LMFDB - Embedded newform 405.2.r.a.368.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [405,2,Mod(8,405)] 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("405.8"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(405, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([2, 27])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	405.r (of order $36$, degree $12$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.23394128186$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			368.14
Character	$\chi$	$=$	405.368
Dual form			405.2.r.a.197.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.19031 + 0.191628i) q^{2} +(2.79113 + 0.492152i) q^{4} +(2.15257 - 0.605349i) q^{5} +(0.000530458 + 0.000371431i) q^{7} +(1.77162 + 0.474704i) q^{8} +(4.83080 - 0.913412i) q^{10} +(-0.925209 + 2.54199i) q^{11} +(-0.277011 - 3.16625i) q^{13} +(0.00109069 + 0.000915200i) q^{14} +(-1.53710 - 0.559459i) q^{16} +(-6.58840 + 1.76536i) q^{17} +(1.52337 - 0.879517i) q^{19} +(6.30603 - 0.630218i) q^{20} +(-2.51361 + 5.39046i) q^{22} +(2.93096 + 4.18584i) q^{23} +(4.26710 - 2.60611i) q^{25} -6.98815i q^{26} +(0.00129778 + 0.00129778i) q^{28} +(4.37718 - 3.67289i) q^{29} +(-0.944975 + 5.35922i) q^{31} +(-6.58407 - 3.07020i) q^{32} +(-14.7689 + 2.60416i) q^{34} +(0.00136669 + 0.000478418i) q^{35} +(-0.0678960 - 0.253391i) q^{37} +(3.50519 - 1.63450i) q^{38} +(4.10090 - 0.0506152i) q^{40} +(-7.56097 + 9.01082i) q^{41} +(-3.67622 - 7.88368i) q^{43} +(-3.83342 + 6.63969i) q^{44} +(5.61759 + 9.72995i) q^{46} +(0.403711 - 0.576559i) q^{47} +(-2.39414 - 6.57785i) q^{49} +(9.84570 - 4.89050i) q^{50} +(0.785101 - 8.97374i) q^{52} +(-5.73786 + 5.73786i) q^{53} +(-0.452784 + 6.03188i) q^{55} +(0.000763450 + 0.000909845i) q^{56} +(10.2912 - 7.20599i) q^{58} +(2.11198 - 0.768697i) q^{59} +(-1.14333 - 6.48417i) q^{61} +(-3.09676 + 11.5573i) q^{62} +(-10.9996 - 6.35064i) q^{64} +(-2.51297 - 6.64787i) q^{65} +(2.47165 - 0.216242i) q^{67} +(-19.2579 + 1.68485i) q^{68} +(0.00290181 + 0.00130978i) q^{70} +(10.4316 + 6.02267i) q^{71} +(-0.375408 + 1.40104i) q^{73} +(-0.100157 - 0.568017i) q^{74} +(4.68478 - 1.70512i) q^{76} +(-0.00143496 + 0.00100477i) q^{77} +(3.36157 + 4.00616i) q^{79} +(-3.64738 - 0.273791i) q^{80} +(-18.2876 + 18.2876i) q^{82} +(1.39592 - 15.9554i) q^{83} +(-13.1133 + 7.78833i) q^{85} +(-6.54134 - 17.9722i) q^{86} +(-2.84581 + 4.06424i) q^{88} +(-2.99426 - 5.18621i) q^{89} +(0.00102910 - 0.00178245i) q^{91} +(6.12062 + 13.1257i) q^{92} +(0.994737 - 1.18548i) q^{94} +(2.74674 - 2.81539i) q^{95} +(7.62753 - 3.55678i) q^{97} +(-3.98342 - 14.8663i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35}+ \cdots - 324 q^{98}+O(q^{100}) $ 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Character values

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

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{18}\right)$

Coefficient data

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

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

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

$2$	2.19031	+	0.191628i	1.54878	+	0.135501i	0.829219	−	0.558923i	$-0.188785\pi$
$2$	2.19031	+	0.191628i	1.54878	+	0.135501i	0.719566	+	0.694425i	$0.244341\pi$
$3$		0			0
$3$		0			0
$4$	2.79113	+	0.492152i	1.39557	+	0.246076i
$5$	2.15257	−	0.605349i	0.962658	−	0.270720i
$5$	2.15257	−	0.605349i	0.962658	−	0.270720i
$6$		0			0
$7$	0.000530458	0	0.000371431i	0.000200494	0	0.000140388i	0.573677	−	0.819082i	$-0.305517\pi$
$7$	0.000530458	0	0.000371431i	0.000200494	0	0.000140388i	−0.573476	+	0.819222i	$0.694405\pi$
$8$	1.77162	+	0.474704i	0.626362	+	0.167833i
$9$		0			0
$10$	4.83080	−	0.913412i	1.52763	−	0.288846i
$11$	−0.925209	+	2.54199i	−0.278961	+	0.766439i	0.718520	+	0.695506i	$0.244820\pi$
$11$	−0.925209	+	2.54199i	−0.278961	+	0.766439i	−0.997481	+	0.0709326i	$0.977402\pi$
$12$		0			0
$13$	−0.277011	−	3.16625i	−0.0768289	−	0.878159i	−0.932625	−	0.360846i	$-0.882488\pi$
$13$	−0.277011	−	3.16625i	−0.0768289	−	0.878159i	0.855797	−	0.517313i	$-0.173068\pi$
$14$	0.00109069		0.000915200i	0.000291500		0.000244597i
$15$		0			0
$16$	−1.53710	−	0.559459i	−0.384275	−	0.139865i
$17$	−6.58840	+	1.76536i	−1.59792	+	0.428162i	−0.944414	−	0.328759i	$-0.893370\pi$
$17$	−6.58840	+	1.76536i	−1.59792	+	0.428162i	−0.653507	+	0.756921i	$0.726703\pi$
$18$		0			0
$19$	1.52337	−	0.879517i	0.349485	−	0.201775i	−0.314974	−	0.949100i	$-0.601996\pi$
$19$	1.52337	−	0.879517i	0.349485	−	0.201775i	0.664458	+	0.747325i	$0.268662\pi$
$20$	6.30603	−	0.630218i	1.41007	−	0.140921i
$21$		0			0
$22$	−2.51361	+	5.39046i	−0.535904	+	1.14925i
$23$	2.93096	+	4.18584i	0.611147	+	0.872808i	0.998799	−	0.0489979i	$-0.0156028\pi$
$23$	2.93096	+	4.18584i	0.611147	+	0.872808i	−0.387652	+	0.921806i	$0.626714\pi$
$24$		0			0
$25$	4.26710	−	2.60611i	0.853421	−	0.521222i
$26$		−	6.98815i		−	1.37049i
$27$		0			0
$28$	0.00129778	+	0.00129778i	0.000245257	+	0.000245257i
$29$	4.37718	−	3.67289i	0.812822	−	0.682038i	−0.138458	−	0.990368i	$-0.544215\pi$
$29$	4.37718	−	3.67289i	0.812822	−	0.682038i	0.951279	+	0.308330i	$0.0997701\pi$
$30$		0			0
$31$	−0.944975	+	5.35922i	−0.169723	+	0.962544i	0.774338	+	0.632772i	$0.218083\pi$
$31$	−0.944975	+	5.35922i	−0.169723	+	0.962544i	−0.944061	+	0.329772i	$0.893028\pi$
$32$	−6.58407	−	3.07020i	−1.16391	−	0.542740i
$33$		0			0
$34$	−14.7689	+	2.60416i	−2.53285	+	0.446610i
$35$	0.00136669		0.000478418i	0.000231013		8.08674e-5i
$36$		0			0
$37$	−0.0678960	−	0.253391i	−0.0111620	−	0.0416573i	0.960120	−	0.279587i	$-0.0901977\pi$
$37$	−0.0678960	−	0.253391i	−0.0111620	−	0.0416573i	−0.971282	+	0.237930i	$0.923531\pi$
$38$	3.50519	−	1.63450i	0.568617	−	0.265151i
$39$		0			0
$40$	4.10090	−	0.0506152i	0.648408	−	0.00800297i
$41$	−7.56097	+	9.01082i	−1.18083	+	1.40725i	−0.287537	+	0.957770i	$0.592836\pi$
$41$	−7.56097	+	9.01082i	−1.18083	+	1.40725i	−0.893289	+	0.449483i	$0.851608\pi$
$42$		0			0
$43$	−3.67622	−	7.88368i	−0.560618	−	1.20225i	−0.958574	−	0.284845i	$-0.908058\pi$
$43$	−3.67622	−	7.88368i	−0.560618	−	1.20225i	0.397955	−	0.917405i	$-0.369720\pi$
$44$	−3.83342	+	6.63969i	−0.577910	+	1.00097i
$45$		0			0
$46$	5.61759	+	9.72995i	0.828268	+	1.43460i
$47$	0.403711	−	0.576559i	0.0588873	−	0.0840997i	−0.788628	−	0.614870i	$-0.789208\pi$
$47$	0.403711	−	0.576559i	0.0588873	−	0.0840997i	0.847516	+	0.530770i	$0.178097\pi$
$48$		0			0
$49$	−2.39414	−	6.57785i	−0.342020	−	0.939693i
$50$	9.84570	−	4.89050i	1.39239	−	0.691622i
$51$		0			0
$52$	0.785101	−	8.97374i	0.108874	−	1.24443i
$53$	−5.73786	+	5.73786i	−0.788156	+	0.788156i	−0.981192	−	0.193036i	$-0.938167\pi$
$53$	−5.73786	+	5.73786i	−0.788156	+	0.788156i	0.193036	+	0.981192i	$0.438167\pi$
$54$		0			0
$55$	−0.452784	+	6.03188i	−0.0610534	+	0.813339i
$56$	0.000763450	0	0.000909845i	0.000102020	0	0.000121583i
$57$		0			0
$58$	10.2912	−	7.20599i	1.35130	−	0.946193i
$59$	2.11198	−	0.768697i	0.274956	−	0.100076i	−0.200862	−	0.979620i	$-0.564374\pi$
$59$	2.11198	−	0.768697i	0.274956	−	0.100076i	0.475818	+	0.879544i	$0.342152\pi$
$60$		0			0
$61$	−1.14333	−	6.48417i	−0.146389	−	0.830213i	−0.966241	−	0.257638i	$-0.917056\pi$
$61$	−1.14333	−	6.48417i	−0.146389	−	0.830213i	0.819852	−	0.572575i	$-0.194055\pi$
$62$	−3.09676	+	11.5573i	−0.393290	+	1.46778i
$63$		0			0
$64$	−10.9996	−	6.35064i	−1.37495	−	0.793830i
$65$	−2.51297	−	6.64787i	−0.311695	−	0.824567i
$66$		0			0
$67$	2.47165	−	0.216242i	0.301960	−	0.0264181i	0.0648313	−	0.997896i	$-0.479349\pi$
$67$	2.47165	−	0.216242i	0.301960	−	0.0264181i	0.237129	+	0.971478i	$0.423794\pi$
$68$	−19.2579	+	1.68485i	−2.33536	+	0.204318i
$69$		0			0
$70$	0.00290181	+	0.00130978i	0.000346832	+	0.000156549i
$71$	10.4316	+	6.02267i	1.23800	+	0.714759i	0.968685	−	0.248294i	$-0.0798698\pi$
$71$	10.4316	+	6.02267i	1.23800	+	0.714759i	0.269314	+	0.963052i	$0.413203\pi$
