LMFDB - Embedded newform 936.2.q.g.313.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(313,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.313"); S:= CuspForms(chi, 2); N := Newforms(S);

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

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

Newform invariants

comment:select newform

sage:traces = [22,0,0,0,-3,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			313.4
Character	$\chi$	$=$	936.313
Dual form			936.2.q.g.625.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.722210 - 1.57430i) q^{3} +(-1.89006 - 3.27368i) q^{5} +(-0.659907 + 1.14299i) q^{7} +(-1.95682 + 2.27395i) q^{9} +(-2.20538 + 3.81984i) q^{11} +(-0.500000 - 0.866025i) q^{13} +(-3.78872 + 5.33980i) q^{15} -3.06205 q^{17} +7.13223 q^{19} +(2.27600 + 0.213409i) q^{21} +(-1.08498 - 1.87925i) q^{23} +(-4.64465 + 8.04477i) q^{25} +(4.99311 + 1.43836i) q^{27} +(-4.17231 + 7.22665i) q^{29} +(-0.669313 - 1.15928i) q^{31} +(7.60631 + 0.713205i) q^{33} +4.98905 q^{35} +1.24930 q^{37} +(-1.00228 + 1.41260i) q^{39} +(-1.62494 - 2.81448i) q^{41} +(5.93250 - 10.2754i) q^{43} +(11.1427 + 2.10812i) q^{45} +(-0.203201 + 0.351955i) q^{47} +(2.62905 + 4.55364i) q^{49} +(2.21144 + 4.82058i) q^{51} +2.17588 q^{53} +16.6732 q^{55} +(-5.15097 - 11.2282i) q^{57} +(4.05223 + 7.01866i) q^{59} +(-4.39869 + 7.61875i) q^{61} +(-1.30778 - 3.73723i) q^{63} +(-1.89006 + 3.27368i) q^{65} +(4.69012 + 8.12353i) q^{67} +(-2.17491 + 3.06530i) q^{69} -9.45879 q^{71} -12.2720 q^{73} +(16.0193 + 1.50205i) q^{75} +(-2.91070 - 5.04147i) q^{77} +(-3.64033 + 6.30524i) q^{79} +(-1.34167 - 8.89943i) q^{81} +(-6.04966 + 10.4783i) q^{83} +(5.78746 + 10.0242i) q^{85} +(14.3902 + 1.34929i) q^{87} -5.47746 q^{89} +1.31981 q^{91} +(-1.34167 + 1.89094i) q^{93} +(-13.4803 - 23.3486i) q^{95} +(-6.70181 + 11.6079i) q^{97} +(-4.37056 - 12.4897i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 3 q^{5} - 4 q^{7} - 4 q^{9} + 5 q^{11} - 11 q^{13} + 5 q^{15} + 8 q^{17} + 10 q^{19} + 4 q^{21} + 9 q^{23} - 24 q^{25} - 12 q^{27} - 16 q^{29} - q^{31} + 9 q^{33} + 18 q^{37} + 3 q^{39} - 6 q^{41}+ \cdots - 109 q^{99}+O(q^{100}) $ 22 * q - 3 * q^5 - 4 * q^7 - 4 * q^9 + 5 * q^11 - 11 * q^13 + 5 * q^15 + 8 * q^17 + 10 * q^19 + 4 * q^21 + 9 * q^23 - 24 * q^25 - 12 * q^27 - 16 * q^29 - q^31 + 9 * q^33 + 18 * q^37 + 3 * q^39 - 6 * q^41 - 7 * q^43 - 21 * q^45 + 21 * q^47 - 27 * q^49 - 11 * q^51 + 32 * q^53 + 34 * q^55 + 2 * q^57 + 11 * q^59 - 2 * q^61 - 27 * q^63 - 3 * q^65 - 18 * q^67 + 7 * q^69 - 30 * q^71 + 18 * q^73 + 62 * q^75 - 9 * q^77 - 30 * q^79 + 4 * q^81 - 16 * q^83 - 32 * q^85 + 33 * q^87 + 26 * q^89 + 8 * q^91 + 20 * q^95 - 10 * q^97 - 109 * q^99

Character values

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

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.722210	−	1.57430i	−0.416968	−	0.908921i
$3$	−0.722210	−	1.57430i	−0.416968	−	0.908921i
$4$		0			0
$5$	−1.89006	−	3.27368i	−0.845260	−	1.46403i	−0.885395	−	0.464839i	$-0.846112\pi$
$5$	−1.89006	−	3.27368i	−0.845260	−	1.46403i	0.0401347	−	0.999194i	$-0.487221\pi$
$6$		0			0
$7$	−0.659907	+	1.14299i	−0.249421	+	0.432011i	−0.963365	−	0.268192i	$-0.913574\pi$
$7$	−0.659907	+	1.14299i	−0.249421	+	0.432011i	0.713944	+	0.700203i	$0.246907\pi$
$8$		0			0
$9$	−1.95682	+	2.27395i	−0.652275	+	0.757982i
$10$		0			0
$11$	−2.20538	+	3.81984i	−0.664948	+	1.15172i	0.314351	+	0.949307i	$0.398213\pi$
$11$	−2.20538	+	3.81984i	−0.664948	+	1.15172i	−0.979299	+	0.202417i	$0.935120\pi$
$12$		0			0
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i
$14$		0			0
$15$	−3.78872	+	5.33980i	−0.978244	+	1.37873i
$16$		0			0
$17$	−3.06205			−0.742656			−0.371328	−	0.928502i	$-0.621098\pi$
$17$	−3.06205			−0.742656			−0.371328	+	0.928502i	$0.621098\pi$
$18$		0			0
$19$	7.13223			1.63624			0.818122	−	0.575044i	$-0.195015\pi$
$19$	7.13223			1.63624			0.818122	+	0.575044i	$0.195015\pi$
$20$		0			0
$21$	2.27600	+	0.213409i	0.496664	+	0.0465697i
$22$		0			0
$23$	−1.08498	−	1.87925i	−0.226235	−	0.391850i	0.730454	−	0.682961i	$-0.239308\pi$
$23$	−1.08498	−	1.87925i	−0.226235	−	0.391850i	−0.956689	+	0.291111i	$0.905975\pi$
$24$		0			0
$25$	−4.64465	+	8.04477i	−0.928930	+	1.60895i
$26$		0			0
$27$	4.99311	+	1.43836i	0.960924	+	0.276812i
$28$		0			0
$29$	−4.17231	+	7.22665i	−0.774778	+	1.34195i	0.160141	+	0.987094i	$0.448805\pi$
$29$	−4.17231	+	7.22665i	−0.774778	+	1.34195i	−0.934919	+	0.354861i	$0.884528\pi$
$30$		0			0
$31$	−0.669313	−	1.15928i	−0.120212	−	0.208213i	0.799639	−	0.600481i	$-0.205024\pi$
$31$	−0.669313	−	1.15928i	−0.120212	−	0.208213i	−0.919851	+	0.392267i	$0.871691\pi$
$32$		0			0
$33$	7.60631	+	0.713205i	1.32409	+	0.124153i
$34$		0			0
$35$	4.98905			0.843304
$36$		0			0
$37$	1.24930			0.205384			0.102692	−	0.994713i	$-0.467254\pi$
$37$	1.24930			0.205384			0.102692	+	0.994713i	$0.467254\pi$
$38$		0			0
$39$	−1.00228	+	1.41260i	−0.160493	+	0.226197i
$40$		0			0
$41$	−1.62494	−	2.81448i	−0.253773	−	0.439548i	0.710788	−	0.703406i	$-0.248338\pi$
$41$	−1.62494	−	2.81448i	−0.253773	−	0.439548i	−0.964562	+	0.263858i	$0.915005\pi$
$42$		0			0
$43$	5.93250	−	10.2754i	0.904698	−	1.56698i	0.0833760	−	0.996518i	$-0.473430\pi$
$43$	5.93250	−	10.2754i	0.904698	−	1.56698i	0.821322	−	0.570465i	$-0.193237\pi$
$44$		0			0
$45$	11.1427	+	2.10812i	1.66105	+	0.314260i
$46$		0			0
$47$	−0.203201	+	0.351955i	−0.0296400	+	0.0513380i	−0.880465	−	0.474111i	$-0.842769\pi$
$47$	−0.203201	+	0.351955i	−0.0296400	+	0.0513380i	0.850825	+	0.525449i	$0.176103\pi$
$48$		0			0
$49$	2.62905	+	4.55364i	0.375578	+	0.650520i
$50$		0			0
$51$	2.21144	+	4.82058i	0.309664	+	0.675016i
$52$		0			0
$53$	2.17588			0.298881			0.149440	−	0.988771i	$-0.452253\pi$
$53$	2.17588			0.298881			0.149440	+	0.988771i	$0.452253\pi$
$54$		0			0
$55$	16.6732			2.24822
$56$		0			0
$57$	−5.15097	−	11.2282i	−0.682262	−	1.48722i
$58$		0			0
$59$	4.05223	+	7.01866i	0.527555	+	0.913752i	0.999484	+	0.0321154i	$0.0102244\pi$
$59$	4.05223	+	7.01866i	0.527555	+	0.913752i	−0.471929	+	0.881636i	$0.656442\pi$
$60$		0			0
$61$	−4.39869	+	7.61875i	−0.563194	+	0.975481i	0.434021	+	0.900903i	$0.357094\pi$
$61$	−4.39869	+	7.61875i	−0.563194	+	0.975481i	−0.997215	+	0.0745784i	$0.976239\pi$
$62$		0			0
$63$	−1.30778	−	3.73723i	−0.164765	−	0.470847i
$64$		0			0
$65$	−1.89006	+	3.27368i	−0.234433	+	0.406050i
$66$		0			0
$67$	4.69012	+	8.12353i	0.572990	+	0.992448i	0.996257	+	0.0864426i	$0.0275499\pi$
$67$	4.69012	+	8.12353i	0.572990	+	0.992448i	−0.423267	+	0.906005i	$0.639117\pi$
$68$		0			0
