LMFDB - Embedded newform 896.2.ba.f.417.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [896,2,Mod(289,896)] 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("896.289"); 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([0, 9, 4])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,-4,0,0,0,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$7.15459602111$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			417.9
Character	$\chi$	$=$	896.417
Dual form			896.2.ba.f.737.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.60845 - 0.430984i) q^{3} +(-1.94900 - 0.522232i) q^{5} +(-1.89075 + 1.85069i) q^{7} +(-0.196696 + 0.113563i) q^{9} +(-1.63411 - 6.09856i) q^{11} +(-1.13388 - 1.13388i) q^{13} -3.35995 q^{15} +(-0.960789 + 1.66414i) q^{17} +(-1.63324 + 6.09532i) q^{19} +(-2.24357 + 3.79164i) q^{21} +(-0.924606 + 0.533821i) q^{23} +(-0.804265 - 0.464342i) q^{25} +(-3.79985 + 3.79985i) q^{27} +(-5.08936 - 5.08936i) q^{29} +(-0.198293 + 0.343454i) q^{31} +(-5.25677 - 9.10499i) q^{33} +(4.65156 - 2.61958i) q^{35} +(-0.327303 - 0.0877006i) q^{37} +(-2.31247 - 1.33510i) q^{39} -7.26189i q^{41} +(-1.75565 + 1.75565i) q^{43} +(0.442666 - 0.118612i) q^{45} +(-1.08118 - 1.87265i) q^{47} +(0.149895 - 6.99839i) q^{49} +(-0.828170 + 3.09077i) q^{51} +(-0.111394 - 0.415727i) q^{53} +12.7395i q^{55} +10.5079i q^{57} +(2.32453 + 8.67527i) q^{59} +(2.72673 - 10.1763i) q^{61} +(0.161735 - 0.578743i) q^{63} +(1.61777 + 2.80206i) q^{65} +(-7.87441 + 2.10994i) q^{67} +(-1.25712 + 1.25712i) q^{69} +2.78982i q^{71} +(2.05730 + 1.18779i) q^{73} +(-1.49375 - 0.400248i) q^{75} +(14.3762 + 8.50666i) q^{77} +(5.10829 + 8.84782i) q^{79} +(-4.13352 + 7.15947i) q^{81} +(-1.17951 - 1.17951i) q^{83} +(2.74164 - 2.74164i) q^{85} +(-10.3794 - 5.99257i) q^{87} +(11.0470 - 6.37800i) q^{89} +(4.24233 + 0.0454269i) q^{91} +(-0.170922 + 0.637891i) q^{93} +(6.36634 - 11.0268i) q^{95} -2.21148 q^{97} +(1.01399 + 1.01399i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{5} + 4 q^{11} + 24 q^{13} - 40 q^{15} + 8 q^{17} + 4 q^{19} + 8 q^{21} + 24 q^{27} - 24 q^{29} + 28 q^{31} + 16 q^{33} - 28 q^{35} + 24 q^{37} + 40 q^{43} + 28 q^{45} - 20 q^{47} - 24 q^{51}+ \cdots + 24 q^{99}+O(q^{100}) $ 48 * q - 4 * q^5 + 4 * q^11 + 24 * q^13 - 40 * q^15 + 8 * q^17 + 4 * q^19 + 8 * q^21 + 24 * q^27 - 24 * q^29 + 28 * q^31 + 16 * q^33 - 28 * q^35 + 24 * q^37 + 40 * q^43 + 28 * q^45 - 20 * q^47 - 24 * q^51 + 16 * q^53 + 20 * q^59 - 8 * q^61 - 16 * q^63 + 8 * q^65 - 48 * q^67 + 40 * q^69 + 4 * q^75 + 20 * q^77 - 36 * q^79 + 8 * q^83 - 64 * q^91 - 8 * q^93 - 4 * q^95 - 48 * q^97 + 24 * q^99

Character values

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

$n$	$127$	$129$	$645$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{4}\right)$

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
$3$	1.60845	−	0.430984i	0.928642	−	0.248829i	0.237366	−	0.971420i	$-0.423716\pi$
$3$	1.60845	−	0.430984i	0.928642	−	0.248829i	0.691275	+	0.722591i	$0.257049\pi$
$4$		0			0
$5$	−1.94900	−	0.522232i	−0.871618	−	0.233549i	−0.204831	−	0.978797i	$-0.565664\pi$
$5$	−1.94900	−	0.522232i	−0.871618	−	0.233549i	−0.666787	+	0.745248i	$0.732331\pi$
$6$		0			0
$7$	−1.89075	+	1.85069i	−0.714638	+	0.699495i
$7$	−1.89075	+	1.85069i	−0.714638	+	0.699495i
$8$		0			0
$9$	−0.196696	+	0.113563i	−0.0655654	+	0.0378542i
$10$		0			0
$11$	−1.63411	−	6.09856i	−0.492701	−	1.83879i	−0.542542	−	0.840029i	$-0.682538\pi$
$11$	−1.63411	−	6.09856i	−0.492701	−	1.83879i	0.0498403	−	0.998757i	$-0.484129\pi$
$12$		0			0
$13$	−1.13388	−	1.13388i	−0.314480	−	0.314480i	0.532162	−	0.846642i	$-0.321380\pi$
$13$	−1.13388	−	1.13388i	−0.314480	−	0.314480i	−0.846642	+	0.532162i	$0.821380\pi$
$14$		0			0
$15$	−3.35995			−0.867535
$16$		0			0
$17$	−0.960789	+	1.66414i	−0.233026	+	0.403612i	−0.958697	−	0.284429i	$-0.908196\pi$
$17$	−0.960789	+	1.66414i	−0.233026	+	0.403612i	0.725671	+	0.688041i	$0.241529\pi$
$18$		0			0
$19$	−1.63324	+	6.09532i	−0.374690	+	1.39836i	0.479107	+	0.877756i	$0.340960\pi$
$19$	−1.63324	+	6.09532i	−0.374690	+	1.39836i	−0.853797	+	0.520605i	$0.825706\pi$
$20$		0			0
$21$	−2.24357	+	3.79164i	−0.489588	+	0.827403i
$22$		0			0
$23$	−0.924606	+	0.533821i	−0.192794	+	0.111309i	−0.593290	−	0.804989i	$-0.702171\pi$
$23$	−0.924606	+	0.533821i	−0.192794	+	0.111309i	0.400496	+	0.916298i	$0.368838\pi$
$24$		0			0
$25$	−0.804265	−	0.464342i	−0.160853	−	0.0928685i
$26$		0			0
$27$	−3.79985	+	3.79985i	−0.731281	+	0.731281i
$28$		0			0
$29$	−5.08936	−	5.08936i	−0.945070	−	0.945070i	0.0534979	−	0.998568i	$-0.482963\pi$
$29$	−5.08936	−	5.08936i	−0.945070	−	0.945070i	−0.998568	+	0.0534979i	$0.982963\pi$
$30$		0			0
$31$	−0.198293	+	0.343454i	−0.0356145	+	0.0616861i	−0.883283	−	0.468840i	$-0.844672\pi$
$31$	−0.198293	+	0.343454i	−0.0356145	+	0.0616861i	0.847669	+	0.530526i	$0.178006\pi$
$32$		0			0
$33$	−5.25677	−	9.10499i	−0.915086	−	1.58498i
$34$		0			0
$35$	4.65156	−	2.61958i	0.786257	−	0.442789i
$36$		0			0
$37$	−0.327303	−	0.0877006i	−0.0538083	−	0.0144179i	0.231814	−	0.972760i	$-0.425534\pi$
$37$	−0.327303	−	0.0877006i	−0.0538083	−	0.0144179i	−0.285623	+	0.958342i	$0.592200\pi$
$38$		0			0
$39$	−2.31247	−	1.33510i	−0.370291	−	0.213788i
$40$		0			0
$41$		−	7.26189i		−	1.13412i	−0.823678	−	0.567058i	$-0.808081\pi$
$41$		−	7.26189i		−	1.13412i	0.823678	−	0.567058i	$-0.191919\pi$
$42$		0			0
$43$	−1.75565	+	1.75565i	−0.267734	+	0.267734i	−0.828187	−	0.560452i	$-0.810627\pi$
$43$	−1.75565	+	1.75565i	−0.267734	+	0.267734i	0.560452	+	0.828187i	$0.310627\pi$
$44$		0			0
$45$	0.442666	−	0.118612i	0.0659888	−	0.0176816i
$46$		0			0
$47$	−1.08118	−	1.87265i	−0.157706	−	0.273155i	0.776335	−	0.630320i	$-0.217076\pi$
$47$	−1.08118	−	1.87265i	−0.157706	−	0.273155i	−0.934041	+	0.357166i	$0.883743\pi$
$48$		0			0
$49$	0.149895	−	6.99839i	0.0214136	−	0.999771i
$50$		0			0
$51$	−0.828170	+	3.09077i	−0.115967	+	0.432795i
$52$		0			0
$53$	−0.111394	−	0.415727i	−0.0153011	−	0.0571045i	0.957853	−	0.287258i	$-0.0927438\pi$
$53$	−0.111394	−	0.415727i	−0.0153011	−	0.0571045i	−0.973154	+	0.230154i	$0.926077\pi$
$54$		0			0
$55$			12.7395i			1.71779i
$56$		0			0
$57$			10.5079i			1.39181i
$58$		0			0
$59$	2.32453	+	8.67527i	0.302628	+	1.12942i	0.934968	+	0.354732i	$0.115428\pi$
$59$	2.32453	+	8.67527i	0.302628	+	1.12942i	−0.632340	+	0.774691i	$0.717905\pi$
$60$		0			0
$61$	2.72673	−	10.1763i	0.349122	−	1.30294i	−0.538601	−	0.842561i	$-0.681047\pi$
$61$	2.72673	−	10.1763i	0.349122	−	1.30294i	0.887722	−	0.460379i	$-0.152287\pi$
$62$		0			0
$63$	0.161735	−	0.578743i	0.0203767	−	0.0729147i
$64$		0			0
$65$	1.61777	+	2.80206i	0.200660	+	0.347553i
$66$		0			0
$67$	−7.87441	+	2.10994i	−0.962012	+	0.257770i	−0.705452	−	0.708758i	$-0.749256\pi$
$67$	−7.87441	+	2.10994i	−0.962012	+	0.257770i	−0.256560	+	0.966528i	$0.582589\pi$
$68$		0			0
$69$	−1.25712	+	1.25712i	−0.151339	+	0.151339i
$70$		0			0
$71$			2.78982i			0.331090i	0.986202	+	0.165545i	$0.0529384\pi$
