LMFDB - Embedded newform 684.2.cf.c.127.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,2,Mod(91,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 11]))

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

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

chi := DirichletCharacter("684.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	684.cf (of order $18$, degree $6$, 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:	$5.46176749826$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 228)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			127.3
Character	$\chi$	$=$	684.127
Dual form			684.2.cf.c.307.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.13356 + 0.845604i) q^{2} +(0.569909 - 1.91708i) q^{4} +(-0.162908 - 0.923898i) q^{5} +(2.27351 + 1.31261i) q^{7} +(0.975067 + 2.65504i) q^{8} +(0.965918 + 0.909537i) q^{10} +(5.14137 - 2.96837i) q^{11} +(-1.39481 - 3.83220i) q^{13} +(-3.68710 + 0.434566i) q^{14} +(-3.35041 - 2.18512i) q^{16} +(-2.94059 + 2.46745i) q^{17} +(-4.31383 - 0.625180i) q^{19} +(-1.86403 - 0.214229i) q^{20} +(-3.31798 + 7.71239i) q^{22} +(-0.401333 - 0.0707658i) q^{23} +(3.87141 - 1.40908i) q^{25} +(4.82161 + 3.16457i) q^{26} +(3.81207 - 3.61043i) q^{28} +(4.15634 - 4.95333i) q^{29} +(-3.66403 + 6.34629i) q^{31} +(5.64563 - 0.356152i) q^{32} +(1.24685 - 5.28357i) q^{34} +(0.842345 - 2.31432i) q^{35} -2.51566i q^{37} +(5.41864 - 2.93911i) q^{38} +(2.29414 - 1.33339i) q^{40} +(1.57709 - 4.33302i) q^{41} +(11.3090 - 1.99407i) q^{43} +(-2.76050 - 11.5481i) q^{44} +(0.514774 - 0.259151i) q^{46} +(2.45354 - 2.92401i) q^{47} +(-0.0541088 - 0.0937192i) q^{49} +(-3.19695 + 4.87096i) q^{50} +(-8.14155 + 0.489954i) q^{52} +(4.84195 + 0.853766i) q^{53} +(-3.58005 - 4.26653i) q^{55} +(-1.26821 + 7.31614i) q^{56} +(-0.522897 + 9.12951i) q^{58} +(-1.21047 + 1.01570i) q^{59} +(1.11276 - 6.31077i) q^{61} +(-1.21305 - 10.2922i) q^{62} +(-6.09849 + 5.17769i) q^{64} +(-3.31333 + 1.91295i) q^{65} +(2.22499 + 1.86699i) q^{67} +(3.05443 + 7.04358i) q^{68} +(1.00215 + 3.33571i) q^{70} +(1.17754 + 6.67818i) q^{71} +(11.1504 + 4.05843i) q^{73} +(2.12725 + 2.85164i) q^{74} +(-3.65701 + 7.91368i) q^{76} +15.5853 q^{77} +(4.29071 + 1.56169i) q^{79} +(-1.47302 + 3.45141i) q^{80} +(1.87629 + 6.24532i) q^{82} +(0.641515 + 0.370379i) q^{83} +(2.75872 + 2.31484i) q^{85} +(-11.1332 + 11.8233i) q^{86} +(12.8943 + 10.7562i) q^{88} +(-5.87516 - 16.1419i) q^{89} +(1.85908 - 10.5434i) q^{91} +(-0.364387 + 0.729058i) q^{92} +(-0.308673 + 5.38926i) q^{94} +(0.125156 + 4.08739i) q^{95} +(2.43876 + 2.90640i) q^{97} +(0.140585 + 0.0604816i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 3 q^{2} - 3 q^{4} - 3 q^{8} - 6 q^{10} - 6 q^{13} + 9 q^{14} - 27 q^{16} - 18 q^{19} - 30 q^{20} + 12 q^{22} - 18 q^{28} + 12 q^{31} + 63 q^{32} - 39 q^{34} + 48 q^{38} + 33 q^{40} + 12 q^{41} + 18 q^{43}+ \cdots - 117 q^{98}+O(q^{100}) $ 60 * q + 3 * q^2 - 3 * q^4 - 3 * q^8 - 6 * q^10 - 6 * q^13 + 9 * q^14 - 27 * q^16 - 18 * q^19 - 30 * q^20 + 12 * q^22 - 18 * q^28 + 12 * q^31 + 63 * q^32 - 39 * q^34 + 48 * q^38 + 33 * q^40 + 12 * q^41 + 18 * q^43 + 9 * q^44 - 69 * q^46 + 30 * q^49 + 27 * q^50 - 3 * q^52 - 12 * q^53 + 42 * q^56 - 36 * q^58 - 27 * q^62 + 21 * q^64 + 36 * q^65 - 42 * q^67 - 93 * q^68 + 132 * q^70 + 24 * q^71 + 18 * q^73 - 27 * q^74 + 66 * q^76 + 72 * q^77 - 12 * q^79 - 6 * q^80 - 9 * q^82 - 60 * q^85 - 123 * q^86 + 36 * q^88 + 12 * q^89 + 84 * q^91 + 99 * q^92 - 24 * q^95 + 12 * q^97 - 117 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$-1$	$1$

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 $

$2$	−1.13356	+	0.845604i	−0.801547	+	0.597932i
$2$	−1.13356	+	0.845604i	−0.801547	+	0.597932i
$3$		0			0
$3$		0			0
$4$	0.569909	−	1.91708i	0.284954	−	0.958541i
$5$	−0.162908	−	0.923898i	−0.0728547	−	0.413180i	−0.999322	−	0.0368055i	$-0.988282\pi$
$5$	−0.162908	−	0.923898i	−0.0728547	−	0.413180i	0.926468	−	0.376374i	$-0.122829\pi$
$6$		0			0
$7$	2.27351	+	1.31261i	0.859305	+	0.496120i	0.863780	−	0.503870i	$-0.168091\pi$
$7$	2.27351	+	1.31261i	0.859305	+	0.496120i	−0.00447442	+	0.999990i	$0.501424\pi$
$8$	0.975067	+	2.65504i	0.344738	+	0.938699i
$9$		0			0
$10$	0.965918	+	0.909537i	0.305450	+	0.287621i
$11$	5.14137	−	2.96837i	1.55018	−	0.894998i	0.552057	−	0.833807i	$-0.313843\pi$
$11$	5.14137	−	2.96837i	1.55018	−	0.894998i	0.998126	−	0.0611917i	$-0.0194901\pi$
$12$		0			0
$13$	−1.39481	−	3.83220i	−0.386850	−	1.06286i	−0.968411	−	0.249358i	$-0.919780\pi$
$13$	−1.39481	−	3.83220i	−0.386850	−	1.06286i	0.581562	−	0.813502i	$-0.302442\pi$
$14$	−3.68710	+	0.434566i	−0.985419	+	0.116143i
$15$		0			0
$16$	−3.35041	−	2.18512i	−0.837602	−	0.546281i
$17$	−2.94059	+	2.46745i	−0.713198	+	0.598444i	−0.925495	−	0.378761i	$-0.876350\pi$
$17$	−2.94059	+	2.46745i	−0.713198	+	0.598444i	0.212296	+	0.977205i	$0.431906\pi$
$18$		0			0
$19$	−4.31383	−	0.625180i	−0.989661	−	0.143426i
$19$	−4.31383	−	0.625180i	−0.989661	−	0.143426i
$20$	−1.86403	−	0.214229i	−0.416810	−	0.0479031i
$21$		0			0
$22$	−3.31798	+	7.71239i	−0.707396	+	1.64429i
$23$	−0.401333	−	0.0707658i	−0.0836836	−	0.0147557i	0.131650	−	0.991296i	$-0.457973\pi$
$23$	−0.401333	−	0.0707658i	−0.0836836	−	0.0147557i	−0.215333	+	0.976541i	$0.569084\pi$
$24$		0			0
$25$	3.87141	−	1.40908i	0.774283	−	0.281816i
$26$	4.82161	+	3.16457i	0.945596	+	0.620623i
$27$		0			0
$28$	3.81207	−	3.61043i	0.720414	−	0.682308i
$29$	4.15634	−	4.95333i	0.771813	−	0.919811i	−0.226720	−	0.973960i	$-0.572800\pi$
$29$	4.15634	−	4.95333i	0.771813	−	0.919811i	0.998533	+	0.0541493i	$0.0172447\pi$
$30$		0			0
$31$	−3.66403	+	6.34629i	−0.658080	+	1.13983i	0.323032	+	0.946388i	$0.395298\pi$
$31$	−3.66403	+	6.34629i	−0.658080	+	1.13983i	−0.981112	+	0.193440i	$0.938036\pi$
$32$	5.64563	−	0.356152i	0.998016	−	0.0629594i
$33$		0			0
$34$	1.24685	−	5.28357i	0.213833	−	0.906125i
$35$	0.842345	−	2.31432i	0.142382	−	0.391192i
$36$		0			0
$37$		−	2.51566i		−	0.413571i	−0.978386	−	0.206786i	$-0.933700\pi$
$37$		−	2.51566i		−	0.413571i	0.978386	−	0.206786i	$-0.0663003\pi$
$38$	5.41864	−	2.93911i	0.879019	−	0.476787i
$39$		0			0
$40$	2.29414	−	1.33339i	0.362736	−	0.210828i
$41$	1.57709	−	4.33302i	0.246300	−	0.676703i	−0.753514	−	0.657431i	$-0.771643\pi$
$41$	1.57709	−	4.33302i	0.246300	−	0.676703i	0.999814	−	0.0192719i	$-0.00613482\pi$
$42$		0			0
$43$	11.3090	−	1.99407i	1.72460	−	0.304093i	0.778422	−	0.627741i	$-0.216020\pi$
$43$	11.3090	−	1.99407i	1.72460	−	0.304093i	0.946178	+	0.323648i	$0.104909\pi$
$44$	−2.76050	−	11.5481i	−0.416161	−	1.74095i
$45$		0			0
$46$	0.514774	−	0.259151i	0.0758992	−	0.0382098i
$47$	2.45354	−	2.92401i	0.357886	−	0.426511i	−0.556819	−	0.830634i	$-0.687978\pi$
$47$	2.45354	−	2.92401i	0.357886	−	0.426511i	0.914705	+	0.404122i	$0.132423\pi$
$48$		0			0
$49$	−0.0541088	−	0.0937192i	−0.00772983	−	0.0133885i
$50$	−3.19695	+	4.87096i	−0.452117	+	0.688857i
$51$		0			0
$52$	−8.14155	+	0.489954i	−1.12903	+	0.0679444i
$53$	4.84195	+	0.853766i	0.665092	+	0.117274i	0.495995	−	0.868326i	$-0.334804\pi$
$53$	4.84195	+	0.853766i	0.665092	+	0.117274i	0.169098	+	0.985599i	$0.445915\pi$
$54$		0			0
$55$	−3.58005	−	4.26653i	−0.482733	−	0.575299i
$56$	−1.26821	+	7.31614i	−0.169472	+	0.977660i
$57$		0			0
$58$	−0.522897	+	9.12951i	−0.0686597	+	1.19876i
$59$	−1.21047	+	1.01570i	−0.157589	+	0.132233i	−0.718173	−	0.695865i	$-0.755021\pi$
$59$	−1.21047	+	1.01570i	−0.157589	+	0.132233i	0.560584	+	0.828098i	$0.310577\pi$
$60$		0			0
$61$	1.11276	−	6.31077i	0.142474	−	0.808012i	−0.826886	−	0.562369i	$-0.809890\pi$
$61$	1.11276	−	6.31077i	0.142474	−	0.808012i	0.969360	−	0.245643i	$-0.0789989\pi$
$62$	−1.21305	−	10.2922i	−0.154058	−	1.30711i
$63$		0			0
$64$	−6.09849	+	5.17769i	−0.762311	+	0.647211i
$65$	−3.31333	+	1.91295i	−0.410969	+	0.237273i
$66$		0			0
