LMFDB - Embedded newform 735.2.q.c.79.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [735,2,Mod(79,735)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(735, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("735.79"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.q (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			79.3
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	735.79
Dual form			735.2.q.c.214.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.448288 + 0.258819i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.866025 - 1.50000i) q^{4} +(-0.792893 - 2.09077i) q^{5} -0.517638 q^{6} -1.93185i q^{8} +(0.500000 - 0.866025i) q^{9} +(0.185687 - 1.14248i) q^{10} +(-1.73205 - 3.00000i) q^{11} +(1.50000 + 0.866025i) q^{12} +4.00000i q^{13} +(1.73205 + 1.41421i) q^{15} +(-1.23205 + 2.13397i) q^{16} +(-3.46410 + 2.00000i) q^{17} +(0.448288 - 0.258819i) q^{18} +(-2.63896 + 4.57081i) q^{19} +(-2.44949 + 3.00000i) q^{20} -1.79315i q^{22} +(3.01790 + 1.74238i) q^{23} +(0.965926 + 1.67303i) q^{24} +(-3.74264 + 3.31552i) q^{25} +(-1.03528 + 1.79315i) q^{26} +1.00000i q^{27} +4.92820 q^{29} +(0.410432 + 1.08226i) q^{30} +(-3.67423 - 6.36396i) q^{31} +(-4.45069 + 2.56961i) q^{32} +(3.00000 + 1.73205i) q^{33} -2.07055 q^{34} -1.73205 q^{36} +(-9.14162 - 5.27792i) q^{37} +(-2.36603 + 1.36603i) q^{38} +(-2.00000 - 3.46410i) q^{39} +(-4.03906 + 1.53175i) q^{40} -8.48528 q^{41} +(-3.00000 + 5.19615i) q^{44} +(-2.20711 - 0.358719i) q^{45} +(0.901924 + 1.56218i) q^{46} +(5.19615 + 3.00000i) q^{47} -2.46410i q^{48} +(-2.53590 + 0.517638i) q^{50} +(2.00000 - 3.46410i) q^{51} +(6.00000 - 3.46410i) q^{52} +(6.36396 - 3.67423i) q^{53} +(-0.258819 + 0.448288i) q^{54} +(-4.89898 + 6.00000i) q^{55} -5.27792i q^{57} +(2.20925 + 1.27551i) q^{58} +(0.378937 + 0.656339i) q^{59} +(0.621320 - 3.82282i) q^{60} +(0.328169 - 0.568406i) q^{61} -3.80385i q^{62} +2.26795 q^{64} +(8.36308 - 3.17157i) q^{65} +(0.896575 + 1.55291i) q^{66} +(-10.9348 + 6.31319i) q^{67} +(6.00000 + 3.46410i) q^{68} -3.48477 q^{69} -6.39230 q^{71} +(-1.67303 - 0.965926i) q^{72} +(-2.53590 + 1.46410i) q^{73} +(-2.73205 - 4.73205i) q^{74} +(1.58346 - 4.74264i) q^{75} +9.14162 q^{76} -2.07055i q^{78} +(-2.26795 + 3.92820i) q^{79} +(5.43854 + 0.883921i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.80385 - 2.19615i) q^{82} +6.00000i q^{83} +(6.92820 + 5.65685i) q^{85} +(-4.26795 + 2.46410i) q^{87} +(-5.79555 + 3.34607i) q^{88} +(7.72741 - 13.3843i) q^{89} +(-0.896575 - 0.732051i) q^{90} -6.03579i q^{92} +(6.36396 + 3.67423i) q^{93} +(1.55291 + 2.68973i) q^{94} +(11.6489 + 1.89329i) q^{95} +(2.56961 - 4.45069i) q^{96} -18.9282i q^{97} -3.46410 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{5} + 4 q^{9} + 12 q^{10} + 12 q^{12} + 4 q^{16} + 4 q^{25} - 16 q^{29} + 4 q^{30} + 24 q^{33} - 12 q^{38} - 16 q^{39} - 12 q^{40} - 24 q^{44} - 12 q^{45} + 28 q^{46} - 48 q^{50} + 16 q^{51}+ \cdots + 16 q^{95}+O(q^{100}) $ 8 * q - 12 * q^5 + 4 * q^9 + 12 * q^10 + 12 * q^12 + 4 * q^16 + 4 * q^25 - 16 * q^29 + 4 * q^30 + 24 * q^33 - 12 * q^38 - 16 * q^39 - 12 * q^40 - 24 * q^44 - 12 * q^45 + 28 * q^46 - 48 * q^50 + 16 * q^51 + 48 * q^52 - 12 * q^60 + 32 * q^64 + 48 * q^68 + 32 * q^71 - 48 * q^73 - 8 * q^74 - 32 * q^79 - 12 * q^80 - 4 * q^81 - 72 * q^82 - 48 * q^87 + 16 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$

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 $

$2$	0.448288	+	0.258819i	0.316987	+	0.183013i	0.650049	−	0.759892i	$-0.274748\pi$
$2$	0.448288	+	0.258819i	0.316987	+	0.183013i	−0.333062	+	0.942905i	$0.608082\pi$
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	−0.866025	−	1.50000i	−0.433013	−	0.750000i
$5$	−0.792893	−	2.09077i	−0.354593	−	0.935021i
$5$	−0.792893	−	2.09077i	−0.354593	−	0.935021i
$6$	−0.517638			−0.211325
$7$		0			0
$7$		0			0
$8$		−	1.93185i		−	0.683013i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	0.185687	−	1.14248i	0.0587193	−	0.361285i
$11$	−1.73205	−	3.00000i	−0.522233	−	0.904534i	−0.999665	−	0.0258656i	$-0.991766\pi$
$11$	−1.73205	−	3.00000i	−0.522233	−	0.904534i	0.477432	−	0.878668i	$-0.341568\pi$
$12$	1.50000	+	0.866025i	0.433013	+	0.250000i
$13$			4.00000i			1.10940i	0.832050	+	0.554700i	$0.187167\pi$
$13$			4.00000i			1.10940i	−0.832050	+	0.554700i	$0.812833\pi$
$14$		0			0
$15$	1.73205	+	1.41421i	0.447214	+	0.365148i
$16$	−1.23205	+	2.13397i	−0.308013	+	0.533494i
$17$	−3.46410	+	2.00000i	−0.840168	+	0.485071i	−0.857321	−	0.514782i	$-0.827873\pi$
$17$	−3.46410	+	2.00000i	−0.840168	+	0.485071i	0.0171533	+	0.999853i	$0.494540\pi$
$18$	0.448288	−	0.258819i	0.105662	−	0.0610042i
$19$	−2.63896	+	4.57081i	−0.605419	+	1.04862i	0.386567	+	0.922261i	$0.373661\pi$
$19$	−2.63896	+	4.57081i	−0.605419	+	1.04862i	−0.991985	+	0.126354i	$0.959672\pi$
$20$	−2.44949	+	3.00000i	−0.547723	+	0.670820i
$21$		0			0
$22$		−	1.79315i		−	0.382301i
$23$	3.01790	+	1.74238i	0.629275	+	0.363312i	0.780471	−	0.625192i	$-0.214979\pi$
$23$	3.01790	+	1.74238i	0.629275	+	0.363312i	−0.151196	+	0.988504i	$0.548313\pi$
$24$	0.965926	+	1.67303i	0.197169	+	0.341506i
$25$	−3.74264	+	3.31552i	−0.748528	+	0.663103i
$26$	−1.03528	+	1.79315i	−0.203034	+	0.351666i
$27$			1.00000i			0.192450i
$28$		0			0
$29$	4.92820			0.915144			0.457572	−	0.889172i	$-0.348719\pi$
$29$	4.92820			0.915144			0.457572	+	0.889172i	$0.348719\pi$
$30$	0.410432	+	1.08226i	0.0749342	+	0.197593i
$31$	−3.67423	−	6.36396i	−0.659912	−	1.14300i	−0.980638	−	0.195829i	$-0.937260\pi$
$31$	−3.67423	−	6.36396i	−0.659912	−	1.14300i	0.320726	−	0.947172i	$-0.396073\pi$
$32$	−4.45069	+	2.56961i	−0.786779	+	0.454247i
$33$	3.00000	+	1.73205i	0.522233	+	0.301511i
$34$	−2.07055			−0.355097
$35$		0			0
$36$	−1.73205			−0.288675
$37$	−9.14162	−	5.27792i	−1.50287	−	0.867684i	−0.999994	−	0.00332716i	$-0.998941\pi$
$37$	−9.14162	−	5.27792i	−1.50287	−	0.867684i	−0.502879	−	0.864357i	$-0.667726\pi$
$38$	−2.36603	+	1.36603i	−0.383820	+	0.221599i
$39$	−2.00000	−	3.46410i	−0.320256	−	0.554700i
$40$	−4.03906	+	1.53175i	−0.638631	+	0.242191i
$41$	−8.48528			−1.32518			−0.662589	−	0.748983i	$-0.730542\pi$
$41$	−8.48528			−1.32518			−0.662589	+	0.748983i	$0.730542\pi$
$42$		0			0
$43$		0			0		1.00000			$0$
$43$		0			0		−1.00000			$\pi$
$44$	−3.00000	+	5.19615i	−0.452267	+	0.783349i
$45$	−2.20711	−	0.358719i	−0.329016	−	0.0534747i
$46$	0.901924	+	1.56218i	0.132981	+	0.230331i
$47$	5.19615	+	3.00000i	0.757937	+	0.437595i	0.828554	−	0.559908i	$-0.189164\pi$
$47$	5.19615	+	3.00000i	0.757937	+	0.437595i	−0.0706177	+	0.997503i	$0.522497\pi$
$48$		−	2.46410i		−	0.355662i
$49$		0			0
$50$	−2.53590	+	0.517638i	−0.358630	+	0.0732051i
$51$	2.00000	−	3.46410i	0.280056	−	0.485071i
$52$	6.00000	−	3.46410i	0.832050	−	0.480384i
$53$	6.36396	−	3.67423i	0.874157	−	0.504695i	0.00542976	−	0.999985i	$-0.498272\pi$
$53$	6.36396	−	3.67423i	0.874157	−	0.504695i	0.868728	+	0.495290i	$0.164938\pi$
$54$	−0.258819	+	0.448288i	−0.0352208	+	0.0610042i
$55$	−4.89898	+	6.00000i	−0.660578	+	0.809040i
$56$		0			0
$57$		−	5.27792i		−	0.699077i
$58$	2.20925	+	1.27551i	0.290089	+	0.167483i
$59$	0.378937	+	0.656339i	0.0493334	+	0.0854480i	0.889638	−	0.456667i	$-0.150957\pi$
$59$	0.378937	+	0.656339i	0.0493334	+	0.0854480i	−0.840304	+	0.542115i	$0.817624\pi$
$60$	0.621320	−	3.82282i	0.0802121	−	0.493524i
$61$	0.328169	−	0.568406i	0.0420178	−	0.0727769i	−0.844252	−	0.535947i	$-0.819955\pi$
$61$	0.328169	−	0.568406i	0.0420178	−	0.0727769i	0.886269	+	0.463170i	$0.153288\pi$
$62$		−	3.80385i		−	0.483089i
$63$		0			0
$64$	2.26795			0.283494
$65$	8.36308	−	3.17157i	1.03731	−	0.393385i
$66$	0.896575	+	1.55291i	0.110361	+	0.191151i
$67$	−10.9348	+	6.31319i	−1.33589	+	0.771279i	−0.986196	−	0.165583i	$-0.947049\pi$
$67$	−10.9348	+	6.31319i	−1.33589	+	0.771279i	−0.349699	+	0.936862i	$0.613716\pi$
$68$	6.00000	+	3.46410i	0.727607	+	0.420084i
$69$	−3.48477			−0.419517
$70$		0			0
$71$	−6.39230			−0.758627			−0.379314	−	0.925268i	$-0.623840\pi$
$71$	−6.39230			−0.758627			−0.379314	+	0.925268i	$0.623840\pi$
$72$	−1.67303	−	0.965926i	−0.197169	−	0.113835i
