LMFDB - Embedded newform 912.2.bn.n.65.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(65,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))

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

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

chi := DirichletCharacter("912.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.bn (of order $6$, degree $2$, not 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:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} - 6 x^{14} + 5 x^{13} + 21 x^{12} - 4 x^{11} - 94 x^{10} - 6 x^{9} + 364 x^{8} + \cdots + 6561 $ x^16 - x^15 - 6x^14 + 5x^13 + 21x^12 - 4x^11 - 94x^10 - 6x^9 + 364x^8 - 18x^7 - 846x^6 - 108x^5 + 1701x^4 + 1215x^3 - 4374x^2 - 2187x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 456)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.2
Root			$-1.63023 + 0.585107i$ of defining polynomial
Character	$\chi$	$=$	912.65
Dual form			912.2.bn.n.449.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32183 - 1.11927i) q^{3} +(-2.85312 - 1.64725i) q^{5} +4.86833 q^{7} +(0.494481 + 2.95897i) q^{9} +O(q^{10})$	\(q+(-1.32183 - 1.11927i) q^{3} +(-2.85312 - 1.64725i) q^{5} +4.86833 q^{7} +(0.494481 + 2.95897i) q^{9} +4.65610i q^{11} +(0.131680 - 0.0760256i) q^{13} +(1.92763 + 5.37080i) q^{15} +(-2.37145 - 1.36916i) q^{17} +(1.11847 + 4.21296i) q^{19} +(-6.43512 - 5.44897i) q^{21} +(4.87999 - 2.81746i) q^{23} +(2.92687 + 5.06949i) q^{25} +(2.65826 - 4.46472i) q^{27} +(3.39039 + 5.87234i) q^{29} +2.83096i q^{31} +(5.21142 - 6.15459i) q^{33} +(-13.8899 - 8.01937i) q^{35} -5.14080i q^{37} +(-0.259152 - 0.0468923i) q^{39} +(0.166117 - 0.287723i) q^{41} +(2.12547 - 3.68143i) q^{43} +(3.46335 - 9.25683i) q^{45} +(7.83895 - 4.52582i) q^{47} +16.7007 q^{49} +(1.60221 + 4.46408i) q^{51} +(-0.486173 - 0.842076i) q^{53} +(7.66977 - 13.2844i) q^{55} +(3.23699 - 6.82069i) q^{57} +(3.30452 - 5.72359i) q^{59} +(1.39736 + 2.42029i) q^{61} +(2.40730 + 14.4052i) q^{63} -0.500933 q^{65} +(3.73878 - 2.15859i) q^{67} +(-9.60403 - 1.73780i) q^{69} +(-7.75734 + 13.4361i) q^{71} +(3.13060 - 5.42236i) q^{73} +(1.80528 - 9.97697i) q^{75} +22.6675i q^{77} +(8.38726 + 4.84239i) q^{79} +(-8.51098 + 2.92631i) q^{81} -4.12833i q^{83} +(4.51069 + 7.81274i) q^{85} +(2.09118 - 11.5570i) q^{87} +(-1.77429 - 3.07316i) q^{89} +(0.641063 - 0.370118i) q^{91} +(3.16860 - 3.74205i) q^{93} +(3.74866 - 13.8625i) q^{95} +(-9.51040 - 5.49083i) q^{97} +(-13.7773 + 2.30235i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{3} + 3 q^{5} - 5 q^{9}+O(q^{10}) $ 16 * q - q^3 + 3 * q^5 - 5 * q^9	$ 16 q - q^{3} + 3 q^{5} - 5 q^{9} - 3 q^{13} - 12 q^{15} - 3 q^{17} - 11 q^{19} - 12 q^{21} + 3 q^{23} + 11 q^{25} - 4 q^{27} + 5 q^{29} + 14 q^{33} - 24 q^{35} + 9 q^{39} + 6 q^{41} - 13 q^{43} + 33 q^{45} - 27 q^{47} + 8 q^{49} + 18 q^{51} - 7 q^{53} + 12 q^{55} - 36 q^{57} + 10 q^{59} - q^{61} + 26 q^{63} - 30 q^{65} + 24 q^{67} - 41 q^{69} - 27 q^{71} + 2 q^{73} - 21 q^{75} + 21 q^{79} - 13 q^{81} - 5 q^{85} + 23 q^{87} + 25 q^{89} + 78 q^{91} + 22 q^{93} - 13 q^{95} - 60 q^{97} + 20 q^{99}+O(q^{100}) $ 16 * q - q^3 + 3 * q^5 - 5 * q^9 - 3 * q^13 - 12 * q^15 - 3 * q^17 - 11 * q^19 - 12 * q^21 + 3 * q^23 + 11 * q^25 - 4 * q^27 + 5 * q^29 + 14 * q^33 - 24 * q^35 + 9 * q^39 + 6 * q^41 - 13 * q^43 + 33 * q^45 - 27 * q^47 + 8 * q^49 + 18 * q^51 - 7 * q^53 + 12 * q^55 - 36 * q^57 + 10 * q^59 - q^61 + 26 * q^63 - 30 * q^65 + 24 * q^67 - 41 * q^69 - 27 * q^71 + 2 * q^73 - 21 * q^75 + 21 * q^79 - 13 * q^81 - 5 * q^85 + 23 * q^87 + 25 * q^89 + 78 * q^91 + 22 * q^93 - 13 * q^95 - 60 * q^97 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$	$1$

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			0
$2$		0			0
$3$	−1.32183	−	1.11927i	−0.763160	−	0.646209i
$3$	−1.32183	−	1.11927i	−0.763160	−	0.646209i
$4$		0			0
$5$	−2.85312	−	1.64725i	−1.27596	−	0.736673i	−0.299853	−	0.953985i	$-0.596938\pi$
$5$	−2.85312	−	1.64725i	−1.27596	−	0.736673i	−0.976102	+	0.217312i	$0.930271\pi$
$6$		0			0
$7$	4.86833			1.84006			0.920028	−	0.391852i	$-0.128165\pi$
$7$	4.86833			1.84006			0.920028	+	0.391852i	$0.128165\pi$
$8$		0			0
$9$	0.494481	+	2.95897i	0.164827	+	0.986322i
$10$		0			0
$11$			4.65610i			1.40387i	0.712242	+	0.701934i	$0.247680\pi$
$11$			4.65610i			1.40387i	−0.712242	+	0.701934i	$0.752320\pi$
$12$		0			0
$13$	0.131680	−	0.0760256i	0.0365215	−	0.0210857i	−0.481628	−	0.876376i	$-0.659954\pi$
$13$	0.131680	−	0.0760256i	0.0365215	−	0.0210857i	0.518150	+	0.855290i	$0.326621\pi$
$14$		0			0
$15$	1.92763	+	5.37080i	0.497713	+	1.38673i
$16$		0			0
$17$	−2.37145	−	1.36916i	−0.575161	−	0.332069i	0.184047	−	0.982917i	$-0.441080\pi$
$17$	−2.37145	−	1.36916i	−0.575161	−	0.332069i	−0.759208	+	0.650848i	$0.774413\pi$
$18$		0			0
$19$	1.11847	+	4.21296i	0.256595	+	0.966519i
$19$	1.11847	+	4.21296i	0.256595	+	0.966519i
$20$		0			0
$21$	−6.43512	−	5.44897i	−1.40426	−	1.18906i
$22$		0			0
$23$	4.87999	−	2.81746i	1.01755	−	0.587482i	0.104156	−	0.994561i	$-0.466786\pi$
$23$	4.87999	−	2.81746i	1.01755	−	0.587482i	0.913393	+	0.407079i	$0.133453\pi$
$24$		0			0
$25$	2.92687	+	5.06949i	0.585374	+	1.01390i
$26$		0			0
$27$	2.65826	−	4.46472i	0.511581	−	0.859235i
$28$		0			0
$29$	3.39039	+	5.87234i	0.629581	+	1.09047i	0.987636	+	0.156765i	$0.0501066\pi$
$29$	3.39039	+	5.87234i	0.629581	+	1.09047i	−0.358055	+	0.933700i	$0.616560\pi$
$30$		0			0
$31$			2.83096i			0.508455i	0.967144	+	0.254228i	$0.0818212\pi$
$31$			2.83096i			0.508455i	−0.967144	+	0.254228i	$0.918179\pi$
$32$		0			0
$33$	5.21142	−	6.15459i	0.907192	−	1.07138i
$34$		0			0
$35$	−13.8899	−	8.01937i	−2.34783	−	1.35552i
$36$		0			0
$37$		−	5.14080i		−	0.845142i	−0.906330	−	0.422571i	$-0.861128\pi$
$37$		−	5.14080i		−	0.845142i	0.906330	−	0.422571i	$-0.138872\pi$
$38$		0			0
$39$	−0.259152	−	0.0468923i	−0.0414976	−	0.00750877i
$40$		0			0
$41$	0.166117	−	0.287723i	0.0259431	−	0.0449348i	−0.852762	−	0.522299i	$-0.825074\pi$
$41$	0.166117	−	0.287723i	0.0259431	−	0.0449348i	0.878705	+	0.477364i	$0.158408\pi$
$42$		0			0
$43$	2.12547	−	3.68143i	0.324132	−	0.561413i	−0.657204	−	0.753712i	$-0.728261\pi$
$43$	2.12547	−	3.68143i	0.324132	−	0.561413i	0.981336	+	0.192300i	$0.0615945\pi$
$44$		0			0
$45$	3.46335	−	9.25683i	0.516285	−	1.37993i
$46$		0			0
$47$	7.83895	−	4.52582i	1.14343	−	0.660158i	0.196151	−	0.980574i	$-0.437156\pi$
$47$	7.83895	−	4.52582i	1.14343	−	0.660158i	0.947277	+	0.320415i	$0.103822\pi$
$48$		0			0
$49$	16.7007			2.38581
$50$		0			0
$51$	1.60221	+	4.46408i	0.224354	+	0.625096i
$52$		0			0
$53$	−0.486173	−	0.842076i	−0.0667810	−	0.115668i	0.830702	−	0.556718i	$-0.187940\pi$
$53$	−0.486173	−	0.842076i	−0.0667810	−	0.115668i	−0.897483	+	0.441050i	$0.854606\pi$
$54$		0			0
$55$	7.66977	−	13.2844i	1.03419	−	1.79127i
$56$		0			0
$57$	3.23699	−	6.82069i	0.428750	−	0.903423i
