LMFDB - Embedded newform 896.2.z.b.159.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [896,2,Mod(31,896)] 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("896.31"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(896, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.z (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [56,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$7.15459602111$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			159.13
Character	$\chi$	$=$	896.159
Dual form			896.2.z.b.479.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.61463 + 0.700587i) q^{3} +(-0.120751 - 0.450647i) q^{5} +(-2.37326 + 1.16946i) q^{7} +(3.74737 + 2.16355i) q^{9} +(1.93537 + 0.518581i) q^{11} +(4.51607 + 4.51607i) q^{13} -1.26287i q^{15} +(-4.68066 + 2.70238i) q^{17} +(0.510379 + 1.90476i) q^{19} +(-7.02450 + 1.39503i) q^{21} +(0.951245 - 1.64761i) q^{23} +(4.14162 - 2.39117i) q^{25} +(2.54010 + 2.54010i) q^{27} +(1.12415 - 1.12415i) q^{29} +(-0.434075 - 0.751840i) q^{31} +(4.69696 + 2.71179i) q^{33} +(0.813586 + 0.928290i) q^{35} +(7.90732 - 2.11876i) q^{37} +(8.64394 + 14.9717i) q^{39} +3.24226 q^{41} +(-6.35727 + 6.35727i) q^{43} +(0.522499 - 1.94999i) q^{45} +(-1.49266 + 2.58536i) q^{47} +(4.26473 - 5.55087i) q^{49} +(-14.1314 + 3.78650i) q^{51} +(1.81663 - 6.77976i) q^{53} -0.934789i q^{55} +5.33780i q^{57} +(2.22228 - 8.29366i) q^{59} +(-0.469703 + 0.125856i) q^{61} +(-11.4237 - 0.752254i) q^{63} +(1.48984 - 2.58047i) q^{65} +(1.03224 - 3.85238i) q^{67} +(3.64144 - 3.64144i) q^{69} -12.1916 q^{71} +(-7.79109 - 13.4946i) q^{73} +(12.5040 - 3.35044i) q^{75} +(-5.19960 + 1.03261i) q^{77} +(-1.07130 - 0.618516i) q^{79} +(-1.62878 - 2.82113i) q^{81} +(-9.03560 + 9.03560i) q^{83} +(1.78301 + 1.78301i) q^{85} +(3.72680 - 2.15167i) q^{87} +(-1.16364 + 2.01548i) q^{89} +(-15.9992 - 5.43644i) q^{91} +(-0.608215 - 2.26989i) q^{93} +(0.796746 - 0.460002i) q^{95} +4.69704i q^{97} +(6.13058 + 6.13058i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 6 q^{3} + 6 q^{5} - 8 q^{7} - 2 q^{11} - 12 q^{17} + 6 q^{19} + 10 q^{21} - 12 q^{23} + 24 q^{29} - 12 q^{33} + 2 q^{35} - 6 q^{37} - 4 q^{39} - 12 q^{45} - 8 q^{49} + 34 q^{51} - 6 q^{53} - 42 q^{59}+ \cdots + 16 q^{99}+O(q^{100}) $ 56 * q + 6 * q^3 + 6 * q^5 - 8 * q^7 - 2 * q^11 - 12 * q^17 + 6 * q^19 + 10 * q^21 - 12 * q^23 + 24 * q^29 - 12 * q^33 + 2 * q^35 - 6 * q^37 - 4 * q^39 - 12 * q^45 - 8 * q^49 + 34 * q^51 - 6 * q^53 - 42 * q^59 + 6 * q^61 - 4 * q^65 - 6 * q^67 - 80 * q^71 - 24 * q^75 - 10 * q^77 - 8 * q^81 + 28 * q^85 - 12 * q^87 - 16 * q^91 - 10 * q^93 + 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$645$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.61463	+	0.700587i	1.50955	+	0.404484i	0.916287	−	0.400521i	$-0.131171\pi$
$3$	2.61463	+	0.700587i	1.50955	+	0.404484i	0.593268	+	0.805005i	$0.297838\pi$
$4$		0			0
$5$	−0.120751	−	0.450647i	−0.0540013	−	0.201536i	0.933655	−	0.358175i	$-0.116601\pi$
$5$	−0.120751	−	0.450647i	−0.0540013	−	0.201536i	−0.987656	+	0.156639i	$0.949934\pi$
$6$		0			0
$7$	−2.37326	+	1.16946i	−0.897008	+	0.442014i
$7$	−2.37326	+	1.16946i	−0.897008	+	0.442014i
$8$		0			0
$9$	3.74737	+	2.16355i	1.24912	+	0.721182i
$10$		0			0
$11$	1.93537	+	0.518581i	0.583536	+	0.156358i	0.538497	−	0.842627i	$-0.318992\pi$
$11$	1.93537	+	0.518581i	0.583536	+	0.156358i	0.0450390	+	0.998985i	$0.485659\pi$
$12$		0			0
$13$	4.51607	+	4.51607i	1.25253	+	1.25253i	0.954581	+	0.297952i	$0.0963035\pi$
$13$	4.51607	+	4.51607i	1.25253	+	1.25253i	0.297952	+	0.954581i	$0.403696\pi$
$14$		0			0
$15$		−	1.26287i		−	0.326072i
$16$		0			0
$17$	−4.68066	+	2.70238i	−1.13523	+	0.655424i	−0.945244	−	0.326364i	$-0.894177\pi$
$17$	−4.68066	+	2.70238i	−1.13523	+	0.655424i	−0.189983	+	0.981787i	$0.560843\pi$
$18$		0			0
$19$	0.510379	+	1.90476i	0.117089	+	0.436982i	0.999435	−	0.0336198i	$-0.0107035\pi$
$19$	0.510379	+	1.90476i	0.117089	+	0.436982i	−0.882346	+	0.470602i	$0.844037\pi$
$20$		0			0
$21$	−7.02450	+	1.39503i	−1.53287	+	0.304420i
$22$		0			0
$23$	0.951245	−	1.64761i	0.198348	−	0.343549i	−0.749645	−	0.661841i	$-0.769776\pi$
$23$	0.951245	−	1.64761i	0.198348	−	0.343549i	0.947993	+	0.318291i	$0.103109\pi$
$24$		0			0
$25$	4.14162	−	2.39117i	0.828325	−	0.478234i
$26$		0			0
$27$	2.54010	+	2.54010i	0.488843	+	0.488843i
$28$		0			0
$29$	1.12415	−	1.12415i	0.208749	−	0.208749i	−0.594986	−	0.803736i	$-0.702843\pi$
$29$	1.12415	−	1.12415i	0.208749	−	0.208749i	0.803736	+	0.594986i	$0.202843\pi$
$30$		0			0
$31$	−0.434075	−	0.751840i	−0.0779622	−	0.135035i	0.824408	−	0.565995i	$-0.191508\pi$
$31$	−0.434075	−	0.751840i	−0.0779622	−	0.135035i	−0.902371	+	0.430961i	$0.858175\pi$
$32$		0			0
$33$	4.69696	+	2.71179i	0.817636	+	0.472062i
$34$		0			0
$35$	0.813586	+	0.928290i	0.137521	+	0.156910i
$36$		0			0
$37$	7.90732	−	2.11876i	1.29996	−	0.348322i	0.458522	−	0.888683i	$-0.348379\pi$
$37$	7.90732	−	2.11876i	1.29996	−	0.348322i	0.841433	+	0.540361i	$0.181712\pi$
$38$		0			0
$39$	8.64394	+	14.9717i	1.38414	+	2.39740i
$40$		0			0
$41$	3.24226			0.506356			0.253178	−	0.967420i	$-0.418524\pi$
$41$	3.24226			0.506356			0.253178	+	0.967420i	$0.418524\pi$
$42$		0			0
$43$	−6.35727	+	6.35727i	−0.969475	+	0.969475i	−0.999548	−	0.0300731i	$-0.990426\pi$
$43$	−6.35727	+	6.35727i	−0.969475	+	0.969475i	0.0300731	+	0.999548i	$0.490426\pi$
$44$		0			0
$45$	0.522499	−	1.94999i	0.0778895	−	0.290688i
$46$		0			0
$47$	−1.49266	+	2.58536i	−0.217727	+	0.377114i	−0.954113	−	0.299448i	$-0.903198\pi$
$47$	−1.49266	+	2.58536i	−0.217727	+	0.377114i	0.736386	+	0.676562i	$0.236531\pi$
$48$		0			0
$49$	4.26473	−	5.55087i	0.609246	−	0.792981i
$50$		0			0
$51$	−14.1314	+	3.78650i	−1.97880	+	0.530217i
$52$		0			0
$53$	1.81663	−	6.77976i	0.249533	−	0.931272i	−0.721517	−	0.692397i	$-0.756555\pi$
$53$	1.81663	−	6.77976i	0.249533	−	0.931272i	0.971050	−	0.238875i	$-0.0767786\pi$
$54$		0			0
$55$		−	0.934789i		−	0.126047i
$56$		0			0
$57$			5.33780i			0.707009i
$58$		0			0
$59$	2.22228	−	8.29366i	0.289316	−	1.07974i	−0.656311	−	0.754491i	$-0.727884\pi$
$59$	2.22228	−	8.29366i	0.289316	−	1.07974i	0.945627	−	0.325253i	$-0.105449\pi$
$60$		0			0
$61$	−0.469703	+	0.125856i	−0.0601393	+	0.0161143i	−0.288763	−	0.957401i	$-0.593244\pi$
$61$	−0.469703	+	0.125856i	−0.0601393	+	0.0161143i	0.228624	+	0.973515i	$0.426577\pi$
$62$		0			0
$63$	−11.4237	−	0.752254i	−1.43925	−	0.0947751i
$64$		0			0
$65$	1.48984	−	2.58047i	0.184792	−	0.320068i
$66$		0			0
$67$	1.03224	−	3.85238i	0.126108	−	0.470643i	−0.873768	−	0.486342i	$-0.838331\pi$
$67$	1.03224	−	3.85238i	0.126108	−	0.470643i	0.999877	+	0.0156996i	$0.00499753\pi$
$68$		0			0
$69$	3.64144	−	3.64144i	0.438378	−	0.438378i
$70$		0			0
$71$	−12.1916			−1.44687			−0.723437	−	0.690390i	$-0.757439\pi$
$71$	−12.1916			−1.44687			−0.723437	+	0.690390i	$0.757439\pi$
$72$		0			0
$73$	−7.79109	−	13.4946i	−0.911878	−	1.57942i	−0.811408	−	0.584480i	$-0.801299\pi$