$72$		0			0
$73$	−0.375408	+	1.40104i	−0.0439381	+	0.163979i	−0.984409	−	0.175895i	$-0.943718\pi$
$73$	−0.375408	+	1.40104i	−0.0439381	+	0.163979i	0.940471	+	0.339875i	$0.110385\pi$
$74$	−0.100157	−	0.568017i	−0.0116430	−	0.0660306i
$75$		0			0
$76$	4.68478	−	1.70512i	0.537381	−	0.195591i
$77$	−0.00143496	+	0.00100477i	−0.000163529	+	0.000114504i
$78$		0			0
$79$	3.36157	+	4.00616i	0.378206	+	0.450729i	0.921247	−	0.388978i	$-0.127172\pi$
$79$	3.36157	+	4.00616i	0.378206	+	0.450729i	−0.543041	+	0.839706i	$0.682727\pi$
$80$	−3.64738	−	0.273791i	−0.407790	−	0.0306108i
$81$		0			0
$82$	−18.2876	+	18.2876i	−2.01953	+	2.01953i
$83$	1.39592	−	15.9554i	0.153222	−	1.75134i	−0.398372	−	0.917224i	$-0.630425\pi$
$83$	1.39592	−	15.9554i	0.153222	−	1.75134i	0.551594	−	0.834113i	$-0.314020\pi$
$84$		0			0
$85$	−13.1133	+	7.78833i	−1.42234	+	0.844763i
$86$	−6.54134	−	17.9722i	−0.705371	−	1.93799i
$87$		0			0
$88$	−2.84581	+	4.06424i	−0.303364	+	0.433249i
$89$	−2.99426	−	5.18621i	−0.317391	−	0.549737i	0.662552	−	0.749016i	$-0.269473\pi$
$89$	−2.99426	−	5.18621i	−0.317391	−	0.549737i	−0.979943	+	0.199279i	$0.936140\pi$
$90$		0			0
$91$	0.00102910	−	0.00178245i	0.000107879	−	0.000186852i
$92$	6.12062	+	13.1257i	0.638118	+	1.36845i
$93$		0			0
$94$	0.994737	−	1.18548i	0.102599	−	0.122273i
$95$	2.74674	−	2.81539i	0.281810	−	0.288853i
$96$		0			0
$97$	7.62753	−	3.55678i	0.774459	−	0.361136i	0.00512815	−	0.999987i	$-0.498368\pi$
$97$	7.62753	−	3.55678i	0.774459	−	0.361136i	0.769331	+	0.638851i	$0.220590\pi$
$98$	−3.98342	−	14.8663i	−0.402386	−	1.50173i
$99$		0			0
$100$	13.1927	−	5.17394i	1.31927	−	0.517394i
$101$	−11.3335	+	1.99841i	−1.12773	+	0.198849i	−0.706231	−	0.707981i	$-0.749606\pi$
$101$	−11.3335	+	1.99841i	−1.12773	+	0.198849i	−0.421496	+	0.906830i	$0.638495\pi$
$102$		0			0
$103$	6.21507	+	2.89813i	0.612389	+	0.285562i	0.703963	−	0.710237i	$-0.251412\pi$
$103$	6.21507	+	2.89813i	0.612389	+	0.285562i	−0.0915740	+	0.995798i	$0.529190\pi$
$104$	1.01227	−	5.74088i	0.0992615	−	0.562940i
$105$		0			0
$106$	−13.6672	+	11.4682i	−1.32748	+	1.11389i
$107$	9.67551	+	9.67551i	0.935367	+	0.935367i	0.998034	−	0.0626673i	$-0.0199607\pi$
$107$	9.67551	+	9.67551i	0.935367	+	0.935367i	−0.0626673	+	0.998034i	$0.519961\pi$
$108$		0			0
$109$			3.73835i			0.358069i	0.983843	+	0.179034i	$0.0572974\pi$
$109$			3.73835i			0.358069i	−0.983843	+	0.179034i	$0.942703\pi$
$110$	−2.14761	+	13.1249i	−0.204767	+	1.25141i
$111$		0			0
$112$	−0.000607567	0	0.000867696i	−5.74097e−5	0	8.19895e-5i
$113$	0.472320	−	1.01289i	0.0444322	−	0.0952851i	−0.882839	−	0.469676i	$-0.844371\pi$
$113$	0.472320	−	1.01289i	0.0444322	−	0.0952851i	0.927271	+	0.374391i	$0.122148\pi$
$114$		0			0
$115$	8.84298	+	7.23605i	0.824612	+	0.674766i
$116$	14.0249	−	8.09728i	1.30218	−	0.751814i
$117$		0			0
$118$	4.77320	−	1.27897i	0.439408	−	0.117739i
$119$	−0.00415058	−	0.00151069i	−0.000380483	−	0.000138484i
$120$		0			0
$121$	2.82079	+	2.36692i	0.256435	+	0.215175i
$122$	−1.26171	−	14.4215i	−0.114230	−	1.30566i
$123$		0			0
$124$	−5.27510	+	14.4932i	−0.473718	+	1.30153i
$125$	7.60763	−	8.19292i	0.680447	−	0.732797i
$126$		0			0
$127$	−10.0914	−	2.70398i	−0.895467	−	0.239940i	−0.218398	−	0.975860i	$-0.570083\pi$
$127$	−10.0914	−	2.70398i	−0.895467	−	0.239940i	−0.677068	+	0.735920i	$0.736750\pi$
$128$	−10.9739	−	7.68398i	−0.969962	−	0.679175i
$129$		0			0
$130$	−4.23027	−	15.0425i	−0.371019	−	1.31931i
$131$	14.3376	+	2.52811i	1.25269	+	0.220882i	0.760345	−	0.649520i	$-0.225030\pi$
$131$	14.3376	+	2.52811i	1.25269	+	0.220882i	0.492341	+	0.870402i	$0.336141\pi$
$132$		0			0
$133$	0.00113476		9.92788e-5i	9.83964e−5		8.60857e-6i
$134$	5.45513			0.471251
$135$		0			0
$136$	−12.5102			−1.07274
$137$	7.28394	+	0.637262i	0.622309	+	0.0544450i	0.393950	−	0.919132i	$-0.371108\pi$
$137$	7.28394	+	0.637262i	0.622309	+	0.0544450i	0.228359	+	0.973577i	$0.426664\pi$
$138$		0			0
$139$	3.00586	+	0.530014i	0.254953	+	0.0449552i	0.299664	−	0.954045i	$-0.403125\pi$
$139$	3.00586	+	0.530014i	0.254953	+	0.0449552i	−0.0447106	+	0.999000i	$0.514237\pi$
$140$	0.00357917	+	0.00200795i	0.000302495	+	0.000169703i
$141$		0			0
$142$	21.6943	+	15.1905i	1.82054	+	1.27476i
$143$	8.30486	+	2.22528i	0.694487	+	0.186087i
$144$		0			0
$145$	7.19880	−	10.5559i	0.597828	−	0.876617i
$146$	−1.09074	+	2.99678i	−0.0902701	+	0.248015i
$147$		0			0
$148$	−0.0647997	−	0.740664i	−0.00532650	−	0.0608822i
$149$	7.76525	+	6.51582i	0.636154	+	0.533797i	0.902834	−	0.429988i	$-0.141482\pi$
$149$	7.76525	+	6.51582i	0.636154	+	0.533797i	−0.266680	+	0.963785i	$0.585927\pi$
$150$		0			0
$151$	17.4779	+	6.36142i	1.42233	+	0.517685i	0.934722	−	0.355379i	$-0.115648\pi$
$151$	17.4779	+	6.36142i	1.42233	+	0.517685i	0.487605	+	0.873064i	$0.337870\pi$
$152$	3.11634	−	0.835020i	0.252768	−	0.0677291i
$153$		0			0
$154$	−0.00333555	+	0.00192578i	−0.000268786	+	0.000155184i
$155$	1.21008	+	12.1081i	0.0971956	+	0.972548i
$156$		0			0
$157$	−0.136723	+	0.293204i	−0.0109117	+	0.0234002i	−0.911688	−	0.410883i	$-0.865220\pi$
$157$	−0.136723	+	0.293204i	−0.0109117	+	0.0234002i	0.900776	+	0.434283i	$0.142998\pi$
$158$	6.59520	+	9.41892i	0.524686	+	0.749329i
$159$		0			0
$160$	−16.0312	−	2.62316i	−1.26738	−	0.207379i
$161$			0.00330906i			0.000260790i
$162$		0			0
$163$	−3.86594	−	3.86594i	−0.302804	−	0.302804i	0.539306	−	0.842110i	$-0.318687\pi$
$163$	−3.86594	−	3.86594i	−0.302804	−	0.302804i	−0.842110	+	0.539306i	$0.818687\pi$
$164$	−25.5384	+	21.4292i	−1.99421	+	1.67334i
$165$		0			0
$166$	6.11500	−	34.6799i	0.474616	−	2.69168i
$167$	−16.6893	−	7.78235i	−1.29146	−	0.602217i	−0.349182	−	0.937055i	$-0.613541\pi$
$167$	−16.6893	−	7.78235i	−1.29146	−	0.602217i	−0.942276	+	0.334838i	$0.891318\pi$
$168$		0			0
$169$	2.85412	−	0.503259i	0.219548	−	0.0387122i
$170$	−30.2147	+	14.5460i	−2.31736	+	1.11563i
$171$		0			0
$172$	−6.38085	−	23.8136i	−0.486535	−	1.81577i
$173$	2.69896	−	1.25855i	0.205198	−	0.0956855i	−0.317302	−	0.948324i	$-0.602777\pi$
$173$	2.69896	−	1.25855i	0.205198	−	0.0956855i	0.522501	+	0.852639i	$0.324999\pi$
$174$		0			0
$175$	0.00323151		0.000202501i	0.000244279		1.53077e-5i
$176$	2.84428	−	3.38968i	0.214395	−	0.255506i
$177$		0			0
$178$	−5.56454	−	11.9332i	−0.417080	−	0.894431i
$179$	−8.26245	+	14.3110i	−0.617564	+	1.06965i	0.372365	+	0.928087i	$0.378547\pi$
$179$	−8.26245	+	14.3110i	−0.617564	+	1.06965i	−0.989929	+	0.141566i	$0.954786\pi$
$180$		0			0
$181$	4.81540	+	8.34051i	0.357926	+	0.619945i	0.987614	−	0.156902i	$-0.0501508\pi$
$181$	4.81540	+	8.34051i	0.357926	+	0.619945i	−0.629688	+	0.776848i	$0.716817\pi$
$182$	0.00259561	−	0.00370692i	0.000192400	−	0.000274775i
$183$		0			0
$184$	3.20550	+	8.80705i	0.236313	+	0.649264i
$185$	−0.299541	−	0.504341i	−0.0220227	−	0.0370799i
$186$		0			0
$187$	1.60813	−	18.3810i	0.117598	−	1.34415i
$188$	1.41056	−	1.41056i	0.102876	−	0.102876i
$189$		0			0
$190$	6.55572	−	5.64023i	0.475602	−	0.409185i
$191$	−0.797244	−	0.950119i	−0.0576866	−	0.0687482i	0.736430	−	0.676514i	$-0.236510\pi$
$191$	−0.797244	−	0.950119i	−0.0576866	−	0.0687482i	−0.794116	+	0.607766i	$0.792066\pi$
$192$		0			0
$193$	−14.5052	+	10.1567i	−1.04411	+	0.731093i	−0.964056	−	0.265698i	$-0.914398\pi$
$193$	−14.5052	+	10.1567i	−1.04411	+	0.731093i	−0.0800524	+	0.996791i	$0.525509\pi$
$194$	17.3883	−	6.32881i	1.24840	−	0.454382i
$195$		0			0
$196$	−3.44506	−	19.5379i	−0.246076	−	1.39557i
$197$	4.39615	−	16.4067i	0.313213	−	1.16893i	−0.612429	−	0.790526i	$-0.709807\pi$
$197$	4.39615	−	16.4067i	0.313213	−	1.16893i	0.925642	−	0.378401i	$-0.123526\pi$
$198$		0			0
$199$	9.13371	+	5.27335i	0.647472	+	0.373818i	0.787487	−	0.616331i	$-0.211382\pi$
$199$	9.13371	+	5.27335i	0.647472	+	0.373818i	−0.140015	+	0.990149i	$0.544715\pi$
$200$	8.79682	−	2.59143i	0.622029	−	0.183241i
$201$		0			0
$202$	−25.2069	+	2.20532i	−1.77355	+	0.155166i
