LMFDB - Embedded newform 648.2.v.b.35.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [648,2,Mod(35,648)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(648, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 13]))

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

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

chi := DirichletCharacter("648.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			35.24
Character	$\chi$	$=$	648.35
Dual form			648.2.v.b.611.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.03887 + 0.959554i) q^{2} +(0.158512 + 1.99371i) q^{4} +(-0.588722 - 0.214277i) q^{5} +(-4.57427 - 0.806567i) q^{7} +(-1.74840 + 2.22331i) q^{8} +O(q^{10})$	\(q+(1.03887 + 0.959554i) q^{2} +(0.158512 + 1.99371i) q^{4} +(-0.588722 - 0.214277i) q^{5} +(-4.57427 - 0.806567i) q^{7} +(-1.74840 + 2.22331i) q^{8} +(-0.405997 - 0.787518i) q^{10} +(1.37081 + 3.76628i) q^{11} +(-0.583330 - 0.695185i) q^{13} +(-3.97814 - 5.22718i) q^{14} +(-3.94975 + 0.632053i) q^{16} +(-2.52763 + 1.45933i) q^{17} +(-2.50619 + 4.34085i) q^{19} +(0.333887 - 1.20771i) q^{20} +(-2.18985 + 5.22805i) q^{22} +(0.819150 + 4.64563i) q^{23} +(-3.52954 - 2.96164i) q^{25} +(0.0610627 - 1.28195i) q^{26} +(0.882983 - 9.24761i) q^{28} +(-6.21586 - 5.21572i) q^{29} +(4.29253 - 0.756889i) q^{31} +(-4.70977 - 3.13337i) q^{32} +(-4.02619 - 0.909343i) q^{34} +(2.52015 + 1.45501i) q^{35} +(3.72940 - 2.15317i) q^{37} +(-6.76889 + 2.10476i) q^{38} +(1.50573 - 0.934270i) q^{40} +(5.41092 + 6.44848i) q^{41} +(5.48086 - 1.99487i) q^{43} +(-7.29157 + 3.33000i) q^{44} +(-3.60674 + 5.61224i) q^{46} +(-1.38464 + 7.85268i) q^{47} +(13.6955 + 4.98477i) q^{49} +(-0.824893 - 6.46355i) q^{50} +(1.29353 - 1.27318i) q^{52} +3.06833 q^{53} -2.51103i q^{55} +(9.79089 - 8.75982i) q^{56} +(-1.45271 - 11.3829i) q^{58} +(0.537968 - 1.47805i) q^{59} +(-3.32732 - 0.586696i) q^{61} +(5.18567 + 3.33260i) q^{62} +(-1.88621 - 7.77446i) q^{64} +(0.194457 + 0.534265i) q^{65} +(9.02325 - 7.57140i) q^{67} +(-3.31014 - 4.80804i) q^{68} +(1.22195 + 3.92978i) q^{70} +(3.19304 + 5.53051i) q^{71} +(-2.18272 + 3.78059i) q^{73} +(5.94045 + 1.34169i) q^{74} +(-9.05165 - 4.30854i) q^{76} +(-3.23271 - 18.3336i) q^{77} +(-5.52630 + 6.58598i) q^{79} +(2.46074 + 0.474238i) q^{80} +(-0.566412 + 11.8912i) q^{82} +(-6.42426 + 7.65613i) q^{83} +(1.80077 - 0.317525i) q^{85} +(7.60810 + 3.18677i) q^{86} +(-10.7703 - 3.53721i) q^{88} +(1.88520 + 1.08842i) q^{89} +(2.10759 + 3.65046i) q^{91} +(-9.13219 + 2.36954i) q^{92} +(-8.97354 + 6.82930i) q^{94} +(2.40560 - 2.01853i) q^{95} +(-0.312612 + 0.113782i) q^{97} +(9.44477 + 18.3202i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 6 q^{2} - 6 q^{4} + 9 q^{8}+O(q^{10}) $ 192 * q + 6 * q^2 - 6 * q^4 + 9 * q^8	$ 192 q + 6 q^{2} - 6 q^{4} + 9 q^{8} - 3 q^{10} + 30 q^{11} - 9 q^{14} - 6 q^{16} + 18 q^{17} - 6 q^{19} + 27 q^{20} - 18 q^{22} - 12 q^{25} - 12 q^{28} + 36 q^{32} + 12 q^{34} + 18 q^{35} + 102 q^{38} + 9 q^{40} - 18 q^{41} - 42 q^{43} + 81 q^{44} - 3 q^{46} - 12 q^{49} - 57 q^{50} + 21 q^{52} + 69 q^{56} - 33 q^{58} + 84 q^{59} - 90 q^{62} - 51 q^{64} + 12 q^{65} + 30 q^{67} - 63 q^{68} - 33 q^{70} - 6 q^{73} - 51 q^{74} + 30 q^{76} - 12 q^{82} + 72 q^{83} - 42 q^{86} - 78 q^{88} - 144 q^{89} - 6 q^{91} + 3 q^{92} - 33 q^{94} - 42 q^{97} - 162 q^{98}+O(q^{100}) $ 192 * q + 6 * q^2 - 6 * q^4 + 9 * q^8 - 3 * q^10 + 30 * q^11 - 9 * q^14 - 6 * q^16 + 18 * q^17 - 6 * q^19 + 27 * q^20 - 18 * q^22 - 12 * q^25 - 12 * q^28 + 36 * q^32 + 12 * q^34 + 18 * q^35 + 102 * q^38 + 9 * q^40 - 18 * q^41 - 42 * q^43 + 81 * q^44 - 3 * q^46 - 12 * q^49 - 57 * q^50 + 21 * q^52 + 69 * q^56 - 33 * q^58 + 84 * q^59 - 90 * q^62 - 51 * q^64 + 12 * q^65 + 30 * q^67 - 63 * q^68 - 33 * q^70 - 6 * q^73 - 51 * q^74 + 30 * q^76 - 12 * q^82 + 72 * q^83 - 42 * q^86 - 78 * q^88 - 144 * q^89 - 6 * q^91 + 3 * q^92 - 33 * q^94 - 42 * q^97 - 162 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{13}{18}\right)$

Coefficient data

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

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

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

$2$	1.03887	+	0.959554i	0.734594	+	0.678507i
$2$	1.03887	+	0.959554i	0.734594	+	0.678507i
$3$		0			0
$3$		0			0
$4$	0.158512	+	1.99371i	0.0792560	+	0.996854i
$5$	−0.588722	−	0.214277i	−0.263285	−	0.0958277i	0.207005	−	0.978340i	$-0.433628\pi$
$5$	−0.588722	−	0.214277i	−0.263285	−	0.0958277i	−0.470290	+	0.882512i	$0.655851\pi$
$6$		0			0
$7$	−4.57427	−	0.806567i	−1.72891	−	0.304854i	−0.781271	−	0.624192i	$-0.785428\pi$
$7$	−4.57427	−	0.806567i	−1.72891	−	0.304854i	−0.947641	+	0.319339i	$0.896539\pi$
$8$	−1.74840	+	2.22331i	−0.618152	+	0.786059i
$9$		0			0
$10$	−0.405997	−	0.787518i	−0.128387	−	0.249035i
$11$	1.37081	+	3.76628i	0.413316	+	1.13558i	0.955416	+	0.295262i	$0.0954070\pi$
$11$	1.37081	+	3.76628i	0.413316	+	1.13558i	−0.542100	+	0.840314i	$0.682371\pi$
$12$		0			0
$13$	−0.583330	−	0.695185i	−0.161787	−	0.192810i	0.679061	−	0.734082i	$-0.262387\pi$
$13$	−0.583330	−	0.695185i	−0.161787	−	0.192810i	−0.840847	+	0.541272i	$0.817943\pi$
$14$	−3.97814	−	5.22718i	−1.06320	−	1.39702i
$15$		0			0
$16$	−3.94975	+	0.632053i	−0.987437	+	0.158013i
$17$	−2.52763	+	1.45933i	−0.613041	+	0.353939i	−0.774155	−	0.632997i	$-0.781825\pi$
$17$	−2.52763	+	1.45933i	−0.613041	+	0.353939i	0.161114	+	0.986936i	$0.448491\pi$
$18$		0			0
$19$	−2.50619	+	4.34085i	−0.574959	+	0.995859i	0.421087	+	0.907020i	$0.361649\pi$
$19$	−2.50619	+	4.34085i	−0.574959	+	0.995859i	−0.996046	+	0.0888386i	$0.971684\pi$
$20$	0.333887	−	1.20771i	0.0746594	−	0.270051i
$21$		0			0
$22$	−2.18985	+	5.22805i	−0.466877	+	1.11462i
$23$	0.819150	+	4.64563i	0.170805	+	0.968681i	0.942876	+	0.333145i	$0.108110\pi$
$23$	0.819150	+	4.64563i	0.170805	+	0.968681i	−0.772071	+	0.635536i	$0.780779\pi$
$24$		0			0
$25$	−3.52954	−	2.96164i	−0.705909	−	0.592328i
$26$	0.0610627	−	1.28195i	0.0119754	−	0.251410i
$27$		0			0
$28$	0.882983	−	9.24761i	0.166868	−	1.74763i
$29$	−6.21586	−	5.21572i	−1.15426	−	0.968535i	−0.154445	−	0.988001i	$-0.549359\pi$
$29$	−6.21586	−	5.21572i	−1.15426	−	0.968535i	−0.999811	+	0.0194661i	$0.993803\pi$
$30$		0			0
$31$	4.29253	−	0.756889i	0.770961	−	0.135941i	0.225688	−	0.974200i	$-0.427537\pi$
$31$	4.29253	−	0.756889i	0.770961	−	0.135941i	0.545273	+	0.838258i	$0.316426\pi$
$32$	−4.70977	−	3.13337i	−0.832578	−	0.553907i
$33$		0			0
$34$	−4.02619	−	0.909343i	−0.690486	−	0.155951i
$35$	2.52015	+	1.45501i	0.425982	+	0.245941i
$36$		0			0
$37$	3.72940	−	2.15317i	0.613109	−	0.353979i	−0.161072	−	0.986943i	$-0.551495\pi$
$37$	3.72940	−	2.15317i	0.613109	−	0.353979i	0.774181	+	0.632964i	$0.218162\pi$
$38$	−6.76889	+	2.10476i	−1.09806	+	0.341438i
$39$		0			0
$40$	1.50573	−	0.934270i	0.238076	−	0.147721i
$41$	5.41092	+	6.44848i	0.845043	+	1.00708i	0.999817	+	0.0191334i	$0.00609071\pi$
$41$	5.41092	+	6.44848i	0.845043	+	1.00708i	−0.154774	+	0.987950i	$0.549465\pi$
$42$		0			0
$43$	5.48086	−	1.99487i	0.835823	−	0.304215i	0.111577	−	0.993756i	$-0.464410\pi$
$43$	5.48086	−	1.99487i	0.835823	−	0.304215i	0.724247	+	0.689541i	$0.242188\pi$
$44$	−7.29157	+	3.33000i	−1.09925	+	0.502017i
$45$		0			0
$46$	−3.60674	+	5.61224i	−0.531785	+	0.827480i
$47$	−1.38464	+	7.85268i	−0.201971	+	1.14543i	0.700166	+	0.713980i	$0.253109\pi$
$47$	−1.38464	+	7.85268i	−0.201971	+	1.14543i	−0.902136	+	0.431451i	$0.858002\pi$
$48$		0			0
$49$	13.6955	+	4.98477i	1.95651	+	0.712110i
$50$	−0.824893	−	6.46355i	−0.116657	−	0.914084i
$51$		0			0
$52$	1.29353	−	1.27318i	0.179381	−	0.176559i
$53$	3.06833			0.421467			0.210734	−	0.977544i	$-0.432415\pi$
$53$	3.06833			0.421467			0.210734	+	0.977544i	$0.432415\pi$
$54$		0			0
$55$		−	2.51103i		−	0.338587i
$56$	9.79089	−	8.75982i	1.30836	−	1.17058i
$57$		0			0
$58$	−1.45271	−	11.3829i	−0.190751	−	1.49465i
$59$	0.537968	−	1.47805i	0.0700375	−	0.192426i	−0.899735	−	0.436436i	$-0.856241\pi$