$73$	−7.79109	−	13.4946i	−0.911878	−	1.57942i	−0.100470	−	0.994940i	$-0.532035\pi$
$74$		0			0
$75$	12.5040	−	3.35044i	1.44384	−	0.386876i
$76$		0			0
$77$	−5.19960	+	1.03261i	−0.592549	+	0.117677i
$78$		0			0
$79$	−1.07130	−	0.618516i	−0.120531	−	0.0695885i	0.438522	−	0.898720i	$-0.355502\pi$
$79$	−1.07130	−	0.618516i	−0.120531	−	0.0695885i	−0.559053	+	0.829132i	$0.688835\pi$
$80$		0			0
$81$	−1.62878	−	2.82113i	−0.180976	−	0.313459i
$82$		0			0
$83$	−9.03560	+	9.03560i	−0.991786	+	0.991786i	−0.999967	−	0.00818066i	$-0.997396\pi$
$83$	−9.03560	+	9.03560i	−0.991786	+	0.991786i	0.00818066	+	0.999967i	$0.497396\pi$
$84$		0			0
$85$	1.78301	+	1.78301i	0.193395	+	0.193395i
$86$		0			0
$87$	3.72680	−	2.15167i	0.399554	−	0.230683i
$88$		0			0
$89$	−1.16364	+	2.01548i	−0.123345	+	0.213640i	−0.921085	−	0.389362i	$-0.872696\pi$
$89$	−1.16364	+	2.01548i	−0.123345	+	0.213640i	0.797740	+	0.603002i	$0.206029\pi$
$90$		0			0
$91$	−15.9992	−	5.43644i	−1.67717	−	0.569894i
$92$		0			0
$93$	−0.608215	−	2.26989i	−0.0630689	−	0.235376i
$94$		0			0
$95$	0.796746	−	0.460002i	0.0817444	−	0.0471952i
$96$		0			0
$97$			4.69704i			0.476912i	0.971153	+	0.238456i	$0.0766414\pi$
$97$			4.69704i			0.476912i	−0.971153	+	0.238456i	$0.923359\pi$
$98$		0			0
$99$	6.13058	+	6.13058i	0.616146	+	0.616146i
$100$		0			0
$101$	−5.35584	−	1.43509i	−0.532926	−	0.142797i	−0.0176866	−	0.999844i	$-0.505630\pi$
$101$	−5.35584	−	1.43509i	−0.532926	−	0.142797i	−0.515239	+	0.857047i	$0.672297\pi$
$102$		0			0
$103$	−0.958115	−	0.553168i	−0.0944059	−	0.0545053i	0.452054	−	0.891991i	$-0.350692\pi$
$103$	−0.958115	−	0.553168i	−0.0944059	−	0.0545053i	−0.546460	+	0.837485i	$0.684025\pi$
$104$		0			0
$105$	1.47688	+	2.99712i	0.144128	+	0.292489i
$106$		0			0
$107$	1.60020	+	5.97202i	0.154697	+	0.577337i	0.999131	+	0.0416773i	$0.0132702\pi$
$107$	1.60020	+	5.97202i	0.154697	+	0.577337i	−0.844434	+	0.535659i	$0.820063\pi$
$108$		0			0
$109$	10.5236	+	2.81979i	1.00798	+	0.270087i	0.724785	−	0.688975i	$-0.241939\pi$
$109$	10.5236	+	2.81979i	1.00798	+	0.270087i	0.283194	+	0.959063i	$0.408606\pi$
$110$		0			0
$111$	22.1591			2.10324
$112$		0			0
$113$	−2.81872			−0.265163			−0.132582	−	0.991172i	$-0.542327\pi$
$113$	−2.81872			−0.265163			−0.132582	+	0.991172i	$0.542327\pi$
$114$		0			0
$115$	−0.857352	−	0.229727i	−0.0799485	−	0.0214221i
$116$		0			0
$117$	7.15267	+	26.6941i	0.661264	+	2.46787i
$118$		0			0
$119$	7.94810	−	11.8873i	0.728601	−	1.08971i
$120$		0			0
$121$	−6.04954	−	3.49271i	−0.549958	−	0.317519i
$122$		0			0
$123$	8.47731	+	2.27149i	0.764373	+	0.204813i
$124$		0			0
$125$	−3.22716	−	3.22716i	−0.288646	−	0.288646i
$126$		0			0
$127$			9.34725i			0.829434i	0.909950	+	0.414717i	$0.136119\pi$
$127$			9.34725i			0.829434i	−0.909950	+	0.414717i	$0.863881\pi$
$128$		0			0
$129$	−21.0757	+	12.1681i	−1.85561	+	1.07134i
$130$		0			0
$131$	−4.80174	−	17.9203i	−0.419530	−	1.56571i	−0.775586	−	0.631242i	$-0.782545\pi$
$131$	−4.80174	−	17.9203i	−0.419530	−	1.56571i	0.356056	−	0.934465i	$-0.384121\pi$
$132$		0			0
$133$	−3.43880	−	3.92362i	−0.298182	−	0.340221i
$134$		0			0
$135$	0.837971	−	1.45141i	0.0721211	−	0.124917i
$136$		0			0
$137$	13.1541	−	7.59453i	1.12383	−	0.648844i	0.181455	−	0.983399i	$-0.441919\pi$
$137$	13.1541	−	7.59453i	1.12383	−	0.648844i	0.942376	+	0.334555i	$0.108586\pi$
$138$		0			0
$139$	−1.13113	−	1.13113i	−0.0959413	−	0.0959413i	0.657507	−	0.753448i	$-0.271611\pi$
$139$	−1.13113	−	1.13113i	−0.0959413	−	0.0959413i	−0.753448	+	0.657507i	$0.771611\pi$
$140$		0			0
$141$	−5.71402	+	5.71402i	−0.481207	+	0.481207i
$142$		0			0
$143$	6.39833	+	11.0822i	0.535055	+	0.926742i
$144$		0			0
$145$	−0.642337	−	0.370853i	−0.0533431	−	0.0307977i
$146$		0			0
$147$	15.0395	−	11.5256i	1.24044	−	0.950618i
$148$		0			0
$149$	9.81380	−	2.62960i	0.803978	−	0.215425i	0.166648	−	0.986016i	$-0.446706\pi$
$149$	9.81380	−	2.62960i	0.803978	−	0.215425i	0.637330	+	0.770591i	$0.280039\pi$
$150$		0			0
$151$	−5.83900	−	10.1134i	−0.475171	−	0.823020i	0.524425	−	0.851457i	$-0.324280\pi$
$151$	−5.83900	−	10.1134i	−0.475171	−	0.823020i	−0.999596	+	0.0284368i	$0.990947\pi$
$152$		0			0
$153$	−23.3869			−1.89072
$154$		0			0
$155$	−0.286400	+	0.286400i	−0.0230042	+	0.0230042i
$156$		0			0
$157$	−0.576431	+	2.15127i	−0.0460042	+	0.171690i	−0.985106	−	0.171950i	$-0.944993\pi$
$157$	−0.576431	+	2.15127i	−0.0460042	+	0.171690i	0.939101	+	0.343640i	$0.111660\pi$
$158$		0			0
$159$	9.49962	−	16.4538i	0.753369	−	1.30487i
$160$		0			0
$161$	−0.330743	+	5.02264i	−0.0260662	+	0.395839i
$162$		0			0
$163$	14.1740	−	3.79792i	1.11020	−	0.297476i	0.343286	−	0.939231i	$-0.388460\pi$
$163$	14.1740	−	3.79792i	1.11020	−	0.297476i	0.766910	+	0.641755i	$0.221793\pi$
$164$		0			0
$165$	0.654901	−	2.44412i	0.0509839	−	0.190275i
$166$		0			0
$167$		−	5.94995i		−	0.460421i	−0.973141	−	0.230210i	$-0.926059\pi$
$167$		−	5.94995i		−	0.460421i	0.973141	−	0.230210i	$-0.0739415\pi$
$168$		0			0
$169$			27.7898i			2.13768i
$170$		0			0
$171$	−2.20846	+	8.24207i	−0.168885	+	0.630287i
$172$		0			0
$173$	8.87194	−	2.37723i	0.674521	−	0.180737i	0.0947304	−	0.995503i	$-0.469801\pi$
$173$	8.87194	−	2.37723i	0.674521	−	0.180737i	0.579790	+	0.814766i	$0.303134\pi$
$174$		0			0
$175$	−7.03278	+	10.5183i	−0.531628	+	0.795111i
$176$		0			0
$177$	11.6209	−	20.1279i	0.873478	−	1.51291i
$178$		0			0
$179$	0.984716	−	3.67501i	0.0736011	−	0.274683i	−0.919311	−	0.393531i	$-0.871253\pi$
$179$	0.984716	−	3.67501i	0.0736011	−	0.274683i	0.992912	+	0.118848i	$0.0379201\pi$
$180$		0			0
$181$	−5.13439	+	5.13439i	−0.381636	+	0.381636i	−0.871691	−	0.490055i	$-0.836977\pi$
$181$	−5.13439	+	5.13439i	−0.381636	+	0.381636i	0.490055	+	0.871691i	$0.336977\pi$
$182$		0			0
$183$	−1.31627			−0.0973015
$184$		0			0
$185$	−1.90963	−	3.30757i	−0.140398	−	0.243177i
$186$		0			0
$187$	−10.4602	+	2.80281i	−0.764927	+	0.204962i
$188$		0			0
$189$	−8.99887	−	3.05777i	−0.654572	−	0.222420i
$190$		0			0
$191$	−15.2400	−	8.79882i	−1.10273	−	0.636660i	−0.165791	−	0.986161i	$-0.553018\pi$
$191$	−15.2400	−	8.79882i	−1.10273	−	0.636660i	−0.936936	+	0.349501i	$0.886351\pi$
$192$		0			0
$193$	3.28968	+	5.69790i	0.236797	+	0.410144i	0.959793	−	0.280708i	$-0.0905692\pi$
$193$	3.28968	+	5.69790i	0.236797	+	0.410144i	−0.722997	+	0.690851i	$0.757236\pi$
$194$		0			0
$195$	5.70321	−	5.70321i	0.408415	−	0.408415i
$196$		0			0
$197$	−14.8776	−	14.8776i	−1.05998	−	1.05998i	−0.998082	−	0.0619015i	$-0.980284\pi$
$197$	−14.8776	−	14.8776i	−1.05998	−	1.05998i	−0.0619015	−	0.998082i	$-0.519716\pi$
$198$		0			0
$199$	6.43322	−	3.71422i	0.456039	−	0.263294i	−0.254338	−	0.967115i	$-0.581858\pi$
$199$	6.43322	−	3.71422i	0.456039	−	0.263294i	0.710377	+	0.703821i	$0.248524\pi$
$200$		0			0
$201$	5.39785	−	9.34935i	0.380735	−	0.659452i
$202$		0			0
$203$	−1.35325	+	3.98255i	−0.0949796	+	0.279520i
$204$		0			0
$205$	−0.391505	−	1.46112i	−0.0273439	−	0.102049i
