LMFDB - Embedded newform 612.2.bd.f.415.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [612,2,Mod(91,612)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("612.91"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(612, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 0, 15])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 612 = 2^{2} \cdot 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	612.bd (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [144,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(20)] == traces)

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

Self dual:	no
Analytic conductor:	$4.88684460370$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$18$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 204)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			415.4
Character	$\chi$	$=$	612.415
Dual form			612.2.bd.f.379.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.16052 - 0.808208i) q^{2} +(0.693599 + 1.87588i) q^{4} +(0.754921 + 3.79524i) q^{5} +(4.91130 + 0.976917i) q^{7} +(0.711166 - 2.73756i) q^{8} +(2.19125 - 5.01458i) q^{10} +(-0.713223 - 1.06741i) q^{11} +(0.586054 - 0.586054i) q^{13} +(-4.91009 - 5.10308i) q^{14} +(-3.03784 + 2.60222i) q^{16} +(3.49411 + 2.18889i) q^{17} +(-1.96871 - 0.815467i) q^{19} +(-6.59580 + 4.04852i) q^{20} +(-0.0349849 + 1.81518i) q^{22} +(3.25840 - 2.17719i) q^{23} +(-9.21456 + 3.81680i) q^{25} +(-1.15378 + 0.206472i) q^{26} +(1.57389 + 9.89058i) q^{28} +(-3.15662 + 0.627891i) q^{29} +(-2.74031 + 4.10117i) q^{31} +(5.62860 - 0.564710i) q^{32} +(-2.28590 - 5.36420i) q^{34} +19.3771i q^{35} +(3.51373 - 5.25867i) q^{37} +(1.62566 + 2.53749i) q^{38} +(10.9266 + 0.632406i) q^{40} +(0.507052 - 2.54912i) q^{41} +(-7.27038 + 3.01149i) q^{43} +(1.50765 - 2.07828i) q^{44} +(-5.54106 - 0.106795i) q^{46} +(-0.936262 - 0.936262i) q^{47} +(16.6993 + 6.91708i) q^{49} +(13.7784 + 3.01782i) q^{50} +(1.50585 + 0.692879i) q^{52} +(3.38920 - 8.18225i) q^{53} +(3.51266 - 3.51266i) q^{55} +(6.16712 - 12.7502i) q^{56} +(4.17078 + 1.82253i) q^{58} +(-0.417091 - 1.00695i) q^{59} +(-7.31011 - 1.45407i) q^{61} +(6.49478 - 2.54473i) q^{62} +(-6.98849 - 3.89372i) q^{64} +(2.66664 + 1.78179i) q^{65} +1.76213 q^{67} +(-1.68257 + 8.07273i) q^{68} +(15.6607 - 22.4874i) q^{70} +(0.757356 + 0.506049i) q^{71} +(-0.143161 - 0.719719i) q^{73} +(-8.32784 + 3.26295i) q^{74} +(0.164220 - 4.25867i) q^{76} +(-2.46007 - 5.93914i) q^{77} +(-1.05421 - 1.57773i) q^{79} +(-12.1694 - 9.56487i) q^{80} +(-2.64867 + 2.54850i) q^{82} +(-3.72584 + 8.99498i) q^{83} +(-5.66958 + 14.9134i) q^{85} +(10.8713 + 2.38109i) q^{86} +(-3.42933 + 1.19338i) q^{88} +(8.39190 + 8.39190i) q^{89} +(3.45081 - 2.30576i) q^{91} +(6.34418 + 4.60226i) q^{92} +(0.329853 + 1.84324i) q^{94} +(1.60867 - 8.08735i) q^{95} +(11.4456 - 2.27668i) q^{97} +(-13.7894 - 21.5239i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 64 q^{26} - 48 q^{28} + 80 q^{32} - 16 q^{34} + 80 q^{38} - 64 q^{40} + 64 q^{44} - 16 q^{46} + 16 q^{53} - 80 q^{56} + 112 q^{58} - 64 q^{61} - 112 q^{62} + 96 q^{64} + 208 q^{65} - 176 q^{68}+ \cdots - 96 q^{94}+O(q^{100}) $ 144 * q + 64 * q^26 - 48 * q^28 + 80 * q^32 - 16 * q^34 + 80 * q^38 - 64 * q^40 + 64 * q^44 - 16 * q^46 + 16 * q^53 - 80 * q^56 + 112 * q^58 - 64 * q^61 - 112 * q^62 + 96 * q^64 + 208 * q^65 - 176 * q^68 + 176 * q^70 - 208 * q^73 - 96 * q^74 + 112 * q^76 + 64 * q^77 - 112 * q^80 + 80 * q^82 - 16 * q^85 - 64 * q^88 - 96 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/612\mathbb{Z}\right)^\times$.