$69$	−2.17491	+	3.06530i	−0.261828	+	0.369019i
$70$		0			0
$71$	−9.45879			−1.12255			−0.561276	−	0.827629i	$-0.689689\pi$
$71$	−9.45879			−1.12255			−0.561276	+	0.827629i	$0.689689\pi$
$72$		0			0
$73$	−12.2720			−1.43633			−0.718165	−	0.695872i	$-0.755018\pi$
$73$	−12.2720			−1.43633			−0.718165	+	0.695872i	$0.755018\pi$
$74$		0			0
$75$	16.0193	+	1.50205i	1.84975	+	0.173441i
$76$		0			0
$77$	−2.91070	−	5.04147i	−0.331705	−	0.574529i
$78$		0			0
$79$	−3.64033	+	6.30524i	−0.409569	+	0.709395i	−0.994841	−	0.101442i	$-0.967654\pi$
$79$	−3.64033	+	6.30524i	−0.409569	+	0.709395i	0.585272	+	0.810837i	$0.300988\pi$
$80$		0			0
$81$	−1.34167	−	8.89943i	−0.149075	−	0.988826i
$82$		0			0
$83$	−6.04966	+	10.4783i	−0.664036	+	1.15014i	0.315510	+	0.948922i	$0.397825\pi$
$83$	−6.04966	+	10.4783i	−0.664036	+	1.15014i	−0.979546	+	0.201222i	$0.935509\pi$
$84$		0			0
$85$	5.78746	+	10.0242i	0.627738	+	1.08727i
$86$		0			0
$87$	14.3902	+	1.34929i	1.54279	+	0.144659i
$88$		0			0
$89$	−5.47746			−0.580609			−0.290305	−	0.956934i	$-0.593757\pi$
$89$	−5.47746			−0.580609			−0.290305	+	0.956934i	$0.593757\pi$
$90$		0			0
$91$	1.31981			0.138354
$92$		0			0
$93$	−1.34167	+	1.89094i	−0.139125	+	0.196082i
$94$		0			0
$95$	−13.4803	−	23.3486i	−1.38305	−	2.39552i
$96$		0			0
$97$	−6.70181	+	11.6079i	−0.680465	+	1.17860i	0.294374	+	0.955690i	$0.404889\pi$
$97$	−6.70181	+	11.6079i	−0.680465	+	1.17860i	−0.974839	+	0.222910i	$0.928444\pi$
$98$		0			0
$99$	−4.37056	−	12.4897i	−0.439257	−	1.25526i
$100$		0			0
$101$	6.65426	−	11.5255i	0.662124	−	1.14683i	−0.317933	−	0.948113i	$-0.602989\pi$
$101$	6.65426	−	11.5255i	0.662124	−	1.14683i	0.980057	−	0.198719i	$-0.0636780\pi$
$102$		0			0
$103$	0.675053	+	1.16923i	0.0665149	+	0.115207i	0.897365	−	0.441289i	$-0.145479\pi$
$103$	0.675053	+	1.16923i	0.0665149	+	0.115207i	−0.830850	+	0.556496i	$0.812145\pi$
$104$		0			0
$105$	−3.60315	−	7.85426i	−0.351631	−	0.766497i
$106$		0			0
$107$	5.74705			0.555588			0.277794	−	0.960641i	$-0.410397\pi$
$107$	5.74705			0.555588			0.277794	+	0.960641i	$0.410397\pi$
$108$		0			0
$109$	−16.1839			−1.55014			−0.775069	−	0.631877i	$-0.782285\pi$
$109$	−16.1839			−1.55014			−0.775069	+	0.631877i	$0.782285\pi$
$110$		0			0
$111$	−0.902257	−	1.96677i	−0.0856384	−	0.186677i
$112$		0			0
$113$	2.55790	+	4.43040i	0.240627	+	0.416777i	0.960893	−	0.276920i	$-0.0893138\pi$
$113$	2.55790	+	4.43040i	0.240627	+	0.416777i	−0.720266	+	0.693698i	$0.755980\pi$
$114$		0			0
$115$	−4.10137	+	7.10378i	−0.382455	+	0.662431i
$116$		0			0
$117$	2.94771	+	0.557686i	0.272516	+	0.0515581i
$118$		0			0
$119$	2.02067	−	3.49990i	0.185234	−	0.320835i
$120$		0			0
$121$	−4.22743	−	7.32212i	−0.384312	−	0.665647i
$122$		0			0
$123$	−3.25728	+	4.59079i	−0.293699	+	0.413937i
$124$		0			0
$125$	16.2141			1.45023
$126$		0			0
$127$	−17.4520			−1.54861			−0.774305	−	0.632812i	$-0.781901\pi$
$127$	−17.4520			−1.54861			−0.774305	+	0.632812i	$0.781901\pi$
$128$		0			0
$129$	−20.4610	−	1.91853i	−1.80149	−	0.168917i
$130$		0			0
$131$	1.53713	+	2.66239i	0.134300	+	0.232614i	0.925330	−	0.379163i	$-0.123788\pi$
$131$	1.53713	+	2.66239i	0.134300	+	0.232614i	−0.791030	+	0.611777i	$0.790455\pi$
$132$		0			0
$133$	−4.70661	+	8.15208i	−0.408115	+	0.706875i
$134$		0			0
$135$	−4.72855	−	19.0644i	−0.406969	−	1.64080i
$136$		0			0
$137$	−6.40458	+	11.0931i	−0.547181	+	0.947745i	0.451286	+	0.892380i	$0.350966\pi$
$137$	−6.40458	+	11.0931i	−0.547181	+	0.947745i	−0.998466	+	0.0553650i	$0.982368\pi$
$138$		0			0
$139$	9.62910	+	16.6781i	0.816730	+	1.41462i	0.908079	+	0.418798i	$0.137549\pi$
$139$	9.62910	+	16.6781i	0.816730	+	1.41462i	−0.0913499	+	0.995819i	$0.529118\pi$
$140$		0			0
$141$	0.700836	+	0.0657139i	0.0590211	+	0.00553411i
$142$		0			0
$143$	4.41077			0.368847
$144$		0			0
$145$	31.5436			2.61956
$146$		0			0
$147$	5.27006	−	7.42758i	0.434667	−	0.612617i
$148$		0			0
$149$	−5.33391	−	9.23860i	−0.436971	−	0.756856i	0.560483	−	0.828166i	$-0.310615\pi$
$149$	−5.33391	−	9.23860i	−0.436971	−	0.756856i	−0.997454	+	0.0713099i	$0.977282\pi$
$150$		0			0
$151$	−4.99869	+	8.65799i	−0.406788	+	0.704577i	−0.994528	−	0.104473i	$-0.966684\pi$
$151$	−4.99869	+	8.65799i	−0.406788	+	0.704577i	0.587740	+	0.809050i	$0.300018\pi$
$152$		0			0
$153$	5.99190	−	6.96294i	0.484416	−	0.562921i
$154$		0			0
$155$	−2.53008	+	4.38223i	−0.203221	+	0.351989i
$156$		0			0
$157$	−6.75613	−	11.7020i	−0.539198	−	0.933919i	−0.998947	−	0.0458699i	$-0.985394\pi$
$157$	−6.75613	−	11.7020i	−0.539198	−	0.933919i	0.459749	−	0.888049i	$-0.347939\pi$
$158$		0			0
$159$	−1.57144	−	3.42549i	−0.124624	−	0.271659i
$160$		0			0
$161$	2.86395			0.225711
$162$		0			0
$163$	−5.22981			−0.409631			−0.204815	−	0.978801i	$-0.565659\pi$
$163$	−5.22981			−0.409631			−0.204815	+	0.978801i	$0.565659\pi$
$164$		0			0
$165$	−12.0416	−	26.2486i	−0.937435	−	2.04345i
$166$		0			0
$167$	4.85695	+	8.41248i	0.375842	+	0.650977i	0.990453	−	0.137853i	$-0.0440202\pi$
$167$	4.85695	+	8.41248i	0.375842	+	0.650977i	−0.614611	+	0.788831i	$0.710687\pi$
$168$		0			0
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$		0			0
$171$	−13.9565	+	16.2183i	−1.06728	+	1.24024i
$172$		0			0
$173$	12.2600	−	21.2350i	0.932113	−	1.61447i	0.152410	−	0.988317i	$-0.451297\pi$
$173$	12.2600	−	21.2350i	0.932113	−	1.61447i	0.779703	−	0.626149i	$-0.215370\pi$
$174$		0			0
$175$	−6.13007	−	10.6176i	−0.463390	−	0.802615i
$176$		0			0
$177$	8.12290	−	11.4484i	0.610555	−	0.860511i
$178$		0			0
$179$	−19.4506			−1.45381			−0.726903	−	0.686740i	$-0.759041\pi$
$179$	−19.4506			−1.45381			−0.726903	+	0.686740i	$0.759041\pi$
$180$		0			0
$181$	15.4476			1.14821			0.574104	−	0.818782i	$-0.305350\pi$
$181$	15.4476			1.14821			0.574104	+	0.818782i	$0.305350\pi$
$182$		0			0
$183$	15.1710	+	1.42250i	1.12147	+	0.105154i
$184$		0			0
$185$	−2.36125	−	4.08981i	−0.173603	−	0.300689i
$186$		0			0
$187$	6.75300	−	11.6965i	0.493828	−	0.855335i
$188$		0			0
$189$	−4.93902	+	4.75790i	−0.359261	+	0.346087i
$190$		0			0
$191$	4.31759	−	7.47829i	0.312410	−	0.541110i	−0.666474	−	0.745529i	$-0.732197\pi$
$191$	4.31759	−	7.47829i	0.312410	−	0.541110i	0.978884	+	0.204419i	$0.0655304\pi$
$192$		0			0
$193$	−9.17262	−	15.8874i	−0.660260	−	1.14360i	−0.980547	−	0.196283i	$-0.937113\pi$
$193$	−9.17262	−	15.8874i	−0.660260	−	1.14360i	0.320287	−	0.947320i	$-0.396220\pi$
$194$		0			0
$195$	6.51876	+	0.611231i	0.466818	+	0.0437712i
$196$		0			0
$197$	−3.26698			−0.232762			−0.116381	−	0.993205i	$-0.537129\pi$
$197$	−3.26698			−0.232762			−0.116381	+	0.993205i	$0.537129\pi$
$198$		0			0
