LMFDB - Embedded newform 405.2.f.b.242.9

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			242.9
Character	$\chi$	$=$	405.242
Dual form			405.2.f.b.323.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.01382 - 1.01382i) q^{2} -0.0556605i q^{4} +(-0.721513 - 2.11646i) q^{5} +(3.46834 + 3.46834i) q^{7} +(1.97121 + 1.97121i) q^{8} +(-2.87720 - 1.41423i) q^{10} -1.61753i q^{11} +(1.71168 - 1.71168i) q^{13} +7.03254 q^{14} +4.10822 q^{16} +(-0.839316 + 0.839316i) q^{17} -3.33104i q^{19} +(-0.117803 + 0.0401598i) q^{20} +(-1.63988 - 1.63988i) q^{22} +(-3.66638 - 3.66638i) q^{23} +(-3.95884 + 3.05411i) q^{25} -3.47066i q^{26} +(0.193050 - 0.193050i) q^{28} +6.55782 q^{29} -7.88102 q^{31} +(0.222578 - 0.222578i) q^{32} +1.70183i q^{34} +(4.83817 - 9.84307i) q^{35} +(1.82308 + 1.82308i) q^{37} +(-3.37707 - 3.37707i) q^{38} +(2.74974 - 5.59425i) q^{40} +6.27343i q^{41} +(1.47910 - 1.47910i) q^{43} -0.0900325 q^{44} -7.43410 q^{46} +(-2.29888 + 2.29888i) q^{47} +17.0588i q^{49} +(-0.917230 + 7.10987i) q^{50} +(-0.0952728 - 0.0952728i) q^{52} +(0.605237 + 0.605237i) q^{53} +(-3.42344 + 1.16707i) q^{55} +13.6737i q^{56} +(6.64844 - 6.64844i) q^{58} -6.13485 q^{59} -9.91828 q^{61} +(-7.98993 + 7.98993i) q^{62} +7.76514i q^{64} +(-4.85770 - 2.38771i) q^{65} +(-3.52409 - 3.52409i) q^{67} +(0.0467168 + 0.0467168i) q^{68} +(-5.07407 - 14.8841i) q^{70} +4.41355i q^{71} +(9.23878 - 9.23878i) q^{73} +3.69656 q^{74} -0.185407 q^{76} +(5.61014 - 5.61014i) q^{77} -4.16388i q^{79} +(-2.96414 - 8.69491i) q^{80} +(6.36012 + 6.36012i) q^{82} +(-7.74767 - 7.74767i) q^{83} +(2.38196 + 1.17081i) q^{85} -2.99909i q^{86} +(3.18849 - 3.18849i) q^{88} -12.9410 q^{89} +11.8734 q^{91} +(-0.204073 + 0.204073i) q^{92} +4.66130i q^{94} +(-7.05002 + 2.40339i) q^{95} +(-3.15941 - 3.15941i) q^{97} +(17.2945 + 17.2945i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.01382	−	1.01382i	0.716879	−	0.716879i	−0.251086	−	0.967965i	$-0.580788\pi$
$2$	1.01382	−	1.01382i	0.716879	−	0.716879i	0.967965	+	0.251086i	$0.0807877\pi$
$3$		0			0
$3$		0			0
$4$		−	0.0556605i		−	0.0278302i
$5$	−0.721513	−	2.11646i	−0.322670	−	0.946511i
$5$	−0.721513	−	2.11646i	−0.322670	−	0.946511i
$6$		0			0
$7$	3.46834	+	3.46834i	1.31091	+	1.31091i	0.920745	+	0.390164i	$0.127582\pi$
$7$	3.46834	+	3.46834i	1.31091	+	1.31091i	0.390164	+	0.920745i	$0.372418\pi$
$8$	1.97121	+	1.97121i	0.696928	+	0.696928i
$9$		0			0
$10$	−2.87720	−	1.41423i	−0.909849	−	0.447218i
$11$		−	1.61753i		−	0.487703i	−0.969813	−	0.243852i	$-0.921589\pi$
$11$		−	1.61753i		−	0.487703i	0.969813	−	0.243852i	$-0.0784110\pi$
$12$		0			0
$13$	1.71168	−	1.71168i	0.474734	−	0.474734i	−0.428709	−	0.903443i	$-0.641031\pi$
$13$	1.71168	−	1.71168i	0.474734	−	0.474734i	0.903443	+	0.428709i	$0.141031\pi$
$14$	7.03254			1.87953
$15$		0			0
$16$	4.10822			1.02706
$17$	−0.839316	+	0.839316i	−0.203564	+	0.203564i	−0.801525	−	0.597961i	$-0.795978\pi$
$17$	−0.839316	+	0.839316i	−0.203564	+	0.203564i	0.597961	+	0.801525i	$0.295978\pi$
$18$		0			0
$19$		−	3.33104i		−	0.764192i	−0.924123	−	0.382096i	$-0.875202\pi$
$19$		−	3.33104i		−	0.764192i	0.924123	−	0.382096i	$-0.124798\pi$
$20$	−0.117803	+	0.0401598i	−0.0263416	+	0.00897999i
$21$		0			0
$22$	−1.63988	−	1.63988i	−0.349624	−	0.349624i
$23$	−3.66638	−	3.66638i	−0.764494	−	0.764494i	0.212638	−	0.977131i	$-0.431795\pi$
$23$	−3.66638	−	3.66638i	−0.764494	−	0.764494i	−0.977131	+	0.212638i	$0.931795\pi$
$24$		0			0
$25$	−3.95884	+	3.05411i	−0.791768	+	0.610822i
$26$		−	3.47066i		−	0.680653i
$27$		0			0
$28$	0.193050	−	0.193050i	0.0364829	−	0.0364829i
$29$	6.55782			1.21776			0.608878	−	0.793264i	$-0.291620\pi$
$29$	6.55782			1.21776			0.608878	+	0.793264i	$0.291620\pi$
$30$		0			0
$31$	−7.88102			−1.41547			−0.707736	−	0.706477i	$-0.750284\pi$
$31$	−7.88102			−1.41547			−0.707736	+	0.706477i	$0.750284\pi$
$32$	0.222578	−	0.222578i	0.0393466	−	0.0393466i
$33$		0			0
$34$			1.70183i			0.291862i
$35$	4.83817	−	9.84307i	0.817799	−	1.66378i
$36$		0			0
$37$	1.82308	+	1.82308i	0.299713	+	0.299713i	0.840902	−	0.541188i	$-0.182025\pi$
$37$	1.82308	+	1.82308i	0.299713	+	0.299713i	−0.541188	+	0.840902i	$0.682025\pi$
$38$	−3.37707	−	3.37707i	−0.547833	−	0.547833i
$39$		0			0
$40$	2.74974	−	5.59425i	0.434772	−	0.884528i
$41$			6.27343i			0.979744i	0.871794	+	0.489872i	$0.162957\pi$
$41$			6.27343i			0.979744i	−0.871794	+	0.489872i	$0.837043\pi$
$42$		0			0
$43$	1.47910	−	1.47910i	0.225561	−	0.225561i	−0.585274	−	0.810835i	$-0.699013\pi$
$43$	1.47910	−	1.47910i	0.225561	−	0.225561i	0.810835	+	0.585274i	$0.199013\pi$
$44$	−0.0900325			−0.0135729
$45$		0			0
$46$	−7.43410			−1.09610
$47$	−2.29888	+	2.29888i	−0.335326	+	0.335326i	−0.854605	−	0.519279i	$-0.826201\pi$
$47$	−2.29888	+	2.29888i	−0.335326	+	0.335326i	0.519279	+	0.854605i	$0.326201\pi$
$48$		0			0
$49$			17.0588i			2.43697i
$50$	−0.917230	+	7.10987i	−0.129716	+	1.00549i
$51$		0			0
$52$	−0.0952728	−	0.0952728i	−0.0132120	−	0.0132120i
$53$	0.605237	+	0.605237i	0.0831357	+	0.0831357i	0.747452	−	0.664316i	$-0.231277\pi$
$53$	0.605237	+	0.605237i	0.0831357	+	0.0831357i	−0.664316	+	0.747452i	$0.731277\pi$
$54$		0			0
$55$	−3.42344	+	1.16707i	−0.461617	+	0.157367i
$56$			13.6737i			1.82722i
$57$		0			0
$58$	6.64844	−	6.64844i	0.872984	−	0.872984i
$59$	−6.13485			−0.798689			−0.399345	−	0.916801i	$-0.630762\pi$
$59$	−6.13485			−0.798689			−0.399345	+	0.916801i	$0.630762\pi$
$60$		0			0
$61$	−9.91828			−1.26991			−0.634953	−	0.772551i	$-0.718980\pi$
$61$	−9.91828			−1.26991			−0.634953	+	0.772551i	$0.718980\pi$
$62$	−7.98993	+	7.98993i	−1.01472	+	1.01472i
$63$		0			0
$64$			7.76514i			0.970642i
$65$	−4.85770	−	2.38771i	−0.602524	−	0.296159i
$66$		0			0
$67$	−3.52409	−	3.52409i	−0.430536	−	0.430536i	0.458275	−	0.888811i	$-0.348468\pi$
$67$	−3.52409	−	3.52409i	−0.430536	−	0.430536i	−0.888811	+	0.458275i	$0.848468\pi$
$68$	0.0467168	+	0.0467168i	0.00566524	+	0.00566524i
$69$		0			0
$70$	−5.07407	−	14.8841i	−0.606467	−	1.77899i
$71$			4.41355i			0.523792i	0.965096	+	0.261896i	$0.0843477\pi$
$71$			4.41355i			0.523792i	−0.965096	+	0.261896i	$0.915652\pi$
$72$		0			0
$73$	9.23878	−	9.23878i	1.08132	−	1.08132i	0.0849307	−	0.996387i	$-0.472933\pi$
$73$	9.23878	−	9.23878i	1.08132	−	1.08132i	0.996387	−	0.0849307i	$-0.0270669\pi$
$74$	3.69656			0.429716
$75$		0			0
$76$	−0.185407			−0.0212677
$77$	5.61014	−	5.61014i	0.639335	−	0.639335i
$78$		0			0
$79$		−	4.16388i		−	0.468473i	−0.972180	−	0.234237i	$-0.924741\pi$
$79$		−	4.16388i		−	0.468473i	0.972180	−	0.234237i	$-0.0752591\pi$
$80$	−2.96414	−	8.69491i	−0.331400	−	0.972120i
$81$		0			0
$82$	6.36012	+	6.36012i	0.702358	+	0.702358i
$83$	−7.74767	−	7.74767i	−0.850417	−	0.850417i	0.139767	−	0.990184i	$-0.455365\pi$
$83$	−7.74767	−	7.74767i	−0.850417	−	0.850417i	−0.990184	+	0.139767i	$0.955365\pi$