$n$	$37$	$137$	$307$
$\chi(n)$	$e\left(\frac{11}{16}\right)$	$1$	$-1$

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 $

$2$	−1.16052	−	0.808208i	−0.820609	−	0.571489i
$2$	−1.16052	−	0.808208i	−0.820609	−	0.571489i
$3$		0			0
$3$		0			0
$4$	0.693599	+	1.87588i	0.346800	+	0.937939i
$5$	0.754921	+	3.79524i	0.337611	+	1.69728i	0.660483	+	0.750841i	$0.270352\pi$
$5$	0.754921	+	3.79524i	0.337611	+	1.69728i	−0.322872	+	0.946443i	$0.604648\pi$
$6$		0			0
$7$	4.91130	+	0.976917i	1.85630	+	0.369240i	0.991201	−	0.132368i	$-0.0422582\pi$
$7$	4.91130	+	0.976917i	1.85630	+	0.369240i	0.865095	+	0.501608i	$0.167258\pi$
$8$	0.711166	−	2.73756i	0.251435	−	0.967874i
$9$		0			0
$10$	2.19125	−	5.01458i	0.692933	−	1.58575i
$11$	−0.713223	−	1.06741i	−0.215045	−	0.321837i	0.708227	−	0.705985i	$-0.249495\pi$
$11$	−0.713223	−	1.06741i	−0.215045	−	0.321837i	−0.923272	+	0.384148i	$0.874495\pi$
$12$		0			0
$13$	0.586054	−	0.586054i	0.162542	−	0.162542i	−0.621150	−	0.783692i	$-0.713334\pi$
$13$	0.586054	−	0.586054i	0.162542	−	0.162542i	0.783692	+	0.621150i	$0.213334\pi$
$14$	−4.91009	−	5.10308i	−1.31228	−	1.36386i
$15$		0			0
$16$	−3.03784	+	2.60222i	−0.759460	+	0.650554i
$17$	3.49411	+	2.18889i	0.847445	+	0.530883i
$17$	3.49411	+	2.18889i	0.847445	+	0.530883i
$18$		0			0
$19$	−1.96871	−	0.815467i	−0.451653	−	0.187081i	0.145248	−	0.989395i	$-0.453602\pi$
$19$	−1.96871	−	0.815467i	−0.451653	−	0.187081i	−0.596902	+	0.802314i	$0.703602\pi$
$20$	−6.59580	+	4.04852i	−1.47487	+	0.905276i
$21$		0			0
$22$	−0.0349849	+	1.81518i	−0.00745881	+	0.386998i
$23$	3.25840	−	2.17719i	0.679424	−	0.453976i	−0.167373	−	0.985894i	$-0.553528\pi$
$23$	3.25840	−	2.17719i	0.679424	−	0.453976i	0.846796	+	0.531917i	$0.178528\pi$
$24$		0			0
$25$	−9.21456	+	3.81680i	−1.84291	+	0.763359i
$26$	−1.15378	+	0.206472i	−0.226275	+	0.0404925i
$27$		0			0
$28$	1.57389	+	9.89058i	0.297438	+	1.86914i
$29$	−3.15662	+	0.627891i	−0.586170	+	0.116596i	−0.479261	−	0.877672i	$-0.659095\pi$
$29$	−3.15662	+	0.627891i	−0.586170	+	0.116596i	−0.106909	+	0.994269i	$0.534095\pi$
$30$		0			0
$31$	−2.74031	+	4.10117i	−0.492175	+	0.736592i	−0.991540	−	0.129800i	$-0.958567\pi$
$31$	−2.74031	+	4.10117i	−0.492175	+	0.736592i	0.499365	+	0.866391i	$0.333567\pi$
$32$	5.62860	−	0.564710i	0.995005	−	0.0998275i
$33$		0			0
$34$	−2.28590	−	5.36420i	−0.392028	−	0.919953i
$35$			19.3771i			3.27532i
$36$		0			0
$37$	3.51373	−	5.25867i	0.577654	−	0.864520i	−0.421450	−	0.906852i	$-0.638479\pi$
$37$	3.51373	−	5.25867i	0.577654	−	0.864520i	0.999104	+	0.0423318i	$0.0134787\pi$
$38$	1.62566	+	2.53749i	0.263716	+	0.411636i
$39$		0			0
$40$	10.9266	+	0.632406i	1.72764	+	0.0999922i
$41$	0.507052	−	2.54912i	0.0791883	−	0.398106i	−0.920780	−	0.390083i	$-0.872446\pi$
$41$	0.507052	−	2.54912i	0.0791883	−	0.398106i	0.999968	−	0.00802299i	$-0.00255382\pi$
$42$		0			0
$43$	−7.27038	+	3.01149i	−1.10872	+	0.459248i	−0.860497	−	0.509455i	$-0.829847\pi$
$43$	−7.27038	+	3.01149i	−1.10872	+	0.459248i	−0.248225	+	0.968703i	$0.579847\pi$
$44$	1.50765	−	2.07828i	0.227286	−	0.313312i
$45$		0			0
$46$	−5.54106	−	0.106795i	−0.816984	−	0.0157461i
$47$	−0.936262	−	0.936262i	−0.136568	−	0.136568i	0.635518	−	0.772086i	$-0.280787\pi$