$58$		0			0
$59$	3.30452	−	5.72359i	0.430212	−	0.745148i	−0.566680	−	0.823938i	$-0.691772\pi$
$59$	3.30452	−	5.72359i	0.430212	−	0.745148i	0.996891	+	0.0787898i	$0.0251056\pi$
$60$		0			0
$61$	1.39736	+	2.42029i	0.178913	+	0.309887i	0.941509	−	0.336989i	$-0.109409\pi$
$61$	1.39736	+	2.42029i	0.178913	+	0.309887i	−0.762595	+	0.646876i	$0.776075\pi$
$62$		0			0
$63$	2.40730	+	14.4052i	0.303291	+	1.81489i
$64$		0			0
$65$	−0.500933			−0.0621331
$66$		0			0
$67$	3.73878	−	2.15859i	0.456765	−	0.263713i	−0.253918	−	0.967226i	$-0.581719\pi$
$67$	3.73878	−	2.15859i	0.456765	−	0.263713i	0.710683	+	0.703512i	$0.248386\pi$
$68$		0			0
$69$	−9.60403	−	1.73780i	−1.15619	−	0.209207i
$70$		0			0
$71$	−7.75734	+	13.4361i	−0.920627	+	1.59457i	−0.122181	+	0.992508i	$0.538989\pi$
$71$	−7.75734	+	13.4361i	−0.920627	+	1.59457i	−0.798447	+	0.602066i	$0.794345\pi$
$72$		0			0
$73$	3.13060	−	5.42236i	0.366409	−	0.634639i	−0.622592	−	0.782547i	$-0.713920\pi$
$73$	3.13060	−	5.42236i	0.366409	−	0.634639i	0.989001	+	0.147907i	$0.0472537\pi$
$74$		0			0
$75$	1.80528	−	9.97697i	0.208456	−	1.15204i
$76$		0			0
$77$			22.6675i			2.58320i
$78$		0			0
$79$	8.38726	+	4.84239i	0.943641	+	0.544811i	0.891100	−	0.453807i	$-0.149935\pi$
$79$	8.38726	+	4.84239i	0.943641	+	0.544811i	0.0525412	+	0.998619i	$0.483268\pi$
$80$		0			0
$81$	−8.51098	+	2.92631i	−0.945664	+	0.325145i
$82$		0			0
$83$		−	4.12833i		−	0.453144i	−0.973994	−	0.226572i	$-0.927248\pi$
$83$		−	4.12833i		−	0.453144i	0.973994	−	0.226572i	$-0.0727518\pi$
$84$		0			0
$85$	4.51069	+	7.81274i	0.489253	+	0.847411i
$86$		0			0
$87$	2.09118	−	11.5570i	0.224198	−	1.23904i
$88$		0			0
$89$	−1.77429	−	3.07316i	−0.188074	−	0.325754i	0.756534	−	0.653954i	$-0.226891\pi$
$89$	−1.77429	−	3.07316i	−0.188074	−	0.325754i	−0.944608	+	0.328201i	$0.893558\pi$
$90$		0			0
$91$	0.641063	−	0.370118i	0.0672017	−	0.0387989i
$92$		0			0
$93$	3.16860	−	3.74205i	0.328568	−	0.388033i
$94$		0			0
$95$	3.74866	−	13.8625i	0.384604	−	1.42226i
$96$		0			0
$97$	−9.51040	−	5.49083i	−0.965634	−	0.557509i	−0.0677318	−	0.997704i	$-0.521576\pi$
$97$	−9.51040	−	5.49083i	−0.965634	−	0.557509i	−0.897903	+	0.440194i	$0.854910\pi$
$98$		0			0
$99$	−13.7773	+	2.30235i	−1.38467	+	0.231395i
$100$		0			0
$101$	11.0216	−	6.36332i	1.09669	−	0.633174i	0.161340	−	0.986899i	$-0.448419\pi$
$101$	11.0216	−	6.36332i	1.09669	−	0.633174i	0.935349	+	0.353725i	$0.115085\pi$
$102$		0			0
$103$			11.8504i			1.16765i	0.811879	+	0.583826i	$0.198445\pi$
$103$			11.8504i			1.16765i	−0.811879	+	0.583826i	$0.801555\pi$
$104$		0			0
$105$	9.38437	+	26.1468i	0.915820	+	2.55167i
$106$		0			0
$107$	−8.27966			−0.800425			−0.400213	−	0.916422i	$-0.631064\pi$
$107$	−8.27966			−0.800425			−0.400213	+	0.916422i	$0.631064\pi$
$108$		0			0
$109$	−1.36125	−	0.785918i	−0.130384	−	0.0752772i	0.433389	−	0.901207i	$-0.357318\pi$
$109$	−1.36125	−	0.785918i	−0.130384	−	0.0752772i	−0.563773	+	0.825930i	$0.690651\pi$
$110$		0			0
$111$	−5.75393	+	6.79527i	−0.546139	+	0.644979i
$112$		0			0
$113$	2.64722			0.249029			0.124515	−	0.992218i	$-0.460263\pi$
$113$	2.64722			0.249029			0.124515	+	0.992218i	$0.460263\pi$
$114$		0			0
$115$	−18.5643			−1.73113
$116$		0			0
$117$	0.290071	+	0.352044i	0.0268170	+	0.0325465i
$118$		0			0
$119$	−11.5450	−	6.66551i	−1.05833	−	0.611026i
$120$		0			0
$121$	−10.6793			−0.970844
$122$		0			0
$123$	−0.541618	+	0.194392i	−0.0488360	+	0.0175278i
$124$		0			0
$125$		−	2.81266i		−	0.251572i
$126$		0			0
$127$	−16.5358	+	9.54696i	−1.46732	+	0.847156i	−0.999331	−	0.0365804i	$-0.988353\pi$
$127$	−16.5358	+	9.54696i	−1.46732	+	0.847156i	−0.467986	+	0.883736i	$0.655020\pi$
$128$		0			0
$129$	−6.93003	+	2.48726i	−0.610155	+	0.218991i
$130$		0			0
$131$	19.1064	+	11.0311i	1.66933	+	0.963788i	0.968000	+	0.250951i	$0.0807433\pi$
$131$	19.1064	+	11.0311i	1.66933	+	0.963788i	0.701330	+	0.712837i	$0.252590\pi$
$132$		0			0
$133$	5.44510	+	20.5101i	0.472150	+	1.77845i
$134$		0			0
$135$	−14.9388	+	8.35956i	−1.28573	+	0.719477i
$136$		0			0
$137$	−6.01441	+	3.47242i	−0.513846	+	0.296669i	−0.734413	−	0.678703i	$-0.762542\pi$
$137$	−6.01441	+	3.47242i	−0.513846	+	0.296669i	0.220567	+	0.975372i	$0.429209\pi$
$138$		0			0
$139$	2.87631	+	4.98192i	0.243966	+	0.422561i	0.961840	−	0.273611i	$-0.0882182\pi$
$139$	2.87631	+	4.98192i	0.243966	+	0.422561i	−0.717875	+	0.696172i	$0.754885\pi$
$140$		0			0
$141$	−15.4274	−	2.79151i	−1.29922	−	0.235087i
$142$		0			0
$143$	0.353983	+	0.613117i	0.0296015	+	0.0512714i
$144$		0			0
$145$		−	22.3393i		−	1.85518i
$146$		0			0
$147$	−22.0755	−	18.6925i	−1.82075	−	1.54173i
$148$		0			0
$149$	13.3389	+	7.70122i	1.09277	+	0.630908i	0.934311	−	0.356458i	$-0.116016\pi$
$149$	13.3389	+	7.70122i	1.09277	+	0.630908i	0.158454	+	0.987366i	$0.449349\pi$
$150$		0			0
$151$		−	11.0189i		−	0.896704i	−0.893857	−	0.448352i	$-0.852011\pi$
$151$		−	11.0189i		−	0.896704i	0.893857	−	0.448352i	$-0.147989\pi$
$152$		0			0
$153$	2.87865	−	7.69406i	0.232725	−	0.622028i
$154$		0			0
$155$	4.66330	−	8.07707i	0.374565	−	0.648766i
$156$		0			0
$157$	0.210692	−	0.364930i	0.0168151	−	0.0291246i	−0.857495	−	0.514492i	$-0.827981\pi$
$157$	0.210692	−	0.364930i	0.0168151	−	0.0291246i	0.874311	+	0.485367i	$0.161314\pi$
$158$		0			0
$159$	−0.299869	+	1.65724i	−0.0237812	+	0.131428i
$160$		0			0
$161$	23.7574	−	13.7164i	1.87235	−	1.08100i
$162$		0			0
$163$	14.5885			1.14266			0.571331	−	0.820720i	$-0.306427\pi$
$163$	14.5885			1.14266			0.571331	+	0.820720i	$0.306427\pi$
$164$		0			0
$165$	−25.0070	+	8.97526i	−1.94679	+	0.698723i
$166$		0			0
$167$	−3.38965	−	5.87104i	−0.262299	−	0.454315i	0.704554	−	0.709651i	$-0.251147\pi$
$167$	−3.38965	−	5.87104i	−0.262299	−	0.454315i	−0.966852	+	0.255336i	$0.917814\pi$
$168$		0			0
$169$	−6.48844	+	11.2383i	−0.499111	+	0.864485i
$170$		0			0
$171$	−11.9129	+	5.39275i	−0.911006	+	0.412394i
$172$		0			0
$173$	3.66905	−	6.35499i	0.278953	−	0.483161i	−0.692172	−	0.721733i	$-0.743346\pi$
$173$	3.66905	−	6.35499i	0.278953	−	0.483161i	0.971125	+	0.238572i	$0.0766793\pi$
$174$		0			0
$175$	14.2490	+	24.6800i	1.07712	+	1.86563i
$176$		0			0
$177$	−10.7743	+	3.86699i	−0.809842	+	0.290661i
$178$		0			0
$179$	12.1321			0.906799			0.453399	−	0.891308i	$-0.350211\pi$
$179$	12.1321			0.906799			0.453399	+	0.891308i	$0.350211\pi$
$180$		0			0
$181$	1.69123	−	0.976433i	0.125708	−	0.0725777i	−0.435827	−	0.900030i	$-0.643544\pi$
$181$	1.69123	−	0.976433i	0.125708	−	0.0725777i	0.561536	+	0.827453i	$0.310211\pi$
$182$		0			0
$183$	0.861884	−	4.76324i	0.0637123	−	0.352109i
$184$		0			0
$185$	−8.46819	+	14.6673i	−0.622593	+	1.07836i
$186$		0			0
$187$	6.37493	−	11.0417i	0.466181	−	0.807450i
$188$		0			0
$189$	12.9413	−	21.7357i	0.941339	−	1.58104i
$190$		0			0
$191$		−	6.07874i		−	0.439842i	−0.975518	−	0.219921i	$-0.929420\pi$