$206$		0			0
$207$	7.12934	−	4.11612i	0.495523	−	0.286090i
$208$		0			0
$209$			3.95109i			0.273303i
$210$		0			0
$211$	9.11727	+	9.11727i	0.627659	+	0.627659i	0.947478	−	0.319820i	$-0.103622\pi$
$211$	9.11727	+	9.11727i	0.627659	+	0.627659i	−0.319820	+	0.947478i	$0.603622\pi$
$212$		0			0
$213$	−31.8764	−	8.54126i	−2.18414	−	0.585237i
$214$		0			0
$215$	3.63253	+	2.09724i	0.247736	+	0.143031i
$216$		0			0
$217$	1.90942	+	1.27668i	0.129620	+	0.0866666i
$218$		0			0
$219$	−10.9167	−	40.7416i	−0.737681	−	2.75306i
$220$		0			0
$221$	−33.3423	−	8.93405i	−2.24285	−	0.600969i
$222$		0			0
$223$	−6.72926			−0.450624			−0.225312	−	0.974287i	$-0.572340\pi$
$223$	−6.72926			−0.450624			−0.225312	+	0.974287i	$0.572340\pi$
$224$		0			0
$225$	20.6936			1.37957
$226$		0			0
$227$	7.46500	+	2.00024i	0.495469	+	0.132761i	0.497896	−	0.867236i	$-0.334106\pi$
$227$	7.46500	+	2.00024i	0.495469	+	0.132761i	−0.00242728	+	0.999997i	$0.500773\pi$
$228$		0			0
$229$	3.94509	+	14.7233i	0.260699	+	0.972941i	0.964831	+	0.262872i	$0.0846696\pi$
$229$	3.94509	+	14.7233i	0.260699	+	0.972941i	−0.704132	+	0.710069i	$0.748664\pi$
$230$		0			0
$231$	−14.3184	−	0.942877i	−0.942084	−	0.0620367i
$232$		0			0
$233$	12.7954	+	7.38741i	0.838253	+	0.483965i	0.856670	−	0.515865i	$-0.172529\pi$
$233$	12.7954	+	7.38741i	0.838253	+	0.483965i	−0.0184173	+	0.999830i	$0.505863\pi$
$234$		0			0
$235$	1.34533	+	0.360479i	0.0877594	+	0.0235151i
$236$		0			0
$237$	−2.36773	−	2.36773i	−0.153800	−	0.153800i
$238$		0			0
$239$		−	28.5488i		−	1.84667i	−0.383998	−	0.923334i	$-0.625453\pi$
$239$		−	28.5488i		−	1.84667i	0.383998	−	0.923334i	$-0.374547\pi$
$240$		0			0
$241$	19.8792	−	11.4772i	1.28053	−	0.739314i	0.303584	−	0.952805i	$-0.401817\pi$
$241$	19.8792	−	11.4772i	1.28053	−	0.739314i	0.976945	+	0.213491i	$0.0684834\pi$
$242$		0			0
$243$	−5.07143	−	18.9268i	−0.325332	−	1.21416i
$244$		0			0
$245$	−3.01645	−	1.25162i	−0.192714	−	0.0799628i
$246$		0			0
$247$	−6.29713	+	10.9069i	−0.400676	+	0.693992i
$248$		0			0
$249$	−29.9549	+	17.2945i	−1.89832	+	1.09599i
$250$		0			0
$251$	10.2808	+	10.2808i	0.648918	+	0.648918i	0.952732	−	0.303813i	$-0.0982599\pi$
$251$	10.2808	+	10.2808i	0.648918	+	0.648918i	−0.303813	+	0.952732i	$0.598260\pi$
$252$		0			0
$253$	2.69543	−	2.69543i	0.169460	−	0.169460i
$254$		0			0
$255$	3.41276	+	5.91107i	0.213715	+	0.370165i
$256$		0			0
$257$	2.17812	+	1.25754i	0.135867	+	0.0784431i	0.566393	−	0.824135i	$-0.308338\pi$
$257$	2.17812	+	1.25754i	0.135867	+	0.0784431i	−0.430526	+	0.902578i	$0.641672\pi$
$258$		0			0
$259$	−16.2883	+	14.2757i	−1.01211	+	0.887046i
$260$		0			0
$261$	6.64475	−	1.78046i	0.411300	−	0.110207i
$262$		0			0
$263$	−4.54781	−	7.87703i	−0.280430	−	0.485718i	0.691061	−	0.722797i	$-0.257144\pi$
$263$	−4.54781	−	7.87703i	−0.280430	−	0.485718i	−0.971491	+	0.237078i	$0.923810\pi$
$264$		0			0
$265$	−3.27464			−0.201159
$266$		0			0
$267$	−4.45449	+	4.45449i	−0.272611	+	0.272611i
$268$		0			0
$269$	−1.47548	+	5.50656i	−0.0899615	+	0.335741i	−0.996207	−	0.0870099i	$-0.972269\pi$
$269$	−1.47548	+	5.50656i	−0.0899615	+	0.335741i	0.906246	+	0.422751i	$0.138935\pi$
$270$		0			0
$271$	−5.76007	+	9.97673i	−0.349899	+	0.606043i	−0.986231	−	0.165372i	$-0.947118\pi$
$271$	−5.76007	+	9.97673i	−0.349899	+	0.606043i	0.636332	+	0.771415i	$0.280451\pi$
$272$		0			0
$273$	−38.0232	−	25.4231i	−2.30127	−	1.53868i
$274$		0			0
$275$	9.25560	−	2.48003i	0.558134	−	0.149551i
$276$		0			0
$277$	−5.40800	+	20.1829i	−0.324935	+	1.21268i	0.589442	+	0.807811i	$0.299348\pi$
$277$	−5.40800	+	20.1829i	−0.324935	+	1.21268i	−0.914377	+	0.404864i	$0.867319\pi$
$278$		0			0
$279$		−	3.75657i		−	0.224900i
$280$		0			0
$281$		−	19.8360i		−	1.18331i	−0.806190	−	0.591657i	$-0.798474\pi$
$281$		−	19.8360i		−	1.18331i	0.806190	−	0.591657i	$-0.201526\pi$
$282$		0			0
$283$	−5.26602	+	19.6531i	−0.313033	+	1.16825i	0.612775	+	0.790258i	$0.290053\pi$
$283$	−5.26602	+	19.6531i	−0.313033	+	1.16825i	−0.925807	+	0.377996i	$0.876613\pi$
$284$		0			0
$285$	2.40546	−	0.644542i	0.142487	−	0.0381794i
$286$		0			0
$287$	−7.69473	+	3.79170i	−0.454206	+	0.223817i
$288$		0			0
$289$	6.10572	−	10.5754i	0.359160	−	0.622083i
$290$		0			0
$291$	−3.29069	+	12.2810i	−0.192903	+	0.719926i
$292$		0			0
$293$	6.75509	−	6.75509i	0.394636	−	0.394636i	−0.481700	−	0.876336i	$-0.659980\pi$
$293$	6.75509	−	6.75509i	0.394636	−	0.394636i	0.876336	+	0.481700i	$0.159980\pi$
$294$		0			0
$295$	−4.00586			−0.233230
$296$		0			0
$297$	3.59879	+	6.23329i	0.208823	+	0.361692i
$298$		0			0
$299$	11.7366	−	3.14481i	0.678745	−	0.181869i
$300$		0			0
$301$	7.65288	−	22.5220i	0.441105	−	1.29815i
$302$		0			0
$303$	−12.9981	−	7.50446i	−0.746721	−	0.431120i
$304$		0			0
$305$	0.113434	+	0.196473i	0.00649520	+	0.0112500i
$306$		0			0
$307$	−2.36930	+	2.36930i	−0.135223	+	0.135223i	−0.771479	−	0.636255i	$-0.780483\pi$
$307$	−2.36930	+	2.36930i	−0.135223	+	0.135223i	0.636255	+	0.771479i	$0.280483\pi$
$308$		0			0
$309$	−2.11757	−	2.11757i	−0.120464	−	0.120464i
$310$		0			0
$311$	−13.1239	+	7.57707i	−0.744186	+	0.429656i	−0.823589	−	0.567186i	$-0.808032\pi$
$311$	−13.1239	+	7.57707i	−0.744186	+	0.429656i	0.0794032	+	0.996843i	$0.474699\pi$
$312$		0			0
$313$	−3.32791	+	5.76411i	−0.188105	+	0.325807i	−0.944618	−	0.328171i	$-0.893568\pi$
$313$	−3.32791	+	5.76411i	−0.188105	+	0.325807i	0.756514	+	0.653978i	$0.226901\pi$
$314$		0			0
$315$	1.04041	+	5.23888i	0.0586206	+	0.295177i
$316$		0			0
$317$	−6.86233	−	25.6106i	−0.385427	−	1.43843i	−0.837493	−	0.546449i	$-0.815979\pi$
$317$	−6.86233	−	25.6106i	−0.385427	−	1.43843i	0.452065	−	0.891985i	$-0.350687\pi$
$318$		0			0
$319$	2.75861	−	1.59268i	0.154453	−	0.0891732i
$320$		0			0
$321$			16.7357i			0.934094i
$322$		0			0
$323$	−7.53630	−	7.53630i	−0.419331	−	0.419331i
$324$		0			0
$325$	29.5026	+	7.90519i	1.63651	+	0.438501i
$326$		0			0
$327$	25.5398	+	14.7454i	1.41235	+	0.815423i
$328$		0			0
$329$	0.518991	−	7.88134i	0.0286129	−	0.434513i
$330$		0			0
$331$	−2.45530	−	9.16331i	−0.134956	−	0.503661i	−0.999998	−	0.00196237i	$-0.999375\pi$
$331$	−2.45530	−	9.16331i	−0.134956	−	0.503661i	0.865043	−	0.501699i	$-0.167291\pi$
$332$		0			0
$333$	34.2157	+	9.16806i	1.87501	+	0.502407i
$334$		0			0
$335$	−1.86071			−0.101661
$336$		0			0
$337$	−16.0354			−0.873502			−0.436751	−	0.899582i	$-0.643871\pi$
$337$	−16.0354			−0.873502			−0.436751	+	0.899582i	$0.643871\pi$
$338$		0			0
$339$	−7.36991	−	1.97476i	−0.400278	−	0.107254i
$340$		0			0
$341$	−0.450207	−	1.68019i	−0.0243801	−	0.0909876i
$342$		0			0
$343$	−3.62978	+	18.1611i	−0.195990	+	0.980606i
$344$		0			0
$345$	−2.08071	−	1.20130i	−0.112022	−	0.0646758i
$346$		0			0
$347$	3.06636	+	0.821629i	0.164611	+	0.0441074i	0.340183	−	0.940359i	$-0.389511\pi$
$347$	3.06636	+	0.821629i	0.164611	+	0.0441074i	−0.175572	+	0.984467i	$0.556178\pi$
$348$		0			0
$349$	2.21348	+	2.21348i	0.118485	+	0.118485i	0.763863	−	0.645378i	$-0.223300\pi$
