LMFDB - Embedded newform 405.2.r.a.287.3

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			287.3
Character	$\chi$	$=$	405.287
Dual form			405.2.r.a.278.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.191628 + 2.19031i) q^{2} +(-2.79113 - 0.492152i) q^{4} +(-2.03807 + 0.919920i) q^{5} +(-0.000371431 + 0.000530458i) q^{7} +(0.474704 - 1.77162i) q^{8} +(-1.62436 - 4.64030i) q^{10} +(-0.925209 + 2.54199i) q^{11} +(-3.16625 + 0.277011i) q^{13} +(-0.00109069 - 0.000915200i) q^{14} +(-1.53710 - 0.559459i) q^{16} +(-1.76536 - 6.58840i) q^{17} +(-1.52337 + 0.879517i) q^{19} +(6.14128 - 1.56458i) q^{20} +(-5.39046 - 2.51361i) q^{22} +(4.18584 - 2.93096i) q^{23} +(3.30749 - 3.74973i) q^{25} -6.98815i q^{26} +(0.00129778 - 0.00129778i) q^{28} +(-4.37718 + 3.67289i) q^{29} +(-0.944975 + 5.35922i) q^{31} +(3.07020 - 6.58407i) q^{32} +(14.7689 - 2.60416i) q^{34} +(0.000269024 - 0.00142280i) q^{35} +(0.253391 - 0.0678960i) q^{37} +(-1.63450 - 3.50519i) q^{38} +(0.662267 + 4.04738i) q^{40} +(-7.56097 + 9.01082i) q^{41} +(-7.88368 + 3.67622i) q^{43} +(3.83342 - 6.63969i) q^{44} +(5.61759 + 9.72995i) q^{46} +(0.576559 + 0.403711i) q^{47} +(2.39414 + 6.57785i) q^{49} +(7.57928 + 7.96300i) q^{50} +(8.97374 + 0.785101i) q^{52} +(5.73786 + 5.73786i) q^{53} +(-0.452784 - 6.03188i) q^{55} +(0.000763450 + 0.000909845i) q^{56} +(-7.20599 - 10.2912i) q^{58} +(-2.11198 + 0.768697i) q^{59} +(-1.14333 - 6.48417i) q^{61} +(-11.5573 - 3.09676i) q^{62} +(10.9996 + 6.35064i) q^{64} +(6.19822 - 3.47726i) q^{65} +(0.216242 + 2.47165i) q^{67} +(1.68485 + 19.2579i) q^{68} +(0.00306482 + 0.000861895i) q^{70} +(10.4316 + 6.02267i) q^{71} +(1.40104 + 0.375408i) q^{73} +(0.100157 + 0.568017i) q^{74} +(4.68478 - 1.70512i) q^{76} +(-0.00100477 - 0.00143496i) q^{77} +(-3.36157 - 4.00616i) q^{79} +(3.64738 - 0.273791i) q^{80} +(-18.2876 - 18.2876i) q^{82} +(-15.9554 - 1.39592i) q^{83} +(9.65872 + 11.8037i) q^{85} +(-6.54134 - 17.9722i) q^{86} +(4.06424 + 2.84581i) q^{88} +(2.99426 + 5.18621i) q^{89} +(0.00102910 - 0.00178245i) q^{91} +(-13.1257 + 6.12062i) q^{92} +(-0.994737 + 1.18548i) q^{94} +(2.29565 - 3.19390i) q^{95} +(3.55678 + 7.62753i) q^{97} +(-14.8663 + 3.98342i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{18}\right)$

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 $

$2$	−0.191628	+	2.19031i	−0.135501	+	1.54878i	0.558923	+	0.829219i	$0.311215\pi$
$2$	−0.191628	+	2.19031i	−0.135501	+	1.54878i	−0.694425	+	0.719566i	$0.744341\pi$
$3$		0			0
$3$		0			0
$4$	−2.79113	−	0.492152i	−1.39557	−	0.246076i
$5$	−2.03807	+	0.919920i	−0.911455	+	0.411401i
$5$	−2.03807	+	0.919920i	−0.911455	+	0.411401i
$6$		0			0
$7$	−0.000371431	0	0.000530458i	−0.000140388	0	0.000200494i	−0.819222	−	0.573476i	$-0.805595\pi$
$7$	−0.000371431	0	0.000530458i	−0.000140388	0	0.000200494i	0.819082	+	0.573677i	$0.194483\pi$
$8$	0.474704	−	1.77162i	0.167833	−	0.626362i
$9$		0			0
$10$	−1.62436	−	4.64030i	−0.513668	−	1.46739i
$11$	−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
$13$	−3.16625	+	0.277011i	−0.878159	+	0.0768289i	−0.517313	−	0.855797i	$-0.673068\pi$
$13$	−3.16625	+	0.277011i	−0.878159	+	0.0768289i	−0.360846	+	0.932625i	$0.617512\pi$
$14$	−0.00109069		0.000915200i	−0.000291500		0.000244597i
$15$		0			0
$16$	−1.53710	−	0.559459i	−0.384275	−	0.139865i
$17$	−1.76536	−	6.58840i	−0.428162	−	1.59792i	−0.756921	−	0.653507i	$-0.773297\pi$
$17$	−1.76536	−	6.58840i	−0.428162	−	1.59792i	0.328759	−	0.944414i	$-0.393370\pi$
$18$		0			0
$19$	−1.52337	+	0.879517i	−0.349485	+	0.201775i	−0.664458	−	0.747325i	$-0.731338\pi$
$19$	−1.52337	+	0.879517i	−0.349485	+	0.201775i	0.314974	+	0.949100i	$0.398004\pi$
$20$	6.14128	−	1.56458i	1.37323	−	0.349850i
$21$		0			0
$22$	−5.39046	−	2.51361i	−1.14925	−	0.535904i
$23$	4.18584	−	2.93096i	0.872808	−	0.611147i	−0.0489979	−	0.998799i	$-0.515603\pi$
$23$	4.18584	−	2.93096i	0.872808	−	0.611147i	0.921806	+	0.387652i	$0.126714\pi$
$24$		0			0
$25$	3.30749	−	3.74973i	0.661499	−	0.749946i
$26$		−	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	−0.951279	−	0.308330i	$-0.900230\pi$
$29$	−4.37718	+	3.67289i	−0.812822	+	0.682038i	0.138458	+	0.990368i	$0.455785\pi$
$30$		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	$0.893028\pi$
$32$	3.07020	−	6.58407i	0.542740	−	1.16391i
$33$		0			0
$34$	14.7689	−	2.60416i	2.53285	−	0.446610i
$35$	0.000269024	−	0.00142280i	4.54734e−5	−	0.000240497i
$36$		0			0
$37$	0.253391	−	0.0678960i	0.0416573	−	0.0111620i	−0.237930	−	0.971282i	$-0.576469\pi$
$37$	0.253391	−	0.0678960i	0.0416573	−	0.0111620i	0.279587	+	0.960120i	$0.409802\pi$
$38$	−1.63450	−	3.50519i	−0.265151	−	0.568617i
$39$		0			0
$40$	0.662267	+	4.04738i	0.104714	+	0.639947i
$41$	−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
$43$	−7.88368	+	3.67622i	−1.20225	+	0.560618i	−0.917405	−	0.397955i	$-0.869720\pi$
$43$	−7.88368	+	3.67622i	−1.20225	+	0.560618i	−0.284845	+	0.958574i	$0.591942\pi$
$44$	3.83342	−	6.63969i	0.577910	−	1.00097i
$45$		0			0
$46$	5.61759	+	9.72995i	0.828268	+	1.43460i
$47$	0.576559	+	0.403711i	0.0840997	+	0.0588873i	0.614870	−	0.788628i	$-0.289208\pi$
$47$	0.576559	+	0.403711i	0.0840997	+	0.0588873i	−0.530770	+	0.847516i	$0.678097\pi$
$48$		0			0
$49$	2.39414	+	6.57785i	0.342020	+	0.939693i
$50$	7.57928	+	7.96300i	1.07187	+	1.12614i
$51$		0			0
$52$	8.97374	+	0.785101i	1.24443	+	0.108874i
$53$	5.73786	+	5.73786i	0.788156	+	0.788156i	0.981192	−	0.193036i	$-0.0618333\pi$
$53$	5.73786	+	5.73786i	0.788156	+	0.788156i	−0.193036	+	0.981192i	$0.561833\pi$
$54$		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
$58$	−7.20599	−	10.2912i	−0.946193	−	1.35130i
$59$	−2.11198	+	0.768697i	−0.274956	+	0.100076i	−0.475818	−	0.879544i	$-0.657848\pi$
$59$	−2.11198	+	0.768697i	−0.274956	+	0.100076i	0.200862	+	0.979620i	$0.435626\pi$
$60$		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	$-0.194055\pi$
$62$	−11.5573	−	3.09676i	−1.46778	−	0.393290i
$63$		0			0
$64$	10.9996	+	6.35064i	1.37495	+	0.793830i
$65$	6.19822	−	3.47726i	0.768794	−	0.431301i
$66$		0			0
$67$	0.216242	+	2.47165i	0.0264181	+	0.301960i	0.997896	+	0.0648313i	$0.0206509\pi$
$67$	0.216242	+	2.47165i	0.0264181	+	0.301960i	−0.971478	+	0.237129i	$0.923794\pi$
$68$	1.68485	+	19.2579i	0.204318	+	2.33536i
$69$		0			0
$70$	0.00306482		0.000861895i	0.000366316		0.000103016i
$71$	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
$73$	1.40104	+	0.375408i	0.163979	+	0.0439381i	0.339875	−	0.940471i	$-0.389615\pi$
$73$	1.40104	+	0.375408i	0.163979	+	0.0439381i	−0.175895	+	0.984409i	$0.556282\pi$
$74$	0.100157	+	0.568017i	0.0116430	+	0.0660306i
$75$		0			0
$76$	4.68478	−	1.70512i	0.537381	−	0.195591i
$77$	−0.00100477	−	0.00143496i	−0.000114504	−	0.000163529i
$78$		0			0
$79$	−3.36157	−	4.00616i	−0.378206	−	0.450729i	0.543041	−	0.839706i	$-0.317273\pi$
