LMFDB - Embedded newform 820.2.bi.a.269.20

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)

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);

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")

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			269.20
Character	$\chi$	$=$	820.269
Dual form			820.2.bi.a.189.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+3.03349 q^{3} +(1.93569 - 1.11942i) q^{5} +(0.0669129 - 0.205937i) q^{7} +6.20209 q^{9} +(-2.13114 + 2.93326i) q^{11} +(-0.699493 - 2.15282i) q^{13} +(5.87191 - 3.39575i) q^{15} +(2.80914 + 2.04096i) q^{17} +(-2.36798 - 0.769403i) q^{19} +(0.202980 - 0.624708i) q^{21} +(-5.90545 + 1.91880i) q^{23} +(2.49381 - 4.33370i) q^{25} +9.71351 q^{27} +(3.38875 + 4.66421i) q^{29} +(-0.260464 - 0.189238i) q^{31} +(-6.46479 + 8.89802i) q^{33} +(-0.101006 - 0.473534i) q^{35} +(-4.68159 - 6.44365i) q^{37} +(-2.12191 - 6.53056i) q^{39} +(1.70127 - 6.17298i) q^{41} +(-5.69152 + 1.84929i) q^{43} +(12.0053 - 6.94273i) q^{45} +(-3.16195 - 9.73150i) q^{47} +(5.62519 + 4.08694i) q^{49} +(8.52152 + 6.19124i) q^{51} +(-8.51902 + 6.18943i) q^{53} +(-0.841683 + 8.06352i) q^{55} +(-7.18325 - 2.33398i) q^{57} +(1.33099 + 4.09637i) q^{59} +(-1.56003 + 4.80128i) q^{61} +(0.415000 - 1.27724i) q^{63} +(-3.76391 - 3.38417i) q^{65} +(-5.42363 + 3.94050i) q^{67} +(-17.9141 + 5.82066i) q^{69} +(9.55669 - 13.1537i) q^{71} +6.64621i q^{73} +(7.56495 - 13.1462i) q^{75} +(0.461465 + 0.635152i) q^{77} -0.296675i q^{79} +10.8596 q^{81} +3.09381i q^{83} +(7.72232 + 0.806068i) q^{85} +(10.2798 + 14.1489i) q^{87} +(-9.05444 - 2.94197i) q^{89} -0.490149 q^{91} +(-0.790117 - 0.574054i) q^{93} +(-5.44496 + 1.16143i) q^{95} +(3.18534 - 2.31429i) q^{97} +(-13.2175 + 18.1923i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{9}{10}\right)$	$-1$

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	$-0.160404\pi$
$3$	3.03349			1.75139			0.875694	+	0.482866i	$0.160404\pi$
$4$		0			0
$5$	1.93569	−	1.11942i	0.865668	−	0.500619i
$5$	1.93569	−	1.11942i	0.865668	−	0.500619i
$6$		0			0
$7$	0.0669129	−	0.205937i	0.0252907	−	0.0778368i	−0.937615	−	0.347677i	$-0.886971\pi$
$7$	0.0669129	−	0.205937i	0.0252907	−	0.0778368i	0.962905	+	0.269840i	$0.0869707\pi$
$8$		0			0
$9$	6.20209			2.06736
$10$		0			0
$11$	−2.13114	+	2.93326i	−0.642562	+	0.884411i	−0.998749	−	0.0500038i	$-0.984077\pi$
$11$	−2.13114	+	2.93326i	−0.642562	+	0.884411i	0.356187	+	0.934415i	$0.384077\pi$
$12$		0			0
$13$	−0.699493	−	2.15282i	−0.194004	−	0.597084i	−0.999987	−	0.00514462i	$-0.998362\pi$
$13$	−0.699493	−	2.15282i	−0.194004	−	0.597084i	0.805982	−	0.591940i	$-0.201638\pi$
$14$		0			0
$15$	5.87191	−	3.39575i	1.51612	−	0.876778i
$16$		0			0
$17$	2.80914	+	2.04096i	0.681317	+	0.495006i	0.873794	−	0.486296i	$-0.161652\pi$
$17$	2.80914	+	2.04096i	0.681317	+	0.495006i	−0.192477	+	0.981301i	$0.561652\pi$
$18$		0			0
$19$	−2.36798	−	0.769403i	−0.543252	−	0.176513i	0.0245198	−	0.999699i	$-0.492194\pi$
$19$	−2.36798	−	0.769403i	−0.543252	−	0.176513i	−0.567772	+	0.823186i	$0.692194\pi$
$20$		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	$-0.824131\pi$
$23$	−5.90545	+	1.91880i	−1.23137	+	0.400097i	−0.380160	+	0.924921i	$0.624131\pi$
$24$		0			0
$25$	2.49381	−	4.33370i	0.498761	−	0.866739i
$26$		0			0
$27$	9.71351			1.86937
$28$		0			0
$29$	3.38875	+	4.66421i	0.629275	+	0.866123i	0.997987	−	0.0634209i	$-0.0202011\pi$
$29$	3.38875	+	4.66421i	0.629275	+	0.866123i	−0.368712	+	0.929544i	$0.620201\pi$
$30$		0			0
$31$	−0.260464	−	0.189238i	−0.0467808	−	0.0339882i	0.564149	−	0.825673i	$-0.309204\pi$
$31$	−0.260464	−	0.189238i	−0.0467808	−	0.0339882i	−0.610930	+	0.791685i	$0.709204\pi$
$32$		0			0
$33$	−6.46479	+	8.89802i	−1.12538	+	1.54895i
$34$		0			0
$35$	−0.101006	−	0.473534i	−0.0170732	−	0.0800418i
$36$		0			0
$37$	−4.68159	−	6.44365i	−0.769648	−	1.05933i	−0.996350	−	0.0853656i	$-0.972794\pi$
$37$	−4.68159	−	6.44365i	−0.769648	−	1.05933i	0.226702	−	0.973964i	$-0.427206\pi$
$38$		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	$-0.750828\pi$
$43$	−5.69152	+	1.84929i	−0.867949	+	0.282014i	−0.159005	+	0.987278i	$0.550828\pi$
$44$		0			0
$45$	12.0053	−	6.94273i	1.78965	−	1.03496i
$46$		0			0
$47$	−3.16195	−	9.73150i	−0.461218	−	1.41948i	−0.863677	−	0.504046i	$-0.831844\pi$
$47$	−3.16195	−	9.73150i	−0.461218	−	1.41948i	0.402458	−	0.915438i	$-0.368156\pi$
$48$		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	$-0.957334\pi$
$53$	−8.51902	+	6.18943i	−1.17018	+	0.850184i	−0.179147	+	0.983822i	$0.557334\pi$
$54$		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	0.999551	−	0.0299716i	$-0.00954167\pi$
$59$	1.33099	+	4.09637i	0.173280	+	0.533302i	−0.826270	+	0.563274i	$0.809542\pi$
$60$		0			0
$61$	−1.56003	+	4.80128i	−0.199742	+	0.614741i	0.800147	+	0.599804i	$0.204755\pi$
$61$	−1.56003	+	4.80128i	−0.199742	+	0.614741i	−0.999888	+	0.0149371i	$0.995245\pi$
$62$		0			0
$63$	0.415000	−	1.27724i	0.0522850	−	0.160917i
