LMFDB - Embedded newform 820.2.bi.a.189.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(189,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 5, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.189"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.bi (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			189.1
Character	$\chi$	$=$	820.189
Dual form			820.2.bi.a.269.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.03349 q^{3} +(1.66279 + 1.49503i) q^{5} +(-0.0669129 - 0.205937i) q^{7} +6.20209 q^{9} +(-2.13114 - 2.93326i) q^{11} +(0.699493 - 2.15282i) q^{13} +(-5.04407 - 4.53517i) q^{15} +(-2.80914 + 2.04096i) q^{17} +(-2.36798 + 0.769403i) q^{19} +(0.202980 + 0.624708i) q^{21} +(5.90545 + 1.91880i) q^{23} +(0.529751 + 4.97186i) q^{25} -9.71351 q^{27} +(3.38875 - 4.66421i) q^{29} +(-0.260464 + 0.189238i) q^{31} +(6.46479 + 8.89802i) q^{33} +(0.196620 - 0.442467i) q^{35} +(4.68159 - 6.44365i) q^{37} +(-2.12191 + 6.53056i) q^{39} +(1.70127 + 6.17298i) q^{41} +(5.69152 + 1.84929i) q^{43} +(10.3128 + 9.27233i) q^{45} +(3.16195 - 9.73150i) q^{47} +(5.62519 - 4.08694i) q^{49} +(8.52152 - 6.19124i) q^{51} +(8.51902 + 6.18943i) q^{53} +(0.841683 - 8.06352i) q^{55} +(7.18325 - 2.33398i) q^{57} +(1.33099 - 4.09637i) q^{59} +(-1.56003 - 4.80128i) q^{61} +(-0.415000 - 1.27724i) q^{63} +(4.38164 - 2.53392i) q^{65} +(5.42363 + 3.94050i) q^{67} +(-17.9141 - 5.82066i) q^{69} +(9.55669 + 13.1537i) q^{71} +6.64621i q^{73} +(-1.60700 - 15.0821i) q^{75} +(-0.461465 + 0.635152i) q^{77} +0.296675i q^{79} +10.8596 q^{81} +3.09381i q^{83} +(-7.72232 - 0.806068i) q^{85} +(-10.2798 + 14.1489i) q^{87} +(-9.05444 + 2.94197i) q^{89} -0.490149 q^{91} +(0.790117 - 0.574054i) q^{93} +(-5.08774 - 2.26085i) q^{95} +(-3.18534 - 2.31429i) q^{97} +(-13.2175 - 18.1923i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 68 q^{9} + 10 q^{15} - 26 q^{21} + 10 q^{25} - 20 q^{29} + 4 q^{31} + 15 q^{35} - 8 q^{39} + 4 q^{41} - 4 q^{45} + 18 q^{49} + 52 q^{51} - 36 q^{59} - 42 q^{61} - 15 q^{65} + 30 q^{69} - 20 q^{75}+ \cdots + 80 q^{99}+O(q^{100}) $ 80 * q + 68 * q^9 + 10 * q^15 - 26 * q^21 + 10 * q^25 - 20 * q^29 + 4 * q^31 + 15 * q^35 - 8 * q^39 + 4 * q^41 - 4 * q^45 + 18 * q^49 + 52 * q^51 - 36 * q^59 - 42 * q^61 - 15 * q^65 + 30 * q^69 - 20 * q^75 + 32 * q^81 + 10 * q^89 - 132 * q^91 + 50 * q^95 + 80 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{1}{10}\right)$	$-1$

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
$3$	−3.03349			−1.75139			−0.875694	−	0.482866i	$-0.839596\pi$
$3$	−3.03349			−1.75139			−0.875694	+	0.482866i	$0.839596\pi$
$4$		0			0
$5$	1.66279	+	1.49503i	0.743623	+	0.668599i
$5$	1.66279	+	1.49503i	0.743623	+	0.668599i
$6$		0			0
$7$	−0.0669129	−	0.205937i	−0.0252907	−	0.0778368i	0.937615	−	0.347677i	$-0.113029\pi$
$7$	−0.0669129	−	0.205937i	−0.0252907	−	0.0778368i	−0.962905	+	0.269840i	$0.913029\pi$
$8$		0			0
$9$	6.20209			2.06736
$10$		0			0
$11$	−2.13114	−	2.93326i	−0.642562	−	0.884411i	0.356187	−	0.934415i	$-0.384077\pi$
$11$	−2.13114	−	2.93326i	−0.642562	−	0.884411i	−0.998749	+	0.0500038i	$0.984077\pi$
$12$		0			0
$13$	0.699493	−	2.15282i	0.194004	−	0.597084i	−0.805982	−	0.591940i	$-0.798362\pi$
$13$	0.699493	−	2.15282i	0.194004	−	0.597084i	0.999987	−	0.00514462i	$-0.00163759\pi$
$14$		0			0
$15$	−5.04407	−	4.53517i	−1.30237	−	1.17098i
$16$		0			0
$17$	−2.80914	+	2.04096i	−0.681317	+	0.495006i	−0.873794	−	0.486296i	$-0.838348\pi$
$17$	−2.80914	+	2.04096i	−0.681317	+	0.495006i	0.192477	+	0.981301i	$0.438348\pi$
$18$		0			0
$19$	−2.36798	+	0.769403i	−0.543252	+	0.176513i	−0.567772	−	0.823186i	$-0.692194\pi$
$19$	−2.36798	+	0.769403i	−0.543252	+	0.176513i	0.0245198	+	0.999699i	$0.492194\pi$
$20$		0			0
$21$	0.202980	+	0.624708i	0.0442938	+	0.136322i
$22$		0			0
$23$	5.90545	+	1.91880i	1.23137	+	0.400097i	0.851211	−	0.524824i	$-0.175869\pi$
$23$	5.90545	+	1.91880i	1.23137	+	0.400097i	0.380160	+	0.924921i	$0.375869\pi$
$24$		0			0
$25$	0.529751	+	4.97186i	0.105950	+	0.994371i
$26$		0			0
$27$	−9.71351			−1.86937
$28$		0			0
$29$	3.38875	−	4.66421i	0.629275	−	0.866123i	−0.368712	−	0.929544i	$-0.620201\pi$
$29$	3.38875	−	4.66421i	0.629275	−	0.866123i	0.997987	+	0.0634209i	$0.0202011\pi$
$30$		0			0
$31$	−0.260464	+	0.189238i	−0.0467808	+	0.0339882i	−0.610930	−	0.791685i	$-0.709204\pi$
$31$	−0.260464	+	0.189238i	−0.0467808	+	0.0339882i	0.564149	+	0.825673i	$0.309204\pi$
$32$		0			0
$33$	6.46479	+	8.89802i	1.12538	+	1.54895i
$34$		0			0
$35$	0.196620	−	0.442467i	0.0332349	−	0.0747905i
$36$		0			0
$37$	4.68159	−	6.44365i	0.769648	−	1.05933i	−0.226702	−	0.973964i	$-0.572794\pi$
$37$	4.68159	−	6.44365i	0.769648	−	1.05933i	0.996350	−	0.0853656i	$-0.0272058\pi$
$38$		0			0
$39$	−2.12191	+	6.53056i	−0.339777	+	1.04573i
$40$		0			0
$41$	1.70127	+	6.17298i	0.265694	+	0.964058i
$41$	1.70127	+	6.17298i	0.265694	+	0.964058i
$42$		0			0
$43$	5.69152	+	1.84929i	0.867949	+	0.282014i	0.708945	−	0.705264i	$-0.249172\pi$
$43$	5.69152	+	1.84929i	0.867949	+	0.282014i	0.159005	+	0.987278i	$0.449172\pi$
$44$		0			0
$45$	10.3128	+	9.27233i	1.53734	+	1.38224i
$46$		0			0
$47$	3.16195	−	9.73150i	0.461218	−	1.41948i	−0.402458	−	0.915438i	$-0.631844\pi$
$47$	3.16195	−	9.73150i	0.461218	−	1.41948i	0.863677	−	0.504046i	$-0.168156\pi$
$48$		0			0
$49$	5.62519	−	4.08694i	0.803598	−	0.583848i
$50$		0			0
$51$	8.52152	−	6.19124i	1.19325	−	0.866948i
$52$		0			0
$53$	8.51902	+	6.18943i	1.17018	+	0.850184i	0.991030	−	0.133639i	$-0.0426661\pi$
$53$	8.51902	+	6.18943i	1.17018	+	0.850184i	0.179147	+	0.983822i	$0.442666\pi$
$54$		0			0
$55$	0.841683	−	8.06352i	0.113493	−	1.08728i
$56$		0			0
$57$	7.18325	−	2.33398i	0.951445	−	0.309143i
$58$		0			0
$59$	1.33099	−	4.09637i	0.173280	−	0.533302i	−0.826270	−	0.563274i	$-0.809542\pi$
$59$	1.33099	−	4.09637i	0.173280	−	0.533302i	0.999551	+	0.0299716i	$0.00954167\pi$
$60$		0			0
$61$	−1.56003	−	4.80128i	−0.199742	−	0.614741i	−0.999888	−	0.0149371i	$-0.995245\pi$
$61$	−1.56003	−	4.80128i	−0.199742	−	0.614741i	0.800147	−	0.599804i	$-0.204755\pi$
$62$		0			0
$63$	−0.415000	−	1.27724i	−0.0522850	−	0.160917i
$64$		0			0
$65$	4.38164	−	2.53392i	0.543476	−	0.314294i
$66$		0			0
$67$	5.42363	+	3.94050i	0.662602	+	0.481408i	0.867540	−	0.497367i	$-0.165700\pi$
$67$	5.42363	+	3.94050i	0.662602	+	0.481408i	−0.204939	+	0.978775i	$0.565700\pi$
$68$		0			0
$69$	−17.9141	−	5.82066i	−2.15661	−	0.700725i
$70$		0			0
$71$	9.55669	+	13.1537i	1.13417	+	1.56105i	0.779895	+	0.625910i	$0.215272\pi$
$71$	9.55669	+	13.1537i	1.13417	+	1.56105i	0.354275	+	0.935141i	$0.384728\pi$
$72$		0			0
$73$			6.64621i			0.777880i	0.921263	+	0.388940i	$0.127159\pi$
