LMFDB - Embedded newform 684.2.cf.b.127.1

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			127.1
Character	$\chi$	$=$	684.127
Dual form			684.2.cf.b.307.1

$q$-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 $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.39185	+	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	−0.620569	−	0.784152i	$-0.713098\pi$
$5$	−0.683388	−	3.87569i	−0.305621	−	1.73326i	0.314949	−	0.949109i	$-0.398013\pi$
$6$		0			0
$7$	0.181667	+	0.104885i	0.0686636	+	0.0396430i	0.533939	−	0.845523i	$-0.320711\pi$
$7$	0.181667	+	0.104885i	0.0686636	+	0.0396430i	−0.465275	+	0.885166i	$0.654045\pi$
$8$	−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	−0.608777	−	0.793341i	$-0.708340\pi$
$11$	−0.749928	+	0.432971i	−0.226112	+	0.130546i	0.382665	+	0.923887i	$0.375006\pi$
$12$		0			0
$13$	−0.989139	−	2.71764i	−0.274338	−	0.753737i	−0.997978	−	0.0635596i	$-0.979755\pi$
$13$	−0.989139	−	2.71764i	−0.274338	−	0.753737i	0.723640	−	0.690177i	$-0.242468\pi$
$14$	−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	−0.351980	−	0.936008i	$-0.614492\pi$
$17$	2.09737	−	1.75990i	0.508687	−	0.426839i	0.860667	+	0.509169i	$0.170047\pi$
$18$		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	0.451382	−	0.892331i	$-0.350931\pi$
$23$	2.73529	+	0.482305i	0.570347	+	0.100568i	0.118965	+	0.992898i	$0.462042\pi$
$24$		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	−0.102408	+	0.994743i	$0.532655\pi$
$29$	−5.73119	+	6.83016i	−1.06425	+	1.26833i	−0.961847	+	0.273587i	$0.911790\pi$
$30$		0			0
$31$	−2.99093	+	5.18044i	−0.537186	+	0.930434i	0.461868	+	0.886949i	$0.347179\pi$
$31$	−2.99093	+	5.18044i	−0.537186	+	0.930434i	−0.999054	+	0.0434852i	$0.986154\pi$
$32$	−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	$-0.996044\pi$
$37$		−	0.151178i		−	0.0248535i	0.999923	−	0.0124267i	$-0.00395566\pi$
$38$	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	−0.688555	−	0.725184i	$-0.741755\pi$
$41$	1.95326	−	5.36654i	0.305048	−	0.838113i	0.993603	−	0.112929i	$-0.0360232\pi$
$42$		0			0
$43$	−10.1816	+	1.79529i	−1.55268	+	0.273780i	−0.883181	−	0.469032i	$-0.844603\pi$
$43$	−10.1816	+	1.79529i	−1.55268	+	0.273780i	−0.669501	+	0.742812i	$0.733492\pi$
$44$	−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	−0.587592	−	0.809158i	$-0.699924\pi$
$47$	2.13422	−	2.54346i	0.311307	−	0.371002i	0.898899	+	0.438156i	$0.144368\pi$
$48$		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	−0.510423	−	0.859923i	$-0.670511\pi$
$53$	−9.34894	−	1.64847i	−1.28418	−	0.226435i	−0.773752	+	0.633488i	$0.781622\pi$
$54$		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	−0.434495	−	0.900674i	$-0.643073\pi$
$59$	2.89615	−	2.43016i	0.377047	−	0.316380i	0.811542	+	0.584295i	$0.198629\pi$
$60$		0			0
$61$	1.46504	−	8.30867i	0.187579	−	1.06382i	−0.735017	−	0.678049i	$-0.762826\pi$
$61$	1.46504	−	8.30867i	0.187579	−	1.06382i	0.922596	−	0.385767i	$-0.126063\pi$
$62$	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	0.0641890	−	0.997938i	$-0.479554\pi$
$67$	−7.42773	−	6.23260i	−0.907442	−	0.761434i	−0.971631	+	0.236504i	$0.923998\pi$
$68$	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	0.833257	+	0.552885i	$0.186473\pi$
$71$	2.01679	+	11.4378i	0.239349	+	1.35742i	−0.593908	+	0.804533i	$0.702416\pi$
$72$		0			0
$73$	6.12889	+	2.23073i	0.717332	+	0.261088i	0.674793	−	0.738007i	$-0.264233\pi$
$73$	6.12889	+	2.23073i	0.717332	+	0.261088i	0.0425394	+	0.999095i	$0.486455\pi$
$74$	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	0.996943	+	0.0781264i	$0.0248938\pi$
$79$	16.0953	+	5.85822i	1.81087	+	0.659101i	0.813922	+	0.580975i	$0.197328\pi$