$203$	0.00368613		0.000322495i	0.000258716		2.26347e-5i
$204$		0			0
$205$	−10.8208	+	23.9734i	−0.755759	+	1.67438i
$206$	13.0576	+	7.53880i	0.909765	+	0.525253i
$207$		0			0
$208$	−1.34559	+	5.02181i	−0.0932999	+	0.348200i
$209$	0.826290	+	4.68612i	0.0571557	+	0.324146i
$210$		0			0
$211$	0.169003	−	0.0615119i	0.0116346	−	0.00423465i	−0.336196	−	0.941792i	$-0.609141\pi$
$211$	0.169003	−	0.0615119i	0.0116346	−	0.00423465i	0.347831	+	0.937557i	$0.386918\pi$
$212$	−18.8390	+	13.1912i	−1.29387	+	0.905978i
$213$		0			0
$214$	19.3383	+	23.0465i	1.32194	+	1.57543i
$215$	−12.6857	−	14.7448i	−0.865157	−	1.00558i
$216$		0			0
$217$	−0.00249185	+	0.00249185i	−0.000169158	+	0.000169158i
$218$	−0.716371	+	8.18815i	−0.0485187	+	0.554572i
$219$		0			0
$220$	−4.23238	+	16.6129i	−0.285347	+	1.12004i
$221$	7.41460	+	20.3715i	0.498760	+	1.37033i
$222$		0			0
$223$	10.5728	−	15.0996i	0.708010	−	1.01114i	−0.290516	−	0.956870i	$-0.593827\pi$
$223$	10.5728	−	15.0996i	0.708010	−	1.01114i	0.998526	−	0.0542728i	$-0.0172841\pi$
$224$	−0.00235221	−	0.00407414i	−0.000157163	−	0.000272215i
$225$		0			0
$226$	1.22863	−	2.12804i	0.0817271	−	0.141555i
$227$	−6.61613	−	14.1883i	−0.439128	−	0.941713i	−0.993959	−	0.109750i	$-0.964995\pi$
$227$	−6.61613	−	14.1883i	−0.439128	−	0.941713i	0.554831	−	0.831963i	$-0.312783\pi$
$228$		0			0
$229$	4.54463	−	5.41608i	0.300318	−	0.357904i	−0.594690	−	0.803955i	$-0.702725\pi$
$229$	4.54463	−	5.41608i	0.300318	−	0.357904i	0.895008	+	0.446050i	$0.147170\pi$
$230$	17.9823	+	17.5438i	1.18571	+	1.15680i
$231$		0			0
$232$	9.49823	−	4.42910i	0.623590	−	0.290785i
$233$	−0.591957	−	2.20921i	−0.0387804	−	0.144730i	0.943821	−	0.330457i	$-0.107203\pi$
$233$	−0.591957	−	2.20921i	−0.0387804	−	0.144730i	−0.982601	+	0.185726i	$0.940536\pi$
$234$		0			0
$235$	0.519996	−	1.48547i	0.0339208	−	0.0969013i
$236$	6.27313	−	1.10612i	0.408346	−	0.0720024i
$237$		0			0
$238$	−0.00880157	−	0.00410424i	−0.000570521	−	0.000266038i
$239$	−1.33675	+	7.58107i	−0.0864670	+	0.490379i	0.910563	+	0.413369i	$0.135648\pi$
$239$	−1.33675	+	7.58107i	−0.0864670	+	0.490379i	−0.997030	+	0.0770092i	$0.975463\pi$
$240$		0			0
$241$	−7.35154	+	6.16868i	−0.473555	+	0.397359i	−0.848089	−	0.529853i	$-0.822247\pi$
$241$	−7.35154	+	6.16868i	−0.473555	+	0.397359i	0.374535	+	0.927213i	$0.377802\pi$
$242$	5.72484	+	5.72484i	0.368007	+	0.368007i
$243$		0			0
$244$		−	18.6609i		−	1.19464i
$245$	−9.13545	−	12.7100i	−0.583642	−	0.812011i
$246$		0			0
$247$	−3.20676	−	4.57972i	−0.204041	−	0.291401i
$248$	−4.21818	+	9.04592i	−0.267855	+	0.574416i
$249$		0			0
$250$	18.2331	−	16.4872i	1.15316	−	1.04274i
$251$	4.10987	−	2.37283i	0.259413	−	0.149772i	−0.364654	−	0.931143i	$-0.618813\pi$
$251$	4.10987	−	2.37283i	0.259413	−	0.149772i	0.624067	+	0.781371i	$0.285479\pi$
$252$		0			0
$253$	−13.3521	+	3.57769i	−0.839440	+	0.224927i
$254$	−21.5852	−	7.85635i	−1.35437	−	0.492951i
$255$		0			0
$256$	−3.10423	−	2.60476i	−0.194015	−	0.162798i
$257$	−1.05277	−	12.0332i	−0.0656701	−	0.750612i	−0.955629	−	0.294572i	$-0.904823\pi$
$257$	−1.05277	−	12.0332i	−0.0656701	−	0.750612i	0.889959	−	0.456040i	$-0.150733\pi$
$258$		0			0
$259$	5.81013e−5	0	0.000159632i	3.61024e−6	0	9.91906e-6i
$260$	−3.74226	−	19.7919i	−0.232085	−	1.22744i
$261$		0			0
$262$	30.9195	+	8.28485i	1.91021	+	0.511840i
$263$	7.01542	+	4.91225i	0.432589	+	0.302902i	0.769515	−	0.638629i	$-0.220498\pi$
$263$	7.01542	+	4.91225i	0.432589	+	0.302902i	−0.336926	+	0.941531i	$0.609387\pi$
$264$		0			0
$265$	−8.87774	+	15.8246i	−0.545355	+	0.972095i
$266$	0.00246646		0.000434903i	0.000151228		2.66656e-5i
$267$		0			0
$268$	7.00513	+	0.612870i	0.427907	+	0.0374370i
$269$	17.3406			1.05728			0.528638	−	0.848847i	$-0.322703\pi$
$269$	17.3406			1.05728			0.528638	+	0.848847i	$0.322703\pi$
$270$		0			0
$271$	−11.8573			−0.720278			−0.360139	−	0.932899i	$-0.617271\pi$
$271$	−11.8573			−0.720278			−0.360139	+	0.932899i	$0.617271\pi$
$272$	11.1147	+	0.972407i	0.673926	+	0.0589609i
$273$		0			0
$274$	15.8320	+	2.79161i	0.956446	+	0.168647i
$275$	2.67675	+	13.2581i	0.161414	+	0.799495i
$276$		0			0
$277$	−16.3872	−	11.4745i	−0.984613	−	0.689433i	−0.0338740	−	0.999426i	$-0.510784\pi$
$277$	−16.3872	−	11.4745i	−0.984613	−	0.689433i	−0.950739	+	0.309993i	$0.899673\pi$
$278$	6.48220	+	1.73690i	0.388776	+	0.104172i
$279$		0			0
$280$	0.00219415	+	0.00149635i	0.000131126	+	8.94240e-5i
$281$	2.66069	−	7.31019i	0.158724	−	0.436089i	−0.834683	−	0.550730i	$-0.814349\pi$
$281$	2.66069	−	7.31019i	0.158724	−	0.436089i	0.993407	+	0.114641i	$0.0365716\pi$
$282$		0			0
$283$	1.30970	+	14.9700i	0.0778538	+	0.889873i	0.930238	+	0.366957i	$0.119600\pi$
$283$	1.30970	+	14.9700i	0.0778538	+	0.889873i	−0.852384	+	0.522916i	$0.824844\pi$
$284$	26.1518	+	21.9440i	1.55182	+	1.30213i
$285$		0			0
$286$	17.7638	+	6.46550i	1.05040	+	0.382313i
$287$	−0.00735767	+	0.00197148i	−0.000434310	+	0.000116373i
$288$		0			0
$289$	25.5680	−	14.7617i	1.50400	−	0.868336i
$290$	17.7904	−	21.7412i	1.04469	−	1.27669i
$291$		0			0
$292$	−1.73734	+	3.72573i	−0.101670	+	0.218032i
$293$	−12.9347	−	18.4726i	−0.755651	−	1.07918i	−0.994147	−	0.108038i	$-0.965543\pi$
$293$	−12.9347	−	18.4726i	−0.755651	−	1.07918i	0.238495	−	0.971144i	$-0.423346\pi$
$294$		0			0
$295$	4.08085	−	2.93316i	0.237596	−	0.170775i
$296$		−	0.481143i		−	0.0279659i
$297$		0			0
$298$	15.7597	+	15.7597i	0.912936	+	0.912936i
$299$	12.4415	−	10.4396i	0.719510	−	0.603740i
$300$		0			0
$301$	0.000978160	−	0.00554742i	5.63802e−5	−	0.000319748i
$302$	37.0629	+	17.2827i	2.13273	+	0.994510i
$303$		0			0
$304$	−2.83362	+	0.499644i	−0.162519	+	0.0286566i
$305$	−6.38629	−	13.2655i	−0.365678	−	0.759581i
$306$		0			0
$307$	−1.30818	−	4.88220i	−0.0746619	−	0.278642i	0.918495	−	0.395434i	$-0.129406\pi$
$307$	−1.30818	−	4.88220i	−0.0746619	−	0.278642i	−0.993156	+	0.116792i	$0.962739\pi$
$308$	−0.00449965	+	0.00209822i	−0.000256392	+	0.000119557i
$309$		0			0
$310$	0.330192	+	26.7525i	0.0187536	+	1.51944i
$311$	−12.6744	+	15.1048i	−0.718699	+	0.856512i	−0.994504	−	0.104702i	$-0.966611\pi$
$311$	−12.6744	+	15.1048i	−0.718699	+	0.856512i	0.275805	+	0.961214i	$0.411056\pi$
$312$		0			0
$313$	−11.4671	−	24.5912i	−0.648157	−	1.38998i	−0.905787	−	0.423734i	$-0.860719\pi$
$313$	−11.4671	−	24.5912i	−0.648157	−	1.38998i	0.257629	−	0.966244i	$-0.417059\pi$
$314$	−0.355652	+	0.616007i	−0.0200706	+	0.0347633i
$315$		0			0
$316$	7.41094	+	12.8361i	0.416898	+	0.722089i
$317$	−0.143177	+	0.204479i	−0.00804165	+	0.0114847i	−0.823153	−	0.567820i	$-0.807787\pi$
$317$	−0.143177	+	0.204479i	−0.00804165	+	0.0114847i	0.815111	+	0.579305i	$0.196676\pi$
$318$		0			0
$319$	5.28664	+	14.5249i	0.295995	+	0.813240i
$320$	−27.5218	−	7.01157i	−1.53852	−	0.391959i
$321$		0			0
$322$	−0.000634107		0.00724787i	−3.53374e−5		0.000403908i
$323$	−8.48389	+	8.48389i	−0.472056	+	0.472056i
$324$		0			0
$325$	−9.43362	−	12.7888i	−0.523283	−	0.709394i
$326$	−7.72680	−	9.20844i	−0.427948	−	0.510009i
$327$		0			0
$328$	−17.6726	+	12.3745i	−0.975808	+	0.683268i
$329$	0.000428303	0	0.000155890i	2.36131e−5	0	8.59448e-6i
$330$		0			0
$331$	0.820786	+	4.65491i	0.0451145	+	0.255857i	0.999021	−	0.0442484i	$-0.0140893\pi$
$331$	0.820786	+	4.65491i	0.0451145	+	0.255857i	−0.953906	+	0.300105i	$0.902978\pi$
$332$	11.7487	−	43.8467i	0.644794	−	2.40640i
$333$		0			0
$334$	−35.0635	−	20.2439i	−1.91859	−	1.10770i
$335$	5.18950	−	1.96169i	0.283533	−	0.107178i
$336$		0			0
$337$	10.7791	−	0.943046i	0.587173	−	0.0513710i	0.210302	−	0.977637i	$-0.432555\pi$
$337$	10.7791	−	0.943046i	0.587173	−	0.0513710i	0.376872	+	0.926266i	$0.377000\pi$
$338$	6.34786	−	0.555366i	0.345278	−	0.0302079i
$339$		0			0
$340$	−40.4340	+	15.2845i	−2.19284	+	0.828919i
$341$	−12.7488	−	7.36051i	−0.690385	−	0.398594i
$342$		0			0
$343$	0.00234645	−	0.00875706i	0.000126696	−	0.000472837i