$191$		−	6.07874i		−	0.439842i	0.975518	−	0.219921i	$-0.0705799\pi$
$192$		0			0
$193$	−0.110281	−	0.0636710i	−0.00793823	−	0.00458314i	0.496026	−	0.868308i	$-0.334792\pi$
$193$	−0.110281	−	0.0636710i	−0.00793823	−	0.00458314i	−0.503964	+	0.863725i	$0.668126\pi$
$194$		0			0
$195$	0.662149	+	0.560678i	0.0474175	+	0.0401510i
$196$		0			0
$197$		0	0.000205150i		0	1.46163e-5i	−1.00000		7.30815e-6i	$-0.999998\pi$
$197$		0	0.000205150i		0	1.46163e-5i	1.00000		7.30815e-6i	$-2.32626e-6\pi$
$198$		0			0
$199$	1.12547	+	1.94938i	0.0797828	+	0.138188i	0.903156	−	0.429312i	$-0.141244\pi$
$199$	1.12547	+	1.94938i	0.0797828	+	0.138188i	−0.823373	+	0.567500i	$0.807911\pi$
$200$		0			0
$201$	−7.35808	−	1.33141i	−0.518999	−	0.0939102i
$202$		0			0
$203$	16.5056	+	28.5885i	1.15846	+	2.00652i
$204$		0			0
$205$	−0.947904	+	0.547273i	−0.0662045	+	0.0382232i
$206$		0			0
$207$	10.7498	+	13.0466i	0.747166	+	0.906798i
$208$		0			0
$209$	−19.6160	+	5.20773i	−1.35686	+	0.360226i
$210$		0			0
$211$	−15.6337	−	9.02615i	−1.07627	−	0.621386i	−0.146383	−	0.989228i	$-0.546763\pi$
$211$	−15.6337	−	9.02615i	−1.07627	−	0.621386i	−0.929888	+	0.367842i	$0.880097\pi$
$212$		0			0
$213$	25.2925	−	9.07775i	1.73301	−	0.621997i
$214$		0			0
$215$	−12.1285	+	7.00238i	−0.827155	+	0.477558i
$216$		0			0
$217$			13.7820i			0.935586i
$218$		0			0
$219$	−10.2072	+	3.66347i	−0.689739	+	0.247554i
$220$		0			0
$221$	−0.416364			−0.0280077
$222$		0			0
$223$	22.2258	+	12.8321i	1.48835	+	0.859300i	0.999912	−	0.0132968i	$-0.00423263\pi$
$223$	22.2258	+	12.8321i	1.48835	+	0.859300i	0.488440	+	0.872597i	$0.337566\pi$
$224$		0			0
$225$	−13.5532	+	11.1673i	−0.903545	+	0.744485i
$226$		0			0
$227$	3.17727			0.210883			0.105441	−	0.994426i	$-0.466374\pi$
$227$	3.17727			0.210883			0.105441	+	0.994426i	$0.466374\pi$
$228$		0			0
$229$	−11.0362			−0.729292			−0.364646	−	0.931146i	$-0.618810\pi$
$229$	−11.0362			−0.729292			−0.364646	+	0.931146i	$0.618810\pi$
$230$		0			0
$231$	25.3709	−	29.9626i	1.66929	−	1.97139i
$232$		0			0
$233$	−18.5816	−	10.7281i	−1.21732	−	0.702820i	−0.252976	−	0.967473i	$-0.581409\pi$
$233$	−18.5816	−	10.7281i	−1.21732	−	0.702820i	−0.964344	+	0.264653i	$0.914743\pi$
$234$		0			0
$235$	−29.8206			−1.94528
$236$		0			0
$237$	−5.66663	−	15.7884i	−0.368087	−	1.02557i
$238$		0			0
$239$			26.4261i			1.70936i	0.519153	+	0.854681i	$0.326247\pi$
$239$			26.4261i			1.70936i	−0.519153	+	0.854681i	$0.673753\pi$
$240$		0			0
$241$	4.86568	−	2.80920i	0.313426	−	0.180956i	−0.335033	−	0.942206i	$-0.608747\pi$
$241$	4.86568	−	2.80920i	0.313426	−	0.180956i	0.648458	+	0.761250i	$0.275414\pi$
$242$		0			0
$243$	14.5254	+	5.65797i	0.931805	+	0.362959i
$244$		0			0
$245$	−47.6490	−	27.5102i	−3.04419	−	1.75756i
$246$		0			0
$247$	0.467574	+	0.469731i	0.0297510	+	0.0298882i
$248$		0			0
$249$	−4.62071	+	5.45697i	−0.292826	+	0.345821i
$250$		0			0
$251$	−18.1764	+	10.4942i	−1.14728	+	0.662385i	−0.948224	−	0.317602i	$-0.897122\pi$
$251$	−18.1764	+	10.4942i	−1.14728	+	0.662385i	−0.199061	+	0.979987i	$0.563789\pi$
$252$		0			0
$253$	13.1184	+	22.7217i	0.824747	+	1.42850i
$254$		0			0
$255$	2.78217	−	15.3758i	0.174226	−	0.962870i
$256$		0			0
$257$	−12.0071	−	20.7968i	−0.748980	−	1.29727i	−0.948312	−	0.317339i	$-0.897211\pi$
$257$	−12.0071	−	20.7968i	−0.748980	−	1.29727i	0.199333	−	0.979932i	$-0.436123\pi$
$258$		0			0
$259$		−	25.0271i		−	1.55511i
$260$		0			0
$261$	−15.6996	+	12.9358i	−0.971779	+	0.800708i
$262$		0			0
$263$	17.4431	+	10.0708i	1.07558	+	0.620989i	0.929702	−	0.368313i	$-0.120064\pi$
$263$	17.4431	+	10.0708i	1.07558	+	0.620989i	0.145883	+	0.989302i	$0.453398\pi$
$264$		0			0
$265$			3.20340i			0.196783i
$266$		0			0
$267$	−1.09437	+	6.04810i	−0.0669745	+	0.370138i
$268$		0			0
$269$	5.60624	−	9.71029i	0.341818	−	0.592047i	−0.642952	−	0.765906i	$-0.722291\pi$
$269$	5.60624	−	9.71029i	0.341818	−	0.592047i	0.984770	+	0.173860i	$0.0556239\pi$
$270$		0			0
$271$	11.6149	−	20.1175i	0.705553	−	1.22205i	−0.260939	−	0.965355i	$-0.584032\pi$
$271$	11.6149	−	20.1175i	0.705553	−	1.22205i	0.966492	−	0.256698i	$-0.0826347\pi$
$272$		0			0
$273$	−1.26164	−	0.228287i	−0.0763579	−	0.0138166i
$274$		0			0
$275$	−23.6041	+	13.6278i	−1.42338	+	0.821788i
$276$		0			0
$277$	13.1424			0.789651			0.394825	−	0.918756i	$-0.370805\pi$
$277$	13.1424			0.789651			0.394825	+	0.918756i	$0.370805\pi$
$278$		0			0
$279$	−8.37671	+	1.39985i	−0.501501	+	0.0838071i
$280$		0			0
$281$	13.0401	+	22.5862i	0.777910	+	1.34738i	0.933144	+	0.359502i	$0.117053\pi$
$281$	13.0401	+	22.5862i	0.777910	+	1.34738i	−0.155235	+	0.987878i	$0.549613\pi$
$282$		0			0
$283$	−4.84667	+	8.39468i	−0.288105	+	0.499012i	−0.973357	−	0.229293i	$-0.926358\pi$
$283$	−4.84667	+	8.39468i	−0.288105	+	0.499012i	0.685253	+	0.728306i	$0.259692\pi$
$284$		0			0
$285$	−20.4709	+	14.1281i	−1.21259	+	0.836879i
$286$		0			0
$287$	0.808713	−	1.40073i	0.0477368	−	0.0826826i
$288$		0			0
$289$	−4.75082	−	8.22866i	−0.279460	−	0.484039i
$290$		0			0
$291$	6.42544	+	17.9026i	0.376666	+	1.04947i
$292$		0			0
$293$	3.78224			0.220961			0.110480	−	0.993878i	$-0.464761\pi$
$293$	3.78224			0.220961			0.110480	+	0.993878i	$0.464761\pi$
$294$		0			0
$295$	−18.8564	+	10.8867i	−1.09786	+	0.633851i
$296$		0			0
$297$	20.7882	+	12.3771i	1.20625	+	0.718193i
$298$		0			0
$299$	0.428399	−	0.742009i	0.0247749	−	0.0429115i
$300$		0			0
$301$	10.3475	−	17.9224i	0.596421	−	1.03303i
$302$		0			0
$303$	−21.6909	−	3.92487i	−1.24611	−	0.225478i
$304$		0			0
$305$		−	9.20719i		−	0.527202i
$306$		0			0
$307$	−21.8068	−	12.5902i	−1.24458	−	0.718558i	−0.274556	−	0.961571i	$-0.588531\pi$
$307$	−21.8068	−	12.5902i	−1.24458	−	0.718558i	−0.970023	+	0.243013i	$0.921864\pi$
$308$		0			0
$309$	13.2637	−	15.6642i	0.754548	−	0.891106i
$310$		0			0
$311$			10.0429i			0.569482i	0.958605	+	0.284741i	$0.0919076\pi$
$311$			10.0429i			0.569482i	−0.958605	+	0.284741i	$0.908092\pi$
$312$		0			0
$313$	−7.66058	−	13.2685i	−0.433002	−	0.749981i	0.564128	−	0.825687i	$-0.309212\pi$
$313$	−7.66058	−	13.2685i	−0.433002	−	0.749981i	−0.997130	+	0.0757060i	$0.975879\pi$
$314$		0			0
$315$	16.8607	−	45.0653i	0.949994	−	2.53914i
$316$		0			0
$317$	1.84541	+	3.19634i	0.103648	+	0.179524i	0.913185	−	0.407545i	$-0.133615\pi$
$317$	1.84541	+	3.19634i	0.103648	+	0.179524i	−0.809537	+	0.587069i	$0.800282\pi$
$318$		0			0
$319$	−27.3422	+	15.7860i	−1.53087	+	0.883848i
$320$		0			0
$321$	10.9443	+	9.26716i	0.610853	+	0.517242i
$322$		0			0
$323$	3.11580	−	11.5222i	0.173368	−	0.641111i
$324$		0			0
$325$	0.770822	+	0.445034i	0.0427575	+	0.0246861i
$326$		0			0
$327$	0.919691	+	2.56245i	0.0508590	+	0.141704i
$328$		0			0
$329$	38.1626	−	22.0332i	2.10397	−	1.21473i
$330$		0			0
$331$			10.4541i			0.574609i	0.957839	+	0.287305i	$0.0927592\pi$
$331$			10.4541i			0.574609i	−0.957839	+	0.287305i	$0.907241\pi$
$332$		0			0