$80$	−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	−0.999951	−	0.00988648i	$-0.996853\pi$
$83$	−13.7430	−	7.93452i	−1.50849	−	0.870926i	−0.508538	−	0.861040i	$-0.669814\pi$
$84$		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	0.902296	−	0.431117i	$-0.141880\pi$
$89$	−0.622825	−	1.71120i	−0.0660193	−	0.181387i	−0.968315	+	0.249730i	$0.919658\pi$
$90$		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	0.335974	−	0.941871i	$-0.390935\pi$
$97$	−6.40106	−	7.62849i	−0.649929	−	0.774555i	−0.985903	+	0.167316i	$0.946490\pi$
$98$	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	0.354086	−	0.935213i	$-0.384792\pi$
$101$	12.3259	−	4.48627i	1.22647	−	0.446400i	0.872389	+	0.488813i	$0.162570\pi$
$102$		0			0
$103$	3.05588	+	5.29294i	0.301105	+	0.521529i	0.976386	−	0.216031i	$-0.0693113\pi$
$103$	3.05588	+	5.29294i	0.301105	+	0.521529i	−0.675282	+	0.737560i	$0.735978\pi$
$104$	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	−0.909384	−	0.415958i	$-0.863446\pi$
$107$	−0.977120	+	1.69242i	−0.0944618	+	0.163613i	0.814922	+	0.579571i	$0.196780\pi$
$108$		0			0
$109$	6.99424	−	1.23327i	0.669927	−	0.118126i	0.171669	−	0.985155i	$-0.445084\pi$
$109$	6.99424	−	1.23327i	0.669927	−	0.118126i	0.498258	+	0.867029i	$0.333973\pi$
$110$	−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	$-0.835803\pi$
$113$		−	10.4870i		−	0.986531i	0.869879	−	0.493265i	$-0.164197\pi$
$114$		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	−0.961305	−	0.275486i	$-0.911161\pi$
$127$	−17.1366	+	6.23722i	−1.52063	+	0.553464i	−0.559324	+	0.828949i	$0.688939\pi$
$128$	−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	0.310151	−	0.950687i	$-0.399620\pi$
$131$	−7.78238	−	9.27469i	−0.679950	−	0.810333i	−0.990101	+	0.140354i	$0.955176\pi$
$132$		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	−0.673625	−	0.739073i	$-0.735264\pi$
$137$	2.48319	−	14.0829i	0.212153	−	1.20318i	0.885778	−	0.464109i	$-0.153625\pi$
$138$		0			0
$139$	4.90177	+	13.4675i	0.415763	+	1.14230i	0.954079	+	0.299556i	$0.0968386\pi$
$139$	4.90177	+	13.4675i	0.415763	+	1.14230i	−0.538316	+	0.842743i	$0.680939\pi$
$140$	−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	0.681895	−	0.731450i	$-0.261156\pi$
$149$	8.96072	+	3.26144i	0.734091	+	0.267187i	0.0521954	+	0.998637i	$0.483378\pi$
$150$		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	0.948214	−	0.317631i	$-0.102887\pi$
$157$	−0.644692	−	3.65623i	−0.0514520	−	0.291799i	−0.999666	+	0.0258325i	$0.991776\pi$
$158$	−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	−0.201043	−	0.979582i	$-0.564433\pi$
$163$	6.98080	−	4.03037i	0.546778	−	0.315683i	0.747822	+	0.663900i	$0.231100\pi$
$164$	−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	−0.853988	−	0.520292i	$-0.825823\pi$
$167$	1.63408	−	9.26731i	0.126449	−	0.717126i	0.980437	−	0.196834i	$-0.0630659\pi$
$168$		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	0.994451	−	0.105196i	$-0.0335471\pi$
$173$	9.44603	+	11.2573i	0.718169	+	0.855880i	−0.276283	+	0.961076i	$0.589103\pi$
$174$		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	0.673064	−	0.739584i	$-0.264978\pi$
$179$	−4.06680	−	7.04391i	−0.303967	−	0.526486i	−0.977031	+	0.213098i	$0.931645\pi$
$180$		0			0
$181$	2.72615	−	3.24890i	0.202633	−	0.241489i	−0.655152	−	0.755497i	$-0.727396\pi$
$181$	2.72615	−	3.24890i	0.202633	−	0.241489i	0.857785	+	0.514008i	$0.171840\pi$
$182$	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	$0.155109\pi$
$191$			12.9422i			0.936468i	−0.883605	+	0.468234i	$0.844891\pi$
$192$		0			0
$193$	0.0498843	−	0.137056i	0.00359075	−	0.00986551i	−0.937884	−	0.346948i	$-0.887218\pi$
