LMFDB - Embedded newform 728.2.h.b.27.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [728,2,Mod(27,728)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("728.27"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(728, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 728 = 2^{3} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	728.h (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,1,0,1,0,10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$5.81310926715$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			27.9
Character	$\chi$	$=$	728.27
Dual form			728.2.h.b.27.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.25982 - 0.642544i) q^{2} +2.44281i q^{3} +(1.17427 + 1.61897i) q^{4} -3.85137 q^{5} +(1.56961 - 3.07749i) q^{6} +(-2.49284 + 0.886436i) q^{7} +(-0.439107 - 2.79413i) q^{8} -2.96733 q^{9} +(4.85202 + 2.47467i) q^{10} -1.81225 q^{11} +(-3.95485 + 2.86853i) q^{12} +1.00000 q^{13} +(3.71009 + 0.485010i) q^{14} -9.40816i q^{15} +(-1.24216 + 3.80224i) q^{16} -3.46118i q^{17} +(3.73828 + 1.90664i) q^{18} +4.50271i q^{19} +(-4.52256 - 6.23527i) q^{20} +(-2.16540 - 6.08953i) q^{21} +(2.28311 + 1.16445i) q^{22} -0.813440i q^{23} +(6.82554 - 1.07266i) q^{24} +9.83303 q^{25} +(-1.25982 - 0.642544i) q^{26} +0.0798187i q^{27} +(-4.36239 - 2.99492i) q^{28} -2.95921i q^{29} +(-6.04516 + 11.8526i) q^{30} -7.74273 q^{31} +(4.00800 - 3.99198i) q^{32} -4.42699i q^{33} +(-2.22396 + 4.36046i) q^{34} +(9.60083 - 3.41399i) q^{35} +(-3.48445 - 4.80402i) q^{36} -0.986953i q^{37} +(2.89319 - 5.67259i) q^{38} +2.44281i q^{39} +(1.69116 + 10.7612i) q^{40} -3.45219i q^{41} +(-1.18479 + 9.06305i) q^{42} +5.13822 q^{43} +(-2.12808 - 2.93399i) q^{44} +11.4283 q^{45} +(-0.522671 + 1.02479i) q^{46} +12.5979 q^{47} +(-9.28816 - 3.03436i) q^{48} +(5.42846 - 4.41948i) q^{49} +(-12.3878 - 6.31816i) q^{50} +8.45502 q^{51} +(1.17427 + 1.61897i) q^{52} +1.21088i q^{53} +(0.0512870 - 0.100557i) q^{54} +6.97966 q^{55} +(3.57144 + 6.57608i) q^{56} -10.9993 q^{57} +(-1.90142 + 3.72806i) q^{58} +12.8822i q^{59} +(15.2316 - 11.0478i) q^{60} +4.69520 q^{61} +(9.75441 + 4.97504i) q^{62} +(7.39705 - 2.63034i) q^{63} +(-7.61437 + 2.45385i) q^{64} -3.85137 q^{65} +(-2.84454 + 5.57720i) q^{66} -2.12856 q^{67} +(5.60357 - 4.06438i) q^{68} +1.98708 q^{69} +(-14.2889 - 1.86795i) q^{70} -3.99821i q^{71} +(1.30297 + 8.29110i) q^{72} -9.25114i q^{73} +(-0.634161 + 1.24338i) q^{74} +24.0202i q^{75} +(-7.28978 + 5.28742i) q^{76} +(4.51765 - 1.60645i) q^{77} +(1.56961 - 3.07749i) q^{78} -11.8410i q^{79} +(4.78401 - 14.6438i) q^{80} -9.09696 q^{81} +(-2.21819 + 4.34913i) q^{82} -17.6272i q^{83} +(7.31602 - 10.6565i) q^{84} +13.3303i q^{85} +(-6.47322 - 3.30154i) q^{86} +7.22879 q^{87} +(0.795774 + 5.06368i) q^{88} -0.651173i q^{89} +(-14.3975 - 7.34316i) q^{90} +(-2.49284 + 0.886436i) q^{91} +(1.31694 - 0.955202i) q^{92} -18.9140i q^{93} +(-15.8711 - 8.09472i) q^{94} -17.3416i q^{95} +(9.75166 + 9.79079i) q^{96} -10.3289i q^{97} +(-9.67857 + 2.07971i) q^{98} +5.37755 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + q^{2} + q^{4} + 10 q^{6} - 5 q^{8} - 48 q^{9} - 4 q^{11} - 10 q^{12} + 48 q^{13} - 6 q^{14} + 5 q^{16} - 15 q^{18} + 22 q^{20} - 6 q^{22} + 48 q^{25} + q^{26} - 26 q^{28} - 26 q^{30} - 19 q^{32}+ \cdots + 20 q^{99}+O(q^{100}) $ 48 * q + q^2 + q^4 + 10 * q^6 - 5 * q^8 - 48 * q^9 - 4 * q^11 - 10 * q^12 + 48 * q^13 - 6 * q^14 + 5 * q^16 - 15 * q^18 + 22 * q^20 - 6 * q^22 + 48 * q^25 + q^26 - 26 * q^28 - 26 * q^30 - 19 * q^32 - 36 * q^34 + 12 * q^35 - 5 * q^36 + 10 * q^38 + 48 * q^40 + 39 * q^42 - 4 * q^43 - 30 * q^44 - 24 * q^45 + 2 * q^46 - 48 * q^48 + 11 * q^50 - 40 * q^51 + q^52 - 62 * q^54 - 14 * q^56 + 2 * q^58 + 18 * q^60 + 36 * q^62 - 20 * q^63 - 11 * q^64 - 32 * q^66 - 4 * q^67 - 62 * q^68 - 37 * q^70 + 13 * q^72 - 44 * q^74 + 48 * q^76 + 20 * q^77 + 10 * q^78 - 32 * q^80 + 64 * q^81 + 50 * q^82 - 45 * q^84 + 2 * q^86 + 40 * q^87 - 66 * q^88 - 74 * q^90 - 24 * q^92 + 26 * q^94 + 84 * q^96 - 20 * q^98 + 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/728\mathbb{Z}\right)^\times$.

$n$	$183$	$365$	$521$	$561$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.25982	−	0.642544i	−0.890825	−	0.454347i
$2$	−1.25982	−	0.642544i	−0.890825	−	0.454347i
$3$			2.44281i			1.41036i	0.709030	+	0.705179i	$0.249133\pi$
$3$			2.44281i			1.41036i	−0.709030	+	0.705179i	$0.750867\pi$
$4$	1.17427	+	1.61897i	0.587137	+	0.809487i
$5$	−3.85137			−1.72238			−0.861192	−	0.508280i	$-0.830282\pi$
$5$	−3.85137			−1.72238			−0.861192	+	0.508280i	$0.830282\pi$
$6$	1.56961	−	3.07749i	0.640792	−	1.25638i
$7$	−2.49284	+	0.886436i	−0.942203	+	0.335041i
$7$	−2.49284	+	0.886436i	−0.942203	+	0.335041i
$8$	−0.439107	−	2.79413i	−0.155248	−	0.987876i
$9$	−2.96733			−0.989108
$10$	4.85202	+	2.47467i	1.53434	+	0.782560i
$11$	−1.81225			−0.546415			−0.273208	−	0.961955i	$-0.588085\pi$
$11$	−1.81225			−0.546415			−0.273208	+	0.961955i	$0.588085\pi$
$12$	−3.95485	+	2.86853i	−1.14167	+	0.828073i
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$	3.71009	+	0.485010i	0.991563	+	0.129624i
$15$		−	9.40816i		−	2.42918i
$16$	−1.24216	+	3.80224i	−0.310540	+	0.950560i
$17$		−	3.46118i		−	0.839461i	−0.907649	−	0.419730i	$-0.862125\pi$
$17$		−	3.46118i		−	0.839461i	0.907649	−	0.419730i	$-0.137875\pi$
$18$	3.73828	+	1.90664i	0.881122	+	0.449399i
$19$			4.50271i			1.03299i	0.856289	+	0.516496i	$0.172764\pi$
$19$			4.50271i			1.03299i	−0.856289	+	0.516496i	$0.827236\pi$
$20$	−4.52256	−	6.23527i	−1.01128	−	1.39425i
$21$	−2.16540	−	6.08953i	−0.472528	−	1.32884i
$22$	2.28311	+	1.16445i	0.486760	+	0.248262i
$23$		−	0.813440i		−	0.169614i	−0.996397	−	0.0848070i	$-0.972973\pi$
$23$		−	0.813440i		−	0.169614i	0.996397	−	0.0848070i	$-0.0270274\pi$
$24$	6.82554	−	1.07266i	1.39326	−	0.218955i
$25$	9.83303			1.96661
$26$	−1.25982	−	0.642544i	−0.247070	−	0.126013i
$27$			0.0798187i			0.0153611i
$28$	−4.36239	−	2.99492i	−0.824414	−	0.565987i
$29$		−	2.95921i		−	0.549511i	−0.961514	−	0.274756i	$-0.911403\pi$
$29$		−	2.95921i		−	0.549511i	0.961514	−	0.274756i	$-0.0885970\pi$
$30$	−6.04516	+	11.8526i	−1.10369	+	2.16397i
$31$	−7.74273			−1.39063			−0.695317	−	0.718703i	$-0.744736\pi$
$31$	−7.74273			−1.39063			−0.695317	+	0.718703i	$0.744736\pi$
$32$	4.00800	−	3.99198i	0.708521	−	0.705690i
$33$		−	4.42699i		−	0.770641i
$34$	−2.22396	+	4.36046i	−0.381407	+	0.747812i
$35$	9.60083	−	3.41399i	1.62284	−	0.577070i
$36$	−3.48445	−	4.80402i	−0.580742	−	0.800671i
$37$		−	0.986953i		−	0.162254i	−0.996704	−	0.0811271i	$-0.974148\pi$
$37$		−	0.986953i		−	0.162254i	0.996704	−	0.0811271i	$-0.0258520\pi$
$38$	2.89319	−	5.67259i	0.469337	−	0.920215i
$39$			2.44281i			0.391163i
$40$	1.69116	+	10.7612i	0.267396	+	1.70150i
$41$		−	3.45219i		−	0.539142i	−0.962981	−	0.269571i	$-0.913118\pi$
$41$		−	3.45219i		−	0.539142i	0.962981	−	0.269571i	$-0.0868819\pi$
$42$	−1.18479	+	9.06305i	−0.182817	+	1.39846i
$43$	5.13822			0.783572			0.391786	−	0.920056i	$-0.371857\pi$
$43$	5.13822			0.783572			0.391786	+	0.920056i	$0.371857\pi$
$44$	−2.12808	−	2.93399i	−0.320821	−	0.442316i
$45$	11.4283			1.70362
$46$	−0.522671	+	1.02479i	−0.0770637	+	0.151096i
$47$	12.5979			1.83759			0.918797	−	0.394729i	$-0.129162\pi$
$47$	12.5979			1.83759			0.918797	+	0.394729i	$0.129162\pi$
$48$	−9.28816	−	3.03436i	−1.34063	−	0.437972i
$49$	5.42846	−	4.41948i	0.775494	−	0.631354i
$50$	−12.3878	−	6.31816i	−1.75190	−	0.893522i
$51$	8.45502			1.18394
$52$	1.17427	+	1.61897i	0.162843	+	0.224511i
$53$			1.21088i			0.166328i	0.996536	+	0.0831639i	$0.0265025\pi$
$53$			1.21088i			0.166328i	−0.996536	+	0.0831639i	$0.973498\pi$
$54$	0.0512870	−	0.100557i	0.00697928	−	0.0136841i
$55$	6.97966			0.941137
$56$	3.57144	+	6.57608i	0.477254	+	0.878765i
$57$	−10.9993			−1.45689
$58$	−1.90142	+	3.72806i	−0.249669	+	0.489518i
$59$			12.8822i			1.67712i	0.544807	+	0.838561i	$0.316603\pi$
$59$			12.8822i			1.67712i	−0.544807	+	0.838561i	$0.683397\pi$
$60$	15.2316	−	11.0478i	1.96639	−	1.42626i
$61$	4.69520			0.601159			0.300579	−	0.953757i	$-0.402820\pi$
$61$	4.69520			0.601159			0.300579	+	0.953757i	$0.402820\pi$
