LMFDB - Embedded newform 867.2.e.i.829.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [867,2,Mod(616,867)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(867, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([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("867.616"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 867 = 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	867.e (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,0,0,0,0,0,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$6.92302985525$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
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:	$ 2 $
Twist minimal:	no (minimal twist has level 51)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			829.4
Root			$0.923880 + 0.382683i$ of defining polynomial
Character	$\chi$	$=$	867.829
Dual form			867.2.e.i.616.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.84776i q^{2} +(0.707107 + 0.707107i) q^{3} -1.41421 q^{4} +(-1.14065 - 1.14065i) q^{5} +(-1.30656 + 1.30656i) q^{6} +(0.107651 - 0.107651i) q^{7} +1.08239i q^{8} +1.00000i q^{9} +(2.10765 - 2.10765i) q^{10} +(-3.55487 + 3.55487i) q^{11} +(-1.00000 - 1.00000i) q^{12} +3.94495 q^{13} +(0.198912 + 0.198912i) q^{14} -1.61313i q^{15} -4.82843 q^{16} -1.84776 q^{18} +6.57900i q^{19} +(1.61313 + 1.61313i) q^{20} +0.152241 q^{21} +(-6.56854 - 6.56854i) q^{22} +(-2.43835 + 2.43835i) q^{23} +(-0.765367 + 0.765367i) q^{24} -2.39782i q^{25} +7.28931i q^{26} +(-0.707107 + 0.707107i) q^{27} +(-0.152241 + 0.152241i) q^{28} +(-1.58579 - 1.58579i) q^{29} +2.98067 q^{30} +(1.82042 + 1.82042i) q^{31} -6.75699i q^{32} -5.02734 q^{33} -0.245584 q^{35} -1.41421i q^{36} +(-7.54920 - 7.54920i) q^{37} -12.1564 q^{38} +(2.78950 + 2.78950i) q^{39} +(1.23463 - 1.23463i) q^{40} +(-0.195705 + 0.195705i) q^{41} +0.281305i q^{42} +6.34277i q^{43} +(5.02734 - 5.02734i) q^{44} +(1.14065 - 1.14065i) q^{45} +(-4.50548 - 4.50548i) q^{46} -9.82164 q^{47} +(-3.41421 - 3.41421i) q^{48} +6.97682i q^{49} +4.43060 q^{50} -5.57900 q^{52} +2.12612i q^{53} +(-1.30656 - 1.30656i) q^{54} +8.10973 q^{55} +(0.116520 + 0.116520i) q^{56} +(-4.65205 + 4.65205i) q^{57} +(2.93015 - 2.93015i) q^{58} +1.32381i q^{59} +2.28130i q^{60} +(5.85369 - 5.85369i) q^{61} +(-3.36370 + 3.36370i) q^{62} +(0.107651 + 0.107651i) q^{63} +2.82843 q^{64} +(-4.49981 - 4.49981i) q^{65} -9.28931i q^{66} +7.10973 q^{67} -3.44834 q^{69} -0.453780i q^{70} +(4.62951 + 4.62951i) q^{71} -1.08239 q^{72} +(5.88764 + 5.88764i) q^{73} +(13.9491 - 13.9491i) q^{74} +(1.69552 - 1.69552i) q^{75} -9.30411i q^{76} +0.765367i q^{77} +(-5.15432 + 5.15432i) q^{78} +(-0.376412 + 0.376412i) q^{79} +(5.50756 + 5.50756i) q^{80} -1.00000 q^{81} +(-0.361616 - 0.361616i) q^{82} -2.20345i q^{83} -0.215301 q^{84} -11.7199 q^{86} -2.24264i q^{87} +(-3.84776 - 3.84776i) q^{88} +7.64847 q^{89} +(2.10765 + 2.10765i) q^{90} +(0.424676 - 0.424676i) q^{91} +(3.44834 - 3.44834i) q^{92} +2.57446i q^{93} -18.1480i q^{94} +(7.50435 - 7.50435i) q^{95} +(4.77791 - 4.77791i) q^{96} +(2.55007 + 2.55007i) q^{97} -12.8915 q^{98} +(-3.55487 - 3.55487i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 16 q^{10} - 8 q^{11} - 8 q^{12} + 8 q^{13} - 8 q^{14} - 16 q^{16} - 8 q^{20} + 16 q^{21} - 16 q^{22} - 16 q^{28} - 24 q^{29} + 16 q^{30} + 32 q^{31} - 8 q^{33} + 32 q^{35} - 16 q^{37} - 32 q^{38}+ \cdots - 8 q^{99}+O(q^{100}) $ 8 * q + 16 * q^10 - 8 * q^11 - 8 * q^12 + 8 * q^13 - 8 * q^14 - 16 * q^16 - 8 * q^20 + 16 * q^21 - 16 * q^22 - 16 * q^28 - 24 * q^29 + 16 * q^30 + 32 * q^31 - 8 * q^33 + 32 * q^35 - 16 * q^37 - 32 * q^38 + 8 * q^39 + 16 * q^40 - 16 * q^41 + 8 * q^44 - 16 * q^46 - 16 * q^47 - 16 * q^48 + 32 * q^50 - 16 * q^52 + 24 * q^55 - 8 * q^57 + 32 * q^61 + 8 * q^65 + 16 * q^67 - 24 * q^69 + 24 * q^71 - 32 * q^73 + 8 * q^74 - 16 * q^75 - 16 * q^78 - 16 * q^79 - 16 * q^80 - 8 * q^81 - 16 * q^82 - 32 * q^86 - 16 * q^88 - 32 * q^89 + 16 * q^90 + 24 * q^92 + 24 * q^95 + 16 * q^97 - 64 * q^98 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/867\mathbb{Z}\right)^\times$.

$n$	$290$	$292$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$			1.84776i			1.30656i	0.757115	+	0.653281i	$0.226608\pi$
$2$			1.84776i			1.30656i	−0.757115	+	0.653281i	$0.773392\pi$
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$	−1.41421			−0.707107
$5$	−1.14065	−	1.14065i	−0.510115	−	0.510115i	0.404446	−	0.914562i	$-0.367464\pi$
$5$	−1.14065	−	1.14065i	−0.510115	−	0.510115i	−0.914562	+	0.404446i	$0.867464\pi$
$6$	−1.30656	+	1.30656i	−0.533402	+	0.533402i
$7$	0.107651	−	0.107651i	0.0406881	−	0.0406881i	−0.686470	−	0.727158i	$-0.740841\pi$
$7$	0.107651	−	0.107651i	0.0406881	−	0.0406881i	0.727158	+	0.686470i	$0.240841\pi$
$8$			1.08239i			0.382683i
$9$			1.00000i			0.333333i
$10$	2.10765	−	2.10765i	0.666498	−	0.666498i
$11$	−3.55487	+	3.55487i	−1.07183	+	1.07183i	−0.0746204	+	0.997212i	$0.523774\pi$
$11$	−3.55487	+	3.55487i	−1.07183	+	1.07183i	−0.997212	+	0.0746204i	$0.976226\pi$
$12$	−1.00000	−	1.00000i	−0.288675	−	0.288675i
$13$	3.94495			1.09413			0.547066	−	0.837090i	$-0.315745\pi$
$13$	3.94495			1.09413			0.547066	+	0.837090i	$0.315745\pi$
$14$	0.198912	+	0.198912i	0.0531616	+	0.0531616i
$15$		−	1.61313i		−	0.416507i
$16$	−4.82843			−1.20711
$17$		0			0
$17$		0			0
$18$	−1.84776			−0.435521
$19$			6.57900i			1.50933i	0.656113	+	0.754663i	$0.272200\pi$
$19$			6.57900i			1.50933i	−0.656113	+	0.754663i	$0.727800\pi$
$20$	1.61313	+	1.61313i	0.360706	+	0.360706i
$21$	0.152241			0.0332217
$22$	−6.56854	−	6.56854i	−1.40042	−	1.40042i
$23$	−2.43835	+	2.43835i	−0.508430	+	0.508430i	−0.914044	−	0.405614i	$-0.867058\pi$
$23$	−2.43835	+	2.43835i	−0.508430	+	0.508430i	0.405614	+	0.914044i	$0.367058\pi$
$24$	−0.765367	+	0.765367i	−0.156230	+	0.156230i
$25$		−	2.39782i		−	0.479565i
$26$			7.28931i			1.42955i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−0.152241	+	0.152241i	−0.0287708	+	0.0287708i
$29$	−1.58579	−	1.58579i	−0.294473	−	0.294473i	0.544371	−	0.838844i	$-0.316768\pi$
$29$	−1.58579	−	1.58579i	−0.294473	−	0.294473i	−0.838844	+	0.544371i	$0.816768\pi$
$30$	2.98067			0.544193
$31$	1.82042	+	1.82042i	0.326957	+	0.326957i	0.851428	−	0.524471i	$-0.175737\pi$
$31$	1.82042	+	1.82042i	0.326957	+	0.326957i	−0.524471	+	0.851428i	$0.675737\pi$
$32$		−	6.75699i		−	1.19448i
$33$	−5.02734			−0.875147
$34$		0			0
$35$	−0.245584			−0.0415112
$36$		−	1.41421i		−	0.235702i
$37$	−7.54920	−	7.54920i	−1.24108	−	1.24108i	−0.959553	−	0.281529i	$-0.909159\pi$
$37$	−7.54920	−	7.54920i	−1.24108	−	1.24108i	−0.281529	−	0.959553i	$-0.590841\pi$
$38$	−12.1564			−1.97203
$39$	2.78950	+	2.78950i	0.446677	+	0.446677i
$40$	1.23463	−	1.23463i	0.195213	−	0.195213i
$41$	−0.195705	+	0.195705i	−0.0305640	+	0.0305640i	−0.722224	−	0.691660i	$-0.756880\pi$
$41$	−0.195705	+	0.195705i	−0.0305640	+	0.0305640i	0.691660	+	0.722224i	$0.256880\pi$
$42$			0.281305i			0.0434062i
$43$			6.34277i			0.967264i	0.875272	+	0.483632i	$0.160683\pi$
$43$			6.34277i			0.967264i	−0.875272	+	0.483632i	$0.839317\pi$
$44$	5.02734	−	5.02734i	0.757900	−	0.757900i
$45$	1.14065	−	1.14065i	0.170038	−	0.170038i
$46$	−4.50548	−	4.50548i	−0.664296	−	0.664296i
$47$	−9.82164			−1.43263			−0.716317	−	0.697775i	$-0.754173\pi$
$47$	−9.82164			−1.43263			−0.716317	+	0.697775i	$0.754173\pi$
$48$	−3.41421	−	3.41421i	−0.492799	−	0.492799i
$49$			6.97682i			0.996689i
$50$	4.43060			0.626582
$51$		0			0
$52$	−5.57900			−0.773668
$53$			2.12612i			0.292045i	0.989281	+	0.146023i	$0.0466472\pi$
$53$			2.12612i			0.292045i	−0.989281	+	0.146023i	$0.953353\pi$
$54$	−1.30656	−	1.30656i	−0.177801	−	0.177801i
$55$	8.10973			1.09352
$56$	0.116520	+	0.116520i	0.0155707	+	0.0155707i
$57$	−4.65205	+	4.65205i	−0.616180	+	0.616180i
$58$	2.93015	−	2.93015i	0.384748	−	0.384748i
$59$			1.32381i			0.172346i	0.996280	+	0.0861729i	$0.0274638\pi$
$59$			1.32381i			0.172346i	−0.996280	+	0.0861729i	$0.972536\pi$
$60$			2.28130i			0.294515i
