LMFDB - Embedded newform 735.2.q.c.79.4

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			79.4
Root			$-0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	735.79
Dual form			735.2.q.c.214.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.67303 + 0.965926i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.866025 + 1.50000i) q^{4} +(-0.792893 - 2.09077i) q^{5} +1.93185 q^{6} -0.517638i q^{8} +(0.500000 - 0.866025i) q^{9} +(0.692993 - 4.26380i) q^{10} +(1.73205 + 3.00000i) q^{11} +(1.50000 + 0.866025i) q^{12} -4.00000i q^{13} +(-1.73205 - 1.41421i) q^{15} +(2.23205 - 3.86603i) q^{16} +(3.46410 - 2.00000i) q^{17} +(1.67303 - 0.965926i) q^{18} +(-0.189469 + 0.328169i) q^{19} +(2.44949 - 3.00000i) q^{20} +6.69213i q^{22} +(5.46739 + 3.15660i) q^{23} +(-0.258819 - 0.448288i) q^{24} +(-3.74264 + 3.31552i) q^{25} +(3.86370 - 6.69213i) q^{26} -1.00000i q^{27} -8.92820 q^{29} +(-1.53175 - 4.03906i) q^{30} +(3.67423 + 6.36396i) q^{31} +(6.57201 - 3.79435i) q^{32} +(3.00000 + 1.73205i) q^{33} +7.72741 q^{34} +1.73205 q^{36} +(0.656339 + 0.378937i) q^{37} +(-0.633975 + 0.366025i) q^{38} +(-2.00000 - 3.46410i) q^{39} +(-1.08226 + 0.410432i) q^{40} -8.48528 q^{41} +(-3.00000 + 5.19615i) q^{44} +(-2.20711 - 0.358719i) q^{45} +(6.09808 + 10.5622i) q^{46} +(-5.19615 - 3.00000i) q^{47} -4.46410i q^{48} +(-9.46410 + 1.93185i) q^{50} +(2.00000 - 3.46410i) q^{51} +(6.00000 - 3.46410i) q^{52} +(6.36396 - 3.67423i) q^{53} +(0.965926 - 1.67303i) q^{54} +(4.89898 - 6.00000i) q^{55} +0.378937i q^{57} +(-14.9372 - 8.62398i) q^{58} +(5.27792 + 9.14162i) q^{59} +(0.621320 - 3.82282i) q^{60} +(-4.57081 + 7.91688i) q^{61} +14.1962i q^{62} +5.73205 q^{64} +(-8.36308 + 3.17157i) q^{65} +(3.34607 + 5.79555i) q^{66} +(-6.03579 + 3.48477i) q^{67} +(6.00000 + 3.46410i) q^{68} +6.31319 q^{69} +14.3923 q^{71} +(-0.448288 - 0.258819i) q^{72} +(-9.46410 + 5.46410i) q^{73} +(0.732051 + 1.26795i) q^{74} +(-1.58346 + 4.74264i) q^{75} -0.656339 q^{76} -7.72741i q^{78} +(-5.73205 + 9.92820i) q^{79} +(-9.85275 - 1.60136i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-14.1962 - 8.19615i) q^{82} -6.00000i q^{83} +(-6.92820 - 5.65685i) q^{85} +(-7.73205 + 4.46410i) q^{87} +(1.55291 - 0.896575i) q^{88} +(-2.07055 + 3.58630i) q^{89} +(-3.34607 - 2.73205i) q^{90} +10.9348i q^{92} +(6.36396 + 3.67423i) q^{93} +(-5.79555 - 10.0382i) q^{94} +(0.836355 + 0.135932i) q^{95} +(3.79435 - 6.57201i) q^{96} +5.07180i 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 $

$2$	1.67303	+	0.965926i	1.18301	+	0.683013i	0.956710	−	0.291044i	$-0.0940027\pi$
$2$	1.67303	+	0.965926i	1.18301	+	0.683013i	0.226303	+	0.974057i	$0.427336\pi$
$3$	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
$6$	1.93185			0.788675
$7$		0			0
$7$		0			0
$8$		−	0.517638i		−	0.183013i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	0.692993	−	4.26380i	0.219144	−	1.34833i
$11$	1.73205	+	3.00000i	0.522233	+	0.904534i	0.999665	+	0.0258656i	$0.00823419\pi$
$11$	1.73205	+	3.00000i	0.522233	+	0.904534i	−0.477432	+	0.878668i	$0.658432\pi$
$12$	1.50000	+	0.866025i	0.433013	+	0.250000i
$13$		−	4.00000i		−	1.10940i	−0.832050	−	0.554700i	$-0.812833\pi$
$13$		−	4.00000i		−	1.10940i	0.832050	−	0.554700i	$-0.187167\pi$
$14$		0			0
$15$	−1.73205	−	1.41421i	−0.447214	−	0.365148i
$16$	2.23205	−	3.86603i	0.558013	−	0.966506i
$17$	3.46410	−	2.00000i	0.840168	−	0.485071i	−0.0171533	−	0.999853i	$-0.505460\pi$
$17$	3.46410	−	2.00000i	0.840168	−	0.485071i	0.857321	+	0.514782i	$0.172127\pi$
$18$	1.67303	−	0.965926i	0.394338	−	0.227671i
$19$	−0.189469	+	0.328169i	−0.0434671	+	0.0752872i	−0.886940	−	0.461884i	$-0.847174\pi$
$19$	−0.189469	+	0.328169i	−0.0434671	+	0.0752872i	0.843473	+	0.537171i	$0.180507\pi$
$20$	2.44949	−	3.00000i	0.547723	−	0.670820i
$21$		0			0
$22$			6.69213i			1.42677i
$23$	5.46739	+	3.15660i	1.14003	+	0.658196i	0.946438	−	0.322886i	$-0.104653\pi$
$23$	5.46739	+	3.15660i	1.14003	+	0.658196i	0.193591	+	0.981082i	$0.437987\pi$
$24$	−0.258819	−	0.448288i	−0.0528312	−	0.0915064i
$25$	−3.74264	+	3.31552i	−0.748528	+	0.663103i
$26$	3.86370	−	6.69213i	0.757735	−	1.31243i
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$	−8.92820			−1.65793			−0.828963	−	0.559304i	$-0.811069\pi$
$29$	−8.92820			−1.65793			−0.828963	+	0.559304i	$0.811069\pi$
$30$	−1.53175	−	4.03906i	−0.279658	−	0.737428i
$31$	3.67423	+	6.36396i	0.659912	+	1.14300i	0.980638	+	0.195829i	$0.0627398\pi$
$31$	3.67423	+	6.36396i	0.659912	+	1.14300i	−0.320726	+	0.947172i	$0.603927\pi$
$32$	6.57201	−	3.79435i	1.16178	−	0.670753i
$33$	3.00000	+	1.73205i	0.522233	+	0.301511i
$34$	7.72741			1.32524
$35$		0			0
$36$	1.73205			0.288675
$37$	0.656339	+	0.378937i	0.107901	+	0.0622969i	0.552980	−	0.833195i	$-0.313491\pi$
$37$	0.656339	+	0.378937i	0.107901	+	0.0622969i	−0.445078	+	0.895492i	$0.646824\pi$
$38$	−0.633975	+	0.366025i	−0.102844	+	0.0593772i
$39$	−2.00000	−	3.46410i	−0.320256	−	0.554700i
$40$	−1.08226	+	0.410432i	−0.171121	+	0.0648950i
$41$	−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
$46$	6.09808	+	10.5622i	0.899112	+	1.55731i
$47$	−5.19615	−	3.00000i	−0.757937	−	0.437595i	0.0706177	−	0.997503i	$-0.477503\pi$
$47$	−5.19615	−	3.00000i	−0.757937	−	0.437595i	−0.828554	+	0.559908i	$0.810836\pi$
$48$		−	4.46410i		−	0.644338i
$49$		0			0
$50$	−9.46410	+	1.93185i	−1.33843	+	0.273205i
$51$	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	$0.164938\pi$
$54$	0.965926	−	1.67303i	0.131446	−	0.227671i
$55$	4.89898	−	6.00000i	0.660578	−	0.809040i
$56$		0			0
$57$			0.378937i			0.0501915i
$58$	−14.9372	−	8.62398i	−1.96135	−	1.13238i
$59$	5.27792	+	9.14162i	0.687126	+	1.19014i	0.972764	+	0.231800i	$0.0744614\pi$
$59$	5.27792	+	9.14162i	0.687126	+	1.19014i	−0.285637	+	0.958338i	$0.592205\pi$
$60$	0.621320	−	3.82282i	0.0802121	−	0.493524i
$61$	−4.57081	+	7.91688i	−0.585232	+	1.01365i	0.409614	+	0.912259i	$0.365663\pi$
$61$	−4.57081	+	7.91688i	−0.585232	+	1.01365i	−0.994846	+	0.101393i	$0.967670\pi$
$62$			14.1962i			1.80291i
$63$		0			0
$64$	5.73205			0.716506
$65$	−8.36308	+	3.17157i	−1.03731	+	0.393385i
$66$	3.34607	+	5.79555i	0.411872	+	0.713384i
$67$	−6.03579	+	3.48477i	−0.737389	+	0.425732i	−0.821119	−	0.570757i	$-0.806650\pi$
$67$	−6.03579	+	3.48477i	−0.737389	+	0.425732i	0.0837300	+	0.996488i	$0.473317\pi$
$68$	6.00000	+	3.46410i	0.727607	+	0.420084i
$69$	6.31319			0.760019
$70$		0			0
$71$	14.3923			1.70805			0.854026	−	0.520230i	$-0.174154\pi$
$71$	14.3923			1.70805			0.854026	+	0.520230i	$0.174154\pi$
$72$	−0.448288	−	0.258819i	−0.0528312	−	0.0305021i
$73$	−9.46410	+	5.46410i	−1.10769	+	0.639525i	−0.938230	−	0.346012i	$-0.887535\pi$
$73$	−9.46410	+	5.46410i	−1.10769	+	0.639525i	−0.169459	+	0.985537i	$0.554202\pi$
$74$	0.732051	+	1.26795i	0.0850992	+	0.147396i
$75$	−1.58346	+	4.74264i	−0.182843	+	0.547633i
$76$	−0.656339			−0.0752872
$77$		0			0
$78$		−	7.72741i		−	0.874957i
$79$	−5.73205	+	9.92820i	−0.644906	+	1.11701i	0.339417	+	0.940636i	$0.389770\pi$
$79$	−5.73205	+	9.92820i	−0.644906	+	1.11701i	−0.984323	+	0.176374i	$0.943563\pi$
$80$	−9.85275	−	1.60136i	−1.10157	−	0.179038i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−14.1962	−	8.19615i	−1.56770	−	0.905114i
$83$		−	6.00000i		−	0.658586i	−0.944228	−	0.329293i	$-0.893190\pi$
$83$		−	6.00000i		−	0.658586i	0.944228	−	0.329293i	$-0.106810\pi$
$84$		0			0
$85$	−6.92820	−	5.65685i	−0.751469	−	0.613572i
$86$		0			0
$87$	−7.73205	+	4.46410i	−0.828963	+	0.478602i
$88$	1.55291	−	0.896575i	0.165541	−	0.0955753i
$89$	−2.07055	+	3.58630i	−0.219478	+	0.380147i	−0.954649	−	0.297735i	$-0.903769\pi$
