LMFDB - Embedded newform 405.2.r.a.197.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,2,Mod(8,405)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			197.14
Character	$\chi$	$=$	405.197
Dual form			405.2.r.a.368.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{13}{18}\right)$

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	0.719566	−	0.694425i	$-0.244341\pi$
$2$	2.19031	−	0.191628i	1.54878	−	0.135501i	0.829219	+	0.558923i	$0.188785\pi$
$3$		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	−0.573476	−	0.819222i	$-0.694405\pi$
$7$	0.000530458	0	0.000371431i	0.000200494	0	0.000140388i	0.573677	+	0.819082i	$0.305517\pi$
$8$	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	−0.997481	−	0.0709326i	$-0.977402\pi$
$11$	−0.925209	−	2.54199i	−0.278961	−	0.766439i	0.718520	−	0.695506i	$-0.244820\pi$
$12$		0			0
$13$	−0.277011	+	3.16625i	−0.0768289	+	0.878159i	0.855797	+	0.517313i	$0.173068\pi$
$13$	−0.277011	+	3.16625i	−0.0768289	+	0.878159i	−0.932625	+	0.360846i	$0.882488\pi$
$14$	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	−0.653507	−	0.756921i	$-0.726703\pi$
$17$	−6.58840	−	1.76536i	−1.59792	−	0.428162i	−0.944414	+	0.328759i	$0.893370\pi$
$18$		0			0
$19$	1.52337	+	0.879517i	0.349485	+	0.201775i	0.664458	−	0.747325i	$-0.268662\pi$
$19$	1.52337	+	0.879517i	0.349485	+	0.201775i	−0.314974	+	0.949100i	$0.601996\pi$
$20$	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	−0.387652	−	0.921806i	$-0.626714\pi$
$23$	2.93096	−	4.18584i	0.611147	−	0.872808i	0.998799	+	0.0489979i	$0.0156028\pi$
$24$		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	0.951279	−	0.308330i	$-0.0997701\pi$
$29$	4.37718	+	3.67289i	0.812822	+	0.682038i	−0.138458	+	0.990368i	$0.544215\pi$
$30$		0			0
$31$	−0.944975	−	5.35922i	−0.169723	−	0.962544i	−0.944061	−	0.329772i	$-0.893028\pi$
$31$	−0.944975	−	5.35922i	−0.169723	−	0.962544i	0.774338	−	0.632772i	$-0.218083\pi$
$32$	−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	−0.971282	−	0.237930i	$-0.923531\pi$
$37$	−0.0678960	+	0.253391i	−0.0111620	+	0.0416573i	0.960120	+	0.279587i	$0.0901977\pi$
$38$	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	−0.893289	−	0.449483i	$-0.851608\pi$
$41$	−7.56097	−	9.01082i	−1.18083	−	1.40725i	−0.287537	−	0.957770i	$-0.592836\pi$
$42$		0			0
$43$	−3.67622	+	7.88368i	−0.560618	+	1.20225i	0.397955	+	0.917405i	$0.369720\pi$
$43$	−3.67622	+	7.88368i	−0.560618	+	1.20225i	−0.958574	+	0.284845i	$0.908058\pi$
$44$	−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	0.847516	−	0.530770i	$-0.178097\pi$
$47$	0.403711	+	0.576559i	0.0588873	+	0.0840997i	−0.788628	+	0.614870i	$0.789208\pi$
$48$		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	0.193036	−	0.981192i	$-0.438167\pi$
$53$	−5.73786	−	5.73786i	−0.788156	−	0.788156i	−0.981192	+	0.193036i	$0.938167\pi$
$54$		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	0.475818	−	0.879544i	$-0.342152\pi$
$59$	2.11198	+	0.768697i	0.274956	+	0.100076i	−0.200862	+	0.979620i	$0.564374\pi$
$60$		0			0
$61$	−1.14333	+	6.48417i	−0.146389	+	0.830213i	0.819852	+	0.572575i	$0.194055\pi$
$61$	−1.14333	+	6.48417i	−0.146389	+	0.830213i	−0.966241	+	0.257638i	$0.917056\pi$
$62$	−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	0.237129	−	0.971478i	$-0.423794\pi$
$67$	2.47165	+	0.216242i	0.301960	+	0.0264181i	0.0648313	+	0.997896i	$0.479349\pi$
$68$	−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	0.269314	−	0.963052i	$-0.413203\pi$
$71$	10.4316	−	6.02267i	1.23800	−	0.714759i	0.968685	+	0.248294i	$0.0798698\pi$
$72$		0			0
$73$	−0.375408	−	1.40104i	−0.0439381	−	0.163979i	0.940471	−	0.339875i	$-0.110385\pi$
$73$	−0.375408	−	1.40104i	−0.0439381	−	0.163979i	−0.984409	+	0.175895i	$0.943718\pi$
$74$	−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	−0.543041	−	0.839706i	$-0.682727\pi$
