LMFDB - Embedded newform 936.2.be.a.757.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(685,936)] 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("936.685"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.be (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,1,0,-1,0,0,-2,10,0,-3,0,0,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(14)] == traces)

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			757.6
Character	$\chi$	$=$	936.757
Dual form			936.2.be.a.685.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.332845 - 1.37449i) q^{2} +(-1.77843 + 0.914983i) q^{4} -2.24007i q^{5} +(0.471952 - 0.817445i) q^{7} +(1.84957 + 2.13988i) q^{8} +(-3.07895 + 0.745597i) q^{10} +(-4.82849 + 2.78773i) q^{11} +(0.108823 + 3.60391i) q^{13} +(-1.28065 - 0.376609i) q^{14} +(2.32561 - 3.25446i) q^{16} +(-3.03119 + 5.25017i) q^{17} +(-1.43961 - 0.831159i) q^{19} +(2.04963 + 3.98380i) q^{20} +(5.43884 + 5.70881i) q^{22} +(-1.07746 - 1.86621i) q^{23} -0.0179136 q^{25} +(4.91730 - 1.34912i) q^{26} +(-0.0913848 + 1.88560i) q^{28} +(-1.68452 + 0.972558i) q^{29} -1.91161 q^{31} +(-5.24728 - 2.11329i) q^{32} +(8.22520 + 2.41883i) q^{34} +(-1.83113 - 1.05721i) q^{35} +(-4.54154 + 2.62206i) q^{37} +(-0.663250 + 2.25537i) q^{38} +(4.79348 - 4.14317i) q^{40} +(0.332039 + 0.575109i) q^{41} +(-6.97919 - 4.02944i) q^{43} +(6.03640 - 9.37576i) q^{44} +(-2.20645 + 2.10211i) q^{46} +10.5778 q^{47} +(3.05452 + 5.29059i) q^{49} +(0.00596244 + 0.0246219i) q^{50} +(-3.49105 - 6.30972i) q^{52} +10.3882i q^{53} +(6.24471 + 10.8162i) q^{55} +(2.62214 - 0.502004i) q^{56} +(1.89745 + 1.99164i) q^{58} +(0.411368 + 0.237503i) q^{59} +(3.06666 + 1.77054i) q^{61} +(0.636270 + 2.62748i) q^{62} +(-1.15816 + 7.91572i) q^{64} +(8.07301 - 0.243772i) q^{65} +(-3.91067 + 2.25783i) q^{67} +(0.586933 - 12.1105i) q^{68} +(-0.843631 + 2.86876i) q^{70} +(-5.81695 + 10.0753i) q^{71} -1.91680 q^{73} +(5.11561 + 5.36954i) q^{74} +(3.32074 + 0.160939i) q^{76} +5.26270i q^{77} +13.6120 q^{79} +(-7.29022 - 5.20954i) q^{80} +(0.679962 - 0.647806i) q^{82} -11.5623i q^{83} +(11.7607 + 6.79007i) q^{85} +(-3.21542 + 10.9340i) q^{86} +(-14.8961 - 5.17627i) q^{88} +(0.373638 + 0.647161i) q^{89} +(2.99736 + 1.61192i) q^{91} +(3.62373 + 2.33306i) q^{92} +(-3.52077 - 14.5391i) q^{94} +(-1.86185 + 3.22483i) q^{95} +(0.640742 - 1.10980i) q^{97} +(6.25516 - 5.95935i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + q^{2} - q^{4} - 2 q^{7} + 10 q^{8} - 3 q^{10} - 8 q^{14} - q^{16} + 11 q^{20} - 2 q^{22} + 14 q^{23} - 12 q^{25} + 3 q^{26} - 4 q^{28} - 8 q^{31} + 21 q^{32} + 14 q^{34} - 12 q^{38} + 54 q^{40}+ \cdots + 17 q^{98}+O(q^{100}) $ 24 * q + q^2 - q^4 - 2 * q^7 + 10 * q^8 - 3 * q^10 - 8 * q^14 - q^16 + 11 * q^20 - 2 * q^22 + 14 * q^23 - 12 * q^25 + 3 * q^26 - 4 * q^28 - 8 * q^31 + 21 * q^32 + 14 * q^34 - 12 * q^38 + 54 * q^40 + 4 * q^41 + 24 * q^46 + 8 * q^47 + 6 * q^49 - 32 * q^50 - 4 * q^52 + 8 * q^55 - 8 * q^56 + 33 * q^58 + 14 * q^62 + 26 * q^64 - 30 * q^65 - 23 * q^68 - 16 * q^70 - 30 * q^71 - 12 * q^73 + 7 * q^74 + 14 * q^76 - 48 * q^79 - 29 * q^80 - q^82 + 96 * q^86 + 4 * q^88 + 22 * q^89 + 80 * q^92 - 42 * q^94 - 60 * q^95 + 2 * q^97 + 17 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.332845	−	1.37449i	−0.235357	−	0.971909i
$2$	−0.332845	−	1.37449i	−0.235357	−	0.971909i
$3$		0			0
$3$		0			0
$4$	−1.77843	+	0.914983i	−0.889214	+	0.457491i
$5$		−	2.24007i		−	1.00179i	−0.865508	−	0.500895i	$-0.833004\pi$
$5$		−	2.24007i		−	1.00179i	0.865508	−	0.500895i	$-0.166996\pi$
$6$		0			0
$7$	0.471952	−	0.817445i	0.178381	−	0.308965i	−0.762945	−	0.646463i	$-0.776247\pi$
$7$	0.471952	−	0.817445i	0.178381	−	0.308965i	0.941326	+	0.337498i	$0.109581\pi$
$8$	1.84957	+	2.13988i	0.653923	+	0.756561i
$9$		0			0
$10$	−3.07895	+	0.745597i	−0.973648	+	0.235778i
$11$	−4.82849	+	2.78773i	−1.45584	+	0.840532i	−0.998803	−	0.0489128i	$-0.984424\pi$
$11$	−4.82849	+	2.78773i	−1.45584	+	0.840532i	−0.457042	+	0.889445i	$0.651091\pi$
$12$		0			0
$13$	0.108823	+	3.60391i	0.0301821	+	0.999544i
$13$	0.108823	+	3.60391i	0.0301821	+	0.999544i
$14$	−1.28065	−	0.376609i	−0.342269	−	0.100653i
$15$		0			0
$16$	2.32561	−	3.25446i	0.581403	−	0.813616i
$17$	−3.03119	+	5.25017i	−0.735170	+	1.27335i	0.219478	+	0.975617i	$0.429565\pi$
$17$	−3.03119	+	5.25017i	−0.735170	+	1.27335i	−0.954649	+	0.297735i	$0.903769\pi$
$18$		0			0
$19$	−1.43961	−	0.831159i	−0.330269	−	0.190681i	0.325692	−	0.945476i	$-0.394403\pi$
$19$	−1.43961	−	0.831159i	−0.330269	−	0.190681i	−0.655961	+	0.754795i	$0.727736\pi$
$20$	2.04963	+	3.98380i	0.458310	+	0.890806i
$21$		0			0
$22$	5.43884	+	5.70881i	1.15956	+	1.21712i
$23$	−1.07746	−	1.86621i	−0.224665	−	0.389131i	0.731554	−	0.681784i	$-0.238795\pi$
$23$	−1.07746	−	1.86621i	−0.224665	−	0.389131i	−0.956219	+	0.292652i	$0.905462\pi$
$24$		0			0
$25$	−0.0179136			−0.00358271
$26$	4.91730	−	1.34912i	0.964363	−	0.264584i
$27$		0			0
$28$	−0.0913848	+	1.88560i	−0.0172701	+	0.356344i
$29$	−1.68452	+	0.972558i	−0.312807	+	0.180599i	−0.648182	−	0.761485i	$-0.724470\pi$
$29$	−1.68452	+	0.972558i	−0.312807	+	0.180599i	0.335375	+	0.942085i	$0.391137\pi$
$30$		0			0
$31$	−1.91161			−0.343335			−0.171668	−	0.985155i	$-0.554916\pi$
$31$	−1.91161			−0.343335			−0.171668	+	0.985155i	$0.554916\pi$
$32$	−5.24728	−	2.11329i	−0.927598	−	0.373581i
$33$		0			0
$34$	8.22520	+	2.41883i	1.41061	+	0.414826i
$35$	−1.83113	−	1.05721i	−0.309518	−	0.178700i
$36$		0			0
$37$	−4.54154	+	2.62206i	−0.746624	+	0.431064i	−0.824473	−	0.565902i	$-0.808528\pi$
$37$	−4.54154	+	2.62206i	−0.746624	+	0.431064i	0.0778488	+	0.996965i	$0.475195\pi$
$38$	−0.663250	+	2.25537i	−0.107593	+	0.365870i
$39$		0			0
$40$	4.79348	−	4.14317i	0.757915	−	0.655093i
$41$	0.332039	+	0.575109i	0.0518558	+	0.0898169i	0.890788	−	0.454419i	$-0.150153\pi$
$41$	0.332039	+	0.575109i	0.0518558	+	0.0898169i	−0.838932	+	0.544236i	$0.816820\pi$
$42$		0			0
$43$	−6.97919	−	4.02944i	−1.06432	−	0.614483i	−0.137693	−	0.990475i	$-0.543969\pi$
$43$	−6.97919	−	4.02944i	−1.06432	−	0.614483i	−0.926623	+	0.375992i	$0.877302\pi$
$44$	6.03640	−	9.37576i	0.910021	−	1.41345i
$45$		0			0
$46$	−2.20645	+	2.10211i	−0.325324	+	0.309939i
$47$	10.5778			1.54293			0.771466	−	0.636270i	$-0.219524\pi$
$47$	10.5778			1.54293			0.771466	+	0.636270i	$0.219524\pi$
$48$		0			0
$49$	3.05452	+	5.29059i	0.436360	+	0.755798i
$50$	0.00596244	+	0.0246219i	0.000843216	+	0.00348207i
$51$		0			0
$52$	−3.49105	−	6.30972i	−0.484121	−	0.875001i
$53$			10.3882i			1.42693i	0.700691	+	0.713465i	$0.252875\pi$
$53$			10.3882i			1.42693i	−0.700691	+	0.713465i	$0.747125\pi$
$54$		0			0
$55$	6.24471	+	10.8162i	0.842037	+	1.45845i
$56$	2.62214	−	0.502004i	0.350399	−	0.0670831i
$57$		0			0
$58$	1.89745	+	1.99164i	0.249148	+	0.261515i
$59$	0.411368	+	0.237503i	0.0535555	+	0.0309203i	0.526539	−	0.850151i	$-0.323490\pi$
$59$	0.411368	+	0.237503i	0.0535555	+	0.0309203i	−0.472983	+	0.881071i	$0.656823\pi$
$60$		0			0
$61$	3.06666	+	1.77054i	0.392646	+	0.226694i	0.683306	−	0.730132i	$-0.260541\pi$
$61$	3.06666	+	1.77054i	0.392646	+	0.226694i	−0.290660	+	0.956826i	$0.593875\pi$
$62$	0.636270	+	2.62748i	0.0808064	+	0.333691i
$63$		0			0
$64$	−1.15816	+	7.91572i	−0.144770	+	0.989465i
$65$	8.07301	−	0.243772i	1.00133	−	0.0302362i
$66$		0			0
$67$	−3.91067	+	2.25783i	−0.477764	+	0.275837i	−0.719484	−	0.694509i	$-0.755622\pi$
$67$	−3.91067	+	2.25783i	−0.477764	+	0.275837i	0.241720	+	0.970346i	$0.422288\pi$
$68$	0.586933	−	12.1105i	0.0711761	−	1.46862i
$69$		0			0