$67$	2.22499	+	1.86699i	0.271826	+	0.228089i	0.768503	−	0.639846i	$-0.221002\pi$
$67$	2.22499	+	1.86699i	0.271826	+	0.228089i	−0.496677	+	0.867936i	$0.665446\pi$
$68$	3.05443	+	7.04358i	0.370405	+	0.854159i
$69$		0			0
$70$	1.00215	+	3.33571i	0.119780	+	0.398694i
$71$	1.17754	+	6.67818i	0.139749	+	0.792555i	0.971434	+	0.237308i	$0.0762651\pi$
$71$	1.17754	+	6.67818i	0.139749	+	0.792555i	−0.831686	+	0.555247i	$0.812624\pi$
$72$		0			0
$73$	11.1504	+	4.05843i	1.30506	+	0.475003i	0.898642	−	0.438684i	$-0.144555\pi$
$73$	11.1504	+	4.05843i	1.30506	+	0.475003i	0.406419	+	0.913687i	$0.366777\pi$
$74$	2.12725	+	2.85164i	0.247288	+	0.331497i
$75$		0			0
$76$	−3.65701	+	7.91368i	−0.419488	+	0.907761i
$77$	15.5853			1.77611
$78$		0			0
$79$	4.29071	+	1.56169i	0.482742	+	0.175704i	0.571916	−	0.820312i	$-0.306200\pi$
$79$	4.29071	+	1.56169i	0.482742	+	0.175704i	−0.0891737	+	0.996016i	$0.528423\pi$
$80$	−1.47302	+	3.45141i	−0.164689	+	0.385879i
$81$		0			0
$82$	1.87629	+	6.24532i	0.207202	+	0.689680i
$83$	0.641515	+	0.370379i	0.0704154	+	0.0406543i	0.534794	−	0.844982i	$-0.320389\pi$
$83$	0.641515	+	0.370379i	0.0704154	+	0.0406543i	−0.464379	+	0.885637i	$0.653722\pi$
$84$		0			0
$85$	2.75872	+	2.31484i	0.299225	+	0.251080i
$86$	−11.1332	+	11.8233i	−1.20052	+	1.27494i
$87$		0			0
$88$	12.8943	+	10.7562i	1.37454	+	1.14661i
$89$	−5.87516	−	16.1419i	−0.622766	−	1.71103i	−0.700114	−	0.714031i	$-0.746868\pi$
$89$	−5.87516	−	16.1419i	−0.622766	−	1.71103i	0.0773486	−	0.997004i	$-0.475355\pi$
$90$		0			0
$91$	1.85908	−	10.5434i	0.194885	−	1.10525i
$92$	−0.364387	+	0.729058i	−0.0379899	+	0.0760095i
$93$		0			0
$94$	−0.308673	+	5.38926i	−0.0318371	+	0.555860i
$95$	0.125156	+	4.08739i	0.0128407	+	0.419357i
$96$		0			0
$97$	2.43876	+	2.90640i	0.247618	+	0.295100i	0.875509	−	0.483201i	$-0.160526\pi$
$97$	2.43876	+	2.90640i	0.247618	+	0.295100i	−0.627891	+	0.778301i	$0.716082\pi$
$98$	0.140585	+	0.0604816i	0.0142012	+	0.00610956i
$99$		0			0
$100$	−0.494968	−	8.22487i	−0.0494968	−	0.822487i
$101$	−9.11983	+	3.31935i	−0.907457	+	0.330287i	−0.753237	−	0.657749i	$-0.771509\pi$
$101$	−9.11983	+	3.31935i	−0.907457	+	0.330287i	−0.154220	+	0.988037i	$0.549286\pi$
$102$		0			0
$103$	−7.76969	−	13.4575i	−0.765570	−	1.32601i	−0.939945	−	0.341327i	$-0.889124\pi$
$103$	−7.76969	−	13.4575i	−0.765570	−	1.32601i	0.174374	−	0.984679i	$-0.444210\pi$
$104$	8.81461	−	7.43992i	0.864344	−	0.729544i
$105$		0			0
$106$	−6.21058	+	3.12657i	−0.603224	+	0.303680i
$107$	−8.60129	+	14.8979i	−0.831518	+	1.44023i	0.0653163	+	0.997865i	$0.479194\pi$
$107$	−8.60129	+	14.8979i	−0.831518	+	1.44023i	−0.896834	+	0.442367i	$0.854139\pi$
$108$		0			0
$109$	−3.11205	+	0.548739i	−0.298081	+	0.0525597i	−0.320688	−	0.947185i	$-0.603914\pi$
$109$	−3.11205	+	0.548739i	−0.298081	+	0.0525597i	0.0226078	+	0.999744i	$0.492803\pi$
$110$	7.66599	+	1.80906i	0.730923	+	0.172487i
$111$		0			0
$112$	−4.74896	−	9.36568i	−0.448735	−	0.884973i
$113$			19.3153i			1.81703i	0.417850	+	0.908516i	$0.362784\pi$
$113$			19.3153i			1.81703i	−0.417850	+	0.908516i	$0.637216\pi$
$114$		0			0
$115$			0.382319i			0.0356514i
$116$	−7.12721	−	10.7910i	−0.661745	−	1.00192i
$117$		0			0
$118$	0.513253	−	2.17493i	0.0472487	−	0.200219i
$119$	−9.92426	+	1.74991i	−0.909755	+	0.160414i
$120$		0			0
$121$	12.1225	−	20.9968i	1.10204	−	1.90880i
$122$	4.07504	+	8.09458i	0.368936	+	0.732849i
$123$		0			0
$124$	10.0782	+	10.6411i	0.905049	+	0.955595i
$125$	−4.27791	−	7.40955i	−0.382628	−	0.662731i
$126$		0			0
$127$	−13.9783	+	5.08769i	−1.24037	+	0.451459i	−0.877138	−	0.480238i	$-0.840550\pi$
$127$	−13.9783	+	5.08769i	−1.24037	+	0.451459i	−0.363236	+	0.931697i	$0.618328\pi$
$128$	2.53472	−	11.0261i	0.224040	−	0.974580i
$129$		0			0
$130$	2.13826	−	4.97021i	0.187537	−	0.435917i
$131$	−2.07131	−	2.46849i	−0.180971	−	0.215673i	0.667931	−	0.744223i	$-0.267180\pi$
$131$	−2.07131	−	2.46849i	−0.180971	−	0.215673i	−0.848902	+	0.528551i	$0.822736\pi$
$132$		0			0
$133$	−8.98691	−	7.08373i	−0.779264	−	0.614237i
$134$	−4.10089	−	0.234881i	−0.354263	−	0.0202906i
$135$		0			0
$136$	−9.41845	−	5.40146i	−0.807626	−	0.463172i
$137$	−1.36502	+	7.74139i	−0.116621	+	0.661391i	0.869314	+	0.494261i	$0.164561\pi$
$137$	−1.36502	+	7.74139i	−0.116621	+	0.661391i	−0.985935	+	0.167130i	$0.946550\pi$
$138$		0			0
$139$	0.00238476	+	0.00655208i	0.000202273	+	0.000555740i	0.939794	−	0.341742i	$-0.111017\pi$
$139$	0.00238476	+	0.00655208i	0.000202273	+	0.000555740i	−0.939591	+	0.342298i	$0.888795\pi$
$140$	−3.95669	−	2.93380i	−0.334401	−	0.247951i
$141$		0			0
$142$	−6.98191	−	6.57438i	−0.585909	−	0.551709i
$143$	−18.5466	−	15.5625i	−1.55095	−	1.30140i
$144$		0			0
$145$	−5.25348	−	3.03310i	−0.436277	−	0.251885i
$146$	−16.0715	+	4.82839i	−1.33009	+	0.399600i
$147$		0			0
$148$	−4.82272	−	1.43369i	−0.396425	−	0.117849i
$149$	10.8510	+	3.94945i	0.888950	+	0.323552i	0.745816	−	0.666152i	$-0.232060\pi$
$149$	10.8510	+	3.94945i	0.888950	+	0.323552i	0.143134	+	0.989703i	$0.454282\pi$
$150$		0			0
$151$	3.85210			0.313480			0.156740	−	0.987640i	$-0.449902\pi$
$151$	3.85210			0.313480			0.156740	+	0.987640i	$0.449902\pi$
$152$	−2.54640	−	12.0630i	−0.206540	−	0.978438i
$153$		0			0
$154$	−17.6668	+	13.1790i	−1.42363	+	1.06199i
$155$	6.46023	+	2.35133i	0.518898	+	0.188863i
$156$		0			0
$157$	3.30340	+	18.7345i	0.263640	+	1.49518i	0.772880	+	0.634553i	$0.218816\pi$
$157$	3.30340	+	18.7345i	0.263640	+	1.49518i	−0.509240	+	0.860625i	$0.670073\pi$
$158$	−6.18433	+	1.85797i	−0.491999	+	0.147812i
$159$		0			0
$160$	−1.24877	−	5.15797i	−0.0987237	−	0.407773i
$161$	−0.819545	−	0.687680i	−0.0645892	−	0.0541968i
$162$		0			0
$163$	5.72920	−	3.30775i	0.448745	−	0.259083i	−0.258555	−	0.965997i	$-0.583246\pi$
$163$	5.72920	−	3.30775i	0.448745	−	0.259083i	0.707300	+	0.706913i	$0.249913\pi$
$164$	−7.40795	−	5.49283i	−0.578464	−	0.428918i
$165$		0			0
$166$	−1.04039	+	0.122621i	−0.0807497	+	0.00951726i
$167$	0.143711	−	0.815026i	0.0111207	−	0.0630686i	−0.978742	−	0.205093i	$-0.934250\pi$
$167$	0.143711	−	0.815026i	0.0111207	−	0.0630686i	0.989863	+	0.142025i	$0.0453613\pi$
$168$		0			0
$169$	−2.78168	+	2.33410i	−0.213975	+	0.179546i
$170$	−5.08460	−	0.291223i	−0.389971	−	0.0223358i
$171$		0			0
$172$	2.62227	−	22.8166i	0.199946	−	1.73975i
$173$	−3.66715	−	4.37034i	−0.278808	−	0.332271i	0.608408	−	0.793624i	$-0.291808\pi$
$173$	−3.66715	−	4.37034i	−0.278808	−	0.332271i	−0.887216	+	0.461354i	$0.847364\pi$
$174$		0			0
$175$	10.6513	+	1.87810i	0.805160	+	0.141971i
$176$	−23.7120	−	1.28928i	−1.78736	−	0.0971829i
$177$		0			0
$178$	20.3095	+	13.3297i	1.52226	+	0.999103i
$179$	2.18671	+	3.78750i	0.163442	+	0.283091i	0.936101	−	0.351731i	$-0.114407\pi$
$179$	2.18671	+	3.78750i	0.163442	+	0.283091i	−0.772659	+	0.634822i	$0.781074\pi$
$180$		0			0
$181$	−5.17743	+	6.17022i	−0.384835	+	0.458628i	−0.923334	−	0.383998i	$-0.874547\pi$
$181$	−5.17743	+	6.17022i	−0.384835	+	0.458628i	0.538499	+	0.842626i	$0.318992\pi$
$182$	6.80813	+	13.5236i	0.504652	+	1.00243i
$183$		0			0
$184$	−0.203440	−	1.13456i	−0.0149978	−	0.0836406i
$185$	−2.32421	+	0.409821i	−0.170879	+	0.0301306i
$186$		0			0
$187$	−7.79437	+	21.4149i	−0.569981	+	1.56601i
$188$	−4.20728	−	6.37006i	−0.306848	−	0.464584i
$189$		0			0
$190$	−3.59818	−	4.52746i	−0.261040	−	0.328457i
$191$		−	3.21322i		−	0.232501i	−0.993220	−	0.116250i	$-0.962913\pi$
$191$		−	3.21322i		−	0.232501i	0.993220	−	0.116250i	$-0.0370875\pi$
$192$		0			0
$193$	−2.03628	+	5.59463i	−0.146575	+	0.402711i	−0.991153	−	0.132721i	$-0.957629\pi$
$193$	−2.03628	+	5.59463i	−0.146575	+	0.402711i	0.844579	+	0.535431i	$0.179851\pi$
$194$	−5.22213	−	1.23235i	−0.374927	−	0.0884775i
$195$		0			0
$196$	−0.210505	+	0.0503197i	−0.0150360	+	0.00359426i
$197$	6.98997	−	12.1070i	0.498015	−	0.862587i	−0.501982	−	0.864878i	$-0.667396\pi$