$59$	0.537968	−	1.47805i	0.0700375	−	0.192426i	0.969773	+	0.244010i	$0.0784628\pi$
$60$		0			0
$61$	−3.32732	−	0.586696i	−0.426020	−	0.0751188i	−0.0434723	−	0.999055i	$-0.513842\pi$
$61$	−3.32732	−	0.586696i	−0.426020	−	0.0751188i	−0.382547	+	0.923936i	$0.624953\pi$
$62$	5.18567	+	3.33260i	0.658580	+	0.423241i
$63$		0			0
$64$	−1.88621	−	7.77446i	−0.235777	−	0.971807i
$65$	0.194457	+	0.534265i	0.0241194	+	0.0662675i
$66$		0			0
$67$	9.02325	−	7.57140i	1.10237	−	0.924994i	0.104783	−	0.994495i	$-0.466585\pi$
$67$	9.02325	−	7.57140i	1.10237	−	0.924994i	0.997582	+	0.0695008i	$0.0221406\pi$
$68$	−3.31014	−	4.80804i	−0.401413	−	0.583060i
$69$		0			0
$70$	1.22195	+	3.92978i	0.146051	+	0.469699i
$71$	3.19304	+	5.53051i	0.378944	+	0.656350i	0.990909	−	0.134535i	$-0.0429540\pi$
$71$	3.19304	+	5.53051i	0.378944	+	0.656350i	−0.611965	+	0.790885i	$0.709621\pi$
$72$		0			0
$73$	−2.18272	+	3.78059i	−0.255469	+	0.442485i	−0.965023	−	0.262166i	$-0.915563\pi$
$73$	−2.18272	+	3.78059i	−0.255469	+	0.442485i	0.709554	+	0.704651i	$0.248896\pi$
$74$	5.94045	+	1.34169i	0.690563	+	0.155968i
$75$		0			0
$76$	−9.05165	−	4.30854i	−1.03830	−	0.494223i
$77$	−3.23271	−	18.3336i	−0.368402	−	2.08931i
$78$		0			0
$79$	−5.52630	+	6.58598i	−0.621757	+	0.740981i	−0.981371	−	0.192120i	$-0.938464\pi$
$79$	−5.52630	+	6.58598i	−0.621757	+	0.740981i	0.359615	+	0.933101i	$0.382908\pi$
$80$	2.46074	+	0.474238i	0.275119	+	0.0530214i
$81$		0			0
$82$	−0.566412	+	11.8912i	−0.0625498	+	1.31317i
$83$	−6.42426	+	7.65613i	−0.705154	+	0.840370i	−0.993099	−	0.117277i	$-0.962583\pi$
$83$	−6.42426	+	7.65613i	−0.705154	+	0.840370i	0.287945	+	0.957647i	$0.407028\pi$
$84$		0			0
$85$	1.80077	−	0.317525i	0.195321	−	0.0344404i
$86$	7.60810	+	3.18677i	0.820403	+	0.343638i
$87$		0			0
$88$	−10.7703	−	3.53721i	−1.14812	−	0.377068i
$89$	1.88520	+	1.08842i	0.199830	+	0.115372i	0.596576	−	0.802556i	$-0.296527\pi$
$89$	1.88520	+	1.08842i	0.199830	+	0.115372i	−0.396746	+	0.917928i	$0.629861\pi$
$90$		0			0
$91$	2.10759	+	3.65046i	0.220936	+	0.382672i
$92$	−9.13219	+	2.36954i	−0.952097	+	0.247041i
$93$		0			0
$94$	−8.97354	+	6.82930i	−0.925550	+	0.704389i
$95$	2.40560	−	2.01853i	0.246809	−	0.207097i
$96$		0			0
$97$	−0.312612	+	0.113782i	−0.0317410	+	0.0115528i	−0.357842	−	0.933782i	$-0.616487\pi$
$97$	−0.312612	+	0.113782i	−0.0317410	+	0.0115528i	0.326101	+	0.945335i	$0.394265\pi$
$98$	9.44477	+	18.3202i	0.954066	+	1.85062i
$99$		0			0
$100$	5.34517	−	7.50634i	0.534517	−	0.750634i
$101$	−1.17640	+	6.67170i	−0.117056	+	0.663859i	0.868655	+	0.495417i	$0.164985\pi$
$101$	−1.17640	+	6.67170i	−0.117056	+	0.663859i	−0.985712	+	0.168442i	$0.946126\pi$
$102$		0			0
$103$	−4.03772	+	11.0936i	−0.397849	+	1.09308i	0.565481	+	0.824761i	$0.308690\pi$
$103$	−4.03772	+	11.0936i	−0.397849	+	1.09308i	−0.963330	+	0.268319i	$0.913532\pi$
$104$	2.56550	−	0.0814625i	0.251568	−	0.00798805i
$105$		0			0
$106$	3.18760	+	2.94423i	0.309607	+	0.285969i
$107$		−	11.7674i		−	1.13759i	−0.822478	−	0.568797i	$-0.807409\pi$
$107$		−	11.7674i		−	1.13759i	0.822478	−	0.568797i	$-0.192591\pi$
$108$		0			0
$109$		−	4.09964i		−	0.392674i	−0.980536	−	0.196337i	$-0.937095\pi$
$109$		−	4.09964i		−	0.392674i	0.980536	−	0.196337i	$-0.0629047\pi$
$110$	2.40947	−	2.60864i	0.229734	−	0.248724i
$111$		0			0
$112$	18.5770	+	0.294554i	1.75536	+	0.0278328i
$113$	−0.0392698	+	0.107893i	−0.00369419	+	0.0101497i	−0.941526	−	0.336940i	$-0.890608\pi$
$113$	−0.0392698	+	0.107893i	−0.00369419	+	0.0101497i	0.937832	+	0.347090i	$0.112830\pi$
$114$		0			0
$115$	0.513202	−	2.91051i	0.0478563	−	0.271407i
$116$	9.41334	−	13.2194i	0.874007	−	1.22739i
$117$		0			0
$118$	1.97715	−	1.01930i	0.182012	−	0.0938343i
$119$	12.7391	−	4.63666i	1.16779	−	0.425042i
$120$		0			0
$121$	−3.87924	+	3.25507i	−0.352658	+	0.295916i
$122$	−2.89369	−	3.80225i	−0.261983	−	0.344239i
$123$		0			0
$124$	2.18943	+	8.43808i	0.196617	+	0.757762i
$125$	3.00957	+	5.21273i	0.269184	+	0.466241i
$126$		0			0
$127$	−10.7644	−	6.21480i	−0.955182	−	0.551475i	−0.0604953	−	0.998168i	$-0.519268\pi$
$127$	−10.7644	−	6.21480i	−0.955182	−	0.551475i	−0.894687	+	0.446694i	$0.852601\pi$
$128$	5.50048	−	9.88659i	0.486178	−	0.873860i
$129$		0			0
$130$	−0.310641	+	0.741625i	−0.0272450	+	0.0650448i
$131$	−0.499778	+	0.0881243i	−0.0436658	+	0.00769945i	−0.195438	−	0.980716i	$-0.562613\pi$
$131$	−0.499778	+	0.0881243i	−0.0436658	+	0.00769945i	0.151773	+	0.988415i	$0.451502\pi$
$132$		0			0
$133$	14.9652	−	17.8348i	1.29765	−	1.54647i
$134$	16.6392	+	0.792571i	1.43741	+	0.0684677i
$135$		0			0
$136$	1.17476	−	8.17119i	0.100735	−	0.700674i
$137$	−5.79017	+	6.90045i	−0.494687	+	0.589545i	−0.954403	−	0.298521i	$-0.903507\pi$
$137$	−5.79017	+	6.90045i	−0.494687	+	0.589545i	0.459716	+	0.888066i	$0.347951\pi$
$138$		0			0
$139$	3.21820	+	18.2513i	0.272965	+	1.54806i	0.745354	+	0.666669i	$0.232280\pi$
$139$	3.21820	+	18.2513i	0.272965	+	1.54806i	−0.472389	+	0.881390i	$0.656608\pi$
$140$	−2.50139	+	5.25507i	−0.211406	+	0.444135i
$141$		0			0
$142$	−1.98966	+	8.80938i	−0.166968	+	0.739267i
$143$	1.81863	−	3.14995i	0.152081	−	0.263412i
$144$		0			0
$145$	2.54180	+	4.40253i	0.211085	+	0.365610i
$146$	−5.89525	+	1.83311i	−0.487895	+	0.151709i
$147$		0			0
$148$	4.88394	+	7.09402i	0.401458	+	0.583125i
$149$	9.83276	−	8.25067i	0.805531	−	0.675921i	−0.144006	−	0.989577i	$-0.545998\pi$
$149$	9.83276	−	8.25067i	0.805531	−	0.675921i	0.949537	+	0.313656i	$0.101554\pi$
$150$		0			0
$151$	8.03472	+	22.0752i	0.653856	+	1.79645i	0.602989	+	0.797749i	$0.293976\pi$
$151$	8.03472	+	22.0752i	0.653856	+	1.79645i	0.0508665	+	0.998705i	$0.483802\pi$
$152$	−5.26924	−	13.1616i	−0.427391	−	1.06754i
$153$		0			0
$154$	14.2337	−	22.1483i	1.14699	−	1.78476i
$155$	−2.68929	−	0.474195i	−0.216009	−	0.0380882i
$156$		0			0
$157$	1.30901	−	3.59647i	0.104470	−	0.287029i	−0.876434	−	0.481522i	$-0.840084\pi$
$157$	1.30901	−	3.59647i	0.104470	−	0.287029i	0.980904	+	0.194493i	$0.0623062\pi$
$158$	−12.0607	+	1.53922i	−0.959500	+	0.122454i
$159$		0			0
$160$	2.10134	+	2.85388i	0.166125	+	0.225619i
$161$		−	21.9111i		−	1.72683i
$162$		0			0
$163$	−9.80547			−0.768023			−0.384012	−	0.923328i	$-0.625458\pi$
$163$	−9.80547			−0.768023			−0.384012	+	0.923328i	$0.625458\pi$
$164$	−11.9987	+	11.8100i	−0.936941	+	0.922202i
$165$		0			0
$166$	−14.0205	+	1.78932i	−1.08820	+	0.138878i
$167$	−5.51424	−	2.00702i	−0.426705	−	0.155308i	0.119736	−	0.992806i	$-0.461795\pi$
$167$	−5.51424	−	2.00702i	−0.426705	−	0.155308i	−0.546440	+	0.837498i	$0.684018\pi$
$168$		0			0
$169$	2.11442	−	11.9915i	0.162647	−	0.922420i
$170$	2.17546	+	1.39807i	0.166850	+	0.107227i
$171$		0			0
$172$	4.84597	+	10.6110i	0.369502	+	0.809083i
$173$	−16.3275	+	5.94273i	−1.24136	+	0.451817i	−0.877473	−	0.479627i	$-0.840772\pi$
$173$	−16.3275	+	5.94273i	−1.24136	+	0.451817i	−0.363885	+	0.931444i	$0.618550\pi$
$174$		0			0
$175$	13.7563	+	16.3941i	1.03988	+	1.23928i
$176$	−7.79486	−	14.0094i	−0.587560	−	1.05600i
$177$		0			0
$178$	0.914081	+	2.93967i	0.0685133	+	0.220338i
$179$	−2.25513	+	1.30200i	−0.168556	+	0.0973161i	−0.581905	−	0.813257i	$-0.697692\pi$
$179$	−2.25513	+	1.30200i	−0.168556	+	0.0973161i	0.413349	+	0.910573i	$0.364359\pi$
$180$		0			0
$181$	16.9999	+	9.81488i	1.26359	+	0.729535i	0.973767	−	0.227546i	$-0.0730701\pi$
$181$	16.9999	+	9.81488i	1.26359	+	0.729535i	0.289823	+	0.957080i	$0.406403\pi$
$182$	−1.31329	+	5.81471i	−0.0973477	+	0.431015i
$183$		0			0
$184$	−11.7609	−	6.30119i	−0.867024	−	0.464530i
$185$	−2.65695	+	0.468492i	−0.195343	+	0.0344442i
$186$		0			0
$187$	−8.96115	−	7.51930i	−0.655304	−	0.549866i
$188$	−15.8754	−	1.51582i	−1.15784	−	0.110553i
$189$		0			0
$190$	4.43600	+	0.211299i	0.321821	+	0.0153293i
$191$	11.2413	+	9.43260i	0.813394	+	0.682519i	0.951415	−	0.307910i	$-0.0996297\pi$
$191$	11.2413	+	9.43260i	0.813394	+	0.682519i	−0.138021	+	0.990429i	$0.544074\pi$
$192$		0			0
$193$	−3.08198	−	17.4788i	−0.221846	−	1.25815i	−0.868624	−	0.495472i	$-0.834995\pi$
$193$	−3.08198	−	17.4788i	−0.221846	−	1.25815i	0.646778	−	0.762678i	$-0.276116\pi$