$344$	−2.77045	−	15.7120i	−0.149373	−	0.847134i
$345$		0			0
$346$	6.15274	−	2.23942i	0.330774	−	0.120392i
$347$	−19.7058	+	13.7981i	−1.05786	+	0.740723i	−0.966906	−	0.255132i	$-0.917881\pi$
$347$	−19.7058	+	13.7981i	−1.05786	+	0.740723i	−0.0909561	+	0.995855i	$0.528992\pi$
$348$		0			0
$349$	0.752338	+	0.896601i	0.0402717	+	0.0479940i	0.785804	−	0.618475i	$-0.212249\pi$
$349$	0.752338	+	0.896601i	0.0402717	+	0.0479940i	−0.745533	+	0.666469i	$0.767805\pi$
$350$	0.00703921	+	0.00106279i	0.000376262	+	5.68084e-5i
$351$		0			0
$352$	13.8961	−	13.8961i	0.740662	−	0.740662i
$353$	−1.76656	+	20.1919i	−0.0940245	+	1.07470i	0.791830	+	0.610741i	$0.209129\pi$
$353$	−1.76656	+	20.1919i	−0.0940245	+	1.07470i	−0.885855	+	0.463963i	$0.846427\pi$
$354$		0			0
$355$	26.1005	+	6.64946i	1.38527	+	0.352917i
$356$	−5.80497	−	15.9490i	−0.307663	−	0.845296i
$357$		0			0
$358$	−20.8397	+	29.7622i	−1.10141	+	1.57298i
$359$	13.1082	+	22.7040i	0.691823	+	1.19827i	0.971240	+	0.238102i	$0.0765253\pi$
$359$	13.1082	+	22.7040i	0.691823	+	1.19827i	−0.279418	+	0.960170i	$0.590141\pi$
$360$		0			0
$361$	−7.95290	+	13.7748i	−0.418574	+	0.724991i
$362$	8.94895	+	19.1911i	0.470347	+	1.00866i
$363$		0			0
$364$	0.00374959	−	0.00446858i	0.000196532	−	0.000234217i
$365$	0.0400278	+	3.24309i	0.00209515	+	0.169751i
$366$		0			0
$367$	−19.0178	+	8.86817i	−0.992723	+	0.462914i	−0.849963	−	0.526843i	$-0.823376\pi$
$367$	−19.0178	+	8.86817i	−0.992723	+	0.462914i	−0.142761	+	0.989757i	$0.545598\pi$
$368$	−2.16337	−	8.07380i	−0.112773	−	0.420876i
$369$		0			0
$370$	−0.559443	−	1.16207i	−0.0290840	−	0.0604129i
$371$	−0.00517492		0.000912477i	−0.000268668		4.73735e-5i
$372$		0			0
$373$	−1.52296	−	0.710169i	−0.0788560	−	0.0367712i	0.382790	−	0.923835i	$-0.374963\pi$
$373$	−1.52296	−	0.710169i	−0.0788560	−	0.0367712i	−0.461646	+	0.887064i	$0.652741\pi$
$374$	7.04459	−	39.9519i	0.364267	−	2.06586i
$375$		0			0
$376$	0.988917	−	0.829800i	0.0509995	−	0.0427937i
$377$	−12.8418	−	12.8418i	−0.661386	−	0.661386i
$378$		0			0
$379$			11.6637i			0.599126i	0.954077	+	0.299563i	$0.0968408\pi$
$379$			11.6637i			0.599126i	−0.954077	+	0.299563i	$0.903159\pi$
$380$	9.05211	−	6.50631i	0.464364	−	0.333767i
$381$		0			0
$382$	−1.56415	−	2.23383i	−0.0800286	−	0.114293i
$383$	4.44907	−	9.54105i	0.227337	−	0.487525i	−0.759243	−	0.650808i	$-0.774430\pi$
$383$	4.44907	−	9.54105i	0.227337	−	0.487525i	0.986579	+	0.163283i	$0.0522082\pi$
$384$		0			0
$385$	−0.00248061	+	0.00303148i	−0.000126424	+	0.000154499i
$386$	−33.7173	+	19.4667i	−1.71616	+	0.990828i
$387$		0			0
$388$	23.0399	−	6.17353i	1.16968	−	0.313414i
$389$	−36.8621	−	13.4167i	−1.86898	−	0.680254i	−0.970427	−	0.241396i	$-0.922395\pi$
$389$	−36.8621	−	13.4167i	−1.86898	−	0.680254i	−0.898557	−	0.438858i	$-0.855383\pi$
$390$		0			0
$391$	−26.6998	−	22.4038i	−1.35027	−	1.13301i
$392$	−1.11898	−	12.7900i	−0.0565168	−	0.645990i
$393$		0			0
$394$	12.7729	−	35.0933i	0.643491	−	1.76798i
$395$	9.66114	+	6.58862i	0.486105	+	0.331509i
$396$		0			0
$397$	−10.0653	−	2.69699i	−0.505162	−	0.135358i	−0.00276748	−	0.999996i	$-0.500881\pi$
$397$	−10.0653	−	2.69699i	−0.505162	−	0.135358i	−0.502395	+	0.864638i	$0.667548\pi$
$398$	18.9952	+	13.3006i	0.952141	+	0.666697i
$399$		0			0
$400$	−8.01698	+	1.61858i	−0.400849	+	0.0809292i
$401$	−26.3401	−	4.64448i	−1.31536	−	0.231934i	−0.528433	−	0.848975i	$-0.677220\pi$
$401$	−26.3401	−	4.64448i	−1.31536	−	0.231934i	−0.786931	+	0.617041i	$0.788331\pi$
$402$		0			0
$403$	17.2304	+	1.50746i	0.858306	+	0.0750921i
$404$	−32.6169			−1.62275
$405$		0			0
$406$	0.00813559			0.000403762
$407$	0.706936	+	0.0618489i	0.0350415	+	0.00306574i
$408$		0			0
$409$	−33.6400	−	5.93165i	−1.66339	−	0.293301i	−0.738705	−	0.674028i	$-0.764562\pi$
$409$	−33.6400	−	5.93165i	−1.66339	−	0.293301i	−0.924687	+	0.380727i	$0.875674\pi$
$410$	−28.2950	+	50.4357i	−1.39739	+	2.49084i
$411$		0			0
$412$	15.9208	+	11.1478i	0.784359	+	0.549214i
$413$	0.00140583		0.000376692i	6.91766e−5		1.85358e-5i
$414$		0			0
$415$	−6.65380	−	35.1902i	−0.326622	−	1.72742i
$416$	−7.89716	+	21.6973i	−0.387190	+	1.06380i
$417$		0			0
$418$	0.911843	+	10.4224i	0.0445997	+	0.509777i
$419$	−12.2431	−	10.2731i	−0.598112	−	0.501876i	0.292726	−	0.956196i	$-0.405438\pi$
$419$	−12.2431	−	10.2731i	−0.598112	−	0.501876i	−0.890838	+	0.454321i	$0.849882\pi$
$420$		0			0
$421$	29.9345	+	10.8953i	1.45892	+	0.531002i	0.945067	−	0.326878i	$-0.105997\pi$
$421$	29.9345	+	10.8953i	1.45892	+	0.531002i	0.513850	+	0.857880i	$0.328219\pi$
$422$	0.381956	−	0.102345i	0.0185933	−	0.00498206i
$423$		0			0
$424$	−12.8891	+	7.44152i	−0.625950	+	0.361392i
$425$	−23.5127	+	24.7030i	−1.14053	+	1.19827i
$426$		0			0
$427$	0.00180193	−	0.00386425i	8.72015e−5	−	0.000187004i
$428$	22.2438	+	31.7675i	1.07520	+	1.53554i
$429$		0			0
$430$	−24.9601	−	34.7266i	−1.20368	−	1.67466i
$431$		−	5.93676i		−	0.285963i	−0.989725	−	0.142982i	$-0.954331\pi$
$431$		−	5.93676i		−	0.285963i	0.989725	−	0.142982i	$-0.0456690\pi$
$432$		0			0
$433$	−7.73933	−	7.73933i	−0.371929	−	0.371929i	0.496251	−	0.868179i	$-0.334710\pi$
$433$	−7.73933	−	7.73933i	−0.371929	−	0.371929i	−0.868179	+	0.496251i	$0.834710\pi$
$434$	−0.00593543	+	0.00498042i	−0.000284910	+	0.000239068i
$435$		0			0
$436$	−1.83984	+	10.4342i	−0.0881122	+	0.499709i
$437$	8.14644	+	3.79875i	0.389697	+	0.181719i
$438$		0			0
$439$	−28.6483	+	5.05146i	−1.36731	+	0.241093i	−0.808642	−	0.588300i	$-0.799797\pi$
$439$	−28.6483	+	5.05146i	−1.36731	+	0.241093i	−0.558665	+	0.829394i	$0.688686\pi$
$440$	−3.66552	+	10.4713i	−0.174747	+	0.499198i
$441$		0			0
$442$	12.3366	+	46.0407i	0.586791	+	2.18993i
$443$	−24.6030	+	11.4725i	−1.16892	+	0.545077i	−0.907461	−	0.420137i	$-0.861982\pi$
$443$	−24.6030	+	11.4725i	−1.16892	+	0.545077i	−0.261461	+	0.965214i	$0.584204\pi$
$444$		0			0
$445$	−9.58481	−	9.35110i	−0.454364	−	0.443284i
$446$	26.0513	−	31.0468i	1.23357	−	1.47011i
$447$		0			0
$448$	−0.00347602	−	0.00745435i	−0.000164227	−	0.000352185i
$449$	1.73698	−	3.00854i	0.0819733	−	0.141982i	−0.822124	−	0.569308i	$-0.807211\pi$
$449$	1.73698	−	3.00854i	0.0819733	−	0.141982i	0.904097	+	0.427326i	$0.140544\pi$
$450$		0			0
$451$	−15.9099	−	27.5568i	−0.749169	−	1.29760i
$452$	1.81681	−	2.59467i	0.0854554	−	0.122043i
$453$		0			0
$454$	−11.7725	−	32.3447i	−0.552511	−	1.51801i
$455$	0.00113620	−	0.00445981i	5.32659e−5	−	0.000209079i
$456$		0			0
$457$	−2.05624	+	23.5029i	−0.0961868	+	1.09942i	0.782703	+	0.622395i	$0.213840\pi$
$457$	−2.05624	+	23.5029i	−0.0961868	+	1.09942i	−0.878890	+	0.477025i	$0.841715\pi$
$458$	10.9920	−	10.9920i	0.513624	−	0.513624i
$459$		0			0
$460$	21.1207	+	24.5489i	0.984757	+	1.14460i
$461$	−5.14645	−	6.13330i	−0.239694	−	0.285656i	0.632765	−	0.774344i	$-0.281920\pi$
$461$	−5.14645	−	6.13330i	−0.239694	−	0.285656i	−0.872459	+	0.488688i	$0.837476\pi$
$462$		0			0
$463$	1.93475	−	1.35473i	0.0899154	−	0.0629594i	−0.527754	−	0.849397i	$-0.676966\pi$
$463$	1.93475	−	1.35473i	0.0899154	−	0.0629594i	0.617670	+	0.786438i	$0.288077\pi$
$464$	−8.78299	+	3.19675i	−0.407740	+	0.148405i
$465$		0			0
$466$	−0.873225	−	4.95230i	−0.0404514	−	0.229411i
$467$	−5.32380	+	19.8687i	−0.246356	+	0.919414i	0.726341	+	0.687335i	$0.241220\pi$
$467$	−5.32380	+	19.8687i	−0.246356	+	0.919414i	−0.972697	+	0.232079i	$0.925447\pi$
$468$		0			0
$469$	0.00139143		0.000803341i	6.42501e−5		3.70948e-5i
$470$	1.42361	−	3.15399i	0.0656662	−	0.145483i
$471$		0			0
$472$	4.10653	−	0.359274i	0.189018	−	0.0165369i
$473$	23.4415	−	2.05087i	1.07784	−	0.0942989i
$474$		0			0
$475$	4.20825	−	7.72306i	0.193088	−	0.354358i
$476$	−0.0108413	−	0.00625924i	−0.000496911	−	0.000286892i
$477$		0			0
$478$	−4.38064	+	16.3488i	−0.200366	+	0.747775i
$479$	−3.74161	−	21.2197i	−0.170958	−	0.969553i	−0.942706	−	0.333624i	$-0.891728\pi$
$479$	−3.74161	−	21.2197i	−0.170958	−	0.969553i	0.771748	−	0.635929i	$-0.219383\pi$
