LMFDB - Embedded newform 820.2.bg.b.681.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(441,820)] 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, 0, 7])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.441"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			681.6
Character	$\chi$	$=$	820.681
Dual form			820.2.bg.b.761.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.94063i q^{3} +(-0.809017 - 0.587785i) q^{5} +(-0.0642499 + 0.0208760i) q^{7} -0.766036 q^{9} +(-2.16777 - 2.98368i) q^{11} +(-6.64164 - 2.15800i) q^{13} +(1.14067 - 1.57000i) q^{15} +(-1.45177 - 1.99819i) q^{17} +(-4.29550 + 1.39569i) q^{19} +(-0.0405126 - 0.124685i) q^{21} +(0.787726 - 2.42437i) q^{23} +(0.309017 + 0.951057i) q^{25} +4.33529i q^{27} +(-1.87679 + 2.58318i) q^{29} +(6.91829 - 5.02643i) q^{31} +(5.79021 - 4.20683i) q^{33} +(0.0642499 + 0.0208760i) q^{35} +(-8.43488 - 6.12830i) q^{37} +(4.18787 - 12.8889i) q^{39} +(6.20927 + 1.56362i) q^{41} +(-1.94594 + 5.98900i) q^{43} +(0.619736 + 0.450264i) q^{45} +(-5.49583 - 1.78570i) q^{47} +(-5.65943 + 4.11181i) q^{49} +(3.87774 - 2.81734i) q^{51} +(-5.45570 + 7.50912i) q^{53} +3.68803i q^{55} +(-2.70852 - 8.33597i) q^{57} +(4.49661 - 13.8391i) q^{59} +(-2.71482 - 8.35535i) q^{61} +(0.0492177 - 0.0159918i) q^{63} +(4.10476 + 5.64971i) q^{65} +(8.16190 - 11.2339i) q^{67} +(4.70480 + 1.52868i) q^{69} +(6.24053 + 8.58935i) q^{71} +0.824160 q^{73} +(-1.84565 + 0.599687i) q^{75} +(0.201566 + 0.146446i) q^{77} -1.29531i q^{79} -10.7113 q^{81} -0.209284 q^{83} +2.46990i q^{85} +(-5.01300 - 3.64216i) q^{87} +(-7.98903 + 2.59579i) q^{89} +0.471775 q^{91} +(9.75444 + 13.4258i) q^{93} +(4.29550 + 1.39569i) q^{95} +(3.17235 - 4.36637i) q^{97} +(1.66059 + 2.28560i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{5} - 5 q^{7} - 42 q^{9} + 5 q^{11} + 5 q^{13} - 5 q^{17} - 25 q^{19} - 6 q^{21} - 22 q^{23} - 8 q^{25} + 5 q^{29} - 9 q^{31} + 24 q^{33} + 5 q^{35} - 11 q^{37} + 20 q^{39} + 16 q^{41} + 26 q^{43}+ \cdots - 20 q^{97}+O(q^{100}) $ 32 * q - 8 * q^5 - 5 * q^7 - 42 * q^9 + 5 * q^11 + 5 * q^13 - 5 * q^17 - 25 * q^19 - 6 * q^21 - 22 * q^23 - 8 * q^25 + 5 * q^29 - 9 * q^31 + 24 * q^33 + 5 * q^35 - 11 * q^37 + 20 * q^39 + 16 * q^41 + 26 * q^43 + 13 * q^45 - 25 * q^47 + 33 * q^49 + 29 * q^51 - 35 * q^53 + 27 * q^57 + 10 * q^59 + 32 * q^61 + 90 * q^63 - 5 * q^65 + 30 * q^67 - 10 * q^69 + 45 * q^71 - 80 * q^73 - 5 * q^75 - 78 * q^77 - 20 * q^81 - 10 * q^83 + 27 * q^87 - 60 * q^89 + 14 * q^91 - 80 * q^93 + 25 * q^95 - 20 * q^97

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
$3$			1.94063i			1.12042i	0.828350	+	0.560211i	$0.189280\pi$
$3$			1.94063i			1.12042i	−0.828350	+	0.560211i	$0.810720\pi$
$4$		0			0
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$6$		0			0
$7$	−0.0642499	+	0.0208760i	−0.0242842	+	0.00789040i	−0.321134	−	0.947034i	$-0.604064\pi$
$7$	−0.0642499	+	0.0208760i	−0.0242842	+	0.00789040i	0.296850	+	0.954924i	$0.404064\pi$
$8$		0			0
$9$	−0.766036			−0.255345
$10$		0			0
$11$	−2.16777	−	2.98368i	−0.653607	−	0.899613i	0.345642	−	0.938366i	$-0.387661\pi$
$11$	−2.16777	−	2.98368i	−0.653607	−	0.899613i	−0.999249	+	0.0387538i	$0.987661\pi$
$12$		0			0
$13$	−6.64164	−	2.15800i	−1.84206	−	0.598521i	−0.998066	−	0.0621668i	$-0.980199\pi$
$13$	−6.64164	−	2.15800i	−1.84206	−	0.598521i	−0.843993	−	0.536354i	$-0.819801\pi$
$14$		0			0
$15$	1.14067	−	1.57000i	0.294520	−	0.405372i
$16$		0			0
$17$	−1.45177	−	1.99819i	−0.352105	−	0.484632i	0.595823	−	0.803116i	$-0.296826\pi$
$17$	−1.45177	−	1.99819i	−0.352105	−	0.484632i	−0.947928	+	0.318484i	$0.896826\pi$
$18$		0			0
$19$	−4.29550	+	1.39569i	−0.985455	+	0.320194i	−0.757039	−	0.653370i	$-0.773355\pi$
$19$	−4.29550	+	1.39569i	−0.985455	+	0.320194i	−0.228416	+	0.973564i	$0.573355\pi$
$20$		0			0
$21$	−0.0405126	−	0.124685i	−0.00884058	−	0.0272085i
$22$		0			0
$23$	0.787726	−	2.42437i	0.164252	−	0.505517i	−0.834728	−	0.550662i	$-0.814375\pi$
$23$	0.787726	−	2.42437i	0.164252	−	0.505517i	0.998980	+	0.0451457i	$0.0143752\pi$
$24$		0			0
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$		0			0
$27$			4.33529i			0.834328i
$28$		0			0
$29$	−1.87679	+	2.58318i	−0.348512	+	0.479685i	−0.946903	−	0.321519i	$-0.895807\pi$
$29$	−1.87679	+	2.58318i	−0.348512	+	0.479685i	0.598392	+	0.801204i	$0.295807\pi$
$30$		0			0
$31$	6.91829	−	5.02643i	1.24256	−	0.902774i	0.244796	−	0.969575i	$-0.421279\pi$
$31$	6.91829	−	5.02643i	1.24256	−	0.902774i	0.997766	+	0.0668004i	$0.0212791\pi$
$32$		0			0
$33$	5.79021	−	4.20683i	1.00795	−	0.732315i
$34$		0			0
$35$	0.0642499	+	0.0208760i	0.0108602	+	0.00352870i
$36$		0			0
$37$	−8.43488	−	6.12830i	−1.38669	−	1.00749i	−0.996220	−	0.0868686i	$-0.972314\pi$
$37$	−8.43488	−	6.12830i	−1.38669	−	1.00749i	−0.390466	−	0.920617i	$-0.627686\pi$
$38$		0			0
$39$	4.18787	−	12.8889i	0.670596	−	2.06388i
$40$		0			0
$41$	6.20927	+	1.56362i	0.969726	+	0.244197i
$41$	6.20927	+	1.56362i	0.969726	+	0.244197i
$42$		0			0
$43$	−1.94594	+	5.98900i	−0.296754	+	0.913314i	0.685873	+	0.727721i	$0.259421\pi$
$43$	−1.94594	+	5.98900i	−0.296754	+	0.913314i	−0.982627	+	0.185593i	$0.940579\pi$
$44$		0			0
$45$	0.619736	+	0.450264i	0.0923848	+	0.0671215i
$46$		0			0
$47$	−5.49583	−	1.78570i	−0.801649	−	0.260472i	−0.120592	−	0.992702i	$-0.538479\pi$
$47$	−5.49583	−	1.78570i	−0.801649	−	0.260472i	−0.681057	+	0.732231i	$0.738479\pi$
$48$		0			0
$49$	−5.65943	+	4.11181i	−0.808490	+	0.587402i
$50$		0			0
$51$	3.87774	−	2.81734i	0.542992	−	0.394507i
$52$		0			0
$53$	−5.45570	+	7.50912i	−0.749397	+	1.03146i	0.248625	+	0.968600i	$0.420021\pi$
$53$	−5.45570	+	7.50912i	−0.749397	+	1.03146i	−0.998023	+	0.0628572i	$0.979979\pi$
$54$		0			0
$55$			3.68803i			0.497294i
$56$		0			0
$57$	−2.70852	−	8.33597i	−0.358752	−	1.10413i
$58$		0			0
$59$	4.49661	−	13.8391i	0.585409	−	1.80170i	−0.0122129	−	0.999925i	$-0.503888\pi$
$59$	4.49661	−	13.8391i	0.585409	−	1.80170i	0.597622	−	0.801778i	$-0.296112\pi$
$60$		0			0
$61$	−2.71482	−	8.35535i	−0.347597	−	1.06979i	−0.960179	−	0.279386i	$-0.909869\pi$
$61$	−2.71482	−	8.35535i	−0.347597	−	1.06979i	0.612582	−	0.790407i	$-0.290131\pi$
$62$		0			0
$63$	0.0492177	−	0.0159918i	0.00620084	−	0.00201478i
$64$		0			0
$65$	4.10476	+	5.64971i	0.509132	+	0.700761i
$66$		0			0
$67$	8.16190	−	11.2339i	0.997135	−	1.37244i	0.0700678	−	0.997542i	$-0.477678\pi$
$67$	8.16190	−	11.2339i	0.997135	−	1.37244i	0.927067	−	0.374896i	$-0.122322\pi$
$68$		0			0
$69$	4.70480	+	1.52868i	0.566392	+	0.184032i
$70$		0			0
$71$	6.24053	+	8.58935i	0.740615	+	1.01937i	0.998583	+	0.0532152i	$0.0169469\pi$
$71$	6.24053	+	8.58935i	0.740615	+	1.01937i	−0.257968	+	0.966153i	$0.583053\pi$