$199$	18.4899			1.31071			0.655357	−	0.755320i	$-0.272518\pi$
$199$	18.4899			1.31071			0.655357	+	0.755320i	$0.272518\pi$
$200$		0			0
$201$	9.40160	−	13.2506i	0.663138	−	0.934622i
$202$		0			0
$203$	−5.50667	−	9.53783i	−0.386493	−	0.669425i
$204$		0			0
$205$	−6.14247	+	10.6391i	−0.429009	+	0.743065i
$206$		0			0
$207$	6.39643	+	1.21016i	0.444583	+	0.0841120i
$208$		0			0
$209$	−15.7293	+	27.2439i	−1.08802	+	1.88450i
$210$		0			0
$211$	−1.54759	−	2.68050i	−0.106540	−	0.184533i	0.807826	−	0.589421i	$-0.200644\pi$
$211$	−1.54759	−	2.68050i	−0.106540	−	0.184533i	−0.914367	+	0.404888i	$0.867311\pi$
$212$		0			0
$213$	6.83123	+	14.8909i	0.468068	+	1.02031i
$214$		0			0
$215$	−44.8511			−3.05882
$216$		0			0
$217$	1.76674			0.119934
$218$		0			0
$219$	8.86298	+	19.3198i	0.598904	+	1.30551i
$220$		0			0
$221$	1.53103	+	2.65181i	0.102988	+	0.178380i
$222$		0			0
$223$	−1.28975	+	2.23391i	−0.0863679	+	0.149594i	−0.905973	−	0.423335i	$-0.860859\pi$
$223$	−1.28975	+	2.23391i	−0.0863679	+	0.149594i	0.819605	+	0.572928i	$0.194193\pi$
$224$		0			0
$225$	−9.20461	−	26.3039i	−0.613641	−	1.75359i
$226$		0			0
$227$	4.97484	−	8.61667i	0.330192	−	0.571909i	−0.652358	−	0.757911i	$-0.726220\pi$
$227$	4.97484	−	8.61667i	0.330192	−	0.571909i	0.982549	+	0.186003i	$0.0595533\pi$
$228$		0			0
$229$	−2.34074	−	4.05428i	−0.154680	−	0.267914i	0.778262	−	0.627939i	$-0.216101\pi$
$229$	−2.34074	−	4.05428i	−0.154680	−	0.267914i	−0.932943	+	0.360025i	$0.882768\pi$
$230$		0			0
$231$	−5.83464	+	8.22330i	−0.383891	+	0.541054i
$232$		0			0
$233$	−15.8323			−1.03721			−0.518604	−	0.855015i	$-0.673548\pi$
$233$	−15.8323			−1.03721			−0.518604	+	0.855015i	$0.673548\pi$
$234$		0			0
$235$	1.53625			0.100214
$236$		0			0
$237$	12.5554	+	1.17726i	0.815561	+	0.0764710i
$238$		0			0
$239$	6.53305	+	11.3156i	0.422588	+	0.731944i	0.996192	−	0.0871889i	$-0.0277884\pi$
$239$	6.53305	+	11.3156i	0.422588	+	0.731944i	−0.573604	+	0.819133i	$0.694455\pi$
$240$		0			0
$241$	−8.30511	+	14.3849i	−0.534979	+	0.926611i	0.464185	+	0.885738i	$0.346347\pi$
$241$	−8.30511	+	14.3849i	−0.534979	+	0.926611i	−0.999164	+	0.0408729i	$0.986986\pi$
$242$		0			0
$243$	−13.0414	+	8.53945i	−0.836605	+	0.547806i
$244$		0			0
$245$	9.93810	−	17.2133i	0.634922	−	1.09972i
$246$		0			0
$247$	−3.56611	−	6.17669i	−0.226906	−	0.393013i
$248$		0			0
$249$	20.8651	+	1.95641i	1.32227	+	0.123983i
$250$		0			0
$251$	−20.1047			−1.26900			−0.634500	−	0.772923i	$-0.718794\pi$
$251$	−20.1047			−1.26900			−0.634500	+	0.772923i	$0.718794\pi$
$252$		0			0
$253$	9.57122			0.601737
$254$		0			0
$255$	11.6013	−	16.3507i	0.726499	−	1.02392i
$256$		0			0
$257$	8.56913	+	14.8422i	0.534527	+	0.925829i	0.999186	+	0.0403387i	$0.0128437\pi$
$257$	8.56913	+	14.8422i	0.534527	+	0.925829i	−0.464659	+	0.885490i	$0.653823\pi$
$258$		0			0
$259$	−0.824422	+	1.42794i	−0.0512271	+	0.0887279i
$260$		0			0
$261$	−8.26854	−	23.6289i	−0.511810	−	1.46259i
$262$		0			0
$263$	10.0441	−	17.3970i	0.619348	−	1.07274i	−0.370256	−	0.928930i	$-0.620730\pi$
$263$	10.0441	−	17.3970i	0.619348	−	1.07274i	0.989605	−	0.143813i	$-0.0459365\pi$
$264$		0			0
$265$	−4.11255	−	7.12314i	−0.252632	−	0.437571i
$266$		0			0
$267$	3.95587	+	8.62315i	0.242096	+	0.527728i
$268$		0			0
$269$	−4.10780			−0.250457			−0.125228	−	0.992128i	$-0.539966\pi$
$269$	−4.10780			−0.250457			−0.125228	+	0.992128i	$0.539966\pi$
$270$		0			0
$271$	13.1958			0.801585			0.400793	−	0.916169i	$-0.368735\pi$
$271$	13.1958			0.801585			0.400793	+	0.916169i	$0.368735\pi$
$272$		0			0
$273$	−0.953183	−	2.07778i	−0.0576893	−	0.125753i
$274$		0			0
$275$	−20.4865	−	35.4836i	−1.23538	−	2.13974i
$276$		0			0
$277$	11.3036	−	19.5785i	0.679170	−	1.17636i	−0.296061	−	0.955169i	$-0.595673\pi$
$277$	11.3036	−	19.5785i	0.679170	−	1.17636i	0.975231	−	0.221188i	$-0.0709935\pi$
$278$		0			0
$279$	3.94588	+	0.746533i	0.236233	+	0.0446938i
$280$		0			0
$281$	−7.61926	+	13.1969i	−0.454527	+	0.787263i	−0.998661	−	0.0517348i	$-0.983525\pi$
$281$	−7.61926	+	13.1969i	−0.454527	+	0.787263i	0.544134	+	0.838998i	$0.316858\pi$
$282$		0			0
$283$	−4.59195	−	7.95348i	−0.272963	−	0.472786i	0.696656	−	0.717405i	$-0.254670\pi$
$283$	−4.59195	−	7.95348i	−0.272963	−	0.472786i	−0.969619	+	0.244620i	$0.921337\pi$
$284$		0			0
$285$	−27.0220	+	38.0847i	−1.60065	+	2.25594i
$286$		0			0
$287$	4.28924			0.253186
$288$		0			0
$289$	−7.62384			−0.448461
$290$		0			0
$291$	23.1144	+	2.16731i	1.35499	+	0.127050i
$292$		0			0
$293$	0.232689	+	0.403030i	0.0135939	+	0.0235453i	0.872742	−	0.488181i	$-0.162339\pi$
$293$	0.232689	+	0.403030i	0.0135939	+	0.0235453i	−0.859148	+	0.511726i	$0.829006\pi$
$294$		0			0
$295$	15.3179	−	26.5314i	0.891842	−	1.54472i
$296$		0			0
$297$	−16.5060	+	15.9007i	−0.957775	+	0.922654i
$298$		0			0
$299$	−1.08498	+	1.87925i	−0.0627462	+	0.108680i
$300$		0			0
$301$	7.82980	+	13.5616i	0.451302	+	0.781678i
$302$		0			0
$303$	−22.9504	−	2.15194i	−1.31846	−	0.123626i
$304$		0			0
$305$	33.2551			1.90418
$306$		0			0
$307$	−13.8035			−0.787810			−0.393905	−	0.919151i	$-0.628876\pi$
$307$	−13.8035			−0.787810			−0.393905	+	0.919151i	$0.628876\pi$
$308$		0			0
$309$	1.35318	−	1.90716i	0.0769797	−	0.108495i
$310$		0			0
$311$	−3.59547	−	6.22754i	−0.203880	−	0.353131i	0.745895	−	0.666063i	$-0.232022\pi$
$311$	−3.59547	−	6.22754i	−0.203880	−	0.353131i	−0.949775	+	0.312932i	$0.898689\pi$
$312$		0			0
$313$	4.14223	−	7.17456i	0.234133	−	0.405530i	−0.724888	−	0.688867i	$-0.758108\pi$
$313$	4.14223	−	7.17456i	0.234133	−	0.405530i	0.959020	+	0.283337i	$0.0914416\pi$
$314$		0			0
$315$	−9.76271	+	11.3448i	−0.550066	+	0.639210i
$316$		0			0
$317$	−2.21178	+	3.83091i	−0.124226	+	0.215165i	−0.921430	−	0.388544i	$-0.872978\pi$
$317$	−2.21178	+	3.83091i	−0.124226	+	0.215165i	0.797204	+	0.603710i	$0.206311\pi$
$318$		0			0
$319$	−18.4031	−	31.8751i	−1.03037	−	1.78466i
$320$		0			0
$321$	−4.15058	−	9.04756i	−0.231663	−	0.504986i
$322$		0			0
$323$	−21.8392			−1.21517
$324$		0			0
$325$	9.28930			0.515278
$326$		0			0
$327$	11.6882	+	25.4783i	0.646358	+	1.40895i
$328$		0			0
$329$	−0.268188	−	0.464516i	−0.0147857	−	0.0256096i
$330$		0			0
$331$	11.7011	−	20.2668i	0.643148	−	1.11397i	−0.341577	−	0.939854i	$-0.610961\pi$
$331$	11.7011	−	20.2668i	0.643148	−	1.11397i	0.984726	−	0.174112i	$-0.0557055\pi$
$332$		0			0
$333$	−2.44466	+	2.84084i	−0.133967	+	0.155677i
$334$		0			0
$335$	17.7292	−	30.7079i	0.968651	−	1.67775i
$336$		0			0
$337$	15.8641	+	27.4774i	0.864171	+	1.49679i	0.867868	+	0.496795i	$0.165490\pi$
$337$	15.8641	+	27.4774i	0.864171	+	1.49679i	−0.00369700	+	0.999993i	$0.501177\pi$