$89$	−2.07055	+	3.58630i	−0.219478	+	0.380147i	0.735170	+	0.677882i	$0.237102\pi$
$90$	−3.34607	−	2.73205i	−0.352706	−	0.287983i
$91$		0			0
$92$			10.9348i			1.14003i
$93$	6.36396	+	3.67423i	0.659912	+	0.381000i
$94$	−5.79555	−	10.0382i	−0.597766	−	1.03536i
$95$	0.836355	+	0.135932i	0.0858082	+	0.0139464i
$96$	3.79435	−	6.57201i	0.387260	−	0.670753i
$97$			5.07180i			0.514963i	0.966283	+	0.257481i	$0.0828926\pi$
$97$			5.07180i			0.514963i	−0.966283	+	0.257481i	$0.917107\pi$
$98$		0			0
$99$	3.46410			0.348155
$100$	−8.21449	−	2.74264i	−0.821449	−	0.274264i
$101$	6.31319	+	10.9348i	0.628186	+	1.08805i	0.987915	+	0.154994i	$0.0495357\pi$
$101$	6.31319	+	10.9348i	0.628186	+	1.08805i	−0.359729	+	0.933057i	$0.617131\pi$
$102$	6.69213	−	3.86370i	0.662620	−	0.382564i
$103$	−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	$0.905842\pi$
$104$	−2.07055			−0.203034
$105$		0			0
$106$	14.1962			1.37885
$107$	13.4722	+	7.77817i	1.30241	+	0.751945i	0.980816	−	0.194935i	$-0.0624494\pi$
$107$	13.4722	+	7.77817i	1.30241	+	0.751945i	0.321590	+	0.946879i	$0.395783\pi$
$108$	1.50000	−	0.866025i	0.144338	−	0.0833333i
$109$	−5.92820	−	10.2679i	−0.567819	−	0.983491i	−0.996781	−	0.0801688i	$-0.974454\pi$
$109$	−5.92820	−	10.2679i	−0.567819	−	0.983491i	0.428962	−	0.903322i	$-0.358879\pi$
$110$	13.9917	−	5.30614i	1.33406	−	0.505921i
$111$	0.757875			0.0719343
$112$		0			0
$113$		−	0.378937i		−	0.0356474i	−0.999841	−	0.0178237i	$-0.994326\pi$
$113$		−	0.378937i		−	0.0356474i	0.999841	−	0.0178237i	$-0.00567377\pi$
$114$	−0.366025	+	0.633975i	−0.0342814	+	0.0593772i
$115$	2.26467	−	13.9339i	0.211181	−	1.29934i
$116$	−7.73205	−	13.3923i	−0.717903	−	1.24344i
$117$	−3.46410	−	2.00000i	−0.320256	−	0.184900i
$118$			20.3923i			1.87726i
$119$		0			0
$120$	−0.732051	+	0.896575i	−0.0668268	+	0.0818458i
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−15.2942	+	8.83013i	−1.38467	+	0.799442i
$123$	−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	$-0.959949\pi$
$127$		−	2.82843i		−	0.250982i	0.992095	−	0.125491i	$-0.0400507\pi$
$128$	−3.55412	−	2.05197i	−0.314142	−	0.181370i
$129$		0			0
$130$	−17.0552	−	2.77197i	−1.49584	−	0.243118i
$131$	−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
$134$	−13.4641			−1.16312
$135$	−2.09077	+	0.792893i	−0.179945	+	0.0682414i
$136$	−1.03528	−	1.79315i	−0.0887742	−	0.153761i
$137$	3.91447	−	2.26002i	0.334436	−	0.193087i	−0.323373	−	0.946272i	$-0.604817\pi$
$137$	3.91447	−	2.26002i	0.334436	−	0.193087i	0.657809	+	0.753185i	$0.271483\pi$
$138$	10.5622	+	6.09808i	0.899112	+	0.519103i
$139$	−5.27792			−0.447667			−0.223834	−	0.974627i	$-0.571857\pi$
$139$	−5.27792			−0.447667			−0.223834	+	0.974627i	$0.571857\pi$
$140$		0			0
$141$	−6.00000			−0.505291
$142$	24.0788	+	13.9019i	2.02065	+	1.16662i
$143$	12.0000	−	6.92820i	1.00349	−	0.579365i
$144$	−2.23205	−	3.86603i	−0.186004	−	0.322169i
$145$	7.07911	+	18.6668i	0.587888	+	1.55020i
$146$	−21.1117			−1.74721
$147$		0			0
$148$			1.31268i			0.107901i
$149$	10.4641	−	18.1244i	0.857253	−	1.48481i	−0.0172868	−	0.999851i	$-0.505503\pi$
$149$	10.4641	−	18.1244i	0.857253	−	1.48481i	0.874539	−	0.484954i	$-0.161164\pi$
$150$	−7.23023	+	6.40508i	−0.590346	+	0.522973i
$151$	6.26795	+	10.8564i	0.510078	+	0.883482i	0.999932	+	0.0116770i	$0.00371698\pi$
$151$	6.26795	+	10.8564i	0.510078	+	0.883482i	−0.489853	+	0.871805i	$0.662950\pi$
$152$	0.169873	+	0.0980762i	0.0137785	+	0.00795503i
$153$		−	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
$157$	16.3923	−	9.46410i	1.30825	−	0.755318i	0.326445	−	0.945216i	$-0.394149\pi$
$157$	16.3923	−	9.46410i	1.30825	−	0.755318i	0.981804	+	0.189899i	$0.0608160\pi$
$158$	−19.1798	+	11.0735i	−1.52586	+	0.880958i
$159$	3.67423	−	6.36396i	0.291386	−	0.504695i
$160$	−13.1440	−	10.7321i	−1.03913	−	0.848443i
$161$		0			0
$162$		−	1.93185i		−	0.151781i
$163$	−14.5211	−	8.38375i	−1.13738	−	0.656666i	−0.191598	−	0.981473i	$-0.561367\pi$
$163$	−14.5211	−	8.38375i	−1.13738	−	0.656666i	−0.945780	+	0.324808i	$0.894700\pi$
$164$	−7.34847	−	12.7279i	−0.573819	−	0.993884i
$165$	1.24264	−	7.64564i	0.0967394	−	0.595212i
$166$	5.79555	−	10.0382i	0.449822	−	0.779115i
$167$			5.07180i			0.392467i	0.980557	+	0.196234i	$0.0628711\pi$
$167$			5.07180i			0.392467i	−0.980557	+	0.196234i	$0.937129\pi$
$168$		0			0
$169$	−3.00000			−0.230769
$170$	−6.12701	−	16.1562i	−0.469920	−	1.23913i
$171$	0.189469	+	0.328169i	0.0144890	+	0.0250957i
$172$		0			0
$173$	13.8564	+	8.00000i	1.05348	+	0.608229i	0.923622	−	0.383304i	$-0.125214\pi$
$173$	13.8564	+	8.00000i	1.05348	+	0.608229i	0.129861	+	0.991532i	$0.458547\pi$
$174$	−17.2480			−1.30756
$175$		0			0
$176$	15.4641			1.16565
$177$	9.14162	+	5.27792i	0.687126	+	0.396713i
$178$	−6.92820	+	4.00000i	−0.519291	+	0.299813i
$179$	−5.19615	−	9.00000i	−0.388379	−	0.672692i	0.603853	−	0.797096i	$-0.293631\pi$
$179$	−5.19615	−	9.00000i	−0.388379	−	0.672692i	−0.992232	+	0.124404i	$0.960298\pi$
$180$	−1.37333	−	3.62132i	−0.102362	−	0.269917i
$181$	−3.48477			−0.259021			−0.129510	−	0.991578i	$-0.541341\pi$
$181$	−3.48477			−0.259021			−0.129510	+	0.991578i	$0.541341\pi$
$182$		0			0
$183$			9.14162i			0.675768i
$184$	1.63397	−	2.83013i	0.120458	−	0.208640i
$185$	0.271864	−	1.67271i	0.0199879	−	0.122980i
$186$	7.09808	+	12.2942i	0.520456	+	0.901457i
$187$	12.0000	+	6.92820i	0.877527	+	0.506640i
$188$		−	10.3923i		−	0.757937i
$189$		0			0
$190$	1.26795	+	1.03528i	0.0919867	+	0.0751068i
$191$	0.267949	−	0.464102i	0.0193881	−	0.0335812i	−0.856169	−	0.516697i	$-0.827162\pi$
$191$	0.267949	−	0.464102i	0.0193881	−	0.0335812i	0.875557	+	0.483115i	$0.160495\pi$
$192$	4.96410	−	2.86603i	0.358253	−	0.206838i
$193$	−14.0406	+	8.10634i	−1.01066	+	0.583507i	−0.911386	−	0.411552i	$-0.864987\pi$
$193$	−14.0406	+	8.10634i	−1.01066	+	0.583507i	−0.0992783	+	0.995060i	$0.531653\pi$
$194$	−4.89898	+	8.48528i	−0.351726	+	0.609208i
$195$	−5.65685	+	6.92820i	−0.405096	+	0.496139i
$196$		0			0
$197$		−	11.4896i		−	0.818598i	−0.912400	−	0.409299i	$-0.865773\pi$
$197$		−	11.4896i		−	0.818598i	0.912400	−	0.409299i	$-0.134227\pi$
$198$	5.79555	+	3.34607i	0.411872	+	0.237795i
$199$	−1.60368	−	2.77766i	−0.113682	−	0.196903i	0.803570	−	0.595210i	$-0.202931\pi$
$199$	−1.60368	−	2.77766i	−0.113682	−	0.196903i	−0.917252	+	0.398307i	$0.869598\pi$
$200$	1.71624	+	1.93733i	0.121356	+	0.136990i
$201$	−3.48477	+	6.03579i	−0.245796	+	0.425732i
$202$			24.3923i			1.71624i
$203$		0			0
$204$	6.92820			0.485071
$205$	6.72792	+	17.7408i	0.469898	+	1.23907i
$206$	−13.3843	−	23.1822i	−0.932526	−	1.61518i
$207$	5.46739	−	3.15660i	0.380010	−	0.219399i
$208$	−15.4641	−	8.92820i	−1.07224	−	0.619060i
$209$	−1.31268			−0.0907998
$210$		0			0
$211$	−13.0718			−0.899900			−0.449950	−	0.893054i	$-0.648558\pi$
$211$	−13.0718			−0.899900			−0.449950	+	0.893054i	$0.648558\pi$
$212$	11.0227	+	6.36396i	0.757042	+	0.437079i
$213$	12.4641	−	7.19615i	0.854026	−	0.493072i
$214$	15.0263	+	26.0263i	1.02718	+	1.77912i
$215$		0			0
$216$	−0.517638			−0.0352208
$217$		0			0
$218$		−	22.9048i		−	1.55131i
$219$	−5.46410	+	9.46410i	−0.369230	+	0.639525i
$220$	13.2426	+	2.15232i	0.892819	+	0.145109i
$221$	−8.00000	−	13.8564i	−0.538138	−	0.932083i
$222$	1.26795	+	0.732051i	0.0850992	+	0.0491320i
$223$		−	8.00000i		−	0.535720i	−0.963458	−	0.267860i	$-0.913684\pi$
$223$		−	8.00000i		−	0.535720i	0.963458	−	0.267860i	$-0.0863164\pi$
$224$		0			0
$225$	1.00000	+	4.89898i	0.0666667	+	0.326599i
$226$	0.366025	−	0.633975i	0.0243476	−	0.0421714i
$227$	3.46410	−	2.00000i	0.229920	−	0.132745i	−0.380615	−	0.924734i	$-0.624288\pi$
$227$	3.46410	−	2.00000i	0.229920	−	0.132745i	0.610535	+	0.791989i	$0.290954\pi$
