LMFDB - Embedded newform 405.2.f.b.242.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [405,2,Mod(242,405)] 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("405.242"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(405, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	405.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.23394128186$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			242.1
Character	$\chi$	$=$	405.242
Dual form			405.2.f.b.323.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.85830 + 1.85830i) q^{2} -4.90659i q^{4} +(-1.97703 + 1.04468i) q^{5} +(0.484523 + 0.484523i) q^{7} +(5.40134 + 5.40134i) q^{8} +(1.73258 - 5.61526i) q^{10} -5.24456i q^{11} +(-0.0638872 + 0.0638872i) q^{13} -1.80078 q^{14} -10.2615 q^{16} +(3.14882 - 3.14882i) q^{17} +2.33738i q^{19} +(5.12584 + 9.70047i) q^{20} +(9.74600 + 9.74600i) q^{22} +(4.18041 + 4.18041i) q^{23} +(2.81727 - 4.13074i) q^{25} -0.237444i q^{26} +(2.37736 - 2.37736i) q^{28} +3.46874 q^{29} +2.93755 q^{31} +(8.26627 - 8.26627i) q^{32} +11.7029i q^{34} +(-1.46409 - 0.451741i) q^{35} +(4.39816 + 4.39816i) q^{37} +(-4.34356 - 4.34356i) q^{38} +(-16.3213 - 5.03590i) q^{40} +4.57937i q^{41} +(-2.57232 + 2.57232i) q^{43} -25.7329 q^{44} -15.5369 q^{46} +(2.47888 - 2.47888i) q^{47} -6.53048i q^{49} +(2.44082 + 12.9115i) q^{50} +(0.313468 + 0.313468i) q^{52} +(0.625281 + 0.625281i) q^{53} +(5.47891 + 10.3686i) q^{55} +5.23414i q^{56} +(-6.44598 + 6.44598i) q^{58} -2.04457 q^{59} +8.82003 q^{61} +(-5.45886 + 5.45886i) q^{62} +10.1996i q^{64} +(0.0595647 - 0.193049i) q^{65} +(-0.0399773 - 0.0399773i) q^{67} +(-15.4500 - 15.4500i) q^{68} +(3.56019 - 1.88125i) q^{70} -12.5803i q^{71} +(7.14603 - 7.14603i) q^{73} -16.3462 q^{74} +11.4686 q^{76} +(2.54111 - 2.54111i) q^{77} +5.35488i q^{79} +(20.2872 - 10.7200i) q^{80} +(-8.50987 - 8.50987i) q^{82} +(3.57664 + 3.57664i) q^{83} +(-2.93577 + 9.51481i) q^{85} -9.56031i q^{86} +(28.3277 - 28.3277i) q^{88} +14.2411 q^{89} -0.0619096 q^{91} +(20.5116 - 20.5116i) q^{92} +9.21302i q^{94} +(-2.44182 - 4.62106i) q^{95} +(-11.2443 - 11.2443i) q^{97} +(12.1356 + 12.1356i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{13} - 24 q^{16} + 36 q^{37} - 36 q^{40} - 24 q^{43} - 48 q^{46} - 36 q^{52} - 60 q^{58} + 72 q^{70} + 12 q^{73} + 48 q^{76} - 96 q^{82} + 60 q^{85} + 96 q^{88} - 48 q^{91} + 24 q^{97}+O(q^{100}) $ 24 * q + 12 * q^13 - 24 * q^16 + 36 * q^37 - 36 * q^40 - 24 * q^43 - 48 * q^46 - 36 * q^52 - 60 * q^58 + 72 * q^70 + 12 * q^73 + 48 * q^76 - 96 * q^82 + 60 * q^85 + 96 * q^88 - 48 * q^91 + 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−1.85830	+	1.85830i	−1.31402	+	1.31402i	−0.395595	+	0.918425i	$0.629462\pi$
$2$	−1.85830	+	1.85830i	−1.31402	+	1.31402i	−0.918425	+	0.395595i	$0.870538\pi$
$3$		0			0
$3$		0			0
$4$		−	4.90659i		−	2.45330i
$5$	−1.97703	+	1.04468i	−0.884153	+	0.467197i
$5$	−1.97703	+	1.04468i	−0.884153	+	0.467197i
$6$		0			0
$7$	0.484523	+	0.484523i	0.183132	+	0.183132i	0.792719	−	0.609587i	$-0.208665\pi$
$7$	0.484523	+	0.484523i	0.183132	+	0.183132i	−0.609587	+	0.792719i	$0.708665\pi$
$8$	5.40134	+	5.40134i	1.90966	+	1.90966i
$9$		0			0
$10$	1.73258	−	5.61526i	0.547889	−	1.77570i
$11$		−	5.24456i		−	1.58130i	−0.612271	−	0.790648i	$-0.709744\pi$
$11$		−	5.24456i		−	1.58130i	0.612271	−	0.790648i	$-0.290256\pi$
$12$		0			0
$13$	−0.0638872	+	0.0638872i	−0.0177191	+	0.0177191i	−0.715911	−	0.698192i	$-0.753988\pi$
$13$	−0.0638872	+	0.0638872i	−0.0177191	+	0.0177191i	0.698192	+	0.715911i	$0.253988\pi$
$14$	−1.80078			−0.481279
$15$		0			0
$16$	−10.2615			−2.56537
$17$	3.14882	−	3.14882i	0.763700	−	0.763700i	−0.213289	−	0.976989i	$-0.568418\pi$
$17$	3.14882	−	3.14882i	0.763700	−	0.763700i	0.976989	+	0.213289i	$0.0684177\pi$
$18$		0			0
$19$			2.33738i			0.536231i	0.963387	+	0.268116i	$0.0864009\pi$
$19$			2.33738i			0.536231i	−0.963387	+	0.268116i	$0.913599\pi$
$20$	5.12584	+	9.70047i	1.14617	+	2.16909i
$21$		0			0
$22$	9.74600	+	9.74600i	2.07785	+	2.07785i
$23$	4.18041	+	4.18041i	0.871675	+	0.871675i	0.992655	−	0.120980i	$-0.0386036\pi$
$23$	4.18041	+	4.18041i	0.871675	+	0.871675i	−0.120980	+	0.992655i	$0.538604\pi$
$24$		0			0
$25$	2.81727	−	4.13074i	0.563454	−	0.826148i
$26$		−	0.237444i		−	0.0465665i
$27$		0			0
$28$	2.37736	−	2.37736i	0.449278	−	0.449278i
$29$	3.46874			0.644129			0.322065	−	0.946718i	$-0.395623\pi$
$29$	3.46874			0.644129			0.322065	+	0.946718i	$0.395623\pi$
$30$		0			0
$31$	2.93755			0.527599			0.263800	−	0.964577i	$-0.415024\pi$
$31$	2.93755			0.527599			0.263800	+	0.964577i	$0.415024\pi$
$32$	8.26627	−	8.26627i	1.46128	−	1.46128i
$33$		0			0
$34$			11.7029i			2.00703i
$35$	−1.46409	−	0.451741i	−0.247476	−	0.0763582i
$36$		0			0
$37$	4.39816	+	4.39816i	0.723053	+	0.723053i	0.969226	−	0.246173i	$-0.0791730\pi$
$37$	4.39816	+	4.39816i	0.723053	+	0.723053i	−0.246173	+	0.969226i	$0.579173\pi$
$38$	−4.34356	−	4.34356i	−0.704619	−	0.704619i
$39$		0			0
$40$	−16.3213	−	5.03590i	−2.58062	−	0.796245i
$41$			4.57937i			0.715178i	0.933879	+	0.357589i	$0.116401\pi$
$41$			4.57937i			0.715178i	−0.933879	+	0.357589i	$0.883599\pi$
$42$		0			0
$43$	−2.57232	+	2.57232i	−0.392275	+	0.392275i	−0.875498	−	0.483223i	$-0.839466\pi$
$43$	−2.57232	+	2.57232i	−0.392275	+	0.392275i	0.483223	+	0.875498i	$0.339466\pi$
$44$	−25.7329			−3.87939
$45$		0			0
$46$	−15.5369			−2.29080
$47$	2.47888	−	2.47888i	0.361581	−	0.361581i	−0.502814	−	0.864395i	$-0.667702\pi$
$47$	2.47888	−	2.47888i	0.361581	−	0.361581i	0.864395	+	0.502814i	$0.167702\pi$
$48$		0			0
$49$		−	6.53048i		−	0.932925i
$50$	2.44082	+	12.9115i	0.345185	+	1.82596i
$51$		0			0
$52$	0.313468	+	0.313468i	0.0434703	+	0.0434703i
$53$	0.625281	+	0.625281i	0.0858890	+	0.0858890i	0.748746	−	0.662857i	$-0.230656\pi$
$53$	0.625281	+	0.625281i	0.0858890	+	0.0858890i	−0.662857	+	0.748746i	$0.730656\pi$
$54$		0			0
$55$	5.47891	+	10.3686i	0.738777	+	1.39811i
$56$			5.23414i			0.699441i
$57$		0			0
$58$	−6.44598	+	6.44598i	−0.846399	+	0.846399i
$59$	−2.04457			−0.266180			−0.133090	−	0.991104i	$-0.542490\pi$
$59$	−2.04457			−0.266180			−0.133090	+	0.991104i	$0.542490\pi$
$60$		0			0
$61$	8.82003			1.12929			0.564645	−	0.825334i	$-0.309013\pi$
$61$	8.82003			1.12929			0.564645	+	0.825334i	$0.309013\pi$
$62$	−5.45886	+	5.45886i	−0.693276	+	0.693276i
$63$		0			0
$64$			10.1996i			1.27495i
$65$	0.0595647	−	0.193049i	0.00738810	−	0.0239447i
$66$		0			0
$67$	−0.0399773	−	0.0399773i	−0.00488401	−	0.00488401i	0.704661	−	0.709545i	$-0.251099\pi$
$67$	−0.0399773	−	0.0399773i	−0.00488401	−	0.00488401i	−0.709545	+	0.704661i	$0.751099\pi$
$68$	−15.4500	−	15.4500i	−1.87358	−	1.87358i
$69$		0			0
$70$	3.56019	−	1.88125i	0.425524	−	0.224852i
$71$		−	12.5803i		−	1.49300i	−0.665383	−	0.746502i	$-0.731732\pi$
$71$		−	12.5803i		−	1.49300i	0.665383	−	0.746502i	$-0.268268\pi$
$72$		0			0
$73$	7.14603	−	7.14603i	0.836379	−	0.836379i	−0.152001	−	0.988380i	$-0.548572\pi$
