LMFDB - Embedded newform 741.2.d.a.740.73

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [741,2,Mod(740,741)] 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("741.740"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(741, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 741 = 3 \cdot 13 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	741.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.91691478978$
Analytic rank:	$0$
Dimension:	$88$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			740.73
Character	$\chi$	$=$	741.740
Dual form			741.2.d.a.740.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.15821i q^{2} +(-0.966847 - 1.43708i) q^{3} -2.65789 q^{4} -0.857839 q^{5} +(3.10153 - 2.08666i) q^{6} +1.81675i q^{7} -1.41987i q^{8} +(-1.13041 + 2.77888i) q^{9} -1.85140i q^{10} +3.67285 q^{11} +(2.56977 + 3.81961i) q^{12} +(1.36529 - 3.33706i) q^{13} -3.92095 q^{14} +(0.829399 + 1.23279i) q^{15} -2.25140 q^{16} +3.08928i q^{17} +(-5.99742 - 2.43968i) q^{18} +(-4.14735 + 1.34145i) q^{19} +2.28004 q^{20} +(2.61083 - 1.75652i) q^{21} +7.92680i q^{22} +3.67504i q^{23} +(-2.04047 + 1.37280i) q^{24} -4.26411 q^{25} +(7.20210 + 2.94659i) q^{26} +(5.08642 - 1.06225i) q^{27} -4.82874i q^{28} -9.35435 q^{29} +(-2.66062 + 1.79002i) q^{30} -0.267933 q^{31} -7.69874i q^{32} +(-3.55108 - 5.27819i) q^{33} -6.66733 q^{34} -1.55848i q^{35} +(3.00452 - 7.38595i) q^{36} -3.40248 q^{37} +(-2.89513 - 8.95087i) q^{38} +(-6.11566 + 1.26439i) q^{39} +1.21802i q^{40} +9.43096i q^{41} +(3.79096 + 5.63473i) q^{42} -1.50171 q^{43} -9.76203 q^{44} +(0.969713 - 2.38383i) q^{45} -7.93152 q^{46} -10.2072 q^{47} +(2.17676 + 3.23545i) q^{48} +3.69940 q^{49} -9.20287i q^{50} +(4.43955 - 2.98686i) q^{51} +(-3.62879 + 8.86955i) q^{52} -12.0534 q^{53} +(2.29256 + 10.9776i) q^{54} -3.15071 q^{55} +2.57955 q^{56} +(5.93762 + 4.66311i) q^{57} -20.1887i q^{58} -6.46120i q^{59} +(-2.20445 - 3.27661i) q^{60} +7.91653 q^{61} -0.578257i q^{62} +(-5.04854 - 2.05369i) q^{63} +12.1127 q^{64} +(-1.17120 + 2.86266i) q^{65} +(11.3915 - 7.66400i) q^{66} +2.15781 q^{67} -8.21097i q^{68} +(5.28134 - 3.55320i) q^{69} +3.36354 q^{70} +9.01484i q^{71} +(3.94564 + 1.60504i) q^{72} +10.5104i q^{73} -7.34328i q^{74} +(4.12274 + 6.12788i) q^{75} +(11.0232 - 3.56542i) q^{76} +6.67267i q^{77} +(-2.72883 - 13.1989i) q^{78} -8.11738i q^{79} +1.93134 q^{80} +(-6.44433 - 6.28257i) q^{81} -20.3540 q^{82} -3.06269 q^{83} +(-6.93929 + 4.66865i) q^{84} -2.65010i q^{85} -3.24101i q^{86} +(9.04422 + 13.4430i) q^{87} -5.21497i q^{88} +6.17584i q^{89} +(5.14482 + 2.09285i) q^{90} +(6.06262 + 2.48040i) q^{91} -9.76785i q^{92} +(0.259050 + 0.385042i) q^{93} -22.0293i q^{94} +(3.55776 - 1.15075i) q^{95} +(-11.0637 + 7.44350i) q^{96} +19.1257 q^{97} +7.98410i q^{98} +(-4.15184 + 10.2064i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 88 q^{4} - 4 q^{9} + 72 q^{16} + 64 q^{25} - 60 q^{30} - 48 q^{36} + 20 q^{39} + 48 q^{42} - 64 q^{43} - 112 q^{49} - 24 q^{55} - 64 q^{61} - 104 q^{64} + 12 q^{66} + 60 q^{81} + 56 q^{82} - 32 q^{87}+O(q^{100}) $ 88 * q - 88 * q^4 - 4 * q^9 + 72 * q^16 + 64 * q^25 - 60 * q^30 - 48 * q^36 + 20 * q^39 + 48 * q^42 - 64 * q^43 - 112 * q^49 - 24 * q^55 - 64 * q^61 - 104 * q^64 + 12 * q^66 + 60 * q^81 + 56 * q^82 - 32 * q^87

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/741\mathbb{Z}\right)^\times$.

$n$	$40$	$248$	$457$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$			2.15821i			1.52609i	0.646346	+	0.763044i	$0.276296\pi$
$2$			2.15821i			1.52609i	−0.646346	+	0.763044i	$0.723704\pi$
$3$	−0.966847	−	1.43708i	−0.558209	−	0.829700i
$3$	−0.966847	−	1.43708i	−0.558209	−	0.829700i
$4$	−2.65789			−1.32895
$5$	−0.857839			−0.383637			−0.191819	−	0.981430i	$-0.561439\pi$
$5$	−0.857839			−0.383637			−0.191819	+	0.981430i	$0.561439\pi$
$6$	3.10153	−	2.08666i	1.26620	−	0.851877i
$7$			1.81675i			0.686669i	0.939213	+	0.343334i	$0.111556\pi$
$7$			1.81675i			0.686669i	−0.939213	+	0.343334i	$0.888444\pi$
$8$		−	1.41987i		−	0.502000i
$9$	−1.13041	+	2.77888i	−0.376805	+	0.926293i
$10$		−	1.85140i		−	0.585464i
$11$	3.67285			1.10741			0.553703	−	0.832714i	$-0.313214\pi$
$11$	3.67285			1.10741			0.553703	+	0.832714i	$0.313214\pi$
$12$	2.56977	+	3.81961i	0.741830	+	1.10263i
$13$	1.36529	−	3.33706i	0.378663	−	0.925535i
$13$	1.36529	−	3.33706i	0.378663	−	0.925535i
$14$	−3.92095			−1.04792
$15$	0.829399	+	1.23279i	0.214150	+	0.318304i
$16$	−2.25140			−0.562850
$17$			3.08928i			0.749260i	0.927174	+	0.374630i	$0.122230\pi$
$17$			3.08928i			0.749260i	−0.927174	+	0.374630i	$0.877770\pi$
$18$	−5.99742	−	2.43968i	−1.41360	−	0.575037i
$19$	−4.14735	+	1.34145i	−0.951467	+	0.307749i
$19$	−4.14735	+	1.34145i	−0.951467	+	0.307749i
$20$	2.28004			0.509833
$21$	2.61083	−	1.75652i	0.569729	−	0.383305i
$22$			7.92680i			1.69000i
$23$			3.67504i			0.766299i	0.923686	+	0.383149i	$0.125161\pi$
$23$			3.67504i			0.766299i	−0.923686	+	0.383149i	$0.874839\pi$
$24$	−2.04047	+	1.37280i	−0.416509	+	0.280221i
$25$	−4.26411			−0.852822
$26$	7.20210	+	2.94659i	1.41245	+	0.577873i
$27$	5.08642	−	1.06225i	0.978881	−	0.204430i
$28$		−	4.82874i		−	0.912545i
$29$	−9.35435			−1.73706			−0.868529	−	0.495637i	$-0.834934\pi$
$29$	−9.35435			−1.73706			−0.868529	+	0.495637i	$0.834934\pi$
$30$	−2.66062	+	1.79002i	−0.485760	+	0.326812i
$31$	−0.267933			−0.0481222			−0.0240611	−	0.999710i	$-0.507660\pi$
$31$	−0.267933			−0.0481222			−0.0240611	+	0.999710i	$0.507660\pi$
$32$		−	7.69874i		−	1.36096i
$33$	−3.55108	−	5.27819i	−0.618164	−	0.918815i
$34$	−6.66733			−1.14344
$35$		−	1.55848i		−	0.263432i
$36$	3.00452	−	7.38595i	0.500753	−	1.23099i
$37$	−3.40248			−0.559364			−0.279682	−	0.960093i	$-0.590229\pi$
$37$	−3.40248			−0.559364			−0.279682	+	0.960093i	$0.590229\pi$
$38$	−2.89513	−	8.95087i	−0.469653	−	1.45202i
$39$	−6.11566	+	1.26439i	−0.979289	+	0.202465i
$40$			1.21802i			0.192586i
$41$			9.43096i			1.47287i	0.676509	+	0.736434i	$0.263492\pi$
$41$			9.43096i			1.47287i	−0.676509	+	0.736434i	$0.736508\pi$
$42$	3.79096	+	5.63473i	0.584957	+	0.869457i
$43$	−1.50171			−0.229008			−0.114504	−	0.993423i	$-0.536528\pi$
$43$	−1.50171			−0.229008			−0.114504	+	0.993423i	$0.536528\pi$
$44$	−9.76203			−1.47168
$45$	0.969713	−	2.38383i	0.144556	−	0.355360i
$46$	−7.93152			−1.16944
$47$	−10.2072			−1.48887			−0.744435	−	0.667695i	$-0.767281\pi$
$47$	−10.2072			−1.48887			−0.744435	+	0.667695i	$0.767281\pi$
$48$	2.17676	+	3.23545i	0.314188	+	0.466996i
$49$	3.69940			0.528486
$50$		−	9.20287i		−	1.30148i
$51$	4.43955	−	2.98686i	0.621661	−	0.418244i
$52$	−3.62879	+	8.86955i	−0.503223	+	1.22998i
$53$	−12.0534			−1.65566			−0.827830	−	0.560979i	$-0.810425\pi$
$53$	−12.0534			−1.65566			−0.827830	+	0.560979i	$0.810425\pi$
$54$	2.29256	+	10.9776i	0.311978	+	1.49386i
$55$	−3.15071			−0.424842
$56$	2.57955			0.344707
$57$	5.93762	+	4.66311i	0.786458	+	0.617644i
$58$		−	20.1887i		−	2.65091i
$59$		−	6.46120i		−	0.841176i	−0.907252	−	0.420588i	$-0.861824\pi$
$59$		−	6.46120i		−	0.841176i	0.907252	−	0.420588i	$-0.138176\pi$
$60$	−2.20445	−	3.27661i	−0.284593	−	0.423008i
$61$	7.91653			1.01361			0.506804	−	0.862061i	$-0.330827\pi$
$61$	7.91653			1.01361			0.506804	+	0.862061i	$0.330827\pi$
$62$		−	0.578257i		−	0.0734387i
$63$	−5.04854	−	2.05369i	−0.636056	−	0.258740i
$64$	12.1127			1.51409
$65$	−1.17120	+	2.86266i	−0.145269	+	0.355069i
$66$	11.3915	−	7.66400i	1.40219	−	0.943373i
$67$	2.15781			0.263618			0.131809	−	0.991275i	$-0.457921\pi$
$67$	2.15781			0.263618			0.131809	+	0.991275i	$0.457921\pi$