$349$	2.21348	+	2.21348i	0.118485	+	0.118485i	−0.645378	+	0.763863i	$0.723300\pi$
$350$		0			0
$351$			22.9426i			1.22458i
$352$		0			0
$353$	−7.11770	+	4.10941i	−0.378837	+	0.218722i	−0.677312	−	0.735696i	$-0.736855\pi$
$353$	−7.11770	+	4.10941i	−0.378837	+	0.218722i	0.298475	+	0.954417i	$0.403522\pi$
$354$		0			0
$355$	1.47214	+	5.49410i	0.0781331	+	0.291597i
$356$		0			0
$357$	29.1094	−	25.5125i	1.54063	−	1.35026i
$358$		0			0
$359$	15.3319	−	26.5556i	0.809184	−	1.40155i	−0.104245	−	0.994552i	$-0.533243\pi$
$359$	15.3319	−	26.5556i	0.809184	−	1.40155i	0.913430	−	0.406997i	$-0.133424\pi$
$360$		0			0
$361$	13.0869	−	7.55570i	0.688782	−	0.397668i
$362$		0			0
$363$	−13.3703	−	13.3703i	−0.701761	−	0.701761i
$364$		0			0
$365$	−5.14051	+	5.14051i	−0.269067	+	0.269067i
$366$		0			0
$367$	8.91168	+	15.4355i	0.465186	+	0.805726i	0.999210	−	0.0397435i	$-0.0126541\pi$
$367$	8.91168	+	15.4355i	0.465186	+	0.805726i	−0.534024	+	0.845469i	$0.679321\pi$
$368$		0			0
$369$	12.1500	+	7.01478i	0.632502	+	0.365175i
$370$		0			0
$371$	3.61732	+	18.2146i	0.187802	+	0.945656i
$372$		0			0
$373$	−2.39939	+	0.642914i	−0.124236	+	0.0332888i	−0.320401	−	0.947282i	$-0.603818\pi$
$373$	−2.39939	+	0.642914i	−0.124236	+	0.0332888i	0.196166	+	0.980571i	$0.437151\pi$
$374$		0			0
$375$	−6.17691	−	10.6987i	−0.318974	−	0.552480i
$376$		0			0
$377$	10.1535			0.522931
$378$		0			0
$379$	0.526070	−	0.526070i	0.0270224	−	0.0270224i	−0.693466	−	0.720489i	$-0.743917\pi$
$379$	0.526070	−	0.526070i	0.0270224	−	0.0270224i	0.720489	+	0.693466i	$0.243917\pi$
$380$		0			0
$381$	−6.54856	+	24.4396i	−0.335493	+	1.25208i
$382$		0			0
$383$	11.8928	−	20.5989i	0.607692	−	1.05255i	−0.383928	−	0.923363i	$-0.625429\pi$
$383$	11.8928	−	20.5989i	0.607692	−	1.05255i	0.991620	−	0.129190i	$-0.0412377\pi$
$384$		0			0
$385$	1.09320	+	2.21850i	0.0557145	+	0.113065i
$386$		0			0
$387$	−37.5773	+	10.0688i	−1.91016	+	0.511826i
$388$		0			0
$389$	−6.27509	+	23.4190i	−0.318160	+	1.18739i	0.602852	+	0.797853i	$0.294031\pi$
$389$	−6.27509	+	23.4190i	−0.318160	+	1.18739i	−0.921012	+	0.389535i	$0.872636\pi$
$390$		0			0
$391$			10.2825i			0.520009i
$392$		0			0
$393$		−	50.2190i		−	2.53321i
$394$		0			0
$395$	−0.149372	+	0.557465i	−0.00751574	+	0.0280491i
$396$		0			0
$397$	−4.07659	+	1.09232i	−0.204598	+	0.0548219i	−0.359662	−	0.933082i	$-0.617108\pi$
$397$	−4.07659	+	1.09232i	−0.204598	+	0.0548219i	0.155064	+	0.987904i	$0.450442\pi$
$398$		0			0
$399$	−6.24235	−	12.6680i	−0.312508	−	0.634193i
$400$		0			0
$401$	−9.01163	+	15.6086i	−0.450019	+	0.779456i	−0.998387	−	0.0567812i	$-0.981916\pi$
$401$	−9.01163	+	15.6086i	−0.450019	+	0.779456i	0.548367	+	0.836238i	$0.315250\pi$
$402$		0			0
$403$	1.43505	−	5.35568i	0.0714849	−	0.266785i
$404$		0			0
$405$	−1.07466	+	1.07466i	−0.0534002	+	0.0534002i
$406$		0			0
$407$	16.4023			0.813034
$408$		0			0
$409$	13.9843	+	24.2215i	0.691478	+	1.19768i	0.971354	+	0.237639i	$0.0763736\pi$
$409$	13.9843	+	24.2215i	0.691478	+	1.19768i	−0.279875	+	0.960036i	$0.590293\pi$
$410$		0			0
$411$	39.7137	−	10.6412i	1.95893	−	0.524894i
$412$		0			0
$413$	4.42506	+	22.2819i	0.217743	+	1.09642i
$414$		0			0
$415$	5.16292	+	2.98081i	0.253438	+	0.146322i
$416$		0			0
$417$	−2.16503	−	3.74994i	−0.106022	−	0.183635i
$418$		0			0
$419$	10.4669	−	10.4669i	0.511342	−	0.511342i	−0.403596	−	0.914937i	$-0.632240\pi$
$419$	10.4669	−	10.4669i	0.511342	−	0.511342i	0.914937	+	0.403596i	$0.132240\pi$
$420$		0			0
$421$	−12.3722	−	12.3722i	−0.602984	−	0.602984i	0.338119	−	0.941103i	$-0.390209\pi$
$421$	−12.3722	−	12.3722i	−0.602984	−	0.602984i	−0.941103	+	0.338119i	$0.890209\pi$
$422$		0			0
$423$	−11.1871	+	6.45887i	−0.543935	+	0.314041i
$424$		0			0
$425$	−12.9237	+	22.3845i	−0.626891	+	1.08581i
$426$		0			0
$427$	0.967542	−	0.847989i	0.0468227	−	0.0410370i
$428$		0			0
$429$	8.96517	+	33.4585i	0.432842	+	1.61539i
$430$		0			0
$431$	−11.8089	+	6.81786i	−0.568814	+	0.328405i	−0.756675	−	0.653791i	$-0.773178\pi$
$431$	−11.8089	+	6.81786i	−0.568814	+	0.328405i	0.187862	+	0.982195i	$0.439844\pi$
$432$		0			0
$433$			19.1575i			0.920649i	0.887751	+	0.460325i	$0.152267\pi$
$433$			19.1575i			0.920649i	−0.887751	+	0.460325i	$0.847733\pi$
$434$		0			0
$435$	−1.41965	−	1.41965i	−0.0680672	−	0.0680672i
$436$		0			0
$437$	3.62379	+	0.970991i	0.173349	+	0.0464488i
$438$		0			0
$439$	7.42387	+	4.28617i	0.354322	+	0.204568i	0.666587	−	0.745427i	$-0.267754\pi$
$439$	7.42387	+	4.28617i	0.354322	+	0.204568i	−0.312265	+	0.949995i	$0.601088\pi$
$440$		0			0
$441$	27.9911	−	11.5742i	1.33291	−	0.551154i
$442$		0			0
$443$	5.42088	+	20.2310i	0.257554	+	0.961204i	0.966652	+	0.256094i	$0.0824356\pi$
$443$	5.42088	+	20.2310i	0.257554	+	0.961204i	−0.709098	+	0.705110i	$0.750898\pi$
$444$		0			0
$445$	1.04878	+	0.281020i	0.0497169	+	0.0133216i
$446$		0			0
$447$	27.5017			1.30079
$448$		0			0
$449$	−24.4270			−1.15278			−0.576391	−	0.817174i	$-0.695539\pi$
$449$	−24.4270			−1.15278			−0.576391	+	0.817174i	$0.695539\pi$
$450$		0			0
$451$	6.27498	+	1.68138i	0.295477	+	0.0791729i
$452$		0			0
$453$	−8.18145	−	30.5336i	−0.384398	−	1.43459i
$454$		0			0
$455$	−0.518009	+	7.86644i	−0.0242846	+	0.368784i
$456$		0			0
$457$	3.12783	+	1.80585i	0.146314	+	0.0844743i	0.571370	−	0.820693i	$-0.306412\pi$
$457$	3.12783	+	1.80585i	0.146314	+	0.0844743i	−0.425056	+	0.905167i	$0.639746\pi$
$458$		0			0
$459$	−18.7537	−	5.02503i	−0.875347	−	0.234548i
$460$		0			0
$461$	25.2872	+	25.2872i	1.17774	+	1.17774i	0.980318	+	0.197423i	$0.0632574\pi$
$461$	25.2872	+	25.2872i	1.17774	+	1.17774i	0.197423	+	0.980318i	$0.436743\pi$
$462$		0			0
$463$			8.01165i			0.372333i	0.982518	+	0.186166i	$0.0596064\pi$
$463$			8.01165i			0.372333i	−0.982518	+	0.186166i	$0.940394\pi$
$464$		0			0
$465$	−0.949477	+	0.548181i	−0.0440309	+	0.0254213i
$466$		0			0
$467$	4.79633	+	17.9002i	0.221948	+	0.828321i	0.983604	+	0.180340i	$0.0577197\pi$
$467$	4.79633	+	17.9002i	0.221948	+	0.828321i	−0.761657	+	0.647981i	$0.775614\pi$
$468$		0			0
$469$	2.05542	+	10.3499i	0.0949107	+	0.477912i
$470$		0			0
$471$	−3.01430	+	5.22093i	−0.138892	+	0.240568i
$472$		0			0
$473$	−15.6004	+	9.00692i	−0.717309	+	0.414139i
$474$		0			0
$475$	6.66840	+	6.66840i	0.305967	+	0.305967i
$476$		0			0
$477$	21.4759	−	21.4759i	0.983314	−	0.983314i
$478$		0			0
$479$	13.6882	+	23.7087i	0.625432	+	1.08328i	0.988457	+	0.151501i	$0.0484106\pi$
$479$	13.6882	+	23.7087i	0.625432	+	1.08328i	−0.363025	+	0.931779i	$0.618256\pi$
$480$		0			0
$481$	45.2785	+	26.1415i	2.06452	+	1.19195i
$482$		0			0
$483$	−4.38357	+	12.9006i	−0.199459	+	0.586998i
$484$		0			0
$485$	2.11671	−	0.567171i	0.0961148	−	0.0257539i
$486$		0			0
$487$	−9.68012	−	16.7665i	−0.438648	−	0.759761i	0.558938	−	0.829210i	$-0.311209\pi$
$487$	−9.68012	−	16.7665i	−0.438648	−	0.759761i	−0.997585	+	0.0694492i	$0.977876\pi$
$488$		0			0
$489$	39.7206			1.79623
$490$		0			0
