LMFDB - Embedded newform 684.2.cf.b.307.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [684,2,Mod(91,684)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [60,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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			307.1
Character	$\chi$	$=$	684.307
Dual form			684.2.cf.b.127.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.39185 - 0.250479i) q^{2} +(1.87452 + 0.697261i) q^{4} +(-0.683388 + 3.87569i) q^{5} +(0.181667 - 0.104885i) q^{7} +(-2.43441 - 1.44001i) q^{8} +(1.92196 - 5.22322i) q^{10} +(-0.749928 - 0.432971i) q^{11} +(-0.989139 + 2.71764i) q^{13} +(-0.279125 + 0.100482i) q^{14} +(3.02765 + 2.61406i) q^{16} +(2.09737 + 1.75990i) q^{17} +(-0.105352 + 4.35763i) q^{19} +(-3.98339 + 6.78856i) q^{20} +(0.935341 + 0.790474i) q^{22} +(2.73529 - 0.482305i) q^{23} +(-9.85547 - 3.58710i) q^{25} +(2.05745 - 3.53480i) q^{26} +(0.413671 - 0.0699406i) q^{28} +(-5.73119 - 6.83016i) q^{29} +(-2.99093 - 5.18044i) q^{31} +(-3.55929 - 4.39676i) q^{32} +(-2.47841 - 2.97487i) q^{34} +(0.282354 + 0.775761i) q^{35} +0.151178i q^{37} +(1.23813 - 6.03879i) q^{38} +(7.24470 - 8.45093i) q^{40} +(1.95326 + 5.36654i) q^{41} +(-10.1816 - 1.79529i) q^{43} +(-1.10386 - 1.33451i) q^{44} +(-3.92793 - 0.0138338i) q^{46} +(2.13422 + 2.54346i) q^{47} +(-3.47800 + 6.02407i) q^{49} +(12.8189 + 7.46131i) q^{50} +(-3.74906 + 4.40458i) q^{52} +(-9.34894 + 1.64847i) q^{53} +(2.19055 - 2.61060i) q^{55} +(-0.593288 - 0.00626872i) q^{56} +(6.26617 + 10.9421i) q^{58} +(2.89615 + 2.43016i) q^{59} +(1.46504 + 8.30867i) q^{61} +(2.86535 + 7.95958i) q^{62} +(3.85272 + 7.01118i) q^{64} +(-9.85675 - 5.69080i) q^{65} +(-7.42773 + 6.23260i) q^{67} +(2.70445 + 4.76139i) q^{68} +(-0.198684 - 1.15047i) q^{70} +(2.01679 - 11.4378i) q^{71} +(6.12889 - 2.23073i) q^{73} +(0.0378669 - 0.210418i) q^{74} +(-3.23589 + 8.09500i) q^{76} -0.181649 q^{77} +(16.0953 - 5.85822i) q^{79} +(-12.2003 + 9.94782i) q^{80} +(-1.37445 - 7.95870i) q^{82} +(-13.7430 + 7.93452i) q^{83} +(-8.25415 + 6.92605i) q^{85} +(13.7216 + 5.04907i) q^{86} +(1.20215 + 2.13394i) q^{88} +(-0.622825 + 1.71120i) q^{89} +(0.105347 + 0.597451i) q^{91} +(5.46365 + 1.00312i) q^{92} +(-2.33344 - 4.07470i) q^{94} +(-16.8168 - 3.38626i) q^{95} +(-6.40106 + 7.62849i) q^{97} +(6.34977 - 7.51347i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 3 q^{2} - 3 q^{4} + 3 q^{8} - 6 q^{10} - 6 q^{13} + 9 q^{14} + 21 q^{16} + 18 q^{19} - 30 q^{20} - 12 q^{22} - 18 q^{28} - 12 q^{31} - 33 q^{32} - 15 q^{34} + 84 q^{38} - 87 q^{40} + 12 q^{41} - 18 q^{43}+ \cdots + 105 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 + 21 * q^16 + 18 * q^19 - 30 * q^20 - 12 * q^22 - 18 * q^28 - 12 * q^31 - 33 * q^32 - 15 * q^34 + 84 * q^38 - 87 * q^40 + 12 * q^41 - 18 * q^43 + 51 * q^44 - 21 * q^46 + 30 * q^49 + 27 * q^50 - 3 * q^52 - 12 * q^53 - 42 * q^56 - 36 * q^58 - 105 * q^62 + 21 * q^64 + 36 * q^65 + 42 * q^67 + 15 * q^68 - 96 * q^70 - 24 * q^71 + 18 * q^73 - 69 * q^74 + 54 * q^76 + 72 * q^77 + 12 * q^79 + 12 * q^80 + 75 * q^82 - 60 * q^85 - 21 * q^86 + 36 * q^88 + 12 * q^89 - 84 * q^91 - 99 * q^92 + 24 * q^95 + 12 * q^97 + 105 * q^98

Character values

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

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$-1$	$1$

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 $

$2$	−1.39185	−	0.250479i	−0.984190	−	0.177115i
$2$	−1.39185	−	0.250479i	−0.984190	−	0.177115i
$3$		0			0
$3$		0			0
$4$	1.87452	+	0.697261i	0.937260	+	0.348631i
$5$	−0.683388	+	3.87569i	−0.305621	+	1.73326i	0.314949	+	0.949109i	$0.398013\pi$
$5$	−0.683388	+	3.87569i	−0.305621	+	1.73326i	−0.620569	+	0.784152i	$0.713098\pi$
$6$		0			0
$7$	0.181667	−	0.104885i	0.0686636	−	0.0396430i	−0.465275	−	0.885166i	$-0.654045\pi$
$7$	0.181667	−	0.104885i	0.0686636	−	0.0396430i	0.533939	+	0.845523i	$0.320711\pi$
$8$	−2.43441	−	1.44001i	−0.860694	−	0.509122i
$9$		0			0
$10$	1.92196	−	5.22322i	0.607776	−	1.65173i
$11$	−0.749928	−	0.432971i	−0.226112	−	0.130546i	0.382665	−	0.923887i	$-0.375006\pi$
$11$	−0.749928	−	0.432971i	−0.226112	−	0.130546i	−0.608777	+	0.793341i	$0.708340\pi$
$12$		0			0
$13$	−0.989139	+	2.71764i	−0.274338	+	0.753737i	0.723640	+	0.690177i	$0.242468\pi$
$13$	−0.989139	+	2.71764i	−0.274338	+	0.753737i	−0.997978	+	0.0635596i	$0.979755\pi$
$14$	−0.279125	+	0.100482i	−0.0745994	+	0.0268548i
$15$		0			0
$16$	3.02765	+	2.61406i	0.756913	+	0.653515i
$17$	2.09737	+	1.75990i	0.508687	+	0.426839i	0.860667	−	0.509169i	$-0.170047\pi$
$17$	2.09737	+	1.75990i	0.508687	+	0.426839i	−0.351980	+	0.936008i	$0.614492\pi$
$18$		0			0
$19$	−0.105352	+	4.35763i	−0.0241694	+	0.999708i
$19$	−0.105352	+	4.35763i	−0.0241694	+	0.999708i
$20$	−3.98339	+	6.78856i	−0.890714	+	1.51797i
$21$		0			0
$22$	0.935341	+	0.790474i	0.199415	+	0.168530i
$23$	2.73529	−	0.482305i	0.570347	−	0.100568i	0.118965	−	0.992898i	$-0.462042\pi$
$23$	2.73529	−	0.482305i	0.570347	−	0.100568i	0.451382	+	0.892331i	$0.350931\pi$
$24$		0			0
$25$	−9.85547	−	3.58710i	−1.97109	−	0.717420i
$26$	2.05745	−	3.53480i	0.403499	−	0.693231i
$27$		0			0
$28$	0.413671	−	0.0699406i	0.0781764	−	0.0132175i
$29$	−5.73119	−	6.83016i	−1.06425	−	1.26833i	−0.961847	−	0.273587i	$-0.911790\pi$
$29$	−5.73119	−	6.83016i	−1.06425	−	1.26833i	−0.102408	−	0.994743i	$-0.532655\pi$
$30$		0			0
$31$	−2.99093	−	5.18044i	−0.537186	−	0.930434i	−0.999054	−	0.0434852i	$-0.986154\pi$
$31$	−2.99093	−	5.18044i	−0.537186	−	0.930434i	0.461868	−	0.886949i	$-0.347179\pi$
$32$	−3.55929	−	4.39676i	−0.629199	−	0.777244i
$33$		0			0
$34$	−2.47841	−	2.97487i	−0.425045	−	0.510187i
$35$	0.282354	+	0.775761i	0.0477265	+	0.131128i
$36$		0			0
$37$			0.151178i			0.0248535i	0.999923	+	0.0124267i	$0.00395566\pi$
$37$			0.151178i			0.0248535i	−0.999923	+	0.0124267i	$0.996044\pi$
$38$	1.23813	−	6.03879i	0.200851	−	0.979622i
$39$		0			0
$40$	7.24470	−	8.45093i	1.14549	−	1.33621i
$41$	1.95326	+	5.36654i	0.305048	+	0.838113i	0.993603	+	0.112929i	$0.0360232\pi$
$41$	1.95326	+	5.36654i	0.305048	+	0.838113i	−0.688555	+	0.725184i	$0.741755\pi$
$42$		0			0
$43$	−10.1816	−	1.79529i	−1.55268	−	0.273780i	−0.669501	−	0.742812i	$-0.733492\pi$
$43$	−10.1816	−	1.79529i	−1.55268	−	0.273780i	−0.883181	+	0.469032i	$0.844603\pi$
$44$	−1.10386	−	1.33451i	−0.166413	−	0.201185i
$45$		0			0
$46$	−3.92793	−	0.0138338i	−0.579142	−	0.00203968i
$47$	2.13422	+	2.54346i	0.311307	+	0.371002i	0.898899	−	0.438156i	$-0.144368\pi$
$47$	2.13422	+	2.54346i	0.311307	+	0.371002i	−0.587592	+	0.809158i	$0.699924\pi$
$48$		0			0
$49$	−3.47800	+	6.02407i	−0.496857	+	0.860581i
$50$	12.8189	+	7.46131i	1.81287	+	1.05519i
$51$		0			0
$52$	−3.74906	+	4.40458i	−0.519902	+	0.610805i
$53$	−9.34894	+	1.64847i	−1.28418	+	0.226435i	−0.773752	−	0.633488i	$-0.781622\pi$
$53$	−9.34894	+	1.64847i	−1.28418	+	0.226435i	−0.510423	+	0.859923i	$0.670511\pi$
$54$		0			0
$55$	2.19055	−	2.61060i	0.295374	−	0.352013i
$56$	−0.593288	−	0.00626872i	−0.0792815	−	0.000837692i
$57$		0			0
$58$	6.26617	+	10.9421i	0.822788	+	1.43677i
$59$	2.89615	+	2.43016i	0.377047	+	0.316380i	0.811542	−	0.584295i	$-0.198629\pi$
$59$	2.89615	+	2.43016i	0.377047	+	0.316380i	−0.434495	+	0.900674i	$0.643073\pi$
$60$		0			0
$61$	1.46504	+	8.30867i	0.187579	+	1.06382i	0.922596	+	0.385767i	$0.126063\pi$
$61$	1.46504	+	8.30867i	0.187579	+	1.06382i	−0.735017	+	0.678049i	$0.762826\pi$
$62$	2.86535	+	7.95958i	0.363899	+	1.01087i
$63$		0			0
$64$	3.85272	+	7.01118i	0.481589	+	0.876397i
$65$	−9.85675	−	5.69080i	−1.22258	−	0.705856i
$66$		0			0
$67$	−7.42773	+	6.23260i	−0.907442	+	0.761434i	−0.971631	−	0.236504i	$-0.923998\pi$
$67$	−7.42773	+	6.23260i	−0.907442	+	0.761434i	0.0641890	+	0.997938i	$0.479554\pi$
$68$	2.70445	+	4.76139i	0.327963	+	0.577403i
$69$		0			0
$70$	−0.198684	−	1.15047i	−0.0237473	−	0.137508i