$333$	15.2115	−	2.54203i	0.833583	−	0.139302i
$334$		0			0
$335$	−14.2229			−0.777082
$336$		0			0
$337$	−12.7470	−	7.35946i	−0.694371	−	0.400895i	0.110877	−	0.993834i	$-0.464634\pi$
$337$	−12.7470	−	7.35946i	−0.694371	−	0.400895i	−0.805247	+	0.592939i	$0.797968\pi$
$338$		0			0
$339$	−3.49918	−	2.96294i	−0.190049	−	0.160925i
$340$		0			0
$341$	−13.1812			−0.713804
$342$		0			0
$343$	47.2261			2.54997
$344$		0			0
$345$	24.5389	+	20.7784i	1.32113	+	1.11867i
$346$		0			0
$347$	−10.7623	−	6.21361i	−0.577750	−	0.333564i	0.182489	−	0.983208i	$-0.441585\pi$
$347$	−10.7623	−	6.21361i	−0.577750	−	0.333564i	−0.760239	+	0.649644i	$0.774918\pi$
$348$		0			0
$349$	−24.9137			−1.33360			−0.666800	−	0.745237i	$-0.732336\pi$
$349$	−24.9137			−1.33360			−0.666800	+	0.745237i	$0.732336\pi$
$350$		0			0
$351$	0.0106069	−	0.790010i	0.000566156	−	0.0421676i
$352$		0			0
$353$			18.6672i			0.993554i	0.867878	+	0.496777i	$0.165483\pi$
$353$			18.6672i			0.993554i	−0.867878	+	0.496777i	$0.834517\pi$
$354$		0			0
$355$	44.2653	−	25.5566i	2.34936	−	1.35640i
$356$		0			0
$357$	7.80007	+	21.7326i	0.412823	+	1.15021i
$358$		0			0
$359$	14.9647	+	8.63986i	0.789806	+	0.455994i	0.839894	−	0.542750i	$-0.182617\pi$
$359$	14.9647	+	8.63986i	0.789806	+	0.455994i	−0.0500885	+	0.998745i	$0.515950\pi$
$360$		0			0
$361$	−16.4980	+	9.42416i	−0.868318	+	0.496009i
$362$		0			0
$363$	14.1162	+	11.9530i	0.740910	+	0.627369i
$364$		0			0
$365$	−17.8640	+	10.3138i	−0.935043	+	0.539847i
$366$		0			0
$367$	1.48274	+	2.56817i	0.0773982	+	0.134058i	0.902127	−	0.431471i	$-0.142005\pi$
$367$	1.48274	+	2.56817i	0.0773982	+	0.134058i	−0.824728	+	0.565529i	$0.808672\pi$
$368$		0			0
$369$	0.933505	+	0.349261i	0.0485963	+	0.0181818i
$370$		0			0
$371$	−2.36685	−	4.09951i	−0.122881	−	0.212836i
$372$		0			0
$373$			31.1963i			1.61528i	0.589675	+	0.807640i	$0.299256\pi$
$373$			31.1963i			1.61528i	−0.589675	+	0.807640i	$0.700744\pi$
$374$		0			0
$375$	−3.14811	+	3.71786i	−0.162568	+	0.191989i
$376$		0			0
$377$	0.892896	+	0.515514i	0.0459865	+	0.0265503i
$378$		0			0
$379$			3.63538i			0.186737i	0.995632	+	0.0933684i	$0.0297634\pi$
$379$			3.63538i			0.186737i	−0.995632	+	0.0933684i	$0.970237\pi$
$380$		0			0
$381$	32.5432	+	5.88852i	1.66724	+	0.301678i
$382$		0			0
$383$	12.7202	−	22.0320i	0.649970	−	1.12578i	−0.333160	−	0.942870i	$-0.608115\pi$
$383$	12.7202	−	22.0320i	0.649970	−	1.12578i	0.983130	−	0.182911i	$-0.0585519\pi$
$384$		0			0
$385$	37.3390	−	64.6730i	1.90297	−	3.29604i
$386$		0			0
$387$	11.9442	+	4.46881i	0.607160	+	0.227163i
$388$		0			0
$389$	18.7935	−	10.8504i	0.952868	−	0.550139i	0.0588977	−	0.998264i	$-0.481241\pi$
$389$	18.7935	−	10.8504i	0.952868	−	0.550139i	0.893971	+	0.448125i	$0.147908\pi$
$390$		0			0
$391$	−15.4302			−0.780339
$392$		0			0
$393$	−12.9087	−	35.9663i	−0.651157	−	1.81426i
$394$		0			0
$395$	−15.9533	−	27.6319i	−0.802696	−	1.39031i
$396$		0			0
$397$	−1.35859	+	2.35315i	−0.0681856	+	0.118101i	−0.898103	−	0.439786i	$-0.855054\pi$
$397$	−1.35859	+	2.35315i	−0.0681856	+	0.118101i	0.829917	+	0.557887i	$0.188388\pi$
$398$		0			0
$399$	15.7588	−	33.2054i	0.788925	−	1.66235i
$400$		0			0
$401$	−8.76597	+	15.1831i	−0.437752	+	0.758208i	−0.997516	−	0.0704439i	$-0.977558\pi$
$401$	−8.76597	+	15.1831i	−0.437752	+	0.758208i	0.559764	+	0.828652i	$0.310892\pi$
$402$		0			0
$403$	0.215225	+	0.372781i	0.0107211	+	0.0185696i
$404$		0			0
$405$	29.1032	+	5.67061i	1.44615	+	0.281775i
$406$		0			0
$407$	23.9361			1.18647
$408$		0			0
$409$	−20.8589	+	12.0429i	−1.03140	+	0.595481i	−0.917387	−	0.397997i	$-0.869705\pi$
$409$	−20.8589	+	12.0429i	−1.03140	+	0.595481i	−0.114018	+	0.993479i	$0.536372\pi$
$410$		0			0
$411$	11.8366	+	2.14178i	0.583857	+	0.105646i
$412$		0			0
$413$	16.0875	−	27.8644i	0.791614	−	1.37112i
$414$		0			0
$415$	−6.80040	+	11.7786i	−0.333819	+	0.578191i
$416$		0			0
$417$	1.77410	−	9.80463i	0.0868780	−	0.480135i
$418$		0			0
$419$		−	1.25695i		−	0.0614060i	−0.999529	−	0.0307030i	$-0.990225\pi$
$419$		−	1.25695i		−	0.0614060i	0.999529	−	0.0307030i	$-0.00977461\pi$
$420$		0			0
$421$	−6.55168	−	3.78262i	−0.319310	−	0.184353i	0.331775	−	0.943358i	$-0.392352\pi$
$421$	−6.55168	−	3.78262i	−0.319310	−	0.184353i	−0.651085	+	0.759005i	$0.725686\pi$
$422$		0			0
$423$	17.2680	+	20.9573i	0.839597	+	1.01898i
$424$		0			0
$425$		−	16.0294i		−	0.777539i
$426$		0			0
$427$	6.80280	+	11.7828i	0.329211	+	0.570209i
$428$		0			0
$429$	0.218335	−	1.20664i	0.0105413	−	0.0582571i
$430$		0			0
$431$	−7.99078	−	13.8404i	−0.384902	−	0.666670i	0.606853	−	0.794814i	$-0.292431\pi$
$431$	−7.99078	−	13.8404i	−0.384902	−	0.666670i	−0.991756	+	0.128144i	$0.959098\pi$
$432$		0			0
$433$	9.65991	−	5.57715i	0.464226	−	0.268021i	−0.249594	−	0.968351i	$-0.580297\pi$
$433$	9.65991	−	5.57715i	0.464226	−	0.268021i	0.713819	+	0.700330i	$0.246964\pi$
$434$		0			0
$435$	−25.0037	+	29.5288i	−1.19883	+	1.41580i
$436$		0			0
$437$	17.3280	+	17.4079i	0.828911	+	0.832735i
$438$		0			0
$439$	−16.0949	−	9.29240i	−0.768168	−	0.443502i	0.0640529	−	0.997947i	$-0.479597\pi$
$439$	−16.0949	−	9.29240i	−0.768168	−	0.443502i	−0.832221	+	0.554445i	$0.812931\pi$
$440$		0			0
$441$	8.25816	+	49.4167i	0.393246	+	2.35318i
$442$		0			0
$443$	5.93810	−	3.42837i	0.282128	−	0.162887i	−0.352258	−	0.935903i	$-0.614586\pi$
$443$	5.93810	−	3.42837i	0.282128	−	0.162887i	0.634386	+	0.773016i	$0.281253\pi$
$444$		0			0
$445$			11.6908i			0.554196i
$446$		0			0
$447$	−9.01207	−	25.1095i	−0.426256	−	1.18764i
$448$		0			0
$449$	30.5307			1.44084			0.720418	−	0.693541i	$-0.243950\pi$
$449$	30.5307			1.44084			0.720418	+	0.693541i	$0.243950\pi$
$450$		0			0
$451$	1.33967	+	0.773458i	0.0630825	+	0.0364207i
$452$		0			0
$453$	−12.3331	+	14.5651i	−0.579459	+	0.684329i
$454$		0			0
$455$	−2.43871			−0.114328
$456$		0			0
$457$	6.22400			0.291147			0.145573	−	0.989347i	$-0.453497\pi$
$457$	6.22400			0.291147			0.145573	+	0.989347i	$0.453497\pi$
$458$		0			0
$459$	−12.4168	+	6.94828i	−0.579567	+	0.324318i
$460$		0			0
$461$	−11.3205	−	6.53590i	−0.527249	−	0.304407i	0.212647	−	0.977129i	$-0.431792\pi$
$461$	−11.3205	−	6.53590i	−0.527249	−	0.304407i	−0.739895	+	0.672722i	$0.765125\pi$
$462$		0			0
$463$	−29.1884			−1.35650			−0.678249	−	0.734832i	$-0.737261\pi$
$463$	−29.1884			−1.35650			−0.678249	+	0.734832i	$0.737261\pi$
$464$		0			0
$465$	−15.2045	+	5.45705i	−0.705092	+	0.253065i
$466$		0			0
$467$		−	7.03591i		−	0.325583i	−0.986660	−	0.162792i	$-0.947950\pi$
$467$		−	7.03591i		−	0.325583i	0.986660	−	0.162792i	$-0.0520498\pi$
$468$		0			0
$469$	18.2016	−	10.5087i	0.840473	−	0.485248i
$470$		0			0
$471$	−0.686954	+	0.246555i	−0.0316532	+	0.0113607i
$472$		0			0
$473$	17.1411	+	9.89643i	0.788149	+	0.455038i
$474$		0			0
$475$	−18.0839	+	18.0009i	−0.829747	+	0.825937i
$476$		0			0
$477$	2.25127	−	1.85496i	0.103079	−	0.0849328i
