LMFDB - Embedded newform 648.2.v.b.611.25

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [648,2,Mod(35,648)] 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("648.35"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(648, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 9, 13])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 648 = 2^{3} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	648.v (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [192] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.17430605098$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$32$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			611.25
Character	$\chi$	$=$	648.611
Dual form			648.2.v.b.35.25

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.20377 + 0.742249i) q^{2} +(0.898133 + 1.78700i) q^{4} +(3.07462 - 1.11907i) q^{5} +(1.33825 - 0.235969i) q^{7} +(-0.245250 + 2.81777i) q^{8} +(4.53177 + 0.935029i) q^{10} +(0.982057 - 2.69818i) q^{11} +(-2.36880 + 2.82303i) q^{13} +(1.78609 + 0.709260i) q^{14} +(-2.38671 + 3.20992i) q^{16} +(-1.94027 - 1.12022i) q^{17} +(-1.22444 - 2.12079i) q^{19} +(4.76119 + 4.48926i) q^{20} +(3.18489 - 2.51906i) q^{22} +(1.08869 - 6.17426i) q^{23} +(4.37075 - 3.66750i) q^{25} +(-4.94689 + 1.64004i) q^{26} +(1.62360 + 2.17951i) q^{28} +(-5.00298 + 4.19800i) q^{29} +(4.65080 + 0.820062i) q^{31} +(-5.25562 + 2.09248i) q^{32} +(-1.50416 - 2.78865i) q^{34} +(3.85054 - 2.22311i) q^{35} +(3.70698 + 2.14023i) q^{37} +(0.100210 - 3.46179i) q^{38} +(2.39924 + 8.93804i) q^{40} +(-7.28211 + 8.67848i) q^{41} +(-3.24005 - 1.17928i) q^{43} +(5.70365 - 0.668391i) q^{44} +(5.89337 - 6.62433i) q^{46} +(2.21737 + 12.5753i) q^{47} +(-4.84262 + 1.76257i) q^{49} +(7.98359 - 1.17064i) q^{50} +(-7.17224 - 1.69759i) q^{52} -4.14210 q^{53} -9.39487i q^{55} +(0.336703 + 3.82875i) q^{56} +(-9.13841 + 1.33998i) q^{58} +(-3.92440 - 10.7822i) q^{59} +(9.59806 - 1.69240i) q^{61} +(4.98981 + 4.43922i) q^{62} +(-7.87971 - 1.38212i) q^{64} +(-4.12400 + 11.3306i) q^{65} +(-6.64683 - 5.57735i) q^{67} +(0.259201 - 4.47336i) q^{68} +(6.28527 + 0.181942i) q^{70} +(3.19451 - 5.53306i) q^{71} +(-2.87137 - 4.97336i) q^{73} +(2.87378 + 5.32784i) q^{74} +(2.69014 - 4.09283i) q^{76} +(0.677549 - 3.84257i) q^{77} +(5.31972 + 6.33979i) q^{79} +(-3.74612 + 12.5402i) q^{80} +(-15.2076 + 5.04177i) q^{82} +(1.56022 + 1.85940i) q^{83} +(-7.21919 - 1.27294i) q^{85} +(-3.02496 - 3.82451i) q^{86} +(7.36201 + 3.42894i) q^{88} +(-1.06132 + 0.612754i) q^{89} +(-2.50390 + 4.33688i) q^{91} +(12.0112 - 3.59982i) q^{92} +(-6.66482 + 16.7837i) q^{94} +(-6.13801 - 5.15040i) q^{95} +(16.9633 + 6.17414i) q^{97} +(-7.13768 - 1.47270i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 6 q^{2} - 6 q^{4} + 9 q^{8} - 3 q^{10} + 30 q^{11} - 9 q^{14} - 6 q^{16} + 18 q^{17} - 6 q^{19} + 27 q^{20} - 18 q^{22} - 12 q^{25} - 12 q^{28} + 36 q^{32} + 12 q^{34} + 18 q^{35} + 102 q^{38} + 9 q^{40}+ \cdots - 162 q^{98}+O(q^{100}) $ 192 * q + 6 * q^2 - 6 * q^4 + 9 * q^8 - 3 * q^10 + 30 * q^11 - 9 * q^14 - 6 * q^16 + 18 * q^17 - 6 * q^19 + 27 * q^20 - 18 * q^22 - 12 * q^25 - 12 * q^28 + 36 * q^32 + 12 * q^34 + 18 * q^35 + 102 * q^38 + 9 * q^40 - 18 * q^41 - 42 * q^43 + 81 * q^44 - 3 * q^46 - 12 * q^49 - 57 * q^50 + 21 * q^52 + 69 * q^56 - 33 * q^58 + 84 * q^59 - 90 * q^62 - 51 * q^64 + 12 * q^65 + 30 * q^67 - 63 * q^68 - 33 * q^70 - 6 * q^73 - 51 * q^74 + 30 * q^76 - 12 * q^82 + 72 * q^83 - 42 * q^86 - 78 * q^88 - 144 * q^89 - 6 * q^91 + 3 * q^92 - 33 * q^94 - 42 * q^97 - 162 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{18}\right)$

Coefficient data

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

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

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

$2$	1.20377	+	0.742249i	0.851195	+	0.524849i
$2$	1.20377	+	0.742249i	0.851195	+	0.524849i
$3$		0			0
$3$		0			0
$4$	0.898133	+	1.78700i	0.449066	+	0.893498i
$5$	3.07462	−	1.11907i	1.37501	−	0.500464i	0.454350	−	0.890823i	$-0.349872\pi$
$5$	3.07462	−	1.11907i	1.37501	−	0.500464i	0.920662	+	0.390360i	$0.127649\pi$
$6$		0			0
$7$	1.33825	−	0.235969i	0.505810	−	0.0891880i	0.0850807	−	0.996374i	$-0.472885\pi$
$7$	1.33825	−	0.235969i	0.505810	−	0.0891880i	0.420730	+	0.907186i	$0.361774\pi$
$8$	−0.245250	+	2.81777i	−0.0867089	+	0.996234i
$9$		0			0
$10$	4.53177	+	0.935029i	1.43307	+	0.295682i
$11$	0.982057	−	2.69818i	0.296101	−	0.813531i	−0.699041	−	0.715082i	$-0.746389\pi$
$11$	0.982057	−	2.69818i	0.296101	−	0.813531i	0.995142	−	0.0984497i	$-0.0313883\pi$
$12$		0			0
$13$	−2.36880	+	2.82303i	−0.656987	+	0.782967i	−0.986950	−	0.161027i	$-0.948519\pi$
$13$	−2.36880	+	2.82303i	−0.656987	+	0.782967i	0.329963	+	0.943994i	$0.392964\pi$
$14$	1.78609	+	0.709260i	0.477354	+	0.189558i
$15$		0			0
$16$	−2.38671	+	3.20992i	−0.596679	+	0.802480i
$17$	−1.94027	−	1.12022i	−0.470585	−	0.271692i	0.245900	−	0.969295i	$-0.420917\pi$
$17$	−1.94027	−	1.12022i	−0.470585	−	0.271692i	−0.716484	+	0.697603i	$0.754250\pi$
$18$		0			0
$19$	−1.22444	−	2.12079i	−0.280906	−	0.486544i	0.690702	−	0.723139i	$-0.257302\pi$
$19$	−1.22444	−	2.12079i	−0.280906	−	0.486544i	−0.971608	+	0.236596i	$0.923968\pi$
$20$	4.76119	+	4.48926i	1.06464	+	1.00383i
$21$		0			0
$22$	3.18489	−	2.51906i	0.679021	−	0.537066i
$23$	1.08869	−	6.17426i	0.227007	−	1.28742i	−0.631803	−	0.775129i	$-0.717685\pi$
$23$	1.08869	−	6.17426i	0.227007	−	1.28742i	0.858810	−	0.512294i	$-0.171204\pi$
$24$		0			0
$25$	4.37075	−	3.66750i	0.874151	−	0.733500i
$26$	−4.94689	+	1.64004i	−0.970164	+	0.321638i
$27$		0			0
$28$	1.62360	+	2.17951i	0.306832	+	0.411889i
$29$	−5.00298	+	4.19800i	−0.929030	+	0.779549i	−0.975643	−	0.219364i	$-0.929602\pi$
$29$	−5.00298	+	4.19800i	−0.929030	+	0.779549i	0.0466128	+	0.998913i	$0.485157\pi$
$30$		0			0
$31$	4.65080	+	0.820062i	0.835309	+	0.147287i	0.574913	−	0.818215i	$-0.305036\pi$
$31$	4.65080	+	0.820062i	0.835309	+	0.147287i	0.260396	+	0.965502i	$0.416147\pi$
$32$	−5.25562	+	2.09248i	−0.929071	+	0.369901i
$33$		0			0
$34$	−1.50416	−	2.78865i	−0.257962	−	0.478249i
$35$	3.85054	−	2.22311i	0.650860	−	0.375774i
$36$		0			0
$37$	3.70698	+	2.14023i	0.609424	+	0.351851i	0.772740	−	0.634723i	$-0.218886\pi$
$37$	3.70698	+	2.14023i	0.609424	+	0.351851i	−0.163316	+	0.986574i	$0.552219\pi$
$38$	0.100210	−	3.46179i	0.0162562	−	0.561577i
$39$		0			0
$40$	2.39924	+	8.93804i	0.379353	+	1.41323i
$41$	−7.28211	+	8.67848i	−1.13727	+	1.35535i	−0.211454	+	0.977388i	$0.567820\pi$
$41$	−7.28211	+	8.67848i	−1.13727	+	1.35535i	−0.925821	+	0.377963i	$0.876625\pi$
$42$		0			0
$43$	−3.24005	−	1.17928i	−0.494103	−	0.179839i	0.0829367	−	0.996555i	$-0.473570\pi$
$43$	−3.24005	−	1.17928i	−0.494103	−	0.179839i	−0.577040	+	0.816716i	$0.695792\pi$
$44$	5.70365	−	0.668391i	0.859858	−	0.100764i
$45$		0			0
$46$	5.89337	−	6.62433i	0.868931	−	0.976704i
$47$	2.21737	+	12.5753i	0.323437	+	1.83430i	0.520439	+	0.853899i	$0.325768\pi$
$47$	2.21737	+	12.5753i	0.323437	+	1.83430i	−0.197002	+	0.980403i	$0.563121\pi$
$48$		0			0
$49$	−4.84262	+	1.76257i	−0.691803	+	0.251796i
$50$	7.98359	−	1.17064i	1.12905	−	0.165554i
$51$		0			0
$52$	−7.17224	−	1.69759i	−0.994611	−	0.235413i
$53$	−4.14210			−0.568961			−0.284481	−	0.958682i	$-0.591821\pi$
$53$	−4.14210			−0.568961			−0.284481	+	0.958682i	$0.591821\pi$
$54$		0			0
$55$		−	9.39487i		−	1.26680i
$56$	0.336703	+	3.82875i	0.0449939	+	0.511639i
$57$		0			0
$58$	−9.13841	+	1.33998i	−1.19993	+	0.175947i
$59$	−3.92440	−	10.7822i	−0.510913	−	1.40372i	−0.880287	−	0.474442i	$-0.842650\pi$
$59$	−3.92440	−	10.7822i	−0.510913	−	1.40372i	0.369373	−	0.929281i	$-0.379572\pi$
$60$		0			0
$61$	9.59806	−	1.69240i	1.22891	−	0.216689i	0.478750	−	0.877951i	$-0.341090\pi$
$61$	9.59806	−	1.69240i	1.22891	−	0.216689i	0.750155	+	0.661262i	$0.229979\pi$
$62$	4.98981	+	4.43922i	0.633707	+	0.563781i