$64$		0			0
$65$	−3.76391	−	3.38417i	−0.466855	−	0.419754i
$66$		0			0
$67$	−5.42363	+	3.94050i	−0.662602	+	0.481408i	−0.867540	−	0.497367i	$-0.834300\pi$
$67$	−5.42363	+	3.94050i	−0.662602	+	0.481408i	0.204939	+	0.978775i	$0.434300\pi$
$68$		0			0
$69$	−17.9141	+	5.82066i	−2.15661	+	0.700725i
$70$		0			0
$71$	9.55669	−	13.1537i	1.13417	−	1.56105i	0.354275	−	0.935141i	$-0.384728\pi$
$71$	9.55669	−	13.1537i	1.13417	−	1.56105i	0.779895	−	0.625910i	$-0.215272\pi$
$72$		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
$75$	7.56495	−	13.1462i	0.873525	−	1.51800i
$76$		0			0
$77$	0.461465	+	0.635152i	0.0525888	+	0.0723823i
$78$		0			0
$79$		−	0.296675i		−	0.0333786i	−0.999861	−	0.0166893i	$-0.994687\pi$
$79$		−	0.296675i		−	0.0333786i	0.999861	−	0.0166893i	$-0.00531261\pi$
$80$		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	−0.213090	−	0.977033i	$-0.568353\pi$
$89$	−9.05444	−	2.94197i	−0.959769	−	0.311848i	−0.746679	+	0.665185i	$0.768353\pi$
$90$		0			0
$91$	−0.490149			−0.0513816
$92$		0			0
$93$	−0.790117	−	0.574054i	−0.0819314	−	0.0595266i
$94$		0			0
$95$	−5.44496	+	1.16143i	−0.558641	+	0.119160i
$96$		0			0
$97$	3.18534	−	2.31429i	0.323423	−	0.234980i	−0.414212	−	0.910180i	$-0.635943\pi$
$97$	3.18534	−	2.31429i	0.323423	−	0.234980i	0.737635	+	0.675200i	$0.235943\pi$
$98$		0			0
$99$	−13.2175	+	18.1923i	−1.32841	+	1.82840i
$100$		0			0
$101$	12.4684	+	4.05121i	1.24065	+	0.403111i	0.854561	−	0.519352i	$-0.173827\pi$
$101$	12.4684	+	4.05121i	1.24065	+	0.403111i	0.386087	+	0.922462i	$0.373827\pi$
$102$		0			0
$103$	−3.95669	−	1.28561i	−0.389864	−	0.126675i	0.107524	−	0.994202i	$-0.465708\pi$
$103$	−3.95669	−	1.28561i	−0.389864	−	0.126675i	−0.497388	+	0.867528i	$0.665708\pi$
$104$		0			0
$105$	−0.306403	−	1.43646i	−0.0299018	−	0.140184i
$106$		0			0
$107$	−2.64208	−	0.858463i	−0.255419	−	0.0829907i	0.178509	−	0.983938i	$-0.442873\pi$
$107$	−2.64208	−	0.858463i	−0.255419	−	0.0829907i	−0.433928	+	0.900948i	$0.642873\pi$
$108$		0			0
$109$			0.107588i			0.0103050i	0.999987	+	0.00515251i	$0.00164010\pi$
$109$			0.107588i			0.0103050i	−0.999987	+	0.00515251i	$0.998360\pi$
$110$		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	$-0.922336\pi$
$113$	−4.68542	+	6.44892i	−0.440767	+	0.606664i	0.529615	+	0.848238i	$0.322336\pi$
$114$		0			0
$115$	−9.28319	+	10.3249i	−0.865662	+	0.962798i
$116$		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
$125$	−0.0239750	−	11.1803i	−0.00214439	−	0.999998i
$126$		0			0
$127$	3.76949	+	5.18825i	0.334488	+	0.460383i	0.942821	−	0.333299i	$-0.108162\pi$
$127$	3.76949	+	5.18825i	0.334488	+	0.460383i	−0.608334	+	0.793681i	$0.708162\pi$
$128$		0			0
$129$	−17.2652	+	5.60981i	−1.52012	+	0.493916i
$130$		0			0
$131$	16.6441	+	12.0926i	1.45420	+	1.05654i	0.984828	+	0.173535i	$0.0555189\pi$
$131$	16.6441	+	12.0926i	1.45420	+	1.05654i	0.469370	+	0.883002i	$0.344481\pi$
$132$		0			0
$133$	−0.316897	+	0.436171i	−0.0274784	+	0.0378208i
$134$		0			0
$135$	18.8024	−	10.8735i	1.61825	−	0.935840i
$136$		0			0
$137$	15.3781			1.31384			0.656918	−	0.753962i	$-0.271860\pi$
$137$	15.3781			1.31384			0.656918	+	0.753962i	$0.271860\pi$
$138$		0			0
$139$	1.01205	−	3.11478i	0.0858412	−	0.264192i	−0.898918	−	0.438118i	$-0.855645\pi$
$139$	1.01205	−	3.11478i	0.0858412	−	0.264192i	0.984759	+	0.173926i	$0.0556453\pi$
$140$		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
$145$	11.7808	+	5.23505i	0.978341	+	0.434748i
$146$		0			0
$147$	17.0640	+	12.3977i	1.40741	+	1.02254i
$148$		0			0
$149$	3.39798	+	4.67691i	0.278373	+	0.383148i	0.925194	−	0.379494i	$-0.123902\pi$
$149$	3.39798	+	4.67691i	0.278373	+	0.383148i	−0.646821	+	0.762642i	$0.723902\pi$
$150$		0			0
$151$	−8.27772	+	2.68960i	−0.673632	+	0.218876i	−0.625805	−	0.779980i	$-0.715229\pi$
$151$	−8.27772	+	2.68960i	−0.673632	+	0.218876i	−0.0478265	+	0.998856i	$0.515229\pi$
$152$		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	−0.461604	−	0.887086i	$-0.652726\pi$
$157$	5.42870	−	16.7078i	0.433258	−	1.33343i	0.894862	−	0.446344i	$-0.147274\pi$
$158$		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	$-0.598618\pi$
$167$	−7.87999			−0.609772			−0.304886	+	0.952389i	$0.598618\pi$
$168$		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
$175$	−0.725599	−	0.803547i	−0.0548502	−	0.0607424i
$176$		0			0
$177$	4.03756	+	12.4263i	0.303481	+	0.934019i
$178$		0			0
$179$	−8.17015	−	11.2452i	−0.610665	−	0.840509i	0.385967	−	0.922513i	$-0.373868\pi$
$179$	−8.17015	−	11.2452i	−0.610665	−	0.840509i	−0.996632	+	0.0820040i	$0.973868\pi$
$180$		0			0
$181$	−4.82223	+	6.63723i	−0.358434	+	0.493342i	−0.949712	−	0.313126i	$-0.898624\pi$
$181$	−4.82223	+	6.63723i	−0.358434	+	0.493342i	0.591278	+	0.806468i	$0.298624\pi$
$182$		0			0
$183$	−4.73234	+	14.5647i	−0.349825	+	1.07665i
$184$		0			0
$185$	−16.2753	−	7.23227i	−1.19658	−	0.531727i
$186$		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	$0.193990\pi$