$71$	2.01679	−	11.4378i	0.239349	−	1.35742i	−0.593908	−	0.804533i	$-0.702416\pi$
$71$	2.01679	−	11.4378i	0.239349	−	1.35742i	0.833257	−	0.552885i	$-0.186473\pi$
$72$		0			0
$73$	6.12889	−	2.23073i	0.717332	−	0.261088i	0.0425394	−	0.999095i	$-0.486455\pi$
$73$	6.12889	−	2.23073i	0.717332	−	0.261088i	0.674793	+	0.738007i	$0.264233\pi$
$74$	0.0378669	−	0.210418i	0.00440194	−	0.0244605i
$75$		0			0
$76$	−3.23589	+	8.09500i	−0.371182	+	0.928560i
$77$	−0.181649			−0.0207009
$78$		0			0
$79$	16.0953	−	5.85822i	1.81087	−	0.659101i	0.813922	−	0.580975i	$-0.197328\pi$
$79$	16.0953	−	5.85822i	1.81087	−	0.659101i	0.996943	−	0.0781264i	$-0.0248938\pi$
$80$	−12.2003	+	9.94782i	−1.36404	+	1.11220i
$81$		0			0
$82$	−1.37445	−	7.95870i	−0.151783	−	0.878891i
$83$	−13.7430	+	7.93452i	−1.50849	+	0.870926i	−0.508538	+	0.861040i	$0.669814\pi$
$83$	−13.7430	+	7.93452i	−1.50849	+	0.870926i	−0.999951	+	0.00988648i	$0.996853\pi$
$84$		0			0
$85$	−8.25415	+	6.92605i	−0.895288	+	0.751236i
$86$	13.7216	+	5.04907i	1.47964	+	0.544455i
$87$		0			0
$88$	1.20215	+	2.13394i	0.128149	+	0.227478i
$89$	−0.622825	+	1.71120i	−0.0660193	+	0.181387i	−0.968315	−	0.249730i	$-0.919658\pi$
$89$	−0.622825	+	1.71120i	−0.0660193	+	0.181387i	0.902296	+	0.431117i	$0.141880\pi$
$90$		0			0
$91$	0.105347	+	0.597451i	0.0110433	+	0.0626299i
$92$	5.46365	+	1.00312i	0.569624	+	0.104582i
$93$		0			0
$94$	−2.33344	−	4.07470i	−0.240676	−	0.420274i
$95$	−16.8168	−	3.38626i	−1.72537	−	0.347423i
$96$		0			0
$97$	−6.40106	+	7.62849i	−0.649929	+	0.774555i	−0.985903	−	0.167316i	$-0.946490\pi$
$97$	−6.40106	+	7.62849i	−0.649929	+	0.774555i	0.335974	+	0.941871i	$0.390935\pi$
$98$	6.34977	−	7.51347i	0.641424	−	0.758975i
$99$		0			0
$100$	−15.9731	−	13.5959i	−1.59731	−	1.35959i
$101$	12.3259	+	4.48627i	1.22647	+	0.446400i	0.872389	−	0.488813i	$-0.162570\pi$
$101$	12.3259	+	4.48627i	1.22647	+	0.446400i	0.354086	+	0.935213i	$0.384792\pi$
$102$		0			0
$103$	3.05588	−	5.29294i	0.301105	−	0.521529i	−0.675282	−	0.737560i	$-0.735978\pi$
$103$	3.05588	−	5.29294i	0.301105	−	0.521529i	0.976386	+	0.216031i	$0.0693113\pi$
$104$	6.32141	−	5.19147i	0.619865	−	0.509066i
$105$		0			0
$106$	13.4253	+	0.0472825i	1.30398	+	0.00459248i
$107$	−0.977120	−	1.69242i	−0.0944618	−	0.163613i	0.814922	−	0.579571i	$-0.196780\pi$
$107$	−0.977120	−	1.69242i	−0.0944618	−	0.163613i	−0.909384	+	0.415958i	$0.863446\pi$
$108$		0			0
$109$	6.99424	+	1.23327i	0.669927	+	0.118126i	0.498258	−	0.867029i	$-0.333973\pi$
$109$	6.99424	+	1.23327i	0.669927	+	0.118126i	0.171669	+	0.985155i	$0.445084\pi$
$110$	−3.70283	+	3.08489i	−0.353051	+	0.294132i
$111$		0			0
$112$	0.824201	+	0.157331i	0.0778797	+	0.0148664i
$113$			10.4870i			0.986531i	0.869879	+	0.493265i	$0.164197\pi$
$113$			10.4870i			0.986531i	−0.869879	+	0.493265i	$0.835803\pi$
$114$		0			0
$115$			10.9307i			1.01930i
$116$	−5.98082	−	16.7994i	−0.555305	−	1.55979i
$117$		0			0
$118$	−3.42232	−	4.10785i	−0.315050	−	0.378158i
$119$	0.565610	+	0.0997324i	0.0518494	+	0.00914245i
$120$		0			0
$121$	−5.12507	−	8.87689i	−0.465916	−	0.806990i
$122$	0.0420213	−	11.9314i	0.00380443	−	1.08022i
$123$		0			0
$124$	−1.99444	−	11.7963i	−0.179106	−	1.05934i
$125$	10.7989	−	18.7042i	0.965883	−	1.67296i
$126$		0			0
$127$	−17.1366	−	6.23722i	−1.52063	−	0.553464i	−0.559324	−	0.828949i	$-0.688939\pi$
$127$	−17.1366	−	6.23722i	−1.52063	−	0.553464i	−0.961305	+	0.275486i	$0.911161\pi$
$128$	−3.60627	−	10.7236i	−0.318752	−	0.947838i
$129$		0			0
$130$	12.2937	+	10.3897i	1.07823	+	0.911235i
$131$	−7.78238	+	9.27469i	−0.679950	+	0.810333i	−0.990101	−	0.140354i	$-0.955176\pi$
$131$	−7.78238	+	9.27469i	−0.679950	+	0.810333i	0.310151	+	0.950687i	$0.399620\pi$
$132$		0			0
$133$	0.437912	+	0.802686i	0.0379718	+	0.0696017i
$134$	11.8995	−	6.81439i	1.02796	−	0.588674i
$135$		0			0
$136$	−2.57157	−	7.30457i	−0.220511	−	0.626361i
$137$	2.48319	+	14.0829i	0.212153	+	1.20318i	0.885778	+	0.464109i	$0.153625\pi$
$137$	2.48319	+	14.0829i	0.212153	+	1.20318i	−0.673625	+	0.739073i	$0.735264\pi$
$138$		0			0
$139$	4.90177	−	13.4675i	0.415763	−	1.14230i	−0.538316	−	0.842743i	$-0.680939\pi$
$139$	4.90177	−	13.4675i	0.415763	−	1.14230i	0.954079	−	0.299556i	$-0.0968386\pi$
$140$	−0.0116298	+	1.65105i	−0.000982902	+	0.139540i
$141$		0			0
$142$	−5.67202	+	15.4146i	−0.475985	+	1.29357i
$143$	1.91844	−	1.60976i	0.160428	−	0.134615i
$144$		0			0
$145$	30.3882	−	17.5446i	2.52360	−	1.45700i
$146$	−9.08928	+	1.56970i	−0.752234	+	0.129909i
$147$		0			0
$148$	−0.105410	+	0.283386i	−0.00866468	+	0.0232942i
$149$	8.96072	−	3.26144i	0.734091	−	0.267187i	0.0521954	−	0.998637i	$-0.483378\pi$
$149$	8.96072	−	3.26144i	0.734091	−	0.267187i	0.681895	+	0.731450i	$0.261156\pi$
$150$		0			0
$151$	13.8409			1.12636			0.563180	−	0.826334i	$-0.309578\pi$
$151$	13.8409			1.12636			0.563180	+	0.826334i	$0.309578\pi$
$152$	6.53151	−	10.4565i	0.529776	−	0.848138i
$153$		0			0
$154$	0.252830	+	0.0454994i	0.0203736	+	0.00366644i
$155$	22.1217	−	8.05165i	1.77686	−	0.646724i
$156$		0			0
$157$	−0.644692	+	3.65623i	−0.0514520	+	0.291799i	−0.999666	−	0.0258325i	$-0.991776\pi$
$157$	−0.644692	+	3.65623i	−0.0514520	+	0.291799i	0.948214	+	0.317631i	$0.102887\pi$
$158$	−23.8697	+	4.12225i	−1.89897	+	0.327948i
$159$		0			0
$160$	19.4728	−	10.7900i	1.53946	−	0.853024i
$161$	0.446324	−	0.374511i	0.0351753	−	0.0295156i
$162$		0			0
$163$	6.98080	+	4.03037i	0.546778	+	0.315683i	0.747822	−	0.663900i	$-0.231100\pi$
$163$	6.98080	+	4.03037i	0.546778	+	0.315683i	−0.201043	+	0.979582i	$0.564433\pi$
$164$	−0.0804527	+	11.4216i	−0.00628230	+	0.891879i
$165$		0			0
$166$	21.1157	−	7.60137i	1.63889	−	0.589980i
$167$	1.63408	+	9.26731i	0.126449	+	0.717126i	0.980437	+	0.196834i	$0.0630659\pi$
$167$	1.63408	+	9.26731i	0.126449	+	0.717126i	−0.853988	+	0.520292i	$0.825823\pi$
$168$		0			0
$169$	3.55142	+	2.98000i	0.273186	+	0.229230i
$170$	13.2234	−	7.57257i	1.01419	−	0.580789i
$171$		0			0
$172$	−17.8339	−	10.4646i	−1.35982	−	0.797915i
$173$	9.44603	−	11.2573i	0.718169	−	0.855880i	−0.276283	−	0.961076i	$-0.589103\pi$
$173$	9.44603	−	11.2573i	0.718169	−	0.855880i	0.994451	+	0.105196i	$0.0335471\pi$
$174$		0			0
$175$	−2.16665	+	0.382038i	−0.163783	+	0.0288794i
$176$	−1.13871	−	3.27124i	−0.0858334	−	0.246579i
$177$		0			0
$178$	1.29550	−	2.22573i	0.0971019	−	0.166826i
$179$	−4.06680	+	7.04391i	−0.303967	+	0.526486i	−0.977031	−	0.213098i	$-0.931645\pi$
$179$	−4.06680	+	7.04391i	−0.303967	+	0.526486i	0.673064	+	0.739584i	$0.264978\pi$
$180$		0			0
$181$	2.72615	+	3.24890i	0.202633	+	0.241489i	0.857785	−	0.514008i	$-0.171840\pi$
$181$	2.72615	+	3.24890i	0.202633	+	0.241489i	−0.655152	+	0.755497i	$0.727396\pi$
$182$	0.00302162	−	0.857952i	0.000223978	−	0.0635956i
$183$		0			0
$184$	−7.35334	−	2.76473i	−0.542096	−	0.203818i
$185$	−0.585918	−	0.103313i	−0.0430775	−	0.00759573i
$186$		0			0
$187$	−0.810889	−	2.22790i	−0.0592981	−	0.162920i
$188$	2.22718	+	6.25587i	0.162434	+	0.456256i
$189$		0			0
$190$	22.5584	+	8.92544i	1.63656	+	0.647520i
$191$		−	12.9422i		−	0.936468i	−0.883605	−	0.468234i	$-0.844891\pi$
$191$		−	12.9422i		−	0.936468i	0.883605	−	0.468234i	$-0.155109\pi$
$192$		0			0
$193$	0.0498843	+	0.137056i	0.00359075	+	0.00986551i	0.941475	−	0.337083i	$-0.109440\pi$
$193$	0.0498843	+	0.137056i	0.00359075	+	0.00986551i	−0.937884	+	0.346948i	$0.887218\pi$
$194$	10.8201	−	9.01441i	0.776840	−	0.647197i
$195$		0			0
$196$	−10.7199	+	8.86717i	−0.765709	+	0.633369i
$197$	5.67982	+	9.83775i	0.404671	+	0.700910i	0.994283	−	0.106776i	$-0.0340528\pi$
$197$	5.67982	+	9.83775i	0.404671	+	0.700910i	−0.589612	+	0.807686i	$0.700719\pi$
$198$		0			0
$199$	2.97672	+	3.54752i	0.211014	+	0.251477i	0.861162	−	0.508331i	$-0.169737\pi$
$199$	2.97672	+	3.54752i	0.211014	+	0.251477i	−0.650148	+	0.759808i	$0.725293\pi$
