LMFDB - Embedded newform 896.2.z.a.607.7

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)

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")

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);

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			607.7
Character	$\chi$	$=$	896.607
Dual form			896.2.z.a.31.7

$q$-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 $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$645$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.204601	+	0.763582i	−0.118127	+	0.440854i	−0.999502	−	0.0315627i	$-0.989952\pi$
$3$	−0.204601	+	0.763582i	−0.118127	+	0.440854i	0.881375	+	0.472417i	$0.156618\pi$
$4$		0			0
$5$	3.81370	−	1.02188i	1.70554	−	0.456998i	0.731214	−	0.682148i	$-0.238954\pi$
$5$	3.81370	−	1.02188i	1.70554	−	0.456998i	0.974324	+	0.225150i	$0.0722873\pi$
$6$		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	0.531751	+	0.846901i	$0.321534\pi$
$11$	−1.16815	+	4.35958i	−0.352209	+	1.31446i	−0.883960	+	0.467562i	$0.845132\pi$
$12$		0			0
$13$	−1.34913	+	1.34913i	−0.374182	+	0.374182i	−0.868998	−	0.494816i	$-0.835236\pi$
$13$	−1.34913	+	1.34913i	−0.374182	+	0.374182i	0.494816	+	0.868998i	$0.335236\pi$
$14$		0			0
$15$			3.12115i			0.805877i
$16$		0			0
$17$	0.989178	−	0.571102i	0.239911	−	0.138513i	−0.375225	−	0.926934i	$-0.622435\pi$
$17$	0.989178	−	0.571102i	0.239911	−	0.138513i	0.615136	+	0.788421i	$0.289101\pi$
$18$		0			0
$19$	−3.01629	+	0.808212i	−0.691984	+	0.185416i	−0.587637	−	0.809125i	$-0.699942\pi$
$19$	−3.01629	+	0.808212i	−0.691984	+	0.185416i	−0.104346	+	0.994541i	$0.533275\pi$
$20$		0			0
$21$	−0.544222	+	2.01947i	−0.118759	+	0.440684i
$22$		0			0
$23$	1.02392	−	1.77348i	0.213502	−	0.369796i	−0.739306	−	0.673369i	$-0.764846\pi$
$23$	1.02392	−	1.77348i	0.213502	−	0.369796i	0.952808	+	0.303573i	$0.0981798\pi$
$24$		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	0.0152539	−	0.999884i	$-0.495144\pi$
$29$	−5.30239	−	5.30239i	−0.984630	−	0.984630i	−0.999884	+	0.0152539i	$0.995144\pi$
$30$		0			0
$31$	−2.07171	−	3.58830i	−0.372089	−	0.644478i	0.617797	−	0.786337i	$-0.288025\pi$
$31$	−2.07171	−	3.58830i	−0.372089	−	0.644478i	−0.989887	+	0.141860i	$0.954692\pi$
$32$		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	0.999993	−	0.00369416i	$-0.00117589\pi$
$37$	0.803695	+	2.99943i	0.132127	+	0.493103i	−0.867867	+	0.496797i	$0.834509\pi$
$38$		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	0.352830	−	0.935688i	$-0.385220\pi$
$43$	−3.82205	−	3.82205i	−0.582858	−	0.582858i	−0.935688	+	0.352830i	$0.885220\pi$
$44$		0			0
$45$	9.05785	+	2.42704i	1.35026	+	0.361802i
$46$		0			0
$47$	−0.814305	+	1.41042i	−0.118779	+	0.205731i	−0.919284	−	0.393595i	$-0.871231\pi$
$47$	−0.814305	+	1.41042i	−0.118779	+	0.205731i	0.800505	+	0.599326i	$0.204565\pi$
$48$		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	0.454049	−	0.890977i	$-0.349979\pi$
$53$	2.92499	+	0.783749i	0.401779	+	0.107656i	−0.0522704	+	0.998633i	$0.516646\pi$
$54$		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	0.682412	−	0.730967i	$-0.260931\pi$
$59$	6.97383	+	1.86863i	0.907915	+	0.243275i	0.225503	+	0.974243i	$0.427597\pi$
$60$		0			0
$61$	−1.68972	−	6.30611i	−0.216346	−	0.807414i	−0.985688	−	0.168578i	$-0.946083\pi$
$61$	−1.68972	−	6.30611i	−0.216346	−	0.807414i	0.769342	−	0.638837i	$-0.220584\pi$
$62$		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	0.296265	−	0.955106i	$-0.404259\pi$
$67$	0.616236	+	0.165120i	0.0752852	+	0.0201726i	−0.220980	+	0.975278i	$0.570926\pi$
$68$		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	0.939530	−	0.342466i	$-0.111262\pi$
$73$	1.47966	+	2.56284i	0.173181	+	0.299958i	−0.766349	+	0.642424i	$0.777929\pi$
$74$		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	0.439006	−	0.898484i	$-0.355331\pi$
$79$	−1.06303	−	0.613742i	−0.119601	−	0.0690514i	−0.558607	+	0.829433i	$0.688664\pi$
$80$		0			0
$81$	1.88313	+	3.26167i	0.209236	+	0.362408i