$72$		0			0
$73$	0.824160			0.0964606			0.0482303	−	0.998836i	$-0.484642\pi$
$73$	0.824160			0.0964606			0.0482303	+	0.998836i	$0.484642\pi$
$74$		0			0
$75$	−1.84565	+	0.599687i	−0.213117	+	0.0692459i
$76$		0			0
$77$	0.201566	+	0.146446i	0.0229706	+	0.0166891i
$78$		0			0
$79$		−	1.29531i		−	0.145734i	−0.997342	−	0.0728670i	$-0.976785\pi$
$79$		−	1.29531i		−	0.145734i	0.997342	−	0.0728670i	$-0.0232149\pi$
$80$		0			0
$81$	−10.7113			−1.19014
$82$		0			0
$83$	−0.209284			−0.0229719			−0.0114860	−	0.999934i	$-0.503656\pi$
$83$	−0.209284			−0.0229719			−0.0114860	+	0.999934i	$0.503656\pi$
$84$		0			0
$85$			2.46990i			0.267898i
$86$		0			0
$87$	−5.01300	−	3.64216i	−0.537450	−	0.390480i
$88$		0			0
$89$	−7.98903	+	2.59579i	−0.846836	+	0.275154i	−0.700120	−	0.714025i	$-0.746870\pi$
$89$	−7.98903	+	2.59579i	−0.846836	+	0.275154i	−0.146716	+	0.989179i	$0.546870\pi$
$90$		0			0
$91$	0.471775			0.0494554
$92$		0			0
$93$	9.75444	+	13.4258i	1.01149	+	1.39219i
$94$		0			0
$95$	4.29550	+	1.39569i	0.440709	+	0.143195i
$96$		0			0
$97$	3.17235	−	4.36637i	0.322104	−	0.443338i	−0.617004	−	0.786960i	$-0.711654\pi$
$97$	3.17235	−	4.36637i	0.322104	−	0.443338i	0.939108	+	0.343622i	$0.111654\pi$
$98$		0			0
$99$	1.66059	+	2.28560i	0.166895	+	0.229712i
$100$		0			0
$101$	10.6923	−	3.47413i	1.06392	−	0.345688i	0.275803	−	0.961214i	$-0.411056\pi$
$101$	10.6923	−	3.47413i	1.06392	−	0.345688i	0.788117	+	0.615526i	$0.211056\pi$
$102$		0			0
$103$	−1.40260	−	4.31676i	−0.138202	−	0.425343i	0.857872	−	0.513863i	$-0.171786\pi$
$103$	−1.40260	−	4.31676i	−0.138202	−	0.425343i	−0.996074	+	0.0885204i	$0.971786\pi$
$104$		0			0
$105$	−0.0405126	+	0.124685i	−0.00395363	+	0.0121680i
$106$		0			0
$107$	4.70386	+	14.4770i	0.454739	+	1.39954i	0.871441	+	0.490500i	$0.163186\pi$
$107$	4.70386	+	14.4770i	0.454739	+	1.39954i	−0.416702	+	0.909043i	$0.636814\pi$
$108$		0			0
$109$			13.5120i			1.29421i	0.762399	+	0.647107i	$0.224021\pi$
$109$			13.5120i			1.29421i	−0.762399	+	0.647107i	$0.775979\pi$
$110$		0			0
$111$	11.8927	−	16.3690i	1.12881	−	1.55367i
$112$		0			0
$113$	−10.6601	+	7.74499i	−1.00281	+	0.728587i	−0.962690	−	0.270608i	$-0.912775\pi$
$113$	−10.6601	+	7.74499i	−1.00281	+	0.728587i	−0.0401244	+	0.999195i	$0.512775\pi$
$114$		0			0
$115$	−2.06229	+	1.49834i	−0.192310	+	0.139721i
$116$		0			0
$117$	5.08773	+	1.65310i	0.470361	+	0.152829i
$118$		0			0
$119$	0.134990	+	0.0980761i	0.0123745	+	0.00899062i
$120$		0			0
$121$	−0.803924	+	2.47423i	−0.0730840	+	0.224930i
$122$		0			0
$123$	−3.03441	+	12.0499i	−0.273603	+	1.08650i
$124$		0			0
$125$	0.309017	−	0.951057i	0.0276393	−	0.0850651i
$126$		0			0
$127$	−14.9976	−	10.8964i	−1.33082	−	0.966900i	−0.999728	−	0.0233028i	$-0.992582\pi$
$127$	−14.9976	−	10.8964i	−1.33082	−	0.966900i	−0.331095	−	0.943597i	$-0.607418\pi$
$128$		0			0
$129$	−11.6224	−	3.77635i	−1.02330	−	0.332489i
$130$		0			0
$131$	−11.5113	+	8.36346i	−1.00575	+	0.730719i	−0.963313	−	0.268381i	$-0.913512\pi$
$131$	−11.5113	+	8.36346i	−1.00575	+	0.730719i	−0.0424349	+	0.999099i	$0.513512\pi$
$132$		0			0
$133$	0.246849	−	0.179346i	0.0214045	−	0.0155513i
$134$		0			0
$135$	2.54822	−	3.50733i	0.219316	−	0.301863i
$136$		0			0
$137$			17.7040i			1.51255i	0.654253	+	0.756276i	$0.272983\pi$
$137$			17.7040i			1.51255i	−0.654253	+	0.756276i	$0.727017\pi$
$138$		0			0
$139$	−0.367427	−	1.13083i	−0.0311648	−	0.0959154i	0.934264	−	0.356582i	$-0.116058\pi$
$139$	−0.367427	−	1.13083i	−0.0311648	−	0.0959154i	−0.965429	+	0.260666i	$0.916058\pi$
$140$		0			0
$141$	3.46538	−	10.6654i	0.291838	−	0.898185i
$142$		0			0
$143$	7.95876	+	24.4945i	0.665545	+	2.04834i
$144$		0			0
$145$	3.03671	−	0.986688i	0.252185	−	0.0819400i
$146$		0			0
$147$	−7.97950	−	10.9828i	−0.658138	−	0.905849i
$148$		0			0
$149$	−1.64715	+	2.26711i	−0.134940	+	0.185729i	−0.871140	−	0.491036i	$-0.836619\pi$
$149$	−1.64715	+	2.26711i	−0.134940	+	0.185729i	0.736199	+	0.676765i	$0.236619\pi$
$150$		0			0
$151$	−2.50829	−	0.814993i	−0.204122	−	0.0663232i	0.205172	−	0.978726i	$-0.434225\pi$
$151$	−2.50829	−	0.814993i	−0.204122	−	0.0663232i	−0.409293	+	0.912403i	$0.634225\pi$
$152$		0			0
$153$	1.11211	+	1.53068i	0.0899084	+	0.123748i
$154$		0			0
$155$	−8.55148			−0.686871
$156$		0			0
$157$	−8.15099	+	2.64842i	−0.650520	+	0.211367i	−0.615643	−	0.788025i	$-0.711104\pi$
$157$	−8.15099	+	2.64842i	−0.650520	+	0.211367i	−0.0348764	+	0.999392i	$0.511104\pi$
$158$		0			0
$159$	−14.5724	−	10.5875i	−1.15567	−	0.839641i
$160$		0			0
$161$			0.172210i			0.0135721i
$162$		0			0
$163$	0.483415			0.0378640			0.0189320	−	0.999821i	$-0.493973\pi$
$163$	0.483415			0.0378640			0.0189320	+	0.999821i	$0.493973\pi$
$164$		0			0
$165$	−7.15709			−0.557179
$166$		0			0
$167$			19.0176i			1.47163i	0.677183	+	0.735815i	$0.263201\pi$
$167$			19.0176i			1.47163i	−0.677183	+	0.735815i	$0.736799\pi$
$168$		0			0
$169$	28.9372	+	21.0241i	2.22594	+	1.61724i
$170$		0			0
$171$	3.29051	−	1.06915i	0.251631	−	0.0817600i
$172$		0			0
$173$	−13.6124			−1.03493			−0.517466	−	0.855704i	$-0.673125\pi$
$173$	−13.6124			−1.03493			−0.517466	+	0.855704i	$0.673125\pi$
$174$		0			0
$175$	−0.0397086	−	0.0546542i	−0.00300169	−	0.00413147i
$176$		0			0
$177$	26.8566	+	8.72625i	2.01867	+	0.655905i
$178$		0			0
$179$	4.50436	−	6.19971i	0.336671	−	0.463388i	−0.606794	−	0.794859i	$-0.707545\pi$
$179$	4.50436	−	6.19971i	0.336671	−	0.463388i	0.943466	+	0.331471i	$0.107545\pi$
$180$		0			0
$181$	−13.6668	−	18.8107i	−1.01584	−	1.39819i	−0.915076	−	0.403280i	$-0.867870\pi$
$181$	−13.6668	−	18.8107i	−1.01584	−	1.39819i	−0.100768	−	0.994910i	$-0.532130\pi$
$182$		0			0
$183$	16.2146	−	5.26845i	1.19862	−	0.389455i
$184$		0			0
$185$	3.22184	+	9.91579i	0.236874	+	0.729024i
$186$		0			0
$187$	−2.81485	+	8.66322i	−0.205842	+	0.633517i
$188$		0			0
$189$	−0.0905038	−	0.278542i	−0.00658318	−	0.0202609i
$190$		0			0
$191$		−	16.1097i		−	1.16566i	−0.812594	−	0.582830i	$-0.801945\pi$
$191$		−	16.1097i		−	1.16566i	0.812594	−	0.582830i	$-0.198055\pi$
$192$		0			0
$193$	−14.8797	+	20.4801i	−1.07106	+	1.47419i	−0.202064	+	0.979372i	$0.564765\pi$
$193$	−14.8797	+	20.4801i	−1.07106	+	1.47419i	−0.868997	+	0.494817i	$0.835235\pi$
$194$		0			0
$195$	−10.9640	+	7.96581i	−0.785148	+	0.570443i
$196$		0			0
$197$	18.1064	−	13.1551i	1.29003	−	0.937259i	0.290220	−	0.956960i	$-0.406271\pi$
$197$	18.1064	−	13.1551i	1.29003	−	0.937259i	0.999806	+	0.0197008i	$0.00627137\pi$
$198$		0			0
$199$	−1.90269	−	0.618222i	−0.134878	−	0.0438246i	0.240800	−	0.970575i	$-0.422590\pi$
$199$	−1.90269	−	0.618222i	−0.134878	−	0.0438246i	−0.375678	+	0.926750i	$0.622590\pi$
$200$		0			0
$201$	21.8008	+	15.8392i	1.53771	+	1.11721i
