LMFDB - Embedded newform 486.2.e.g.55.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [486,2,Mod(55,486)] 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("486.55"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(486, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([16])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 486 = 2 \cdot 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	486.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$3.88072953823$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 33 x^{10} - 110 x^{9} + 318 x^{8} - 678 x^{7} + 1225 x^{6} - 1698 x^{5} + 1905 x^{4} + \cdots + 57 $ x^12 - 6x^11 + 33x^10 - 110x^9 + 318x^8 - 678x^7 + 1225x^6 - 1698x^5 + 1905x^4 - 1584x^3 + 936x^2 - 342*x + 57
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			55.1
Root			$0.500000 + 2.42499i$ of defining polynomial
Character	$\chi$	$=$	486.55
Dual form			486.2.e.g.433.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.939693 - 0.342020i) q^{2} +(0.766044 - 0.642788i) q^{4} +(-0.550137 - 3.11998i) q^{5} +(2.82342 + 2.36913i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.58406 - 2.74367i) q^{10} +(0.396798 - 2.25035i) q^{11} +(-2.91331 - 1.06036i) q^{13} +(3.46344 + 1.26059i) q^{14} +(0.173648 - 0.984808i) q^{16} +(0.862878 + 1.49455i) q^{17} +(1.69740 - 2.93998i) q^{19} +(-2.42692 - 2.03643i) q^{20} +(-0.396798 - 2.25035i) q^{22} +(2.56861 - 2.15532i) q^{23} +(-4.73319 + 1.72274i) q^{25} -3.10027 q^{26} +3.68572 q^{28} +(-0.550137 + 0.200234i) q^{29} +(-3.55290 + 2.98123i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(1.32201 + 1.10929i) q^{34} +(5.83839 - 10.1124i) q^{35} +(3.65360 + 6.32822i) q^{37} +(0.589500 - 3.34322i) q^{38} +(-2.97705 - 1.08356i) q^{40} +(-6.65351 - 2.42168i) q^{41} +(0.287894 - 1.63273i) q^{43} +(-1.14253 - 1.97893i) q^{44} +(1.67654 - 2.90386i) q^{46} +(2.95079 + 2.47601i) q^{47} +(1.14339 + 6.48449i) q^{49} +(-3.85853 + 3.23769i) q^{50} +(-2.91331 + 1.06036i) q^{52} +2.58267 q^{53} -7.23936 q^{55} +(3.46344 - 1.26059i) q^{56} +(-0.448476 + 0.376316i) q^{58} +(1.67799 + 9.51638i) q^{59} +(10.0285 + 8.41495i) q^{61} +(-2.31899 + 4.01660i) q^{62} +(-0.500000 - 0.866025i) q^{64} +(-1.70558 + 9.67281i) q^{65} +(8.08959 + 2.94437i) q^{67} +(1.62168 + 0.590243i) q^{68} +(2.02765 - 11.4994i) q^{70} +(0.993732 + 1.72119i) q^{71} +(-5.32371 + 9.22094i) q^{73} +(5.59764 + 4.69698i) q^{74} +(-0.589500 - 3.34322i) q^{76} +(6.45172 - 5.41363i) q^{77} +(-13.2433 + 4.82016i) q^{79} -3.16812 q^{80} -7.08052 q^{82} +(-2.91156 + 1.05972i) q^{83} +(4.18826 - 3.51437i) q^{85} +(-0.287894 - 1.63273i) q^{86} +(-1.75046 - 1.46881i) q^{88} +(-8.67300 + 15.0221i) q^{89} +(-5.71337 - 9.89585i) q^{91} +(0.582258 - 3.30215i) q^{92} +(3.61968 + 1.31746i) q^{94} +(-10.1065 - 3.67846i) q^{95} +(1.59603 - 9.05153i) q^{97} +(3.29226 + 5.70237i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{5} + 6 q^{7} + 6 q^{8} - 3 q^{10} - 6 q^{11} - 6 q^{13} + 3 q^{14} + 6 q^{17} - 9 q^{19} + 3 q^{20} + 6 q^{22} + 6 q^{23} - 27 q^{25} - 18 q^{26} + 12 q^{28} + 3 q^{29} - 27 q^{31} + 12 q^{34}+ \cdots + 12 q^{98}+O(q^{100}) $ 12 * q + 3 * q^5 + 6 * q^7 + 6 * q^8 - 3 * q^10 - 6 * q^11 - 6 * q^13 + 3 * q^14 + 6 * q^17 - 9 * q^19 + 3 * q^20 + 6 * q^22 + 6 * q^23 - 27 * q^25 - 18 * q^26 + 12 * q^28 + 3 * q^29 - 27 * q^31 + 12 * q^34 - 3 * q^35 - 15 * q^37 + 15 * q^38 + 6 * q^40 - 15 * q^41 + 18 * q^43 + 3 * q^44 + 3 * q^46 + 27 * q^47 + 42 * q^49 - 36 * q^50 - 6 * q^52 + 12 * q^53 + 18 * q^55 + 3 * q^56 - 12 * q^58 + 24 * q^59 + 27 * q^61 + 12 * q^62 - 6 * q^64 - 57 * q^65 + 9 * q^67 + 15 * q^68 - 6 * q^70 - 12 * q^71 - 21 * q^73 + 3 * q^74 - 15 * q^76 + 51 * q^77 - 42 * q^79 - 6 * q^80 + 6 * q^82 - 45 * q^85 - 18 * q^86 - 12 * q^88 - 12 * q^89 - 6 * q^91 + 24 * q^92 - 9 * q^94 - 48 * q^95 - 24 * q^97 + 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/486\mathbb{Z}\right)^\times$.

$n$	$245$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

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 $

$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$3$		0			0
$3$		0			0
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	−0.550137	−	3.11998i	−0.246029	−	1.39530i	−0.818091	−	0.575089i	$-0.804967\pi$
$5$	−0.550137	−	3.11998i	−0.246029	−	1.39530i	0.572062	−	0.820210i	$-0.306144\pi$
$6$		0			0
$7$	2.82342	+	2.36913i	1.06715	+	0.895449i	0.994792	−	0.101930i	$-0.0325017\pi$
$7$	2.82342	+	2.36913i	1.06715	+	0.895449i	0.0723626	+	0.997378i	$0.476946\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$		0			0
$10$	−1.58406	−	2.74367i	−0.500923	−	0.867624i
$11$	0.396798	−	2.25035i	0.119639	−	0.678507i	−0.864709	−	0.502273i	$-0.832497\pi$
$11$	0.396798	−	2.25035i	0.119639	−	0.678507i	0.984348	−	0.176234i	$-0.0563915\pi$
$12$		0			0
$13$	−2.91331	−	1.06036i	−0.808006	−	0.294090i	−0.0952058	−	0.995458i	$-0.530351\pi$
$13$	−2.91331	−	1.06036i	−0.808006	−	0.294090i	−0.712800	+	0.701368i	$0.752573\pi$
$14$	3.46344	+	1.26059i	0.925644	+	0.336907i
$15$		0			0
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	0.862878	+	1.49455i	0.209279	+	0.362481i	0.951487	−	0.307687i	$-0.0995551\pi$
$17$	0.862878	+	1.49455i	0.209279	+	0.362481i	−0.742209	+	0.670169i	$0.766222\pi$
$18$		0			0
$19$	1.69740	−	2.93998i	0.389410	−	0.674478i	−0.602960	−	0.797771i	$-0.706012\pi$
$19$	1.69740	−	2.93998i	0.389410	−	0.674478i	0.992370	+	0.123293i	$0.0393456\pi$
$20$	−2.42692	−	2.03643i	−0.542675	−	0.455359i
$21$		0			0
$22$	−0.396798	−	2.25035i	−0.0845976	−	0.479777i
$23$	2.56861	−	2.15532i	0.535593	−	0.449416i	−0.334434	−	0.942419i	$-0.608545\pi$
$23$	2.56861	−	2.15532i	0.535593	−	0.449416i	0.870028	+	0.493003i	$0.164101\pi$
$24$		0			0
$25$	−4.73319	+	1.72274i	−0.946638	+	0.344548i
$26$	−3.10027			−0.608014
$27$		0			0
$28$	3.68572			0.696535
$29$	−0.550137	+	0.200234i	−0.102158	+	0.0371825i	−0.392593	−	0.919712i	$-0.628422\pi$
$29$	−0.550137	+	0.200234i	−0.102158	+	0.0371825i	0.290436	+	0.956895i	$0.406200\pi$
$30$		0			0
$31$	−3.55290	+	2.98123i	−0.638119	+	0.535445i	−0.903440	−	0.428715i	$-0.858966\pi$
$31$	−3.55290	+	2.98123i	−0.638119	+	0.535445i	0.265321	+	0.964160i	$0.414522\pi$
$32$	−0.173648	−	0.984808i	−0.0306970	−	0.174091i
$33$		0			0
$34$	1.32201	+	1.10929i	0.226722	+	0.190242i
$35$	5.83839	−	10.1124i	0.986868	−	1.70931i
$36$		0			0
$37$	3.65360	+	6.32822i	0.600648	+	1.04035i	0.992723	+	0.120420i	$0.0384240\pi$
$37$	3.65360	+	6.32822i	0.600648	+	1.04035i	−0.392075	+	0.919933i	$0.628243\pi$
$38$	0.589500	−	3.34322i	0.0956296	−	0.542342i
$39$		0			0
$40$	−2.97705	−	1.08356i	−0.470714	−	0.171326i
$41$	−6.65351	−	2.42168i	−1.03910	−	0.378203i	−0.234563	−	0.972101i	$-0.575366\pi$
$41$	−6.65351	−	2.42168i	−1.03910	−	0.378203i	−0.804540	+	0.593898i	$0.797588\pi$
$42$		0			0
$43$	0.287894	−	1.63273i	0.0439034	−	0.248989i	−0.954955	−	0.296749i	$-0.904097\pi$
$43$	0.287894	−	1.63273i	0.0439034	−	0.248989i	0.998859	+	0.0477608i	$0.0152085\pi$
$44$	−1.14253	−	1.97893i	−0.172243	−	0.298334i
$45$		0			0
$46$	1.67654	−	2.90386i	0.247193	−	0.428151i
$47$	2.95079	+	2.47601i	0.430417	+	0.361163i	0.832109	−	0.554612i	$-0.187133\pi$
$47$	2.95079	+	2.47601i	0.430417	+	0.361163i	−0.401692	+	0.915775i	$0.631578\pi$
$48$		0			0
$49$	1.14339	+	6.48449i	0.163342	+	0.926356i
$50$	−3.85853	+	3.23769i	−0.545679	+	0.457879i
$51$		0			0
$52$	−2.91331	+	1.06036i	−0.404003	+	0.147045i
$53$	2.58267			0.354757			0.177379	−	0.984143i	$-0.443238\pi$
$53$	2.58267			0.354757			0.177379	+	0.984143i	$0.443238\pi$
$54$		0			0
$55$	−7.23936			−0.976155
$56$	3.46344	−	1.26059i	0.462822	−	0.168453i
$57$		0			0
$58$	−0.448476	+	0.376316i	−0.0588878	+	0.0494127i
$59$	1.67799	+	9.51638i	0.218456	+	1.23893i	0.874807	+	0.484471i	$0.160988\pi$
$59$	1.67799	+	9.51638i	0.218456	+	1.23893i	−0.656351	+	0.754456i	$0.727901\pi$
$60$		0			0