$228$	−0.568406	+	0.328169i	−0.0376436	+	0.0217335i
$229$	11.6419	−	20.1643i	0.769317	−	1.33250i	−0.168617	−	0.985682i	$-0.553930\pi$
$229$	11.6419	−	20.1643i	0.769317	−	1.33250i	0.937934	−	0.346814i	$-0.112737\pi$
$230$	17.2480	−	21.1244i	1.13730	−	1.39290i
$231$		0			0
$232$			4.62158i			0.303421i
$233$	0.328169	+	0.189469i	0.0214991	+	0.0124125i	0.510711	−	0.859752i	$-0.329382\pi$
$233$	0.328169	+	0.189469i	0.0214991	+	0.0124125i	−0.489212	+	0.872165i	$0.662716\pi$
$234$	−3.86370	−	6.69213i	−0.252578	−	0.437478i
$235$	−2.15232	+	13.2426i	−0.140402	+	0.863855i
$236$	−9.14162	+	15.8338i	−0.595069	+	1.03069i
$237$			11.4641i			0.744673i
$238$		0			0
$239$	15.4641			1.00029			0.500145	−	0.865942i	$-0.333280\pi$
$239$	15.4641			1.00029			0.500145	+	0.865942i	$0.333280\pi$
$240$	−9.33341	+	3.53956i	−0.602469	+	0.228477i
$241$	−2.77766	−	4.81105i	−0.178925	−	0.309907i	0.762588	−	0.646885i	$-0.223929\pi$
$241$	−2.77766	−	4.81105i	−0.178925	−	0.309907i	−0.941513	+	0.336978i	$0.890595\pi$
$242$	−1.67303	+	0.965926i	−0.107547	+	0.0620921i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−15.8338			−1.01365
$245$		0			0
$246$	−16.3923			−1.04514
$247$	1.31268	+	0.757875i	0.0835237	+	0.0482224i
$248$	3.29423	−	1.90192i	0.209184	−	0.120772i
$249$	−3.00000	−	5.19615i	−0.190117	−	0.329293i
$250$	11.5431	+	18.2555i	0.730048	+	1.15458i
$251$	9.04008			0.570605			0.285303	−	0.958438i	$-0.407906\pi$
$251$	9.04008			0.570605			0.285303	+	0.958438i	$0.407906\pi$
$252$		0			0
$253$			21.8695i			1.37493i
$254$	2.73205	−	4.73205i	0.171424	−	0.296915i
$255$	−8.82843	−	1.43488i	−0.552858	−	0.0898555i
$256$	−9.69615	−	16.7942i	−0.606010	−	1.04964i
$257$	−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
$261$	−4.46410	+	7.73205i	−0.276321	+	0.478602i
$262$	−9.46410	+	5.46410i	−0.584694	+	0.337573i
$263$	−18.8516	+	10.8840i	−1.16244	+	0.671136i	−0.951888	−	0.306446i	$-0.900860\pi$
$263$	−18.8516	+	10.8840i	−1.16244	+	0.671136i	−0.210554	+	0.977582i	$0.567527\pi$
$264$	0.896575	−	1.55291i	0.0551804	−	0.0955753i
$265$	−12.7279	−	10.3923i	−0.781870	−	0.638394i
$266$		0			0
$267$			4.14110i			0.253431i
$268$	−10.4543	−	6.03579i	−0.638598	−	0.368695i
$269$	4.14110	+	7.17260i	0.252488	+	0.437321i	0.964210	−	0.265139i	$-0.0854180\pi$
$269$	4.14110	+	7.17260i	0.252488	+	0.437321i	−0.711722	+	0.702461i	$0.752085\pi$
$270$	−4.26380	−	0.692993i	−0.259487	−	0.0421742i
$271$	6.50266	−	11.2629i	0.395009	−	0.684175i	−0.598094	−	0.801426i	$-0.704075\pi$
$271$	6.50266	−	11.2629i	0.395009	−	0.684175i	0.993102	+	0.117251i	$0.0374083\pi$
$272$		−	17.8564i		−	1.08270i
$273$		0			0
$274$	8.73205			0.527522
$275$	−16.4290	−	5.48528i	−0.990705	−	0.330775i
$276$	5.46739	+	9.46979i	0.329098	+	0.570014i
$277$	9.79796	−	5.65685i	0.588702	−	0.339887i	−0.175882	−	0.984411i	$-0.556278\pi$
$277$	9.79796	−	5.65685i	0.588702	−	0.339887i	0.764584	+	0.644524i	$0.222944\pi$
$278$	−8.83013	−	5.09808i	−0.529596	−	0.305762i
$279$	7.34847			0.439941
$280$		0			0
$281$	0.143594			0.00856607			0.00428304	−	0.999991i	$-0.498637\pi$
$281$	0.143594			0.00856607			0.00428304	+	0.999991i	$0.498637\pi$
$282$	−10.0382	−	5.79555i	−0.597766	−	0.345120i
$283$	−25.8564	+	14.9282i	−1.53700	+	0.887390i	−0.537992	+	0.842950i	$0.680817\pi$
$283$	−25.8564	+	14.9282i	−1.53700	+	0.887390i	−0.999012	+	0.0444395i	$0.985850\pi$
$284$	12.4641	+	21.5885i	0.739608	+	1.28104i
$285$	0.792271	−	0.300457i	0.0469301	−	0.0177975i
$286$	26.7685			1.58286
$287$		0			0
$288$		−	7.58871i		−	0.447169i
$289$	−0.500000	+	0.866025i	−0.0294118	+	0.0509427i
$290$	−6.18718	+	38.0681i	−0.363324	+	2.23544i
$291$	2.53590	+	4.39230i	0.148657	+	0.257481i
$292$	−16.3923	−	9.46410i	−0.959287	−	0.553845i
$293$		−	4.53590i		−	0.264990i	−0.991184	−	0.132495i	$-0.957701\pi$
$293$		−	4.53590i		−	0.264990i	0.991184	−	0.132495i	$-0.0422989\pi$
$294$		0			0
$295$	14.9282	−	18.2832i	0.869154	−	1.06449i
$296$	0.196152	−	0.339746i	0.0114011	−	0.0197473i
$297$	3.00000	−	1.73205i	0.174078	−	0.100504i
$298$	35.0136	−	20.2151i	2.02828	−	1.17103i
$299$	12.6264	−	21.8695i	0.730203	−	1.26475i
$300$	−8.48528	+	1.73205i	−0.489898	+	0.100000i
$301$		0			0
$302$			24.2175i			1.39356i
$303$	10.9348	+	6.31319i	0.628186	+	0.362683i
$304$	0.845807	+	1.46498i	0.0485104	+	0.0840225i
$305$	20.1765	+	3.27928i	1.15530	+	0.187771i
$306$	3.86370	−	6.69213i	0.220873	−	0.382564i
$307$		−	4.00000i		−	0.228292i	−0.993464	−	0.114146i	$-0.963587\pi$
$307$		−	4.00000i		−	0.228292i	0.993464	−	0.114146i	$-0.0364132\pi$
$308$		0			0
$309$	−13.8564			−0.788263
$310$	29.6809	−	11.2560i	1.68576	−	0.639300i
$311$	−7.72741	−	13.3843i	−0.438181	−	0.758952i	0.559368	−	0.828919i	$-0.311044\pi$
$311$	−7.72741	−	13.3843i	−0.438181	−	0.758952i	−0.997549	+	0.0699675i	$0.977710\pi$
$312$	−1.79315	+	1.03528i	−0.101517	+	0.0586110i
$313$	9.46410	+	5.46410i	0.534943	+	0.308849i	0.743027	−	0.669262i	$-0.233389\pi$
$313$	9.46410	+	5.46410i	0.534943	+	0.308849i	−0.208084	+	0.978111i	$0.566723\pi$
$314$	36.5665			2.06357
$315$		0			0
$316$	−19.8564			−1.11701
$317$	−25.3035	−	14.6090i	−1.42119	−	0.820524i	−0.424788	−	0.905293i	$-0.639651\pi$
$317$	−25.3035	−	14.6090i	−1.42119	−	0.820524i	−0.996401	+	0.0847694i	$0.972985\pi$
$318$	12.2942	−	7.09808i	0.689426	−	0.398040i
$319$	−15.4641	−	26.7846i	−0.865823	−	1.49965i
$320$	−4.54490	−	11.9844i	−0.254068	−	0.669948i
$321$	15.5563			0.868271
$322$		0			0
$323$			1.51575i			0.0843386i
$324$	0.866025	−	1.50000i	0.0481125	−	0.0833333i
$325$	13.2621	+	14.9706i	0.735647	+	0.830417i
$326$	−16.1962	−	28.0526i	−0.897022	−	1.55369i
$327$	−10.2679	−	5.92820i	−0.567819	−	0.327830i
$328$			4.39230i			0.242524i
$329$		0			0
$330$	9.46410	−	11.5911i	0.520982	−	0.638070i
$331$	−16.3923	+	28.3923i	−0.901003	+	1.56058i	−0.0748075	+	0.997198i	$0.523834\pi$
$331$	−16.3923	+	28.3923i	−0.901003	+	1.56058i	−0.826195	+	0.563384i	$0.809499\pi$
$332$	9.00000	−	5.19615i	0.493939	−	0.285176i
$333$	0.656339	−	0.378937i	0.0359671	−	0.0207656i
$334$	−4.89898	+	8.48528i	−0.268060	+	0.464294i
$335$	12.0716	+	9.85641i	0.659541	+	0.538513i
$336$		0			0
$337$			27.5264i			1.49946i	0.661745	+	0.749729i	$0.269816\pi$
$337$			27.5264i			1.49946i	−0.661745	+	0.749729i	$0.730184\pi$
$338$	−5.01910	−	2.89778i	−0.273003	−	0.157618i
$339$	−0.189469	−	0.328169i	−0.0102905	−	0.0178237i
$340$	2.48528	−	15.2913i	0.134783	−	0.829286i
$341$	−12.7279	+	22.0454i	−0.689256	+	1.19383i
$342$			0.732051i			0.0395848i
$343$		0			0
$344$		0			0
$345$	−5.00569	−	13.1994i	−0.269497	−	0.710634i
$346$	15.4548	+	26.7685i	0.830856	+	1.43908i
$347$	9.88589	−	5.70762i	0.530702	−	0.306401i	−0.210600	−	0.977572i	$-0.567542\pi$
$347$	9.88589	−	5.70762i	0.530702	−	0.306401i	0.741302	+	0.671171i	$0.234208\pi$
$348$	−13.3923	−	7.73205i	−0.717903	−	0.414481i
$349$	−7.82894			−0.419074			−0.209537	−	0.977801i	$-0.567196\pi$
$349$	−7.82894			−0.419074			−0.209537	+	0.977801i	$0.567196\pi$
$350$		0			0
$351$	−4.00000			−0.213504
$352$	22.7661	+	13.1440i	1.21344	+	0.700579i
$353$	−3.92820	+	2.26795i	−0.209077	+	0.120711i	−0.600882	−	0.799337i	$-0.705184\pi$
$353$	−3.92820	+	2.26795i	−0.209077	+	0.120711i	0.391805	+	0.920048i	$0.371851\pi$
$354$	10.1962	+	17.6603i	0.541919	+	0.938632i
$355$	−11.4116	−	30.0910i	−0.605663	−	1.59706i
$356$	−7.17260			−0.380147
$357$		0			0
$358$		−	20.0764i		−	1.06107i
$359$	4.26795	−	7.39230i	0.225254	−	0.390151i	−0.731142	−	0.682226i	$-0.761012\pi$
$359$	4.26795	−	7.39230i	0.225254	−	0.390151i	0.956396	+	0.292075i	$0.0943456\pi$
$360$	−0.185687	+	1.14248i	−0.00978656	+	0.0602141i
$361$	9.42820	+	16.3301i	0.496221	+	0.859480i