$84$		0			0
$85$	2.38196	+	1.17081i	0.258360	+	0.126992i
$86$		−	2.99909i		−	0.323400i
$87$		0			0
$88$	3.18849	−	3.18849i	0.339894	−	0.339894i
$89$	−12.9410			−1.37174			−0.685869	−	0.727725i	$-0.740578\pi$
$89$	−12.9410			−1.37174			−0.685869	+	0.727725i	$0.740578\pi$
$90$		0			0
$91$	11.8734			1.24467
$92$	−0.204073	+	0.204073i	−0.0212760	+	0.0212760i
$93$		0			0
$94$			4.66130i			0.480777i
$95$	−7.05002	+	2.40339i	−0.723317	+	0.246582i
$96$		0			0
$97$	−3.15941	−	3.15941i	−0.320789	−	0.320789i	0.528281	−	0.849070i	$-0.322837\pi$
$97$	−3.15941	−	3.15941i	−0.320789	−	0.320789i	−0.849070	+	0.528281i	$0.822837\pi$
$98$	17.2945	+	17.2945i	1.74701	+	1.74701i
$99$		0			0
$100$	0.169993	+	0.220351i	0.0169993	+	0.0220351i
$101$		−	2.21186i		−	0.220088i	−0.993927	−	0.110044i	$-0.964901\pi$
$101$		−	2.21186i		−	0.220088i	0.993927	−	0.110044i	$-0.0350992\pi$
$102$		0			0
$103$	1.44176	−	1.44176i	0.142061	−	0.142061i	−0.632500	−	0.774561i	$-0.717971\pi$
$103$	1.44176	−	1.44176i	0.142061	−	0.142061i	0.774561	+	0.632500i	$0.217971\pi$
$104$	6.74815			0.661711
$105$		0			0
$106$	1.22720			0.119196
$107$	−11.3639	+	11.3639i	−1.09859	+	1.09859i	−0.104009	+	0.994576i	$0.533167\pi$
$107$	−11.3639	+	11.3639i	−1.09859	+	1.09859i	−0.994576	+	0.104009i	$0.966833\pi$
$108$		0			0
$109$			9.85763i			0.944190i	0.881548	+	0.472095i	$0.156502\pi$
$109$			9.85763i			0.944190i	−0.881548	+	0.472095i	$0.843498\pi$
$110$	−2.28756	+	4.65395i	−0.218110	+	0.443737i
$111$		0			0
$112$	14.2487	+	14.2487i	1.34638	+	1.34638i
$113$	−10.3562	−	10.3562i	−0.974225	−	0.974225i	0.0254509	−	0.999676i	$-0.491898\pi$
$113$	−10.3562	−	10.3562i	−0.974225	−	0.974225i	−0.999676	+	0.0254509i	$0.991898\pi$
$114$		0			0
$115$	−5.11442	+	10.4051i	−0.476922	+	0.970281i
$116$		−	0.365011i		−	0.0338905i
$117$		0			0
$118$	−6.21963	+	6.21963i	−0.572563	+	0.572563i
$119$	−5.82207			−0.533708
$120$		0			0
$121$	8.38360			0.762145
$122$	−10.0553	+	10.0553i	−0.910368	+	0.910368i
$123$		0			0
$124$			0.438661i			0.0393930i
$125$	9.32027	+	6.17516i	0.833630	+	0.552323i
$126$		0			0
$127$	2.69554	+	2.69554i	0.239191	+	0.239191i	0.816515	−	0.577324i	$-0.195903\pi$
$127$	2.69554	+	2.69554i	0.239191	+	0.239191i	−0.577324	+	0.816515i	$0.695903\pi$
$128$	8.31761	+	8.31761i	0.735179	+	0.735179i
$129$		0			0
$130$	−7.34554	+	2.50413i	−0.644246	+	0.219627i
$131$			9.77051i			0.853654i	0.904333	+	0.426827i	$0.140369\pi$
$131$			9.77051i			0.853654i	−0.904333	+	0.426827i	$0.859631\pi$
$132$		0			0
$133$	11.5532	−	11.5532i	1.00179	−	1.00179i
$134$	−7.14558			−0.617284
$135$		0			0
$136$	−3.30894			−0.283739
$137$	2.54611	−	2.54611i	0.217529	−	0.217529i	−0.589927	−	0.807456i	$-0.700844\pi$
$137$	2.54611	−	2.54611i	0.217529	−	0.217529i	0.807456	+	0.589927i	$0.200844\pi$
$138$		0			0
$139$		−	16.1562i		−	1.37035i	−0.728377	−	0.685177i	$-0.759725\pi$
$139$		−	16.1562i		−	1.37035i	0.728377	−	0.685177i	$-0.240275\pi$
$140$	−0.547870	−	0.269295i	−0.0463035	−	0.0227596i
$141$		0			0
$142$	4.47454	+	4.47454i	0.375495	+	0.375495i
$143$	−2.76869	−	2.76869i	−0.231529	−	0.231529i
$144$		0			0
$145$	−4.73155	−	13.8794i	−0.392934	−	1.15262i
$146$		−	18.7329i		−	1.55035i
$147$		0			0
$148$	0.101474	−	0.101474i	0.00834110	−	0.00834110i
$149$	17.1931			1.40851			0.704257	−	0.709945i	$-0.251280\pi$
$149$	17.1931			1.40851			0.704257	+	0.709945i	$0.251280\pi$
$150$		0			0
$151$	−1.67352			−0.136189			−0.0680947	−	0.997679i	$-0.521692\pi$
$151$	−1.67352			−0.136189			−0.0680947	+	0.997679i	$0.521692\pi$
$152$	6.56617	−	6.56617i	0.532587	−	0.532587i
$153$		0			0
$154$		−	11.3753i		−	0.916651i
$155$	5.68626	+	16.6799i	0.456731	+	1.33976i
$156$		0			0
$157$	1.93131	+	1.93131i	0.154135	+	0.154135i	0.779962	−	0.625827i	$-0.215238\pi$
$157$	1.93131	+	1.93131i	0.154135	+	0.154135i	−0.625827	+	0.779962i	$0.715238\pi$
$158$	−4.22143	−	4.22143i	−0.335839	−	0.335839i
$159$		0			0
$160$	−0.631671	−	0.310485i	−0.0499380	−	0.0245460i
$161$		−	25.4325i		−	2.00436i
$162$		0			0
$163$	2.88877	−	2.88877i	0.226266	−	0.226266i	−0.584865	−	0.811131i	$-0.698853\pi$
$163$	2.88877	−	2.88877i	0.226266	−	0.226266i	0.811131	+	0.584865i	$0.198853\pi$
$164$	0.349182			0.0272665
$165$		0			0
$166$	−15.7095			−1.21929
$167$	10.5238	−	10.5238i	0.814359	−	0.814359i	−0.170925	−	0.985284i	$-0.554676\pi$
$167$	10.5238	−	10.5238i	0.814359	−	0.814359i	0.985284	+	0.170925i	$0.0546757\pi$
$168$		0			0
$169$			7.14032i			0.549255i
$170$	3.60186	−	1.22789i	0.276250	−	0.0941751i
$171$		0			0
$172$	−0.0823276	−	0.0823276i	−0.00627742	−	0.00627742i
$173$	−6.10575	−	6.10575i	−0.464212	−	0.464212i	0.435822	−	0.900033i	$-0.356458\pi$
$173$	−6.10575	−	6.10575i	−0.464212	−	0.464212i	−0.900033	+	0.435822i	$0.856458\pi$
$174$		0			0
$175$	−24.3233	−	3.13790i	−1.83867	−	0.237203i
$176$		−	6.64517i		−	0.500899i
$177$		0			0
$178$	−13.1198	+	13.1198i	−0.983370	+	0.983370i
$179$	−3.11270			−0.232654			−0.116327	−	0.993211i	$-0.537112\pi$
$179$	−3.11270			−0.232654			−0.116327	+	0.993211i	$0.537112\pi$
$180$		0			0
$181$	−7.82906			−0.581929			−0.290965	−	0.956734i	$-0.593976\pi$
$181$	−7.82906			−0.581929			−0.290965	+	0.956734i	$0.593976\pi$
$182$	12.0374	−	12.0374i	0.892275	−	0.892275i
$183$		0			0
$184$		−	14.4544i		−	1.06559i
$185$	2.54311	−	5.17387i	0.186973	−	0.380391i
$186$		0			0
$187$	1.35762	+	1.35762i	0.0992789	+	0.0992789i
$188$	0.127957	+	0.127957i	0.00933222	+	0.00933222i
$189$		0			0
$190$	−4.71085	+	9.58405i	−0.341761	+	0.695300i
$191$			13.1341i			0.950353i	0.879891	+	0.475176i	$0.157616\pi$
$191$			13.1341i			0.950353i	−0.879891	+	0.475176i	$0.842384\pi$
$192$		0			0
$193$	−4.26234	+	4.26234i	−0.306810	+	0.306810i	−0.843671	−	0.536861i	$-0.819610\pi$
$193$	−4.26234	+	4.26234i	−0.306810	+	0.306810i	0.536861	+	0.843671i	$0.319610\pi$
$194$	−6.40614			−0.459934
$195$		0			0
$196$	0.949499			0.0678214
$197$	18.4191	−	18.4191i	1.31230	−	1.31230i	0.392590	−	0.919714i	$-0.371579\pi$
$197$	18.4191	−	18.4191i	1.31230	−	1.31230i	0.919714	−	0.392590i	$-0.128421\pi$
$198$		0			0
$199$			3.57649i			0.253531i	0.991933	+	0.126765i	$0.0404596\pi$
$199$			3.57649i			0.253531i	−0.991933	+	0.126765i	$0.959540\pi$
$200$	−13.8240	−	1.78341i	−0.977504	−	0.126106i
$201$		0			0
$202$	−2.24242	−	2.24242i	−0.157776	−	0.157776i
$203$	22.7447	+	22.7447i	1.59637	+	1.59637i
$204$		0			0
$205$	13.2775	−	4.52636i	0.927339	−	0.316134i
$206$		−	2.92337i		−	0.203681i
$207$		0			0
$208$	7.03195	−	7.03195i	0.487578	−	0.487578i
$209$	−5.38805			−0.372699
$210$		0			0
$211$	21.9087			1.50826			0.754130	−	0.656725i	$-0.228059\pi$
$211$	21.9087			1.50826			0.754130	+	0.656725i	$0.228059\pi$
$212$	0.0336878	−	0.0336878i	0.00231369	−	0.00231369i
$213$		0			0
$214$			23.0418i			1.57511i
$215$	−4.19766	−	2.06328i	−0.286278	−	0.140714i
$216$		0			0
$217$	−27.3341	−	27.3341i	−1.85556	−	1.85556i