$68$		−	8.21097i		−	0.995726i
$69$	5.28134	−	3.55320i	0.635798	−	0.427755i
$70$	3.36354			0.402020
$71$			9.01484i			1.06986i	0.844895	+	0.534932i	$0.179663\pi$
$71$			9.01484i			1.06986i	−0.844895	+	0.534932i	$0.820337\pi$
$72$	3.94564	+	1.60504i	0.464999	+	0.189156i
$73$			10.5104i			1.23015i	0.788468	+	0.615076i	$0.210875\pi$
$73$			10.5104i			1.23015i	−0.788468	+	0.615076i	$0.789125\pi$
$74$		−	7.34328i		−	0.853639i
$75$	4.12274	+	6.12788i	0.476053	+	0.707587i
$76$	11.0232	−	3.56542i	1.26445	−	0.408982i
$77$			6.67267i			0.760421i
$78$	−2.72883	−	13.1989i	−0.308980	−	1.49448i
$79$		−	8.11738i		−	0.913277i	−0.889652	−	0.456638i	$-0.849053\pi$
$79$		−	8.11738i		−	0.913277i	0.889652	−	0.456638i	$-0.150947\pi$
$80$	1.93134			0.215930
$81$	−6.44433	−	6.28257i	−0.716036	−	0.698063i
$82$	−20.3540			−2.24773
$83$	−3.06269			−0.336174			−0.168087	−	0.985772i	$-0.553759\pi$
$83$	−3.06269			−0.336174			−0.168087	+	0.985772i	$0.553759\pi$
$84$	−6.93929	+	4.66865i	−0.757139	+	0.509391i
$85$		−	2.65010i		−	0.287444i
$86$		−	3.24101i		−	0.349487i
$87$	9.04422	+	13.4430i	0.969642	+	1.44124i
$88$		−	5.21497i		−	0.555917i
$89$			6.17584i			0.654637i	0.944914	+	0.327319i	$0.106145\pi$
$89$			6.17584i			0.654637i	−0.944914	+	0.327319i	$0.893855\pi$
$90$	5.14482	+	2.09285i	0.542311	+	0.220606i
$91$	6.06262	+	2.48040i	0.635536	+	0.260016i
$92$		−	9.76785i		−	1.01837i
$93$	0.259050	+	0.385042i	0.0268622	+	0.0399270i
$94$		−	22.0293i		−	2.27215i
$95$	3.55776	−	1.15075i	0.365018	−	0.118064i
$96$	−11.0637	+	7.44350i	−1.12919	+	0.759699i
$97$	19.1257			1.94192			0.970962	−	0.239232i	$-0.0768956\pi$
$97$	19.1257			1.94192			0.970962	+	0.239232i	$0.0768956\pi$
$98$			7.98410i			0.806516i
$99$	−4.15184	+	10.2064i	−0.417276	+	1.02578i
$100$	11.3335			1.13335
$101$		−	10.8013i		−	1.07477i	−0.843336	−	0.537386i	$-0.819412\pi$
$101$		−	10.8013i		−	1.07477i	0.843336	−	0.537386i	$-0.180588\pi$
$102$	6.44628	+	9.58150i	0.638277	+	0.948710i
$103$			16.6893i			1.64445i	0.569163	+	0.822225i	$0.307267\pi$
$103$			16.6893i			1.64445i	−0.569163	+	0.822225i	$0.692733\pi$
$104$	−4.73819	−	1.93853i	−0.464618	−	0.190089i
$105$	−2.23967	+	1.50681i	−0.218569	+	0.147050i
$106$		−	26.0138i		−	2.52668i
$107$	−8.63674			−0.834945			−0.417473	−	0.908689i	$-0.637084\pi$
$107$	−8.63674			−0.834945			−0.417473	+	0.908689i	$0.637084\pi$
$108$	−13.5191	+	2.82334i	−1.30088	+	0.271676i
$109$	15.6648			1.50042			0.750208	−	0.661202i	$-0.229953\pi$
$109$	15.6648			1.50042			0.750208	+	0.661202i	$0.229953\pi$
$110$		−	6.79991i		−	0.648346i
$111$	3.28968	+	4.88964i	0.312242	+	0.464105i
$112$		−	4.09024i		−	0.386491i
$113$	18.1242			1.70498			0.852491	−	0.522742i	$-0.175091\pi$
$113$	18.1242			1.70498			0.852491	+	0.522742i	$0.175091\pi$
$114$	−10.0640	+	12.8147i	−0.942580	+	1.20020i
$115$		−	3.15259i		−	0.293981i
$116$	24.8628			2.30846
$117$	7.72995	+	7.56624i	0.714634	+	0.699499i
$118$	13.9447			1.28371
$119$	−5.61246			−0.514494
$120$	1.75039	−	1.17764i	0.159788	−	0.107503i
$121$	2.48982			0.226347
$122$			17.0856i			1.54686i
$123$	13.5531	−	9.11829i	1.22204	−	0.822168i
$124$	0.712136			0.0639517
$125$	7.94712			0.710812
$126$	4.43230	−	10.8958i	0.394860	−	0.970678i
$127$			2.77249i			0.246019i	0.992406	+	0.123009i	$0.0392545\pi$
$127$			2.77249i			0.246019i	−0.992406	+	0.123009i	$0.960746\pi$
$128$			10.7444i			0.949680i
$129$	1.45192	+	2.15808i	0.127835	+	0.190008i
$130$	−6.17824	−	2.52770i	−0.541867	−	0.221694i
$131$			3.46241i			0.302512i	0.988495	+	0.151256i	$0.0483318\pi$
$131$			3.46241i			0.302512i	−0.988495	+	0.151256i	$0.951668\pi$
$132$	9.43839	+	14.0288i	0.821506	+	1.22105i
$133$	−2.43708	−	7.53472i	−0.211322	−	0.653343i
$134$			4.65702i			0.402305i
$135$	−4.36333	+	0.911239i	−0.375535	+	0.0784270i
$136$	4.38637			0.376128
$137$	4.30210			0.367554			0.183777	−	0.982968i	$-0.441168\pi$
$137$	4.30210			0.367554			0.183777	+	0.982968i	$0.441168\pi$
$138$	7.66857	+	11.3983i	0.652792	+	0.970284i
$139$	−16.3045			−1.38293			−0.691467	−	0.722408i	$-0.743035\pi$
$139$	−16.3045			−1.38293			−0.691467	+	0.722408i	$0.743035\pi$
$140$			4.14228i			0.350086i
$141$	9.86878	+	14.6686i	0.831101	+	1.23532i
$142$	−19.4560			−1.63271
$143$	5.01450	−	12.2565i	0.419334	−	1.02494i
$144$	2.54501	−	6.25636i	0.212084	−	0.521363i
$145$	8.02452			0.666400
$146$	−22.6837			−1.87732
$147$	−3.57675	−	5.31635i	−0.295006	−	0.438485i
$148$	9.04342			0.743364
$149$	8.58110			0.702991			0.351496	−	0.936190i	$-0.385673\pi$
$149$	8.58110			0.702991			0.351496	+	0.936190i	$0.385673\pi$
$150$	−13.2253	+	8.89777i	−1.07984	+	0.726500i
$151$	−13.6493			−1.11077			−0.555384	−	0.831594i	$-0.687429\pi$
$151$	−13.6493			−1.11077			−0.555384	+	0.831594i	$0.687429\pi$
$152$	1.90468	+	5.88870i	0.154490	+	0.477636i
$153$	−8.58473	−	3.49217i	−0.694034	−	0.282325i
$154$	−14.4010			−1.16047
$155$	0.229843			0.0184615
$156$	16.2548	−	3.36062i	1.30142	−	0.269065i
$157$	−4.36973			−0.348742			−0.174371	−	0.984680i	$-0.555789\pi$
$157$	−4.36973			−0.348742			−0.174371	+	0.984680i	$0.555789\pi$
$158$	17.5190			1.39374
$159$	11.6538	+	17.3217i	0.924205	+	1.37370i
$160$			6.60428i			0.522114i
$161$	−6.67665			−0.526193
$162$	13.5591	−	13.9082i	1.06531	−	1.09273i
$163$			10.8164i			0.847206i	0.905848	+	0.423603i	$0.139235\pi$
$163$			10.8164i			0.847206i	−0.905848	+	0.423603i	$0.860765\pi$
$164$		−	25.0664i		−	1.95736i
$165$	3.04626	+	4.52784i	0.237151	+	0.352491i
$166$		−	6.60995i		−	0.513032i
$167$			11.2698i			0.872083i	0.899927	+	0.436042i	$0.143620\pi$
$167$			11.2698i			0.872083i	−0.899927	+	0.436042i	$0.856380\pi$
$168$	−2.49403	−	3.70703i	−0.192419	−	0.286004i
$169$	−9.27197	−	9.11211i	−0.713228	−	0.700932i
$170$	5.71949			0.438665
$171$	0.960504	−	13.0414i	0.0734516	−	0.997299i
$172$	3.99138			0.304340
$173$	−4.99832			−0.380015			−0.190008	−	0.981783i	$-0.560851\pi$
$173$	−4.99832			−0.380015			−0.190008	+	0.981783i	$0.560851\pi$
$174$	−29.0128	+	19.5194i	−2.19946	+	1.47976i
$175$		−	7.74685i		−	0.585607i
$176$	−8.26905			−0.623303
$177$	−9.28528	+	6.24699i	−0.697924	+	0.469552i
$178$	−13.3288			−0.999034
$179$	−12.0113			−0.897766			−0.448883	−	0.893591i	$-0.648178\pi$
$179$	−12.0113			−0.897766			−0.448883	+	0.893591i	$0.648178\pi$
$180$	−2.57739	+	6.33596i	−0.192107	+	0.472254i
$181$		−	11.5353i		−	0.857413i	−0.903444	−	0.428706i	$-0.858969\pi$
$181$		−	11.5353i		−	0.857413i	0.903444	−	0.428706i	$-0.141031\pi$
$182$	−5.35323	+	13.0844i	−0.396808	+	0.969884i
$183$	−7.65407	−	11.3767i	−0.565805	−	0.840991i
$184$	5.21808			0.384682
$185$	2.91878			0.214593
$186$	−0.831003	+	0.559086i	−0.0609321	+	0.0409942i
$187$			11.3465i			0.829735i
$188$	27.1296			1.97863
$189$	1.92985	+	9.24077i	0.140376	+	0.672167i
$190$	2.48356	+	7.67841i	0.180176	+	0.557050i
$191$		−	6.21912i		−	0.449999i	−0.974359	−	0.225000i	$-0.927762\pi$
$191$		−	6.21912i		−	0.449999i	0.974359	−	0.225000i	$-0.0722381\pi$
$192$	−11.7112	−	17.4070i	−0.845180	−	1.25624i
$193$	−24.2066			−1.74243			−0.871214	−	0.490904i	$-0.836667\pi$
$193$	−24.2066			−1.74243			−0.871214	+	0.490904i	$0.836667\pi$
$194$			41.2775i			2.96355i
$195$	5.24625	−	1.08465i	0.375692	−	0.0776731i
$196$	−9.83261			−0.702329
$197$	8.86090			0.631313			0.315656	−	0.948874i	$-0.397775\pi$
$197$	8.86090			0.631313			0.315656	+	0.948874i	$0.397775\pi$
$198$	−22.0276	−	8.96057i	−1.56543	−	0.636800i
$199$	22.0238			1.56123			0.780613	−	0.625015i	$-0.214907\pi$
$199$	22.0238			1.56123			0.780613	+	0.625015i	$0.214907\pi$
$200$			6.05448i			0.428117i