$491$	17.1950	−	17.1950i	0.775998	−	0.775998i	−0.203149	−	0.979148i	$-0.565118\pi$
$491$	17.1950	−	17.1950i	0.775998	−	0.775998i	0.979148	+	0.203149i	$0.0651177\pi$
$492$		0			0
$493$	−2.22388	+	8.29964i	−0.100159	+	0.373797i
$494$		0			0
$495$	2.02246	−	3.50300i	0.0909027	−	0.157448i
$496$		0			0
$497$	28.9338	−	14.2576i	1.29786	−	0.639539i
$498$		0			0
$499$	−2.92484	+	0.783708i	−0.130934	+	0.0350836i	−0.323691	−	0.946163i	$-0.604924\pi$
$499$	−2.92484	+	0.783708i	−0.130934	+	0.0350836i	0.192757	+	0.981247i	$0.438257\pi$
$500$		0			0
$501$	4.16846	−	15.5569i	0.186233	−	0.695031i
$502$		0			0
$503$			34.5673i			1.54128i	0.637272	+	0.770639i	$0.280063\pi$
$503$			34.5673i			1.54128i	−0.637272	+	0.770639i	$0.719937\pi$
$504$		0			0
$505$			2.58688i			0.115115i
$506$		0			0
$507$	−19.4692	+	72.6599i	−0.864656	+	3.22694i
$508$		0			0
$509$	15.2307	−	4.08105i	0.675088	−	0.180889i	0.0950424	−	0.995473i	$-0.469701\pi$
$509$	15.2307	−	4.08105i	0.675088	−	0.180889i	0.580046	+	0.814584i	$0.303035\pi$
$510$		0			0
$511$	34.2717	+	22.9147i	1.51609	+	1.01369i
$512$		0			0
$513$	−3.54187	+	6.13470i	−0.156377	+	0.270854i
$514$		0			0
$515$	−0.133591	+	0.498567i	−0.00588671	+	0.0219695i
$516$		0			0
$517$	−4.22957	+	4.22957i	−0.186016	+	0.186016i
$518$		0			0
$519$	24.8623			1.09133
$520$		0			0
$521$	−7.72095	−	13.3731i	−0.338261	−	0.585885i	0.645845	−	0.763469i	$-0.276505\pi$
$521$	−7.72095	−	13.3731i	−0.338261	−	0.585885i	−0.984106	+	0.177584i	$0.943172\pi$
$522$		0			0
$523$	−1.96968	+	0.527773i	−0.0861280	+	0.0230779i	−0.301626	−	0.953426i	$-0.597529\pi$
$523$	−1.96968	+	0.527773i	−0.0861280	+	0.0230779i	0.215498	+	0.976504i	$0.430863\pi$
$524$		0			0
$525$	−25.7571	+	22.5744i	−1.12413	+	0.985229i
$526$		0			0
$527$	4.06352	+	2.34607i	0.177010	+	0.102197i
$528$		0			0
$529$	9.69026	+	16.7840i	0.421316	+	0.729740i
$530$		0			0
$531$	26.2714	−	26.2714i	1.14008	−	1.14008i
$532$		0			0
$533$	14.6423	+	14.6423i	0.634228	+	0.634228i
$534$		0			0
$535$	2.49805	−	1.44225i	0.108000	−	0.0623538i
$536$		0			0
$537$	5.14933	−	8.91890i	0.222210	−	0.384879i
$538$		0			0
$539$	11.1324	−	8.53138i	0.479507	−	0.367473i
$540$		0			0
$541$	−5.40772	−	20.1819i	−0.232496	−	0.867686i	−0.979262	−	0.202599i	$-0.935061\pi$
$541$	−5.40772	−	20.1819i	−0.232496	−	0.867686i	0.746766	−	0.665087i	$-0.231606\pi$
$542$		0			0
$543$	−17.0216	+	9.82741i	−0.730466	+	0.421735i
$544$		0			0
$545$		−	5.08293i		−	0.217729i
$546$		0			0
$547$	−13.0675	−	13.0675i	−0.558728	−	0.558728i	0.370217	−	0.928945i	$-0.379283\pi$
$547$	−13.0675	−	13.0675i	−0.558728	−	0.558728i	−0.928945	+	0.370217i	$0.879283\pi$
$548$		0			0
$549$	−2.03245	−	0.544592i	−0.0867427	−	0.0232426i
$550$		0			0
$551$	2.71498	+	1.56749i	0.115662	+	0.0667775i
$552$		0			0
$553$	3.26581	+	0.215055i	0.138876	+	0.00914507i
$554$		0			0
$555$	−2.67572	−	9.98591i	−0.113578	−	0.423878i
$556$		0			0
$557$	11.6914	+	3.13271i	0.495381	+	0.132737i	0.497856	−	0.867260i	$-0.334121\pi$
$557$	11.6914	+	3.13271i	0.495381	+	0.132737i	−0.00247440	+	0.999997i	$0.500788\pi$
$558$		0			0
$559$	−57.4198			−2.42860
$560$		0			0
$561$	−29.3132			−1.23760
$562$		0			0
$563$	−27.2040	−	7.28930i	−1.14651	−	0.307207i	−0.364946	−	0.931029i	$-0.618913\pi$
$563$	−27.2040	−	7.28930i	−1.14651	−	0.307207i	−0.781567	+	0.623821i	$0.785579\pi$
$564$		0			0
$565$	0.340362	+	1.27025i	0.0143192	+	0.0534398i
$566$		0			0
$567$	7.16472	+	4.79048i	0.300890	+	0.201181i
$568$		0			0
$569$	−20.4277	−	11.7940i	−0.856375	−	0.494428i	0.00642167	−	0.999979i	$-0.497956\pi$
$569$	−20.4277	−	11.7940i	−0.856375	−	0.494428i	−0.862797	+	0.505551i	$0.831289\pi$
$570$		0			0
$571$	−21.7673	−	5.83253i	−0.910933	−	0.244084i	−0.227227	−	0.973842i	$-0.572966\pi$
$571$	−21.7673	−	5.83253i	−0.910933	−	0.244084i	−0.683705	+	0.729758i	$0.739633\pi$
$572$		0			0
$573$	−33.6826	−	33.6826i	−1.40711	−	1.40711i
$574$		0			0
$575$		−	9.09835i		−	0.379427i
$576$		0			0
$577$	−16.2893	+	9.40463i	−0.678132	+	0.391520i	−0.799151	−	0.601130i	$-0.794717\pi$
$577$	−16.2893	+	9.40463i	−0.678132	+	0.391520i	0.121019	+	0.992650i	$0.461384\pi$
$578$		0			0
$579$	4.60942	+	17.2026i	0.191561	+	0.714915i
$580$		0			0
$581$	10.8771	−	32.0106i	0.451256	−	1.32802i
$582$		0			0
$583$	7.03171	−	12.1793i	0.291224	−	0.504414i
$584$		0			0
$585$	11.1659	−	6.44666i	0.461655	−	0.266537i
$586$		0			0
$587$	−12.6185	−	12.6185i	−0.520820	−	0.520820i	0.396999	−	0.917819i	$-0.370052\pi$
$587$	−12.6185	−	12.6185i	−0.520820	−	0.520820i	−0.917819	+	0.396999i	$0.870052\pi$
$588$		0			0
$589$	1.21053	−	1.21053i	0.0498791	−	0.0498791i
$590$		0			0
$591$	−28.4763	−	49.3223i	−1.17136	−	2.02885i
$592$		0			0
$593$	−22.0260	−	12.7167i	−0.904498	−	0.522212i	−0.0258409	−	0.999666i	$-0.508226\pi$
$593$	−22.0260	−	12.7167i	−0.904498	−	0.522212i	−0.878657	+	0.477454i	$0.841560\pi$
$594$		0			0
$595$	−6.31671	−	2.14639i	−0.258960	−	0.0879934i
$596$		0			0
$597$	19.4226	−	5.20427i	0.794914	−	0.212997i
$598$		0			0
$599$	21.1003	+	36.5468i	0.862135	+	1.49326i	0.869864	+	0.493292i	$0.164207\pi$
$599$	21.1003	+	36.5468i	0.862135	+	1.49326i	−0.00772853	+	0.999970i	$0.502460\pi$
$600$		0			0
$601$	−29.8695			−1.21840			−0.609202	−	0.793015i	$-0.708510\pi$
$601$	−29.8695			−1.21840			−0.609202	+	0.793015i	$0.708510\pi$
$602$		0			0
$603$	12.2030	−	12.2030i	0.496944	−	0.496944i
$604$		0			0
$605$	−0.843492	+	3.14796i	−0.0342928	+	0.127983i
$606$		0			0
$607$	14.7137	−	25.4850i	0.597212	−	1.03440i	−0.396018	−	0.918243i	$-0.629608\pi$
$607$	14.7137	−	25.4850i	0.597212	−	1.03440i	0.993231	−	0.116160i	$-0.0370584\pi$
$608$		0			0
$609$	−6.32837	+	9.46480i	−0.256438	+	0.383533i
$610$		0			0
$611$	−18.4166	+	4.93472i	−0.745058	+	0.199638i
$612$		0			0
$613$	−5.94532	+	22.1882i	−0.240129	+	0.896175i	0.735640	+	0.677373i	$0.236882\pi$
$613$	−5.94532	+	22.1882i	−0.240129	+	0.896175i	−0.975769	+	0.218802i	$0.929785\pi$
$614$		0			0
$615$		−	4.09456i		−	0.165108i
$616$		0			0
$617$			31.2064i			1.25632i	0.778084	+	0.628161i	$0.216192\pi$
$617$			31.2064i			1.25632i	−0.778084	+	0.628161i	$0.783808\pi$
$618$		0			0
$619$	4.74503	−	17.7087i	0.190719	−	0.711772i	−0.802615	−	0.596498i	$-0.796559\pi$
$619$	4.74503	−	17.7087i	0.190719	−	0.711772i	0.993334	−	0.115275i	$-0.0367748\pi$
$620$		0			0
$621$	6.60135	−	1.76883i	0.264903	−	0.0709805i
$622$		0			0
$623$	0.404591	−	6.14408i	0.0162096	−	0.246157i
$624$		0			0
$625$	10.8912	−	18.8641i	0.435648	−	0.754565i
$626$		0			0
$627$	−2.76808	+	10.3306i	−0.110547	+	0.412565i
$628$		0			0
$629$	−31.2858	+	31.2858i	−1.24745	+	1.24745i
$630$		0			0
$631$	8.10970			0.322842			0.161421	−	0.986886i	$-0.448392\pi$
$631$	8.10970			0.322842			0.161421	+	0.986886i	$0.448392\pi$
$632$		0			0
$633$	17.4508	+	30.2257i	0.693608	+	1.20136i
$634$		0			0
$635$	4.21231	−	1.12869i	0.167160	−	0.0447905i
$636$		0			0
$637$	44.3279	−	5.80831i	1.75634	−	0.230134i
$638$		0			0
$639$	−45.6864	−	26.3770i	−1.80732	−	1.04346i
