LMFDB - Embedded newform 864.2.bk.a.613.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(37,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("864.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bk (of order $24$, degree $8$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	no (minimal twist has level 288)
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			613.17
Character	$\chi$	$=$	864.613
Dual form			864.2.bk.a.685.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.575751 + 1.29171i) q^{2} +(-1.33702 - 1.48741i) q^{4} +(0.302346 + 2.29654i) q^{5} +(-1.69771 + 0.454899i) q^{7} +(2.69109 - 0.870667i) q^{8} +O(q^{10})$	\(q+(-0.575751 + 1.29171i) q^{2} +(-1.33702 - 1.48741i) q^{4} +(0.302346 + 2.29654i) q^{5} +(-1.69771 + 0.454899i) q^{7} +(2.69109 - 0.870667i) q^{8} +(-3.14054 - 0.931695i) q^{10} +(-2.61252 - 3.40470i) q^{11} +(-1.84196 - 1.41338i) q^{13} +(0.389859 - 2.45485i) q^{14} +(-0.424748 + 3.97738i) q^{16} -1.85832i q^{17} +(2.22188 - 0.920333i) q^{19} +(3.01165 - 3.52024i) q^{20} +(5.90204 - 1.41435i) q^{22} +(-3.80389 - 1.01925i) q^{23} +(-0.353072 + 0.0946054i) q^{25} +(2.88619 - 1.56552i) q^{26} +(2.94649 + 1.91697i) q^{28} +(-4.98542 - 0.656343i) q^{29} +(-3.53119 - 6.11620i) q^{31} +(-4.89307 - 2.83863i) q^{32} +(2.40040 + 1.06993i) q^{34} +(-1.55799 - 3.76132i) q^{35} +(3.25157 + 1.34684i) q^{37} +(-0.0904482 + 3.39990i) q^{38} +(2.81316 + 5.91695i) q^{40} +(11.9515 + 3.20240i) q^{41} +(1.47137 + 1.91753i) q^{43} +(-1.57118 + 8.43803i) q^{44} +(3.50667 - 4.32669i) q^{46} +(-5.58096 - 3.22217i) q^{47} +(-3.38691 + 1.95543i) q^{49} +(0.0810791 - 0.510536i) q^{50} +(0.360463 + 4.62946i) q^{52} +(3.40394 - 8.21784i) q^{53} +(7.02916 - 7.02916i) q^{55} +(-4.17260 + 2.70231i) q^{56} +(3.71817 - 6.06182i) q^{58} +(-1.94627 - 14.7834i) q^{59} +(-13.0401 - 1.71676i) q^{61} +(9.93343 - 1.03986i) q^{62} +(6.48388 - 4.68608i) q^{64} +(2.68899 - 4.65747i) q^{65} +(3.15146 - 4.10706i) q^{67} +(-2.76407 + 2.48461i) q^{68} +(5.75554 + 0.153115i) q^{70} +(-0.786895 - 0.786895i) q^{71} +(6.89191 - 6.89191i) q^{73} +(-3.61182 + 3.42463i) q^{74} +(-4.33961 - 2.07433i) q^{76} +(5.98408 + 4.59174i) q^{77} +(7.90822 + 4.56581i) q^{79} +(-9.26266 + 0.227094i) q^{80} +(-11.0177 + 13.5941i) q^{82} +(-0.457417 + 3.47443i) q^{83} +(4.26771 - 0.561854i) q^{85} +(-3.32404 + 0.796566i) q^{86} +(-9.99487 - 6.88770i) q^{88} +(-3.68687 - 3.68687i) q^{89} +(3.77005 + 1.56161i) q^{91} +(3.56985 + 7.02069i) q^{92} +(7.37534 - 5.35380i) q^{94} +(2.78536 + 4.82439i) q^{95} +(-4.33284 + 7.50470i) q^{97} +(-0.575832 - 5.50074i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 16 q^{8}+O(q^{10}) $ 368 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 16 * q^8	$ 368 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 16 q^{8} - 16 q^{10} + 4 q^{11} - 4 q^{13} + 4 q^{14} - 4 q^{16} - 16 q^{19} + 4 q^{20} - 4 q^{22} + 4 q^{23} - 4 q^{25} + 16 q^{26} - 16 q^{28} + 4 q^{29} - 8 q^{31} + 4 q^{32} + 4 q^{34} + 16 q^{35} - 16 q^{37} + 60 q^{38} - 4 q^{40} + 4 q^{41} - 4 q^{43} + 104 q^{44} - 16 q^{46} - 48 q^{50} - 4 q^{52} + 16 q^{53} - 16 q^{55} + 84 q^{56} - 40 q^{58} + 4 q^{59} - 4 q^{61} + 24 q^{62} - 16 q^{64} + 8 q^{65} - 4 q^{67} - 12 q^{68} - 4 q^{70} + 16 q^{71} - 16 q^{73} + 4 q^{74} + 20 q^{76} + 4 q^{77} - 48 q^{80} - 16 q^{82} - 36 q^{83} + 16 q^{85} - 100 q^{86} - 4 q^{88} + 16 q^{89} - 16 q^{91} + 80 q^{92} - 20 q^{94} + 136 q^{95} - 8 q^{97} - 104 q^{98}+O(q^{100}) $ 368 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 16 * q^8 - 16 * q^10 + 4 * q^11 - 4 * q^13 + 4 * q^14 - 4 * q^16 - 16 * q^19 + 4 * q^20 - 4 * q^22 + 4 * q^23 - 4 * q^25 + 16 * q^26 - 16 * q^28 + 4 * q^29 - 8 * q^31 + 4 * q^32 + 4 * q^34 + 16 * q^35 - 16 * q^37 + 60 * q^38 - 4 * q^40 + 4 * q^41 - 4 * q^43 + 104 * q^44 - 16 * q^46 - 48 * q^50 - 4 * q^52 + 16 * q^53 - 16 * q^55 + 84 * q^56 - 40 * q^58 + 4 * q^59 - 4 * q^61 + 24 * q^62 - 16 * q^64 + 8 * q^65 - 4 * q^67 - 12 * q^68 - 4 * q^70 + 16 * q^71 - 16 * q^73 + 4 * q^74 + 20 * q^76 + 4 * q^77 - 48 * q^80 - 16 * q^82 - 36 * q^83 + 16 * q^85 - 100 * q^86 - 4 * q^88 + 16 * q^89 - 16 * q^91 + 80 * q^92 - 20 * q^94 + 136 * q^95 - 8 * q^97 - 104 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.575751	+	1.29171i	−0.407117	+	0.913376i
$2$	−0.575751	+	1.29171i	−0.407117	+	0.913376i
$3$		0			0
$3$		0			0
$4$	−1.33702	−	1.48741i	−0.668511	−	0.743703i
$5$	0.302346	+	2.29654i	0.135213	+	1.02705i	0.915697	+	0.401870i	$0.131640\pi$
$5$	0.302346	+	2.29654i	0.135213	+	1.02705i	−0.780484	+	0.625176i	$0.785027\pi$
$6$		0			0
$7$	−1.69771	+	0.454899i	−0.641672	+	0.171936i	−0.564961	−	0.825118i	$-0.691109\pi$
$7$	−1.69771	+	0.454899i	−0.641672	+	0.171936i	−0.0767115	+	0.997053i	$0.524442\pi$
$8$	2.69109	−	0.870667i	0.951442	−	0.307827i
$9$		0			0
$10$	−3.14054	−	0.931695i	−0.993126	−	0.294628i
$11$	−2.61252	−	3.40470i	−0.787704	−	1.02656i	−0.998794	−	0.0490891i	$-0.984368\pi$
$11$	−2.61252	−	3.40470i	−0.787704	−	1.02656i	0.211091	−	0.977466i	$-0.432298\pi$
$12$		0			0
$13$	−1.84196	−	1.41338i	−0.510867	−	0.392002i	0.320912	−	0.947109i	$-0.396011\pi$
$13$	−1.84196	−	1.41338i	−0.510867	−	0.392002i	−0.831779	+	0.555107i	$0.812677\pi$
$14$	0.389859	−	2.45485i	0.104194	−	0.656086i
$15$		0			0
$16$	−0.424748	+	3.97738i	−0.106187	+	0.994346i
$17$		−	1.85832i		−	0.450708i	−0.974277	−	0.225354i	$-0.927646\pi$
$17$		−	1.85832i		−	0.450708i	0.974277	−	0.225354i	$-0.0723539\pi$
$18$		0			0
$19$	2.22188	−	0.920333i	0.509734	−	0.211139i	−0.112967	−	0.993599i	$-0.536035\pi$
$19$	2.22188	−	0.920333i	0.509734	−	0.211139i	0.622701	+	0.782460i	$0.286035\pi$
$20$	3.01165	−	3.52024i	0.673425	−	0.787149i
$21$		0			0
$22$	5.90204	−	1.41435i	1.25832	−	0.301541i
$23$	−3.80389	−	1.01925i	−0.793167	−	0.212528i	−0.160585	−	0.987022i	$-0.551338\pi$
$23$	−3.80389	−	1.01925i	−0.793167	−	0.212528i	−0.632582	+	0.774494i	$0.718005\pi$
$24$		0			0
$25$	−0.353072	+	0.0946054i	−0.0706145	+	0.0189211i
$26$	2.88619	−	1.56552i	0.566029	−	0.307023i
$27$		0			0
$28$	2.94649	+	1.91697i	0.556834	+	0.362272i
$29$	−4.98542	−	0.656343i	−0.925770	−	0.121880i	−0.347458	−	0.937696i	$-0.612955\pi$
$29$	−4.98542	−	0.656343i	−0.925770	−	0.121880i	−0.578312	+	0.815816i	$0.696288\pi$
$30$		0			0
$31$	−3.53119	−	6.11620i	−0.634220	−	1.09850i	−0.986680	−	0.162674i	$-0.947988\pi$
$31$	−3.53119	−	6.11620i	−0.634220	−	1.09850i	0.352460	−	0.935827i	$-0.385345\pi$
$32$	−4.89307	−	2.83863i	−0.864981	−	0.501804i
$33$		0			0
$34$	2.40040	+	1.06993i	0.411666	+	0.183491i
$35$	−1.55799	−	3.76132i	−0.263348	−	0.635779i
$36$		0			0
$37$	3.25157	+	1.34684i	0.534554	+	0.221420i	0.633597	−	0.773664i	$-0.281578\pi$
$37$	3.25157	+	1.34684i	0.534554	+	0.221420i	−0.0990423	+	0.995083i	$0.531578\pi$
$38$	−0.0904482	+	3.39990i	−0.0146726	+	0.551537i
$39$		0			0
$40$	2.81316	+	5.91695i	0.444800	+	0.935552i
$41$	11.9515	+	3.20240i	1.86651	+	0.500131i	1.00000		0.000976646i	$0.000310876\pi$
$41$	11.9515	+	3.20240i	1.86651	+	0.500131i	0.866513	+	0.499154i	$0.166356\pi$
$42$		0			0
$43$	1.47137	+	1.91753i	0.224383	+	0.292421i	0.891955	−	0.452123i	$-0.149333\pi$
$43$	1.47137	+	1.91753i	0.224383	+	0.292421i	−0.667573	+	0.744545i	$0.732667\pi$
$44$	−1.57118	+	8.43803i	−0.236864	+	1.27208i
$45$		0			0
$46$	3.50667	−	4.32669i	0.517030	−	0.637935i
$47$	−5.58096	−	3.22217i	−0.814066	−	0.470001i	0.0342998	−	0.999412i	$-0.489080\pi$
$47$	−5.58096	−	3.22217i	−0.814066	−	0.470001i	−0.848366	+	0.529410i	$0.822413\pi$
$48$		0			0
$49$	−3.38691	+	1.95543i	−0.483844	+	0.279347i
$50$	0.0810791	−	0.510536i	0.0114663	−	0.0722006i
$51$		0			0
$52$	0.360463	+	4.62946i	0.0499872	+	0.641991i
$53$	3.40394	−	8.21784i	0.467567	−	1.12881i	−0.497655	−	0.867375i	$-0.665805\pi$
$53$	3.40394	−	8.21784i	0.467567	−	1.12881i	0.965222	−	0.261432i	$-0.0841948\pi$
$54$		0			0
$55$	7.02916	−	7.02916i	0.947812	−	0.947812i
$56$	−4.17260	+	2.70231i	−0.557588	+	0.361111i
$57$		0			0
$58$	3.71817	−	6.06182i	0.488219	−	0.795956i
$59$	−1.94627	−	14.7834i	−0.253383	−	1.92463i	−0.365246	−	0.930911i	$-0.619015\pi$
