LMFDB - Embedded newform 729.2.g.d.514.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [729,2,Mod(28,729)] 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("729.28"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(729, base_ring=CyclotomicField(54)) chi = DirichletCharacter(H, H._module([44])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.g (of order $27$, degree $18$, not minimal)

Newform invariants

comment:select newform

sage:traces = [144,9,0,9,9,0,9,-18,0,-18,9,0,9,9,0,9,-18,0,-18,45] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(20)] == traces)

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

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			514.3
Character	$\chi$	$=$	729.514
Dual form			729.2.g.d.217.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0484354 - 0.831603i) q^{2} +(1.29726 - 0.151628i) q^{4} +(-1.17364 - 0.278158i) q^{5} +(-0.785201 + 1.05471i) q^{7} +(-0.478230 - 2.71217i) q^{8} +(-0.174471 + 0.989477i) q^{10} +(-1.49146 - 1.58086i) q^{11} +(4.07045 - 2.04426i) q^{13} +(0.915130 + 0.601890i) q^{14} +(0.309479 - 0.0733479i) q^{16} +(3.54217 - 1.28924i) q^{17} +(-2.50517 - 0.911807i) q^{19} +(-1.56469 - 0.182886i) q^{20} +(-1.24241 + 1.31687i) q^{22} +(-3.60284 - 4.83945i) q^{23} +(-3.16810 - 1.59108i) q^{25} +(-1.89717 - 3.28599i) q^{26} +(-0.858686 + 1.48729i) q^{28} +(3.47381 - 2.28476i) q^{29} +(2.95363 - 6.84728i) q^{31} +(-1.65571 - 5.53044i) q^{32} +(-1.24371 - 2.88323i) q^{34} +(1.21492 - 1.01944i) q^{35} +(7.47819 + 6.27494i) q^{37} +(-0.636923 + 2.12747i) q^{38} +(-0.193143 + 3.31614i) q^{40} +(-0.336547 + 5.77829i) q^{41} +(1.44983 - 4.84276i) q^{43} +(-2.17451 - 1.82463i) q^{44} +(-3.85000 + 3.23053i) q^{46} +(-1.18743 - 2.75276i) q^{47} +(1.51175 + 5.04961i) q^{49} +(-1.16970 + 2.71167i) q^{50} +(4.97047 - 3.26913i) q^{52} +(-6.22987 + 10.7905i) q^{53} +(1.31071 + 2.27022i) q^{55} +(3.23606 + 1.62521i) q^{56} +(-2.06827 - 2.77817i) q^{58} +(7.48542 - 7.93408i) q^{59} +(-11.7134 - 1.36910i) q^{61} +(-5.83728 - 2.12460i) q^{62} +(-3.92120 + 1.42720i) q^{64} +(-5.34588 + 1.26700i) q^{65} +(0.693545 + 0.456152i) q^{67} +(4.39962 - 2.20957i) q^{68} +(-0.906613 - 0.960954i) q^{70} +(1.25916 - 7.14107i) q^{71} +(-1.41006 - 7.99685i) q^{73} +(4.85605 - 6.52281i) q^{74} +(-3.38811 - 0.802996i) q^{76} +(2.83844 - 0.331766i) q^{77} +(0.668640 + 11.4801i) q^{79} -0.383620 q^{80} +4.82155 q^{82} +(0.277632 + 4.76675i) q^{83} +(-4.51585 + 0.527827i) q^{85} +(-4.09748 - 0.971120i) q^{86} +(-3.57430 + 4.80112i) q^{88} +(0.578632 + 3.28158i) q^{89} +(-1.04003 + 5.89829i) q^{91} +(-5.40761 - 5.73174i) q^{92} +(-2.23169 + 1.12080i) q^{94} +(2.68654 + 1.76697i) q^{95} +(1.32651 - 0.314388i) q^{97} +(4.12605 - 1.50176i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} + 45 q^{20} + 9 q^{22} - 45 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28}+ \cdots + 81 q^{98}+O(q^{100}) $ 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 - 18 * q^10 + 9 * q^11 + 9 * q^13 + 9 * q^14 + 9 * q^16 - 18 * q^17 - 18 * q^19 + 45 * q^20 + 9 * q^22 - 45 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 + 36 * q^29 + 9 * q^31 - 99 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 + 18 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 - 99 * q^47 + 9 * q^49 + 126 * q^50 - 27 * q^52 + 45 * q^53 - 9 * q^55 - 225 * q^56 + 9 * q^58 + 72 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 - 81 * q^65 - 45 * q^67 + 117 * q^68 - 99 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 - 153 * q^76 + 81 * q^77 - 99 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 - 99 * q^85 + 81 * q^86 - 153 * q^88 - 81 * q^89 - 18 * q^91 + 207 * q^92 - 99 * q^94 - 171 * q^95 - 45 * q^97 + 81 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{13}{27}\right)$

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 $

$2$	−0.0484354	−	0.831603i	−0.0342490	−	0.588032i	−0.971155	−	0.238450i	$-0.923361\pi$
$2$	−0.0484354	−	0.831603i	−0.0342490	−	0.588032i	0.936906	−	0.349582i	$-0.113676\pi$
$3$		0			0
$3$		0			0
$4$	1.29726	−	0.151628i	0.648629	−	0.0758139i
$5$	−1.17364	−	0.278158i	−0.524868	−	0.124396i	−0.0403642	−	0.999185i	$-0.512852\pi$
$5$	−1.17364	−	0.278158i	−0.524868	−	0.124396i	−0.484504	+	0.874789i	$0.661000\pi$
$6$		0			0
$7$	−0.785201	+	1.05471i	−0.296778	+	0.398642i	−0.925353	−	0.379107i	$-0.876231\pi$
$7$	−0.785201	+	1.05471i	−0.296778	+	0.398642i	0.628575	+	0.777749i	$0.283639\pi$
$8$	−0.478230	−	2.71217i	−0.169080	−	0.958899i
$9$		0			0
$10$	−0.174471	+	0.989477i	−0.0551727	+	0.312900i
$11$	−1.49146	−	1.58086i	−0.449693	−	0.476646i	0.462376	−	0.886684i	$-0.346997\pi$
$11$	−1.49146	−	1.58086i	−0.449693	−	0.476646i	−0.912069	+	0.410038i	$0.865516\pi$
$12$		0			0
$13$	4.07045	−	2.04426i	1.12894	−	0.566975i	0.216540	−	0.976274i	$-0.430523\pi$
$13$	4.07045	−	2.04426i	1.12894	−	0.566975i	0.912401	+	0.409298i	$0.134226\pi$
$14$	0.915130	+	0.601890i	0.244579	+	0.160862i
$15$		0			0
$16$	0.309479	−	0.0733479i	0.0773698	−	0.0183370i
$17$	3.54217	−	1.28924i	0.859102	−	0.312688i	0.125356	−	0.992112i	$-0.459993\pi$
$17$	3.54217	−	1.28924i	0.859102	−	0.312688i	0.733746	+	0.679424i	$0.237770\pi$
$18$		0			0
$19$	−2.50517	−	0.911807i	−0.574725	−	0.209183i	0.0382728	−	0.999267i	$-0.487814\pi$
$19$	−2.50517	−	0.911807i	−0.574725	−	0.209183i	−0.612998	+	0.790084i	$0.710037\pi$
$20$	−1.56469	−	0.182886i	−0.349876	−	0.0408947i
$21$		0			0
$22$	−1.24241	+	1.31687i	−0.264882	+	0.280758i
$23$	−3.60284	−	4.83945i	−0.751244	−	1.00910i	−0.999187	−	0.0403213i	$-0.987162\pi$
$23$	−3.60284	−	4.83945i	−0.751244	−	1.00910i	0.247943	−	0.968775i	$-0.420246\pi$
$24$		0			0
$25$	−3.16810	−	1.59108i	−0.633620	−	0.318216i
$26$	−1.89717	−	3.28599i	−0.372065	−	0.644435i
$27$		0			0
$28$	−0.858686	+	1.48729i	−0.162276	+	0.281071i
$29$	3.47381	−	2.28476i	0.645070	−	0.424269i	−0.184376	−	0.982856i	$-0.559026\pi$
$29$	3.47381	−	2.28476i	0.645070	−	0.424269i	0.829446	+	0.558587i	$0.188656\pi$
$30$		0			0
$31$	2.95363	−	6.84728i	0.530488	−	1.22981i	−0.416675	−	0.909055i	$-0.636805\pi$
$31$	2.95363	−	6.84728i	0.530488	−	1.22981i	0.947163	−	0.320753i	$-0.103936\pi$
$32$	−1.65571	−	5.53044i	−0.292690	−	0.977654i
$33$		0			0
$34$	−1.24371	−	2.88323i	−0.213294	−	0.494470i
$35$	1.21492	−	1.01944i	0.205359	−	0.172317i
$36$		0			0
$37$	7.47819	+	6.27494i	1.22941	+	1.03159i	0.998277	+	0.0586711i	$0.0186863\pi$
$37$	7.47819	+	6.27494i	1.22941	+	1.03159i	0.231129	+	0.972923i	$0.425758\pi$
$38$	−0.636923	+	2.12747i	−0.103322	+	0.345121i
$39$		0			0
$40$	−0.193143	+	3.31614i	−0.0305387	+	0.524328i
$41$	−0.336547	+	5.77829i	−0.0525599	+	0.902418i	0.864242	+	0.503076i	$0.167798\pi$
$41$	−0.336547	+	5.77829i	−0.0525599	+	0.902418i	−0.916802	+	0.399342i	$0.869239\pi$
$42$		0			0
$43$	1.44983	−	4.84276i	0.221097	−	0.738514i	−0.773416	−	0.633899i	$-0.781454\pi$
$43$	1.44983	−	4.84276i	0.221097	−	0.738514i	0.994513	−	0.104616i	$-0.0333612\pi$
$44$	−2.17451	−	1.82463i	−0.327820	−	0.275074i
$45$		0			0
$46$	−3.85000	+	3.23053i	−0.567652	+	0.476316i
$47$	−1.18743	−	2.75276i	−0.173204	−	0.401531i	0.809397	−	0.587262i	$-0.199794\pi$
$47$	−1.18743	−	2.75276i	−0.173204	−	0.401531i	−0.982601	+	0.185730i	$0.940535\pi$
$48$		0			0
$49$	1.51175	+	5.04961i	0.215965	+	0.721373i
$50$	−1.16970	+	2.71167i	−0.165420	+	0.383488i
$51$		0			0
$52$	4.97047	−	3.26913i	0.689280	−	0.453346i
$53$	−6.22987	+	10.7905i	−0.855739	+	1.48218i	0.0202187	+	0.999796i	$0.493564\pi$
$53$	−6.22987	+	10.7905i	−0.855739	+	1.48218i	−0.875958	+	0.482388i	$0.839770\pi$
$54$		0			0
$55$	1.31071	+	2.27022i	0.176737	+	0.306117i
$56$	3.23606	+	1.62521i	0.432436	+	0.217178i
$57$		0			0
$58$	−2.06827	−	2.77817i	−0.271577	−	0.364791i
$59$	7.48542	−	7.93408i	0.974518	−	1.03293i	−0.0249289	−	0.999689i	$-0.507936\pi$
$59$	7.48542	−	7.93408i	0.974518	−	1.03293i	0.999447	−	0.0332400i	$-0.0105826\pi$
$60$		0			0
$61$	−11.7134	−	1.36910i	−1.49975	−	0.175295i	−0.673746	−	0.738963i	$-0.735316\pi$