$73$			6.64621i			0.777880i	−0.921263	+	0.388940i	$0.872841\pi$
$74$		0			0
$75$	−1.60700	−	15.0821i	−0.185560	−	1.74153i
$76$		0			0
$77$	−0.461465	+	0.635152i	−0.0525888	+	0.0723823i
$78$		0			0
$79$			0.296675i			0.0333786i	0.999861	+	0.0166893i	$0.00531261\pi$
$79$			0.296675i			0.0333786i	−0.999861	+	0.0166893i	$0.994687\pi$
$80$		0			0
$81$	10.8596			1.20662
$82$		0			0
$83$			3.09381i			0.339590i	0.985479	+	0.169795i	$0.0543105\pi$
$83$			3.09381i			0.339590i	−0.985479	+	0.169795i	$0.945690\pi$
$84$		0			0
$85$	−7.72232	−	0.806068i	−0.837604	−	0.0874304i
$86$		0			0
$87$	−10.2798	+	14.1489i	−1.10211	+	1.51692i
$88$		0			0
$89$	−9.05444	+	2.94197i	−0.959769	+	0.311848i	−0.746679	−	0.665185i	$-0.768353\pi$
$89$	−9.05444	+	2.94197i	−0.959769	+	0.311848i	−0.213090	+	0.977033i	$0.568353\pi$
$90$		0			0
$91$	−0.490149			−0.0513816
$92$		0			0
$93$	0.790117	−	0.574054i	0.0819314	−	0.0595266i
$94$		0			0
$95$	−5.08774	−	2.26085i	−0.521991	−	0.231958i
$96$		0			0
$97$	−3.18534	−	2.31429i	−0.323423	−	0.234980i	0.414212	−	0.910180i	$-0.364057\pi$
$97$	−3.18534	−	2.31429i	−0.323423	−	0.234980i	−0.737635	+	0.675200i	$0.764057\pi$
$98$		0			0
$99$	−13.2175	−	18.1923i	−1.32841	−	1.82840i
$100$		0			0
$101$	12.4684	−	4.05121i	1.24065	−	0.403111i	0.386087	−	0.922462i	$-0.373827\pi$
$101$	12.4684	−	4.05121i	1.24065	−	0.403111i	0.854561	+	0.519352i	$0.173827\pi$
$102$		0			0
$103$	3.95669	−	1.28561i	0.389864	−	0.126675i	−0.107524	−	0.994202i	$-0.534292\pi$
$103$	3.95669	−	1.28561i	0.389864	−	0.126675i	0.497388	+	0.867528i	$0.334292\pi$
$104$		0			0
$105$	−0.596446	+	1.34222i	−0.0582072	+	0.130987i
$106$		0			0
$107$	2.64208	−	0.858463i	0.255419	−	0.0829907i	−0.178509	−	0.983938i	$-0.557127\pi$
$107$	2.64208	−	0.858463i	0.255419	−	0.0829907i	0.433928	+	0.900948i	$0.357127\pi$
$108$		0			0
$109$		−	0.107588i		−	0.0103050i	−0.999987	−	0.00515251i	$-0.998360\pi$
$109$		−	0.107588i		−	0.0103050i	0.999987	−	0.00515251i	$-0.00164010\pi$
$110$		0			0
$111$	−14.2016	+	19.5468i	−1.34795	+	1.85530i
$112$		0			0
$113$	4.68542	+	6.44892i	0.440767	+	0.606664i	0.970382	−	0.241574i	$-0.0776637\pi$
$113$	4.68542	+	6.44892i	0.440767	+	0.606664i	−0.529615	+	0.848238i	$0.677664\pi$
$114$		0			0
$115$	6.95086	+	12.0194i	0.648171	+	1.12081i
$116$		0			0
$117$	4.33831	−	13.3520i	0.401077	−	1.23439i
$118$		0			0
$119$	0.608277	+	0.441939i	0.0557606	+	0.0405125i
$120$		0			0
$121$	−0.663075	+	2.04074i	−0.0602796	+	0.185521i
$122$		0			0
$123$	−5.16079	−	18.7257i	−0.465333	−	1.68844i
$124$		0			0
$125$	−6.55223	+	9.05916i	−0.586049	+	0.810276i
$126$		0			0
$127$	−3.76949	+	5.18825i	−0.334488	+	0.460383i	−0.942821	−	0.333299i	$-0.891838\pi$
$127$	−3.76949	+	5.18825i	−0.334488	+	0.460383i	0.608334	+	0.793681i	$0.291838\pi$
$128$		0			0
$129$	−17.2652	−	5.60981i	−1.52012	−	0.493916i
$130$		0			0
$131$	16.6441	−	12.0926i	1.45420	−	1.05654i	0.469370	−	0.883002i	$-0.344481\pi$
$131$	16.6441	−	12.0926i	1.45420	−	1.05654i	0.984828	−	0.173535i	$-0.0555189\pi$
$132$		0			0
$133$	0.316897	+	0.436171i	0.0274784	+	0.0378208i
$134$		0			0
$135$	−16.1515	−	14.5220i	−1.39010	−	1.24986i
$136$		0			0
$137$	−15.3781			−1.31384			−0.656918	−	0.753962i	$-0.728140\pi$
$137$	−15.3781			−1.31384			−0.656918	+	0.753962i	$0.728140\pi$
$138$		0			0
$139$	1.01205	+	3.11478i	0.0858412	+	0.264192i	0.984759	−	0.173926i	$-0.0556453\pi$
$139$	1.01205	+	3.11478i	0.0858412	+	0.264192i	−0.898918	+	0.438118i	$0.855645\pi$
$140$		0			0
$141$	−9.59177	+	29.5204i	−0.807773	+	2.48607i
$142$		0			0
$143$	−7.80549	+	2.53616i	−0.652728	+	0.212084i
$144$		0			0
$145$	12.6079	−	2.68932i	1.04703	−	0.223336i
$146$		0			0
$147$	−17.0640	+	12.3977i	−1.40741	+	1.02254i
$148$		0			0
$149$	3.39798	−	4.67691i	0.278373	−	0.383148i	−0.646821	−	0.762642i	$-0.723902\pi$
$149$	3.39798	−	4.67691i	0.278373	−	0.383148i	0.925194	+	0.379494i	$0.123902\pi$
$150$		0			0
$151$	−8.27772	−	2.68960i	−0.673632	−	0.218876i	−0.0478265	−	0.998856i	$-0.515229\pi$
$151$	−8.27772	−	2.68960i	−0.673632	−	0.218876i	−0.625805	+	0.779980i	$0.715229\pi$
$152$		0			0
$153$	−17.4225	+	12.6582i	−1.40853	+	1.02336i
$154$		0			0
$155$	−0.716016	−	0.0747389i	−0.0575118	−	0.00600317i
$156$		0			0
$157$	−5.42870	−	16.7078i	−0.433258	−	1.33343i	−0.894862	−	0.446344i	$-0.852726\pi$
$157$	−5.42870	−	16.7078i	−0.433258	−	1.33343i	0.461604	−	0.887086i	$-0.347274\pi$
$158$		0			0
$159$	−25.8424	−	18.7756i	−2.04944	−	1.48900i
$160$		0			0
$161$		−	1.34454i		−	0.105965i
$162$		0			0
$163$		−	7.59370i		−	0.594784i	−0.954755	−	0.297392i	$-0.903883\pi$
$163$		−	7.59370i		−	0.594784i	0.954755	−	0.297392i	$-0.0961169\pi$
$164$		0			0
$165$	−2.55324	+	24.4606i	−0.198770	+	1.90426i
$166$		0			0
$167$	7.87999			0.609772			0.304886	−	0.952389i	$-0.401382\pi$
$167$	7.87999			0.609772			0.304886	+	0.952389i	$0.401382\pi$
$168$		0			0
$169$	6.37189	+	4.62945i	0.490145	+	0.356111i
$170$		0			0
$171$	−14.6864	+	4.77190i	−1.12310	+	0.364917i
$172$		0			0
$173$		−	13.9308i		−	1.05914i	−0.848265	−	0.529571i	$-0.822353\pi$
$173$		−	13.9308i		−	1.05914i	0.848265	−	0.529571i	$-0.177647\pi$
$174$		0			0
$175$	0.988441	−	0.441776i	0.0747191	−	0.0333952i
$176$		0			0
$177$	−4.03756	+	12.4263i	−0.303481	+	0.934019i
$178$		0			0
$179$	−8.17015	+	11.2452i	−0.610665	+	0.840509i	−0.996632	−	0.0820040i	$-0.973868\pi$
$179$	−8.17015	+	11.2452i	−0.610665	+	0.840509i	0.385967	+	0.922513i	$0.373868\pi$
$180$		0			0
$181$	−4.82223	−	6.63723i	−0.358434	−	0.493342i	0.591278	−	0.806468i	$-0.298624\pi$
$181$	−4.82223	−	6.63723i	−0.358434	−	0.493342i	−0.949712	+	0.313126i	$0.898624\pi$
$182$		0			0
$183$	4.73234	+	14.5647i	0.349825	+	1.07665i
$184$		0			0
$185$	17.4180	−	3.71532i	1.28060	−	0.273156i
$186$		0			0
$187$	11.9733	+	3.89037i	0.875577	+	0.284492i
$188$		0			0
$189$	0.649959	+	2.00037i	0.0472776	+	0.145505i
$190$		0			0
$191$		−	15.8216i		−	1.14481i	−0.819970	−	0.572406i	$-0.806010\pi$
$191$		−	15.8216i		−	1.14481i	0.819970	−	0.572406i	$-0.193990\pi$
$192$		0			0
$193$	17.3526	+	12.6074i	1.24907	+	0.907502i	0.998168	−	0.0605111i	$-0.0192731\pi$
$193$	17.3526	+	12.6074i	1.24907	+	0.907502i	0.250901	+	0.968013i	$0.419273\pi$
$194$		0			0
$195$	−13.2917	+	7.68664i	−0.951838	+	0.550451i
$196$		0			0
$197$	−13.9828	−	19.2457i	−0.996233	−	1.37120i	−0.927608	−	0.373554i	$-0.878139\pi$
$197$	−13.9828	−	19.2457i	−0.996233	−	1.37120i	−0.0686245	−	0.997643i	$-0.521861\pi$
$198$		0			0
$199$	−18.9316	−	6.15125i	−1.34203	−	0.436050i	−0.452023	−	0.892006i	$-0.649297\pi$
$199$	−18.9316	−	6.15125i	−1.34203	−	0.436050i	−0.890002	+	0.455956i	$0.849297\pi$
$200$		0			0
$201$	−16.4525	−	11.9535i	−1.16047	−	0.843133i
$202$		0			0
$203$	−1.18728	−	0.385772i	−0.0833310	−	0.0270759i