$79$	−3.36157	−	4.00616i	−0.378206	−	0.450729i	−0.921247	+	0.388978i	$0.872828\pi$
$80$	3.64738	−	0.273791i	0.407790	−	0.0306108i
$81$		0			0
$82$	−18.2876	−	18.2876i	−2.01953	−	2.01953i
$83$	−15.9554	−	1.39592i	−1.75134	−	0.153222i	−0.834113	−	0.551594i	$-0.814020\pi$
$83$	−15.9554	−	1.39592i	−1.75134	−	0.153222i	−0.917224	+	0.398372i	$0.869575\pi$
$84$		0			0
$85$	9.65872	+	11.8037i	1.04764	+	1.28029i
$86$	−6.54134	−	17.9722i	−0.705371	−	1.93799i
$87$		0			0
$88$	4.06424	+	2.84581i	0.433249	+	0.303364i
$89$	2.99426	+	5.18621i	0.317391	+	0.549737i	0.979943	−	0.199279i	$-0.0638600\pi$
$89$	2.99426	+	5.18621i	0.317391	+	0.549737i	−0.662552	+	0.749016i	$0.730527\pi$
$90$		0			0
$91$	0.00102910	−	0.00178245i	0.000107879	−	0.000186852i
$92$	−13.1257	+	6.12062i	−1.36845	+	0.638118i
$93$		0			0
$94$	−0.994737	+	1.18548i	−0.102599	+	0.122273i
$95$	2.29565	−	3.19390i	0.235529	−	0.327687i
$96$		0			0
$97$	3.55678	+	7.62753i	0.361136	+	0.774459i	0.999987	+	0.00512815i	$0.00163235\pi$
$97$	3.55678	+	7.62753i	0.361136	+	0.774459i	−0.638851	+	0.769331i	$0.720590\pi$
$98$	−14.8663	+	3.98342i	−1.50173	+	0.402386i
$99$		0			0
$100$	−11.0771	+	8.83821i	−1.10771	+	0.883821i
$101$	−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
$103$	2.89813	−	6.21507i	0.285562	−	0.612389i	−0.710237	−	0.703963i	$-0.751412\pi$
$103$	2.89813	−	6.21507i	0.285562	−	0.612389i	0.995798	+	0.0915740i	$0.0291898\pi$
$104$	−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	$-0.980039\pi$
$107$	−9.67551	+	9.67551i	−0.935367	+	0.935367i	0.0626673	+	0.998034i	$0.480039\pi$
$108$		0			0
$109$		−	3.73835i		−	0.358069i	−0.983843	−	0.179034i	$-0.942703\pi$
$109$		−	3.73835i		−	0.358069i	0.983843	−	0.179034i	$-0.0572974\pi$
$110$	13.2985	+	0.164136i	1.26796	+	0.0156498i
$111$		0			0
$112$	0.000867696	0	0.000607567i	8.19895e−5	0	5.74097e-5i
$113$	−1.01289	−	0.472320i	−0.0952851	−	0.0444322i	0.374391	−	0.927271i	$-0.377852\pi$
$113$	−1.01289	−	0.472320i	−0.0952851	−	0.0444322i	−0.469676	+	0.882839i	$0.655629\pi$
$114$		0			0
$115$	−5.83480	+	9.82414i	−0.544098	+	0.916106i
$116$	14.0249	−	8.09728i	1.30218	−	0.751814i
$117$		0			0
$118$	−1.27897	−	4.77320i	−0.117739	−	0.439408i
$119$	0.00415058	+	0.00151069i	0.000380483	+	0.000138484i
$120$		0			0
$121$	2.82079	+	2.36692i	0.256435	+	0.215175i
$122$	14.4215	−	1.26171i	1.30566	−	0.114230i
$123$		0			0
$124$	5.27510	−	14.4932i	0.473718	−	1.30153i
$125$	−3.29146	+	10.6849i	−0.294397	+	0.955683i
$126$		0			0
$127$	2.70398	−	10.0914i	0.239940	−	0.895467i	−0.735920	−	0.677068i	$-0.763250\pi$
$127$	2.70398	−	10.0914i	0.239940	−	0.895467i	0.975860	−	0.218398i	$-0.0700832\pi$
$128$	−7.68398	+	10.9739i	−0.679175	+	0.969962i
$129$		0			0
$130$	6.42854	+	14.2424i	0.563820	+	1.24914i
$131$	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
$133$	9.92788e−5	−	0.00113476i	8.60857e−6	−	9.83964e-5i
$134$	−5.45513			−0.471251
$135$		0			0
$136$	−12.5102			−1.07274
$137$	−0.637262	+	7.28394i	−0.0544450	+	0.622309i	0.919132	+	0.393950i	$0.128892\pi$
$137$	−0.637262	+	7.28394i	−0.0544450	+	0.622309i	−0.973577	+	0.228359i	$0.926664\pi$
$138$		0			0
$139$	−3.00586	−	0.530014i	−0.254953	−	0.0449552i	0.0447106	−	0.999000i	$-0.485763\pi$
$139$	−3.00586	−	0.530014i	−0.254953	−	0.0449552i	−0.299664	+	0.954045i	$0.596875\pi$
$140$	−0.00145112	+	0.00383882i	−0.000122642	+	0.000324440i
$141$		0			0
$142$	−15.1905	+	21.6943i	−1.27476	+	1.82054i
$143$	2.22528	−	8.30486i	0.186087	−	0.694487i
$144$		0			0
$145$	5.54225	−	11.5123i	0.460259	−	0.956043i
$146$	−1.09074	+	2.99678i	−0.0902701	+	0.248015i
$147$		0			0
$148$	−0.740664	+	0.0647997i	−0.0608822	+	0.00532650i
$149$	−7.76525	−	6.51582i	−0.636154	−	0.533797i	0.266680	−	0.963785i	$-0.414073\pi$
$149$	−7.76525	−	6.51582i	−0.636154	−	0.533797i	−0.902834	+	0.429988i	$0.858518\pi$
$150$		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	$0.337870\pi$
$152$	0.835020	+	3.11634i	0.0677291	+	0.252768i
$153$		0			0
$154$	0.00333555	−	0.00192578i	0.000268786	−	0.000155184i
$155$	−3.00413	−	11.7918i	−0.241297	−	0.947139i
$156$		0			0
$157$	−0.293204	−	0.136723i	−0.0234002	−	0.0109117i	0.410883	−	0.911688i	$-0.365220\pi$
$157$	−0.293204	−	0.136723i	−0.0234002	−	0.0109117i	−0.434283	+	0.900776i	$0.642998\pi$
$158$	9.41892	−	6.59520i	0.749329	−	0.524686i
$159$		0			0
$160$	−0.200481	+	16.2432i	−0.0158494	+	1.28413i
$161$			0.00330906i			0.000260790i
$162$		0			0
$163$	−3.86594	+	3.86594i	−0.302804	+	0.302804i	−0.842110	−	0.539306i	$-0.818687\pi$
$163$	−3.86594	+	3.86594i	−0.302804	+	0.302804i	0.539306	+	0.842110i	$0.318687\pi$
$164$	25.5384	−	21.4292i	1.99421	−	1.67334i
$165$		0			0
$166$	6.11500	−	34.6799i	0.474616	−	2.69168i
$167$	7.78235	−	16.6893i	0.602217	−	1.29146i	−0.334838	−	0.942276i	$-0.608682\pi$
$167$	7.78235	−	16.6893i	0.602217	−	1.29146i	0.937055	−	0.349182i	$-0.113541\pi$
$168$		0			0
$169$	−2.85412	+	0.503259i	−0.219548	+	0.0387122i
$170$	−27.7046	+	18.8937i	−2.12484	+	1.44908i
$171$		0			0
$172$	23.8136	−	6.38085i	1.81577	−	0.486535i
$173$	−1.25855	−	2.69896i	−0.0956855	−	0.205198i	0.852639	−	0.522501i	$-0.175001\pi$
$173$	−1.25855	−	2.69896i	−0.0956855	−	0.205198i	−0.948324	+	0.317302i	$0.897223\pi$
$174$		0			0
$175$	0.000760571		0.00314725i	5.74937e−5		0.000237910i
$176$	2.84428	−	3.38968i	0.214395	−	0.255506i
$177$		0			0
$178$	−11.9332	+	5.56454i	−0.894431	+	0.417080i
$179$	8.26245	−	14.3110i	0.617564	−	1.06965i	−0.372365	−	0.928087i	$-0.621453\pi$
$179$	8.26245	−	14.3110i	0.617564	−	1.06965i	0.989929	−	0.141566i	$-0.0452138\pi$
$180$		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	$0.716817\pi$
$182$	0.00370692	+	0.00259561i	0.000274775	+	0.000192400i
$183$		0			0
$184$	−3.20550	−	8.80705i	−0.236313	−	0.649264i
$185$	−0.453971	+	0.371477i	−0.0333766	+	0.0273115i
$186$		0			0
$187$	18.3810	+	1.60813i	1.34415	+	0.117598i
$188$	−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
$193$	10.1567	+	14.5052i	0.731093	+	1.04411i	0.996791	+	0.0800524i	$0.0255088\pi$
$193$	10.1567	+	14.5052i	0.731093	+	1.04411i	−0.265698	+	0.964056i	$0.585602\pi$
$194$	−17.3883	+	6.32881i	−1.24840	+	0.454382i
$195$		0			0
$196$	−3.44506	−	19.5379i	−0.246076	−	1.39557i
$197$	16.4067	+	4.39615i	1.16893	+	0.313213i	0.790526	−	0.612429i	$-0.209807\pi$
$197$	16.4067	+	4.39615i	1.16893	+	0.313213i	0.378401	+	0.925642i	$0.376474\pi$
$198$		0			0
$199$	−9.13371	−	5.27335i	−0.647472	−	0.373818i	0.140015	−	0.990149i	$-0.455285\pi$
$199$	−9.13371	−	5.27335i	−0.647472	−	0.373818i	−0.787487	+	0.616331i	$0.788618\pi$
$200$	−5.07302	−	7.63963i	−0.358717	−	0.540204i
$201$		0			0
$202$	−2.20532	−	25.2069i	−0.155166	−	1.77355i
$203$	−0.000322495	−	0.00368613i	−2.26347e−5	−	0.000258716i
$204$		0			0
$205$	7.12059	−	25.3202i	0.497324	−	1.76844i
$206$	13.0576	+	7.53880i	0.909765	+	0.525253i
$207$		0			0
$208$	5.02181	+	1.34559i	0.348200	+	0.0932999i