$201$	−2.08627	−	3.10095i	−0.147154	−	0.218724i
$202$	23.3116			1.64020
$203$		−	16.9946i		−	1.19278i
$204$	−11.7998	+	7.93875i	−0.826154	+	0.555823i
$205$		−	8.09024i		−	0.565047i
$206$	−36.0192			−2.50958
$207$	−10.2125	−	4.15432i	−0.709817	−	0.288745i
$208$	−3.07381	+	7.51306i	−0.213130	+	0.520937i
$209$	−15.2326	+	4.92694i	−1.05366	+	0.340803i
$210$	−3.25203	−	4.83369i	−0.224411	−	0.333556i
$211$		−	9.55622i		−	0.657877i	−0.944351	−	0.328939i	$-0.893309\pi$
$211$		−	9.55622i		−	0.657877i	0.944351	−	0.328939i	$-0.106691\pi$
$212$	32.0366			2.20028
$213$	12.9551	−	8.71597i	0.887667	−	0.597208i
$214$		−	18.6399i		−	1.27420i
$215$	1.28822			0.0878561
$216$	−1.50826	−	7.22205i	−0.102624	−	0.491398i
$217$		−	0.486768i		−	0.0330440i
$218$			33.8080i			2.28977i
$219$	15.1043	−	10.1620i	1.02066	−	0.686682i
$220$	8.37425			0.564592
$221$	10.3091	+	4.21776i	0.693466	+	0.283717i
$222$	−10.5529	+	7.09983i	−0.708264	+	0.476509i
$223$	−8.90623			−0.596405			−0.298203	−	0.954503i	$-0.596387\pi$
$223$	−8.90623			−0.596405			−0.298203	+	0.954503i	$0.596387\pi$
$224$	13.9867			0.934527
$225$	4.82021	−	11.8494i	0.321348	−	0.789963i
$226$			39.1159i			2.60195i
$227$			16.4499i			1.09182i	0.837845	+	0.545909i	$0.183816\pi$
$227$			16.4499i			1.09182i	−0.837845	+	0.545909i	$0.816184\pi$
$228$	−15.7816	−	12.3940i	−1.04516	−	0.820815i
$229$		−	17.2830i		−	1.14209i	−0.820918	−	0.571046i	$-0.806538\pi$
$229$		−	17.2830i		−	1.14209i	0.820918	−	0.571046i	$-0.193462\pi$
$230$	6.80397			0.448640
$231$	9.58917	−	6.45145i	0.630921	−	0.424474i
$232$			13.2820i			0.872003i
$233$			8.74673i			0.573017i	0.958078	+	0.286509i	$0.0924947\pi$
$233$			8.74673i			0.573017i	−0.958078	+	0.286509i	$0.907505\pi$
$234$	−16.3296	+	16.6829i	−1.06750	+	1.09059i
$235$	8.75612			0.571186
$236$			17.1732i			1.11788i
$237$	−11.6653	+	7.84826i	−0.757746	+	0.509799i
$238$		−	12.1129i		−	0.785163i
$239$	1.12075			0.0724955			0.0362478	−	0.999343i	$-0.488459\pi$
$239$	1.12075			0.0724955			0.0362478	+	0.999343i	$0.488459\pi$
$240$	−1.86731	−	2.77549i	−0.120534	−	0.179157i
$241$	18.9514			1.22076			0.610382	−	0.792107i	$-0.291016\pi$
$241$	18.9514			1.22076			0.610382	+	0.792107i	$0.291016\pi$
$242$			5.37357i			0.345426i
$243$	−2.79789	+	15.3353i	−0.179485	+	0.983761i
$244$	−21.0413			−1.34703
$245$	−3.17349			−0.202747
$246$	19.6792	+	29.2504i	1.25470	+	1.86494i
$247$	−1.18584	+	15.6714i	−0.0754530	+	0.997149i
$248$			0.380430i			0.0241573i
$249$	2.96116	+	4.40135i	0.187656	+	0.278924i
$250$			17.1516i			1.08476i
$251$		−	8.04287i		−	0.507661i	−0.967249	−	0.253831i	$-0.918309\pi$
$251$		−	8.04287i		−	0.507661i	0.967249	−	0.253831i	$-0.0816906\pi$
$252$	13.4185	+	5.45847i	0.845284	+	0.343851i
$253$			13.4979i			0.848603i
$254$	−5.98363			−0.375446
$255$	−3.80842	+	2.56224i	−0.238492	+	0.160454i
$256$	1.03674			0.0647961
$257$	6.77157			0.422399			0.211199	−	0.977443i	$-0.432263\pi$
$257$	6.77157			0.422399			0.211199	+	0.977443i	$0.432263\pi$
$258$	−4.65760	+	3.13356i	−0.289969	+	0.195087i
$259$		−	6.18147i		−	0.384098i
$260$	3.11292	−	7.60864i	0.193055	−	0.471868i
$261$	10.5743	−	25.9946i	0.654532	−	1.60903i
$262$	−7.47262			−0.461660
$263$		−	28.4700i		−	1.75553i	−0.479087	−	0.877767i	$-0.659032\pi$
$263$		−	28.4700i		−	1.75553i	0.479087	−	0.877767i	$-0.340968\pi$
$264$	−7.49434	+	5.04207i	−0.461245	+	0.310318i
$265$	10.3399			0.635173
$266$	16.2615	−	5.25975i	0.997059	−	0.322496i
$267$	8.87519	−	5.97109i	0.543153	−	0.365425i
$268$	−5.73522			−0.350334
$269$	16.7218			1.01955			0.509773	−	0.860309i	$-0.329730\pi$
$269$	16.7218			1.01955			0.509773	+	0.860309i	$0.329730\pi$
$270$	−1.96665	−	9.41699i	−0.119687	−	0.573100i
$271$			18.0043i			1.09368i	0.837237	+	0.546840i	$0.184170\pi$
$271$			18.0043i			1.09368i	−0.837237	+	0.546840i	$0.815830\pi$
$272$		−	6.95520i		−	0.421721i
$273$	−2.29709	−	11.1107i	−0.139026	−	0.672448i
$274$			9.28486i			0.560919i
$275$	−15.6614			−0.944420
$276$	−14.0372	+	9.44402i	−0.844941	+	0.568463i
$277$	26.1355			1.57033			0.785164	−	0.619288i	$-0.212579\pi$
$277$	26.1355			1.57033			0.785164	+	0.619288i	$0.212579\pi$
$278$		−	35.1887i		−	2.11048i
$279$	0.302875	−	0.744553i	0.0181327	−	0.0445752i
$280$	−2.21284			−0.132243
$281$			13.1761i			0.786020i	0.919534	+	0.393010i	$0.128566\pi$
$281$			13.1761i			0.786020i	−0.919534	+	0.393010i	$0.871434\pi$
$282$	−31.6579	+	21.2990i	−1.88520	+	1.26833i
$283$	13.7919			0.819846			0.409923	−	0.912120i	$-0.365556\pi$
$283$	13.7919			0.819846			0.409923	+	0.912120i	$0.365556\pi$
$284$		−	23.9605i		−	1.42179i
$285$	−5.09353	−	4.00020i	−0.301714	−	0.236951i
$286$	26.4522	+	10.8224i	1.56415	+	0.639940i
$287$	−17.1337			−1.01137
$288$	21.3939	+	8.70277i	1.26065	+	0.512815i
$289$	7.45636			0.438609
$290$			17.3186i			1.01699i
$291$	−18.4917	−	27.4853i	−1.08400	−	1.61122i
$292$		−	27.9355i		−	1.63480i
$293$			16.3002i			0.952270i	0.879372	+	0.476135i	$0.157963\pi$
$293$			16.3002i			0.952270i	−0.879372	+	0.476135i	$0.842037\pi$
$294$	11.4738	−	7.71940i	0.669167	−	0.450205i
$295$			5.54267i			0.322707i
$296$			4.83108i			0.280801i
$297$	18.6816	−	3.90148i	1.08402	−	0.226387i
$298$			18.5199i			1.07283i
$299$	12.2638	+	5.01749i	0.709236	+	0.290169i
$300$	−10.9578	−	16.2872i	−0.632649	−	0.940344i
$301$		−	2.72824i		−	0.157253i
$302$		−	29.4582i		−	1.69513i
$303$	−15.5224	+	10.4432i	−0.891738	+	0.599948i
$304$	9.33734	−	3.02013i	0.535533	−	0.173217i
$305$	−6.79111			−0.388858
$306$	7.53684	−	18.5277i	0.430853	−	1.05916i
$307$	−1.88021			−0.107309			−0.0536546	−	0.998560i	$-0.517087\pi$
$307$	−1.88021			−0.107309			−0.0536546	+	0.998560i	$0.517087\pi$
$308$		−	17.7352i		−	1.01056i
$309$	23.9840	−	16.1360i	1.36440	−	0.917947i
$310$			0.496051i			0.0281738i
$311$		−	9.88672i		−	0.560624i	−0.959909	−	0.280312i	$-0.909562\pi$
$311$		−	9.88672i		−	0.560624i	0.959909	−	0.280312i	$-0.0904380\pi$
$312$	1.79527	+	8.68344i	0.101637	+	0.491603i
$313$	−9.06669			−0.512480			−0.256240	−	0.966613i	$-0.582484\pi$
$313$	−9.06669			−0.512480			−0.256240	+	0.966613i	$0.582484\pi$
$314$		−	9.43081i		−	0.532211i
$315$	4.33083	+	1.76173i	0.244015	+	0.0992623i
$316$			21.5751i			1.21369i
$317$			12.3078i			0.691277i	0.938368	+	0.345638i	$0.112338\pi$
$317$			12.3078i			0.691277i	−0.938368	+	0.345638i	$0.887662\pi$
$318$	−37.3840	+	25.1514i	−2.09639	+	1.41042i
$319$	−34.3571			−1.92363
$320$	−10.3908			−0.580862
$321$	8.35041	+	12.4117i	0.466074	+	0.692754i
$322$		−	14.4096i		−	0.803018i
$323$	−4.14411	−	12.8123i	−0.230584	−	0.712897i
$324$	17.1283	+	16.6984i	0.951573	+	0.927688i
$325$	−5.82175	+	14.2296i	−0.322932	+	0.789317i
$326$	−23.3441			−1.29291
$327$	−15.1455	−	22.5116i	−0.837546	−	1.24490i
$328$	13.3907			0.739379
$329$		−	18.5439i		−	1.02236i
$330$	−9.77204	+	6.57448i	−0.537933	+	0.361913i
$331$	−0.996948			−0.0547972			−0.0273986	−	0.999625i	$-0.508722\pi$
$331$	−0.996948			−0.0547972			−0.0273986	+	0.999625i	$0.508722\pi$
$332$	8.14031			0.446757
$333$	3.84621	−	9.45507i	0.210771	−	0.518135i
$334$	−24.3226			−1.33088
$335$	−1.85105			−0.101134
$336$	−5.87801	+	3.95463i	−0.320672	+	0.215743i
$337$			7.23122i			0.393910i	0.980413	+	0.196955i	$0.0631052\pi$
$337$			7.23122i			0.393910i	−0.980413	+	0.196955i	$0.936895\pi$
$338$	19.6659	−	20.0109i	1.06968	−	1.08845i
$339$	−17.5233	−	26.0460i	−0.951737	−	1.41462i
$340$			7.04369i			0.381997i
$341$	−0.984077			−0.0532908
$342$	28.1461	+	2.07297i	1.52197	+	0.112094i
$343$			19.4382i			1.04956i
$344$			2.13223i			0.114962i
$345$	−4.53054	+	3.04807i	−0.243916	+	0.164103i
$346$		−	10.7875i		−	0.579937i