$63$		0			0
$64$	−7.87971	−	1.38212i	−0.984963	−	0.172765i
$65$	−4.12400	+	11.3306i	−0.511519	+	1.40539i
$66$		0			0
$67$	−6.64683	−	5.57735i	−0.812039	−	0.681382i	0.139054	−	0.990285i	$-0.455594\pi$
$67$	−6.64683	−	5.57735i	−0.812039	−	0.681382i	−0.951094	+	0.308903i	$0.900038\pi$
$68$	0.259201	−	4.47336i	0.0314328	−	0.542474i
$69$		0			0
$70$	6.28527	+	0.181942i	0.751234	+	0.0217462i
$71$	3.19451	−	5.53306i	0.379119	−	0.656653i	−0.611816	−	0.791000i	$-0.709561\pi$
$71$	3.19451	−	5.53306i	0.379119	−	0.656653i	0.990934	+	0.134348i	$0.0428939\pi$
$72$		0			0
$73$	−2.87137	−	4.97336i	−0.336069	−	0.582088i	0.647621	−	0.761963i	$-0.275764\pi$
$73$	−2.87137	−	4.97336i	−0.336069	−	0.582088i	−0.983690	+	0.179875i	$0.942431\pi$
$74$	2.87378	+	5.32784i	0.334070	+	0.619349i
$75$		0			0
$76$	2.69014	−	4.09283i	0.308580	−	0.469479i
$77$	0.677549	−	3.84257i	0.0772138	−	0.437901i
$78$		0			0
$79$	5.31972	+	6.33979i	0.598515	+	0.713283i	0.977219	−	0.212236i	$-0.0680744\pi$
$79$	5.31972	+	6.33979i	0.598515	+	0.713283i	−0.378703	+	0.925518i	$0.623630\pi$
$80$	−3.74612	+	12.5402i	−0.418828	+	1.40204i
$81$		0			0
$82$	−15.2076	+	5.04177i	−1.67940	+	0.556771i
$83$	1.56022	+	1.85940i	0.171257	+	0.204096i	0.844845	−	0.535011i	$-0.179692\pi$
$83$	1.56022	+	1.85940i	0.171257	+	0.204096i	−0.673589	+	0.739106i	$0.735248\pi$
$84$		0			0
$85$	−7.21919	−	1.27294i	−0.783032	−	0.138070i
$86$	−3.02496	−	3.82451i	−0.326190	−	0.412408i
$87$		0			0
$88$	7.36201	+	3.42894i	0.784793	+	0.365526i
$89$	−1.06132	+	0.612754i	−0.112500	+	0.0649518i	−0.555194	−	0.831721i	$-0.687356\pi$
$89$	−1.06132	+	0.612754i	−0.112500	+	0.0649518i	0.442694	+	0.896673i	$0.354023\pi$
$90$		0			0
$91$	−2.50390	+	4.33688i	−0.262480	+	0.454628i
$92$	12.0112	−	3.59982i	1.25225	−	0.375308i
$93$		0			0
$94$	−6.66482	+	16.7837i	−0.687424	+	1.73110i
$95$	−6.13801	−	5.15040i	−0.629747	−	0.528420i
$96$		0			0
$97$	16.9633	+	6.17414i	1.72236	+	0.626889i	0.998041	−	0.0625705i	$-0.0199298\pi$
$97$	16.9633	+	6.17414i	1.72236	+	0.626889i	0.724324	+	0.689460i	$0.242152\pi$
$98$	−7.13768	−	1.47270i	−0.721014	−	0.148765i
$99$		0			0
$100$	10.4793	+	4.51662i	1.04793	+	0.451662i
$101$	−3.06146	−	17.3624i	−0.304627	−	1.72763i	−0.625255	−	0.780420i	$-0.715005\pi$
$101$	−3.06146	−	17.3624i	−0.304627	−	1.72763i	0.320628	−	0.947205i	$-0.396106\pi$
$102$		0			0
$103$	−3.18775	−	8.75828i	−0.314099	−	0.862979i	−0.991818	−	0.127658i	$-0.959254\pi$
$103$	−3.18775	−	8.75828i	−0.314099	−	0.862979i	0.677720	−	0.735320i	$-0.262968\pi$
$104$	−7.37371	−	7.36709i	−0.723051	−	0.722403i
$105$		0			0
$106$	−4.98614	−	3.07447i	−0.484297	−	0.298619i
$107$			3.23586i			0.312823i	0.987692	+	0.156411i	$0.0499926\pi$
$107$			3.23586i			0.312823i	−0.987692	+	0.156411i	$0.950007\pi$
$108$		0			0
$109$		−	7.62757i		−	0.730589i	−0.930892	−	0.365295i	$-0.880968\pi$
$109$		−	7.62757i		−	0.730589i	0.930892	−	0.365295i	$-0.119032\pi$
$110$	6.97333	−	11.3093i	0.664881	−	1.07830i
$111$		0			0
$112$	−2.43657	+	4.85886i	−0.230235	+	0.459119i
$113$	−2.66170	−	7.31296i	−0.250392	−	0.687946i	−0.999670	−	0.0256902i	$-0.991822\pi$
$113$	−2.66170	−	7.31296i	−0.250392	−	0.687946i	0.749278	−	0.662255i	$-0.230401\pi$
$114$		0			0
$115$	−3.56213	−	20.2018i	−0.332170	−	1.88383i
$116$	−11.9952	−	5.16995i	−1.11372	−	0.480018i
$117$		0			0
$118$	3.27900	−	15.8922i	0.301856	−	1.46299i
$119$	−2.86090	−	1.04128i	−0.262258	−	0.0954542i
$120$		0			0
$121$	2.11076	+	1.77114i	0.191887	+	0.161012i
$122$	12.8101	+	5.08689i	1.15977	+	0.460545i
$123$		0			0
$124$	2.71159	+	9.04749i	0.243508	+	0.812489i
$125$	1.15436	−	1.99942i	0.103249	−	0.178833i
$126$		0			0
$127$	−9.21001	+	5.31740i	−0.817256	+	0.471843i	−0.849469	−	0.527638i	$-0.823078\pi$
$127$	−9.21001	+	5.31740i	−0.817256	+	0.471843i	0.0322133	+	0.999481i	$0.489744\pi$
$128$	−8.45949	−	7.51246i	−0.747721	−	0.664014i
$129$		0			0
$130$	−13.3745	+	10.5784i	−1.17302	+	0.927788i
$131$	−18.4239	−	3.24863i	−1.60970	−	0.283834i	−0.704784	−	0.709422i	$-0.748956\pi$
$131$	−18.4239	−	3.24863i	−1.60970	−	0.283834i	−0.904917	+	0.425588i	$0.860067\pi$
$132$		0			0
$133$	−2.13905	−	2.54922i	−0.185479	−	0.221045i
$134$	−3.86148	−	11.6475i	−0.333581	−	1.00619i
$135$		0			0
$136$	3.63236	−	5.19251i	0.311473	−	0.445254i
$137$	4.50049	+	5.36347i	0.384502	+	0.458232i	0.923230	−	0.384248i	$-0.125539\pi$
$137$	4.50049	+	5.36347i	0.384502	+	0.458232i	−0.538727	+	0.842480i	$0.681095\pi$
$138$		0			0
$139$	2.26112	−	12.8235i	0.191786	−	1.08767i	−0.725136	−	0.688606i	$-0.758223\pi$
$139$	2.26112	−	12.8235i	0.191786	−	1.08767i	0.916922	−	0.399067i	$-0.130666\pi$
$140$	7.43099	+	4.88426i	0.628033	+	0.412795i
$141$		0			0
$142$	7.95237	−	4.28941i	0.667348	−	0.359960i
$143$	5.29073	+	9.16382i	0.442433	+	0.766317i
$144$		0			0
$145$	−10.6844	+	18.5059i	−0.887292	+	1.53684i
$146$	0.234997	−	8.11807i	0.0194485	−	0.671856i
$147$		0			0
$148$	−0.495216	+	8.54657i	−0.0407065	+	0.702523i
$149$	−5.35782	−	4.49574i	−0.438929	−	0.368305i	0.396379	−	0.918087i	$-0.370267\pi$
$149$	−5.35782	−	4.49574i	−0.438929	−	0.368305i	−0.835309	+	0.549781i	$0.814711\pi$
$150$		0			0
$151$	−3.81995	+	10.4952i	−0.310863	+	0.854089i	0.681620	+	0.731706i	$0.261276\pi$
$151$	−3.81995	+	10.4952i	−0.310863	+	0.854089i	−0.992483	+	0.122383i	$0.960947\pi$
$152$	6.27621	−	2.93007i	0.509068	−	0.237660i
$153$		0			0
$154$	3.66776	−	4.12267i	0.295556	−	0.332214i
$155$	15.2172	−	2.68320i	1.22227	−	0.215519i
$156$		0			0
$157$	−2.38479	−	6.55217i	−0.190327	−	0.522920i	0.807422	−	0.589974i	$-0.200862\pi$
$157$	−2.38479	−	6.55217i	−0.190327	−	0.522920i	−0.997749	+	0.0670544i	$0.978640\pi$
$158$	1.69802	+	11.5802i	0.135087	+	0.921273i
$159$		0			0
$160$	−13.8174	+	12.3150i	−1.09236	+	0.973585i
$161$		−	8.51960i		−	0.671438i
$162$		0			0
$163$	−2.76444			−0.216528			−0.108264	−	0.994122i	$-0.534529\pi$
$163$	−2.76444			−0.216528			−0.108264	+	0.994122i	$0.534529\pi$
$164$	−22.0487	−	5.21868i	−1.72172	−	0.407510i
$165$		0			0
$166$	0.498013	+	3.39637i	0.0386533	+	0.263609i
$167$	14.0653	−	5.11934i	1.08840	−	0.396146i	0.265374	−	0.964146i	$-0.414505\pi$
$167$	14.0653	−	5.11934i	1.08840	−	0.396146i	0.823029	+	0.567999i	$0.192282\pi$
$168$		0			0
$169$	−0.100838	−	0.571881i	−0.00775677	−	0.0439908i
$170$	−7.74542	−	6.89077i	−0.594047	−	0.528498i
$171$		0			0
$172$	−0.802623	−	6.84911i	−0.0611994	−	0.522240i
$173$	7.26501	+	2.64425i	0.552349	+	0.201038i	0.603090	−	0.797673i	$-0.293936\pi$
$173$	7.26501	+	2.64425i	0.552349	+	0.201038i	−0.0507411	+	0.998712i	$0.516158\pi$
$174$		0			0
$175$	4.98374	−	5.93939i	0.376735	−	0.448975i
$176$	6.31705	+	9.59211i	0.476166	+	0.723032i
$177$		0			0
$178$	−1.73240	−	0.0501485i	−0.129849	−	0.00375879i
$179$	5.90573	+	3.40968i	0.441415	+	0.254851i	0.704198	−	0.710004i	$-0.251307\pi$
$179$	5.90573	+	3.40968i	0.441415	+	0.254851i	−0.262782	+	0.964855i	$0.584640\pi$
$180$		0			0
$181$	−5.60659	+	3.23697i	−0.416734	+	0.240602i	−0.693679	−	0.720284i	$-0.744011\pi$
$181$	−5.60659	+	3.23697i	−0.416734	+	0.240602i	0.276945	+	0.960886i	$0.410678\pi$
$182$	−6.23316	+	3.36209i	−0.462033	+	0.249215i
$183$		0			0
$184$	17.1307	+	4.58192i	1.26289	+	0.337783i
$185$	13.7926	+	2.43201i	1.01405	+	0.178805i
$186$		0			0
$187$	−4.92800	+	4.13508i	−0.360371	+	0.302387i
$188$	−20.4806	+	15.2568i	−1.49370	+	1.11271i
$189$		0			0
$190$	−3.56588	−	10.7558i	−0.258696	−	0.780311i
$191$	6.03023	−	5.05997i	0.436332	−	0.366126i	−0.398003	−	0.917384i	$-0.630296\pi$
$191$	6.03023	−	5.05997i	0.436332	−	0.366126i	0.834335	+	0.551258i	$0.185852\pi$
$192$		0			0
$193$	−3.98502	+	22.6002i	−0.286848	+	1.62680i	0.411761	+	0.911292i	$0.364914\pi$
$193$	−3.98502	+	22.6002i	−0.286848	+	1.62680i	−0.698609	+	0.715504i	$0.746197\pi$
$194$	15.8372	+	20.0233i	1.13705	+	1.43759i
$195$		0			0
$196$	−7.49902	−	7.07073i	−0.535645	−	0.505052i