$73$	−2.53590	+	1.46410i	−0.296804	+	0.171360i	−0.641006	−	0.767535i	$-0.721483\pi$
$73$	−2.53590	+	1.46410i	−0.296804	+	0.171360i	0.344202	+	0.938896i	$0.388149\pi$
$74$	−2.73205	−	4.73205i	−0.317594	−	0.550090i
$75$	1.58346	−	4.74264i	0.182843	−	0.547633i
$76$	9.14162			1.04862
$77$		0			0
$78$		−	2.07055i		−	0.234444i
$79$	−2.26795	+	3.92820i	−0.255164	+	0.441957i	−0.964940	−	0.262470i	$-0.915463\pi$
$79$	−2.26795	+	3.92820i	−0.255164	+	0.441957i	0.709776	+	0.704428i	$0.248796\pi$
$80$	5.43854	+	0.883921i	0.608047	+	0.0988254i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−3.80385	−	2.19615i	−0.420065	−	0.242524i
$83$			6.00000i			0.658586i	0.944228	+	0.329293i	$0.106810\pi$
$83$			6.00000i			0.658586i	−0.944228	+	0.329293i	$0.893190\pi$
$84$		0			0
$85$	6.92820	+	5.65685i	0.751469	+	0.613572i
$86$		0			0
$87$	−4.26795	+	2.46410i	−0.457572	+	0.264179i
$88$	−5.79555	+	3.34607i	−0.617808	+	0.356692i
$89$	7.72741	−	13.3843i	0.819103	−	1.41873i	−0.0872401	−	0.996187i	$-0.527805\pi$
$89$	7.72741	−	13.3843i	0.819103	−	1.41873i	0.906344	−	0.422542i	$-0.138862\pi$
$90$	−0.896575	−	0.732051i	−0.0945074	−	0.0771649i
$91$		0			0
$92$		−	6.03579i		−	0.629275i
$93$	6.36396	+	3.67423i	0.659912	+	0.381000i
$94$	1.55291	+	2.68973i	0.160171	+	0.277424i
$95$	11.6489	+	1.89329i	1.19515	+	0.194248i
$96$	2.56961	−	4.45069i	0.262260	−	0.454247i
$97$		−	18.9282i		−	1.92187i	−0.276778	−	0.960934i	$-0.589267\pi$
$97$		−	18.9282i		−	1.92187i	0.276778	−	0.960934i	$-0.410733\pi$
$98$		0			0
$99$	−3.46410			−0.348155
$100$	8.21449	+	2.74264i	0.821449	+	0.274264i
$101$	−3.48477	−	6.03579i	−0.346747	−	0.600584i	0.638922	−	0.769271i	$-0.279380\pi$
$101$	−3.48477	−	6.03579i	−0.346747	−	0.600584i	−0.985670	+	0.168687i	$0.946047\pi$
$102$	1.79315	−	1.03528i	0.177548	−	0.102508i
$103$	−12.0000	−	6.92820i	−1.18240	−	0.682656i	−0.225828	−	0.974167i	$-0.572509\pi$
$103$	−12.0000	−	6.92820i	−1.18240	−	0.682656i	−0.956567	+	0.291511i	$0.905842\pi$
$104$	7.72741			0.757735
$105$		0			0
$106$	3.80385			0.369462
$107$	−13.4722	−	7.77817i	−1.30241	−	0.751945i	−0.321590	−	0.946879i	$-0.604217\pi$
$107$	−13.4722	−	7.77817i	−1.30241	−	0.751945i	−0.980816	+	0.194935i	$0.937551\pi$
$108$	1.50000	−	0.866025i	0.144338	−	0.0833333i
$109$	7.92820	+	13.7321i	0.759384	+	1.31529i	0.943165	+	0.332325i	$0.107833\pi$
$109$	7.92820	+	13.7321i	0.759384	+	1.31529i	−0.183781	+	0.982967i	$0.558834\pi$
$110$	−3.74907	+	1.42178i	−0.357459	+	0.135561i
$111$	10.5558			1.00192
$112$		0			0
$113$			5.27792i			0.496505i	0.968695	+	0.248252i	$0.0798562\pi$
$113$			5.27792i			0.496505i	−0.968695	+	0.248252i	$0.920144\pi$
$114$	1.36603	−	2.36603i	0.127940	−	0.221599i
$115$	1.25005	−	7.69125i	0.116568	−	0.717213i
$116$	−4.26795	−	7.39230i	−0.396269	−	0.686358i
$117$	3.46410	+	2.00000i	0.320256	+	0.184900i
$118$			0.392305i			0.0361146i
$119$		0			0
$120$	2.73205	−	3.34607i	0.249401	−	0.305453i
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	0.294229	−	0.169873i	0.0266382	−	0.0153796i
$123$	7.34847	−	4.24264i	0.662589	−	0.382546i
$124$	−6.36396	+	11.0227i	−0.571501	+	0.989868i
$125$	9.89949	+	5.19615i	0.885438	+	0.464758i
$126$		0			0
$127$			2.82843i			0.250982i	0.992095	+	0.125491i	$0.0400507\pi$
$127$			2.82843i			0.250982i	−0.992095	+	0.125491i	$0.959949\pi$
$128$	9.91808	+	5.72620i	0.876642	+	0.506130i
$129$		0			0
$130$	4.56993	+	0.742747i	0.400809	+	0.0651433i
$131$	−2.82843	+	4.89898i	−0.247121	+	0.428026i	−0.962726	−	0.270479i	$-0.912818\pi$
$131$	−2.82843	+	4.89898i	−0.247121	+	0.428026i	0.715605	+	0.698505i	$0.246151\pi$
$132$		−	6.00000i		−	0.522233i
$133$		0			0
$134$	−6.53590			−0.564616
$135$	2.09077	−	0.792893i	0.179945	−	0.0682414i
$136$	3.86370	+	6.69213i	0.331310	+	0.573845i
$137$	8.81345	−	5.08845i	0.752984	−	0.434735i	−0.0737871	−	0.997274i	$-0.523509\pi$
$137$	8.81345	−	5.08845i	0.752984	−	0.434735i	0.826771	+	0.562539i	$0.190175\pi$
$138$	−1.56218	−	0.901924i	−0.132981	−	0.0767769i
$139$	−0.378937			−0.0321410			−0.0160705	−	0.999871i	$-0.505116\pi$
$139$	−0.378937			−0.0321410			−0.0160705	+	0.999871i	$0.505116\pi$
$140$		0			0
$141$	−6.00000			−0.505291
$142$	−2.86559	−	1.65445i	−0.240475	−	0.138838i
$143$	12.0000	−	6.92820i	1.00349	−	0.579365i
$144$	1.23205	+	2.13397i	0.102671	+	0.177831i
$145$	−3.90754	−	10.3037i	−0.324503	−	0.855679i
$146$	−1.51575			−0.125444
$147$		0			0
$148$			18.2832i			1.50287i
$149$	3.53590	−	6.12436i	0.289672	−	0.501727i	−0.684059	−	0.729426i	$-0.739787\pi$
$149$	3.53590	−	6.12436i	0.289672	−	0.501727i	0.973731	+	0.227700i	$0.0731204\pi$
$150$	1.93733	−	1.71624i	0.158183	−	0.140130i
$151$	9.73205	+	16.8564i	0.791983	+	1.37175i	0.924737	+	0.380606i	$0.124285\pi$
$151$	9.73205	+	16.8564i	0.791983	+	1.37175i	−0.132754	+	0.991149i	$0.542382\pi$
$152$	8.83013	+	5.09808i	0.716218	+	0.413509i
$153$			4.00000i			0.323381i
$154$		0			0
$155$	−10.3923	+	12.7279i	−0.834730	+	1.02233i
$156$	−3.46410	+	6.00000i	−0.277350	+	0.480384i
$157$	−4.39230	+	2.53590i	−0.350544	+	0.202387i	−0.664925	−	0.746910i	$-0.731536\pi$
$157$	−4.39230	+	2.53590i	−0.350544	+	0.202387i	0.314381	+	0.949297i	$0.398203\pi$
$158$	−2.03339	+	1.17398i	−0.161768	+	0.0933966i
$159$	−3.67423	+	6.36396i	−0.291386	+	0.504695i
$160$	8.90138	+	7.26795i	0.703716	+	0.574582i
$161$		0			0
$162$		−	0.517638i		−	0.0406695i
$163$	−19.4201	−	11.2122i	−1.52110	−	0.878205i	−0.999690	−	0.0248963i	$-0.992074\pi$
$163$	−19.4201	−	11.2122i	−1.52110	−	0.878205i	−0.521406	−	0.853309i	$-0.674592\pi$
$164$	7.34847	+	12.7279i	0.573819	+	0.993884i
$165$	1.24264	−	7.64564i	0.0967394	−	0.595212i
$166$	−1.55291	+	2.68973i	−0.120530	+	0.208763i
$167$		−	18.9282i		−	1.46471i	−0.680924	−	0.732354i	$-0.738422\pi$
$167$		−	18.9282i		−	1.46471i	0.680924	−	0.732354i	$-0.261578\pi$
$168$		0			0
$169$	−3.00000			−0.230769
$170$	1.64173	+	4.32905i	0.125915	+	0.332023i
$171$	2.63896	+	4.57081i	0.201806	+	0.349539i
$172$		0			0
$173$	−13.8564	−	8.00000i	−1.05348	−	0.608229i	−0.129861	−	0.991532i	$-0.541453\pi$
$173$	−13.8564	−	8.00000i	−1.05348	−	0.608229i	−0.923622	+	0.383304i	$0.874786\pi$
$174$	−2.55103			−0.193393
$175$		0			0
$176$	8.53590			0.643418
$177$	−0.656339	−	0.378937i	−0.0493334	−	0.0284827i
$178$	6.92820	−	4.00000i	0.519291	−	0.299813i
$179$	5.19615	+	9.00000i	0.388379	+	0.672692i	0.992232	−	0.124404i	$-0.0397019\pi$
$179$	5.19615	+	9.00000i	0.388379	+	0.672692i	−0.603853	+	0.797096i	$0.706369\pi$
$180$	1.37333	+	3.62132i	0.102362	+	0.269917i
$181$	6.31319			0.469256			0.234628	−	0.972085i	$-0.424613\pi$
$181$	6.31319			0.469256			0.234628	+	0.972085i	$0.424613\pi$
$182$		0			0
$183$			0.656339i			0.0485180i
$184$	3.36603	−	5.83013i	0.248147	−	0.429803i
$185$	−3.78658	+	23.2979i	−0.278395	+	1.71289i
$186$	1.90192	+	3.29423i	0.139456	+	0.241545i
$187$	12.0000	+	6.92820i	0.877527	+	0.506640i
$188$		−	10.3923i		−	0.757937i
$189$		0			0
$190$	4.73205	+	3.86370i	0.343299	+	0.280302i
$191$	3.73205	−	6.46410i	0.270042	−	0.467726i	−0.698831	−	0.715287i	$-0.746296\pi$
$191$	3.73205	−	6.46410i	0.270042	−	0.467726i	0.968872	+	0.247561i	$0.0796292\pi$
$192$	−1.96410	+	1.13397i	−0.141747	+	0.0818376i
$193$	5.55532	−	3.20736i	0.399881	−	0.230871i	−0.286552	−	0.958065i	$-0.592509\pi$
$193$	5.55532	−	3.20736i	0.399881	−	0.230871i	0.686432	+	0.727194i	$0.259176\pi$
$194$	4.89898	−	8.48528i	0.351726	−	0.609208i
$195$	−5.65685	+	6.92820i	−0.405096	+	0.496139i
$196$		0			0
$197$		−	22.8033i		−	1.62467i	−0.583193	−	0.812333i	$-0.698197\pi$
$197$		−	22.8033i		−	1.62467i	0.583193	−	0.812333i	$-0.301803\pi$
$198$	−1.55291	−	0.896575i	−0.110361	−	0.0637168i
$199$	−4.05317	−	7.02030i	−0.287322	−	0.497656i	0.685848	−	0.727745i	$-0.259432\pi$
$199$	−4.05317	−	7.02030i	−0.287322	−	0.497656i	−0.973170	+	0.230089i	$0.926098\pi$
$200$	6.40508	+	7.23023i	0.452908	+	0.511254i
$201$	6.31319	−	10.9348i	0.445298	−	0.771279i
$202$		−	3.60770i		−	0.253837i
$203$		0			0
$204$	−6.92820			−0.485071
$205$	6.72792	+	17.7408i	0.469898	+	1.23907i
$206$	−3.58630	−	6.21166i	−0.249869	−	0.432787i
$207$	3.01790	−	1.74238i	0.209758	−	0.121104i
$208$	−8.53590	−	4.92820i	−0.591858	−	0.341709i