$82$		0			0
$83$	−2.29910	−	2.29910i	−0.252359	−	0.252359i	0.569578	−	0.821937i	$-0.307107\pi$
$83$	−2.29910	−	2.29910i	−0.252359	−	0.252359i	−0.821937	+	0.569578i	$0.807107\pi$
$84$		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	−0.536249	−	0.844060i	$-0.680159\pi$
$89$	4.36654	−	7.56307i	0.462852	−	0.801684i	0.999102	+	0.0423758i	$0.0134927\pi$
$90$		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	$0.140765\pi$
$97$			8.42967i			0.855903i	−0.903802	+	0.427952i	$0.859235\pi$
$98$		0			0
$99$	−7.57992	+	7.57992i	−0.761810	+	0.761810i
$100$		0			0
$101$	3.81352	−	14.2323i	0.379460	−	1.41616i	−0.467258	−	0.884121i	$-0.654758\pi$
$101$	3.81352	−	14.2323i	0.379460	−	1.41616i	0.846718	−	0.532042i	$-0.178575\pi$
$102$		0			0
$103$	−6.87358	−	3.96846i	−0.677274	−	0.391024i	0.121553	−	0.992585i	$-0.461213\pi$
$103$	−6.87358	−	3.96846i	−0.677274	−	0.391024i	−0.798827	+	0.601561i	$0.794546\pi$
$104$		0			0
$105$	−0.0118491	+	8.25777i	−0.00115635	+	0.805876i
$106$		0			0
$107$	8.96762	−	2.40287i	0.866932	−	0.232294i	0.202172	−	0.979350i	$-0.435200\pi$
$107$	8.96762	−	2.40287i	0.866932	−	0.232294i	0.664761	+	0.747056i	$0.268533\pi$
$108$		0			0
$109$	−0.227686	+	0.849736i	−0.0218084	+	0.0813900i	−0.975972	−	0.217894i	$-0.930081\pi$
$109$	−0.227686	+	0.849736i	−0.0218084	+	0.0813900i	0.954164	+	0.299284i	$0.0967479\pi$
$110$		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	$-0.821940\pi$
$127$		−	11.9607i		−	1.06134i	0.847578	−	0.530671i	$-0.178060\pi$
$128$		0			0
$129$	3.70045	−	2.13645i	0.325806	−	0.188104i
$130$		0			0
$131$	−5.36296	+	1.43700i	−0.468564	+	0.125551i	−0.485372	−	0.874307i	$-0.661316\pi$
$131$	−5.36296	+	1.43700i	−0.468564	+	0.125551i	0.0168089	+	0.999859i	$0.494649\pi$
$132$		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	−0.925727	−	0.378192i	$-0.876546\pi$
$137$	−12.4195	+	7.17038i	−1.06107	+	0.612607i	−0.135339	+	0.990799i	$0.543212\pi$
$138$		0			0
$139$	14.6088	−	14.6088i	1.23910	−	1.23910i	0.278731	−	0.960369i	$-0.410086\pi$
$139$	14.6088	−	14.6088i	1.23910	−	1.23910i	0.960369	−	0.278731i	$-0.0899137\pi$
$140$		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	0.970835	+	0.239750i	$0.0770655\pi$
$149$	3.05093	+	11.3862i	0.249942	+	0.932797i	−0.720892	+	0.693047i	$0.756268\pi$
$150$		0			0
$151$	−6.85381	−	11.8712i	−0.557755	−	0.966061i	−0.997683	−	0.0680276i	$-0.978329\pi$
$151$	−6.85381	−	11.8712i	−0.557755	−	0.966061i	0.439928	−	0.898033i	$-0.355004\pi$
$152$		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	0.177599	−	0.984103i	$-0.443167\pi$
$157$	−2.01291	−	0.539359i	−0.160648	−	0.0430455i	−0.338247	+	0.941058i	$0.609834\pi$
$158$		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	0.981795	−	0.189942i	$-0.0608300\pi$
$163$	0.466826	+	1.74222i	0.0365647	+	0.136461i	−0.945231	+	0.326403i	$0.894163\pi$
$164$		0			0
$165$	−13.6069	−	3.64596i	−1.05930	−	0.283837i
$166$		0			0
$167$		−	21.6002i		−	1.67147i	−0.549132	−	0.835735i	$-0.685042\pi$
$167$		−	21.6002i		−	1.67147i	0.549132	−	0.835735i	$-0.314958\pi$
$168$		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	0.996898	+	0.0787035i	$0.0250780\pi$
$173$	2.27429	+	8.48775i	0.172911	+	0.645312i	−0.823987	+	0.566608i	$0.808255\pi$
$174$		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	0.195214	−	0.980761i	$-0.437460\pi$
$179$	−1.68719	−	0.452081i	−0.126106	−	0.0337901i	−0.321320	+	0.946971i	$0.604127\pi$
$180$		0			0
$181$	−5.29547	−	5.29547i	−0.393609	−	0.393609i	0.482362	−	0.875972i	$-0.339779\pi$
$181$	−5.29547	−	5.29547i	−0.393609	−	0.393609i	−0.875972	+	0.482362i	$0.839779\pi$
$182$		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	0.941076	+	0.338195i	$0.109816\pi$
$191$	23.5567	+	13.6004i	1.70450	+	0.984093i	0.763423	+	0.645899i	$0.223517\pi$
$192$		0			0
$193$	−2.88165	−	4.99117i	−0.207426	−	0.359272i	0.743477	−	0.668762i	$-0.233175\pi$
$193$	−2.88165	−	4.99117i	−0.207426	−	0.359272i	−0.950903	+	0.309489i	$0.899842\pi$