$70$	−0.843631	+	2.86876i	−0.100833	+	0.342882i
$71$	−5.81695	+	10.0753i	−0.690345	+	1.19571i	0.281379	+	0.959597i	$0.409208\pi$
$71$	−5.81695	+	10.0753i	−0.690345	+	1.19571i	−0.971725	+	0.236117i	$0.924125\pi$
$72$		0			0
$73$	−1.91680			−0.224345			−0.112172	−	0.993689i	$-0.535781\pi$
$73$	−1.91680			−0.224345			−0.112172	+	0.993689i	$0.535781\pi$
$74$	5.11561	+	5.36954i	0.594678	+	0.624197i
$75$		0			0
$76$	3.32074	+	0.160939i	0.380915	+	0.0184609i
$77$			5.26270i			0.599741i
$78$		0			0
$79$	13.6120			1.53147			0.765737	−	0.643154i	$-0.222374\pi$
$79$	13.6120			1.53147			0.765737	+	0.643154i	$0.222374\pi$
$80$	−7.29022	−	5.20954i	−0.815072	−	0.582444i
$81$		0			0
$82$	0.679962	−	0.647806i	0.0750892	−	0.0715382i
$83$		−	11.5623i		−	1.26913i	−0.772871	−	0.634564i	$-0.781180\pi$
$83$		−	11.5623i		−	1.26913i	0.772871	−	0.634564i	$-0.218820\pi$
$84$		0			0
$85$	11.7607	+	6.79007i	1.27563	+	0.736486i
$86$	−3.21542	+	10.9340i	−0.346727	+	1.17904i
$87$		0			0
$88$	−14.8961	−	5.17627i	−1.58792	−	0.551792i
$89$	0.373638	+	0.647161i	0.0396056	+	0.0685989i	0.885149	−	0.465308i	$-0.154057\pi$
$89$	0.373638	+	0.647161i	0.0396056	+	0.0685989i	−0.845543	+	0.533907i	$0.820723\pi$
$90$		0			0
$91$	2.99736	+	1.61192i	0.314208	+	0.168975i
$92$	3.62373	+	2.33306i	0.377800	+	0.243239i
$93$		0			0
$94$	−3.52077	−	14.5391i	−0.363140	−	1.49959i
$95$	−1.86185	+	3.22483i	−0.191022	+	0.330860i
$96$		0			0
$97$	0.640742	−	1.10980i	0.0650575	−	0.112683i	−0.831662	−	0.555282i	$-0.812610\pi$
$97$	0.640742	−	1.10980i	0.0650575	−	0.112683i	0.896719	+	0.442599i	$0.145944\pi$
$98$	6.25516	−	5.95935i	0.631867	−	0.601985i
$99$		0			0
$100$	0.0318580	−	0.0163906i	0.00318580	−	0.00163906i
$101$	−8.45583	+	4.88197i	−0.841386	+	0.485775i	−0.857735	−	0.514092i	$-0.828129\pi$
$101$	−8.45583	+	4.88197i	−0.841386	+	0.485775i	0.0163490	+	0.999866i	$0.494796\pi$
$102$		0			0
$103$	−15.0755			−1.48544			−0.742719	−	0.669604i	$-0.766464\pi$
$103$	−15.0755			−1.48544			−0.742719	+	0.669604i	$0.766464\pi$
$104$	−7.51065	+	6.89856i	−0.736480	+	0.676460i
$105$		0			0
$106$	14.2785	−	3.45767i	1.38685	−	0.335838i
$107$	−13.6044	+	7.85448i	−1.31518	+	0.759321i	−0.982949	−	0.183876i	$-0.941135\pi$
$107$	−13.6044	+	7.85448i	−1.31518	+	0.759321i	−0.332233	+	0.943197i	$0.607802\pi$
$108$		0			0
$109$		−	9.69920i		−	0.929015i	−0.885569	−	0.464508i	$-0.846231\pi$
$109$		−	9.69920i		−	0.929015i	0.885569	−	0.464508i	$-0.153769\pi$
$110$	12.7881	−	12.1834i	1.21930	−	1.16164i
$111$		0			0
$112$	−1.56277	−	3.43701i	−0.147668	−	0.324767i
$113$	−3.78116	+	6.54916i	−0.355701	+	0.616093i	−0.987238	−	0.159253i	$-0.949091\pi$
$113$	−3.78116	+	6.54916i	−0.355701	+	0.616093i	0.631536	+	0.775346i	$0.282425\pi$
$114$		0			0
$115$	−4.18044	+	2.41358i	−0.389828	+	0.225067i
$116$	2.10592	−	3.27093i	0.195530	−	0.303698i
$117$		0			0
$118$	0.189523	−	0.644472i	0.0174470	−	0.0593284i
$119$	2.86115	+	4.95566i	0.262281	+	0.454284i
$120$		0			0
$121$	10.0429	−	17.3948i	0.912989	−	1.58134i
$122$	1.41286	−	4.80441i	0.127914	−	0.434970i
$123$		0			0
$124$	3.39966	−	1.74909i	0.305299	−	0.157073i
$125$		−	11.1602i		−	0.998201i
$126$		0			0
$127$	−1.53962	−	2.66670i	−0.136619	−	0.236632i	0.789596	−	0.613628i	$-0.210290\pi$
$127$	−1.53962	−	2.66670i	−0.136619	−	0.236632i	−0.926215	+	0.376996i	$0.876957\pi$
$128$	11.2655	−	1.04284i	0.995743	−	0.0921746i
$129$		0			0
$130$	−3.02212	−	11.0151i	−0.265058	−	0.966089i
$131$		−	11.9145i		−	1.04098i	−0.853869	−	0.520488i	$-0.825750\pi$
$131$		−	11.9145i		−	1.04098i	0.853869	−	0.520488i	$-0.174250\pi$
$132$		0			0
$133$	−1.35885	+	0.784534i	−0.117828	+	0.0680278i
$134$	4.40500	+	4.62366i	0.380534	+	0.399423i
$135$		0			0
$136$	−16.8411	+	3.22420i	−1.44411	+	0.276473i
$137$	10.2342	−	17.7261i	0.874365	−	1.51444i	0.0169276	−	0.999857i	$-0.494612\pi$
$137$	10.2342	−	17.7261i	0.874365	−	1.51444i	0.857437	−	0.514588i	$-0.172055\pi$
$138$		0			0
$139$	−7.01589	−	4.05062i	−0.595080	−	0.343570i	0.172024	−	0.985093i	$-0.444969\pi$
$139$	−7.01589	−	4.05062i	−0.595080	−	0.343570i	−0.767104	+	0.641523i	$0.778303\pi$
$140$	4.22387	+	0.204708i	0.356982	+	0.0173010i
$141$		0			0
$142$	15.7845	+	4.64182i	1.32460	+	0.389533i
$143$	−10.5722	−	17.0981i	−0.884090	−	1.42981i
$144$		0			0
$145$	2.17860	+	3.77344i	0.180923	+	0.313367i
$146$	0.637998	+	2.63462i	0.0528011	+	0.218043i
$147$		0			0
$148$	5.67766	−	8.81857i	0.466701	−	0.724882i
$149$	−3.13501	−	1.81000i	−0.256830	−	0.148281i	0.366058	−	0.930592i	$-0.380707\pi$
$149$	−3.13501	−	1.81000i	−0.256830	−	0.148281i	−0.622888	+	0.782311i	$0.714041\pi$
$150$		0			0
$151$	−16.0939			−1.30970			−0.654850	−	0.755759i	$-0.727268\pi$
$151$	−16.0939			−1.30970			−0.654850	+	0.755759i	$0.727268\pi$
$152$	−0.884084	−	4.61788i	−0.0717087	−	0.374559i
$153$		0			0
$154$	7.23351	−	1.75167i	0.582893	−	0.141153i
$155$			4.28214i			0.343950i
$156$		0			0
$157$			15.4274i			1.23124i	0.788042	+	0.615621i	$0.211095\pi$
$157$			15.4274i			1.23124i	−0.788042	+	0.615621i	$0.788905\pi$
$158$	−4.53070	−	18.7096i	−0.360443	−	1.48845i
$159$		0			0
$160$	−4.73392	+	11.7543i	−0.374249	+	0.929258i
$161$	−2.03403			−0.160304
$162$		0			0
$163$	−4.33867	−	2.50493i	−0.339831	−	0.196201i	0.320366	−	0.947294i	$-0.396194\pi$
$163$	−4.33867	−	2.50493i	−0.339831	−	0.196201i	−0.660197	+	0.751092i	$0.729527\pi$
$164$	−1.11672	−	0.718980i	−0.0872014	−	0.0561429i
$165$		0			0
$166$	−15.8922	+	3.84846i	−1.23348	+	0.298698i
$167$	0.532199	+	0.921796i	0.0411828	+	0.0713308i	0.885882	−	0.463910i	$-0.153554\pi$
$167$	0.532199	+	0.921796i	0.0411828	+	0.0713308i	−0.844699	+	0.535241i	$0.820221\pi$
$168$		0			0
$169$	−12.9763	+	0.784378i	−0.998178	+	0.0603368i
$170$	5.41835	−	18.4250i	0.415569	−	1.41314i
$171$		0			0
$172$	16.0988	+	0.780226i	1.22753	+	0.0594916i
$173$	18.9047	+	10.9146i	1.43730	+	0.829825i	0.997661	−	0.0683503i	$-0.0217736\pi$
$173$	18.9047	+	10.9146i	1.43730	+	0.829825i	0.439638	+	0.898175i	$0.355107\pi$
$174$		0			0
$175$	−0.00845434	+	0.0146433i	−0.000639088	+	0.00110693i
$176$	−2.15664	+	22.1973i	−0.162563	+	1.67319i
$177$		0			0
$178$	0.765150	−	0.728965i	0.0573504	−	0.0546383i
$179$	−2.82862	+	1.63310i	−0.211421	+	0.122064i	−0.601972	−	0.798517i	$-0.705618\pi$
$179$	−2.82862	+	1.63310i	−0.211421	+	0.122064i	0.390551	+	0.920581i	$0.372285\pi$
$180$		0			0
$181$			13.1229i			0.975420i	0.873006	+	0.487710i	$0.162168\pi$
$181$			13.1229i			0.975420i	−0.873006	+	0.487710i	$0.837832\pi$
$182$	1.21790	−	4.65635i	0.0902768	−	0.345151i
$183$		0			0
$184$	2.00063	−	5.75731i	0.147488	−	0.424435i
$185$	5.87359	+	10.1734i	0.431835	+	0.747960i
$186$		0			0
$187$		−	33.8005i		−	2.47174i
$188$	−18.8119	+	9.67852i	−1.37200	+	0.705878i
$189$		0			0
$190$	5.05219	+	1.48573i	0.366524	+	0.107786i
$191$	−4.02136	+	6.96520i	−0.290975	+	0.503984i	−0.974041	−	0.226373i	$-0.927313\pi$
$191$	−4.02136	+	6.96520i	−0.290975	+	0.503984i	0.683065	+	0.730357i	$0.260646\pi$
$192$		0			0
$193$	0.417932	+	0.723880i	0.0300834	+	0.0521060i	0.880675	−	0.473721i	$-0.157089\pi$
$193$	0.417932	+	0.723880i	0.0300834	+	0.0521060i	−0.850592	+	0.525827i	$0.823756\pi$
$194$	−1.73867	−	0.511300i	−0.124829	−	0.0367092i
$195$		0			0
$196$	−10.2730	−	6.61409i	−0.733789	−	0.472435i
$197$	6.06608	−	3.50225i	0.432190	−	0.249525i	−0.268089	−	0.963394i	$-0.586392\pi$
$197$	6.06608	−	3.50225i	0.432190	−	0.249525i	0.700279	+	0.713869i	$0.253059\pi$
$198$		0			0
$199$	−7.51756	+	13.0208i	−0.532906	+	0.923019i	0.466356	+	0.884597i	$0.345567\pi$
$199$	−7.51756	+	13.0208i	−0.532906	+	0.923019i	−0.999262	+	0.0384223i	$0.987767\pi$