$478$		0			0
$479$	9.71285	−	5.60772i	0.443791	−	0.256223i	−0.261413	−	0.965227i	$-0.584188\pi$
$479$	9.71285	−	5.60772i	0.443791	−	0.256223i	0.705205	+	0.709004i	$0.250855\pi$
$480$		0			0
$481$	−0.390832	−	0.676942i	−0.0178204	−	0.0308659i
$482$		0			0
$483$	−46.7556	−	8.46019i	−2.12745	−	0.384952i
$484$		0			0
$485$	18.0895	+	31.3320i	0.821404	+	1.42271i
$486$		0			0
$487$		−	7.89794i		−	0.357890i	−0.983859	−	0.178945i	$-0.942732\pi$
$487$		−	7.89794i		−	0.357890i	0.983859	−	0.178945i	$-0.0572684\pi$
$488$		0			0
$489$	−19.2836	−	16.3285i	−0.872034	−	0.738398i
$490$		0			0
$491$	−4.35617	−	2.51503i	−0.196591	−	0.113502i	0.398473	−	0.917180i	$-0.369540\pi$
$491$	−4.35617	−	2.51503i	−0.196591	−	0.113502i	−0.595064	+	0.803678i	$0.702873\pi$
$492$		0			0
$493$		−	18.5679i		−	0.836257i
$494$		0			0
$495$	43.1007	+	16.1257i	1.93723	+	0.724796i
$496$		0			0
$497$	−37.7653	+	65.4115i	−1.69401	+	2.93411i
$498$		0			0
$499$	20.4988	−	35.5049i	0.917651	−	1.58942i	0.114678	−	0.993403i	$-0.463416\pi$
$499$	20.4988	−	35.5049i	0.917651	−	1.58942i	0.802973	−	0.596015i	$-0.203250\pi$
$500$		0			0
$501$	−2.09072	+	11.5544i	−0.0934064	+	0.516215i
$502$		0			0
$503$	−17.0455	+	9.84123i	−0.760022	+	0.438799i	−0.829304	−	0.558798i	$-0.811263\pi$
$503$	−17.0455	+	9.84123i	−0.760022	+	0.438799i	0.0692817	+	0.997597i	$0.477929\pi$
$504$		0			0
$505$	−41.9279			−1.86577
$506$		0			0
$507$	21.1553	−	7.59286i	0.939540	−	0.337211i
$508$		0			0
$509$	−22.3738	−	38.7525i	−0.991699	−	1.71767i	−0.607202	−	0.794547i	$-0.707708\pi$
$509$	−22.3738	−	38.7525i	−0.991699	−	1.71767i	−0.384497	−	0.923126i	$-0.625625\pi$
$510$		0			0
$511$	15.2408	−	26.3979i	0.674214	−	1.16777i
$512$		0			0
$513$	21.7828	+	6.20545i	0.961736	+	0.273977i
$514$		0			0
$515$	19.5205	−	33.8106i	0.860178	−	1.48987i
$516$		0			0
$517$	21.0727	+	36.4989i	0.926775	+	1.60522i
$518$		0			0
$519$	−11.9628	+	4.29358i	−0.525109	+	0.188467i
$520$		0			0
$521$	11.3968			0.499305			0.249652	−	0.968336i	$-0.419684\pi$
$521$	11.3968			0.499305			0.249652	+	0.968336i	$0.419684\pi$
$522$		0			0
$523$	−32.6718	+	18.8631i	−1.42864	+	0.824824i	−0.997013	−	0.0772300i	$-0.975392\pi$
$523$	−32.6718	+	18.8631i	−1.42864	+	0.824824i	−0.431624	+	0.902054i	$0.642059\pi$
$524$		0			0
$525$	8.78871	−	48.5712i	0.383571	−	2.11982i
$526$		0			0
$527$	3.87603	−	6.71347i	0.168842	−	0.292443i
$528$		0			0
$529$	4.37621	−	7.57981i	0.190270	−	0.329557i
$530$		0			0
$531$	18.5699	+	6.94775i	0.805867	+	0.301507i
$532$		0			0
$533$		−	0.0505166i		−	0.00218812i
$534$		0			0
$535$	23.6229	+	13.6387i	1.02131	+	0.589652i
$536$		0			0
$537$	−16.0367	−	13.5791i	−0.692033	−	0.585982i
$538$		0			0
$539$			77.7600i			3.34936i
$540$		0			0
$541$	0.276080	+	0.478184i	0.0118696	+	0.0205587i	0.871899	−	0.489685i	$-0.162888\pi$
$541$	0.276080	+	0.478184i	0.0118696	+	0.0205587i	−0.860030	+	0.510244i	$0.829555\pi$
$542$		0			0
$543$	−3.32842	−	0.602260i	−0.142836	−	0.0258454i
$544$		0			0
$545$	2.58921	+	4.48464i	0.110909	+	0.192101i
$546$		0			0
$547$	1.13486	−	0.655211i	0.0485230	−	0.0280148i	−0.475542	−	0.879693i	$-0.657748\pi$
$547$	1.13486	−	0.655211i	0.0485230	−	0.0280148i	0.524065	+	0.851678i	$0.324415\pi$
$548$		0			0
$549$	−6.47060	+	5.33152i	−0.276159	+	0.227544i
$550$		0			0
$551$	−20.9478	+	20.8516i	−0.892408	+	0.888310i
$552$		0			0
$553$	40.8320	+	23.5744i	1.73635	+	1.00248i
$554$		0			0
$555$	27.6102	−	9.90958i	1.17199	−	0.420638i
$556$		0			0
$557$	−6.76140	+	3.90370i	−0.286490	+	0.165405i	−0.636358	−	0.771394i	$-0.719560\pi$
$557$	−6.76140	+	3.90370i	−0.286490	+	0.165405i	0.349868	+	0.936799i	$0.386226\pi$
$558$		0			0
$559$		−	0.646362i		−	0.0273382i
$560$		0			0
$561$	−20.7852	+	7.46003i	−0.877553	+	0.314963i
$562$		0			0
$563$	−34.7472			−1.46442			−0.732210	−	0.681079i	$-0.761511\pi$
$563$	−34.7472			−1.46442			−0.732210	+	0.681079i	$0.761511\pi$
$564$		0			0
$565$	−7.55283	−	4.36063i	−0.317750	−	0.183453i
$566$		0			0
$567$	−41.4343	+	14.2462i	−1.74008	+	0.598285i
$568$		0			0
$569$	−35.7973			−1.50070			−0.750350	−	0.661041i	$-0.770115\pi$
$569$	−35.7973			−1.50070			−0.750350	+	0.661041i	$0.770115\pi$
$570$		0			0
$571$	16.7301			0.700133			0.350067	−	0.936725i	$-0.386159\pi$
$571$	16.7301			0.700133			0.350067	+	0.936725i	$0.386159\pi$
$572$		0			0
$573$	−6.80373	+	8.03507i	−0.284230	+	0.335670i
$574$		0			0
$575$	28.5662	+	16.4927i	1.19129	+	0.687793i
$576$		0			0
$577$	−9.23873			−0.384613			−0.192307	−	0.981335i	$-0.561597\pi$
$577$	−9.23873			−0.384613			−0.192307	+	0.981335i	$0.561597\pi$
$578$		0			0
$579$	0.0745086	+	0.207597i	0.00309647	+	0.00862742i
$580$		0			0
$581$		−	20.0981i		−	0.833810i
$582$		0			0
$583$	3.92079	−	2.26367i	0.162383	−	0.0937517i
$584$		0			0
$585$	−0.247702	−	1.48224i	−0.0102412	−	0.0612833i
$586$		0			0
$587$	1.72443	+	0.995601i	0.0711749	+	0.0410928i	0.535165	−	0.844747i	$-0.320249\pi$
$587$	1.72443	+	0.995601i	0.0711749	+	0.0410928i	−0.463990	+	0.885840i	$0.653583\pi$
$588$		0			0
$589$	−11.9267	+	3.16635i	−0.491431	+	0.130467i
$590$		0			0
$591$	−0.000229617	0	0.000271173i	−9.44519e−6	0	1.11546e-5i
$592$		0			0
$593$	11.1953	−	6.46361i	0.459736	−	0.265429i	−0.252197	−	0.967676i	$-0.581153\pi$
$593$	11.1953	−	6.46361i	0.459736	−	0.265429i	0.711933	+	0.702247i	$0.247820\pi$
$594$		0			0
$595$	21.9595	+	38.0350i	0.900253	+	1.55928i
$596$		0			0
$597$	0.694188	−	3.83646i	0.0284112	−	0.157016i
$598$		0			0
$599$	−11.8312	−	20.4923i	−0.483411	−	0.837292i	0.516408	−	0.856343i	$-0.327269\pi$
$599$	−11.8312	−	20.4923i	−0.483411	−	0.837292i	−0.999819	+	0.0190507i	$0.993936\pi$
$600$		0			0
$601$		−	35.6062i		−	1.45241i	−0.687481	−	0.726203i	$-0.741283\pi$
$601$		−	35.6062i		−	1.45241i	0.687481	−	0.726203i	$-0.258717\pi$
$602$		0			0
$603$	8.23594	+	9.99555i	0.335394	+	0.407050i
$604$		0			0
$605$	30.4693	+	17.5915i	1.23875	+	0.715195i
$606$		0			0
$607$		−	4.08226i		−	0.165694i	−0.996562	−	0.0828470i	$-0.973599\pi$
$607$		−	4.08226i		−	0.165694i	0.996562	−	0.0828470i	$-0.0264013\pi$
$608$		0			0
$609$	10.1806	−	56.2633i	0.412537	−	2.27991i
$610$		0			0
$611$	0.688156	−	1.19192i	0.0278398	−	0.0482200i
$612$		0			0
$613$	−13.6833	+	23.7002i	−0.552663	+	0.957240i	0.445418	+	0.895323i	$0.353055\pi$
$613$	−13.6833	+	23.7002i	−0.552663	+	0.957240i	−0.998081	+	0.0619178i	$0.980278\pi$
$614$		0			0
$615$	1.86551	+	0.337556i	0.0752248	+	0.0136116i
$616$		0			0
$617$	2.20706	−	1.27425i	0.0888528	−	0.0512992i	−0.454915	−	0.890535i	$-0.650330\pi$
$617$	2.20706	−	1.27425i	0.0888528	−	0.0512992i	0.543768	+	0.839236i	$0.316997\pi$
$618$		0			0
$619$	16.7126			0.671736			0.335868	−	0.941909i	$-0.390970\pi$
$619$	16.7126			0.671736			0.335868	+	0.941909i	$0.390970\pi$
$620$		0			0
$621$	0.393086	−	29.2773i	0.0157740	−	1.17486i
$622$		0			0
$623$	−8.63782	−	14.9611i	−0.346067	−	0.599406i