$71$			2.78982i			0.331090i	−0.986202	+	0.165545i	$0.947062\pi$
$72$		0			0
$73$	2.05730	+	1.18779i	0.240789	+	0.139020i	0.615539	−	0.788106i	$-0.288938\pi$
$73$	2.05730	+	1.18779i	0.240789	+	0.139020i	−0.374750	+	0.927126i	$0.622272\pi$
$74$		0			0
$75$	−1.49375	−	0.400248i	−0.172483	−	0.0462167i
$76$		0			0
$77$	14.3762	+	8.50666i	1.63832	+	0.969424i
$78$		0			0
$79$	5.10829	+	8.84782i	0.574727	+	0.995457i	0.996071	+	0.0885562i	$0.0282253\pi$
$79$	5.10829	+	8.84782i	0.574727	+	0.995457i	−0.421344	+	0.906901i	$0.638441\pi$
$80$		0			0
$81$	−4.13352	+	7.15947i	−0.459280	+	0.795496i
$82$		0			0
$83$	−1.17951	−	1.17951i	−0.129468	−	0.129468i	0.639404	−	0.768871i	$-0.279181\pi$
$83$	−1.17951	−	1.17951i	−0.129468	−	0.129468i	−0.768871	+	0.639404i	$0.779181\pi$
$84$		0			0
$85$	2.74164	−	2.74164i	0.297373	−	0.297373i
$86$		0			0
$87$	−10.3794	−	5.99257i	−1.11279	−	0.642471i
$88$		0			0
$89$	11.0470	−	6.37800i	1.17098	−	0.676066i	0.217070	−	0.976156i	$-0.430350\pi$
$89$	11.0470	−	6.37800i	1.17098	−	0.676066i	0.953911	+	0.300089i	$0.0970165\pi$
$90$		0			0
$91$	4.24233	+	0.0454269i	0.444717	+	0.00476204i
$92$		0			0
$93$	−0.170922	+	0.637891i	−0.0177238	+	0.0661462i
$94$		0			0
$95$	6.36634	−	11.0268i	0.653173	−	1.13133i
$96$		0			0
$97$	−2.21148			−0.224542			−0.112271	−	0.993678i	$-0.535813\pi$
$97$	−2.21148			−0.224542			−0.112271	+	0.993678i	$0.535813\pi$
$98$		0			0
$99$	1.01399	+	1.01399i	0.101910	+	0.101910i
$100$		0			0
$101$	−1.86231	−	6.95024i	−0.185307	−	0.691575i	−0.994565	−	0.104121i	$-0.966797\pi$
$101$	−1.86231	−	6.95024i	−0.185307	−	0.691575i	0.809258	−	0.587454i	$-0.199870\pi$
$102$		0			0
$103$	15.1457	−	8.74438i	1.49235	−	0.861609i	0.492390	−	0.870375i	$-0.336123\pi$
$103$	15.1457	−	8.74438i	1.49235	−	0.861609i	0.999962	+	0.00876536i	$0.00279014\pi$
$104$		0			0
$105$	6.35283	−	6.21822i	0.619973	−	0.606836i
$106$		0			0
$107$	−2.90855	−	0.779344i	−0.281180	−	0.0753420i	0.115473	−	0.993311i	$-0.463162\pi$
$107$	−2.90855	−	0.779344i	−0.281180	−	0.0753420i	−0.396653	+	0.917969i	$0.629828\pi$
$108$		0			0
$109$	−6.86536	+	1.83957i	−0.657583	+	0.176199i	−0.572155	−	0.820146i	$-0.693892\pi$
$109$	−6.86536	+	1.83957i	−0.657583	+	0.176199i	−0.0854277	+	0.996344i	$0.527226\pi$
$110$		0			0
$111$	−0.564250			−0.0535562
$112$		0			0
$113$	−5.96535			−0.561173			−0.280586	−	0.959829i	$-0.590529\pi$
$113$	−5.96535			−0.561173			−0.280586	+	0.959829i	$0.590529\pi$
$114$		0			0
$115$	2.08083	−	0.557557i	0.194039	−	0.0519925i
$116$		0			0
$117$	0.351795	+	0.0942631i	0.0325234	+	0.00871463i
$118$		0			0
$119$	−1.26318	−	4.92459i	−0.115796	−	0.451437i
$120$		0			0
$121$	−24.9959	+	14.4314i	−2.27235	+	1.31194i
$122$		0			0
$123$	−3.12976	−	11.6804i	−0.282201	−	1.05319i
$124$		0			0
$125$	8.45884	+	8.45884i	0.756582	+	0.756582i
$126$		0			0
$127$	6.41296			0.569058			0.284529	−	0.958667i	$-0.408163\pi$
$127$	6.41296			0.569058			0.284529	+	0.958667i	$0.408163\pi$
$128$		0			0
$129$	−2.06723	+	3.58055i	−0.182009	+	0.315250i
$130$		0			0
$131$	3.87298	−	14.4542i	0.338384	−	1.26287i	−0.561769	−	0.827294i	$-0.689879\pi$
$131$	3.87298	−	14.4542i	0.338384	−	1.26287i	0.900154	−	0.435573i	$-0.143454\pi$
$132$		0			0
$133$	−8.19250	−	14.5474i	−0.710380	−	1.26142i
$134$		0			0
$135$	9.39029	−	5.42149i	0.808187	−	0.466607i
$136$		0			0
$137$	1.50928	+	0.871382i	0.128946	+	0.0744472i	0.563086	−	0.826399i	$-0.309614\pi$
$137$	1.50928	+	0.871382i	0.128946	+	0.0744472i	−0.434139	+	0.900846i	$0.642947\pi$
$138$		0			0
$139$	−2.84436	+	2.84436i	−0.241256	+	0.241256i	−0.817370	−	0.576114i	$-0.804569\pi$
$139$	−2.84436	+	2.84436i	−0.241256	+	0.241256i	0.576114	+	0.817370i	$0.304569\pi$
$140$		0			0
$141$	−2.54611	−	2.54611i	−0.214421	−	0.214421i
$142$		0			0
$143$	−5.06214	+	8.76788i	−0.423317	+	0.733207i
$144$		0			0
$145$	7.26132	+	12.5770i	0.603020	+	1.04446i
$146$		0			0
$147$	−2.77510	−	11.3212i	−0.228886	−	0.933757i
$148$		0			0
$149$	17.7848	+	4.76543i	1.45699	+	0.390399i	0.898449	−	0.439077i	$-0.144695\pi$
$149$	17.7848	+	4.76543i	1.45699	+	0.390399i	0.558541	+	0.829477i	$0.311361\pi$
$150$		0			0
$151$	−5.52437	−	3.18949i	−0.449567	−	0.259557i	0.258081	−	0.966123i	$-0.416910\pi$
$151$	−5.52437	−	3.18949i	−0.449567	−	0.259557i	−0.707647	+	0.706566i	$0.750243\pi$
$152$		0			0
$153$		−	0.436439i		−	0.0352840i
$154$		0			0
$155$	0.565835	−	0.565835i	0.0454490	−	0.0454490i
$156$		0			0
$157$	−17.6177	+	4.72065i	−1.40605	+	0.376749i	−0.880512	−	0.474024i	$-0.842801\pi$
$157$	−17.6177	+	4.72065i	−1.40605	+	0.376749i	−0.525534	+	0.850773i	$0.676134\pi$
$158$		0			0
$159$	−0.358344	−	0.620669i	−0.0284185	−	0.0492223i
$160$		0			0
$161$	0.760264	−	2.72048i	0.0599172	−	0.214404i
$162$		0			0
$163$	−2.97338	+	11.0968i	−0.232893	+	0.869170i	0.746194	+	0.665729i	$0.231879\pi$
$163$	−2.97338	+	11.0968i	−0.232893	+	0.869170i	−0.979087	+	0.203441i	$0.934787\pi$
$164$		0			0
$165$	5.49051	+	20.4909i	0.427435	+	1.59521i
$166$		0			0
$167$			21.6693i			1.67682i	0.545040	+	0.838410i	$0.316514\pi$
$167$			21.6693i			1.67682i	−0.545040	+	0.838410i	$0.683486\pi$
$168$		0			0
$169$		−	10.4287i		−	0.802204i
$170$		0			0
$171$	−0.370949	−	1.38440i	−0.0283672	−	0.105868i
$172$		0			0
$173$	−3.31175	+	12.3596i	−0.251788	+	0.939684i	0.718062	+	0.695979i	$0.245030\pi$
$173$	−3.31175	+	12.3596i	−0.251788	+	0.939684i	−0.969849	+	0.243705i	$0.921637\pi$
$174$		0			0
$175$	2.38002	−	0.610487i	0.179913	−	0.0461485i
$176$		0			0
$177$	7.47780	+	12.9519i	0.562066	+	0.973527i
$178$		0			0
$179$	−3.05939	+	0.819762i	−0.228670	+	0.0612719i	−0.371334	−	0.928499i	$-0.621100\pi$
$179$	−3.05939	+	0.819762i	−0.228670	+	0.0612719i	0.142665	+	0.989771i	$0.454433\pi$
$180$		0			0
$181$	14.3765	−	14.3765i	1.06860	−	1.06860i	0.0711279	−	0.997467i	$-0.477340\pi$
$181$	14.3765	−	14.3765i	1.06860	−	1.06860i	0.997467	−	0.0711279i	$-0.0226598\pi$
$182$		0			0
$183$		−	17.5433i		−	1.29684i
$184$		0			0
$185$	0.592113	+	0.341857i	0.0435330	+	0.0251338i
$186$		0			0
$187$	11.7189	+	3.14006i	0.856969	+	0.229624i
$188$		0			0
$189$	0.152235	−	14.2169i	0.0110735	−	1.03413i
$190$		0			0
$191$	−6.12089	−	10.6017i	−0.442892	−	0.767111i	0.555011	−	0.831843i	$-0.312714\pi$
$191$	−6.12089	−	10.6017i	−0.442892	−	0.767111i	−0.997903	+	0.0647319i	$0.979381\pi$
$192$		0			0
$193$	1.08900	−	1.88620i	0.0783877	−	0.135771i	−0.824167	−	0.566347i	$-0.808356\pi$
$193$	1.08900	−	1.88620i	0.0783877	−	0.135771i	0.902554	+	0.430576i	$0.141689\pi$
$194$		0			0
$195$	3.80976	+	3.80976i	0.272823	+	0.272823i
$196$		0			0
$197$	−9.97878	+	9.97878i	−0.710959	+	0.710959i	−0.966736	−	0.255777i	$-0.917669\pi$
$197$	−9.97878	+	9.97878i	−0.710959	+	0.710959i	0.255777	+	0.966736i	$0.417669\pi$
$198$		0			0
$199$	−9.14271	−	5.27854i	−0.648109	−	0.374186i	0.139622	−	0.990205i	$-0.455411\pi$
$199$	−9.14271	−	5.27854i	−0.648109	−	0.374186i	−0.787731	+	0.616019i	$0.788745\pi$
$200$		0			0
$201$	−11.7563	+	6.78749i	−0.829224	+	0.478753i
$202$		0			0