$480$		0			0
$481$	−0.783491	+	0.285167i	−0.0357241	+	0.0130025i
$482$	−17.2843	+	12.1026i	−0.787277	+	0.551257i
$483$		0			0
$484$	6.70831	+	7.99465i	0.304923	+	0.363393i
$485$	14.2657	−	12.2735i	0.647772	−	0.557312i
$486$		0			0
$487$	2.20133	−	2.20133i	0.0997518	−	0.0997518i	−0.655470	−	0.755221i	$-0.727529\pi$
$487$	2.20133	−	2.20133i	0.0997518	−	0.0997518i	0.755221	+	0.655470i	$0.227529\pi$
$488$	1.05251	−	12.0302i	0.0476449	−	0.544583i
$489$		0			0
$490$	−17.5739	−	29.5894i	−0.793908	−	1.33671i
$491$	2.81965	+	7.74693i	0.127249	+	0.349614i	0.986915	−	0.161243i	$-0.0515503\pi$
$491$	2.81965	+	7.74693i	0.127249	+	0.349614i	−0.859666	+	0.510857i	$0.829328\pi$
$492$		0			0
$493$	−22.3546	+	31.9257i	−1.00680	+	1.43786i
$494$	−6.14620	−	10.6455i	−0.276530	−	0.478965i
$495$		0			0
$496$	4.45078	−	7.70898i	0.199846	−	0.346144i
$497$	0.00329650	+	0.00706937i	0.000147868	+	0.000317105i
$498$		0			0
$499$	16.9583	−	20.2101i	0.759156	−	0.904727i	−0.238638	−	0.971109i	$-0.576701\pi$
$499$	16.9583	−	20.2101i	0.759156	−	0.904727i	0.997794	+	0.0663815i	$0.0211454\pi$
$500$	25.2661	−	19.1234i	1.12993	−	0.855225i
$501$		0			0
$502$	9.45659	−	4.40968i	0.422068	−	0.196814i
$503$	−2.01259	−	7.51109i	−0.0897370	−	0.334903i	0.906432	−	0.422352i	$-0.138795\pi$
$503$	−2.01259	−	7.51109i	−0.0897370	−	0.334903i	−0.996169	+	0.0874487i	$0.972129\pi$
$504$		0			0
$505$	−23.1865	+	11.1624i	−1.03178	+	0.496722i
$506$	−29.9309	+	5.27762i	−1.33059	+	0.234619i
$507$		0			0
$508$	−26.8357	−	12.5137i	−1.19064	−	0.555204i
$509$	5.25087	−	29.7791i	0.232741	−	1.31994i	−0.614580	−	0.788855i	$-0.710674\pi$
$509$	5.25087	−	29.7791i	0.232741	−	1.31994i	0.847320	−	0.531082i	$-0.178215\pi$
$510$		0			0
$511$	−0.000719528	0	0.000603755i	−3.18300e−5	0	2.67086e-5i
$512$	12.6456	+	12.6456i	0.558861	+	0.558861i
$513$		0			0
$514$		−	26.5583i		−	1.17144i
$515$	15.1327	+	2.47615i	0.666829	+	0.109112i
$516$		0			0
$517$	1.09209	+	1.55967i	0.0480300	+	0.0685940i
$518$	0.000157850	0	0.000338510i	6.93553e−6	0	1.48733e-5i
$519$		0			0
$520$	−1.29625	−	12.9704i	−0.0568444	−	0.568791i
$521$	−2.44020	+	1.40885i	−0.106907	+	0.0617227i	−0.552500	−	0.833513i	$-0.686326\pi$
$521$	−2.44020	+	1.40885i	−0.106907	+	0.0617227i	0.445593	+	0.895236i	$0.352993\pi$
$522$		0			0
$523$	12.7481	−	3.41584i	0.557436	−	0.149364i	0.0309077	−	0.999522i	$-0.490160\pi$
$523$	12.7481	−	3.41584i	0.557436	−	0.149364i	0.526528	+	0.850158i	$0.323494\pi$
$524$	38.7741	+	14.1126i	1.69385	+	0.616512i
$525$		0			0
$526$	14.4246	+	12.1037i	0.628944	+	0.527747i
$527$	−3.23506	−	36.9769i	−0.140921	−	1.61074i
$528$		0			0
$529$	−1.06428	+	2.92409i	−0.0462731	+	0.127134i
$530$	−22.4774	+	32.9595i	−0.976357	+	1.43167i
$531$		0			0
$532$	0.00311841		0.000835576i	0.000135200		3.62268e-5i
$533$	30.6249	+	21.4438i	1.32651	+	0.928834i
$534$		0			0
$535$	26.6843	+	14.9701i	1.15366	+	0.647216i
$536$	4.48148	+	0.790206i	0.193570	+	0.0341317i
$537$		0			0
$538$	37.9814	+	3.32294i	1.63749	+	0.143262i
$539$	18.9359			0.815627
$540$		0			0
$541$	−11.4416			−0.491911			−0.245956	−	0.969281i	$-0.579102\pi$
$541$	−11.4416			−0.491911			−0.245956	+	0.969281i	$0.579102\pi$
$542$	−25.9711	−	2.27218i	−1.11556	−	0.0975985i
$543$		0			0
$544$	48.7984	+	8.60448i	2.09222	+	0.368914i
$545$	2.26301	+	8.04706i	0.0969366	+	0.344698i
$546$		0			0
$547$	26.2542	+	18.3834i	1.12255	+	0.786018i	0.979048	−	0.203632i	$-0.0652745\pi$
$547$	26.2542	+	18.3834i	1.12255	+	0.786018i	0.143503	+	0.989650i	$0.454163\pi$
$548$	20.0168	+	5.36349i	0.855076	+	0.229117i
$549$		0			0
$550$	3.32229	+	29.5524i	0.141663	+	1.26012i
$551$	3.43769	−	9.44496i	0.146450	−	0.402369i
$552$		0			0
$553$	0.000295160		0.00337369i	1.25515e−5		0.000143464i
$554$	−33.6943	−	28.2729i	−1.43153	−	1.20120i
$555$		0			0
$556$	8.12889	+	2.95868i	0.344742	+	0.125476i
$557$	28.6955	−	7.68893i	1.21587	−	0.325791i	0.406806	−	0.913515i	$-0.366643\pi$
$557$	28.6955	−	7.68893i	1.21587	−	0.325791i	0.809061	+	0.587724i	$0.199976\pi$
$558$		0			0
$559$	−23.9433	+	13.8237i	−1.01269	+	0.584679i
$560$	−0.00183309	−	0.00149998i	−7.74621e−5	−	6.33859e-5i
$561$		0			0
$562$	7.22858	−	15.5017i	0.304919	−	0.653902i
$563$	−3.43987	−	4.91264i	−0.144973	−	0.207043i	0.740098	−	0.672499i	$-0.234779\pi$
$563$	−3.43987	−	4.91264i	−0.144973	−	0.207043i	−0.885071	+	0.465456i	$0.845890\pi$
$564$		0			0
$565$	0.403547	−	2.46624i	0.0169774	−	0.103756i
$566$			33.0399i			1.38877i
$567$		0			0
$568$	15.6218	+	15.6218i	0.655475	+	0.655475i
$569$	8.00903	−	6.72037i	0.335756	−	0.281733i	−0.459284	−	0.888289i	$-0.651894\pi$
$569$	8.00903	−	6.72037i	0.335756	−	0.281733i	0.795040	+	0.606557i	$0.207450\pi$
$570$		0			0
$571$	−1.98699	+	11.2688i	−0.0831531	+	0.471584i	0.914587	+	0.404390i	$0.132516\pi$
$571$	−1.98699	+	11.2688i	−0.0831531	+	0.471584i	−0.997740	+	0.0671948i	$0.978595\pi$
$572$	22.0848	+	10.2983i	0.923411	+	0.430594i
$573$		0			0
$574$	−0.0164934	+	0.00290823i	−0.000688421	+	0.000121387i
$575$	23.4155	+	10.2230i	0.976492	+	0.426329i
$576$		0			0
$577$	11.8211	+	44.1170i	0.492120	+	1.83662i	0.545597	+	0.838047i	$0.316303\pi$
$577$	11.8211	+	44.1170i	0.492120	+	1.83662i	−0.0534774	+	0.998569i	$0.517031\pi$
$578$	58.8308	−	27.4332i	2.44704	−	1.14107i
$579$		0			0
$580$	25.2879	−	25.9199i	1.05002	−	1.07627i
$581$	0.00666682	−	0.00794521i	0.000276586	−	0.000329623i
$582$		0			0
$583$	−9.27687	−	19.8943i	−0.384209	−	0.823938i
$584$	−1.33016	+	2.30390i	−0.0550424	+	0.0953362i
$585$		0			0
$586$	−24.7911	−	42.9394i	−1.02411	−	1.77381i
$587$	−15.9259	+	22.7446i	−0.657334	+	0.938770i	−1.00000		0.000687603i	$-0.999781\pi$
$587$	−15.9259	+	22.7446i	−0.657334	+	0.938770i	0.342666	+	0.939457i	$0.388670\pi$
$588$		0			0
$589$	3.27398	+	8.99519i	0.134902	+	0.370640i
$590$	9.50041	−	5.64253i	0.391126	−	0.232299i
$591$		0			0
$592$	−0.0373990	+	0.427473i	−0.00153709	+	0.0175690i
$593$	−12.5526	+	12.5526i	−0.515474	+	0.515474i	−0.916199	−	0.400725i	$-0.868758\pi$
$593$	−12.5526	+	12.5526i	−0.515474	+	0.515474i	0.400725	+	0.916199i	$0.368758\pi$
$594$		0			0
$595$	−0.00984889		0.000739308i	−0.000403765		3.03087e-5i
$596$	18.4671	+	22.0082i	0.756441	+	0.901491i
$597$		0			0
$598$	29.2513	−	20.4820i	1.19617	−	0.837570i
$599$	−9.47392	+	3.44823i	−0.387094	+	0.140891i	−0.528234	−	0.849099i	$-0.677146\pi$
$599$	−9.47392	+	3.44823i	−0.387094	+	0.140891i	0.141140	+	0.989990i	$0.454923\pi$
$600$		0			0
$601$	−0.977209	−	5.54203i	−0.0398612	−	0.226064i	0.958369	−	0.285533i	$-0.0921705\pi$
$601$	−0.977209	−	5.54203i	−0.0398612	−	0.226064i	−0.998230	+	0.0594686i	$0.981059\pi$
$602$	0.00320552	−	0.0119631i	0.000130647	−	0.000487581i
$603$		0			0
$604$	45.6522	+	26.3573i	1.85756	+	1.07246i
$605$	7.50476	+	3.38740i	0.305112	+	0.137717i
$606$		0			0
$607$	12.1412	−	1.06222i	0.492796	−	0.0431140i	0.161950	−	0.986799i	$-0.448222\pi$
$607$	12.1412	−	1.06222i	0.492796	−	0.0431140i	0.330846	+	0.943685i	$0.392666\pi$
$608$	−12.7303	+	1.11375i	−0.516280	+	0.0451686i
$609$		0			0
$610$	−11.4459	−	30.2794i	−0.463433	−	1.22598i
$611$	−1.93736	−	1.11853i	−0.0783771	−	0.0452511i
$612$		0			0
$613$	5.69311	−	21.2470i	0.229942	−	0.858157i	−0.750422	−	0.660960i	$-0.770149\pi$
$613$	5.69311	−	21.2470i	0.229942	−	0.858157i	0.980364	−	0.197197i	$-0.0631839\pi$
$614$	−1.92976	−	10.9442i	−0.0778789	−	0.441673i
$615$		0			0
$616$	−0.00301917	+	0.00109889i	−0.000121646	+	4.42754e-5i
$617$	5.87642	−	4.11472i	0.236576	−	0.165652i	−0.449277	−	0.893393i	$-0.648318\pi$
$617$	5.87642	−	4.11472i	0.236576	−	0.165652i	0.685853	+	0.727740i	$0.259429\pi$
$618$		0			0
$619$	−0.611202	−	0.728403i	−0.0245663	−	0.0292770i	0.753621	−	0.657309i	$-0.228305\pi$
$619$	−0.611202	−	0.728403i	−0.0245663	−	0.0292770i	−0.778188	+	0.628032i	$0.783861\pi$
$620$	−2.58156	+	34.3909i	−0.103678	+	1.38117i
$621$		0			0
$622$	−30.6554	+	30.6554i	−1.22917	+	1.22917i
