LMFDB - Embedded newform 912.2.bn.d.449.1

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:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 114)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			449.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	912.449
Dual form			912.2.bn.d.65.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 + 0.866025i) q^{3} +(-3.00000 + 1.73205i) q^{5} +2.00000 q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(1.50000 + 0.866025i) q^{3} +(-3.00000 + 1.73205i) q^{5} +2.00000 q^{7} +(1.50000 + 2.59808i) q^{9} +1.73205i q^{11} +(-3.00000 - 1.73205i) q^{13} -6.00000 q^{15} +(-6.00000 + 3.46410i) q^{17} +(-0.500000 + 4.33013i) q^{19} +(3.00000 + 1.73205i) q^{21} +(3.50000 - 6.06218i) q^{25} +5.19615i q^{27} +(3.00000 - 5.19615i) q^{29} -6.92820i q^{31} +(-1.50000 + 2.59808i) q^{33} +(-6.00000 + 3.46410i) q^{35} +6.92820i q^{37} +(-3.00000 - 5.19615i) q^{39} +(1.50000 + 2.59808i) q^{41} +(4.00000 + 6.92820i) q^{43} +(-9.00000 - 5.19615i) q^{45} +(-3.00000 - 1.73205i) q^{47} -3.00000 q^{49} -12.0000 q^{51} +(-3.00000 + 5.19615i) q^{53} +(-3.00000 - 5.19615i) q^{55} +(-4.50000 + 6.06218i) q^{57} +(1.50000 + 2.59808i) q^{59} +(-5.00000 + 8.66025i) q^{61} +(3.00000 + 5.19615i) q^{63} +12.0000 q^{65} +(-4.50000 - 2.59808i) q^{67} +(3.00000 + 5.19615i) q^{71} +(-2.50000 - 4.33013i) q^{73} +(10.5000 - 6.06218i) q^{75} +3.46410i q^{77} +(12.0000 - 6.92820i) q^{79} +(-4.50000 + 7.79423i) q^{81} +5.19615i q^{83} +(12.0000 - 20.7846i) q^{85} +(9.00000 - 5.19615i) q^{87} +(3.00000 - 5.19615i) q^{89} +(-6.00000 - 3.46410i) q^{91} +(6.00000 - 10.3923i) q^{93} +(-6.00000 - 13.8564i) q^{95} +(7.50000 - 4.33013i) q^{97} +(-4.50000 + 2.59808i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{3} - 6 q^{5} + 4 q^{7} + 3 q^{9}+O(q^{10}) $ 2 * q + 3 * q^3 - 6 * q^5 + 4 * q^7 + 3 * q^9	$ 2 q + 3 q^{3} - 6 q^{5} + 4 q^{7} + 3 q^{9} - 6 q^{13} - 12 q^{15} - 12 q^{17} - q^{19} + 6 q^{21} + 7 q^{25} + 6 q^{29} - 3 q^{33} - 12 q^{35} - 6 q^{39} + 3 q^{41} + 8 q^{43} - 18 q^{45} - 6 q^{47} - 6 q^{49} - 24 q^{51} - 6 q^{53} - 6 q^{55} - 9 q^{57} + 3 q^{59} - 10 q^{61} + 6 q^{63} + 24 q^{65} - 9 q^{67} + 6 q^{71} - 5 q^{73} + 21 q^{75} + 24 q^{79} - 9 q^{81} + 24 q^{85} + 18 q^{87} + 6 q^{89} - 12 q^{91} + 12 q^{93} - 12 q^{95} + 15 q^{97} - 9 q^{99}+O(q^{100}) $ 2 * q + 3 * q^3 - 6 * q^5 + 4 * q^7 + 3 * q^9 - 6 * q^13 - 12 * q^15 - 12 * q^17 - q^19 + 6 * q^21 + 7 * q^25 + 6 * q^29 - 3 * q^33 - 12 * q^35 - 6 * q^39 + 3 * q^41 + 8 * q^43 - 18 * q^45 - 6 * q^47 - 6 * q^49 - 24 * q^51 - 6 * q^53 - 6 * q^55 - 9 * q^57 + 3 * q^59 - 10 * q^61 + 6 * q^63 + 24 * q^65 - 9 * q^67 + 6 * q^71 - 5 * q^73 + 21 * q^75 + 24 * q^79 - 9 * q^81 + 24 * q^85 + 18 * q^87 + 6 * q^89 - 12 * q^91 + 12 * q^93 - 12 * q^95 + 15 * q^97 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$	$1$

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
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i
$4$		0			0
$5$	−3.00000	+	1.73205i	−1.34164	+	0.774597i	−0.987048	−	0.160424i	$-0.948714\pi$
$5$	−3.00000	+	1.73205i	−1.34164	+	0.774597i	−0.354593	+	0.935021i	$0.615380\pi$
$6$		0			0
$7$	2.00000			0.755929			0.377964	−	0.925820i	$-0.376624\pi$
$7$	2.00000			0.755929			0.377964	+	0.925820i	$0.376624\pi$
$8$		0			0
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$		0			0
$11$			1.73205i			0.522233i	0.965307	+	0.261116i	$0.0840907\pi$
$11$			1.73205i			0.522233i	−0.965307	+	0.261116i	$0.915909\pi$
$12$		0			0
$13$	−3.00000	−	1.73205i	−0.832050	−	0.480384i	0.0225039	−	0.999747i	$-0.492836\pi$
$13$	−3.00000	−	1.73205i	−0.832050	−	0.480384i	−0.854554	+	0.519362i	$0.826170\pi$
$14$		0			0
$15$	−6.00000			−1.54919
$16$		0			0
$17$	−6.00000	+	3.46410i	−1.45521	+	0.840168i	−0.998770	−	0.0495842i	$-0.984210\pi$
$17$	−6.00000	+	3.46410i	−1.45521	+	0.840168i	−0.456444	+	0.889752i	$0.650877\pi$
$18$		0			0
$19$	−0.500000	+	4.33013i	−0.114708	+	0.993399i
$19$	−0.500000	+	4.33013i	−0.114708	+	0.993399i
$20$		0			0
$21$	3.00000	+	1.73205i	0.654654	+	0.377964i
$22$		0			0
$23$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$23$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$24$		0			0
$25$	3.50000	−	6.06218i	0.700000	−	1.21244i
$26$		0			0
$27$			5.19615i			1.00000i
$28$		0			0
$29$	3.00000	−	5.19615i	0.557086	−	0.964901i	−0.440652	−	0.897678i	$-0.645253\pi$
$29$	3.00000	−	5.19615i	0.557086	−	0.964901i	0.997738	−	0.0672232i	$-0.0214140\pi$
$30$		0			0
$31$		−	6.92820i		−	1.24434i	−0.782881	−	0.622171i	$-0.786251\pi$
$31$		−	6.92820i		−	1.24434i	0.782881	−	0.622171i	$-0.213749\pi$
$32$		0			0
$33$	−1.50000	+	2.59808i	−0.261116	+	0.452267i
$34$		0			0
$35$	−6.00000	+	3.46410i	−1.01419	+	0.585540i
$36$		0			0
$37$			6.92820i			1.13899i	0.821995	+	0.569495i	$0.192861\pi$
$37$			6.92820i			1.13899i	−0.821995	+	0.569495i	$0.807139\pi$
$38$		0			0
$39$	−3.00000	−	5.19615i	−0.480384	−	0.832050i
$40$		0			0
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	0.959058	−	0.283211i	$-0.0913998\pi$
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	−0.724797	+	0.688963i	$0.758066\pi$
$42$		0			0
$43$	4.00000	+	6.92820i	0.609994	+	1.05654i	0.991241	+	0.132068i	$0.0421616\pi$
$43$	4.00000	+	6.92820i	0.609994	+	1.05654i	−0.381246	+	0.924473i	$0.624505\pi$
$44$		0			0
$45$	−9.00000	−	5.19615i	−1.34164	−	0.774597i
$46$		0			0
$47$	−3.00000	−	1.73205i	−0.437595	−	0.252646i	0.264982	−	0.964253i	$-0.414634\pi$
$47$	−3.00000	−	1.73205i	−0.437595	−	0.252646i	−0.702577	+	0.711608i	$0.747967\pi$
$48$		0			0
$49$	−3.00000			−0.428571
$50$		0			0
$51$	−12.0000			−1.68034
$52$		0			0
$53$	−3.00000	+	5.19615i	−0.412082	+	0.713746i	−0.995117	−	0.0987002i	$-0.968532\pi$
$53$	−3.00000	+	5.19615i	−0.412082	+	0.713746i	0.583036	+	0.812447i	$0.301865\pi$
$54$		0			0
$55$	−3.00000	−	5.19615i	−0.404520	−	0.700649i
$56$		0			0
$57$	−4.50000	+	6.06218i	−0.596040	+	0.802955i
$58$		0			0
$59$	1.50000	+	2.59808i	0.195283	+	0.338241i	0.946993	−	0.321253i	$-0.104104\pi$
$59$	1.50000	+	2.59808i	0.195283	+	0.338241i	−0.751710	+	0.659494i	$0.770771\pi$
$60$		0			0
$61$	−5.00000	+	8.66025i	−0.640184	+	1.10883i	0.345207	+	0.938527i	$0.387809\pi$
$61$	−5.00000	+	8.66025i	−0.640184	+	1.10883i	−0.985391	+	0.170305i	$0.945525\pi$
$62$		0			0
$63$	3.00000	+	5.19615i	0.377964	+	0.654654i
$64$		0			0
$65$	12.0000			1.48842
$66$		0			0
$67$	−4.50000	−	2.59808i	−0.549762	−	0.317406i	0.199264	−	0.979946i	$-0.436145\pi$