$73$	7.14603	−	7.14603i	0.836379	−	0.836379i	0.988380	+	0.152001i	$0.0485718\pi$
$74$	−16.3462			−1.90021
$75$		0			0
$76$	11.4686			1.31553
$77$	2.54111	−	2.54111i	0.289586	−	0.289586i
$78$		0			0
$79$			5.35488i			0.602471i	0.953550	+	0.301236i	$0.0973991\pi$
$79$			5.35488i			0.602471i	−0.953550	+	0.301236i	$0.902601\pi$
$80$	20.2872	−	10.7200i	2.26818	−	1.19853i
$81$		0			0
$82$	−8.50987	−	8.50987i	−0.939758	−	0.939758i
$83$	3.57664	+	3.57664i	0.392587	+	0.392587i	0.875609	−	0.483021i	$-0.160461\pi$
$83$	3.57664	+	3.57664i	0.392587	+	0.392587i	−0.483021	+	0.875609i	$0.660461\pi$
$84$		0			0
$85$	−2.93577	+	9.51481i	−0.318429	+	1.03203i
$86$		−	9.56031i		−	1.03091i
$87$		0			0
$88$	28.3277	−	28.3277i	3.01974	−	3.01974i
$89$	14.2411			1.50956			0.754778	−	0.655980i	$-0.227745\pi$
$89$	14.2411			1.50956			0.754778	+	0.655980i	$0.227745\pi$
$90$		0			0
$91$	−0.0619096			−0.00648989
$92$	20.5116	−	20.5116i	2.13848	−	2.13848i
$93$		0			0
$94$			9.21302i			0.950250i
$95$	−2.44182	−	4.62106i	−0.250526	−	0.474111i
$96$		0			0
$97$	−11.2443	−	11.2443i	−1.14168	−	1.14168i	−0.988142	−	0.153542i	$-0.950932\pi$
$97$	−11.2443	−	11.2443i	−1.14168	−	1.14168i	−0.153542	−	0.988142i	$-0.549068\pi$
$98$	12.1356	+	12.1356i	1.22588	+	1.22588i
$99$		0			0
$100$	−20.2679	−	13.8232i	−2.02679	−	1.38232i
$101$		−	3.90591i		−	0.388653i	−0.980937	−	0.194326i	$-0.937748\pi$
$101$		−	3.90591i		−	0.388653i	0.980937	−	0.194326i	$-0.0622521\pi$
$102$		0			0
$103$	10.6613	−	10.6613i	1.05049	−	1.05049i	0.0518339	−	0.998656i	$-0.483493\pi$
$103$	10.6613	−	10.6613i	1.05049	−	1.05049i	0.998656	−	0.0518339i	$-0.0165066\pi$
$104$	−0.690152			−0.0676750
$105$		0			0
$106$	−2.32393			−0.225720
$107$	−5.74908	+	5.74908i	−0.555785	+	0.555785i	−0.928105	−	0.372320i	$-0.878562\pi$
$107$	−5.74908	+	5.74908i	−0.555785	+	0.555785i	0.372320	+	0.928105i	$0.378562\pi$
$108$		0			0
$109$			3.70689i			0.355056i	0.984116	+	0.177528i	$0.0568100\pi$
$109$			3.70689i			0.355056i	−0.984116	+	0.177528i	$0.943190\pi$
$110$	−29.4496	−	9.08661i	−2.80791	−	0.866374i
$111$		0			0
$112$	−4.97192	−	4.97192i	−0.469802	−	0.469802i
$113$	4.17403	+	4.17403i	0.392660	+	0.392660i	0.875634	−	0.482975i	$-0.160444\pi$
$113$	4.17403	+	4.17403i	0.392660	+	0.392660i	−0.482975	+	0.875634i	$0.660444\pi$
$114$		0			0
$115$	−12.6320	−	3.89757i	−1.17794	−	0.363450i
$116$		−	17.0197i		−	1.58024i
$117$		0			0
$118$	3.79943	−	3.79943i	0.349766	−	0.349766i
$119$	3.05134			0.279716
$120$		0			0
$121$	−16.5054			−1.50050
$122$	−16.3903	+	16.3903i	−1.48391	+	1.48391i
$123$		0			0
$124$		−	14.4134i		−	1.29436i
$125$	−1.25450	+	11.1097i	−0.112206	+	0.993685i
$126$		0			0
$127$	−3.83940	−	3.83940i	−0.340692	−	0.340692i	0.515935	−	0.856627i	$-0.327444\pi$
$127$	−3.83940	−	3.83940i	−0.340692	−	0.340692i	−0.856627	+	0.515935i	$0.827444\pi$
$128$	−2.42135	−	2.42135i	−0.214019	−	0.214019i
$129$		0			0
$130$	0.248054	+	0.469433i	0.0217558	+	0.0411720i
$131$		−	21.0386i		−	1.83815i	−0.394082	−	0.919075i	$-0.628937\pi$
$131$		−	21.0386i		−	1.83815i	0.394082	−	0.919075i	$-0.371063\pi$
$132$		0			0
$133$	−1.13251	+	1.13251i	−0.0982013	+	0.0982013i
$134$	0.148580			0.0128354
$135$		0			0
$136$	34.0156			2.91682
$137$	−8.60134	+	8.60134i	−0.734862	+	0.734862i	−0.971579	−	0.236717i	$-0.923929\pi$
$137$	−8.60134	+	8.60134i	−0.734862	+	0.734862i	0.236717	+	0.971579i	$0.423929\pi$
$138$		0			0
$139$		−	5.52076i		−	0.468265i	−0.972205	−	0.234132i	$-0.924775\pi$
$139$		−	5.52076i		−	0.468265i	0.972205	−	0.234132i	$-0.0752249\pi$
$140$	−2.21651	+	7.18368i	−0.187329	+	0.607132i
$141$		0			0
$142$	23.3780	+	23.3780i	1.96184	+	1.96184i
$143$	0.335060	+	0.335060i	0.0280192	+	0.0280192i
$144$		0			0
$145$	−6.85780	+	3.62374i	−0.569509	+	0.300935i
$146$			26.5590i			2.19804i
$147$		0			0
$148$	21.5800	−	21.5800i	1.77386	−	1.77386i
$149$	14.6126			1.19711			0.598557	−	0.801080i	$-0.295741\pi$
$149$	14.6126			1.19711			0.598557	+	0.801080i	$0.295741\pi$
$150$		0			0
$151$	15.6129			1.27056			0.635281	−	0.772281i	$-0.280884\pi$
$151$	15.6129			1.27056			0.635281	+	0.772281i	$0.280884\pi$
$152$	−12.6250	+	12.6250i	−1.02402	+	1.02402i
$153$		0			0
$154$			9.44431i			0.761044i
$155$	−5.80761	+	3.06881i	−0.466479	+	0.246493i
$156$		0			0
$157$	−9.86331	−	9.86331i	−0.787178	−	0.787178i	0.193853	−	0.981031i	$-0.437902\pi$
$157$	−9.86331	−	9.86331i	−0.787178	−	0.787178i	−0.981031	+	0.193853i	$0.937902\pi$
$158$	−9.95100	−	9.95100i	−0.791659	−	0.791659i
$159$		0			0
$160$	−7.70700	+	24.9783i	−0.609292	+	1.97471i
$161$			4.05100i			0.319264i
$162$		0			0
$163$	−12.1643	+	12.1643i	−0.952784	+	0.952784i	−0.998934	−	0.0461509i	$-0.985305\pi$
$163$	−12.1643	+	12.1643i	−0.952784	+	0.952784i	0.0461509	+	0.998934i	$0.485305\pi$
$164$	22.4691			1.75454
$165$		0			0
$166$	−13.2930			−1.03173
$167$	6.73261	−	6.73261i	0.520985	−	0.520985i	−0.396884	−	0.917869i	$-0.629908\pi$
$167$	6.73261	−	6.73261i	0.520985	−	0.520985i	0.917869	+	0.396884i	$0.129908\pi$
$168$		0			0
$169$			12.9918i			0.999372i
$170$	−12.2259	−	23.1370i	−0.937680	−	1.77453i
$171$		0			0
$172$	12.6213	+	12.6213i	0.962367	+	0.962367i
$173$	6.32726	+	6.32726i	0.481053	+	0.481053i	0.905468	−	0.424415i	$-0.139520\pi$
$173$	6.32726	+	6.32726i	0.481053	+	0.481053i	−0.424415	+	0.905468i	$0.639520\pi$
$174$		0			0
$175$	3.36647	−	0.636405i	0.254481	−	0.0481077i
$176$			53.8170i			4.05661i
$177$		0			0
$178$	−26.4643	+	26.4643i	−1.98359	+	1.98359i
$179$	−4.11390			−0.307488			−0.153744	−	0.988111i	$-0.549133\pi$
$179$	−4.11390			−0.307488			−0.153744	+	0.988111i	$0.549133\pi$
$180$		0			0
$181$	−11.0450			−0.820970			−0.410485	−	0.911867i	$-0.634641\pi$
$181$	−11.0450			−0.820970			−0.410485	+	0.911867i	$0.634641\pi$
$182$	0.115047	−	0.115047i	0.00852784	−	0.00852784i
$183$		0			0
$184$			45.1596i			3.32921i
$185$	−13.2900	−	4.10059i	−0.977098	−	0.301482i
$186$		0			0
$187$	−16.5142	−	16.5142i	−1.20764	−	1.20764i
$188$	−12.1628	−	12.1628i	−0.887066	−	0.887066i
$189$		0			0
$190$	13.1250	+	4.04969i	0.952187	+	0.293795i
$191$		−	13.0761i		−	0.946152i	−0.881022	−	0.473076i	$-0.843144\pi$
$191$		−	13.0761i		−	0.946152i	0.881022	−	0.473076i	$-0.156856\pi$
$192$		0			0
$193$	−13.0552	+	13.0552i	−0.939732	+	0.939732i	−0.998284	−	0.0585524i	$-0.981352\pi$
$193$	−13.0552	+	13.0552i	−0.939732	+	0.939732i	0.0585524	+	0.998284i	$0.481352\pi$
$194$	41.7906			3.00039
$195$		0			0
$196$	−32.0424			−2.28874
$197$	−11.1172	+	11.1172i	−0.792070	+	0.792070i	−0.981830	−	0.189761i	$-0.939229\pi$
$197$	−11.1172	+	11.1172i	−0.792070	+	0.792070i	0.189761	+	0.981830i	$0.439229\pi$
$198$		0			0
$199$		−	21.1474i		−	1.49910i	−0.661949	−	0.749549i	$-0.730271\pi$
$199$		−	21.1474i		−	1.49910i	0.661949	−	0.749549i	$-0.269729\pi$
$200$	37.5285	−	7.09449i	2.65367	−	0.501656i
$201$		0			0
$202$	7.25837	+	7.25837i	0.510697	+	0.510697i
$203$	1.68068	+	1.68068i	0.117961	+	0.117961i
$204$		0			0