$218$	9.99386	+	9.99386i	0.676869	+	0.676869i
$219$		0			0
$220$	0.0649596	+	0.190550i	0.00437957	+	0.0128469i
$221$			2.87328i			0.193278i
$222$		0			0
$223$	3.74802	−	3.74802i	0.250986	−	0.250986i	−0.570389	−	0.821375i	$-0.693207\pi$
$223$	3.74802	−	3.74802i	0.250986	−	0.250986i	0.821375	+	0.570389i	$0.193207\pi$
$224$	1.54395			0.103160
$225$		0			0
$226$	−20.9985			−1.39680
$227$	3.12225	−	3.12225i	0.207231	−	0.207231i	−0.595859	−	0.803089i	$-0.703188\pi$
$227$	3.12225	−	3.12225i	0.207231	−	0.207231i	0.803089	+	0.595859i	$0.203188\pi$
$228$		0			0
$229$			0.389796i			0.0257585i	0.999917	+	0.0128792i	$0.00409970\pi$
$229$			0.389796i			0.0257585i	−0.999917	+	0.0128792i	$0.995900\pi$
$230$	5.36380	+	15.7340i	0.353678	+	1.03747i
$231$		0			0
$232$	12.9268	+	12.9268i	0.848688	+	0.848688i
$233$	4.33038	+	4.33038i	0.283692	+	0.283692i	0.834580	−	0.550887i	$-0.185711\pi$
$233$	4.33038	+	4.33038i	0.283692	+	0.283692i	−0.550887	+	0.834580i	$0.685711\pi$
$234$		0			0
$235$	6.52417	+	3.20683i	0.425590	+	0.209190i
$236$			0.341469i			0.0222277i
$237$		0			0
$238$	−5.90253	+	5.90253i	−0.382604	+	0.382604i
$239$	−29.9756			−1.93896			−0.969479	−	0.245175i	$-0.921155\pi$
$239$	−29.9756			−1.93896			−0.969479	+	0.245175i	$0.921155\pi$
$240$		0			0
$241$	2.94744			0.189861			0.0949306	−	0.995484i	$-0.469737\pi$
$241$	2.94744			0.189861			0.0949306	+	0.995484i	$0.469737\pi$
$242$	8.49946	−	8.49946i	0.546366	−	0.546366i
$243$		0			0
$244$			0.552056i			0.0353418i
$245$	36.1043	−	12.3081i	2.30662	−	0.786337i
$246$		0			0
$247$	−5.70166	−	5.70166i	−0.362788	−	0.362788i
$248$	−15.5351	−	15.5351i	−0.986483	−	0.986483i
$249$		0			0
$250$	15.7096	−	3.18857i	0.993560	−	0.201663i
$251$			17.0361i			1.07531i	0.843166	+	0.537653i	$0.180689\pi$
$251$			17.0361i			1.07531i	−0.843166	+	0.537653i	$0.819311\pi$
$252$		0			0
$253$	−5.93048	+	5.93048i	−0.372846	+	0.372846i
$254$	5.46559			0.342942
$255$		0			0
$256$	1.33483			0.0834267
$257$	18.4379	−	18.4379i	1.15013	−	1.15013i	0.163598	−	0.986527i	$-0.447690\pi$
$257$	18.4379	−	18.4379i	1.15013	−	1.15013i	0.986527	−	0.163598i	$-0.0523100\pi$
$258$		0			0
$259$			12.6462i			0.785794i
$260$	−0.132901	+	0.270382i	−0.00824217	+	0.0167684i
$261$		0			0
$262$	9.90554	+	9.90554i	0.611966	+	0.611966i
$263$	−6.04753	−	6.04753i	−0.372907	−	0.372907i	0.495628	−	0.868535i	$-0.334938\pi$
$263$	−6.04753	−	6.04753i	−0.372907	−	0.372907i	−0.868535	+	0.495628i	$0.834938\pi$
$264$		0			0
$265$	0.844276	−	1.71765i	0.0518635	−	0.105514i
$266$		−	23.4257i		−	1.43632i
$267$		0			0
$268$	−0.196152	+	0.196152i	−0.0119819	+	0.0119819i
$269$	11.4103			0.695699			0.347850	−	0.937550i	$-0.386912\pi$
$269$	11.4103			0.695699			0.347850	+	0.937550i	$0.386912\pi$
$270$		0			0
$271$	11.4430			0.695116			0.347558	−	0.937659i	$-0.387011\pi$
$271$	11.4430			0.695116			0.347558	+	0.937659i	$0.387011\pi$
$272$	−3.44810	+	3.44810i	−0.209072	+	0.209072i
$273$		0			0
$274$		−	5.16259i		−	0.311884i
$275$	4.94011	+	6.40354i	0.297900	+	0.386148i
$276$		0			0
$277$	−16.0589	−	16.0589i	−0.964883	−	0.964883i	0.0345209	−	0.999404i	$-0.489009\pi$
$277$	−16.0589	−	16.0589i	−0.964883	−	0.964883i	−0.999404	+	0.0345209i	$0.989009\pi$
$278$	−16.3795	−	16.3795i	−0.982377	−	0.982377i
$279$		0			0
$280$	28.9398	−	9.86571i	1.72948	−	0.589589i
$281$		−	11.6774i		−	0.696614i	−0.937381	−	0.348307i	$-0.886757\pi$
$281$		−	11.6774i		−	0.696614i	0.937381	−	0.348307i	$-0.113243\pi$
$282$		0			0
$283$	−2.83612	+	2.83612i	−0.168590	+	0.168590i	−0.786359	−	0.617769i	$-0.788037\pi$
$283$	−2.83612	+	2.83612i	−0.168590	+	0.168590i	0.617769	+	0.786359i	$0.288037\pi$
$284$	0.245660			0.0145773
$285$		0			0
$286$	−5.61390			−0.331957
$287$	−21.7584	+	21.7584i	−1.28436	+	1.28436i
$288$		0			0
$289$			15.5911i			0.917123i
$290$	−18.8681	−	9.27425i	−1.10797	−	0.544603i
$291$		0			0
$292$	−0.514235	−	0.514235i	−0.0300933	−	0.0300933i
$293$	13.5176	+	13.5176i	0.789709	+	0.789709i	0.981446	−	0.191738i	$-0.0614122\pi$
$293$	13.5176	+	13.5176i	0.789709	+	0.789709i	−0.191738	+	0.981446i	$0.561412\pi$
$294$		0			0
$295$	4.42637	+	12.9842i	0.257713	+	0.755969i
$296$			7.18737i			0.417757i
$297$		0			0
$298$	17.4307	−	17.4307i	1.00973	−	1.00973i
$299$	−12.5513			−0.725862
$300$		0			0
$301$	10.2601			0.591380
$302$	−1.69665	+	1.69665i	−0.0976313	+	0.0976313i
$303$		0			0
$304$		−	13.6846i		−	0.784868i
$305$	7.15616	+	20.9917i	0.409761	+	1.20198i
$306$		0			0
$307$	4.76401	+	4.76401i	0.271896	+	0.271896i	0.829863	−	0.557967i	$-0.188418\pi$
$307$	4.76401	+	4.76401i	0.271896	+	0.271896i	−0.557967	+	0.829863i	$0.688418\pi$
$308$	−0.312263	−	0.312263i	−0.0177928	−	0.0177928i
$309$		0			0
$310$	22.6752	+	11.1456i	1.28787	+	0.633026i
$311$		−	12.9831i		−	0.736203i	−0.929786	−	0.368102i	$-0.880008\pi$
$311$		−	12.9831i		−	0.736203i	0.929786	−	0.368102i	$-0.119992\pi$
$312$		0			0
$313$	5.66676	−	5.66676i	0.320304	−	0.320304i	−0.528579	−	0.848884i	$-0.677275\pi$
$313$	5.66676	−	5.66676i	0.320304	−	0.320304i	0.848884	+	0.528579i	$0.177275\pi$
$314$	3.91600			0.220992
$315$		0			0
$316$	−0.231764			−0.0130377
$317$	−14.1392	+	14.1392i	−0.794135	+	0.794135i	−0.982164	−	0.188029i	$-0.939790\pi$
$317$	−14.1392	+	14.1392i	−0.794135	+	0.794135i	0.188029	+	0.982164i	$0.439790\pi$
$318$		0			0
$319$		−	10.6075i		−	0.593904i
$320$	16.4346	−	5.60265i	0.918724	−	0.313197i
$321$		0			0
$322$	−25.7840	−	25.7840i	−1.43689	−	1.43689i
$323$	2.79579	+	2.79579i	0.155562	+	0.155562i
$324$		0			0
$325$	−1.54860	+	12.0039i	−0.0859009	+	0.665857i
$326$		−	5.85737i		−	0.324410i
$327$		0			0
$328$	−12.3662	+	12.3662i	−0.682811	+	0.682811i
$329$	−15.9466			−0.879165
$330$		0			0
$331$	12.6378			0.694634			0.347317	−	0.937748i	$-0.387093\pi$
$331$	12.6378			0.694634			0.347317	+	0.937748i	$0.387093\pi$
$332$	−0.431239	+	0.431239i	−0.0236673	+	0.0236673i
$333$		0			0
$334$		−	21.3385i		−	1.16759i
$335$	−4.91593	+	10.0013i	−0.268586	+	0.546428i
$336$		0			0
$337$	10.9708	+	10.9708i	0.597618	+	0.597618i	0.939678	−	0.342060i	$-0.111125\pi$
$337$	10.9708	+	10.9708i	0.597618	+	0.597618i	−0.342060	+	0.939678i	$0.611125\pi$
$338$	7.23900	+	7.23900i	0.393749	+	0.393749i
$339$		0			0
$340$	0.0651676	−	0.132581i	0.00353421	−	0.00719022i
$341$			12.7478i			0.690331i
$342$		0			0
$343$	−34.8872	+	34.8872i	−1.88373	+	1.88373i
$344$	5.83124			0.314399
$345$		0			0
$346$	−12.3803			−0.665567
$347$	−12.6764	+	12.6764i	−0.680503	+	0.680503i	−0.960114	−	0.279610i	$-0.909795\pi$
$347$	−12.6764	+	12.6764i	−0.680503	+	0.680503i	0.279610	+	0.960114i	$0.409795\pi$
$348$		0			0
$349$		−	13.0190i		−	0.696891i	−0.937329	−	0.348445i	$-0.886710\pi$
$349$		−	13.0190i		−	0.696891i	0.937329	−	0.348445i	$-0.113290\pi$
$350$	−27.8407	+	21.4782i	−1.48815	+	1.14806i
$351$		0			0
$352$	−0.360026	−	0.360026i	−0.0191895	−	0.0191895i