$623$	0.000337988	−	0.00386323i	1.35412e−5	−	0.000154777i
$624$		0			0
$625$	11.4164	−	22.2411i	0.456655	−	0.889644i
$626$	−20.4041	−	56.0599i	−0.815513	−	2.24060i
$627$		0			0
$628$	−0.525913	+	0.751081i	−0.0209862	+	0.0299714i
$629$	0.894651	+	1.54958i	0.0356721	+	0.0617859i
$630$		0			0
$631$	−19.0880	+	33.0615i	−0.759883	+	1.31616i	0.183027	+	0.983108i	$0.441411\pi$
$631$	−19.0880	+	33.0615i	−0.759883	+	1.31616i	−0.942910	+	0.333048i	$0.891923\pi$
$632$	4.05368	+	8.69315i	0.161247	+	0.345795i
$633$		0			0
$634$	−0.352787	+	0.420435i	−0.0140110	+	0.0166976i
$635$	−23.3593	+	0.288311i	−0.926985	+	0.0114413i
$636$		0			0
$637$	−20.1639	+	9.40257i	−0.798922	+	0.372543i
$638$	8.79602	+	32.8272i	0.348238	+	1.29964i
$639$		0			0
$640$	−28.2735	−	9.89728i	−1.11761	−	0.391224i
$641$	24.5606	−	4.33069i	0.970084	−	0.171052i	0.333916	−	0.942603i	$-0.391630\pi$
$641$	24.5606	−	4.33069i	0.970084	−	0.171052i	0.636168	+	0.771551i	$0.280519\pi$
$642$		0			0
$643$	40.2010	+	18.7461i	1.58537	+	0.739272i	0.997566	−	0.0697279i	$-0.0222131\pi$
$643$	40.2010	+	18.7461i	1.58537	+	0.739272i	0.587808	+	0.809000i	$0.299991\pi$
$644$	−0.00162856	+	0.00923602i	−6.41742e−5	+	0.000363950i
$645$		0			0
$646$	−20.2081	+	16.9566i	−0.795078	+	0.667149i
$647$	−4.55768	−	4.55768i	−0.179181	−	0.179181i	0.611818	−	0.790999i	$-0.290439\pi$
$647$	−4.55768	−	4.55768i	−0.179181	−	0.179181i	−0.790999	+	0.611818i	$0.790439\pi$
$648$		0			0
$649$			6.07983i			0.238654i
$650$	−18.2119	−	29.8192i	−0.714329	−	1.16960i
$651$		0			0
$652$	−8.88773	−	12.6930i	−0.348070	−	0.497096i
$653$	2.85735	−	6.12762i	0.111817	−	0.239792i	−0.842434	−	0.538800i	$-0.818878\pi$
$653$	2.85735	−	6.12762i	0.111817	−	0.239792i	0.954251	+	0.299008i	$0.0966557\pi$
$654$		0			0
$655$	32.3932	−	3.23734i	1.26571	−	0.126493i
$656$	16.6632	−	9.62047i	0.650587	−	0.375616i
$657$		0			0
$658$	0.000967991	0	0.000259372i	3.77362e−5	0	1.01114e-5i
$659$	29.5176	+	10.7435i	1.14984	+	0.418508i	0.845458	−	0.534042i	$-0.179327\pi$
$659$	29.5176	+	10.7435i	1.14984	+	0.418508i	0.304383	+	0.952550i	$0.401550\pi$
$660$		0			0
$661$	−12.6918	−	10.6497i	−0.493654	−	0.414225i	0.361680	−	0.932302i	$-0.382203\pi$
$661$	−12.6918	−	10.6497i	−0.493654	−	0.414225i	−0.855334	+	0.518078i	$0.826648\pi$
$662$	0.905769	+	10.3530i	0.0352037	+	0.402380i
$663$		0			0
$664$	10.0472	−	27.6043i	0.389905	−	1.07126i
$665$	0.00250275		0.000473223i	9.70526e−5		1.83508e-5i
$666$		0			0
$667$	28.2034	+	7.55709i	1.09204	+	0.292612i
$668$	−42.7520	−	29.9353i	−1.65412	−	1.15823i
$669$		0			0
$670$	11.7425	−	3.30226i	0.453654	−	0.127577i
$671$	17.5405	+	3.09287i	0.677144	+	0.119399i
$672$		0			0
$673$	7.80022	+	0.682431i	0.300676	+	0.0263058i	0.236496	−	0.971633i	$-0.424001\pi$
$673$	7.80022	+	0.682431i	0.300676	+	0.0263058i	0.0641806	+	0.997938i	$0.479557\pi$
$674$	23.7902			0.916366
$675$		0			0
$676$	8.21392			0.315920
$677$	−30.1802	−	2.64043i	−1.15992	−	0.101480i	−0.509097	−	0.860709i	$-0.670021\pi$
$677$	−30.1802	−	2.64043i	−1.15992	−	0.101480i	−0.650823	+	0.759229i	$0.725576\pi$
$678$		0			0
$679$	0.00536718		0.000946379i	0.000205974		3.63187e-5i
$680$	−26.9290	+	7.57301i	−1.03268	+	0.290412i
$681$		0			0
$682$	−26.5133	−	18.5648i	−1.01525	−	0.710885i
$683$	−30.0707	−	8.05741i	−1.15062	−	0.308308i	−0.367408	−	0.930060i	$-0.619755\pi$
$683$	−30.0707	−	8.05741i	−1.15062	−	0.308308i	−0.783214	+	0.621752i	$0.786421\pi$
$684$		0			0
$685$	16.0650	−	3.03758i	0.613810	−	0.116060i
$686$	0.00681755	−	0.0187311i	0.000260295	−	0.000715155i
$687$		0			0
$688$	1.24013	+	14.1747i	0.0472793	+	0.540405i
$689$	19.7569	+	16.5780i	0.752679	+	0.631573i
$690$		0			0
$691$	6.70424	+	2.44014i	0.255041	+	0.0928274i	0.466377	−	0.884586i	$-0.345559\pi$
$691$	6.70424	+	2.44014i	0.255041	+	0.0928274i	−0.211336	+	0.977414i	$0.567781\pi$
$692$	8.15256	−	2.18447i	0.309914	−	0.0830411i
$693$		0			0
$694$	−45.8059	+	26.4461i	−1.73877	+	1.00388i
$695$	6.79115	−	0.678702i	0.257603	−	0.0257446i
$696$		0			0
$697$	33.9074	−	72.7146i	1.28433	−	2.75426i
$698$	1.47604	+	2.10801i	0.0558690	+	0.0797892i
$699$		0			0
$700$	0.00891991	+	0.00215560i	0.000337141	+	8.14741e-5i
$701$		−	18.1226i		−	0.684482i	−0.939612	−	0.342241i	$-0.888814\pi$
$701$		−	18.1226i		−	0.684482i	0.939612	−	0.342241i	$-0.111186\pi$
$702$		0			0
$703$	−0.326292	−	0.326292i	−0.0123064	−	0.0123064i
$704$	26.3202	−	22.0853i	0.991981	−	0.832371i
$705$		0			0
$706$	−7.73863	+	43.8880i	−0.291247	+	1.65175i
$707$	−0.00675423	−	0.00314955i	−0.000254019	−	0.000118451i
$708$		0			0
$709$	−20.6080	+	3.63375i	−0.773951	+	0.136469i	−0.546656	−	0.837357i	$-0.684099\pi$
$709$	−20.6080	+	3.63375i	−0.773951	+	0.136469i	−0.227296	+	0.973826i	$0.572988\pi$
$710$	55.8940	+	19.5660i	2.09766	+	0.734298i
$711$		0			0
$712$	−2.84277	−	10.6094i	−0.106537	−	0.397603i
$713$	−25.2025	+	11.7521i	−0.943842	+	0.440121i
$714$		0			0
$715$	19.2238	−	0.237270i	0.718931	−	0.00887339i
$716$	−30.1048	+	35.8774i	−1.12507	+	1.34080i
$717$		0			0
$718$	24.3603	+	52.2408i	0.909117	+	1.94961i
$719$	−4.36807	+	7.56572i	−0.162902	+	0.282154i	−0.935908	−	0.352244i	$-0.885419\pi$
$719$	−4.36807	+	7.56572i	−0.162902	+	0.282154i	0.773007	+	0.634398i	$0.218752\pi$
$720$		0			0
$721$	0.00222038	+	0.00384581i	8.26912e−5	+	0.000143225i
$722$	−20.0590	+	28.6472i	−0.746518	+	1.06614i
$723$		0			0
$724$	9.33561	+	25.6494i	0.346955	+	0.953252i
$725$	9.10592	−	27.0800i	0.338186	−	1.00573i
$726$		0			0
$727$	3.90529	−	44.6377i	0.144839	−	1.65552i	−0.481851	−	0.876253i	$-0.660035\pi$
$727$	3.90529	−	44.6377i	0.144839	−	1.65552i	0.626690	−	0.779268i	$-0.284409\pi$
$728$	0.00266931	−	0.00266931i	9.89311e−5	−	9.89311e-5i
$729$		0			0
$730$	−0.533792	+	7.11105i	−0.0197565	+	0.263192i
$731$	38.1379	+	45.4510i	1.41058	+	1.68106i
$732$		0			0
$733$	−18.4458	+	12.9159i	−0.681312	+	0.477060i	−0.862282	−	0.506429i	$-0.830965\pi$
$733$	−18.4458	+	12.9159i	−0.681312	+	0.477060i	0.180970	+	0.983489i	$0.442076\pi$
$734$	−43.3544	+	15.7797i	−1.60024	+	0.582440i
$735$		0			0
$736$	−6.44625	−	36.5585i	−0.237612	−	1.34756i
$737$	−1.73711	+	6.48298i	−0.0639873	+	0.238804i
$738$		0			0
$739$	−29.3820	−	16.9637i	−1.08084	−	0.624020i	−0.149714	−	0.988729i	$-0.547835\pi$
$739$	−29.3820	−	16.9637i	−1.08084	−	0.624020i	−0.931122	+	0.364709i	$0.881168\pi$
$740$	−0.587846	−	1.55510i	−0.0216096	−	0.0571667i
$741$		0			0
$742$	−0.0115095	+	0.00100695i	−0.000422528	+	3.69664e-5i
$743$	−25.4881	+	2.22992i	−0.935068	+	0.0818078i	−0.544495	−	0.838764i	$-0.683279\pi$
$743$	−25.4881	+	2.22992i	−0.935068	+	0.0818078i	−0.390573	+	0.920572i	$0.627723\pi$
$744$		0			0
$745$	20.6596	+	9.32506i	0.756908	+	0.341644i
$746$	−3.19968	−	1.84733i	−0.117148	−	0.0676357i
$747$		0			0
$748$	13.5347	−	50.5122i	0.494878	−	1.84691i
$749$	0.00153867	+	0.00872624i	5.62218e−5	+	0.000318850i
$750$		0			0
$751$	−18.3171	+	6.66687i	−0.668400	+	0.243278i	−0.653859	−	0.756617i	$-0.726851\pi$
$751$	−18.3171	+	6.66687i	−0.668400	+	0.243278i	−0.0145411	+	0.999894i	$0.504629\pi$
$752$	−0.943105	+	0.660369i	−0.0343915	+	0.0240812i
$753$		0			0
$754$	−25.6667	−	30.5884i	−0.934726	−	1.11396i
$755$	41.4732	+	3.11319i	1.50936	+	0.113301i
$756$		0			0
$757$	37.3446	−	37.3446i	1.35731	−	1.35731i	0.480097	−	0.877215i	$-0.340601\pi$
$757$	37.3446	−	37.3446i	1.35731	−	1.35731i	0.877215	−	0.480097i	$-0.159399\pi$
$758$	−2.23509	+	25.5472i	−0.0811822	+	0.927917i
$759$		0			0
$760$	6.20265	−	3.68391i	0.224994	−	0.133630i
$761$	−13.8978	−	38.1838i	−0.503793	−	1.38416i	−0.887543	−	0.460724i	$-0.847590\pi$
$761$	−13.8978	−	38.1838i	−0.503793	−	1.38416i	0.383750	−	0.923437i	$-0.374632\pi$
$762$		0			0
$763$	−0.00138854	+	0.00198304i	−5.02685e−5	+	7.17908e-5i
$764$	−1.75761	−	3.04427i	−0.0635881	−	0.110138i
$765$		0			0
$766$	11.5732	−	20.0453i	0.418156	−	0.724267i
$767$	−3.01892	−	6.47410i	−0.109007	−	0.233766i