$197$	9.17303	+	15.8882i	0.653551	+	1.13198i	0.982255	+	0.187551i	$0.0600550\pi$
$197$	9.17303	+	15.8882i	0.653551	+	1.13198i	−0.328704	+	0.944433i	$0.606612\pi$
$198$		0			0
$199$	−1.73990	−	1.00453i	−0.123338	−	0.0712092i	0.437062	−	0.899432i	$-0.356019\pi$
$199$	−1.73990	−	1.00453i	−0.123338	−	0.0712092i	−0.560400	+	0.828222i	$0.689352\pi$
$200$	9.26225	+	13.2152i	0.654940	+	0.934459i
$201$		0			0
$202$	9.20194	−	23.1728i	0.647446	−	1.63043i
$203$	−5.70463	+	6.79852i	−0.400387	+	0.477162i
$204$		0			0
$205$	−12.6779	+	34.8322i	−0.885463	+	2.43279i
$206$	2.66350	−	12.9091i	0.185575	−	0.899418i
$207$		0			0
$208$	−3.40804	−	14.3414i	−0.236305	−	0.994399i
$209$	−6.92475	+	1.22102i	−0.478995	+	0.0844598i
$210$		0			0
$211$	4.02245	−	1.46405i	0.276917	−	0.100790i	−0.199828	−	0.979831i	$-0.564038\pi$
$211$	4.02245	−	1.46405i	0.276917	−	0.100790i	0.476746	+	0.879041i	$0.341816\pi$
$212$	−3.72016	−	7.40192i	−0.255501	−	0.508366i
$213$		0			0
$214$	−2.40182	+	3.89524i	−0.164185	+	0.266273i
$215$	−11.2816			−0.769401
$216$		0			0
$217$	6.41744			0.435644
$218$	5.66156	−	9.18186i	0.383449	−	0.621874i
$219$		0			0
$220$	16.7886	−	8.43784i	1.13189	−	0.568879i
$221$	7.75851	−	2.82387i	0.521894	−	0.189954i
$222$		0			0
$223$	14.9594	−	2.63774i	1.00175	−	0.176636i	0.351366	−	0.936238i	$-0.385717\pi$
$223$	14.9594	−	2.63774i	1.00175	−	0.176636i	0.650388	+	0.759602i	$0.274606\pi$
$224$	−6.53957	+	4.04042i	−0.436943	+	0.269962i
$225$		0			0
$226$	2.22396	−	10.7788i	0.147936	−	0.716994i
$227$	6.27979	−	17.2536i	0.416805	−	1.14516i	−0.536698	−	0.843775i	$-0.680328\pi$
$227$	6.27979	−	17.2536i	0.416805	−	1.14516i	0.953502	−	0.301386i	$-0.0974494\pi$
$228$		0			0
$229$	13.7865	−	16.4302i	0.911040	−	1.08574i	−0.0849601	−	0.996384i	$-0.527076\pi$
$229$	13.7865	−	16.4302i	0.911040	−	1.08574i	0.996000	−	0.0893510i	$-0.0284793\pi$
$230$	10.7068	−	26.9624i	0.705986	−	1.77785i
$231$		0			0
$232$	−10.6020	−	15.1268i	−0.696058	−	0.993125i
$233$	−4.91994	−	2.84053i	−0.322316	−	0.186089i	0.330108	−	0.943943i	$-0.392915\pi$
$233$	−4.91994	−	2.84053i	−0.322316	−	0.186089i	−0.652424	+	0.757854i	$0.726248\pi$
$234$		0			0
$235$	20.8903	+	36.1830i	1.36273	+	2.36032i
$236$	15.7431	−	16.6967i	1.02479	−	1.08687i
$237$		0			0
$238$	−2.67098	−	3.37697i	−0.173134	−	0.218896i
$239$	−1.83559	+	10.4102i	−0.118735	+	0.673377i	0.866099	+	0.499873i	$0.166620\pi$
$239$	−1.83559	+	10.4102i	−0.118735	+	0.673377i	−0.984833	+	0.173504i	$0.944491\pi$
$240$		0			0
$241$	5.42614	−	4.55307i	0.349528	−	0.293289i	−0.451072	−	0.892487i	$-0.648958\pi$
$241$	5.42614	−	4.55307i	0.349528	−	0.293289i	0.800601	+	0.599198i	$0.204514\pi$
$242$	1.22625	+	3.69875i	0.0788261	+	0.237765i
$243$		0			0
$244$	11.6446	+	15.6317i	0.745472	+	1.00072i
$245$	−12.9168	+	10.8385i	−0.825223	+	0.692444i
$246$		0			0
$247$	8.88752	+	1.56711i	0.565499	+	0.0997128i
$248$	−3.45136	+	12.9038i	−0.219161	+	0.819391i
$249$		0			0
$250$	2.87365	−	1.55002i	0.181746	−	0.0980316i
$251$	1.58934	−	0.917608i	0.100318	−	0.0579189i	−0.449001	−	0.893531i	$-0.648220\pi$
$251$	1.58934	−	0.917608i	0.100318	−	0.0579189i	0.549320	+	0.835612i	$0.314887\pi$
$252$		0			0
$253$	−15.5901	−	9.00095i	−0.980142	−	0.565885i
$254$	−15.0336	−	0.435183i	−0.943291	−	0.0273058i
$255$		0			0
$256$	−4.60718	−	15.3223i	−0.287949	−	0.957646i
$257$	4.18774	−	4.99076i	0.261224	−	0.311315i	−0.619451	−	0.785035i	$-0.712645\pi$
$257$	4.18774	−	4.99076i	0.261224	−	0.311315i	0.880675	+	0.473720i	$0.157089\pi$
$258$		0			0
$259$	5.46589	+	1.98942i	0.339634	+	0.123617i
$260$	−23.9516	+	2.80681i	−1.48542	+	0.174071i
$261$		0			0
$262$	−19.7668	−	17.5857i	−1.22120	−	1.08645i
$263$	−0.191952	−	1.08861i	−0.0118363	−	0.0671268i	0.978318	−	0.207111i	$-0.0664060\pi$
$263$	−0.191952	−	1.08861i	−0.0118363	−	0.0671268i	−0.990154	+	0.139984i	$0.955295\pi$
$264$		0			0
$265$	−12.7354	+	4.63530i	−0.782329	+	0.284744i
$266$	−0.682771	−	4.65638i	−0.0418634	−	0.285501i
$267$		0			0
$268$	3.99697	−	16.8871i	0.244154	−	1.03154i
$269$	2.45873			0.149911			0.0749556	−	0.997187i	$-0.476118\pi$
$269$	2.45873			0.149911			0.0749556	+	0.997187i	$0.476118\pi$
$270$		0			0
$271$			10.4347i			0.633866i	0.948448	+	0.316933i	$0.102653\pi$
$271$			10.4347i			0.633866i	−0.948448	+	0.316933i	$0.897347\pi$
$272$	8.22667	−	3.55448i	0.498815	−	0.215522i
$273$		0			0
$274$	1.43653	+	9.79688i	0.0867838	+	0.591851i
$275$	−5.60324	−	15.3948i	−0.337888	−	0.928339i
$276$		0			0
$277$	−8.82313	+	1.55576i	−0.530130	+	0.0934763i	−0.432305	−	0.901727i	$-0.642300\pi$
$277$	−8.82313	+	1.55576i	−0.530130	+	0.0934763i	−0.0978251	+	0.995204i	$0.531189\pi$
$278$	12.2401	−	13.7582i	0.734111	−	0.825163i
$279$		0			0
$280$	5.31988	+	11.3952i	0.317924	+	0.680992i
$281$	−8.31065	+	22.8333i	−0.495772	+	1.36212i	0.399554	+	0.916710i	$0.369165\pi$
$281$	−8.31065	+	22.8333i	−0.495772	+	1.36212i	−0.895326	+	0.445412i	$0.853057\pi$
$282$		0			0
$283$	−5.06269	−	4.24810i	−0.300946	−	0.252524i	0.479792	−	0.877382i	$-0.340712\pi$
$283$	−5.06269	−	4.24810i	−0.300946	−	0.252524i	−0.780738	+	0.624859i	$0.785157\pi$
$284$	12.7566	+	0.739162i	0.756968	+	0.0438612i
$285$		0			0
$286$	−0.433000	+	14.9582i	−0.0256038	+	0.884496i
$287$	−7.69742	+	13.3323i	−0.454364	+	0.786982i
$288$		0			0
$289$	−5.99024	−	10.3754i	−0.352367	−	0.610317i
$290$	−26.5976	+	14.3464i	−1.56187	+	0.842452i
$291$		0			0
$292$	6.30851	−	9.59787i	0.369178	−	0.561673i
$293$	−5.28397	+	29.9669i	−0.308693	+	1.75068i	0.296900	+	0.954908i	$0.404047\pi$
$293$	−5.28397	+	29.9669i	−0.308693	+	1.75068i	−0.605593	+	0.795775i	$0.707064\pi$
$294$		0			0
$295$	−24.1321	−	28.7595i	−1.40502	−	1.67444i
$296$	−6.93981	+	9.92054i	−0.403368	+	0.576620i
$297$		0			0
$298$	−3.11263	−	9.38868i	−0.180310	−	0.543872i
$299$	14.8512	+	17.6990i	0.858869	+	1.02356i
$300$		0			0
$301$	−4.61427	−	0.813620i	−0.265962	−	0.0468963i
$302$	−12.3884	+	9.79850i	−0.712873	+	0.563840i
$303$		0			0
$304$	9.72997	+	1.13137i	0.558052	+	0.0648886i
$305$	27.6165	−	15.9444i	1.58131	−	0.912973i
$306$		0			0
$307$	2.83374	−	4.90819i	0.161730	−	0.280125i	−0.773759	−	0.633480i	$-0.781626\pi$
$307$	2.83374	−	4.90819i	0.161730	−	0.280125i	0.935489	+	0.353355i	$0.114959\pi$
$308$	7.47519	−	2.24036i	0.425938	−	0.127656i
$309$		0			0
$310$	20.3096	+	8.06497i	1.15351	+	0.458059i
$311$	−0.654416	−	0.549121i	−0.0371085	−	0.0311378i	0.624045	−	0.781389i	$-0.285488\pi$
$311$	−0.654416	−	0.549121i	−0.0371085	−	0.0311378i	−0.661153	+	0.750251i	$0.729933\pi$
$312$		0			0
$313$	22.1803	+	8.07297i	1.25370	+	0.456311i	0.881652	−	0.471900i	$-0.156432\pi$
$313$	22.1803	+	8.07297i	1.25370	+	0.456311i	0.372053	+	0.928212i	$0.378654\pi$
$314$	1.99259	−	9.65742i	0.112448	−	0.545000i
$315$		0			0
$316$	−6.55138	+	15.2003i	−0.368544	+	0.855084i
$317$	3.58128	+	20.3104i	0.201145	+	1.14075i	0.903392	+	0.428815i	$0.141069\pi$
$317$	3.58128	+	20.3104i	0.201145	+	1.14075i	−0.702248	+	0.711932i	$0.747820\pi$
$318$		0			0
$319$	6.41374	+	17.6216i	0.359101	+	0.986621i
$320$	−25.7738	+	4.56846i	−1.44080	+	0.255385i
$321$		0			0
$322$	6.32366	−	10.2556i	0.352404	−	0.571525i
$323$			5.48655i			0.305280i
$324$		0			0
$325$			21.0263i			1.16633i
$326$	−3.32776	−	2.05191i	−0.184308	−	0.113645i
$327$		0			0
$328$	−22.6681	−	22.6477i	−1.25163	−	1.25051i
$329$	5.93479	+	16.3057i	0.327196	+	0.898962i
$330$		0			0
$331$	3.26084	+	18.4932i	0.179232	+	1.01648i	0.933145	+	0.359501i	$0.117053\pi$
$331$	3.26084	+	18.4932i	0.179232	+	1.01648i	−0.753913	+	0.656975i	$0.771836\pi$
$332$	−1.92146	+	4.45810i	−0.105454	+	0.244670i
$333$		0			0
$334$	20.7312	+	4.27742i	1.13436	+	0.234050i
$335$	−26.6779	−	9.70997i	−1.45757	−	0.530512i
$336$		0			0
$337$	−5.59075	−	4.69119i	−0.304547	−	0.255546i	0.477687	−	0.878530i	$-0.341475\pi$
$337$	−5.59075	−	4.69119i	−0.304547	−	0.255546i	−0.782234	+	0.622985i	$0.785920\pi$
$338$	0.303092	−	0.763260i	0.0164860	−	0.0415159i