$209$	18.2832			1.26468
$210$		0			0
$211$	−26.9282			−1.85381			−0.926907	−	0.375291i	$-0.877543\pi$
$211$	−26.9282			−1.85381			−0.926907	+	0.375291i	$0.877543\pi$
$212$	−11.0227	−	6.36396i	−0.757042	−	0.437079i
$213$	5.53590	−	3.19615i	0.379314	−	0.218997i
$214$	−4.02628	−	6.97372i	−0.275231	−	0.476714i
$215$		0			0
$216$	1.93185			0.131446
$217$		0			0
$218$			8.20788i			0.555908i
$219$	1.46410	−	2.53590i	0.0989348	−	0.171360i
$220$	13.2426	+	2.15232i	0.892819	+	0.145109i
$221$	−8.00000	−	13.8564i	−0.538138	−	0.932083i
$222$	4.73205	+	2.73205i	0.317594	+	0.183363i
$223$			8.00000i			0.535720i	0.963458	+	0.267860i	$0.0863164\pi$
$223$			8.00000i			0.535720i	−0.963458	+	0.267860i	$0.913684\pi$
$224$		0			0
$225$	1.00000	+	4.89898i	0.0666667	+	0.326599i
$226$	−1.36603	+	2.36603i	−0.0908667	+	0.157386i
$227$	−3.46410	+	2.00000i	−0.229920	+	0.132745i	−0.610535	−	0.791989i	$-0.709046\pi$
$227$	−3.46410	+	2.00000i	−0.229920	+	0.132745i	0.380615	+	0.924734i	$0.375712\pi$
$228$	−7.91688	+	4.57081i	−0.524308	+	0.302709i
$229$	6.74290	−	11.6790i	0.445583	−	0.771773i	−0.552509	−	0.833507i	$-0.686330\pi$
$229$	6.74290	−	11.6790i	0.445583	−	0.771773i	0.998093	+	0.0617338i	$0.0196630\pi$
$230$	2.55103	−	3.12436i	0.168210	−	0.206014i
$231$		0			0
$232$		−	9.52056i		−	0.625055i
$233$	−4.57081	−	2.63896i	−0.299444	−	0.172884i	0.342749	−	0.939427i	$-0.388642\pi$
$233$	−4.57081	−	2.63896i	−0.299444	−	0.172884i	−0.642193	+	0.766543i	$0.721975\pi$
$234$	1.03528	+	1.79315i	0.0676781	+	0.117222i
$235$	2.15232	−	13.2426i	0.140402	−	0.863855i
$236$	0.656339	−	1.13681i	0.0427240	−	0.0740002i
$237$		−	4.53590i		−	0.294638i
$238$		0			0
$239$	8.53590			0.552141			0.276071	−	0.961137i	$-0.410968\pi$
$239$	8.53590			0.552141			0.276071	+	0.961137i	$0.410968\pi$
$240$	−5.15187	+	1.95377i	−0.332552	+	0.126115i
$241$	7.02030	+	12.1595i	0.452217	+	0.783263i	0.998523	−	0.0543223i	$-0.0172998\pi$
$241$	7.02030	+	12.1595i	0.452217	+	0.783263i	−0.546306	+	0.837586i	$0.683966\pi$
$242$	−0.448288	+	0.258819i	−0.0288170	+	0.0166375i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	−1.13681			−0.0727769
$245$		0			0
$246$	4.39230			0.280043
$247$	−18.2832	−	10.5558i	−1.16333	−	0.671652i
$248$	−12.2942	+	7.09808i	−0.780684	+	0.450728i
$249$	−3.00000	−	5.19615i	−0.190117	−	0.329293i
$250$	3.09296	+	4.89155i	0.195616	+	0.309369i
$251$	−20.3538			−1.28472			−0.642360	−	0.766403i	$-0.722045\pi$
$251$	−20.3538			−1.28472			−0.642360	+	0.766403i	$0.722045\pi$
$252$		0			0
$253$		−	12.0716i		−	0.758934i
$254$	−0.732051	+	1.26795i	−0.0459330	+	0.0795582i
$255$	−8.82843	−	1.43488i	−0.552858	−	0.0898555i
$256$	0.696152	+	1.20577i	0.0435095	+	0.0753607i
$257$	−3.00000	−	1.73205i	−0.187135	−	0.108042i	0.403506	−	0.914977i	$-0.367792\pi$
$257$	−3.00000	−	1.73205i	−0.187135	−	0.108042i	−0.590641	+	0.806935i	$0.701125\pi$
$258$		0			0
$259$		0			0
$260$	−12.0000	−	9.79796i	−0.744208	−	0.607644i
$261$	2.46410	−	4.26795i	0.152524	−	0.264179i
$262$	−2.53590	+	1.46410i	−0.156668	+	0.0904525i
$263$	−6.60420	+	3.81294i	−0.407232	+	0.235116i	−0.689600	−	0.724191i	$-0.742214\pi$
$263$	−6.60420	+	3.81294i	−0.407232	+	0.235116i	0.282368	+	0.959306i	$0.408880\pi$
$264$	3.34607	−	5.79555i	0.205936	−	0.356692i
$265$	−12.7279	−	10.3923i	−0.781870	−	0.638394i
$266$		0			0
$267$			15.4548i			0.945819i
$268$	18.9396	+	10.9348i	1.15692	+	0.667947i
$269$	−15.4548	−	26.7685i	−0.942297	−	1.63211i	−0.761076	−	0.648663i	$-0.775328\pi$
$269$	−15.4548	−	26.7685i	−0.942297	−	1.63211i	−0.181221	−	0.983442i	$-0.558005\pi$
$270$	1.14248	+	0.185687i	0.0695293	+	0.0113005i
$271$	−0.845807	+	1.46498i	−0.0513791	+	0.0889913i	−0.890571	−	0.454844i	$-0.849695\pi$
$271$	−0.845807	+	1.46498i	−0.0513791	+	0.0889913i	0.839192	+	0.543835i	$0.183028\pi$
$272$		−	9.85641i		−	0.597632i
$273$		0			0
$274$	5.26795			0.318248
$275$	16.4290	+	5.48528i	0.990705	+	0.330775i
$276$	3.01790	+	5.22715i	0.181656	+	0.314637i
$277$	−9.79796	+	5.65685i	−0.588702	+	0.339887i	−0.764584	−	0.644524i	$-0.777056\pi$
$277$	−9.79796	+	5.65685i	−0.588702	+	0.339887i	0.175882	+	0.984411i	$0.443722\pi$
$278$	−0.169873	−	0.0980762i	−0.0101883	−	0.00588222i
$279$	−7.34847			−0.439941
$280$		0			0
$281$	27.8564			1.66177			0.830887	−	0.556441i	$-0.187834\pi$
$281$	27.8564			1.66177			0.830887	+	0.556441i	$0.187834\pi$
$282$	−2.68973	−	1.55291i	−0.160171	−	0.0924747i
$283$	1.85641	−	1.07180i	0.110352	−	0.0637117i	−0.443808	−	0.896122i	$-0.646373\pi$
$283$	1.85641	−	1.07180i	0.110352	−	0.0637117i	0.554160	+	0.832410i	$0.313040\pi$
$284$	5.53590	+	9.58846i	0.328495	+	0.568970i
$285$	−11.0349	+	4.18482i	−0.653652	+	0.247888i
$286$	7.17260			0.424125
$287$		0			0
$288$			5.13922i			0.302831i
$289$	−0.500000	+	0.866025i	−0.0294118	+	0.0509427i
$290$	0.915103	−	5.63039i	0.0537367	−	0.330628i
$291$	9.46410	+	16.3923i	0.554795	+	0.960934i
$292$	4.39230	+	2.53590i	0.257040	+	0.148402i
$293$			11.4641i			0.669740i	0.942264	+	0.334870i	$0.108692\pi$
$293$			11.4641i			0.669740i	−0.942264	+	0.334870i	$0.891308\pi$
$294$		0			0
$295$	1.07180	−	1.31268i	0.0624024	−	0.0764270i
$296$	−10.1962	+	17.6603i	−0.592639	+	1.02648i
$297$	3.00000	−	1.73205i	0.174078	−	0.100504i
$298$	3.17020	−	1.83032i	0.183645	−	0.106027i
$299$	−6.96953	+	12.0716i	−0.403058	+	0.698118i
$300$	−8.48528	+	1.73205i	−0.489898	+	0.100000i
$301$		0			0
$302$			10.0754i			0.579772i
$303$	6.03579	+	3.48477i	0.346747	+	0.200195i
$304$	−6.50266	−	11.2629i	−0.372953	−	0.645974i
$305$	−1.44861	−	0.235442i	−0.0829472	−	0.0134813i
$306$	−1.03528	+	1.79315i	−0.0591828	+	0.102508i
$307$			4.00000i			0.228292i	0.993464	+	0.114146i	$0.0364132\pi$
$307$			4.00000i			0.228292i	−0.993464	+	0.114146i	$0.963587\pi$
$308$		0			0
$309$	13.8564			0.788263
$310$	−7.95297	+	3.01604i	−0.451698	+	0.171300i
$311$	2.07055	+	3.58630i	0.117410	+	0.203361i	0.918741	−	0.394861i	$-0.129207\pi$
$311$	2.07055	+	3.58630i	0.117410	+	0.203361i	−0.801330	+	0.598222i	$0.795874\pi$
$312$	−6.69213	+	3.86370i	−0.378867	+	0.218739i
$313$	2.53590	+	1.46410i	0.143337	+	0.0827559i	0.569954	−	0.821677i	$-0.306961\pi$
$313$	2.53590	+	1.46410i	0.143337	+	0.0827559i	−0.426616	+	0.904433i	$0.640294\pi$
$314$	−2.62536			−0.148157
$315$		0			0
$316$	7.85641			0.441957
$317$	4.09034	+	2.36156i	0.229736	+	0.132638i	0.610450	−	0.792055i	$-0.290988\pi$
$317$	4.09034	+	2.36156i	0.229736	+	0.132638i	−0.380714	+	0.924693i	$0.624322\pi$
$318$	−3.29423	+	1.90192i	−0.184731	+	0.106655i
$319$	−8.53590	−	14.7846i	−0.477919	−	0.827779i
$320$	−1.79824	−	4.74176i	−0.100525	−	0.265072i
$321$	15.5563			0.868271
$322$		0			0
$323$		−	21.1117i		−	1.17468i
$324$	−0.866025	+	1.50000i	−0.0481125	+	0.0833333i
$325$	−13.2621	−	14.9706i	−0.735647	−	0.830417i
$326$	−5.80385	−	10.0526i	−0.321445	−	0.556760i
$327$	−13.7321	−	7.92820i	−0.759384	−	0.438431i
$328$			16.3923i			0.905114i
$329$		0			0
$330$	2.53590	−	3.10583i	0.139597	−	0.170970i
$331$	4.39230	−	7.60770i	0.241423	−	0.418157i	−0.719697	−	0.694288i	$-0.755719\pi$
$331$	4.39230	−	7.60770i	0.241423	−	0.418157i	0.961120	+	0.276132i	$0.0890526\pi$
$332$	9.00000	−	5.19615i	0.493939	−	0.285176i
$333$	−9.14162	+	5.27792i	−0.500958	+	0.289228i
$334$	4.89898	−	8.48528i	0.268060	−	0.464294i
$335$	21.8695	+	17.8564i	1.19486	+	0.975600i
$336$		0			0
$337$		−	17.7284i		−	0.965730i	−0.875695	−	0.482865i	$-0.839596\pi$
$337$		−	17.7284i		−	0.965730i	0.875695	−	0.482865i	$-0.160404\pi$
$338$	−1.34486	−	0.776457i	−0.0731509	−	0.0422337i
$339$	−2.63896	−	4.57081i	−0.143329	−	0.248252i
$340$	2.48528	−	15.2913i	0.134783	−	0.829286i
$341$	−12.7279	+	22.0454i	−0.689256	+	1.19383i
$342$			2.73205i			0.147732i
$343$		0			0
$344$		0			0
$345$	2.76305	+	7.28585i	0.148757	+	0.392257i
$346$	−4.14110	−	7.17260i	−0.222627	−	0.385602i
$347$	−26.8565	+	15.5056i	−1.44173	+	0.832383i	−0.997965	−	0.0637601i	$-0.979691\pi$
$347$	−26.8565	+	15.5056i	−1.44173	+	0.832383i	−0.443765	+	0.896143i	$0.646357\pi$
$348$	7.39230	+	4.26795i	0.396269	+	0.228786i
$349$	−17.6269			−0.943546			−0.471773	−	0.881720i	$-0.656386\pi$
