LMFDB - Embedded newform 864.2.bf.a.49.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [864,2,Mod(49,864)] 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("864.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(864, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 14])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bf (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			49.13
Character	$\chi$	$=$	864.49
Dual form			864.2.bf.a.529.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.684682 - 1.59098i) q^{3} +(-1.15428 - 3.17134i) q^{5} +(-0.593321 - 3.36489i) q^{7} +(-2.06242 + 2.17863i) q^{9} +(0.197048 - 0.541384i) q^{11} +(4.30199 - 5.12691i) q^{13} +(-4.25523 + 4.00779i) q^{15} +(1.15893 - 2.00733i) q^{17} +(0.353289 - 0.203971i) q^{19} +(-4.94723 + 3.24784i) q^{21} +(-1.15186 + 6.53250i) q^{23} +(-4.89486 + 4.10727i) q^{25} +(4.87825 + 1.78960i) q^{27} +(-2.24644 - 2.67721i) q^{29} +(0.382945 - 2.17179i) q^{31} +(-0.996245 + 0.0571774i) q^{33} +(-9.98637 + 5.76564i) q^{35} +(-1.05249 - 0.607656i) q^{37} +(-11.1023 - 3.33407i) q^{39} +(5.09057 + 4.27150i) q^{41} +(-0.442145 + 1.21478i) q^{43} +(9.28978 + 4.02591i) q^{45} +(0.547022 + 3.10232i) q^{47} +(-4.39261 + 1.59878i) q^{49} +(-3.98712 - 0.469453i) q^{51} +9.35460i q^{53} -1.94436 q^{55} +(-0.566405 - 0.422419i) q^{57} +(3.00302 + 8.25072i) q^{59} +(-4.67459 + 0.824257i) q^{61} +(8.55452 + 5.64720i) q^{63} +(-21.2249 - 7.72523i) q^{65} +(9.67062 - 11.5250i) q^{67} +(11.1817 - 2.64011i) q^{69} +(3.92323 - 6.79524i) q^{71} +(0.641809 + 1.11165i) q^{73} +(9.88600 + 4.97543i) q^{75} +(-1.93861 - 0.341829i) q^{77} +(-3.84081 + 3.22282i) q^{79} +(-0.492839 - 8.98650i) q^{81} +(-6.67152 - 7.95081i) q^{83} +(-7.70366 - 1.35836i) q^{85} +(-2.72128 + 5.40708i) q^{87} +(-2.86501 - 4.96234i) q^{89} +(-19.8040 - 11.4338i) q^{91} +(-3.71746 + 0.877728i) q^{93} +(-1.05466 - 0.884962i) q^{95} +(10.5548 + 3.84165i) q^{97} +(0.773079 + 1.54586i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 12 q^{7} - 12 q^{9} + 12 q^{15} - 6 q^{17} + 12 q^{23} - 12 q^{25} + 12 q^{31} + 12 q^{39} - 24 q^{41} + 12 q^{47} - 12 q^{49} + 24 q^{55} - 30 q^{57} + 72 q^{63} - 12 q^{65} + 90 q^{71} - 6 q^{73}+ \cdots - 12 q^{97}+O(q^{100}) $ 204 * q + 12 * q^7 - 12 * q^9 + 12 * q^15 - 6 * q^17 + 12 * q^23 - 12 * q^25 + 12 * q^31 + 12 * q^39 - 24 * q^41 + 12 * q^47 - 12 * q^49 + 24 * q^55 - 30 * q^57 + 72 * q^63 - 12 * q^65 + 90 * q^71 - 6 * q^73 + 12 * q^79 - 12 * q^81 + 48 * q^87 - 6 * q^89 + 42 * q^95 - 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$-1$	$e\left(\frac{7}{9}\right)$	$1$

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
$3$	−0.684682	−	1.59098i	−0.395301	−	0.918551i
$3$	−0.684682	−	1.59098i	−0.395301	−	0.918551i
$4$		0			0
$5$	−1.15428	−	3.17134i	−0.516208	−	1.41827i	−0.874667	−	0.484723i	$-0.838920\pi$
$5$	−1.15428	−	3.17134i	−0.516208	−	1.41827i	0.358460	−	0.933545i	$-0.383302\pi$
$6$		0			0
$7$	−0.593321	−	3.36489i	−0.224254	−	1.27181i	−0.864106	−	0.503311i	$-0.832115\pi$
$7$	−0.593321	−	3.36489i	−0.224254	−	1.27181i	0.639851	−	0.768499i	$-0.278996\pi$
$8$		0			0
$9$	−2.06242	+	2.17863i	−0.687474	+	0.726209i
$10$		0			0
$11$	0.197048	−	0.541384i	0.0594121	−	0.163233i	−0.906435	−	0.422344i	$-0.861207\pi$
$11$	0.197048	−	0.541384i	0.0594121	−	0.163233i	0.965848	+	0.259111i	$0.0834295\pi$
$12$		0			0
$13$	4.30199	−	5.12691i	1.19316	−	1.42195i	0.311379	−	0.950286i	$-0.399209\pi$
$13$	4.30199	−	5.12691i	1.19316	−	1.42195i	0.881779	−	0.471664i	$-0.156346\pi$
$14$		0			0
$15$	−4.25523	+	4.00779i	−1.09870	+	1.03481i
$16$		0			0
$17$	1.15893	−	2.00733i	0.281082	−	0.486849i	−0.690569	−	0.723266i	$-0.742640\pi$
$17$	1.15893	−	2.00733i	0.281082	−	0.486849i	0.971652	+	0.236417i	$0.0759732\pi$
$18$		0			0
$19$	0.353289	−	0.203971i	0.0810500	−	0.0467943i	−0.458927	−	0.888474i	$-0.651766\pi$
$19$	0.353289	−	0.203971i	0.0810500	−	0.0467943i	0.539977	+	0.841680i	$0.318433\pi$
$20$		0			0
$21$	−4.94723	+	3.24784i	−1.07957	+	0.708737i
$22$		0			0
$23$	−1.15186	+	6.53250i	−0.240178	+	1.36212i	0.591250	+	0.806488i	$0.298635\pi$
$23$	−1.15186	+	6.53250i	−0.240178	+	1.36212i	−0.831429	+	0.555631i	$0.812477\pi$
$24$		0			0
$25$	−4.89486	+	4.10727i	−0.978971	+	0.821454i
$26$		0			0
$27$	4.87825	+	1.78960i	0.938820	+	0.344408i
$28$		0			0
$29$	−2.24644	−	2.67721i	−0.417154	−	0.497145i	0.516016	−	0.856579i	$-0.327414\pi$
$29$	−2.24644	−	2.67721i	−0.417154	−	0.497145i	−0.933171	+	0.359434i	$0.882970\pi$
$30$		0			0
$31$	0.382945	−	2.17179i	0.0687790	−	0.390065i	−0.930913	−	0.365241i	$-0.880986\pi$
$31$	0.382945	−	2.17179i	0.0687790	−	0.390065i	0.999692	−	0.0248236i	$-0.00790240\pi$
$32$		0			0
$33$	−0.996245	+	0.0571774i	−0.173424	+	0.00995332i
$34$		0			0
$35$	−9.98637	+	5.76564i	−1.68801	+	0.974570i
$36$		0			0
$37$	−1.05249	−	0.607656i	−0.173028	−	0.0998980i	0.410985	−	0.911642i	$-0.365185\pi$
$37$	−1.05249	−	0.607656i	−0.173028	−	0.0998980i	−0.584013	+	0.811744i	$0.698518\pi$
$38$		0			0
$39$	−11.1023	−	3.33407i	−1.77779	−	0.533878i
$40$		0			0
$41$	5.09057	+	4.27150i	0.795014	+	0.667096i	0.946981	−	0.321290i	$-0.104116\pi$
$41$	5.09057	+	4.27150i	0.795014	+	0.667096i	−0.151967	+	0.988386i	$0.548561\pi$
$42$		0			0
$43$	−0.442145	+	1.21478i	−0.0674265	+	0.185253i	−0.968830	−	0.247728i	$-0.920316\pi$
$43$	−0.442145	+	1.21478i	−0.0674265	+	0.185253i	0.901403	+	0.432981i	$0.142538\pi$
$44$		0			0
$45$	9.28978	+	4.02591i	1.38484	+	0.600148i
$46$		0			0
$47$	0.547022	+	3.10232i	0.0797914	+	0.452520i	0.998359	+	0.0572567i	$0.0182354\pi$
$47$	0.547022	+	3.10232i	0.0797914	+	0.452520i	−0.918568	+	0.395263i	$0.870654\pi$
$48$		0			0
$49$	−4.39261	+	1.59878i	−0.627516	+	0.228397i
$50$		0			0
$51$	−3.98712	−	0.469453i	−0.558308	−	0.0657366i
$52$		0			0
$53$			9.35460i			1.28495i	0.766305	+	0.642477i	$0.222093\pi$
$53$			9.35460i			1.28495i	−0.766305	+	0.642477i	$0.777907\pi$
$54$		0			0
$55$	−1.94436			−0.262178
$56$		0			0
$57$	−0.566405	−	0.422419i	−0.0750221	−	0.0559508i
$58$		0			0
$59$	3.00302	+	8.25072i	0.390959	+	1.07415i	0.966564	+	0.256424i	$0.0825444\pi$
$59$	3.00302	+	8.25072i	0.390959	+	1.07415i	−0.575605	+	0.817728i	$0.695233\pi$
$60$		0			0
$61$	−4.67459	+	0.824257i	−0.598520	+	0.105535i	−0.464697	−	0.885470i	$-0.653837\pi$
$61$	−4.67459	+	0.824257i	−0.598520	+	0.105535i	−0.133824	+	0.991005i	$0.542726\pi$
$62$		0			0
$63$	8.55452	+	5.64720i	1.07777	+	0.711480i
$64$		0			0
$65$	−21.2249	−	7.72523i	−2.63262	−	0.958196i
$66$		0			0
$67$	9.67062	−	11.5250i	1.18145	−	1.40800i	0.288723	−	0.957413i	$-0.406769\pi$
$67$	9.67062	−	11.5250i	1.18145	−	1.40800i	0.892731	−	0.450589i	$-0.148786\pi$
$68$		0			0
$69$	11.1817	−	2.64011i	1.34612	−	0.317831i
$70$		0			0
$71$	3.92323	−	6.79524i	0.465602	−	0.806446i	−0.533627	−	0.845720i	$-0.679171\pi$
$71$	3.92323	−	6.79524i	0.465602	−	0.806446i	0.999228	+	0.0392740i	$0.0125045\pi$
$72$		0			0