$640$		0			0
$641$	−14.0435	−	24.3241i	−0.554685	−	0.960743i	−0.997928	−	0.0643416i	$-0.979505\pi$
$641$	−14.0435	−	24.3241i	−0.554685	−	0.960743i	0.443242	−	0.896402i	$-0.353828\pi$
$642$		0			0
$643$	−21.6759	+	21.6759i	−0.854812	+	0.854812i	−0.990721	−	0.135909i	$-0.956605\pi$
$643$	−21.6759	+	21.6759i	−0.854812	+	0.854812i	0.135909	+	0.990721i	$0.456605\pi$
$644$		0			0
$645$	8.02841	+	8.02841i	0.316118	+	0.316118i
$646$		0			0
$647$	−39.8543	+	23.0099i	−1.56683	+	0.904612i	−0.570299	+	0.821437i	$0.693173\pi$
$647$	−39.8543	+	23.0099i	−1.56683	+	0.904612i	−0.996535	+	0.0831749i	$0.973494\pi$
$648$		0			0
$649$	8.60188	−	14.8989i	0.337653	−	0.584833i
$650$		0			0
$651$	4.09800	+	4.67575i	0.160613	+	0.183257i
$652$		0			0
$653$	−7.84001	−	29.2593i	−0.306803	−	1.14501i	−0.931382	−	0.364043i	$-0.881396\pi$
$653$	−7.84001	−	29.2593i	−0.306803	−	1.14501i	0.624579	−	0.780962i	$-0.285271\pi$
$654$		0			0
$655$	−7.49594	+	4.32778i	−0.292890	+	0.169100i
$656$		0			0
$657$		−	67.4255i		−	2.63052i
$658$		0			0
$659$	7.48634	+	7.48634i	0.291626	+	0.291626i	0.837723	−	0.546096i	$-0.183887\pi$
$659$	7.48634	+	7.48634i	0.291626	+	0.291626i	−0.546096	+	0.837723i	$0.683887\pi$
$660$		0			0
$661$	−10.2052	−	2.73446i	−0.396934	−	0.106358i	0.0548296	−	0.998496i	$-0.482538\pi$
$661$	−10.2052	−	2.73446i	−0.396934	−	0.106358i	−0.451764	+	0.892137i	$0.649205\pi$
$662$		0			0
$663$	−80.9187	−	46.7184i	−3.14262	−	1.81439i
$664$		0			0
$665$	−1.35293	+	2.02347i	−0.0524645	+	0.0784667i
$666$		0			0
$667$	−0.782813	−	2.92150i	−0.0303106	−	0.113121i
$668$		0			0
$669$	−17.5945	−	4.71443i	−0.680242	−	0.182270i
$670$		0			0
$671$	−0.974316			−0.0376130
$672$		0			0
$673$	17.2027			0.663115			0.331557	−	0.943435i	$-0.392426\pi$
$673$	17.2027			0.663115			0.331557	+	0.943435i	$0.392426\pi$
$674$		0			0
$675$	16.5940	+	4.44634i	0.638702	+	0.171140i
$676$		0			0
$677$	−5.18323	−	19.3441i	−0.199208	−	0.743453i	−0.991137	−	0.132841i	$-0.957590\pi$
$677$	−5.18323	−	19.3441i	−0.199208	−	0.743453i	0.791930	−	0.610612i	$-0.209077\pi$
$678$		0			0
$679$	−5.49301	−	11.1473i	−0.210802	−	0.427794i
$680$		0			0
$681$	18.1168	+	10.4598i	0.694238	+	0.400819i
$682$		0			0
$683$	0.930638	+	0.249364i	0.0356099	+	0.00954164i	0.276580	−	0.960991i	$-0.410799\pi$
$683$	0.930638	+	0.249364i	0.0356099	+	0.00954164i	−0.240970	+	0.970533i	$0.577466\pi$
$684$		0			0
$685$	−5.01082	−	5.01082i	−0.191453	−	0.191453i
$686$		0			0
$687$			41.2597i			1.57416i
$688$		0			0
$689$	38.8219	−	22.4138i	1.47900	−	0.853899i
$690$		0			0
$691$	8.97758	+	33.5048i	0.341523	+	1.27458i	0.896622	+	0.442797i	$0.146014\pi$
$691$	8.97758	+	33.5048i	0.341523	+	1.27458i	−0.555099	+	0.831784i	$0.687320\pi$
$692$		0			0
$693$	−21.7189	−	7.37999i	−0.825034	−	0.280343i
$694$		0			0
$695$	−0.373156	+	0.646326i	−0.0141546	+	0.0245165i
$696$		0			0
$697$	−15.1759	+	8.76183i	−0.574829	+	0.331878i
$698$		0			0
$699$	28.2796	+	28.2796i	1.06963	+	1.06963i
$700$		0			0
$701$	−32.4969	+	32.4969i	−1.22739	+	1.22739i	−0.262444	+	0.964947i	$0.584529\pi$
$701$	−32.4969	+	32.4969i	−1.22739	+	1.22739i	−0.964947	+	0.262444i	$0.915471\pi$
$702$		0			0
$703$	8.07146	+	13.9802i	0.304421	+	0.527272i
$704$		0			0
$705$	3.26498	+	1.88504i	0.122966	+	0.0709945i
$706$		0			0
$707$	14.3891	−	2.85759i	0.541157	−	0.107471i
$708$		0			0
$709$	−4.54454	+	1.21770i	−0.170674	+	0.0457319i	−0.343144	−	0.939283i	$-0.611492\pi$
$709$	−4.54454	+	1.21770i	−0.170674	+	0.0457319i	0.172470	+	0.985015i	$0.444825\pi$
$710$		0			0
$711$	−2.67638	−	4.63562i	−0.100372	−	0.173849i
$712$		0			0
$713$	−1.65165			−0.0618547
$714$		0			0
$715$	4.22157	−	4.22157i	0.157878	−	0.157878i
$716$		0			0
$717$	20.0009	−	74.6444i	0.746947	−	2.78765i
$718$		0			0
$719$	9.27548	−	16.0656i	0.345917	−	0.599146i	−0.639603	−	0.768706i	$-0.720901\pi$
$719$	9.27548	−	16.0656i	0.345917	−	0.599146i	0.985520	+	0.169559i	$0.0542345\pi$
$720$		0			0
$721$	2.92076	+	0.192334i	0.108775	+	0.00716289i
$722$		0			0
$723$	60.0174	−	16.0816i	2.23207	−	0.598081i
$724$		0			0
$725$	1.96778	−	7.34384i	0.0730813	−	0.272743i
$726$		0			0
$727$			5.96613i			0.221272i	0.993861	+	0.110636i	$0.0352887\pi$
$727$			5.96613i			0.221272i	−0.993861	+	0.110636i	$0.964711\pi$
$728$		0			0
$729$		−	43.2669i		−	1.60248i
$730$		0			0
$731$	12.5765	−	46.9360i	0.465157	−	1.73599i
$732$		0			0
$733$	−20.8755	+	5.59358i	−0.771055	+	0.206604i	−0.622838	−	0.782351i	$-0.714020\pi$
$733$	−20.8755	+	5.59358i	−0.771055	+	0.206604i	−0.148218	+	0.988955i	$0.547354\pi$
$734$		0			0
$735$	−7.01002	−	5.38579i	−0.258569	−	0.198658i
$736$		0			0
$737$	3.99554	−	6.92048i	0.147178	−	0.254919i
$738$		0			0
$739$	9.37297	−	34.9804i	0.344790	−	1.28677i	−0.548067	−	0.836434i	$-0.684636\pi$
$739$	9.37297	−	34.9804i	0.344790	−	1.28677i	0.892857	−	0.450340i	$-0.148697\pi$
$740$		0			0
$741$	−24.1059	+	24.1059i	−0.885552	+	0.885552i
$742$		0			0
$743$	16.2749			0.597067			0.298533	−	0.954399i	$-0.403503\pi$
$743$	16.2749			0.597067			0.298533	+	0.954399i	$0.403503\pi$
$744$		0			0
$745$	−2.37004	−	4.10504i	−0.0868317	−	0.150397i
$746$		0			0
$747$	−53.4087	+	14.3108i	−1.95412	+	0.523605i
$748$		0			0
$749$	−10.7817	−	12.3018i	−0.393955	−	0.449497i
$750$		0			0
$751$	15.8511	+	9.15166i	0.578416	+	0.333949i	0.760504	−	0.649334i	$-0.224952\pi$
$751$	15.8511	+	9.15166i	0.578416	+	0.333949i	−0.182087	+	0.983282i	$0.558285\pi$
$752$		0			0
$753$	19.6778	+	34.0830i	0.717101	+	1.24205i
$754$		0			0
$755$	−3.85253	+	3.85253i	−0.140208	+	0.140208i
$756$		0			0
$757$	16.6944	+	16.6944i	0.606767	+	0.606767i	0.942100	−	0.335333i	$-0.108849\pi$
$757$	16.6944	+	16.6944i	0.606767	+	0.606767i	−0.335333	+	0.942100i	$0.608849\pi$
$758$		0			0
$759$	8.93593	−	5.15916i	0.324354	−	0.187266i
$760$		0			0
$761$	−4.43390	+	7.67974i	−0.160729	+	0.278390i	−0.935130	−	0.354304i	$-0.884718\pi$
$761$	−4.43390	+	7.67974i	−0.160729	+	0.278390i	0.774401	+	0.632695i	$0.218051\pi$
$762$		0			0
$763$	−28.2729	+	5.61484i	−1.02355	+	0.203271i
$764$		0			0
$765$	2.82398	+	10.5392i	0.102101	+	0.381047i
$766$		0			0
$767$	47.4908	−	27.4188i	1.71479	−	0.990036i
$768$		0			0
$769$			1.14344i			0.0412335i	0.999787	+	0.0206167i	$0.00656298\pi$
$769$			1.14344i			0.0412335i	−0.999787	+	0.0206167i	$0.993437\pi$
$770$		0			0
$771$	4.81396	+	4.81396i	0.173370	+	0.173370i
$772$		0			0
$773$	5.25103	+	1.40701i	0.188866	+	0.0506066i	0.352012	−	0.935995i	$-0.385497\pi$
$773$	5.25103	+	1.40701i	0.188866	+	0.0506066i	−0.163146	+	0.986602i	$0.552164\pi$
$774$		0			0
$775$	−3.59555	−	2.07589i	−0.129156	−	0.0745683i
$776$		0			0
$777$	−52.5892	+	25.9141i	−1.88663	+	0.929664i
$778$		0			0
$779$	1.65478	+	6.17573i	0.0592888	+	0.221269i
$780$		0			0
$781$	−23.5952	−	6.32232i	−0.844304	−	0.226231i
$782$		0			0
$783$	5.71091			0.204091
$784$		0			0
$785$	1.03907			0.0370859
$786$		0			0
$787$	49.2659	+	13.2008i	1.75614	+	0.470556i	0.985919	−	0.167221i	$-0.0534795\pi$
