LMFDB - Embedded newform 816.2.bq.a.529.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [816,2,Mod(49,816)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(816, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 0, 0, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("816.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 816 = 2^{4} \cdot 3 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	816.bq (of order $8$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,-8,0,0,0,0,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$6.51579280494$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{8})$
Coefficient field:	$\Q(\zeta_{16})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 51)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			529.1
Root			$-0.923880 - 0.382683i$ of defining polynomial
Character	$\chi$	$=$	816.529
Dual form			816.2.bq.a.145.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.923880 + 0.382683i) q^{3} +(-0.617317 - 1.49033i) q^{5} +(-0.0582601 + 0.140652i) q^{7} +(0.707107 - 0.707107i) q^{9} +(-4.64466 - 1.92388i) q^{11} +3.94495i q^{13} +(1.14065 + 1.14065i) q^{15} +(-1.26616 + 3.92388i) q^{17} +(4.65205 + 4.65205i) q^{19} -0.152241i q^{21} +(3.18585 + 1.31962i) q^{23} +(1.69552 - 1.69552i) q^{25} +(-0.382683 + 0.923880i) q^{27} +(0.858221 + 2.07193i) q^{29} +(2.37849 - 0.985204i) q^{31} +5.02734 q^{33} +0.245584 q^{35} +(-9.86351 + 4.08560i) q^{37} +(-1.50967 - 3.64466i) q^{39} +(-0.105915 + 0.255701i) q^{41} +(-4.48502 + 4.48502i) q^{43} +(-1.49033 - 0.617317i) q^{45} +9.82164i q^{47} +(4.93336 + 4.93336i) q^{49} +(-0.331821 - 4.10973i) q^{51} +(-1.50339 - 1.50339i) q^{53} +8.10973i q^{55} +(-6.07820 - 2.51767i) q^{57} +(0.936078 - 0.936078i) q^{59} +(-3.16799 + 7.64821i) q^{61} +(0.0582601 + 0.140652i) q^{63} +(5.87929 - 2.43528i) q^{65} +7.10973 q^{67} -3.44834 q^{69} +(-6.04875 + 2.50548i) q^{71} +(3.18637 + 7.69258i) q^{73} +(-0.917608 + 2.21530i) q^{75} +(0.541196 - 0.541196i) q^{77} +(-0.491806 - 0.203713i) q^{79} -1.00000i q^{81} +(1.55807 + 1.55807i) q^{83} +(6.62951 - 0.535270i) q^{85} +(-1.58579 - 1.58579i) q^{87} -7.64847i q^{89} +(-0.554866 - 0.229833i) q^{91} +(-1.82042 + 1.82042i) q^{93} +(4.06132 - 9.80490i) q^{95} +(-1.38009 - 3.33182i) q^{97} +(-4.64466 + 1.92388i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{5} - 8 q^{11} - 8 q^{17} + 8 q^{19} - 8 q^{23} - 16 q^{25} - 8 q^{31} + 8 q^{33} - 32 q^{35} - 8 q^{37} - 16 q^{39} - 24 q^{41} + 8 q^{43} - 8 q^{45} - 8 q^{49} - 32 q^{53} - 16 q^{57} - 16 q^{59}+ \cdots - 8 q^{99}+O(q^{100}) $ 8 * q - 8 * q^5 - 8 * q^11 - 8 * q^17 + 8 * q^19 - 8 * q^23 - 16 * q^25 - 8 * q^31 + 8 * q^33 - 32 * q^35 - 8 * q^37 - 16 * q^39 - 24 * q^41 + 8 * q^43 - 8 * q^45 - 8 * q^49 - 32 * q^53 - 16 * q^57 - 16 * q^59 + 16 * q^61 + 24 * q^65 + 16 * q^67 - 24 * q^69 + 16 * q^71 + 48 * q^73 - 16 * q^75 - 32 * q^83 + 40 * q^85 - 24 * q^87 + 16 * q^91 - 32 * q^93 + 40 * q^95 + 8 * q^97 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/816\mathbb{Z}\right)^\times$.

$n$	$241$	$511$	$545$	$613$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.923880	+	0.382683i	−0.533402	+	0.220942i
$3$	−0.923880	+	0.382683i	−0.533402	+	0.220942i
$4$		0			0
$5$	−0.617317	−	1.49033i	−0.276072	−	0.666498i	0.723647	−	0.690170i	$-0.242464\pi$
$5$	−0.617317	−	1.49033i	−0.276072	−	0.666498i	−0.999720	+	0.0236722i	$0.992464\pi$
$6$		0			0
$7$	−0.0582601	+	0.140652i	−0.0220202	+	0.0531616i	−0.934507	−	0.355944i	$-0.884159\pi$
$7$	−0.0582601	+	0.140652i	−0.0220202	+	0.0531616i	0.912487	+	0.409106i	$0.134159\pi$
$8$		0			0
$9$	0.707107	−	0.707107i	0.235702	−	0.235702i
$10$		0			0
$11$	−4.64466	−	1.92388i	−1.40042	−	0.580072i	−0.450557	−	0.892748i	$-0.648774\pi$
$11$	−4.64466	−	1.92388i	−1.40042	−	0.580072i	−0.949860	+	0.312676i	$0.898774\pi$
$12$		0			0
$13$			3.94495i			1.09413i	0.837090	+	0.547066i	$0.184255\pi$
$13$			3.94495i			1.09413i	−0.837090	+	0.547066i	$0.815745\pi$
$14$		0			0
$15$	1.14065	+	1.14065i	0.294515	+	0.294515i
$16$		0			0
$17$	−1.26616	+	3.92388i	−0.307090	+	0.951681i
$17$	−1.26616	+	3.92388i	−0.307090	+	0.951681i
$18$		0			0
$19$	4.65205	+	4.65205i	1.06725	+	1.06725i	0.997569	+	0.0696854i	$0.0221995\pi$
$19$	4.65205	+	4.65205i	1.06725	+	1.06725i	0.0696854	+	0.997569i	$0.477800\pi$
$20$		0			0
$21$		−	0.152241i		−	0.0332217i
$22$		0			0
$23$	3.18585	+	1.31962i	0.664296	+	0.275160i	0.689245	−	0.724528i	$-0.257942\pi$
$23$	3.18585	+	1.31962i	0.664296	+	0.275160i	−0.0249490	+	0.999689i	$0.507942\pi$
$24$		0			0
$25$	1.69552	−	1.69552i	0.339104	−	0.339104i
$26$		0			0
$27$	−0.382683	+	0.923880i	−0.0736475	+	0.177801i
$28$		0			0
$29$	0.858221	+	2.07193i	0.159368	+	0.384748i	0.983313	−	0.181922i	$-0.0582317\pi$
$29$	0.858221	+	2.07193i	0.159368	+	0.384748i	−0.823945	+	0.566669i	$0.808232\pi$
$30$		0			0
$31$	2.37849	−	0.985204i	0.427190	−	0.176948i	−0.158721	−	0.987324i	$-0.550737\pi$
$31$	2.37849	−	0.985204i	0.427190	−	0.176948i	0.585911	+	0.810376i	$0.300737\pi$
$32$		0			0
$33$	5.02734			0.875147
$34$		0			0
$35$	0.245584			0.0415112
$36$		0			0
$37$	−9.86351	+	4.08560i	−1.62155	+	0.671668i	−0.994248	−	0.107106i	$-0.965841\pi$
$37$	−9.86351	+	4.08560i	−1.62155	+	0.671668i	−0.627303	+	0.778775i	$0.715841\pi$
$38$		0			0
$39$	−1.50967	−	3.64466i	−0.241740	−	0.583612i
$40$		0			0
$41$	−0.105915	+	0.255701i	−0.0165411	+	0.0399338i	−0.931934	−	0.362627i	$-0.881880\pi$
$41$	−0.105915	+	0.255701i	−0.0165411	+	0.0399338i	0.915393	+	0.402561i	$0.131880\pi$
$42$		0			0
$43$	−4.48502	+	4.48502i	−0.683959	+	0.683959i	−0.960890	−	0.276931i	$-0.910683\pi$
$43$	−4.48502	+	4.48502i	−0.683959	+	0.683959i	0.276931	+	0.960890i	$0.410683\pi$
$44$		0			0
$45$	−1.49033	−	0.617317i	−0.222166	−	0.0920241i
$46$		0			0
$47$			9.82164i			1.43263i	0.697775	+	0.716317i	$0.254173\pi$
$47$			9.82164i			1.43263i	−0.697775	+	0.716317i	$0.745827\pi$
$48$		0			0
$49$	4.93336	+	4.93336i	0.704766	+	0.704766i
$50$		0			0
$51$	−0.331821	−	4.10973i	−0.0464643	−	0.575478i
$52$		0			0
$53$	−1.50339	−	1.50339i	−0.206507	−	0.206507i	0.596274	−	0.802781i	$-0.296647\pi$
$53$	−1.50339	−	1.50339i	−0.206507	−	0.206507i	−0.802781	+	0.596274i	$0.796647\pi$
$54$		0			0
$55$			8.10973i			1.09352i
$56$		0			0
$57$	−6.07820	−	2.51767i	−0.805077	−	0.333474i
$58$		0			0
$59$	0.936078	−	0.936078i	0.121867	−	0.121867i	−0.643543	−	0.765410i	$-0.722536\pi$
$59$	0.936078	−	0.936078i	0.121867	−	0.121867i	0.765410	+	0.643543i	$0.222536\pi$
$60$		0			0
$61$	−3.16799	+	7.64821i	−0.405620	+	0.979253i	0.580656	+	0.814149i	$0.302796\pi$
$61$	−3.16799	+	7.64821i	−0.405620	+	0.979253i	−0.986276	+	0.165104i	$0.947204\pi$
$62$		0			0
$63$	0.0582601	+	0.140652i	0.00734008	+	0.0177205i
$64$		0			0
$65$	5.87929	−	2.43528i	0.729236	−	0.302059i
$66$		0			0
$67$	7.10973			0.868592			0.434296	−	0.900770i	$-0.356997\pi$