$62$	9.75441	+	4.97504i	1.23881	+	0.631831i
$63$	7.39705	−	2.63034i	0.931941	−	0.331392i
$64$	−7.61437	+	2.45385i	−0.951796	+	0.306731i
$65$	−3.85137			−0.477703
$66$	−2.84454	+	5.57720i	−0.350138	+	0.686506i
$67$	−2.12856			−0.260045			−0.130023	−	0.991511i	$-0.541505\pi$
$67$	−2.12856			−0.260045			−0.130023	+	0.991511i	$0.541505\pi$
$68$	5.60357	−	4.06438i	0.679533	−	0.492879i
$69$	1.98708			0.239216
$70$	−14.2889	−	1.86795i	−1.70785	−	0.223263i
$71$		−	3.99821i		−	0.474500i	−0.971449	−	0.237250i	$-0.923754\pi$
$71$		−	3.99821i		−	0.474500i	0.971449	−	0.237250i	$-0.0762460\pi$
$72$	1.30297	+	8.29110i	0.153557	+	0.977116i
$73$		−	9.25114i		−	1.08276i	−0.840777	−	0.541382i	$-0.817901\pi$
$73$		−	9.25114i		−	1.08276i	0.840777	−	0.541382i	$-0.182099\pi$
$74$	−0.634161	+	1.24338i	−0.0737197	+	0.144540i
$75$			24.0202i			2.77362i
$76$	−7.28978	+	5.28742i	−0.836195	+	0.606508i
$77$	4.51765	−	1.60645i	0.514834	−	0.183072i
$78$	1.56961	−	3.07749i	0.177724	−	0.348457i
$79$		−	11.8410i		−	1.33222i	−0.745854	−	0.666110i	$-0.767958\pi$
$79$		−	11.8410i		−	1.33222i	0.745854	−	0.666110i	$-0.232042\pi$
$80$	4.78401	−	14.6438i	0.534869	−	1.63723i
$81$	−9.09696			−1.01077
$82$	−2.21819	+	4.34913i	−0.244958	+	0.480281i
$83$		−	17.6272i		−	1.93484i	−0.253182	−	0.967419i	$-0.581477\pi$
$83$		−	17.6272i		−	1.93484i	0.253182	−	0.967419i	$-0.418523\pi$
$84$	7.31602	−	10.6565i	0.798243	−	1.16272i
$85$			13.3303i			1.44587i
$86$	−6.47322	−	3.30154i	−0.698025	−	0.356014i
$87$	7.22879			0.775007
$88$	0.795774	+	5.06368i	0.0848298	+	0.539790i
$89$		−	0.651173i		−	0.0690242i	−0.999404	−	0.0345121i	$-0.989012\pi$
$89$		−	0.651173i		−	0.0690242i	0.999404	−	0.0345121i	$-0.0109877\pi$
$90$	−14.3975	−	7.34316i	−1.51763	−	0.774037i
$91$	−2.49284	+	0.886436i	−0.261320	+	0.0929238i
$92$	1.31694	−	0.955202i	0.137300	−	0.0995867i
$93$		−	18.9140i		−	1.96129i
$94$	−15.8711	−	8.09472i	−1.63697	−	0.834906i
$95$		−	17.3416i		−	1.77921i
$96$	9.75166	+	9.79079i	0.995275	+	0.999268i
$97$		−	10.3289i		−	1.04874i	−0.851490	−	0.524371i	$-0.824301\pi$
$97$		−	10.3289i		−	1.04874i	0.851490	−	0.524371i	$-0.175699\pi$
$98$	−9.67857	+	2.07971i	−0.977684	+	0.210082i
$99$	5.37755			0.540464
$100$	11.5467	+	15.9194i	1.15467	+	1.59194i
$101$	−18.0120			−1.79226			−0.896132	−	0.443788i	$-0.853634\pi$
$101$	−18.0120			−1.79226			−0.896132	+	0.443788i	$0.853634\pi$
$102$	−10.6518	−	5.43272i	−1.05468	−	0.537920i
$103$	−3.56069			−0.350845			−0.175422	−	0.984493i	$-0.556129\pi$
$103$	−3.56069			−0.350845			−0.175422	+	0.984493i	$0.556129\pi$
$104$	−0.439107	−	2.79413i	−0.0430580	−	0.273987i
$105$	8.33974	+	23.4530i	0.813875	+	2.28878i
$106$	0.778046	−	1.52549i	0.0755705	−	0.148169i
$107$	−14.4988			−1.40165			−0.700824	−	0.713334i	$-0.747184\pi$
$107$	−14.4988			−1.40165			−0.700824	+	0.713334i	$0.747184\pi$
$108$	−0.129224	+	0.0937290i	−0.0124346	+	0.00901908i
$109$			17.5262i			1.67870i	0.543589	+	0.839351i	$0.317065\pi$
$109$			17.5262i			1.67870i	−0.543589	+	0.839351i	$0.682935\pi$
$110$	−8.79308	−	4.48474i	−0.838388	−	0.427603i
$111$	2.41094			0.228836
$112$	−0.273945	−	10.5795i	−0.0258854	−	0.999665i
$113$	−9.73680			−0.915962			−0.457981	−	0.888962i	$-0.651427\pi$
$113$	−9.73680			−0.915962			−0.457981	+	0.888962i	$0.651427\pi$
$114$	13.8571	+	7.06752i	1.29783	+	0.661934i
$115$			3.13286i			0.292141i
$116$	4.79089	−	3.47492i	0.444823	−	0.322639i
$117$	−2.96733			−0.274329
$118$	8.27740	−	16.2292i	0.761996	−	1.49402i
$119$	3.06812	+	8.62817i	0.281254	+	0.790943i
$120$	−26.2877	+	4.13119i	−2.39972	+	0.377125i
$121$	−7.71574			−0.701431
$122$	−5.91509	−	3.01687i	−0.535527	−	0.273135i
$123$	8.43305			0.760383
$124$	−9.09209	−	12.5353i	−0.816493	−	1.12570i
$125$	−18.6138			−1.66487
$126$	−11.0090	−	1.43918i	−0.980763	−	0.128213i
$127$			0.775751i			0.0688368i	0.999408	+	0.0344184i	$0.0109579\pi$
$127$			0.775751i			0.0688368i	−0.999408	+	0.0344184i	$0.989042\pi$
$128$	11.1694	+	1.80117i	0.987246	+	0.159202i
$129$			12.5517i			1.10512i
$130$	4.85202	+	2.47467i	0.425550	+	0.217043i
$131$		−	5.40650i		−	0.472368i	−0.971708	−	0.236184i	$-0.924103\pi$
$131$		−	5.40650i		−	0.472368i	0.971708	−	0.236184i	$-0.0758969\pi$
$132$	7.16719	−	5.19850i	0.623824	−	0.452472i
$133$	−3.99137	−	11.2245i	−0.346095	−	0.973289i
$134$	2.68160	+	1.36770i	0.231655	+	0.118151i
$135$		−	0.307411i		−	0.0264577i
$136$	−9.67101	+	1.51983i	−0.829283	+	0.130324i
$137$	5.29585			0.452455			0.226227	−	0.974075i	$-0.427361\pi$
$137$	5.29585			0.452455			0.226227	+	0.974075i	$0.427361\pi$
$138$	−2.50336	−	1.27679i	−0.213100	−	0.108687i
$139$		−	15.7618i		−	1.33690i	−0.743758	−	0.668449i	$-0.766959\pi$
$139$		−	15.7618i		−	1.33690i	0.743758	−	0.668449i	$-0.233041\pi$
$140$	16.8012	+	11.5345i	1.41996	+	0.974846i
$141$			30.7743i			2.59167i
$142$	−2.56902	+	5.03700i	−0.215588	+	0.422696i
$143$	−1.81225			−0.151548
$144$	3.68589	−	11.2825i	0.307158	−	0.940207i
$145$			11.3970i			0.946470i
$146$	−5.94427	+	11.6547i	−0.491951	+	0.964553i
$147$	10.7960	+	13.2607i	0.890435	+	1.09372i
$148$	1.59785	−	1.15895i	0.131343	−	0.0952654i
$149$		−	20.2534i		−	1.65923i	−0.558339	−	0.829613i	$-0.688561\pi$
$149$		−	20.2534i		−	1.65923i	0.558339	−	0.829613i	$-0.311439\pi$
$150$	15.4341	−	30.2611i	1.26019	−	2.47081i
$151$			10.6491i			0.866609i	0.901248	+	0.433304i	$0.142652\pi$
$151$			10.6491i			0.866609i	−0.901248	+	0.433304i	$0.857348\pi$
$152$	12.5812	−	1.97717i	1.02047	−	0.160370i
$153$			10.2705i			0.830318i
$154$	−6.72362	−	0.878961i	−0.541805	−	0.0708287i
$155$	29.8201			2.39521
$156$	−3.95485	+	2.86853i	−0.316641	+	0.229666i
$157$	12.8972			1.02931			0.514653	−	0.857398i	$-0.327921\pi$
$157$	12.8972			1.02931			0.514653	+	0.857398i	$0.327921\pi$
$158$	−7.60838	+	14.9175i	−0.605290	+	1.18677i
$159$	−2.95796			−0.234582
$160$	−15.4363	+	15.3746i	−1.22035	+	1.21547i
$161$	0.721063	+	2.02777i	0.0568277	+	0.159811i
$162$	11.4605	+	5.84520i	0.900422	+	0.459242i
$163$	17.2917			1.35439			0.677195	−	0.735804i	$-0.263195\pi$
$163$	17.2917			1.35439			0.677195	+	0.735804i	$0.263195\pi$
$164$	5.58901	−	4.05382i	0.436429	−	0.316550i
$165$			17.0500i			1.32734i
$166$	−11.3263	+	22.2070i	−0.879088	+	1.72360i
$167$	9.67383			0.748583			0.374292	−	0.927311i	$-0.377886\pi$
$167$	9.67383			0.748583			0.374292	+	0.927311i	$0.377886\pi$
$168$	−16.0641	+	8.72436i	−1.23937	+	0.673099i
$169$	1.00000			0.0769231
$170$	8.56530	−	16.7937i	0.656929	−	1.28802i
$171$		−	13.3610i		−	1.02174i
$172$	6.03369	+	8.31866i	0.460064	+	0.634292i
$173$	7.65616			0.582087			0.291043	−	0.956710i	$-0.405998\pi$
$173$	7.65616			0.582087			0.291043	+	0.956710i	$0.405998\pi$
$174$	−9.10695	−	4.64481i	−0.690396	−	0.352123i
$175$	−24.5121	+	8.71636i	−1.85294	+	0.658895i
$176$	2.25111	−	6.89063i	0.169684	−	0.519400i
$177$	−31.4688			−2.36534
$178$	−0.418407	+	0.820358i	−0.0313610	+	0.0614885i
$179$	−22.6980			−1.69652			−0.848262	−	0.529576i	$-0.822351\pi$
$179$	−22.6980			−1.69652			−0.848262	+	0.529576i	$0.822351\pi$
$180$	13.4199	+	18.5021i	1.00026	+	1.37906i
$181$	−16.7233			−1.24303			−0.621517	−	0.783400i	$-0.713483\pi$
$181$	−16.7233			−1.24303			−0.621517	+	0.783400i	$0.713483\pi$
$182$	3.71009	+	0.485010i	0.275010	+	0.0359513i
$183$			11.4695i			0.847849i
$184$	−2.27286	+	0.357188i	−0.167558	+	0.0263322i
$185$			3.80112i			0.279464i
$186$	−12.1531	+	23.8282i	−0.891108	+	1.74717i
$187$			6.27255i			0.458694i
$188$	14.7934	+	20.3957i	1.07892	+	1.48751i
$189$	−0.0707542	−	0.198975i	−0.00514661	−	0.0144733i
$190$	−11.1427	+	21.8472i	−0.808379	+	1.58496i
$191$			8.61903i			0.623651i	0.950139	+	0.311826i	$0.100940\pi$
$191$			8.61903i			0.623651i	−0.950139	+	0.311826i	$0.899060\pi$
$192$	−5.99429	−	18.6005i	−0.432601	−	1.34237i
$193$	−18.9038			−1.36072			−0.680361	−	0.732877i	$-0.738177\pi$
$193$	−18.9038			−1.36072			−0.680361	+	0.732877i	$0.738177\pi$
$194$	−6.63678	+	13.0125i	−0.476493	+	0.934245i
$195$		−	9.40816i		−	0.673733i
$196$	13.5295	+	3.59886i	0.966395	+	0.257061i
$197$		−	4.49011i		−	0.319907i	−0.987125	−	0.159954i	$-0.948865\pi$