$194$		0			0
$195$	−4.21084	−	4.21084i	−0.301545	−	0.301545i
$196$		0			0
$197$	−12.7740	+	12.7740i	−0.910107	+	0.910107i	−0.996280	−	0.0861731i	$-0.972536\pi$
$197$	−12.7740	+	12.7740i	−0.910107	+	0.910107i	0.0861731	+	0.996280i	$0.472536\pi$
$198$		0			0
$199$	4.76949	−	2.75367i	0.338100	−	0.195202i	−0.321331	−	0.946967i	$-0.604130\pi$
$199$	4.76949	−	2.75367i	0.338100	−	0.195202i	0.659432	+	0.751764i	$0.270797\pi$
$200$		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	0.433192	−	0.901302i	$-0.357387\pi$
$211$	19.3846	−	19.3846i	1.33449	−	1.33449i	0.901302	−	0.433192i	$-0.142613\pi$
$212$		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	−0.851702	−	0.524026i	$-0.824429\pi$
$227$	2.22844	−	8.31664i	0.147907	−	0.551995i	0.999609	−	0.0279688i	$-0.00890392\pi$
$228$		0			0
$229$	−24.4498	+	6.55130i	−1.61569	+	0.432922i	−0.949731	−	0.313067i	$-0.898643\pi$
$229$	−24.4498	+	6.55130i	−1.61569	+	0.432922i	−0.665957	+	0.745990i	$0.731977\pi$
$230$		0			0
$231$	−8.16831	−	4.73162i	−0.537435	−	0.311317i
$232$		0			0
$233$	−13.4837	−	7.78481i	−0.883346	−	0.510000i	−0.0115857	−	0.999933i	$-0.503688\pi$
$233$	−13.4837	−	7.78481i	−0.883346	−	0.510000i	−0.871760	+	0.489933i	$0.837021\pi$
$234$		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	$0.122672\pi$
$239$			11.6230i			0.751832i	−0.926654	+	0.375916i	$0.877328\pi$
$240$		0			0
$241$	2.43625	−	1.40657i	0.156933	−	0.0906051i	−0.419477	−	0.907766i	$-0.637787\pi$
$241$	2.43625	−	1.40657i	0.156933	−	0.0906051i	0.576410	+	0.817161i	$0.304453\pi$
$242$		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	−0.767262	−	0.641334i	$-0.778381\pi$
$251$	−1.99507	+	1.99507i	−0.125928	+	0.125928i	0.641334	+	0.767262i	$0.278381\pi$
$252$		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	0.846298	−	0.532709i	$-0.178826\pi$
$257$	12.9550	+	7.47955i	0.808108	+	0.466561i	−0.0381904	+	0.999270i	$0.512159\pi$
$258$		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	0.998742	−	0.0501505i	$-0.0159701\pi$
$263$	7.39409	+	12.8069i	0.455939	+	0.789710i	−0.542802	+	0.839860i	$0.682637\pi$
$264$		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	0.882356	−	0.470583i	$-0.155956\pi$
$269$	23.1455	+	6.20182i	1.41121	+	0.378132i	0.528851	+	0.848715i	$0.322623\pi$
$270$		0			0
$271$	−7.37718	+	12.7776i	−0.448131	+	0.776186i	−0.998264	−	0.0588906i	$-0.981244\pi$
$271$	−7.37718	+	12.7776i	−0.448131	+	0.776186i	0.550133	+	0.835077i	$0.314577\pi$
$272$		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	0.749496	−	0.662009i	$-0.230296\pi$
$277$	17.7680	+	4.76091i	1.06757	+	0.286055i	0.318077	+	0.948065i	$0.396963\pi$
$278$		0			0
$279$		−	9.84094i		−	0.589162i
$280$		0			0
$281$			31.9694i			1.90713i	0.301185	+	0.953566i	$0.402618\pi$
$281$			31.9694i			1.90713i	−0.301185	+	0.953566i	$0.597382\pi$
$282$		0			0
$283$	−3.17648	−	0.851136i	−0.188822	−	0.0505948i	0.163169	−	0.986598i	$-0.447829\pi$
$283$	−3.17648	−	0.851136i	−0.188822	−	0.0505948i	−0.351991	+	0.936003i	$0.614495\pi$
$284$		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	0.473090	−	0.881014i	$-0.343139\pi$
$293$	−6.98254	−	6.98254i	−0.407925	−	0.407925i	−0.881014	+	0.473090i	$0.843139\pi$
$294$		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	−0.900967	−	0.433888i	$-0.857141\pi$
$307$	−23.3885	−	23.3885i	−1.33485	−	1.33485i	−0.433888	−	0.900967i	$-0.642859\pi$
$308$		0			0
$309$	4.43659	−	4.43659i	0.252389	−	0.252389i
$310$		0			0
$311$	−21.8118	+	12.5931i	−1.23684	+	0.714087i	−0.968446	−	0.249223i	$-0.919825\pi$
$311$	−21.8118	+	12.5931i	−1.23684	+	0.714087i	−0.268390	+	0.963310i	$0.586491\pi$
$312$		0			0
$313$	4.22602	−	7.31969i	0.238869	−	0.413733i	−0.721521	−	0.692393i	$-0.756557\pi$
$313$	4.22602	−	7.31969i	0.238869	−	0.413733i	0.960390	+	0.278659i	$0.0898900\pi$
$314$		0			0
$315$	23.9556	+	6.45573i	1.34974	+	0.363739i
$316$		0			0
$317$	−18.4857	+	4.95323i	−1.03826	+	0.278201i	−0.737393	−	0.675464i	$-0.763943\pi$
