LMFDB - Embedded newform 900.2.be.d.893.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [900,2,Mod(257,900)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("900.257"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(900, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 10, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.be (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,6,0,0,0,-6,0,6,0,-6,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			893.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	900.893
Dual form			900.2.be.d.257.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.50000 - 0.866025i) q^{3} +(0.232051 + 0.866025i) q^{7} +(1.50000 - 2.59808i) q^{9} +(1.09808 + 0.633975i) q^{11} +(0.633975 - 2.36603i) q^{13} +(3.00000 + 3.00000i) q^{17} -4.19615i q^{19} +(1.09808 + 1.09808i) q^{21} +(1.50000 + 0.401924i) q^{23} -5.19615i q^{27} +(3.86603 - 6.69615i) q^{29} +(2.09808 + 3.63397i) q^{31} +2.19615 q^{33} +(-6.46410 + 6.46410i) q^{37} +(-1.09808 - 4.09808i) q^{39} +(5.59808 - 3.23205i) q^{41} +(-4.09808 + 1.09808i) q^{43} +(8.59808 - 2.30385i) q^{47} +(5.36603 - 3.09808i) q^{49} +(7.09808 + 1.90192i) q^{51} +(-8.19615 + 8.19615i) q^{53} +(-3.63397 - 6.29423i) q^{57} +(-1.26795 - 2.19615i) q^{59} +(1.59808 - 2.76795i) q^{61} +(2.59808 + 0.696152i) q^{63} +(-10.9641 - 2.93782i) q^{67} +(2.59808 - 0.696152i) q^{69} +11.6603i q^{71} +(-9.46410 - 9.46410i) q^{73} +(-0.294229 + 1.09808i) q^{77} +(-1.73205 - 1.00000i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(2.59808 + 9.69615i) q^{83} -13.3923i q^{87} -2.66025 q^{89} +2.19615 q^{91} +(6.29423 + 3.63397i) q^{93} +(2.66025 + 9.92820i) q^{97} +(3.29423 - 1.90192i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{3} - 6 q^{7} + 6 q^{9} - 6 q^{11} + 6 q^{13} + 12 q^{17} - 6 q^{21} + 6 q^{23} + 12 q^{29} - 2 q^{31} - 12 q^{33} - 12 q^{37} + 6 q^{39} + 12 q^{41} - 6 q^{43} + 24 q^{47} + 18 q^{49} + 18 q^{51}+ \cdots - 18 q^{99}+O(q^{100}) $ 4 * q + 6 * q^3 - 6 * q^7 + 6 * q^9 - 6 * q^11 + 6 * q^13 + 12 * q^17 - 6 * q^21 + 6 * q^23 + 12 * q^29 - 2 * q^31 - 12 * q^33 - 12 * q^37 + 6 * q^39 + 12 * q^41 - 6 * q^43 + 24 * q^47 + 18 * q^49 + 18 * q^51 - 12 * q^53 - 18 * q^57 - 12 * q^59 - 4 * q^61 - 30 * q^67 - 24 * q^73 + 30 * q^77 - 18 * q^81 + 24 * q^89 - 12 * q^91 - 6 * q^93 - 24 * q^97 - 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.232051	+	0.866025i	0.0877070	+	0.327327i	0.995813	−	0.0914134i	$-0.0291385\pi$
$7$	0.232051	+	0.866025i	0.0877070	+	0.327327i	−0.908106	+	0.418740i	$0.862472\pi$
$8$		0			0
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$		0			0
$11$	1.09808	+	0.633975i	0.331082	+	0.191151i	0.656322	−	0.754481i	$-0.272111\pi$
$11$	1.09808	+	0.633975i	0.331082	+	0.191151i	−0.325239	+	0.945632i	$0.605445\pi$
$12$		0			0
$13$	0.633975	−	2.36603i	0.175833	−	0.656217i	−0.820575	−	0.571538i	$-0.806347\pi$
$13$	0.633975	−	2.36603i	0.175833	−	0.656217i	0.996408	−	0.0846790i	$-0.0269865\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.00000	+	3.00000i	0.727607	+	0.727607i	0.970143	−	0.242536i	$-0.0779791\pi$
$17$	3.00000	+	3.00000i	0.727607	+	0.727607i	−0.242536	+	0.970143i	$0.577979\pi$
$18$		0			0
$19$		−	4.19615i		−	0.962663i	−0.876539	−	0.481332i	$-0.840153\pi$
$19$		−	4.19615i		−	0.962663i	0.876539	−	0.481332i	$-0.159847\pi$
$20$		0			0
$21$	1.09808	+	1.09808i	0.239620	+	0.239620i
$22$		0			0
$23$	1.50000	+	0.401924i	0.312772	+	0.0838069i	0.411790	−	0.911279i	$-0.364904\pi$
$23$	1.50000	+	0.401924i	0.312772	+	0.0838069i	−0.0990186	+	0.995086i	$0.531570\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		−	5.19615i		−	1.00000i
$28$		0			0
$29$	3.86603	−	6.69615i	0.717903	−	1.24344i	−0.243926	−	0.969794i	$-0.578436\pi$
$29$	3.86603	−	6.69615i	0.717903	−	1.24344i	0.961829	−	0.273651i	$-0.0882312\pi$
$30$		0			0
$31$	2.09808	+	3.63397i	0.376826	+	0.652681i	0.990598	−	0.136802i	$-0.0436823\pi$
$31$	2.09808	+	3.63397i	0.376826	+	0.652681i	−0.613773	+	0.789483i	$0.710349\pi$
$32$		0			0
$33$	2.19615			0.382301
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−6.46410	+	6.46410i	−1.06269	+	1.06269i	−0.0647930	+	0.997899i	$0.520639\pi$
$37$	−6.46410	+	6.46410i	−1.06269	+	1.06269i	−0.997899	+	0.0647930i	$0.979361\pi$
$38$		0			0
$39$	−1.09808	−	4.09808i	−0.175833	−	0.656217i
$40$		0			0
$41$	5.59808	−	3.23205i	0.874273	−	0.504762i	0.00550690	−	0.999985i	$-0.498247\pi$
$41$	5.59808	−	3.23205i	0.874273	−	0.504762i	0.868766	+	0.495223i	$0.164914\pi$
$42$		0			0
$43$	−4.09808	+	1.09808i	−0.624951	+	0.167455i	−0.557377	−	0.830259i	$-0.688192\pi$
$43$	−4.09808	+	1.09808i	−0.624951	+	0.167455i	−0.0675734	+	0.997714i	$0.521526\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	8.59808	−	2.30385i	1.25416	−	0.336051i	0.430217	−	0.902726i	$-0.358437\pi$
$47$	8.59808	−	2.30385i	1.25416	−	0.336051i	0.823941	+	0.566675i	$0.191770\pi$
$48$		0			0
$49$	5.36603	−	3.09808i	0.766575	−	0.442582i
$50$		0			0
$51$	7.09808	+	1.90192i	0.993929	+	0.266323i
$52$		0			0
$53$	−8.19615	+	8.19615i	−1.12583	+	1.12583i	−0.134980	+	0.990848i	$0.543097\pi$
$53$	−8.19615	+	8.19615i	−1.12583	+	1.12583i	−0.990848	+	0.134980i	$0.956903\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−3.63397	−	6.29423i	−0.481332	−	0.833691i
$58$		0			0
$59$	−1.26795	−	2.19615i	−0.165073	−	0.285915i	0.771608	−	0.636098i	$-0.219453\pi$
$59$	−1.26795	−	2.19615i	−0.165073	−	0.285915i	−0.936681	+	0.350183i	$0.886119\pi$
$60$		0			0
$61$	1.59808	−	2.76795i	0.204613	−	0.354400i	−0.745397	−	0.666621i	$-0.767740\pi$
$61$	1.59808	−	2.76795i	0.204613	−	0.354400i	0.950009	+	0.312222i	$0.101073\pi$
$62$		0			0
$63$	2.59808	+	0.696152i	0.327327	+	0.0877070i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−10.9641	−	2.93782i	−1.33948	−	0.358912i	−0.483238	−	0.875489i	$-0.660539\pi$
$67$	−10.9641	−	2.93782i	−1.33948	−	0.358912i	−0.856241	+	0.516577i	$0.827206\pi$
$68$		0			0
$69$	2.59808	−	0.696152i	0.312772	−	0.0838069i
$70$		0			0
$71$			11.6603i			1.38382i	0.721985	+	0.691909i	$0.243230\pi$
$71$			11.6603i			1.38382i	−0.721985	+	0.691909i	$0.756770\pi$
$72$		0			0
$73$	−9.46410	−	9.46410i	−1.10769	−	1.10769i	−0.993454	−	0.114236i	$-0.963558\pi$
$73$	−9.46410	−	9.46410i	−1.10769	−	1.10769i	−0.114236	−	0.993454i	$-0.536442\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.294229	+	1.09808i	−0.0335305	+	0.125137i