$73$	0.641809	+	1.11165i	0.0751180	+	0.130108i	0.901138	−	0.433533i	$-0.142733\pi$
$73$	0.641809	+	1.11165i	0.0751180	+	0.130108i	−0.826020	+	0.563641i	$0.809400\pi$
$74$		0			0
$75$	9.88600	+	4.97543i	1.14154	+	0.574513i
$76$		0			0
$77$	−1.93861	−	0.341829i	−0.220925	−	0.0389551i
$78$		0			0
$79$	−3.84081	+	3.22282i	−0.432125	+	0.362596i	−0.832753	−	0.553645i	$-0.813236\pi$
$79$	−3.84081	+	3.22282i	−0.432125	+	0.362596i	0.400628	+	0.916241i	$0.368792\pi$
$80$		0			0
$81$	−0.492839	−	8.98650i	−0.0547599	−	0.998500i
$82$		0			0
$83$	−6.67152	−	7.95081i	−0.732295	−	0.872715i	0.263468	−	0.964668i	$-0.415134\pi$
$83$	−6.67152	−	7.95081i	−0.732295	−	0.872715i	−0.995763	+	0.0919529i	$0.970689\pi$
$84$		0			0
$85$	−7.70366	−	1.35836i	−0.835580	−	0.147335i
$86$		0			0
$87$	−2.72128	+	5.40708i	−0.291752	+	0.579700i
$88$		0			0
$89$	−2.86501	−	4.96234i	−0.303690	−	0.526007i	0.673278	−	0.739389i	$-0.264886\pi$
$89$	−2.86501	−	4.96234i	−0.303690	−	0.526007i	−0.976969	+	0.213382i	$0.931552\pi$
$90$		0			0
$91$	−19.8040	−	11.4338i	−2.07602	−	1.19859i
$92$		0			0
$93$	−3.71746	+	0.877728i	−0.385483	+	0.0910161i
$94$		0			0
$95$	−1.05466	−	0.884962i	−0.108205	−	0.0907952i
$96$		0			0
$97$	10.5548	+	3.84165i	1.07168	+	0.390061i	0.816806	−	0.576913i	$-0.195743\pi$
$97$	10.5548	+	3.84165i	1.07168	+	0.390061i	0.254877	+	0.966974i	$0.417965\pi$
$98$		0			0
$99$	0.773079	+	1.54586i	0.0776974	+	0.155364i
$100$		0			0
$101$	−12.2411	+	2.15844i	−1.21804	+	0.214773i	−0.745481	−	0.666527i	$-0.767780\pi$
$101$	−12.2411	+	2.15844i	−1.21804	+	0.214773i	−0.472557	+	0.881300i	$0.656669\pi$
$102$		0			0
$103$	14.8537	−	5.40632i	1.46358	−	0.532701i	0.517233	−	0.855844i	$-0.326962\pi$
$103$	14.8537	−	5.40632i	1.46358	−	0.532701i	0.946350	+	0.323144i	$0.104740\pi$
$104$		0			0
$105$	16.0105	+	11.9405i	1.56246	+	1.16527i
$106$		0			0
$107$		−	2.44491i		−	0.236359i	−0.992992	−	0.118179i	$-0.962294\pi$
$107$		−	2.44491i		−	0.236359i	0.992992	−	0.118179i	$-0.0377058\pi$
$108$		0			0
$109$		−	16.2522i		−	1.55668i	−0.627843	−	0.778340i	$-0.716062\pi$
$109$		−	16.2522i		−	1.55668i	0.627843	−	0.778340i	$-0.283938\pi$
$110$		0			0
$111$	−0.246146	+	2.09054i	−0.0233631	+	0.198425i
$112$		0			0
$113$	−11.4376	+	4.16294i	−1.07596	+	0.391617i	−0.818402	−	0.574646i	$-0.805140\pi$
$113$	−11.4376	+	4.16294i	−1.07596	+	0.391617i	−0.257556	+	0.966263i	$0.582917\pi$
$114$		0			0
$115$	22.0464	−	3.88737i	2.05583	−	0.362499i
$116$		0			0
$117$	2.29712	+	19.9463i	0.212369	+	1.84403i
$118$		0			0
$119$	−7.44207	−	2.70869i	−0.682213	−	0.248305i
$120$		0			0
$121$	8.17222	+	6.85731i	0.742929	+	0.623392i
$122$		0			0
$123$	3.31044	−	11.0236i	0.298492	−	0.993965i
$124$		0			0
$125$	4.06195	+	2.34517i	0.363312	+	0.209758i
$126$		0			0
$127$	4.79341	+	8.30243i	0.425346	+	0.736722i	0.996453	−	0.0841546i	$-0.0268189\pi$
$127$	4.79341	+	8.30243i	0.425346	+	0.736722i	−0.571106	+	0.820876i	$0.693486\pi$
$128$		0			0
$129$	2.23542	−	0.128297i	0.196818	−	0.0112960i
$130$		0			0
$131$	−0.406480	−	0.0716734i	−0.0355143	−	0.00626213i	0.155863	−	0.987779i	$-0.450184\pi$
$131$	−0.406480	−	0.0716734i	−0.0355143	−	0.00626213i	−0.191377	+	0.981517i	$0.561295\pi$
$132$		0			0
$133$	−0.895956	−	1.06776i	−0.0776892	−	0.0925864i
$134$		0			0
$135$	0.0445910	−	17.5363i	0.00383778	−	1.50928i
$136$		0			0
$137$	12.0727	−	10.1302i	1.03144	−	0.865480i	0.0404177	−	0.999183i	$-0.487131\pi$
$137$	12.0727	−	10.1302i	1.03144	−	0.865480i	0.991021	+	0.133703i	$0.0426867\pi$
$138$		0			0
$139$	−2.17442	−	0.383409i	−0.184432	−	0.0325204i	0.0806691	−	0.996741i	$-0.474294\pi$
$139$	−2.17442	−	0.383409i	−0.184432	−	0.0325204i	−0.265101	+	0.964221i	$0.585405\pi$
$140$		0			0
$141$	4.56118	−	2.99440i	0.384121	−	0.252174i
$142$		0			0
$143$	−1.92793	−	3.33928i	−0.161222	−	0.279244i
$144$		0			0
$145$	−5.89733	+	10.2145i	−0.489747	+	0.848267i
$146$		0			0
$147$	5.55117	+	5.89389i	0.457853	+	0.486120i
$148$		0			0
$149$	−4.40044	+	5.24424i	−0.360498	+	0.429625i	−0.915558	−	0.402186i	$-0.868251\pi$
$149$	−4.40044	+	5.24424i	−0.360498	+	0.429625i	0.555060	+	0.831810i	$0.312695\pi$
$150$		0			0
$151$	−11.0866	−	4.03519i	−0.902213	−	0.328379i	−0.151074	−	0.988522i	$-0.548273\pi$
$151$	−11.0866	−	4.03519i	−0.902213	−	0.328379i	−0.751139	+	0.660144i	$0.770495\pi$
$152$		0			0
$153$	1.98302	+	6.66484i	0.160318	+	0.538821i
$154$		0			0
$155$	−7.32952	+	1.29239i	−0.588721	+	0.103807i
$156$		0			0
$157$	4.12184	+	11.3247i	0.328959	+	0.903808i	0.988376	+	0.152030i	$0.0485810\pi$
$157$	4.12184	+	11.3247i	0.328959	+	0.903808i	−0.659417	+	0.751778i	$0.729197\pi$
$158$		0			0
$159$	14.8830	−	6.40493i	1.18030	−	0.507944i
$160$		0			0
$161$	22.6646			1.78622
$162$		0			0
$163$			13.3972i			1.04935i	0.851303	+	0.524675i	$0.175813\pi$
$163$			13.3972i			1.04935i	−0.851303	+	0.524675i	$0.824187\pi$
$164$		0			0
$165$	1.33127	+	3.09344i	0.103639	+	0.240824i
$166$		0			0
$167$	6.36473	−	2.31657i	0.492517	−	0.179262i	−0.0838081	−	0.996482i	$-0.526708\pi$
$167$	6.36473	−	2.31657i	0.492517	−	0.179262i	0.576325	+	0.817220i	$0.304486\pi$
$168$		0			0
$169$	−5.52068	−	31.3093i	−0.424668	−	2.40841i
$170$		0			0
$171$	−0.284253	+	1.19036i	−0.0217373	+	0.0910291i
$172$		0			0
$173$	0.576454	−	1.58380i	0.0438270	−	0.120414i	−0.915848	−	0.401524i	$-0.868481\pi$
$173$	0.576454	−	1.58380i	0.0438270	−	0.120414i	0.959675	+	0.281111i	$0.0907028\pi$
$174$		0			0
$175$	16.7247	+	14.0337i	1.26427	+	1.06085i
$176$		0			0
$177$	11.0706	−	10.4269i	0.832117	−	0.783730i
$178$		0			0
$179$	−10.3190	−	5.95768i	−0.771279	−	0.445298i	0.0620517	−	0.998073i	$-0.480236\pi$
$179$	−10.3190	−	5.95768i	−0.771279	−	0.445298i	−0.833331	+	0.552775i	$0.813569\pi$
$180$		0			0
$181$	14.3027	−	8.25769i	1.06311	−	0.613789i	0.136822	−	0.990596i	$-0.456311\pi$
$181$	14.3027	−	8.25769i	1.06311	−	0.613789i	0.926292	+	0.376806i	$0.122978\pi$
$182$		0			0
$183$	4.51198	+	6.87282i	0.333536	+	0.508054i
$184$		0			0
$185$	−0.712223	+	4.03922i	−0.0523636	+	0.296969i
$186$		0			0
$187$	−0.858372	−	1.02297i	−0.0627703	−	0.0748068i
$188$		0			0
$189$	3.12744	−	17.4766i	0.227487	−	1.27123i
$190$		0			0
$191$	10.1267	−	8.49734i	0.732745	−	0.614846i	−0.198134	−	0.980175i	$-0.563488\pi$
$191$	10.1267	−	8.49734i	0.732745	−	0.614846i	0.930878	+	0.365329i	$0.119044\pi$
$192$		0			0
$193$	−0.0307325	+	0.174293i	−0.00221218	+	0.0125459i	−0.985894	−	0.167372i	$-0.946472\pi$
$193$	−0.0307325	+	0.174293i	−0.00221218	+	0.0125459i	0.983682	+	0.179918i	$0.0575831\pi$
$194$		0			0
$195$	2.24163	+	39.0576i	0.160527	+	2.79698i
$196$		0			0
$197$	−0.841221	+	0.485679i	−0.0599345	+	0.0346032i	−0.529668	−	0.848205i	$-0.677683\pi$
$197$	−0.841221	+	0.485679i	−0.0599345	+	0.0346032i	0.469733	+	0.882808i	$0.344350\pi$
$198$		0			0
$199$	−2.04926	+	3.54942i	−0.145268	+	0.251612i	−0.929473	−	0.368890i	$-0.879738\pi$
$199$	−2.04926	+	3.54942i	−0.145268	+	0.251612i	0.784205	+	0.620502i	$0.213071\pi$
$200$		0			0