$209$	−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	$0.386918\pi$
$212$	−13.1912	−	18.8390i	−0.905978	−	1.29387i
$213$		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
$218$	8.18815	+	0.716371i	0.554572	+	0.0485187i
$219$		0			0
$220$	−1.70482	+	17.0586i	−0.114939	+	1.15009i
$221$	7.41460	+	20.3715i	0.498760	+	1.37033i
$222$		0			0
$223$	−15.0996	−	10.5728i	−1.01114	−	0.708010i	−0.0542728	−	0.998526i	$-0.517284\pi$
$223$	−15.0996	−	10.5728i	−1.01114	−	0.708010i	−0.956870	+	0.290516i	$0.906173\pi$
$224$	0.00235221	+	0.00407414i	0.000157163	+	0.000272215i
$225$		0			0
$226$	1.22863	−	2.12804i	0.0817271	−	0.141555i
$227$	14.1883	−	6.61613i	0.941713	−	0.439128i	0.109750	−	0.993959i	$-0.464995\pi$
$227$	14.1883	−	6.61613i	0.941713	−	0.439128i	0.831963	+	0.554831i	$0.187217\pi$
$228$		0			0
$229$	−4.54463	+	5.41608i	−0.300318	+	0.357904i	−0.895008	−	0.446050i	$-0.852830\pi$
$229$	−4.54463	+	5.41608i	−0.300318	+	0.357904i	0.594690	+	0.803955i	$0.297275\pi$
$230$	−20.3998	−	14.6626i	−1.34513	−	0.966825i
$231$		0			0
$232$	4.42910	+	9.49823i	0.290785	+	0.623590i
$233$	−2.20921	+	0.591957i	−0.144730	+	0.0387804i	−0.330457	−	0.943821i	$-0.607203\pi$
$233$	−2.20921	+	0.591957i	−0.144730	+	0.0387804i	0.185726	+	0.982601i	$0.440536\pi$
$234$		0			0
$235$	−1.54645	−	0.292404i	−0.100879	−	0.0190744i
$236$	6.27313	−	1.10612i	0.408346	−	0.0720024i
$237$		0			0
$238$	−0.00410424	+	0.00880157i	−0.000266038	+	0.000570521i
$239$	1.33675	−	7.58107i	0.0864670	−	0.490379i	−0.910563	−	0.413369i	$-0.864352\pi$
$239$	1.33675	−	7.58107i	0.0864670	−	0.490379i	0.997030	−	0.0770092i	$-0.0245371\pi$
$240$		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
$245$	−10.9305	−	11.2037i	−0.698326	−	0.715780i
$246$		0			0
$247$	4.57972	−	3.20676i	0.291401	−	0.204041i
$248$	9.04592	+	4.21818i	0.574416	+	0.267855i
$249$		0			0
$250$	−22.7725	−	9.25685i	−1.44026	−	0.585454i
$251$	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
$253$	3.57769	+	13.3521i	0.224927	+	0.839440i
$254$	21.5852	+	7.85635i	1.35437	+	0.492951i
$255$		0			0
$256$	−3.10423	−	2.60476i	−0.194015	−	0.162798i
$257$	12.0332	−	1.05277i	0.750612	−	0.0656701i	0.294572	−	0.955629i	$-0.404823\pi$
$257$	12.0332	−	1.05277i	0.750612	−	0.0656701i	0.456040	+	0.889959i	$0.349267\pi$
$258$		0			0
$259$	−5.81013e−5	0	0.000159632i	−3.61024e−6	0	9.91906e-6i
$260$	−19.0114	+	6.65503i	−1.17904	+	0.412728i
$261$		0			0
$262$	−8.28485	+	30.9195i	−0.511840	+	1.91021i
$263$	4.91225	−	7.01542i	0.302902	−	0.432589i	−0.638629	−	0.769515i	$-0.720498\pi$
$263$	4.91225	−	7.01542i	0.302902	−	0.432589i	0.941531	+	0.336926i	$0.109387\pi$
$264$		0			0
$265$	−16.9726	−	6.41581i	−1.04262	−	0.394120i
$266$	0.00246646		0.000434903i	0.000151228		2.66656e-5i
$267$		0			0
$268$	0.612870	−	7.00513i	0.0374370	−	0.427907i
$269$	−17.3406			−1.05728			−0.528638	−	0.848847i	$-0.677297\pi$
$269$	−17.3406			−1.05728			−0.528638	+	0.848847i	$0.677297\pi$
$270$		0			0
$271$	−11.8573			−0.720278			−0.360139	−	0.932899i	$-0.617271\pi$
$271$	−11.8573			−0.720278			−0.360139	+	0.932899i	$0.617271\pi$
$272$	−0.972407	+	11.1147i	−0.0589609	+	0.673926i
$273$		0			0
$274$	−15.8320	−	2.79161i	−0.956446	−	0.168647i
$275$	6.47166	+	11.8769i	0.390256	+	0.716204i
$276$		0			0
$277$	11.4745	−	16.3872i	0.689433	−	0.984613i	−0.309993	−	0.950739i	$-0.600327\pi$
$277$	11.4745	−	16.3872i	0.689433	−	0.984613i	0.999426	−	0.0338740i	$-0.0107845\pi$
$278$	1.73690	−	6.48220i	0.104172	−	0.388776i
$279$		0			0
$280$	−0.00239295	−	0.00115202i	−0.000143006	−	6.88462e-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
$283$	14.9700	−	1.30970i	0.889873	−	0.0778538i	0.366957	−	0.930238i	$-0.380400\pi$
$283$	14.9700	−	1.30970i	0.889873	−	0.0778538i	0.522916	+	0.852384i	$0.324844\pi$
$284$	−26.1518	−	21.9440i	−1.55182	−	1.30213i
$285$		0			0
$286$	17.7638	+	6.46550i	1.05040	+	0.382313i
$287$	−0.00197148	−	0.00735767i	−0.000116373	−	0.000434310i
$288$		0			0
$289$	−25.5680	+	14.7617i	−1.50400	+	0.868336i
$290$	24.1534	+	14.3453i	1.41834	+	0.842387i
$291$		0			0
$292$	−3.72573	−	1.73734i	−0.218032	−	0.101670i
$293$	−18.4726	+	12.9347i	−1.07918	+	0.755651i	−0.971144	−	0.238495i	$-0.923346\pi$
$293$	−18.4726	+	12.9347i	−1.07918	+	0.755651i	−0.108038	+	0.994147i	$0.534457\pi$
$294$		0			0
$295$	3.59723	−	3.50951i	0.209439	−	0.204332i
$296$		−	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
$302$	−17.2827	+	37.0629i	−0.994510	+	2.13273i
$303$		0			0
$304$	2.83362	−	0.499644i	0.162519	−	0.0286566i
$305$	8.29512	+	12.1634i	0.474977	+	0.696477i
$306$		0			0
$307$	4.88220	−	1.30818i	0.278642	−	0.0746619i	−0.116792	−	0.993156i	$-0.537261\pi$
$307$	4.88220	−	1.30818i	0.278642	−	0.0746619i	0.395434	+	0.918495i	$0.370594\pi$
$308$	0.00209822	+	0.00449965i	0.000119557	+	0.000256392i
$309$		0			0
$310$	26.4034	−	4.32034i	1.49961	−	0.245379i
$311$	−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
$313$	−24.5912	+	11.4671i	−1.38998	+	0.648157i	−0.966244	−	0.257629i	$-0.917059\pi$
$313$	−24.5912	+	11.4671i	−1.38998	+	0.648157i	−0.423734	+	0.905787i	$0.639281\pi$
$314$	0.355652	−	0.616007i	0.0200706	−	0.0347633i
$315$		0			0
$316$	7.41094	+	12.8361i	0.416898	+	0.722089i
$317$	−0.204479	−	0.143177i	−0.0114847	−	0.00804165i	0.567820	−	0.823153i	$-0.307787\pi$
$317$	−0.204479	−	0.143177i	−0.0114847	−	0.00804165i	−0.579305	+	0.815111i	$0.696676\pi$
$318$		0			0
$319$	−5.28664	−	14.5249i	−0.295995	−	0.813240i
$320$	−28.2602	−	2.82429i	−1.57979	−	0.157883i
$321$		0			0
$322$	−0.00724787		0.000634107i	−0.000403908		3.53374e-5i
$323$	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
$328$	12.3745	+	17.6726i	0.683268	+	0.975808i
$329$	−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	$0.902978\pi$
$332$	43.8467	+	11.7487i	2.40640	+	0.644794i
$333$		0			0
$334$	35.0635	+	20.2439i	1.91859	+	1.10770i
$335$	−2.71444	−	4.83849i	−0.148306	−	0.264355i
$336$		0			0
$337$	0.943046	+	10.7791i	0.0513710	+	0.587173i	0.977637	+	0.210302i	$0.0674446\pi$
$337$	0.943046	+	10.7791i	0.0513710	+	0.587173i	−0.926266	+	0.376872i	$0.877000\pi$
$338$	−0.555366	−	6.34786i	−0.0302079	−	0.345278i
$339$		0			0
$340$	−21.1496	−	37.6991i	−1.14700	−	2.04452i
$341$	−12.7488	−	7.36051i	−0.690385	−	0.398594i
$342$		0			0
$343$	−0.00875706	−	0.00234645i	−0.000472837	−	0.000126696i
$344$	2.77045	+	15.7120i	0.149373	+	0.847134i
$345$		0			0
$346$	6.15274	−	2.23942i	0.330774	−	0.120392i
$347$	−13.7981	−	19.7058i	−0.740723	−	1.05786i	−0.995855	−	0.0909561i	$-0.971008\pi$
$347$	−13.7981	−	19.7058i	−0.740723	−	1.05786i	0.255132	−	0.966906i	$-0.417881\pi$
$348$		0			0
$349$	−0.752338	−	0.896601i	−0.0402717	−	0.0479940i	0.745533	−	0.666469i	$-0.232195\pi$
$349$	−0.752338	−	0.896601i	−0.0402717	−	0.0479940i	−0.785804	+	0.618475i	$0.787751\pi$
$350$	−0.00703921	+	0.00106279i	−0.000376262	+	5.68084e-5i
$351$		0			0
$352$	13.8961	+	13.8961i	0.740662	+	0.740662i