$61$	−11.7134	−	1.36910i	−1.49975	−	0.175295i	−0.826001	+	0.563668i	$0.809390\pi$
$62$	−5.83728	−	2.12460i	−0.741336	−	0.269824i
$63$		0			0
$64$	−3.92120	+	1.42720i	−0.490150	+	0.178400i
$65$	−5.34588	+	1.26700i	−0.663075	+	0.157152i
$66$		0			0
$67$	0.693545	+	0.456152i	0.0847300	+	0.0557278i	0.591167	−	0.806549i	$-0.298667\pi$
$67$	0.693545	+	0.456152i	0.0847300	+	0.0557278i	−0.506437	+	0.862277i	$0.669038\pi$
$68$	4.39962	−	2.20957i	0.533533	−	0.267950i
$69$		0			0
$70$	−0.906613	−	0.960954i	−0.108361	−	0.114856i
$71$	1.25916	−	7.14107i	0.149435	−	0.847489i	−0.814263	−	0.580496i	$-0.802859\pi$
$71$	1.25916	−	7.14107i	0.149435	−	0.847489i	0.963698	−	0.266993i	$-0.0860301\pi$
$72$		0			0
$73$	−1.41006	−	7.99685i	−0.165035	−	0.935960i	−0.949028	−	0.315191i	$-0.897931\pi$
$73$	−1.41006	−	7.99685i	−0.165035	−	0.935960i	0.783993	−	0.620769i	$-0.213180\pi$
$74$	4.85605	−	6.52281i	0.564505	−	0.758261i
$75$		0			0
$76$	−3.38811	−	0.802996i	−0.388643	−	0.0921100i
$77$	2.83844	−	0.331766i	0.323470	−	0.0378082i
$78$		0			0
$79$	0.668640	+	11.4801i	0.0752278	+	1.29161i	0.798898	+	0.601466i	$0.205417\pi$
$79$	0.668640	+	11.4801i	0.0752278	+	1.29161i	−0.723670	+	0.690146i	$0.757546\pi$
$80$	−0.383620			−0.0428900
$81$		0			0
$82$	4.82155			0.532451
$83$	0.277632	+	4.76675i	0.0304740	+	0.523219i	0.978658	+	0.205497i	$0.0658810\pi$
$83$	0.277632	+	4.76675i	0.0304740	+	0.523219i	−0.948184	+	0.317722i	$0.897082\pi$
$84$		0			0
$85$	−4.51585	+	0.527827i	−0.489813	+	0.0572509i
$86$	−4.09748	−	0.971120i	−0.441842	−	0.104719i
$87$		0			0
$88$	−3.57430	+	4.80112i	−0.381022	+	0.511801i
$89$	0.578632	+	3.28158i	0.0613348	+	0.347847i	0.999995	+	0.00300484i	$0.000956472\pi$
$89$	0.578632	+	3.28158i	0.0613348	+	0.347847i	−0.938661	+	0.344842i	$0.887932\pi$
$90$		0			0
$91$	−1.04003	+	5.89829i	−0.109025	+	0.618309i
$92$	−5.40761	−	5.73174i	−0.563783	−	0.597575i
$93$		0			0
$94$	−2.23169	+	1.12080i	−0.230181	+	0.115601i
$95$	2.68654	+	1.76697i	0.275634	+	0.181287i
$96$		0			0
$97$	1.32651	−	0.314388i	0.134686	−	0.0319212i	−0.162720	−	0.986672i	$-0.552027\pi$
$97$	1.32651	−	0.314388i	0.134686	−	0.0319212i	0.297406	+	0.954751i	$0.403879\pi$
$98$	4.12605	−	1.50176i	0.416794	−	0.151701i
$99$		0			0
$100$	−4.35110	−	1.58367i	−0.435110	−	0.158367i
$101$	−2.29919	−	0.268737i	−0.228778	−	0.0267403i	0.000931520	−	1.00000i	$-0.499703\pi$
$101$	−2.29919	−	0.268737i	−0.228778	−	0.0267403i	−0.229709	+	0.973259i	$0.573778\pi$
$102$		0			0
$103$	−3.12210	+	3.30923i	−0.307629	+	0.326068i	−0.862682	−	0.505747i	$-0.831217\pi$
$103$	−3.12210	+	3.30923i	−0.307629	+	0.326068i	0.555052	+	0.831815i	$0.312698\pi$
$104$	−7.49100	−	10.0622i	−0.734553	−	0.986676i
$105$		0			0
$106$	9.27513	+	4.65814i	0.900880	+	0.452439i
$107$	6.14665	+	10.6463i	0.594219	+	1.02922i	0.993657	+	0.112457i	$0.0358721\pi$
$107$	6.14665	+	10.6463i	0.594219	+	1.02922i	−0.399438	+	0.916760i	$0.630795\pi$
$108$		0			0
$109$	4.45327	−	7.71330i	0.426546	−	0.738800i	−0.570017	−	0.821633i	$-0.693063\pi$
$109$	4.45327	−	7.71330i	0.426546	−	0.738800i	0.996563	+	0.0828329i	$0.0263968\pi$
$110$	1.82444	−	1.19995i	0.173953	−	0.114411i
$111$		0			0
$112$	−0.165643	+	0.384003i	−0.0156518	+	0.0362849i
$113$	4.98772	+	16.6601i	0.469205	+	1.56725i	0.785667	+	0.618649i	$0.212320\pi$
$113$	4.98772	+	16.6601i	0.469205	+	1.56725i	−0.316462	+	0.948605i	$0.602495\pi$
$114$		0			0
$115$	2.88231	+	6.68194i	0.268777	+	0.623095i
$116$	4.16000	−	3.49065i	0.386246	−	0.324099i
$117$		0			0
$118$	−6.96056	−	5.84061i	−0.640772	−	0.537671i
$119$	−1.42154	+	4.74827i	−0.130312	+	0.435273i
$120$		0			0
$121$	0.364942	−	6.26581i	0.0331765	−	0.569619i
$122$	−0.571205	+	9.80721i	−0.0517145	+	0.887903i
$123$		0			0
$124$	2.79338	−	9.33055i	0.250853	−	0.837908i
$125$	7.89548	+	6.62509i	0.706193	+	0.592566i
$126$		0			0
$127$	4.35255	−	3.65222i	0.386226	−	0.324082i	−0.428915	−	0.903345i	$-0.641104\pi$
$127$	4.35255	−	3.65222i	0.386226	−	0.324082i	0.815141	+	0.579263i	$0.196660\pi$
$128$	−3.19633	−	7.40992i	−0.282518	−	0.654950i
$129$		0			0
$130$	1.31257	+	4.38428i	0.115120	+	0.384527i
$131$	−7.73087	+	17.9222i	−0.675449	+	1.56587i	0.142000	+	0.989867i	$0.454647\pi$
$131$	−7.73087	+	17.9222i	−0.675449	+	1.56587i	−0.817449	+	0.576001i	$0.804612\pi$
$132$		0			0
$133$	2.92875	−	1.92627i	0.253955	−	0.167029i
$134$	0.345745	−	0.598848i	0.0298678	−	0.0517326i
$135$		0			0
$136$	−5.19062	−	8.99042i	−0.445092	−	0.770922i
$137$	14.1679	+	7.11536i	1.21044	+	0.607907i	0.935422	−	0.353532i	$-0.115020\pi$
$137$	14.1679	+	7.11536i	1.21044	+	0.607907i	0.275019	+	0.961439i	$0.411316\pi$
$138$		0			0
$139$	−6.23388	−	8.37355i	−0.528751	−	0.710236i	0.454855	−	0.890565i	$-0.349691\pi$
$139$	−6.23388	−	8.37355i	−0.528751	−	0.710236i	−0.983606	+	0.180330i	$0.942284\pi$
$140$	1.42149	−	1.50669i	0.120138	−	0.127339i
$141$		0			0
$142$	−5.99952	−	0.701243i	−0.503469	−	0.0588470i
$143$	−9.30261	−	3.38587i	−0.777923	−	0.283141i
$144$		0			0
$145$	−4.71253	+	1.71522i	−0.391354	+	0.142441i
$146$	−6.58191	+	1.55994i	−0.544722	+	0.129102i
$147$		0			0
$148$	10.6526	+	7.00632i	0.875638	+	0.575916i
$149$	−2.60504	+	1.30830i	−0.213413	+	0.107180i	−0.552295	−	0.833649i	$-0.686248\pi$
$149$	−2.60504	+	1.30830i	−0.213413	+	0.107180i	0.338882	+	0.940829i	$0.389951\pi$
$150$		0			0
$151$	8.75633	+	9.28117i	0.712580	+	0.755291i	0.977946	−	0.208857i	$-0.0669743\pi$
$151$	8.75633	+	9.28117i	0.712580	+	0.755291i	−0.265366	+	0.964148i	$0.585493\pi$
$152$	−1.27493	+	7.23051i	−0.103411	+	0.586472i
$153$		0			0
$154$	−0.413378	−	2.34439i	−0.0333110	−	0.188916i
$155$	−5.37113	+	7.21468i	−0.431420	+	0.579497i
$156$		0			0
$157$	−1.23639	−	0.293029i	−0.0986743	−	0.0233862i	0.180982	−	0.983486i	$-0.442072\pi$
$157$	−1.23639	−	0.293029i	−0.0986743	−	0.0233862i	−0.279656	+	0.960100i	$0.590221\pi$
$158$	9.51450	−	1.11209i	0.756933	−	0.0884728i
$159$		0			0
$160$	0.404868	+	6.95131i	0.0320076	+	0.549549i
$161$	7.93316			0.625221
$162$		0			0
$163$	12.3636			0.968391			0.484195	−	0.874960i	$-0.339112\pi$
$163$	12.3636			0.968391			0.484195	+	0.874960i	$0.339112\pi$
$164$	0.439561	+	7.54697i	0.0343240	+	0.589320i
$165$		0			0
$166$	3.95060	−	0.461759i	0.306626	−	0.0358394i
$167$	3.71075	+	0.879464i	0.287146	+	0.0680550i	0.371665	−	0.928367i	$-0.378787\pi$
$167$	3.71075	+	0.879464i	0.287146	+	0.0680550i	−0.0845184	+	0.996422i	$0.526935\pi$
$168$		0			0
$169$	4.62654	−	6.21452i	0.355888	−	0.478040i
$170$	0.657669	+	3.72983i	0.0504409	+	0.286065i
$171$		0			0
$172$	1.14650	−	6.50215i	0.0874201	−	0.495784i
$173$	16.5179	+	17.5080i	1.25584	+	1.33111i	0.921364	+	0.388702i	$0.127076\pi$
$173$	16.5179	+	17.5080i	1.25584	+	1.33111i	0.334471	+	0.942406i	$0.391442\pi$
$174$		0			0
$175$	4.16572	−	2.09210i	0.314899	−	0.158148i
$176$	−0.577529	−	0.379847i	−0.0435329	−	0.0286320i
$177$		0			0
$178$	2.70095	−	0.640136i	0.202445	−	0.0479803i
$179$	5.95691	−	2.16814i	0.445240	−	0.162054i	−0.109664	−	0.993969i	$-0.534977\pi$
$179$	5.95691	−	2.16814i	0.445240	−	0.162054i	0.554904	+	0.831915i	$0.312755\pi$
$180$		0			0
$181$	−5.82014	−	2.11836i	−0.432608	−	0.157456i	0.116532	−	0.993187i	$-0.462822\pi$
$181$	−5.82014	−	2.11836i	−0.432608	−	0.157456i	−0.549140	+	0.835731i	$0.685045\pi$
$182$	4.95541	+	0.579205i	0.367320	+	0.0429335i
$183$		0			0
$184$	−11.4025	+	12.0859i	−0.840601	+	0.890985i
$185$	−7.03128	−	9.44465i	−0.516950	−	0.694385i
$186$		0			0
$187$	−7.32112	−	3.67680i	−0.535373	−	0.268875i
$188$	−1.95779	−	3.39100i	−0.142787	−	0.247314i
$189$		0			0
$190$	1.33929	−	2.31972i	0.0971625	−	0.168290i
$191$	−5.64176	+	3.71064i	−0.408223	+	0.268493i	−0.736970	−	0.675925i	$-0.763744\pi$
$191$	−5.64176	+	3.71064i	−0.408223	+	0.268493i	0.328747	+	0.944418i	$0.393374\pi$
$192$		0			0
$193$	−6.30224	+	14.6102i	−0.453645	+	1.05167i	0.525918	+	0.850535i	$0.323722\pi$
$193$	−6.30224	+	14.6102i	−0.453645	+	1.05167i	−0.979564	+	0.201133i	$0.935538\pi$
$194$	−0.325696	−	1.08790i	−0.0233836	−	0.0781066i
$195$		0			0
$196$	2.72680	+	6.32143i	0.194771	+	0.451531i