$201$	−24.9573	−	7.49478i	−1.76035	−	0.528641i
$202$		0			0
$203$	−7.67565	+	9.14748i	−0.538725	+	0.642027i
$204$		0			0
$205$	7.67047	−	21.0745i	0.535729	−	1.47190i
$206$		0			0
$207$	−11.8563	−	15.9822i	−0.824068	−	1.11084i
$208$		0			0
$209$	−0.0408121	−	0.231457i	−0.00282303	−	0.0160102i
$210$		0			0
$211$	−1.28341	−	3.52613i	−0.0883534	−	0.242749i	0.887644	−	0.460530i	$-0.152340\pi$
$211$	−1.28341	−	3.52613i	−0.0883534	−	0.242749i	−0.975998	+	0.217781i	$0.930118\pi$
$212$		0			0
$213$	−13.4972	−	1.58920i	−0.924815	−	0.108890i
$214$		0			0
$215$	4.36285			0.297544
$216$		0			0
$217$	−7.53504			−0.511512
$218$		0			0
$219$	1.32917	−	1.78223i	0.0898169	−	0.120432i
$220$		0			0
$221$	−5.30569	−	14.5773i	−0.356899	−	0.980572i
$222$		0			0
$223$	−0.680991	−	3.86209i	−0.0456025	−	0.258625i	0.953480	−	0.301457i	$-0.0974730\pi$
$223$	−0.680991	−	3.86209i	−0.0456025	−	0.258625i	−0.999082	+	0.0428323i	$0.986362\pi$
$224$		0			0
$225$	1.14704	−	19.1350i	0.0764691	−	1.27567i
$226$		0			0
$227$	4.04735	−	11.1200i	0.268632	−	0.738061i	−0.729882	−	0.683573i	$-0.760425\pi$
$227$	4.04735	−	11.1200i	0.268632	−	0.738061i	0.998514	−	0.0544879i	$-0.0173526\pi$
$228$		0			0
$229$	−6.81207	+	8.11831i	−0.450154	+	0.536473i	−0.942624	−	0.333857i	$-0.891650\pi$
$229$	−6.81207	+	8.11831i	−0.450154	+	0.536473i	0.492470	+	0.870330i	$0.336094\pi$
$230$		0			0
$231$	0.783489	+	3.31833i	0.0515498	+	0.218330i
$232$		0			0
$233$	−0.565006	+	0.978619i	−0.0370148	+	0.0641115i	−0.883939	−	0.467602i	$-0.845118\pi$
$233$	−0.565006	+	0.978619i	−0.0370148	+	0.0641115i	0.846925	+	0.531713i	$0.178452\pi$
$234$		0			0
$235$	9.20711	−	5.31572i	0.600605	−	0.346760i
$236$		0			0
$237$	7.75717	+	3.90404i	0.503883	+	0.253594i
$238$		0			0
$239$	−1.00787	+	5.71591i	−0.0651936	+	0.369731i	0.934704	+	0.355427i	$0.115665\pi$
$239$	−1.00787	+	5.71591i	−0.0651936	+	0.369731i	−0.999898	+	0.0143045i	$0.995447\pi$
$240$		0			0
$241$	22.5974	−	18.9615i	1.45563	−	1.22142i	0.527286	−	0.849688i	$-0.323210\pi$
$241$	22.5974	−	18.9615i	1.45563	−	1.22142i	0.928342	−	0.371728i	$-0.121235\pi$
$242$		0			0
$243$	−13.9599	+	6.93699i	−0.895527	+	0.445008i
$244$		0			0
$245$	10.1406	+	12.0851i	0.647857	+	0.772086i
$246$		0			0
$247$	0.474102	−	2.68876i	0.0301664	−	0.171082i
$248$		0			0
$249$	−8.08169	+	16.0580i	−0.512157	+	1.01764i
$250$		0			0
$251$	5.20730	−	3.00644i	0.328682	−	0.189765i	−0.326574	−	0.945172i	$-0.605894\pi$
$251$	5.20730	−	3.00644i	0.328682	−	0.189765i	0.655256	+	0.755407i	$0.272561\pi$
$252$		0			0
$253$	3.30962	+	1.91081i	0.208074	+	0.120132i
$254$		0			0
$255$	3.11343	+	13.1864i	0.194971	+	0.825765i
$256$		0			0
$257$	19.8936	+	16.6927i	1.24093	+	1.04126i	0.997451	+	0.0713589i	$0.0227336\pi$
$257$	19.8936	+	16.6927i	1.24093	+	1.04126i	0.243480	+	0.969906i	$0.421711\pi$
$258$		0			0
$259$	−1.42023	+	3.90205i	−0.0882489	+	0.242462i
$260$		0			0
$261$	10.4658	+	0.627364i	0.647814	+	0.0388329i
$262$		0			0
$263$	2.41565	+	13.6998i	0.148956	+	0.844769i	0.964106	+	0.265519i	$0.0855433\pi$
$263$	2.41565	+	13.6998i	0.148956	+	0.844769i	−0.815150	+	0.579250i	$0.803346\pi$
$264$		0			0
$265$	29.6667	−	10.7978i	1.82241	−	0.663303i
$266$		0			0
$267$	−5.93336	+	7.95579i	−0.363115	+	0.486887i
$268$		0			0
$269$			3.89404i			0.237424i	0.992929	+	0.118712i	$0.0378765\pi$
$269$			3.89404i			0.237424i	−0.992929	+	0.118712i	$0.962123\pi$
$270$		0			0
$271$	−27.1005			−1.64624			−0.823119	−	0.567869i	$-0.807768\pi$
$271$	−27.1005			−1.64624			−0.823119	+	0.567869i	$0.807768\pi$
$272$		0			0
$273$	−4.63154	+	39.3362i	−0.280314	+	2.38073i
$274$		0			0
$275$	1.25909	+	3.45933i	0.0759261	+	0.208605i
$276$		0			0
$277$	−7.05421	+	1.24385i	−0.423847	+	0.0747356i	−0.381503	−	0.924368i	$-0.624593\pi$
$277$	−7.05421	+	1.24385i	−0.423847	+	0.0747356i	−0.0423435	+	0.999103i	$0.513482\pi$
$278$		0			0
$279$	3.94173	+	5.31344i	0.235985	+	0.318107i
$280$		0			0
$281$	−0.728892	−	0.265295i	−0.0434820	−	0.0158262i	0.320188	−	0.947354i	$-0.396254\pi$
$281$	−0.728892	−	0.265295i	−0.0434820	−	0.0158262i	−0.363670	+	0.931528i	$0.618476\pi$
$282$		0			0
$283$	−0.982704	+	1.17114i	−0.0584157	+	0.0696171i	−0.794461	−	0.607315i	$-0.792247\pi$
$283$	−0.982704	+	1.17114i	−0.0584157	+	0.0696171i	0.736045	+	0.676932i	$0.236691\pi$
$284$		0			0
$285$	−0.685850	+	2.28385i	−0.0406263	+	0.135284i
$286$		0			0
$287$	11.3528	−	19.6636i	0.670134	−	1.16071i
$288$		0			0
$289$	5.81375	+	10.0697i	0.341985	+	0.592336i
$290$		0			0
$291$	−1.11473	−	19.4228i	−0.0653469	−	1.13859i
$292$		0			0
$293$	−15.6621	−	2.76164i	−0.914987	−	0.161337i	−0.303720	−	0.952761i	$-0.598229\pi$
$293$	−15.6621	−	2.76164i	−0.914987	−	0.161337i	−0.611267	+	0.791424i	$0.709340\pi$
$294$		0			0
$295$	22.6996	−	19.0472i	1.32162	−	1.10897i
$296$		0			0
$297$	1.93011	−	2.28837i	0.111996	−	0.132785i
$298$		0			0
$299$	28.5363	+	34.0082i	1.65029	+	1.96674i
$300$		0			0
$301$	4.34995	+	0.767013i	0.250727	+	0.0442099i
$302$		0			0
$303$	11.8153	+	17.9975i	0.678772	+	1.03393i
$304$		0			0
$305$	8.00977	+	13.8733i	0.458638	+	0.794385i
$306$		0			0
$307$	−0.370582	−	0.213955i	−0.0211502	−	0.0122111i	0.489388	−	0.872066i	$-0.337220\pi$
$307$	−0.370582	−	0.213955i	−0.0211502	−	0.0122111i	−0.510538	+	0.859855i	$0.670554\pi$
$308$		0			0
$309$	−18.7714	−	19.9304i	−1.06787	−	1.13380i
$310$		0			0
$311$	−8.46179	−	7.10028i	−0.479824	−	0.402620i	0.370539	−	0.928817i	$-0.379173\pi$
$311$	−8.46179	−	7.10028i	−0.479824	−	0.402620i	−0.850363	+	0.526197i	$0.823617\pi$
$312$		0			0
$313$	−26.1193	−	9.50664i	−1.47635	−	0.537347i	−0.526533	−	0.850155i	$-0.676508\pi$
$313$	−26.1193	−	9.50664i	−1.47635	−	0.537347i	−0.949817	+	0.312807i	$0.898731\pi$
$314$		0			0
$315$	8.03493	−	33.6478i	0.452717	−	1.89584i
$316$		0			0
$317$	−3.46040	+	0.610163i	−0.194356	+	0.0342701i	−0.269979	−	0.962866i	$-0.587017\pi$
$317$	−3.46040	+	0.610163i	−0.194356	+	0.0342701i	0.0756229	+	0.997136i	$0.475905\pi$
$318$		0			0
$319$	−1.89205	+	0.688651i	−0.105935	+	0.0385571i
$320$		0			0
$321$	−3.88980	+	1.67399i	−0.217108	+	0.0934329i
$322$		0			0
$323$		−	0.945557i		−	0.0526122i
$324$		0			0
$325$			42.7649i			2.37217i
$326$		0			0
$327$	−25.8569	+	11.1276i	−1.42989	+	0.615358i
$328$		0			0
$329$	10.1144	−	3.68134i	0.557625	−	0.202959i
$330$		0			0
$331$	−17.1533	+	3.02459i	−0.942832	+	0.166247i	−0.623876	−	0.781523i	$-0.714443\pi$
$331$	−17.1533	+	3.02459i	−0.942832	+	0.166247i	−0.318956	+	0.947770i	$0.603332\pi$
$332$		0			0
$333$	3.49454	−	1.03974i	0.191499	−	0.0569776i
$334$		0			0
$335$	−47.7123	−	17.3659i	−2.60680	−	0.948798i
$336$		0			0
$337$	−2.18023	−	1.82943i	−0.118765	−	0.0996554i	0.581471	−	0.813567i	$-0.302477\pi$
$337$	−2.18023	−	1.82943i	−0.118765	−	0.0996554i	−0.700236	+	0.713912i	$0.746922\pi$
$338$		0			0
$339$	14.4543	+	15.3467i	0.785048	+	0.833516i
$340$		0			0
$341$	−1.10031	−	0.635266i	−0.0595853	−	0.0344016i
$342$		0			0
$343$	−3.97285	−	6.88117i	−0.214514	−	0.371548i