$338$		0			0
$339$	5.12744	−	7.22657i	0.278484	−	0.392493i
$340$		0			0
$341$	5.90436			0.319739
$342$		0			0
$343$	−16.1784			−0.873552
$344$		0			0
$345$	14.1455	+	1.32635i	0.761569	+	0.0714084i
$346$		0			0
$347$	15.6119	+	27.0407i	0.838092	+	1.45162i	0.891488	+	0.453045i	$0.149662\pi$
$347$	15.6119	+	27.0407i	0.838092	+	1.45162i	−0.0533955	+	0.998573i	$0.517004\pi$
$348$		0			0
$349$	−13.8233	+	23.9426i	−0.739944	+	1.28162i	0.212577	+	0.977144i	$0.431814\pi$
$349$	−13.8233	+	23.9426i	−0.739944	+	1.28162i	−0.952520	+	0.304475i	$0.901519\pi$
$350$		0			0
$351$	−1.25090	−	5.04334i	−0.0667682	−	0.269193i
$352$		0			0
$353$	−2.49914	+	4.32864i	−0.133016	+	0.230390i	−0.924838	−	0.380362i	$-0.875799\pi$
$353$	−2.49914	+	4.32864i	−0.133016	+	0.230390i	0.791822	+	0.610752i	$0.209133\pi$
$354$		0			0
$355$	17.8777	+	30.9650i	0.948848	+	1.64345i
$356$		0			0
$357$	−6.96923	−	0.653470i	−0.368851	−	0.0345853i
$358$		0			0
$359$	−10.1761			−0.537075			−0.268537	−	0.963269i	$-0.586540\pi$
$359$	−10.1761			−0.537075			−0.268537	+	0.963269i	$0.586540\pi$
$360$		0			0
$361$	31.8686			1.67730
$362$		0			0
$363$	−8.47410	+	11.9433i	−0.444775	+	0.626863i
$364$		0			0
$365$	23.1948	+	40.1746i	1.21407	+	2.10284i
$366$		0			0
$367$	3.85242	−	6.67258i	0.201094	−	0.348306i	−0.747787	−	0.663939i	$-0.768884\pi$
$367$	3.85242	−	6.67258i	0.201094	−	0.348306i	0.948881	+	0.315633i	$0.102217\pi$
$368$		0			0
$369$	9.57971	+	1.81241i	0.498700	+	0.0943505i
$370$		0			0
$371$	−1.43588	+	2.48702i	−0.0745472	+	0.129120i
$372$		0			0
$373$	−14.6275	−	25.3356i	−0.757384	−	1.31183i	−0.944180	−	0.329429i	$-0.893144\pi$
$373$	−14.6275	−	25.3356i	−0.757384	−	1.31183i	0.186797	−	0.982399i	$-0.440189\pi$
$374$		0			0
$375$	−11.7100	−	25.5257i	−0.604700	−	1.31814i
$376$		0			0
$377$	8.34461			0.429769
$378$		0			0
$379$	−20.9948			−1.07843			−0.539215	−	0.842168i	$-0.681279\pi$
$379$	−20.9948			−1.07843			−0.539215	+	0.842168i	$0.681279\pi$
$380$		0			0
$381$	12.6040	+	27.4746i	0.645722	+	1.40757i
$382$		0			0
$383$	8.49637	+	14.7161i	0.434144	+	0.751960i	0.997225	−	0.0744417i	$-0.0237175\pi$
$383$	8.49637	+	14.7161i	0.434144	+	0.751960i	−0.563081	+	0.826402i	$0.690384\pi$
$384$		0			0
$385$	−11.0028	+	19.0574i	−0.560753	+	0.971253i
$386$		0			0
$387$	11.7568	+	33.5973i	0.597634	+	1.70785i
$388$		0			0
$389$	−11.5122	+	19.9398i	−0.583694	+	1.01099i	0.411343	+	0.911481i	$0.365060\pi$
$389$	−11.5122	+	19.9398i	−0.583694	+	1.01099i	−0.995037	+	0.0995069i	$0.968273\pi$
$390$		0			0
$391$	3.32228	+	5.75435i	0.168015	+	0.291010i
$392$		0			0
$393$	3.08126	−	4.34271i	0.155429	−	0.219061i
$394$		0			0
$395$	27.5218			1.38477
$396$		0			0
$397$	−10.2161			−0.512731			−0.256365	−	0.966580i	$-0.582525\pi$
$397$	−10.2161			−0.512731			−0.256365	+	0.966580i	$0.582525\pi$
$398$		0			0
$399$	16.2330	+	1.52208i	0.812665	+	0.0761994i
$400$		0			0
$401$	−17.0998	−	29.6177i	−0.853921	−	1.47904i	−0.877642	−	0.479317i	$-0.840885\pi$
$401$	−17.0998	−	29.6177i	−0.853921	−	1.47904i	0.0237206	−	0.999719i	$-0.492449\pi$
$402$		0			0
$403$	−0.669313	+	1.15928i	−0.0333408	+	0.0577480i
$404$		0			0
$405$	−26.5980	+	21.2127i	−1.32167	+	1.05407i
$406$		0			0
$407$	−2.75518	+	4.77212i	−0.136569	+	0.236545i
$408$		0			0
$409$	−14.9088	−	25.8229i	−0.737195	−	1.27686i	−0.953754	−	0.300590i	$-0.902817\pi$
$409$	−14.9088	−	25.8229i	−0.737195	−	1.27686i	0.216558	−	0.976270i	$-0.430517\pi$
$410$		0			0
$411$	22.0892	+	2.07120i	1.08958	+	0.102165i
$412$		0			0
$413$	−10.6964			−0.526334
$414$		0			0
$415$	45.7368			2.24513
$416$		0			0
$417$	19.3020	−	27.2042i	0.945225	−	1.33219i
$418$		0			0
$419$	−7.45668	−	12.9153i	−0.364283	−	0.630956i	0.624378	−	0.781122i	$-0.285352\pi$
$419$	−7.45668	−	12.9153i	−0.364283	−	0.630956i	−0.988661	+	0.150166i	$0.952019\pi$
$420$		0			0
$421$	−6.46463	+	11.1971i	−0.315067	+	0.545712i	−0.979452	−	0.201679i	$-0.935360\pi$
$421$	−6.46463	+	11.1971i	−0.315067	+	0.545712i	0.664385	+	0.747391i	$0.268694\pi$
$422$		0			0
$423$	−0.402698	−	1.15078i	−0.0195799	−	0.0559530i
$424$		0			0
$425$	14.2222	−	24.6335i	0.689876	−	1.19490i
$426$		0			0
$427$	−5.80545	−	10.0553i	−0.280946	−	0.486612i
$428$		0			0
$429$	−3.18550	−	6.94386i	−0.153797	−	0.335253i
$430$		0			0
$431$	9.00134			0.433579			0.216790	−	0.976218i	$-0.430441\pi$
$431$	9.00134			0.433579			0.216790	+	0.976218i	$0.430441\pi$
$432$		0			0
$433$	11.7638			0.565333			0.282667	−	0.959218i	$-0.408781\pi$
$433$	11.7638			0.565333			0.282667	+	0.959218i	$0.408781\pi$
$434$		0			0
$435$	−22.7811	−	49.6591i	−1.09227	−	2.38097i
$436$		0			0
$437$	−7.73835	−	13.4032i	−0.370175	−	0.641163i
$438$		0			0
$439$	−15.8633	+	27.4760i	−0.757114	+	1.31136i	0.187202	+	0.982321i	$0.440058\pi$
$439$	−15.8633	+	27.4760i	−0.757114	+	1.31136i	−0.944316	+	0.329039i	$0.893275\pi$
$440$		0			0
$441$	−15.4993	−	2.93236i	−0.738063	−	0.139636i
$442$		0			0
$443$	1.83382	−	3.17626i	0.0871272	−	0.150909i	−0.819168	−	0.573553i	$-0.805565\pi$
$443$	1.83382	−	3.17626i	0.0871272	−	0.150909i	0.906296	+	0.422644i	$0.138898\pi$
$444$		0			0
$445$	10.3527	+	17.9314i	0.490766	+	0.850031i
$446$		0			0
$447$	−10.6921	+	15.0694i	−0.505719	+	0.712757i
$448$		0			0
$449$	39.4850			1.86341			0.931706	−	0.363213i	$-0.118320\pi$
$449$	39.4850			1.86341			0.931706	+	0.363213i	$0.118320\pi$
$450$		0			0
$451$	14.3345			0.674984
$452$		0			0
$453$	17.2404	+	1.61654i	0.810022	+	0.0759517i
$454$		0			0
$455$	−2.49453	−	4.32065i	−0.116945	−	0.202555i
$456$		0			0
$457$	−12.1028	+	20.9626i	−0.566144	+	0.980590i	0.430798	+	0.902448i	$0.358232\pi$
$457$	−12.1028	+	20.9626i	−0.566144	+	0.980590i	−0.996942	+	0.0781417i	$0.975101\pi$
$458$		0			0
$459$	−15.2892	−	4.40432i	−0.713637	−	0.205576i
$460$		0			0
$461$	4.62828	−	8.01641i	0.215560	−	0.373362i	−0.737885	−	0.674926i	$-0.764176\pi$
$461$	4.62828	−	8.01641i	0.215560	−	0.373362i	0.953446	+	0.301564i	$0.0975089\pi$
$462$		0			0
$463$	−4.06304	−	7.03739i	−0.188826	−	0.327055i	0.756033	−	0.654533i	$-0.227135\pi$
$463$	−4.06304	−	7.03739i	−0.188826	−	0.327055i	−0.944859	+	0.327478i	$0.893801\pi$
$464$		0			0
$465$	8.72618	+	0.818210i	0.404667	+	0.0379436i
$466$		0			0
$467$	3.39825			0.157252			0.0786261	−	0.996904i	$-0.474947\pi$
$467$	3.39825			0.157252			0.0786261	+	0.996904i	$0.474947\pi$
$468$		0			0
$469$	−12.3802			−0.571664
$470$		0			0
$471$	−13.5430	+	19.0874i	−0.624030	+	0.879503i
$472$		0			0
$473$	26.1669	+	45.3224i	1.20315	+	2.08392i
$474$		0			0
$475$	−33.1267	+	57.3771i	−1.51996	+	2.63264i
$476$		0			0
$477$	−4.25782	+	4.94784i	−0.194952	+	0.226546i