$347$			5.57916i			0.299505i	0.988724	+	0.149752i	$0.0478477\pi$
$347$			5.57916i			0.299505i	−0.988724	+	0.149752i	$0.952152\pi$
$348$	−24.0386	−	35.7300i	−1.28860	−	1.91533i
$349$			20.1829i			1.08037i	0.841548	+	0.540183i	$0.181645\pi$
$349$			20.1829i			1.08037i	−0.841548	+	0.540183i	$0.818355\pi$
$350$	16.7194			0.893687
$351$	3.39963	−	18.4240i	0.181459	−	0.983398i
$352$		−	28.2763i		−	1.50713i
$353$	15.6090			0.830781			0.415390	−	0.909643i	$-0.363645\pi$
$353$	15.6090			0.830781			0.415390	+	0.909643i	$0.363645\pi$
$354$	−13.4823	−	20.0396i	−0.716578	−	1.06509i
$355$		−	7.73328i		−	0.410440i
$356$		−	16.4147i		−	0.869977i
$357$	5.42639	+	8.06557i	0.287195	+	0.426875i
$358$		−	25.9229i		−	1.37007i
$359$	16.3148			0.861060			0.430530	−	0.902576i	$-0.358327\pi$
$359$	16.3148			0.861060			0.430530	+	0.902576i	$0.358327\pi$
$360$	−3.38473	−	1.37687i	−0.178391	−	0.0725672i
$361$	15.4010	−	11.1269i	0.810581	−	0.585627i
$362$	24.8957			1.30849
$363$	−2.40727	−	3.57808i	−0.126349	−	0.187800i
$364$	−16.1138	−	6.59262i	−0.844592	−	0.345547i
$365$		−	9.01624i		−	0.471932i
$366$	24.5534	−	16.5191i	1.28343	−	0.863469i
$367$	9.03812			0.471786			0.235893	−	0.971779i	$-0.424198\pi$
$367$	9.03812			0.471786			0.235893	+	0.971779i	$0.424198\pi$
$368$		−	8.27398i		−	0.431311i
$369$	−26.2075	−	10.6609i	−1.36431	−	0.554984i
$370$			6.29935i			0.327488i
$371$		−	21.8981i		−	1.13689i
$372$	−0.688527	−	1.02340i	−0.0356985	−	0.0530608i
$373$			24.9763i			1.29322i	0.762819	+	0.646612i	$0.223815\pi$
$373$			24.9763i			1.29322i	−0.762819	+	0.646612i	$0.776185\pi$
$374$	−24.4881			−1.26625
$375$	−7.68364	−	11.4207i	−0.396782	−	0.589761i
$376$			14.4929i			0.747413i
$377$	−12.7714	+	31.2160i	−0.657760	+	1.60771i
$378$	−19.9436	+	4.16503i	−1.02579	+	0.214226i
$379$	−27.6507			−1.42032			−0.710161	−	0.704039i	$-0.751378\pi$
$379$	−27.6507			−1.42032			−0.710161	+	0.704039i	$0.751378\pi$
$380$	−9.45613	+	3.05856i	−0.485089	+	0.156901i
$381$	3.98430	−	2.68057i	0.204122	−	0.137330i
$382$	13.4222			0.686739
$383$		−	8.36436i		−	0.427399i	−0.976899	−	0.213700i	$-0.931449\pi$
$383$		−	8.36436i		−	0.427399i	0.976899	−	0.213700i	$-0.0685513\pi$
$384$	15.4406	−	10.3882i	0.787950	−	0.530120i
$385$		−	5.72407i		−	0.291726i
$386$		−	52.2430i		−	2.65910i
$387$	1.69755	−	4.17306i	0.0862914	−	0.212129i
$388$	−50.8341			−2.58071
$389$		−	19.5268i		−	0.990049i	−0.868879	−	0.495025i	$-0.835159\pi$
$389$		−	19.5268i		−	0.990049i	0.868879	−	0.495025i	$-0.164841\pi$
$390$	2.34090	+	11.3225i	0.118536	+	0.573339i
$391$	−11.3532			−0.574157
$392$		−	5.25267i		−	0.265300i
$393$	4.97577	−	3.34762i	0.250994	−	0.168865i
$394$			19.1237i			0.963439i
$395$			6.96340i			0.350367i
$396$	11.0351	−	27.1275i	0.554537	−	1.36321i
$397$		−	30.8413i		−	1.54788i	−0.633257	−	0.773941i	$-0.718282\pi$
$397$		−	30.8413i		−	1.54788i	0.633257	−	0.773941i	$-0.281718\pi$
$398$			47.5321i			2.38257i
$399$	−8.47173	+	10.7872i	−0.424117	+	0.540036i
$400$	9.60022			0.480011
$401$		−	2.05184i		−	0.102464i	−0.998687	−	0.0512320i	$-0.983685\pi$
$401$		−	2.05184i		−	0.102464i	0.998687	−	0.0512320i	$-0.0163148\pi$
$402$	6.69252	−	4.50262i	0.333792	−	0.224570i
$403$	−0.365806	+	0.894109i	−0.0182221	+	0.0445387i
$404$			28.7087i			1.42831i
$405$	5.52819	+	5.38943i	0.274698	+	0.267803i
$406$	36.6779			1.82029
$407$	−12.4968			−0.619443
$408$	−4.24095	−	6.30358i	−0.209958	−	0.312074i
$409$	24.9857			1.23546			0.617732	−	0.786388i	$-0.288051\pi$
$409$	24.9857			1.23546			0.617732	+	0.786388i	$0.288051\pi$
$410$	17.4605			0.862311
$411$	−4.15948	−	6.18248i	−0.205172	−	0.304959i
$412$		−	44.3584i		−	2.18538i
$413$	11.7384			0.577610
$414$	8.96591	−	22.0407i	0.440650	−	1.08324i
$415$	2.62730			0.128969
$416$	−25.6912	−	10.5110i	−1.25961	−	0.515345i
$417$	15.7640	+	23.4310i	0.771966	+	1.14742i
$418$	−10.6334	−	32.8752i	−0.520096	−	1.60798i
$419$		−	12.7988i		−	0.625261i	−0.949875	−	0.312630i	$-0.898790\pi$
$419$		−	12.7988i		−	0.625261i	0.949875	−	0.312630i	$-0.101210\pi$
$420$	5.95280	−	4.00495i	0.290467	−	0.195421i
$421$	2.56762			0.125138			0.0625692	−	0.998041i	$-0.480071\pi$
$421$	2.56762			0.125138			0.0625692	+	0.998041i	$0.480071\pi$
$422$	20.6244			1.00398
$423$	11.5383	−	28.3645i	0.561014	−	1.37913i
$424$			17.1142i			0.831141i
$425$		−	13.1730i		−	0.638986i
$426$	18.8109	+	27.9598i	0.911393	+	1.35466i
$427$			14.3824i			0.696013i
$428$	22.9555			1.10960
$429$	−22.4619	+	4.64393i	−1.08447	+	0.224211i
$430$			2.78026i			0.134076i
$431$		−	14.5986i		−	0.703188i	−0.936153	−	0.351594i	$-0.885640\pi$
$431$		−	14.5986i		−	0.703188i	0.936153	−	0.351594i	$-0.114360\pi$
$432$	−11.4515	+	2.39155i	−0.550963	+	0.115063i
$433$			10.7949i			0.518769i	0.965774	+	0.259384i	$0.0835197\pi$
$433$			10.7949i			0.518769i	−0.965774	+	0.259384i	$0.916480\pi$
$434$	1.05055			0.0504281
$435$	−7.75849	−	11.5319i	−0.371991	−	0.552913i
$436$	−41.6353			−1.99397
$437$	−4.92987	−	15.2417i	−0.235828	−	0.729108i
$438$	21.9317	+	32.5984i	1.04794	+	1.55761i
$439$			34.9387i			1.66753i	0.552119	+	0.833765i	$0.313819\pi$
$439$			34.9387i			1.66753i	−0.552119	+	0.833765i	$0.686181\pi$
$440$			4.47360i			0.213271i
$441$	−4.18186	+	10.2802i	−0.199136	+	0.489533i
$442$	−9.10283	+	22.2493i	−0.432978	+	1.05829i
$443$			40.3072i			1.91505i	0.288344	+	0.957527i	$0.406895\pi$
$443$			40.3072i			1.91505i	−0.288344	+	0.957527i	$0.593105\pi$
$444$	−8.74360	−	12.9961i	−0.414953	−	0.616770i
$445$		−	5.29787i		−	0.251143i
$446$		−	19.2216i		−	0.910167i
$447$	−8.29661	−	12.3318i	−0.392416	−	0.583272i
$448$			22.0059i			1.03968i
$449$		−	16.7190i		−	0.789018i	−0.918892	−	0.394509i	$-0.870915\pi$
$449$		−	16.7190i		−	0.789018i	0.918892	−	0.394509i	$-0.129085\pi$
$450$	25.5737	+	10.4031i	1.20555	+	0.490405i
$451$			34.6385i			1.63106i
$452$	−48.1722			−2.26583
$453$	13.1968	+	19.6152i	0.620041	+	0.921605i
$454$	−35.5024			−1.66621
$455$	−5.20075	−	2.12778i	−0.243815	−	0.0997519i
$456$	6.62101	−	8.43065i	0.310057	−	0.394801i
$457$			29.4340i			1.37687i	0.725300	+	0.688433i	$0.241701\pi$
$457$			29.4340i			1.37687i	−0.725300	+	0.688433i	$0.758299\pi$
$458$	37.3004			1.74293
$459$	3.28159	+	15.7134i	0.153171	+	0.733437i
$460$			8.37924i			0.390684i
$461$	−13.4731			−0.627503			−0.313752	−	0.949505i	$-0.601586\pi$
$461$	−13.4731			−0.627503			−0.313752	+	0.949505i	$0.601586\pi$
$462$	13.9236	+	20.6955i	0.647785	+	0.962842i
$463$		−	19.8337i		−	0.921748i	−0.887465	−	0.460874i	$-0.847536\pi$
$463$		−	19.8337i		−	0.921748i	0.887465	−	0.460874i	$-0.152464\pi$
$464$	21.0604			0.977703
$465$	−0.222223	−	0.330304i	−0.0103054	−	0.0153175i
$466$	−18.8773			−0.874475
$467$			16.6061i			0.768439i	0.923242	+	0.384220i	$0.125529\pi$
$467$			16.6061i			0.768439i	−0.923242	+	0.384220i	$0.874471\pi$
$468$	−20.5454	−	20.1102i	−0.949709	−	0.929596i
$469$			3.92021i			0.181018i
$470$			18.8976i			0.871681i
$471$	4.22486	+	6.27966i	0.194671	+	0.289351i
$472$	−9.17406			−0.422270
$473$	−5.51555			−0.253605
$474$	−16.9382	−	25.1763i	−0.777999	−	1.15639i
$475$	17.6848	−	5.72009i	0.811433	−	0.262456i
$476$	14.9173			0.683734
$477$	13.6253	−	33.4949i	0.623861	−	1.53363i
$478$			2.41883i			0.110635i
$479$	−39.7954			−1.81830			−0.909148	−	0.416473i	$-0.863266\pi$
$479$	−39.7954			−1.81830			−0.909148	+	0.416473i	$0.863266\pi$
$480$	9.49090	−	6.38533i	0.433198	−	0.291449i
$481$	−4.64537	+	11.3543i	−0.211811	+	0.517711i
$482$			40.9011i			1.86299i
$483$	6.45529	+	9.59489i	0.293726	+	0.436583i
$484$	−6.61767			−0.300803
$485$	−16.4068			−0.744995