$200$	18.8268	+	22.9245i	1.33126	+	1.62101i
$201$		0			0
$202$	−16.0322	−	9.33162i	−1.12802	−	0.656570i
$203$	−1.75755	−	0.639696i	−0.123356	−	0.0448979i
$204$		0			0
$205$	−22.1339	+	3.90280i	−1.54590	+	0.272583i
$206$	−5.57911	+	6.60157i	−0.388715	+	0.459953i
$207$		0			0
$208$	−10.0988	+	5.64240i	−0.700229	+	0.391230i
$209$	1.96573	−	3.22229i	0.135973	−	0.222890i
$210$		0			0
$211$	1.45050	+	1.21712i	0.0998568	+	0.0837898i	0.691349	−	0.722521i	$-0.257017\pi$
$211$	1.45050	+	1.21712i	0.0998568	+	0.0837898i	−0.591492	+	0.806311i	$0.701461\pi$
$212$	−18.6742	−	3.42856i	−1.28255	−	0.235475i
$213$		0			0
$214$	0.936093	+	2.60035i	0.0639900	+	0.177757i
$215$	13.9160	−	38.2339i	0.949063	−	2.60753i
$216$		0			0
$217$	−1.08670	−	0.627409i	−0.0737703	−	0.0425913i
$218$	−9.42606	−	3.46845i	−0.638414	−	0.234913i
$219$		0			0
$220$	5.92650	−	3.36623i	0.399565	−	0.226951i
$221$	−6.85736	+	3.95910i	−0.461276	+	0.266318i
$222$		0			0
$223$	−1.35879	+	7.70607i	−0.0909911	+	0.516036i	0.904911	+	0.425600i	$0.139937\pi$
$223$	−1.35879	+	7.70607i	−0.0909911	+	0.516036i	−0.995902	+	0.0904358i	$0.971174\pi$
$224$	−1.10776	−	0.425428i	−0.0740153	−	0.0284251i
$225$		0			0
$226$	2.62677	−	14.5963i	0.174730	−	0.970934i
$227$	27.2136			1.80623			0.903114	−	0.429400i	$-0.141275\pi$
$227$	27.2136			1.80623			0.903114	+	0.429400i	$0.141275\pi$
$228$		0			0
$229$	7.86096			0.519467			0.259733	−	0.965680i	$-0.416365\pi$
$229$	7.86096			0.519467			0.259733	+	0.965680i	$0.416365\pi$
$230$	2.73792	−	15.2140i	0.180533	−	1.00318i
$231$		0			0
$232$	4.11653	+	24.8804i	0.270264	+	1.63348i
$233$	0.324927	−	1.84275i	0.0212866	−	0.120723i	−0.972313	−	0.233683i	$-0.924922\pi$
$233$	0.324927	−	1.84275i	0.0212866	−	0.120723i	0.993599	+	0.112960i	$0.0360333\pi$
$234$		0			0
$235$	−11.3162	+	6.53338i	−0.738185	+	0.426191i
$236$	3.73444	+	6.57475i	0.243091	+	0.427980i
$237$		0			0
$238$	−0.762267	−	0.280487i	−0.0494104	−	0.0181812i
$239$	3.69843	+	2.13529i	0.239232	+	0.138121i	0.614824	−	0.788665i	$-0.289227\pi$
$239$	3.69843	+	2.13529i	0.239232	+	0.138121i	−0.375592	+	0.926785i	$0.622561\pi$
$240$		0			0
$241$	1.49461	−	4.10641i	0.0962764	−	0.264517i	−0.882200	−	0.470874i	$-0.843939\pi$
$241$	1.49461	−	4.10641i	0.0962764	−	0.264517i	0.978477	+	0.206357i	$0.0661608\pi$
$242$	4.90988	+	13.6391i	0.315619	+	0.876752i
$243$		0			0
$244$	−3.04706	+	16.5963i	−0.195068	+	1.06247i
$245$	−20.9706	−	17.5964i	−1.33976	−	1.12419i
$246$		0			0
$247$	−11.7382	−	4.59661i	−0.746886	−	0.292475i
$248$	−0.178760	+	16.9183i	−0.0113512	+	1.07431i
$249$		0			0
$250$	−19.7155	+	23.3287i	−1.24692	+	1.47544i
$251$	−9.14449	+	1.61242i	−0.577195	+	0.101775i	−0.454622	−	0.890684i	$-0.650226\pi$
$251$	−9.14449	+	1.61242i	−0.577195	+	0.101775i	−0.122573	+	0.992460i	$0.539115\pi$
$252$		0			0
$253$	−2.26009	−	0.822606i	−0.142091	−	0.0517168i
$254$	22.2894	+	12.9737i	1.39856	+	0.814040i
$255$		0			0
$256$	2.33337	+	15.8289i	0.145836	+	0.989309i
$257$	9.61171	+	11.4548i	0.599562	+	0.714530i	0.977414	−	0.211336i	$-0.0677814\pi$
$257$	9.61171	+	11.4548i	0.599562	+	0.714530i	−0.377851	+	0.925866i	$0.623337\pi$
$258$		0			0
$259$	0.0158563	+	0.0274640i	0.000985265	+	0.00170653i
$260$	−14.5087	−	17.5402i	−0.899792	−	1.08780i
$261$		0			0
$262$	13.1551	−	10.9597i	0.812723	−	0.677092i
$263$	8.49957	+	23.3524i	0.524106	+	1.43997i	0.865911	+	0.500198i	$0.166739\pi$
$263$	8.49957	+	23.3524i	0.524106	+	1.43997i	−0.341805	+	0.939771i	$0.611038\pi$
$264$		0			0
$265$		−	37.3601i		−	2.29501i
$266$	−0.408454	−	1.22691i	−0.0250439	−	0.0752267i
$267$		0			0
$268$	−18.2692	+	6.50408i	−1.11597	+	0.397300i
$269$	2.09029	+	5.74304i	0.127448	+	0.350159i	0.986962	−	0.160952i	$-0.0514563\pi$
$269$	2.09029	+	5.74304i	0.127448	+	0.350159i	−0.859515	+	0.511111i	$0.829234\pi$
$270$		0			0
$271$	3.74612	+	0.660543i	0.227561	+	0.0401251i	0.286266	−	0.958150i	$-0.407586\pi$
$271$	3.74612	+	0.660543i	0.227561	+	0.0401251i	−0.0587049	+	0.998275i	$0.518697\pi$
$272$	1.74962	+	10.8110i	0.106086	+	0.655514i
$273$		0			0
$274$	0.0712245	−	20.2233i	0.00430283	−	1.22174i
$275$	5.83778	+	6.95720i	0.352032	+	0.419535i
$276$		0			0
$277$	8.61685	−	14.9248i	0.517736	−	0.896745i	−0.482052	−	0.876143i	$-0.660108\pi$
$277$	8.61685	−	14.9248i	0.517736	−	0.896745i	0.999788	−	0.0206025i	$-0.00655846\pi$
$278$	−10.1959	+	17.5170i	−0.611509	+	1.05060i
$279$		0			0
$280$	0.429742	−	2.29512i	0.0256820	−	0.137159i
$281$	18.1477	−	3.19992i	1.08260	−	0.190891i	0.396234	−	0.918149i	$-0.370317\pi$
$281$	18.1477	−	3.19992i	1.08260	−	0.190891i	0.686364	+	0.727258i	$0.259206\pi$
$282$		0			0
$283$	−0.208397	+	0.248357i	−0.0123879	+	0.0147633i	−0.772203	−	0.635376i	$-0.780845\pi$
$283$	−0.208397	+	0.248357i	−0.0123879	+	0.0147633i	0.759815	+	0.650139i	$0.225290\pi$
$284$	11.7557	−	20.0342i	0.697570	−	1.18881i
$285$		0			0
$286$	−3.07340	+	1.76003i	−0.181734	+	0.104073i
$287$	0.917715	+	0.770054i	0.0541710	+	0.0454548i
$288$		0			0
$289$	−1.65032	−	9.35941i	−0.0970774	−	0.550553i
$290$	−46.6905	+	16.8080i	−2.74176	+	0.986999i
$291$		0			0
$292$	13.0441	+	0.0918814i	0.763350	+	0.00537695i
$293$	−24.6394	−	14.2255i	−1.43945	−	0.831065i	−0.441636	−	0.897194i	$-0.645602\pi$
$293$	−24.6394	−	14.2255i	−1.43945	−	0.831065i	−0.997811	+	0.0661289i	$0.978935\pi$
$294$		0			0
$295$	−11.3977	+	9.56383i	−0.663601	+	0.556828i
$296$	0.217698	−	0.368029i	0.0126535	−	0.0213912i
$297$		0			0
$298$	−13.2889	+	2.29497i	−0.769808	+	0.132944i
$299$	−1.39485	+	7.91059i	−0.0806663	+	0.457481i
$300$		0			0
$301$	−2.03796	+	0.741757i	−0.117466	+	0.0427542i
$302$	−19.2646	−	3.46687i	−1.10855	−	0.199496i
$303$		0			0
$304$	−11.7101	+	12.9180i	−0.671618	+	0.740897i
$305$	−33.2030			−1.90120
$306$		0			0
$307$	7.20630	−	2.62288i	0.411285	−	0.149696i	−0.128087	−	0.991763i	$-0.540884\pi$
$307$	7.20630	−	2.62288i	0.411285	−	0.149696i	0.539372	+	0.842067i	$0.318662\pi$
$308$	−0.340505	−	0.126657i	−0.0194021	−	0.00721695i
$309$		0			0
$310$	−32.8070	+	5.66570i	−1.86331	+	0.321790i
$311$	−23.6264	+	13.6407i	−1.33973	+	0.773493i	−0.986767	−	0.162144i	$-0.948159\pi$
$311$	−23.6264	+	13.6407i	−1.33973	+	0.773493i	−0.352962	+	0.935638i	$0.614826\pi$
$312$		0			0
$313$	−22.1900	+	18.6196i	−1.25425	+	1.05244i	−0.257985	+	0.966149i	$0.583059\pi$
$313$	−22.1900	+	18.6196i	−1.25425	+	1.05244i	−0.996270	+	0.0862959i	$0.972497\pi$
$314$	1.81313	−	4.92746i	0.102321	−	0.278073i
$315$		0			0
$316$	34.2557	+	0.241294i	1.92703	+	0.0135738i
$317$	3.22555	−	8.86213i	0.181165	−	0.497747i	−0.815555	−	0.578680i	$-0.803568\pi$
$317$	3.22555	−	8.86213i	0.181165	−	0.497747i	0.996719	+	0.0809336i	$0.0257902\pi$
$318$		0			0
$319$	1.34071	+	7.60357i	0.0750656	+	0.425718i
$320$	−29.8060	+	10.1406i	−1.66621	+	0.566875i
$321$		0			0
$322$	−0.715026	+	0.409469i	−0.0398468	+	0.0228188i
$323$	−7.88995	+	8.95414i	−0.439009	+	0.498222i
$324$		0			0
$325$	19.4969	−	23.2355i	1.08149	−	1.28887i
$326$	−8.70674	−	7.35823i	−0.482222	−	0.407535i
$327$		0			0
$328$	2.97286	−	15.8771i	0.164149	−	0.876666i
$329$	0.654488	+	0.238214i	0.0360831	+	0.0131332i
$330$		0			0
$331$	−10.9079	+	18.8930i	−0.599552	+	1.03846i	0.393335	+	0.919395i	$0.371321\pi$
$331$	−10.9079	+	18.8930i	−0.599552	+	1.03846i	−0.992887	+	0.119060i	$0.962012\pi$
$332$	−31.2939	+	5.29096i	−1.71748	+	0.290379i
$333$		0			0
$334$	0.0468697	−	13.3081i	0.00256459	−	0.728184i
$335$	−19.0796	−	33.0468i	−1.04243	−	1.80554i
$336$		0			0
$337$	14.5666	+	2.56848i	0.793492	+	0.139914i	0.555679	−	0.831397i	$-0.312458\pi$
$337$	14.5666	+	2.56848i	0.793492	+	0.139914i	0.237813	+	0.971311i	$0.423569\pi$
$338$	−4.19664	−	5.03728i	−0.228267	−	0.273992i
$339$		0			0
$340$	−20.3018	+	7.22773i	−1.10102	+	0.391979i
$341$			5.17994i			0.280509i
$342$		0			0
$343$			2.92756i			0.158073i
$344$	22.2010	+	19.0322i	1.19700	+	1.02615i
$345$		0			0