$47$	−0.936262	−	0.936262i	−0.136568	−	0.136568i	−0.772086	+	0.635518i	$0.780787\pi$
$48$		0			0
$49$	16.6993	+	6.91708i	2.38561	+	0.988154i
$50$	13.7784	+	3.01782i	1.94856	+	0.426785i
$51$		0			0
$52$	1.50585	+	0.692879i	0.208824	+	0.0960851i
$53$	3.38920	−	8.18225i	0.465542	−	1.12392i	−0.500547	−	0.865709i	$-0.666868\pi$
$53$	3.38920	−	8.18225i	0.465542	−	1.12392i	0.966089	−	0.258209i	$-0.0831323\pi$
$54$		0			0
$55$	3.51266	−	3.51266i	0.473648	−	0.473648i
$56$	6.16712	−	12.7502i	0.824116	−	1.70382i
$57$		0			0
$58$	4.17078	+	1.82253i	0.547650	+	0.239310i
$59$	−0.417091	−	1.00695i	−0.0543006	−	0.131093i	0.894401	−	0.447266i	$-0.147602\pi$
$59$	−0.417091	−	1.00695i	−0.0543006	−	0.131093i	−0.948702	+	0.316173i	$0.897602\pi$
$60$		0			0
$61$	−7.31011	−	1.45407i	−0.935964	−	0.186175i	−0.296533	−	0.955023i	$-0.595830\pi$
$61$	−7.31011	−	1.45407i	−0.935964	−	0.186175i	−0.639432	+	0.768848i	$0.720830\pi$
$62$	6.49478	−	2.54473i	0.824838	−	0.323181i
$63$		0			0
$64$	−6.98849	−	3.89372i	−0.873561	−	0.486715i
$65$	2.66664	+	1.78179i	0.330756	+	0.221004i
$66$		0			0
$67$	1.76213			0.215278			0.107639	−	0.994190i	$-0.465671\pi$
$67$	1.76213			0.215278			0.107639	+	0.994190i	$0.465671\pi$
$68$	−1.68257	+	8.07273i	−0.204042	+	0.978962i
$69$		0			0
$70$	15.6607	−	22.4874i	1.87181	−	2.68776i
$71$	0.757356	+	0.506049i	0.0898816	+	0.0600570i	0.599699	−	0.800226i	$-0.295287\pi$
$71$	0.757356	+	0.506049i	0.0898816	+	0.0600570i	−0.509817	+	0.860283i	$0.670287\pi$
$72$		0			0
$73$	−0.143161	−	0.719719i	−0.0167557	−	0.0842367i	0.971503	−	0.237029i	$-0.0761735\pi$
$73$	−0.143161	−	0.719719i	−0.0167557	−	0.0842367i	−0.988258	+	0.152792i	$0.951174\pi$
$74$	−8.32784	+	3.26295i	−0.968092	+	0.379310i
$75$		0			0
$76$	0.164220	−	4.25867i	0.0188373	−	0.488503i
$77$	−2.46007	−	5.93914i	−0.280351	−	0.676828i
$78$		0			0
$79$	−1.05421	−	1.57773i	−0.118608	−	0.177509i	0.767415	−	0.641151i	$-0.221543\pi$
$79$	−1.05421	−	1.57773i	−0.118608	−	0.177509i	−0.886023	+	0.463641i	$0.846543\pi$
$80$	−12.1694	−	9.56487i	−1.36058	−	1.06938i
$81$		0			0
$82$	−2.64867	+	2.54850i	−0.292496	+	0.281435i
$83$	−3.72584	+	8.99498i	−0.408964	+	0.987327i	0.576447	+	0.817135i	$0.304439\pi$
$83$	−3.72584	+	8.99498i	−0.408964	+	0.987327i	−0.985411	+	0.170192i	$0.945561\pi$
$84$		0			0
$85$	−5.66958	+	14.9134i	−0.614952	+	1.61759i
$86$	10.8713	+	2.38109i	1.17228	+	0.256760i
$87$		0			0
$88$	−3.42933	+	1.19338i	−0.365568	+	0.127215i
$89$	8.39190	+	8.39190i	0.889540	+	0.889540i	0.994479	−	0.104939i	$-0.0334647\pi$
$89$	8.39190	+	8.39190i	0.889540	+	0.889540i	−0.104939	+	0.994479i	$0.533465\pi$
$90$		0			0
$91$	3.45081	−	2.30576i	0.361743	−	0.241709i
$92$	6.34418	+	4.60226i	0.661426	+	0.479819i
$93$		0			0
$94$	0.329853	+	1.84324i	0.0340218	+	0.190116i
$95$	1.60867	−	8.08735i	0.165046	−	0.829745i
$96$		0			0
$97$	11.4456	−	2.27668i	1.16213	−	0.231162i	0.423898	−	0.905710i	$-0.360662\pi$
$97$	11.4456	−	2.27668i	1.16213	−	0.231162i	0.738231	+	0.674548i	$0.235662\pi$
$98$	−13.7894	−	21.5239i	−1.39294	−	2.17424i
$99$		0			0
$100$	−13.5511	−	14.6381i	−1.35511	−	1.46381i
$101$		−	0.179506i		−	0.0178615i	−0.999960	−	0.00893076i	$-0.997157\pi$
$101$		−	0.179506i		−	0.0178615i	0.999960	−	0.00893076i	$-0.00284279\pi$
$102$		0			0