$349$	−17.6269			−0.943546			−0.471773	+	0.881720i	$0.656386\pi$
$350$		0			0
$351$	−4.00000			−0.213504
$352$	15.4176	+	8.90138i	0.821763	+	0.474445i
$353$	9.92820	−	5.73205i	0.528425	−	0.305086i	−0.211950	−	0.977281i	$-0.567981\pi$
$353$	9.92820	−	5.73205i	0.528425	−	0.305086i	0.740375	+	0.672194i	$0.234648\pi$
$354$	−0.196152	−	0.339746i	−0.0104254	−	0.0180573i
$355$	5.06842	+	13.3648i	0.269004	+	0.709332i
$356$	−26.7685			−1.41873
$357$		0			0
$358$			5.37945i			0.284313i
$359$	7.73205	−	13.3923i	0.408082	−	0.706819i	−0.586593	−	0.809882i	$-0.699531\pi$
$359$	7.73205	−	13.3923i	0.408082	−	0.706819i	0.994675	+	0.103063i	$0.0328644\pi$
$360$	−0.692993	+	4.26380i	−0.0365239	+	0.224722i
$361$	−4.42820	−	7.66987i	−0.233063	−	0.403678i
$362$	2.83013	+	1.63397i	0.148748	+	0.0858798i
$363$		−	1.00000i		−	0.0524864i
$364$		0			0
$365$	5.07180	+	4.14110i	0.265470	+	0.216755i
$366$	−0.169873	+	0.294229i	−0.00887940	+	0.0153796i
$367$	−3.46410	+	2.00000i	−0.180825	+	0.104399i	−0.587680	−	0.809093i	$-0.699959\pi$
$367$	−3.46410	+	2.00000i	−0.180825	+	0.104399i	0.406855	+	0.913493i	$0.366625\pi$
$368$	−7.43640	+	4.29341i	−0.387649	+	0.223809i
$369$	−4.24264	+	7.34847i	−0.220863	+	0.382546i
$370$	−7.72741	+	9.46410i	−0.401729	+	0.492015i
$371$		0			0
$372$		−	12.7279i		−	0.659912i
$373$	6.21166	+	3.58630i	0.321627	+	0.185692i	0.652118	−	0.758118i	$-0.273881\pi$
$373$	6.21166	+	3.58630i	0.321627	+	0.185692i	−0.330490	+	0.943809i	$0.607214\pi$
$374$	3.58630	+	6.21166i	0.185443	+	0.321197i
$375$	−11.1713	+	0.449747i	−0.576883	+	0.0232249i
$376$	5.79555	−	10.0382i	0.298883	−	0.517680i
$377$			19.7128i			1.01526i
$378$		0			0
$379$	−11.4641			−0.588871			−0.294436	−	0.955671i	$-0.595132\pi$
$379$	−11.4641			−0.588871			−0.294436	+	0.955671i	$0.595132\pi$
$380$	−7.24833	−	19.1130i	−0.371831	−	0.980478i
$381$	−1.41421	−	2.44949i	−0.0724524	−	0.125491i
$382$	3.34607	−	1.93185i	0.171200	−	0.0988421i
$383$	20.6603	+	11.9282i	1.05569	+	0.609503i	0.924237	−	0.381820i	$-0.124702\pi$
$383$	20.6603	+	11.9282i	1.05569	+	0.609503i	0.131453	+	0.991322i	$0.458036\pi$
$384$	−11.4524			−0.584428
$385$		0			0
$386$	3.32051			0.169009
$387$		0			0
$388$	−28.3923	+	16.3923i	−1.44140	+	0.832193i
$389$	5.53590	+	9.58846i	0.280681	+	0.486154i	0.971553	−	0.236823i	$-0.0761063\pi$
$389$	5.53590	+	9.58846i	0.280681	+	0.486154i	−0.690872	+	0.722978i	$0.742773\pi$
$390$	−4.32905	+	1.64173i	−0.219210	+	0.0831321i
$391$	−13.9391			−0.704929
$392$		0			0
$393$		−	5.65685i		−	0.285351i
$394$	5.90192	−	10.2224i	0.297335	−	0.514999i
$395$	10.0112	+	1.62712i	0.503719	+	0.0818690i
$396$	3.00000	+	5.19615i	0.150756	+	0.261116i
$397$	20.5359	+	11.8564i	1.03067	+	0.595056i	0.917176	−	0.398483i	$-0.130463\pi$
$397$	20.5359	+	11.8564i	1.03067	+	0.595056i	0.113491	+	0.993539i	$0.463797\pi$
$398$		−	4.19615i		−	0.210334i
$399$		0			0
$400$	−2.46410	−	12.0716i	−0.123205	−	0.603579i
$401$	−1.00000	+	1.73205i	−0.0499376	+	0.0864945i	−0.889914	−	0.456129i	$-0.849236\pi$
$401$	−1.00000	+	1.73205i	−0.0499376	+	0.0864945i	0.839976	+	0.542623i	$0.182569\pi$
$402$	5.66025	−	3.26795i	0.282308	−	0.162990i
$403$	25.4558	−	14.6969i	1.26805	−	0.732107i
$404$	−6.03579	+	10.4543i	−0.300292	+	0.520121i
$405$	−1.41421	+	1.73205i	−0.0702728	+	0.0860663i
$406$		0			0
$407$			36.5665i			1.81253i
$408$	−6.69213	−	3.86370i	−0.331310	−	0.191282i
$409$	5.70762	+	9.88589i	0.282224	+	0.488826i	0.971932	−	0.235261i	$-0.0755946\pi$
$409$	5.70762	+	9.88589i	0.282224	+	0.488826i	−0.689708	+	0.724087i	$0.742261\pi$
$410$	−1.57561	+	9.69429i	−0.0778136	+	0.478767i
$411$	−5.08845	+	8.81345i	−0.250995	+	0.434735i
$412$			24.0000i			1.18240i
$413$		0			0
$414$	1.80385			0.0886543
$415$	12.5446	−	4.75736i	0.615791	−	0.233530i
$416$	−10.2784	−	17.8028i	−0.503942	−	0.872852i
$417$	0.328169	−	0.189469i	0.0160705	−	0.00927832i
$418$	8.19615	+	4.73205i	0.400887	+	0.231452i
$419$	−21.1117			−1.03137			−0.515686	−	0.856778i	$-0.672463\pi$
$419$	−21.1117			−1.03137			−0.515686	+	0.856778i	$0.672463\pi$
$420$		0			0
$421$	12.7846			0.623084			0.311542	−	0.950232i	$-0.399155\pi$
$421$	12.7846			0.623084			0.311542	+	0.950232i	$0.399155\pi$
$422$	−12.0716	−	6.96953i	−0.587635	−	0.339272i
$423$	5.19615	−	3.00000i	0.252646	−	0.145865i
$424$	−7.09808	−	12.2942i	−0.344713	−	0.597061i
$425$	6.33386	−	18.9706i	0.307237	−	0.920207i
$426$	3.30890			0.160317
$427$		0			0
$428$			26.9444i			1.30241i
$429$	−6.92820	+	12.0000i	−0.334497	+	0.579365i
$430$		0			0
$431$	−18.6603	−	32.3205i	−0.898833	−	1.55682i	−0.828988	−	0.559266i	$-0.811083\pi$
$431$	−18.6603	−	32.3205i	−0.898833	−	1.55682i	−0.0698447	−	0.997558i	$-0.522250\pi$
$432$	−2.13397	−	1.23205i	−0.102671	−	0.0592771i
$433$		−	17.8564i		−	0.858124i	−0.903275	−	0.429062i	$-0.858844\pi$
$433$		−	17.8564i		−	0.858124i	0.903275	−	0.429062i	$-0.141156\pi$
$434$		0			0
$435$	8.53590	+	6.96953i	0.409265	+	0.334163i
$436$	13.7321	−	23.7846i	0.657646	−	1.13908i
$437$	−15.9282	+	9.19615i	−0.761949	+	0.439912i
$438$	1.31268	−	0.757875i	0.0627222	−	0.0362127i
$439$	−6.50266	+	11.2629i	−0.310355	+	0.537551i	−0.978439	−	0.206535i	$-0.933781\pi$
$439$	−6.50266	+	11.2629i	−0.310355	+	0.537551i	0.668084	+	0.744086i	$0.267115\pi$
$440$	11.5911	+	9.46410i	0.552584	+	0.451183i
$441$		0			0
$442$		−	8.28221i		−	0.393945i
$443$	10.8468	+	6.26243i	0.515349	+	0.297537i	0.735030	−	0.678035i	$-0.237168\pi$
$443$	10.8468	+	6.26243i	0.515349	+	0.297537i	−0.219681	+	0.975572i	$0.570502\pi$
$444$	−9.14162	−	15.8338i	−0.433842	−	0.751437i
$445$	−34.1104	−	5.54394i	−1.61699	−	0.262808i
$446$	−2.07055	+	3.58630i	−0.0980435	+	0.169816i
$447$			7.07180i			0.334485i
$448$		0			0
$449$	−35.8564			−1.69217			−0.846084	−	0.533049i	$-0.821046\pi$
$449$	−35.8564			−1.69217			−0.846084	+	0.533049i	$0.821046\pi$
$450$	−0.819661	+	2.45497i	−0.0386392	+	0.115728i
$451$	14.6969	+	25.4558i	0.692052	+	1.19867i
$452$	7.91688	−	4.57081i	0.372378	−	0.214993i
$453$	−16.8564	−	9.73205i	−0.791983	−	0.457252i
$454$	−2.07055			−0.0971758
$455$		0			0
$456$	−10.1962			−0.477479
$457$	18.9396	+	10.9348i	0.885956	+	0.511507i	0.872618	−	0.488404i	$-0.162421\pi$
$457$	18.9396	+	10.9348i	0.885956	+	0.511507i	0.0133385	+	0.999911i	$0.495754\pi$
$458$	6.04552	−	3.49038i	0.282488	−	0.163095i
$459$	−2.00000	−	3.46410i	−0.0933520	−	0.161690i
$460$	−12.6195	+	4.78574i	−0.588385	+	0.223136i
$461$	−32.4254			−1.51020			−0.755100	−	0.655609i	$-0.772412\pi$
$461$	−32.4254			−1.51020			−0.755100	+	0.655609i	$0.772412\pi$
$462$		0			0
$463$		−	22.4243i		−	1.04215i	−0.853512	−	0.521074i	$-0.825532\pi$
$463$		−	22.4243i		−	1.04215i	0.853512	−	0.521074i	$-0.174468\pi$
$464$	−6.07180	+	10.5167i	−0.281876	+	0.488224i
$465$	2.63604	−	16.2189i	0.122243	−	0.752131i
$466$	−1.36603	−	2.36603i	−0.0632799	−	0.109604i
$467$	−8.53590	−	4.92820i	−0.394994	−	0.228050i	0.289328	−	0.957230i	$-0.406568\pi$
$467$	−8.53590	−	4.92820i	−0.394994	−	0.228050i	−0.684322	+	0.729180i	$0.739902\pi$
$468$		−	6.92820i		−	0.320256i
$469$		0			0
$470$	4.39230	−	5.37945i	0.202602	−	0.248136i
$471$	2.53590	−	4.39230i	0.116848	−	0.202387i
$472$	1.26795	−	0.732051i	0.0583621	−	0.0336954i
$473$		0			0
$474$	1.17398	−	2.03339i	0.0539225	−	0.0933966i
$475$	−5.27792	−	25.8564i	−0.242167	−	1.18637i
$476$		0			0
$477$		−	7.34847i		−	0.336463i
$478$	3.82654	+	2.20925i	0.175022	+	0.101049i
$479$	12.6264	+	21.8695i	0.576914	+	0.999245i	0.995831	+	0.0912201i	$0.0290767\pi$
$479$	12.6264	+	21.8695i	0.576914	+	0.999245i	−0.418916	+	0.908025i	$0.637590\pi$
$480$	−11.3428	−	1.84354i	−0.517726	−	0.0841456i
$481$	21.1117	−	36.5665i	0.962609	−	1.66729i
$482$			7.26795i			0.331046i
$483$		0			0
$484$	1.73205			0.0787296
$485$	−39.5745	+	15.0080i	−1.79699	+	0.681480i
$486$	0.258819	+	0.448288i	0.0117403	+	0.0203347i
$487$	13.3843	−	7.72741i	0.606499	−	0.350162i	−0.165095	−	0.986278i	$-0.552793\pi$
$487$	13.3843	−	7.72741i	0.606499	−	0.350162i	0.771594	+	0.636115i	$0.219460\pi$
$488$	−1.09808	−	0.633975i	−0.0497076	−	0.0286987i
$489$	22.4243			1.01406
$490$		0			0
$491$	41.3205			1.86477			0.932384	−	0.361469i	$-0.117725\pi$
$491$	41.3205			1.86477			0.932384	+	0.361469i	$0.117725\pi$
