LMFDB - Embedded newform 510.2.u.a.151.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [510,2,Mod(121,510)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(510, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 0, 7]))

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

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

chi := DirichletCharacter("510.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 510 = 2 \cdot 3 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	510.u (of order $8$, degree $4$, 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:	$4.07237050309$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{8})$
Coefficient field:	$\Q(\zeta_{16})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			151.2
Root			$0.923880 + 0.382683i$ of defining polynomial
Character	$\chi$	$=$	510.151
Dual form			510.2.u.a.331.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 - 0.707107i) q^{2} +(0.382683 + 0.923880i) q^{3} +1.00000i q^{4} +(0.923880 - 0.382683i) q^{5} +(0.382683 - 0.923880i) q^{6} +(-4.26197 - 1.76537i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.707107 + 0.707107i) q^{9} +(-0.923880 - 0.382683i) q^{10} +(-1.95541 + 4.72078i) q^{11} +(-0.923880 + 0.382683i) q^{12} +3.23463i q^{13} +(1.76537 + 4.26197i) q^{14} +(0.707107 + 0.707107i) q^{15} -1.00000 q^{16} +(-2.22304 - 3.47247i) q^{17} +1.00000 q^{18} +(2.82843 + 2.82843i) q^{19} +(0.382683 + 0.923880i) q^{20} -4.61313i q^{21} +(4.72078 - 1.95541i) q^{22} +(-2.38329 + 5.75378i) q^{23} +(0.923880 + 0.382683i) q^{24} +(0.707107 - 0.707107i) q^{25} +(2.28723 - 2.28723i) q^{26} +(-0.923880 - 0.382683i) q^{27} +(1.76537 - 4.26197i) q^{28} +(-7.70144 + 3.19004i) q^{29} -1.00000i q^{30} +(1.45314 + 3.50819i) q^{31} +(0.707107 + 0.707107i) q^{32} -5.10973 q^{33} +(-0.883480 + 4.02734i) q^{34} -4.61313 q^{35} +(-0.707107 - 0.707107i) q^{36} +(-2.86709 - 6.92177i) q^{37} -4.00000i q^{38} +(-2.98841 + 1.23784i) q^{39} +(0.382683 - 0.923880i) q^{40} +(-8.83938 - 3.66139i) q^{41} +(-3.26197 + 3.26197i) q^{42} +(5.83889 - 5.83889i) q^{43} +(-4.72078 - 1.95541i) q^{44} +(-0.382683 + 0.923880i) q^{45} +(5.75378 - 2.38329i) q^{46} +12.4525i q^{47} +(-0.382683 - 0.923880i) q^{48} +(10.0981 + 10.0981i) q^{49} -1.00000 q^{50} +(2.35743 - 3.38268i) q^{51} -3.23463 q^{52} +(0.965872 + 0.965872i) q^{53} +(0.382683 + 0.923880i) q^{54} +5.10973i q^{55} +(-4.26197 + 1.76537i) q^{56} +(-1.53073 + 3.69552i) q^{57} +(7.70144 + 3.19004i) q^{58} +(1.67705 - 1.67705i) q^{59} +(-0.707107 + 0.707107i) q^{60} +(1.13291 + 0.469266i) q^{61} +(1.45314 - 3.50819i) q^{62} +(4.26197 - 1.76537i) q^{63} -1.00000i q^{64} +(1.23784 + 2.98841i) q^{65} +(3.61313 + 3.61313i) q^{66} -2.74444 q^{67} +(3.47247 - 2.22304i) q^{68} -6.22784 q^{69} +(3.26197 + 3.26197i) q^{70} +(3.48181 + 8.40583i) q^{71} +1.00000i q^{72} +(8.50756 - 3.52395i) q^{73} +(-2.86709 + 6.92177i) q^{74} +(0.923880 + 0.382683i) q^{75} +(-2.82843 + 2.82843i) q^{76} +(16.6678 - 16.6678i) q^{77} +(2.98841 + 1.23784i) q^{78} +(-1.38207 + 3.33662i) q^{79} +(-0.923880 + 0.382683i) q^{80} -1.00000i q^{81} +(3.66139 + 8.83938i) q^{82} +(-7.96550 - 7.96550i) q^{83} +4.61313 q^{84} +(-3.38268 - 2.35743i) q^{85} -8.25744 q^{86} +(-5.89443 - 5.89443i) q^{87} +(1.95541 + 4.72078i) q^{88} -9.03188i q^{89} +(0.923880 - 0.382683i) q^{90} +(5.71031 - 13.7859i) q^{91} +(-5.75378 - 2.38329i) q^{92} +(-2.68506 + 2.68506i) q^{93} +(8.80525 - 8.80525i) q^{94} +(3.69552 + 1.53073i) q^{95} +(-0.382683 + 0.923880i) q^{96} +(-5.54712 + 2.29769i) q^{97} -14.2809i q^{98} +(-1.95541 - 4.72078i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{7} + 8 q^{14} - 8 q^{16} + 8 q^{18} + 16 q^{22} + 24 q^{23} + 8 q^{28} - 32 q^{29} - 8 q^{31} - 8 q^{34} - 16 q^{35} - 16 q^{37} - 8 q^{41} + 32 q^{43} - 16 q^{44} + 16 q^{46} + 16 q^{49} - 8 q^{50}+ \cdots - 40 q^{97}+O(q^{100}) $ 8 * q - 8 * q^7 + 8 * q^14 - 8 * q^16 + 8 * q^18 + 16 * q^22 + 24 * q^23 + 8 * q^28 - 32 * q^29 - 8 * q^31 - 8 * q^34 - 16 * q^35 - 16 * q^37 - 8 * q^41 + 32 * q^43 - 16 * q^44 + 16 * q^46 + 16 * q^49 - 8 * q^50 + 8 * q^51 - 32 * q^52 - 8 * q^56 + 32 * q^58 + 16 * q^59 + 16 * q^61 - 8 * q^62 + 8 * q^63 - 8 * q^65 + 8 * q^66 + 16 * q^68 - 16 * q^69 + 8 * q^71 + 8 * q^73 - 16 * q^74 + 48 * q^77 - 48 * q^79 - 8 * q^82 + 32 * q^83 + 16 * q^84 - 24 * q^85 - 32 * q^86 - 8 * q^87 + 16 * q^91 - 16 * q^92 + 16 * q^93 - 40 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/510\mathbb{Z}\right)^\times$.

$n$	$241$	$307$	$341$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$1$	$1$

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 $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	0.382683	+	0.923880i	0.220942	+	0.533402i
$3$	0.382683	+	0.923880i	0.220942	+	0.533402i
$4$			1.00000i			0.500000i
$5$	0.923880	−	0.382683i	0.413171	−	0.171141i
$5$	0.923880	−	0.382683i	0.413171	−	0.171141i
$6$	0.382683	−	0.923880i	0.156230	−	0.377172i
$7$	−4.26197	−	1.76537i	−1.61087	−	0.667246i	−0.617974	−	0.786198i	$-0.712046\pi$
$7$	−4.26197	−	1.76537i	−1.61087	−	0.667246i	−0.992900	+	0.118952i	$0.962046\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−0.707107	+	0.707107i	−0.235702	+	0.235702i
$10$	−0.923880	−	0.382683i	−0.292156	−	0.121015i
$11$	−1.95541	+	4.72078i	−0.589578	+	1.42337i	0.294328	+	0.955704i	$0.404904\pi$
$11$	−1.95541	+	4.72078i	−0.589578	+	1.42337i	−0.883907	+	0.467663i	$0.845096\pi$
$12$	−0.923880	+	0.382683i	−0.266701	+	0.110471i
$13$			3.23463i			0.897126i	0.893751	+	0.448563i	$0.148064\pi$
$13$			3.23463i			0.897126i	−0.893751	+	0.448563i	$0.851936\pi$
$14$	1.76537	+	4.26197i	0.471814	+	1.13906i
$15$	0.707107	+	0.707107i	0.182574	+	0.182574i
$16$	−1.00000			−0.250000
$17$	−2.22304	−	3.47247i	−0.539167	−	0.842199i
$17$	−2.22304	−	3.47247i	−0.539167	−	0.842199i
$18$	1.00000			0.235702
$19$	2.82843	+	2.82843i	0.648886	+	0.648886i	0.952724	−	0.303838i	$-0.0982682\pi$
$19$	2.82843	+	2.82843i	0.648886	+	0.648886i	−0.303838	+	0.952724i	$0.598268\pi$
$20$	0.382683	+	0.923880i	0.0855706	+	0.206586i
$21$		−	4.61313i		−	1.00667i
$22$	4.72078	−	1.95541i	1.00647	−	0.416895i
$23$	−2.38329	+	5.75378i	−0.496951	+	1.19975i	0.454167	+	0.890917i	$0.349937\pi$
$23$	−2.38329	+	5.75378i	−0.496951	+	1.19975i	−0.951118	+	0.308829i	$0.900063\pi$
$24$	0.923880	+	0.382683i	0.188586	+	0.0781149i
$25$	0.707107	−	0.707107i	0.141421	−	0.141421i
$26$	2.28723	−	2.28723i	0.448563	−	0.448563i
$27$	−0.923880	−	0.382683i	−0.177801	−	0.0736475i
$28$	1.76537	−	4.26197i	0.333623	−	0.805437i
$29$	−7.70144	+	3.19004i	−1.43012	+	0.592376i	−0.957382	−	0.288826i	$-0.906735\pi$
$29$	−7.70144	+	3.19004i	−1.43012	+	0.592376i	−0.472741	+	0.881202i	$0.656735\pi$
$30$		−	1.00000i		−	0.182574i
$31$	1.45314	+	3.50819i	0.260992	+	0.630090i	0.999000	−	0.0447012i	$-0.0142336\pi$
$31$	1.45314	+	3.50819i	0.260992	+	0.630090i	−0.738008	+	0.674791i	$0.764234\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−5.10973			−0.889490
$34$	−0.883480	+	4.02734i	−0.151516	+	0.690683i
$35$	−4.61313			−0.779761
$36$	−0.707107	−	0.707107i	−0.117851	−	0.117851i
$37$	−2.86709	−	6.92177i	−0.471347	−	1.13793i	−0.963568	−	0.267462i	$-0.913815\pi$
$37$	−2.86709	−	6.92177i	−0.471347	−	1.13793i	0.492222	−	0.870470i	$-0.336185\pi$
$38$		−	4.00000i		−	0.648886i
$39$	−2.98841	+	1.23784i	−0.478529	+	0.198213i
$40$	0.382683	−	0.923880i	0.0605076	−	0.146078i
$41$	−8.83938	−	3.66139i	−1.38048	−	0.571813i	−0.435870	−	0.900010i	$-0.643559\pi$
$41$	−8.83938	−	3.66139i	−1.38048	−	0.571813i	−0.944609	+	0.328197i	$0.893559\pi$
$42$	−3.26197	+	3.26197i	−0.503333	+	0.503333i
$43$	5.83889	−	5.83889i	0.890422	−	0.890422i	−0.104140	−	0.994563i	$-0.533209\pi$
$43$	5.83889	−	5.83889i	0.890422	−	0.890422i	0.994563	+	0.104140i	$0.0332091\pi$
$44$	−4.72078	−	1.95541i	−0.711684	−	0.294789i
$45$	−0.382683	+	0.923880i	−0.0570471	+	0.137724i
$46$	5.75378	−	2.38329i	0.848348	−	0.351397i
$47$			12.4525i			1.81638i	0.418553	+	0.908192i	$0.362537\pi$
$47$			12.4525i			1.81638i	−0.418553	+	0.908192i	$0.637463\pi$
$48$	−0.382683	−	0.923880i	−0.0552356	−	0.133351i
$49$	10.0981	+	10.0981i	1.44259	+	1.44259i
$50$	−1.00000			−0.141421
$51$	2.35743	−	3.38268i	0.330106	−	0.473670i
$52$	−3.23463			−0.448563
$53$	0.965872	+	0.965872i	0.132673	+	0.132673i	0.770325	−	0.637652i	$-0.220094\pi$
$53$	0.965872	+	0.965872i	0.132673	+	0.132673i	−0.637652	+	0.770325i	$0.720094\pi$
$54$	0.382683	+	0.923880i	0.0520766	+	0.125724i
$55$			5.10973i			0.688996i
$56$	−4.26197	+	1.76537i	−0.569530	+	0.235907i
$57$	−1.53073	+	3.69552i	−0.202751	+	0.489483i
$58$	7.70144	+	3.19004i	1.01125	+	0.418873i
$59$	1.67705	−	1.67705i	0.218333	−	0.218333i	−0.589463	−	0.807796i	$-0.700660\pi$
$59$	1.67705	−	1.67705i	0.218333	−	0.218333i	0.807796	+	0.589463i	$0.200660\pi$
$60$	−0.707107	+	0.707107i	−0.0912871	+	0.0912871i
$61$	1.13291	+	0.469266i	0.145054	+	0.0600834i	0.454029	−	0.890987i	$-0.349986\pi$