$79$	3.36157	−	4.00616i	0.378206	−	0.450729i	0.921247	+	0.388978i	$0.127172\pi$
$80$	−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	0.551594	+	0.834113i	$0.314020\pi$
$83$	1.39592	+	15.9554i	0.153222	+	1.75134i	−0.398372	+	0.917224i	$0.630425\pi$
$84$		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	−0.979943	−	0.199279i	$-0.936140\pi$
$89$	−2.99426	+	5.18621i	−0.317391	+	0.549737i	0.662552	+	0.749016i	$0.269473\pi$
$90$		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	0.769331	−	0.638851i	$-0.220590\pi$
$97$	7.62753	+	3.55678i	0.774459	+	0.361136i	0.00512815	+	0.999987i	$0.498368\pi$
$98$	−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	−0.421496	−	0.906830i	$-0.638495\pi$
$101$	−11.3335	−	1.99841i	−1.12773	−	0.198849i	−0.706231	+	0.707981i	$0.749606\pi$
$102$		0			0
$103$	6.21507	−	2.89813i	0.612389	−	0.285562i	−0.0915740	−	0.995798i	$-0.529190\pi$
$103$	6.21507	−	2.89813i	0.612389	−	0.285562i	0.703963	+	0.710237i	$0.251412\pi$
$104$	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	−0.0626673	−	0.998034i	$-0.519961\pi$
$107$	9.67551	−	9.67551i	0.935367	−	0.935367i	0.998034	+	0.0626673i	$0.0199607\pi$
$108$		0			0
$109$		−	3.73835i		−	0.358069i	−0.983843	−	0.179034i	$-0.942703\pi$
$109$		−	3.73835i		−	0.358069i	0.983843	−	0.179034i	$-0.0572974\pi$
$110$	−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	0.927271	−	0.374391i	$-0.122148\pi$
$113$	0.472320	+	1.01289i	0.0444322	+	0.0952851i	−0.882839	+	0.469676i	$0.844371\pi$
$114$		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	−0.677068	−	0.735920i	$-0.736750\pi$
$127$	−10.0914	+	2.70398i	−0.895467	+	0.239940i	−0.218398	+	0.975860i	$0.570083\pi$
$128$	−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	0.492341	−	0.870402i	$-0.336141\pi$
$131$	14.3376	−	2.52811i	1.25269	−	0.220882i	0.760345	+	0.649520i	$0.225030\pi$
$132$		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	0.228359	−	0.973577i	$-0.426664\pi$
$137$	7.28394	−	0.637262i	0.622309	−	0.0544450i	0.393950	+	0.919132i	$0.371108\pi$
$138$		0			0
$139$	3.00586	−	0.530014i	0.254953	−	0.0449552i	−0.0447106	−	0.999000i	$-0.514237\pi$
$139$	3.00586	−	0.530014i	0.254953	−	0.0449552i	0.299664	+	0.954045i	$0.403125\pi$
$140$	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	−0.266680	−	0.963785i	$-0.585927\pi$
$149$	7.76525	−	6.51582i	0.636154	−	0.533797i	0.902834	+	0.429988i	$0.141482\pi$
$150$		0			0
$151$	17.4779	−	6.36142i	1.42233	−	0.517685i	0.487605	−	0.873064i	$-0.337870\pi$
$151$	17.4779	−	6.36142i	1.42233	−	0.517685i	0.934722	+	0.355379i	$0.115648\pi$
$152$	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	0.900776	−	0.434283i	$-0.142998\pi$
$157$	−0.136723	−	0.293204i	−0.0109117	−	0.0234002i	−0.911688	+	0.410883i	$0.865220\pi$
$158$	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	−0.842110	−	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
$167$	−16.6893	+	7.78235i	−1.29146	+	0.602217i	−0.942276	−	0.334838i	$-0.891318\pi$
$167$	−16.6893	+	7.78235i	−1.29146	+	0.602217i	−0.349182	+	0.937055i	$0.613541\pi$
$168$		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	0.522501	−	0.852639i	$-0.324999\pi$
$173$	2.69896	+	1.25855i	0.205198	+	0.0956855i	−0.317302	+	0.948324i	$0.602777\pi$
$174$		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	−0.989929	−	0.141566i	$-0.954786\pi$
$179$	−8.26245	−	14.3110i	−0.617564	−	1.06965i	0.372365	−	0.928087i	$-0.378547\pi$
$180$		0			0
$181$	4.81540	−	8.34051i	0.357926	−	0.619945i	−0.629688	−	0.776848i	$-0.716817\pi$
$181$	4.81540	−	8.34051i	0.357926	−	0.619945i	0.987614	+	0.156902i	$0.0501508\pi$
$182$	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	−0.794116	−	0.607766i	$-0.792066\pi$
$191$	−0.797244	+	0.950119i	−0.0576866	+	0.0687482i	0.736430	+	0.676514i	$0.236510\pi$