$339$		0			0
$340$	−4.20906	−	14.0439i	−0.228268	−	0.761640i
$341$	6.78002	−	11.7433i	0.367159	−	0.635938i
$342$		0			0
$343$	−14.3026	+	8.25759i	−0.772266	+	0.445868i
$344$	4.11757	−	8.84052i	0.222005	−	0.476649i
$345$		0			0
$346$	6.78273	+	8.57552i	0.364642	+	0.461023i
$347$	22.5534	+	3.97677i	1.21073	+	0.213484i	0.742331	−	0.670034i	$-0.233720\pi$
$347$	22.5534	+	3.97677i	1.21073	+	0.213484i	0.468398	+	0.883518i	$0.344831\pi$
$348$		0			0
$349$	10.5079	+	12.5229i	0.562476	+	0.670333i	0.970069	−	0.242831i	$-0.0780760\pi$
$349$	10.5079	+	12.5229i	0.562476	+	0.670333i	−0.407592	+	0.913164i	$0.633632\pi$
$350$	10.4078	−	3.45049i	0.556320	−	0.184437i
$351$		0			0
$352$	0.484555	+	16.2355i	0.0258269	+	0.865357i
$353$	−2.82906	−	3.37155i	−0.150576	−	0.179449i	0.685484	−	0.728088i	$-0.259591\pi$
$353$	−2.82906	−	3.37155i	−0.150576	−	0.179449i	−0.836060	+	0.548639i	$0.815146\pi$
$354$		0			0
$355$	3.63003	−	20.5869i	0.192662	−	1.09264i
$356$	−2.04820	−	1.34624i	−0.108554	−	0.0713507i
$357$		0			0
$358$	4.57833	+	8.48800i	0.241972	+	0.448605i
$359$	1.38464	+	2.39827i	0.0730784	+	0.126576i	0.900249	−	0.435375i	$-0.143384\pi$
$359$	1.38464	+	2.39827i	0.0730784	+	0.126576i	−0.827171	+	0.561951i	$0.810051\pi$
$360$		0			0
$361$	6.50149	−	11.2609i	0.342184	−	0.592679i
$362$	−9.15169	−	0.264917i	−0.481002	−	0.0139237i
$363$		0			0
$364$	−9.99882	−	0.579364i	−0.524080	−	0.0303669i
$365$	−14.3939	−	12.0779i	−0.753413	−	0.632188i
$366$		0			0
$367$	3.78468	−	10.3983i	0.197559	−	0.542788i	−0.800869	−	0.598839i	$-0.795629\pi$
$367$	3.78468	−	10.3983i	0.197559	−	0.542788i	0.998428	+	0.0560511i	$0.0178510\pi$
$368$	17.2205	+	18.2308i	0.897681	+	0.950347i
$369$		0			0
$370$	14.7980	+	13.1651i	0.769312	+	0.684423i
$371$	−5.54316	+	0.977409i	−0.287787	+	0.0507445i
$372$		0			0
$373$	3.74325	+	10.2845i	0.193818	+	0.532510i	0.998092	−	0.0617485i	$-0.0196677\pi$
$373$	3.74325	+	10.2845i	0.193818	+	0.532510i	−0.804274	+	0.594259i	$0.797445\pi$
$374$	−9.00144	+	1.31989i	−0.465453	+	0.0682500i
$375$		0			0
$376$	−35.9783	+	3.16396i	−1.85544	+	0.163169i
$377$		−	24.0678i		−	1.23955i
$378$		0			0
$379$	−9.42607			−0.484185			−0.242092	−	0.970253i	$-0.577834\pi$
$379$	−9.42607			−0.484185			−0.242092	+	0.970253i	$0.577834\pi$
$380$	3.69100	−	15.5943i	0.189344	−	0.799973i
$381$		0			0
$382$	11.0148	−	1.61511i	0.563565	−	0.0826362i
$383$	12.6302	−	4.59701i	0.645372	−	0.234896i	0.00146378	−	0.999999i	$-0.499534\pi$
$383$	12.6302	−	4.59701i	0.645372	−	0.234896i	0.643908	+	0.765103i	$0.277312\pi$
$384$		0			0
$385$	−2.21690	−	12.5727i	−0.112984	−	0.640762i
$386$	−21.5720	+	24.2476i	−1.09799	+	1.23417i
$387$		0			0
$388$	4.20214	+	35.8586i	0.213331	+	1.82044i
$389$	−7.86520	−	2.86270i	−0.398781	−	0.145145i	0.134841	−	0.990867i	$-0.456948\pi$
$389$	−7.86520	−	2.86270i	−0.398781	−	0.145145i	−0.533623	+	0.845723i	$0.679170\pi$
$390$		0			0
$391$	−9.02886	+	10.7602i	−0.456609	+	0.544165i
$392$	−3.77887	−	14.0777i	−0.190862	−	0.711030i
$393$		0			0
$394$	−0.750732	+	25.9344i	−0.0378213	+	1.30656i
$395$	23.4508	+	13.5393i	1.17994	+	0.681237i
$396$		0			0
$397$	18.5938	−	10.7351i	0.933195	−	0.538780i	0.0453741	−	0.998970i	$-0.485552\pi$
$397$	18.5938	−	10.7351i	0.933195	−	0.538780i	0.887820	+	0.460190i	$0.152219\pi$
$398$	−1.34883	−	2.50066i	−0.0676106	−	0.125347i
$399$		0			0
$400$	1.34063	+	22.7830i	0.0670317	+	1.13915i
$401$	28.7000	+	5.06058i	1.43321	+	0.252713i	0.835716	−	0.549161i	$-0.185053\pi$
$401$	28.7000	+	5.06058i	1.43321	+	0.252713i	0.597492	+	0.801875i	$0.296164\pi$
$402$		0			0
$403$	−13.3319	+	11.1868i	−0.664108	+	0.557253i
$404$	28.2770	−	21.0646i	1.40683	−	1.04800i
$405$		0			0
$406$	−11.9133	+	3.94960i	−0.591246	+	0.196016i
$407$	9.41517	−	7.90027i	0.466693	−	0.391602i
$408$		0			0
$409$	3.08156	−	17.4764i	0.152373	−	0.864152i	−0.808775	−	0.588119i	$-0.799869\pi$
$409$	3.08156	−	17.4764i	0.152373	−	0.864152i	0.961148	−	0.276034i	$-0.0890201\pi$
$410$	−41.1155	+	32.5199i	−2.03055	+	1.60604i
$411$		0			0
$412$	12.7880	−	13.5626i	0.630019	−	0.668181i
$413$	−7.79609	−	13.5032i	−0.383621	−	0.664450i
$414$		0			0
$415$	6.87789	+	3.97095i	0.337622	+	0.194926i
$416$	6.54241	−	19.7934i	0.320768	−	0.970452i
$417$		0			0
$418$	−9.24212	−	3.67006i	−0.452047	−	0.179508i
$419$	−23.7288	+	28.2789i	−1.15923	+	1.38151i	−0.248436	+	0.968648i	$0.579916\pi$
$419$	−23.7288	+	28.2789i	−1.15923	+	1.38151i	−0.910792	+	0.412866i	$0.864528\pi$
$420$		0			0
$421$	8.97583	−	24.6609i	0.437455	−	1.20190i	−0.503687	−	0.863886i	$-0.668023\pi$
$421$	8.97583	−	24.6609i	0.437455	−	1.20190i	0.941142	−	0.338012i	$-0.109754\pi$
$422$	5.92881	+	1.22328i	0.288610	+	0.0595482i
$423$		0			0
$424$	1.01585	−	11.6715i	0.0493340	−	0.566818i
$425$	−12.5888	+	2.21975i	−0.610648	+	0.107674i
$426$		0			0
$427$	12.4452	−	4.52969i	0.602267	−	0.219207i
$428$	−5.78248	+	2.90624i	−0.279507	+	0.140478i
$429$		0			0
$430$	−13.5805	−	8.37378i	−0.654910	−	0.403819i
$431$	12.1132			0.583473			0.291736	−	0.956499i	$-0.405767\pi$
$431$	12.1132			0.583473			0.291736	+	0.956499i	$0.405767\pi$
$432$		0			0
$433$	21.9408			1.05441			0.527203	−	0.849739i	$-0.323241\pi$
$433$	21.9408			1.05441			0.527203	+	0.849739i	$0.323241\pi$
$434$	7.72513	+	4.76334i	0.370818	+	0.228647i
$435$		0			0
$436$	13.6304	−	6.85057i	0.652780	−	0.328083i
$437$	−14.4274	+	5.25114i	−0.690155	+	0.251196i
$438$		0			0
$439$	18.3248	−	3.23116i	0.874596	−	0.154215i	0.281708	−	0.959500i	$-0.409099\pi$
$439$	18.3248	−	3.23116i	0.874596	−	0.154215i	0.592888	+	0.805285i	$0.297988\pi$
$440$	26.4726	+	2.30409i	1.26203	+	0.109843i
$441$		0			0
$442$	11.4355	+	2.35946i	0.543931	+	0.112228i
$443$	−0.178768	+	0.491160i	−0.00849351	+	0.0233357i	−0.943867	−	0.330326i	$-0.892841\pi$
$443$	−0.178768	+	0.491160i	−0.00849351	+	0.0233357i	0.935373	+	0.353662i	$0.115064\pi$
$444$		0			0
$445$	−2.57744	+	3.07168i	−0.122183	+	0.145612i
$446$	19.9655	+	7.92834i	0.945395	+	0.375418i
$447$		0			0
$448$	−10.8711	+	0.00975332i	−0.513613	+	0.000460801i
$449$	−8.98007	−	5.18465i	−0.423796	−	0.244679i	0.272904	−	0.962041i	$-0.412016\pi$
$449$	−8.98007	−	5.18465i	−0.423796	−	0.244679i	−0.696700	+	0.717363i	$0.745349\pi$
$450$		0			0
$451$	16.2646	+	28.1712i	0.765872	+	1.32653i
$452$	10.6777	−	11.3245i	0.502236	−	0.532658i
$453$		0			0
$454$	20.3659	−	16.1082i	0.955819	−	0.755996i
$455$	−2.84526	+	16.1363i	−0.133388	+	0.756481i
$456$		0			0
$457$	−5.85958	+	4.91677i	−0.274099	+	0.229997i	−0.769467	−	0.638687i	$-0.779478\pi$
$457$	−5.85958	+	4.91677i	−0.274099	+	0.229997i	0.495367	+	0.868684i	$0.335033\pi$
$458$	28.7911	−	9.54511i	1.34532	−	0.446014i
$459$		0			0
$460$	32.9014	−	24.5095i	1.53403	−	1.14276i
$461$	−3.98250	+	3.34172i	−0.185484	+	0.155639i	−0.730801	−	0.682590i	$-0.760853\pi$
$461$	−3.98250	+	3.34172i	−0.185484	+	0.155639i	0.545318	+	0.838229i	$0.316409\pi$
$462$		0			0
$463$	−24.6573	−	4.34774i	−1.14592	−	0.202057i	−0.431727	−	0.902004i	$-0.642096\pi$
$463$	−24.6573	−	4.34774i	−1.14592	−	0.202057i	−0.714194	+	0.699948i	$0.753207\pi$
$464$	−1.53456	−	26.0786i	−0.0712400	−	1.21067i
$465$		0			0
$466$	−3.81411	−	7.07117i	−0.176685	−	0.327566i
$467$	−5.51602	+	3.18467i	−0.255251	+	0.147369i	−0.622166	−	0.782885i	$-0.713747\pi$
$467$	−5.51602	+	3.18467i	−0.255251	+	0.147369i	0.366915	+	0.930254i	$0.380414\pi$
$468$		0			0
$469$	−10.2112	−	5.89543i	−0.471509	−	0.272226i
$470$	−1.70969	+	59.0619i	−0.0788619	+	2.72432i
$471$		0			0
$472$	31.3443	−	8.41374i	1.44274	−	0.387274i
$473$	−6.36383	+	7.58412i	−0.292609	+	0.348718i
$474$		0			0
$475$	−13.1297	−	4.77883i	−0.602434	−	0.219268i
$476$	−0.708700	−	6.04763i	−0.0324832	−	0.277193i
$477$		0			0
$478$	−9.93657	+	11.1690i	−0.454488	+	0.510858i
$479$	3.99003	+	22.6286i	0.182309	+	1.03393i	0.929364	+	0.369164i	$0.120356\pi$
$479$	3.99003	+	22.6286i	0.182309	+	1.03393i	−0.747055	+	0.664762i	$0.768533\pi$