$197$		−	4.49011i		−	0.319907i	0.987125	−	0.159954i	$-0.0511345\pi$
$198$	−6.77472	−	3.45531i	−0.481458	−	0.245558i
$199$	9.15280			0.648825			0.324413	−	0.945916i	$-0.394833\pi$
$199$	9.15280			0.648825			0.324413	+	0.945916i	$0.394833\pi$
$200$	−4.31776	−	27.4748i	−0.305311	−	1.94276i
$201$		−	5.19968i		−	0.366757i
$202$	22.6919	+	11.5735i	1.59659	+	0.814310i
$203$	2.62315	+	7.37682i	0.184109	+	0.517751i
$204$	9.92851	+	13.6885i	0.695135	+	0.958384i
$205$			13.2957i			0.928609i
$206$	4.48581	+	2.28790i	0.312541	+	0.159405i
$207$			2.41374i			0.167767i
$208$	−1.24216	+	3.80224i	−0.0861283	+	0.263638i
$209$		−	8.16005i		−	0.564443i
$210$	4.56305	−	34.9051i	0.314880	−	2.40868i
$211$	8.77366			0.604004			0.302002	−	0.953307i	$-0.402345\pi$
$211$	8.77366			0.604004			0.302002	+	0.953307i	$0.402345\pi$
$212$	−1.96039	+	1.42191i	−0.134640	+	0.0976572i
$213$	9.76686			0.669214
$214$	18.2658	+	9.31609i	1.24862	+	0.636835i
$215$	−19.7892			−1.34961
$216$	0.223024	−	0.0350490i	0.0151749	−	0.00238478i
$217$	19.3013	−	6.86343i	1.31026	−	0.465920i
$218$	11.2613	−	22.0798i	0.762714	−	1.49543i
$219$	22.5988			1.52708
$220$	8.19603	+	11.2999i	0.552576	+	0.761838i
$221$		−	3.46118i		−	0.232824i
$222$	−3.03734	−	1.54914i	−0.203853	−	0.103971i
$223$	1.21343			0.0812571			0.0406286	−	0.999174i	$-0.487064\pi$
$223$	1.21343			0.0812571			0.0406286	+	0.999174i	$0.487064\pi$
$224$	−6.45265	+	13.5042i	−0.431136	+	0.902287i
$225$	−29.1778			−1.94519
$226$	12.2666	+	6.25633i	0.815961	+	0.416165i
$227$		−	27.1333i		−	1.80090i	−0.434958	−	0.900451i	$-0.643237\pi$
$227$		−	27.1333i		−	1.80090i	0.434958	−	0.900451i	$-0.356763\pi$
$228$	−12.9162	−	17.8075i	−0.855394	−	1.17933i
$229$	0.338616			0.0223764			0.0111882	−	0.999937i	$-0.496439\pi$
$229$	0.338616			0.0223764			0.0111882	+	0.999937i	$0.496439\pi$
$230$	2.01300	−	3.94683i	0.132733	−	0.260246i
$231$	3.92425	+	11.0358i	0.258197	+	0.726100i
$232$	−8.26843	+	1.29941i	−0.542849	+	0.0853105i
$233$	−2.38874			−0.156492			−0.0782459	−	0.996934i	$-0.524932\pi$
$233$	−2.38874			−0.156492			−0.0782459	+	0.996934i	$0.524932\pi$
$234$	3.73828	+	1.90664i	0.244379	+	0.124641i
$235$	−48.5192			−3.16504
$236$	−20.8560	+	15.1273i	−1.35761	+	0.984701i
$237$	28.9254			1.87891
$238$	1.67871	−	12.8413i	0.108815	−	0.832378i
$239$			22.6748i			1.46671i	0.679846	+	0.733355i	$0.262047\pi$
$239$			22.6748i			1.46671i	−0.679846	+	0.733355i	$0.737953\pi$
$240$	35.7721	+	11.6864i	2.30908	+	0.754356i
$241$		−	24.4172i		−	1.57285i	−0.617685	−	0.786426i	$-0.711929\pi$
$241$		−	24.4172i		−	1.57285i	0.617685	−	0.786426i	$-0.288071\pi$
$242$	9.72041	+	4.95770i	0.624852	+	0.318693i
$243$		−	21.9827i		−	1.41019i
$244$	5.51345	+	7.60141i	0.352963	+	0.486631i
$245$	−20.9070	+	17.0210i	−1.33570	+	1.08743i
$246$	−10.6241	−	5.41861i	−0.677368	−	0.345478i
$247$			4.50271i			0.286501i
$248$	3.39989	+	21.6342i	0.215893	+	1.37377i
$249$	43.0599			2.72881
$250$	23.4500	+	11.9602i	1.48311	+	0.756428i
$251$			10.9009i			0.688057i	0.938959	+	0.344029i	$0.111792\pi$
$251$			10.9009i			0.688057i	−0.938959	+	0.344029i	$0.888208\pi$
$252$	12.9446	+	8.88690i	0.815435	+	0.559822i
$253$			1.47416i			0.0926797i
$254$	0.498454	−	0.977304i	0.0312758	−	0.0613215i
$255$	−32.5634			−2.03920
$256$	−12.9141	−	9.44598i	−0.807130	−	0.590374i
$257$			27.1459i			1.69331i	0.532140	+	0.846657i	$0.321388\pi$
$257$			27.1459i			1.69331i	−0.532140	+	0.846657i	$0.678612\pi$
$258$	8.06503	−	15.8129i	0.502107	−	0.984465i
$259$	0.874871	+	2.46031i	0.0543619	+	0.152876i
$260$	−4.52256	−	6.23527i	−0.280477	−	0.386695i
$261$			8.78094i			0.543526i
$262$	−3.47392	+	6.81120i	−0.214619	+	0.420797i
$263$		−	27.3617i		−	1.68720i	−0.536975	−	0.843598i	$-0.680433\pi$
$263$		−	27.3617i		−	1.68720i	0.536975	−	0.843598i	$-0.319567\pi$
$264$	−12.3696	+	1.94393i	−0.761297	+	0.119640i
$265$		−	4.66356i		−	0.286480i
$266$	−2.18386	+	16.7055i	−0.133901	+	1.02428i
$267$	1.59069			0.0973488
$268$	−2.49952	−	3.44609i	−0.152682	−	0.210503i
$269$	−29.3298			−1.78827			−0.894134	−	0.447799i	$-0.852208\pi$
$269$	−29.3298			−1.78827			−0.894134	+	0.447799i	$0.852208\pi$
$270$	−0.197525	+	0.387281i	−0.0120210	+	0.0235692i
$271$	−4.63752			−0.281709			−0.140855	−	0.990030i	$-0.544985\pi$
$271$	−4.63752			−0.281709			−0.140855	+	0.990030i	$0.544985\pi$
$272$	13.1603	+	4.29934i	0.797958	+	0.260686i
$273$	−2.16540	−	6.08953i	−0.131056	−	0.368555i
$274$	−6.67180	−	3.40282i	−0.403058	−	0.205572i
$275$	−17.8200			−1.07458
$276$	2.33338	+	3.21703i	0.140453	+	0.193643i
$277$			2.25309i			0.135375i	0.997707	+	0.0676876i	$0.0215621\pi$
$277$			2.25309i			0.135375i	−0.997707	+	0.0676876i	$0.978438\pi$
$278$	−10.1276	+	19.8570i	−0.607416	+	1.19094i
$279$	22.9752			1.37549
$280$	−13.7549	−	25.3269i	−0.822015	−	1.51357i
$281$	−7.46920			−0.445575			−0.222788	−	0.974867i	$-0.571516\pi$
$281$	−7.46920			−0.445575			−0.222788	+	0.974867i	$0.571516\pi$
$282$	19.7739	−	38.7700i	1.17752	−	2.30872i
$283$		−	0.265875i		−	0.0158047i	−0.999969	−	0.00790233i	$-0.997485\pi$
$283$		−	0.265875i		−	0.0158047i	0.999969	−	0.00790233i	$-0.00251541\pi$
$284$	6.47299	−	4.69499i	0.384102	−	0.278596i
$285$	42.3622			2.50932
$286$	2.28311	+	1.16445i	0.135003	+	0.0688555i
$287$	3.06015	+	8.60575i	0.180635	+	0.507981i
$288$	−11.8930	+	11.8455i	−0.700804	+	0.698004i
$289$	5.02020			0.295306
$290$	7.32308	−	14.3581i	0.430026	−	0.843138i
$291$	25.2316			1.47910
$292$	14.9774	−	10.8634i	0.876484	−	0.635731i
$293$	−4.28179			−0.250145			−0.125072	−	0.992148i	$-0.539916\pi$
$293$	−4.28179			−0.250145			−0.125072	+	0.992148i	$0.539916\pi$
$294$	−5.08033	−	23.6429i	−0.296291	−	1.37888i
$295$		−	49.6142i		−	2.88865i
$296$	−2.75768	+	0.433378i	−0.160287	+	0.0251896i
$297$		−	0.144652i		−	0.00839354i
$298$	−13.0137	+	25.5156i	−0.753865	+	1.47808i
$299$		−	0.813440i		−	0.0470425i
$300$	−38.8882	+	28.2064i	−2.24521	+	1.62849i
$301$	−12.8088	+	4.55471i	−0.738284	+	0.262529i
$302$	6.84249	−	13.4159i	0.393741	−	0.771996i
$303$		−	44.0000i		−	2.52773i
$304$	−17.1204	−	5.59309i	−0.981922	−	0.320785i
$305$	−18.0829			−1.03543
$306$	6.59922	−	12.9389i	0.377252	−	0.739667i
$307$		−	2.40502i		−	0.137262i	−0.997642	−	0.0686309i	$-0.978137\pi$
$307$		−	2.40502i		−	0.137262i	0.997642	−	0.0686309i	$-0.0218631\pi$
$308$	7.90576	+	5.42755i	0.450472	+	0.309264i
$309$		−	8.69808i		−	0.494817i
$310$	−37.5678	−	19.1607i	−2.13371	−	1.08826i
$311$	18.9445			1.07424			0.537121	−	0.843505i	$-0.319512\pi$
$311$	18.9445			1.07424			0.537121	+	0.843505i	$0.319512\pi$
$312$	6.82554	−	1.07266i	0.386420	−	0.0607272i
$313$		−	2.60232i		−	0.147092i	−0.997292	−	0.0735460i	$-0.976568\pi$
$313$		−	2.60232i		−	0.147092i	0.997292	−	0.0735460i	$-0.0234316\pi$
$314$	−16.2481	−	8.28700i	−0.916931	−	0.467662i
$315$	−28.4888	+	10.1304i	−1.60516	+	0.570785i
$316$	19.1703	−	13.9046i	1.07841	−	0.782195i
$317$			2.67627i			0.150314i	0.997172	+	0.0751571i	$0.0239458\pi$
$317$			2.67627i			0.150314i	−0.997172	+	0.0751571i	$0.976054\pi$
$318$	3.72649	+	1.90062i	0.208971	+	0.106581i
$319$			5.36284i			0.300261i
$320$	29.3257	−	9.45068i	1.63936	−	0.528309i
$321$		−	35.4177i		−	1.97682i
$322$	0.394527	−	3.01794i	0.0219861	−	0.168183i
$323$	15.5847			0.867157
$324$	−10.6823	−	14.7277i	−0.593462	−	0.818208i
$325$	9.83303			0.545439
$326$	−21.7844	−	11.1107i	−1.20652	−	0.615363i
$327$	−42.8131			−2.36757
$328$	−9.64589	+	1.51588i	−0.532605	+	0.0837006i
$329$	−31.4045	+	11.1672i	−1.73139	+	0.615670i
$330$	10.9554	−	21.4798i	0.603073	−	1.18243i
$331$	15.6728			0.861453			0.430726	−	0.902483i	$-0.358257\pi$
$331$	15.6728			0.861453			0.430726	+	0.902483i	$0.358257\pi$
$332$	28.5380	−	20.6992i	1.56623	−	1.13602i
$333$			2.92861i			0.160487i
$334$	−12.1872	−	6.21586i	−0.666856	−	0.340117i
$335$	8.19788			0.447898
$336$	25.8436	−	0.669196i	1.40988	−	0.0365076i
$337$	27.0995			1.47620			0.738102	−	0.674690i	$-0.235723\pi$
$337$	27.0995			1.47620			0.738102	+	0.674690i	$0.235723\pi$
$338$	−1.25982	−	0.642544i	−0.0685250	−	0.0349498i
$339$		−	23.7852i		−	1.29183i
$340$	−21.5814	+	15.6534i	−1.17042	+	0.848926i
$341$	14.0318			0.759864
$342$	−8.58504	+	16.8324i	−0.464226	+	0.910193i