$194$	−0.433944	−	0.181764i	−0.0311554	−	0.0130499i
$195$		0			0
$196$	−7.76727	+	28.0951i	−0.554805	+	2.00679i
$197$	−0.959735	+	1.66231i	−0.0683783	+	0.118435i	−0.898188	−	0.439612i	$-0.855116\pi$
$197$	−0.959735	+	1.66231i	−0.0683783	+	0.118435i	0.829809	+	0.558047i	$0.188449\pi$
$198$		0			0
$199$	14.5078	−	8.37608i	1.02843	−	0.593765i	0.111896	−	0.993720i	$-0.464308\pi$
$199$	14.5078	−	8.37608i	1.02843	−	0.593765i	0.916535	+	0.399955i	$0.130974\pi$
$200$	12.7557	−	2.66915i	0.901963	−	0.188737i
$201$		0			0
$202$	−7.62399	+	5.80223i	−0.536422	+	0.408243i
$203$	24.2262	+	28.8716i	1.70034	+	2.02639i
$204$		0			0
$205$	−1.80376	−	4.95580i	−0.125980	−	0.346128i
$206$	−14.8395	+	7.65037i	−1.03392	+	0.533027i
$207$		0			0
$208$	2.74340	+	2.37711i	0.190221	+	0.164823i
$209$	−19.7844	−	3.48852i	−1.36851	−	0.241306i
$210$		0			0
$211$	−6.38063	−	2.32236i	−0.439261	−	0.159878i	0.112917	−	0.993604i	$-0.463981\pi$
$211$	−6.38063	−	2.32236i	−0.439261	−	0.159878i	−0.552177	+	0.833727i	$0.686203\pi$
$212$	0.486367	+	6.11735i	0.0334038	+	0.420141i
$213$		0			0
$214$	11.2914	−	12.2248i	0.771866	−	0.835670i
$215$	−3.65416			−0.249212
$216$		0			0
$217$	−20.2457			−1.37437
$218$	3.93382	−	4.25900i	0.266432	−	0.288456i
$219$		0			0
$220$	5.00626	−	0.398028i	0.337522	−	0.0268350i
$221$	2.48895	+	0.905902i	0.167425	+	0.0609376i
$222$		0			0
$223$	−27.4675	−	4.84327i	−1.83936	−	0.324329i	−0.857582	−	0.514348i	$-0.828034\pi$
$223$	−27.4675	−	4.84327i	−1.83936	−	0.324329i	−0.981780	+	0.190019i	$0.939145\pi$
$224$	19.0165	+	18.1316i	1.27059	+	1.21147i
$225$		0			0
$226$	−0.144325	+	0.0744054i	−0.00960037	+	0.00494937i
$227$	−7.70763	−	21.1766i	−0.511574	−	1.40554i	−0.879597	−	0.475720i	$-0.842187\pi$
$227$	−7.70763	−	21.1766i	−0.511574	−	1.40554i	0.368023	−	0.929817i	$-0.380035\pi$
$228$		0			0
$229$	−11.0943	−	13.2216i	−0.733130	−	0.873710i	0.262706	−	0.964876i	$-0.415385\pi$
$229$	−11.0943	−	13.2216i	−0.733130	−	0.873710i	−0.995836	+	0.0911658i	$0.970941\pi$
$230$	3.32595	−	2.53121i	0.219306	−	0.166903i
$231$		0			0
$232$	22.4640	−	4.70062i	1.47483	−	0.308611i
$233$	12.5406	−	7.24033i	0.821564	−	0.474330i	−0.0293918	−	0.999568i	$-0.509357\pi$
$233$	12.5406	−	7.24033i	0.821564	−	0.474330i	0.850955	+	0.525238i	$0.176024\pi$
$234$		0			0
$235$	2.49782	−	4.32635i	0.162940	−	0.282220i
$236$	3.03208	+	0.838262i	0.197372	+	0.0545662i
$237$		0			0
$238$	17.6834	+	7.40697i	1.14625	+	0.480123i
$239$	3.39066	+	19.2294i	0.219324	+	1.24385i	0.873244	+	0.487283i	$0.162012\pi$
$239$	3.39066	+	19.2294i	0.219324	+	1.24385i	−0.653920	+	0.756563i	$0.726877\pi$
$240$		0			0
$241$	1.60322	+	1.34526i	0.103272	+	0.0866558i	0.692962	−	0.720974i	$-0.256305\pi$
$241$	1.60322	+	1.34526i	0.103272	+	0.0866558i	−0.589689	+	0.807630i	$0.700750\pi$
$242$	−7.15345	−	0.340739i	−0.459841	−	0.0219036i
$243$		0			0
$244$	0.642281	−	6.72670i	0.0411178	−	0.430633i
$245$	−6.99475	−	5.86929i	−0.446878	−	0.374975i
$246$		0			0
$247$	4.47963	−	0.789880i	0.285032	−	0.0502588i
$248$	−5.82225	+	10.8670i	−0.369713	+	0.690053i
$249$		0			0
$250$	−1.87534	+	8.30321i	−0.118607	+	0.525141i
$251$	−7.71685	−	4.45533i	−0.487083	−	0.281218i	0.236280	−	0.971685i	$-0.424072\pi$
$251$	−7.71685	−	4.45533i	−0.487083	−	0.281218i	−0.723364	+	0.690467i	$0.757405\pi$
$252$		0			0
$253$	−16.3738	+	9.45345i	−1.02942	+	0.594333i
$254$	−5.21935	−	16.7854i	−0.327491	−	1.05321i
$255$		0			0
$256$	15.2010	−	4.99290i	0.950064	−	0.312056i
$257$	7.13593	+	8.50427i	0.445127	+	0.530482i	0.941223	−	0.337786i	$-0.109678\pi$
$257$	7.13593	+	8.50427i	0.445127	+	0.530482i	−0.496096	+	0.868268i	$0.665234\pi$
$258$		0			0
$259$	−18.7959	+	6.84116i	−1.16792	+	0.425089i
$260$	−1.03435	+	0.472377i	−0.0641474	+	0.0292956i
$261$		0			0
$262$	−0.603765	−	0.388014i	−0.0373007	−	0.0239716i
$263$	3.30401	−	18.7379i	0.203734	−	1.15543i	−0.695686	−	0.718346i	$-0.744900\pi$
$263$	3.30401	−	18.7379i	0.203734	−	1.15543i	0.899420	−	0.437085i	$-0.143989\pi$
$264$		0			0
$265$	−1.80639	−	0.657473i	−0.110966	−	0.0403883i
$266$	32.6604	−	4.16819i	2.00254	−	0.255568i
$267$		0			0
$268$	16.5255	+	16.7896i	1.00945	+	1.02559i
$269$	2.37780			0.144977			0.0724886	−	0.997369i	$-0.476906\pi$
$269$	2.37780			0.144977			0.0724886	+	0.997369i	$0.476906\pi$
$270$		0			0
$271$			18.7598i			1.13957i	0.821792	+	0.569787i	$0.192974\pi$
$271$			18.7598i			1.13957i	−0.821792	+	0.569787i	$0.807026\pi$
$272$	9.06113	−	7.36158i	0.549412	−	0.446361i
$273$		0			0
$274$	−12.6366	+	1.61271i	−0.763405	+	0.0974274i
$275$	6.31601	−	17.3531i	0.380870	−	1.04643i
$276$		0			0
$277$	−4.07892	−	0.719224i	−0.245079	−	0.0432140i	0.0497594	−	0.998761i	$-0.484155\pi$
$277$	−4.07892	−	0.719224i	−0.245079	−	0.0432140i	−0.294838	+	0.955547i	$0.595266\pi$
$278$	−14.1698	+	22.0489i	−0.849851	+	1.32240i
$279$		0			0
$280$	−7.64115	+	3.05913i	−0.456646	+	0.182818i
$281$	5.40819	+	14.8589i	0.322625	+	0.886406i	0.989922	+	0.141614i	$0.0452291\pi$
$281$	5.40819	+	14.8589i	0.322625	+	0.886406i	−0.667297	+	0.744792i	$0.732549\pi$
$282$		0			0
$283$	6.74592	−	5.66050i	0.401003	−	0.336482i	−0.419878	−	0.907581i	$-0.637927\pi$
$283$	6.74592	−	5.66050i	0.401003	−	0.336482i	0.820881	+	0.571099i	$0.193483\pi$
$284$	−10.5201	+	7.24264i	−0.624252	+	0.429772i
$285$		0			0
$286$	4.91187	−	1.52733i	0.290445	−	0.0903129i
$287$	−19.5499	−	33.8614i	−1.15399	−	1.99877i
$288$		0			0
$289$	−4.24072	+	7.34514i	−0.249454	+	0.432067i
$290$	−1.58386	+	7.01266i	−0.0930073	+	0.411798i
$291$		0			0
$292$	−7.88338	−	3.75245i	−0.461340	−	0.219595i
$293$	1.65024	+	9.35900i	0.0964083	+	0.546759i	0.994307	+	0.106556i	$0.0339823\pi$
$293$	1.65024	+	9.35900i	0.0964083	+	0.546759i	−0.897898	+	0.440203i	$0.854907\pi$
$294$		0			0
$295$	−0.633427	+	0.754889i	−0.0368796	+	0.0439514i
$296$	−1.73331	+	12.0562i	−0.100746	+	0.700752i
$297$		0			0
$298$	18.1319	+	0.863676i	1.05036	+	0.0500314i
$299$	2.75174	−	3.27940i	0.159137	−	0.189652i
$300$		0			0
$301$	−26.6799	+	4.70439i	−1.53781	+	0.271157i
$302$	−12.8353	+	30.6431i	−0.738589	+	1.76331i
$303$		0			0
$304$	7.15517	−	18.7293i	0.410377	−	1.07420i
$305$	1.83315	+	1.05837i	0.104966	+	0.0606021i
$306$		0			0
$307$	−7.38935	−	12.7987i	−0.421733	−	0.730462i	0.574376	−	0.818591i	$-0.305245\pi$
$307$	−7.38935	−	12.7987i	−0.421733	−	0.730462i	−0.996109	+	0.0881289i	$0.971911\pi$
$308$	36.0395	−	9.35119i	2.05354	−	0.532833i
$309$		0			0
$310$	−2.33882	−	3.07315i	−0.132836	−	0.174543i
$311$	−22.8823	+	19.2005i	−1.29753	+	1.08876i	−0.306969	+	0.951720i	$0.599315\pi$
$311$	−22.8823	+	19.2005i	−1.29753	+	1.08876i	−0.990565	+	0.137041i	$0.956241\pi$
$312$		0			0
$313$	4.41539	−	1.60707i	0.249572	−	0.0908369i	−0.214205	−	0.976789i	$-0.568716\pi$
$313$	4.41539	−	1.60707i	0.249572	−	0.0908369i	0.463777	+	0.885952i	$0.346494\pi$
$314$	4.81090	−	2.48021i	0.271495	−	0.139966i
$315$		0			0
$316$	−14.0065	−	9.97387i	−0.787928	−	0.561074i
$317$	1.83138	−	10.3863i	0.102861	−	0.583352i	−0.889193	−	0.457533i	$-0.848733\pi$
$317$	1.83138	−	10.3863i	0.102861	−	0.583352i	0.992053	−	0.125819i	$-0.0401558\pi$
$318$		0			0
$319$	11.1231	−	30.5604i	0.622773	−	1.71106i
$320$	−0.555435	+	4.98117i	−0.0310498	+	0.278456i
$321$		0			0
$322$	21.0249	−	22.7628i	1.17167	−	1.26852i
$323$		−	14.6294i		−	0.814003i
$324$		0			0
$325$			4.18130i			0.231937i
$326$	−10.1866	−	9.40888i	−0.564185	−	0.521109i
$327$		0			0
$328$	−23.7974	+	0.755639i	−1.31399	+	0.0417232i
$329$	12.6674	−	34.8035i	0.698378	−	1.91878i
$330$		0			0
$331$	2.08554	−	11.8277i	0.114632	−	0.650108i	−0.872300	−	0.488971i	$-0.837373\pi$
$331$	2.08554	−	11.8277i	0.114632	−	0.650108i	0.986932	−	0.161138i	$-0.0515163\pi$
$332$	−16.2824	−	11.5945i	−0.893614	−	0.636331i
$333$		0			0
$334$	−3.80275	−	7.37625i	−0.208077	−	0.403610i
$335$	−6.93457	+	2.52398i	−0.378876	+	0.137900i
$336$		0			0
$337$	−8.14386	+	6.83351i	−0.443624	+	0.372245i	−0.837064	−	0.547106i	$-0.815730\pi$
$337$	−8.14386	+	6.83351i	−0.443624	+	0.372245i	0.393439	+	0.919351i	$0.371285\pi$