$478$		0			0
$479$	−15.5576	+	26.9466i	−0.710847	+	1.23122i	0.253693	+	0.967285i	$0.418355\pi$
$479$	−15.5576	+	26.9466i	−0.710847	+	1.23122i	−0.964540	+	0.263938i	$0.914979\pi$
$480$		0			0
$481$	−0.624650	−	1.08193i	−0.0284816	−	0.0493315i
$482$		0			0
$483$	−2.06838	−	4.50872i	−0.0941144	−	0.205154i
$484$		0			0
$485$	50.6672			2.30068
$486$		0			0
$487$	5.20054			0.235659			0.117829	−	0.993034i	$-0.462406\pi$
$487$	5.20054			0.235659			0.117829	+	0.993034i	$0.462406\pi$
$488$		0			0
$489$	3.77702	+	8.23328i	0.170803	+	0.372322i
$490$		0			0
$491$	17.2623	+	29.8992i	0.779037	+	1.34933i	0.932497	+	0.361177i	$0.117625\pi$
$491$	17.2623	+	29.8992i	0.779037	+	1.34933i	−0.153460	+	0.988155i	$0.549042\pi$
$492$		0			0
$493$	12.7758	−	22.1284i	0.575394	−	0.996611i
$494$		0			0
$495$	−32.6266	+	37.9140i	−1.46646	+	1.70411i
$496$		0			0
$497$	6.24192	−	10.8113i	0.279988	−	0.484954i
$498$		0			0
$499$	−4.65602	−	8.06446i	−0.208432	−	0.361015i	0.742789	−	0.669526i	$-0.233503\pi$
$499$	−4.65602	−	8.06446i	−0.208432	−	0.361015i	−0.951221	+	0.308511i	$0.900169\pi$
$500$		0			0
$501$	9.73601	−	13.7219i	0.434973	−	0.613047i
$502$		0			0
$503$	−16.3420			−0.728656			−0.364328	−	0.931271i	$-0.618701\pi$
$503$	−16.3420			−0.728656			−0.364328	+	0.931271i	$0.618701\pi$
$504$		0			0
$505$	−50.3078			−2.23867
$506$		0			0
$507$	1.72449	+	0.161696i	0.0765871	+	0.00718119i
$508$		0			0
$509$	−19.7266	−	34.1675i	−0.874368	−	1.51445i	−0.857435	−	0.514593i	$-0.827943\pi$
$509$	−19.7266	−	34.1675i	−0.874368	−	1.51445i	−0.0169335	−	0.999857i	$-0.505390\pi$
$510$		0			0
$511$	8.09839	−	14.0268i	0.358252	−	0.620510i
$512$		0			0
$513$	35.6120	+	10.2587i	1.57231	+	0.452932i
$514$		0			0
$515$	2.55178	−	4.41981i	0.112445	−	0.194760i
$516$		0			0
$517$	−0.896274	−	1.55239i	−0.0394181	−	0.0682741i
$518$		0			0
$519$	−42.2845	−	3.96480i	−1.85608	−	0.174036i
$520$		0			0
$521$	−24.7139			−1.08274			−0.541368	−	0.840786i	$-0.682093\pi$
$521$	−24.7139			−1.08274			−0.541368	+	0.840786i	$0.682093\pi$
$522$		0			0
$523$	25.3771			1.10966			0.554832	−	0.831963i	$-0.312783\pi$
$523$	25.3771			1.10966			0.554832	+	0.831963i	$0.312783\pi$
$524$		0			0
$525$	−12.2881	+	17.3187i	−0.536295	+	0.755850i
$526$		0			0
$527$	2.04947	+	3.54978i	0.0892763	+	0.154631i
$528$		0			0
$529$	9.14562	−	15.8407i	0.397636	−	0.688725i
$530$		0			0
$531$	−23.8896	−	4.51974i	−1.03672	−	0.196140i
$532$		0			0
$533$	−1.62494	+	2.81448i	−0.0703840	+	0.121909i
$534$		0			0
$535$	−10.8623	−	18.8140i	−0.469616	−	0.813400i
$536$		0			0
$537$	14.0474	+	30.6210i	0.606191	+	1.32140i
$538$		0			0
$539$	−23.1922			−0.998959
$540$		0			0
$541$	−22.0818			−0.949370			−0.474685	−	0.880156i	$-0.657438\pi$
$541$	−22.0818			−0.949370			−0.474685	+	0.880156i	$0.657438\pi$
$542$		0			0
$543$	−11.1564	−	24.3191i	−0.478766	−	1.04363i
$544$		0			0
$545$	30.5886	+	52.9809i	1.31027	+	2.26945i
$546$		0			0
$547$	−3.02667	+	5.24235i	−0.129411	+	0.224147i	−0.923449	−	0.383722i	$-0.874642\pi$
$547$	−3.02667	+	5.24235i	−0.129411	+	0.224147i	0.794037	+	0.607869i	$0.207975\pi$
$548$		0			0
$549$	−8.71718	−	24.9110i	−0.372040	−	1.06317i
$550$		0			0
$551$	−29.7578	+	51.5421i	−1.26773	+	2.19577i
$552$		0			0
$553$	−4.80456	−	8.32174i	−0.204311	−	0.353876i
$554$		0			0
$555$	−4.73325	+	6.67101i	−0.200915	+	0.283169i
$556$		0			0
$557$	27.8981			1.18208			0.591039	−	0.806643i	$-0.298718\pi$
$557$	27.8981			1.18208			0.591039	+	0.806643i	$0.298718\pi$
$558$		0			0
$559$	−11.8650			−0.501836
$560$		0			0
$561$	−23.2909	−	2.18387i	−0.983343	−	0.0922030i
$562$		0			0
$563$	10.9423	+	18.9526i	0.461162	+	0.798755i	0.999019	−	0.0442804i	$-0.0140995\pi$
$563$	10.9423	+	18.9526i	0.461162	+	0.798755i	−0.537858	+	0.843036i	$0.680766\pi$
$564$		0			0
$565$	9.66915	−	16.7475i	0.406784	−	0.704571i
$566$		0			0
$567$	11.0574	+	4.33928i	0.464366	+	0.182233i
$568$		0			0
$569$	0.0845017	−	0.146361i	0.00354249	−	0.00613578i	−0.864249	−	0.503065i	$-0.832206\pi$
$569$	0.0845017	−	0.146361i	0.00354249	−	0.00613578i	0.867791	+	0.496929i	$0.165539\pi$
$570$		0			0
$571$	−12.7297	−	22.0485i	−0.532722	−	0.922701i	−0.999270	−	0.0382052i	$-0.987836\pi$
$571$	−12.7297	−	22.0485i	−0.532722	−	0.922701i	0.466548	−	0.884496i	$-0.345497\pi$
$572$		0			0
$573$	−14.8913	−	1.39628i	−0.622091	−	0.0583303i
$574$		0			0
$575$	20.1575			0.840625
$576$		0			0
$577$	−2.82205			−0.117484			−0.0587418	−	0.998273i	$-0.518709\pi$
$577$	−2.82205			−0.117484			−0.0587418	+	0.998273i	$0.518709\pi$
$578$		0			0
$579$	−18.3870	+	25.9145i	−0.764138	+	1.07697i
$580$		0			0
$581$	−7.98442	−	13.8294i	−0.331250	−	0.573741i
$582$		0			0
$583$	−4.79866	+	8.31151i	−0.198740	+	0.344228i
$584$		0			0
$585$	−3.74566	−	10.7039i	−0.154864	−	0.442552i
$586$		0			0
$587$	14.4040	−	24.9485i	0.594518	−	1.02973i	−0.399097	−	0.916909i	$-0.630676\pi$
$587$	14.4040	−	24.9485i	0.594518	−	1.02973i	0.993615	−	0.112826i	$-0.0359903\pi$
$588$		0			0
$589$	−4.77369	−	8.26827i	−0.196696	−	0.340688i
$590$		0			0
$591$	2.35944	+	5.14319i	0.0970545	+	0.211563i
$592$		0			0
$593$	27.6059			1.13364			0.566819	−	0.823842i	$-0.308174\pi$
$593$	27.6059			1.13364			0.566819	+	0.823842i	$0.308174\pi$
$594$		0			0
$595$	−15.2767			−0.626285
$596$		0			0
$597$	−13.3536	−	29.1086i	−0.546526	−	1.19133i
$598$		0			0
$599$	20.9533	+	36.2921i	0.856127	+	1.48285i	0.875596	+	0.483044i	$0.160469\pi$
$599$	20.9533	+	36.2921i	0.856127	+	1.48285i	−0.0194691	+	0.999810i	$0.506198\pi$
$600$		0			0
$601$	10.1877	−	17.6457i	0.415566	−	0.719781i	−0.579922	−	0.814672i	$-0.696917\pi$
$601$	10.1877	−	17.6457i	0.415566	−	0.719781i	0.995488	+	0.0948909i	$0.0302502\pi$
$602$		0			0
$603$	−27.6502	−	5.23124i	−1.12600	−	0.213032i
$604$		0			0
$605$	−15.9802	+	27.6785i	−0.649687	+	1.12529i
$606$		0			0
$607$	−21.4089	−	37.0812i	−0.868959	−	1.50508i	−0.863062	−	0.505098i	$-0.831456\pi$
$607$	−21.4089	−	37.0812i	−0.868959	−	1.50508i	−0.00589722	−	0.999983i	$-0.501877\pi$
$608$		0			0
$609$	−11.0384	+	15.5575i	−0.447299	+	0.630420i
$610$		0			0
$611$	0.406403			0.0164413
$612$		0			0
$613$	26.9648			1.08910			0.544549	−	0.838729i	$-0.316701\pi$
$613$	26.9648			1.08910			0.544549	+	0.838729i	$0.316701\pi$
$614$		0			0
$615$	21.1852	+	1.98643i	0.854270	+	0.0801006i
$616$		0			0
$617$	12.2801	+	21.2697i	0.494378	+	0.856287i	0.999979	−	0.00647995i	$-0.00206265\pi$
$617$	12.2801	+	21.2697i	0.494378	+	0.856287i	−0.505601	+	0.862767i	$0.668729\pi$
$618$		0			0
$619$	8.80180	−	15.2452i	0.353774	−	0.612755i	−0.633133	−	0.774043i	$-0.718231\pi$