$61$	10.0285	+	8.41495i	1.28402	+	1.07742i	0.992676	+	0.120807i	$0.0385481\pi$
$61$	10.0285	+	8.41495i	1.28402	+	1.07742i	0.291348	+	0.956617i	$0.405896\pi$
$62$	−2.31899	+	4.01660i	−0.294512	+	0.510109i
$63$		0			0
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−1.70558	+	9.67281i	−0.211551	+	1.19976i
$66$		0			0
$67$	8.08959	+	2.94437i	0.988301	+	0.359712i	0.785062	−	0.619417i	$-0.212631\pi$
$67$	8.08959	+	2.94437i	0.988301	+	0.359712i	0.203239	+	0.979129i	$0.434853\pi$
$68$	1.62168	+	0.590243i	0.196658	+	0.0715775i
$69$		0			0
$70$	2.02765	−	11.4994i	0.242351	−	1.37444i
$71$	0.993732	+	1.72119i	0.117934	+	0.204268i	0.918949	−	0.394377i	$-0.129039\pi$
$71$	0.993732	+	1.72119i	0.117934	+	0.204268i	−0.801015	+	0.598645i	$0.795706\pi$
$72$		0			0
$73$	−5.32371	+	9.22094i	−0.623094	+	1.07923i	0.365812	+	0.930689i	$0.380791\pi$
$73$	−5.32371	+	9.22094i	−0.623094	+	1.07923i	−0.988906	+	0.148541i	$0.952542\pi$
$74$	5.59764	+	4.69698i	0.650712	+	0.546012i
$75$		0			0
$76$	−0.589500	−	3.34322i	−0.0676203	−	0.383494i
$77$	6.45172	−	5.41363i	0.735241	−	0.616941i
$78$		0			0
$79$	−13.2433	+	4.82016i	−1.48998	+	0.542310i	−0.953445	−	0.301566i	$-0.902491\pi$
$79$	−13.2433	+	4.82016i	−1.48998	+	0.542310i	−0.536539	+	0.843876i	$0.680268\pi$
$80$	−3.16812			−0.354206
$81$		0			0
$82$	−7.08052			−0.781912
$83$	−2.91156	+	1.05972i	−0.319586	+	0.116320i	−0.496832	−	0.867847i	$-0.665503\pi$
$83$	−2.91156	+	1.05972i	−0.319586	+	0.116320i	0.177246	+	0.984167i	$0.443281\pi$
$84$		0			0
$85$	4.18826	−	3.51437i	0.454281	−	0.381187i
$86$	−0.287894	−	1.63273i	−0.0310444	−	0.176062i
$87$		0			0
$88$	−1.75046	−	1.46881i	−0.186600	−	0.156576i
$89$	−8.67300	+	15.0221i	−0.919336	+	1.59234i	−0.118911	+	0.992905i	$0.537940\pi$
$89$	−8.67300	+	15.0221i	−0.919336	+	1.59234i	−0.800425	+	0.599432i	$0.795393\pi$
$90$		0			0
$91$	−5.71337	−	9.89585i	−0.598924	−	1.03737i
$92$	0.582258	−	3.30215i	0.0607046	−	0.344273i
$93$		0			0
$94$	3.61968	+	1.31746i	0.373341	+	0.135885i
$95$	−10.1065	−	3.67846i	−1.03690	−	0.377402i
$96$		0			0
$97$	1.59603	−	9.05153i	0.162052	−	0.919044i	−0.790000	−	0.613107i	$-0.789919\pi$
$97$	1.59603	−	9.05153i	0.162052	−	0.919044i	0.952052	−	0.305937i	$-0.0989695\pi$
$98$	3.29226	+	5.70237i	0.332569	+	0.576026i
$99$		0			0
$100$	−2.51848	+	4.36213i	−0.251848	+	0.436213i
$101$	−9.16203	−	7.68785i	−0.911656	−	0.764970i	0.0607775	−	0.998151i	$-0.480642\pi$
$101$	−9.16203	−	7.68785i	−0.911656	−	0.764970i	−0.972433	+	0.233181i	$0.925086\pi$
$102$		0			0
$103$	−2.21340	−	12.5528i	−0.218093	−	1.23687i	−0.875458	−	0.483294i	$-0.839440\pi$
$103$	−2.21340	−	12.5528i	−0.218093	−	1.23687i	0.657365	−	0.753572i	$-0.271671\pi$
$104$	−2.37495	+	1.99282i	−0.232883	+	0.195412i
$105$		0			0
$106$	2.42692	−	0.883326i	0.235723	−	0.0857962i
$107$	−6.09894			−0.589607			−0.294803	−	0.955558i	$-0.595254\pi$
$107$	−6.09894			−0.589607			−0.294803	+	0.955558i	$0.595254\pi$
$108$		0			0
$109$	11.2390			1.07650			0.538250	−	0.842785i	$-0.319086\pi$
$109$	11.2390			1.07650			0.538250	+	0.842785i	$0.319086\pi$
$110$	−6.80277	+	2.47601i	−0.648619	+	0.236078i
$111$		0			0
$112$	2.82342	−	2.36913i	0.266789	−	0.223862i
$113$	1.22195	+	6.93005i	0.114952	+	0.651924i	0.986774	+	0.162102i	$0.0518273\pi$
$113$	1.22195	+	6.93005i	0.114952	+	0.651924i	−0.871822	+	0.489822i	$0.837062\pi$
$114$		0			0
$115$	−8.13767	−	6.82831i	−0.758841	−	0.636744i
$116$	−0.292722	+	0.507009i	−0.0271786	+	0.0470746i
$117$		0			0
$118$	4.83159	+	8.36857i	0.444784	+	0.770389i
$119$	−1.10452	+	6.26402i	−0.101251	+	0.574221i
$120$		0			0
$121$	5.42998	+	1.97635i	0.493635	+	0.179668i
$122$	12.3018	+	4.47750i	1.11376	+	0.405374i
$123$		0			0
$124$	−0.805376	+	4.56751i	−0.0723249	+	0.410175i
$125$	0.0585380	+	0.101391i	0.00523579	+	0.00906866i
$126$		0			0
$127$	−2.99250	+	5.18316i	−0.265541	+	0.459931i	−0.967705	−	0.252084i	$-0.918884\pi$
$127$	−2.99250	+	5.18316i	−0.265541	+	0.459931i	0.702164	+	0.712015i	$0.252217\pi$
$128$	−0.766044	−	0.642788i	−0.0677094	−	0.0568149i
$129$		0			0
$130$	1.70558	+	9.67281i	0.149589	+	0.848362i
$131$	−12.5746	+	10.5514i	−1.09865	+	0.921878i	−0.997334	−	0.0729758i	$-0.976750\pi$
$131$	−12.5746	+	10.5514i	−1.09865	+	0.921878i	−0.101318	+	0.994854i	$0.532306\pi$
$132$		0			0
$133$	11.7577	−	4.27945i	1.01952	−	0.371075i
$134$	8.60876			0.743684
$135$		0			0
$136$	1.72576			0.147982
$137$	−0.198424	+	0.0722205i	−0.0169525	+	0.00617021i	−0.350482	−	0.936569i	$-0.613982\pi$
$137$	−0.198424	+	0.0722205i	−0.0169525	+	0.00617021i	0.333530	+	0.942739i	$0.391760\pi$
$138$		0			0
$139$	2.81254	−	2.36000i	0.238557	−	0.200173i	−0.515669	−	0.856788i	$-0.672457\pi$
$139$	2.81254	−	2.36000i	0.238557	−	0.200173i	0.754226	+	0.656615i	$0.228012\pi$
$140$	−2.02765	−	11.4994i	−0.171368	−	0.971875i
$141$		0			0
$142$	1.52249	+	1.27752i	0.127764	+	0.107207i
$143$	−3.54217	+	6.13522i	−0.296211	+	0.513053i
$144$		0			0
$145$	0.927377	+	1.60626i	0.0770145	+	0.133393i
$146$	−1.84891	+	10.4857i	−0.153017	+	0.867800i
$147$		0			0
$148$	6.86652	+	2.49921i	0.564424	+	0.205434i
$149$	14.5412	+	5.29255i	1.19126	+	0.433583i	0.860166	−	0.510015i	$-0.170360\pi$
$149$	14.5412	+	5.29255i	1.19126	+	0.433583i	0.331094	+	0.943598i	$0.392582\pi$
$150$		0			0
$151$	3.49827	−	19.8397i	0.284685	−	1.61453i	−0.421723	−	0.906725i	$-0.638575\pi$
$151$	3.49827	−	19.8397i	0.284685	−	1.61453i	0.706408	−	0.707804i	$-0.250314\pi$
$152$	−1.69740	−	2.93998i	−0.137677	−	0.238464i
$153$		0			0
$154$	4.21106	−	7.29377i	0.339337	−	0.587748i
$155$	11.2560	+	9.44489i	0.904102	+	0.758632i
$156$		0			0
$157$	3.12522	+	17.7240i	0.249420	+	1.41453i	0.810000	+	0.586430i	$0.199467\pi$
$157$	3.12522	+	17.7240i	0.249420	+	1.41453i	−0.560580	+	0.828100i	$0.689422\pi$
$158$	−10.7960	+	9.05893i	−0.858885	+	0.720690i
$159$		0			0
$160$	−2.97705	+	1.08356i	−0.235357	+	0.0856629i
$161$	12.3585			0.973989
$162$		0			0
$163$	3.05289			0.239121			0.119560	−	0.992827i	$-0.461851\pi$
$163$	3.05289			0.239121			0.119560	+	0.992827i	$0.461851\pi$
$164$	−6.65351	+	2.42168i	−0.519552	+	0.189101i
$165$		0			0
$166$	−2.37353	+	1.99163i	−0.184222	+	0.154580i
$167$	0.712165	+	4.03889i	0.0551090	+	0.312539i	0.999885	−	0.0151788i	$-0.00483174\pi$
$167$	0.712165	+	4.03889i	0.0551090	+	0.312539i	−0.944776	+	0.327717i	$0.893721\pi$
$168$		0			0
$169$	−2.59559	−	2.17795i	−0.199660	−	0.167535i
$170$	2.73370	−	4.73490i	0.209665	−	0.363150i
$171$		0			0
$172$	−0.828957	−	1.43580i	−0.0632074	−	0.109478i
$173$	2.95672	−	16.7684i	0.224796	−	1.27488i	−0.638280	−	0.769804i	$-0.720354\pi$
$173$	2.95672	−	16.7684i	0.224796	−	1.27488i	0.863076	−	0.505075i	$-0.168535\pi$
$174$		0			0
$175$	−17.4452	−	6.34953i	−1.31873	−	0.479980i
$176$	−2.14726	−	0.781539i	−0.161856	−	0.0589107i
$177$		0			0
$178$	−3.01210	+	17.0825i	−0.225767	+	1.28039i
$179$	−7.27802	−	12.6059i	−0.543985	−	0.942210i	−0.998670	−	0.0515575i	$-0.983581\pi$
$179$	−7.27802	−	12.6059i	−0.543985	−	0.942210i	0.454685	−	0.890652i	$-0.349752\pi$
$180$		0			0
$181$	6.51190	−	11.2789i	0.484026	−	0.838357i	−0.515806	−	0.856706i	$-0.672507\pi$
$181$	6.51190	−	11.2789i	0.484026	−	0.838357i	0.999832	+	0.0183482i	$0.00584075\pi$
$182$	−8.75339	−	7.34497i	−0.648845	−	0.544445i
$183$		0			0
$184$	−0.582258	−	3.30215i	−0.0429246	−	0.243438i
$185$	17.7340	−	14.8806i	1.30383	−	1.09404i
$186$		0			0
$187$	3.70565	−	1.34875i	0.270984	−	0.0986300i
$188$	3.85198			0.280935
$189$		0			0
$190$	−10.7551			−0.780258
$191$	3.38559	−	1.23226i	0.244973	−	0.0891629i	−0.216616	−	0.976257i	$-0.569502\pi$
$191$	3.38559	−	1.23226i	0.244973	−	0.0891629i	0.461589	+	0.887094i	$0.347280\pi$
$192$		0			0
$193$	1.12982	−	0.948028i	0.0813259	−	0.0682405i	−0.601218	−	0.799085i	$-0.705318\pi$
$193$	1.12982	−	0.948028i	0.0813259	−	0.0682405i	0.682544	+	0.730844i	$0.260873\pi$
$194$	−1.59603	−	9.05153i	−0.114588	−	0.649862i
$195$		0			0
$196$	5.04404	+	4.23245i	0.360288	+	0.302318i