$362$	−5.83013	−	3.36603i	−0.306425	−	0.176914i
$363$			1.00000i			0.0524864i
$364$		0			0
$365$	18.9282	+	15.4548i	0.990747	+	0.808942i
$366$	−8.83013	+	15.2942i	−0.461558	+	0.799442i
$367$	3.46410	−	2.00000i	0.180825	−	0.104399i	−0.406855	−	0.913493i	$-0.633375\pi$
$367$	3.46410	−	2.00000i	0.180825	−	0.104399i	0.587680	+	0.809093i	$0.300041\pi$
$368$	24.4070	−	14.0914i	1.27230	−	0.734563i
$369$	−4.24264	+	7.34847i	−0.220863	+	0.382546i
$370$	2.07055	−	2.53590i	0.107643	−	0.131835i
$371$		0			0
$372$			12.7279i			0.659912i
$373$	−23.1822	−	13.3843i	−1.20033	−	0.693011i	−0.239701	−	0.970847i	$-0.577050\pi$
$373$	−23.1822	−	13.3843i	−1.20033	−	0.693011i	−0.960629	+	0.277836i	$0.910383\pi$
$374$	13.3843	+	23.1822i	0.692084	+	1.19872i
$375$	11.1713	−	0.449747i	0.576883	−	0.0232249i
$376$	−1.55291	+	2.68973i	−0.0800854	+	0.138712i
$377$			35.7128i			1.83930i
$378$		0			0
$379$	−4.53590			−0.232993			−0.116497	−	0.993191i	$-0.537166\pi$
$379$	−4.53590			−0.232993			−0.116497	+	0.993191i	$0.537166\pi$
$380$	0.520407	+	1.37225i	0.0266963	+	0.0703951i
$381$	−1.41421	−	2.44949i	−0.0724524	−	0.125491i
$382$	0.896575	−	0.517638i	0.0458728	−	0.0264847i
$383$	3.33975	+	1.92820i	0.170653	+	0.0985266i	0.582894	−	0.812548i	$-0.301920\pi$
$383$	3.33975	+	1.92820i	0.170653	+	0.0985266i	−0.412241	+	0.911075i	$0.635254\pi$
$384$	−4.10394			−0.209428
$385$		0			0
$386$	−31.3205			−1.59417
$387$		0			0
$388$	−7.60770	+	4.39230i	−0.386222	+	0.222985i
$389$	12.4641	+	21.5885i	0.631955	+	1.09458i	0.987152	+	0.159787i	$0.0510806\pi$
$389$	12.4641	+	21.5885i	0.631955	+	1.09458i	−0.355197	+	0.934792i	$0.615586\pi$
$390$	−16.1562	+	6.12701i	−0.818103	+	0.310253i
$391$	25.2528			1.27709
$392$		0			0
$393$			5.65685i			0.285351i
$394$	11.0981	−	19.2224i	0.559113	−	0.968412i
$395$	25.3025	+	4.11240i	1.27311	+	0.206917i
$396$	3.00000	+	5.19615i	0.150756	+	0.261116i
$397$	27.4641	+	15.8564i	1.37838	+	0.795810i	0.991965	−	0.126513i	$-0.0403786\pi$
$397$	27.4641	+	15.8564i	1.37838	+	0.795810i	0.386419	+	0.922323i	$0.373712\pi$
$398$		−	6.19615i		−	0.310585i
$399$		0			0
$400$	4.46410	+	21.8695i	0.223205	+	1.09348i
$401$	−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	$0.182569\pi$
$402$	−11.6603	+	6.73205i	−0.581561	+	0.335764i
$403$	25.4558	−	14.6969i	1.26805	−	0.732107i
$404$	−10.9348	+	18.9396i	−0.544025	+	0.942279i
$405$	−1.41421	+	1.73205i	−0.0702728	+	0.0860663i
$406$		0			0
$407$			2.62536i			0.130134i
$408$	−1.79315	−	1.03528i	−0.0887742	−	0.0512538i
$409$	15.5056	+	26.8565i	0.766702	+	1.32797i	0.939342	+	0.342981i	$0.111437\pi$
$409$	15.5056	+	26.8565i	0.766702	+	1.32797i	−0.172641	+	0.984985i	$0.555230\pi$
$410$	−5.88024	+	36.1796i	−0.290404	+	1.78678i
$411$	2.26002	−	3.91447i	0.111479	−	0.193087i
$412$		−	24.0000i		−	1.18240i
$413$		0			0
$414$	12.1962			0.599408
$415$	−12.5446	+	4.75736i	−0.615791	+	0.233530i
$416$	−15.1774	−	26.2880i	−0.744134	−	1.28888i
$417$	−4.57081	+	2.63896i	−0.223834	+	0.129230i
$418$	−2.19615	−	1.26795i	−0.107417	−	0.0620174i
$419$	−1.51575			−0.0740492			−0.0370246	−	0.999314i	$-0.511788\pi$
$419$	−1.51575			−0.0740492			−0.0370246	+	0.999314i	$0.511788\pi$
$420$		0			0
$421$	−28.7846			−1.40288			−0.701438	−	0.712730i	$-0.747458\pi$
$421$	−28.7846			−1.40288			−0.701438	+	0.712730i	$0.747458\pi$
$422$	−21.8695	−	12.6264i	−1.06459	−	0.614643i
$423$	−5.19615	+	3.00000i	−0.252646	+	0.145865i
$424$	−1.90192	−	3.29423i	−0.0923656	−	0.159982i
$425$	−6.33386	+	18.9706i	−0.307237	+	0.920207i
$426$	27.8038			1.34710
$427$		0			0
$428$			26.9444i			1.30241i
$429$	6.92820	−	12.0000i	0.334497	−	0.579365i
$430$		0			0
$431$	−1.33975	−	2.32051i	−0.0645333	−	0.111775i	0.831954	−	0.554845i	$-0.187223\pi$
$431$	−1.33975	−	2.32051i	−0.0645333	−	0.111775i	−0.896487	+	0.443070i	$0.853889\pi$
$432$	−3.86603	−	2.23205i	−0.186004	−	0.107390i
$433$		−	9.85641i		−	0.473669i	−0.971550	−	0.236834i	$-0.923890\pi$
$433$		−	9.85641i		−	0.473669i	0.971550	−	0.236834i	$-0.0761099\pi$
$434$		0			0
$435$	15.4641	+	12.6264i	0.741447	+	0.605389i
$436$	10.2679	−	17.7846i	0.491746	−	0.851728i
$437$	−2.07180	+	1.19615i	−0.0991075	+	0.0572197i
$438$	−18.2832	+	10.5558i	−0.873607	+	0.504377i
$439$	0.845807	−	1.46498i	0.0403682	−	0.0699198i	−0.845135	−	0.534552i	$-0.820480\pi$
$439$	0.845807	−	1.46498i	0.0403682	−	0.0699198i	0.885504	+	0.464633i	$0.153814\pi$
$440$	−3.10583	−	2.53590i	−0.148065	−	0.120894i
$441$		0			0
$442$		−	30.9096i		−	1.47022i
$443$	23.0943	+	13.3335i	1.09724	+	0.633493i	0.935495	−	0.353339i	$-0.114954\pi$
$443$	23.0943	+	13.3335i	1.09724	+	0.633493i	0.161747	+	0.986832i	$0.448287\pi$
$444$	0.656339	+	1.13681i	0.0311485	+	0.0539507i
$445$	9.13986	+	1.48549i	0.433271	+	0.0704192i
$446$	7.72741	−	13.3843i	0.365903	−	0.633763i
$447$		−	20.9282i		−	0.989870i
$448$		0			0
$449$	−8.14359			−0.384320			−0.192160	−	0.981364i	$-0.561549\pi$
$449$	−8.14359			−0.384320			−0.192160	+	0.981364i	$0.561549\pi$
$450$	−3.05902	+	9.16208i	−0.144204	+	0.431905i
$451$	−14.6969	−	25.4558i	−0.692052	−	1.19867i
$452$	0.568406	−	0.328169i	0.0267356	−	0.0154358i
$453$	10.8564	+	6.26795i	0.510078	+	0.294494i
$454$	7.72741			0.362665
$455$		0			0
$456$	0.196152			0.00918568
$457$	−10.4543	−	6.03579i	−0.489031	−	0.282342i	0.235141	−	0.971961i	$-0.424445\pi$
$457$	−10.4543	−	6.03579i	−0.489031	−	0.282342i	−0.724173	+	0.689619i	$0.757778\pi$
$458$	38.9545	−	22.4904i	1.82022	−	1.05091i
$459$	−2.00000	−	3.46410i	−0.0933520	−	0.161690i
$460$	22.8621	−	8.67011i	1.06595	−	0.404246i
$461$	−12.8295			−0.597527			−0.298764	−	0.954327i	$-0.596574\pi$
$461$	−12.8295			−0.597527			−0.298764	+	0.954327i	$0.596574\pi$
$462$		0			0
$463$		−	16.7675i		−	0.779251i	−0.920973	−	0.389626i	$-0.872604\pi$
$463$		−	16.7675i		−	0.779251i	0.920973	−	0.389626i	$-0.127396\pi$
$464$	−19.9282	+	34.5167i	−0.925144	+	1.60240i
$465$	2.63604	−	16.2189i	0.122243	−	0.752131i
$466$	0.366025	+	0.633975i	0.0169558	+	0.0293683i
$467$	−15.4641	−	8.92820i	−0.715593	−	0.413148i	0.0975353	−	0.995232i	$-0.468904\pi$
$467$	−15.4641	−	8.92820i	−0.715593	−	0.413148i	−0.813129	+	0.582084i	$0.802237\pi$
$468$		−	6.92820i		−	0.320256i
$469$		0			0
$470$	−16.3923	+	20.0764i	−0.756121	+	0.926055i
$471$	9.46410	−	16.3923i	0.436083	−	0.755318i
$472$	4.73205	−	2.73205i	0.217810	−	0.125753i
$473$		0			0
$474$	−11.0735	+	19.1798i	−0.508621	+	0.880958i
$475$	−0.378937	−	1.85641i	−0.0173868	−	0.0851778i
$476$		0			0
$477$		−	7.34847i		−	0.336463i
$478$	25.8719	+	14.9372i	1.18336	+	0.683210i
$479$	−6.96953	−	12.0716i	−0.318446	−	0.551565i	0.661718	−	0.749753i	$-0.269828\pi$
$479$	−6.96953	−	12.0716i	−0.318446	−	0.551565i	−0.980164	+	0.198188i	$0.936494\pi$
$480$	−16.7491	−	2.72222i	−0.764488	−	0.124252i
$481$	1.51575	−	2.62536i	0.0691122	−	0.119706i
$482$		−	10.7321i		−	0.488832i
$483$		0			0
$484$	−1.73205			−0.0787296
$485$	10.6040	−	4.02139i	0.481501	−	0.182602i
$486$	−0.965926	−	1.67303i	−0.0438153	−	0.0758903i
$487$	3.58630	−	2.07055i	0.162511	−	0.0938257i	−0.416539	−	0.909118i	$-0.636757\pi$
$487$	3.58630	−	2.07055i	0.162511	−	0.0938257i	0.579050	+	0.815292i	$0.303424\pi$
$488$	4.09808	+	2.36603i	0.185511	+	0.107105i
$489$	−16.7675			−0.758252
$490$		0			0
$491$	6.67949			0.301441			0.150721	−	0.988576i	$-0.451841\pi$
$491$	6.67949			0.301441			0.150721	+	0.988576i	$0.451841\pi$
$492$	−12.7279	−	7.34847i	−0.573819	−	0.331295i
$493$	−30.9282	+	17.8564i	−1.39294	+	0.804212i
$494$	1.46410	+	2.53590i	0.0658730	+	0.114095i
$495$	−2.74666	−	7.24264i	−0.123453	−	0.325532i
$496$	32.8043			1.47296
$497$		0			0
$498$		−	11.5911i		−	0.519410i
$499$	8.12436	−	14.0718i	0.363696	−	0.629940i	−0.624870	−	0.780729i	$-0.714848\pi$