$193$	0.0498843	−	0.137056i	0.00359075	−	0.00986551i	0.941475	+	0.337083i	$0.109440\pi$
$194$	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	−0.589612	−	0.807686i	$-0.700719\pi$
$197$	5.67982	−	9.83775i	0.404671	−	0.700910i	0.994283	+	0.106776i	$0.0340528\pi$
$198$		0			0
$199$	2.97672	−	3.54752i	0.211014	−	0.251477i	−0.650148	−	0.759808i	$-0.725293\pi$
$199$	2.97672	−	3.54752i	0.211014	−	0.251477i	0.861162	+	0.508331i	$0.169737\pi$
$200$	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	−0.591492	−	0.806311i	$-0.701461\pi$
$211$	1.45050	−	1.21712i	0.0998568	−	0.0837898i	0.691349	+	0.722521i	$0.257017\pi$
$212$	−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	−0.995902	−	0.0904358i	$-0.971174\pi$
$223$	−1.35879	−	7.70607i	−0.0909911	−	0.516036i	0.904911	−	0.425600i	$-0.139937\pi$
$224$	−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	0.993599	−	0.112960i	$-0.0360333\pi$
$233$	0.324927	+	1.84275i	0.0212866	+	0.120723i	−0.972313	+	0.233683i	$0.924922\pi$
$234$		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	−0.375592	−	0.926785i	$-0.622561\pi$
$239$	3.69843	−	2.13529i	0.239232	−	0.138121i	0.614824	+	0.788665i	$0.289227\pi$
$240$		0			0
$241$	1.49461	+	4.10641i	0.0962764	+	0.264517i	0.978477	−	0.206357i	$-0.0661608\pi$
$241$	1.49461	+	4.10641i	0.0962764	+	0.264517i	−0.882200	+	0.470874i	$0.843939\pi$
$242$	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	−0.122573	−	0.992460i	$-0.539115\pi$
$251$	−9.14449	−	1.61242i	−0.577195	−	0.101775i	−0.454622	+	0.890684i	$0.650226\pi$
$252$		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	−0.377851	−	0.925866i	$-0.623337\pi$
$257$	9.61171	−	11.4548i	0.599562	−	0.714530i	0.977414	+	0.211336i	$0.0677814\pi$
$258$		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	−0.341805	−	0.939771i	$-0.611038\pi$
$263$	8.49957	−	23.3524i	0.524106	−	1.43997i	0.865911	−	0.500198i	$-0.166739\pi$
$264$		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	−0.859515	−	0.511111i	$-0.829234\pi$
$269$	2.09029	−	5.74304i	0.127448	−	0.350159i	0.986962	+	0.160952i	$0.0514563\pi$
$270$		0			0
$271$	3.74612	−	0.660543i	0.227561	−	0.0401251i	−0.0587049	−	0.998275i	$-0.518697\pi$
$271$	3.74612	−	0.660543i	0.227561	−	0.0401251i	0.286266	+	0.958150i	$0.407586\pi$
$272$	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	0.999788	+	0.0206025i	$0.00655846\pi$
$277$	8.61685	+	14.9248i	0.517736	+	0.896745i	−0.482052	+	0.876143i	$0.660108\pi$
$278$	−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	0.686364	−	0.727258i	$-0.259206\pi$
$281$	18.1477	+	3.19992i	1.08260	+	0.190891i	0.396234	+	0.918149i	$0.370317\pi$
$282$		0			0
$283$	−0.208397	−	0.248357i	−0.0123879	−	0.0147633i	0.759815	−	0.650139i	$-0.225290\pi$
$283$	−0.208397	−	0.248357i	−0.0123879	−	0.0147633i	−0.772203	+	0.635376i	$0.780845\pi$
$284$	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	−0.997811	−	0.0661289i	$-0.978935\pi$
$293$	−24.6394	+	14.2255i	−1.43945	+	0.831065i	−0.441636	+	0.897194i	$0.645602\pi$
$294$		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	0.539372	−	0.842067i	$-0.318662\pi$
$307$	7.20630	+	2.62288i	0.411285	+	0.149696i	−0.128087	+	0.991763i	$0.540884\pi$
$308$	−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	−0.352962	−	0.935638i	$-0.614826\pi$
$311$	−23.6264	−	13.6407i	−1.33973	−	0.773493i	−0.986767	+	0.162144i	$0.948159\pi$
$312$		0			0
$313$	−22.1900	−	18.6196i	−1.25425	−	1.05244i	−0.996270	−	0.0862959i	$-0.972497\pi$
$313$	−22.1900	−	18.6196i	−1.25425	−	1.05244i	−0.257985	−	0.966149i	$-0.583059\pi$