$67$	−4.50000	−	2.59808i	−0.549762	−	0.317406i	−0.749026	+	0.662540i	$0.769478\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	0.987294	−	0.158901i	$-0.0507952\pi$
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	−0.631260	+	0.775571i	$0.717462\pi$
$72$		0			0
$73$	−2.50000	−	4.33013i	−0.292603	−	0.506803i	0.681822	−	0.731519i	$-0.261188\pi$
$73$	−2.50000	−	4.33013i	−0.292603	−	0.506803i	−0.974424	+	0.224716i	$0.927855\pi$
$74$		0			0
$75$	10.5000	−	6.06218i	1.21244	−	0.700000i
$76$		0			0
$77$			3.46410i			0.394771i
$78$		0			0
$79$	12.0000	−	6.92820i	1.35011	−	0.779484i	0.361842	−	0.932240i	$-0.382148\pi$
$79$	12.0000	−	6.92820i	1.35011	−	0.779484i	0.988264	+	0.152756i	$0.0488148\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$		0			0
$83$			5.19615i			0.570352i	0.958475	+	0.285176i	$0.0920520\pi$
$83$			5.19615i			0.570352i	−0.958475	+	0.285176i	$0.907948\pi$
$84$		0			0
$85$	12.0000	−	20.7846i	1.30158	−	2.25441i
$86$		0			0
$87$	9.00000	−	5.19615i	0.964901	−	0.557086i
$88$		0			0
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	−0.662071	−	0.749441i	$-0.730322\pi$
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	0.980071	+	0.198650i	$0.0636557\pi$
$90$		0			0
$91$	−6.00000	−	3.46410i	−0.628971	−	0.363137i
$92$		0			0
$93$	6.00000	−	10.3923i	0.622171	−	1.07763i
$94$		0			0
$95$	−6.00000	−	13.8564i	−0.615587	−	1.42164i
$96$		0			0
$97$	7.50000	−	4.33013i	0.761510	−	0.439658i	−0.0683279	−	0.997663i	$-0.521766\pi$
$97$	7.50000	−	4.33013i	0.761510	−	0.439658i	0.829837	+	0.558005i	$0.188433\pi$
$98$		0			0
$99$	−4.50000	+	2.59808i	−0.452267	+	0.261116i
$100$		0			0
$101$	−9.00000	−	5.19615i	−0.895533	−	0.517036i	−0.0197851	−	0.999804i	$-0.506298\pi$
$101$	−9.00000	−	5.19615i	−0.895533	−	0.517036i	−0.875748	+	0.482768i	$0.839632\pi$
$102$		0			0
$103$			10.3923i			1.02398i	0.858990	+	0.511992i	$0.171092\pi$
$103$			10.3923i			1.02398i	−0.858990	+	0.511992i	$0.828908\pi$
$104$		0			0
$105$	−12.0000			−1.17108
$106$		0			0
$107$	12.0000			1.16008			0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000			1.16008			0.580042	+	0.814587i	$0.303036\pi$
$108$		0			0
$109$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$109$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$110$		0			0
$111$	−6.00000	+	10.3923i	−0.569495	+	0.986394i
$112$		0			0
$113$	15.0000			1.41108			0.705541	−	0.708669i	$-0.250704\pi$
$113$	15.0000			1.41108			0.705541	+	0.708669i	$0.250704\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		−	10.3923i		−	0.960769i
$118$		0			0
$119$	−12.0000	+	6.92820i	−1.10004	+	0.635107i
$120$		0			0
$121$	8.00000			0.727273
$122$		0			0
$123$			5.19615i			0.468521i
$124$		0			0
$125$			6.92820i			0.619677i
$126$		0			0
$127$	9.00000	+	5.19615i	0.798621	+	0.461084i	0.842989	−	0.537931i	$-0.180794\pi$
$127$	9.00000	+	5.19615i	0.798621	+	0.461084i	−0.0443678	+	0.999015i	$0.514127\pi$
$128$		0			0
$129$			13.8564i			1.21999i
$130$		0			0
$131$	16.5000	−	9.52628i	1.44161	−	0.832315i	0.443654	−	0.896198i	$-0.353682\pi$
$131$	16.5000	−	9.52628i	1.44161	−	0.832315i	0.997957	+	0.0638831i	$0.0203485\pi$
$132$		0			0
$133$	−1.00000	+	8.66025i	−0.0867110	+	0.750939i
$134$		0			0
$135$	−9.00000	−	15.5885i	−0.774597	−	1.34164i
$136$		0			0
$137$	−1.50000	−	0.866025i	−0.128154	−	0.0739895i	0.434553	−	0.900646i	$-0.356906\pi$
$137$	−1.50000	−	0.866025i	−0.128154	−	0.0739895i	−0.562706	+	0.826657i	$0.690240\pi$
$138$		0			0
$139$	0.500000	−	0.866025i	0.0424094	−	0.0734553i	−0.844042	−	0.536278i	$-0.819830\pi$
$139$	0.500000	−	0.866025i	0.0424094	−	0.0734553i	0.886451	+	0.462822i	$0.153163\pi$
$140$		0			0
$141$	−3.00000	−	5.19615i	−0.252646	−	0.437595i
$142$		0			0
$143$	3.00000	−	5.19615i	0.250873	−	0.434524i
$144$		0			0
$145$			20.7846i			1.72607i
$146$		0			0
$147$	−4.50000	−	2.59808i	−0.371154	−	0.214286i
$148$		0			0
$149$	−6.00000	+	3.46410i	−0.491539	+	0.283790i	−0.725213	−	0.688525i	$-0.758259\pi$
$149$	−6.00000	+	3.46410i	−0.491539	+	0.283790i	0.233674	+	0.972315i	$0.424925\pi$
$150$		0			0
$151$			6.92820i			0.563809i	0.959442	+	0.281905i	$0.0909662\pi$
$151$			6.92820i			0.563809i	−0.959442	+	0.281905i	$0.909034\pi$
$152$		0			0
$153$	−18.0000	−	10.3923i	−1.45521	−	0.840168i
$154$		0			0
$155$	12.0000	+	20.7846i	0.963863	+	1.66946i
$156$		0			0
$157$	10.0000	+	17.3205i	0.798087	+	1.38233i	0.920860	+	0.389892i	$0.127488\pi$
$157$	10.0000	+	17.3205i	0.798087	+	1.38233i	−0.122774	+	0.992435i	$0.539179\pi$
$158$		0			0
$159$	−9.00000	+	5.19615i	−0.713746	+	0.412082i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	17.0000			1.33154			0.665771	−	0.746156i	$-0.268103\pi$
$163$	17.0000			1.33154			0.665771	+	0.746156i	$0.268103\pi$
$164$		0			0
$165$		−	10.3923i		−	0.809040i
$166$		0			0
$167$	6.00000	−	10.3923i	0.464294	−	0.804181i	−0.534875	−	0.844931i	$-0.679641\pi$
$167$	6.00000	−	10.3923i	0.464294	−	0.804181i	0.999169	+	0.0407502i	$0.0129748\pi$
$168$		0			0
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$		0			0
$171$	−12.0000	+	5.19615i	−0.917663	+	0.397360i
$172$		0			0
$173$	−9.00000	−	15.5885i	−0.684257	−	1.18517i	−0.973670	−	0.227964i	$-0.926793\pi$
$173$	−9.00000	−	15.5885i	−0.684257	−	1.18517i	0.289412	−	0.957205i	$-0.406540\pi$
$174$		0			0
$175$	7.00000	−	12.1244i	0.529150	−	0.916515i
$176$		0			0
$177$			5.19615i			0.390567i
$178$		0			0
$179$	−3.00000			−0.224231			−0.112115	−	0.993695i	$-0.535763\pi$
$179$	−3.00000			−0.224231			−0.112115	+	0.993695i	$0.535763\pi$
$180$		0			0
$181$	6.00000	+	3.46410i	0.445976	+	0.257485i	0.706129	−	0.708083i	$-0.250440\pi$
$181$	6.00000	+	3.46410i	0.445976	+	0.257485i	−0.260153	+	0.965567i	$0.583773\pi$
$182$		0			0
$183$	−15.0000	+	8.66025i	−1.10883	+	0.640184i
$184$		0			0
$185$	−12.0000	−	20.7846i	−0.882258	−	1.52811i
$186$		0			0
$187$	−6.00000	−	10.3923i	−0.438763	−	0.759961i
$188$		0			0
$189$			10.3923i			0.755929i
$190$		0			0
$191$		−	6.92820i		−	0.501307i	−0.968077	−	0.250654i	$-0.919354\pi$
$191$		−	6.92820i		−	0.501307i	0.968077	−	0.250654i	$-0.0806455\pi$
$192$		0			0
$193$	18.0000	−	10.3923i	1.29567	−	0.748054i	0.316016	−	0.948754i	$-0.397655\pi$
$193$	18.0000	−	10.3923i	1.29567	−	0.748054i	0.979653	+	0.200700i	$0.0643215\pi$
$194$		0			0
$195$	18.0000	+	10.3923i	1.28901	+	0.744208i
$196$		0			0
$197$			20.7846i			1.48084i	0.672143	+	0.740421i	$0.265374\pi$
$197$			20.7846i			1.48084i	−0.672143	+	0.740421i	$0.734626\pi$