$338$	13.7031	−	10.4287i	0.745348	−	0.567246i
$339$		0			0
$340$	0.918496	+	3.53989i	0.0498125	+	0.191977i
$341$	8.73492	+	15.1293i	0.473022	+	0.819298i
$342$		0			0
$343$	−30.4687	−	17.5911i	−1.64516	−	0.949832i
$344$	−5.14751	+	15.6735i	−0.277535	+	0.845057i
$345$		0			0
$346$	−22.6646	−	9.49339i	−1.21845	−	0.510368i
$347$	−13.6704	+	2.41047i	−0.733868	+	0.129401i	−0.528078	−	0.849196i	$-0.677087\pi$
$347$	−13.6704	+	2.41047i	−0.733868	+	0.129401i	−0.205789	+	0.978596i	$0.565976\pi$
$348$		0			0
$349$	13.0999	−	15.6119i	0.701223	−	0.835685i	−0.291441	−	0.956589i	$-0.594135\pi$
$349$	13.0999	−	15.6119i	0.701223	−	0.835685i	0.992664	+	0.120904i	$0.0385792\pi$
$350$	−1.44001	+	30.2314i	−0.0769715	+	1.61593i
$351$		0			0
$352$	5.34494	−	22.0336i	0.284886	−	1.17439i
$353$	2.23673	−	2.66563i	0.119049	−	0.141877i	−0.703228	−	0.710964i	$-0.748259\pi$
$353$	2.23673	−	2.66563i	0.119049	−	0.141877i	0.822277	+	0.569087i	$0.192703\pi$
$354$		0			0
$355$	−0.694751	−	3.94013i	−0.0368735	−	0.209120i
$356$	−1.87116	+	3.93106i	−0.0991714	+	0.208346i
$357$		0			0
$358$	−3.59213	−	0.811307i	−0.189850	−	0.0428789i
$359$	−0.993822	+	1.72135i	−0.0524519	+	0.0908494i	−0.891059	−	0.453887i	$-0.850037\pi$
$359$	−0.993822	+	1.72135i	−0.0524519	+	0.0908494i	0.838607	+	0.544736i	$0.183370\pi$
$360$		0			0
$361$	−3.06198	−	5.30350i	−0.161157	−	0.279132i
$362$	8.24279	+	26.5087i	0.433232	+	1.39327i
$363$		0			0
$364$	−6.94387	+	4.78057i	−0.363958	+	0.250570i
$365$	2.09511	−	1.75801i	0.109663	−	0.0920184i
$366$		0			0
$367$	−1.09533	−	3.00938i	−0.0571755	−	0.157089i	0.907817	−	0.419368i	$-0.137748\pi$
$367$	−1.09533	−	3.00938i	−0.0571755	−	0.157089i	−0.964992	+	0.262279i	$0.915526\pi$
$368$	−6.17173	−	17.8313i	−0.321723	−	0.929522i
$369$		0			0
$370$	−3.20978	−	2.06279i	−0.166868	−	0.107239i
$371$	−14.0354	−	2.47481i	−0.728679	−	0.128486i
$372$		0			0
$373$	0.734328	−	2.01755i	0.0380221	−	0.104465i	−0.919229	−	0.393724i	$-0.871187\pi$
$373$	0.734328	−	2.01755i	0.0380221	−	0.104465i	0.957251	+	0.289259i	$0.0934089\pi$
$374$	−2.09432	−	16.4103i	−0.108295	−	0.848556i
$375$		0			0
$376$	−15.0380	−	16.8081i	−0.775528	−	0.866811i
$377$			7.36366i			0.379248i
$378$		0			0
$379$	10.2488			0.526447			0.263223	−	0.964735i	$-0.415214\pi$
$379$	10.2488			0.526447			0.263223	+	0.964735i	$0.415214\pi$
$380$	4.40568	+	4.47609i	0.226007	+	0.229619i
$381$		0			0
$382$	2.62722	+	20.5859i	0.134420	+	1.05327i
$383$	20.9591	+	7.62848i	1.07096	+	0.389797i	0.816535	−	0.577296i	$-0.195892\pi$
$383$	20.9591	+	7.62848i	1.07096	+	0.389797i	0.254423	+	0.967093i	$0.418114\pi$
$384$		0			0
$385$	−2.02531	+	11.4861i	−0.103219	+	0.585387i
$386$	13.5701	−	21.1156i	0.690697	−	1.07475i
$387$		0			0
$388$	−0.276400	−	0.605222i	−0.0140321	−	0.0307255i
$389$	−8.94456	+	3.25555i	−0.453507	+	0.165063i	−0.558667	−	0.829392i	$-0.688687\pi$
$389$	−8.94456	+	3.25555i	−0.453507	+	0.165063i	0.105160	+	0.994455i	$0.466465\pi$
$390$		0			0
$391$	−8.85001	−	10.5470i	−0.447564	−	0.533387i
$392$	−35.0279	+	21.7341i	−1.76918	+	1.09774i
$393$		0			0
$394$	−2.59212	+	0.806010i	−0.130589	+	0.0406062i
$395$	4.66468	−	2.69315i	0.234706	−	0.135507i
$396$		0			0
$397$	31.4195	+	18.1401i	1.57690	+	0.910424i	0.995289	+	0.0969571i	$0.0309110\pi$
$397$	31.4195	+	18.1401i	1.57690	+	0.910424i	0.581612	+	0.813467i	$0.302422\pi$
$398$	23.1091	+	5.21934i	1.15835	+	0.261622i
$399$		0			0
$400$	15.8127	+	9.46687i	0.790636	+	0.473343i
$401$	−32.5501	+	5.73946i	−1.62547	+	0.286615i	−0.910802	−	0.412844i	$-0.864535\pi$
$401$	−32.5501	+	5.73946i	−1.62547	+	0.286615i	−0.714673	+	0.699459i	$0.753424\pi$
$402$		0			0
$403$	−3.03014	−	2.54259i	−0.150942	−	0.126655i
$404$	−13.4879	−	1.28786i	−0.671048	−	0.0640732i
$405$		0			0
$406$	−2.53598	+	53.2403i	−0.125859	+	2.64227i
$407$	13.2217	+	11.0944i	0.655377	+	0.549927i
$408$		0			0
$409$	3.81109	+	21.6138i	0.188446	+	1.06873i	0.921447	+	0.388504i	$0.127008\pi$
$409$	3.81109	+	21.6138i	0.188446	+	1.06873i	−0.733001	+	0.680228i	$0.761881\pi$
$410$	2.88148	−	6.87925i	0.142306	−	0.339742i
$411$		0			0
$412$	−22.7573	−	6.29158i	−1.12117	−	0.309964i
$413$	−3.65296	+	6.32711i	−0.179750	+	0.311337i
$414$		0			0
$415$	5.42264	−	3.13076i	0.266187	−	0.153683i
$416$	0.569076	+	5.10196i	0.0279012	+	0.250144i
$417$		0			0
$418$	−17.2060	−	22.6083i	−0.841574	−	1.10581i
$419$	−10.2635	−	12.2316i	−0.501405	−	0.597551i	0.454675	−	0.890658i	$-0.349755\pi$
$419$	−10.2635	−	12.2316i	−0.501405	−	0.597551i	−0.956080	+	0.293106i	$0.905311\pi$
$420$		0			0
$421$	9.89676	+	27.1911i	0.482338	+	1.32521i	0.907483	+	0.420088i	$0.138001\pi$
$421$	9.89676	+	27.1911i	0.482338	+	1.32521i	−0.425145	+	0.905125i	$0.639777\pi$
$422$	−4.40023	−	8.53519i	−0.214200	−	0.415487i
$423$		0			0
$424$	−5.36466	+	6.82184i	−0.260531	+	0.331298i
$425$	13.2434	+	2.33517i	0.642399	+	0.113272i
$426$		0			0
$427$	14.7468	+	5.36741i	0.713650	+	0.259747i
$428$	23.4607	−	1.86527i	1.13402	−	0.0901612i
$429$		0			0
$430$	−3.79621	−	3.50636i	−0.183069	−	0.169092i
$431$	−30.7042			−1.47897			−0.739484	−	0.673174i	$-0.764930\pi$
$431$	−30.7042			−1.47897			−0.739484	+	0.673174i	$0.764930\pi$
$432$		0			0
$433$	24.3318			1.16931			0.584657	−	0.811281i	$-0.301229\pi$
$433$	24.3318			1.16931			0.584657	+	0.811281i	$0.301229\pi$
$434$	−21.0327	−	19.4268i	−1.00960	−	0.932517i
$435$		0			0
$436$	8.17348	−	0.649842i	0.391439	−	0.0311218i
$437$	−22.2189	−	8.08703i	−1.06288	−	0.386855i
$438$		0			0
$439$	15.6481	+	2.75919i	0.746844	+	0.131689i	0.534102	−	0.845420i	$-0.320650\pi$
$439$	15.6481	+	2.75919i	0.746844	+	0.131689i	0.212741	+	0.977109i	$0.431761\pi$
$440$	5.58279	+	4.39027i	0.266149	+	0.209298i
$441$		0			0
$442$	1.71644	+	3.32940i	0.0816425	+	0.158363i
$443$	7.27214	+	19.9800i	0.345510	+	0.949280i	0.983766	+	0.179456i	$0.0574338\pi$
$443$	7.27214	+	19.9800i	0.345510	+	0.949280i	−0.638256	+	0.769824i	$0.720344\pi$
$444$		0			0
$445$	−0.876633	−	1.04473i	−0.0415564	−	0.0495250i
$446$	−23.8879	−	31.3881i	−1.13112	−	1.48627i
$447$		0			0
$448$	2.35742	+	37.0838i	0.111378	+	1.75205i
$449$	−10.3738	+	5.98931i	−0.489569	+	0.282653i	−0.724396	−	0.689384i	$-0.757881\pi$
$449$	−10.3738	+	5.98931i	−0.489569	+	0.282653i	0.234827	+	0.972037i	$0.424548\pi$
$450$		0			0
$451$	−16.8694	+	29.2187i	−0.794350	+	1.37585i
$452$	−0.221331	−	0.0611902i	−0.0104106	−	0.00287814i
$453$		0			0
$454$	12.3128	−	29.3956i	0.577868	−	1.37961i
$455$	−0.458576	−	2.60072i	−0.0214984	−	0.121923i
$456$		0			0
$457$	−19.6891	−	16.5211i	−0.921015	−	0.772823i	0.0531674	−	0.998586i	$-0.483068\pi$
$457$	−19.6891	−	16.5211i	−0.921015	−	0.772823i	−0.974182	+	0.225762i	$0.927513\pi$
$458$	1.16134	−	24.3811i	0.0542660	−	1.13926i
$459$		0			0
$460$	5.88406	+	0.561824i	0.274346	+	0.0261952i
$461$	19.7573	+	16.5784i	0.920190	+	0.772131i	0.974030	−	0.226418i	$-0.0727017\pi$
$461$	19.7573	+	16.5784i	0.920190	+	0.772131i	−0.0538400	+	0.998550i	$0.517146\pi$
$462$		0			0
$463$	23.8682	−	4.20861i	1.10925	−	0.195591i	0.411133	−	0.911575i	$-0.365133\pi$
$463$	23.8682	−	4.20861i	1.10925	−	0.195591i	0.698116	+	0.715985i	$0.254022\pi$
$464$	27.8477	+	16.6720i	1.29280	+	0.773980i
$465$		0			0
$466$	19.9756	+	4.51162i	0.925352	+	0.208997i
$467$	−1.80364	−	1.04133i	−0.0834624	−	0.0481870i	0.457688	−	0.889113i	$-0.348678\pi$
$467$	−1.80364	−	1.04133i	−0.0834624	−	0.0481870i	−0.541150	+	0.840926i	$0.682011\pi$
$468$		0			0
$469$	−47.3816	+	27.3558i	−2.18788	+	1.26317i
$470$	6.74629	−	2.09773i	0.311183	−	0.0967613i
$471$		0			0
$472$	2.34559	+	3.78030i	0.107965	+	0.174002i
$473$	15.0265	+	17.9079i	0.690918	+	0.823404i
$474$		0			0
$475$	21.7017	−	7.89878i	0.995744	−	0.362421i
$476$	11.2634	+	24.6631i	0.516259	+	1.13043i
$477$		0			0
$478$	−14.9292	+	23.2304i	−0.682845	+	1.06253i
$479$	2.00257	−	11.3572i	0.0914999	−	0.518922i	−0.904264	−	0.426974i	$-0.859580\pi$
$479$	2.00257	−	11.3572i	0.0914999	−	0.518922i	0.995764	−	0.0919478i	$-0.0293093\pi$
$480$		0			0
$481$	−3.67232	−	1.33661i	−0.167443	−	0.0609444i
