LMFDB - Embedded newform 896.2.z.a.31.7

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			31.7
Character	$\chi$	$=$	896.31
Dual form			896.2.z.a.607.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.204601 - 0.763582i) q^{3} +(3.81370 + 1.02188i) q^{5} +(2.64575 - 0.00379639i) q^{7} +(2.05688 - 1.18754i) q^{9} +(-1.16815 - 4.35958i) q^{11} +(-1.34913 - 1.34913i) q^{13} -3.12115i q^{15} +(0.989178 + 0.571102i) q^{17} +(-3.01629 - 0.808212i) q^{19} +(-0.544222 - 2.01947i) q^{21} +(1.02392 + 1.77348i) q^{23} +(9.16994 + 5.29427i) q^{25} +(-3.00457 - 3.00457i) q^{27} +(-5.30239 + 5.30239i) q^{29} +(-2.07171 + 3.58830i) q^{31} +(-3.08989 + 1.78395i) q^{33} +(10.0940 + 2.68915i) q^{35} +(0.803695 - 2.99943i) q^{37} +(-0.754139 + 1.30621i) q^{39} -8.08732 q^{41} +(-3.82205 + 3.82205i) q^{43} +(9.05785 - 2.42704i) q^{45} +(-0.814305 - 1.41042i) q^{47} +(6.99997 - 0.0200886i) q^{49} +(0.233696 - 0.872167i) q^{51} +(2.92499 - 0.783749i) q^{53} -17.8198i q^{55} +2.46854i q^{57} +(6.97383 - 1.86863i) q^{59} +(-1.68972 + 6.30611i) q^{61} +(5.43748 - 3.14974i) q^{63} +(-3.76654 - 6.52383i) q^{65} +(0.616236 - 0.165120i) q^{67} +(1.14470 - 1.14470i) q^{69} +2.40482 q^{71} +(1.47966 - 2.56284i) q^{73} +(2.16643 - 8.08521i) q^{75} +(-3.10717 - 11.5299i) q^{77} +(-1.06303 + 0.613742i) q^{79} +(1.88313 - 3.26167i) q^{81} +(-2.29910 + 2.29910i) q^{83} +(3.18883 + 3.18883i) q^{85} +(5.13369 + 2.96394i) q^{87} +(4.36654 + 7.56307i) q^{89} +(-3.57459 - 3.56434i) q^{91} +(3.16383 + 0.847747i) q^{93} +(-10.6773 - 6.16455i) q^{95} -8.42967i q^{97} +(-7.57992 - 7.57992i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

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

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
$3$	−0.204601	−	0.763582i	−0.118127	−	0.440854i	0.881375	−	0.472417i	$-0.156618\pi$
$3$	−0.204601	−	0.763582i	−0.118127	−	0.440854i	−0.999502	+	0.0315627i	$0.989952\pi$
$4$		0			0
$5$	3.81370	+	1.02188i	1.70554	+	0.456998i	0.974324	−	0.225150i	$-0.0722873\pi$
$5$	3.81370	+	1.02188i	1.70554	+	0.456998i	0.731214	+	0.682148i	$0.238954\pi$
$6$		0			0
$7$	2.64575	−	0.00379639i	0.999999	−	0.00143490i
$7$	2.64575	−	0.00379639i	0.999999	−	0.00143490i
$8$		0			0
$9$	2.05688	−	1.18754i	0.685627	−	0.395847i
$10$		0			0
$11$	−1.16815	−	4.35958i	−0.352209	−	1.31446i	−0.883960	−	0.467562i	$-0.845132\pi$
$11$	−1.16815	−	4.35958i	−0.352209	−	1.31446i	0.531751	−	0.846901i	$-0.321534\pi$
$12$		0			0
$13$	−1.34913	−	1.34913i	−0.374182	−	0.374182i	0.494816	−	0.868998i	$-0.335236\pi$
$13$	−1.34913	−	1.34913i	−0.374182	−	0.374182i	−0.868998	+	0.494816i	$0.835236\pi$
$14$		0			0
$15$		−	3.12115i		−	0.805877i
$16$		0			0
$17$	0.989178	+	0.571102i	0.239911	+	0.138513i	0.615136	−	0.788421i	$-0.289101\pi$
$17$	0.989178	+	0.571102i	0.239911	+	0.138513i	−0.375225	+	0.926934i	$0.622435\pi$
$18$		0			0
$19$	−3.01629	−	0.808212i	−0.691984	−	0.185416i	−0.104346	−	0.994541i	$-0.533275\pi$
$19$	−3.01629	−	0.808212i	−0.691984	−	0.185416i	−0.587637	+	0.809125i	$0.699942\pi$
$20$		0			0
$21$	−0.544222	−	2.01947i	−0.118759	−	0.440684i
$22$		0			0
$23$	1.02392	+	1.77348i	0.213502	+	0.369796i	0.952808	−	0.303573i	$-0.0981798\pi$
$23$	1.02392	+	1.77348i	0.213502	+	0.369796i	−0.739306	+	0.673369i	$0.764846\pi$
$24$		0			0
$25$	9.16994	+	5.29427i	1.83399	+	1.05885i
$26$		0			0
$27$	−3.00457	−	3.00457i	−0.578229	−	0.578229i
$28$		0			0
$29$	−5.30239	+	5.30239i	−0.984630	+	0.984630i	−0.999884	−	0.0152539i	$-0.995144\pi$
$29$	−5.30239	+	5.30239i	−0.984630	+	0.984630i	0.0152539	+	0.999884i	$0.495144\pi$
$30$		0			0
$31$	−2.07171	+	3.58830i	−0.372089	+	0.644478i	−0.989887	−	0.141860i	$-0.954692\pi$
$31$	−2.07171	+	3.58830i	−0.372089	+	0.644478i	0.617797	+	0.786337i	$0.288025\pi$
$32$		0			0
$33$	−3.08989	+	1.78395i	−0.537881	+	0.310546i
$34$		0			0
$35$	10.0940	+	2.68915i	1.70619	+	0.454550i
$36$		0			0
$37$	0.803695	−	2.99943i	0.132127	−	0.493103i	−0.867867	−	0.496797i	$-0.834509\pi$
$37$	0.803695	−	2.99943i	0.132127	−	0.493103i	0.999993	+	0.00369416i	$0.00117589\pi$
$38$		0			0
$39$	−0.754139	+	1.30621i	−0.120759	+	0.209161i
$40$		0			0
$41$	−8.08732			−1.26303			−0.631514	−	0.775365i	$-0.717566\pi$
$41$	−8.08732			−1.26303			−0.631514	+	0.775365i	$0.717566\pi$
$42$		0			0
$43$	−3.82205	+	3.82205i	−0.582858	+	0.582858i	−0.935688	−	0.352830i	$-0.885220\pi$
$43$	−3.82205	+	3.82205i	−0.582858	+	0.582858i	0.352830	+	0.935688i	$0.385220\pi$
$44$		0			0
$45$	9.05785	−	2.42704i	1.35026	−	0.361802i
$46$		0			0
$47$	−0.814305	−	1.41042i	−0.118779	−	0.205731i	0.800505	−	0.599326i	$-0.204565\pi$
$47$	−0.814305	−	1.41042i	−0.118779	−	0.205731i	−0.919284	+	0.393595i	$0.871231\pi$
$48$		0			0
$49$	6.99997	−	0.0200886i	0.999996	−	0.00286980i
$50$		0			0
$51$	0.233696	−	0.872167i	0.0327240	−	0.122128i
$52$		0			0
$53$	2.92499	−	0.783749i	0.401779	−	0.107656i	−0.0522704	−	0.998633i	$-0.516646\pi$
$53$	2.92499	−	0.783749i	0.401779	−	0.107656i	0.454049	+	0.890977i	$0.349979\pi$
$54$		0			0
$55$		−	17.8198i		−	2.40283i
$56$		0			0
$57$			2.46854i			0.326966i
$58$		0			0
$59$	6.97383	−	1.86863i	0.907915	−	0.243275i	0.225503	−	0.974243i	$-0.427597\pi$
$59$	6.97383	−	1.86863i	0.907915	−	0.243275i	0.682412	+	0.730967i	$0.260931\pi$
$60$		0			0
$61$	−1.68972	+	6.30611i	−0.216346	+	0.807414i	0.769342	+	0.638837i	$0.220584\pi$
$61$	−1.68972	+	6.30611i	−0.216346	+	0.807414i	−0.985688	+	0.168578i	$0.946083\pi$
$62$		0			0
$63$	5.43748	−	3.14974i	0.685058	−	0.396830i
$64$		0			0
$65$	−3.76654	−	6.52383i	−0.467181	−	0.809182i
$66$		0			0
$67$	0.616236	−	0.165120i	0.0752852	−	0.0201726i	−0.220980	−	0.975278i	$-0.570926\pi$
$67$	0.616236	−	0.165120i	0.0752852	−	0.0201726i	0.296265	+	0.955106i	$0.404259\pi$
$68$		0			0
$69$	1.14470	−	1.14470i	0.137806	−	0.137806i
$70$		0			0
$71$	2.40482			0.285400			0.142700	−	0.989766i	$-0.454422\pi$
$71$	2.40482			0.285400			0.142700	+	0.989766i	$0.454422\pi$
$72$		0			0
$73$	1.47966	−	2.56284i	0.173181	−	0.299958i	−0.766349	−	0.642424i	$-0.777929\pi$
$73$	1.47966	−	2.56284i	0.173181	−	0.299958i	0.939530	+	0.342466i	$0.111262\pi$
$74$		0			0
$75$	2.16643	−	8.08521i	0.250157	−	0.933600i
$76$		0			0
$77$	−3.10717	−	11.5299i	−0.354095	−	1.31396i
$78$		0			0
$79$	−1.06303	+	0.613742i	−0.119601	+	0.0690514i	−0.558607	−	0.829433i	$-0.688664\pi$
$79$	−1.06303	+	0.613742i	−0.119601	+	0.0690514i	0.439006	+	0.898484i	$0.355331\pi$
$80$		0			0
$81$	1.88313	−	3.26167i	0.209236	−	0.362408i
$82$		0			0
$83$	−2.29910	+	2.29910i	−0.252359	+	0.252359i	−0.821937	−	0.569578i	$-0.807107\pi$
$83$	−2.29910	+	2.29910i	−0.252359	+	0.252359i	0.569578	+	0.821937i	$0.307107\pi$
$84$		0			0
$85$	3.18883	+	3.18883i	0.345877	+	0.345877i
$86$		0			0
$87$	5.13369	+	2.96394i	0.550389	+	0.317767i
$88$		0			0