$203$	19.0415	+	0.203897i	1.33645	+	0.0143108i
$204$		0			0
$205$	−3.79239	+	14.1534i	−0.264872	+	0.988516i
$206$		0			0
$207$	0.121244	−	0.210001i	0.00842706	−	0.0145961i
$208$		0			0
$209$	39.8416			2.75590
$210$		0			0
$211$	−5.20378	−	5.20378i	−0.358243	−	0.358243i	0.504922	−	0.863165i	$-0.331521\pi$
$211$	−5.20378	−	5.20378i	−0.358243	−	0.358243i	−0.863165	+	0.504922i	$0.831521\pi$
$212$		0			0
$213$	1.20237	+	4.48730i	0.0823849	+	0.307464i
$214$		0			0
$215$	4.33862	−	2.50490i	0.295891	−	0.170833i
$216$		0			0
$217$	−0.260703	−	1.01636i	−0.0176977	−	0.0689953i
$218$		0			0
$219$	3.82100	+	1.02383i	0.258199	+	0.0691843i
$220$		0			0
$221$	2.97634	−	0.797507i	0.200210	−	0.0536461i
$222$		0			0
$223$	−22.3888			−1.49926			−0.749632	−	0.661855i	$-0.769770\pi$
$223$	−22.3888			−1.49926			−0.749632	+	0.661855i	$0.769770\pi$
$224$		0			0
$225$	0.210928			0.0140619
$226$		0			0
$227$	17.9753	−	4.81647i	1.19306	−	0.319680i	0.392967	−	0.919552i	$-0.371448\pi$
$227$	17.9753	−	4.81647i	1.19306	−	0.319680i	0.800096	+	0.599872i	$0.204782\pi$
$228$		0			0
$229$	−8.12426	−	2.17689i	−0.536866	−	0.143853i	−0.0198093	−	0.999804i	$-0.506306\pi$
$229$	−8.12426	−	2.17689i	−0.536866	−	0.143853i	−0.517057	+	0.855951i	$0.672973\pi$
$230$		0			0
$231$	26.7898	+	7.48664i	1.76264	+	0.492585i
$232$		0			0
$233$	14.9278	−	8.61859i	0.977955	−	0.564623i	0.0763032	−	0.997085i	$-0.475688\pi$
$233$	14.9278	−	8.61859i	0.977955	−	0.564623i	0.901652	+	0.432462i	$0.142355\pi$
$234$		0			0
$235$	1.12925	+	4.21442i	0.0736642	+	0.274919i
$236$		0			0
$237$	12.0297	+	12.0297i	0.781414	+	0.781414i
$238$		0			0
$239$	−0.572679			−0.0370435			−0.0185218	−	0.999828i	$-0.505896\pi$
$239$	−0.572679			−0.0370435			−0.0185218	+	0.999828i	$0.505896\pi$
$240$		0			0
$241$	5.89318	−	10.2073i	0.379613	−	0.657510i	−0.611393	−	0.791327i	$-0.709390\pi$
$241$	5.89318	−	10.2073i	0.379613	−	0.657510i	0.991006	+	0.133818i	$0.0427237\pi$
$242$		0			0
$243$	0.609557	−	2.27490i	0.0391031	−	0.145935i
$244$		0			0
$245$	−3.94693	+	13.5616i	−0.252160	+	0.866417i
$246$		0			0
$247$	8.76321	−	5.05944i	0.557590	−	0.321925i
$248$		0			0
$249$	−2.40553	−	1.38883i	−0.152444	−	0.0880137i
$250$		0			0
$251$	5.57539	−	5.57539i	0.351916	−	0.351916i	−0.508906	−	0.860822i	$-0.669950\pi$
$251$	5.57539	−	5.57539i	0.351916	−	0.351916i	0.860822	+	0.508906i	$0.169950\pi$
$252$		0			0
$253$	4.76645	+	4.76645i	0.299664	+	0.299664i
$254$		0			0
$255$	3.22820	−	5.59141i	0.202158	−	0.350148i
$256$		0			0
$257$	−14.5328	−	25.1715i	−0.906528	−	1.57015i	−0.818853	−	0.574004i	$-0.805390\pi$
$257$	−14.5328	−	25.1715i	−0.906528	−	1.57015i	−0.0876753	−	0.996149i	$-0.527944\pi$
$258$		0			0
$259$	0.781156	−	0.439916i	0.0485387	−	0.0273351i
$260$		0			0
$261$	1.57902	+	0.423097i	0.0977388	+	0.0261890i
$262$		0			0
$263$	−15.3142	−	8.84163i	−0.944311	−	0.545198i	−0.0530021	−	0.998594i	$-0.516879\pi$
$263$	−15.3142	−	8.84163i	−0.944311	−	0.545198i	−0.891309	+	0.453396i	$0.850212\pi$
$264$		0			0
$265$			0.868424i			0.0533469i
$266$		0			0
$267$	15.0198	−	15.0198i	0.919198	−	0.919198i
$268$		0			0
$269$	−14.4268	+	3.86566i	−0.879620	+	0.235693i	−0.670243	−	0.742142i	$-0.733810\pi$
$269$	−14.4268	+	3.86566i	−0.879620	+	0.235693i	−0.209377	+	0.977835i	$0.567144\pi$
$270$		0			0
$271$	6.93172	+	12.0061i	0.421072	+	0.729319i	0.996045	−	0.0888543i	$-0.0283205\pi$
$271$	6.93172	+	12.0061i	0.421072	+	0.729319i	−0.574972	+	0.818173i	$0.694987\pi$
$272$		0			0
$273$	6.84317	−	1.75531i	0.414168	−	0.106236i
$274$		0			0
$275$	−1.51757	+	5.66364i	−0.0915128	+	0.341531i
$276$		0			0
$277$	0.597472	+	2.22980i	0.0358986	+	0.133975i	0.981550	−	0.191208i	$-0.0612406\pi$
$277$	0.597472	+	2.22980i	0.0358986	+	0.133975i	−0.945651	+	0.325184i	$0.894574\pi$
$278$		0			0
$279$		−	0.0900747i		−	0.00539263i
$280$		0			0
$281$			0.680351i			0.0405863i	0.999794	+	0.0202932i	$0.00645996\pi$
$281$			0.680351i			0.0405863i	−0.999794	+	0.0202932i	$0.993540\pi$
$282$		0			0
$283$	−0.0985120	−	0.367652i	−0.00585593	−	0.0218546i	0.962936	−	0.269730i	$-0.0869344\pi$
$283$	−0.0985120	−	0.367652i	−0.00585593	−	0.0218546i	−0.968792	+	0.247875i	$0.920268\pi$
$284$		0			0
$285$	5.48759	−	20.4799i	0.325056	−	1.21313i
$286$		0			0
$287$	13.4395	+	13.7304i	0.793309	+	0.810482i
$288$		0			0
$289$	6.65377	+	11.5247i	0.391398	+	0.677921i
$290$		0			0
$291$	−3.55707	+	0.953115i	−0.208519	+	0.0558726i
$292$		0			0
$293$	−7.49220	+	7.49220i	−0.437699	+	0.437699i	−0.891237	−	0.453538i	$-0.850162\pi$
$293$	−7.49220	+	7.49220i	−0.437699	+	0.437699i	0.453538	+	0.891237i	$0.350162\pi$
$294$		0			0
$295$		−	18.1220i		−	1.05510i
$296$		0			0
$297$	29.3829	+	16.9643i	1.70497	+	0.984366i
$298$		0			0
$299$	1.65367	+	0.443101i	0.0956345	+	0.0256252i
$300$		0			0
$301$	0.0703375	−	6.56867i	0.00405418	−	0.378612i
$302$		0			0
$303$	−5.99089	−	10.3765i	−0.344168	−	0.596116i
$304$		0			0
$305$	−10.6288	+	18.4096i	−0.608602	+	1.05413i
$306$		0			0
$307$	6.27988	+	6.27988i	0.358412	+	0.358412i	0.863227	−	0.504816i	$-0.168439\pi$
$307$	6.27988	+	6.27988i	0.358412	+	0.358412i	−0.504816	+	0.863227i	$0.668439\pi$
$308$		0			0
$309$	20.5925	−	20.5925i	1.17147	−	1.17147i
$310$		0			0
$311$	8.55685	+	4.94030i	0.485215	+	0.280139i	0.722587	−	0.691280i	$-0.242953\pi$
$311$	8.55685	+	4.94030i	0.485215	+	0.280139i	−0.237372	+	0.971419i	$0.576286\pi$
$312$		0			0
$313$	−14.8734	+	8.58714i	−0.840692	+	0.485374i	−0.857499	−	0.514485i	$-0.827983\pi$
$313$	−14.8734	+	8.58714i	−0.840692	+	0.485374i	0.0168075	+	0.999859i	$0.494650\pi$
$314$		0			0
$315$	−0.617459	+	1.04350i	−0.0347899	+	0.0587948i
$316$		0			0
$317$	5.49870	−	20.5214i	0.308838	−	1.15260i	−0.620754	−	0.784006i	$-0.713173\pi$
$317$	5.49870	−	20.5214i	0.308838	−	1.15260i	0.929591	−	0.368592i	$-0.120160\pi$
$318$		0			0
$319$	−22.7212	+	39.3543i	−1.27214	+	2.20342i
$320$		0			0
$321$	−5.01416			−0.279863
$322$		0			0
$323$	−8.57424	−	8.57424i	−0.477084	−	0.477084i
$324$		0			0
$325$	0.385429	+	1.43844i	0.0213798	+	0.0797904i
$326$		0			0
$327$	−10.2498	+	5.91773i	−0.566815	+	0.327251i
$328$		0			0
$329$	5.50994	+	1.53980i	0.303773	+	0.0848921i
$330$		0			0
$331$	−23.3748	−	6.26326i	−1.28479	−	0.344260i	−0.449113	−	0.893475i	$-0.648260\pi$
$331$	−23.3748	−	6.26326i	−1.28479	−	0.344260i	−0.835681	+	0.549215i	$0.814927\pi$
$332$		0			0
$333$	0.0743388	−	0.0199190i	0.00407374	−	0.00109156i
$334$		0			0
$335$	16.4491			0.898709
$336$		0			0
$337$	−4.26739			−0.232460			−0.116230	−	0.993222i	$-0.537081\pi$
$337$	−4.26739			−0.232460			−0.116230	+	0.993222i	$0.537081\pi$
$338$		0			0
$339$	−9.59499	+	2.57097i	−0.521128	+	0.139636i
$340$		0			0
$341$	2.41861	+	0.648063i	0.130975	+	0.0350946i
$342$		0			0
$343$	12.6684	+	13.5096i	0.684032	+	0.729452i
$344$		0			0
$345$	3.10663	−	1.79361i	0.167255	−	0.0965648i
$346$		0			0
$347$	0.0139833	+	0.0521865i	0.000750664	+	0.00280152i	0.966300	−	0.257418i	$-0.0828717\pi$
$347$	0.0139833	+	0.0521865i	0.000750664	+	0.00280152i	−0.965549	+	0.260220i	$0.916205\pi$