$197$	1.26931	−	2.19851i	0.0904346	−	0.156637i	−0.817259	−	0.576270i	$-0.804508\pi$
$197$	1.26931	−	2.19851i	0.0904346	−	0.156637i	0.907694	+	0.419633i	$0.137841\pi$
$198$		0			0
$199$	0.925891	+	1.60369i	0.0656347	+	0.113683i	0.896975	−	0.442081i	$-0.145759\pi$
$199$	0.925891	+	1.60369i	0.0656347	+	0.113683i	−0.831341	+	0.555763i	$0.812426\pi$
$200$	−0.874658	+	4.96043i	−0.0618477	+	0.350755i
$201$		0			0
$202$	−11.2389	−	4.09062i	−0.790766	−	0.287815i
$203$	−2.02765	−	0.738005i	−0.142313	−	0.0517978i
$204$		0			0
$205$	−3.89526	+	22.0911i	−0.272057	+	1.54291i
$206$	−6.37324	−	11.0388i	−0.444045	−	0.769108i
$207$		0			0
$208$	−1.55014	+	2.68492i	−0.107483	+	0.186165i
$209$	−5.94247	−	4.98632i	−0.411049	−	0.344911i
$210$		0			0
$211$	−3.29728	−	18.6998i	−0.226994	−	1.28735i	−0.858836	−	0.512251i	$-0.828812\pi$
$211$	−3.29728	−	18.6998i	−0.226994	−	1.28735i	0.631842	−	0.775098i	$-0.282299\pi$
$212$	1.97844	−	1.66011i	0.135880	−	0.114017i
$213$		0			0
$214$	−5.73113	+	2.08596i	−0.391772	+	0.142593i
$215$	−5.25247			−0.358215
$216$		0			0
$217$	−17.0943			−1.16043
$218$	10.5612	−	3.84396i	0.715295	−	0.260346i
$219$		0			0
$220$	−5.54567	+	4.65337i	−0.373889	+	0.313730i
$221$	−0.929073	−	5.26903i	−0.0624962	−	0.354433i
$222$		0			0
$223$	−5.55716	−	4.66301i	−0.372135	−	0.312259i	0.437470	−	0.899233i	$-0.355874\pi$
$223$	−5.55716	−	4.66301i	−0.372135	−	0.312259i	−0.809606	+	0.586974i	$0.800319\pi$
$224$	1.84286	−	3.19193i	0.123131	−	0.213270i
$225$		0			0
$226$	3.51848	+	6.09418i	0.234046	+	0.405379i
$227$	4.95369	−	28.0938i	0.328788	−	1.86465i	−0.152807	−	0.988256i	$-0.548831\pi$
$227$	4.95369	−	28.0938i	0.328788	−	1.86465i	0.481595	−	0.876394i	$-0.340058\pi$
$228$		0			0
$229$	−1.74349	−	0.634578i	−0.115213	−	0.0419341i	0.283770	−	0.958892i	$-0.408415\pi$
$229$	−1.74349	−	0.634578i	−0.115213	−	0.0419341i	−0.398983	+	0.916958i	$0.630637\pi$
$230$	−9.98233	−	3.63327i	−0.658215	−	0.239571i
$231$		0			0
$232$	−0.101661	+	0.576550i	−0.00667439	+	0.0378524i
$233$	4.26735	+	7.39126i	0.279563	+	0.484218i	0.971276	−	0.237955i	$-0.0764770\pi$
$233$	4.26735	+	7.39126i	0.279563	+	0.484218i	−0.691713	+	0.722172i	$0.743144\pi$
$234$		0			0
$235$	6.10176	−	10.5686i	0.398035	−	0.689417i
$236$	7.40243	+	6.21138i	0.481857	+	0.404326i
$237$		0			0
$238$	1.10452	+	6.26402i	0.0715951	+	0.406036i
$239$	5.58290	−	4.68461i	0.361128	−	0.303022i	−0.444112	−	0.895971i	$-0.646481\pi$
$239$	5.58290	−	4.68461i	0.361128	−	0.303022i	0.805240	+	0.592949i	$0.202036\pi$
$240$		0			0
$241$	1.25441	−	0.456569i	0.0808039	−	0.0294102i	−0.301302	−	0.953529i	$-0.597421\pi$
$241$	1.25441	−	0.456569i	0.0808039	−	0.0294102i	0.382106	+	0.924119i	$0.375199\pi$
$242$	5.77847			0.371454
$243$		0			0
$244$	13.0913			0.838087
$245$	19.6025	−	7.13472i	1.25236	−	0.455821i
$246$		0			0
$247$	−8.06247	+	6.76521i	−0.513003	+	0.430460i
$248$	0.805376	+	4.56751i	0.0511414	+	0.290037i
$249$		0			0
$250$	0.0896853	+	0.0752549i	0.00567220	+	0.00475954i
$251$	−1.43928	+	2.49291i	−0.0908466	+	0.157351i	−0.907868	−	0.419257i	$-0.862291\pi$
$251$	−1.43928	+	2.49291i	−0.0908466	+	0.157351i	0.817021	+	0.576608i	$0.195624\pi$
$252$		0			0
$253$	−3.83102	−	6.63552i	−0.240854	−	0.417171i
$254$	−1.03928	+	5.89407i	−0.0652104	+	0.369827i
$255$		0			0
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	−24.2233	−	8.81657i	−1.51101	−	0.549962i	−0.552125	−	0.833761i	$-0.686183\pi$
$257$	−24.2233	−	8.81657i	−1.51101	−	0.549962i	−0.958884	+	0.283799i	$0.908405\pi$
$258$		0			0
$259$	−4.67674	+	26.5231i	−0.290599	+	1.64807i
$260$	4.91101	+	8.50613i	0.304568	+	0.527528i
$261$		0			0
$262$	−8.20752	+	14.2158i	−0.507062	+	0.878257i
$263$	11.5441	+	9.68661i	0.711837	+	0.597302i	0.925114	−	0.379690i	$-0.123969\pi$
$263$	11.5441	+	9.68661i	0.711837	+	0.597302i	−0.213277	+	0.976992i	$0.568414\pi$
$264$		0			0
$265$	−1.42082	−	8.05789i	−0.0872805	−	0.494993i
$266$	9.58495	−	8.04273i	0.587691	−	0.493131i
$267$		0			0
$268$	8.08959	−	2.94437i	0.494150	−	0.179856i
$269$	−16.0615			−0.979286			−0.489643	−	0.871923i	$-0.662873\pi$
$269$	−16.0615			−0.979286			−0.489643	+	0.871923i	$0.662873\pi$
$270$		0			0
$271$	9.41446			0.571888			0.285944	−	0.958246i	$-0.407693\pi$
$271$	9.41446			0.571888			0.285944	+	0.958246i	$0.407693\pi$
$272$	1.62168	−	0.590243i	0.0983288	−	0.0357887i
$273$		0			0
$274$	−0.161757	+	0.135730i	−0.00977209	+	0.00819976i
$275$	1.99865	+	11.3349i	0.120523	+	0.683521i
$276$		0			0
$277$	4.27051	+	3.58339i	0.256590	+	0.215305i	0.762004	−	0.647572i	$-0.224216\pi$
$277$	4.27051	+	3.58339i	0.256590	+	0.215305i	−0.505414	+	0.862877i	$0.668660\pi$
$278$	1.83576	−	3.17962i	0.110101	−	0.190701i
$279$		0			0
$280$	−5.83839	−	10.1124i	−0.348911	−	0.604331i
$281$	−4.86298	+	27.5793i	−0.290101	+	1.64525i	0.396372	+	0.918090i	$0.370269\pi$
$281$	−4.86298	+	27.5793i	−0.290101	+	1.64525i	−0.686473	+	0.727155i	$0.740842\pi$
$282$		0			0
$283$	−5.78401	−	2.10521i	−0.343824	−	0.125142i	0.164336	−	0.986404i	$-0.447452\pi$
$283$	−5.78401	−	2.10521i	−0.343824	−	0.125142i	−0.508160	+	0.861263i	$0.669674\pi$
$284$	1.86760	+	0.679753i	0.110822	+	0.0403359i
$285$		0			0
$286$	−1.23018	+	6.97671i	−0.0727422	+	0.412542i
$287$	−13.0484	−	22.6005i	−0.770222	−	1.33406i
$288$		0			0
$289$	7.01088	−	12.1432i	0.412405	−	0.714306i
$290$	1.42082	+	1.19221i	0.0834337	+	0.0700092i
$291$		0			0
$292$	1.84891	+	10.4857i	0.108199	+	0.613628i
$293$	−1.78879	+	1.50097i	−0.104502	+	0.0876878i	−0.693542	−	0.720416i	$-0.743951\pi$
$293$	−1.78879	+	1.50097i	−0.104502	+	0.0876878i	0.589039	+	0.808104i	$0.299506\pi$
$294$		0			0
$295$	28.7678	−	10.4706i	1.67493	−	0.609624i
$296$	7.30720			0.424722
$297$		0			0
$298$	15.4744			0.896408
$299$	−9.76857	+	3.55547i	−0.564931	+	0.205618i
$300$		0			0
$301$	4.68100	−	3.92782i	0.269808	−	0.226396i
$302$	−3.49827	−	19.8397i	−0.201303	−	1.14164i
$303$		0			0
$304$	−2.60057	−	2.18213i	−0.149153	−	0.125154i
$305$	20.7374	−	35.9183i	1.18742	−	2.05668i
$306$		0			0
$307$	−3.41265	−	5.91088i	−0.194770	−	0.337351i	0.752055	−	0.659100i	$-0.229063\pi$
$307$	−3.41265	−	5.91088i	−0.194770	−	0.337351i	−0.946825	+	0.321749i	$0.895729\pi$
$308$	1.46249	−	8.29417i	0.0833328	−	0.472604i
$309$		0			0
$310$	13.8075	+	5.02552i	0.784214	+	0.285430i
$311$	8.07686	+	2.93974i	0.457997	+	0.166697i	0.560707	−	0.828014i	$-0.310529\pi$
$311$	8.07686	+	2.93974i	0.457997	+	0.166697i	−0.102710	+	0.994711i	$0.532752\pi$
$312$		0			0
$313$	−3.76276	+	21.3397i	−0.212684	+	1.20619i	0.672196	+	0.740373i	$0.265351\pi$
$313$	−3.76276	+	21.3397i	−0.212684	+	1.20619i	−0.884880	+	0.465818i	$0.845760\pi$
$314$	8.99872	+	15.5862i	0.507827	+	0.879582i
$315$		0			0
$316$	−7.04660	+	12.2051i	−0.396402	+	0.686588i
$317$	−27.0567	−	22.7032i	−1.51965	−	1.27514i	−0.841559	−	0.540166i	$-0.818362\pi$
$317$	−27.0567	−	22.7032i	−1.51965	−	1.27514i	−0.678094	−	0.734975i	$-0.737194\pi$
$318$		0			0
$319$	0.232303	+	1.31746i	0.0130065	+	0.0737633i
$320$	−2.42692	+	2.03643i	−0.135669	+	0.113840i
$321$		0			0
$322$	11.6132	−	4.22687i	0.647180	−	0.235554i
$323$	5.85859			0.325981
$324$		0			0
$325$	15.6159			0.866217
$326$	2.86878	−	1.04415i	0.158887	−	0.0578302i
$327$		0			0
$328$	−5.42399	+	4.55127i	−0.299490	+	0.251302i
$329$	2.46534	+	13.9816i	0.135919	+	0.770832i
$330$		0			0
$331$	−19.7744	−	16.5927i	−1.08690	−	0.912017i	−0.0904242	−	0.995903i	$-0.528822\pi$
$331$	−19.7744	−	16.5927i	−1.08690	−	0.912017i	−0.996475	+	0.0838863i	$0.973267\pi$
$332$	−1.54921	+	2.68331i	−0.0850240	+	0.147266i
$333$		0			0
$334$	2.05060	+	3.55174i	0.112204	+	0.194343i
$335$	4.73600	−	26.8592i	0.258755	−	1.46748i
$336$		0			0
$337$	3.18047	+	1.15760i	0.173251	+	0.0630583i	0.427189	−	0.904162i	$-0.359504\pi$
$337$	3.18047	+	1.15760i	0.173251	+	0.0630583i	−0.253938	+	0.967220i	$0.581726\pi$
$338$	−3.18396	−	1.15887i	−0.173184	−	0.0630340i
$339$		0			0