$197$	−8.88023	+	7.45140i	−0.632690	+	0.530890i	−0.901764	−	0.432229i	$-0.857727\pi$
$197$	−8.88023	+	7.45140i	−0.632690	+	0.530890i	0.269073	+	0.963120i	$0.413283\pi$
$198$		0			0
$199$	3.29385	+	2.76387i	0.233495	+	0.195925i	0.752026	−	0.659133i	$-0.229077\pi$
$199$	3.29385	+	2.76387i	0.233495	+	0.195925i	−0.518531	+	0.855059i	$0.673521\pi$
$200$	−2.80021	+	9.35334i	−0.198005	+	0.661381i
$201$		0			0
$202$	−0.112120	+	1.92503i	−0.00788875	+	0.135445i
$203$	−0.317883	+	5.45785i	−0.0223110	+	0.383066i
$204$		0			0
$205$	2.00227	−	6.68803i	0.139844	−	0.467112i
$206$	2.90318	+	2.43606i	0.202274	+	0.169728i
$207$		0			0
$208$	1.10978	−	0.931215i	0.0769493	−	0.0645682i
$209$	2.29493	+	5.32024i	0.158743	+	0.368009i
$210$		0			0
$211$	−4.09591	−	13.6813i	−0.281974	−	0.941858i	−0.975235	−	0.221172i	$-0.929012\pi$
$211$	−4.09591	−	13.6813i	−0.281974	−	0.941858i	0.693261	−	0.720687i	$-0.256173\pi$
$212$	−6.44563	+	14.9426i	−0.442687	+	1.02626i
$213$		0			0
$214$	8.55579	−	5.62723i	0.584862	−	0.384669i
$215$	−3.04863	+	5.28038i	−0.207915	+	0.360119i
$216$		0			0
$217$	4.90269	+	8.49171i	0.332816	+	0.576455i
$218$	−6.63010	−	3.32976i	−0.449047	−	0.225520i
$219$		0			0
$220$	2.04456	+	2.74633i	0.137844	+	0.185157i
$221$	11.7827	−	12.4889i	0.792589	−	0.840095i
$222$		0			0
$223$	20.0537	+	2.34394i	1.34290	+	0.156962i	0.756995	−	0.653421i	$-0.226667\pi$
$223$	20.0537	+	2.34394i	1.34290	+	0.156962i	0.585901	+	0.810383i	$0.300741\pi$
$224$	7.13306	+	2.59622i	0.476598	+	0.173467i
$225$		0			0
$226$	13.6130	−	4.95474i	0.905526	−	0.329585i
$227$	2.65003	−	0.628068i	0.175889	−	0.0416863i	−0.141728	−	0.989906i	$-0.545266\pi$
$227$	2.65003	−	0.628068i	0.175889	−	0.0416863i	0.317616	+	0.948219i	$0.397118\pi$
$228$		0			0
$229$	−1.27542	−	0.838856i	−0.0842821	−	0.0554332i	0.506669	−	0.862141i	$-0.330877\pi$
$229$	−1.27542	−	0.838856i	−0.0842821	−	0.0554332i	−0.590951	+	0.806708i	$0.701247\pi$
$230$	5.41712	−	2.72058i	0.357194	−	0.179390i
$231$		0			0
$232$	−7.85794	−	8.32893i	−0.515899	−	0.546821i
$233$	−1.13347	+	6.42825i	−0.0742563	+	0.421128i	0.924906	+	0.380197i	$0.124144\pi$
$233$	−1.13347	+	6.42825i	−0.0742563	+	0.421128i	−0.999162	+	0.0409317i	$0.986967\pi$
$234$		0			0
$235$	0.627909	+	3.56105i	0.0409602	+	0.232297i
$236$	8.50750	−	11.4276i	0.553791	−	0.743870i
$237$		0			0
$238$	4.01753	+	0.952171i	0.260417	+	0.0617201i
$239$	16.7833	−	1.96169i	1.08562	−	0.126891i	0.445589	−	0.895238i	$-0.352994\pi$
$239$	16.7833	−	1.96169i	1.08562	−	0.126891i	0.640034	+	0.768347i	$0.278920\pi$
$240$		0			0
$241$	0.732563	+	12.5776i	0.0471885	+	0.810196i	0.936017	+	0.351955i	$0.114483\pi$
$241$	0.732563	+	12.5776i	0.0471885	+	0.810196i	−0.888828	+	0.458240i	$0.848480\pi$
$242$	−5.22835			−0.336091
$243$		0			0
$244$	−15.4029			−0.986070
$245$	−0.369667	−	6.34694i	−0.0236172	−	0.405491i
$246$		0			0
$247$	−12.0611	+	1.40975i	−0.767432	+	0.0897000i
$248$	−19.9835	−	4.73619i	−1.26896	−	0.300748i
$249$		0			0
$250$	5.12703	−	6.88679i	0.324262	−	0.435559i
$251$	−4.48052	−	25.4103i	−0.282808	−	1.60388i	−0.713012	−	0.701152i	$-0.752669\pi$
$251$	−4.48052	−	25.4103i	−0.282808	−	1.60388i	0.430204	−	0.902732i	$-0.358442\pi$
$252$		0			0
$253$	−2.27699	+	12.9134i	−0.143153	+	0.811861i
$254$	−3.24801	−	3.44269i	−0.203799	−	0.216014i
$255$		0			0
$256$	−13.4653	+	6.76252i	−0.841580	+	0.422658i
$257$	−12.0914	−	7.95265i	−0.754242	−	0.496073i	0.113224	−	0.993570i	$-0.463882\pi$
$257$	−12.0914	−	7.95265i	−0.754242	−	0.496073i	−0.867466	+	0.497497i	$0.834253\pi$
$258$		0			0
$259$	−12.4901	+	2.96021i	−0.776097	+	0.183938i
$260$	−6.74288	+	2.45421i	−0.418176	+	0.152204i
$261$		0			0
$262$	15.2786	+	5.56095i	0.943914	+	0.343557i
$263$	10.3839	+	1.21371i	0.640300	+	0.0748403i	0.430047	−	0.902807i	$-0.358497\pi$
$263$	10.3839	+	1.21371i	0.640300	+	0.0748403i	0.210253	+	0.977647i	$0.432571\pi$
$264$		0			0
$265$	10.3131	−	10.9312i	0.633528	−	0.671501i
$266$	−1.74375	−	2.34226i	−0.106916	−	0.143613i
$267$		0			0
$268$	0.968872	+	0.486586i	0.0591833	+	0.0297230i
$269$	0.105374	+	0.182513i	0.00642476	+	0.0111280i	0.869220	−	0.494426i	$-0.164622\pi$
$269$	0.105374	+	0.182513i	0.00642476	+	0.0111280i	−0.862795	+	0.505554i	$0.831288\pi$
$270$		0			0
$271$	5.70846	−	9.88735i	0.346765	−	0.600614i	−0.638908	−	0.769283i	$-0.720614\pi$
$271$	5.70846	−	9.88735i	0.346765	−	0.600614i	0.985673	+	0.168669i	$0.0539470\pi$
$272$	1.00166	−	0.658805i	0.0607348	−	0.0399459i
$273$		0			0
$274$	5.23093	−	12.1267i	0.316012	−	0.732599i
$275$	2.20983	+	7.38135i	0.133258	+	0.445112i
$276$		0			0
$277$	−4.41607	−	10.2376i	−0.265336	−	0.615117i	0.732508	−	0.680759i	$-0.238350\pi$
$277$	−4.41607	−	10.2376i	−0.265336	−	0.615117i	−0.997843	+	0.0656416i	$0.979091\pi$
$278$	−6.66153	+	5.58969i	−0.399532	+	0.335247i
$279$		0			0
$280$	−3.34591	−	2.80755i	−0.199956	−	0.167783i
$281$	6.22453	−	20.7914i	0.371325	−	1.24031i	−0.544510	−	0.838754i	$-0.683284\pi$
$281$	6.22453	−	20.7914i	0.371325	−	1.24031i	0.915834	−	0.401556i	$-0.131531\pi$
$282$		0			0
$283$	0.0172412	−	0.296021i	0.00102488	−	0.0175966i	−0.997757	−	0.0669409i	$-0.978676\pi$
$283$	0.0172412	−	0.296021i	0.00102488	−	0.0175966i	0.998782	+	0.0493443i	$0.0157132\pi$
$284$	0.550676	−	9.45474i	0.0326766	−	0.561035i
$285$		0			0
$286$	−2.36513	+	7.90008i	−0.139853	+	0.467141i
$287$	−5.83015	−	4.89208i	−0.344143	−	0.288770i
$288$		0			0
$289$	−2.13795	+	1.79396i	−0.125762	+	0.105527i
$290$	1.65464	+	3.83588i	0.0971636	+	0.225250i
$291$		0			0
$292$	−3.04176	−	10.1602i	−0.178005	−	0.594579i
$293$	−5.74578	+	13.3202i	−0.335672	+	0.778175i	0.663868	+	0.747850i	$0.268914\pi$
$293$	−5.74578	+	13.3202i	−0.335672	+	0.778175i	−0.999540	+	0.0303252i	$0.990346\pi$
$294$		0			0
$295$	−10.9921	+	7.22964i	−0.639986	+	0.420926i
$296$	13.4425	−	23.2830i	0.781327	−	1.35330i
$297$		0			0
$298$	1.21416	+	2.10299i	0.0703346	+	0.121823i
$299$	−24.5583	−	12.3336i	−1.42024	−	0.713273i
$300$		0			0
$301$	3.96929	+	5.33168i	0.228786	+	0.307313i
$302$	7.29413	−	7.73133i	0.419730	−	0.444888i
$303$		0			0
$304$	−0.842177	−	0.0984364i	−0.0483022	−	0.00564571i
$305$	13.3665	+	4.86501i	0.765364	+	0.278570i
$306$		0			0
$307$	−3.56052	+	1.29592i	−0.203210	+	0.0739622i	−0.441620	−	0.897202i	$-0.645596\pi$
$307$	−3.56052	+	1.29592i	−0.203210	+	0.0739622i	0.238410	+	0.971165i	$0.423374\pi$
$308$	3.63189	−	0.860773i	0.206946	−	0.0490471i
$309$		0			0
$310$	6.25990	+	4.11720i	0.355539	+	0.233841i
$311$	11.0181	−	5.53348i	0.624777	−	0.313775i	−0.108096	−	0.994141i	$-0.534475\pi$
$311$	11.0181	−	5.53348i	0.624777	−	0.313775i	0.732873	+	0.680366i	$0.238179\pi$
$312$		0			0
$313$	−4.67044	−	4.95038i	−0.263989	−	0.279812i	0.581797	−	0.813334i	$-0.302350\pi$
$313$	−4.67044	−	4.95038i	−0.263989	−	0.279812i	−0.845786	+	0.533522i	$0.820868\pi$
$314$	−0.183799	+	1.04238i	−0.0103724	+	0.0588246i
$315$		0			0
$316$	2.60810	+	14.7913i	0.146717	+	0.832074i
$317$	−8.91947	+	11.9809i	−0.500967	+	0.672916i	−0.978630	−	0.205627i	$-0.934077\pi$
$317$	−8.91947	+	11.9809i	−0.500967	+	0.672916i	0.477663	+	0.878543i	$0.341484\pi$
$318$		0			0
$319$	−8.79293	−	2.08396i	−0.492310	−	0.116680i
$320$	4.99907	−	0.584307i	0.279456	−	0.0326638i
$321$		0			0
$322$	−0.384246	−	6.59724i	−0.0214132	−	0.367650i
$323$	−10.0493			−0.559156
$324$		0			0
$325$	−16.1482			−0.895740
$326$	−0.598835	−	10.2816i	−0.0331664	−	0.569445i
$327$		0			0
$328$	15.8327	−	1.85058i	0.874214	−	0.102181i
$329$	3.83572	+	0.909083i	0.211470	+	0.0501194i
$330$		0			0
$331$	−2.20579	+	2.96289i	−0.121241	+	0.162855i	−0.858600	−	0.512646i	$-0.828665\pi$
$331$	−2.20579	+	2.96289i	−0.121241	+	0.162855i	0.737359	+	0.675501i	$0.236073\pi$
$332$	1.08293	+	6.14162i	0.0594337	+	0.337065i
$333$		0			0
$334$	0.551633	−	3.12847i	0.0301840	−	0.171182i
$335$	−0.687091	−	0.728274i	−0.0375398	−	0.0397898i
$336$		0			0
$337$	16.4827	−	8.27793i	0.897870	−	0.450927i	0.0608800	−	0.998145i	$-0.480609\pi$
$337$	16.4827	−	8.27793i	0.897870	−	0.450927i	0.836990	+	0.547218i	$0.184313\pi$