$480$		0			0
$481$	−14.8230	+	5.39513i	−0.675871	+	0.245997i
$482$	9.91135	−	1.45331i	0.451449	−	0.0661966i
$483$		0			0
$484$	−1.26927	+	5.36263i	−0.0576942	+	0.243756i
$485$	59.0651			2.68201
$486$		0			0
$487$			17.1809i			0.778541i	0.921124	+	0.389270i	$0.127273\pi$
$487$			17.1809i			0.778541i	−0.921124	+	0.389270i	$0.872727\pi$
$488$	2.41487	+	27.4602i	0.109316	+	1.24307i
$489$		0			0
$490$	−23.5937	+	3.45957i	−1.06585	+	0.156288i
$491$	−4.32122	−	11.8724i	−0.195014	−	0.535796i	0.803189	−	0.595724i	$-0.203135\pi$
$491$	−4.32122	−	11.8724i	−0.195014	−	0.535796i	−0.998203	+	0.0599285i	$0.980913\pi$
$492$		0			0
$493$	14.4098	−	2.54084i	0.648985	−	0.114433i
$494$	9.53536	+	8.48319i	0.429016	+	0.381677i
$495$		0			0
$496$	−13.7325	+	12.9715i	−0.616606	+	0.582435i
$497$	2.96942	−	8.15841i	0.133197	−	0.365955i
$498$		0			0
$499$	1.80634	+	1.51570i	0.0808628	+	0.0678519i	0.682323	−	0.731051i	$-0.260970\pi$
$499$	1.80634	+	1.51570i	0.0808628	+	0.0678519i	−0.601460	+	0.798903i	$0.705414\pi$
$500$	4.60972	+	0.267102i	0.206153	+	0.0119452i
$501$		0			0
$502$	2.59430	+	0.0750982i	0.115789	+	0.00335180i
$503$	−9.09713	+	15.7567i	−0.405621	+	0.702556i	−0.994394	−	0.105743i	$-0.966278\pi$
$503$	−9.09713	+	15.7567i	−0.405621	+	0.702556i	0.588773	+	0.808299i	$0.299611\pi$
$504$		0			0
$505$	−28.8426	−	49.9569i	−1.28348	−	2.22305i
$506$	−12.0860	−	22.4068i	−0.537288	−	0.996106i
$507$		0			0
$508$	−17.7740	−	11.6825i	−0.788593	−	0.518328i
$509$	2.07234	−	11.7528i	0.0918549	−	0.520935i	−0.903811	−	0.427932i	$-0.859242\pi$
$509$	2.07234	−	11.7528i	0.0918549	−	0.520935i	0.995666	−	0.0930030i	$-0.0296466\pi$
$510$		0			0
$511$	−5.01617	−	5.97804i	−0.221902	−	0.264453i
$512$	5.82699	−	21.8643i	0.257519	−	0.966273i
$513$		0			0
$514$	8.74547	−	2.89939i	0.385746	−	0.127886i
$515$	−19.6023	−	23.3611i	−0.863779	−	1.02941i
$516$		0			0
$517$	36.1081	+	6.36683i	1.58803	+	0.280013i
$518$	5.10303	+	6.45186i	0.224214	+	0.283478i
$519$		0			0
$520$	−30.9157	−	14.3993i	−1.35574	−	0.631452i
$521$	−12.2664	+	7.08202i	−0.537402	+	0.310269i	−0.744025	−	0.668152i	$-0.767086\pi$
$521$	−12.2664	+	7.08202i	−0.537402	+	0.310269i	0.206624	+	0.978421i	$0.433752\pi$
$522$		0			0
$523$	8.17227	−	14.1548i	0.357349	−	0.618946i	−0.630168	−	0.776459i	$-0.717014\pi$
$523$	8.17227	−	14.1548i	0.357349	−	0.618946i	0.987517	+	0.157513i	$0.0503475\pi$
$524$	−10.7418	−	35.8411i	−0.469258	−	1.56573i
$525$		0			0
$526$	0.576956	−	1.45292i	0.0251565	−	0.0633503i
$527$	−8.10516	−	6.80104i	−0.353066	−	0.296258i
$528$		0			0
$529$	−15.3234	−	5.57725i	−0.666233	−	0.242489i
$530$	−18.7711	−	3.87298i	−0.815362	−	0.168232i
$531$		0			0
$532$	2.63430	−	6.11201i	0.114211	−	0.264989i
$533$	−7.24972	−	41.1152i	−0.314020	−	1.78090i
$534$		0			0
$535$	3.62116	+	9.94906i	0.156556	+	0.430135i
$536$	17.3458	−	17.3614i	0.749226	−	0.749899i
$537$		0			0
$538$	2.95974	+	1.82499i	0.127604	+	0.0786808i
$539$			14.7972i			0.637360i
$540$		0			0
$541$		−	10.8601i		−	0.466912i	−0.972367	−	0.233456i	$-0.924996\pi$
$541$		−	10.8601i		−	0.466912i	0.972367	−	0.233456i	$-0.0750035\pi$
$542$	−7.74518	+	12.5611i	−0.332684	+	0.539543i
$543$		0			0
$544$	12.5413	+	1.82746i	0.537706	+	0.0783517i
$545$	−8.53579	−	23.4519i	−0.365633	−	1.00457i
$546$		0			0
$547$	0.544866	+	3.09009i	0.0232968	+	0.132123i	0.994238	−	0.107196i	$-0.0341872\pi$
$547$	0.544866	+	3.09009i	0.0232968	+	0.132123i	−0.970941	+	0.239318i	$0.923076\pi$
$548$	−5.54247	+	12.8595i	−0.236763	+	0.549329i
$549$		0			0
$550$	4.68173	−	22.6908i	0.199630	−	0.967538i
$551$	15.0289	+	5.47009i	0.640255	+	0.233034i
$552$		0			0
$553$	8.61510	+	7.22893i	0.366351	+	0.307405i
$554$	−11.7758	−	4.67618i	−0.500305	−	0.198672i
$555$		0			0
$556$	24.9463	−	7.47656i	1.05796	−	0.317077i
$557$	−4.03028	+	6.98066i	−0.170769	+	0.295780i	−0.938689	−	0.344766i	$-0.887958\pi$
$557$	−4.03028	+	6.98066i	−0.170769	+	0.295780i	0.767920	+	0.640546i	$0.221292\pi$
$558$		0			0
$559$	11.0042	−	6.35327i	0.465427	−	0.268715i
$560$	−2.05413	+	17.6659i	−0.0868030	+	0.746519i
$561$		0			0
$562$	−26.9521	+	21.3175i	−1.13691	+	0.899226i
$563$	−1.45495	−	0.256547i	−0.0613187	−	0.0108121i	0.142905	−	0.989736i	$-0.454356\pi$
$563$	−1.45495	−	0.256547i	−0.0613187	−	0.0108121i	−0.204223	+	0.978924i	$0.565467\pi$
$564$		0			0
$565$	−16.3674	−	19.5060i	−0.688583	−	0.820622i
$566$	−2.94118	−	8.87152i	−0.123627	−	0.372898i
$567$		0			0
$568$	14.8074	+	10.3584i	0.621307	+	0.434628i
$569$	−6.48819	−	7.73232i	−0.271999	−	0.324156i	0.612703	−	0.790314i	$-0.290082\pi$
$569$	−6.48819	−	7.73232i	−0.271999	−	0.324156i	−0.884702	+	0.466158i	$0.845638\pi$
$570$		0			0
$571$	−4.99821	+	28.3463i	−0.209169	+	1.18626i	0.681575	+	0.731749i	$0.261295\pi$
$571$	−4.99821	+	28.3463i	−0.209169	+	1.18626i	−0.890743	+	0.454507i	$0.849816\pi$
$572$	−11.6239	+	17.6849i	−0.486021	+	0.739441i
$573$		0			0
$574$	−19.1618	+	10.3357i	−0.799800	+	0.431402i
$575$	−17.8857	−	30.9789i	−0.745885	−	1.29191i
$576$		0			0
$577$	5.35695	−	9.27852i	0.223013	−	0.386270i	−0.732709	−	0.680543i	$-0.761744\pi$
$577$	5.35695	−	9.27852i	0.223013	−	0.386270i	0.955721	+	0.294273i	$0.0950774\pi$
$578$	0.490248	−	16.9358i	0.0203916	−	0.704438i
$579$		0			0
$580$	−42.6661	−	2.47221i	−1.77161	−	0.102653i
$581$	2.52673	+	2.12018i	0.104826	+	0.0879597i
$582$		0			0
$583$	−4.06778	+	11.1761i	−0.168470	+	0.462868i
$584$	14.7180	−	6.87116i	0.609036	−	0.284331i
$585$		0			0
$586$	−28.6036	+	32.1512i	−1.18160	+	1.32816i
$587$	7.19613	−	1.26887i	0.297016	−	0.0523720i	−0.0231543	−	0.999732i	$-0.507371\pi$
$587$	7.19613	−	1.26887i	0.297016	−	0.0523720i	0.320171	+	0.947360i	$0.396260\pi$
$588$		0			0
$589$	−3.95545	−	10.8675i	−0.162981	−	0.447788i
$590$	−7.70281	−	52.5319i	−0.317120	−	2.16270i
$591$		0			0
$592$	−15.7175	+	6.79100i	−0.645983	+	0.279108i
$593$		−	13.1080i		−	0.538281i	−0.963101	−	0.269140i	$-0.913260\pi$
$593$		−	13.1080i		−	0.538281i	0.963101	−	0.269140i	$-0.0867395\pi$
$594$		0			0
$595$	−9.96145			−0.408380
$596$	3.22184	−	13.6122i	0.131972	−	0.557576i
$597$		0			0
$598$	4.74042	+	32.3289i	0.193850	+	1.32203i
$599$	−6.88675	+	2.50657i	−0.281385	+	0.102416i	−0.478857	−	0.877893i	$-0.658949\pi$
$599$	−6.88675	+	2.50657i	−0.281385	+	0.102416i	0.197473	+	0.980308i	$0.436727\pi$
$600$		0			0
$601$	0.0524110	+	0.297238i	0.00213789	+	0.0121246i	0.985858	−	0.167583i	$-0.0535961\pi$
$601$	0.0524110	+	0.297238i	0.00213789	+	0.0121246i	−0.983720	+	0.179707i	$0.942485\pi$
$602$	−4.95062	−	4.40435i	−0.201772	−	0.179508i
$603$		0			0
$604$	−22.1857	+	2.59987i	−0.902725	+	0.105787i
$605$	8.47180	+	3.08348i	0.344428	+	0.125361i
$606$		0			0
$607$	9.41990	−	11.2262i	0.382342	−	0.455657i	−0.540210	−	0.841530i	$-0.681655\pi$
$607$	9.41990	−	11.2262i	0.382342	−	0.455657i	0.922552	+	0.385873i	$0.126100\pi$
$608$	10.8729	+	8.58398i	0.440955	+	0.348126i
$609$		0			0
$610$	45.0786	+	1.30491i	1.82518	+	0.0528342i
$611$	−40.7530	−	23.5288i	−1.64869	−	0.951873i
$612$		0			0
$613$	11.7747	−	6.79811i	0.475574	−	0.274573i	−0.242996	−	0.970027i	$-0.578130\pi$
$613$	11.7747	−	6.79811i	0.475574	−	0.274573i	0.718570	+	0.695454i	$0.244797\pi$
$614$	7.05428	−	3.80499i	0.284687	−	0.153557i
$615$		0			0
$616$	10.6613	+	2.85157i	0.429557	+	0.114893i
$617$	21.9238	+	3.86576i	0.882620	+	0.155630i	0.596547	−	0.802578i	$-0.296539\pi$
$617$	21.9238	+	3.86576i	0.882620	+	0.155630i	0.286073	+	0.958208i	$0.407650\pi$
$618$		0			0
$619$	−26.2499	+	22.0263i	−1.05507	+	0.885311i	−0.993618	−	0.112799i	$-0.964018\pi$
$619$	−26.2499	+	22.0263i	−1.05507	+	0.885311i	−0.0614548	+	0.998110i	$0.519574\pi$
$620$	18.4619	+	24.7831i	0.741447	+	0.995315i
$621$		0			0
$622$	−0.380184	−	1.14676i	−0.0152440	−	0.0459807i
$623$	−1.27572	+	1.07046i	−0.0511106	+	0.0428869i
$624$		0			0
$625$	−3.64210	+	20.6554i	−0.145684	+	0.826216i