$103$			10.5801i			1.04249i	0.853408	+	0.521243i	$0.174531\pi$
$103$			10.5801i			1.04249i	−0.853408	+	0.521243i	$0.825469\pi$
$104$	−1.18758	−	2.02114i	−0.116452	−	0.198189i
$105$		0			0
$106$	−10.5462	+	6.75646i	−1.02434	+	0.656246i
$107$	−7.98170	+	1.58766i	−0.771620	+	0.153485i	−0.565172	−	0.824973i	$-0.691190\pi$
$107$	−7.98170	+	1.58766i	−0.771620	+	0.153485i	−0.206448	+	0.978458i	$0.566190\pi$
$108$		0			0
$109$	1.10769	−	5.56873i	0.106097	−	0.533387i	−0.890781	−	0.454433i	$-0.849842\pi$
$109$	1.10769	−	5.56873i	0.106097	−	0.533387i	0.996878	−	0.0789542i	$-0.0251581\pi$
$110$	−6.91547	+	1.23754i	−0.659364	+	0.117995i
$111$		0			0
$112$	−17.4619	+	9.81254i	−1.64999	+	0.927197i
$113$	−10.1459	+	6.77928i	−0.954446	+	0.637741i	−0.932174	−	0.362011i	$-0.882090\pi$
$113$	−10.1459	+	6.77928i	−0.954446	+	0.637741i	−0.0222726	+	0.999752i	$0.507090\pi$
$114$		0			0
$115$	10.7228	+	10.7228i	0.999907	+	0.999907i
$116$	−3.36728	−	5.48593i	−0.312644	−	0.509356i
$117$		0			0
$118$	−0.329781	+	1.50567i	−0.0303588	+	0.138608i
$119$	15.0222	+	14.1637i	1.37709	+	1.29839i
$120$		0			0
$121$	3.57883	−	8.64007i	0.325348	−	0.785461i
$122$	7.30832	+	7.59557i	0.661664	+	0.687671i
$123$		0			0
$124$	−9.59397	−	2.29593i	−0.861564	−	0.206180i
$125$	−10.6928	−	16.0028i	−0.956390	−	1.43134i
$126$		0			0
$127$	2.45881	+	5.93609i	0.218184	+	0.526743i	0.994636	−	0.103433i	$-0.0329828\pi$
$127$	2.45881	+	5.93609i	0.218184	+	0.526743i	−0.776452	+	0.630176i	$0.782983\pi$
$128$	4.96332	+	10.1669i	0.438700	+	0.898634i
$129$		0			0
$130$	−1.65462	−	4.22300i	−0.145120	−	0.370382i
$131$	−1.98893	−	9.99903i	−0.173774	−	0.873619i	−0.965031	−	0.262136i	$-0.915573\pi$
$131$	−1.98893	−	9.99903i	−0.173774	−	0.873619i	0.791257	−	0.611483i	$-0.209427\pi$
$132$		0			0
$133$	−8.87228	−	5.92827i	−0.769324	−	0.514046i
$134$	−2.04498	−	1.42416i	−0.176659	−	0.123029i
$135$		0			0
$136$	8.47710	−	8.00867i	0.726905	−	0.686738i
$137$	−22.2609			−1.90187			−0.950936	−	0.309386i	$-0.899876\pi$
$137$	−22.2609			−1.90187			−0.950936	+	0.309386i	$0.899876\pi$
$138$		0			0
$139$	0.976901	+	0.652744i	0.0828597	+	0.0553651i	0.596310	−	0.802754i	$-0.296633\pi$
$139$	0.976901	+	0.652744i	0.0828597	+	0.0553651i	−0.513450	+	0.858119i	$0.671633\pi$
$140$	−36.3490	+	13.4399i	−3.07205	+	1.13588i
$141$		0			0
$142$	−0.469931	−	1.19938i	−0.0394358	−	0.100650i
$143$	−1.04355	−	0.207575i	−0.0872659	−	0.0173583i
$144$		0			0
$145$	−4.76599	−	11.5061i	−0.395794	−	0.955532i
$146$	−0.415542	+	0.950949i	−0.0343905	+	0.0787011i
$147$		0			0
$148$	12.3017	+	2.94392i	1.01120	+	0.241989i
$149$	−0.335607	+	0.335607i	−0.0274940	+	0.0274940i	−0.720720	−	0.693226i	$-0.756189\pi$
$149$	−0.335607	+	0.335607i	−0.0274940	+	0.0274940i	0.693226	+	0.720720i	$0.256189\pi$
$150$		0			0
$151$	5.13011	−	12.3852i	0.417483	−	1.00789i	−0.565592	−	0.824685i	$-0.691352\pi$
$151$	5.13011	−	12.3852i	0.417483	−	1.00789i	0.983074	−	0.183207i	$-0.0586478\pi$
$152$	−3.63247	+	4.80954i	−0.294632	+	0.390105i
$153$		0			0
$154$	−1.94511	+	8.88073i	−0.156741	+	0.715629i
$155$	−17.6336	−	7.30410i	−1.41637	−	0.586679i
$156$		0			0
$157$	−8.32983	−	8.32983i	−0.664793	−	0.664793i	0.291713	−	0.956506i	$-0.405775\pi$