$67$	7.10973			0.868592			0.434296	+	0.900770i	$0.356997\pi$
$68$		0			0
$69$	−3.44834			−0.415132
$70$		0			0
$71$	−6.04875	+	2.50548i	−0.717855	+	0.297345i	−0.711551	−	0.702635i	$-0.752007\pi$
$71$	−6.04875	+	2.50548i	−0.717855	+	0.297345i	−0.00630431	+	0.999980i	$0.502007\pi$
$72$		0			0
$73$	3.18637	+	7.69258i	0.372936	+	0.900348i	0.993250	+	0.115994i	$0.0370053\pi$
$73$	3.18637	+	7.69258i	0.372936	+	0.900348i	−0.620314	+	0.784354i	$0.712995\pi$
$74$		0			0
$75$	−0.917608	+	2.21530i	−0.105956	+	0.255801i
$76$		0			0
$77$	0.541196	−	0.541196i	0.0616750	−	0.0616750i
$78$		0			0
$79$	−0.491806	−	0.203713i	−0.0553325	−	0.0229195i	0.354846	−	0.934925i	$-0.384533\pi$
$79$	−0.491806	−	0.203713i	−0.0553325	−	0.0229195i	−0.410178	+	0.912005i	$0.634533\pi$
$80$		0			0
$81$		−	1.00000i		−	0.111111i
$82$		0			0
$83$	1.55807	+	1.55807i	0.171021	+	0.171021i	0.787428	−	0.616407i	$-0.211412\pi$
$83$	1.55807	+	1.55807i	0.171021	+	0.171021i	−0.616407	+	0.787428i	$0.711412\pi$
$84$		0			0
$85$	6.62951	−	0.535270i	0.719072	−	0.0580581i
$86$		0			0
$87$	−1.58579	−	1.58579i	−0.170014	−	0.170014i
$88$		0			0
$89$		−	7.64847i		−	0.810737i	−0.914153	−	0.405368i	$-0.867143\pi$
$89$		−	7.64847i		−	0.810737i	0.914153	−	0.405368i	$-0.132857\pi$
$90$		0			0
$91$	−0.554866	−	0.229833i	−0.0581657	−	0.0240930i
$92$		0			0
$93$	−1.82042	+	1.82042i	−0.188769	+	0.188769i
$94$		0			0
$95$	4.06132	−	9.80490i	0.416683	−	1.00596i
$96$		0			0
$97$	−1.38009	−	3.33182i	−0.140126	−	0.338295i	0.838200	−	0.545363i	$-0.183608\pi$
$97$	−1.38009	−	3.33182i	−0.140126	−	0.338295i	−0.978327	+	0.207067i	$0.933608\pi$
$98$		0			0
$99$	−4.64466	+	1.92388i	−0.466805	+	0.193357i
$100$		0			0
$101$	−9.13707			−0.909173			−0.454586	−	0.890703i	$-0.650213\pi$
$101$	−9.13707			−0.909173			−0.454586	+	0.890703i	$0.650213\pi$
$102$		0			0
$103$	−7.57862			−0.746744			−0.373372	−	0.927682i	$-0.621798\pi$
$103$	−7.57862			−0.746744			−0.373372	+	0.927682i	$0.621798\pi$
$104$		0			0
$105$	−0.226890	+	0.0939809i	−0.0221422	+	0.00917159i
$106$		0			0
$107$	−7.06688	−	17.0610i	−0.683181	−	1.64934i	−0.758087	−	0.652154i	$-0.773866\pi$
$107$	−7.06688	−	17.0610i	−0.683181	−	1.64934i	0.0749059	−	0.997191i	$-0.476134\pi$
$108$		0			0
$109$	4.10973	−	9.92177i	0.393641	−	0.950333i	−0.595499	−	0.803356i	$-0.703046\pi$
$109$	4.10973	−	9.92177i	0.393641	−	0.950333i	0.989140	−	0.146977i	$-0.0469544\pi$
$110$		0			0
$111$	7.54920	−	7.54920i	0.716539	−	0.716539i
$112$		0			0
$113$	1.54747	+	0.640982i	0.145574	+	0.0602985i	0.454281	−	0.890859i	$-0.349896\pi$
$113$	1.54747	+	0.640982i	0.145574	+	0.0602985i	−0.308707	+	0.951157i	$0.599896\pi$
$114$		0			0
$115$		−	5.56261i		−	0.518716i
$116$		0			0
$117$	2.78950	+	2.78950i	0.257889	+	0.257889i
$118$		0			0
$119$	−0.478136	−	0.406694i	−0.0438306	−	0.0372816i
$120$		0			0
$121$	10.0933	+	10.0933i	0.917577	+	0.917577i
$122$		0			0
$123$		−	0.276769i		−	0.0249554i
$124$		0			0
$125$	−11.0252	−	4.56680i	−0.986127	−	0.408467i
$126$		0			0
$127$	−8.61339	+	8.61339i	−0.764315	+	0.764315i	−0.977099	−	0.212784i	$-0.931747\pi$
$127$	−8.61339	+	8.61339i	−0.764315	+	0.764315i	0.212784	+	0.977099i	$0.431747\pi$
$128$		0			0
$129$	2.42727	−	5.85996i	0.213710	−	0.515940i
$130$		0			0
$131$	3.99948	+	9.65561i	0.349436	+	0.843614i	0.996687	+	0.0813367i	$0.0259189\pi$
$131$	3.99948	+	9.65561i	0.349436	+	0.843614i	−0.647250	+	0.762278i	$0.724081\pi$
$132$		0			0
$133$	−0.925351	+	0.383293i	−0.0802381	+	0.0332357i
$134$		0			0
$135$	1.61313			0.138836
$136$		0			0
$137$	13.4928			1.15276			0.576382	−	0.817180i	$-0.304464\pi$
$137$	13.4928			1.15276			0.576382	+	0.817180i	$0.304464\pi$
$138$		0			0
$139$	4.92241	−	2.03893i	0.417513	−	0.172940i	−0.164030	−	0.986455i	$-0.552449\pi$
$139$	4.92241	−	2.03893i	0.417513	−	0.172940i	0.581543	+	0.813516i	$0.302449\pi$
$140$		0			0
$141$	−3.75858	−	9.07401i	−0.316529	−	0.764170i
$142$		0			0
$143$	7.58960	−	18.3229i	0.634675	−	1.53224i
$144$		0			0
$145$	2.55807	−	2.55807i	0.212436	−	0.212436i
$146$		0			0
$147$	−6.44574	−	2.66991i	−0.531636	−	0.220211i
$148$		0			0
$149$		−	9.31890i		−	0.763434i	−0.924279	−	0.381717i	$-0.875333\pi$
$149$		−	9.31890i		−	0.763434i	0.924279	−	0.381717i	$-0.124667\pi$
$150$		0			0
$151$	8.45929	+	8.45929i	0.688407	+	0.688407i	0.961880	−	0.273472i	$-0.0881722\pi$
$151$	8.45929	+	8.45929i	0.688407	+	0.688407i	−0.273472	+	0.961880i	$0.588172\pi$
$152$		0			0
$153$	1.87929	+	3.66991i	0.151932	+	0.296695i
$154$		0			0
$155$	−2.93657	−	2.93657i	−0.235871	−	0.235871i
$156$		0			0
$157$		−	18.1548i		−	1.44891i	−0.689321	−	0.724456i	$-0.742091\pi$
$157$		−	18.1548i		−	1.44891i	0.689321	−	0.724456i	$-0.257909\pi$
$158$		0			0
$159$	1.96428	+	0.813631i	0.155777	+	0.0645251i
$160$		0			0
$161$	−0.371216	+	0.371216i	−0.0292559	+	0.0292559i
$162$		0			0
$163$	−7.93015	+	19.1451i	−0.621137	+	1.49956i	0.229232	+	0.973372i	$0.426379\pi$
$163$	−7.93015	+	19.1451i	−0.621137	+	1.49956i	−0.850369	+	0.526186i	$0.823621\pi$
$164$		0			0
$165$	−3.10346	−	7.49242i	−0.241604	−	0.583284i
$166$		0			0
$167$	7.47308	−	3.09545i	0.578285	−	0.239533i	−0.0743169	−	0.997235i	$-0.523678\pi$
$167$	7.47308	−	3.09545i	0.578285	−	0.239533i	0.652601	+	0.757701i	$0.273678\pi$
$168$		0			0
$169$	−2.56261			−0.197124
$170$		0			0
$171$	6.57900			0.503109
$172$		0			0
$173$	−1.07228	+	0.444151i	−0.0815236	+	0.0337682i	−0.423073	−	0.906096i	$-0.639048\pi$
$173$	−1.07228	+	0.444151i	−0.0815236	+	0.0337682i	0.341549	+	0.939864i	$0.389048\pi$
$174$		0			0
$175$	0.139697	+	0.337260i	0.0105601	+	0.0254944i
$176$		0			0
$177$	−0.506602	+	1.22304i	−0.0380785	+	0.0919297i
$178$		0			0
$179$	−2.04826	+	2.04826i	−0.153094	+	0.153094i	−0.779499	−	0.626404i	$-0.784526\pi$
$179$	−2.04826	+	2.04826i	−0.153094	+	0.153094i	0.626404	+	0.779499i	$0.284526\pi$
$180$		0			0
$181$	0.778548	+	0.322485i	0.0578690	+	0.0239701i	0.411430	−	0.911441i	$-0.365029\pi$
$181$	0.778548	+	0.322485i	0.0578690	+	0.0239701i	−0.353561	+	0.935411i	$0.615029\pi$
$182$		0			0
$183$		−	8.27836i		−	0.611954i
$184$		0			0
$185$	12.1778	+	12.1778i	0.895331	+	0.895331i
$186$		0			0
$187$	13.4300	−	15.7891i	0.982096	−	1.15462i
$188$		0			0
$189$	−0.107651	−	0.107651i	−0.00783043	−	0.00783043i
$190$		0			0
$191$		−	9.97069i		−	0.721454i	−0.932671	−	0.360727i	$-0.882529\pi$
$191$		−	9.97069i		−	0.721454i	0.932671	−	0.360727i	$-0.117471\pi$
$192$		0			0
$193$	3.44993	+	1.42901i	0.248332	+	0.102862i	0.503377	−	0.864067i	$-0.332091\pi$
$193$	3.44993	+	1.42901i	0.248332	+	0.102862i	−0.255046	+	0.966929i	$0.582091\pi$
$194$		0			0
$195$	−4.49981	+	4.49981i	−0.322238	+	0.322238i
$196$		0			0
$197$	−6.20151	+	14.9718i	−0.441839	+	1.06669i	0.533464	+	0.845823i	$0.320890\pi$
$197$	−6.20151	+	14.9718i	−0.441839	+	1.06669i	−0.975303	+	0.220871i	$0.929110\pi$
$198$		0			0