$197$	6.98997	−	12.1070i	0.498015	−	0.862587i	0.999997	+	0.00229054i	$0.000729101\pi$
$198$		0			0
$199$	−6.33587	+	7.55079i	−0.449138	+	0.535261i	−0.942342	−	0.334652i	$-0.891381\pi$
$199$	−6.33587	+	7.55079i	−0.449138	+	0.535261i	0.493204	+	0.869914i	$0.335826\pi$
$200$	7.51605	+	8.90482i	0.531465	+	0.629666i
$201$		0			0
$202$	7.53101	−	11.4744i	0.529880	−	0.807339i
$203$	15.9513	−	5.80578i	1.11956	−	0.407486i
$204$		0			0
$205$	−4.26018	−	0.751186i	−0.297544	−	0.0524651i
$206$	20.1871	+	8.68478i	1.40650	+	0.605097i
$207$		0			0
$208$	−3.70066	+	15.8872i	−0.256594	+	1.10158i
$209$	−24.0348	+	9.59078i	−1.66252	+	0.663408i
$210$		0			0
$211$	−11.1612	+	9.36536i	−0.768369	+	0.644738i	−0.940291	−	0.340373i	$-0.889447\pi$
$211$	−11.1612	+	9.36536i	−0.768369	+	0.644738i	0.171922	+	0.985111i	$0.445002\pi$
$212$	4.39621	−	8.79584i	0.301933	−	0.604101i
$213$		0			0
$214$	−2.84763	−	24.1609i	−0.194660	−	1.65160i
$215$	−3.68464	−	10.1235i	−0.251291	−	0.690415i
$216$		0			0
$217$	−16.6604	+	9.61889i	−1.13098	+	0.652973i
$218$	3.06368	−	3.25359i	0.207498	−	0.220361i
$219$		0			0
$220$	−10.2196	+	4.43171i	−0.689005	+	0.298786i
$221$	13.5573	+	7.82731i	0.911963	+	0.526522i
$222$		0			0
$223$	−0.947405	−	5.37300i	−0.0634429	−	0.359803i	−0.999958	−	0.00917516i	$-0.997079\pi$
$223$	−0.947405	−	5.37300i	−0.0634429	−	0.359803i	0.936515	−	0.350628i	$-0.114032\pi$
$224$	13.3029	+	6.60080i	0.888836	+	0.441034i
$225$		0			0
$226$	−16.3331	−	21.8950i	−1.08646	−	1.45644i
$227$	−4.73837			−0.314497			−0.157248	−	0.987559i	$-0.550262\pi$
$227$	−4.73837			−0.314497			−0.157248	+	0.987559i	$0.550262\pi$
$228$		0			0
$229$	−25.7074			−1.69879			−0.849397	−	0.527755i	$-0.823034\pi$
$229$	−25.7074			−1.69879			−0.849397	+	0.527755i	$0.823034\pi$
$230$	−0.323290	−	0.433381i	−0.0213171	−	0.0285763i
$231$		0			0
$232$	17.2040	+	6.20542i	1.12950	+	0.407406i
$233$	−2.50999	−	14.2349i	−0.164435	−	0.932556i	−0.949645	−	0.313327i	$-0.898556\pi$
$233$	−2.50999	−	14.2349i	−0.164435	−	0.932556i	0.785210	−	0.619229i	$-0.212555\pi$
$234$		0			0
$235$	−3.10119	−	1.79047i	−0.202300	−	0.116798i
$236$	1.25733	+	2.89942i	0.0818451	+	0.188736i
$237$		0			0
$238$	9.76999	−	10.3756i	0.633294	−	0.672551i
$239$	−13.1429	+	7.58808i	−0.850146	+	0.490832i	−0.860700	−	0.509112i	$-0.829974\pi$
$239$	−13.1429	+	7.58808i	−0.850146	+	0.490832i	0.0105542	+	0.999944i	$0.496640\pi$
$240$		0			0
$241$	−1.91914	−	5.27279i	−0.123623	−	0.339650i	0.862408	−	0.506214i	$-0.168955\pi$
$241$	−1.91914	−	5.27279i	−0.123623	−	0.339650i	−0.986031	+	0.166563i	$0.946733\pi$
$242$	4.01339	+	34.0519i	0.257991	+	2.18894i
$243$		0			0
$244$	−11.4641	−	5.72982i	−0.733914	−	0.366814i
$245$	−0.0777723	+	0.0652587i	−0.00496869	+	0.00416922i
$246$		0			0
$247$	3.62114	+	17.4035i	0.230408	+	1.10736i
$248$	−20.4223	−	3.54010i	−1.29682	−	0.224797i
$249$		0			0
$250$	11.1148	+	4.78175i	0.702962	+	0.302424i
$251$	20.4595	+	3.60756i	1.29139	+	0.227707i	0.776810	−	0.629735i	$-0.216837\pi$
$251$	20.4595	+	3.60756i	1.29139	+	0.227707i	0.514580	+	0.857442i	$0.327948\pi$
$252$		0			0
$253$	−2.27346	+	0.827472i	−0.142931	+	0.0520227i
$254$	11.5431	−	17.5873i	0.724276	−	1.10353i
$255$		0			0
$256$	6.45047	+	14.6421i	0.403154	+	0.915132i
$257$	10.5434	−	12.5652i	0.657681	−	0.783793i	−0.329370	−	0.944201i	$-0.606836\pi$
$257$	10.5434	−	12.5652i	0.657681	−	0.783793i	0.987051	+	0.160408i	$0.0512809\pi$
$258$		0			0
$259$	3.30208	−	5.71936i	0.205181	−	0.355384i
$260$	1.77899	+	7.44214i	0.110328	+	0.461542i
$261$		0			0
$262$	4.43531	+	1.04667i	0.274014	+	0.0646635i
$263$	−4.15539	+	11.4168i	−0.256232	+	0.703992i	0.743159	+	0.669114i	$0.233326\pi$
$263$	−4.15539	+	11.4168i	−0.256232	+	0.703992i	−0.999392	+	0.0348776i	$0.988896\pi$
$264$		0			0
$265$		−	4.61255i		−	0.283347i
$266$	16.1772	+	0.430457i	0.991889	+	0.0263930i
$267$		0			0
$268$	4.84722	−	3.20148i	0.296091	−	0.195562i
$269$	−5.91660	+	16.2557i	−0.360741	+	0.991129i	0.618027	+	0.786157i	$0.287932\pi$
$269$	−5.91660	+	16.2557i	−0.360741	+	0.991129i	−0.978768	+	0.204972i	$0.934290\pi$
$270$		0			0
$271$	−6.08103	+	1.07225i	−0.369396	+	0.0651345i	−0.355265	−	0.934766i	$-0.615609\pi$
$271$	−6.08103	+	1.07225i	−0.369396	+	0.0651345i	−0.0141312	+	0.999900i	$0.504498\pi$
$272$	15.2439	−	1.84140i	0.924295	−	0.111652i
$273$		0			0
$274$	−4.99882	−	9.92957i	−0.301990	−	0.599867i
$275$	15.7217	−	18.7364i	0.948055	−	1.12985i
$276$		0			0
$277$	13.7725	+	23.8547i	0.827511	+	1.43329i	0.899985	+	0.435920i	$0.143577\pi$
$277$	13.7725	+	23.8547i	0.827511	+	1.43329i	−0.0724748	+	0.997370i	$0.523090\pi$
$278$	−0.00824373	−	0.00541060i	−0.000494426	−	0.000324506i
$279$		0			0
$280$	6.96597	−	0.0201599i	0.416296	−	0.00120478i
$281$	−7.27059	−	1.28200i	−0.433727	−	0.0764778i	−0.0474780	−	0.998872i	$-0.515118\pi$
$281$	−7.27059	−	1.28200i	−0.433727	−	0.0764778i	−0.386249	+	0.922394i	$0.626230\pi$
$282$		0			0
$283$	−5.57965	−	6.64957i	−0.331676	−	0.395276i	0.574272	−	0.818664i	$-0.305285\pi$
$283$	−5.57965	−	6.64957i	−0.331676	−	0.395276i	−0.905948	+	0.423388i	$0.860841\pi$
$284$	13.4737	+	1.54851i	0.799518	+	0.0918870i
$285$		0			0
$286$	34.1833	+	1.95787i	2.02130	+	0.115771i
$287$	9.27308	−	7.78104i	0.547373	−	0.459300i
$288$		0			0
$289$	−0.393247	+	2.23021i	−0.0231321	+	0.131189i
$290$	8.51992	−	1.00417i	0.500307	−	0.0589668i
$291$		0			0
$292$	14.1351	−	19.0634i	0.827193	−	1.11560i
$293$	−8.59522	+	4.96245i	−0.502138	+	0.289910i	−0.729596	−	0.683878i	$-0.760292\pi$
$293$	−8.59522	+	4.96245i	−0.502138	+	0.289910i	0.227458	+	0.973788i	$0.426959\pi$
$294$		0			0
$295$	1.13560	+	0.952881i	0.0661171	+	0.0554789i
$296$	6.67917	−	2.45293i	0.388219	−	0.142574i
$297$		0			0
$298$	−15.6399	+	4.69873i	−0.905997	+	0.272190i
$299$	0.288593	+	1.63669i	0.0166897	+	0.0946522i
$300$		0			0
$301$	28.3284	+	10.3107i	1.63282	+	0.594299i
$302$	−4.36658	+	3.25735i	−0.251269	+	0.187440i
$303$		0			0
$304$	13.0870	+	11.5209i	0.750591	+	0.660767i
$305$	−6.01179			−0.344234
$306$		0			0
$307$	23.6159	+	8.59549i	1.34783	+	0.490571i	0.912271	−	0.409588i	$-0.134328\pi$
$307$	23.6159	+	8.59549i	1.34783	+	0.490571i	0.435562	+	0.900159i	$0.356550\pi$
$308$	8.88218	−	29.8782i	0.506109	−	1.70247i
$309$		0			0
$310$	−9.31134	+	2.79742i	−0.528848	+	0.158883i
$311$	−17.9579	−	10.3680i	−1.01830	−	0.587916i	−0.104689	−	0.994505i	$-0.533385\pi$
$311$	−17.9579	−	10.3680i	−1.01830	−	0.587916i	−0.913611	+	0.406589i	$0.866718\pi$
$312$		0			0
$313$	13.2291	+	11.1005i	0.747752	+	0.627439i	0.934907	−	0.354892i	$-0.115482\pi$
$313$	13.2291	+	11.1005i	0.747752	+	0.627439i	−0.187155	+	0.982330i	$0.559927\pi$
$314$	−19.5866	−	18.4433i	−1.10533	−	1.04082i
$315$		0			0
$316$	5.43920	−	7.33561i	0.305979	−	0.412661i
$317$	1.69445	+	4.65547i	0.0951699	+	0.261477i	0.978138	−	0.207955i	$-0.0666808\pi$
$317$	1.69445	+	4.65547i	0.0951699	+	0.261477i	−0.882968	+	0.469432i	$0.844459\pi$
$318$		0			0
$319$	6.66595	−	37.8045i	0.373222	−	2.11665i
$320$	5.77715	+	4.79089i	0.322952	+	0.267819i
$321$		0			0
$322$	1.51051	+	0.0865150i	0.0841772	+	0.00482129i
$323$	14.2278	−	8.80576i	0.791657	−	0.489966i
$324$		0			0
$325$	−10.7997	−	12.8706i	−0.599062	−	0.713934i
$326$	−3.69733	+	8.59416i	−0.204776	+	0.475987i
$327$		0			0
$328$	13.0421	−	0.0377445i	0.720130	−	0.00208409i
$329$	9.41623	−	3.42723i	0.519134	−	0.188949i
$330$		0			0
$331$	6.79791	+	11.7743i	0.373647	+	0.647175i	0.990123	−	0.140198i	$-0.0447739\pi$
$331$	6.79791	+	11.7743i	0.373647	+	0.647175i	−0.616477	+	0.787373i	$0.711441\pi$
$332$	1.07565	−	1.01875i	0.0590340	−	0.0559114i
$333$		0			0
$334$	0.526284	+	1.04540i	0.0287970	+	0.0572019i
$335$	1.36244	−	2.35981i	0.0744380	−	0.128930i
$336$		0			0
$337$	−7.24750	+	1.27793i	−0.394797	+	0.0696133i	−0.367522	−	0.930015i	$-0.619794\pi$
$337$	−7.24750	+	1.27793i	−0.394797	+	0.0696133i	−0.0272743	+	0.999628i	$0.508683\pi$