$338$	−5.39211	−	3.54644i	−0.293292	−	0.192901i
$339$		0			0
$340$	−5.77819	+	1.36946i	−0.313366	+	0.0742692i
$341$	−15.2298	+	5.54319i	−0.824740	+	0.300181i
$342$		0			0
$343$	−15.1621	−	5.51854i	−0.818675	−	0.297973i
$344$	−13.8278	−	1.61623i	−0.745543	−	0.0871415i
$345$		0			0
$346$	13.7596	−	14.5844i	0.739723	−	0.784061i
$347$	−20.0622	−	26.9481i	−1.07699	−	1.44665i	−0.885196	−	0.465218i	$-0.845976\pi$
$347$	−20.0622	−	26.9481i	−1.07699	−	1.44665i	−0.191796	−	0.981435i	$-0.561431\pi$
$348$		0			0
$349$	−29.4341	−	14.7824i	−1.57557	−	0.791282i	−0.575916	−	0.817509i	$-0.695354\pi$
$349$	−29.4341	−	14.7824i	−1.57557	−	0.791282i	−0.999656	+	0.0262270i	$0.991651\pi$
$350$	−1.94157	−	3.36289i	−0.103781	−	0.179754i
$351$		0			0
$352$	−6.27342	+	10.8659i	−0.334374	+	0.579154i
$353$	−11.1466	+	7.33122i	−0.593273	+	0.390202i	−0.810344	−	0.585954i	$-0.800720\pi$
$353$	−11.1466	+	7.33122i	−0.593273	+	0.390202i	0.217072	+	0.976156i	$0.430350\pi$
$354$		0			0
$355$	−3.46415	+	8.03081i	−0.183858	+	0.426231i
$356$	1.24821	+	4.16933i	0.0661552	+	0.220974i
$357$		0			0
$358$	−2.09155	−	4.84877i	−0.110542	−	0.256265i
$359$	6.91454	−	5.80199i	0.364936	−	0.306217i	−0.441819	−	0.897104i	$-0.645667\pi$
$359$	6.91454	−	5.80199i	0.364936	−	0.306217i	0.806754	+	0.590887i	$0.201222\pi$
$360$		0			0
$361$	−9.11037	−	7.64450i	−0.479493	−	0.402342i
$362$	−1.47973	+	4.94265i	−0.0777730	+	0.259780i
$363$		0			0
$364$	−0.454840	+	7.80931i	−0.0238401	+	0.409319i
$365$	−0.569483	+	9.77765i	−0.0298081	+	0.511786i
$366$		0			0
$367$	−7.34329	+	24.5283i	−0.383316	+	1.28037i	0.521019	+	0.853545i	$0.325552\pi$
$367$	−7.34329	+	24.5283i	−0.383316	+	1.28037i	−0.904336	+	0.426821i	$0.859633\pi$
$368$	−1.46997	−	1.23345i	−0.0766274	−	0.0642980i
$369$		0			0
$370$	−7.51364	+	6.30469i	−0.390616	+	0.327765i
$371$	−6.48908	−	15.0434i	−0.336896	−	0.781013i
$372$		0			0
$373$	6.27172	+	20.9490i	0.324737	+	1.08470i	0.952053	+	0.305933i	$0.0989685\pi$
$373$	6.27172	+	20.9490i	0.324737	+	1.08470i	−0.627315	+	0.778765i	$0.715846\pi$
$374$	−2.70304	+	6.26635i	−0.139771	+	0.324025i
$375$		0			0
$376$	−6.89811	+	4.53696i	−0.355743	+	0.233976i
$377$	9.46934	−	16.4014i	0.487696	−	0.844714i
$378$		0			0
$379$	−5.26717	−	9.12300i	−0.270556	−	0.468617i	0.698448	−	0.715661i	$-0.253874\pi$
$379$	−5.26717	−	9.12300i	−0.270556	−	0.468617i	−0.969004	+	0.247043i	$0.920541\pi$
$380$	3.75306	+	1.88486i	0.192528	+	0.0966913i
$381$		0			0
$382$	3.35904	+	4.51198i	0.171864	+	0.230853i
$383$	−15.0071	+	15.9066i	−0.766829	+	0.812791i	−0.986668	−	0.162745i	$-0.947965\pi$
$383$	−15.0071	+	15.9066i	−0.766829	+	0.812791i	0.219839	+	0.975536i	$0.429447\pi$
$384$		0			0
$385$	−3.42359	−	0.400161i	−0.174482	−	0.0203941i
$386$	12.4552	+	4.53331i	0.633952	+	0.230740i
$387$		0			0
$388$	1.67315	−	0.608977i	0.0849414	−	0.0309161i
$389$	23.7332	−	5.62487i	1.20332	−	0.285192i	0.420414	−	0.907332i	$-0.361885\pi$
$389$	23.7332	−	5.62487i	1.20332	−	0.285192i	0.782906	+	0.622140i	$0.213737\pi$
$390$		0			0
$391$	−19.0011	−	12.4972i	−0.960927	−	0.632012i
$392$	12.9725	−	6.51502i	0.655208	−	0.329058i
$393$		0			0
$394$	6.62672	+	7.02392i	0.333850	+	0.353860i
$395$	2.40854	−	13.6595i	0.121187	−	0.687285i
$396$		0			0
$397$	4.16728	+	23.6338i	0.209150	+	1.18615i	0.890775	+	0.454445i	$0.150163\pi$
$397$	4.16728	+	23.6338i	0.209150	+	1.18615i	−0.681625	+	0.731702i	$0.738726\pi$
$398$	2.13890	−	2.87304i	0.107214	−	0.144013i
$399$		0			0
$400$	−1.09716	−	0.260033i	−0.0548582	−	0.0130016i
$401$	36.6641	−	4.28542i	1.83092	−	0.214004i	0.870425	−	0.492301i	$-0.163844\pi$
$401$	36.6641	−	4.28542i	1.83092	−	0.214004i	0.960495	+	0.278297i	$0.0897700\pi$
$402$		0			0
$403$	−1.97501	−	33.9095i	−0.0983820	−	1.68915i
$404$	−3.02339			−0.150419
$405$		0			0
$406$	4.55416			0.226019
$407$	−1.23364	−	21.1808i	−0.0611493	−	1.04989i
$408$		0			0
$409$	2.83591	−	0.331470i	0.140227	−	0.0163901i	−0.0456900	−	0.998956i	$-0.514549\pi$
$409$	2.83591	−	0.331470i	0.140227	−	0.0163901i	0.185917	+	0.982566i	$0.440475\pi$
$410$	−5.65877	−	1.34115i	−0.279467	−	0.0662348i
$411$		0			0
$412$	−3.54840	+	4.76632i	−0.174817	+	0.234820i
$413$	2.49058	+	14.1248i	0.122553	+	0.695035i
$414$		0			0
$415$	1.00007	−	5.67169i	0.0490916	−	0.278412i
$416$	−18.0451	−	19.1267i	−0.884736	−	0.937765i
$417$		0			0
$418$	4.31317	−	2.16616i	0.210964	−	0.105950i
$419$	−28.7197	−	18.8893i	−1.40305	−	0.922801i	−0.999971	−	0.00763598i	$-0.997569\pi$
$419$	−28.7197	−	18.8893i	−1.40305	−	0.922801i	−0.403080	−	0.915165i	$-0.632060\pi$
$420$		0			0
$421$	6.08312	−	1.44172i	0.296473	−	0.0702654i	−0.0796876	−	0.996820i	$-0.525392\pi$
$421$	6.08312	−	1.44172i	0.296473	−	0.0702654i	0.376161	+	0.926555i	$0.377244\pi$
$422$	−11.1790	+	4.06883i	−0.544186	+	0.198067i
$423$		0			0
$424$	32.2449	+	11.7362i	1.56595	+	0.569960i
$425$	−13.2732	−	1.55142i	−0.643846	−	0.0752548i
$426$		0			0
$427$	10.6414	−	11.2792i	0.514972	−	0.545838i
$428$	9.58807	+	12.8790i	0.463457	+	0.622531i
$429$		0			0
$430$	4.53885	+	2.27949i	0.218883	+	0.109927i
$431$	−1.50862	−	2.61301i	−0.0726679	−	0.125864i	0.827402	−	0.561610i	$-0.189818\pi$
$431$	−1.50862	−	2.61301i	−0.0726679	−	0.125864i	−0.900070	+	0.435746i	$0.856485\pi$
$432$		0			0
$433$	−15.3659	+	26.6146i	−0.738439	+	1.27901i	0.214759	+	0.976667i	$0.431104\pi$
$433$	−15.3659	+	26.6146i	−0.738439	+	1.27901i	−0.953198	+	0.302347i	$0.902230\pi$
$434$	6.82427	−	4.48839i	0.327575	−	0.215450i
$435$		0			0
$436$	4.60750	−	10.6814i	0.220659	−	0.511546i
$437$	4.61308	+	15.4087i	0.220673	+	0.737100i
$438$		0			0
$439$	0.181258	+	0.420203i	0.00865097	+	0.0200552i	0.922487	−	0.386029i	$-0.126153\pi$
$439$	0.181258	+	0.420203i	0.00865097	+	0.0200552i	−0.913836	+	0.406084i	$0.866894\pi$
$440$	5.53042	−	4.64057i	0.263652	−	0.221231i
$441$		0			0
$442$	−10.9565	−	9.19361i	−0.521148	−	0.437296i
$443$	10.0119	−	33.4420i	0.475679	−	1.58888i	−0.297520	−	0.954716i	$-0.596159\pi$
$443$	10.0119	−	33.4420i	0.475679	−	1.58888i	0.773199	−	0.634163i	$-0.218655\pi$
$444$		0			0
$445$	0.233693	−	4.01235i	0.0110781	−	0.190204i
$446$	0.977921	−	16.7903i	0.0463059	−	0.795042i
$447$		0			0
$448$	1.57365	−	5.25635i	0.0743479	−	0.248339i
$449$	−5.48196	−	4.59991i	−0.258710	−	0.217083i	0.504202	−	0.863586i	$-0.331787\pi$
$449$	−5.48196	−	4.59991i	−0.258710	−	0.217083i	−0.762912	+	0.646502i	$0.776231\pi$
$450$		0			0
$451$	9.63661	−	8.08607i	0.453770	−	0.380758i
$452$	8.99650	+	20.8562i	0.423160	+	0.980995i
$453$		0			0
$454$	−0.650658	−	2.17335i	−0.0305369	−	0.102000i
$455$	2.86128	−	6.63319i	0.134139	−	0.310969i
$456$		0			0
$457$	10.5960	−	6.96910i	0.495660	−	0.326001i	−0.276947	−	0.960885i	$-0.589323\pi$
$457$	10.5960	−	6.96910i	0.495660	−	0.326001i	0.772607	+	0.634884i	$0.218952\pi$
$458$	−0.635820	+	1.10127i	−0.0297099	+	0.0514591i
$459$		0			0
$460$	4.75227	+	8.23117i	0.221576	+	0.383780i
$461$	0.412693	+	0.207262i	0.0192210	+	0.00965317i	0.458384	−	0.888754i	$-0.348429\pi$
$461$	0.412693	+	0.207262i	0.0192210	+	0.00965317i	−0.439163	+	0.898408i	$0.644725\pi$
$462$		0			0
$463$	22.1551	+	29.7595i	1.02964	+	1.38304i	0.921267	+	0.388931i	$0.127156\pi$
$463$	22.1551	+	29.7595i	1.02964	+	1.38304i	0.108369	+	0.994111i	$0.465437\pi$
$464$	0.907489	−	0.961882i	0.0421291	−	0.0446543i
$465$		0			0
$466$	5.40065	+	0.631245i	0.250180	+	0.0292419i
$467$	−25.8480	−	9.40792i	−1.19611	−	0.435347i	−0.334242	−	0.942487i	$-0.608480\pi$
$467$	−25.8480	−	9.40792i	−1.19611	−	0.435347i	−0.861863	+	0.507141i	$0.830702\pi$
$468$		0			0
$469$	−1.02568	+	0.373316i	−0.0473614	+	0.0172381i
$470$	2.93096	−	0.694651i	0.135195	−	0.0320419i
$471$		0			0
$472$	−25.0984	−	16.5075i	−1.15525	−	0.759817i
$473$	−9.81808	+	4.93082i	−0.451436	+	0.226720i
$474$		0			0
$475$	6.48587	+	6.87462i	0.297592	+	0.315429i
$476$	−1.12413	+	6.37527i	−0.0515245	+	0.292210i
$477$		0			0
$478$	−2.44425	−	13.8620i	−0.111798	−	0.634035i
$479$	−8.51578	+	11.4387i	−0.389096	+	0.522646i	−0.952909	−	0.303256i	$-0.901926\pi$