$199$	−6.30411	−	15.2195i	−0.446886	−	1.07888i	−0.973482	−	0.228763i	$-0.926532\pi$
$199$	−6.30411	−	15.2195i	−0.446886	−	1.07888i	0.526596	−	0.850116i	$-0.323468\pi$
$200$		0			0
$201$	−6.56854	+	2.72078i	−0.463309	+	0.191909i
$202$		0			0
$203$	−0.341422			−0.0239631
$204$		0			0
$205$	0.446463			0.0311823
$206$		0			0
$207$	3.18585	−	1.31962i	0.221432	−	0.0917202i
$208$		0			0
$209$	−12.6572	−	30.5572i	−0.875517	−	2.11368i
$210$		0			0
$211$	4.09040	−	9.87510i	0.281595	−	0.679830i	−0.718278	−	0.695756i	$-0.755070\pi$
$211$	4.09040	−	9.87510i	0.281595	−	0.679830i	0.999873	+	0.0159259i	$0.00506960\pi$
$212$		0			0
$213$	4.62951	−	4.62951i	0.317209	−	0.317209i
$214$		0			0
$215$	9.45285	+	3.91550i	0.644679	+	0.267035i
$216$		0			0
$217$			0.391939i			0.0266065i
$218$		0			0
$219$	−5.88764	−	5.88764i	−0.397850	−	0.397850i
$220$		0			0
$221$	−15.4795	−	4.99495i	−1.04126	−	0.335997i
$222$		0			0
$223$	−3.83004	−	3.83004i	−0.256479	−	0.256479i	0.567142	−	0.823620i	$-0.308049\pi$
$223$	−3.83004	−	3.83004i	−0.256479	−	0.256479i	−0.823620	+	0.567142i	$0.808049\pi$
$224$		0			0
$225$		−	2.39782i		−	0.159855i
$226$		0			0
$227$	11.3625	+	4.70650i	0.754155	+	0.312381i	0.726436	−	0.687235i	$-0.241176\pi$
$227$	11.3625	+	4.70650i	0.754155	+	0.312381i	0.0277193	+	0.999616i	$0.491176\pi$
$228$		0			0
$229$	−21.2951	+	21.2951i	−1.40722	+	1.40722i	−0.633362	+	0.773856i	$0.718326\pi$
$229$	−21.2951	+	21.2951i	−1.40722	+	1.40722i	−0.773856	+	0.633362i	$0.781674\pi$
$230$		0			0
$231$	−0.292893	+	0.707107i	−0.0192710	+	0.0465242i
$232$		0			0
$233$	−3.36196	−	8.11649i	−0.220249	−	0.531729i	0.774674	−	0.632360i	$-0.217914\pi$
$233$	−3.36196	−	8.11649i	−0.220249	−	0.531729i	−0.994924	+	0.100631i	$0.967914\pi$
$234$		0			0
$235$	14.6375	−	6.06306i	0.954847	−	0.395510i
$236$		0			0
$237$	0.532327			0.0345783
$238$		0			0
$239$	−14.6501			−0.947634			−0.473817	−	0.880623i	$-0.657124\pi$
$239$	−14.6501			−0.947634			−0.473817	+	0.880623i	$0.657124\pi$
$240$		0			0
$241$	15.6646	−	6.48849i	1.00905	−	0.417960i	0.183939	−	0.982938i	$-0.441115\pi$
$241$	15.6646	−	6.48849i	1.00905	−	0.417960i	0.825106	+	0.564977i	$0.191115\pi$
$242$		0			0
$243$	0.382683	+	0.923880i	0.0245492	+	0.0592669i
$244$		0			0
$245$	4.30691	−	10.3978i	0.275158	−	0.664291i
$246$		0			0
$247$	−18.3521	+	18.3521i	−1.16772	+	1.16772i
$248$		0			0
$249$	−2.03572	−	0.843223i	−0.129009	−	0.0534371i
$250$		0			0
$251$		−	13.9453i		−	0.880217i	−0.897945	−	0.440109i	$-0.854940\pi$
$251$		−	13.9453i		−	0.880217i	0.897945	−	0.440109i	$-0.145060\pi$
$252$		0			0
$253$	−12.2584	−	12.2584i	−0.770678	−	0.770678i
$254$		0			0
$255$	−5.92003	+	3.03153i	−0.370727	+	0.189842i
$256$		0			0
$257$	13.9019	+	13.9019i	0.867180	+	0.867180i	0.992159	−	0.124980i	$-0.0398865\pi$
$257$	13.9019	+	13.9019i	0.867180	+	0.867180i	−0.124980	+	0.992159i	$0.539887\pi$
$258$		0			0
$259$		−	1.62535i		−	0.100994i
$260$		0			0
$261$	2.07193	+	0.858221i	0.128249	+	0.0531226i
$262$		0			0
$263$	−19.7085	+	19.7085i	−1.21528	+	1.21528i	−0.246015	+	0.969266i	$0.579121\pi$
$263$	−19.7085	+	19.7085i	−1.21528	+	1.21528i	−0.969266	+	0.246015i	$0.920879\pi$
$264$		0			0
$265$	−1.31249	+	3.16863i	−0.0806256	+	0.194647i
$266$		0			0
$267$	2.92694	+	7.06627i	0.179126	+	0.432449i
$268$		0			0
$269$	0.189698	−	0.0785753i	0.0115661	−	0.00479082i	−0.376893	−	0.926257i	$-0.623008\pi$
$269$	0.189698	−	0.0785753i	0.0115661	−	0.00479082i	0.388459	+	0.921466i	$0.373008\pi$
$270$		0			0
$271$	−8.21077			−0.498768			−0.249384	−	0.968405i	$-0.580228\pi$
$271$	−8.21077			−0.498768			−0.249384	+	0.968405i	$0.580228\pi$
$272$		0			0
$273$	0.600582			0.0363489
$274$		0			0
$275$	−11.1371	+	4.61313i	−0.671591	+	0.278182i
$276$		0			0
$277$	9.01896	+	21.7737i	0.541897	+	1.30825i	0.923383	+	0.383880i	$0.125412\pi$
$277$	9.01896	+	21.7737i	0.541897	+	1.30825i	−0.381486	+	0.924374i	$0.624588\pi$
$278$		0			0
$279$	0.985204	−	2.37849i	0.0589826	−	0.142397i
$280$		0			0
$281$	−7.17941	+	7.17941i	−0.428288	+	0.428288i	−0.888045	−	0.459757i	$-0.847936\pi$
$281$	−7.17941	+	7.17941i	−0.428288	+	0.428288i	0.459757	+	0.888045i	$0.347936\pi$
$282$		0			0
$283$	8.75762	+	3.62753i	0.520587	+	0.215634i	0.627475	−	0.778637i	$-0.284089\pi$
$283$	8.75762	+	3.62753i	0.520587	+	0.215634i	−0.106888	+	0.994271i	$0.534089\pi$
$284$		0			0
$285$			10.6128i			0.628645i
$286$		0			0
$287$	−0.0297943	−	0.0297943i	−0.00175870	−	0.00175870i
$288$		0			0
$289$	−13.7937	−	9.93654i	−0.811392	−	0.584503i
$290$		0			0
$291$	2.55007	+	2.55007i	0.149487	+	0.149487i
$292$		0			0
$293$			9.28515i			0.542444i	0.962517	+	0.271222i	$0.0874278\pi$
$293$			9.28515i			0.542444i	−0.962517	+	0.271222i	$0.912572\pi$
$294$		0			0
$295$	−1.97292	−	0.817212i	−0.114868	−	0.0475799i
$296$		0			0
$297$	3.55487	−	3.55487i	0.206274	−	0.206274i
$298$		0			0
$299$	−5.20584	+	12.5680i	−0.301062	+	0.726827i
$300$		0			0
$301$	−0.369530	−	0.892125i	−0.0212994	−	0.0514213i
$302$		0			0
$303$	8.44155	−	3.49661i	0.484955	−	0.200875i
$304$		0			0
$305$	13.3540			0.764650
$306$		0			0
$307$	27.1418			1.54906			0.774531	−	0.632536i	$-0.217986\pi$
$307$	27.1418			1.54906			0.774531	+	0.632536i	$0.217986\pi$
$308$		0			0
$309$	7.00174	−	2.90021i	0.398315	−	0.164987i
$310$		0			0
$311$	0.989538	+	2.38896i	0.0561115	+	0.135465i	0.949449	−	0.313921i	$-0.101643\pi$
$311$	0.989538	+	2.38896i	0.0561115	+	0.135465i	−0.893338	+	0.449386i	$0.851643\pi$
$312$		0			0
$313$	9.80071	−	23.6610i	0.553969	−	1.33740i	−0.360506	−	0.932757i	$-0.617396\pi$
$313$	9.80071	−	23.6610i	0.553969	−	1.33740i	0.914475	−	0.404643i	$-0.132604\pi$
$314$		0			0
$315$	0.173654	−	0.173654i	0.00978429	−	0.00978429i
$316$		0			0
$317$	23.6497	+	9.79601i	1.32830	+	0.550199i	0.930169	−	0.367131i	$-0.119660\pi$
$317$	23.6497	+	9.79601i	1.32830	+	0.550199i	0.398128	+	0.917330i	$0.369660\pi$
$318$		0			0
$319$		−	11.2745i		−	0.631252i
$320$		0			0
$321$	13.0579	+	13.0579i	0.728820	+	0.728820i
$322$		0			0
$323$	−24.1444	+	12.3638i	−1.34343	+	0.687942i
$324$		0			0
$325$	6.68873	+	6.68873i	0.371024	+	0.371024i
$326$		0			0
$327$			10.7392i			0.593882i
$328$		0			0
$329$	−1.38144	−	0.572209i	−0.0761610	−	0.0315469i
$330$		0			0
$331$	−0.235588	+	0.235588i	−0.0129491	+	0.0129491i	−0.713552	−	0.700603i	$-0.752915\pi$
$331$	−0.235588	+	0.235588i	−0.0129491	+	0.0129491i	0.700603	+	0.713552i	$0.252915\pi$
$332$		0			0
$333$	−4.08560	+	9.86351i	−0.223889	+	0.540517i
$334$		0			0
$335$	−4.38896	−	10.5959i	−0.239794	−	0.578914i
$336$		0			0
$337$	−3.46953	+	1.43713i	−0.188997	+	0.0782853i	−0.475175	−	0.879891i	$-0.657615\pi$
$337$	−3.46953	+	1.43713i	−0.188997	+	0.0782853i	0.286178	+	0.958177i	$0.407615\pi$
$338$		0			0
$339$	−1.67497			−0.0909717
$340$		0			0
$341$	−12.9427			−0.700886
$342$		0			0
$343$	−1.96587	+	0.814291i	−0.106147	+	0.0439676i
$344$		0			0
$345$	2.12872	+	5.13918i	0.114606	+	0.276684i