$353$	11.6752	+	11.6752i	0.621406	+	0.621406i	0.945891	−	0.324485i	$-0.105191\pi$
$353$	11.6752	+	11.6752i	0.621406	+	0.621406i	−0.324485	+	0.945891i	$0.605191\pi$
$354$		0			0
$355$	9.34111	−	3.18443i	0.495775	−	0.169012i
$356$			0.720300i			0.0381758i
$357$		0			0
$358$	−3.15571	+	3.15571i	−0.166785	+	0.166785i
$359$	7.45388			0.393401			0.196700	−	0.980464i	$-0.436977\pi$
$359$	7.45388			0.393401			0.196700	+	0.980464i	$0.436977\pi$
$360$		0			0
$361$	7.90419			0.416010
$362$	−7.93725	+	7.93725i	−0.417173	+	0.417173i
$363$		0			0
$364$		−	0.660877i		−	0.0346394i
$365$	−26.2194	−	12.8876i	−1.37239	−	0.674570i
$366$		0			0
$367$	8.39436	+	8.39436i	0.438182	+	0.438182i	0.891400	−	0.453218i	$-0.149724\pi$
$367$	8.39436	+	8.39436i	0.438182	+	0.438182i	−0.453218	+	0.891400i	$0.649724\pi$
$368$	−15.0623	−	15.0623i	−0.785177	−	0.785177i
$369$		0			0
$370$	−2.66711	−	7.82363i	−0.138657	−	0.406731i
$371$			4.19834i			0.217967i
$372$		0			0
$373$	17.5386	−	17.5386i	0.908115	−	0.908115i	−0.0880047	−	0.996120i	$-0.528049\pi$
$373$	17.5386	−	17.5386i	0.908115	−	0.908115i	0.996120	+	0.0880047i	$0.0280491\pi$
$374$	2.75276			0.142342
$375$		0			0
$376$	−9.06316			−0.467397
$377$	11.2249	−	11.2249i	0.578110	−	0.578110i
$378$		0			0
$379$			7.68175i			0.394585i	0.980345	+	0.197292i	$0.0632149\pi$
$379$			7.68175i			0.394585i	−0.980345	+	0.197292i	$0.936785\pi$
$380$	0.133774	+	0.392408i	0.00686244	+	0.0201301i
$381$		0			0
$382$	13.3156	+	13.3156i	0.681288	+	0.681288i
$383$	3.13137	+	3.13137i	0.160006	+	0.160006i	0.782569	−	0.622564i	$-0.213909\pi$
$383$	3.13137	+	3.13137i	0.160006	+	0.160006i	−0.622564	+	0.782569i	$0.713909\pi$
$384$		0			0
$385$	−15.9214	−	7.82587i	−0.811432	−	0.398843i
$386$			8.64249i			0.439891i
$387$		0			0
$388$	−0.175854	+	0.175854i	−0.00892765	+	0.00892765i
$389$	2.96156			0.150157			0.0750785	−	0.997178i	$-0.476079\pi$
$389$	2.96156			0.150157			0.0750785	+	0.997178i	$0.476079\pi$
$390$		0			0
$391$	6.15451			0.311247
$392$	−33.6264	+	33.6264i	−1.69839	+	1.69839i
$393$		0			0
$394$		−	37.3472i		−	1.88153i
$395$	−8.81271	+	3.00430i	−0.443415	+	0.151162i
$396$		0			0
$397$	2.38141	+	2.38141i	0.119520	+	0.119520i	0.764337	−	0.644817i	$-0.223067\pi$
$397$	2.38141	+	2.38141i	0.119520	+	0.119520i	−0.644817	+	0.764337i	$0.723067\pi$
$398$	3.62592	+	3.62592i	0.181751	+	0.181751i
$399$		0			0
$400$	−16.2638	+	12.5470i	−0.813190	+	0.627349i
$401$			38.7685i			1.93601i	0.250940	+	0.968003i	$0.419260\pi$
$401$			38.7685i			1.93601i	−0.250940	+	0.968003i	$0.580740\pi$
$402$		0			0
$403$	−13.4898	+	13.4898i	−0.671973	+	0.671973i
$404$	−0.123113			−0.00612510
$405$		0			0
$406$	46.1181			2.28880
$407$	2.94889	−	2.94889i	0.146171	−	0.146171i
$408$		0			0
$409$			23.9460i			1.18405i	0.805919	+	0.592026i	$0.201672\pi$
$409$			23.9460i			1.18405i	−0.805919	+	0.592026i	$0.798328\pi$
$410$	8.87206	−	18.0499i	0.438160	−	0.891420i
$411$		0			0
$412$	−0.0802490	−	0.0802490i	−0.00395359	−	0.00395359i
$413$	−21.2777	−	21.2777i	−1.04701	−	1.04701i
$414$		0			0
$415$	−10.8076	+	21.9877i	−0.530525	+	1.07933i
$416$		−	0.761963i		−	0.0373583i
$417$		0			0
$418$	−5.46251	+	5.46251i	−0.267180	+	0.267180i
$419$	2.81461			0.137503			0.0687513	−	0.997634i	$-0.478098\pi$
$419$	2.81461			0.137503			0.0687513	+	0.997634i	$0.478098\pi$
$420$		0			0
$421$	−27.4241			−1.33657			−0.668285	−	0.743906i	$-0.732971\pi$
$421$	−27.4241			−1.33657			−0.668285	+	0.743906i	$0.732971\pi$
$422$	22.2115	−	22.2115i	1.08124	−	1.08124i
$423$		0			0
$424$			2.38610i			0.115879i
$425$	0.759352	−	5.88608i	0.0368340	−	0.285517i
$426$		0			0
$427$	−34.4000	−	34.4000i	−1.66473	−	1.66473i
$428$	0.632518	+	0.632518i	0.0305739	+	0.0305739i
$429$		0			0
$430$	−6.34746	+	2.16388i	−0.306102	+	0.104351i
$431$		−	11.9733i		−	0.576733i	−0.957520	−	0.288366i	$-0.906888\pi$
$431$		−	11.9733i		−	0.576733i	0.957520	−	0.288366i	$-0.0931121\pi$
$432$		0			0
$433$	−2.03195	+	2.03195i	−0.0976494	+	0.0976494i	−0.754244	−	0.656594i	$-0.771996\pi$
$433$	−2.03195	+	2.03195i	−0.0976494	+	0.0976494i	0.656594	+	0.754244i	$0.271996\pi$
$434$	−55.4236			−2.66042
$435$		0			0
$436$	0.548680			0.0262770
$437$	−12.2129	+	12.2129i	−0.584220	+	0.584220i
$438$		0			0
$439$		−	36.6162i		−	1.74760i	−0.486287	−	0.873799i	$-0.661649\pi$
$439$		−	36.6162i		−	1.74760i	0.486287	−	0.873799i	$-0.338351\pi$
$440$	−9.04886	−	4.44779i	−0.431387	−	0.212040i
$441$		0			0
$442$	2.91299	+	2.91299i	0.138557	+	0.138557i
$443$	16.4513	+	16.4513i	0.781624	+	0.781624i	0.980105	−	0.198481i	$-0.0636007\pi$
$443$	16.4513	+	16.4513i	0.781624	+	0.781624i	−0.198481	+	0.980105i	$0.563601\pi$
$444$		0			0
$445$	9.33707	+	27.3891i	0.442619	+	1.29837i
$446$		−	7.59963i		−	0.359853i
$447$		0			0
$448$	−26.9321	+	26.9321i	−1.27242	+	1.27242i
$449$	30.9394			1.46012			0.730061	−	0.683383i	$-0.239492\pi$
$449$	30.9394			1.46012			0.730061	+	0.683383i	$0.239492\pi$
$450$		0			0
$451$	10.1474			0.477825
$452$	−0.576429	+	0.576429i	−0.0271129	+	0.0271129i
$453$		0			0
$454$		−	6.33079i		−	0.297119i
$455$	−8.56678	−	25.1295i	−0.401617	−	1.17809i
$456$		0			0
$457$	−8.75684	−	8.75684i	−0.409627	−	0.409627i	0.471981	−	0.881609i	$-0.343539\pi$
$457$	−8.75684	−	8.75684i	−0.409627	−	0.409627i	−0.881609	+	0.471981i	$0.843539\pi$
$458$	0.395183	+	0.395183i	0.0184657	+	0.0184657i
$459$		0			0
$460$	0.579153	+	0.284671i	0.0270032	+	0.0132729i
$461$			13.7285i			0.639398i	0.947519	+	0.319699i	$0.103582\pi$
$461$			13.7285i			0.639398i	−0.947519	+	0.319699i	$0.896418\pi$
$462$		0			0
$463$	−23.2746	+	23.2746i	−1.08166	+	1.08166i	−0.0853083	+	0.996355i	$0.527188\pi$
$463$	−23.2746	+	23.2746i	−1.08166	+	1.08166i	−0.996355	+	0.0853083i	$0.972812\pi$
$464$	26.9410			1.25070
$465$		0			0
$466$	8.78044			0.406746
$467$	7.35920	−	7.35920i	0.340543	−	0.340543i	−0.516028	−	0.856572i	$-0.672590\pi$
$467$	7.35920	−	7.35920i	0.340543	−	0.340543i	0.856572	+	0.516028i	$0.172590\pi$
$468$		0			0
$469$		−	24.4455i		−	1.12879i
$470$	9.86548	−	3.36319i	0.455061	−	0.155132i
$471$		0			0
$472$	−12.0931	−	12.0931i	−0.556629	−	0.556629i
$473$	−2.39249	−	2.39249i	−0.110007	−	0.110007i
$474$		0			0
$475$	10.1734	+	13.1870i	0.466786	+	0.605063i
$476$			0.324059i			0.0148532i
$477$		0			0
$478$	−30.3898	+	30.3898i	−1.39000	+	1.39000i
$479$	28.1197			1.28482			0.642410	−	0.766361i	$-0.277935\pi$
$479$	28.1197			1.28482			0.642410	+	0.766361i	$0.277935\pi$
$480$		0			0
$481$	6.24107			0.284568
$482$	2.98817	−	2.98817i	0.136107	−	0.136107i
$483$		0			0
$484$		−	0.466635i		−	0.0212107i
$485$	−4.40722	+	8.96633i	−0.200122	+	0.407140i
$486$		0			0
$487$	−16.9394	−	16.9394i	−0.767596	−	0.767596i	0.210087	−	0.977683i	$-0.432625\pi$
$487$	−16.9394	−	16.9394i	−0.767596	−	0.767596i	−0.977683	+	0.210087i	$0.932625\pi$
$488$	−19.5510	−	19.5510i	−0.885032	−	0.885032i
$489$		0			0