$204$		0			0
$205$	−6.39996	+	12.8078i	−0.446992	+	0.894538i
$206$		0			0
$207$	36.6261	+	11.9005i	2.54569	+	0.827144i
$208$		0			0
$209$	7.30335	+	5.30619i	0.505183	+	0.367037i
$210$		0			0
$211$	−23.7692	−	7.72308i	−1.63634	−	0.531679i	−0.660622	−	0.750718i	$-0.729708\pi$
$211$	−23.7692	−	7.72308i	−1.63634	−	0.531679i	−0.975716	+	0.219040i	$0.929708\pi$
$212$		0			0
$213$	−28.9902	−	39.9015i	−1.98637	−	2.73401i
$214$		0			0
$215$	6.69907	+	11.5840i	0.456873	+	0.790022i
$216$		0			0
$217$	0.0563996	+	0.0409767i	0.00382865	+	0.00278168i
$218$		0			0
$219$		−	20.1612i		−	1.36237i
$220$		0			0
$221$	2.42884	+	7.47521i	0.163382	+	0.502837i
$222$		0			0
$223$	−3.38854	−	1.10100i	−0.226913	−	0.0737286i	0.193354	−	0.981129i	$-0.438064\pi$
$223$	−3.38854	−	1.10100i	−0.226913	−	0.0737286i	−0.420267	+	0.907401i	$0.638064\pi$
$224$		0			0
$225$	3.28556	+	30.8359i	0.219037	+	2.05573i
$226$		0			0
$227$	8.63058	+	26.5622i	0.572832	+	1.76300i	0.643446	+	0.765492i	$0.277504\pi$
$227$	8.63058	+	26.5622i	0.572832	+	1.76300i	−0.0706139	+	0.997504i	$0.522496\pi$
$228$		0			0
$229$	−1.63343	−	2.24823i	−0.107940	−	0.148567i	0.751629	−	0.659586i	$-0.229268\pi$
$229$	−1.63343	−	2.24823i	−0.107940	−	0.148567i	−0.859570	+	0.511019i	$0.829268\pi$
$230$		0			0
$231$	1.39985	−	1.92673i	0.0921035	−	0.126770i
$232$		0			0
$233$	−2.55997	+	7.87877i	−0.167709	+	0.516155i	−0.999226	−	0.0393445i	$-0.987473\pi$
$233$	−2.55997	+	7.87877i	−0.167709	+	0.516155i	0.831517	+	0.555500i	$0.187473\pi$
$234$		0			0
$235$	19.8066	−	11.4542i	1.29204	−	0.747191i
$236$		0			0
$237$		−	0.899963i		−	0.0584589i
$238$		0			0
$239$	18.6883	−	6.07219i	1.20885	−	0.392778i	0.365837	−	0.930679i	$-0.380783\pi$
$239$	18.6883	−	6.07219i	1.20885	−	0.392778i	0.843008	+	0.537901i	$0.180783\pi$
$240$		0			0
$241$	−15.6811	−	11.3930i	−1.01011	−	0.733888i	−0.0458777	−	0.998947i	$-0.514608\pi$
$241$	−15.6811	−	11.3930i	−1.01011	−	0.733888i	−0.964232	+	0.265059i	$0.914608\pi$
$242$		0			0
$243$	−3.80204			−0.243901
$244$		0			0
$245$	15.4636	+	1.61412i	0.987934	+	0.103122i
$246$		0			0
$247$			5.63602i			0.358611i
$248$		0			0
$249$		−	9.38505i		−	0.594753i
$250$		0			0
$251$	−0.306537	−	0.222712i	−0.0193485	−	0.0140575i	0.578069	−	0.815988i	$-0.303806\pi$
$251$	−0.306537	−	0.222712i	−0.0193485	−	0.0140575i	−0.597417	+	0.801930i	$0.703806\pi$
$252$		0			0
$253$	−6.95699	−	21.4114i	−0.437382	−	1.34612i
$254$		0			0
$255$	23.4256	+	2.44520i	1.46697	+	0.153125i
$256$		0			0
$257$	19.4489	−	14.1305i	1.21319	−	0.881435i	0.217675	−	0.976021i	$-0.430153\pi$
$257$	19.4489	−	14.1305i	1.21319	−	0.881435i	0.995517	+	0.0945859i	$0.0301527\pi$
$258$		0			0
$259$	−1.64024	−	0.532947i	−0.101920	−	0.0331157i
$260$		0			0
$261$	21.0173	−	28.9279i	1.30094	−	1.79059i
$262$		0			0
$263$	23.2139	−	16.8659i	1.43143	−	1.03999i	0.441682	−	0.897172i	$-0.354382\pi$
$263$	23.2139	−	16.8659i	1.43143	−	1.03999i	0.989748	−	0.142823i	$-0.0456181\pi$
$264$		0			0
$265$	4.91195	+	23.0280i	0.301739	+	1.41460i
$266$		0			0
$267$	27.4666	−	8.92444i	1.68093	−	0.546167i
$268$		0			0
$269$	−4.56554	+	14.0513i	−0.278366	+	0.856722i	0.709943	+	0.704259i	$0.248721\pi$
$269$	−4.56554	+	14.0513i	−0.278366	+	0.856722i	−0.988309	+	0.152463i	$0.951279\pi$
$270$		0			0
$271$	4.94944	+	15.2328i	0.300657	+	0.925327i	0.981262	+	0.192677i	$0.0617169\pi$
$271$	4.94944	+	15.2328i	0.300657	+	0.925327i	−0.680605	+	0.732650i	$0.738283\pi$
$272$		0			0
$273$	1.48686			0.0899892
$274$		0			0
$275$	13.4548	−	12.1496i	0.811353	−	0.732649i
$276$		0			0
$277$	−11.0870	−	15.2600i	−0.666154	−	0.916882i	0.333511	−	0.942746i	$-0.391766\pi$
$277$	−11.0870	−	15.2600i	−0.666154	−	0.916882i	−0.999665	+	0.0258637i	$0.991766\pi$
$278$		0			0
$279$	−1.61542	+	1.17367i	−0.0967128	+	0.0702660i
$280$		0			0
$281$	18.5113	+	6.01469i	1.10429	+	0.358806i	0.803753	−	0.594963i	$-0.202833\pi$
$281$	18.5113	+	6.01469i	1.10429	+	0.358806i	0.300540	+	0.953769i	$0.402833\pi$
$282$		0			0
$283$	−13.2502	+	18.2374i	−0.787645	+	1.08410i	0.206753	+	0.978393i	$0.433710\pi$
$283$	−13.2502	+	18.2374i	−0.787645	+	1.08410i	−0.994397	+	0.105706i	$0.966290\pi$
$284$		0			0
$285$	15.4336	+	6.85828i	0.914209	+	0.406249i
$286$		0			0
$287$	1.15741	−	0.763406i	0.0683195	−	0.0450624i
$288$		0			0
$289$	−1.52753	+	4.70126i	−0.0898548	+	0.276545i
$290$		0			0
$291$	9.66272	+	7.02038i	0.566439	+	0.411542i
$292$		0			0
$293$	0.460758	−	1.41807i	0.0269178	−	0.0828444i	−0.936695	−	0.350146i	$-0.886132\pi$
$293$	0.460758	−	1.41807i	0.0269178	−	0.0828444i	0.963613	+	0.267302i	$0.0861320\pi$
$294$		0			0
$295$	8.33737	−	4.82153i	0.485421	−	0.280721i
$296$		0			0
$297$	20.7008	+	28.4922i	1.20118	+	1.65329i
$298$		0			0
$299$	8.26163	−	11.3712i	0.477783	−	0.657611i
$300$		0			0
$301$		−	1.29584i		−	0.0746907i
$302$		0			0
$303$	−37.8227	+	12.2893i	−2.17286	+	0.706004i
$304$		0			0
$305$	4.58407	−	10.3158i	0.262483	−	0.590683i
$306$		0			0
$307$	−23.8434	+	7.74721i	−1.36082	+	0.442156i	−0.896316	−	0.443416i	$-0.853766\pi$
$307$	−23.8434	+	7.74721i	−1.36082	+	0.442156i	−0.464502	+	0.885572i	$0.653766\pi$
$308$		0			0
$309$	−12.0026	+	3.89988i	−0.682804	+	0.221856i
$310$		0			0
$311$	13.7018	+	18.8590i	0.776960	+	1.06939i	0.995611	+	0.0935907i	$0.0298345\pi$
$311$	13.7018	+	18.8590i	0.776960	+	1.06939i	−0.218651	+	0.975803i	$0.570165\pi$
$312$		0			0
$313$	1.81588	+	1.31932i	0.102640	+	0.0745722i	0.637921	−	0.770102i	$-0.279794\pi$
$313$	1.81588	+	1.31932i	0.102640	+	0.0745722i	−0.535282	+	0.844674i	$0.679794\pi$
$314$		0			0
$315$	1.21945	−	2.74422i	0.0687085	−	0.154619i
$316$		0			0
$317$	−11.6186	+	8.44142i	−0.652567	+	0.474118i	−0.864145	−	0.503244i	$-0.832140\pi$
$317$	−11.6186	+	8.44142i	−0.652567	+	0.474118i	0.211578	+	0.977361i	$0.432140\pi$
$318$		0			0
$319$	−20.9032			−1.17036
$320$		0			0
$321$	−8.01472	+	2.60414i	−0.447338	+	0.145349i
$322$		0			0
$323$	5.08167	−	6.99432i	0.282752	−	0.389174i
$324$		0			0
$325$	11.0741	+	2.33732i	0.614278	+	0.129651i
$326$		0			0
$327$			0.326366i			0.0180481i
$328$		0			0
$329$	−2.21565			−0.122153
$330$		0			0
$331$			7.60835i			0.418193i	0.977895	+	0.209096i	$0.0670522\pi$
$331$			7.60835i			0.418193i	−0.977895	+	0.209096i	$0.932948\pi$
$332$		0			0
$333$	29.0356	−	39.9641i	1.59114	−	2.19002i
$334$		0			0
$335$	3.12719	+	14.6607i	0.170857	+	0.801001i
$336$		0			0
$337$		−	22.8389i		−	1.24411i	−0.782972	−	0.622057i	$-0.786297\pi$
$337$		−	22.8389i		−	1.24411i	0.782972	−	0.622057i	$-0.213703\pi$
$338$		0			0
$339$	−14.2132	−	19.5628i	−0.771954	−	1.06250i
$340$		0			0
$341$	1.11017	+	0.360716i	0.0601191	+	0.0195339i
$342$		0			0
$343$	−2.44431	−	1.77589i	−0.131980	−	0.0958893i