$346$		0			0
$347$	−1.26668	+	3.05804i	−0.0679989	+	0.164164i	−0.954225	−	0.299088i	$-0.903318\pi$
$347$	−1.26668	+	3.05804i	−0.0679989	+	0.164164i	0.886227	+	0.463252i	$0.153318\pi$
$348$		0			0
$349$	1.82779	−	1.82779i	0.0978393	−	0.0978393i	−0.656493	−	0.754332i	$-0.727961\pi$
$349$	1.82779	−	1.82779i	0.0978393	−	0.0978393i	0.754332	+	0.656493i	$0.227961\pi$
$350$		0			0
$351$	−3.64466	−	1.50967i	−0.194537	−	0.0805800i
$352$		0			0
$353$		−	13.2848i		−	0.707079i	−0.935420	−	0.353539i	$-0.884978\pi$
$353$		−	13.2848i		−	0.707079i	0.935420	−	0.353539i	$-0.115022\pi$
$354$		0			0
$355$	7.46799	+	7.46799i	0.396360	+	0.396360i
$356$		0			0
$357$	0.597375	+	0.192762i	0.0316164	+	0.0102020i
$358$		0			0
$359$	10.4143	+	10.4143i	0.549647	+	0.549647i	0.926339	−	0.376692i	$-0.122938\pi$
$359$	10.4143	+	10.4143i	0.549647	+	0.549647i	−0.376692	+	0.926339i	$0.622938\pi$
$360$		0			0
$361$			24.2832i			1.27806i
$362$		0			0
$363$	−13.1876	−	5.46248i	−0.692169	−	0.286706i
$364$		0			0
$365$	9.49751	−	9.49751i	0.497122	−	0.497122i
$366$		0			0
$367$	0.168365	−	0.406470i	0.00878861	−	0.0212176i	−0.919424	−	0.393267i	$-0.871345\pi$
$367$	0.168365	−	0.406470i	0.00878861	−	0.0212176i	0.928213	+	0.372049i	$0.121345\pi$
$368$		0			0
$369$	0.105915	+	0.255701i	0.00551370	+	0.0133113i
$370$		0			0
$371$	0.299044	−	0.123868i	0.0155256	−	0.00643090i
$372$		0			0
$373$	0.827899			0.0428670			0.0214335	−	0.999770i	$-0.493177\pi$
$373$	0.827899			0.0428670			0.0214335	+	0.999770i	$0.493177\pi$
$374$		0			0
$375$	11.9336			0.616250
$376$		0			0
$377$	−8.17365	+	3.38564i	−0.420965	+	0.174369i
$378$		0			0
$379$	−7.58033	−	18.3005i	−0.389375	−	0.940035i	−0.990072	−	0.140558i	$-0.955110\pi$
$379$	−7.58033	−	18.3005i	−0.389375	−	0.940035i	0.600697	−	0.799477i	$-0.294890\pi$
$380$		0			0
$381$	4.66153	−	11.2539i	0.238818	−	0.576557i
$382$		0			0
$383$	11.7966	−	11.7966i	0.602776	−	0.602776i	−0.338273	−	0.941048i	$-0.609843\pi$
$383$	11.7966	−	11.7966i	0.602776	−	0.602776i	0.941048	+	0.338273i	$0.109843\pi$
$384$		0			0
$385$	−1.14065	−	0.472474i	−0.0581330	−	0.0240795i
$386$		0			0
$387$			6.34277i			0.322421i
$388$		0			0
$389$	−12.2315	−	12.2315i	−0.620163	−	0.620163i	0.325410	−	0.945573i	$-0.394498\pi$
$389$	−12.2315	−	12.2315i	−0.620163	−	0.620163i	−0.945573	+	0.325410i	$0.894498\pi$
$390$		0			0
$391$	−9.21185	+	10.8300i	−0.465863	+	0.547699i
$392$		0			0
$393$	−7.39008	−	7.39008i	−0.372780	−	0.372780i
$394$		0			0
$395$			0.858710i			0.0432064i
$396$		0			0
$397$	−5.95039	−	2.46473i	−0.298641	−	0.123701i	0.228331	−	0.973583i	$-0.426673\pi$
$397$	−5.95039	−	2.46473i	−0.298641	−	0.123701i	−0.526973	+	0.849882i	$0.676673\pi$
$398$		0			0
$399$	0.708233	−	0.708233i	0.0354560	−	0.0354560i
$400$		0			0
$401$	−8.06407	+	19.4684i	−0.402700	+	0.972204i	0.584308	+	0.811532i	$0.301366\pi$
$401$	−8.06407	+	19.4684i	−0.402700	+	0.972204i	−0.987008	+	0.160672i	$0.948634\pi$
$402$		0			0
$403$	3.88658	+	9.38303i	0.193604	+	0.467402i
$404$		0			0
$405$	−1.49033	+	0.617317i	−0.0740553	+	0.0306747i
$406$		0			0
$407$	53.6728			2.66046
$408$		0			0
$409$	−27.6232			−1.36588			−0.682939	−	0.730475i	$-0.739299\pi$
$409$	−27.6232			−1.36588			−0.682939	+	0.730475i	$0.739299\pi$
$410$		0			0
$411$	−12.4657	+	5.16346i	−0.614887	+	0.254694i
$412$		0			0
$413$	0.0771255	+	0.186197i	0.00379510	+	0.00916218i
$414$		0			0
$415$	1.36023	−	3.28387i	0.0667708	−	0.161199i
$416$		0			0
$417$	−3.76745	+	3.76745i	−0.184493	+	0.184493i
$418$		0			0
$419$	11.1336	+	4.61170i	0.543914	+	0.225297i	0.637685	−	0.770297i	$-0.279892\pi$
$419$	11.1336	+	4.61170i	0.543914	+	0.225297i	−0.0937711	+	0.995594i	$0.529892\pi$
$420$		0			0
$421$		−	14.0183i		−	0.683210i	−0.939844	−	0.341605i	$-0.889029\pi$
$421$		−	14.0183i		−	0.683210i	0.939844	−	0.341605i	$-0.110971\pi$
$422$		0			0
$423$	6.94495	+	6.94495i	0.337675	+	0.337675i
$424$		0			0
$425$	4.50621	+	8.79981i	0.218583	+	0.426854i
$426$		0			0
$427$	−0.891171	−	0.891171i	−0.0431268	−	0.0431268i
$428$		0			0
$429$			19.8326i			0.957526i
$430$		0			0
$431$	−3.18166	−	1.31789i	−0.153255	−	0.0634804i	0.304737	−	0.952436i	$-0.401431\pi$
$431$	−3.18166	−	1.31789i	−0.153255	−	0.0634804i	−0.457992	+	0.888956i	$0.651431\pi$
$432$		0			0
$433$	−3.93561	+	3.93561i	−0.189133	+	0.189133i	−0.795321	−	0.606188i	$-0.792698\pi$
$433$	−3.93561	+	3.93561i	−0.189133	+	0.189133i	0.606188	+	0.795321i	$0.292698\pi$
$434$		0			0
$435$	−1.38442	+	3.34228i	−0.0663778	+	0.160250i
$436$		0			0
$437$	8.68180	+	20.9597i	0.415307	+	1.00264i
$438$		0			0
$439$	−16.2477	+	6.73002i	−0.775461	+	0.321206i	−0.735082	−	0.677978i	$-0.762856\pi$
$439$	−16.2477	+	6.73002i	−0.775461	+	0.321206i	−0.0403786	+	0.999184i	$0.512856\pi$
$440$		0			0
$441$	6.97682			0.332230
$442$		0			0
$443$	−5.87632			−0.279192			−0.139596	−	0.990209i	$-0.544580\pi$
$443$	−5.87632			−0.279192			−0.139596	+	0.990209i	$0.544580\pi$
$444$		0			0
$445$	−11.3988	+	4.72153i	−0.540354	+	0.223822i
$446$		0			0
$447$	3.56619	+	8.60954i	0.168675	+	0.407217i
$448$		0			0
$449$	−15.3001	+	36.9378i	−0.722058	+	1.74320i	−0.0546546	+	0.998505i	$0.517406\pi$
$449$	−15.3001	+	36.9378i	−0.722058	+	1.74320i	−0.667403	+	0.744697i	$0.732594\pi$
$450$		0			0
$451$	0.983875	−	0.983875i	0.0463289	−	0.0463289i
$452$		0			0
$453$	−11.0526	−	4.57814i	−0.519296	−	0.215100i
$454$		0			0
$455$			0.968815i			0.0454188i
$456$		0			0
$457$	12.5092	+	12.5092i	0.585154	+	0.585154i	0.936315	−	0.351161i	$-0.114213\pi$
$457$	12.5092	+	12.5092i	0.585154	+	0.585154i	−0.351161	+	0.936315i	$0.614213\pi$
$458$		0			0
$459$	−3.14065	−	2.67139i	−0.146593	−	0.124690i
$460$		0			0
$461$	21.1186	+	21.1186i	0.983591	+	0.983591i	0.999868	−	0.0162762i	$-0.00518111\pi$
$461$	21.1186	+	21.1186i	0.983591	+	0.983591i	−0.0162762	+	0.999868i	$0.505181\pi$
$462$		0			0
$463$		−	9.45213i		−	0.439278i	−0.975581	−	0.219639i	$-0.929512\pi$
$463$		−	9.45213i		−	0.439278i	0.975581	−	0.219639i	$-0.0704879\pi$
$464$		0			0
$465$	3.83681	+	1.58926i	0.177928	+	0.0737001i
$466$		0			0
$467$	−14.1488	+	14.1488i	−0.654726	+	0.654726i	−0.954127	−	0.299401i	$-0.903213\pi$
$467$	−14.1488	+	14.1488i	−0.654726	+	0.654726i	0.299401	+	0.954127i	$0.403213\pi$
$468$		0			0
$469$	−0.414214	+	1.00000i	−0.0191266	+	0.0461757i
$470$		0			0
$471$	6.94755	+	16.7729i	0.320126	+	0.772852i
$472$		0			0
$473$	29.4600	−	12.2027i	1.35457	−	0.561082i
$474$		0			0
$475$	15.7753			0.723820
$476$		0			0
$477$	−2.12612			−0.0973484
$478$		0			0
$479$	−1.11392	+	0.461402i	−0.0508964	+	0.0210820i	−0.407986	−	0.912988i	$-0.633769\pi$
$479$	−1.11392	+	0.461402i	−0.0508964	+	0.0210820i	0.357090	+	0.934070i	$0.383769\pi$
$480$		0			0
$481$	−16.1175	−	38.9110i	−0.734894	−	1.77419i
$482$		0			0
$483$	0.200901	−	0.485017i	0.00914130	−	0.0220690i
$484$		0			0
$485$	−4.11358	+	4.11358i	−0.186788	+	0.186788i