$343$	−9.61467	+	15.8290i	−0.519144	+	0.854687i
$344$	−2.25623	−	14.3569i	−0.121648	−	0.774072i
$345$	−7.65298			−0.412023
$346$	−9.64535	−	4.91942i	−0.518537	−	0.264469i
$347$	−2.59125			−0.139106			−0.0695528	−	0.997578i	$-0.522157\pi$
$347$	−2.59125			−0.139106			−0.0695528	+	0.997578i	$0.522157\pi$
$348$	8.48858	+	11.7032i	0.455036	+	0.627359i
$349$	12.4308			0.665408			0.332704	−	0.943031i	$-0.392039\pi$
$349$	12.4308			0.665408			0.332704	+	0.943031i	$0.392039\pi$
$350$	36.4814	+	4.76912i	1.95001	+	0.254920i
$351$			0.0798187i			0.00426041i
$352$	−7.26351	+	7.23449i	−0.387147	+	0.385599i
$353$		−	12.9113i		−	0.687198i	−0.939116	−	0.343599i	$-0.888354\pi$
$353$		−	12.9113i		−	0.687198i	0.939116	−	0.343599i	$-0.111646\pi$
$354$	39.6450	+	20.2201i	2.10711	+	1.07469i
$355$			15.3986i			0.817271i
$356$	1.05423	−	0.764656i	0.0558742	−	0.0405267i
$357$	−21.0770	+	7.49484i	−1.11551	+	0.396669i
$358$	28.5953	+	14.5844i	1.51131	+	0.770811i
$359$			15.4518i			0.815517i	0.913090	+	0.407759i	$0.133690\pi$
$359$			15.4518i			0.815517i	−0.913090	+	0.407759i	$0.866310\pi$
$360$	−5.01823	−	31.9321i	−0.264484	−	1.68297i
$361$	−1.27441			−0.0670740
$362$	21.0683	+	10.7455i	1.10733	+	0.564769i
$363$		−	18.8481i		−	0.989268i
$364$	−4.36239	−	2.99492i	−0.228651	−	0.156976i
$365$			35.6295i			1.86494i
$366$	7.36965	−	14.4494i	0.385218	−	0.755285i
$367$	−31.0339			−1.61995			−0.809977	−	0.586461i	$-0.800521\pi$
$367$	−31.0339			−1.61995			−0.809977	+	0.586461i	$0.800521\pi$
$368$	3.09290	+	1.01042i	0.161228	+	0.0526719i
$369$			10.2438i			0.533270i
$370$	2.44239	−	4.78871i	0.126974	−	0.248953i
$371$	−1.07337	−	3.01854i	−0.0557267	−	0.156715i
$372$	30.6213	−	22.2102i	1.58764	−	1.15155i
$373$		−	23.1844i		−	1.20044i	−0.799835	−	0.600220i	$-0.795080\pi$
$373$		−	23.1844i		−	1.20044i	0.799835	−	0.600220i	$-0.204920\pi$
$374$	4.03039	−	7.90225i	0.208406	−	0.408616i
$375$		−	45.4700i		−	2.34806i
$376$	−5.53184	−	35.2003i	−0.285283	−	1.81531i
$377$		−	2.95921i		−	0.152407i
$378$	−0.0387128	+	0.296134i	−0.00199117	+	0.0152315i
$379$	−9.21018			−0.473095			−0.236547	−	0.971620i	$-0.576016\pi$
$379$	−9.21018			−0.473095			−0.236547	+	0.971620i	$0.576016\pi$
$380$	28.0756	−	20.3638i	1.44025	−	1.04464i
$381$	−1.89501			−0.0970845
$382$	5.53811	−	10.8584i	0.283354	−	0.555564i
$383$	−1.04939			−0.0536214			−0.0268107	−	0.999641i	$-0.508535\pi$
$383$	−1.04939			−0.0536214			−0.0268107	+	0.999641i	$0.508535\pi$
$384$	−4.39991	+	27.2848i	−0.224532	+	1.39237i
$385$	−17.3991	+	6.18702i	−0.886742	+	0.315320i
$386$	23.8153	+	12.1465i	1.21216	+	0.618240i
$387$	−15.2468			−0.775038
$388$	16.7222	−	12.1290i	0.848944	−	0.615755i
$389$		−	33.8614i		−	1.71684i	−0.512948	−	0.858419i	$-0.671447\pi$
$389$		−	33.8614i		−	1.71684i	0.512948	−	0.858419i	$-0.328553\pi$
$390$	−6.04516	+	11.8526i	−0.306109	+	0.600178i
$391$	−2.81547			−0.142384
$392$	−14.7323	−	13.2272i	−0.744093	−	0.668076i
$393$	13.2071			0.666208
$394$	−2.88510	+	5.65672i	−0.145349	+	0.284981i
$395$			45.6041i			2.29459i
$396$	6.31471	+	8.70611i	0.317326	+	0.437499i
$397$	15.8664			0.796314			0.398157	−	0.917317i	$-0.369650\pi$
$397$	15.8664			0.796314			0.398157	+	0.917317i	$0.369650\pi$
$398$	−11.5309	−	5.88108i	−0.577989	−	0.294792i
$399$	27.4194	−	9.75015i	1.37269	−	0.488118i
$400$	−12.2142	+	37.3876i	−0.610710	+	1.86938i
$401$	−2.08850			−0.104295			−0.0521473	−	0.998639i	$-0.516607\pi$
$401$	−2.08850			−0.104295			−0.0521473	+	0.998639i	$0.516607\pi$
$402$	−3.34102	+	6.55064i	−0.166635	+	0.326716i
$403$	−7.74273			−0.385693
$404$	−21.1511	−	29.1610i	−1.05230	−	1.45082i
$405$	35.0357			1.74094
$406$	1.43525	−	10.9789i	0.0712300	−	0.544875i
$407$			1.78861i			0.0886581i
$408$	−3.71266	−	23.6245i	−0.183804	−	1.16958i
$409$		−	1.03994i		−	0.0514215i	−0.999669	−	0.0257107i	$-0.991815\pi$
$409$		−	1.03994i		−	0.0514215i	0.999669	−	0.0257107i	$-0.00818488\pi$
$410$	8.54305	−	16.7501i	0.421911	−	0.827228i
$411$			12.9368i			0.638123i
$412$	−4.18122	−	5.76466i	−0.205994	−	0.284004i
$413$	−11.4193	−	32.1133i	−0.561906	−	1.58019i
$414$	1.55094	−	3.04087i	0.0762243	−	0.149451i
$415$			67.8889i			3.33253i
$416$	4.00800	−	3.99198i	0.196508	−	0.195723i
$417$	38.5031			1.88550
$418$	−5.24319	+	10.2802i	−0.256453	+	0.502820i
$419$			17.2962i			0.844973i	0.906369	+	0.422486i	$0.138843\pi$
$419$			17.2962i			0.844973i	−0.906369	+	0.422486i	$0.861157\pi$
$420$	−28.1767	+	41.0421i	−1.37488	+	2.00265i
$421$		−	21.9062i		−	1.06764i	−0.845597	−	0.533821i	$-0.820755\pi$
$421$		−	21.9062i		−	1.06764i	0.845597	−	0.533821i	$-0.179245\pi$
$422$	−11.0532	−	5.63746i	−0.538061	−	0.274427i
$423$	−37.3821			−1.81758
$424$	3.38337	−	0.531708i	0.164311	−	0.0258220i
$425$		−	34.0339i		−	1.65089i
$426$	−12.3045	−	6.27564i	−0.596153	−	0.304056i
$427$	−11.7044	+	4.16200i	−0.566414	+	0.201413i
$428$	−17.0255	−	23.4731i	−0.822960	−	1.13462i
$429$		−	4.42699i		−	0.213737i
$430$	24.9307	+	12.7154i	1.20227	+	0.613192i
$431$			23.8919i			1.15083i	0.817860	+	0.575417i	$0.195160\pi$
$431$			23.8919i			1.15083i	−0.817860	+	0.575417i	$0.804840\pi$
$432$	−0.303490	−	0.0991475i	−0.0146017	−	0.00477024i
$433$		−	2.82638i		−	0.135827i	−0.997691	−	0.0679135i	$-0.978366\pi$
$433$		−	2.82638i		−	0.135827i	0.997691	−	0.0679135i	$-0.0216342\pi$
$434$	−28.7262	−	3.75530i	−1.37890	−	0.180260i
$435$	−27.8407			−1.33486
$436$	−28.3744	+	20.5805i	−1.35889	+	0.985629i
$437$	3.66269			0.175210
$438$	−28.4703	−	14.5207i	−1.36036	−	0.693827i
$439$	1.33988			0.0639489			0.0319745	−	0.999489i	$-0.489820\pi$
$439$	1.33988			0.0639489			0.0319745	+	0.999489i	$0.489820\pi$
$440$	−3.06482	−	19.5021i	−0.146109	−	0.929726i
$441$	−16.1080	+	13.1140i	−0.767048	+	0.624478i
$442$	−2.22396	+	4.36046i	−0.105783	+	0.207406i
$443$	−7.54624			−0.358533			−0.179266	−	0.983801i	$-0.557372\pi$
$443$	−7.54624			−0.358533			−0.179266	+	0.983801i	$0.557372\pi$
$444$	2.83111	+	3.90325i	0.134358	+	0.185240i
$445$			2.50791i			0.118886i
$446$	−1.52870	−	0.779681i	−0.0723859	−	0.0369190i
$447$	49.4753			2.34010
$448$	16.8062	−	12.8667i	0.794018	−	0.607894i
$449$	17.7511			0.837725			0.418862	−	0.908050i	$-0.362429\pi$
$449$	17.7511			0.837725			0.418862	+	0.908050i	$0.362429\pi$
$450$	36.7587	+	18.7480i	1.73282	+	0.883790i
$451$			6.25625i			0.294595i
$452$	−11.4337	−	15.7636i	−0.537795	−	0.741459i
$453$	−26.0137			−1.22223
$454$	−17.4344	+	34.1830i	−0.818235	+	1.60429i
$455$	9.60083	−	3.41399i	0.450094	−	0.160050i
$456$	4.82986	+	30.7334i	0.226179	+	1.43923i
$457$	1.09635			0.0512851			0.0256425	−	0.999671i	$-0.491837\pi$
$457$	1.09635			0.0512851			0.0256425	+	0.999671i	$0.491837\pi$
$458$	−0.426594	−	0.217576i	−0.0199334	−	0.0101667i
$459$	0.276267			0.0128950
$460$	−5.07202	+	3.67884i	−0.236484	+	0.171527i
$461$	−3.61769			−0.168493			−0.0842463	−	0.996445i	$-0.526848\pi$
$461$	−3.61769			−0.168493			−0.0842463	+	0.996445i	$0.526848\pi$
$462$	2.14714	−	16.4245i	0.0998938	−	0.764139i
$463$			3.14597i			0.146206i	0.997324	+	0.0731029i	$0.0232901\pi$
$463$			3.14597i			0.146206i	−0.997324	+	0.0731029i	$0.976710\pi$
$464$	11.2516	+	3.67581i	0.522344	+	0.170645i
$465$			72.8448i			3.37810i
$466$	3.00938	+	1.53487i	0.139407	+	0.0711016i
$467$			22.1648i			1.02567i	0.858488	+	0.512833i	$0.171404\pi$
$467$			22.1648i			1.02567i	−0.858488	+	0.512833i	$0.828596\pi$
$468$	−3.48445	−	4.80402i	−0.161069	−	0.222066i
$469$	5.30616	−	1.88684i	0.245016	−	0.0871260i
$470$	61.1253	+	31.1757i	2.81950	+	1.43803i
$471$			31.5054i			1.45169i
$472$	35.9947	−	5.65668i	1.65679	−	0.260370i
$473$	−9.31177			−0.428155
$474$	−36.4407	−	18.5858i	−1.67378	−	0.853676i
$475$			44.2753i			2.03149i
$476$	−10.3660	+	15.0990i	−0.475123	+	0.692063i
$477$		−	3.59309i		−	0.164516i
$478$	14.5695	−	28.5661i	0.666396	−	1.30658i
$479$	22.6530			1.03504			0.517521	−	0.855671i	$-0.326855\pi$
$479$	22.6530			1.03504			0.517521	+	0.855671i	$0.326855\pi$
$480$	−37.5572	−	37.7079i	−1.71425	−	1.72112i
$481$		−	0.986953i		−	0.0450012i
$482$	−15.6891	+	30.7612i	−0.714621	+	1.40114i
$483$	−4.95347	+	1.76142i	−0.225391	+	0.0801474i
$484$	−9.06039	−	12.4916i	−0.411836	−	0.567799i