$346$	−15.9672	+	13.3026i	−0.858404	+	0.715150i
$347$	6.08482	+	1.07292i	0.326650	+	0.0575972i	0.334568	−	0.942371i	$-0.391409\pi$
$347$	6.08482	+	1.07292i	0.326650	+	0.0575972i	−0.00791847	+	0.999969i	$0.502521\pi$
$348$		0			0
$349$	5.62591	+	9.74437i	0.301148	+	0.521604i	0.976396	−	0.215987i	$-0.0692967\pi$
$349$	5.62591	+	9.74437i	0.301148	+	0.521604i	−0.675248	+	0.737591i	$0.735963\pi$
$350$	3.11135	+	0.0109579i	0.166309	+	0.000585723i
$351$		0			0
$352$	0.765540	+	4.83832i	0.0408034	+	0.257883i
$353$	9.41068	−	16.2998i	0.500880	−	0.867550i	−0.499119	−	0.866533i	$-0.666343\pi$
$353$	9.41068	−	16.2998i	0.500880	−	0.867550i	0.999999	−	0.00101645i	$-0.000323547\pi$
$354$		0			0
$355$	42.9511	+	15.6329i	2.27961	+	0.829710i
$356$	−2.36065	+	2.77340i	−0.125114	+	0.146990i
$357$		0			0
$358$	7.42475	−	8.78545i	0.392410	−	0.464325i
$359$	7.58505	−	9.03951i	0.400324	−	0.477087i	−0.527795	−	0.849372i	$-0.676981\pi$
$359$	7.58505	−	9.03951i	0.400324	−	0.477087i	0.928119	+	0.372285i	$0.121425\pi$
$360$		0			0
$361$	−18.9778	−	0.918170i	−0.998832	−	0.0483247i
$362$	−2.98062	−	5.20483i	−0.156658	−	0.273560i
$363$		0			0
$364$	−0.219105	+	1.19339i	−0.0114842	+	0.0625505i
$365$	4.45721	+	25.2781i	0.233301	+	1.32312i
$366$		0			0
$367$	−5.33801	+	14.6661i	−0.278642	+	0.765562i	0.718875	+	0.695139i	$0.244657\pi$
$367$	−5.33801	+	14.6661i	−0.278642	+	0.765562i	−0.997517	+	0.0704230i	$0.977565\pi$
$368$	9.54228	+	5.68996i	0.497426	+	0.296609i
$369$		0			0
$370$	0.789635	+	0.290557i	0.0410512	+	0.0151053i
$371$	−1.52549	+	1.28004i	−0.0791996	+	0.0664563i
$372$		0			0
$373$	13.4824	−	7.78405i	0.698090	−	0.403043i	−0.108545	−	0.994091i	$-0.534619\pi$
$373$	13.4824	−	7.78405i	0.698090	−	0.403043i	0.806636	+	0.591049i	$0.201286\pi$
$374$	0.570598	+	3.30402i	0.0295049	+	0.170847i
$375$		0			0
$376$	−1.53294	−	9.26513i	−0.0790554	−	0.477813i
$377$	24.2308	−	8.81931i	1.24795	−	0.454217i
$378$		0			0
$379$	22.0194			1.13106			0.565530	−	0.824728i	$-0.308672\pi$
$379$	22.0194			1.13106			0.565530	+	0.824728i	$0.308672\pi$
$380$	−29.1623	−	18.0733i	−1.49600	−	0.927142i
$381$		0			0
$382$	−3.24176	+	18.0137i	−0.165863	+	0.921662i
$383$	−21.8207	+	7.94210i	−1.11499	+	0.405822i	−0.832821	−	0.553543i	$-0.813275\pi$
$383$	−21.8207	+	7.94210i	−1.11499	+	0.405822i	−0.282167	+	0.959365i	$0.591053\pi$
$384$		0			0
$385$	0.124137	−	0.704016i	0.00632661	−	0.0358800i
$386$	−0.0351021	−	0.203257i	−0.00178665	−	0.0103455i
$387$		0			0
$388$	−17.3180	+	9.83654i	−0.879187	+	0.499375i
$389$	4.51226	−	3.78624i	0.228781	−	0.191970i	−0.521190	−	0.853440i	$-0.674512\pi$
$389$	4.51226	−	3.78624i	0.228781	−	0.191970i	0.749971	+	0.661471i	$0.230067\pi$
$390$		0			0
$391$	6.58572	+	3.80227i	0.333054	+	0.192289i
$392$	17.1416	−	9.65669i	0.865783	−	0.487737i
$393$		0			0
$394$	−5.44134	−	15.1154i	−0.274131	−	0.761502i
$395$	11.7053	+	66.3839i	0.588956	+	3.34014i
$396$		0			0
$397$	−3.96864	−	3.33009i	−0.199180	−	0.167132i	0.537742	−	0.843109i	$-0.319277\pi$
$397$	−3.96864	−	3.33009i	−0.199180	−	0.167132i	−0.736923	+	0.675977i	$0.763722\pi$
$398$	−3.25458	−	5.68323i	−0.163138	−	0.284875i
$399$		0			0
$400$	−20.4621	−	36.6233i	−1.02310	−	1.83116i
$401$	−16.6724	+	19.8694i	−0.832582	+	0.992232i	0.167398	+	0.985889i	$0.446463\pi$
$401$	−16.6724	+	19.8694i	−0.832582	+	0.992232i	−0.999980	+	0.00634288i	$0.997981\pi$
$402$		0			0
$403$	17.0370	−	3.00408i	0.848673	−	0.149644i
$404$	19.9771	+	17.0040i	0.993897	+	0.845980i
$405$		0			0
$406$	2.28603	+	1.33059i	0.113454	+	0.0660363i
$407$	0.0654556	−	0.113372i	0.00324451	−	0.00561966i
$408$		0			0
$409$	7.25219	+	8.64283i	0.358598	+	0.427360i	0.914938	−	0.403594i	$-0.132239\pi$
$409$	7.25219	+	8.64283i	0.358598	+	0.427360i	−0.556340	+	0.830955i	$0.687795\pi$
$410$	31.7847	+	0.111943i	1.56974	+	0.00552845i
$411$		0			0
$412$	9.41887	−	7.79097i	0.464034	−	0.383834i
$413$	0.781022	+	0.137715i	0.0384316	+	0.00677653i
$414$		0			0
$415$	−21.3599	−	58.6859i	−1.04852	−	2.88078i
$416$	15.4694	−	5.32385i	0.758451	−	0.261023i
$417$		0			0
$418$	−3.54313	+	3.99259i	−0.173300	+	0.195284i
$419$		−	15.2915i		−	0.747037i	−0.927623	−	0.373518i	$-0.878151\pi$
$419$		−	15.2915i		−	0.747037i	0.927623	−	0.373518i	$-0.121849\pi$
$420$		0			0
$421$	13.5067	+	37.1092i	0.658274	+	1.80859i	0.584617	+	0.811310i	$0.301245\pi$
$421$	13.5067	+	37.1092i	0.658274	+	1.80859i	0.0736575	+	0.997284i	$0.476533\pi$
$422$	−1.71403	−	2.05737i	−0.0834376	−	0.100151i
$423$		0			0
$424$	25.1330	+	9.44955i	1.22057	+	0.458911i
$425$	−14.3576	−	24.8681i	−0.696447	−	1.20628i
$426$		0			0
$427$	1.13761	+	1.35575i	0.0550527	+	0.0656092i
$428$	−0.651572	−	3.85379i	−0.0314949	−	0.186280i
$429$		0			0
$430$	−28.9458	+	49.7303i	−1.39589	+	2.39821i
$431$	8.12496	+	2.95725i	0.391366	+	0.142445i	0.530205	−	0.847869i	$-0.322115\pi$
$431$	8.12496	+	2.95725i	0.391366	+	0.142445i	−0.138839	+	0.990315i	$0.544337\pi$
$432$		0			0
$433$	−7.20103	+	1.26974i	−0.346059	+	0.0610196i	−0.343977	−	0.938978i	$-0.611774\pi$
$433$	−7.20103	+	1.26974i	−0.346059	+	0.0610196i	−0.00208276	+	0.999998i	$0.500663\pi$
$434$	1.35538	+	1.14546i	0.0650604	+	0.0549838i
$435$		0			0
$436$	12.2509	+	7.18861i	0.586714	+	0.344272i
$437$	1.81354	+	11.9702i	0.0867532	+	0.572611i
$438$		0			0
$439$	11.4550	+	9.61190i	0.546718	+	0.458751i	0.873828	−	0.486235i	$-0.161630\pi$
$439$	11.4550	+	9.61190i	0.546718	+	0.458751i	−0.327110	+	0.944986i	$0.606075\pi$
$440$	−9.09201	+	3.20084i	−0.433444	+	0.152594i
$441$		0			0
$442$	10.5361	−	3.79287i	0.501153	−	0.180408i
$443$	−6.11614	+	16.8039i	−0.290586	+	0.798380i	0.705395	+	0.708815i	$0.250770\pi$
$443$	−6.11614	+	16.8039i	−0.290586	+	0.798380i	−0.995981	+	0.0895648i	$0.971452\pi$
$444$		0			0
$445$	−6.20644	−	3.58329i	−0.294213	−	0.169864i
$446$	3.82144	−	10.3854i	0.180951	−	0.491762i
$447$		0			0
$448$	1.43528	+	0.869604i	0.0678106	+	0.0410849i
$449$	15.4628	−	8.92745i	0.729735	−	0.421313i	−0.0885903	−	0.996068i	$-0.528236\pi$
$449$	15.4628	−	8.92745i	0.729735	−	0.421313i	0.818325	+	0.574756i	$0.194903\pi$
$450$		0			0
$451$	0.858752	−	4.87022i	0.0404371	−	0.229330i
$452$	−7.31215	+	19.6580i	−0.343935	+	0.924636i
$453$		0			0
$454$	−37.8774	−	6.81643i	−1.77767	−	0.319911i
$455$	−2.38753			−0.111929
$456$		0			0
$457$	33.7501			1.57876			0.789382	−	0.613902i	$-0.210401\pi$
$457$	33.7501			1.57876			0.789382	+	0.613902i	$0.210401\pi$
$458$	−10.9413	−	1.96901i	−0.511254	−	0.0920056i
$459$		0			0
$460$	−7.62157	+	20.4899i	−0.355357	+	0.955345i
$461$	−2.27764	+	12.9171i	−0.106080	+	0.601611i	0.884703	+	0.466155i	$0.154361\pi$
$461$	−2.27764	+	12.9171i	−0.106080	+	0.601611i	−0.990783	+	0.135456i	$0.956750\pi$
$462$		0			0
$463$	−28.6823	+	16.5597i	−1.33298	+	0.769595i	−0.985755	−	0.168188i	$-0.946208\pi$
$463$	−28.6823	+	16.5597i	−1.33298	+	0.769595i	−0.347223	+	0.937783i	$0.612875\pi$
$464$	0.502410	−	35.6610i	0.0233238	−	1.65552i
$465$		0			0
$466$	−0.913821	+	2.48345i	−0.0423319	+	0.115044i
$467$	16.1123	+	9.30244i	0.745588	+	0.430465i	0.824098	−	0.566448i	$-0.191683\pi$
$467$	16.1123	+	9.30244i	0.745588	+	0.430465i	−0.0785095	+	0.996913i	$0.525016\pi$
$468$		0			0
$469$	−0.695663	+	1.91132i	−0.0321227	+	0.0882565i
$470$	17.3869	−	6.25906i	0.801999	−	0.288709i
$471$		0			0
$472$	−3.55096	−	10.0865i	−0.163446	−	0.464269i
$473$	6.85817	+	5.75469i	0.315339	+	0.264601i
$474$		0			0
$475$	16.6695	−	42.5686i	0.764850	−	1.95318i
$476$	0.990709	+	0.581328i	0.0454091	+	0.0266451i
$477$		0			0
$478$	−4.61284	−	3.89840i	−0.210986	−	0.178309i
$479$	−15.1913	+	2.67863i	−0.694106	+	0.122390i	−0.509561	−	0.860434i	$-0.670192\pi$
$479$	−15.1913	+	2.67863i	−0.694106	+	0.122390i	−0.184545	+	0.982824i	$0.559081\pi$
$480$		0			0
$481$	−0.410846	−	0.149536i	−0.0187330	−	0.00681825i
$482$	−3.10885	+	5.34116i	−0.141604	+	0.243283i