$338$	1.17947	−	4.99804i	0.0641545	−	0.271857i
$339$		0			0
$340$	6.00995	−	3.96944i	0.325936	−	0.215273i
$341$			43.5049i			2.35592i
$342$		0			0
$343$		−	18.6606i		−	1.00758i
$344$	16.3213	+	28.0814i	0.879988	+	1.51405i
$345$		0			0
$346$	7.85250	+	1.85308i	0.422153	+	0.0996221i
$347$	−7.29437	+	1.28619i	−0.391582	+	0.0690465i	−0.365973	−	0.930625i	$-0.619264\pi$
$347$	−7.29437	+	1.28619i	−0.391582	+	0.0690465i	−0.0256094	+	0.999672i	$0.508153\pi$
$348$		0			0
$349$	−10.0951	+	17.4851i	−0.540376	+	0.935958i	0.458507	+	0.888691i	$0.348385\pi$
$349$	−10.0951	+	17.4851i	−0.540376	+	0.935958i	−0.998882	+	0.0472671i	$0.984949\pi$
$350$	−13.6620	+	6.87781i	−0.730262	+	0.367634i
$351$		0			0
$352$	27.9691	−	18.5895i	1.49076	−	0.990821i
$353$	10.6908	+	18.5171i	0.569016	+	0.985564i	0.996664	+	0.0816189i	$0.0260090\pi$
$353$	10.6908	+	18.5171i	0.569016	+	0.985564i	−0.427648	+	0.903945i	$0.640658\pi$
$354$		0			0
$355$	5.97813	−	2.17586i	0.317286	−	0.115483i
$356$	−34.2936	+	2.06377i	−1.81756	+	0.109380i
$357$		0			0
$358$	−5.68148	−	2.44426i	−0.300276	−	0.129183i
$359$	13.3436	+	15.9023i	0.704248	+	0.839290i	0.993000	−	0.118114i	$-0.0376848\pi$
$359$	13.3436	+	15.9023i	0.704248	+	0.839290i	−0.288752	+	0.957404i	$0.593240\pi$
$360$		0			0
$361$	18.2183	+	5.39384i	0.958858	+	0.283887i
$362$	0.651357	−	11.3723i	0.0342345	−	0.597717i
$363$		0			0
$364$	−19.1530	−	9.57277i	−1.00389	−	0.501749i
$365$	1.93308	−	10.9630i	0.101182	−	0.573831i
$366$		0			0
$367$	3.99066	+	10.9643i	0.208311	+	0.572330i	0.999215	−	0.0396103i	$-0.0126116\pi$
$367$	3.99066	+	10.9643i	0.208311	+	0.572330i	−0.790904	+	0.611940i	$0.790389\pi$
$368$	1.19000	+	1.11406i	0.0620328	+	0.0580742i
$369$		0			0
$370$	2.28808	−	2.42992i	0.118952	−	0.126325i
$371$	9.88754	+	8.29663i	0.513336	+	0.430740i
$372$		0			0
$373$	−22.7922	−	13.1591i	−1.18013	−	0.681351i	−0.224089	−	0.974569i	$-0.571941\pi$
$373$	−22.7922	−	13.1591i	−1.18013	−	0.681351i	−0.956046	+	0.293218i	$0.905274\pi$
$374$	−9.27311	−	30.8659i	−0.479501	−	1.59604i
$375$		0			0
$376$	10.1557	+	3.66314i	0.523743	+	0.188912i
$377$	−24.7794	−	9.01898i	−1.27621	−	0.464501i
$378$		0			0
$379$	−15.1616			−0.778798			−0.389399	−	0.921069i	$-0.627317\pi$
$379$	−15.1616			−0.778798			−0.389399	+	0.921069i	$0.627317\pi$
$380$	7.90719	+	2.08950i	0.405630	+	0.107189i
$381$		0			0
$382$	2.71711	+	3.64238i	0.139020	+	0.186360i
$383$	29.2153	+	10.6335i	1.49283	+	0.543346i	0.954193	−	0.299193i	$-0.0967173\pi$
$383$	29.2153	+	10.6335i	1.49283	+	0.543346i	0.538637	+	0.842538i	$0.318940\pi$
$384$		0			0
$385$	−2.53897	−	14.3992i	−0.129398	−	0.733851i
$386$	−2.42260	−	8.06373i	−0.123307	−	0.410433i
$387$		0			0
$388$	6.96167	−	3.01892i	0.353425	−	0.153262i
$389$	−26.2800	−	22.0515i	−1.33245	−	1.11806i	−0.983499	−	0.180913i	$-0.942095\pi$
$389$	−26.2800	−	22.0515i	−1.33245	−	1.11806i	−0.348947	−	0.937142i	$-0.613461\pi$
$390$		0			0
$391$	1.35477	−	0.782175i	0.0685135	−	0.0395563i
$392$	0.196069	−	0.235044i	0.00990297	−	0.0118715i
$393$		0			0
$394$	2.31417	+	19.6347i	0.116586	+	0.989183i
$395$	0.743851	−	4.21859i	0.0374272	−	0.212260i
$396$		0			0
$397$	−6.93811	+	5.82177i	−0.348214	+	0.292186i	−0.800072	−	0.599904i	$-0.795206\pi$
$397$	−6.93811	+	5.82177i	−0.348214	+	0.292186i	0.451859	+	0.892090i	$0.350761\pi$
$398$	0.797097	−	13.9169i	0.0399548	−	0.697591i
$399$		0			0
$400$	−16.0498	−	3.73853i	−0.802492	−	0.186926i
$401$	5.10512	+	6.08405i	0.254938	+	0.303823i	0.878300	−	0.478110i	$-0.158678\pi$
$401$	5.10512	+	6.08405i	0.254938	+	0.303823i	−0.623362	+	0.781933i	$0.714234\pi$
$402$		0			0
$403$	29.4309	+	5.18945i	1.46606	+	0.258505i
$404$	1.16599	+	19.3752i	0.0580101	+	0.963952i
$405$		0			0
$406$	−13.1723	+	20.0696i	−0.653730	+	0.996040i
$407$	−7.46741	−	12.9339i	−0.370146	−	0.641111i
$408$		0			0
$409$	−17.5748	+	20.9449i	−0.869020	+	1.03566i	0.130005	+	0.991513i	$0.458501\pi$
$409$	−17.5748	+	20.9449i	−0.869020	+	1.03566i	−0.999025	+	0.0441446i	$0.985944\pi$
$410$	5.46437	−	2.75092i	0.269866	−	0.135858i
$411$		0			0
$412$	−30.2271	+	7.22559i	−1.48918	+	0.355979i
$413$	−4.08522	+	0.720335i	−0.201021	+	0.0354454i
$414$		0			0
$415$	0.237684	−	0.653032i	0.0116675	−	0.0320561i
$416$	−9.23940	−	21.1384i	−0.452999	−	1.03640i
$417$		0			0
$418$	19.1348	−	31.1956i	0.935916	−	1.52583i
$419$			13.4784i			0.658462i	0.944249	+	0.329231i	$0.106789\pi$
$419$			13.4784i			0.658462i	−0.944249	+	0.329231i	$0.893211\pi$
$420$		0			0
$421$	13.2512	−	36.4074i	0.645825	−	1.77439i	0.0132242	−	0.999913i	$-0.495790\pi$
$421$	13.2512	−	36.4074i	0.645825	−	1.77439i	0.632601	−	0.774478i	$-0.281987\pi$
$422$	4.73249	−	20.0541i	0.230374	−	0.976220i
$423$		0			0
$424$	2.45444	+	13.6880i	0.119198	+	0.664750i
$425$	−7.90742	+	13.6960i	−0.383566	+	0.664356i
$426$		0			0
$427$	10.8135	−	12.8870i	0.523300	−	0.623644i
$428$	23.6585	+	24.9798i	1.14358	+	1.20744i
$429$		0			0
$430$	12.7372	+	8.35980i	0.614243	+	0.403145i
$431$	−37.1856	+	13.5345i	−1.79117	+	0.651932i	−0.792029	+	0.610484i	$0.790975\pi$
$431$	−37.1856	+	13.5345i	−1.79117	+	0.651932i	−0.999141	+	0.0414488i	$0.986803\pi$
$432$		0			0
$433$	35.8179	+	6.31566i	1.72130	+	0.303511i	0.945052	−	0.326919i	$-0.106011\pi$
$433$	35.8179	+	6.31566i	1.72130	+	0.303511i	0.776246	+	0.630431i	$0.217122\pi$
$434$	10.7518	−	24.9917i	0.516102	−	1.19964i
$435$		0			0
$436$	−0.721609	+	6.27879i	−0.0345588	+	0.300700i
$437$	1.68704	+	0.556177i	0.0807021	+	0.0266055i
$438$		0			0
$439$	−8.70974	+	7.30834i	−0.415693	+	0.348808i	−0.826522	−	0.562905i	$-0.809684\pi$
$439$	−8.70974	+	7.30834i	−0.415693	+	0.348808i	0.410829	+	0.911713i	$0.365239\pi$
$440$	7.83704	−	13.6653i	0.373616	−	0.651469i
$441$		0			0
$442$	−21.9868	+	2.59139i	−1.04581	+	0.123260i
$443$	7.73933	+	21.2636i	0.367707	+	1.01027i	0.976231	+	0.216731i	$0.0695395\pi$
$443$	7.73933	+	21.2636i	0.367707	+	1.01027i	−0.608525	+	0.793535i	$0.708238\pi$
$444$		0			0
$445$	−13.9563	+	8.05769i	−0.661594	+	0.381971i
$446$	5.61737	+	5.28948i	0.265990	+	0.250464i
$447$		0			0
$448$	−20.6612	+	3.76657i	−0.976152	+	0.177954i
$449$	26.6431	+	15.3824i	1.25737	+	0.725941i	0.972562	−	0.232644i	$-0.0747378\pi$
$449$	26.6431	+	15.3824i	1.25737	+	0.725941i	0.284805	+	0.958585i	$0.408071\pi$
$450$		0			0
$451$	−4.75361	−	26.9590i	−0.223839	−	1.26945i
$452$	37.0291	+	11.0080i	1.74170	+	0.517771i
$453$		0			0
$454$	5.37122	−	4.00679i	0.252084	−	0.188048i
$455$	−10.0439			−0.470863
$456$		0			0
$457$	−24.2691			−1.13526			−0.567631	−	0.823283i	$-0.692140\pi$
$457$	−24.2691			−1.13526			−0.567631	+	0.823283i	$0.692140\pi$
$458$	29.1409	−	21.7383i	1.36166	−	1.01576i
$459$		0			0
$460$	0.732936	+	0.217887i	0.0341733	+	0.0101590i
$461$	−6.43606	−	36.5007i	−0.299757	−	1.70001i	−0.647212	−	0.762310i	$-0.724065\pi$
$461$	−6.43606	−	36.5007i	−0.299757	−	1.70001i	0.347455	−	0.937697i	$-0.387046\pi$
$462$		0			0
$463$	−18.1684	−	10.4895i	−0.844355	−	0.487489i	0.0143872	−	0.999896i	$-0.495420\pi$
$463$	−18.1684	−	10.4895i	−0.844355	−	0.487489i	−0.858742	+	0.512408i	$0.828754\pi$
$464$	−24.7491	+	7.51357i	−1.14895	+	0.348809i
$465$		0			0
$466$	14.8823	+	14.0136i	0.689408	+	0.649167i
$467$	34.2174	−	19.7554i	1.58339	−	0.914172i	0.589032	−	0.808110i	$-0.299509\pi$
$467$	34.2174	−	19.7554i	1.58339	−	0.914172i	0.994360	−	0.106062i	$-0.0338242\pi$
$468$		0			0
$469$	2.60791	+	7.16517i	0.120422	+	0.330857i
$470$	5.02942	−	0.592773i	0.231990	−	0.0273426i
$471$		0			0
$472$	−3.87701	−	2.22346i	−0.178454	−	0.102343i
$473$	52.2244	−	43.8215i	2.40128	−	2.01491i
$474$		0			0
$475$	−17.5816	+	3.65820i	−0.806697	+	0.167850i
$476$	−2.30119	+	20.0229i	−0.105475	+	0.917748i
$477$		0			0
$478$	8.48178	−	19.7152i	0.387947	−	0.901754i
$479$	−12.6442	−	2.22951i	−0.577728	−	0.101869i	−0.122854	−	0.992425i	$-0.539205\pi$
$479$	−12.6442	−	2.22951i	−0.577728	−	0.101869i	−0.454874	+	0.890556i	$0.650316\pi$