$317$	−18.4857	+	4.95323i	−1.03826	+	0.278201i	−0.300868	+	0.953666i	$0.597276\pi$
$318$		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	−0.621222	−	0.783635i	$-0.713364\pi$
$331$	−13.9616	+	3.74100i	−0.767399	+	0.205624i	−0.146177	+	0.989258i	$0.546697\pi$
$332$		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	−0.999977	−	0.00683892i	$-0.997823\pi$
$347$	−2.43191	+	9.07603i	−0.130552	+	0.487227i	0.869425	+	0.494066i	$0.164490\pi$
$348$		0			0
$349$	8.35069	−	8.35069i	0.447002	−	0.447002i	−0.447355	−	0.894357i	$-0.647634\pi$
$349$	8.35069	−	8.35069i	0.447002	−	0.447002i	0.894357	+	0.447355i	$0.147634\pi$
$350$		0			0
$351$		−	8.10712i		−	0.432726i
$352$		0			0
$353$	16.9374	−	9.77882i	0.901488	−	0.520474i	0.0238051	−	0.999717i	$-0.492422\pi$
$353$	16.9374	−	9.77882i	0.901488	−	0.520474i	0.877683	+	0.479242i	$0.159089\pi$
$354$		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	−0.999186	−	0.0403489i	$-0.987153\pi$
$359$	−8.80385	+	15.2487i	−0.464650	+	0.804797i	0.534536	+	0.845146i	$0.320486\pi$
$360$		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	−0.871631	−	0.490163i	$-0.836937\pi$
$367$	−16.4811	−	28.5462i	−0.860309	−	1.49010i	0.0113220	−	0.999936i	$-0.496396\pi$
$368$		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	−0.995644	−	0.0932356i	$-0.970279\pi$
$373$	−3.47655	−	12.9747i	−0.180009	−	0.671802i	0.815635	−	0.578566i	$-0.196388\pi$
$374$		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	0.722781	−	0.691077i	$-0.242863\pi$
$379$	0.617225	+	0.617225i	0.0317047	+	0.0317047i	−0.691077	+	0.722781i	$0.742863\pi$
$380$		0			0
$381$	9.13298	+	2.44718i	0.467897	+	0.125373i
$382$		0			0
$383$	−0.214398	+	0.371348i	−0.0109552	+	0.0189750i	−0.871451	−	0.490483i	$-0.836821\pi$
$383$	−0.214398	+	0.371348i	−0.0109552	+	0.0189750i	0.860496	+	0.509457i	$0.170154\pi$
$384$		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	−0.00674269	−	0.999977i	$-0.502146\pi$
$389$	−10.1095	−	2.70883i	−0.512571	−	0.137343i	−0.505828	+	0.862634i	$0.668813\pi$
$390$		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	−0.870639	−	0.491922i	$-0.836294\pi$
$397$	−7.22485	−	26.9635i	−0.362605	−	1.35326i	0.508034	−	0.861337i	$-0.330372\pi$
$398$		0			0
$399$	0.00937155	−	6.53114i	0.000469165	−	0.326966i
$400$		0			0
$401$	−13.1880	+	22.8422i	−0.658575	+	1.14069i	0.322410	+	0.946600i	$0.395507\pi$
$401$	−13.1880	+	22.8422i	−0.658575	+	1.14069i	−0.980985	+	0.194085i	$0.937826\pi$
$402$		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	0.556962	−	0.830538i	$-0.311967\pi$
$409$	−8.91434	−	15.4401i	−0.440786	−	0.763463i	−0.997748	+	0.0670744i	$0.978634\pi$
$410$		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	0.999167	−	0.0408093i	$-0.0129936\pi$
$419$	19.6171	+	19.6171i	0.958358	+	0.958358i	−0.0408093	+	0.999167i	$0.512994\pi$
$420$		0			0
$421$	5.25405	−	5.25405i	0.256067	−	0.256067i	−0.567385	−	0.823452i	$-0.692045\pi$
$421$	5.25405	−	5.25405i	0.256067	−	0.256067i	0.823452	+	0.567385i	$0.192045\pi$
$422$		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	−0.941431	−	0.337205i	$-0.890518\pi$
$431$	−23.2543	+	13.4259i	−1.12012	+	0.646701i	−0.178687	+	0.983906i	$0.557185\pi$
$432$		0			0
$433$		−	18.6517i		−	0.896344i	−0.893947	−	0.448172i	$-0.852075\pi$
$433$		−	18.6517i		−	0.896344i	0.893947	−	0.448172i	$-0.147925\pi$
$434$		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	0.856389	−	0.516332i	$-0.172703\pi$
$439$	17.5460	+	10.1302i	0.837427	+	0.483488i	−0.0189621	+	0.999820i	$0.506036\pi$
$440$		0			0
$441$	14.3742	+	8.35407i	0.684488	+	0.397813i
$442$		0			0
$443$	34.1538	−	9.15149i	1.62270	−	0.434800i	0.670904	−	0.741544i	$-0.265906\pi$
$443$	34.1538	−	9.15149i	1.62270	−	0.434800i	0.951792	+	0.306744i	$0.0992394\pi$
$444$		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	0.388133	−	0.921604i	$-0.373120\pi$
$457$	−4.61613	−	2.66512i	−0.215933	−	0.124669i	−0.604066	+	0.796934i	$0.706454\pi$