$205$	−4.78400	−	9.05354i	−0.334129	−	0.632327i
$206$			39.6239i			2.76073i
$207$		0			0
$208$	0.655577	−	0.655577i	0.0454561	−	0.0454561i
$209$	12.2585			0.847940
$210$		0			0
$211$	4.58636			0.315738			0.157869	−	0.987460i	$-0.449538\pi$
$211$	4.58636			0.315738			0.157869	+	0.987460i	$0.449538\pi$
$212$	3.06800	−	3.06800i	0.210711	−	0.210711i
$213$		0			0
$214$		−	21.3671i		−	1.46062i
$215$	2.39828	−	7.77281i	0.163562	−	0.530101i
$216$		0			0
$217$	1.42331	+	1.42331i	0.0966205	+	0.0966205i
$218$	−6.88853	−	6.88853i	−0.466550	−	0.466550i
$219$		0			0
$220$	50.8747	−	26.8828i	3.42997	−	1.81244i
$221$			0.402338i			0.0270642i
$222$		0			0
$223$	−16.6563	+	16.6563i	−1.11539	+	1.11539i	−0.122982	+	0.992409i	$0.539246\pi$
$223$	−16.6563	+	16.6563i	−1.11539	+	1.11539i	−0.992409	+	0.122982i	$0.960754\pi$
$224$	8.01039			0.535217
$225$		0			0
$226$	−15.5132			−1.03192
$227$	−16.3479	+	16.3479i	−1.08505	+	1.08505i	−0.0890170	+	0.996030i	$0.528373\pi$
$227$	−16.3479	+	16.3479i	−1.08505	+	1.08505i	−0.996030	+	0.0890170i	$0.971627\pi$
$228$		0			0
$229$			23.6439i			1.56243i	0.624261	+	0.781216i	$0.285400\pi$
$229$			23.6439i			1.56243i	−0.624261	+	0.781216i	$0.714600\pi$
$230$	30.7170	−	16.2312i	2.02542	−	1.07025i
$231$		0			0
$232$	18.7358	+	18.7358i	1.23007	+	1.23007i
$233$	0.0231441	+	0.0231441i	0.00151622	+	0.00151622i	0.707864	−	0.706348i	$-0.249659\pi$
$233$	0.0231441	+	0.0231441i	0.00151622	+	0.00151622i	−0.706348	+	0.707864i	$0.749659\pi$
$234$		0			0
$235$	−2.31116	+	7.49045i	−0.150764	+	0.488623i
$236$			10.0319i			0.653018i
$237$		0			0
$238$	−5.67033	+	5.67033i	−0.367553	+	0.367553i
$239$	−13.5197			−0.874517			−0.437258	−	0.899336i	$-0.644050\pi$
$239$	−13.5197			−0.874517			−0.437258	+	0.899336i	$0.644050\pi$
$240$		0			0
$241$	22.1681			1.42797			0.713985	−	0.700161i	$-0.246888\pi$
$241$	22.1681			1.42797			0.713985	+	0.700161i	$0.246888\pi$
$242$	30.6722	−	30.6722i	1.97168	−	1.97168i
$243$		0			0
$244$		−	43.2763i		−	2.77048i
$245$	6.82229	+	12.9109i	0.435860	+	0.824849i
$246$		0			0
$247$	−0.149329	−	0.149329i	−0.00950155	−	0.00950155i
$248$	15.8667	+	15.8667i	1.00754	+	1.00754i
$249$		0			0
$250$	−18.3140	−	22.9765i	−1.15828	−	1.45316i
$251$		−	6.07581i		−	0.383501i	−0.981444	−	0.191751i	$-0.938583\pi$
$251$		−	6.07581i		−	0.383501i	0.981444	−	0.191751i	$-0.0614165\pi$
$252$		0			0
$253$	21.9244	−	21.9244i	1.37838	−	1.37838i
$254$	14.2696			0.895352
$255$		0			0
$256$	−11.3999			−0.712494
$257$	8.64540	−	8.64540i	0.539285	−	0.539285i	−0.384034	−	0.923319i	$-0.625465\pi$
$257$	8.64540	−	8.64540i	0.539285	−	0.539285i	0.923319	+	0.384034i	$0.125465\pi$
$258$		0			0
$259$			4.26202i			0.264829i
$260$	−0.947211	−	0.292260i	−0.0587435	−	0.0181252i
$261$		0			0
$262$	39.0961	+	39.0961i	2.41537	+	2.41537i
$263$	−21.1631	−	21.1631i	−1.30497	−	1.30497i	−0.924998	−	0.379973i	$-0.875933\pi$
$263$	−21.1631	−	21.1631i	−1.30497	−	1.30497i	−0.379973	−	0.924998i	$-0.624067\pi$
$264$		0			0
$265$	−1.88942	−	0.582976i	−0.116066	−	0.0358120i
$266$		−	4.20911i		−	0.258077i
$267$		0			0
$268$	−0.196152	+	0.196152i	−0.0119819	+	0.0119819i
$269$	2.19392			0.133766			0.0668828	−	0.997761i	$-0.478695\pi$
$269$	2.19392			0.133766			0.0668828	+	0.997761i	$0.478695\pi$
$270$		0			0
$271$	−15.6614			−0.951361			−0.475681	−	0.879618i	$-0.657798\pi$
$271$	−15.6614			−0.951361			−0.475681	+	0.879618i	$0.657798\pi$
$272$	−32.3115	+	32.3115i	−1.95917	+	1.95917i
$273$		0			0
$274$		−	31.9678i		−	1.93125i
$275$	−21.6639	−	14.7753i	−1.30638	−	0.890987i
$276$		0			0
$277$	12.8816	+	12.8816i	0.773981	+	0.773981i	0.978800	−	0.204819i	$-0.0656605\pi$
$277$	12.8816	+	12.8816i	0.773981	+	0.773981i	−0.204819	+	0.978800i	$0.565660\pi$
$278$	10.2593	+	10.2593i	0.615309	+	0.615309i
$279$		0			0
$280$	−5.46802	−	10.3480i	−0.326777	−	0.618413i
$281$			0.677466i			0.0404142i	0.999796	+	0.0202071i	$0.00643256\pi$
$281$			0.677466i			0.0404142i	−0.999796	+	0.0202071i	$0.993567\pi$
$282$		0			0
$283$	13.9010	−	13.9010i	0.826328	−	0.826328i	−0.160679	−	0.987007i	$-0.551368\pi$
$283$	13.9010	−	13.9010i	0.826328	−	0.826328i	0.987007	+	0.160679i	$0.0513684\pi$
$284$	−61.7263			−3.66278
$285$		0			0
$286$	−1.24529			−0.0736355
$287$	−2.21881	+	2.21881i	−0.130972	+	0.130972i
$288$		0			0
$289$		−	2.83007i		−	0.166475i
$290$	6.00986	−	19.4779i	0.352911	−	1.14378i
$291$		0			0
$292$	−35.0626	−	35.0626i	−2.05189	−	2.05189i
$293$	9.08093	+	9.08093i	0.530514	+	0.530514i	0.920725	−	0.390212i	$-0.127598\pi$
$293$	9.08093	+	9.08093i	0.530514	+	0.530514i	−0.390212	+	0.920725i	$0.627598\pi$
$294$		0			0
$295$	4.04216	−	2.13593i	0.235344	−	0.124358i
$296$			47.5119i			2.76157i
$297$		0			0
$298$	−27.1547	+	27.1547i	−1.57303	+	1.57303i
$299$	−0.534149			−0.0308906
$300$		0			0
$301$	−2.49269			−0.143676
$302$	−29.0136	+	29.0136i	−1.66954	+	1.66954i
$303$		0			0
$304$		−	23.9850i		−	1.37563i
$305$	−17.4374	+	9.21415i	−0.998465	+	0.527601i
$306$		0			0
$307$	−11.2227	−	11.2227i	−0.640513	−	0.640513i	0.310169	−	0.950681i	$-0.399614\pi$
$307$	−11.2227	−	11.2227i	−0.640513	−	0.640513i	−0.950681	+	0.310169i	$0.899614\pi$
$308$	−12.4682	−	12.4682i	−0.710441	−	0.710441i
$309$		0			0
$310$	5.08953	−	16.4951i	0.289066	−	0.936859i
$311$			24.3872i			1.38287i	0.722437	+	0.691437i	$0.243022\pi$
$311$			24.3872i			1.38287i	−0.722437	+	0.691437i	$0.756978\pi$
$312$		0			0
$313$	10.6942	−	10.6942i	0.604474	−	0.604474i	−0.337023	−	0.941497i	$-0.609420\pi$
$313$	10.6942	−	10.6942i	0.604474	−	0.604474i	0.941497	+	0.337023i	$0.109420\pi$
$314$	36.6581			2.06874
$315$		0			0
$316$	26.2742			1.47804
$317$	−11.4112	+	11.4112i	−0.640916	+	0.640916i	−0.950781	−	0.309864i	$-0.899716\pi$
$317$	−11.4112	+	11.4112i	−0.640916	+	0.640916i	0.309864	+	0.950781i	$0.399716\pi$
$318$		0			0
$319$		−	18.1920i		−	1.01856i
$320$	−10.6553	−	20.1648i	−0.595651	−	1.12725i
$321$		0			0
$322$	−7.52800	−	7.52800i	−0.419519	−	0.419519i
$323$	7.35997	+	7.35997i	0.409520	+	0.409520i
$324$		0			0
$325$	0.0839138	+	0.443889i	0.00465470	+	0.0246225i
$326$		−	45.2101i		−	2.50395i
$327$		0			0
$328$	−24.7347	+	24.7347i	−1.36575	+	1.36575i
$329$	2.40214			0.132434
$330$		0			0
$331$	−6.41769			−0.352748			−0.176374	−	0.984323i	$-0.556437\pi$
$331$	−6.41769			−0.352748			−0.176374	+	0.984323i	$0.556437\pi$
$332$	17.5491	−	17.5491i	0.963133	−	0.963133i
$333$		0			0
$334$			25.0225i			1.36917i
$335$	0.120800	+	0.0372725i	0.00660000	+	0.00203642i
$336$		0			0
$337$	11.9893	+	11.9893i	0.653100	+	0.653100i	0.953738	−	0.300638i	$-0.0971997\pi$
$337$	11.9893	+	11.9893i	0.653100	+	0.653100i	−0.300638	+	0.953738i	$0.597200\pi$
$338$	−24.1428	−	24.1428i	−1.31319	−	1.31319i
$339$		0			0
$340$	46.6853	+	14.4046i	2.53187	+	0.781202i
$341$		−	15.4062i		−	0.834290i
$342$		0			0
$343$	6.55582	−	6.55582i	0.353981	−	0.353981i
$344$	−27.7879			−1.49822
$345$		0			0
$346$	−23.5160			−1.26423
$347$	−3.80833	+	3.80833i	−0.204442	+	0.204442i	−0.801900	−	0.597458i	$-0.796177\pi$