$59$	−1.94627	−	14.7834i	−0.253383	−	1.92463i	0.111863	−	0.993724i	$-0.464318\pi$
$60$		0			0
$61$	−13.0401	−	1.71676i	−1.66961	−	0.219809i	−0.764392	−	0.644751i	$-0.776961\pi$
$61$	−13.0401	−	1.71676i	−1.66961	−	0.219809i	−0.905220	+	0.424943i	$0.860294\pi$
$62$	9.93343	−	1.03986i	1.26155	−	0.132062i
$63$		0			0
$64$	6.48388	−	4.68608i	0.810485	−	0.585760i
$65$	2.68899	−	4.65747i	0.333528	−	0.577688i
$66$		0			0
$67$	3.15146	−	4.10706i	0.385012	−	0.501757i	−0.560136	−	0.828401i	$-0.689251\pi$
$67$	3.15146	−	4.10706i	0.385012	−	0.501757i	0.945148	+	0.326644i	$0.105918\pi$
$68$	−2.76407	+	2.48461i	−0.335193	+	0.301303i
$69$		0			0
$70$	5.75554	+	0.153115i	0.687919	+	0.0183008i
$71$	−0.786895	−	0.786895i	−0.0933873	−	0.0933873i	0.658870	−	0.752257i	$-0.271035\pi$
$71$	−0.786895	−	0.786895i	−0.0933873	−	0.0933873i	−0.752257	+	0.658870i	$0.771035\pi$
$72$		0			0
$73$	6.89191	−	6.89191i	0.806637	−	0.806637i	−0.177486	−	0.984123i	$-0.556797\pi$
$73$	6.89191	−	6.89191i	0.806637	−	0.806637i	0.984123	+	0.177486i	$0.0567966\pi$
$74$	−3.61182	+	3.42463i	−0.419866	+	0.398105i
$75$		0			0
$76$	−4.33961	−	2.07433i	−0.497787	−	0.237942i
$77$	5.98408	+	4.59174i	0.681949	+	0.523278i
$78$		0			0
$79$	7.90822	+	4.56581i	0.889745	+	0.513694i	0.873859	−	0.486180i	$-0.161610\pi$
$79$	7.90822	+	4.56581i	0.889745	+	0.513694i	0.0158857	+	0.999874i	$0.494943\pi$
$80$	−9.26266	+	0.227094i	−1.03560	+	0.0253898i
$81$		0			0
$82$	−11.0177	+	13.5941i	−1.21670	+	1.50122i
$83$	−0.457417	+	3.47443i	−0.0502080	+	0.381368i	0.947831	+	0.318773i	$0.103271\pi$
$83$	−0.457417	+	3.47443i	−0.0502080	+	0.381368i	−0.998039	+	0.0625947i	$0.980062\pi$
$84$		0			0
$85$	4.26771	−	0.561854i	0.462898	−	0.0609416i
$86$	−3.32404	+	0.796566i	−0.358440	+	0.0858959i
$87$		0			0
$88$	−9.99487	−	6.88770i	−1.06546	−	0.734232i
$89$	−3.68687	−	3.68687i	−0.390808	−	0.390808i	0.484168	−	0.874975i	$-0.339123\pi$
$89$	−3.68687	−	3.68687i	−0.390808	−	0.390808i	−0.874975	+	0.484168i	$0.839123\pi$
$90$		0			0
$91$	3.77005	+	1.56161i	0.395209	+	0.163701i
$92$	3.56985	+	7.02069i	0.372183	+	0.731958i
$93$		0			0
$94$	7.37534	−	5.35380i	0.760708	−	0.552203i
$95$	2.78536	+	4.82439i	0.285772	+	0.494972i
$96$		0			0
$97$	−4.33284	+	7.50470i	−0.439933	+	0.761987i	−0.997684	−	0.0680218i	$-0.978331\pi$
$97$	−4.33284	+	7.50470i	−0.439933	+	0.761987i	0.557750	+	0.830009i	$0.311665\pi$
$98$	−0.575832	−	5.50074i	−0.0581679	−	0.555659i
$99$		0			0
$100$	0.612782	+	0.398672i	0.0612782	+	0.0398672i
$101$	6.79246	−	5.21204i	0.675875	−	0.518617i	−0.212834	−	0.977088i	$-0.568269\pi$
$101$	6.79246	−	5.21204i	0.675875	−	0.518617i	0.888709	+	0.458471i	$0.151603\pi$
$102$		0			0
$103$	−1.37995	+	5.15005i	−0.135971	+	0.507449i	0.864021	+	0.503455i	$0.167938\pi$
$103$	−1.37995	+	5.15005i	−0.135971	+	0.507449i	−0.999992	+	0.00399421i	$0.998729\pi$
$104$	−6.18746	−	2.19981i	−0.606730	−	0.215709i
$105$		0			0
$106$	8.65523	+	9.12833i	0.840671	+	0.886622i
$107$	2.80668	−	6.77594i	0.271332	−	0.655055i	−0.728208	−	0.685356i	$-0.759647\pi$
$107$	2.80668	−	6.77594i	0.271332	−	0.655055i	0.999541	+	0.0303013i	$0.00964668\pi$
$108$		0			0
$109$	−16.4296	+	6.80536i	−1.57367	+	0.651835i	−0.987395	−	0.158277i	$-0.949406\pi$
$109$	−16.4296	+	6.80536i	−1.57367	+	0.651835i	−0.586275	+	0.810112i	$0.699406\pi$
$110$	5.03258	+	13.1267i	0.479837	+	1.25158i
$111$		0			0
$112$	−1.08821	−	6.94564i	−0.102826	−	0.656302i
$113$	−7.30520	+	4.21766i	−0.687216	+	0.396764i	−0.802568	−	0.596561i	$-0.796534\pi$
$113$	−7.30520	+	4.21766i	−0.687216	+	0.396764i	0.115353	+	0.993325i	$0.463200\pi$
$114$		0			0
$115$	1.19066	−	9.04398i	0.111030	−	0.843355i
$116$	5.68937	+	8.29289i	0.528245	+	0.769975i
$117$		0			0
$118$	20.2164	+	5.99754i	1.86107	+	0.552119i
$119$	0.845346	+	3.15487i	0.0774927	+	0.289207i
$120$		0			0
$121$	−1.91972	+	7.16449i	−0.174520	+	0.651318i
$122$	9.72540	−	15.8556i	0.880496	−	1.43550i
$123$		0			0
$124$	−4.37599	+	13.4298i	−0.392975	+	1.20603i
$125$	4.10815	+	9.91795i	0.367444	+	0.887088i
$126$		0			0
$127$	−6.45329			−0.572637			−0.286318	−	0.958135i	$-0.592431\pi$
$127$	−6.45329			−0.572637			−0.286318	+	0.958135i	$0.592431\pi$
$128$	2.31994	+	11.0733i	0.205056	+	0.978750i
$129$		0			0
$130$	4.46790	+	6.15494i	0.391861	+	0.539824i
$131$	8.57663	−	11.1773i	0.749343	−	0.976563i	−0.250621	−	0.968085i	$-0.580635\pi$
$131$	8.57663	−	11.1773i	0.749343	−	0.976563i	0.999964	−	0.00847780i	$-0.00269860\pi$
$132$		0			0
$133$	−3.35344	+	2.57318i	−0.290780	+	0.223123i
$134$	3.49067	+	6.43541i	0.301548	+	0.555935i
$135$		0			0
$136$	−1.61797	−	5.00089i	−0.138740	−	0.428823i
$137$	4.18811	+	15.6302i	0.357814	+	1.33538i	0.876906	+	0.480662i	$0.159604\pi$
$137$	4.18811	+	15.6302i	0.357814	+	1.33538i	−0.519092	+	0.854718i	$0.673730\pi$
$138$		0			0
$139$	−21.8599	+	2.87791i	−1.85413	+	0.244101i	−0.973334	−	0.229393i	$-0.926326\pi$
$139$	−21.8599	+	2.87791i	−1.85413	+	0.244101i	−0.880797	+	0.473494i	$0.842993\pi$
$140$	−3.51154	+	7.34632i	−0.296779	+	0.620878i
$141$		0			0
$142$	1.46950	−	0.563383i	0.123317	−	0.0472781i
$143$			9.96381i			0.833216i
$144$		0			0
$145$		−	11.6477i		−	0.967288i
$146$	4.93431	+	12.8704i	0.408367	+	1.06516i
$147$		0			0
$148$	−2.34411	−	6.63716i	−0.192685	−	0.545571i
$149$	−11.2907	+	1.48645i	−0.924971	+	0.121775i	−0.577940	−	0.816079i	$-0.696143\pi$
$149$	−11.2907	+	1.48645i	−0.924971	+	0.121775i	−0.347031	+	0.937854i	$0.612810\pi$
$150$		0			0
$151$	−3.79793	−	14.1741i	−0.309071	−	1.15347i	−0.929384	−	0.369115i	$-0.879661\pi$
$151$	−3.79793	−	14.1741i	−0.309071	−	1.15347i	0.620313	−	0.784355i	$-0.287006\pi$
$152$	5.17797	−	4.41121i	0.419989	−	0.357797i
$153$		0			0
$154$	−9.37654	+	5.08598i	−0.755583	+	0.409840i
$155$	12.9785	−	9.95873i	1.04246	−	0.799905i
$156$		0			0
$157$	1.03401	−	1.34755i	0.0825233	−	0.107546i	−0.750267	−	0.661135i	$-0.770075\pi$
$157$	1.03401	−	1.34755i	0.0825233	−	0.107546i	0.832791	+	0.553588i	$0.186742\pi$
$158$	−10.4509	+	7.58635i	−0.831427	+	0.603537i
$159$		0			0
$160$	5.03965	−	12.0954i	0.398419	−	0.956226i
$161$	6.92155			0.545494
$162$		0			0
$163$	−3.09378	−	7.46904i	−0.242323	−	0.585020i	0.755189	−	0.655507i	$-0.227545\pi$
$163$	−3.09378	−	7.46904i	−0.242323	−	0.585020i	−0.997513	+	0.0704864i	$0.977545\pi$
$164$	−11.2162	−	22.0584i	−0.875835	−	1.72247i
$165$		0			0
$166$	−4.22459	−	2.59126i	−0.327892	−	0.201120i
$167$	−5.50569	+	20.5475i	−0.426043	+	1.59001i	0.335591	+	0.942008i	$0.391064\pi$
$167$	−5.50569	+	20.5475i	−0.426043	+	1.59001i	−0.761634	+	0.648007i	$0.775603\pi$
$168$		0			0
$169$	−1.96949	−	7.35024i	−0.151499	−	0.565403i
$170$	−1.73138	+	5.83612i	−0.132791	+	0.447610i
$171$		0			0
$172$	0.884889	−	4.75231i	0.0674721	−	0.362361i
$173$	0.719274	−	5.46343i	0.0546854	−	0.415377i	−0.942105	−	0.335319i	$-0.891156\pi$
$173$	0.719274	−	5.46343i	0.0546854	−	0.415377i	0.996790	−	0.0800582i	$-0.0255106\pi$
$174$		0			0
$175$	0.556377	−	0.321224i	0.0420581	−	0.0242823i
$176$	14.6515	−	8.94485i	1.10440	−	0.674243i
$177$		0			0
$178$	6.88509	−	2.63964i	0.516059	−	0.197850i
$179$	−20.4046	+	8.45184i	−1.52511	+	0.631721i	−0.978607	−	0.205738i	$-0.934041\pi$
$179$	−20.4046	+	8.45184i	−1.52511	+	0.631721i	−0.546501	+	0.837458i	$0.684041\pi$
$180$		0			0
$181$	−7.15352	+	17.2701i	−0.531717	+	1.28368i	0.398669	+	0.917095i	$0.369472\pi$
$181$	−7.15352	+	17.2701i	−0.531717	+	1.28368i	−0.930385	+	0.366583i	$0.880528\pi$
$182$	−4.18775	+	3.97071i	−0.310417	+	0.294329i
$183$		0			0
$184$	−11.1240	+	0.569034i	−0.820074	+	0.0419498i
$185$	−2.10999	+	7.87458i	−0.155129	+	0.578951i
$186$		0			0
$187$	−6.32701	+	4.85489i	−0.462677	+	0.355024i
$188$	2.66919	+	12.6092i	0.194671	+	0.919624i
$189$		0			0
$190$	−7.83538	+	0.820228i	−0.568438	+	0.0595056i
$191$	7.49890	−	12.9885i	0.542601	−	0.939813i	−0.456152	−	0.889902i	$-0.650773\pi$
$191$	7.49890	−	12.9885i	0.542601	−	0.939813i	0.998754	−	0.0499114i	$-0.0158939\pi$
$192$		0			0
$193$	−0.624997	−	1.08253i	−0.0449883	−	0.0779220i	0.842654	−	0.538455i	$-0.180992\pi$
$193$	−0.624997	−	1.08253i	−0.0449883	−	0.0779220i	−0.887643	+	0.460533i	$0.847658\pi$