$348$		0			0
$349$	15.4928	+	15.4928i	0.829309	+	0.829309i	0.987421	−	0.158112i	$-0.0505407\pi$
$349$	15.4928	+	15.4928i	0.829309	+	0.829309i	−0.158112	+	0.987421i	$0.550541\pi$
$350$		0			0
$351$	8.61710			0.459947
$352$		0			0
$353$	−8.38161	+	14.5174i	−0.446108	+	0.772682i	−0.998129	−	0.0611484i	$-0.980524\pi$
$353$	−8.38161	+	14.5174i	−0.446108	+	0.772682i	0.552020	+	0.833831i	$0.313857\pi$
$354$		0			0
$355$	1.45693	−	5.43735i	0.0773259	−	0.288584i
$356$		0			0
$357$	−4.15420	−	7.37657i	−0.219863	−	0.390410i
$358$		0			0
$359$	−29.8777	+	17.2499i	−1.57689	+	0.910415i	−0.581595	+	0.813479i	$0.697571\pi$
$359$	−29.8777	+	17.2499i	−1.57689	+	0.910415i	−0.995291	+	0.0969365i	$0.969096\pi$
$360$		0			0
$361$	−18.0310	−	10.4102i	−0.948998	−	0.547904i
$362$		0			0
$363$	−33.9851	+	33.9851i	−1.78375	+	1.78375i
$364$		0			0
$365$	−3.38938	−	3.38938i	−0.177408	−	0.177408i
$366$		0			0
$367$	10.2644	−	17.7785i	0.535799	−	0.928032i	−0.463325	−	0.886189i	$-0.653344\pi$
$367$	10.2644	−	17.7785i	0.535799	−	0.928032i	0.999124	−	0.0418433i	$-0.0133230\pi$
$368$		0			0
$369$	0.824679	+	1.42839i	0.0429311	+	0.0743588i
$370$		0			0
$371$	0.980000	+	0.579882i	0.0508791	+	0.0301060i
$372$		0			0
$373$	−15.2773	−	4.09353i	−0.791027	−	0.211955i	−0.159386	−	0.987216i	$-0.550951\pi$
$373$	−15.2773	−	4.09353i	−0.791027	−	0.211955i	−0.631641	+	0.775261i	$0.717618\pi$
$374$		0			0
$375$	17.2513	+	9.96003i	0.890853	+	0.514334i
$376$		0			0
$377$			11.5414i			0.594412i
$378$		0			0
$379$	−11.2717	+	11.2717i	−0.578987	+	0.578987i	−0.934624	−	0.355637i	$-0.884264\pi$
$379$	−11.2717	+	11.2717i	−0.578987	+	0.578987i	0.355637	+	0.934624i	$0.384264\pi$
$380$		0			0
$381$	10.3150	−	2.76388i	0.528451	−	0.141598i
$382$		0			0
$383$	−5.14594	−	8.91303i	−0.262945	−	0.455434i	0.704078	−	0.710123i	$-0.251360\pi$
$383$	−5.14594	−	8.91303i	−0.262945	−	0.455434i	−0.967023	+	0.254688i	$0.918027\pi$
$384$		0			0
$385$	−23.5768	−	24.0872i	−1.20158	−	1.22760i
$386$		0			0
$387$	0.145954	−	0.544707i	0.00741925	−	0.0276890i
$388$		0			0
$389$	−5.30513	−	19.7990i	−0.268981	−	1.00385i	−0.959769	−	0.280792i	$-0.909403\pi$
$389$	−5.30513	−	19.7990i	−0.268981	−	1.00385i	0.690788	−	0.723058i	$-0.257264\pi$
$390$		0			0
$391$		−	2.05156i		−	0.103752i
$392$		0			0
$393$		−	24.9181i		−	1.25695i
$394$		0			0
$395$	−5.33543	−	19.9121i	−0.268454	−	1.00189i
$396$		0			0
$397$	2.02632	−	7.56231i	0.101698	−	0.379542i	−0.896252	−	0.443546i	$-0.853720\pi$
$397$	2.02632	−	7.56231i	0.101698	−	0.379542i	0.997950	+	0.0640041i	$0.0203871\pi$
$398$		0			0
$399$	−19.4469	−	19.8679i	−0.973565	−	0.994640i
$400$		0			0
$401$	−7.09985	−	12.2973i	−0.354549	−	0.614098i	0.632491	−	0.774567i	$-0.282032\pi$
$401$	−7.09985	−	12.2973i	−0.354549	−	0.614098i	−0.987041	+	0.160470i	$0.948699\pi$
$402$		0			0
$403$	0.614273	−	0.164594i	0.0305991	−	0.00819901i
$404$		0			0
$405$	11.7951	−	11.7951i	0.586104	−	0.586104i
$406$		0			0
$407$			2.13939i			0.106046i
$408$		0			0
$409$	−22.8759	−	13.2074i	−1.13114	−	0.653065i	−0.186920	−	0.982375i	$-0.559851\pi$
$409$	−22.8759	−	13.2074i	−1.13114	−	0.653065i	−0.944222	+	0.329310i	$0.893184\pi$
$410$		0			0
$411$	2.80316	+	0.751104i	0.138270	+	0.0370492i
$412$		0			0
$413$	−20.4503	−	12.1008i	−1.00630	−	0.595442i
$414$		0			0
$415$	1.68288	+	2.91483i	0.0826092	+	0.143083i
$416$		0			0
$417$	−3.34915	+	5.80091i	−0.164009	+	0.284072i
$418$		0			0
$419$	15.6893	+	15.6893i	0.766471	+	0.766471i	0.977483	−	0.211012i	$-0.0676759\pi$
$419$	15.6893	+	15.6893i	0.766471	+	0.766471i	−0.211012	+	0.977483i	$0.567676\pi$
$420$		0			0
$421$	−25.7068	+	25.7068i	−1.25287	+	1.25287i	−0.298444	+	0.954427i	$0.596468\pi$
$421$	−25.7068	+	25.7068i	−1.25287	+	1.25287i	−0.954427	+	0.298444i	$0.903532\pi$
$422$		0			0
$423$	0.425327	+	0.245563i	0.0206801	+	0.0119397i
$424$		0			0
$425$	1.54546	−	0.892270i	0.0749657	−	0.0432815i
$426$		0			0
$427$	13.6776	+	24.2872i	0.661905	+	1.17534i
$428$		0			0
$429$	−4.36340	+	16.2844i	−0.210667	+	0.786220i
$430$		0			0
$431$	12.3981	−	21.4741i	0.597194	−	1.03437i	−0.396039	−	0.918234i	$-0.629616\pi$
$431$	12.3981	−	21.4741i	0.597194	−	1.03437i	0.993233	−	0.116137i	$-0.0370510\pi$
$432$		0			0
$433$	5.22863			0.251272			0.125636	−	0.992076i	$-0.459903\pi$
$433$	5.22863			0.251272			0.125636	+	0.992076i	$0.459903\pi$
$434$		0			0
$435$	17.1000	+	17.1000i	0.819881	+	0.819881i
$436$		0			0
$437$	−1.74371	−	6.50762i	−0.0834131	−	0.311302i
$438$		0			0
$439$	−19.1771	+	11.0719i	−0.915273	+	0.528433i	−0.882124	−	0.471017i	$-0.843887\pi$
$439$	−19.1771	+	11.0719i	−0.915273	+	0.528433i	−0.0331491	+	0.999450i	$0.510554\pi$
$440$		0			0
$441$	0.765272	+	1.39358i	0.0364415	+	0.0663610i
$442$		0			0
$443$	−21.8067	−	5.84309i	−1.03607	−	0.277614i	−0.299585	−	0.954070i	$-0.596848\pi$
$443$	−21.8067	−	5.84309i	−1.03607	−	0.277614i	−0.736483	+	0.676456i	$0.763515\pi$
$444$		0			0
$445$	−24.8614	+	6.66159i	−1.17854	+	0.315790i
$446$		0			0
$447$	30.6599			1.45017
$448$		0			0
$449$	−36.3678			−1.71630			−0.858152	−	0.513396i	$-0.828387\pi$
$449$	−36.3678			−1.71630			−0.858152	+	0.513396i	$0.828387\pi$
$450$		0			0
$451$	−44.2871	+	11.8667i	−2.08540	+	0.558781i
$452$		0			0
$453$	−10.2603	−	2.74924i	−0.482072	−	0.129171i
$454$		0			0
$455$	−8.24456	−	2.30402i	−0.386511	−	0.108014i
$456$		0			0
$457$	21.5807	−	12.4596i	1.00950	−	0.582837i	0.0984570	−	0.995141i	$-0.468609\pi$
$457$	21.5807	−	12.4596i	1.00950	−	0.582837i	0.911046	+	0.412304i	$0.135276\pi$
$458$		0			0
$459$	−2.67261	−	9.97431i	−0.124747	−	0.465561i
$460$		0			0
$461$	1.60588	+	1.60588i	0.0747933	+	0.0747933i	0.743514	−	0.668721i	$-0.233158\pi$
$461$	1.60588	+	1.60588i	0.0747933	+	0.0747933i	−0.668721	+	0.743514i	$0.733158\pi$
$462$		0			0
$463$	−14.8176			−0.688634			−0.344317	−	0.938853i	$-0.611890\pi$
$463$	−14.8176			−0.688634			−0.344317	+	0.938853i	$0.611890\pi$
$464$		0			0
$465$	0.666254	−	1.15399i	0.0308968	−	0.0535148i
$466$		0			0
$467$	3.21315	−	11.9916i	0.148687	−	0.554907i	−0.850877	−	0.525365i	$-0.823929\pi$
$467$	3.21315	−	11.9916i	0.148687	−	0.554907i	0.999564	−	0.0295414i	$-0.00940469\pi$
$468$		0			0
$469$	10.9837	−	18.5625i	0.507181	−	0.857135i
$470$		0			0
$471$	−26.3028	+	15.1859i	−1.21197	+	0.699730i
$472$		0			0
$473$	13.5759	+	7.83804i	0.624220	+	0.360393i
$474$		0			0
$475$	4.14387	−	4.14387i	0.190134	−	0.190134i
$476$		0			0
$477$	0.0691218	+	0.0691218i	0.00316487	+	0.00316487i
$478$		0			0
$479$	1.02709	−	1.77897i	0.0469288	−	0.0812831i	−0.841607	−	0.540091i	$-0.818390\pi$
$479$	1.02709	−	1.77897i	0.0469288	−	0.0812831i	0.888536	+	0.458808i	$0.151723\pi$
$480$		0			0
$481$	0.271679	+	0.470563i	0.0123875	+	0.0214558i
$482$		0			0
$483$	0.0503645	−	4.70344i	0.00229166	−	0.214014i
$484$		0			0
$485$	4.31018	+	1.15491i	0.195715	+	0.0524417i
$486$		0			0
$487$	−35.4045	−	20.4408i	−1.60433	−	0.926261i	−0.990607	−	0.136740i	$-0.956338\pi$
$487$	−35.4045	−	20.4408i	−1.60433	−	0.926261i	−0.613724	−	0.789521i	$-0.710329\pi$