$78$		0			0
$79$	−1.73205	−	1.00000i	−0.194871	−	0.112509i	0.399390	−	0.916781i	$-0.369222\pi$
$79$	−1.73205	−	1.00000i	−0.194871	−	0.112509i	−0.594261	+	0.804272i	$0.702555\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$		0			0
$83$	2.59808	+	9.69615i	0.285176	+	1.06429i	0.948711	+	0.316146i	$0.102389\pi$
$83$	2.59808	+	9.69615i	0.285176	+	1.06429i	−0.663535	+	0.748145i	$0.730945\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		−	13.3923i		−	1.43581i
$88$		0			0
$89$	−2.66025			−0.281986			−0.140993	−	0.990011i	$-0.545030\pi$
$89$	−2.66025			−0.281986			−0.140993	+	0.990011i	$0.545030\pi$
$90$		0			0
$91$	2.19615			0.230219
$92$		0			0
$93$	6.29423	+	3.63397i	0.652681	+	0.376826i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	2.66025	+	9.92820i	0.270108	+	1.00806i	0.959049	+	0.283239i	$0.0914091\pi$
$97$	2.66025	+	9.92820i	0.270108	+	1.00806i	−0.688941	+	0.724817i	$0.741924\pi$
$98$		0			0
$99$	3.29423	−	1.90192i	0.331082	−	0.191151i
$100$		0			0
$101$	−11.1962	−	6.46410i	−1.11406	−	0.643202i	−0.174181	−	0.984714i	$-0.555728\pi$
$101$	−11.1962	−	6.46410i	−1.11406	−	0.643202i	−0.939878	+	0.341511i	$0.889061\pi$
$102$		0			0
$103$	0.169873	−	0.633975i	0.0167381	−	0.0624674i	−0.957052	−	0.289917i	$-0.906372\pi$
$103$	0.169873	−	0.633975i	0.0167381	−	0.0624674i	0.973790	+	0.227450i	$0.0730388\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	13.0981	+	13.0981i	1.26624	+	1.26624i	0.948016	+	0.318223i	$0.103086\pi$
$107$	13.0981	+	13.0981i	1.26624	+	1.26624i	0.318223	+	0.948016i	$0.396914\pi$
$108$		0			0
$109$			1.19615i			0.114571i	0.998358	+	0.0572853i	$0.0182445\pi$
$109$			1.19615i			0.114571i	−0.998358	+	0.0572853i	$0.981756\pi$
$110$		0			0
$111$	−4.09808	+	15.2942i	−0.388972	+	1.45166i
$112$		0			0
$113$	−5.19615	−	1.39230i	−0.488813	−	0.130977i	0.00599034	−	0.999982i	$-0.498093\pi$
$113$	−5.19615	−	1.39230i	−0.488813	−	0.130977i	−0.494803	+	0.869005i	$0.664760\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−5.19615	−	5.19615i	−0.480384	−	0.480384i
$118$		0			0
$119$	−1.90192	+	3.29423i	−0.174349	+	0.301981i
$120$		0			0
$121$	−4.69615	−	8.13397i	−0.426923	−	0.739452i
$122$		0			0
$123$	5.59808	−	9.69615i	0.504762	−	0.874273i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−13.0981	+	13.0981i	−1.16227	+	1.16227i	−0.178288	+	0.983978i	$0.557056\pi$
$127$	−13.0981	+	13.0981i	−1.16227	+	1.16227i	−0.983978	+	0.178288i	$0.942944\pi$
$128$		0			0
$129$	−5.19615	+	5.19615i	−0.457496	+	0.457496i
$130$		0			0
$131$	6.80385	−	3.92820i	0.594455	−	0.343209i	−0.172402	−	0.985027i	$-0.555153\pi$
$131$	6.80385	−	3.92820i	0.594455	−	0.343209i	0.766857	+	0.641818i	$0.221820\pi$
$132$		0			0
$133$	3.63397	−	0.973721i	0.315106	−	0.0844323i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	19.3923	−	5.19615i	1.65680	−	0.443937i	0.695292	−	0.718727i	$-0.255275\pi$
$137$	19.3923	−	5.19615i	1.65680	−	0.443937i	0.961504	+	0.274790i	$0.0886083\pi$
$138$		0			0
$139$	−10.7321	+	6.19615i	−0.910281	+	0.525551i	−0.880521	−	0.474006i	$-0.842807\pi$
$139$	−10.7321	+	6.19615i	−0.910281	+	0.525551i	−0.0297592	+	0.999557i	$0.509474\pi$
$140$		0			0
$141$	10.9019	−	10.9019i	0.918108	−	0.918108i
$142$		0			0
$143$	2.19615	−	2.19615i	0.183651	−	0.183651i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	5.36603	−	9.29423i	0.442582	−	0.766575i
$148$		0			0
$149$	9.69615	+	16.7942i	0.794340	+	1.37584i	0.923258	+	0.384182i	$0.125516\pi$
$149$	9.69615	+	16.7942i	0.794340	+	1.37584i	−0.128918	+	0.991655i	$0.541150\pi$
$150$		0			0
$151$	−5.29423	+	9.16987i	−0.430838	+	0.746234i	−0.996946	−	0.0780978i	$-0.975115\pi$
$151$	−5.29423	+	9.16987i	−0.430838	+	0.746234i	0.566107	+	0.824331i	$0.308449\pi$
$152$		0			0
$153$	12.2942	−	3.29423i	0.993929	−	0.266323i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−3.00000	−	0.803848i	−0.239426	−	0.0641540i	0.137111	−	0.990556i	$-0.456218\pi$
$157$	−3.00000	−	0.803848i	−0.239426	−	0.0641540i	−0.376537	+	0.926402i	$0.622885\pi$
$158$		0			0
$159$	−5.19615	+	19.3923i	−0.412082	+	1.53791i
$160$		0			0
$161$			1.39230i			0.109729i
$162$		0			0
$163$	−3.92820	−	3.92820i	−0.307681	−	0.307681i	0.536329	−	0.844009i	$-0.319811\pi$
$163$	−3.92820	−	3.92820i	−0.307681	−	0.307681i	−0.844009	+	0.536329i	$0.819811\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−2.89230	+	10.7942i	−0.223813	+	0.835282i	0.759063	+	0.651017i	$0.225657\pi$
$167$	−2.89230	+	10.7942i	−0.223813	+	0.835282i	−0.982876	+	0.184266i	$0.941009\pi$
$168$		0			0
$169$	6.06218	+	3.50000i	0.466321	+	0.269231i
$170$		0			0
$171$	−10.9019	−	6.29423i	−0.833691	−	0.481332i
$172$		0			0
$173$	1.60770	+	6.00000i	0.122231	+	0.456172i	0.999726	−	0.0234141i	$-0.00745363\pi$
$173$	1.60770	+	6.00000i	0.122231	+	0.456172i	−0.877495	+	0.479586i	$0.840787\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−3.80385	−	2.19615i	−0.285915	−	0.165073i
$178$		0			0
$179$	−16.7321			−1.25061			−0.625306	−	0.780380i	$-0.715026\pi$
$179$	−16.7321			−1.25061			−0.625306	+	0.780380i	$0.715026\pi$
$180$		0			0
$181$	−9.39230			−0.698125			−0.349062	−	0.937100i	$-0.613500\pi$
$181$	−9.39230			−0.698125			−0.349062	+	0.937100i	$0.613500\pi$
$182$		0			0
$183$		−	5.53590i		−	0.409225i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	1.39230	+	5.19615i	0.101815	+	0.379980i
$188$		0			0
$189$	4.50000	−	1.20577i	0.327327	−	0.0877070i
$190$		0			0
$191$	−16.9019	−	9.75833i	−1.22298	−	0.706088i	−0.257428	−	0.966297i	$-0.582875\pi$
$191$	−16.9019	−	9.75833i	−1.22298	−	0.706088i	−0.965552	+	0.260209i	$0.916208\pi$
$192$		0			0
$193$	5.36603	−	20.0263i	0.386255	−	1.44152i	−0.449924	−	0.893067i	$-0.648549\pi$
$193$	5.36603	−	20.0263i	0.386255	−	1.44152i	0.836179	−	0.548456i	$-0.184784\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	2.19615	+	2.19615i	0.156469	+	0.156469i	0.781000	−	0.624531i	$-0.214710\pi$
$197$	2.19615	+	2.19615i	0.156469	+	0.156469i	−0.624531	+	0.781000i	$0.714710\pi$
$198$		0			0
$199$			20.5885i			1.45948i	0.683726	+	0.729739i	$0.260358\pi$
$199$			20.5885i			1.45948i	−0.683726	+	0.729739i	$0.739642\pi$
$200$		0			0
$201$	−18.9904	+	5.08846i	−1.33948	+	0.358912i
$202$		0			0
$203$	6.69615	+	1.79423i	0.469978	+	0.125930i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	3.29423	−	3.29423i	0.228965	−	0.228965i
$208$		0			0
$209$	2.66025	−	4.60770i	0.184014	−	0.318721i