$61$	5.85369	−	5.85369i	0.749488	−	0.749488i	−0.224895	−	0.974383i	$-0.572204\pi$
$61$	5.85369	−	5.85369i	0.749488	−	0.749488i	0.974383	+	0.224895i	$0.0722040\pi$
$62$	−3.36370	+	3.36370i	−0.427190	+	0.427190i
$63$	0.107651	+	0.107651i	0.0135627	+	0.0135627i
$64$	2.82843			0.353553
$65$	−4.49981	−	4.49981i	−0.558133	−	0.558133i
$66$		−	9.28931i		−	1.14344i
$67$	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
$70$		−	0.453780i		−	0.0542370i
$71$	4.62951	+	4.62951i	0.549422	+	0.549422i	0.926274	−	0.376851i	$-0.122993\pi$
$71$	4.62951	+	4.62951i	0.549422	+	0.549422i	−0.376851	+	0.926274i	$0.622993\pi$
$72$	−1.08239			−0.127561
$73$	5.88764	+	5.88764i	0.689096	+	0.689096i	0.962032	−	0.272936i	$-0.0879947\pi$
$73$	5.88764	+	5.88764i	0.689096	+	0.689096i	−0.272936	+	0.962032i	$0.587995\pi$
$74$	13.9491	−	13.9491i	1.62155	−	1.62155i
$75$	1.69552	−	1.69552i	0.195782	−	0.195782i
$76$		−	9.30411i		−	1.06725i
$77$			0.765367i			0.0872216i
$78$	−5.15432	+	5.15432i	−0.583612	+	0.583612i
$79$	−0.376412	+	0.376412i	−0.0423496	+	0.0423496i	−0.727964	−	0.685615i	$-0.759533\pi$
$79$	−0.376412	+	0.376412i	−0.0423496	+	0.0423496i	0.685615	+	0.727964i	$0.259533\pi$
$80$	5.50756	+	5.50756i	0.615764	+	0.615764i
$81$	−1.00000			−0.111111
$82$	−0.361616	−	0.361616i	−0.0399338	−	0.0399338i
$83$		−	2.20345i		−	0.241860i	−0.992661	−	0.120930i	$-0.961412\pi$
$83$		−	2.20345i		−	0.241860i	0.992661	−	0.120930i	$-0.0385876\pi$
$84$	−0.215301			−0.0234913
$85$		0			0
$86$	−11.7199			−1.26379
$87$		−	2.24264i		−	0.240436i
$88$	−3.84776	−	3.84776i	−0.410172	−	0.410172i
$89$	7.64847			0.810737			0.405368	−	0.914153i	$-0.367143\pi$
$89$	7.64847			0.810737			0.405368	+	0.914153i	$0.367143\pi$
$90$	2.10765	+	2.10765i	0.222166	+	0.222166i
$91$	0.424676	−	0.424676i	0.0445181	−	0.0445181i
$92$	3.44834	−	3.44834i	0.359514	−	0.359514i
$93$			2.57446i			0.266959i
$94$		−	18.1480i		−	1.87183i
$95$	7.50435	−	7.50435i	0.769930	−	0.769930i
$96$	4.77791	−	4.77791i	0.487643	−	0.487643i
$97$	2.55007	+	2.55007i	0.258920	+	0.258920i	0.824615	−	0.565695i	$-0.191392\pi$
$97$	2.55007	+	2.55007i	0.258920	+	0.258920i	−0.565695	+	0.824615i	$0.691392\pi$
$98$	−12.8915			−1.30224
$99$	−3.55487	−	3.55487i	−0.357277	−	0.357277i
$100$			3.39104i			0.339104i
$101$	9.13707			0.909173			0.454586	−	0.890703i	$-0.349787\pi$
$101$	9.13707			0.909173			0.454586	+	0.890703i	$0.349787\pi$
$102$		0			0
$103$	7.57862			0.746744			0.373372	−	0.927682i	$-0.378202\pi$
$103$	7.57862			0.746744			0.373372	+	0.927682i	$0.378202\pi$
$104$			4.26998i			0.418706i
$105$	−0.173654	−	0.173654i	−0.0169469	−	0.0169469i
$106$	−3.92856			−0.381575
$107$	13.0579	+	13.0579i	1.26235	+	1.26235i	0.949949	+	0.312404i	$0.101134\pi$
$107$	13.0579	+	13.0579i	1.26235	+	1.26235i	0.312404	+	0.949949i	$0.398866\pi$
$108$	1.00000	−	1.00000i	0.0962250	−	0.0962250i
$109$	7.59379	−	7.59379i	0.727354	−	0.727354i	−0.242738	−	0.970092i	$-0.578046\pi$
$109$	7.59379	−	7.59379i	0.727354	−	0.727354i	0.970092	+	0.242738i	$0.0780456\pi$
$110$			14.9848i			1.42875i
$111$		−	10.6762i		−	1.01334i
$112$	−0.519783	+	0.519783i	−0.0491149	+	0.0491149i
$113$	−1.18438	+	1.18438i	−0.111417	+	0.111417i	−0.760617	−	0.649200i	$-0.775104\pi$
$113$	−1.18438	+	1.18438i	−0.111417	+	0.111417i	0.649200	+	0.760617i	$0.275104\pi$
$114$	−8.59588	−	8.59588i	−0.805077	−	0.805077i
$115$	5.56261			0.518716
$116$	2.24264	+	2.24264i	0.208224	+	0.208224i
$117$			3.94495i			0.364711i
$118$	−2.44609			−0.225181
$119$		0			0
$120$	1.74603			0.159390
$121$		−	14.2741i		−	1.29765i
$122$	10.8162	+	10.8162i	0.979253	+	0.979253i
$123$	−0.276769			−0.0249554
$124$	−2.57446	−	2.57446i	−0.231194	−	0.231194i
$125$	−8.43835	+	8.43835i	−0.754749	+	0.754749i
$126$	−0.198912	+	0.198912i	−0.0177205	+	0.0177205i
$127$		−	12.1812i		−	1.08090i	−0.841375	−	0.540452i	$-0.818253\pi$
$127$		−	12.1812i		−	1.08090i	0.841375	−	0.540452i	$-0.181747\pi$
$128$		−	8.28772i		−	0.732538i
$129$	−4.48502	+	4.48502i	−0.394884	+	0.394884i
$130$	8.31457	−	8.31457i	0.729236	−	0.729236i
$131$	7.39008	+	7.39008i	0.645674	+	0.645674i	0.951945	−	0.306270i	$-0.0990811\pi$
$131$	7.39008	+	7.39008i	0.645674	+	0.645674i	−0.306270	+	0.951945i	$0.599081\pi$
$132$	7.10973			0.618823
$133$	0.708233	+	0.708233i	0.0614116	+	0.0614116i
$134$			13.1371i			1.13487i
$135$	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	$0.304464\pi$
$138$		−	6.37170i		−	0.542395i
$139$	−3.76745	−	3.76745i	−0.319551	−	0.319551i	0.529044	−	0.848595i	$-0.322551\pi$
$139$	−3.76745	−	3.76745i	−0.319551	−	0.319551i	−0.848595	+	0.529044i	$0.822551\pi$
$140$	0.347308			0.0293529
$141$	−6.94495	−	6.94495i	−0.584870	−	0.584870i
$142$	−8.55423	+	8.55423i	−0.717855	+	0.717855i
$143$	−14.0238	+	14.0238i	−1.17273	+	1.17273i
$144$		−	4.82843i		−	0.402369i
$145$			3.61766i			0.300430i
$146$	−10.8789	+	10.8789i	−0.900348	+	0.900348i
$147$	−4.93336	+	4.93336i	−0.406897	+	0.406897i
$148$	10.6762	+	10.6762i	0.877577	+	0.877577i
$149$	−9.31890			−0.763434			−0.381717	−	0.924279i	$-0.624667\pi$
$149$	−9.31890			−0.763434			−0.381717	+	0.924279i	$0.624667\pi$
$150$	3.13291	+	3.13291i	0.255801	+	0.255801i
$151$		−	11.9632i		−	0.973555i	−0.873526	−	0.486778i	$-0.838172\pi$
$151$		−	11.9632i		−	0.973555i	0.873526	−	0.486778i	$-0.161828\pi$
$152$	−7.12106			−0.577594
$153$		0			0
$154$	−1.41421			−0.113961
$155$		−	4.15293i		−	0.333571i
$156$	−3.94495	−	3.94495i	−0.315849	−	0.315849i
$157$	18.1548			1.44891			0.724456	−	0.689321i	$-0.242091\pi$
$157$	18.1548			1.44891			0.724456	+	0.689321i	$0.242091\pi$
$158$	−0.695518	−	0.695518i	−0.0553325	−	0.0553325i
$159$	−1.50339	+	1.50339i	−0.119227	+	0.119227i
$160$	−7.70737	+	7.70737i	−0.609321	+	0.609321i
$161$			0.524979i			0.0413741i
$162$		−	1.84776i		−	0.145174i
$163$	−14.6530	+	14.6530i	−1.14771	+	1.14771i	−0.160711	+	0.987002i	$0.551379\pi$
$163$	−14.6530	+	14.6530i	−1.14771	+	1.14771i	−0.987002	+	0.160711i	$0.948621\pi$
$164$	0.276769	−	0.276769i	0.0216120	−	0.0216120i
$165$	5.73445	+	5.73445i	0.446426	+	0.446426i
$166$	4.07144			0.316005
$167$	5.71965	+	5.71965i	0.442600	+	0.442600i	0.892885	−	0.450285i	$-0.148678\pi$
$167$	5.71965	+	5.71965i	0.442600	+	0.442600i	−0.450285	+	0.892885i	$0.648678\pi$
$168$			0.164784i			0.0127134i
$169$	2.56261			0.197124
$170$		0			0
$171$	−6.57900			−0.503109
$172$		−	8.97003i		−	0.683959i
$173$	−0.820684	−	0.820684i	−0.0623954	−	0.0623954i	0.675221	−	0.737616i	$-0.264048\pi$
$173$	−0.820684	−	0.820684i	−0.0623954	−	0.0623954i	−0.737616	+	0.675221i	$0.764048\pi$
$174$	4.14386			0.314145
$175$	−0.258127	−	0.258127i	−0.0195126	−	0.0195126i
$176$	17.1644	−	17.1644i	1.29382	−	1.29382i
$177$	−0.936078	+	0.936078i	−0.0703599	+	0.0703599i
$178$			14.1325i			1.05928i
$179$			2.89668i			0.216508i	0.994123	+	0.108254i	$0.0345260\pi$
$179$			2.89668i			0.216508i	−0.994123	+	0.108254i	$0.965474\pi$
$180$	−1.61313	+	1.61313i	−0.120235	+	0.120235i
$181$	−0.595875	+	0.595875i	−0.0442910	+	0.0442910i	−0.728905	−	0.684614i	$-0.759971\pi$
$181$	−0.595875	+	0.595875i	−0.0442910	+	0.0442910i	0.684614	+	0.728905i	$0.259971\pi$
$182$	0.784699	+	0.784699i	0.0581657	+	0.0581657i
$183$	8.27836			0.611954
$184$	−2.63925	−	2.63925i	−0.194568	−	0.194568i
$185$			17.2220i			1.26619i
$186$	−4.75699			−0.348799
$187$		0			0
$188$	13.8899			1.01302
$189$			0.152241i			0.0110739i
$190$	13.8662	+	13.8662i	1.00596	+	1.00596i
$191$	−9.97069			−0.721454			−0.360727	−	0.932671i	$-0.617471\pi$
$191$	−9.97069			−0.721454			−0.360727	+	0.932671i	$0.617471\pi$
$192$	2.00000	+	2.00000i	0.144338	+	0.144338i
$193$	2.64047	−	2.64047i	0.190065	−	0.190065i	−0.605659	−	0.795724i	$-0.707091\pi$
$193$	2.64047	−	2.64047i	0.190065	−	0.190065i	0.795724	+	0.605659i	$0.207091\pi$
$194$	−4.71191	+	4.71191i	−0.338295	+	0.338295i
$195$		−	6.36370i		−	0.455714i
$196$		−	9.86672i		−	0.704766i
$197$	11.4589	−	11.4589i	0.816413	−	0.816413i	−0.169174	−	0.985586i	$-0.554110\pi$
$197$	11.4589	−	11.4589i	0.816413	−	0.816413i	0.985586	+	0.169174i	$0.0541099\pi$