$480$		0			0
$481$	−9.64049	+	3.50885i	−0.439569	+	0.159990i
$482$	6.63415	+	4.35419i	0.302177	+	0.198328i
$483$		0			0
$484$	−33.3438	−	35.2060i	−1.51563	−	1.60027i
$485$	2.28792	−	2.72664i	0.103889	−	0.123810i
$486$		0			0
$487$	−16.9204	+	29.3070i	−0.766736	+	1.32803i	0.172587	+	0.984994i	$0.444787\pi$
$487$	−16.9204	+	29.3070i	−0.766736	+	1.32803i	−0.939324	+	0.343032i	$0.888546\pi$
$488$	17.8404	−	3.19900i	0.807596	−	0.144812i
$489$		0			0
$490$	0.0329764	−	0.139739i	0.00148972	−	0.00631277i
$491$	−11.0221	+	30.2830i	−0.497420	+	1.36665i	0.396339	+	0.918104i	$0.370280\pi$
$491$	−11.0221	+	30.2830i	−0.497420	+	1.36665i	−0.893759	+	0.448547i	$0.851942\pi$
$492$		0			0
$493$			24.8213i			1.11789i
$494$	−18.8212	−	16.6658i	−0.846806	−	0.749829i
$495$		0			0
$496$	26.1434	−	13.2563i	1.17387	−	0.595225i
$497$	−6.08870	+	16.7286i	−0.273115	+	0.750378i
$498$		0			0
$499$	13.9952	−	2.46774i	0.626513	−	0.110471i	0.148627	−	0.988893i	$-0.452515\pi$
$499$	13.9952	−	2.46774i	0.626513	−	0.110471i	0.477885	+	0.878422i	$0.341403\pi$
$500$	−16.6427	+	3.97833i	−0.744286	+	0.177916i
$501$		0			0
$502$	−26.2426	+	13.2112i	−1.17126	+	0.589646i
$503$	−9.64008	+	11.4886i	−0.429830	+	0.512251i	−0.936873	−	0.349669i	$-0.886294\pi$
$503$	−9.64008	+	11.4886i	−0.429830	+	0.512251i	0.507043	+	0.861921i	$0.330738\pi$
$504$		0			0
$505$	4.55243	+	7.88505i	0.202581	+	0.350880i
$506$	1.87739	−	2.86043i	0.0834600	−	0.127162i
$507$		0			0
$508$	1.78716	+	29.6971i	0.0792922	+	1.31760i
$509$	17.9890	+	3.17194i	0.797348	+	0.140594i	0.557457	−	0.830206i	$-0.311777\pi$
$509$	17.9890	+	3.17194i	0.797348	+	0.140594i	0.239891	+	0.970800i	$0.422888\pi$
$510$		0			0
$511$	20.0235	+	23.8631i	0.885786	+	1.05564i
$512$	−19.6934	−	11.1432i	−0.870334	−	0.492462i
$513$		0			0
$514$	−1.32644	+	23.1589i	−0.0585066	+	1.02150i
$515$	−11.1676	+	9.37074i	−0.492104	+	0.412924i
$516$		0			0
$517$	3.93500	−	22.3165i	0.173061	−	0.981478i
$518$	1.09322	+	9.27548i	0.0480333	+	0.407541i
$519$		0			0
$520$	−8.30970	−	6.93178i	−0.364404	−	0.303979i
$521$	5.73358	−	3.31029i	0.251193	−	0.145026i	−0.369117	−	0.929383i	$-0.620340\pi$
$521$	5.73358	−	3.31029i	0.251193	−	0.145026i	0.620310	+	0.784356i	$0.287007\pi$
$522$		0			0
$523$	−4.96107	−	4.16283i	−0.216932	−	0.182028i	0.527845	−	0.849341i	$-0.323000\pi$
$523$	−4.96107	−	4.16283i	−0.216932	−	0.182028i	−0.744778	+	0.667313i	$0.767445\pi$
$524$	−5.91275	+	2.56405i	−0.258300	+	0.112011i
$525$		0			0
$526$	−4.94374	−	16.4555i	−0.215557	−	0.717492i
$527$	−4.88473	−	27.7027i	−0.212782	−	1.20675i
$528$		0			0
$529$	−21.4569	−	7.80966i	−0.932907	−	0.339551i
$530$	3.90039	+	5.22859i	0.169422	+	0.227116i
$531$		0			0
$532$	−18.7018	+	13.1916i	−0.810827	+	0.571927i
$533$	−18.8047			−0.814522
$534$		0			0
$535$	15.1653	+	5.51973i	0.655654	+	0.238639i
$536$	−2.78742	+	7.72789i	−0.120398	+	0.333794i
$537$		0			0
$538$	−7.03909	−	23.4299i	−0.303477	−	1.01013i
$539$	−0.556387	−	0.321230i	−0.0239653	−	0.0138364i
$540$		0			0
$541$	−28.8161	−	24.1796i	−1.23890	−	1.03956i	−0.997609	−	0.0691090i	$-0.977984\pi$
$541$	−28.8161	−	24.1796i	−1.23890	−	1.03956i	−0.241292	−	0.970453i	$-0.577571\pi$
$542$	5.98650	−	6.35760i	0.257142	−	0.273082i
$543$		0			0
$544$	−15.7227	+	14.9776i	−0.674106	+	0.642160i
$545$	1.01396	+	2.78583i	0.0434332	+	0.119332i
$546$		0			0
$547$	1.80391	−	10.2305i	0.0771298	−	0.437425i	−0.921649	−	0.388024i	$-0.873158\pi$
$547$	1.80391	−	10.2305i	0.0771298	−	0.437425i	0.998779	−	0.0494007i	$-0.0157311\pi$
$548$	14.0629	+	7.02873i	0.600739	+	0.300252i
$549$		0			0
$550$	−1.97790	+	34.5332i	−0.0843380	+	1.47250i
$551$	−21.0265	+	18.7694i	−0.895758	+	0.799603i
$552$		0			0
$553$	7.70506	+	9.18254i	0.327653	+	0.390481i
$554$	−35.7836	−	15.3946i	−1.52030	−	0.654054i
$555$		0			0
$556$	0.0139200		0.000837696i	0.000590338		3.55262e-5i
$557$	−32.8112	+	11.9423i	−1.39026	+	0.506012i	−0.925271	−	0.379306i	$-0.876163\pi$
$557$	−32.8112	+	11.9423i	−1.39026	+	0.506012i	−0.464985	+	0.885318i	$0.653940\pi$
$558$		0			0
$559$	−23.4155	−	40.5568i	−0.990370	−	1.71537i
$560$	−7.87928	+	5.91330i	−0.332961	+	0.249883i
$561$		0			0
$562$	9.32571	−	4.69482i	0.393381	−	0.198039i
$563$	10.3868	−	17.9905i	0.437753	−	0.758210i	−0.559763	−	0.828653i	$-0.689108\pi$
$563$	10.3868	−	17.9905i	0.437753	−	0.758210i	0.997516	+	0.0704427i	$0.0224412\pi$
$564$		0			0
$565$	17.8454	−	3.14662i	0.750761	−	0.132379i
$566$	11.9478	+	2.81950i	0.502202	+	0.118513i
$567$		0			0
$568$	−16.5827	+	9.63811i	−0.695793	+	0.404406i
$569$			0.315660i			0.0132332i	0.999978	+	0.00661658i	$0.00210614\pi$
$569$			0.315660i			0.0132332i	−0.999978	+	0.00661658i	$0.997894\pi$
$570$		0			0
$571$			21.2742i			0.890299i	0.895456	+	0.445150i	$0.146850\pi$
$571$			21.2742i			0.890299i	−0.895456	+	0.445150i	$0.853150\pi$
$572$	−40.4044	+	26.6862i	−1.68939	+	1.11581i
$573$		0			0
$574$	−3.93190	+	16.6616i	−0.164114	+	0.695442i
$575$	−1.65344	+	0.291546i	−0.0689532	+	0.0121583i
$576$		0			0
$577$	11.4507	−	19.8332i	0.476699	−	0.825667i	−0.522944	−	0.852367i	$-0.675166\pi$
$577$	11.4507	−	19.8332i	0.476699	−	0.825667i	0.999643	+	0.0266997i	$0.00849980\pi$
$578$	−1.44011	−	2.86061i	−0.0599006	−	0.118986i
$579$		0			0
$580$	−8.80869	+	8.34276i	−0.365761	+	0.346414i
$581$	0.972325	+	1.68412i	0.0403389	+	0.0698689i
$582$		0			0
$583$	27.4286	−	9.98318i	1.13597	−	0.413461i
$584$	0.0971304	+	33.5621i	0.00401929	+	1.38881i
$585$		0			0
$586$	5.54692	−	12.8934i	0.229141	−	0.532621i
$587$	−9.56479	−	11.3989i	−0.394781	−	0.470482i	0.531640	−	0.846970i	$-0.321576\pi$
$587$	−9.56479	−	11.3989i	−0.394781	−	0.470482i	−0.926421	+	0.376488i	$0.877131\pi$
$588$		0			0
$589$	19.7736	−	25.0862i	0.814757	−	1.03366i
$590$	−2.09303	−	0.119879i	−0.0861686	−	0.00493535i
$591$		0			0
$592$	−5.49702	+	8.42847i	−0.225926	+	0.346408i
$593$	0.999120	−	5.66629i	0.0410289	−	0.232687i	−0.957397	−	0.288776i	$-0.906752\pi$
$593$	0.999120	−	5.66629i	0.0410289	−	0.232687i	0.998426	+	0.0560888i	$0.0178630\pi$
$594$		0			0
$595$	3.23348	+	8.88393i	0.132560	+	0.364205i
$596$	13.7555	−	18.5515i	0.563448	−	0.759898i
$597$		0			0
$598$	−1.71113	−	1.61125i	−0.0699732	−	0.0658889i
$599$	12.8004	+	10.7408i	0.523008	+	0.438856i	0.865679	−	0.500599i	$-0.166887\pi$
$599$	12.8004	+	10.7408i	0.523008	+	0.438856i	−0.342671	+	0.939456i	$0.611331\pi$
$600$		0			0
$601$	−2.32187	−	1.34053i	−0.0947110	−	0.0546814i	0.451896	−	0.892070i	$-0.350748\pi$
$601$	−2.32187	−	1.34053i	−0.0947110	−	0.0546814i	−0.546607	+	0.837389i	$0.684081\pi$
$602$	−40.8307	+	12.2668i	−1.66414	+	0.499959i
$603$		0			0
$604$	2.19535	−	7.38480i	0.0893274	−	0.300483i
$605$	−21.3737	−	7.77940i	−0.868965	−	0.316277i
$606$		0			0
$607$	−35.3587			−1.43517			−0.717583	−	0.696473i	$-0.754752\pi$
$607$	−35.3587			−1.43517			−0.717583	+	0.696473i	$0.754752\pi$
$608$	−24.5770	−	1.99316i	−0.996728	−	0.0808332i
$609$		0			0
$610$	6.81471	−	5.08359i	0.275920	−	0.205829i
$611$	−14.6276	−	5.32402i	−0.591770	−	0.215387i
$612$		0			0
$613$	−4.31337	−	24.4623i	−0.174215	−	0.988024i	−0.939046	−	0.343792i	$-0.888288\pi$
$613$	−4.31337	−	24.4623i	−0.174215	−	0.988024i	0.764831	−	0.644232i	$-0.222823\pi$
$614$	−34.0384	+	10.2262i	−1.37368	+	0.412697i
$615$		0			0
$616$	15.1967	+	41.3795i	0.612292	+	1.66723i
$617$	2.84603	+	2.38810i	0.114577	+	0.0961415i	0.698276	−	0.715829i	$-0.253951\pi$
$617$	2.84603	+	2.38810i	0.114577	+	0.0961415i	−0.583699	+	0.811970i	$0.698395\pi$
$618$		0			0
$619$	30.3051	−	17.4967i	1.21807	−	0.703250i	0.253562	−	0.967319i	$-0.418398\pi$
$619$	30.3051	−	17.4967i	1.21807	−	0.703250i	0.964504	+	0.264069i	$0.0850646\pi$
$620$	8.18943	−	11.0447i	0.328896	−	0.443568i
$621$		0			0
$622$	29.1236	−	3.43254i	1.16775	−	0.137632i
$623$	7.83076	−	44.4105i	0.313733	−	1.77927i
$624$		0			0
$625$	9.63126	−	8.08159i	0.385251	−	0.323264i