$200$	−0.0331324	−	0.0383328i	−0.00234282	−	0.00271054i
$201$		0			0
$202$	9.52469	+	9.99748i	0.670155	+	0.703420i
$203$			1.83600i			0.128862i
$204$		0			0
$205$	1.28828	−	0.743791i	0.0899777	−	0.0519486i
$206$	5.01782	+	20.7211i	0.349608	+	1.44371i
$207$		0			0
$208$	11.9819	+	8.02714i	0.830793	+	0.556582i
$209$	9.26819			0.641094
$210$		0			0
$211$	−5.82236	+	3.36154i	−0.400828	+	0.231418i	−0.686841	−	0.726808i	$-0.741003\pi$
$211$	−5.82236	+	3.36154i	−0.400828	+	0.231418i	0.286013	+	0.958226i	$0.407670\pi$
$212$	−9.50503	−	18.4747i	−0.652808	−	1.26885i
$213$		0			0
$214$	15.3240	+	16.0847i	1.04753	+	1.09953i
$215$	−9.02622	+	15.6339i	−0.615583	+	1.06622i
$216$		0			0
$217$	−0.902189	+	1.56264i	−0.0612446	+	0.106079i
$218$	−13.3314	+	3.22833i	−0.902918	+	0.218650i
$219$		0			0
$220$	−21.0024	−	13.5220i	−1.41598	−	0.911650i
$221$	−19.2510	−	10.3528i	−1.29496	−	0.696403i
$222$		0			0
$223$	−10.4340	−	18.0723i	−0.698715	−	1.21021i	−0.968912	−	0.247404i	$-0.920422\pi$
$223$	−10.4340	−	18.0723i	−0.698715	−	1.21021i	0.270198	−	0.962805i	$-0.412911\pi$
$224$	−4.20397	+	3.29199i	−0.280889	+	0.219956i
$225$		0			0
$226$	10.2603	+	3.01730i	0.682503	+	0.200707i
$227$	16.7688	+	9.68145i	1.11298	+	0.642580i	0.939600	−	0.342274i	$-0.111197\pi$
$227$	16.7688	+	9.68145i	1.11298	+	0.642580i	0.173382	+	0.984855i	$0.444531\pi$
$228$		0			0
$229$		−	17.6044i		−	1.16333i	−0.813428	−	0.581666i	$-0.802401\pi$
$229$		−	17.6044i		−	1.16333i	0.813428	−	0.581666i	$-0.197599\pi$
$230$	4.70887	+	4.94261i	0.310494	+	0.325906i
$231$		0			0
$232$	−5.19680	−	1.80585i	−0.341186	−	0.118560i
$233$	−15.3281			−1.00417			−0.502087	−	0.864817i	$-0.667434\pi$
$233$	−15.3281			−1.00417			−0.502087	+	0.864817i	$0.667434\pi$
$234$		0			0
$235$		−	23.6950i		−	1.54569i
$236$	−0.948900	−	0.0459881i	−0.0617681	−	0.00299357i
$237$		0			0
$238$	5.85916	−	5.58208i	0.379793	−	0.361832i
$239$	14.0854			0.911111			0.455556	−	0.890207i	$-0.349441\pi$
$239$	14.0854			0.911111			0.455556	+	0.890207i	$0.349441\pi$
$240$		0			0
$241$	−7.24993	+	12.5572i	−0.467009	+	0.808883i	−0.999290	−	0.0376849i	$-0.988002\pi$
$241$	−7.24993	+	12.5572i	−0.467009	+	0.808883i	0.532281	+	0.846568i	$0.321335\pi$
$242$	−27.2516	−	8.01404i	−1.75180	−	0.515162i
$243$		0			0
$244$	−7.07386	−	0.342832i	−0.452857	−	0.0219476i
$245$	11.8513	−	6.84234i	0.757151	−	0.437141i
$246$		0			0
$247$	2.83876	−	5.27867i	0.180626	−	0.335874i
$248$	−3.53566	−	4.09061i	−0.224515	−	0.259754i
$249$		0			0
$250$	−15.3396	+	3.71463i	−0.970160	+	0.234934i
$251$	−24.8381	−	14.3403i	−1.56777	−	0.905151i	−0.996429	−	0.0844378i	$-0.973091\pi$
$251$	−24.8381	−	14.3403i	−1.56777	−	0.905151i	−0.571340	−	0.820714i	$-0.693576\pi$
$252$		0			0
$253$	10.4050	+	6.00731i	0.654155	+	0.377677i
$254$	−3.15289	+	3.00379i	−0.197830	+	0.188475i
$255$		0			0
$256$	−5.18305	−	15.1372i	−0.323940	−	0.946077i
$257$	−5.81269	−	10.0679i	−0.362586	−	0.628017i	0.625800	−	0.779984i	$-0.284773\pi$
$257$	−5.81269	−	10.0679i	−0.362586	−	0.628017i	−0.988386	+	0.151967i	$0.951439\pi$
$258$		0			0
$259$			4.94994i			0.307574i
$260$	−14.1342	+	7.82019i	−0.876567	+	0.484988i
$261$		0			0
$262$	−16.3763	+	3.96569i	−1.01173	+	0.245001i
$263$	−8.47469	−	14.6786i	−0.522572	−	0.905121i	−0.999655	−	0.0262631i	$-0.991639\pi$
$263$	−8.47469	−	14.6786i	−0.522572	−	0.905121i	0.477083	−	0.878858i	$-0.341694\pi$
$264$		0			0
$265$	23.2703			1.42948
$266$	1.53062	+	1.60660i	0.0938483	+	0.0985068i
$267$		0			0
$268$	4.88897	−	7.59358i	0.298642	−	0.463852i
$269$	6.45180	+	3.72495i	0.393373	+	0.227114i	0.683621	−	0.729837i	$-0.260404\pi$
$269$	6.45180	+	3.72495i	0.393373	+	0.227114i	−0.290247	+	0.956952i	$0.593738\pi$
$270$		0			0
$271$	7.61248	+	13.1852i	0.462425	+	0.800944i	0.999081	−	0.0428569i	$-0.0136459\pi$
$271$	7.61248	+	13.1852i	0.462425	+	0.800944i	−0.536656	+	0.843801i	$0.680313\pi$
$272$	10.0371	+	22.0747i	0.608589	+	1.33848i
$273$		0			0
$274$	−27.7707	−	8.16669i	−1.67769	−	0.493368i
$275$	0.0864954	−	0.0499382i	0.00521587	−	0.00301138i
$276$		0			0
$277$	13.9928	+	8.07878i	0.840749	+	0.485407i	0.857519	−	0.514453i	$-0.172005\pi$
$277$	13.9928	+	8.07878i	0.840749	+	0.485407i	−0.0167699	+	0.999859i	$0.505338\pi$
$278$	−3.23233	+	10.9915i	−0.193862	+	0.659225i
$279$		0			0
$280$	−1.12452	−	5.87378i	−0.0672032	−	0.351026i
$281$	−27.7204			−1.65366			−0.826831	−	0.562450i	$-0.809859\pi$
$281$	−27.7204			−1.65366			−0.826831	+	0.562450i	$0.809859\pi$
$282$		0			0
$283$	−3.28760	+	1.89810i	−0.195428	+	0.112830i	−0.594521	−	0.804080i	$-0.702658\pi$
$283$	−3.28760	+	1.89810i	−0.195428	+	0.112830i	0.399093	+	0.916910i	$0.369325\pi$
$284$	1.12635	−	23.2405i	0.0668363	−	1.37907i
$285$		0			0
$286$	−19.9822	+	20.2223i	−1.18157	+	1.19577i
$287$	0.626827			0.0370004
$288$		0			0
$289$	−9.87617	−	17.1060i	−0.580951	−	1.00624i
$290$	4.46141	−	4.25043i	0.261983	−	0.249594i
$291$		0			0
$292$	3.40889	−	1.75384i	0.199490	−	0.102636i
$293$	4.14791	+	2.39480i	0.242324	+	0.139906i	0.616244	−	0.787555i	$-0.288653\pi$
$293$	4.14791	+	2.39480i	0.242324	+	0.139906i	−0.373921	+	0.927461i	$0.621987\pi$
$294$		0			0
$295$	0.532024	−	0.921493i	0.0309756	−	0.0536514i
$296$	−14.0108	−	4.86865i	−0.814360	−	0.282984i
$297$		0			0
$298$	−1.44435	+	4.91148i	−0.0836687	+	0.284514i
$299$	6.60839	−	4.08614i	0.382173	−	0.236308i
$300$		0			0
$301$	−6.58768	+	3.80340i	−0.379708	+	0.219224i
$302$	5.35677	+	22.1208i	0.308247	+	1.27291i
$303$		0			0
$304$	−6.05295	+	2.75220i	−0.347160	+	0.157849i
$305$	3.96613	−	6.86954i	0.227100	−	0.393349i
$306$		0			0
$307$			8.95981i			0.511363i	0.966761	+	0.255682i	$0.0822999\pi$
$307$			8.95981i			0.511363i	−0.966761	+	0.255682i	$0.917700\pi$
$308$	−4.81528	−	9.35934i	−0.274376	−	0.533298i
$309$		0			0
$310$	5.88575	−	1.42529i	0.334288	−	0.0809511i
$311$	−9.35196			−0.530301			−0.265150	−	0.964207i	$-0.585422\pi$
$311$	−9.35196			−0.530301			−0.265150	+	0.964207i	$0.585422\pi$
$312$		0			0
$313$	−11.7834			−0.666039			−0.333019	−	0.942920i	$-0.608067\pi$
$313$	−11.7834			−0.666039			−0.333019	+	0.942920i	$0.608067\pi$
$314$	21.2048	−	5.13494i	1.19665	−	0.289782i
$315$		0			0
$316$	−24.2080	+	12.4548i	−1.36181	+	0.700636i
$317$		−	0.828044i		−	0.0465076i	−0.999730	−	0.0232538i	$-0.992597\pi$
$317$		−	0.828044i		−	0.0465076i	0.999730	−	0.0232538i	$-0.00740258\pi$
$318$		0			0
$319$	5.42246	−	9.39197i	0.303599	−	0.525850i
$320$	17.7318	+	2.59436i	0.991236	+	0.145029i
$321$		0			0
$322$	0.677017	+	2.79575i	0.0377287	+	0.155801i
$323$	8.72745	−	5.03879i	0.485608	−	0.280366i
$324$		0			0
$325$	−0.00194941	−	0.0645588i	−0.000108134	−	0.00358108i
$326$	−1.99889	+	6.79720i	−0.110708	+	0.376462i
$327$		0			0
$328$	−0.616532	+	1.77423i	−0.0340423	+	0.0979655i
$329$	4.99222	−	8.64678i	0.275230	−	0.476712i
$330$		0			0
$331$	12.8419	+	7.41425i	0.705853	+	0.407524i	0.809524	−	0.587087i	$-0.199726\pi$
$331$	12.8419	+	7.41425i	0.705853	+	0.407524i	−0.103671	+	0.994612i	$0.533059\pi$
$332$	10.5793	+	20.5627i	0.580615	+	1.12853i
$333$		0			0
$334$	1.08986	−	1.03832i	0.0596343	−	0.0568142i
$335$	5.05769	+	8.76018i	0.276331	+	0.478620i
$336$		0			0
$337$	5.53901			0.301729			0.150865	−	0.988554i	$-0.451794\pi$
$337$	5.53901			0.301729			0.150865	+	0.988554i	$0.451794\pi$
$338$	5.39722	+	17.5747i	0.293570	+	0.955938i
$339$		0			0
$340$	−27.1284	−	1.31477i	−1.47125	−	0.0713035i
$341$	9.23019	−	5.32906i	0.499843	−	0.288585i
$342$		0			0
$343$	12.3737			0.668116
$344$	−4.28601	−	22.3873i	−0.231086	−	1.20704i
$345$		0			0
$346$	8.70969	−	29.6172i	0.468236	−	1.59223i