$89$	4.36654	+	7.56307i	0.462852	+	0.801684i	0.999102	−	0.0423758i	$-0.0134927\pi$
$89$	4.36654	+	7.56307i	0.462852	+	0.801684i	−0.536249	+	0.844060i	$0.680159\pi$
$90$		0			0
$91$	−3.57459	−	3.56434i	−0.374719	−	0.373645i
$92$		0			0
$93$	3.16383	+	0.847747i	0.328074	+	0.0879073i
$94$		0			0
$95$	−10.6773	−	6.16455i	−1.09547	−	0.632470i
$96$		0			0
$97$		−	8.42967i		−	0.855903i	−0.903802	−	0.427952i	$-0.859235\pi$
$97$		−	8.42967i		−	0.855903i	0.903802	−	0.427952i	$-0.140765\pi$
$98$		0			0
$99$	−7.57992	−	7.57992i	−0.761810	−	0.761810i
$100$		0			0
$101$	3.81352	+	14.2323i	0.379460	+	1.41616i	0.846718	+	0.532042i	$0.178575\pi$
$101$	3.81352	+	14.2323i	0.379460	+	1.41616i	−0.467258	+	0.884121i	$0.654758\pi$
$102$		0			0
$103$	−6.87358	+	3.96846i	−0.677274	+	0.391024i	−0.798827	−	0.601561i	$-0.794546\pi$
$103$	−6.87358	+	3.96846i	−0.677274	+	0.391024i	0.121553	+	0.992585i	$0.461213\pi$
$104$		0			0
$105$	−0.0118491	−	8.25777i	−0.00115635	−	0.805876i
$106$		0			0
$107$	8.96762	+	2.40287i	0.866932	+	0.232294i	0.664761	−	0.747056i	$-0.268533\pi$
$107$	8.96762	+	2.40287i	0.866932	+	0.232294i	0.202172	+	0.979350i	$0.435200\pi$
$108$		0			0
$109$	−0.227686	−	0.849736i	−0.0218084	−	0.0813900i	0.954164	−	0.299284i	$-0.0967479\pi$
$109$	−0.227686	−	0.849736i	−0.0218084	−	0.0813900i	−0.975972	+	0.217894i	$0.930081\pi$
$110$		0			0
$111$	−2.45475			−0.232994
$112$		0			0
$113$	1.91230			0.179894			0.0899469	−	0.995947i	$-0.471330\pi$
$113$	1.91230			0.179894			0.0899469	+	0.995947i	$0.471330\pi$
$114$		0			0
$115$	2.09264	+	7.80983i	0.195140	+	0.728271i
$116$		0			0
$117$	−4.37715	−	1.17285i	−0.404668	−	0.108430i
$118$		0			0
$119$	2.61928	+	1.50724i	0.240109	+	0.138168i
$120$		0			0
$121$	−8.11511	+	4.68526i	−0.737737	+	0.425933i
$122$		0			0
$123$	1.65468	+	6.17533i	0.149197	+	0.556811i
$124$		0			0
$125$	15.6022	+	15.6022i	1.39550	+	1.39550i
$126$		0			0
$127$			11.9607i			1.06134i	0.847578	+	0.530671i	$0.178060\pi$
$127$			11.9607i			1.06134i	−0.847578	+	0.530671i	$0.821940\pi$
$128$		0			0
$129$	3.70045	+	2.13645i	0.325806	+	0.188104i
$130$		0			0
$131$	−5.36296	−	1.43700i	−0.468564	−	0.125551i	0.0168089	−	0.999859i	$-0.494649\pi$
$131$	−5.36296	−	1.43700i	−0.468564	−	0.125551i	−0.485372	+	0.874307i	$0.661316\pi$
$132$		0			0
$133$	−7.98340	−	2.12687i	−0.692249	−	0.184423i
$134$		0			0
$135$	−8.38821	−	14.5288i	−0.721943	−	1.25044i
$136$		0			0
$137$	−12.4195	−	7.17038i	−1.06107	−	0.612607i	−0.135339	−	0.990799i	$-0.543212\pi$
$137$	−12.4195	−	7.17038i	−1.06107	−	0.612607i	−0.925727	+	0.378192i	$0.876546\pi$
$138$		0			0
$139$	14.6088	+	14.6088i	1.23910	+	1.23910i	0.960369	+	0.278731i	$0.0899137\pi$
$139$	14.6088	+	14.6088i	1.23910	+	1.23910i	0.278731	+	0.960369i	$0.410086\pi$
$140$		0			0
$141$	−0.910361	+	0.910361i	−0.0766663	+	0.0766663i
$142$		0			0
$143$	−4.30567	+	7.45764i	−0.360058	+	0.623639i
$144$		0			0
$145$	−25.6401	+	14.8033i	−2.12930	+	1.22935i
$146$		0			0
$147$	−1.44754	−	5.34094i	−0.119391	−	0.440513i
$148$		0			0
$149$	3.05093	−	11.3862i	0.249942	−	0.932797i	−0.720892	−	0.693047i	$-0.756268\pi$
$149$	3.05093	−	11.3862i	0.249942	−	0.932797i	0.970835	−	0.239750i	$-0.0770655\pi$
$150$		0			0
$151$	−6.85381	+	11.8712i	−0.557755	+	0.966061i	0.439928	+	0.898033i	$0.355004\pi$
$151$	−6.85381	+	11.8712i	−0.557755	+	0.966061i	−0.997683	+	0.0680276i	$0.978329\pi$
$152$		0			0
$153$	2.71283			0.219319
$154$		0			0
$155$	−11.5677	+	11.5677i	−0.929138	+	0.929138i
$156$		0			0
$157$	−2.01291	+	0.539359i	−0.160648	+	0.0430455i	−0.338247	−	0.941058i	$-0.609834\pi$
$157$	−2.01291	+	0.539359i	−0.160648	+	0.0430455i	0.177599	+	0.984103i	$0.443167\pi$
$158$		0			0
$159$	−1.19691	−	2.07311i	−0.0949214	−	0.164409i
$160$		0			0
$161$	2.71576	+	4.68829i	0.214032	+	0.369489i
$162$		0			0
$163$	0.466826	−	1.74222i	0.0365647	−	0.136461i	−0.945231	−	0.326403i	$-0.894163\pi$
$163$	0.466826	−	1.74222i	0.0365647	−	0.136461i	0.981795	+	0.189942i	$0.0608300\pi$
$164$		0			0
$165$	−13.6069	+	3.64596i	−1.05930	+	0.283837i
$166$		0			0
$167$			21.6002i			1.67147i	0.549132	+	0.835735i	$0.314958\pi$
$167$			21.6002i			1.67147i	−0.549132	+	0.835735i	$0.685042\pi$
$168$		0			0
$169$		−	9.35968i		−	0.719976i
$170$		0			0
$171$	−7.16393	+	1.91957i	−0.547839	+	0.146793i
$172$		0			0
$173$	2.27429	−	8.48775i	0.172911	−	0.645312i	−0.823987	−	0.566608i	$-0.808255\pi$
$173$	2.27429	−	8.48775i	0.172911	−	0.645312i	0.996898	−	0.0787035i	$-0.0250780\pi$
$174$		0			0
$175$	24.2815	+	13.9725i	1.83551	+	1.05622i
$176$		0			0
$177$	−2.85371	−	4.94277i	−0.214498	−	0.371521i
$178$		0			0
$179$	−1.68719	+	0.452081i	−0.126106	+	0.0337901i	−0.321320	−	0.946971i	$-0.604127\pi$
$179$	−1.68719	+	0.452081i	−0.126106	+	0.0337901i	0.195214	+	0.980761i	$0.437460\pi$
$180$		0			0
$181$	−5.29547	+	5.29547i	−0.393609	+	0.393609i	−0.875972	−	0.482362i	$-0.839779\pi$
$181$	−5.29547	+	5.29547i	−0.393609	+	0.393609i	0.482362	+	0.875972i	$0.339779\pi$
$182$		0			0
$183$	5.16095			0.381508
$184$		0			0
$185$	6.13010	−	10.6176i	0.450694	−	0.780625i
$186$		0			0
$187$	1.33426	−	4.97953i	0.0975709	−	0.364140i
$188$		0			0
$189$	−7.96073	−	7.93792i	−0.579058	−	0.577399i
$190$		0			0
$191$	23.5567	−	13.6004i	1.70450	−	0.984093i	0.763423	−	0.645899i	$-0.223517\pi$
$191$	23.5567	−	13.6004i	1.70450	−	0.984093i	0.941076	−	0.338195i	$-0.109816\pi$
$192$		0			0
$193$	−2.88165	+	4.99117i	−0.207426	+	0.359272i	−0.950903	−	0.309489i	$-0.899842\pi$
$193$	−2.88165	+	4.99117i	−0.207426	+	0.359272i	0.743477	+	0.668762i	$0.233175\pi$
$194$		0			0
$195$	−4.21084	+	4.21084i	−0.301545	+	0.301545i
$196$		0			0
$197$	−12.7740	−	12.7740i	−0.910107	−	0.910107i	0.0861731	−	0.996280i	$-0.472536\pi$
$197$	−12.7740	−	12.7740i	−0.910107	−	0.910107i	−0.996280	+	0.0861731i	$0.972536\pi$
$198$		0			0
$199$	4.76949	+	2.75367i	0.338100	+	0.195202i	0.659432	−	0.751764i	$-0.270797\pi$
$199$	4.76949	+	2.75367i	0.338100	+	0.195202i	−0.321331	+	0.946967i	$0.604130\pi$
$200$		0			0
$201$	−0.252165	−	0.436763i	−0.0177863	−	0.0308069i
$202$		0			0
$203$	−14.0087	+	14.0489i	−0.983216	+	0.986042i
$204$		0			0
$205$	−30.8426	−	8.26425i	−2.15414	−	0.577201i
$206$		0			0
$207$	4.21216	+	2.43189i	0.292765	+	0.169028i
$208$		0			0
$209$			14.0939i			0.974893i
$210$		0			0
$211$	19.3846	+	19.3846i	1.33449	+	1.33449i	0.901302	+	0.433192i	$0.142613\pi$
$211$	19.3846	+	19.3846i	1.33449	+	1.33449i	0.433192	+	0.901302i	$0.357387\pi$
$212$		0			0
$213$	−0.492029	−	1.83628i	−0.0337133	−	0.125820i
$214$		0			0
$215$	−18.4818	+	10.6705i	−1.26045	+	0.727722i
$216$		0			0
$217$	−5.46759	+	9.50161i	−0.371164	+	0.645011i
$218$		0			0
$219$	−2.25968	−	0.605480i	−0.152695	−	0.0409145i
$220$		0			0
$221$	−0.564040	−	2.10503i	−0.0379414	−	0.141599i
$222$		0			0