$353$	20.1919	+	1.76656i	1.07470	+	0.0940245i	0.610741	−	0.791830i	$-0.290871\pi$
$353$	20.1919	+	1.76656i	1.07470	+	0.0940245i	0.463963	+	0.885855i	$0.346427\pi$
$354$		0			0
$355$	−26.8007	−	2.67843i	−1.42243	−	0.142157i
$356$	−5.80497	−	15.9490i	−0.307663	−	0.845296i
$357$		0			0
$358$	29.7622	+	20.8397i	1.57298	+	1.10141i
$359$	−13.1082	−	22.7040i	−0.691823	−	1.19827i	−0.971240	−	0.238102i	$-0.923475\pi$
$359$	−13.1082	−	22.7040i	−0.691823	−	1.19827i	0.279418	−	0.960170i	$-0.409859\pi$
$360$		0			0
$361$	−7.95290	+	13.7748i	−0.418574	+	0.724991i
$362$	−19.1911	+	8.94895i	−1.00866	+	0.470347i
$363$		0			0
$364$	−0.00374959	+	0.00446858i	−0.000196532	+	0.000234217i
$365$	−3.20077	+	0.523737i	−0.167536	+	0.0274136i
$366$		0			0
$367$	−8.86817	−	19.0178i	−0.462914	−	0.992723i	−0.989757	−	0.142761i	$-0.954402\pi$
$367$	−8.86817	−	19.0178i	−0.462914	−	0.992723i	0.526843	−	0.849963i	$-0.323376\pi$
$368$	−8.07380	+	2.16337i	−0.420876	+	0.112773i
$369$		0			0
$370$	−0.726657	−	1.06552i	−0.0377771	−	0.0553940i
$371$	−0.00517492		0.000912477i	−0.000268668		4.73735e-5i
$372$		0			0
$373$	−0.710169	+	1.52296i	−0.0367712	+	0.0788560i	−0.923835	−	0.382790i	$-0.874963\pi$
$373$	−0.710169	+	1.52296i	−0.0367712	+	0.0788560i	0.887064	+	0.461646i	$0.152741\pi$
$374$	−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	$-0.903159\pi$
$379$		−	11.6637i		−	0.599126i	0.954077	−	0.299563i	$-0.0968408\pi$
$380$	−7.97935	+	7.78478i	−0.409332	+	0.399351i
$381$		0			0
$382$	2.23383	−	1.56415i	0.114293	−	0.0800286i
$383$	−9.54105	−	4.44907i	−0.487525	−	0.227337i	0.163283	−	0.986579i	$-0.447792\pi$
$383$	−9.54105	−	4.44907i	−0.487525	−	0.227337i	−0.650808	+	0.759243i	$0.725570\pi$
$384$		0			0
$385$	0.00336784	+	0.00200024i	0.000171641	+	0.000101942i
$386$	−33.7173	+	19.4667i	−1.71616	+	0.990828i
$387$		0			0
$388$	−6.17353	−	23.0399i	−0.313414	−	1.16968i
$389$	36.8621	+	13.4167i	1.86898	+	0.680254i	0.970427	+	0.241396i	$0.0776054\pi$
$389$	36.8621	+	13.4167i	1.86898	+	0.680254i	0.898557	+	0.438858i	$0.144617\pi$
$390$		0			0
$391$	−26.6998	−	22.4038i	−1.35027	−	1.13301i
$392$	12.7900	−	1.11898i	0.645990	−	0.0565168i
$393$		0			0
$394$	−12.7729	+	35.0933i	−0.643491	+	1.76798i
$395$	10.5365	+	5.07248i	0.530148	+	0.255224i
$396$		0			0
$397$	2.69699	−	10.0653i	0.135358	−	0.505162i	−0.864638	−	0.502395i	$-0.832452\pi$
$397$	2.69699	−	10.0653i	0.135358	−	0.505162i	0.999996	−	0.00276748i	$-0.000880917\pi$
$398$	13.3006	−	18.9952i	0.666697	−	0.952141i
$399$		0			0
$400$	−7.18177	+	3.91331i	−0.359088	+	0.195665i
$401$	−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
$403$	1.50746	−	17.2304i	0.0750921	−	0.858306i
$404$	32.6169			1.62275
$405$		0			0
$406$	0.00813559			0.000403762
$407$	−0.0618489	+	0.706936i	−0.00306574	+	0.0350415i
$408$		0			0
$409$	33.6400	+	5.93165i	1.66339	+	0.293301i	0.924687	−	0.380727i	$-0.124326\pi$
$409$	33.6400	+	5.93165i	1.66339	+	0.293301i	0.738705	+	0.674028i	$0.235438\pi$
$410$	54.0947	+	20.4484i	2.67154	+	1.00987i
$411$		0			0
$412$	−11.1478	+	15.9208i	−0.549214	+	0.784359i
$413$	0.000376692	−	0.00140583i	1.85358e−5	−	6.91766e-5i
$414$		0			0
$415$	33.8025	−	11.8327i	1.65930	−	0.580847i
$416$	−7.89716	+	21.6973i	−0.387190	+	1.06380i
$417$		0			0
$418$	10.4224	−	0.911843i	0.509777	−	0.0445997i
$419$	12.2431	+	10.2731i	0.598112	+	0.501876i	0.890838	−	0.454321i	$-0.150118\pi$
$419$	12.2431	+	10.2731i	0.598112	+	0.501876i	−0.292726	+	0.956196i	$0.594562\pi$
$420$		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	$0.328219\pi$
$422$	0.102345	+	0.381956i	0.00498206	+	0.0185933i
$423$		0			0
$424$	12.8891	−	7.44152i	0.625950	−	0.361392i
$425$	−30.5436	−	15.1715i	−1.48158	−	0.735924i
$426$		0			0
$427$	0.00386425	+	0.00180193i	0.000187004	+	8.72015e-5i
$428$	31.7675	−	22.2438i	1.53554	−	1.07520i
$429$		0			0
$430$	29.8647	+	30.6111i	1.44020	+	1.47620i
$431$		−	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	−0.868179	−	0.496251i	$-0.834710\pi$
$433$	−7.73933	+	7.73933i	−0.371929	+	0.371929i	0.496251	+	0.868179i	$0.334710\pi$
$434$	0.00593543	−	0.00498042i	0.000284910	−	0.000239068i
$435$		0			0
$436$	−1.83984	+	10.4342i	−0.0881122	+	0.499709i
$437$	−3.79875	+	8.14644i	−0.181719	+	0.389697i
$438$		0			0
$439$	28.6483	−	5.05146i	1.36731	−	0.241093i	0.558665	−	0.829394i	$-0.311314\pi$
$439$	28.6483	−	5.05146i	1.36731	−	0.241093i	0.808642	+	0.588300i	$0.200203\pi$
$440$	−10.9011	−	2.06120i	−0.519691	−	0.0982637i
$441$		0			0
$442$	−46.0407	+	12.3366i	−2.18993	+	0.586791i
$443$	11.4725	+	24.6030i	0.545077	+	1.16892i	0.965214	+	0.261461i	$0.0842043\pi$
$443$	11.4725	+	24.6030i	0.545077	+	1.16892i	−0.420137	+	0.907461i	$0.638018\pi$
$444$		0			0
$445$	−10.8734	−	7.81540i	−0.515449	−	0.370485i
$446$	26.0513	−	31.0468i	1.23357	−	1.47011i
$447$		0			0
$448$	−0.00745435	+	0.00347602i	−0.000352185	+	0.000164227i
$449$	−1.73698	+	3.00854i	−0.0819733	+	0.141982i	−0.904097	−	0.427326i	$-0.859456\pi$
$449$	−1.73698	+	3.00854i	−0.0819733	+	0.141982i	0.822124	+	0.569308i	$0.192789\pi$
$450$		0			0
$451$	−15.9099	−	27.5568i	−0.749169	−	1.29760i
$452$	2.59467	+	1.81681i	0.122043	+	0.0854554i
$453$		0			0
$454$	11.7725	+	32.3447i	0.552511	+	1.51801i
$455$	−0.000457667		0.00457946i	−2.14557e−5		0.000214688i
$456$		0			0
$457$	−23.5029	−	2.05624i	−1.09942	−	0.0961868i	−0.477025	−	0.878890i	$-0.658285\pi$
$457$	−23.5029	−	2.05624i	−1.09942	−	0.0961868i	−0.622395	+	0.782703i	$0.713840\pi$
$458$	−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
$463$	−1.35473	−	1.93475i	−0.0629594	−	0.0899154i	0.786438	−	0.617670i	$-0.211923\pi$
$463$	−1.35473	−	1.93475i	−0.0629594	−	0.0899154i	−0.849397	+	0.527754i	$0.823034\pi$
$464$	8.78299	−	3.19675i	0.407740	−	0.148405i
$465$		0			0
$466$	−0.873225	−	4.95230i	−0.0404514	−	0.229411i
$467$	−19.8687	−	5.32380i	−0.919414	−	0.246356i	−0.232079	−	0.972697i	$-0.574553\pi$
$467$	−19.8687	−	5.32380i	−0.919414	−	0.246356i	−0.687335	+	0.726341i	$0.741220\pi$
$468$		0			0
$469$	−0.00139143		0.000803341i	−6.42501e−5		3.70948e-5i
$470$	0.936800	−	3.33118i	0.0432114	−	0.153656i
$471$		0			0
$472$	0.359274	+	4.10653i	0.0165369	+	0.189018i
$473$	−2.05087	−	23.4415i	−0.0942989	−	1.07784i
$474$		0			0
$475$	−1.74058	+	8.62122i	−0.0798632	+	0.395569i
$476$	−0.0108413	−	0.00625924i	−0.000496911	−	0.000286892i
$477$		0			0
$478$	16.3488	+	4.38064i	0.747775	+	0.200366i
$479$	3.74161	+	21.2197i	0.170958	+	0.969553i	0.942706	+	0.333624i	$0.108272\pi$
$479$	3.74161	+	21.2197i	0.170958	+	0.969553i	−0.771748	+	0.635929i	$0.780617\pi$
$480$		0			0
$481$	−0.783491	+	0.285167i	−0.0357241	+	0.0130025i
$482$	−12.1026	−	17.2843i	−0.551257	−	0.787277i
$483$		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	0.755221	−	0.655470i	$-0.227529\pi$
$487$	2.20133	+	2.20133i	0.0997518	+	0.0997518i	−0.655470	+	0.755221i	$0.727529\pi$