$486$		0			0
$487$	−11.0508	−	4.57738i	−0.500759	−	0.207421i	0.117983	−	0.993016i	$-0.462357\pi$
$487$	−11.0508	−	4.57738i	−0.500759	−	0.207421i	−0.618742	+	0.785595i	$0.712357\pi$
$488$		0			0
$489$		−	20.7225i		−	0.937103i
$490$		0			0
$491$	22.1064	+	22.1064i	0.997649	+	0.997649i	0.999997	−	0.00234871i	$-0.000747617\pi$
$491$	22.1064	+	22.1064i	0.997649	+	0.997649i	−0.00234871	+	0.999997i	$0.500748\pi$
$492$		0			0
$493$	−9.21665	+	0.744156i	−0.415097	+	0.0335151i
$494$		0			0
$495$	5.73445	+	5.73445i	0.257744	+	0.257744i
$496$		0			0
$497$		−	0.996740i		−	0.0447099i
$498$		0			0
$499$	−38.2107	−	15.8274i	−1.71055	−	0.708531i	−0.999988	−	0.00489302i	$-0.998442\pi$
$499$	−38.2107	−	15.8274i	−1.71055	−	0.708531i	−0.710558	−	0.703638i	$-0.751558\pi$
$500$		0			0
$501$	−5.71965	+	5.71965i	−0.255535	+	0.255535i
$502$		0			0
$503$	1.17972	−	2.84810i	0.0526013	−	0.126991i	−0.895394	−	0.445274i	$-0.853106\pi$
$503$	1.17972	−	2.84810i	0.0526013	−	0.126991i	0.947996	+	0.318283i	$0.103106\pi$
$504$		0			0
$505$	5.64047	+	13.6173i	0.250997	+	0.605961i
$506$		0			0
$507$	2.36754	−	0.980668i	0.105146	−	0.0435530i
$508$		0			0
$509$	33.8077			1.49850			0.749249	−	0.662288i	$-0.230415\pi$
$509$	33.8077			1.49850			0.749249	+	0.662288i	$0.230415\pi$
$510$		0			0
$511$	−1.26762			−0.0560760
$512$		0			0
$513$	−6.07820	+	2.51767i	−0.268359	+	0.111158i
$514$		0			0
$515$	4.67841	+	11.2947i	0.206155	+	0.497703i
$516$		0			0
$517$	18.8956	−	45.6181i	0.831030	−	2.00628i
$518$		0			0
$519$	0.820684	−	0.820684i	0.0360240	−	0.0360240i
$520$		0			0
$521$	−37.8381	−	15.6731i	−1.65772	−	0.686649i	−0.659818	−	0.751425i	$-0.729367\pi$
$521$	−37.8381	−	15.6731i	−1.65772	−	0.686649i	−0.997900	+	0.0647762i	$0.979367\pi$
$522$		0			0
$523$		−	9.06788i		−	0.396511i	−0.980150	−	0.198255i	$-0.936472\pi$
$523$		−	9.06788i		−	0.396511i	0.980150	−	0.198255i	$-0.0635275\pi$
$524$		0			0
$525$	−0.258127	−	0.258127i	−0.0112656	−	0.0112656i
$526$		0			0
$527$	0.854262	+	10.5803i	0.0372122	+	0.460887i
$528$		0			0
$529$	−7.85521	−	7.85521i	−0.341531	−	0.341531i
$530$		0			0
$531$		−	1.32381i		−	0.0574486i
$532$		0			0
$533$	−1.00873	−	0.417828i	−0.0436928	−	0.0180981i
$534$		0			0
$535$	−21.0640	+	21.0640i	−0.910677	+	0.910677i
$536$		0			0
$537$	1.10851	−	2.67619i	0.0478359	−	0.115486i
$538$		0			0
$539$	−13.4226	−	32.4049i	−0.578151	−	1.39578i
$540$		0			0
$541$	11.9569	−	4.95269i	0.514065	−	0.212933i	−0.110543	−	0.993871i	$-0.535259\pi$
$541$	11.9569	−	4.95269i	0.514065	−	0.212933i	0.624608	+	0.780939i	$0.285259\pi$
$542$		0			0
$543$	−0.842695			−0.0361635
$544$		0			0
$545$	−17.3238			−0.742068
$546$		0			0
$547$	−9.84840	+	4.07934i	−0.421087	+	0.174420i	−0.583157	−	0.812359i	$-0.698183\pi$
$547$	−9.84840	+	4.07934i	−0.421087	+	0.174420i	0.162070	+	0.986779i	$0.448183\pi$
$548$		0			0
$549$	3.16799	+	7.64821i	0.135207	+	0.326418i
$550$		0			0
$551$	−5.64624	+	13.6312i	−0.240538	+	0.580710i
$552$		0			0
$553$	0.0573053	−	0.0573053i	0.00243687	−	0.00243687i
$554$		0			0
$555$	−15.9111	−	6.59059i	−0.675388	−	0.279755i
$556$		0			0
$557$			30.1933i			1.27933i	0.768653	+	0.639667i	$0.220928\pi$
$557$			30.1933i			1.27933i	−0.768653	+	0.639667i	$0.779072\pi$
$558$		0			0
$559$	−17.6932	−	17.6932i	−0.748341	−	0.748341i
$560$		0			0
$561$	−6.36543	+	19.7267i	−0.268749	+	0.832861i
$562$		0			0
$563$	21.1592	+	21.1592i	0.891755	+	0.891755i	0.994688	−	0.102934i	$-0.0328229\pi$
$563$	21.1592	+	21.1592i	0.891755	+	0.891755i	−0.102934	+	0.994688i	$0.532823\pi$
$564$		0			0
$565$		−	2.70193i		−	0.113671i
$566$		0			0
$567$	0.140652	+	0.0582601i	0.00590684	+	0.00244669i
$568$		0			0
$569$	−18.1692	+	18.1692i	−0.761694	+	0.761694i	−0.976628	−	0.214935i	$-0.931046\pi$
$569$	−18.1692	+	18.1692i	−0.761694	+	0.761694i	0.214935	+	0.976628i	$0.431046\pi$
$570$		0			0
$571$	10.7206	−	25.8818i	0.448643	−	1.08312i	−0.524187	−	0.851603i	$-0.675631\pi$
$571$	10.7206	−	25.8818i	0.448643	−	1.08312i	0.972831	−	0.231518i	$-0.0743692\pi$
$572$		0			0
$573$	3.81562	+	9.21172i	0.159400	+	0.384825i
$574$		0			0
$575$	7.63912	−	3.16423i	0.318573	−	0.131957i
$576$		0			0
$577$	11.8072			0.491538			0.245769	−	0.969328i	$-0.420959\pi$
$577$	11.8072			0.491538			0.245769	+	0.969328i	$0.420959\pi$
$578$		0			0
$579$	−3.73418			−0.155187
$580$		0			0
$581$	−0.309920	+	0.128373i	−0.0128576	+	0.00532581i
$582$		0			0
$583$	4.09040	+	9.87510i	0.169407	+	0.408985i
$584$		0			0
$585$	2.43528	−	5.87929i	0.100686	−	0.243079i
$586$		0			0
$587$	−5.26250	+	5.26250i	−0.217207	+	0.217207i	−0.807320	−	0.590114i	$-0.799083\pi$
$587$	−5.26250	+	5.26250i	−0.217207	+	0.217207i	0.590114	+	0.807320i	$0.299083\pi$
$588$		0			0
$589$	15.6481	+	6.48165i	0.644769	+	0.267072i
$590$		0			0
$591$		−	16.2053i		−	0.666598i
$592$		0			0
$593$	−5.41074	−	5.41074i	−0.222193	−	0.222193i	0.587229	−	0.809421i	$-0.300219\pi$
$593$	−5.41074	−	5.41074i	−0.222193	−	0.222193i	−0.809421	+	0.587229i	$0.800219\pi$
$594$		0			0
$595$	−0.310949	+	0.963641i	−0.0127477	+	0.0395054i
$596$		0			0
$597$	11.6485	+	11.6485i	0.476740	+	0.476740i
$598$		0			0
$599$		−	16.1547i		−	0.660062i	−0.943970	−	0.330031i	$-0.892941\pi$
$599$		−	16.1547i		−	0.660062i	0.943970	−	0.330031i	$-0.107059\pi$
$600$		0			0
$601$	−26.5316	−	10.9897i	−1.08225	−	0.448281i	−0.230949	−	0.972966i	$-0.574183\pi$
$601$	−26.5316	−	10.9897i	−1.08225	−	0.448281i	−0.851296	+	0.524685i	$0.824183\pi$
$602$		0			0
$603$	5.02734	−	5.02734i	0.204729	−	0.204729i
$604$		0			0
$605$	8.81166	−	21.2732i	0.358245	−	0.864880i
$606$		0			0
$607$	9.87815	+	23.8480i	0.400942	+	0.967959i	0.987438	+	0.158007i	$0.0505069\pi$
$607$	9.87815	+	23.8480i	0.400942	+	0.967959i	−0.586496	+	0.809952i	$0.699493\pi$
$608$		0			0
$609$	0.315433	−	0.130656i	0.0127820	−	0.00529447i
$610$		0			0
$611$	−38.7458			−1.56749
$612$		0			0
$613$	49.1769			1.98623			0.993117	−	0.117123i	$-0.0373670\pi$
$613$	49.1769			1.98623			0.993117	+	0.117123i	$0.0373670\pi$
$614$		0			0
$615$	−0.412478	+	0.170854i	−0.0166327	+	0.00688949i
$616$		0			0
$617$	1.35880	+	3.28044i	0.0547034	+	0.132066i	0.948868	−	0.315672i	$-0.102230\pi$
$617$	1.35880	+	3.28044i	0.0547034	+	0.132066i	−0.894165	+	0.447738i	$0.852230\pi$
$618$		0			0
$619$	13.4709	−	32.5216i	0.541440	−	1.30715i	−0.382266	−	0.924052i	$-0.624856\pi$
$619$	13.4709	−	32.5216i	0.541440	−	1.30715i	0.923707	−	0.383101i	$-0.125144\pi$
$620$		0			0
$621$	−2.43835	+	2.43835i	−0.0978474	+	0.0978474i
$622$		0			0
$623$	1.07578	+	0.445601i	0.0431000	+	0.0178526i
$624$		0			0
$625$			7.26131i			0.290453i
$626$		0			0
$627$	23.3875	+	23.3875i	0.934005	+	0.934005i
$628$		0			0
$629$	−3.54259	−	43.8763i	−0.141252	−	1.74946i
$630$		0			0
$631$	22.2124	+	22.2124i	0.884262	+	0.884262i	0.993964	−	0.109702i	$-0.0349898\pi$
$631$	22.2124	+	22.2124i	0.884262	+	0.884262i	−0.109702	+	0.993964i	$0.534990\pi$