$488$		0			0
$489$			19.1302i			0.865098i
$490$		0			0
$491$	0.278015	−	0.278015i	0.0125466	−	0.0125466i	−0.700806	−	0.713352i	$-0.747176\pi$
$491$	0.278015	−	0.278015i	0.0125466	−	0.0125466i	0.713352	+	0.700806i	$0.247176\pi$
$492$		0			0
$493$	13.3592	−	3.57958i	0.601667	−	0.161216i
$494$		0			0
$495$	−1.44673	−	2.50580i	−0.0650255	−	0.112628i
$496$		0			0
$497$	−5.16309	−	5.27486i	−0.231596	−	0.236610i
$498$		0			0
$499$	3.19039	−	11.9067i	0.142822	−	0.533018i	−0.857021	−	0.515281i	$-0.827687\pi$
$499$	3.19039	−	11.9067i	0.142822	−	0.533018i	0.999843	−	0.0177363i	$-0.00564595\pi$
$500$		0			0
$501$	9.33912	+	34.8541i	0.417241	+	1.55717i
$502$		0			0
$503$			0.367839i			0.0164011i	0.999966	+	0.00820057i	$0.00261035\pi$
$503$			0.367839i			0.0164011i	−0.999966	+	0.00820057i	$0.997390\pi$
$504$		0			0
$505$			14.5186i			0.646068i
$506$		0			0
$507$	−4.49459	−	16.7740i	−0.199612	−	0.744960i
$508$		0			0
$509$	2.09820	−	7.83060i	0.0930012	−	0.347085i	−0.903708	−	0.428150i	$-0.859165\pi$
$509$	2.09820	−	7.83060i	0.0930012	−	0.347085i	0.996709	+	0.0810649i	$0.0258321\pi$
$510$		0			0
$511$	−6.08808	+	1.56162i	−0.269321	+	0.0690822i
$512$		0			0
$513$	−16.9552	−	29.3673i	−0.748591	−	1.29660i
$514$		0			0
$515$	−34.0855	+	9.13319i	−1.50199	+	0.402457i
$516$		0			0
$517$	−9.65374	+	9.65374i	−0.424571	+	0.424571i
$518$		0			0
$519$			21.3072i			0.935282i
$520$		0			0
$521$	−11.5215	−	6.65193i	−0.504766	−	0.291427i	0.225914	−	0.974147i	$-0.427463\pi$
$521$	−11.5215	−	6.65193i	−0.504766	−	0.291427i	−0.730679	+	0.682721i	$0.760797\pi$
$522$		0			0
$523$	27.4536	+	7.35616i	1.20046	+	0.321663i	0.803013	−	0.595962i	$-0.203229\pi$
$523$	27.4536	+	7.35616i	1.20046	+	0.321663i	0.397448	+	0.917625i	$0.369896\pi$
$524$		0			0
$525$	3.56504	−	2.00769i	0.155591	−	0.0876229i
$526$		0			0
$527$	−0.381036	−	0.659973i	−0.0165982	−	0.0287489i
$528$		0			0
$529$	−10.9301	+	18.9314i	−0.475220	+	0.823106i
$530$		0			0
$531$	−1.44241	−	1.44241i	−0.0625954	−	0.0625954i
$532$		0			0
$533$	−8.23408	+	8.23408i	−0.356657	+	0.356657i
$534$		0			0
$535$	5.26176	+	3.03788i	0.227486	+	0.131339i
$536$		0			0
$537$	−4.56759	+	2.63710i	−0.197106	+	0.113799i
$538$		0			0
$539$	−42.9251	+	10.5220i	−1.84892	+	0.453213i
$540$		0			0
$541$	4.75802	−	17.7572i	0.204563	−	0.763441i	−0.785019	−	0.619472i	$-0.787347\pi$
$541$	4.75802	−	17.7572i	0.204563	−	0.763441i	0.989582	−	0.143969i	$-0.0459866\pi$
$542$		0			0
$543$	16.9279	−	29.3199i	0.726445	−	1.25824i
$544$		0			0
$545$	14.3413			0.614312
$546$		0			0
$547$	22.9801	+	22.9801i	0.982558	+	0.982558i	0.999850	−	0.0172930i	$-0.00550479\pi$
$547$	22.9801	+	22.9801i	0.982558	+	0.982558i	−0.0172930	+	0.999850i	$0.505505\pi$
$548$		0			0
$549$	0.619309	+	2.31129i	0.0264315	+	0.0986436i
$550$		0			0
$551$	39.3334	−	22.7091i	1.67566	−	0.967442i
$552$		0			0
$553$	−26.0331	−	7.27518i	−1.10704	−	0.309372i
$554$		0			0
$555$	1.09972	+	0.294670i	0.0466806	+	0.0125080i
$556$		0			0
$557$	−4.50327	+	1.20665i	−0.190810	+	0.0511273i	−0.352958	−	0.935639i	$-0.614824\pi$
$557$	−4.50327	+	1.20665i	−0.190810	+	0.0511273i	0.162149	+	0.986766i	$0.448158\pi$
$558$		0			0
$559$	3.98138			0.168394
$560$		0			0
$561$	20.2026			0.852954
$562$		0			0
$563$	4.04301	−	1.08332i	0.170393	−	0.0456566i	−0.172614	−	0.984990i	$-0.555221\pi$
$563$	4.04301	−	1.08332i	0.170393	−	0.0456566i	0.343007	+	0.939333i	$0.388555\pi$
$564$		0			0
$565$	11.6264	+	3.11530i	0.489128	+	0.131061i
$566$		0			0
$567$	−5.43448	−	21.1866i	−0.228227	−	0.889755i
$568$		0			0
$569$	3.88173	−	2.24111i	0.162730	−	0.0939524i	−0.416423	−	0.909171i	$-0.636717\pi$
$569$	3.88173	−	2.24111i	0.162730	−	0.0939524i	0.579154	+	0.815218i	$0.303383\pi$
$570$		0			0
$571$	0.126176	+	0.470896i	0.00528031	+	0.0197064i	0.968516	−	0.248952i	$-0.0800863\pi$
$571$	0.126176	+	0.470896i	0.00528031	+	0.0197064i	−0.963235	+	0.268659i	$0.913420\pi$
$572$		0			0
$573$	−14.4143	−	14.4143i	−0.602167	−	0.602167i
$574$		0			0
$575$	0.991504			0.0413486
$576$		0			0
$577$	5.31982	−	9.21420i	0.221467	−	0.383592i	−0.733787	−	0.679380i	$-0.762249\pi$
$577$	5.31982	−	9.21420i	0.221467	−	0.383592i	0.955254	+	0.295788i	$0.0955821\pi$
$578$		0			0
$579$	0.938680	−	3.50320i	0.0390102	−	0.145588i
$580$		0			0
$581$	4.41305	+	0.0472550i	0.183084	+	0.00196047i
$582$		0			0
$583$	−2.35331	+	1.35868i	−0.0974641	+	0.0562709i
$584$		0			0
$585$	−0.636420	−	0.367437i	−0.0263127	−	0.0151917i
$586$		0			0
$587$	13.2861	−	13.2861i	0.548376	−	0.548376i	−0.377595	−	0.925971i	$-0.623249\pi$
$587$	13.2861	−	13.2861i	0.548376	−	0.548376i	0.925971	+	0.377595i	$0.123249\pi$
$588$		0			0
$589$	−1.76960	−	1.76960i	−0.0729151	−	0.0729151i
$590$		0			0
$591$	−11.7497	+	20.3511i	−0.483319	+	0.837133i
$592$		0			0
$593$	0.198497	+	0.343806i	0.00815128	+	0.0141184i	0.870072	−	0.492924i	$-0.164072\pi$
$593$	0.198497	+	0.343806i	0.00815128	+	0.0141184i	−0.861921	+	0.507043i	$0.830739\pi$
$594$		0			0
$595$	−0.109840	+	10.2577i	−0.00450298	+	0.420524i
$596$		0			0
$597$	−16.9806	−	4.54994i	−0.694970	−	0.186217i
$598$		0			0
$599$	11.9718	+	6.91190i	0.489153	+	0.282412i	0.724223	−	0.689566i	$-0.242199\pi$
$599$	11.9718	+	6.91190i	0.489153	+	0.282412i	−0.235070	+	0.971978i	$0.575532\pi$
$600$		0			0
$601$		−	8.73396i		−	0.356266i	−0.984006	−	0.178133i	$-0.942994\pi$
$601$		−	8.73396i		−	0.356266i	0.984006	−	0.178133i	$-0.0570057\pi$
$602$		0			0
$603$	1.30926	−	1.30926i	0.0533170	−	0.0533170i
$604$		0			0
$605$	56.2535	−	15.0731i	2.28703	−	0.612807i
$606$		0			0
$607$	14.3937	+	24.9305i	0.584220	+	1.01190i	0.994972	+	0.100152i	$0.0319330\pi$
$607$	14.3937	+	24.9305i	0.584220	+	1.01190i	−0.410752	+	0.911747i	$0.634734\pi$
$608$		0			0
$609$	30.7153	−	7.87864i	1.24465	−	0.319259i
$610$		0			0
$611$	−0.897436	+	3.34928i	−0.0363064	+	0.135497i
$612$		0			0
$613$	−9.13486	−	34.0918i	−0.368954	−	1.37695i	−0.861981	−	0.506940i	$-0.830777\pi$
$613$	−9.13486	−	34.0918i	−0.368954	−	1.37695i	0.493028	−	0.870014i	$-0.335890\pi$
$614$		0			0
$615$			24.3996i			0.983886i
$616$		0			0
$617$			33.4612i			1.34710i	0.739143	+	0.673548i	$0.235231\pi$
$617$			33.4612i			1.34710i	−0.739143	+	0.673548i	$0.764769\pi$
$618$		0			0
$619$	2.41362	+	9.00777i	0.0970118	+	0.362053i	0.997317	−	0.0732067i	$-0.0233233\pi$
$619$	2.41362	+	9.00777i	0.0970118	+	0.362053i	−0.900305	+	0.435260i	$0.856657\pi$
$620$		0			0
$621$	1.48492	−	5.54180i	0.0595878	−	0.222385i
$622$		0			0
$623$	−9.08349	+	32.5038i	−0.363922	+	1.30224i
$624$		0			0
$625$	−9.74706	−	16.8824i	−0.389882	−	0.675296i
$626$		0			0
$627$	64.0834	−	17.1711i	2.55924	−	0.685747i
$628$		0			0
$629$	0.460415	−	0.460415i	0.0183580	−	0.0183580i
$630$		0			0
$631$			22.2587i			0.886105i	0.896496	+	0.443053i	$0.146104\pi$
$631$			22.2587i			0.886105i	−0.896496	+	0.443053i	$0.853896\pi$
$632$		0			0
$633$	−10.6128	−	6.12730i	−0.421821	−	0.243538i
$634$		0			0
$635$	−12.4988	−	3.34905i	−0.496001	−	0.132903i
$636$		0			0