$344$		0			0
$345$	−21.2795	−	32.4137i	−1.14565	−	1.74509i
$346$		0			0
$347$	−25.7859	−	4.54675i	−1.38426	−	0.244082i	−0.568599	−	0.822615i	$-0.692514\pi$
$347$	−25.7859	−	4.54675i	−1.38426	−	0.244082i	−0.815659	+	0.578533i	$0.803626\pi$
$348$		0			0
$349$	−3.27963	−	3.90851i	−0.175555	−	0.209218i	0.671091	−	0.741375i	$-0.265826\pi$
$349$	−3.27963	−	3.90851i	−0.175555	−	0.209218i	−0.846646	+	0.532157i	$0.821382\pi$
$350$		0			0
$351$	30.1613	−	17.3115i	1.60989	−	0.924021i
$352$		0			0
$353$	−11.4022	+	9.56754i	−0.606875	+	0.509229i	−0.893647	−	0.448770i	$-0.851862\pi$
$353$	−11.4022	+	9.56754i	−0.606875	+	0.509229i	0.286772	+	0.957999i	$0.407418\pi$
$354$		0			0
$355$	−26.0785	−	4.59835i	−1.38410	−	0.244055i
$356$		0			0
$357$	0.785982	+	13.6948i	0.0415986	+	0.724803i
$358$		0			0
$359$	7.74329	+	13.4118i	0.408675	+	0.707846i	0.994742	−	0.102417i	$-0.0326575\pi$
$359$	7.74329	+	13.4118i	0.408675	+	0.707846i	−0.586066	+	0.810263i	$0.699324\pi$
$360$		0			0
$361$	−9.41679	+	16.3104i	−0.495621	+	0.858440i
$362$		0			0
$363$	5.31445	−	17.6969i	0.278936	−	0.928846i
$364$		0			0
$365$	2.78459	−	3.31854i	0.145752	−	0.173700i
$366$		0			0
$367$	−24.0744	−	8.76237i	−1.25667	−	0.457392i	−0.374023	−	0.927419i	$-0.622022\pi$
$367$	−24.0744	−	8.76237i	−1.25667	−	0.457392i	−0.882652	+	0.470027i	$0.844244\pi$
$368$		0			0
$369$	−19.8049	+	2.28084i	−1.03100	+	0.118736i
$370$		0			0
$371$	31.4772	−	5.55028i	1.63422	−	0.288156i
$372$		0			0
$373$	4.86012	+	13.3531i	0.251648	+	0.691396i	0.999617	+	0.0276634i	$0.00880666\pi$
$373$	4.86012	+	13.3531i	0.251648	+	0.691396i	−0.747970	+	0.663733i	$0.768971\pi$
$374$		0			0
$375$	0.949965	−	8.06816i	0.0490560	−	0.416638i
$376$		0			0
$377$	−23.3900			−1.20465
$378$		0			0
$379$			1.93137i			0.0992080i	0.998769	+	0.0496040i	$0.0157959\pi$
$379$			1.93137i			0.0992080i	−0.998769	+	0.0496040i	$0.984204\pi$
$380$		0			0
$381$	9.92702	−	13.3107i	0.508577	−	0.681930i
$382$		0			0
$383$	−12.4377	+	4.52695i	−0.635537	+	0.231317i	−0.639639	−	0.768675i	$-0.720916\pi$
$383$	−12.4377	+	4.52695i	−0.635537	+	0.231317i	0.00410258	+	0.999992i	$0.498694\pi$
$384$		0			0
$385$	1.15363	+	6.54257i	0.0587945	+	0.333440i
$386$		0			0
$387$	−1.73467	−	3.46866i	−0.0881783	−	0.176322i
$388$		0			0
$389$	−8.22522	+	22.5986i	−0.417035	+	1.14579i	0.536339	+	0.844003i	$0.319807\pi$
$389$	−8.22522	+	22.5986i	−0.417035	+	1.14579i	−0.953374	+	0.301792i	$0.902415\pi$
$390$		0			0
$391$	11.7780	+	9.88288i	0.595637	+	0.499799i
$392$		0			0
$393$	0.164279	+	0.695774i	0.00828677	+	0.0350972i
$394$		0			0
$395$	14.6540	+	8.46051i	0.737325	+	0.425695i
$396$		0			0
$397$	28.6833	−	16.5603i	1.43957	−	0.831137i	0.441752	−	0.897137i	$-0.354357\pi$
$397$	28.6833	−	16.5603i	1.43957	−	0.831137i	0.997820	+	0.0659997i	$0.0210236\pi$
$398$		0			0
$399$	−1.08534	+	2.15652i	−0.0543347	+	0.107961i
$400$		0			0
$401$	1.94567	−	11.0344i	0.0971620	−	0.551033i	−0.896901	−	0.442231i	$-0.854187\pi$
$401$	1.94567	−	11.0344i	0.0971620	−	0.551033i	0.994063	−	0.108802i	$-0.0347016\pi$
$402$		0			0
$403$	−9.48715	−	11.3063i	−0.472588	−	0.563209i
$404$		0			0
$405$	−27.9304	+	11.9359i	−1.38787	+	0.593097i
$406$		0			0
$407$	−0.536366	+	0.450065i	−0.0265867	+	0.0223089i
$408$		0			0
$409$	1.95004	−	11.0592i	0.0964233	−	0.546844i	−0.897879	−	0.440243i	$-0.854892\pi$
$409$	1.95004	−	11.0592i	0.0964233	−	0.546844i	0.994302	−	0.106601i	$-0.0339966\pi$
$410$		0			0
$411$	−24.3829	−	12.2714i	−1.20272	−	0.605305i
$412$		0			0
$413$	25.9810	−	15.0001i	1.27844	−	0.738109i
$414$		0			0
$415$	−17.5140	+	30.3351i	−0.859728	+	1.48909i
$416$		0			0
$417$	0.878792	+	3.72197i	0.0430347	+	0.182266i
$418$		0			0
$419$	8.95678	−	10.6743i	0.437567	−	0.521472i	−0.501522	−	0.865145i	$-0.667226\pi$
$419$	8.95678	−	10.6743i	0.437567	−	0.521472i	0.939090	+	0.343672i	$0.111671\pi$
$420$		0			0
$421$	4.06687	−	11.1736i	0.198207	−	0.544570i	−0.800276	−	0.599632i	$-0.795314\pi$
$421$	4.06687	−	11.1736i	0.198207	−	0.544570i	0.998483	+	0.0550623i	$0.0175358\pi$
$422$		0			0
$423$	−7.88699	−	5.20653i	−0.383478	−	0.253150i
$424$		0			0
$425$	2.57184	+	14.5856i	0.124753	+	0.707507i
$426$		0			0
$427$	5.54707	+	15.2404i	0.268442	+	0.737537i
$428$		0			0
$429$	−3.99269	+	5.35364i	−0.192769	+	0.258476i
$430$		0			0
$431$	28.2506			1.36079			0.680393	−	0.732848i	$-0.261809\pi$
$431$	28.2506			1.36079			0.680393	+	0.732848i	$0.261809\pi$
$432$		0			0
$433$	−27.8524			−1.33850			−0.669251	−	0.743036i	$-0.733385\pi$
$433$	−27.8524			−1.33850			−0.669251	+	0.743036i	$0.733385\pi$
$434$		0			0
$435$	20.2888	+	2.38886i	0.972774	+	0.114537i
$436$		0			0
$437$	0.925505	+	2.54280i	0.0442729	+	0.121639i
$438$		0			0
$439$	2.13242	+	12.0935i	0.101775	+	0.577193i	0.992460	+	0.122572i	$0.0391142\pi$
$439$	2.13242	+	12.0935i	0.101775	+	0.577193i	−0.890685	+	0.454621i	$0.849775\pi$
$440$		0			0
$441$	5.57627	−	12.8672i	0.265537	−	0.612725i
$442$		0			0
$443$	7.22670	−	19.8552i	0.343351	−	0.943348i	−0.641064	−	0.767487i	$-0.721507\pi$
$443$	7.22670	−	19.8552i	0.343351	−	0.943348i	0.984415	−	0.175861i	$-0.0562710\pi$
$444$		0			0
$445$	−12.4303	+	14.8138i	−0.589252	+	0.702243i
$446$		0			0
$447$	11.3564	+	3.41036i	0.537137	+	0.161305i
$448$		0			0
$449$	13.8708	−	24.0249i	0.654604	−	1.13381i	−0.327389	−	0.944890i	$-0.606169\pi$
$449$	13.8708	−	24.0249i	0.654604	−	1.13381i	0.981993	−	0.188917i	$-0.0604978\pi$
$450$		0			0
$451$	3.31561	−	1.91427i	0.156126	−	0.0901393i
$452$		0			0
$453$	1.17089	+	20.4013i	0.0550133	+	0.958538i
$454$		0			0
$455$	−13.4014	+	76.0030i	−0.628266	+	3.56307i
$456$		0			0
$457$	−26.0906	+	21.8926i	−1.22047	+	1.02409i	−0.221668	+	0.975122i	$0.571150\pi$
$457$	−26.0906	+	21.8926i	−1.22047	+	1.02409i	−0.998800	+	0.0489720i	$0.984405\pi$
$458$		0			0
$459$	9.24588	−	7.71824i	0.431561	−	0.360256i
$460$		0			0
$461$	−8.93591	−	10.6494i	−0.416187	−	0.495992i	0.516698	−	0.856168i	$-0.327161\pi$
$461$	−8.93591	−	10.6494i	−0.416187	−	0.495992i	−0.932884	+	0.360176i	$0.882717\pi$
$462$		0			0
$463$	−3.22751	+	18.3041i	−0.149995	+	0.850665i	0.813224	+	0.581950i	$0.197710\pi$
$463$	−3.22751	+	18.3041i	−0.149995	+	0.850665i	−0.963220	+	0.268715i	$0.913401\pi$
$464$		0			0
$465$	7.07455	+	10.7762i	0.328075	+	0.499735i
$466$		0			0
$467$	8.34116	−	4.81577i	0.385983	−	0.222847i	−0.294435	−	0.955671i	$-0.595132\pi$
$467$	8.34116	−	4.81577i	0.385983	−	0.222847i	0.680418	+	0.732824i	$0.261798\pi$
$468$		0			0
$469$	−44.5181	−	25.7026i	−2.05566	−	1.18683i
$470$		0			0
$471$	15.1952	−	14.3116i	0.700156	−	0.659442i
$472$		0			0
$473$	0.570541	+	0.478741i	0.0262335	+	0.0220125i
$474$		0			0
$475$	−0.891532	+	2.44946i	−0.0409063	+	0.112389i
$476$		0			0
$477$	−20.3802	−	19.2931i	−0.933145	−	0.883372i
$478$		0			0
$479$	−5.05443	−	28.6651i	−0.230943	−	1.30974i	−0.850992	−	0.525179i	$-0.823998\pi$
$479$	−5.05443	−	28.6651i	−0.230943	−	1.30974i	0.620049	−	0.784563i	$-0.287113\pi$
$480$		0			0