$202$		0			0
$203$	0.0666570	−	0.205149i	0.00467840	−	0.0143986i
$204$		0			0
$205$	−4.10433	−	4.91472i	−0.286659	−	0.343259i
$206$		0			0
$207$	−0.603427	+	1.85716i	−0.0419410	+	0.129081i
$208$		0			0
$209$	13.4759	+	9.79085i	0.932151	+	0.677247i
$210$		0			0
$211$	−3.71026	−	1.20554i	−0.255425	−	0.0829925i	0.178506	−	0.983939i	$-0.442874\pi$
$211$	−3.71026	−	1.20554i	−0.255425	−	0.0829925i	−0.433930	+	0.900946i	$0.642874\pi$
$212$		0			0
$213$	−16.6687	+	12.1105i	−1.14212	+	0.829801i
$214$		0			0
$215$	5.09455	−	3.70141i	0.347445	−	0.252434i
$216$		0			0
$217$	−0.339567	+	0.467374i	−0.0230513	+	0.0317274i
$218$		0			0
$219$			1.59939i			0.108077i
$220$		0			0
$221$	5.33003	+	16.4041i	0.358537	+	1.10346i
$222$		0			0
$223$	3.57388	−	10.9993i	0.239325	−	0.736565i	−0.757194	−	0.653190i	$-0.773430\pi$
$223$	3.57388	−	10.9993i	0.239325	−	0.736565i	0.996518	−	0.0833749i	$-0.0265699\pi$
$224$		0			0
$225$	−0.236718	−	0.728543i	−0.0157812	−	0.0485695i
$226$		0			0
$227$	13.2607	−	4.30865i	0.880142	−	0.285975i	0.166126	−	0.986105i	$-0.446874\pi$
$227$	13.2607	−	4.30865i	0.880142	−	0.285975i	0.714016	+	0.700129i	$0.246874\pi$
$228$		0			0
$229$	8.95349	+	12.3234i	0.591663	+	0.814355i	0.994913	−	0.100735i	$-0.0321195\pi$
$229$	8.95349	+	12.3234i	0.591663	+	0.814355i	−0.403250	+	0.915090i	$0.632120\pi$
$230$		0			0
$231$	−0.284198	+	0.391165i	−0.0186989	+	0.0257368i
$232$		0			0
$233$	9.86652	+	3.20583i	0.646377	+	0.210021i	0.613816	−	0.789449i	$-0.289634\pi$
$233$	9.86652	+	3.20583i	0.646377	+	0.210021i	0.0325611	+	0.999470i	$0.489634\pi$
$234$		0			0
$235$	3.39661	+	4.67503i	0.221570	+	0.304965i
$236$		0			0
$237$	2.51372			0.163284
$238$		0			0
$239$	4.75836	−	1.54609i	0.307793	−	0.100008i	−0.151048	−	0.988526i	$-0.548265\pi$
$239$	4.75836	−	1.54609i	0.307793	−	0.100008i	0.458841	+	0.888518i	$0.348265\pi$
$240$		0			0
$241$	−2.05525	−	1.49323i	−0.132391	−	0.0961874i	0.519619	−	0.854398i	$-0.326074\pi$
$241$	−2.05525	−	1.49323i	−0.132391	−	0.0961874i	−0.652010	+	0.758211i	$0.726074\pi$
$242$		0			0
$243$		−	7.78076i		−	0.499136i
$244$		0			0
$245$	6.99544			0.446922
$246$		0			0
$247$	31.5411			2.00691
$248$		0			0
$249$		−	0.406142i		−	0.0257382i
$250$		0			0
$251$	−16.5929	−	12.0554i	−1.04733	−	0.760931i	−0.0756289	−	0.997136i	$-0.524096\pi$
$251$	−16.5929	−	12.0554i	−1.04733	−	0.760931i	−0.971703	+	0.236205i	$0.924096\pi$
$252$		0			0
$253$	−8.94116	+	2.90516i	−0.562126	+	0.182646i
$254$		0			0
$255$	−4.79315			−0.300159
$256$		0			0
$257$	−8.93361	−	12.2961i	−0.557264	−	0.767007i	0.433712	−	0.901052i	$-0.357204\pi$
$257$	−8.93361	−	12.2961i	−0.557264	−	0.767007i	−0.990975	+	0.134044i	$0.957204\pi$
$258$		0			0
$259$	0.669874	+	0.217655i	0.0416240	+	0.0135244i
$260$		0			0
$261$	1.43769	−	1.97881i	0.0889908	−	0.122485i
$262$		0			0
$263$	−1.38565	−	1.90718i	−0.0854425	−	0.117602i	0.764156	−	0.645031i	$-0.223156\pi$
$263$	−1.38565	−	1.90718i	−0.0854425	−	0.117602i	−0.849599	+	0.527430i	$0.823156\pi$
$264$		0			0
$265$	8.82750	−	2.86823i	0.542269	−	0.176194i
$266$		0			0
$267$	−5.03747	−	15.5037i	−0.308288	−	0.948813i
$268$		0			0
$269$	6.32616	−	19.4699i	0.385713	−	1.18710i	−0.550249	−	0.835000i	$-0.685467\pi$
$269$	6.32616	−	19.4699i	0.385713	−	1.18710i	0.935962	−	0.352101i	$-0.114533\pi$
$270$		0			0
$271$	−7.84685	−	24.1501i	−0.476662	−	1.46702i	−0.843703	−	0.536811i	$-0.819629\pi$
$271$	−7.84685	−	24.1501i	−0.476662	−	1.46702i	0.367040	−	0.930205i	$-0.380371\pi$
$272$		0			0
$273$			0.915539i			0.0554109i
$274$		0			0
$275$	2.16777	−	2.98368i	0.130721	−	0.179923i
$276$		0			0
$277$	−1.35971	+	0.987889i	−0.0816972	+	0.0593565i	−0.627884	−	0.778307i	$-0.716079\pi$
$277$	−1.35971	+	0.987889i	−0.0816972	+	0.0593565i	0.546187	+	0.837663i	$0.316079\pi$
$278$		0			0
$279$	−5.29966	+	3.85043i	−0.317282	+	0.230519i
$280$		0			0
$281$	−15.5785	−	5.06177i	−0.929338	−	0.301960i	−0.195046	−	0.980794i	$-0.562486\pi$
$281$	−15.5785	−	5.06177i	−0.929338	−	0.301960i	−0.734292	+	0.678834i	$0.762486\pi$
$282$		0			0
$283$	15.1035	+	10.9734i	0.897813	+	0.652299i	0.937903	−	0.346897i	$-0.112765\pi$
$283$	15.1035	+	10.9734i	0.897813	+	0.652299i	−0.0400905	+	0.999196i	$0.512765\pi$
$284$		0			0
$285$	−2.70852	+	8.33597i	−0.160439	+	0.493780i
$286$		0			0
$287$	−0.431587	+	0.0291626i	−0.0254758	+	0.00172141i
$288$		0			0
$289$	3.36817	−	10.3662i	0.198127	−	0.609774i
$290$		0			0
$291$	8.47349	+	6.15635i	0.496725	+	0.360892i
$292$		0			0
$293$	6.18814	+	2.01065i	0.361515	+	0.117463i	0.484142	−	0.874990i	$-0.339132\pi$
$293$	6.18814	+	2.01065i	0.361515	+	0.117463i	−0.122627	+	0.992453i	$0.539132\pi$
$294$		0			0
$295$	−11.7723	+	8.55306i	−0.685409	+	0.497979i
$296$		0			0
$297$	12.9351	−	9.39791i	0.750572	−	0.545322i
$298$		0			0
$299$	−10.4636	+	14.4019i	−0.605125	+	0.832883i
$300$		0			0
$301$		−	0.425416i		−	0.0245206i
$302$		0			0
$303$	6.74198	+	20.7497i	0.387317	+	1.19204i
$304$		0			0
$305$	−2.71482	+	8.35535i	−0.155450	+	0.478426i
$306$		0			0
$307$	−2.82885	−	8.70629i	−0.161451	−	0.496894i	0.837306	−	0.546734i	$-0.184129\pi$
$307$	−2.82885	−	8.70629i	−0.161451	−	0.496894i	−0.998757	+	0.0498394i	$0.984129\pi$
$308$		0			0
$309$	8.37722	−	2.72192i	0.476563	−	0.154845i
$310$		0			0
$311$	14.9409	+	20.5644i	0.847222	+	1.16610i	0.984468	+	0.175564i	$0.0561748\pi$
$311$	14.9409	+	20.5644i	0.847222	+	1.16610i	−0.137246	+	0.990537i	$0.543825\pi$
$312$		0			0
$313$	7.89594	−	10.8678i	0.446305	−	0.614286i	−0.525294	−	0.850921i	$-0.676045\pi$
$313$	7.89594	−	10.8678i	0.446305	−	0.614286i	0.971599	+	0.236635i	$0.0760446\pi$
$314$		0			0
$315$	−0.0492177	−	0.0159918i	−0.00277310	−	0.000901035i
$316$		0			0
$317$	−0.650998	−	0.896023i	−0.0365637	−	0.0503256i	0.790344	−	0.612664i	$-0.209902\pi$
$317$	−0.650998	−	0.896023i	−0.0365637	−	0.0503256i	−0.826907	+	0.562338i	$0.809902\pi$
$318$		0			0
$319$	11.7758			0.659320
$320$		0			0
$321$	−28.0944	+	9.12844i	−1.56808	+	0.509500i
$322$		0			0
$323$	9.02493	+	6.55699i	0.502160	+	0.364841i
$324$		0			0
$325$		−	6.98343i		−	0.387371i
$326$		0			0
$327$	−26.2217			−1.45007
$328$		0			0
$329$	0.390385			0.0215226
$330$		0			0
$331$			22.8344i			1.25509i	0.778579	+	0.627546i	$0.215941\pi$
$331$			22.8344i			1.25509i	−0.778579	+	0.627546i	$0.784059\pi$
$332$		0			0
$333$	6.46142	+	4.69449i	0.354083	+	0.257257i
$334$		0			0
$335$	−13.2062	+	4.29096i	−0.721533	+	0.234440i
$336$		0			0
$337$	0.652804			0.0355605			0.0177803	−	0.999842i	$-0.494340\pi$
$337$	0.652804			0.0355605			0.0177803	+	0.999842i	$0.494340\pi$
$338$		0			0
$339$	−15.0301	−	20.6872i	−0.816325	−	1.12357i
$340$		0			0
$341$	−29.9945	−	9.74581i	−1.62429	−	0.527765i