$637$	−8.10527	+	7.76534i	−0.321142	+	0.307674i
$638$		0			0
$639$	−0.316819	−	0.548747i	−0.0125332	−	0.0217081i
$640$		0			0
$641$	4.13758	−	7.16649i	0.163424	−	0.283059i	−0.772670	−	0.634808i	$-0.781079\pi$
$641$	4.13758	−	7.16649i	0.163424	−	0.283059i	0.936095	+	0.351748i	$0.114413\pi$
$642$		0			0
$643$	−4.19175	−	4.19175i	−0.165307	−	0.165307i	0.619606	−	0.784913i	$-0.287292\pi$
$643$	−4.19175	−	4.19175i	−0.165307	−	0.165307i	−0.784913	+	0.619606i	$0.787292\pi$
$644$		0			0
$645$	5.89890	−	5.89890i	0.232269	−	0.232269i
$646$		0			0
$647$	18.2428	+	10.5325i	0.717199	+	0.414075i	0.813721	−	0.581256i	$-0.197439\pi$
$647$	18.2428	+	10.5325i	0.717199	+	0.414075i	−0.0965221	+	0.995331i	$0.530772\pi$
$648$		0			0
$649$	49.1081	−	28.3526i	1.92766	−	1.11294i
$650$		0			0
$651$	−0.857366	−	1.52242i	−0.0336028	−	0.0596683i
$652$		0			0
$653$	−4.43173	+	16.5394i	−0.173427	+	0.647239i	0.823387	+	0.567480i	$0.192082\pi$
$653$	−4.43173	+	16.5394i	−0.173427	+	0.647239i	−0.996814	+	0.0797585i	$0.974585\pi$
$654$		0			0
$655$	−15.0969	+	26.1485i	−0.589883	+	1.02171i
$656$		0			0
$657$	−0.539552			−0.0210499
$658$		0			0
$659$	−19.9513	−	19.9513i	−0.777192	−	0.777192i	0.202161	−	0.979352i	$-0.435204\pi$
$659$	−19.9513	−	19.9513i	−0.777192	−	0.777192i	−0.979352	+	0.202161i	$0.935204\pi$
$660$		0			0
$661$	5.55822	+	20.7436i	0.216190	+	0.806831i	0.985744	+	0.168250i	$0.0538117\pi$
$661$	5.55822	+	20.7436i	0.216190	+	0.806831i	−0.769555	+	0.638581i	$0.779522\pi$
$662$		0			0
$663$	4.44359	−	2.56551i	0.172575	−	0.0996361i
$664$		0			0
$665$	8.37005	+	32.6311i	0.324577	+	1.26538i
$666$		0			0
$667$	7.42246	+	1.98884i	0.287399	+	0.0770083i
$668$		0			0
$669$	−36.0114	+	9.64922i	−1.39228	+	0.373060i
$670$		0			0
$671$	−66.5165			−2.56784
$672$		0			0
$673$	21.0339			0.810796			0.405398	−	0.914140i	$-0.367133\pi$
$673$	21.0339			0.810796			0.405398	+	0.914140i	$0.367133\pi$
$674$		0			0
$675$	4.82051	−	1.29165i	0.185542	−	0.0497157i
$676$		0			0
$677$	−6.02033	−	1.61314i	−0.231380	−	0.0619982i	0.141266	−	0.989972i	$-0.454883\pi$
$677$	−6.02033	−	1.61314i	−0.231380	−	0.0619982i	−0.372646	+	0.927974i	$0.621549\pi$
$678$		0			0
$679$	4.18137	−	4.09277i	0.160466	−	0.157066i
$680$		0			0
$681$	26.8367	−	15.4942i	1.02838	−	0.593737i
$682$		0			0
$683$	5.78001	+	21.5713i	0.221166	+	0.825402i	0.983904	+	0.178695i	$0.0571876\pi$
$683$	5.78001	+	21.5713i	0.221166	+	0.825402i	−0.762739	+	0.646707i	$0.776146\pi$
$684$		0			0
$685$	−2.48651	−	2.48651i	−0.0950048	−	0.0950048i
$686$		0			0
$687$	−14.0057			−0.534351
$688$		0			0
$689$	−0.345076	+	0.597689i	−0.0131463	+	0.0227701i
$690$		0			0
$691$	−9.94413	+	37.1120i	−0.378292	+	1.41181i	0.470182	+	0.882570i	$0.344188\pi$
$691$	−9.94413	+	37.1120i	−0.378292	+	1.41181i	−0.848474	+	0.529237i	$0.822478\pi$
$692$		0			0
$693$	−3.79379	−	0.0406240i	−0.144114	−	0.00154318i
$694$		0			0
$695$	7.02907	−	4.05824i	0.266628	−	0.153938i
$696$		0			0
$697$	12.0848	+	6.97715i	0.457743	+	0.264278i
$698$		0			0
$699$	20.2963	−	20.2963i	0.767676	−	0.767676i
$700$		0			0
$701$	−1.40129	−	1.40129i	−0.0529259	−	0.0529259i	0.680148	−	0.733074i	$-0.261915\pi$
$701$	−1.40129	−	1.40129i	−0.0529259	−	0.0529259i	−0.733074	+	0.680148i	$0.761915\pi$
$702$		0			0
$703$	1.06913	−	1.85178i	0.0403229	−	0.0698413i
$704$		0			0
$705$	3.63270	+	6.29202i	0.136815	+	0.236971i
$706$		0			0
$707$	16.3839	+	9.69463i	0.616181	+	0.364604i
$708$		0			0
$709$	8.42034	+	2.25622i	0.316232	+	0.0847342i	0.413444	−	0.910530i	$-0.364326\pi$
$709$	8.42034	+	2.25622i	0.316232	+	0.0847342i	−0.0972117	+	0.995264i	$0.530992\pi$
$710$		0			0
$711$	−2.00956	−	1.16022i	−0.0753645	−	0.0435117i
$712$		0			0
$713$		−	0.423412i		−	0.0158569i
$714$		0			0
$715$	14.4450	−	14.4450i	0.540211	−	0.540211i
$716$		0			0
$717$	−0.921129	+	0.246816i	−0.0344002	+	0.00921750i
$718$		0			0
$719$	−13.3330	−	23.0934i	−0.497236	−	0.861239i	0.502758	−	0.864427i	$-0.332319\pi$
$719$	−13.3330	−	23.0934i	−0.497236	−	0.861239i	−0.999995	+	0.00318810i	$0.998985\pi$
$720$		0			0
$721$	−12.4537	+	44.5635i	−0.463799	+	1.65963i
$722$		0			0
$723$	5.07974	−	18.9578i	0.188917	−	0.705050i
$724$		0			0
$725$	1.72999	+	6.45640i	0.0642501	+	0.239785i
$726$		0			0
$727$		−	37.7224i		−	1.39905i	−0.714610	−	0.699523i	$-0.753396\pi$
$727$		−	37.7224i		−	1.39905i	0.714610	−	0.699523i	$-0.246604\pi$
$728$		0			0
$729$		−	28.7229i		−	1.06381i
$730$		0			0
$731$	−1.23483	−	4.60846i	−0.0456719	−	0.170450i
$732$		0			0
$733$	−5.88050	+	21.9463i	−0.217201	+	0.810606i	0.768179	+	0.640235i	$0.221163\pi$
$733$	−5.88050	+	21.9463i	−0.217201	+	0.810606i	−0.985380	+	0.170371i	$0.945504\pi$
$734$		0			0
$735$	−0.503639	+	23.5142i	−0.0185770	+	0.867336i
$736$		0			0
$737$	25.7352	+	44.5747i	0.947969	+	1.64193i
$738$		0			0
$739$	−25.3304	+	6.78727i	−0.931795	+	0.249674i	−0.692620	−	0.721303i	$-0.743544\pi$
$739$	−25.3304	+	6.78727i	−0.931795	+	0.249674i	−0.239175	+	0.970977i	$0.576877\pi$
$740$		0			0
$741$	11.9147	−	11.9147i	0.437697	−	0.437697i
$742$		0			0
$743$		−	20.7110i		−	0.759812i	−0.925025	−	0.379906i	$-0.875956\pi$
$743$		−	20.7110i		−	0.759812i	0.925025	−	0.379906i	$-0.124044\pi$
$744$		0			0
$745$	−32.1739	−	18.5756i	−1.17876	−	0.680558i
$746$		0			0
$747$	0.365952	+	0.0980566i	0.0133895	+	0.00358770i
$748$		0			0
$749$	6.94168	−	3.90928i	0.253643	−	0.142842i
$750$		0			0
$751$	7.73865	+	13.4037i	0.282387	+	0.489109i	0.971972	−	0.235096i	$-0.0755403\pi$
$751$	7.73865	+	13.4037i	0.282387	+	0.489109i	−0.689585	+	0.724205i	$0.742207\pi$
$752$		0			0
$753$	6.56486	−	11.3707i	0.239237	−	0.414370i
$754$		0			0
$755$	9.10132	+	9.10132i	0.331231	+	0.331231i
$756$		0			0
$757$	−18.4631	+	18.4631i	−0.671051	+	0.671051i	−0.957958	−	0.286907i	$-0.907373\pi$
$757$	−18.4631	+	18.4631i	−0.671051	+	0.671051i	0.286907	+	0.957958i	$0.407373\pi$
$758$		0			0
$759$	9.72088	+	5.61235i	0.352846	+	0.203715i
$760$		0			0
$761$	−11.1420	+	6.43283i	−0.403897	+	0.233190i	−0.688164	−	0.725555i	$-0.741583\pi$
$761$	−11.1420	+	6.43283i	−0.403897	+	0.233190i	0.284267	+	0.958745i	$0.408250\pi$
$762$		0			0
$763$	9.57624	−	16.1838i	0.346683	−	0.585894i
$764$		0			0
$765$	−0.227923	+	0.850618i	−0.00824056	+	0.0307542i
$766$		0			0
$767$	7.20094	−	12.4724i	0.260011	−	0.450352i
$768$		0			0
$769$	−16.5676			−0.597443			−0.298722	−	0.954340i	$-0.596560\pi$
$769$	−16.5676			−0.597443			−0.298722	+	0.954340i	$0.596560\pi$
$770$		0			0
$771$	−34.2238	−	34.2238i	−1.23254	−	1.23254i
$772$		0			0
$773$	12.6807	+	47.3250i	0.456093	+	1.70216i	0.684856	+	0.728679i	$0.259865\pi$
$773$	12.6807	+	47.3250i	0.456093	+	1.70216i	−0.228763	+	0.973482i	$0.573468\pi$
$774$		0			0
$775$	0.318960	−	0.184152i	0.0114574	−	0.00661492i
$776$		0			0
$777$	1.06686	−	1.04425i	0.0382733	−	0.0374623i
$778$		0			0
$779$	44.2635	+	11.8604i	1.58591	+	0.424942i
$780$		0			0
$781$	17.0139	−	4.55886i	0.608805	−	0.163129i
$782$		0			0
$783$	38.6776			1.38222
$784$		0			0
$785$	36.8021			1.31352
$786$		0			0