$492$	−12.7279	−	7.34847i	−0.573819	−	0.331295i
$493$	−17.0718	+	9.85641i	−0.768875	+	0.443910i
$494$	−5.46410	−	9.46410i	−0.245842	−	0.425810i
$495$	2.74666	+	7.24264i	0.123453	+	0.325532i
$496$	18.1074			0.813045
$497$		0			0
$498$		−	3.10583i		−	0.139176i
$499$	−16.1244	+	27.9282i	−0.721825	+	1.25024i	0.238442	+	0.971157i	$0.423363\pi$
$499$	−16.1244	+	27.9282i	−0.721825	+	1.25024i	−0.960267	+	0.279081i	$0.909970\pi$
$500$	−0.778985	−	19.3492i	−0.0348373	−	0.865324i
$501$	9.46410	+	16.3923i	0.422825	+	0.732354i
$502$	−9.12436	−	5.26795i	−0.407240	−	0.235120i
$503$			23.8564i			1.06370i	0.846837	+	0.531852i	$0.178504\pi$
$503$			23.8564i			1.06370i	−0.846837	+	0.531852i	$0.821496\pi$
$504$		0			0
$505$	−9.85641	+	12.0716i	−0.438604	+	0.537178i
$506$	3.12436	−	5.41154i	0.138895	−	0.240572i
$507$	2.59808	−	1.50000i	0.115385	−	0.0666173i
$508$	4.24264	−	2.44949i	0.188237	−	0.108679i
$509$	1.51575	−	2.62536i	0.0671844	−	0.116367i	−0.830476	−	0.557054i	$-0.811932\pi$
$509$	1.51575	−	2.62536i	0.0671844	−	0.116367i	0.897661	+	0.440687i	$0.145265\pi$
$510$	−3.58630	−	2.92820i	−0.158804	−	0.129663i
$511$		0			0
$512$		−	22.1841i		−	0.980408i
$513$	−4.57081	−	2.63896i	−0.201806	−	0.116513i
$514$	−0.896575	−	1.55291i	−0.0395462	−	0.0684961i
$515$	−4.97056	+	30.5826i	−0.219029	+	1.34763i
$516$		0			0
$517$		−	20.7846i		−	0.914106i
$518$		0			0
$519$	16.0000			0.702322
$520$	−6.12701	−	16.1562i	−0.268687	−	0.708498i
$521$	−14.1421	−	24.4949i	−0.619578	−	1.07314i	−0.989563	−	0.144103i	$-0.953970\pi$
$521$	−14.1421	−	24.4949i	−0.619578	−	1.07314i	0.369984	−	0.929038i	$-0.379363\pi$
$522$	2.20925	−	1.27551i	0.0966964	−	0.0558277i
$523$	37.8564	+	21.8564i	1.65535	+	0.955714i	0.974821	+	0.222988i	$0.0715811\pi$
$523$	37.8564	+	21.8564i	1.65535	+	0.955714i	0.680524	+	0.732726i	$0.261752\pi$
$524$	9.79796			0.428026
$525$		0			0
$526$	−3.94744			−0.172117
$527$	25.4558	+	14.6969i	1.10887	+	0.640209i
$528$	−7.39230	+	4.26795i	−0.321709	+	0.185739i
$529$	−5.42820	−	9.40192i	−0.236009	−	0.408779i
$530$	−3.01604	−	7.95297i	−0.131009	−	0.345455i
$531$	0.757875			0.0328890
$532$		0			0
$533$		−	33.9411i		−	1.47015i
$534$	−4.00000	+	6.92820i	−0.173097	+	0.299813i
$535$	−5.58037	+	34.3345i	−0.241260	+	1.48441i
$536$	12.1962	+	21.1244i	0.526794	+	0.912433i
$537$	−9.00000	−	5.19615i	−0.388379	−	0.224231i
$538$		−	16.0000i		−	0.689809i
$539$		0			0
$540$	−3.00000	−	2.44949i	−0.129099	−	0.105409i
$541$	−13.3205	+	23.0718i	−0.572693	+	0.991934i	0.423595	+	0.905852i	$0.360768\pi$
$541$	−13.3205	+	23.0718i	−0.572693	+	0.991934i	−0.996288	+	0.0860822i	$0.972565\pi$
$542$	−0.758330	+	0.437822i	−0.0325731	+	0.0188061i
$543$	−5.46739	+	3.15660i	−0.234628	+	0.135463i
$544$	10.2784	−	17.8028i	0.440684	−	0.763287i
$545$	22.4243	−	27.4641i	0.960553	−	1.17643i
$546$		0			0
$547$			10.0010i			0.427613i	0.976876	+	0.213807i	$0.0685862\pi$
$547$			10.0010i			0.427613i	−0.976876	+	0.213807i	$0.931414\pi$
$548$	−15.2653	−	8.81345i	−0.652103	−	0.376492i
$549$	−0.328169	−	0.568406i	−0.0140059	−	0.0242590i
$550$	5.94522	+	6.71112i	0.253505	+	0.286163i
$551$	−13.0053	+	22.5259i	−0.554045	+	0.959635i
$552$			6.73205i			0.286535i
$553$		0			0
$554$	−5.85641			−0.248815
$555$	−8.36965	−	22.0698i	−0.355272	−	0.936812i
$556$	0.328169	+	0.568406i	0.0139175	+	0.0241058i
$557$	7.67664	−	4.43211i	0.325270	−	0.187795i	−0.328469	−	0.944515i	$-0.606533\pi$
$557$	7.67664	−	4.43211i	0.325270	−	0.187795i	0.653739	+	0.756720i	$0.273199\pi$
$558$	−3.29423	−	1.90192i	−0.139456	−	0.0805149i
$559$		0			0
$560$		0			0
$561$	−13.8564			−0.585018
$562$	12.4877	+	7.20977i	0.526761	+	0.304126i
$563$	3.58846	−	2.07180i	0.151235	−	0.0873158i	−0.422473	−	0.906376i	$-0.638838\pi$
$563$	3.58846	−	2.07180i	0.151235	−	0.0873158i	0.573708	+	0.819060i	$0.305504\pi$
$564$	5.19615	+	9.00000i	0.218797	+	0.378968i
$565$	11.0349	−	4.18482i	0.464242	−	0.176057i
$566$	1.10961			0.0466402
$567$		0			0
$568$			12.3490i			0.518152i
$569$	−7.92820	+	13.7321i	−0.332368	+	0.575678i	−0.982976	−	0.183736i	$-0.941181\pi$
$569$	−7.92820	+	13.7321i	−0.332368	+	0.575678i	0.650608	+	0.759414i	$0.274514\pi$
$570$	−6.02993	−	0.980040i	−0.252566	−	0.0410494i
$571$	7.85641	+	13.6077i	0.328780	+	0.569464i	0.982270	−	0.187471i	$-0.0600291\pi$
$571$	7.85641	+	13.6077i	0.328780	+	0.569464i	−0.653490	+	0.756935i	$0.726696\pi$
$572$	−20.7846	−	12.0000i	−0.869048	−	0.501745i
$573$			7.46410i			0.311817i
$574$		0			0
$575$	−17.0718	+	3.48477i	−0.711943	+	0.145325i
$576$	1.13397	−	1.96410i	0.0472489	−	0.0818376i
$577$	−3.46410	+	2.00000i	−0.144212	+	0.0832611i	−0.570370	−	0.821388i	$-0.693200\pi$
$577$	−3.46410	+	2.00000i	−0.144212	+	0.0832611i	0.426158	+	0.904649i	$0.359867\pi$
$578$	−0.448288	+	0.258819i	−0.0186463	+	0.0107655i
$579$	−3.20736	+	5.55532i	−0.133294	+	0.230871i
$580$	−12.0716	+	14.7846i	−0.501245	+	0.613898i
$581$		0			0
$582$			9.79796i			0.406138i
$583$	−22.0454	−	12.7279i	−0.913027	−	0.527137i
$584$	2.82843	+	4.89898i	0.117041	+	0.202721i
$585$	1.43488	−	8.82843i	0.0593249	−	0.365011i
$586$	−2.96713	+	5.13922i	−0.122571	+	0.212299i
$587$			4.14359i			0.171024i	0.996337	+	0.0855122i	$0.0272527\pi$
$587$			4.14359i			0.171024i	−0.996337	+	0.0855122i	$0.972747\pi$
$588$		0			0
$589$	38.7846			1.59809
$590$	0.820219	−	0.311056i	0.0337679	−	0.0128060i
$591$	11.4016	+	19.7482i	0.469001	+	0.812333i
$592$	22.5259	−	13.0053i	0.925808	−	0.534516i
$593$	−21.9282	−	12.6603i	−0.900483	−	0.519894i	−0.0231264	−	0.999733i	$-0.507362\pi$
$593$	−21.9282	−	12.6603i	−0.900483	−	0.519894i	−0.877357	+	0.479838i	$0.840695\pi$
$594$	1.79315			0.0735739
$595$		0			0
$596$	−12.2487			−0.501727
$597$	7.02030	+	4.05317i	0.287322	+	0.165885i
$598$	−6.24871	+	3.60770i	−0.255529	+	0.147530i
$599$	14.6603	+	25.3923i	0.599002	+	1.03750i	0.992969	+	0.118377i	$0.0377691\pi$
$599$	14.6603	+	25.3923i	0.599002	+	1.03750i	−0.393967	+	0.919125i	$0.628898\pi$
$600$	−9.16208	−	3.05902i	−0.374040	−	0.124884i
$601$	25.1512			1.02594			0.512970	−	0.858406i	$-0.328545\pi$
$601$	25.1512			1.02594			0.512970	+	0.858406i	$0.328545\pi$
$602$		0			0
$603$			12.6264i			0.514186i
$604$	16.8564	−	29.1962i	0.685877	−	1.18797i
$605$	2.20711	+	0.358719i	0.0897317	+	0.0145840i
$606$	1.80385	+	3.12436i	0.0732763	+	0.126918i
$607$	−10.3923	−	6.00000i	−0.421811	−	0.243532i	0.274041	−	0.961718i	$-0.411640\pi$
$607$	−10.3923	−	6.00000i	−0.421811	−	0.243532i	−0.695852	+	0.718186i	$0.744973\pi$
$608$		−	27.1244i		−	1.10004i
$609$		0			0
$610$	−0.588457	−	0.480473i	−0.0238259	−	0.0194538i
$611$	−12.0000	+	20.7846i	−0.485468	+	0.840855i
$612$	6.00000	−	3.46410i	0.242536	−	0.140028i
$613$	−8.48528	+	4.89898i	−0.342717	+	0.197868i	−0.661473	−	0.749969i	$-0.730068\pi$
$613$	−8.48528	+	4.89898i	−0.342717	+	0.197868i	0.318756	+	0.947837i	$0.396735\pi$
$614$	−1.03528	+	1.79315i	−0.0417803	+	0.0723657i
$615$	−14.6969	−	12.0000i	−0.592638	−	0.483887i
$616$		0			0
$617$			27.1475i			1.09292i	0.837487	+	0.546458i	$0.184024\pi$
$617$			27.1475i			1.09292i	−0.837487	+	0.546458i	$0.815976\pi$
$618$	6.21166	+	3.58630i	0.249869	+	0.144262i
$619$	10.3664	+	17.9551i	0.416659	+	0.721675i	0.995601	−	0.0936937i	$-0.0298674\pi$
$619$	10.3664	+	17.9551i	0.416659	+	0.721675i	−0.578942	+	0.815369i	$0.696534\pi$
$620$	28.0919	+	4.56575i	1.12820	+	0.183365i
$621$	−1.74238	+	3.01790i	−0.0699194	+	0.121104i
$622$			2.14359i			0.0859503i
$623$		0			0
$624$	9.85641			0.394572
$625$	3.01472	−	24.8176i	0.120589	−	0.992703i
$626$	0.757875	+	1.31268i	0.0302908	+	0.0524651i
$627$	−15.8338	+	9.14162i	−0.632339	+	0.365081i
$628$	7.60770	+	4.39230i	0.303580	+	0.175272i
$629$	42.2233			1.68355
$630$		0			0
$631$	−25.3205			−1.00799			−0.503997	−	0.863706i	$-0.668138\pi$
$631$	−25.3205			−1.00799			−0.503997	+	0.863706i	$0.668138\pi$
$632$	7.58871	+	4.38134i	0.301863	+	0.174280i
$633$	23.3205	−	13.4641i	0.926907	−	0.535150i
$634$	1.22243	+	2.11731i	0.0485490	+	0.0840893i
$635$	5.91359	−	2.24264i	0.234674	−	0.0889965i
$636$	12.7279			0.504695
$637$		0			0
$638$		−	8.83701i		−	0.349861i
$639$	−3.19615	+	5.53590i	−0.126438	+	0.218997i