$344$		0			0
$345$	−21.0854	−	36.4608i	−1.13520	−	1.96298i
$346$		0			0
$347$	−1.85432	−	5.70702i	−0.0995453	−	0.306369i	0.888866	−	0.458167i	$-0.151494\pi$
$347$	−1.85432	−	5.70702i	−0.0995453	−	0.306369i	−0.988412	+	0.151798i	$0.951494\pi$
$348$		0			0
$349$	−3.00764	−	9.25656i	−0.160995	−	0.495492i	0.837724	−	0.546094i	$-0.183886\pi$
$349$	−3.00764	−	9.25656i	−0.160995	−	0.495492i	−0.998719	+	0.0506020i	$0.983886\pi$
$350$		0			0
$351$	−6.79453	+	20.9114i	−0.362665	+	1.11617i
$352$		0			0
$353$	−20.8449	+	6.77291i	−1.10946	+	0.360486i	−0.805737	−	0.592274i	$-0.798230\pi$
$353$	−20.8449	+	6.77291i	−1.10946	+	0.360486i	−0.303725	+	0.952760i	$0.598230\pi$
$354$		0			0
$355$	−3.77437	+	36.1594i	−0.200323	+	1.91914i
$356$		0			0
$357$	−1.84520	−	1.34062i	−0.0976586	−	0.0709531i
$358$		0			0
$359$	16.5684	−	12.0376i	0.874447	−	0.635323i	−0.0573298	−	0.998355i	$-0.518259\pi$
$359$	16.5684	−	12.0376i	0.874447	−	0.635323i	0.931776	+	0.363033i	$0.118259\pi$
$360$		0			0
$361$	−10.3560	+	7.52406i	−0.545051	+	0.396003i
$362$		0			0
$363$	2.01144	−	6.19056i	0.105573	−	0.324920i
$364$		0			0
$365$	−9.93631	+	11.0513i	−0.520090	+	0.578450i
$366$		0			0
$367$	−6.95645	−	2.26029i	−0.363124	−	0.117986i	0.121772	−	0.992558i	$-0.461142\pi$
$367$	−6.95645	−	2.26029i	−0.363124	−	0.117986i	−0.484896	+	0.874572i	$0.661142\pi$
$368$		0			0
$369$	10.5514	+	38.2854i	0.549285	+	1.99306i
$370$		0			0
$371$	0.704599	−	2.16853i	0.0365809	−	0.112585i
$372$		0			0
$373$	−5.00847	+	6.89357i	−0.259329	+	0.356936i	−0.918751	−	0.394837i	$-0.870801\pi$
$373$	−5.00847	+	6.89357i	−0.259329	+	0.356936i	0.659422	+	0.751773i	$0.270801\pi$
$374$		0			0
$375$	19.8761	−	27.4809i	1.02640	−	1.41911i
$376$		0			0
$377$	−7.67080	−	10.5579i	−0.395066	−	0.543762i
$378$		0			0
$379$	−20.5006	+	14.8946i	−1.05304	+	0.765082i	−0.972789	−	0.231692i	$-0.925574\pi$
$379$	−20.5006	+	14.8946i	−1.05304	+	0.765082i	−0.0802558	+	0.996774i	$0.525574\pi$
$380$		0			0
$381$	11.4347	−	15.7385i	0.585818	−	0.806310i
$382$		0			0
$383$	−32.7360			−1.67273			−0.836366	−	0.548172i	$-0.815324\pi$
$383$	−32.7360			−1.67273			−0.836366	+	0.548172i	$0.815324\pi$
$384$		0			0
$385$	−1.71689	+	0.366220i	−0.0875010	+	0.0186643i
$386$		0			0
$387$	35.2993	+	11.4694i	1.79437	+	0.583025i
$388$		0			0
$389$	−0.117127	−	0.360481i	−0.00593860	−	0.0182771i	0.948043	−	0.318141i	$-0.103059\pi$
$389$	−0.117127	−	0.360481i	−0.00593860	−	0.0182771i	−0.953982	+	0.299864i	$0.903059\pi$
$390$		0			0
$391$	−20.5054	+	6.66262i	−1.03700	+	0.336943i
$392$		0			0
$393$	−50.4896	+	36.6829i	−2.54687	+	1.85041i
$394$		0			0
$395$	−0.443540	+	0.493309i	−0.0223169	+	0.0248211i
$396$		0			0
$397$	−12.0907	+	37.2112i	−0.606813	+	1.86758i	−0.123001	+	0.992407i	$0.539252\pi$
$397$	−12.0907	+	37.2112i	−0.606813	+	1.86758i	−0.483812	+	0.875172i	$0.660748\pi$
$398$		0			0
$399$	−0.961304	−	1.32312i	−0.0481254	−	0.0662390i
$400$		0			0
$401$	32.5757			1.62675			0.813377	−	0.581737i	$-0.197627\pi$
$401$	32.5757			1.62675			0.813377	+	0.581737i	$0.197627\pi$
$402$		0			0
$403$	0.225203	+	0.693103i	0.0112182	+	0.0345259i
$404$		0			0
$405$	18.0573	+	16.2355i	0.897273	+	0.806748i
$406$		0			0
$407$	−28.8780			−1.43143
$408$		0			0
$409$	−7.90131			−0.390695			−0.195347	−	0.980734i	$-0.562583\pi$
$409$	−7.90131			−0.390695			−0.195347	+	0.980734i	$0.562583\pi$
$410$		0			0
$411$	46.6493			2.30104
$412$		0			0
$413$	−0.932654			−0.0458929
$414$		0			0
$415$	−4.62535	+	5.14436i	−0.227049	+	0.252527i
$416$		0			0
$417$	−3.07005	−	9.44866i	−0.150341	−	0.462703i
$418$		0			0
$419$	7.27081			0.355202			0.177601	−	0.984103i	$-0.443166\pi$
$419$	7.27081			0.355202			0.177601	+	0.984103i	$0.443166\pi$
$420$		0			0
$421$	10.1349	+	13.9495i	0.493945	+	0.679858i	0.981110	−	0.193453i	$-0.0619686\pi$
$421$	10.1349	+	13.9495i	0.493945	+	0.679858i	−0.487164	+	0.873310i	$0.661969\pi$
$422$		0			0
$423$	19.6107	−	60.3556i	0.953506	−	2.93459i
$424$		0			0
$425$	−11.6355	−	12.8855i	−0.564405	−	0.625036i
$426$		0			0
$427$	−0.884374	+	0.642535i	−0.0427979	+	0.0310945i
$428$		0			0
$429$	23.6779	−	7.69342i	1.14318	−	0.371442i
$430$		0			0
$431$	5.95343	+	18.3228i	0.286767	+	0.882577i	0.985864	+	0.167550i	$0.0535856\pi$
$431$	5.95343	+	18.3228i	0.286767	+	0.882577i	−0.699097	+	0.715027i	$0.746414\pi$
$432$		0			0
$433$	−10.6175	−	3.44984i	−0.510246	−	0.165789i	0.0425684	−	0.999094i	$-0.486446\pi$
$433$	−10.6175	−	3.44984i	−0.510246	−	0.165789i	−0.552814	+	0.833305i	$0.686446\pi$
$434$		0			0
$435$	−38.2461	+	8.15804i	−1.83376	+	0.391148i
$436$		0			0
$437$	−15.4603			−0.739567
$438$		0			0
$439$	1.25895	−	1.73280i	0.0600865	−	0.0827020i	−0.777916	−	0.628368i	$-0.783723\pi$
$439$	1.25895	−	1.73280i	0.0600865	−	0.0827020i	0.838003	+	0.545666i	$0.183723\pi$
$440$		0			0
$441$	34.8879	−	25.3475i	1.66133	−	1.20703i
$442$		0			0
$443$	−8.98635	−	12.3687i	−0.426954	−	0.587652i	0.540296	−	0.841475i	$-0.318312\pi$
$443$	−8.98635	−	12.3687i	−0.426954	−	0.587652i	−0.967251	+	0.253822i	$0.918312\pi$
$444$		0			0
$445$	−19.4540	−	8.64482i	−0.922207	−	0.409804i
$446$		0			0
$447$	−10.3077	+	14.1874i	−0.487540	+	0.671041i
$448$		0			0
$449$	4.20676	−	12.9471i	0.198529	−	0.611011i	−0.801388	−	0.598145i	$-0.795905\pi$
$449$	4.20676	−	12.9471i	0.198529	−	0.611011i	0.999917	−	0.0128657i	$-0.00409541\pi$
$450$		0			0
$451$	14.4813	−	18.1457i	0.681898	−	0.854449i
$452$		0			0
$453$	25.1104	+	8.15887i	1.17979	+	0.383337i
$454$		0			0
$455$	−0.815016	−	0.732790i	−0.0382085	−	0.0343537i
$456$		0			0
$457$	11.1170	−	34.2145i	0.520030	−	1.60049i	−0.253910	−	0.967228i	$-0.581717\pi$
$457$	11.1170	−	34.2145i	0.520030	−	1.60049i	0.773939	−	0.633260i	$-0.218283\pi$
$458$		0			0
$459$	27.2866	−	19.8249i	1.27363	−	0.925347i
$460$		0			0
$461$	31.0216	−	22.5385i	1.44482	−	1.04972i	0.457811	−	0.889050i	$-0.348634\pi$
$461$	31.0216	−	22.5385i	1.44482	−	1.04972i	0.987008	−	0.160673i	$-0.0513664\pi$
$462$		0			0
$463$	23.2603	+	16.8996i	1.08100	+	0.785391i	0.977857	−	0.209275i	$-0.0671105\pi$
$463$	23.2603	+	16.8996i	1.08100	+	0.785391i	0.103142	+	0.994667i	$0.467110\pi$
$464$		0			0
$465$	2.17203	+	0.226720i	0.100725	+	0.0105139i
$466$		0			0
$467$	−10.6732	+	3.46792i	−0.493896	+	0.160476i	−0.545366	−	0.838198i	$-0.683609\pi$
$467$	−10.6732	+	3.46792i	−0.493896	+	0.160476i	0.0514702	+	0.998675i	$0.483609\pi$
$468$		0			0
$469$	0.448582	−	1.38059i	0.0207136	−	0.0637499i
$470$		0			0
$471$	16.4679	+	50.6831i	0.758802	+	2.33535i
$472$		0			0
$473$	−6.70498	−	20.6358i	−0.308295	−	0.948835i
$474$		0			0
$475$	−5.07980	−	11.3657i	−0.233077	−	0.521492i
$476$		0			0
$477$	52.8357	+	38.3874i	2.41918	+	1.75764i
$478$		0			0