$486$	−33.0969	−	6.03846i	−1.50131	−	0.273910i
$487$	−15.8530			−0.718367			−0.359184	−	0.933267i	$-0.616945\pi$
$487$	−15.8530			−0.718367			−0.359184	+	0.933267i	$0.616945\pi$
$488$		−	11.2404i		−	0.508831i
$489$	15.5441	−	10.4578i	0.702927	−	0.472918i
$490$		−	6.84907i		−	0.309410i
$491$		−	4.80604i		−	0.216894i	−0.994102	−	0.108447i	$-0.965412\pi$
$491$		−	4.80604i		−	0.216894i	0.994102	−	0.108447i	$-0.0345877\pi$
$492$	−36.0226	+	24.2354i	−1.62402	+	1.09262i
$493$		−	28.8982i		−	1.30151i
$494$	−33.8223	−	2.55929i	−1.52174	−	0.115148i
$495$	3.56161	−	8.75545i	0.160083	−	0.393528i
$496$	0.603224			0.0270856
$497$	−16.3778			−0.734643
$498$	−9.49905	+	6.39081i	−0.425663	+	0.286379i
$499$		−	37.4295i		−	1.67558i	−0.545996	−	0.837788i	$-0.683849\pi$
$499$		−	37.4295i		−	1.67558i	0.545996	−	0.837788i	$-0.316151\pi$
$500$	−21.1226			−0.944630
$501$	16.1956	−	10.8962i	0.723568	−	0.486805i
$502$	17.3582			0.774736
$503$			3.96345i			0.176721i	0.996089	+	0.0883607i	$0.0281628\pi$
$503$			3.96345i			0.176721i	−0.996089	+	0.0883607i	$0.971837\pi$
$504$	−2.91597	+	7.16827i	−0.129887	+	0.319300i
$505$			9.26579i			0.412322i
$506$	−29.1313			−1.29504
$507$	−4.13028	+	22.1346i	−0.183432	+	0.983032i
$508$		−	7.36897i		−	0.326945i
$509$			14.4113i			0.638770i	0.947625	+	0.319385i	$0.103476\pi$
$509$			14.4113i			0.638770i	−0.947625	+	0.319385i	$0.896524\pi$
$510$	−5.52987	−	8.21938i	−0.244867	−	0.363960i
$511$	−19.0949			−0.844707
$512$			23.7263i			1.04856i
$513$	−19.6702	+	11.2287i	−0.868460	+	0.495759i
$514$			14.6145i			0.644618i
$515$		−	14.3168i		−	0.630872i
$516$	−3.85905	−	5.73594i	−0.169885	−	0.252511i
$517$	−37.4894			−1.64878
$518$	13.3409			0.586167
$519$	4.83261	+	7.18300i	0.212128	+	0.315299i
$520$	4.06461	+	1.66295i	0.178245	+	0.0729251i
$521$	−2.11238			−0.0925449			−0.0462725	−	0.998929i	$-0.514734\pi$
$521$	−2.11238			−0.0925449			−0.0462725	+	0.998929i	$0.514734\pi$
$522$	56.1019	+	22.8216i	2.45551	+	0.998874i
$523$		−	8.40511i		−	0.367530i	−0.982970	−	0.183765i	$-0.941172\pi$
$523$		−	8.40511i		−	0.367530i	0.982970	−	0.183765i	$-0.0588285\pi$
$524$		−	9.20271i		−	0.402022i
$525$	−11.1329	+	7.49001i	−0.485878	+	0.326891i
$526$	61.4443			2.67910
$527$		−	0.827720i		−	0.0360560i
$528$	7.99490	+	11.8833i	0.347933	+	0.517154i
$529$	9.49409			0.412786
$530$			22.3157i			0.969330i
$531$	17.9549	+	7.30383i	0.779176	+	0.316959i
$532$	6.47750	+	20.0265i	0.280835	+	0.868257i
$533$	31.4717	+	12.8760i	1.36319	+	0.557721i
$534$	12.8869	+	19.1546i	0.557670	+	0.828899i
$535$	7.40893			0.320316
$536$		−	3.06381i		−	0.132336i
$537$	11.6131	+	17.2612i	0.501141	+	0.744877i
$538$			36.0892i			1.55592i
$539$	13.5873			0.585248
$540$	11.5972	−	2.42197i	0.499066	−	0.104225i
$541$			2.64466i			0.113703i	0.998383	+	0.0568515i	$0.0181061\pi$
$541$			2.64466i			0.113703i	−0.998383	+	0.0568515i	$0.981894\pi$
$542$	−38.8571			−1.66905
$543$	−16.5772	+	11.1529i	−0.711396	+	0.478616i
$544$	23.7836			1.01971
$545$	−13.4379			−0.575615
$546$	23.9792	−	4.95762i	1.02621	−	0.212167i
$547$		−	4.78305i		−	0.204508i	−0.994758	−	0.102254i	$-0.967394\pi$
$547$		−	4.78305i		−	0.204508i	0.994758	−	0.102254i	$-0.0326055\pi$
$548$	−11.4345			−0.488459
$549$	−8.94896	+	21.9991i	−0.381932	+	0.938898i
$550$		−	33.8008i		−	1.44127i
$551$	38.7958	−	12.5484i	1.65276	−	0.534579i
$552$	−5.04508	−	7.49881i	−0.214733	−	0.319170i
$553$	14.7473			0.627119
$554$			56.4059i			2.39646i
$555$	−2.82201	−	4.19453i	−0.119788	−	0.178048i
$556$	43.3357			1.83784
$557$	−9.41694			−0.399009			−0.199504	−	0.979897i	$-0.563933\pi$
$557$	−9.41694			−0.399009			−0.199504	+	0.979897i	$0.563933\pi$
$558$	1.60691	+	0.653670i	0.0680257	+	0.0276721i
$559$	−2.05027	+	5.01129i	−0.0867170	+	0.211955i
$560$			3.50877i			0.148272i
$561$	16.3058	−	10.9703i	0.688431	−	0.463166i
$562$	−28.4368			−1.19954
$563$	5.62182			0.236932			0.118466	−	0.992958i	$-0.462202\pi$
$563$	5.62182			0.236932			0.118466	+	0.992958i	$0.462202\pi$
$564$	−26.2301	−	38.9875i	−1.10449	−	1.64167i
$565$	−15.5477			−0.654095
$566$			29.7660i			1.25116i
$567$	11.4139	−	11.7078i	0.479338	−	0.491680i
$568$	12.7999			0.537072
$569$	9.26480			0.388401			0.194200	−	0.980962i	$-0.437789\pi$
$569$	9.26480			0.388401			0.194200	+	0.980962i	$0.437789\pi$
$570$	8.63329	−	10.9929i	0.361609	−	0.460443i
$571$	10.6847			0.447140			0.223570	−	0.974688i	$-0.428229\pi$
$571$	10.6847			0.447140			0.223570	+	0.974688i	$0.428229\pi$
$572$	−13.3280	+	32.5765i	−0.557272	+	1.36209i
$573$	−8.93739	+	6.01293i	−0.373365	+	0.251194i
$574$		−	36.9783i		−	1.54344i
$575$		−	15.6708i		−	0.653517i
$576$	−13.6924	+	33.6598i	−0.570517	+	1.40249i
$577$			11.3439i			0.472252i	0.971722	+	0.236126i	$0.0758778\pi$
$577$			11.3439i			0.472252i	−0.971722	+	0.236126i	$0.924122\pi$
$578$			16.0924i			0.669356i
$579$	23.4041	+	34.7869i	0.972639	+	1.44569i
$580$	−21.3283			−0.885610
$581$		−	5.56417i		−	0.230840i
$582$	59.3191	−	39.9090i	2.45886	−	1.65428i
$583$	−44.2703			−1.83349
$584$	14.9234			0.617535
$585$	−6.63105	−	6.49061i	−0.274160	−	0.268354i
$586$	−35.1794			−1.45325
$587$	8.07861			0.333440			0.166720	−	0.986004i	$-0.446682\pi$
$587$	8.07861			0.333440			0.166720	+	0.986004i	$0.446682\pi$
$588$	9.50662	+	14.1303i	0.392047	+	0.582722i
$589$	1.11121	−	0.359418i	0.0457867	−	0.0148096i
$590$	−11.9623			−0.492479
$591$	−8.56713	−	12.7338i	−0.352405	−	0.523800i
$592$	7.66034			0.314838
$593$	−15.8318			−0.650133			−0.325066	−	0.945691i	$-0.605387\pi$
$593$	−15.8318			−0.650133			−0.325066	+	0.945691i	$0.605387\pi$
$594$	8.42024	+	40.3190i	0.345487	+	1.65431i
$595$	4.81459			0.197379
$596$	−22.8076			−0.934237
$597$	−21.2936	−	31.6500i	−0.871491	−	1.29535i
$598$	−10.8288	+	26.4680i	−0.442824	+	1.08236i
$599$	−17.6984			−0.723138			−0.361569	−	0.932345i	$-0.617759\pi$
$599$	−17.6984			−0.723138			−0.361569	+	0.932345i	$0.617759\pi$
$600$	8.70079	−	5.85376i	0.355208	−	0.238979i
$601$		−	2.15360i		−	0.0878473i	−0.999035	−	0.0439236i	$-0.986014\pi$
$601$		−	2.15360i		−	0.0878473i	0.999035	−	0.0439236i	$-0.0139858\pi$
$602$	5.88812			0.239982
$603$	−2.43922	+	5.99629i	−0.0993327	+	0.244188i
$604$	36.2785			1.47615
$605$	−2.13586			−0.0868352
$606$	−22.5387	−	33.5007i	−0.915573	−	1.36087i
$607$		−	27.2405i		−	1.10566i	−0.833294	−	0.552829i	$-0.813548\pi$
$607$		−	27.2405i		−	1.10566i	0.833294	−	0.552829i	$-0.186452\pi$
$608$	10.3275	+	31.9294i	0.418834	+	1.29491i
$609$	−24.4226	+	16.4311i	−0.989653	+	0.665823i
$610$		−	14.6567i		−	0.593431i
$611$	−13.9358	+	34.0620i	−0.563780	+	1.37800i
$612$	22.8173	+	9.28179i	0.922334	+	0.375194i
$613$		−	13.7766i		−	0.556432i	−0.960519	−	0.278216i	$-0.910257\pi$
$613$		−	13.7766i		−	0.556432i	0.960519	−	0.278216i	$-0.0897431\pi$
$614$		−	4.05789i		−	0.163763i
$615$	−11.6263	+	7.82202i	−0.468820	+	0.315414i
$616$	9.47431			0.381731
$617$	−41.3065			−1.66294			−0.831469	−	0.555571i	$-0.812500\pi$
$617$	−41.3065			−1.66294			−0.831469	+	0.555571i	$0.812500\pi$
$618$	34.8250	+	51.7626i	1.40087	+	2.08220i
$619$			34.8380i			1.40026i	0.714017	+	0.700129i	$0.246874\pi$
$619$			34.8380i			1.40026i	−0.714017	+	0.700129i	$0.753126\pi$
$620$	−0.610898			−0.0245343
$621$	3.90381	+	18.6928i	0.156655	+	0.750115i
$622$	21.3377			0.855562
$623$	−11.2200			−0.449519
$624$	13.7688	−	2.84665i	0.551193	−	0.113957i
$625$	14.5032			0.580129
$626$		−	19.5679i		−	0.782089i
$627$	21.8080	+	17.1269i	0.870928	+	0.683983i
$628$	11.6143			0.463459
$629$		−	10.5112i		−	0.419109i
$630$	−3.80220	+	9.34687i	−0.151483	+	0.372388i
$631$		−	8.39841i		−	0.334335i	−0.985928	−	0.167168i	$-0.946538\pi$