$61$	1.13291	+	0.469266i	0.145054	+	0.0600834i	−0.308975	+	0.951070i	$0.599986\pi$
$62$	1.45314	−	3.50819i	0.184549	−	0.445541i
$63$	4.26197	−	1.76537i	0.536958	−	0.222415i
$64$		−	1.00000i		−	0.125000i
$65$	1.23784	+	2.98841i	0.153535	+	0.370667i
$66$	3.61313	+	3.61313i	0.444745	+	0.444745i
$67$	−2.74444			−0.335287			−0.167643	−	0.985848i	$-0.553616\pi$
$67$	−2.74444			−0.335287			−0.167643	+	0.985848i	$0.553616\pi$
$68$	3.47247	−	2.22304i	0.421099	−	0.269584i
$69$	−6.22784			−0.749744
$70$	3.26197	+	3.26197i	0.389880	+	0.389880i
$71$	3.48181	+	8.40583i	0.413215	+	0.997589i	0.984269	+	0.176676i	$0.0565346\pi$
$71$	3.48181	+	8.40583i	0.413215	+	0.997589i	−0.571054	+	0.820912i	$0.693465\pi$
$72$			1.00000i			0.117851i
$73$	8.50756	−	3.52395i	0.995734	−	0.412447i	0.175503	−	0.984479i	$-0.443845\pi$
$73$	8.50756	−	3.52395i	0.995734	−	0.412447i	0.820231	+	0.572032i	$0.193845\pi$
$74$	−2.86709	+	6.92177i	−0.333293	+	0.804639i
$75$	0.923880	+	0.382683i	0.106680	+	0.0441885i
$76$	−2.82843	+	2.82843i	−0.324443	+	0.324443i
$77$	16.6678	−	16.6678i	1.89947	−	1.89947i
$78$	2.98841	+	1.23784i	0.338371	+	0.140158i
$79$	−1.38207	+	3.33662i	−0.155495	+	0.375399i	−0.982359	−	0.187003i	$-0.940123\pi$
$79$	−1.38207	+	3.33662i	−0.155495	+	0.375399i	0.826864	+	0.562402i	$0.190123\pi$
$80$	−0.923880	+	0.382683i	−0.103293	+	0.0427853i
$81$		−	1.00000i		−	0.111111i
$82$	3.66139	+	8.83938i	0.404333	+	0.976146i
$83$	−7.96550	−	7.96550i	−0.874327	−	0.874327i	0.118613	−	0.992941i	$-0.462155\pi$
$83$	−7.96550	−	7.96550i	−0.874327	−	0.874327i	−0.992941	+	0.118613i	$0.962155\pi$
$84$	4.61313			0.503333
$85$	−3.38268	−	2.35743i	−0.366904	−	0.255699i
$86$	−8.25744			−0.890422
$87$	−5.89443	−	5.89443i	−0.631949	−	0.631949i
$88$	1.95541	+	4.72078i	0.208447	+	0.503236i
$89$		−	9.03188i		−	0.957377i	−0.877985	−	0.478688i	$-0.841112\pi$
$89$		−	9.03188i		−	0.957377i	0.877985	−	0.478688i	$-0.158888\pi$
$90$	0.923880	−	0.382683i	0.0973855	−	0.0403384i
$91$	5.71031	−	13.7859i	0.598604	−	1.44516i
$92$	−5.75378	−	2.38329i	−0.599873	−	0.248475i
$93$	−2.68506	+	2.68506i	−0.278427	+	0.278427i
$94$	8.80525	−	8.80525i	0.908192	−	0.908192i
$95$	3.69552	+	1.53073i	0.379152	+	0.157050i
$96$	−0.382683	+	0.923880i	−0.0390575	+	0.0942931i
$97$	−5.54712	+	2.29769i	−0.563225	+	0.233295i	−0.646085	−	0.763266i	$-0.723595\pi$
$97$	−5.54712	+	2.29769i	−0.563225	+	0.233295i	0.0828596	+	0.996561i	$0.473595\pi$
$98$		−	14.2809i		−	1.44259i
$99$	−1.95541	−	4.72078i	−0.196526	−	0.474456i
$100$	0.707107	+	0.707107i	0.0707107	+	0.0707107i
$101$	6.96882			0.693423			0.346712	−	0.937972i	$-0.387298\pi$
$101$	6.96882			0.693423			0.346712	+	0.937972i	$0.387298\pi$
$102$	−4.05887	+	0.724967i	−0.401888	+	0.0717824i
$103$	−17.5854			−1.73274			−0.866371	−	0.499401i	$-0.833554\pi$
$103$	−17.5854			−1.73274			−0.866371	+	0.499401i	$0.833554\pi$
$104$	2.28723	+	2.28723i	0.224281	+	0.224281i
$105$	−1.76537	−	4.26197i	−0.172282	−	0.415926i
$106$		−	1.36595i		−	0.132673i
$107$	2.57741	−	1.06760i	0.249167	−	0.103208i	−0.254605	−	0.967045i	$-0.581945\pi$
$107$	2.57741	−	1.06760i	0.249167	−	0.103208i	0.503772	+	0.863837i	$0.331945\pi$
$108$	0.382683	−	0.923880i	0.0368237	−	0.0889003i
$109$	13.9958	+	5.79724i	1.34055	+	0.555275i	0.933647	−	0.358195i	$-0.116608\pi$
$109$	13.9958	+	5.79724i	1.34055	+	0.555275i	0.406906	+	0.913470i	$0.366608\pi$
$110$	3.61313	−	3.61313i	0.344498	−	0.344498i
$111$	5.29769	−	5.29769i	0.502835	−	0.502835i
$112$	4.26197	+	1.76537i	0.402719	+	0.166811i
$113$	0.898012	−	2.16799i	0.0844778	−	0.203948i	−0.875996	−	0.482319i	$-0.839795\pi$
$113$	0.898012	−	2.16799i	0.0844778	−	0.203948i	0.960473	+	0.278371i	$0.0897946\pi$
$114$	3.69552	−	1.53073i	0.346117	−	0.143366i
$115$			6.22784i			0.580750i
$116$	−3.19004	−	7.70144i	−0.296188	−	0.715061i
$117$	−2.28723	−	2.28723i	−0.211455	−	0.211455i
$118$	−2.37170			−0.218333
$119$	3.34436	+	18.7241i	0.306577	+	1.71643i
$120$	1.00000			0.0912871
$121$	−10.6839	−	10.6839i	−0.971266	−	0.971266i
$122$	−0.469266	−	1.13291i	−0.0424854	−	0.102569i
$123$		−	9.56767i		−	0.862688i
$124$	−3.50819	+	1.45314i	−0.315045	+	0.130496i
$125$	0.382683	−	0.923880i	0.0342282	−	0.0826343i
$126$	−4.26197	−	1.76537i	−0.379687	−	0.157271i
$127$	5.79430	−	5.79430i	0.514161	−	0.514161i	−0.401638	−	0.915799i	$-0.631559\pi$
$127$	5.79430	−	5.79430i	0.514161	−	0.514161i	0.915799	+	0.401638i	$0.131559\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	7.62888	+	3.15998i	0.671685	+	0.278221i
$130$	1.23784	−	2.98841i	0.108566	−	0.262101i
$131$	6.02440	−	2.49539i	0.526354	−	0.218023i	−0.103651	−	0.994614i	$-0.533053\pi$
$131$	6.02440	−	2.49539i	0.526354	−	0.218023i	0.630005	+	0.776591i	$0.283053\pi$
$132$		−	5.10973i		−	0.444745i
$133$	−7.06147	−	17.0479i	−0.612307	−	1.47824i
$134$	1.94061	+	1.94061i	0.167643	+	0.167643i
$135$	−1.00000			−0.0860663
$136$	−4.02734	−	0.883480i	−0.345342	−	0.0757578i
$137$	11.5076			0.983157			0.491578	−	0.870833i	$-0.336420\pi$
$137$	11.5076			0.983157			0.491578	+	0.870833i	$0.336420\pi$
$138$	4.40375	+	4.40375i	0.374872	+	0.374872i
$139$	−8.09040	−	19.5320i	−0.686219	−	1.65668i	−0.752264	−	0.658862i	$-0.771038\pi$
$139$	−8.09040	−	19.5320i	−0.686219	−	1.65668i	0.0660451	−	0.997817i	$-0.478962\pi$
$140$		−	4.61313i		−	0.389880i
$141$	−11.5046	+	4.76537i	−0.968863	+	0.401316i
$142$	3.48181	−	8.40583i	0.292187	−	0.705402i
$143$	−15.2700	−	6.32503i	−1.27694	−	0.528926i
$144$	0.707107	−	0.707107i	0.0589256	−	0.0589256i
$145$	−5.89443	+	5.89443i	−0.489506	+	0.489506i
$146$	−8.50756	−	3.52395i	−0.704090	−	0.291644i
$147$	−5.46508	+	13.1939i	−0.450752	+	1.08821i
$148$	6.92177	−	2.86709i	0.568966	−	0.235673i
$149$			20.4592i			1.67608i	0.545609	+	0.838040i	$0.316298\pi$
$149$			20.4592i			1.67608i	−0.545609	+	0.838040i	$0.683702\pi$
$150$	−0.382683	−	0.923880i	−0.0312460	−	0.0754344i
$151$	10.8120	+	10.8120i	0.879871	+	0.879871i	0.993521	−	0.113650i	$-0.0362542\pi$
$151$	10.8120	+	10.8120i	0.879871	+	0.879871i	−0.113650	+	0.993521i	$0.536254\pi$
$152$	4.00000			0.324443
$153$	4.02734	+	0.883480i	0.325591	+	0.0714251i
$154$	−23.5718			−1.89947
$155$	2.68506	+	2.68506i	0.215669	+	0.215669i
$156$	−1.23784	−	2.98841i	−0.0991066	−	0.239264i
$157$		−	1.82267i		−	0.145465i	−0.997351	−	0.0727325i	$-0.976828\pi$
$157$		−	1.82267i		−	0.145465i	0.997351	−	0.0727325i	$-0.0231719\pi$
$158$	3.33662	−	1.38207i	0.265447	−	0.109952i
$159$	−0.522726	+	1.26197i	−0.0414549	+	0.100081i
$160$	0.923880	+	0.382683i	0.0730391	+	0.0302538i
$161$	20.3151	−	20.3151i	1.60105	−	1.60105i
$162$	−0.707107	+	0.707107i	−0.0555556	+	0.0555556i
$163$	7.17872	+	2.97352i	0.562281	+	0.232904i	0.645675	−	0.763612i	$-0.276576\pi$
$163$	7.17872	+	2.97352i	0.562281	+	0.232904i	−0.0833943	+	0.996517i	$0.526576\pi$
$164$	3.66139	−	8.83938i	0.285907	−	0.690239i
$165$	−4.72078	+	1.95541i	−0.367512	+	0.152228i
$166$			11.2649i			0.874327i
$167$	−1.86388	−	4.49981i	−0.144232	−	0.348206i	0.835211	−	0.549930i	$-0.185346\pi$
$167$	−1.86388	−	4.49981i	−0.144232	−	0.348206i	−0.979442	+	0.201724i	$0.935346\pi$
$168$	−3.26197	−	3.26197i	−0.251667	−	0.251667i
$169$	2.53715			0.195165
$170$	0.724967	+	4.05887i	0.0556024	+	0.311301i
$171$	−4.00000			−0.305888
$172$	5.83889	+	5.83889i	0.445211	+	0.445211i
$173$	−0.331821	−	0.801088i	−0.0252279	−	0.0609056i	0.910764	−	0.412928i	$-0.135494\pi$
$173$	−0.331821	−	0.801088i	−0.0252279	−	0.0609056i	−0.935991	+	0.352023i	$0.885494\pi$
$174$			8.33598i			0.631949i
$175$	−4.26197	+	1.76537i	−0.322175	+	0.133449i
$176$	1.95541	−	4.72078i	0.147395	−	0.355842i
$177$	2.19117	+	0.907612i	0.164698	+	0.0682203i
$178$	−6.38650	+	6.38650i	−0.478688	+	0.478688i
$179$	−12.2818	+	12.2818i	−0.917984	+	0.917984i	−0.996883	−	0.0788984i	$-0.974860\pi$
$179$	−12.2818	+	12.2818i	−0.917984	+	0.917984i	0.0788984	+	0.996883i	$0.474860\pi$
$180$	−0.923880	−	0.382683i	−0.0688619	−	0.0285235i
$181$	−2.37396	+	5.73124i	−0.176455	+	0.426000i	−0.987218	−	0.159374i	$-0.949052\pi$
$181$	−2.37396	+	5.73124i	−0.176455	+	0.426000i	0.810763	+	0.585374i	$0.199052\pi$
$182$	−13.7859	+	5.71031i	−1.02188	+	0.423277i
$183$			1.22625i			0.0906471i
$184$	2.38329	+	5.75378i	0.175699	+	0.424174i
$185$	−5.29769	−	5.29769i	−0.389494	−	0.389494i
$186$	3.79724			0.278427
$187$	20.7397	−	3.70439i	1.51664	−	0.270892i
$188$	−12.4525			−0.908192
$189$	3.26197	+	3.26197i	0.237274	+	0.237274i
$190$	−1.53073	−	3.69552i	−0.111051	−	0.268101i
$191$		−	2.35916i		−	0.170703i	−0.996351	−	0.0853514i	$-0.972799\pi$
$191$		−	2.35916i		−	0.170703i	0.996351	−	0.0853514i	$-0.0272013\pi$
$192$	0.923880	−	0.382683i	0.0666753	−	0.0276178i
$193$	0.592575	−	1.43060i	0.0426545	−	0.102977i	−0.901116	−	0.433577i	$-0.857251\pi$
$193$	0.592575	−	1.43060i	0.0426545	−	0.102977i	0.943771	+	0.330600i	$0.107251\pi$
$194$	5.54712	+	2.29769i	0.398260	+	0.164965i
$195$	−2.28723	+	2.28723i	−0.163792	+	0.163792i
$196$	−10.0981	+	10.0981i	−0.721296	+	0.721296i