$342$		0			0
$343$	0.555739	−	0.764909i	0.0300071	−	0.0413012i
$344$		0			0
$345$	−2.90773	−	4.00215i	−0.156547	−	0.215468i
$346$		0			0
$347$	−7.10614	+	2.30893i	−0.381478	+	0.123950i	−0.493477	−	0.869759i	$-0.664274\pi$
$347$	−7.10614	+	2.30893i	−0.381478	+	0.123950i	0.112000	+	0.993708i	$0.464274\pi$
$348$		0			0
$349$	−9.07135	−	27.9187i	−0.485578	−	1.49446i	−0.831142	−	0.556061i	$-0.812312\pi$
$349$	−9.07135	−	27.9187i	−0.485578	−	1.49446i	0.345564	−	0.938395i	$-0.387688\pi$
$350$		0			0
$351$	9.35556	−	28.7934i	0.499363	−	1.53688i
$352$		0			0
$353$	4.03909	+	12.4311i	0.214979	+	0.661638i	0.999155	+	0.0410994i	$0.0130860\pi$
$353$	4.03909	+	12.4311i	0.214979	+	0.661638i	−0.784176	+	0.620539i	$0.786914\pi$
$354$		0			0
$355$		−	10.6170i		−	0.563493i
$356$		0			0
$357$	−0.190329	+	0.261966i	−0.0100733	+	0.0138647i
$358$		0			0
$359$	−5.70996	+	4.14853i	−0.301360	+	0.218951i	−0.728180	−	0.685385i	$-0.759634\pi$
$359$	−5.70996	+	4.14853i	−0.301360	+	0.218951i	0.426820	+	0.904337i	$0.359634\pi$
$360$		0			0
$361$	1.13204	−	0.822476i	0.0595811	−	0.0432882i
$362$		0			0
$363$	−4.80155	−	1.56012i	−0.252016	−	0.0818850i
$364$		0			0
$365$	−0.666759	−	0.484429i	−0.0348998	−	0.0253562i
$366$		0			0
$367$	10.4150	−	32.0542i	0.543661	−	1.67322i	−0.180492	−	0.983576i	$-0.557769\pi$
$367$	10.4150	−	32.0542i	0.543661	−	1.67322i	0.724153	−	0.689640i	$-0.242231\pi$
$368$		0			0
$369$	−4.75652	−	1.19779i	−0.247615	−	0.0623545i
$370$		0			0
$371$	0.193767	−	0.596353i	0.0100599	−	0.0309611i
$372$		0			0
$373$	−5.56073	−	4.04011i	−0.287924	−	0.209189i	0.434442	−	0.900700i	$-0.356945\pi$
$373$	−5.56073	−	4.04011i	−0.287924	−	0.209189i	−0.722366	+	0.691511i	$0.756945\pi$
$374$		0			0
$375$	1.84565	+	0.599687i	0.0953088	+	0.0309677i
$376$		0			0
$377$	18.0395	−	13.1065i	0.929081	−	0.675017i
$378$		0			0
$379$	3.39533	−	2.46685i	0.174406	−	0.126714i	−0.497157	−	0.867660i	$-0.665623\pi$
$379$	3.39533	−	2.46685i	0.174406	−	0.126714i	0.671564	+	0.740947i	$0.265623\pi$
$380$		0			0
$381$	21.1459	−	29.1048i	1.08334	−	1.49108i
$382$		0			0
$383$		−	6.69530i		−	0.342114i	−0.985261	−	0.171057i	$-0.945282\pi$
$383$		−	6.69530i		−	0.342114i	0.985261	−	0.171057i	$-0.0547182\pi$
$384$		0			0
$385$	−0.0769914	−	0.236955i	−0.00392385	−	0.0120764i
$386$		0			0
$387$	1.49066	−	4.58779i	0.0757747	−	0.233210i
$388$		0			0
$389$	2.70933	+	8.33846i	0.137369	+	0.422777i	0.995951	−	0.0898988i	$-0.0286544\pi$
$389$	2.70933	+	8.33846i	0.137369	+	0.422777i	−0.858582	+	0.512676i	$0.828654\pi$
$390$		0			0
$391$	−5.98795	+	1.94560i	−0.302824	+	0.0983933i
$392$		0			0
$393$	−16.2304	−	22.3392i	−0.818713	−	1.12686i
$394$		0			0
$395$	−0.761366	+	1.04793i	−0.0383085	+	0.0527271i
$396$		0			0
$397$	6.77472	+	2.20124i	0.340014	+	0.110477i	0.474047	−	0.880500i	$-0.342793\pi$
$397$	6.77472	+	2.20124i	0.340014	+	0.110477i	−0.134033	+	0.990977i	$0.542793\pi$
$398$		0			0
$399$	0.348044	+	0.479041i	0.0174240	+	0.0239821i
$400$		0			0
$401$	−15.6859			−0.783317			−0.391659	−	0.920111i	$-0.628099\pi$
$401$	−15.6859			−0.783317			−0.391659	+	0.920111i	$0.628099\pi$
$402$		0			0
$403$	−56.7958	+	18.4541i	−2.82920	+	0.919263i
$404$		0			0
$405$	8.66562	+	6.29594i	0.430598	+	0.312848i
$406$		0			0
$407$			38.4517i			1.90598i
$408$		0			0
$409$	−17.0981			−0.845448			−0.422724	−	0.906258i	$-0.638926\pi$
$409$	−17.0981			−0.845448			−0.422724	+	0.906258i	$0.638926\pi$
$410$		0			0
$411$	−34.3568			−1.69470
$412$		0			0
$413$			0.983035i			0.0483720i
$414$		0			0
$415$	0.169314	+	0.123014i	0.00831132	+	0.00603852i
$416$		0			0
$417$	2.19451	−	0.713040i	0.107466	−	0.0349177i
$418$		0			0
$419$	17.7479			0.867044			0.433522	−	0.901143i	$-0.357271\pi$
$419$	17.7479			0.867044			0.433522	+	0.901143i	$0.357271\pi$
$420$		0			0
$421$	−19.4854	−	26.8194i	−0.949662	−	1.30710i	−0.951678	−	0.307099i	$-0.900642\pi$
$421$	−19.4854	−	26.8194i	−0.949662	−	1.30710i	0.00201586	−	0.999998i	$-0.499358\pi$
$422$		0			0
$423$	4.21000	+	1.36791i	0.204697	+	0.0665102i
$424$		0			0
$425$	1.45177	−	1.99819i	0.0704211	−	0.0969263i
$426$		0			0
$427$	0.348853	+	0.480156i	0.0168822	+	0.0232364i
$428$		0			0
$429$	−47.5348	+	15.4450i	−2.29500	+	0.745691i
$430$		0			0
$431$	−0.910426	−	2.80200i	−0.0438537	−	0.134968i	0.926732	−	0.375722i	$-0.122605\pi$
$431$	−0.910426	−	2.80200i	−0.0438537	−	0.134968i	−0.970586	+	0.240754i	$0.922605\pi$
$432$		0			0
$433$	0.244000	−	0.750954i	0.0117259	−	0.0360885i	−0.945022	−	0.327006i	$-0.893960\pi$
$433$	0.244000	−	0.750954i	0.0117259	−	0.0360885i	0.956748	+	0.290917i	$0.0939604\pi$
$434$		0			0
$435$	1.91479	+	5.89313i	0.0918074	+	0.282554i
$436$		0			0
$437$			11.5133i			0.550757i
$438$		0			0
$439$	0.326113	−	0.448857i	0.0155645	−	0.0214228i	−0.801164	−	0.598445i	$-0.795785\pi$
$439$	0.326113	−	0.448857i	0.0155645	−	0.0214228i	0.816728	+	0.577022i	$0.195785\pi$
$440$		0			0
$441$	4.33532	−	3.14980i	0.206444	−	0.149990i
$442$		0			0
$443$	0.985864	−	0.716272i	0.0468398	−	0.0340311i	−0.564119	−	0.825693i	$-0.690784\pi$
$443$	0.985864	−	0.716272i	0.0468398	−	0.0340311i	0.610959	+	0.791662i	$0.290784\pi$
$444$		0			0
$445$	7.98903	+	2.59579i	0.378716	+	0.123052i
$446$		0			0
$447$	−4.39962	−	3.19651i	−0.208095	−	0.151190i
$448$		0			0
$449$	−0.324897	+	0.999929i	−0.0153328	+	0.0471896i	−0.958430	−	0.285327i	$-0.907898\pi$
$449$	−0.324897	+	0.999929i	−0.0153328	+	0.0471896i	0.943097	+	0.332517i	$0.107898\pi$
$450$		0			0
$451$	−8.79493	−	21.9160i	−0.414137	−	1.03199i
$452$		0			0
$453$	1.58160	−	4.86766i	0.0743100	−	0.228703i
$454$		0			0
$455$	−0.381674	−	0.277302i	−0.0178931	−	0.0130001i
$456$		0			0
$457$	−35.2539	−	11.4547i	−1.64911	−	0.535828i	−0.670563	−	0.741853i	$-0.733947\pi$
$457$	−35.2539	−	11.4547i	−1.64911	−	0.535828i	−0.978547	+	0.206024i	$0.933947\pi$
$458$		0			0
$459$	8.66273	−	6.29384i	0.404341	−	0.293771i
$460$		0			0
$461$	11.6544	−	8.46739i	0.542798	−	0.394366i	−0.282325	−	0.959319i	$-0.591106\pi$
$461$	11.6544	−	8.46739i	0.542798	−	0.394366i	0.825123	+	0.564953i	$0.191106\pi$
$462$		0			0
$463$	11.5198	−	15.8557i	0.535373	−	0.736877i	−0.452565	−	0.891732i	$-0.649491\pi$
$463$	11.5198	−	15.8557i	0.535373	−	0.736877i	0.987937	+	0.154854i	$0.0494908\pi$
$464$		0			0
$465$		−	16.5952i		−	0.769586i
$466$		0			0
$467$	9.07143	+	27.9190i	0.419776	+	1.29194i	0.907909	+	0.419168i	$0.137678\pi$
$467$	9.07143	+	27.9190i	0.419776	+	1.29194i	−0.488133	+	0.872769i	$0.662322\pi$
$468$		0			0
$469$	−0.289882	+	0.892164i	−0.0133855	+	0.0411963i
$470$		0			0
$471$	−5.13959	−	15.8180i	−0.236820	−	0.728856i
$472$		0			0
$473$	22.0876	−	7.17670i	1.01559	−	0.329985i
$474$		0			0
$475$	−2.65477	−	3.65397i	−0.121809	−	0.167656i