$194$	−7.19925	−	9.91761i	−0.516876	−	0.712043i
$195$		0			0
$196$	7.43689	+	2.42325i	0.531206	+	0.173089i
$197$	−0.313242	−	0.129749i	−0.0223176	−	0.00924423i	0.371497	−	0.928434i	$-0.378845\pi$
$197$	−0.313242	−	0.129749i	−0.0223176	−	0.00924423i	−0.393814	+	0.919190i	$0.628845\pi$
$198$		0			0
$199$	4.29098	+	4.29098i	0.304179	+	0.304179i	0.842646	−	0.538467i	$-0.180996\pi$
$199$	4.29098	+	4.29098i	0.304179	+	0.304179i	−0.538467	+	0.842646i	$0.680996\pi$
$200$	−0.867778	+	0.562000i	−0.0613612	+	0.0397394i
$201$		0			0
$202$	2.82167	+	11.7747i	0.198532	+	0.828466i
$203$	8.76235	−	1.15359i	0.614996	−	0.0809658i
$204$		0			0
$205$	−3.74096	+	28.4154i	−0.261280	+	1.98462i
$206$	−5.85785	−	4.74764i	−0.408136	−	0.330784i
$207$		0			0
$208$	6.40394	−	6.72585i	0.444034	−	0.466354i
$209$	−8.93816	−	5.16045i	−0.618265	−	0.356956i
$210$		0			0
$211$	−6.19977	−	4.75725i	−0.426810	−	0.327503i	0.372919	−	0.927864i	$-0.378357\pi$
$211$	−6.19977	−	4.75725i	−0.426810	−	0.327503i	−0.799729	+	0.600361i	$0.795023\pi$
$212$	−16.7744	+	5.92439i	−1.15207	+	0.406889i
$213$		0			0
$214$	7.13658	+	7.52667i	0.487847	+	0.514513i
$215$	−3.95884	+	3.95884i	−0.269990	+	0.269990i
$216$		0			0
$217$	8.77716	+	8.77716i	0.595833	+	0.595833i
$218$	0.668815	−	25.1404i	0.0452978	−	1.70272i
$219$		0			0
$220$	−19.8533	−	1.05707i	−1.33851	−	0.0712677i
$221$	−2.62652	+	3.42294i	−0.176679	+	0.230252i
$222$		0			0
$223$	8.01763	−	13.8869i	0.536900	−	0.929938i	−0.462169	−	0.886792i	$-0.652929\pi$
$223$	8.01763	−	13.8869i	0.536900	−	0.929938i	0.999069	−	0.0431461i	$-0.0137381\pi$
$224$	9.59828	+	2.59331i	0.641312	+	0.173273i
$225$		0			0
$226$	−1.24201	−	11.8645i	−0.0826172	−	0.789216i
$227$	−23.3168	−	3.06972i	−1.54759	−	0.203744i	−0.692192	−	0.721714i	$-0.743355\pi$
$227$	−23.3168	−	3.06972i	−1.54759	−	0.203744i	−0.855399	+	0.517970i	$0.826688\pi$
$228$		0			0
$229$	−0.971767	−	7.38131i	−0.0642162	−	0.487770i	−0.993088	−	0.117370i	$-0.962554\pi$
$229$	−0.971767	−	7.38131i	−0.0642162	−	0.487770i	0.928872	−	0.370401i	$-0.120780\pi$
$230$	10.9967	+	6.74507i	0.725098	+	0.444757i
$231$		0			0
$232$	−13.9877	+	2.57437i	−0.918335	+	0.169015i
$233$	−5.74620	+	5.74620i	−0.376446	+	0.376446i	−0.869818	−	0.493372i	$-0.835764\pi$
$233$	−5.74620	+	5.74620i	−0.376446	+	0.376446i	0.493372	+	0.869818i	$0.335764\pi$
$234$		0			0
$235$	5.71247	−	13.7911i	0.372640	−	0.899633i
$236$	−19.3867	+	22.6606i	−1.26197	+	1.47508i
$237$		0			0
$238$	−4.56189	−	0.724482i	−0.295703	−	0.0469612i
$239$	6.52718	−	3.76847i	0.422208	−	0.243762i	−0.273814	−	0.961783i	$-0.588285\pi$
$239$	6.52718	−	3.76847i	0.422208	−	0.243762i	0.696021	+	0.718021i	$0.254952\pi$
$240$		0			0
$241$	−13.4698	−	7.77681i	−0.867668	−	0.500948i	−0.00109546	−	0.999999i	$-0.500349\pi$
$241$	−13.4698	−	7.77681i	−0.867668	−	0.500948i	−0.866573	+	0.499051i	$0.833682\pi$
$242$	−8.14916	−	6.60468i	−0.523848	−	0.424565i
$243$		0			0
$244$	14.8814	+	21.6912i	0.952682	+	1.38864i
$245$	−5.51475	−	7.18697i	−0.352325	−	0.459158i
$246$		0			0
$247$	−5.39340	−	1.44516i	−0.343174	−	0.0919531i
$248$	−14.8279	−	13.3847i	−0.941572	−	0.849930i
$249$		0			0
$250$	−15.1764	−	0.403739i	−0.959838	−	0.0255347i
$251$	−4.10085	−	1.69863i	−0.258843	−	0.107216i	0.249488	−	0.968378i	$-0.419738\pi$
$251$	−4.10085	−	1.69863i	−0.258843	−	0.107216i	−0.508332	+	0.861161i	$0.669738\pi$
$252$		0			0
$253$	6.46750	+	15.6139i	0.406608	+	0.981639i
$254$	3.71549	−	8.33577i	0.233130	−	0.523032i
$255$		0			0
$256$	−15.6392	−	3.37877i	−0.977449	−	0.211173i
$257$	10.8708	+	18.8289i	0.678105	+	1.17451i	0.975551	+	0.219773i	$0.0705317\pi$
$257$	10.8708	+	18.8289i	0.678105	+	1.17451i	−0.297446	+	0.954738i	$0.596135\pi$
$258$		0			0
$259$	−6.13288	−	0.807409i	−0.381079	−	0.0501699i
$260$	−10.5228	+	2.22752i	−0.652595	+	0.138145i
$261$		0			0
$262$	9.49978	+	17.5138i	0.586898	+	1.08201i
$263$	20.3111	−	5.44235i	1.25244	−	0.335590i	0.429160	−	0.903228i	$-0.358810\pi$
$263$	20.3111	−	5.44235i	1.25244	−	0.335590i	0.823278	+	0.567638i	$0.192143\pi$
$264$		0			0
$265$	19.9018	+	5.33267i	1.22256	+	0.327583i
$266$	−1.39306	−	5.81318i	−0.0854139	−	0.356429i
$267$		0			0
$268$	−10.3224	+	0.803733i	−0.630543	+	0.0490958i
$269$	−25.8978	+	10.7272i	−1.57902	+	0.654051i	−0.988258	−	0.152796i	$-0.951172\pi$
$269$	−25.8978	+	10.7272i	−1.57902	+	0.654051i	−0.590761	+	0.806847i	$0.701172\pi$
$270$		0			0
$271$			23.6586i			1.43716i	0.695446	+	0.718578i	$0.255207\pi$
$271$			23.6586i			1.43716i	−0.695446	+	0.718578i	$0.744793\pi$
$272$	7.39124	+	0.789316i	0.448160	+	0.0478593i
$273$		0			0
$274$	−22.6010	−	3.58931i	−1.36538	−	0.216838i
$275$	1.24451	+	0.954947i	0.0750468	+	0.0575855i
$276$		0			0
$277$	2.47944	+	3.23127i	0.148975	+	0.194148i	0.861880	−	0.507113i	$-0.169287\pi$
$277$	2.47944	+	3.23127i	0.148975	+	0.194148i	−0.712904	+	0.701261i	$0.752621\pi$
$278$	8.86843	−	29.8936i	0.531893	−	1.79290i
$279$		0			0
$280$	−7.46753	−	8.76554i	−0.446271	−	0.523841i
$281$	14.4950	−	3.88392i	0.864699	−	0.231695i	0.200905	−	0.979611i	$-0.435612\pi$
$281$	14.4950	−	3.88392i	0.864699	−	0.231695i	0.663794	+	0.747915i	$0.268945\pi$
$282$		0			0
$283$	−1.13568	−	8.62638i	−0.0675094	−	0.512785i	−0.991474	−	0.130306i	$-0.958404\pi$
$283$	−1.13568	−	8.62638i	−0.0675094	−	0.512785i	0.923964	−	0.382479i	$-0.124929\pi$
$284$	−0.118336	+	2.22253i	−0.00702196	+	0.131883i
$285$		0			0
$286$	−12.8703	−	5.73667i	−0.761039	−	0.339217i
$287$	−21.7469			−1.28368
$288$		0			0
$289$	13.5467			0.796862
$290$	15.0454	+	6.70617i	0.883497	+	0.393800i
$291$		0			0
$292$	−19.4657	−	1.03643i	−1.13914	−	0.0606525i
$293$	−1.15773	−	8.79383i	−0.0676353	−	0.513741i	−0.991409	−	0.130801i	$-0.958245\pi$
$293$	−1.15773	−	8.79383i	−0.0676353	−	0.513741i	0.923773	−	0.382940i	$-0.125088\pi$
$294$		0			0
$295$	33.3623	−	8.93940i	1.94243	−	0.520472i
$296$	9.92289	+	0.793439i	0.576757	+	0.0461177i
$297$		0			0
$298$	4.58058	−	15.4401i	0.265346	−	0.894423i
$299$	5.56602	+	7.25378i	0.321891	+	0.419497i
$300$		0			0
$301$	−3.37024	−	2.58608i	−0.194258	−	0.149059i
$302$	20.4954	+	3.25492i	1.17938	+	0.187299i
$303$		0			0
$304$	2.71678	+	9.22818i	0.155818	+	0.529273i
$305$		−	30.4662i		−	1.74449i
$306$		0			0
$307$	−21.6584	+	8.97121i	−1.23611	+	0.512014i	−0.902497	−	0.430696i	$-0.858268\pi$
$307$	−21.6584	+	8.97121i	−1.23611	+	0.512014i	−0.333614	+	0.942710i	$0.608268\pi$
$308$	−1.17106	−	15.0400i	−0.0667271	−	0.856984i
$309$		0			0
$310$	5.39141	+	22.4982i	0.306211	+	1.27781i
$311$	−7.91425	−	2.12062i	−0.448776	−	0.120249i	0.0273506	−	0.999626i	$-0.491293\pi$
$311$	−7.91425	−	2.12062i	−0.448776	−	0.120249i	−0.476127	+	0.879377i	$0.657960\pi$
$312$		0			0
$313$	11.2322	−	3.00966i	0.634882	−	0.170116i	0.0729977	−	0.997332i	$-0.476743\pi$
$313$	11.2322	−	3.00966i	0.634882	−	0.170116i	0.561884	+	0.827216i	$0.310077\pi$
$314$	1.14531	+	2.11150i	0.0646337	+	0.119159i
$315$		0			0
$316$	−3.78225	−	17.8673i	−0.212768	−	1.00512i
$317$	−4.12855	−	0.543534i	−0.231883	−	0.0305279i	0.0136893	−	0.999906i	$-0.495642\pi$
$317$	−4.12855	−	0.543534i	−0.231883	−	0.0305279i	−0.245572	+	0.969378i	$0.578976\pi$
$318$		0			0
$319$	10.7899	+	18.6886i	0.604116	+	1.04636i
$320$	12.7222	+	13.4737i	0.711190	+	0.753203i
$321$		0			0
$322$	−3.98509	+	8.94062i	−0.222080	+	0.498241i
$323$	−1.71027	−	4.12896i	−0.0951620	−	0.229741i
$324$		0			0
$325$	0.784059	+	0.324768i	0.0434917	+	0.0180149i
$326$	11.4291	+	0.304049i	0.632997	+	0.0168397i
$327$		0			0
$328$	34.9508	−	1.78786i	1.92983	−	0.0987179i
$329$	10.9406	+	2.93152i	0.603174	+	0.161620i
$330$		0			0
$331$	11.5621	+	15.0681i	0.635513	+	0.828216i	0.994457	−	0.105143i	$-0.0335299\pi$
$331$	11.5621	+	15.0681i	0.635513	+	0.828216i	−0.358944	+	0.933359i	$0.616863\pi$
$332$	5.77946	−	3.96502i	0.317189	−	0.217609i
$333$		0			0
$334$	−23.3715	−	18.9420i	−1.27883	−	1.03646i
$335$	10.3849	+	5.99571i	0.567386	+	0.327581i
$336$		0			0
$337$	25.9301	−	14.9707i	1.41250	−	0.815508i	0.416878	−	0.908963i	$-0.363124\pi$
$337$	25.9301	−	14.9707i	1.41250	−	0.815508i	0.995624	+	0.0934545i	$0.0297910\pi$