$157$	−8.32983	−	8.32983i	−0.664793	−	0.664793i	−0.956506	+	0.291713i	$0.905775\pi$
$158$	−0.0517109	+	2.68301i	−0.00411390	+	0.213449i
$159$		0			0
$160$	6.39235	+	20.9356i	0.505360	+	1.65510i
$161$	18.1299	−	7.50966i	1.42884	−	0.591844i
$162$		0			0
$163$	4.18519	−	21.0404i	0.327809	−	1.64801i	−0.368032	−	0.929813i	$-0.619968\pi$
$163$	4.18519	−	21.0404i	0.327809	−	1.64801i	0.695842	−	0.718195i	$-0.255032\pi$
$164$	5.13354	−	0.816903i	0.400862	−	0.0637894i
$165$		0			0
$166$	11.5937	−	7.42757i	0.899847	−	0.576491i
$167$	−4.57365	+	6.84495i	−0.353920	+	0.529678i	−0.965124	−	0.261795i	$-0.915686\pi$
$167$	−4.57365	+	6.84495i	−0.353920	+	0.529678i	0.611204	+	0.791473i	$0.290686\pi$
$168$		0			0
$169$			12.3131i			0.947160i
$170$	18.6328	−	12.7251i	1.42907	−	0.975969i
$171$		0			0
$172$	−10.6919	−	11.5496i	−0.815251	−	0.880647i
$173$	5.94943	−	8.90395i	0.452327	−	0.676955i	−0.533294	−	0.845930i	$-0.679046\pi$
$173$	5.94943	−	8.90395i	0.452327	−	0.676955i	0.985620	+	0.168976i	$0.0540459\pi$
$174$		0			0
$175$	−48.9841	+	9.74355i	−3.70285	+	0.736543i
$176$	4.94430	+	1.38667i	0.372690	+	0.104524i
$177$		0			0
$178$	−2.95654	−	16.5213i	−0.221602	−	1.23833i
$179$	18.2130	−	7.54407i	1.36130	−	0.563870i	0.421887	−	0.906649i	$-0.361368\pi$
$179$	18.2130	−	7.54407i	1.36130	−	0.563870i	0.939416	+	0.342778i	$0.111368\pi$
$180$		0			0
$181$	−3.29611	+	2.20239i	−0.244998	+	0.163702i	−0.672007	−	0.740545i	$-0.734567\pi$
$181$	−3.29611	+	2.20239i	−0.244998	+	0.163702i	0.427009	+	0.904247i	$0.359567\pi$
$182$	−5.86826	−	0.113102i	−0.434984	−	0.00838366i
$183$		0			0
$184$	−3.64294	−	10.4684i	−0.268561	−	0.771742i
$185$	22.6105	+	9.36558i	1.66236	+	0.688571i
$186$		0			0
$187$	−0.155631	−	5.29082i	−0.0113809	−	0.386903i
$188$	1.10692	−	2.40570i	0.0807306	−	0.175454i
$189$		0			0
$190$	−8.40315	+	8.08536i	−0.609629	+	0.586574i
$191$	13.1036	−	13.1036i	0.948146	−	0.948146i	−0.0505742	−	0.998720i	$-0.516105\pi$
$191$	13.1036	−	13.1036i	0.948146	−	0.948146i	0.998720	+	0.0505742i	$0.0161051\pi$
$192$		0			0
$193$	−11.7503	−	17.5856i	−0.845805	−	1.26584i	−0.962121	−	0.272624i	$-0.912109\pi$
$193$	−11.7503	−	17.5856i	−0.845805	−	1.26584i	0.116316	−	0.993212i	$-0.462891\pi$
$194$	−15.1229	−	6.60833i	−1.08576	−	0.474451i
$195$		0			0
$196$	−1.39297	+	36.1235i	−0.0994978	+	2.58025i
$197$	−7.64795	−	1.52127i	−0.544894	−	0.108386i	−0.0850346	−	0.996378i	$-0.527100\pi$
$197$	−7.64795	−	1.52127i	−0.544894	−	0.108386i	−0.459859	+	0.887992i	$0.652100\pi$
$198$		0			0
$199$	−1.29565	−	6.51369i	−0.0918464	−	0.461743i	−0.999148	−	0.0412634i	$-0.986862\pi$
$199$	−1.29565	−	6.51369i	−0.0918464	−	0.461743i	0.907302	−	0.420480i	$-0.138138\pi$
$200$	3.89563	+	27.9398i	0.275463	+	1.97564i
$201$		0			0
$202$	−0.145078	+	0.208320i	−0.0102077	+	0.0146573i
$203$	−16.1165			−1.13116
$204$		0			0
$205$	10.0573			0.702434
$206$	8.55090	−	12.2784i	0.595770	−	0.855474i
$207$		0			0
$208$	−0.255299	+	3.30538i	−0.0177018	+	0.229187i
$209$	0.533690	+	2.68304i	0.0369161	+	0.185590i
$210$		0			0
$211$	−12.5920	−	2.50470i	−0.866867	−	0.172431i	−0.258427	−	0.966031i	$-0.583204\pi$
$211$	−12.5920	−	2.50470i	−0.866867	−	0.172431i	−0.608440	+	0.793600i	$0.708204\pi$
$212$	17.6996	+	0.682521i	1.21562	+	0.0468757i
$213$		0			0