$631$		−	8.39841i		−	0.334335i	0.985928	−	0.167168i	$-0.0534621\pi$
$632$	−11.5256			−0.458464
$633$	−13.7331	+	9.23940i	−0.545841	+	0.367233i
$634$	−26.5629			−1.05495
$635$		−	2.37835i		−	0.0943819i
$636$	−30.9745	−	46.0392i	−1.22822	−	1.82557i
$637$	5.05075	−	12.3451i	0.200118	−	0.489132i
$638$		−	74.1500i		−	2.93563i
$639$	−25.0511	−	10.1905i	−0.991008	−	0.403130i
$640$		−	9.21697i		−	0.364333i
$641$	−20.7795			−0.820742			−0.410371	−	0.911919i	$-0.634601\pi$
$641$	−20.7795			−0.820742			−0.410371	+	0.911919i	$0.634601\pi$
$642$	−26.7871	+	18.0220i	−1.05720	+	0.711271i
$643$			27.1734i			1.07161i	0.844340	+	0.535807i	$0.179993\pi$
$643$			27.1734i			1.07161i	−0.844340	+	0.535807i	$0.820007\pi$
$644$	17.7458			0.699282
$645$	−1.24551	−	1.85128i	−0.0490421	−	0.0728942i
$646$	27.6517	−	8.94387i	1.08794	−	0.351892i
$647$			5.74840i			0.225993i	0.993595	+	0.112996i	$0.0360448\pi$
$647$			5.74840i			0.225993i	−0.993595	+	0.112996i	$0.963955\pi$
$648$	−8.92043	+	9.15010i	−0.350427	+	0.359450i
$649$		−	23.7310i		−	0.931523i
$650$	−30.7106	−	12.5646i	−1.20457	−	0.492823i
$651$	−0.699527	+	0.470631i	−0.0274166	+	0.0184455i
$652$		−	28.7488i		−	1.12589i
$653$			40.3384i			1.57856i	0.614031	+	0.789282i	$0.289547\pi$
$653$			40.3384i			1.57856i	−0.614031	+	0.789282i	$0.710453\pi$
$654$	48.5849	−	32.6872i	1.89982	−	1.27817i
$655$		−	2.97019i		−	0.116055i
$656$		−	21.2328i		−	0.829003i
$657$	−29.2072	−	11.8811i	−1.13948	−	0.463527i
$658$	40.0218			1.56021
$659$	21.2889			0.829299			0.414649	−	0.909981i	$-0.363904\pi$
$659$	21.2889			0.829299			0.414649	+	0.909981i	$0.363904\pi$
$660$	−8.09662	−	12.0345i	−0.315160	−	0.468442i
$661$	−3.67929			−0.143108			−0.0715539	−	0.997437i	$-0.522796\pi$
$661$	−3.67929			−0.143108			−0.0715539	+	0.997437i	$0.522796\pi$
$662$		−	2.15163i		−	0.0836254i
$663$	−3.90607	−	18.8930i	−0.151699	−	0.733743i
$664$			4.34863i			0.168759i
$665$	2.09062	+	6.46358i	0.0810709	+	0.250647i
$666$	20.4061	+	8.30095i	0.790720	+	0.321655i
$667$		−	34.3776i		−	1.33111i
$668$		−	29.9539i		−	1.15895i
$669$	8.61096	+	12.7990i	0.332919	+	0.494838i
$670$		−	3.99497i		−	0.154339i
$671$	29.0762			1.12248
$672$	−13.5230	−	20.1001i	−0.521662	−	0.775377i
$673$			30.1463i			1.16206i	0.813884	+	0.581028i	$0.197349\pi$
$673$			30.1463i			1.16206i	−0.813884	+	0.581028i	$0.802651\pi$
$674$	−15.6065			−0.601141
$675$	−21.6890	+	4.52955i	−0.834812	+	0.174343i
$676$	24.6439	+	24.2190i	0.947842	+	0.931500i
$677$	−0.634202			−0.0243744			−0.0121872	−	0.999926i	$-0.503879\pi$
$677$	−0.634202			−0.0243744			−0.0121872	+	0.999926i	$0.503879\pi$
$678$	56.2128	−	37.8191i	2.15884	−	1.45243i
$679$			34.7468i			1.33346i
$680$	−3.76280			−0.144297
$681$	23.6399	−	15.9045i	0.905881	−	0.609463i
$682$		−	2.12385i		−	0.0813264i
$683$			11.1644i			0.427195i	0.976922	+	0.213597i	$0.0685181\pi$
$683$			11.1644i			0.427195i	−0.976922	+	0.213597i	$0.931482\pi$
$684$	−2.55291	+	34.6625i	−0.0976131	+	1.32536i
$685$	−3.69051			−0.141007
$686$	−41.9518			−1.60173
$687$	−24.8371	+	16.7100i	−0.947594	+	0.637526i
$688$	3.38094			0.128897
$689$	−16.4564	+	40.2229i	−0.626938	+	1.53237i
$690$	−6.57840	−	9.77787i	−0.250435	−	0.372237i
$691$			23.0728i			0.877732i	0.898552	+	0.438866i	$0.144620\pi$
$691$			23.0728i			0.877732i	−0.898552	+	0.438866i	$0.855380\pi$
$692$	13.2850			0.505020
$693$	−18.5425	−	7.54288i	−0.704372	−	0.286530i
$694$	−12.0410			−0.457071
$695$	13.9867			0.530545
$696$	19.0873	−	12.8416i	0.723501	−	0.486760i
$697$	−29.1349			−1.10356
$698$	−43.5590			−1.64873
$699$	12.5698	−	8.45675i	0.475432	−	0.319864i
$700$			20.5903i			0.778239i
$701$		−	29.7860i		−	1.12500i	−0.826796	−	0.562501i	$-0.809839\pi$
$701$		−	29.7860i		−	1.12500i	0.826796	−	0.562501i	$-0.190161\pi$
$702$	39.7629	+	7.33714i	1.50075	+	0.276923i
$703$	14.1113	−	4.56425i	0.532217	−	0.172144i
$704$	44.4883			1.67671
$705$	−8.46583	−	12.5833i	−0.318841	−	0.473913i
$706$			33.6875i			1.26784i
$707$	19.6234			0.738012
$708$	24.6793	−	16.6038i	0.927503	−	0.624010i
$709$		−	14.3758i		−	0.539893i	−0.962875	−	0.269947i	$-0.912994\pi$
$709$		−	14.3758i		−	0.539893i	0.962875	−	0.269947i	$-0.0870061\pi$
$710$	16.6901			0.626368
$711$	22.5572	+	9.17600i	0.845961	+	0.344127i
$712$	8.76888			0.328628
$713$		−	0.984664i		−	0.0368760i
$714$	−17.4072	+	11.7113i	−0.651450	+	0.438285i
$715$	−4.30163	+	10.5141i	−0.160872	+	0.393206i
$716$	31.9247			1.19308
$717$	−1.08360	−	1.61062i	−0.0404677	−	0.0601496i
$718$			35.2108i			1.31405i
$719$			21.3182i			0.795036i	0.917594	+	0.397518i	$0.130128\pi$
$719$			21.3182i			0.795036i	−0.917594	+	0.397518i	$0.869872\pi$
$720$	−2.18321	+	5.36695i	−0.0813635	+	0.200014i
$721$	−30.3204			−1.12919
$722$	24.0143	+	33.2387i	0.893718	+	1.23702i
$723$	−18.3231	−	27.2347i	−0.681442	−	1.01287i
$724$			30.6596i			1.13945i
$725$	39.8880			1.48140
$726$	7.72226	−	5.19541i	0.286600	−	0.192820i
$727$	35.9481			1.33324			0.666621	−	0.745397i	$-0.267740\pi$
$727$	35.9481			1.33324			0.666621	+	0.745397i	$0.267740\pi$
$728$	3.52184	−	8.60813i	0.130528	−	0.319039i
$729$	24.7432	−	10.8061i	0.916417	−	0.400226i
$730$	19.4590			0.720210
$731$		−	4.63919i		−	0.171587i
$732$	20.3437	+	30.2381i	0.751925	+	1.11763i
$733$		−	17.2584i		−	0.637452i	−0.947847	−	0.318726i	$-0.896745\pi$
$733$		−	17.2584i		−	0.637452i	0.947847	−	0.318726i	$-0.103255\pi$
$734$			19.5062i			0.719987i
$735$	3.06828	+	4.56057i	0.113175	+	0.168219i
$736$	28.2932			1.04290
$737$	7.92531			0.291932
$738$	23.0085	−	56.5614i	0.846954	−	2.08205i
$739$			11.7619i			0.432670i	0.976319	+	0.216335i	$0.0694104\pi$
$739$			11.7619i			0.432670i	−0.976319	+	0.216335i	$0.930590\pi$
$740$	−7.75779			−0.285182
$741$	23.6677	−	13.4477i	0.869454	−	0.494015i
$742$	47.2607			1.73500
$743$		−	49.4580i		−	1.81444i	−0.420658	−	0.907219i	$-0.638201\pi$
$743$		−	49.4580i		−	1.81444i	0.420658	−	0.907219i	$-0.361799\pi$
$744$	0.546709	−	0.367817i	0.0200433	−	0.0134848i
$745$	−7.36120			−0.269694
$746$	−53.9043			−1.97357
$747$	3.46211	−	8.51086i	0.126672	−	0.311396i
$748$		−	30.1576i		−	1.10267i
$749$		−	15.6908i		−	0.573331i
$750$	24.6482	−	16.5830i	0.900027	−	0.605524i
$751$		−	37.9459i		−	1.38466i	−0.721579	−	0.692332i	$-0.756583\pi$
$751$		−	37.9459i		−	1.38466i	0.721579	−	0.692332i	$-0.243417\pi$
$752$	22.9804			0.838010
$753$	−11.5583	+	7.77622i	−0.421207	+	0.283381i
$754$	−67.3709	−	27.5634i	−2.45350	−	1.00380i
$755$	11.7089			0.426132
$756$	−5.12932	−	24.5610i	−0.186552	−	0.893273i
$757$	−36.0703			−1.31100			−0.655498	−	0.755197i	$-0.727541\pi$
$757$	−36.0703			−1.31100			−0.655498	+	0.755197i	$0.727541\pi$
$758$		−	59.6762i		−	2.16754i
$759$	19.3975	−	13.0504i	0.704086	−	0.473698i
$760$	−1.63391	−	5.05155i	−0.0592681	−	0.183239i
$761$	26.8339			0.972730			0.486365	−	0.873756i	$-0.338323\pi$
$761$	26.8339			0.972730			0.486365	+	0.873756i	$0.338323\pi$
$762$	5.78525	+	8.59897i	0.209577	+	0.311508i
$763$			28.4591i			1.03029i
$764$			16.5297i			0.598025i
$765$	7.36431	+	2.99572i	0.266257	+	0.108310i
$766$	18.0521			0.652249
$767$	−21.5614	−	8.82141i	−0.778538	−	0.318522i
$768$	−1.00237	−	1.48988i	−0.0361698	−	0.0537613i
$769$		−	3.49339i		−	0.125975i	−0.998014	−	0.0629874i	$-0.979937\pi$
$769$		−	3.49339i		−	0.125975i	0.998014	−	0.0629874i	$-0.0200628\pi$
$770$	12.3538			0.445199
$771$	−6.54707	−	9.73131i	−0.235787	−	0.350464i
$772$	64.3384			2.31559
$773$			37.5373i			1.35012i	0.737761	+	0.675062i	$0.235883\pi$
$773$			37.5373i			1.35012i	−0.737761	+	0.675062i	$0.764117\pi$