$482$	0.374690	+	2.93593i	0.0170667	+	0.133728i
$483$		0			0
$484$	−7.10457	−	7.21811i	−0.322935	−	0.328096i
$485$	0.208423			0.00946398
$486$		0			0
$487$		−	29.2353i		−	1.32478i	−0.749160	−	0.662389i	$-0.769542\pi$
$487$		−	29.2353i		−	1.32478i	0.749160	−	0.662389i	$-0.230458\pi$
$488$	7.12189	−	6.37188i	0.322393	−	0.288442i
$489$		0			0
$490$	−1.63475	−	12.8093i	−0.0738504	−	0.578664i
$491$	1.76088	−	4.83798i	0.0794674	−	0.218335i	−0.893596	−	0.448872i	$-0.851826\pi$
$491$	1.76088	−	4.83798i	0.0794674	−	0.218335i	0.973064	+	0.230537i	$0.0740482\pi$
$492$		0			0
$493$	23.3228	+	4.11245i	1.05041	+	0.185215i
$494$	5.41170	+	3.47786i	0.243484	+	0.156476i
$495$		0			0
$496$	−16.4760	+	5.70263i	−0.739795	+	0.256056i
$497$	−10.1451	−	27.8734i	−0.455070	−	1.25029i
$498$		0			0
$499$	−19.4599	+	16.3288i	−0.871144	+	0.730977i	−0.964339	−	0.264671i	$-0.914737\pi$
$499$	−19.4599	+	16.3288i	−0.871144	+	0.730977i	0.0931946	+	0.995648i	$0.470292\pi$
$500$	−9.91561	+	6.82649i	−0.443440	+	0.305290i
$501$		0			0
$502$	−3.74170	−	12.0333i	−0.167000	−	0.537070i
$503$	−3.28486	−	5.68954i	−0.146465	−	0.253684i	0.783454	−	0.621450i	$-0.213456\pi$
$503$	−3.28486	−	5.68954i	−0.146465	−	0.253684i	−0.929918	+	0.367766i	$0.880123\pi$
$504$		0			0
$505$	2.12217	−	3.67570i	0.0944352	−	0.163567i
$506$	−26.0814	−	5.89067i	−1.15946	−	0.261872i
$507$		0			0
$508$	10.6842	−	22.4461i	0.474036	−	0.995885i
$509$	0.0426035	+	0.241616i	0.00188837	+	0.0107095i	0.985737	−	0.168291i	$-0.0538248\pi$
$509$	0.0426035	+	0.241616i	0.00188837	+	0.0107095i	−0.983849	+	0.179000i	$0.942714\pi$
$510$		0			0
$511$	13.0337	−	15.5329i	0.576576	−	0.687136i
$512$	20.5829	+	9.39921i	0.909643	+	0.415390i
$513$		0			0
$514$	−0.746986	+	15.6822i	−0.0329481	+	0.691711i
$515$	4.75419	−	5.66583i	0.209495	−	0.249666i
$516$		0			0
$517$	−31.4735	+	5.54962i	−1.38420	+	0.244072i
$518$	−26.0910	−	10.9286i	−1.14637	−	0.480176i
$519$		0			0
$520$	−1.52783	−	0.501771i	−0.0669996	−	0.0220041i
$521$	−29.9500	−	17.2916i	−1.31213	−	0.757560i	−0.329683	−	0.944092i	$-0.606942\pi$
$521$	−29.9500	−	17.2916i	−1.31213	−	0.757560i	−0.982449	+	0.186532i	$0.940275\pi$
$522$		0			0
$523$	12.9546	+	22.4380i	0.566466	+	0.981147i	0.996912	+	0.0785309i	$0.0250229\pi$
$523$	12.9546	+	22.4380i	0.566466	+	0.981147i	−0.430446	+	0.902616i	$0.641644\pi$
$524$	−0.254915	−	0.982442i	−0.0111360	−	0.0429182i
$525$		0			0
$526$	21.4125	−	16.2960i	0.933630	−	0.710538i
$527$	−9.74539	+	8.17735i	−0.424516	+	0.356211i
$528$		0			0
$529$	0.702032	−	0.255519i	0.0305231	−	0.0111095i
$530$	−1.24573	−	2.41636i	−0.0541111	−	0.104960i
$531$		0			0
$532$	37.9296	+	27.0092i	1.64445	+	1.17100i
$533$	1.32654	−	7.52318i	0.0574588	−	0.325865i
$534$		0			0
$535$	−2.52148	+	6.92771i	−0.109013	+	0.299511i
$536$	1.05735	+	33.2993i	0.0456707	+	1.43831i
$537$		0			0
$538$	2.47023	+	2.28163i	0.106499	+	0.0983681i
$539$			58.4144i			2.51609i
$540$		0			0
$541$			12.5921i			0.541376i	0.962667	+	0.270688i	$0.0872512\pi$
$541$			12.5921i			0.541376i	−0.962667	+	0.270688i	$0.912749\pi$
$542$	−18.0010	+	19.4890i	−0.773210	+	0.837124i
$543$		0			0
$544$	16.4772	+	1.04691i	0.706454	+	0.0448857i
$545$	−0.878460	+	2.41355i	−0.0376291	+	0.103385i
$546$		0			0
$547$	−3.19463	+	18.1176i	−0.136592	+	0.774654i	0.837145	+	0.546981i	$0.184223\pi$
$547$	−3.19463	+	18.1176i	−0.136592	+	0.774654i	−0.973738	+	0.227673i	$0.926888\pi$
$548$	−14.6753	−	10.4501i	−0.626898	−	0.446406i
$549$		0			0
$550$	23.2128	−	11.9671i	0.989796	−	0.510279i
$551$	38.2188	−	13.9105i	1.62817	−	0.592607i
$552$		0			0
$553$	30.5908	−	25.6687i	1.30085	−	1.09155i
$554$	−3.54734	−	4.66113i	−0.150712	−	0.198032i
$555$		0			0
$556$	−35.8777	+	9.30922i	−1.52156	+	0.394799i
$557$	8.10237	+	14.0337i	0.343308	+	0.594628i	0.985045	−	0.172298i	$-0.0551191\pi$
$557$	8.10237	+	14.0337i	0.343308	+	0.594628i	−0.641737	+	0.766925i	$0.721786\pi$
$558$		0			0
$559$	−4.58395	−	2.64655i	−0.193881	−	0.111937i
$560$	−10.8736	−	4.15404i	−0.459493	−	0.175540i
$561$		0			0
$562$	−8.63947	+	20.6259i	−0.364434	+	0.870052i
$563$	−18.5122	+	3.26419i	−0.780194	+	0.137569i	−0.549541	−	0.835467i	$-0.685197\pi$
$563$	−18.5122	+	3.26419i	−0.780194	+	0.137569i	−0.230653	+	0.973036i	$0.574086\pi$
$564$		0			0
$565$	0.0462380	−	0.0551042i	0.00194525	−	0.00231825i
$566$	12.4397	+	0.592539i	0.522880	+	0.0249063i
$567$		0			0
$568$	−17.8787	−	2.57041i	−0.750175	−	0.107852i
$569$	11.3736	−	13.5546i	0.476807	−	0.568237i	−0.473004	−	0.881060i	$-0.656830\pi$
$569$	11.3736	−	13.5546i	0.476807	−	0.568237i	0.949811	+	0.312823i	$0.101275\pi$
$570$		0			0
$571$	−6.91365	−	39.2093i	−0.289327	−	1.64086i	−0.689405	−	0.724376i	$-0.742128\pi$
$571$	−6.91365	−	39.2093i	−0.289327	−	1.64086i	0.400078	−	0.916481i	$-0.368983\pi$
$572$	6.56836	+	3.12651i	0.274637	+	0.130726i
$573$		0			0
$574$	12.1820	−	53.9368i	0.508466	−	2.25128i
$575$	10.8675	−	18.8230i	0.453204	−	0.784973i
$576$		0			0
$577$	1.07337	+	1.85913i	0.0446850	+	0.0773967i	0.887503	−	0.460802i	$-0.152438\pi$
$577$	1.07337	+	1.85913i	0.0446850	+	0.0773967i	−0.842818	+	0.538199i	$0.819105\pi$
$578$	−11.4536	+	3.56147i	−0.476408	+	0.148137i
$579$		0			0
$580$	−8.37445	+	5.76546i	−0.347730	+	0.239398i
$581$	35.5615	−	29.8396i	1.47534	−	1.23796i
$582$		0			0
$583$	4.20611	+	11.5562i	0.174199	+	0.478608i
$584$	−4.58915	−	11.4628i	−0.189901	−	0.474336i
$585$		0			0
$586$	−7.26607	+	11.3063i	−0.300159	+	0.467059i
$587$	34.2197	+	6.03386i	1.41240	+	0.249044i	0.827228	−	0.561866i	$-0.189916\pi$
$587$	34.2197	+	6.03386i	1.41240	+	0.249044i	0.585171	+	0.810910i	$0.301027\pi$
$588$		0			0
$589$	−7.47236	+	20.5301i	−0.307893	+	0.845930i
$590$	−1.38241	+	0.176426i	−0.0569128	+	0.00726334i
$591$		0			0
$592$	−13.3693	+	10.8616i	−0.549473	+	0.446411i
$593$			41.3775i			1.69917i	0.527450	+	0.849586i	$0.323148\pi$
$593$			41.3775i			1.69917i	−0.527450	+	0.849586i	$0.676852\pi$
$594$		0			0
$595$	−8.49333			−0.348193
$596$	18.0080	+	18.2958i	0.737638	+	0.749426i
$597$		0			0
$598$	6.00547	−	0.766431i	0.245582	−	0.0313417i
$599$	−31.9356	−	11.6236i	−1.30485	−	0.474928i	−0.406280	−	0.913749i	$-0.633174\pi$
$599$	−31.9356	−	11.6236i	−1.30485	−	0.474928i	−0.898575	+	0.438821i	$0.855396\pi$
$600$		0			0
$601$	−0.244918	+	1.38900i	−0.00999041	+	0.0566584i	−0.989395	−	0.145247i	$-0.953602\pi$
$601$	−0.244918	+	1.38900i	−0.00999041	+	0.0566584i	0.979405	+	0.201906i	$0.0647134\pi$
$602$	−32.2312	−	20.7136i	−1.31364	−	0.844222i
$603$		0			0
$604$	−42.7379	+	19.5181i	−1.73898	+	0.794179i
$605$	2.98128	−	1.08510i	0.121206	−	0.0441155i
$606$		0			0
$607$	−0.276419	−	0.329424i	−0.0112195	−	0.0133709i	0.760406	−	0.649449i	$-0.225000\pi$
$607$	−0.276419	−	0.329424i	−0.0112195	−	0.0133709i	−0.771625	+	0.636078i	$0.780556\pi$
$608$	25.4051	−	12.5916i	1.03031	−	0.510656i
$609$		0			0
$610$	0.888847	+	2.85852i	0.0359884	+	0.115738i
$611$	6.26677	−	3.61812i	0.253526	−	0.146374i
$612$		0			0
$613$	11.9125	+	6.87769i	0.481142	+	0.277787i	0.720892	−	0.693047i	$-0.243732\pi$
$613$	11.9125	+	6.87769i	0.481142	+	0.277787i	−0.239750	+	0.970835i	$0.577066\pi$
$614$	4.60448	−	20.3867i	0.185822	−	0.822742i
$615$		0			0
$616$	46.4134	+	24.8671i	1.87005	+	1.00193i
$617$	16.8375	−	2.96891i	0.677854	−	0.119524i	0.175886	−	0.984410i	$-0.443721\pi$
$617$	16.8375	−	2.96891i	0.677854	−	0.119524i	0.501967	+	0.864887i	$0.332610\pi$
$618$		0			0
$619$	20.7852	+	17.4409i	0.835429	+	0.701008i	0.956531	−	0.291632i	$-0.0941982\pi$
$619$	20.7852	+	17.4409i	0.835429	+	0.701008i	−0.121101	+	0.992640i	$0.538643\pi$
$620$	0.519121	−	5.43683i	0.0208484	−	0.218348i
$621$		0			0
$622$	−42.1957	−	2.00990i	−1.69189	−	0.0805896i
$623$	−7.74551	−	6.49925i	−0.310317	−	0.260387i
$624$		0			0
$625$	3.34558	+	18.9737i	0.133823	+	0.758949i
$626$	6.12909	+	2.56726i	0.244968	+	0.102608i
$627$		0			0
$628$	7.37780	+	2.03970i	0.294406	+	0.0813927i
$629$	−6.28436	+	10.8848i	−0.250574	+	0.434006i
$630$		0			0
$631$	36.5260	−	21.0883i	1.45408	−	0.839512i	0.455369	−	0.890303i	$-0.349507\pi$