$198$		0			0
$199$	7.00000	−	12.1244i	0.496217	−	0.859473i	−0.503774	−	0.863836i	$-0.668055\pi$
$199$	7.00000	−	12.1244i	0.496217	−	0.859473i	0.999990	+	0.00436292i	$0.00138876\pi$
$200$		0			0
$201$	−4.50000	−	7.79423i	−0.317406	−	0.549762i
$202$		0			0
$203$	6.00000	−	10.3923i	0.421117	−	0.729397i
$204$		0			0
$205$	−9.00000	−	5.19615i	−0.628587	−	0.362915i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−7.50000	−	0.866025i	−0.518786	−	0.0599042i
$210$		0			0
$211$	−9.00000	+	5.19615i	−0.619586	+	0.357718i	−0.776708	−	0.629861i	$-0.783112\pi$
$211$	−9.00000	+	5.19615i	−0.619586	+	0.357718i	0.157122	+	0.987579i	$0.449778\pi$
$212$		0			0
$213$			10.3923i			0.712069i
$214$		0			0
$215$	−24.0000	−	13.8564i	−1.63679	−	0.944999i
$216$		0			0
$217$		−	13.8564i		−	0.940634i
$218$		0			0
$219$		−	8.66025i		−	0.585206i
$220$		0			0
$221$	24.0000			1.61441
$222$		0			0
$223$	−12.0000	+	6.92820i	−0.803579	+	0.463947i	−0.844721	−	0.535207i	$-0.820234\pi$
$223$	−12.0000	+	6.92820i	−0.803579	+	0.463947i	0.0411418	+	0.999153i	$0.486900\pi$
$224$		0			0
$225$	21.0000			1.40000
$226$		0			0
$227$	−21.0000			−1.39382			−0.696909	−	0.717159i	$-0.745442\pi$
$227$	−21.0000			−1.39382			−0.696909	+	0.717159i	$0.745442\pi$
$228$		0			0
$229$	4.00000			0.264327			0.132164	−	0.991228i	$-0.457808\pi$
$229$	4.00000			0.264327			0.132164	+	0.991228i	$0.457808\pi$
$230$		0			0
$231$	−3.00000	+	5.19615i	−0.197386	+	0.341882i
$232$		0			0
$233$	−1.50000	+	0.866025i	−0.0982683	+	0.0567352i	−0.548329	−	0.836263i	$-0.684736\pi$
$233$	−1.50000	+	0.866025i	−0.0982683	+	0.0567352i	0.450060	+	0.892998i	$0.351402\pi$
$234$		0			0
$235$	12.0000			0.782794
$236$		0			0
$237$	24.0000			1.55897
$238$		0			0
$239$		−	6.92820i		−	0.448148i	−0.974572	−	0.224074i	$-0.928064\pi$
$239$		−	6.92820i		−	0.448148i	0.974572	−	0.224074i	$-0.0719358\pi$
$240$		0			0
$241$	4.50000	+	2.59808i	0.289870	+	0.167357i	0.637883	−	0.770133i	$-0.279810\pi$
$241$	4.50000	+	2.59808i	0.289870	+	0.167357i	−0.348013	+	0.937490i	$0.613143\pi$
$242$		0			0
$243$	−13.5000	+	7.79423i	−0.866025	+	0.500000i
$244$		0			0
$245$	9.00000	−	5.19615i	0.574989	−	0.331970i
$246$		0			0
$247$	9.00000	−	12.1244i	0.572656	−	0.771454i
$248$		0			0
$249$	−4.50000	+	7.79423i	−0.285176	+	0.493939i
$250$		0			0
$251$	7.50000	+	4.33013i	0.473396	+	0.273315i	0.717660	−	0.696393i	$-0.245213\pi$
$251$	7.50000	+	4.33013i	0.473396	+	0.273315i	−0.244264	+	0.969709i	$0.578546\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	36.0000	−	20.7846i	2.25441	−	1.30158i
$256$		0			0
$257$	7.50000	−	12.9904i	0.467837	−	0.810318i	−0.531487	−	0.847066i	$-0.678367\pi$
$257$	7.50000	−	12.9904i	0.467837	−	0.810318i	0.999325	+	0.0367485i	$0.0117000\pi$
$258$		0			0
$259$			13.8564i			0.860995i
$260$		0			0
$261$	18.0000			1.11417
$262$		0			0
$263$	−3.00000	+	1.73205i	−0.184988	+	0.106803i	−0.589634	−	0.807671i	$-0.700728\pi$
$263$	−3.00000	+	1.73205i	−0.184988	+	0.106803i	0.404646	+	0.914473i	$0.367395\pi$
$264$		0			0
$265$		−	20.7846i		−	1.27679i
$266$		0			0
$267$	9.00000	−	5.19615i	0.550791	−	0.317999i
$268$		0			0
$269$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$269$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$270$		0			0
$271$	13.0000	+	22.5167i	0.789694	+	1.36779i	0.926155	+	0.377144i	$0.123094\pi$
$271$	13.0000	+	22.5167i	0.789694	+	1.36779i	−0.136461	+	0.990645i	$0.543573\pi$
$272$		0			0
$273$	−6.00000	−	10.3923i	−0.363137	−	0.628971i
$274$		0			0
$275$	10.5000	+	6.06218i	0.633174	+	0.365563i
$276$		0			0
$277$	−2.00000			−0.120168			−0.0600842	−	0.998193i	$-0.519137\pi$
$277$	−2.00000			−0.120168			−0.0600842	+	0.998193i	$0.519137\pi$
$278$		0			0
$279$	18.0000	−	10.3923i	1.07763	−	0.622171i
$280$		0			0
$281$	−7.50000	+	12.9904i	−0.447412	+	0.774941i	−0.998217	−	0.0596933i	$-0.980988\pi$
$281$	−7.50000	+	12.9904i	−0.447412	+	0.774941i	0.550804	+	0.834634i	$0.314321\pi$
$282$		0			0
$283$	−0.500000	−	0.866025i	−0.0297219	−	0.0514799i	0.850782	−	0.525519i	$-0.176129\pi$
$283$	−0.500000	−	0.866025i	−0.0297219	−	0.0514799i	−0.880504	+	0.474039i	$0.842796\pi$
$284$		0			0
$285$	3.00000	−	25.9808i	0.177705	−	1.53897i
$286$		0			0
$287$	3.00000	+	5.19615i	0.177084	+	0.306719i
$288$		0			0
$289$	15.5000	−	26.8468i	0.911765	−	1.57922i
$290$		0			0
$291$	15.0000			0.879316
$292$		0			0
$293$	−6.00000			−0.350524			−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000			−0.350524			−0.175262	+	0.984522i	$0.556077\pi$
$294$		0			0
$295$	−9.00000	−	5.19615i	−0.524000	−	0.302532i
$296$		0			0
$297$	−9.00000			−0.522233
$298$		0			0
$299$		0			0
$300$		0			0
$301$	8.00000	+	13.8564i	0.461112	+	0.798670i
$302$		0			0
$303$	−9.00000	−	15.5885i	−0.517036	−	0.895533i
$304$		0			0
$305$		−	34.6410i		−	1.98354i
$306$		0			0
$307$	4.50000	−	2.59808i	0.256829	−	0.148280i	−0.366058	−	0.930592i	$-0.619293\pi$
$307$	4.50000	−	2.59808i	0.256829	−	0.148280i	0.622887	+	0.782312i	$0.285960\pi$
$308$		0			0
$309$	−9.00000	+	15.5885i	−0.511992	+	0.886796i
$310$		0			0
$311$			13.8564i			0.785725i	0.919597	+	0.392862i	$0.128515\pi$
$311$			13.8564i			0.785725i	−0.919597	+	0.392862i	$0.871485\pi$
$312$		0			0
$313$	−15.5000	+	26.8468i	−0.876112	+	1.51747i	−0.0205381	+	0.999789i	$0.506538\pi$
$313$	−15.5000	+	26.8468i	−0.876112	+	1.51747i	−0.855574	+	0.517681i	$0.826795\pi$
$314$		0			0
$315$	−18.0000	−	10.3923i	−1.01419	−	0.585540i
$316$		0			0
$317$	3.00000	−	5.19615i	0.168497	−	0.291845i	−0.769395	−	0.638774i	$-0.779442\pi$
$317$	3.00000	−	5.19615i	0.168497	−	0.291845i	0.937892	+	0.346929i	$0.112775\pi$
$318$		0			0
$319$	9.00000	+	5.19615i	0.503903	+	0.290929i
$320$		0			0
$321$	18.0000	+	10.3923i	1.00466	+	0.580042i
$322$		0			0
$323$	−12.0000	−	27.7128i	−0.667698	−	1.54198i
$324$		0			0
$325$	−21.0000	+	12.1244i	−1.16487	+	0.672538i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−6.00000	−	3.46410i	−0.330791	−	0.190982i
$330$		0			0
$331$		−	8.66025i		−	0.476011i	−0.971264	−	0.238005i	$-0.923506\pi$
$331$		−	8.66025i		−	0.476011i	0.971264	−	0.238005i	$-0.0764936\pi$
$332$		0			0
$333$	−18.0000	+	10.3923i	−0.986394	+	0.569495i
$334$		0			0
$335$	18.0000			0.983445
$336$		0			0
$337$	−22.5000	+	12.9904i	−1.22565	+	0.707631i	−0.966118	−	0.258102i	$-0.916903\pi$
$337$	−22.5000	+	12.9904i	−1.22565	+	0.707631i	−0.259536	+	0.965734i	$0.583569\pi$
$338$		0			0
$339$	22.5000	+	12.9904i	1.22203	+	0.705541i