$476$		0			0
$477$	4.17926	−	5.75225i	0.191355	−	0.263378i
$478$		0			0
$479$	31.6373	+	10.2796i	1.44554	+	0.469686i	0.923621	−	0.383306i	$-0.125215\pi$
$479$	31.6373	+	10.2796i	1.44554	+	0.469686i	0.521923	+	0.852992i	$0.325215\pi$
$480$		0			0
$481$	42.7965	+	58.9044i	1.95135	+	2.68581i
$482$		0			0
$483$	−0.334196			−0.0152064
$484$		0			0
$485$	−5.13297	+	1.66780i	−0.233076	+	0.0757311i
$486$		0			0
$487$	−2.89179	−	2.10101i	−0.131040	−	0.0952059i	0.520335	−	0.853962i	$-0.325807\pi$
$487$	−2.89179	−	2.10101i	−0.131040	−	0.0952059i	−0.651374	+	0.758757i	$0.725807\pi$
$488$		0			0
$489$			0.938129i			0.0424236i
$490$		0			0
$491$	37.8790			1.70945			0.854727	−	0.519077i	$-0.173724\pi$
$491$	37.8790			1.70945			0.854727	+	0.519077i	$0.173724\pi$
$492$		0			0
$493$	7.88635			0.355183
$494$		0			0
$495$		−	2.82516i		−	0.126982i
$496$		0			0
$497$	−0.580265	−	0.421587i	−0.0260284	−	0.0189108i
$498$		0			0
$499$	5.77057	−	1.87497i	0.258326	−	0.0839352i	−0.176991	−	0.984212i	$-0.556636\pi$
$499$	5.77057	−	1.87497i	0.258326	−	0.0839352i	0.435317	+	0.900277i	$0.356636\pi$
$500$		0			0
$501$	−36.9062			−1.64885
$502$		0			0
$503$	−13.9476	−	19.1972i	−0.621893	−	0.855963i	0.375596	−	0.926784i	$-0.377438\pi$
$503$	−13.9476	−	19.1972i	−0.621893	−	0.855963i	−0.997489	+	0.0708208i	$0.977438\pi$
$504$		0			0
$505$	−10.6923	−	3.47413i	−0.475799	−	0.154597i
$506$		0			0
$507$	−40.7999	+	56.1563i	−1.81199	+	2.49399i
$508$		0			0
$509$	4.53891	+	6.24728i	0.201184	+	0.276906i	0.897674	−	0.440661i	$-0.145256\pi$
$509$	4.53891	+	6.24728i	0.201184	+	0.276906i	−0.696490	+	0.717567i	$0.745256\pi$
$510$		0			0
$511$	−0.0529521	+	0.0172052i	−0.00234246	+	0.000761113i
$512$		0			0
$513$	−6.05074	−	18.6223i	−0.267147	−	0.822193i
$514$		0			0
$515$	−1.40260	+	4.31676i	−0.0618059	+	0.190219i
$516$		0			0
$517$	6.58572	+	20.2688i	0.289640	+	0.891420i
$518$		0			0
$519$		−	26.4166i		−	1.15956i
$520$		0			0
$521$	13.4398	−	18.4983i	0.588808	−	0.810425i	−0.405819	−	0.913954i	$-0.633014\pi$
$521$	13.4398	−	18.4983i	0.588808	−	0.810425i	0.994626	+	0.103529i	$0.0330135\pi$
$522$		0			0
$523$	0.0282957	−	0.0205580i	0.00123728	−	0.000898939i	−0.587166	−	0.809466i	$-0.699757\pi$
$523$	0.0282957	−	0.0205580i	0.00123728	−	0.000898939i	0.588404	+	0.808567i	$0.299757\pi$
$524$		0			0
$525$	0.106063	−	0.0770596i	0.00462899	−	0.00336316i
$526$		0			0
$527$	−20.0875	−	6.52683i	−0.875026	−	0.284313i
$528$		0			0
$529$	13.3503	+	9.69958i	0.580449	+	0.421721i
$530$		0			0
$531$	−3.44456	+	10.6013i	−0.149481	+	0.460056i
$532$		0			0
$533$	−37.8655	−	23.7846i	−1.64013	−	1.03023i
$534$		0			0
$535$	4.70386	−	14.4770i	0.203365	−	0.625895i
$536$		0			0
$537$	12.0313	+	8.74128i	0.519190	+	0.377214i
$538$		0			0
$539$	24.5367	+	7.97244i	1.05687	+	0.343397i
$540$		0			0
$541$	4.72581	−	3.43350i	0.203179	−	0.147618i	−0.481543	−	0.876422i	$-0.659924\pi$
$541$	4.72581	−	3.43350i	0.203179	−	0.147618i	0.684722	+	0.728804i	$0.259924\pi$
$542$		0			0
$543$	36.5046	−	26.5222i	1.56656	−	1.13817i
$544$		0			0
$545$	7.94215	−	10.9314i	0.340204	−	0.468251i
$546$		0			0
$547$		−	19.7029i		−	0.842437i	−0.906959	−	0.421218i	$-0.861603\pi$
$547$		−	19.7029i		−	0.842437i	0.906959	−	0.421218i	$-0.138397\pi$
$548$		0			0
$549$	2.07965	+	6.40050i	0.0887572	+	0.273167i
$550$		0			0
$551$	4.45643	−	13.7155i	0.189850	−	0.584300i
$552$		0			0
$553$	0.0270410	+	0.0832236i	0.00114990	+	0.00353903i
$554$		0			0
$555$	−19.2429	+	6.25239i	−0.816814	+	0.265399i
$556$		0			0
$557$	−5.01166	−	6.89796i	−0.212351	−	0.292276i	0.689533	−	0.724254i	$-0.257816\pi$
$557$	−5.01166	−	6.89796i	−0.212351	−	0.292276i	−0.901884	+	0.431978i	$0.857816\pi$
$558$		0			0
$559$	25.8485	−	35.5774i	1.09328	−	1.50477i
$560$		0			0
$561$	−16.8121	−	5.46257i	−0.709806	−	0.230630i
$562$		0			0
$563$	1.52512	+	2.09915i	0.0642762	+	0.0884686i	0.839945	−	0.542672i	$-0.182587\pi$
$563$	1.52512	+	2.09915i	0.0642762	+	0.0884686i	−0.775669	+	0.631140i	$0.782587\pi$
$564$		0			0
$565$	13.1766			0.554342
$566$		0			0
$567$	0.688199	−	0.223609i	0.0289017	−	0.00939072i
$568$		0			0
$569$	−19.1514	−	13.9143i	−0.802871	−	0.583320i	0.108884	−	0.994054i	$-0.465272\pi$
$569$	−19.1514	−	13.9143i	−0.802871	−	0.583320i	−0.911755	+	0.410735i	$0.865272\pi$
$570$		0			0
$571$			30.8979i			1.29304i	0.762898	+	0.646519i	$0.223776\pi$
$571$			30.8979i			1.29304i	−0.762898	+	0.646519i	$0.776224\pi$
$572$		0			0
$573$	31.2630			1.30603
$574$		0			0
$575$	2.54914			0.106306
$576$		0			0
$577$		−	41.8453i		−	1.74204i	−0.491245	−	0.871021i	$-0.663458\pi$
$577$		−	41.8453i		−	1.74204i	0.491245	−	0.871021i	$-0.336542\pi$
$578$		0			0
$579$	−39.7442	−	28.8759i	−1.65171	−	1.20004i
$580$		0			0
$581$	0.0134465	−	0.00436902i	0.000557854	−	0.000181258i
$582$		0			0
$583$	34.2315			1.41772
$584$		0			0
$585$	−3.14439	−	4.32788i	−0.130005	−	0.178936i
$586$		0			0
$587$	17.9302	+	5.82588i	0.740060	+	0.240460i	0.654698	−	0.755890i	$-0.272796\pi$
$587$	17.9302	+	5.82588i	0.740060	+	0.240460i	0.0853611	+	0.996350i	$0.472796\pi$
$588$		0			0
$589$	−22.7022	+	31.2469i	−0.935427	+	1.28750i
$590$		0			0
$591$	25.5291	+	35.1377i	1.05013	+	1.44537i
$592$		0			0
$593$	−27.7752	+	9.02472i	−1.14059	+	0.370601i	−0.817592	−	0.575798i	$-0.804691\pi$
$593$	−27.7752	+	9.02472i	−1.14059	+	0.370601i	−0.323000	+	0.946399i	$0.604691\pi$
$594$		0			0
$595$	−0.0515616	−	0.158690i	−0.00211382	−	0.00650567i
$596$		0			0
$597$	1.19974	−	3.69242i	0.0491021	−	0.151121i
$598$		0			0
$599$	8.22746	+	25.3215i	0.336165	+	1.03461i	0.966145	+	0.257998i	$0.0830629\pi$
$599$	8.22746	+	25.3215i	0.336165	+	1.03461i	−0.629980	+	0.776611i	$0.716937\pi$
$600$		0			0
$601$			9.76291i			0.398237i	0.979975	+	0.199119i	$0.0638079\pi$
$601$			9.76291i			0.398237i	−0.979975	+	0.199119i	$0.936192\pi$
$602$		0			0
$603$	−6.25231	+	8.60556i	−0.254614	+	0.350446i
$604$		0			0
$605$	2.10470	−	1.52916i	0.0855683	−	0.0621690i
$606$		0			0
$607$	9.43044	−	6.85162i	0.382770	−	0.278098i	−0.379717	−	0.925103i	$-0.623978\pi$
$607$	9.43044	−	6.85162i	0.382770	−	0.278098i	0.762486	+	0.647004i	$0.223978\pi$
$608$		0			0
$609$	0.398118	+	0.129356i	0.0161326	+	0.00524179i
$610$		0			0
$611$	32.6478	+	23.7200i	1.32079	+	0.959608i
$612$		0			0
$613$	1.28802	−	3.96413i	0.0520228	−	0.160110i	−0.921670	−	0.387975i	$-0.873175\pi$
$613$	1.28802	−	3.96413i	0.0520228	−	0.160110i	0.973693	+	0.227865i	$0.0731746\pi$
$614$		0			0
$615$	9.53763	−	7.96498i	0.384595	−	0.321179i
$616$		0			0
$617$	10.8596	−	33.4224i	0.437191	−	1.34553i	−0.453634	−	0.891188i	$-0.649873\pi$
$617$	10.8596	−	33.4224i	0.437191	−	1.34553i	0.890825	−	0.454346i	$-0.150127\pi$
$618$		0			0