$631$	36.5260	−	21.0883i	1.45408	−	0.839512i	0.998709	+	0.0507908i	$0.0161742\pi$
$632$	−4.98052	−	23.8016i	−0.198114	−	0.946776i
$633$		0			0
$634$	11.8688	−	9.03271i	0.471369	−	0.358735i
$635$	5.00552	+	5.96535i	0.198638	+	0.236728i
$636$		0			0
$637$	−4.52368	−	12.4287i	−0.179235	−	0.492443i
$638$	40.8799	−	21.0752i	1.61845	−	0.834375i
$639$		0			0
$640$	−5.35673	+	4.64183i	−0.211743	+	0.183484i
$641$	27.2082	+	4.79753i	1.07466	+	0.189491i	0.682852	−	0.730557i	$-0.260739\pi$
$641$	27.2082	+	4.79753i	1.07466	+	0.189491i	0.391806	+	0.920048i	$0.371850\pi$
$642$		0			0
$643$	−6.31128	−	2.29712i	−0.248892	−	0.0905894i	0.214561	−	0.976711i	$-0.431168\pi$
$643$	−6.31128	−	2.29712i	−0.248892	−	0.0905894i	−0.463454	+	0.886121i	$0.653390\pi$
$644$	43.6843	−	3.47317i	1.72140	−	0.136862i
$645$		0			0
$646$	14.0377	−	15.1981i	0.552307	−	0.597961i
$647$	3.89370			0.153077			0.0765386	−	0.997067i	$-0.475613\pi$
$647$	3.89370			0.153077			0.0765386	+	0.997067i	$0.475613\pi$
$648$		0			0
$649$	6.30422			0.247462
$650$	−4.01218	+	4.34384i	−0.157371	+	0.170379i
$651$		0			0
$652$	−1.55428	−	19.5492i	−0.0608705	−	0.765607i
$653$	46.1107	+	16.7829i	1.80445	+	0.656767i	0.997840	+	0.0656846i	$0.0209231\pi$
$653$	46.1107	+	16.7829i	1.80445	+	0.656767i	0.806611	+	0.591082i	$0.201299\pi$
$654$		0			0
$655$	0.313113	+	0.0552103i	0.0122343	+	0.00215724i
$656$	−25.4475	−	22.0499i	−0.993560	−	0.860903i
$657$		0			0
$658$	46.5557	−	24.0013i	1.81493	−	0.935668i
$659$	6.99121	+	19.2082i	0.272339	+	0.748245i	0.998176	+	0.0603781i	$0.0192306\pi$
$659$	6.99121	+	19.2082i	0.272339	+	0.748245i	−0.725837	+	0.687867i	$0.758547\pi$
$660$		0			0
$661$	−1.63166	−	1.94453i	−0.0634642	−	0.0756336i	0.733378	−	0.679821i	$-0.237942\pi$
$661$	−1.63166	−	1.94453i	−0.0634642	−	0.0756336i	−0.796843	+	0.604187i	$0.793498\pi$
$662$	13.5159	−	10.2863i	0.525311	−	0.399787i
$663$		0			0
$664$	−5.78980	−	27.6691i	−0.224688	−	1.07377i
$665$	−12.6319	+	7.29305i	−0.489845	+	0.282812i
$666$		0			0
$667$	19.1386	−	33.1490i	0.741050	−	1.28354i
$668$	3.12734	−	11.3119i	0.121000	−	0.437671i
$669$		0			0
$670$	−9.62602	−	4.03200i	−0.371886	−	0.155770i
$671$	−2.35147	−	13.3359i	−0.0907776	−	0.514825i
$672$		0			0
$673$	16.2031	+	13.5960i	0.624582	+	0.524087i	0.899240	−	0.437455i	$-0.144120\pi$
$673$	16.2031	+	13.5960i	0.624582	+	0.524087i	−0.274658	+	0.961542i	$0.588565\pi$
$674$	−15.0176	−	0.715329i	−0.578454	−	0.0275534i
$675$		0			0
$676$	24.2426	+	2.31474i	0.932409	+	0.0890286i
$677$	−9.66175	−	8.10717i	−0.371331	−	0.311584i	0.437957	−	0.898996i	$-0.355702\pi$
$677$	−9.66175	−	8.10717i	−0.371331	−	0.311584i	−0.809288	+	0.587412i	$0.800147\pi$
$678$		0			0
$679$	1.52175	−	0.268325i	0.0583992	−	0.0102974i
$680$	−2.44251	+	4.55884i	−0.0936660	+	0.174823i
$681$		0			0
$682$	−5.44293	+	24.0991i	−0.208421	+	0.922800i
$683$	18.7608	+	10.8315i	0.717860	+	0.414457i	0.813965	−	0.580914i	$-0.197305\pi$
$683$	18.7608	+	10.8315i	0.717860	+	0.414457i	−0.0961043	+	0.995371i	$0.530638\pi$
$684$		0			0
$685$	4.88741	−	2.82175i	0.186738	−	0.107813i
$686$	−14.7735	−	47.5114i	−0.564054	−	1.81399i
$687$		0			0
$688$	−20.3872	+	11.3434i	−0.777253	+	0.432464i
$689$	−1.78985	−	2.13306i	−0.0681877	−	0.0812630i
$690$		0			0
$691$	19.0830	−	6.94564i	0.725951	−	0.264225i	0.0475010	−	0.998871i	$-0.484874\pi$
$691$	19.0830	−	6.94564i	0.725951	−	0.264225i	0.678450	+	0.734647i	$0.262652\pi$
$692$	−14.4362	−	31.6103i	−0.548781	−	1.20164i
$693$		0			0
$694$	−16.5148	−	10.6134i	−0.626894	−	0.402878i
$695$	2.01622	−	11.4346i	0.0764796	−	0.433738i
$696$		0			0
$697$	−23.0873	−	8.40307i	−0.874492	−	0.318289i
$698$	28.5896	−	3.64867i	1.08213	−	0.138104i
$699$		0			0
$700$	−30.5046	+	30.0248i	−1.15297	+	1.13483i
$701$	38.5604			1.45640			0.728202	−	0.685362i	$-0.240356\pi$
$701$	38.5604			1.45640			0.728202	+	0.685362i	$0.240356\pi$
$702$		0			0
$703$			21.5850i			0.814093i
$704$	26.6951	−	17.7613i	1.00611	−	0.669406i
$705$		0			0
$706$	4.88149	−	0.622987i	0.183717	−	0.0234464i
$707$	10.7623	−	29.5693i	0.404760	−	1.11207i
$708$		0			0
$709$	−12.2287	−	2.15625i	−0.459258	−	0.0809796i	−0.0607673	−	0.998152i	$-0.519355\pi$
$709$	−12.2287	−	2.15625i	−0.459258	−	0.0809796i	−0.398491	+	0.917172i	$0.630466\pi$
$710$	3.05901	−	4.75994i	0.114803	−	0.178637i
$711$		0			0
$712$	−5.71596	+	2.28839i	−0.214215	+	0.0857609i
$713$	7.03246	+	19.3215i	0.263368	+	0.723596i
$714$		0			0
$715$	−1.74563	+	1.46476i	−0.0652828	+	0.0547788i
$716$	−2.95327	−	4.28969i	−0.110369	−	0.160313i
$717$		0			0
$718$	−2.68418	+	0.834637i	−0.100173	+	0.0311484i
$719$	−3.49686	−	6.05674i	−0.130411	−	0.225878i	0.793424	−	0.608669i	$-0.208296\pi$
$719$	−3.49686	−	6.05674i	−0.130411	−	0.225878i	−0.923835	+	0.382791i	$0.874963\pi$
$720$		0			0
$721$	27.4173	−	47.4882i	1.02107	−	1.76855i
$722$	1.90799	−	8.44780i	0.0710081	−	0.314395i
$723$		0			0
$724$	−16.8733	+	35.4486i	−0.627092	+	1.31744i
$725$	6.49205	+	36.8182i	0.241109	+	1.36739i
$726$		0			0
$727$	−8.35207	+	9.95361i	−0.309761	+	0.369159i	−0.898355	−	0.439270i	$-0.855237\pi$
$727$	−8.35207	+	9.95361i	−0.309761	+	0.369159i	0.588594	+	0.808429i	$0.299682\pi$
$728$	−11.8010	−	1.69662i	−0.437375	−	0.0628809i
$729$		0			0
$730$	3.86346	+	0.184028i	0.142993	+	0.00681117i
$731$	−10.9424	+	13.0407i	−0.404720	+	0.482327i
$732$		0			0
$733$	47.3767	−	8.35378i	1.74990	−	0.308554i	0.795247	−	0.606285i	$-0.207341\pi$
$733$	47.3767	−	8.35378i	1.74990	−	0.308554i	0.954650	+	0.297731i	$0.0962300\pi$
$734$	1.74976	−	4.17739i	0.0645849	−	0.154190i
$735$		0			0
$736$	10.6985	−	24.4466i	0.394352	−	0.901113i
$737$	40.8852	+	23.6051i	1.50603	+	0.869505i
$738$		0			0
$739$	−8.56966	−	14.8431i	−0.315240	−	0.546012i	0.664249	−	0.747512i	$-0.268752\pi$
$739$	−8.56966	−	14.8431i	−0.315240	−	0.546012i	−0.979488	+	0.201500i	$0.935418\pi$
$740$	−1.35520	−	5.22293i	−0.0498180	−	0.191999i
$741$		0			0
$742$	−12.2062	−	16.0387i	−0.448105	−	0.588799i
$743$	2.86000	−	2.39983i	0.104923	−	0.0880412i	−0.588817	−	0.808267i	$-0.700406\pi$
$743$	2.86000	−	2.39983i	0.104923	−	0.0880412i	0.693740	+	0.720225i	$0.255962\pi$
$744$		0			0
$745$	−7.55669	+	2.75041i	−0.276856	+	0.100767i
$746$	2.69882	−	1.39135i	0.0988109	−	0.0509409i
$747$		0			0
$748$	13.5708	−	19.0578i	0.496199	−	0.696823i
$749$	−9.49118	+	53.8271i	−0.346800	+	1.96680i
$750$		0			0
$751$	−3.19769	+	8.78557i	−0.116685	+	0.320590i	−0.984263	−	0.176712i	$-0.943454\pi$
$751$	−3.19769	+	8.78557i	−0.116685	+	0.320590i	0.867577	+	0.497302i	$0.165676\pi$
$752$	0.505664	−	31.8913i	0.0184397	−	1.16296i
$753$		0			0
$754$	−7.06583	+	7.64990i	−0.257322	+	0.278593i
$755$		−	14.7178i		−	0.535636i
$756$		0			0
$757$		−	15.4500i		−	0.561539i	−0.959775	−	0.280770i	$-0.909410\pi$
$757$		−	15.4500i		−	0.561539i	0.959775	−	0.280770i	$-0.0905897\pi$
$758$	10.6472	+	9.83430i	0.386724	+	0.357198i
$759$		0			0
$760$	0.281890	+	8.87758i	0.0102252	+	0.322024i
$761$	−4.45855	+	12.2498i	−0.161622	+	0.444053i	−0.993897	−	0.110309i	$-0.964816\pi$
$761$	−4.45855	+	12.2498i	−0.161622	+	0.444053i	0.832275	+	0.554363i	$0.187038\pi$
$762$		0			0
$763$	−3.30663	+	18.7529i	−0.119708	+	0.678899i
$764$	−17.0240	+	23.9071i	−0.615906	+	0.864929i
$765$		0			0
$766$	14.4539	+	28.0364i	0.522239	+	1.01300i
$767$	−1.34133	+	0.488206i	−0.0484328	+	0.0176281i
$768$		0			0
$769$	−7.85539	+	6.59146i	−0.283273	+	0.237694i	−0.773341	−	0.633990i	$-0.781416\pi$
$769$	−7.85539	+	6.59146i	−0.283273	+	0.237694i	0.490069	+	0.871684i	$0.336972\pi$
$770$	−13.1256	+	9.98921i	−0.473013	+	0.359986i
$771$		0			0
$772$	34.3591	−	8.91517i	1.23661	−	0.320864i
$773$	−11.5460	−	19.9983i	−0.415281	−	0.719288i	0.580177	−	0.814491i	$-0.302983\pi$
$773$	−11.5460	−	19.9983i	−0.415281	−	0.719288i	−0.995458	+	0.0952026i	$0.969650\pi$
$774$		0			0
$775$	−17.3923	−	10.0415i	−0.624750	−	0.360700i
$776$	0.293599	−	0.893969i	0.0105396	−	0.0320916i
$777$		0			0
$778$	−12.4161	−	5.20068i	−0.445140	−	0.186454i
$779$	−41.5527	+	7.32686i	−1.48878	+	0.262512i