$619$	8.80180	−	15.2452i	0.353774	−	0.612755i	0.986907	+	0.161288i	$0.0515648\pi$
$620$		0			0
$621$	−2.71442	−	10.9439i	−0.108926	−	0.439163i
$622$		0			0
$623$	3.61461	−	6.26069i	0.144816	−	0.250829i
$624$		0			0
$625$	−7.42228	−	12.8558i	−0.296891	−	0.514231i
$626$		0			0
$627$	54.2499	+	5.08674i	2.16653	+	0.203145i
$628$		0			0
$629$	−3.82542			−0.152529
$630$		0			0
$631$	11.6431			0.463503			0.231752	−	0.972775i	$-0.425554\pi$
$631$	11.6431			0.463503			0.231752	+	0.972775i	$0.425554\pi$
$632$		0			0
$633$	−3.10222	+	4.37225i	−0.123302	+	0.173781i
$634$		0			0
$635$	32.9852	+	57.1321i	1.30898	+	2.26722i
$636$		0			0
$637$	2.62905	−	4.55364i	0.104167	−	0.180422i
$638$		0			0
$639$	18.5092	−	21.5088i	0.732212	−	0.850874i
$640$		0			0
$641$	16.3997	−	28.4051i	0.647750	−	1.12194i	−0.335909	−	0.941894i	$-0.609044\pi$
$641$	16.3997	−	28.4051i	0.647750	−	1.12194i	0.983659	−	0.180041i	$-0.0576230\pi$
$642$		0			0
$643$	3.44097	+	5.95994i	0.135699	+	0.235037i	0.925864	−	0.377857i	$-0.123339\pi$
$643$	3.44097	+	5.95994i	0.135699	+	0.235037i	−0.790165	+	0.612894i	$0.790005\pi$
$644$		0			0
$645$	32.3919	+	70.6090i	1.27543	+	2.78023i
$646$		0			0
$647$	8.22182			0.323233			0.161617	−	0.986854i	$-0.448329\pi$
$647$	8.22182			0.323233			0.161617	+	0.986854i	$0.448329\pi$
$648$		0			0
$649$	−35.7468			−1.40319
$650$		0			0
$651$	−1.27596	−	2.78137i	−0.0500086	−	0.109010i
$652$		0			0
$653$	−20.1786	−	34.9503i	−0.789649	−	1.36771i	−0.926182	−	0.377077i	$-0.876929\pi$
$653$	−20.1786	−	34.9503i	−0.789649	−	1.36771i	0.136533	−	0.990635i	$-0.456404\pi$
$654$		0			0
$655$	5.81054	−	10.0641i	0.227037	−	0.393239i
$656$		0			0
$657$	24.0142	−	27.9059i	0.936883	−	1.08871i
$658$		0			0
$659$	0.0788685	−	0.136604i	0.00307228	−	0.00532135i	−0.864485	−	0.502658i	$-0.832355\pi$
$659$	0.0788685	−	0.136604i	0.00307228	−	0.00532135i	0.867557	+	0.497337i	$0.165689\pi$
$660$		0			0
$661$	12.8347	+	22.2304i	0.499214	+	0.864663i	1.00000		0.000907872i	$-0.000288985\pi$
$661$	12.8347	+	22.2304i	0.499214	+	0.864663i	−0.500786	+	0.865571i	$0.666956\pi$
$662$		0			0
$663$	3.06902	−	4.32546i	0.119191	−	0.167987i
$664$		0			0
$665$	35.5831			1.37985
$666$		0			0
$667$	18.1075			0.701127
$668$		0			0
$669$	4.44830	+	0.417095i	0.171981	+	0.0161258i
$670$		0			0
$671$	−19.4016	−	33.6045i	−0.748990	−	1.29729i
$672$		0			0
$673$	−8.87413	+	15.3704i	−0.342072	+	0.592487i	−0.984817	−	0.173593i	$-0.944462\pi$
$673$	−8.87413	+	15.3704i	−0.342072	+	0.592487i	0.642745	+	0.766080i	$0.277796\pi$
$674$		0			0
$675$	−34.7625	+	33.4877i	−1.33801	+	1.28894i
$676$		0			0
$677$	18.6184	−	32.2480i	0.715564	−	1.23939i	−0.247178	−	0.968970i	$-0.579503\pi$
$677$	18.6184	−	32.2480i	0.715564	−	1.23939i	0.962742	−	0.270422i	$-0.0871633\pi$
$678$		0			0
$679$	−8.84514	−	15.3202i	−0.339445	−	0.587937i
$680$		0			0
$681$	−17.1581	−	1.60883i	−0.657499	−	0.0616504i
$682$		0			0
$683$	13.1276			0.502315			0.251158	−	0.967946i	$-0.419189\pi$
$683$	13.1276			0.502315			0.251158	+	0.967946i	$0.419189\pi$
$684$		0			0
$685$	48.4202			1.85004
$686$		0			0
$687$	−4.69214	+	6.61306i	−0.179016	+	0.252304i
$688$		0			0
$689$	−1.08794	−	1.88437i	−0.0414473	−	0.0717888i
$690$		0			0
$691$	−2.44120	+	4.22828i	−0.0928676	+	0.160851i	−0.908717	−	0.417414i	$-0.862937\pi$
$691$	−2.44120	+	4.22828i	−0.0928676	+	0.160851i	0.815849	+	0.578265i	$0.196270\pi$
$692$		0			0
$693$	17.1598	+	3.24651i	0.651846	+	0.123325i
$694$		0			0
$695$	36.3991	−	63.0452i	1.38070	−	2.39144i
$696$		0			0
$697$	4.97565	+	8.61808i	0.188466	+	0.326433i
$698$		0			0
$699$	11.4342	+	24.9247i	0.432483	+	0.942740i
$700$		0			0
$701$	−1.88397			−0.0711565			−0.0355782	−	0.999367i	$-0.511327\pi$
$701$	−1.88397			−0.0711565			−0.0355782	+	0.999367i	$0.511327\pi$
$702$		0			0
$703$	8.91029			0.336058
$704$		0			0
$705$	−1.10950	−	2.41852i	−0.0417861	−	0.0910866i
$706$		0			0
$707$	8.78239	+	15.2115i	0.330296	+	0.572089i
$708$		0			0
$709$	−10.2918	+	17.8259i	−0.386516	+	0.669466i	−0.991978	−	0.126408i	$-0.959655\pi$
$709$	−10.2918	+	17.8259i	−0.386516	+	0.669466i	0.605462	+	0.795874i	$0.292988\pi$
$710$		0			0
$711$	−7.21429	−	20.6162i	−0.270557	−	0.773167i
$712$		0			0
$713$	−1.45239	+	2.51561i	−0.0543923	+	0.0942102i
$714$		0			0
$715$	−8.33661	−	14.4394i	−0.311772	−	0.540004i
$716$		0			0
$717$	13.0959	−	18.4572i	0.489074	−	0.689297i
$718$		0			0
$719$	8.09546			0.301910			0.150955	−	0.988541i	$-0.451765\pi$
$719$	8.09546			0.301910			0.150955	+	0.988541i	$0.451765\pi$
$720$		0			0
$721$	−1.78189			−0.0663610
$722$		0			0
$723$	28.6441	+	2.68581i	1.06529	+	0.0998864i
$724$		0			0
$725$	−38.7578	−	67.1305i	−1.43943	−	2.49316i
$726$		0			0
$727$	−16.8348	+	29.1587i	−0.624367	+	1.08144i	0.364296	+	0.931283i	$0.381310\pi$
$727$	−16.8348	+	29.1587i	−0.624367	+	1.08144i	−0.988663	+	0.150152i	$0.952024\pi$
$728$		0			0
$729$	22.8623	+	14.3637i	0.846750	+	0.531990i
$730$		0			0
$731$	−18.1656	+	31.4638i	−0.671880	+	1.16373i
$732$		0			0
$733$	19.7069	+	34.1334i	0.727891	+	1.26074i	0.957773	+	0.287526i	$0.0928327\pi$
$733$	19.7069	+	34.1334i	0.727891	+	1.26074i	−0.229882	+	0.973219i	$0.573834\pi$
$734$		0			0
$735$	−34.2763	−	3.21391i	−1.26430	−	0.118547i
$736$		0			0
$737$	−41.3741			−1.52403
$738$		0			0
$739$	13.3865			0.492429			0.246215	−	0.969215i	$-0.420813\pi$
$739$	13.3865			0.492429			0.246215	+	0.969215i	$0.420813\pi$
$740$		0			0
$741$	−7.14846	+	10.0750i	−0.262605	+	0.370114i
$742$		0			0
$743$	9.03777	+	15.6539i	0.331564	+	0.574285i	0.982819	−	0.184574i	$-0.0590905\pi$
$743$	9.03777	+	15.6539i	0.331564	+	0.574285i	−0.651255	+	0.758859i	$0.725757\pi$
$744$		0			0
$745$	−20.1628	+	34.9230i	−0.738708	+	1.27948i
$746$		0			0
$747$	−11.9890	−	34.2608i	−0.438655	−	1.25354i
$748$		0			0
$749$	−3.79252	+	6.56883i	−0.138576	+	0.240020i
$750$		0			0
$751$	−10.4782	−	18.1488i	−0.382356	−	0.662260i	0.609042	−	0.793138i	$-0.291554\pi$
$751$	−10.4782	−	18.1488i	−0.382356	−	0.662260i	−0.991399	+	0.130877i	$0.958221\pi$
$752$		0			0
$753$	14.5198	+	31.6508i	0.529132	+	1.15342i
$754$		0			0
$755$	37.7913			1.37537
$756$		0			0
$757$	40.0649			1.45618			0.728092	−	0.685479i	$-0.240407\pi$
$757$	40.0649			1.45618			0.728092	+	0.685479i	$0.240407\pi$
$758$		0			0
$759$	−6.91243	−	15.0679i	−0.250905	−	0.546932i
$760$		0			0
$761$	−0.455916	−	0.789670i	−0.0165269	−	0.0286255i	0.857644	−	0.514244i	$-0.171928\pi$
$761$	−0.455916	−	0.789670i	−0.0165269	−	0.0286255i	−0.874171	+	0.485619i	$0.838594\pi$
$762$		0			0
$763$	10.6799	−	18.4981i	0.386638	−	0.669676i
$764$		0			0
$765$	−34.1195	−	6.45517i	−1.23359	−	0.233387i