$483$		0			0
$484$	−3.41754	−	20.2134i	−0.155343	−	0.918792i
$485$	−25.1912	−	30.0217i	−1.14387	−	1.36322i
$486$		0			0
$487$	0.954158	+	1.65265i	0.0432370	+	0.0748887i	0.886834	−	0.462088i	$-0.152900\pi$
$487$	0.954158	+	1.65265i	0.0432370	+	0.0748887i	−0.843597	+	0.536977i	$0.819566\pi$
$488$	8.39809	−	22.3364i	0.380164	−	1.01112i
$489$		0			0
$490$	24.7805	+	29.7444i	1.11947	+	1.34371i
$491$	−12.5011	−	34.3464i	−0.564166	−	1.55003i	−0.813469	−	0.581608i	$-0.802424\pi$
$491$	−12.5011	−	34.3464i	−0.564166	−	1.55003i	0.249304	−	0.968425i	$-0.419798\pi$
$492$		0			0
$493$		−	24.4117i		−	1.09945i
$494$	15.1866	+	9.33799i	0.683276	+	0.420136i
$495$		0			0
$496$	4.48649	−	23.5030i	0.201449	−	1.05532i
$497$	−0.833274	−	2.28940i	−0.0373775	−	0.102694i
$498$		0			0
$499$	−8.46805	−	1.49315i	−0.379082	−	0.0668424i	−0.0191394	−	0.999817i	$-0.506093\pi$
$499$	−8.46805	−	1.49315i	−0.379082	−	0.0668424i	−0.359943	+	0.932974i	$0.617204\pi$
$500$	33.2845	−	27.5318i	1.48853	−	1.23126i
$501$		0			0
$502$	13.1317	+	0.0462485i	0.586096	+	0.00206417i
$503$	−11.4192	−	13.6089i	−0.509159	−	0.606792i	0.448823	−	0.893621i	$-0.351843\pi$
$503$	−11.4192	−	13.6089i	−0.509159	−	0.606792i	−0.957982	+	0.286829i	$0.907399\pi$
$504$		0			0
$505$	−25.8108	+	44.7055i	−1.14856	+	1.98937i
$506$	2.93968	+	1.71105i	0.130685	+	0.0760657i
$507$		0			0
$508$	−27.7740	−	23.6405i	−1.23227	−	1.04888i
$509$	13.5154	−	2.38313i	0.599059	−	0.105630i	0.134108	−	0.990967i	$-0.457183\pi$
$509$	13.5154	−	2.38313i	0.599059	−	0.105630i	0.464951	+	0.885336i	$0.346072\pi$
$510$		0			0
$511$	0.879444	−	1.04808i	0.0389043	−	0.0463644i
$512$	0.717101	−	22.6161i	0.0316917	−	0.999498i
$513$		0			0
$514$	−10.5089	−	18.3509i	−0.463529	−	0.809426i
$515$	18.4254	+	15.4608i	0.811921	+	0.681283i
$516$		0			0
$517$	−0.499264	−	2.83146i	−0.0219576	−	0.124528i
$518$	−0.0151906	−	0.0421976i	−0.000667435	−	0.00185405i
$519$		0			0
$520$	15.8005	+	28.0476i	0.692900	+	1.22997i
$521$	6.24273	+	3.60424i	0.273499	+	0.157905i	0.630477	−	0.776208i	$-0.282859\pi$
$521$	6.24273	+	3.60424i	0.273499	+	0.157905i	−0.356978	+	0.934113i	$0.616193\pi$
$522$		0			0
$523$	−28.6996	+	24.0819i	−1.25495	+	1.05303i	−0.258747	+	0.965945i	$0.583309\pi$
$523$	−28.6996	+	24.0819i	−1.25495	+	1.05303i	−0.996201	+	0.0870811i	$0.972246\pi$
$524$	−21.0551	+	11.9592i	−0.919797	+	0.522441i
$525$		0			0
$526$	−5.98088	−	34.6321i	−0.260779	−	1.51003i
$527$	2.84398	−	16.1290i	0.123886	−	0.702591i
$528$		0			0
$529$	−14.3637	+	5.22798i	−0.624511	+	0.227303i
$530$	−9.35793	+	51.9999i	−0.406482	+	2.25873i
$531$		0			0
$532$	0.261194	+	1.80999i	0.0113242	+	0.0784730i
$533$	−16.5164			−0.715403
$534$		0			0
$535$	7.22705	−	2.63043i	0.312453	−	0.113723i
$536$	27.0572	−	4.47668i	1.16869	−	0.193363i
$537$		0			0
$538$	−1.47088	−	8.51705i	−0.0634140	−	0.367196i
$539$	5.21650	−	3.01174i	0.224690	−	0.129725i
$540$		0			0
$541$	−1.58880	+	1.33316i	−0.0683079	+	0.0573172i	−0.676302	−	0.736624i	$-0.736419\pi$
$541$	−1.58880	+	1.33316i	−0.0683079	+	0.0573172i	0.607994	+	0.793941i	$0.291974\pi$
$542$	−5.04861	−	1.85771i	−0.216856	−	0.0797953i
$543$		0			0
$544$	0.272721	−	15.4856i	0.0116928	−	0.663940i
$545$	−9.55957	+	26.2647i	−0.409487	+	1.12506i
$546$		0			0
$547$	2.71682	+	15.4078i	0.116163	+	0.658791i	0.986168	+	0.165749i	$0.0530041\pi$
$547$	2.71682	+	15.4078i	0.116163	+	0.658791i	−0.870005	+	0.493042i	$0.835885\pi$
$548$	−5.16465	+	28.1301i	−0.220623	+	1.20166i
$549$		0			0
$550$	−6.38272	−	11.1457i	−0.272160	−	0.475252i
$551$	30.3671	−	24.2548i	1.29368	−	1.03329i
$552$		0			0
$553$	2.30954	−	2.75241i	0.0982118	−	0.117044i
$554$	−15.7318	+	18.6148i	−0.668378	+	0.790869i
$555$		0			0
$556$	18.5788	−	21.8273i	0.787919	−	0.925684i
$557$	1.47433	+	0.536611i	0.0624693	+	0.0227370i	0.373066	−	0.927805i	$-0.378307\pi$
$557$	1.47433	+	0.536611i	0.0624693	+	0.0227370i	−0.310597	+	0.950542i	$0.600529\pi$
$558$		0			0
$559$	14.9500	−	25.8941i	0.632317	−	1.09521i
$560$	−1.17302	+	3.08683i	−0.0495690	+	0.130442i
$561$		0			0
$562$	−26.0604	−	0.0917822i	−1.09929	−	0.00387160i
$563$	2.67277	+	4.62937i	0.112644	+	0.195105i	0.916835	−	0.399265i	$-0.130735\pi$
$563$	2.67277	+	4.62937i	0.112644	+	0.195105i	−0.804192	+	0.594370i	$0.797401\pi$
$564$		0			0
$565$	−40.6442	−	7.16667i	−1.70991	−	0.301504i
$566$	0.352266	−	0.293479i	0.0148069	−	0.0123358i
$567$		0			0
$568$	−21.3803	+	24.9401i	−0.897098	+	1.04646i
$569$		−	7.29290i		−	0.305734i	−0.988247	−	0.152867i	$-0.951149\pi$
$569$		−	7.29290i		−	0.305734i	0.988247	−	0.152867i	$-0.0488507\pi$
$570$		0			0
$571$		−	35.8008i		−	1.49822i	−0.662448	−	0.749108i	$-0.730482\pi$
$571$		−	35.8008i		−	1.49822i	0.662448	−	0.749108i	$-0.269518\pi$
$572$	4.71858	−	1.67988i	0.197294	−	0.0702393i
$573$		0			0
$574$	−1.08444	−	1.30167i	−0.0452638	−	0.0543307i
$575$	−28.6876	−	5.05840i	−1.19636	−	0.210950i
$576$		0			0
$577$	−7.89890	−	13.6813i	−0.328836	−	0.569560i	0.653445	−	0.756974i	$-0.273323\pi$
$577$	−7.89890	−	13.6813i	−0.328836	−	0.569560i	−0.982281	+	0.187414i	$0.939990\pi$
$578$	−0.0473354	+	13.4403i	−0.00196889	+	0.559043i
$579$		0			0
$580$	69.1965	−	11.6993i	2.87323	−	0.485786i
$581$	−1.66443	+	2.88288i	−0.0690522	+	0.119602i
$582$		0			0
$583$	7.72477	+	2.81159i	0.319927	+	0.116444i
$584$	−18.1325	−	3.39517i	−0.750329	−	0.140493i
$585$		0			0
$586$	30.7312	+	25.9715i	1.26950	+	1.07287i
$587$	11.0661	−	13.1881i	0.456749	−	0.544332i	−0.487691	−	0.873016i	$-0.662161\pi$
$587$	11.0661	−	13.1881i	0.456749	−	0.544332i	0.944440	+	0.328684i	$0.106605\pi$
$588$		0			0
$589$	22.8895	−	12.4876i	0.943146	−	0.514541i
$590$	18.2595	−	10.4566i	0.751733	−	0.430490i
$591$		0			0
$592$	−0.395188	+	0.457714i	−0.0162421	+	0.0188119i
$593$	−0.342331	−	1.94146i	−0.0140579	−	0.0797260i	0.976972	−	0.213369i	$-0.0684436\pi$
$593$	−0.342331	−	1.94146i	−0.0140579	−	0.0797260i	−0.991030	+	0.133643i	$0.957333\pi$
$594$		0			0
$595$	−0.773063	+	2.12397i	−0.0316925	+	0.0870744i
$596$	19.0711	+	0.134335i	0.781184	+	0.00550257i
$597$		0			0
$598$	3.92287	−	10.6610i	0.160418	−	0.435961i
$599$	−17.5707	+	14.7435i	−0.717918	+	0.602404i	−0.926808	−	0.375535i	$-0.877459\pi$
$599$	−17.5707	+	14.7435i	−0.717918	+	0.602404i	0.208891	+	0.977939i	$0.433015\pi$
$600$		0			0
$601$	7.34871	−	4.24278i	0.299760	−	0.173067i	−0.342575	−	0.939491i	$-0.611299\pi$
$601$	7.34871	−	4.24278i	0.299760	−	0.173067i	0.642335	+	0.766424i	$0.277966\pi$
$602$	3.02234	−	0.521952i	0.123181	−	0.0212732i
$603$		0			0
$604$	25.9451	+	9.65075i	1.05569	+	0.392683i
$605$	37.9065	−	13.7968i	1.54112	−	0.560920i
$606$		0			0
$607$	−16.4542			−0.667855			−0.333928	−	0.942599i	$-0.608374\pi$
$607$	−16.4542			−0.667855			−0.333928	+	0.942599i	$0.608374\pi$
$608$	19.5344	−	15.0468i	0.792225	−	0.610230i
$609$		0			0
$610$	46.2138	+	8.31666i	1.87114	+	0.336732i
$611$	−9.02324	+	3.28419i	−0.365041	+	0.132864i
$612$		0			0
$613$	−3.12517	+	17.7237i	−0.126224	+	0.715853i	0.854349	+	0.519700i	$0.173956\pi$
$613$	−3.12517	+	17.7237i	−0.126224	+	0.715853i	−0.980573	+	0.196154i	$0.937155\pi$
$614$	−10.6871	+	1.84564i	−0.431296	+	0.0744839i
$615$		0			0
$616$	0.442209	+	0.261578i	0.0178171	+	0.0105393i
$617$	0.667321	−	0.559949i	0.0268653	−	0.0225427i	−0.629256	−	0.777198i	$-0.716640\pi$
$617$	0.667321	−	0.559949i	0.0268653	−	0.0225427i	0.656121	+	0.754655i	$0.272196\pi$
$618$		0			0
$619$	17.2683	+	9.96987i	0.694073	+	0.400723i	0.805136	−	0.593090i	$-0.202092\pi$
$619$	17.2683	+	9.96987i	0.694073	+	0.400723i	−0.111063	+	0.993813i	$0.535426\pi$
$620$	47.0817	+	0.331639i	1.89085	+	0.0133189i
$621$		0			0
$622$	36.3012	−	13.0680i	1.45555	−	0.523977i
$623$	0.0663330	+	0.376193i	0.00265757	+	0.0150719i
$624$		0			0
$625$	24.9407	+	20.9277i	0.997628	+	0.837109i
$626$	35.5491	−	20.3577i	1.42083	−	0.813658i
$627$		0			0