$619$	−22.6502	−	16.4563i	−0.910387	−	0.661435i	0.0307259	−	0.999528i	$-0.490218\pi$
$619$	−22.6502	−	16.4563i	−0.910387	−	0.661435i	−0.941113	+	0.338093i	$0.890218\pi$
$620$		0			0
$621$	10.5104	+	3.41503i	0.421766	+	0.137040i
$622$		0			0
$623$	0.459104	−	0.333559i	0.0183936	−	0.0133637i
$624$		0			0
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$		0			0
$627$	−19.0004	+	26.1518i	−0.758803	+	1.04440i
$628$		0			0
$629$			25.7513i			1.02677i
$630$		0			0
$631$	12.7296	+	39.1777i	0.506758	+	1.55964i	0.797795	+	0.602929i	$0.206000\pi$
$631$	12.7296	+	39.1777i	0.506758	+	1.55964i	−0.291037	+	0.956712i	$0.594000\pi$
$632$		0			0
$633$	2.33950	−	7.20023i	0.0929866	−	0.286183i
$634$		0			0
$635$	5.72858	+	17.6308i	0.227332	+	0.699655i
$636$		0			0
$637$	46.4611	−	15.0961i	1.84086	−	0.598131i
$638$		0			0
$639$	−4.78047	−	6.57975i	−0.189112	−	0.260291i
$640$		0			0
$641$	9.11952	−	12.5519i	0.360200	−	0.495772i	−0.590005	−	0.807400i	$-0.700874\pi$
$641$	9.11952	−	12.5519i	0.360200	−	0.495772i	0.950204	+	0.311628i	$0.100874\pi$
$642$		0			0
$643$	−27.0140	−	8.77737i	−1.06533	−	0.346146i	−0.276661	−	0.960968i	$-0.589228\pi$
$643$	−27.0140	−	8.77737i	−1.06533	−	0.346146i	−0.788666	+	0.614822i	$0.789228\pi$
$644$		0			0
$645$	7.18305	+	9.88662i	0.282832	+	0.389285i
$646$		0			0
$647$	10.0176			0.393831			0.196916	−	0.980420i	$-0.436908\pi$
$647$	10.0176			0.393831			0.196916	+	0.980420i	$0.436908\pi$
$648$		0			0
$649$	−51.0392	+	16.5836i	−2.00346	+	0.650964i
$650$		0			0
$651$	−0.906999	−	0.658974i	−0.0355481	−	0.0258272i
$652$		0			0
$653$		−	13.3533i		−	0.522555i	−0.965264	−	0.261277i	$-0.915856\pi$
$653$		−	13.3533i		−	0.522555i	0.965264	−	0.261277i	$-0.0841437\pi$
$654$		0			0
$655$	14.2288			0.555964
$656$		0			0
$657$	−0.631336			−0.0246307
$658$		0			0
$659$			26.4985i			1.03223i	0.856518	+	0.516117i	$0.172623\pi$
$659$			26.4985i			1.03223i	−0.856518	+	0.516117i	$0.827377\pi$
$660$		0			0
$661$	9.81156	+	7.12851i	0.381625	+	0.277267i	0.762015	−	0.647559i	$-0.224210\pi$
$661$	9.81156	+	7.12851i	0.381625	+	0.277267i	−0.380390	+	0.924826i	$0.624210\pi$
$662$		0			0
$663$	−31.8343	+	10.3436i	−1.23634	+	0.401712i
$664$		0			0
$665$	−0.305122			−0.0118321
$666$		0			0
$667$	4.78420	+	6.58489i	0.185245	+	0.254968i
$668$		0			0
$669$	21.3455	+	6.93557i	0.825264	+	0.268145i
$670$		0			0
$671$	−19.0446	+	26.2126i	−0.735208	+	1.01193i
$672$		0			0
$673$	−20.4676	−	28.1713i	−0.788969	−	1.08592i	−0.994236	−	0.107216i	$-0.965806\pi$
$673$	−20.4676	−	28.1713i	−0.788969	−	1.08592i	0.205267	−	0.978706i	$-0.434194\pi$
$674$		0			0
$675$	−4.12311	+	1.33968i	−0.158699	+	0.0515643i
$676$		0			0
$677$	−5.69465	−	17.5263i	−0.218863	−	0.673591i	−0.998857	−	0.0478038i	$-0.984778\pi$
$677$	−5.69465	−	17.5263i	−0.218863	−	0.673591i	0.779994	−	0.625787i	$-0.215222\pi$
$678$		0			0
$679$	−0.112671	+	0.346765i	−0.00432390	+	0.0133076i
$680$		0			0
$681$	8.36149	+	25.7340i	0.320413	+	0.986130i
$682$		0			0
$683$			16.8516i			0.644808i	0.946602	+	0.322404i	$0.104491\pi$
$683$			16.8516i			0.644808i	−0.946602	+	0.322404i	$0.895509\pi$
$684$		0			0
$685$	10.4061	−	14.3228i	0.397598	−	0.547246i
$686$		0			0
$687$	−23.9152	+	17.3754i	−0.912421	+	0.662912i
$688$		0			0
$689$	52.4394	−	38.0995i	1.99778	−	1.45147i
$690$		0			0
$691$	5.47247	+	1.77811i	0.208183	+	0.0676426i	0.411252	−	0.911522i	$-0.365092\pi$
$691$	5.47247	+	1.77811i	0.208183	+	0.0676426i	−0.203069	+	0.979164i	$0.565092\pi$
$692$		0			0
$693$	−0.154407	−	0.112183i	−0.00586543	−	0.00426149i
$694$		0			0
$695$	−0.367427	+	1.13083i	−0.0139373	+	0.0428947i
$696$		0			0
$697$	−5.89002	−	14.6773i	−0.223100	−	0.555943i
$698$		0			0
$699$	−6.22132	+	19.1472i	−0.235312	+	0.724215i
$700$		0			0
$701$	15.3673	+	11.1650i	0.580417	+	0.421697i	0.838874	−	0.544325i	$-0.183214\pi$
$701$	15.3673	+	11.1650i	0.580417	+	0.421697i	−0.258458	+	0.966023i	$0.583214\pi$
$702$		0			0
$703$	44.7852	+	14.5516i	1.68911	+	0.548824i
$704$		0			0
$705$	−9.07249	+	6.59155i	−0.341690	+	0.248252i
$706$		0			0
$707$	−0.614450	+	0.446424i	−0.0231088	+	0.0167895i
$708$		0			0
$709$	−7.80384	+	10.7411i	−0.293079	+	0.403389i	−0.930011	−	0.367531i	$-0.880203\pi$
$709$	−7.80384	+	10.7411i	−0.293079	+	0.403389i	0.636932	+	0.770920i	$0.280203\pi$
$710$		0			0
$711$			0.992255i			0.0372125i
$712$		0			0
$713$	−6.73623	−	20.7320i	−0.252274	−	0.776419i
$714$		0			0
$715$	7.95876	−	24.4945i	0.297641	−	0.916044i
$716$		0			0
$717$	3.00038	+	9.23421i	0.112051	+	0.344858i
$718$		0			0
$719$	−5.85943	+	1.90384i	−0.218520	+	0.0710014i	−0.416231	−	0.909259i	$-0.636649\pi$
$719$	−5.85943	+	1.90384i	−0.218520	+	0.0710014i	0.197711	+	0.980260i	$0.436649\pi$
$720$		0			0
$721$	0.180234	+	0.248070i	0.00671225	+	0.00923862i
$722$		0			0
$723$	2.89780	−	3.98848i	0.107770	−	0.148333i
$724$		0			0
$725$	−3.03671	−	0.986688i	−0.112781	−	0.0366447i
$726$		0			0
$727$	−17.1762	−	23.6410i	−0.637028	−	0.876794i	0.361424	−	0.932401i	$-0.382291\pi$
$727$	−17.1762	−	23.6410i	−0.637028	−	0.876794i	−0.998453	+	0.0556071i	$0.982291\pi$
$728$		0			0
$729$	−17.0343			−0.630901
$730$		0			0
$731$	14.7922	−	4.80628i	0.547110	−	0.177767i
$732$		0			0
$733$	6.09089	+	4.42529i	0.224972	+	0.163452i	0.694562	−	0.719433i	$-0.255598\pi$
$733$	6.09089	+	4.42529i	0.224972	+	0.163452i	−0.469590	+	0.882885i	$0.655598\pi$
$734$		0			0
$735$			13.5755i			0.500741i
$736$		0			0
$737$	−51.2114			−1.88640
$738$		0			0
$739$	37.6564			1.38521			0.692607	−	0.721315i	$-0.256462\pi$
$739$	37.6564			1.38521			0.692607	+	0.721315i	$0.256462\pi$
$740$		0			0
$741$			61.2094i			2.24859i
$742$		0			0
$743$	26.7577	+	19.4406i	0.981645	+	0.713207i	0.958076	−	0.286515i	$-0.0924968\pi$
$743$	26.7577	+	19.4406i	0.981645	+	0.713207i	0.0235697	+	0.999722i	$0.492497\pi$
$744$		0			0
$745$	2.66515	−	0.865960i	0.0976436	−	0.0317263i
$746$		0			0
$747$	0.160319			0.00586577
$748$		0			0
$749$	−0.604444	−	0.831946i	−0.0220859	−	0.0303987i
$750$		0			0
$751$	−4.66882	−	1.51699i	−0.170368	−	0.0553559i	0.222591	−	0.974912i	$-0.428549\pi$
$751$	−4.66882	−	1.51699i	−0.170368	−	0.0553559i	−0.392959	+	0.919556i	$0.628549\pi$
$752$		0			0
$753$	23.3951	−	32.2006i	0.852564	−	1.17345i
$754$		0			0
$755$	1.55021	+	2.13368i	0.0564179	+	0.0776526i
$756$		0			0
$757$	−29.3213	+	9.52708i	−1.06570	+	0.346268i	−0.788813	−	0.614634i	$-0.789304\pi$
$757$	−29.3213	+	9.52708i	−1.06570	+	0.346268i	−0.276890	+	0.960902i	$0.589304\pi$
$758$		0			0
$759$	−5.63783	−	17.3515i	−0.204640	−	0.629818i
$760$		0			0
$761$	−13.7918	+	42.4469i	−0.499953	+	1.53870i	0.309139	+	0.951017i	$0.399959\pi$
$761$	−13.7918	+	42.4469i	−0.499953	+	1.53870i	−0.809092	+	0.587682i	$0.800041\pi$