$479$	−8.51578	+	11.4387i	−0.389096	+	0.522646i	0.563813	+	0.825902i	$0.309334\pi$
$480$		0			0
$481$	43.2672	+	10.2545i	1.97282	+	0.467566i
$482$	10.4241	−	1.21840i	0.474805	−	0.0554967i
$483$		0			0
$484$	−0.476647	−	8.18372i	−0.0216658	−	0.371987i
$485$	−1.64429			−0.0746634
$486$		0			0
$487$	9.07752			0.411342			0.205671	−	0.978621i	$-0.434062\pi$
$487$	9.07752			0.411342			0.205671	+	0.978621i	$0.434062\pi$
$488$	1.88846	+	32.4235i	0.0854864	+	1.46774i
$489$		0			0
$490$	−5.26023	+	0.614833i	−0.237633	+	0.0277753i
$491$	−27.1313	−	6.43024i	−1.22442	−	0.290193i	−0.432960	−	0.901413i	$-0.642531\pi$
$491$	−27.1313	−	6.43024i	−1.22442	−	0.290193i	−0.791460	+	0.611220i	$0.790679\pi$
$492$		0			0
$493$	9.35920	−	12.5716i	0.421517	−	0.566196i
$494$	1.75653	+	9.96180i	0.0790302	+	0.448203i
$495$		0			0
$496$	0.411853	−	2.33573i	0.0184927	−	0.104878i
$497$	6.54304	+	6.93522i	0.293495	+	0.311087i
$498$		0			0
$499$	−21.2606	+	10.6775i	−0.951755	+	0.477989i	−0.855749	−	0.517392i	$-0.826903\pi$
$499$	−21.2606	+	10.6775i	−0.951755	+	0.477989i	−0.0960058	+	0.995381i	$0.530607\pi$
$500$	11.2470	+	7.39729i	0.502982	+	0.330817i
$501$		0			0
$502$	−20.9143	+	4.95677i	−0.933450	+	0.221232i
$503$	7.57016	−	2.75531i	0.337537	−	0.122853i	−0.167690	−	0.985840i	$-0.553631\pi$
$503$	7.57016	−	2.75531i	0.337537	−	0.122853i	0.505227	+	0.862986i	$0.331409\pi$
$504$		0			0
$505$	2.62367	+	0.954939i	0.116752	+	0.0424942i
$506$	10.8491	+	1.26808i	0.482303	+	0.0563732i
$507$		0			0
$508$	5.09260	−	5.39784i	0.225948	−	0.239491i
$509$	−11.5280	−	15.4848i	−0.510971	−	0.686353i	0.469519	−	0.882922i	$-0.344427\pi$
$509$	−11.5280	−	15.4848i	−0.510971	−	0.686353i	−0.980490	+	0.196569i	$0.937020\pi$
$510$		0			0
$511$	9.54151	+	4.79193i	0.422092	+	0.211982i
$512$	−1.79397	−	3.10725i	−0.0792832	−	0.137323i
$513$		0			0
$514$	−6.02780	+	10.4405i	−0.265875	+	0.460509i
$515$	4.58471	−	3.01541i	0.202027	−	0.132875i
$516$		0			0
$517$	−2.58072	+	5.98279i	−0.113500	+	0.263123i
$518$	3.06668	+	10.2434i	0.134742	+	0.450071i
$519$		0			0
$520$	5.99288	+	13.8930i	0.262805	+	0.609251i
$521$	2.04454	−	1.71557i	0.0895727	−	0.0751604i	−0.596902	−	0.802314i	$-0.703602\pi$
$521$	2.04454	−	1.71557i	0.0895727	−	0.0751604i	0.686474	+	0.727154i	$0.259157\pi$
$522$		0			0
$523$	11.7693	+	9.87562i	0.514636	+	0.431831i	0.862757	−	0.505619i	$-0.168736\pi$
$523$	11.7693	+	9.87562i	0.514636	+	0.431831i	−0.348121	+	0.937450i	$0.613180\pi$
$524$	−7.31144	+	24.4219i	−0.319402	+	1.06688i
$525$		0			0
$526$	0.506373	−	8.69408i	0.0220789	−	0.379080i
$527$	1.63444	−	28.0622i	0.0711971	−	1.22241i
$528$		0			0
$529$	−3.84339	+	12.8378i	−0.167104	+	0.558166i
$530$	−9.58997	−	8.04694i	−0.416562	−	0.349537i
$531$		0			0
$532$	3.50727	−	2.94295i	0.152059	−	0.127593i
$533$	10.4424	+	24.2083i	0.452312	+	1.04858i
$534$		0			0
$535$	−4.25260	−	14.2047i	−0.183856	−	0.614122i
$536$	0.905489	−	2.09916i	0.0391112	−	0.0906699i
$537$		0			0
$538$	0.146675	−	0.0964694i	0.00632359	−	0.00415909i
$539$	5.72799	−	9.92117i	0.246722	−	0.427335i
$540$		0			0
$541$	9.39421	+	16.2713i	0.403889	+	0.699556i	0.994191	−	0.107626i	$-0.0343250\pi$
$541$	9.39421	+	16.2713i	0.403889	+	0.699556i	−0.590303	+	0.807182i	$0.700992\pi$
$542$	−8.49884	−	4.26828i	−0.365057	−	0.183338i
$543$		0			0
$544$	−12.9949	−	17.4552i	−0.557151	−	0.748384i
$545$	−7.37206	+	7.81393i	−0.315785	+	0.334712i
$546$		0			0
$547$	11.3834	+	1.33052i	0.486717	+	0.0568891i	0.355913	−	0.934519i	$-0.384170\pi$
$547$	11.3834	+	1.33052i	0.486717	+	0.0568891i	0.130804	+	0.991408i	$0.458244\pi$
$548$	19.4583	+	7.08223i	0.831216	+	0.302538i
$549$		0			0
$550$	6.03132	−	2.19522i	0.257176	−	0.0936045i
$551$	−10.7857	+	2.55627i	−0.459488	+	0.108901i
$552$		0			0
$553$	−12.6332	−	8.30896i	−0.537217	−	0.353333i
$554$	−8.29972	+	4.16828i	−0.352621	+	0.177093i
$555$		0			0
$556$	−9.35662	−	9.91744i	−0.396809	−	0.420593i
$557$	4.33665	−	24.5943i	0.183750	−	1.04210i	−0.743802	−	0.668400i	$-0.766979\pi$
$557$	4.33665	−	24.5943i	0.183750	−	1.04210i	0.927551	−	0.373695i	$-0.121909\pi$
$558$		0			0
$559$	−3.99840	−	22.6761i	−0.169114	−	0.959095i
$560$	0.301219	−	0.404607i	0.0127288	−	0.0170978i
$561$		0			0
$562$	−17.5917	−	4.16930i	−0.742060	−	0.175871i
$563$	17.4623	−	2.04106i	0.735950	−	0.0860202i	0.260143	−	0.965570i	$-0.416230\pi$
$563$	17.4623	−	2.04106i	0.735950	−	0.0860202i	0.475807	+	0.879550i	$0.342156\pi$
$564$		0			0
$565$	−1.21964	−	20.9404i	−0.0513106	−	0.880970i
$566$	−0.247007			−0.0103825
$567$		0			0
$568$	−19.9700			−0.837922
$569$	−0.929683	−	15.9620i	−0.0389743	−	0.669164i	−0.960058	−	0.279800i	$-0.909732\pi$
$569$	−0.929683	−	15.9620i	−0.0389743	−	0.669164i	0.921084	−	0.389364i	$-0.127305\pi$
$570$		0			0
$571$	−10.2603	+	1.19926i	−0.429380	+	0.0501873i	−0.328038	−	0.944664i	$-0.606388\pi$
$571$	−10.2603	+	1.19926i	−0.429380	+	0.0501873i	−0.101341	+	0.994852i	$0.532313\pi$
$572$	−12.5813	−	2.98182i	−0.526050	−	0.124676i
$573$		0			0
$574$	−3.78588	+	5.08532i	−0.158020	+	0.212257i
$575$	3.71420	+	21.0643i	0.154893	+	0.878441i
$576$		0			0
$577$	6.79785	−	38.5525i	0.282998	−	1.60496i	−0.429351	−	0.903138i	$-0.641258\pi$
$577$	6.79785	−	38.5525i	0.282998	−	1.60496i	0.712349	−	0.701825i	$-0.247631\pi$
$578$	1.59541	+	1.69104i	0.0663604	+	0.0703379i
$579$		0			0
$580$	−5.85330	+	2.93964i	−0.243045	+	0.122062i
$581$	−5.24553	−	3.45004i	−0.217621	−	0.143132i
$582$		0			0
$583$	26.3498	−	6.24502i	1.09130	−	0.258642i
$584$	−21.0145	+	7.64866i	−0.869587	+	0.316504i
$585$		0			0
$586$	11.3554	+	4.13304i	0.469088	+	0.170734i
$587$	17.6814	+	2.06665i	0.729788	+	0.0853000i	0.472869	−	0.881133i	$-0.343218\pi$
$587$	17.6814	+	2.06665i	0.729788	+	0.0853000i	0.256919	+	0.966433i	$0.417293\pi$
$588$		0			0
$589$	−13.6427	+	14.4605i	−0.562139	+	0.595833i
$590$	6.54460	+	8.79092i	0.269437	+	0.361916i
$591$		0			0
$592$	2.77460	+	1.39346i	0.114035	+	0.0572707i
$593$	6.92687	+	11.9977i	0.284452	+	0.492686i	0.972476	−	0.233002i	$-0.0748549\pi$
$593$	6.92687	+	11.9977i	0.284452	+	0.492686i	−0.688024	+	0.725688i	$0.741522\pi$
$594$		0			0
$595$	2.98914	−	5.17735i	0.122543	−	0.212251i
$596$	−3.18104	+	2.09220i	−0.130300	+	0.0856999i
$597$		0			0
$598$	−9.06720	+	21.0201i	−0.370786	+	0.859577i
$599$	−1.03796	−	3.46703i	−0.0424099	−	0.141659i	0.934163	−	0.356848i	$-0.116149\pi$
$599$	−1.03796	−	3.46703i	−0.0424099	−	0.141659i	−0.976572	+	0.215189i	$0.930963\pi$
$600$		0			0
$601$	−4.11249	−	9.53383i	−0.167752	−	0.388893i	0.813515	−	0.581543i	$-0.197551\pi$
$601$	−4.11249	−	9.53383i	−0.167752	−	0.388893i	−0.981267	+	0.192650i	$0.938292\pi$
$602$	4.24159	−	3.55912i	0.172874	−	0.145059i
$603$		0			0
$604$	12.7665	+	10.7124i	0.519462	+	0.435880i
$605$	−2.17120	+	7.25231i	−0.0882718	+	0.294848i
$606$		0			0
$607$	−0.781051	+	13.4101i	−0.0317019	+	0.544301i	0.944645	+	0.328093i	$0.106406\pi$
$607$	−0.781051	+	13.4101i	−0.0317019	+	0.544301i	−0.976347	+	0.216208i	$0.930631\pi$
$608$	−0.894873	+	15.3644i	−0.0362919	+	0.623108i
$609$		0			0
$610$	3.39835	−	11.3513i	0.137595	−	0.459599i
$611$	−10.4607	−	8.77758i	−0.423195	−	0.355103i
$612$		0			0
$613$	22.2652	−	18.6827i	0.899281	−	0.754587i	−0.0707686	−	0.997493i	$-0.522545\pi$
$613$	22.2652	−	18.6827i	0.899281	−	0.754587i	0.970050	+	0.242906i	$0.0781007\pi$
$614$	1.25015	+	2.89817i	0.0504519	+	0.116961i
$615$		0			0
$616$	−2.25723	−	7.53968i	−0.0909465	−	0.303782i
$617$	4.92341	−	11.4138i	0.198209	−	0.459500i	−0.789904	−	0.613231i	$-0.789870\pi$
$617$	4.92341	−	11.4138i	0.198209	−	0.459500i	0.988113	+	0.153730i	$0.0491288\pi$
$618$		0			0
$619$	−28.8790	+	18.9940i	−1.16074	+	0.763434i	−0.975660	−	0.219289i	$-0.929626\pi$
$619$	−28.8790	+	18.9940i	−1.16074	+	0.763434i	−0.185085	+	0.982723i	$0.559256\pi$
$620$	−5.87380	+	10.1737i	−0.235898	+	0.408586i
$621$		0			0
$622$	−5.13533	−	8.89464i	−0.205908	−	0.356643i
$623$	−3.91545	−	1.96641i	−0.156869	−	0.0787827i
$624$		0			0
$625$	3.16157	+	4.24673i	0.126463	+	0.169869i
$626$	−3.89053	+	4.12373i	−0.155497	+	0.164817i