$197$	4.57446	+	1.89480i	0.325917	+	0.134999i	0.539642	−	0.841895i	$-0.318560\pi$
$197$	4.57446	+	1.89480i	0.325917	+	0.134999i	−0.213725	+	0.976894i	$0.568560\pi$
$198$	−1.95541	+	4.72078i	−0.138965	+	0.335491i
$199$	9.56287	−	3.96107i	0.677894	−	0.280793i	−0.0170522	−	0.999855i	$-0.505428\pi$
$199$	9.56287	−	3.96107i	0.677894	−	0.280793i	0.694946	+	0.719062i	$0.255428\pi$
$200$		−	1.00000i		−	0.0707107i
$201$	−1.05025	−	2.53553i	−0.0740791	−	0.178843i
$202$	−4.92770	−	4.92770i	−0.346712	−	0.346712i
$203$	38.4549			2.69901
$204$	3.38268	+	2.35743i	0.236835	+	0.165053i
$205$	−9.56767			−0.668235
$206$	12.4348	+	12.4348i	0.866371	+	0.866371i
$207$	−2.38329	−	5.75378i	−0.165650	−	0.399915i
$208$		−	3.23463i		−	0.224281i
$209$	−18.8831	+	7.82164i	−1.30617	+	0.541034i
$210$	−1.76537	+	4.26197i	−0.121822	+	0.294104i
$211$	−2.12068	−	0.878415i	−0.145994	−	0.0604726i	0.308490	−	0.951228i	$-0.400176\pi$
$211$	−2.12068	−	0.878415i	−0.145994	−	0.0604726i	−0.454484	+	0.890755i	$0.650176\pi$
$212$	−0.965872	+	0.965872i	−0.0663364	+	0.0663364i
$213$	−6.43355	+	6.43355i	−0.440819	+	0.440819i
$214$	−2.57741	−	1.06760i	−0.176188	−	0.0729794i
$215$	3.15998	−	7.62888i	0.215509	−	0.520285i
$216$	−0.923880	+	0.382683i	−0.0628620	+	0.0260383i
$217$		−	17.5172i		−	1.18914i
$218$	−5.79724	−	13.9958i	−0.392639	−	0.947914i
$219$	6.51140	+	6.51140i	0.440000	+	0.440000i
$220$	−5.10973			−0.344498
$221$	11.2322	−	7.19073i	0.755558	−	0.483701i
$222$	−7.49207			−0.502835
$223$	18.5577	+	18.5577i	1.24272	+	1.24272i	0.958870	+	0.283845i	$0.0916103\pi$
$223$	18.5577	+	18.5577i	1.24272	+	1.24272i	0.283845	+	0.958870i	$0.408390\pi$
$224$	−1.76537	−	4.26197i	−0.117954	−	0.284765i
$225$			1.00000i			0.0666667i
$226$	−2.16799	+	0.898012i	−0.144213	+	0.0597348i
$227$	1.60737	−	3.88054i	0.106685	−	0.257560i	−0.861518	−	0.507728i	$-0.830486\pi$
$227$	1.60737	−	3.88054i	0.106685	−	0.257560i	0.968203	+	0.250167i	$0.0804856\pi$
$228$	−3.69552	−	1.53073i	−0.244742	−	0.101375i
$229$	8.90628	−	8.90628i	0.588544	−	0.588544i	−0.348693	−	0.937237i	$-0.613374\pi$
$229$	8.90628	−	8.90628i	0.588544	−	0.588544i	0.937237	+	0.348693i	$0.113374\pi$
$230$	4.40375	−	4.40375i	0.290375	−	0.290375i
$231$	21.7775	+	9.02055i	1.43286	+	0.593509i
$232$	−3.19004	+	7.70144i	−0.209437	+	0.505625i
$233$	−19.3215	+	8.00321i	−1.26579	+	0.524308i	−0.911682	−	0.410897i	$-0.865216\pi$
$233$	−19.3215	+	8.00321i	−1.26579	+	0.524308i	−0.354109	+	0.935204i	$0.615216\pi$
$234$			3.23463i			0.211455i
$235$	4.76537	+	11.5046i	0.310858	+	0.750478i
$236$	1.67705	+	1.67705i	0.109167	+	0.109167i
$237$	−3.61153			−0.234594
$238$	10.8751	−	15.6047i	0.704928	−	1.01151i
$239$	−24.2741			−1.57016			−0.785082	−	0.619392i	$-0.787379\pi$
$239$	−24.2741			−1.57016			−0.785082	+	0.619392i	$0.787379\pi$
$240$	−0.707107	−	0.707107i	−0.0456435	−	0.0456435i
$241$	2.24426	+	5.41811i	0.144565	+	0.349011i	0.979532	−	0.201289i	$-0.0645131\pi$
$241$	2.24426	+	5.41811i	0.144565	+	0.349011i	−0.834967	+	0.550301i	$0.814513\pi$
$242$			15.1094i			0.971266i
$243$	0.923880	−	0.382683i	0.0592669	−	0.0245492i
$244$	−0.469266	+	1.13291i	−0.0300417	+	0.0725271i
$245$	13.1939	+	5.46508i	0.842925	+	0.349151i
$246$	−6.76537	+	6.76537i	−0.431344	+	0.431344i
$247$	−9.14892	+	9.14892i	−0.582132	+	0.582132i
$248$	3.50819	+	1.45314i	0.222771	+	0.0922746i
$249$	4.31090	−	10.4074i	0.273192	−	0.659544i
$250$	−0.923880	+	0.382683i	−0.0584313	+	0.0242030i
$251$			3.18412i			0.200980i	0.994938	+	0.100490i	$0.0320410\pi$
$251$			3.18412i			0.200980i	−0.994938	+	0.100490i	$0.967959\pi$
$252$	1.76537	+	4.26197i	0.111208	+	0.268479i
$253$	−22.5020	−	22.5020i	−1.41469	−	1.41469i
$254$	−8.19438			−0.514161
$255$	0.883480	−	4.02734i	0.0553257	−	0.252202i
$256$	1.00000			0.0625000
$257$	7.64272	+	7.64272i	0.476740	+	0.476740i	0.904087	−	0.427348i	$-0.140552\pi$
$257$	7.64272	+	7.64272i	0.476740	+	0.476740i	−0.427348	+	0.904087i	$0.640552\pi$
$258$	−3.15998	−	7.62888i	−0.196732	−	0.474953i
$259$			34.5619i			2.14757i
$260$	−2.98841	+	1.23784i	−0.185333	+	0.0767676i
$261$	3.19004	−	7.70144i	0.197459	−	0.476707i
$262$	−6.02440	−	2.49539i	−0.372188	−	0.154166i
$263$	−18.4866	+	18.4866i	−1.13993	+	1.13993i	−0.151473	+	0.988461i	$0.548402\pi$
$263$	−18.4866	+	18.4866i	−1.13993	+	1.13993i	−0.988461	+	0.151473i	$0.951598\pi$
$264$	−3.61313	+	3.61313i	−0.222373	+	0.222373i
$265$	1.26197	+	0.522726i	0.0775224	+	0.0321108i
$266$	−7.06147	+	17.0479i	−0.432966	+	1.04527i
$267$	8.34436	−	3.45635i	0.510667	−	0.211525i
$268$		−	2.74444i		−	0.167643i
$269$	4.91761	+	11.8722i	0.299832	+	0.723858i	0.999952	+	0.00983272i	$0.00312990\pi$
$269$	4.91761	+	11.8722i	0.299832	+	0.723858i	−0.700120	+	0.714025i	$0.746870\pi$
$270$	0.707107	+	0.707107i	0.0430331	+	0.0430331i
$271$	−6.64954			−0.403931			−0.201965	−	0.979393i	$-0.564733\pi$
$271$	−6.64954			−0.403931			−0.201965	+	0.979393i	$0.564733\pi$
$272$	2.22304	+	3.47247i	0.134792	+	0.210550i
$273$	14.9218			0.903107
$274$	−8.13707	−	8.13707i	−0.491578	−	0.491578i
$275$	1.95541	+	4.72078i	0.117916	+	0.284674i
$276$		−	6.22784i		−	0.374872i
$277$	−19.1585	+	7.93570i	−1.15112	+	0.476810i	−0.874910	−	0.484286i	$-0.839079\pi$
$277$	−19.1585	+	7.93570i	−1.15112	+	0.476810i	−0.276212	+	0.961097i	$0.589079\pi$
$278$	−8.09040	+	19.5320i	−0.485230	+	1.17145i
$279$	−3.50819	−	1.45314i	−0.210030	−	0.0869973i
$280$	−3.26197	+	3.26197i	−0.194940	+	0.194940i
$281$	13.0888	−	13.0888i	0.780813	−	0.780813i	−0.199155	−	0.979968i	$-0.563820\pi$
$281$	13.0888	−	13.0888i	0.780813	−	0.780813i	0.979968	+	0.199155i	$0.0638198\pi$
$282$	11.5046	+	4.76537i	0.685090	+	0.283773i
$283$	−12.1862	+	29.4201i	−0.724394	+	1.74884i	−0.0639674	+	0.997952i	$0.520375\pi$
$283$	−12.1862	+	29.4201i	−0.724394	+	1.74884i	−0.660427	+	0.750890i	$0.729625\pi$
$284$	−8.40583	+	3.48181i	−0.498794	+	0.206607i
$285$			4.00000i			0.236940i
$286$	6.32503	+	15.2700i	0.374007	+	0.902933i
$287$	31.2095	+	31.2095i	1.84224	+	1.84224i
$288$	−1.00000			−0.0589256
$289$	−7.11615	+	15.4389i	−0.418597	+	0.908172i
$290$	8.33598			0.489506
$291$	−4.24558	−	4.24558i	−0.248881	−	0.248881i
$292$	3.52395	+	8.50756i	0.206223	+	0.497867i
$293$		−	0.145584i		−	0.00850509i	−0.999991	−	0.00425255i	$-0.998646\pi$
$293$		−	0.145584i		−	0.00850509i	0.999991	−	0.00425255i	$-0.00135363\pi$
$294$	13.1939	−	5.46508i	0.769482	−	0.318730i
$295$	0.907612	−	2.19117i	0.0528432	−	0.127575i
$296$	−6.92177	−	2.86709i	−0.402320	−	0.166646i
$297$	3.61313	−	3.61313i	0.209655	−	0.209655i
$298$	14.4668	−	14.4668i	0.838040	−	0.838040i
$299$	−18.6114	−	7.70908i	−1.07632	−	0.445828i
$300$	−0.382683	+	0.923880i	−0.0220942	+	0.0533402i
$301$	−35.1930	+	14.5774i	−2.02849	+	0.840228i
$302$		−	15.2905i		−	0.879871i
$303$	2.66685	+	6.43835i	0.153207	+	0.369873i
$304$	−2.82843	−	2.82843i	−0.162221	−	0.162221i
$305$	1.22625			0.0702150
$306$	−2.22304	−	3.47247i	−0.127083	−	0.198508i
$307$	−8.52742			−0.486685			−0.243343	−	0.969940i	$-0.578244\pi$
$307$	−8.52742			−0.486685			−0.243343	+	0.969940i	$0.578244\pi$
$308$	16.6678	+	16.6678i	0.949736	+	0.949736i
$309$	−6.72965	−	16.2468i	−0.382836	−	0.924248i
$310$		−	3.79724i		−	0.215669i
$311$	3.80819	−	1.57741i	0.215943	−	0.0894464i	−0.272090	−	0.962272i	$-0.587715\pi$
$311$	3.80819	−	1.57741i	0.215943	−	0.0894464i	0.488033	+	0.872825i	$0.337715\pi$
$312$	−1.23784	+	2.98841i	−0.0700789	+	0.169185i
$313$	−12.3965	−	5.13479i	−0.700690	−	0.290235i	0.00375585	−	0.999993i	$-0.498804\pi$
$313$	−12.3965	−	5.13479i	−0.700690	−	0.290235i	−0.704446	+	0.709758i	$0.748804\pi$
$314$	−1.28882	+	1.28882i	−0.0727325	+	0.0727325i
$315$	3.26197	−	3.26197i	0.183791	−	0.183791i
$316$	−3.33662	−	1.38207i	−0.187700	−	0.0777477i
$317$	−6.70231	+	16.1808i	−0.376439	+	0.908804i	0.616188	+	0.787599i	$0.288676\pi$
$317$	−6.70231	+	16.1808i	−0.376439	+	0.908804i	−0.992627	+	0.121205i	$0.961324\pi$
$318$	1.26197	−	0.522726i	0.0707679	−	0.0293130i
$319$		−	42.5946i		−	2.38484i
$320$	−0.382683	−	0.923880i	−0.0213927	−	0.0516464i
$321$	1.97266	+	1.97266i	0.110103	+	0.110103i
$322$	−28.7298			−1.60105
$323$	3.53392	−	16.1094i	0.196633	−	0.896349i
$324$	1.00000			0.0555556
$325$	2.28723	+	2.28723i	0.126873	+	0.126873i
$326$	−2.97352	−	7.17872i	−0.164688	−	0.397592i
$327$			15.1489i			0.837737i
$328$	−8.83938	+	3.66139i	−0.488073	+	0.202166i
$329$	21.9832	−	53.0722i	1.21198	−	2.92597i
$330$	4.72078	+	1.95541i	0.259870	+	0.107642i
$331$	−7.58541	+	7.58541i	−0.416932	+	0.416932i	−0.884145	−	0.467213i	$-0.845258\pi$
$331$	−7.58541	+	7.58541i	−0.416932	+	0.416932i	0.467213	+	0.884145i	$0.345258\pi$
$332$	7.96550	−	7.96550i	0.437164	−	0.437164i
$333$	6.92177	+	2.86709i	0.379311	+	0.157116i
$334$	−1.86388	+	4.49981i	−0.101987	+	0.246219i
$335$	−2.53553	+	1.05025i	−0.138531	+	0.0573814i
$336$			4.61313i			0.251667i
$337$	2.62951	+	6.34821i	0.143239	+	0.345809i	0.979175	−	0.203017i	$-0.0650748\pi$
$337$	2.62951	+	6.34821i	0.143239	+	0.345809i	−0.835936	+	0.548826i	$0.815075\pi$