$485$			39.7804i			1.80634i
$486$	−14.1248	+	27.6942i	−0.640716	+	1.25623i
$487$		−	0.888954i		−	0.0402824i	−0.999797	−	0.0201412i	$-0.993588\pi$
$487$		−	0.888954i		−	0.0402824i	0.999797	−	0.0201412i	$-0.00641157\pi$
$488$	−2.06170	−	13.1190i	−0.0933286	−	0.593870i
$489$			42.2403i			1.91017i
$490$	37.2758	−	8.00972i	1.68395	−	0.361842i
$491$	1.30699			0.0589837			0.0294918	−	0.999565i	$-0.490611\pi$
$491$	1.30699			0.0589837			0.0294918	+	0.999565i	$0.490611\pi$
$492$	9.90272	+	13.6529i	0.446449	+	0.615520i
$493$	−10.2424			−0.461293
$494$	2.89319	−	5.67259i	0.130171	−	0.255222i
$495$	−20.7109			−0.930886
$496$	9.61770	−	29.4397i	0.431848	−	1.32188i
$497$	3.54415	+	9.96687i	0.158977	+	0.447075i
$498$	−54.2476	−	27.6679i	−2.43089	−	1.23983i
$499$	−28.7592			−1.28744			−0.643720	−	0.765262i	$-0.722610\pi$
$499$	−28.7592			−1.28744			−0.643720	+	0.765262i	$0.722610\pi$
$500$	−21.8577	−	30.1353i	−0.977506	−	1.34769i
$501$			23.6313i			1.05577i
$502$	7.00429	−	13.7331i	0.312617	−	0.612938i
$503$	11.8526			0.528479			0.264240	−	0.964457i	$-0.414879\pi$
$503$	11.8526			0.528479			0.264240	+	0.964457i	$0.414879\pi$
$504$	−10.5976	−	19.5134i	−0.472056	−	0.869194i
$505$	69.3710			3.08697
$506$	0.947213	−	1.85717i	0.0421088	−	0.0825613i
$507$			2.44281i			0.108489i
$508$	−1.25592	+	0.910945i	−0.0557225	+	0.0404166i
$509$	−15.4601			−0.685259			−0.342629	−	0.939471i	$-0.611318\pi$
$509$	−15.4601			−0.685259			−0.342629	+	0.939471i	$0.611318\pi$
$510$	41.0239	+	20.9234i	1.81657	+	0.926504i
$511$	8.20055	+	23.0616i	0.362771	+	1.02018i
$512$	10.1999	+	20.1981i	0.450777	+	0.892637i
$513$	−0.359400			−0.0158679
$514$	17.4424	−	34.1988i	0.769352	−	1.50845i
$515$	13.7135			0.604289
$516$	−20.3209	+	14.7392i	−0.894578	+	0.648855i
$517$	−22.8306			−1.00409
$518$	0.478682	−	3.66169i	0.0210321	−	0.160885i
$519$			18.7025i			0.820950i
$520$	1.69116	+	10.7612i	0.0741624	+	0.471911i
$521$		−	34.6336i		−	1.51733i	−0.651484	−	0.758663i	$-0.725853\pi$
$521$		−	34.6336i		−	1.51733i	0.651484	−	0.758663i	$-0.274147\pi$
$522$	5.64214	−	11.0624i	0.246950	−	0.484187i
$523$		−	25.9793i		−	1.13600i	−0.823030	−	0.567998i	$-0.807718\pi$
$523$		−	25.9793i		−	1.13600i	0.823030	−	0.567998i	$-0.192282\pi$
$524$	8.75299	−	6.34872i	0.382376	−	0.277345i
$525$	−21.2924	−	59.8785i	−0.929277	−	2.61331i
$526$	−17.5811	+	34.4707i	−0.766573	+	1.50300i
$527$			26.7990i			1.16738i
$528$	16.8325	+	5.49903i	0.732540	+	0.239315i
$529$	22.3383			0.971231
$530$	−2.99654	+	5.87523i	−0.130161	+	0.255204i
$531$		−	38.2258i		−	1.65886i
$532$	13.4853	−	19.6426i	0.584660	−	0.851614i
$533$		−	3.45219i		−	0.149531i
$534$	−2.00398	−	1.02209i	−0.0867207	−	0.0442302i
$535$	55.8401			2.41418
$536$	0.934668	+	5.94749i	0.0403715	+	0.256892i
$537$		−	55.4468i		−	2.39271i
$538$	36.9501	+	18.8457i	1.59303	+	0.812495i
$539$	−9.83775	+	8.00922i	−0.423742	+	0.344982i
$540$	0.497691	−	0.360985i	0.0214172	−	0.0155343i
$541$		−	12.5538i		−	0.539732i	−0.962898	−	0.269866i	$-0.913021\pi$
$541$		−	12.5538i		−	0.539732i	0.962898	−	0.269866i	$-0.0869794\pi$
$542$	5.84242	+	2.97981i	0.250954	+	0.127994i
$543$		−	40.8519i		−	1.75312i
$544$	−13.8170	−	13.8724i	−0.592399	−	0.594776i
$545$		−	67.4997i		−	2.89137i
$546$	−1.18479	+	9.06305i	−0.0507042	+	0.387863i
$547$	−19.8173			−0.847327			−0.423663	−	0.905820i	$-0.639256\pi$
$547$	−19.8173			−0.847327			−0.423663	+	0.905820i	$0.639256\pi$
$548$	6.21878	+	8.57385i	0.265653	+	0.366257i
$549$	−13.9322			−0.594611
$550$	22.4499	+	11.4501i	0.957265	+	0.488234i
$551$	13.3245			0.567641
$552$	−0.872542	−	5.55217i	−0.0371378	−	0.236316i
$553$	10.4963	+	29.5177i	0.446349	+	1.25522i
$554$	1.44771	−	2.83848i	0.0615074	−	0.120596i
$555$	−9.28542			−0.394144
$556$	25.5179	−	18.5087i	1.08220	−	0.784942i
$557$			22.7061i			0.962089i	0.876696	+	0.481044i	$0.159742\pi$
$557$			22.7061i			0.962089i	−0.876696	+	0.481044i	$0.840258\pi$
$558$	−28.9445	−	14.7626i	−1.22532	−	0.624949i
$559$	5.13822			0.217324
$560$	1.05506	+	40.7454i	0.0445845	+	1.72181i
$561$	−15.3226			−0.646922
$562$	9.40982	+	4.79929i	0.396929	+	0.202446i
$563$			6.86719i			0.289417i	0.989474	+	0.144709i	$0.0462245\pi$
$563$			6.86719i			0.289417i	−0.989474	+	0.144709i	$0.953775\pi$
$564$	−49.8229	+	36.1375i	−2.09792	+	1.52166i
$565$	37.5000			1.57764
$566$	−0.170837	+	0.334954i	−0.00718080	+	0.0140792i
$567$	22.6772	−	8.06387i	0.952354	−	0.338651i
$568$	−11.1715	+	1.75564i	−0.468747	+	0.0736651i
$569$	0.587660			0.0246360			0.0123180	−	0.999924i	$-0.496079\pi$
$569$	0.587660			0.0246360			0.0123180	+	0.999924i	$0.496079\pi$
$570$	−53.3686	−	27.2196i	−2.23537	−	1.14010i
$571$	−11.7541			−0.491894			−0.245947	−	0.969283i	$-0.579099\pi$
$571$	−11.7541			−0.491894			−0.245947	+	0.969283i	$0.579099\pi$
$572$	−2.12808	−	2.93399i	−0.0889796	−	0.122676i
$573$	−21.0547			−0.879571
$574$	1.67435	−	12.8079i	0.0698859	−	0.534593i
$575$		−	7.99859i		−	0.333564i
$576$	22.5943	−	7.28137i	0.941430	−	0.303390i
$577$		−	19.3871i		−	0.807095i	−0.914959	−	0.403547i	$-0.867777\pi$
$577$		−	19.3871i		−	0.807095i	0.914959	−	0.403547i	$-0.132223\pi$
$578$	−6.32453	−	3.22570i	−0.263066	−	0.134171i
$579$		−	46.1783i		−	1.91910i
$580$	−18.4515	+	13.3832i	−0.766155	+	0.555707i
$581$	15.6254	+	43.9417i	0.648251	+	1.82301i
$582$	−31.7872	−	16.2124i	−1.31762	−	0.672026i
$583$		−	2.19443i		−	0.0908840i
$584$	−25.8489	+	4.06224i	−1.06964	+	0.168097i
$585$	11.4283			0.472500
$586$	5.39427	+	2.75124i	0.222835	+	0.113653i
$587$		−	41.4962i		−	1.71273i	−0.516368	−	0.856367i	$-0.672716\pi$
$587$		−	41.4962i		−	1.71273i	0.516368	−	0.856367i	$-0.327284\pi$
$588$	−8.79133	+	33.0501i	−0.362549	+	1.36296i
$589$		−	34.8633i		−	1.43652i
$590$	−31.8793	+	62.5048i	−1.31245	+	2.57328i
$591$	10.9685			0.451184
$592$	3.75264	+	1.22595i	0.154232	+	0.0503864i
$593$			23.4256i			0.961976i	0.876727	+	0.480988i	$0.159722\pi$
$593$			23.4256i			0.961976i	−0.876727	+	0.480988i	$0.840278\pi$
$594$	−0.0929451	+	0.182235i	−0.00381358	+	0.00747717i
$595$	−11.8165	−	33.2302i	−0.484428	−	1.36231i
$596$	32.7898	−	23.7831i	1.34312	−	0.974193i
$597$			22.3586i			0.915075i
$598$	−0.522671	+	1.02479i	−0.0213736	+	0.0419066i
$599$		−	16.8992i		−	0.690485i	−0.938514	−	0.345242i	$-0.887797\pi$
$599$		−	16.8992i		−	0.690485i	0.938514	−	0.345242i	$-0.112203\pi$
$600$	67.1158	−	10.5475i	2.73999	−	0.430598i
$601$			41.1108i			1.67695i	0.544943	+	0.838473i	$0.316551\pi$
$601$			41.1108i			1.67695i	−0.544943	+	0.838473i	$0.683449\pi$
$602$	19.0633	+	2.49209i	0.776961	+	0.101570i
$603$	6.31614			0.257213
$604$	−17.2406	+	12.5049i	−0.701509	+	0.508818i
$605$	29.7161			1.20813
$606$	−28.2719	+	55.4319i	−1.14847	+	2.25177i
$607$	35.6288			1.44613			0.723064	−	0.690781i	$-0.242733\pi$
$607$	35.6288			1.44613			0.723064	+	0.690781i	$0.242733\pi$
$608$	17.9747	+	18.0469i	0.728972	+	0.731897i
$609$	−18.0202	+	6.40786i	−0.730215	+	0.259660i
$610$	22.7812	+	11.6191i	0.922383	+	0.470443i
$611$	12.5979			0.509657
$612$	−16.6276	+	12.0603i	−0.672132	+	0.487510i
$613$		−	15.0402i		−	0.607466i	−0.952757	−	0.303733i	$-0.901767\pi$
$613$		−	15.0402i		−	0.607466i	0.952757	−	0.303733i	$-0.0982331\pi$
$614$	−1.54533	+	3.02989i	−0.0623646	+	0.122276i
$615$	−32.4788			−1.30967
$616$	−6.47236	−	11.9175i	−0.260779	−	0.480171i
$617$	−20.9019			−0.841479			−0.420739	−	0.907182i	$-0.638229\pi$
$617$	−20.9019			−0.841479			−0.420739	+	0.907182i	$0.638229\pi$
$618$	−5.58890	+	10.9580i	−0.224819	+	0.440795i
$619$			32.1484i			1.29215i	0.763272	+	0.646077i	$0.223591\pi$
$619$			32.1484i			1.29215i	−0.763272	+	0.646077i	$0.776409\pi$
$620$	35.0170	+	48.2780i	1.40632	+	1.93889i
$621$	0.0649277			0.00260546
$622$	−23.8666	−	12.1727i	−0.956962	−	0.488079i
$623$	0.577223	+	1.62327i	0.0231260	+	0.0650348i
$624$	−9.28816	−	3.03436i	−0.371824	−	0.121472i
$625$	22.5234			0.900935
$626$	−1.67211	+	3.27845i	−0.0668308	+	0.131033i
$627$	19.9335			0.796066
$628$	15.1448	+	20.8802i	0.604344	+	0.833211i
$629$	−3.41603			−0.136206
$630$	42.3999	+	5.54282i	1.68925	+	0.220831i
$631$		−	20.4474i		−	0.813998i	−0.913429	−	0.406999i	$-0.866575\pi$