$223$	−22.1379			−1.48247			−0.741233	−	0.671248i	$-0.765759\pi$
$223$	−22.1379			−1.48247			−0.741233	+	0.671248i	$0.765759\pi$
$224$		0			0
$225$	25.1486			1.67658
$226$		0			0
$227$	2.22844	+	8.31664i	0.147907	+	0.551995i	0.999609	+	0.0279688i	$0.00890392\pi$
$227$	2.22844	+	8.31664i	0.147907	+	0.551995i	−0.851702	+	0.524026i	$0.824429\pi$
$228$		0			0
$229$	−24.4498	−	6.55130i	−1.61569	−	0.432922i	−0.665957	−	0.745990i	$-0.731977\pi$
$229$	−24.4498	−	6.55130i	−1.61569	−	0.432922i	−0.949731	+	0.313067i	$0.898643\pi$
$230$		0			0
$231$	−8.16831	+	4.73162i	−0.537435	+	0.311317i
$232$		0			0
$233$	−13.4837	+	7.78481i	−0.883346	+	0.510000i	−0.871760	−	0.489933i	$-0.837021\pi$
$233$	−13.4837	+	7.78481i	−0.883346	+	0.510000i	−0.0115857	+	0.999933i	$0.503688\pi$
$234$		0			0
$235$	−1.66424	−	6.21103i	−0.108563	−	0.405163i
$236$		0			0
$237$	0.686140	+	0.686140i	0.0445696	+	0.0445696i
$238$		0			0
$239$		−	11.6230i		−	0.751832i	−0.926654	−	0.375916i	$-0.877328\pi$
$239$		−	11.6230i		−	0.751832i	0.926654	−	0.375916i	$-0.122672\pi$
$240$		0			0
$241$	2.43625	+	1.40657i	0.156933	+	0.0906051i	0.576410	−	0.817161i	$-0.304453\pi$
$241$	2.43625	+	1.40657i	0.156933	+	0.0906051i	−0.419477	+	0.907766i	$0.637787\pi$
$242$		0			0
$243$	−15.1888	−	4.06982i	−0.974361	−	0.261079i
$244$		0			0
$245$	26.7163	+	7.07650i	1.70684	+	0.452101i
$246$		0			0
$247$	2.97899	+	5.15975i	0.189548	+	0.328307i
$248$		0			0
$249$	2.22595	+	1.28515i	0.141064	+	0.0814432i
$250$		0			0
$251$	−1.99507	−	1.99507i	−0.125928	−	0.125928i	0.641334	−	0.767262i	$-0.278381\pi$
$251$	−1.99507	−	1.99507i	−0.125928	−	0.125928i	−0.767262	+	0.641334i	$0.778381\pi$
$252$		0			0
$253$	6.53554	−	6.53554i	0.410886	−	0.410886i
$254$		0			0
$255$	1.78250	−	3.08737i	0.111624	−	0.193339i
$256$		0			0
$257$	12.9550	−	7.47955i	0.808108	−	0.466561i	−0.0381904	−	0.999270i	$-0.512159\pi$
$257$	12.9550	−	7.47955i	0.808108	−	0.466561i	0.846298	+	0.532709i	$0.178826\pi$
$258$		0			0
$259$	2.11499	−	7.93879i	0.131419	−	0.493292i
$260$		0			0
$261$	−4.60958	+	17.2032i	−0.285326	+	1.06485i
$262$		0			0
$263$	7.39409	−	12.8069i	0.455939	−	0.789710i	−0.542802	−	0.839860i	$-0.682637\pi$
$263$	7.39409	−	12.8069i	0.455939	−	0.789710i	0.998742	+	0.0501505i	$0.0159701\pi$
$264$		0			0
$265$	11.9559			0.734447
$266$		0			0
$267$	4.88162	−	4.88162i	0.298750	−	0.298750i
$268$		0			0
$269$	23.1455	−	6.20182i	1.41121	−	0.378132i	0.528851	−	0.848715i	$-0.322623\pi$
$269$	23.1455	−	6.20182i	1.41121	−	0.378132i	0.882356	+	0.470583i	$0.155956\pi$
$270$		0			0
$271$	−7.37718	−	12.7776i	−0.448131	−	0.776186i	0.550133	−	0.835077i	$-0.314577\pi$
$271$	−7.37718	−	12.7776i	−0.448131	−	0.776186i	−0.998264	+	0.0588906i	$0.981244\pi$
$272$		0			0
$273$	−1.99030	+	3.45876i	−0.120459	+	0.209334i
$274$		0			0
$275$	12.3690	−	46.1616i	0.745877	−	2.78365i
$276$		0			0
$277$	17.7680	−	4.76091i	1.06757	−	0.286055i	0.318077	−	0.948065i	$-0.396963\pi$
$277$	17.7680	−	4.76091i	1.06757	−	0.286055i	0.749496	+	0.662009i	$0.230296\pi$
$278$		0			0
$279$			9.84094i			0.589162i
$280$		0			0
$281$		−	31.9694i		−	1.90713i	−0.301185	−	0.953566i	$-0.597382\pi$
$281$		−	31.9694i		−	1.90713i	0.301185	−	0.953566i	$-0.402618\pi$
$282$		0			0
$283$	−3.17648	+	0.851136i	−0.188822	+	0.0505948i	−0.351991	−	0.936003i	$-0.614495\pi$
$283$	−3.17648	+	0.851136i	−0.188822	+	0.0505948i	0.163169	+	0.986598i	$0.447829\pi$
$284$		0			0
$285$	−2.52255	+	9.41428i	−0.149423	+	0.557654i
$286$		0			0
$287$	−21.3970	+	0.0307026i	−1.26303	+	0.00181232i
$288$		0			0
$289$	−7.84768	−	13.5926i	−0.461628	−	0.799564i
$290$		0			0
$291$	−6.43674	+	1.72472i	−0.377329	+	0.101105i
$292$		0			0
$293$	−6.98254	+	6.98254i	−0.407925	+	0.407925i	−0.881014	−	0.473090i	$-0.843139\pi$
$293$	−6.98254	+	6.98254i	−0.407925	+	0.407925i	0.473090	+	0.881014i	$0.343139\pi$
$294$		0			0
$295$	28.5056			1.65966
$296$		0			0
$297$	−9.58888	+	16.6084i	−0.556403	+	0.963719i
$298$		0			0
$299$	1.01126	−	3.77406i	0.0584824	−	0.218259i
$300$		0			0
$301$	−10.0977	+	10.1267i	−0.582021	+	0.583694i
$302$		0			0
$303$	10.0872	−	5.82388i	0.579497	−	0.334573i
$304$		0			0
$305$	−12.8881	+	22.3229i	−0.737973	+	1.27821i
$306$		0			0
$307$	−23.3885	+	23.3885i	−1.33485	+	1.33485i	−0.433888	+	0.900967i	$0.642859\pi$
$307$	−23.3885	+	23.3885i	−1.33485	+	1.33485i	−0.900967	+	0.433888i	$0.857141\pi$
$308$		0			0
$309$	4.43659	+	4.43659i	0.252389	+	0.252389i
$310$		0			0
$311$	−21.8118	−	12.5931i	−1.23684	−	0.714087i	−0.268390	−	0.963310i	$-0.586491\pi$
$311$	−21.8118	−	12.5931i	−1.23684	−	0.714087i	−0.968446	+	0.249223i	$0.919825\pi$
$312$		0			0
$313$	4.22602	+	7.31969i	0.238869	+	0.413733i	0.960390	−	0.278659i	$-0.0898900\pi$
$313$	4.22602	+	7.31969i	0.238869	+	0.413733i	−0.721521	+	0.692393i	$0.756557\pi$
$314$		0			0
$315$	23.9556	−	6.45573i	1.34974	−	0.363739i
$316$		0			0
$317$	−18.4857	−	4.95323i	−1.03826	−	0.278201i	−0.300868	−	0.953666i	$-0.597276\pi$
$317$	−18.4857	−	4.95323i	−1.03826	−	0.278201i	−0.737393	+	0.675464i	$0.763943\pi$
$318$		0			0
$319$	29.3102	+	16.9222i	1.64106	+	0.947464i
$320$		0			0
$321$		−	7.33914i		−	0.409631i
$322$		0			0
$323$	−2.52207	−	2.52207i	−0.140332	−	0.140332i
$324$		0			0
$325$	−5.22880	−	19.5141i	−0.290041	−	1.08245i
$326$		0			0
$327$	−0.602258	+	0.347714i	−0.0333050	+	0.0192286i
$328$		0			0
$329$	−2.15980	−	3.72852i	−0.119074	−	0.205560i
$330$		0			0
$331$	−13.9616	−	3.74100i	−0.767399	−	0.205624i	−0.146177	−	0.989258i	$-0.546697\pi$
$331$	−13.9616	−	3.74100i	−0.767399	−	0.205624i	−0.621222	+	0.783635i	$0.713364\pi$
$332$		0			0
$333$	−1.90884	−	7.12389i	−0.104604	−	0.390387i
$334$		0			0
$335$	2.51887			0.137621
$336$		0			0
$337$	−13.7159			−0.747152			−0.373576	−	0.927600i	$-0.621868\pi$
$337$	−13.7159			−0.747152			−0.373576	+	0.927600i	$0.621868\pi$
$338$		0			0
$339$	−0.391258	−	1.46020i	−0.0212502	−	0.0793069i
$340$		0			0
$341$	18.0635	+	4.84011i	0.978196	+	0.262107i
$342$		0			0
$343$	18.5201	−	0.0797240i	0.999991	−	0.00430469i
$344$		0			0
$345$	5.53529	−	3.19580i	0.298010	−	0.172056i
$346$		0			0
$347$	−2.43191	−	9.07603i	−0.130552	−	0.487227i	0.869425	−	0.494066i	$-0.164490\pi$
$347$	−2.43191	−	9.07603i	−0.130552	−	0.487227i	−0.999977	+	0.00683892i	$0.997823\pi$
$348$		0			0
$349$	8.35069	+	8.35069i	0.447002	+	0.447002i	0.894357	−	0.447355i	$-0.147634\pi$
$349$	8.35069	+	8.35069i	0.447002	+	0.447002i	−0.447355	+	0.894357i	$0.647634\pi$
$350$		0			0
$351$			8.10712i			0.432726i
$352$		0			0
$353$	16.9374	+	9.77882i	0.901488	+	0.520474i	0.877683	−	0.479242i	$-0.159089\pi$
$353$	16.9374	+	9.77882i	0.901488	+	0.520474i	0.0238051	+	0.999717i	$0.492422\pi$
$354$		0			0
$355$	9.17127	+	2.45743i	0.486760	+	0.130427i
$356$		0			0
$357$	0.614991	−	2.30842i	0.0325488	−	0.122175i
$358$		0			0