$768$		0			0
$769$	1.03060	−	1.22823i	0.0371646	−	0.0442910i	−0.747142	−	0.664664i	$-0.768575\pi$
$769$	1.03060	−	1.22823i	0.0371646	−	0.0442910i	0.784307	+	0.620373i	$0.213019\pi$
$770$	−0.00601423	+	0.00616454i	−0.000216738	+	0.000222155i
$771$		0			0
$772$	−45.4846	+	21.2098i	−1.63703	+	0.763358i
$773$	8.72934	+	32.5784i	0.313973	+	1.17176i	0.924942	+	0.380108i	$0.124113\pi$
$773$	8.72934	+	32.5784i	0.313973	+	1.17176i	−0.610970	+	0.791654i	$0.709220\pi$
$774$		0			0
$775$	9.93442	+	25.3311i	0.356855	+	0.909919i
$776$	15.2015	−	2.68044i	0.545702	−	0.0962220i
$777$		0			0
$778$	−78.1685	−	36.4506i	−2.80248	−	1.30682i
$779$	−3.59298	+	20.3768i	−0.128732	+	0.730074i
$780$		0			0
$781$	−24.9609	+	20.9447i	−0.893172	+	0.749460i
$782$	−54.1877	−	54.1877i	−1.93775	−	1.93775i
$783$		0			0
$784$			11.4502i			0.408937i
$785$	−0.116815	+	0.713906i	−0.00416932	+	0.0254804i
$786$		0			0
$787$	−1.32801	−	1.89659i	−0.0473384	−	0.0676063i	0.794785	−	0.606891i	$-0.207584\pi$
$787$	−1.32801	−	1.89659i	−0.0473384	−	0.0676063i	−0.842123	+	0.539285i	$0.818695\pi$
$788$	20.3448	−	43.6296i	0.724754	−	1.55424i
$789$		0			0
$790$	19.8983	+	16.2825i	0.707952	+	0.579304i
$791$	0.000626766	0	0.000361864i	2.22852e−5	0	1.28664e-5i
$792$		0			0
$793$	−20.2138	+	5.41626i	−0.717812	+	0.192337i
$794$	−21.5293	−	7.83603i	−0.764047	−	0.278090i
$795$		0			0
$796$	22.8981	+	19.2138i	0.811602	+	0.681015i
$797$	1.45181	+	16.5943i	0.0514259	+	0.587801i	0.977567	+	0.210624i	$0.0675495\pi$
$797$	1.45181	+	16.5943i	0.0514259	+	0.587801i	−0.926141	+	0.377177i	$0.876895\pi$
$798$		0			0
$799$	−1.64198	+	4.51129i	−0.0580889	+	0.159598i
$800$	−36.0962	+	4.05794i	−1.27619	+	0.143470i
$801$		0			0
$802$	−56.8031	−	15.2204i	−2.00579	−	0.537449i
$803$	−3.21410	−	2.25054i	−0.113423	−	0.0794197i
$804$		0			0
$805$	0.00200314	+	0.00712298i	7.06013e−5	+	0.000251052i
$806$	37.4510	+	6.60363i	1.31916	+	0.232603i
$807$		0			0
$808$	−21.0273	−	1.83965i	−0.739739	−	0.0647188i
$809$	−38.2899			−1.34620			−0.673100	−	0.739551i	$-0.735038\pi$
$809$	−38.2899			−1.34620			−0.673100	+	0.739551i	$0.735038\pi$
$810$		0			0
$811$	48.1974			1.69244			0.846220	−	0.532833i	$-0.178873\pi$
$811$	48.1974			1.69244			0.846220	+	0.532833i	$0.178873\pi$
$812$	0.0104472		0.000914012i	0.000366625		3.20755e-5i
$813$		0			0
$814$	1.53656	+	0.270937i	0.0538564	+	0.00949633i
$815$	−10.6620	−	5.98146i	−0.373472	−	0.209522i
$816$		0			0
$817$	−12.5341	−	8.77644i	−0.438511	−	0.307049i
$818$	−72.5455	−	19.4385i	−2.53649	−	0.679652i
$819$		0			0
$820$	−42.0009	+	61.5875i	−1.46674	+	2.15073i
$821$	−5.73809	+	15.7653i	−0.200261	+	0.550212i	−0.998651	−	0.0519288i	$-0.983463\pi$
$821$	−5.73809	+	15.7653i	−0.200261	+	0.550212i	0.798390	+	0.602141i	$0.205685\pi$
$822$		0			0
$823$	−3.01595	−	34.4725i	−0.105130	−	1.20164i	−0.847185	−	0.531298i	$-0.821705\pi$
$823$	−3.01595	−	34.4725i	−0.105130	−	1.20164i	0.742056	−	0.670338i	$-0.233851\pi$
$824$	9.63498	+	8.08471i	0.335651	+	0.281644i
$825$		0			0
$826$	0.00300703	+	0.00109447i	0.000104628	+	3.80815e-5i
$827$	−19.5339	+	5.23409i	−0.679261	+	0.182007i	−0.581923	−	0.813244i	$-0.697699\pi$
$827$	−19.5339	+	5.23409i	−0.679261	+	0.182007i	−0.0973378	+	0.995251i	$0.531033\pi$
$828$		0			0
$829$	45.7476	−	26.4124i	1.58888	−	0.917340i	0.595387	−	0.803439i	$-0.296999\pi$
$829$	45.7476	−	26.4124i	1.58888	−	0.917340i	0.993492	−	0.113900i	$-0.0363344\pi$
$830$	−7.83048	−	78.3526i	−0.271800	−	2.71966i
$831$		0			0
$832$	−17.0607	+	36.5867i	−0.591473	+	1.26842i
$833$	27.3858	+	39.1110i	0.948861	+	1.35511i
$834$		0			0
$835$	−40.6359	−	6.64919i	−1.40626	−	0.230105i
$836$			13.4862i			0.466432i
$837$		0			0
$838$	−24.8475	−	24.8475i	−0.858342	−	0.858342i
$839$	1.94021	−	1.62803i	0.0669835	−	0.0562059i	−0.608681	−	0.793415i	$-0.708301\pi$
$839$	1.94021	−	1.62803i	0.0669835	−	0.0562059i	0.675665	+	0.737209i	$0.263857\pi$
$840$		0			0
$841$	0.633784	−	3.59437i	0.0218546	−	0.123944i
$842$	63.4780	+	29.6003i	2.18760	+	1.02009i
$843$		0			0
$844$	0.501982	−	0.0885129i	0.0172789	−	0.00304674i
$845$	5.83905	−	2.81104i	0.200869	−	0.0967028i
$846$		0			0
$847$	0.000617162		0.00230328i	2.12059e−5		7.91417e-5i
$848$	12.0298	−	5.60957i	0.413104	−	0.192634i
$849$		0			0
$850$	−56.2339	+	49.6017i	−1.92881	+	1.70132i
$851$	0.861655	−	1.02688i	0.0295371	−	0.0352010i
$852$		0			0
$853$	17.6637	+	37.8798i	0.604792	+	1.29698i	0.935526	+	0.353257i	$0.114926\pi$
$853$	17.6637	+	37.8798i	0.604792	+	1.29698i	−0.330734	+	0.943724i	$0.607296\pi$
$854$	0.00468729	−	0.00811862i	0.000160396	−	0.000277813i
$855$		0			0
$856$	12.5483	+	21.7343i	0.428893	+	0.742864i
$857$	15.3891	−	21.9778i	0.525680	−	0.750749i	−0.465242	−	0.885183i	$-0.654033\pi$
$857$	15.3891	−	21.9778i	0.525680	−	0.750749i	0.990923	+	0.134434i	$0.0429217\pi$
$858$		0			0
$859$	7.80591	+	21.4466i	0.266334	+	0.731747i	0.998707	+	0.0508429i	$0.0161908\pi$
$859$	7.80591	+	21.4466i	0.266334	+	0.731747i	−0.732372	+	0.680904i	$0.761587\pi$
$860$	−28.1508	−	47.3979i	−0.959934	−	1.61625i
$861$		0			0
$862$	1.13765	−	13.0034i	0.0387484	−	0.442896i
$863$	7.93097	−	7.93097i	0.269973	−	0.269973i	−0.559116	−	0.829089i	$-0.688859\pi$
$863$	7.93097	−	7.93097i	0.269973	−	0.269973i	0.829089	+	0.559116i	$0.188859\pi$
$864$		0			0
$865$	5.04784	−	4.34292i	0.171632	−	0.147664i
$866$	−15.4685	−	18.4346i	−0.525641	−	0.626434i
$867$		0			0
$868$	−0.00818145	+	0.00572871i	−0.000277696	+	0.000194445i
$869$	−13.2938	+	4.83854i	−0.450961	+	0.164136i
$870$		0			0
$871$	−1.36935	−	7.76596i	−0.0463986	−	0.263139i
$872$	−1.77461	+	6.62293i	−0.0600959	+	0.224281i
$873$		0			0
$874$	17.1153	+	9.88153i	0.578934	+	0.334248i
$875$	0.00707863	−	0.00152029i	0.000239301	−	5.13953e-5i
$876$		0			0
$877$	0.977840	−	0.0855499i	0.0330193	−	0.00288882i	−0.0706341	−	0.997502i	$-0.522502\pi$
$877$	0.977840	−	0.0855499i	0.0330193	−	0.00288882i	0.103653	+	0.994613i	$0.466947\pi$
$878$	−63.7167	+	5.57448i	−2.15033	+	0.188130i
$879$		0			0
$880$	4.07056	−	9.01829i	0.137219	−	0.304007i
$881$	−22.3414	−	12.8988i	−0.752701	−	0.434572i	0.0739682	−	0.997261i	$-0.476434\pi$
$881$	−22.3414	−	12.8988i	−0.752701	−	0.434572i	−0.826669	+	0.562689i	$0.809767\pi$
$882$		0			0
$883$	−12.4224	+	46.3611i	−0.418048	+	1.56018i	0.360604	+	0.932719i	$0.382571\pi$
$883$	−12.4224	+	46.3611i	−0.418048	+	1.56018i	−0.778652	+	0.627457i	$0.784096\pi$
$884$	10.6693	+	60.5085i	0.358847	+	2.03512i
$885$		0			0
$886$	−56.0866	+	20.4139i	−1.88427	+	0.685817i
$887$	5.46649	−	3.82768i	0.183547	−	0.128521i	−0.478192	−	0.878255i	$-0.658708\pi$
$887$	5.46649	−	3.82768i	0.183547	−	0.128521i	0.661739	+	0.749734i	$0.269819\pi$
$888$		0			0
$889$	−0.00434872	−	0.00518260i	−0.000145851	−	0.000173819i
$890$	−19.2018	−	22.3185i	−0.643646	−	0.748119i
$891$		0			0
$892$	36.9415	−	36.9415i	1.23689	−	1.23689i
$893$	0.107907	−	1.23338i	0.00361097	−	0.0412735i
$894$		0			0
$895$	−9.12235	+	35.8070i	−0.304926	+	1.19690i
$896$	−0.00296711	−	0.00815206i	−9.91241e−5	−	0.000272341i
$897$		0			0
$898$	4.38105	−	6.25679i	0.146198	−	0.208792i
$899$	15.5475	+	26.9291i	0.518538	+	0.898134i
$900$		0			0
$901$	27.6739	−	47.9327i	0.921953	−	1.59687i
$902$	−29.5671	−	63.4068i	−0.984476	−	2.11121i
$903$		0			0
$904$	1.31760	−	1.57025i	0.0438226	−	0.0522258i
$905$	15.4144	+	15.0385i	0.512392	+	0.499898i
$906$		0			0
$907$	1.07303	−	0.500360i	0.0356292	−	0.0166142i	−0.404722	−	0.914440i	$-0.632632\pi$
$907$	1.07303	−	0.500360i	0.0356292	−	0.0166142i	0.440351	+	0.897826i	$0.354854\pi$
$908$	−11.4837	−	42.8576i	−0.381099	−	1.42228i
$909$		0			0
$910$	0.00334326	−	0.00955065i	0.000110828	−	0.000316601i
$911$	27.0446	−	4.76870i	0.896028	−	0.157994i	0.293375	−	0.955997i	$-0.405221\pi$
$911$	27.0446	−	4.76870i	0.896028	−	0.157994i	0.602653	+	0.798003i	$0.294110\pi$
$912$		0			0
$913$	39.2670	+	18.3105i	1.29955	+	0.605990i
$914$	−9.00761	+	51.0847i	−0.297945	+	1.68973i