$314$	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	0.996719	−	0.0809336i	$-0.0257902\pi$
$317$	3.22555	+	8.86213i	0.181165	+	0.497747i	−0.815555	+	0.578680i	$0.803568\pi$
$318$		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	−0.992887	−	0.119060i	$-0.962012\pi$
$331$	−10.9079	−	18.8930i	−0.599552	−	1.03846i	0.393335	−	0.919395i	$-0.371321\pi$
$332$	−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	0.237813	−	0.971311i	$-0.423569\pi$
$337$	14.5666	−	2.56848i	0.793492	−	0.139914i	0.555679	+	0.831397i	$0.312458\pi$
$338$	−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	−0.00791847	−	0.999969i	$-0.502521\pi$
$347$	6.08482	−	1.07292i	0.326650	−	0.0575972i	0.334568	+	0.942371i	$0.391409\pi$
$348$		0			0
$349$	5.62591	−	9.74437i	0.301148	−	0.521604i	−0.675248	−	0.737591i	$-0.735963\pi$
$349$	5.62591	−	9.74437i	0.301148	−	0.521604i	0.976396	+	0.215987i	$0.0692967\pi$
$350$	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	0.999999	+	0.00101645i	$0.000323547\pi$
$353$	9.41068	+	16.2998i	0.500880	+	0.867550i	−0.499119	+	0.866533i	$0.666343\pi$
$354$		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	0.928119	−	0.372285i	$-0.121425\pi$
$359$	7.58505	+	9.03951i	0.400324	+	0.477087i	−0.527795	+	0.849372i	$0.676981\pi$
$360$		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	−0.997517	−	0.0704230i	$-0.977565\pi$
$367$	−5.33801	−	14.6661i	−0.278642	−	0.765562i	0.718875	−	0.695139i	$-0.244657\pi$
$368$	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	0.806636	−	0.591049i	$-0.201286\pi$
$373$	13.4824	+	7.78405i	0.698090	+	0.403043i	−0.108545	+	0.994091i	$0.534619\pi$
$374$	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	−0.282167	−	0.959365i	$-0.591053\pi$
$383$	−21.8207	−	7.94210i	−1.11499	−	0.405822i	−0.832821	+	0.553543i	$0.813275\pi$
$384$		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	0.749971	−	0.661471i	$-0.230067\pi$
$389$	4.51226	+	3.78624i	0.228781	+	0.191970i	−0.521190	+	0.853440i	$0.674512\pi$
$390$		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	−0.736923	−	0.675977i	$-0.763722\pi$
$397$	−3.96864	+	3.33009i	−0.199180	+	0.167132i	0.537742	+	0.843109i	$0.319277\pi$
$398$	−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	−0.999980	−	0.00634288i	$-0.997981\pi$
$401$	−16.6724	−	19.8694i	−0.832582	−	0.992232i	0.167398	−	0.985889i	$-0.446463\pi$
$402$		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	−0.556340	−	0.830955i	$-0.687795\pi$
$409$	7.25219	−	8.64283i	0.358598	−	0.427360i	0.914938	+	0.403594i	$0.132239\pi$
$410$	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	$0.121849\pi$
$419$			15.2915i			0.747037i	−0.927623	+	0.373518i	$0.878151\pi$
$420$		0			0
$421$	13.5067	−	37.1092i	0.658274	−	1.80859i	0.0736575	−	0.997284i	$-0.476533\pi$
$421$	13.5067	−	37.1092i	0.658274	−	1.80859i	0.584617	−	0.811310i	$-0.301245\pi$
$422$	−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	−0.138839	−	0.990315i	$-0.544337\pi$
$431$	8.12496	−	2.95725i	0.391366	−	0.142445i	0.530205	+	0.847869i	$0.322115\pi$
$432$		0			0
$433$	−7.20103	−	1.26974i	−0.346059	−	0.0610196i	−0.00208276	−	0.999998i	$-0.500663\pi$
$433$	−7.20103	−	1.26974i	−0.346059	−	0.0610196i	−0.343977	+	0.938978i	$0.611774\pi$
$434$	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	−0.327110	−	0.944986i	$-0.606075\pi$
$439$	11.4550	−	9.61190i	0.546718	−	0.458751i	0.873828	+	0.486235i	$0.161630\pi$
$440$	−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	−0.995981	−	0.0895648i	$-0.971452\pi$
$443$	−6.11614	−	16.8039i	−0.290586	−	0.798380i	0.705395	−	0.708815i	$-0.250770\pi$
$444$		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	0.818325	−	0.574756i	$-0.194903\pi$