$359$	−8.80385	−	15.2487i	−0.464650	−	0.804797i	0.534536	−	0.845146i	$-0.320486\pi$
$359$	−8.80385	−	15.2487i	−0.464650	−	0.804797i	−0.999186	+	0.0403489i	$0.987153\pi$
$360$		0			0
$361$	−8.00970	−	4.62440i	−0.421563	−	0.243390i
$362$		0			0
$363$	5.23794	+	5.23794i	0.274920	+	0.274920i
$364$		0			0
$365$	8.26189	−	8.26189i	0.432447	−	0.432447i
$366$		0			0
$367$	−16.4811	+	28.5462i	−0.860309	+	1.49010i	0.0113220	+	0.999936i	$0.496396\pi$
$367$	−16.4811	+	28.5462i	−0.860309	+	1.49010i	−0.871631	+	0.490163i	$0.836937\pi$
$368$		0			0
$369$	−16.6347	+	9.60402i	−0.865966	+	0.499966i
$370$		0			0
$371$	7.73582	−	2.08471i	0.401624	−	0.108233i
$372$		0			0
$373$	−3.47655	+	12.9747i	−0.180009	+	0.671802i	0.815635	+	0.578566i	$0.196388\pi$
$373$	−3.47655	+	12.9747i	−0.180009	+	0.671802i	−0.995644	+	0.0932356i	$0.970279\pi$
$374$		0			0
$375$	8.72133	−	15.1058i	0.450368	−	0.780059i
$376$		0			0
$377$	14.3073			0.736861
$378$		0			0
$379$	0.617225	−	0.617225i	0.0317047	−	0.0317047i	−0.691077	−	0.722781i	$-0.742863\pi$
$379$	0.617225	−	0.617225i	0.0317047	−	0.0317047i	0.722781	+	0.691077i	$0.242863\pi$
$380$		0			0
$381$	9.13298	−	2.44718i	0.467897	−	0.125373i
$382$		0			0
$383$	−0.214398	−	0.371348i	−0.0109552	−	0.0189750i	0.860496	−	0.509457i	$-0.170154\pi$
$383$	−0.214398	−	0.371348i	−0.0109552	−	0.0189750i	−0.871451	+	0.490483i	$0.836821\pi$
$384$		0			0
$385$	−0.0676511	−	47.1468i	−0.00344782	−	2.40282i
$386$		0			0
$387$	−3.32267	+	12.4004i	−0.168901	+	0.630346i
$388$		0			0
$389$	−10.1095	+	2.70883i	−0.512571	+	0.137343i	−0.505828	−	0.862634i	$-0.668813\pi$
$389$	−10.1095	+	2.70883i	−0.512571	+	0.137343i	−0.00674269	+	0.999977i	$0.502146\pi$
$390$		0			0
$391$			2.33905i			0.118291i
$392$		0			0
$393$			4.38907i			0.221399i
$394$		0			0
$395$	−4.68126	+	1.25434i	−0.235540	+	0.0631126i
$396$		0			0
$397$	−7.22485	+	26.9635i	−0.362605	+	1.35326i	0.508034	+	0.861337i	$0.330372\pi$
$397$	−7.22485	+	26.9635i	−0.362605	+	1.35326i	−0.870639	+	0.491922i	$0.836294\pi$
$398$		0			0
$399$	0.00937155	+	6.53114i	0.000469165	+	0.326966i
$400$		0			0
$401$	−13.1880	−	22.8422i	−0.658575	−	1.14069i	−0.980985	−	0.194085i	$-0.937826\pi$
$401$	−13.1880	−	22.8422i	−0.658575	−	1.14069i	0.322410	−	0.946600i	$-0.395507\pi$
$402$		0			0
$403$	7.63610	−	2.04609i	0.380381	−	0.101923i
$404$		0			0
$405$	10.5147	−	10.5147i	0.522480	−	0.522480i
$406$		0			0
$407$	−14.0151			−0.694702
$408$		0			0
$409$	−8.91434	+	15.4401i	−0.440786	+	0.763463i	−0.997748	−	0.0670744i	$-0.978634\pi$
$409$	−8.91434	+	15.4401i	−0.440786	+	0.763463i	0.556962	+	0.830538i	$0.311967\pi$
$410$		0			0
$411$	−2.93414	+	10.9503i	−0.144730	+	0.540141i
$412$		0			0
$413$	18.4439	−	4.97041i	0.907565	−	0.244578i
$414$		0			0
$415$	−11.1175	+	6.41868i	−0.545735	+	0.315081i
$416$		0			0
$417$	8.16602	−	14.1440i	0.399892	−	0.692633i
$418$		0			0
$419$	19.6171	−	19.6171i	0.958358	−	0.958358i	−0.0408093	−	0.999167i	$-0.512994\pi$
$419$	19.6171	−	19.6171i	0.958358	−	0.958358i	0.999167	+	0.0408093i	$0.0129936\pi$
$420$		0			0
$421$	5.25405	+	5.25405i	0.256067	+	0.256067i	0.823452	−	0.567385i	$-0.192045\pi$
$421$	5.25405	+	5.25405i	0.256067	+	0.256067i	−0.567385	+	0.823452i	$0.692045\pi$
$422$		0			0
$423$	−3.34986	−	1.93404i	−0.162876	−	0.0940363i
$424$		0			0
$425$	6.04714	+	10.4740i	0.293329	+	0.508061i
$426$		0			0
$427$	−4.44663	+	16.6908i	−0.215187	+	0.807724i
$428$		0			0
$429$	6.57546	+	1.76189i	0.317466	+	0.0850648i
$430$		0			0
$431$	−23.2543	−	13.4259i	−1.12012	−	0.646701i	−0.178687	−	0.983906i	$-0.557185\pi$
$431$	−23.2543	−	13.4259i	−1.12012	−	0.646701i	−0.941431	+	0.337205i	$0.890518\pi$
$432$		0			0
$433$			18.6517i			0.896344i	0.893947	+	0.448172i	$0.147925\pi$
$433$			18.6517i			0.896344i	−0.893947	+	0.448172i	$0.852075\pi$
$434$		0			0
$435$	16.5496	+	16.5496i	0.793491	+	0.793491i
$436$		0			0
$437$	−1.65509	−	6.17686i	−0.0791735	−	0.295479i
$438$		0			0
$439$	17.5460	−	10.1302i	0.837427	−	0.483488i	−0.0189621	−	0.999820i	$-0.506036\pi$
$439$	17.5460	−	10.1302i	0.837427	−	0.483488i	0.856389	+	0.516332i	$0.172703\pi$
$440$		0			0
$441$	14.3742	−	8.35407i	0.684488	−	0.397813i
$442$		0			0
$443$	34.1538	+	9.15149i	1.62270	+	0.434800i	0.951792	−	0.306744i	$-0.0992394\pi$
$443$	34.1538	+	9.15149i	1.62270	+	0.434800i	0.670904	+	0.741544i	$0.265906\pi$
$444$		0			0
$445$	8.92414	+	33.3053i	0.423045	+	1.57882i
$446$		0			0
$447$	−9.31855			−0.440752
$448$		0			0
$449$	14.0702			0.664012			0.332006	−	0.943277i	$-0.392275\pi$
$449$	14.0702			0.664012			0.332006	+	0.943277i	$0.392275\pi$
$450$		0			0
$451$	9.44718	+	35.2573i	0.444850	+	1.66020i
$452$		0			0
$453$	10.4669	+	2.80460i	0.491777	+	0.131771i
$454$		0			0
$455$	−9.99008	−	17.2461i	−0.468342	−	0.808511i
$456$		0			0
$457$	−4.61613	+	2.66512i	−0.215933	+	0.124669i	−0.604066	−	0.796934i	$-0.706454\pi$
$457$	−4.61613	+	2.66512i	−0.215933	+	0.124669i	0.388133	+	0.921604i	$0.373120\pi$
$458$		0			0
$459$	−1.25614	−	4.68797i	−0.0586314	−	0.218816i
$460$		0			0
$461$	2.32075	+	2.32075i	0.108088	+	0.108088i	0.759082	−	0.650995i	$-0.225648\pi$
$461$	2.32075	+	2.32075i	0.108088	+	0.108088i	−0.650995	+	0.759082i	$0.725648\pi$
$462$		0			0
$463$		−	15.2932i		−	0.710736i	−0.934727	−	0.355368i	$-0.884356\pi$
$463$		−	15.2932i		−	0.710736i	0.934727	−	0.355368i	$-0.115644\pi$
$464$		0			0
$465$	11.1996	+	6.46610i	0.519370	+	0.299858i
$466$		0			0
$467$	−29.0012	−	7.77086i	−1.34202	−	0.359592i	−0.484835	−	0.874606i	$-0.661120\pi$
$467$	−29.0012	−	7.77086i	−1.34202	−	0.359592i	−0.857182	+	0.515014i	$0.827787\pi$
$468$		0			0
$469$	1.62978	−	0.439205i	0.0752561	−	0.0202806i
$470$		0			0
$471$	0.823689	+	1.42667i	0.0379536	+	0.0657375i
$472$		0			0
$473$	21.1273	+	12.1978i	0.971433	+	0.560857i
$474$		0			0
$475$	−23.3803	−	23.3803i	−1.07276	−	1.07276i
$476$		0			0
$477$	5.08563	−	5.08563i	0.232855	−	0.232855i
$478$		0			0
$479$	17.2367	−	29.8548i	0.787564	−	1.36410i	−0.139892	−	0.990167i	$-0.544676\pi$
$479$	17.2367	−	29.8548i	0.787564	−	1.36410i	0.927456	−	0.373933i	$-0.121991\pi$
$480$		0			0
$481$	−5.13092	+	2.96234i	−0.233950	+	0.135071i
$482$		0			0
$483$	3.02425	−	3.03294i	0.137608	−	0.138003i
$484$		0			0
$485$	8.61409	−	32.1482i	0.391146	−	1.45978i
$486$		0			0
$487$	−7.45142	+	12.9062i	−0.337656	+	0.584837i	−0.983991	−	0.178216i	$-0.942967\pi$
$487$	−7.45142	+	12.9062i	−0.337656	+	0.584837i	0.646335	+	0.763053i	$0.276301\pi$
$488$		0			0
$489$	−1.42584			−0.0644787
$490$		0			0
$491$	30.5248	−	30.5248i	1.37756	−	1.37756i	0.528844	−	0.848719i	$-0.322626\pi$
$491$	30.5248	−	30.5248i	1.37756	−	1.37756i	0.848719	−	0.528844i	$-0.177374\pi$
$492$		0			0
$493$	−8.27322	+	2.21680i	−0.372607	+	0.0998398i
$494$		0			0
$495$	−21.1618	−	36.6533i	−0.951151	−	1.64744i
$496$		0			0