$192$		0			0
$193$	−14.5052	−	10.1567i	−1.04411	−	0.731093i	−0.0800524	−	0.996791i	$-0.525509\pi$
$193$	−14.5052	−	10.1567i	−1.04411	−	0.731093i	−0.964056	+	0.265698i	$0.914398\pi$
$194$	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	0.925642	+	0.378401i	$0.123526\pi$
$197$	4.39615	+	16.4067i	0.313213	+	1.16893i	−0.612429	+	0.790526i	$0.709807\pi$
$198$		0			0
$199$	9.13371	−	5.27335i	0.647472	−	0.373818i	−0.140015	−	0.990149i	$-0.544715\pi$
$199$	9.13371	−	5.27335i	0.647472	−	0.373818i	0.787487	+	0.616331i	$0.211382\pi$
$200$	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	0.347831	−	0.937557i	$-0.386918\pi$
$211$	0.169003	+	0.0615119i	0.0116346	+	0.00423465i	−0.336196	+	0.941792i	$0.609141\pi$
$212$	−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	0.998526	+	0.0542728i	$0.0172841\pi$
$223$	10.5728	+	15.0996i	0.708010	+	1.01114i	−0.290516	+	0.956870i	$0.593827\pi$
$224$	−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	0.554831	+	0.831963i	$0.312783\pi$
$227$	−6.61613	+	14.1883i	−0.439128	+	0.941713i	−0.993959	+	0.109750i	$0.964995\pi$
$228$		0			0
$229$	4.54463	+	5.41608i	0.300318	+	0.357904i	0.895008	−	0.446050i	$-0.147170\pi$
$229$	4.54463	+	5.41608i	0.300318	+	0.357904i	−0.594690	+	0.803955i	$0.702725\pi$
$230$	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	−0.982601	−	0.185726i	$-0.940536\pi$
$233$	−0.591957	+	2.20921i	−0.0387804	+	0.144730i	0.943821	+	0.330457i	$0.107203\pi$
$234$		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	−0.997030	−	0.0770092i	$-0.975463\pi$
$239$	−1.33675	−	7.58107i	−0.0864670	−	0.490379i	0.910563	−	0.413369i	$-0.135648\pi$
$240$		0			0
$241$	−7.35154	−	6.16868i	−0.473555	−	0.397359i	0.374535	−	0.927213i	$-0.377802\pi$
$241$	−7.35154	−	6.16868i	−0.473555	−	0.397359i	−0.848089	+	0.529853i	$0.822247\pi$
$242$	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	0.624067	−	0.781371i	$-0.285479\pi$
$251$	4.10987	+	2.37283i	0.259413	+	0.149772i	−0.364654	+	0.931143i	$0.618813\pi$
$252$		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	0.889959	+	0.456040i	$0.150733\pi$
$257$	−1.05277	+	12.0332i	−0.0656701	+	0.750612i	−0.955629	+	0.294572i	$0.904823\pi$
$258$		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	−0.336926	−	0.941531i	$-0.609387\pi$
$263$	7.01542	−	4.91225i	0.432589	−	0.302902i	0.769515	+	0.638629i	$0.220498\pi$
$264$		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	−0.950739	−	0.309993i	$-0.899673\pi$
$277$	−16.3872	+	11.4745i	−0.984613	+	0.689433i	−0.0338740	+	0.999426i	$0.510784\pi$
$278$	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	0.993407	−	0.114641i	$-0.0365716\pi$
$281$	2.66069	+	7.31019i	0.158724	+	0.436089i	−0.834683	+	0.550730i	$0.814349\pi$
$282$		0			0
$283$	1.30970	−	14.9700i	0.0778538	−	0.889873i	−0.852384	−	0.522916i	$-0.824844\pi$
$283$	1.30970	−	14.9700i	0.0778538	−	0.889873i	0.930238	−	0.366957i	$-0.119600\pi$
$284$	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	0.238495	+	0.971144i	$0.423346\pi$
$293$	−12.9347	+	18.4726i	−0.755651	+	1.07918i	−0.994147	+	0.108038i	$0.965543\pi$
$294$		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	−0.993156	−	0.116792i	$-0.962739\pi$
$307$	−1.30818	+	4.88220i	−0.0746619	+	0.278642i	0.918495	+	0.395434i	$0.129406\pi$
$308$	−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	0.275805	−	0.961214i	$-0.411056\pi$
$311$	−12.6744	−	15.1048i	−0.718699	−	0.856512i	−0.994504	+	0.104702i	$0.966611\pi$
$312$		0			0
$313$	−11.4671	+	24.5912i	−0.648157	+	1.38998i	0.257629	+	0.966244i	$0.417059\pi$
$313$	−11.4671	+	24.5912i	−0.648157	+	1.38998i	−0.905787	+	0.423734i	$0.860719\pi$
$314$	−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	0.815111	−	0.579305i	$-0.196676\pi$