$347$	13.9803	+	8.07154i	0.750503	+	0.433303i	0.825876	−	0.563852i	$-0.190681\pi$
$347$	13.9803	+	8.07154i	0.750503	+	0.433303i	−0.0753728	+	0.997155i	$0.524015\pi$
$348$		0			0
$349$	20.7087	−	11.9562i	1.10851	−	0.640000i	0.170068	−	0.985432i	$-0.445601\pi$
$349$	20.7087	−	11.9562i	1.10851	−	0.640000i	0.938444	+	0.345432i	$0.112268\pi$
$350$	0.0229411	+	0.00674641i	0.00122625	+	0.000360611i
$351$		0			0
$352$	31.2278	−	4.42400i	1.66445	−	0.235800i
$353$	2.77899	+	4.81335i	0.147911	+	0.256189i	0.930455	−	0.366406i	$-0.119412\pi$
$353$	2.77899	+	4.81335i	0.147911	+	0.256189i	−0.782544	+	0.622595i	$0.786079\pi$
$354$		0			0
$355$	22.5693	+	13.0304i	1.19785	+	0.691581i
$356$	−1.25663	−	0.809056i	−0.0666013	−	0.0428799i
$357$		0			0
$358$	3.18617	+	3.34433i	0.168395	+	0.176753i
$359$	8.55135			0.451323			0.225661	−	0.974206i	$-0.427546\pi$
$359$	8.55135			0.451323			0.225661	+	0.974206i	$0.427546\pi$
$360$		0			0
$361$	−8.11835	−	14.0614i	−0.427282	−	0.740073i
$362$	18.0373	−	4.36791i	0.948019	−	0.229572i
$363$		0			0
$364$	−6.80546	−	0.124146i	−0.356703	−	0.00650701i
$365$			4.29377i			0.224746i
$366$		0			0
$367$	1.96700	+	3.40695i	0.102677	+	0.177841i	0.912787	−	0.408437i	$-0.133926\pi$
$367$	1.96700	+	3.40695i	0.102677	+	0.177841i	−0.810110	+	0.586278i	$0.800593\pi$
$368$	−8.57925	−	0.833539i	−0.447224	−	0.0434512i
$369$		0			0
$370$	12.0282	−	11.4593i	0.625314	−	0.595742i
$371$	8.49179	+	4.90274i	0.440872	+	0.254537i
$372$		0			0
$373$	6.86329	+	3.96253i	0.355368	+	0.205172i	0.667047	−	0.745016i	$-0.267558\pi$
$373$	6.86329	+	3.96253i	0.355368	+	0.205172i	−0.311679	+	0.950187i	$0.600891\pi$
$374$	−46.4584	+	11.2503i	−2.40230	+	0.581741i
$375$		0			0
$376$	19.5644	+	22.6352i	1.00896	+	1.16732i
$377$	−3.68832	−	5.96502i	−0.189958	−	0.307214i
$378$		0			0
$379$	−22.8779	+	13.2086i	−1.17516	+	0.678479i	−0.954890	−	0.296959i	$-0.904027\pi$
$379$	−22.8779	+	13.2086i	−1.17516	+	0.678479i	−0.220271	+	0.975439i	$0.570694\pi$
$380$	0.360514	−	7.43868i	0.0184940	−	0.381596i
$381$		0			0
$382$	10.9121	+	3.20897i	0.558310	+	0.164185i
$383$	0.947088	−	1.64041i	0.0483940	−	0.0838208i	−0.840814	−	0.541325i	$-0.817923\pi$
$383$	0.947088	−	1.64041i	0.0483940	−	0.0838208i	0.889208	+	0.457504i	$0.151256\pi$
$384$		0			0
$385$	11.7888			0.600814
$386$	0.855857	−	0.815382i	0.0435620	−	0.0415019i
$387$		0			0
$388$	−0.124068	+	2.55996i	−0.00629859	+	0.129962i
$389$			25.0808i			1.27165i	0.771835	+	0.635823i	$0.219339\pi$
$389$			25.0808i			1.27165i	−0.771835	+	0.635823i	$0.780661\pi$
$390$		0			0
$391$	13.0639			0.660669
$392$	−5.67165	+	16.3216i	−0.286462	+	0.824367i
$393$		0			0
$394$	−6.83286	−	7.17203i	−0.344235	−	0.361322i
$395$		−	30.4919i		−	1.53422i
$396$		0			0
$397$	−7.99993	−	4.61876i	−0.401505	−	0.231809i	0.285628	−	0.958341i	$-0.407798\pi$
$397$	−7.99993	−	4.61876i	−0.401505	−	0.231809i	−0.687133	+	0.726532i	$0.741131\pi$
$398$	20.3991	+	5.99888i	1.02251	+	0.300696i
$399$		0			0
$400$	−0.0416600	+	0.0582990i	−0.00208300	+	0.00291495i
$401$	2.21136	+	3.83018i	0.110430	+	0.191270i	0.915944	−	0.401307i	$-0.131444\pi$
$401$	2.21136	+	3.83018i	0.110430	+	0.191270i	−0.805514	+	0.592577i	$0.798111\pi$
$402$		0			0
$403$	−0.208028	−	6.88927i	−0.0103626	−	0.343179i
$404$	10.5712	−	16.4192i	0.525935	−	0.816884i
$405$		0			0
$406$	2.52356	−	0.611105i	0.125242	−	0.0303286i
$407$	14.6192	−	25.3212i	0.724646	−	1.25512i
$408$		0			0
$409$	−13.2341	+	22.9221i	−0.654384	+	1.13343i	0.327664	+	0.944794i	$0.393738\pi$
$409$	−13.2341	+	22.9221i	−0.654384	+	1.13343i	−0.982048	+	0.188631i	$0.939595\pi$
$410$	−1.45113	−	1.52316i	−0.0716662	−	0.0752236i
$411$		0			0
$412$	26.8108	−	13.7939i	1.32087	−	0.679575i
$413$	0.388292	−	0.224180i	0.0191066	−	0.0110312i
$414$		0			0
$415$	−25.9004			−1.27140
$416$	7.04509	−	19.1407i	0.345414	−	0.938450i
$417$		0			0
$418$	−3.08487	−	12.7390i	−0.150886	−	0.623085i
$419$	4.30501	−	2.48550i	0.210314	−	0.121425i	−0.391144	−	0.920330i	$-0.627920\pi$
$419$	4.30501	−	2.48550i	0.210314	−	0.121425i	0.601457	+	0.798905i	$0.294587\pi$
$420$		0			0
$421$		−	24.0575i		−	1.17249i	−0.810134	−	0.586244i	$-0.800606\pi$
$421$		−	24.0575i		−	1.17249i	0.810134	−	0.586244i	$-0.199394\pi$
$422$	6.55834	+	6.88388i	0.319255	+	0.335102i
$423$		0			0
$424$	−22.2295	+	19.2137i	−1.07956	+	0.933102i
$425$	0.0542993	−	0.0940492i	0.00263390	−	0.00456205i
$426$		0			0
$427$	2.89464	−	1.67122i	0.140081	−	0.0808760i
$428$	17.0077	−	26.4164i	0.822096	−	1.27688i
$429$		0			0
$430$	24.4929	+	7.20276i	1.18115	+	0.347348i
$431$	5.28961	+	9.16188i	0.254792	+	0.441312i	0.964839	−	0.262842i	$-0.0846598\pi$
$431$	5.28961	+	9.16188i	0.254792	+	0.441312i	−0.710047	+	0.704154i	$0.751326\pi$
$432$		0			0
$433$	6.11293	−	10.5879i	0.293769	−	0.508822i	−0.680929	−	0.732349i	$-0.738424\pi$
$433$	6.11293	−	10.5879i	0.293769	−	0.508822i	0.974698	+	0.223527i	$0.0717572\pi$
$434$	2.44811	+	0.719930i	0.117513	+	0.0345578i
$435$		0			0
$436$	8.87460	+	17.2493i	0.425016	+	0.826093i
$437$			3.58215i			0.171357i
$438$		0			0
$439$	−6.46417	−	11.1963i	−0.308518	−	0.534369i	0.669520	−	0.742794i	$-0.266500\pi$
$439$	−6.46417	−	11.1963i	−0.308518	−	0.534369i	−0.978038	+	0.208425i	$0.933166\pi$
$440$	−11.5952	+	33.3682i	−0.552780	+	1.59077i
$441$		0			0
$442$	−7.82215	+	29.9061i	−0.372062	+	1.42249i
$443$		−	14.0440i		−	0.667248i	−0.942706	−	0.333624i	$-0.891728\pi$
$443$		−	14.0440i		−	0.667248i	0.942706	−	0.333624i	$-0.108272\pi$
$444$		0			0
$445$	1.44969	−	0.836976i	0.0687217	−	0.0396765i
$446$	−21.3672	+	20.3567i	−1.01177	+	0.963918i
$447$		0			0
$448$	5.92407	+	4.68257i	0.279886	+	0.221231i
$449$	0.857113	−	1.48456i	0.0404497	−	0.0700609i	−0.845092	−	0.534621i	$-0.820454\pi$
$449$	0.857113	−	1.48456i	0.0404497	−	0.0700609i	0.885541	+	0.464560i	$0.153788\pi$
$450$		0			0
$451$	−3.20650	−	1.85127i	−0.150988	−	0.0871730i
$452$	0.732151	−	15.1069i	0.0344375	−	0.710569i
$453$		0			0
$454$	7.72562	−	26.2709i	0.362581	−	1.23295i
$455$	3.61080	−	6.71429i	0.169277	−	0.314771i
$456$		0			0
$457$	14.5822	+	25.2571i	0.682126	+	1.18148i	0.974331	+	0.225121i	$0.0722778\pi$
$457$	14.5822	+	25.2571i	0.682126	+	1.18148i	−0.292205	+	0.956356i	$0.594389\pi$
$458$	−24.1970	+	5.85954i	−1.13065	+	0.273798i
$459$		0			0
$460$	5.22623	−	8.11740i	0.243674	−	0.378476i
$461$	22.4501	+	12.9616i	1.04561	+	0.603681i	0.921416	−	0.388577i	$-0.127033\pi$
$461$	22.4501	+	12.9616i	1.04561	+	0.603681i	0.124190	+	0.992258i	$0.460367\pi$
$462$		0			0
$463$	36.7003			1.70561			0.852803	−	0.522233i	$-0.174901\pi$
$463$	36.7003			1.70561			0.852803	+	0.522233i	$0.174901\pi$
$464$	−0.752388	+	7.74400i	−0.0349287	+	0.359506i
$465$		0			0
$466$	5.10187	+	21.0682i	0.236340	+	0.975967i
$467$			27.9836i			1.29492i	0.762097	+	0.647462i	$0.224170\pi$
$467$			27.9836i			1.29492i	−0.762097	+	0.647462i	$0.775830\pi$
$468$		0			0
$469$			4.26234i			0.196817i
$470$	−32.5685	+	7.88678i	−1.50227	+	0.363790i
$471$		0			0
$472$	0.252627	+	1.31956i	0.0116281	+	0.0607375i
$473$	44.9319			2.06597
$474$		0			0
$475$	0.0257885	+	0.0148890i	0.00118326	+	0.000683155i
$476$	−9.62269	−	6.19537i	−0.441055	−	0.283965i
$477$		0			0
$478$	−4.68827	−	19.3603i	−0.214437	−	0.885517i
$479$	−16.2482	−	28.1426i	−0.742397	−	1.28587i	−0.951401	−	0.307955i	$-0.900355\pi$
$479$	−16.2482	−	28.1426i	−0.742397	−	1.28587i	0.209004	−	0.977915i	$-0.432978\pi$
$480$		0			0
$481$	−9.94388	−	16.0819i	−0.453402	−	0.733273i
$482$	19.6729	+	5.78531i	0.896074	+	0.263514i
$483$		0			0
$484$	−1.94462	+	40.1244i	−0.0883918	+	1.82384i