$210$		0			0
$211$	0.901924	+	1.56218i	0.0620910	+	0.107545i	0.895400	−	0.445263i	$-0.146890\pi$
$211$	0.901924	+	1.56218i	0.0620910	+	0.107545i	−0.833309	+	0.552808i	$0.813556\pi$
$212$		0			0
$213$	10.0981	+	17.4904i	0.691909	+	1.19842i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−2.66025	+	2.66025i	−0.180590	+	0.180590i
$218$		0			0
$219$	−22.3923	−	6.00000i	−1.51313	−	0.405442i
$220$		0			0
$221$	9.00000	−	5.19615i	0.605406	−	0.349531i
$222$		0			0
$223$	−15.6962	+	4.20577i	−1.05109	+	0.281639i	−0.742703	−	0.669621i	$-0.766457\pi$
$223$	−15.6962	+	4.20577i	−1.05109	+	0.281639i	−0.308389	+	0.951260i	$0.599790\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−1.09808	+	0.294229i	−0.0728819	+	0.0195286i	−0.295076	−	0.955474i	$-0.595345\pi$
$227$	−1.09808	+	0.294229i	−0.0728819	+	0.0195286i	0.222194	+	0.975003i	$0.428678\pi$
$228$		0			0
$229$	−4.33013	+	2.50000i	−0.286143	+	0.165205i	−0.636201	−	0.771523i	$-0.719495\pi$
$229$	−4.33013	+	2.50000i	−0.286143	+	0.165205i	0.350058	+	0.936728i	$0.386162\pi$
$230$		0			0
$231$	0.509619	+	1.90192i	0.0335305	+	0.125137i
$232$		0			0
$233$	−11.1962	+	11.1962i	−0.733484	+	0.733484i	−0.971308	−	0.237824i	$-0.923566\pi$
$233$	−11.1962	+	11.1962i	−0.733484	+	0.733484i	0.237824	+	0.971308i	$0.423566\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−3.46410			−0.225018
$238$		0			0
$239$	9.00000	+	15.5885i	0.582162	+	1.00833i	0.995223	+	0.0976302i	$0.0311262\pi$
$239$	9.00000	+	15.5885i	0.582162	+	1.00833i	−0.413061	+	0.910703i	$0.635540\pi$
$240$		0			0
$241$	4.59808	−	7.96410i	0.296188	−	0.513013i	−0.679072	−	0.734071i	$-0.737618\pi$
$241$	4.59808	−	7.96410i	0.296188	−	0.513013i	0.975261	+	0.221058i	$0.0709511\pi$
$242$		0			0
$243$	−13.5000	−	7.79423i	−0.866025	−	0.500000i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−9.92820	−	2.66025i	−0.631716	−	0.169268i
$248$		0			0
$249$	12.2942	+	12.2942i	0.779115	+	0.779115i
$250$		0			0
$251$			24.5885i			1.55201i	0.630727	+	0.776005i	$0.282757\pi$
$251$			24.5885i			1.55201i	−0.630727	+	0.776005i	$0.717243\pi$
$252$		0			0
$253$	1.39230	+	1.39230i	0.0875335	+	0.0875335i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	6.00000	−	22.3923i	0.374270	−	1.39679i	−0.480139	−	0.877192i	$-0.659414\pi$
$257$	6.00000	−	22.3923i	0.374270	−	1.39679i	0.854409	−	0.519601i	$-0.173919\pi$
$258$		0			0
$259$	−7.09808	−	4.09808i	−0.441053	−	0.254642i
$260$		0			0
$261$	−11.5981	−	20.0885i	−0.717903	−	1.24344i
$262$		0			0
$263$	1.09808	+	4.09808i	0.0677103	+	0.252698i	0.991482	−	0.130246i	$-0.0415768\pi$
$263$	1.09808	+	4.09808i	0.0677103	+	0.252698i	−0.923771	+	0.382944i	$0.874910\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−3.99038	+	2.30385i	−0.244207	+	0.140993i
$268$		0			0
$269$	−16.8564			−1.02775			−0.513877	−	0.857864i	$-0.671791\pi$
$269$	−16.8564			−1.02775			−0.513877	+	0.857864i	$0.671791\pi$
$270$		0			0
$271$	−0.196152			−0.0119154			−0.00595771	−	0.999982i	$-0.501896\pi$
$271$	−0.196152			−0.0119154			−0.00595771	+	0.999982i	$0.501896\pi$
$272$		0			0
$273$	3.29423	−	1.90192i	0.199376	−	0.115110i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−2.49038	−	9.29423i	−0.149632	−	0.558436i	−0.999505	−	0.0314483i	$-0.989988\pi$
$277$	−2.49038	−	9.29423i	−0.149632	−	0.558436i	0.849873	−	0.526988i	$-0.176679\pi$
$278$		0			0
$279$	12.5885			0.753651
$280$		0			0
$281$	−16.7942	−	9.69615i	−1.00186	−	0.578424i	−0.0930617	−	0.995660i	$-0.529665\pi$
$281$	−16.7942	−	9.69615i	−1.00186	−	0.578424i	−0.908798	+	0.417236i	$0.862999\pi$
$282$		0			0
$283$	−6.69615	+	24.9904i	−0.398045	+	1.48552i	0.418487	+	0.908223i	$0.362561\pi$
$283$	−6.69615	+	24.9904i	−0.398045	+	1.48552i	−0.816531	+	0.577301i	$0.804106\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	4.09808	+	4.09808i	0.241902	+	0.241902i
$288$		0			0
$289$			1.00000i			0.0588235i
$290$		0			0
$291$	12.5885	+	12.5885i	0.737948	+	0.737948i
$292$		0			0
$293$	−18.2942	−	4.90192i	−1.06876	−	0.286373i	−0.318777	−	0.947830i	$-0.603272\pi$
$293$	−18.2942	−	4.90192i	−1.06876	−	0.286373i	−0.749984	+	0.661456i	$0.769939\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	3.29423	−	5.70577i	0.191151	−	0.331082i
$298$		0			0
$299$	1.90192	−	3.29423i	0.109991	−	0.190510i
$300$		0			0
$301$	−1.90192	−	3.29423i	−0.109625	−	0.189876i
$302$		0			0
$303$	−22.3923			−1.28640
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−1.90192	+	1.90192i	−0.108549	+	0.108549i	−0.759295	−	0.650747i	$-0.774456\pi$
$307$	−1.90192	+	1.90192i	−0.108549	+	0.108549i	0.650747	+	0.759295i	$0.274456\pi$
$308$		0			0
$309$	−0.294229	−	1.09808i	−0.0167381	−	0.0624674i
$310$		0			0
$311$	16.9019	−	9.75833i	0.958420	−	0.553344i	0.0627337	−	0.998030i	$-0.480018\pi$
$311$	16.9019	−	9.75833i	0.958420	−	0.553344i	0.895686	+	0.444686i	$0.146685\pi$
$312$		0			0
$313$	5.36603	−	1.43782i	0.303306	−	0.0812705i	−0.103956	−	0.994582i	$-0.533150\pi$
$313$	5.36603	−	1.43782i	0.303306	−	0.0812705i	0.407262	+	0.913311i	$0.366484\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−21.2942	+	5.70577i	−1.19600	+	0.320468i	−0.801256	−	0.598322i	$-0.795834\pi$
$317$	−21.2942	+	5.70577i	−1.19600	+	0.320468i	−0.394747	+	0.918790i	$0.629168\pi$
$318$		0			0
$319$	8.49038	−	4.90192i	0.475370	−	0.274455i
$320$		0			0
$321$	30.9904	+	8.30385i	1.72971	+	0.463476i
$322$		0			0
$323$	12.5885	−	12.5885i	0.700440	−	0.700440i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	1.03590	+	1.79423i	0.0572853	+	0.0992211i
$328$		0			0
$329$	3.99038	+	6.91154i	0.219997	+	0.381046i
$330$		0			0
$331$	−1.80385	+	3.12436i	−0.0991484	+	0.171730i	−0.911332	−	0.411671i	$-0.864945\pi$
$331$	−1.80385	+	3.12436i	−0.0991484	+	0.171730i	0.812184	+	0.583401i	$0.198279\pi$
$332$		0			0
$333$	7.09808	+	26.4904i	0.388972	+	1.45166i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	22.8564	+	6.12436i	1.24507	+	0.333615i	0.820429	−	0.571748i	$-0.193735\pi$
$337$	22.8564	+	6.12436i	1.24507	+	0.333615i	0.424639	+	0.905363i	$0.360401\pi$
$338$		0			0
$339$	−9.00000	+	2.41154i	−0.488813	+	0.130977i
$340$		0			0
$341$			5.32051i			0.288122i
$342$		0			0
$343$	8.36603	+	8.36603i	0.451723	+	0.451723i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−2.70577	+	10.0981i	−0.145253	+	0.542093i	0.854491	+	0.519467i	$0.173869\pi$
$347$	−2.70577	+	10.0981i	−0.145253	+	0.542093i	−0.999744	+	0.0226262i	$0.992797\pi$