$766$		0			0
$767$	4.05223	−	7.01866i	0.146317	−	0.253429i
$768$		0			0
$769$	−12.3273	−	21.3514i	−0.444532	−	0.769952i	0.553487	−	0.832858i	$-0.313297\pi$
$769$	−12.3273	−	21.3514i	−0.444532	−	0.769952i	−0.998019	+	0.0629054i	$0.979963\pi$
$770$		0			0
$771$	17.1773	−	24.2095i	0.618624	−	0.871884i
$772$		0			0
$773$	−41.8304			−1.50454			−0.752268	−	0.658858i	$-0.771040\pi$
$773$	−41.8304			−1.50454			−0.752268	+	0.658858i	$0.771040\pi$
$774$		0			0
$775$	12.4349			0.446674
$776$		0			0
$777$	2.84341	+	0.266612i	0.102007	+	0.00956465i
$778$		0			0
$779$	−11.5894	−	20.0735i	−0.415235	−	0.719208i
$780$		0			0
$781$	20.8602	−	36.1310i	0.746438	−	1.29287i
$782$		0			0
$783$	−31.2273	+	30.0822i	−1.11597	+	1.07505i
$784$		0			0
$785$	−25.5390	+	44.2348i	−0.911526	+	1.57881i
$786$		0			0
$787$	8.80612	+	15.2526i	0.313904	+	0.543698i	0.979204	−	0.202878i	$-0.0650296\pi$
$787$	8.80612	+	15.2526i	0.313904	+	0.543698i	−0.665300	+	0.746576i	$0.731696\pi$
$788$		0			0
$789$	−34.6420	−	3.24820i	−1.23329	−	0.115639i
$790$		0			0
$791$	−6.75189			−0.240070
$792$		0			0
$793$	8.79738			0.312404
$794$		0			0
$795$	−8.24382	+	11.6188i	−0.292378	+	0.412076i
$796$		0			0
$797$	1.39125	+	2.40971i	0.0492805	+	0.0853563i	0.889613	−	0.456714i	$-0.150974\pi$
$797$	1.39125	+	2.40971i	0.0492805	+	0.0853563i	−0.840333	+	0.542071i	$0.817641\pi$
$798$		0			0
$799$	0.622213	−	1.07771i	0.0220123	−	0.0381265i
$800$		0			0
$801$	10.7184	−	12.4554i	0.378717	−	0.440092i
$802$		0			0
$803$	27.0645	−	46.8771i	0.955085	−	1.65426i
$804$		0			0
$805$	−5.41304	−	9.37567i	−0.190785	−	0.330449i
$806$		0			0
$807$	2.96669	+	6.46690i	0.104433	+	0.227646i
$808$		0			0
$809$	20.0046			0.703324			0.351662	−	0.936127i	$-0.385617\pi$
$809$	20.0046			0.703324			0.351662	+	0.936127i	$0.385617\pi$
$810$		0			0
$811$	21.7172			0.762593			0.381297	−	0.924453i	$-0.375478\pi$
$811$	21.7172			0.762593			0.381297	+	0.924453i	$0.375478\pi$
$812$		0			0
$813$	−9.53011	−	20.7741i	−0.334236	−	0.728578i
$814$		0			0
$815$	9.88466	+	17.1207i	0.346244	+	0.599713i
$816$		0			0
$817$	42.3119	−	73.2864i	1.48031	−	2.56397i
$818$		0			0
$819$	−2.58265	+	3.00119i	−0.0902449	+	0.104870i
$820$		0			0
$821$	−25.6483	+	44.4242i	−0.895133	+	1.55042i	−0.0614936	+	0.998107i	$0.519586\pi$
$821$	−25.6483	+	44.4242i	−0.895133	+	1.55042i	−0.833640	+	0.552309i	$0.813747\pi$
$822$		0			0
$823$	−7.54360	−	13.0659i	−0.262953	−	0.455449i	0.704072	−	0.710129i	$-0.251363\pi$
$823$	−7.54360	−	13.0659i	−0.262953	−	0.455449i	−0.967025	+	0.254680i	$0.918030\pi$
$824$		0			0
$825$	−41.0662	+	57.8784i	−1.42974	+	2.01507i
$826$		0			0
$827$	24.8406			0.863792			0.431896	−	0.901923i	$-0.357845\pi$
$827$	24.8406			0.863792			0.431896	+	0.901923i	$0.357845\pi$
$828$		0			0
$829$	−23.4924			−0.815924			−0.407962	−	0.912999i	$-0.633760\pi$
$829$	−23.4924			−0.815924			−0.407962	+	0.912999i	$0.633760\pi$
$830$		0			0
$831$	−38.9860	−	3.65552i	−1.35241	−	0.126808i
$832$		0			0
$833$	−8.05027	−	13.9435i	−0.278925	−	0.483113i
$834$		0			0
$835$	18.3598	−	31.8002i	0.635368	−	1.10049i
$836$		0			0
$837$	−1.67449	−	6.75114i	−0.0578788	−	0.233353i
$838$		0			0
$839$	22.7569	−	39.4161i	0.785656	−	1.36080i	−0.142950	−	0.989730i	$-0.545659\pi$
$839$	22.7569	−	39.4161i	0.785656	−	1.36080i	0.928606	−	0.371066i	$-0.121008\pi$
$840$		0			0
$841$	−20.3163	−	35.1889i	−0.700562	−	1.21341i
$842$		0			0
$843$	26.2786	+	2.46401i	0.905084	+	0.0848651i
$844$		0			0
$845$	3.78012			0.130040
$846$		0			0
$847$	11.1588			0.383422
$848$		0			0
$849$	−9.20480	+	12.9732i	−0.315908	+	0.445238i
$850$		0			0
$851$	−1.35547	−	2.34774i	−0.0464649	−	0.0804796i
$852$		0			0
$853$	8.22123	−	14.2396i	0.281489	−	0.487554i	−0.690262	−	0.723559i	$-0.742505\pi$
$853$	8.22123	−	14.2396i	0.281489	−	0.487554i	0.971752	+	0.236005i	$0.0758382\pi$
$854$		0			0
$855$	79.4722	+	15.0356i	2.71789	+	0.514206i
$856$		0			0
$857$	−7.08343	+	12.2689i	−0.241965	+	0.419096i	−0.961274	−	0.275594i	$-0.911125\pi$
$857$	−7.08343	+	12.2689i	−0.241965	+	0.419096i	0.719309	+	0.694690i	$0.244459\pi$
$858$		0			0
$859$	−26.9365	−	46.6554i	−0.919062	−	1.59186i	−0.800844	−	0.598874i	$-0.795615\pi$
$859$	−26.9365	−	46.6554i	−0.919062	−	1.59186i	−0.118218	−	0.992988i	$-0.537718\pi$
$860$		0			0
$861$	−3.09773	−	6.75254i	−0.105570	−	0.230126i
$862$		0			0
$863$	−23.9687			−0.815905			−0.407952	−	0.913003i	$-0.633757\pi$
$863$	−23.9687			−0.815905			−0.407952	+	0.913003i	$0.633757\pi$
$864$		0			0
$865$	−92.6887			−3.15151
$866$		0			0
$867$	5.50602	+	12.0022i	0.186994	+	0.407616i
$868$		0			0
$869$	−16.0566	−	27.8109i	−0.544684	−	0.943421i
$870$		0			0
$871$	4.69012	−	8.12353i	0.158919	−	0.275255i
$872$		0			0
$873$	−13.2814	−	37.9541i	−0.449508	−	1.28455i
$874$		0			0
$875$	−10.6998	+	18.5325i	−0.361718	+	0.626514i
$876$		0			0
$877$	7.89845	+	13.6805i	0.266712	+	0.461958i	0.968011	−	0.250909i	$-0.0807295\pi$
$877$	7.89845	+	13.6805i	0.266712	+	0.461958i	−0.701299	+	0.712867i	$0.747396\pi$
$878$		0			0
$879$	0.466438	−	0.657395i	0.0157326	−	0.0221734i
$880$		0			0
$881$	−47.9966			−1.61705			−0.808523	−	0.588464i	$-0.799733\pi$
$881$	−47.9966			−1.61705			−0.808523	+	0.588464i	$0.799733\pi$
$882$		0			0
$883$	−30.6008			−1.02980			−0.514899	−	0.857251i	$-0.672171\pi$
$883$	−30.6008			−1.02980			−0.514899	+	0.857251i	$0.672171\pi$
$884$		0			0
$885$	−52.8310	−	4.95369i	−1.77590	−	0.166517i
$886$		0			0
$887$	−17.1661	−	29.7326i	−0.576382	−	0.998323i	−0.995890	−	0.0905710i	$-0.971131\pi$
$887$	−17.1661	−	29.7326i	−0.576382	−	0.998323i	0.419508	−	0.907752i	$-0.362203\pi$
$888$		0			0
$889$	11.5167	−	19.9475i	0.386257	−	0.669016i
$890$		0			0
$891$	36.9533	+	14.5017i	1.23798	+	0.485825i
$892$		0			0
$893$	−1.44928	+	2.51022i	−0.0484983	+	0.0840015i
$894$		0			0
$895$	36.7628	+	63.6750i	1.22884	+	2.12842i
$896$		0			0
$897$	3.74208	+	0.350876i	0.124944	+	0.0117154i
$898$		0			0
$899$	11.1703			0.372551
$900$		0			0
$901$	−6.66266			−0.221966
$902$		0			0
$903$	15.6952	−	22.1208i	0.522305	−	0.736133i
$904$		0			0
$905$	−29.1968	−	50.5704i	−0.970535	−	1.68102i
$906$		0			0
$907$	−8.32595	+	14.4210i	−0.276459	+	0.478840i	−0.970502	−	0.241093i	$-0.922494\pi$
$907$	−8.32595	+	14.4210i	−0.276459	+	0.478840i	0.694044	+	0.719933i	$0.255828\pi$
$908$		0			0
$909$	13.1872	+	37.6849i	0.437392	+	1.24993i
$910$		0			0
$911$	4.00817	−	6.94235i	0.132797	−	0.230010i	−0.791957	−	0.610577i	$-0.790938\pi$
$911$	4.00817	−	6.94235i	0.132797	−	0.230010i	0.924754	+	0.380566i	$0.124271\pi$
$912$		0			0
$913$	−26.6836	−	46.2174i	−0.883099	−	1.52957i