$774$	9.00637	+	3.66368i	0.323727	+	0.131688i
$775$	1.14250			0.0410397
$776$		−	27.1561i		−	0.974846i
$777$	−8.88329	+	5.97653i	−0.318686	+	0.214407i
$778$	42.1431			1.51090
$779$	−12.6511	−	39.1135i	−0.453274	−	1.40139i
$780$	−13.9440	+	2.88287i	−0.499274	+	0.103223i
$781$			33.1101i			1.18477i
$782$		−	24.5027i		−	0.876214i
$783$	−47.5801	+	9.93666i	−1.70037	+	0.355107i
$784$	−8.32883			−0.297458
$785$	3.74852			0.133790
$786$	7.22488	+	10.7388i	0.257703	+	0.383040i
$787$	−26.0445			−0.928387			−0.464194	−	0.885734i	$-0.653656\pi$
$787$	−26.0445			−0.928387			−0.464194	+	0.885734i	$0.653656\pi$
$788$	−23.5513			−0.838980
$789$	−40.9137	+	27.5261i	−1.45657	+	0.979956i
$790$	−15.0285			−0.534691
$791$			32.9272i			1.17076i
$792$	14.4918	+	5.89507i	0.514942	+	0.209472i
$793$	10.8084	−	26.4180i	0.383816	−	0.938129i
$794$	66.5622			2.36221
$795$	−9.99707	−	14.8592i	−0.354559	−	0.527003i
$796$	−58.5369			−2.07478
$797$	18.9794			0.672284			0.336142	−	0.941811i	$-0.390878\pi$
$797$	18.9794			0.672284			0.336142	+	0.941811i	$0.390878\pi$
$798$	−23.2811	−	18.2838i	−0.824142	−	0.647240i
$799$		−	31.5328i		−	1.11555i
$800$			32.8283i			1.16066i
$801$	−17.1619	−	6.98125i	−0.606386	−	0.246670i
$802$	4.42831			0.156369
$803$			38.6032i			1.36228i
$804$	5.54508	+	8.24199i	0.195560	+	0.290672i
$805$	5.72749			0.201867
$806$	−1.92968	−	0.789488i	−0.0679700	−	0.0278085i
$807$	−16.1674	−	24.0306i	−0.569120	−	0.845917i
$808$	−15.3365			−0.539535
$809$		−	45.7368i		−	1.60802i	−0.594616	−	0.804010i	$-0.702696\pi$
$809$		−	45.7368i		−	1.60802i	0.594616	−	0.804010i	$-0.297304\pi$
$810$	−11.6315	+	11.9310i	−0.408691	+	0.419214i
$811$	−2.70738			−0.0950689			−0.0475344	−	0.998870i	$-0.515136\pi$
$811$	−2.70738			−0.0950689			−0.0475344	+	0.998870i	$0.515136\pi$
$812$			45.1697i			1.58514i
$813$	25.8736	−	17.4074i	0.907427	−	0.610503i
$814$		−	26.9708i		−	0.945325i
$815$		−	9.27873i		−	0.325020i
$816$	−9.99520	+	6.72461i	−0.349902	+	0.235408i
$817$	6.22811	−	2.01446i	0.217894	−	0.0704772i
$818$			53.9246i			1.88543i
$819$	−13.7460	+	14.0434i	−0.480324	+	0.490717i
$820$			21.5030i			0.750916i
$821$	15.2253			0.531366			0.265683	−	0.964061i	$-0.414403\pi$
$821$	15.2253			0.531366			0.265683	+	0.964061i	$0.414403\pi$
$822$	13.3431	−	8.97704i	0.465395	−	0.313110i
$823$	−24.0896			−0.839712			−0.419856	−	0.907591i	$-0.637919\pi$
$823$	−24.0896			−0.839712			−0.419856	+	0.907591i	$0.637919\pi$
$824$	23.6967			0.825513
$825$	15.1422	+	22.5068i	0.527184	+	0.783586i
$826$			25.3340i			0.881483i
$827$			16.9309i			0.588747i	0.955691	+	0.294373i	$0.0951109\pi$
$827$			16.9309i			0.588747i	−0.955691	+	0.294373i	$0.904889\pi$
$828$	27.1437	+	11.0417i	0.943308	+	0.383726i
$829$			27.5950i			0.958415i	0.877702	+	0.479207i	$0.159076\pi$
$829$			27.5950i			0.958415i	−0.877702	+	0.479207i	$0.840924\pi$
$830$			5.67027i			0.196818i
$831$	−25.2690	−	37.5588i	−0.876571	−	1.30290i
$832$	16.5374	−	40.4210i	0.573331	−	1.40134i
$833$			11.4285i			0.395973i
$834$	−50.5691	+	34.0221i	−1.75106	+	1.17809i
$835$		−	9.66767i		−	0.334564i
$836$	40.4866	−	13.0953i	1.40026	−	0.452909i
$837$	−1.36282	+	0.284612i	−0.0471059	+	0.00983762i
$838$	27.6225			0.954203
$839$		−	25.0645i		−	0.865321i	−0.901557	−	0.432661i	$-0.857575\pi$
$839$		−	25.0645i		−	0.865321i	0.901557	−	0.432661i	$-0.142425\pi$
$840$	2.13948	+	3.18004i	0.0738190	+	0.109722i
$841$	58.5038			2.01737
$842$			5.54148i			0.190972i
$843$	18.9351	−	12.7393i	0.652161	−	0.438763i
$844$			25.3994i			0.874283i
$845$	7.95386	+	7.81672i	0.273621	+	0.268903i
$846$	61.2167	+	24.9022i	2.10467	+	0.856156i
$847$			4.52339i			0.155426i
$848$	27.1370			0.931888
$849$	−13.3347	−	19.8202i	−0.457646	−	0.680226i
$850$	28.4302			0.975149
$851$		−	12.5042i		−	0.428640i
$852$	−34.4332	+	23.1661i	−1.17966	+	0.793657i
$853$			44.4341i			1.52140i	0.649106	+	0.760698i	$0.275143\pi$
$853$			44.4341i			1.52140i	−0.649106	+	0.760698i	$0.724857\pi$
$854$	−31.0403			−1.06218
$855$	−0.823958	+	11.1874i	−0.0281788	+	0.382601i
$856$			12.2630i			0.419142i
$857$	−12.3062			−0.420371			−0.210186	−	0.977662i	$-0.567407\pi$
$857$	−12.3062			−0.420371			−0.210186	+	0.977662i	$0.567407\pi$
$858$	−10.0226	−	48.4776i	−0.342166	−	1.65500i
$859$	−7.51594			−0.256441			−0.128220	−	0.991746i	$-0.540926\pi$
$859$	−7.51594			−0.256441			−0.128220	+	0.991746i	$0.540926\pi$
$860$	−3.42396			−0.116756
$861$	16.5657	+	24.6226i	0.564557	+	0.839136i
$862$	31.5068			1.07313
$863$		−	18.1537i		−	0.617960i	−0.951069	−	0.308980i	$-0.900012\pi$
$863$		−	18.1537i		−	0.617960i	0.951069	−	0.308980i	$-0.0999876\pi$
$864$	−8.17799	−	39.1590i	−0.278221	−	1.33222i
$865$	4.28776			0.145788
$866$	−23.2977			−0.791687
$867$	−7.20915	−	10.7154i	−0.244836	−	0.363914i
$868$			1.29378i			0.0439137i
$869$		−	29.8139i		−	1.01137i
$870$	24.8883	−	16.7445i	0.843793	−	0.567691i
$871$	2.94603	−	7.20074i	0.0998225	−	0.243988i
$872$		−	22.2420i		−	0.753208i
$873$	−21.6200	+	53.1481i	−0.731727	+	1.79879i
$874$	32.8948	−	10.6397i	1.11268	−	0.359894i
$875$			14.4380i			0.488092i
$876$	−40.1457	+	27.0094i	−1.35640	+	0.912563i
$877$	40.6939			1.37413			0.687067	−	0.726594i	$-0.258898\pi$
$877$	40.6939			1.37413			0.687067	+	0.726594i	$0.258898\pi$
$878$	−75.4051			−2.54480
$879$	23.4248	−	15.7598i	0.790099	−	0.531566i
$880$	7.09351			0.239122
$881$			5.77172i			0.194454i	0.995262	+	0.0972271i	$0.0309973\pi$
$881$			5.77172i			0.194454i	−0.995262	+	0.0972271i	$0.969003\pi$
$882$	−22.1868	−	9.02535i	−0.747070	−	0.303899i
$883$	−8.40361			−0.282804			−0.141402	−	0.989952i	$-0.545161\pi$
$883$	−8.40361			−0.282804			−0.141402	+	0.989952i	$0.545161\pi$
$884$	−27.4005	−	11.2103i	−0.921579	−	0.377045i
$885$	7.96527	−	5.35891i	0.267750	−	0.180138i
$886$	−86.9916			−2.92254
$887$	46.5170			1.56189			0.780944	−	0.624601i	$-0.214739\pi$
$887$	46.5170			1.56189			0.780944	+	0.624601i	$0.214739\pi$
$888$	6.94266	−	4.67091i	0.232980	−	0.156745i
$889$	−5.03693			−0.168933
$890$	11.4339			0.383267
$891$	−23.6690	−	23.0749i	−0.792943	−	0.773039i
$892$	23.6718			0.792590
$893$	42.3328	−	13.6924i	1.41661	−	0.458199i
$894$	26.6146	−	17.9059i	0.890124	−	0.598862i
$895$	10.3038			0.344416
$896$	−19.5200			−0.652116
$897$	−4.64670	−	22.4753i	−0.155149	−	0.750428i
$898$	36.0832			1.20411
$899$	2.50634			0.0835911
$900$	−12.8116	+	31.4945i	−0.427053	+	1.04982i
$901$		−	37.2363i		−	1.24052i
$902$	−74.7573			−2.48914
$903$	−3.92070	+	2.63779i	−0.130473	+	0.0877800i
$904$		−	25.7340i		−	0.855901i
$905$			9.89544i			0.328935i
$906$	−42.3339	+	28.4816i	−1.40645	+	0.946238i
$907$		−	18.5854i		−	0.617117i	−0.951205	−	0.308559i	$-0.900153\pi$
$907$		−	18.5854i		−	0.617117i	0.951205	−	0.308559i	$-0.0998466\pi$
$908$		−	43.7220i		−	1.45097i
$909$	30.0156	+	12.2100i	0.995553	+	0.404979i
$910$	4.59221	−	11.2243i	0.152230	−	0.372083i
$911$	−23.0943			−0.765149			−0.382575	−	0.923925i	$-0.624963\pi$
$911$	−23.0943			−0.765149			−0.382575	+	0.923925i	$0.624963\pi$
$912$	−13.3680	−	10.4985i	−0.442657	−	0.347641i
$913$	−11.2488			−0.372281
$914$	−63.5250			−2.10122
$915$	6.56596	+	9.75939i	0.217064	+	0.322635i
$916$			45.9363i			1.51778i
$917$	−6.29035			−0.207726
$918$	−33.9128	+	7.08237i	−1.11929	+	0.233753i
$919$	−4.92461			−0.162448			−0.0812239	−	0.996696i	$-0.525883\pi$
$919$	−4.92461			−0.162448			−0.0812239	+	0.996696i	$0.525883\pi$
$920$	−4.47627			−0.147578
$921$	1.81787	+	2.70202i	0.0599010	+	0.0890344i
$922$		−	29.0778i		−	0.957625i
$923$	30.0831	+	12.3079i	0.990197	+	0.405118i
$924$	−25.4870	+	17.1472i	−0.838460	+	0.564103i