$340$	0.949403	−	5.38433i	0.0514886	−	0.292006i
$341$	5.29904	+	9.17821i	0.286959	+	0.497028i
$342$		0			0
$343$	0.765664	−	1.32617i	0.0413420	−	0.0716064i
$344$	−1.27004	−	1.06569i	−0.0684758	−	0.0574580i
$345$		0			0
$346$	−2.95672	−	16.7684i	−0.158954	−	0.901476i
$347$	12.4099	−	10.4132i	0.666200	−	0.559009i	−0.245738	−	0.969336i	$-0.579030\pi$
$347$	12.4099	−	10.4132i	0.666200	−	0.559009i	0.911938	+	0.410328i	$0.134586\pi$
$348$		0			0
$349$	−4.22160	+	1.53654i	−0.225977	+	0.0822489i	−0.452527	−	0.891751i	$-0.649477\pi$
$349$	−4.22160	+	1.53654i	−0.225977	+	0.0822489i	0.226550	+	0.973999i	$0.427255\pi$
$350$	−18.5648			−0.992330
$351$		0			0
$352$	−2.28507			−0.121795
$353$	−21.8259	+	7.94399i	−1.16168	+	0.422816i	−0.849696	−	0.527272i	$-0.823215\pi$
$353$	−21.8259	+	7.94399i	−1.16168	+	0.422816i	−0.311981	+	0.950088i	$0.600993\pi$
$354$		0			0
$355$	4.82341	−	4.04732i	0.256000	−	0.214809i
$356$	3.01210	+	17.0825i	0.159641	+	0.905370i
$357$		0			0
$358$	−11.1506	−	9.35645i	−0.589327	−	0.494504i
$359$	−5.77697	+	10.0060i	−0.304897	+	0.528097i	−0.977238	−	0.212144i	$-0.931955\pi$
$359$	−5.77697	+	10.0060i	−0.304897	+	0.528097i	0.672341	+	0.740241i	$0.265289\pi$
$360$		0			0
$361$	3.73768	+	6.47385i	0.196720	+	0.340729i
$362$	2.26156	−	12.8259i	0.118865	−	0.674117i
$363$		0			0
$364$	−10.7376	−	3.90818i	−0.562804	−	0.204844i
$365$	31.6980	+	11.5371i	1.65915	+	0.603881i
$366$		0			0
$367$	2.70365	−	15.3332i	0.141130	−	0.800385i	−0.829264	−	0.558857i	$-0.811240\pi$
$367$	2.70365	−	15.3332i	0.141130	−	0.800385i	0.970394	−	0.241529i	$-0.0776488\pi$
$368$	−1.67654	−	2.90386i	−0.0873959	−	0.151374i
$369$		0			0
$370$	11.5750	−	20.0485i	0.601757	−	1.04227i
$371$	7.29198	+	6.11870i	0.378581	+	0.317667i
$372$		0			0
$373$	−1.69433	−	9.60903i	−0.0877291	−	0.497537i	−0.996734	−	0.0807517i	$-0.974268\pi$
$373$	−1.69433	−	9.60903i	−0.0877291	−	0.497537i	0.909005	−	0.416785i	$-0.136843\pi$
$374$	3.02087	−	2.53481i	0.156206	−	0.131072i
$375$		0			0
$376$	3.61968	−	1.31746i	0.186671	−	0.0679426i
$377$	1.81504			0.0934792
$378$		0			0
$379$	−18.7904			−0.965197			−0.482599	−	0.875842i	$-0.660307\pi$
$379$	−18.7904			−0.965197			−0.482599	+	0.875842i	$0.660307\pi$
$380$	−10.1065	+	3.67846i	−0.518452	+	0.188701i
$381$		0			0
$382$	2.75996	−	2.31588i	0.141212	−	0.118491i
$383$	−5.34281	−	30.3006i	−0.273005	−	1.54829i	−0.745229	−	0.666809i	$-0.767660\pi$
$383$	−5.34281	−	30.3006i	−0.273005	−	1.54829i	0.472224	−	0.881479i	$-0.343451\pi$
$384$		0			0
$385$	−20.4398	−	17.1510i	−1.04171	−	0.874096i
$386$	0.737435	−	1.27727i	0.0375344	−	0.0650116i
$387$		0			0
$388$	−4.59558	−	7.95978i	−0.233305	−	0.404097i
$389$	−5.14010	+	29.1510i	−0.260614	+	1.47801i	0.520628	+	0.853784i	$0.325698\pi$
$389$	−5.14010	+	29.1510i	−0.260614	+	1.47801i	−0.781241	+	0.624229i	$0.785413\pi$
$390$		0			0
$391$	5.43763	+	1.97914i	0.274993	+	0.100089i
$392$	6.18743	+	2.25204i	0.312512	+	0.113745i
$393$		0			0
$394$	0.440827	−	2.50005i	0.0222085	−	0.125951i
$395$	22.3244	+	38.6670i	1.12326	+	1.94555i
$396$		0			0
$397$	−8.07134	+	13.9800i	−0.405089	+	0.701635i	−0.994332	−	0.106321i	$-0.966093\pi$
$397$	−8.07134	+	13.9800i	−0.405089	+	0.701635i	0.589243	+	0.807956i	$0.299426\pi$
$398$	1.41855	+	1.19030i	0.0711054	+	0.0596645i
$399$		0			0
$400$	0.874658	+	4.96043i	0.0437329	+	0.248022i
$401$	−19.4287	+	16.3026i	−0.970223	+	0.814114i	−0.982586	−	0.185810i	$-0.940509\pi$
$401$	−19.4287	+	16.3026i	−0.970223	+	0.814114i	0.0123625	+	0.999924i	$0.496065\pi$
$402$		0			0
$403$	13.5118	−	4.91791i	0.673073	−	0.244978i
$404$	−11.9602			−0.595041
$405$		0			0
$406$	−2.15778			−0.107089
$407$	15.6905	−	5.71086i	0.777747	−	0.283077i
$408$		0			0
$409$	−17.4438	+	14.6371i	−0.862542	+	0.723759i	−0.962514	−	0.271231i	$-0.912569\pi$
$409$	−17.4438	+	14.6371i	−0.862542	+	0.723759i	0.0999721	+	0.994990i	$0.468125\pi$
$410$	3.89526	+	22.0911i	0.192373	+	1.09100i
$411$		0			0
$412$	−9.76437	−	8.19328i	−0.481056	−	0.403654i
$413$	−17.8079	+	30.8442i	−0.876269	+	1.51774i
$414$		0			0
$415$	4.90808	+	8.50104i	0.240928	+	0.417300i
$416$	−0.538357	+	3.05317i	−0.0263951	+	0.149694i
$417$		0			0
$418$	−7.28951	−	2.65317i	−0.356542	−	0.129771i
$419$	−4.62588	−	1.68368i	−0.225989	−	0.0822533i	0.226544	−	0.974001i	$-0.427257\pi$
$419$	−4.62588	−	1.68368i	−0.225989	−	0.0822533i	−0.452533	+	0.891748i	$0.649480\pi$
$420$		0			0
$421$	3.42393	−	19.4180i	0.166872	−	0.946378i	−0.780241	−	0.625479i	$-0.784904\pi$
$421$	3.42393	−	19.4180i	0.166872	−	0.946378i	0.947113	−	0.320899i	$-0.103985\pi$
$422$	−9.49415	−	16.4443i	−0.462168	−	0.800498i
$423$		0			0
$424$	1.29134	−	2.23666i	0.0627128	−	0.108622i
$425$	−6.65888	−	5.58746i	−0.323003	−	0.271032i
$426$		0			0
$427$	8.37870	+	47.5180i	0.405474	+	2.29955i
$428$	−4.67206	+	3.92032i	−0.225833	+	0.189496i
$429$		0			0
$430$	−4.93570	+	1.79645i	−0.238021	+	0.0866325i
$431$	6.16323			0.296873			0.148436	−	0.988922i	$-0.452576\pi$
$431$	6.16323			0.296873			0.148436	+	0.988922i	$0.452576\pi$
$432$		0			0
$433$	−14.7838			−0.710466			−0.355233	−	0.934778i	$-0.615599\pi$
$433$	−14.7838			−0.710466			−0.355233	+	0.934778i	$0.615599\pi$
$434$	−16.0634	+	5.84659i	−0.771066	+	0.280645i
$435$		0			0
$436$	8.60957	−	7.22429i	0.412324	−	0.345981i
$437$	−1.97665	−	11.2101i	−0.0945558	−	0.536253i
$438$		0			0
$439$	22.8029	+	19.1339i	1.08832	+	0.913210i	0.996585	−	0.0825729i	$-0.0263137\pi$
$439$	22.8029	+	19.1339i	1.08832	+	0.913210i	0.0917368	+	0.995783i	$0.470758\pi$
$440$	−3.61968	+	6.26947i	−0.172561	+	0.298885i
$441$		0			0
$442$	−2.67516	−	4.63351i	−0.127244	−	0.220394i
$443$	−5.29182	+	30.0114i	−0.251422	+	1.42588i	0.553671	+	0.832736i	$0.313227\pi$
$443$	−5.29182	+	30.0114i	−0.251422	+	1.42588i	−0.805093	+	0.593149i	$0.797885\pi$
$444$		0			0
$445$	51.6400	+	18.7954i	2.44797	+	0.890989i
$446$	−6.81687	−	2.48114i	−0.322788	−	0.117485i
$447$		0			0
$448$	0.640018	−	3.62972i	0.0302380	−	0.171488i
$449$	5.92055	+	10.2547i	0.279408	+	0.483949i	0.971238	−	0.238112i	$-0.0765284\pi$
$449$	5.92055	+	10.2547i	0.279408	+	0.483949i	−0.691830	+	0.722061i	$0.743195\pi$
$450$		0			0
$451$	−8.08973	+	14.0118i	−0.380930	+	0.659791i
$452$	5.39062	+	4.52327i	0.253553	+	0.212757i
$453$		0			0
$454$	−4.95369	−	28.0938i	−0.232488	−	1.31851i
$455$	−27.7318	+	23.2697i	−1.30008	+	1.09090i
$456$		0			0
$457$	0.175152	−	0.0637502i	0.00819327	−	0.00298211i	−0.337920	−	0.941175i	$-0.609723\pi$
$457$	0.175152	−	0.0637502i	0.00819327	−	0.00298211i	0.346114	+	0.938193i	$0.387501\pi$
$458$	−1.85538			−0.0866963
$459$		0			0
$460$	−10.6230			−0.495299
$461$	9.77783	−	3.55884i	0.455399	−	0.165752i	−0.104128	−	0.994564i	$-0.533205\pi$
$461$	9.77783	−	3.55884i	0.455399	−	0.165752i	0.559527	+	0.828812i	$0.310983\pi$
$462$		0			0
$463$	19.7551	−	16.5765i	0.918096	−	0.770374i	−0.0555458	−	0.998456i	$-0.517690\pi$
$463$	19.7551	−	16.5765i	0.918096	−	0.770374i	0.973642	+	0.228082i	$0.0732454\pi$
$464$	0.101661	+	0.576550i	0.00471951	+	0.0267657i
$465$		0			0
$466$	6.53795	+	5.48600i	0.302865	+	0.254134i
$467$	10.8506	−	18.7937i	0.502104	−	0.869670i	−0.497893	−	0.867239i	$-0.665893\pi$
$467$	10.8506	−	18.7937i	0.502104	−	0.869670i	0.999997	−	0.00243153i	$-0.000773982\pi$
$468$		0			0
$469$	15.8647	+	27.4785i	0.732566	+	1.26884i
$470$	2.11912	−	12.0181i	0.0977477	−	0.554355i
$471$		0			0
$472$	9.08043	+	3.30500i	0.417960	+	0.152125i
$473$	−3.55998	−	1.29573i	−0.163688	−	0.0595775i
$474$		0			0
$475$	−2.96929	+	16.8397i	−0.136240	+	0.772657i
$476$	3.18032	+	5.50848i	0.145770	+	0.252481i
$477$		0			0
$478$	3.64398	−	6.31156i	0.166672	−	0.288684i
$479$	29.9686	+	25.1466i	1.36930	+	1.14898i	0.972986	+	0.230864i	$0.0741553\pi$
$479$	29.9686	+	25.1466i	1.36930	+	1.14898i	0.396314	+	0.918115i	$0.370289\pi$
$480$		0			0
$481$	−3.93388	−	22.3102i	−0.179370	−	1.01726i
$482$	1.02261	−	0.858069i	0.0465785	−	0.0390840i