$481$	−7.64321	+	2.78190i	−0.348500	+	0.126844i
$482$		0			0
$483$	−15.5180	−	36.0588i	−0.706094	−	1.64073i
$484$		0			0
$485$		−	37.9074i		−	1.72129i
$486$		0			0
$487$	13.1429			0.595563			0.297782	−	0.954634i	$-0.403753\pi$
$487$	13.1429			0.595563			0.297782	+	0.954634i	$0.403753\pi$
$488$		0			0
$489$	21.3147	−	9.17282i	0.963882	−	0.414809i
$490$		0			0
$491$	−4.01945	−	11.0433i	−0.181395	−	0.498379i	0.815352	−	0.578965i	$-0.196543\pi$
$491$	−4.01945	−	11.0433i	−0.181395	−	0.498379i	−0.996748	+	0.0805856i	$0.974321\pi$
$492$		0			0
$493$	−7.97752	+	1.40665i	−0.359289	+	0.0633524i
$494$		0			0
$495$	4.01010	−	4.23604i	0.180240	−	0.190396i
$496$		0			0
$497$	−25.1930	−	9.16949i	−1.13006	−	0.411308i
$498$		0			0
$499$	−23.2598	+	27.7199i	−1.04125	+	1.24091i	−0.0713387	+	0.997452i	$0.522727\pi$
$499$	−23.2598	+	27.7199i	−1.04125	+	1.24091i	−0.969911	+	0.243461i	$0.921717\pi$
$500$		0			0
$501$	−8.04343	−	8.54003i	−0.359354	−	0.381540i
$502$		0			0
$503$	−1.18773	+	2.05720i	−0.0529581	+	0.0917261i	−0.891289	−	0.453435i	$-0.850198\pi$
$503$	−1.18773	+	2.05720i	−0.0529581	+	0.0917261i	0.838331	+	0.545161i	$0.183532\pi$
$504$		0			0
$505$	20.9748	+	36.3294i	0.933366	+	1.61664i
$506$		0			0
$507$	−46.0326	+	30.2202i	−2.04438	+	1.34213i
$508$		0			0
$509$	40.5051	+	7.14215i	1.79536	+	0.316570i	0.969090	−	0.246706i	$-0.0793482\pi$
$509$	40.5051	+	7.14215i	1.79536	+	0.316570i	0.826269	+	0.563276i	$0.190459\pi$
$510$		0			0
$511$	3.35977	−	2.81918i	0.148627	−	0.124713i
$512$		0			0
$513$	2.08846	−	0.362779i	0.0922077	−	0.0160171i
$514$		0			0
$515$	−34.2906	−	40.8660i	−1.51103	−	1.80077i
$516$		0			0
$517$	1.78734	+	0.315155i	0.0786069	+	0.0138605i
$518$		0			0
$519$	−2.91447	+	0.167270i	−0.127931	+	0.00734234i
$520$		0			0
$521$	−5.21530	−	9.03316i	−0.228486	−	0.395750i	0.728873	−	0.684649i	$-0.240044\pi$
$521$	−5.21530	−	9.03316i	−0.228486	−	0.395750i	−0.957360	+	0.288899i	$0.906711\pi$
$522$		0			0
$523$	14.6626	+	8.46543i	0.641149	+	0.370167i	0.785057	−	0.619424i	$-0.212634\pi$
$523$	14.6626	+	8.46543i	0.641149	+	0.370167i	−0.143908	+	0.989591i	$0.545967\pi$
$524$		0			0
$525$	10.8762	−	36.2173i	0.474677	−	1.58065i
$526$		0			0
$527$	−3.91569	−	3.28565i	−0.170570	−	0.143125i
$528$		0			0
$529$	−19.7338	−	7.18252i	−0.857992	−	0.312283i
$530$		0			0
$531$	−24.1687	−	10.4740i	−1.04883	−	0.454533i
$532$		0			0
$533$	43.7992	−	7.72298i	1.89715	−	0.334519i
$534$		0			0
$535$	−7.75366	+	2.82210i	−0.335220	+	0.122010i
$536$		0			0
$537$	−2.41330	+	20.4964i	−0.104142	+	0.884486i
$538$		0			0
$539$			2.69313i			0.116001i
$540$		0			0
$541$			29.4745i			1.26721i	0.773658	+	0.633603i	$0.218425\pi$
$541$			29.4745i			1.26721i	−0.773658	+	0.633603i	$0.781575\pi$
$542$		0			0
$543$	−22.9306	−	17.1015i	−0.984048	−	0.733894i
$544$		0			0
$545$	−51.5414	+	18.7595i	−2.20779	+	0.803570i
$546$		0			0
$547$	31.4846	−	5.55158i	1.34618	−	0.237369i	0.546333	−	0.837568i	$-0.316023\pi$
$547$	31.4846	−	5.55158i	1.34618	−	0.237369i	0.799850	+	0.600199i	$0.204912\pi$
$548$		0			0
$549$	7.84523	−	11.8842i	0.334826	−	0.507204i
$550$		0			0
$551$	−1.33972	−	0.487617i	−0.0570739	−	0.0207732i
$552$		0			0
$553$	13.1233	+	11.0117i	0.558059	+	0.468267i
$554$		0			0
$555$	6.91395	−	1.63245i	0.293481	−	0.0692935i
$556$		0			0
$557$	7.19468	+	4.15385i	0.304849	+	0.176004i	0.644619	−	0.764504i	$-0.277016\pi$
$557$	7.19468	+	4.15385i	0.304849	+	0.176004i	−0.339770	+	0.940508i	$0.610349\pi$
$558$		0			0
$559$	4.32598	+	7.49282i	0.182970	+	0.316913i
$560$		0			0
$561$	−1.03981	+	2.06606i	−0.0439007	+	0.0872290i
$562$		0			0
$563$	6.57453	+	1.15927i	0.277083	+	0.0488573i	0.310463	−	0.950585i	$-0.399516\pi$
$563$	6.57453	+	1.15927i	0.277083	+	0.0488573i	−0.0333796	+	0.999443i	$0.510627\pi$
$564$		0			0
$565$	26.4043	+	31.4674i	1.11084	+	1.32384i
$566$		0			0
$567$	−29.9462	+	6.99023i	−1.25762	+	0.293562i
$568$		0			0
$569$	−24.2709	+	20.3657i	−1.01749	+	0.853775i	−0.989310	−	0.145827i	$-0.953416\pi$
$569$	−24.2709	+	20.3657i	−1.01749	+	0.853775i	−0.0281798	+	0.999603i	$0.508971\pi$
$570$		0			0
$571$	32.6020	+	5.74861i	1.36435	+	0.240572i	0.807416	−	0.589983i	$-0.200866\pi$
$571$	32.6020	+	5.74861i	1.36435	+	0.240572i	0.556936	+	0.830555i	$0.311977\pi$
$572$		0			0
$573$	−20.4527	−	10.2934i	−0.854423	−	0.430014i
$574$		0			0
$575$	−21.1926	−	36.7066i	−0.883791	−	1.53077i
$576$		0			0
$577$	15.0611	−	26.0866i	0.627001	−	1.08600i	−0.361149	−	0.932508i	$-0.617615\pi$
$577$	15.0611	−	26.0866i	0.627001	−	1.08600i	0.988150	−	0.153490i	$-0.0490512\pi$
$578$		0			0
$579$	0.298338	−	0.0704404i	0.0123985	−	0.00292740i
$580$		0			0
$581$	−22.7953	+	27.1663i	−0.945707	+	1.12705i
$582$		0			0
$583$	5.06443	+	1.84330i	0.209747	+	0.0763418i
$584$		0			0
$585$	60.6050	−	30.3085i	2.50571	−	1.25310i
$586$		0			0
$587$	−15.0318	+	2.65051i	−0.620427	+	0.109398i	−0.475022	−	0.879974i	$-0.657560\pi$
$587$	−15.0318	+	2.65051i	−0.620427	+	0.109398i	−0.145406	+	0.989372i	$0.546449\pi$
$588$		0			0
$589$	−0.307693	−	0.845379i	−0.0126783	−	0.0348332i
$590$		0			0
$591$	1.34867	+	1.00583i	0.0554770	+	0.0413743i
$592$		0			0
$593$	27.1813			1.11620			0.558101	−	0.829773i	$-0.311530\pi$
$593$	27.1813			1.11620			0.558101	+	0.829773i	$0.311530\pi$
$594$		0			0
$595$			26.7279i			1.09574i
$596$		0			0
$597$	7.05014	+	0.830102i	0.288543	+	0.0339738i
$598$		0			0
$599$	39.7660	−	14.4737i	1.62480	−	0.591378i	0.640509	−	0.767951i	$-0.278723\pi$
$599$	39.7660	−	14.4737i	1.62480	−	0.591378i	0.984288	+	0.176573i	$0.0565012\pi$
$600$		0			0
$601$	−0.648834	−	3.67972i	−0.0264665	−	0.150099i	0.968711	−	0.248193i	$-0.0798366\pi$
$601$	−0.648834	−	3.67972i	−0.0264665	−	0.150099i	−0.995177	+	0.0980937i	$0.968726\pi$
$602$		0			0
$603$	5.16379	+	44.8381i	0.210286	+	1.82595i
$604$		0			0
$605$	12.3139	−	33.8321i	0.500631	−	1.37547i
$606$		0			0
$607$	−35.5497	−	29.8298i	−1.44292	−	1.21075i	−0.937550	−	0.347850i	$-0.886912\pi$
$607$	−35.5497	−	29.8298i	−1.44292	−	1.21075i	−0.505370	−	0.862903i	$-0.668644\pi$
$608$		0			0
$609$	19.8088	+	5.94867i	0.802694	+	0.241052i
$610$		0			0
$611$	18.2586	+	10.5416i	0.738664	+	0.426468i
$612$		0			0
$613$	−21.9670	+	12.6827i	−0.887239	+	0.512248i	−0.873038	−	0.487652i	$-0.837854\pi$
$613$	−21.9670	+	12.6827i	−0.887239	+	0.512248i	−0.0142005	+	0.999899i	$0.504520\pi$
$614$		0			0
$615$	−38.7808	+	2.22575i	−1.56379	+	0.0897507i
$616$		0			0
$617$	1.23909	−	7.02722i	0.0498838	−	0.282905i	−0.949654	−	0.313300i	$-0.898565\pi$
$617$	1.23909	−	7.02722i	0.0498838	−	0.282905i	0.999538	+	0.0303950i	$0.00967653\pi$
$618$		0			0
$619$	17.2889	+	20.6041i	0.694900	+	0.828149i	0.991939	−	0.126716i	$-0.0404437\pi$
$619$	17.2889	+	20.6041i	0.694900	+	0.828149i	−0.297039	+	0.954865i	$0.595999\pi$
$620$		0			0
$621$	−17.3096	+	29.8058i	−0.694610	+	1.19607i
$622$		0			0
$623$	−14.9979	+	12.5847i	−0.600877	+	0.504196i
$624$		0			0
$625$	−2.79914	+	15.8747i	−0.111966	+	0.634989i
$626$		0			0