$497$	6.36255	−	0.00912964i	0.285399	−	0.000409520i
$498$		0			0
$499$	2.86434	−	10.6899i	0.128225	−	0.478544i	−0.871709	−	0.490025i	$-0.836988\pi$
$499$	2.86434	−	10.6899i	0.128225	−	0.478544i	0.999934	+	0.0114806i	$0.00365448\pi$
$500$		0			0
$501$	16.4935	−	4.41942i	0.736875	−	0.197445i
$502$		0			0
$503$		−	25.6811i		−	1.14507i	−0.819882	−	0.572533i	$-0.805961\pi$
$503$		−	25.6811i		−	1.14507i	0.819882	−	0.572533i	$-0.194039\pi$
$504$		0			0
$505$			58.1745i			2.58873i
$506$		0			0
$507$	−7.14688	+	1.91500i	−0.317404	+	0.0850482i
$508$		0			0
$509$	−3.97493	+	14.8346i	−0.176186	+	0.657534i	0.820161	+	0.572133i	$0.193884\pi$
$509$	−3.97493	+	14.8346i	−0.176186	+	0.657534i	−0.996347	+	0.0854009i	$0.972783\pi$
$510$		0			0
$511$	3.90508	−	6.78626i	0.172750	−	0.300206i
$512$		0			0
$513$	6.63431	+	11.4910i	0.292912	+	0.507338i
$514$		0			0
$515$	−30.2691	+	8.11057i	−1.33381	+	0.357394i
$516$		0			0
$517$	−5.19760	+	5.19760i	−0.228590	+	0.228590i
$518$		0			0
$519$	−6.94641			−0.304914
$520$		0			0
$521$	14.9189	−	25.8403i	0.653609	−	1.13208i	−0.328632	−	0.944458i	$-0.606588\pi$
$521$	14.9189	−	25.8403i	0.653609	−	1.13208i	0.982241	−	0.187626i	$-0.0600792\pi$
$522$		0			0
$523$	9.32633	−	34.8063i	0.407812	−	1.52198i	−0.390998	−	0.920392i	$-0.627870\pi$
$523$	9.32633	−	34.8063i	0.407812	−	1.52198i	0.798810	−	0.601583i	$-0.205463\pi$
$524$		0			0
$525$	5.70113	−	21.3997i	0.248818	−	0.933958i
$526$		0			0
$527$	−4.09857	+	2.36631i	−0.178537	+	0.103078i
$528$		0			0
$529$	9.40318	−	16.2868i	0.408834	−	0.708121i
$530$		0			0
$531$	12.1253	−	12.1253i	0.526191	−	0.526191i
$532$		0			0
$533$	10.9109	+	10.9109i	0.472602	+	0.472602i
$534$		0			0
$535$	31.7444	+	18.3276i	1.37243	+	0.792372i
$536$		0			0
$537$	0.690401	+	1.19581i	0.0297930	+	0.0516030i
$538$		0			0
$539$	−8.26457	−	30.4935i	−0.355980	−	1.31345i
$540$		0			0
$541$	13.0674	+	3.50141i	0.561813	+	0.150537i	0.528539	−	0.848909i	$-0.322740\pi$
$541$	13.0674	+	3.50141i	0.561813	+	0.150537i	0.0332740	+	0.999446i	$0.489407\pi$
$542$		0			0
$543$	5.12698	+	2.96007i	0.220020	+	0.127029i
$544$		0			0
$545$		−	3.47331i		−	0.148780i
$546$		0			0
$547$	−19.9064	−	19.9064i	−0.851134	−	0.851134i	0.139139	−	0.990273i	$-0.455567\pi$
$547$	−19.9064	−	19.9064i	−0.851134	−	0.851134i	−0.990273	+	0.139139i	$0.955567\pi$
$548$		0			0
$549$	4.01321	+	14.9775i	0.171280	+	0.639225i
$550$		0			0
$551$	20.2790	−	11.7081i	0.863914	−	0.498781i
$552$		0			0
$553$	−2.81019	+	1.62784i	−0.119501	+	0.0692229i
$554$		0			0
$555$	−9.36167	−	2.50845i	−0.397381	−	0.106478i
$556$		0			0
$557$	−3.45569	−	12.8968i	−0.146422	−	0.546456i	−0.999688	−	0.0249794i	$-0.992048\pi$
$557$	−3.45569	−	12.8968i	−0.146422	−	0.546456i	0.853265	−	0.521477i	$-0.174619\pi$
$558$		0			0
$559$	10.3129			0.436190
$560$		0			0
$561$	−4.07527			−0.172058
$562$		0			0
$563$	6.53907	+	24.4041i	0.275589	+	1.02851i	0.955446	+	0.295167i	$0.0953751\pi$
$563$	6.53907	+	24.4041i	0.275589	+	1.02851i	−0.679857	+	0.733345i	$0.737958\pi$
$564$		0			0
$565$	7.29293	+	1.95413i	0.306816	+	0.0822110i
$566$		0			0
$567$	4.96990	−	8.63671i	0.208716	−	0.362708i
$568$		0			0
$569$	10.8718	−	6.27682i	0.455768	−	0.263138i	−0.254495	−	0.967074i	$-0.581909\pi$
$569$	10.8718	−	6.27682i	0.455768	−	0.263138i	0.710263	+	0.703936i	$0.248576\pi$
$570$		0			0
$571$	10.2203	+	38.1427i	0.427706	+	1.59622i	0.757942	+	0.652322i	$0.226205\pi$
$571$	10.2203	+	38.1427i	0.427706	+	1.59622i	−0.330235	+	0.943899i	$0.607128\pi$
$572$		0			0
$573$	−15.2048	−	15.2048i	−0.635188	−	0.635188i
$574$		0			0
$575$			21.6836i			0.904268i
$576$		0			0
$577$	−20.1944	−	11.6592i	−0.840702	−	0.485380i	0.0168006	−	0.999859i	$-0.494652\pi$
$577$	−20.1944	−	11.6592i	−0.840702	−	0.485380i	−0.857503	+	0.514479i	$0.827985\pi$
$578$		0			0
$579$	4.40076	+	1.17918i	0.182889	+	0.0490050i
$580$		0			0
$581$	−6.07411	+	6.09157i	−0.251997	+	0.252721i
$582$		0			0
$583$	−6.83364	−	11.8362i	−0.283020	−	0.490206i
$584$		0			0
$585$	−15.4946	−	8.94583i	−0.640624	−	0.369865i
$586$		0			0
$587$	−24.2488	−	24.2488i	−1.00085	−	1.00085i	−1.00000		0.000853494i	$-0.999728\pi$
$587$	−24.2488	−	24.2488i	−1.00085	−	1.00085i	−0.000853494	−	1.00000i	$-0.500272\pi$
$588$		0			0
$589$	9.14897	−	9.14897i	0.376977	−	0.376977i
$590$		0			0
$591$	−7.14040	+	12.3675i	−0.293717	+	0.508732i
$592$		0			0
$593$	33.2134	−	19.1758i	1.36391	−	0.787454i	0.373768	−	0.927522i	$-0.378066\pi$
$593$	33.2134	−	19.1758i	1.36391	−	0.787454i	0.990142	+	0.140068i	$0.0447322\pi$
$594$		0			0
$595$	8.44895	+	8.42474i	0.346373	+	0.345381i
$596$		0			0
$597$	1.12681	−	4.20530i	0.0461171	−	0.172112i
$598$		0			0
$599$	0.398968	−	0.691033i	0.0163014	−	0.0282348i	−0.857760	−	0.514051i	$-0.828144\pi$
$599$	0.398968	−	0.691033i	0.0163014	−	0.0282348i	0.874061	+	0.485816i	$0.161478\pi$
$600$		0			0
$601$	4.37578			0.178492			0.0892459	−	0.996010i	$-0.471554\pi$
$601$	4.37578			0.178492			0.0892459	+	0.996010i	$0.471554\pi$
$602$		0			0
$603$	1.07144	−	1.07144i	0.0436323	−	0.0436323i
$604$		0			0
$605$	−35.7363	+	9.57552i	−1.45289	+	0.389300i
$606$		0			0
$607$	3.27685	+	5.67568i	0.133003	+	0.230369i	0.924833	−	0.380373i	$-0.124205\pi$
$607$	3.27685	+	5.67568i	0.133003	+	0.230369i	−0.791830	+	0.610742i	$0.790871\pi$
$608$		0			0
$609$	13.5937	+	7.82234i	0.550844	+	0.316977i
$610$		0			0
$611$	−0.804235	+	3.00145i	−0.0325359	+	0.121425i
$612$		0			0
$613$	18.1595	−	4.86583i	0.733457	−	0.196529i	0.127289	−	0.991866i	$-0.459373\pi$
$613$	18.1595	−	4.86583i	0.733457	−	0.196529i	0.606168	+	0.795337i	$0.292706\pi$
$614$		0			0
$615$			25.2417i			1.01785i
$616$		0			0
$617$			22.2202i			0.894552i	0.894396	+	0.447276i	$0.147606\pi$
$617$			22.2202i			0.894552i	−0.894396	+	0.447276i	$0.852394\pi$
$618$		0			0
$619$	−8.23929	+	2.20771i	−0.331165	+	0.0887354i	−0.420570	−	0.907260i	$-0.638170\pi$
$619$	−8.23929	+	2.20771i	−0.331165	+	0.0887354i	0.0894053	+	0.995995i	$0.471503\pi$
$620$		0			0
$621$	2.25210	−	8.40496i	0.0903738	−	0.337280i
$622$		0			0
$623$	11.5815	+	19.9934i	0.464002	+	0.801019i
$624$		0			0
$625$	17.0872	+	29.5959i	0.683489	+	1.18384i
$626$		0			0
$627$	10.7618	−	2.88362i	0.429785	−	0.115161i
$628$		0			0
$629$	2.50798	−	2.50798i	0.0999997	−	0.0999997i
$630$		0			0
$631$	−45.0684			−1.79415			−0.897073	−	0.441882i	$-0.854311\pi$
$631$	−45.0684			−1.79415			−0.897073	+	0.441882i	$0.854311\pi$
$632$		0			0
$633$	10.8356	−	18.7679i	0.430678	−	0.745956i
$634$		0			0
$635$	−12.2224	+	45.6146i	−0.485031	+	1.81016i
$636$		0			0
$637$	−9.47099	−	9.41679i	−0.375254	−	0.373107i
$638$		0			0
$639$	4.94643	−	2.85582i	0.195678	−	0.112975i
$640$		0			0
$641$	−14.4649	+	25.0540i	−0.571329	+	0.989572i	0.425100	+	0.905146i	$0.360239\pi$
$641$	−14.4649	+	25.0540i	−0.571329	+	0.989572i	−0.996430	+	0.0844254i	$0.973095\pi$