$348$		0			0
$349$	−2.25833	−	1.30385i	−0.120886	−	0.0697934i	0.438338	−	0.898810i	$-0.355567\pi$
$349$	−2.25833	−	1.30385i	−0.120886	−	0.0697934i	−0.559224	+	0.829017i	$0.688901\pi$
$350$		0			0
$351$	−12.2942	−	3.29423i	−0.656217	−	0.175833i
$352$		0			0
$353$	−2.19615	−	8.19615i	−0.116889	−	0.436237i	0.882532	−	0.470253i	$-0.155837\pi$
$353$	−2.19615	−	8.19615i	−0.116889	−	0.436237i	−0.999421	+	0.0340153i	$0.989170\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$			6.58846i			0.348698i
$358$		0			0
$359$	8.87564			0.468439			0.234219	−	0.972184i	$-0.424747\pi$
$359$	8.87564			0.468439			0.234219	+	0.972184i	$0.424747\pi$
$360$		0			0
$361$	1.39230			0.0732792
$362$		0			0
$363$	−14.0885	−	8.13397i	−0.739452	−	0.426923i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−3.63397	−	13.5622i	−0.189692	−	0.707940i	−0.993577	−	0.113156i	$-0.963904\pi$
$367$	−3.63397	−	13.5622i	−0.189692	−	0.707940i	0.803885	−	0.594784i	$-0.202763\pi$
$368$		0			0
$369$		−	19.3923i		−	1.00952i
$370$		0			0
$371$	−9.00000	−	5.19615i	−0.467257	−	0.269771i
$372$		0			0
$373$	3.92820	−	14.6603i	0.203395	−	0.759079i	−0.786538	−	0.617542i	$-0.788129\pi$
$373$	3.92820	−	14.6603i	0.203395	−	0.759079i	0.989933	−	0.141538i	$-0.0452046\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−13.3923	−	13.3923i	−0.689739	−	0.689739i
$378$		0			0
$379$		−	34.7846i		−	1.78677i	−0.449297	−	0.893383i	$-0.648325\pi$
$379$		−	34.7846i		−	1.78677i	0.449297	−	0.893383i	$-0.351675\pi$
$380$		0			0
$381$	−8.30385	+	30.9904i	−0.425419	+	1.58769i
$382$		0			0
$383$	20.4904	+	5.49038i	1.04701	+	0.280545i	0.741015	−	0.671488i	$-0.234345\pi$
$383$	20.4904	+	5.49038i	1.04701	+	0.280545i	0.305994	+	0.952033i	$0.401011\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−3.29423	+	12.2942i	−0.167455	+	0.624951i
$388$		0			0
$389$	14.8923	−	25.7942i	0.755070	−	1.30782i	−0.190270	−	0.981732i	$-0.560936\pi$
$389$	14.8923	−	25.7942i	0.755070	−	1.30782i	0.945340	−	0.326087i	$-0.105730\pi$
$390$		0			0
$391$	3.29423	+	5.70577i	0.166596	+	0.288553i
$392$		0			0
$393$	6.80385	−	11.7846i	0.343209	−	0.594455i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	26.7846	−	26.7846i	1.34428	−	1.34428i	0.452534	−	0.891747i	$-0.350520\pi$
$397$	26.7846	−	26.7846i	1.34428	−	1.34428i	0.891747	−	0.452534i	$-0.149480\pi$
$398$		0			0
$399$	4.60770	−	4.60770i	0.230673	−	0.230673i
$400$		0			0
$401$	9.00000	−	5.19615i	0.449439	−	0.259483i	−0.258154	−	0.966104i	$-0.583114\pi$
$401$	9.00000	−	5.19615i	0.449439	−	0.259483i	0.707593	+	0.706620i	$0.249781\pi$
$402$		0			0
$403$	9.92820	−	2.66025i	0.494559	−	0.132517i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−11.1962	+	3.00000i	−0.554973	+	0.148704i
$408$		0			0
$409$	2.07180	−	1.19615i	0.102444	−	0.0591459i	−0.447903	−	0.894082i	$-0.647829\pi$
$409$	2.07180	−	1.19615i	0.102444	−	0.0591459i	0.550347	+	0.834936i	$0.314496\pi$
$410$		0			0
$411$	24.5885	−	24.5885i	1.21286	−	1.21286i
$412$		0			0
$413$	1.60770	−	1.60770i	0.0791095	−	0.0791095i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−10.7321	+	18.5885i	−0.525551	+	0.910281i
$418$		0			0
$419$	−16.0981	−	27.8827i	−0.786442	−	1.36216i	−0.928134	−	0.372247i	$-0.878587\pi$
$419$	−16.0981	−	27.8827i	−0.786442	−	1.36216i	0.141691	−	0.989911i	$-0.454746\pi$
$420$		0			0
$421$	3.19615	−	5.53590i	0.155771	−	0.269803i	−0.777569	−	0.628798i	$-0.783547\pi$
$421$	3.19615	−	5.53590i	0.155771	−	0.269803i	0.933339	+	0.358995i	$0.116880\pi$
$422$		0			0
$423$	6.91154	−	25.7942i	0.336051	−	1.25416i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	2.76795	+	0.741670i	0.133950	+	0.0358919i
$428$		0			0
$429$	1.39230	−	5.19615i	0.0672211	−	0.250873i
$430$		0			0
$431$			36.2487i			1.74604i	0.487685	+	0.873019i	$0.337841\pi$
$431$			36.2487i			1.74604i	−0.487685	+	0.873019i	$0.662159\pi$
$432$		0			0
$433$	0.803848	+	0.803848i	0.0386304	+	0.0386304i	0.726158	−	0.687528i	$-0.241304\pi$
$433$	0.803848	+	0.803848i	0.0386304	+	0.0386304i	−0.687528	+	0.726158i	$0.741304\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1.68653	−	6.29423i	0.0806778	−	0.301094i
$438$		0			0
$439$	22.8564	+	13.1962i	1.09088	+	0.629818i	0.933810	−	0.357770i	$-0.116463\pi$
$439$	22.8564	+	13.1962i	1.09088	+	0.629818i	0.157067	+	0.987588i	$0.449796\pi$
$440$		0			0
$441$		−	18.5885i		−	0.885165i
$442$		0			0
$443$	−6.10770	−	22.7942i	−0.290185	−	1.08299i	−0.944966	−	0.327168i	$-0.893906\pi$
$443$	−6.10770	−	22.7942i	−0.290185	−	1.08299i	0.654781	−	0.755819i	$-0.272761\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	29.0885	+	16.7942i	1.37584	+	0.794340i
$448$		0			0
$449$	−7.85641			−0.370767			−0.185383	−	0.982666i	$-0.559353\pi$
$449$	−7.85641			−0.370767			−0.185383	+	0.982666i	$0.559353\pi$
$450$		0			0
$451$	8.19615			0.385942
$452$		0			0
$453$			18.3397i			0.861676i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	6.50962	+	24.2942i	0.304507	+	1.13644i	0.933369	+	0.358919i	$0.116855\pi$
$457$	6.50962	+	24.2942i	0.304507	+	1.13644i	−0.628862	+	0.777517i	$0.716479\pi$
$458$		0			0
$459$	15.5885	−	15.5885i	0.727607	−	0.727607i
$460$		0			0
$461$	13.2846	+	7.66987i	0.618726	+	0.357222i	0.776373	−	0.630274i	$-0.217057\pi$
$461$	13.2846	+	7.66987i	0.618726	+	0.357222i	−0.157647	+	0.987496i	$0.550391\pi$
$462$		0			0
$463$	−6.97372	+	26.0263i	−0.324096	+	1.20954i	0.591121	+	0.806583i	$0.298686\pi$
$463$	−6.97372	+	26.0263i	−0.324096	+	1.20954i	−0.915217	+	0.402961i	$0.867981\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−15.0000	−	15.0000i	−0.694117	−	0.694117i	0.269018	−	0.963135i	$-0.413301\pi$
$467$	−15.0000	−	15.0000i	−0.694117	−	0.694117i	−0.963135	+	0.269018i	$0.913301\pi$
$468$		0			0
$469$		−	10.1769i		−	0.469926i
$470$		0			0
$471$	−5.19615	+	1.39230i	−0.239426	+	0.0641540i
$472$		0			0
$473$	−5.19615	−	1.39230i	−0.238919	−	0.0640182i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	9.00000	+	33.5885i	0.412082	+	1.53791i
$478$		0			0
$479$	7.73205	−	13.3923i	0.353286	−	0.611910i	−0.633537	−	0.773713i	$-0.718397\pi$
$479$	7.73205	−	13.3923i	0.353286	−	0.611910i	0.986823	+	0.161803i	$0.0517308\pi$
$480$		0			0
$481$	11.1962	+	19.3923i	0.510501	+	0.884213i
$482$		0			0
$483$	1.20577	+	2.08846i	0.0548645	+	0.0950281i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	19.7321	−	19.7321i	0.894145	−	0.894145i	−0.100766	−	0.994910i	$-0.532129\pi$