$338$	−1.79403	−	1.79403i	−0.0975826	−	0.0975826i
$339$	2.34662			0.127451
$340$	2.35743	−	3.38268i	0.127849	−	0.183452i
$341$	−19.4029			−1.05073
$342$	2.82843	+	2.82843i	0.152944	+	0.152944i
$343$	−12.8535	−	31.0311i	−0.694025	−	1.67552i
$344$		−	8.25744i		−	0.445211i
$345$	−5.75378	+	2.38329i	−0.309773	+	0.128312i
$346$	−0.331821	+	0.801088i	−0.0178388	+	0.0430667i
$347$	5.49276	+	2.27518i	0.294867	+	0.122138i	0.525213	−	0.850971i	$-0.323986\pi$
$347$	5.49276	+	2.27518i	0.294867	+	0.122138i	−0.230346	+	0.973109i	$0.573986\pi$
$348$	5.89443	−	5.89443i	0.315975	−	0.315975i
$349$	11.0551	−	11.0551i	0.591763	−	0.591763i	−0.346344	−	0.938108i	$-0.612577\pi$
$349$	11.0551	−	11.0551i	0.591763	−	0.591763i	0.938108	+	0.346344i	$0.112577\pi$
$350$	4.26197	+	1.76537i	0.227812	+	0.0943628i
$351$	1.23784	−	2.98841i	0.0660710	−	0.159510i
$352$	−4.72078	+	1.95541i	−0.251618	+	0.104224i
$353$			25.7425i			1.37014i	0.728479	+	0.685068i	$0.240227\pi$
$353$			25.7425i			1.37014i	−0.728479	+	0.685068i	$0.759773\pi$
$354$	−0.907612	−	2.19117i	−0.0482390	−	0.116459i
$355$	6.43355	+	6.43355i	0.341457	+	0.341457i
$356$	9.03188			0.478688
$357$	−16.0190	+	10.2552i	−0.847813	+	0.542762i
$358$	17.3691			0.917984
$359$	1.11517	+	1.11517i	0.0588564	+	0.0588564i	0.735922	−	0.677066i	$-0.236749\pi$
$359$	1.11517	+	1.11517i	0.0588564	+	0.0588564i	−0.677066	+	0.735922i	$0.736749\pi$
$360$	0.382683	+	0.923880i	0.0201692	+	0.0486927i
$361$		−	3.00000i		−	0.157895i
$362$	5.73124	−	2.37396i	0.301227	−	0.124772i
$363$	5.78210	−	13.9592i	0.303482	−	0.732669i
$364$	13.7859	+	5.71031i	0.722578	+	0.299302i
$365$	6.51140	−	6.51140i	0.340822	−	0.340822i
$366$	0.867091	−	0.867091i	0.0453236	−	0.0453236i
$367$	3.53233	+	1.46314i	0.184386	+	0.0763752i	0.472966	−	0.881081i	$-0.343183\pi$
$367$	3.53233	+	1.46314i	0.184386	+	0.0763752i	−0.288580	+	0.957456i	$0.593183\pi$
$368$	2.38329	−	5.75378i	0.124238	−	0.299936i
$369$	8.83938	−	3.66139i	0.460160	−	0.190604i
$370$			7.49207i			0.389494i
$371$	−2.41140	−	5.82164i	−0.125194	−	0.302244i
$372$	−2.68506	−	2.68506i	−0.139214	−	0.139214i
$373$	−8.52742			−0.441533			−0.220766	−	0.975327i	$-0.570856\pi$
$373$	−8.52742			−0.441533			−0.220766	+	0.975327i	$0.570856\pi$
$374$	−17.2846	−	12.0458i	−0.893766	−	0.622874i
$375$	1.00000			0.0516398
$376$	8.80525	+	8.80525i	0.454096	+	0.454096i
$377$	−10.3186	−	24.9113i	−0.531436	−	1.28300i
$378$		−	4.61313i		−	0.237274i
$379$	0.532327	−	0.220497i	0.0273438	−	0.0113262i	−0.368970	−	0.929441i	$-0.620289\pi$
$379$	0.532327	−	0.220497i	0.0273438	−	0.0113262i	0.396313	+	0.918115i	$0.370289\pi$
$380$	−1.53073	+	3.69552i	−0.0785250	+	0.189576i
$381$	7.57062	+	3.13585i	0.387854	+	0.160655i
$382$	−1.66818	+	1.66818i	−0.0853514	+	0.0853514i
$383$	−5.91952	+	5.91952i	−0.302473	+	0.302473i	−0.841981	−	0.539508i	$-0.818610\pi$
$383$	−5.91952	+	5.91952i	−0.302473	+	0.302473i	0.539508	+	0.841981i	$0.318610\pi$
$384$	−0.923880	−	0.382683i	−0.0471465	−	0.0195287i
$385$	9.02055	−	21.7775i	0.459730	−	1.10989i
$386$	−1.43060	+	0.592575i	−0.0728157	+	0.0301613i
$387$			8.25744i			0.419749i
$388$	−2.29769	−	5.54712i	−0.116648	−	0.281612i
$389$	−15.1472	−	15.1472i	−0.767991	−	0.767991i	0.209761	−	0.977753i	$-0.432731\pi$
$389$	−15.1472	−	15.1472i	−0.767991	−	0.767991i	−0.977753	+	0.209761i	$0.932731\pi$
$390$	3.23463			0.163792
$391$	25.2780	−	4.51498i	1.27836	−	0.228332i
$392$	14.2809			0.721296
$393$	4.61087	+	4.61087i	0.232588	+	0.232588i
$394$	−1.89480	−	4.57446i	−0.0954589	−	0.230458i
$395$			3.61153i			0.181716i
$396$	4.72078	−	1.95541i	0.237228	−	0.0982630i
$397$	−2.24019	+	5.40829i	−0.112432	+	0.271434i	−0.970073	−	0.242815i	$-0.921929\pi$
$397$	−2.24019	+	5.40829i	−0.112432	+	0.271434i	0.857641	+	0.514249i	$0.171929\pi$
$398$	−9.56287	−	3.96107i	−0.479344	−	0.198551i
$399$	13.0479	−	13.0479i	0.653212	−	0.653212i
$400$	−0.707107	+	0.707107i	−0.0353553	+	0.0353553i
$401$	−12.4339	−	5.15027i	−0.620917	−	0.257192i	0.0499710	−	0.998751i	$-0.484087\pi$
$401$	−12.4339	−	5.15027i	−0.620917	−	0.257192i	−0.670889	+	0.741558i	$0.734087\pi$
$402$	−1.05025	+	2.53553i	−0.0523818	+	0.126461i
$403$	−11.3477	+	4.70038i	−0.565270	+	0.234143i
$404$			6.96882i			0.346712i
$405$	−0.382683	−	0.923880i	−0.0190157	−	0.0459079i
$406$	−27.1918	−	27.1918i	−1.34950	−	1.34950i
$407$	38.2825			1.89759
$408$	−0.724967	−	4.05887i	−0.0358912	−	0.200944i
$409$	12.5762			0.621852			0.310926	−	0.950434i	$-0.399361\pi$
$409$	12.5762			0.621852			0.310926	+	0.950434i	$0.399361\pi$
$410$	6.76537	+	6.76537i	0.334118	+	0.334118i
$411$	4.40375	+	10.6316i	0.217221	+	0.524418i
$412$		−	17.5854i		−	0.866371i
$413$	−10.1081	+	4.18693i	−0.497389	+	0.206025i
$414$	−2.38329	+	5.75378i	−0.117132	+	0.282783i
$415$	−10.4074	−	4.31090i	−0.510880	−	0.211614i
$416$	−2.28723	+	2.28723i	−0.112141	+	0.112141i
$417$	14.9491	−	14.9491i	0.732061	−	0.732061i
$418$	18.8831	+	7.82164i	0.923603	+	0.382569i
$419$	2.27631	−	5.49550i	0.111205	−	0.268473i	−0.858473	−	0.512859i	$-0.828586\pi$
$419$	2.27631	−	5.49550i	0.111205	−	0.268473i	0.969678	+	0.244386i	$0.0785864\pi$
$420$	4.26197	−	1.76537i	0.207963	−	0.0861411i
$421$		−	17.3255i		−	0.844392i	−0.906505	−	0.422196i	$-0.861259\pi$
$421$		−	17.3255i		−	0.844392i	0.906505	−	0.422196i	$-0.138741\pi$
$422$	0.878415	+	2.12068i	0.0427606	+	0.103233i
$423$	−8.80525	−	8.80525i	−0.428126	−	0.428126i
$424$	1.36595			0.0663364
$425$	−4.02734	−	0.883480i	−0.195355	−	0.0428551i
$426$	9.09841			0.440819
$427$	−4.00000	−	4.00000i	−0.193574	−	0.193574i
$428$	1.06760	+	2.57741i	0.0516042	+	0.124584i
$429$		−	16.5281i		−	0.797985i
$430$	−7.62888	+	3.15998i	−0.367897	+	0.152388i
$431$	−2.94654	+	7.11358i	−0.141930	+	0.342649i	−0.978820	−	0.204722i	$-0.934371\pi$
$431$	−2.94654	+	7.11358i	−0.141930	+	0.342649i	0.836890	+	0.547370i	$0.184371\pi$
$432$	0.923880	+	0.382683i	0.0444502	+	0.0184119i
$433$	−26.3971	+	26.3971i	−1.26856	+	1.26856i	−0.321732	+	0.946831i	$0.604265\pi$
$433$	−26.3971	+	26.3971i	−1.26856	+	1.26856i	−0.946831	+	0.321732i	$0.895735\pi$
$434$	−12.3865	+	12.3865i	−0.594571	+	0.594571i
$435$	−7.70144	−	3.19004i	−0.369256	−	0.152951i
$436$	−5.79724	+	13.9958i	−0.277638	+	0.670276i
$437$	−23.0151	+	9.53317i	−1.10096	+	0.456033i
$438$		−	9.20851i		−	0.440000i
$439$	−11.1941	−	27.0250i	−0.534266	−	1.28983i	−0.928674	−	0.370897i	$-0.879050\pi$
$439$	−11.1941	−	27.0250i	−0.534266	−	1.28983i	0.394408	−	0.918935i	$-0.370950\pi$
$440$	3.61313	+	3.61313i	0.172249	+	0.172249i
$441$	−14.2809			−0.680044
$442$	−13.0270	−	2.85773i	−0.619630	−	0.135929i
$443$	−9.66136			−0.459025			−0.229513	−	0.973306i	$-0.573713\pi$
$443$	−9.66136			−0.459025			−0.229513	+	0.973306i	$0.573713\pi$
$444$	5.29769	+	5.29769i	0.251417	+	0.251417i
$445$	−3.45635	−	8.34436i	−0.163847	−	0.395561i
$446$		−	26.2446i		−	1.24272i
$447$	−18.9018	+	7.82938i	−0.894024	+	0.370317i
$448$	−1.76537	+	4.26197i	−0.0834057	+	0.201359i
$449$	14.1348	+	5.85483i	0.667063	+	0.276307i	0.690407	−	0.723421i	$-0.257431\pi$
$449$	14.1348	+	5.85483i	0.667063	+	0.276307i	−0.0233440	+	0.999727i	$0.507431\pi$
$450$	0.707107	−	0.707107i	0.0333333	−	0.0333333i
$451$	34.5692	−	34.5692i	1.62780	−	1.62780i
$452$	2.16799	+	0.898012i	0.101974	+	0.0422389i
$453$	−5.85143	+	14.1266i	−0.274924	+	0.663726i
$454$	−3.88054	+	1.60737i	−0.182123	+	0.0754377i
$455$		−	14.9218i		−	0.699543i
$456$	1.53073	+	3.69552i	0.0716832	+	0.173058i
$457$	22.3707	+	22.3707i	1.04646	+	1.04646i	0.998867	+	0.0475888i	$0.0151537\pi$
$457$	22.3707	+	22.3707i	1.04646	+	1.04646i	0.0475888	+	0.998867i	$0.484846\pi$
$458$	−12.5954			−0.588544
$459$	0.724967	+	4.05887i	0.0338386	+	0.189452i
$460$	−6.22784			−0.290375
$461$	10.7703	+	10.7703i	0.501621	+	0.501621i	0.911941	−	0.410320i	$-0.134583\pi$
$461$	10.7703	+	10.7703i	0.501621	+	0.501621i	−0.410320	+	0.911941i	$0.634583\pi$
$462$	−9.02055	−	21.7775i	−0.419674	−	1.01318i
$463$			26.4086i			1.22731i	0.789574	+	0.613656i	$0.210302\pi$
$463$			26.4086i			1.22731i	−0.789574	+	0.613656i	$0.789698\pi$
$464$	7.70144	−	3.19004i	0.357531	−	0.148094i
$465$	−1.45314	+	3.50819i	−0.0673878	+	0.162689i
$466$	19.3215	+	8.00321i	0.895049	+	0.370741i
$467$	6.10201	−	6.10201i	0.282367	−	0.282367i	−0.551685	−	0.834052i	$-0.686015\pi$
$467$	6.10201	−	6.10201i	0.282367	−	0.282367i	0.834052	+	0.551685i	$0.186015\pi$
$468$	2.28723	−	2.28723i	0.105727	−	0.105727i
$469$	11.6967	+	4.84495i	0.540105	+	0.223719i
$470$	4.76537	−	11.5046i	0.219810	−	0.530668i
$471$	1.68393	−	0.697506i	0.0775914	−	0.0321394i
$472$		−	2.37170i		−	0.109167i
$473$	16.1467	+	38.9815i	0.742425	+	1.79237i
$474$	2.55374	+	2.55374i	0.117297	+	0.117297i
$475$	4.00000			0.183533
$476$	−18.7241	+	3.34436i	−0.858217	+	0.153289i
$477$	−1.36595			−0.0625425
$478$	17.1644	+	17.1644i	0.785082	+	0.785082i
$479$	2.77725	+	6.70488i	0.126896	+	0.306354i	0.974541	−	0.224210i	$-0.0719802\pi$