$458$		0			0
$459$	−1.25614	+	4.68797i	−0.0586314	+	0.218816i
$460$		0			0
$461$	2.32075	−	2.32075i	0.108088	−	0.108088i	−0.650995	−	0.759082i	$-0.725648\pi$
$461$	2.32075	−	2.32075i	0.108088	−	0.108088i	0.759082	+	0.650995i	$0.225648\pi$
$462$		0			0
$463$			15.2932i			0.710736i	0.934727	+	0.355368i	$0.115644\pi$
$463$			15.2932i			0.710736i	−0.934727	+	0.355368i	$0.884356\pi$
$464$		0			0
$465$	11.1996	−	6.46610i	0.519370	−	0.299858i
$466$		0			0
$467$	−29.0012	+	7.77086i	−1.34202	+	0.359592i	−0.857182	−	0.515014i	$-0.827787\pi$
$467$	−29.0012	+	7.77086i	−1.34202	+	0.359592i	−0.484835	+	0.874606i	$0.661120\pi$
$468$		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	0.927456	+	0.373933i	$0.121991\pi$
$479$	17.2367	+	29.8548i	0.787564	+	1.36410i	−0.139892	+	0.990167i	$0.544676\pi$
$480$		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	0.646335	−	0.763053i	$-0.276301\pi$
$487$	−7.45142	−	12.9062i	−0.337656	−	0.584837i	−0.983991	+	0.178216i	$0.942967\pi$
$488$		0			0
$489$	−1.42584			−0.0644787
$490$		0			0
$491$	30.5248	+	30.5248i	1.37756	+	1.37756i	0.848719	+	0.528844i	$0.177374\pi$
$491$	30.5248	+	30.5248i	1.37756	+	1.37756i	0.528844	+	0.848719i	$0.322626\pi$
$492$		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	0.999934	−	0.0114806i	$-0.00365448\pi$
$499$	2.86434	+	10.6899i	0.128225	+	0.478544i	−0.871709	+	0.490025i	$0.836988\pi$
$500$		0			0
$501$	16.4935	+	4.41942i	0.736875	+	0.197445i
$502$		0			0
$503$			25.6811i			1.14507i	0.819882	+	0.572533i	$0.194039\pi$
$503$			25.6811i			1.14507i	−0.819882	+	0.572533i	$0.805961\pi$
$504$		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	−0.996347	−	0.0854009i	$-0.972783\pi$
$509$	−3.97493	−	14.8346i	−0.176186	−	0.657534i	0.820161	−	0.572133i	$-0.193884\pi$
$510$		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	0.982241	+	0.187626i	$0.0600792\pi$
$521$	14.9189	+	25.8403i	0.653609	+	1.13208i	−0.328632	+	0.944458i	$0.606588\pi$
$522$		0			0
$523$	9.32633	+	34.8063i	0.407812	+	1.52198i	0.798810	+	0.601583i	$0.205463\pi$
$523$	9.32633	+	34.8063i	0.407812	+	1.52198i	−0.390998	+	0.920392i	$0.627870\pi$
$524$		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	0.0332740	−	0.999446i	$-0.489407\pi$
$541$	13.0674	−	3.50141i	0.561813	−	0.150537i	0.528539	+	0.848909i	$0.322740\pi$
$542$		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	−0.990273	−	0.139139i	$-0.955567\pi$
$547$	−19.9064	+	19.9064i	−0.851134	+	0.851134i	0.139139	+	0.990273i	$0.455567\pi$
$548$		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	0.853265	+	0.521477i	$0.174619\pi$
$557$	−3.45569	+	12.8968i	−0.146422	+	0.546456i	−0.999688	+	0.0249794i	$0.992048\pi$
$558$		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	−0.679857	−	0.733345i	$-0.737958\pi$
$563$	6.53907	−	24.4041i	0.275589	−	1.02851i	0.955446	−	0.295167i	$-0.0953751\pi$
$564$		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	0.710263	−	0.703936i	$-0.248576\pi$
$569$	10.8718	+	6.27682i	0.455768	+	0.263138i	−0.254495	+	0.967074i	$0.581909\pi$
$570$		0			0
$571$	10.2203	−	38.1427i	0.427706	−	1.59622i	−0.330235	−	0.943899i	$-0.607128\pi$
$571$	10.2203	−	38.1427i	0.427706	−	1.59622i	0.757942	−	0.652322i	$-0.226205\pi$
$572$		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	−0.857503	−	0.514479i	$-0.827985\pi$
$577$	−20.1944	+	11.6592i	−0.840702	+	0.485380i	0.0168006	+	0.999859i	$0.494652\pi$
$578$		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	−0.000853494		1.00000i	$0.500272\pi$
$587$	−24.2488	+	24.2488i	−1.00085	+	1.00085i	−1.00000		0.000853494i	$0.999728\pi$
$588$		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	0.990142	−	0.140068i	$-0.0447322\pi$
$593$	33.2134	+	19.1758i	1.36391	+	0.787454i	0.373768	+	0.927522i	$0.378066\pi$
$594$		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	0.874061	−	0.485816i	$-0.161478\pi$
$599$	0.398968	+	0.691033i	0.0163014	+	0.0282348i	−0.857760	+	0.514051i	$0.828144\pi$