$317$	−0.143177	−	0.204479i	−0.00804165	−	0.0114847i	−0.823153	+	0.567820i	$0.807787\pi$
$318$		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	−0.953906	−	0.300105i	$-0.902978\pi$
$331$	0.820786	−	4.65491i	0.0451145	−	0.255857i	0.999021	+	0.0442484i	$0.0140893\pi$
$332$	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	0.376872	−	0.926266i	$-0.377000\pi$
$337$	10.7791	+	0.943046i	0.587173	+	0.0513710i	0.210302	+	0.977637i	$0.432555\pi$
$338$	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	−0.0909561	−	0.995855i	$-0.528992\pi$
$347$	−19.7058	−	13.7981i	−1.05786	−	0.740723i	−0.966906	+	0.255132i	$0.917881\pi$
$348$		0			0
$349$	0.752338	−	0.896601i	0.0402717	−	0.0479940i	−0.745533	−	0.666469i	$-0.767805\pi$
$349$	0.752338	−	0.896601i	0.0402717	−	0.0479940i	0.785804	+	0.618475i	$0.212249\pi$
$350$	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	−0.885855	−	0.463963i	$-0.846427\pi$
$353$	−1.76656	−	20.1919i	−0.0940245	−	1.07470i	0.791830	−	0.610741i	$-0.209129\pi$
$354$		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	−0.279418	−	0.960170i	$-0.590141\pi$
$359$	13.1082	−	22.7040i	0.691823	−	1.19827i	0.971240	−	0.238102i	$-0.0765253\pi$
$360$		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	−0.142761	−	0.989757i	$-0.545598\pi$
$367$	−19.0178	−	8.86817i	−0.992723	−	0.462914i	−0.849963	+	0.526843i	$0.823376\pi$
$368$	−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	−0.461646	−	0.887064i	$-0.652741\pi$
$373$	−1.52296	+	0.710169i	−0.0788560	+	0.0367712i	0.382790	+	0.923835i	$0.374963\pi$
$374$	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	$-0.0968408\pi$
$380$	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	0.986579	−	0.163283i	$-0.0522082\pi$
$383$	4.44907	+	9.54105i	0.227337	+	0.487525i	−0.759243	+	0.650808i	$0.774430\pi$
$384$		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	−0.898557	+	0.438858i	$0.855383\pi$
$389$	−36.8621	+	13.4167i	−1.86898	+	0.680254i	−0.970427	+	0.241396i	$0.922395\pi$
$390$		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	−0.502395	−	0.864638i	$-0.667548\pi$
$397$	−10.0653	+	2.69699i	−0.505162	+	0.135358i	−0.00276748	+	0.999996i	$0.500881\pi$
$398$	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	−0.786931	−	0.617041i	$-0.788331\pi$
$401$	−26.3401	+	4.64448i	−1.31536	+	0.231934i	−0.528433	+	0.848975i	$0.677220\pi$
$402$		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	−0.924687	−	0.380727i	$-0.875674\pi$
$409$	−33.6400	+	5.93165i	−1.66339	+	0.293301i	−0.738705	+	0.674028i	$0.764562\pi$
$410$	−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	−0.890838	−	0.454321i	$-0.849882\pi$
$419$	−12.2431	+	10.2731i	−0.598112	+	0.501876i	0.292726	+	0.956196i	$0.405438\pi$
$420$		0			0
$421$	29.9345	−	10.8953i	1.45892	−	0.531002i	0.513850	−	0.857880i	$-0.328219\pi$
$421$	29.9345	−	10.8953i	1.45892	−	0.531002i	0.945067	+	0.326878i	$0.105997\pi$
$422$	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	$0.0456690\pi$
$431$			5.93676i			0.285963i	−0.989725	+	0.142982i	$0.954331\pi$
$432$		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
$437$	8.14644	−	3.79875i	0.389697	−	0.181719i
$438$		0			0
$439$	−28.6483	−	5.05146i	−1.36731	−	0.241093i	−0.558665	−	0.829394i	$-0.688686\pi$
$439$	−28.6483	−	5.05146i	−1.36731	−	0.241093i	−0.808642	+	0.588300i	$0.799797\pi$
$440$	−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	−0.261461	−	0.965214i	$-0.584204\pi$
$443$	−24.6030	−	11.4725i	−1.16892	−	0.545077i	−0.907461	+	0.420137i	$0.861982\pi$
$444$		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	0.904097	−	0.427326i	$-0.140544\pi$
$449$	1.73698	+	3.00854i	0.0819733	+	0.141982i	−0.822124	+	0.569308i	$0.807211\pi$
$450$		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	−0.878890	−	0.477025i	$-0.841715\pi$