$191$			15.8216i			1.14481i	−0.819970	+	0.572406i	$0.806010\pi$
$192$		0			0
$193$	−17.3526	+	12.6074i	−1.24907	+	0.907502i	−0.998168	−	0.0605111i	$-0.980727\pi$
$193$	−17.3526	+	12.6074i	−1.24907	+	0.907502i	−0.250901	+	0.968013i	$0.580727\pi$
$194$		0			0
$195$	−11.4178	−	10.2659i	−0.817645	−	0.735153i
$196$		0			0
$197$	13.9828	−	19.2457i	0.996233	−	1.37120i	0.0686245	−	0.997643i	$-0.478139\pi$
$197$	13.9828	−	19.2457i	0.996233	−	1.37120i	0.927608	−	0.373554i	$-0.121861\pi$
$198$		0			0
$199$	−18.9316	+	6.15125i	−1.34203	+	0.436050i	−0.890002	−	0.455956i	$-0.849297\pi$
$199$	−18.9316	+	6.15125i	−1.34203	+	0.436050i	−0.452023	+	0.892006i	$0.649297\pi$
$200$		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
$205$	−3.61701	−	13.8534i	−0.252623	−	0.967565i
$206$		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	−0.975716	−	0.219040i	$-0.929708\pi$
$211$	−23.7692	+	7.72308i	−1.63634	+	0.531679i	−0.660622	+	0.750718i	$0.729708\pi$
$212$		0			0
$213$	28.9902	−	39.9015i	1.98637	−	2.73401i
$214$		0			0
$215$	−8.94691	+	9.95085i	−0.610174	+	0.678642i
$216$		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	$-0.561936\pi$
$223$	3.38854	−	1.10100i	0.226913	−	0.0737286i	0.420267	+	0.907401i	$0.361936\pi$
$224$		0			0
$225$	15.4668	−	26.8780i	1.03112	−	1.79186i
$226$		0			0
$227$	−8.63058	+	26.5622i	−0.572832	+	1.76300i	0.0706139	+	0.997504i	$0.477504\pi$
$227$	−8.63058	+	26.5622i	−0.572832	+	1.76300i	−0.643446	+	0.765492i	$0.722496\pi$
$228$		0			0
$229$	−1.63343	+	2.24823i	−0.107940	+	0.148567i	−0.859570	−	0.511019i	$-0.829268\pi$
$229$	−1.63343	+	2.24823i	−0.107940	+	0.148567i	0.751629	+	0.659586i	$0.229268\pi$
$230$		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	$-0.0125270\pi$
$233$	2.55997	+	7.87877i	0.167709	+	0.516155i	−0.831517	+	0.555500i	$0.812527\pi$
$234$		0			0
$235$	−17.0142	−	15.2976i	−1.10988	−	0.997907i
$236$		0			0
$237$		−	0.899963i		−	0.0584589i
$238$		0			0
$239$	18.6883	+	6.07219i	1.20885	+	0.392778i	0.843008	−	0.537901i	$-0.180783\pi$
$239$	18.6883	+	6.07219i	1.20885	+	0.392778i	0.365837	+	0.930679i	$0.380783\pi$
$240$		0			0
$241$	−15.6811	+	11.3930i	−1.01011	+	0.733888i	−0.964232	−	0.265059i	$-0.914608\pi$
$241$	−15.6811	+	11.3930i	−1.01011	+	0.733888i	−0.0458777	+	0.998947i	$0.514608\pi$
$242$		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	−0.597417	−	0.801930i	$-0.703806\pi$
$251$	−0.306537	+	0.222712i	−0.0193485	+	0.0140575i	0.578069	+	0.815988i	$0.303806\pi$
$252$		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	$-0.569847\pi$
$257$	−19.4489	−	14.1305i	−1.21319	−	0.881435i	−0.995517	+	0.0945859i	$0.969847\pi$
$258$		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	−0.989748	−	0.142823i	$-0.954382\pi$
$263$	−23.2139	−	16.8659i	−1.43143	−	1.03999i	−0.441682	−	0.897172i	$-0.645618\pi$
$264$		0			0
$265$	−9.56164	+	21.5172i	−0.587367	+	1.32179i
$266$		0			0
$267$	−27.4666	−	8.92444i	−1.68093	−	0.546167i
$268$		0			0
$269$	−4.56554	−	14.0513i	−0.278366	−	0.856722i	−0.988309	−	0.152463i	$-0.951279\pi$
$269$	−4.56554	−	14.0513i	−0.278366	−	0.856722i	0.709943	−	0.704259i	$-0.248721\pi$
$270$		0			0
$271$	4.94944	−	15.2328i	0.300657	−	0.925327i	−0.680605	−	0.732650i	$-0.738283\pi$
$271$	4.94944	−	15.2328i	0.300657	−	0.925327i	0.981262	−	0.192677i	$-0.0617169\pi$
$272$		0			0
$273$	−1.48686			−0.0899892
$274$		0			0
$275$	7.39721	+	16.5507i	0.446069	+	0.998044i
$276$		0			0
$277$	11.0870	−	15.2600i	0.666154	−	0.916882i	−0.333511	−	0.942746i	$-0.608234\pi$
$277$	11.0870	−	15.2600i	0.666154	−	0.916882i	0.999665	+	0.0258637i	$0.00823359\pi$
$278$		0			0
$279$	−1.61542	−	1.17367i	−0.0967128	−	0.0702660i
$280$		0			0
$281$	18.5113	−	6.01469i	1.10429	−	0.358806i	0.300540	−	0.953769i	$-0.402833\pi$
$281$	18.5113	−	6.01469i	1.10429	−	0.358806i	0.803753	+	0.594963i	$0.202833\pi$
$282$		0			0
$283$	13.2502	+	18.2374i	0.787645	+	1.08410i	0.994397	+	0.105706i	$0.0337104\pi$
$283$	13.2502	+	18.2374i	0.787645	+	1.08410i	−0.206753	+	0.978393i	$0.566290\pi$
$284$		0			0
$285$	−16.5173	+	3.52319i	−0.978398	+	0.208696i
$286$		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	$-0.113868\pi$
$293$	−0.460758	−	1.41807i	−0.0269178	−	0.0828444i	−0.963613	+	0.267302i	$0.913868\pi$
$294$		0			0
$295$	7.16194	+	6.43938i	0.416984	+	0.374915i
$296$		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
$305$	2.35490	+	11.0401i	0.134841	+	0.632156i
$306$		0			0
$307$	23.8434	+	7.74721i	1.36082	+	0.442156i	0.896316	−	0.443416i	$-0.146234\pi$
$307$	23.8434	+	7.74721i	1.36082	+	0.442156i	0.464502	+	0.885572i	$0.346234\pi$
$308$		0			0
$309$	−12.0026	−	3.89988i	−0.682804	−	0.221856i
$310$		0			0
$311$	13.7018	−	18.8590i	0.776960	−	1.06939i	−0.218651	−	0.975803i	$-0.570165\pi$
$311$	13.7018	−	18.8590i	0.776960	−	1.06939i	0.995611	−	0.0935907i	$-0.0298345\pi$
$312$		0			0
$313$	−1.81588	+	1.31932i	−0.102640	+	0.0745722i	−0.637921	−	0.770102i	$-0.720206\pi$