$628$	−3.75783	+	6.40416i	−0.149954	+	0.255554i
$629$	−0.266058	+	0.317076i	−0.0106084	+	0.0126426i
$630$		0			0
$631$	−22.0544	+	3.88878i	−0.877970	+	0.154810i	−0.594427	−	0.804150i	$-0.702621\pi$
$631$	−22.0544	+	3.88878i	−0.877970	+	0.154810i	−0.283543	+	0.958959i	$0.591510\pi$
$632$	−47.6185	−	8.91619i	−1.89416	−	0.354667i
$633$		0			0
$634$	−6.70927	+	11.5269i	−0.266459	+	0.457790i
$635$	35.8845	−	62.1537i	1.42403	−	2.46650i
$636$		0			0
$637$	−12.9310	−	15.4106i	−0.512345	−	0.610589i
$638$	0.0384552	−	10.9189i	0.00152246	−	0.432283i
$639$		0			0
$640$	44.0257	−	6.64841i	1.74027	−	0.262802i
$641$	−45.2010	−	7.97015i	−1.78533	−	0.314802i	−0.819327	−	0.573327i	$-0.805653\pi$
$641$	−45.2010	−	7.97015i	−1.78533	−	0.314802i	−0.966005	+	0.258525i	$0.916764\pi$
$642$		0			0
$643$	7.82012	+	21.4856i	0.308395	+	0.847310i	0.992970	+	0.118367i	$0.0377658\pi$
$643$	7.82012	+	21.4856i	0.308395	+	0.847310i	−0.684575	+	0.728943i	$0.740012\pi$
$644$	1.09778	−	0.390823i	0.0432584	−	0.0154006i
$645$		0			0
$646$	13.2245	−	10.4866i	0.520311	−	0.412590i
$647$		−	6.37749i		−	0.250725i	−0.992111	−	0.125362i	$-0.959991\pi$
$647$		−	6.37749i		−	0.250725i	0.992111	−	0.125362i	$-0.0400094\pi$
$648$		0			0
$649$	−1.11972	−	3.07639i	−0.0439527	−	0.120759i
$650$	−32.9568	+	27.4568i	−1.29267	+	1.07695i
$651$		0			0
$652$	10.2754	+	12.4224i	0.402417	+	0.486501i
$653$	20.6208	+	35.7162i	0.806953	+	1.39768i	0.914964	+	0.403535i	$0.132219\pi$
$653$	20.6208	+	35.7162i	0.806953	+	1.39768i	−0.108011	+	0.994150i	$0.534448\pi$
$654$		0			0
$655$	−30.6274	−	36.5003i	−1.19671	−	1.42618i
$656$	−8.11467	+	21.3540i	−0.316824	+	0.833733i
$657$		0			0
$658$	−0.851285	−	0.495495i	−0.0331865	−	0.0193164i
$659$	−11.8817	−	4.32460i	−0.462847	−	0.168462i	0.100062	−	0.994981i	$-0.468096\pi$
$659$	−11.8817	−	4.32460i	−0.462847	−	0.168462i	−0.562909	+	0.826519i	$0.690318\pi$
$660$		0			0
$661$	0.353109	−	0.0622626i	0.0137343	−	0.00242173i	−0.166777	−	0.985995i	$-0.553336\pi$
$661$	0.353109	−	0.0622626i	0.0137343	−	0.00242173i	0.180511	+	0.983573i	$0.442225\pi$
$662$	19.9145	−	23.5642i	0.774000	−	0.915847i
$663$		0			0
$664$	44.8819	+	0.474225i	1.74176	+	0.0184035i
$665$	−3.41022	+	1.14867i	−0.132243	+	0.0445433i
$666$		0			0
$667$	−18.9707	−	15.9183i	−0.734547	−	0.616358i
$668$	−3.39863	+	18.5111i	−0.131497	+	0.716218i
$669$		0			0
$670$	18.2785	+	50.7755i	0.706160	+	1.96163i
$671$	2.49874	−	6.86522i	0.0964627	−	0.265029i
$672$		0			0
$673$	−6.45905	−	3.72913i	−0.248978	−	0.143747i	0.370318	−	0.928905i	$-0.379249\pi$
$673$	−6.45905	−	3.72913i	−0.248978	−	0.143747i	−0.619296	+	0.785157i	$0.712582\pi$
$674$	−19.6312	−	7.22358i	−0.756166	−	0.278242i
$675$		0			0
$676$	4.57937	+	8.06233i	0.176130	+	0.310090i
$677$	−9.14972	+	5.28259i	−0.351652	+	0.203026i	−0.665413	−	0.746476i	$-0.731744\pi$
$677$	−9.14972	+	5.28259i	−0.351652	+	0.203026i	0.313761	+	0.949502i	$0.398411\pi$
$678$		0			0
$679$	−0.362743	+	2.05722i	−0.0139208	+	0.0789489i
$680$	30.0676	−	4.97477i	1.15304	−	0.190774i
$681$		0			0
$682$	1.29747	−	7.20972i	0.0496826	−	0.276075i
$683$	0.943220			0.0360913			0.0180457	−	0.999837i	$-0.494256\pi$
$683$	0.943220			0.0360913			0.0180457	+	0.999837i	$0.494256\pi$
$684$		0			0
$685$	−56.2778			−2.15027
$686$	0.733293	−	4.07474i	0.0279972	−	0.155574i
$687$		0			0
$688$	−26.1334	−	32.0509i	−0.996326	−	1.22193i
$689$	4.76746	−	27.0376i	0.181626	−	1.03005i
$690$		0			0
$691$	−10.4176	+	6.01463i	−0.396306	+	0.228807i	−0.684889	−	0.728648i	$-0.740149\pi$
$691$	−10.4176	+	6.01463i	−0.396306	+	0.228807i	0.288583	+	0.957455i	$0.406816\pi$
$692$	25.5561	−	14.5158i	0.971497	−	0.551807i
$693$		0			0
$694$	−8.20044	−	3.01746i	−0.311284	−	0.114541i
$695$	48.8461	+	28.2013i	1.85284	+	1.06974i
$696$		0			0
$697$	−5.34787	+	14.6932i	−0.202565	+	0.556543i
$698$	−5.38970	−	14.9719i	−0.204003	−	0.566696i
$699$		0			0
$700$	−4.32780	−	0.794580i	−0.163576	−	0.0300323i
$701$	21.1942	+	17.7840i	0.800494	+	0.671694i	0.948319	−	0.317320i	$-0.102783\pi$
$701$	21.1942	+	17.7840i	0.800494	+	0.671694i	−0.147825	+	0.989014i	$0.547227\pi$
$702$		0			0
$703$	−0.658776	−	0.0159269i	−0.0248462	−	0.000600694i
$704$	0.146377	−	6.92599i	0.00551679	−	0.261033i
$705$		0			0
$706$	−17.1811	+	20.3297i	−0.646618	+	0.765120i
$707$	2.70975	−	0.477803i	0.101911	−	0.0179696i
$708$		0			0
$709$	18.1451	+	6.60427i	0.681453	+	0.248029i	0.659471	−	0.751730i	$-0.270780\pi$
$709$	18.1451	+	6.60427i	0.681453	+	0.248029i	0.0219818	+	0.999758i	$0.493002\pi$
$710$	−55.8660	−	32.5171i	−2.09661	−	1.22035i
$711$		0			0
$712$	3.98036	−	3.26888i	0.149170	−	0.122506i
$713$	−10.6796	−	12.7274i	−0.399954	−	0.476647i
$714$		0			0
$715$	4.92790	+	8.53537i	0.184293	+	0.319205i
$716$	−12.5347	+	10.3683i	−0.468446	+	0.387483i
$717$		0			0
$718$	−12.8215	+	10.6818i	−0.478494	+	0.398641i
$719$	−4.78669	−	13.1513i	−0.178513	−	0.490462i	0.817873	−	0.575399i	$-0.195153\pi$
$719$	−4.78669	−	13.1513i	−0.178513	−	0.490462i	−0.996386	+	0.0849373i	$0.972931\pi$
$720$		0			0
$721$		−	1.28207i		−	0.0477467i
$722$	26.1844	+	6.03150i	0.974481	+	0.224469i
$723$		0			0
$724$	2.84489	+	7.99096i	0.105730	+	0.296982i
$725$	31.9831	+	87.8728i	1.18782	+	3.26352i
$726$		0			0
$727$	−7.95695	−	1.40303i	−0.295107	−	0.0520353i	0.0241345	−	0.999709i	$-0.492317\pi$
$727$	−7.95695	−	1.40303i	−0.295107	−	0.0520353i	−0.319241	+	0.947673i	$0.603428\pi$
$728$	0.603881	−	1.60614i	0.0223813	−	0.0595276i
$729$		0			0
$730$	0.127845	−	36.2999i	0.00473174	−	1.34352i
$731$	−18.1951	−	21.6840i	−0.672969	−	0.802013i
$732$		0			0
$733$	−11.3292	+	19.6227i	−0.418452	+	0.724780i	−0.995784	−	0.0917295i	$-0.970760\pi$
$733$	−11.3292	+	19.6227i	−0.418452	+	0.724780i	0.577332	+	0.816509i	$0.304094\pi$
$734$	11.1033	−	19.0760i	0.409829	−	0.704107i
$735$		0			0
$736$	−11.8563	−	10.3097i	−0.437027	−	0.380022i
$737$	8.26880	−	1.45801i	0.304585	−	0.0537066i
$738$		0			0
$739$	9.18420	−	10.9453i	0.337846	−	0.402630i	−0.570195	−	0.821509i	$-0.693133\pi$
$739$	9.18420	−	10.9453i	0.337846	−	0.402630i	0.908042	+	0.418879i	$0.137577\pi$
$740$	−1.02628	−	0.602200i	−0.0377268	−	0.0221373i
$741$		0			0
$742$	2.44389	−	1.39953i	0.0897179	−	0.0513782i
$743$	−31.0594	−	26.0620i	−1.13946	−	0.956121i	−0.140040	−	0.990146i	$-0.544723\pi$
$743$	−31.0594	−	26.0620i	−1.13946	−	0.956121i	−0.999421	+	0.0340249i	$0.989167\pi$
$744$		0			0
$745$	6.51665	+	36.9578i	0.238752	+	1.35403i
$746$	−20.7152	+	7.45721i	−0.758439	+	0.273028i
$747$		0			0
$748$	0.0333996	−	4.74164i	0.00122121	−	0.173372i
$749$	−0.355021	−	0.204971i	−0.0129722	−	0.00748949i
$750$		0			0
$751$	−13.7493	+	11.5370i	−0.501718	+	0.420991i	−0.858204	−	0.513310i	$-0.828419\pi$
$751$	−13.7493	+	11.5370i	−0.501718	+	0.420991i	0.356486	+	0.934301i	$0.383975\pi$
$752$	−0.187091	+	13.2797i	−0.00682249	+	0.484260i
$753$		0			0
$754$	−35.9349	+	6.20588i	−1.30867	+	0.226005i
$755$	−9.45874	+	53.6432i	−0.344239	+	1.95227i
$756$		0			0
$757$	44.5914	−	16.2299i	1.62070	−	0.589887i	0.637185	−	0.770711i	$-0.280099\pi$
$757$	44.5914	−	16.2299i	1.62070	−	0.589887i	0.983516	+	0.180824i	$0.0578764\pi$
$758$	−30.6478	−	5.51539i	−1.11318	−	0.200328i
$759$		0			0
$760$	36.0627	+	32.4600i	1.30813	+	1.17745i
$761$	35.8628			1.30003			0.650014	−	0.759923i	$-0.274763\pi$
$761$	35.8628			1.30003			0.650014	+	0.759923i	$0.274763\pi$
$762$		0			0
$763$	1.39997	−	0.509549i	0.0506825	−	0.0184469i
$764$	9.02412	−	24.2605i	0.326481	−	0.877714i
$765$		0			0
$766$	32.3606	−	5.58861i	1.16924	−	0.201925i
$767$	−9.46898	+	5.46692i	−0.341905	+	0.197399i
$768$		0			0
$769$	12.1897	−	10.2284i	0.439573	−	0.368845i	−0.395977	−	0.918261i	$-0.629594\pi$
$769$	12.1897	−	10.2284i	0.439573	−	0.368845i	0.835550	+	0.549415i	$0.185149\pi$
$770$	−0.349122	+	0.948795i	−0.0125815	+	0.0341922i
$771$		0			0
$772$	−0.00205468	+	0.291697i	−7.39495e−5	+	0.0104984i