$449$	15.4628	+	8.92745i	0.729735	+	0.421313i	−0.0885903	+	0.996068i	$0.528236\pi$
$450$		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	−0.990783	−	0.135456i	$-0.956750\pi$
$461$	−2.27764	−	12.9171i	−0.106080	−	0.601611i	0.884703	−	0.466155i	$-0.154361\pi$
$462$		0			0
$463$	−28.6823	−	16.5597i	−1.33298	−	0.769595i	−0.347223	−	0.937783i	$-0.612875\pi$
$463$	−28.6823	−	16.5597i	−1.33298	−	0.769595i	−0.985755	+	0.168188i	$0.946208\pi$
$464$	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	−0.0785095	−	0.996913i	$-0.525016\pi$
$467$	16.1123	−	9.30244i	0.745588	−	0.430465i	0.824098	+	0.566448i	$0.191683\pi$
$468$		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	−0.184545	−	0.982824i	$-0.559081\pi$
$479$	−15.1913	−	2.67863i	−0.694106	−	0.122390i	−0.509561	+	0.860434i	$0.670192\pi$
$480$		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	−0.843597	−	0.536977i	$-0.819566\pi$
$487$	0.954158	−	1.65265i	0.0432370	−	0.0748887i	0.886834	+	0.462088i	$0.152900\pi$
$488$	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	0.249304	+	0.968425i	$0.419798\pi$
$491$	−12.5011	+	34.3464i	−0.564166	+	1.55003i	−0.813469	+	0.581608i	$0.802424\pi$
$492$		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	−0.359943	−	0.932974i	$-0.617204\pi$
$499$	−8.46805	+	1.49315i	−0.379082	+	0.0668424i	−0.0191394	+	0.999817i	$0.506093\pi$
$500$	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	−0.957982	−	0.286829i	$-0.907399\pi$
$503$	−11.4192	+	13.6089i	−0.509159	+	0.606792i	0.448823	+	0.893621i	$0.351843\pi$
$504$		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	0.464951	−	0.885336i	$-0.346072\pi$
$509$	13.5154	+	2.38313i	0.599059	+	0.105630i	0.134108	+	0.990967i	$0.457183\pi$
$510$		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	−0.356978	−	0.934113i	$-0.616193\pi$
$521$	6.24273	−	3.60424i	0.273499	−	0.157905i	0.630477	+	0.776208i	$0.282859\pi$
$522$		0			0
$523$	−28.6996	−	24.0819i	−1.25495	−	1.05303i	−0.996201	−	0.0870811i	$-0.972246\pi$
$523$	−28.6996	−	24.0819i	−1.25495	−	1.05303i	−0.258747	−	0.965945i	$-0.583309\pi$
$524$	−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	0.607994	−	0.793941i	$-0.291974\pi$
$541$	−1.58880	−	1.33316i	−0.0683079	−	0.0573172i	−0.676302	+	0.736624i	$0.736419\pi$
$542$	−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	−0.870005	−	0.493042i	$-0.835885\pi$
$547$	2.71682	−	15.4078i	0.116163	−	0.658791i	0.986168	−	0.165749i	$-0.0530041\pi$
$548$	−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	−0.310597	−	0.950542i	$-0.600529\pi$
$557$	1.47433	−	0.536611i	0.0624693	−	0.0227370i	0.373066	+	0.927805i	$0.378307\pi$
$558$		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	−0.804192	−	0.594370i	$-0.797401\pi$
$563$	2.67277	−	4.62937i	0.112644	−	0.195105i	0.916835	+	0.399265i	$0.130735\pi$
$564$		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	$0.0488507\pi$
$569$			7.29290i			0.305734i	−0.988247	+	0.152867i	$0.951149\pi$
$570$		0			0
$571$			35.8008i			1.49822i	0.662448	+	0.749108i	$0.269518\pi$
$571$			35.8008i			1.49822i	−0.662448	+	0.749108i	$0.730482\pi$
$572$	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	−0.982281	−	0.187414i	$-0.939990\pi$
$577$	−7.89890	+	13.6813i	−0.328836	+	0.569560i	0.653445	+	0.756974i	$0.273323\pi$
$578$	−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	0.944440	−	0.328684i	$-0.106605\pi$
$587$	11.0661	+	13.1881i	0.456749	+	0.544332i	−0.487691	+	0.873016i	$0.662161\pi$
$588$		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	−0.991030	−	0.133643i	$-0.957333\pi$
$593$	−0.342331	+	1.94146i	−0.0140579	+	0.0797260i	0.976972	+	0.213369i	$0.0684436\pi$