$198$	6.56854	−	6.56854i	0.466805	−	0.466805i
$199$	−11.6485	−	11.6485i	−0.825738	−	0.825738i	0.161186	−	0.986924i	$-0.448468\pi$
$199$	−11.6485	−	11.6485i	−0.825738	−	0.825738i	−0.986924	+	0.161186i	$0.948468\pi$
$200$	2.59539			0.183522
$201$	5.02734	+	5.02734i	0.354601	+	0.354601i
$202$			16.8831i			1.18789i
$203$	−0.341422			−0.0239631
$204$		0			0
$205$	0.446463			0.0311823
$206$			14.0035i			0.975668i
$207$	−2.43835	−	2.43835i	−0.169477	−	0.169477i
$208$	−19.0479			−1.32073
$209$	−23.3875	−	23.3875i	−1.61774	−	1.61774i
$210$	0.320871	−	0.320871i	0.0221422	−	0.0221422i
$211$	−7.55807	+	7.55807i	−0.520319	+	0.520319i	−0.917668	−	0.397349i	$-0.869930\pi$
$211$	−7.55807	+	7.55807i	−0.520319	+	0.520319i	0.397349	+	0.917668i	$0.369930\pi$
$212$		−	3.00679i		−	0.206507i
$213$			6.54712i			0.448601i
$214$	−24.1278	+	24.1278i	−1.64934	+	1.64934i
$215$	7.23490	−	7.23490i	0.493416	−	0.493416i
$216$	−0.765367	−	0.765367i	−0.0520766	−	0.0520766i
$217$	0.391939			0.0266065
$218$	14.0315	+	14.0315i	0.950333	+	0.950333i
$219$			8.32638i			0.562645i
$220$	−11.4689			−0.773233
$221$		0			0
$222$	19.7270			1.32399
$223$		−	5.41650i		−	0.362715i	−0.983417	−	0.181358i	$-0.941951\pi$
$223$		−	5.41650i		−	0.362715i	0.983417	−	0.181358i	$-0.0580492\pi$
$224$	−0.727394	−	0.727394i	−0.0486010	−	0.0486010i
$225$	2.39782			0.159855
$226$	−2.18845	−	2.18845i	−0.145574	−	0.145574i
$227$	−8.69647	+	8.69647i	−0.577205	+	0.577205i	−0.934132	−	0.356927i	$-0.883824\pi$
$227$	−8.69647	+	8.69647i	−0.577205	+	0.577205i	0.356927	+	0.934132i	$0.383824\pi$
$228$	6.57900	−	6.57900i	0.435705	−	0.435705i
$229$			30.1158i			1.99011i	0.0993441	+	0.995053i	$0.468326\pi$
$229$			30.1158i			1.99011i	−0.0993441	+	0.995053i	$0.531674\pi$
$230$			10.2784i			0.677735i
$231$	−0.541196	+	0.541196i	−0.0356081	+	0.0356081i
$232$	1.71644	−	1.71644i	0.112690	−	0.112690i
$233$	6.21209	+	6.21209i	0.406968	+	0.406968i	0.880680	−	0.473712i	$-0.157086\pi$
$233$	6.21209	+	6.21209i	0.406968	+	0.406968i	−0.473712	+	0.880680i	$0.657086\pi$
$234$	−7.28931			−0.476517
$235$	11.2031	+	11.2031i	0.730808	+	0.730808i
$236$		−	1.87216i		−	0.121867i
$237$	−0.532327			−0.0345783
$238$		0			0
$239$	14.6501			0.947634			0.473817	−	0.880623i	$-0.342876\pi$
$239$	14.6501			0.947634			0.473817	+	0.880623i	$0.342876\pi$
$240$			7.78886i			0.502769i
$241$	11.9892	+	11.9892i	0.772290	+	0.772290i	0.978506	−	0.206216i	$-0.0661151\pi$
$241$	11.9892	+	11.9892i	0.772290	+	0.772290i	−0.206216	+	0.978506i	$0.566115\pi$
$242$	26.3752			1.69546
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	−8.27836	+	8.27836i	−0.529968	+	0.529968i
$245$	7.95813	−	7.95813i	0.508426	−	0.508426i
$246$		−	0.511402i		−	0.0326058i
$247$			25.9538i			1.65140i
$248$	−1.97041	+	1.97041i	−0.125121	+	0.125121i
$249$	1.55807	−	1.55807i	0.0987389	−	0.0987389i
$250$	−15.5920	−	15.5920i	−0.986127	−	0.986127i
$251$	13.9453			0.880217			0.440109	−	0.897945i	$-0.354940\pi$
$251$	13.9453			0.880217			0.440109	+	0.897945i	$0.354940\pi$
$252$	−0.152241	−	0.152241i	−0.00959028	−	0.00959028i
$253$		−	17.3360i		−	1.08990i
$254$	22.5079			1.41227
$255$		0			0
$256$	20.9706			1.31066
$257$		−	19.6603i		−	1.22638i	−0.789936	−	0.613189i	$-0.789887\pi$
$257$		−	19.6603i		−	1.22638i	0.789936	−	0.613189i	$-0.210113\pi$
$258$	−8.28723	−	8.28723i	−0.515940	−	0.515940i
$259$	−1.62535			−0.100994
$260$	6.36370	+	6.36370i	0.394660	+	0.394660i
$261$	1.58579	−	1.58579i	0.0981577	−	0.0981577i
$262$	−13.6551	+	13.6551i	−0.843614	+	0.843614i
$263$		−	27.8721i		−	1.71867i	−0.511415	−	0.859334i	$-0.670879\pi$
$263$		−	27.8721i		−	1.71867i	0.511415	−	0.859334i	$-0.329121\pi$
$264$		−	5.44155i		−	0.334904i
$265$	2.42516	−	2.42516i	0.148977	−	0.148977i
$266$	−1.30864	+	1.30864i	−0.0802381	+	0.0802381i
$267$	5.40829	+	5.40829i	0.330982	+	0.330982i
$268$	−10.0547			−0.614187
$269$	−0.145188	−	0.145188i	−0.00885228	−	0.00885228i	0.702667	−	0.711519i	$-0.251992\pi$
$269$	−0.145188	−	0.145188i	−0.00885228	−	0.00885228i	−0.711519	+	0.702667i	$0.751992\pi$
$270$			2.98067i			0.181398i
$271$	−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
$274$			24.9314i			1.50616i
$275$	8.52395	+	8.52395i	0.514013	+	0.514013i
$276$	4.87669			0.293542
$277$	16.6649	+	16.6649i	1.00129	+	1.00129i	0.999999	+	0.00129534i	$0.000412320\pi$
$277$	16.6649	+	16.6649i	1.00129	+	1.00129i	0.00129534	+	0.999999i	$0.499588\pi$
$278$	6.96134	−	6.96134i	0.417513	−	0.417513i
$279$	−1.82042	+	1.82042i	−0.108986	+	0.108986i
$280$		−	0.265818i		−	0.0158857i
$281$		−	10.1532i		−	0.605690i	−0.953040	−	0.302845i	$-0.902064\pi$
$281$		−	10.1532i		−	0.605690i	0.953040	−	0.302845i	$-0.0979365\pi$
$282$	12.8326	−	12.8326i	0.764170	−	0.764170i
$283$	6.70279	−	6.70279i	0.398440	−	0.398440i	−0.479243	−	0.877682i	$-0.659089\pi$
$283$	6.70279	−	6.70279i	0.398440	−	0.398440i	0.877682	+	0.479243i	$0.159089\pi$
$284$	−6.54712	−	6.54712i	−0.388500	−	0.388500i
$285$	10.6128			0.628645
$286$	−25.9125	−	25.9125i	−1.53224	−	1.53224i
$287$			0.0421355i			0.00248718i
$288$	6.75699			0.398159
$289$		0			0
$290$	−6.68457			−0.392531
$291$			3.60634i			0.211407i
$292$	−8.32638	−	8.32638i	−0.487265	−	0.487265i
$293$	−9.28515			−0.542444			−0.271222	−	0.962517i	$-0.587428\pi$
$293$	−9.28515			−0.542444			−0.271222	+	0.962517i	$0.587428\pi$
$294$	−9.11566	−	9.11566i	−0.531636	−	0.531636i
$295$	1.51001	−	1.51001i	0.0879163	−	0.0879163i
$296$	8.17120	−	8.17120i	0.474941	−	0.474941i
$297$		−	5.02734i		−	0.291716i
$298$		−	17.2191i		−	0.997475i
$299$	−9.61915	+	9.61915i	−0.556290	+	0.556290i
$300$	−2.39782	+	2.39782i	−0.138438	+	0.138438i
$301$	0.682803	+	0.682803i	0.0393561	+	0.0393561i
$302$	22.1052			1.27201
$303$	6.46088	+	6.46088i	0.371168	+	0.371168i
$304$		−	31.7662i		−	1.82192i
$305$	−13.3540			−0.764650
$306$		0			0
$307$	−27.1418			−1.54906			−0.774531	−	0.632536i	$-0.782014\pi$
$307$	−27.1418			−1.54906			−0.774531	+	0.632536i	$0.782014\pi$
$308$		−	1.08239i		−	0.0616750i
$309$	5.35890	+	5.35890i	0.304857	+	0.304857i
$310$	7.67362			0.435832
$311$	−1.82843	−	1.82843i	−0.103681	−	0.103681i	0.653364	−	0.757044i	$-0.273357\pi$
$311$	−1.82843	−	1.82843i	−0.103681	−	0.103681i	−0.757044	+	0.653364i	$0.773357\pi$
$312$	−3.01933	+	3.01933i	−0.170936	+	0.170936i
$313$	18.1094	−	18.1094i	1.02360	−	1.02360i	0.0238868	−	0.999715i	$-0.492396\pi$
$313$	18.1094	−	18.1094i	1.02360	−	1.02360i	0.999715	−	0.0238868i	$-0.00760412\pi$
$314$			33.5457i			1.89309i
$315$		−	0.245584i		−	0.0138371i
$316$	0.532327	−	0.532327i	0.0299457	−	0.0299457i
$317$	−18.1007	+	18.1007i	−1.01663	+	1.01663i	−0.0167751	+	0.999859i	$0.505340\pi$
$317$	−18.1007	+	18.1007i	−1.01663	+	1.01663i	−0.999859	+	0.0167751i	$0.994660\pi$
$318$	−2.77791	−	2.77791i	−0.155777	−	0.155777i
$319$	11.2745			0.631252
$320$	−3.22625	−	3.22625i	−0.180353	−	0.180353i
$321$			18.4666i			1.03071i
$322$	−0.970034			−0.0540579
$323$		0			0
$324$	1.41421			0.0785674
$325$		−	9.45929i		−	0.524707i
$326$	−27.0752	−	27.0752i	−1.49956	−	1.49956i
$327$	10.7392			0.593882
$328$	−0.211830	−	0.211830i	−0.0116963	−	0.0116963i
$329$	−1.05731	+	1.05731i	−0.0582911	+	0.0582911i
$330$	−10.5959	+	10.5959i	−0.583284	+	0.583284i
$331$		−	0.333172i		−	0.0183128i	−0.999958	−	0.00915639i	$-0.997085\pi$
$331$		−	0.333172i		−	0.0183128i	0.999958	−	0.00915639i	$-0.00291461\pi$
$332$			3.11615i			0.171021i
$333$	7.54920	−	7.54920i	0.413694	−	0.413694i
$334$	−10.5685	+	10.5685i	−0.578285	+	0.578285i
$335$	−8.10973	−	8.10973i	−0.443082	−	0.443082i
$336$	−0.735084			−0.0401021
$337$	2.65546	+	2.65546i	0.144652	+	0.144652i	0.775724	−	0.631072i	$-0.217385\pi$
$337$	2.65546	+	2.65546i	0.144652	+	0.144652i	−0.631072	+	0.775724i	$0.717385\pi$
$338$			4.73508i			0.257555i
$339$	−1.67497			−0.0909717
$340$		0			0
$341$	−12.9427			−0.700886
$342$		−	12.1564i		−	0.657343i
$343$	1.50461	+	1.50461i	0.0812415	+	0.0812415i
$344$	−6.86537			−0.370156
$345$	3.93336	+	3.93336i	0.211765	+	0.211765i