$488$	−12.0302	−	1.05251i	−0.544583	−	0.0476449i
$489$		0			0
$490$	26.6342	−	21.7943i	1.20321	−	0.984568i
$491$	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
$493$	31.9257	+	22.3546i	1.43786	+	1.00680i
$494$	6.14620	+	10.6455i	0.276530	+	0.478965i
$495$		0			0
$496$	4.45078	−	7.70898i	0.199846	−	0.346144i
$497$	−0.00706937	+	0.00329650i	−0.000317105	+	0.000147868i
$498$		0			0
$499$	−16.9583	+	20.2101i	−0.759156	+	0.904727i	−0.997794	−	0.0663815i	$-0.978855\pi$
$499$	−16.9583	+	20.2101i	−0.759156	+	0.904727i	0.238638	+	0.971109i	$0.423299\pi$
$500$	14.4455	−	28.2030i	0.646022	−	1.26127i
$501$		0			0
$502$	4.40968	+	9.45659i	0.196814	+	0.422068i
$503$	−7.51109	+	2.01259i	−0.334903	+	0.0897370i	−0.422352	−	0.906432i	$-0.638795\pi$
$503$	−7.51109	+	2.01259i	−0.334903	+	0.0897370i	0.0874487	+	0.996169i	$0.472129\pi$
$504$		0			0
$505$	21.2602	−	14.4988i	0.946066	−	0.645190i
$506$	−29.9309	+	5.27762i	−1.33059	+	0.234619i
$507$		0			0
$508$	−12.5137	+	26.8357i	−0.555204	+	1.19064i
$509$	−5.25087	+	29.7791i	−0.232741	+	1.31994i	0.614580	+	0.788855i	$0.289326\pi$
$509$	−5.25087	+	29.7791i	−0.232741	+	1.31994i	−0.847320	+	0.531082i	$0.821785\pi$
$510$		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
$515$	−0.189245	+	15.3328i	−0.00833913	+	0.675645i
$516$		0			0
$517$	−1.55967	+	1.09209i	−0.0685940	+	0.0480300i
$518$	−0.000338510	0	0.000157850i	−1.48733e−5	0	6.93553e-6i
$519$		0			0
$520$	−3.21807	−	12.6316i	−0.141122	−	0.553930i
$521$	−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
$523$	−3.41584	−	12.7481i	−0.149364	−	0.557436i	−0.999522	−	0.0309077i	$-0.990160\pi$
$523$	−3.41584	−	12.7481i	−0.149364	−	0.557436i	0.850158	−	0.526528i	$-0.176506\pi$
$524$	−38.7741	−	14.1126i	−1.69385	−	0.616512i
$525$		0			0
$526$	14.4246	+	12.1037i	0.628944	+	0.527747i
$527$	36.9769	−	3.23506i	1.61074	−	0.140921i
$528$		0			0
$529$	1.06428	−	2.92409i	0.0462731	−	0.127134i
$530$	17.3051	−	35.9458i	0.751683	−	1.56138i
$531$		0			0
$532$	−0.000835576		0.00311841i	−3.62268e−5		0.000135200i
$533$	21.4438	−	30.6249i	0.928834	−	1.32651i
$534$		0			0
$535$	10.8187	−	28.6201i	0.467734	−	1.23736i
$536$	4.48148	+	0.790206i	0.193570	+	0.0341317i
$537$		0			0
$538$	3.32294	−	37.9814i	0.143262	−	1.63749i
$539$	−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	$0.579102\pi$
$542$	2.27218	−	25.9711i	0.0975985	−	1.11556i
$543$		0			0
$544$	−48.7984	−	8.60448i	−2.09222	−	0.368914i
$545$	3.43898	+	7.61904i	0.147310	+	0.326364i
$546$		0			0
$547$	−18.3834	+	26.2542i	−0.786018	+	1.12255i	0.203632	+	0.979048i	$0.434726\pi$
$547$	−18.3834	+	26.2542i	−0.786018	+	1.12255i	−0.989650	+	0.143503i	$0.954163\pi$
$548$	5.36349	−	20.0168i	0.229117	−	0.855076i
$549$		0			0
$550$	−27.2543	+	11.8990i	−1.16213	+	0.507376i
$551$	3.43769	−	9.44496i	0.146450	−	0.402369i
$552$		0			0
$553$	0.00337369		0.000295160i	0.000143464		1.25515e-5i
$554$	33.6943	+	28.2729i	1.43153	+	1.20120i
$555$		0			0
$556$	8.12889	+	2.95868i	0.344742	+	0.125476i
$557$	7.68893	+	28.6955i	0.325791	+	1.21587i	0.913515	+	0.406806i	$0.133357\pi$
$557$	7.68893	+	28.6955i	0.325791	+	1.21587i	−0.587724	+	0.809061i	$0.699976\pi$
$558$		0			0
$559$	23.9433	−	13.8237i	1.01269	−	0.584679i
$560$	−0.00120951	+	0.00203648i	−5.11113e−5	+	8.60569e-5i
$561$		0			0
$562$	15.5017	+	7.22858i	0.653902	+	0.304919i
$563$	−4.91264	+	3.43987i	−0.207043	+	0.144973i	−0.672499	−	0.740098i	$-0.734779\pi$
$563$	−4.91264	+	3.43987i	−0.207043	+	0.144973i	0.465456	+	0.885071i	$0.345890\pi$
$564$		0			0
$565$	2.49885	+	0.0308420i	0.105127	+	0.00129753i
$566$			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	−0.795040	−	0.606557i	$-0.792550\pi$
$569$	−8.00903	+	6.72037i	−0.335756	+	0.281733i	0.459284	+	0.888289i	$0.348106\pi$
$570$		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	$0.978595\pi$
$572$	−10.2983	+	22.0848i	−0.430594	+	0.923411i
$573$		0			0
$574$	0.0164934	−	0.00290823i	0.000688421	−	0.000121387i
$575$	2.85434	−	25.3899i	0.119034	−	1.05883i
$576$		0			0
$577$	−44.1170	+	11.8211i	−1.83662	+	0.492120i	−0.998569	−	0.0534774i	$-0.982969\pi$
$577$	−44.1170	+	11.8211i	−1.83662	+	0.492120i	−0.838047	+	0.545597i	$0.816303\pi$
$578$	−27.4332	−	58.8308i	−1.14107	−	2.44704i
$579$		0			0
$580$	−21.1349	+	29.4047i	−0.877581	+	1.22096i
$581$	0.00666682	−	0.00794521i	0.000276586	−	0.000329623i
$582$		0			0
$583$	−19.8943	+	9.27687i	−0.823938	+	0.384209i
$584$	1.33016	−	2.30390i	0.0550424	−	0.0953362i
$585$		0			0
$586$	−24.7911	−	42.9394i	−1.02411	−	1.77381i
$587$	−22.7446	−	15.9259i	−0.938770	−	0.657334i	0.000687603	−	1.00000i	$-0.499781\pi$
$587$	−22.7446	−	15.9259i	−0.938770	−	0.657334i	−0.939457	+	0.342666i	$0.888670\pi$
$588$		0			0
$589$	−3.27398	−	8.99519i	−0.134902	−	0.370640i
$590$	6.99760	+	8.55157i	0.288087	+	0.352063i
$591$		0			0
$592$	−0.427473	−	0.0373990i	−0.0175690	−	0.00153709i
$593$	12.5526	+	12.5526i	0.515474	+	0.515474i	0.916199	−	0.400725i	$-0.131242\pi$
$593$	12.5526	+	12.5526i	0.515474	+	0.515474i	−0.400725	+	0.916199i	$0.631242\pi$
$594$		0			0
$595$	−0.00984889		0.000739308i	−0.000403765		3.03087e-5i
$596$	18.4671	+	22.0082i	0.756441	+	0.901491i
$597$		0			0
$598$	−20.4820	−	29.2513i	−0.837570	−	1.19617i
$599$	9.47392	−	3.44823i	0.387094	−	0.140891i	−0.141140	−	0.989990i	$-0.545077\pi$
$599$	9.47392	−	3.44823i	0.387094	−	0.140891i	0.528234	+	0.849099i	$0.322854\pi$
$600$		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	$0.981059\pi$
$602$	0.0119631	+	0.00320552i	0.000487581	+	0.000130647i
$603$		0			0
$604$	−45.6522	−	26.3573i	−1.85756	−	1.07246i
$605$	−7.92636	−	2.22906i	−0.322252	−	0.0906243i
$606$		0			0
$607$	1.06222	+	12.1412i	0.0431140	+	0.492796i	0.986799	+	0.161950i	$0.0517784\pi$
$607$	1.06222	+	12.1412i	0.0431140	+	0.492796i	−0.943685	+	0.330846i	$0.892666\pi$
$608$	1.11375	+	12.7303i	0.0451686	+	0.516280i
$609$		0			0
$610$	−28.2313	+	15.8381i	−1.14305	+	0.641264i
$611$	−1.93736	−	1.11853i	−0.0783771	−	0.0452511i
$612$		0			0
$613$	−21.2470	−	5.69311i	−0.858157	−	0.229942i	−0.197197	−	0.980364i	$-0.563184\pi$
$613$	−21.2470	−	5.69311i	−0.858157	−	0.229942i	−0.660960	+	0.750422i	$0.729851\pi$
$614$	1.92976	+	10.9442i	0.0778789	+	0.441673i
$615$		0			0
$616$	−0.00301917	+	0.00109889i	−0.000121646	+	4.42754e-5i
$617$	4.11472	+	5.87642i	0.165652	+	0.236576i	0.893393	−	0.449277i	$-0.148318\pi$
$617$	4.11472	+	5.87642i	0.165652	+	0.236576i	−0.727740	+	0.685853i	$0.759429\pi$
$618$		0			0
$619$	0.611202	+	0.728403i	0.0245663	+	0.0292770i	0.778188	−	0.628032i	$-0.216139\pi$
$619$	0.611202	+	0.728403i	0.0245663	+	0.0292770i	−0.753621	+	0.657309i	$0.771695\pi$
$620$	2.58156	+	34.3909i	0.103678	+	1.38117i
$621$		0			0
$622$	−30.6554	−	30.6554i	−1.22917	−	1.22917i
$623$	−0.00386323		0.000337988i	−0.000154777		1.35412e-5i
$624$		0			0
$625$	−3.12097	−	24.8044i	−0.124839	−	0.992177i