$915$		0			0
$916$	15.3502	−	12.8803i	0.507185	−	0.425578i
$917$	0.00666650	+	0.00666650i	0.000220147	+	0.000220147i
$918$		0			0
$919$			21.2332i			0.700419i	0.936671	+	0.350209i	$0.113890\pi$
$919$			21.2332i			0.700419i	−0.936671	+	0.350209i	$0.886110\pi$
$920$	12.2314	+	17.0173i	0.403258	+	0.561045i
$921$		0			0
$922$	−10.0970	−	14.4200i	−0.332528	−	0.474899i
$923$	16.1796	−	34.6972i	0.532557	−	1.14207i
$924$		0			0
$925$	−0.950085	−	0.904303i	−0.0312386	−	0.0297333i
$926$	4.49731	−	2.59652i	0.147791	−	0.0853270i
$927$		0			0
$928$	−40.0962	+	10.7437i	−1.31622	+	0.352680i
$929$	28.3403	+	10.3150i	0.929816	+	0.338425i	0.762136	−	0.647416i	$-0.224150\pi$
$929$	28.3403	+	10.3150i	0.929816	+	0.338425i	0.167679	+	0.985842i	$0.446373\pi$
$930$		0			0
$931$	−9.43249	−	7.91479i	−0.309137	−	0.259397i
$932$	−0.564962	−	6.45754i	−0.0185059	−	0.211524i
$933$		0			0
$934$	−15.4682	+	42.4985i	−0.506135	+	1.39059i
$935$	−7.66529	−	40.5397i	−0.250682	−	1.32579i
$936$		0			0
$937$	16.5394	+	4.43173i	0.540320	+	0.144778i	0.518650	−	0.854987i	$-0.326435\pi$
$937$	16.5394	+	4.43173i	0.540320	+	0.144778i	0.0216704	+	0.999765i	$0.493102\pi$
$938$	0.00289372	+	0.00202620i	9.44832e−5	+	6.61579e-5i
$939$		0			0
$940$	2.18245	−	3.89022i	0.0711838	−	0.126885i
$941$	21.0459	+	3.71097i	0.686078	+	0.120974i	0.505812	−	0.862644i	$-0.331193\pi$
$941$	21.0459	+	3.71097i	0.686078	+	0.120974i	0.180266	+	0.983618i	$0.442304\pi$
$942$		0			0
$943$	−59.8787	−	5.23871i	−1.94992	−	0.170596i
$944$	−3.67638			−0.119656
$945$		0			0
$946$	51.7372			1.68212
$947$	28.3818	+	2.48308i	0.922284	+	0.0806894i	0.538398	−	0.842691i	$-0.319030\pi$
$947$	28.3818	+	2.48308i	0.922284	+	0.0806894i	0.383886	+	0.923380i	$0.374585\pi$
$948$		0			0
$949$	4.54003	+	0.800530i	0.147376	+	0.0259863i
$950$	10.6973	−	16.1095i	0.347067	−	0.522661i
$951$		0			0
$952$	−0.00663611	−	0.00464666i	−0.000215078	−	0.000150599i
$953$	−48.9558	−	13.1177i	−1.58583	−	0.424923i	−0.645108	−	0.764091i	$-0.723188\pi$
$953$	−48.9558	−	13.1177i	−1.58583	−	0.424923i	−0.940726	+	0.339169i	$0.889854\pi$
$954$		0			0
$955$	−2.29128	−	1.56258i	−0.0741440	−	0.0505641i
$956$	−7.46208	+	20.5019i	−0.241341	+	0.663078i
$957$		0			0
$958$	−4.12901	−	47.1948i	−0.133402	−	1.52479i
$959$	0.00362713	+	0.00304352i	0.000117126	+	9.82804e-5i
$960$		0			0
$961$	1.30221	+	0.473965i	0.0420067	+	0.0152892i
$962$	−1.77074	+	0.474467i	−0.0570908	+	0.0152974i
$963$		0			0
$964$	−23.5551	+	13.5995i	−0.758657	+	0.438011i
$965$	−25.0752	+	30.6436i	−0.807198	+	0.986454i
$966$		0			0
$967$	−22.4321	+	48.1057i	−0.721366	+	1.54697i	0.111663	+	0.993746i	$0.464382\pi$
$967$	−22.4321	+	48.1057i	−0.721366	+	1.54697i	−0.833029	+	0.553229i	$0.813396\pi$
$968$	3.87378	+	5.53233i	0.124508	+	0.177816i
$969$		0			0
$970$	33.5983	−	24.1492i	1.07878	−	0.775383i
$971$		−	12.4548i		−	0.399695i	−0.979827	−	0.199847i	$-0.935955\pi$
$971$		−	12.4548i		−	0.399695i	0.979827	−	0.199847i	$-0.0640447\pi$
$972$		0			0
$973$	0.00139762	+	0.00139762i	4.48056e−5	+	4.48056e-5i
$974$	5.24344	−	4.39976i	0.168011	−	0.140978i
$975$		0			0
$976$	−1.87021	+	10.6065i	−0.0598639	+	0.339505i
$977$	17.1398	+	7.99244i	0.548352	+	0.255701i	0.676992	−	0.735991i	$-0.263283\pi$
$977$	17.1398	+	7.99244i	0.548352	+	0.255701i	−0.128639	+	0.991691i	$0.541061\pi$
$978$		0			0
$979$	15.9536	−	2.81305i	0.509879	−	0.0899055i
$980$	−19.2430	−	39.9713i	−0.614695	−	1.27684i
$981$		0			0
$982$	4.69139	+	17.5085i	0.149708	+	0.558719i
$983$	−12.0933	+	5.63921i	−0.385717	+	0.179863i	−0.605798	−	0.795619i	$-0.707146\pi$
$983$	−12.0933	+	5.63921i	−0.385717	+	0.179863i	0.220080	+	0.975482i	$0.429368\pi$
$984$		0			0
$985$	−0.468739	−	37.9777i	−0.0149353	−	1.21007i
$986$	−55.0815	+	65.6436i	−1.75415	+	2.09052i
$987$		0			0
$988$	−6.69656	−	14.3608i	−0.213046	−	0.456878i
$989$	22.2250	−	38.4948i	0.706713	−	1.22406i
$990$		0			0
$991$	−2.99736	−	5.19158i	−0.0952142	−	0.164916i	0.814484	−	0.580186i	$-0.197020\pi$
$991$	−2.99736	−	5.19158i	−0.0952142	−	0.164916i	−0.909698	+	0.415270i	$0.863687\pi$
$992$	22.6757	−	32.3842i	0.719953	−	1.02820i
$993$		0			0
$994$	0.00586569	+	0.0161158i	0.000186048	+	0.000511163i
$995$	22.8532	+	5.82217i	0.724494	+	0.184575i
$996$		0			0
$997$	−3.98279	+	45.5235i	−0.126136	+	1.44174i	0.624498	+	0.781026i	$0.285304\pi$
$997$	−3.98279	+	45.5235i	−0.126136	+	1.44174i	−0.750634	+	0.660718i	$0.770252\pi$
$998$	41.0167	−	41.0167i	1.29836	−	1.29836i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.r.a.368.14		192
3.2	odd	2		135.2.q.a.113.3	yes	192
5.2	odd	4	inner	405.2.r.a.287.3		192
15.2	even	4		135.2.q.a.32.14	✓	192
15.8	even	4		675.2.ba.b.32.3		192
15.14	odd	2		675.2.ba.b.518.14		192
27.11	odd	18	inner	405.2.r.a.278.3		192
27.16	even	9		135.2.q.a.38.14	yes	192
135.43	odd	36		675.2.ba.b.632.14		192
135.92	even	36	inner	405.2.r.a.197.14		192
135.97	odd	36		135.2.q.a.92.3	yes	192
135.124	even	18		675.2.ba.b.443.3		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.14	✓	192	15.2	even	4
135.2.q.a.38.14	yes	192	27.16	even	9
135.2.q.a.92.3	yes	192	135.97	odd	36
135.2.q.a.113.3	yes	192	3.2	odd	2
405.2.r.a.197.14		192	135.92	even	36	inner
405.2.r.a.278.3		192	27.11	odd	18	inner
405.2.r.a.287.3		192	5.2	odd	4	inner
405.2.r.a.368.14		192	1.1	even	1	trivial
675.2.ba.b.32.3		192	15.8	even	4
675.2.ba.b.443.3		192	135.124	even	18
675.2.ba.b.518.14		192	15.14	odd	2
675.2.ba.b.632.14		192	135.43	odd	36

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.r (of order \(36\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.19031 + 0.191628i) q^{2} +(2.79113 + 0.492152i) q^{4} +(2.15257 - 0.605349i) q^{5} +(0.000530458 + 0.000371431i) q^{7} +(1.77162 + 0.474704i) q^{8} +(4.83080 - 0.913412i) q^{10} +(-0.925209 + 2.54199i) q^{11} +(-0.277011 - 3.16625i) q^{13} +(0.00109069 + 0.000915200i) q^{14} +(-1.53710 - 0.559459i) q^{16} +(-6.58840 + 1.76536i) q^{17} +(1.52337 - 0.879517i) q^{19} +(6.30603 - 0.630218i) q^{20} +(-2.51361 + 5.39046i) q^{22} +(2.93096 + 4.18584i) q^{23} +(4.26710 - 2.60611i) q^{25} -6.98815i q^{26} +(0.00129778 + 0.00129778i) q^{28} +(4.37718 - 3.67289i) q^{29} +(-0.944975 + 5.35922i) q^{31} +(-6.58407 - 3.07020i) q^{32} +(-14.7689 + 2.60416i) q^{34} +(0.00136669 + 0.000478418i) q^{35} +(-0.0678960 - 0.253391i) q^{37} +(3.50519 - 1.63450i) q^{38} +(4.10090 - 0.0506152i) q^{40} +(-7.56097 + 9.01082i) q^{41} +(-3.67622 - 7.88368i) q^{43} +(-3.83342 + 6.63969i) q^{44} +(5.61759 + 9.72995i) q^{46} +(0.403711 - 0.576559i) q^{47} +(-2.39414 - 6.57785i) q^{49} +(9.84570 - 4.89050i) q^{50} +(0.785101 - 8.97374i) q^{52} +(-5.73786 + 5.73786i) q^{53} +(-0.452784 + 6.03188i) q^{55} +(0.000763450 + 0.000909845i) q^{56} +(10.2912 - 7.20599i) q^{58} +(2.11198 - 0.768697i) q^{59} +(-1.14333 - 6.48417i) q^{61} +(-3.09676 + 11.5573i) q^{62} +(-10.9996 - 6.35064i) q^{64} +(-2.51297 - 6.64787i) q^{65} +(2.47165 - 0.216242i) q^{67} +(-19.2579 + 1.68485i) q^{68} +(0.00290181 + 0.00130978i) q^{70} +(10.4316 + 6.02267i) q^{71} +(-0.375408 + 1.40104i) q^{73} +(-0.100157 - 0.568017i) q^{74} +(4.68478 - 1.70512i) q^{76} +(-0.00143496 + 0.00100477i) q^{77} +(3.36157 + 4.00616i) q^{79} +(-3.64738 - 0.273791i) q^{80} +(-18.2876 + 18.2876i) q^{82} +(1.39592 - 15.9554i) q^{83} +(-13.1133 + 7.78833i) q^{85} +(-6.54134 - 17.9722i) q^{86} +(-2.84581 + 4.06424i) q^{88} +(-2.99426 - 5.18621i) q^{89} +(0.00102910 - 0.00178245i) q^{91} +(6.12062 + 13.1257i) q^{92} +(0.994737 - 1.18548i) q^{94} +(2.74674 - 2.81539i) q^{95} +(7.62753 - 3.55678i) q^{97} +(-3.98342 - 14.8663i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35}+ \cdots - 324 q^{98}+O(q^{100}) \) 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Introduction

L-functions

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Database

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