$338$	10.6283	+	1.68790i	0.578104	+	0.0918097i
$339$		0			0
$340$	−6.54172	−	5.59660i	−0.354775	−	0.303518i
$341$	−11.5985	+	28.0013i	−0.628095	+	1.51636i
$342$		0			0
$343$	13.5601	−	13.5601i	0.732176	−	0.732176i
$344$	5.62913	+	3.87917i	0.303502	+	0.209151i
$345$		0			0
$346$	6.64303	+	4.07467i	0.357132	+	0.219056i
$347$	−1.11787	−	8.49110i	−0.0600106	−	0.455826i	−0.994898	−	0.100882i	$-0.967833\pi$
$347$	−1.11787	−	8.49110i	−0.0600106	−	0.455826i	0.934888	−	0.354944i	$-0.115500\pi$
$348$		0			0
$349$	−8.64822	−	1.13856i	−0.462928	−	0.0609457i	−0.104545	−	0.994520i	$-0.533339\pi$
$349$	−8.64822	−	1.13856i	−0.462928	−	0.0609457i	−0.358383	+	0.933574i	$0.616672\pi$
$350$	0.0945936	+	0.903622i	0.00505624	+	0.0483006i
$351$		0			0
$352$	3.11854	+	24.0754i	0.166219	+	1.28322i
$353$	−0.687258	+	1.19037i	−0.0365790	+	0.0633567i	−0.883735	−	0.467987i	$-0.844979\pi$
$353$	−0.687258	+	1.19037i	−0.0365790	+	0.0633567i	0.847156	+	0.531344i	$0.178313\pi$
$354$		0			0
$355$	1.56923	−	2.04505i	0.0832858	−	0.108540i
$356$	−0.554446	+	10.4133i	−0.0293856	+	0.551904i
$357$		0			0
$358$	0.830627	−	31.2229i	0.0439000	−	1.65018i
$359$	−5.66910	−	5.66910i	−0.299204	−	0.299204i	0.541498	−	0.840702i	$-0.317857\pi$
$359$	−5.66910	−	5.66910i	−0.299204	−	0.299204i	−0.840702	+	0.541498i	$0.817857\pi$
$360$		0			0
$361$	−9.34529	+	9.34529i	−0.491857	+	0.491857i
$362$	−18.1893	−	19.1835i	−0.956009	−	1.00826i
$363$		0			0
$364$	−2.71790	−	7.69549i	−0.142457	−	0.403353i
$365$	17.9113	+	13.7438i	0.937521	+	0.719385i
$366$		0			0
$367$	30.7867	+	17.7747i	1.60705	+	0.927832i	0.990025	+	0.140890i	$0.0449964\pi$
$367$	30.7867	+	17.7747i	1.60705	+	0.927832i	0.617027	+	0.786942i	$0.288337\pi$
$368$	5.66965	−	14.6966i	0.295551	−	0.766115i
$369$		0			0
$370$	−8.95683	−	7.25929i	−0.465644	−	0.377392i
$371$	−2.04060	+	15.4999i	−0.105943	+	0.804716i
$372$		0			0
$373$	23.0614	−	3.03609i	1.19407	−	0.157203i	0.492830	−	0.870125i	$-0.335962\pi$
$373$	23.0614	−	3.03609i	1.19407	−	0.157203i	0.701243	+	0.712923i	$0.252629\pi$
$374$	−2.62831	−	10.9679i	−0.135907	−	0.567134i
$375$		0			0
$376$	−17.8243	−	3.81197i	−0.919216	−	0.196587i
$377$	8.25528	+	8.25528i	0.425169	+	0.425169i
$378$		0			0
$379$	−5.76133	−	2.38642i	−0.295939	−	0.122582i	0.229774	−	0.973244i	$-0.426201\pi$
$379$	−5.76133	−	2.38642i	−0.295939	−	0.122582i	−0.525713	+	0.850662i	$0.676201\pi$
$380$	3.45173	−	10.5933i	0.177070	−	0.543423i
$381$		0			0
$382$	12.4598	+	17.1645i	0.637500	+	0.878213i
$383$	14.3541	+	24.8620i	0.733458	+	1.27039i	0.955396	+	0.295326i	$0.0954283\pi$
$383$	14.3541	+	24.8620i	0.733458	+	1.27039i	−0.221938	+	0.975061i	$0.571238\pi$
$384$		0			0
$385$	−8.73588	+	15.1310i	−0.445222	+	0.771147i
$386$	1.75815	−	0.184048i	0.0894876	−	0.00936780i
$387$		0			0
$388$	16.9556	−	3.58926i	0.860792	−	0.182217i
$389$	1.74939	−	1.34235i	0.0886974	−	0.0680599i	−0.563461	−	0.826143i	$-0.690530\pi$
$389$	1.74939	−	1.34235i	0.0886974	−	0.0680599i	0.652158	+	0.758083i	$0.273864\pi$
$390$		0			0
$391$	−1.89409	+	7.06884i	−0.0957882	+	0.357487i
$392$	−7.41193	+	8.21110i	−0.374359	+	0.414723i
$393$		0			0
$394$	0.347947	−	0.329914i	0.0175293	−	0.0166208i
$395$	−8.09458	+	19.5420i	−0.407282	+	0.983267i
$396$		0			0
$397$	6.18835	−	2.56330i	0.310584	−	0.128648i	−0.221947	−	0.975059i	$-0.571241\pi$
$397$	6.18835	−	2.56330i	0.310584	−	0.128648i	0.532531	+	0.846411i	$0.321241\pi$
$398$	−8.01322	+	3.07216i	−0.401667	+	0.153993i
$399$		0			0
$400$	−0.226316	−	1.44449i	−0.0113158	−	0.0722244i
$401$	−2.39063	+	1.38023i	−0.119382	+	0.0689254i	−0.558502	−	0.829503i	$-0.688624\pi$
$401$	−2.39063	+	1.38023i	−0.119382	+	0.0689254i	0.439120	+	0.898429i	$0.355290\pi$
$402$		0			0
$403$	−2.14024	+	16.2567i	−0.106613	+	0.809804i
$404$	−16.8341	−	3.13453i	−0.837526	−	0.155949i
$405$		0			0
$406$	−3.55484	+	11.9826i	−0.176424	+	0.594685i
$407$	−3.90918	−	14.5893i	−0.193771	−	0.723163i
$408$		0			0
$409$	3.26654	−	12.1909i	0.161520	−	0.602801i	−0.836938	−	0.547297i	$-0.815657\pi$
$409$	3.26654	−	12.1909i	0.161520	−	0.602801i	0.998458	−	0.0555039i	$-0.0176765\pi$
$410$	−34.5506	−	21.1924i	−1.70633	−	1.04662i
$411$		0			0
$412$	9.50523	−	4.83318i	0.468289	−	0.238114i
$413$	10.0291	+	24.2125i	0.493502	+	1.19142i
$414$		0			0
$415$	−8.11747			−0.398471
$416$	5.00076	+	12.1444i	0.245182	+	0.595430i
$417$		0			0
$418$	11.8120	−	8.57436i	0.577741	−	0.419386i
$419$	−1.04787	+	1.36561i	−0.0511919	+	0.0667146i	−0.818248	−	0.574866i	$-0.805054\pi$
$419$	−1.04787	+	1.36561i	−0.0511919	+	0.0667146i	0.767056	+	0.641580i	$0.221721\pi$
$420$		0			0
$421$	27.1791	−	20.8553i	1.32463	−	1.01642i	0.327186	−	0.944960i	$-0.393899\pi$
$421$	27.1791	−	20.8553i	1.32463	−	1.01642i	0.997443	−	0.0714643i	$-0.0227672\pi$
$422$	9.71450	−	5.26930i	0.472895	−	0.256506i
$423$		0			0
$424$	2.00530	−	25.0786i	0.0973858	−	1.21793i
$425$	0.175807	+	0.656120i	0.00852789	+	0.0318265i
$426$		0			0
$427$	22.9192	−	3.01737i	1.10914	−	0.146021i
$428$	−13.8312	+	4.88489i	−0.668554	+	0.236120i
$429$		0			0
$430$	−2.83436	−	7.39296i	−0.136685	−	0.356520i
$431$		−	6.06871i		−	0.292319i	−0.989261	−	0.146160i	$-0.953309\pi$
$431$		−	6.06871i		−	0.292319i	0.989261	−	0.146160i	$-0.0466913\pi$
$432$		0			0
$433$		−	22.3463i		−	1.07390i	−0.843615	−	0.536948i	$-0.819577\pi$
$433$		−	22.3463i		−	1.07390i	0.843615	−	0.536948i	$-0.180423\pi$
$434$	−16.3910	+	6.28407i	−0.786793	+	0.301645i
$435$		0			0
$436$	32.0890	+	15.3385i	1.53679	+	0.734583i
$437$	−9.38985	+	1.23620i	−0.449177	+	0.0591353i
$438$		0			0
$439$	−1.07159	−	3.99922i	−0.0511440	−	0.190872i	0.935628	−	0.352989i	$-0.114835\pi$
$439$	−1.07159	−	3.99922i	−0.0511440	−	0.190872i	−0.986772	+	0.162117i	$0.948168\pi$
$440$	12.7960	−	25.0361i	0.610026	−	1.19355i
$441$		0			0
$442$	−2.90922	−	5.36346i	−0.138378	−	0.255114i
$443$	18.0020	−	13.8134i	0.855299	−	0.656294i	−0.0850983	−	0.996373i	$-0.527120\pi$
$443$	18.0020	−	13.8134i	0.855299	−	0.656294i	0.940397	+	0.340079i	$0.110454\pi$
$444$		0			0
$445$	7.35236	−	9.58178i	0.348535	−	0.454220i
$446$	13.3217	+	18.3519i	0.630802	+	0.868986i
$447$		0			0
$448$	−8.87602	+	10.9051i	−0.419353	+	0.515217i
$449$	30.9160			1.45901			0.729507	−	0.683973i	$-0.239749\pi$
$449$	30.9160			1.45901			0.729507	+	0.683973i	$0.239749\pi$
$450$		0			0
$451$	−20.3203	−	49.0576i	−0.956847	−	2.31003i
$452$	16.0406	+	5.22669i	0.754485	+	0.245843i
$453$		0			0
$454$	17.3899	−	28.3511i	0.816146	−	1.33058i
$455$	−2.44644	+	9.13023i	−0.114691	+	0.428032i
$456$		0			0
$457$	−3.89417	−	14.5332i	−0.182161	−	0.679836i	−0.995220	−	0.0976544i	$-0.968866\pi$
$457$	−3.89417	−	14.5332i	−0.182161	−	0.679836i	0.813059	−	0.582181i	$-0.197801\pi$
$458$	10.0940	+	2.99455i	0.471661	+	0.139926i
$459$		0			0
$460$	−15.0440	+	10.3210i	−0.701430	+	0.481219i
$461$	−0.821111	+	6.23695i	−0.0382429	+	0.290484i	0.961627	+	0.274360i	$0.0884660\pi$
$461$	−0.821111	+	6.23695i	−0.0382429	+	0.290484i	−0.999870	+	0.0161240i	$0.994867\pi$
$462$		0			0
$463$	−34.3974	+	19.8593i	−1.59858	+	0.922941i	−0.606819	+	0.794840i	$0.707555\pi$
$463$	−34.3974	+	19.8593i	−1.59858	+	0.922941i	−0.991761	+	0.128101i	$0.959112\pi$
$464$	4.72808	−	19.5502i	0.219495	−	0.907594i
$465$		0			0
$466$	−4.11404	−	10.7308i	−0.190579	−	0.497095i
$467$	25.1605	−	10.4218i	1.16429	−	0.482265i	0.284989	−	0.958531i	$-0.408010\pi$
$467$	25.1605	−	10.4218i	1.16429	−	0.482265i	0.879301	+	0.476266i	$0.158010\pi$
$468$		0			0
$469$	−3.48195	+	8.40617i	−0.160782	+	0.388161i
$470$	14.5251	+	15.3191i	0.669995	+	0.706617i
$471$		0			0
$472$	−18.1090	−	38.0888i	−0.833534	−	1.75318i
$473$	2.68463	−	10.0192i	0.123439	−	0.460682i
$474$		0			0
$475$	−0.697416	+	0.535146i	−0.0319996	+	0.0245542i
$476$	3.56233	−	5.47551i	0.163279	−	0.250969i
$477$		0			0
$478$	1.10973	+	10.6009i	0.0507579	+	0.484874i
$479$	−5.20509	+	9.01548i	−0.237827	+	0.411928i	−0.960090	−	0.279690i	$-0.909768\pi$
$479$	−5.20509	+	9.01548i	−0.237827	+	0.411928i	0.722264	+	0.691618i	$0.243102\pi$
$480$		0			0
$481$	−4.08564	−	7.07654i	−0.186289	−	0.322663i
$482$	17.8006	−	12.9216i	0.810797	−	0.588562i