$627$	−0.340300	+	0.223406i	−0.0135903	+	0.00892197i
$628$		0			0
$629$	−2.43953	+	1.40846i	−0.0972705	+	0.0561592i
$630$		0			0
$631$	11.7466	−	20.3457i	0.467624	−	0.809949i	−0.531691	−	0.846938i	$-0.678443\pi$
$631$	11.7466	−	20.3457i	0.467624	−	0.809949i	0.999316	+	0.0369893i	$0.0117767\pi$
$632$		0			0
$633$	−4.73127	+	4.45615i	−0.188051	+	0.177116i
$634$		0			0
$635$	20.7970	−	24.7848i	0.825302	−	0.983557i
$636$		0			0
$637$	−10.7002	+	29.3985i	−0.423956	+	1.16481i
$638$		0			0
$639$	6.71294	+	22.5619i	0.265560	+	0.892535i
$640$		0			0
$641$	−7.57282	−	42.9476i	−0.299108	−	1.69633i	−0.650019	−	0.759918i	$-0.725239\pi$
$641$	−7.57282	−	42.9476i	−0.299108	−	1.69633i	0.350911	−	0.936409i	$-0.385872\pi$
$642$		0			0
$643$	0.120739	+	0.331727i	0.00476148	+	0.0130820i	0.942051	−	0.335471i	$-0.108895\pi$
$643$	0.120739	+	0.331727i	0.00476148	+	0.0130820i	−0.937289	+	0.348553i	$0.886673\pi$
$644$		0			0
$645$	−2.98717	−	6.94120i	−0.117620	−	0.273310i
$646$		0			0
$647$	26.0967			1.02597			0.512984	−	0.858398i	$-0.328540\pi$
$647$	26.0967			1.02597			0.512984	+	0.858398i	$0.328540\pi$
$648$		0			0
$649$	5.05855			0.198565
$650$		0			0
$651$	5.15911	+	11.9881i	0.202201	+	0.469850i
$652$		0			0
$653$	0.281991	+	0.774764i	0.0110352	+	0.0303189i	0.945088	−	0.326816i	$-0.105976\pi$
$653$	0.281991	+	0.774764i	0.0110352	+	0.0303189i	−0.934053	+	0.357135i	$0.883754\pi$
$654$		0			0
$655$	0.241889	+	1.37182i	0.00945137	+	0.0536014i
$656$		0			0
$657$	−3.74554	−	0.894418i	−0.146127	−	0.0348946i
$658$		0			0
$659$	−14.2971	+	39.2809i	−0.556935	+	1.53017i	0.267123	+	0.963662i	$0.413927\pi$
$659$	−14.2971	+	39.2809i	−0.556935	+	1.53017i	−0.824058	+	0.566505i	$0.808295\pi$
$660$		0			0
$661$	1.06741	−	1.27208i	0.0415173	−	0.0494784i	−0.744886	−	0.667192i	$-0.767496\pi$
$661$	1.06741	−	1.27208i	0.0415173	−	0.0494784i	0.786404	+	0.617713i	$0.211941\pi$
$662$		0			0
$663$	−19.5594	+	18.4220i	−0.759624	+	0.715452i
$664$		0			0
$665$	−2.35205	+	4.07387i	−0.0912086	+	0.157978i
$666$		0			0
$667$	20.0764	−	11.5911i	0.777362	−	0.448810i
$668$		0			0
$669$	−5.67824	+	3.72775i	−0.219533	+	0.144123i
$670$		0			0
$671$	−0.474878	+	2.69317i	−0.0183325	+	0.103969i
$672$		0			0
$673$	−4.23311	+	3.55200i	−0.163175	+	0.136920i	−0.720719	−	0.693227i	$-0.756188\pi$
$673$	−4.23311	+	3.55200i	−0.163175	+	0.136920i	0.557544	+	0.830147i	$0.311744\pi$
$674$		0			0
$675$	−31.2287	+	11.2765i	−1.20199	+	0.434032i
$676$		0			0
$677$	−2.08429	−	2.48396i	−0.0801056	−	0.0954662i	0.724503	−	0.689272i	$-0.242069\pi$
$677$	−2.08429	−	2.48396i	−0.0801056	−	0.0954662i	−0.804609	+	0.593805i	$0.797625\pi$
$678$		0			0
$679$	6.66432	−	37.7952i	0.255753	−	1.45045i
$680$		0			0
$681$	−20.4628	+	1.17442i	−0.784137	+	0.0450040i
$682$		0			0
$683$	22.4547	−	12.9642i	0.859206	−	0.496063i	−0.00454025	−	0.999990i	$-0.501445\pi$
$683$	22.4547	−	12.9642i	0.859206	−	0.496063i	0.863746	+	0.503927i	$0.168112\pi$
$684$		0			0
$685$	−46.0615	−	26.5936i	−1.75992	−	1.01609i
$686$		0			0
$687$	17.5801	+	5.27939i	0.670724	+	0.201421i
$688$		0			0
$689$	47.9602	+	40.2434i	1.82714	+	1.53315i
$690$		0			0
$691$	−10.2247	+	28.0920i	−0.388964	+	1.06867i	0.578504	+	0.815679i	$0.303637\pi$
$691$	−10.2247	+	28.0920i	−0.388964	+	1.06867i	−0.967469	+	0.252991i	$0.918586\pi$
$692$		0			0
$693$	4.74295	−	3.51852i	0.180170	−	0.133657i
$694$		0			0
$695$	1.29396	+	7.33841i	0.0490827	+	0.278362i
$696$		0			0
$697$	14.4739	−	5.26808i	0.548240	−	0.199543i
$698$		0			0
$699$	1.94381	+	0.228869i	0.0735217	+	0.00865663i
$700$		0			0
$701$			24.6223i			0.929973i	0.885318	+	0.464987i	$0.153941\pi$
$701$			24.6223i			0.929973i	−0.885318	+	0.464987i	$0.846059\pi$
$702$		0			0
$703$	−0.495778			−0.0186986
$704$		0			0
$705$	−14.7611	−	11.0087i	−0.555937	−	0.414612i
$706$		0			0
$707$	14.5258	+	39.9094i	0.546300	+	1.50095i
$708$		0			0
$709$	26.4148	−	4.65765i	0.992030	−	0.174922i	0.346001	−	0.938234i	$-0.387540\pi$
$709$	26.4148	−	4.65765i	0.992030	−	0.174922i	0.646029	+	0.763313i	$0.276428\pi$
$710$		0			0
$711$	0.900037	−	15.0145i	0.0337540	−	0.563088i
$712$		0			0
$713$	13.7461	+	5.00317i	0.514796	+	0.187370i
$714$		0			0
$715$	−8.36463	+	9.96858i	−0.312819	+	0.372804i
$716$		0			0
$717$	9.78395	−	2.31008i	0.365388	−	0.0862716i
$718$		0			0
$719$	−9.26666	+	16.0503i	−0.345588	+	0.598576i	−0.985460	−	0.169905i	$-0.945654\pi$
$719$	−9.26666	+	16.0503i	−0.345588	+	0.598576i	0.639872	+	0.768481i	$0.278987\pi$
$720$		0			0
$721$	−27.0047	−	46.7736i	−1.00571	−	1.74194i
$722$		0			0
$723$	−45.6393	−	22.9694i	−1.69735	−	0.854241i
$724$		0			0
$725$	21.9920	+	3.87779i	0.816764	+	0.144017i
$726$		0			0
$727$	−4.82234	+	4.04643i	−0.178851	+	0.150074i	−0.727818	−	0.685770i	$-0.759466\pi$
$727$	−4.82234	+	4.04643i	−0.178851	+	0.150074i	0.548967	+	0.835844i	$0.315021\pi$
$728$		0			0
$729$	20.5947	+	17.4602i	0.762766	+	0.646675i
$730$		0			0
$731$	1.92605	+	2.29538i	0.0712377	+	0.0848978i
$732$		0			0
$733$	22.4113	+	3.95172i	0.827781	+	0.145960i	0.571458	−	0.820631i	$-0.306378\pi$
$733$	22.4113	+	3.95172i	0.827781	+	0.145960i	0.256323	+	0.966591i	$0.417489\pi$
$734$		0			0
$735$	12.2840	−	24.4078i	0.453102	−	0.900297i
$736$		0			0
$737$	−4.33388	−	7.50649i	−0.159640	−	0.276505i
$738$		0			0
$739$	−37.2940	−	21.5317i	−1.37188	−	0.792056i	−0.380717	−	0.924692i	$-0.624323\pi$
$739$	−37.2940	−	21.5317i	−1.37188	−	0.792056i	−0.991165	+	0.132636i	$0.957656\pi$
$740$		0			0
$741$	−4.60237	+	1.08666i	−0.169072	+	0.0399196i
$742$		0			0
$743$	27.0616	+	22.7074i	0.992794	+	0.833053i	0.985970	−	0.166924i	$-0.0533834\pi$
$743$	27.0616	+	22.7074i	0.992794	+	0.833053i	0.00682406	+	0.999977i	$0.497828\pi$
$744$		0			0
$745$	21.7106	+	7.90201i	0.795415	+	0.289507i
$746$		0			0
$747$	31.0814	+	1.86316i	1.13721	+	0.0681693i
$748$		0			0
$749$	−8.22687	+	1.45062i	−0.300603	+	0.0530045i
$750$		0			0
$751$	23.5008	−	8.55359i	0.857557	−	0.312125i	0.124439	−	0.992227i	$-0.460287\pi$
$751$	23.5008	−	8.55359i	0.857557	−	0.312125i	0.733117	+	0.680102i	$0.238065\pi$
$752$		0			0
$753$	−8.34852	−	6.22625i	−0.304237	−	0.226897i
$754$		0			0
$755$			39.8171i			1.44909i
$756$		0			0
$757$			31.3025i			1.13771i	0.822439	+	0.568853i	$0.192613\pi$
$757$			31.3025i			1.13771i	−0.822439	+	0.568853i	$0.807387\pi$
$758$		0			0
$759$	0.774019	−	6.57383i	0.0280951	−	0.238615i
$760$		0			0
$761$	−2.59308	+	0.943805i	−0.0939992	+	0.0342129i	−0.388592	−	0.921410i	$-0.627038\pi$
$761$	−2.59308	+	0.943805i	−0.0939992	+	0.0342129i	0.294592	+	0.955623i	$0.404816\pi$
$762$		0			0
$763$	−54.6869	+	9.64278i	−1.97980	+	0.349092i
$764$		0			0
$765$	18.8476	−	13.9819i	0.681435	−	0.505517i
$766$		0			0
$767$	55.2197	+	20.0983i	1.99387	+	0.725708i
$768$		0			0
$769$	3.61913	+	3.03681i	0.130509	+	0.109510i	0.705706	−	0.708505i	$-0.250630\pi$
$769$	3.61913	+	3.03681i	0.130509	+	0.109510i	−0.575197	+	0.818015i	$0.695074\pi$
$770$		0			0
$771$	12.9370	−	43.0796i	0.465914	−	1.55147i