$600$		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	−0.791830	−	0.610742i	$-0.790871\pi$
$607$	3.27685	−	5.67568i	0.133003	−	0.230369i	0.924833	+	0.380373i	$0.124205\pi$
$608$		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	0.606168	−	0.795337i	$-0.292706\pi$
$613$	18.1595	+	4.86583i	0.733457	+	0.196529i	0.127289	+	0.991866i	$0.459373\pi$
$614$		0			0
$615$		−	25.2417i		−	1.01785i
$616$		0			0
$617$		−	22.2202i		−	0.894552i	−0.894396	−	0.447276i	$-0.852394\pi$
$617$		−	22.2202i		−	0.894552i	0.894396	−	0.447276i	$-0.147606\pi$
$618$		0			0
$619$	−8.23929	−	2.20771i	−0.331165	−	0.0887354i	0.0894053	−	0.995995i	$-0.471503\pi$
$619$	−8.23929	−	2.20771i	−0.331165	−	0.0887354i	−0.420570	+	0.907260i	$0.638170\pi$
$620$		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	−0.996430	−	0.0844254i	$-0.973095\pi$
$641$	−14.4649	−	25.0540i	−0.571329	−	0.989572i	0.425100	−	0.905146i	$-0.360239\pi$
$642$		0			0
$643$	27.4126	+	27.4126i	1.08105	+	1.08105i	0.996412	+	0.0846366i	$0.0269729\pi$
$643$	27.4126	+	27.4126i	1.08105	+	1.08105i	0.0846366	+	0.996412i	$0.473027\pi$
$644$		0			0
$645$	11.9292	−	11.9292i	0.469712	−	0.469712i
$646$		0			0
$647$	25.8281	−	14.9119i	1.01541	−	0.586247i	0.102638	−	0.994719i	$-0.467272\pi$
$647$	25.8281	−	14.9119i	1.01541	−	0.586247i	0.912771	+	0.408472i	$0.133938\pi$
$648$		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	−0.00375078	−	0.999993i	$-0.501194\pi$
$653$	12.5980	−	3.37562i	0.492997	−	0.132098i	0.496748	+	0.867895i	$0.334527\pi$
$654$		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	−0.937733	−	0.347358i	$-0.887079\pi$
$659$	−15.1555	+	15.1555i	−0.590375	+	0.590375i	0.347358	+	0.937733i	$0.387079\pi$
$660$		0			0
$661$	−0.571930	+	2.13447i	−0.0222455	+	0.0830213i	−0.976156	−	0.217069i	$-0.930350\pi$
$661$	−0.571930	+	2.13447i	−0.0222455	+	0.0830213i	0.953911	+	0.300091i	$0.0970169\pi$
$662$		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	−0.762763	−	0.646678i	$-0.776158\pi$
$677$	−28.6211	+	7.66899i	−1.10000	+	0.294743i	−0.337234	+	0.941421i	$0.609491\pi$
$678$		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	−0.982036	−	0.188693i	$-0.939575\pi$
$683$	−0.972755	+	3.63037i	−0.0372214	+	0.138912i	0.944815	+	0.327605i	$0.106242\pi$
$684$		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	0.0146470	−	0.999893i	$-0.495338\pi$
$691$	13.8605	−	3.71391i	0.527278	−	0.141284i	0.512631	+	0.858609i	$0.328671\pi$
$692$		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	0.418863	−	0.908050i	$-0.362429\pi$
$701$	−12.9519	−	12.9519i	−0.489187	−	0.489187i	−0.908050	+	0.418863i	$0.862429\pi$
$702$		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	0.968991	−	0.247094i	$-0.0794757\pi$
$709$	0.167036	+	0.623389i	0.00627319	+	0.0234119i	−0.962718	+	0.270506i	$0.912809\pi$
$710$		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	−0.418344	−	0.908289i	$-0.637389\pi$
$719$	15.4833	−	26.8178i	0.577429	−	1.00014i	0.995773	−	0.0918476i	$-0.0292772\pi$
$720$		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	$0.100685\pi$
$727$			16.7744i			0.622128i	−0.950389	+	0.311064i	$0.899315\pi$
$728$		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	−0.944282	−	0.329139i	$-0.893242\pi$
$733$	−7.88067	−	29.4110i	−0.291079	−	1.08632i	0.653203	−	0.757183i	$-0.273425\pi$
$734$		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	0.686977	−	0.726679i	$-0.258937\pi$
$739$	24.9711	+	6.69098i	0.918577	+	0.246132i	0.231600	+	0.972811i	$0.425604\pi$
$740$		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	0.810377	−	0.585909i	$-0.199262\pi$
$751$	19.4065	+	11.2044i	0.708154	+	0.408853i	−0.102223	+	0.994761i	$0.532596\pi$
$752$		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	−0.867106	−	0.498124i	$-0.834022\pi$
$757$	−10.1520	+	10.1520i	−0.368982	+	0.368982i	0.498124	+	0.867106i	$0.334022\pi$
$758$		0			0
$759$	−6.32760	+	3.65324i	−0.229677	+	0.132604i
$760$		0			0