$485$	−2.48602	−	1.43531i	−0.112885	−	0.0651739i
$486$		0			0
$487$	−5.79695	+	10.0406i	−0.262685	+	0.454983i	−0.966954	−	0.254949i	$-0.917941\pi$
$487$	−5.79695	+	10.0406i	−0.262685	+	0.454983i	0.704270	+	0.709933i	$0.251275\pi$
$488$	1.88328	+	9.83703i	0.0852521	+	0.445302i
$489$		0			0
$490$	−13.3494	−	14.0120i	−0.603062	−	0.632997i
$491$	36.2077	−	20.9045i	1.63403	−	0.943407i	0.651197	−	0.758909i	$-0.274267\pi$
$491$	36.2077	−	20.9045i	1.63403	−	0.943407i	0.982833	−	0.184498i	$-0.0590661\pi$
$492$		0			0
$493$		−	11.7920i		−	0.531085i
$494$	−8.20033	−	2.14485i	−0.368950	−	0.0965016i
$495$		0			0
$496$	−4.44567	+	6.22126i	−0.199616	+	0.279343i
$497$	5.49065	+	9.51008i	0.246289	+	0.426585i
$498$		0			0
$499$			17.9011i			0.801363i	0.916217	+	0.400682i	$0.131227\pi$
$499$			17.9011i			0.801363i	−0.916217	+	0.400682i	$0.868773\pi$
$500$	10.2114	+	19.8477i	0.456668	+	0.887614i
$501$		0			0
$502$	−11.4433	+	38.9128i	−0.510739	+	1.73676i
$503$	7.29456	−	12.6345i	0.325248	−	0.563346i	−0.656314	−	0.754488i	$-0.727886\pi$
$503$	7.29456	−	12.6345i	0.325248	−	0.563346i	0.981563	+	0.191141i	$0.0612188\pi$
$504$		0			0
$505$	10.9360	+	18.9416i	0.486644	+	0.842892i
$506$	4.79373	−	16.3010i	0.213107	−	0.724668i
$507$		0			0
$508$	5.17810	+	3.33381i	0.229741	+	0.147914i
$509$	−1.08621	+	0.627122i	−0.0481453	+	0.0277967i	−0.523879	−	0.851792i	$-0.675516\pi$
$509$	−1.08621	+	0.627122i	−0.0481453	+	0.0277967i	0.475734	+	0.879589i	$0.342182\pi$
$510$		0			0
$511$	−0.904639	+	1.56688i	−0.0400189	+	0.0693147i
$512$	−19.0808	+	12.1624i	−0.843259	+	0.537507i
$513$		0			0
$514$	−11.9034	+	11.3405i	−0.525038	+	0.500209i
$515$			33.7703i			1.48810i
$516$		0			0
$517$	−51.0749	+	29.4881i	−2.24627	+	1.29688i
$518$	6.80363	−	1.64756i	0.298934	−	0.0723898i
$519$		0			0
$520$	15.4533	+	16.8244i	0.677670	+	0.737798i
$521$	−8.42526			−0.369117			−0.184559	−	0.982822i	$-0.559086\pi$
$521$	−8.42526			−0.369117			−0.184559	+	0.982822i	$0.559086\pi$
$522$		0			0
$523$	20.6677	−	11.9325i	0.903736	−	0.521772i	0.0253256	−	0.999679i	$-0.491938\pi$
$523$	20.6677	−	11.9325i	0.903736	−	0.521772i	0.878410	+	0.477907i	$0.158604\pi$
$524$	10.9016	+	21.1891i	0.476238	+	0.925651i
$525$		0			0
$526$	−17.3548	+	16.5341i	−0.756704	+	0.720919i
$527$	5.79445	−	10.0363i	0.252410	−	0.437187i
$528$		0			0
$529$	9.17818	−	15.8971i	0.399051	−	0.691177i
$530$	−7.74541	−	31.9847i	−0.336439	−	1.38933i
$531$		0			0
$532$	1.69879	−	2.63857i	0.0736518	−	0.114396i
$533$	−2.03651	+	1.25922i	−0.0882109	+	0.0545431i
$534$		0			0
$535$	17.5946	+	30.4747i	0.760680	+	1.31754i
$536$	−12.0645	−	4.19234i	−0.521109	−	0.181082i
$537$		0			0
$538$	2.97244	−	10.1077i	0.128151	−	0.435776i
$539$	−29.4975	−	17.0304i	−1.27055	−	0.733550i
$540$		0			0
$541$			19.4928i			0.838059i	0.907973	+	0.419030i	$0.137630\pi$
$541$			19.4928i			0.838059i	−0.907973	+	0.419030i	$0.862370\pi$
$542$	15.5891	−	14.8519i	0.669610	−	0.637943i
$543$		0			0
$544$	27.0006	−	21.1433i	1.15764	−	0.906513i
$545$	−21.7269			−0.930678
$546$		0			0
$547$		−	2.18538i		−	0.0934399i	−0.998908	−	0.0467200i	$-0.985123\pi$
$547$		−	2.18538i		−	0.0934399i	0.998908	−	0.0467200i	$-0.0148768\pi$
$548$	−1.98166	+	40.8887i	−0.0846523	+	1.74668i
$549$		0			0
$550$	−0.0974289	−	0.102265i	−0.00415438	−	0.00436060i
$551$	3.23340			0.137747
$552$		0			0
$553$	6.42423	−	11.1271i	0.273186	−	0.473172i
$554$	6.44672	−	21.9220i	0.273895	−	0.931375i
$555$		0			0
$556$	16.1835	+	0.784328i	0.686333	+	0.0332629i
$557$	29.5902	−	17.0839i	1.25378	−	0.723869i	0.281921	−	0.959438i	$-0.409028\pi$
$557$	29.5902	−	17.0839i	1.25378	−	0.723869i	0.971858	+	0.235568i	$0.0756951\pi$
$558$		0			0
$559$	13.7622	−	25.5908i	0.582080	−	1.08238i
$560$	−7.69915	+	3.50071i	−0.325348	+	0.147932i
$561$		0			0
$562$	9.22661	+	38.1014i	0.389201	+	1.60721i
$563$	20.4379	+	11.7998i	0.861353	+	0.497302i	0.864465	−	0.502693i	$-0.167657\pi$
$563$	20.4379	+	11.7998i	0.861353	+	0.497302i	−0.00311215	+	0.999995i	$0.500991\pi$
$564$		0			0
$565$	14.6706	+	8.47006i	0.617195	+	0.356338i
$566$	3.70317	+	3.88699i	0.155656	+	0.163382i
$567$		0			0
$568$	−32.3187	+	6.18736i	−1.35606	+	0.259616i
$569$	1.38906	+	2.40592i	0.0582323	+	0.100861i	0.893672	−	0.448721i	$-0.148120\pi$
$569$	1.38906	+	2.40592i	0.0582323	+	0.100861i	−0.835440	+	0.549582i	$0.814787\pi$
$570$		0			0
$571$			19.2497i			0.805577i	0.915293	+	0.402788i	$0.131959\pi$
$571$			19.2497i			0.805577i	−0.915293	+	0.402788i	$0.868041\pi$
$572$	34.4463	+	20.7343i	1.44027	+	0.866946i
$573$		0			0
$574$	−0.208636	−	0.861565i	−0.00870831	−	0.0359610i
$575$	0.0193011	+	0.0334304i	0.000804910	+	0.00139415i
$576$		0			0
$577$	6.64617			0.276683			0.138342	−	0.990385i	$-0.455823\pi$
$577$	6.64617			0.276683			0.138342	+	0.990385i	$0.455823\pi$
$578$	−20.2248	+	19.2683i	−0.841240	+	0.801457i
$579$		0			0
$580$	−7.32711	−	4.71742i	−0.304242	−	0.195880i
$581$	−9.45154	−	5.45685i	−0.392116	−	0.226388i
$582$		0			0
$583$	−28.9595	−	50.1594i	−1.19938	−	2.07739i
$584$	−3.54526	−	4.10172i	−0.146704	−	0.169730i
$585$		0			0
$586$	1.91101	−	6.49835i	0.0789430	−	0.268444i
$587$	−23.1016	+	13.3377i	−0.953505	+	0.550507i	−0.894168	−	0.447731i	$-0.852232\pi$
$587$	−23.1016	+	13.3377i	−0.953505	+	0.550507i	−0.0593374	+	0.998238i	$0.518899\pi$
$588$		0			0
$589$	2.75197	+	1.58885i	0.113393	+	0.0654675i
$590$	−1.44366	−	0.424546i	−0.0594346	−	0.0174783i
$591$		0			0
$592$	−2.02847	+	20.8781i	−0.0833696	+	0.858087i
$593$	−6.61409			−0.271608			−0.135804	−	0.990736i	$-0.543362\pi$
$593$	−6.61409			−0.271608			−0.135804	+	0.990736i	$0.543362\pi$
$594$		0			0
$595$	11.1010	−	6.40917i	0.455097	−	0.262751i
$596$	7.23150	+	0.350473i	0.296214	+	0.0143559i
$597$		0			0
$598$	−7.81592	−	7.72310i	−0.319617	−	0.315821i
$599$	−11.9319			−0.487523			−0.243762	−	0.969835i	$-0.578381\pi$
$599$	−11.9319			−0.487523			−0.243762	+	0.969835i	$0.578381\pi$
$600$		0			0
$601$	6.15610	+	10.6627i	0.251113	+	0.434940i	0.963832	−	0.266509i	$-0.0858702\pi$
$601$	6.15610	+	10.6627i	0.251113	+	0.434940i	−0.712720	+	0.701449i	$0.752537\pi$
$602$	7.42040	+	7.78874i	0.302433	+	0.317445i
$603$		0			0
$604$	28.6218	−	14.7256i	1.16460	−	0.599177i
$605$	−38.9655	−	22.4968i	−1.58417	−	0.914623i
$606$		0			0
$607$	4.35738	−	7.54720i	0.176860	−	0.306331i	−0.763943	−	0.645284i	$-0.776739\pi$
$607$	4.35738	−	7.54720i	0.176860	−	0.306331i	0.940804	+	0.338952i	$0.110073\pi$
$608$	5.79756	+	7.40364i	0.235122	+	0.300257i
$609$		0			0
$610$	−10.7622	−	3.16490i	−0.435749	−	0.128143i
$611$	1.15111	+	38.1215i	0.0465690	+	1.54223i
$612$		0			0
$613$	30.7480	−	17.7523i	1.24190	−	0.717010i	0.272418	−	0.962179i	$-0.412177\pi$
$613$	30.7480	−	17.7523i	1.24190	−	0.717010i	0.969480	+	0.245169i	$0.0788433\pi$
$614$	12.3151	−	2.98223i	0.496999	−	0.120353i
$615$		0			0
$616$	−11.2615	+	9.73375i	−0.453740	+	0.392184i
$617$	−12.0318	+	20.8396i	−0.484380	+	0.838971i	−0.999839	−	0.0179431i	$-0.994288\pi$
$617$	−12.0318	+	20.8396i	−0.484380	+	0.838971i	0.515459	+	0.856914i	$0.327622\pi$
$618$		0			0
$619$			21.6806i			0.871417i	0.900088	+	0.435708i	$0.143502\pi$
$619$			21.6806i			0.871417i	−0.900088	+	0.435708i	$0.856498\pi$
$620$	−3.91809	−	7.61548i	−0.157354	−	0.305845i
$621$		0			0
$622$	3.11275	+	12.8541i	0.124810	+	0.515404i
$623$	0.705358			0.0282596
$624$		0			0
$625$	−25.0892			−1.00357
$626$	3.92206	+	16.1962i	0.156757	+	0.647329i
$627$		0			0
$628$	−14.1158	−	27.4365i	−0.563283	−	1.09484i
$629$		−	31.7918i		−	1.26762i
$630$		0			0
$631$	−9.48379	+	16.4264i	−0.377544	+	0.653925i	−0.990704	−	0.136033i	$-0.956565\pi$