$479$	2.77725	+	6.70488i	0.126896	+	0.306354i	−0.847645	+	0.530564i	$0.821980\pi$
$480$			1.00000i			0.0456435i
$481$	22.3894	−	9.27399i	1.02087	−	0.422857i
$482$	2.24426	−	5.41811i	0.102223	−	0.246788i
$483$	26.5429	+	10.9944i	1.20774	+	0.500264i
$484$	10.6839	−	10.6839i	0.485633	−	0.485633i
$485$	−4.24558	+	4.24558i	−0.192782	+	0.192782i
$486$	−0.923880	−	0.382683i	−0.0419080	−	0.0173589i
$487$	2.95468	−	7.13323i	0.133889	−	0.323237i	−0.842689	−	0.538401i	$-0.819029\pi$
$487$	2.95468	−	7.13323i	0.133889	−	0.323237i	0.976578	+	0.215164i	$0.0690285\pi$
$488$	1.13291	−	0.469266i	0.0512844	−	0.0212427i
$489$			7.77019i			0.351380i
$490$	−5.46508	−	13.1939i	−0.246887	−	0.596038i
$491$	1.07647	+	1.07647i	0.0485802	+	0.0485802i	0.730980	−	0.682399i	$-0.239063\pi$
$491$	1.07647	+	1.07647i	0.0485802	+	0.0485802i	−0.682399	+	0.730980i	$0.739063\pi$
$492$	9.56767			0.431344
$493$	28.1980	+	19.6515i	1.26997	+	0.885057i
$494$	12.9385			0.582132
$495$	−3.61313	−	3.61313i	−0.162398	−	0.162398i
$496$	−1.45314	−	3.50819i	−0.0652480	−	0.157523i
$497$		−	41.9721i		−	1.88271i
$498$	−10.4074	+	4.31090i	−0.466368	+	0.193176i
$499$	−4.17855	+	10.0879i	−0.187057	+	0.451597i	−0.989391	−	0.145280i	$-0.953592\pi$
$499$	−4.17855	+	10.0879i	−0.187057	+	0.451597i	0.802333	+	0.596876i	$0.203592\pi$
$500$	0.923880	+	0.382683i	0.0413171	+	0.0171141i
$501$	3.44401	−	3.44401i	0.153867	−	0.153867i
$502$	2.25151	−	2.25151i	0.100490	−	0.100490i
$503$	7.10750	+	2.94402i	0.316908	+	0.131268i	0.535467	−	0.844556i	$-0.320136\pi$
$503$	7.10750	+	2.94402i	0.316908	+	0.131268i	−0.218559	+	0.975824i	$0.570136\pi$
$504$	1.76537	−	4.26197i	0.0786357	−	0.189843i
$505$	6.43835	−	2.66685i	0.286503	−	0.118673i
$506$			31.8226i			1.41469i
$507$	0.970925	+	2.34402i	0.0431203	+	0.104102i
$508$	5.79430	+	5.79430i	0.257080	+	0.257080i
$509$	10.6762			0.473214			0.236607	−	0.971605i	$-0.423965\pi$
$509$	10.6762			0.473214			0.236607	+	0.971605i	$0.423965\pi$
$510$	−3.47247	+	2.22304i	−0.153764	+	0.0984381i
$511$	−42.4800			−1.87921
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−1.53073	−	3.69552i	−0.0675835	−	0.163161i
$514$		−	10.8084i		−	0.476740i
$515$	−16.2468	+	6.72965i	−0.715920	+	0.296544i
$516$	−3.15998	+	7.62888i	−0.139111	+	0.335843i
$517$	−58.7855	−	24.3497i	−2.58538	−	1.07090i
$518$	24.4389	−	24.4389i	1.07378	−	1.07378i
$519$	0.613126	−	0.613126i	0.0269132	−	0.0269132i
$520$	2.98841	+	1.23784i	0.131051	+	0.0542829i
$521$	−12.7019	+	30.6652i	−0.556482	+	1.34347i	0.356053	+	0.934466i	$0.384122\pi$
$521$	−12.7019	+	30.6652i	−0.556482	+	1.34347i	−0.912534	+	0.409000i	$0.865878\pi$
$522$	−7.70144	+	3.19004i	−0.337083	+	0.139624i
$523$		−	13.6526i		−	0.596988i	−0.954412	−	0.298494i	$-0.903516\pi$
$523$		−	13.6526i		−	0.596988i	0.954412	−	0.298494i	$-0.0964843\pi$
$524$	2.49539	+	6.02440i	0.109011	+	0.263177i
$525$	−3.26197	−	3.26197i	−0.142364	−	0.142364i
$526$	26.1440			1.13993
$527$	8.95171	−	12.8449i	0.389943	−	0.559531i
$528$	5.10973			0.222373
$529$	−11.1624	−	11.1624i	−0.485323	−	0.485323i
$530$	−0.522726	−	1.26197i	−0.0227058	−	0.0548166i
$531$			2.37170i			0.102923i
$532$	17.0479	−	7.06147i	0.739120	−	0.306153i
$533$	11.8433	−	28.5921i	0.512988	−	1.23846i
$534$	−8.34436	−	3.45635i	−0.361096	−	0.149571i
$535$	1.97266	−	1.97266i	0.0852856	−	0.0852856i
$536$	−1.94061	+	1.94061i	−0.0838217	+	0.0838217i
$537$	−16.0469	−	6.64686i	−0.692476	−	0.286833i
$538$	4.91761	−	11.8722i	0.212013	−	0.511845i
$539$	−67.4171	+	27.9251i	−2.90386	+	1.20282i
$540$		−	1.00000i		−	0.0430331i
$541$	7.61859	+	18.3929i	0.327549	+	0.790773i	0.998773	+	0.0495188i	$0.0157688\pi$
$541$	7.61859	+	18.3929i	0.327549	+	0.790773i	−0.671224	+	0.741254i	$0.734231\pi$
$542$	4.70193	+	4.70193i	0.201965	+	0.201965i
$543$	−6.20345			−0.266215
$544$	0.883480	−	4.02734i	0.0378789	−	0.172671i
$545$	15.1489			0.648909
$546$	−10.5513	−	10.5513i	−0.451553	−	0.451553i
$547$	9.16167	+	22.1182i	0.391725	+	0.945707i	0.989564	+	0.144091i	$0.0460259\pi$
$547$	9.16167	+	22.1182i	0.391725	+	0.945707i	−0.597840	+	0.801616i	$0.703974\pi$
$548$			11.5076i			0.491578i
$549$	−1.13291	+	0.469266i	−0.0483514	+	0.0200278i
$550$	1.95541	−	4.72078i	0.0833789	−	0.201295i
$551$	−30.8058	−	12.7602i	−1.31237	−	0.543602i
$552$	−4.40375	+	4.40375i	−0.187436	+	0.187436i
$553$	11.7807	−	11.7807i	0.500967	−	0.500967i
$554$	19.1585	+	7.93570i	0.813966	+	0.337156i
$555$	2.86709	−	6.92177i	0.121701	−	0.293813i
$556$	19.5320	−	8.09040i	0.828339	−	0.343109i
$557$		−	43.3001i		−	1.83469i	−0.398098	−	0.917343i	$-0.630330\pi$
$557$		−	43.3001i		−	1.83469i	0.398098	−	0.917343i	$-0.369670\pi$
$558$	1.45314	+	3.50819i	0.0615164	+	0.148514i
$559$	18.8867	+	18.8867i	0.798821	+	0.798821i
$560$	4.61313			0.194940
$561$	11.3592	+	17.7434i	0.479584	+	0.749127i
$562$	−18.5104			−0.780813
$563$	−5.18834	−	5.18834i	−0.218662	−	0.218662i	0.589272	−	0.807935i	$-0.299415\pi$
$563$	−5.18834	−	5.18834i	−0.218662	−	0.218662i	−0.807935	+	0.589272i	$0.799415\pi$
$564$	−4.76537	−	11.5046i	−0.200658	−	0.484432i
$565$		−	2.34662i		−	0.0987229i
$566$	29.4201	−	12.1862i	1.23662	−	0.512224i
$567$	−1.76537	+	4.26197i	−0.0741384	+	0.178986i
$568$	8.40583	+	3.48181i	0.352701	+	0.146093i
$569$	25.3565	−	25.3565i	1.06300	−	1.06300i	0.0651241	−	0.997877i	$-0.479256\pi$
$569$	25.3565	−	25.3565i	1.06300	−	1.06300i	0.997877	−	0.0651241i	$-0.0207443\pi$
$570$	2.82843	−	2.82843i	0.118470	−	0.118470i
$571$	−35.3987	−	14.6626i	−1.48139	−	0.613611i	−0.511965	−	0.859006i	$-0.671082\pi$
$571$	−35.3987	−	14.6626i	−1.48139	−	0.613611i	−0.969423	+	0.245395i	$0.921082\pi$
$572$	6.32503	−	15.2700i	0.264463	−	0.638470i
$573$	2.17958	−	0.902812i	0.0910533	−	0.0377155i
$574$		−	44.1369i		−	1.84224i
$575$	2.38329	+	5.75378i	0.0993902	+	0.239949i
$576$	0.707107	+	0.707107i	0.0294628	+	0.0294628i
$577$	11.2911			0.470053			0.235026	−	0.971989i	$-0.424482\pi$
$577$	11.2911			0.470053			0.235026	+	0.971989i	$0.424482\pi$
$578$	15.9488	−	5.88509i	0.663385	−	0.244788i
$579$	1.54847			0.0643523
$580$	−5.89443	−	5.89443i	−0.244753	−	0.244753i
$581$	19.8867	+	48.0108i	0.825040	+	1.99182i
$582$			6.00416i			0.248881i
$583$	−6.44834	+	2.67099i	−0.267063	+	0.110621i
$584$	3.52395	−	8.50756i	0.145822	−	0.352045i
$585$	−2.98841	−	1.23784i	−0.123556	−	0.0511784i
$586$	−0.102943	+	0.102943i	−0.00425255	+	0.00425255i
$587$	−16.7525	+	16.7525i	−0.691449	+	0.691449i	−0.962551	−	0.271102i	$-0.912612\pi$
$587$	−16.7525	+	16.7525i	−0.691449	+	0.691449i	0.271102	+	0.962551i	$0.412612\pi$
$588$	−13.1939	−	5.46508i	−0.544106	−	0.225376i
$589$	−5.81257	+	14.0328i	−0.239503	+	0.578211i
$590$	−2.19117	+	0.907612i	−0.0902090	+	0.0373658i
$591$			4.95136i			0.203672i
$592$	2.86709	+	6.92177i	0.117837	+	0.284483i
$593$	22.0907	+	22.0907i	0.907156	+	0.907156i	0.996042	−	0.0888861i	$-0.0283307\pi$
$593$	22.0907	+	22.0907i	0.907156	+	0.907156i	−0.0888861	+	0.996042i	$0.528331\pi$
$594$	−5.10973			−0.209655
$595$	10.2552	+	16.0190i	0.420422	+	0.656713i
$596$	−20.4592			−0.838040
$597$	7.31911	+	7.31911i	0.299551	+	0.299551i
$598$	7.70908	+	18.6114i	0.315248	+	0.761075i
$599$		−	39.0402i		−	1.59514i	−0.603227	−	0.797570i	$-0.706119\pi$
$599$		−	39.0402i		−	1.59514i	0.603227	−	0.797570i	$-0.293881\pi$
$600$	0.923880	−	0.382683i	0.0377172	−	0.0156230i
$601$	−5.78725	+	13.9716i	−0.236067	+	0.569915i	−0.996869	−	0.0790680i	$-0.974806\pi$
$601$	−5.78725	+	13.9716i	−0.236067	+	0.569915i	0.760803	+	0.648983i	$0.224806\pi$
$602$	35.1930	+	14.5774i	1.43436	+	0.594131i
$603$	1.94061	−	1.94061i	0.0790279	−	0.0790279i
$604$	−10.8120	+	10.8120i	−0.439936	+	0.439936i
$605$	−13.9592	−	5.78210i	−0.567523	−	0.235076i
$606$	2.66685	−	6.43835i	0.108333	−	0.261540i
$607$	21.9503	−	9.09212i	0.890936	−	0.369038i	0.110208	−	0.993909i	$-0.464848\pi$
$607$	21.9503	−	9.09212i	0.890936	−	0.369038i	0.780728	+	0.624871i	$0.214848\pi$
$608$			4.00000i			0.162221i
$609$	14.7161	+	35.5277i	0.596325	+	1.43966i
$610$	−0.867091	−	0.867091i	−0.0351075	−	0.0351075i
$611$	−40.2793			−1.62953
$612$	−0.883480	+	4.02734i	−0.0357126	+	0.162796i
$613$	23.1238			0.933961			0.466980	−	0.884268i	$-0.345342\pi$
$613$	23.1238			0.933961			0.466980	+	0.884268i	$0.345342\pi$
$614$	6.02979	+	6.02979i	0.243343	+	0.243343i
$615$	−3.66139	−	8.83938i	−0.147642	−	0.356438i
$616$		−	23.5718i		−	0.949736i
$617$	−1.33450	+	0.552768i	−0.0537250	+	0.0222536i	−0.409384	−	0.912362i	$-0.634256\pi$
$617$	−1.33450	+	0.552768i	−0.0537250	+	0.0222536i	0.355659	+	0.934616i	$0.384256\pi$
$618$	−6.72965	+	16.2468i	−0.270706	+	0.653542i
$619$	4.44834	+	1.84256i	0.178794	+	0.0740589i	0.470285	−	0.882515i	$-0.344151\pi$
$619$	4.44834	+	1.84256i	0.178794	+	0.0740589i	−0.291491	+	0.956574i	$0.594151\pi$
$620$	−2.68506	+	2.68506i	−0.107834	+	0.107834i
$621$	4.40375	−	4.40375i	0.176716	−	0.176716i
$622$	−3.80819	−	1.57741i	−0.152695	−	0.0632482i
$623$	−15.9446	+	38.4936i	−0.638806	+	1.54221i
$624$	2.98841	−	1.23784i	0.119632	−	0.0495533i