$761$	10.0149	−	17.3464i	0.363041	−	0.628805i	−0.625419	−	0.780289i	$-0.715072\pi$
$761$	10.0149	−	17.3464i	0.363041	−	0.628805i	0.988460	+	0.151484i	$0.0484053\pi$
$762$		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	$-0.632346\pi$
$769$		−	50.7365i		−	1.82960i	0.403902	−	0.914802i	$-0.367654\pi$
$770$		0			0
$771$	−8.36185	+	8.36185i	−0.301144	+	0.301144i
$772$		0			0
$773$	7.73070	−	28.8514i	0.278054	−	1.03771i	−0.675713	−	0.737165i	$-0.736164\pi$
$773$	7.73070	−	28.8514i	0.278054	−	1.03771i	0.953767	−	0.300547i	$-0.0971692\pi$
$774$		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	0.528438	+	0.848972i	$0.322778\pi$
$787$	−9.92221	+	37.0302i	−0.353688	+	1.31998i	−0.882127	+	0.471012i	$0.843889\pi$
$788$		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	−0.957042	−	0.289949i	$-0.906361\pi$
$797$	−18.8328	+	18.8328i	−0.667092	+	0.667092i	0.289949	+	0.957042i	$0.406361\pi$
$798$		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	−0.166663	−	0.986014i	$-0.553299\pi$
$809$	17.1772	−	9.91725i	0.603918	−	0.348672i	0.770581	+	0.637342i	$0.219966\pi$
$810$		0			0
$811$	3.89894	−	3.89894i	0.136910	−	0.136910i	−0.635330	−	0.772240i	$-0.719136\pi$
$811$	3.89894	−	3.89894i	0.136910	−	0.136910i	0.772240	+	0.635330i	$0.219136\pi$
$812$		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	0.996585	+	0.0825677i	$0.0263121\pi$
$821$	5.00859	+	18.6923i	0.174801	+	0.652366i	−0.821784	+	0.569798i	$0.807021\pi$
$822$		0			0
$823$	−20.0886	−	34.7944i	−0.700243	−	1.21286i	−0.968381	−	0.249476i	$-0.919742\pi$
$823$	−20.0886	−	34.7944i	−0.700243	−	1.21286i	0.268138	−	0.963381i	$-0.413592\pi$
$824$		0			0
$825$	−37.7789			−1.31529
$826$		0			0
$827$	11.2802	+	11.2802i	0.392250	+	0.392250i	0.875489	−	0.483239i	$-0.160540\pi$
$827$	11.2802	+	11.2802i	0.392250	+	0.392250i	−0.483239	+	0.875489i	$0.660540\pi$
$828$		0			0
$829$	40.7143	+	10.9094i	1.41407	+	0.378898i	0.883375	−	0.468668i	$-0.155266\pi$
$829$	40.7143	+	10.9094i	1.41407	+	0.378898i	0.530691	+	0.847565i	$0.321933\pi$
$830$		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	$-0.842975\pi$
$839$		−	27.4328i		−	0.947087i	0.880771	−	0.473543i	$-0.157025\pi$
$840$		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	0.843530	−	0.537082i	$-0.180473\pi$
$853$	8.95019	+	8.95019i	0.306449	+	0.306449i	−0.537082	+	0.843530i	$0.680473\pi$
$854$		0			0
$855$	−29.2826			−1.00144
$856$		0			0
$857$	−26.8241	−	46.4607i	−0.916294	−	1.58707i	−0.804995	−	0.593281i	$-0.797832\pi$
$857$	−26.8241	−	46.4607i	−0.916294	−	1.58707i	−0.111299	−	0.993787i	$-0.535501\pi$
$858$		0			0
$859$	−3.41188	−	12.7333i	−0.116412	−	0.434455i	0.882977	−	0.469417i	$-0.155536\pi$
$859$	−3.41188	−	12.7333i	−0.116412	−	0.434455i	−0.999389	+	0.0349617i	$0.988869\pi$
$860$		0			0
$861$	4.40130	−	16.3321i	0.149996	−	0.556596i
$862$		0			0
$863$	−6.64111	−	3.83425i	−0.226066	−	0.130519i	0.382690	−	0.923877i	$-0.374998\pi$
$863$	−6.64111	−	3.83425i	−0.226066	−	0.130519i	−0.608756	+	0.793358i	$0.708331\pi$
$864$		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	−0.500674	−	0.865636i	$-0.666915\pi$
$877$	−14.8501	+	3.97908i	−0.501453	+	0.134364i	−0.000778781		1.00000i	$0.500248\pi$
$878$		0			0
$879$	6.76038	−	3.90311i	0.228022	−	0.131649i
$880$		0			0
$881$			21.5605i			0.726392i	0.931713	+	0.363196i	$0.118314\pi$
$881$			21.5605i			0.726392i	−0.931713	+	0.363196i	$0.881686\pi$
$882$		0			0
$883$	3.61325	−	3.61325i	0.121596	−	0.121596i	−0.643690	−	0.765286i	$-0.722598\pi$
$883$	3.61325	−	3.61325i	0.121596	−	0.121596i	0.765286	+	0.643690i	$0.222598\pi$
$884$		0			0
$885$	−5.83228	+	21.7664i	−0.196050	+	0.731668i
$886$		0			0
$887$	31.1537	+	17.9866i	1.04604	+	0.603930i	0.921537	−	0.388290i	$-0.126934\pi$
$887$	31.1537	+	17.9866i	1.04604	+	0.603930i	0.124500	+	0.992220i	$0.460267\pi$
$888$		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	−0.833409	−	0.552656i	$-0.813614\pi$