$631$	−9.48379	+	16.4264i	−0.377544	+	0.653925i	0.613161	+	0.789958i	$0.289898\pi$
$632$	25.1765	+	29.1281i	1.00147	+	1.15865i
$633$		0			0
$634$	−1.13814	+	0.275611i	−0.0452011	+	0.0109459i
$635$	−5.97360	+	3.44886i	−0.237055	+	0.136864i
$636$		0			0
$637$	−18.7344	+	11.5840i	−0.742284	+	0.458973i
$638$	−14.7140	−	4.32702i	−0.582532	−	0.171309i
$639$		0			0
$640$	−2.33603	−	25.2356i	−0.0923395	−	0.997525i
$641$	12.4294	−	21.5284i	0.490934	−	0.850322i	−0.509012	−	0.860759i	$-0.669989\pi$
$641$	12.4294	−	21.5284i	0.490934	−	0.850322i	0.999946	+	0.0104375i	$0.00332243\pi$
$642$		0			0
$643$	3.25429	+	1.87887i	0.128337	+	0.0740952i	0.562794	−	0.826597i	$-0.309726\pi$
$643$	3.25429	+	1.87887i	0.128337	+	0.0740952i	−0.434457	+	0.900692i	$0.643060\pi$
$644$	3.61738	−	1.86110i	0.142545	−	0.0733377i
$645$		0			0
$646$	−9.83064	−	10.3186i	−0.386781	−	0.405981i
$647$	24.0878	+	41.7213i	0.946989	+	1.64023i	0.751718	+	0.659484i	$0.229225\pi$
$647$	24.0878	+	41.7213i	0.946989	+	1.64023i	0.195271	+	0.980749i	$0.437441\pi$
$648$		0			0
$649$	−2.64838			−0.103958
$650$	−0.0880864	+	0.0241675i	−0.00345503	+	0.000947929i
$651$		0			0
$652$	10.0080	+	0.485034i	0.391943	+	0.0189954i
$653$	−21.5793	+	12.4588i	−0.844463	+	0.487551i	−0.858779	−	0.512346i	$-0.828776\pi$
$653$	−21.5793	+	12.4588i	−0.844463	+	0.487551i	0.0143156	+	0.999898i	$0.495443\pi$
$654$		0			0
$655$	−26.6894			−1.04284
$656$	2.64387	+	0.256872i	0.103226	+	0.0100291i
$657$		0			0
$658$	−13.5465	−	3.98370i	−0.528098	−	0.155301i
$659$	−1.75765	−	1.01478i	−0.0684684	−	0.0395302i	0.465375	−	0.885114i	$-0.345919\pi$
$659$	−1.75765	−	1.01478i	−0.0684684	−	0.0395302i	−0.533843	+	0.845583i	$0.679253\pi$
$660$		0			0
$661$	−9.61763	+	5.55274i	−0.374082	+	0.215977i	−0.675240	−	0.737598i	$-0.735960\pi$
$661$	−9.61763	+	5.55274i	−0.374082	+	0.215977i	0.301158	+	0.953574i	$0.402627\pi$
$662$	5.91644	−	20.1188i	0.229949	−	0.781938i
$663$		0			0
$664$	24.7419	−	21.3853i	0.960172	−	0.829911i
$665$	1.75741	+	3.04393i	0.0681495	+	0.118038i
$666$		0			0
$667$	3.62999	+	2.09578i	0.140554	+	0.0811488i
$668$	−1.78991	−	1.15240i	−0.0692536	−	0.0445875i
$669$		0			0
$670$	10.3573	−	9.86751i	0.400138	−	0.381215i
$671$	−19.7432			−0.762176
$672$		0			0
$673$	−17.0389	−	29.5122i	−0.656800	−	1.13761i	−0.981439	−	0.191773i	$-0.938576\pi$
$673$	−17.0389	−	29.5122i	−0.656800	−	1.13761i	0.324639	−	0.945838i	$-0.394757\pi$
$674$	−1.84363	−	7.61330i	−0.0710141	−	0.293253i
$675$		0			0
$676$	22.3598	−	13.2681i	0.859990	−	0.510310i
$677$		−	28.8974i		−	1.11062i	−0.831645	−	0.555308i	$-0.812600\pi$
$677$		−	28.8974i		−	1.11062i	0.831645	−	0.555308i	$-0.187400\pi$
$678$		0			0
$679$	−0.604799	−	1.04754i	−0.0232100	−	0.0402010i
$680$	7.22243	+	37.7253i	0.276968	+	1.44670i
$681$		0			0
$682$	−10.3969	−	10.9130i	−0.398120	−	0.417882i
$683$	−18.5350	−	10.7012i	−0.709221	−	0.409469i	0.101551	−	0.994830i	$-0.467619\pi$
$683$	−18.5350	−	10.7012i	−0.709221	−	0.409469i	−0.810773	+	0.585361i	$0.800953\pi$
$684$		0			0
$685$	−39.7078	−	22.9253i	−1.51716	−	0.875930i
$686$	−4.11852	−	17.0075i	−0.157246	−	0.649348i
$687$		0			0
$688$	−29.3445	+	13.3426i	−1.11875	+	0.508682i
$689$	−37.4381	+	1.13048i	−1.42628	+	0.0430678i
$690$		0			0
$691$	42.9878	−	24.8190i	1.63533	−	0.944159i	0.652921	−	0.757426i	$-0.273543\pi$
$691$	42.9878	−	24.8190i	1.63533	−	0.944159i	0.982411	−	0.186733i	$-0.0597900\pi$
$692$	−43.6074	−	2.11342i	−1.65770	−	0.0803401i
$693$		0			0
$694$	6.44094	−	21.9023i	0.244495	−	0.831401i
$695$	−9.07368	+	15.7161i	−0.344184	+	0.596145i
$696$		0			0
$697$	−4.02589			−0.152491
$698$	−23.3264	−	24.4843i	−0.882918	−	0.926744i
$699$		0			0
$700$	0.00163703	−	0.0337777i	6.18738e−5	−	0.00127668i
$701$		−	23.3855i		−	0.883258i	−0.897198	−	0.441629i	$-0.854401\pi$
$701$		−	23.3855i		−	0.883258i	0.897198	−	0.441629i	$-0.145599\pi$
$702$		0			0
$703$	8.71738			0.328782
$704$	−16.4747	−	41.4496i	−0.620915	−	1.56219i
$705$		0			0
$706$	5.69091	−	5.42178i	0.214180	−	0.204051i
$707$			9.21623i			0.346612i
$708$		0			0
$709$	−41.1118	−	23.7359i	−1.54399	−	0.891421i	−0.998581	−	0.0532487i	$-0.983042\pi$
$709$	−41.1118	−	23.7359i	−1.54399	−	0.891421i	−0.545405	−	0.838172i	$-0.683624\pi$
$710$	10.3980	−	35.3583i	0.390230	−	1.32697i
$711$		0			0
$712$	−0.693774	+	1.99651i	−0.0260003	+	0.0748224i
$713$	2.05968	+	3.56746i	0.0771355	+	0.133603i
$714$		0			0
$715$	−38.3009	+	23.6824i	−1.43237	+	0.885672i
$716$	3.53624	−	5.49250i	0.132155	−	0.205264i
$717$		0			0
$718$	−2.84628	−	11.7537i	−0.106222	−	0.438645i
$719$	−22.6840	+	39.2899i	−0.845972	+	1.46527i	0.0388023	+	0.999247i	$0.487646\pi$
$719$	−22.6840	+	39.2899i	−0.845972	+	1.46527i	−0.884774	+	0.466020i	$0.845688\pi$
$720$		0			0
$721$	−7.11493	+	12.3234i	−0.264974	+	0.458948i
$722$	−16.6250	+	15.8388i	−0.618720	+	0.589460i
$723$		0			0
$724$	−12.0073	−	23.3382i	−0.446246	−	0.867357i
$725$	0.0301757	−	0.0174220i	0.00112070	−	0.000647036i
$726$		0			0
$727$	27.1042			1.00524			0.502619	−	0.864508i	$-0.332370\pi$
$727$	27.1042			1.00524			0.502619	+	0.864508i	$0.332370\pi$
$728$	2.09453	+	9.39533i	0.0776284	+	0.348214i
$729$		0			0
$730$	5.90173	−	1.42916i	0.218433	−	0.0528956i
$731$	42.3104	−	24.4279i	1.56491	−	0.903500i
$732$		0			0
$733$			21.1225i			0.780179i	0.920777	+	0.390090i	$0.127556\pi$
$733$			21.1225i			0.780179i	−0.920777	+	0.390090i	$0.872444\pi$
$734$	4.02810	−	3.83760i	0.148680	−	0.141649i
$735$		0			0
$736$	1.70987	+	12.0695i	0.0630268	+	0.444888i
$737$	12.5884	−	21.8038i	0.463701	−	0.803153i
$738$		0			0
$739$	25.6746	−	14.8233i	0.944457	−	0.545283i	0.0531023	−	0.998589i	$-0.483089\pi$
$739$	25.6746	−	14.8233i	0.944457	−	0.545283i	0.891355	+	0.453307i	$0.149756\pi$
$740$	−19.7542	−	12.7184i	−0.726179	−	0.467536i
$741$		0			0
$742$	3.91230	−	13.3037i	0.143625	−	0.488394i
$743$	−5.52318	−	9.56643i	−0.202626	−	0.350958i	0.746748	−	0.665107i	$-0.231614\pi$
$743$	−5.52318	−	9.56643i	−0.202626	−	0.350958i	−0.949374	+	0.314149i	$0.898281\pi$
$744$		0			0
$745$	−4.05452	+	7.02264i	−0.148546	+	0.257290i
$746$	3.16202	−	10.7524i	0.115770	−	0.393674i
$747$		0			0
$748$	30.9269	+	60.1118i	1.13080	+	2.19790i
$749$			14.8277i			0.541794i
$750$		0			0
$751$	18.6034	+	32.2220i	0.678846	+	1.17580i	0.975329	+	0.220758i	$0.0708530\pi$
$751$	18.6034	+	32.2220i	0.678846	+	1.17580i	−0.296483	+	0.955038i	$0.595814\pi$
$752$	24.5999	−	34.4251i	0.897066	−	1.25535i
$753$		0			0
$754$	−6.97120	+	7.05498i	−0.253876	+	0.256927i
$755$			36.0514i			1.31204i
$756$		0			0
$757$	17.2083	−	9.93522i	0.625446	−	0.361102i	−0.153540	−	0.988142i	$-0.549067\pi$
$757$	17.2083	−	9.93522i	0.625446	−	0.361102i	0.778986	+	0.627041i	$0.215734\pi$
$758$	25.7698	+	27.0490i	0.936003	+	0.982464i
$759$		0			0
$760$	−10.3444	+	1.98041i	−0.375230	+	0.0718370i
$761$	4.52926	−	7.84491i	0.164186	−	0.284378i	−0.772180	−	0.635404i	$-0.780834\pi$
$761$	4.52926	−	7.84491i	0.164186	−	0.284378i	0.936366	+	0.351026i	$0.114167\pi$
$762$		0			0
$763$	−7.92857	−	4.57756i	−0.287033	−	0.165719i
$764$	0.778662	−	16.0666i	0.0281710	−	0.581269i
$765$		0			0
$766$	−2.56995	−	0.755759i	−0.0928560	−	0.0273067i
$767$	−0.811174	+	1.50838i	−0.0292898	+	0.0544644i
$768$		0			0
$769$	−5.28678	−	9.15697i	−0.190646	−	0.330209i	0.754818	−	0.655934i	$-0.227725\pi$
$769$	−5.28678	−	9.15697i	−0.190646	−	0.330209i	−0.945465	+	0.325725i	$0.894392\pi$
$770$	−3.92385	−	16.2036i	−0.141406	−	0.583936i
$771$		0			0
$772$	−1.40560	−	0.904968i	−0.0505887	−	0.0325705i