$483$		0			0
$484$	13.2232	−	6.72368i	0.601055	−	0.305622i
$485$	−18.5449	−	7.68155i	−0.842080	−	0.348801i
$486$		0			0
$487$	−2.62552	−	2.62552i	−0.118974	−	0.118974i	0.645113	−	0.764087i	$-0.276810\pi$
$487$	−2.62552	−	2.62552i	−0.118974	−	0.118974i	−0.764087	+	0.645113i	$0.776810\pi$
$488$	−36.5867	+	6.73362i	−1.65620	+	0.304817i
$489$		0			0
$490$	12.4586	−	2.98555i	0.562822	−	0.134873i
$491$	−17.5722	+	2.31343i	−0.793024	+	0.104404i	−0.516145	−	0.856501i	$-0.672633\pi$
$491$	−17.5722	+	2.31343i	−0.793024	+	0.104404i	−0.276879	+	0.960905i	$0.589300\pi$
$492$		0			0
$493$	−1.21969	+	9.26450i	−0.0549323	+	0.417252i
$494$	4.97197	−	6.13465i	0.223700	−	0.276011i
$495$		0			0
$496$	25.8263	−	11.4470i	1.15964	−	0.513988i
$497$	1.69387	+	0.977958i	0.0759806	+	0.0438674i
$498$		0			0
$499$	17.5034	+	13.4308i	0.783559	+	0.601246i	0.921134	−	0.389245i	$-0.127264\pi$
$499$	17.5034	+	13.4308i	0.783559	+	0.601246i	−0.137575	+	0.990491i	$0.543931\pi$
$500$	9.25932	−	19.3710i	0.414090	−	0.866297i
$501$		0			0
$502$	4.55520	−	4.31911i	0.203308	−	0.192771i
$503$	11.3945	−	11.3945i	0.508054	−	0.508054i	−0.405875	−	0.913929i	$-0.633033\pi$
$503$	11.3945	−	11.3945i	0.508054	−	0.508054i	0.913929	+	0.405875i	$0.133033\pi$
$504$		0			0
$505$	14.0233	+	14.0233i	0.624031	+	0.624031i
$506$	−23.8923	−	0.635611i	−1.06214	−	0.0282563i
$507$		0			0
$508$	8.62818	+	9.59865i	0.382814	+	0.425871i
$509$	21.8821	−	28.5173i	0.969907	−	1.26401i	0.00538989	−	0.999985i	$-0.498284\pi$
$509$	21.8821	−	28.5173i	0.969907	−	1.26401i	0.964517	−	0.264022i	$-0.0850490\pi$
$510$		0			0
$511$	−8.56531	+	14.8355i	−0.378907	+	0.656286i
$512$	13.3687	−	18.2559i	0.590817	−	0.806806i
$513$		0			0
$514$	−30.5803	+	3.20123i	−1.34884	+	0.141200i
$515$	−12.2445	−	1.61202i	−0.539559	−	0.0710342i
$516$		0			0
$517$	3.60984	+	27.4194i	0.158761	+	1.20591i
$518$	4.57395	−	7.45702i	0.200968	−	0.327643i
$519$		0			0
$520$	3.18120	−	14.8749i	0.139505	−	0.652306i
$521$	8.86700	−	8.86700i	0.388470	−	0.388470i	−0.485671	−	0.874142i	$-0.661425\pi$
$521$	8.86700	−	8.86700i	0.388470	−	0.388470i	0.874142	+	0.485671i	$0.161425\pi$
$522$		0			0
$523$	6.58354	−	15.8941i	0.287878	−	0.695000i	−0.712097	−	0.702081i	$-0.752254\pi$
$523$	6.58354	−	15.8941i	0.287878	−	0.695000i	0.999975	+	0.00708176i	$0.00225421\pi$
$524$	−28.0923	+	2.18734i	−1.22722	+	0.0955544i
$525$		0			0
$526$	−4.66423	+	29.3695i	−0.203370	+	1.28057i
$527$	−11.3658	+	6.56206i	−0.495103	+	0.285848i
$528$		0			0
$529$	−6.48785	−	3.74576i	−0.282080	−	0.162859i
$530$	−18.3467	+	22.6370i	−0.796932	+	0.983290i
$531$		0			0
$532$	8.31099	+	1.54752i	0.360327	+	0.0670935i
$533$	−17.4880	−	22.7908i	−0.757488	−	0.987178i
$534$		0			0
$535$	16.4098	+	4.39700i	0.709459	+	0.190099i
$536$	4.90496	−	13.7963i	0.211862	−	0.595910i
$537$		0			0
$538$	1.05425	−	39.6287i	0.0454518	−	1.70851i
$539$	15.5060	+	6.42280i	0.667891	+	0.276650i
$540$		0			0
$541$	−7.03001	−	16.9719i	−0.302244	−	0.729681i	−0.999912	−	0.0132601i	$-0.995779\pi$
$541$	−7.03001	−	16.9719i	−0.302244	−	0.729681i	0.697668	−	0.716421i	$-0.254221\pi$
$542$	−30.5600	−	13.6215i	−1.31266	−	0.585091i
$543$		0			0
$544$	−5.27508	+	9.09288i	−0.226167	+	0.389854i
$545$	−20.5962	−	35.6737i	−0.882245	−	1.52809i
$546$		0			0
$547$	1.12181	+	0.147689i	0.0479650	+	0.00631471i	0.154470	−	0.987997i	$-0.450633\pi$
$547$	1.12181	+	0.147689i	0.0479650	+	0.00631471i	−0.106506	+	0.994312i	$0.533966\pi$
$548$	17.6489	−	27.1274i	0.753923	−	1.15882i
$549$		0			0
$550$	−1.95004	+	1.05773i	−0.0831500	+	0.0451019i
$551$	−11.6811	+	3.12993i	−0.497630	+	0.133340i
$552$		0			0
$553$	−15.5028	−	4.15397i	−0.659247	−	0.176645i
$554$	−5.60140	+	1.34231i	−0.237981	+	0.0570292i
$555$		0			0
$556$	33.5077	+	28.6667i	1.42104	+	1.21574i
$557$	−22.7424	+	9.42021i	−0.963626	+	0.399147i	−0.808336	−	0.588722i	$-0.799631\pi$
$557$	−22.7424	+	9.42021i	−0.963626	+	0.399147i	−0.155290	+	0.987869i	$0.549631\pi$
$558$		0			0
$559$		−	5.61164i		−	0.237347i
$560$	15.6220	−	4.59911i	0.660148	−	0.194348i
$561$		0			0
$562$	−3.32861	+	20.9595i	−0.140409	+	0.884122i
$563$	−8.34473	−	6.40314i	−0.351689	−	0.269860i	0.417775	−	0.908550i	$-0.362810\pi$
$563$	−8.34473	−	6.40314i	−0.351689	−	0.269860i	−0.769464	+	0.638690i	$0.779477\pi$
$564$		0			0
$565$	−11.8947	−	15.5015i	−0.500415	−	0.652154i
$566$	11.7966	+	3.49967i	0.495850	+	0.147102i
$567$		0			0
$568$	−2.80273	−	1.43248i	−0.117600	−	0.0601055i
$569$	25.1811	−	6.74726i	1.05565	−	0.282860i	0.311064	−	0.950389i	$-0.399315\pi$
$569$	25.1811	−	6.74726i	1.05565	−	0.282860i	0.744584	+	0.667529i	$0.232648\pi$
$570$		0			0
$571$	−0.199249	−	1.51344i	−0.00833829	−	0.0633356i	0.986770	−	0.162127i	$-0.0518356\pi$
$571$	−0.199249	−	1.51344i	−0.00833829	−	0.0633356i	−0.995108	+	0.0987918i	$0.968502\pi$
$572$	14.8202	−	13.3218i	0.619665	−	0.557014i
$573$		0			0
$574$	12.5208	−	28.0907i	0.522608	−	1.17248i
$575$	1.43948			0.0600303
$576$		0			0
$577$	−7.93730			−0.330434			−0.165217	−	0.986257i	$-0.552832\pi$
$577$	−7.93730			−0.330434			−0.165217	+	0.986257i	$0.552832\pi$
$578$	−7.79950	+	17.4983i	−0.324417	+	0.727835i
$579$		0			0
$580$	−17.3248	+	15.5732i	−0.719374	+	0.646642i
$581$	−0.803953	−	6.10663i	−0.0333536	−	0.253346i
$582$		0			0
$583$	−36.8721	+	9.87986i	−1.52709	+	0.409182i
$584$	12.5462	−	24.5473i	0.519164	−	1.01577i
$585$		0			0
$586$	12.0256	+	3.56761i	0.496774	+	0.147377i
$587$	22.0089	+	28.6826i	0.908405	+	1.18386i	0.982436	+	0.186600i	$0.0597470\pi$
$587$	22.0089	+	28.6826i	0.908405	+	1.18386i	−0.0740310	+	0.997256i	$0.523586\pi$
$588$		0			0
$589$	−13.4748	−	10.3396i	−0.555220	−	0.426035i
$590$	−7.66128	+	48.2412i	−0.315410	+	1.98606i
$591$		0			0
$592$	−6.73801	+	12.3607i	−0.276930	+	0.508020i
$593$		−	3.46481i		−	0.142283i	−0.997466	−	0.0711414i	$-0.977336\pi$
$593$		−	3.46481i		−	0.142283i	0.997466	−	0.0711414i	$-0.0226641\pi$
$594$		0			0
$595$	−6.98972	+	2.89524i	−0.286551	+	0.118693i
$596$	17.3069	+	14.8064i	0.708917	+	0.606496i
$597$		0			0
$598$	−12.5744	+	3.01331i	−0.514206	+	0.123223i
$599$	−13.5724	−	3.63671i	−0.554552	−	0.148592i	−0.0293500	−	0.999569i	$-0.509344\pi$
$599$	−13.5724	−	3.63671i	−0.554552	−	0.148592i	−0.525202	+	0.850977i	$0.676010\pi$
$600$		0			0
$601$	−16.3972	+	4.39361i	−0.668854	+	0.179219i	−0.577239	−	0.816576i	$-0.695870\pi$
$601$	−16.3972	+	4.39361i	−0.668854	+	0.179219i	−0.0916156	+	0.995794i	$0.529203\pi$
$602$	5.28088	−	2.86443i	0.215233	−	0.116746i
$603$		0			0
$604$	−16.0047	+	24.6001i	−0.651221	+	1.00096i
$605$	−17.0340	−	2.24257i	−0.692530	−	0.0911734i
$606$		0			0
$607$	11.5502	+	20.0056i	0.468809	+	0.812001i	0.999364	−	0.0356492i	$-0.0113499\pi$
$607$	11.5502	+	20.0056i	0.468809	+	0.812001i	−0.530555	+	0.847650i	$0.678017\pi$
$608$	−13.4843	−	1.80385i	−0.546861	−	0.0731557i
$609$		0			0
$610$	39.3534	+	17.5409i	1.59337	+	0.710212i
$611$	5.72573	+	13.8231i	0.231638	+	0.559224i
$612$		0			0
$613$	31.7359	+	13.1454i	1.28180	+	0.530940i	0.916532	−	0.399962i	$-0.130977\pi$
$613$	31.7359	+	13.1454i	1.28180	+	0.530940i	0.365270	+	0.930902i	$0.380977\pi$
$614$	0.881670	−	33.1416i	0.0355813	−	1.33748i
$615$		0			0
$616$	20.1015	+	7.14664i	0.809914	+	0.287946i
$617$	10.0400	+	2.69022i	0.404196	+	0.108304i	0.455189	−	0.890395i	$-0.349572\pi$
$617$	10.0400	+	2.69022i	0.404196	+	0.108304i	−0.0509925	+	0.998699i	$0.516238\pi$
$618$		0			0
$619$	8.69790	+	11.3353i	0.349598	+	0.455605i	0.934743	−	0.355323i	$-0.115629\pi$
$619$	8.69790	+	11.3353i	0.349598	+	0.455605i	−0.585145	+	0.810928i	$0.698963\pi$
$620$	−32.1652	−	5.98921i	−1.29178	−	0.240532i
$621$		0			0
$622$	7.29586	−	9.00196i	0.292537	−	0.360946i
$623$	7.93638	+	4.58207i	0.317964	+	0.183577i
$624$		0			0
$625$	−23.1177	+	13.3470i	−0.924708	+	0.533881i
$626$	−2.57935	+	16.2415i	−0.103092	+	0.649143i
$627$		0			0
$628$	−3.38686	+	0.263710i	−0.135150	+	0.0105232i
$629$	2.50286	−	6.04244i	0.0997956	−	0.240928i
$630$		0			0
$631$	−13.2206	+	13.2206i	−0.526306	+	0.526306i	−0.919469	−	0.393163i	$-0.871381\pi$
$631$	−13.2206	+	13.2206i	−0.526306	+	0.526306i	0.393163	+	0.919469i	$0.371381\pi$