$346$	1.51643	−	1.51643i	0.0815236	−	0.0815236i
$347$	2.34052	−	2.34052i	0.125646	−	0.125646i	−0.641488	−	0.767133i	$-0.721682\pi$
$347$	2.34052	−	2.34052i	0.125646	−	0.125646i	0.767133	+	0.641488i	$0.221682\pi$
$348$			3.17157i			0.170014i
$349$			2.58488i			0.138366i	0.997604	+	0.0691828i	$0.0220392\pi$
$349$			2.58488i			0.138366i	−0.997604	+	0.0691828i	$0.977961\pi$
$350$	0.476957	−	0.476957i	0.0254944	−	0.0254944i
$351$	−2.78950	+	2.78950i	−0.148892	+	0.148892i
$352$	24.0202	+	24.0202i	1.28028	+	1.28028i
$353$	−13.2848			−0.707079			−0.353539	−	0.935420i	$-0.615022\pi$
$353$	−13.2848			−0.707079			−0.353539	+	0.935420i	$0.615022\pi$
$354$	−1.72965	−	1.72965i	−0.0919297	−	0.0919297i
$355$		−	10.5613i		−	0.560537i
$356$	−10.8166			−0.573277
$357$		0			0
$358$	−5.35237			−0.282882
$359$			14.7281i			0.777319i	0.921382	+	0.388659i	$0.127062\pi$
$359$			14.7281i			0.777319i	−0.921382	+	0.388659i	$0.872938\pi$
$360$	1.23463	+	1.23463i	0.0650709	+	0.0650709i
$361$	−24.2832			−1.27806
$362$	−1.10103	−	1.10103i	−0.0578690	−	0.0578690i
$363$	10.0933	−	10.0933i	0.529763	−	0.529763i
$364$	−0.600582	+	0.600582i	−0.0314791	+	0.0314791i
$365$		−	13.4315i		−	0.703037i
$366$			15.2964i			0.799557i
$367$	0.311099	−	0.311099i	0.0162392	−	0.0162392i	−0.698941	−	0.715180i	$-0.746345\pi$
$367$	0.311099	−	0.311099i	0.0162392	−	0.0162392i	0.715180	+	0.698941i	$0.246345\pi$
$368$	11.7734	−	11.7734i	0.613730	−	0.613730i
$369$	−0.195705	−	0.195705i	−0.0101880	−	0.0101880i
$370$	−31.8222			−1.65436
$371$	0.228878	+	0.228878i	0.0118828	+	0.0118828i
$372$		−	3.64084i		−	0.188769i
$373$	−0.827899			−0.0428670			−0.0214335	−	0.999770i	$-0.506823\pi$
$373$	−0.827899			−0.0428670			−0.0214335	+	0.999770i	$0.506823\pi$
$374$		0			0
$375$	−11.9336			−0.616250
$376$		−	10.6309i		−	0.548245i
$377$	−6.25584	−	6.25584i	−0.322192	−	0.322192i
$378$	−0.281305			−0.0144687
$379$	14.0066	+	14.0066i	0.719472	+	0.719472i	0.968497	−	0.249025i	$-0.0801103\pi$
$379$	14.0066	+	14.0066i	0.719472	+	0.719472i	−0.249025	+	0.968497i	$0.580110\pi$
$380$	−10.6128	+	10.6128i	−0.544423	+	0.544423i
$381$	8.61339	−	8.61339i	0.441277	−	0.441277i
$382$		−	18.4234i		−	0.942625i
$383$		−	16.6828i		−	0.852453i	−0.904616	−	0.426227i	$-0.859843\pi$
$383$		−	16.6828i		−	0.852453i	0.904616	−	0.426227i	$-0.140157\pi$
$384$	5.86030	−	5.86030i	0.299057	−	0.299057i
$385$	0.873017	−	0.873017i	0.0444931	−	0.0444931i
$386$	4.87894	+	4.87894i	0.248332	+	0.248332i
$387$	−6.34277			−0.322421
$388$	−3.60634	−	3.60634i	−0.183084	−	0.183084i
$389$		−	17.2980i		−	0.877042i	−0.898721	−	0.438521i	$-0.855502\pi$
$389$		−	17.2980i		−	0.877042i	0.898721	−	0.438521i	$-0.144498\pi$
$390$	11.7586			0.595419
$391$		0			0
$392$	−7.55166			−0.381416
$393$			10.4512i			0.527191i
$394$	21.1733	+	21.1733i	1.06669	+	1.06669i
$395$	0.858710			0.0432064
$396$	5.02734	+	5.02734i	0.252633	+	0.252633i
$397$	−4.55423	+	4.55423i	−0.228570	+	0.228570i	−0.812095	−	0.583525i	$-0.801673\pi$
$397$	−4.55423	+	4.55423i	−0.228570	+	0.228570i	0.583525	+	0.812095i	$0.301673\pi$
$398$	21.5236	−	21.5236i	1.07888	−	1.07888i
$399$			1.00159i			0.0501424i
$400$			11.5777i			0.578886i
$401$	14.9004	−	14.9004i	0.744093	−	0.744093i	−0.229270	−	0.973363i	$-0.573634\pi$
$401$	14.9004	−	14.9004i	0.744093	−	0.744093i	0.973363	+	0.229270i	$0.0736339\pi$
$402$	−9.28931	+	9.28931i	−0.463309	+	0.463309i
$403$	7.18146	+	7.18146i	0.357734	+	0.357734i
$404$	−12.9218			−0.642882
$405$	1.14065	+	1.14065i	0.0566795	+	0.0566795i
$406$		−	0.630865i		−	0.0313093i
$407$	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	$0.739299\pi$
$410$			0.824955i			0.0407416i
$411$	9.54082	+	9.54082i	0.470614	+	0.470614i
$412$	−10.7178			−0.528028
$413$	0.142509	+	0.142509i	0.00701243	+	0.00701243i
$414$	4.50548	−	4.50548i	0.221432	−	0.221432i
$415$	−2.51337	+	2.51337i	−0.123376	+	0.123376i
$416$		−	26.6560i		−	1.30692i
$417$		−	5.32798i		−	0.260912i
$418$	43.2144	−	43.2144i	2.11368	−	2.11368i
$419$	8.52132	−	8.52132i	0.416294	−	0.416294i	−0.467630	−	0.883924i	$-0.654892\pi$
$419$	8.52132	−	8.52132i	0.416294	−	0.416294i	0.883924	+	0.467630i	$0.154892\pi$
$420$	0.245584	+	0.245584i	0.0119833	+	0.0119833i
$421$	−14.0183			−0.683210			−0.341605	−	0.939844i	$-0.610971\pi$
$421$	−14.0183			−0.683210			−0.341605	+	0.939844i	$0.610971\pi$
$422$	−13.9655	−	13.9655i	−0.679830	−	0.679830i
$423$		−	9.82164i		−	0.477544i
$424$	−2.30130			−0.111761
$425$		0			0
$426$	−12.0975			−0.586126
$427$		−	1.26031i		−	0.0609905i
$428$	−18.4666	−	18.4666i	−0.892619	−	0.892619i
$429$	−19.8326			−0.957526
$430$	13.3683	+	13.3683i	0.644679	+	0.644679i
$431$	2.43514	−	2.43514i	0.117296	−	0.117296i	−0.646022	−	0.763319i	$-0.723569\pi$
$431$	2.43514	−	2.43514i	0.117296	−	0.117296i	0.763319	+	0.646022i	$0.223569\pi$
$432$	3.41421	−	3.41421i	0.164266	−	0.164266i
$433$			5.56579i			0.267475i	0.991017	+	0.133738i	$0.0426979\pi$
$433$			5.56579i			0.267475i	−0.991017	+	0.133738i	$0.957302\pi$
$434$			0.724208i			0.0347631i
$435$	−2.55807	+	2.55807i	−0.122650	+	0.122650i
$436$	−10.7392	+	10.7392i	−0.514317	+	0.514317i
$437$	−16.0419	−	16.0419i	−0.767387	−	0.767387i
$438$	−15.3852			−0.735131
$439$	−12.4355	−	12.4355i	−0.593512	−	0.593512i	0.345066	−	0.938578i	$-0.387856\pi$
$439$	−12.4355	−	12.4355i	−0.593512	−	0.593512i	−0.938578	+	0.345066i	$0.887856\pi$
$440$			8.77791i			0.418470i
$441$	−6.97682			−0.332230
$442$		0			0
$443$	5.87632			0.279192			0.139596	−	0.990209i	$-0.455420\pi$
$443$	5.87632			0.279192			0.139596	+	0.990209i	$0.455420\pi$
$444$			15.0984i			0.716539i
$445$	−8.72425	−	8.72425i	−0.413569	−	0.413569i
$446$	10.0084			0.473911
$447$	−6.58946	−	6.58946i	−0.311671	−	0.311671i
$448$	0.304482	−	0.304482i	0.0143854	−	0.0143854i
$449$	−28.2710	+	28.2710i	−1.33419	+	1.33419i	−0.432606	+	0.901583i	$0.642406\pi$
$449$	−28.2710	+	28.2710i	−1.33419	+	1.33419i	−0.901583	+	0.432606i	$0.857594\pi$
$450$			4.43060i			0.208861i
$451$		−	1.39141i		−	0.0655189i
$452$	1.67497	−	1.67497i	0.0787838	−	0.0787838i
$453$	8.45929	−	8.45929i	0.397452	−	0.397452i
$454$	−16.0690	−	16.0690i	−0.754155	−	0.754155i
$455$	−0.968815			−0.0454188
$456$	−5.03535	−	5.03535i	−0.235802	−	0.235802i
$457$			17.6906i			0.827533i	0.910383	+	0.413767i	$0.135787\pi$
$457$			17.6906i			0.827533i	−0.910383	+	0.413767i	$0.864213\pi$
$458$	−55.6467			−2.60020
$459$		0			0
$460$	−7.86672			−0.366788
$461$		−	29.8662i		−	1.39101i	−0.718522	−	0.695504i	$-0.755181\pi$
$461$		−	29.8662i		−	1.39101i	0.718522	−	0.695504i	$-0.244819\pi$
$462$	−1.00000	−	1.00000i	−0.0465242	−	0.0465242i
$463$	−9.45213			−0.439278			−0.219639	−	0.975581i	$-0.570488\pi$
$463$	−9.45213			−0.439278			−0.219639	+	0.975581i	$0.570488\pi$
$464$	7.65685	+	7.65685i	0.355461	+	0.355461i
$465$	2.93657	−	2.93657i	0.136180	−	0.136180i
$466$	−11.4785	+	11.4785i	−0.531729	+	0.531729i
$467$		−	20.0094i		−	0.925923i	−0.886378	−	0.462961i	$-0.846787\pi$
$467$		−	20.0094i		−	0.925923i	0.886378	−	0.462961i	$-0.153213\pi$
$468$		−	5.57900i		−	0.257889i
$469$	0.765367	−	0.765367i	0.0353414	−	0.0353414i
$470$	−20.7006	+	20.7006i	−0.954847	+	0.954847i
$471$	12.8374	+	12.8374i	0.591516	+	0.591516i
$472$	−1.43289			−0.0659539
$473$	−22.5477	−	22.5477i	−1.03674	−	1.03674i
$474$		−	0.983611i		−	0.0451788i
$475$	15.7753			0.723820
$476$		0			0
$477$	−2.12612			−0.0973484
$478$			27.0698i			1.23814i
$479$	0.852559	+	0.852559i	0.0389544	+	0.0389544i	0.726316	−	0.687361i	$-0.241231\pi$
$479$	0.852559	+	0.852559i	0.0389544	+	0.0389544i	−0.687361	+	0.726316i	$0.741231\pi$
$480$	−10.8999			−0.497509
$481$	−29.7812	−	29.7812i	−1.35791	−	1.35791i
$482$	−22.1531	+	22.1531i	−1.00905	+	1.00905i
$483$	−0.371216	+	0.371216i	−0.0168909	+	0.0168909i
$484$			20.1867i			0.917577i
$485$		−	5.81748i		−	0.264158i
$486$	1.30656	−	1.30656i	0.0592669	−	0.0592669i
$487$	−8.45790	+	8.45790i	−0.383264	+	0.383264i	−0.872277	−	0.489013i	$-0.837357\pi$
$487$	−8.45790	+	8.45790i	−0.383264	+	0.383264i	0.489013	+	0.872277i	$0.337357\pi$