$642$		0			0
$643$	27.4126	−	27.4126i	1.08105	−	1.08105i	0.0846366	−	0.996412i	$-0.473027\pi$
$643$	27.4126	−	27.4126i	1.08105	−	1.08105i	0.996412	−	0.0846366i	$-0.0269729\pi$
$644$		0			0
$645$	11.9292	+	11.9292i	0.469712	+	0.469712i
$646$		0			0
$647$	25.8281	+	14.9119i	1.01541	+	0.586247i	0.912771	−	0.408472i	$-0.133938\pi$
$647$	25.8281	+	14.9119i	1.01541	+	0.586247i	0.102638	+	0.994719i	$0.467272\pi$
$648$		0			0
$649$	−16.2929	−	28.2201i	−0.639553	−	1.10774i
$650$		0			0
$651$	8.37393	+	2.23091i	0.328200	+	0.0874364i
$652$		0			0
$653$	12.5980	+	3.37562i	0.492997	+	0.132098i	0.496748	−	0.867895i	$-0.334527\pi$
$653$	12.5980	+	3.37562i	0.492997	+	0.132098i	−0.00375078	+	0.999993i	$0.501194\pi$
$654$		0			0
$655$	−18.9843	−	10.9606i	−0.741776	−	0.428265i
$656$		0			0
$657$		−	7.02862i		−	0.274213i
$658$		0			0
$659$	−15.1555	−	15.1555i	−0.590375	−	0.590375i	0.347358	−	0.937733i	$-0.387079\pi$
$659$	−15.1555	−	15.1555i	−0.590375	−	0.590375i	−0.937733	+	0.347358i	$0.887079\pi$
$660$		0			0
$661$	−0.571930	−	2.13447i	−0.0222455	−	0.0830213i	0.953911	−	0.300091i	$-0.0970169\pi$
$661$	−0.571930	−	2.13447i	−0.0222455	−	0.0830213i	−0.976156	+	0.217069i	$0.930350\pi$
$662$		0			0
$663$	−1.49196	+	0.861381i	−0.0579428	+	0.0334533i
$664$		0			0
$665$	−28.2729	−	16.2693i	−1.09638	−	0.630897i
$666$		0			0
$667$	−14.8329	−	3.97446i	−0.574332	−	0.153892i
$668$		0			0
$669$	4.52945	+	16.9041i	0.175118	+	0.653551i
$670$		0			0
$671$	29.4658			1.13752
$672$		0			0
$673$	−50.4864			−1.94611			−0.973054	−	0.230577i	$-0.925939\pi$
$673$	−50.4864			−1.94611			−0.973054	+	0.230577i	$0.925939\pi$
$674$		0			0
$675$	−11.6447	−	43.4587i	−0.448205	−	1.67273i
$676$		0			0
$677$	−28.6211	−	7.66899i	−1.10000	−	0.294743i	−0.337234	−	0.941421i	$-0.609491\pi$
$677$	−28.6211	−	7.66899i	−1.10000	−	0.294743i	−0.762763	+	0.646678i	$0.776158\pi$
$678$		0			0
$679$	−0.0320023	−	22.3028i	−0.00122814	−	0.855903i
$680$		0			0
$681$	5.89450	−	3.40319i	0.225878	−	0.130410i
$682$		0			0
$683$	−0.972755	−	3.63037i	−0.0372214	−	0.138912i	0.944815	−	0.327605i	$-0.106242\pi$
$683$	−0.972755	−	3.63037i	−0.0372214	−	0.138912i	−0.982036	+	0.188693i	$0.939575\pi$
$684$		0			0
$685$	−40.0368	−	40.0368i	−1.52973	−	1.52973i
$686$		0			0
$687$			20.0098i			0.763423i
$688$		0			0
$689$	−5.00358	−	2.88882i	−0.190621	−	0.110055i
$690$		0			0
$691$	13.8605	+	3.71391i	0.527278	+	0.141284i	0.512631	−	0.858609i	$-0.328671\pi$
$691$	13.8605	+	3.71391i	0.527278	+	0.141284i	0.0146470	+	0.999893i	$0.495338\pi$
$692$		0			0
$693$	−20.0833	−	20.0258i	−0.762903	−	0.760717i
$694$		0			0
$695$	40.7851	+	70.6418i	1.54707	+	2.67960i
$696$		0			0
$697$	−7.99980	−	4.61869i	−0.303014	−	0.174945i
$698$		0			0
$699$	8.70312	+	8.70312i	0.329182	+	0.329182i
$700$		0			0
$701$	−12.9519	+	12.9519i	−0.489187	+	0.489187i	−0.908050	−	0.418863i	$-0.862429\pi$
$701$	−12.9519	+	12.9519i	−0.489187	+	0.489187i	0.418863	+	0.908050i	$0.362429\pi$
$702$		0			0
$703$	−4.84835	+	8.39758i	−0.182859	+	0.316721i
$704$		0			0
$705$	−4.40212	+	2.54157i	−0.165794	+	0.0957210i
$706$		0			0
$707$	10.1437	+	37.6405i	0.381492	+	1.41562i
$708$		0			0
$709$	0.167036	−	0.623389i	0.00627319	−	0.0234119i	−0.962718	−	0.270506i	$-0.912809\pi$
$709$	0.167036	−	0.623389i	0.00627319	−	0.0234119i	0.968991	+	0.247094i	$0.0794757\pi$
$710$		0			0
$711$	−1.45769	+	2.52479i	−0.0546676	+	0.0946870i
$712$		0			0
$713$	−8.48503			−0.317767
$714$		0			0
$715$	−24.0413	+	24.0413i	−0.899094	+	0.899094i
$716$		0			0
$717$	−8.87514	+	2.37809i	−0.331448	+	0.0888113i
$718$		0			0
$719$	15.4833	+	26.8178i	0.577429	+	1.00014i	0.995773	+	0.0918476i	$0.0292772\pi$
$719$	15.4833	+	26.8178i	0.577429	+	1.00014i	−0.418344	+	0.908289i	$0.637389\pi$
$720$		0			0
$721$	−18.1707	+	10.5257i	−0.676712	+	0.391996i
$722$		0			0
$723$	0.575572	−	2.14806i	0.0214057	−	0.0798873i
$724$		0			0
$725$	−76.6949	+	20.5503i	−2.84838	+	0.763221i
$726$		0			0
$727$		−	16.7744i		−	0.622128i	−0.950389	−	0.311064i	$-0.899315\pi$
$727$		−	16.7744i		−	0.622128i	0.950389	−	0.311064i	$-0.100685\pi$
$728$		0			0
$729$			1.13181i			0.0419187i
$730$		0			0
$731$	−5.96348	+	1.59791i	−0.220567	+	0.0591008i
$732$		0			0
$733$	−7.88067	+	29.4110i	−0.291079	+	1.08632i	0.653203	+	0.757183i	$0.273425\pi$
$733$	−7.88067	+	29.4110i	−0.291079	+	1.08632i	−0.944282	+	0.329139i	$0.893242\pi$
$734$		0			0
$735$	−0.0626995	−	21.8480i	−0.00231271	−	0.805874i
$736$		0			0
$737$	−1.43971	−	2.49365i	−0.0530323	−	0.0918546i
$738$		0			0
$739$	24.9711	−	6.69098i	0.918577	−	0.246132i	0.231600	−	0.972811i	$-0.425604\pi$
$739$	24.9711	−	6.69098i	0.918577	−	0.246132i	0.686977	+	0.726679i	$0.258937\pi$
$740$		0			0
$741$	3.33039	−	3.33039i	0.122345	−	0.122345i
$742$		0			0
$743$	−16.7597			−0.614855			−0.307427	−	0.951572i	$-0.599468\pi$
$743$	−16.7597			−0.614855			−0.307427	+	0.951572i	$0.599468\pi$
$744$		0			0
$745$	23.2707	−	40.3060i	0.852572	−	1.47670i
$746$		0			0
$747$	−1.99870	+	7.45925i	−0.0731286	+	0.272920i
$748$		0			0
$749$	23.7352	+	6.32334i	0.867265	+	0.231050i
$750$		0			0
$751$	19.4065	−	11.2044i	0.708154	−	0.408853i	−0.102223	−	0.994761i	$-0.532596\pi$
$751$	19.4065	−	11.2044i	0.708154	−	0.408853i	0.810377	+	0.585909i	$0.199262\pi$
$752$		0			0
$753$	−1.11521	+	1.93159i	−0.0406404	+	0.0703912i
$754$		0			0
$755$	−38.2692	+	38.2692i	−1.39276	+	1.39276i
$756$		0			0
$757$	−10.1520	−	10.1520i	−0.368982	−	0.368982i	0.498124	−	0.867106i	$-0.334022\pi$
$757$	−10.1520	−	10.1520i	−0.368982	−	0.368982i	−0.867106	+	0.498124i	$0.834022\pi$
$758$		0			0
$759$	−6.32760	−	3.65324i	−0.229677	−	0.132604i
$760$		0			0
$761$	10.0149	+	17.3464i	0.363041	+	0.628805i	0.988460	−	0.151484i	$-0.0484053\pi$
$761$	10.0149	+	17.3464i	0.363041	+	0.628805i	−0.625419	+	0.780289i	$0.715072\pi$
$762$		0			0
$763$	−0.605626	−	2.24732i	−0.0219251	−	0.0813586i
$764$		0			0
$765$	10.3459	+	2.77218i	0.374057	+	0.100228i
$766$		0			0
$767$	−11.9297	−	6.88759i	−0.430755	−	0.248696i
$768$		0			0
$769$			50.7365i			1.82960i	0.403902	+	0.914802i	$0.367654\pi$
$769$			50.7365i			1.82960i	−0.403902	+	0.914802i	$0.632346\pi$
$770$		0			0
$771$	−8.36185	−	8.36185i	−0.301144	−	0.301144i
$772$		0			0
$773$	7.73070	+	28.8514i	0.278054	+	1.03771i	0.953767	+	0.300547i	$0.0971692\pi$
$773$	7.73070	+	28.8514i	0.278054	+	1.03771i	−0.675713	+	0.737165i	$0.736164\pi$
$774$		0			0
$775$	−37.9949	+	21.9363i	−1.36482	+	0.787977i
$776$		0			0
$777$	−6.49464	+	0.00931918i	−0.232994	+	0.000334324i
$778$		0			0
$779$	24.3937	+	6.53627i	0.873994	+	0.234186i
$780$		0			0
$781$	−2.80918	−	10.4840i	−0.100520	−	0.375148i
$782$		0			0
$783$	31.8628			1.13868
$784$		0			0
$785$	−8.22781			−0.293663
$786$		0			0
$787$	−9.92221	−	37.0302i	−0.353688	−	1.31998i	−0.882127	−	0.471012i	$-0.843889\pi$