$479$	27.2184	+	8.84381i	1.24364	+	0.404084i	0.855638	−	0.517574i	$-0.173165\pi$
$479$	27.2184	+	8.84381i	1.24364	+	0.404084i	0.388004	+	0.921658i	$0.373165\pi$
$480$		0			0
$481$	−10.5973	−	14.5859i	−0.483194	−	0.665059i
$482$		0			0
$483$			4.07866i			0.185585i
$484$		0			0
$485$	−1.83662	−	8.61037i	−0.0833968	−	0.390977i
$486$		0			0
$487$	8.68645	−	11.9559i	0.393621	−	0.541772i	−0.565508	−	0.824743i	$-0.691320\pi$
$487$	8.68645	−	11.9559i	0.393621	−	0.541772i	0.959129	+	0.282971i	$0.0913199\pi$
$488$		0			0
$489$			23.0354i			1.04170i
$490$		0			0
$491$	−20.4369			−0.922303			−0.461151	−	0.887321i	$-0.652564\pi$
$491$	−20.4369			−0.922303			−0.461151	+	0.887321i	$0.652564\pi$
$492$		0			0
$493$			20.0188i			0.901599i
$494$		0			0
$495$	5.22019	−	50.0106i	0.234630	−	2.24781i
$496$		0			0
$497$	2.06935	−	2.84822i	0.0928232	−	0.127760i
$498$		0			0
$499$	39.2117	−	12.7407i	1.75536	−	0.570350i	0.758655	−	0.651493i	$-0.225857\pi$
$499$	39.2117	−	12.7407i	1.75536	−	0.570350i	0.996702	+	0.0811430i	$0.0258570\pi$
$500$		0			0
$501$	−23.9039			−1.06795
$502$		0			0
$503$	21.6666	−	15.7417i	0.966068	−	0.701890i	0.0115160	−	0.999934i	$-0.496334\pi$
$503$	21.6666	−	15.7417i	0.966068	−	0.701890i	0.954552	+	0.298044i	$0.0963343\pi$
$504$		0			0
$505$	26.7890	+	11.9043i	1.19209	+	0.529733i
$506$		0			0
$507$	−19.3291	−	14.0434i	−0.858435	−	0.623689i
$508$		0			0
$509$	6.45239	+	8.88095i	0.285997	+	0.393641i	0.927709	−	0.373305i	$-0.121775\pi$
$509$	6.45239	+	8.88095i	0.285997	+	0.393641i	−0.641712	+	0.766946i	$0.721775\pi$
$510$		0			0
$511$	1.36870	−	0.444717i	0.0605477	−	0.0196731i
$512$		0			0
$513$	23.0014	−	7.47360i	1.01554	−	0.329968i
$514$		0			0
$515$	8.50117	+	3.77769i	0.374606	+	0.166465i
$516$		0			0
$517$	−35.2836	+	11.4643i	−1.55177	+	0.504200i
$518$		0			0
$519$			42.2591i			1.85497i
$520$		0			0
$521$	−16.3163	+	22.4575i	−0.714832	+	0.983881i	0.284848	+	0.958573i	$0.408057\pi$
$521$	−16.3163	+	22.4575i	−0.714832	+	0.983881i	−0.999680	+	0.0253086i	$0.991943\pi$
$522$		0			0
$523$	−7.26772	−	10.0032i	−0.317795	−	0.437408i	0.619997	−	0.784604i	$-0.287134\pi$
$523$	−7.26772	−	10.0032i	−0.317795	−	0.437408i	−0.937792	+	0.347196i	$0.887134\pi$
$524$		0			0
$525$	−2.99843	+	1.34013i	−0.130862	+	0.0584879i
$526$		0			0
$527$	0.345453	−	1.06320i	0.0150482	−	0.0463135i
$528$		0			0
$529$	12.5851	+	9.14363i	0.547179	+	0.397549i
$530$		0			0
$531$	8.25493	−	25.4060i	0.358233	−	1.10253i
$532$		0			0
$533$	14.4793	+	0.655433i	0.627169	+	0.0283900i
$534$		0			0
$535$	5.67665	+	2.52255i	0.245423	+	0.109059i
$536$		0			0
$537$	24.7841	−	34.1124i	1.06951	−	1.47206i
$538$		0			0
$539$	−23.9761	−	7.79030i	−1.03272	−	0.335552i
$540$		0			0
$541$	−31.1045	+	22.5987i	−1.33728	+	0.971594i	−0.337746	+	0.941237i	$0.609664\pi$
$541$	−31.1045	+	22.5987i	−1.33728	+	0.971594i	−0.999539	+	0.0303569i	$0.990336\pi$
$542$		0			0
$543$	14.6282	+	20.1340i	0.627757	+	0.864033i
$544$		0			0
$545$	0.160847	−	0.178896i	0.00688993	−	0.00766305i
$546$		0			0
$547$	−29.4222			−1.25800			−0.629001	−	0.777405i	$-0.716536\pi$
$547$	−29.4222			−1.25800			−0.629001	+	0.777405i	$0.716536\pi$
$548$		0			0
$549$	−9.67545	−	29.7780i	−0.412938	−	1.27089i
$550$		0			0
$551$	−4.43583	+	13.6521i	−0.188973	+	0.581598i
$552$		0			0
$553$	0.0610964	−	0.0198514i	0.00259808	−	0.000844168i
$554$		0			0
$555$	−52.8373	+	11.2704i	−2.24282	+	0.478402i
$556$		0			0
$557$	21.0050	−	15.2611i	0.890013	−	0.646632i	−0.0458688	−	0.998947i	$-0.514606\pi$
$557$	21.0050	−	15.2611i	0.890013	−	0.646632i	0.935881	+	0.352316i	$0.114606\pi$
$558$		0			0
$559$	7.96236	−	10.9593i	0.336772	−	0.463527i
$560$		0			0
$561$	−36.3210	−	11.8014i	−1.53348	−	0.498257i
$562$		0			0
$563$	−35.2718	+	25.6265i	−1.48653	+	1.08003i	−0.511150	+	0.859492i	$0.670780\pi$
$563$	−35.2718	+	25.6265i	−1.48653	+	1.08003i	−0.975379	+	0.220535i	$0.929220\pi$
$564$		0			0
$565$	−1.85048	+	17.7281i	−0.0778505	+	0.745826i
$566$		0			0
$567$	−0.726648	−	2.23639i	−0.0305163	−	0.0939197i
$568$		0			0
$569$	21.2820	+	15.4623i	0.892188	+	0.648212i	0.936448	−	0.350808i	$-0.114093\pi$
$569$	21.2820	+	15.4623i	0.892188	+	0.648212i	−0.0442597	+	0.999020i	$0.514093\pi$
$570$		0			0
$571$		−	22.4839i		−	0.940924i	−0.882420	−	0.470462i	$-0.844087\pi$
$571$		−	22.4839i		−	0.940924i	0.882420	−	0.470462i	$-0.155913\pi$
$572$		0			0
$573$			47.9948i			2.00501i
$574$		0			0
$575$	−6.41156	+	30.3775i	−0.267381	+	1.26683i
$576$		0			0
$577$	−19.4507			−0.809744			−0.404872	−	0.914373i	$-0.632684\pi$
$577$	−19.4507			−0.809744			−0.404872	+	0.914373i	$0.632684\pi$
$578$		0			0
$579$	−52.6391	−	38.2445i	−2.18760	−	1.58939i
$580$		0			0
$581$	0.637129	−	0.207016i	0.0264326	−	0.00858846i
$582$		0			0
$583$		−	38.1790i		−	1.58121i
$584$		0			0
$585$	27.1753	−	15.7156i	1.12356	−	0.649760i
$586$		0			0
$587$	7.56585	−	23.2853i	0.312276	−	0.961087i	−0.664585	−	0.747212i	$-0.731392\pi$
$587$	7.56585	−	23.2853i	0.312276	−	0.961087i	0.976861	−	0.213874i	$-0.0686083\pi$
$588$		0			0
$589$	0.471174	−	0.648515i	0.0194144	−	0.0267216i
$590$		0			0
$591$	42.4167	+	58.3816i	1.74479	+	2.40150i
$592$		0			0
$593$	12.3480	+	38.0032i	0.507071	+	1.56060i	0.797262	+	0.603634i	$0.206281\pi$
$593$	12.3480	+	38.0032i	0.507071	+	1.56060i	−0.290191	+	0.956969i	$0.593719\pi$
$594$		0			0
$595$	0.350724	+	1.64425i	0.0143783	+	0.0674075i
$596$		0			0
$597$	57.4289	+	18.6598i	2.35041	+	0.763694i
$598$		0			0
$599$	−2.59508	−	7.98683i	−0.106032	−	0.326333i	0.883939	−	0.467602i	$-0.154882\pi$
$599$	−2.59508	−	7.98683i	−0.106032	−	0.326333i	−0.989971	+	0.141269i	$0.954882\pi$
$600$		0			0
$601$		−	44.2909i		−	1.80666i	−0.428941	−	0.903332i	$-0.641113\pi$
$601$		−	44.2909i		−	1.80666i	0.428941	−	0.903332i	$-0.358887\pi$
$602$		0			0
$603$	33.6378	+	24.4393i	1.36984	+	0.995245i
$604$		0			0
$605$	−4.15352	+	2.40200i	−0.168865	+	0.0976551i
$606$		0			0
$607$	6.25546	+	8.60991i	0.253901	+	0.349465i	0.916873	−	0.399179i	$-0.130705\pi$
$607$	6.25546	+	8.60991i	0.253901	+	0.349465i	−0.662971	+	0.748645i	$0.730705\pi$
$608$		0			0
$609$	3.60162	+	1.17024i	0.145945	+	0.0474204i
$610$		0			0
$611$	−18.7384	−	13.6142i	−0.758073	−	0.550773i
$612$		0			0
$613$	18.7307	+	6.08596i	0.756524	+	0.245810i	0.661786	−	0.749693i	$-0.269799\pi$
$613$	18.7307	+	6.08596i	0.756524	+	0.245810i	0.0947380	+	0.995502i	$0.469799\pi$
$614$		0			0
$615$	19.4142	−	38.8525i	0.782857	−	1.56668i
$616$		0			0
$617$	−13.1219	−	4.26358i	−0.528270	−	0.171645i	0.0327254	−	0.999464i	$-0.489581\pi$
$617$	−13.1219	−	4.26358i	−0.528270	−	0.171645i	−0.560995	+	0.827819i	$0.689581\pi$
$618$		0			0
$619$	19.6216	+	14.2559i	0.788659	+	0.572995i	0.907565	−	0.419911i	$-0.137939\pi$