$488$	6.33598	+	6.33598i	0.286816	+	0.286816i
$489$	−20.7225			−0.937103
$490$	14.7047	+	14.7047i	0.664291	+	0.664291i
$491$		−	31.2632i		−	1.41089i	−0.708766	−	0.705444i	$-0.750748\pi$
$491$		−	31.2632i		−	1.41089i	0.708766	−	0.705444i	$-0.249252\pi$
$492$	0.391410			0.0176461
$493$		0			0
$494$	−47.9564			−2.15766
$495$			8.10973i			0.364505i
$496$	−8.78976	−	8.78976i	−0.394672	−	0.394672i
$497$	0.996740			0.0447099
$498$	2.87894	+	2.87894i	0.129009	+	0.129009i
$499$	29.2452	−	29.2452i	1.30920	−	1.30920i	0.387199	−	0.921996i	$-0.373442\pi$
$499$	29.2452	−	29.2452i	1.30920	−	1.30920i	0.921996	−	0.387199i	$-0.126558\pi$
$500$	11.9336	−	11.9336i	0.533688	−	0.533688i
$501$			8.08881i			0.361381i
$502$			25.7675i			1.15006i
$503$	2.17984	−	2.17984i	0.0971945	−	0.0971945i	−0.656838	−	0.754032i	$-0.728106\pi$
$503$	2.17984	−	2.17984i	0.0971945	−	0.0971945i	0.754032	+	0.656838i	$0.228106\pi$
$504$	−0.116520	+	0.116520i	−0.00519022	+	0.00519022i
$505$	−10.4222	−	10.4222i	−0.463783	−	0.463783i
$506$	32.0327			1.42403
$507$	1.81204	+	1.81204i	0.0804754	+	0.0804754i
$508$			17.2268i			0.764315i
$509$	−33.8077			−1.49850			−0.749249	−	0.662288i	$-0.769585\pi$
$509$	−33.8077			−1.49850			−0.749249	+	0.662288i	$0.769585\pi$
$510$		0			0
$511$	1.26762			0.0560760
$512$			22.1731i			0.979922i
$513$	−4.65205	−	4.65205i	−0.205393	−	0.205393i
$514$	36.3275			1.60234
$515$	−8.64458	−	8.64458i	−0.380925	−	0.380925i
$516$	6.34277	−	6.34277i	0.279225	−	0.279225i
$517$	34.9146	−	34.9146i	1.53554	−	1.53554i
$518$		−	3.00326i		−	0.131956i
$519$		−	1.16062i		−	0.0509457i
$520$	4.87056	−	4.87056i	0.213588	−	0.213588i
$521$	28.9600	−	28.9600i	1.26876	−	1.26876i	0.322034	−	0.946728i	$-0.395633\pi$
$521$	28.9600	−	28.9600i	1.26876	−	1.26876i	0.946728	−	0.322034i	$-0.104367\pi$
$522$	2.93015	+	2.93015i	0.128249	+	0.128249i
$523$	9.06788			0.396511			0.198255	−	0.980150i	$-0.436472\pi$
$523$	9.06788			0.396511			0.198255	+	0.980150i	$0.436472\pi$
$524$	−10.4512	−	10.4512i	−0.456561	−	0.456561i
$525$		−	0.365047i		−	0.0159320i
$526$	51.5009			2.24555
$527$		0			0
$528$	24.2741			1.05640
$529$			11.1089i			0.482997i
$530$	4.48112	+	4.48112i	0.194647	+	0.194647i
$531$	−1.32381			−0.0574486
$532$	−1.00159	−	1.00159i	−0.0434246	−	0.0434246i
$533$	−0.772046	+	0.772046i	−0.0334410	+	0.0334410i
$534$	−9.99321	+	9.99321i	−0.432449	+	0.432449i
$535$		−	29.7890i		−	1.28789i
$536$			7.69552i			0.332396i
$537$	−2.04826	+	2.04826i	−0.0883891	+	0.0883891i
$538$	0.268273	−	0.268273i	0.0115661	−	0.0115661i
$539$	−24.8017	−	24.8017i	−1.06828	−	1.06828i
$540$	−2.28130			−0.0981717
$541$	−9.15138	−	9.15138i	−0.393449	−	0.393449i	0.482466	−	0.875915i	$-0.339741\pi$
$541$	−9.15138	−	9.15138i	−0.393449	−	0.393449i	−0.875915	+	0.482466i	$0.839741\pi$
$542$		−	15.1715i		−	0.651672i
$543$	−0.842695			−0.0361635
$544$		0			0
$545$	−17.3238			−0.742068
$546$			1.10973i			0.0474921i
$547$	7.53764	+	7.53764i	0.322286	+	0.322286i	0.849644	−	0.527357i	$-0.176817\pi$
$547$	7.53764	+	7.53764i	0.322286	+	0.322286i	−0.527357	+	0.849644i	$0.676817\pi$
$548$	−19.0816			−0.815127
$549$	5.85369	+	5.85369i	0.249829	+	0.249829i
$550$	−15.7502	+	15.7502i	−0.671591	+	0.671591i
$551$	10.4329	−	10.4329i	0.444456	−	0.444456i
$552$		−	3.73246i		−	0.158864i
$553$			0.0810419i			0.00344625i
$554$	−30.7926	+	30.7926i	−1.30825	+	1.30825i
$555$	−12.1778	+	12.1778i	−0.516920	+	0.516920i
$556$	5.32798	+	5.32798i	0.225957	+	0.225957i
$557$	30.1933			1.27933			0.639667	−	0.768653i	$-0.279072\pi$
$557$	30.1933			1.27933			0.639667	+	0.768653i	$0.279072\pi$
$558$	−3.36370	−	3.36370i	−0.142397	−	0.142397i
$559$			25.0219i			1.05831i
$560$	1.18578			0.0501085
$561$		0			0
$562$	18.7607			0.791372
$563$			29.9236i			1.26113i	0.776136	+	0.630566i	$0.217177\pi$
$563$			29.9236i			1.26113i	−0.776136	+	0.630566i	$0.782823\pi$
$564$	9.82164	+	9.82164i	0.413566	+	0.413566i
$565$	2.70193			0.113671
$566$	12.3852	+	12.3852i	0.520587	+	0.520587i
$567$	−0.107651	+	0.107651i	−0.00452090	+	0.00452090i
$568$	−5.01095	+	5.01095i	−0.210255	+	0.210255i
$569$			25.6952i			1.07720i	0.842562	+	0.538599i	$0.181046\pi$
$569$			25.6952i			1.07720i	−0.842562	+	0.538599i	$0.818954\pi$
$570$			19.6098i			0.821365i
$571$	19.8091	−	19.8091i	0.828985	−	0.828985i	−0.158392	−	0.987376i	$-0.550631\pi$
$571$	19.8091	−	19.8091i	0.828985	−	0.828985i	0.987376	+	0.158392i	$0.0506308\pi$
$572$	19.8326	−	19.8326i	0.829242	−	0.829242i
$573$	−7.05035	−	7.05035i	−0.294532	−	0.294532i
$574$	−0.0778563			−0.00324966
$575$	5.84673	+	5.84673i	0.243825	+	0.243825i
$576$			2.82843i			0.117851i
$577$	−11.8072			−0.491538			−0.245769	−	0.969328i	$-0.579041\pi$
$577$	−11.8072			−0.491538			−0.245769	+	0.969328i	$0.579041\pi$
$578$		0			0
$579$	3.73418			0.155187
$580$		−	5.11615i		−	0.212436i
$581$	−0.237203	−	0.237203i	−0.00984082	−	0.00984082i
$582$	−6.66364			−0.276217
$583$	−7.55807	−	7.55807i	−0.313023	−	0.313023i
$584$	−6.37274	+	6.37274i	−0.263706	+	0.263706i
$585$	4.49981	−	4.49981i	0.186044	−	0.186044i
$586$		−	17.1567i		−	0.708738i
$587$			7.44230i			0.307177i	0.988135	+	0.153588i	$0.0490830\pi$
$587$			7.44230i			0.307177i	−0.988135	+	0.153588i	$0.950917\pi$
$588$	6.97682	−	6.97682i	0.287719	−	0.287719i
$589$	−11.9765	+	11.9765i	−0.493485	+	0.493485i
$590$	2.79014	+	2.79014i	0.114868	+	0.114868i
$591$	16.2053			0.666598
$592$	36.4508	+	36.4508i	1.49812	+	1.49812i
$593$		−	7.65194i		−	0.314228i	−0.987580	−	0.157114i	$-0.949781\pi$
$593$		−	7.65194i		−	0.314228i	0.987580	−	0.157114i	$-0.0502190\pi$
$594$	9.28931			0.381145
$595$		0			0
$596$	13.1789			0.539830
$597$		−	16.4734i		−	0.674213i
$598$	−17.7739	−	17.7739i	−0.726827	−	0.726827i
$599$	−16.1547			−0.660062			−0.330031	−	0.943970i	$-0.607059\pi$
$599$	−16.1547			−0.660062			−0.330031	+	0.943970i	$0.607059\pi$
$600$	1.83522	+	1.83522i	0.0749224	+	0.0749224i
$601$	−20.3064	+	20.3064i	−0.828315	+	0.828315i	−0.987284	−	0.158969i	$-0.949183\pi$
$601$	−20.3064	+	20.3064i	−0.828315	+	0.828315i	0.158969	+	0.987284i	$0.449183\pi$
$602$	−1.26166	+	1.26166i	−0.0514213	+	0.0514213i
$603$			7.10973i			0.289531i
$604$			16.9186i			0.688407i
$605$	−16.2818	+	16.2818i	−0.661951	+	0.661951i
$606$	−11.9382	+	11.9382i	−0.484955	+	0.484955i
$607$	18.2524	+	18.2524i	0.740844	+	0.740844i	0.972740	−	0.231897i	$-0.0744931\pi$
$607$	18.2524	+	18.2524i	0.740844	+	0.740844i	−0.231897	+	0.972740i	$0.574493\pi$
$608$	44.4542			1.80286
$609$	−0.241422	−	0.241422i	−0.00978290	−	0.00978290i
$610$		−	24.6750i		−	0.999063i
$611$	−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	$0.0373670\pi$
$614$		−	50.1514i		−	2.02395i
$615$	0.315697	+	0.315697i	0.0127301	+	0.0127301i
$616$	−0.828427			−0.0333783
$617$	2.51074	+	2.51074i	0.101079	+	0.101079i	0.755838	−	0.654759i	$-0.227230\pi$
$617$	2.51074	+	2.51074i	0.101079	+	0.101079i	−0.654759	+	0.755838i	$0.727230\pi$
$618$	−9.90195	+	9.90195i	−0.398315	+	0.398315i
$619$	−24.8909	+	24.8909i	−1.00045	+	1.00045i	−0.000451537		1.00000i	$0.500144\pi$
$619$	−24.8909	+	24.8909i	−1.00045	+	1.00045i	−1.00000		0.000451537i	$0.999856\pi$
$620$			5.87313i			0.235871i
$621$		−	3.44834i		−	0.138377i
$622$	3.37849	−	3.37849i	0.135465	−	0.135465i
$623$	0.823363	−	0.823363i	0.0329873	−	0.0329873i
$624$	−13.4689	−	13.4689i	−0.539187	−	0.539187i
$625$	7.26131			0.290453
$626$	33.4617	+	33.4617i	1.33740	+	1.33740i
$627$		−	33.0749i		−	1.32088i
$628$	−25.6748			−1.02454
$629$		0			0
$630$	0.453780			0.0180790
$631$			31.4131i			1.25054i	0.780410	+	0.625268i	$0.215010\pi$
$631$			31.4131i			1.25054i	−0.780410	+	0.625268i	$0.784990\pi$
$632$	−0.407425	−	0.407425i	−0.0162065	−	0.0162065i
$633$	−10.6887			−0.424839
$634$	−33.4457	−	33.4457i	−1.32830	−	1.32830i
$635$	−13.8945	+	13.8945i	−0.551386	+	0.551386i
$636$	2.12612	−	2.12612i	0.0843062	−	0.0843062i
$637$			27.5232i			1.09051i
$638$			20.8326i			0.824770i
$639$	−4.62951	+	4.62951i	−0.183141	+	0.183141i
$640$	−9.45341	+	9.45341i	−0.373679	+	0.373679i