$632$	25.2570	+	5.40157i	1.00467	+	0.214863i
$633$		0			0
$634$	3.07911	−	5.01995i	0.122287	−	0.199368i
$635$	−1.95112	−	14.8203i	−0.0774280	−	0.588124i
$636$		0			0
$637$	9.00232	+	1.18518i	0.356685	+	0.0469585i
$638$	−30.3525	+	3.17738i	−1.20167	+	0.125794i
$639$		0			0
$640$	−24.7289	+	8.67582i	−0.977495	+	0.342942i
$641$	−24.8380	+	43.0207i	−0.981042	+	1.69921i	−0.322687	+	0.946506i	$0.604586\pi$
$641$	−24.8380	+	43.0207i	−0.981042	+	1.69921i	−0.658354	+	0.752708i	$0.728747\pi$
$642$		0			0
$643$	−7.88034	+	10.2699i	−0.310770	+	0.405004i	−0.922459	−	0.386095i	$-0.873824\pi$
$643$	−7.88034	+	10.2699i	−0.310770	+	0.405004i	0.611689	+	0.791099i	$0.290490\pi$
$644$	−9.25425	−	10.2951i	−0.364669	−	0.405685i
$645$		0			0
$646$	6.31810	+	0.168081i	0.248582	+	0.00661307i
$647$	2.03731	+	2.03731i	0.0800948	+	0.0800948i	0.746019	−	0.665924i	$-0.231963\pi$
$647$	2.03731	+	2.03731i	0.0800948	+	0.0800948i	−0.665924	+	0.746019i	$0.731963\pi$
$648$		0			0
$649$	−45.2484	+	45.2484i	−1.77615	+	1.77615i
$650$	−0.870928	+	0.825790i	−0.0341606	+	0.0323901i
$651$		0			0
$652$	−6.97304	+	14.5880i	−0.273085	+	0.571309i
$653$	−22.6018	−	17.3430i	−0.884478	−	0.678684i	0.0631690	−	0.998003i	$-0.479879\pi$
$653$	−22.6018	−	17.3430i	−0.884478	−	0.678684i	−0.947647	+	0.319319i	$0.896546\pi$
$654$		0			0
$655$	28.2622	+	16.3172i	1.10430	+	0.637566i
$656$	−17.8135	+	46.1756i	−0.695502	+	1.80285i
$657$		0			0
$658$	−10.0857	+	12.4442i	−0.393182	+	0.485126i
$659$	−0.681616	+	5.17738i	−0.0265520	+	0.201682i	−0.999579	−	0.0290081i	$-0.990765\pi$
$659$	−0.681616	+	5.17738i	−0.0265520	+	0.201682i	0.973027	+	0.230690i	$0.0740985\pi$
$660$		0			0
$661$	−18.2899	+	2.40791i	−0.711393	+	0.0936567i	−0.477533	−	0.878614i	$-0.658469\pi$
$661$	−18.2899	+	2.40791i	−0.711393	+	0.0936567i	−0.233860	+	0.972270i	$0.575136\pi$
$662$	−26.1205	+	6.25946i	−1.01520	+	0.243281i
$663$		0			0
$664$	1.79412	+	9.74824i	0.0696254	+	0.378305i
$665$	−6.92333	−	6.92333i	−0.268475	−	0.268475i
$666$		0			0
$667$	18.2950	+	7.57806i	0.708387	+	0.293423i
$668$	37.9237	−	19.2833i	1.46731	−	0.746093i
$669$		0			0
$670$	−13.7238	+	9.96220i	−0.530197	+	0.384873i
$671$	28.2224	+	48.8827i	1.08951	+	1.88709i
$672$		0			0
$673$	25.3190	−	43.8538i	0.975976	−	1.69044i	0.299299	−	0.954159i	$-0.403247\pi$
$673$	25.3190	−	43.8538i	0.975976	−	1.69044i	0.676677	−	0.736280i	$-0.263419\pi$
$674$	4.40856	+	42.1135i	0.169811	+	1.62215i
$675$		0			0
$676$	−8.29954	+	12.7569i	−0.319213	+	0.490649i
$677$	28.1946	−	21.6345i	1.08361	−	0.831482i	0.0971132	−	0.995273i	$-0.469039\pi$
$677$	28.1946	−	21.6345i	1.08361	−	0.831482i	0.986495	+	0.163792i	$0.0523724\pi$
$678$		0			0
$679$	3.94201	−	14.7118i	0.151280	−	0.564586i
$680$	10.9956	−	5.22775i	0.421661	−	0.200475i
$681$		0			0
$682$	−29.4917	−	31.1037i	−1.12929	−	1.19102i
$683$	8.93273	−	21.5655i	0.341801	−	0.825182i	−0.655732	−	0.754993i	$-0.727640\pi$
$683$	8.93273	−	21.5655i	0.341801	−	0.825182i	0.997534	−	0.0701882i	$-0.0223600\pi$
$684$		0			0
$685$	−34.6292	+	14.3439i	−1.32312	+	0.548052i
$686$	9.70845	+	25.3229i	0.370670	+	0.966834i
$687$		0			0
$688$	−8.25173	+	5.03776i	−0.314594	+	0.192063i
$689$	−17.8849	+	10.3258i	−0.681360	+	0.393383i
$690$		0			0
$691$	3.02974	−	23.0132i	0.115257	−	0.875463i	−0.831952	−	0.554847i	$-0.812777\pi$
$691$	3.02974	−	23.0132i	0.115257	−	0.875463i	0.947209	−	0.320616i	$-0.103890\pi$
$692$	−9.08802	+	6.23487i	−0.345475	+	0.237014i
$693$		0			0
$694$	11.6116	+	3.44479i	0.440772	+	0.130762i
$695$	−13.2185	−	49.3321i	−0.501406	−	1.87127i
$696$		0			0
$697$	5.95107	−	22.2097i	0.225413	−	0.841252i
$698$	6.44991	−	10.5154i	0.244133	−	0.398016i
$699$		0			0
$700$	−1.22168	−	0.398074i	−0.0461751	−	0.0150458i
$701$	−7.72776	−	18.6565i	−0.291873	−	0.704645i	0.708126	−	0.706087i	$-0.249541\pi$
$701$	−7.72776	−	18.6565i	−0.291873	−	0.704645i	−0.999999	+	0.00144185i	$0.999541\pi$
$702$		0			0
$703$	8.46414			0.319231
$704$	−32.8939	−	9.83320i	−1.23974	−	0.370603i
$705$		0			0
$706$	−1.14192	−	1.57309i	−0.0429766	−	0.0592040i
$707$	−9.16064	+	11.9384i	−0.344521	+	0.448989i
$708$		0			0
$709$	−2.20742	+	1.69381i	−0.0829013	+	0.0636124i	−0.649381	−	0.760464i	$-0.724972\pi$
$709$	−2.20742	+	1.69381i	−0.0829013	+	0.0636124i	0.566479	+	0.824076i	$0.308305\pi$
$710$	1.73813	+	3.20442i	0.0652309	+	0.120260i
$711$		0			0
$712$	−13.1317	−	6.71165i	−0.492132	−	0.251530i
$713$	7.19833	+	26.8645i	0.269579	+	1.00608i
$714$		0			0
$715$	−22.8823	+	3.01252i	−0.855751	+	0.112662i
$716$	39.8526	+	19.0495i	1.48936	+	0.711915i
$717$		0			0
$718$	10.5868	−	4.05884i	0.395097	−	0.151474i
$719$			21.4415i			0.799633i	0.916595	+	0.399816i	$0.130926\pi$
$719$			21.4415i			0.799633i	−0.916595	+	0.399816i	$0.869074\pi$
$720$		0			0
$721$		−	9.37100i		−	0.348994i
$722$	−6.69083	−	17.4519i	−0.249007	−	0.649494i
$723$		0			0
$724$	35.2521	−	12.4503i	1.31013	−	0.462713i
$725$	1.82231	−	0.239911i	0.0676788	−	0.00891009i
$726$		0			0
$727$	−2.39788	−	8.94901i	−0.0889325	−	0.331900i	0.907097	−	0.420921i	$-0.138293\pi$
$727$	−2.39788	−	8.94901i	−0.0889325	−	0.331900i	−0.996030	+	0.0890205i	$0.971626\pi$
$728$	11.5052	+	0.919957i	0.426410	+	0.0340959i
$729$		0			0
$730$	−28.0655	+	15.2232i	−1.03875	+	0.563435i
$731$	3.56338	−	2.73428i	0.131797	−	0.101131i
$732$		0			0
$733$	11.6914	−	15.2365i	0.431832	−	0.562774i	−0.525860	−	0.850571i	$-0.676256\pi$
$733$	11.6914	−	15.2365i	0.431832	−	0.562774i	0.957691	+	0.287797i	$0.0929229\pi$
$734$	−40.6852	+	29.5336i	−1.50172	+	1.09011i
$735$		0			0
$736$	15.7195	+	15.7851i	0.579427	+	0.581848i
$737$	−22.2166			−0.818357
$738$		0			0
$739$	1.58086	+	3.81654i	0.0581529	+	0.140394i	0.950285	−	0.311380i	$-0.100791\pi$
$739$	1.58086	+	3.81654i	0.0581529	+	0.140394i	−0.892132	+	0.451774i	$0.850791\pi$
$740$	14.5338	−	7.39007i	0.534273	−	0.271665i
$741$		0			0
$742$	−18.8465	−	11.5600i	−0.691877	−	0.424380i
$743$	0.523506	−	1.95375i	0.0192056	−	0.0716762i	−0.955658	−	0.294479i	$-0.904854\pi$
$743$	0.523506	−	1.95375i	0.0192056	−	0.0716762i	0.974864	+	0.222803i	$0.0715206\pi$
$744$		0			0
$745$	−6.82740	−	25.4802i	−0.250136	−	0.933522i
$746$	−9.35587	+	31.5366i	−0.342543	+	1.15464i
$747$		0			0
$748$	15.6805	+	2.91974i	0.573337	+	0.106756i
$749$	−1.68256	+	12.7803i	−0.0614793	+	0.466982i
$750$		0			0
$751$	−13.0403	+	7.52882i	−0.475847	+	0.274730i	−0.718684	−	0.695337i	$-0.755255\pi$
$751$	−13.0403	+	7.52882i	−0.475847	+	0.274730i	0.242837	+	0.970067i	$0.421922\pi$
$752$	15.1863	−	20.8290i	0.553787	−	0.759556i
$753$		0			0
$754$	−15.4164	+	5.91043i	−0.561432	+	0.215245i
$755$	31.4031	−	13.0076i	1.14287	−	0.473394i
$756$		0			0
$757$	10.9898	−	26.5317i	0.399430	−	0.964310i	−0.588371	−	0.808591i	$-0.700231\pi$
$757$	10.9898	−	26.5317i	0.399430	−	0.964310i	0.987801	−	0.155719i	$-0.0497694\pi$
$758$	6.39965	−	6.06797i	0.232446	−	0.220399i
$759$		0			0
$760$	11.6961	+	10.5577i	0.424261	+	0.382969i
$761$	6.33331	−	23.6362i	0.229582	−	0.856813i	−0.750934	−	0.660377i	$-0.770397\pi$
$761$	6.33331	−	23.6362i	0.229582	−	0.856813i	0.980517	−	0.196436i	$-0.0629367\pi$
$762$		0			0
$763$	24.7968	−	19.0273i	0.897706	−	0.688834i
$764$	−29.3453	+	6.21197i	−1.06168	+	0.224741i
$765$		0			0
$766$	−40.3788	+	4.22696i	−1.45894	+	0.152726i
$767$	−17.3097	+	29.9812i	−0.625016	+	1.08256i
$768$		0			0
$769$	−1.81707	−	3.14725i	−0.0655252	−	0.113493i	0.831402	−	0.555672i	$-0.187539\pi$
$769$	−1.81707	−	3.14725i	−0.0655252	−	0.113493i	−0.896927	+	0.442179i	$0.854206\pi$
$770$	−14.5151	−	19.9959i	−0.523089	−	0.720602i
$771$		0			0
$772$	−0.774522	+	2.37699i	−0.0278756	+	0.0855496i
$773$	3.52157	+	1.45868i	0.126662	+	0.0524652i	0.445114	−	0.895474i	$-0.353163\pi$
$773$	3.52157	+	1.45868i	0.126662	+	0.0524652i	−0.318452	+	0.947939i	$0.603163\pi$
$774$		0			0
$775$	1.82539	+	1.82539i	0.0655699	+	0.0655699i
$776$	−5.12595	+	23.9682i	−0.184011	+	0.860410i
$777$		0			0
$778$	0.726715	+	3.03256i	0.0260540	+	0.108722i
$779$	29.5021	−	3.88403i	1.05702	−	0.139160i
$780$		0			0
$781$	−0.623364	+	4.73492i	−0.0223057	+	0.169429i