$787$	−9.92221	−	37.0302i	−0.353688	−	1.31998i	0.528438	−	0.848972i	$-0.322778\pi$
$788$		0			0
$789$	−11.2920	−	3.02568i	−0.402005	−	0.107717i
$790$		0			0
$791$	5.05946	−	0.00725983i	0.179894	−	0.000258130i
$792$		0			0
$793$	10.7874	−	6.22812i	0.383073	−	0.221167i
$794$		0			0
$795$	−2.44620	−	9.12933i	−0.0867577	−	0.323784i
$796$		0			0
$797$	−18.8328	−	18.8328i	−0.667092	−	0.667092i	0.289949	−	0.957042i	$-0.406361\pi$
$797$	−18.8328	−	18.8328i	−0.667092	−	0.667092i	−0.957042	+	0.289949i	$0.906361\pi$
$798$		0			0
$799$		−	1.86021i		−	0.0658094i
$800$		0			0
$801$	17.9629	+	10.3709i	0.634688	+	0.366437i
$802$		0			0
$803$	−12.9014	−	3.45692i	−0.455280	−	0.121992i
$804$		0			0
$805$	5.56624	+	20.6549i	0.196184	+	0.727990i
$806$		0			0
$807$	−9.47120	−	16.4046i	−0.333402	−	0.577469i
$808$		0			0
$809$	17.1772	+	9.91725i	0.603918	+	0.348672i	0.770581	−	0.637342i	$-0.219966\pi$
$809$	17.1772	+	9.91725i	0.603918	+	0.348672i	−0.166663	+	0.986014i	$0.553299\pi$
$810$		0			0
$811$	3.89894	+	3.89894i	0.136910	+	0.136910i	0.772240	−	0.635330i	$-0.219136\pi$
$811$	3.89894	+	3.89894i	0.136910	+	0.136910i	−0.635330	+	0.772240i	$0.719136\pi$
$812$		0			0
$813$	−8.24740	+	8.24740i	−0.289249	+	0.289249i
$814$		0			0
$815$	3.56067	−	6.16726i	0.124725	−	0.216030i
$816$		0			0
$817$	14.6174	−	8.43938i	0.511400	−	0.295257i
$818$		0			0
$819$	−11.5853	−	3.08646i	−0.404823	−	0.107850i
$820$		0			0
$821$	5.00859	−	18.6923i	0.174801	−	0.652366i	−0.821784	−	0.569798i	$-0.807021\pi$
$821$	5.00859	−	18.6923i	0.174801	−	0.652366i	0.996585	−	0.0825677i	$-0.0263121\pi$
$822$		0			0
$823$	−20.0886	+	34.7944i	−0.700243	+	1.21286i	0.268138	+	0.963381i	$0.413592\pi$
$823$	−20.0886	+	34.7944i	−0.700243	+	1.21286i	−0.968381	+	0.249476i	$0.919742\pi$
$824$		0			0
$825$	−37.7789			−1.31529
$826$		0			0
$827$	11.2802	−	11.2802i	0.392250	−	0.392250i	−0.483239	−	0.875489i	$-0.660540\pi$
$827$	11.2802	−	11.2802i	0.392250	−	0.392250i	0.875489	+	0.483239i	$0.160540\pi$
$828$		0			0
$829$	40.7143	−	10.9094i	1.41407	−	0.378898i	0.530691	−	0.847565i	$-0.321933\pi$
$829$	40.7143	−	10.9094i	1.41407	−	0.378898i	0.883375	+	0.468668i	$0.155266\pi$
$830$		0			0
$831$	−7.27069	−	12.5932i	−0.252217	−	0.436853i
$832$		0			0
$833$	6.93569	+	3.97783i	0.240307	+	0.137824i
$834$		0			0
$835$	−22.0727	+	82.3765i	−0.763858	+	2.85076i
$836$		0			0
$837$	17.0059	−	4.55671i	0.587809	−	0.157503i
$838$		0			0
$839$			27.4328i			0.947087i	0.880771	+	0.473543i	$0.157025\pi$
$839$			27.4328i			0.947087i	−0.880771	+	0.473543i	$0.842975\pi$
$840$		0			0
$841$		−	27.2308i		−	0.938992i
$842$		0			0
$843$	−24.4112	+	6.54097i	−0.840767	+	0.225283i
$844$		0			0
$845$	9.56445	−	35.6950i	0.329027	−	1.22795i
$846$		0			0
$847$	−21.4527	+	12.4268i	−0.737125	+	0.426991i
$848$		0			0
$849$	1.29982	+	2.25136i	0.0446098	+	0.0772665i
$850$		0			0
$851$	6.14234	−	1.64584i	0.210557	−	0.0564185i
$852$		0			0
$853$	8.95019	−	8.95019i	0.306449	−	0.306449i	−0.537082	−	0.843530i	$-0.680473\pi$
$853$	8.95019	−	8.95019i	0.306449	−	0.306449i	0.843530	+	0.537082i	$0.180473\pi$
$854$		0			0
$855$	−29.2826			−1.00144
$856$		0			0
$857$	−26.8241	+	46.4607i	−0.916294	+	1.58707i	−0.111299	+	0.993787i	$0.535501\pi$
$857$	−26.8241	+	46.4607i	−0.916294	+	1.58707i	−0.804995	+	0.593281i	$0.797832\pi$
$858$		0			0
$859$	−3.41188	+	12.7333i	−0.116412	+	0.434455i	−0.999389	−	0.0349617i	$-0.988869\pi$
$859$	−3.41188	+	12.7333i	−0.116412	+	0.434455i	0.882977	+	0.469417i	$0.155536\pi$
$860$		0			0
$861$	4.40130	+	16.3321i	0.149996	+	0.556596i
$862$		0			0
$863$	−6.64111	+	3.83425i	−0.226066	+	0.130519i	−0.608756	−	0.793358i	$-0.708331\pi$
$863$	−6.64111	+	3.83425i	−0.226066	+	0.130519i	0.382690	+	0.923877i	$0.374998\pi$
$864$		0			0
$865$	17.3469	−	30.0457i	0.589812	−	1.02158i
$866$		0			0
$867$	−8.77341	+	8.77341i	−0.297961	+	0.297961i
$868$		0			0
$869$	3.91744	+	3.91744i	0.132890	+	0.132890i
$870$		0			0
$871$	−1.05415	−	0.608615i	−0.0357186	−	0.0206221i
$872$		0			0
$873$	−10.0106	−	17.3388i	−0.338807	−	0.586830i
$874$		0			0
$875$	41.3387	+	41.2203i	1.39750	+	1.39350i
$876$		0			0
$877$	−14.8501	−	3.97908i	−0.501453	−	0.134364i	−0.000778781	−	1.00000i	$-0.500248\pi$
$877$	−14.8501	−	3.97908i	−0.501453	−	0.134364i	−0.500674	+	0.865636i	$0.666915\pi$
$878$		0			0
$879$	6.76038	+	3.90311i	0.228022	+	0.131649i
$880$		0			0
$881$		−	21.5605i		−	0.726392i	−0.931713	−	0.363196i	$-0.881686\pi$
$881$		−	21.5605i		−	0.726392i	0.931713	−	0.363196i	$-0.118314\pi$
$882$		0			0
$883$	3.61325	+	3.61325i	0.121596	+	0.121596i	0.765286	−	0.643690i	$-0.222598\pi$
$883$	3.61325	+	3.61325i	0.121596	+	0.121596i	−0.643690	+	0.765286i	$0.722598\pi$
$884$		0			0
$885$	−5.83228	−	21.7664i	−0.196050	−	0.731668i
$886$		0			0
$887$	31.1537	−	17.9866i	1.04604	−	0.603930i	0.124500	−	0.992220i	$-0.460267\pi$
$887$	31.1537	−	17.9866i	1.04604	−	0.603930i	0.921537	+	0.388290i	$0.126934\pi$
$888$		0			0
$889$	0.0454076	+	31.6450i	0.00152292	+	1.06134i
$890$		0			0
$891$	−16.4193	−	4.39954i	−0.550067	−	0.147390i
$892$		0			0
$893$	1.31626	+	4.91235i	0.0440470	+	0.164386i
$894$		0			0
$895$	−6.89640			−0.230521
$896$		0			0
$897$	−3.08871			−0.103129
$898$		0			0
$899$	−8.04158	−	30.0116i	−0.268202	−	1.00094i
$900$		0			0
$901$	3.34094	+	0.895202i	0.111303	+	0.0298235i
$902$		0			0
$903$	9.79857	+	5.63847i	0.326076	+	0.187637i
$904$		0			0
$905$	−25.6067	+	14.7840i	−0.851194	+	0.491437i
$906$		0			0
$907$	4.95935	+	18.5085i	0.164672	+	0.614566i	0.998082	+	0.0619098i	$0.0197191\pi$
$907$	4.95935	+	18.5085i	0.164672	+	0.614566i	−0.833409	+	0.552656i	$0.813614\pi$
$908$		0			0
$909$	24.7454	+	24.7454i	0.820752	+	0.820752i
$910$		0			0
$911$		−	16.9566i		−	0.561797i	−0.959737	−	0.280899i	$-0.909368\pi$
$911$		−	16.9566i		−	0.561797i	0.959737	−	0.280899i	$-0.0906325\pi$
$912$		0			0
$913$	12.7088	+	7.33743i	0.420600	+	0.242833i
$914$		0			0
$915$	19.6823	+	5.27386i	0.650677	+	0.174348i
$916$		0			0
$917$	−14.1945	−	3.78158i	−0.468743	−	0.124879i
$918$		0			0
$919$	−19.0403	−	32.9788i	−0.628083	−	1.08787i	−0.987936	−	0.154863i	$-0.950507\pi$
$919$	−19.0403	−	32.9788i	−0.628083	−	1.08787i	0.359853	−	0.933009i	$-0.382827\pi$
$920$		0			0
$921$	22.6444	+	13.0737i	0.746158	+	0.430794i
$922$		0			0
$923$	−3.24442	−	3.24442i	−0.106791	−	0.106791i
$924$		0			0
$925$	23.2496	−	23.2496i	0.764443	−	0.764443i
$926$		0			0
$927$	−9.42543	+	16.3253i	−0.309572	+	0.536194i
$928$		0			0
$929$	−3.92408	+	2.26557i	−0.128745	+	0.0743309i	−0.562989	−	0.826464i	$-0.690349\pi$
$929$	−3.92408	+	2.26557i	−0.128745	+	0.0743309i	0.434244	+	0.900795i	$0.357015\pi$
$930$		0			0
$931$	−21.1302	−	5.59686i	−0.692513	−	0.183430i
$932$		0			0
$933$	−5.15311	+	19.2317i	−0.168705	+	0.629617i
$934$		0			0