$787$	5.05999	−	1.35582i	0.180369	−	0.0483298i	−0.167504	−	0.985871i	$-0.553571\pi$
$787$	5.05999	−	1.35582i	0.180369	−	0.0483298i	0.347873	+	0.937542i	$0.386904\pi$
$788$		0			0
$789$	−28.4427	−	7.62121i	−1.01259	−	0.271322i
$790$		0			0
$791$	11.2790	−	11.0400i	0.401035	−	0.392537i
$792$		0			0
$793$	−14.6304	+	8.44687i	−0.519541	+	0.299957i
$794$		0			0
$795$	0.374277	+	1.39682i	0.0132742	+	0.0495401i
$796$		0			0
$797$	−20.4204	−	20.4204i	−0.723329	−	0.723329i	0.245953	−	0.969282i	$-0.420899\pi$
$797$	−20.4204	−	20.4204i	−0.723329	−	0.723329i	−0.969282	+	0.245953i	$0.920899\pi$
$798$		0			0
$799$	4.15514			0.146998
$800$		0			0
$801$	−1.44860	+	2.50906i	−0.0511839	+	0.0886532i
$802$		0			0
$803$	3.88193	−	14.4876i	0.136990	−	0.511255i
$804$		0			0
$805$	−2.90248	+	4.90518i	−0.102299	+	0.172885i
$806$		0			0
$807$	−21.5389	+	12.4355i	−0.758205	+	0.437750i
$808$		0			0
$809$	−33.6734	−	19.4413i	−1.18389	−	0.683521i	−0.226981	−	0.973899i	$-0.572886\pi$
$809$	−33.6734	−	19.4413i	−1.18389	−	0.683521i	−0.956912	+	0.290378i	$0.906219\pi$
$810$		0			0
$811$	−12.4718	+	12.4718i	−0.437945	+	0.437945i	−0.891320	−	0.453375i	$-0.850220\pi$
$811$	−12.4718	+	12.4718i	−0.437945	+	0.437945i	0.453375	+	0.891320i	$0.350220\pi$
$812$		0			0
$813$	16.3238	+	16.3238i	0.572501	+	0.572501i
$814$		0			0
$815$	11.5902	−	20.0749i	0.405988	−	0.703192i
$816$		0			0
$817$	−7.83387	−	13.5687i	−0.274072	−	0.474707i
$818$		0			0
$819$	−0.839609	+	0.472835i	−0.0293383	+	0.0165222i
$820$		0			0
$821$	18.4979	+	4.95650i	0.645581	+	0.172983i	0.566730	−	0.823903i	$-0.308208\pi$
$821$	18.4979	+	4.95650i	0.645581	+	0.172983i	0.0788511	+	0.996886i	$0.474875\pi$
$822$		0			0
$823$	8.96748	+	5.17738i	0.312587	+	0.180472i	0.648083	−	0.761569i	$-0.275571\pi$
$823$	8.96748	+	5.17738i	0.312587	+	0.180472i	−0.335497	+	0.942041i	$0.608904\pi$
$824$		0			0
$825$			9.76376i			0.339931i
$826$		0			0
$827$	9.65786	−	9.65786i	0.335837	−	0.335837i	−0.518961	−	0.854798i	$-0.673681\pi$
$827$	9.65786	−	9.65786i	0.335837	−	0.335837i	0.854798	+	0.518961i	$0.173681\pi$
$828$		0			0
$829$	−25.6983	+	6.88583i	−0.892538	+	0.239155i	−0.675809	−	0.737077i	$-0.736205\pi$
$829$	−25.6983	+	6.88583i	−0.892538	+	0.239155i	−0.216729	+	0.976232i	$0.569539\pi$
$830$		0			0
$831$	1.92201	+	3.32902i	0.0666739	+	0.115483i
$832$		0			0
$833$	11.5023	+	6.97343i	0.398530	+	0.241615i
$834$		0			0
$835$	11.3164	−	42.2334i	0.391620	−	1.46155i
$836$		0			0
$837$	−0.551588	−	2.05855i	−0.0190657	−	0.0711540i
$838$		0			0
$839$		−	46.4429i		−	1.60339i	−0.597736	−	0.801693i	$-0.703933\pi$
$839$		−	46.4429i		−	1.60339i	0.597736	−	0.801693i	$-0.296067\pi$
$840$		0			0
$841$			22.8031i			0.786315i
$842$		0			0
$843$	0.293220	+	1.09431i	0.0100990	+	0.0376902i
$844$		0			0
$845$	−5.44618	+	20.3254i	−0.187354	+	0.699216i
$846$		0			0
$847$	20.5531	−	73.5459i	0.706211	−	2.52707i
$848$		0			0
$849$	−0.316904	−	0.548894i	−0.0108761	−	0.0188380i
$850$		0			0
$851$	0.349443	−	0.0936330i	0.0119788	−	0.00320970i
$852$		0			0
$853$	31.3013	−	31.3013i	1.07174	−	1.07174i	0.0745177	−	0.997220i	$-0.476258\pi$
$853$	31.3013	−	31.3013i	1.07174	−	1.07174i	0.997220	−	0.0745177i	$-0.0237417\pi$
$854$		0			0
$855$			2.89191i			0.0989014i
$856$		0			0
$857$	22.8393	+	13.1863i	0.780175	+	0.450434i	0.836492	−	0.547979i	$-0.184602\pi$
$857$	22.8393	+	13.1863i	0.780175	+	0.450434i	−0.0563171	+	0.998413i	$0.517936\pi$
$858$		0			0
$859$	2.91867	+	0.782055i	0.0995837	+	0.0266834i	0.308267	−	0.951300i	$-0.400251\pi$
$859$	2.91867	+	0.782055i	0.0995837	+	0.0266834i	−0.208683	+	0.977983i	$0.566918\pi$
$860$		0			0
$861$	27.5344	+	16.2926i	0.938371	+	0.555250i
$862$		0			0
$863$	−3.50456	−	6.07008i	−0.119297	−	0.206628i	0.800192	−	0.599743i	$-0.204731\pi$
$863$	−3.50456	−	6.07008i	−0.119297	−	0.206628i	−0.919489	+	0.393115i	$0.871397\pi$
$864$		0			0
$865$	12.9092	−	22.3594i	0.438925	−	0.760241i
$866$		0			0
$867$	15.6692	+	15.6692i	0.532155	+	0.532155i
$868$		0			0
$869$	45.6115	−	45.6115i	1.54726	−	1.54726i
$870$		0			0
$871$	11.3210	+	6.53619i	0.383598	+	0.221470i
$872$		0			0
$873$	0.434991	−	0.251142i	0.0147222	−	0.00849987i
$874$		0			0
$875$	−31.6483	−	0.338890i	−1.06991	−	0.0114566i
$876$		0			0
$877$	−10.6267	+	39.6594i	−0.358838	+	1.33920i	0.516748	+	0.856138i	$0.327143\pi$
$877$	−10.6267	+	39.6594i	−0.358838	+	1.33920i	−0.875585	+	0.483063i	$0.839524\pi$
$878$		0			0
$879$	−8.82185	+	15.2799i	−0.297554	+	0.515378i
$880$		0			0
$881$	−13.6166			−0.458755			−0.229377	−	0.973338i	$-0.573669\pi$
$881$	−13.6166			−0.458755			−0.229377	+	0.973338i	$0.573669\pi$
$882$		0			0
$883$	−35.2238	−	35.2238i	−1.18537	−	1.18537i	−0.978332	−	0.207042i	$-0.933616\pi$
$883$	−35.2238	−	35.2238i	−1.18537	−	1.18537i	−0.207042	−	0.978332i	$-0.566384\pi$
$884$		0			0
$885$	−7.81030	−	29.1484i	−0.262540	−	0.979814i
$886$		0			0
$887$	−5.44911	+	3.14604i	−0.182963	+	0.105634i	−0.588684	−	0.808363i	$-0.700354\pi$
$887$	−5.44911	+	3.14604i	−0.182963	+	0.105634i	0.405721	+	0.913997i	$0.367020\pi$
$888$		0			0
$889$	−12.1253	+	11.8684i	−0.406670	+	0.398053i
$890$		0			0
$891$	50.4171	+	13.5092i	1.68904	+	0.452576i
$892$		0			0
$893$	13.1802	−	3.53163i	0.441060	−	0.118182i
$894$		0			0
$895$	6.39085			0.213623
$896$		0			0
$897$	2.85083			0.0951864
$898$		0			0
$899$	2.75714	−	0.738774i	0.0919559	−	0.0246395i
$900$		0			0
$901$	0.798852	+	0.214052i	0.0266136	+	0.00713110i
$902$		0			0
$903$	−2.71786	−	10.5957i	−0.0904447	−	0.352604i
$904$		0			0
$905$	−35.5276	+	20.5118i	−1.18098	+	0.681837i
$906$		0			0
$907$	−11.6035	−	43.3049i	−0.385289	−	1.43792i	−0.837711	−	0.546113i	$-0.816107\pi$
$907$	−11.6035	−	43.3049i	−0.385289	−	1.43792i	0.452423	−	0.891804i	$-0.350560\pi$
$908$		0			0
$909$	1.15560	+	1.15560i	0.0383288	+	0.0383288i
$910$		0			0
$911$	42.8973			1.42125			0.710625	−	0.703571i	$-0.248412\pi$
$911$	42.8973			1.42125			0.710625	+	0.703571i	$0.248412\pi$
$912$		0			0
$913$	−5.26585	+	9.12073i	−0.174274	+	0.301852i
$914$		0			0
$915$	−9.16166	+	34.1918i	−0.302875	+	1.13035i
$916$		0			0
$917$	19.4273	+	34.4970i	0.641547	+	1.13919i
$918$		0			0
$919$	26.2242	−	15.1405i	0.865056	−	0.499440i	−0.000646343	−	1.00000i	$-0.500206\pi$
$919$	26.2242	−	15.1405i	0.865056	−	0.499440i	0.865702	+	0.500560i	$0.166872\pi$
$920$		0			0
$921$	12.8074	+	7.39438i	0.422019	+	0.243653i
$922$		0			0
$923$	3.16330	−	3.16330i	0.104121	−	0.104121i
$924$		0			0
$925$	0.222515	+	0.222515i	0.00731626	+	0.00731626i
$926$		0			0
$927$	−1.98607	+	3.43997i	−0.0652311	+	0.112984i
$928$		0			0
$929$	6.93334	+	12.0089i	0.227475	+	0.393999i	0.957059	−	0.289892i	$-0.0936195\pi$
$929$	6.93334	+	12.0089i	0.227475	+	0.393999i	−0.729584	+	0.683891i	$0.760286\pi$
$930$		0			0
$931$	42.4126	+	12.3437i	1.39002	+	0.404548i
$932$		0			0
$933$	15.8925	+	4.25838i	0.520297	+	0.139413i
$934$		0			0
$935$	−21.2002	−	12.2399i	−0.693321	−	0.400289i
$936$		0			0
$937$			46.7544i			1.52740i	0.645572	+	0.763699i	$0.276619\pi$