$907$	4.95935	−	18.5085i	0.164672	−	0.614566i	0.998082	−	0.0619098i	$-0.0197191\pi$
$908$		0			0
$909$	24.7454	−	24.7454i	0.820752	−	0.820752i
$910$		0			0
$911$			16.9566i			0.561797i	0.959737	+	0.280899i	$0.0906325\pi$
$911$			16.9566i			0.561797i	−0.959737	+	0.280899i	$0.909368\pi$
$912$		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	0.359853	+	0.933009i	$0.382827\pi$
$919$	−19.0403	+	32.9788i	−0.628083	+	1.08787i	−0.987936	+	0.154863i	$0.950507\pi$
$920$		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	0.434244	−	0.900795i	$-0.357015\pi$
$929$	−3.92408	−	2.26557i	−0.128745	−	0.0743309i	−0.562989	+	0.826464i	$0.690349\pi$
$930$		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	0.223144	−	0.974785i	$-0.428368\pi$
$941$	−2.17799	−	0.583589i	−0.0710003	−	0.0190245i	−0.294144	+	0.955761i	$0.595035\pi$
$942$		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	−0.999980	−	0.00637300i	$-0.997971\pi$
$947$	−4.22082	−	15.7523i	−0.137158	−	0.511882i	0.862821	−	0.505509i	$-0.168695\pi$
$948$		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	$0.149490\pi$
$953$			27.9419i			0.905126i	−0.891733	+	0.452563i	$0.850510\pi$
$954$		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	−0.957832	−	0.287330i	$-0.907232\pi$
$971$	−8.47546	−	31.6308i	−0.271990	−	1.01508i	0.685841	−	0.727751i	$-0.259434\pi$
$972$		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	0.999940	+	0.0109296i	$0.00347908\pi$
$977$	15.9234	+	27.5802i	0.509435	+	0.882368i	−0.490505	+	0.871438i	$0.663188\pi$
$978$		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	−0.959660	−	0.281162i	$-0.909280\pi$
$983$	−37.4979	+	21.6494i	−1.19600	+	0.690509i	−0.236337	+	0.971671i	$0.575947\pi$
$984$		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	−0.215952	−	0.976404i	$-0.569285\pi$
$991$	16.4220	−	9.48127i	0.521663	−	0.301183i	0.737615	+	0.675222i	$0.235952\pi$
$992$		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	0.723742	+	0.690070i	$0.242420\pi$
$997$	−7.83295	+	29.2330i	−0.248072	+	0.925818i	−0.971814	+	0.235747i	$0.924246\pi$
$998$		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.607.7		56
4.3	odd	2		896.2.z.b.607.8		56
7.3	odd	6	inner	896.2.z.a.479.7		56
8.3	odd	2		112.2.v.a.19.5	yes	56
8.5	even	2		448.2.z.a.47.8		56
16.3	odd	4		448.2.z.a.271.8		56
16.5	even	4		896.2.z.b.159.8		56
16.11	odd	4	inner	896.2.z.a.159.7		56
16.13	even	4		112.2.v.a.75.6	yes	56
28.3	even	6		896.2.z.b.479.8		56
56.3	even	6		112.2.v.a.3.6	✓	56
56.11	odd	6		784.2.w.f.227.6		56
56.19	even	6		784.2.j.a.195.28		56
56.27	even	2		784.2.w.f.19.5		56
56.45	odd	6		448.2.z.a.367.8		56
56.51	odd	6		784.2.j.a.195.27		56
112.3	even	12		448.2.z.a.143.8		56
112.13	odd	4		784.2.w.f.411.6		56
112.45	odd	12		112.2.v.a.59.5	yes	56
112.59	even	12	inner	896.2.z.a.31.7		56
112.61	odd	12		784.2.j.a.587.27		56
112.93	even	12		784.2.j.a.587.28		56
112.101	odd	12		896.2.z.b.31.8		56
112.109	even	12		784.2.w.f.619.5		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.v.a.3.6	✓	56	56.3	even	6
112.2.v.a.19.5	yes	56	8.3	odd	2
112.2.v.a.59.5	yes	56	112.45	odd	12
112.2.v.a.75.6	yes	56	16.13	even	4
448.2.z.a.47.8		56	8.5	even	2
448.2.z.a.143.8		56	112.3	even	12
448.2.z.a.271.8		56	16.3	odd	4
448.2.z.a.367.8		56	56.45	odd	6
784.2.j.a.195.27		56	56.51	odd	6
784.2.j.a.195.28		56	56.19	even	6
784.2.j.a.587.27		56	112.61	odd	12
784.2.j.a.587.28		56	112.93	even	12
784.2.w.f.19.5		56	56.27	even	2
784.2.w.f.227.6		56	56.11	odd	6
784.2.w.f.411.6		56	112.13	odd	4
784.2.w.f.619.5		56	112.109	even	12
896.2.z.a.31.7		56	112.59	even	12	inner
896.2.z.a.159.7		56	16.11	odd	4	inner
896.2.z.a.479.7		56	7.3	odd	6	inner
896.2.z.a.607.7		56	1.1	even	1	trivial
896.2.z.b.31.8		56	112.101	odd	12
896.2.z.b.159.8		56	16.5	even	4
896.2.z.b.479.8		56	28.3	even	6
896.2.z.b.607.8		56	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
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

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more