$490$	24.1250	−	49.0814i	1.08986	−	2.21727i
$491$			28.3850i			1.28100i	0.767959	+	0.640498i	$0.221272\pi$
$491$			28.3850i			1.28100i	−0.767959	+	0.640498i	$0.778728\pi$
$492$		0			0
$493$	−5.50408	+	5.50408i	−0.247891	+	0.247891i
$494$	−11.5609			−0.520150
$495$		0			0
$496$	−32.3770			−1.45377
$497$	−15.3077	+	15.3077i	−0.686644	+	0.686644i
$498$		0			0
$499$		−	4.65424i		−	0.208353i	−0.994559	−	0.104176i	$-0.966779\pi$
$499$		−	4.65424i		−	0.208353i	0.994559	−	0.104176i	$-0.0332206\pi$
$500$	0.343712	−	0.518771i	0.0153713	−	0.0232001i
$501$		0			0
$502$	17.2715	+	17.2715i	0.770864	+	0.770864i
$503$	−19.7355	−	19.7355i	−0.879964	−	0.879964i	0.113567	−	0.993530i	$-0.463772\pi$
$503$	−19.7355	−	19.7355i	−0.879964	−	0.879964i	−0.993530	+	0.113567i	$0.963772\pi$
$504$		0			0
$505$	−4.68131	+	1.59588i	−0.208316	+	0.0710158i
$506$			12.0249i			0.534571i
$507$		0			0
$508$	0.150035	−	0.150035i	0.00665674	−	0.00665674i
$509$	20.2386			0.897058			0.448529	−	0.893768i	$-0.351948\pi$
$509$	20.2386			0.897058			0.448529	+	0.893768i	$0.351948\pi$
$510$		0			0
$511$	64.0865			2.83502
$512$	−15.2819	+	15.2819i	−0.675373	+	0.675373i
$513$		0			0
$514$		−	37.3854i		−	1.64900i
$515$	−4.09168	−	2.01118i	−0.180301	−	0.0886234i
$516$		0			0
$517$	3.71851	+	3.71851i	0.163540	+	0.163540i
$518$	12.8209	+	12.8209i	0.563319	+	0.563319i
$519$		0			0
$520$	−4.86888	−	14.2822i	−0.213514	−	0.626317i
$521$			24.4368i			1.07060i	0.844663	+	0.535298i	$0.179801\pi$
$521$			24.4368i			1.07060i	−0.844663	+	0.535298i	$0.820199\pi$
$522$		0			0
$523$	21.7734	−	21.7734i	0.952084	−	0.952084i	−0.0468197	−	0.998903i	$-0.514909\pi$
$523$	21.7734	−	21.7734i	0.952084	−	0.952084i	0.998903	+	0.0468197i	$0.0149086\pi$
$524$	0.543832			0.0237574
$525$		0			0
$526$	−12.2622			−0.534658
$527$	6.61467	−	6.61467i	0.288139	−	0.288139i
$528$		0			0
$529$			3.88472i			0.168901i
$530$	−0.885443	−	2.59733i	−0.0384612	−	0.112821i
$531$		0			0
$532$	−0.643055	−	0.643055i	−0.0278800	−	0.0278800i
$533$	10.7381	+	10.7381i	0.465118	+	0.465118i
$534$		0			0
$535$	32.2504	+	15.8520i	1.39430	+	0.685343i
$536$		−	13.8934i		−	0.600105i
$537$		0			0
$538$	11.5680	−	11.5680i	0.498732	−	0.498732i
$539$	27.5931			1.18852
$540$		0			0
$541$	−22.4453			−0.964998			−0.482499	−	0.875897i	$-0.660271\pi$
$541$	−22.4453			−0.964998			−0.482499	+	0.875897i	$0.660271\pi$
$542$	11.6012	−	11.6012i	0.498314	−	0.498314i
$543$		0			0
$544$			0.373626i			0.0160191i
$545$	20.8633	−	7.11240i	0.893686	−	0.304662i
$546$		0			0
$547$	−6.74486	−	6.74486i	−0.288389	−	0.288389i	0.548054	−	0.836443i	$-0.315369\pi$
$547$	−6.74486	−	6.74486i	−0.288389	−	0.288389i	−0.836443	+	0.548054i	$0.815369\pi$
$548$	−0.141718	−	0.141718i	−0.00605388	−	0.00605388i
$549$		0			0
$550$	11.5004	+	1.48365i	0.490379	+	0.0632629i
$551$		−	21.8443i		−	0.930600i
$552$		0			0
$553$	14.4418	−	14.4418i	0.614126	−	0.614126i
$554$	−32.5616			−1.38341
$555$		0			0
$556$	−0.899263			−0.0381373
$557$	−6.89207	+	6.89207i	−0.292026	+	0.292026i	−0.837880	−	0.545854i	$-0.816205\pi$
$557$	−6.89207	+	6.89207i	−0.292026	+	0.292026i	0.545854	+	0.837880i	$0.316205\pi$
$558$		0			0
$559$		−	5.06349i		−	0.214163i
$560$	19.8763	−	40.4375i	0.839925	−	1.70880i
$561$		0			0
$562$	−11.8387	−	11.8387i	−0.499387	−	0.499387i
$563$	−12.2175	−	12.2175i	−0.514905	−	0.514905i	0.401120	−	0.916025i	$-0.368621\pi$
$563$	−12.2175	−	12.2175i	−0.514905	−	0.514905i	−0.916025	+	0.401120i	$0.868621\pi$
$564$		0			0
$565$	−14.4463	+	29.3905i	−0.607762	+	1.23647i
$566$			5.75063i			0.241717i
$567$		0			0
$568$	−8.70003	+	8.70003i	−0.365045	+	0.365045i
$569$	28.7094			1.20356			0.601780	−	0.798662i	$-0.294458\pi$
$569$	28.7094			1.20356			0.601780	+	0.798662i	$0.294458\pi$
$570$		0			0
$571$	−28.2097			−1.18054			−0.590270	−	0.807206i	$-0.700979\pi$
$571$	−28.2097			−1.18054			−0.590270	+	0.807206i	$0.700979\pi$
$572$	−0.154107	+	0.154107i	−0.00644352	+	0.00644352i
$573$		0			0
$574$			44.1181i			1.84146i
$575$	25.7122	+	3.31708i	1.07227	+	0.138332i
$576$		0			0
$577$	31.2061	+	31.2061i	1.29913	+	1.29913i	0.928969	+	0.370158i	$0.120696\pi$
$577$	31.2061	+	31.2061i	1.29913	+	1.29913i	0.370158	+	0.928969i	$0.379304\pi$
$578$	15.8066	+	15.8066i	0.657466	+	0.657466i
$579$		0			0
$580$	−0.772533	+	0.263360i	−0.0320777	+	0.0109354i
$581$		−	53.7431i		−	2.22964i
$582$		0			0
$583$	0.978989	−	0.978989i	0.0405456	−	0.0405456i
$584$	36.4231			1.50720
$585$		0			0
$586$	27.4089			1.13225
$587$	−14.8414	+	14.8414i	−0.612570	+	0.612570i	−0.943615	−	0.331045i	$-0.892599\pi$
$587$	−14.8414	+	14.8414i	−0.612570	+	0.612570i	0.331045	+	0.943615i	$0.392599\pi$
$588$		0			0
$589$			26.2520i			1.08169i
$590$	17.6512	+	8.67608i	0.726687	+	0.357189i
$591$		0			0
$592$	7.48964	+	7.48964i	0.307822	+	0.307822i
$593$	−5.45456	−	5.45456i	−0.223992	−	0.223992i	0.586185	−	0.810177i	$-0.300629\pi$
$593$	−5.45456	−	5.45456i	−0.223992	−	0.223992i	−0.810177	+	0.586185i	$0.800629\pi$
$594$		0			0
$595$	4.20070	+	12.3222i	0.172212	+	0.505161i
$596$		−	0.956976i		−	0.0391993i
$597$		0			0
$598$	−12.7248	+	12.7248i	−0.520355	+	0.520355i
$599$	−20.5629			−0.840176			−0.420088	−	0.907483i	$-0.638001\pi$
$599$	−20.5629			−0.840176			−0.420088	+	0.907483i	$0.638001\pi$
$600$		0			0
$601$	19.4810			0.794648			0.397324	−	0.917678i	$-0.369939\pi$
$601$	19.4810			0.794648			0.397324	+	0.917678i	$0.369939\pi$
$602$	10.4018	−	10.4018i	0.423948	−	0.423948i
$603$		0			0
$604$			0.0931491i			0.00379018i
$605$	−6.04887	−	17.7436i	−0.245922	−	0.721379i
$606$		0			0
$607$	−18.3043	−	18.3043i	−0.742948	−	0.742948i	0.230196	−	0.973144i	$-0.426063\pi$
$607$	−18.3043	−	18.3043i	−0.742948	−	0.742948i	−0.973144	+	0.230196i	$0.926063\pi$
$608$	−0.741415	−	0.741415i	−0.0300684	−	0.0300684i
$609$		0			0
$610$	28.5368	+	14.0267i	1.15542	+	0.567925i
$611$			7.86989i			0.318382i
$612$		0			0
$613$	25.3784	−	25.3784i	1.02503	−	1.02503i	0.0253472	−	0.999679i	$-0.491931\pi$
$613$	25.3784	−	25.3784i	1.02503	−	1.02503i	0.999679	−	0.0253472i	$-0.00806913\pi$
$614$	9.65969			0.389833
$615$		0			0
$616$	22.1175			0.891141
$617$	16.0954	−	16.0954i	0.647976	−	0.647976i	−0.304527	−	0.952504i	$-0.598498\pi$
$617$	16.0954	−	16.0954i	0.647976	−	0.647976i	0.952504	+	0.304527i	$0.0984985\pi$
$618$		0			0
$619$			25.3641i			1.01947i	0.860331	+	0.509735i	$0.170257\pi$
$619$			25.3641i			1.01947i	−0.860331	+	0.509735i	$0.829743\pi$
$620$	0.928411	−	0.316500i	0.0372859	−	0.0127109i
$621$		0			0
$622$	−13.1625	−	13.1625i	−0.527768	−	0.527768i
$623$	−44.8836	−	44.8836i	−1.79823	−	1.79823i
$624$		0			0
$625$	6.34481	−	24.1815i	0.253792	−	0.967259i
$626$		−	11.4901i		−	0.459239i
$627$		0			0
$628$	0.107498	−	0.107498i	0.00428962	−	0.00428962i
$629$	−3.06029			−0.122022
$630$		0			0
$631$	−21.4057			−0.852147			−0.426074	−	0.904689i	$-0.640104\pi$