$787$	49.2659	+	13.2008i	1.75614	+	0.470556i	0.770220	+	0.637778i	$0.220146\pi$
$788$		0			0
$789$	−6.37227	−	23.7816i	−0.226859	−	0.846648i
$790$		0			0
$791$	6.68956	−	3.29639i	0.237854	−	0.117206i
$792$		0			0
$793$	−2.68959	−	1.55283i	−0.0955101	−	0.0551428i
$794$		0			0
$795$	−8.56196	−	2.29417i	−0.303661	−	0.0813658i
$796$		0			0
$797$	26.5433	+	26.5433i	0.940211	+	0.940211i	0.998311	−	0.0581002i	$-0.0185043\pi$
$797$	26.5433	+	26.5433i	0.940211	+	0.940211i	−0.0581002	+	0.998311i	$0.518504\pi$
$798$		0			0
$799$		−	16.1349i		−	0.570813i
$800$		0			0
$801$	−8.72116	+	5.03516i	−0.308147	+	0.177909i
$802$		0			0
$803$	−8.08063	−	30.1573i	−0.285159	−	1.06423i
$804$		0			0
$805$	2.30338	−	0.457438i	0.0811833	−	0.0161226i
$806$		0			0
$807$	−7.71565	+	13.3639i	−0.271604	+	0.470432i
$808$		0			0
$809$	−17.6346	+	10.1813i	−0.620000	+	0.357957i	−0.776869	−	0.629662i	$-0.783193\pi$
$809$	−17.6346	+	10.1813i	−0.620000	+	0.357957i	0.156869	+	0.987619i	$0.449860\pi$
$810$		0			0
$811$	31.8932	+	31.8932i	1.11992	+	1.11992i	0.991752	+	0.128171i	$0.0409107\pi$
$811$	31.8932	+	31.8932i	1.11992	+	1.11992i	0.128171	+	0.991752i	$0.459089\pi$
$812$		0			0
$813$	−22.0500	+	22.0500i	−0.773327	+	0.773327i
$814$		0			0
$815$	−3.42304	−	5.92889i	−0.119904	−	0.207680i
$816$		0			0
$817$	−15.3537	−	8.86446i	−0.537158	−	0.310128i
$818$		0			0
$819$	−48.1928	−	54.9873i	−1.68399	−	1.92141i
$820$		0			0
$821$	−23.6777	+	6.34443i	−0.826359	+	0.221422i	−0.647125	−	0.762384i	$-0.724029\pi$
$821$	−23.6777	+	6.34443i	−0.826359	+	0.221422i	−0.179234	+	0.983806i	$0.557362\pi$
$822$		0			0
$823$	−5.16976	−	8.95429i	−0.180207	−	0.312127i	0.761744	−	0.647878i	$-0.224343\pi$
$823$	−5.16976	−	8.95429i	−0.180207	−	0.312127i	−0.941951	+	0.335751i	$0.891010\pi$
$824$		0			0
$825$	25.9374			0.903024
$826$		0			0
$827$	−33.0264	+	33.0264i	−1.14844	+	1.14844i	−0.161581	+	0.986859i	$0.551659\pi$
$827$	−33.0264	+	33.0264i	−1.14844	+	1.14844i	−0.986859	+	0.161581i	$0.948341\pi$
$828$		0			0
$829$	−9.70111	+	36.2050i	−0.336934	+	1.25745i	0.564824	+	0.825211i	$0.308944\pi$
$829$	−9.70111	+	36.2050i	−0.336934	+	1.25745i	−0.901758	+	0.432242i	$0.857723\pi$
$830$		0			0
$831$	−28.2798	+	48.9821i	−0.981015	+	1.69917i
$832$		0			0
$833$	−4.96118	+	37.5066i	−0.171895	+	1.29953i
$834$		0			0
$835$	−2.68133	+	0.718460i	−0.0927912	+	0.0248633i
$836$		0			0
$837$	0.807156	−	3.01235i	0.0278994	−	0.104122i
$838$		0			0
$839$		−	41.5802i		−	1.43551i	−0.696296	−	0.717754i	$-0.745170\pi$
$839$		−	41.5802i		−	1.43551i	0.696296	−	0.717754i	$-0.254830\pi$
$840$		0			0
$841$			26.4726i			0.912847i
$842$		0			0
$843$	13.8968	−	51.8636i	0.478632	−	1.78628i
$844$		0			0
$845$	12.5234	−	3.35563i	0.430818	−	0.115437i
$846$		0			0
$847$	18.4417	+	1.21440i	0.633665	+	0.0417272i
$848$		0			0
$849$	−27.5374	+	47.6961i	−0.945080	+	1.63693i
$850$		0			0
$851$	4.03092	−	15.0436i	0.138178	−	0.515688i
$852$		0			0
$853$	3.78632	−	3.78632i	0.129641	−	0.129641i	−0.639309	−	0.768950i	$-0.720779\pi$
$853$	3.78632	−	3.78632i	0.129641	−	0.129641i	0.768950	+	0.639309i	$0.220779\pi$
$854$		0			0
$855$	3.98094			0.136145
$856$		0			0
$857$	−9.93943	−	17.2156i	−0.339524	−	0.588073i	0.644819	−	0.764335i	$-0.276933\pi$
$857$	−9.93943	−	17.2156i	−0.339524	−	0.588073i	−0.984343	+	0.176262i	$0.943599\pi$
$858$		0			0
$859$	12.3699	−	3.31449i	0.422054	−	0.113089i	−0.0415399	−	0.999137i	$-0.513226\pi$
$859$	12.3699	−	3.31449i	0.422054	−	0.113089i	0.463594	+	0.886048i	$0.346560\pi$
$860$		0			0
$861$	−22.7753	+	4.52304i	−0.776179	+	0.154145i
$862$		0			0
$863$	20.9940	+	12.1209i	0.714643	+	0.412599i	0.812778	−	0.582574i	$-0.197954\pi$
$863$	20.9940	+	12.1209i	0.714643	+	0.412599i	−0.0981346	+	0.995173i	$0.531288\pi$
$864$		0			0
$865$	−2.14258	−	3.71106i	−0.0728500	−	0.126180i
$866$		0			0
$867$	23.3732	−	23.3732i	0.793794	−	0.793794i
$868$		0			0
$869$	−1.75262	−	1.75262i	−0.0594534	−	0.0594534i
$870$		0			0
$871$	22.0593	−	12.7359i	0.747450	−	0.431541i
$872$		0			0
$873$	−10.1623	+	17.6016i	−0.343941	+	0.595723i
$874$		0			0
$875$	11.4329	+	3.88485i	0.386503	+	0.131332i
$876$		0			0
$877$	5.60738	+	20.9270i	0.189348	+	0.706656i	0.993658	+	0.112446i	$0.0358685\pi$
$877$	5.60738	+	20.9270i	0.189348	+	0.706656i	−0.804310	+	0.594210i	$0.797465\pi$
$878$		0			0
$879$	22.3946	−	12.9295i	0.755349	−	0.436101i
$880$		0			0
$881$			15.3375i			0.516733i	0.966047	+	0.258367i	$0.0831842\pi$
$881$			15.3375i			0.516733i	−0.966047	+	0.258367i	$0.916816\pi$
$882$		0			0
$883$	−35.7596	−	35.7596i	−1.20341	−	1.20341i	−0.973124	−	0.230282i	$-0.926035\pi$
$883$	−35.7596	−	35.7596i	−1.20341	−	1.20341i	−0.230282	−	0.973124i	$-0.573965\pi$
$884$		0			0
$885$	−10.4738	−	2.80645i	−0.352074	−	0.0943378i
$886$		0			0
$887$	28.0000	+	16.1658i	0.940148	+	0.542795i	0.890007	−	0.455947i	$-0.150699\pi$
$887$	28.0000	+	16.1658i	0.940148	+	0.542795i	0.0501414	+	0.998742i	$0.484033\pi$
$888$		0			0
$889$	−10.9312	−	22.1835i	−0.366622	−	0.744009i
$890$		0			0
$891$	−1.68931	−	6.30459i	−0.0565940	−	0.211212i
$892$		0			0
$893$	−5.68632	−	1.52364i	−0.190285	−	0.0509868i
$894$		0			0
$895$	−1.77504			−0.0593330
$896$		0			0
$897$	32.8900			1.09817
$898$		0			0
$899$	−1.33315	−	0.357216i	−0.0444629	−	0.0119138i
$900$		0			0
$901$	9.81846	+	36.6430i	0.327100	+	1.22075i
$902$		0			0
$903$	35.7881	−	53.5252i	1.19095	−	1.78121i
$904$		0			0
$905$	2.93378	+	1.69382i	0.0975220	+	0.0563044i
$906$		0			0
$907$	30.5807	+	8.19408i	1.01542	+	0.272080i	0.727891	−	0.685693i	$-0.240501\pi$
$907$	30.5807	+	8.19408i	1.01542	+	0.272080i	0.287525	+	0.957773i	$0.407168\pi$
$908$		0			0
$909$	−16.9654	−	16.9654i	−0.562707	−	0.562707i
$910$		0			0
$911$			7.17911i			0.237854i	0.992903	+	0.118927i	$0.0379455\pi$
$911$			7.17911i			0.237854i	−0.992903	+	0.118927i	$0.962054\pi$
$912$		0			0
$913$	−22.1729	+	12.8015i	−0.733817	+	0.423669i
$914$		0			0
$915$	0.158940	+	0.593173i	0.00525441	+	0.0196097i
$916$		0			0
$917$	32.3529	+	36.9142i	1.06839	+	1.21901i
$918$		0			0
$919$	−1.18242	+	2.04801i	−0.0390044	+	0.0675576i	−0.884869	−	0.465841i	$-0.845752\pi$
$919$	−1.18242	+	2.04801i	−0.0390044	+	0.0675576i	0.845864	+	0.533398i	$0.179085\pi$
$920$		0			0
$921$	−7.85475	+	4.53494i	−0.258823	+	0.149431i
$922$		0			0
$923$	−55.0580	−	55.0580i	−1.81226	−	1.81226i
$924$		0			0
$925$	27.6828	−	27.6828i	0.910206	−	0.910206i
$926$		0			0
$927$	−2.39361	−	4.14585i	−0.0786164	−	0.136168i
$928$		0			0
$929$	−50.6476	−	29.2414i	−1.66169	−	0.959379i	−0.971906	−	0.235367i	$-0.924371\pi$
$929$	−50.6476	−	29.2414i	−1.66169	−	0.959379i	−0.689787	−	0.724012i	$-0.742296\pi$
$930$		0			0
$931$	12.7497	+	5.29023i	0.417854	+	0.173380i
$932$		0			0
$933$	−39.6224	+	10.6168i	−1.29718	+	0.347578i
$934$		0			0
$935$	2.52615	+	4.37543i	0.0826141	+	0.143092i
$936$		0			0
$937$	−13.4613			−0.439761			−0.219881	−	0.975527i	$-0.570567\pi$
$937$	−13.4613			−0.439761			−0.219881	+	0.975527i	$0.570567\pi$