$483$		0			0
$484$	5.42998	−	1.97635i	0.246817	−	0.0898342i
$485$	−29.1187			−1.32221
$486$		0			0
$487$	−10.4833			−0.475043			−0.237522	−	0.971382i	$-0.576335\pi$
$487$	−10.4833			−0.475043			−0.237522	+	0.971382i	$0.576335\pi$
$488$	12.3018	−	4.47750i	0.556878	−	0.202687i
$489$		0			0
$490$	15.9801	−	13.4089i	0.721907	−	0.605752i
$491$	−1.19071	−	6.75285i	−0.0537360	−	0.304752i	0.946080	−	0.323933i	$-0.105005\pi$
$491$	−1.19071	−	6.75285i	−0.0537360	−	0.304752i	−0.999816	+	0.0191811i	$0.993894\pi$
$492$		0			0
$493$	−0.773960	−	0.649430i	−0.0348574	−	0.0292488i
$494$	−5.26240	+	9.11475i	−0.236767	+	0.410092i
$495$		0			0
$496$	2.31899	+	4.01660i	0.104126	+	0.180351i
$497$	−1.27201	+	7.21395i	−0.0570576	+	0.323590i
$498$		0			0
$499$	−17.6415	−	6.42099i	−0.789743	−	0.287443i	−0.0845136	−	0.996422i	$-0.526934\pi$
$499$	−17.6415	−	6.42099i	−0.789743	−	0.287443i	−0.705229	+	0.708980i	$0.749156\pi$
$500$	0.110015	+	0.0400423i	0.00492004	+	0.00179075i
$501$		0			0
$502$	−0.499857	+	2.83483i	−0.0223097	+	0.126525i
$503$	−6.21350	−	10.7621i	−0.277046	−	0.479858i	0.693603	−	0.720357i	$-0.256022\pi$
$503$	−6.21350	−	10.7621i	−0.277046	−	0.479858i	−0.970649	+	0.240499i	$0.922689\pi$
$504$		0			0
$505$	−18.9456	+	32.8148i	−0.843069	+	1.46024i
$506$	−5.86946	−	4.92506i	−0.260929	−	0.218946i
$507$		0			0
$508$	1.03928	+	5.89407i	0.0461107	+	0.261507i
$509$	−25.2624	+	21.1977i	−1.11974	+	0.939570i	−0.998591	−	0.0530649i	$-0.983101\pi$
$509$	−25.2624	+	21.1977i	−1.11974	+	0.939570i	−0.121145	+	0.992635i	$0.538657\pi$
$510$		0			0
$511$	−36.8768	+	13.4220i	−1.63133	+	0.593756i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−25.7779			−1.13702
$515$	−37.9470	+	13.8116i	−1.67214	+	0.608610i
$516$		0			0
$517$	6.74275	−	5.65784i	0.296546	−	0.248832i
$518$	4.67674	+	26.5231i	0.205484	+	1.16536i
$519$		0			0
$520$	7.52411	+	6.31348i	0.329954	+	0.276864i
$521$	7.16598	−	12.4118i	0.313947	−	0.543773i	−0.665266	−	0.746607i	$-0.731682\pi$
$521$	7.16598	−	12.4118i	0.313947	−	0.543773i	0.979213	+	0.202834i	$0.0650151\pi$
$522$		0			0
$523$	2.85442	+	4.94400i	0.124815	+	0.216186i	0.921661	−	0.387997i	$-0.126833\pi$
$523$	2.85442	+	4.94400i	0.124815	+	0.216186i	−0.796846	+	0.604183i	$0.793500\pi$
$524$	−2.85044	+	16.1657i	−0.124522	+	0.706200i
$525$		0			0
$526$	14.1609	+	5.15414i	0.617444	+	0.224731i
$527$	−7.52131	−	2.73753i	−0.327633	−	0.119249i
$528$		0			0
$529$	−2.04155	+	11.5782i	−0.0887629	+	0.503399i
$530$	−4.09110	−	7.08599i	−0.177706	−	0.307796i
$531$		0			0
$532$	6.25613	−	10.8359i	0.271238	−	0.469798i
$533$	16.8159	+	14.1102i	0.728376	+	0.611180i
$534$		0			0
$535$	3.35526	+	19.0286i	0.145060	+	0.822678i
$536$	6.59469	−	5.53361i	0.284847	−	0.239015i
$537$		0			0
$538$	−15.0929	+	5.49335i	−0.650699	+	0.236835i
$539$	15.0461			0.648081
$540$		0			0
$541$	18.0099			0.774305			0.387153	−	0.922016i	$-0.373459\pi$
$541$	18.0099			0.774305			0.387153	+	0.922016i	$0.373459\pi$
$542$	8.84670	−	3.21994i	0.379998	−	0.138308i
$543$		0			0
$544$	1.32201	−	1.10929i	0.0566805	−	0.0475606i
$545$	−6.18299	−	35.0655i	−0.264850	−	1.50204i
$546$		0			0
$547$	−15.8017	−	13.2592i	−0.675634	−	0.566924i	0.239093	−	0.970997i	$-0.423150\pi$
$547$	−15.8017	−	13.2592i	−0.675634	−	0.566924i	−0.914727	+	0.404072i	$0.867594\pi$
$548$	−0.105579	+	0.182869i	−0.00451012	+	0.00781176i
$549$		0			0
$550$	5.75489	+	9.96776i	0.245389	+	0.425027i
$551$	−0.345119	+	1.95727i	−0.0147026	+	0.0833825i
$552$		0			0
$553$	−48.8110	−	17.7657i	−2.07565	−	0.755476i
$554$	5.23856	+	1.90668i	0.222565	+	0.0810071i
$555$		0			0
$556$	0.637551	−	3.61573i	0.0270382	−	0.153341i
$557$	−1.90209	−	3.29452i	−0.0805942	−	0.139593i	0.822911	−	0.568170i	$-0.192348\pi$
$557$	−1.90209	−	3.29452i	−0.0805942	−	0.139593i	−0.903505	+	0.428577i	$0.859015\pi$
$558$		0			0
$559$	−2.57000	+	4.45136i	−0.108699	+	0.188273i
$560$	−8.94493	−	7.50569i	−0.377992	−	0.317173i
$561$		0			0
$562$	4.86298	+	27.5793i	0.205133	+	1.16336i
$563$	8.48116	−	7.11654i	0.357438	−	0.299926i	−0.446330	−	0.894868i	$-0.647269\pi$
$563$	8.48116	−	7.11654i	0.357438	−	0.299926i	0.803769	+	0.594942i	$0.202825\pi$
$564$		0			0
$565$	20.9494	−	7.62496i	0.881348	−	0.320784i
$566$	−6.15522			−0.258723
$567$		0			0
$568$	1.98746			0.0833921
$569$	43.8980	−	15.9776i	1.84030	−	0.669815i	0.850761	−	0.525553i	$-0.176142\pi$
$569$	43.8980	−	15.9776i	1.84030	−	0.669815i	0.989540	−	0.144261i	$-0.0460805\pi$
$570$		0			0
$571$	−24.2730	+	20.3675i	−1.01580	+	0.852354i	−0.989093	−	0.147290i	$-0.952945\pi$
$571$	−24.2730	+	20.3675i	−1.01580	+	0.852354i	−0.0267020	+	0.999643i	$0.508501\pi$
$572$	1.23018	+	6.97671i	0.0514365	+	0.291711i
$573$		0			0
$574$	−19.9913	−	16.7747i	−0.834421	−	0.700162i
$575$	−8.44468	+	14.6266i	−0.352167	+	0.609972i
$576$		0			0
$577$	−22.1642	−	38.3895i	−0.922707	−	1.59818i	−0.795208	−	0.606336i	$-0.792639\pi$
$577$	−22.1642	−	38.3895i	−0.922707	−	1.59818i	−0.127499	−	0.991839i	$-0.540695\pi$
$578$	2.43485	−	13.8087i	0.101277	−	0.574368i
$579$		0			0
$580$	1.74290	+	0.634363i	0.0723699	+	0.0263405i
$581$	−10.7312	−	3.90584i	−0.445206	−	0.162042i
$582$		0			0
$583$	1.02480	−	5.81192i	0.0424428	−	0.240705i
$584$	5.32371	+	9.22094i	0.220297	+	0.381565i
$585$		0			0
$586$	−1.16755	+	2.02226i	−0.0482310	+	0.0835386i
$587$	−31.4420	−	26.3830i	−1.29775	−	1.08894i	−0.990529	−	0.137305i	$-0.956156\pi$
$587$	−31.4420	−	26.3830i	−1.29775	−	1.08894i	−0.307223	−	0.951638i	$-0.599400\pi$
$588$		0			0
$589$	2.73409	+	15.5058i	0.112656	+	0.638905i
$590$	23.4518	−	19.6784i	0.965493	−	0.810145i
$591$		0			0
$592$	6.86652	−	2.49921i	0.282212	−	0.102717i
$593$	9.69265			0.398029			0.199015	−	0.979996i	$-0.436226\pi$
$593$	9.69265			0.398029			0.199015	+	0.979996i	$0.436226\pi$
$594$		0			0
$595$	20.1513			0.826121
$596$	14.5412	−	5.29255i	0.595630	−	0.216791i
$597$		0			0
$598$	−7.96341	+	6.68210i	−0.325648	+	0.273251i
$599$	5.18130	+	29.3846i	0.211702	+	1.20062i	0.886538	+	0.462655i	$0.153103\pi$
$599$	5.18130	+	29.3846i	0.211702	+	1.20062i	−0.674836	+	0.737967i	$0.735786\pi$
$600$		0			0
$601$	9.61439	+	8.06743i	0.392179	+	0.329077i	0.817461	−	0.575983i	$-0.195381\pi$
$601$	9.61439	+	8.06743i	0.392179	+	0.329077i	−0.425282	+	0.905061i	$0.639825\pi$
$602$	3.05530	−	5.29194i	0.124525	−	0.215683i
$603$		0			0
$604$	−10.0729	−	17.4467i	−0.409859	−	0.709896i
$605$	3.17895	−	18.0287i	0.129243	−	0.732972i
$606$		0			0
$607$	2.61247	+	0.950862i	0.106037	+	0.0385943i	0.394494	−	0.918899i	$-0.370920\pi$
$607$	2.61247	+	0.950862i	0.106037	+	0.0385943i	−0.288457	+	0.957493i	$0.593142\pi$
$608$	−3.19007	−	1.16109i	−0.129374	−	0.0470884i
$609$		0			0
$610$	7.20204	−	40.8448i	0.291602	−	1.65376i
$611$	−5.97110	−	10.3422i	−0.241565	−	0.418403i
$612$		0			0
$613$	4.29646	−	7.44168i	0.173532	−	0.300567i	−0.766120	−	0.642697i	$-0.777815\pi$
$613$	4.29646	−	7.44168i	0.173532	−	0.300567i	0.939652	+	0.342131i	$0.111149\pi$
$614$	−5.22848	−	4.38721i	−0.211004	−	0.177053i
$615$		0			0
$616$	−1.46249	−	8.29417i	−0.0589252	−	0.334181i
$617$	15.3814	−	12.9066i	0.619233	−	0.519598i	−0.278329	−	0.960486i	$-0.589781\pi$
$617$	15.3814	−	12.9066i	0.619233	−	0.519598i	0.897562	+	0.440887i	$0.145336\pi$
$618$		0			0
$619$	−7.88576	+	2.87018i	−0.316955	+	0.115362i	−0.495599	−	0.868552i	$-0.665051\pi$
$619$	−7.88576	+	2.87018i	−0.316955	+	0.115362i	0.178643	+	0.983914i	$0.442829\pi$
$620$	14.6936			0.590111
$621$		0			0
$622$	8.59522			0.344637
$623$	−60.0769	+	21.8662i	−2.40693	+	0.876051i
$624$		0			0
$625$	−19.0085	+	15.9500i	−0.760341	+	0.638002i
$626$	3.76276	+	21.3397i	0.150390	+	0.852906i
$627$		0			0
$628$	13.7868	+	11.5685i	0.550155	+	0.461635i
$629$	−6.30522	+	10.9210i	−0.251405	+	0.435447i
$630$		0			0
$631$	−8.78157	−	15.2101i	−0.349589	−	0.605506i	0.636588	−	0.771204i	$-0.280345\pi$
$631$	−8.78157	−	15.2101i	−0.349589	−	0.605506i	−0.986176	+	0.165699i	$0.947012\pi$