$937$			46.7544i			1.52740i	−0.645572	+	0.763699i	$0.723381\pi$
$938$		0			0
$939$	−20.2222	+	20.2222i	−0.659927	+	0.659927i
$940$		0			0
$941$	−8.04407	+	2.15540i	−0.262229	+	0.0702641i	−0.387538	−	0.921854i	$-0.626674\pi$
$941$	−8.04407	+	2.15540i	−0.262229	+	0.0702641i	0.125309	+	0.992118i	$0.460008\pi$
$942$		0			0
$943$	3.87655	+	6.71439i	0.126238	+	0.218651i
$944$		0			0
$945$	−7.72123	+	27.6292i	−0.251172	+	0.898778i
$946$		0			0
$947$	−1.89988	+	7.09044i	−0.0617378	+	0.230408i	−0.989900	−	0.141767i	$-0.954722\pi$
$947$	−1.89988	+	7.09044i	−0.0617378	+	0.230408i	0.928162	+	0.372176i	$0.121388\pi$
$948$		0			0
$949$	−0.985926	−	3.67953i	−0.0320045	−	0.119442i
$950$		0			0
$951$		−	35.3776i		−	1.14720i
$952$		0			0
$953$		−	41.3553i		−	1.33963i	−0.742528	−	0.669815i	$-0.766373\pi$
$953$		−	41.3553i		−	1.33963i	0.742528	−	0.669815i	$-0.233627\pi$
$954$		0			0
$955$	6.39305	+	23.8592i	0.206874	+	0.772065i
$956$		0			0
$957$	−19.5850	+	73.0921i	−0.633093	+	2.36273i
$958$		0			0
$959$	−4.46633	+	1.14564i	−0.144225	+	0.0369945i
$960$		0			0
$961$	15.4214	+	26.7106i	0.497463	+	0.861632i
$962$		0			0
$963$	0.660606	−	0.177009i	0.0212877	−	0.00570403i
$964$		0			0
$965$	−3.10748	+	3.10748i	−0.100033	+	0.100033i
$966$		0			0
$967$			40.5984i			1.30556i	0.757549	+	0.652778i	$0.226397\pi$
$967$			40.5984i			1.30556i	−0.757549	+	0.652778i	$0.773603\pi$
$968$		0			0
$969$	−17.4866	−	10.0959i	−0.561752	−	0.324328i
$970$		0			0
$971$	−31.4132	−	8.41714i	−1.00810	−	0.270119i	−0.283263	−	0.959042i	$-0.591417\pi$
$971$	−31.4132	−	8.41714i	−1.00810	−	0.270119i	−0.724834	+	0.688924i	$0.758084\pi$
$972$		0			0
$973$	0.113955	−	10.6420i	0.00365323	−	0.341168i
$974$		0			0
$975$	1.23989	+	2.14755i	0.0397083	+	0.0687768i
$976$		0			0
$977$	8.34286	−	14.4503i	0.266912	−	0.462305i	−0.701151	−	0.713013i	$-0.747330\pi$
$977$	8.34286	−	14.4503i	0.266912	−	0.462305i	0.968063	+	0.250708i	$0.0806635\pi$
$978$		0			0
$979$	−56.9486	−	56.9486i	−1.82009	−	1.82009i
$980$		0			0
$981$	1.14148	−	1.14148i	0.0364448	−	0.0364448i
$982$		0			0
$983$	−10.1999	−	5.88892i	−0.325326	−	0.187827i	0.328438	−	0.944526i	$-0.393478\pi$
$983$	−10.1999	−	5.88892i	−0.325326	−	0.187827i	−0.653764	+	0.756698i	$0.726811\pi$
$984$		0			0
$985$	24.6599	−	14.2374i	0.785728	−	0.453640i
$986$		0			0
$987$	9.52612	+	0.102006i	0.303220	+	0.00324688i
$988$		0			0
$989$	0.686082	−	2.56049i	0.0218161	−	0.0814189i
$990$		0			0
$991$	15.8872	−	27.5175i	0.504675	−	0.874122i	−0.495311	−	0.868716i	$-0.664946\pi$
$991$	15.8872	−	27.5175i	0.504675	−	0.874122i	0.999985	−	0.00540613i	$-0.00172083\pi$
$992$		0			0
$993$	−40.2967			−1.27878
$994$		0			0
$995$	15.0625	+	15.0625i	0.477513	+	0.477513i
$996$		0			0
$997$	0.309461	+	1.15492i	0.00980073	+	0.0365768i	0.970653	−	0.240484i	$-0.0773062\pi$
$997$	0.309461	+	1.15492i	0.00980073	+	0.0365768i	−0.960852	+	0.277061i	$0.910640\pi$
$998$		0			0
$999$	1.57695	−	0.910453i	0.0498925	−	0.0288055i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.ba.f.417.9		48
4.3	odd	2		896.2.ba.e.417.4		48
7.2	even	3	inner	896.2.ba.f.289.4		48
8.3	odd	2		448.2.ba.c.81.9		48
8.5	even	2		112.2.w.c.109.2	yes	48
16.3	odd	4		448.2.ba.c.305.4		48
16.5	even	4	inner	896.2.ba.f.865.4		48
16.11	odd	4		896.2.ba.e.865.9		48
16.13	even	4		112.2.w.c.53.10	yes	48
28.23	odd	6		896.2.ba.e.289.9		48
56.5	odd	6		784.2.x.o.765.10		48
56.13	odd	2		784.2.x.o.557.2		48
56.37	even	6		112.2.w.c.93.10	yes	48
56.45	odd	6		784.2.m.k.589.6		24
56.51	odd	6		448.2.ba.c.401.4		48
56.53	even	6		784.2.m.j.589.6		24
112.13	odd	4		784.2.x.o.165.10		48
112.37	even	12	inner	896.2.ba.f.737.9		48
112.45	odd	12		784.2.m.k.197.6		24
112.51	odd	12		448.2.ba.c.177.9		48
112.61	odd	12		784.2.x.o.373.2		48
112.93	even	12		112.2.w.c.37.2	✓	48
112.107	odd	12		896.2.ba.e.737.4		48
112.109	even	12		784.2.m.j.197.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.w.c.37.2	✓	48	112.93	even	12
112.2.w.c.53.10	yes	48	16.13	even	4
112.2.w.c.93.10	yes	48	56.37	even	6
112.2.w.c.109.2	yes	48	8.5	even	2
448.2.ba.c.81.9		48	8.3	odd	2
448.2.ba.c.177.9		48	112.51	odd	12
448.2.ba.c.305.4		48	16.3	odd	4
448.2.ba.c.401.4		48	56.51	odd	6
784.2.m.j.197.6		24	112.109	even	12
784.2.m.j.589.6		24	56.53	even	6
784.2.m.k.197.6		24	112.45	odd	12
784.2.m.k.589.6		24	56.45	odd	6
784.2.x.o.165.10		48	112.13	odd	4
784.2.x.o.373.2		48	112.61	odd	12
784.2.x.o.557.2		48	56.13	odd	2
784.2.x.o.765.10		48	56.5	odd	6
896.2.ba.e.289.9		48	28.23	odd	6
896.2.ba.e.417.4		48	4.3	odd	2
896.2.ba.e.737.4		48	112.107	odd	12
896.2.ba.e.865.9		48	16.11	odd	4
896.2.ba.f.289.4		48	7.2	even	3	inner
896.2.ba.f.417.9		48	1.1	even	1	trivial
896.2.ba.f.737.9		48	112.37	even	12	inner
896.2.ba.f.865.4		48	16.5	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.60845 - 0.430984i) q^{3} +(-1.94900 - 0.522232i) q^{5} +(-1.89075 + 1.85069i) q^{7} +(-0.196696 + 0.113563i) q^{9} +(-1.63411 - 6.09856i) q^{11} +(-1.13388 - 1.13388i) q^{13} -3.35995 q^{15} +(-0.960789 + 1.66414i) q^{17} +(-1.63324 + 6.09532i) q^{19} +(-2.24357 + 3.79164i) q^{21} +(-0.924606 + 0.533821i) q^{23} +(-0.804265 - 0.464342i) q^{25} +(-3.79985 + 3.79985i) q^{27} +(-5.08936 - 5.08936i) q^{29} +(-0.198293 + 0.343454i) q^{31} +(-5.25677 - 9.10499i) q^{33} +(4.65156 - 2.61958i) q^{35} +(-0.327303 - 0.0877006i) q^{37} +(-2.31247 - 1.33510i) q^{39} -7.26189i q^{41} +(-1.75565 + 1.75565i) q^{43} +(0.442666 - 0.118612i) q^{45} +(-1.08118 - 1.87265i) q^{47} +(0.149895 - 6.99839i) q^{49} +(-0.828170 + 3.09077i) q^{51} +(-0.111394 - 0.415727i) q^{53} +12.7395i q^{55} +10.5079i q^{57} +(2.32453 + 8.67527i) q^{59} +(2.72673 - 10.1763i) q^{61} +(0.161735 - 0.578743i) q^{63} +(1.61777 + 2.80206i) q^{65} +(-7.87441 + 2.10994i) q^{67} +(-1.25712 + 1.25712i) q^{69} +2.78982i q^{71} +(2.05730 + 1.18779i) q^{73} +(-1.49375 - 0.400248i) q^{75} +(14.3762 + 8.50666i) q^{77} +(5.10829 + 8.84782i) q^{79} +(-4.13352 + 7.15947i) q^{81} +(-1.17951 - 1.17951i) q^{83} +(2.74164 - 2.74164i) q^{85} +(-10.3794 - 5.99257i) q^{87} +(11.0470 - 6.37800i) q^{89} +(4.24233 + 0.0454269i) q^{91} +(-0.170922 + 0.637891i) q^{93} +(6.36634 - 11.0268i) q^{95} -2.21148 q^{97} +(1.01399 + 1.01399i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{5} + 4 q^{11} + 24 q^{13} - 40 q^{15} + 8 q^{17} + 4 q^{19} + 8 q^{21} + 24 q^{27} - 24 q^{29} + 28 q^{31} + 16 q^{33} - 28 q^{35} + 24 q^{37} + 40 q^{43} + 28 q^{45} - 20 q^{47} - 24 q^{51}+ \cdots + 24 q^{99}+O(q^{100}) \) 48 * q - 4 * q^5 + 4 * q^11 + 24 * q^13 - 40 * q^15 + 8 * q^17 + 4 * q^19 + 8 * q^21 + 24 * q^27 - 24 * q^29 + 28 * q^31 + 16 * q^33 - 28 * q^35 + 24 * q^37 + 40 * q^43 + 28 * q^45 - 20 * q^47 - 24 * q^51 + 16 * q^53 + 20 * q^59 - 8 * q^61 - 16 * q^63 + 8 * q^65 - 48 * q^67 + 40 * q^69 + 4 * q^75 + 20 * q^77 - 36 * q^79 + 8 * q^83 - 64 * q^91 - 8 * q^93 - 4 * q^95 - 48 * q^97 + 24 * q^99

Introduction

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Database

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