$773$	22.3264	+	12.8902i	0.803026	+	0.463627i	0.844528	−	0.535511i	$-0.179881\pi$
$773$	22.3264	+	12.8902i	0.803026	+	0.463627i	−0.0415022	+	0.999138i	$0.513214\pi$
$774$		0			0
$775$	0.0342437			0.00123007
$776$	3.55993	−	0.681542i	0.127794	−	0.0244659i
$777$		0			0
$778$	34.4732	−	8.34802i	1.23592	−	0.299291i
$779$		−	1.10391i		−	0.0395517i
$780$		0			0
$781$		−	64.8644i		−	2.32103i
$782$	−4.34825	−	17.9561i	−0.155493	−	0.642110i
$783$		0			0
$784$	24.3217	+	2.36303i	0.868631	+	0.0843940i
$785$	34.5585			1.23345
$786$		0			0
$787$	12.1719	+	7.02745i	0.433881	+	0.250502i	0.700999	−	0.713162i	$-0.252738\pi$
$787$	12.1719	+	7.02745i	0.433881	+	0.250502i	−0.267117	+	0.963664i	$0.586071\pi$
$788$	−7.58358	+	11.7789i	−0.270154	+	0.419604i
$789$		0			0
$790$	−41.9108	+	10.1491i	−1.49112	+	0.361088i
$791$	3.56905	+	6.18178i	0.126901	+	0.219799i
$792$		0			0
$793$	−6.04714	+	11.2447i	−0.214740	+	0.399309i
$794$	−3.68569	+	12.5331i	−0.130800	+	0.444784i
$795$		0			0
$796$	1.45564	−	30.0350i	0.0515936	−	1.06456i
$797$	−19.1331	−	11.0465i	−0.677731	−	0.391288i	0.121269	−	0.992620i	$-0.461304\pi$
$797$	−19.1331	−	11.0465i	−0.677731	−	0.391288i	−0.798999	+	0.601332i	$0.794637\pi$
$798$		0			0
$799$	−32.0633	+	55.5353i	−1.13432	+	1.96470i
$800$	0.0939975	+	0.0378566i	0.00332331	+	0.00133843i
$801$		0			0
$802$	4.52849	−	4.31434i	0.159907	−	0.152345i
$803$	9.25526	−	5.34353i	0.326611	−	0.188569i
$804$		0			0
$805$			4.55637i			0.160591i
$806$	−9.39997	+	2.57899i	−0.331100	+	0.0908411i
$807$		0			0
$808$	−26.0865	−	9.06487i	−0.917720	−	0.318901i
$809$	2.02317	+	3.50424i	0.0711310	+	0.123202i	0.899397	−	0.437132i	$-0.144006\pi$
$809$	2.02317	+	3.50424i	0.0711310	+	0.123202i	−0.828266	+	0.560335i	$0.810672\pi$
$810$		0			0
$811$			18.7132i			0.657109i	0.944485	+	0.328555i	$0.106561\pi$
$811$			18.7132i			0.657109i	−0.944485	+	0.328555i	$0.893439\pi$
$812$	−1.67991	−	3.26520i	−0.0589533	−	0.114586i
$813$		0			0
$814$	−39.6695	−	11.6658i	−1.39042	−	0.408888i
$815$	−5.61122	+	9.71893i	−0.196553	+	0.340439i
$816$		0			0
$817$	6.69820	+	11.6016i	0.234340	+	0.405889i
$818$	35.9110	+	10.5606i	1.25560	+	0.369241i
$819$		0			0
$820$	−1.61056	+	2.50154i	−0.0562434	+	0.0873575i
$821$	6.46202	−	3.73085i	0.225526	−	0.130208i	−0.382980	−	0.923757i	$-0.625102\pi$
$821$	6.46202	−	3.73085i	0.225526	−	0.130208i	0.608506	+	0.793549i	$0.291769\pi$
$822$		0			0
$823$	−9.81336	+	16.9972i	−0.342072	+	0.592486i	−0.984817	−	0.173594i	$-0.944462\pi$
$823$	−9.81336	+	16.9972i	−0.342072	+	0.592486i	0.642745	+	0.766080i	$0.277795\pi$
$824$	−27.8833	−	32.2598i	−0.971361	−	1.12382i
$825$		0			0
$826$	−0.437374	−	0.459085i	−0.0152182	−	0.0159736i
$827$		−	19.2616i		−	0.669792i	−0.942255	−	0.334896i	$-0.891299\pi$
$827$		−	19.2616i		−	0.669792i	0.942255	−	0.334896i	$-0.108701\pi$
$828$		0			0
$829$	18.7148	−	10.8050i	0.649993	−	0.375273i	−0.138461	−	0.990368i	$-0.544215\pi$
$829$	18.7148	−	10.8050i	0.649993	−	0.375273i	0.788453	+	0.615094i	$0.210882\pi$
$830$	8.62081	+	35.5997i	0.299233	+	1.23568i
$831$		0			0
$832$	−28.6536	−	3.31248i	−0.993384	−	0.114840i
$833$	−37.0353			−1.28320
$834$		0			0
$835$	2.06489	−	1.19216i	0.0714584	−	0.0412565i
$836$	−16.4828	+	8.48023i	−0.570070	+	0.293295i
$837$		0			0
$838$	−4.84919	−	5.08989i	−0.167512	−	0.175827i
$839$	21.0839	−	36.5183i	0.727895	−	1.26075i	−0.229876	−	0.973220i	$-0.573832\pi$
$839$	21.0839	−	36.5183i	0.727895	−	1.26075i	0.957771	−	0.287532i	$-0.0928347\pi$
$840$		0			0
$841$	−12.6083	+	21.8382i	−0.434768	+	0.753040i
$842$	−33.0667	+	8.00741i	−1.13955	+	0.275954i
$843$		0			0
$844$	7.27889	−	11.3056i	0.250550	−	0.389155i
$845$	1.75706	+	29.0679i	0.0604448	+	0.999965i
$846$		0			0
$847$	−9.47952	−	16.4190i	−0.325720	−	0.564164i
$848$	33.8080	+	24.1590i	1.16097	+	0.829622i
$849$		0			0
$850$	−0.147343	−	0.0433299i	−0.00505381	−	0.00148620i
$851$	9.78661	+	5.65030i	0.335481	+	0.193690i
$852$		0			0
$853$		−	40.2417i		−	1.37785i	−0.724833	−	0.688924i	$-0.758083\pi$
$853$		−	40.2417i		−	1.37785i	0.724833	−	0.688924i	$-0.241917\pi$
$854$	−3.26054	−	3.42238i	−0.111573	−	0.117112i
$855$		0			0
$856$	−41.9699	−	14.5842i	−1.43450	−	0.498479i
$857$	−7.37621			−0.251966			−0.125983	−	0.992032i	$-0.540209\pi$
$857$	−7.37621			−0.251966			−0.125983	+	0.992032i	$0.540209\pi$
$858$		0			0
$859$			31.9493i			1.09010i	0.838405	+	0.545048i	$0.183489\pi$
$859$			31.9493i			1.09010i	−0.838405	+	0.545048i	$0.816511\pi$
$860$	1.74776	−	36.0625i	0.0595981	−	1.22972i
$861$		0			0
$862$	10.8323	−	10.3200i	0.368948	−	0.351500i
$863$	16.1143			0.548536			0.274268	−	0.961653i	$-0.411564\pi$
$863$	16.1143			0.548536			0.274268	+	0.961653i	$0.411564\pi$
$864$		0			0
$865$	24.4496	−	42.3479i	0.831310	−	1.43987i
$866$	−16.5876	−	4.87801i	−0.563669	−	0.165761i
$867$		0			0
$868$	0.174692	−	3.60452i	0.00592944	−	0.122346i
$869$	−65.7256	+	37.9467i	−2.22959	+	1.28725i
$870$		0			0
$871$	−8.56257	−	13.8480i	−0.290132	−	0.469221i
$872$	20.7551	−	17.9394i	0.702857	−	0.607504i
$873$		0			0
$874$	4.92362	−	1.19230i	0.166544	−	0.0403302i
$875$	−9.12287	−	5.26709i	−0.308409	−	0.178060i
$876$		0			0
$877$	−0.181562	−	0.104825i	−0.00613091	−	0.00353968i	0.496931	−	0.867790i	$-0.334460\pi$
$877$	−0.181562	−	0.104825i	−0.00613091	−	0.00353968i	−0.503062	+	0.864250i	$0.667793\pi$
$878$	−13.2376	+	12.6115i	−0.446746	+	0.425619i
$879$		0			0
$880$	49.7236	+	4.83102i	1.67618	+	0.162854i
$881$	20.1008	+	34.8157i	0.677214	+	1.17297i	0.975816	+	0.218592i	$0.0701464\pi$
$881$	20.1008	+	34.8157i	0.677214	+	1.17297i	−0.298602	+	0.954378i	$0.596520\pi$
$882$		0			0
$883$			4.69019i			0.157837i	0.996881	+	0.0789187i	$0.0251467\pi$
$883$			4.69019i			0.157837i	−0.996881	+	0.0789187i	$0.974853\pi$
$884$	43.7091	+	0.797345i	1.47010	+	0.0268176i
$885$		0			0
$886$	−19.3032	+	4.67446i	−0.648505	+	0.157042i
$887$	11.6991	+	20.2635i	0.392819	+	0.680382i	0.992820	−	0.119617i	$-0.0381667\pi$
$887$	11.6991	+	20.2635i	0.392819	+	0.680382i	−0.600002	+	0.799999i	$0.704833\pi$
$888$		0			0
$889$	−2.90651			−0.0974813
$890$	−1.63293	−	1.71399i	−0.0547361	−	0.0574531i
$891$		0			0
$892$	35.0920	+	22.5933i	1.17497	+	0.756479i
$893$	−15.2279	−	8.79184i	−0.509583	−	0.294208i
$894$		0			0
$895$	3.65827	+	6.33631i	0.122282	+	0.211799i
$896$	4.46434	−	9.70113i	0.149143	−	0.324092i
$897$		0			0
$898$	−2.32580	−	0.683961i	−0.0776129	−	0.0228241i
$899$	3.22015	−	1.85915i	0.107398	−	0.0620062i
$900$		0			0
$901$	−54.5398	−	31.4886i	−1.81698	−	1.04904i
$902$	−1.47728	+	5.02348i	−0.0491881	+	0.167263i
$903$		0			0
$904$	−21.0079	+	4.02193i	−0.698713	+	0.133767i
$905$	29.3963			0.977166
$906$		0			0
$907$	−3.93422	+	2.27142i	−0.130634	+	0.0754213i	−0.563893	−	0.825848i	$-0.690697\pi$
$907$	−3.93422	+	2.27142i	−0.130634	+	0.0754213i	0.433259	+	0.901269i	$0.357363\pi$
$908$	−38.6804	−	1.87463i	−1.28365	−	0.0622119i
$909$		0			0
$910$	−10.4305	−	2.72818i	−0.345769	−	0.0904384i
$911$	29.5451			0.978873			0.489436	−	0.872039i	$-0.337203\pi$
$911$	29.5451			0.978873			0.489436	+	0.872039i	$0.337203\pi$
$912$		0			0
$913$	32.2326	+	55.8285i	1.06674	+	1.84765i
$914$	29.8619	−	28.4497i	0.987745	−	0.941033i
$915$		0			0
$916$	16.1077	+	31.3082i	0.532214	+	1.03445i
$917$	−9.73946	−	5.62308i	−0.321625	−	0.185691i
$918$		0			0
$919$	15.5647	−	26.9588i	0.513431	−	0.889288i	−0.486448	−	0.873710i	$-0.661708\pi$
$919$	15.5647	−	26.9588i	0.513431	−	0.889288i	0.999879	−	0.0155787i	$-0.00495905\pi$
$920$	−12.8968	−	4.48154i	−0.425194	−	0.147752i
$921$		0			0
$922$	10.3431	−	35.1716i	0.340632	−	1.15831i
$923$	−36.9433	−	19.8673i	−1.21600	−	0.653942i