$214$	10.5461	+	4.60837i	0.720913	+	0.315022i
$215$	−16.9179	−	25.3194i	−1.15379	−	1.72677i
$216$		0			0
$217$	−17.4650	+	17.4650i	−1.18560	+	1.18560i
$218$	−5.78618	+	5.56736i	−0.391890	+	0.377069i
$219$		0			0
$220$	9.02571	+	4.15295i	0.608514	+	0.279992i
$221$	3.33054	−	0.764930i	0.224036	−	0.0514548i
$222$		0			0
$223$	20.6044	+	8.53462i	1.37977	+	0.571521i	0.944421	−	0.328740i	$-0.106624\pi$
$223$	20.6044	+	8.53462i	1.37977	+	0.571521i	0.435352	+	0.900260i	$0.356624\pi$
$224$	28.1954	+	2.72522i	1.88388	+	0.182086i
$225$		0			0
$226$	17.2536	+	0.332536i	1.14769	+	0.0221200i
$227$	6.70771	−	4.48195i	0.445206	−	0.297477i	−0.312687	−	0.949856i	$-0.601229\pi$
$227$	6.70771	−	4.48195i	0.445206	−	0.297477i	0.757893	+	0.652379i	$0.226229\pi$
$228$		0			0
$229$	−0.0700762	+	0.0290265i	−0.00463077	+	0.00191813i	−0.384998	−	0.922918i	$-0.625798\pi$
$229$	−0.0700762	+	0.0290265i	−0.00463077	+	0.00191813i	0.380367	+	0.924836i	$0.375798\pi$
$230$	−3.77774	−	21.1103i	−0.249097	−	1.39197i
$231$		0			0
$232$	−0.525992	+	9.08797i	−0.0345330	+	0.596655i
$233$	−7.75274	+	1.54212i	−0.507899	+	0.101027i	−0.442387	−	0.896824i	$-0.645868\pi$
$233$	−7.75274	+	1.54212i	−0.507899	+	0.101027i	−0.0655122	+	0.997852i	$0.520868\pi$
$234$		0			0
$235$	2.84654	−	4.26014i	0.185688	−	0.277901i
$236$	1.59961	−	1.48083i	0.104126	−	0.0963937i
$237$		0			0
$238$	−5.98632	−	28.5783i	−0.388036	−	1.85246i
$239$		−	13.2508i		−	0.857122i	−0.903513	−	0.428561i	$-0.859021\pi$
$239$		−	13.2508i		−	0.857122i	0.903513	−	0.428561i	$-0.140979\pi$
$240$		0			0
$241$	10.4235	−	15.5999i	0.671436	−	1.00488i	−0.326776	−	0.945102i	$-0.605962\pi$
$241$	10.4235	−	15.5999i	0.671436	−	1.00488i	0.998212	−	0.0597735i	$-0.0190379\pi$
$242$	−11.1363	+	7.13450i	−0.715867	+	0.458623i
$243$		0			0
$244$	−2.34263	−	14.7214i	−0.149971	−	0.942443i
$245$	−13.6453	+	68.5997i	−0.871769	+	4.38268i
$246$		0			0
$247$	−1.63168	+	0.675864i	−0.103821	+	0.0430042i
$248$	9.27838	+	10.4184i	0.589178	+	0.661568i
$249$		0			0
$250$	−0.524500	+	27.2136i	−0.0331723	+	1.72114i
$251$	11.7830	+	11.7830i	0.743738	+	0.743738i	0.973295	−	0.229557i	$-0.0737279\pi$
$251$	11.7830	+	11.7830i	0.743738	+	0.743738i	−0.229557	+	0.973295i	$0.573728\pi$
$252$		0			0
$253$	−4.64793	−	1.92524i	−0.292213	−	0.121039i
$254$	1.94411	−	8.87616i	0.121984	−	0.556940i
$255$		0			0
$256$	2.45694	−	15.8102i	0.153559	−	0.988140i
$257$	4.90695	−	11.8464i	0.306087	−	0.738960i	−0.693737	−	0.720228i	$-0.744037\pi$
$257$	4.90695	−	11.8464i	0.306087	−	0.738960i	0.999825	−	0.0187319i	$-0.00596289\pi$
$258$		0			0
$259$	22.3943	−	22.3943i	1.39151	−	1.39151i
$260$	−1.49285	+	6.23814i	−0.0925823	+	0.386873i
$261$		0			0
$262$	−5.77311	+	13.2115i	−0.356664	+	0.816210i
$263$	3.12396	+	7.54191i	0.192632	+	0.465054i	0.990455	−	0.137837i	$-0.0440151\pi$
$263$	3.12396	+	7.54191i	0.192632	+	0.465054i	−0.797823	+	0.602892i	$0.794015\pi$
$264$		0			0
$265$	33.6122	+	6.68588i	2.06478	+	0.410710i
$266$	5.50516	+	14.0505i	0.337543	+	0.861492i
$267$		0			0
$268$	1.22221	+	3.30553i	0.0746583	+	0.201918i
$269$	18.6773	+	12.4798i	1.13877	+	0.760904i	0.974250	−	0.225469i	$-0.0723916\pi$
$269$	18.6773	+	12.4798i	1.13877	+	0.760904i	0.164523	+	0.986373i	$0.447392\pi$
$270$		0			0