$619$	19.6216	+	14.2559i	0.788659	+	0.572995i	−0.118906	+	0.992906i	$0.537939\pi$
$620$		0			0
$621$	−57.3626	−	18.6382i	−2.30188	−	0.747927i
$622$		0			0
$623$	1.21172	+	1.66779i	0.0485465	+	0.0668185i
$624$		0			0
$625$	−24.4387	+	5.26769i	−0.977549	+	0.210708i
$626$		0			0
$627$	−22.1547	−	16.0963i	−0.884772	−	0.642825i
$628$		0			0
$629$			27.6561i			1.10272i
$630$		0			0
$631$	−4.72928	−	14.5552i	−0.188270	−	0.579435i	0.811720	−	0.584047i	$-0.198532\pi$
$631$	−4.72928	−	14.5552i	−0.188270	−	0.579435i	−0.999989	+	0.00461250i	$0.998532\pi$
$632$		0			0
$633$	72.1037	+	23.4279i	2.86586	+	0.931176i
$634$		0			0
$635$	−14.0245	+	2.99147i	−0.556545	+	0.118713i
$636$		0			0
$637$	−4.86365	−	14.9688i	−0.192705	−	0.593085i
$638$		0			0
$639$	59.2714	+	81.5801i	2.34474	+	3.22726i
$640$		0			0
$641$	−6.44630	+	8.87257i	−0.254613	+	0.350445i	−0.917120	−	0.398610i	$-0.869493\pi$
$641$	−6.44630	+	8.87257i	−0.254613	+	0.350445i	0.662507	+	0.749056i	$0.269493\pi$
$642$		0			0
$643$	1.16761	−	3.59352i	0.0460458	−	0.141715i	−0.925390	−	0.379015i	$-0.876263\pi$
$643$	1.16761	−	3.59352i	0.0460458	−	0.141715i	0.971436	+	0.237301i	$0.0762627\pi$
$644$		0			0
$645$	−20.3216	−	35.1400i	−0.800162	−	1.38364i
$646$		0			0
$647$			10.9551i			0.430689i	0.976538	+	0.215344i	$0.0690874\pi$
$647$			10.9551i			0.430689i	−0.976538	+	0.215344i	$0.930913\pi$
$648$		0			0
$649$	−14.8522	+	4.82579i	−0.583002	+	0.189429i
$650$		0			0
$651$	−0.171088	−	0.124303i	−0.00670546	−	0.00487180i
$652$		0			0
$653$	16.8284			0.658544			0.329272	−	0.944235i	$-0.393197\pi$
$653$	16.8284			0.658544			0.329272	+	0.944235i	$0.393197\pi$
$654$		0			0
$655$	45.7544	+	4.77592i	1.78777	+	0.186611i
$656$		0			0
$657$			41.2204i			1.60816i
$658$		0			0
$659$		−	7.74006i		−	0.301510i	−0.988571	−	0.150755i	$-0.951830\pi$
$659$		−	7.74006i		−	0.301510i	0.988571	−	0.150755i	$-0.0481705\pi$
$660$		0			0
$661$	−20.9801	−	15.2429i	−0.816031	−	0.592881i	0.0995420	−	0.995033i	$-0.468262\pi$
$661$	−20.9801	−	15.2429i	−0.816031	−	0.592881i	−0.915573	+	0.402152i	$0.868262\pi$
$662$		0			0
$663$	−7.36788	−	22.6760i	−0.286145	−	0.880663i
$664$		0			0
$665$	−0.125157	+	1.19903i	−0.00485338	+	0.0464965i
$666$		0			0
$667$	28.9618	−	21.0419i	1.12140	−	0.814747i
$668$		0			0
$669$	10.2791	+	3.33989i	0.397413	+	0.129127i
$670$		0			0
$671$	−10.7588	+	14.8082i	−0.415337	+	0.571663i
$672$		0			0
$673$	−15.6237	+	11.3513i	−0.602250	+	0.437560i	−0.846677	−	0.532107i	$-0.821400\pi$
$673$	−15.6237	+	11.3513i	−0.602250	+	0.437560i	0.244427	+	0.969668i	$0.421400\pi$
$674$		0			0
$675$	−5.14574	−	48.2942i	−0.198059	−	1.85884i
$676$		0			0
$677$	9.62811	−	3.12836i	0.370038	−	0.120233i	−0.118094	−	0.993002i	$-0.537678\pi$
$677$	9.62811	−	3.12836i	0.370038	−	0.120233i	0.488132	+	0.872770i	$0.337678\pi$
$678$		0			0
$679$	−0.263456	+	0.810835i	−0.0101105	+	0.0311170i
$680$		0			0
$681$	−26.1808	−	80.5763i	−1.00325	−	3.08769i
$682$		0			0
$683$	−3.32384			−0.127183			−0.0635917	−	0.997976i	$-0.520256\pi$
$683$	−3.32384			−0.127183			−0.0635917	+	0.997976i	$0.520256\pi$
$684$		0			0
$685$	−25.5705	−	22.9907i	−0.976999	−	0.878430i
$686$		0			0
$687$	4.95501	+	6.81998i	0.189045	+	0.260199i
$688$		0			0
$689$	19.2837	−	14.0104i	0.734651	−	0.533755i
$690$		0			0
$691$	30.6771	+	9.96760i	1.16701	+	0.379185i	0.827527	−	0.561426i	$-0.189747\pi$
$691$	30.6771	+	9.96760i	1.16701	+	0.379185i	0.339486	+	0.940611i	$0.389747\pi$
$692$		0			0
$693$	−2.86205	+	3.93927i	−0.108720	+	0.149640i
$694$		0			0
$695$	−2.97386	+	6.69228i	−0.112805	+	0.253852i
$696$		0			0
$697$	−17.3779	−	13.8686i	−0.658236	−	0.525309i
$698$		0			0
$699$	7.76564	−	23.9002i	0.293724	−	0.903988i
$700$		0			0
$701$	−5.06793	−	3.68207i	−0.191413	−	0.139070i	0.487951	−	0.872871i	$-0.337744\pi$
$701$	−5.06793	−	3.68207i	−0.191413	−	0.139070i	−0.679364	+	0.733801i	$0.737744\pi$
$702$		0			0
$703$	−6.12814	+	18.8605i	−0.231127	+	0.711336i
$704$		0			0
$705$	−60.0831	+	34.7463i	−2.26286	+	1.30862i
$706$		0			0
$707$	−1.66859	−	2.29661i	−0.0627537	−	0.0863730i
$708$		0			0
$709$	−7.29109	+	10.0353i	−0.273823	+	0.376885i	−0.923676	−	0.383175i	$-0.874830\pi$
$709$	−7.29109	+	10.0353i	−0.273823	+	0.376885i	0.649853	+	0.760060i	$0.274830\pi$
$710$		0			0
$711$			1.84001i			0.0690056i
$712$		0			0
$713$	−1.90127	+	0.617760i	−0.0712031	+	0.0231353i
$714$		0			0
$715$	−16.7705	−	7.45236i	−0.627183	−	0.278703i
$716$		0			0
$717$	−56.6908	+	18.4200i	−2.11716	+	0.687906i
$718$		0			0
$719$	−26.1545	+	8.49812i	−0.975399	+	0.316926i	−0.752994	−	0.658028i	$-0.771391\pi$
$719$	−26.1545	+	8.49812i	−0.975399	+	0.316926i	−0.222405	+	0.974954i	$0.571391\pi$
$720$		0			0
$721$	−0.529507	−	0.728804i	−0.0197199	−	0.0271421i
$722$		0			0
$723$	47.5686	+	34.5606i	1.76909	+	1.28532i
$724$		0			0
$725$	24.9850	+	14.3775i	0.927920	+	0.533967i
$726$		0			0
$727$	−14.3554	+	10.4298i	−0.532414	+	0.386821i	−0.821260	−	0.570554i	$-0.806728\pi$
$727$	−14.3554	+	10.4298i	−0.532414	+	0.386821i	0.288846	+	0.957376i	$0.406728\pi$
$728$		0			0
$729$	−21.0454			−0.779458
$730$		0			0
$731$	−19.7626	+	6.42127i	−0.730947	+	0.237499i
$732$		0			0
$733$	20.9217	−	28.7962i	0.772759	−	1.06361i	−0.223285	−	0.974753i	$-0.571678\pi$
$733$	20.9217	−	28.7962i	0.772759	−	1.06361i	0.996044	−	0.0888585i	$-0.0283219\pi$
$734$		0			0
$735$	−46.9088	−	4.89641i	−1.73026	−	0.180607i
$736$		0			0
$737$		−	24.3066i		−	0.895347i
$738$		0			0
$739$	22.0790			0.812190			0.406095	−	0.913831i	$-0.366890\pi$
$739$	22.0790			0.812190			0.406095	+	0.913831i	$0.366890\pi$
$740$		0			0
$741$		−	17.0968i		−	0.628068i
$742$		0			0
$743$	−5.62014	+	7.73546i	−0.206183	+	0.283787i	−0.899568	−	0.436781i	$-0.856119\pi$
$743$	−5.62014	+	7.73546i	−0.206183	+	0.283787i	0.693385	+	0.720567i	$0.256119\pi$
$744$		0			0
$745$	12.6423	−	2.69664i	0.463177	−	0.0987974i
$746$		0			0
$747$			19.1881i			0.702055i
$748$		0			0
$749$	−0.353578	−	0.486658i	−0.0129195	−	0.0177821i
$750$		0			0
$751$	−34.2566	−	11.1307i	−1.25004	−	0.406163i	−0.392106	−	0.919920i	$-0.628253\pi$
$751$	−34.2566	−	11.1307i	−1.25004	−	0.406163i	−0.857936	+	0.513757i	$0.828253\pi$
$752$		0			0
$753$	0.929879	+	0.675597i	0.0338867	+	0.0246201i
$754$		0			0
$755$	−9.74309	−	16.8477i	−0.354587	−	0.613151i
$756$		0			0
$757$	14.5655	+	44.8279i	0.529391	+	1.62930i	0.755467	+	0.655187i	$0.227410\pi$
$757$	14.5655	+	44.8279i	0.529391	+	1.62930i	−0.226076	+	0.974110i	$0.572590\pi$
$758$		0			0
$759$	21.1040	+	64.9514i	0.766026	+	2.35759i
$760$		0			0
$761$	−0.410675	+	1.26393i	−0.0148870	+	0.0458173i	−0.958224	−	0.286019i	$-0.907668\pi$
$761$	−0.410675	+	1.26393i	−0.0148870	+	0.0458173i	0.943337	+	0.331836i	$0.107668\pi$