$487$	19.7321	−	19.7321i	0.894145	−	0.894145i	0.994910	+	0.100766i	$0.0321292\pi$
$488$		0			0
$489$	−9.29423	−	2.49038i	−0.420300	−	0.112619i
$490$		0			0
$491$	37.9808	−	21.9282i	1.71405	−	0.989606i	0.785121	−	0.619342i	$-0.212601\pi$
$491$	37.9808	−	21.9282i	1.71405	−	0.989606i	0.928927	−	0.370264i	$-0.120733\pi$
$492$		0			0
$493$	31.6865	−	8.49038i	1.42709	−	0.382388i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−10.0981	+	2.70577i	−0.452961	+	0.121370i
$498$		0			0
$499$	9.33975	−	5.39230i	0.418104	−	0.241393i	−0.276162	−	0.961111i	$-0.589062\pi$
$499$	9.33975	−	5.39230i	0.418104	−	0.241393i	0.694266	+	0.719719i	$0.255729\pi$
$500$		0			0
$501$	5.00962	+	18.6962i	0.223813	+	0.835282i
$502$		0			0
$503$	24.2942	−	24.2942i	1.08323	−	1.08323i	0.0870195	−	0.996207i	$-0.472266\pi$
$503$	24.2942	−	24.2942i	1.08323	−	1.08323i	0.996207	−	0.0870195i	$-0.0277342\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	12.1244			0.538462
$508$		0			0
$509$	7.79423	+	13.5000i	0.345473	+	0.598377i	0.985440	−	0.170026i	$-0.0543851\pi$
$509$	7.79423	+	13.5000i	0.345473	+	0.598377i	−0.639966	+	0.768403i	$0.721052\pi$
$510$		0			0
$511$	6.00000	−	10.3923i	0.265424	−	0.459728i
$512$		0			0
$513$	−21.8038			−0.962663
$514$		0			0
$515$		0			0
$516$		0			0
$517$	10.9019	+	2.92116i	0.479466	+	0.128473i
$518$		0			0
$519$	7.60770	+	7.60770i	0.333941	+	0.333941i
$520$		0			0
$521$			12.8038i			0.560947i	0.959862	+	0.280473i	$0.0904914\pi$
$521$			12.8038i			0.560947i	−0.959862	+	0.280473i	$0.909509\pi$
$522$		0			0
$523$	15.6340	+	15.6340i	0.683626	+	0.683626i	0.960815	−	0.277189i	$-0.0894029\pi$
$523$	15.6340	+	15.6340i	0.683626	+	0.683626i	−0.277189	+	0.960815i	$0.589403\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−4.60770	+	17.1962i	−0.200714	+	0.749076i
$528$		0			0
$529$	−17.8301	−	10.2942i	−0.775223	−	0.447575i
$530$		0			0
$531$	−7.60770			−0.330146
$532$		0			0
$533$	−4.09808	−	15.2942i	−0.177507	−	0.662467i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−25.0981	+	14.4904i	−1.08306	+	0.625306i
$538$		0			0
$539$	7.85641			0.338399
$540$		0			0
$541$	27.3923			1.17769			0.588844	−	0.808247i	$-0.299583\pi$
$541$	27.3923			1.17769			0.588844	+	0.808247i	$0.299583\pi$
$542$		0			0
$543$	−14.0885	+	8.13397i	−0.604594	+	0.349062i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−9.01666	−	33.6506i	−0.385525	−	1.43880i	−0.837338	−	0.546685i	$-0.815890\pi$
$547$	−9.01666	−	33.6506i	−0.385525	−	1.43880i	0.451814	−	0.892112i	$-0.350777\pi$
$548$		0			0
$549$	−4.79423	−	8.30385i	−0.204613	−	0.354400i
$550$		0			0
$551$	−28.0981	−	16.2224i	−1.19702	−	0.691099i
$552$		0			0
$553$	0.464102	−	1.73205i	0.0197356	−	0.0736543i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−28.3923	−	28.3923i	−1.20302	−	1.20302i	−0.973243	−	0.229777i	$-0.926200\pi$
$557$	−28.3923	−	28.3923i	−1.20302	−	1.20302i	−0.229777	−	0.973243i	$-0.573800\pi$
$558$		0			0
$559$			10.3923i			0.439548i
$560$		0			0
$561$	6.58846	+	6.58846i	0.278165	+	0.278165i
$562$		0			0
$563$	24.9904	+	6.69615i	1.05322	+	0.282209i	0.743581	−	0.668645i	$-0.233126\pi$
$563$	24.9904	+	6.69615i	1.05322	+	0.282209i	0.309638	+	0.950855i	$0.399792\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	5.70577	−	5.70577i	0.239620	−	0.239620i
$568$		0			0
$569$	12.9282	−	22.3923i	0.541978	−	0.938734i	−0.456812	−	0.889563i	$-0.651009\pi$
$569$	12.9282	−	22.3923i	0.541978	−	0.938734i	0.998790	−	0.0491709i	$-0.0156579\pi$
$570$		0			0
$571$	−6.19615	−	10.7321i	−0.259301	−	0.449122i	0.706754	−	0.707459i	$-0.250159\pi$
$571$	−6.19615	−	10.7321i	−0.259301	−	0.449122i	−0.966055	+	0.258337i	$0.916825\pi$
$572$		0			0
$573$	−33.8038			−1.41218
$574$		0			0
$575$		0			0
$576$		0			0
$577$	13.2679	−	13.2679i	0.552352	−	0.552352i	−0.374767	−	0.927119i	$-0.622277\pi$
$577$	13.2679	−	13.2679i	0.552352	−	0.552352i	0.927119	+	0.374767i	$0.122277\pi$
$578$		0			0
$579$	−9.29423	−	34.6865i	−0.386255	−	1.44152i
$580$		0			0
$581$	−7.79423	+	4.50000i	−0.323359	+	0.186691i
$582$		0			0
$583$	−14.1962	+	3.80385i	−0.587945	+	0.157539i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−9.69615	+	2.59808i	−0.400203	+	0.107234i	−0.453306	−	0.891355i	$-0.649756\pi$
$587$	−9.69615	+	2.59808i	−0.400203	+	0.107234i	0.0531030	+	0.998589i	$0.483089\pi$
$588$		0			0
$589$	15.2487	−	8.80385i	0.628312	−	0.362756i
$590$		0			0
$591$	5.19615	+	1.39230i	0.213741	+	0.0572718i
$592$		0			0
$593$	−3.58846	+	3.58846i	−0.147360	+	0.147360i	−0.776938	−	0.629577i	$-0.783228\pi$
$593$	−3.58846	+	3.58846i	−0.147360	+	0.147360i	0.629577	+	0.776938i	$0.283228\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	17.8301	+	30.8827i	0.729739	+	1.26394i
$598$		0			0
$599$	10.2679	+	17.7846i	0.419537	+	0.726659i	0.995893	−	0.0905394i	$-0.0288591\pi$
$599$	10.2679	+	17.7846i	0.419537	+	0.726659i	−0.576356	+	0.817199i	$0.695526\pi$
$600$		0			0
$601$	−19.7846	+	34.2679i	−0.807031	+	1.39782i	0.107880	+	0.994164i	$0.465594\pi$
$601$	−19.7846	+	34.2679i	−0.807031	+	1.39782i	−0.914911	+	0.403655i	$0.867740\pi$
$602$		0			0
$603$	−24.0788	+	24.0788i	−0.980566	+	0.980566i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	11.4282	+	3.06218i	0.463856	+	0.124290i	0.483176	−	0.875523i	$-0.339483\pi$
$607$	11.4282	+	3.06218i	0.463856	+	0.124290i	−0.0193193	+	0.999813i	$0.506150\pi$
$608$		0			0
$609$	11.5981	−	3.10770i	0.469978	−	0.125930i
$610$		0			0
$611$		−	21.8038i		−	0.882089i
$612$		0			0
$613$	7.05256	+	7.05256i	0.284850	+	0.284850i	0.835040	−	0.550190i	$-0.185445\pi$
$613$	7.05256	+	7.05256i	0.284850	+	0.284850i	−0.550190	+	0.835040i	$0.685445\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	3.58846	−	13.3923i	0.144466	−	0.539154i	−0.855313	−	0.518112i	$-0.826635\pi$
$617$	3.58846	−	13.3923i	0.144466	−	0.539154i	0.999779	−	0.0210418i	$-0.00669832\pi$
$618$		0			0
$619$	−32.0263	−	18.4904i	−1.28724	−	0.743191i	−0.309083	−	0.951035i	$-0.600022\pi$
$619$	−32.0263	−	18.4904i	−1.28724	−	0.743191i	−0.978162	+	0.207844i	$0.933355\pi$
$620$		0			0
$621$	2.08846	−	7.79423i	0.0838069	−	0.312772i
$622$		0			0
$623$	−0.617314	−	2.30385i	−0.0247322	−	0.0923017i
$624$		0			0
$625$		0			0
$626$		0			0
$627$		−	9.21539i		−	0.368027i
$628$		0			0
$629$	−38.7846			−1.54644
$630$		0			0
$631$	−30.7846			−1.22552			−0.612758	−	0.790271i	$-0.709940\pi$