$340$		0			0
$341$	12.0000			0.649836
$342$		0			0
$343$	−20.0000			−1.07990
$344$		0			0
$345$		0			0
$346$		0			0
$347$	7.50000	−	4.33013i	0.402621	−	0.232453i	−0.284993	−	0.958530i	$-0.591991\pi$
$347$	7.50000	−	4.33013i	0.402621	−	0.232453i	0.687614	+	0.726076i	$0.258658\pi$
$348$		0			0
$349$	8.00000			0.428230			0.214115	−	0.976808i	$-0.431313\pi$
$349$	8.00000			0.428230			0.214115	+	0.976808i	$0.431313\pi$
$350$		0			0
$351$	9.00000	−	15.5885i	0.480384	−	0.832050i
$352$		0			0
$353$			25.9808i			1.38282i	0.722464	+	0.691408i	$0.243009\pi$
$353$			25.9808i			1.38282i	−0.722464	+	0.691408i	$0.756991\pi$
$354$		0			0
$355$	−18.0000	−	10.3923i	−0.955341	−	0.551566i
$356$		0			0
$357$	−24.0000			−1.27021
$358$		0			0
$359$	−6.00000	+	3.46410i	−0.316668	+	0.182828i	−0.649906	−	0.760014i	$-0.725192\pi$
$359$	−6.00000	+	3.46410i	−0.316668	+	0.182828i	0.333238	+	0.942843i	$0.391859\pi$
$360$		0			0
$361$	−18.5000	−	4.33013i	−0.973684	−	0.227901i
$362$		0			0
$363$	12.0000	+	6.92820i	0.629837	+	0.363636i
$364$		0			0
$365$	15.0000	+	8.66025i	0.785136	+	0.453298i
$366$		0			0
$367$	−2.00000	+	3.46410i	−0.104399	+	0.180825i	−0.913493	−	0.406855i	$-0.866625\pi$
$367$	−2.00000	+	3.46410i	−0.104399	+	0.180825i	0.809093	+	0.587680i	$0.199959\pi$
$368$		0			0
$369$	−4.50000	+	7.79423i	−0.234261	+	0.405751i
$370$		0			0
$371$	−6.00000	+	10.3923i	−0.311504	+	0.539542i
$372$		0			0
$373$		−	6.92820i		−	0.358729i	−0.983783	−	0.179364i	$-0.942596\pi$
$373$		−	6.92820i		−	0.358729i	0.983783	−	0.179364i	$-0.0574041\pi$
$374$		0			0
$375$	−6.00000	+	10.3923i	−0.309839	+	0.536656i
$376$		0			0
$377$	−18.0000	+	10.3923i	−0.927047	+	0.535231i
$378$		0			0
$379$			10.3923i			0.533817i	0.963722	+	0.266908i	$0.0860021\pi$
$379$			10.3923i			0.533817i	−0.963722	+	0.266908i	$0.913998\pi$
$380$		0			0
$381$	9.00000	+	15.5885i	0.461084	+	0.798621i
$382$		0			0
$383$	−9.00000	−	15.5885i	−0.459879	−	0.796533i	0.539076	−	0.842257i	$-0.318774\pi$
$383$	−9.00000	−	15.5885i	−0.459879	−	0.796533i	−0.998954	+	0.0457244i	$0.985440\pi$
$384$		0			0
$385$	−6.00000	−	10.3923i	−0.305788	−	0.529641i
$386$		0			0
$387$	−12.0000	+	20.7846i	−0.609994	+	1.05654i
$388$		0			0
$389$	−30.0000	−	17.3205i	−1.52106	−	0.878185i	−0.999691	−	0.0248535i	$-0.992088\pi$
$389$	−30.0000	−	17.3205i	−1.52106	−	0.878185i	−0.521369	−	0.853331i	$-0.674579\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	33.0000			1.66463
$394$		0			0
$395$	−24.0000	+	41.5692i	−1.20757	+	2.09157i
$396$		0			0
$397$	−10.0000	−	17.3205i	−0.501886	−	0.869291i	−0.999998	−	0.00217869i	$-0.999307\pi$
$397$	−10.0000	−	17.3205i	−0.501886	−	0.869291i	0.498112	−	0.867113i	$-0.334027\pi$
$398$		0			0
$399$	−9.00000	+	12.1244i	−0.450564	+	0.606977i
$400$		0			0
$401$	1.50000	+	2.59808i	0.0749064	+	0.129742i	0.901046	−	0.433724i	$-0.142801\pi$
$401$	1.50000	+	2.59808i	0.0749064	+	0.129742i	−0.826139	+	0.563466i	$0.809468\pi$
$402$		0			0
$403$	−12.0000	+	20.7846i	−0.597763	+	1.03536i
$404$		0			0
$405$		−	31.1769i		−	1.54919i
$406$		0			0
$407$	−12.0000			−0.594818
$408$		0			0
$409$	−16.5000	−	9.52628i	−0.815872	−	0.471044i	0.0331186	−	0.999451i	$-0.489456\pi$
$409$	−16.5000	−	9.52628i	−0.815872	−	0.471044i	−0.848991	+	0.528407i	$0.822789\pi$
$410$		0			0
$411$	−1.50000	−	2.59808i	−0.0739895	−	0.128154i
$412$		0			0
$413$	3.00000	+	5.19615i	0.147620	+	0.255686i
$414$		0			0
$415$	−9.00000	−	15.5885i	−0.441793	−	0.765207i
$416$		0			0
$417$	1.50000	−	0.866025i	0.0734553	−	0.0424094i
$418$		0			0
$419$		−	10.3923i		−	0.507697i	−0.967244	−	0.253849i	$-0.918303\pi$
$419$		−	10.3923i		−	0.507697i	0.967244	−	0.253849i	$-0.0816965\pi$
$420$		0			0
$421$	−12.0000	+	6.92820i	−0.584844	+	0.337660i	−0.763056	−	0.646332i	$-0.776302\pi$
$421$	−12.0000	+	6.92820i	−0.584844	+	0.337660i	0.178212	+	0.983992i	$0.442969\pi$
$422$		0			0
$423$		−	10.3923i		−	0.505291i
$424$		0			0
$425$			48.4974i			2.35247i
$426$		0			0
$427$	−10.0000	+	17.3205i	−0.483934	+	0.838198i
$428$		0			0
$429$	9.00000	−	5.19615i	0.434524	−	0.250873i
$430$		0			0
$431$	−3.00000	+	5.19615i	−0.144505	+	0.250290i	−0.929188	−	0.369607i	$-0.879492\pi$
$431$	−3.00000	+	5.19615i	−0.144505	+	0.250290i	0.784683	+	0.619897i	$0.212826\pi$
$432$		0			0
$433$	−12.0000	−	6.92820i	−0.576683	−	0.332948i	0.183131	−	0.983089i	$-0.441377\pi$
$433$	−12.0000	−	6.92820i	−0.576683	−	0.332948i	−0.759814	+	0.650140i	$0.774710\pi$
$434$		0			0
$435$	−18.0000	+	31.1769i	−0.863034	+	1.49482i
$436$		0			0
$437$		0			0
$438$		0			0
$439$	12.0000	−	6.92820i	0.572729	−	0.330665i	−0.185510	−	0.982642i	$-0.559394\pi$
$439$	12.0000	−	6.92820i	0.572729	−	0.330665i	0.758238	+	0.651977i	$0.226060\pi$
$440$		0			0
$441$	−4.50000	−	7.79423i	−0.214286	−	0.371154i
$442$		0			0
$443$	10.5000	+	6.06218i	0.498870	+	0.288023i	0.728247	−	0.685315i	$-0.240335\pi$
$443$	10.5000	+	6.06218i	0.498870	+	0.288023i	−0.229377	+	0.973338i	$0.573669\pi$
$444$		0			0
$445$			20.7846i			0.985285i
$446$		0			0
$447$	−12.0000			−0.567581
$448$		0			0
$449$	3.00000			0.141579			0.0707894	−	0.997491i	$-0.477448\pi$
$449$	3.00000			0.141579			0.0707894	+	0.997491i	$0.477448\pi$
$450$		0			0
$451$	−4.50000	+	2.59808i	−0.211897	+	0.122339i
$452$		0			0
$453$	−6.00000	+	10.3923i	−0.281905	+	0.488273i
$454$		0			0
$455$	24.0000			1.12514
$456$		0			0
$457$	17.0000			0.795226			0.397613	−	0.917553i	$-0.369839\pi$
$457$	17.0000			0.795226			0.397613	+	0.917553i	$0.369839\pi$
$458$		0			0
$459$	−18.0000	−	31.1769i	−0.840168	−	1.45521i
$460$		0			0
$461$	21.0000	−	12.1244i	0.978068	−	0.564688i	0.0763814	−	0.997079i	$-0.475663\pi$
$461$	21.0000	−	12.1244i	0.978068	−	0.564688i	0.901686	+	0.432391i	$0.142330\pi$
$462$		0			0
$463$	−14.0000			−0.650635			−0.325318	−	0.945605i	$-0.605471\pi$
$463$	−14.0000			−0.650635			−0.325318	+	0.945605i	$0.605471\pi$
$464$		0			0
$465$			41.5692i			1.92773i
$466$		0			0
$467$			12.1244i			0.561048i	0.959847	+	0.280524i	$0.0905083\pi$
$467$			12.1244i			0.561048i	−0.959847	+	0.280524i	$0.909492\pi$
$468$		0			0
$469$	−9.00000	−	5.19615i	−0.415581	−	0.239936i
$470$		0			0
$471$			34.6410i			1.59617i
$472$		0			0
$473$	−12.0000	+	6.92820i	−0.551761	+	0.318559i
$474$		0			0
$475$	24.5000	+	18.1865i	1.12414	+	0.834455i
$476$		0			0
$477$	−18.0000			−0.824163
$478$		0			0
$479$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$479$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$480$		0			0