$624$		0			0
$625$	10.0012	−	17.3226i	0.400048	−	0.692904i
$626$		0			0
$627$	31.7579	+	15.0718i	1.26829	+	0.601908i
$628$		0			0
$629$	−7.03856	+	12.1911i	−0.280646	+	0.486093i
$630$		0			0
$631$	−5.39766	−	9.34902i	−0.214877	−	0.372178i	0.738357	−	0.674410i	$-0.235602\pi$
$631$	−5.39766	−	9.34902i	−0.214877	−	0.372178i	−0.953235	+	0.302231i	$0.902269\pi$
$632$		0			0
$633$	10.5625	+	29.4294i	0.419822	+	1.16971i
$634$		0			0
$635$	62.9049			2.49631
$636$		0			0
$637$	2.19915	−	1.26968i	0.0871334	−	0.0503065i
$638$		0			0
$639$	−43.5929	−	16.3098i	−1.72451	−	0.645207i
$640$		0			0
$641$	17.2478	−	29.8741i	0.681247	−	1.17996i	−0.293353	−	0.956004i	$-0.594771\pi$
$641$	17.2478	−	29.8741i	0.681247	−	1.17996i	0.974600	−	0.223951i	$-0.0718955\pi$
$642$		0			0
$643$	6.66166	−	11.5383i	0.262710	−	0.455028i	−0.704251	−	0.709951i	$-0.748717\pi$
$643$	6.66166	−	11.5383i	0.262710	−	0.455028i	0.966961	+	0.254924i	$0.0820503\pi$
$644$		0			0
$645$	23.8693	+	4.31904i	0.939855	+	0.170062i
$646$		0			0
$647$		−	21.9757i		−	0.863955i	−0.901884	−	0.431977i	$-0.857816\pi$
$647$		−	21.9757i		−	0.863955i	0.901884	−	0.431977i	$-0.142184\pi$
$648$		0			0
$649$	26.6496	+	15.3862i	1.04609	+	0.603960i
$650$		0			0
$651$	15.4258	−	18.2176i	0.604585	−	0.714002i
$652$		0			0
$653$			12.9296i			0.505975i	0.967470	+	0.252988i	$0.0814132\pi$
$653$			12.9296i			0.505975i	−0.967470	+	0.252988i	$0.918587\pi$
$654$		0			0
$655$	−36.3418	−	62.9459i	−1.41999	−	2.45950i
$656$		0			0
$657$	17.5926	+	6.58209i	0.686353	+	0.256792i
$658$		0			0
$659$	−12.8663	−	22.2851i	−0.501199	−	0.868102i	−0.999999	−	0.00138516i	$-0.999559\pi$
$659$	−12.8663	−	22.2851i	−0.501199	−	0.868102i	0.498800	−	0.866717i	$-0.333774\pi$
$660$		0			0
$661$	−0.941644	+	0.543658i	−0.0366257	+	0.0211459i	−0.518201	−	0.855259i	$-0.673398\pi$
$661$	−0.941644	+	0.543658i	−0.0366257	+	0.0211459i	0.481575	+	0.876405i	$0.340065\pi$
$662$		0			0
$663$	0.550363	+	0.466023i	0.0213743	+	0.0180988i
$664$		0			0
$665$	18.2497	−	67.4872i	0.707694	−	2.61704i
$666$		0			0
$667$	33.0902	+	19.1046i	1.28126	+	0.739734i
$668$		0			0
$669$	−15.0163	−	41.8385i	−0.580563	−	1.61757i
$670$		0			0
$671$	−11.2691	+	6.50624i	−0.435040	+	0.251171i
$672$		0			0
$673$		−	17.8691i		−	0.688805i	−0.938822	−	0.344402i	$-0.888082\pi$
$673$		−	17.8691i		−	0.688805i	0.938822	−	0.344402i	$-0.111918\pi$
$674$		0			0
$675$	30.4142	+	0.408351i	1.17064	+	0.0157174i
$676$		0			0
$677$	−21.5790			−0.829349			−0.414674	−	0.909970i	$-0.636104\pi$
$677$	−21.5790			−0.829349			−0.414674	+	0.909970i	$0.636104\pi$
$678$		0			0
$679$	−46.2998	−	26.7312i	−1.77682	−	1.02585i
$680$		0			0
$681$	−4.19981	−	3.55621i	−0.160937	−	0.136274i
$682$		0			0
$683$	−7.03565			−0.269212			−0.134606	−	0.990899i	$-0.542977\pi$
$683$	−7.03565			−0.269212			−0.134606	+	0.990899i	$0.542977\pi$
$684$		0			0
$685$	22.8798			0.874192
$686$		0			0
$687$	14.5880	+	12.3524i	0.556566	+	0.471275i
$688$		0			0
$689$	−0.128039	−	0.0739232i	−0.00487789	−	0.00281625i
$690$		0			0
$691$	−33.3219			−1.26762			−0.633812	−	0.773487i	$-0.718511\pi$
$691$	−33.3219			−1.26762			−0.633812	+	0.773487i	$0.718511\pi$
$692$		0			0
$693$	−67.0723	+	11.2086i	−2.54786	+	0.425780i
$694$		0			0
$695$		−	18.9520i		−	0.718892i
$696$		0			0
$697$	−0.787876	+	0.454880i	−0.0298429	+	0.0172298i
$698$		0			0
$699$	12.5541	+	34.9785i	0.474841	+	1.32301i
$700$		0			0
$701$	−11.7215	−	6.76742i	−0.442715	−	0.255602i	0.262033	−	0.965059i	$-0.415607\pi$
$701$	−11.7215	−	6.76742i	−0.442715	−	0.255602i	−0.704749	+	0.709457i	$0.748940\pi$
$702$		0			0
$703$	21.6580	−	5.74985i	0.816846	−	0.216860i
$704$		0			0
$705$	39.4179	+	33.3773i	1.48456	+	1.25706i
$706$		0			0
$707$	53.6568	−	30.9787i	2.01797	−	1.16508i
$708$		0			0
$709$	−12.3267	−	21.3505i	−0.462940	−	0.801835i	0.536166	−	0.844113i	$-0.319872\pi$
$709$	−12.3267	−	21.3505i	−0.462940	−	0.801835i	−0.999106	+	0.0422772i	$0.986539\pi$
$710$		0			0
$711$	−10.1811	+	27.2121i	−0.381822	+	1.02053i
$712$		0			0
$713$	7.97612	+	13.8151i	0.298708	+	0.517378i
$714$		0			0
$715$		−	2.33240i		−	0.0872266i
$716$		0			0
$717$	29.5779	−	34.9309i	1.10461	−	1.30452i
$718$		0			0
$719$	10.1664	+	5.86960i	0.379144	+	0.218899i	0.677446	−	0.735573i	$-0.263087\pi$
$719$	10.1664	+	5.86960i	0.379144	+	0.218899i	−0.298302	+	0.954472i	$0.596420\pi$
$720$		0			0
$721$			57.6916i			2.14855i
$722$		0			0
$723$	−9.57585	−	1.73270i	−0.356130	−	0.0644399i
$724$		0			0
$725$	−19.8465	+	34.3751i	−0.737080	+	1.27666i
$726$		0			0
$727$	8.77988	−	15.2072i	0.325628	−	0.564003i	−0.656012	−	0.754751i	$-0.727758\pi$
$727$	8.77988	−	15.2072i	0.325628	−	0.564003i	0.981639	+	0.190747i	$0.0610911\pi$
$728$		0			0
$729$	−12.8674	−	23.7367i	−0.476569	−	0.879137i
$730$		0			0
$731$	−10.0809	+	5.82022i	−0.372856	+	0.215268i
$732$		0			0
$733$	9.79201			0.361676			0.180838	−	0.983513i	$-0.442119\pi$
$733$	9.79201			0.361676			0.180838	+	0.983513i	$0.442119\pi$
$734$		0			0
$735$	32.1928	+	89.6959i	1.18745	+	3.30848i
$736$		0			0
$737$	10.0506	+	17.4081i	0.370219	+	0.641237i
$738$		0			0
$739$	−15.3380	+	26.5662i	−0.564218	+	0.977254i	0.432904	+	0.901440i	$0.357489\pi$
$739$	−15.3380	+	26.5662i	−0.564218	+	0.977254i	−0.997122	+	0.0758139i	$0.975845\pi$
$740$		0			0
$741$	−0.0922995	−	1.14424i	−0.00339071	−	0.0420349i
$742$		0			0
$743$	4.16076	−	7.20665i	0.152644	−	0.264386i	−0.779555	−	0.626334i	$-0.784555\pi$
$743$	4.16076	−	7.20665i	0.152644	−	0.264386i	0.932199	+	0.361947i	$0.117888\pi$
$744$		0			0
$745$	−25.3717	−	43.9450i	−0.929546	−	1.61002i
$746$		0			0
$747$	12.2156	−	2.04138i	0.446946	−	0.0746903i
$748$		0			0
$749$	−40.3082			−1.47283
$750$		0			0
$751$	−8.35220	+	4.82215i	−0.304776	+	0.175963i	−0.644586	−	0.764531i	$-0.722970\pi$
$751$	−8.35220	+	4.82215i	−0.304776	+	0.175963i	0.339810	+	0.940494i	$0.389637\pi$
$752$		0			0
$753$	35.7719	+	6.47275i	1.30360	+	0.235880i
$754$		0			0
$755$	−18.1509	+	31.4382i	−0.660578	+	1.14415i
$756$		0			0
$757$	−26.0414	+	45.1051i	−0.946492	+	1.63937i	−0.193757	+	0.981050i	$0.562067\pi$
$757$	−26.0414	+	45.1051i	−0.946492	+	1.63937i	−0.752735	+	0.658323i	$0.771266\pi$
$758$		0			0
$759$	8.09137	−	44.7173i	0.293698	−	1.62314i
$760$		0			0
$761$			4.30369i			0.156009i	0.996953	+	0.0780043i	$0.0248548\pi$
$761$			4.30369i			0.156009i	−0.996953	+	0.0780043i	$0.975145\pi$
$762$		0			0
$763$	−6.62701	−	3.82611i	−0.239914	−	0.138514i
$764$		0			0
$765$	−20.8872	+	17.2102i	−0.755178	+	0.622237i
$766$		0			0
$767$		−	1.00491i		−	0.0362853i
$768$		0			0
$769$	−18.5444	−	32.1199i	−0.668729	−	1.15827i	−0.978260	−	0.207383i	$-0.933505\pi$
$769$	−18.5444	−	32.1199i	−0.668729	−	1.15827i	0.309531	−	0.950890i	$-0.399828\pi$
$770$		0			0
$771$	−7.40590	+	40.9290i	−0.266717	+	1.47402i
$772$		0			0
$773$	1.15766	+	2.00513i	0.0416383	+	0.0721197i	0.886093	−	0.463507i	$-0.153409\pi$