$641$	−18.7917	−	18.7917i	−0.742227	−	0.742227i	0.230779	−	0.973006i	$-0.425873\pi$
$641$	−18.7917	−	18.7917i	−0.742227	−	0.742227i	−0.973006	+	0.230779i	$0.925873\pi$
$642$	−34.1219			−1.34668
$643$	11.3312	+	11.3312i	0.446857	+	0.446857i	0.894308	−	0.447451i	$-0.147668\pi$
$643$	11.3312	+	11.3312i	0.446857	+	0.446857i	−0.447451	+	0.894308i	$0.647668\pi$
$644$		−	0.742432i		−	0.0292559i
$645$	10.2317			0.402872
$646$		0			0
$647$	41.6554			1.63764			0.818822	−	0.574048i	$-0.194628\pi$
$647$	41.6554			1.63764			0.818822	+	0.574048i	$0.194628\pi$
$648$		−	1.08239i		−	0.0425204i
$649$	−4.70598	−	4.70598i	−0.184726	−	0.184726i
$650$	17.4785			0.685563
$651$	0.277142	+	0.277142i	0.0108621	+	0.0108621i
$652$	20.7225	−	20.7225i	0.811555	−	0.811555i
$653$	−8.71609	+	8.71609i	−0.341087	+	0.341087i	−0.856776	−	0.515689i	$-0.827536\pi$
$653$	−8.71609	+	8.71609i	−0.341087	+	0.341087i	0.515689	+	0.856776i	$0.327536\pi$
$654$			19.8435i			0.775944i
$655$		−	16.8590i		−	0.658737i
$656$	0.944947	−	0.944947i	0.0368940	−	0.0368940i
$657$	−5.88764	+	5.88764i	−0.229699	+	0.229699i
$658$	−1.95365	−	1.95365i	−0.0761610	−	0.0761610i
$659$	−3.46449			−0.134957			−0.0674786	−	0.997721i	$-0.521495\pi$
$659$	−3.46449			−0.134957			−0.0674786	+	0.997721i	$0.521495\pi$
$660$	−8.10973	−	8.10973i	−0.315671	−	0.315671i
$661$			28.3233i			1.10165i	0.834621	+	0.550825i	$0.185687\pi$
$661$			28.3233i			1.10165i	−0.834621	+	0.550825i	$0.814313\pi$
$662$	0.615621			0.0239268
$663$		0			0
$664$	2.38500			0.0925558
$665$		−	1.61570i		−	0.0626540i
$666$	13.9491	+	13.9491i	0.540517	+	0.540517i
$667$	7.73339			0.299438
$668$	−8.08881	−	8.08881i	−0.312965	−	0.312965i
$669$	3.83004	−	3.83004i	0.148078	−	0.148078i
$670$	14.9848	−	14.9848i	0.578914	−	0.578914i
$671$			41.6181i			1.60665i
$672$		−	1.02869i		−	0.0396826i
$673$	−20.0879	+	20.0879i	−0.774332	+	0.774332i	−0.978861	−	0.204529i	$-0.934434\pi$
$673$	−20.0879	+	20.0879i	−0.774332	+	0.774332i	0.204529	+	0.978861i	$0.434434\pi$
$674$	−4.90666	+	4.90666i	−0.188997	+	0.188997i
$675$	1.69552	+	1.69552i	0.0652605	+	0.0652605i
$676$	−3.62408			−0.139388
$677$	−13.6459	−	13.6459i	−0.524456	−	0.524456i	0.394458	−	0.918914i	$-0.370932\pi$
$677$	−13.6459	−	13.6459i	−0.524456	−	0.524456i	−0.918914	+	0.394458i	$0.870932\pi$
$678$		−	3.09494i		−	0.118860i
$679$	0.549032			0.0210699
$680$		0			0
$681$	−12.2987			−0.471286
$682$		−	23.9150i		−	0.915752i
$683$	13.7740	+	13.7740i	0.527046	+	0.527046i	0.919690	−	0.392645i	$-0.128440\pi$
$683$	13.7740	+	13.7740i	0.527046	+	0.527046i	−0.392645	+	0.919690i	$0.628440\pi$
$684$	9.30411			0.355751
$685$	−15.3905	−	15.3905i	−0.588043	−	0.588043i
$686$	−2.78016	+	2.78016i	−0.106147	+	0.106147i
$687$	−21.2951	+	21.2951i	−0.812457	+	0.812457i
$688$		−	30.6256i		−	1.16759i
$689$			8.38743i			0.319536i
$690$	−7.26790	+	7.26790i	−0.276684	+	0.276684i
$691$	5.33116	−	5.33116i	0.202807	−	0.202807i	−0.598395	−	0.801202i	$-0.704194\pi$
$691$	5.33116	−	5.33116i	0.202807	−	0.202807i	0.801202	+	0.598395i	$0.204194\pi$
$692$	1.16062	+	1.16062i	0.0441202	+	0.0441202i
$693$	−0.765367			−0.0290739
$694$	4.32472	+	4.32472i	0.164164	+	0.164164i
$695$			8.59470i			0.326015i
$696$	2.42742			0.0920110
$697$		0			0
$698$	−4.77624			−0.180783
$699$			8.78523i			0.332288i
$700$	0.365047	+	0.365047i	0.0137975	+	0.0137975i
$701$	39.0875			1.47632			0.738158	−	0.674628i	$-0.235696\pi$
$701$	39.0875			1.47632			0.738158	+	0.674628i	$0.235696\pi$
$702$	−5.15432	−	5.15432i	−0.194537	−	0.194537i
$703$	49.6662	−	49.6662i	1.87320	−	1.87320i
$704$	−10.0547	+	10.0547i	−0.378950	+	0.378950i
$705$			15.8435i			0.596702i
$706$		−	24.5471i		−	0.923843i
$707$	0.983611	−	0.983611i	0.0369925	−	0.0369925i
$708$	1.32381	−	1.32381i	0.0497520	−	0.0497520i
$709$	4.74669	+	4.74669i	0.178266	+	0.178266i	0.790599	−	0.612334i	$-0.209769\pi$
$709$	4.74669	+	4.74669i	0.178266	+	0.178266i	−0.612334	+	0.790599i	$0.709769\pi$
$710$	19.5148			0.732377
$711$	−0.376412	−	0.376412i	−0.0141165	−	0.0141165i
$712$			8.27865i			0.310255i
$713$	−8.87762			−0.332470
$714$		0			0
$715$	31.9925			1.19645
$716$		−	4.09653i		−	0.153094i
$717$	10.3592	+	10.3592i	0.386870	+	0.386870i
$718$	−27.2140			−1.01562
$719$	5.23700	+	5.23700i	0.195307	+	0.195307i	0.797985	−	0.602678i	$-0.205900\pi$
$719$	5.23700	+	5.23700i	0.195307	+	0.195307i	−0.602678	+	0.797985i	$0.705900\pi$
$720$	−5.50756	+	5.50756i	−0.205255	+	0.205255i
$721$	0.815843	−	0.815843i	0.0303836	−	0.0303836i
$722$		−	44.8695i		−	1.66987i
$723$			16.9552i			0.630572i
$724$	0.842695	−	0.842695i	0.0313185	−	0.0313185i
$725$	−3.80244	+	3.80244i	−0.141219	+	0.141219i
$726$	18.6501	+	18.6501i	0.692169	+	0.692169i
$727$	6.36054			0.235899			0.117950	−	0.993020i	$-0.462368\pi$
$727$	6.36054			0.235899			0.117950	+	0.993020i	$0.462368\pi$
$728$	0.459666	+	0.459666i	0.0170364	+	0.0170364i
$729$		−	1.00000i		−	0.0370370i
$730$	24.8182			0.918562
$731$		0			0
$732$	−11.7074			−0.432717
$733$			41.3337i			1.52670i	0.645988	+	0.763348i	$0.276446\pi$
$733$			41.3337i			1.52670i	−0.645988	+	0.763348i	$0.723554\pi$
$734$	0.574836	+	0.574836i	0.0212176	+	0.0212176i
$735$	11.2545			0.415128
$736$	16.4759	+	16.4759i	0.607309	+	0.607309i
$737$	−25.2741	+	25.2741i	−0.930985	+	0.930985i
$738$	0.361616	−	0.361616i	0.0133113	−	0.0133113i
$739$			23.1653i			0.852150i	0.904688	+	0.426075i	$0.140104\pi$
$739$			23.1653i			0.852150i	−0.904688	+	0.426075i	$0.859896\pi$
$740$		−	24.3556i		−	0.895331i
$741$	−18.3521	+	18.3521i	−0.674182	+	0.674182i
$742$	−0.422912	+	0.422912i	−0.0155256	+	0.0155256i
$743$	26.9764	+	26.9764i	0.989670	+	0.989670i	0.999947	−	0.0102773i	$-0.00327141\pi$
$743$	26.9764	+	26.9764i	0.989670	+	0.989670i	−0.0102773	+	0.999947i	$0.503271\pi$
$744$	−2.78658			−0.102161
$745$	10.6296	+	10.6296i	0.389439	+	0.389439i
$746$		−	1.52976i		−	0.0560084i
$747$	2.20345			0.0806200
$748$		0			0
$749$	2.81138			0.102726
$750$		−	22.0505i		−	0.805169i
$751$	−24.1882	−	24.1882i	−0.882640	−	0.882640i	0.111163	−	0.993802i	$-0.464543\pi$
$751$	−24.1882	−	24.1882i	−0.882640	−	0.882640i	−0.993802	+	0.111163i	$0.964543\pi$
$752$	47.4231			1.72934
$753$	9.86079	+	9.86079i	0.359347	+	0.359347i
$754$	11.5593	−	11.5593i	0.420965	−	0.420965i
$755$	−13.6459	+	13.6459i	−0.496625	+	0.496625i
$756$		−	0.215301i		−	0.00783043i
$757$		−	7.02190i		−	0.255215i	−0.991825	−	0.127608i	$-0.959270\pi$
$757$		−	7.02190i		−	0.255215i	0.991825	−	0.127608i	$-0.0407298\pi$
$758$	−25.8809	+	25.8809i	−0.940035	+	0.940035i
$759$	12.2584	−	12.2584i	0.444951	−	0.444951i
$760$	8.12265	+	8.12265i	0.294639	+	0.294639i
$761$	−47.2917			−1.71432			−0.857161	−	0.515048i	$-0.827774\pi$
$761$	−47.2917			−1.71432			−0.857161	+	0.515048i	$0.827774\pi$
$762$	15.9155	+	15.9155i	0.576557	+	0.576557i
$763$		−	1.63495i		−	0.0591893i
$764$	14.1007			0.510145
$765$		0			0
$766$	30.8259			1.11378
$767$			5.22238i			0.188569i
$768$	14.8284	+	14.8284i	0.535075	+	0.535075i
$769$	−6.39156			−0.230486			−0.115243	−	0.993337i	$-0.536765\pi$
$769$	−6.39156			−0.230486			−0.115243	+	0.993337i	$0.536765\pi$
$770$	1.61313	+	1.61313i	0.0581330	+	0.0581330i
$771$	13.9019	−	13.9019i	0.500666	−	0.500666i
$772$	−3.73418	+	3.73418i	−0.134396	+	0.134396i
$773$			3.67729i			0.132263i	0.997811	+	0.0661315i	$0.0210657\pi$
$773$			3.67729i			0.132263i	−0.997811	+	0.0661315i	$0.978934\pi$
$774$		−	11.7199i		−	0.421264i
$775$	4.36505	−	4.36505i	0.156797	−	0.156797i
$776$	−2.76017	+	2.76017i	−0.0990844	+	0.0990844i
$777$	−1.14930	−	1.14930i	−0.0412308	−	0.0412308i
$778$	31.9625			1.14591
$779$	−1.28754	−	1.28754i	−0.0461310	−	0.0461310i
$780$			8.99963i			0.322238i
$781$	−32.9146			−1.17778
$782$		0			0
$783$	2.24264			0.0801454
$784$		−	33.6871i		−	1.20311i
$785$	−20.7083	−	20.7083i	−0.739112	−	0.739112i
$786$	−19.3112			−0.688808
$787$	−2.87375	−	2.87375i	−0.102438	−	0.102438i	0.654030	−	0.756468i	$-0.273077\pi$
$787$	−2.87375	−	2.87375i	−0.102438	−	0.102438i	−0.756468	+	0.654030i	$0.773077\pi$