$626$	20.7079	+	26.1813i	0.827653	+	1.04642i
$627$		0			0
$628$	9.56684	−	10.1463i	0.381758	−	0.404883i
$629$	−4.79503	−	8.30523i	−0.191190	−	0.331151i
$630$		0			0
$631$	−4.33363	−	2.50202i	−0.172519	−	0.0996040i	0.411254	−	0.911521i	$-0.365091\pi$
$631$	−4.33363	−	2.50202i	−0.172519	−	0.0996040i	−0.583773	+	0.811917i	$0.698424\pi$
$632$	−19.1688	+	13.4349i	−0.762493	+	0.534413i
$633$		0			0
$634$	−10.7644	+	27.1073i	−0.427507	+	1.07657i
$635$	−22.3667	+	26.6556i	−0.887597	+	1.05780i
$636$		0			0
$637$	6.49542	−	17.8460i	0.257358	−	0.707085i
$638$	−5.35894	+	25.9730i	−0.212163	+	1.02828i
$639$		0			0
$640$	−34.4167	−	13.6312i	−1.36044	−	0.538820i
$641$	−21.6772	+	3.82227i	−0.856197	+	0.150971i	−0.584482	−	0.811407i	$-0.698702\pi$
$641$	−21.6772	+	3.82227i	−0.856197	+	0.150971i	−0.271716	+	0.962378i	$0.587591\pi$
$642$		0			0
$643$	17.8842	−	6.50931i	0.705283	−	0.256702i	0.0356184	−	0.999365i	$-0.488660\pi$
$643$	17.8842	−	6.50931i	0.705283	−	0.256702i	0.669665	+	0.742663i	$0.266438\pi$
$644$	15.2245	−	7.65173i	0.599929	−	0.301520i
$645$		0			0
$646$	−4.07239	+	6.60455i	−0.160226	+	0.259853i
$647$	10.3985			0.408809			0.204405	−	0.978886i	$-0.434474\pi$
$647$	10.3985			0.408809			0.204405	+	0.978886i	$0.434474\pi$
$648$		0			0
$649$	−32.9463			−1.29325
$650$	−15.6068	+	25.3109i	−0.612148	+	0.992775i
$651$		0			0
$652$	−2.48284	−	4.94005i	−0.0972354	−	0.193467i
$653$	14.2393	−	5.18267i	0.557225	−	0.202813i	−0.0480285	−	0.998846i	$-0.515294\pi$
$653$	14.2393	−	5.18267i	0.557225	−	0.202813i	0.605254	+	0.796033i	$0.293072\pi$
$654$		0			0
$655$	−60.2819	+	10.6293i	−2.35541	+	0.415322i
$656$	−10.4769	−	44.0881i	−0.409055	−	1.72135i
$657$		0			0
$658$	−4.95876	+	24.0334i	−0.193312	+	0.936921i
$659$	−3.21036	+	8.82040i	−0.125058	+	0.343594i	−0.986384	−	0.164459i	$-0.947412\pi$
$659$	−3.21036	+	8.82040i	−0.125058	+	0.343594i	0.861326	+	0.508053i	$0.169635\pi$
$660$		0			0
$661$	−15.4507	+	18.4135i	−0.600964	+	0.716201i	−0.977673	−	0.210131i	$-0.932611\pi$
$661$	−15.4507	+	18.4135i	−0.600964	+	0.716201i	0.376709	+	0.926332i	$0.377056\pi$
$662$	−9.80122	+	24.6819i	−0.380935	+	0.959289i
$663$		0			0
$664$	−5.62201	+	3.94034i	−0.218176	+	0.152915i
$665$	−9.42952	−	5.44414i	−0.365661	−	0.211115i
$666$		0			0
$667$	20.4729	+	35.4600i	0.792712	+	1.37302i
$668$	21.7807	+	20.5367i	0.842721	+	0.794590i
$669$		0			0
$670$	−24.9069	−	31.4902i	−0.962238	−	1.21657i
$671$	4.85945	−	27.5593i	0.187597	−	1.06392i
$672$		0			0
$673$	7.81263	−	6.55558i	0.301155	−	0.252699i	−0.479670	−	0.877449i	$-0.659244\pi$
$673$	7.81263	−	6.55558i	0.301155	−	0.252699i	0.780825	+	0.624750i	$0.214799\pi$
$674$	−3.24795	−	9.79685i	−0.125106	−	0.377361i
$675$		0			0
$676$	0.931383	−	0.693822i	0.0358224	−	0.0266855i
$677$	33.3112	−	27.9514i	1.28025	−	1.07426i	0.287044	−	0.957917i	$-0.407327\pi$
$677$	33.3112	−	27.9514i	1.28025	−	1.07426i	0.993209	−	0.116342i	$-0.0371170\pi$
$678$		0			0
$679$	24.1580	+	4.25972i	0.927101	+	0.163473i
$680$	5.35736	−	20.0299i	0.205445	−	0.768111i
$681$		0			0
$682$	16.8781	−	9.10384i	0.646295	−	0.348604i
$683$	−29.8941	+	17.2593i	−1.14386	+	0.660411i	−0.947385	−	0.320097i	$-0.896284\pi$
$683$	−29.8941	+	17.2593i	−1.14386	+	0.660411i	−0.196480	+	0.980508i	$0.562951\pi$
$684$		0			0
$685$	19.8394	+	11.4543i	0.758024	+	0.437645i
$686$	−23.3462	−	0.675812i	−0.891363	−	0.0258026i
$687$		0			0
$688$	11.5185	−	7.58570i	0.439138	−	0.289202i
$689$	9.81181	−	11.6933i	0.373800	−	0.445478i
$690$		0			0
$691$	−28.1515	−	10.2463i	−1.07093	−	0.389788i	−0.254408	−	0.967097i	$-0.581881\pi$
$691$	−28.1515	−	10.2463i	−1.07093	−	0.389788i	−0.816526	+	0.577309i	$0.804103\pi$
$692$	1.79968	+	15.3574i	0.0684137	+	0.583802i
$693$		0			0
$694$	24.1974	+	21.5273i	0.918519	+	0.817167i
$695$	−7.39827	−	41.9577i	−0.280632	−	1.59154i
$696$		0			0
$697$	23.8510	−	8.68106i	0.903422	−	0.328819i
$698$	3.35406	+	22.8742i	0.126953	+	0.865799i
$699$		0			0
$700$	15.0897	+	3.57156i	0.570338	+	0.134992i
$701$	−44.3573			−1.67535			−0.837677	−	0.546167i	$-0.816087\pi$
$701$	−44.3573			−1.67535			−0.837677	+	0.546167i	$0.816087\pi$
$702$		0			0
$703$		−	10.4823i		−	0.395348i
$704$	−11.4675	+	19.9035i	−0.432198	+	0.750143i
$705$		0			0
$706$	−0.903020	−	6.15844i	−0.0339856	−	0.231776i
$707$	−8.19400	−	22.5128i	−0.308167	−	0.846682i
$708$		0			0
$709$	−19.2193	+	3.38888i	−0.721795	+	0.127272i	−0.522465	−	0.852660i	$-0.674988\pi$
$709$	−19.2193	+	3.38888i	−0.721795	+	0.127272i	−0.199330	+	0.979932i	$0.563877\pi$
$710$	19.6504	−	22.0876i	0.737465	−	0.828932i
$711$		0			0
$712$	−1.46631	−	3.14084i	−0.0549524	−	0.117708i
$713$	10.1266	−	27.8225i	0.379242	−	1.04196i
$714$		0			0
$715$	26.5220	+	22.2546i	0.991865	+	0.832274i
$716$	−0.788948	+	13.6159i	−0.0294844	+	0.508849i
$717$		0			0
$718$	−0.113321	+	3.91471i	−0.00422909	+	0.146096i
$719$	20.6637	−	35.7906i	0.770626	−	1.33476i	−0.166595	−	0.986025i	$-0.553277\pi$
$719$	20.6637	−	35.7906i	0.770626	−	1.33476i	0.937220	−	0.348737i	$-0.113389\pi$
$720$		0			0
$721$	−6.33269	−	10.9685i	−0.235842	−	0.408490i
$722$	16.1847	−	8.72984i	0.602332	−	0.324891i
$723$		0			0
$724$	−10.8199	−	7.11173i	−0.402119	−	0.264305i
$725$	−6.47064	+	36.6968i	−0.240314	+	1.36289i
$726$		0			0
$727$	5.83712	+	6.95641i	0.216487	+	0.257999i	0.863348	−	0.504609i	$-0.168363\pi$
$727$	5.83712	+	6.95641i	0.216487	+	0.257999i	−0.646861	+	0.762608i	$0.723919\pi$
$728$	−11.6063	−	8.11903i	−0.430157	−	0.300911i
$729$		0			0
$730$	−8.36216	−	25.2230i	−0.309498	−	0.933544i
$731$	4.96552	+	5.91768i	0.183657	+	0.218873i
$732$		0			0
$733$	−44.2086	−	7.79517i	−1.63288	−	0.287921i	−0.719337	−	0.694661i	$-0.755554\pi$
$733$	−44.2086	−	7.79517i	−1.63288	−	0.287921i	−0.913544	+	0.406740i	$0.866665\pi$
$734$	12.2740	−	9.70804i	0.453043	−	0.358330i
$735$		0			0
$736$	7.19776	+	34.7276i	0.265313	+	1.28008i
$737$	−21.5762	+	12.4571i	−0.794771	+	0.458861i
$738$		0			0
$739$	24.0347	−	41.6292i	0.884129	−	1.53136i	0.0374202	−	0.999300i	$-0.488086\pi$
$739$	24.0347	−	41.6292i	0.884129	−	1.53136i	0.846709	−	0.532057i	$-0.178581\pi$
$740$	8.04161	+	26.8316i	0.295615	+	0.986350i
$741$		0			0
$742$	−7.39818	−	2.93783i	−0.271596	−	0.107851i
$743$	−32.1593	−	26.9848i	−1.17981	−	0.989977i	−0.999980	−	0.00627899i	$-0.998001\pi$
$743$	−32.1593	−	26.9848i	−1.17981	−	0.989977i	−0.179828	−	0.983698i	$-0.557554\pi$
$744$		0			0
$745$	−21.5043	−	7.82693i	−0.787857	−	0.286756i
$746$	−3.12763	+	15.1586i	−0.114511	+	0.554995i
$747$		0			0
$748$	−11.8154	−	5.09246i	−0.432013	−	0.186199i
$749$	0.763565	+	4.33039i	0.0279000	+	0.158229i
$750$		0			0
$751$	−13.3606	−	36.7079i	−0.487534	−	1.33949i	−0.902906	−	0.429838i	$-0.858571\pi$
$751$	−13.3606	−	36.7079i	−0.487534	−	1.33949i	0.415371	−	0.909652i	$-0.363652\pi$
$752$	−45.6581	−	22.8962i	−1.66498	−	0.834937i
$753$		0			0
$754$	17.8643	−	28.9721i	0.650579	−	1.05510i
$755$			36.5436i			1.32996i
$756$		0			0
$757$			46.6422i			1.69524i	0.530604	+	0.847620i	$0.321965\pi$
$757$			46.6422i			1.69524i	−0.530604	+	0.847620i	$0.678035\pi$
$758$	−11.3468	−	6.99649i	−0.412136	−	0.254124i
$759$		0			0
$760$	16.0180	−	16.0324i	0.581034	−	0.581556i
$761$	−7.07189	−	19.4299i	−0.256356	−	0.704332i	−0.999385	−	0.0350727i	$-0.988834\pi$
$761$	−7.07189	−	19.4299i	−0.256356	−	0.704332i	0.743029	−	0.669259i	$-0.233388\pi$
$762$		0			0
$763$	−1.79987	−	10.2076i	−0.0651598	−	0.369540i
$764$	14.4581	+	6.23148i	0.523075	+	0.225447i
$765$		0			0
$766$	18.6160	+	3.84099i	0.672623	+	0.138781i
$767$	39.7346	+	14.4622i	1.43473	+	0.522200i
$768$		0			0
$769$	−31.2082	−	26.1868i	−1.12540	−	0.944321i	−0.126533	−	0.991962i	$-0.540385\pi$
$769$	−31.2082	−	26.1868i	−1.12540	−	0.944321i	−0.998864	+	0.0476419i	$0.984829\pi$
$770$	6.66341	−	16.7801i	0.240133	−	0.604713i
$771$		0			0
$772$	−43.9655	+	13.1767i	−1.58235	+	0.474241i
$773$	−10.3871	+	17.9910i	−0.373598	+	0.647090i	−0.990116	−	0.140250i	$-0.955209\pi$