$313$	−1.81588	+	1.31932i	−0.102640	+	0.0745722i	0.535282	+	0.844674i	$0.320206\pi$
$314$		0			0
$315$	−0.626451	−	2.93690i	−0.0352965	−	0.165475i
$316$		0			0
$317$	11.6186	+	8.44142i	0.652567	+	0.474118i	0.864145	−	0.503244i	$-0.167860\pi$
$317$	11.6186	+	8.44142i	0.652567	+	0.474118i	−0.211578	+	0.977361i	$0.567860\pi$
$318$		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	$-0.932948\pi$
$331$		−	7.60835i		−	0.418193i	0.977895	−	0.209096i	$-0.0670522\pi$
$332$		0			0
$333$	−29.0356	−	39.9641i	−1.59114	−	2.19002i
$334$		0			0
$335$	−6.08741	+	13.6989i	−0.332591	+	0.748450i
$336$		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
$345$	−28.1605	+	31.3204i	−1.51611	+	1.68623i
$346$		0			0
$347$	1.85432	−	5.70702i	0.0995453	−	0.306369i	−0.888866	−	0.458167i	$-0.848506\pi$
$347$	1.85432	−	5.70702i	0.0995453	−	0.306369i	0.988412	+	0.151798i	$0.0485063\pi$
$348$		0			0
$349$	−3.00764	+	9.25656i	−0.160995	+	0.495492i	−0.998719	−	0.0506020i	$-0.983886\pi$
$349$	−3.00764	+	9.25656i	−0.160995	+	0.495492i	0.837724	+	0.546094i	$0.183886\pi$
$350$		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	$-0.201770\pi$
$353$	20.8449	+	6.77291i	1.10946	+	0.360486i	0.303725	+	0.952760i	$0.401770\pi$
$354$		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	0.931776	−	0.363033i	$-0.118259\pi$
$359$	16.5684	+	12.0376i	0.874447	+	0.635323i	−0.0573298	+	0.998355i	$0.518259\pi$
$360$		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
$365$	7.43989	+	12.8650i	0.389422	+	0.673386i
$366$		0			0
$367$	6.95645	−	2.26029i	0.363124	−	0.117986i	−0.121772	−	0.992558i	$-0.538858\pi$
$367$	6.95645	−	2.26029i	0.363124	−	0.117986i	0.484896	+	0.874572i	$0.338858\pi$
$368$		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	$-0.129199\pi$
$373$	5.00847	+	6.89357i	0.259329	+	0.356936i	−0.659422	+	0.751773i	$0.729199\pi$
$374$		0			0
$375$	−0.0727280	−	33.9154i	−0.00375566	−	1.75138i
$376$		0			0
$377$	7.67080	−	10.5579i	0.395066	−	0.543762i
$378$		0			0
$379$	−20.5006	−	14.8946i	−1.05304	−	0.765082i	−0.0802558	−	0.996774i	$-0.525574\pi$
$379$	−20.5006	−	14.8946i	−1.05304	−	0.765082i	−0.972789	+	0.231692i	$0.925574\pi$
$380$		0			0
$381$	11.4347	+	15.7385i	0.585818	+	0.806310i
$382$		0			0
$383$	32.7360			1.67273			0.836366	−	0.548172i	$-0.184676\pi$
$383$	32.7360			1.67273			0.836366	+	0.548172i	$0.184676\pi$
$384$		0			0
$385$	1.60426	+	0.712887i	0.0817604	+	0.0363321i
$386$		0			0
$387$	−35.2993	+	11.4694i	−1.79437	+	0.583025i
$388$		0			0
$389$	−0.117127	+	0.360481i	−0.00593860	+	0.0182771i	−0.953982	−	0.299864i	$-0.903059\pi$
$389$	−0.117127	+	0.360481i	−0.00593860	+	0.0182771i	0.948043	+	0.318141i	$0.103059\pi$
$390$		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
$395$	−0.332104	−	0.574272i	−0.0167100	−	0.0288948i
$396$		0			0
$397$	12.0907	+	37.2112i	0.606813	+	1.86758i	0.483812	+	0.875172i	$0.339252\pi$
$397$	12.0907	+	37.2112i	0.606813	+	1.86758i	0.123001	+	0.992407i	$0.460748\pi$
$398$		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
$405$	21.0209	−	12.1564i	1.04454	−	0.604058i
$406$		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
$415$	3.46326	+	5.98866i	0.170005	+	0.293972i
$416$		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	−0.487164	−	0.873310i	$-0.661969\pi$
$421$	10.1349	−	13.9495i	0.493945	−	0.679858i	0.981110	+	0.193453i	$0.0619686\pi$
$422$		0			0
$423$	−19.6107	−	60.3556i	−0.953506	−	2.93459i
$424$		0			0
$425$	15.8504	−	7.08421i	0.768856	−	0.343635i
$426$		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	−0.699097	−	0.715027i	$-0.746414\pi$
$431$	5.95343	−	18.3228i	0.286767	−	0.882577i	0.985864	−	0.167550i	$-0.0535856\pi$
$432$		0			0
$433$	10.6175	−	3.44984i	0.510246	−	0.165789i	−0.0425684	−	0.999094i	$-0.513554\pi$
$433$	10.6175	−	3.44984i	0.510246	−	0.165789i	0.552814	+	0.833305i	$0.313554\pi$
$434$		0			0
$435$	35.7369	+	15.8805i	1.71345	+	0.761412i
$436$		0			0
$437$	15.4603			0.739567
$438$		0			0
$439$	1.25895	+	1.73280i	0.0600865	+	0.0827020i	0.838003	−	0.545666i	$-0.183723\pi$
$439$	1.25895	+	1.73280i	0.0600865	+	0.0827020i	−0.777916	+	0.628368i	$0.783723\pi$
$440$		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	$-0.681688\pi$
$443$	8.98635	−	12.3687i	0.426954	−	0.587652i	0.967251	+	0.253822i	$0.0816879\pi$
$444$		0			0
$445$	−20.8199	+	4.44096i	−0.986958	+	0.210522i
$446$		0			0
$447$	10.3077	+	14.1874i	0.487540	+	0.671041i
$448$		0			0
$449$	4.20676	+	12.9471i	0.198529	+	0.611011i	0.999917	+	0.0128657i	$0.00409541\pi$
$449$	4.20676	+	12.9471i	0.198529	+	0.611011i	−0.801388	+	0.598145i	$0.795905\pi$
$450$		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
$455$	−0.948778	+	0.548682i	−0.0444794	+	0.0257226i
$456$		0			0
$457$	−11.1170	−	34.2145i	−0.520030	−	1.60049i	−0.773939	−	0.633260i	$-0.781717\pi$
$457$	−11.1170	−	34.2145i	−0.520030	−	1.60049i	0.253910	−	0.967228i	$-0.418283\pi$
$458$		0			0
$459$	27.2866	+	19.8249i	1.27363	+	0.925347i