$625$		−	1.00000i		−	0.0400000i
$626$	5.13479	+	12.3965i	0.205227	+	0.495463i
$627$	−14.4525	−	14.4525i	−0.577177	−	0.577177i
$628$	1.82267			0.0727325
$629$	−17.6620	+	25.3433i	−0.704230	+	1.01050i
$630$	−4.61313			−0.183791
$631$	−19.7247	−	19.7247i	−0.785229	−	0.785229i	0.195479	−	0.980708i	$-0.437374\pi$
$631$	−19.7247	−	19.7247i	−0.785229	−	0.785229i	−0.980708	+	0.195479i	$0.937374\pi$
$632$	1.38207	+	3.33662i	0.0549759	+	0.132724i
$633$		−	2.29541i		−	0.0912344i
$634$	16.1808	−	6.70231i	0.642622	−	0.266183i
$635$	3.13585	−	7.57062i	0.124442	−	0.300431i
$636$	−1.26197	−	0.522726i	−0.0500405	−	0.0207274i
$637$	−32.6638	+	32.6638i	−1.29419	+	1.29419i
$638$	−30.1190	+	30.1190i	−1.19242	+	1.19242i
$639$	−8.40583	−	3.48181i	−0.332530	−	0.137738i
$640$	−0.382683	+	0.923880i	−0.0151269	+	0.0365195i
$641$	16.9500	−	7.02092i	0.669485	−	0.277310i	−0.0219385	−	0.999759i	$-0.506984\pi$
$641$	16.9500	−	7.02092i	0.669485	−	0.277310i	0.691424	+	0.722449i	$0.256984\pi$
$642$		−	2.78976i		−	0.110103i
$643$	8.35549	+	20.1719i	0.329508	+	0.795503i	0.998629	+	0.0523494i	$0.0166710\pi$
$643$	8.35549	+	20.1719i	0.329508	+	0.795503i	−0.669121	+	0.743154i	$0.733329\pi$
$644$	20.3151	+	20.3151i	0.800525	+	0.800525i
$645$	8.25744			0.325136
$646$	−13.8899	+	8.89218i	−0.546491	+	0.349858i
$647$	11.9054			0.468049			0.234024	−	0.972231i	$-0.424810\pi$
$647$	11.9054			0.468049			0.234024	+	0.972231i	$0.424810\pi$
$648$	−0.707107	−	0.707107i	−0.0277778	−	0.0277778i
$649$	4.63765	+	11.1963i	0.182044	+	0.439493i
$650$		−	3.23463i		−	0.126873i
$651$	16.1837	−	6.70353i	0.634291	−	0.262732i
$652$	−2.97352	+	7.17872i	−0.116452	+	0.281140i
$653$	−1.94526	−	0.805755i	−0.0761241	−	0.0315316i	0.344297	−	0.938861i	$-0.388117\pi$
$653$	−1.94526	−	0.805755i	−0.0761241	−	0.0315316i	−0.420421	+	0.907329i	$0.638117\pi$
$654$	10.7119	−	10.7119i	0.418869	−	0.418869i
$655$	4.61087	−	4.61087i	0.180162	−	0.180162i
$656$	8.83938	+	3.66139i	0.345120	+	0.142953i
$657$	−3.52395	+	8.50756i	−0.137482	+	0.331911i
$658$	−53.0722	+	21.9832i	−2.06897	+	0.856996i
$659$		−	34.9841i		−	1.36279i	−0.731918	−	0.681393i	$-0.761374\pi$
$659$		−	34.9841i		−	1.36279i	0.731918	−	0.681393i	$-0.238626\pi$
$660$	−1.95541	−	4.72078i	−0.0761142	−	0.183756i
$661$	16.7502	+	16.7502i	0.651508	+	0.651508i	0.953356	−	0.301848i	$-0.0976034\pi$
$661$	16.7502	+	16.7502i	0.651508	+	0.651508i	−0.301848	+	0.953356i	$0.597603\pi$
$662$	10.7274			0.416932
$663$	10.9417	+	7.62541i	0.424942	+	0.296146i
$664$	−11.2649			−0.437164
$665$	−13.0479	−	13.0479i	−0.505975	−	0.505975i
$666$	−2.86709	−	6.92177i	−0.111098	−	0.268213i
$667$		−	51.9152i		−	2.01016i
$668$	4.49981	−	1.86388i	0.174103	−	0.0721158i
$669$	−10.0434	+	24.2468i	−0.388299	+	0.937436i
$670$	2.53553	+	1.05025i	0.0979562	+	0.0405748i
$671$	−4.43060	+	4.43060i	−0.171042	+	0.171042i
$672$	3.26197	−	3.26197i	0.125833	−	0.125833i
$673$	−25.5631	−	10.5886i	−0.985387	−	0.408160i	−0.168968	−	0.985621i	$-0.554044\pi$
$673$	−25.5631	−	10.5886i	−0.985387	−	0.408160i	−0.816418	+	0.577461i	$0.804044\pi$
$674$	2.62951	−	6.34821i	0.101285	−	0.244524i
$675$	−0.923880	+	0.382683i	−0.0355601	+	0.0147295i
$676$			2.53715i			0.0975826i
$677$	−12.5971	−	30.4121i	−0.484146	−	1.16883i	−0.957623	−	0.288026i	$-0.907001\pi$
$677$	−12.5971	−	30.4121i	−0.484146	−	1.16883i	0.473476	−	0.880807i	$-0.342999\pi$
$678$	−1.65931	−	1.65931i	−0.0637254	−	0.0637254i
$679$	27.6980			1.06295
$680$	−4.05887	+	0.724967i	−0.155651	+	0.0278012i
$681$	4.20026			0.160954
$682$	13.7199	+	13.7199i	0.525363	+	0.525363i
$683$	−12.5835	−	30.3793i	−0.481496	−	1.16243i	−0.958899	−	0.283749i	$-0.908422\pi$
$683$	−12.5835	−	30.3793i	−0.481496	−	1.16243i	0.477403	−	0.878684i	$-0.341578\pi$
$684$		−	4.00000i		−	0.152944i
$685$	10.6316	−	4.40375i	0.406212	−	0.168259i
$686$	−12.8535	+	31.0311i	−0.490749	+	1.18477i
$687$	11.6366	+	4.82005i	0.443965	+	0.183896i
$688$	−5.83889	+	5.83889i	−0.222606	+	0.222606i
$689$	−3.12424	+	3.12424i	−0.119024	+	0.119024i
$690$	5.75378	+	2.38329i	0.219043	+	0.0907304i
$691$	−13.4972	+	32.5850i	−0.513456	+	1.23959i	0.428404	+	0.903588i	$0.359076\pi$
$691$	−13.4972	+	32.5850i	−0.513456	+	1.23959i	−0.941860	+	0.336006i	$0.890924\pi$
$692$	0.801088	−	0.331821i	0.0304528	−	0.0126140i
$693$			23.5718i			0.895420i
$694$	−2.27518	−	5.49276i	−0.0863645	−	0.208502i
$695$	−14.9491	−	14.9491i	−0.567052	−	0.567052i
$696$	−8.33598			−0.315975
$697$	6.93625	+	38.8339i	0.262729	+	1.47094i
$698$	−15.6342			−0.591763
$699$	−14.7880	−	14.7880i	−0.559333	−	0.559333i
$700$	−1.76537	−	4.26197i	−0.0667246	−	0.161087i
$701$		−	22.1766i		−	0.837598i	−0.908079	−	0.418799i	$-0.862451\pi$
$701$		−	22.1766i		−	0.837598i	0.908079	−	0.418799i	$-0.137549\pi$
$702$	−2.98841	+	1.23784i	−0.112790	+	0.0467193i
$703$	11.4684	−	27.6871i	0.432538	−	1.04424i
$704$	4.72078	+	1.95541i	0.177921	+	0.0736973i
$705$	−8.80525	+	8.80525i	−0.331625	+	0.331625i
$706$	18.2027	−	18.2027i	0.685068	−	0.685068i
$707$	−29.7009	−	12.3025i	−1.11702	−	0.462684i
$708$	−0.907612	+	2.19117i	−0.0341101	+	0.0823492i
$709$	3.13066	−	1.29676i	0.117574	−	0.0487009i	−0.323121	−	0.946358i	$-0.604732\pi$
$709$	3.13066	−	1.29676i	0.117574	−	0.0487009i	0.440695	+	0.897657i	$0.354732\pi$
$710$		−	9.09841i		−	0.341457i
$711$	−1.38207	−	3.33662i	−0.0518318	−	0.125133i
$712$	−6.38650	−	6.38650i	−0.239344	−	0.239344i
$713$	−23.6486			−0.885648
$714$	18.5786	+	4.07560i	0.695288	+	0.152526i
$715$	−16.5281			−0.618116
$716$	−12.2818	−	12.2818i	−0.458992	−	0.458992i
$717$	−9.28931	−	22.4264i	−0.346916	−	0.837529i
$718$		−	1.57709i		−	0.0588564i
$719$	30.5438	−	12.6517i	1.13909	−	0.471827i	0.268230	−	0.963355i	$-0.413561\pi$
$719$	30.5438	−	12.6517i	1.13909	−	0.471827i	0.870862	+	0.491528i	$0.163561\pi$
$720$	0.382683	−	0.923880i	0.0142618	−	0.0344310i
$721$	74.9485	+	31.0447i	2.79123	+	1.15617i
$722$	−2.12132	+	2.12132i	−0.0789474	+	0.0789474i
$723$	−4.14684	+	4.14684i	−0.154223	+	0.154223i
$724$	−5.73124	−	2.37396i	−0.213000	−	0.0882274i
$725$	−3.19004	+	7.70144i	−0.118475	+	0.286024i
$726$	−13.9592	+	5.78210i	−0.518075	+	0.214594i
$727$			27.6774i			1.02650i	0.858239	+	0.513250i	$0.171559\pi$
$727$			27.6774i			1.02650i	−0.858239	+	0.513250i	$0.828441\pi$
$728$	−5.71031	−	13.7859i	−0.211638	−	0.510940i
$729$	0.707107	+	0.707107i	0.0261891	+	0.0261891i
$730$	−9.20851			−0.340822
$731$	−33.2555	−	7.29528i	−1.23000	−	0.269826i
$732$	−1.22625			−0.0453236
$733$	7.60197	+	7.60197i	0.280785	+	0.280785i	0.833422	−	0.552637i	$-0.186378\pi$
$733$	7.60197	+	7.60197i	0.280785	+	0.280785i	−0.552637	+	0.833422i	$0.686378\pi$
$734$	−1.46314	−	3.53233i	−0.0540054	−	0.130381i
$735$			14.2809i			0.526760i
$736$	−5.75378	+	2.38329i	−0.212087	+	0.0878493i
$737$	5.36651	−	12.9559i	0.197678	−	0.477237i
$738$	−8.83938	−	3.66139i	−0.325382	−	0.134778i
$739$	−11.6273	+	11.6273i	−0.427716	+	0.427716i	−0.887850	−	0.460134i	$-0.847801\pi$
$739$	−11.6273	+	11.6273i	−0.427716	+	0.427716i	0.460134	+	0.887850i	$0.347801\pi$
$740$	5.29769	−	5.29769i	0.194747	−	0.194747i
$741$	−11.9536	−	4.95136i	−0.439128	−	0.181893i
$742$	−2.41140	+	5.82164i	−0.0885253	+	0.213719i
$743$	17.7106	−	7.33596i	0.649738	−	0.269130i	−0.0333750	−	0.999443i	$-0.510626\pi$
$743$	17.7106	−	7.33596i	0.649738	−	0.269130i	0.683113	+	0.730313i	$0.260626\pi$
$744$			3.79724i			0.139214i
$745$	7.82938	+	18.9018i	0.286846	+	0.692508i
$746$	6.02979	+	6.02979i	0.220766	+	0.220766i
$747$	11.2649			0.412162
$748$	3.70439	+	20.7397i	0.135446	+	0.758320i
$749$	−12.8695			−0.470242
$750$	−0.707107	−	0.707107i	−0.0258199	−	0.0258199i
$751$	−2.09345	−	5.05404i	−0.0763912	−	0.184425i	0.881071	−	0.472985i	$-0.156823\pi$
$751$	−2.09345	−	5.05404i	−0.0763912	−	0.184425i	−0.957462	+	0.288560i	$0.906823\pi$
$752$		−	12.4525i		−	0.454096i
$753$	−2.94174	+	1.21851i	−0.107203	+	0.0444049i
$754$	−10.3186	+	24.9113i	−0.375782	+	0.907218i
$755$	14.1266	+	5.85143i	0.514120	+	0.212955i
$756$	−3.26197	+	3.26197i	−0.118637	+	0.118637i
$757$	−26.5151	+	26.5151i	−0.963707	+	0.963707i	−0.999364	−	0.0356573i	$-0.988648\pi$
$757$	−26.5151	+	26.5151i	−0.963707	+	0.963707i	0.0356573	+	0.999364i	$0.488648\pi$
$758$	−0.532327	−	0.220497i	−0.0193350	−	0.00800881i
$759$	12.1780	−	29.4003i	0.442033	−	1.06716i
$760$	3.69552	−	1.53073i	0.134051	−	0.0555255i
$761$		−	18.8762i		−	0.684260i	−0.939653	−	0.342130i	$-0.888852\pi$
$761$		−	18.8762i		−	0.684260i	0.939653	−	0.342130i	$-0.111148\pi$
$762$	−3.13585	−	7.57062i	−0.113600	−	0.274255i
$763$	−49.4154	−	49.4154i	−1.78896	−	1.78896i
$764$	2.35916			0.0853514
$765$	4.05887	−	0.724967i	0.146749	−	0.0262112i
$766$	8.37146			0.302473
$767$	5.42464	+	5.42464i	0.195872	+	0.195872i
$768$	0.382683	+	0.923880i	0.0138089	+	0.0333376i
$769$			24.5762i			0.886240i	0.896462	+	0.443120i	$0.146128\pi$
$769$			24.5762i			0.886240i	−0.896462	+	0.443120i	$0.853872\pi$
$770$	−21.7775	+	9.02055i	−0.784808	+	0.325078i