$499$	8.12436	−	14.0718i	0.363696	−	0.629940i	0.988566	+	0.150789i	$0.0481813\pi$
$500$	0.778985	+	19.3492i	0.0348373	+	0.865324i
$501$	2.53590	+	4.39230i	0.113296	+	0.196234i
$502$	15.1244	+	8.73205i	0.675033	+	0.389731i
$503$			3.85641i			0.171949i	0.996297	+	0.0859743i	$0.0274003\pi$
$503$			3.85641i			0.171949i	−0.996297	+	0.0859743i	$0.972600\pi$
$504$		0			0
$505$	17.8564	−	21.8695i	0.794600	−	0.973182i
$506$	−21.1244	+	36.5885i	−0.939092	+	1.62656i
$507$	−2.59808	+	1.50000i	−0.115385	+	0.0666173i
$508$	4.24264	−	2.44949i	0.188237	−	0.108679i
$509$	21.1117	−	36.5665i	0.935758	−	1.62078i	0.162482	−	0.986712i	$-0.448050\pi$
$509$	21.1117	−	36.5665i	0.935758	−	1.62078i	0.773276	−	0.634069i	$-0.218617\pi$
$510$	−13.3843	−	10.9282i	−0.592665	−	0.483909i
$511$		0			0
$512$		−	29.2552i		−	1.29291i
$513$	0.328169	+	0.189469i	0.0144890	+	0.00836525i
$514$	−3.34607	−	5.79555i	−0.147589	−	0.255631i
$515$	−4.97056	+	30.5826i	−0.219029	+	1.34763i
$516$		0			0
$517$		−	20.7846i		−	0.914106i
$518$		0			0
$519$	16.0000			0.702322
$520$	1.64173	+	4.32905i	0.0719945	+	0.189841i
$521$	−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	$-0.379363\pi$
$522$	−14.9372	+	8.62398i	−0.653782	+	0.377461i
$523$	10.1436	+	5.85641i	0.443548	+	0.256083i	0.705102	−	0.709106i	$-0.250901\pi$
$523$	10.1436	+	5.85641i	0.443548	+	0.256083i	−0.261553	+	0.965189i	$0.584235\pi$
$524$	−9.79796			−0.428026
$525$		0			0
$526$	−42.0526			−1.83358
$527$	25.4558	+	14.6969i	1.10887	+	0.640209i
$528$	13.3923	−	7.73205i	0.582825	−	0.336494i
$529$	8.42820	+	14.5981i	0.366444	+	0.634699i
$530$	−11.2560	−	29.6809i	−0.488931	−	1.28926i
$531$	10.5558			0.458084
$532$		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
$536$	1.80385	+	3.12436i	0.0779143	+	0.134952i
$537$	−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
$541$	21.3205	−	36.9282i	0.916640	−	1.58767i	0.112158	−	0.993690i	$-0.464224\pi$
$541$	21.3205	−	36.9282i	0.916640	−	1.58767i	0.804482	−	0.593977i	$-0.202443\pi$
$542$	21.7583	−	12.5622i	0.934600	−	0.539592i
$543$	−3.01790	+	1.74238i	−0.129510	+	0.0747728i
$544$	15.1774	−	26.2880i	0.650726	−	1.12709i
$545$	−16.7675	+	20.5359i	−0.718240	+	0.879661i
$546$		0			0
$547$		−	29.5969i		−	1.26547i	−0.774367	−	0.632737i	$-0.781931\pi$
$547$		−	29.5969i		−	1.26547i	0.774367	−	0.632737i	$-0.218069\pi$
$548$	6.78006	+	3.91447i	0.289630	+	0.167218i
$549$	4.57081	+	7.91688i	0.195077	+	0.337884i
$550$	−22.1879	−	25.0462i	−0.946094	−	1.06798i
$551$	1.69161	−	2.92996i	0.0720652	−	0.124821i
$552$		−	3.26795i		−	0.139093i
$553$		0			0
$554$	21.8564			0.928590
$555$	−0.600914	−	1.58454i	−0.0255074	−	0.0672601i
$556$	−4.57081	−	7.91688i	−0.193846	−	0.335750i
$557$	−11.9193	+	6.88160i	−0.505036	+	0.291583i	−0.730791	−	0.682601i	$-0.760849\pi$
$557$	−11.9193	+	6.88160i	−0.505036	+	0.291583i	0.225755	+	0.974184i	$0.427515\pi$
$558$	12.2942	+	7.09808i	0.520456	+	0.300486i
$559$		0			0
$560$		0			0
$561$	13.8564			0.585018
$562$	0.240237	+	0.138701i	0.0101338	+	0.00585074i
$563$	−27.5885	+	15.9282i	−1.16271	+	0.671294i	−0.951953	−	0.306244i	$-0.900928\pi$
$563$	−27.5885	+	15.9282i	−1.16271	+	0.671294i	−0.210762	+	0.977537i	$0.567594\pi$
$564$	−5.19615	−	9.00000i	−0.218797	−	0.378968i
$565$	−0.792271	+	0.300457i	−0.0333311	+	0.0126403i
$566$	−57.6781			−2.42439
$567$		0			0
$568$		−	7.45001i		−	0.312595i
$569$	5.92820	−	10.2679i	0.248523	−	0.430455i	−0.714593	−	0.699540i	$-0.753388\pi$
$569$	5.92820	−	10.2679i	0.248523	−	0.430455i	0.963116	+	0.269086i	$0.0867214\pi$
$570$	1.61571	+	0.262601i	0.0676748	+	0.0109991i
$571$	−19.8564	−	34.3923i	−0.830965	−	1.43927i	−0.897274	−	0.441474i	$-0.854456\pi$
$571$	−19.8564	−	34.3923i	−0.830965	−	1.43927i	0.0663093	−	0.997799i	$-0.478878\pi$
$572$	20.7846	+	12.0000i	0.869048	+	0.501745i
$573$		−	0.535898i		−	0.0223875i
$574$		0			0
$575$	−30.9282	+	6.31319i	−1.28980	+	0.263278i
$576$	2.86603	−	4.96410i	0.119418	−	0.206838i
$577$	3.46410	−	2.00000i	0.144212	−	0.0832611i	−0.426158	−	0.904649i	$-0.640133\pi$
$577$	3.46410	−	2.00000i	0.144212	−	0.0832611i	0.570370	+	0.821388i	$0.306800\pi$
$578$	−1.67303	+	0.965926i	−0.0695890	+	0.0401772i
$579$	−8.10634	+	14.0406i	−0.336888	+	0.583507i
$580$	−21.8695	+	26.7846i	−0.908083	+	1.11217i
$581$		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
$586$	4.38134	−	7.58871i	0.180992	−	0.313487i
$587$		−	31.8564i		−	1.31485i	−0.753518	−	0.657427i	$-0.771645\pi$
$587$		−	31.8564i		−	1.31485i	0.753518	−	0.657427i	$-0.228355\pi$
$588$		0			0
$589$	−2.78461			−0.114738
$590$	42.6356	−	16.1689i	1.75528	−	0.665664i
$591$	−5.74479	−	9.95026i	−0.236309	−	0.409299i
$592$	2.92996	−	1.69161i	0.120421	−	0.0695249i
$593$	−8.07180	−	4.66025i	−0.331469	−	0.191374i	0.325024	−	0.945706i	$-0.394628\pi$
$593$	−8.07180	−	4.66025i	−0.331469	−	0.191374i	−0.656493	+	0.754332i	$0.727961\pi$
$594$	6.69213			0.274581
$595$		0			0
$596$	36.2487			1.48481
$597$	−2.77766	−	1.60368i	−0.113682	−	0.0656343i
$598$	42.2487	−	24.3923i	1.72768	−	0.997476i
$599$	−2.66025	−	4.60770i	−0.108695	−	0.188265i	0.806547	−	0.591170i	$-0.201334\pi$
$599$	−2.66025	−	4.60770i	−0.108695	−	0.188265i	−0.915242	+	0.402905i	$0.868001\pi$
$600$	2.45497	+	0.819661i	0.100224	+	0.0334625i
$601$	−33.6365			−1.37206			−0.686031	−	0.727572i	$-0.740649\pi$
$601$	−33.6365			−1.37206			−0.686031	+	0.727572i	$0.740649\pi$
$602$		0			0
$603$			6.96953i			0.283821i
$604$	−10.8564	+	18.8038i	−0.441741	+	0.765118i
$605$	2.20711	+	0.358719i	0.0897317	+	0.0145840i
$606$	12.1962	+	21.1244i	0.495435	+	0.858118i
$607$	10.3923	+	6.00000i	0.421811	+	0.243532i	0.695852	−	0.718186i	$-0.255027\pi$
$607$	10.3923	+	6.00000i	0.421811	+	0.243532i	−0.274041	+	0.961718i	$0.588360\pi$
$608$			2.87564i			0.116623i
$609$		0			0
$610$	30.5885	+	24.9754i	1.23849	+	1.01122i
$611$	−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	$0.396735\pi$
$614$	3.86370	−	6.69213i	0.155926	−	0.270072i
$615$	14.6969	+	12.0000i	0.592638	+	0.483887i
$616$		0			0
$617$		−	12.4505i		−	0.501239i	−0.968086	−	0.250620i	$-0.919366\pi$
$617$		−	12.4505i		−	0.501239i	0.968086	−	0.250620i	$-0.0806343\pi$
$618$	−23.1822	−	13.3843i	−0.932526	−	0.538394i
$619$	−1.88108	−	3.25813i	−0.0756071	−	0.130955i	0.825743	−	0.564047i	$-0.190756\pi$
$619$	−1.88108	−	3.25813i	−0.0756071	−	0.130955i	−0.901350	+	0.433091i	$0.857423\pi$
$620$	28.0919	+	4.56575i	1.12820	+	0.183365i
$621$	3.15660	−	5.46739i	0.126670	−	0.219399i
$622$		−	29.8564i		−	1.19713i
$623$		0			0
$624$	−17.8564			−0.714828
$625$	3.01472	−	24.8176i	0.120589	−	0.992703i
$626$	10.5558	+	18.2832i	0.421896	+	0.730745i
$627$	−1.13681	+	0.656339i	−0.0453999	+	0.0262116i
$628$	28.3923	+	16.3923i	1.13298	+	0.654124i
$629$	3.03150			0.120874
$630$		0			0
$631$	9.32051			0.371044			0.185522	−	0.982640i	$-0.440602\pi$
$631$	9.32051			0.371044			0.185522	+	0.982640i	$0.440602\pi$
$632$	5.13922	+	2.96713i	0.204427	+	0.118026i
$633$	−11.3205	+	6.53590i	−0.449950	+	0.259779i
$634$	−28.2224	−	48.8827i	−1.12086	−	1.94138i
$635$	−5.91359	+	2.24264i	−0.234674	+	0.0889965i
$636$	12.7279			0.504695
$637$		0			0
$638$		−	59.7487i		−	2.36547i
$639$	7.19615	−	12.4641i	0.284675	−	0.493072i
$640$	−1.47216	+	9.05783i	−0.0581924	+	0.358042i
$641$	−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	$0.896612\pi$
$642$	26.0263	+	15.0263i	1.02718	+	0.593040i
$643$			4.00000i			0.157745i	0.996885	+	0.0788723i	$0.0251319\pi$
$643$			4.00000i			0.157745i	−0.996885	+	0.0788723i	$0.974868\pi$
$644$		0			0
$645$		0			0
$646$	−1.46410	+	2.53590i	−0.0576043	+	0.0997736i