$481$	12.0000	−	20.7846i	0.547153	−	0.947697i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−15.0000	+	25.9808i	−0.681115	+	1.17973i
$486$		0			0
$487$			6.92820i			0.313947i	0.987603	+	0.156973i	$0.0501737\pi$
$487$			6.92820i			0.313947i	−0.987603	+	0.156973i	$0.949826\pi$
$488$		0			0
$489$	25.5000	+	14.7224i	1.15315	+	0.665771i
$490$		0			0
$491$	−27.0000	+	15.5885i	−1.21849	+	0.703497i	−0.964595	−	0.263734i	$-0.915046\pi$
$491$	−27.0000	+	15.5885i	−1.21849	+	0.703497i	−0.253897	+	0.967231i	$0.581713\pi$
$492$		0			0
$493$			41.5692i			1.87218i
$494$		0			0
$495$	9.00000	−	15.5885i	0.404520	−	0.700649i
$496$		0			0
$497$	6.00000	+	10.3923i	0.269137	+	0.466159i
$498$		0			0
$499$	−20.5000	−	35.5070i	−0.917706	−	1.58951i	−0.802890	−	0.596127i	$-0.796706\pi$
$499$	−20.5000	−	35.5070i	−0.917706	−	1.58951i	−0.114816	−	0.993387i	$-0.536628\pi$
$500$		0			0
$501$	18.0000	−	10.3923i	0.804181	−	0.464294i
$502$		0			0
$503$	18.0000	+	10.3923i	0.802580	+	0.463370i	0.844373	−	0.535756i	$-0.179973\pi$
$503$	18.0000	+	10.3923i	0.802580	+	0.463370i	−0.0417923	+	0.999126i	$0.513307\pi$
$504$		0			0
$505$	36.0000			1.60198
$506$		0			0
$507$		−	1.73205i		−	0.0769231i
$508$		0			0
$509$	12.0000	−	20.7846i	0.531891	−	0.921262i	−0.467416	−	0.884037i	$-0.654815\pi$
$509$	12.0000	−	20.7846i	0.531891	−	0.921262i	0.999307	−	0.0372243i	$-0.0118516\pi$
$510$		0			0
$511$	−5.00000	−	8.66025i	−0.221187	−	0.383107i
$512$		0			0
$513$	−22.5000	−	2.59808i	−0.993399	−	0.114708i
$514$		0			0
$515$	−18.0000	−	31.1769i	−0.793175	−	1.37382i
$516$		0			0
$517$	3.00000	−	5.19615i	0.131940	−	0.228527i
$518$		0			0
$519$		−	31.1769i		−	1.36851i
$520$		0			0
$521$	−21.0000			−0.920027			−0.460013	−	0.887912i	$-0.652155\pi$
$521$	−21.0000			−0.920027			−0.460013	+	0.887912i	$0.652155\pi$
$522$		0			0
$523$	−15.0000	−	8.66025i	−0.655904	−	0.378686i	0.134810	−	0.990871i	$-0.456957\pi$
$523$	−15.0000	−	8.66025i	−0.655904	−	0.378686i	−0.790715	+	0.612185i	$0.790291\pi$
$524$		0			0
$525$	21.0000	−	12.1244i	0.916515	−	0.529150i
$526$		0			0
$527$	24.0000	+	41.5692i	1.04546	+	1.81078i
$528$		0			0
$529$	−11.5000	−	19.9186i	−0.500000	−	0.866025i
$530$		0			0
$531$	−4.50000	+	7.79423i	−0.195283	+	0.338241i
$532$		0			0
$533$		−	10.3923i		−	0.450141i
$534$		0			0
$535$	−36.0000	+	20.7846i	−1.55642	+	0.898597i
$536$		0			0
$537$	−4.50000	−	2.59808i	−0.194189	−	0.112115i
$538$		0			0
$539$		−	5.19615i		−	0.223814i
$540$		0			0
$541$	−10.0000	+	17.3205i	−0.429934	+	0.744667i	−0.996867	−	0.0790969i	$-0.974796\pi$
$541$	−10.0000	+	17.3205i	−0.429934	+	0.744667i	0.566933	+	0.823764i	$0.308130\pi$
$542$		0			0
$543$	6.00000	+	10.3923i	0.257485	+	0.445976i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	21.0000	+	12.1244i	0.897895	+	0.518400i	0.876517	−	0.481371i	$-0.159861\pi$
$547$	21.0000	+	12.1244i	0.897895	+	0.518400i	0.0213785	+	0.999771i	$0.493195\pi$
$548$		0			0
$549$	−30.0000			−1.28037
$550$		0			0
$551$	21.0000	+	15.5885i	0.894630	+	0.664091i
$552$		0			0
$553$	24.0000	−	13.8564i	1.02058	−	0.589234i
$554$		0			0
$555$		−	41.5692i		−	1.76452i
$556$		0			0
$557$	12.0000	+	6.92820i	0.508456	+	0.293557i	0.732199	−	0.681091i	$-0.238494\pi$
$557$	12.0000	+	6.92820i	0.508456	+	0.293557i	−0.223743	+	0.974648i	$0.571827\pi$
$558$		0			0
$559$		−	27.7128i		−	1.17213i
$560$		0			0
$561$		−	20.7846i		−	0.877527i
$562$		0			0
$563$	21.0000			0.885044			0.442522	−	0.896758i	$-0.354084\pi$
$563$	21.0000			0.885044			0.442522	+	0.896758i	$0.354084\pi$
$564$		0			0
$565$	−45.0000	+	25.9808i	−1.89316	+	1.09302i
$566$		0			0
$567$	−9.00000	+	15.5885i	−0.377964	+	0.654654i
$568$		0			0
$569$	6.00000			0.251533			0.125767	−	0.992060i	$-0.459861\pi$
$569$	6.00000			0.251533			0.125767	+	0.992060i	$0.459861\pi$
$570$		0			0
$571$	43.0000			1.79949			0.899747	−	0.436412i	$-0.143751\pi$
$571$	43.0000			1.79949			0.899747	+	0.436412i	$0.143751\pi$
$572$		0			0
$573$	6.00000	−	10.3923i	0.250654	−	0.434145i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−29.0000			−1.20729			−0.603643	−	0.797255i	$-0.706285\pi$
$577$	−29.0000			−1.20729			−0.603643	+	0.797255i	$0.706285\pi$
$578$		0			0
$579$	36.0000			1.49611
$580$		0			0
$581$			10.3923i			0.431145i
$582$		0			0
$583$	−9.00000	−	5.19615i	−0.372742	−	0.215203i
$584$		0			0
$585$	18.0000	+	31.1769i	0.744208	+	1.28901i
$586$		0			0
$587$	33.0000	−	19.0526i	1.36206	−	0.786383i	0.372158	−	0.928169i	$-0.378618\pi$
$587$	33.0000	−	19.0526i	1.36206	−	0.786383i	0.989897	+	0.141786i	$0.0452845\pi$
$588$		0			0
$589$	30.0000	+	3.46410i	1.23613	+	0.142736i
$590$		0			0
$591$	−18.0000	+	31.1769i	−0.740421	+	1.28245i
$592$		0			0
$593$	22.5000	+	12.9904i	0.923964	+	0.533451i	0.884898	−	0.465786i	$-0.154228\pi$
$593$	22.5000	+	12.9904i	0.923964	+	0.533451i	0.0390666	+	0.999237i	$0.487562\pi$
$594$		0			0
$595$	24.0000	−	41.5692i	0.983904	−	1.70417i
$596$		0			0
$597$	21.0000	−	12.1244i	0.859473	−	0.496217i
$598$		0			0
$599$	−18.0000	+	31.1769i	−0.735460	+	1.27385i	0.219061	+	0.975711i	$0.429701\pi$
$599$	−18.0000	+	31.1769i	−0.735460	+	1.27385i	−0.954521	+	0.298143i	$0.903633\pi$
$600$		0			0
$601$			8.66025i			0.353259i	0.984277	+	0.176630i	$0.0565195\pi$
$601$			8.66025i			0.353259i	−0.984277	+	0.176630i	$0.943481\pi$
$602$		0			0
$603$		−	15.5885i		−	0.634811i
$604$		0			0
$605$	−24.0000	+	13.8564i	−0.975739	+	0.563343i
$606$		0			0
$607$			31.1769i			1.26543i	0.774384	+	0.632716i	$0.218060\pi$
$607$			31.1769i			1.26543i	−0.774384	+	0.632716i	$0.781940\pi$
$608$		0			0
$609$	18.0000	−	10.3923i	0.729397	−	0.421117i
$610$		0			0
$611$	6.00000	+	10.3923i	0.242734	+	0.420428i
$612$		0			0
$613$	−17.0000	−	29.4449i	−0.686624	−	1.18927i	−0.972924	−	0.231127i	$-0.925759\pi$
$613$	−17.0000	−	29.4449i	−0.686624	−	1.18927i	0.286300	−	0.958140i	$-0.407575\pi$
$614$		0			0
$615$	−9.00000	−	15.5885i	−0.362915	−	0.628587i
$616$		0			0
$617$	−1.50000	−	0.866025i	−0.0603877	−	0.0348649i	0.469502	−	0.882931i	$-0.344433\pi$
$617$	−1.50000	−	0.866025i	−0.0603877	−	0.0348649i	−0.529890	+	0.848066i	$0.677767\pi$
$618$		0			0
$619$	−40.0000			−1.60774			−0.803868	−	0.594808i	$-0.797228\pi$
$619$	−40.0000			−1.60774			−0.803868	+	0.594808i	$0.797228\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	6.00000	−	10.3923i	0.240385	−	0.416359i
$624$		0			0
$625$	5.50000	+	9.52628i	0.220000	+	0.381051i
$626$		0			0
$627$	−10.5000	−	7.79423i	−0.419330	−	0.311272i