$627$		0			0
$628$	−1.64834	−	0.192664i	−0.0657761	−	0.00768812i
$629$	34.5789	+	12.5857i	1.37875	+	0.501825i
$630$		0			0
$631$	12.4258	−	4.52262i	0.494663	−	0.180042i	−0.0826292	−	0.996580i	$-0.526332\pi$
$631$	12.4258	−	4.52262i	0.494663	−	0.180042i	0.577292	+	0.816538i	$0.304109\pi$
$632$	30.8163	−	7.30359i	1.22581	−	0.290521i
$633$		0			0
$634$	10.3954	+	6.83716i	0.412854	+	0.271538i
$635$	−6.12422	+	3.07570i	−0.243032	+	0.122055i
$636$		0			0
$637$	16.4762	+	17.4638i	0.652813	+	0.691941i
$638$	−1.30714	+	7.41317i	−0.0517502	+	0.293490i
$639$		0			0
$640$	1.69021	+	9.58567i	0.0668115	+	0.378907i
$641$	−3.14875	+	4.22950i	−0.124368	+	0.167055i	−0.859946	−	0.510384i	$-0.829503\pi$
$641$	−3.14875	+	4.22950i	−0.124368	+	0.167055i	0.735578	+	0.677440i	$0.236911\pi$
$642$		0			0
$643$	4.25864	+	1.00932i	0.167944	+	0.0398035i	0.313728	−	0.949513i	$-0.398422\pi$
$643$	4.25864	+	1.00932i	0.167944	+	0.0398035i	−0.145783	+	0.989317i	$0.546570\pi$
$644$	10.2914	−	1.20289i	0.405537	−	0.0474004i
$645$		0			0
$646$	0.486740	+	8.35700i	0.0191505	+	0.328802i
$647$	5.42624			0.213327			0.106664	−	0.994295i	$-0.465983\pi$
$647$	5.42624			0.213327			0.106664	+	0.994295i	$0.465983\pi$
$648$		0			0
$649$	−23.7069			−0.930576
$650$	0.782143	+	13.4289i	0.0306782	+	0.526724i
$651$		0			0
$652$	16.0388	−	1.87466i	0.628127	−	0.0734175i
$653$	10.8018	+	2.56007i	0.422706	+	0.100183i	0.436463	−	0.899722i	$-0.356231\pi$
$653$	10.8018	+	2.56007i	0.422706	+	0.100183i	−0.0137571	+	0.999905i	$0.504379\pi$
$654$		0			0
$655$	14.0585	−	18.8838i	0.549310	−	0.737851i
$656$	0.319672	+	1.81295i	0.0124811	+	0.0707837i
$657$		0			0
$658$	0.570212	−	3.23383i	0.0222292	−	0.126068i
$659$	5.10241	+	5.40824i	0.198762	+	0.210675i	0.819087	−	0.573670i	$-0.194481\pi$
$659$	5.10241	+	5.40824i	0.198762	+	0.210675i	−0.620325	+	0.784345i	$0.712999\pi$
$660$		0			0
$661$	−3.42406	+	1.71963i	−0.133180	+	0.0668858i	−0.514142	−	0.857705i	$-0.671889\pi$
$661$	−3.42406	+	1.71963i	−0.133180	+	0.0668858i	0.380961	+	0.924591i	$0.375593\pi$
$662$	2.57079	+	1.69083i	0.0999165	+	0.0657161i
$663$		0			0
$664$	12.7955	−	3.03259i	0.496562	−	0.117687i
$665$	−3.97311	+	1.44609i	−0.154071	+	0.0560771i
$666$		0			0
$667$	−23.5726	−	8.57971i	−0.912733	−	0.332208i
$668$	4.94716	+	0.578240i	0.191411	+	0.0223728i
$669$		0			0
$670$	−0.572355	+	0.606661i	−0.0221120	+	0.0234374i
$671$	15.3057	+	20.5592i	0.590871	+	0.793678i
$672$		0			0
$673$	37.6141	+	18.8905i	1.44992	+	0.728177i	0.987372	−	0.158418i	$-0.0506395\pi$
$673$	37.6141	+	18.8905i	1.44992	+	0.728177i	0.462547	+	0.886595i	$0.346936\pi$
$674$	−7.68230	−	13.3061i	−0.295911	−	0.512533i
$675$		0			0
$676$	5.05953	−	8.76336i	0.194597	−	0.337052i
$677$	2.08236	−	1.36959i	0.0800315	−	0.0526376i	−0.508863	−	0.860848i	$-0.669934\pi$
$677$	2.08236	−	1.36959i	0.0800315	−	0.0526376i	0.588894	+	0.808210i	$0.299563\pi$
$678$		0			0
$679$	−0.709986	+	1.64593i	−0.0272468	+	0.0631651i
$680$	3.59117	+	11.9953i	0.137715	+	0.460001i
$681$		0			0
$682$	5.34740	+	12.3967i	0.204762	+	0.474693i
$683$	−11.7411	+	9.85194i	−0.449260	+	0.376974i	−0.839161	−	0.543883i	$-0.816954\pi$
$683$	−11.7411	+	9.85194i	−0.449260	+	0.376974i	0.389901	+	0.920857i	$0.372509\pi$
$684$		0			0
$685$	−14.6488	−	12.2918i	−0.559701	−	0.469645i
$686$	−3.85486	+	12.8761i	−0.147179	+	0.491613i
$687$		0			0
$688$	0.0934850	−	1.60508i	0.00356408	−	0.0611930i
$689$	−3.29993	+	56.6575i	−0.125717	+	2.15848i
$690$		0			0
$691$	−10.6430	+	35.5501i	−0.404879	+	1.35239i	0.476165	+	0.879356i	$0.342027\pi$
$691$	−10.6430	+	35.5501i	−0.404879	+	1.35239i	−0.881044	+	0.473035i	$0.843159\pi$
$692$	24.0827	+	20.2078i	0.915488	+	0.768186i
$693$		0			0
$694$	−21.4384	+	17.9890i	−0.813792	+	0.682853i
$695$	4.98717	+	11.5616i	0.189174	+	0.438555i
$696$		0			0
$697$	6.25752	+	20.9016i	0.237021	+	0.791704i
$698$	−10.8674	+	25.1935i	−0.411338	+	0.953588i
$699$		0			0
$700$	5.08679	−	3.34564i	0.192263	−	0.126453i
$701$	−3.35489	+	5.81083i	−0.126712	+	0.219472i	−0.922401	−	0.386234i	$-0.873776\pi$
$701$	−3.35489	+	5.81083i	−0.126712	+	0.219472i	0.795689	+	0.605706i	$0.207109\pi$
$702$		0			0
$703$	−13.0126	−	22.5385i	−0.490779	−	0.850054i
$704$	8.10452	+	4.07024i	0.305450	+	0.153403i
$705$		0			0
$706$	6.63656	+	8.91444i	0.249770	+	0.335499i
$707$	2.08876	−	2.21396i	0.0785560	−	0.0832645i
$708$		0			0
$709$	23.6203	+	2.76081i	0.887078	+	0.103685i	0.547413	−	0.836862i	$-0.315613\pi$
$709$	23.6203	+	2.76081i	0.887078	+	0.103685i	0.339664	+	0.940547i	$0.389687\pi$
$710$	6.84623	+	2.49182i	0.256934	+	0.0935165i
$711$		0			0
$712$	8.62351	−	3.13870i	0.323180	−	0.117628i
$713$	−43.7786	+	10.3757i	−1.63952	+	0.388573i
$714$		0			0
$715$	9.97612	+	6.56140i	0.373086	+	0.245382i
$716$	7.39890	−	3.71587i	0.276510	−	0.138868i
$717$		0			0
$718$	−5.15986	−	5.46913i	−0.192564	−	0.204106i
$719$	−7.41202	+	42.0356i	−0.276422	+	1.56766i	0.457988	+	0.888958i	$0.348570\pi$
$719$	−7.41202	+	42.0356i	−0.276422	+	1.56766i	−0.734410	+	0.678706i	$0.762541\pi$
$720$		0			0
$721$	−1.03880	−	5.89131i	−0.0386868	−	0.219404i
$722$	−5.91593	+	7.94647i	−0.220168	+	0.295737i
$723$		0			0
$724$	−7.87144	−	1.86556i	−0.292540	−	0.0693332i
$725$	−14.6406	+	1.71124i	−0.543739	+	0.0635539i
$726$		0			0
$727$	−1.10799	−	19.0235i	−0.0410932	−	0.705544i	−0.954448	−	0.298378i	$-0.903554\pi$
$727$	−1.10799	−	19.0235i	−0.0410932	−	0.705544i	0.913354	−	0.407165i	$-0.133483\pi$
$728$	16.4946			0.611329
$729$		0			0
$730$	8.15871			0.301967
$731$	−1.10797	−	19.0231i	−0.0409796	−	0.703593i
$732$		0			0
$733$	17.8418	−	2.08541i	0.659001	−	0.0770262i	0.219982	−	0.975504i	$-0.429400\pi$
$733$	17.8418	−	2.08541i	0.659001	−	0.0770262i	0.439019	+	0.898478i	$0.355326\pi$
$734$	20.7535	+	4.91866i	0.766025	+	0.181551i
$735$		0			0
$736$	−20.7991	+	27.9380i	−0.766665	+	1.02981i
$737$	−0.313285	−	1.77673i	−0.0115400	−	0.0654466i
$738$		0			0
$739$	2.16602	−	12.2841i	0.0796782	−	0.451878i	−0.918700	−	0.394955i	$-0.870760\pi$
$739$	2.16602	−	12.2841i	0.0796782	−	0.451878i	0.998379	−	0.0569224i	$-0.0181288\pi$
$740$	−10.5535	−	11.1860i	−0.387953	−	0.411206i
$741$		0			0
$742$	−12.1958	+	6.12497i	−0.447722	+	0.224855i
$743$	21.6533	+	14.2416i	0.794384	+	0.522474i	0.880633	−	0.473799i	$-0.157118\pi$
$743$	21.6533	+	14.2416i	0.794384	+	0.522474i	−0.0862493	+	0.996274i	$0.527488\pi$
$744$		0			0
$745$	3.42130	−	0.810863i	0.125347	−	0.0297077i
$746$	17.1175	−	6.23026i	0.626716	−	0.228106i
$747$		0			0
$748$	−10.0549	−	3.65968i	−0.367643	−	0.133811i
$749$	−16.0551	−	1.87657i	−0.586640	−	0.0685684i
$750$		0			0
$751$	−7.20276	+	7.63448i	−0.262832	+	0.278586i	−0.845328	−	0.534248i	$-0.820595\pi$
$751$	−7.20276	+	7.63448i	−0.262832	+	0.278586i	0.582495	+	0.812834i	$0.302076\pi$
$752$	−0.569393	−	0.764827i	−0.0207636	−	0.0278904i
$753$		0			0
$754$	−14.0981	−	7.08032i	−0.513422	−	0.257850i
$755$	−7.69516	−	13.3284i	−0.280056	−	0.485070i
$756$		0			0
$757$	−0.0864170	+	0.149679i	−0.00314088	+	0.00544016i	−0.867592	−	0.497277i	$-0.834333\pi$
$757$	−0.0864170	+	0.149679i	−0.00314088	+	0.00544016i	0.864451	+	0.502718i	$0.167666\pi$
$758$	−7.33160	+	4.82207i	−0.266296	+	0.175145i
$759$		0			0
$760$	3.50754	−	8.13139i	0.127232	−	0.294957i
$761$	−0.537224	−	1.79445i	−0.0194743	−	0.0650488i	0.947700	−	0.319162i	$-0.103402\pi$
$761$	−0.537224	−	1.79445i	−0.0194743	−	0.0650488i	−0.967174	+	0.254113i	$0.918216\pi$
$762$		0			0
$763$	4.63856	+	10.7534i	0.167927	+	0.389299i
$764$	−6.75618	+	5.66911i	−0.244430	+	0.205101i
$765$		0			0
$766$	13.9549	+	11.7095i	0.504211	+	0.423083i
$767$	14.2497	−	47.5974i	0.514528	−	1.71864i
$768$		0			0
$769$	1.62282	−	27.8628i	0.0585204	−	1.00476i	−0.833430	−	0.552624i	$-0.813626\pi$
$769$	1.62282	−	27.8628i	0.0585204	−	1.00476i	0.891951	−	0.452132i	$-0.149337\pi$
$770$	−0.166952	+	2.86645i	−0.00601653	+	0.103300i
$771$		0			0
$772$	−5.96032	+	19.9089i	−0.214517	+	0.716536i
$773$	0.0418155	+	0.0350873i	0.00150400	+	0.00126200i	0.643539	−	0.765413i	$-0.277465\pi$