$935$	10.1770	−	17.6270i	0.332822	−	0.576464i
$936$		0			0
$937$	−37.0969			−1.21190			−0.605952	−	0.795501i	$-0.707208\pi$
$937$	−37.0969			−1.21190			−0.605952	+	0.795501i	$0.707208\pi$
$938$		0			0
$939$	4.72453	−	4.72453i	0.154179	−	0.154179i
$940$		0			0
$941$	−2.17799	+	0.583589i	−0.0710003	+	0.0190245i	−0.294144	−	0.955761i	$-0.595035\pi$
$941$	−2.17799	+	0.583589i	−0.0710003	+	0.0190245i	0.223144	+	0.974785i	$0.428368\pi$
$942$		0			0
$943$	−8.28076	−	14.3427i	−0.269659	−	0.467062i
$944$		0			0
$945$	−22.2483	−	38.4077i	−0.723736	−	1.24940i
$946$		0			0
$947$	−4.22082	+	15.7523i	−0.137158	+	0.511882i	0.862821	+	0.505509i	$0.168695\pi$
$947$	−4.22082	+	15.7523i	−0.137158	+	0.511882i	−0.999980	+	0.00637300i	$0.997971\pi$
$948$		0			0
$949$	−5.45387	+	1.46136i	−0.177040	+	0.0474378i
$950$		0			0
$951$			15.1288i			0.490585i
$952$		0			0
$953$		−	27.9419i		−	0.905126i	−0.891733	−	0.452563i	$-0.850510\pi$
$953$		−	27.9419i		−	0.905126i	0.891733	−	0.452563i	$-0.149490\pi$
$954$		0			0
$955$	103.736	−	27.7960i	3.35682	−	0.899456i
$956$		0			0
$957$	6.92462	−	25.8430i	0.223841	−	0.835387i
$958$		0			0
$959$	−32.8860	−	18.9239i	−1.06194	−	0.611084i
$960$		0			0
$961$	6.91607	+	11.9790i	0.223099	+	0.386419i
$962$		0			0
$963$	21.2988	−	5.70700i	0.686345	−	0.183906i
$964$		0			0
$965$	−16.0901	+	16.0901i	−0.517960	+	0.517960i
$966$		0			0
$967$	47.4478			1.52582			0.762910	−	0.646505i	$-0.223770\pi$
$967$	47.4478			1.52582			0.762910	+	0.646505i	$0.223770\pi$
$968$		0			0
$969$	−1.40979	+	2.44183i	−0.0452890	+	0.0784428i
$970$		0			0
$971$	−8.47546	+	31.6308i	−0.271990	+	1.01508i	0.685841	+	0.727751i	$0.259434\pi$
$971$	−8.47546	+	31.6308i	−0.271990	+	1.01508i	−0.957832	+	0.287330i	$0.907232\pi$
$972$		0			0
$973$	38.7066	+	38.5957i	1.24088	+	1.23732i
$974$		0			0
$975$	−13.8308	+	7.98523i	−0.442941	+	0.255732i
$976$		0			0
$977$	15.9234	−	27.5802i	0.509435	−	0.882368i	−0.490505	−	0.871438i	$-0.663188\pi$
$977$	15.9234	−	27.5802i	0.509435	−	0.882368i	0.999940	−	0.0109296i	$-0.00347908\pi$
$978$		0			0
$979$	27.8711	−	27.8711i	0.890763	−	0.890763i
$980$		0			0
$981$	−1.47742	−	1.47742i	−0.0471704	−	0.0471704i
$982$		0			0
$983$	−37.4979	−	21.6494i	−1.19600	−	0.690509i	−0.236337	−	0.971671i	$-0.575947\pi$
$983$	−37.4979	−	21.6494i	−1.19600	−	0.690509i	−0.959660	+	0.281162i	$0.909280\pi$
$984$		0			0
$985$	−35.6626	−	61.7695i	−1.13631	−	1.96814i
$986$		0			0
$987$	−2.40513	+	2.41204i	−0.0765562	+	0.0767762i
$988$		0			0
$989$	−10.6918	−	2.86486i	−0.339980	−	0.0910973i
$990$		0			0
$991$	16.4220	+	9.48127i	0.521663	+	0.301183i	0.737615	−	0.675222i	$-0.235952\pi$
$991$	16.4220	+	9.48127i	0.521663	+	0.301183i	−0.215952	+	0.976404i	$0.569285\pi$
$992$		0			0
$993$			11.4262i			0.362601i
$994$		0			0
$995$	15.3755	+	15.3755i	0.487436	+	0.487436i
$996$		0			0
$997$	−7.83295	−	29.2330i	−0.248072	−	0.925818i	−0.971814	−	0.235747i	$-0.924246\pi$
$997$	−7.83295	−	29.2330i	−0.248072	−	0.925818i	0.723742	−	0.690070i	$-0.242420\pi$
$998$		0			0
$999$	−11.4267	+	6.59723i	−0.361526	+	0.208727i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.z.a.31.7		56
4.3	odd	2		896.2.z.b.31.8		56
7.5	odd	6	inner	896.2.z.a.159.7		56
8.3	odd	2		112.2.v.a.59.5	yes	56
8.5	even	2		448.2.z.a.143.8		56
16.3	odd	4	inner	896.2.z.a.479.7		56
16.5	even	4		112.2.v.a.3.6	✓	56
16.11	odd	4		448.2.z.a.367.8		56
16.13	even	4		896.2.z.b.479.8		56
28.19	even	6		896.2.z.b.159.8		56
56.3	even	6		784.2.j.a.587.28		56
56.5	odd	6		448.2.z.a.271.8		56
56.11	odd	6		784.2.j.a.587.27		56
56.19	even	6		112.2.v.a.75.6	yes	56
56.27	even	2		784.2.w.f.619.5		56
56.51	odd	6		784.2.w.f.411.6		56
112.5	odd	12		112.2.v.a.19.5	yes	56
112.19	even	12	inner	896.2.z.a.607.7		56
112.37	even	12		784.2.w.f.19.5		56
112.53	even	12		784.2.j.a.195.28		56
112.61	odd	12		896.2.z.b.607.8		56
112.69	odd	4		784.2.w.f.227.6		56
112.75	even	12		448.2.z.a.47.8		56
112.101	odd	12		784.2.j.a.195.27		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.v.a.3.6	✓	56	16.5	even	4
112.2.v.a.19.5	yes	56	112.5	odd	12
112.2.v.a.59.5	yes	56	8.3	odd	2
112.2.v.a.75.6	yes	56	56.19	even	6
448.2.z.a.47.8		56	112.75	even	12
448.2.z.a.143.8		56	8.5	even	2
448.2.z.a.271.8		56	56.5	odd	6
448.2.z.a.367.8		56	16.11	odd	4
784.2.j.a.195.27		56	112.101	odd	12
784.2.j.a.195.28		56	112.53	even	12
784.2.j.a.587.27		56	56.11	odd	6
784.2.j.a.587.28		56	56.3	even	6
784.2.w.f.19.5		56	112.37	even	12
784.2.w.f.227.6		56	112.69	odd	4
784.2.w.f.411.6		56	56.51	odd	6
784.2.w.f.619.5		56	56.27	even	2
896.2.z.a.31.7		56	1.1	even	1	trivial
896.2.z.a.159.7		56	7.5	odd	6	inner
896.2.z.a.479.7		56	16.3	odd	4	inner
896.2.z.a.607.7		56	112.19	even	12	inner
896.2.z.b.31.8		56	4.3	odd	2
896.2.z.b.159.8		56	28.19	even	6
896.2.z.b.479.8		56	16.13	even	4
896.2.z.b.607.8		56	112.61	odd	12

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)

\(f(q)\)	\(=\)	\(q+(-0.204601 - 0.763582i) q^{3} +(3.81370 + 1.02188i) q^{5} +(2.64575 - 0.00379639i) q^{7} +(2.05688 - 1.18754i) q^{9} +(-1.16815 - 4.35958i) q^{11} +(-1.34913 - 1.34913i) q^{13} -3.12115i q^{15} +(0.989178 + 0.571102i) q^{17} +(-3.01629 - 0.808212i) q^{19} +(-0.544222 - 2.01947i) q^{21} +(1.02392 + 1.77348i) q^{23} +(9.16994 + 5.29427i) q^{25} +(-3.00457 - 3.00457i) q^{27} +(-5.30239 + 5.30239i) q^{29} +(-2.07171 + 3.58830i) q^{31} +(-3.08989 + 1.78395i) q^{33} +(10.0940 + 2.68915i) q^{35} +(0.803695 - 2.99943i) q^{37} +(-0.754139 + 1.30621i) q^{39} -8.08732 q^{41} +(-3.82205 + 3.82205i) q^{43} +(9.05785 - 2.42704i) q^{45} +(-0.814305 - 1.41042i) q^{47} +(6.99997 - 0.0200886i) q^{49} +(0.233696 - 0.872167i) q^{51} +(2.92499 - 0.783749i) q^{53} -17.8198i q^{55} +2.46854i q^{57} +(6.97383 - 1.86863i) q^{59} +(-1.68972 + 6.30611i) q^{61} +(5.43748 - 3.14974i) q^{63} +(-3.76654 - 6.52383i) q^{65} +(0.616236 - 0.165120i) q^{67} +(1.14470 - 1.14470i) q^{69} +2.40482 q^{71} +(1.47966 - 2.56284i) q^{73} +(2.16643 - 8.08521i) q^{75} +(-3.10717 - 11.5299i) q^{77} +(-1.06303 + 0.613742i) q^{79} +(1.88313 - 3.26167i) q^{81} +(-2.29910 + 2.29910i) q^{83} +(3.18883 + 3.18883i) q^{85} +(5.13369 + 2.96394i) q^{87} +(4.36654 + 7.56307i) q^{89} +(-3.57459 - 3.56434i) q^{91} +(3.16383 + 0.847747i) q^{93} +(-10.6773 - 6.16455i) q^{95} -8.42967i q^{97} +(-7.57992 - 7.57992i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 6 q^{3} + 6 q^{5} + 8 q^{7} + 2 q^{11} - 12 q^{17} - 6 q^{19} + 10 q^{21} + 12 q^{23} + 24 q^{29} - 12 q^{33} - 2 q^{35} - 6 q^{37} + 4 q^{39} - 12 q^{45} - 8 q^{49} - 34 q^{51} - 6 q^{53} + 42 q^{59}+ \cdots - 16 q^{99}+O(q^{100}) \) 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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Groups

Database

Properties

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