$788$	−16.2053	+	16.2053i	−0.577291	+	0.577291i
$789$	19.7085	−	19.7085i	0.701643	−	0.701643i
$790$			1.58669i			0.0564519i
$791$			0.254999i			0.00906670i
$792$	3.84776	−	3.84776i	0.136724	−	0.136724i
$793$	23.0925	−	23.0925i	0.820038	−	0.820038i
$794$	−8.41512	−	8.41512i	−0.298641	−	0.298641i
$795$	3.42970			0.121639
$796$	16.4734	+	16.4734i	0.583885	+	0.583885i
$797$			13.8056i			0.489020i	0.969647	+	0.244510i	$0.0786271\pi$
$797$			13.8056i			0.489020i	−0.969647	+	0.244510i	$0.921373\pi$
$798$	−1.85070			−0.0655141
$799$		0			0
$800$	−16.2021			−0.572830
$801$			7.64847i			0.270246i
$802$	27.5324	+	27.5324i	0.972204	+	0.972204i
$803$	−41.8596			−1.47719
$804$	−7.10973	−	7.10973i	−0.250741	−	0.250741i
$805$	0.598818	−	0.598818i	0.0211056	−	0.0211056i
$806$	−13.2696	+	13.2696i	−0.467402	+	0.467402i
$807$		−	0.205327i		−	0.00722786i
$808$			9.88989i			0.347925i
$809$	−13.3282	+	13.3282i	−0.468596	+	0.468596i	−0.901459	−	0.432864i	$-0.857503\pi$
$809$	−13.3282	+	13.3282i	−0.468596	+	0.468596i	0.432864	+	0.901459i	$0.357503\pi$
$810$	−2.10765	+	2.10765i	−0.0740553	+	0.0740553i
$811$	1.83816	+	1.83816i	0.0645465	+	0.0645465i	0.738643	−	0.674097i	$-0.235467\pi$
$811$	1.83816	+	1.83816i	0.0645465	+	0.0645465i	−0.674097	+	0.738643i	$0.735467\pi$
$812$	0.482843			0.0169445
$813$	−5.80589	−	5.80589i	−0.203621	−	0.203621i
$814$			99.1744i			3.47606i
$815$	33.4280			1.17093
$816$		0			0
$817$	−41.7291			−1.45992
$818$		−	51.0410i		−	1.78461i
$819$	0.424676	+	0.424676i	0.0148394	+	0.0148394i
$820$	−0.631394			−0.0220492
$821$	9.19758	+	9.19758i	0.320998	+	0.320998i	0.849150	−	0.528152i	$-0.177115\pi$
$821$	9.19758	+	9.19758i	0.320998	+	0.320998i	−0.528152	+	0.849150i	$0.677115\pi$
$822$	−17.6291	+	17.6291i	−0.614887	+	0.614887i
$823$	−15.3119	+	15.3119i	−0.533741	+	0.533741i	−0.921684	−	0.387943i	$-0.873186\pi$
$823$	−15.3119	+	15.3119i	−0.533741	+	0.533741i	0.387943	+	0.921684i	$0.373186\pi$
$824$			8.20304i			0.285767i
$825$			12.0547i			0.419690i
$826$	−0.263323	+	0.263323i	−0.00916218	+	0.00916218i
$827$	33.8522	−	33.8522i	1.17716	−	1.17716i	0.196690	−	0.980466i	$-0.436981\pi$
$827$	33.8522	−	33.8522i	1.17716	−	1.17716i	0.980466	−	0.196690i	$-0.0630193\pi$
$828$	3.44834	+	3.44834i	0.119838	+	0.119838i
$829$	−12.9906			−0.451181			−0.225590	−	0.974222i	$-0.572431\pi$
$829$	−12.9906			−0.451181			−0.225590	+	0.974222i	$0.572431\pi$
$830$	−4.64410	−	4.64410i	−0.161199	−	0.161199i
$831$			23.5677i			0.817554i
$832$	11.1580			0.386834
$833$		0			0
$834$	9.84482			0.340898
$835$		−	13.0483i		−	0.451554i
$836$	33.0749	+	33.0749i	1.14392	+	1.14392i
$837$	−2.57446			−0.0889864
$838$	15.7453	+	15.7453i	0.543914	+	0.543914i
$839$	13.3450	−	13.3450i	0.460721	−	0.460721i	−0.438171	−	0.898892i	$-0.644374\pi$
$839$	13.3450	−	13.3450i	0.460721	−	0.460721i	0.898892	+	0.438171i	$0.144374\pi$
$840$	0.187962	−	0.187962i	0.00648529	−	0.00648529i
$841$		−	23.9706i		−	0.826571i
$842$		−	25.9024i		−	0.892657i
$843$	7.17941	−	7.17941i	0.247272	−	0.247272i
$844$	10.6887	−	10.6887i	0.367921	−	0.367921i
$845$	−2.92305	−	2.92305i	−0.100556	−	0.100556i
$846$	18.1480			0.623942
$847$	−1.53662	−	1.53662i	−0.0527989	−	0.0527989i
$848$		−	10.2658i		−	0.352530i
$849$	9.47918			0.325325
$850$		0			0
$851$	36.8151			1.26201
$852$		−	9.25903i		−	0.317209i
$853$	4.26803	+	4.26803i	0.146135	+	0.146135i	0.776389	−	0.630254i	$-0.217049\pi$
$853$	4.26803	+	4.26803i	0.146135	+	0.146135i	−0.630254	+	0.776389i	$0.717049\pi$
$854$	2.32874			0.0796879
$855$	7.50435	+	7.50435i	0.256643	+	0.256643i
$856$	−14.1338	+	14.1338i	−0.483082	+	0.483082i
$857$	11.3727	−	11.3727i	0.388485	−	0.388485i	−0.485662	−	0.874147i	$-0.661421\pi$
$857$	11.3727	−	11.3727i	0.388485	−	0.388485i	0.874147	+	0.485662i	$0.161421\pi$
$858$		−	36.6458i		−	1.25107i
$859$		−	57.8556i		−	1.97401i	−0.160699	−	0.987003i	$-0.551375\pi$
$859$		−	57.8556i		−	1.97401i	0.160699	−	0.987003i	$-0.448625\pi$
$860$	−10.2317	+	10.2317i	−0.348898	+	0.348898i
$861$	−0.0297943	+	0.0297943i	−0.00101539	+	0.00101539i
$862$	4.49955	+	4.49955i	0.153255	+	0.153255i
$863$	7.56067			0.257368			0.128684	−	0.991686i	$-0.458925\pi$
$863$	7.56067			0.257368			0.128684	+	0.991686i	$0.458925\pi$
$864$	4.77791	+	4.77791i	0.162548	+	0.162548i
$865$			1.87223i			0.0636577i
$866$	−10.2842			−0.349473
$867$		0			0
$868$	−0.554285			−0.0188137
$869$		−	2.67619i		−	0.0907834i
$870$	−4.72670	−	4.72670i	−0.160250	−	0.160250i
$871$	28.0475			0.950354
$872$	8.21946	+	8.21946i	0.278346	+	0.278346i
$873$	−2.55007	+	2.55007i	−0.0863066	+	0.0863066i
$874$	29.6415	−	29.6415i	1.00264	−	1.00264i
$875$			1.81679i			0.0614186i
$876$		−	11.7753i		−	0.397850i
$877$	−12.2796	+	12.2796i	−0.414653	+	0.414653i	−0.883356	−	0.468703i	$-0.844721\pi$
$877$	−12.2796	+	12.2796i	−0.414653	+	0.414653i	0.468703	+	0.883356i	$0.344721\pi$
$878$	22.9777	−	22.9777i	0.775461	−	0.775461i
$879$	−6.56559	−	6.56559i	−0.221452	−	0.221452i
$880$	−39.1572			−1.31999
$881$	−29.0634	−	29.0634i	−0.979170	−	0.979170i	0.0206174	−	0.999787i	$-0.493437\pi$
$881$	−29.0634	−	29.0634i	−0.979170	−	0.979170i	−0.999787	+	0.0206174i	$0.993437\pi$
$882$		−	12.8915i		−	0.434079i
$883$	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
$886$			10.8580i			0.364782i
$887$	−15.2031	−	15.2031i	−0.510470	−	0.510470i	0.404200	−	0.914670i	$-0.367550\pi$
$887$	−15.2031	−	15.2031i	−0.510470	−	0.510470i	−0.914670	+	0.404200i	$0.867550\pi$
$888$	11.5558			0.387788
$889$	−1.31131	−	1.31131i	−0.0439799	−	0.0439799i
$890$	16.1203	−	16.1203i	0.540354	−	0.540354i
$891$	3.55487	−	3.55487i	0.119092	−	0.119092i
$892$			7.66008i			0.256479i
$893$		−	64.6165i		−	2.16231i
$894$	12.1757	−	12.1757i	0.407217	−	0.407217i
$895$	3.30411	−	3.30411i	0.110444	−	0.110444i
$896$	−0.892178	−	0.892178i	−0.0298056	−	0.0298056i
$897$	−13.6035			−0.454208
$898$	−52.2379	−	52.2379i	−1.74320	−	1.74320i
$899$		−	5.77359i		−	0.192560i
$900$	−3.39104			−0.113035
$901$		0			0
$902$	2.57099			0.0856046
$903$			0.965630i			0.0321341i
$904$	−1.28196	−	1.28196i	−0.0426375	−	0.0426375i
$905$	1.35937			0.0451871
$906$	15.6307	+	15.6307i	0.519296	+	0.519296i
$907$	−10.4700	+	10.4700i	−0.347652	+	0.347652i	−0.859234	−	0.511582i	$-0.829060\pi$
$907$	−10.4700	+	10.4700i	−0.347652	+	0.347652i	0.511582	+	0.859234i	$0.329060\pi$
$908$	12.2987	−	12.2987i	0.408146	−	0.408146i
$909$			9.13707i			0.303058i
$910$		−	1.79014i		−	0.0593425i
$911$	−33.6024	+	33.6024i	−1.11330	+	1.11330i	−0.120595	+	0.992702i	$0.538480\pi$
$911$	−33.6024	+	33.6024i	−1.11330	+	1.11330i	−0.992702	+	0.120595i	$0.961520\pi$
$912$	22.4621	−	22.4621i	0.743795	−	0.743795i
$913$	7.83296	+	7.83296i	0.259233	+	0.259233i
$914$	−32.6880			−1.08122
$915$	−9.44273	−	9.44273i	−0.312167	−	0.312167i
$916$		−	42.5901i		−	1.40722i
$917$	1.59109			0.0525425
$918$		0			0
$919$	−52.4090			−1.72881			−0.864407	−	0.502793i	$-0.832306\pi$
$919$	−52.4090			−1.72881			−0.864407	+	0.502793i	$0.832306\pi$
$920$			6.02092i			0.198504i
$921$	−19.1921	−	19.1921i	−0.632402	−	0.632402i
$922$	55.1856			1.81744
$923$	18.2632	+	18.2632i	0.601140	+	0.601140i
$924$	0.765367	−	0.765367i	0.0251787	−	0.0251787i
$925$	−18.1017	+	18.1017i	−0.595179	+	0.595179i
$926$		−	17.4653i		−	0.573944i
$927$			7.57862i			0.248915i
$928$	−10.7151	+	10.7151i	−0.351742	+	0.351742i
$929$	−32.4544	+	32.4544i	−1.06480	+	1.06480i	−0.0670456	+	0.997750i	$0.521357\pi$
$929$	−32.4544	+	32.4544i	−1.06480	+	1.06480i	−0.997750	+	0.0670456i	$0.978643\pi$
$930$	5.42607	+	5.42607i	0.177928	+	0.177928i
$931$	−45.9005			−1.50433
$932$	−8.78523	−	8.78523i	−0.287770	−	0.287770i
$933$		−	2.58579i		−	0.0846548i
$934$	36.9725			1.20978
$935$		0			0
$936$	−4.26998			−0.139569
$937$		−	21.7579i		−	0.710799i	−0.934714	−	0.355400i	$-0.884345\pi$
$937$		−	21.7579i		−	0.710799i	0.934714	−	0.355400i	$-0.115655\pi$
$938$	1.41421	+	1.41421i	0.0461757	+	0.0461757i
$939$	25.6105			0.835767
$940$	−15.8435	−	15.8435i	−0.516759	−	0.516759i
$941$	38.2560	−	38.2560i	1.24711	−	1.24711i	0.290121	−	0.956990i	$-0.406304\pi$