$271$	−24.6416			−1.49687			−0.748436	−	0.663207i	$-0.769195\pi$
$271$	−24.6416			−1.49687			−0.748436	+	0.663207i	$0.769195\pi$
$272$	−16.3105	+	2.44294i	−0.988969	+	0.148125i
$273$		0			0
$274$	25.8341	+	17.9914i	1.56069	+	1.08690i
$275$	10.6461	+	7.11352i	0.641986	+	0.428961i
$276$		0			0
$277$	4.95046	+	24.8876i	0.297444	+	1.49535i	0.783482	+	0.621415i	$0.213442\pi$
$277$	4.95046	+	24.8876i	0.297444	+	1.49535i	−0.486037	+	0.873938i	$0.661558\pi$
$278$	−0.606157	−	1.54706i	−0.0363549	−	0.0927865i
$279$		0			0
$280$	53.0459	+	13.7803i	3.17010	+	0.823531i
$281$	1.14859	+	2.77293i	0.0685189	+	0.165419i	0.954429	−	0.298437i	$-0.0964653\pi$
$281$	1.14859	+	2.77293i	0.0685189	+	0.165419i	−0.885910	+	0.463856i	$0.846465\pi$
$282$		0			0
$283$	5.70411	+	8.53680i	0.339074	+	0.507460i	0.961347	−	0.275340i	$-0.0887906\pi$
$283$	5.70411	+	8.53680i	0.339074	+	0.507460i	−0.622273	+	0.782800i	$0.713791\pi$
$284$	−0.423985	+	1.77170i	−0.0251589	+	0.105131i
$285$		0			0
$286$	1.04329	+	1.08430i	0.0616912	+	0.0641159i
$287$	4.98057	−	12.0242i	0.293994	−	0.709764i
$288$		0			0
$289$	7.41756	+	15.2964i	0.436327	+	0.899788i
$290$	−3.76833	+	17.2050i	−0.221284	+	1.01031i
$291$		0			0
$292$	1.25081	−	0.767749i	0.0731980	−	0.0449291i
$293$	−22.4441	−	22.4441i	−1.31120	−	1.31120i	−0.920534	−	0.390663i	$-0.872246\pi$
$293$	−22.4441	−	22.4441i	−1.31120	−	1.31120i	−0.390663	−	0.920534i	$-0.627754\pi$
$294$		0			0
$295$	3.50673	−	2.34312i	0.204170	−	0.136422i
$296$	−11.8971	−	13.3588i	−0.691504	−	0.776467i
$297$		0			0
$298$	0.660719	−	0.118238i	0.0382744	−	0.00684931i
$299$	0.633646	−	3.18555i	0.0366447	−	0.184225i
$300$		0			0
$301$	−38.6489	+	7.68775i	−2.22769	+	0.443115i
$302$	−15.9634	+	10.2270i	−0.918590	+	0.588499i
$303$		0			0
$304$	8.10265	−	2.64576i	0.464719	−	0.151744i
$305$		−	28.8414i		−	1.65145i
$306$		0			0
$307$			7.69557i			0.439210i	0.975589	+	0.219605i	$0.0704768\pi$
$307$			7.69557i			0.439210i	−0.975589	+	0.219605i	$0.929523\pi$
$308$	9.43480	−	8.73418i	0.537598	−	0.497676i
$309$		0			0
$310$	14.5609	+	22.7282i	0.827005	+	1.29087i
$311$	−6.46031	+	1.28504i	−0.366331	+	0.0728677i	−0.374823	−	0.927096i	$-0.622297\pi$
$311$	−6.46031	+	1.28504i	−0.366331	+	0.0728677i	0.00849263	+	0.999964i	$0.497297\pi$
$312$		0			0
$313$	5.19563	−	26.1202i	0.293675	−	1.47640i	−0.498918	−	0.866649i	$-0.666269\pi$
$313$	5.19563	−	26.1202i	0.293675	−	1.47640i	0.792592	−	0.609752i	$-0.208731\pi$
$314$	2.93467	+	16.3991i	0.165613	+	0.925457i
$315$		0			0
$316$	2.22844	−	3.07188i	0.125360	−	0.172807i
$317$	−3.71014	+	2.47904i	−0.208382	+	0.139237i	−0.655382	−	0.755297i	$-0.727492\pi$
$317$	−3.71014	+	2.47904i	−0.208382	+	0.139237i	0.447000	+	0.894534i	$0.352492\pi$
$318$		0			0
$319$	2.92159	+	2.92159i	0.163578	+	0.163578i
$320$	9.50187	−	29.4624i	0.531170	−	1.64700i
$321$		0			0
$322$	−27.1094	−	5.93766i	−1.51075	−	0.330893i
$323$	−5.09392	−	7.15861i	−0.283434	−	0.398316i
$324$		0			0
$325$	−3.16338	+	7.63708i	−0.175473	+	0.423629i
$326$	−21.8620	+	21.0352i	−1.21082	+	1.16503i
$327$		0			0
$328$	−6.61779	−	3.20094i	−0.365406	−	0.176742i
$329$	−3.68361	−	5.51291i	−0.203084	−	0.303937i
$330$		0			0
$331$	−9.09378	−	21.9543i	−0.499839	−	1.20672i	−0.949570	−	0.313555i	$-0.898480\pi$