$773$	0.0418155	+	0.0350873i	0.00150400	+	0.00126200i	−0.642035	+	0.766675i	$0.721910\pi$
$774$		0			0
$775$	−20.2520	+	16.9934i	−0.727472	+	0.610422i
$776$	−1.48705	−	3.44737i	−0.0533819	−	0.123753i
$777$		0			0
$778$	−5.82718	−	19.4641i	−0.208915	−	0.697823i
$779$	6.11180	−	14.1687i	0.218978	−	0.507648i
$780$		0			0
$781$	−13.1670	+	8.66007i	−0.471152	+	0.309882i
$782$	−9.47240	+	16.4067i	−0.338732	+	0.586702i
$783$		0			0
$784$	0.838235	+	1.45187i	0.0299370	+	0.0518524i
$785$	1.36957	+	0.687821i	0.0488819	+	0.0245494i
$786$		0			0
$787$	−20.2554	−	27.2077i	−0.722025	−	0.969848i	−0.999957	−	0.00924767i	$-0.997056\pi$
$787$	−20.2554	−	27.2077i	−0.722025	−	0.969848i	0.277932	−	0.960601i	$-0.410351\pi$
$788$	−10.3901	+	11.0129i	−0.370133	+	0.392318i
$789$		0			0
$790$	−11.4760	−	1.34135i	−0.408296	−	0.0477230i
$791$	−21.4879	−	7.82097i	−0.764023	−	0.278082i
$792$		0			0
$793$	−50.4776	+	18.3724i	−1.79251	+	0.652422i
$794$	19.4521	−	4.61023i	0.690330	−	0.163611i
$795$		0			0
$796$	4.69206	+	3.08601i	0.166306	+	0.109381i
$797$	13.0138	−	6.53577i	0.460972	−	0.231509i	−0.203129	−	0.979152i	$-0.565111\pi$
$797$	13.0138	−	6.53577i	0.460972	−	0.231509i	0.664101	+	0.747643i	$0.268815\pi$
$798$		0			0
$799$	−7.75504	−	8.21986i	−0.274354	−	0.290798i
$800$	−3.55394	+	20.1554i	−0.125651	+	0.712600i
$801$		0			0
$802$	−5.33961	−	30.2825i	−0.188548	−	1.06931i
$803$	−10.5388	+	14.1561i	−0.371907	+	0.499558i
$804$		0			0
$805$	−9.31069	−	2.20667i	−0.328159	−	0.0777750i
$806$	−28.1036	+	3.28484i	−0.989908	+	0.115704i
$807$		0			0
$808$	0.370679	+	6.36432i	0.0130405	+	0.223896i
$809$	28.0189			0.985092			0.492546	−	0.870286i	$-0.336066\pi$
$809$	28.0189			0.985092			0.492546	+	0.870286i	$0.336066\pi$
$810$		0			0
$811$	29.1924			1.02508			0.512542	−	0.858662i	$-0.328704\pi$
$811$	29.1924			1.02508			0.512542	+	0.858662i	$0.328704\pi$
$812$	0.415184	+	7.12844i	0.0145701	+	0.250159i
$813$		0			0
$814$	−17.5543	+	2.05180i	−0.615276	+	0.0719155i
$815$	−14.5104	−	3.43903i	−0.508278	−	0.120464i
$816$		0			0
$817$	−8.04773	+	10.8100i	−0.281554	+	0.378193i
$818$	−0.413009	−	2.34229i	−0.0144405	−	0.0818964i
$819$		0			0
$820$	1.58337	−	8.97971i	0.0552935	−	0.313585i
$821$	20.4884	+	21.7164i	0.715049	+	0.757908i	0.978384	−	0.206797i	$-0.0663039\pi$
$821$	20.4884	+	21.7164i	0.715049	+	0.757908i	−0.263335	+	0.964704i	$0.584822\pi$
$822$		0			0
$823$	−35.9168	+	18.0381i	−1.25198	+	0.628769i	−0.946277	−	0.323357i	$-0.895188\pi$
$823$	−35.9168	+	18.0381i	−1.25198	+	0.628769i	−0.305705	+	0.952126i	$0.598892\pi$
$824$	10.4683	+	6.88510i	0.364680	+	0.239854i
$825$		0			0
$826$	11.6256	−	2.75531i	0.404505	−	0.0958695i
$827$	39.9498	−	14.5405i	1.38919	−	0.505623i	0.464238	−	0.885710i	$-0.346328\pi$
$827$	39.9498	−	14.5405i	1.38919	−	0.505623i	0.924951	+	0.380087i	$0.124106\pi$
$828$		0			0
$829$	5.90599	+	2.14960i	0.205124	+	0.0746589i	0.442539	−	0.896749i	$-0.354078\pi$
$829$	5.90599	+	2.14960i	0.205124	+	0.0746589i	−0.237415	+	0.971408i	$0.576300\pi$
$830$	−4.76503	−	0.556952i	−0.165397	−	0.0193321i
$831$		0			0
$832$	−13.0435	+	13.8253i	−0.452202	+	0.479306i
$833$	11.8651	+	15.9376i	0.411100	+	0.552204i
$834$		0			0
$835$	−4.11046	−	2.06435i	−0.142248	−	0.0714398i
$836$	3.78381	+	6.55375i	0.130866	+	0.226666i
$837$		0			0
$838$	−14.3173	+	24.7983i	−0.494584	+	0.856644i
$839$	−13.8375	+	9.10107i	−0.477724	+	0.314204i	−0.765435	−	0.643513i	$-0.777476\pi$
$839$	−13.8375	+	9.10107i	−0.477724	+	0.314204i	0.287711	+	0.957717i	$0.407106\pi$
$840$		0			0
$841$	−4.63910	+	10.7546i	−0.159969	+	0.370849i
$842$	−1.49358	−	4.98891i	−0.0514722	−	0.171929i
$843$		0			0
$844$	−7.38791	−	17.1271i	−0.254303	−	0.589539i
$845$	−7.15852	+	6.00671i	−0.246261	+	0.206637i
$846$		0			0
$847$	6.32205	+	5.30483i	0.217228	+	0.182276i
$848$	−1.13656	+	3.79637i	−0.0390296	+	0.130368i
$849$		0			0
$850$	−0.647271	+	11.1132i	−0.0222012	+	0.381180i
$851$	3.42459	−	58.7980i	0.117393	−	2.01557i
$852$		0			0
$853$	14.9484	−	49.9311i	0.511823	−	1.70961i	−0.176586	−	0.984285i	$-0.556505\pi$
$853$	14.9484	−	49.9311i	0.511823	−	1.70961i	0.688409	−	0.725323i	$-0.258309\pi$
$854$	−9.89523	−	8.30308i	−0.338608	−	0.284126i
$855$		0			0
$856$	25.9351	−	21.7622i	0.886445	−	0.743815i
$857$	−15.4005	−	35.7024i	−0.526071	−	1.21957i	−0.949536	−	0.313658i	$-0.898445\pi$
$857$	−15.4005	−	35.7024i	−0.526071	−	1.21957i	0.423465	−	0.905913i	$-0.360814\pi$
$858$		0			0
$859$	6.22471	+	20.7920i	0.212384	+	0.709413i	0.996095	+	0.0882870i	$0.0281393\pi$
$859$	6.22471	+	20.7920i	0.212384	+	0.709413i	−0.783711	+	0.621126i	$0.786676\pi$
$860$	−3.15421	+	7.31228i	−0.107558	+	0.249347i
$861$		0			0
$862$	−2.09992	+	1.38114i	−0.0715236	+	0.0470418i
$863$	−21.9404	+	38.0020i	−0.746861	+	1.29360i	0.202459	+	0.979291i	$0.435107\pi$
$863$	−21.9404	+	38.0020i	−0.746861	+	1.29360i	−0.949320	+	0.314311i	$0.898227\pi$
$864$		0			0
$865$	−14.5161	−	25.1427i	−0.493564	−	0.854877i
$866$	22.8770	+	11.4893i	0.777392	+	0.390421i
$867$		0			0
$868$	7.64764	+	10.2726i	0.259578	+	0.348673i
$869$	17.1512	−	18.1792i	0.581813	−	0.616686i
$870$		0			0
$871$	3.75553	+	0.438959i	0.127251	+	0.0148736i
$872$	−23.0495	−	8.38933i	−0.780554	−	0.284099i
$873$		0			0
$874$	12.5905	−	4.58258i	0.425881	−	0.155008i
$875$	−13.1871	+	3.12539i	−0.445804	+	0.105658i
$876$		0			0
$877$	20.9882	+	13.8042i	0.708721	+	0.466133i	0.851995	−	0.523550i	$-0.175393\pi$
$877$	20.9882	+	13.8042i	0.708721	+	0.466133i	−0.143274	+	0.989683i	$0.545763\pi$
$878$	0.340663	−	0.171087i	0.0114968	−	0.00577392i
$879$		0			0
$880$	0.572155	+	0.606449i	0.0192873	+	0.0204434i
$881$	0.463850	−	2.63063i	0.0156275	−	0.0886281i	−0.975996	−	0.217786i	$-0.930116\pi$
$881$	0.463850	−	2.63063i	0.0156275	−	0.0886281i	0.991624	+	0.129158i	$0.0412275\pi$
$882$		0			0
$883$	6.82642	+	38.7145i	0.229727	+	1.30285i	0.853439	+	0.521193i	$0.174513\pi$
$883$	6.82642	+	38.7145i	0.229727	+	1.30285i	−0.623711	+	0.781655i	$0.714376\pi$
$884$	13.3915	−	17.9879i	0.450406	−	0.605000i
$885$		0			0
$886$	−28.2954	−	6.70614i	−0.950604	−	0.225297i
$887$	−33.1937	+	3.87979i	−1.11454	+	0.130271i	−0.653367	−	0.757041i	$-0.726644\pi$
$887$	−33.1937	+	3.87979i	−1.11454	+	0.130271i	−0.461169	+	0.887312i	$0.652570\pi$
$888$		0			0
$889$	0.434402	+	7.45839i	0.0145694	+	0.250146i
$890$	−3.34800			−0.112225
$891$		0			0
$892$	26.3703			0.882942
$893$	0.464714	+	7.97883i	0.0155511	+	0.267001i
$894$		0			0
$895$	−7.59436	+	0.887653i	−0.253851	+	0.0296710i
$896$	10.3251	+	2.44708i	0.344936	+	0.0817513i
$897$		0			0
$898$	−3.55978	+	4.78161i	−0.118791	+	0.159565i
$899$	−5.38405	−	30.5345i	−0.179568	−	1.01838i
$900$		0			0
$901$	−8.15573	+	46.2534i	−0.271707	+	1.54093i
$902$	−7.19116	−	7.62218i	−0.239439	−	0.253791i
$903$		0			0
$904$	42.7999	−	21.4949i	1.42350	−	0.714911i
$905$	6.24152	+	4.10511i	0.207475	+	0.136459i
$906$		0			0
$907$	−11.9717	+	2.83735i	−0.397515	+	0.0942127i	−0.424511	−	0.905423i	$-0.639554\pi$
$907$	−11.9717	+	2.83735i	−0.397515	+	0.0942127i	0.0269963	+	0.999636i	$0.491406\pi$
$908$	3.34254	−	1.21658i	0.110926	−	0.0403738i
$909$		0			0
$910$	−5.65477	−	2.05817i	−0.187454	−	0.0682276i
$911$	21.7054	+	2.53700i	0.719131	+	0.0840544i	0.467784	−	0.883843i	$-0.345052\pi$
$911$	21.7054	+	2.53700i	0.719131	+	0.0840544i	0.251347	+	0.967897i	$0.419126\pi$
$912$		0			0
$913$	7.12148	−	7.54833i	0.235687	−	0.249813i
$914$	−6.30875	−	8.47412i	−0.208675	−	0.280299i
$915$		0			0
$916$	−1.78174	−	0.894825i	−0.0588704	−	0.0295658i
$917$	−12.8324	−	22.2263i	−0.423762	−	0.733977i
$918$		0			0
$919$	27.9349	−	48.3846i	0.921487	−	1.59606i	0.124370	−	0.992236i	$-0.460309\pi$
$919$	27.9349	−	48.3846i	0.921487	−	1.59606i	0.797116	−	0.603826i	$-0.206358\pi$
$920$	16.7442	−	11.0128i	0.552040	−	0.363082i
$921$		0			0
$922$	0.152371	−	0.353236i	0.00501807	−	0.0116332i
$923$	−9.47282	−	31.6414i	−0.311802	−	1.04149i
$924$		0			0
$925$	−13.7077	−	31.7780i	−0.450707	−	1.04486i
$926$	23.6750	−	19.8657i	0.778009	−	0.652827i
$927$		0			0
$928$	−18.3873	−	15.4288i	−0.603594	−	0.506476i