$773$	−10.3871	+	17.9910i	−0.373598	+	0.647090i	0.616518	+	0.787341i	$0.288543\pi$
$774$		0			0
$775$	23.3351	−	13.4725i	0.838221	−	0.483947i
$776$	−21.5576	+	46.2846i	−0.773873	+	1.66152i
$777$		0			0
$778$	−7.34307	−	9.28397i	−0.263262	−	0.332847i
$779$	27.3218	+	4.81757i	0.978905	+	0.172607i
$780$		0			0
$781$	−11.7920	−	14.0531i	−0.421950	−	0.502861i
$782$	−18.8554	+	6.25113i	−0.674268	+	0.223540i
$783$		0			0
$784$	5.90025	−	19.7512i	0.210723	−	0.705399i
$785$	−14.6647	−	17.4767i	−0.523405	−	0.623769i
$786$		0			0
$787$	5.43029	−	30.7967i	0.193569	−	1.09778i	−0.720873	−	0.693067i	$-0.756259\pi$
$787$	5.43029	−	30.7967i	0.193569	−	1.09778i	0.914442	−	0.404717i	$-0.132630\pi$
$788$	−20.1535	+	30.6618i	−0.717938	+	1.09228i
$789$		0			0
$790$	18.1799	+	33.7046i	0.646810	+	1.19916i
$791$	−5.28765	−	9.15848i	−0.188007	−	0.325638i
$792$		0			0
$793$	−17.9582	+	31.1045i	−0.637715	+	1.10455i
$794$	30.3508	+	0.878576i	1.07711	+	0.0311795i
$795$		0			0
$796$	0.232433	−	4.01139i	0.00823838	−	0.142180i
$797$	34.7586	+	29.1659i	1.23121	+	1.03311i	0.998159	+	0.0606447i	$0.0193157\pi$
$797$	34.7586	+	29.1659i	1.23121	+	1.03311i	0.233052	+	0.972464i	$0.425129\pi$
$798$		0			0
$799$	9.78479	−	26.8835i	0.346161	−	0.951069i
$800$	−15.2969	+	28.4207i	−0.540826	+	1.00482i
$801$		0			0
$802$	30.7920	+	27.3943i	1.08730	+	0.967327i
$803$	−16.2389	+	2.86335i	−0.573057	+	0.101045i
$804$		0			0
$805$	−9.53403	−	26.1945i	−0.336030	−	0.923236i
$806$	−24.3519	+	3.57075i	−0.857760	+	0.125774i
$807$		0			0
$808$	49.6742	−	4.36838i	1.74753	−	0.153679i
$809$		−	4.07482i		−	0.143263i	−0.997431	−	0.0716315i	$-0.977179\pi$
$809$		−	4.07482i		−	0.143263i	0.997431	−	0.0716315i	$-0.0228206\pi$
$810$		0			0
$811$	−27.7403			−0.974095			−0.487047	−	0.873376i	$-0.661926\pi$
$811$	−27.7403			−0.974095			−0.487047	+	0.873376i	$0.661926\pi$
$812$	−17.2724	−	4.08819i	−0.606144	−	0.143467i
$813$		0			0
$814$	17.1977	−	2.52172i	0.602779	−	0.0883861i
$815$	−8.49962	+	3.09361i	−0.297729	+	0.108364i
$816$		0			0
$817$	1.46624	+	8.31544i	0.0512971	+	0.290921i
$818$	16.6813	−	18.7503i	0.583249	−	0.655589i
$819$		0			0
$820$	−73.6315	+	8.62861i	−2.57132	+	0.301324i
$821$	−20.0519	−	7.29828i	−0.699815	−	0.254712i	−0.0324830	−	0.999472i	$-0.510341\pi$
$821$	−20.0519	−	7.29828i	−0.699815	−	0.254712i	−0.667332	+	0.744761i	$0.732564\pi$
$822$		0			0
$823$	8.84276	−	10.5384i	0.308239	−	0.367345i	−0.589579	−	0.807710i	$-0.700707\pi$
$823$	8.84276	−	10.5384i	0.308239	−	0.367345i	0.897819	+	0.440365i	$0.145151\pi$
$824$	25.4606	−	6.83440i	0.886964	−	0.238088i
$825$		0			0
$826$	0.638042	−	22.0414i	0.0222003	−	0.766920i
$827$	39.9803	+	23.0826i	1.39025	+	0.802662i	0.993343	−	0.115196i	$-0.0367495\pi$
$827$	39.9803	+	23.0826i	1.39025	+	0.802662i	0.396909	+	0.917858i	$0.370083\pi$
$828$		0			0
$829$	48.1207	−	27.7825i	1.67130	−	0.964925i	0.704387	−	0.709816i	$-0.251222\pi$
$829$	48.1207	−	27.7825i	1.67130	−	0.964925i	0.966912	−	0.255110i	$-0.0821116\pi$
$830$	5.33198	+	9.88523i	0.185076	+	0.343121i
$831$		0			0
$832$	22.5672	−	18.9707i	0.782377	−	0.657689i
$833$	11.3704	+	2.00492i	0.393963	+	0.0694663i
$834$		0			0
$835$	37.5165	−	31.4801i	1.29831	−	1.08941i
$836$	−8.40131	−	11.2779i	−0.290565	−	0.390053i
$837$		0			0
$838$	−49.5540	+	16.4286i	−1.71182	+	0.567518i
$839$	−35.4959	+	29.7846i	−1.22546	+	1.02828i	−0.226935	+	0.973910i	$0.572870\pi$
$839$	−35.4959	+	29.7846i	−1.22546	+	1.02828i	−0.998521	+	0.0543696i	$0.982685\pi$
$840$		0			0
$841$	2.37082	−	13.4456i	0.0817525	−	0.463641i
$842$	29.1094	−	23.0238i	1.00317	−	0.793452i
$843$		0			0
$844$	6.22896	+	5.87320i	0.214410	+	0.202164i
$845$	−0.950013	−	1.64547i	−0.0326814	−	0.0566059i
$846$		0			0
$847$	3.24265	+	1.87215i	0.111419	+	0.0643277i
$848$	9.88601	−	13.2958i	0.339487	−	0.456580i
$849$		0			0
$850$	−16.8017	−	6.67197i	−0.576293	−	0.228847i
$851$	17.2501	−	20.5578i	0.591325	−	0.704713i
$852$		0			0
$853$	−7.11678	+	19.5532i	−0.243674	+	0.669489i	0.756211	+	0.654328i	$0.227048\pi$
$853$	−7.11678	+	19.5532i	−0.243674	+	0.669489i	−0.999885	+	0.0151612i	$0.995174\pi$
$854$	18.3434	+	3.78474i	0.627698	+	0.129511i
$855$		0			0
$856$	−9.11794	−	0.793595i	−0.311645	−	0.0271245i
$857$	52.7015	−	9.29269i	1.80025	−	0.317432i	0.829676	−	0.558245i	$-0.188525\pi$
$857$	52.7015	−	9.29269i	1.80025	−	0.317432i	0.970572	+	0.240813i	$0.0774139\pi$
$858$		0			0
$859$	−6.25960	+	2.27831i	−0.213575	+	0.0777349i	−0.446592	−	0.894738i	$-0.647362\pi$
$859$	−6.25960	+	2.27831i	−0.213575	+	0.0777349i	0.233017	+	0.972473i	$0.425140\pi$
$860$	−10.1324	−	20.1602i	−0.345512	−	0.687458i
$861$		0			0
$862$	14.5815	+	8.99102i	0.496649	+	0.306235i
$863$	−26.7202			−0.909566			−0.454783	−	0.890602i	$-0.650283\pi$
$863$	−26.7202			−0.909566			−0.454783	+	0.890602i	$0.650283\pi$
$864$		0			0
$865$	25.2963			0.860099
$866$	26.4117	+	16.2855i	0.897505	+	0.553404i
$867$		0			0
$868$	5.76371	+	11.4679i	0.195633	+	0.389247i
$869$	22.3302	−	8.12751i	0.757499	−	0.275707i
$870$		0			0
$871$	31.4900	−	5.55254i	1.06700	−	0.188141i
$872$	21.4928	+	1.87066i	0.727837	+	0.0633485i
$873$		0			0
$874$	−21.2649	−	4.38754i	−0.719297	−	0.148411i
$875$	1.07302	−	2.94811i	0.0362748	−	0.0996643i
$876$		0			0
$877$	−19.4723	+	23.2062i	−0.657534	+	0.783618i	−0.987030	−	0.160539i	$-0.948677\pi$
$877$	−19.4723	+	23.2062i	−0.657534	+	0.783618i	0.329496	+	0.944157i	$0.393121\pi$
$878$	24.4572	+	9.71200i	0.825391	+	0.327764i
$879$		0			0
$880$	30.1568	+	22.4229i	1.01658	+	0.755875i
$881$	26.4220	+	15.2548i	0.890181	+	0.513946i	0.874002	−	0.485923i	$-0.161516\pi$
$881$	26.4220	+	15.2548i	0.890181	+	0.513946i	0.0161793	+	0.999869i	$0.494850\pi$
$882$		0			0
$883$	−21.5979	−	37.4087i	−0.726827	−	1.25890i	−0.958218	−	0.286040i	$-0.907661\pi$
$883$	−21.5979	−	37.4087i	−0.726827	−	1.25890i	0.231391	−	0.972861i	$-0.425672\pi$
$884$	12.0144	+	11.3282i	0.404089	+	0.381010i
$885$		0			0
$886$	−0.579759	+	0.458555i	−0.0194774	+	0.0154055i
$887$	−7.61863	+	43.2074i	−0.255809	+	1.45076i	0.538180	+	0.842830i	$0.319112\pi$
$887$	−7.61863	+	43.2074i	−0.255809	+	1.45076i	−0.793989	+	0.607933i	$0.791999\pi$
$888$		0			0
$889$	−11.0705	+	9.28928i	−0.371294	+	0.311553i
$890$	−5.38260	+	1.78449i	−0.180425	+	0.0598164i
$891$		0			0
$892$	18.1491	+	24.3633i	0.607678	+	0.815744i
$893$	23.9547	−	20.1004i	0.801612	−	0.672633i
$894$		0			0
$895$	21.9736	+	3.87453i	0.734495	+	0.129511i
$896$	−13.0936	−	8.05735i	−0.437427	−	0.269177i
$897$		0			0
$898$	−6.96166	−	12.9066i	−0.232314	−	0.430698i
$899$	−26.7105	+	15.4213i	−0.890845	+	0.514329i
$900$		0			0
$901$	8.03679	+	4.64005i	0.267744	+	0.154582i
$902$	−1.33112	+	45.9841i	−0.0443214	+	1.53110i
$903$		0			0
$904$	21.2591	−	5.70657i	0.707066	−	0.189798i
$905$	−13.6157	+	16.2266i	−0.452603	+	0.539391i
$906$		0			0
$907$	35.4010	+	12.8849i	1.17547	+	0.427836i	0.854600	−	0.519287i	$-0.173802\pi$
$907$	35.4010	+	12.8849i	1.17547	+	0.427836i	0.320870	+	0.947123i	$0.396025\pi$
$908$	36.4722	−	4.27405i	1.21037	−	0.141839i
$909$		0			0
$910$	−15.4022	+	17.3125i	−0.510578	+	0.573904i
$911$	−4.75504	−	26.9672i	−0.157541	−	0.893462i	−0.956425	−	0.291977i	$-0.905687\pi$
$911$	−4.75504	−	26.9672i	−0.157541	−	0.893462i	0.798884	−	0.601485i	$-0.205424\pi$
$912$		0			0
$913$	6.54922	−	2.38372i	0.216748	−	0.0788897i
$914$	−10.7031	+	1.56940i	−0.354026	+	0.0519112i
$915$		0			0
$916$	41.7428	+	9.88004i	1.37922	+	0.326446i
$917$	−25.4223			−0.839518
$918$		0			0
$919$		−	40.1046i		−	1.32293i	−0.749976	−	0.661465i	$-0.769935\pi$
$919$		−	40.1046i		−	1.32293i	0.749976	−	0.661465i	$-0.230065\pi$
$920$	57.7978	−	5.08278i	1.90554	−	0.167574i
$921$		0			0
$922$	−7.27441	+	1.06666i	−0.239570	+	0.0351284i
$923$	8.05281	+	22.1249i	0.265061	+	0.728250i
$924$		0			0
$925$	24.0516	−	4.24094i	0.790810	−	0.139441i
$926$	−26.4546	−	23.5355i	−0.869353	−	0.773425i