$938$		0			0
$939$	−12.7395	+	12.7395i	−0.415738	+	0.415738i
$940$		0			0
$941$	3.99761	−	14.9193i	0.130318	−	0.486355i	−0.869655	−	0.493660i	$-0.835659\pi$
$941$	3.99761	−	14.9193i	0.130318	−	0.486355i	0.999973	+	0.00730539i	$0.00232540\pi$
$942$		0			0
$943$	3.08419	−	5.34197i	0.100435	−	0.173959i
$944$		0			0
$945$	−0.291359	+	4.42454i	−0.00947790	+	0.143930i
$946$		0			0
$947$	30.1683	−	8.08357i	0.980338	−	0.262681i	0.267151	−	0.963655i	$-0.413918\pi$
$947$	30.1683	−	8.08357i	0.980338	−	0.262681i	0.713187	+	0.700974i	$0.247251\pi$
$948$		0			0
$949$	25.7573	−	96.1276i	0.836118	−	3.12043i
$950$		0			0
$951$		−	71.7697i		−	2.32729i
$952$		0			0
$953$		−	15.7802i		−	0.511170i	−0.966787	−	0.255585i	$-0.917732\pi$
$953$		−	15.7802i		−	0.511170i	0.966787	−	0.255585i	$-0.0822680\pi$
$954$		0			0
$955$	−2.12492	+	7.93032i	−0.0687609	+	0.256619i
$956$		0			0
$957$	8.32855	−	2.23163i	0.269224	−	0.0721383i
$958$		0			0
$959$	−22.3366	+	33.4070i	−0.721287	+	1.07877i
$960$		0			0
$961$	15.1232	−	26.1941i	0.487844	−	0.844970i
$962$		0			0
$963$	−6.92420	+	25.8415i	−0.223129	+	0.832729i
$964$		0			0
$965$	2.17051	−	2.17051i	0.0698712	−	0.0698712i
$966$		0			0
$967$	−44.7046			−1.43760			−0.718801	−	0.695216i	$-0.755309\pi$
$967$	−44.7046			−1.43760			−0.718801	+	0.695216i	$0.755309\pi$
$968$		0			0
$969$	−14.4248	−	24.9844i	−0.463390	−	0.802615i
$970$		0			0
$971$	−56.2271	+	15.0660i	−1.80441	+	0.483491i	−0.994653	−	0.103269i	$-0.967070\pi$
$971$	−56.2271	+	15.0660i	−1.80441	+	0.483491i	−0.809761	+	0.586761i	$0.800403\pi$
$972$		0			0
$973$	4.00728	+	1.36166i	0.128468	+	0.0436527i
$974$		0			0
$975$	71.5999	+	41.3382i	2.29303	+	1.32388i
$976$		0			0
$977$	10.4344	+	18.0729i	0.333827	+	0.578204i	0.983259	−	0.182215i	$-0.0583267\pi$
$977$	10.4344	+	18.0729i	0.333827	+	0.578204i	−0.649432	+	0.760420i	$0.724993\pi$
$978$		0			0
$979$	−3.29726	+	3.29726i	−0.105381	+	0.105381i
$980$		0			0
$981$	33.3351	+	33.3351i	1.06431	+	1.06431i
$982$		0			0
$983$	36.5230	−	21.0866i	1.16490	−	0.672558i	0.212430	−	0.977176i	$-0.431862\pi$
$983$	36.5230	−	21.0866i	1.16490	−	0.672558i	0.952474	+	0.304619i	$0.0985291\pi$
$984$		0			0
$985$	−4.90806	+	8.50102i	−0.156384	+	0.270865i
$986$		0			0
$987$	6.87853	−	20.2432i	0.218946	−	0.644347i
$988$		0			0
$989$	4.42695	+	16.5216i	0.140769	+	0.525356i
$990$		0			0
$991$	−14.7987	+	8.54402i	−0.470095	+	0.271410i	−0.716280	−	0.697813i	$-0.754156\pi$
$991$	−14.7987	+	8.54402i	−0.470095	+	0.271410i	0.246184	+	0.969223i	$0.420823\pi$
$992$		0			0
$993$		−	25.6788i		−	0.814891i
$994$		0			0
$995$	−2.45062	−	2.45062i	−0.0776898	−	0.0776898i
$996$		0			0
$997$	27.4427	+	7.35325i	0.869119	+	0.232880i	0.665707	−	0.746214i	$-0.268130\pi$
$997$	27.4427	+	7.35325i	0.869119	+	0.232880i	0.203412	+	0.979093i	$0.434797\pi$
$998$		0			0
$999$	25.4673	+	14.7035i	0.805749	+	0.465199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.z.b.159.13		56
4.3	odd	2		896.2.z.a.159.2		56
7.3	odd	6	inner	896.2.z.b.31.13		56
8.3	odd	2		448.2.z.a.271.13		56
8.5	even	2		112.2.v.a.75.7	yes	56
16.3	odd	4	inner	896.2.z.b.607.13		56
16.5	even	4		448.2.z.a.47.13		56
16.11	odd	4		112.2.v.a.19.13	yes	56
16.13	even	4		896.2.z.a.607.2		56
28.3	even	6		896.2.z.a.31.2		56
56.3	even	6		448.2.z.a.143.13		56
56.5	odd	6		784.2.j.a.587.7		56
56.13	odd	2		784.2.w.f.411.7		56
56.37	even	6		784.2.j.a.587.8		56
56.45	odd	6		112.2.v.a.59.13	yes	56
56.53	even	6		784.2.w.f.619.13		56
112.3	even	12	inner	896.2.z.b.479.13		56
112.11	odd	12		784.2.w.f.227.7		56
112.27	even	4		784.2.w.f.19.13		56
112.45	odd	12		896.2.z.a.479.2		56
112.59	even	12		112.2.v.a.3.7	✓	56
112.75	even	12		784.2.j.a.195.8		56
112.101	odd	12		448.2.z.a.367.13		56
112.107	odd	12		784.2.j.a.195.7		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.v.a.3.7	✓	56	112.59	even	12
112.2.v.a.19.13	yes	56	16.11	odd	4
112.2.v.a.59.13	yes	56	56.45	odd	6
112.2.v.a.75.7	yes	56	8.5	even	2
448.2.z.a.47.13		56	16.5	even	4
448.2.z.a.143.13		56	56.3	even	6
448.2.z.a.271.13		56	8.3	odd	2
448.2.z.a.367.13		56	112.101	odd	12
784.2.j.a.195.7		56	112.107	odd	12
784.2.j.a.195.8		56	112.75	even	12
784.2.j.a.587.7		56	56.5	odd	6
784.2.j.a.587.8		56	56.37	even	6
784.2.w.f.19.13		56	112.27	even	4
784.2.w.f.227.7		56	112.11	odd	12
784.2.w.f.411.7		56	56.13	odd	2
784.2.w.f.619.13		56	56.53	even	6
896.2.z.a.31.2		56	28.3	even	6
896.2.z.a.159.2		56	4.3	odd	2
896.2.z.a.479.2		56	112.45	odd	12
896.2.z.a.607.2		56	16.13	even	4
896.2.z.b.31.13		56	7.3	odd	6	inner
896.2.z.b.159.13		56	1.1	even	1	trivial
896.2.z.b.479.13		56	112.3	even	12	inner
896.2.z.b.607.13		56	16.3	odd	4	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:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.z (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.61463 + 0.700587i) q^{3} +(-0.120751 - 0.450647i) q^{5} +(-2.37326 + 1.16946i) q^{7} +(3.74737 + 2.16355i) q^{9} +(1.93537 + 0.518581i) q^{11} +(4.51607 + 4.51607i) q^{13} -1.26287i q^{15} +(-4.68066 + 2.70238i) q^{17} +(0.510379 + 1.90476i) q^{19} +(-7.02450 + 1.39503i) q^{21} +(0.951245 - 1.64761i) q^{23} +(4.14162 - 2.39117i) q^{25} +(2.54010 + 2.54010i) q^{27} +(1.12415 - 1.12415i) q^{29} +(-0.434075 - 0.751840i) q^{31} +(4.69696 + 2.71179i) q^{33} +(0.813586 + 0.928290i) q^{35} +(7.90732 - 2.11876i) q^{37} +(8.64394 + 14.9717i) q^{39} +3.24226 q^{41} +(-6.35727 + 6.35727i) q^{43} +(0.522499 - 1.94999i) q^{45} +(-1.49266 + 2.58536i) q^{47} +(4.26473 - 5.55087i) q^{49} +(-14.1314 + 3.78650i) q^{51} +(1.81663 - 6.77976i) q^{53} -0.934789i q^{55} +5.33780i q^{57} +(2.22228 - 8.29366i) q^{59} +(-0.469703 + 0.125856i) q^{61} +(-11.4237 - 0.752254i) q^{63} +(1.48984 - 2.58047i) q^{65} +(1.03224 - 3.85238i) q^{67} +(3.64144 - 3.64144i) q^{69} -12.1916 q^{71} +(-7.79109 - 13.4946i) q^{73} +(12.5040 - 3.35044i) q^{75} +(-5.19960 + 1.03261i) q^{77} +(-1.07130 - 0.618516i) q^{79} +(-1.62878 - 2.82113i) q^{81} +(-9.03560 + 9.03560i) q^{83} +(1.78301 + 1.78301i) q^{85} +(3.72680 - 2.15167i) q^{87} +(-1.16364 + 2.01548i) q^{89} +(-15.9992 - 5.43644i) q^{91} +(-0.608215 - 2.26989i) q^{93} +(0.796746 - 0.460002i) q^{95} +4.69704i q^{97} +(6.13058 + 6.13058i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 6 q^{3} + 6 q^{5} - 8 q^{7} - 2 q^{11} - 12 q^{17} + 6 q^{19} + 10 q^{21} - 12 q^{23} + 24 q^{29} - 12 q^{33} + 2 q^{35} - 6 q^{37} - 4 q^{39} - 12 q^{45} - 8 q^{49} + 34 q^{51} - 6 q^{53} - 42 q^{59}+ \cdots + 16 q^{99}+O(q^{100}) \) 56 * q + 6 * q^3 + 6 * q^5 - 8 * q^7 - 2 * q^11 - 12 * q^17 + 6 * q^19 + 10 * q^21 - 12 * q^23 + 24 * q^29 - 12 * q^33 + 2 * q^35 - 6 * q^37 - 4 * q^39 - 12 * q^45 - 8 * q^49 + 34 * q^51 - 6 * q^53 - 42 * q^59 + 6 * q^61 - 4 * q^65 - 6 * q^67 - 80 * q^71 - 24 * q^75 - 10 * q^77 - 8 * q^81 + 28 * q^85 - 12 * q^87 - 16 * q^91 - 10 * q^93 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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