$941$	38.2560	−	38.2560i	1.24711	−	1.24711i	0.956990	−	0.290121i	$-0.0936955\pi$
$942$	−23.7204	+	23.7204i	−0.772852	+	0.772852i
$943$		−	0.954393i		−	0.0310793i
$944$		−	6.39194i		−	0.208040i
$945$	0.173654	−	0.173654i	0.00564896	−	0.00564896i
$946$	41.6627	−	41.6627i	1.35457	−	1.35457i
$947$	−4.08430	−	4.08430i	−0.132722	−	0.132722i	0.637625	−	0.770347i	$-0.279917\pi$
$947$	−4.08430	−	4.08430i	−0.132722	−	0.132722i	−0.770347	+	0.637625i	$0.779917\pi$
$948$	0.752823			0.0244506
$949$	23.2264	+	23.2264i	0.753962	+	0.753962i
$950$			29.1489i			0.945716i
$951$	−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	$0.670245\pi$
$954$		−	3.92856i		−	0.127192i
$955$	11.3731	+	11.3731i	0.368025	+	0.368025i
$956$	−20.7183			−0.670078
$957$	7.97229	+	7.97229i	0.257707	+	0.257707i
$958$	−1.57532	+	1.57532i	−0.0508964	+	0.0508964i
$959$	1.45250	−	1.45250i	0.0469038	−	0.0469038i
$960$		−	4.56261i		−	0.147258i
$961$		−	24.3721i		−	0.786198i
$962$	55.0285	−	55.0285i	1.77419	−	1.77419i
$963$	−13.0579	+	13.0579i	−0.420785	+	0.420785i
$964$	−16.9552	−	16.9552i	−0.546091	−	0.546091i
$965$	−6.02371			−0.193910
$966$	−0.685918	−	0.685918i	−0.0220690	−	0.0220690i
$967$			5.82126i			0.187199i	0.995610	+	0.0935996i	$0.0298374\pi$
$967$			5.82126i			0.187199i	−0.995610	+	0.0935996i	$0.970163\pi$
$968$	15.4502			0.496589
$969$		0			0
$970$	10.7493			0.345139
$971$		−	21.9049i		−	0.702963i	−0.936195	−	0.351481i	$-0.885678\pi$
$971$		−	21.9049i		−	0.702963i	0.936195	−	0.351481i	$-0.114322\pi$
$972$	1.00000	+	1.00000i	0.0320750	+	0.0320750i
$973$	−0.811136			−0.0260038
$974$	−15.6282	−	15.6282i	−0.500759	−	0.500759i
$975$	6.68873	−	6.68873i	0.214211	−	0.214211i
$976$	−28.2641	+	28.2641i	−0.904712	+	0.904712i
$977$		−	28.0473i		−	0.897312i	−0.893705	−	0.448656i	$-0.851903\pi$
$977$		−	28.0473i		−	0.897312i	0.893705	−	0.448656i	$-0.148097\pi$
$978$		−	38.2902i		−	1.22438i
$979$	−27.1893	+	27.1893i	−0.868974	+	0.868974i
$980$	−11.2545	+	11.2545i	−0.359512	+	0.359512i
$981$	7.59379	+	7.59379i	0.242451	+	0.242451i
$982$	57.7668			1.84341
$983$	22.1516	+	22.1516i	0.706526	+	0.706526i	0.965803	−	0.259277i	$-0.0834842\pi$
$983$	22.1516	+	22.1516i	0.706526	+	0.706526i	−0.259277	+	0.965803i	$0.583484\pi$
$984$		−	0.299572i		−	0.00955001i
$985$	−26.1412			−0.832929
$986$		0			0
$987$	−1.49526			−0.0475945
$988$		−	36.7042i		−	1.16772i
$989$	−15.4659	−	15.4659i	−0.491786	−	0.491786i
$990$	−14.9848			−0.476249
$991$	12.7274	+	12.7274i	0.404299	+	0.404299i	0.879745	−	0.475446i	$-0.157713\pi$
$991$	12.7274	+	12.7274i	0.404299	+	0.404299i	−0.475446	+	0.879745i	$0.657713\pi$
$992$	12.3005	−	12.3005i	0.390543	−	0.390543i
$993$	0.235588	−	0.235588i	0.00747616	−	0.00747616i
$994$			1.84174i			0.0584163i
$995$			26.5737i			0.842443i
$996$	−2.20345	+	2.20345i	−0.0698189	+	0.0698189i
$997$	−39.2915	+	39.2915i	−1.24438	+	1.24438i	−0.286208	+	0.958167i	$0.592395\pi$
$997$	−39.2915	+	39.2915i	−1.24438	+	1.24438i	−0.958167	+	0.286208i	$0.907605\pi$
$998$	54.0381	+	54.0381i	1.71055	+	1.71055i
$999$	10.6762			0.337780

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.2.e.i.829.4		8
17.2	even	8		867.2.a.n.1.1		4
17.3	odd	16		867.2.h.f.712.2		8
17.4	even	4	inner	867.2.e.i.616.1		8
17.5	odd	16		867.2.h.g.733.1		8
17.6	odd	16		51.2.h.a.43.1	yes	8
17.7	odd	16		867.2.h.f.688.2		8
17.8	even	8		867.2.d.e.577.7		8
17.9	even	8		867.2.d.e.577.8		8
17.10	odd	16		867.2.h.b.688.2		8
17.11	odd	16		867.2.h.g.757.1		8
17.12	odd	16		51.2.h.a.19.1	✓	8
17.13	even	4		867.2.e.h.616.1		8
17.14	odd	16		867.2.h.b.712.2		8
17.15	even	8		867.2.a.m.1.1		4
17.16	even	2		867.2.e.h.829.4		8
51.2	odd	8		2601.2.a.bd.1.4		4
51.23	even	16		153.2.l.e.145.2		8
51.29	even	16		153.2.l.e.19.2		8
51.32	odd	8		2601.2.a.bc.1.4		4
68.23	even	16		816.2.bq.a.145.1		8
68.63	even	16		816.2.bq.a.529.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.h.a.19.1	✓	8	17.12	odd	16
51.2.h.a.43.1	yes	8	17.6	odd	16
153.2.l.e.19.2		8	51.29	even	16
153.2.l.e.145.2		8	51.23	even	16
816.2.bq.a.145.1		8	68.23	even	16
816.2.bq.a.529.1		8	68.63	even	16
867.2.a.m.1.1		4	17.15	even	8
867.2.a.n.1.1		4	17.2	even	8
867.2.d.e.577.7		8	17.8	even	8
867.2.d.e.577.8		8	17.9	even	8
867.2.e.h.616.1		8	17.13	even	4
867.2.e.h.829.4		8	17.16	even	2
867.2.e.i.616.1		8	17.4	even	4	inner
867.2.e.i.829.4		8	1.1	even	1	trivial
867.2.h.b.688.2		8	17.10	odd	16
867.2.h.b.712.2		8	17.14	odd	16
867.2.h.f.688.2		8	17.7	odd	16
867.2.h.f.712.2		8	17.3	odd	16
867.2.h.g.733.1		8	17.5	odd	16
867.2.h.g.757.1		8	17.11	odd	16
2601.2.a.bc.1.4		4	51.32	odd	8
2601.2.a.bd.1.4		4	51.2	odd	8

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:	\( N \)	\(=\)	\( 867 = 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	867.e (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.84776i q^{2} +(0.707107 + 0.707107i) q^{3} -1.41421 q^{4} +(-1.14065 - 1.14065i) q^{5} +(-1.30656 + 1.30656i) q^{6} +(0.107651 - 0.107651i) q^{7} +1.08239i q^{8} +1.00000i q^{9} +(2.10765 - 2.10765i) q^{10} +(-3.55487 + 3.55487i) q^{11} +(-1.00000 - 1.00000i) q^{12} +3.94495 q^{13} +(0.198912 + 0.198912i) q^{14} -1.61313i q^{15} -4.82843 q^{16} -1.84776 q^{18} +6.57900i q^{19} +(1.61313 + 1.61313i) q^{20} +0.152241 q^{21} +(-6.56854 - 6.56854i) q^{22} +(-2.43835 + 2.43835i) q^{23} +(-0.765367 + 0.765367i) q^{24} -2.39782i q^{25} +7.28931i q^{26} +(-0.707107 + 0.707107i) q^{27} +(-0.152241 + 0.152241i) q^{28} +(-1.58579 - 1.58579i) q^{29} +2.98067 q^{30} +(1.82042 + 1.82042i) q^{31} -6.75699i q^{32} -5.02734 q^{33} -0.245584 q^{35} -1.41421i q^{36} +(-7.54920 - 7.54920i) q^{37} -12.1564 q^{38} +(2.78950 + 2.78950i) q^{39} +(1.23463 - 1.23463i) q^{40} +(-0.195705 + 0.195705i) q^{41} +0.281305i q^{42} +6.34277i q^{43} +(5.02734 - 5.02734i) q^{44} +(1.14065 - 1.14065i) q^{45} +(-4.50548 - 4.50548i) q^{46} -9.82164 q^{47} +(-3.41421 - 3.41421i) q^{48} +6.97682i q^{49} +4.43060 q^{50} -5.57900 q^{52} +2.12612i q^{53} +(-1.30656 - 1.30656i) q^{54} +8.10973 q^{55} +(0.116520 + 0.116520i) q^{56} +(-4.65205 + 4.65205i) q^{57} +(2.93015 - 2.93015i) q^{58} +1.32381i q^{59} +2.28130i q^{60} +(5.85369 - 5.85369i) q^{61} +(-3.36370 + 3.36370i) q^{62} +(0.107651 + 0.107651i) q^{63} +2.82843 q^{64} +(-4.49981 - 4.49981i) q^{65} -9.28931i q^{66} +7.10973 q^{67} -3.44834 q^{69} -0.453780i q^{70} +(4.62951 + 4.62951i) q^{71} -1.08239 q^{72} +(5.88764 + 5.88764i) q^{73} +(13.9491 - 13.9491i) q^{74} +(1.69552 - 1.69552i) q^{75} -9.30411i q^{76} +0.765367i q^{77} +(-5.15432 + 5.15432i) q^{78} +(-0.376412 + 0.376412i) q^{79} +(5.50756 + 5.50756i) q^{80} -1.00000 q^{81} +(-0.361616 - 0.361616i) q^{82} -2.20345i q^{83} -0.215301 q^{84} -11.7199 q^{86} -2.24264i q^{87} +(-3.84776 - 3.84776i) q^{88} +7.64847 q^{89} +(2.10765 + 2.10765i) q^{90} +(0.424676 - 0.424676i) q^{91} +(3.44834 - 3.44834i) q^{92} +2.57446i q^{93} -18.1480i q^{94} +(7.50435 - 7.50435i) q^{95} +(4.77791 - 4.77791i) q^{96} +(2.55007 + 2.55007i) q^{97} -12.8915 q^{98} +(-3.55487 - 3.55487i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 16 q^{10} - 8 q^{11} - 8 q^{12} + 8 q^{13} - 8 q^{14} - 16 q^{16} - 8 q^{20} + 16 q^{21} - 16 q^{22} - 16 q^{28} - 24 q^{29} + 16 q^{30} + 32 q^{31} - 8 q^{33} + 32 q^{35} - 16 q^{37} - 32 q^{38}+ \cdots - 8 q^{99}+O(q^{100}) \) 8 * q + 16 * q^10 - 8 * q^11 - 8 * q^12 + 8 * q^13 - 8 * q^14 - 16 * q^16 - 8 * q^20 + 16 * q^21 - 16 * q^22 - 16 * q^28 - 24 * q^29 + 16 * q^30 + 32 * q^31 - 8 * q^33 + 32 * q^35 - 16 * q^37 - 32 * q^38 + 8 * q^39 + 16 * q^40 - 16 * q^41 + 8 * q^44 - 16 * q^46 - 16 * q^47 - 16 * q^48 + 32 * q^50 - 16 * q^52 + 24 * q^55 - 8 * q^57 + 32 * q^61 + 8 * q^65 + 16 * q^67 - 24 * q^69 + 24 * q^71 - 32 * q^73 + 8 * q^74 - 16 * q^75 - 16 * q^78 - 16 * q^79 - 16 * q^80 - 8 * q^81 - 16 * q^82 - 32 * q^86 - 16 * q^88 - 32 * q^89 + 16 * q^90 + 24 * q^92 + 24 * q^95 + 16 * q^97 - 64 * q^98 - 8 * q^99

Introduction

L-functions

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