$762$		0			0
$763$	−0.0221562	+	0.00719900i	−0.000802110	+	0.000260621i
$764$		0			0
$765$	−47.8945	−	4.99931i	−1.73163	−	0.180750i
$766$		0			0
$767$	−7.88772	−	5.73076i	−0.284809	−	0.206926i
$768$		0			0
$769$	−5.97772	+	4.34307i	−0.215562	+	0.156615i	−0.690327	−	0.723498i	$-0.742533\pi$
$769$	−5.97772	+	4.34307i	−0.215562	+	0.156615i	0.474765	+	0.880113i	$0.342533\pi$
$770$		0			0
$771$	−58.9983	+	42.8647i	−2.12477	+	1.54374i
$772$		0			0
$773$	−3.80483	+	11.7101i	−0.136850	+	0.421181i	−0.995873	−	0.0907555i	$-0.971072\pi$
$773$	−3.80483	+	11.7101i	−0.136850	+	0.421181i	0.859023	+	0.511937i	$0.171072\pi$
$774$		0			0
$775$	−1.07885	−	1.19474i	−0.0387534	−	0.0429164i
$776$		0			0
$777$	4.97567	+	1.61669i	0.178501	+	0.0579985i
$778$		0			0
$779$	−8.77808	−	13.3085i	−0.314507	−	0.476828i
$780$		0			0
$781$	18.2165	−	56.0645i	0.651836	−	2.00615i
$782$		0			0
$783$	−32.9166	+	45.3059i	−1.17635	+	1.61910i
$784$		0			0
$785$	15.9520	−	35.8977i	0.569350	−	1.28124i
$786$		0			0
$787$	−3.86233	−	5.31604i	−0.137677	−	0.189496i	0.734611	−	0.678489i	$-0.237365\pi$
$787$	−3.86233	−	5.31604i	−0.137677	−	0.189496i	−0.872288	+	0.488992i	$0.837365\pi$
$788$		0			0
$789$	−70.4192	+	51.1626i	−2.50699	+	1.82144i
$790$		0			0
$791$	1.01456	−	1.39642i	0.0360734	−	0.0496508i
$792$		0			0
$793$	−11.4275			−0.405803
$794$		0			0
$795$	−14.9004	−	69.8552i	−0.528462	−	2.47751i
$796$		0			0
$797$	−45.0875	−	14.6498i	−1.59708	−	0.518923i	−0.630698	−	0.776029i	$-0.717231\pi$
$797$	−45.0875	−	14.6498i	−1.59708	−	0.518923i	−0.966383	+	0.257106i	$0.917231\pi$
$798$		0			0
$799$	10.9792	+	33.7906i	0.388417	+	1.19543i
$800$		0			0
$801$	−56.1564	+	18.2463i	−1.98419	+	0.644702i
$802$		0			0
$803$	19.4951	−	14.1640i	0.687966	−	0.499837i
$804$		0			0
$805$	2.01013	−	2.23569i	0.0708479	−	0.0787977i
$806$		0			0
$807$	13.8495	−	42.6245i	0.487527	−	1.50045i
$808$		0			0
$809$	−31.5672	−	43.4486i	−1.10984	−	1.52757i	−0.821644	−	0.570000i	$-0.806943\pi$
$809$	−31.5672	−	43.4486i	−1.10984	−	1.52757i	−0.288200	−	0.957570i	$-0.593057\pi$
$810$		0			0
$811$	23.3409			0.819611			0.409805	−	0.912173i	$-0.365597\pi$
$811$	23.3409			0.819611			0.409805	+	0.912173i	$0.365597\pi$
$812$		0			0
$813$	−15.0141	−	46.2086i	−0.526567	−	1.62061i
$814$		0			0
$815$	11.3528	−	12.6267i	0.397672	−	0.442295i
$816$		0			0
$817$	−14.9003			−0.521294
$818$		0			0
$819$	−3.03995			−0.106224
$820$		0			0
$821$	−28.3435			−0.989196			−0.494598	−	0.869122i	$-0.664685\pi$
$821$	−28.3435			−0.989196			−0.494598	+	0.869122i	$0.664685\pi$
$822$		0			0
$823$	−9.38237			−0.327049			−0.163524	−	0.986539i	$-0.552286\pi$
$823$	−9.38237			−0.327049			−0.163524	+	0.986539i	$0.552286\pi$
$824$		0			0
$825$	−40.8150	+	36.8558i	−1.42100	+	1.28315i
$826$		0			0
$827$	2.17753	+	6.70176i	0.0757202	+	0.233043i	0.981752	−	0.190167i	$-0.0609031\pi$
$827$	2.17753	+	6.70176i	0.0757202	+	0.233043i	−0.906031	+	0.423210i	$0.860903\pi$
$828$		0			0
$829$	−15.0278			−0.521936			−0.260968	−	0.965347i	$-0.584042\pi$
$829$	−15.0278			−0.521936			−0.260968	+	0.965347i	$0.584042\pi$
$830$		0			0
$831$	33.6324	+	46.2910i	1.16669	+	1.60582i
$832$		0			0
$833$	−7.46067	+	22.9616i	−0.258497	+	0.795572i
$834$		0			0
$835$	13.1028	+	11.7808i	0.453440	+	0.407693i
$836$		0			0
$837$	2.53002	−	1.83817i	0.0874504	−	0.0635364i
$838$		0			0
$839$	3.18838	−	1.03597i	0.110075	−	0.0357656i	−0.253462	−	0.967345i	$-0.581569\pi$
$839$	3.18838	−	1.03597i	0.110075	−	0.0357656i	0.363537	+	0.931580i	$0.381569\pi$
$840$		0			0
$841$	−1.30977	−	4.03107i	−0.0451646	−	0.139002i
$842$		0			0
$843$	−56.1540	−	18.2455i	−1.93405	−	0.628410i
$844$		0			0
$845$	3.67394	+	17.2240i	0.126387	+	0.592523i
$846$		0			0
$847$	0.464631			0.0159649
$848$		0			0
$849$	40.1945	−	55.3230i	1.37947	−	1.89868i
$850$		0			0
$851$	40.0109	−	29.0696i	1.37156	−	0.996494i
$852$		0			0
$853$	−1.07832	−	1.48418i	−0.0369209	−	0.0508172i	0.790157	−	0.612904i	$-0.209999\pi$
$853$	−1.07832	−	1.48418i	−0.0369209	−	0.0508172i	−0.827078	+	0.562087i	$0.809999\pi$
$854$		0			0
$855$	−31.5546	−	14.0220i	−1.07914	−	0.479542i
$856$		0			0
$857$	−4.14968	+	5.71154i	−0.141750	+	0.195102i	−0.873989	−	0.485945i	$-0.838475\pi$
$857$	−4.14968	+	5.71154i	−0.141750	+	0.195102i	0.732239	+	0.681048i	$0.238475\pi$
$858$		0			0
$859$	−0.646894	+	1.99093i	−0.0220717	+	0.0679298i	−0.961486	−	0.274855i	$-0.911370\pi$
$859$	−0.646894	+	1.99093i	−0.0220717	+	0.0679298i	0.939414	+	0.342785i	$0.111370\pi$
$860$		0			0
$861$	−3.51099	+	2.31579i	−0.119654	+	0.0789218i
$862$		0			0
$863$	52.5051	+	17.0600i	1.78730	+	0.580728i	0.999385	−	0.0350622i	$-0.0111629\pi$
$863$	52.5051	+	17.0600i	1.78730	+	0.580728i	0.787911	+	0.615790i	$0.211163\pi$
$864$		0			0
$865$	20.8271	−	23.1641i	0.708142	−	0.787603i
$866$		0			0
$867$	4.63376	−	14.2612i	0.157371	−	0.484337i
$868$		0			0
$869$	0.870226	−	0.632256i	0.0295204	−	0.0214478i
$870$		0			0
$871$	12.2770	−	8.91973i	0.415989	−	0.302234i
$872$		0			0
$873$	−19.7558	−	14.3534i	−0.668631	−	0.485789i
$874$		0			0
$875$	2.30404	+	0.743170i	0.0778908	+	0.0251237i
$876$		0			0
$877$	−10.9460	+	3.55657i	−0.369620	+	0.120097i	−0.487936	−	0.872879i	$-0.662250\pi$
$877$	−10.9460	+	3.55657i	−0.369620	+	0.120097i	0.118317	+	0.992976i	$0.462250\pi$
$878$		0			0
$879$	−1.39771	+	4.30170i	−0.0471435	+	0.145093i
$880$		0			0
$881$	15.9839	+	49.1932i	0.538510	+	1.65736i	0.735941	+	0.677046i	$0.236740\pi$
$881$	15.9839	+	49.1932i	0.538510	+	1.65736i	−0.197431	+	0.980317i	$0.563260\pi$
$882$		0			0
$883$	9.82569	+	30.2404i	0.330661	+	1.01767i	0.968820	+	0.247765i	$0.0796960\pi$
$883$	9.82569	+	30.2404i	0.330661	+	1.01767i	−0.638160	+	0.769904i	$0.720304\pi$
$884$		0			0
$885$	−25.2914	+	14.6261i	−0.850160	+	0.491651i
$886$		0			0
$887$	−38.4297	−	27.9208i	−1.29034	−	0.937490i	−0.290532	−	0.956865i	$-0.593832\pi$
$887$	−38.4297	−	27.9208i	−1.29034	−	0.937490i	−0.999812	+	0.0193750i	$0.993832\pi$
$888$		0			0
$889$	1.32068	+	0.429115i	0.0442942	+	0.0143920i
$890$		0			0
$891$	−23.1433	−	31.8541i	−0.775331	−	1.06715i
$892$		0			0
$893$			25.4768i			0.852549i
$894$		0			0
$895$	−30.3973	+	6.48385i	−1.01607	+	0.216731i
$896$		0			0
$897$	−25.0616	+	34.4944i	−0.836783	+	1.15173i
$898$		0			0
$899$			1.85614i			0.0619059i
$900$		0			0
$901$	−36.5635			−1.21811
$902$		0			0
$903$			3.93091i			0.130812i
$904$		0			0
$905$	1.90452	−	18.2457i	0.0633084	−	0.606509i
$906$		0			0
$907$	11.0779	−	15.2475i	0.367837	−	0.506284i	−0.584475	−	0.811412i	$-0.698699\pi$
$907$	11.0779	−	15.2475i	0.367837	−	0.506284i	0.952311	+	0.305128i	$0.0986993\pi$
$908$		0			0
$909$	77.3298	−	25.1260i	2.56487	−	0.833376i
$910$		0			0