$647$	−25.1769	+	14.5359i	−0.989807	+	0.571465i	−0.905216	−	0.424951i	$-0.860291\pi$
$647$	−25.1769	+	14.5359i	−0.989807	+	0.571465i	−0.0845901	+	0.996416i	$0.526958\pi$
$648$	−0.448288	+	0.258819i	−0.0176104	+	0.0101674i
$649$	−18.2832	+	31.6675i	−0.717680	+	1.24306i
$650$	7.72741	+	37.8564i	0.303094	+	1.48485i
$651$		0			0
$652$		−	29.0421i		−	1.13738i
$653$	16.1619	+	9.33109i	0.632465	+	0.365154i	0.781706	−	0.623647i	$-0.214350\pi$
$653$	16.1619	+	9.33109i	0.632465	+	0.365154i	−0.149241	+	0.988801i	$0.547683\pi$
$654$	−11.4524	−	19.8362i	−0.447825	−	0.775655i
$655$	12.4853	+	2.02922i	0.487840	+	0.0792883i
$656$	−18.9396	+	32.8043i	−0.739466	+	1.28079i
$657$			10.9282i			0.426350i
$658$		0			0
$659$	10.3923			0.404827			0.202413	−	0.979300i	$-0.435122\pi$
$659$	10.3923			0.404827			0.202413	+	0.979300i	$0.435122\pi$
$660$	12.5446	−	4.75736i	0.488299	−	0.185180i
$661$	11.6419	+	20.1643i	0.452817	+	0.784301i	0.998560	−	0.0536512i	$-0.0170859\pi$
$661$	11.6419	+	20.1643i	0.452817	+	0.784301i	−0.545743	+	0.837953i	$0.683753\pi$
$662$	−54.8497	+	31.6675i	−2.13179	+	1.23079i
$663$	−13.8564	−	8.00000i	−0.538138	−	0.310694i
$664$	−3.10583			−0.120530
$665$		0			0
$666$	1.46410			0.0567328
$667$	−48.8139	−	28.1827i	−1.89008	−	1.09124i
$668$	−7.60770	+	4.39230i	−0.294351	+	0.169943i
$669$	−4.00000	−	6.92820i	−0.154649	−	0.267860i
$670$	10.6756	+	28.1503i	0.412434	+	1.08754i
$671$	−31.6675			−1.22251
$672$		0			0
$673$			12.0716i			0.465325i	0.972557	+	0.232663i	$0.0747438\pi$
$673$			12.0716i			0.465325i	−0.972557	+	0.232663i	$0.925256\pi$
$674$	−26.5885	+	46.0526i	−1.02415	+	1.77388i
$675$	3.31552	+	3.74264i	0.127614	+	0.144054i
$676$	−2.59808	−	4.50000i	−0.0999260	−	0.173077i
$677$	−33.9282	−	19.5885i	−1.30397	−	0.752846i	−0.322885	−	0.946438i	$-0.604653\pi$
$677$	−33.9282	−	19.5885i	−1.30397	−	0.752846i	−0.981082	+	0.193593i	$0.937986\pi$
$678$		−	0.732051i		−	0.0281142i
$679$		0			0
$680$	−2.92820	+	3.58630i	−0.112291	+	0.137528i
$681$	2.00000	−	3.46410i	0.0766402	−	0.132745i
$682$	−42.5885	+	24.5885i	−1.63080	+	0.941541i
$683$	−19.6839	+	11.3645i	−0.753182	+	0.434850i	−0.826842	−	0.562434i	$-0.809865\pi$
$683$	−19.6839	+	11.3645i	−0.753182	+	0.434850i	0.0736607	+	0.997283i	$0.476532\pi$
$684$	−0.328169	+	0.568406i	−0.0125479	+	0.0217335i
$685$	−7.82894	−	6.39230i	−0.299129	−	0.244237i
$686$		0			0
$687$		−	23.2838i		−	0.888331i
$688$		0			0
$689$	−14.6969	−	25.4558i	−0.559909	−	0.969790i
$690$	4.37500	−	26.9182i	0.166553	−	1.02476i
$691$	3.01790	−	5.22715i	0.114806	−	0.198850i	−0.802896	−	0.596119i	$-0.796709\pi$
$691$	3.01790	−	5.22715i	0.114806	−	0.198850i	0.917702	+	0.397269i	$0.130042\pi$
$692$			27.7128i			1.05348i
$693$		0			0
$694$	22.0526			0.837104
$695$	4.18482	+	11.0349i	0.158739	+	0.418578i
$696$	2.31079	+	4.00240i	0.0875902	+	0.151711i
$697$	−29.3939	+	16.9706i	−1.11337	+	0.642806i
$698$	−13.0981	−	7.56218i	−0.495769	−	0.286233i
$699$	0.378937			0.0143327
$700$		0			0
$701$	−24.9282			−0.941525			−0.470763	−	0.882260i	$-0.656021\pi$
$701$	−24.9282			−0.941525			−0.470763	+	0.882260i	$0.656021\pi$
$702$	−6.69213	−	3.86370i	−0.252578	−	0.145826i
$703$	−0.248711	+	0.143594i	−0.00938032	+	0.00541573i
$704$	9.92820	+	17.1962i	0.374183	+	0.648104i
$705$	4.75736	+	12.5446i	0.179173	+	0.472458i
$706$	−8.76268			−0.329788
$707$		0			0
$708$			18.2832i			0.687126i
$709$	1.46410	−	2.53590i	0.0549855	−	0.0952377i	−0.837222	−	0.546862i	$-0.815822\pi$
$709$	1.46410	−	2.53590i	0.0549855	−	0.0952377i	0.892208	+	0.451625i	$0.149155\pi$
$710$	9.97376	−	61.3660i	0.374309	−	2.30302i
$711$	5.73205	+	9.92820i	0.214969	+	0.372337i
$712$	1.85641	+	1.07180i	0.0695718	+	0.0401673i
$713$			46.3923i			1.73741i
$714$		0			0
$715$	−24.0000	−	19.5959i	−0.897549	−	0.732846i
$716$	9.00000	−	15.5885i	0.336346	−	0.582568i
$717$	13.3923	−	7.73205i	0.500145	−	0.288759i
$718$	14.2808	−	8.24504i	0.532956	−	0.307702i
$719$	7.34847	−	12.7279i	0.274052	−	0.474671i	−0.695844	−	0.718193i	$-0.744969\pi$
$719$	7.34847	−	12.7279i	0.274052	−	0.474671i	0.969895	+	0.243522i	$0.0783027\pi$
$720$	−6.31319	+	7.73205i	−0.235279	+	0.288157i
$721$		0			0
$722$			36.4278i			1.35570i
$723$	−4.81105	−	2.77766i	−0.178925	−	0.103302i
$724$	−3.01790	−	5.22715i	−0.112159	−	0.194265i
$725$	33.4151	−	29.6016i	1.24100	−	1.09938i
$726$	−0.965926	+	1.67303i	−0.0358489	+	0.0620921i
$727$			31.7128i			1.17616i	0.808802	+	0.588082i	$0.200117\pi$
$727$			31.7128i			1.17616i	−0.808802	+	0.588082i	$0.799883\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	16.7393	+	44.1396i	0.619549	+	1.63368i
$731$		0			0
$732$	−13.7124	+	7.91688i	−0.506826	+	0.292616i
$733$	−8.53590	−	4.92820i	−0.315281	−	0.182027i	0.334006	−	0.942571i	$-0.391599\pi$
$733$	−8.53590	−	4.92820i	−0.315281	−	0.182027i	−0.649287	+	0.760543i	$0.724933\pi$
$734$	7.72741			0.285224
$735$		0			0
$736$	47.9090			1.76595
$737$	−20.9086	−	12.0716i	−0.770178	−	0.444662i
$738$	−14.1962	+	8.19615i	−0.522568	+	0.301705i
$739$	0.928203	+	1.60770i	0.0341445	+	0.0591400i	0.882593	−	0.470138i	$-0.155796\pi$
$739$	0.928203	+	1.60770i	0.0341445	+	0.0591400i	−0.848448	+	0.529278i	$0.822463\pi$
$740$	2.74451	−	1.04081i	0.100890	−	0.0382611i
$741$	1.51575			0.0556825
$742$		0			0
$743$			37.0197i			1.35812i	0.734081	+	0.679061i	$0.237613\pi$
$743$			37.0197i			1.35812i	−0.734081	+	0.679061i	$0.762387\pi$
$744$	1.90192	−	3.29423i	0.0697279	−	0.120772i
$745$	−46.1908	−	7.50735i	−1.69230	−	0.275048i
$746$	−25.8564	−	44.7846i	−0.946670	−	1.63968i
$747$	−5.19615	−	3.00000i	−0.190117	−	0.109764i
$748$			24.0000i			0.877527i
$749$		0			0
$750$	19.1244	+	10.0382i	0.698323	+	0.366543i
$751$	−2.39230	+	4.14359i	−0.0872964	+	0.151202i	−0.906367	−	0.422490i	$-0.861156\pi$
$751$	−2.39230	+	4.14359i	−0.0872964	+	0.151202i	0.819071	+	0.573692i	$0.194489\pi$
$752$	−23.1962	+	13.3923i	−0.845877	+	0.488367i
$753$	7.82894	−	4.52004i	0.285303	−	0.164719i
$754$	−34.4959	+	59.7487i	−1.25627	+	2.17592i
$755$	17.7284	−	21.7128i	0.645204	−	0.790210i
$756$		0			0
$757$			34.2929i			1.24640i	0.782064	+	0.623198i	$0.214167\pi$
$757$			34.2929i			1.24640i	−0.782064	+	0.623198i	$0.785833\pi$
$758$	−7.58871	−	4.38134i	−0.275634	−	0.159137i
$759$	10.9348	+	18.9396i	0.396907	+	0.687463i
$760$	0.0703637	−	0.432929i	0.00255236	−	0.0157040i
$761$	−20.3538	+	35.2538i	−0.737824	+	1.27795i	0.215649	+	0.976471i	$0.430813\pi$
$761$	−20.3538	+	35.2538i	−0.737824	+	1.27795i	−0.953473	+	0.301478i	$0.902520\pi$
$762$		−	5.46410i		−	0.197944i
$763$		0			0
$764$	0.928203			0.0335812
$765$	−8.36308	+	3.17157i	−0.302368	+	0.114668i
$766$	3.72500	+	6.45189i	0.134590	+	0.233116i
$767$	36.5665	−	21.1117i	1.32034	−	0.762298i
$768$	−16.7942	−	9.69615i	−0.606010	−	0.349880i
$769$	−19.4944			−0.702985			−0.351493	−	0.936191i	$-0.614326\pi$
$769$	−19.4944			−0.702985			−0.351493	+	0.936191i	$0.614326\pi$
$770$		0			0
$771$	−3.46410			−0.124757
$772$	−24.3190	−	14.0406i	−0.875261	−	0.505332i
$773$	−8.78461	+	5.07180i	−0.315960	+	0.182420i	−0.649591	−	0.760284i	$-0.725060\pi$
$773$	−8.78461	+	5.07180i	−0.315960	+	0.182420i	0.333630	+	0.942704i	$0.391726\pi$
$774$		0			0
$775$	−34.8511	−	11.6360i	−1.25189	−	0.417979i
$776$	2.62536			0.0942448
$777$		0			0
$778$			48.1576i			1.72653i
$779$	1.60770	−	2.78461i	0.0576017	−	0.0997690i
$780$	−15.2913	−	2.48528i	−0.547516	−	0.0889873i
$781$	24.9282	+	43.1769i	0.892001	+	1.54499i
$782$	42.2487	+	24.3923i	1.51081	+	0.872267i
$783$			8.92820i			0.319068i
$784$		0			0
$785$	−32.7846	−	26.7685i	−1.17013	−	0.955410i
$786$	−5.46410	+	9.46410i	−0.194898	+	0.337573i
$787$	−15.7128	+	9.07180i	−0.560101	+	0.323375i	−0.753186	−	0.657807i	$-0.771484\pi$