$628$		0			0
$629$	−24.0000	−	41.5692i	−0.956943	−	1.65747i
$630$		0			0
$631$	−1.00000	+	1.73205i	−0.0398094	+	0.0689519i	−0.885244	−	0.465128i	$-0.846008\pi$
$631$	−1.00000	+	1.73205i	−0.0398094	+	0.0689519i	0.845434	+	0.534080i	$0.179342\pi$
$632$		0			0
$633$	−18.0000			−0.715436
$634$		0			0
$635$	−36.0000			−1.42862
$636$		0			0
$637$	9.00000	+	5.19615i	0.356593	+	0.205879i
$638$		0			0
$639$	−9.00000	+	15.5885i	−0.356034	+	0.616670i
$640$		0			0
$641$	22.5000	+	38.9711i	0.888697	+	1.53927i	0.841417	+	0.540386i	$0.181722\pi$
$641$	22.5000	+	38.9711i	0.888697	+	1.53927i	0.0472793	+	0.998882i	$0.484945\pi$
$642$		0			0
$643$	−24.5000	−	42.4352i	−0.966186	−	1.67348i	−0.706395	−	0.707818i	$-0.749680\pi$
$643$	−24.5000	−	42.4352i	−0.966186	−	1.67348i	−0.259791	−	0.965665i	$-0.583654\pi$
$644$		0			0
$645$	−24.0000	−	41.5692i	−0.944999	−	1.63679i
$646$		0			0
$647$		−	24.2487i		−	0.953315i	−0.879089	−	0.476658i	$-0.841848\pi$
$647$		−	24.2487i		−	0.953315i	0.879089	−	0.476658i	$-0.158152\pi$
$648$		0			0
$649$	−4.50000	+	2.59808i	−0.176640	+	0.101983i
$650$		0			0
$651$	12.0000	−	20.7846i	0.470317	−	0.814613i
$652$		0			0
$653$			6.92820i			0.271122i	0.990769	+	0.135561i	$0.0432836\pi$
$653$			6.92820i			0.271122i	−0.990769	+	0.135561i	$0.956716\pi$
$654$		0			0
$655$	−33.0000	+	57.1577i	−1.28942	+	2.23334i
$656$		0			0
$657$	7.50000	−	12.9904i	0.292603	−	0.506803i
$658$		0			0
$659$	18.0000	−	31.1769i	0.701180	−	1.21448i	−0.266872	−	0.963732i	$-0.585990\pi$
$659$	18.0000	−	31.1769i	0.701180	−	1.21448i	0.968052	−	0.250748i	$-0.0806766\pi$
$660$		0			0
$661$	−33.0000	−	19.0526i	−1.28355	−	0.741059i	−0.306055	−	0.952014i	$-0.599009\pi$
$661$	−33.0000	−	19.0526i	−1.28355	−	0.741059i	−0.977496	+	0.210955i	$0.932343\pi$
$662$		0			0
$663$	36.0000	+	20.7846i	1.39812	+	0.807207i
$664$		0			0
$665$	−12.0000	−	27.7128i	−0.465340	−	1.07466i
$666$		0			0
$667$		0			0
$668$		0			0
$669$	−24.0000			−0.927894
$670$		0			0
$671$	−15.0000	−	8.66025i	−0.579069	−	0.334325i
$672$		0			0
$673$			20.7846i			0.801188i	0.916256	+	0.400594i	$0.131196\pi$
$673$			20.7846i			0.801188i	−0.916256	+	0.400594i	$0.868804\pi$
$674$		0			0
$675$	31.5000	+	18.1865i	1.21244	+	0.700000i
$676$		0			0
$677$	42.0000			1.61419			0.807096	−	0.590421i	$-0.201038\pi$
$677$	42.0000			1.61419			0.807096	+	0.590421i	$0.201038\pi$
$678$		0			0
$679$	15.0000	−	8.66025i	0.575647	−	0.332350i
$680$		0			0
$681$	−31.5000	−	18.1865i	−1.20708	−	0.696909i
$682$		0			0
$683$	36.0000			1.37750			0.688751	−	0.724998i	$-0.258159\pi$
$683$	36.0000			1.37750			0.688751	+	0.724998i	$0.258159\pi$
$684$		0			0
$685$	6.00000			0.229248
$686$		0			0
$687$	6.00000	+	3.46410i	0.228914	+	0.132164i
$688$		0			0
$689$	18.0000	−	10.3923i	0.685745	−	0.395915i
$690$		0			0
$691$	−20.0000			−0.760836			−0.380418	−	0.924815i	$-0.624220\pi$
$691$	−20.0000			−0.760836			−0.380418	+	0.924815i	$0.624220\pi$
$692$		0			0
$693$	−9.00000	+	5.19615i	−0.341882	+	0.197386i
$694$		0			0
$695$			3.46410i			0.131401i
$696$		0			0
$697$	−18.0000	−	10.3923i	−0.681799	−	0.393637i
$698$		0			0
$699$	−3.00000			−0.113470
$700$		0			0
$701$	9.00000	−	5.19615i	0.339925	−	0.196256i	−0.320314	−	0.947312i	$-0.603788\pi$
$701$	9.00000	−	5.19615i	0.339925	−	0.196256i	0.660239	+	0.751056i	$0.270455\pi$
$702$		0			0
$703$	−30.0000	−	3.46410i	−1.13147	−	0.130651i
$704$		0			0
$705$	18.0000	+	10.3923i	0.677919	+	0.391397i
$706$		0			0
$707$	−18.0000	−	10.3923i	−0.676960	−	0.390843i
$708$		0			0
$709$	−4.00000	+	6.92820i	−0.150223	+	0.260194i	−0.931309	−	0.364229i	$-0.881333\pi$
$709$	−4.00000	+	6.92820i	−0.150223	+	0.260194i	0.781086	+	0.624423i	$0.214666\pi$
$710$		0			0
$711$	36.0000	+	20.7846i	1.35011	+	0.779484i
$712$		0			0
$713$		0			0
$714$		0			0
$715$			20.7846i			0.777300i
$716$		0			0
$717$	6.00000	−	10.3923i	0.224074	−	0.388108i
$718$		0			0
$719$	−3.00000	+	1.73205i	−0.111881	+	0.0645946i	−0.554896	−	0.831919i	$-0.687242\pi$
$719$	−3.00000	+	1.73205i	−0.111881	+	0.0645946i	0.443015	+	0.896514i	$0.353909\pi$
$720$		0			0
$721$			20.7846i			0.774059i
$722$		0			0
$723$	4.50000	+	7.79423i	0.167357	+	0.289870i
$724$		0			0
$725$	−21.0000	−	36.3731i	−0.779920	−	1.35086i
$726$		0			0
$727$	4.00000	+	6.92820i	0.148352	+	0.256953i	0.930618	−	0.365991i	$-0.119270\pi$
$727$	4.00000	+	6.92820i	0.148352	+	0.256953i	−0.782267	+	0.622944i	$0.785937\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	−48.0000	−	27.7128i	−1.77534	−	1.02500i
$732$		0			0
$733$	−4.00000			−0.147743			−0.0738717	−	0.997268i	$-0.523536\pi$
$733$	−4.00000			−0.147743			−0.0738717	+	0.997268i	$0.523536\pi$
$734$		0			0
$735$	18.0000			0.663940
$736$		0			0
$737$	4.50000	−	7.79423i	0.165760	−	0.287104i
$738$		0			0
$739$	−5.50000	−	9.52628i	−0.202321	−	0.350430i	0.746955	−	0.664875i	$-0.231515\pi$
$739$	−5.50000	−	9.52628i	−0.202321	−	0.350430i	−0.949276	+	0.314445i	$0.898182\pi$
$740$		0			0
$741$	24.0000	−	10.3923i	0.881662	−	0.381771i
$742$		0			0
$743$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$743$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$744$		0			0
$745$	12.0000	−	20.7846i	0.439646	−	0.761489i
$746$		0			0
$747$	−13.5000	+	7.79423i	−0.493939	+	0.285176i
$748$		0			0
$749$	24.0000			0.876941
$750$		0			0
$751$	33.0000	+	19.0526i	1.20419	+	0.695238i	0.961483	−	0.274863i	$-0.0886324\pi$
$751$	33.0000	+	19.0526i	1.20419	+	0.695238i	0.242704	+	0.970100i	$0.421966\pi$
$752$		0			0
$753$	7.50000	+	12.9904i	0.273315	+	0.473396i
$754$		0			0
$755$	−12.0000	−	20.7846i	−0.436725	−	0.756429i
$756$		0			0
$757$	19.0000	+	32.9090i	0.690567	+	1.19610i	0.971652	+	0.236414i	$0.0759722\pi$
$757$	19.0000	+	32.9090i	0.690567	+	1.19610i	−0.281086	+	0.959683i	$0.590695\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$			8.66025i			0.313934i	0.987604	+	0.156967i	$0.0501716\pi$
$761$			8.66025i			0.313934i	−0.987604	+	0.156967i	$0.949828\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	72.0000			2.60317
$766$		0			0
$767$		−	10.3923i		−	0.375244i
$768$		0			0
$769$	7.00000	−	12.1244i	0.252426	−	0.437215i	−0.711767	−	0.702416i	$-0.752105\pi$
$769$	7.00000	−	12.1244i	0.252426	−	0.437215i	0.964193	+	0.265200i	$0.0854381\pi$
$770$		0			0
$771$	22.5000	−	12.9904i	0.810318	−	0.467837i
$772$		0			0
$773$	−3.00000	+	5.19615i	−0.107903	+	0.186893i	−0.914920	−	0.403634i	$-0.867747\pi$
$773$	−3.00000	+	5.19615i	−0.107903	+	0.186893i	0.807018	+	0.590527i	$0.201080\pi$