$460$		0			0
$461$	31.0216	+	22.5385i	1.44482	+	1.04972i	0.987008	+	0.160673i	$0.0513664\pi$
$461$	31.0216	+	22.5385i	1.44482	+	1.04972i	0.457811	+	0.889050i	$0.348634\pi$
$462$		0			0
$463$	−23.2603	+	16.8996i	−1.08100	+	0.785391i	−0.977857	−	0.209275i	$-0.932890\pi$
$463$	−23.2603	+	16.8996i	−1.08100	+	0.785391i	−0.103142	+	0.994667i	$0.532890\pi$
$464$		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	$-0.316391\pi$
$467$	10.6732	+	3.46792i	0.493896	+	0.160476i	−0.0514702	+	0.998675i	$0.516391\pi$
$468$		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
$475$	−9.23964	+	8.34336i	−0.423944	+	0.382820i
$476$		0			0
$477$	−52.8357	+	38.3874i	−2.41918	+	1.75764i
$478$		0			0
$479$	27.2184	−	8.84381i	1.24364	−	0.404084i	0.388004	−	0.921658i	$-0.373165\pi$
$479$	27.2184	−	8.84381i	1.24364	−	0.404084i	0.855638	+	0.517574i	$0.173165\pi$
$480$		0			0
$481$	−10.5973	+	14.5859i	−0.483194	+	0.665059i
$482$		0			0
$483$			4.07866i			0.185585i
$484$		0			0
$485$	3.57519	−	8.04548i	0.162341	−	0.365326i
$486$		0			0
$487$	−8.68645	−	11.9559i	−0.393621	−	0.541772i	0.565508	−	0.824743i	$-0.308680\pi$
$487$	−8.68645	−	11.9559i	−0.393621	−	0.541772i	−0.959129	+	0.282971i	$0.908680\pi$
$488$		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	0.996702	−	0.0811430i	$-0.0258570\pi$
$499$	39.2117	+	12.7407i	1.75536	+	0.570350i	0.758655	+	0.651493i	$0.225857\pi$
$500$		0			0
$501$	−23.9039			−1.06795
$502$		0			0
$503$	−21.6666	−	15.7417i	−0.966068	−	0.701890i	−0.0115160	−	0.999934i	$-0.503666\pi$
$503$	−21.6666	−	15.7417i	−0.966068	−	0.701890i	−0.954552	+	0.298044i	$0.903666\pi$
$504$		0			0
$505$	28.6699	−	6.11540i	1.27579	−	0.272132i
$506$		0			0
$507$	19.3291	−	14.0434i	0.858435	−	0.623689i
$508$		0			0
$509$	6.45239	−	8.88095i	0.285997	−	0.393641i	−0.641712	−	0.766946i	$-0.721775\pi$
$509$	6.45239	−	8.88095i	0.285997	−	0.393641i	0.927709	+	0.373305i	$0.121775\pi$
$510$		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
$515$	−9.09806	+	1.94065i	−0.400908	+	0.0855153i
$516$		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	−0.999680	−	0.0253086i	$-0.991943\pi$
$521$	−16.3163	−	22.4575i	−0.714832	−	0.983881i	0.284848	−	0.958573i	$-0.408057\pi$
$522$		0			0
$523$	7.26772	−	10.0032i	0.317795	−	0.437408i	−0.619997	−	0.784604i	$-0.712866\pi$
$523$	7.26772	−	10.0032i	0.317795	−	0.437408i	0.937792	+	0.347196i	$0.112866\pi$
$524$		0			0
$525$	−2.20110	−	2.43755i	−0.0960639	−	0.106384i
$526$		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
$535$	−6.07523	+	1.29587i	−0.262655	+	0.0560253i
$536$		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	−0.999539	−	0.0303569i	$-0.990336\pi$
$541$	−31.1045	−	22.5987i	−1.33728	−	0.971594i	−0.337746	−	0.941237i	$-0.609664\pi$
$542$		0			0
$543$	−14.6282	+	20.1340i	−0.627757	+	0.864033i
$544$		0			0
$545$	0.120436	+	0.208257i	0.00515889	+	0.00892073i
$546$		0			0
$547$	29.4222			1.25800			0.629001	−	0.777405i	$-0.283464\pi$
$547$	29.4222			1.25800			0.629001	+	0.777405i	$0.283464\pi$
$548$		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
$555$	−49.3709	−	21.9391i	−2.09568	−	0.931261i
$556$		0			0
$557$	−21.0050	−	15.2611i	−0.890013	−	0.646632i	0.0458688	−	0.998947i	$-0.485394\pi$
$557$	−21.0050	−	15.2611i	−0.890013	−	0.646632i	−0.935881	+	0.352316i	$0.885394\pi$
$558$		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	0.975379	+	0.220535i	$0.0707802\pi$
$563$	35.2718	+	25.6265i	1.48653	+	1.08003i	0.511150	+	0.859492i	$0.329220\pi$
$564$		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	−0.0442597	−	0.999020i	$-0.514093\pi$
$569$	21.2820	−	15.4623i	0.892188	−	0.648212i	0.936448	+	0.350808i	$0.114093\pi$
$570$		0			0
$571$			22.4839i			0.940924i	0.882420	+	0.470462i	$0.155913\pi$
$571$			22.4839i			0.940924i	−0.882420	+	0.470462i	$0.844087\pi$
$572$		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	$-0.367316\pi$
$577$	19.4507			0.809744			0.404872	+	0.914373i	$0.367316\pi$
$578$		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
$585$	−23.3441	−	20.9889i	−0.965158	−	0.867784i
$586$		0			0
$587$	−7.56585	−	23.2853i	−0.312276	−	0.961087i	−0.976861	−	0.213874i	$-0.931392\pi$
$587$	−7.56585	−	23.2853i	−0.312276	−	0.961087i	0.664585	−	0.747212i	$-0.268608\pi$
$588$		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	0.290191	+	0.956969i	$0.406281\pi$
$593$	−12.3480	+	38.0032i	−0.507071	+	1.56060i	−0.797262	+	0.603634i	$0.793719\pi$
$594$		0			0
$595$	0.682722	−	1.53637i	0.0279889	−	0.0629852i
$596$		0			0
$597$	−57.4289	+	18.6598i	−2.35041	+	0.763694i
$598$		0			0
$599$	−2.59508	+	7.98683i	−0.106032	+	0.326333i	−0.989971	−	0.141269i	$-0.954882\pi$
$599$	−2.59508	+	7.98683i	−0.106032	+	0.326333i	0.883939	+	0.467602i	$0.154882\pi$
$600$		0			0
$601$			44.2909i			1.80666i	0.428941	+	0.903332i	$0.358887\pi$
$601$			44.2909i			1.80666i	−0.428941	+	0.903332i	$0.641113\pi$
$602$		0			0
$603$	−33.6378	+	24.4393i	−1.36984	+	0.995245i