$762$		0			0
$763$	−0.282077	−	0.868144i	−0.0102119	−	0.0314289i
$764$		0			0
$765$		−	1.89203i		−	0.0684064i
$766$		0			0
$767$	−59.7297	+	82.2109i	−2.15672	+	2.96846i
$768$		0			0
$769$	−9.79153	+	7.11396i	−0.353092	+	0.256536i	−0.750165	−	0.661251i	$-0.770026\pi$
$769$	−9.79153	+	7.11396i	−0.353092	+	0.256536i	0.397073	+	0.917787i	$0.370026\pi$
$770$		0			0
$771$	23.8621	−	17.3368i	0.859372	−	0.624370i
$772$		0			0
$773$	−1.44387	−	0.469143i	−0.0519325	−	0.0168739i	0.282936	−	0.959139i	$-0.408692\pi$
$773$	−1.44387	−	0.469143i	−0.0519325	−	0.0168739i	−0.334868	+	0.942265i	$0.608692\pi$
$774$		0			0
$775$	6.91829	+	5.02643i	0.248512	+	0.180555i
$776$		0			0
$777$	−0.422388	+	1.29998i	−0.0151531	+	0.0466364i
$778$		0			0
$779$	−28.8543	+	1.94970i	−1.03381	+	0.0698553i
$780$		0			0
$781$	12.0998	−	37.2395i	0.432966	−	1.33253i
$782$		0			0
$783$	−11.1989	−	8.13645i	−0.400214	−	0.290773i
$784$		0			0
$785$	8.15099	+	2.64842i	0.290921	+	0.0945260i
$786$		0			0
$787$	−27.8693	+	20.2482i	−0.993434	+	0.721772i	−0.960670	−	0.277691i	$-0.910431\pi$
$787$	−27.8693	+	20.2482i	−0.993434	+	0.721772i	−0.0327635	+	0.999463i	$0.510431\pi$
$788$		0			0
$789$	3.70112	−	2.68902i	0.131763	−	0.0957317i
$790$		0			0
$791$	0.523223	−	0.720154i	0.0186037	−	0.0256057i
$792$		0			0
$793$			61.3518i			2.17867i
$794$		0			0
$795$	5.56616	+	17.1309i	0.197411	+	0.607570i
$796$		0			0
$797$	8.92632	−	27.4724i	0.316186	−	0.973122i	−0.659077	−	0.752076i	$-0.729053\pi$
$797$	8.92632	−	27.4724i	0.316186	−	0.973122i	0.975263	−	0.221046i	$-0.0709472\pi$
$798$		0			0
$799$	4.41050	+	13.5741i	0.156032	+	0.480218i
$800$		0			0
$801$	6.11988	−	1.98847i	0.216235	−	0.0702591i
$802$		0			0
$803$	−1.78659	−	2.45903i	−0.0630473	−	0.0867772i
$804$		0			0
$805$	0.101223	−	0.139321i	0.00356763	−	0.00491042i
$806$		0			0
$807$	37.7839	+	12.2767i	1.33005	+	0.432161i
$808$		0			0
$809$	−9.39782	−	12.9350i	−0.330410	−	0.454770i	0.611200	−	0.791476i	$-0.290687\pi$
$809$	−9.39782	−	12.9350i	−0.330410	−	0.454770i	−0.941610	+	0.336706i	$0.890687\pi$
$810$		0			0
$811$	−15.4721			−0.543300			−0.271650	−	0.962396i	$-0.587569\pi$
$811$	−15.4721			−0.543300			−0.271650	+	0.962396i	$0.587569\pi$
$812$		0			0
$813$	46.8664	−	15.2278i	1.64368	−	0.534063i
$814$		0			0
$815$	−0.391091	−	0.284144i	−0.0136993	−	0.00995314i
$816$		0			0
$817$		−	28.4417i		−	0.995049i
$818$		0			0
$819$	−0.361396			−0.0126282
$820$		0			0
$821$	2.91335			0.101677			0.0508384	−	0.998707i	$-0.483811\pi$
$821$	2.91335			0.101677			0.0508384	+	0.998707i	$0.483811\pi$
$822$		0			0
$823$		−	8.75688i		−	0.305246i	−0.988285	−	0.152623i	$-0.951228\pi$
$823$		−	8.75688i		−	0.305246i	0.988285	−	0.152623i	$-0.0487720\pi$
$824$		0			0
$825$	5.79021	+	4.20683i	0.201589	+	0.146463i
$826$		0			0
$827$	−31.9069	+	10.3672i	−1.10951	+	0.360502i	−0.805755	−	0.592249i	$-0.798240\pi$
$827$	−31.9069	+	10.3672i	−1.10951	+	0.360502i	−0.303755	+	0.952750i	$0.598240\pi$
$828$		0			0
$829$	2.61019			0.0906557			0.0453279	−	0.998972i	$-0.485567\pi$
$829$	2.61019			0.0906557			0.0453279	+	0.998972i	$0.485567\pi$
$830$		0			0
$831$	−1.91713	−	2.63870i	−0.0665043	−	0.0915354i
$832$		0			0
$833$	16.4323	+	5.33919i	0.569347	+	0.184992i
$834$		0			0
$835$	11.1783	−	15.3856i	0.386841	−	0.532441i
$836$		0			0
$837$	21.7911	+	29.9928i	0.753209	+	1.03670i
$838$		0			0
$839$	43.7743	−	14.2231i	1.51126	−	0.491037i	0.567979	−	0.823043i	$-0.307726\pi$
$839$	43.7743	−	14.2231i	1.51126	−	0.491037i	0.943277	+	0.332006i	$0.107726\pi$
$840$		0			0
$841$	5.81101	+	17.8844i	0.200380	+	0.616705i
$842$		0			0
$843$	9.82302	−	30.2321i	0.338323	−	1.04125i
$844$		0			0
$845$	−11.0530	−	34.0177i	−0.380235	−	1.17024i
$846$		0			0
$847$		−	0.175751i		−	0.00603889i
$848$		0			0
$849$	−21.2952	+	29.3104i	−0.730850	+	1.00593i
$850$		0			0
$851$	−21.5017	+	15.6219i	−0.737067	+	0.535511i
$852$		0			0
$853$	−39.5271	+	28.7181i	−1.35338	+	0.983290i	−0.354548	+	0.935038i	$0.615365\pi$
$853$	−39.5271	+	28.7181i	−1.35338	+	0.983290i	−0.998835	+	0.0482522i	$0.984635\pi$
$854$		0			0
$855$	−3.29051	−	1.06915i	−0.112533	−	0.0365642i
$856$		0			0
$857$	31.4340	+	22.8382i	1.07377	+	0.780137i	0.976585	−	0.215130i	$-0.0690175\pi$
$857$	31.4340	+	22.8382i	1.07377	+	0.780137i	0.0971806	+	0.995267i	$0.469018\pi$
$858$		0			0
$859$	−5.24341	+	16.1376i	−0.178903	+	0.550606i	−0.999790	−	0.0204838i	$-0.993479\pi$
$859$	−5.24341	+	16.1376i	−0.178903	+	0.550606i	0.820887	+	0.571090i	$0.193479\pi$
$860$		0			0
$861$	−0.0565937	−	0.837550i	−0.00192871	−	0.0285436i
$862$		0			0
$863$	8.38682	−	25.8120i	0.285491	−	0.878650i	−0.700761	−	0.713397i	$-0.747156\pi$
$863$	8.38682	−	25.8120i	0.285491	−	0.878650i	0.986251	−	0.165253i	$-0.0528441\pi$
$864$		0			0
$865$	11.0127	+	8.00117i	0.374442	+	0.272048i
$866$		0			0
$867$	20.1168	+	6.53636i	0.683204	+	0.221986i
$868$		0			0
$869$	−3.86479	+	2.80794i	−0.131104	+	0.0952528i
$870$		0			0
$871$	−78.4511	+	56.9981i	−2.65821	+	1.93131i
$872$		0			0
$873$	−2.43013	+	3.34479i	−0.0822476	+	0.113204i
$874$		0			0
$875$			0.0675563i			0.00228382i
$876$		0			0
$877$	14.2285	+	43.7909i	0.480463	+	1.47871i	0.838446	+	0.544985i	$0.183465\pi$
$877$	14.2285	+	43.7909i	0.480463	+	1.47871i	−0.357983	+	0.933728i	$0.616535\pi$
$878$		0			0
$879$	−3.90192	+	12.0089i	−0.131608	+	0.405049i
$880$		0			0
$881$	−8.40334	−	25.8628i	−0.283116	−	0.871341i	−0.986957	−	0.160984i	$-0.948533\pi$
$881$	−8.40334	−	25.8628i	−0.283116	−	0.871341i	0.703841	−	0.710357i	$-0.251467\pi$
$882$		0			0
$883$	2.65356	−	0.862193i	0.0892993	−	0.0290151i	−0.264027	−	0.964515i	$-0.585051\pi$
$883$	2.65356	−	0.862193i	0.0892993	−	0.0290151i	0.353326	+	0.935500i	$0.385051\pi$
$884$		0			0
$885$	−16.5983	−	22.8456i	−0.557946	−	0.767947i
$886$		0			0
$887$	−11.8487	+	16.3083i	−0.397839	+	0.547578i	−0.960200	−	0.279314i	$-0.909893\pi$
$887$	−11.8487	+	16.3083i	−0.397839	+	0.547578i	0.562361	+	0.826892i	$0.309893\pi$
$888$		0			0
$889$	1.19107	+	0.387002i	0.0399472	+	0.0129796i
$890$		0			0
$891$	23.2196	+	31.9591i	0.777886	+	1.07067i
$892$		0			0
$893$	26.0996			0.873391
$894$		0			0
$895$	−7.28820	+	2.36808i	−0.243618	+	0.0791562i
$896$		0			0
$897$	−27.9487	−	20.3059i	−0.933180	−	0.677995i
$898$		0			0
$899$			27.3048i			0.910666i
$900$		0			0
$901$	22.9250			0.763744
$902$		0			0
$903$	0.825574			0.0274734
$904$		0			0
$905$			23.2513i			0.772901i
$906$		0			0
$907$	36.9633	+	26.8554i	1.22735	+	0.891720i	0.996689	−	0.0813143i	$-0.0259118\pi$
$907$	36.9633	+	26.8554i	1.22735	+	0.891720i	0.230659	+	0.973035i	$0.425912\pi$
$908$		0			0
$909$	−8.19065	+	2.66130i	−0.271667	+	0.0882699i
$910$		0			0