$632$		0			0
$633$			10.6887i			0.424839i
$634$		0			0
$635$	18.1540	+	7.51964i	0.720420	+	0.298408i
$636$		0			0
$637$	−19.4618	+	19.4618i	−0.771106	+	0.771106i
$638$		0			0
$639$	−2.50548	+	6.04875i	−0.0991151	+	0.239285i
$640$		0			0
$641$	10.1700	+	24.5525i	0.401691	+	0.969767i	0.987256	+	0.159141i	$0.0508726\pi$
$641$	10.1700	+	24.5525i	0.401691	+	0.969767i	−0.585565	+	0.810625i	$0.699127\pi$
$642$		0			0
$643$	14.8049	−	6.13238i	0.583847	−	0.241837i	−0.0711538	−	0.997465i	$-0.522668\pi$
$643$	14.8049	−	6.13238i	0.583847	−	0.241837i	0.655001	+	0.755628i	$0.272668\pi$
$644$		0			0
$645$	−10.2317			−0.402872
$646$		0			0
$647$	−41.6554			−1.63764			−0.818822	−	0.574048i	$-0.805372\pi$
$647$	−41.6554			−1.63764			−0.818822	+	0.574048i	$0.805372\pi$
$648$		0			0
$649$	−6.14866	+	2.54686i	−0.241356	+	0.0999729i
$650$		0			0
$651$	−0.149988	−	0.362104i	−0.00587851	−	0.0141920i
$652$		0			0
$653$	−4.71711	+	11.3881i	−0.184595	+	0.445652i	−0.988903	−	0.148560i	$-0.952536\pi$
$653$	−4.71711	+	11.3881i	−0.184595	+	0.445652i	0.804308	+	0.594212i	$0.202536\pi$
$654$		0			0
$655$	11.9211	−	11.9211i	0.465797	−	0.465797i
$656$		0			0
$657$	7.69258	+	3.18637i	0.300116	+	0.124312i
$658$		0			0
$659$			3.46449i			0.134957i	0.997721	+	0.0674786i	$0.0214955\pi$
$659$			3.46449i			0.134957i	−0.997721	+	0.0674786i	$0.978505\pi$
$660$		0			0
$661$	20.0276	+	20.0276i	0.778984	+	0.778984i	0.979658	−	0.200674i	$-0.0643134\pi$
$661$	20.0276	+	20.0276i	0.778984	+	0.778984i	−0.200674	+	0.979658i	$0.564313\pi$
$662$		0			0
$663$	16.2127	−	1.30902i	0.629648	−	0.0508380i
$664$		0			0
$665$	1.14247	+	1.14247i	0.0443031	+	0.0443031i
$666$		0			0
$667$			7.73339i			0.299438i
$668$		0			0
$669$	5.00419	+	2.07280i	0.193473	+	0.0801392i
$670$		0			0
$671$	29.4285	−	29.4285i	1.13607	−	1.13607i
$672$		0			0
$673$	10.8715	−	26.2461i	0.419065	−	1.01171i	−0.563554	−	0.826079i	$-0.690566\pi$
$673$	10.8715	−	26.2461i	0.419065	−	1.01171i	0.982619	−	0.185634i	$-0.0594338\pi$
$674$		0			0
$675$	0.917608	+	2.21530i	0.0353187	+	0.0852670i
$676$		0			0
$677$	17.8293	−	7.38512i	0.685234	−	0.283833i	−0.0127789	−	0.999918i	$-0.504068\pi$
$677$	17.8293	−	7.38512i	0.685234	−	0.283833i	0.698013	+	0.716085i	$0.254068\pi$
$678$		0			0
$679$	0.549032			0.0210699
$680$		0			0
$681$	−12.2987			−0.471286
$682$		0			0
$683$	−17.9965	+	7.45441i	−0.688618	+	0.285235i	−0.699424	−	0.714707i	$-0.746560\pi$
$683$	−17.9965	+	7.45441i	−0.688618	+	0.285235i	0.0108060	+	0.999942i	$0.496560\pi$
$684$		0			0
$685$	−8.32930	−	20.1087i	−0.318246	−	0.768315i
$686$		0			0
$687$	11.5248	−	27.8233i	0.439699	−	1.06153i
$688$		0			0
$689$	5.93081	−	5.93081i	0.225946	−	0.225946i
$690$		0			0
$691$	6.96550	+	2.88520i	0.264980	+	0.109758i	0.511218	−	0.859451i	$-0.329194\pi$
$691$	6.96550	+	2.88520i	0.264980	+	0.109758i	−0.246238	+	0.969209i	$0.579194\pi$
$692$		0			0
$693$		−	0.765367i		−	0.0290739i
$694$		0			0
$695$	−6.07737	−	6.07737i	−0.230528	−	0.230528i
$696$		0			0
$697$	−0.869234	−	0.739356i	−0.0329246	−	0.0280051i
$698$		0			0
$699$	6.21209	+	6.21209i	0.234963	+	0.234963i
$700$		0			0
$701$		−	39.0875i		−	1.47632i	−0.674628	−	0.738158i	$-0.735696\pi$
$701$		−	39.0875i		−	1.47632i	0.674628	−	0.738158i	$-0.264304\pi$
$702$		0			0
$703$	−64.8920	−	26.8792i	−2.44745	−	1.01377i
$704$		0			0
$705$	−11.2031	+	11.2031i	−0.421932	+	0.421932i
$706$		0			0
$707$	0.532327	−	1.28515i	0.0200202	−	0.0483330i
$708$		0			0
$709$	−2.56889	−	6.20186i	−0.0964768	−	0.232916i	0.868272	−	0.496089i	$-0.165231\pi$
$709$	−2.56889	−	6.20186i	−0.0964768	−	0.232916i	−0.964749	+	0.263173i	$0.915231\pi$
$710$		0			0
$711$	−0.491806	+	0.203713i	−0.0184442	+	0.00763982i
$712$		0			0
$713$	8.87762			0.332470
$714$		0			0
$715$	−31.9925			−1.19645
$716$		0			0
$717$	13.5349	−	5.60634i	0.505470	−	0.209373i
$718$		0			0
$719$	−2.83424	−	6.84246i	−0.105699	−	0.255181i	0.862177	−	0.506607i	$-0.169100\pi$
$719$	−2.83424	−	6.84246i	−0.105699	−	0.255181i	−0.967876	+	0.251426i	$0.919100\pi$
$720$		0			0
$721$	0.441531	−	1.06595i	0.0164435	−	0.0396981i
$722$		0			0
$723$	−11.9892	+	11.9892i	−0.445882	+	0.445882i
$724$		0			0
$725$	4.96812	+	2.05786i	0.184512	+	0.0764272i
$726$		0			0
$727$		−	6.36054i		−	0.235899i	−0.993020	−	0.117950i	$-0.962368\pi$
$727$		−	6.36054i		−	0.235899i	0.993020	−	0.117950i	$-0.0376322\pi$
$728$		0			0
$729$	−0.707107	−	0.707107i	−0.0261891	−	0.0261891i
$730$		0			0
$731$	−11.9199	−	23.2774i	−0.440874	−	0.860947i
$732$		0			0
$733$	−29.2273	−	29.2273i	−1.07954	−	1.07954i	−0.996551	−	0.0829857i	$-0.973554\pi$
$733$	−29.2273	−	29.2273i	−1.07954	−	1.07954i	−0.0829857	−	0.996551i	$-0.526446\pi$
$734$		0			0
$735$			11.2545i			0.415128i
$736$		0			0
$737$	−33.0223	−	13.6783i	−1.21639	−	0.503845i
$738$		0			0
$739$	16.3803	−	16.3803i	0.602561	−	0.602561i	−0.338430	−	0.940991i	$-0.609896\pi$
$739$	16.3803	−	16.3803i	0.602561	−	0.602561i	0.940991	+	0.338430i	$0.109896\pi$
$740$		0			0
$741$	9.93209	−	23.9782i	0.364864	−	0.880861i
$742$		0			0
$743$	14.5995	+	35.2464i	0.535606	+	1.29307i	0.927764	+	0.373168i	$0.121729\pi$
$743$	14.5995	+	35.2464i	0.535606	+	1.29307i	−0.392158	+	0.919898i	$0.628271\pi$
$744$		0			0
$745$	−13.8883	+	5.75271i	−0.508827	+	0.210763i
$746$		0			0
$747$	2.20345			0.0806200
$748$		0			0
$749$	2.81138			0.102726
$750$		0			0
$751$	31.6034	−	13.0906i	1.15322	−	0.477681i	0.277611	−	0.960694i	$-0.410457\pi$
$751$	31.6034	−	13.0906i	1.15322	−	0.477681i	0.875613	+	0.483013i	$0.160457\pi$
$752$		0			0
$753$	5.33662	+	12.8837i	0.194477	+	0.469510i
$754$		0			0
$755$	7.38511	−	17.8292i	0.268772	−	0.648872i
$756$		0			0
$757$	−4.96523	+	4.96523i	−0.180465	+	0.180465i	−0.791558	−	0.611094i	$-0.790730\pi$
$757$	−4.96523	+	4.96523i	−0.180465	+	0.180465i	0.611094	+	0.791558i	$0.290730\pi$
$758$		0			0
$759$	16.0164	+	6.63419i	0.581357	+	0.240806i
$760$		0			0
$761$		−	47.2917i		−	1.71432i	−0.515048	−	0.857161i	$-0.672226\pi$
$761$		−	47.2917i		−	1.71432i	0.515048	−	0.857161i	$-0.327774\pi$
$762$		0			0
$763$	1.15609	+	1.15609i	0.0418531	+	0.0418531i
$764$		0			0
$765$	4.30928	−	5.06627i	0.155802	−	0.183171i
$766$		0			0
$767$	3.69278	+	3.69278i	0.133338	+	0.133338i
$768$		0			0
$769$			6.39156i			0.230486i	0.993337	+	0.115243i	$0.0367646\pi$
$769$			6.39156i			0.230486i	−0.993337	+	0.115243i	$0.963235\pi$
$770$		0			0
$771$	−18.1638	−	7.52368i	−0.654152	−	0.270959i
$772$		0			0
$773$	−2.60024	+	2.60024i	−0.0935241	+	0.0935241i	−0.752321	−	0.658797i	$-0.771066\pi$
$773$	−2.60024	+	2.60024i	−0.0935241	+	0.0935241i	0.658797	+	0.752321i	$0.271066\pi$
$774$		0			0
$775$	2.36235	−	5.70321i	0.0848580	−	0.204865i
$776$		0			0
$777$	0.621995	+	1.50163i	0.0223140	+	0.0538707i
$778$		0			0
$779$	−1.68226	+	0.696813i	−0.0602731	+	0.0249659i
$780$		0			0
$781$	32.9146			1.17778
$782$		0			0
$783$	−2.24264			−0.0801454