$347$	−3.80833	+	3.80833i	−0.204442	+	0.204442i	0.597458	+	0.801900i	$0.296177\pi$
$348$		0			0
$349$		−	7.06928i		−	0.378410i	−0.981938	−	0.189205i	$-0.939409\pi$
$349$		−	7.06928i		−	0.378410i	0.981938	−	0.189205i	$-0.0605910\pi$
$350$	−5.07329	+	7.43856i	−0.271179	+	0.397608i
$351$		0			0
$352$	−43.3530	−	43.3530i	−2.31072	−	2.31072i
$353$	21.0411	+	21.0411i	1.11990	+	1.11990i	0.991755	+	0.128149i	$0.0409035\pi$
$353$	21.0411	+	21.0411i	1.11990	+	1.11990i	0.128149	+	0.991755i	$0.459097\pi$
$354$		0			0
$355$	13.1424	+	24.8715i	0.697527	+	1.32004i
$356$		−	69.8754i		−	3.70339i
$357$		0			0
$358$	7.64489	−	7.64489i	0.404045	−	0.404045i
$359$	13.5719			0.716299			0.358149	−	0.933664i	$-0.383408\pi$
$359$	13.5719			0.716299			0.358149	+	0.933664i	$0.383408\pi$
$360$		0			0
$361$	13.5367			0.712456
$362$	20.5250	−	20.5250i	1.07877	−	1.07877i
$363$		0			0
$364$			0.303765i			0.0159216i
$365$	−6.66254	+	21.5932i	−0.348733	+	1.13024i
$366$		0			0
$367$	8.69358	+	8.69358i	0.453801	+	0.453801i	0.896614	−	0.442813i	$-0.146019\pi$
$367$	8.69358	+	8.69358i	0.453801	+	0.453801i	−0.442813	+	0.896614i	$0.646019\pi$
$368$	−42.8972	−	42.8972i	−2.23617	−	2.23617i
$369$		0			0
$370$	32.3170	−	17.0767i	1.68008	−	0.887774i
$371$			0.605926i			0.0314581i
$372$		0			0
$373$	12.9869	−	12.9869i	0.672434	−	0.672434i	−0.285843	−	0.958277i	$-0.592273\pi$
$373$	12.9869	−	12.9869i	0.672434	−	0.672434i	0.958277	+	0.285843i	$0.0922734\pi$
$374$	61.3767			3.17371
$375$		0			0
$376$	26.7785			1.38100
$377$	−0.221608	+	0.221608i	−0.0114134	+	0.0114134i
$378$		0			0
$379$			11.7691i			0.604536i	0.953223	+	0.302268i	$0.0977438\pi$
$379$			11.7691i			0.604536i	−0.953223	+	0.302268i	$0.902256\pi$
$380$	−22.6737	+	11.9810i	−1.16313	+	0.614614i
$381$		0			0
$382$	24.2993	+	24.2993i	1.24326	+	1.24326i
$383$	3.98843	+	3.98843i	0.203799	+	0.203799i	0.801626	−	0.597826i	$-0.203969\pi$
$383$	3.98843	+	3.98843i	0.203799	+	0.203799i	−0.597826	+	0.801626i	$0.703969\pi$
$384$		0			0
$385$	−2.36918	+	7.67850i	−0.120745	+	0.391333i
$386$		−	48.5210i		−	2.46965i
$387$		0			0
$388$	−55.1711	+	55.1711i	−2.80089	+	2.80089i
$389$	−10.0768			−0.510916			−0.255458	−	0.966820i	$-0.582226\pi$
$389$	−10.0768			−0.510916			−0.255458	+	0.966820i	$0.582226\pi$
$390$		0			0
$391$	26.3267			1.33140
$392$	35.2733	−	35.2733i	1.78157	−	1.78157i
$393$		0			0
$394$		−	41.3184i		−	2.08159i
$395$	−5.59416	−	10.5867i	−0.281473	−	0.532677i
$396$		0			0
$397$	−9.61428	−	9.61428i	−0.482527	−	0.482527i	0.423411	−	0.905938i	$-0.360833\pi$
$397$	−9.61428	−	9.61428i	−0.482527	−	0.482527i	−0.905938	+	0.423411i	$0.860833\pi$
$398$	39.2983	+	39.2983i	1.96984	+	1.96984i
$399$		0			0
$400$	−28.9093	+	42.3875i	−1.44547	+	2.11937i
$401$			29.1528i			1.45582i	0.685672	+	0.727911i	$0.259508\pi$
$401$			29.1528i			1.45582i	−0.685672	+	0.727911i	$0.740492\pi$
$402$		0			0
$403$	−0.187672	+	0.187672i	−0.00934859	+	0.00934859i
$404$	−19.1647			−0.953480
$405$		0			0
$406$	−6.24645			−0.310006
$407$	23.0664	−	23.0664i	1.14336	−	1.14336i
$408$		0			0
$409$			24.1470i			1.19399i	0.802244	+	0.596996i	$0.203639\pi$
$409$			24.1470i			1.19399i	−0.802244	+	0.596996i	$0.796361\pi$
$410$	25.7144	+	7.93411i	1.26994	+	0.391838i
$411$		0			0
$412$	−52.3107	−	52.3107i	−2.57716	−	2.57716i
$413$	−0.990638	−	0.990638i	−0.0487461	−	0.0487461i
$414$		0			0
$415$	−10.8076	−	3.33465i	−0.530523	−	0.163692i
$416$			1.05622i			0.0517853i
$417$		0			0
$418$	−22.7801	+	22.7801i	−1.11421	+	1.11421i
$419$	−20.8299			−1.01761			−0.508803	−	0.860883i	$-0.669912\pi$
$419$	−20.8299			−1.01761			−0.508803	+	0.860883i	$0.669912\pi$
$420$		0			0
$421$	5.54985			0.270483			0.135242	−	0.990813i	$-0.456819\pi$
$421$	5.54985			0.270483			0.135242	+	0.990813i	$0.456819\pi$
$422$	−8.52286	+	8.52286i	−0.414886	+	0.414886i
$423$		0			0
$424$			6.75471i			0.328038i
$425$	−4.13587	−	21.8780i	−0.200619	−	1.06124i
$426$		0			0
$427$	4.27351	+	4.27351i	0.206809	+	0.206809i
$428$	28.2084	+	28.2084i	1.36350	+	1.36350i
$429$		0			0
$430$	9.98750	+	18.9010i	0.481640	+	0.911486i
$431$		−	10.4835i		−	0.504972i	−0.967601	−	0.252486i	$-0.918752\pi$
$431$		−	10.4835i		−	0.504972i	0.967601	−	0.252486i	$-0.0812481\pi$
$432$		0			0
$433$	4.34442	−	4.34442i	0.208780	−	0.208780i	−0.594969	−	0.803749i	$-0.702836\pi$
$433$	4.34442	−	4.34442i	0.208780	−	0.208780i	0.803749	+	0.594969i	$0.202836\pi$
$434$	−5.28988			−0.253923
$435$		0			0
$436$	18.1882			0.871057
$437$	−9.77119	+	9.77119i	−0.467420	+	0.467420i
$438$		0			0
$439$			32.8157i			1.56621i	0.621890	+	0.783105i	$0.286365\pi$
$439$			32.8157i			1.56621i	−0.621890	+	0.783105i	$0.713635\pi$
$440$	−26.4111	+	85.5980i	−1.25910	+	4.08072i
$441$		0			0
$442$	−0.747666	−	0.747666i	−0.0355629	−	0.0355629i
$443$	−25.1989	−	25.1989i	−1.19724	−	1.19724i	−0.974990	−	0.222247i	$-0.928661\pi$
$443$	−25.1989	−	25.1989i	−1.19724	−	1.19724i	−0.222247	−	0.974990i	$-0.571339\pi$
$444$		0			0
$445$	−28.1551	+	14.8775i	−1.33468	+	0.705260i
$446$		−	61.9051i		−	2.93129i
$447$		0			0
$448$	−4.94192	+	4.94192i	−0.233484	+	0.233484i
$449$	−17.5910			−0.830173			−0.415086	−	0.909782i	$-0.636249\pi$
$449$	−17.5910			−0.830173			−0.415086	+	0.909782i	$0.636249\pi$
$450$		0			0
$451$	24.0168			1.13091
$452$	20.4803	−	20.4803i	0.963310	−	0.963310i
$453$		0			0
$454$		−	60.7587i		−	2.85155i
$455$	0.122397	−	0.0646760i	0.00573805	−	0.00303206i
$456$		0			0
$457$	3.15387	+	3.15387i	0.147532	+	0.147532i	0.777014	−	0.629483i	$-0.216733\pi$
$457$	3.15387	+	3.15387i	0.147532	+	0.147532i	−0.629483	+	0.777014i	$0.716733\pi$
$458$	−43.9375	−	43.9375i	−2.05307	−	2.05307i
$459$		0			0
$460$	−19.1238	+	61.9800i	−0.891652	+	2.88983i
$461$		−	14.4147i		−	0.671361i	−0.941976	−	0.335681i	$-0.891034\pi$
$461$		−	14.4147i		−	0.671361i	0.941976	−	0.335681i	$-0.108966\pi$
$462$		0			0
$463$	−2.38794	+	2.38794i	−0.110977	+	0.110977i	−0.760415	−	0.649438i	$-0.775004\pi$
$463$	−2.38794	+	2.38794i	−0.110977	+	0.110977i	0.649438	+	0.760415i	$0.275004\pi$
$464$	−35.5944			−1.65243
$465$		0			0
$466$	−0.0860178			−0.00398470
$467$	−10.5757	+	10.5757i	−0.489385	+	0.489385i	−0.908112	−	0.418727i	$-0.862476\pi$
$467$	−10.5757	+	10.5757i	−0.489385	+	0.489385i	0.418727	+	0.908112i	$0.362476\pi$
$468$		0			0
$469$		−	0.0387398i		−	0.00178884i
$470$	−9.62470	−	18.2144i	−0.443954	−	0.840167i
$471$		0			0
$472$	−11.0434	−	11.0434i	−0.508313	−	0.508313i
$473$	13.4907	+	13.4907i	0.620303	+	0.620303i
$474$		0			0
$475$	9.65510	+	6.58502i	0.443006	+	0.302142i
$476$		−	14.9717i		−	0.686227i
$477$		0			0
$478$	25.1237	−	25.1237i	1.14913	−	1.14913i
$479$	16.0825			0.734827			0.367413	−	0.930058i	$-0.380243\pi$
$479$	16.0825			0.734827			0.367413	+	0.930058i	$0.380243\pi$
$480$		0			0
$481$	−0.561972			−0.0256237
$482$	−41.1950	+	41.1950i	−1.87638	+	1.87638i
$483$		0			0
$484$			80.9855i			3.68116i
$485$	33.9770	+	10.4835i	1.54281	+	0.476032i