$604$		0			0
$605$	−3.56795	−	3.20798i	−0.145058	−	0.130423i
$606$		0			0
$607$	−6.25546	+	8.60991i	−0.253901	+	0.349465i	−0.916873	−	0.399179i	$-0.869295\pi$
$607$	−6.25546	+	8.60991i	−0.253901	+	0.349465i	0.662971	+	0.748645i	$0.269295\pi$
$608$		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	$-0.730201\pi$
$613$	−18.7307	+	6.08596i	−0.756524	+	0.245810i	−0.0947380	+	0.995502i	$0.530201\pi$
$614$		0			0
$615$	−10.9722	−	42.0243i	−0.442441	−	1.69458i
$616$		0			0
$617$	13.1219	−	4.26358i	0.528270	−	0.171645i	−0.0327254	−	0.999464i	$-0.510419\pi$
$617$	13.1219	−	4.26358i	0.528270	−	0.171645i	0.560995	+	0.827819i	$0.310419\pi$
$618$		0			0
$619$	19.6216	−	14.2559i	0.788659	−	0.572995i	−0.118906	−	0.992906i	$-0.537939\pi$
$619$	19.6216	−	14.2559i	0.788659	−	0.572995i	0.907565	+	0.419911i	$0.137939\pi$
$620$		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
$625$	−12.5619	−	21.6148i	−0.502474	−	0.864592i
$626$		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	−0.999989	−	0.00461250i	$-0.998532\pi$
$631$	−4.72928	+	14.5552i	−0.188270	+	0.579435i	0.811720	+	0.584047i	$0.198532\pi$
$632$		0			0
$633$	−72.1037	+	23.4279i	−2.86586	+	0.931176i
$634$		0			0
$635$	13.1044	+	5.82323i	0.520032	+	0.231088i
$636$		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	0.662507	−	0.749056i	$-0.269493\pi$
$641$	−6.44630	−	8.87257i	−0.254613	−	0.350445i	−0.917120	+	0.398610i	$0.869493\pi$
$642$		0			0
$643$	−1.16761	−	3.59352i	−0.0460458	−	0.141715i	0.925390	−	0.379015i	$-0.123737\pi$
$643$	−1.16761	−	3.59352i	−0.0460458	−	0.141715i	−0.971436	+	0.237301i	$0.923737\pi$
$644$		0			0
$645$	−27.1404	+	30.1858i	−1.06865	+	1.18857i
$646$		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	$-0.606803\pi$
$653$	−16.8284			−0.658544			−0.329272	+	0.944235i	$0.606803\pi$
$654$		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	$0.0481705\pi$
$659$			7.74006i			0.301510i	−0.988571	+	0.150755i	$0.951830\pi$
$660$		0			0
$661$	−20.9801	+	15.2429i	−0.816031	+	0.592881i	−0.915573	−	0.402152i	$-0.868262\pi$
$661$	−20.9801	+	15.2429i	−0.816031	+	0.592881i	0.0995420	+	0.995033i	$0.468262\pi$
$662$		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	$-0.178600\pi$
$673$	15.6237	+	11.3513i	0.602250	+	0.437560i	−0.244427	+	0.969668i	$0.578600\pi$
$674$		0			0
$675$	24.2236	−	42.0954i	0.932367	−	1.62025i
$676$		0			0
$677$	−9.62811	−	3.12836i	−0.370038	−	0.120233i	0.118094	−	0.993002i	$-0.462322\pi$
$677$	−9.62811	−	3.12836i	−0.370038	−	0.120233i	−0.488132	+	0.872770i	$0.662322\pi$
$678$		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	$-0.479744\pi$
$683$	3.32384			0.127183			0.0635917	+	0.997976i	$0.479744\pi$
$684$		0			0
$685$	29.7672	−	17.2145i	1.13735	−	0.657731i
$686$		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	0.339486	−	0.940611i	$-0.389747\pi$
$691$	30.6771	−	9.96760i	1.16701	−	0.379185i	0.827527	+	0.561426i	$0.189747\pi$
$692$		0			0
$693$	2.86205	+	3.93927i	0.108720	+	0.149640i
$694$		0			0
$695$	−1.52772	−	7.16216i	−0.0579495	−	0.271676i
$696$		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	−0.679364	−	0.733801i	$-0.737744\pi$
$701$	−5.06793	+	3.68207i	−0.191413	+	0.139070i	0.487951	+	0.872871i	$0.337744\pi$
$702$		0			0
$703$	6.12814	+	18.8605i	0.231127	+	0.711336i
$704$		0			0
$705$	−51.6124	−	46.4053i	−1.94384	−	1.74772i
$706$		0			0
$707$	1.66859	−	2.29661i	0.0627537	−	0.0863730i
$708$		0			0
$709$	−7.29109	−	10.0353i	−0.273823	−	0.376885i	0.649853	−	0.760060i	$-0.274830\pi$
$709$	−7.29109	−	10.0353i	−0.273823	−	0.376885i	−0.923676	+	0.383175i	$0.874830\pi$
$710$		0			0
$711$		−	1.84001i		−	0.0690056i
$712$		0			0
$713$	1.90127	+	0.617760i	0.0712031	+	0.0231353i
$714$		0			0
$715$	17.9480	−	3.82838i	0.671219	−	0.143173i
$716$		0			0
$717$	56.6908	+	18.4200i	2.11716	+	0.687906i
$718$		0			0
$719$	−26.1545	−	8.49812i	−0.975399	−	0.316926i	−0.222405	−	0.974954i	$-0.571391\pi$
$719$	−26.1545	−	8.49812i	−0.975399	−	0.316926i	−0.752994	+	0.658028i	$0.771391\pi$
$720$		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
$725$	28.6642	−	3.05416i	1.06456	−	0.113429i
$726$		0			0
$727$	14.3554	+	10.4298i	0.532414	+	0.386821i	0.821260	−	0.570554i	$-0.193272\pi$
$727$	14.3554	+	10.4298i	0.532414	+	0.386821i	−0.288846	+	0.957376i	$0.593272\pi$
$728$		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	−0.996044	−	0.0888585i	$-0.971678\pi$
$733$	−20.9217	−	28.7962i	−0.772759	−	1.06361i	0.223285	−	0.974753i	$-0.428322\pi$
$734$		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	$-0.143881\pi$
$743$	5.62014	+	7.73546i	0.206183	+	0.283787i	−0.693385	+	0.720567i	$0.743881\pi$
$744$		0			0
$745$	11.8129	+	5.24931i	0.432790	+	0.192320i
$746$		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	−0.857936	−	0.513757i	$-0.828253\pi$
$751$	−34.2566	+	11.1307i	−1.25004	+	0.406163i	−0.392106	+	0.919920i	$0.628253\pi$
$752$		0			0