$631$		−	20.4474i		−	0.813998i	0.913429	−	0.406999i	$-0.133425\pi$
$632$	−33.0854	+	5.19948i	−1.31607	+	0.206824i
$633$			21.4324i			0.851861i
$634$	1.71962	−	3.37160i	0.0682948	−	0.133904i
$635$		−	2.98770i		−	0.118563i
$636$	−3.47346	−	4.78886i	−0.137732	−	0.189891i
$637$	5.42846	−	4.41948i	0.215083	−	0.175106i
$638$	3.44586	−	6.75619i	0.136423	−	0.267480i
$639$			11.8640i			0.469332i
$640$	−43.0175	−	6.93696i	−1.70042	−	0.274207i
$641$	19.9013			0.786056			0.393028	−	0.919527i	$-0.371428\pi$
$641$	19.9013			0.786056			0.393028	+	0.919527i	$0.371428\pi$
$642$	−22.7574	+	44.6198i	−0.898165	+	1.76100i
$643$		−	36.6222i		−	1.44424i	−0.691768	−	0.722120i	$-0.743168\pi$
$643$		−	36.6222i		−	1.44424i	0.691768	−	0.722120i	$-0.256832\pi$
$644$	−2.43619	+	3.54855i	−0.0959993	+	0.139832i
$645$		−	48.3413i		−	1.90343i
$646$	−19.6339	−	10.0139i	−0.772485	−	0.393990i
$647$	−33.4255			−1.31409			−0.657045	−	0.753851i	$-0.728194\pi$
$647$	−33.4255			−1.31409			−0.657045	+	0.753851i	$0.728194\pi$
$648$	3.99454	+	25.4181i	0.156920	+	0.998518i
$649$		−	23.3459i		−	0.916405i
$650$	−12.3878	−	6.31816i	−0.485890	−	0.247818i
$651$	16.7661	+	47.1495i	0.657114	+	1.84794i
$652$	20.3052	+	27.9948i	0.795213	+	1.09636i
$653$			15.8386i			0.619811i	0.950767	+	0.309905i	$0.100297\pi$
$653$			15.8386i			0.619811i	−0.950767	+	0.309905i	$0.899703\pi$
$654$	53.9367	+	27.5093i	2.10909	+	1.07570i
$655$			20.8224i			0.813600i
$656$	13.1261	+	4.28817i	0.512487	+	0.167425i
$657$			27.4511i			1.07097i
$658$	46.7394	+	6.11011i	1.82209	+	0.238197i
$659$	−35.1659			−1.36987			−0.684935	−	0.728604i	$-0.740169\pi$
$659$	−35.1659			−1.36987			−0.684935	+	0.728604i	$0.740169\pi$
$660$	−27.6035	+	20.0214i	−1.07446	+	0.779330i
$661$	−48.9746			−1.90489			−0.952446	−	0.304707i	$-0.901441\pi$
$661$	−48.9746			−1.90489			−0.952446	+	0.304707i	$0.901441\pi$
$662$	−19.7448	−	10.0704i	−0.767404	−	0.391399i
$663$	8.45502			0.328366
$664$	−49.2528	+	7.74024i	−1.91138	+	0.300379i
$665$	15.3722	+	43.2298i	0.596109	+	1.67638i
$666$	1.88176	−	3.68951i	0.0729168	−	0.142966i
$667$	−2.40714			−0.0932049
$668$	11.3597	+	15.6617i	0.439521	+	0.605969i
$669$			2.96417i			0.114602i
$670$	−10.3278	−	5.26750i	−0.398999	−	0.203501i
$671$	−8.50890			−0.328482
$672$	−32.9882	−	15.7626i	−1.27255	−	0.608055i
$673$	−12.2361			−0.471666			−0.235833	−	0.971794i	$-0.575782\pi$
$673$	−12.2361			−0.471666			−0.235833	+	0.971794i	$0.575782\pi$
$674$	−34.1404	−	17.4126i	−1.31504	−	0.670709i
$675$			0.784860i			0.0302093i
$676$	1.17427	+	1.61897i	0.0451644	+	0.0622683i
$677$	−12.6987			−0.488051			−0.244025	−	0.969769i	$-0.578468\pi$
$677$	−12.6987			−0.488051			−0.244025	+	0.969769i	$0.578468\pi$
$678$	−15.2830	+	29.9649i	−0.586941	+	1.15080i
$679$	9.15592	+	25.7483i	0.351372	+	0.988128i
$680$	37.2466	−	5.85343i	1.42834	−	0.224469i
$681$	66.2816			2.53992
$682$	−17.6775	−	9.01604i	−0.676905	−	0.345242i
$683$	−14.5785			−0.557831			−0.278916	−	0.960316i	$-0.589975\pi$
$683$	−14.5785			−0.557831			−0.278916	+	0.960316i	$0.589975\pi$
$684$	21.6311	−	15.6895i	0.827087	−	0.599903i
$685$	−20.3963			−0.779301
$686$	22.2836	−	13.7638i	0.850791	−	0.525505i
$687$			0.827175i			0.0315587i
$688$	−6.38249	+	19.5368i	−0.243330	+	0.744832i
$689$			1.21088i			0.0461310i
$690$	9.64135	+	4.91738i	0.367040	+	0.187201i
$691$			23.6667i			0.900323i	0.892947	+	0.450162i	$0.148634\pi$
$691$			23.6667i			0.900323i	−0.892947	+	0.450162i	$0.851366\pi$
$692$	8.99043	+	12.3951i	0.341765	+	0.471192i
$693$	−13.4053	+	4.76685i	−0.509227	+	0.181078i
$694$	3.26450	+	1.66499i	0.123919	+	0.0632023i
$695$			60.7045i			2.30265i
$696$	−3.17421	−	20.1982i	−0.120318	−	0.765611i
$697$	−11.9487			−0.452588
$698$	−15.6606	−	7.98736i	−0.592762	−	0.302326i
$699$		−	5.83525i		−	0.220709i
$700$	−42.8955	−	29.4491i	−1.62130	−	1.11307i
$701$			7.44505i			0.281196i	0.990067	+	0.140598i	$0.0449025\pi$
$701$			7.44505i			0.281196i	−0.990067	+	0.140598i	$0.955098\pi$
$702$	0.0512870	−	0.100557i	0.00193570	−	0.00379527i
$703$	4.44397			0.167607
$704$	13.7992	−	4.44700i	0.520076	−	0.167603i
$705$		−	118.523i		−	4.46384i
$706$	−8.29606	+	16.2658i	−0.312226	+	0.612173i
$707$	44.9010	−	15.9665i	1.68868	−	0.600483i
$708$	−36.9531	−	50.9473i	−1.38878	−	1.91472i
$709$		−	44.0918i		−	1.65590i	−0.560800	−	0.827951i	$-0.689506\pi$
$709$		−	44.0918i		−	1.65590i	0.560800	−	0.827951i	$-0.310494\pi$
$710$	9.89425	−	19.3994i	0.371325	−	0.728045i
$711$			35.1362i			1.31771i
$712$	−1.81946	+	0.285935i	−0.0681873	+	0.0107159i
$713$			6.29825i			0.235871i
$714$	31.3689	+	4.10077i	1.17395	+	0.153467i
$715$	6.97966			0.261024
$716$	−26.6536	−	36.7474i	−0.996093	−	1.37332i
$717$	−55.3902			−2.06859
$718$	9.92849	−	19.4665i	0.370528	−	0.726483i
$719$	−24.0504			−0.896929			−0.448464	−	0.893801i	$-0.648029\pi$
$719$	−24.0504			−0.896929			−0.448464	+	0.893801i	$0.648029\pi$
$720$	−14.1957	+	43.4530i	−0.529043	+	1.61940i
$721$	8.87621	−	3.15632i	0.330567	−	0.117548i
$722$	1.60552	+	0.818862i	0.0597512	+	0.0304749i
$723$	59.6467			2.21828
$724$	−19.6378	−	27.0746i	−0.729832	−	1.00622i
$725$		−	29.0980i		−	1.08067i
$726$	−12.1107	+	23.7451i	−0.449471	+	0.881264i
$727$	−36.9514			−1.37045			−0.685226	−	0.728330i	$-0.740297\pi$
$727$	−36.9514			−1.37045			−0.685226	+	0.728330i	$0.740297\pi$
$728$	3.57144	+	6.57608i	0.132367	+	0.243726i
$729$	26.4087			0.978099
$730$	22.8936	−	44.8867i	0.847328	−	1.66133i
$731$		−	17.7843i		−	0.657778i
$732$	−18.5688	+	13.4683i	−0.686323	+	0.497804i
$733$	22.0569			0.814692			0.407346	−	0.913274i	$-0.366454\pi$
$733$	22.0569			0.814692			0.407346	+	0.913274i	$0.366454\pi$
$734$	39.0970	+	19.9406i	1.44310	+	0.736022i
$735$	−41.5792	−	51.0718i	−1.53367	−	1.88381i
$736$	−3.24724	−	3.26027i	−0.119695	−	0.120175i
$737$	3.85750			0.142093
$738$	6.58208	−	12.9053i	0.242290	−	0.475050i
$739$	36.0166			1.32489			0.662445	−	0.749110i	$-0.269519\pi$
$739$	36.0166			1.32489			0.662445	+	0.749110i	$0.269519\pi$
$740$	−6.15392	+	4.46356i	−0.226223	+	0.164084i
$741$	−10.9993			−0.404068
$742$	−0.587291	+	4.49249i	−0.0215601	+	0.164924i
$743$			10.2860i			0.377358i	0.982039	+	0.188679i	$0.0604206\pi$
$743$			10.2860i			0.377358i	−0.982039	+	0.188679i	$0.939579\pi$
$744$	−52.8483	+	8.30528i	−1.93751	+	0.304486i
$745$			78.0034i			2.85782i
$746$	−14.8970	+	29.2080i	−0.545417	+	1.06938i
$747$			52.3057i			1.91376i
$748$	−10.1551	+	7.36569i	−0.371307	+	0.269316i
$749$	36.1430	−	12.8522i	1.32064	−	0.469610i
$750$	−29.2165	+	57.2838i	−1.06683	+	2.09171i
$751$		−	34.8371i		−	1.27122i	−0.772009	−	0.635612i	$-0.780748\pi$
$751$		−	34.8371i		−	1.27122i	0.772009	−	0.635612i	$-0.219252\pi$
$752$	−15.6486	+	47.9003i	−0.570646	+	1.74674i
$753$	−26.6288			−0.970407
$754$	−1.90142	+	3.72806i	−0.0692457	+	0.135768i
$755$		−	41.0135i		−	1.49263i
$756$	0.239050	−	0.348200i	0.00869418	−	0.0126639i
$757$			6.93156i			0.251932i	0.992035	+	0.125966i	$0.0402030\pi$
$757$			6.93156i			0.251932i	−0.992035	+	0.125966i	$0.959797\pi$
$758$	11.6031	+	5.91794i	0.421445	+	0.214949i
$759$	−3.60110			−0.130711
$760$	−48.4547	+	7.61482i	−1.75764	+	0.276219i
$761$		−	32.8554i		−	1.19101i	−0.803352	−	0.595504i	$-0.796952\pi$
$761$		−	32.8554i		−	1.19101i	0.803352	−	0.595504i	$-0.203048\pi$
$762$	2.38737	+	1.21763i	0.0864853	+	0.0441101i
$763$	−15.5358	−	43.6899i	−0.562435	−	1.58168i
$764$	−13.9540	+	10.1211i	−0.504838	+	0.366169i
$765$		−	39.5553i		−	1.43013i
$766$	1.32204	+	0.674281i	0.0477673	+	0.0243627i
$767$			12.8822i			0.465150i
$768$	23.0747	−	31.5467i	0.832638	−	1.13834i
$769$			29.5660i			1.06618i	0.846059	+	0.533089i	$0.178969\pi$
$769$			29.5660i			1.06618i	−0.846059	+	0.533089i	$0.821031\pi$
$770$	25.8951	+	3.38520i	0.933196	+	0.121994i
$771$	−66.3122			−2.38818
$772$	−22.1982	−	30.6047i	−0.798930	−	1.10149i
$773$	28.4754			1.02419			0.512094	−	0.858929i	$-0.328870\pi$
$773$	28.4754			1.02419			0.512094	+	0.858929i	$0.328870\pi$
$774$	19.2081	+	9.79673i	0.690423	+	0.352136i
$775$	−76.1345			−2.73483
$776$	−28.8604	+	4.53550i	−1.03603	+	0.162815i
$777$	−6.01008	+	2.13715i	−0.215610	+	0.0766697i