$772$		0			0
$773$	17.3435	+	10.0133i	0.623803	+	0.360153i	0.778348	−	0.627833i	$-0.216058\pi$
$773$	17.3435	+	10.0133i	0.623803	+	0.360153i	−0.154545	+	0.987986i	$0.549391\pi$
$774$		0			0
$775$	7.04567	+	12.2035i	0.253088	+	0.438361i
$776$		0			0
$777$	7.18049	−	0.412109i	0.257599	−	0.0147843i
$778$		0			0
$779$	2.66971	+	0.470742i	0.0956522	+	0.0168661i
$780$		0			0
$781$	−2.90577	−	3.46296i	−0.103977	−	0.123914i
$782$		0			0
$783$	−6.16759	−	17.0803i	−0.220412	−	0.610401i
$784$		0			0
$785$	31.1567	−	26.1436i	1.11203	−	0.933105i
$786$		0			0
$787$	41.5062	+	7.31867i	1.47954	+	0.260882i	0.854393	−	0.519627i	$-0.173929\pi$
$787$	41.5062	+	7.31867i	1.47954	+	0.260882i	0.625144	+	0.780510i	$0.285040\pi$
$788$		0			0
$789$	20.1422	−	13.2233i	0.717081	−	0.470762i
$790$		0			0
$791$	20.7940	+	36.0163i	0.739350	+	1.28059i
$792$		0			0
$793$	−15.8842	+	27.5122i	−0.564063	+	0.976986i
$794$		0			0
$795$	−37.4913	−	39.8060i	−1.32968	−	1.41177i
$796$		0			0
$797$	32.1711	−	38.3400i	1.13956	−	1.35807i	0.215189	−	0.976572i	$-0.430963\pi$
$797$	32.1711	−	38.3400i	1.13956	−	1.35807i	0.924369	−	0.381500i	$-0.124592\pi$
$798$		0			0
$799$	6.86134	+	2.49732i	0.242737	+	0.0883489i
$800$		0			0
$801$	16.7200	+	3.99265i	0.590771	+	0.141073i
$802$		0			0
$803$	0.728294	−	0.128418i	0.0257009	−	0.00453177i
$804$		0			0
$805$	−26.1611	−	71.8771i	−0.922059	−	2.53334i
$806$		0			0
$807$	6.19534	−	2.66618i	0.218086	−	0.0938541i
$808$		0			0
$809$	7.89082			0.277426			0.138713	−	0.990333i	$-0.455703\pi$
$809$	7.89082			0.277426			0.138713	+	0.990333i	$0.455703\pi$
$810$		0			0
$811$			16.9433i			0.594960i	0.954728	+	0.297480i	$0.0961461\pi$
$811$			16.9433i			0.594960i	−0.954728	+	0.297480i	$0.903854\pi$
$812$		0			0
$813$	18.5552	+	43.1163i	0.650760	+	1.51215i
$814$		0			0
$815$	42.4871	−	15.4641i	1.48826	−	0.541682i
$816$		0			0
$817$	0.0915762	+	0.519355i	0.00320385	+	0.0181699i
$818$		0			0
$819$	65.7541	−	19.5641i	2.29764	−	0.683625i
$820$		0			0
$821$	16.2209	−	44.5665i	0.566112	−	1.55538i	−0.244410	−	0.969672i	$-0.578594\pi$
$821$	16.2209	−	44.5665i	0.566112	−	1.55538i	0.810522	−	0.585708i	$-0.199184\pi$
$822$		0			0
$823$	3.65996	+	3.07107i	0.127578	+	0.107051i	0.704344	−	0.709858i	$-0.251241\pi$
$823$	3.65996	+	3.07107i	0.127578	+	0.107051i	−0.576766	+	0.816909i	$0.695686\pi$
$824$		0			0
$825$	4.64163	−	4.37172i	0.161601	−	0.152204i
$826$		0			0
$827$	−25.0451	−	14.4598i	−0.870903	−	0.502816i	−0.00325451	−	0.999995i	$-0.501036\pi$
$827$	−25.0451	−	14.4598i	−0.870903	−	0.502816i	−0.867648	+	0.497179i	$0.834369\pi$
$828$		0			0
$829$	17.1833	−	9.92077i	0.596800	−	0.344563i	−0.170982	−	0.985274i	$-0.554694\pi$
$829$	17.1833	−	9.92077i	0.596800	−	0.344563i	0.767782	+	0.640711i	$0.221361\pi$
$830$		0			0
$831$	6.80883	+	10.3715i	0.236196	+	0.359782i
$832$		0			0
$833$	−1.88146	+	10.6703i	−0.0651888	+	0.369704i
$834$		0			0
$835$	−14.6933	−	17.5108i	−0.508482	−	0.605986i
$836$		0			0
$837$	5.75473	−	9.90922i	0.198913	−	0.342513i
$838$		0			0
$839$	−26.2638	+	22.0379i	−0.906725	+	0.760833i	−0.971493	−	0.237067i	$-0.923814\pi$
$839$	−26.2638	+	22.0379i	−0.906725	+	0.760833i	0.0647677	+	0.997900i	$0.479369\pi$
$840$		0			0
$841$	2.91487	−	16.5310i	0.100513	−	0.570036i
$842$		0			0
$843$	0.0769808	+	1.34129i	0.00265136	+	0.0461966i
$844$		0			0
$845$	−92.9203	+	53.6476i	−3.19656	+	1.84553i
$846$		0			0
$847$	18.2253	−	31.5672i	0.626230	−	1.08466i
$848$		0			0
$849$	2.53610	+	0.761601i	0.0870387	+	0.0261381i
$850$		0			0
$851$	5.18183	−	6.17546i	0.177631	−	0.211692i
$852$		0			0
$853$	−11.5939	+	31.8539i	−0.396967	+	1.09066i	0.566787	+	0.823865i	$0.308186\pi$
$853$	−11.5939	+	31.8539i	−0.396967	+	1.09066i	−0.963754	+	0.266793i	$0.914036\pi$
$854$		0			0
$855$	4.10315	−	0.472540i	0.140325	−	0.0161605i
$856$		0			0
$857$	0.670084	+	3.80024i	0.0228896	+	0.129814i	0.994111	−	0.108364i	$-0.0345611\pi$
$857$	0.670084	+	3.80024i	0.0228896	+	0.129814i	−0.971222	+	0.238177i	$0.923450\pi$
$858$		0			0
$859$	−7.37600	−	20.2654i	−0.251666	−	0.691446i	−0.999617	−	0.0276917i	$-0.991184\pi$
$859$	−7.37600	−	20.2654i	−0.251666	−	0.691446i	0.747951	−	0.663754i	$-0.231038\pi$
$860$		0			0
$861$	−39.0574	−	4.59872i	−1.33107	−	0.156724i
$862$		0			0
$863$	−30.2497			−1.02971			−0.514857	−	0.857276i	$-0.672155\pi$
$863$	−30.2497			−1.02971			−0.514857	+	0.857276i	$0.672155\pi$
$864$		0			0
$865$	−5.68815			−0.193403
$866$		0			0
$867$	12.0401	−	16.1441i	0.408904	−	0.548282i
$868$		0			0
$869$	0.987962	+	2.71440i	0.0335143	+	0.0920799i
$870$		0			0
$871$	−17.4847	−	99.1608i	−0.592447	−	3.35994i
$872$		0			0
$873$	−30.1381	+	15.0720i	−1.02002	+	0.510109i
$874$		0			0
$875$	5.48119	−	15.0594i	0.185298	−	0.509102i
$876$		0			0
$877$	10.0265	−	11.9491i	0.338571	−	0.403493i	−0.569715	−	0.821842i	$-0.692947\pi$
$877$	10.0265	−	11.9491i	0.338571	−	0.403493i	0.908286	+	0.418349i	$0.137391\pi$
$878$		0			0
$879$	6.32982	+	26.8088i	0.213499	+	0.904239i
$880$		0			0
$881$	18.2832	−	31.6674i	0.615977	−	1.06690i	−0.374235	−	0.927334i	$-0.622095\pi$
$881$	18.2832	−	31.6674i	0.615977	−	1.06690i	0.990212	−	0.139569i	$-0.0445719\pi$
$882$		0			0
$883$	26.1355	−	15.0893i	0.879529	−	0.507796i	0.00902592	−	0.999959i	$-0.497127\pi$
$883$	26.1355	−	15.0893i	0.879529	−	0.507796i	0.870503	+	0.492163i	$0.163794\pi$
$884$		0			0
$885$	−45.8457	−	23.0732i	−1.54109	−	0.775598i
$886$		0			0
$887$	7.16882	−	40.6564i	0.240705	−	1.36511i	−0.589553	−	0.807730i	$-0.700696\pi$
$887$	7.16882	−	40.6564i	0.240705	−	1.36511i	0.830258	−	0.557379i	$-0.188193\pi$
$888$		0			0
$889$	25.0927	−	21.0553i	0.841584	−	0.706172i
$890$		0			0
$891$	−4.96226	−	1.50395i	−0.166242	−	0.0503843i
$892$		0			0
$893$	0.826041	+	0.984438i	0.0276424	+	0.0329430i
$894$		0			0
$895$	−6.98289	+	39.6019i	−0.233412	+	1.32375i
$896$		0			0
$897$	34.5680	−	68.6854i	1.15419	−	2.29334i
$898$		0			0
$899$	−6.67459	+	3.85358i	−0.222610	+	0.128524i
$900$		0			0
$901$	18.7778	+	10.8414i	0.625578	+	0.361178i
$902$		0			0
$903$	−1.75803	−	7.44583i	−0.0585036	−	0.247782i
$904$		0			0
$905$	−42.6973	−	35.8273i	−1.41931	−	1.19094i
$906$		0			0
$907$	13.9229	−	38.2529i	0.462303	−	1.27017i	−0.461446	−	0.887168i	$-0.652669\pi$
$907$	13.9229	−	38.2529i	0.462303	−	1.27017i	0.923749	−	0.382999i	$-0.125109\pi$
$908$		0			0
$909$	20.5439	−	31.1205i	0.681399	−	1.03220i
$910$		0			0
$911$	−7.42318	−	42.0989i	−0.245941	−	1.39480i	−0.818298	−	0.574795i	$-0.805082\pi$
$911$	−7.42318	−	42.0989i	−0.245941	−	1.39480i	0.572357	−	0.820005i	$-0.306029\pi$
$912$		0			0
$913$	−5.61905	+	2.04517i	−0.185963	+	0.0676852i
$914$		0			0
$915$	16.5880	−	22.2422i	0.548383	−	0.735304i
$916$		0			0
$917$			1.41029i			0.0465717i
$918$		0			0
$919$	4.00742			0.132193			0.0660963	−	0.997813i	$-0.478946\pi$
$919$	4.00742			0.132193			0.0660963	+	0.997813i	$0.478946\pi$
$920$		0			0
$921$	−0.0866677	+	0.736078i	−0.00285580	+	0.0242546i
$922$		0			0