$753$	−0.929879	+	0.675597i	−0.0338867	+	0.0246201i
$754$		0			0
$755$	−13.0123	+	14.4725i	−0.473568	+	0.526707i
$756$		0			0
$757$	−14.5655	+	44.8279i	−0.529391	+	1.62930i	0.226076	+	0.974110i	$0.427410\pi$
$757$	−14.5655	+	44.8279i	−0.529391	+	1.62930i	−0.755467	+	0.655187i	$0.772590\pi$
$758$		0			0
$759$	21.1040	−	64.9514i	0.766026	−	2.35759i
$760$		0			0
$761$	−0.410675	−	1.26393i	−0.0148870	−	0.0458173i	0.943337	−	0.331836i	$-0.107668\pi$
$761$	−0.410675	−	1.26393i	−0.0148870	−	0.0458173i	−0.958224	+	0.286019i	$0.907668\pi$
$762$		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	0.474765	−	0.880113i	$-0.342533\pi$
$769$	−5.97772	−	4.34307i	−0.215562	−	0.156615i	−0.690327	+	0.723498i	$0.742533\pi$
$770$		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	$-0.0289282\pi$
$773$	3.80483	+	11.7101i	0.136850	+	0.421181i	−0.859023	+	0.511937i	$0.828928\pi$
$774$		0			0
$775$	−1.46965	+	0.656850i	−0.0527914	+	0.0235947i
$776$		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
$785$	−8.19475	−	38.4182i	−0.292483	−	1.37120i
$786$		0			0
$787$	3.86233	−	5.31604i	0.137677	−	0.189496i	−0.734611	−	0.678489i	$-0.762635\pi$
$787$	3.86233	−	5.31604i	0.137677	−	0.189496i	0.872288	+	0.488992i	$0.162635\pi$
$788$		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
$795$	−29.0052	+	65.2722i	−1.02871	+	2.31497i
$796$		0			0
$797$	45.0875	−	14.6498i	1.59708	−	0.518923i	0.630698	−	0.776029i	$-0.282769\pi$
$797$	45.0875	−	14.6498i	1.59708	−	0.518923i	0.966383	+	0.257106i	$0.0827688\pi$
$798$		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
$805$	1.50510	+	2.60262i	0.0530479	+	0.0917302i
$806$		0			0
$807$	−13.8495	−	42.6245i	−0.487527	−	1.50045i
$808$		0			0
$809$	−31.5672	+	43.4486i	−1.10984	+	1.52757i	−0.288200	+	0.957570i	$0.593057\pi$
$809$	−31.5672	+	43.4486i	−1.10984	+	1.52757i	−0.821644	+	0.570000i	$0.806943\pi$
$810$		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
$815$	−8.50052	−	14.6991i	−0.297760	−	0.514886i
$816$		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	$-0.447714\pi$
$823$	9.38237			0.327049			0.163524	+	0.986539i	$0.447714\pi$
$824$		0			0
$825$	22.4394	+	50.2064i	0.781239	+	1.74796i
$826$		0			0
$827$	−2.17753	+	6.70176i	−0.0757202	+	0.233043i	−0.981752	−	0.190167i	$-0.939097\pi$
$827$	−2.17753	+	6.70176i	−0.0757202	+	0.233043i	0.906031	+	0.423210i	$0.139097\pi$
$828$		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
$835$	−15.2532	+	8.82100i	−0.527860	+	0.305263i
$836$		0			0
$837$	−2.53002	−	1.83817i	−0.0874504	−	0.0635364i
$838$		0			0
$839$	3.18838	+	1.03597i	0.110075	+	0.0357656i	0.363537	−	0.931580i	$-0.381569\pi$
$839$	3.18838	+	1.03597i	0.110075	+	0.0357656i	−0.253462	+	0.967345i	$0.581569\pi$
$840$		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
$845$	7.15173	−	16.0940i	0.246027	−	0.553650i
$846$		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	$-0.790001\pi$
$853$	1.07832	−	1.48418i	0.0369209	−	0.0508172i	0.827078	+	0.562087i	$0.190001\pi$
$854$		0			0
$855$	−33.7701	+	7.20330i	−1.15491	+	0.246348i
$856$		0			0
$857$	4.14968	+	5.71154i	0.141750	+	0.195102i	0.873989	−	0.485945i	$-0.161525\pi$
$857$	4.14968	+	5.71154i	0.141750	+	0.195102i	−0.732239	+	0.681048i	$0.761525\pi$
$858$		0			0
$859$	−0.646894	−	1.99093i	−0.0220717	−	0.0679298i	0.939414	−	0.342785i	$-0.111370\pi$
$859$	−0.646894	−	1.99093i	−0.0220717	−	0.0679298i	−0.961486	+	0.274855i	$0.911370\pi$
$860$		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	$-0.988837\pi$
$863$	−52.5051	+	17.0600i	−1.78730	+	0.580728i	−0.787911	+	0.615790i	$0.788837\pi$
$864$		0			0
$865$	−15.5944	−	26.9658i	−0.530227	−	0.916866i
$866$		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	$-0.337750\pi$
$877$	10.9460	+	3.55657i	0.369620	+	0.120097i	−0.118317	+	0.992976i	$0.537750\pi$
$878$		0			0
$879$	−1.39771	−	4.30170i	−0.0471435	−	0.145093i
$880$		0			0
$881$	15.9839	−	49.1932i	0.538510	−	1.65736i	−0.197431	−	0.980317i	$-0.563260\pi$
$881$	15.9839	−	49.1932i	0.538510	−	1.65736i	0.735941	−	0.677046i	$-0.236740\pi$
$882$		0			0
$883$	−9.82569	+	30.2404i	−0.330661	+	1.01767i	0.638160	+	0.769904i	$0.279696\pi$
$883$	−9.82569	+	30.2404i	−0.330661	+	1.01767i	−0.968820	+	0.247765i	$0.920304\pi$
$884$		0			0
$885$	21.7257	+	19.5338i	0.730302	+	0.656622i
$886$		0			0
$887$	38.4297	−	27.9208i	1.29034	−	0.937490i	0.290532	−	0.956865i	$-0.406168\pi$
$887$	38.4297	−	27.9208i	1.29034	−	0.937490i	0.999812	+	0.0193750i	$0.00616765\pi$
$888$		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
$895$	−28.4030	−	12.6215i	−0.949408	−	0.421891i
$896$		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	$-0.301301\pi$
$907$	−11.0779	−	15.2475i	−0.367837	−	0.506284i	−0.952311	+	0.305128i	$0.901301\pi$
$908$		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
$915$	7.14358	+	33.4902i	0.236159	+	1.10715i
$916$		0			0
$917$	3.60401	−	2.61847i	0.119015	−	0.0864695i
$918$		0			0