$486$		0			0
$487$	−3.27106	−	3.27106i	−0.148226	−	0.148226i	0.629099	−	0.777325i	$-0.283424\pi$
$487$	−3.27106	−	3.27106i	−0.148226	−	0.148226i	−0.777325	+	0.629099i	$0.783424\pi$
$488$	47.6400	+	47.6400i	2.15656	+	2.15656i
$489$		0			0
$490$	−36.6703	−	11.3145i	−1.65660	−	0.511139i
$491$			13.4883i			0.608719i	0.952557	+	0.304360i	$0.0984425\pi$
$491$			13.4883i			0.608719i	−0.952557	+	0.304360i	$0.901558\pi$
$492$		0			0
$493$	10.9224	−	10.9224i	0.491921	−	0.491921i
$494$	0.554996			0.0249704
$495$		0			0
$496$	−30.1436			−1.35349
$497$	6.09543	−	6.09543i	0.273417	−	0.273417i
$498$		0			0
$499$		−	2.90316i		−	0.129963i	−0.997886	−	0.0649817i	$-0.979301\pi$
$499$		−	2.90316i		−	0.129963i	0.997886	−	0.0649817i	$-0.0206989\pi$
$500$	54.5110	+	6.15532i	2.43780	+	0.275274i
$501$		0			0
$502$	11.2907	+	11.2907i	0.503929	+	0.503929i
$503$	−19.6808	−	19.6808i	−0.877522	−	0.877522i	0.115756	−	0.993278i	$-0.463071\pi$
$503$	−19.6808	−	19.6808i	−0.877522	−	0.877522i	−0.993278	+	0.115756i	$0.963071\pi$
$504$		0			0
$505$	4.08044	+	7.72209i	0.181577	+	0.343628i
$506$			81.4845i			3.62243i
$507$		0			0
$508$	−18.8384	+	18.8384i	−0.835819	+	0.835819i
$509$	−26.9370			−1.19396			−0.596980	−	0.802256i	$-0.703633\pi$
$509$	−26.9370			−1.19396			−0.596980	+	0.802256i	$0.703633\pi$
$510$		0			0
$511$	6.92482			0.306336
$512$	26.0272	−	26.0272i	1.15025	−	1.15025i
$513$		0			0
$514$			32.1316i			1.41726i
$515$	−9.93999	+	32.2154i	−0.438008	+	1.41958i
$516$		0			0
$517$	−13.0006	−	13.0006i	−0.571767	−	0.571767i
$518$	−7.92013	−	7.92013i	−0.347990	−	0.347990i
$519$		0			0
$520$	1.36445	−	0.720991i	0.0598351	−	0.0316176i
$521$			22.3103i			0.977434i	0.872442	+	0.488717i	$0.162535\pi$
$521$			22.3103i			0.977434i	−0.872442	+	0.488717i	$0.837465\pi$
$522$		0			0
$523$	6.60413	−	6.60413i	0.288778	−	0.288778i	−0.547819	−	0.836597i	$-0.684542\pi$
$523$	6.60413	−	6.60413i	0.288778	−	0.288778i	0.836597	+	0.547819i	$0.184542\pi$
$524$	−103.228			−4.50953
$525$		0			0
$526$	78.6549			3.42951
$527$	9.24980	−	9.24980i	0.402927	−	0.402927i
$528$		0			0
$529$			11.9516i			0.519636i
$530$	4.59447	−	2.42777i	0.199571	−	0.105456i
$531$		0			0
$532$	5.55678	+	5.55678i	0.240917	+	0.240917i
$533$	−0.292563	−	0.292563i	−0.0126723	−	0.0126723i
$534$		0			0
$535$	5.36011	−	17.3721i	0.231738	−	0.751060i
$536$		−	0.431862i		−	0.0186536i
$537$		0			0
$538$	−4.07697	+	4.07697i	−0.175771	+	0.175771i
$539$	−34.2495			−1.47523
$540$		0			0
$541$	4.79329			0.206080			0.103040	−	0.994677i	$-0.467143\pi$
$541$	4.79329			0.206080			0.103040	+	0.994677i	$0.467143\pi$
$542$	29.1036	−	29.1036i	1.25011	−	1.25011i
$543$		0			0
$544$		−	52.0579i		−	2.23197i
$545$	−3.87253	−	7.32862i	−0.165881	−	0.313924i
$546$		0			0
$547$	−25.1971	−	25.1971i	−1.07735	−	1.07735i	−0.996746	−	0.0806044i	$-0.974315\pi$
$547$	−25.1971	−	25.1971i	−1.07735	−	1.07735i	−0.0806044	−	0.996746i	$-0.525685\pi$
$548$	42.2033	+	42.2033i	1.80283	+	1.80283i
$549$		0			0
$550$	67.7153	−	12.8011i	2.88739	−	0.545839i
$551$			8.10776i			0.345402i
$552$		0			0
$553$	−2.59456	+	2.59456i	−0.110332	+	0.110332i
$554$	−47.8759			−2.03405
$555$		0			0
$556$	−27.0881			−1.14879
$557$	9.03850	−	9.03850i	0.382974	−	0.382974i	−0.489199	−	0.872172i	$-0.662711\pi$
$557$	9.03850	−	9.03850i	0.382974	−	0.382974i	0.872172	+	0.489199i	$0.162711\pi$
$558$		0			0
$559$		−	0.328677i		−	0.0139015i
$560$	15.0237	+	4.63553i	0.634867	+	0.195887i
$561$		0			0
$562$	−1.25894	−	1.25894i	−0.0531051	−	0.0531051i
$563$	−3.62845	−	3.62845i	−0.152921	−	0.152921i	0.626500	−	0.779421i	$-0.284487\pi$
$563$	−3.62845	−	3.62845i	−0.152921	−	0.152921i	−0.779421	+	0.626500i	$0.784487\pi$
$564$		0			0
$565$	−12.6127	−	3.89162i	−0.530621	−	0.163722i
$566$			51.6645i			2.17162i
$567$		0			0
$568$	67.9503	−	67.9503i	2.85113	−	2.85113i
$569$	−38.9268			−1.63190			−0.815948	−	0.578126i	$-0.803784\pi$
$569$	−38.9268			−1.63190			−0.815948	+	0.578126i	$0.803784\pi$
$570$		0			0
$571$	28.2374			1.18170			0.590848	−	0.806783i	$-0.298793\pi$
$571$	28.2374			1.18170			0.590848	+	0.806783i	$0.298793\pi$
$572$	1.64401	−	1.64401i	0.0687393	−	0.0687393i
$573$		0			0
$574$		−	8.24645i		−	0.344200i
$575$	29.0455	−	5.49083i	1.21128	−	0.228984i
$576$		0			0
$577$	−12.1777	−	12.1777i	−0.506962	−	0.506962i	0.406630	−	0.913593i	$-0.366704\pi$
$577$	−12.1777	−	12.1777i	−0.506962	−	0.506962i	−0.913593	+	0.406630i	$0.866704\pi$
$578$	5.25914	+	5.25914i	0.218751	+	0.218751i
$579$		0			0
$580$	17.7802	+	33.6484i	0.738284	+	1.39717i
$581$			3.46593i			0.143791i
$582$		0			0
$583$	3.27933	−	3.27933i	0.135816	−	0.135816i
$584$	77.1962			3.19440
$585$		0			0
$586$	−33.7503			−1.39421
$587$	−0.0889004	+	0.0889004i	−0.00366931	+	0.00366931i	−0.708939	−	0.705270i	$-0.750826\pi$
$587$	−0.0889004	+	0.0889004i	−0.00366931	+	0.00366931i	0.705270	+	0.708939i	$0.250826\pi$
$588$		0			0
$589$			6.86616i			0.282915i
$590$	−3.54237	+	11.4808i	−0.145837	+	0.472656i
$591$		0			0
$592$	−45.1316	−	45.1316i	−1.85490	−	1.85490i
$593$	3.86396	+	3.86396i	0.158674	+	0.158674i	0.781979	−	0.623305i	$-0.214210\pi$
$593$	3.86396	+	3.86396i	0.158674	+	0.158674i	−0.623305	+	0.781979i	$0.714210\pi$
$594$		0			0
$595$	−6.03259	+	3.18769i	−0.247312	+	0.130683i
$596$		−	71.6983i		−	2.93688i
$597$		0			0
$598$	0.992612	−	0.992612i	0.0405909	−	0.0405909i
$599$	27.3735			1.11845			0.559225	−	0.829016i	$-0.311099\pi$
$599$	27.3735			1.11845			0.559225	+	0.829016i	$0.311099\pi$
$600$		0			0
$601$	−5.98852			−0.244277			−0.122138	−	0.992513i	$-0.538975\pi$
$601$	−5.98852			−0.244277			−0.122138	+	0.992513i	$0.538975\pi$
$602$	4.63219	−	4.63219i	0.188794	−	0.188794i
$603$		0			0
$604$		−	76.6063i		−	3.11707i
$605$	32.6317	−	17.2430i	1.32667	−	0.701027i
$606$		0			0
$607$	−9.28582	−	9.28582i	−0.376900	−	0.376900i	0.493083	−	0.869982i	$-0.335870\pi$
$607$	−9.28582	−	9.28582i	−0.376900	−	0.376900i	−0.869982	+	0.493083i	$0.835870\pi$
$608$	19.3214	+	19.3214i	0.783587	+	0.783587i
$609$		0			0
$610$	15.2814	−	49.5268i	0.618725	−	2.00528i
$611$			0.316737i			0.0128138i
$612$		0			0
$613$	−23.8814	+	23.8814i	−0.964560	+	0.964560i	−0.999393	−	0.0348332i	$-0.988910\pi$
$613$	−23.8814	+	23.8814i	−0.964560	+	0.964560i	0.0348332	+	0.999393i	$0.488910\pi$
$614$	41.7103			1.68329
$615$		0			0
$616$	27.4508			1.10602
$617$	26.9091	−	26.9091i	1.08332	−	1.08332i	0.0871206	−	0.996198i	$-0.472233\pi$
$617$	26.9091	−	26.9091i	1.08332	−	1.08332i	0.996198	−	0.0871206i	$-0.0277666\pi$
$618$		0			0
$619$		−	49.6022i		−	1.99368i	−0.0794249	−	0.996841i	$-0.525308\pi$
$619$		−	49.6022i		−	1.99368i	0.0794249	−	0.996841i	$-0.474692\pi$
$620$	15.0574	+	28.4956i	0.604720	+	1.14441i
$621$		0			0
$622$	−45.3189	−	45.3189i	−1.81712	−	1.81712i
$623$	6.90014	+	6.90014i	0.276448	+	0.276448i
$624$		0			0
$625$	−9.12599	−	23.2748i	−0.365040	−	0.930992i
$626$			39.7463i			1.58858i
$627$		0			0
$628$	−48.3953	+	48.3953i	−1.93118	+	1.93118i
$629$	27.6980			1.10439