$640$	4.10820	−	25.2767i	0.162391	−	0.999149i
$641$	−5.00000	−	8.66025i	−0.197488	−	0.342059i	0.750225	−	0.661182i	$-0.229945\pi$
$641$	−5.00000	−	8.66025i	−0.197488	−	0.342059i	−0.947713	+	0.319123i	$0.896612\pi$
$642$	6.97372	+	4.02628i	0.275231	+	0.158905i
$643$		−	4.00000i		−	0.157745i	−0.996885	−	0.0788723i	$-0.974868\pi$
$643$		−	4.00000i		−	0.157745i	0.996885	−	0.0788723i	$-0.0251319\pi$
$644$		0			0
$645$		0			0
$646$	5.46410	−	9.46410i	0.214982	−	0.372360i
$647$	37.1769	−	21.4641i	1.46158	−	0.843841i	0.462491	−	0.886624i	$-0.346956\pi$
$647$	37.1769	−	21.4641i	1.46158	−	0.843841i	0.999084	+	0.0427831i	$0.0136224\pi$
$648$	−1.67303	+	0.965926i	−0.0657229	+	0.0379452i
$649$	1.31268	−	2.27362i	0.0515271	−	0.0892476i
$650$	−2.07055	−	10.1436i	−0.0812137	−	0.397864i
$651$		0			0
$652$			38.8401i			1.52110i
$653$	−3.43400	−	1.98262i	−0.134383	−	0.0775859i	0.431301	−	0.902208i	$-0.358055\pi$
$653$	−3.43400	−	1.98262i	−0.134383	−	0.0775859i	−0.565684	+	0.824622i	$0.691388\pi$
$654$	−4.10394	−	7.10823i	−0.160477	−	0.277954i
$655$	12.4853	+	2.02922i	0.487840	+	0.0792883i
$656$	10.4543	−	18.1074i	0.408172	−	0.706974i
$657$			2.92820i			0.114240i
$658$		0			0
$659$	−10.3923			−0.404827			−0.202413	−	0.979300i	$-0.564878\pi$
$659$	−10.3923			−0.404827			−0.202413	+	0.979300i	$0.564878\pi$
$660$	−12.5446	+	4.75736i	−0.488299	+	0.185180i
$661$	6.74290	+	11.6790i	0.262268	+	0.454262i	0.966844	−	0.255366i	$-0.0821961\pi$
$661$	6.74290	+	11.6790i	0.262268	+	0.454262i	−0.704576	+	0.709629i	$0.748863\pi$
$662$	3.93803	−	2.27362i	0.153056	−	0.0883669i
$663$	13.8564	+	8.00000i	0.538138	+	0.310694i
$664$	11.5911			0.449822
$665$		0			0
$666$	−5.46410			−0.211730
$667$	14.8728	+	8.58682i	0.575877	+	0.332483i
$668$	−28.3923	+	16.3923i	−1.09853	+	0.634237i
$669$	−4.00000	−	6.92820i	−0.154649	−	0.267860i
$670$	5.18227	+	13.6651i	0.200209	+	0.527927i
$671$	−2.27362			−0.0877723
$672$		0			0
$673$		−	21.8695i		−	0.843009i	−0.906826	−	0.421504i	$-0.861502\pi$
$673$		−	21.8695i		−	0.843009i	0.906826	−	0.421504i	$-0.138498\pi$
$674$	4.58846	−	7.94744i	0.176741	−	0.306124i
$675$	−3.31552	−	3.74264i	−0.127614	−	0.144054i
$676$	2.59808	+	4.50000i	0.0999260	+	0.173077i
$677$	−20.0718	−	11.5885i	−0.771422	−	0.445381i	0.0619598	−	0.998079i	$-0.480265\pi$
$677$	−20.0718	−	11.5885i	−0.771422	−	0.445381i	−0.833382	+	0.552698i	$0.813598\pi$
$678$		−	2.73205i		−	0.104924i
$679$		0			0
$680$	10.9282	−	13.3843i	0.419077	−	0.513263i
$681$	2.00000	−	3.46410i	0.0766402	−	0.132745i
$682$	−11.4115	+	6.58846i	−0.436971	+	0.252285i
$683$	36.6544	−	21.1624i	1.40254	−	0.809758i	0.407889	−	0.913031i	$-0.366265\pi$
$683$	36.6544	−	21.1624i	1.40254	−	0.809758i	0.994653	+	0.103273i	$0.0329317\pi$
$684$	4.57081	−	7.91688i	0.174769	−	0.302709i
$685$	−17.6269	−	14.3923i	−0.673489	−	0.549902i
$686$		0			0
$687$			13.4858i			0.514515i
$688$		0			0
$689$	14.6969	+	25.4558i	0.559909	+	0.969790i
$690$	−0.647075	+	3.98128i	−0.0246337	+	0.151565i
$691$	5.46739	−	9.46979i	0.207989	−	0.360248i	−0.743092	−	0.669189i	$-0.766641\pi$
$691$	5.46739	−	9.46979i	0.207989	−	0.360248i	0.951081	+	0.308942i	$0.0999748\pi$
$692$			27.7128i			1.05348i
$693$		0			0
$694$	−16.0526			−0.609347
$695$	0.300457	+	0.792271i	0.0113970	+	0.0300526i
$696$	4.76028	+	8.24504i	0.180438	+	0.312528i
$697$	29.3939	−	16.9706i	1.11337	−	0.642806i
$698$	−7.90192	−	4.56218i	−0.299092	−	0.172681i
$699$	5.27792			0.199629
$700$		0			0
$701$	−11.0718			−0.418176			−0.209088	−	0.977897i	$-0.567050\pi$
$701$	−11.0718			−0.418176			−0.209088	+	0.977897i	$0.567050\pi$
$702$	−1.79315	−	1.03528i	−0.0676781	−	0.0390740i
$703$	48.2487	−	27.8564i	1.81973	−	1.05062i
$704$	−3.92820	−	6.80385i	−0.148050	−	0.256430i
$705$	4.75736	+	12.5446i	0.179173	+	0.472458i
$706$	5.93426			0.223339
$707$		0			0
$708$			1.31268i			0.0493334i
$709$	−5.46410	+	9.46410i	−0.205209	+	0.355432i	−0.950199	−	0.311643i	$-0.899121\pi$
$709$	−5.46410	+	9.46410i	−0.205209	+	0.355432i	0.744991	+	0.667075i	$0.232454\pi$
$710$	−1.18697	+	7.30310i	−0.0445461	+	0.274080i
$711$	2.26795	+	3.92820i	0.0850547	+	0.147319i
$712$	−25.8564	−	14.9282i	−0.969010	−	0.559458i
$713$		−	25.6077i		−	0.959016i
$714$		0			0
$715$	−24.0000	−	19.5959i	−0.897549	−	0.732846i
$716$	9.00000	−	15.5885i	0.336346	−	0.582568i
$717$	−7.39230	+	4.26795i	−0.276071	+	0.159389i
$718$	6.93237	−	4.00240i	0.258714	−	0.149368i
$719$	−7.34847	+	12.7279i	−0.274052	+	0.474671i	−0.969895	−	0.243522i	$-0.921697\pi$
$719$	−7.34847	+	12.7279i	−0.274052	+	0.474671i	0.695844	+	0.718193i	$0.255031\pi$
$720$	3.48477	−	4.26795i	0.129870	−	0.159057i
$721$		0			0
$722$		−	4.58441i		−	0.170614i
$723$	−12.1595	−	7.02030i	−0.452217	−	0.261088i
$724$	−5.46739	−	9.46979i	−0.203194	−	0.351942i
$725$	−18.4445	+	16.3395i	−0.685011	+	0.606835i
$726$	0.258819	−	0.448288i	0.00960568	−	0.0166375i
$727$			23.7128i			0.879460i	0.898130	+	0.439730i	$0.144926\pi$
$727$			23.7128i			0.879460i	−0.898130	+	0.439730i	$0.855074\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	1.20183	+	3.16908i	0.0444816	+	0.117293i
$731$		0			0
$732$	0.984508	−	0.568406i	0.0363885	−	0.0210089i
$733$	−15.4641	−	8.92820i	−0.571180	−	0.329771i	0.186441	−	0.982466i	$-0.440305\pi$
$733$	−15.4641	−	8.92820i	−0.571180	−	0.329771i	−0.757620	+	0.652696i	$0.773638\pi$
$734$	−2.07055			−0.0764255
$735$		0			0
$736$	−17.9090			−0.660133
$737$	37.8792	+	21.8695i	1.39530	+	0.805575i
$738$	−3.80385	+	2.19615i	−0.140022	+	0.0808415i
$739$	−12.9282	−	22.3923i	−0.475572	−	0.823714i	0.524037	−	0.851696i	$-0.324425\pi$
$739$	−12.9282	−	22.3923i	−0.475572	−	0.823714i	−0.999608	+	0.0279814i	$0.991092\pi$
$740$	38.2261	−	14.4967i	1.40522	−	0.532908i
$741$	21.1117			0.775556
$742$		0			0
$743$			51.1619i			1.87695i	0.345351	+	0.938474i	$0.387760\pi$
$743$			51.1619i			1.87695i	−0.345351	+	0.938474i	$0.612240\pi$
$744$	7.09808	−	12.2942i	0.260228	−	0.450728i
$745$	−15.6082	−	2.53679i	−0.571841	−	0.0929408i
$746$	1.85641	+	3.21539i	0.0679679	+	0.117724i
$747$	5.19615	+	3.00000i	0.190117	+	0.109764i
$748$		−	24.0000i		−	0.877527i
$749$		0			0
$750$	−5.12436	−	2.68973i	−0.187115	−	0.0982149i
$751$	18.3923	−	31.8564i	0.671145	−	1.16246i	−0.306435	−	0.951892i	$-0.599136\pi$
$751$	18.3923	−	31.8564i	0.671145	−	1.16246i	0.977580	−	0.210565i	$-0.0675304\pi$
$752$	−12.8038	+	7.39230i	−0.466908	+	0.269570i
$753$	17.6269	−	10.1769i	0.642360	−	0.370867i
$754$	−5.10205	+	8.83701i	−0.185806	+	0.321825i
$755$	27.5264	−	33.7128i	1.00179	−	1.22693i
$756$		0			0
$757$			34.2929i			1.24640i	0.782064	+	0.623198i	$0.214167\pi$
$757$			34.2929i			1.24640i	−0.782064	+	0.623198i	$0.785833\pi$
$758$	−5.13922	−	2.96713i	−0.186665	−	0.107771i
$759$	6.03579	+	10.4543i	0.219085	+	0.379467i
$760$	3.65756	−	22.5040i	0.132674	−	0.816306i
$761$	9.04008	−	15.6579i	0.327703	−	0.567598i	−0.654353	−	0.756189i	$-0.727059\pi$
$761$	9.04008	−	15.6579i	0.327703	−	0.567598i	0.982056	+	0.188591i	$0.0603922\pi$
$762$		−	1.46410i		−	0.0530388i
$763$		0			0
$764$	−12.9282			−0.467726
$765$	8.36308	−	3.17157i	0.302368	−	0.114668i
$766$	6.17449	+	10.6945i	0.223093	+	0.386409i
$767$	−2.62536	+	1.51575i	−0.0947961	+	0.0547305i
$768$	−1.20577	−	0.696152i	−0.0435095	−	0.0251202i
$769$	39.2934			1.41696			0.708478	−	0.705733i	$-0.249382\pi$
$769$	39.2934			1.41696			0.708478	+	0.705733i	$0.249382\pi$
$770$		0			0
$771$	3.46410			0.124757
$772$	−9.62209	−	5.55532i	−0.346307	−	0.199940i
$773$	32.7846	−	18.9282i	1.17918	−	0.680800i	0.223356	−	0.974737i	$-0.428299\pi$
$773$	32.7846	−	18.9282i	1.17918	−	0.680800i	0.955825	+	0.293937i	$0.0949655\pi$
$774$		0			0
$775$	34.8511	+	11.6360i	1.25189	+	0.417979i
$776$	−36.5665			−1.31266
$777$		0			0
$778$			5.73118i			0.205473i
$779$	22.3923	−	38.7846i	0.802288	−	1.38960i
$780$	15.2913	+	2.48528i	0.547516	+	0.0889873i
$781$	11.0718	+	19.1769i	0.396180	+	0.686204i
$782$	−6.24871	−	3.60770i	−0.223453	−	0.129011i
$783$			4.92820i			0.176120i
$784$		0			0
$785$	8.78461	+	7.17260i	0.313536	+	0.256001i
$786$	1.46410	−	2.53590i	0.0522228	−	0.0904525i