$780$		0			0
$781$	−16.4524	+	19.6072i	−0.588712	+	0.701600i
$782$	0.926416	−	19.4491i	0.0331286	−	0.695498i
$783$		0			0
$784$	−57.2446	−	11.0323i	−2.04445	−	0.394010i
$785$	−1.54128	+	1.83683i	−0.0550107	+	0.0655593i
$786$		0			0
$787$	−2.55103	−	14.4676i	−0.0909343	−	0.515714i	−0.995918	−	0.0902670i	$-0.971228\pi$
$787$	−2.55103	−	14.4676i	−0.0909343	−	0.515714i	0.904983	−	0.425447i	$-0.139883\pi$
$788$	−3.46629	−	1.64994i	−0.123481	−	0.0587765i
$789$		0			0
$790$	7.43024	+	1.67817i	0.264356	+	0.0597066i
$791$	0.266653	−	0.461857i	0.00948110	−	0.0164217i
$792$		0			0
$793$	1.53306	+	2.65534i	0.0544406	+	0.0942939i
$794$	15.2345	+	48.9939i	0.540652	+	1.73873i
$795$		0			0
$796$	18.9991	+	27.5966i	0.673406	+	0.978136i
$797$	−37.4213	+	31.4002i	−1.32553	+	1.11225i	−0.340431	+	0.940269i	$0.610573\pi$
$797$	−37.4213	+	31.4002i	−1.32553	+	1.11225i	−0.985100	+	0.171983i	$0.944983\pi$
$798$		0			0
$799$	−7.95979	−	21.8693i	−0.281597	−	0.773681i
$800$	7.34343	+	25.0080i	0.259629	+	0.884167i
$801$		0			0
$802$	−39.3227	−	25.2710i	−1.38853	−	0.892350i
$803$	−17.2309	−	3.03827i	−0.608064	−	0.107218i
$804$		0			0
$805$	−4.69505	+	12.8995i	−0.165479	+	0.454649i
$806$	−0.708177	−	5.54901i	−0.0249445	−	0.195455i
$807$		0			0
$808$	−12.7764	−	14.2803i	−0.449474	−	0.502379i
$809$			22.9120i			0.805542i	0.915301	+	0.402771i	$0.131953\pi$
$809$			22.9120i			0.805542i	−0.915301	+	0.402771i	$0.868047\pi$
$810$		0			0
$811$	28.0030			0.983320			0.491660	−	0.870787i	$-0.336390\pi$
$811$	28.0030			0.983320			0.491660	+	0.870787i	$0.336390\pi$
$812$	−53.7215	+	52.8764i	−1.88525	+	1.85560i
$813$		0			0
$814$	3.09006	+	24.2126i	0.108307	+	0.848651i
$815$	5.77270	+	2.10109i	0.202209	+	0.0735980i
$816$		0			0
$817$	−5.07665	+	28.7911i	−0.177610	+	1.00727i
$818$	−16.7803	+	26.1109i	−0.586711	+	0.912946i
$819$		0			0
$820$	9.59450	−	4.38173i	0.335055	−	0.153017i
$821$	4.83141	−	1.75849i	0.168617	−	0.0613717i	−0.256332	−	0.966589i	$-0.582514\pi$
$821$	4.83141	−	1.75849i	0.168617	−	0.0613717i	0.424950	+	0.905217i	$0.360292\pi$
$822$		0			0
$823$	13.1233	+	15.6398i	0.457450	+	0.545168i	0.944632	−	0.328133i	$-0.106419\pi$
$823$	13.1233	+	15.6398i	0.457450	+	0.545168i	−0.487181	+	0.873301i	$0.661975\pi$
$824$	−17.6049	−	28.3730i	−0.613294	−	0.988422i
$825$		0			0
$826$	−9.86617	+	3.06785i	−0.343288	+	0.106744i
$827$	7.13738	−	4.12077i	0.248191	−	0.143293i	−0.370745	−	0.928735i	$-0.620897\pi$
$827$	7.13738	−	4.12077i	0.248191	−	0.143293i	0.618936	+	0.785442i	$0.287564\pi$
$828$		0			0
$829$	11.9497	+	6.89919i	0.415032	+	0.239619i	0.692949	−	0.720986i	$-0.256311\pi$
$829$	11.9497	+	6.89919i	0.415032	+	0.239619i	−0.277918	+	0.960605i	$0.589644\pi$
$830$	8.63756	+	1.95085i	0.299814	+	0.0677151i
$831$		0			0
$832$	−4.30441	+	5.84634i	−0.149228	+	0.202685i
$833$	−41.8917	+	7.38664i	−1.45146	+	0.255932i
$834$		0			0
$835$	2.81630	+	2.36315i	0.0974620	+	0.0817803i
$836$	3.81903	−	39.9972i	0.132084	−	1.38333i
$837$		0			0
$838$	1.07438	−	22.5554i	0.0371138	−	0.779164i
$839$	−39.2115	−	32.9024i	−1.35373	−	1.13592i	−0.977863	−	0.209244i	$-0.932900\pi$
$839$	−39.2115	−	32.9024i	−1.35373	−	1.13592i	−0.375869	−	0.926673i	$-0.622656\pi$
$840$		0			0
$841$	6.39731	+	36.2809i	0.220597	+	1.25107i
$842$	−15.8099	+	37.7446i	−0.544844	+	1.30076i
$843$		0			0
$844$	3.61870	−	13.0892i	0.124561	−	0.450550i
$845$	−3.81430	+	6.60656i	−0.131216	+	0.227273i
$846$		0			0
$847$	20.3701	−	11.7607i	0.699926	−	0.404102i
$848$	−12.1191	+	1.93935i	−0.416172	+	0.0665974i
$849$		0			0
$850$	11.5175	+	15.1337i	0.395046	+	0.519081i
$851$	13.0578	+	15.5616i	0.447614	+	0.533446i
$852$		0			0
$853$	−15.2286	−	41.8402i	−0.521417	−	1.43258i	−0.868943	−	0.494912i	$-0.835200\pi$
$853$	−15.2286	−	41.8402i	−0.521417	−	1.43258i	0.347526	−	0.937670i	$-0.387022\pi$
$854$	10.1698	+	19.7265i	0.348002	+	0.675025i
$855$		0			0
$856$	26.1625	+	20.5740i	0.894216	+	0.703206i
$857$	2.44277	+	0.430726i	0.0834434	+	0.0147133i	0.215214	−	0.976567i	$-0.430955\pi$
$857$	2.44277	+	0.430726i	0.0834434	+	0.0147133i	−0.131771	+	0.991280i	$0.542066\pi$
$858$		0			0
$859$	22.1180	+	8.05028i	0.754655	+	0.274672i	0.690563	−	0.723272i	$-0.257363\pi$
$859$	22.1180	+	8.05028i	0.754655	+	0.274672i	0.0640917	+	0.997944i	$0.479585\pi$
$860$	−0.579228	−	7.28533i	−0.0197515	−	0.248428i
$861$		0			0
$862$	−31.8977	−	29.4623i	−1.08644	−	1.00349i
$863$	24.1686			0.822708			0.411354	−	0.911476i	$-0.365056\pi$
$863$	24.1686			0.822708			0.411354	+	0.911476i	$0.365056\pi$
$864$		0			0
$865$	10.8858			0.370127
$866$	25.2777	+	23.3477i	0.858970	+	0.793387i
$867$		0			0
$868$	−3.20918	−	40.3640i	−0.108927	−	1.37004i
$869$	−32.3802	−	11.7854i	−1.09842	−	0.399793i
$870$		0			0
$871$	−10.5271	−	1.85620i	−0.356696	−	0.0628951i
$872$	9.11477	+	7.16780i	0.308665	+	0.242732i
$873$		0			0
$874$	−15.3227	−	29.7217i	−0.518298	−	1.00535i
$875$	−9.56217	−	26.2719i	−0.323260	−	0.888151i
$876$		0			0
$877$	−12.5608	−	14.9694i	−0.424148	−	0.505480i	0.511077	−	0.859535i	$-0.329247\pi$
$877$	−12.5608	−	14.9694i	−0.424148	−	0.505480i	−0.935224	+	0.354056i	$0.884802\pi$
$878$	13.6088	+	17.8817i	0.459275	+	0.603477i
$879$		0			0
$880$	1.58710	+	9.91792i	0.0535012	+	0.334333i
$881$	39.3096	−	22.6954i	1.32437	−	0.764627i	0.339950	−	0.940444i	$-0.389590\pi$
$881$	39.3096	−	22.6954i	1.32437	−	0.764627i	0.984423	+	0.175817i	$0.0562566\pi$
$882$		0			0
$883$	21.0724	−	36.4984i	0.709142	−	1.22827i	−0.256034	−	0.966668i	$-0.582416\pi$
$883$	21.0724	−	36.4984i	0.709142	−	1.22827i	0.965176	−	0.261602i	$-0.0842509\pi$
$884$	−1.41158	+	5.10583i	−0.0474765	+	0.171728i
$885$		0			0
$886$	−11.6171	+	27.7347i	−0.390284	+	0.931766i
$887$	1.04275	+	5.91374i	0.0350122	+	0.198564i	0.997297	−	0.0734815i	$-0.0234110\pi$
$887$	1.04275	+	5.91374i	0.0350122	+	0.198564i	−0.962284	+	0.272045i	$0.912300\pi$
$888$		0			0
$889$	44.2264	+	37.1104i	1.48331	+	1.24464i
$890$	0.0917655	−	1.92652i	0.00307599	−	0.0645770i
$891$		0			0
$892$	5.30213	−	55.5300i	0.177528	−	1.85928i
$893$	−30.6171	−	25.6908i	−1.02456	−	0.859711i
$894$		0			0
$895$	1.60663	−	0.283293i	0.0537039	−	0.00946944i
$896$	−33.1349	+	40.7874i	−1.10696	+	1.36261i
$897$		0			0
$898$	−16.5241	−	3.73208i	−0.551416	−	0.124541i
$899$	−30.6295	−	17.6839i	−1.02155	−	0.589792i
$900$		0			0
$901$	−7.75560	+	4.47770i	−0.258377	+	0.149174i
$902$	−45.5621	+	14.1674i	−1.51705	+	0.471722i
$903$		0			0
$904$	−0.171220	−	0.275948i	−0.00569469	−	0.00917790i
$905$	−7.90510	−	9.42093i	−0.262774	−	0.313162i
$906$		0			0
$907$	−24.0330	+	8.74731i	−0.798004	+	0.290450i	−0.708659	−	0.705551i	$-0.750699\pi$
$907$	−24.0330	+	8.74731i	−0.798004	+	0.290450i	−0.0893447	+	0.996001i	$0.528477\pi$
$908$	40.9981	−	18.7235i	1.36057	−	0.621362i
$909$		0			0
$910$	2.01913	−	3.14184i	0.0669334	−	0.104151i
$911$	−4.86428	+	27.5867i	−0.161161	+	0.913988i	0.791774	+	0.610814i	$0.209158\pi$
$911$	−4.86428	+	27.5867i	−0.161161	+	0.913988i	−0.952935	+	0.303175i	$0.901953\pi$
$912$		0			0
$913$	−37.6416	−	13.7004i	−1.24575	−	0.453418i
$914$	−4.60155	−	36.0560i	−0.152206	−	1.19263i
$915$		0			0
$916$	24.6015	−	24.2145i	0.812857	−	0.800070i
$917$	2.35720			0.0778414
$918$		0			0
$919$			49.4765i			1.63208i	0.577996	+	0.816040i	$0.303835\pi$
$919$			49.4765i			1.63208i	−0.577996	+	0.816040i	$0.696165\pi$
$920$	5.57369	+	6.22974i	0.183759	+	0.205388i
$921$		0			0
$922$	4.61750	+	36.1810i	0.152069	+	1.19156i
$923$	1.98213	−	5.44586i	0.0652427	−	0.179253i
$924$		0			0
$925$	−19.5400	−	3.44542i	−0.642470	−	0.113285i
$926$	28.8344	+	18.5306i	0.947557	+	0.608954i
$927$		0			0
$928$	12.9325	+	44.0415i	0.424529	+	1.44573i
$929$	−6.23688	−	17.1357i	−0.204625	−	0.562203i	0.794350	−	0.607460i	$-0.207812\pi$
$929$	−6.23688	−	17.1357i	−0.204625	−	0.562203i	−0.998975	+	0.0452568i	$0.985589\pi$
$930$		0			0
$931$	−55.9618	+	46.9575i	−1.83407	+	1.53897i
$932$	16.4230	+	23.8547i	0.537952	+	0.781386i
$933$		0			0
$934$	−0.874536	−	2.81250i	−0.0286157	−	0.0920277i