$457$	−2.05624	−	23.5029i	−0.0961868	−	1.09942i	0.782703	−	0.622395i	$-0.213840\pi$
$458$	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	−0.872459	−	0.488688i	$-0.837476\pi$
$461$	−5.14645	+	6.13330i	−0.239694	+	0.285656i	0.632765	+	0.774344i	$0.281920\pi$
$462$		0			0
$463$	1.93475	+	1.35473i	0.0899154	+	0.0629594i	0.617670	−	0.786438i	$-0.288077\pi$
$463$	1.93475	+	1.35473i	0.0899154	+	0.0629594i	−0.527754	+	0.849397i	$0.676966\pi$
$464$	−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	−0.972697	−	0.232079i	$-0.925447\pi$
$467$	−5.32380	−	19.8687i	−0.246356	−	0.919414i	0.726341	−	0.687335i	$-0.241220\pi$
$468$		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	0.771748	+	0.635929i	$0.219383\pi$
$479$	−3.74161	+	21.2197i	−0.170958	+	0.969553i	−0.942706	+	0.333624i	$0.891728\pi$
$480$		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	0.755221	−	0.655470i	$-0.227529\pi$
$487$	2.20133	+	2.20133i	0.0997518	+	0.0997518i	−0.655470	+	0.755221i	$0.727529\pi$
$488$	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	−0.859666	−	0.510857i	$-0.829328\pi$
$491$	2.81965	−	7.74693i	0.127249	−	0.349614i	0.986915	+	0.161243i	$0.0515503\pi$
$492$		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	0.997794	−	0.0663815i	$-0.0211454\pi$
$499$	16.9583	+	20.2101i	0.759156	+	0.904727i	−0.238638	+	0.971109i	$0.576701\pi$
$500$	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	−0.996169	−	0.0874487i	$-0.972129\pi$
$503$	−2.01259	+	7.51109i	−0.0897370	+	0.334903i	0.906432	+	0.422352i	$0.138795\pi$
$504$		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	0.847320	+	0.531082i	$0.178215\pi$
$509$	5.25087	+	29.7791i	0.232741	+	1.31994i	−0.614580	+	0.788855i	$0.710674\pi$
$510$		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	0.445593	−	0.895236i	$-0.352993\pi$
$521$	−2.44020	−	1.40885i	−0.106907	−	0.0617227i	−0.552500	+	0.833513i	$0.686326\pi$
$522$		0			0
$523$	12.7481	+	3.41584i	0.557436	+	0.149364i	0.526528	−	0.850158i	$-0.323494\pi$
$523$	12.7481	+	3.41584i	0.557436	+	0.149364i	0.0309077	+	0.999522i	$0.490160\pi$
$524$	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	0.143503	−	0.989650i	$-0.454163\pi$
$547$	26.2542	−	18.3834i	1.12255	−	0.786018i	0.979048	+	0.203632i	$0.0652745\pi$
$548$	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	0.809061	−	0.587724i	$-0.199976\pi$
$557$	28.6955	+	7.68893i	1.21587	+	0.325791i	0.406806	+	0.913515i	$0.366643\pi$
$558$		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	−0.885071	−	0.465456i	$-0.845890\pi$
$563$	−3.43987	+	4.91264i	−0.144973	+	0.207043i	0.740098	+	0.672499i	$0.234779\pi$
$564$		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	0.795040	−	0.606557i	$-0.207450\pi$
$569$	8.00903	+	6.72037i	0.335756	+	0.281733i	−0.459284	+	0.888289i	$0.651894\pi$
$570$		0			0
$571$	−1.98699	−	11.2688i	−0.0831531	−	0.471584i	−0.997740	−	0.0671948i	$-0.978595\pi$
$571$	−1.98699	−	11.2688i	−0.0831531	−	0.471584i	0.914587	−	0.404390i	$-0.132516\pi$
$572$	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	−0.0534774	−	0.998569i	$-0.517031\pi$
$577$	11.8211	−	44.1170i	0.492120	−	1.83662i	0.545597	−	0.838047i	$-0.316303\pi$
$578$	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	0.342666	−	0.939457i	$-0.388670\pi$
$587$	−15.9259	−	22.7446i	−0.657334	−	0.938770i	−1.00000		0.000687603i	$0.999781\pi$
$588$		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	0.400725	−	0.916199i	$-0.368758\pi$
$593$	−12.5526	−	12.5526i	−0.515474	−	0.515474i	−0.916199	+	0.400725i	$0.868758\pi$
$594$		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	0.141140	−	0.989990i	$-0.454923\pi$
$599$	−9.47392	−	3.44823i	−0.387094	−	0.140891i	−0.528234	+	0.849099i	$0.677146\pi$
$600$		0			0
$601$	−0.977209	+	5.54203i	−0.0398612	+	0.226064i	−0.998230	−	0.0594686i	$-0.981059\pi$