$773$	2.36474	−	6.49707i	0.0850538	−	0.233683i	−0.889873	−	0.456208i	$-0.849207\pi$
$773$	2.36474	−	6.49707i	0.0850538	−	0.233683i	0.974927	+	0.222524i	$0.0714296\pi$
$774$		0			0
$775$	10.8943	+	61.7844i	0.391333	+	2.21936i
$776$	26.5679	−	9.35325i	0.953734	−	0.335762i
$777$		0			0
$778$	−7.22879	+	4.13967i	−0.259165	+	0.148414i
$779$	−23.5912	+	7.94621i	−0.845241	+	0.284702i
$780$		0			0
$781$	−6.46469	+	7.70432i	−0.231325	+	0.275682i
$782$	−8.21397	−	6.94179i	−0.293731	−	0.248238i
$783$		0			0
$784$	−26.2775	+	9.14710i	−0.938481	+	0.326682i
$785$	−13.7298	−	4.99725i	−0.490039	−	0.178359i
$786$		0			0
$787$	−24.7329	+	42.8387i	−0.881633	+	1.52703i	−0.0321080	+	0.999484i	$0.510222\pi$
$787$	−24.7329	+	42.8387i	−0.881633	+	1.52703i	−0.849525	+	0.527549i	$0.823111\pi$
$788$	3.78747	+	22.4014i	0.134923	+	0.798016i
$789$		0			0
$790$	0.335738	−	95.3287i	0.0119450	−	3.39164i
$791$	1.09993	+	1.90513i	0.0391090	+	0.0677387i
$792$		0			0
$793$	−24.0291	−	4.23698i	−0.853298	−	0.150459i
$794$	4.68966	+	5.62906i	0.166430	+	0.199768i
$795$		0			0
$796$	3.10638	+	8.72544i	0.110103	+	0.309265i
$797$		−	10.0163i		−	0.354797i	−0.984139	−	0.177398i	$-0.943232\pi$
$797$		−	10.0163i		−	0.354797i	0.984139	−	0.177398i	$-0.0567681\pi$
$798$		0			0
$799$			9.09058i			0.321602i
$800$	19.3069	+	56.0996i	0.682601	+	1.98342i
$801$		0			0
$802$	28.1825	−	23.4793i	0.995158	−	0.829082i
$803$	−5.56207	−	0.980742i	−0.196281	−	0.0346097i
$804$		0			0
$805$	1.14647	+	1.98575i	0.0404079	+	0.0699885i
$806$	−24.4655	−	0.0861650i	−0.861760	−	0.00303503i
$807$		0			0
$808$	−23.5461	−	28.6709i	−0.828348	−	1.00864i
$809$	−18.8758	+	32.6938i	−0.663638	+	1.14945i	0.316015	+	0.948754i	$0.397655\pi$
$809$	−18.8758	+	32.6938i	−0.663638	+	1.14945i	−0.979653	+	0.200700i	$0.935678\pi$
$810$		0			0
$811$	−13.3406	−	4.85559i	−0.468453	−	0.170503i	0.0969984	−	0.995285i	$-0.469076\pi$
$811$	−13.3406	−	4.85559i	−0.468453	−	0.170503i	−0.565451	+	0.824782i	$0.691298\pi$
$812$	−2.84853	−	2.42460i	−0.0999638	−	0.0850866i
$813$		0			0
$814$	−0.119502	+	0.141403i	−0.00418855	+	0.00495616i
$815$	−20.3910	+	24.3011i	−0.714267	+	0.851230i
$816$		0			0
$817$	8.89587	−	44.1785i	0.311227	−	1.54561i
$818$	−7.92915	−	13.8461i	−0.277236	−	0.484117i
$819$		0			0
$820$	−44.2117	−	8.11721i	−1.54394	−	0.283465i
$821$	−4.21822	−	23.9227i	−0.147217	−	0.834909i	−0.965560	−	0.260179i	$-0.916218\pi$
$821$	−4.21822	−	23.9227i	−0.147217	−	0.834909i	0.818343	−	0.574730i	$-0.194893\pi$
$822$		0			0
$823$	8.50271	−	23.3610i	0.296386	−	0.814313i	−0.698711	−	0.715404i	$-0.746243\pi$
$823$	8.50271	−	23.3610i	0.296386	−	0.814313i	0.995097	−	0.0989088i	$-0.0315352\pi$
$824$	−15.0612	+	8.48468i	−0.524681	+	0.295578i
$825$		0			0
$826$	−1.05258	−	0.387310i	−0.0366238	−	0.0134762i
$827$	19.8813	−	16.6824i	0.691341	−	0.580104i	−0.227954	−	0.973672i	$-0.573204\pi$
$827$	19.8813	−	16.6824i	0.691341	−	0.580104i	0.919296	+	0.393568i	$0.128759\pi$
$828$		0			0
$829$	−18.9765	+	10.9561i	−0.659081	+	0.380521i	−0.791927	−	0.610616i	$-0.790922\pi$
$829$	−18.9765	+	10.9561i	−0.659081	+	0.380521i	0.132846	+	0.991137i	$0.457589\pi$
$830$	15.0303	+	87.0324i	0.521710	+	3.02094i
$831$		0			0
$832$	−22.8647	+	3.53526i	−0.792691	+	0.122563i
$833$	−17.8964	+	6.51376i	−0.620074	+	0.225688i
$834$		0			0
$835$	−37.0339			−1.28161
$836$	5.93158	−	4.66962i	0.205148	−	0.161502i
$837$		0			0
$838$	−3.83019	+	21.2835i	−0.132312	+	0.735226i
$839$	25.2502	−	9.19034i	0.871735	−	0.317286i	0.132866	−	0.991134i	$-0.457582\pi$
$839$	25.2502	−	9.19034i	0.871735	−	0.317286i	0.738870	+	0.673848i	$0.235360\pi$
$840$		0			0
$841$	−8.76882	+	49.7305i	−0.302373	+	1.71484i
$842$	−9.50422	−	55.0338i	−0.327537	−	1.89659i
$843$		0			0
$844$	1.87035	+	3.29289i	0.0643801	+	0.113346i
$845$	−13.9765	+	11.7277i	−0.480807	+	0.403445i
$846$		0			0
$847$	−1.86211	−	1.07509i	−0.0639829	−	0.0369405i
$848$	−32.6146	−	19.4477i	−1.11999	−	0.667837i
$849$		0			0
$850$	13.7548	+	38.2091i	0.471785	+	1.31056i
$851$	0.0729138	+	0.413515i	0.00249945	+	0.0141751i
$852$		0			0
$853$	−1.64649	−	1.38157i	−0.0563748	−	0.0473041i	0.614165	−	0.789178i	$-0.289493\pi$
$853$	−1.64649	−	1.38157i	−0.0563748	−	0.0473041i	−0.670540	+	0.741874i	$0.733937\pi$
$854$	−1.24380	−	2.17195i	−0.0425619	−	0.0743227i
$855$		0			0
$856$	−0.0583998	+	5.52712i	−0.00199606	+	0.188913i
$857$	33.5911	−	40.0323i	1.14745	−	1.36748i	0.228291	−	0.973593i	$-0.426686\pi$
$857$	33.5911	−	40.0323i	1.14745	−	1.36748i	0.919160	−	0.393885i	$-0.128869\pi$
$858$		0			0
$859$	20.1780	−	3.55792i	0.688463	−	0.121395i	0.181537	−	0.983384i	$-0.441893\pi$
$859$	20.1780	−	3.55792i	0.688463	−	0.121395i	0.506926	+	0.861989i	$0.330782\pi$
$860$	52.7448	−	61.9671i	1.79858	−	2.11306i
$861$		0			0
$862$	−10.5680	−	6.15119i	−0.359949	−	0.209510i
$863$	−0.450739	+	0.780702i	−0.0153433	+	0.0265754i	−0.873595	−	0.486653i	$-0.838217\pi$
$863$	−0.450739	+	0.780702i	−0.0153433	+	0.0265754i	0.858252	+	0.513229i	$0.171551\pi$
$864$		0			0
$865$	37.1746	+	44.3030i	1.26398	+	1.50635i
$866$	10.3408	+	0.0364194i	0.351396	+	0.00123758i
$867$		0			0
$868$	−1.59958	−	1.93381i	−0.0542933	−	0.0656377i
$869$	−14.6068	−	2.57557i	−0.495501	−	0.0873701i
$870$		0			0
$871$	−9.59090	−	26.3508i	−0.324975	−	0.892862i
$872$	−15.2509	−	13.0741i	−0.516462	−	0.442745i
$873$		0			0
$874$	0.474098	−	17.1150i	0.0160366	−	0.578923i
$875$		−	4.53059i		−	0.153162i
$876$		0			0
$877$	−8.87885	−	24.3944i	−0.299817	−	0.823742i	−0.994530	−	0.104454i	$-0.966691\pi$
$877$	−8.87885	−	24.3944i	−0.299817	−	0.823742i	0.694712	−	0.719288i	$-0.255532\pi$
$878$	−13.5361	−	16.2476i	−0.456823	−	0.548330i
$879$		0			0
$880$	13.4565	−	2.17775i	0.453618	−	0.0734120i
$881$	10.6496	+	18.4456i	0.358793	+	0.621448i	0.987759	−	0.155985i	$-0.0498551\pi$
$881$	10.6496	+	18.4456i	0.358793	+	0.621448i	−0.628966	+	0.777432i	$0.716522\pi$
$882$		0			0
$883$	−30.6480	−	36.5249i	−1.03139	−	1.22916i	−0.972985	−	0.230867i	$-0.925844\pi$
$883$	−30.6480	−	36.5249i	−1.03139	−	1.22916i	−0.0584021	−	0.998293i	$-0.518601\pi$
$884$	−15.6148	+	2.64004i	−0.525182	+	0.0887942i
$885$		0			0
$886$	12.7218	−	21.8567i	0.427398	−	0.734290i
$887$	−2.16889	−	0.789412i	−0.0728242	−	0.0265059i	0.305351	−	0.952240i	$-0.401226\pi$
$887$	−2.16889	−	0.789412i	−0.0728242	−	0.0265059i	−0.378175	+	0.925734i	$0.623448\pi$
$888$		0			0
$889$	−3.76735	+	0.664285i	−0.126353	+	0.0222794i
$890$	7.74092	+	6.54200i	0.259476	+	0.219288i
$891$		0			0
$892$	−7.92021	+	13.4977i	−0.265188	+	0.451938i
$893$	−11.3083	+	9.03216i	−0.378417	+	0.302250i
$894$		0			0
$895$	−24.5208	−	20.5754i	−0.819639	−	0.687759i
$896$	−1.77988	−	1.56987i	−0.0594618	−	0.0524457i
$897$		0			0
$898$	−23.7581	+	8.55261i	−0.792819	+	0.285404i
$899$	−18.2417	+	50.1186i	−0.608394	+	1.67155i
$900$		0			0
$901$	−22.5093	−	12.9958i	−0.749894	−	0.432952i
$902$	−2.41515	+	6.56355i	−0.0804156	+	0.218542i
$903$		0			0
$904$	15.1014	−	25.5296i	0.502264	−	0.849101i
$905$	−14.4547	+	8.34544i	−0.480491	+	0.277412i
$906$		0			0
$907$	−2.26633	+	12.8530i	−0.0752523	+	0.426777i	0.923785	+	0.382911i	$0.125079\pi$
$907$	−2.26633	+	12.8530i	−0.0752523	+	0.426777i	−0.999037	+	0.0438658i	$0.986033\pi$
$908$	51.0124	+	18.9750i	1.69291	+	0.629707i
$909$		0			0
$910$	3.32309	+	0.598025i	0.110159	+	0.0198243i
$911$	−40.1054			−1.32875			−0.664376	−	0.747398i	$-0.731303\pi$
$911$	−40.1054			−1.32875			−0.664376	+	0.747398i	$0.731303\pi$
$912$		0			0
$913$	13.7417			0.454783
$914$	−46.9753	−	8.45370i	−1.55380	−	0.279624i
$915$		0			0
$916$	14.7355	+	5.48114i	0.486875	+	0.181102i
$917$	−0.441022	+	2.50116i	−0.0145638	+	0.0825956i
$918$		0			0
$919$	38.9363	−	22.4799i	1.28439	−	0.741544i	0.306743	−	0.951792i	$-0.400761\pi$
$919$	38.9363	−	22.4799i	1.28439	−	0.741544i	0.977648	+	0.210249i	$0.0674274\pi$