$594$		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	0.208891	−	0.977939i	$-0.433015\pi$
$599$	−17.5707	−	14.7435i	−0.717918	−	0.602404i	−0.926808	+	0.375535i	$0.877459\pi$
$600$		0			0
$601$	7.34871	+	4.24278i	0.299760	+	0.173067i	0.642335	−	0.766424i	$-0.277966\pi$
$601$	7.34871	+	4.24278i	0.299760	+	0.173067i	−0.342575	+	0.939491i	$0.611299\pi$
$602$	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	−0.980573	−	0.196154i	$-0.937155\pi$
$613$	−3.12517	−	17.7237i	−0.126224	−	0.715853i	0.854349	−	0.519700i	$-0.173956\pi$
$614$	−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	0.656121	−	0.754655i	$-0.272196\pi$
$617$	0.667321	+	0.559949i	0.0268653	+	0.0225427i	−0.629256	+	0.777198i	$0.716640\pi$
$618$		0			0
$619$	17.2683	−	9.96987i	0.694073	−	0.400723i	−0.111063	−	0.993813i	$-0.535426\pi$
$619$	17.2683	−	9.96987i	0.694073	−	0.400723i	0.805136	+	0.593090i	$0.202092\pi$
$620$	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	−0.283543	−	0.958959i	$-0.591510\pi$
$631$	−22.0544	−	3.88878i	−0.877970	−	0.154810i	−0.594427	+	0.804150i	$0.702621\pi$
$632$	−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	−0.966005	−	0.258525i	$-0.916764\pi$
$641$	−45.2010	+	7.97015i	−1.78533	+	0.314802i	−0.819327	+	0.573327i	$0.805653\pi$
$642$		0			0
$643$	7.82012	−	21.4856i	0.308395	−	0.847310i	−0.684575	−	0.728943i	$-0.740012\pi$
$643$	7.82012	−	21.4856i	0.308395	−	0.847310i	0.992970	−	0.118367i	$-0.0377658\pi$
$644$	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	$0.0400094\pi$
$647$			6.37749i			0.250725i	−0.992111	+	0.125362i	$0.959991\pi$
$648$		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	−0.108011	−	0.994150i	$-0.534448\pi$
$653$	20.6208	−	35.7162i	0.806953	−	1.39768i	0.914964	−	0.403535i	$-0.132219\pi$
$654$		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	−0.562909	−	0.826519i	$-0.690318\pi$
$659$	−11.8817	+	4.32460i	−0.462847	+	0.168462i	0.100062	+	0.994981i	$0.468096\pi$
$660$		0			0
$661$	0.353109	+	0.0622626i	0.0137343	+	0.00242173i	0.180511	−	0.983573i	$-0.442225\pi$
$661$	0.353109	+	0.0622626i	0.0137343	+	0.00242173i	−0.166777	+	0.985995i	$0.553336\pi$
$662$	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	−0.619296	−	0.785157i	$-0.712582\pi$
$673$	−6.45905	+	3.72913i	−0.248978	+	0.143747i	0.370318	+	0.928905i	$0.379249\pi$
$674$	−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	0.313761	−	0.949502i	$-0.398411\pi$
$677$	−9.14972	−	5.28259i	−0.351652	−	0.203026i	−0.665413	+	0.746476i	$0.731744\pi$
$678$		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	0.288583	−	0.957455i	$-0.406816\pi$
$691$	−10.4176	−	6.01463i	−0.396306	−	0.228807i	−0.684889	+	0.728648i	$0.740149\pi$
$692$	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	−0.147825	−	0.989014i	$-0.547227\pi$
$701$	21.1942	−	17.7840i	0.800494	−	0.671694i	0.948319	+	0.317320i	$0.102783\pi$
$702$		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	0.0219818	−	0.999758i	$-0.493002\pi$
$709$	18.1451	−	6.60427i	0.681453	−	0.248029i	0.659471	+	0.751730i	$0.270780\pi$
$710$	−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	−0.996386	−	0.0849373i	$-0.972931\pi$
$719$	−4.78669	+	13.1513i	−0.178513	+	0.490462i	0.817873	+	0.575399i	$0.195153\pi$
$720$		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	−0.319241	−	0.947673i	$-0.603428\pi$
$727$	−7.95695	+	1.40303i	−0.295107	+	0.0520353i	0.0241345	+	0.999709i	$0.492317\pi$
$728$	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	0.577332	−	0.816509i	$-0.304094\pi$
$733$	−11.3292	−	19.6227i	−0.418452	−	0.724780i	−0.995784	+	0.0917295i	$0.970760\pi$