$601$	−0.977209	+	5.54203i	−0.0398612	+	0.226064i	0.958369	+	0.285533i	$0.0921705\pi$
$602$	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	0.330846	−	0.943685i	$-0.392666\pi$
$607$	12.1412	+	1.06222i	0.492796	+	0.0431140i	0.161950	+	0.986799i	$0.448222\pi$
$608$	−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	0.980364	+	0.197197i	$0.0631839\pi$
$613$	5.69311	+	21.2470i	0.229942	+	0.858157i	−0.750422	+	0.660960i	$0.770149\pi$
$614$	−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	0.685853	−	0.727740i	$-0.259429\pi$
$617$	5.87642	+	4.11472i	0.236576	+	0.165652i	−0.449277	+	0.893393i	$0.648318\pi$
$618$		0			0
$619$	−0.611202	+	0.728403i	−0.0245663	+	0.0292770i	−0.778188	−	0.628032i	$-0.783861\pi$
$619$	−0.611202	+	0.728403i	−0.0245663	+	0.0292770i	0.753621	+	0.657309i	$0.228305\pi$
$620$	−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	−0.942910	−	0.333048i	$-0.891923\pi$
$631$	−19.0880	−	33.0615i	−0.759883	−	1.31616i	0.183027	−	0.983108i	$-0.441411\pi$
$632$	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	0.636168	−	0.771551i	$-0.280519\pi$
$641$	24.5606	+	4.33069i	0.970084	+	0.171052i	0.333916	+	0.942603i	$0.391630\pi$
$642$		0			0
$643$	40.2010	−	18.7461i	1.58537	−	0.739272i	0.587808	−	0.809000i	$-0.299991\pi$
$643$	40.2010	−	18.7461i	1.58537	−	0.739272i	0.997566	+	0.0697279i	$0.0222131\pi$
$644$	−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	−0.790999	−	0.611818i	$-0.790439\pi$
$647$	−4.55768	+	4.55768i	−0.179181	+	0.179181i	0.611818	+	0.790999i	$0.290439\pi$
$648$		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	0.954251	−	0.299008i	$-0.0966557\pi$
$653$	2.85735	+	6.12762i	0.111817	+	0.239792i	−0.842434	+	0.538800i	$0.818878\pi$
$654$		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	0.304383	−	0.952550i	$-0.401550\pi$
$659$	29.5176	−	10.7435i	1.14984	−	0.418508i	0.845458	+	0.534042i	$0.179327\pi$
$660$		0			0
$661$	−12.6918	+	10.6497i	−0.493654	+	0.414225i	−0.855334	−	0.518078i	$-0.826648\pi$
$661$	−12.6918	+	10.6497i	−0.493654	+	0.414225i	0.361680	+	0.932302i	$0.382203\pi$
$662$	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	0.0641806	−	0.997938i	$-0.479557\pi$
$673$	7.80022	−	0.682431i	0.300676	−	0.0263058i	0.236496	+	0.971633i	$0.424001\pi$
$674$	23.7902			0.916366
$675$		0			0
$676$	8.21392			0.315920
$677$	−30.1802	+	2.64043i	−1.15992	+	0.101480i	−0.650823	−	0.759229i	$-0.725576\pi$
$677$	−30.1802	+	2.64043i	−1.15992	+	0.101480i	−0.509097	+	0.860709i	$0.670021\pi$
$678$		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	−0.783214	−	0.621752i	$-0.786421\pi$
$683$	−30.0707	+	8.05741i	−1.15062	+	0.308308i	−0.367408	+	0.930060i	$0.619755\pi$
$684$		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	−0.211336	−	0.977414i	$-0.567781\pi$
$691$	6.70424	−	2.44014i	0.255041	−	0.0928274i	0.466377	+	0.884586i	$0.345559\pi$
$692$	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	$0.111186\pi$
$701$			18.1226i			0.684482i	−0.939612	+	0.342241i	$0.888814\pi$
$702$		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	−0.227296	−	0.973826i	$-0.572988\pi$
$709$	−20.6080	−	3.63375i	−0.773951	−	0.136469i	−0.546656	+	0.837357i	$0.684099\pi$
$710$	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	0.773007	−	0.634398i	$-0.218752\pi$
$719$	−4.36807	−	7.56572i	−0.162902	−	0.282154i	−0.935908	+	0.352244i	$0.885419\pi$
$720$		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	0.626690	+	0.779268i	$0.284409\pi$
$727$	3.90529	+	44.6377i	0.144839	+	1.65552i	−0.481851	+	0.876253i	$0.660035\pi$
$728$	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	0.180970	−	0.983489i	$-0.442076\pi$
$733$	−18.4458	−	12.9159i	−0.681312	−	0.477060i	−0.862282	+	0.506429i	$0.830965\pi$
$734$	−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	−0.931122	−	0.364709i	$-0.881168\pi$