$631$	−30.7846			−1.22552			−0.612758	+	0.790271i	$0.709940\pi$
$632$		0			0
$633$	2.70577	+	1.56218i	0.107545	+	0.0620910i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−3.92820	−	14.6603i	−0.155641	−	0.580860i
$638$		0			0
$639$	30.2942	+	17.4904i	1.19842	+	0.691909i
$640$		0			0
$641$	9.99038	+	5.76795i	0.394596	+	0.227820i	0.684150	−	0.729342i	$-0.260173\pi$
$641$	9.99038	+	5.76795i	0.394596	+	0.227820i	−0.289553	+	0.957162i	$0.593507\pi$
$642$		0			0
$643$	−6.40192	+	23.8923i	−0.252467	+	0.942221i	0.717015	+	0.697058i	$0.245508\pi$
$643$	−6.40192	+	23.8923i	−0.252467	+	0.942221i	−0.969482	+	0.245163i	$0.921159\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−19.9019	−	19.9019i	−0.782425	−	0.782425i	0.197814	−	0.980240i	$-0.436616\pi$
$647$	−19.9019	−	19.9019i	−0.782425	−	0.782425i	−0.980240	+	0.197814i	$0.936616\pi$
$648$		0			0
$649$		−	3.21539i		−	0.126215i
$650$		0			0
$651$	−1.68653	+	6.29423i	−0.0661005	+	0.246690i
$652$		0			0
$653$	−43.6865	−	11.7058i	−1.70959	−	0.458082i	−0.734263	−	0.678865i	$-0.762472\pi$
$653$	−43.6865	−	11.7058i	−1.70959	−	0.458082i	−0.975323	+	0.220783i	$0.929139\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−38.7846	+	10.3923i	−1.51313	+	0.405442i
$658$		0			0
$659$	−5.19615	+	9.00000i	−0.202413	+	0.350590i	−0.949306	−	0.314355i	$-0.898212\pi$
$659$	−5.19615	+	9.00000i	−0.202413	+	0.350590i	0.746892	+	0.664945i	$0.231545\pi$
$660$		0			0
$661$	1.00000	+	1.73205i	0.0388955	+	0.0673690i	0.884818	−	0.465937i	$-0.154283\pi$
$661$	1.00000	+	1.73205i	0.0388955	+	0.0673690i	−0.845922	+	0.533306i	$0.820949\pi$
$662$		0			0
$663$	9.00000	−	15.5885i	0.349531	−	0.605406i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	8.49038	−	8.49038i	0.328749	−	0.328749i
$668$		0			0
$669$	−19.9019	+	19.9019i	−0.769453	+	0.769453i
$670$		0			0
$671$	3.50962	−	2.02628i	0.135487	−	0.0782237i
$672$		0			0
$673$	−21.7583	+	5.83013i	−0.838722	+	0.224735i	−0.652515	−	0.757776i	$-0.726286\pi$
$673$	−21.7583	+	5.83013i	−0.838722	+	0.224735i	−0.186207	+	0.982511i	$0.559619\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−37.6865	+	10.0981i	−1.44841	+	0.388101i	−0.895471	−	0.445120i	$-0.853161\pi$
$677$	−37.6865	+	10.0981i	−1.44841	+	0.388101i	−0.552940	+	0.833221i	$0.686494\pi$
$678$		0			0
$679$	−7.98076	+	4.60770i	−0.306274	+	0.176827i
$680$		0			0
$681$	−1.39230	+	1.39230i	−0.0533532	+	0.0533532i
$682$		0			0
$683$	3.00000	−	3.00000i	0.114792	−	0.114792i	−0.647378	−	0.762169i	$-0.724134\pi$
$683$	3.00000	−	3.00000i	0.114792	−	0.114792i	0.762169	+	0.647378i	$0.224134\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−4.33013	+	7.50000i	−0.165205	+	0.286143i
$688$		0			0
$689$	14.1962	+	24.5885i	0.540830	+	0.936746i
$690$		0			0
$691$	19.5885	−	33.9282i	0.745180	−	1.29069i	−0.204931	−	0.978777i	$-0.565697\pi$
$691$	19.5885	−	33.9282i	0.745180	−	1.29069i	0.950111	−	0.311913i	$-0.100970\pi$
$692$		0			0
$693$	2.41154	+	2.41154i	0.0916069	+	0.0916069i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	26.4904	+	7.09808i	1.00339	+	0.268859i
$698$		0			0
$699$	−7.09808	+	26.4904i	−0.268474	+	1.00196i
$700$		0			0
$701$			11.5359i			0.435705i	0.975982	+	0.217852i	$0.0699052\pi$
$701$			11.5359i			0.435705i	−0.975982	+	0.217852i	$0.930095\pi$
$702$		0			0
$703$	27.1244	+	27.1244i	1.02301	+	1.02301i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	3.00000	−	11.1962i	0.112827	−	0.421075i
$708$		0			0
$709$	25.1147	+	14.5000i	0.943204	+	0.544559i	0.890963	−	0.454076i	$-0.150030\pi$
$709$	25.1147	+	14.5000i	0.943204	+	0.544559i	0.0522406	+	0.998635i	$0.483364\pi$
$710$		0			0
$711$	−5.19615	+	3.00000i	−0.194871	+	0.112509i
$712$		0			0
$713$	1.68653	+	6.29423i	0.0631612	+	0.235721i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	27.0000	+	15.5885i	1.00833	+	0.582162i
$718$		0			0
$719$	23.3205			0.869708			0.434854	−	0.900501i	$-0.356800\pi$
$719$	23.3205			0.869708			0.434854	+	0.900501i	$0.356800\pi$
$720$		0			0
$721$	0.588457			0.0219153
$722$		0			0
$723$		−	15.9282i		−	0.592376i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−6.40192	−	23.8923i	−0.237434	−	0.886117i	−0.977036	−	0.213072i	$-0.931653\pi$
$727$	−6.40192	−	23.8923i	−0.237434	−	0.886117i	0.739602	−	0.673044i	$-0.235014\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	−15.5885	−	9.00000i	−0.576560	−	0.332877i
$732$		0			0
$733$	4.39230	−	16.3923i	0.162233	−	0.605464i	−0.836143	−	0.548511i	$-0.815195\pi$
$733$	4.39230	−	16.3923i	0.162233	−	0.605464i	0.998377	−	0.0569527i	$-0.0181384\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−10.1769	−	10.1769i	−0.374871	−	0.374871i
$738$		0			0
$739$			32.3923i			1.19157i	0.803144	+	0.595785i	$0.203159\pi$
$739$			32.3923i			1.19157i	−0.803144	+	0.595785i	$0.796841\pi$
$740$		0			0
$741$	−17.1962	+	4.60770i	−0.631716	+	0.169268i
$742$		0			0
$743$	9.69615	+	2.59808i	0.355717	+	0.0953142i	0.432252	−	0.901753i	$-0.357719\pi$
$743$	9.69615	+	2.59808i	0.355717	+	0.0953142i	−0.0765349	+	0.997067i	$0.524386\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	29.0885	+	7.79423i	1.06429	+	0.285176i
$748$		0			0
$749$	−8.30385	+	14.3827i	−0.303416	+	0.525532i
$750$		0			0
$751$	−4.49038	−	7.77757i	−0.163856	−	0.283807i	0.772392	−	0.635146i	$-0.219060\pi$
$751$	−4.49038	−	7.77757i	−0.163856	−	0.283807i	−0.936249	+	0.351338i	$0.885727\pi$
$752$		0			0
$753$	21.2942	+	36.8827i	0.776005	+	1.34408i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	13.7321	−	13.7321i	0.499100	−	0.499100i	−0.412058	−	0.911158i	$-0.635190\pi$
$757$	13.7321	−	13.7321i	0.499100	−	0.499100i	0.911158	+	0.412058i	$0.135190\pi$
$758$		0			0
$759$	3.29423	+	0.882686i	0.119573	+	0.0320395i
$760$		0			0
$761$	−17.8923	+	10.3301i	−0.648596	+	0.374467i	−0.787918	−	0.615780i	$-0.788841\pi$
$761$	−17.8923	+	10.3301i	−0.648596	+	0.374467i	0.139322	+	0.990247i	$0.455508\pi$
$762$		0			0
$763$	−1.03590	+	0.277568i	−0.0375020	+	0.0100486i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−6.00000	+	1.60770i	−0.216647	+	0.0580505i
$768$		0			0
$769$	−42.0622	+	24.2846i	−1.51680	+	0.875725i	−0.516996	+	0.855988i	$0.672950\pi$
$769$	−42.0622	+	24.2846i	−1.51680	+	0.875725i	−0.999805	+	0.0197374i	$0.993717\pi$
$770$		0			0
$771$	−10.3923	−	38.7846i	−0.374270	−	1.39679i
$772$		0			0
$773$	4.39230	−	4.39230i	0.157980	−	0.157980i	−0.623691	−	0.781671i	$-0.714368\pi$