$782$	−8.04036	−	6.51650i	−0.287523	−	0.233030i
$783$		0			0
$784$	−6.33893	−	14.3016i	−0.226390	−	0.510772i
$785$	3.40735	+	1.96723i	0.121613	+	0.0702135i
$786$		0			0
$787$	12.9142	+	9.90945i	0.460343	+	0.353234i	0.812749	−	0.582613i	$-0.197970\pi$
$787$	12.9142	+	9.90945i	0.460343	+	0.353234i	−0.352406	+	0.935847i	$0.614636\pi$
$788$	0.225822	+	0.639395i	0.00804456	+	0.0227775i
$789$		0			0
$790$	−20.5822	−	21.7072i	−0.732280	−	0.772307i
$791$	10.4835	−	10.4835i	0.372749	−	0.372749i
$792$		0			0
$793$	21.5929	+	21.5929i	0.766785	+	0.766785i
$794$	−0.251915	+	9.46936i	−0.00894012	+	0.336055i
$795$		0			0
$796$	0.645293	−	12.1195i	0.0228718	−	0.429566i
$797$	−9.20430	+	11.9953i	−0.326033	+	0.424895i	−0.927396	−	0.374082i	$-0.877958\pi$
$797$	−9.20430	+	11.9953i	−0.326033	+	0.424895i	0.601363	+	0.798976i	$0.294625\pi$
$798$		0			0
$799$	−5.98781	+	10.3712i	−0.211833	+	0.366906i
$800$	1.99616	+	0.539332i	0.0705749	+	0.0190683i
$801$		0			0
$802$	−0.406448	−	3.88266i	−0.0143522	−	0.137102i
$803$	−41.4701	−	5.45964i	−1.46345	−	0.192667i
$804$		0			0
$805$	2.09270	+	15.8956i	0.0737580	+	0.560247i
$806$	−19.7667	−	12.1244i	−0.696252	−	0.427063i
$807$		0			0
$808$	13.7411	−	19.9400i	0.483412	−	0.701487i
$809$	31.8739	−	31.8739i	1.12063	−	1.12063i	0.128980	−	0.991647i	$-0.458830\pi$
$809$	31.8739	−	31.8739i	1.12063	−	1.12063i	0.991647	−	0.128980i	$-0.0411703\pi$
$810$		0			0
$811$	−7.59731	+	18.3415i	−0.266778	+	0.644058i	−0.999328	−	0.0366546i	$-0.988330\pi$
$811$	−7.59731	+	18.3415i	−0.266778	+	0.644058i	0.732550	+	0.680713i	$0.238330\pi$
$812$	−13.4313	−	11.4908i	−0.471346	−	0.403248i
$813$		0			0
$814$	21.0958	+	3.35026i	0.739407	+	0.117427i
$815$	16.2176	−	9.36323i	0.568077	−	0.327980i
$816$		0			0
$817$	5.03399	+	2.90637i	0.176117	+	0.101681i
$818$	13.8664	+	11.2383i	0.484826	+	0.392939i
$819$		0			0
$820$	47.2670	−	32.4277i	1.65063	−	1.13242i
$821$	−6.74524	−	8.79056i	−0.235410	−	0.306793i	0.660677	−	0.750670i	$-0.270269\pi$
$821$	−6.74524	−	8.79056i	−0.235410	−	0.306793i	−0.896088	+	0.443877i	$0.853603\pi$
$822$		0			0
$823$	18.3772	+	4.92417i	0.640590	+	0.171646i	0.564471	−	0.825453i	$-0.309080\pi$
$823$	18.3772	+	4.92417i	0.640590	+	0.171646i	0.0761196	+	0.997099i	$0.475747\pi$
$824$	0.770409	+	15.0607i	0.0268385	+	0.524664i
$825$		0			0
$826$	−37.0498	−	0.985641i	−1.28913	−	0.0342948i
$827$	−9.16153	−	3.79483i	−0.318578	−	0.131959i	0.217664	−	0.976024i	$-0.430156\pi$
$827$	−9.16153	−	3.79483i	−0.318578	−	0.131959i	−0.536241	+	0.844065i	$0.680156\pi$
$828$		0			0
$829$	−1.43211	−	3.45742i	−0.0497393	−	0.120081i	0.897057	−	0.441915i	$-0.145701\pi$
$829$	−1.43211	−	3.45742i	−0.0497393	−	0.120081i	−0.946796	+	0.321834i	$0.895701\pi$
$830$	4.67364	−	10.4854i	0.162225	−	0.363954i
$831$		0			0
$832$	−18.5663	−	0.532655i	−0.643670	−	0.0184665i
$833$	3.63381	+	6.29395i	0.125904	+	0.218072i
$834$		0			0
$835$	−48.8529	−	6.43161i	−1.69062	−	0.222575i
$836$	4.27483	+	20.1943i	0.147848	+	0.698434i
$837$		0			0
$838$	−1.16066	−	2.13980i	−0.0400944	−	0.0739181i
$839$	−11.9369	+	3.19848i	−0.412107	+	0.110424i	−0.458915	−	0.888480i	$-0.651762\pi$
$839$	−11.9369	+	3.19848i	−0.412107	+	0.110424i	0.0468078	+	0.998904i	$0.485095\pi$
$840$		0			0
$841$	−3.58819	−	0.961452i	−0.123731	−	0.0331535i
$842$	11.2905	+	47.1150i	0.389097	+	1.62369i
$843$		0			0
$844$	1.21327	+	15.5821i	0.0417623	+	0.536358i
$845$	16.2847	−	6.74534i	0.560210	−	0.232047i
$846$		0			0
$847$		−	13.0365i		−	0.447939i
$848$	31.2397	+	17.0293i	1.07278	+	0.584788i
$849$		0			0
$850$	−0.948737	−	0.150671i	−0.0325414	−	0.00516796i
$851$	−10.9958	−	8.43741i	−0.376933	−	0.289231i
$852$		0			0
$853$	−27.8305	−	36.2695i	−0.952899	−	1.24184i	−0.970278	−	0.241994i	$-0.922199\pi$
$853$	−27.8305	−	36.2695i	−0.952899	−	1.24184i	0.0173784	−	0.999849i	$-0.494468\pi$
$854$	−9.29818	+	31.3422i	−0.318177	+	1.07251i
$855$		0			0
$856$	1.65345	−	20.6783i	0.0565136	−	0.706770i
$857$	24.0251	−	6.43751i	0.820682	−	0.219901i	0.176037	−	0.984383i	$-0.443672\pi$
$857$	24.0251	−	6.43751i	0.820682	−	0.219901i	0.644645	+	0.764482i	$0.277005\pi$
$858$		0			0
$859$	7.03901	+	53.4666i	0.240168	+	1.82426i	0.508653	+	0.860972i	$0.330144\pi$
$859$	7.03901	+	53.4666i	0.240168	+	1.82426i	−0.268485	+	0.963284i	$0.586523\pi$
$860$	11.1814	+	0.595344i	0.381284	+	0.0203011i
$861$		0			0
$862$	7.83900	+	3.49406i	0.266997	+	0.119008i
$863$	−1.48658			−0.0506037			−0.0253019	−	0.999680i	$-0.508055\pi$
$863$	−1.48658			−0.0506037			−0.0253019	+	0.999680i	$0.508055\pi$
$864$		0			0
$865$	12.7645			0.434005
$866$	28.8650	+	12.8659i	0.980871	+	0.437202i
$867$		0			0
$868$	1.31994	−	24.7905i	0.0448018	−	0.841443i
$869$	−5.11515	−	38.8534i	−0.173519	−	1.31801i
$870$		0			0
$871$	−11.6097	+	3.11081i	−0.393380	+	0.105406i
$872$	−38.2882	+	32.6185i	−1.29660	+	1.10460i
$873$		0			0
$874$	3.80941	−	12.8407i	0.128855	−	0.434343i
$875$	−11.4861	−	14.9690i	−0.388301	−	0.506043i
$876$		0			0
$877$	−21.6332	−	16.5997i	−0.730502	−	0.560534i	0.175157	−	0.984540i	$-0.443957\pi$
$877$	−21.6332	−	16.5997i	−0.730502	−	0.560534i	−0.905659	+	0.424007i	$0.860623\pi$
$878$	5.78279	+	0.918375i	0.195160	+	0.0309937i
$879$		0			0
$880$	24.9721	+	30.9433i	0.841808	+	1.04310i
$881$			16.3864i			0.552073i	0.961147	+	0.276036i	$0.0890211\pi$
$881$			16.3864i			0.552073i	−0.961147	+	0.276036i	$0.910979\pi$
$882$		0			0
$883$	−35.6527	+	14.7678i	−1.19981	+	0.496977i	−0.890937	−	0.454127i	$-0.849951\pi$
$883$	−35.6527	+	14.7678i	−1.19981	+	0.496977i	−0.308872	+	0.951104i	$0.599951\pi$
$884$	8.60301	−	0.669854i	0.289351	−	0.0225296i
$885$		0			0
$886$	7.47822	+	31.2063i	0.251236	+	1.04840i
$887$	−0.902923	−	0.241937i	−0.0303172	−	0.00812347i	0.243629	−	0.969869i	$-0.421662\pi$
$887$	−0.902923	−	0.241937i	−0.0303172	−	0.00812347i	−0.273946	+	0.961745i	$0.588329\pi$
$888$		0			0
$889$	10.9558	−	2.93559i	0.367445	−	0.0984566i
$890$	8.14373	+	15.0138i	0.272979	+	0.503264i
$891$		0			0
$892$	−31.3752	+	6.64167i	−1.05052	+	0.222380i
$893$	−15.3657	−	2.02293i	−0.514193	−	0.0676948i
$894$		0			0
$895$	−25.5793	−	44.3046i	−0.855021	−	1.48094i
$896$	−8.97581	−	17.7438i	−0.299861	−	0.592780i
$897$		0			0
$898$	−17.7999	+	39.9344i	−0.593991	+	1.33263i
$899$	13.5901	+	32.8095i	0.453257	+	1.09426i
$900$		0			0
$901$	−15.2714	−	6.32560i	−0.508763	−	0.210736i
$902$	75.0676	+	1.99704i	2.49948	+	0.0664940i
$903$		0			0
$904$	−15.9867	+	17.7105i	−0.531711	+	0.589042i
$905$	−41.8244	−	11.2068i	−1.39029	−	0.372527i
$906$		0			0
$907$	−8.66795	−	11.2963i	−0.287815	−	0.375087i	0.626960	−	0.779051i	$-0.284299\pi$
$907$	−8.66795	−	11.2963i	−0.287815	−	0.375087i	−0.914775	+	0.403964i	$0.867632\pi$
$908$	26.6092	+	38.7858i	0.883056	+	1.28715i
$909$		0			0
$910$	−10.3851	−	8.41682i	−0.344261	−	0.279015i
$911$	12.0229	+	6.94141i	0.398336	+	0.229979i	0.685766	−	0.727822i	$-0.259468\pi$
$911$	12.0229	+	6.94141i	0.398336	+	0.229979i	−0.287430	+	0.957802i	$0.592801\pi$
$912$		0			0
$913$	13.0244	−	7.51964i	0.431044	−	0.248864i
$914$	21.0148	+	3.33739i	0.695107	+	0.110391i
$915$		0			0
$916$	−9.67972	+	11.3144i	−0.319827	+	0.373837i
$917$	−9.47605	+	22.8772i	−0.312927	+	0.755472i
$918$		0			0
$919$	26.8207	−	26.8207i	0.884735	−	0.884735i	−0.109277	−	0.994011i	$-0.534853\pi$
$919$	26.8207	−	26.8207i	0.884735	−	0.884735i	0.994011	+	0.109277i	$0.0348534\pi$
$920$	−4.67012	−	25.3748i	−0.153969	−	0.836582i
$921$		0			0
$922$	−7.58357	−	4.65157i	−0.249752	−	0.153191i
$923$	0.337243	+	2.56161i	0.0111005	+	0.0843166i
$924$		0			0
$925$	−1.27546	−	0.167917i	−0.0419368	−	0.00552108i
$926$	−5.84814	−	55.8654i	−0.192182	−	1.83585i
$927$		0			0
$928$	22.5309	+	17.3633i	0.739614	+	0.569979i
$929$	−13.2213	+	22.9000i	−0.433777	+	0.751323i	−0.997195	−	0.0748486i	$-0.976153\pi$
$929$	−13.2213	+	22.9000i	−0.433777	+	0.751323i	0.563418	+	0.826172i	$0.309486\pi$
$930$		0			0
$931$	−5.72566	+	7.46182i	−0.187651	+	0.244551i
$932$	16.2297	+	0.864135i	0.531622	+	0.0283057i
$933$		0			0
$934$	−1.02423	+	38.5004i	−0.0335139	+	1.25977i
$935$	−13.0624	−	13.0624i	−0.427186	−	0.427186i
$936$		0			0