$626$	−24.3826	−	1.39652i	−0.974524	−	0.0558163i
$627$		0			0
$628$	37.7983	+	4.34408i	1.50831	+	0.173347i
$629$	6.20725	+	7.39752i	0.247499	+	0.294958i
$630$		0			0
$631$	−32.6231	−	5.75233i	−1.29871	−	0.228997i	−0.518801	−	0.854895i	$-0.673621\pi$
$631$	−32.6231	−	5.75233i	−1.29871	−	0.228997i	−0.779904	+	0.625899i	$0.784732\pi$
$632$	0.0373759	+	12.9148i	0.00148673	+	0.513721i
$633$		0			0
$634$	−5.85744	−	3.84441i	−0.232629	−	0.152681i
$635$	6.97769	+	12.0857i	0.276901	+	0.479607i
$636$		0			0
$637$	−0.283679	+	0.338076i	−0.0112398	+	0.0133951i
$638$	24.4114	+	48.4904i	0.966456	+	1.91975i
$639$		0			0
$640$	−10.5999	−	0.545581i	−0.418999	−	0.0215660i
$641$	−11.5354	+	2.03399i	−0.455619	+	0.0803379i	−0.396748	−	0.917928i	$-0.629861\pi$
$641$	−11.5354	+	2.03399i	−0.455619	+	0.0803379i	−0.0588712	+	0.998266i	$0.518750\pi$
$642$		0			0
$643$	−14.1267	+	38.8127i	−0.557101	+	1.53062i	0.266720	+	0.963774i	$0.414060\pi$
$643$	−14.1267	+	38.8127i	−0.557101	+	1.53062i	−0.823822	+	0.566849i	$0.808162\pi$
$644$	−1.78540	+	1.17922i	−0.0703548	+	0.0464678i
$645$		0			0
$646$	−8.68188	+	22.0129i	−0.341584	+	0.866088i
$647$		−	15.5407i		−	0.610967i	−0.952197	−	0.305484i	$-0.901182\pi$
$647$		−	15.5407i		−	0.610967i	0.952197	−	0.305484i	$-0.0988181\pi$
$648$		0			0
$649$	−3.20848	+	8.81521i	−0.125944	+	0.346027i
$650$	23.1256	+	5.45731i	0.907060	+	0.214053i
$651$		0			0
$652$	−3.07612	−	12.8685i	−0.120470	−	0.503968i
$653$	9.90157	−	17.1500i	0.387478	−	0.671132i	−0.604631	−	0.796506i	$-0.706679\pi$
$653$	9.90157	−	17.1500i	0.387478	−	0.671132i	0.992110	+	0.125373i	$0.0400128\pi$
$654$		0			0
$655$	−1.94320	+	2.31581i	−0.0759270	+	0.0904863i
$656$	−14.7521	+	11.0712i	−0.575971	+	0.432259i
$657$		0			0
$658$	−7.77577	+	11.8474i	−0.303131	+	0.461858i
$659$	20.5503	−	7.47970i	0.800526	−	0.291368i	0.0908217	−	0.995867i	$-0.471051\pi$
$659$	20.5503	−	7.47970i	0.800526	−	0.291368i	0.709705	+	0.704499i	$0.248828\pi$
$660$		0			0
$661$	39.3132	+	6.93199i	1.52911	+	0.269623i	0.874005	−	0.485917i	$-0.161514\pi$
$661$	39.3132	+	6.93199i	1.52911	+	0.269623i	0.655103	+	0.755540i	$0.272625\pi$
$662$	−17.6622	−	7.59854i	−0.686462	−	0.295326i
$663$		0			0
$664$	−0.357851	+	2.06439i	−0.0138873	+	0.0801139i
$665$	−5.08061	+	9.45699i	−0.197017	+	0.366726i
$666$		0			0
$667$	−2.01860	+	1.69381i	−0.0781605	+	0.0655845i
$668$	−1.48057	−	0.739997i	−0.0572850	−	0.0286313i
$669$		0			0
$670$	0.451063	+	3.82707i	0.0174261	+	0.147853i
$671$	−13.0116	−	35.7491i	−0.502308	−	1.38008i
$672$		0			0
$673$	22.9216	−	13.2338i	0.883561	−	0.510124i	0.0117304	−	0.999931i	$-0.496266\pi$
$673$	22.9216	−	13.2338i	0.883561	−	0.510124i	0.871831	+	0.489807i	$0.162933\pi$
$674$	7.13485	−	7.57712i	0.274824	−	0.291860i
$675$		0			0
$676$	2.88937	+	6.66293i	0.111129	+	0.256266i
$677$	20.4055	+	11.7811i	0.784248	+	0.452786i	0.837934	−	0.545772i	$-0.183764\pi$
$677$	20.4055	+	11.7811i	0.784248	+	0.452786i	−0.0536855	+	0.998558i	$0.517097\pi$
$678$		0			0
$679$	1.72957	+	9.80886i	0.0663747	+	0.376429i
$680$	−3.45606	+	9.58163i	−0.132534	+	0.367439i
$681$		0			0
$682$	−36.7879	−	49.3153i	−1.40868	−	1.88838i
$683$	12.5259			0.479292			0.239646	−	0.970860i	$-0.422969\pi$
$683$	12.5259			0.479292			0.239646	+	0.970860i	$0.422969\pi$
$684$		0			0
$685$	7.37462			0.281770
$686$	15.7795	+	21.1529i	0.602464	+	0.807622i
$687$		0			0
$688$	−42.2469	−	18.0305i	−1.61065	−	0.687407i
$689$	−3.48178	−	19.7461i	−0.132645	−	0.752268i
$690$		0			0
$691$	−17.6035	−	10.1634i	−0.669667	−	0.386633i	0.126283	−	0.991994i	$-0.459695\pi$
$691$	−17.6035	−	10.1634i	−0.669667	−	0.386633i	−0.795951	+	0.605362i	$0.793029\pi$
$692$	−10.4682	+	4.53953i	−0.397943	+	0.172567i
$693$		0			0
$694$	7.18098	−	7.62612i	0.272586	−	0.289484i
$695$	0.00566495	−	0.00327066i	0.000214884	−	0.000124063i
$696$		0			0
$697$	6.05392	+	16.6330i	0.229309	+	0.630020i
$698$	−3.34217	−	28.3568i	−0.126503	−	1.07332i
$699$		0			0
$700$	9.67073	−	19.3490i	0.365519	−	0.731323i
$701$	18.7774	−	15.7561i	0.709211	−	0.595099i	−0.215167	−	0.976577i	$-0.569029\pi$
$701$	18.7774	−	15.7561i	0.709211	−	0.595099i	0.924378	+	0.381479i	$0.124585\pi$
$702$		0			0
$703$	−1.57274	+	10.8521i	−0.0593169	+	0.409295i
$704$	−15.9853	+	44.7230i	−0.602469	+	1.68556i
$705$		0			0
$706$	−27.7768	−	11.9500i	−1.04539	−	0.449743i
$707$	−25.0910	−	4.42422i	−0.943645	−	0.166390i
$708$		0			0
$709$	24.6478	−	8.97106i	0.925667	−	0.336915i	0.165176	−	0.986264i	$-0.447181\pi$
$709$	24.6478	−	8.97106i	0.925667	−	0.336915i	0.760491	+	0.649349i	$0.224958\pi$
$710$	−4.93664	+	7.52159i	−0.185269	+	0.282280i
$711$		0			0
$712$	37.1287	−	31.3382i	1.39146	−	1.17445i
$713$	1.91960	−	2.28769i	0.0718894	−	0.0856745i
$714$		0			0
$715$	−11.3567	+	19.6704i	−0.424718	+	0.735632i
$716$	8.50717	−	2.03358i	0.317928	−	0.0759984i
$717$		0			0
$718$	−28.5728	−	6.74276i	−1.06633	−	0.251638i
$719$	4.64524	−	12.7627i	0.173238	−	0.475968i	−0.822438	−	0.568854i	$-0.807387\pi$
$719$	4.64524	−	12.7627i	0.173238	−	0.475968i	0.995677	+	0.0928858i	$0.0296091\pi$
$720$		0			0
$721$		−	40.7943i		−	1.51926i
$722$	−25.2126	+	9.29122i	−0.938314	+	0.345784i
$723$		0			0
$724$	8.87815	+	13.4420i	0.329954	+	0.499568i
$725$	9.11127	−	25.0330i	0.338384	−	0.929703i
$726$		0			0
$727$	−18.5330	+	3.26787i	−0.687352	+	0.121199i	−0.506407	−	0.862295i	$-0.669027\pi$
$727$	−18.5330	+	3.26787i	−0.687352	+	0.121199i	−0.180945	+	0.983493i	$0.557916\pi$
$728$	29.8058	−	5.34455i	1.10468	−	0.198082i
$729$		0			0
$730$	7.07912	+	14.0618i	0.262010	+	0.520452i
$731$	−28.3347	+	33.7680i	−1.04800	+	1.24896i
$732$		0			0
$733$	11.3569	+	19.6706i	0.419475	+	0.726552i	0.995887	−	0.0906076i	$-0.0288809\pi$
$733$	11.3569	+	19.6706i	0.419475	+	0.726552i	−0.576412	+	0.817159i	$0.695548\pi$
$734$	−13.7951	−	9.05411i	−0.509185	−	0.334193i
$735$		0			0
$736$	−2.29098	−	0.256582i	−0.0844466	−	0.00945774i
$737$	16.9814	+	2.99429i	0.625520	+	0.110296i
$738$		0			0
$739$	22.4003	+	26.6956i	0.824008	+	0.982015i	0.999997	−	0.00237743i	$-0.000756759\pi$
$739$	22.4003	+	26.6956i	0.824008	+	0.982015i	−0.175989	+	0.984392i	$0.556312\pi$
$740$	−0.538927	+	4.68926i	−0.0198114	+	0.172381i
$741$		0			0
$742$	−18.2238	−	1.04377i	−0.669015	−	0.0383182i
$743$	−18.5624	+	15.5757i	−0.680987	+	0.571416i	−0.916295	−	0.400505i	$-0.868835\pi$
$743$	−18.5624	+	15.5757i	−0.680987	+	0.571416i	0.235307	+	0.971921i	$0.424390\pi$
$744$		0			0
$745$	1.88117	−	10.6686i	0.0689207	−	0.390869i
$746$	36.9636	−	4.35658i	1.35333	−	0.159506i
$747$		0			0
$748$	36.6120	+	27.1470i	1.33867	+	0.992591i
$749$	−39.1102	+	22.5803i	−1.42906	+	0.825065i
$750$		0			0
$751$	−25.2781	−	21.2109i	−0.922412	−	0.773995i	0.0520279	−	0.998646i	$-0.483432\pi$
$751$	−25.2781	−	21.2109i	−0.922412	−	0.773995i	−0.974439	+	0.224650i	$0.927876\pi$
$752$	−14.6097	+	4.43535i	−0.532761	+	0.161741i
$753$		0			0
$754$	35.7154	−	10.7300i	1.30068	−	0.390765i
$755$	−0.627539	−	3.55895i	−0.0228385	−	0.129523i
$756$		0			0
$757$	18.3827	+	6.69076i	0.668131	+	0.243180i	0.653743	−	0.756717i	$-0.273198\pi$
$757$	18.3827	+	6.69076i	0.668131	+	0.243180i	0.0143881	+	0.999896i	$0.495420\pi$
$758$	17.1865	−	12.8207i	0.624243	−	0.465668i
$759$		0			0
$760$	−10.7301	+	4.31777i	−0.389223	+	0.156622i
$761$	7.99819			0.289934			0.144967	−	0.989436i	$-0.453692\pi$
$761$	7.99819			0.289934			0.144967	+	0.989436i	$0.453692\pi$
$762$		0			0
$763$	−7.79556	−	2.83735i	−0.282218	−	0.102719i
$764$	−6.16001	−	1.83124i	−0.222861	−	0.0662521i
$765$		0			0
$766$	−42.1089	+	12.6509i	−1.52146	+	0.457094i
$767$	5.58073	+	3.22204i	0.201509	+	0.116341i
$768$		0			0
$769$	9.49371	+	7.96617i	0.342352	+	0.287267i	0.797710	−	0.603041i	$-0.206044\pi$
$769$	9.49371	+	7.96617i	0.342352	+	0.287267i	−0.455358	+	0.890308i	$0.650489\pi$
$770$	15.0541	+	14.1754i	0.542512	+	0.510845i
$771$		0			0