$771$	−4.13621	+	9.98569i	−0.148962	+	0.359626i
$772$	1.43060	+	0.592575i	0.0514885	+	0.0213272i
$773$	33.1703	−	33.1703i	1.19305	−	1.19305i	0.216847	−	0.976206i	$-0.430423\pi$
$773$	33.1703	−	33.1703i	1.19305	−	1.19305i	0.976206	−	0.216847i	$-0.0695773\pi$
$774$	5.83889	−	5.83889i	0.209875	−	0.209875i
$775$	3.50819	+	1.45314i	0.126018	+	0.0521984i
$776$	−2.29769	+	5.54712i	−0.0824824	+	0.199130i
$777$	−31.9310	+	13.2263i	−1.14552	+	0.474489i
$778$			21.4213i			0.767991i
$779$	−14.6456	−	35.3575i	−0.524732	−	1.26681i
$780$	−2.28723	−	2.28723i	−0.0818960	−	0.0818960i
$781$	−46.4904			−1.66356
$782$	−21.0668	−	14.6817i	−0.753348	−	0.525016i
$783$	8.33598			0.297904
$784$	−10.0981	−	10.0981i	−0.360648	−	0.360648i
$785$	−0.697506	−	1.68393i	−0.0248951	−	0.0601020i
$786$		−	6.52076i		−	0.232588i
$787$	47.2599	−	19.5757i	1.68464	−	0.697799i	0.685105	−	0.728444i	$-0.259756\pi$
$787$	47.2599	−	19.5757i	1.68464	−	0.697799i	0.999530	+	0.0306456i	$0.00975633\pi$
$788$	−1.89480	+	4.57446i	−0.0674996	+	0.162958i
$789$	−24.1539	−	10.0049i	−0.859903	−	0.356184i
$790$	2.55374	−	2.55374i	0.0908580	−	0.0908580i
$791$	−7.65460	+	7.65460i	−0.272166	+	0.272166i
$792$	−4.72078	−	1.95541i	−0.167745	−	0.0694825i
$793$	−1.51790	+	3.66454i	−0.0539024	+	0.130132i
$794$	5.40829	−	2.24019i	0.191933	−	0.0795012i
$795$			1.36595i			0.0484452i
$796$	3.96107	+	9.56287i	0.140396	+	0.338947i
$797$	19.6633	+	19.6633i	0.696509	+	0.696509i	0.963656	−	0.267147i	$-0.0860809\pi$
$797$	19.6633	+	19.6633i	0.696509	+	0.696509i	−0.267147	+	0.963656i	$0.586081\pi$
$798$	−18.4525			−0.653212
$799$	43.2410	−	27.6825i	1.52976	−	0.979335i
$800$	1.00000			0.0353553
$801$	6.38650	+	6.38650i	0.225656	+	0.225656i
$802$	5.15027	+	12.4339i	0.181863	+	0.439055i
$803$			47.0530i			1.66047i
$804$	2.53553	−	1.05025i	0.0894214	−	0.0370396i
$805$	10.9944	−	26.5429i	0.387503	−	0.935514i
$806$	11.3477	+	4.70038i	0.399706	+	0.165564i
$807$	−9.08655	+	9.08655i	−0.319862	+	0.319862i
$808$	4.92770	−	4.92770i	0.173356	−	0.173356i
$809$	28.5664	+	11.8326i	1.00434	+	0.416012i	0.823387	−	0.567480i	$-0.192082\pi$
$809$	28.5664	+	11.8326i	1.00434	+	0.416012i	0.180954	+	0.983492i	$0.442082\pi$
$810$	−0.382683	+	0.923880i	−0.0134461	+	0.0324618i
$811$	22.0386	−	9.12869i	0.773880	−	0.320552i	0.0394372	−	0.999222i	$-0.487444\pi$
$811$	22.0386	−	9.12869i	0.773880	−	0.320552i	0.734443	+	0.678670i	$0.237444\pi$
$812$			38.4549i			1.34950i
$813$	−2.54467	−	6.14337i	−0.0892454	−	0.215457i
$814$	−27.0698	−	27.0698i	−0.948796	−	0.948796i
$815$	7.77019			0.272178
$816$	−2.35743	+	3.38268i	−0.0825264	+	0.118418i
$817$	33.0297			1.15556
$818$	−8.89271	−	8.89271i	−0.310926	−	0.310926i
$819$	5.71031	+	13.7859i	0.199535	+	0.481719i
$820$		−	9.56767i		−	0.334118i
$821$	−36.6939	+	15.1991i	−1.28063	+	0.530453i	−0.916178	−	0.400771i	$-0.868742\pi$
$821$	−36.6939	+	15.1991i	−1.28063	+	0.530453i	−0.364448	+	0.931224i	$0.618742\pi$
$822$	4.40375	−	10.6316i	0.153598	−	0.370819i
$823$	−19.5924	−	8.11546i	−0.682950	−	0.282887i	0.0141097	−	0.999900i	$-0.495509\pi$
$823$	−19.5924	−	8.11546i	−0.682950	−	0.282887i	−0.697059	+	0.717013i	$0.745509\pi$
$824$	−12.4348	+	12.4348i	−0.433186	+	0.433186i
$825$	−3.61313	+	3.61313i	−0.125793	+	0.125793i
$826$	10.1081	+	4.18693i	0.351707	+	0.145682i
$827$	−15.2605	+	36.8422i	−0.530661	+	1.28113i	0.400425	+	0.916329i	$0.368862\pi$
$827$	−15.2605	+	36.8422i	−0.530661	+	1.28113i	−0.931086	+	0.364799i	$0.881138\pi$
$828$	5.75378	−	2.38329i	0.199958	−	0.0828252i
$829$			20.7092i			0.719262i	0.933095	+	0.359631i	$0.117097\pi$
$829$			20.7092i			0.719262i	−0.933095	+	0.359631i	$0.882903\pi$
$830$	4.31090	+	10.4074i	0.149633	+	0.361247i
$831$	−14.6633	−	14.6633i	−0.508663	−	0.508663i
$832$	3.23463			0.112141
$833$	12.6169	−	57.5142i	0.437150	−	1.99275i
$834$	−21.1412			−0.732061
$835$	−3.44401	−	3.44401i	−0.119185	−	0.119185i
$836$	−7.82164	−	18.8831i	−0.270517	−	0.653086i
$837$		−	3.79724i		−	0.131252i
$838$	−5.49550	+	2.27631i	−0.189839	+	0.0786339i
$839$	−10.7610	+	25.9794i	−0.371512	+	0.896908i	0.621983	+	0.783031i	$0.286327\pi$
$839$	−10.7610	+	25.9794i	−0.371512	+	0.896908i	−0.993495	+	0.113878i	$0.963673\pi$
$840$	−4.26197	−	1.76537i	−0.147052	−	0.0609109i
$841$	28.6298	−	28.6298i	0.987234	−	0.987234i
$842$	−12.2510	+	12.2510i	−0.422196	+	0.422196i
$843$	17.1014	+	7.08361i	0.589002	+	0.243973i
$844$	0.878415	−	2.12068i	0.0302363	−	0.0729969i
$845$	2.34402	−	0.970925i	0.0806367	−	0.0334008i
$846$			12.4525i			0.428126i
$847$	26.6736	+	64.3957i	0.916514	+	2.21266i
$848$	−0.965872	−	0.965872i	−0.0331682	−	0.0331682i
$849$	−31.8441			−1.09289
$850$	2.22304	+	3.47247i	0.0762498	+	0.119105i
$851$	46.6594			1.59947
$852$	−6.43355	−	6.43355i	−0.220410	−	0.220410i
$853$	3.07843	+	7.43199i	0.105404	+	0.254467i	0.967778	−	0.251804i	$-0.0810238\pi$
$853$	3.07843	+	7.43199i	0.105404	+	0.254467i	−0.862375	+	0.506270i	$0.831024\pi$
$854$			5.65685i			0.193574i
$855$	−3.69552	+	1.53073i	−0.126384	+	0.0523500i
$856$	1.06760	−	2.57741i	0.0364897	−	0.0880939i
$857$	16.2008	+	6.71058i	0.553408	+	0.229229i	0.641820	−	0.766855i	$-0.278179\pi$
$857$	16.2008	+	6.71058i	0.553408	+	0.229229i	−0.0884127	+	0.996084i	$0.528179\pi$
$858$	−11.6871	+	11.6871i	−0.398992	+	0.398992i
$859$	29.3019	−	29.3019i	0.999766	−	0.999766i	−0.000233562	−	1.00000i	$-0.500074\pi$
$859$	29.3019	−	29.3019i	0.999766	−	0.999766i	1.00000		0.000233562i	$7.43451e-5\pi$
$860$	7.62888	+	3.15998i	0.260143	+	0.107755i
$861$	−16.8905	+	40.7772i	−0.575625	+	1.38968i
$862$	7.11358	−	2.94654i	0.242289	−	0.100360i
$863$			29.7790i			1.01369i	0.862038	+	0.506844i	$0.169188\pi$
$863$			29.7790i			1.01369i	−0.862038	+	0.506844i	$0.830812\pi$
$864$	−0.382683	−	0.923880i	−0.0130192	−	0.0314310i
$865$	−0.613126	−	0.613126i	−0.0208469	−	0.0208469i
$866$	37.3311			1.26856
$867$	−16.9869	−	0.666241i	−0.576907	−	0.0226267i
$868$	17.5172			0.594571
$869$	−13.0489	−	13.0489i	−0.442654	−	0.442654i
$870$	3.19004	+	7.70144i	0.108153	+	0.261103i
$871$		−	8.87726i		−	0.300795i
$872$	13.9958	−	5.79724i	0.473957	−	0.196319i
$873$	2.29769	−	5.54712i	0.0777651	−	0.187742i
$874$	23.0151	+	9.53317i	0.778498	+	0.322464i
$875$	−3.26197	+	3.26197i	−0.110275	+	0.110275i
$876$	−6.51140	+	6.51140i	−0.220000	+	0.220000i
$877$	−32.8998	−	13.6275i	−1.11095	−	0.460170i	−0.249684	−	0.968327i	$-0.580327\pi$
$877$	−32.8998	−	13.6275i	−1.11095	−	0.460170i	−0.861264	+	0.508158i	$0.830327\pi$
$878$	−11.1941	+	27.0250i	−0.377783	+	0.912049i
$879$	0.134502	−	0.0557125i	0.00453663	−	0.00187913i
$880$		−	5.10973i		−	0.172249i
$881$	11.0643	+	26.7115i	0.372765	+	0.899934i	0.993280	+	0.115739i	$0.0369238\pi$
$881$	11.0643	+	26.7115i	0.372765	+	0.899934i	−0.620515	+	0.784195i	$0.713076\pi$
$882$	10.0981	+	10.0981i	0.340022	+	0.340022i
$883$	47.8658			1.61081			0.805406	−	0.592723i	$-0.201947\pi$
$883$	47.8658			1.61081			0.805406	+	0.592723i	$0.201947\pi$
$884$	7.19073	+	11.2322i	0.241851	+	0.377779i
$885$	2.37170			0.0797240
$886$	6.83161	+	6.83161i	0.229513	+	0.229513i
$887$	14.4425	+	34.8673i	0.484932	+	1.17073i	0.957240	+	0.289296i	$0.0934211\pi$
$887$	14.4425	+	34.8673i	0.484932	+	1.17073i	−0.472308	+	0.881434i	$0.656579\pi$
$888$		−	7.49207i		−	0.251417i
$889$	−34.9242	+	14.4661i	−1.17132	+	0.485177i
$890$	−3.45635	+	8.34436i	−0.115857	+	0.279704i
$891$	4.72078	+	1.95541i	0.158152	+	0.0655087i
$892$	−18.5577	+	18.5577i	−0.621358	+	0.621358i
$893$	−35.2210	+	35.2210i	−1.17863	+	1.17863i
$894$	18.9018	+	7.82938i	0.632171	+	0.261854i
$895$	−6.64686	+	16.0469i	−0.222180	+	0.536390i
$896$	4.26197	−	1.76537i	0.142383	−	0.0589768i
$897$		−	20.1448i		−	0.672615i
$898$	−5.85483	−	14.1348i	−0.195378	−	0.471685i
$899$	−22.3826	−	22.3826i	−0.746501	−	0.746501i
$900$	−1.00000			−0.0333333
$901$	1.20679	−	5.50114i	0.0402040	−	0.183270i
$902$	−48.8882			−1.62780
$903$	−26.9355	−	26.9355i	−0.896358	−	0.896358i
$904$	−0.898012	−	2.16799i	−0.0298674	−	0.0721063i
$905$			6.20345i			0.206210i
$906$	14.1266	−	5.85143i	0.469325	−	0.194401i
$907$	−10.1582	+	24.5239i	−0.337296	+	0.814304i	0.660677	+	0.750670i	$0.270269\pi$
$907$	−10.1582	+	24.5239i	−0.337296	+	0.814304i	−0.997973	+	0.0636343i	$0.979731\pi$
$908$	3.88054	+	1.60737i	0.128780	+	0.0533425i
$909$	−4.92770	+	4.92770i	−0.163441	+	0.163441i
$910$	−10.5513	+	10.5513i	−0.349772	+	0.349772i
$911$	12.2775	+	5.08549i	0.406770	+	0.168490i	0.576681	−	0.816970i	$-0.304348\pi$
$911$	12.2775	+	5.08549i	0.406770	+	0.168490i	−0.169910	+	0.985460i	$0.554348\pi$
$912$	1.53073	−	3.69552i	0.0506877	−	0.122371i
$913$	53.1791	−	22.0275i	1.75997	−	0.729005i
$914$		−	31.6369i		−	1.04646i
$915$	0.469266	+	1.13291i	0.0155135	+	0.0374528i
$916$	8.90628	+	8.90628i	0.294272	+	0.294272i
$917$	−30.0811			−0.993365
$918$	2.35743	−	3.38268i	0.0778066	−	0.111645i
$919$	−34.2273			−1.12905			−0.564527	−	0.825415i	$-0.690941\pi$
$919$	−34.2273			−1.12905			−0.564527	+	0.825415i	$0.690941\pi$