$739$	−29.3820	+	16.9637i	−1.08084	+	0.624020i	−0.149714	+	0.988729i	$0.547835\pi$
$740$	−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	−0.390573	−	0.920572i	$-0.627723\pi$
$743$	−25.4881	−	2.22992i	−0.935068	−	0.0818078i	−0.544495	+	0.838764i	$0.683279\pi$
$744$		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	−0.0145411	−	0.999894i	$-0.504629\pi$
$751$	−18.3171	−	6.66687i	−0.668400	−	0.243278i	−0.653859	+	0.756617i	$0.726851\pi$
$752$	−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	0.877215	+	0.480097i	$0.159399\pi$
$757$	37.3446	+	37.3446i	1.35731	+	1.35731i	0.480097	+	0.877215i	$0.340601\pi$
$758$	−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	0.383750	+	0.923437i	$0.374632\pi$
$761$	−13.8978	+	38.1838i	−0.503793	+	1.38416i	−0.887543	+	0.460724i	$0.847590\pi$
$762$		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	0.784307	−	0.620373i	$-0.213019\pi$
$769$	1.03060	+	1.22823i	0.0371646	+	0.0442910i	−0.747142	+	0.664664i	$0.768575\pi$
$770$	−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	−0.610970	−	0.791654i	$-0.709220\pi$
$773$	8.72934	−	32.5784i	0.313973	−	1.17176i	0.924942	−	0.380108i	$-0.124113\pi$
$774$		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	−0.842123	−	0.539285i	$-0.818695\pi$
$787$	−1.32801	+	1.89659i	−0.0473384	+	0.0676063i	0.794785	+	0.606891i	$0.207584\pi$
$788$	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	−0.926141	−	0.377177i	$-0.876895\pi$
$797$	1.45181	−	16.5943i	0.0514259	−	0.587801i	0.977567	−	0.210624i	$-0.0675495\pi$
$798$		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	0.798390	−	0.602141i	$-0.205685\pi$
$821$	−5.73809	−	15.7653i	−0.200261	−	0.550212i	−0.998651	+	0.0519288i	$0.983463\pi$
$822$		0			0
$823$	−3.01595	+	34.4725i	−0.105130	+	1.20164i	0.742056	+	0.670338i	$0.233851\pi$
$823$	−3.01595	+	34.4725i	−0.105130	+	1.20164i	−0.847185	+	0.531298i	$0.821705\pi$
$824$	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	−0.0973378	−	0.995251i	$-0.531033\pi$
$827$	−19.5339	−	5.23409i	−0.679261	−	0.182007i	−0.581923	+	0.813244i	$0.697699\pi$
$828$		0			0
$829$	45.7476	+	26.4124i	1.58888	+	0.917340i	0.993492	+	0.113900i	$0.0363344\pi$
$829$	45.7476	+	26.4124i	1.58888	+	0.917340i	0.595387	+	0.803439i	$0.296999\pi$
$830$	−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	0.675665	−	0.737209i	$-0.263857\pi$
$839$	1.94021	+	1.62803i	0.0669835	+	0.0562059i	−0.608681	+	0.793415i	$0.708301\pi$
$840$		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	−0.330734	−	0.943724i	$-0.607296\pi$
$853$	17.6637	−	37.8798i	0.604792	−	1.29698i	0.935526	−	0.353257i	$-0.114926\pi$
$854$	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	0.990923	−	0.134434i	$-0.0429217\pi$
$857$	15.3891	+	21.9778i	0.525680	+	0.750749i	−0.465242	+	0.885183i	$0.654033\pi$
$858$		0			0
$859$	7.80591	−	21.4466i	0.266334	−	0.731747i	−0.732372	−	0.680904i	$-0.761587\pi$
$859$	7.80591	−	21.4466i	0.266334	−	0.731747i	0.998707	−	0.0508429i	$-0.0161908\pi$
$860$	−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	0.829089	−	0.559116i	$-0.188859\pi$
$863$	7.93097	+	7.93097i	0.269973	+	0.269973i	−0.559116	+	0.829089i	$0.688859\pi$
$864$		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	0.103653	−	0.994613i	$-0.466947\pi$
$877$	0.977840	+	0.0855499i	0.0330193	+	0.00288882i	−0.0706341	+	0.997502i	$0.522502\pi$
$878$	−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	−0.826669	−	0.562689i	$-0.809767\pi$
$881$	−22.3414	+	12.8988i	−0.752701	+	0.434572i	0.0739682	+	0.997261i	$0.476434\pi$
$882$		0			0
$883$	−12.4224	−	46.3611i	−0.418048	−	1.56018i	−0.778652	−	0.627457i	$-0.784096\pi$
$883$	−12.4224	−	46.3611i	−0.418048	−	1.56018i	0.360604	−	0.932719i	$-0.382571\pi$
$884$	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	0.661739	−	0.749734i	$-0.269819\pi$