$935$	3.66441	+	6.34695i	0.119839	+	0.207567i
$936$		0			0
$937$	−11.2761	+	19.5307i	−0.368373	+	0.638041i	−0.989311	−	0.145819i	$-0.953418\pi$
$937$	−11.2761	+	19.5307i	−0.368373	+	0.638041i	0.620938	+	0.783859i	$0.286752\pi$
$938$	−75.4728	−	17.0460i	−2.46427	−	0.556573i
$939$		0			0
$940$	9.02142	+	4.29415i	0.294246	+	0.140060i
$941$	−10.3351	−	58.6135i	−0.336916	−	1.91075i	−0.407434	−	0.913235i	$-0.633576\pi$
$941$	−10.3351	−	58.6135i	−0.336916	−	1.91075i	0.0705179	−	0.997511i	$-0.477535\pi$
$942$		0			0
$943$	−25.5249	+	30.4194i	−0.831206	+	0.990592i
$944$	−1.19063	+	6.17797i	−0.0387516	+	0.201076i
$945$		0			0
$946$	−1.57296	+	33.0227i	−0.0511415	+	1.07366i
$947$	33.2910	−	39.6746i	1.08181	−	1.28925i	0.127045	−	0.991897i	$-0.459451\pi$
$947$	33.2910	−	39.6746i	1.08181	−	1.28925i	0.954767	−	0.297356i	$-0.0961047\pi$
$948$		0			0
$949$	3.90146	−	0.687933i	0.126647	−	0.0223312i
$950$	30.1246	+	12.6182i	0.977372	+	0.409387i
$951$		0			0
$952$	−11.9643	+	36.4297i	−0.387765	+	1.18069i
$953$	−19.9155	−	11.4982i	−0.645125	−	0.372463i	0.141461	−	0.989944i	$-0.454820\pi$
$953$	−19.9155	−	11.4982i	−0.645125	−	0.372463i	−0.786586	+	0.617481i	$0.788153\pi$
$954$		0			0
$955$	−4.59683	−	7.96194i	−0.148750	−	0.257642i
$956$	−37.8004	+	9.80808i	−1.22255	+	0.317216i
$957$		0			0
$958$	12.9782	−	9.87706i	0.419307	−	0.319113i
$959$	32.0515	−	26.8944i	1.03500	−	0.868464i
$960$		0			0
$961$	−11.2775	+	4.10469i	−0.363791	+	0.132409i
$962$	−2.53252	−	4.91236i	−0.0816516	−	0.158381i
$963$		0			0
$964$	−2.42793	+	3.40959i	−0.0781983	+	0.109816i
$965$	−1.93088	+	10.9505i	−0.0621571	+	0.352511i
$966$		0			0
$967$	5.56318	−	15.2847i	0.178900	−	0.491523i	−0.817536	−	0.575877i	$-0.804661\pi$
$967$	5.56318	−	15.2847i	0.178900	−	0.491523i	0.996436	+	0.0843543i	$0.0268828\pi$
$968$	−0.454573	−	14.3159i	−0.0146105	−	0.460131i
$969$		0			0
$970$	0.216524	+	0.199993i	0.00695218	+	0.00642138i
$971$			38.0842i			1.22218i	0.791561	+	0.611090i	$0.209269\pi$
$971$			38.0842i			1.22218i	−0.791561	+	0.611090i	$0.790731\pi$
$972$		0			0
$973$		−	86.0823i		−	2.75967i
$974$	28.0529	−	30.3718i	0.898872	−	0.973174i
$975$		0			0
$976$	13.5129	+	0.214259i	0.432537	+	0.00685825i
$977$	10.6918	−	29.3754i	0.342060	−	0.939803i	−0.642736	−	0.766088i	$-0.722201\pi$
$977$	10.6918	−	29.3754i	0.342060	−	0.939803i	0.984796	−	0.173715i	$-0.0555771\pi$
$978$		0			0
$979$	−1.51503	+	8.59219i	−0.0484207	+	0.274608i
$980$	10.5929	−	14.8758i	0.338378	−	0.475191i
$981$		0			0
$982$	6.47163	−	3.33638i	0.206518	−	0.106468i
$983$	−52.5891	+	19.1409i	−1.67733	+	0.610498i	−0.992940	−	0.118617i	$-0.962154\pi$
$983$	−52.5891	+	19.1409i	−1.67733	+	0.610498i	−0.684390	+	0.729116i	$0.739932\pi$
$984$		0			0
$985$	0.921212	−	0.772989i	0.0293523	−	0.0246295i
$986$	20.2833	+	26.6518i	0.645953	+	0.848767i
$987$		0			0
$988$	2.28486	+	8.80587i	0.0726912	+	0.280152i
$989$	13.7571	+	23.8280i	0.437450	+	0.757685i
$990$		0			0
$991$	−33.9036	−	19.5742i	−1.07698	−	0.621796i	−0.146901	−	0.989151i	$-0.546930\pi$
$991$	−33.9036	−	19.5742i	−1.07698	−	0.621796i	−0.930081	+	0.367355i	$0.880263\pi$
$992$	−22.5885	−	9.88533i	−0.717184	−	0.313859i
$993$		0			0
$994$	16.2066	−	38.6917i	0.514042	−	1.22723i
$995$	−10.3359	+	1.82249i	−0.327669	+	0.0577769i
$996$		0			0
$997$	−9.08868	+	10.8315i	−0.287841	+	0.343036i	−0.890517	−	0.454950i	$-0.849657\pi$
$997$	−9.08868	+	10.8315i	−0.287841	+	0.343036i	0.602675	+	0.797986i	$0.294101\pi$
$998$	−35.8847	−	1.70929i	−1.13591	−	0.0541066i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.2.v.b.35.24		192
3.2	odd	2		216.2.v.b.11.9	✓	192
8.3	odd	2	inner	648.2.v.b.35.7		192
12.11	even	2		864.2.bh.b.335.14		192
24.5	odd	2		864.2.bh.b.335.13		192
24.11	even	2		216.2.v.b.11.26	yes	192
27.5	odd	18	inner	648.2.v.b.611.7		192
27.22	even	9		216.2.v.b.59.26	yes	192
108.103	odd	18		864.2.bh.b.815.13		192
216.59	even	18	inner	648.2.v.b.611.24		192
216.157	even	18		864.2.bh.b.815.14		192
216.211	odd	18		216.2.v.b.59.9	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.11.9	✓	192	3.2	odd	2
216.2.v.b.11.26	yes	192	24.11	even	2
216.2.v.b.59.9	yes	192	216.211	odd	18
216.2.v.b.59.26	yes	192	27.22	even	9
648.2.v.b.35.7		192	8.3	odd	2	inner
648.2.v.b.35.24		192	1.1	even	1	trivial
648.2.v.b.611.7		192	27.5	odd	18	inner
648.2.v.b.611.24		192	216.59	even	18	inner
864.2.bh.b.335.13		192	24.5	odd	2
864.2.bh.b.335.14		192	12.11	even	2
864.2.bh.b.815.13		192	108.103	odd	18
864.2.bh.b.815.14		192	216.157	even	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.03887 + 0.959554i) q^{2} +(0.158512 + 1.99371i) q^{4} +(-0.588722 - 0.214277i) q^{5} +(-4.57427 - 0.806567i) q^{7} +(-1.74840 + 2.22331i) q^{8} +O(q^{10})\)	\(q+(1.03887 + 0.959554i) q^{2} +(0.158512 + 1.99371i) q^{4} +(-0.588722 - 0.214277i) q^{5} +(-4.57427 - 0.806567i) q^{7} +(-1.74840 + 2.22331i) q^{8} +(-0.405997 - 0.787518i) q^{10} +(1.37081 + 3.76628i) q^{11} +(-0.583330 - 0.695185i) q^{13} +(-3.97814 - 5.22718i) q^{14} +(-3.94975 + 0.632053i) q^{16} +(-2.52763 + 1.45933i) q^{17} +(-2.50619 + 4.34085i) q^{19} +(0.333887 - 1.20771i) q^{20} +(-2.18985 + 5.22805i) q^{22} +(0.819150 + 4.64563i) q^{23} +(-3.52954 - 2.96164i) q^{25} +(0.0610627 - 1.28195i) q^{26} +(0.882983 - 9.24761i) q^{28} +(-6.21586 - 5.21572i) q^{29} +(4.29253 - 0.756889i) q^{31} +(-4.70977 - 3.13337i) q^{32} +(-4.02619 - 0.909343i) q^{34} +(2.52015 + 1.45501i) q^{35} +(3.72940 - 2.15317i) q^{37} +(-6.76889 + 2.10476i) q^{38} +(1.50573 - 0.934270i) q^{40} +(5.41092 + 6.44848i) q^{41} +(5.48086 - 1.99487i) q^{43} +(-7.29157 + 3.33000i) q^{44} +(-3.60674 + 5.61224i) q^{46} +(-1.38464 + 7.85268i) q^{47} +(13.6955 + 4.98477i) q^{49} +(-0.824893 - 6.46355i) q^{50} +(1.29353 - 1.27318i) q^{52} +3.06833 q^{53} -2.51103i q^{55} +(9.79089 - 8.75982i) q^{56} +(-1.45271 - 11.3829i) q^{58} +(0.537968 - 1.47805i) q^{59} +(-3.32732 - 0.586696i) q^{61} +(5.18567 + 3.33260i) q^{62} +(-1.88621 - 7.77446i) q^{64} +(0.194457 + 0.534265i) q^{65} +(9.02325 - 7.57140i) q^{67} +(-3.31014 - 4.80804i) q^{68} +(1.22195 + 3.92978i) q^{70} +(3.19304 + 5.53051i) q^{71} +(-2.18272 + 3.78059i) q^{73} +(5.94045 + 1.34169i) q^{74} +(-9.05165 - 4.30854i) q^{76} +(-3.23271 - 18.3336i) q^{77} +(-5.52630 + 6.58598i) q^{79} +(2.46074 + 0.474238i) q^{80} +(-0.566412 + 11.8912i) q^{82} +(-6.42426 + 7.65613i) q^{83} +(1.80077 - 0.317525i) q^{85} +(7.60810 + 3.18677i) q^{86} +(-10.7703 - 3.53721i) q^{88} +(1.88520 + 1.08842i) q^{89} +(2.10759 + 3.65046i) q^{91} +(-9.13219 + 2.36954i) q^{92} +(-8.97354 + 6.82930i) q^{94} +(2.40560 - 2.01853i) q^{95} +(-0.312612 + 0.113782i) q^{97} +(9.44477 + 18.3202i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 6 q^{2} - 6 q^{4} + 9 q^{8}+O(q^{10}) \) 192 * q + 6 * q^2 - 6 * q^4 + 9 * q^8	\( 192 q + 6 q^{2} - 6 q^{4} + 9 q^{8} - 3 q^{10} + 30 q^{11} - 9 q^{14} - 6 q^{16} + 18 q^{17} - 6 q^{19} + 27 q^{20} - 18 q^{22} - 12 q^{25} - 12 q^{28} + 36 q^{32} + 12 q^{34} + 18 q^{35} + 102 q^{38} + 9 q^{40} - 18 q^{41} - 42 q^{43} + 81 q^{44} - 3 q^{46} - 12 q^{49} - 57 q^{50} + 21 q^{52} + 69 q^{56} - 33 q^{58} + 84 q^{59} - 90 q^{62} - 51 q^{64} + 12 q^{65} + 30 q^{67} - 63 q^{68} - 33 q^{70} - 6 q^{73} - 51 q^{74} + 30 q^{76} - 12 q^{82} + 72 q^{83} - 42 q^{86} - 78 q^{88} - 144 q^{89} - 6 q^{91} + 3 q^{92} - 33 q^{94} - 42 q^{97} - 162 q^{98}+O(q^{100}) \) 192 * q + 6 * q^2 - 6 * q^4 + 9 * q^8 - 3 * q^10 + 30 * q^11 - 9 * q^14 - 6 * q^16 + 18 * q^17 - 6 * q^19 + 27 * q^20 - 18 * q^22 - 12 * q^25 - 12 * q^28 + 36 * q^32 + 12 * q^34 + 18 * q^35 + 102 * q^38 + 9 * q^40 - 18 * q^41 - 42 * q^43 + 81 * q^44 - 3 * q^46 - 12 * q^49 - 57 * q^50 + 21 * q^52 + 69 * q^56 - 33 * q^58 + 84 * q^59 - 90 * q^62 - 51 * q^64 + 12 * q^65 + 30 * q^67 - 63 * q^68 - 33 * q^70 - 6 * q^73 - 51 * q^74 + 30 * q^76 - 12 * q^82 + 72 * q^83 - 42 * q^86 - 78 * q^88 - 144 * q^89 - 6 * q^91 + 3 * q^92 - 33 * q^94 - 42 * q^97 - 162 * q^98

Introduction

L-functions

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