$630$		0			0
$631$	−14.6385			−0.582749			−0.291375	−	0.956609i	$-0.594113\pi$
$631$	−14.6385			−0.582749			−0.291375	+	0.956609i	$0.594113\pi$
$632$	−28.9235	+	28.9235i	−1.15052	+	1.15052i
$633$		0			0
$634$		−	42.4109i		−	1.68435i
$635$	11.6016	+	3.57964i	0.460394	+	0.142054i
$636$		0			0
$637$	0.417214	+	0.417214i	0.0165306	+	0.0165306i
$638$	33.8064	+	33.8064i	1.33841	+	1.33841i
$639$		0			0
$640$	7.31663	+	2.25753i	0.289215	+	0.0892367i
$641$		−	6.91608i		−	0.273169i	−0.990628	−	0.136584i	$-0.956387\pi$
$641$		−	6.91608i		−	0.273169i	0.990628	−	0.136584i	$-0.0436125\pi$
$642$		0			0
$643$	−20.9969	+	20.9969i	−0.828037	+	0.828037i	−0.987245	−	0.159208i	$-0.949106\pi$
$643$	−20.9969	+	20.9969i	−0.828037	+	0.828037i	0.159208	+	0.987245i	$0.449106\pi$
$644$	19.8766			0.783249
$645$		0			0
$646$	−27.3541			−1.07623
$647$	2.08629	−	2.08629i	0.0820205	−	0.0820205i	−0.664906	−	0.746927i	$-0.731529\pi$
$647$	2.08629	−	2.08629i	0.0820205	−	0.0820205i	0.746927	+	0.664906i	$0.231529\pi$
$648$		0			0
$649$			10.7229i			0.420909i
$650$	−0.980818	−	0.668943i	−0.0384708	−	0.0262381i
$651$		0			0
$652$	59.6854	+	59.6854i	2.33746	+	2.33746i
$653$	−22.7402	−	22.7402i	−0.889893	−	0.889893i	0.104620	−	0.994512i	$-0.466638\pi$
$653$	−22.7402	−	22.7402i	−0.889893	−	0.889893i	−0.994512	+	0.104620i	$0.966638\pi$
$654$		0			0
$655$	21.9787	+	41.5939i	0.858779	+	1.62521i
$656$		−	46.9911i		−	1.83469i
$657$		0			0
$658$	−4.46392	+	4.46392i	−0.174022	+	0.174022i
$659$	28.7505			1.11996			0.559980	−	0.828506i	$-0.310809\pi$
$659$	28.7505			1.11996			0.559980	+	0.828506i	$0.310809\pi$
$660$		0			0
$661$	−10.6289			−0.413415			−0.206708	−	0.978403i	$-0.566275\pi$
$661$	−10.6289			−0.413415			−0.206708	+	0.978403i	$0.566275\pi$
$662$	11.9260	−	11.9260i	0.463518	−	0.463518i
$663$		0			0
$664$			38.6373i			1.49942i
$665$	1.05589	−	3.42213i	0.0409456	−	0.132704i
$666$		0			0
$667$	14.5008	+	14.5008i	0.561472	+	0.561472i
$668$	−33.0342	−	33.0342i	−1.27813	−	1.27813i
$669$		0			0
$670$	−0.293747	+	0.155219i	−0.0113484	+	0.00599664i
$671$		−	46.2572i		−	1.78574i
$672$		0			0
$673$	29.1119	−	29.1119i	1.12218	−	1.12218i	0.130768	−	0.991413i	$-0.458256\pi$
$673$	29.1119	−	29.1119i	1.12218	−	1.12218i	0.991413	−	0.130768i	$-0.0417442\pi$
$674$	−44.5596			−1.71637
$675$		0			0
$676$	63.7457			2.45176
$677$	−33.3164	+	33.3164i	−1.28045	+	1.28045i	−0.340044	+	0.940409i	$0.610442\pi$
$677$	−33.3164	+	33.3164i	−1.28045	+	1.28045i	−0.940409	+	0.340044i	$0.889558\pi$
$678$		0			0
$679$		−	10.8962i		−	0.418158i
$680$	−67.2498	+	35.5356i	−2.57891	+	1.36273i
$681$		0			0
$682$	28.6293	+	28.6293i	1.09627	+	1.09627i
$683$	3.17588	+	3.17588i	0.121522	+	0.121522i	0.765252	−	0.643730i	$-0.222614\pi$
$683$	3.17588	+	3.17588i	0.121522	+	0.121522i	−0.643730	+	0.765252i	$0.722614\pi$
$684$		0			0
$685$	8.01939	−	25.9907i	0.306405	−	0.993055i
$686$			24.3654i			0.930276i
$687$		0			0
$688$	26.3958	−	26.3958i	1.00633	−	1.00633i
$689$	−0.0798949			−0.00304375
$690$		0			0
$691$	−37.1786			−1.41434			−0.707171	−	0.707043i	$-0.750029\pi$
$691$	−37.1786			−1.41434			−0.707171	+	0.707043i	$0.750029\pi$
$692$	31.0453	−	31.0453i	1.18017	−	1.18017i
$693$		0			0
$694$		−	14.1541i		−	0.537281i
$695$	5.76745	+	10.9147i	0.218772	+	0.414018i
$696$		0			0
$697$	14.4196	+	14.4196i	0.546181	+	0.546181i
$698$	13.1369	+	13.1369i	0.497238	+	0.497238i
$699$		0			0
$700$	−3.12258	−	16.5179i	−0.118022	−	0.624317i
$701$			3.87768i			0.146458i	0.997315	+	0.0732290i	$0.0233304\pi$
$701$			3.87768i			0.146458i	−0.997315	+	0.0732290i	$0.976670\pi$
$702$		0			0
$703$	−10.2802	+	10.2802i	−0.387724	+	0.387724i
$704$	53.4923			2.01607
$705$		0			0
$706$	−78.2015			−2.94315
$707$	1.89250	−	1.89250i	0.0711748	−	0.0711748i
$708$		0			0
$709$		−	11.7484i		−	0.441219i	−0.975362	−	0.220609i	$-0.929195\pi$
$709$		−	11.7484i		−	0.441219i	0.975362	−	0.220609i	$-0.0708046\pi$
$710$	−70.6415	−	21.7963i	−2.65113	−	0.818000i
$711$		0			0
$712$	76.9211	+	76.9211i	2.88274	+	2.88274i
$713$	12.2802	+	12.2802i	0.459895	+	0.459895i
$714$		0			0
$715$	−1.01246	−	0.312391i	−0.0378637	−	0.0116828i
$716$			20.1853i			0.754358i
$717$		0			0
$718$	−25.2208	+	25.2208i	−0.941231	+	0.941231i
$719$	−7.25104			−0.270418			−0.135209	−	0.990817i	$-0.543171\pi$
$719$	−7.25104			−0.270418			−0.135209	+	0.990817i	$0.543171\pi$
$720$		0			0
$721$	10.3313			0.384757
$722$	−25.1552	+	25.1552i	−0.936181	+	0.936181i
$723$		0			0
$724$			54.1935i			2.01408i
$725$	9.77238	−	14.3285i	0.362937	−	0.532146i
$726$		0			0
$727$	18.2889	+	18.2889i	0.678298	+	0.678298i	0.959615	−	0.281317i	$-0.0907711\pi$
$727$	18.2889	+	18.2889i	0.678298	+	0.678298i	−0.281317	+	0.959615i	$0.590771\pi$
$728$	−0.334394	−	0.334394i	−0.0123935	−	0.0123935i
$729$		0			0
$730$	−27.7458	−	52.5078i	−1.02692	−	1.94340i
$731$			16.1995i			0.599161i
$732$		0			0
$733$	19.1199	−	19.1199i	0.706211	−	0.706211i	−0.259526	−	0.965736i	$-0.583566\pi$
$733$	19.1199	−	19.1199i	0.706211	−	0.706211i	0.965736	+	0.259526i	$0.0835662\pi$
$734$	−32.3106			−1.19261
$735$		0			0
$736$	69.1128			2.54753
$737$	−0.209664	+	0.209664i	−0.00772306	+	0.00772306i
$738$		0			0
$739$			40.0776i			1.47428i	0.675740	+	0.737140i	$0.263824\pi$
$739$			40.0776i			1.47428i	−0.675740	+	0.737140i	$0.736176\pi$
$740$	−20.1199	+	65.2085i	−0.739624	+	2.39711i
$741$		0			0
$742$	−1.12600	−	1.12600i	−0.0413366	−	0.0413366i
$743$	2.76057	+	2.76057i	0.101275	+	0.101275i	0.755929	−	0.654654i	$-0.227186\pi$
$743$	2.76057	+	2.76057i	0.101275	+	0.101275i	−0.654654	+	0.755929i	$0.727186\pi$
$744$		0			0
$745$	−28.8896	+	15.2656i	−1.05843	+	0.559288i
$746$			48.2671i			1.76718i
$747$		0			0
$748$	−81.0283	+	81.0283i	−2.96269	+	2.96269i
$749$	−5.57112			−0.203564
$750$		0			0
$751$	−23.8913			−0.871806			−0.435903	−	0.899994i	$-0.643571\pi$
$751$	−23.8913			−0.871806			−0.435903	+	0.899994i	$0.643571\pi$
$752$	−25.4369	+	25.4369i	−0.927589	+	0.927589i
$753$		0			0
$754$		−	0.823631i		−	0.0299949i
$755$	−30.8672	+	16.3106i	−1.12337	+	0.593603i
$756$		0			0
$757$	17.6447	+	17.6447i	0.641309	+	0.641309i	0.950877	−	0.309568i	$-0.100185\pi$
$757$	17.6447	+	17.6447i	0.641309	+	0.641309i	−0.309568	+	0.950877i	$0.600185\pi$
$758$	−21.8705	−	21.8705i	−0.794373	−	0.794373i
$759$		0			0
$760$	11.7708	−	38.1490i	0.426972	−	1.38381i
$761$			5.21490i			0.189040i	0.995523	+	0.0945200i	$0.0301316\pi$
$761$			5.21490i			0.189040i	−0.995523	+	0.0945200i	$0.969868\pi$
$762$		0			0
$763$	−1.79607	+	1.79607i	−0.0650222	+	0.0650222i
$764$	−64.1590			−2.32119
$765$		0			0
$766$	−14.8234			−0.535593
$767$	0.130622	−	0.130622i	0.00471647	−	0.00471647i
$768$		0			0
$769$		−	29.6344i		−	1.06864i	−0.845281	−	0.534322i	$-0.820567\pi$
$769$		−	29.6344i		−	1.06864i	0.845281	−	0.534322i	$-0.179433\pi$
$770$	−9.86633	−	18.6717i	−0.355558	−	0.672880i
$771$		0			0
$772$	64.0564	+	64.0564i	2.30544	+	2.30544i