$772$	9.56488	+	7.09215i	0.344248	+	0.255252i
$773$	11.5697	+	31.7874i	0.416132	+	1.14331i	0.953875	+	0.300204i	$0.0970547\pi$
$773$	11.5697	+	31.7874i	0.416132	+	1.14331i	−0.537743	+	0.843109i	$0.680723\pi$
$774$		0			0
$775$	−5.24256	+	29.7320i	−0.188318	+	1.06801i
$776$	−5.33866	+	9.30893i	−0.191647	+	0.334171i
$777$		0			0
$778$	48.4367	+	2.77423i	1.73654	+	0.0994611i
$779$	−9.51221	+	17.7059i	−0.340810	+	0.634381i
$780$		0			0
$781$	25.8775	+	30.8397i	0.925971	+	1.10353i
$782$	−0.874297	+	2.03224i	−0.0312648	+	0.0726726i
$783$		0			0
$784$	−0.0235015	+	0.432232i	−0.000839339	+	0.0154369i
$785$	16.7706	−	6.10401i	0.598570	−	0.217862i
$786$		0			0
$787$	7.27170	+	12.5950i	0.259208	+	0.448962i	0.966030	−	0.258430i	$-0.0832051\pi$
$787$	7.27170	+	12.5950i	0.259208	+	0.448962i	−0.706822	+	0.707392i	$0.749872\pi$
$788$	−19.2264	−	20.3002i	−0.684914	−	0.723166i
$789$		0			0
$790$	2.72405	+	5.41102i	0.0969175	+	0.192515i
$791$	−25.3535	+	43.9135i	−0.901466	+	1.56139i
$792$		0			0
$793$	−25.7362	+	4.53799i	−0.913920	+	0.161149i
$794$	2.94185	−	12.4662i	0.104402	−	0.442409i
$795$		0			0
$796$	10.8646	+	16.4496i	0.385086	+	0.583042i
$797$			3.14479i			0.111394i	0.998448	+	0.0556971i	$0.0177381\pi$
$797$			3.14479i			0.111394i	−0.998448	+	0.0556971i	$0.982262\pi$
$798$		0			0
$799$			14.6523i			0.518362i
$800$	21.3547	−	9.33396i	0.755004	−	0.330005i
$801$		0			0
$802$	−10.9316	−	2.57971i	−0.386010	−	0.0910928i
$803$	69.3755	−	12.2328i	2.44821	−	0.431685i
$804$		0			0
$805$	−0.501835	+	0.869205i	−0.0176874	+	0.0306354i
$806$	−37.7498	+	19.0043i	−1.32968	+	0.669398i
$807$		0			0
$808$	−17.7055	−	20.9769i	−0.622876	−	0.737966i
$809$	7.09419	+	12.2875i	0.249419	+	0.432006i	0.963365	−	0.268195i	$-0.0864272\pi$
$809$	7.09419	+	12.2875i	0.249419	+	0.432006i	−0.713946	+	0.700201i	$0.753094\pi$
$810$		0			0
$811$	5.23170	−	1.90418i	0.183710	−	0.0668649i	−0.248527	−	0.968625i	$-0.579947\pi$
$811$	5.23170	−	1.90418i	0.183710	−	0.0668649i	0.432237	+	0.901760i	$0.357724\pi$
$812$	−2.03940	−	33.8886i	−0.0715690	−	1.18926i
$813$		0			0
$814$	19.4017	+	8.34689i	0.680030	+	0.292558i
$815$	−3.98936	−	4.75434i	−0.139741	−	0.166537i
$816$		0			0
$817$	−50.0316	+	1.53197i	−1.75038	+	0.0535967i
$818$	2.21104	−	38.6036i	0.0773072	−	1.34974i
$819$		0			0
$820$	−3.86800	+	7.73902i	−0.135076	+	0.270258i
$821$	4.88607	−	27.7103i	0.170525	−	0.967096i	−0.772658	−	0.634823i	$-0.781073\pi$
$821$	4.88607	−	27.7103i	0.170525	−	0.967096i	0.943183	−	0.332274i	$-0.107816\pi$
$822$		0			0
$823$	−13.8813	−	38.1386i	−0.483872	−	1.32943i	−0.906148	−	0.422961i	$-0.860991\pi$
$823$	−13.8813	−	38.1386i	−0.483872	−	1.32943i	0.422276	−	0.906467i	$-0.361231\pi$
$824$	28.1542	−	33.7508i	0.980800	−	1.17577i
$825$		0			0
$826$	4.02172	−	4.27102i	0.139934	−	0.148608i
$827$	−28.7314	−	24.1085i	−0.999088	−	0.838334i	−0.0122298	−	0.999925i	$-0.503893\pi$
$827$	−28.7314	−	24.1085i	−0.999088	−	0.838334i	−0.986858	+	0.161591i	$0.948337\pi$
$828$		0			0
$829$	29.0901	+	16.7952i	1.01034	+	0.583320i	0.911291	−	0.411762i	$-0.135087\pi$
$829$	29.0901	+	16.7952i	1.01034	+	0.583320i	0.0990493	+	0.995083i	$0.468420\pi$
$830$	0.282777	+	0.941236i	0.00981534	+	0.0326708i
$831$		0			0
$832$	28.3481	+	16.1487i	0.982794	+	0.559857i
$833$	0.390359	+	0.142079i	0.0135252	+	0.00492275i
$834$		0			0
$835$	−0.776413			−0.0268689
$836$	4.68868	+	51.5425i	0.162161	+	1.78264i
$837$		0			0
$838$	−11.3974	−	15.2785i	−0.393715	−	0.527788i
$839$	−2.98358	−	1.08593i	−0.103005	−	0.0374906i	0.290004	−	0.957026i	$-0.406343\pi$
$839$	−2.98358	−	1.08593i	−0.103005	−	0.0374906i	−0.393008	+	0.919535i	$0.628566\pi$
$840$		0			0
$841$	−2.22455	−	12.6160i	−0.0767085	−	0.435035i
$842$	15.7652	+	52.4752i	0.543306	+	1.80842i
$843$		0			0
$844$	11.5933	+	26.7343i	0.399058	+	0.920234i
$845$	2.60963	+	2.18974i	0.0897741	+	0.0753294i
$846$		0			0
$847$	55.1211	−	31.8242i	1.89398	−	1.09349i
$848$	−14.3569	−	13.4407i	−0.493018	−	0.461556i
$849$		0			0
$850$	−2.61791	−	22.2118i	−0.0897936	−	0.761859i
$851$	−0.178022	+	1.00961i	−0.00610253	+	0.0346091i
$852$		0			0
$853$	31.0068	−	26.0178i	1.06165	−	0.890833i	0.0673834	−	0.997727i	$-0.478535\pi$
$853$	31.0068	−	26.0178i	1.06165	−	0.890833i	0.994270	+	0.106894i	$0.0340905\pi$
$854$	−1.36041	+	23.7520i	−0.0465522	+	0.812778i
$855$		0			0
$856$	−47.9413	−	8.31036i	−1.63860	−	0.284042i
$857$	−4.59201	−	5.47255i	−0.156860	−	0.186939i	0.681891	−	0.731454i	$-0.261158\pi$
$857$	−4.59201	−	5.47255i	−0.156860	−	0.186939i	−0.838751	+	0.544515i	$0.816714\pi$
$858$		0			0
$859$	33.5177	+	5.91007i	1.14361	+	0.201649i	0.713184	−	0.700977i	$-0.247253\pi$
$859$	33.5177	+	5.91007i	1.14361	+	0.201649i	0.430425	+	0.902626i	$0.358364\pi$
$860$	−21.5074	+	1.29431i	−0.733398	+	0.0441355i
$861$		0			0
$862$	30.7073	−	46.7864i	1.04589	−	1.59355i
$863$	−3.20642	−	5.55368i	−0.109148	−	0.189049i	0.806277	−	0.591538i	$-0.201479\pi$
$863$	−3.20642	−	5.55368i	−0.109148	−	0.189049i	−0.915425	+	0.402488i	$0.868146\pi$
$864$		0			0
$865$	−3.44034	+	4.10003i	−0.116975	+	0.139405i
$866$	−45.9422	+	23.1286i	−1.56118	+	0.785941i
$867$		0			0
$868$	8.94529	+	37.4213i	0.303623	+	1.27016i
$869$	26.6958	−	4.70719i	0.905593	−	0.159680i
$870$		0			0
$871$	4.05124	−	11.1307i	0.137271	−	0.377149i
$872$	−4.49138	−	7.72757i	−0.152097	−	0.261689i
$873$		0			0
$874$	−2.38266	+	0.796109i	−0.0805948	+	0.0269288i
$875$		−	22.4609i		−	0.759317i
$876$		0			0
$877$	2.85384	−	7.84086i	0.0963673	−	0.264767i	−0.882137	−	0.470993i	$-0.843896\pi$
$877$	2.85384	−	7.84086i	0.0963673	−	0.264767i	0.978504	+	0.206226i	$0.0661181\pi$
$878$	3.69304	−	15.6494i	0.124634	−	0.528142i
$879$		0			0
$880$	2.67171	+	22.1175i	0.0900634	+	0.745580i
$881$	9.44775	−	16.3640i	0.318303	−	0.551316i	−0.661831	−	0.749653i	$-0.730220\pi$
$881$	9.44775	−	16.3640i	0.318303	−	0.551316i	0.980134	+	0.198336i	$0.0635538\pi$
$882$		0			0
$883$	7.40855	−	8.82916i	0.249317	−	0.297125i	−0.626842	−	0.779146i	$-0.715653\pi$
$883$	7.40855	−	8.82916i	0.249317	−	0.297125i	0.876159	+	0.482021i	$0.160097\pi$
$884$	22.7320	−	21.5296i	0.764561	−	0.724119i
$885$		0			0
$886$	−26.7536	−	17.5592i	−0.898805	−	0.589912i
$887$	15.5662	−	5.66563i	0.522661	−	0.190233i	−0.0671973	−	0.997740i	$-0.521406\pi$
$887$	15.5662	−	5.66563i	0.522661	−	0.190233i	0.589859	+	0.807507i	$0.299183\pi$
$888$		0			0
$889$	−38.4579	−	6.78117i	−1.28984	−	0.227433i
$890$	9.00670	−	20.9354i	0.301905	−	0.701756i
$891$		0			0
$892$	−10.8404	−	1.24587i	−0.362964	−	0.0417147i
$893$	−12.4122	+	11.0798i	−0.415358	+	0.370772i
$894$		0			0
$895$	3.14303	−	2.63731i	0.105060	−	0.0881556i
$896$	20.2357	−	21.7409i	0.676027	−	0.726311i
$897$		0			0
$898$	−43.2090	+	5.09266i	−1.44190	+	0.169944i
$899$	16.2063	+	44.5265i	0.540511	+	1.48504i
$900$		0			0
$901$	−16.3448	+	9.43668i	−0.544525	+	0.314381i
$902$	28.1852	+	26.5400i	0.938463	+	0.883685i
$903$		0			0
$904$	−51.2830	+	18.8337i	−1.70565	+	0.626401i
$905$	6.54409	+	3.77823i	0.217533	+	0.125593i
$906$		0			0
$907$	−3.05694	−	17.3368i	−0.101504	−	0.575658i	−0.992559	−	0.121763i	$-0.961145\pi$
$907$	−3.05694	−	17.3368i	−0.101504	−	0.575658i	0.891055	−	0.453895i	$-0.149966\pi$
$908$	−2.70044	+	9.08385i	−0.0896173	+	0.301458i
$909$		0			0
$910$	11.3853	−	8.49312i	0.377419	−	0.281544i
$911$	30.1503			0.998923			0.499462	−	0.866336i	$-0.333531\pi$
$911$	30.1503			0.998923			0.499462	+	0.866336i	$0.333531\pi$
$912$		0			0
$913$	4.39769			0.145542
$914$	27.5105	−	20.5220i	0.909965	−	0.678809i
$915$		0			0
$916$	−14.6509	+	49.2832i	−0.484079	+	1.62836i
$917$	−1.46897	−	8.33094i	−0.0485097	−	0.275112i
$918$		0			0
$919$	11.6050	+	6.70014i	0.382813	+	0.221017i	0.679041	−	0.734100i	$-0.262396\pi$
$919$	11.6050	+	6.70014i	0.382813	+	0.221017i	−0.296228	+	0.955117i	$0.595729\pi$
$920$	−1.01507	+	0.372786i	−0.0334659	+	0.0122904i
$921$		0			0