$626$	−20.4041	−	56.0599i	−0.815513	−	2.24060i
$627$		0			0
$628$	0.751081	+	0.525913i	0.0299714	+	0.0209862i
$629$	−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	$0.891923\pi$
$632$	−8.69315	+	4.05368i	−0.345795	+	0.161247i
$633$		0			0
$634$	0.352787	−	0.420435i	0.0140110	−	0.0166976i
$635$	3.77236	+	23.0545i	0.149702	+	0.914888i
$636$		0			0
$637$	−9.40257	−	20.1639i	−0.372543	−	0.798922i
$638$	32.8272	−	8.79602i	1.29964	−	0.348238i
$639$		0			0
$640$	5.56545	−	29.4342i	0.219994	−	1.16349i
$641$	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
$643$	18.7461	−	40.2010i	0.739272	−	1.58537i	−0.0697279	−	0.997566i	$-0.522213\pi$
$643$	18.7461	−	40.2010i	0.739272	−	1.58537i	0.809000	−	0.587808i	$-0.200009\pi$
$644$	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	$-0.709561\pi$
$647$	4.55768	−	4.55768i	0.179181	−	0.179181i	0.790999	+	0.611818i	$0.209561\pi$
$648$		0			0
$649$		−	6.07983i		−	0.238654i
$650$	−26.2037	−	23.1133i	−1.02779	−	0.906577i
$651$		0			0
$652$	12.6930	−	8.88773i	0.497096	−	0.348070i
$653$	−6.12762	−	2.85735i	−0.239792	−	0.111817i	0.299008	−	0.954251i	$-0.403344\pi$
$653$	−6.12762	−	2.85735i	−0.239792	−	0.111817i	−0.538800	+	0.842434i	$0.681122\pi$
$654$		0			0
$655$	−31.5469	+	8.03701i	−1.23264	+	0.314032i
$656$	16.6632	−	9.62047i	0.650587	−	0.375616i
$657$		0			0
$658$	−0.000259372	0	0.000967991i	−1.01114e−5	0	3.77362e-5i
$659$	−29.5176	−	10.7435i	−1.14984	−	0.418508i	−0.304383	−	0.952550i	$-0.598450\pi$
$659$	−29.5176	−	10.7435i	−1.14984	−	0.418508i	−0.845458	+	0.534042i	$0.820673\pi$
$660$		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	$0.826648\pi$
$662$	−10.3530	+	0.905769i	−0.402380	+	0.0352037i
$663$		0			0
$664$	−10.0472	+	27.6043i	−0.389905	+	1.07126i
$665$	0.000841553		0.00240406i	3.26340e−5		9.32254e-5i
$666$		0			0
$667$	−7.55709	+	28.2034i	−0.292612	+	1.09204i
$668$	−29.9353	+	42.7520i	−1.15823	+	1.65412i
$669$		0			0
$670$	11.1180	−	5.01828i	0.429524	−	0.193873i
$671$	17.5405	+	3.09287i	0.677144	+	0.119399i
$672$		0			0
$673$	0.682431	−	7.80022i	0.0263058	−	0.300676i	−0.971633	−	0.236496i	$-0.924001\pi$
$673$	0.682431	−	7.80022i	0.0263058	−	0.300676i	0.997938	−	0.0641806i	$-0.0204434\pi$
$674$	−23.7902			−0.916366
$675$		0			0
$676$	8.21392			0.315920
$677$	2.64043	−	30.1802i	0.101480	−	1.15992i	−0.759229	−	0.650823i	$-0.774424\pi$
$677$	2.64043	−	30.1802i	0.101480	−	1.15992i	0.860709	−	0.509097i	$-0.170021\pi$
$678$		0			0
$679$	−0.00536718		0.000946379i	−0.000205974		3.63187e-5i
$680$	25.4966	−	11.5083i	0.977751	−	0.441325i
$681$		0			0
$682$	18.5648	−	26.5133i	0.710885	−	1.01525i
$683$	−8.05741	+	30.0707i	−0.308308	+	1.15062i	0.621752	+	0.783214i	$0.286421\pi$
$683$	−8.05741	+	30.0707i	−0.308308	+	1.15062i	−0.930060	+	0.367408i	$0.880245\pi$
$684$		0			0
$685$	−5.40186	−	15.4314i	−0.206394	−	0.589605i
$686$	0.00681755	−	0.0187311i	0.000260295	−	0.000715155i
$687$		0			0
$688$	14.1747	−	1.24013i	0.540405	−	0.0472793i
$689$	−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	$0.567781\pi$
$692$	2.18447	+	8.15256i	0.0830411	+	0.309914i
$693$		0			0
$694$	45.8059	−	26.4461i	1.73877	−	1.00388i
$695$	6.61373	−	1.68494i	0.250873	−	0.0639135i
$696$		0			0
$697$	72.7146	+	33.9074i	2.75426	+	1.28433i
$698$	2.10801	−	1.47604i	0.0797892	−	0.0558690i
$699$		0			0
$700$	−0.000573927	−	0.00915871i	−2.16924e−5	−	0.000346167i
$701$		−	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
$707$	0.00314955	−	0.00675423i	0.000118451	−	0.000254019i
$708$		0			0
$709$	20.6080	−	3.63375i	0.773951	−	0.136469i	0.227296	−	0.973826i	$-0.427012\pi$
$709$	20.6080	−	3.63375i	0.773951	−	0.136469i	0.546656	+	0.837357i	$0.315901\pi$
$710$	11.0024	−	58.1886i	0.412911	−	2.18378i
$711$		0			0
$712$	10.6094	−	2.84277i	0.397603	−	0.106537i
$713$	11.7521	+	25.2025i	0.440121	+	0.943842i
$714$		0			0
$715$	3.10452	+	18.9730i	0.116102	+	0.709550i
$716$	−30.1048	+	35.8774i	−1.12507	+	1.34080i
$717$		0			0
$718$	52.2408	−	24.3603i	1.94961	−	0.909117i
$719$	4.36807	−	7.56572i	0.162902	−	0.282154i	−0.773007	−	0.634398i	$-0.781248\pi$
$719$	4.36807	−	7.56572i	0.162902	−	0.282154i	0.935908	+	0.352244i	$0.114581\pi$
$720$		0			0
$721$	0.00222038	+	0.00384581i	8.26912e−5	+	0.000143225i
$722$	−28.6472	−	20.0590i	−1.06614	−	0.746518i
$723$		0			0
$724$	−9.33561	−	25.6494i	−0.346955	−	0.953252i
$725$	−0.705142	+	28.5613i	−0.0261883	+	1.06074i
$726$		0			0
$727$	44.6377	+	3.90529i	1.65552	+	0.144839i	0.876253	−	0.481851i	$-0.160035\pi$
$727$	44.6377	+	3.90529i	1.65552	+	0.144839i	0.779268	+	0.626690i	$0.215591\pi$
$728$	−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
$733$	12.9159	+	18.4458i	0.477060	+	0.681312i	0.983489	−	0.180970i	$-0.0579237\pi$
$733$	12.9159	+	18.4458i	0.477060	+	0.681312i	−0.506429	+	0.862282i	$0.669035\pi$
$734$	43.3544	−	15.7797i	1.60024	−	0.582440i
$735$		0			0
$736$	−6.44625	−	36.5585i	−0.237612	−	1.34756i
$737$	−6.48298	−	1.73711i	−0.238804	−	0.0639873i
$738$		0			0
$739$	29.3820	+	16.9637i	1.08084	+	0.624020i	0.931122	−	0.364709i	$-0.118832\pi$
$739$	29.3820	+	16.9637i	1.08084	+	0.624020i	0.149714	+	0.988729i	$0.452165\pi$
$740$	1.44992	−	0.813418i	0.0533000	−	0.0299018i
$741$		0			0
$742$	−0.00100695	−	0.0115095i	−3.69664e−5	−	0.000422528i
$743$	2.22992	+	25.4881i	0.0818078	+	0.935068i	0.920572	+	0.390573i	$0.127723\pi$
$743$	2.22992	+	25.4881i	0.0818078	+	0.935068i	−0.838764	+	0.544495i	$0.816721\pi$
$744$		0			0
$745$	21.8202	+	6.13631i	0.799430	+	0.224817i
$746$	−3.19968	−	1.84733i	−0.117148	−	0.0676357i
$747$		0			0
$748$	−50.5122	−	13.5347i	−1.84691	−	0.494878i
$749$	−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	$0.504629\pi$
$752$	−0.660369	−	0.943105i	−0.0240812	−	0.0343915i
$753$		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	0.877215	+	0.480097i	$0.159399\pi$
$757$	37.3446	+	37.3446i	1.35731	+	1.35731i	0.480097	+	0.877215i	$0.340601\pi$
$758$	25.5472	+	2.23509i	0.927917	+	0.0811822i
$759$		0			0
$760$	−4.56862	−	5.58318i	−0.165721	−	0.202523i
$761$	−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
$763$	0.00198304	+	0.00138854i	7.17908e−5	+	5.02685e-5i
$764$	1.75761	+	3.04427i	0.0635881	+	0.110138i
$765$		0			0
$766$	11.5732	−	20.0453i	0.418156	−	0.724267i
$767$	6.47410	−	3.01892i	0.233766	−	0.109007i
$768$		0			0
$769$	−1.03060	+	1.22823i	−0.0371646	+	0.0442910i	−0.784307	−	0.620373i	$-0.786981\pi$
$769$	−1.03060	+	1.22823i	−0.0371646	+	0.0442910i	0.747142	+	0.664664i	$0.231425\pi$
$770$	−0.00502653	+	0.00699332i	−0.000181144	+	0.000252022i
$771$		0			0
$772$	−21.2098	−	45.4846i	−0.763358	−	1.63703i
$773$	32.5784	−	8.72934i	1.17176	−	0.313973i	0.380108	−	0.924942i	$-0.375887\pi$
$773$	32.5784	−	8.72934i	1.17176	−	0.313973i	0.791654	+	0.610970i	$0.209220\pi$
$774$		0			0
$775$	16.9701	+	21.2690i	0.609585	+	0.764005i
$776$	15.2015	−	2.68044i	0.545702	−	0.0962220i