$787$	−15.7128	+	9.07180i	−0.560101	+	0.323375i	0.193085	+	0.981182i	$0.438151\pi$
$788$	17.2344	−	9.95026i	0.613949	−	0.354463i
$789$	−10.8840	+	18.8516i	−0.387481	+	0.671136i
$790$	38.3596	+	31.3205i	1.36477	+	1.11433i
$791$		0			0
$792$		−	1.79315i		−	0.0637168i
$793$	31.6675	+	18.2832i	1.12455	+	0.649257i
$794$	30.6322	+	53.0566i	1.08710	+	1.88291i
$795$	−16.2189	−	2.63604i	−0.575224	−	0.0934907i
$796$	2.77766	−	4.81105i	0.0984515	−	0.170523i
$797$		−	37.8564i		−	1.34094i	−0.741935	−	0.670471i	$-0.766092\pi$
$797$		−	37.8564i		−	1.34094i	0.741935	−	0.670471i	$-0.233908\pi$
$798$		0			0
$799$	−24.0000			−0.849059
$800$	−12.0164	+	35.9905i	−0.424845	+	1.27246i
$801$	2.07055	+	3.58630i	0.0731594	+	0.126716i
$802$	−3.34607	+	1.93185i	−0.118154	+	0.0682161i
$803$	−32.7846	−	18.9282i	−1.15694	−	0.667962i
$804$	−12.0716			−0.425732
$805$		0			0
$806$	56.7846			2.00015
$807$	7.17260	+	4.14110i	0.252488	+	0.145774i
$808$	5.66025	−	3.26795i	0.199127	−	0.114966i
$809$	−16.8564	−	29.1962i	−0.592640	−	1.02648i	−0.993875	−	0.110507i	$-0.964752\pi$
$809$	−16.8564	−	29.1962i	−0.592640	−	1.02648i	0.401236	−	0.915975i	$-0.368581\pi$
$810$	−4.03906	+	1.53175i	−0.141918	+	0.0538203i
$811$	−8.66115			−0.304134			−0.152067	−	0.988370i	$-0.548593\pi$
$811$	−8.66115			−0.304134			−0.152067	+	0.988370i	$0.548593\pi$
$812$		0			0
$813$		−	13.0053i		−	0.456117i
$814$	−2.53590	+	4.39230i	−0.0888832	+	0.153950i
$815$	−6.01483	+	37.0076i	−0.210690	+	1.29632i
$816$	−8.92820	−	15.4641i	−0.312550	−	0.541352i
$817$		0			0
$818$			59.9090i			2.09467i
$819$		0			0
$820$	−20.7846	+	25.4558i	−0.725830	+	0.888957i
$821$	11.3923	−	19.7321i	0.397594	−	0.688653i	−0.595834	−	0.803107i	$-0.703179\pi$
$821$	11.3923	−	19.7321i	0.397594	−	0.688653i	0.993429	+	0.114454i	$0.0365119\pi$
$822$	7.56218	−	4.36603i	0.263761	−	0.152283i
$823$	−41.2896	+	23.8386i	−1.43926	+	0.830960i	−0.997799	−	0.0663179i	$-0.978875\pi$
$823$	−41.2896	+	23.8386i	−1.43926	+	0.830960i	−0.441466	+	0.897278i	$0.645542\pi$
$824$	−3.58630	+	6.21166i	−0.124935	+	0.216393i
$825$	−16.9706	+	3.46410i	−0.590839	+	0.120605i
$826$		0			0
$827$		−	50.6071i		−	1.75978i	−0.475177	−	0.879890i	$-0.657616\pi$
$827$		−	50.6071i		−	1.75978i	0.475177	−	0.879890i	$-0.342384\pi$
$828$	9.46979	+	5.46739i	0.329098	+	0.190005i
$829$	17.9551	+	31.0991i	0.623605	+	1.08012i	0.988809	+	0.149188i	$0.0476661\pi$
$829$	17.9551	+	31.0991i	0.623605	+	1.08012i	−0.365203	+	0.930928i	$0.619001\pi$
$830$	−25.5828	−	4.15796i	−0.887993	−	0.144325i
$831$	5.65685	−	9.79796i	0.196234	−	0.339887i
$832$		−	22.9282i		−	0.794892i
$833$		0			0
$834$	−10.1962			−0.353064
$835$	10.6040	−	4.02139i	0.366965	−	0.139166i
$836$	−1.13681	−	1.96902i	−0.0393175	−	0.0680999i
$837$	6.36396	−	3.67423i	0.219971	−	0.127000i
$838$	−2.53590	−	1.46410i	−0.0876012	−	0.0505766i
$839$	9.04008			0.312098			0.156049	−	0.987749i	$-0.450124\pi$
$839$	9.04008			0.312098			0.156049	+	0.987749i	$0.450124\pi$
$840$		0			0
$841$	50.7128			1.74872
$842$	−48.1576	−	27.8038i	−1.65962	−	0.958182i
$843$	0.124356	−	0.0717968i	0.00428304	−	0.00247281i
$844$	−11.3205	−	19.6077i	−0.389668	−	0.674925i
$845$	2.37868	+	6.27231i	0.0818291	+	0.215774i
$846$	−11.5911			−0.398511
$847$		0			0
$848$		−	32.8043i		−	1.12650i
$849$	−14.9282	+	25.8564i	−0.512335	+	0.887390i
$850$	−28.9209	+	25.6203i	−0.991979	+	0.878770i
$851$	2.39230	+	4.14359i	0.0820072	+	0.142041i
$852$	21.5885	+	12.4641i	0.739608	+	0.427013i
$853$		−	26.9282i		−	0.922004i	−0.887399	−	0.461002i	$-0.847490\pi$
$853$		−	26.9282i		−	0.922004i	0.887399	−	0.461002i	$-0.152510\pi$
$854$		0			0
$855$	0.535898	−	0.656339i	0.0183273	−	0.0224463i
$856$	4.02628	−	6.97372i	0.137615	−	0.238357i
$857$	15.4641	−	8.92820i	0.528244	−	0.304982i	−0.212057	−	0.977257i	$-0.568016\pi$
$857$	15.4641	−	8.92820i	0.528244	−	0.304982i	0.740301	+	0.672276i	$0.234683\pi$
$858$	23.1822	−	13.3843i	0.791428	−	0.456931i
$859$	23.7506	−	41.1373i	0.810361	−	1.40359i	−0.102251	−	0.994759i	$-0.532604\pi$
$859$	23.7506	−	41.1373i	0.810361	−	1.40359i	0.912612	−	0.408828i	$-0.134062\pi$
$860$		0			0
$861$		0			0
$862$		−	5.17638i		−	0.176308i
$863$	−45.6202	−	26.3388i	−1.55293	−	0.896584i	−0.997901	−	0.0647515i	$-0.979375\pi$
$863$	−45.6202	−	26.3388i	−1.55293	−	0.896584i	−0.555027	−	0.831832i	$-0.687292\pi$
$864$	−3.79435	−	6.57201i	−0.129087	−	0.223584i
$865$	5.73951	−	35.3137i	0.195149	−	1.20070i
$866$	9.52056	−	16.4901i	0.323522	−	0.560356i
$867$			1.00000i			0.0339618i
$868$		0			0
$869$	−39.7128			−1.34716
$870$	13.6758	+	36.0615i	0.463653	+	1.22260i
$871$	13.9391	+	24.1432i	0.472307	+	0.818060i
$872$	−5.31508	+	3.06866i	−0.179991	+	0.103918i
$873$	4.39230	+	2.53590i	0.148657	+	0.0858272i
$874$	−4.62158			−0.156327
$875$		0			0
$876$	−18.9282			−0.639525
$877$	−29.3939	−	16.9706i	−0.992561	−	0.573055i	−0.0865220	−	0.996250i	$-0.527575\pi$
$877$	−29.3939	−	16.9706i	−0.992561	−	0.573055i	−0.906039	+	0.423195i	$0.860909\pi$
$878$	2.83013	−	1.63397i	0.0955122	−	0.0551440i
$879$	−2.26795	−	3.92820i	−0.0764960	−	0.132495i
$880$	−12.2614	−	32.3319i	−0.413331	−	1.08991i
$881$	10.0010			0.336943			0.168472	−	0.985707i	$-0.446117\pi$
$881$	10.0010			0.336943			0.168472	+	0.985707i	$0.446117\pi$
$882$		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
$885$	3.78658	−	23.2979i	0.127285	−	0.783149i
$886$	25.7583	+	44.6147i	0.865368	+	1.49886i
$887$	36.1244	+	20.8564i	1.21294	+	0.700290i	0.963398	−	0.268075i	$-0.0863875\pi$
$887$	36.1244	+	20.8564i	1.21294	+	0.700290i	0.249539	+	0.968365i	$0.419721\pi$
$888$		−	0.392305i		−	0.0131649i
$889$		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
$893$	1.96902	−	1.13681i	0.0658906	−	0.0380420i
$894$	20.2151	−	35.0136i	0.676094	−	1.17103i
$895$	−14.6969	+	18.0000i	−0.491264	+	0.601674i
$896$		0			0
$897$		−	25.2528i		−	0.843166i
$898$	−13.6245	−	7.86611i	−0.454655	−	0.262495i
$899$	−32.8043	−	56.8187i	−1.09409	−	1.89501i
$900$	−6.48244	+	5.74264i	−0.216081	+	0.191421i
$901$	14.6969	−	25.4558i	0.489626	−	0.848057i
$902$		−	56.7846i		−	1.89072i
$903$		0			0
$904$	−0.196152			−0.00652393
$905$	2.76305	+	7.28585i	0.0918468	+	0.242190i
$906$	12.1087	+	20.9730i	0.402286	+	0.696780i
$907$	45.0518	−	26.0106i	1.49592	−	0.863669i	0.495930	−	0.868362i	$-0.334827\pi$
$907$	45.0518	−	26.0106i	1.49592	−	0.863669i	0.999989	+	0.00469302i	$0.00149384\pi$
$908$	6.00000	+	3.46410i	0.199117	+	0.114960i
$909$	12.6264			0.418791
$910$		0			0
$911$	30.3923			1.00694			0.503471	−	0.864012i	$-0.332056\pi$
$911$	30.3923			1.00694			0.503471	+	0.864012i	$0.332056\pi$
$912$	1.46498	+	0.845807i	0.0485104	+	0.0280075i
$913$	18.0000	−	10.3923i	0.595713	−	0.343935i
$914$	−11.6603	−	20.1962i	−0.385687	−	0.668029i
$915$	19.1130	−	7.24833i	0.631857	−	0.239622i
$916$	40.3286			1.33250
$917$		0			0
$918$		−	7.72741i		−	0.255042i
$919$	−11.4641	+	19.8564i	−0.378166	+	0.655002i	−0.990795	−	0.135368i	$-0.956778\pi$
$919$	−11.4641	+	19.8564i	−0.378166	+	0.655002i	0.612630	+	0.790370i	$0.290112\pi$
$920$	−7.21271	−	1.17228i	−0.237796	−	0.0386488i
$921$	−2.00000	−	3.46410i	−0.0659022	−	0.114146i
$922$	−21.4641	−	12.3923i	−0.706883	−	0.408119i
$923$		−	57.5692i		−	1.89491i
$924$		0			0
$925$	−3.71281	+	0.757875i	−0.122077	+	0.0249188i
$926$	16.1962	−	28.0526i	0.532239	−	0.921864i
$927$	−12.0000	+	6.92820i	−0.394132	+	0.227552i
$928$	−58.6763	+	33.8768i	−1.92614	+	1.11206i
$929$	−20.3538	+	35.2538i	−0.667786	+	1.15664i	0.310736	+	0.950496i	$0.399425\pi$
$929$	−20.3538	+	35.2538i	−0.667786	+	1.15664i	−0.978522	+	0.206143i	$0.933909\pi$
$930$	20.0764	−	24.5885i	0.658331	−	0.806287i
$931$		0			0
$932$			0.656339i			0.0214991i