$778$	−21.7574	+	42.6591i	−0.780041	+	1.52940i
$779$	15.5442			0.556930
$780$	15.2316	−	11.0478i	0.545378	−	0.395573i
$781$			7.24576i			0.259274i
$782$	3.54697	+	1.80906i	0.126839	+	0.0646919i
$783$	0.236200			0.00844110
$784$	10.0609	+	26.1300i	0.359318	+	0.933215i
$785$	−49.6717			−1.77286
$786$	−16.6385	−	8.48612i	−0.593475	−	0.302690i
$787$			39.7645i			1.41745i	0.705484	+	0.708726i	$0.250730\pi$
$787$			39.7645i			1.41745i	−0.705484	+	0.708726i	$0.749270\pi$
$788$	7.26938	−	5.27263i	0.258961	−	0.187830i
$789$	66.8395			2.37955
$790$	29.3027	−	57.4528i	1.04254	−	2.04408i
$791$	24.2723	−	8.63106i	0.863022	−	0.306885i
$792$	−2.36132	−	15.0256i	−0.0839058	−	0.533911i
$793$	4.69520			0.166731
$794$	−19.9888	−	10.1949i	−0.709376	−	0.361803i
$795$	11.3922			0.404039
$796$	10.7479	+	14.8182i	0.380949	+	0.525216i
$797$	−1.40341			−0.0497114			−0.0248557	−	0.999691i	$-0.507913\pi$
$797$	−1.40341			−0.0497114			−0.0248557	+	0.999691i	$0.507913\pi$
$798$	−40.8083	−	5.33475i	−1.44460	−	0.188848i
$799$		−	43.6037i		−	1.54259i
$800$	39.4108	−	39.2533i	1.39338	−	1.38781i
$801$			1.93224i			0.0682724i
$802$	2.63112	+	1.34195i	0.0929082	+	0.0473860i
$803$			16.7654i			0.591639i
$804$	8.41815	−	6.10585i	0.296885	−	0.215337i
$805$	−2.77708	−	7.80970i	−0.0978792	−	0.275256i
$806$	9.75441	+	4.97504i	0.343585	+	0.175238i
$807$		−	71.6471i		−	2.52210i
$808$	7.90921	+	50.3280i	0.278245	+	1.77053i
$809$	14.9618			0.526027			0.263014	−	0.964792i	$-0.415284\pi$
$809$	14.9618			0.526027			0.263014	+	0.964792i	$0.415284\pi$
$810$	−44.1386	−	22.5120i	−1.55087	−	0.790991i
$811$		−	3.70960i		−	0.130262i	−0.997877	−	0.0651308i	$-0.979254\pi$
$811$		−	3.70960i		−	0.130262i	0.997877	−	0.0651308i	$-0.0207464\pi$
$812$	−8.86259	+	12.9092i	−0.311016	+	0.453025i
$813$		−	11.3286i		−	0.397311i
$814$	1.14926	−	2.25332i	0.0402816	−	0.0789788i
$815$	−66.5967			−2.33278
$816$	−10.5025	+	32.1480i	−0.367660	+	1.12541i
$817$			23.1359i			0.809424i
$818$	−0.668204	+	1.31013i	−0.0233632	+	0.0458075i
$819$	7.39705	−	2.63034i	0.258474	−	0.0919117i
$820$	−21.5253	+	15.6128i	−0.751698	+	0.545221i
$821$			36.0973i			1.25981i	0.776674	+	0.629903i	$0.216905\pi$
$821$			36.0973i			1.25981i	−0.776674	+	0.629903i	$0.783095\pi$
$822$	8.31244	−	16.2979i	0.289929	−	0.568456i
$823$			7.14831i			0.249175i	0.992209	+	0.124587i	$0.0397607\pi$
$823$			7.14831i			0.249175i	−0.992209	+	0.124587i	$0.960239\pi$
$824$	1.56352	+	9.94903i	0.0544679	+	0.346591i
$825$		−	43.5308i		−	1.51555i
$826$	−6.24801	+	47.7942i	−0.217396	+	1.66297i
$827$	−45.0128			−1.56525			−0.782625	−	0.622493i	$-0.786120\pi$
$827$	−45.0128			−1.56525			−0.782625	+	0.622493i	$0.786120\pi$
$828$	−3.90779	+	2.83440i	−0.135805	+	0.0985021i
$829$	1.70523			0.0592250			0.0296125	−	0.999561i	$-0.490573\pi$
$829$	1.70523			0.0592250			0.0296125	+	0.999561i	$0.490573\pi$
$830$	43.6216	−	85.5275i	1.51413	−	2.96870i
$831$	−5.50388			−0.190927
$832$	−7.61437	+	2.45385i	−0.263981	+	0.0850719i
$833$	−15.2966	−	18.7889i	−0.529997	−	0.650997i
$834$	−48.5068	−	24.7399i	−1.67965	−	0.856673i
$835$	−37.2575			−1.28935
$836$	13.2109	−	9.58214i	0.456909	−	0.331405i
$837$		−	0.618014i		−	0.0213617i
$838$	11.1135	−	21.7900i	0.383911	−	0.752723i
$839$	9.92632			0.342694			0.171347	−	0.985211i	$-0.445188\pi$
$839$	9.92632			0.342694			0.171347	+	0.985211i	$0.445188\pi$
$840$	61.8688	−	33.6007i	2.13468	−	1.15934i
$841$	20.2431			0.698037
$842$	−14.0757	+	27.5978i	−0.485080	+	0.951082i
$843$		−	18.2458i		−	0.628420i
$844$	10.3027	+	14.2043i	0.354633	+	0.488933i
$845$	−3.85137			−0.132491
$846$	47.0946	+	24.0197i	1.61915	+	0.825813i
$847$	19.2341	−	6.83951i	0.660890	−	0.235008i
$848$	−4.60407	−	1.50411i	−0.158105	−	0.0516514i
$849$	0.649483			0.0222902
$850$	−21.8683	+	42.8765i	−0.750077	+	1.47065i
$851$	−0.802828			−0.0275206
$852$	11.4690	+	15.8123i	0.392921	+	0.541721i
$853$	−7.29950			−0.249930			−0.124965	−	0.992161i	$-0.539882\pi$
$853$	−7.29950			−0.249930			−0.124965	+	0.992161i	$0.539882\pi$
$854$	17.4196	+	2.27722i	0.596087	+	0.0779248i
$855$			51.4582i			1.75983i
$856$	6.36651	+	40.5115i	0.217603	+	1.38465i
$857$		−	42.5363i		−	1.45301i	−0.687160	−	0.726506i	$-0.741143\pi$
$857$		−	42.5363i		−	1.45301i	0.687160	−	0.726506i	$-0.258857\pi$
$858$	−2.84454	+	5.57720i	−0.0971109	+	0.190402i
$859$			18.3243i			0.625217i	0.949882	+	0.312609i	$0.101203\pi$
$859$			18.3243i			0.625217i	−0.949882	+	0.312609i	$0.898797\pi$
$860$	−23.2379	−	32.0382i	−0.792407	−	1.09249i
$861$	−21.0222	+	7.47536i	−0.716435	+	0.254760i
$862$	15.3516	−	30.0995i	0.522878	−	1.02519i
$863$		−	31.0819i		−	1.05804i	−0.848610	−	0.529019i	$-0.822560\pi$
$863$		−	31.0819i		−	1.05804i	0.848610	−	0.529019i	$-0.177440\pi$
$864$	0.318635	+	0.319913i	0.0108402	+	0.0108837i
$865$	−29.4867			−1.00258
$866$	−1.81607	+	3.56072i	−0.0617127	+	0.120998i
$867$			12.2634i			0.416487i
$868$	33.7768	+	23.1888i	1.14646	+	0.787081i
$869$			21.4589i			0.727945i
$870$	35.0742	+	17.8889i	1.18913	+	0.606490i
$871$	−2.12856			−0.0721236
$872$	48.9705	−	7.69587i	1.65835	−	0.260615i
$873$			30.6492i			1.03732i
$874$	−4.61431	−	2.35344i	−0.156081	−	0.0796062i
$875$	46.4011	−	16.4999i	1.56864	−	0.557800i
$876$	26.5372	+	36.5869i	0.896608	+	1.23616i
$877$		−	50.5638i		−	1.70742i	−0.520752	−	0.853708i	$-0.674348\pi$
$877$		−	50.5638i		−	1.70742i	0.520752	−	0.853708i	$-0.325652\pi$
$878$	−1.68800	−	0.860931i	−0.0569673	−	0.0290550i
$879$		−	10.4596i		−	0.352794i
$880$	−8.66985	+	26.5383i	−0.292260	+	0.894607i
$881$			0.189942i			0.00639930i	0.999995	+	0.00319965i	$0.00101848\pi$
$881$			0.189942i			0.00639930i	−0.999995	+	0.00319965i	$0.998982\pi$
$882$	28.7195	−	6.17117i	0.967035	−	0.207794i
$883$	−32.9338			−1.10831			−0.554156	−	0.832413i	$-0.686959\pi$
$883$	−32.9338			−1.10831			−0.554156	+	0.832413i	$0.686959\pi$
$884$	5.60357	−	4.06438i	0.188468	−	0.136700i
$885$	121.198			4.07403
$886$	9.50688	+	4.84879i	0.319390	+	0.162898i
$887$	−36.6972			−1.23217			−0.616086	−	0.787679i	$-0.711283\pi$
$887$	−36.6972			−1.23217			−0.616086	+	0.787679i	$0.711283\pi$
$888$	−1.05866	−	6.73649i	−0.0355264	−	0.226062i
$889$	−0.687654	−	1.93382i	−0.0230632	−	0.0648583i
$890$	1.61144	−	3.15950i	0.0540156	−	0.105907i
$891$	16.4860			0.552302
$892$	1.42490	+	1.96451i	0.0477091	+	0.0657766i
$893$			56.7248i			1.89822i
$894$	−62.3298	−	31.7901i	−2.08462	−	1.06322i
$895$	87.4182			2.92207
$896$	−29.4401	+	5.41096i	−0.983526	+	0.180767i
$897$	1.98708			0.0663467
$898$	−22.3631	−	11.4058i	−0.746266	−	0.380618i
$899$			22.9123i			0.764170i
$900$	−34.2627	−	47.2381i	−1.14209	−	1.57460i
$901$	4.19109			0.139626
$902$	4.01992	−	7.88172i	0.133849	−	0.262433i
$903$	−11.1263	−	31.2894i	−0.370260	−	1.04124i
$904$	4.27550	+	27.2059i	0.142201	+	0.904856i
$905$	64.4077			2.14098
$906$	32.7724	+	16.7149i	1.08879	+	0.555316i
$907$	−30.6366			−1.01727			−0.508636	−	0.860982i	$-0.669850\pi$
$907$	−30.6366			−1.01727			−0.508636	+	0.860982i	$0.669850\pi$
$908$	43.9282	−	31.8620i	1.45781	−	1.05738i
$909$	53.4476			1.77274
$910$	−14.2889	−	1.86795i	−0.473673	−	0.0619220i
$911$		−	32.3852i		−	1.07297i	−0.843910	−	0.536484i	$-0.819752\pi$
$911$		−	32.3852i		−	1.07297i	0.843910	−	0.536484i	$-0.180248\pi$
$912$	13.6629	−	41.8219i	0.452422	−	1.38486i
$913$			31.9450i			1.05722i
$914$	−1.38120	−	0.704453i	−0.0456860	−	0.0233012i
$915$		−	44.1732i		−	1.46032i
$916$	0.397628	+	0.548211i	0.0131380	+	0.0181134i
$917$	4.79252	+	13.4775i	0.158263	+	0.445067i
$918$	−0.348046	−	0.177514i	−0.0114872	−	0.00585883i
$919$		−	34.3537i		−	1.13322i	−0.823985	−	0.566612i	$-0.808254\pi$
$919$		−	34.3537i		−	1.13322i	0.823985	−	0.566612i	$-0.191746\pi$
$920$	8.75363	−	1.37566i	0.288599	−	0.0453542i
$921$	5.87502			0.193588
$922$	4.55762	+	2.32452i	0.150097	+	0.0765541i
$923$		−	3.99821i		−	0.131603i
$924$	−13.2585	+	19.3123i	−0.436172	+	0.635327i
$925$		−	9.70475i		−	0.319090i
$926$	2.02143	−	3.96335i	0.0664282	−	0.130244i
$927$	10.5657			0.347024
$928$	−11.8131	−	11.8605i	−0.387784	−	0.389340i
$929$			41.2449i			1.35320i	0.736350	+	0.676601i	$0.236548\pi$
$929$			41.2449i			1.35320i	−0.736350	+	0.676601i	$0.763452\pi$