$774$		0			0
$775$	−42.0000	−	24.2487i	−1.50868	−	0.871039i
$776$		0			0
$777$	−12.0000	+	20.7846i	−0.430498	+	0.745644i
$778$		0			0
$779$	−12.0000	+	5.19615i	−0.429945	+	0.186171i
$780$		0			0
$781$	−9.00000	+	5.19615i	−0.322045	+	0.185933i
$782$		0			0
$783$	27.0000	+	15.5885i	0.964901	+	0.557086i
$784$		0			0
$785$	−60.0000	−	34.6410i	−2.14149	−	1.23639i
$786$		0			0
$787$			1.73205i			0.0617409i	0.999523	+	0.0308705i	$0.00982794\pi$
$787$			1.73205i			0.0617409i	−0.999523	+	0.0308705i	$0.990172\pi$
$788$		0			0
$789$	−6.00000			−0.213606
$790$		0			0
$791$	30.0000			1.06668
$792$		0			0
$793$	30.0000	−	17.3205i	1.06533	−	0.615069i
$794$		0			0
$795$	18.0000	−	31.1769i	0.638394	−	1.10573i
$796$		0			0
$797$	−12.0000			−0.425062			−0.212531	−	0.977154i	$-0.568171\pi$
$797$	−12.0000			−0.425062			−0.212531	+	0.977154i	$0.568171\pi$
$798$		0			0
$799$	24.0000			0.849059
$800$		0			0
$801$	18.0000			0.635999
$802$		0			0
$803$	7.50000	−	4.33013i	0.264669	−	0.152807i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	32.9090i		−	1.15702i	−0.815676	−	0.578509i	$-0.803635\pi$
$809$		−	32.9090i		−	1.15702i	0.815676	−	0.578509i	$-0.196365\pi$
$810$		0			0
$811$	27.0000	+	15.5885i	0.948098	+	0.547385i	0.892490	−	0.451068i	$-0.148957\pi$
$811$	27.0000	+	15.5885i	0.948098	+	0.547385i	0.0556086	+	0.998453i	$0.482290\pi$
$812$		0			0
$813$			45.0333i			1.57939i
$814$		0			0
$815$	−51.0000	+	29.4449i	−1.78645	+	1.03141i
$816$		0			0
$817$	−32.0000	+	13.8564i	−1.11954	+	0.484774i
$818$		0			0
$819$		−	20.7846i		−	0.726273i
$820$		0			0
$821$	−33.0000	−	19.0526i	−1.15171	−	0.664939i	−0.202405	−	0.979302i	$-0.564876\pi$
$821$	−33.0000	−	19.0526i	−1.15171	−	0.664939i	−0.949303	+	0.314363i	$0.898209\pi$
$822$		0			0
$823$	11.0000	−	19.0526i	0.383436	−	0.664130i	−0.608115	−	0.793849i	$-0.708074\pi$
$823$	11.0000	−	19.0526i	0.383436	−	0.664130i	0.991551	+	0.129719i	$0.0414074\pi$
$824$		0			0
$825$	10.5000	+	18.1865i	0.365563	+	0.633174i
$826$		0			0
$827$	−4.50000	+	7.79423i	−0.156480	+	0.271032i	−0.933597	−	0.358325i	$-0.883348\pi$
$827$	−4.50000	+	7.79423i	−0.156480	+	0.271032i	0.777117	+	0.629356i	$0.216681\pi$
$828$		0			0
$829$		−	20.7846i		−	0.721879i	−0.932589	−	0.360940i	$-0.882456\pi$
$829$		−	20.7846i		−	0.721879i	0.932589	−	0.360940i	$-0.117544\pi$
$830$		0			0
$831$	−3.00000	−	1.73205i	−0.104069	−	0.0600842i
$832$		0			0
$833$	18.0000	−	10.3923i	0.623663	−	0.360072i
$834$		0			0
$835$			41.5692i			1.43856i
$836$		0			0
$837$	36.0000			1.24434
$838$		0			0
$839$	−21.0000	−	36.3731i	−0.725001	−	1.25574i	−0.958974	−	0.283495i	$-0.908506\pi$
$839$	−21.0000	−	36.3731i	−0.725001	−	1.25574i	0.233973	−	0.972243i	$-0.424827\pi$
$840$		0			0
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$		0			0
$843$	−22.5000	+	12.9904i	−0.774941	+	0.447412i
$844$		0			0
$845$	3.00000	+	1.73205i	0.103203	+	0.0595844i
$846$		0			0
$847$	16.0000			0.549767
$848$		0			0
$849$		−	1.73205i		−	0.0594438i
$850$		0			0
$851$		0			0
$852$		0			0
$853$	5.00000	+	8.66025i	0.171197	+	0.296521i	0.938839	−	0.344358i	$-0.111903\pi$
$853$	5.00000	+	8.66025i	0.171197	+	0.296521i	−0.767642	+	0.640879i	$0.778570\pi$
$854$		0			0
$855$	27.0000	−	36.3731i	0.923381	−	1.24393i
$856$		0			0
$857$	10.5000	+	18.1865i	0.358673	+	0.621240i	0.987739	−	0.156112i	$-0.0498959\pi$
$857$	10.5000	+	18.1865i	0.358673	+	0.621240i	−0.629066	+	0.777352i	$0.716563\pi$
$858$		0			0
$859$	24.5000	−	42.4352i	0.835929	−	1.44787i	−0.0573424	−	0.998355i	$-0.518263\pi$
$859$	24.5000	−	42.4352i	0.835929	−	1.44787i	0.893272	−	0.449517i	$-0.148404\pi$
$860$		0			0
$861$			10.3923i			0.354169i
$862$		0			0
$863$	12.0000			0.408485			0.204242	−	0.978920i	$-0.434527\pi$
$863$	12.0000			0.408485			0.204242	+	0.978920i	$0.434527\pi$
$864$		0			0
$865$	54.0000	+	31.1769i	1.83606	+	1.06005i
$866$		0			0
$867$	46.5000	−	26.8468i	1.57922	−	0.911765i
$868$		0			0
$869$	12.0000	+	20.7846i	0.407072	+	0.705070i
$870$		0			0
$871$	9.00000	+	15.5885i	0.304953	+	0.528195i
$872$		0			0
$873$	22.5000	+	12.9904i	0.761510	+	0.439658i
$874$		0			0
$875$			13.8564i			0.468432i
$876$		0			0
$877$	−33.0000	+	19.0526i	−1.11433	+	0.643359i	−0.939948	−	0.341319i	$-0.889126\pi$
$877$	−33.0000	+	19.0526i	−1.11433	+	0.643359i	−0.174383	+	0.984678i	$0.555793\pi$
$878$		0			0
$879$	−9.00000	−	5.19615i	−0.303562	−	0.175262i
$880$		0			0
$881$		−	19.0526i		−	0.641897i	−0.947097	−	0.320949i	$-0.895998\pi$
$881$		−	19.0526i		−	0.641897i	0.947097	−	0.320949i	$-0.104002\pi$
$882$		0			0
$883$	−5.50000	+	9.52628i	−0.185090	+	0.320585i	−0.943607	−	0.331068i	$-0.892591\pi$
$883$	−5.50000	+	9.52628i	−0.185090	+	0.320585i	0.758517	+	0.651653i	$0.225924\pi$
$884$		0			0
$885$	−9.00000	−	15.5885i	−0.302532	−	0.524000i
$886$		0			0
$887$	−18.0000	+	31.1769i	−0.604381	+	1.04682i	0.387768	+	0.921757i	$0.373246\pi$
$887$	−18.0000	+	31.1769i	−0.604381	+	1.04682i	−0.992149	+	0.125061i	$0.960087\pi$
$888$		0			0
$889$	18.0000	+	10.3923i	0.603701	+	0.348547i
$890$		0			0
$891$	−13.5000	−	7.79423i	−0.452267	−	0.261116i
$892$		0			0
$893$	9.00000	−	12.1244i	0.301174	−	0.405726i
$894$		0			0
$895$	9.00000	−	5.19615i	0.300837	−	0.173688i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−36.0000	−	20.7846i	−1.20067	−	0.693206i
$900$		0			0
$901$		−	41.5692i		−	1.38487i
$902$		0			0
$903$			27.7128i			0.922225i
$904$		0			0
$905$	−24.0000			−0.797787
$906$		0			0
$907$	−1.50000	+	0.866025i	−0.0498067	+	0.0287559i	−0.524697	−	0.851289i	$-0.675821\pi$
$907$	−1.50000	+	0.866025i	−0.0498067	+	0.0287559i	0.474890	+	0.880045i	$0.342488\pi$
$908$		0			0
$909$		−	31.1769i		−	1.03407i
$910$		0			0
$911$	36.0000			1.19273			0.596367	−	0.802712i	$-0.296610\pi$
$911$	36.0000			1.19273			0.596367	+	0.802712i	$0.296610\pi$
$912$		0			0
$913$	−9.00000			−0.297857
$914$		0			0
$915$	30.0000	−	51.9615i	0.991769	−	1.71780i
$916$		0			0
$917$	33.0000	−	19.0526i	1.08976	−	0.629171i
$918$		0			0
$919$	26.0000			0.857661			0.428830	−	0.903385i	$-0.358926\pi$
$919$	26.0000			0.857661			0.428830	+	0.903385i	$0.358926\pi$
$920$		0			0
$921$	9.00000			0.296560
$922$		0			0
$923$		−	20.7846i		−	0.684134i
$924$		0			0
$925$	42.0000	+	24.2487i	1.38095	+	0.797293i
$926$		0			0
$927$	−27.0000	+	15.5885i	−0.886796	+	0.511992i
$928$		0			0
$929$	31.5000	−	18.1865i	1.03348	−	0.596681i	0.115501	−	0.993307i	$-0.463153\pi$
$929$	31.5000	−	18.1865i	1.03348	−	0.596681i	0.917980	+	0.396627i	$0.129819\pi$