$631$	−21.4057			−0.852147			−0.426074	+	0.904689i	$0.640104\pi$
$632$	8.20789	−	8.20789i	0.326492	−	0.326492i
$633$		0			0
$634$			28.6691i			1.13860i
$635$	3.76015	−	7.64989i	0.149217	−	0.303577i
$636$		0			0
$637$	29.1991	+	29.1991i	1.15691	+	1.15691i
$638$	−10.7541	−	10.7541i	−0.425757	−	0.425757i
$639$		0			0
$640$	11.6027	−	23.6052i	0.458635	−	0.933076i
$641$		−	44.1570i		−	1.74410i	−0.489419	−	0.872049i	$-0.662791\pi$
$641$		−	44.1570i		−	1.74410i	0.489419	−	0.872049i	$-0.337209\pi$
$642$		0			0
$643$	27.8297	−	27.8297i	1.09749	−	1.09749i	0.102792	−	0.994703i	$-0.467222\pi$
$643$	27.8297	−	27.8297i	1.09749	−	1.09749i	0.994703	−	0.102792i	$-0.0327776\pi$
$644$	−1.41559			−0.0557819
$645$		0			0
$646$	5.66886			0.223038
$647$	1.68320	−	1.68320i	0.0661734	−	0.0661734i	−0.673246	−	0.739419i	$-0.735100\pi$
$647$	1.68320	−	1.68320i	0.0661734	−	0.0661734i	0.739419	+	0.673246i	$0.235100\pi$
$648$		0			0
$649$			9.92330i			0.389523i
$650$	10.5998	+	13.7398i	0.415758	+	0.538919i
$651$		0			0
$652$	−0.160790	−	0.160790i	−0.00629703	−	0.00629703i
$653$	23.5783	+	23.5783i	0.922691	+	0.922691i	0.997219	−	0.0745277i	$-0.0237449\pi$
$653$	23.5783	+	23.5783i	0.922691	+	0.922691i	−0.0745277	+	0.997219i	$0.523745\pi$
$654$		0			0
$655$	20.6789	−	7.04955i	0.807993	−	0.275449i
$656$			25.7726i			1.00625i
$657$		0			0
$658$	−16.1670	+	16.1670i	−0.630255	+	0.630255i
$659$	35.8952			1.39828			0.699139	−	0.714986i	$-0.253567\pi$
$659$	35.8952			1.39828			0.699139	+	0.714986i	$0.253567\pi$
$660$		0			0
$661$	−29.5683			−1.15007			−0.575037	−	0.818127i	$-0.695012\pi$
$661$	−29.5683			−1.15007			−0.575037	+	0.818127i	$0.695012\pi$
$662$	12.8124	−	12.8124i	0.497968	−	0.497968i
$663$		0			0
$664$		−	30.5446i		−	1.18536i
$665$	−32.7876	−	16.1161i	−1.27145	−	0.624956i
$666$		0			0
$667$	−24.0435	−	24.0435i	−0.930967	−	0.930967i
$668$	−0.585762	−	0.585762i	−0.0226638	−	0.0226638i
$669$		0			0
$670$	5.15563	+	15.1234i	0.199179	+	0.584266i
$671$			16.0431i			0.619337i
$672$		0			0
$673$	6.23060	−	6.23060i	0.240172	−	0.240172i	−0.576749	−	0.816921i	$-0.695679\pi$
$673$	6.23060	−	6.23060i	0.240172	−	0.240172i	0.816921	+	0.576749i	$0.195679\pi$
$674$	22.2449			0.856840
$675$		0			0
$676$	0.397434			0.0152859
$677$	6.31135	−	6.31135i	0.242565	−	0.242565i	−0.575346	−	0.817910i	$-0.695132\pi$
$677$	6.31135	−	6.31135i	0.242565	−	0.242565i	0.817910	+	0.575346i	$0.195132\pi$
$678$		0			0
$679$		−	21.9158i		−	0.841052i
$680$	2.38744	+	7.00324i	0.0915541	+	0.268562i
$681$		0			0
$682$	12.9239	+	12.9239i	0.494884	+	0.494884i
$683$	18.4463	+	18.4463i	0.705828	+	0.705828i	0.965655	−	0.259827i	$-0.0836655\pi$
$683$	18.4463	+	18.4463i	0.705828	+	0.705828i	−0.259827	+	0.965655i	$0.583666\pi$
$684$		0			0
$685$	−7.22580	−	3.55170i	−0.276084	−	0.135703i
$686$			70.7387i			2.70082i
$687$		0			0
$688$	6.07648	−	6.07648i	0.231664	−	0.231664i
$689$	2.07194			0.0789347
$690$		0			0
$691$	−45.1966			−1.71936			−0.859679	−	0.510834i	$-0.829337\pi$
$691$	−45.1966			−1.71936			−0.859679	+	0.510834i	$0.829337\pi$
$692$	−0.339849	+	0.339849i	−0.0129191	+	0.0129191i
$693$		0			0
$694$			25.7031i			0.975677i
$695$	−34.1941	+	11.6569i	−1.29705	+	0.442172i
$696$		0			0
$697$	−5.26539	−	5.26539i	−0.199441	−	0.199441i
$698$	−13.1989	−	13.1989i	−0.499586	−	0.499586i
$699$		0			0
$700$	−0.174657	+	1.35385i	−0.00660142	+	0.0511706i
$701$			3.15549i			0.119181i	0.998223	+	0.0595906i	$0.0189795\pi$
$701$			3.15549i			0.119181i	−0.998223	+	0.0595906i	$0.981020\pi$
$702$		0			0
$703$	6.07276	−	6.07276i	0.229039	−	0.229039i
$704$	12.5603			0.473385
$705$		0			0
$706$	23.6730			0.890946
$707$	7.67147	−	7.67147i	0.288515	−	0.288515i
$708$		0			0
$709$			12.5063i			0.469684i	0.972034	+	0.234842i	$0.0754573\pi$
$709$			12.5063i			0.469684i	−0.972034	+	0.234842i	$0.924543\pi$
$710$	6.24177	−	12.6986i	0.234249	−	0.476572i
$711$		0			0
$712$	−25.5093	−	25.5093i	−0.956003	−	0.956003i
$713$	28.8948	+	28.8948i	1.08212	+	1.08212i
$714$		0			0
$715$	−3.86218	+	7.85747i	−0.144438	+	0.293853i
$716$			0.173254i			0.00647481i
$717$		0			0
$718$	7.55689	−	7.55689i	0.282021	−	0.282021i
$719$	−49.6035			−1.84990			−0.924949	−	0.380092i	$-0.875892\pi$
$719$	−49.6035			−1.84990			−0.924949	+	0.380092i	$0.875892\pi$
$720$		0			0
$721$	10.0010			0.372458
$722$	8.01342	−	8.01342i	0.298229	−	0.298229i
$723$		0			0
$724$			0.435769i			0.0161952i
$725$	−25.9613	+	20.0283i	−0.964180	+	0.743833i
$726$		0			0
$727$	−31.2570	−	31.2570i	−1.15926	−	1.15926i	−0.984636	−	0.174621i	$-0.944130\pi$
$727$	−31.2570	−	31.2570i	−1.15926	−	1.15926i	−0.174621	−	0.984636i	$-0.555870\pi$
$728$	23.4049	+	23.4049i	0.867443	+	0.867443i
$729$		0			0
$730$	−39.6475	+	13.5160i	−1.46742	+	0.500251i
$731$			2.48287i			0.0918322i
$732$		0			0
$733$	−9.43633	+	9.43633i	−0.348539	+	0.348539i	−0.859565	−	0.511026i	$-0.829265\pi$
$733$	−9.43633	+	9.43633i	−0.348539	+	0.348539i	0.511026	+	0.859565i	$0.329265\pi$
$734$	17.0207			0.628247
$735$		0			0
$736$	−1.63211			−0.0601604
$737$	−5.70031	+	5.70031i	−0.209974	+	0.209974i
$738$		0			0
$739$		−	31.2347i		−	1.14899i	−0.818509	−	0.574493i	$-0.805199\pi$
$739$		−	31.2347i		−	1.14899i	0.818509	−	0.574493i	$-0.194801\pi$
$740$	−0.287980	−	0.141551i	−0.0105864	−	0.00520352i
$741$		0			0
$742$	4.25636	+	4.25636i	0.156256	+	0.156256i
$743$	7.92674	+	7.92674i	0.290804	+	0.290804i	0.837398	−	0.546594i	$-0.184076\pi$
$743$	7.92674	+	7.92674i	0.290804	+	0.290804i	−0.546594	+	0.837398i	$0.684076\pi$
$744$		0			0
$745$	−12.4050	−	36.3886i	−0.454486	−	1.33317i
$746$		−	35.5620i		−	1.30202i
$747$		0			0
$748$	0.0755657	−	0.0755657i	0.00276296	−	0.00276296i
$749$	−78.8275			−2.88029
$750$		0			0
$751$	−24.6957			−0.901158			−0.450579	−	0.892737i	$-0.648782\pi$
$751$	−24.6957			−0.901158			−0.450579	+	0.892737i	$0.648782\pi$
$752$	−9.44432	+	9.44432i	−0.344399	+	0.344399i
$753$		0			0
$754$		−	22.7600i		−	0.828870i
$755$	1.20747	+	3.54195i	0.0439443	+	0.128905i
$756$		0			0
$757$	−2.00912	−	2.00912i	−0.0730226	−	0.0730226i	0.669652	−	0.742675i	$-0.266443\pi$
$757$	−2.00912	−	2.00912i	−0.0730226	−	0.0730226i	−0.742675	+	0.669652i	$0.766443\pi$
$758$	7.78791	+	7.78791i	0.282870	+	0.282870i
$759$		0			0
$760$	−18.6346	−	9.15949i	−0.675950	−	0.332250i
$761$			15.4780i			0.561077i	0.959843	+	0.280539i	$0.0905131\pi$
$761$			15.4780i			0.561077i	−0.959843	+	0.280539i	$0.909487\pi$
$762$		0			0
$763$	−34.1896	+	34.1896i	−1.23775	+	1.23775i
$764$	0.731052			0.0264486
$765$		0			0
$766$	6.34929			0.229409
$767$	−10.5009	+	10.5009i	−0.379165	+	0.379165i
$768$		0			0
$769$		−	28.8170i		−	1.03917i	−0.854420	−	0.519584i	$-0.826087\pi$
$769$		−	28.8170i		−	1.03917i	0.854420	−	0.519584i	$-0.173913\pi$
$770$	−24.0755	+	8.20745i	−0.867621	+	0.295776i
$771$		0			0
$772$	0.237244	+	0.237244i	0.00853860	+	0.00853860i