$632$	−2.44726	+	13.8791i	−0.0973467	+	0.552080i
$633$		0			0
$634$	−33.1899	−	12.0801i	−1.31814	−	0.479763i
$635$	17.8177	+	6.48510i	0.707072	+	0.257353i
$636$		0			0
$637$	3.54483	−	20.1037i	0.140451	−	0.796538i
$638$	0.668890	+	1.15855i	0.0264816	+	0.0458675i
$639$		0			0
$640$	−1.58406	+	2.74367i	−0.0626154	+	0.108453i
$641$	10.2762	+	8.62276i	0.405886	+	0.340579i	0.822763	−	0.568384i	$-0.192431\pi$
$641$	10.2762	+	8.62276i	0.405886	+	0.340579i	−0.416878	+	0.908963i	$0.636876\pi$
$642$		0			0
$643$	−1.81204	−	10.2766i	−0.0714597	−	0.405268i	−0.999465	−	0.0327016i	$-0.989589\pi$
$643$	−1.81204	−	10.2766i	−0.0714597	−	0.405268i	0.928005	−	0.372567i	$-0.121522\pi$
$644$	9.46719	−	7.94392i	0.373060	−	0.313034i
$645$		0			0
$646$	5.50527	−	2.00376i	0.216602	−	0.0788367i
$647$	37.9585			1.49230			0.746152	−	0.665775i	$-0.231899\pi$
$647$	37.9585			1.49230			0.746152	+	0.665775i	$0.231899\pi$
$648$		0			0
$649$	22.0810			0.866756
$650$	14.6742	−	5.34097i	0.575569	−	0.209490i
$651$		0			0
$652$	2.33865	−	1.96236i	0.0915886	−	0.0768520i
$653$	4.74169	+	26.8914i	0.185557	+	1.05234i	0.925238	+	0.379387i	$0.123865\pi$
$653$	4.74169	+	26.8914i	0.185557	+	1.05234i	−0.739682	+	0.672957i	$0.765024\pi$
$654$		0			0
$655$	39.8379	+	33.4280i	1.55660	+	1.30614i
$656$	−3.54026	+	6.13191i	−0.138224	+	0.239411i
$657$		0			0
$658$	7.09866	+	12.2952i	0.276735	+	0.479318i
$659$	5.96567	−	33.8330i	0.232389	−	1.31795i	−0.615653	−	0.788017i	$-0.711108\pi$
$659$	5.96567	−	33.8330i	0.232389	−	1.31795i	0.848042	−	0.529929i	$-0.177781\pi$
$660$		0			0
$661$	23.0955	+	8.40607i	0.898310	+	0.326958i	0.749576	−	0.661919i	$-0.230258\pi$
$661$	23.0955	+	8.40607i	0.898310	+	0.326958i	0.148735	+	0.988877i	$0.452480\pi$
$662$	−24.2569	−	8.82879i	−0.942771	−	0.343141i
$663$		0			0
$664$	−0.538035	+	3.05135i	−0.0208798	+	0.118415i
$665$	−19.8202	−	34.3295i	−0.768593	−	1.33124i
$666$		0			0
$667$	−0.981523	+	1.70005i	−0.0380047	+	0.0658261i
$668$	3.14170	+	2.63620i	0.121556	+	0.101998i
$669$		0			0
$670$	−4.73600	−	26.8592i	−0.182968	−	1.03766i
$671$	22.9159	−	19.2287i	0.884659	−	0.742317i
$672$		0			0
$673$	−40.2897	+	14.6643i	−1.55306	+	0.565266i	−0.969132	−	0.246543i	$-0.920705\pi$
$673$	−40.2897	+	14.6643i	−1.55306	+	0.565266i	−0.583923	+	0.811809i	$0.698483\pi$
$674$	3.38459			0.130369
$675$		0			0
$676$	−3.38830			−0.130319
$677$	7.03588	−	2.56085i	0.270411	−	0.0984215i	−0.203256	−	0.979126i	$-0.565152\pi$
$677$	7.03588	−	2.56085i	0.270411	−	0.0984215i	0.473667	+	0.880704i	$0.342930\pi$
$678$		0			0
$679$	25.9506	−	21.7751i	0.995891	−	0.835652i
$680$	−0.949403	−	5.38433i	−0.0364079	−	0.206480i
$681$		0			0
$682$	8.11860	+	6.81232i	0.310877	+	0.260857i
$683$	8.37724	−	14.5098i	0.320546	−	0.555202i	−0.660055	−	0.751218i	$-0.729467\pi$
$683$	8.37724	−	14.5098i	0.320546	−	0.555202i	0.980601	+	0.196015i	$0.0628002\pi$
$684$		0			0
$685$	0.334487	+	0.579349i	0.0127801	+	0.0221358i
$686$	0.265912	−	1.50806i	0.0101526	−	0.0575781i
$687$		0			0
$688$	−1.55793	−	0.567040i	−0.0593955	−	0.0216182i
$689$	−7.52411	−	2.73855i	−0.286646	−	0.104331i
$690$		0			0
$691$	−2.59664	+	14.7263i	−0.0987808	+	0.560214i	0.894742	+	0.446583i	$0.147359\pi$
$691$	−2.59664	+	14.7263i	−0.0987808	+	0.560214i	−0.993523	+	0.113631i	$0.963752\pi$
$692$	−8.51355	−	14.7459i	−0.323637	−	0.560555i
$693$		0			0
$694$	8.10001	−	14.0296i	0.307472	−	0.532558i
$695$	−8.91045	−	7.47676i	−0.337993	−	0.283610i
$696$		0			0
$697$	−2.12185	−	12.0336i	−0.0803707	−	0.455805i
$698$	−3.44148	+	2.88774i	−0.130262	+	0.109303i
$699$		0			0
$700$	−17.4452	+	6.34953i	−0.659367	+	0.239990i
$701$	42.1025			1.59019			0.795094	−	0.606486i	$-0.207421\pi$
$701$	42.1025			1.59019			0.795094	+	0.606486i	$0.207421\pi$
$702$		0			0
$703$	24.8065			0.935593
$704$	−2.14726	+	0.781539i	−0.0809279	+	0.0294554i
$705$		0			0
$706$	−17.7927	+	14.9298i	−0.669636	+	0.561891i
$707$	−7.65473	−	43.4122i	−0.287886	−	1.63268i
$708$		0			0
$709$	21.8212	+	18.3102i	0.819513	+	0.687653i	0.952858	−	0.303416i	$-0.0981273\pi$
$709$	21.8212	+	18.3102i	0.819513	+	0.687653i	−0.133345	+	0.991070i	$0.542572\pi$
$710$	3.14826	−	5.45294i	0.118152	−	0.204645i
$711$		0			0
$712$	8.67300	+	15.0221i	0.325035	+	0.562976i
$713$	−2.70050	+	15.3153i	−0.101134	+	0.573562i
$714$		0			0
$715$	21.0905	+	7.67630i	0.788738	+	0.287077i
$716$	−13.6782	−	4.97846i	−0.511179	−	0.186054i
$717$		0			0
$718$	−2.00632	+	11.3784i	−0.0748752	+	0.424639i
$719$	1.26744	+	2.19526i	0.0472674	+	0.0818695i	0.888691	−	0.458506i	$-0.151615\pi$
$719$	1.26744	+	2.19526i	0.0472674	+	0.0818695i	−0.841424	+	0.540376i	$0.818282\pi$
$720$		0			0
$721$	23.4900	−	40.6858i	0.874812	−	1.51522i
$722$	5.72645	+	4.80507i	0.213117	+	0.178826i
$723$		0			0
$724$	−2.26156	−	12.8259i	−0.0840502	−	0.476672i
$725$	2.25895	−	1.89549i	0.0838954	−	0.0703966i
$726$		0			0
$727$	−18.6843	+	6.80052i	−0.692961	+	0.252217i	−0.664403	−	0.747375i	$-0.731314\pi$
$727$	−18.6843	+	6.80052i	−0.692961	+	0.252217i	−0.0285587	+	0.999592i	$0.509092\pi$
$728$	−11.4267			−0.423503
$729$		0			0
$730$	33.7323			1.24849
$731$	2.68861	−	0.978573i	0.0994417	−	0.0361938i
$732$		0			0
$733$	−7.66892	+	6.43499i	−0.283258	+	0.237682i	−0.773335	−	0.633997i	$-0.781413\pi$
$733$	−7.66892	+	6.43499i	−0.283258	+	0.237682i	0.490077	+	0.871679i	$0.336969\pi$
$734$	−2.70365	−	15.3332i	−0.0997937	−	0.565958i
$735$		0			0
$736$	−2.56861	−	2.15532i	−0.0946804	−	0.0794463i
$737$	9.83580	−	17.0361i	0.362306	−	0.627533i
$738$		0			0
$739$	20.1957	+	34.9800i	0.742911	+	1.28676i	0.951164	+	0.308685i	$0.0998890\pi$
$739$	20.1957	+	34.9800i	0.742911	+	1.28676i	−0.208253	+	0.978075i	$0.566778\pi$
$740$	4.01996	−	22.7983i	0.147777	−	0.838084i
$741$		0			0
$742$	8.94493	+	3.25569i	0.328379	+	0.119520i
$743$	33.5002	+	12.1931i	1.22900	+	0.447321i	0.873256	−	0.487261i	$-0.162004\pi$
$743$	33.5002	+	12.1931i	1.22900	+	0.447321i	0.355748	+	0.934582i	$0.384226\pi$
$744$		0			0
$745$	8.51304	−	48.2799i	0.311894	−	1.76884i
$746$	−4.87863	−	8.45004i	−0.178619	−	0.309378i
$747$		0			0
$748$	1.97173	−	3.41514i	0.0720937	−	0.124870i
$749$	−17.2199	−	14.4492i	−0.629201	−	0.527963i
$750$		0			0
$751$	−1.64423	−	9.32488i	−0.0599987	−	0.340270i	0.940001	−	0.341172i	$-0.110824\pi$
$751$	−1.64423	−	9.32488i	−0.0599987	−	0.340270i	−1.00000		0.000902410i	$0.999713\pi$
$752$	2.95079	−	2.47601i	0.107604	−	0.0902906i
$753$		0			0
$754$	1.70558	−	0.620779i	0.0621135	−	0.0226075i
$755$	−63.8240			−2.32279
$756$		0			0
$757$	−37.9651			−1.37987			−0.689933	−	0.723873i	$-0.742360\pi$
$757$	−37.9651			−1.37987			−0.689933	+	0.723873i	$0.742360\pi$
$758$	−17.6572	+	6.42669i	−0.641338	+	0.233428i
$759$		0			0
$760$	−8.23889	+	6.91325i	−0.298856	+	0.250770i
$761$	−7.79433	−	44.2038i	−0.282544	−	1.60239i	−0.713928	−	0.700219i	$-0.753086\pi$
$761$	−7.79433	−	44.2038i	−0.282544	−	1.60239i	0.431384	−	0.902169i	$-0.358026\pi$
$762$		0			0
$763$	31.7325	+	26.6267i	1.14879	+	0.963951i
$764$	1.80144	−	3.12018i	0.0651737	−	0.112884i
$765$		0			0
$766$	−15.3840	−	26.6459i	−0.555847	−	0.962755i
$767$	5.20225	−	29.5034i	0.187842	−	1.06531i
$768$		0			0
$769$	−42.9786	−	15.6429i	−1.54985	−	0.564098i	−0.581465	−	0.813571i	$-0.697520\pi$
$769$	−42.9786	−	15.6429i	−1.54985	−	0.564098i	−0.968382	+	0.249473i	$0.919742\pi$
$770$	−25.0731	−	9.12586i	−0.903572	−	0.328873i
$771$		0			0
$772$	0.256108	−	1.45246i	0.00921754	−	0.0522753i
$773$	−10.2853	−	17.8147i	−0.369938	−	0.640752i	0.619617	−	0.784904i	$-0.287288\pi$
$773$	−10.2853	−	17.8147i	−0.369938	−	0.640752i	−0.989556	+	0.144152i	$0.953954\pi$
$774$		0			0
$775$	11.6806	−	20.2315i	0.419581	−	0.726735i
$776$	−7.04084	−	5.90797i	−0.252751	−	0.212084i
$777$		0			0
$778$	5.14010	+	29.1510i	0.184282	+	1.04511i
$779$	−18.4133	+	15.4506i	−0.659726	+	0.553576i
$780$		0			0
$781$	4.26760	−	1.55328i	0.152707	−	0.0555807i
$782$	5.78661			0.206929