$929$	−12.3051	+	41.1019i	−0.403718	+	1.34851i	0.478673	+	0.877993i	$0.341118\pi$
$929$	−12.3051	+	41.1019i	−0.403718	+	1.34851i	−0.882391	+	0.470518i	$0.844067\pi$
$930$		0			0
$931$	0.817071	−	14.0286i	0.0267784	−	0.459767i
$932$	−0.495707	+	8.51096i	−0.0162374	+	0.278786i
$933$		0			0
$934$	−6.57170	+	21.9510i	−0.215032	+	0.718258i
$935$	7.56964	+	6.35168i	0.247554	+	0.207722i
$936$		0			0
$937$	−10.4519	+	8.77015i	−0.341447	+	0.286508i	−0.797345	−	0.603524i	$-0.793763\pi$
$937$	−10.4519	+	8.77015i	−0.341447	+	0.286508i	0.455898	+	0.890032i	$0.349318\pi$
$938$	0.360130	+	0.834875i	0.0117587	+	0.0272597i
$939$		0			0
$940$	1.35451	+	4.52439i	0.0441794	+	0.147569i
$941$	17.6077	−	40.8193i	0.573995	−	1.33067i	−0.345814	−	0.938303i	$-0.612397\pi$
$941$	17.6077	−	40.8193i	0.573995	−	1.33067i	0.919809	−	0.392367i	$-0.128344\pi$
$942$		0			0
$943$	29.1763	−	19.1896i	0.950112	−	0.624898i
$944$	1.73463	−	3.00447i	0.0564575	−	0.0977873i
$945$		0			0
$946$	4.57603	+	7.92592i	0.148780	+	0.257694i
$947$	−3.87411	−	1.94565i	−0.125892	−	0.0632251i	0.384739	−	0.923026i	$-0.374292\pi$
$947$	−3.87411	−	1.94565i	−0.125892	−	0.0632251i	−0.510630	+	0.859800i	$0.670588\pi$
$948$		0			0
$949$	−22.0872	−	29.6683i	−0.716981	−	0.963073i
$950$	5.40281	−	5.72664i	0.175290	−	0.185797i
$951$		0			0
$952$	13.5579	+	1.58470i	0.439416	+	0.0513603i
$953$	−34.6339	−	12.6057i	−1.12190	−	0.408339i	−0.286556	−	0.958063i	$-0.592511\pi$
$953$	−34.6339	−	12.6057i	−1.12190	−	0.408339i	−0.835346	+	0.549724i	$0.814733\pi$
$954$		0			0
$955$	7.65355	−	2.78566i	0.247663	−	0.0901419i
$956$	21.4749	−	5.08964i	0.694547	−	0.164611i
$957$		0			0
$958$	9.92490	+	6.52771i	0.320659	+	0.210901i
$959$	−18.6292	+	9.35595i	−0.601569	+	0.302119i
$960$		0			0
$961$	−16.8879	−	17.9001i	−0.544770	−	0.577422i
$962$	6.43203	−	36.4778i	0.207377	−	1.17609i
$963$		0			0
$964$	2.85744	+	16.2054i	0.0920320	+	0.521939i
$965$	11.4605	−	15.3942i	0.368928	−	0.495556i
$966$		0			0
$967$	−9.95790	−	2.36007i	−0.320225	−	0.0758946i	0.0673601	−	0.997729i	$-0.478542\pi$
$967$	−9.95790	−	2.36007i	−0.320225	−	0.0758946i	−0.387585	+	0.921834i	$0.626691\pi$
$968$	−17.1685	+	2.00671i	−0.551817	+	0.0644981i
$969$		0			0
$970$	0.0796419	+	1.36740i	0.00255715	+	0.0439045i
$971$	−43.9486			−1.41038			−0.705188	−	0.709020i	$-0.749138\pi$
$971$	−43.9486			−1.41038			−0.705188	+	0.709020i	$0.749138\pi$
$972$		0			0
$973$	13.7265			0.440051
$974$	−0.439673	−	7.54889i	−0.0140880	−	0.241882i
$975$		0			0
$976$	−3.72547	+	0.435446i	−0.119250	+	0.0139383i
$977$	57.4171	+	13.6081i	1.83694	+	0.435362i	0.994617	−	0.103619i	$-0.0330421\pi$
$977$	57.4171	+	13.6081i	1.83694	+	0.435362i	0.842318	+	0.538980i	$0.181190\pi$
$978$		0			0
$979$	4.32471	−	5.80909i	0.138218	−	0.185659i
$980$	−1.44193	−	8.17758i	−0.0460607	−	0.261223i
$981$		0			0
$982$	−4.03329	+	22.8740i	−0.128708	+	0.729937i
$983$	18.3835	+	19.4854i	0.586344	+	0.621488i	0.950827	−	0.309722i	$-0.100236\pi$
$983$	18.3835	+	19.4854i	0.586344	+	0.621488i	−0.364483	+	0.931210i	$0.618754\pi$
$984$		0			0
$985$	12.4949	−	6.27516i	0.398120	−	0.199943i
$986$	−10.9079	−	7.17423i	−0.347378	−	0.228474i
$987$		0			0
$988$	−15.4327	+	3.65761i	−0.490979	+	0.116364i
$989$	−28.6598	+	10.4313i	−0.911329	+	0.331697i
$990$		0			0
$991$	8.60252	+	3.13106i	0.273268	+	0.0994614i	0.475019	−	0.879975i	$-0.342441\pi$
$991$	8.60252	+	3.13106i	0.273268	+	0.0994614i	−0.201751	+	0.979437i	$0.564663\pi$
$992$	−42.7589	−	4.99779i	−1.35760	−	0.158680i
$993$		0			0
$994$	5.45043	−	5.77712i	0.172877	−	0.183239i
$995$	−3.09701	−	4.16000i	−0.0981817	−	0.131881i
$996$		0			0
$997$	37.8253	+	18.9966i	1.19794	+	0.601628i	0.932034	−	0.362370i	$-0.118032\pi$
$997$	37.8253	+	18.9966i	1.19794	+	0.601628i	0.265907	+	0.963999i	$0.414329\pi$
$998$	9.90918	+	17.1632i	0.313670	+	0.543292i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.d.514.3		144
3.2	odd	2		729.2.g.a.514.6		144
9.2	odd	6		729.2.g.b.28.6		144
9.4	even	3		81.2.g.a.13.6	✓	144
9.5	odd	6		243.2.g.a.10.3		144
9.7	even	3		729.2.g.c.28.3		144
81.2	odd	54		729.2.g.a.217.6		144
81.22	even	27		6561.2.a.c.1.49		72
81.25	even	27		729.2.g.c.703.3		144
81.29	odd	54		243.2.g.a.73.3		144
81.52	even	27		81.2.g.a.25.6	yes	144
81.56	odd	54		729.2.g.b.703.6		144
81.59	odd	54		6561.2.a.d.1.24		72
81.79	even	27	inner	729.2.g.d.217.3		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.13.6	✓	144	9.4	even	3
81.2.g.a.25.6	yes	144	81.52	even	27
243.2.g.a.10.3		144	9.5	odd	6
243.2.g.a.73.3		144	81.29	odd	54
729.2.g.a.217.6		144	81.2	odd	54
729.2.g.a.514.6		144	3.2	odd	2
729.2.g.b.28.6		144	9.2	odd	6
729.2.g.b.703.6		144	81.56	odd	54
729.2.g.c.28.3		144	9.7	even	3
729.2.g.c.703.3		144	81.25	even	27
729.2.g.d.217.3		144	81.79	even	27	inner
729.2.g.d.514.3		144	1.1	even	1	trivial
6561.2.a.c.1.49		72	81.22	even	27
6561.2.a.d.1.24		72	81.59	odd	54

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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0484354 - 0.831603i) q^{2} +(1.29726 - 0.151628i) q^{4} +(-1.17364 - 0.278158i) q^{5} +(-0.785201 + 1.05471i) q^{7} +(-0.478230 - 2.71217i) q^{8} +(-0.174471 + 0.989477i) q^{10} +(-1.49146 - 1.58086i) q^{11} +(4.07045 - 2.04426i) q^{13} +(0.915130 + 0.601890i) q^{14} +(0.309479 - 0.0733479i) q^{16} +(3.54217 - 1.28924i) q^{17} +(-2.50517 - 0.911807i) q^{19} +(-1.56469 - 0.182886i) q^{20} +(-1.24241 + 1.31687i) q^{22} +(-3.60284 - 4.83945i) q^{23} +(-3.16810 - 1.59108i) q^{25} +(-1.89717 - 3.28599i) q^{26} +(-0.858686 + 1.48729i) q^{28} +(3.47381 - 2.28476i) q^{29} +(2.95363 - 6.84728i) q^{31} +(-1.65571 - 5.53044i) q^{32} +(-1.24371 - 2.88323i) q^{34} +(1.21492 - 1.01944i) q^{35} +(7.47819 + 6.27494i) q^{37} +(-0.636923 + 2.12747i) q^{38} +(-0.193143 + 3.31614i) q^{40} +(-0.336547 + 5.77829i) q^{41} +(1.44983 - 4.84276i) q^{43} +(-2.17451 - 1.82463i) q^{44} +(-3.85000 + 3.23053i) q^{46} +(-1.18743 - 2.75276i) q^{47} +(1.51175 + 5.04961i) q^{49} +(-1.16970 + 2.71167i) q^{50} +(4.97047 - 3.26913i) q^{52} +(-6.22987 + 10.7905i) q^{53} +(1.31071 + 2.27022i) q^{55} +(3.23606 + 1.62521i) q^{56} +(-2.06827 - 2.77817i) q^{58} +(7.48542 - 7.93408i) q^{59} +(-11.7134 - 1.36910i) q^{61} +(-5.83728 - 2.12460i) q^{62} +(-3.92120 + 1.42720i) q^{64} +(-5.34588 + 1.26700i) q^{65} +(0.693545 + 0.456152i) q^{67} +(4.39962 - 2.20957i) q^{68} +(-0.906613 - 0.960954i) q^{70} +(1.25916 - 7.14107i) q^{71} +(-1.41006 - 7.99685i) q^{73} +(4.85605 - 6.52281i) q^{74} +(-3.38811 - 0.802996i) q^{76} +(2.83844 - 0.331766i) q^{77} +(0.668640 + 11.4801i) q^{79} -0.383620 q^{80} +4.82155 q^{82} +(0.277632 + 4.76675i) q^{83} +(-4.51585 + 0.527827i) q^{85} +(-4.09748 - 0.971120i) q^{86} +(-3.57430 + 4.80112i) q^{88} +(0.578632 + 3.28158i) q^{89} +(-1.04003 + 5.89829i) q^{91} +(-5.40761 - 5.73174i) q^{92} +(-2.23169 + 1.12080i) q^{94} +(2.68654 + 1.76697i) q^{95} +(1.32651 - 0.314388i) q^{97} +(4.12605 - 1.50176i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} + 45 q^{20} + 9 q^{22} - 45 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28}+ \cdots + 81 q^{98}+O(q^{100}) \) 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 - 18 * q^10 + 9 * q^11 + 9 * q^13 + 9 * q^14 + 9 * q^16 - 18 * q^17 - 18 * q^19 + 45 * q^20 + 9 * q^22 - 45 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 + 36 * q^29 + 9 * q^31 - 99 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 + 18 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 - 99 * q^47 + 9 * q^49 + 126 * q^50 - 27 * q^52 + 45 * q^53 - 9 * q^55 - 225 * q^56 + 9 * q^58 + 72 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 - 81 * q^65 - 45 * q^67 + 117 * q^68 - 99 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 - 153 * q^76 + 81 * q^77 - 99 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 - 99 * q^85 + 81 * q^86 - 153 * q^88 - 81 * q^89 - 18 * q^91 + 207 * q^92 - 99 * q^94 - 171 * q^95 - 45 * q^97 + 81 * q^98

Introduction

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