$924$		0			0
$925$	0.0813551	−	0.0469704i	0.00267494	−	0.00154438i
$926$	−12.2155	−	50.4440i	−0.401426	−	1.65769i
$927$		0			0
$928$	10.8945	−	1.54341i	0.357628	−	0.0506648i
$929$	−11.9251	+	20.6548i	−0.391249	+	0.677663i	−0.992615	−	0.121311i	$-0.961290\pi$
$929$	−11.9251	+	20.6548i	−0.391249	+	0.677663i	0.601366	+	0.798974i	$0.294624\pi$
$930$		0			0
$931$		−	10.1552i		−	0.332822i
$932$	27.2599	−	14.0249i	0.892926	−	0.459401i
$933$		0			0
$934$	38.4630	−	9.31419i	1.25855	−	0.304770i
$935$	−75.7155			−2.47616
$936$		0			0
$937$	−9.97996			−0.326031			−0.163016	−	0.986623i	$-0.552122\pi$
$937$	−9.97996			−0.326031			−0.163016	+	0.986623i	$0.552122\pi$
$938$	5.85854	−	1.41870i	0.191288	−	0.0463222i
$939$		0			0
$940$	21.6806	+	42.1399i	0.707142	+	1.37445i
$941$			12.2242i			0.398498i	0.979949	+	0.199249i	$0.0638502\pi$
$941$			12.2242i			0.398498i	−0.979949	+	0.199249i	$0.936150\pi$
$942$		0			0
$943$	0.715515	−	1.23931i	0.0233004	−	0.0403575i
$944$	1.72963	−	0.786440i	0.0562946	−	0.0255965i
$945$		0			0
$946$	−14.9554	−	61.7583i	−0.486241	−	2.00794i
$947$	2.80497	−	1.61945i	0.0911494	−	0.0526251i	−0.453732	−	0.891138i	$-0.649908\pi$
$947$	2.80497	−	1.61945i	0.0911494	−	0.0526251i	0.544882	+	0.838513i	$0.316574\pi$
$948$		0			0
$949$	−0.208593	−	6.90798i	−0.00677120	−	0.224242i
$950$	0.0118812	−	0.0404017i	0.000385476	−	0.00131080i
$951$		0			0
$952$	−5.31260	+	15.2884i	−0.172182	+	0.495499i
$953$	3.08301	−	5.33994i	0.0998686	−	0.172977i	−0.811762	−	0.583989i	$-0.801491\pi$
$953$	3.08301	−	5.33994i	0.0998686	−	0.172977i	0.911630	+	0.411012i	$0.134824\pi$
$954$		0			0
$955$	15.6025	+	9.00813i	0.504886	+	0.291496i
$956$	−25.0499	+	12.8879i	−0.810173	+	0.416826i
$957$		0			0
$958$	−33.2736	+	31.7000i	−1.07502	+	1.02418i
$959$	−9.66009	−	16.7318i	−0.311941	−	0.540297i
$960$		0			0
$961$	−27.3457			−0.882121
$962$	−18.7946	+	19.0205i	−0.605964	+	0.613246i
$963$		0			0
$964$	1.40381	−	28.9657i	0.0452138	−	0.932922i
$965$	1.62154	−	0.936197i	0.0521993	−	0.0301373i
$966$		0			0
$967$	44.1828			1.42082			0.710411	−	0.703787i	$-0.248509\pi$
$967$	44.1828			1.42082			0.710411	+	0.703787i	$0.248509\pi$
$968$	55.7978	−	10.6824i	1.79341	−	0.343345i
$969$		0			0
$970$	−1.14535	+	3.89474i	−0.0367749	+	0.125053i
$971$	−33.2299	−	19.1853i	−1.06640	−	0.615686i	−0.139204	−	0.990264i	$-0.544454\pi$
$971$	−33.2299	−	19.1853i	−1.06640	−	0.615686i	−0.927195	+	0.374578i	$0.877788\pi$
$972$		0			0
$973$	−6.62233	+	3.82340i	−0.212302	+	0.122573i
$974$	15.7302	+	4.62586i	0.504027	+	0.148222i
$975$		0			0
$976$	12.8940	−	5.86275i	0.412728	−	0.187662i
$977$	9.04005	+	15.6578i	0.289217	+	0.500938i	0.973623	−	0.228163i	$-0.0732718\pi$
$977$	9.04005	+	15.6578i	0.289217	+	0.500938i	−0.684406	+	0.729101i	$0.739938\pi$
$978$		0			0
$979$	−3.60822	−	2.08321i	−0.115319	−	0.0665796i
$980$	−14.8160	+	23.0123i	−0.473281	+	0.735102i
$981$		0			0
$982$	−40.7845	−	42.8090i	−1.30149	−	1.36609i
$983$	−18.8329			−0.600677			−0.300339	−	0.953833i	$-0.597100\pi$
$983$	−18.8329			−0.600677			−0.300339	+	0.953833i	$0.597100\pi$
$984$		0			0
$985$	−7.84529	−	13.5884i	−0.249972	−	0.432964i
$986$	−16.2080	+	3.92491i	−0.516167	+	0.124995i
$987$		0			0
$988$	−0.218634	+	11.9851i	−0.00695568	+	0.381298i
$989$			17.3662i			0.552212i
$990$		0			0
$991$	−24.8600	−	43.0588i	−0.789704	−	1.36781i	−0.926148	−	0.377160i	$-0.876901\pi$
$991$	−24.8600	−	43.0588i	−0.789704	−	1.36781i	0.136444	−	0.990648i	$-0.456433\pi$
$992$	10.0308	+	4.03979i	0.318477	+	0.128264i
$993$		0			0
$994$	11.2439	−	10.7122i	0.356636	−	0.339771i
$995$	29.1675	+	16.8399i	0.924671	+	0.533859i
$996$		0			0
$997$	41.6202	+	24.0294i	1.31812	+	0.761020i	0.983427	−	0.181306i	$-0.0580324\pi$
$997$	41.6202	+	24.0294i	1.31812	+	0.761020i	0.334698	+	0.942325i	$0.391366\pi$
$998$	24.6048	−	5.95829i	0.778852	−	0.188606i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.be.a.757.6		24
3.2	odd	2		104.2.r.a.29.7	✓	24
8.5	even	2	inner	936.2.be.a.757.3		24
12.11	even	2		416.2.z.a.81.8		24
13.9	even	3	inner	936.2.be.a.685.3		24
24.5	odd	2		104.2.r.a.29.10	yes	24
24.11	even	2		416.2.z.a.81.5		24
39.35	odd	6		104.2.r.a.61.10	yes	24
104.61	even	6	inner	936.2.be.a.685.6		24
156.35	even	6		416.2.z.a.113.5		24
312.35	even	6		416.2.z.a.113.8		24
312.269	odd	6		104.2.r.a.61.7	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.r.a.29.7	✓	24	3.2	odd	2
104.2.r.a.29.10	yes	24	24.5	odd	2
104.2.r.a.61.7	yes	24	312.269	odd	6
104.2.r.a.61.10	yes	24	39.35	odd	6
416.2.z.a.81.5		24	24.11	even	2
416.2.z.a.81.8		24	12.11	even	2
416.2.z.a.113.5		24	156.35	even	6
416.2.z.a.113.8		24	312.35	even	6
936.2.be.a.685.3		24	13.9	even	3	inner
936.2.be.a.685.6		24	104.61	even	6	inner
936.2.be.a.757.3		24	8.5	even	2	inner
936.2.be.a.757.6		24	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.332845 - 1.37449i) q^{2} +(-1.77843 + 0.914983i) q^{4} -2.24007i q^{5} +(0.471952 - 0.817445i) q^{7} +(1.84957 + 2.13988i) q^{8} +(-3.07895 + 0.745597i) q^{10} +(-4.82849 + 2.78773i) q^{11} +(0.108823 + 3.60391i) q^{13} +(-1.28065 - 0.376609i) q^{14} +(2.32561 - 3.25446i) q^{16} +(-3.03119 + 5.25017i) q^{17} +(-1.43961 - 0.831159i) q^{19} +(2.04963 + 3.98380i) q^{20} +(5.43884 + 5.70881i) q^{22} +(-1.07746 - 1.86621i) q^{23} -0.0179136 q^{25} +(4.91730 - 1.34912i) q^{26} +(-0.0913848 + 1.88560i) q^{28} +(-1.68452 + 0.972558i) q^{29} -1.91161 q^{31} +(-5.24728 - 2.11329i) q^{32} +(8.22520 + 2.41883i) q^{34} +(-1.83113 - 1.05721i) q^{35} +(-4.54154 + 2.62206i) q^{37} +(-0.663250 + 2.25537i) q^{38} +(4.79348 - 4.14317i) q^{40} +(0.332039 + 0.575109i) q^{41} +(-6.97919 - 4.02944i) q^{43} +(6.03640 - 9.37576i) q^{44} +(-2.20645 + 2.10211i) q^{46} +10.5778 q^{47} +(3.05452 + 5.29059i) q^{49} +(0.00596244 + 0.0246219i) q^{50} +(-3.49105 - 6.30972i) q^{52} +10.3882i q^{53} +(6.24471 + 10.8162i) q^{55} +(2.62214 - 0.502004i) q^{56} +(1.89745 + 1.99164i) q^{58} +(0.411368 + 0.237503i) q^{59} +(3.06666 + 1.77054i) q^{61} +(0.636270 + 2.62748i) q^{62} +(-1.15816 + 7.91572i) q^{64} +(8.07301 - 0.243772i) q^{65} +(-3.91067 + 2.25783i) q^{67} +(0.586933 - 12.1105i) q^{68} +(-0.843631 + 2.86876i) q^{70} +(-5.81695 + 10.0753i) q^{71} -1.91680 q^{73} +(5.11561 + 5.36954i) q^{74} +(3.32074 + 0.160939i) q^{76} +5.26270i q^{77} +13.6120 q^{79} +(-7.29022 - 5.20954i) q^{80} +(0.679962 - 0.647806i) q^{82} -11.5623i q^{83} +(11.7607 + 6.79007i) q^{85} +(-3.21542 + 10.9340i) q^{86} +(-14.8961 - 5.17627i) q^{88} +(0.373638 + 0.647161i) q^{89} +(2.99736 + 1.61192i) q^{91} +(3.62373 + 2.33306i) q^{92} +(-3.52077 - 14.5391i) q^{94} +(-1.86185 + 3.22483i) q^{95} +(0.640742 - 1.10980i) q^{97} +(6.25516 - 5.95935i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + q^{2} - q^{4} - 2 q^{7} + 10 q^{8} - 3 q^{10} - 8 q^{14} - q^{16} + 11 q^{20} - 2 q^{22} + 14 q^{23} - 12 q^{25} + 3 q^{26} - 4 q^{28} - 8 q^{31} + 21 q^{32} + 14 q^{34} - 12 q^{38} + 54 q^{40}+ \cdots + 17 q^{98}+O(q^{100}) \) 24 * q + q^2 - q^4 - 2 * q^7 + 10 * q^8 - 3 * q^10 - 8 * q^14 - q^16 + 11 * q^20 - 2 * q^22 + 14 * q^23 - 12 * q^25 + 3 * q^26 - 4 * q^28 - 8 * q^31 + 21 * q^32 + 14 * q^34 - 12 * q^38 + 54 * q^40 + 4 * q^41 + 24 * q^46 + 8 * q^47 + 6 * q^49 - 32 * q^50 - 4 * q^52 + 8 * q^55 - 8 * q^56 + 33 * q^58 + 14 * q^62 + 26 * q^64 - 30 * q^65 - 23 * q^68 - 16 * q^70 - 30 * q^71 - 12 * q^73 + 7 * q^74 + 14 * q^76 - 48 * q^79 - 29 * q^80 - q^82 + 96 * q^86 + 4 * q^88 + 22 * q^89 + 80 * q^92 - 42 * q^94 - 60 * q^95 + 2 * q^97 + 17 * q^98

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