$784$		0			0
$785$	−27.0567	+	11.2073i	−0.965696	+	0.400004i
$786$		0			0
$787$	1.55526	+	3.75473i	0.0554391	+	0.133842i	0.949172	−	0.314757i	$-0.101923\pi$
$787$	1.55526	+	3.75473i	0.0554391	+	0.133842i	−0.893733	+	0.448599i	$0.851923\pi$
$788$		0			0
$789$	10.6662	−	25.7505i	0.379726	−	0.916741i
$790$		0			0
$791$	−0.180311	+	0.180311i	−0.00641113	+	0.00641113i
$792$		0			0
$793$	−30.1718	−	12.4976i	−1.07143	−	0.443801i
$794$		0			0
$795$		−	3.42970i		−	0.121639i
$796$		0			0
$797$	9.76205	+	9.76205i	0.345790	+	0.345790i	0.858539	−	0.512749i	$-0.171373\pi$
$797$	9.76205	+	9.76205i	0.345790	+	0.345790i	−0.512749	+	0.858539i	$0.671373\pi$
$798$		0			0
$799$	−38.5389	−	12.4358i	−1.36341	−	0.439947i
$800$		0			0
$801$	−5.40829	−	5.40829i	−0.191092	−	0.191092i
$802$		0			0
$803$		−	41.8596i		−	1.47719i
$804$		0			0
$805$	0.782394	+	0.324078i	0.0275758	+	0.0114223i
$806$		0			0
$807$	−0.145188	+	0.145188i	−0.00511087	+	0.00511087i
$808$		0			0
$809$	7.21319	−	17.4142i	0.253602	−	0.612250i	−0.744887	−	0.667190i	$-0.767497\pi$
$809$	7.21319	−	17.4142i	0.253602	−	0.612250i	0.998490	+	0.0549401i	$0.0174968\pi$
$810$		0			0
$811$	0.994804	+	2.40167i	0.0349323	+	0.0843340i	0.940383	−	0.340118i	$-0.110467\pi$
$811$	0.994804	+	2.40167i	0.0349323	+	0.0843340i	−0.905451	+	0.424452i	$0.860467\pi$
$812$		0			0
$813$	7.58576	−	3.14212i	0.266044	−	0.110199i
$814$		0			0
$815$	33.4280			1.17093
$816$		0			0
$817$	−41.7291			−1.45992
$818$		0			0
$819$	−0.554866	+	0.229833i	−0.0193886	+	0.00803101i
$820$		0			0
$821$	4.97770	+	12.0172i	0.173723	+	0.419404i	0.986627	−	0.162993i	$-0.0521149\pi$
$821$	4.97770	+	12.0172i	0.173723	+	0.419404i	−0.812904	+	0.582397i	$0.802115\pi$
$822$		0			0
$823$	8.28676	−	20.0060i	0.288858	−	0.697366i	−0.711125	−	0.703065i	$-0.751814\pi$
$823$	8.28676	−	20.0060i	0.288858	−	0.697366i	0.999984	+	0.00569929i	$0.00181415\pi$
$824$		0			0
$825$	8.52395	−	8.52395i	0.296766	−	0.296766i
$826$		0			0
$827$	44.2300	+	18.3207i	1.53803	+	0.637072i	0.981102	−	0.193490i	$-0.0619807\pi$
$827$	44.2300	+	18.3207i	1.53803	+	0.637072i	0.556926	+	0.830562i	$0.311981\pi$
$828$		0			0
$829$		−	12.9906i		−	0.451181i	−0.974222	−	0.225590i	$-0.927569\pi$
$829$		−	12.9906i		−	0.451181i	0.974222	−	0.225590i	$-0.0724311\pi$
$830$		0			0
$831$	−16.6649	−	16.6649i	−0.578098	−	0.578098i
$832$		0			0
$833$	−25.6043	+	13.1115i	−0.887138	+	0.454285i
$834$		0			0
$835$	−9.22652	−	9.22652i	−0.319297	−	0.319297i
$836$		0			0
$837$			2.57446i			0.0889864i
$838$		0			0
$839$	−17.4361	−	7.22226i	−0.601961	−	0.249340i	0.0608263	−	0.998148i	$-0.480626\pi$
$839$	−17.4361	−	7.22226i	−0.601961	−	0.249340i	−0.662787	+	0.748808i	$0.730626\pi$
$840$		0			0
$841$	16.9497	−	16.9497i	0.584474	−	0.584474i
$842$		0			0
$843$	3.88547	−	9.38035i	0.133823	−	0.323076i
$844$		0			0
$845$	1.58194	+	3.81914i	0.0544204	+	0.131383i
$846$		0			0
$847$	−2.00769	+	0.831613i	−0.0689851	+	0.0285746i
$848$		0			0
$849$	−9.47918			−0.325325
$850$		0			0
$851$	−36.8151			−1.26201
$852$		0			0
$853$	5.57645	−	2.30984i	0.190934	−	0.0790875i	−0.285168	−	0.958478i	$-0.592049\pi$
$853$	5.57645	−	2.30984i	0.190934	−	0.0790875i	0.476102	+	0.879390i	$0.342049\pi$
$854$		0			0
$855$	−4.06132	−	9.80490i	−0.138894	−	0.335321i
$856$		0			0
$857$	6.15488	−	14.8592i	0.210247	−	0.507581i	−0.783214	−	0.621752i	$-0.786421\pi$
$857$	6.15488	−	14.8592i	0.210247	−	0.507581i	0.993461	+	0.114171i	$0.0364213\pi$
$858$		0			0
$859$	40.9101	−	40.9101i	1.39583	−	1.39583i	0.584285	−	0.811548i	$-0.301375\pi$
$859$	40.9101	−	40.9101i	1.39583	−	1.39583i	0.811548	−	0.584285i	$-0.198625\pi$
$860$		0			0
$861$	0.0389281	+	0.0161246i	0.00132667	+	0.000549524i
$862$		0			0
$863$		−	7.56067i		−	0.257368i	−0.991686	−	0.128684i	$-0.958925\pi$
$863$		−	7.56067i		−	0.257368i	0.991686	−	0.128684i	$-0.0410753\pi$
$864$		0			0
$865$	1.32387	+	1.32387i	0.0450128	+	0.0450128i
$866$		0			0
$867$	16.5462	+	3.90156i	0.561940	+	0.132504i
$868$		0			0
$869$	1.89235	+	1.89235i	0.0641936	+	0.0641936i
$870$		0			0
$871$			28.0475i			0.950354i
$872$		0			0
$873$	−3.33182	−	1.38009i	−0.112765	−	0.0467088i
$874$		0			0
$875$	1.28466	−	1.28466i	0.0434295	−	0.0434295i
$876$		0			0
$877$	6.64567	−	16.0441i	0.224408	−	0.541770i	−0.771071	−	0.636749i	$-0.780279\pi$
$877$	6.64567	−	16.0441i	0.224408	−	0.541770i	0.995479	+	0.0949797i	$0.0302786\pi$
$878$		0			0
$879$	−3.55327	−	8.57836i	−0.119849	−	0.289341i
$880$		0			0
$881$	37.9731	−	15.7290i	1.27935	−	0.529923i	0.363554	−	0.931573i	$-0.381563\pi$
$881$	37.9731	−	15.7290i	1.27935	−	0.529923i	0.915793	+	0.401650i	$0.131563\pi$
$882$		0			0
$883$	28.3729			0.954824			0.477412	−	0.878680i	$-0.341575\pi$
$883$	28.3729			0.954824			0.477412	+	0.878680i	$0.341575\pi$
$884$		0			0
$885$	2.13548			0.0717833
$886$		0			0
$887$	19.8638	−	8.22786i	0.666961	−	0.276264i	−0.0234033	−	0.999726i	$-0.507450\pi$
$887$	19.8638	−	8.22786i	0.666961	−	0.276264i	0.690364	+	0.723462i	$0.257450\pi$
$888$		0			0
$889$	−0.709676	−	1.71331i	−0.0238018	−	0.0574626i
$890$		0			0
$891$	−1.92388	+	4.64466i	−0.0644524	+	0.155602i
$892$		0			0
$893$	−45.6908	+	45.6908i	−1.52898	+	1.52898i
$894$		0			0
$895$	4.31703	+	1.78817i	0.144302	+	0.0597719i
$896$		0			0
$897$		−	13.6035i		−	0.454208i
$898$		0			0
$899$	4.08255	+	4.08255i	0.136161	+	0.136161i
$900$		0			0
$901$	7.80268	−	3.99560i	0.259945	−	0.133113i
$902$		0			0
$903$	0.682803	+	0.682803i	0.0227223	+	0.0227223i
$904$		0			0
$905$		−	1.35937i		−	0.0451871i
$906$		0			0
$907$	13.6798	+	5.66635i	0.454229	+	0.188148i	0.598055	−	0.801455i	$-0.295940\pi$
$907$	13.6798	+	5.66635i	0.454229	+	0.188148i	−0.143826	+	0.989603i	$0.545940\pi$
$908$		0			0
$909$	−6.46088	+	6.46088i	−0.214294	+	0.214294i
$910$		0			0
$911$	−18.1855	+	43.9036i	−0.602512	+	1.45459i	0.268475	+	0.963287i	$0.413480\pi$
$911$	−18.1855	+	43.9036i	−0.602512	+	1.45459i	−0.870987	+	0.491306i	$0.836520\pi$
$912$		0			0
$913$	−4.23917	−	10.2343i	−0.140296	−	0.338705i
$914$		0			0
$915$	−12.3375	+	5.11037i	−0.407866	+	0.168944i
$916$		0			0
$917$	−1.59109			−0.0525425
$918$		0			0
$919$	52.4090			1.72881			0.864407	−	0.502793i	$-0.167694\pi$
$919$	52.4090			1.72881			0.864407	+	0.502793i	$0.167694\pi$
$920$		0			0
$921$	−25.0757	+	10.3867i	−0.826273	+	0.342253i
$922$		0			0
$923$	−9.88397	−	23.8620i	−0.325335	−	0.785428i
$924$		0			0
$925$	−9.79655	+	23.6510i	−0.322109	+	0.777639i
$926$		0			0
$927$	−5.35890	+	5.35890i	−0.176009	+	0.176009i
$928$		0			0
$929$	42.4038	+	17.5642i	1.39122	+	0.576263i	0.947458	−	0.319880i	$-0.103643\pi$
$929$	42.4038	+	17.5642i	1.39122	+	0.576263i	0.443764	+	0.896143i	$0.353643\pi$
$930$		0			0
$931$			45.9005i			1.50433i
$932$		0			0
$933$	−1.82843	−	1.82843i	−0.0598600	−	0.0598600i
$934$		0			0
$935$	−31.8216	−	10.2682i	−1.04068	−	0.335807i
$936$		0			0