$919$	12.4602	−	17.1499i	0.411023	−	0.565724i	−0.552445	−	0.833550i	$-0.686305\pi$
$919$	12.4602	−	17.1499i	0.411023	−	0.565724i	0.963468	+	0.267825i	$0.0863050\pi$
$920$		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
$925$	−39.5998	+	4.21935i	−1.30203	+	0.138731i
$926$		0			0
$927$	−24.5397	−	7.97344i	−0.805990	−	0.261882i
$928$		0			0
$929$		−	28.5637i		−	0.937146i	−0.883425	−	0.468573i	$-0.844768\pi$
$929$		−	28.5637i		−	0.937146i	0.883425	−	0.468573i	$-0.155232\pi$
$930$		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
$935$	−18.8217	+	20.9337i	−0.615537	+	0.684606i
$936$		0			0
$937$	−16.1122	−	49.5883i	−0.526363	−	1.61998i	−0.761605	−	0.648041i	$-0.775588\pi$
$937$	−16.1122	−	49.5883i	−0.526363	−	1.61998i	0.235242	−	0.971937i	$-0.424412\pi$
$938$		0			0
$939$	−5.50847	+	4.00214i	−0.179762	+	0.130605i
$940$		0			0
$941$	2.59917	+	7.99943i	0.0847306	+	0.260774i	0.984442	−	0.175712i	$-0.0562228\pi$
$941$	2.59917	+	7.99943i	0.0847306	+	0.260774i	−0.899711	+	0.436486i	$0.856223\pi$
$942$		0			0
$943$	1.79793	+	39.7186i	0.0585488	+	1.29342i
$944$		0			0
$945$	−0.981127	−	4.59967i	−0.0319161	−	0.149627i
$946$		0			0
$947$	21.9425	+	30.2013i	0.713036	+	0.981410i	0.999726	+	0.0233866i	$0.00744487\pi$
$947$	21.9425	+	30.2013i	0.713036	+	0.981410i	−0.286690	+	0.958023i	$0.592555\pi$
$948$		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	−0.106092	−	0.994356i	$-0.533834\pi$
$953$	26.9310	−	37.0674i	0.872381	−	1.20073i	0.978473	−	0.206373i	$-0.0661661\pi$
$954$		0			0
$955$	17.7110	+	30.6258i	0.573115	+	0.991028i
$956$		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
$965$	−19.4764	+	43.8289i	−0.626966	+	1.41090i
$966$		0			0
$967$	−15.6547	−	11.3738i	−0.503423	−	0.365758i	0.306900	−	0.951742i	$-0.400708\pi$
$967$	−15.6547	−	11.3738i	−0.503423	−	0.365758i	−0.810323	+	0.585984i	$0.800708\pi$
$968$		0			0
$969$	−15.4152	−	21.2172i	−0.495208	−	0.681595i
$970$		0			0
$971$	6.30955	−	2.05010i	0.202483	−	0.0657907i	−0.206020	−	0.978548i	$-0.566051\pi$
$971$	6.30955	−	2.05010i	0.202483	−	0.0657907i	0.408503	+	0.912757i	$0.366051\pi$
$972$		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	−0.641106	−	0.767452i	$-0.721524\pi$
$977$	10.2728	−	31.6165i	0.328657	−	1.01150i	0.969763	−	0.244049i	$-0.0784758\pi$
$978$		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	0.617447	−	0.786613i	$-0.288167\pi$
$991$	20.6073	+	6.69571i	0.654612	+	0.212696i	0.0371654	+	0.999309i	$0.488167\pi$
$992$		0			0
$993$		−	23.0799i		−	0.732418i
$994$		0			0
$995$	−29.7599	+	33.0993i	−0.943453	+	1.04932i
$996$		0			0
$997$	8.92215	+	27.4596i	0.282567	+	0.869653i	0.987117	+	0.159999i	$0.0511490\pi$
$997$	8.92215	+	27.4596i	0.282567	+	0.869653i	−0.704550	+	0.709655i	$0.748851\pi$
$998$		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.269.20	yes	80
5.4	even	2	inner	820.2.bi.a.269.1	yes	80
41.25	even	10	inner	820.2.bi.a.189.1	✓	80
205.189	even	10	inner	820.2.bi.a.189.20	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.bi.a.189.1	✓	80	41.25	even	10	inner
820.2.bi.a.189.20	yes	80	205.189	even	10	inner
820.2.bi.a.269.1	yes	80	5.4	even	2	inner
820.2.bi.a.269.20	yes	80	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+3.03349 q^{3} +(1.93569 - 1.11942i) q^{5} +(0.0669129 - 0.205937i) q^{7} +6.20209 q^{9} +(-2.13114 + 2.93326i) q^{11} +(-0.699493 - 2.15282i) q^{13} +(5.87191 - 3.39575i) q^{15} +(2.80914 + 2.04096i) q^{17} +(-2.36798 - 0.769403i) q^{19} +(0.202980 - 0.624708i) q^{21} +(-5.90545 + 1.91880i) q^{23} +(2.49381 - 4.33370i) q^{25} +9.71351 q^{27} +(3.38875 + 4.66421i) q^{29} +(-0.260464 - 0.189238i) q^{31} +(-6.46479 + 8.89802i) q^{33} +(-0.101006 - 0.473534i) q^{35} +(-4.68159 - 6.44365i) q^{37} +(-2.12191 - 6.53056i) q^{39} +(1.70127 - 6.17298i) q^{41} +(-5.69152 + 1.84929i) q^{43} +(12.0053 - 6.94273i) q^{45} +(-3.16195 - 9.73150i) q^{47} +(5.62519 + 4.08694i) q^{49} +(8.52152 + 6.19124i) q^{51} +(-8.51902 + 6.18943i) q^{53} +(-0.841683 + 8.06352i) q^{55} +(-7.18325 - 2.33398i) q^{57} +(1.33099 + 4.09637i) q^{59} +(-1.56003 + 4.80128i) q^{61} +(0.415000 - 1.27724i) q^{63} +(-3.76391 - 3.38417i) q^{65} +(-5.42363 + 3.94050i) q^{67} +(-17.9141 + 5.82066i) q^{69} +(9.55669 - 13.1537i) q^{71} +6.64621i q^{73} +(7.56495 - 13.1462i) q^{75} +(0.461465 + 0.635152i) q^{77} -0.296675i q^{79} +10.8596 q^{81} +3.09381i q^{83} +(7.72232 + 0.806068i) q^{85} +(10.2798 + 14.1489i) q^{87} +(-9.05444 - 2.94197i) q^{89} -0.490149 q^{91} +(-0.790117 - 0.574054i) q^{93} +(-5.44496 + 1.16143i) q^{95} +(3.18534 - 2.31429i) q^{97} +(-13.2175 + 18.1923i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 68 q^{9} + 10 q^{15} - 26 q^{21} + 10 q^{25} - 20 q^{29} + 4 q^{31} + 15 q^{35} - 8 q^{39} + 4 q^{41} - 4 q^{45} + 18 q^{49} + 52 q^{51} - 36 q^{59} - 42 q^{61} - 15 q^{65} + 30 q^{69} - 20 q^{75}+ \cdots + 80 q^{99}+O(q^{100}) \) 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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