$734$	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	0.908042	−	0.418879i	$-0.137577\pi$
$739$	9.18420	+	10.9453i	0.337846	+	0.402630i	−0.570195	+	0.821509i	$0.693133\pi$
$740$	−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	−0.999421	−	0.0340249i	$-0.989167\pi$
$743$	−31.0594	+	26.0620i	−1.13946	+	0.956121i	−0.140040	+	0.990146i	$0.544723\pi$
$744$		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	0.356486	−	0.934301i	$-0.383975\pi$
$751$	−13.7493	−	11.5370i	−0.501718	−	0.420991i	−0.858204	+	0.513310i	$0.828419\pi$
$752$	−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	0.983516	−	0.180824i	$-0.0578764\pi$
$757$	44.5914	+	16.2299i	1.62070	+	0.589887i	0.637185	+	0.770711i	$0.280099\pi$
$758$	−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	0.835550	−	0.549415i	$-0.185149\pi$
$769$	12.1897	+	10.2284i	0.439573	+	0.368845i	−0.395977	+	0.918261i	$0.629594\pi$
$770$	−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	0.974927	−	0.222524i	$-0.0714296\pi$
$773$	2.36474	+	6.49707i	0.0850538	+	0.233683i	−0.889873	+	0.456208i	$0.849207\pi$
$774$		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	−0.849525	−	0.527549i	$-0.823111\pi$
$787$	−24.7329	−	42.8387i	−0.881633	−	1.52703i	−0.0321080	−	0.999484i	$-0.510222\pi$
$788$	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	$0.0567681\pi$
$797$			10.0163i			0.354797i	−0.984139	+	0.177398i	$0.943232\pi$
$798$		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	−0.979653	−	0.200700i	$-0.935678\pi$
$809$	−18.8758	−	32.6938i	−0.663638	−	1.14945i	0.316015	−	0.948754i	$-0.397655\pi$
$810$		0			0
$811$	−13.3406	+	4.85559i	−0.468453	+	0.170503i	−0.565451	−	0.824782i	$-0.691298\pi$
$811$	−13.3406	+	4.85559i	−0.468453	+	0.170503i	0.0969984	+	0.995285i	$0.469076\pi$
$812$	−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	0.818343	+	0.574730i	$0.194893\pi$
$821$	−4.21822	+	23.9227i	−0.147217	+	0.834909i	−0.965560	+	0.260179i	$0.916218\pi$
$822$		0			0
$823$	8.50271	+	23.3610i	0.296386	+	0.814313i	0.995097	+	0.0989088i	$0.0315352\pi$
$823$	8.50271	+	23.3610i	0.296386	+	0.814313i	−0.698711	+	0.715404i	$0.746243\pi$
$824$	−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	0.919296	−	0.393568i	$-0.128759\pi$
$827$	19.8813	+	16.6824i	0.691341	+	0.580104i	−0.227954	+	0.973672i	$0.573204\pi$
$828$		0			0
$829$	−18.9765	−	10.9561i	−0.659081	−	0.380521i	0.132846	−	0.991137i	$-0.457589\pi$
$829$	−18.9765	−	10.9561i	−0.659081	−	0.380521i	−0.791927	+	0.610616i	$0.790922\pi$
$830$	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	0.738870	−	0.673848i	$-0.235360\pi$
$839$	25.2502	+	9.19034i	0.871735	+	0.317286i	0.132866	+	0.991134i	$0.457582\pi$
$840$		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	−0.670540	−	0.741874i	$-0.733937\pi$
$853$	−1.64649	+	1.38157i	−0.0563748	+	0.0473041i	0.614165	+	0.789178i	$0.289493\pi$
$854$	−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	0.919160	+	0.393885i	$0.128869\pi$
$857$	33.5911	+	40.0323i	1.14745	+	1.36748i	0.228291	+	0.973593i	$0.426686\pi$
$858$		0			0
$859$	20.1780	+	3.55792i	0.688463	+	0.121395i	0.506926	−	0.861989i	$-0.330782\pi$
$859$	20.1780	+	3.55792i	0.688463	+	0.121395i	0.181537	+	0.983384i	$0.441893\pi$
$860$	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	0.858252	−	0.513229i	$-0.171551\pi$
$863$	−0.450739	−	0.780702i	−0.0153433	−	0.0265754i	−0.873595	+	0.486653i	$0.838217\pi$
$864$		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	0.694712	+	0.719288i	$0.255532\pi$
$877$	−8.87885	+	24.3944i	−0.299817	+	0.823742i	−0.994530	+	0.104454i	$0.966691\pi$