$887$	5.46649	+	3.82768i	0.183547	+	0.128521i	−0.478192	+	0.878255i	$0.658708\pi$
$888$		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	0.440351	−	0.897826i	$-0.354854\pi$
$907$	1.07303	+	0.500360i	0.0356292	+	0.0166142i	−0.404722	+	0.914440i	$0.632632\pi$
$908$	−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	0.602653	−	0.798003i	$-0.294110\pi$
$911$	27.0446	+	4.76870i	0.896028	+	0.157994i	0.293375	+	0.955997i	$0.405221\pi$
$912$		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	$-0.886110\pi$
$919$		−	21.2332i		−	0.700419i	0.936671	−	0.350209i	$-0.113890\pi$
$920$	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	0.167679	−	0.985842i	$-0.446373\pi$
$929$	28.3403	−	10.3150i	0.929816	−	0.338425i	0.762136	+	0.647416i	$0.224150\pi$
$930$		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	0.0216704	−	0.999765i	$-0.493102\pi$
$937$	16.5394	−	4.43173i	0.540320	−	0.144778i	0.518650	+	0.854987i	$0.326435\pi$
$938$	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	0.180266	−	0.983618i	$-0.442304\pi$
$941$	21.0459	−	3.71097i	0.686078	−	0.120974i	0.505812	+	0.862644i	$0.331193\pi$
$942$		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	0.383886	−	0.923380i	$-0.374585\pi$
$947$	28.3818	−	2.48308i	0.922284	−	0.0806894i	0.538398	+	0.842691i	$0.319030\pi$
$948$		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	−0.940726	−	0.339169i	$-0.889854\pi$
$953$	−48.9558	+	13.1177i	−1.58583	+	0.424923i	−0.645108	+	0.764091i	$0.723188\pi$
$954$		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	−0.833029	−	0.553229i	$-0.813396\pi$
$967$	−22.4321	−	48.1057i	−0.721366	−	1.54697i	0.111663	−	0.993746i	$-0.464382\pi$
$968$	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	$0.0640447\pi$
$971$			12.4548i			0.399695i	−0.979827	+	0.199847i	$0.935955\pi$
$972$		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	−0.128639	−	0.991691i	$-0.541061\pi$
$977$	17.1398	−	7.99244i	0.548352	−	0.255701i	0.676992	+	0.735991i	$0.263283\pi$
$978$		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	0.220080	−	0.975482i	$-0.429368\pi$
$983$	−12.0933	−	5.63921i	−0.385717	−	0.179863i	−0.605798	+	0.795619i	$0.707146\pi$
$984$		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	−0.909698	−	0.415270i	$-0.863687\pi$
$991$	−2.99736	+	5.19158i	−0.0952142	+	0.164916i	0.814484	+	0.580186i	$0.197020\pi$
$992$	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	−0.750634	−	0.660718i	$-0.770252\pi$
$997$	−3.98279	−	45.5235i	−0.126136	−	1.44174i	0.624498	−	0.781026i	$-0.285304\pi$
$998$	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.197.14		192
3.2	odd	2		135.2.q.a.92.3	yes	192
5.3	odd	4	inner	405.2.r.a.278.3		192
15.2	even	4		675.2.ba.b.443.3		192
15.8	even	4		135.2.q.a.38.14	yes	192
15.14	odd	2		675.2.ba.b.632.14		192
27.5	odd	18	inner	405.2.r.a.287.3		192
27.22	even	9		135.2.q.a.32.14	✓	192
135.22	odd	36		675.2.ba.b.518.14		192
135.49	even	18		675.2.ba.b.32.3		192
135.103	odd	36		135.2.q.a.113.3	yes	192
135.113	even	36	inner	405.2.r.a.368.14		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.14	✓	192	27.22	even	9
135.2.q.a.38.14	yes	192	15.8	even	4
135.2.q.a.92.3	yes	192	3.2	odd	2
135.2.q.a.113.3	yes	192	135.103	odd	36
405.2.r.a.197.14		192	1.1	even	1	trivial
405.2.r.a.278.3		192	5.3	odd	4	inner
405.2.r.a.287.3		192	27.5	odd	18	inner
405.2.r.a.368.14		192	135.113	even	36	inner
675.2.ba.b.32.3		192	135.49	even	18
675.2.ba.b.443.3		192	15.2	even	4
675.2.ba.b.518.14		192	135.22	odd	36
675.2.ba.b.632.14		192	15.14	odd	2

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 $\F_{q}$

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

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

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