$773$	−9.60685	−	9.60685i	−0.345535	−	0.345535i	0.512909	−	0.858443i	$-0.328568\pi$
$773$	−9.60685	−	9.60685i	−0.345535	−	0.345535i	−0.858443	+	0.512909i	$0.828568\pi$
$774$		0			0
$775$	8.27587	−	12.1342i	0.297278	−	0.435875i
$776$		−	121.468i		−	4.36046i
$777$		0			0
$778$	18.7259	−	18.7259i	0.671354	−	0.671354i
$779$	−10.7037			−0.383501
$780$		0			0
$781$	−65.9780			−2.36088
$782$	−48.9230	+	48.9230i	−1.74948	+	1.74948i
$783$		0			0
$784$			67.0123i			2.39330i
$785$	29.8041	+	9.19599i	1.06375	+	0.328219i
$786$		0			0
$787$	−22.1540	−	22.1540i	−0.789704	−	0.789704i	0.191741	−	0.981446i	$-0.438587\pi$
$787$	−22.1540	−	22.1540i	−0.789704	−	0.789704i	−0.981446	+	0.191741i	$0.938587\pi$
$788$	54.5477	+	54.5477i	1.94318	+	1.94318i
$789$		0			0
$790$	30.0691	+	9.27774i	1.06981	+	0.330087i
$791$			4.04482i			0.143817i
$792$		0			0
$793$	−0.563487	+	0.563487i	−0.0200100	+	0.0200100i
$794$	35.7325			1.26810
$795$		0			0
$796$	−103.762			−3.67773
$797$	17.3182	−	17.3182i	0.613441	−	0.613441i	−0.330400	−	0.943841i	$-0.607184\pi$
$797$	17.3182	−	17.3182i	0.613441	−	0.613441i	0.943841	+	0.330400i	$0.107184\pi$
$798$		0			0
$799$		−	15.6110i		−	0.552279i
$800$	−10.8575	−	57.4341i	−0.383870	−	2.03060i
$801$		0			0
$802$	−54.1748	−	54.1748i	−1.91298	−	1.91298i
$803$	−37.4778	−	37.4778i	−1.32256	−	1.32256i
$804$		0			0
$805$	−4.23202	−	8.00894i	−0.149159	−	0.282278i
$806$		−	0.697502i		−	0.0245685i
$807$		0			0
$808$	21.0971	−	21.0971i	0.742195	−	0.742195i
$809$	18.8659			0.663288			0.331644	−	0.943405i	$-0.392397\pi$
$809$	18.8659			0.663288			0.331644	+	0.943405i	$0.392397\pi$
$810$		0			0
$811$	17.4687			0.613409			0.306705	−	0.951805i	$-0.400774\pi$
$811$	17.4687			0.613409			0.306705	+	0.951805i	$0.400774\pi$
$812$	8.24643	−	8.24643i	0.289393	−	0.289393i
$813$		0			0
$814$			85.7289i			3.00480i
$815$	11.3413	−	36.7571i	0.397269	−	1.28754i
$816$		0			0
$817$	−6.01248	−	6.01248i	−0.210350	−	0.210350i
$818$	−44.8725	−	44.8725i	−1.56893	−	1.56893i
$819$		0			0
$820$	−44.4220	+	23.4731i	−1.55129	+	0.819717i
$821$			11.2614i			0.393026i	0.980501	+	0.196513i	$0.0629618\pi$
$821$			11.2614i			0.393026i	−0.980501	+	0.196513i	$0.937038\pi$
$822$		0			0
$823$	−37.6209	+	37.6209i	−1.31138	+	1.31138i	−0.390982	+	0.920398i	$0.627865\pi$
$823$	−37.6209	+	37.6209i	−1.31138	+	1.31138i	−0.920398	+	0.390982i	$0.872135\pi$
$824$	115.171			4.01216
$825$		0			0
$826$	3.68182			0.128107
$827$	0.283990	−	0.283990i	0.00987531	−	0.00987531i	−0.702152	−	0.712027i	$-0.747777\pi$
$827$	0.283990	−	0.283990i	0.00987531	−	0.00987531i	0.712027	+	0.702152i	$0.247777\pi$
$828$		0			0
$829$		−	5.96210i		−	0.207072i	−0.994626	−	0.103536i	$-0.966984\pi$
$829$		−	5.96210i		−	0.207072i	0.994626	−	0.103536i	$-0.0330158\pi$
$830$	26.2806	−	13.8870i	0.912212	−	0.482023i
$831$		0			0
$832$	−0.651622	−	0.651622i	−0.0225909	−	0.0225909i
$833$	−20.5633	−	20.5633i	−0.712475	−	0.712475i
$834$		0			0
$835$	−6.27709	+	20.3440i	−0.217228	+	0.704033i
$836$		−	60.1476i		−	2.08025i
$837$		0			0
$838$	38.7083	−	38.7083i	1.33716	−	1.33716i
$839$	27.3250			0.943364			0.471682	−	0.881769i	$-0.343647\pi$
$839$	27.3250			0.943364			0.471682	+	0.881769i	$0.343647\pi$
$840$		0			0
$841$	−16.9678			−0.585097
$842$	−10.3133	+	10.3133i	−0.355420	+	0.355420i
$843$		0			0
$844$		−	22.5034i		−	0.774599i
$845$	−13.5724	−	25.6852i	−0.466904	−	0.883598i
$846$		0			0
$847$	−7.99726	−	7.99726i	−0.274789	−	0.274789i
$848$	−6.41631	−	6.41631i	−0.220337	−	0.220337i
$849$		0			0
$850$	48.3417	+	32.9703i	1.65811	+	1.13087i
$851$			36.7722i			1.26054i
$852$		0			0
$853$	16.9693	−	16.9693i	0.581018	−	0.581018i	−0.354165	−	0.935183i	$-0.615235\pi$
$853$	16.9693	−	16.9693i	0.581018	−	0.581018i	0.935183	+	0.354165i	$0.115235\pi$
$854$	−15.8830			−0.543503
$855$		0			0
$856$	−62.1055			−2.12272
$857$	−6.32883	+	6.32883i	−0.216189	+	0.216189i	−0.806890	−	0.590702i	$-0.798851\pi$
$857$	−6.32883	+	6.32883i	−0.216189	+	0.216189i	0.590702	+	0.806890i	$0.298851\pi$
$858$		0			0
$859$			29.6635i			1.01211i	0.862502	+	0.506053i	$0.168896\pi$
$859$			29.6635i			1.01211i	−0.862502	+	0.506053i	$0.831104\pi$
$860$	−38.1380	−	11.7674i	−1.30050	−	0.401265i
$861$		0			0
$862$	19.4815	+	19.4815i	0.663543	+	0.663543i
$863$	17.4721	+	17.4721i	0.594758	+	0.594758i	0.938913	−	0.344155i	$-0.111835\pi$
$863$	17.4721	+	17.4721i	0.594758	+	0.594758i	−0.344155	+	0.938913i	$0.611835\pi$
$864$		0			0
$865$	−19.1192	−	5.89918i	−0.650071	−	0.200578i
$866$			16.1465i			0.548681i
$867$		0			0
$868$	6.98360	−	6.98360i	0.237039	−	0.237039i
$869$	28.0840			0.952685
$870$		0			0
$871$	0.00510808			0.000173081
$872$	−20.0222	+	20.0222i	−0.678036	+	0.678036i
$873$		0			0
$874$		−	36.3157i		−	1.22840i
$875$	−5.99075	+	4.77508i	−0.202524	+	0.161427i
$876$		0			0
$877$	−6.97108	−	6.97108i	−0.235397	−	0.235397i	0.579544	−	0.814941i	$-0.303231\pi$
$877$	−6.97108	−	6.97108i	−0.235397	−	0.235397i	−0.814941	+	0.579544i	$0.803231\pi$
$878$	−60.9816	−	60.9816i	−2.05803	−	2.05803i
$879$		0			0
$880$	−56.2217	−	106.398i	−1.89523	−	3.58666i
$881$			5.20934i			0.175507i	0.996142	+	0.0877535i	$0.0279688\pi$
$881$			5.20934i			0.175507i	−0.996142	+	0.0877535i	$0.972031\pi$
$882$		0			0
$883$	−19.0043	+	19.0043i	−0.639547	+	0.639547i	−0.950444	−	0.310897i	$-0.899371\pi$
$883$	−19.0043	+	19.0043i	−0.639547	+	0.639547i	0.310897	+	0.950444i	$0.399371\pi$
$884$	1.97411			0.0663965
$885$		0			0
$886$	93.6546			3.14639
$887$	35.7776	−	35.7776i	1.20129	−	1.20129i	0.227521	−	0.973773i	$-0.426938\pi$
$887$	35.7776	−	35.7776i	1.20129	−	1.20129i	0.973773	−	0.227521i	$-0.0730620\pi$
$888$		0			0
$889$		−	3.72056i		−	0.124783i
$890$	24.6738	−	79.9676i	0.827069	−	2.68052i
$891$		0			0
$892$	81.7259	+	81.7259i	2.73638	+	2.73638i
$893$	5.79407	+	5.79407i	0.193891	+	0.193891i
$894$		0			0
$895$	8.13330	−	4.29773i	0.271866	−	0.143657i
$896$		−	2.34640i		−	0.0783878i
$897$		0			0
$898$	32.6895	−	32.6895i	1.09086	−	1.09086i
$899$	10.1896			0.339842
$900$		0			0
$901$	3.93779			0.131187
$902$	−44.6305	+	44.6305i	−1.48603	+	1.48603i
$903$		0			0
$904$			45.0907i			1.49969i
$905$	21.8363	−	11.5386i	0.725863	−	0.383555i
$906$		0			0
$907$	−17.9021	−	17.9021i	−0.594430	−	0.594430i	0.344395	−	0.938825i	$-0.388084\pi$
$907$	−17.9021	−	17.9021i	−0.594430	−	0.594430i	−0.938825	+	0.344395i	$0.888084\pi$
$908$	80.2124	+	80.2124i	2.66194	+	2.66194i
$909$		0			0
$910$	−0.107263	+	0.347638i	−0.00355574	+	0.0115241i
$911$			30.6549i			1.01564i	0.861462	+	0.507822i	$0.169549\pi$
$911$			30.6549i			1.01564i	−0.861462	+	0.507822i	$0.830451\pi$
$912$		0			0
$913$	18.7579	−	18.7579i	0.620796	−	0.620796i
$914$	−11.7217			−0.387719
$915$		0			0
$916$	116.011			3.83311
$917$	10.1937	−	10.1937i	0.336625	−	0.336625i
$918$		0			0
$919$		−	13.3831i		−	0.441469i	−0.975334	−	0.220734i	$-0.929155\pi$
$919$		−	13.3831i		−	0.441469i	0.975334	−	0.220734i	$-0.0708454\pi$
$920$	−47.1775	−	89.2817i	−1.55540	−	2.94353i
$921$		0			0