$937$	15.3852	+	15.3852i	0.502611	+	0.502611i	0.912248	−	0.409637i	$-0.134345\pi$
$937$	15.3852	+	15.3852i	0.502611	+	0.502611i	−0.409637	+	0.912248i	$0.634345\pi$
$938$		0			0
$939$			25.6105i			0.835767i
$940$		0			0
$941$	49.9839	+	20.7040i	1.62943	+	0.674932i	0.995168	−	0.0981874i	$-0.0313045\pi$
$941$	49.9839	+	20.7040i	1.62943	+	0.674932i	0.634261	+	0.773119i	$0.281304\pi$
$942$		0			0
$943$	−0.674858	+	0.674858i	−0.0219764	+	0.0219764i
$944$		0			0
$945$	−0.0939809	+	0.226890i	−0.00305720	+	0.00738073i
$946$		0			0
$947$	−2.21041	−	5.33640i	−0.0718286	−	0.173410i	0.883888	−	0.467699i	$-0.154917\pi$
$947$	−2.21041	−	5.33640i	−0.0718286	−	0.173410i	−0.955716	+	0.294290i	$0.904917\pi$
$948$		0			0
$949$	−30.3468	+	12.5701i	−0.985099	+	0.408041i
$950$		0			0
$951$	−25.5982			−0.830078
$952$		0			0
$953$	−31.4698			−1.01941			−0.509704	−	0.860350i	$-0.670245\pi$
$953$	−31.4698			−1.01941			−0.509704	+	0.860350i	$0.670245\pi$
$954$		0			0
$955$	−14.8597	+	6.15507i	−0.480847	+	0.199174i
$956$		0			0
$957$	4.31457	+	10.4163i	0.139470	+	0.336711i
$958$		0			0
$959$	−0.786089	+	1.89779i	−0.0253841	+	0.0612828i
$960$		0			0
$961$	−17.2337	+	17.2337i	−0.555926	+	0.555926i
$962$		0			0
$963$	−17.0610	−	7.06688i	−0.549781	−	0.227727i
$964$		0			0
$965$		−	6.02371i		−	0.193910i
$966$		0			0
$967$	−4.11626	−	4.11626i	−0.132370	−	0.132370i	0.637818	−	0.770187i	$-0.279837\pi$
$967$	−4.11626	−	4.11626i	−0.132370	−	0.132370i	−0.770187	+	0.637818i	$0.779837\pi$
$968$		0			0
$969$	17.5750	−	20.6623i	0.564592	−	0.663770i
$970$		0			0
$971$	−15.4891	−	15.4891i	−0.497070	−	0.497070i	0.413455	−	0.910525i	$-0.364322\pi$
$971$	−15.4891	−	15.4891i	−0.497070	−	0.497070i	−0.910525	+	0.413455i	$0.864322\pi$
$972$		0			0
$973$			0.811136i			0.0260038i
$974$		0			0
$975$	−8.73925	−	3.61991i	−0.279880	−	0.115930i
$976$		0			0
$977$	19.8324	−	19.8324i	0.634495	−	0.634495i	−0.314697	−	0.949192i	$-0.601903\pi$
$977$	19.8324	−	19.8324i	0.634495	−	0.634495i	0.949192	+	0.314697i	$0.101903\pi$
$978$		0			0
$979$	−14.7147	+	35.5245i	−0.470285	+	1.13537i
$980$		0			0
$981$	−4.10973	−	9.92177i	−0.131214	−	0.316778i
$982$		0			0
$983$	28.9425	−	11.9884i	0.923121	−	0.382369i	0.130056	−	0.991507i	$-0.458484\pi$
$983$	28.9425	−	11.9884i	0.923121	−	0.382369i	0.793065	+	0.609137i	$0.208484\pi$
$984$		0			0
$985$	26.1412			0.832929
$986$		0			0
$987$	1.49526			0.0475945
$988$		0			0
$989$	−20.2071	+	8.37007i	−0.642549	+	0.266153i
$990$		0			0
$991$	−6.88802	−	16.6291i	−0.218805	−	0.528242i	0.775919	−	0.630833i	$-0.217287\pi$
$991$	−6.88802	−	16.6291i	−0.218805	−	0.528242i	−0.994724	+	0.102591i	$0.967287\pi$
$992$		0			0
$993$	0.127499	−	0.307810i	0.00404607	−	0.00976807i
$994$		0			0
$995$	−18.7905	+	18.7905i	−0.595697	+	0.595697i
$996$		0			0
$997$	51.3369	+	21.2644i	1.62586	+	0.673451i	0.994758	−	0.102253i	$-0.0326050\pi$
$997$	51.3369	+	21.2644i	1.62586	+	0.673451i	0.631097	+	0.775704i	$0.282605\pi$
$998$		0			0
$999$		−	10.6762i		−	0.337780i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	816.2.bq.a.529.1		8
4.3	odd	2		51.2.h.a.19.1	✓	8
12.11	even	2		153.2.l.e.19.2		8
17.9	even	8	inner	816.2.bq.a.145.1		8
68.3	even	16		867.2.a.n.1.1		4
68.7	even	16		867.2.e.h.829.4		8
68.11	even	16		867.2.e.h.616.1		8
68.15	odd	8		867.2.h.b.688.2		8
68.19	odd	8		867.2.h.f.688.2		8
68.23	even	16		867.2.e.i.616.1		8
68.27	even	16		867.2.e.i.829.4		8
68.31	even	16		867.2.a.m.1.1		4
68.39	even	16		867.2.d.e.577.8		8
68.43	odd	8		51.2.h.a.43.1	yes	8
68.47	odd	4		867.2.h.f.712.2		8
68.55	odd	4		867.2.h.b.712.2		8
68.59	odd	8		867.2.h.g.757.1		8
68.63	even	16		867.2.d.e.577.7		8
68.67	odd	2		867.2.h.g.733.1		8
204.71	odd	16		2601.2.a.bd.1.4		4
204.167	odd	16		2601.2.a.bc.1.4		4
204.179	even	8		153.2.l.e.145.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.h.a.19.1	✓	8	4.3	odd	2
51.2.h.a.43.1	yes	8	68.43	odd	8
153.2.l.e.19.2		8	12.11	even	2
153.2.l.e.145.2		8	204.179	even	8
816.2.bq.a.145.1		8	17.9	even	8	inner
816.2.bq.a.529.1		8	1.1	even	1	trivial
867.2.a.m.1.1		4	68.31	even	16
867.2.a.n.1.1		4	68.3	even	16
867.2.d.e.577.7		8	68.63	even	16
867.2.d.e.577.8		8	68.39	even	16
867.2.e.h.616.1		8	68.11	even	16
867.2.e.h.829.4		8	68.7	even	16
867.2.e.i.616.1		8	68.23	even	16
867.2.e.i.829.4		8	68.27	even	16
867.2.h.b.688.2		8	68.15	odd	8
867.2.h.b.712.2		8	68.55	odd	4
867.2.h.f.688.2		8	68.19	odd	8
867.2.h.f.712.2		8	68.47	odd	4
867.2.h.g.733.1		8	68.67	odd	2
867.2.h.g.757.1		8	68.59	odd	8
2601.2.a.bc.1.4		4	204.167	odd	16
2601.2.a.bd.1.4		4	204.71	odd	16

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:	\( N \)	\(=\)	\( 816 = 2^{4} \cdot 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	816.bq (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.923880 + 0.382683i) q^{3} +(-0.617317 - 1.49033i) q^{5} +(-0.0582601 + 0.140652i) q^{7} +(0.707107 - 0.707107i) q^{9} +(-4.64466 - 1.92388i) q^{11} +3.94495i q^{13} +(1.14065 + 1.14065i) q^{15} +(-1.26616 + 3.92388i) q^{17} +(4.65205 + 4.65205i) q^{19} -0.152241i q^{21} +(3.18585 + 1.31962i) q^{23} +(1.69552 - 1.69552i) q^{25} +(-0.382683 + 0.923880i) q^{27} +(0.858221 + 2.07193i) q^{29} +(2.37849 - 0.985204i) q^{31} +5.02734 q^{33} +0.245584 q^{35} +(-9.86351 + 4.08560i) q^{37} +(-1.50967 - 3.64466i) q^{39} +(-0.105915 + 0.255701i) q^{41} +(-4.48502 + 4.48502i) q^{43} +(-1.49033 - 0.617317i) q^{45} +9.82164i q^{47} +(4.93336 + 4.93336i) q^{49} +(-0.331821 - 4.10973i) q^{51} +(-1.50339 - 1.50339i) q^{53} +8.10973i q^{55} +(-6.07820 - 2.51767i) q^{57} +(0.936078 - 0.936078i) q^{59} +(-3.16799 + 7.64821i) q^{61} +(0.0582601 + 0.140652i) q^{63} +(5.87929 - 2.43528i) q^{65} +7.10973 q^{67} -3.44834 q^{69} +(-6.04875 + 2.50548i) q^{71} +(3.18637 + 7.69258i) q^{73} +(-0.917608 + 2.21530i) q^{75} +(0.541196 - 0.541196i) q^{77} +(-0.491806 - 0.203713i) q^{79} -1.00000i q^{81} +(1.55807 + 1.55807i) q^{83} +(6.62951 - 0.535270i) q^{85} +(-1.58579 - 1.58579i) q^{87} -7.64847i q^{89} +(-0.554866 - 0.229833i) q^{91} +(-1.82042 + 1.82042i) q^{93} +(4.06132 - 9.80490i) q^{95} +(-1.38009 - 3.33182i) q^{97} +(-4.64466 + 1.92388i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{5} - 8 q^{11} - 8 q^{17} + 8 q^{19} - 8 q^{23} - 16 q^{25} - 8 q^{31} + 8 q^{33} - 32 q^{35} - 8 q^{37} - 16 q^{39} - 24 q^{41} + 8 q^{43} - 8 q^{45} - 8 q^{49} - 32 q^{53} - 16 q^{57} - 16 q^{59}+ \cdots - 8 q^{99}+O(q^{100}) \) 8 * q - 8 * q^5 - 8 * q^11 - 8 * q^17 + 8 * q^19 - 8 * q^23 - 16 * q^25 - 8 * q^31 + 8 * q^33 - 32 * q^35 - 8 * q^37 - 16 * q^39 - 24 * q^41 + 8 * q^43 - 8 * q^45 - 8 * q^49 - 32 * q^53 - 16 * q^57 - 16 * q^59 + 16 * q^61 + 24 * q^65 + 16 * q^67 - 24 * q^69 + 16 * q^71 + 48 * q^73 - 16 * q^75 - 32 * q^83 + 40 * q^85 - 24 * q^87 + 16 * q^91 - 32 * q^93 + 40 * q^95 + 8 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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