$911$	−19.2673			−0.638355			−0.319177	−	0.947695i	$-0.603407\pi$
$911$	−19.2673			−0.638355			−0.319177	+	0.947695i	$0.603407\pi$
$912$		0			0
$913$	9.07494	−	6.59333i	0.300337	−	0.218207i
$914$		0			0
$915$	−13.9057	+	31.2930i	−0.459710	+	1.03451i
$916$		0			0
$917$	−3.60401	−	2.61847i	−0.119015	−	0.0864695i
$918$		0			0
$919$	12.4602	+	17.1499i	0.411023	+	0.565724i	0.963468	−	0.267825i	$-0.0863050\pi$
$919$	12.4602	+	17.1499i	0.411023	+	0.565724i	−0.552445	+	0.833550i	$0.686305\pi$
$920$		0			0
$921$	72.3290	−	23.5011i	2.38332	−	0.774388i
$922$		0			0
$923$	35.0023	−	11.3729i	1.15211	−	0.374344i
$924$		0			0
$925$	34.5170	+	19.8627i	1.13491	+	0.653080i
$926$		0			0
$927$	24.5397	−	7.97344i	0.805990	−	0.261882i
$928$		0			0
$929$			28.5637i			0.937146i	0.883425	+	0.468573i	$0.155232\pi$
$929$			28.5637i			0.937146i	−0.883425	+	0.468573i	$0.844768\pi$
$930$		0			0
$931$	−10.1758	+	14.0058i	−0.333499	+	0.459022i
$932$		0			0
$933$	−41.5645	−	57.2086i	−1.36076	−	1.87292i
$934$		0			0
$935$	14.0929	+	24.3694i	0.460888	+	0.796965i
$936$		0			0
$937$	16.1122	−	49.5883i	0.526363	−	1.61998i	−0.235242	−	0.971937i	$-0.575588\pi$
$937$	16.1122	−	49.5883i	0.526363	−	1.61998i	0.761605	−	0.648041i	$-0.224412\pi$
$938$		0			0
$939$	−5.50847	−	4.00214i	−0.179762	−	0.130605i
$940$		0			0
$941$	2.59917	−	7.99943i	0.0847306	−	0.260774i	−0.899711	−	0.436486i	$-0.856223\pi$
$941$	2.59917	−	7.99943i	0.0847306	−	0.260774i	0.984442	+	0.175712i	$0.0562228\pi$
$942$		0			0
$943$	−1.79793	+	39.7186i	−0.0585488	+	1.29342i
$944$		0			0
$945$	−1.90987	+	4.29791i	−0.0621281	+	0.139811i
$946$		0			0
$947$	−21.9425	+	30.2013i	−0.713036	+	0.981410i	0.286690	+	0.958023i	$0.407445\pi$
$947$	−21.9425	+	30.2013i	−0.713036	+	0.981410i	−0.999726	+	0.0233866i	$0.992555\pi$
$948$		0			0
$949$	14.3081	+	4.64898i	0.464460	+	0.150912i
$950$		0			0
$951$	35.2450	−	25.6070i	1.14290	−	0.830364i
$952$		0			0
$953$	−26.9310	−	37.0674i	−0.872381	−	1.20073i	−0.978473	−	0.206373i	$-0.933834\pi$
$953$	−26.9310	−	37.0674i	−0.872381	−	1.20073i	0.106092	−	0.994356i	$-0.466166\pi$
$954$		0			0
$955$	23.6539	−	26.3081i	0.765421	−	0.851309i
$956$		0			0
$957$	63.4099			2.04975
$958$		0			0
$959$	1.02899	+	3.16691i	0.0332278	+	0.102265i
$960$		0			0
$961$	−9.54750	+	29.3842i	−0.307984	+	0.947877i
$962$		0			0
$963$	16.3864	−	5.32426i	0.528044	−	0.171572i
$964$		0			0
$965$	10.0053	+	46.9062i	0.322081	+	1.50997i
$966$		0			0
$967$	15.6547	−	11.3738i	0.503423	−	0.365758i	−0.306900	−	0.951742i	$-0.599292\pi$
$967$	15.6547	−	11.3738i	0.503423	−	0.365758i	0.810323	+	0.585984i	$0.199292\pi$
$968$		0			0
$969$	−15.4152	+	21.2172i	−0.495208	+	0.681595i
$970$		0			0
$971$	6.30955	+	2.05010i	0.202483	+	0.0657907i	0.408503	−	0.912757i	$-0.366051\pi$
$971$	6.30955	+	2.05010i	0.202483	+	0.0657907i	−0.206020	+	0.978548i	$0.566051\pi$
$972$		0			0
$973$	0.573728	−	0.416837i	0.0183929	−	0.0133632i
$974$		0			0
$975$	−33.5931	−	7.09025i	−1.07584	−	0.227070i
$976$		0			0
$977$	−10.2728	−	31.6165i	−0.328657	−	1.01150i	−0.969763	−	0.244049i	$-0.921524\pi$
$977$	−10.2728	−	31.6165i	−0.328657	−	1.01150i	0.641106	−	0.767452i	$-0.278476\pi$
$978$		0			0
$979$	27.9258	+	20.2893i	0.892513	+	0.648449i
$980$		0			0
$981$		−	0.667268i		−	0.0213042i
$982$		0			0
$983$			53.4952i			1.70623i	0.521722	+	0.853115i	$0.325290\pi$
$983$			53.4952i			1.70623i	−0.521722	+	0.853115i	$0.674710\pi$
$984$		0			0
$985$	5.52244	−	52.9063i	0.175960	−	1.68573i
$986$		0			0
$987$	6.72115			0.213937
$988$		0			0
$989$	30.0626	+	21.8417i	0.955935	+	0.694527i
$990$		0			0
$991$	20.6073	−	6.69571i	0.654612	−	0.212696i	0.0371654	−	0.999309i	$-0.488167\pi$
$991$	20.6073	−	6.69571i	0.654612	−	0.212696i	0.617447	+	0.786613i	$0.288167\pi$
$992$		0			0
$993$		−	23.0799i		−	0.732418i
$994$		0			0
$995$	−22.2830	−	38.5316i	−0.706418	−	1.22153i
$996$		0			0
$997$	−8.92215	+	27.4596i	−0.282567	+	0.869653i	0.704550	+	0.709655i	$0.251149\pi$
$997$	−8.92215	+	27.4596i	−0.282567	+	0.869653i	−0.987117	+	0.159999i	$0.948851\pi$
$998$		0			0
$999$	−45.4746	+	62.5905i	−1.43875	+	1.98027i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.bi.a.189.1	✓	80
5.4	even	2	inner	820.2.bi.a.189.20	yes	80
41.23	even	10	inner	820.2.bi.a.269.20	yes	80
205.64	even	10	inner	820.2.bi.a.269.1	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.bi.a.189.1	✓	80	1.1	even	1	trivial
820.2.bi.a.189.20	yes	80	5.4	even	2	inner
820.2.bi.a.269.1	yes	80	205.64	even	10	inner
820.2.bi.a.269.20	yes	80	41.23	even	10	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:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.bi (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q-3.03349 q^{3} +(1.66279 + 1.49503i) q^{5} +(-0.0669129 - 0.205937i) q^{7} +6.20209 q^{9} +(-2.13114 - 2.93326i) q^{11} +(0.699493 - 2.15282i) q^{13} +(-5.04407 - 4.53517i) q^{15} +(-2.80914 + 2.04096i) q^{17} +(-2.36798 + 0.769403i) q^{19} +(0.202980 + 0.624708i) q^{21} +(5.90545 + 1.91880i) q^{23} +(0.529751 + 4.97186i) q^{25} -9.71351 q^{27} +(3.38875 - 4.66421i) q^{29} +(-0.260464 + 0.189238i) q^{31} +(6.46479 + 8.89802i) q^{33} +(0.196620 - 0.442467i) q^{35} +(4.68159 - 6.44365i) q^{37} +(-2.12191 + 6.53056i) q^{39} +(1.70127 + 6.17298i) q^{41} +(5.69152 + 1.84929i) q^{43} +(10.3128 + 9.27233i) q^{45} +(3.16195 - 9.73150i) q^{47} +(5.62519 - 4.08694i) q^{49} +(8.52152 - 6.19124i) q^{51} +(8.51902 + 6.18943i) q^{53} +(0.841683 - 8.06352i) q^{55} +(7.18325 - 2.33398i) q^{57} +(1.33099 - 4.09637i) q^{59} +(-1.56003 - 4.80128i) q^{61} +(-0.415000 - 1.27724i) q^{63} +(4.38164 - 2.53392i) q^{65} +(5.42363 + 3.94050i) q^{67} +(-17.9141 - 5.82066i) q^{69} +(9.55669 + 13.1537i) q^{71} +6.64621i q^{73} +(-1.60700 - 15.0821i) q^{75} +(-0.461465 + 0.635152i) q^{77} +0.296675i q^{79} +10.8596 q^{81} +3.09381i q^{83} +(-7.72232 - 0.806068i) q^{85} +(-10.2798 + 14.1489i) q^{87} +(-9.05444 + 2.94197i) q^{89} -0.490149 q^{91} +(0.790117 - 0.574054i) q^{93} +(-5.08774 - 2.26085i) q^{95} +(-3.18534 - 2.31429i) q^{97} +(-13.2175 - 18.1923i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 68 q^{9} + 10 q^{15} - 26 q^{21} + 10 q^{25} - 20 q^{29} + 4 q^{31} + 15 q^{35} - 8 q^{39} + 4 q^{41} - 4 q^{45} + 18 q^{49} + 52 q^{51} - 36 q^{59} - 42 q^{61} - 15 q^{65} + 30 q^{69} - 20 q^{75}+ \cdots + 80 q^{99}+O(q^{100}) \) 80 * q + 68 * q^9 + 10 * q^15 - 26 * q^21 + 10 * q^25 - 20 * q^29 + 4 * q^31 + 15 * q^35 - 8 * q^39 + 4 * q^41 - 4 * q^45 + 18 * q^49 + 52 * q^51 - 36 * q^59 - 42 * q^61 - 15 * q^65 + 30 * q^69 - 20 * q^75 + 32 * q^81 + 10 * q^89 - 132 * q^91 + 50 * q^95 + 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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