$920$	15.7404	−	26.6099i	0.518946	−	0.877302i
$921$		0			0
$922$	6.40561	−	17.4083i	0.210958	−	0.573311i
$923$	29.0889	+	16.7945i	0.957474	+	0.552798i
$924$		0			0
$925$	0.542290	−	1.48993i	0.0178304	−	0.0489886i
$926$	44.0694	−	15.8644i	1.44821	−	0.521337i
$927$		0			0
$928$	−9.63163	+	49.5092i	−0.316174	+	1.62522i
$929$	28.4647	+	23.8847i	0.933896	+	0.783632i	0.976513	−	0.215460i	$-0.0691249\pi$
$929$	28.4647	+	23.8847i	0.933896	+	0.783632i	−0.0426166	+	0.999092i	$0.513569\pi$
$930$		0			0
$931$	−25.8842	−	15.7905i	−0.848321	−	0.517511i
$932$	1.89396	−	3.22771i	0.0620387	−	0.105727i
$933$		0			0
$934$	−20.0959	−	16.9834i	−0.657558	−	0.555715i
$935$	9.18879	−	1.62023i	0.300506	−	0.0529873i
$936$		0			0
$937$	−10.4385	−	3.79929i	−0.341010	−	0.124117i	0.165838	−	0.986153i	$-0.446967\pi$
$937$	−10.4385	−	3.79929i	−0.341010	−	0.124117i	−0.506848	+	0.862036i	$0.669189\pi$
$938$	1.44701	−	2.48603i	0.0472464	−	0.0811717i
$939$		0			0
$940$	−25.7678	+	4.35665i	−0.840454	+	0.142098i
$941$	−11.3300	−	13.5026i	−0.369348	−	0.440172i	0.549074	−	0.835774i	$-0.314980\pi$
$941$	−11.3300	−	13.5026i	−0.369348	−	0.440172i	−0.918422	+	0.395602i	$0.870536\pi$
$942$		0			0
$943$	7.93104	+	13.7370i	0.258270	+	0.447337i
$944$	2.41596	+	14.9284i	0.0786327	+	0.485878i
$945$		0			0
$946$	−8.10414	−	9.72751i	−0.263488	−	0.316269i
$947$	7.23906	+	19.8892i	0.235238	+	0.646311i	0.999998	+	0.00199576i	$0.000635272\pi$
$947$	7.23906	+	19.8892i	0.235238	+	0.646311i	−0.764760	+	0.644315i	$0.777143\pi$
$948$		0			0
$949$			18.8626i			0.612306i
$950$	−33.8641	+	55.0739i	−1.09870	+	1.78683i
$951$		0			0
$952$	−1.23331	−	1.05728i	−0.0399719	−	0.0342665i
$953$	−20.9991	−	57.6945i	−0.680227	−	1.86891i	−0.439194	−	0.898392i	$-0.644736\pi$
$953$	−20.9991	−	57.6945i	−0.680227	−	1.86891i	−0.241033	−	0.970517i	$-0.577486\pi$
$954$		0			0
$955$	50.1601	+	8.84458i	1.62314	+	0.286204i
$956$	5.44393	+	6.58142i	0.176069	+	0.212858i
$957$		0			0
$958$	21.8150	+	0.0768302i	0.704810	+	0.00248227i
$959$	1.92820	+	2.29794i	0.0622649	+	0.0742044i
$960$		0			0
$961$	−2.39129	+	4.14183i	−0.0771384	+	0.133608i
$962$	0.534383	+	0.311041i	0.0172292	+	0.0100284i
$963$		0			0
$964$	5.66492	−	6.65542i	0.182455	−	0.214357i
$965$	−0.565277	+	0.0996736i	−0.0181969	+	0.00320861i
$966$		0			0
$967$	34.6635	−	41.3104i	1.11470	−	1.32845i	0.175741	−	0.984436i	$-0.443768\pi$
$967$	34.6635	−	41.3104i	1.11470	−	1.32845i	0.938964	−	0.344017i	$-0.111788\pi$
$968$	−0.306312	+	28.9902i	−0.00984523	+	0.931779i
$969$		0			0
$970$	27.5427	+	48.0958i	0.884343	+	1.54426i
$971$	24.1138	+	20.2338i	0.773847	+	0.649335i	0.941691	−	0.336479i	$-0.109236\pi$
$971$	24.1138	+	20.2338i	0.773847	+	0.649335i	−0.167844	+	0.985814i	$0.553680\pi$
$972$		0			0
$973$	−0.522056	−	2.96072i	−0.0167363	−	0.0949165i
$974$	−0.914095	−	2.53925i	−0.0292895	−	0.0813627i
$975$		0			0
$976$	−17.2837	+	28.9855i	−0.553239	+	0.927803i
$977$	7.25341	+	4.18776i	0.232057	+	0.133978i	0.611521	−	0.791228i	$-0.290558\pi$
$977$	7.25341	+	4.18776i	0.232057	+	0.133978i	−0.379464	+	0.925207i	$0.623891\pi$
$978$		0			0
$979$	1.20797	−	1.01361i	0.0386070	−	0.0323951i
$980$	−27.0405	−	47.6068i	−0.863777	−	1.52074i
$981$		0			0
$982$	8.79663	+	50.9365i	0.280712	+	1.62545i
$983$	3.94998	−	22.4014i	0.125985	−	0.714495i	−0.854733	−	0.519067i	$-0.826279\pi$
$983$	3.94998	−	22.4014i	0.125985	−	0.714495i	0.980718	−	0.195428i	$-0.0626095\pi$
$984$		0			0
$985$	−42.0096	+	15.2902i	−1.33854	+	0.487187i
$986$	−6.11462	+	33.9775i	−0.194729	+	1.08207i
$987$		0			0
$988$	−18.7985	−	16.8011i	−0.598061	−	0.534513i
$989$	−28.7155			−0.913101
$990$		0			0
$991$	47.7300	−	17.3723i	1.51619	−	0.551849i	0.555998	−	0.831184i	$-0.312336\pi$
$991$	47.7300	−	17.3723i	1.51619	−	0.551849i	0.960194	+	0.279335i	$0.0901139\pi$
$992$	−12.1316	+	31.5890i	−0.385177	+	1.00295i
$993$		0			0
$994$	0.586350	+	3.39523i	0.0185979	+	0.107690i
$995$	−15.7833	+	9.11250i	−0.500365	+	0.288886i
$996$		0			0
$997$	40.2848	−	33.8029i	1.27583	−	1.07055i	0.282027	−	0.959407i	$-0.408993\pi$
$997$	40.2848	−	33.8029i	1.27583	−	1.07055i	0.993804	−	0.111143i	$-0.0354512\pi$
$998$	11.4123	+	4.19931i	0.361250	+	0.132927i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.cf.b.307.1		60
3.2	odd	2		228.2.w.b.79.10	yes	60
4.3	odd	2		684.2.cf.c.307.6		60
12.11	even	2		228.2.w.a.79.5	✓	60
19.13	odd	18		684.2.cf.c.127.6		60
57.32	even	18		228.2.w.a.127.5	yes	60
76.51	even	18	inner	684.2.cf.b.127.1		60
228.203	odd	18		228.2.w.b.127.10	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.w.a.79.5	✓	60	12.11	even	2
228.2.w.a.127.5	yes	60	57.32	even	18
228.2.w.b.79.10	yes	60	3.2	odd	2
228.2.w.b.127.10	yes	60	228.203	odd	18
684.2.cf.b.127.1		60	76.51	even	18	inner
684.2.cf.b.307.1		60	1.1	even	1	trivial
684.2.cf.c.127.6		60	19.13	odd	18
684.2.cf.c.307.6		60	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	684.cf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39185 - 0.250479i) q^{2} +(1.87452 + 0.697261i) q^{4} +(-0.683388 + 3.87569i) q^{5} +(0.181667 - 0.104885i) q^{7} +(-2.43441 - 1.44001i) q^{8} +(1.92196 - 5.22322i) q^{10} +(-0.749928 - 0.432971i) q^{11} +(-0.989139 + 2.71764i) q^{13} +(-0.279125 + 0.100482i) q^{14} +(3.02765 + 2.61406i) q^{16} +(2.09737 + 1.75990i) q^{17} +(-0.105352 + 4.35763i) q^{19} +(-3.98339 + 6.78856i) q^{20} +(0.935341 + 0.790474i) q^{22} +(2.73529 - 0.482305i) q^{23} +(-9.85547 - 3.58710i) q^{25} +(2.05745 - 3.53480i) q^{26} +(0.413671 - 0.0699406i) q^{28} +(-5.73119 - 6.83016i) q^{29} +(-2.99093 - 5.18044i) q^{31} +(-3.55929 - 4.39676i) q^{32} +(-2.47841 - 2.97487i) q^{34} +(0.282354 + 0.775761i) q^{35} +0.151178i q^{37} +(1.23813 - 6.03879i) q^{38} +(7.24470 - 8.45093i) q^{40} +(1.95326 + 5.36654i) q^{41} +(-10.1816 - 1.79529i) q^{43} +(-1.10386 - 1.33451i) q^{44} +(-3.92793 - 0.0138338i) q^{46} +(2.13422 + 2.54346i) q^{47} +(-3.47800 + 6.02407i) q^{49} +(12.8189 + 7.46131i) q^{50} +(-3.74906 + 4.40458i) q^{52} +(-9.34894 + 1.64847i) q^{53} +(2.19055 - 2.61060i) q^{55} +(-0.593288 - 0.00626872i) q^{56} +(6.26617 + 10.9421i) q^{58} +(2.89615 + 2.43016i) q^{59} +(1.46504 + 8.30867i) q^{61} +(2.86535 + 7.95958i) q^{62} +(3.85272 + 7.01118i) q^{64} +(-9.85675 - 5.69080i) q^{65} +(-7.42773 + 6.23260i) q^{67} +(2.70445 + 4.76139i) q^{68} +(-0.198684 - 1.15047i) q^{70} +(2.01679 - 11.4378i) q^{71} +(6.12889 - 2.23073i) q^{73} +(0.0378669 - 0.210418i) q^{74} +(-3.23589 + 8.09500i) q^{76} -0.181649 q^{77} +(16.0953 - 5.85822i) q^{79} +(-12.2003 + 9.94782i) q^{80} +(-1.37445 - 7.95870i) q^{82} +(-13.7430 + 7.93452i) q^{83} +(-8.25415 + 6.92605i) q^{85} +(13.7216 + 5.04907i) q^{86} +(1.20215 + 2.13394i) q^{88} +(-0.622825 + 1.71120i) q^{89} +(0.105347 + 0.597451i) q^{91} +(5.46365 + 1.00312i) q^{92} +(-2.33344 - 4.07470i) q^{94} +(-16.8168 - 3.38626i) q^{95} +(-6.40106 + 7.62849i) q^{97} +(6.34977 - 7.51347i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 3 q^{2} - 3 q^{4} + 3 q^{8} - 6 q^{10} - 6 q^{13} + 9 q^{14} + 21 q^{16} + 18 q^{19} - 30 q^{20} - 12 q^{22} - 18 q^{28} - 12 q^{31} - 33 q^{32} - 15 q^{34} + 84 q^{38} - 87 q^{40} + 12 q^{41} - 18 q^{43}+ \cdots + 105 q^{98}+O(q^{100}) \) 60 * q - 3 * q^2 - 3 * q^4 + 3 * q^8 - 6 * q^10 - 6 * q^13 + 9 * q^14 + 21 * q^16 + 18 * q^19 - 30 * q^20 - 12 * q^22 - 18 * q^28 - 12 * q^31 - 33 * q^32 - 15 * q^34 + 84 * q^38 - 87 * q^40 + 12 * q^41 - 18 * q^43 + 51 * q^44 - 21 * q^46 + 30 * q^49 + 27 * q^50 - 3 * q^52 - 12 * q^53 - 42 * q^56 - 36 * q^58 - 105 * q^62 + 21 * q^64 + 36 * q^65 + 42 * q^67 + 15 * q^68 - 96 * q^70 - 24 * q^71 + 18 * q^73 - 69 * q^74 + 54 * q^76 + 72 * q^77 + 12 * q^79 + 12 * q^80 + 75 * q^82 - 60 * q^85 - 21 * q^86 + 36 * q^88 + 12 * q^89 - 84 * q^91 - 99 * q^92 + 24 * q^95 + 12 * q^97 + 105 * q^98

Introduction

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