$925$	14.5086			0.477038
$926$	42.8053			1.40667
$927$	−46.3776	−	18.8659i	−1.52324	−	0.619637i
$928$			72.0167i			2.36406i
$929$	−1.28750			−0.0422416			−0.0211208	−	0.999777i	$-0.506723\pi$
$929$	−1.28750			−0.0422416			−0.0211208	+	0.999777i	$0.506723\pi$
$930$	0.712867	−	0.479606i	0.0233758	−	0.0157269i
$931$	−15.3427	+	4.96256i	−0.502837	+	0.162641i
$932$		−	23.2478i		−	0.761509i
$933$	−14.2080	+	9.55894i	−0.465150	+	0.312946i
$934$	−35.8396			−1.17271
$935$		−	9.73343i		−	0.318317i
$936$	10.7431	−	10.9755i	0.351148	−	0.358746i
$937$	13.3116			0.434872			0.217436	−	0.976075i	$-0.430231\pi$
$937$	13.3116			0.434872			0.217436	+	0.976075i	$0.430231\pi$
$938$	−8.46065			−0.276250
$939$	8.76610	+	13.0296i	0.286071	+	0.425205i
$940$	−23.2728			−0.759075
$941$		−	2.87618i		−	0.0937608i	−0.998901	−	0.0468804i	$-0.985072\pi$
$941$		−	2.87618i		−	0.0937608i	0.998901	−	0.0468804i	$-0.0149280\pi$
$942$	−13.5529	+	9.11815i	−0.441576	+	0.297085i
$943$	−34.6591			−1.12866
$944$			14.5467i			0.473456i
$945$	−1.65550	−	7.92709i	−0.0538534	−	0.257868i
$946$		−	11.9037i		−	0.387024i
$947$	−23.7631			−0.772197			−0.386098	−	0.922458i	$-0.626177\pi$
$947$	−23.7631			−0.772197			−0.386098	+	0.922458i	$0.626177\pi$
$948$	31.0052	−	20.8598i	1.00700	−	0.677496i
$949$	35.0739	+	14.3498i	1.13855	+	0.465813i
$950$	12.3452	+	38.1675i	0.400530	+	1.23832i
$951$	17.6874	−	11.8998i	0.573552	−	0.385877i
$952$			7.96896i			0.258276i
$953$	−25.0414			−0.811170			−0.405585	−	0.914057i	$-0.632932\pi$
$953$	−25.0414			−0.811170			−0.405585	+	0.914057i	$0.632932\pi$
$954$	72.2892	+	29.4064i	2.34045	+	0.952067i
$955$			5.33500i			0.172637i
$956$	−2.97884			−0.0963426
$957$	33.2181	+	49.3740i	1.07379	+	1.59604i
$958$		−	85.8869i		−	2.77488i
$959$			7.81587i			0.252388i
$960$	10.0463	+	14.9324i	0.324243	+	0.481941i
$961$	−30.9282			−0.997684
$962$	−24.5050	−	10.0257i	−0.790072	−	0.323242i
$963$	9.76310	−	24.0005i	0.314611	−	0.773404i
$964$	−50.3706			−1.62233
$965$	20.7653			0.668460
$966$	−20.7078	+	13.9319i	−0.666264	+	0.448252i
$967$		−	6.13314i		−	0.197228i	−0.995126	−	0.0986142i	$-0.968559\pi$
$967$		−	6.13314i		−	0.197228i	0.995126	−	0.0986142i	$-0.0314410\pi$
$968$		−	3.53522i		−	0.113626i
$969$	−14.4057	+	18.3430i	−0.462776	+	0.589261i
$970$		−	35.4094i		−	1.13693i
$971$	13.5663			0.435362			0.217681	−	0.976020i	$-0.430151\pi$
$971$	13.5663			0.435362			0.217681	+	0.976020i	$0.430151\pi$
$972$	7.43650	−	40.7596i	0.238526	−	1.30736i
$973$		−	29.6214i		−	0.949617i
$974$		−	34.2141i		−	1.09629i
$975$	26.0779	−	5.39152i	0.835160	−	0.172667i
$976$	−17.8233			−0.570509
$977$		−	5.06439i		−	0.162024i	−0.996713	−	0.0810121i	$-0.974185\pi$
$977$		−	5.06439i		−	0.162024i	0.996713	−	0.0810121i	$-0.0258152\pi$
$978$	22.5702	+	33.5474i	0.721715	+	1.07273i
$979$			22.6829i			0.724949i
$980$	8.43479			0.269440
$981$	−17.7077	+	43.5306i	−0.565364	+	1.38982i
$982$	10.3725			0.330999
$983$		−	39.6366i		−	1.26421i	−0.774882	−	0.632106i	$-0.782191\pi$
$983$		−	39.6366i		−	1.26421i	0.774882	−	0.632106i	$-0.217809\pi$
$984$	−12.9468	−	19.2436i	−0.412728	−	0.613463i
$985$	−7.60122			−0.242195
$986$	62.3685			1.98622
$987$	−26.6492	+	17.9292i	−0.848253	+	0.570691i
$988$	3.15183	−	41.6530i	0.100273	−	1.32516i
$989$		−	5.51884i		−	0.175489i
$990$	18.8961	+	7.68672i	0.600559	+	0.244300i
$991$			28.7752i			0.914074i	0.889448	+	0.457037i	$0.151089\pi$
$991$			28.7752i			0.914074i	−0.889448	+	0.457037i	$0.848911\pi$
$992$			2.06275i			0.0654923i
$993$	0.963896	+	1.43270i	0.0305883	+	0.0454653i
$994$		−	35.3467i		−	1.12113i
$995$	−18.8929			−0.598944
$996$	−7.87043	−	11.6983i	−0.249384	−	0.370675i
$997$	−55.6956			−1.76390			−0.881948	−	0.471347i	$-0.843768\pi$
$997$	−55.6956			−1.76390			−0.881948	+	0.471347i	$0.843768\pi$
$998$	80.7810			2.55708
$999$	−17.3064	+	3.61428i	−0.547551	+	0.114351i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	741.2.d.a.740.73	yes	88
3.2	odd	2	inner	741.2.d.a.740.15	yes	88
13.12	even	2	inner	741.2.d.a.740.13	✓	88
19.18	odd	2	inner	741.2.d.a.740.16	yes	88
39.38	odd	2	inner	741.2.d.a.740.75	yes	88
57.56	even	2	inner	741.2.d.a.740.74	yes	88
247.246	odd	2	inner	741.2.d.a.740.76	yes	88
741.740	even	2	inner	741.2.d.a.740.14	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
741.2.d.a.740.13	✓	88	13.12	even	2	inner
741.2.d.a.740.14	yes	88	741.740	even	2	inner
741.2.d.a.740.15	yes	88	3.2	odd	2	inner
741.2.d.a.740.16	yes	88	19.18	odd	2	inner
741.2.d.a.740.73	yes	88	1.1	even	1	trivial
741.2.d.a.740.74	yes	88	57.56	even	2	inner
741.2.d.a.740.75	yes	88	39.38	odd	2	inner
741.2.d.a.740.76	yes	88	247.246	odd	2	inner

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:	\( N \)	\(=\)	\( 741 = 3 \cdot 13 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	741.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.15821i q^{2} +(-0.966847 - 1.43708i) q^{3} -2.65789 q^{4} -0.857839 q^{5} +(3.10153 - 2.08666i) q^{6} +1.81675i q^{7} -1.41987i q^{8} +(-1.13041 + 2.77888i) q^{9} -1.85140i q^{10} +3.67285 q^{11} +(2.56977 + 3.81961i) q^{12} +(1.36529 - 3.33706i) q^{13} -3.92095 q^{14} +(0.829399 + 1.23279i) q^{15} -2.25140 q^{16} +3.08928i q^{17} +(-5.99742 - 2.43968i) q^{18} +(-4.14735 + 1.34145i) q^{19} +2.28004 q^{20} +(2.61083 - 1.75652i) q^{21} +7.92680i q^{22} +3.67504i q^{23} +(-2.04047 + 1.37280i) q^{24} -4.26411 q^{25} +(7.20210 + 2.94659i) q^{26} +(5.08642 - 1.06225i) q^{27} -4.82874i q^{28} -9.35435 q^{29} +(-2.66062 + 1.79002i) q^{30} -0.267933 q^{31} -7.69874i q^{32} +(-3.55108 - 5.27819i) q^{33} -6.66733 q^{34} -1.55848i q^{35} +(3.00452 - 7.38595i) q^{36} -3.40248 q^{37} +(-2.89513 - 8.95087i) q^{38} +(-6.11566 + 1.26439i) q^{39} +1.21802i q^{40} +9.43096i q^{41} +(3.79096 + 5.63473i) q^{42} -1.50171 q^{43} -9.76203 q^{44} +(0.969713 - 2.38383i) q^{45} -7.93152 q^{46} -10.2072 q^{47} +(2.17676 + 3.23545i) q^{48} +3.69940 q^{49} -9.20287i q^{50} +(4.43955 - 2.98686i) q^{51} +(-3.62879 + 8.86955i) q^{52} -12.0534 q^{53} +(2.29256 + 10.9776i) q^{54} -3.15071 q^{55} +2.57955 q^{56} +(5.93762 + 4.66311i) q^{57} -20.1887i q^{58} -6.46120i q^{59} +(-2.20445 - 3.27661i) q^{60} +7.91653 q^{61} -0.578257i q^{62} +(-5.04854 - 2.05369i) q^{63} +12.1127 q^{64} +(-1.17120 + 2.86266i) q^{65} +(11.3915 - 7.66400i) q^{66} +2.15781 q^{67} -8.21097i q^{68} +(5.28134 - 3.55320i) q^{69} +3.36354 q^{70} +9.01484i q^{71} +(3.94564 + 1.60504i) q^{72} +10.5104i q^{73} -7.34328i q^{74} +(4.12274 + 6.12788i) q^{75} +(11.0232 - 3.56542i) q^{76} +6.67267i q^{77} +(-2.72883 - 13.1989i) q^{78} -8.11738i q^{79} +1.93134 q^{80} +(-6.44433 - 6.28257i) q^{81} -20.3540 q^{82} -3.06269 q^{83} +(-6.93929 + 4.66865i) q^{84} -2.65010i q^{85} -3.24101i q^{86} +(9.04422 + 13.4430i) q^{87} -5.21497i q^{88} +6.17584i q^{89} +(5.14482 + 2.09285i) q^{90} +(6.06262 + 2.48040i) q^{91} -9.76785i q^{92} +(0.259050 + 0.385042i) q^{93} -22.0293i q^{94} +(3.55776 - 1.15075i) q^{95} +(-11.0637 + 7.44350i) q^{96} +19.1257 q^{97} +7.98410i q^{98} +(-4.15184 + 10.2064i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 88 q^{4} - 4 q^{9} + 72 q^{16} + 64 q^{25} - 60 q^{30} - 48 q^{36} + 20 q^{39} + 48 q^{42} - 64 q^{43} - 112 q^{49} - 24 q^{55} - 64 q^{61} - 104 q^{64} + 12 q^{66} + 60 q^{81} + 56 q^{82} - 32 q^{87}+O(q^{100}) \) 88 * q - 88 * q^4 - 4 * q^9 + 72 * q^16 + 64 * q^25 - 60 * q^30 - 48 * q^36 + 20 * q^39 + 48 * q^42 - 64 * q^43 - 112 * q^49 - 24 * q^55 - 64 * q^61 - 104 * q^64 + 12 * q^66 + 60 * q^81 + 56 * q^82 - 32 * q^87

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