$927$		0			0
$928$	17.5096	−	32.5317i	0.574779	−	1.06791i
$929$	−1.55733	+	4.27874i	−0.0510945	+	0.140381i	−0.962615	−	0.270874i	$-0.912687\pi$
$929$	−1.55733	+	4.27874i	−0.0510945	+	0.140381i	0.911520	+	0.411255i	$0.134909\pi$
$930$		0			0
$931$	9.66755	+	8.11204i	0.316841	+	0.265861i
$932$	0.657256	−	11.3431i	0.0215291	−	0.371555i
$933$		0			0
$934$	−9.00384	−	0.260638i	−0.294615	−	0.00852832i
$935$	−10.5243	+	18.2286i	−0.344181	+	0.596138i
$936$		0			0
$937$	−20.7897	−	36.0087i	−0.679168	−	1.17635i	−0.975232	−	0.221186i	$-0.929007\pi$
$937$	−20.7897	−	36.0087i	−0.679168	−	1.17635i	0.296063	−	0.955168i	$-0.404326\pi$
$938$	−7.91606	−	14.6760i	−0.258469	−	0.479188i
$939$		0			0
$940$	−45.8967	+	69.8280i	−1.49698	+	2.27754i
$941$	0.174402	−	0.989083i	0.00568534	−	0.0322432i	−0.981833	−	0.189747i	$-0.939233\pi$
$941$	0.174402	−	0.989083i	0.00568534	−	0.0322432i	0.987518	+	0.157503i	$0.0503445\pi$
$942$		0			0
$943$	45.6553	+	54.4098i	1.48674	+	1.77183i
$944$	43.9764	+	13.1370i	1.43131	+	0.427574i
$945$		0			0
$946$	−13.2899	+	4.40600i	−0.432092	+	0.143251i
$947$	−17.8652	−	21.2910i	−0.580543	−	0.691864i	0.393216	−	0.919446i	$-0.371362\pi$
$947$	−17.8652	−	21.2910i	−0.580543	−	0.691864i	−0.973759	+	0.227582i	$0.926918\pi$
$948$		0			0
$949$	20.8417	+	3.67495i	0.676549	+	0.119294i
$950$	−12.2581	−	15.4982i	−0.397706	−	0.502827i
$951$		0			0
$952$	3.63573	−	7.80600i	0.117835	−	0.252994i
$953$	−13.5698	+	7.83453i	−0.439569	+	0.253785i	−0.703415	−	0.710780i	$-0.748342\pi$
$953$	−13.5698	+	7.83453i	−0.439569	+	0.253785i	0.263846	+	0.964565i	$0.415009\pi$
$954$		0			0
$955$	12.8782	−	22.3057i	0.416729	−	0.721796i
$956$	−20.2515	+	6.06951i	−0.654981	+	0.196302i
$957$		0			0
$958$	−11.9929	+	30.2012i	−0.387475	+	0.975757i
$959$	7.28838	+	6.11568i	0.235354	+	0.197486i
$960$		0			0
$961$	−8.17302	−	2.97474i	−0.263646	−	0.0959592i
$962$	−21.8481	−	4.50785i	−0.704410	−	0.145339i
$963$		0			0
$964$	13.0097	+	5.60723i	0.419015	+	0.180597i
$965$	13.0388	+	73.9465i	0.419733	+	2.38042i
$966$		0			0
$967$	20.0933	+	55.2059i	0.646157	+	1.77530i	0.631457	+	0.775411i	$0.282457\pi$
$967$	20.0933	+	55.2059i	0.646157	+	1.77530i	0.0147000	+	0.999892i	$0.495321\pi$
$968$	−5.50832	+	5.51327i	−0.177044	+	0.177203i
$969$		0			0
$970$	71.1009	+	43.8410i	2.28291	+	1.40765i
$971$		−	3.85494i		−	0.123711i	−0.998085	−	0.0618554i	$-0.980298\pi$
$971$		−	3.85494i		−	0.123711i	0.998085	−	0.0618554i	$-0.0197018\pi$
$972$		0			0
$973$		−	17.6945i		−	0.567261i
$974$	−12.7525	+	20.6819i	−0.408617	+	0.662690i
$975$		0			0
$976$	−17.4754	+	34.8483i	−0.559373	+	1.11547i
$977$	−1.13249	−	3.11148i	−0.0362314	−	0.0995450i	0.920258	−	0.391313i	$-0.127979\pi$
$977$	−1.13249	−	3.11148i	−0.0362314	−	0.0995450i	−0.956489	+	0.291768i	$0.905757\pi$
$978$		0			0
$979$	0.611042	+	3.46539i	0.0195290	+	0.110754i
$980$	−30.9693	−	13.3479i	−0.989278	−	0.426382i
$981$		0			0
$982$	3.61055	−	17.4991i	0.115217	−	0.558420i
$983$	52.1125	+	18.9674i	1.66213	+	0.604966i	0.990695	−	0.136097i	$-0.0434560\pi$
$983$	52.1125	+	18.9674i	1.66213	+	0.604966i	0.671435	+	0.741063i	$0.265678\pi$
$984$		0			0
$985$	45.9836	+	38.5848i	1.46516	+	1.22941i
$986$	19.2320	+	7.63707i	0.612473	+	0.243214i
$987$		0			0
$988$	5.18175	+	17.2894i	0.164853	+	0.550050i
$989$	−10.8086	+	18.7211i	−0.343694	+	0.595295i
$990$		0			0
$991$	−52.1447	+	30.1057i	−1.65643	+	0.956341i	−0.682088	+	0.731270i	$0.738928\pi$
$991$	−52.1447	+	30.1057i	−1.65643	+	0.956341i	−0.974343	+	0.225070i	$0.927739\pi$
$992$	−26.1588	+	5.42175i	−0.830543	+	0.172141i
$993$		0			0
$994$	9.63007	−	7.61682i	0.305447	−	0.241591i
$995$	−6.47366	−	1.14148i	−0.205229	−	0.0361874i
$996$		0			0
$997$	20.0612	+	23.9080i	0.635343	+	0.757172i	0.983627	−	0.180217i	$-0.0576799\pi$
$997$	20.0612	+	23.9080i	0.635343	+	0.757172i	−0.348284	+	0.937389i	$0.613235\pi$
$998$	1.04939	+	3.16531i	0.0332180	+	0.100196i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.2.v.b.611.25		192
3.2	odd	2		216.2.v.b.59.8	yes	192
8.3	odd	2	inner	648.2.v.b.611.22		192
12.11	even	2		864.2.bh.b.815.7		192
24.5	odd	2		864.2.bh.b.815.8		192
24.11	even	2		216.2.v.b.59.11	yes	192
27.11	odd	18	inner	648.2.v.b.35.22		192
27.16	even	9		216.2.v.b.11.11	yes	192
108.43	odd	18		864.2.bh.b.335.8		192
216.11	even	18	inner	648.2.v.b.35.25		192
216.43	odd	18		216.2.v.b.11.8	✓	192
216.205	even	18		864.2.bh.b.335.7		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.11.8	✓	192	216.43	odd	18
216.2.v.b.11.11	yes	192	27.16	even	9
216.2.v.b.59.8	yes	192	3.2	odd	2
216.2.v.b.59.11	yes	192	24.11	even	2
648.2.v.b.35.22		192	27.11	odd	18	inner
648.2.v.b.35.25		192	216.11	even	18	inner
648.2.v.b.611.22		192	8.3	odd	2	inner
648.2.v.b.611.25		192	1.1	even	1	trivial
864.2.bh.b.335.7		192	216.205	even	18
864.2.bh.b.335.8		192	108.43	odd	18
864.2.bh.b.815.7		192	12.11	even	2
864.2.bh.b.815.8		192	24.5	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	648.v (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.20377 + 0.742249i) q^{2} +(0.898133 + 1.78700i) q^{4} +(3.07462 - 1.11907i) q^{5} +(1.33825 - 0.235969i) q^{7} +(-0.245250 + 2.81777i) q^{8} +(4.53177 + 0.935029i) q^{10} +(0.982057 - 2.69818i) q^{11} +(-2.36880 + 2.82303i) q^{13} +(1.78609 + 0.709260i) q^{14} +(-2.38671 + 3.20992i) q^{16} +(-1.94027 - 1.12022i) q^{17} +(-1.22444 - 2.12079i) q^{19} +(4.76119 + 4.48926i) q^{20} +(3.18489 - 2.51906i) q^{22} +(1.08869 - 6.17426i) q^{23} +(4.37075 - 3.66750i) q^{25} +(-4.94689 + 1.64004i) q^{26} +(1.62360 + 2.17951i) q^{28} +(-5.00298 + 4.19800i) q^{29} +(4.65080 + 0.820062i) q^{31} +(-5.25562 + 2.09248i) q^{32} +(-1.50416 - 2.78865i) q^{34} +(3.85054 - 2.22311i) q^{35} +(3.70698 + 2.14023i) q^{37} +(0.100210 - 3.46179i) q^{38} +(2.39924 + 8.93804i) q^{40} +(-7.28211 + 8.67848i) q^{41} +(-3.24005 - 1.17928i) q^{43} +(5.70365 - 0.668391i) q^{44} +(5.89337 - 6.62433i) q^{46} +(2.21737 + 12.5753i) q^{47} +(-4.84262 + 1.76257i) q^{49} +(7.98359 - 1.17064i) q^{50} +(-7.17224 - 1.69759i) q^{52} -4.14210 q^{53} -9.39487i q^{55} +(0.336703 + 3.82875i) q^{56} +(-9.13841 + 1.33998i) q^{58} +(-3.92440 - 10.7822i) q^{59} +(9.59806 - 1.69240i) q^{61} +(4.98981 + 4.43922i) q^{62} +(-7.87971 - 1.38212i) q^{64} +(-4.12400 + 11.3306i) q^{65} +(-6.64683 - 5.57735i) q^{67} +(0.259201 - 4.47336i) q^{68} +(6.28527 + 0.181942i) q^{70} +(3.19451 - 5.53306i) q^{71} +(-2.87137 - 4.97336i) q^{73} +(2.87378 + 5.32784i) q^{74} +(2.69014 - 4.09283i) q^{76} +(0.677549 - 3.84257i) q^{77} +(5.31972 + 6.33979i) q^{79} +(-3.74612 + 12.5402i) q^{80} +(-15.2076 + 5.04177i) q^{82} +(1.56022 + 1.85940i) q^{83} +(-7.21919 - 1.27294i) q^{85} +(-3.02496 - 3.82451i) q^{86} +(7.36201 + 3.42894i) q^{88} +(-1.06132 + 0.612754i) q^{89} +(-2.50390 + 4.33688i) q^{91} +(12.0112 - 3.59982i) q^{92} +(-6.66482 + 16.7837i) q^{94} +(-6.13801 - 5.15040i) q^{95} +(16.9633 + 6.17414i) q^{97} +(-7.13768 - 1.47270i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 6 q^{2} - 6 q^{4} + 9 q^{8} - 3 q^{10} + 30 q^{11} - 9 q^{14} - 6 q^{16} + 18 q^{17} - 6 q^{19} + 27 q^{20} - 18 q^{22} - 12 q^{25} - 12 q^{28} + 36 q^{32} + 12 q^{34} + 18 q^{35} + 102 q^{38} + 9 q^{40}+ \cdots - 162 q^{98}+O(q^{100}) \) 192 * q + 6 * q^2 - 6 * q^4 + 9 * q^8 - 3 * q^10 + 30 * q^11 - 9 * q^14 - 6 * q^16 + 18 * q^17 - 6 * q^19 + 27 * q^20 - 18 * q^22 - 12 * q^25 - 12 * q^28 + 36 * q^32 + 12 * q^34 + 18 * q^35 + 102 * q^38 + 9 * q^40 - 18 * q^41 - 42 * q^43 + 81 * q^44 - 3 * q^46 - 12 * q^49 - 57 * q^50 + 21 * q^52 + 69 * q^56 - 33 * q^58 + 84 * q^59 - 90 * q^62 - 51 * q^64 + 12 * q^65 + 30 * q^67 - 63 * q^68 - 33 * q^70 - 6 * q^73 - 51 * q^74 + 30 * q^76 - 12 * q^82 + 72 * q^83 - 42 * q^86 - 78 * q^88 - 144 * q^89 - 6 * q^91 + 3 * q^92 - 33 * q^94 - 42 * q^97 - 162 * q^98

Introduction

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