$773$	1.15766	+	2.00513i	0.0416383	+	0.0721197i	−0.844455	+	0.535626i	$0.820076\pi$
$774$		0			0
$775$	−14.3515	+	8.28585i	−0.515522	+	0.297637i
$776$		0			0
$777$	−28.0120	+	33.0817i	−1.00493	+	1.18680i
$778$		0			0
$779$	1.39796	+	0.378033i	0.0500872	+	0.0135445i
$780$		0			0
$781$	−62.5599	−	36.1190i	−2.23857	−	1.29244i
$782$		0			0
$783$	35.2308	+	0.473020i	1.25905	+	0.0169044i
$784$		0			0
$785$	−1.20226	+	0.694126i	−0.0429106	+	0.0247744i
$786$		0			0
$787$			28.4149i			1.01288i	0.862274	+	0.506441i	$0.169039\pi$
$787$			28.4149i			1.01288i	−0.862274	+	0.506441i	$0.830961\pi$
$788$		0			0
$789$	−11.7849	−	32.8353i	−0.419555	−	1.16897i
$790$		0			0
$791$	12.8875			0.458228
$792$		0			0
$793$	0.368009	+	0.212470i	0.0130684	+	0.00754503i
$794$		0			0
$795$	3.58546	−	4.23435i	0.127163	−	0.150177i
$796$		0			0
$797$	−51.0888			−1.80966			−0.904829	−	0.425776i	$-0.860001\pi$
$797$	−51.0888			−1.80966			−0.904829	+	0.425776i	$0.860001\pi$
$798$		0			0
$799$	−24.7862			−0.876873
$800$		0			0
$801$	8.21602	−	6.76968i	0.290299	−	0.239195i
$802$		0			0
$803$	25.2471	+	14.5764i	0.890949	+	0.514390i
$804$		0			0
$805$	−90.3771			−3.18537
$806$		0			0
$807$	−18.2789	+	6.56049i	−0.643448	+	0.230940i
$808$		0			0
$809$			36.2226i			1.27352i	0.771062	+	0.636760i	$0.219726\pi$
$809$			36.2226i			1.27352i	−0.771062	+	0.636760i	$0.780274\pi$
$810$		0			0
$811$	−1.27893	+	0.738391i	−0.0449094	+	0.0259284i	−0.522287	−	0.852770i	$-0.674921\pi$
$811$	−1.27893	+	0.738391i	−0.0449094	+	0.0259284i	0.477377	+	0.878698i	$0.341588\pi$
$812$		0			0
$813$	−37.8698	+	13.5919i	−1.32815	+	0.476688i
$814$		0			0
$815$	−41.6228	−	24.0310i	−1.45798	−	0.841768i
$816$		0			0
$817$	17.8870	+	4.83696i	0.625787	+	0.169224i
$818$		0			0
$819$	1.41216	+	1.71387i	0.0493449	+	0.0598874i
$820$		0			0
$821$	39.5215	−	22.8177i	1.37931	−	0.796345i	0.387234	−	0.921982i	$-0.373431\pi$
$821$	39.5215	−	22.8177i	1.37931	−	0.796345i	0.992076	+	0.125637i	$0.0400974\pi$
$822$		0			0
$823$	5.10684	+	8.84530i	0.178013	+	0.308328i	0.941200	−	0.337850i	$-0.109700\pi$
$823$	5.10684	+	8.84530i	0.178013	+	0.308328i	−0.763187	+	0.646178i	$0.776366\pi$
$824$		0			0
$825$	46.4538	+	8.40558i	1.61731	+	0.292645i
$826$		0			0
$827$	−16.7913	−	29.0834i	−0.583891	−	1.01133i	−0.995013	−	0.0997487i	$-0.968196\pi$
$827$	−16.7913	−	29.0834i	−0.583891	−	1.01133i	0.411121	−	0.911581i	$-0.365137\pi$
$828$		0			0
$829$		−	46.6012i		−	1.61853i	−0.587447	−	0.809263i	$-0.699867\pi$
$829$		−	46.6012i		−	1.61853i	0.587447	−	0.809263i	$-0.300133\pi$
$830$		0			0
$831$	−17.3721	−	14.7099i	−0.602630	−	0.510280i
$832$		0			0
$833$	−39.6048	−	22.8658i	−1.37222	−	0.792254i
$834$		0			0
$835$			22.3344i			0.772913i
$836$		0			0
$837$	12.6394	+	7.52541i	0.436882	+	0.260116i
$838$		0			0
$839$	−22.7133	+	39.3406i	−0.784150	+	1.35819i	0.145356	+	0.989379i	$0.453567\pi$
$839$	−22.7133	+	39.3406i	−0.784150	+	1.35819i	−0.929506	+	0.368808i	$0.879766\pi$
$840$		0			0
$841$	−8.48956	+	14.7043i	−0.292743	+	0.507046i
$842$		0			0
$843$	8.04311	−	44.4506i	0.277019	−	1.53096i
$844$		0			0
$845$	37.0246	−	21.3762i	1.27369	−	0.735363i
$846$		0			0
$847$	−51.9903			−1.78641
$848$		0			0
$849$	15.8024	−	5.67164i	0.542336	−	0.194650i
$850$		0			0
$851$	−14.4840	−	25.0871i	−0.496506	−	0.859973i
$852$		0			0
$853$	0.639941	−	1.10841i	0.0219112	−	0.0379513i	−0.854862	−	0.518856i	$-0.826358\pi$
$853$	0.639941	−	1.10841i	0.0219112	−	0.0379513i	0.876773	+	0.480904i	$0.159692\pi$
$854$		0			0
$855$	42.8723	+	4.23742i	1.46620	+	0.144917i
$856$		0			0
$857$	−24.6870	+	42.7592i	−0.843293	+	1.46063i	0.0438025	+	0.999040i	$0.486053\pi$
$857$	−24.6870	+	42.7592i	−0.843293	+	1.46063i	−0.887095	+	0.461586i	$0.847281\pi$
$858$		0			0
$859$	−12.0526	−	20.8757i	−0.411229	−	0.712270i	0.583795	−	0.811901i	$-0.301567\pi$
$859$	−12.0526	−	20.8757i	−0.411229	−	0.712270i	−0.995024	+	0.0996309i	$0.968234\pi$
$860$		0			0
$861$	−2.63678	+	0.946366i	−0.0898611	+	0.0322521i
$862$		0			0
$863$	−43.8592			−1.49298			−0.746492	−	0.665395i	$-0.768263\pi$
$863$	−43.8592			−1.49298			−0.746492	+	0.665395i	$0.768263\pi$
$864$		0			0
$865$	−20.9365	+	12.0877i	−0.711863	+	0.410994i
$866$		0			0
$867$	−2.93029	+	16.1943i	−0.0995177	+	0.549989i
$868$		0			0
$869$	−22.5467	+	39.0520i	−0.764843	+	1.32475i
$870$		0			0
$871$	0.328216	−	0.568486i	0.0111212	−	0.0192624i
$872$		0			0
$873$	11.5445	−	30.8561i	0.390721	−	1.04432i
$874$		0			0
$875$		−	13.6929i		−	0.462906i
$876$		0			0
$877$	20.4325	+	11.7967i	0.689956	+	0.398347i	0.803596	−	0.595176i	$-0.202917\pi$
$877$	20.4325	+	11.7967i	0.689956	+	0.398347i	−0.113639	+	0.993522i	$0.536251\pi$
$878$		0			0
$879$	−4.99948	−	4.23333i	−0.168628	−	0.142787i
$880$		0			0
$881$		−	1.41851i		−	0.0477908i	−0.999714	−	0.0238954i	$-0.992393\pi$
$881$		−	1.41851i		−	0.0477908i	0.999714	−	0.0238954i	$-0.00760687\pi$
$882$		0			0
$883$	14.0948	+	24.4128i	0.474327	+	0.821558i	0.999568	−	0.0293956i	$-0.00935825\pi$
$883$	14.0948	+	24.4128i	0.474327	+	0.821558i	−0.525241	+	0.850953i	$0.676025\pi$
$884$		0			0
$885$	37.1102	+	6.71490i	1.24744	+	0.225719i
$886$		0			0
$887$	0.855400	+	1.48160i	0.0287215	+	0.0497472i	0.880029	−	0.474920i	$-0.157523\pi$
$887$	0.855400	+	1.48160i	0.0287215	+	0.0497472i	−0.851307	+	0.524667i	$0.824190\pi$
$888$		0			0
$889$	−80.5019	+	46.4778i	−2.69995	+	1.55881i
$890$		0			0
$891$	−13.6252	−	39.6280i	−0.456461	−	1.32759i
$892$		0			0
$893$	27.8347	+	27.9631i	0.931454	+	0.935751i
$894$		0			0
$895$	−34.6145	−	19.9847i	−1.15703	−	0.668014i
$896$		0			0
$897$	−1.39678	+	0.501318i	−0.0466370	+	0.0167385i
$898$		0			0
$899$	−16.6243	+	9.59807i	−0.554453	+	0.320113i
$900$		0			0
$901$			2.66259i			0.0887037i
$902$		0			0
$903$	−33.7377	+	12.1088i	−1.12272	+	0.402956i
$904$		0			0
$905$	−6.43372			−0.213864
$906$		0			0
$907$	−29.5788	−	17.0773i	−0.982148	−	0.567043i	−0.0792301	−	0.996856i	$-0.525246\pi$
$907$	−29.5788	−	17.0773i	−0.982148	−	0.567043i	−0.902918	+	0.429813i	$0.858580\pi$
$908$		0			0
$909$	24.2788	+	29.4660i	0.805277	+	0.977325i
$910$		0			0
$911$	50.4785			1.67243			0.836213	−	0.548405i	$-0.184765\pi$
$911$	50.4785			1.67243			0.836213	+	0.548405i	$0.184765\pi$
$912$		0			0
$913$	19.2219			0.636154
$914$		0			0
$915$	−10.3053	+	12.1704i	−0.340683	+	0.402340i
$916$		0			0
$917$	93.0161	+	53.7029i	3.07166	+	1.77342i
$918$		0			0
$919$	−9.14869			−0.301788			−0.150894	−	0.988550i	$-0.548215\pi$
$919$	−9.14869			−0.301788			−0.150894	+	0.988550i	$0.548215\pi$
$920$		0			0
$921$	14.7332	+	41.0497i	0.485474	+	1.35263i
$922$		0			0
$923$			2.35903i			0.0776483i
$924$		0			0
$925$	26.0612	−	15.0465i	0.856888	−	0.494724i
$926$		0			0
$927$	−35.0649	+	5.85979i	−1.15168	+	0.192461i
$928$		0			0
$929$	7.92666	+	4.57646i	0.260065	+	0.150149i	0.624364	−	0.781133i	$-0.285358\pi$