$773$	−28.0031	−	28.0031i	−1.00720	−	1.00720i	−0.999974	−	0.00722642i	$-0.997700\pi$
$773$	−28.0031	−	28.0031i	−1.00720	−	1.00720i	−0.00722642	−	0.999974i	$-0.502300\pi$
$774$		0			0
$775$	31.1997	−	24.0695i	1.12073	−	0.864602i
$776$		−	12.4557i		−	0.447134i
$777$		0			0
$778$	3.00249	−	3.00249i	0.107644	−	0.107644i
$779$	20.8970			0.748713
$780$		0			0
$781$	7.13904			0.255455
$782$	6.23956	−	6.23956i	0.223126	−	0.223126i
$783$		0			0
$784$			70.0812i			2.50290i
$785$	2.69408	−	5.48101i	0.0961558	−	0.195626i
$786$		0			0
$787$	31.9257	+	31.9257i	1.13803	+	1.13803i	0.988803	+	0.149224i	$0.0476777\pi$
$787$	31.9257	+	31.9257i	1.13803	+	1.13803i	0.149224	+	0.988803i	$0.452322\pi$
$788$	−1.02521	−	1.02521i	−0.0365217	−	0.0365217i
$789$		0			0
$790$	−5.88868	+	11.9803i	−0.209510	+	0.426240i
$791$		−	71.8373i		−	2.55424i
$792$		0			0
$793$	−16.9769	+	16.9769i	−0.602867	+	0.602867i
$794$	4.82864			0.171362
$795$		0			0
$796$	0.199069			0.00705583
$797$	0.999124	−	0.999124i	0.0353908	−	0.0353908i	−0.689190	−	0.724581i	$-0.742033\pi$
$797$	0.999124	−	0.999124i	0.0353908	−	0.0353908i	0.724581	+	0.689190i	$0.242033\pi$
$798$		0			0
$799$		−	3.85898i		−	0.136521i
$800$	−0.201372	+	1.56093i	−0.00711958	+	0.0551871i
$801$		0			0
$802$	39.3042	+	39.3042i	1.38788	+	1.38788i
$803$	−14.9440	−	14.9440i	−0.527362	−	0.527362i
$804$		0			0
$805$	−53.8270	+	18.3499i	−1.89715	+	0.646749i
$806$			27.3524i			0.963446i
$807$		0			0
$808$	4.36003	−	4.36003i	0.153385	−	0.153385i
$809$	11.8160			0.415430			0.207715	−	0.978189i	$-0.433397\pi$
$809$	11.8160			0.415430			0.207715	+	0.978189i	$0.433397\pi$
$810$		0			0
$811$	35.4386			1.24442			0.622209	−	0.782851i	$-0.286235\pi$
$811$	35.4386			1.24442			0.622209	+	0.782851i	$0.286235\pi$
$812$	1.26598	−	1.26598i	0.0444273	−	0.0444273i
$813$		0			0
$814$		−	5.97929i		−	0.209574i
$815$	−8.19825	−	4.02969i	−0.287172	−	0.141154i
$816$		0			0
$817$	−4.92694	−	4.92694i	−0.172372	−	0.172372i
$818$	24.2769	+	24.2769i	0.848822	+	0.848822i
$819$		0			0
$820$	−0.251939	−	0.739031i	−0.00879810	−	0.0258081i
$821$		−	32.3725i		−	1.12981i	−0.825156	−	0.564905i	$-0.808913\pi$
$821$		−	32.3725i		−	1.12981i	0.825156	−	0.564905i	$-0.191087\pi$
$822$		0			0
$823$	−17.7970	+	17.7970i	−0.620366	+	0.620366i	−0.945625	−	0.325259i	$-0.894549\pi$
$823$	−17.7970	+	17.7970i	−0.620366	+	0.620366i	0.325259	+	0.945625i	$0.394549\pi$
$824$	5.68402			0.198012
$825$		0			0
$826$	−43.1436			−1.50116
$827$	6.35269	−	6.35269i	0.220905	−	0.220905i	−0.587975	−	0.808879i	$-0.700075\pi$
$827$	6.35269	−	6.35269i	0.220905	−	0.220905i	0.808879	+	0.587975i	$0.200075\pi$
$828$		0			0
$829$		−	43.0187i		−	1.49410i	−0.664768	−	0.747050i	$-0.731470\pi$
$829$		−	43.0187i		−	1.49410i	0.664768	−	0.747050i	$-0.268530\pi$
$830$	11.3346	+	33.2485i	0.393429	+	1.15407i
$831$		0			0
$832$	13.2914	+	13.2914i	0.460797	+	0.460797i
$833$	−14.3177	−	14.3177i	−0.496079	−	0.496079i
$834$		0			0
$835$	−29.8664	−	14.6802i	−1.03357	−	0.508030i
$836$			0.299902i			0.0103723i
$837$		0			0
$838$	2.85351	−	2.85351i	0.0985727	−	0.0985727i
$839$	0.0133946			0.000462433			0.000231217	−	1.00000i	$-0.499926\pi$
$839$	0.0133946			0.000462433			0.000231217		1.00000i	$0.499926\pi$
$840$		0			0
$841$	14.0050			0.482930
$842$	−27.8031	+	27.8031i	−0.958158	+	0.958158i
$843$		0			0
$844$		−	1.21945i		−	0.0419753i
$845$	15.1122	−	5.15183i	0.519876	−	0.177228i
$846$		0			0
$847$	29.0772	+	29.0772i	0.999104	+	0.999104i
$848$	2.48645	+	2.48645i	0.0853850	+	0.0853850i
$849$		0			0
$850$	−5.19758	−	6.73727i	−0.178276	−	0.231087i
$851$		−	13.3683i		−	0.458258i
$852$		0			0
$853$	26.5731	−	26.5731i	0.909845	−	0.909845i	−0.0864147	−	0.996259i	$-0.527541\pi$
$853$	26.5731	−	26.5731i	0.909845	−	0.909845i	0.996259	+	0.0864147i	$0.0275410\pi$
$854$	−69.7507			−2.38682
$855$		0			0
$856$	−44.8011			−1.53127
$857$	−6.90887	+	6.90887i	−0.236003	+	0.236003i	−0.815193	−	0.579190i	$-0.803369\pi$
$857$	−6.90887	+	6.90887i	−0.236003	+	0.236003i	0.579190	+	0.815193i	$0.303369\pi$
$858$		0			0
$859$			22.2489i			0.759123i	0.925166	+	0.379562i	$0.123925\pi$
$859$			22.2489i			0.759123i	−0.925166	+	0.379562i	$0.876075\pi$
$860$	−0.114843	+	0.233644i	−0.00391611	+	0.00796718i
$861$		0			0
$862$	−12.1387	−	12.1387i	−0.413447	−	0.413447i
$863$	30.8443	+	30.8443i	1.04995	+	1.04995i	0.998685	+	0.0512663i	$0.0163257\pi$
$863$	30.8443	+	30.8443i	1.04995	+	1.04995i	0.0512663	+	0.998685i	$0.483674\pi$
$864$		0			0
$865$	−8.51722	+	17.3280i	−0.289594	+	0.589169i
$866$			4.12007i			0.140006i
$867$		0			0
$868$	−1.52143	+	1.52143i	−0.0516406	+	0.0516406i
$869$	−6.73520			−0.228476
$870$		0			0
$871$	−12.0642			−0.408780
$872$	−19.4315	+	19.4315i	−0.658032	+	0.658032i
$873$		0			0
$874$			24.7633i			0.837630i
$875$	10.9083	+	53.7434i	0.368768	+	1.81686i
$876$		0			0
$877$	21.2794	+	21.2794i	0.718554	+	0.718554i	0.968309	−	0.249755i	$-0.0803500\pi$
$877$	21.2794	+	21.2794i	0.718554	+	0.718554i	−0.249755	+	0.968309i	$0.580350\pi$
$878$	−37.1223	−	37.1223i	−1.25282	−	1.25282i
$879$		0			0
$880$	−14.0643	+	4.79457i	−0.474106	+	0.161625i
$881$		−	20.9422i		−	0.705560i	−0.935706	−	0.352780i	$-0.885236\pi$
$881$		−	20.9422i		−	0.705560i	0.935706	−	0.352780i	$-0.114764\pi$
$882$		0			0
$883$	6.78718	−	6.78718i	0.228407	−	0.228407i	−0.583620	−	0.812027i	$-0.698364\pi$
$883$	6.78718	−	6.78718i	0.228407	−	0.228407i	0.812027	+	0.583620i	$0.198364\pi$
$884$	0.159928			0.00537896
$885$		0			0
$886$	33.3573			1.12066
$887$	−27.9379	+	27.9379i	−0.938062	+	0.938062i	−0.998191	−	0.0601287i	$-0.980849\pi$
$887$	−27.9379	+	27.9379i	−0.938062	+	0.938062i	0.0601287	+	0.998191i	$0.480849\pi$
$888$		0			0
$889$			18.6981i			0.627115i
$890$	37.2337	+	18.3015i	1.24808	+	0.613467i
$891$		0			0
$892$	−0.208617	−	0.208617i	−0.00698500	−	0.00698500i
$893$	7.65766	+	7.65766i	0.256254	+	0.256254i
$894$		0			0
$895$	2.24585	+	6.58791i	0.0750705	+	0.220209i
$896$			57.6966i			1.92751i
$897$		0			0
$898$	31.3670	−	31.3670i	1.04673	−	1.04673i
$899$	−51.6823			−1.72370
$900$		0			0
$901$	−1.01597			−0.0338469
$902$	10.2877	−	10.2877i	0.342542	−	0.342542i
$903$		0			0
$904$		−	40.8283i		−	1.35793i
$905$	5.64876	+	16.5699i	0.187771	+	0.550803i
$906$		0			0
$907$	−29.9894	−	29.9894i	−0.995783	−	0.995783i	0.00420831	−	0.999991i	$-0.498660\pi$
$907$	−29.9894	−	29.9894i	−0.995783	−	0.995783i	−0.999991	+	0.00420831i	$0.998660\pi$
$908$	−0.173786	−	0.173786i	−0.00576729	−	0.00576729i
$909$		0			0
$910$	−34.1620	−	16.7916i	−1.13246	−	0.556638i
$911$			26.9986i			0.894502i	0.894408	+	0.447251i	$0.147597\pi$
$911$			26.9986i			0.894502i	−0.894408	+	0.447251i	$0.852403\pi$
$912$		0			0
$913$	−12.5321	+	12.5321i	−0.414751	+	0.414751i
$914$	−17.7557			−0.587306
$915$		0			0
$916$	0.0216962			0.000716864
$917$	−33.8875	+	33.8875i	−1.11906	+	1.11906i
$918$		0			0