$923$	−17.9609	−	49.3471i	−0.591189	−	1.62428i
$924$		0			0
$925$	7.64760	−	1.34848i	0.251452	−	0.0443377i
$926$		0			0
$927$	−18.8563	+	43.5109i	−0.619323	+	1.42909i
$928$		0			0
$929$	46.5451	+	16.9410i	1.52710	+	0.555818i	0.962908	−	0.269829i	$-0.0869671\pi$
$929$	46.5451	+	16.9410i	1.52710	+	0.555818i	0.564188	+	0.825646i	$0.309189\pi$
$930$		0			0
$931$	−1.22576	+	1.46080i	−0.0401725	+	0.0478758i
$932$		0			0
$933$	−5.50276	+	18.3239i	−0.180152	+	0.599899i
$934$		0			0
$935$	−2.25339	+	3.90298i	−0.0736936	+	0.127641i
$936$		0			0
$937$	4.84280	+	8.38798i	0.158207	+	0.274023i	0.934222	−	0.356691i	$-0.116095\pi$
$937$	4.84280	+	8.38798i	0.158207	+	0.274023i	−0.776015	+	0.630715i	$0.782762\pi$
$938$		0			0
$939$	2.75855	+	48.0642i	0.0900218	+	1.56852i
$940$		0			0
$941$	5.10500	+	0.900150i	0.166418	+	0.0293440i	0.256236	−	0.966614i	$-0.417517\pi$
$941$	5.10500	+	0.900150i	0.166418	+	0.0293440i	−0.0898181	+	0.995958i	$0.528629\pi$
$942$		0			0
$943$	−33.7672	+	28.3340i	−1.09961	+	0.922682i
$944$		0			0
$945$	−59.0342	+	10.2546i	−1.92038	+	0.333583i
$946$		0			0
$947$	19.6357	+	23.4009i	0.638075	+	0.760428i	0.984065	−	0.177811i	$-0.0569014\pi$
$947$	19.6357	+	23.4009i	0.638075	+	0.760428i	−0.345990	+	0.938238i	$0.612457\pi$
$948$		0			0
$949$	8.46036	+	1.49179i	0.274635	+	0.0484256i
$950$		0			0
$951$	3.34003	+	5.08766i	0.108308	+	0.164979i
$952$		0			0
$953$	8.71927	+	15.1022i	0.282445	+	0.489209i	0.971986	−	0.235037i	$-0.0755213\pi$
$953$	8.71927	+	15.1022i	0.282445	+	0.489209i	−0.689542	+	0.724246i	$0.742188\pi$
$954$		0			0
$955$	−38.6370	−	22.3071i	−1.25027	−	0.721841i
$956$		0			0
$957$	2.39108	+	2.53871i	0.0772928	+	0.0820648i
$958$		0			0
$959$	−41.2500	−	34.6128i	−1.33203	−	1.11771i
$960$		0			0
$961$	24.5605	+	8.93927i	0.792273	+	0.288364i
$962$		0			0
$963$	5.32656	+	5.04244i	0.171646	+	0.162490i
$964$		0			0
$965$	0.588217	−	0.103718i	0.0189354	−	0.00333882i
$966$		0			0
$967$	46.2859	−	16.8467i	1.48845	−	0.541752i	0.535411	−	0.844592i	$-0.320157\pi$
$967$	46.2859	−	16.8467i	1.48845	−	0.541752i	0.953042	+	0.302839i	$0.0979345\pi$
$968$		0			0
$969$	−1.50436	+	0.647406i	−0.0483270	+	0.0207977i
$970$		0			0
$971$		−	13.2201i		−	0.424253i	−0.977242	−	0.212126i	$-0.931961\pi$
$971$		−	13.2201i		−	0.424253i	0.977242	−	0.212126i	$-0.0680388\pi$
$972$		0			0
$973$			7.54418i			0.241855i
$974$		0			0
$975$	68.0381	−	29.2804i	2.17896	−	0.937723i
$976$		0			0
$977$	−22.1311	+	8.05506i	−0.708037	+	0.257704i	−0.670838	−	0.741604i	$-0.734066\pi$
$977$	−22.1311	+	8.05506i	−0.708037	+	0.257704i	−0.0371983	+	0.999308i	$0.511843\pi$
$978$		0			0
$979$	−3.25108	+	0.573253i	−0.103905	+	0.0183212i
$980$		0			0
$981$	35.4075	+	33.5189i	1.13048	+	1.07018i
$982$		0			0
$983$	44.1620	+	16.0737i	1.40855	+	0.512670i	0.930704	−	0.365773i	$-0.119195\pi$
$983$	44.1620	+	16.0737i	1.40855	+	0.512670i	0.477846	+	0.878444i	$0.341418\pi$
$984$		0			0
$985$	2.51126	+	2.10719i	0.0800153	+	0.0671408i
$986$		0			0
$987$	−12.7821	−	13.5712i	−0.406858	−	0.431977i
$988$		0			0
$989$	−7.42628	−	4.28756i	−0.236142	−	0.136337i
$990$		0			0
$991$	10.5119	+	18.2072i	0.333922	+	0.578370i	0.983277	−	0.182115i	$-0.0582943\pi$
$991$	10.5119	+	18.2072i	0.333922	+	0.578370i	−0.649355	+	0.760486i	$0.724961\pi$
$992$		0			0
$993$	16.5566	+	25.2197i	0.525409	+	0.800322i
$994$		0			0
$995$	13.6219	+	2.40190i	0.431842	+	0.0761454i
$996$		0			0
$997$	−1.15413	−	1.37543i	−0.0365515	−	0.0435604i	0.747459	−	0.664308i	$-0.231274\pi$
$997$	−1.15413	−	1.37543i	−0.0365515	−	0.0435604i	−0.784011	+	0.620748i	$0.786829\pi$
$998$		0			0
$999$	−4.04686	−	4.84784i	−0.128037	−	0.153379i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bf.a.49.13		204
4.3	odd	2		216.2.t.a.157.27	yes	204
8.3	odd	2		216.2.t.a.157.12	✓	204
8.5	even	2	inner	864.2.bf.a.49.22		204
12.11	even	2		648.2.t.a.37.8		204
24.11	even	2		648.2.t.a.37.23		204
27.16	even	9	inner	864.2.bf.a.529.22		204
108.11	even	18		648.2.t.a.613.23		204
108.43	odd	18		216.2.t.a.205.12	yes	204
216.11	even	18		648.2.t.a.613.8		204
216.43	odd	18		216.2.t.a.205.27	yes	204
216.205	even	18	inner	864.2.bf.a.529.13		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.157.12	✓	204	8.3	odd	2
216.2.t.a.157.27	yes	204	4.3	odd	2
216.2.t.a.205.12	yes	204	108.43	odd	18
216.2.t.a.205.27	yes	204	216.43	odd	18
648.2.t.a.37.8		204	12.11	even	2
648.2.t.a.37.23		204	24.11	even	2
648.2.t.a.613.8		204	216.11	even	18
648.2.t.a.613.23		204	108.11	even	18
864.2.bf.a.49.13		204	1.1	even	1	trivial
864.2.bf.a.49.22		204	8.5	even	2	inner
864.2.bf.a.529.13		204	216.205	even	18	inner
864.2.bf.a.529.22		204	27.16	even	9	inner

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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bf (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.684682 - 1.59098i) q^{3} +(-1.15428 - 3.17134i) q^{5} +(-0.593321 - 3.36489i) q^{7} +(-2.06242 + 2.17863i) q^{9} +(0.197048 - 0.541384i) q^{11} +(4.30199 - 5.12691i) q^{13} +(-4.25523 + 4.00779i) q^{15} +(1.15893 - 2.00733i) q^{17} +(0.353289 - 0.203971i) q^{19} +(-4.94723 + 3.24784i) q^{21} +(-1.15186 + 6.53250i) q^{23} +(-4.89486 + 4.10727i) q^{25} +(4.87825 + 1.78960i) q^{27} +(-2.24644 - 2.67721i) q^{29} +(0.382945 - 2.17179i) q^{31} +(-0.996245 + 0.0571774i) q^{33} +(-9.98637 + 5.76564i) q^{35} +(-1.05249 - 0.607656i) q^{37} +(-11.1023 - 3.33407i) q^{39} +(5.09057 + 4.27150i) q^{41} +(-0.442145 + 1.21478i) q^{43} +(9.28978 + 4.02591i) q^{45} +(0.547022 + 3.10232i) q^{47} +(-4.39261 + 1.59878i) q^{49} +(-3.98712 - 0.469453i) q^{51} +9.35460i q^{53} -1.94436 q^{55} +(-0.566405 - 0.422419i) q^{57} +(3.00302 + 8.25072i) q^{59} +(-4.67459 + 0.824257i) q^{61} +(8.55452 + 5.64720i) q^{63} +(-21.2249 - 7.72523i) q^{65} +(9.67062 - 11.5250i) q^{67} +(11.1817 - 2.64011i) q^{69} +(3.92323 - 6.79524i) q^{71} +(0.641809 + 1.11165i) q^{73} +(9.88600 + 4.97543i) q^{75} +(-1.93861 - 0.341829i) q^{77} +(-3.84081 + 3.22282i) q^{79} +(-0.492839 - 8.98650i) q^{81} +(-6.67152 - 7.95081i) q^{83} +(-7.70366 - 1.35836i) q^{85} +(-2.72128 + 5.40708i) q^{87} +(-2.86501 - 4.96234i) q^{89} +(-19.8040 - 11.4338i) q^{91} +(-3.71746 + 0.877728i) q^{93} +(-1.05466 - 0.884962i) q^{95} +(10.5548 + 3.84165i) q^{97} +(0.773079 + 1.54586i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 12 q^{7} - 12 q^{9} + 12 q^{15} - 6 q^{17} + 12 q^{23} - 12 q^{25} + 12 q^{31} + 12 q^{39} - 24 q^{41} + 12 q^{47} - 12 q^{49} + 24 q^{55} - 30 q^{57} + 72 q^{63} - 12 q^{65} + 90 q^{71} - 6 q^{73}+ \cdots - 12 q^{97}+O(q^{100}) \) 204 * q + 12 * q^7 - 12 * q^9 + 12 * q^15 - 6 * q^17 + 12 * q^23 - 12 * q^25 + 12 * q^31 + 12 * q^39 - 24 * q^41 + 12 * q^47 - 12 * q^49 + 24 * q^55 - 30 * q^57 + 72 * q^63 - 12 * q^65 + 90 * q^71 - 6 * q^73 + 12 * q^79 - 12 * q^81 + 48 * q^87 - 6 * q^89 + 42 * q^95 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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