$929$	7.92666	+	4.57646i	0.260065	+	0.150149i	−0.364299	+	0.931282i	$0.618691\pi$
$930$		0			0
$931$	18.6792	+	70.3592i	0.612188	+	2.30593i
$932$		0			0
$933$	11.2407	−	13.2751i	0.368005	−	0.434606i
$934$		0			0
$935$	−36.3769	+	21.0022i	−1.18965	+	0.686846i
$936$		0			0
$937$	6.30822	+	10.9262i	0.206081	+	0.356942i	0.950477	−	0.310796i	$-0.100596\pi$
$937$	6.30822	+	10.9262i	0.206081	+	0.356942i	−0.744396	+	0.667739i	$0.767262\pi$
$938$		0			0
$939$	−4.72502	+	26.1130i	−0.154195	+	0.852166i
$940$		0			0
$941$	1.79732	+	3.11304i	0.0585908	+	0.101482i	0.893833	−	0.448400i	$-0.148006\pi$
$941$	1.79732	+	3.11304i	0.0585908	+	0.101482i	−0.835242	+	0.549882i	$0.814673\pi$
$942$		0			0
$943$		−	1.87211i		−	0.0609644i
$944$		0			0
$945$	−72.7272	+	40.6971i	−2.36582	+	1.32388i
$946$		0			0
$947$	6.51039	+	3.75877i	0.211559	+	0.122144i	0.602036	−	0.798469i	$-0.294356\pi$
$947$	6.51039	+	3.75877i	0.211559	+	0.122144i	−0.390477	+	0.920613i	$0.627690\pi$
$948$		0			0
$949$		−	0.952023i		−	0.0309040i
$950$		0			0
$951$	1.13824	−	6.29053i	0.0369100	−	0.203985i
$952$		0			0
$953$	6.21944	−	10.7724i	0.201468	−	0.348952i	−0.747534	−	0.664224i	$-0.768762\pi$
$953$	6.21944	−	10.7724i	0.201468	−	0.348952i	0.949001	+	0.315272i	$0.102096\pi$
$954$		0			0
$955$	−10.0132	+	17.3434i	−0.324020	+	0.561219i
$956$		0			0
$957$	53.8106	+	9.73675i	1.73945	+	0.314745i
$958$		0			0
$959$	−29.2802	+	16.9049i	−0.945506	+	0.545888i
$960$		0			0
$961$	22.9857			0.741473
$962$		0			0
$963$	−4.09414	−	24.4993i	−0.131932	−	0.789477i
$964$		0			0
$965$	0.209764	+	0.363322i	0.00675255	+	0.0116958i
$966$		0			0
$967$	−5.23156	+	9.06132i	−0.168235	+	0.291392i	−0.937800	−	0.347177i	$-0.887140\pi$
$967$	−5.23156	+	9.06132i	−0.168235	+	0.291392i	0.769564	+	0.638570i	$0.220474\pi$
$968$		0			0
$969$	−17.0150	+	11.7430i	−0.546599	+	0.377239i
$970$		0			0
$971$	−11.9412	+	20.6828i	−0.383211	+	0.663741i	−0.991519	−	0.129960i	$-0.958515\pi$
$971$	−11.9412	+	20.6828i	−0.383211	+	0.663741i	0.608308	+	0.793701i	$0.291848\pi$
$972$		0			0
$973$	14.0029	+	24.2537i	0.448911	+	0.777537i
$974$		0			0
$975$	−0.520785	−	1.45102i	−0.0166785	−	0.0464697i
$976$		0			0
$977$	−35.5627			−1.13775			−0.568876	−	0.822424i	$-0.692621\pi$
$977$	−35.5627			−1.13775			−0.568876	+	0.822424i	$0.692621\pi$
$978$		0			0
$979$	14.3089	−	8.26126i	0.457315	−	0.264031i
$980$		0			0
$981$	1.65239	−	4.41651i	0.0527568	−	0.141008i
$982$		0			0
$983$	0.362470	−	0.627817i	0.0115610	−	0.0200243i	−0.860187	−	0.509979i	$-0.829653\pi$
$983$	0.362470	−	0.627817i	0.0115610	−	0.0200243i	0.871748	+	0.489954i	$0.162987\pi$
$984$		0			0
$985$	−0.000337933	0	0.000585317i	−1.07674e−5	0	1.86497e-5i
$986$		0			0
$987$	−75.1056	−	13.5900i	−2.39064	−	0.432574i
$988$		0			0
$989$		−	23.9538i		−	0.761686i
$990$		0			0
$991$	33.3654	+	19.2635i	1.05989	+	0.611926i	0.925401	−	0.378989i	$-0.123728\pi$
$991$	33.3654	+	19.2635i	1.05989	+	0.611926i	0.134487	+	0.990915i	$0.457062\pi$
$992$		0			0
$993$	11.7009	−	13.8186i	0.371318	−	0.438519i
$994$		0			0
$995$		−	7.41576i		−	0.235095i
$996$		0			0
$997$	−3.71967	−	6.44265i	−0.117803	−	0.204041i	0.801094	−	0.598539i	$-0.204252\pi$
$997$	−3.71967	−	6.44265i	−0.117803	−	0.204041i	−0.918897	+	0.394498i	$0.870918\pi$
$998$		0			0
$999$	−22.9522	−	13.6656i	−0.726176	−	0.432359i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.bn.n.65.2		16
3.2	odd	2		912.2.bn.o.65.2		16
4.3	odd	2		456.2.bf.d.65.7	yes	16
12.11	even	2		456.2.bf.c.65.7	✓	16
19.12	odd	6		912.2.bn.o.449.2		16
57.50	even	6	inner	912.2.bn.n.449.2		16
76.31	even	6		456.2.bf.c.449.7	yes	16
228.107	odd	6		456.2.bf.d.449.7	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.bf.c.65.7	✓	16	12.11	even	2
456.2.bf.c.449.7	yes	16	76.31	even	6
456.2.bf.d.65.7	yes	16	4.3	odd	2
456.2.bf.d.449.7	yes	16	228.107	odd	6
912.2.bn.n.65.2		16	1.1	even	1	trivial
912.2.bn.n.449.2		16	57.50	even	6	inner
912.2.bn.o.65.2		16	3.2	odd	2
912.2.bn.o.449.2		16	19.12	odd	6

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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.bn (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.32183 - 1.11927i) q^{3} +(-2.85312 - 1.64725i) q^{5} +4.86833 q^{7} +(0.494481 + 2.95897i) q^{9} +O(q^{10})\)	\(q+(-1.32183 - 1.11927i) q^{3} +(-2.85312 - 1.64725i) q^{5} +4.86833 q^{7} +(0.494481 + 2.95897i) q^{9} +4.65610i q^{11} +(0.131680 - 0.0760256i) q^{13} +(1.92763 + 5.37080i) q^{15} +(-2.37145 - 1.36916i) q^{17} +(1.11847 + 4.21296i) q^{19} +(-6.43512 - 5.44897i) q^{21} +(4.87999 - 2.81746i) q^{23} +(2.92687 + 5.06949i) q^{25} +(2.65826 - 4.46472i) q^{27} +(3.39039 + 5.87234i) q^{29} +2.83096i q^{31} +(5.21142 - 6.15459i) q^{33} +(-13.8899 - 8.01937i) q^{35} -5.14080i q^{37} +(-0.259152 - 0.0468923i) q^{39} +(0.166117 - 0.287723i) q^{41} +(2.12547 - 3.68143i) q^{43} +(3.46335 - 9.25683i) q^{45} +(7.83895 - 4.52582i) q^{47} +16.7007 q^{49} +(1.60221 + 4.46408i) q^{51} +(-0.486173 - 0.842076i) q^{53} +(7.66977 - 13.2844i) q^{55} +(3.23699 - 6.82069i) q^{57} +(3.30452 - 5.72359i) q^{59} +(1.39736 + 2.42029i) q^{61} +(2.40730 + 14.4052i) q^{63} -0.500933 q^{65} +(3.73878 - 2.15859i) q^{67} +(-9.60403 - 1.73780i) q^{69} +(-7.75734 + 13.4361i) q^{71} +(3.13060 - 5.42236i) q^{73} +(1.80528 - 9.97697i) q^{75} +22.6675i q^{77} +(8.38726 + 4.84239i) q^{79} +(-8.51098 + 2.92631i) q^{81} -4.12833i q^{83} +(4.51069 + 7.81274i) q^{85} +(2.09118 - 11.5570i) q^{87} +(-1.77429 - 3.07316i) q^{89} +(0.641063 - 0.370118i) q^{91} +(3.16860 - 3.74205i) q^{93} +(3.74866 - 13.8625i) q^{95} +(-9.51040 - 5.49083i) q^{97} +(-13.7773 + 2.30235i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{3} + 3 q^{5} - 5 q^{9}+O(q^{10}) \) 16 * q - q^3 + 3 * q^5 - 5 * q^9	\( 16 q - q^{3} + 3 q^{5} - 5 q^{9} - 3 q^{13} - 12 q^{15} - 3 q^{17} - 11 q^{19} - 12 q^{21} + 3 q^{23} + 11 q^{25} - 4 q^{27} + 5 q^{29} + 14 q^{33} - 24 q^{35} + 9 q^{39} + 6 q^{41} - 13 q^{43} + 33 q^{45} - 27 q^{47} + 8 q^{49} + 18 q^{51} - 7 q^{53} + 12 q^{55} - 36 q^{57} + 10 q^{59} - q^{61} + 26 q^{63} - 30 q^{65} + 24 q^{67} - 41 q^{69} - 27 q^{71} + 2 q^{73} - 21 q^{75} + 21 q^{79} - 13 q^{81} - 5 q^{85} + 23 q^{87} + 25 q^{89} + 78 q^{91} + 22 q^{93} - 13 q^{95} - 60 q^{97} + 20 q^{99}+O(q^{100}) \) 16 * q - q^3 + 3 * q^5 - 5 * q^9 - 3 * q^13 - 12 * q^15 - 3 * q^17 - 11 * q^19 - 12 * q^21 + 3 * q^23 + 11 * q^25 - 4 * q^27 + 5 * q^29 + 14 * q^33 - 24 * q^35 + 9 * q^39 + 6 * q^41 - 13 * q^43 + 33 * q^45 - 27 * q^47 + 8 * q^49 + 18 * q^51 - 7 * q^53 + 12 * q^55 - 36 * q^57 + 10 * q^59 - q^61 + 26 * q^63 - 30 * q^65 + 24 * q^67 - 41 * q^69 - 27 * q^71 + 2 * q^73 - 21 * q^75 + 21 * q^79 - 13 * q^81 - 5 * q^85 + 23 * q^87 + 25 * q^89 + 78 * q^91 + 22 * q^93 - 13 * q^95 - 60 * q^97 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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