$911$	−48.1984			−1.59688			−0.798441	−	0.602073i	$-0.794342\pi$
$911$	−48.1984			−1.59688			−0.798441	+	0.602073i	$0.794342\pi$
$912$		0			0
$913$	0.453679	+	0.624436i	0.0150146	+	0.0206658i
$914$		0			0
$915$	−16.2146	−	5.26845i	−0.536039	−	0.174170i
$916$		0			0
$917$	0.565004	−	0.777662i	0.0186581	−	0.0256806i
$918$		0			0
$919$	−14.0615	−	19.3540i	−0.463845	−	0.638428i	0.511456	−	0.859310i	$-0.329107\pi$
$919$	−14.0615	−	19.3540i	−0.463845	−	0.638428i	−0.975301	+	0.220882i	$0.929107\pi$
$920$		0			0
$921$	16.8957	−	5.48974i	0.556731	−	0.180893i
$922$		0			0
$923$	−22.9115	−	70.5144i	−0.754142	−	2.32101i
$924$		0			0
$925$	3.22184	−	9.91579i	0.105933	−	0.326029i
$926$		0			0
$927$	1.07444	+	3.30679i	0.0352893	+	0.108609i
$928$		0			0
$929$		−	39.0200i		−	1.28021i	−0.768289	−	0.640103i	$-0.778892\pi$
$929$		−	39.0200i		−	1.28021i	0.768289	−	0.640103i	$-0.221108\pi$
$930$		0			0
$931$	18.5712	−	25.5611i	0.608648	−	0.837732i
$932$		0			0
$933$	−39.9079	+	28.9948i	−1.30652	+	0.949246i
$934$		0			0
$935$	7.36937	−	5.35416i	0.241004	−	0.175100i
$936$		0			0
$937$	29.8908	+	9.71211i	0.976490	+	0.317281i	0.753433	−	0.657524i	$-0.228396\pi$
$937$	29.8908	+	9.71211i	0.976490	+	0.317281i	0.223057	+	0.974805i	$0.428396\pi$
$938$		0			0
$939$	21.0904	+	15.3231i	0.688259	+	0.500050i
$940$		0			0
$941$	−4.20289	+	12.9352i	−0.137010	+	0.421674i	−0.995897	−	0.0904910i	$-0.971156\pi$
$941$	−4.20289	+	12.9352i	−0.137010	+	0.421674i	0.858887	+	0.512165i	$0.171156\pi$
$942$		0			0
$943$	8.68201	−	13.8219i	0.282725	−	0.450103i
$944$		0			0
$945$	−0.0905038	+	0.278542i	−0.00294409	+	0.00906097i
$946$		0			0
$947$	−21.3393	−	15.5039i	−0.693433	−	0.503809i	0.184354	−	0.982860i	$-0.440981\pi$
$947$	−21.3393	−	15.5039i	−0.693433	−	0.503809i	−0.877787	+	0.479051i	$0.840981\pi$
$948$		0			0
$949$	−5.47377	−	1.77854i	−0.177686	−	0.0577337i
$950$		0			0
$951$	1.73885	−	1.26335i	0.0563859	−	0.0409668i
$952$		0			0
$953$	42.6504	−	30.9873i	1.38158	−	1.00378i	0.384851	−	0.922979i	$-0.374253\pi$
$953$	42.6504	−	30.9873i	1.38158	−	1.00378i	0.996730	−	0.0807987i	$-0.0257471\pi$
$954$		0			0
$955$	−9.46907	+	13.0331i	−0.306412	+	0.421740i
$956$		0			0
$957$			22.8525i			0.738717i
$958$		0			0
$959$	−0.369589	−	1.13748i	−0.0119346	−	0.0367311i
$960$		0			0
$961$	13.0182	−	40.0659i	0.419942	−	1.29245i
$962$		0			0
$963$	−3.60332	−	11.0899i	−0.116115	−	0.357367i
$964$		0			0
$965$	24.0758	−	7.82270i	0.775027	−	0.251822i
$966$		0			0
$967$	−9.52511	−	13.1102i	−0.306307	−	0.421595i	0.627918	−	0.778279i	$-0.283907\pi$
$967$	−9.52511	−	13.1102i	−0.306307	−	0.421595i	−0.934225	+	0.356684i	$0.883907\pi$
$968$		0			0
$969$	−12.7247	+	17.5140i	−0.408776	+	0.562631i
$970$		0			0
$971$	9.74627	+	3.16676i	0.312773	+	0.101626i	0.461197	−	0.887298i	$-0.347420\pi$
$971$	9.74627	+	3.16676i	0.312773	+	0.101626i	−0.148424	+	0.988924i	$0.547420\pi$
$972$		0			0
$973$	0.0472143	+	0.0649849i	0.00151362	+	0.00208332i
$974$		0			0
$975$	13.5522			0.434019
$976$		0			0
$977$	−2.75088	+	0.893814i	−0.0880083	+	0.0285956i	−0.352690	−	0.935740i	$-0.614733\pi$
$977$	−2.75088	+	0.893814i	−0.0880083	+	0.0285956i	0.264682	+	0.964336i	$0.414733\pi$
$978$		0			0
$979$	25.0634	+	18.2096i	0.801029	+	0.581982i
$980$		0			0
$981$		−	10.3507i		−	0.330471i
$982$		0			0
$983$	−23.3711			−0.745421			−0.372710	−	0.927948i	$-0.621572\pi$
$983$	−23.3711			−0.745421			−0.372710	+	0.927948i	$0.621572\pi$
$984$		0			0
$985$	−22.3807			−0.713109
$986$		0			0
$987$			0.757591i			0.0241144i
$988$		0			0
$989$	12.9867	+	9.43539i	0.412953	+	0.300028i
$990$		0			0
$991$	−19.9091	+	6.46887i	−0.632435	+	0.205491i	−0.607653	−	0.794202i	$-0.707889\pi$
$991$	−19.9091	+	6.46887i	−0.632435	+	0.205491i	−0.0247815	+	0.999693i	$0.507889\pi$
$992$		0			0
$993$	−44.3131			−1.40623
$994$		0			0
$995$	1.17593	+	1.61853i	0.0372794	+	0.0513107i
$996$		0			0
$997$	−14.9744	−	4.86547i	−0.474244	−	0.154091i	0.0621364	−	0.998068i	$-0.480209\pi$
$997$	−14.9744	−	4.86547i	−0.474244	−	0.154091i	−0.536380	+	0.843977i	$0.680209\pi$
$998$		0			0
$999$	26.5680	−	36.5677i	0.840573	−	1.15695i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.bg.b.681.6	✓	32
41.23	even	10	inner	820.2.bg.b.761.3	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.bg.b.681.6	✓	32	1.1	even	1	trivial
820.2.bg.b.761.3	yes	32	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.bg (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+1.94063i q^{3} +(-0.809017 - 0.587785i) q^{5} +(-0.0642499 + 0.0208760i) q^{7} -0.766036 q^{9} +(-2.16777 - 2.98368i) q^{11} +(-6.64164 - 2.15800i) q^{13} +(1.14067 - 1.57000i) q^{15} +(-1.45177 - 1.99819i) q^{17} +(-4.29550 + 1.39569i) q^{19} +(-0.0405126 - 0.124685i) q^{21} +(0.787726 - 2.42437i) q^{23} +(0.309017 + 0.951057i) q^{25} +4.33529i q^{27} +(-1.87679 + 2.58318i) q^{29} +(6.91829 - 5.02643i) q^{31} +(5.79021 - 4.20683i) q^{33} +(0.0642499 + 0.0208760i) q^{35} +(-8.43488 - 6.12830i) q^{37} +(4.18787 - 12.8889i) q^{39} +(6.20927 + 1.56362i) q^{41} +(-1.94594 + 5.98900i) q^{43} +(0.619736 + 0.450264i) q^{45} +(-5.49583 - 1.78570i) q^{47} +(-5.65943 + 4.11181i) q^{49} +(3.87774 - 2.81734i) q^{51} +(-5.45570 + 7.50912i) q^{53} +3.68803i q^{55} +(-2.70852 - 8.33597i) q^{57} +(4.49661 - 13.8391i) q^{59} +(-2.71482 - 8.35535i) q^{61} +(0.0492177 - 0.0159918i) q^{63} +(4.10476 + 5.64971i) q^{65} +(8.16190 - 11.2339i) q^{67} +(4.70480 + 1.52868i) q^{69} +(6.24053 + 8.58935i) q^{71} +0.824160 q^{73} +(-1.84565 + 0.599687i) q^{75} +(0.201566 + 0.146446i) q^{77} -1.29531i q^{79} -10.7113 q^{81} -0.209284 q^{83} +2.46990i q^{85} +(-5.01300 - 3.64216i) q^{87} +(-7.98903 + 2.59579i) q^{89} +0.471775 q^{91} +(9.75444 + 13.4258i) q^{93} +(4.29550 + 1.39569i) q^{95} +(3.17235 - 4.36637i) q^{97} +(1.66059 + 2.28560i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{5} - 5 q^{7} - 42 q^{9} + 5 q^{11} + 5 q^{13} - 5 q^{17} - 25 q^{19} - 6 q^{21} - 22 q^{23} - 8 q^{25} + 5 q^{29} - 9 q^{31} + 24 q^{33} + 5 q^{35} - 11 q^{37} + 20 q^{39} + 16 q^{41} + 26 q^{43}+ \cdots - 20 q^{97}+O(q^{100}) \) 32 * q - 8 * q^5 - 5 * q^7 - 42 * q^9 + 5 * q^11 + 5 * q^13 - 5 * q^17 - 25 * q^19 - 6 * q^21 - 22 * q^23 - 8 * q^25 + 5 * q^29 - 9 * q^31 + 24 * q^33 + 5 * q^35 - 11 * q^37 + 20 * q^39 + 16 * q^41 + 26 * q^43 + 13 * q^45 - 25 * q^47 + 33 * q^49 + 29 * q^51 - 35 * q^53 + 27 * q^57 + 10 * q^59 + 32 * q^61 + 90 * q^63 - 5 * q^65 + 30 * q^67 - 10 * q^69 + 45 * q^71 - 80 * q^73 - 5 * q^75 - 78 * q^77 - 20 * q^81 - 10 * q^83 + 27 * q^87 - 60 * q^89 + 14 * q^91 - 80 * q^93 + 25 * q^95 - 20 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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