$919$			13.9943i			0.461630i	0.972998	+	0.230815i	$0.0741392\pi$
$919$			13.9943i			0.461630i	−0.972998	+	0.230815i	$0.925861\pi$
$920$	−30.5922	+	10.4290i	−1.00860	+	0.343835i
$921$		0			0
$922$	13.9182	+	13.9182i	0.458371	+	0.458371i
$923$	7.55457	+	7.55457i	0.248662	+	0.248662i
$924$		0			0
$925$	−12.7852	−	1.64939i	−0.420375	−	0.0542318i
$926$			47.1925i			1.55084i
$927$		0			0
$928$	1.45963	−	1.45963i	0.0479145	−	0.0479145i
$929$	−24.9978			−0.820152			−0.410076	−	0.912051i	$-0.634498\pi$
$929$	−24.9978			−0.820152			−0.410076	+	0.912051i	$0.634498\pi$
$930$		0			0
$931$	56.8234			1.86231
$932$	0.241031	−	0.241031i	0.00789523	−	0.00789523i
$933$		0			0
$934$		−	14.9218i		−	0.488257i
$935$	1.89381	−	3.85289i	0.0619342	−	0.126003i
$936$		0			0
$937$	−4.06172	−	4.06172i	−0.132691	−	0.132691i	0.637642	−	0.770333i	$-0.279910\pi$
$937$	−4.06172	−	4.06172i	−0.132691	−	0.132691i	−0.770333	+	0.637642i	$0.779910\pi$
$938$	−24.7833	−	24.7833i	−0.809203	−	0.809203i
$939$		0			0
$940$	0.178494	−	0.363139i	0.00582182	−	0.0118443i
$941$		−	36.8257i		−	1.20048i	−0.799819	−	0.600242i	$-0.795071\pi$
$941$		−	36.8257i		−	1.20048i	0.799819	−	0.600242i	$-0.204929\pi$
$942$		0			0
$943$	23.0008	−	23.0008i	0.749008	−	0.749008i
$944$	−25.2033			−0.820298
$945$		0			0
$946$	−4.85111			−0.157723
$947$	25.1992	−	25.1992i	0.818863	−	0.818863i	−0.167080	−	0.985943i	$-0.553434\pi$
$947$	25.1992	−	25.1992i	0.818863	−	0.818863i	0.985943	+	0.167080i	$0.0534338\pi$
$948$		0			0
$949$		−	31.6276i		−	1.02668i
$950$	23.6832	+	3.05533i	0.768386	+	0.0991279i
$951$		0			0
$952$	−11.4765	−	11.4765i	−0.371956	−	0.371956i
$953$	21.3106	+	21.3106i	0.690317	+	0.690317i	0.962302	−	0.271985i	$-0.0876800\pi$
$953$	21.3106	+	21.3106i	0.690317	+	0.690317i	−0.271985	+	0.962302i	$0.587680\pi$
$954$		0			0
$955$	27.7979	−	9.47645i	0.899520	−	0.306651i
$956$			1.66845i			0.0539617i
$957$		0			0
$958$	28.5083	−	28.5083i	0.921060	−	0.921060i
$959$	17.6616			0.570321
$960$		0			0
$961$	31.1105			1.00356
$962$	6.32732	−	6.32732i	0.204001	−	0.204001i
$963$		0			0
$964$		−	0.164056i		−	0.00528388i
$965$	12.0964	+	5.94576i	0.389398	+	0.191401i
$966$		0			0
$967$	29.4988	+	29.4988i	0.948617	+	0.948617i	0.998743	−	0.0501258i	$-0.0159622\pi$
$967$	29.4988	+	29.4988i	0.948617	+	0.948617i	−0.0501258	+	0.998743i	$0.515962\pi$
$968$	16.5258	+	16.5258i	0.531160	+	0.531160i
$969$		0			0
$970$	4.62211	+	13.5584i	0.148407	+	0.435333i
$971$			19.7355i			0.633341i	0.948536	+	0.316671i	$0.102565\pi$
$971$			19.7355i			0.633341i	−0.948536	+	0.316671i	$0.897435\pi$
$972$		0			0
$973$	56.0353	−	56.0353i	1.79641	−	1.79641i
$974$	−34.3469			−1.10055
$975$		0			0
$976$	−40.7465			−1.30426
$977$	36.7121	−	36.7121i	1.17452	−	1.17452i	0.193406	−	0.981119i	$-0.438047\pi$
$977$	36.7121	−	36.7121i	1.17452	−	1.17452i	0.981119	−	0.193406i	$-0.0619534\pi$
$978$		0			0
$979$			20.9324i			0.669002i
$980$	−0.685076	−	2.00958i	−0.0218839	−	0.0641937i
$981$		0			0
$982$	28.7773	+	28.7773i	0.918319	+	0.918319i
$983$	−13.9875	−	13.9875i	−0.446131	−	0.446131i	0.447935	−	0.894066i	$-0.352160\pi$
$983$	−13.9875	−	13.9875i	−0.446131	−	0.446131i	−0.894066	+	0.447935i	$0.852160\pi$
$984$		0			0
$985$	−52.2729	−	25.6937i	−1.66555	−	0.818669i
$986$			11.1603i			0.355416i
$987$		0			0
$988$	−0.317357	+	0.317357i	−0.0100965	+	0.0100965i
$989$	−10.8459			−0.344880
$990$		0			0
$991$	−25.8065			−0.819771			−0.409886	−	0.912137i	$-0.634431\pi$
$991$	−25.8065			−0.819771			−0.409886	+	0.912137i	$0.634431\pi$
$992$	−1.75414	+	1.75414i	−0.0556940	+	0.0556940i
$993$		0			0
$994$			31.0385i			0.984480i
$995$	7.56952	−	2.58049i	0.239970	−	0.0818069i
$996$		0			0
$997$	19.8057	+	19.8057i	0.627253	+	0.627253i	0.947376	−	0.320123i	$-0.103724\pi$
$997$	19.8057	+	19.8057i	0.627253	+	0.627253i	−0.320123	+	0.947376i	$0.603724\pi$
$998$	−4.71856	−	4.71856i	−0.149364	−	0.149364i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.f.b.242.9	yes	24
3.2	odd	2	inner	405.2.f.b.242.4	✓	24
5.3	odd	4	inner	405.2.f.b.323.4	yes	24
9.2	odd	6		405.2.m.e.377.5		24
9.4	even	3		405.2.m.d.107.5		24
9.5	odd	6		405.2.m.d.107.2		24
9.7	even	3		405.2.m.e.377.2		24
15.8	even	4	inner	405.2.f.b.323.9	yes	24
45.13	odd	12		405.2.m.e.188.5		24
45.23	even	12		405.2.m.e.188.2		24
45.38	even	12		405.2.m.d.53.5		24
45.43	odd	12		405.2.m.d.53.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
405.2.f.b.242.4	✓	24	3.2	odd	2	inner
405.2.f.b.242.9	yes	24	1.1	even	1	trivial
405.2.f.b.323.4	yes	24	5.3	odd	4	inner
405.2.f.b.323.9	yes	24	15.8	even	4	inner
405.2.m.d.53.2		24	45.43	odd	12
405.2.m.d.53.5		24	45.38	even	12
405.2.m.d.107.2		24	9.5	odd	6
405.2.m.d.107.5		24	9.4	even	3
405.2.m.e.188.2		24	45.23	even	12
405.2.m.e.188.5		24	45.13	odd	12
405.2.m.e.377.2		24	9.7	even	3
405.2.m.e.377.5		24	9.2	odd	6

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)

\(f(q)\)	\(=\)	\(q+(1.01382 - 1.01382i) q^{2} -0.0556605i q^{4} +(-0.721513 - 2.11646i) q^{5} +(3.46834 + 3.46834i) q^{7} +(1.97121 + 1.97121i) q^{8} +(-2.87720 - 1.41423i) q^{10} -1.61753i q^{11} +(1.71168 - 1.71168i) q^{13} +7.03254 q^{14} +4.10822 q^{16} +(-0.839316 + 0.839316i) q^{17} -3.33104i q^{19} +(-0.117803 + 0.0401598i) q^{20} +(-1.63988 - 1.63988i) q^{22} +(-3.66638 - 3.66638i) q^{23} +(-3.95884 + 3.05411i) q^{25} -3.47066i q^{26} +(0.193050 - 0.193050i) q^{28} +6.55782 q^{29} -7.88102 q^{31} +(0.222578 - 0.222578i) q^{32} +1.70183i q^{34} +(4.83817 - 9.84307i) q^{35} +(1.82308 + 1.82308i) q^{37} +(-3.37707 - 3.37707i) q^{38} +(2.74974 - 5.59425i) q^{40} +6.27343i q^{41} +(1.47910 - 1.47910i) q^{43} -0.0900325 q^{44} -7.43410 q^{46} +(-2.29888 + 2.29888i) q^{47} +17.0588i q^{49} +(-0.917230 + 7.10987i) q^{50} +(-0.0952728 - 0.0952728i) q^{52} +(0.605237 + 0.605237i) q^{53} +(-3.42344 + 1.16707i) q^{55} +13.6737i q^{56} +(6.64844 - 6.64844i) q^{58} -6.13485 q^{59} -9.91828 q^{61} +(-7.98993 + 7.98993i) q^{62} +7.76514i q^{64} +(-4.85770 - 2.38771i) q^{65} +(-3.52409 - 3.52409i) q^{67} +(0.0467168 + 0.0467168i) q^{68} +(-5.07407 - 14.8841i) q^{70} +4.41355i q^{71} +(9.23878 - 9.23878i) q^{73} +3.69656 q^{74} -0.185407 q^{76} +(5.61014 - 5.61014i) q^{77} -4.16388i q^{79} +(-2.96414 - 8.69491i) q^{80} +(6.36012 + 6.36012i) q^{82} +(-7.74767 - 7.74767i) q^{83} +(2.38196 + 1.17081i) q^{85} -2.99909i q^{86} +(3.18849 - 3.18849i) q^{88} -12.9410 q^{89} +11.8734 q^{91} +(-0.204073 + 0.204073i) q^{92} +4.66130i q^{94} +(-7.05002 + 2.40339i) q^{95} +(-3.15941 - 3.15941i) q^{97} +(17.2945 + 17.2945i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{13} - 24 q^{16} + 36 q^{37} - 36 q^{40} - 24 q^{43} - 48 q^{46} - 36 q^{52} - 60 q^{58} + 72 q^{70} + 12 q^{73} + 48 q^{76} - 96 q^{82} + 60 q^{85} + 96 q^{88} - 48 q^{91} + 24 q^{97}+O(q^{100}) \) 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

Related objects

Downloads

Learn more