$878$	−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	−0.628966	−	0.777432i	$-0.716522\pi$
$881$	10.6496	−	18.4456i	0.358793	−	0.621448i	0.987759	+	0.155985i	$0.0498551\pi$
$882$		0			0
$883$	−30.6480	+	36.5249i	−1.03139	+	1.22916i	−0.0584021	+	0.998293i	$0.518601\pi$
$883$	−30.6480	+	36.5249i	−1.03139	+	1.22916i	−0.972985	+	0.230867i	$0.925844\pi$
$884$	−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	−0.378175	−	0.925734i	$-0.623448\pi$
$887$	−2.16889	+	0.789412i	−0.0728242	+	0.0265059i	0.305351	+	0.952240i	$0.401226\pi$
$888$		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	−0.999037	−	0.0438658i	$-0.986033\pi$
$907$	−2.26633	−	12.8530i	−0.0752523	−	0.426777i	0.923785	−	0.382911i	$-0.125079\pi$
$908$	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	0.977648	−	0.210249i	$-0.0674274\pi$
$919$	38.9363	+	22.4799i	1.28439	+	0.741544i	0.306743	+	0.951792i	$0.400761\pi$
$920$	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	−0.0426166	−	0.999092i	$-0.513569\pi$
$929$	28.4647	−	23.8847i	0.933896	−	0.783632i	0.976513	+	0.215460i	$0.0691249\pi$
$930$		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	−0.506848	−	0.862036i	$-0.669189\pi$
$937$	−10.4385	+	3.79929i	−0.341010	+	0.124117i	0.165838	+	0.986153i	$0.446967\pi$
$938$	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	−0.918422	−	0.395602i	$-0.870536\pi$
$941$	−11.3300	+	13.5026i	−0.369348	+	0.440172i	0.549074	+	0.835774i	$0.314980\pi$
$942$		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	−0.764760	−	0.644315i	$-0.777143\pi$
$947$	7.23906	−	19.8892i	0.235238	−	0.646311i	0.999998	−	0.00199576i	$-0.000635272\pi$
$948$		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	−0.241033	+	0.970517i	$0.577486\pi$
$953$	−20.9991	+	57.6945i	−0.680227	+	1.86891i	−0.439194	+	0.898392i	$0.644736\pi$
$954$		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	0.938964	+	0.344017i	$0.111788\pi$
$967$	34.6635	+	41.3104i	1.11470	+	1.32845i	0.175741	+	0.984436i	$0.443768\pi$
$968$	−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	−0.167844	−	0.985814i	$-0.553680\pi$
$971$	24.1138	−	20.2338i	0.773847	−	0.649335i	0.941691	+	0.336479i	$0.109236\pi$
$972$		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	−0.379464	−	0.925207i	$-0.623891\pi$
$977$	7.25341	−	4.18776i	0.232057	−	0.133978i	0.611521	+	0.791228i	$0.290558\pi$
$978$		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	0.980718	+	0.195428i	$0.0626095\pi$
$983$	3.94998	+	22.4014i	0.125985	+	0.714495i	−0.854733	+	0.519067i	$0.826279\pi$
$984$		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	0.960194	−	0.279335i	$-0.0901139\pi$
$991$	47.7300	+	17.3723i	1.51619	+	0.551849i	0.555998	+	0.831184i	$0.312336\pi$
$992$	−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	0.993804	+	0.111143i	$0.0354512\pi$
$997$	40.2848	+	33.8029i	1.27583	+	1.07055i	0.282027	+	0.959407i	$0.408993\pi$
$998$	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.127.1		60
3.2	odd	2		228.2.w.b.127.10	yes	60
4.3	odd	2		684.2.cf.c.127.6		60
12.11	even	2		228.2.w.a.127.5	yes	60
19.3	odd	18		684.2.cf.c.307.6		60
57.41	even	18		228.2.w.a.79.5	✓	60
76.3	even	18	inner	684.2.cf.b.307.1		60
228.155	odd	18		228.2.w.b.79.10	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.w.a.79.5	✓	60	57.41	even	18
228.2.w.a.127.5	yes	60	12.11	even	2
228.2.w.b.79.10	yes	60	228.155	odd	18
228.2.w.b.127.10	yes	60	3.2	odd	2
684.2.cf.b.127.1		60	1.1	even	1	trivial
684.2.cf.b.307.1		60	76.3	even	18	inner
684.2.cf.c.127.6		60	4.3	odd	2
684.2.cf.c.307.6		60	19.3	odd	18

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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