$777$		0			0
$778$	−36.4506	+	78.1685i	−1.30682	+	2.80248i
$779$	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
$785$	0.723345	+	0.00892787i	0.0258173	+	0.000318649i
$786$		0			0
$787$	1.89659	−	1.32801i	0.0676063	−	0.0473384i	−0.539285	−	0.842123i	$-0.681305\pi$
$787$	1.89659	−	1.32801i	0.0676063	−	0.0473384i	0.606891	+	0.794785i	$0.292416\pi$
$788$	−43.6296	−	20.3448i	−1.55424	−	0.724754i
$789$		0			0
$790$	−13.1294	+	22.1062i	−0.467123	+	0.786502i
$791$	0.000626766	0	0.000361864i	2.22852e−5	0	1.28664e-5i
$792$		0			0
$793$	5.41626	+	20.2138i	0.192337	+	0.717812i
$794$	21.5293	+	7.83603i	0.764047	+	0.278090i
$795$		0			0
$796$	22.8981	+	19.2138i	0.811602	+	0.681015i
$797$	−16.5943	+	1.45181i	−0.587801	+	0.0514259i	−0.377177	−	0.926141i	$-0.623105\pi$
$797$	−16.5943	+	1.45181i	−0.587801	+	0.0514259i	−0.210624	+	0.977567i	$0.567550\pi$
$798$		0			0
$799$	1.64198	−	4.51129i	0.0580889	−	0.159598i
$800$	−14.5338	−	33.2892i	−0.513848	−	1.17695i
$801$		0			0
$802$	15.2204	−	56.8031i	0.537449	−	2.00579i
$803$	−2.25054	+	3.21410i	−0.0794197	+	0.113423i
$804$		0			0
$805$	−0.00304407	−	0.00674411i	−0.000107289	−	0.000237699i
$806$	37.4510	+	6.60363i	1.31916	+	0.232603i
$807$		0			0
$808$	−1.83965	+	21.0273i	−0.0647188	+	0.739739i
$809$	38.2899			1.34620			0.673100	−	0.739551i	$-0.264962\pi$
$809$	38.2899			1.34620			0.673100	+	0.739551i	$0.264962\pi$
$810$		0			0
$811$	48.1974			1.69244			0.846220	−	0.532833i	$-0.178873\pi$
$811$	48.1974			1.69244			0.846220	+	0.532833i	$0.178873\pi$
$812$	−0.000914012		0.0104472i	−3.20755e−5		0.000366625i
$813$		0			0
$814$	−1.53656	−	0.270937i	−0.0538564	−	0.00949633i
$815$	4.32272	−	11.4354i	0.151418	−	0.400566i
$816$		0			0
$817$	8.77644	−	12.5341i	0.307049	−	0.438511i
$818$	−19.4385	+	72.5455i	−0.679652	+	2.53649i
$819$		0			0
$820$	−32.3359	+	67.1676i	−1.12922	+	2.34560i
$821$	−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
$823$	−34.4725	+	3.01595i	−1.20164	+	0.105130i	−0.670338	−	0.742056i	$-0.733851\pi$
$823$	−34.4725	+	3.01595i	−1.20164	+	0.105130i	−0.531298	+	0.847185i	$0.678295\pi$
$824$	−9.63498	−	8.08471i	−0.335651	−	0.281644i
$825$		0			0
$826$	0.00300703	+	0.00109447i	0.000104628	+	3.80815e-5i
$827$	−5.23409	−	19.5339i	−0.182007	−	0.679261i	−0.995251	−	0.0973378i	$-0.968967\pi$
$827$	−5.23409	−	19.5339i	−0.182007	−	0.679261i	0.813244	−	0.581923i	$-0.197699\pi$
$828$		0			0
$829$	−45.7476	+	26.4124i	−1.58888	+	0.917340i	−0.595387	+	0.803439i	$0.703001\pi$
$829$	−45.7476	+	26.4124i	−1.58888	+	0.917340i	−0.993492	+	0.113900i	$0.963666\pi$
$830$	19.4399	+	76.3055i	0.674769	+	2.64860i
$831$		0			0
$832$	−36.5867	−	17.0607i	−1.26842	−	0.591473i
$833$	39.1110	−	27.3858i	1.35511	−	0.948861i
$834$		0			0
$835$	−0.508179	+	41.1732i	−0.0175863	+	1.42486i
$836$			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	−0.675665	−	0.737209i	$-0.736143\pi$
$839$	−1.94021	+	1.62803i	−0.0669835	+	0.0562059i	0.608681	+	0.793415i	$0.291699\pi$
$840$		0			0
$841$	0.633784	−	3.59437i	0.0218546	−	0.123944i
$842$	−29.6003	+	63.4780i	−1.02009	+	2.18760i
$843$		0			0
$844$	−0.501982	+	0.0885129i	−0.0172789	+	0.00304674i
$845$	5.35396	−	3.65125i	0.184182	−	0.125607i
$846$		0			0
$847$	−0.00230328		0.000617162i	−7.91417e−5		2.12059e-5i
$848$	−5.60957	−	12.0298i	−0.192634	−	0.413104i
$849$		0			0
$850$	39.0832	−	63.9928i	1.34054	−	2.19493i
$851$	0.861655	−	1.02688i	0.0295371	−	0.0352010i
$852$		0			0
$853$	37.8798	−	17.6637i	1.29698	−	0.604792i	0.353257	−	0.935526i	$-0.385074\pi$
$853$	37.8798	−	17.6637i	1.29698	−	0.604792i	0.943724	+	0.330734i	$0.107296\pi$
$854$	−0.00468729	+	0.00811862i	−0.000160396	+	0.000277813i
$855$		0			0
$856$	12.5483	+	21.7343i	0.428893	+	0.742864i
$857$	21.9778	+	15.3891i	0.750749	+	0.525680i	0.885183	−	0.465242i	$-0.154033\pi$
$857$	21.9778	+	15.3891i	0.750749	+	0.525680i	−0.134434	+	0.990923i	$0.542922\pi$
$858$		0			0
$859$	−7.80591	−	21.4466i	−0.266334	−	0.731747i	−0.998707	−	0.0508429i	$-0.983809\pi$
$859$	−7.80591	−	21.4466i	−0.266334	−	0.731747i	0.732372	−	0.680904i	$-0.238413\pi$
$860$	−42.6641	+	34.9113i	−1.45483	+	1.19047i
$861$		0			0
$862$	13.0034	+	1.13765i	0.442896	+	0.0387484i
$863$	−7.93097	−	7.93097i	−0.269973	−	0.269973i	0.559116	−	0.829089i	$-0.311141\pi$
$863$	−7.93097	−	7.93097i	−0.269973	−	0.269973i	−0.829089	+	0.559116i	$0.811141\pi$
$864$		0			0
$865$	5.04784	+	4.34292i	0.171632	+	0.147664i
$866$	−15.4685	−	18.4346i	−0.525641	−	0.626434i
$867$		0			0
$868$	0.00572871	+	0.00818145i	0.000194445	+	0.000277696i
$869$	13.2938	−	4.83854i	0.450961	−	0.164136i
$870$		0			0
$871$	−1.36935	−	7.76596i	−0.0463986	−	0.263139i
$872$	−6.62293	−	1.77461i	−0.224281	−	0.0600959i
$873$		0			0
$874$	−17.1153	−	9.88153i	−0.578934	−	0.334248i
$875$	−0.00444532	−	0.00571467i	−0.000150279	−	0.000193191i
$876$		0			0
$877$	0.0855499	+	0.977840i	0.00288882	+	0.0330193i	0.997502	−	0.0706341i	$-0.0225023\pi$
$877$	0.0855499	+	0.977840i	0.00288882	+	0.0330193i	−0.994613	+	0.103653i	$0.966947\pi$
$878$	5.57448	+	63.7167i	0.188130	+	2.15033i
$879$		0			0
$880$	−2.67861	+	9.52492i	−0.0902961	+	0.321085i
$881$	−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
$883$	46.3611	+	12.4224i	1.56018	+	0.418048i	0.932719	−	0.360604i	$-0.117429\pi$
$883$	46.3611	+	12.4224i	1.56018	+	0.418048i	0.627457	+	0.778652i	$0.284096\pi$
$884$	−10.6693	−	60.5085i	−0.358847	−	2.03512i
$885$		0			0
$886$	−56.0866	+	20.4139i	−1.88427	+	0.685817i
$887$	3.82768	+	5.46649i	0.128521	+	0.183547i	0.878255	−	0.478192i	$-0.158708\pi$
$887$	3.82768	+	5.46649i	0.128521	+	0.183547i	−0.749734	+	0.661739i	$0.769819\pi$
$888$		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
$893$	−1.23338	−	0.107907i	−0.0412735	−	0.00361097i
$894$		0			0
$895$	−3.67452	+	36.7676i	−0.122826	+	1.22901i
$896$	−0.00296711	−	0.00815206i	−9.91241e−5	−	0.000272341i
$897$		0			0
$898$	−6.25679	−	4.38105i	−0.208792	−	0.146198i
$899$	−15.5475	−	26.9291i	−0.518538	−	0.898134i
$900$		0			0
$901$	27.6739	−	47.9327i	0.921953	−	1.59687i
$902$	63.4068	−	29.5671i	2.11121	−	0.984476i
$903$		0			0
$904$	−1.31760	+	1.57025i	−0.0438226	+	0.0522258i
$905$	−17.4867	−	12.5688i	−0.581279	−	0.417801i
$906$		0			0
$907$	0.500360	+	1.07303i	0.0166142	+	0.0356292i	0.914440	−	0.404722i	$-0.132632\pi$
$907$	0.500360	+	1.07303i	0.0166142	+	0.0356292i	−0.897826	+	0.440351i	$0.854854\pi$
$908$	−42.8576	+	11.4837i	−1.42228	+	0.381099i
$909$		0			0
$910$	−0.00994274	−	0.00187998i	−0.000329599	−	6.23208e-5i
$911$	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
$913$	18.3105	−	39.2670i	0.605990	−	1.29955i
$914$	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	$-0.886110\pi$
$919$		−	21.2332i		−	0.700419i	0.936671	−	0.350209i	$-0.113890\pi$
$920$	14.6348	+	15.0006i	0.482496	+	0.494556i
$921$		0			0
$922$	14.4200	−	10.0970i	0.474899	−	0.332528i