$920$	4.40375	+	4.40375i	0.145187	+	0.145187i
$921$	−3.26330	−	7.87831i	−0.107529	−	0.259599i
$922$		−	15.2314i		−	0.501621i
$923$	−27.1898	+	11.2624i	−0.894963	+	0.370706i
$924$	−9.02055	+	21.7775i	−0.296754	+	0.716428i
$925$	−6.92177	−	2.86709i	−0.227586	−	0.0942694i
$926$	18.6737	−	18.6737i	0.613656	−	0.613656i
$927$	12.4348	−	12.4348i	0.408411	−	0.408411i
$928$	−7.70144	−	3.19004i	−0.252812	−	0.104718i
$929$	−6.33636	+	15.2973i	−0.207889	+	0.501889i	−0.993090	−	0.117352i	$-0.962559\pi$
$929$	−6.33636	+	15.2973i	−0.207889	+	0.501889i	0.785201	+	0.619241i	$0.212559\pi$
$930$	3.50819	−	1.45314i	0.115038	−	0.0476504i
$931$			57.1237i			1.87215i
$932$	−8.00321	−	19.3215i	−0.262154	−	0.632895i
$933$	2.91466	+	2.91466i	0.0954218	+	0.0954218i
$934$	−8.62955			−0.282367
$935$	17.7434	−	11.3592i	0.580272	−	0.371484i
$936$	−3.23463			−0.105727
$937$	−20.6878	−	20.6878i	−0.675841	−	0.675841i	0.283215	−	0.959056i	$-0.408599\pi$
$937$	−20.6878	−	20.6878i	−0.675841	−	0.675841i	−0.959056	+	0.283215i	$0.908599\pi$
$938$	−4.84495	−	11.6967i	−0.158193	−	0.381912i
$939$		−	13.4178i		−	0.437875i
$940$	−11.5046	+	4.76537i	−0.375239	+	0.155429i
$941$	8.80089	−	21.2472i	0.286901	−	0.692639i	−0.713064	−	0.701099i	$-0.752693\pi$
$941$	8.80089	−	21.2472i	0.286901	−	0.692639i	0.999964	+	0.00845993i	$0.00269291\pi$
$942$	−1.68393	−	0.697506i	−0.0548654	−	0.0227260i
$943$	42.1337	−	42.1337i	1.37206	−	1.37206i
$944$	−1.67705	+	1.67705i	−0.0545833	+	0.0545833i
$945$	4.26197	+	1.76537i	0.138642	+	0.0574274i
$946$	16.1467	−	38.9815i	0.524974	−	1.26740i
$947$	−19.8187	+	8.20917i	−0.644021	+	0.266762i	−0.680697	−	0.732565i	$-0.738323\pi$
$947$	−19.8187	+	8.20917i	−0.644021	+	0.266762i	0.0366761	+	0.999327i	$0.488323\pi$
$948$		−	3.61153i		−	0.117297i
$949$	11.3987	+	27.5188i	0.370016	+	0.893299i
$950$	−2.82843	−	2.82843i	−0.0917663	−	0.0917663i
$951$	−17.5140			−0.567929
$952$	15.6047	+	10.8751i	0.505753	+	0.352464i
$953$	2.27834			0.0738026			0.0369013	−	0.999319i	$-0.488251\pi$
$953$	2.27834			0.0738026			0.0369013	+	0.999319i	$0.488251\pi$
$954$	0.965872	+	0.965872i	0.0312713	+	0.0312713i
$955$	−0.902812	−	2.17958i	−0.0292143	−	0.0705296i
$956$		−	24.2741i		−	0.785082i
$957$	39.3523	−	16.3003i	1.27208	−	0.526913i
$958$	2.77725	−	6.70488i	0.0897289	−	0.216625i
$959$	−49.0449	−	20.3151i	−1.58374	−	0.656007i
$960$	0.707107	−	0.707107i	0.0228218	−	0.0228218i
$961$	11.7245	−	11.7245i	0.378210	−	0.378210i
$962$	−22.3894	−	9.27399i	−0.721863	−	0.299005i
$963$	−1.06760	+	2.57741i	−0.0344028	+	0.0830557i
$964$	−5.41811	+	2.24426i	−0.174506	+	0.0722826i
$965$		−	1.54847i		−	0.0498471i
$966$	−10.9944	−	26.5429i	−0.353740	−	0.854004i
$967$	−20.1157	−	20.1157i	−0.646878	−	0.646878i	0.305359	−	0.952237i	$-0.401224\pi$
$967$	−20.1157	−	20.1157i	−0.646878	−	0.646878i	−0.952237	+	0.305359i	$0.901224\pi$
$968$	−15.1094			−0.485633
$969$	16.2355	−	2.89987i	0.521559	−	0.0931572i
$970$	6.00416			0.192782
$971$	14.7761	+	14.7761i	0.474189	+	0.474189i	0.903267	−	0.429078i	$-0.141162\pi$
$971$	14.7761	+	14.7761i	0.474189	+	0.474189i	−0.429078	+	0.903267i	$0.641162\pi$
$972$	0.382683	+	0.923880i	0.0122746	+	0.0296334i
$973$			97.5272i			3.12658i
$974$	−7.13323	+	2.95468i	−0.228563	+	0.0946740i
$975$	−1.23784	+	2.98841i	−0.0396426	+	0.0957058i
$976$	−1.13291	−	0.469266i	−0.0362635	−	0.0150208i
$977$	36.6434	−	36.6434i	1.17233	−	1.17233i	0.190674	−	0.981653i	$-0.438933\pi$
$977$	36.6434	−	36.6434i	1.17233	−	1.17233i	0.981653	−	0.190674i	$-0.0610673\pi$
$978$	5.49435	−	5.49435i	0.175690	−	0.175690i
$979$	42.6375	+	17.6610i	1.36270	+	0.564449i
$980$	−5.46508	+	13.1939i	−0.174575	+	0.421462i
$981$	−13.9958	+	5.79724i	−0.446851	+	0.185092i
$982$		−	1.52235i		−	0.0485802i
$983$	−13.0470	−	31.4982i	−0.416134	−	1.00464i	−0.983457	−	0.181140i	$-0.942021\pi$
$983$	−13.0470	−	31.4982i	−0.416134	−	1.00464i	0.567324	−	0.823495i	$-0.307979\pi$
$984$	−6.76537	−	6.76537i	−0.215672	−	0.215672i
$985$	4.95136			0.157764
$986$	−6.04331	−	33.8347i	−0.192458	−	1.07752i
$987$	57.4450			1.82849
$988$	−9.14892	−	9.14892i	−0.291066	−	0.291066i
$989$	19.6799	+	47.5115i	0.625784	+	1.51078i
$990$			5.10973i			0.162398i
$991$	32.7096	−	13.5488i	1.03906	−	0.430391i	0.203082	−	0.979162i	$-0.434904\pi$
$991$	32.7096	−	13.5488i	1.03906	−	0.430391i	0.835973	+	0.548771i	$0.184904\pi$
$992$	−1.45314	+	3.50819i	−0.0461373	+	0.111385i
$993$	−9.91082	−	4.10520i	−0.314510	−	0.130274i
$994$	−29.6788	+	29.6788i	−0.941353	+	0.941353i
$995$	7.31911	−	7.31911i	0.232031	−	0.232031i
$996$	10.4074	+	4.31090i	0.329772	+	0.136596i
$997$	16.4274	−	39.6593i	0.520262	−	1.25602i	−0.417479	−	0.908686i	$-0.637086\pi$
$997$	16.4274	−	39.6593i	0.520262	−	1.25602i	0.937741	−	0.347336i	$-0.112914\pi$
$998$	10.0879	−	4.17855i	0.319327	−	0.132270i
$999$			7.49207i			0.237039i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	510.2.u.a.151.2	✓	8
17.5	odd	16		8670.2.a.by.1.4		4
17.8	even	8	inner	510.2.u.a.331.2	yes	8
17.12	odd	16		8670.2.a.bz.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
510.2.u.a.151.2	✓	8	1.1	even	1	trivial
510.2.u.a.331.2	yes	8	17.8	even	8	inner
8670.2.a.by.1.4		4	17.5	odd	16
8670.2.a.bz.1.1		4	17.12	odd	16

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:	\( N \)	\(=\)	\( 510 = 2 \cdot 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	510.u (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.382683 + 0.923880i) q^{3} +1.00000i q^{4} +(0.923880 - 0.382683i) q^{5} +(0.382683 - 0.923880i) q^{6} +(-4.26197 - 1.76537i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.707107 + 0.707107i) q^{9} +(-0.923880 - 0.382683i) q^{10} +(-1.95541 + 4.72078i) q^{11} +(-0.923880 + 0.382683i) q^{12} +3.23463i q^{13} +(1.76537 + 4.26197i) q^{14} +(0.707107 + 0.707107i) q^{15} -1.00000 q^{16} +(-2.22304 - 3.47247i) q^{17} +1.00000 q^{18} +(2.82843 + 2.82843i) q^{19} +(0.382683 + 0.923880i) q^{20} -4.61313i q^{21} +(4.72078 - 1.95541i) q^{22} +(-2.38329 + 5.75378i) q^{23} +(0.923880 + 0.382683i) q^{24} +(0.707107 - 0.707107i) q^{25} +(2.28723 - 2.28723i) q^{26} +(-0.923880 - 0.382683i) q^{27} +(1.76537 - 4.26197i) q^{28} +(-7.70144 + 3.19004i) q^{29} -1.00000i q^{30} +(1.45314 + 3.50819i) q^{31} +(0.707107 + 0.707107i) q^{32} -5.10973 q^{33} +(-0.883480 + 4.02734i) q^{34} -4.61313 q^{35} +(-0.707107 - 0.707107i) q^{36} +(-2.86709 - 6.92177i) q^{37} -4.00000i q^{38} +(-2.98841 + 1.23784i) q^{39} +(0.382683 - 0.923880i) q^{40} +(-8.83938 - 3.66139i) q^{41} +(-3.26197 + 3.26197i) q^{42} +(5.83889 - 5.83889i) q^{43} +(-4.72078 - 1.95541i) q^{44} +(-0.382683 + 0.923880i) q^{45} +(5.75378 - 2.38329i) q^{46} +12.4525i q^{47} +(-0.382683 - 0.923880i) q^{48} +(10.0981 + 10.0981i) q^{49} -1.00000 q^{50} +(2.35743 - 3.38268i) q^{51} -3.23463 q^{52} +(0.965872 + 0.965872i) q^{53} +(0.382683 + 0.923880i) q^{54} +5.10973i q^{55} +(-4.26197 + 1.76537i) q^{56} +(-1.53073 + 3.69552i) q^{57} +(7.70144 + 3.19004i) q^{58} +(1.67705 - 1.67705i) q^{59} +(-0.707107 + 0.707107i) q^{60} +(1.13291 + 0.469266i) q^{61} +(1.45314 - 3.50819i) q^{62} +(4.26197 - 1.76537i) q^{63} -1.00000i q^{64} +(1.23784 + 2.98841i) q^{65} +(3.61313 + 3.61313i) q^{66} -2.74444 q^{67} +(3.47247 - 2.22304i) q^{68} -6.22784 q^{69} +(3.26197 + 3.26197i) q^{70} +(3.48181 + 8.40583i) q^{71} +1.00000i q^{72} +(8.50756 - 3.52395i) q^{73} +(-2.86709 + 6.92177i) q^{74} +(0.923880 + 0.382683i) q^{75} +(-2.82843 + 2.82843i) q^{76} +(16.6678 - 16.6678i) q^{77} +(2.98841 + 1.23784i) q^{78} +(-1.38207 + 3.33662i) q^{79} +(-0.923880 + 0.382683i) q^{80} -1.00000i q^{81} +(3.66139 + 8.83938i) q^{82} +(-7.96550 - 7.96550i) q^{83} +4.61313 q^{84} +(-3.38268 - 2.35743i) q^{85} -8.25744 q^{86} +(-5.89443 - 5.89443i) q^{87} +(1.95541 + 4.72078i) q^{88} -9.03188i q^{89} +(0.923880 - 0.382683i) q^{90} +(5.71031 - 13.7859i) q^{91} +(-5.75378 - 2.38329i) q^{92} +(-2.68506 + 2.68506i) q^{93} +(8.80525 - 8.80525i) q^{94} +(3.69552 + 1.53073i) q^{95} +(-0.382683 + 0.923880i) q^{96} +(-5.54712 + 2.29769i) q^{97} -14.2809i q^{98} +(-1.95541 - 4.72078i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{7} + 8 q^{14} - 8 q^{16} + 8 q^{18} + 16 q^{22} + 24 q^{23} + 8 q^{28} - 32 q^{29} - 8 q^{31} - 8 q^{34} - 16 q^{35} - 16 q^{37} - 8 q^{41} + 32 q^{43} - 16 q^{44} + 16 q^{46} + 16 q^{49} - 8 q^{50}+ \cdots - 40 q^{97}+O(q^{100}) \) 8 * q - 8 * q^7 + 8 * q^14 - 8 * q^16 + 8 * q^18 + 16 * q^22 + 24 * q^23 + 8 * q^28 - 32 * q^29 - 8 * q^31 - 8 * q^34 - 16 * q^35 - 16 * q^37 - 8 * q^41 + 32 * q^43 - 16 * q^44 + 16 * q^46 + 16 * q^49 - 8 * q^50 + 8 * q^51 - 32 * q^52 - 8 * q^56 + 32 * q^58 + 16 * q^59 + 16 * q^61 - 8 * q^62 + 8 * q^63 - 8 * q^65 + 8 * q^66 + 16 * q^68 - 16 * q^69 + 8 * q^71 + 8 * q^73 - 16 * q^74 + 48 * q^77 - 48 * q^79 - 8 * q^82 + 32 * q^83 + 16 * q^84 - 24 * q^85 - 32 * q^86 - 8 * q^87 + 16 * q^91 - 16 * q^92 + 16 * q^93 - 40 * q^97

Introduction

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