$783$		0			0
$784$	6.58452			0.235162
$785$	53.5793	−	19.5013i	1.91233	−	0.696031i
$786$		0			0
$787$	34.1376	−	28.6449i	1.21688	−	1.02108i	0.217893	−	0.975973i	$-0.430082\pi$
$787$	34.1376	−	28.6449i	1.21688	−	1.02108i	0.998982	−	0.0451069i	$-0.0143629\pi$
$788$	−0.440827	−	2.50005i	−0.0157038	−	0.0890607i
$789$		0			0
$790$	34.2030	+	28.6997i	1.21689	+	1.02109i
$791$	−12.9681	+	22.4614i	−0.461093	+	0.798637i
$792$		0			0
$793$	−20.2934	−	35.1492i	−0.720639	−	1.24818i
$794$	−2.80315	+	15.8974i	−0.0994800	+	0.564179i
$795$		0			0
$796$	1.74011	+	0.633347i	0.0616764	+	0.0224484i
$797$	41.2150	+	15.0010i	1.45991	+	0.531364i	0.945341	−	0.326084i	$-0.105729\pi$
$797$	41.2150	+	15.0010i	1.45991	+	0.531364i	0.514571	+	0.857448i	$0.327951\pi$
$798$		0			0
$799$	−1.15434	+	6.54659i	−0.0408376	+	0.231602i
$800$	2.51848	+	4.36213i	0.0890416	+	0.154225i
$801$		0			0
$802$	−12.6812	+	21.9645i	−0.447788	+	0.775592i
$803$	18.6379	+	15.6391i	0.657718	+	0.551891i
$804$		0			0
$805$	−6.79890	−	38.5585i	−0.239630	−	1.35901i
$806$	11.0150	−	9.24264i	0.387985	−	0.325558i
$807$		0			0
$808$	−11.2389	+	4.09062i	−0.395383	+	0.143908i
$809$	15.5821			0.547836			0.273918	−	0.961753i	$-0.411680\pi$
$809$	15.5821			0.547836			0.273918	+	0.961753i	$0.411680\pi$
$810$		0			0
$811$	−30.4691			−1.06992			−0.534958	−	0.844879i	$-0.679673\pi$
$811$	−30.4691			−1.06992			−0.534958	+	0.844879i	$0.679673\pi$
$812$	−2.02765	+	0.738005i	−0.0711566	+	0.0258989i
$813$		0			0
$814$	12.7910	−	10.7329i	0.448324	−	0.376188i
$815$	−1.67951	−	9.52498i	−0.0588307	−	0.333645i
$816$		0			0
$817$	−4.31152	−	3.61779i	−0.150841	−	0.126570i
$818$	−11.3857	+	19.7205i	−0.398090	+	0.689512i
$819$		0			0
$820$	11.2159	+	19.4266i	0.391678	+	0.678406i
$821$	0.330108	−	1.87214i	0.0115209	−	0.0653381i	−0.978505	−	0.206222i	$-0.933883\pi$
$821$	0.330108	−	1.87214i	0.0115209	−	0.0653381i	0.990026	+	0.140884i	$0.0449943\pi$
$822$		0			0
$823$	20.7118	+	7.53847i	0.721967	+	0.262775i	0.676761	−	0.736203i	$-0.263383\pi$
$823$	20.7118	+	7.53847i	0.721967	+	0.262775i	0.0452067	+	0.998978i	$0.485605\pi$
$824$	−11.9778	−	4.35955i	−0.417265	−	0.151872i
$825$		0			0
$826$	−6.18462	+	35.0747i	−0.215190	+	1.22041i
$827$	24.2488	+	42.0001i	0.843213	+	1.46049i	0.887164	+	0.461454i	$0.152672\pi$
$827$	24.2488	+	42.0001i	0.843213	+	1.46049i	−0.0439508	+	0.999034i	$0.513994\pi$
$828$		0			0
$829$	10.1593	−	17.5964i	0.352846	−	0.611148i	−0.633900	−	0.773415i	$-0.718547\pi$
$829$	10.1593	−	17.5964i	0.352846	−	0.611148i	0.986747	+	0.162267i	$0.0518805\pi$
$830$	7.51961	+	6.30970i	0.261010	+	0.219013i
$831$		0			0
$832$	0.538357	+	3.05317i	0.0186642	+	0.105850i
$833$	−8.70477	+	7.30417i	−0.301603	+	0.253075i
$834$		0			0
$835$	12.2095	−	4.44389i	0.422527	−	0.153787i
$836$	−7.75734			−0.268293
$837$		0			0
$838$	−4.92276			−0.170054
$839$	−4.76081	+	1.73279i	−0.164361	+	0.0598227i	−0.422890	−	0.906181i	$-0.638984\pi$
$839$	−4.76081	+	1.73279i	−0.164361	+	0.0598227i	0.258529	+	0.966004i	$0.416762\pi$
$840$		0			0
$841$	−21.9527	+	18.4205i	−0.756991	+	0.635191i
$842$	−3.42393	−	19.4180i	−0.117996	−	0.669190i
$843$		0			0
$844$	−14.5459	−	12.2054i	−0.500690	−	0.420129i
$845$	−5.36726	+	9.29636i	−0.184639	+	0.319804i
$846$		0			0
$847$	10.6489	+	18.4444i	0.365901	+	0.633758i
$848$	0.448476	−	2.54343i	0.0154007	−	0.0873419i
$849$		0			0
$850$	−8.16833	−	2.97303i	−0.280171	−	0.101974i
$851$	23.0240	+	8.38007i	0.789254	+	0.287265i
$852$		0			0
$853$	4.59609	−	26.0657i	0.157367	−	0.892474i	−0.799222	−	0.601036i	$-0.794755\pi$
$853$	4.59609	−	26.0657i	0.157367	−	0.892474i	0.956590	−	0.291439i	$-0.0941339\pi$
$854$	24.1255	+	41.7866i	0.825558	+	1.42991i
$855$		0			0
$856$	−3.04947	+	5.28184i	−0.104229	+	0.180529i
$857$	14.0275	+	11.7705i	0.479171	+	0.402072i	0.850127	−	0.526578i	$-0.176525\pi$
$857$	14.0275	+	11.7705i	0.479171	+	0.402072i	−0.370955	+	0.928651i	$0.620970\pi$
$858$		0			0
$859$	−1.63913	−	9.29596i	−0.0559263	−	0.317174i	0.943992	−	0.329969i	$-0.107038\pi$
$859$	−1.63913	−	9.29596i	−0.0559263	−	0.317174i	−0.999918	+	0.0127948i	$0.995927\pi$
$860$	−4.02362	+	3.37622i	−0.137204	+	0.115128i
$861$		0			0
$862$	5.79155	−	2.10795i	0.197261	−	0.0717971i
$863$	14.2154			0.483898			0.241949	−	0.970289i	$-0.422213\pi$
$863$	14.2154			0.483898			0.241949	+	0.970289i	$0.422213\pi$
$864$		0			0
$865$	−53.9438			−1.83414
$866$	−13.8923	+	5.05637i	−0.472079	+	0.171823i
$867$		0			0
$868$	−13.0950	+	10.9880i	−0.444472	+	0.372957i
$869$	5.59215	+	31.7146i	0.189701	+	1.07585i
$870$		0			0
$871$	−20.4454	−	17.1557i	−0.692765	−	0.581299i
$872$	5.61950	−	9.73326i	0.190300	−	0.329610i
$873$		0			0
$874$	−5.69153	−	9.85801i	−0.192519	−	0.333452i
$875$	−0.0749307	+	0.424953i	−0.00253312	+	0.0143660i
$876$		0			0
$877$	−36.7471	−	13.3748i	−1.24086	−	0.451636i	−0.363557	−	0.931572i	$-0.618438\pi$
$877$	−36.7471	−	13.3748i	−1.24086	−	0.451636i	−0.877304	+	0.479935i	$0.840660\pi$
$878$	27.9719	+	10.1809i	0.944005	+	0.343590i
$879$		0			0
$880$	−1.25710	+	7.12937i	−0.0423769	+	0.240331i
$881$	−11.4469	−	19.8266i	−0.385657	−	0.667977i	0.606203	−	0.795310i	$-0.292692\pi$
$881$	−11.4469	−	19.8266i	−0.385657	−	0.667977i	−0.991860	+	0.127333i	$0.959358\pi$
$882$		0			0
$883$	8.57546	−	14.8531i	0.288587	−	0.499847i	−0.684886	−	0.728651i	$-0.740148\pi$
$883$	8.57546	−	14.8531i	0.288587	−	0.499847i	0.973473	+	0.228803i	$0.0734812\pi$
$884$	−4.09858	−	3.43912i	−0.137850	−	0.115670i
$885$		0			0
$886$	5.29182	+	30.0114i	0.177782	+	1.00825i
$887$	−13.9857	+	11.7354i	−0.469594	+	0.394036i	−0.846646	−	0.532156i	$-0.821382\pi$
$887$	−13.9857	+	11.7354i	−0.469594	+	0.394036i	0.377053	+	0.926192i	$0.376938\pi$
$888$		0			0
$889$	−20.7287	+	7.54463i	−0.695218	+	0.253039i
$890$	54.9541			1.84207
$891$		0			0
$892$	−7.25436			−0.242894
$893$	12.2881	−	4.47249i	0.411205	−	0.149666i
$894$		0			0
$895$	−35.3263	+	29.6423i	−1.18083	+	0.990833i
$896$	−0.640018	−	3.62972i	−0.0213815	−	0.121261i
$897$		0			0
$898$	9.07081	+	7.61132i	0.302697	+	0.253993i
$899$	1.35764	−	2.35150i	0.0452797	−	0.0784268i
$900$		0			0
$901$	2.22853	+	3.85993i	0.0742431	+	0.128593i
$902$	−2.80953	+	15.9337i	−0.0935472	+	0.530533i
$903$		0			0
$904$	6.61257	+	2.40678i	0.219931	+	0.0800483i
$905$	−38.7726	−	14.1121i	−1.28884	−	0.469101i
$906$		0			0
$907$	5.06908	−	28.7482i	0.168316	−	0.954567i	−0.777263	−	0.629175i	$-0.783393\pi$
$907$	5.06908	−	28.7482i	0.168316	−	0.954567i	0.945579	−	0.325392i	$-0.105496\pi$
$908$	−14.2636	−	24.7053i	−0.473354	−	0.819873i
$909$		0			0
$910$	−18.1006	+	31.3512i	−0.600030	+	1.03928i
$911$	−41.8535	−	35.1193i	−1.38667	−	1.16355i	−0.966669	−	0.256029i	$-0.917586\pi$
$911$	−41.8535	−	35.1193i	−1.38667	−	1.16355i	−0.420000	−	0.907524i	$-0.637970\pi$
$912$		0			0
$913$	1.22945	+	6.97254i	0.0406888	+	0.230757i
$914$	0.142785	−	0.119811i	0.00472292	−	0.00396300i
$915$		0			0
$916$	−1.74349	+	0.634578i	−0.0576065	+	0.0209671i
$917$	−60.5012			−1.99793
$918$		0			0
$919$	41.0995			1.35575			0.677873	−	0.735179i	$-0.262902\pi$
$919$	41.0995			1.35575			0.677873	+	0.735179i	$0.262902\pi$
$920$	−9.98233	+	3.63327i	−0.329108	+	0.119785i
$921$		0			0
$922$	7.97096	−	6.68843i	0.262510	−	0.220272i
$923$	−1.06997	−	6.06807i	−0.0352183	−	0.199733i
$924$		0			0
$925$	−28.1950	−	23.6585i	−0.927047	−	0.777885i
$926$	12.8942	−	22.3334i	0.423730	−	0.733922i
$927$		0			0
$928$	0.292722	+	0.507009i	0.00960907	+	0.0166434i
$929$	−2.53458	+	14.3743i	−0.0831570	+	0.471606i	0.914582	+	0.404400i	$0.132520\pi$
$929$	−2.53458	+	14.3743i	−0.0831570	+	0.471606i	−0.997739	+	0.0672063i	$0.978591\pi$
$930$		0			0
$931$	21.0051	+	7.64522i	0.688413	+	0.250562i
$932$	8.01999	+	2.91904i	0.262703	+	0.0956162i
$933$		0			0
$934$	3.76836	−	21.3714i	0.123305	−	0.699295i
$935$	−6.24668	−	10.8196i	−0.204288	−	0.353838i
$936$		0			0
$937$	−12.4641	+	21.5885i	−0.407185	+	0.705265i	−0.994573	−	0.104041i	$-0.966823\pi$