$923$	−34.6972	−	16.1796i	−1.14207	−	0.532557i
$924$		0			0
$925$	0.583498	−	1.17471i	0.0191853	−	0.0386244i
$926$	4.49731	−	2.59652i	0.147791	−	0.0853270i
$927$		0			0
$928$	10.7437	+	40.0962i	0.352680	+	1.31622i
$929$	−28.3403	−	10.3150i	−0.929816	−	0.338425i	−0.167679	−	0.985842i	$-0.553627\pi$
$929$	−28.3403	−	10.3150i	−0.929816	−	0.338425i	−0.762136	+	0.647416i	$0.775850\pi$
$930$		0			0
$931$	−9.43249	−	7.91479i	−0.309137	−	0.259397i
$932$	6.45754	−	0.564962i	0.211524	−	0.0185059i
$933$		0			0
$934$	15.4682	−	42.4985i	0.506135	−	1.39059i
$935$	−38.9411	+	13.6315i	−1.27351	+	0.445799i
$936$		0			0
$937$	−4.43173	+	16.5394i	−0.144778	+	0.540320i	0.854987	+	0.518650i	$0.173565\pi$
$937$	−4.43173	+	16.5394i	−0.144778	+	0.540320i	−0.999765	+	0.0216704i	$0.993102\pi$
$938$	0.00202620	−	0.00289372i	6.61579e−5	−	9.44832e-5i
$939$		0			0
$940$	4.17244	+	1.57723i	0.136090	+	0.0514435i
$941$	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
$943$	−5.23871	+	59.8787i	−0.170596	+	1.94992i
$944$	3.67638			0.119656
$945$		0			0
$946$	51.7372			1.68212
$947$	−2.48308	+	28.3818i	−0.0806894	+	0.922284i	0.842691	+	0.538398i	$0.180970\pi$
$947$	−2.48308	+	28.3818i	−0.0806894	+	0.922284i	−0.923380	+	0.383886i	$0.874585\pi$
$948$		0			0
$949$	−4.54003	−	0.800530i	−0.147376	−	0.0259863i
$950$	−18.5496	−	5.46447i	−0.601829	−	0.177291i
$951$		0			0
$952$	0.00464666	−	0.00663611i	0.000150599	−	0.000215078i
$953$	−13.1177	+	48.9558i	−0.424923	+	1.58583i	0.339169	+	0.940726i	$0.389854\pi$
$953$	−13.1177	+	48.9558i	−0.424923	+	1.58583i	−0.764091	+	0.645108i	$0.776812\pi$
$954$		0			0
$955$	2.49888	+	1.20301i	0.0808617	+	0.0389285i
$956$	−7.46208	+	20.5019i	−0.241341	+	0.663078i
$957$		0			0
$958$	−47.1948	+	4.12901i	−1.52479	+	0.133402i
$959$	−0.00362713	−	0.00304352i	−0.000117126	−	9.82804e-5i
$960$		0			0
$961$	1.30221	+	0.473965i	0.0420067	+	0.0152892i
$962$	−0.474467	−	1.77074i	−0.0152974	−	0.0570908i
$963$		0			0
$964$	23.5551	−	13.5995i	0.758657	−	0.438011i
$965$	−34.0437	−	20.2194i	−1.09591	−	0.650885i
$966$		0			0
$967$	−48.1057	−	22.4321i	−1.54697	−	0.721366i	−0.553229	−	0.833029i	$-0.686604\pi$
$967$	−48.1057	−	22.4321i	−1.54697	−	0.721366i	−0.993746	+	0.111663i	$0.964382\pi$
$968$	5.53233	−	3.87378i	0.177816	−	0.124508i
$969$		0			0
$970$	29.6166	−	28.8944i	0.950931	−	0.927743i
$971$		−	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
$977$	−7.99244	+	17.1398i	−0.255701	+	0.548352i	−0.991691	−	0.128639i	$-0.958939\pi$
$977$	−7.99244	+	17.1398i	−0.255701	+	0.548352i	0.735991	+	0.676992i	$0.236717\pi$
$978$		0			0
$979$	−15.9536	+	2.81305i	−0.509879	+	0.0899055i
$980$	24.9946	+	36.6506i	0.798424	+	1.17076i
$981$		0			0
$982$	−17.5085	+	4.69139i	−0.558719	+	0.149708i
$983$	5.63921	+	12.0933i	0.179863	+	0.385717i	0.975482	−	0.220080i	$-0.0706319\pi$
$983$	5.63921	+	12.0933i	0.179863	+	0.385717i	−0.795619	+	0.605798i	$0.792854\pi$
$984$		0			0
$985$	−37.4821	+	6.13314i	−1.19428	+	0.195418i
$986$	−55.0815	+	65.6436i	−1.75415	+	2.09052i
$987$		0			0
$988$	−14.3608	+	6.69656i	−0.456878	+	0.213046i
$989$	−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	$0.863687\pi$
$992$	32.3842	+	22.6757i	1.02820	+	0.719953i
$993$		0			0
$994$	−0.00586569	−	0.0161158i	−0.000186048	−	0.000511163i
$995$	23.4662	+	2.34519i	0.743930	+	0.0743476i
$996$		0			0
$997$	−45.5235	−	3.98279i	−1.44174	−	0.126136i	−0.660718	−	0.750634i	$-0.729748\pi$
$997$	−45.5235	−	3.98279i	−1.44174	−	0.126136i	−0.781026	+	0.624498i	$0.785304\pi$
$998$	−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.287.3		192
3.2	odd	2		135.2.q.a.32.14	✓	192
5.3	odd	4	inner	405.2.r.a.368.14		192
15.2	even	4		675.2.ba.b.518.14		192
15.8	even	4		135.2.q.a.113.3	yes	192
15.14	odd	2		675.2.ba.b.32.3		192
27.11	odd	18	inner	405.2.r.a.197.14		192
27.16	even	9		135.2.q.a.92.3	yes	192
135.38	even	36	inner	405.2.r.a.278.3		192
135.43	odd	36		135.2.q.a.38.14	yes	192
135.97	odd	36		675.2.ba.b.443.3		192
135.124	even	18		675.2.ba.b.632.14		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.14	✓	192	3.2	odd	2
135.2.q.a.38.14	yes	192	135.43	odd	36
135.2.q.a.92.3	yes	192	27.16	even	9
135.2.q.a.113.3	yes	192	15.8	even	4
405.2.r.a.197.14		192	27.11	odd	18	inner
405.2.r.a.278.3		192	135.38	even	36	inner
405.2.r.a.287.3		192	1.1	even	1	trivial
405.2.r.a.368.14		192	5.3	odd	4	inner
675.2.ba.b.32.3		192	15.14	odd	2
675.2.ba.b.443.3		192	135.97	odd	36
675.2.ba.b.518.14		192	15.2	even	4
675.2.ba.b.632.14		192	135.124	even	18

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)

\(f(q)\)	\(=\)	\(q+(-0.191628 + 2.19031i) q^{2} +(-2.79113 - 0.492152i) q^{4} +(-2.03807 + 0.919920i) q^{5} +(-0.000371431 + 0.000530458i) q^{7} +(0.474704 - 1.77162i) q^{8} +(-1.62436 - 4.64030i) q^{10} +(-0.925209 + 2.54199i) q^{11} +(-3.16625 + 0.277011i) q^{13} +(-0.00109069 - 0.000915200i) q^{14} +(-1.53710 - 0.559459i) q^{16} +(-1.76536 - 6.58840i) q^{17} +(-1.52337 + 0.879517i) q^{19} +(6.14128 - 1.56458i) q^{20} +(-5.39046 - 2.51361i) q^{22} +(4.18584 - 2.93096i) q^{23} +(3.30749 - 3.74973i) q^{25} -6.98815i q^{26} +(0.00129778 - 0.00129778i) q^{28} +(-4.37718 + 3.67289i) q^{29} +(-0.944975 + 5.35922i) q^{31} +(3.07020 - 6.58407i) q^{32} +(14.7689 - 2.60416i) q^{34} +(0.000269024 - 0.00142280i) q^{35} +(0.253391 - 0.0678960i) q^{37} +(-1.63450 - 3.50519i) q^{38} +(0.662267 + 4.04738i) q^{40} +(-7.56097 + 9.01082i) q^{41} +(-7.88368 + 3.67622i) q^{43} +(3.83342 - 6.63969i) q^{44} +(5.61759 + 9.72995i) q^{46} +(0.576559 + 0.403711i) q^{47} +(2.39414 + 6.57785i) q^{49} +(7.57928 + 7.96300i) q^{50} +(8.97374 + 0.785101i) q^{52} +(5.73786 + 5.73786i) q^{53} +(-0.452784 - 6.03188i) q^{55} +(0.000763450 + 0.000909845i) q^{56} +(-7.20599 - 10.2912i) q^{58} +(-2.11198 + 0.768697i) q^{59} +(-1.14333 - 6.48417i) q^{61} +(-11.5573 - 3.09676i) q^{62} +(10.9996 + 6.35064i) q^{64} +(6.19822 - 3.47726i) q^{65} +(0.216242 + 2.47165i) q^{67} +(1.68485 + 19.2579i) q^{68} +(0.00306482 + 0.000861895i) q^{70} +(10.4316 + 6.02267i) q^{71} +(1.40104 + 0.375408i) q^{73} +(0.100157 + 0.568017i) q^{74} +(4.68478 - 1.70512i) q^{76} +(-0.00100477 - 0.00143496i) q^{77} +(-3.36157 - 4.00616i) q^{79} +(3.64738 - 0.273791i) q^{80} +(-18.2876 - 18.2876i) q^{82} +(-15.9554 - 1.39592i) q^{83} +(9.65872 + 11.8037i) q^{85} +(-6.54134 - 17.9722i) q^{86} +(4.06424 + 2.84581i) q^{88} +(2.99426 + 5.18621i) q^{89} +(0.00102910 - 0.00178245i) q^{91} +(-13.1257 + 6.12062i) q^{92} +(-0.994737 + 1.18548i) q^{94} +(2.29565 - 3.19390i) q^{95} +(3.55678 + 7.62753i) q^{97} +(-14.8663 + 3.98342i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35}+ \cdots - 324 q^{98}+O(q^{100}) \) 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

Modular forms

Varieties

Fields

Representations

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Database

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