$773$	4.39230	−	4.39230i	0.157980	−	0.157980i	0.781671	+	0.623691i	$0.214368\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−14.1962			−0.509284
$778$		0			0
$779$	−13.5622	−	23.4904i	−0.485915	−	0.841630i
$780$		0			0
$781$	−7.39230	+	12.8038i	−0.264517	+	0.458158i
$782$		0			0
$783$	−34.7942	−	20.0885i	−1.24344	−	0.717903i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	0.633975	+	0.169873i	0.0225988	+	0.00605532i	0.270101	−	0.962832i	$-0.412943\pi$
$787$	0.633975	+	0.169873i	0.0225988	+	0.00605532i	−0.247502	+	0.968887i	$0.579610\pi$
$788$		0			0
$789$	5.19615	+	5.19615i	0.184988	+	0.184988i
$790$		0			0
$791$		−	4.82309i		−	0.171489i
$792$		0			0
$793$	−5.53590	−	5.53590i	−0.196586	−	0.196586i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−9.50962	+	35.4904i	−0.336848	+	1.25713i	0.565004	+	0.825088i	$0.308875\pi$
$797$	−9.50962	+	35.4904i	−0.336848	+	1.25713i	−0.901852	+	0.432046i	$0.857792\pi$
$798$		0			0
$799$	32.7058	+	18.8827i	1.15705	+	0.668021i
$800$		0			0
$801$	−3.99038	+	6.91154i	−0.140993	+	0.244207i
$802$		0			0
$803$	−4.39230	−	16.3923i	−0.155001	−	0.578472i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−25.2846	+	14.5981i	−0.890060	+	0.513877i
$808$		0			0
$809$	−33.7128			−1.18528			−0.592640	−	0.805468i	$-0.701914\pi$
$809$	−33.7128			−1.18528			−0.592640	+	0.805468i	$0.701914\pi$
$810$		0			0
$811$	14.3923			0.505382			0.252691	−	0.967547i	$-0.418684\pi$
$811$	14.3923			0.505382			0.252691	+	0.967547i	$0.418684\pi$
$812$		0			0
$813$	−0.294229	+	0.169873i	−0.0103190	+	0.00595771i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	4.60770	+	17.1962i	0.161203	+	0.601617i
$818$		0			0
$819$	3.29423	−	5.70577i	0.115110	−	0.199376i
$820$		0			0
$821$	5.81347	+	3.35641i	0.202891	+	0.117139i	0.598003	−	0.801494i	$-0.295961\pi$
$821$	5.81347	+	3.35641i	0.202891	+	0.117139i	−0.395112	+	0.918633i	$0.629294\pi$
$822$		0			0
$823$	1.08142	−	4.03590i	0.0376958	−	0.140683i	−0.944513	−	0.328473i	$-0.893466\pi$
$823$	1.08142	−	4.03590i	0.0376958	−	0.140683i	0.982209	+	0.187791i	$0.0601326\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	14.4904	+	14.4904i	0.503880	+	0.503880i	0.912641	−	0.408761i	$-0.134039\pi$
$827$	14.4904	+	14.4904i	0.503880	+	0.503880i	−0.408761	+	0.912641i	$0.634039\pi$
$828$		0			0
$829$			17.9808i			0.624498i	0.950000	+	0.312249i	$0.101082\pi$
$829$			17.9808i			0.624498i	−0.950000	+	0.312249i	$0.898918\pi$
$830$		0			0
$831$	−11.7846	−	11.7846i	−0.408804	−	0.408804i
$832$		0			0
$833$	25.3923	+	6.80385i	0.879791	+	0.235739i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	18.8827	−	10.9019i	0.652681	−	0.376826i
$838$		0			0
$839$	−22.5622	+	39.0788i	−0.778933	+	1.34915i	0.153624	+	0.988129i	$0.450905\pi$
$839$	−22.5622	+	39.0788i	−0.778933	+	1.34915i	−0.932557	+	0.361022i	$0.882428\pi$
$840$		0			0
$841$	−15.3923	−	26.6603i	−0.530769	−	0.919319i
$842$		0			0
$843$	−33.5885			−1.15685
$844$		0			0
$845$		0			0
$846$		0			0
$847$	5.95448	−	5.95448i	0.204598	−	0.204598i
$848$		0			0
$849$	11.5981	+	43.2846i	0.398045	+	1.48552i
$850$		0			0
$851$	−12.2942	+	7.09808i	−0.421441	+	0.243319i
$852$		0			0
$853$	39.4186	−	10.5622i	1.34967	−	0.361642i	0.489655	−	0.871916i	$-0.337123\pi$
$853$	39.4186	−	10.5622i	1.34967	−	0.361642i	0.860012	+	0.510274i	$0.170456\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	34.6865	−	9.29423i	1.18487	−	0.317485i	0.388013	−	0.921654i	$-0.373161\pi$
$857$	34.6865	−	9.29423i	1.18487	−	0.317485i	0.796856	+	0.604169i	$0.206495\pi$
$858$		0			0
$859$	20.6147	−	11.9019i	0.703366	−	0.406088i	−0.105234	−	0.994447i	$-0.533559\pi$
$859$	20.6147	−	11.9019i	0.703366	−	0.406088i	0.808600	+	0.588359i	$0.200226\pi$
$860$		0			0
$861$	9.69615	+	2.59808i	0.330444	+	0.0885422i
$862$		0			0
$863$	10.0981	−	10.0981i	0.343743	−	0.343743i	−0.514030	−	0.857772i	$-0.671848\pi$
$863$	10.0981	−	10.0981i	0.343743	−	0.343743i	0.857772	+	0.514030i	$0.171848\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	0.866025	+	1.50000i	0.0294118	+	0.0509427i
$868$		0			0
$869$	−1.26795	−	2.19615i	−0.0430122	−	0.0744994i
$870$		0			0
$871$	−13.9019	+	24.0788i	−0.471049	+	0.815880i
$872$		0			0
$873$	29.7846	+	7.98076i	1.00806	+	0.270108i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	3.63397	+	0.973721i	0.122711	+	0.0328802i	0.319652	−	0.947535i	$-0.396434\pi$
$877$	3.63397	+	0.973721i	0.122711	+	0.0328802i	−0.196941	+	0.980415i	$0.563101\pi$
$878$		0			0
$879$	−31.6865	+	8.49038i	−1.06876	+	0.286373i
$880$		0			0
$881$			19.1436i			0.644964i	0.946576	+	0.322482i	$0.104517\pi$
$881$			19.1436i			0.644964i	−0.946576	+	0.322482i	$0.895483\pi$
$882$		0			0
$883$	−6.75833	−	6.75833i	−0.227436	−	0.227436i	0.584185	−	0.811621i	$-0.301414\pi$
$883$	−6.75833	−	6.75833i	−0.227436	−	0.227436i	−0.811621	+	0.584185i	$0.801414\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	4.90192	−	18.2942i	0.164590	−	0.614260i	−0.833502	−	0.552517i	$-0.813667\pi$
$887$	4.90192	−	18.2942i	0.164590	−	0.614260i	0.998092	−	0.0617430i	$-0.0196659\pi$
$888$		0			0
$889$	−14.3827	−	8.30385i	−0.482380	−	0.278502i
$890$		0			0
$891$		−	11.4115i		−	0.382301i
$892$		0			0
$893$	−9.66730	−	36.0788i	−0.323504	−	1.20733i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		−	6.58846i		−	0.219982i
$898$		0			0
$899$	32.4449			1.08210
$900$		0			0
$901$	−49.1769			−1.63832
$902$		0			0
$903$	−5.70577	−	3.29423i	−0.189876	−	0.109625i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	10.3301	+	38.5526i	0.343006	+	1.28012i	0.894924	+	0.446218i	$0.147229\pi$
$907$	10.3301	+	38.5526i	0.343006	+	1.28012i	−0.551918	+	0.833898i	$0.686104\pi$
$908$		0			0
$909$	−33.5885	+	19.3923i	−1.11406	+	0.643202i
$910$		0			0
$911$	−28.9808	−	16.7321i	−0.960175	−	0.554358i	−0.0639484	−	0.997953i	$-0.520369\pi$
$911$	−28.9808	−	16.7321i	−0.960175	−	0.554358i	−0.896227	+	0.443596i	$0.853703\pi$
$912$		0			0
$913$	−3.29423	+	12.2942i	−0.109023	+	0.406880i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	4.98076	+	4.98076i	0.164479	+	0.164479i
$918$		0			0
$919$		−	21.6077i		−	0.712772i	−0.934339	−	0.356386i	$-0.884009\pi$
$919$		−	21.6077i		−	0.712772i	0.934339	−	0.356386i	$-0.115991\pi$
$920$		0			0
$921$	−1.20577	+	4.50000i	−0.0397315	+	0.148280i
$922$		0			0