$937$	−6.06603	+	6.06603i	−0.198169	+	0.198169i	−0.799215	−	0.601046i	$-0.794751\pi$
$937$	−6.06603	+	6.06603i	−0.198169	+	0.198169i	0.601046	+	0.799215i	$0.294751\pi$
$938$	−8.85359	−	9.33753i	−0.289080	−	0.304881i
$939$		0			0
$940$	−28.1507	+	9.94227i	−0.918174	+	0.324281i
$941$	8.93688	+	6.85751i	0.291334	+	0.223548i	0.744079	−	0.668092i	$-0.232889\pi$
$941$	8.93688	+	6.85751i	0.291334	+	0.223548i	−0.452745	+	0.891640i	$0.649555\pi$
$942$		0			0
$943$	−42.1982	−	24.3632i	−1.37416	−	0.793374i
$944$	59.6259	−	1.46186i	1.94066	−	0.0475793i
$945$		0			0
$946$	11.3962	+	9.23631i	0.370522	+	0.300298i
$947$	−4.99125	+	37.9123i	−0.162194	+	1.23198i	0.695767	+	0.718268i	$0.255065\pi$
$947$	−4.99125	+	37.9123i	−0.162194	+	1.23198i	−0.857960	+	0.513716i	$0.828269\pi$
$948$		0			0
$949$	−22.4355	+	2.95369i	−0.728288	+	0.0958810i
$950$	−0.289715	−	1.20897i	−0.00939959	−	0.0392241i
$951$		0			0
$952$	5.02174	+	7.75402i	0.162756	+	0.251309i
$953$	−21.1060	−	21.1060i	−0.683689	−	0.683689i	0.277140	−	0.960829i	$-0.410613\pi$
$953$	−21.1060	−	21.1060i	−0.683689	−	0.683689i	−0.960829	+	0.277140i	$0.910613\pi$
$954$		0			0
$955$	32.0959	+	13.2945i	1.03860	+	0.430201i
$956$	−14.3322	−	4.67003i	−0.463537	−	0.151040i
$957$		0			0
$958$	−8.64853	−	11.9141i	−0.279421	−	0.384928i
$959$	−14.2203	−	24.6303i	−0.459199	−	0.795355i
$960$		0			0
$961$	−9.43857	+	16.3481i	−0.304470	+	0.527357i
$962$	11.4931	−	1.20313i	0.370554	−	0.0387906i
$963$		0			0
$964$	6.44218	+	30.4329i	0.207489	+	0.980176i
$965$	2.29711	−	1.76263i	0.0739465	−	0.0567411i
$966$		0			0
$967$	6.07416	−	22.6691i	0.195332	−	0.728988i	−0.796849	−	0.604179i	$-0.793501\pi$
$967$	6.07416	−	22.6691i	0.195332	−	0.728988i	0.992181	−	0.124810i	$-0.0398320\pi$
$968$	1.07176	+	20.9517i	0.0344475	+	0.673413i
$969$		0			0
$970$	20.5996	−	19.5319i	0.661412	−	0.627133i
$971$	−1.72920	+	4.17465i	−0.0554926	+	0.133971i	−0.949194	−	0.314691i	$-0.898099\pi$
$971$	−1.72920	+	4.17465i	−0.0554926	+	0.133971i	0.893702	+	0.448662i	$0.148099\pi$
$972$		0			0
$973$	35.8025	−	14.8299i	1.14777	−	0.475424i
$974$	4.90306	−	1.87976i	0.157104	−	0.0602315i
$975$		0			0
$976$	12.3670	−	51.1363i	0.395857	−	1.63683i
$977$	−17.3350	+	10.0084i	−0.554597	+	0.320197i	−0.750974	−	0.660332i	$-0.770416\pi$
$977$	−17.3350	+	10.0084i	−0.554597	+	0.320197i	0.196377	+	0.980528i	$0.437082\pi$
$978$		0			0
$979$	−2.92067	+	22.1847i	−0.0933451	+	0.709027i
$980$	−3.31659	+	17.8118i	−0.105945	+	0.568977i
$981$		0			0
$982$	7.12896	−	24.0302i	0.227494	−	0.766833i
$983$	9.78459	+	36.5166i	0.312080	+	1.16470i	0.926678	+	0.375857i	$0.122652\pi$
$983$	9.78459	+	36.5166i	0.312080	+	1.16470i	−0.614598	+	0.788841i	$0.710682\pi$
$984$		0			0
$985$	0.203267	−	0.758603i	0.00647662	−	0.0241711i
$986$	−11.2648	−	6.90953i	−0.358744	−	0.220044i
$987$		0			0
$988$	5.06155	+	9.95437i	0.161029	+	0.316691i
$989$	−3.64251	−	8.79379i	−0.115825	−	0.279626i
$990$		0			0
$991$	−52.8446			−1.67866			−0.839332	−	0.543619i	$-0.817054\pi$
$991$	−52.8446			−1.67866			−0.839332	+	0.543619i	$0.817054\pi$
$992$	−0.0832846	+	39.9507i	−0.00264429	+	1.26844i
$993$		0			0
$994$	−2.23849	+	1.62493i	−0.0710005	+	0.0515397i
$995$	−8.55705	+	11.1518i	−0.271277	+	0.353535i
$996$		0			0
$997$	48.4313	−	37.1627i	1.53384	−	1.17695i	0.611078	−	0.791570i	$-0.290736\pi$
$997$	48.4313	−	37.1627i	1.53384	−	1.17695i	0.922757	−	0.385383i	$-0.125931\pi$
$998$	−27.4263	+	14.8765i	−0.868165	+	0.470906i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bk.a.613.17		368
3.2	odd	2		288.2.bc.a.133.30	yes	368
9.4	even	3	inner	864.2.bk.a.37.15		368
9.5	odd	6		288.2.bc.a.229.32	yes	368
32.13	even	8	inner	864.2.bk.a.397.15		368
96.77	odd	8		288.2.bc.a.205.32	yes	368
288.13	even	24	inner	864.2.bk.a.685.17		368
288.77	odd	24		288.2.bc.a.13.30	✓	368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bc.a.13.30	✓	368	288.77	odd	24
288.2.bc.a.133.30	yes	368	3.2	odd	2
288.2.bc.a.205.32	yes	368	96.77	odd	8
288.2.bc.a.229.32	yes	368	9.5	odd	6
864.2.bk.a.37.15		368	9.4	even	3	inner
864.2.bk.a.397.15		368	32.13	even	8	inner
864.2.bk.a.613.17		368	1.1	even	1	trivial
864.2.bk.a.685.17		368	288.13	even	24	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bk (of order \(24\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.575751 + 1.29171i) q^{2} +(-1.33702 - 1.48741i) q^{4} +(0.302346 + 2.29654i) q^{5} +(-1.69771 + 0.454899i) q^{7} +(2.69109 - 0.870667i) q^{8} +O(q^{10})\)	\(q+(-0.575751 + 1.29171i) q^{2} +(-1.33702 - 1.48741i) q^{4} +(0.302346 + 2.29654i) q^{5} +(-1.69771 + 0.454899i) q^{7} +(2.69109 - 0.870667i) q^{8} +(-3.14054 - 0.931695i) q^{10} +(-2.61252 - 3.40470i) q^{11} +(-1.84196 - 1.41338i) q^{13} +(0.389859 - 2.45485i) q^{14} +(-0.424748 + 3.97738i) q^{16} -1.85832i q^{17} +(2.22188 - 0.920333i) q^{19} +(3.01165 - 3.52024i) q^{20} +(5.90204 - 1.41435i) q^{22} +(-3.80389 - 1.01925i) q^{23} +(-0.353072 + 0.0946054i) q^{25} +(2.88619 - 1.56552i) q^{26} +(2.94649 + 1.91697i) q^{28} +(-4.98542 - 0.656343i) q^{29} +(-3.53119 - 6.11620i) q^{31} +(-4.89307 - 2.83863i) q^{32} +(2.40040 + 1.06993i) q^{34} +(-1.55799 - 3.76132i) q^{35} +(3.25157 + 1.34684i) q^{37} +(-0.0904482 + 3.39990i) q^{38} +(2.81316 + 5.91695i) q^{40} +(11.9515 + 3.20240i) q^{41} +(1.47137 + 1.91753i) q^{43} +(-1.57118 + 8.43803i) q^{44} +(3.50667 - 4.32669i) q^{46} +(-5.58096 - 3.22217i) q^{47} +(-3.38691 + 1.95543i) q^{49} +(0.0810791 - 0.510536i) q^{50} +(0.360463 + 4.62946i) q^{52} +(3.40394 - 8.21784i) q^{53} +(7.02916 - 7.02916i) q^{55} +(-4.17260 + 2.70231i) q^{56} +(3.71817 - 6.06182i) q^{58} +(-1.94627 - 14.7834i) q^{59} +(-13.0401 - 1.71676i) q^{61} +(9.93343 - 1.03986i) q^{62} +(6.48388 - 4.68608i) q^{64} +(2.68899 - 4.65747i) q^{65} +(3.15146 - 4.10706i) q^{67} +(-2.76407 + 2.48461i) q^{68} +(5.75554 + 0.153115i) q^{70} +(-0.786895 - 0.786895i) q^{71} +(6.89191 - 6.89191i) q^{73} +(-3.61182 + 3.42463i) q^{74} +(-4.33961 - 2.07433i) q^{76} +(5.98408 + 4.59174i) q^{77} +(7.90822 + 4.56581i) q^{79} +(-9.26266 + 0.227094i) q^{80} +(-11.0177 + 13.5941i) q^{82} +(-0.457417 + 3.47443i) q^{83} +(4.26771 - 0.561854i) q^{85} +(-3.32404 + 0.796566i) q^{86} +(-9.99487 - 6.88770i) q^{88} +(-3.68687 - 3.68687i) q^{89} +(3.77005 + 1.56161i) q^{91} +(3.56985 + 7.02069i) q^{92} +(7.37534 - 5.35380i) q^{94} +(2.78536 + 4.82439i) q^{95} +(-4.33284 + 7.50470i) q^{97} +(-0.575832 - 5.50074i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 16 q^{8}+O(q^{10}) \) 368 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 16 * q^8	\( 368 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 16 q^{8} - 16 q^{10} + 4 q^{11} - 4 q^{13} + 4 q^{14} - 4 q^{16} - 16 q^{19} + 4 q^{20} - 4 q^{22} + 4 q^{23} - 4 q^{25} + 16 q^{26} - 16 q^{28} + 4 q^{29} - 8 q^{31} + 4 q^{32} + 4 q^{34} + 16 q^{35} - 16 q^{37} + 60 q^{38} - 4 q^{40} + 4 q^{41} - 4 q^{43} + 104 q^{44} - 16 q^{46} - 48 q^{50} - 4 q^{52} + 16 q^{53} - 16 q^{55} + 84 q^{56} - 40 q^{58} + 4 q^{59} - 4 q^{61} + 24 q^{62} - 16 q^{64} + 8 q^{65} - 4 q^{67} - 12 q^{68} - 4 q^{70} + 16 q^{71} - 16 q^{73} + 4 q^{74} + 20 q^{76} + 4 q^{77} - 48 q^{80} - 16 q^{82} - 36 q^{83} + 16 q^{85} - 100 q^{86} - 4 q^{88} + 16 q^{89} - 16 q^{91} + 80 q^{92} - 20 q^{94} + 136 q^{95} - 8 q^{97} - 104 q^{98}+O(q^{100}) \) 368 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 16 * q^8 - 16 * q^10 + 4 * q^11 - 4 * q^13 + 4 * q^14 - 4 * q^16 - 16 * q^19 + 4 * q^20 - 4 * q^22 + 4 * q^23 - 4 * q^25 + 16 * q^26 - 16 * q^28 + 4 * q^29 - 8 * q^31 + 4 * q^32 + 4 * q^34 + 16 * q^35 - 16 * q^37 + 60 * q^38 - 4 * q^40 + 4 * q^41 - 4 * q^43 + 104 * q^44 - 16 * q^46 - 48 * q^50 - 4 * q^52 + 16 * q^53 - 16 * q^55 + 84 * q^56 - 40 * q^58 + 4 * q^59 - 4 * q^61 + 24 * q^62 - 16 * q^64 + 8 * q^65 - 4 * q^67 - 12 * q^68 - 4 * q^70 + 16 * q^71 - 16 * q^73 + 4 * q^74 + 20 * q^76 + 4 * q^77 - 48 * q^80 - 16 * q^82 - 36 * q^83 + 16 * q^85 - 100 * q^86 - 4 * q^88 + 16 * q^89 - 16 * q^91 + 80 * q^92 - 20 * q^94 + 136 * q^95 - 8 * q^97 - 104 * q^98

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