$937$	−12.4641	+	21.5885i	−0.407185	+	0.705265i	0.587388	+	0.809305i	$0.300156\pi$
$938$	24.3062	+	20.3953i	0.793625	+	0.665931i
$939$		0			0
$940$	−2.11912	−	12.0181i	−0.0691180	−	0.391988i
$941$	−15.9677	+	13.3985i	−0.520531	+	0.436778i	−0.864817	−	0.502087i	$-0.832566\pi$
$941$	−15.9677	+	13.3985i	−0.520531	+	0.436778i	0.344285	+	0.938865i	$0.388121\pi$
$942$		0			0
$943$	−22.3098	+	8.12010i	−0.726507	+	0.264427i
$944$	9.66319			0.314510
$945$		0			0
$946$	−3.78845			−0.123173
$947$	33.7472	−	12.2830i	1.09664	−	0.399143i	0.270561	−	0.962703i	$-0.412791\pi$
$947$	33.7472	−	12.2830i	1.09664	−	0.399143i	0.826075	+	0.563560i	$0.190569\pi$
$948$		0			0
$949$	25.2871	−	21.2184i	0.820854	−	0.688778i
$950$	2.96929	+	16.8397i	0.0963364	+	0.546351i
$951$		0			0
$952$	4.87254	+	4.08855i	0.157920	+	0.132511i
$953$	2.90103	−	5.02474i	0.0939737	−	0.162767i	−0.815206	−	0.579171i	$-0.803376\pi$
$953$	2.90103	−	5.02474i	0.0939737	−	0.162767i	0.909180	+	0.416404i	$0.136710\pi$
$954$		0			0
$955$	−5.70716	−	9.88509i	−0.184679	−	0.319874i
$956$	1.26554	−	7.17724i	0.0409305	−	0.232129i
$957$		0			0
$958$	36.7619	+	13.3802i	1.18772	+	0.432296i
$959$	−0.731336	−	0.266184i	−0.0236161	−	0.00859554i
$960$		0			0
$961$	−1.64778	+	9.34502i	−0.0531542	+	0.301452i
$962$	−11.3272	−	19.6192i	−0.365202	−	0.632549i
$963$		0			0
$964$	0.667459	−	1.15607i	0.0214974	−	0.0372346i
$965$	−3.57939	−	3.00346i	−0.115225	−	0.0966848i
$966$		0			0
$967$	5.15021	+	29.2083i	0.165620	+	0.939276i	0.948423	+	0.317007i	$0.102678\pi$
$967$	5.15021	+	29.2083i	0.165620	+	0.939276i	−0.782803	+	0.622269i	$0.786211\pi$
$968$	4.42656	−	3.71433i	0.142275	−	0.119383i
$969$		0			0
$970$	−27.3626	+	9.95917i	−0.878560	+	0.319770i
$971$	−47.1522			−1.51318			−0.756592	−	0.653887i	$-0.773137\pi$
$971$	−47.1522			−1.51318			−0.756592	+	0.653887i	$0.773137\pi$
$972$		0			0
$973$	13.5322			0.433821
$974$	−9.85107	+	3.58550i	−0.315649	+	0.114887i
$975$		0			0
$976$	10.0285	−	8.41495i	0.321006	−	0.269356i
$977$	4.13334	+	23.4413i	0.132237	+	0.749954i	0.976744	+	0.214409i	$0.0687827\pi$
$977$	4.13334	+	23.4413i	0.132237	+	0.749954i	−0.844507	+	0.535545i	$0.820106\pi$
$978$		0			0
$979$	30.3635	+	25.4780i	0.970423	+	0.814282i
$980$	10.4303	−	18.0657i	0.333183	−	0.577089i
$981$		0			0
$982$	−3.42851	−	5.93835i	−0.109408	−	0.189501i
$983$	−1.92441	+	10.9139i	−0.0613792	+	0.348099i	0.938616	+	0.344964i	$0.112109\pi$
$983$	−1.92441	+	10.9139i	−0.0613792	+	0.348099i	−0.999995	+	0.00313478i	$0.999002\pi$
$984$		0			0
$985$	−7.55761	−	2.75075i	−0.240806	−	0.0876460i
$986$	−0.949403	−	0.345554i	−0.0302351	−	0.0110047i
$987$		0			0
$988$	−1.82761	+	10.3649i	−0.0581441	+	0.329752i
$989$	−2.77957	−	4.81435i	−0.0883851	−	0.153087i
$990$		0			0
$991$	−5.71846	+	9.90466i	−0.181653	+	0.314632i	−0.942443	−	0.334365i	$-0.891478\pi$
$991$	−5.71846	+	9.90466i	−0.181653	+	0.314632i	0.760791	+	0.648997i	$0.224811\pi$
$992$	3.55290	+	2.98123i	0.112805	+	0.0946542i
$993$		0			0
$994$	1.27201	+	7.21395i	0.0403458	+	0.228812i
$995$	4.49412	−	3.77102i	0.142473	−	0.119549i
$996$		0			0
$997$	26.2123	−	9.54049i	0.830151	−	0.302150i	0.108230	−	0.994126i	$-0.465482\pi$
$997$	26.2123	−	9.54049i	0.830151	−	0.302150i	0.721921	+	0.691976i	$0.243259\pi$
$998$	−18.7737			−0.594271
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	486.2.e.g.55.1		12
3.2	odd	2		486.2.e.f.55.2		12
9.2	odd	6		486.2.e.h.379.1		12
9.4	even	3		162.2.e.b.73.1		12
9.5	odd	6		54.2.e.b.25.1	yes	12
9.7	even	3		486.2.e.e.379.2		12
27.2	odd	18		1458.2.a.g.1.5		6
27.4	even	9	inner	486.2.e.g.433.1		12
27.5	odd	18		54.2.e.b.13.1	✓	12
27.7	even	9		1458.2.c.g.487.5		12
27.11	odd	18		1458.2.c.f.973.2		12
27.13	even	9		486.2.e.e.109.2		12
27.14	odd	18		486.2.e.h.109.1		12
27.16	even	9		1458.2.c.g.973.5		12
27.20	odd	18		1458.2.c.f.487.2		12
27.22	even	9		162.2.e.b.91.1		12
27.23	odd	18		486.2.e.f.433.2		12
27.25	even	9		1458.2.a.f.1.2		6
36.23	even	6		432.2.u.b.241.2		12
108.59	even	18		432.2.u.b.337.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.2.e.b.13.1	✓	12	27.5	odd	18
54.2.e.b.25.1	yes	12	9.5	odd	6
162.2.e.b.73.1		12	9.4	even	3
162.2.e.b.91.1		12	27.22	even	9
432.2.u.b.241.2		12	36.23	even	6
432.2.u.b.337.2		12	108.59	even	18
486.2.e.e.109.2		12	27.13	even	9
486.2.e.e.379.2		12	9.7	even	3
486.2.e.f.55.2		12	3.2	odd	2
486.2.e.f.433.2		12	27.23	odd	18
486.2.e.g.55.1		12	1.1	even	1	trivial
486.2.e.g.433.1		12	27.4	even	9	inner
486.2.e.h.109.1		12	27.14	odd	18
486.2.e.h.379.1		12	9.2	odd	6
1458.2.a.f.1.2		6	27.25	even	9
1458.2.a.g.1.5		6	27.2	odd	18
1458.2.c.f.487.2		12	27.20	odd	18
1458.2.c.f.973.2		12	27.11	odd	18
1458.2.c.g.487.5		12	27.7	even	9
1458.2.c.g.973.5		12	27.16	even	9

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:	\( N \)	\(=\)	\( 486 = 2 \cdot 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	486.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 - 0.342020i) q^{2} +(0.766044 - 0.642788i) q^{4} +(-0.550137 - 3.11998i) q^{5} +(2.82342 + 2.36913i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.58406 - 2.74367i) q^{10} +(0.396798 - 2.25035i) q^{11} +(-2.91331 - 1.06036i) q^{13} +(3.46344 + 1.26059i) q^{14} +(0.173648 - 0.984808i) q^{16} +(0.862878 + 1.49455i) q^{17} +(1.69740 - 2.93998i) q^{19} +(-2.42692 - 2.03643i) q^{20} +(-0.396798 - 2.25035i) q^{22} +(2.56861 - 2.15532i) q^{23} +(-4.73319 + 1.72274i) q^{25} -3.10027 q^{26} +3.68572 q^{28} +(-0.550137 + 0.200234i) q^{29} +(-3.55290 + 2.98123i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(1.32201 + 1.10929i) q^{34} +(5.83839 - 10.1124i) q^{35} +(3.65360 + 6.32822i) q^{37} +(0.589500 - 3.34322i) q^{38} +(-2.97705 - 1.08356i) q^{40} +(-6.65351 - 2.42168i) q^{41} +(0.287894 - 1.63273i) q^{43} +(-1.14253 - 1.97893i) q^{44} +(1.67654 - 2.90386i) q^{46} +(2.95079 + 2.47601i) q^{47} +(1.14339 + 6.48449i) q^{49} +(-3.85853 + 3.23769i) q^{50} +(-2.91331 + 1.06036i) q^{52} +2.58267 q^{53} -7.23936 q^{55} +(3.46344 - 1.26059i) q^{56} +(-0.448476 + 0.376316i) q^{58} +(1.67799 + 9.51638i) q^{59} +(10.0285 + 8.41495i) q^{61} +(-2.31899 + 4.01660i) q^{62} +(-0.500000 - 0.866025i) q^{64} +(-1.70558 + 9.67281i) q^{65} +(8.08959 + 2.94437i) q^{67} +(1.62168 + 0.590243i) q^{68} +(2.02765 - 11.4994i) q^{70} +(0.993732 + 1.72119i) q^{71} +(-5.32371 + 9.22094i) q^{73} +(5.59764 + 4.69698i) q^{74} +(-0.589500 - 3.34322i) q^{76} +(6.45172 - 5.41363i) q^{77} +(-13.2433 + 4.82016i) q^{79} -3.16812 q^{80} -7.08052 q^{82} +(-2.91156 + 1.05972i) q^{83} +(4.18826 - 3.51437i) q^{85} +(-0.287894 - 1.63273i) q^{86} +(-1.75046 - 1.46881i) q^{88} +(-8.67300 + 15.0221i) q^{89} +(-5.71337 - 9.89585i) q^{91} +(0.582258 - 3.30215i) q^{92} +(3.61968 + 1.31746i) q^{94} +(-10.1065 - 3.67846i) q^{95} +(1.59603 - 9.05153i) q^{97} +(3.29226 + 5.70237i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{5} + 6 q^{7} + 6 q^{8} - 3 q^{10} - 6 q^{11} - 6 q^{13} + 3 q^{14} + 6 q^{17} - 9 q^{19} + 3 q^{20} + 6 q^{22} + 6 q^{23} - 27 q^{25} - 18 q^{26} + 12 q^{28} + 3 q^{29} - 27 q^{31} + 12 q^{34}+ \cdots + 12 q^{98}+O(q^{100}) \) 12 * q + 3 * q^5 + 6 * q^7 + 6 * q^8 - 3 * q^10 - 6 * q^11 - 6 * q^13 + 3 * q^14 + 6 * q^17 - 9 * q^19 + 3 * q^20 + 6 * q^22 + 6 * q^23 - 27 * q^25 - 18 * q^26 + 12 * q^28 + 3 * q^29 - 27 * q^31 + 12 * q^34 - 3 * q^35 - 15 * q^37 + 15 * q^38 + 6 * q^40 - 15 * q^41 + 18 * q^43 + 3 * q^44 + 3 * q^46 + 27 * q^47 + 42 * q^49 - 36 * q^50 - 6 * q^52 + 12 * q^53 + 18 * q^55 + 3 * q^56 - 12 * q^58 + 24 * q^59 + 27 * q^61 + 12 * q^62 - 6 * q^64 - 57 * q^65 + 9 * q^67 + 15 * q^68 - 6 * q^70 - 12 * q^71 - 21 * q^73 + 3 * q^74 - 15 * q^76 + 51 * q^77 - 42 * q^79 - 6 * q^80 + 6 * q^82 - 45 * q^85 - 18 * q^86 - 12 * q^88 - 12 * q^89 - 6 * q^91 + 24 * q^92 - 9 * q^94 - 48 * q^95 - 24 * q^97 + 12 * q^98

Introduction

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