$933$	−13.3843	−	7.72741i	−0.438181	−	0.252984i
$934$	−17.2480	−	29.8744i	−0.564371	−	0.977519i
$935$	4.97056	−	30.5826i	0.162555	−	1.00016i
$936$	−1.03528	+	1.79315i	−0.0338391	+	0.0586110i
$937$			24.7846i			0.809678i	0.914388	+	0.404839i	$0.132672\pi$
$937$			24.7846i			0.809678i	−0.914388	+	0.404839i	$0.867328\pi$
$938$		0			0
$939$	10.9282			0.356628
$940$	−21.7279	+	8.23999i	−0.708687	+	0.268759i
$941$	19.6975	+	34.1170i	0.642119	+	1.11218i	0.984959	+	0.172788i	$0.0552777\pi$
$941$	19.6975	+	34.1170i	0.642119	+	1.11218i	−0.342840	+	0.939394i	$0.611389\pi$
$942$	31.6675	−	18.2832i	1.03178	−	0.595700i
$943$	−46.3923	−	26.7846i	−1.51074	−	0.872227i
$944$	47.1223			1.53370
$945$		0			0
$946$		0			0
$947$	15.9217	+	9.19239i	0.517385	+	0.298712i	0.735864	−	0.677129i	$-0.236776\pi$
$947$	15.9217	+	9.19239i	0.517385	+	0.298712i	−0.218479	+	0.975842i	$0.570110\pi$
$948$	−17.1962	+	9.92820i	−0.558505	+	0.322453i
$949$	21.8564	+	37.8564i	0.709489	+	1.22887i
$950$	1.15918	−	3.47185i	0.0376086	−	0.112642i
$951$	−29.2180			−0.947459
$952$		0			0
$953$			19.6231i			0.635655i	0.948148	+	0.317828i	$0.102953\pi$
$953$			19.6231i			0.635655i	−0.948148	+	0.317828i	$0.897047\pi$
$954$	7.09808	−	12.2942i	0.229809	−	0.398040i
$955$	−1.18278	−	0.192237i	−0.0382740	−	0.00622065i
$956$	13.3923	+	23.1962i	0.433138	+	0.750217i
$957$	−26.7846	−	15.4641i	−0.865823	−	0.499883i
$958$		−	26.9282i		−	0.870011i
$959$		0			0
$960$	−9.92820	−	8.10634i	−0.320431	−	0.261631i
$961$	−11.5000	+	19.9186i	−0.370968	+	0.642535i
$962$	5.07180	−	2.92820i	0.163521	−	0.0944091i
$963$	13.4722	−	7.77817i	0.434135	−	0.250648i
$964$	4.81105	−	8.33298i	0.154953	−	0.268387i
$965$	28.0812	+	22.9282i	0.903966	+	0.738085i
$966$		0			0
$967$		−	29.5969i		−	0.951774i	−0.879507	−	0.475887i	$-0.842127\pi$
$967$		−	29.5969i		−	0.951774i	0.879507	−	0.475887i	$-0.157873\pi$
$968$	0.448288	+	0.258819i	0.0144085	+	0.00831876i
$969$	0.757875	+	1.31268i	0.0243464	+	0.0421693i
$970$	21.6251	+	3.51472i	0.694341	+	0.112851i
$971$	28.4601	−	49.2944i	0.913329	−	1.58193i	0.104000	−	0.994577i	$-0.466836\pi$
$971$	28.4601	−	49.2944i	0.913329	−	1.58193i	0.809329	−	0.587355i	$-0.199831\pi$
$972$		−	1.73205i		−	0.0555556i
$973$		0			0
$974$	8.00000			0.256337
$975$	18.9706	+	6.33386i	0.607544	+	0.202846i
$976$	20.4046	+	35.3417i	0.653134	+	1.13126i
$977$	−43.7626	+	25.2664i	−1.40009	+	0.808343i	−0.994401	−	0.105668i	$-0.966302\pi$
$977$	−43.7626	+	25.2664i	−1.40009	+	0.808343i	−0.405690	+	0.914011i	$0.632969\pi$
$978$	−28.0526	−	16.1962i	−0.897022	−	0.517896i
$979$	−14.3452			−0.458475
$980$		0			0
$981$	−11.8564			−0.378546
$982$	11.1750	+	6.45189i	0.356609	+	0.205888i
$983$	−14.5359	+	8.39230i	−0.463623	+	0.267673i	−0.713566	−	0.700588i	$-0.752921\pi$
$983$	−14.5359	+	8.39230i	−0.463623	+	0.267673i	0.249943	+	0.968260i	$0.419588\pi$
$984$	2.19615	+	3.80385i	0.0700108	+	0.121262i
$985$	−24.0221	+	9.11001i	−0.765406	+	0.290269i
$986$	−68.9919			−2.19715
$987$		0			0
$988$			2.62536i			0.0835237i
$989$		0			0
$990$	2.40060	−	14.7702i	0.0762960	−	0.469429i
$991$	14.3923	+	24.9282i	0.457187	+	0.791870i	0.998811	−	0.0487502i	$-0.0155238\pi$
$991$	14.3923	+	24.9282i	0.457187	+	0.791870i	−0.541624	+	0.840621i	$0.682190\pi$
$992$	48.2942	+	27.8827i	1.53334	+	0.885276i
$993$			32.7846i			1.04039i
$994$		0			0
$995$	−4.53590	+	5.55532i	−0.143798	+	0.176115i
$996$	5.19615	−	9.00000i	0.164646	−	0.285176i
$997$	12.2487	−	7.07180i	0.387921	−	0.223966i	−0.293338	−	0.956009i	$-0.594766\pi$
$997$	12.2487	−	7.07180i	0.387921	−	0.223966i	0.681259	+	0.732043i	$0.261433\pi$
$998$	27.1846	−	15.6950i	0.860514	−	0.496818i
$999$	0.378937	−	0.656339i	0.0119890	−	0.0207656i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.q.c.79.4		8
5.4	even	2		735.2.q.d.79.1		8
7.2	even	3		735.2.d.f.589.2	yes	8
7.3	odd	6	inner	735.2.q.c.214.1		8
7.4	even	3		735.2.q.d.214.1		8
7.5	odd	6		735.2.d.f.589.1	✓	8
7.6	odd	2		735.2.q.d.79.4		8
21.2	odd	6		2205.2.d.t.1324.8		8
21.5	even	6		2205.2.d.t.1324.7		8
35.2	odd	12		3675.2.a.bu.1.4		4
35.4	even	6	inner	735.2.q.c.214.4		8
35.9	even	6		735.2.d.f.589.7	yes	8
35.12	even	12		3675.2.a.bs.1.4		4
35.19	odd	6		735.2.d.f.589.8	yes	8
35.23	odd	12		3675.2.a.bs.1.1		4
35.24	odd	6		735.2.q.d.214.4		8
35.33	even	12		3675.2.a.bu.1.1		4
35.34	odd	2	inner	735.2.q.c.79.1		8
105.44	odd	6		2205.2.d.t.1324.2		8
105.89	even	6		2205.2.d.t.1324.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
735.2.d.f.589.1	✓	8	7.5	odd	6
735.2.d.f.589.2	yes	8	7.2	even	3
735.2.d.f.589.7	yes	8	35.9	even	6
735.2.d.f.589.8	yes	8	35.19	odd	6
735.2.q.c.79.1		8	35.34	odd	2	inner
735.2.q.c.79.4		8	1.1	even	1	trivial
735.2.q.c.214.1		8	7.3	odd	6	inner
735.2.q.c.214.4		8	35.4	even	6	inner
735.2.q.d.79.1		8	5.4	even	2
735.2.q.d.79.4		8	7.6	odd	2
735.2.q.d.214.1		8	7.4	even	3
735.2.q.d.214.4		8	35.24	odd	6
2205.2.d.t.1324.1		8	105.89	even	6
2205.2.d.t.1324.2		8	105.44	odd	6
2205.2.d.t.1324.7		8	21.5	even	6
2205.2.d.t.1324.8		8	21.2	odd	6
3675.2.a.bs.1.1		4	35.23	odd	12
3675.2.a.bs.1.4		4	35.12	even	12
3675.2.a.bu.1.1		4	35.33	even	12
3675.2.a.bu.1.4		4	35.2	odd	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+(1.67303 + 0.965926i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.866025 + 1.50000i) q^{4} +(-0.792893 - 2.09077i) q^{5} +1.93185 q^{6} -0.517638i q^{8} +(0.500000 - 0.866025i) q^{9} +(0.692993 - 4.26380i) q^{10} +(1.73205 + 3.00000i) q^{11} +(1.50000 + 0.866025i) q^{12} -4.00000i q^{13} +(-1.73205 - 1.41421i) q^{15} +(2.23205 - 3.86603i) q^{16} +(3.46410 - 2.00000i) q^{17} +(1.67303 - 0.965926i) q^{18} +(-0.189469 + 0.328169i) q^{19} +(2.44949 - 3.00000i) q^{20} +6.69213i q^{22} +(5.46739 + 3.15660i) q^{23} +(-0.258819 - 0.448288i) q^{24} +(-3.74264 + 3.31552i) q^{25} +(3.86370 - 6.69213i) q^{26} -1.00000i q^{27} -8.92820 q^{29} +(-1.53175 - 4.03906i) q^{30} +(3.67423 + 6.36396i) q^{31} +(6.57201 - 3.79435i) q^{32} +(3.00000 + 1.73205i) q^{33} +7.72741 q^{34} +1.73205 q^{36} +(0.656339 + 0.378937i) q^{37} +(-0.633975 + 0.366025i) q^{38} +(-2.00000 - 3.46410i) q^{39} +(-1.08226 + 0.410432i) q^{40} -8.48528 q^{41} +(-3.00000 + 5.19615i) q^{44} +(-2.20711 - 0.358719i) q^{45} +(6.09808 + 10.5622i) q^{46} +(-5.19615 - 3.00000i) q^{47} -4.46410i q^{48} +(-9.46410 + 1.93185i) q^{50} +(2.00000 - 3.46410i) q^{51} +(6.00000 - 3.46410i) q^{52} +(6.36396 - 3.67423i) q^{53} +(0.965926 - 1.67303i) q^{54} +(4.89898 - 6.00000i) q^{55} +0.378937i q^{57} +(-14.9372 - 8.62398i) q^{58} +(5.27792 + 9.14162i) q^{59} +(0.621320 - 3.82282i) q^{60} +(-4.57081 + 7.91688i) q^{61} +14.1962i q^{62} +5.73205 q^{64} +(-8.36308 + 3.17157i) q^{65} +(3.34607 + 5.79555i) q^{66} +(-6.03579 + 3.48477i) q^{67} +(6.00000 + 3.46410i) q^{68} +6.31319 q^{69} +14.3923 q^{71} +(-0.448288 - 0.258819i) q^{72} +(-9.46410 + 5.46410i) q^{73} +(0.732051 + 1.26795i) q^{74} +(-1.58346 + 4.74264i) q^{75} -0.656339 q^{76} -7.72741i q^{78} +(-5.73205 + 9.92820i) q^{79} +(-9.85275 - 1.60136i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-14.1962 - 8.19615i) q^{82} -6.00000i q^{83} +(-6.92820 - 5.65685i) q^{85} +(-7.73205 + 4.46410i) q^{87} +(1.55291 - 0.896575i) q^{88} +(-2.07055 + 3.58630i) q^{89} +(-3.34607 - 2.73205i) q^{90} +10.9348i q^{92} +(6.36396 + 3.67423i) q^{93} +(-5.79555 - 10.0382i) q^{94} +(0.836355 + 0.135932i) q^{95} +(3.79435 - 6.57201i) q^{96} +5.07180i 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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Representations

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Database

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