$787$	39.7128	−	22.9282i	1.41561	−	0.817302i	0.419700	−	0.907663i	$-0.362135\pi$
$787$	39.7128	−	22.9282i	1.41561	−	0.817302i	0.995909	+	0.0903608i	$0.0288020\pi$
$788$	−34.2049	+	19.7482i	−1.21850	+	0.703501i
$789$	3.81294	−	6.60420i	0.135744	−	0.235116i
$790$	4.06678	+	3.32051i	0.144689	+	0.118138i
$791$		0			0
$792$			6.69213i			0.237795i
$793$	2.27362	+	1.31268i	0.0807388	+	0.0466145i
$794$	6.13733	+	10.6302i	0.217806	+	0.377250i
$795$	16.2189	+	2.63604i	0.575224	+	0.0934907i
$796$	−7.02030	+	12.1595i	−0.248828	+	0.430983i
$797$			10.1436i			0.359305i	0.983730	+	0.179652i	$0.0574973\pi$
$797$			10.1436i			0.359305i	−0.983730	+	0.179652i	$0.942503\pi$
$798$		0			0
$799$	−24.0000			−0.849059
$800$	8.13777	−	24.3735i	0.287713	−	0.861732i
$801$	−7.72741	−	13.3843i	−0.273034	−	0.472910i
$802$	−0.896575	+	0.517638i	−0.0316592	+	0.0182784i
$803$	8.78461	+	5.07180i	0.310002	+	0.178980i
$804$	−21.8695			−0.771279
$805$		0			0
$806$	15.2154			0.535939
$807$	26.7685	+	15.4548i	0.942297	+	0.544035i
$808$	−11.6603	+	6.73205i	−0.410206	+	0.236833i
$809$	10.8564	+	18.8038i	0.381691	+	0.661108i	0.991304	−	0.131591i	$-0.0420085\pi$
$809$	10.8564	+	18.8038i	0.381691	+	0.661108i	−0.609613	+	0.792699i	$0.708675\pi$
$810$	−1.08226	+	0.410432i	−0.0380268	+	0.0144211i
$811$	25.6317			0.900051			0.450026	−	0.893016i	$-0.351415\pi$
$811$	25.6317			0.900051			0.450026	+	0.893016i	$0.351415\pi$
$812$		0			0
$813$		−	1.69161i		−	0.0593275i
$814$	−9.46410	+	16.3923i	−0.331717	+	0.574550i
$815$	−8.04405	+	49.4929i	−0.281771	+	1.73366i
$816$	4.92820	+	8.53590i	0.172522	+	0.298816i
$817$		0			0
$818$			5.90897i			0.206602i
$819$		0			0
$820$	20.7846	−	25.4558i	0.725830	−	0.888957i
$821$	−9.39230	+	16.2679i	−0.327794	+	0.567755i	−0.982074	−	0.188497i	$-0.939638\pi$
$821$	−9.39230	+	16.2679i	−0.327794	+	0.567755i	0.654280	+	0.756252i	$0.272972\pi$
$822$	−4.56218	+	2.63397i	−0.159124	+	0.0918704i
$823$	−26.5927	+	15.3533i	−0.926962	+	0.535182i	−0.885849	−	0.463973i	$-0.846423\pi$
$823$	−26.5927	+	15.3533i	−0.926962	+	0.535182i	−0.0411123	+	0.999155i	$0.513090\pi$
$824$	−13.3843	+	23.1822i	−0.466263	+	0.807591i
$825$	−16.9706	+	3.46410i	−0.590839	+	0.120605i
$826$		0			0
$827$		−	8.18067i		−	0.284470i	−0.989833	−	0.142235i	$-0.954571\pi$
$827$		−	8.18067i		−	0.284470i	0.989833	−	0.142235i	$-0.0454289\pi$
$828$	−5.22715	−	3.01790i	−0.181656	−	0.104879i
$829$	3.25813	+	5.64325i	0.113160	+	0.195998i	0.917043	−	0.398789i	$-0.130570\pi$
$829$	3.25813	+	5.64325i	0.113160	+	0.195998i	−0.803883	+	0.594788i	$0.797236\pi$
$830$	6.85490	+	1.11412i	0.237937	+	0.0386717i
$831$	5.65685	−	9.79796i	0.196234	−	0.339887i
$832$			9.07180i			0.314508i
$833$		0			0
$834$	0.196152			0.00679220
$835$	−39.5745	+	15.0080i	−1.36953	+	0.519375i
$836$	−15.8338	−	27.4249i	−0.547622	−	0.948509i
$837$	6.36396	−	3.67423i	0.219971	−	0.127000i
$838$	−9.46410	−	5.46410i	−0.326932	−	0.188754i
$839$	−20.3538			−0.702691			−0.351345	−	0.936246i	$-0.614276\pi$
$839$	−20.3538			−0.702691			−0.351345	+	0.936246i	$0.614276\pi$
$840$		0			0
$841$	−4.71281			−0.162511
$842$	5.73118	+	3.30890i	0.197510	+	0.114032i
$843$	−24.1244	+	13.9282i	−0.830887	+	0.479713i
$844$	23.3205	+	40.3923i	0.802725	+	1.39036i
$845$	2.37868	+	6.27231i	0.0818291	+	0.215774i
$846$	3.10583			0.106781
$847$		0			0
$848$			18.1074i			0.621810i
$849$	−1.07180	+	1.85641i	−0.0367840	+	0.0637117i
$850$	7.74933	−	6.86495i	0.265800	−	0.235466i
$851$	−18.3923	−	31.8564i	−0.630480	−	1.09202i
$852$	−9.58846	−	5.53590i	−0.328495	−	0.189657i
$853$			13.0718i			0.447570i	0.974639	+	0.223785i	$0.0718413\pi$
$853$			13.0718i			0.447570i	−0.974639	+	0.223785i	$0.928159\pi$
$854$		0			0
$855$	7.46410	−	9.14162i	0.255267	−	0.312637i
$856$	−15.0263	+	26.0263i	−0.513588	+	0.889560i
$857$	8.53590	−	4.92820i	0.291581	−	0.168344i	−0.347074	−	0.937838i	$-0.612825\pi$
$857$	8.53590	−	4.92820i	0.291581	−	0.168344i	0.638655	+	0.769494i	$0.279491\pi$
$858$	−6.21166	+	3.58630i	−0.212062	+	0.122434i
$859$	1.70522	−	2.95352i	0.0581813	−	0.100773i	−0.835468	−	0.549539i	$-0.814803\pi$
$859$	1.70522	−	2.95352i	0.0581813	−	0.100773i	0.893649	+	0.448767i	$0.148137\pi$
$860$		0			0
$861$		0			0
$862$		−	19.3185i		−	0.657991i
$863$	−13.7768	−	7.95404i	−0.468968	−	0.270759i	0.246840	−	0.969056i	$-0.420608\pi$
$863$	−13.7768	−	7.95404i	−0.468968	−	0.270759i	−0.715808	+	0.698298i	$0.753941\pi$
$864$	−2.56961	−	4.45069i	−0.0874198	−	0.151416i
$865$	−5.73951	+	35.3137i	−0.195149	+	1.20070i
$866$	4.62158	−	8.00481i	0.157048	−	0.272014i
$867$		−	1.00000i		−	0.0339618i
$868$		0			0
$869$	15.7128			0.533021
$870$	2.02269	+	5.33361i	0.0685756	+	0.180826i
$871$	−25.2528	−	43.7391i	−0.855658	−	1.48204i
$872$	26.5283	−	15.3161i	0.898361	−	0.518669i
$873$	−16.3923	−	9.46410i	−0.554795	−	0.320311i
$874$	−9.52056			−0.322038
$875$		0			0
$876$	−5.07180			−0.171360
$877$	29.3939	+	16.9706i	0.992561	+	0.573055i	0.906039	−	0.423195i	$-0.139091\pi$
$877$	29.3939	+	16.9706i	0.992561	+	0.573055i	0.0865220	+	0.996250i	$0.472425\pi$
$878$	−5.83013	+	3.36603i	−0.196757	+	0.113598i
$879$	−5.73205	−	9.92820i	−0.193337	−	0.334870i
$880$	−6.76806	−	17.8466i	−0.228151	−	0.601609i
$881$	29.5969			0.997147			0.498573	−	0.866848i	$-0.333857\pi$
$881$	29.5969			0.997147			0.498573	+	0.866848i	$0.333857\pi$
$882$		0			0
$883$		−	29.3939i		−	0.989183i	−0.869126	−	0.494591i	$-0.835318\pi$
$883$		−	29.3939i		−	0.989183i	0.869126	−	0.494591i	$-0.164682\pi$
$884$	−13.8564	+	24.0000i	−0.466041	+	0.807207i
$885$	−0.271864	+	1.67271i	−0.00913862	+	0.0562275i
$886$	3.24167	+	5.61474i	0.108906	+	0.188631i
$887$	11.8756	+	6.85641i	0.398745	+	0.230216i	0.685942	−	0.727656i	$-0.259390\pi$
$887$	11.8756	+	6.85641i	0.398745	+	0.230216i	−0.287197	+	0.957871i	$0.592724\pi$
$888$		−	20.3923i		−	0.684321i
$889$		0			0
$890$	−13.8564	−	11.3137i	−0.464468	−	0.379236i
$891$	−1.73205	+	3.00000i	−0.0580259	+	0.100504i
$892$	12.0000	−	6.92820i	0.401790	−	0.231973i
$893$	−27.4249	+	15.8338i	−0.917738	+	0.529856i
$894$	−1.83032	+	3.17020i	−0.0612149	+	0.106027i
$895$	14.6969	−	18.0000i	0.491264	−	0.601674i
$896$		0			0
$897$		−	13.9391i		−	0.465412i
$898$	−16.0740	−	9.28032i	−0.536396	−	0.309688i
$899$	−18.1074	−	31.3629i	−0.603915	−	1.04601i
$900$	6.48244	−	5.74264i	0.216081	−	0.191421i
$901$	−14.6969	+	25.4558i	−0.489626	+	0.848057i
$902$			15.2154i			0.506617i
$903$		0			0
$904$	10.1962			0.339119
$905$	−5.00569	−	13.1994i	−0.166395	−	0.438764i
$906$	−5.03768	−	8.72552i	−0.167366	−	0.289886i
$907$	5.85993	−	3.38323i	0.194576	−	0.112338i	−0.399547	−	0.916713i	$-0.630833\pi$
$907$	5.85993	−	3.38323i	0.194576	−	0.112338i	0.594123	+	0.804374i	$0.297499\pi$
$908$	6.00000	+	3.46410i	0.199117	+	0.114960i
$909$	−6.96953			−0.231165
$910$		0			0
$911$	9.60770			0.318317			0.159159	−	0.987253i	$-0.449122\pi$
$911$	9.60770			0.318317			0.159159	+	0.987253i	$0.449122\pi$
$912$	11.2629	+	6.50266i	0.372953	+	0.215325i
$913$	18.0000	−	10.3923i	0.595713	−	0.343935i
$914$	5.66025	+	9.80385i	0.187225	+	0.324282i
$915$	1.37225	−	0.520407i	0.0453653	−	0.0172041i
$916$	−23.3581			−0.771773
$917$		0			0
$918$		−	2.07055i		−	0.0683384i
$919$	−4.53590	+	7.85641i	−0.149625	+	0.259159i	−0.931089	−	0.364792i	$-0.881140\pi$
$919$	−4.53590	+	7.85641i	−0.149625	+	0.259159i	0.781464	+	0.623951i	$0.214473\pi$
$920$	−14.8584	−	2.41492i	−0.489865	−	0.0796175i
$921$	−2.00000	−	3.46410i	−0.0659022	−	0.114146i
$922$	−14.5359	−	8.39230i	−0.478714	−	0.276386i
$923$		−	25.5692i		−	0.841621i
$924$		0			0
$925$	51.7128	−	10.5558i	1.70031	−	0.347074i
$926$	5.80385	−	10.0526i	0.190726	−	0.330348i
$927$	−12.0000	+	6.92820i	−0.394132	+	0.227552i
$928$	−21.9339	+	12.6636i	−0.720016	+	0.415701i
$929$	9.04008	−	15.6579i	0.296596	−	0.513719i	−0.678759	−	0.734361i	$-0.737482\pi$
$929$	9.04008	−	15.6579i	0.296596	−	0.513719i	0.975355	+	0.220642i	$0.0708153\pi$
$930$	5.37945	−	6.58846i	0.176399	−	0.216044i
$931$		0			0
$932$			9.14162i			0.299444i
$933$	−3.58630	−	2.07055i	−0.117410	−	0.0677868i
$934$	−2.55103	−	4.41851i	−0.0834721	−	0.144578i
$935$	4.97056	−	30.5826i	0.162555	−	1.00016i
$936$	3.86370	−	6.69213i	0.126289	−	0.218739i