$922$	26.7870	+	26.7870i	0.882182	+	0.882182i
$923$	0.803718	+	0.803718i	0.0264547	+	0.0264547i
$924$		0			0
$925$	30.5585	−	5.77685i	1.00476	−	0.189942i
$926$		−	8.87502i		−	0.291651i
$927$		0			0
$928$	28.6736	−	28.6736i	0.941256	−	0.941256i
$929$	−12.6669			−0.415587			−0.207793	−	0.978173i	$-0.566628\pi$
$929$	−12.6669			−0.415587			−0.207793	+	0.978173i	$0.566628\pi$
$930$		0			0
$931$	15.2642			0.500264
$932$	0.113559	−	0.113559i	0.00371975	−	0.00371975i
$933$		0			0
$934$		−	39.3057i		−	1.28612i
$935$	49.9010	+	15.3969i	1.63194	+	0.503531i
$936$		0			0
$937$	−4.20232	−	4.20232i	−0.137284	−	0.137284i	0.635125	−	0.772409i	$-0.280948\pi$
$937$	−4.20232	−	4.20232i	−0.137284	−	0.137284i	−0.772409	+	0.635125i	$0.780948\pi$
$938$	0.0719904	+	0.0719904i	0.00235057	+	0.00235057i
$939$		0			0
$940$	36.7526	+	11.3399i	1.19874	+	0.369868i
$941$		−	10.0360i		−	0.327163i	−0.986530	−	0.163582i	$-0.947695\pi$
$941$		−	10.0360i		−	0.327163i	0.986530	−	0.163582i	$-0.0523047\pi$
$942$		0			0
$943$	−19.1436	+	19.1436i	−0.623403	+	0.623403i
$944$	20.9803			0.682849
$945$		0			0
$946$	−50.1396			−1.63018
$947$	36.9920	−	36.9920i	1.20208	−	1.20208i	0.228547	−	0.973533i	$-0.426603\pi$
$947$	36.9920	−	36.9920i	1.20208	−	1.20208i	0.973533	−	0.228547i	$-0.0733974\pi$
$948$		0			0
$949$			0.913079i			0.0296398i
$950$	−30.1791	+	5.70513i	−0.979139	+	0.185099i
$951$		0			0
$952$	16.4813	+	16.4813i	0.534163	+	0.534163i
$953$	−24.9004	−	24.9004i	−0.806605	−	0.806605i	0.177514	−	0.984118i	$-0.443195\pi$
$953$	−24.9004	−	24.9004i	−0.806605	−	0.806605i	−0.984118	+	0.177514i	$0.943195\pi$
$954$		0			0
$955$	13.6604	+	25.8518i	0.442039	+	0.836543i
$956$			66.3357i			2.14545i
$957$		0			0
$958$	−29.8861	+	29.8861i	−0.965577	+	0.965577i
$959$	−8.33508			−0.269154
$960$		0			0
$961$	−22.3708			−0.721639
$962$	1.04432	−	1.04432i	0.0336701	−	0.0336701i
$963$		0			0
$964$		−	108.770i		−	3.50324i
$965$	12.1719	−	39.4490i	0.391827	−	1.26991i
$966$		0			0
$967$	−37.8961	−	37.8961i	−1.21866	−	1.21866i	−0.968103	−	0.250554i	$-0.919387\pi$
$967$	−37.8961	−	37.8961i	−1.21866	−	1.21866i	−0.250554	−	0.968103i	$-0.580613\pi$
$968$	−89.1515	−	89.1515i	−2.86544	−	2.86544i
$969$		0			0
$970$	−82.6211	+	43.6580i	−2.65281	+	1.40177i
$971$			37.7759i			1.21229i	0.795355	+	0.606143i	$0.207284\pi$
$971$			37.7759i			1.21229i	−0.795355	+	0.606143i	$0.792716\pi$
$972$		0			0
$973$	2.67493	−	2.67493i	0.0857544	−	0.0857544i
$974$	12.1573			0.389543
$975$		0			0
$976$	−90.5066			−2.89704
$977$	−22.6848	+	22.6848i	−0.725752	+	0.725752i	−0.969771	−	0.244018i	$-0.921534\pi$
$977$	−22.6848	+	22.6848i	−0.725752	+	0.725752i	0.244018	+	0.969771i	$0.421534\pi$
$978$		0			0
$979$		−	74.6885i		−	2.38705i
$980$	63.3487	−	33.4742i	2.02360	−	1.06929i
$981$		0			0
$982$	−25.0654	−	25.0654i	−0.799869	−	0.799869i
$983$	−10.3858	−	10.3858i	−0.331256	−	0.331256i	0.521807	−	0.853064i	$-0.325258\pi$
$983$	−10.3858	−	10.3858i	−0.331256	−	0.331256i	−0.853064	+	0.521807i	$0.825258\pi$
$984$		0			0
$985$	10.3651	−	33.5931i	0.330258	−	1.07036i
$986$			40.5944i			1.29279i
$987$		0			0
$988$	−0.732694	+	0.732694i	−0.0233101	+	0.0233101i
$989$	−21.5067			−0.683873
$990$		0			0
$991$	21.6843			0.688825			0.344412	−	0.938818i	$-0.388078\pi$
$991$	21.6843			0.688825			0.344412	+	0.938818i	$0.388078\pi$
$992$	24.2826	−	24.2826i	0.770973	−	0.770973i
$993$		0			0
$994$			22.6543i			0.718551i
$995$	22.0923	+	41.8089i	0.700374	+	1.32543i
$996$		0			0
$997$	19.8482	+	19.8482i	0.628598	+	0.628598i	0.947715	−	0.319117i	$-0.103386\pi$
$997$	19.8482	+	19.8482i	0.628598	+	0.628598i	−0.319117	+	0.947715i	$0.603386\pi$
$998$	5.39496	+	5.39496i	0.170774	+	0.170774i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.f.b.242.1	✓	24
3.2	odd	2	inner	405.2.f.b.242.12	yes	24
5.3	odd	4	inner	405.2.f.b.323.12	yes	24
9.2	odd	6		405.2.m.e.377.1		24
9.4	even	3		405.2.m.d.107.1		24
9.5	odd	6		405.2.m.d.107.6		24
9.7	even	3		405.2.m.e.377.6		24
15.8	even	4	inner	405.2.f.b.323.1	yes	24
45.13	odd	12		405.2.m.e.188.1		24
45.23	even	12		405.2.m.e.188.6		24
45.38	even	12		405.2.m.d.53.1		24
45.43	odd	12		405.2.m.d.53.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
405.2.f.b.242.1	✓	24	1.1	even	1	trivial
405.2.f.b.242.12	yes	24	3.2	odd	2	inner
405.2.f.b.323.1	yes	24	15.8	even	4	inner
405.2.f.b.323.12	yes	24	5.3	odd	4	inner
405.2.m.d.53.1		24	45.38	even	12
405.2.m.d.53.6		24	45.43	odd	12
405.2.m.d.107.1		24	9.4	even	3
405.2.m.d.107.6		24	9.5	odd	6
405.2.m.e.188.1		24	45.13	odd	12
405.2.m.e.188.6		24	45.23	even	12
405.2.m.e.377.1		24	9.2	odd	6
405.2.m.e.377.6		24	9.7	even	3

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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	405.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.85830 + 1.85830i) q^{2} -4.90659i q^{4} +(-1.97703 + 1.04468i) q^{5} +(0.484523 + 0.484523i) q^{7} +(5.40134 + 5.40134i) q^{8} +(1.73258 - 5.61526i) q^{10} -5.24456i q^{11} +(-0.0638872 + 0.0638872i) q^{13} -1.80078 q^{14} -10.2615 q^{16} +(3.14882 - 3.14882i) q^{17} +2.33738i q^{19} +(5.12584 + 9.70047i) q^{20} +(9.74600 + 9.74600i) q^{22} +(4.18041 + 4.18041i) q^{23} +(2.81727 - 4.13074i) q^{25} -0.237444i q^{26} +(2.37736 - 2.37736i) q^{28} +3.46874 q^{29} +2.93755 q^{31} +(8.26627 - 8.26627i) q^{32} +11.7029i q^{34} +(-1.46409 - 0.451741i) q^{35} +(4.39816 + 4.39816i) q^{37} +(-4.34356 - 4.34356i) q^{38} +(-16.3213 - 5.03590i) q^{40} +4.57937i q^{41} +(-2.57232 + 2.57232i) q^{43} -25.7329 q^{44} -15.5369 q^{46} +(2.47888 - 2.47888i) q^{47} -6.53048i q^{49} +(2.44082 + 12.9115i) q^{50} +(0.313468 + 0.313468i) q^{52} +(0.625281 + 0.625281i) q^{53} +(5.47891 + 10.3686i) q^{55} +5.23414i q^{56} +(-6.44598 + 6.44598i) q^{58} -2.04457 q^{59} +8.82003 q^{61} +(-5.45886 + 5.45886i) q^{62} +10.1996i q^{64} +(0.0595647 - 0.193049i) q^{65} +(-0.0399773 - 0.0399773i) q^{67} +(-15.4500 - 15.4500i) q^{68} +(3.56019 - 1.88125i) q^{70} -12.5803i q^{71} +(7.14603 - 7.14603i) q^{73} -16.3462 q^{74} +11.4686 q^{76} +(2.54111 - 2.54111i) q^{77} +5.35488i q^{79} +(20.2872 - 10.7200i) q^{80} +(-8.50987 - 8.50987i) q^{82} +(3.57664 + 3.57664i) q^{83} +(-2.93577 + 9.51481i) q^{85} -9.56031i q^{86} +(28.3277 - 28.3277i) q^{88} +14.2411 q^{89} -0.0619096 q^{91} +(20.5116 - 20.5116i) q^{92} +9.21302i q^{94} +(-2.44182 - 4.62106i) q^{95} +(-11.2443 - 11.2443i) q^{97} +(12.1356 + 12.1356i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{13} - 24 q^{16} + 36 q^{37} - 36 q^{40} - 24 q^{43} - 48 q^{46} - 36 q^{52} - 60 q^{58} + 72 q^{70} + 12 q^{73} + 48 q^{76} - 96 q^{82} + 60 q^{85} + 96 q^{88} - 48 q^{91} + 24 q^{97}+O(q^{100}) \) 24 * q + 12 * q^13 - 24 * q^16 + 36 * q^37 - 36 * q^40 - 24 * q^43 - 48 * q^46 - 36 * q^52 - 60 * q^58 + 72 * q^70 + 12 * q^73 + 48 * q^76 - 96 * q^82 + 60 * q^85 + 96 * q^88 - 48 * q^91 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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