$930$	46.8060	−	91.7711i	1.53483	−	3.00929i
$931$	19.8996	+	24.4428i	0.652184	+	0.801080i
$932$	−2.80504	−	3.86732i	−0.0918821	−	0.126678i
$933$			46.2778i			1.51507i
$934$	14.2419	−	27.9236i	0.466009	−	0.913689i
$935$		−	24.1579i		−	0.790047i
$936$	1.30297	+	8.29110i	0.0425890	+	0.271003i
$937$			24.8231i			0.810936i	0.914109	+	0.405468i	$0.132891\pi$
$937$			24.8231i			0.810936i	−0.914109	+	0.405468i	$0.867109\pi$
$938$	−7.89716	−	1.03237i	−0.257851	−	0.0337082i
$939$	6.35698			0.207452
$940$	−56.9749	−	78.5514i	−1.85831	−	2.56206i
$941$	−22.0956			−0.720295			−0.360147	−	0.932895i	$-0.617274\pi$
$941$	−22.0956			−0.720295			−0.360147	+	0.932895i	$0.617274\pi$
$942$	20.2436	−	39.6910i	0.659571	−	1.29320i
$943$	−2.80815			−0.0914460
$944$	−48.9813	−	16.0018i	−1.59421	−	0.520814i
$945$	0.272500	+	0.766325i	0.00886444	+	0.0249286i
$946$	11.7311	+	5.98322i	0.381411	+	0.194531i
$947$	−49.5764			−1.61102			−0.805508	−	0.592585i	$-0.798107\pi$
$947$	−49.5764			−1.61102			−0.805508	+	0.592585i	$0.798107\pi$
$948$	33.9663	+	46.8295i	1.10318	+	1.52095i
$949$		−	9.25114i		−	0.300305i
$950$	28.4488	−	55.7788i	0.923002	−	1.80970i
$951$	−6.53761			−0.211997
$952$	22.7610	−	12.3614i	0.737689	−	0.400636i
$953$	46.4982			1.50622			0.753112	−	0.657892i	$-0.228552\pi$
$953$	46.4982			1.50622			0.753112	+	0.657892i	$0.228552\pi$
$954$	−2.30872	+	4.52663i	−0.0747474	+	0.146555i
$955$		−	33.1951i		−	1.07417i
$956$	−36.7099	+	26.6264i	−1.18728	+	0.861160i
$957$	−13.1004			−0.423476
$958$	−28.5386	−	14.5555i	−0.922040	−	0.470268i
$959$	−13.2017	+	4.69443i	−0.426305	+	0.151591i
$960$	23.0862	+	71.6372i	0.745104	+	2.31208i
$961$	28.9498			0.933865
$962$	−0.634161	+	1.24338i	−0.0204462	+	0.0400882i
$963$	43.0225			1.38638
$964$	39.5309	−	28.6725i	1.27320	−	0.923480i
$965$	72.8053			2.34369
$966$	7.37225	+	0.963754i	0.237198	+	0.0310083i
$967$			31.7620i			1.02140i	0.859760	+	0.510699i	$0.170613\pi$
$967$			31.7620i			1.02140i	−0.859760	+	0.510699i	$0.829387\pi$
$968$	3.38804	+	21.5588i	0.108896	+	0.692926i
$969$			38.0705i			1.22300i
$970$	25.5607	−	50.1160i	0.820704	−	1.60913i
$971$		−	1.85166i		−	0.0594226i	−0.999559	−	0.0297113i	$-0.990541\pi$
$971$		−	1.85166i		−	0.0594226i	0.999559	−	0.0297113i	$-0.00945879\pi$
$972$	35.5894	−	25.8137i	1.14153	−	0.827975i
$973$	13.9718	+	39.2916i	0.447916	+	1.25963i
$974$	−0.571192	+	1.11992i	−0.0183022	+	0.0358845i
$975$			24.0202i			0.769263i
$976$	−5.83219	+	17.8523i	−0.186684	+	0.571438i
$977$	−40.6090			−1.29920			−0.649598	−	0.760278i	$-0.725063\pi$
$977$	−40.6090			−1.29920			−0.649598	+	0.760278i	$0.725063\pi$
$978$	27.1413	−	53.2151i	0.867882	−	1.70163i
$979$			1.18009i			0.0377159i
$980$	−52.1072	−	13.8605i	−1.66450	−	0.442758i
$981$		−	52.0058i		−	1.66042i
$982$	−1.64657	−	0.839799i	−0.0525441	−	0.0267991i
$983$	23.1405			0.738066			0.369033	−	0.929416i	$-0.379689\pi$
$983$	23.1405			0.738066			0.369033	+	0.929416i	$0.379689\pi$
$984$	−3.70302	−	23.5631i	−0.118048	−	0.751164i
$985$			17.2931i			0.551003i
$986$	12.9035	+	6.58117i	0.410931	+	0.209587i
$987$	−27.2795	−	76.7153i	−0.868315	−	2.44188i
$988$	−7.28978	+	5.28742i	−0.231919	+	0.168215i
$989$		−	4.17964i		−	0.132905i
$990$	26.0919	+	13.3077i	0.829256	+	0.422946i
$991$		−	3.02612i		−	0.0961279i	−0.998844	−	0.0480640i	$-0.984695\pi$
$991$		−	3.02612i		−	0.0961279i	0.998844	−	0.0480640i	$-0.0153051\pi$
$992$	−31.0329	+	30.9088i	−0.985294	+	0.981357i
$993$			38.2856i			1.21496i
$994$	1.93917	−	14.8337i	0.0615067	−	0.470496i
$995$	−35.2508			−1.11753
$996$	50.5642	+	69.7130i	1.60219	+	2.20894i
$997$	25.0174			0.792308			0.396154	−	0.918184i	$-0.370345\pi$
$997$	25.0174			0.792308			0.396154	+	0.918184i	$0.370345\pi$
$998$	36.2313	+	18.4791i	1.14688	+	0.584944i
$999$	0.0787773			0.00249240

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	728.2.h.b.27.9	yes	48
4.3	odd	2		2912.2.h.b.2575.7		48
7.6	odd	2		728.2.h.a.27.9	✓	48
8.3	odd	2		728.2.h.a.27.10	yes	48
8.5	even	2		2912.2.h.a.2575.7		48
28.27	even	2		2912.2.h.a.2575.42		48
56.13	odd	2		2912.2.h.b.2575.42		48
56.27	even	2	inner	728.2.h.b.27.10	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.h.a.27.9	✓	48	7.6	odd	2
728.2.h.a.27.10	yes	48	8.3	odd	2
728.2.h.b.27.9	yes	48	1.1	even	1	trivial
728.2.h.b.27.10	yes	48	56.27	even	2	inner
2912.2.h.a.2575.7		48	8.5	even	2
2912.2.h.a.2575.42		48	28.27	even	2
2912.2.h.b.2575.7		48	4.3	odd	2
2912.2.h.b.2575.42		48	56.13	odd	2

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:	\( N \)	\(=\)	\( 728 = 2^{3} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	728.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.25982 - 0.642544i) q^{2} +2.44281i q^{3} +(1.17427 + 1.61897i) q^{4} -3.85137 q^{5} +(1.56961 - 3.07749i) q^{6} +(-2.49284 + 0.886436i) q^{7} +(-0.439107 - 2.79413i) q^{8} -2.96733 q^{9} +(4.85202 + 2.47467i) q^{10} -1.81225 q^{11} +(-3.95485 + 2.86853i) q^{12} +1.00000 q^{13} +(3.71009 + 0.485010i) q^{14} -9.40816i q^{15} +(-1.24216 + 3.80224i) q^{16} -3.46118i q^{17} +(3.73828 + 1.90664i) q^{18} +4.50271i q^{19} +(-4.52256 - 6.23527i) q^{20} +(-2.16540 - 6.08953i) q^{21} +(2.28311 + 1.16445i) q^{22} -0.813440i q^{23} +(6.82554 - 1.07266i) q^{24} +9.83303 q^{25} +(-1.25982 - 0.642544i) q^{26} +0.0798187i q^{27} +(-4.36239 - 2.99492i) q^{28} -2.95921i q^{29} +(-6.04516 + 11.8526i) q^{30} -7.74273 q^{31} +(4.00800 - 3.99198i) q^{32} -4.42699i q^{33} +(-2.22396 + 4.36046i) q^{34} +(9.60083 - 3.41399i) q^{35} +(-3.48445 - 4.80402i) q^{36} -0.986953i q^{37} +(2.89319 - 5.67259i) q^{38} +2.44281i q^{39} +(1.69116 + 10.7612i) q^{40} -3.45219i q^{41} +(-1.18479 + 9.06305i) q^{42} +5.13822 q^{43} +(-2.12808 - 2.93399i) q^{44} +11.4283 q^{45} +(-0.522671 + 1.02479i) q^{46} +12.5979 q^{47} +(-9.28816 - 3.03436i) q^{48} +(5.42846 - 4.41948i) q^{49} +(-12.3878 - 6.31816i) q^{50} +8.45502 q^{51} +(1.17427 + 1.61897i) q^{52} +1.21088i q^{53} +(0.0512870 - 0.100557i) q^{54} +6.97966 q^{55} +(3.57144 + 6.57608i) q^{56} -10.9993 q^{57} +(-1.90142 + 3.72806i) q^{58} +12.8822i q^{59} +(15.2316 - 11.0478i) q^{60} +4.69520 q^{61} +(9.75441 + 4.97504i) q^{62} +(7.39705 - 2.63034i) q^{63} +(-7.61437 + 2.45385i) q^{64} -3.85137 q^{65} +(-2.84454 + 5.57720i) q^{66} -2.12856 q^{67} +(5.60357 - 4.06438i) q^{68} +1.98708 q^{69} +(-14.2889 - 1.86795i) q^{70} -3.99821i q^{71} +(1.30297 + 8.29110i) q^{72} -9.25114i q^{73} +(-0.634161 + 1.24338i) q^{74} +24.0202i q^{75} +(-7.28978 + 5.28742i) q^{76} +(4.51765 - 1.60645i) q^{77} +(1.56961 - 3.07749i) q^{78} -11.8410i q^{79} +(4.78401 - 14.6438i) q^{80} -9.09696 q^{81} +(-2.21819 + 4.34913i) q^{82} -17.6272i q^{83} +(7.31602 - 10.6565i) q^{84} +13.3303i q^{85} +(-6.47322 - 3.30154i) q^{86} +7.22879 q^{87} +(0.795774 + 5.06368i) q^{88} -0.651173i q^{89} +(-14.3975 - 7.34316i) q^{90} +(-2.49284 + 0.886436i) q^{91} +(1.31694 - 0.955202i) q^{92} -18.9140i q^{93} +(-15.8711 - 8.09472i) q^{94} -17.3416i q^{95} +(9.75166 + 9.79079i) q^{96} -10.3289i q^{97} +(-9.67857 + 2.07971i) q^{98} +5.37755 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + q^{2} + q^{4} + 10 q^{6} - 5 q^{8} - 48 q^{9} - 4 q^{11} - 10 q^{12} + 48 q^{13} - 6 q^{14} + 5 q^{16} - 15 q^{18} + 22 q^{20} - 6 q^{22} + 48 q^{25} + q^{26} - 26 q^{28} - 26 q^{30} - 19 q^{32}+ \cdots + 20 q^{99}+O(q^{100}) \) 48 * q + q^2 + q^4 + 10 * q^6 - 5 * q^8 - 48 * q^9 - 4 * q^11 - 10 * q^12 + 48 * q^13 - 6 * q^14 + 5 * q^16 - 15 * q^18 + 22 * q^20 - 6 * q^22 + 48 * q^25 + q^26 - 26 * q^28 - 26 * q^30 - 19 * q^32 - 36 * q^34 + 12 * q^35 - 5 * q^36 + 10 * q^38 + 48 * q^40 + 39 * q^42 - 4 * q^43 - 30 * q^44 - 24 * q^45 + 2 * q^46 - 48 * q^48 + 11 * q^50 - 40 * q^51 + q^52 - 62 * q^54 - 14 * q^56 + 2 * q^58 + 18 * q^60 + 36 * q^62 - 20 * q^63 - 11 * q^64 - 32 * q^66 - 4 * q^67 - 62 * q^68 - 37 * q^70 + 13 * q^72 - 44 * q^74 + 48 * q^76 + 20 * q^77 + 10 * q^78 - 32 * q^80 + 64 * q^81 + 50 * q^82 - 45 * q^84 + 2 * q^86 + 40 * q^87 - 66 * q^88 - 74 * q^90 - 24 * q^92 + 26 * q^94 + 84 * q^96 - 20 * q^98 + 20 * q^99

Introduction

L-functions

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