$937$			16.7846i			0.548329i	0.961683	+	0.274165i	$0.0884013\pi$
$937$			16.7846i			0.548329i	−0.961683	+	0.274165i	$0.911599\pi$
$938$		0			0
$939$	−2.92820			−0.0955583
$940$	−21.7279	+	8.23999i	−0.708687	+	0.268759i
$941$	0.101536	+	0.175865i	0.00330998	+	0.00573305i	0.867676	−	0.497131i	$-0.165613\pi$
$941$	0.101536	+	0.175865i	0.00330998	+	0.00573305i	−0.864366	+	0.502864i	$0.832280\pi$
$942$	2.27362	−	1.31268i	0.0740787	−	0.0427693i
$943$	−25.6077	−	14.7846i	−0.833901	−	0.481453i
$944$	−1.86748			−0.0607813
$945$		0			0
$946$		0			0
$947$	−15.9217	−	9.19239i	−0.517385	−	0.298712i	0.218479	−	0.975842i	$-0.429890\pi$
$947$	−15.9217	−	9.19239i	−0.517385	−	0.298712i	−0.735864	+	0.677129i	$0.763224\pi$
$948$	−6.80385	+	3.92820i	−0.220979	+	0.127582i
$949$	−5.85641	−	10.1436i	−0.190107	−	0.329275i
$950$	4.32611	−	12.9571i	0.140357	−	0.420385i
$951$	−4.72311			−0.153157
$952$		0			0
$953$		−	53.9160i		−	1.74651i	−0.487264	−	0.873255i	$-0.662005\pi$
$953$		−	53.9160i		−	1.74651i	0.487264	−	0.873255i	$-0.337995\pi$
$954$	1.90192	−	3.29423i	0.0615771	−	0.106655i
$955$	−16.4741	−	2.67752i	−0.533088	−	0.0866425i
$956$	−7.39230	−	12.8038i	−0.239084	−	0.414106i
$957$	14.7846	+	8.53590i	0.477919	+	0.275926i
$958$			13.0718i			0.422331i
$959$		0			0
$960$	3.92820	+	3.20736i	0.126782	+	0.103517i
$961$	−11.5000	+	19.9186i	−0.370968	+	0.642535i
$962$	18.9282	−	10.9282i	0.610270	−	0.352339i
$963$	−13.4722	+	7.77817i	−0.434135	+	0.250648i
$964$	12.1595	−	21.0609i	0.391632	−	0.678326i
$965$	−11.1106	−	9.07180i	−0.357664	−	0.292031i
$966$		0			0
$967$			10.0010i			0.321611i	0.986986	+	0.160806i	$0.0514093\pi$
$967$			10.0010i			0.321611i	−0.986986	+	0.160806i	$0.948591\pi$
$968$	1.67303	+	0.965926i	0.0537733	+	0.0310460i
$969$	10.5558	+	18.2832i	0.339102	+	0.587342i
$970$	−21.6251	−	3.51472i	−0.694341	−	0.112851i
$971$	−5.83272	+	10.1026i	−0.187181	+	0.324207i	−0.944309	−	0.329059i	$-0.893268\pi$
$971$	−5.83272	+	10.1026i	−0.187181	+	0.324207i	0.757128	+	0.653266i	$0.226602\pi$
$972$		−	1.73205i		−	0.0555556i
$973$		0			0
$974$	8.00000			0.256337
$975$	18.9706	+	6.33386i	0.607544	+	0.202846i
$976$	0.808643	+	1.40061i	0.0258840	+	0.0448324i
$977$	39.5200	−	22.8169i	1.26436	−	0.729977i	0.290443	−	0.956892i	$-0.406197\pi$
$977$	39.5200	−	22.8169i	1.26436	−	0.729977i	0.973914	+	0.226916i	$0.0728642\pi$
$978$	10.0526	+	5.80385i	0.321445	+	0.185587i
$979$	−53.5370			−1.71105
$980$		0			0
$981$	15.8564			0.506256
$982$	18.5235	+	10.6945i	0.591108	+	0.341276i
$983$	−21.4641	+	12.3923i	−0.684599	+	0.395253i	−0.801585	−	0.597880i	$-0.796010\pi$
$983$	−21.4641	+	12.3923i	−0.684599	+	0.395253i	0.116987	+	0.993133i	$0.462676\pi$
$984$	−8.19615	−	14.1962i	−0.261284	−	0.452557i
$985$	−47.6764	+	18.0806i	−1.51910	+	0.576095i
$986$	−10.2041			−0.324965
$987$		0			0
$988$			36.5665i			1.16333i
$989$		0			0
$990$	−0.643238	+	3.95768i	−0.0204435	+	0.125783i
$991$	−6.39230	−	11.0718i	−0.203058	−	0.351707i	0.746454	−	0.665437i	$-0.231755\pi$
$991$	−6.39230	−	11.0718i	−0.203058	−	0.351707i	−0.949512	+	0.313730i	$0.898421\pi$
$992$	32.7058	+	18.8827i	1.03841	+	0.599526i
$993$			8.78461i			0.278771i
$994$		0			0
$995$	−11.4641	+	14.0406i	−0.363436	+	0.445117i
$996$	−5.19615	+	9.00000i	−0.164646	+	0.285176i
$997$	−36.2487	+	20.9282i	−1.14801	+	0.662803i	−0.948401	−	0.317073i	$-0.897300\pi$
$997$	−36.2487	+	20.9282i	−1.14801	+	0.662803i	−0.199607	+	0.979876i	$0.563967\pi$
$998$	−14.4567	+	8.34658i	−0.457619	+	0.264206i
$999$	5.27792	−	9.14162i	0.166986	−	0.289228i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.q.c.79.3		8
5.4	even	2		735.2.q.d.79.2		8
7.2	even	3		735.2.d.f.589.3	✓	8
7.3	odd	6	inner	735.2.q.c.214.2		8
7.4	even	3		735.2.q.d.214.2		8
7.5	odd	6		735.2.d.f.589.4	yes	8
7.6	odd	2		735.2.q.d.79.3		8
21.2	odd	6		2205.2.d.t.1324.6		8
21.5	even	6		2205.2.d.t.1324.5		8
35.2	odd	12		3675.2.a.bs.1.3		4
35.4	even	6	inner	735.2.q.c.214.3		8
35.9	even	6		735.2.d.f.589.6	yes	8
35.12	even	12		3675.2.a.bu.1.3		4
35.19	odd	6		735.2.d.f.589.5	yes	8
35.23	odd	12		3675.2.a.bu.1.2		4
35.24	odd	6		735.2.q.d.214.3		8
35.33	even	12		3675.2.a.bs.1.2		4
35.34	odd	2	inner	735.2.q.c.79.2		8
105.44	odd	6		2205.2.d.t.1324.4		8
105.89	even	6		2205.2.d.t.1324.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
735.2.d.f.589.3	✓	8	7.2	even	3
735.2.d.f.589.4	yes	8	7.5	odd	6
735.2.d.f.589.5	yes	8	35.19	odd	6
735.2.d.f.589.6	yes	8	35.9	even	6
735.2.q.c.79.2		8	35.34	odd	2	inner
735.2.q.c.79.3		8	1.1	even	1	trivial
735.2.q.c.214.2		8	7.3	odd	6	inner
735.2.q.c.214.3		8	35.4	even	6	inner
735.2.q.d.79.2		8	5.4	even	2
735.2.q.d.79.3		8	7.6	odd	2
735.2.q.d.214.2		8	7.4	even	3
735.2.q.d.214.3		8	35.24	odd	6
2205.2.d.t.1324.3		8	105.89	even	6
2205.2.d.t.1324.4		8	105.44	odd	6
2205.2.d.t.1324.5		8	21.5	even	6
2205.2.d.t.1324.6		8	21.2	odd	6
3675.2.a.bs.1.2		4	35.33	even	12
3675.2.a.bs.1.3		4	35.2	odd	12
3675.2.a.bu.1.2		4	35.23	odd	12
3675.2.a.bu.1.3		4	35.12	even	12

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:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.448288 + 0.258819i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.866025 - 1.50000i) q^{4} +(-0.792893 - 2.09077i) q^{5} -0.517638 q^{6} -1.93185i q^{8} +(0.500000 - 0.866025i) q^{9} +(0.185687 - 1.14248i) q^{10} +(-1.73205 - 3.00000i) q^{11} +(1.50000 + 0.866025i) q^{12} +4.00000i q^{13} +(1.73205 + 1.41421i) q^{15} +(-1.23205 + 2.13397i) q^{16} +(-3.46410 + 2.00000i) q^{17} +(0.448288 - 0.258819i) q^{18} +(-2.63896 + 4.57081i) q^{19} +(-2.44949 + 3.00000i) q^{20} -1.79315i q^{22} +(3.01790 + 1.74238i) q^{23} +(0.965926 + 1.67303i) q^{24} +(-3.74264 + 3.31552i) q^{25} +(-1.03528 + 1.79315i) q^{26} +1.00000i q^{27} +4.92820 q^{29} +(0.410432 + 1.08226i) q^{30} +(-3.67423 - 6.36396i) q^{31} +(-4.45069 + 2.56961i) q^{32} +(3.00000 + 1.73205i) q^{33} -2.07055 q^{34} -1.73205 q^{36} +(-9.14162 - 5.27792i) q^{37} +(-2.36603 + 1.36603i) q^{38} +(-2.00000 - 3.46410i) q^{39} +(-4.03906 + 1.53175i) q^{40} -8.48528 q^{41} +(-3.00000 + 5.19615i) q^{44} +(-2.20711 - 0.358719i) q^{45} +(0.901924 + 1.56218i) q^{46} +(5.19615 + 3.00000i) q^{47} -2.46410i q^{48} +(-2.53590 + 0.517638i) q^{50} +(2.00000 - 3.46410i) q^{51} +(6.00000 - 3.46410i) q^{52} +(6.36396 - 3.67423i) q^{53} +(-0.258819 + 0.448288i) q^{54} +(-4.89898 + 6.00000i) q^{55} -5.27792i q^{57} +(2.20925 + 1.27551i) q^{58} +(0.378937 + 0.656339i) q^{59} +(0.621320 - 3.82282i) q^{60} +(0.328169 - 0.568406i) q^{61} -3.80385i q^{62} +2.26795 q^{64} +(8.36308 - 3.17157i) q^{65} +(0.896575 + 1.55291i) q^{66} +(-10.9348 + 6.31319i) q^{67} +(6.00000 + 3.46410i) q^{68} -3.48477 q^{69} -6.39230 q^{71} +(-1.67303 - 0.965926i) q^{72} +(-2.53590 + 1.46410i) q^{73} +(-2.73205 - 4.73205i) q^{74} +(1.58346 - 4.74264i) q^{75} +9.14162 q^{76} -2.07055i q^{78} +(-2.26795 + 3.92820i) q^{79} +(5.43854 + 0.883921i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.80385 - 2.19615i) q^{82} +6.00000i q^{83} +(6.92820 + 5.65685i) q^{85} +(-4.26795 + 2.46410i) q^{87} +(-5.79555 + 3.34607i) q^{88} +(7.72741 - 13.3843i) q^{89} +(-0.896575 - 0.732051i) q^{90} -6.03579i q^{92} +(6.36396 + 3.67423i) q^{93} +(1.55291 + 2.68973i) q^{94} +(11.6489 + 1.89329i) q^{95} +(2.56961 - 4.45069i) q^{96} -18.9282i q^{97} -3.46410 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{5} + 4 q^{9} + 12 q^{10} + 12 q^{12} + 4 q^{16} + 4 q^{25} - 16 q^{29} + 4 q^{30} + 24 q^{33} - 12 q^{38} - 16 q^{39} - 12 q^{40} - 24 q^{44} - 12 q^{45} + 28 q^{46} - 48 q^{50} + 16 q^{51}+ \cdots + 16 q^{95}+O(q^{100}) \) 8 * q - 12 * q^5 + 4 * q^9 + 12 * q^10 + 12 * q^12 + 4 * q^16 + 4 * q^25 - 16 * q^29 + 4 * q^30 + 24 * q^33 - 12 * q^38 - 16 * q^39 - 12 * q^40 - 24 * q^44 - 12 * q^45 + 28 * q^46 - 48 * q^50 + 16 * q^51 + 48 * q^52 - 12 * q^60 + 32 * q^64 + 48 * q^68 + 32 * q^71 - 48 * q^73 - 8 * q^74 - 32 * q^79 - 12 * q^80 - 4 * q^81 - 72 * q^82 - 48 * q^87 + 16 * q^95

Introduction

L-functions

Modular forms

Varieties

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Database

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