$930$		0			0
$931$	1.50000	−	12.9904i	0.0491605	−	0.425743i
$932$		0			0
$933$	−12.0000	+	20.7846i	−0.392862	+	0.680458i
$934$		0			0
$935$	36.0000	+	20.7846i	1.17733	+	0.679729i
$936$		0			0
$937$	3.50000	−	6.06218i	0.114340	−	0.198043i	−0.803176	−	0.595742i	$-0.796858\pi$
$937$	3.50000	−	6.06218i	0.114340	−	0.198043i	0.917516	+	0.397699i	$0.130191\pi$
$938$		0			0
$939$	−46.5000	+	26.8468i	−1.51747	+	0.876112i
$940$		0			0
$941$	−27.0000	+	46.7654i	−0.880175	+	1.52451i	−0.0290288	+	0.999579i	$0.509241\pi$
$941$	−27.0000	+	46.7654i	−0.880175	+	1.52451i	−0.851146	+	0.524929i	$0.824092\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$	−18.0000	−	31.1769i	−0.585540	−	1.01419i
$946$		0			0
$947$	45.0000	−	25.9808i	1.46230	−	0.844261i	0.463186	−	0.886261i	$-0.346706\pi$
$947$	45.0000	−	25.9808i	1.46230	−	0.844261i	0.999118	+	0.0419998i	$0.0133729\pi$
$948$		0			0
$949$			17.3205i			0.562247i
$950$		0			0
$951$	9.00000	−	5.19615i	0.291845	−	0.168497i
$952$		0			0
$953$	25.5000	+	44.1673i	0.826026	+	1.43072i	0.901133	+	0.433544i	$0.142737\pi$
$953$	25.5000	+	44.1673i	0.826026	+	1.43072i	−0.0751066	+	0.997176i	$0.523930\pi$
$954$		0			0
$955$	12.0000	+	20.7846i	0.388311	+	0.672574i
$956$		0			0
$957$	9.00000	+	15.5885i	0.290929	+	0.503903i
$958$		0			0
$959$	−3.00000	−	1.73205i	−0.0968751	−	0.0559308i
$960$		0			0
$961$	−17.0000			−0.548387
$962$		0			0
$963$	18.0000	+	31.1769i	0.580042	+	1.00466i
$964$		0			0
$965$	−36.0000	+	62.3538i	−1.15888	+	2.00724i
$966$		0			0
$967$	−25.0000	−	43.3013i	−0.803946	−	1.39247i	−0.917000	−	0.398886i	$-0.869397\pi$
$967$	−25.0000	−	43.3013i	−0.803946	−	1.39247i	0.113055	−	0.993589i	$-0.463936\pi$
$968$		0			0
$969$	6.00000	−	51.9615i	0.192748	−	1.66924i
$970$		0			0
$971$	−4.50000	−	7.79423i	−0.144412	−	0.250129i	0.784741	−	0.619823i	$-0.212796\pi$
$971$	−4.50000	−	7.79423i	−0.144412	−	0.250129i	−0.929153	+	0.369694i	$0.879462\pi$
$972$		0			0
$973$	1.00000	−	1.73205i	0.0320585	−	0.0555270i
$974$		0			0
$975$	−42.0000			−1.34508
$976$		0			0
$977$	−27.0000			−0.863807			−0.431903	−	0.901920i	$-0.642158\pi$
$977$	−27.0000			−0.863807			−0.431903	+	0.901920i	$0.642158\pi$
$978$		0			0
$979$	9.00000	+	5.19615i	0.287641	+	0.166070i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	18.0000	+	31.1769i	0.574111	+	0.994389i	0.996138	+	0.0878058i	$0.0279855\pi$
$983$	18.0000	+	31.1769i	0.574111	+	0.994389i	−0.422027	+	0.906583i	$0.638681\pi$
$984$		0			0
$985$	−36.0000	−	62.3538i	−1.14706	−	1.98676i
$986$		0			0
$987$	−6.00000	−	10.3923i	−0.190982	−	0.330791i
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−6.00000	+	3.46410i	−0.190596	+	0.110041i	−0.592262	−	0.805746i	$-0.701765\pi$
$991$	−6.00000	+	3.46410i	−0.190596	+	0.110041i	0.401665	+	0.915786i	$0.368431\pi$
$992$		0			0
$993$	7.50000	−	12.9904i	0.238005	−	0.412237i
$994$		0			0
$995$			48.4974i			1.53747i
$996$		0			0
$997$	13.0000	−	22.5167i	0.411714	−	0.713110i	−0.583363	−	0.812211i	$-0.698264\pi$
$997$	13.0000	−	22.5167i	0.411714	−	0.713110i	0.995077	+	0.0991016i	$0.0315969\pi$
$998$		0			0
$999$	−36.0000			−1.13899

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.bn.d.449.1		2
3.2	odd	2		912.2.bn.b.449.1		2
4.3	odd	2		114.2.h.a.107.1	yes	2
12.11	even	2		114.2.h.d.107.1	yes	2
19.8	odd	6		912.2.bn.b.65.1		2
57.8	even	6	inner	912.2.bn.d.65.1		2
76.27	even	6		114.2.h.d.65.1	yes	2
228.179	odd	6		114.2.h.a.65.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.h.a.65.1	✓	2	228.179	odd	6
114.2.h.a.107.1	yes	2	4.3	odd	2
114.2.h.d.65.1	yes	2	76.27	even	6
114.2.h.d.107.1	yes	2	12.11	even	2
912.2.bn.b.65.1		2	19.8	odd	6
912.2.bn.b.449.1		2	3.2	odd	2
912.2.bn.d.65.1		2	57.8	even	6	inner
912.2.bn.d.449.1		2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.50000 + 0.866025i) q^{3} +(-3.00000 + 1.73205i) q^{5} +2.00000 q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.50000 + 0.866025i) q^{3} +(-3.00000 + 1.73205i) q^{5} +2.00000 q^{7} +(1.50000 + 2.59808i) q^{9} +1.73205i q^{11} +(-3.00000 - 1.73205i) q^{13} -6.00000 q^{15} +(-6.00000 + 3.46410i) q^{17} +(-0.500000 + 4.33013i) q^{19} +(3.00000 + 1.73205i) q^{21} +(3.50000 - 6.06218i) q^{25} +5.19615i q^{27} +(3.00000 - 5.19615i) q^{29} -6.92820i q^{31} +(-1.50000 + 2.59808i) q^{33} +(-6.00000 + 3.46410i) q^{35} +6.92820i q^{37} +(-3.00000 - 5.19615i) q^{39} +(1.50000 + 2.59808i) q^{41} +(4.00000 + 6.92820i) q^{43} +(-9.00000 - 5.19615i) q^{45} +(-3.00000 - 1.73205i) q^{47} -3.00000 q^{49} -12.0000 q^{51} +(-3.00000 + 5.19615i) q^{53} +(-3.00000 - 5.19615i) q^{55} +(-4.50000 + 6.06218i) q^{57} +(1.50000 + 2.59808i) q^{59} +(-5.00000 + 8.66025i) q^{61} +(3.00000 + 5.19615i) q^{63} +12.0000 q^{65} +(-4.50000 - 2.59808i) q^{67} +(3.00000 + 5.19615i) q^{71} +(-2.50000 - 4.33013i) q^{73} +(10.5000 - 6.06218i) q^{75} +3.46410i q^{77} +(12.0000 - 6.92820i) q^{79} +(-4.50000 + 7.79423i) q^{81} +5.19615i q^{83} +(12.0000 - 20.7846i) q^{85} +(9.00000 - 5.19615i) q^{87} +(3.00000 - 5.19615i) q^{89} +(-6.00000 - 3.46410i) q^{91} +(6.00000 - 10.3923i) q^{93} +(-6.00000 - 13.8564i) q^{95} +(7.50000 - 4.33013i) q^{97} +(-4.50000 + 2.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{3} - 6 q^{5} + 4 q^{7} + 3 q^{9}+O(q^{10}) \) 2 * q + 3 * q^3 - 6 * q^5 + 4 * q^7 + 3 * q^9	\( 2 q + 3 q^{3} - 6 q^{5} + 4 q^{7} + 3 q^{9} - 6 q^{13} - 12 q^{15} - 12 q^{17} - q^{19} + 6 q^{21} + 7 q^{25} + 6 q^{29} - 3 q^{33} - 12 q^{35} - 6 q^{39} + 3 q^{41} + 8 q^{43} - 18 q^{45} - 6 q^{47} - 6 q^{49} - 24 q^{51} - 6 q^{53} - 6 q^{55} - 9 q^{57} + 3 q^{59} - 10 q^{61} + 6 q^{63} + 24 q^{65} - 9 q^{67} + 6 q^{71} - 5 q^{73} + 21 q^{75} + 24 q^{79} - 9 q^{81} + 24 q^{85} + 18 q^{87} + 6 q^{89} - 12 q^{91} + 12 q^{93} - 12 q^{95} + 15 q^{97} - 9 q^{99}+O(q^{100}) \) 2 * q + 3 * q^3 - 6 * q^5 + 4 * q^7 + 3 * q^9 - 6 * q^13 - 12 * q^15 - 12 * q^17 - q^19 + 6 * q^21 + 7 * q^25 + 6 * q^29 - 3 * q^33 - 12 * q^35 - 6 * q^39 + 3 * q^41 + 8 * q^43 - 18 * q^45 - 6 * q^47 - 6 * q^49 - 24 * q^51 - 6 * q^53 - 6 * q^55 - 9 * q^57 + 3 * q^59 - 10 * q^61 + 6 * q^63 + 24 * q^65 - 9 * q^67 + 6 * q^71 - 5 * q^73 + 21 * q^75 + 24 * q^79 - 9 * q^81 + 24 * q^85 + 18 * q^87 + 6 * q^89 - 12 * q^91 + 12 * q^93 - 12 * q^95 + 15 * q^97 - 9 * q^99

Introduction

L-functions

Modular forms

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Database

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