$923$	27.5885	+	7.39230i	0.908085	+	0.243321i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−1.39230	−	1.39230i	−0.0457293	−	0.0457293i
$928$		0			0
$929$	−2.53590	+	4.39230i	−0.0832001	+	0.144107i	−0.904623	−	0.426213i	$-0.859847\pi$
$929$	−2.53590	+	4.39230i	−0.0832001	+	0.144107i	0.821423	+	0.570320i	$0.193181\pi$
$930$		0			0
$931$	−13.0000	−	22.5167i	−0.426058	−	0.737954i
$932$		0			0
$933$	16.9019	−	29.2750i	0.553344	−	0.958420i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−32.4449	+	32.4449i	−1.05993	+	1.05993i	−0.0618415	+	0.998086i	$0.519697\pi$
$937$	−32.4449	+	32.4449i	−1.05993	+	1.05993i	−0.998086	+	0.0618415i	$0.980303\pi$
$938$		0			0
$939$	6.80385	−	6.80385i	0.222035	−	0.222035i
$940$		0			0
$941$	2.08846	−	1.20577i	0.0680818	−	0.0393070i	−0.465573	−	0.885010i	$-0.654152\pi$
$941$	2.08846	−	1.20577i	0.0680818	−	0.0393070i	0.533654	+	0.845703i	$0.320818\pi$
$942$		0			0
$943$	9.69615	−	2.59808i	0.315750	−	0.0846050i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−30.1865	+	8.08846i	−0.980931	+	0.262840i	−0.713436	−	0.700720i	$-0.752862\pi$
$947$	−30.1865	+	8.08846i	−0.980931	+	0.262840i	−0.267494	+	0.963559i	$0.586196\pi$
$948$		0			0
$949$	−28.3923	+	16.3923i	−0.921653	+	0.532117i
$950$		0			0
$951$	−27.0000	+	27.0000i	−0.875535	+	0.875535i
$952$		0			0
$953$	−6.80385	+	6.80385i	−0.220398	+	0.220398i	−0.808666	−	0.588268i	$-0.799810\pi$
$953$	−6.80385	+	6.80385i	−0.220398	+	0.220398i	0.588268	+	0.808666i	$0.299810\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	8.49038	−	14.7058i	0.274455	−	0.475370i
$958$		0			0
$959$	9.00000	+	15.5885i	0.290625	+	0.503378i
$960$		0			0
$961$	6.69615	−	11.5981i	0.216005	−	0.374131i
$962$		0			0
$963$	53.6769	−	14.3827i	1.72971	−	0.463476i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−23.2583	−	6.23205i	−0.747937	−	0.200409i	−0.135334	−	0.990800i	$-0.543211\pi$
$967$	−23.2583	−	6.23205i	−0.747937	−	0.200409i	−0.612603	+	0.790391i	$0.709878\pi$
$968$		0			0
$969$	7.98076	−	29.7846i	0.256379	−	0.956820i
$970$		0			0
$971$		−	40.0526i		−	1.28535i	−0.766140	−	0.642674i	$-0.777825\pi$
$971$		−	40.0526i		−	1.28535i	0.766140	−	0.642674i	$-0.222175\pi$
$972$		0			0
$973$	−7.85641	−	7.85641i	−0.251865	−	0.251865i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	10.0981	−	37.6865i	0.323066	−	1.20570i	−0.593176	−	0.805073i	$-0.702126\pi$
$977$	10.0981	−	37.6865i	0.323066	−	1.20570i	0.916242	−	0.400626i	$-0.131207\pi$
$978$		0			0
$979$	−2.92116	−	1.68653i	−0.0933607	−	0.0539018i
$980$		0			0
$981$	3.10770	+	1.79423i	0.0992211	+	0.0572853i
$982$		0			0
$983$	5.59808	+	20.8923i	0.178551	+	0.666361i	0.995920	+	0.0902460i	$0.0287653\pi$
$983$	5.59808	+	20.8923i	0.178551	+	0.666361i	−0.817369	+	0.576115i	$0.804568\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	11.9711	+	6.91154i	0.381046	+	0.219997i
$988$		0			0
$989$	−6.58846			−0.209501
$990$		0			0
$991$	8.00000			0.254128			0.127064	−	0.991894i	$-0.459445\pi$
$991$	8.00000			0.254128			0.127064	+	0.991894i	$0.459445\pi$
$992$		0			0
$993$			6.24871i			0.198297i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−12.8038	−	47.7846i	−0.405502	−	1.51335i	−0.803128	−	0.595806i	$-0.796833\pi$
$997$	−12.8038	−	47.7846i	−0.405502	−	1.51335i	0.397626	−	0.917547i	$-0.369834\pi$
$998$		0			0
$999$	33.5885	+	33.5885i	1.06269	+	1.06269i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.be.d.893.1	yes	4
3.2	odd	2		2700.2.bf.a.1493.1		4
5.2	odd	4		900.2.be.b.857.1	yes	4
5.3	odd	4		900.2.be.c.857.1	yes	4
5.4	even	2		900.2.be.a.893.1	yes	4
9.4	even	3		2700.2.bf.b.2393.1		4
9.5	odd	6		900.2.be.b.293.1	yes	4
15.2	even	4		2700.2.bf.b.2357.1		4
15.8	even	4		2700.2.bf.c.2357.1		4
15.14	odd	2		2700.2.bf.d.1493.1		4
45.4	even	6		2700.2.bf.c.2393.1		4
45.13	odd	12		2700.2.bf.d.557.1		4
45.14	odd	6		900.2.be.c.293.1	yes	4
45.22	odd	12		2700.2.bf.a.557.1		4
45.23	even	12		900.2.be.a.257.1	✓	4
45.32	even	12	inner	900.2.be.d.257.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
900.2.be.a.257.1	✓	4	45.23	even	12
900.2.be.a.893.1	yes	4	5.4	even	2
900.2.be.b.293.1	yes	4	9.5	odd	6
900.2.be.b.857.1	yes	4	5.2	odd	4
900.2.be.c.293.1	yes	4	45.14	odd	6
900.2.be.c.857.1	yes	4	5.3	odd	4
900.2.be.d.257.1	yes	4	45.32	even	12	inner
900.2.be.d.893.1	yes	4	1.1	even	1	trivial
2700.2.bf.a.557.1		4	45.22	odd	12
2700.2.bf.a.1493.1		4	3.2	odd	2
2700.2.bf.b.2357.1		4	15.2	even	4
2700.2.bf.b.2393.1		4	9.4	even	3
2700.2.bf.c.2357.1		4	15.8	even	4
2700.2.bf.c.2393.1		4	45.4	even	6
2700.2.bf.d.557.1		4	45.13	odd	12
2700.2.bf.d.1493.1		4	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 - 0.866025i) q^{3} +(0.232051 + 0.866025i) q^{7} +(1.50000 - 2.59808i) q^{9} +(1.09808 + 0.633975i) q^{11} +(0.633975 - 2.36603i) q^{13} +(3.00000 + 3.00000i) q^{17} -4.19615i q^{19} +(1.09808 + 1.09808i) q^{21} +(1.50000 + 0.401924i) q^{23} -5.19615i q^{27} +(3.86603 - 6.69615i) q^{29} +(2.09808 + 3.63397i) q^{31} +2.19615 q^{33} +(-6.46410 + 6.46410i) q^{37} +(-1.09808 - 4.09808i) q^{39} +(5.59808 - 3.23205i) q^{41} +(-4.09808 + 1.09808i) q^{43} +(8.59808 - 2.30385i) q^{47} +(5.36603 - 3.09808i) q^{49} +(7.09808 + 1.90192i) q^{51} +(-8.19615 + 8.19615i) q^{53} +(-3.63397 - 6.29423i) q^{57} +(-1.26795 - 2.19615i) q^{59} +(1.59808 - 2.76795i) q^{61} +(2.59808 + 0.696152i) q^{63} +(-10.9641 - 2.93782i) q^{67} +(2.59808 - 0.696152i) q^{69} +11.6603i q^{71} +(-9.46410 - 9.46410i) q^{73} +(-0.294229 + 1.09808i) q^{77} +(-1.73205 - 1.00000i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(2.59808 + 9.69615i) q^{83} -13.3923i q^{87} -2.66025 q^{89} +2.19615 q^{91} +(6.29423 + 3.63397i) q^{93} +(2.66025 + 9.92820i) q^{97} +(3.29423 - 1.90192i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{3} - 6 q^{7} + 6 q^{9} - 6 q^{11} + 6 q^{13} + 12 q^{17} - 6 q^{21} + 6 q^{23} + 12 q^{29} - 2 q^{31} - 12 q^{33} - 12 q^{37} + 6 q^{39} + 12 q^{41} - 6 q^{43} + 24 q^{47} + 18 q^{49} + 18 q^{51}+ \cdots - 18 q^{99}+O(q^{100}) \) 4 * q + 6 * q^3 - 6 * q^7 + 6 * q^9 - 6 * q^11 + 6 * q^13 + 12 * q^17 - 6 * q^21 + 6 * q^23 + 12 * q^29 - 2 * q^31 - 12 * q^33 - 12 * q^37 + 6 * q^39 + 12 * q^41 - 6 * q^43 + 24 * q^47 + 18 * q^49 + 18 * q^51 - 12 * q^53 - 18 * q^57 - 12 * q^59 - 4 * q^61 - 30 * q^67 - 24 * q^73 + 30 * q^77 - 18 * q^81 + 24 * q^89 - 12 * q^91 - 6 * q^93 - 24 * q^97 - 18 * q^99

Introduction

L-functions

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