$914$		0			0
$915$	−24.0172	−	52.3535i	−0.793984	−	1.73075i
$916$		0			0
$917$	−4.05746			−0.133989
$918$		0			0
$919$	3.98767			0.131541			0.0657705	−	0.997835i	$-0.479049\pi$
$919$	3.98767			0.131541			0.0657705	+	0.997835i	$0.479049\pi$
$920$		0			0
$921$	9.96906	+	21.7309i	0.328492	+	0.716057i
$922$		0			0
$923$	4.72939	+	8.19155i	0.155670	+	0.269628i
$924$		0			0
$925$	−5.80256	+	10.0503i	−0.190787	+	0.330453i
$926$		0			0
$927$	−3.97972	−	0.752936i	−0.130711	−	0.0247296i
$928$		0			0
$929$	3.22140	−	5.57962i	0.105691	−	0.183062i	−0.808330	−	0.588730i	$-0.799628\pi$
$929$	3.22140	−	5.57962i	0.105691	−	0.183062i	0.914020	+	0.405669i	$0.132961\pi$
$930$		0			0
$931$	18.7509	+	32.4776i	0.614537	+	1.06441i
$932$		0			0
$933$	−7.20731	+	10.1579i	−0.235957	+	0.332556i
$934$		0			0
$935$	−51.0542			−1.66965
$936$		0			0
$937$	12.2388			0.399824			0.199912	−	0.979814i	$-0.435934\pi$
$937$	12.2388			0.399824			0.199912	+	0.979814i	$0.435934\pi$
$938$		0			0
$939$	−14.2864	−	1.33957i	−0.466221	−	0.0437151i
$940$		0			0
$941$	−9.99773	−	17.3166i	−0.325917	−	0.564504i	0.655781	−	0.754951i	$-0.272340\pi$
$941$	−9.99773	−	17.3166i	−0.325917	−	0.564504i	−0.981697	+	0.190447i	$0.939006\pi$
$942$		0			0
$943$	−3.52607	+	6.10733i	−0.114825	+	0.198882i
$944$		0			0
$945$	24.9109	+	7.17604i	0.810351	+	0.233437i
$946$		0			0
$947$	−17.6942	+	30.6472i	−0.574983	+	0.995899i	0.421061	+	0.907032i	$0.361658\pi$
$947$	−17.6942	+	30.6472i	−0.574983	+	0.995899i	−0.996044	+	0.0888669i	$0.971675\pi$
$948$		0			0
$949$	6.13601	+	10.6279i	0.199183	+	0.344996i
$950$		0			0
$951$	7.62836	+	0.715272i	0.247366	+	0.0231943i
$952$		0			0
$953$	11.3690			0.368278			0.184139	−	0.982900i	$-0.441050\pi$
$953$	11.3690			0.368278			0.184139	+	0.982900i	$0.441050\pi$
$954$		0			0
$955$	−32.6420			−1.05627
$956$		0			0
$957$	−36.8899	+	51.9924i	−1.19248	+	1.68068i
$958$		0			0
$959$	−8.45286	−	14.6408i	−0.272957	−	0.472776i
$960$		0			0
$961$	14.6040	−	25.2949i	0.471098	−	0.815966i
$962$		0			0
$963$	−11.2460	+	13.0685i	−0.362396	+	0.421126i
$964$		0			0
$965$	−34.6736	+	60.0564i	−1.11618	+	1.93329i
$966$		0			0
$967$	−29.3632	−	50.8586i	−0.944258	−	1.63550i	−0.757229	−	0.653149i	$-0.773447\pi$
$967$	−29.3632	−	50.8586i	−0.944258	−	1.63550i	−0.187029	−	0.982354i	$-0.559886\pi$
$968$		0			0
$969$	15.7725	+	34.3815i	0.506686	+	1.10449i
$970$		0			0
$971$	15.1168			0.485121			0.242560	−	0.970136i	$-0.422013\pi$
$971$	15.1168			0.485121			0.242560	+	0.970136i	$0.422013\pi$
$972$		0			0
$973$	−25.4172			−0.814839
$974$		0			0
$975$	−6.70883	−	14.6241i	−0.214854	−	0.468347i
$976$		0			0
$977$	−27.1415	−	47.0105i	−0.868335	−	1.50400i	−0.863698	−	0.504010i	$-0.831857\pi$
$977$	−27.1415	−	47.0105i	−0.868335	−	1.50400i	−0.00463697	−	0.999989i	$-0.501476\pi$
$978$		0			0
$979$	12.0799	−	20.9230i	0.386075	−	0.668701i
$980$		0			0
$981$	31.6691	−	36.8014i	1.01112	−	1.17498i
$982$		0			0
$983$	−15.7221	+	27.2316i	−0.501459	+	0.868552i	0.498540	+	0.866867i	$0.333870\pi$
$983$	−15.7221	+	27.2316i	−0.501459	+	0.868552i	−0.999999	+	0.00168512i	$0.999464\pi$
$984$		0			0
$985$	6.17478	+	10.6950i	0.196745	+	0.340772i
$986$		0			0
$987$	−0.537597	+	0.757686i	−0.0171119	+	0.0241174i
$988$		0			0
$989$	−25.7467			−0.818697
$990$		0			0
$991$	−42.6265			−1.35408			−0.677038	−	0.735948i	$-0.736737\pi$
$991$	−42.6265			−1.35408			−0.677038	+	0.735948i	$0.736737\pi$
$992$		0			0
$993$	−40.3566	−	3.78404i	−1.28068	−	0.120083i
$994$		0			0
$995$	−34.9470	−	60.5300i	−1.10789	−	1.91893i
$996$		0			0
$997$	5.60659	−	9.71091i	0.177563	−	0.307548i	−0.763483	−	0.645829i	$-0.776512\pi$
$997$	5.60659	−	9.71091i	0.177563	−	0.307548i	0.941045	+	0.338281i	$0.109845\pi$
$998$		0			0
$999$	6.23789	+	1.79694i	0.197358	+	0.0568526i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.q.g.313.4	✓	22
3.2	odd	2		2808.2.q.g.937.11		22
9.2	odd	6		8424.2.a.be.1.1		11
9.4	even	3	inner	936.2.q.g.625.4	yes	22
9.5	odd	6		2808.2.q.g.1873.11		22
9.7	even	3		8424.2.a.bf.1.11		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.q.g.313.4	✓	22	1.1	even	1	trivial
936.2.q.g.625.4	yes	22	9.4	even	3	inner
2808.2.q.g.937.11		22	3.2	odd	2
2808.2.q.g.1873.11		22	9.5	odd	6
8424.2.a.be.1.1		11	9.2	odd	6
8424.2.a.bf.1.11		11	9.7	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.722210 - 1.57430i) q^{3} +(-1.89006 - 3.27368i) q^{5} +(-0.659907 + 1.14299i) q^{7} +(-1.95682 + 2.27395i) q^{9} +(-2.20538 + 3.81984i) q^{11} +(-0.500000 - 0.866025i) q^{13} +(-3.78872 + 5.33980i) q^{15} -3.06205 q^{17} +7.13223 q^{19} +(2.27600 + 0.213409i) q^{21} +(-1.08498 - 1.87925i) q^{23} +(-4.64465 + 8.04477i) q^{25} +(4.99311 + 1.43836i) q^{27} +(-4.17231 + 7.22665i) q^{29} +(-0.669313 - 1.15928i) q^{31} +(7.60631 + 0.713205i) q^{33} +4.98905 q^{35} +1.24930 q^{37} +(-1.00228 + 1.41260i) q^{39} +(-1.62494 - 2.81448i) q^{41} +(5.93250 - 10.2754i) q^{43} +(11.1427 + 2.10812i) q^{45} +(-0.203201 + 0.351955i) q^{47} +(2.62905 + 4.55364i) q^{49} +(2.21144 + 4.82058i) q^{51} +2.17588 q^{53} +16.6732 q^{55} +(-5.15097 - 11.2282i) q^{57} +(4.05223 + 7.01866i) q^{59} +(-4.39869 + 7.61875i) q^{61} +(-1.30778 - 3.73723i) q^{63} +(-1.89006 + 3.27368i) q^{65} +(4.69012 + 8.12353i) q^{67} +(-2.17491 + 3.06530i) q^{69} -9.45879 q^{71} -12.2720 q^{73} +(16.0193 + 1.50205i) q^{75} +(-2.91070 - 5.04147i) q^{77} +(-3.64033 + 6.30524i) q^{79} +(-1.34167 - 8.89943i) q^{81} +(-6.04966 + 10.4783i) q^{83} +(5.78746 + 10.0242i) q^{85} +(14.3902 + 1.34929i) q^{87} -5.47746 q^{89} +1.31981 q^{91} +(-1.34167 + 1.89094i) q^{93} +(-13.4803 - 23.3486i) q^{95} +(-6.70181 + 11.6079i) q^{97} +(-4.37056 - 12.4897i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 3 q^{5} - 4 q^{7} - 4 q^{9} + 5 q^{11} - 11 q^{13} + 5 q^{15} + 8 q^{17} + 10 q^{19} + 4 q^{21} + 9 q^{23} - 24 q^{25} - 12 q^{27} - 16 q^{29} - q^{31} + 9 q^{33} + 18 q^{37} + 3 q^{39} - 6 q^{41}+ \cdots - 109 q^{99}+O(q^{100}) \) 22 * q - 3 * q^5 - 4 * q^7 - 4 * q^9 + 5 * q^11 - 11 * q^13 + 5 * q^15 + 8 * q^17 + 10 * q^19 + 4 * q^21 + 9 * q^23 - 24 * q^25 - 12 * q^27 - 16 * q^29 - q^31 + 9 * q^33 + 18 * q^37 + 3 * q^39 - 6 * q^41 - 7 * q^43 - 21 * q^45 + 21 * q^47 - 27 * q^49 - 11 * q^51 + 32 * q^53 + 34 * q^55 + 2 * q^57 + 11 * q^59 - 2 * q^61 - 27 * q^63 - 3 * q^65 - 18 * q^67 + 7 * q^69 - 30 * q^71 + 18 * q^73 + 62 * q^75 - 9 * q^77 - 30 * q^79 + 4 * q^81 - 16 * q^83 - 32 * q^85 + 33 * q^87 + 26 * q^89 + 8 * q^91 + 20 * q^95 - 10 * q^97 - 109 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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