$922$	38.1608	+	35.9333i	1.25676	+	1.18340i
$923$	23.9497	−	13.8274i	0.788313	−	0.455133i
$924$		0			0
$925$	−3.54476	−	9.73915i	−0.116551	−	0.320221i
$926$	29.4648	−	3.47276i	0.968275	−	0.114122i
$927$		0			0
$928$	21.7010	−	29.4450i	0.712371	−	0.966579i
$929$	−23.6357	+	19.8327i	−0.775461	+	0.650689i	−0.942101	−	0.335329i	$-0.891153\pi$
$929$	−23.6357	+	19.8327i	−0.775461	+	0.650689i	0.166640	+	0.986018i	$0.446708\pi$
$930$		0			0
$931$	0.174825	+	0.438117i	0.00572966	+	0.0143587i
$932$	−28.7199	−	3.30071i	−0.940750	−	0.108118i
$933$		0			0
$934$	−22.0821	+	51.3283i	−0.722550	+	1.67951i
$935$	21.0549	+	3.71255i	0.688569	+	0.121413i
$936$		0			0
$937$	−24.9043	+	9.06443i	−0.813588	+	0.296122i	−0.715105	−	0.699017i	$-0.753621\pi$
$937$	−24.9043	+	9.06443i	−0.813588	+	0.296122i	−0.0984830	+	0.995139i	$0.531399\pi$
$938$	−9.01511	−	5.91688i	−0.294354	−	0.193193i
$939$		0			0
$940$	−5.19988	+	4.92484i	−0.169602	+	0.160630i
$941$	19.3496	−	23.0600i	0.630780	−	0.751734i	−0.352104	−	0.935961i	$-0.614534\pi$
$941$	19.3496	−	23.0600i	0.630780	−	0.751734i	0.982884	+	0.184227i	$0.0589781\pi$
$942$		0			0
$943$	−0.939566	+	1.62738i	−0.0305965	+	0.0529947i
$944$	6.27499	−	0.757996i	0.204233	−	0.0246707i
$945$		0			0
$946$	−22.1438	+	93.8354i	−0.719957	+	3.05085i
$947$	−8.91757	+	24.5008i	−0.289782	+	0.796170i	0.706314	+	0.707898i	$0.250357\pi$
$947$	−8.91757	+	24.5008i	−0.289782	+	0.796170i	−0.996096	+	0.0882717i	$0.971866\pi$
$948$		0			0
$949$		−	48.3914i		−	1.57085i
$950$	16.8363	−	19.0138i	0.546243	−	0.616890i
$951$		0			0
$952$	−14.3229	−	24.6430i	−0.464208	−	0.798685i
$953$	0.413730	−	1.13671i	0.0134020	−	0.0368217i	−0.932811	−	0.360365i	$-0.882652\pi$
$953$	0.413730	−	1.13671i	0.0134020	−	0.0368217i	0.946213	+	0.323544i	$0.104874\pi$
$954$		0			0
$955$	−2.96869	+	0.523460i	−0.0960646	+	0.0169388i
$956$	7.05669	+	29.5206i	0.228230	+	0.954764i
$957$		0			0
$958$	16.2182	−	8.16470i	0.523987	−	0.263790i
$959$	−13.2648	+	15.8084i	−0.428343	+	0.510479i
$960$		0			0
$961$	−11.3503	−	19.6592i	−0.366138	−	0.634169i
$962$	7.96096	−	12.1295i	0.256672	−	0.391071i
$963$		0			0
$964$	−11.2021	+	0.674137i	−0.360796	+	0.0217125i
$965$	5.50060	+	0.969904i	0.177071	+	0.0312223i
$966$		0			0
$967$	22.9011	+	27.2925i	0.736451	+	0.877668i	0.996118	−	0.0880305i	$-0.0280573\pi$
$967$	22.9011	+	27.2925i	0.736451	+	0.877668i	−0.259667	+	0.965698i	$0.583613\pi$
$968$	67.5675	+	11.7125i	2.17170	+	0.376452i
$969$		0			0
$970$	−0.287837	+	5.02548i	−0.00924188	+	0.161358i
$971$	10.6081	−	8.90129i	0.340432	−	0.285656i	−0.456503	−	0.889722i	$-0.650898\pi$
$971$	10.6081	−	8.90129i	0.340432	−	0.285656i	0.796934	+	0.604066i	$0.206454\pi$
$972$		0			0
$973$	−0.00317855	+	0.0180265i	−0.000101900	+	0.000577902i
$974$	−5.60184	−	47.5291i	−0.179495	−	1.52293i
$975$		0			0
$976$	−17.5180	+	18.7122i	−0.560738	+	0.598961i
$977$	−6.07278	+	3.50612i	−0.194285	+	0.112171i	−0.593987	−	0.804475i	$-0.702447\pi$
$977$	−6.07278	+	3.50612i	−0.194285	+	0.112171i	0.399702	+	0.916645i	$0.369114\pi$
$978$		0			0
$979$	−78.1215	−	65.5517i	−2.49677	−	2.09504i
$980$	0.0807831	+	0.186287i	0.00258052	+	0.00595073i
$981$		0			0
$982$	−13.1132	−	43.6478i	−0.418459	−	1.39286i
$983$	−1.42112	−	8.05956i	−0.0453266	−	0.257060i	0.953721	−	0.300693i	$-0.0972179\pi$
$983$	−1.42112	−	8.05956i	−0.0453266	−	0.257060i	−0.999048	+	0.0436329i	$0.986107\pi$
$984$		0			0
$985$	−12.3243	−	4.48570i	−0.392686	−	0.142926i
$986$	−20.9890	−	28.1364i	−0.668425	−	0.896045i
$987$		0			0
$988$	35.4276	+	2.97635i	1.12710	+	0.0946904i
$989$	−4.67977			−0.148808
$990$		0			0
$991$	50.4787	+	18.3727i	1.60351	+	0.583629i	0.980141	−	0.198300i	$-0.0635420\pi$
$991$	50.4787	+	18.3727i	1.60351	+	0.583629i	0.623367	+	0.781929i	$0.285764\pi$
$992$	−18.4255	+	37.1338i	−0.585011	+	1.17900i
$993$		0			0
$994$	−7.24384	−	24.1114i	−0.229761	−	0.764768i
$995$	8.00833	+	4.62361i	0.253881	+	0.146578i
$996$		0			0
$997$	8.97721	+	7.53277i	0.284311	+	0.238565i	0.773778	−	0.633456i	$-0.218364\pi$
$997$	8.97721	+	7.53277i	0.284311	+	0.238565i	−0.489467	+	0.872022i	$0.662809\pi$
$998$	−13.7777	+	14.6317i	−0.436125	+	0.463160i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.cf.c.127.3		60
3.2	odd	2		228.2.w.a.127.8	yes	60
4.3	odd	2		684.2.cf.b.127.8		60
12.11	even	2		228.2.w.b.127.3	yes	60
19.3	odd	18		684.2.cf.b.307.8		60
57.41	even	18		228.2.w.b.79.3	yes	60
76.3	even	18	inner	684.2.cf.c.307.3		60
228.155	odd	18		228.2.w.a.79.8	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.w.a.79.8	✓	60	228.155	odd	18
228.2.w.a.127.8	yes	60	3.2	odd	2
228.2.w.b.79.3	yes	60	57.41	even	18
228.2.w.b.127.3	yes	60	12.11	even	2
684.2.cf.b.127.8		60	4.3	odd	2
684.2.cf.b.307.8		60	19.3	odd	18
684.2.cf.c.127.3		60	1.1	even	1	trivial
684.2.cf.c.307.3		60	76.3	even	18	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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	684.cf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.13356 + 0.845604i) q^{2} +(0.569909 - 1.91708i) q^{4} +(-0.162908 - 0.923898i) q^{5} +(2.27351 + 1.31261i) q^{7} +(0.975067 + 2.65504i) q^{8} +(0.965918 + 0.909537i) q^{10} +(5.14137 - 2.96837i) q^{11} +(-1.39481 - 3.83220i) q^{13} +(-3.68710 + 0.434566i) q^{14} +(-3.35041 - 2.18512i) q^{16} +(-2.94059 + 2.46745i) q^{17} +(-4.31383 - 0.625180i) q^{19} +(-1.86403 - 0.214229i) q^{20} +(-3.31798 + 7.71239i) q^{22} +(-0.401333 - 0.0707658i) q^{23} +(3.87141 - 1.40908i) q^{25} +(4.82161 + 3.16457i) q^{26} +(3.81207 - 3.61043i) q^{28} +(4.15634 - 4.95333i) q^{29} +(-3.66403 + 6.34629i) q^{31} +(5.64563 - 0.356152i) q^{32} +(1.24685 - 5.28357i) q^{34} +(0.842345 - 2.31432i) q^{35} -2.51566i q^{37} +(5.41864 - 2.93911i) q^{38} +(2.29414 - 1.33339i) q^{40} +(1.57709 - 4.33302i) q^{41} +(11.3090 - 1.99407i) q^{43} +(-2.76050 - 11.5481i) q^{44} +(0.514774 - 0.259151i) q^{46} +(2.45354 - 2.92401i) q^{47} +(-0.0541088 - 0.0937192i) q^{49} +(-3.19695 + 4.87096i) q^{50} +(-8.14155 + 0.489954i) q^{52} +(4.84195 + 0.853766i) q^{53} +(-3.58005 - 4.26653i) q^{55} +(-1.26821 + 7.31614i) q^{56} +(-0.522897 + 9.12951i) q^{58} +(-1.21047 + 1.01570i) q^{59} +(1.11276 - 6.31077i) q^{61} +(-1.21305 - 10.2922i) q^{62} +(-6.09849 + 5.17769i) q^{64} +(-3.31333 + 1.91295i) q^{65} +(2.22499 + 1.86699i) q^{67} +(3.05443 + 7.04358i) q^{68} +(1.00215 + 3.33571i) q^{70} +(1.17754 + 6.67818i) q^{71} +(11.1504 + 4.05843i) q^{73} +(2.12725 + 2.85164i) q^{74} +(-3.65701 + 7.91368i) q^{76} +15.5853 q^{77} +(4.29071 + 1.56169i) q^{79} +(-1.47302 + 3.45141i) q^{80} +(1.87629 + 6.24532i) q^{82} +(0.641515 + 0.370379i) q^{83} +(2.75872 + 2.31484i) q^{85} +(-11.1332 + 11.8233i) q^{86} +(12.8943 + 10.7562i) q^{88} +(-5.87516 - 16.1419i) q^{89} +(1.85908 - 10.5434i) q^{91} +(-0.364387 + 0.729058i) q^{92} +(-0.308673 + 5.38926i) q^{94} +(0.125156 + 4.08739i) q^{95} +(2.43876 + 2.90640i) q^{97} +(0.140585 + 0.0604816i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 3 q^{2} - 3 q^{4} - 3 q^{8} - 6 q^{10} - 6 q^{13} + 9 q^{14} - 27 q^{16} - 18 q^{19} - 30 q^{20} + 12 q^{22} - 18 q^{28} + 12 q^{31} + 63 q^{32} - 39 q^{34} + 48 q^{38} + 33 q^{40} + 12 q^{41} + 18 q^{43}+ \cdots - 117 q^{98}+O(q^{100}) \) 60 * q + 3 * q^2 - 3 * q^4 - 3 * q^8 - 6 * q^10 - 6 * q^13 + 9 * q^14 - 27 * q^16 - 18 * q^19 - 30 * q^20 + 12 * q^22 - 18 * q^28 + 12 * q^31 + 63 * q^32 - 39 * q^34 + 48 * q^38 + 33 * q^40 + 12 * q^41 + 18 * q^43 + 9 * q^44 - 69 * q^46 + 30 * q^49 + 27 * q^50 - 3 * q^52 - 12 * q^53 + 42 * q^56 - 36 * q^58 - 27 * q^62 + 21 * q^64 + 36 * q^65 - 42 * q^67 - 93 * q^68 + 132 * q^70 + 24 * q^71 + 18 * q^73 - 27 * q^74 + 66 * q^76 + 72 * q^77 - 12 * q^79 - 6 * q^80 - 9 * q^82 - 60 * q^85 - 123 * q^86 + 36 * q^88 + 12 * q^89 + 84 * q^91 + 99 * q^92 - 24 * q^95 + 12 * q^97 - 117 * q^98

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