$331$	−9.09378	−	21.9543i	−0.499839	−	1.20672i	0.449731	−	0.893164i	$-0.351520\pi$
$332$	−19.4577	−	0.750315i	−1.06788	−	0.0411789i
$333$		0			0
$334$	10.8399	−	4.24722i	0.593136	−	0.232398i
$335$	1.33026	+	6.68769i	0.0726801	+	0.365388i
$336$		0			0
$337$	12.4898	+	8.34541i	0.680362	+	0.454603i	0.847125	−	0.531394i	$-0.178332\pi$
$337$	12.4898	+	8.34541i	0.680362	+	0.454603i	−0.166763	+	0.985997i	$0.553332\pi$
$338$	9.95153	−	14.2895i	0.541292	−	0.777249i
$339$		0			0
$340$	−31.9082	−	0.291501i	−1.73046	−	0.0158089i
$341$	6.33210			0.342902
$342$		0			0
$343$	46.1126	+	30.8115i	2.48985	+	1.66366i
$344$	3.07369	+	22.0448i	0.165722	+	1.18857i
$345$		0			0
$346$	−14.1007	+	5.52481i	−0.758056	+	0.297015i
$347$	−5.48826	−	1.09168i	−0.294625	−	0.0586046i	0.0455645	−	0.998961i	$-0.485491\pi$
$347$	−5.48826	−	1.09168i	−0.294625	−	0.0586046i	−0.340190	+	0.940357i	$0.610491\pi$
$348$		0			0
$349$	3.62630	+	8.75465i	0.194111	+	0.468626i	0.990728	−	0.135858i	$-0.0433792\pi$
$349$	3.62630	+	8.75465i	0.194111	+	0.468626i	−0.796617	+	0.604484i	$0.793379\pi$
$350$	64.7217	+	28.2818i	3.45952	+	1.51173i
$351$		0			0
$352$	−4.61722	−	5.60527i	−0.246099	−	0.298762i
$353$	13.2228	−	13.2228i	0.703776	−	0.703776i	−0.261443	−	0.965219i	$-0.584198\pi$
$353$	13.2228	−	13.2228i	0.703776	−	0.703776i	0.965219	+	0.261443i	$0.0841983\pi$
$354$		0			0
$355$	−1.34883	+	3.25638i	−0.0715887	+	0.172830i
$356$	−9.92157	+	21.5628i	−0.525842	+	1.14283i
$357$		0			0
$358$	−27.2337	−	5.96487i	−1.43934	−	0.315253i
$359$	−17.0544	−	7.06417i	−0.900098	−	0.372833i	−0.115840	−	0.993268i	$-0.536956\pi$
$359$	−17.0544	−	7.06417i	−0.900098	−	0.372833i	−0.784258	+	0.620435i	$0.786956\pi$
$360$		0			0
$361$	−10.2242	−	10.2242i	−0.538115	−	0.538115i
$362$	5.60518	+	0.108031i	0.294602	+	0.00567800i
$363$		0			0
$364$	6.71880	+	4.87403i	0.352161	+	0.255469i
$365$	2.62343	−	1.08666i	0.137317	−	0.0568784i
$366$		0			0
$367$	3.71204	−	18.6617i	0.193767	−	0.974131i	−0.754414	−	0.656399i	$-0.772079\pi$
$367$	3.71204	−	18.6617i	0.193767	−	0.974131i	0.948181	−	0.317732i	$-0.102921\pi$
$368$	−4.23297	+	15.0930i	−0.220659	+	0.786779i
$369$		0			0
$370$	−18.6705	−	29.1429i	−0.970635	−	1.51507i
$371$	24.6387	−	36.8745i	1.27918	−	1.91443i
$372$		0			0
$373$			3.82522i			0.198062i	0.995084	+	0.0990312i	$0.0315744\pi$
$373$			3.82522i			0.198062i	−0.995084	+	0.0990312i	$0.968426\pi$
$374$	−4.09547	+	6.26587i	−0.211772	+	0.324000i
$375$		0			0
$376$	−3.22891	+	1.89724i	−0.166518	+	0.0978425i
$377$	−1.48197	+	2.21793i	−0.0763254	+	0.114229i
$378$		0			0
$379$	37.2781	−	7.41508i	1.91485	−	0.380887i	0.915097	−	0.403233i	$-0.132114\pi$
$379$	37.2781	−	7.41508i	1.91485	−	0.380887i	0.999750	+	0.0223462i	$0.00711360\pi$
$380$	16.2867	−	2.59170i	0.835488	−	0.132952i
$381$		0			0
$382$	−25.7975	+	4.61653i	−1.31991	+	0.236202i
$383$	−1.67224	+	0.692666i	−0.0854476	+	0.0353936i	−0.424998	−	0.905194i	$-0.639725\pi$
$383$	−1.67224	+	0.692666i	−0.0854476	+	0.0353936i	0.339550	+	0.940588i	$0.389725\pi$
$384$		0			0
$385$	20.6833	−	13.8202i	1.05412	−	0.704340i
$386$	−0.576374	+	29.9050i	−0.0293366	+	1.52213i
$387$		0			0
$388$	12.2095	+	19.8915i	0.619842	+	1.00984i
$389$	−16.2377	−	6.72587i	−0.823284	−	0.341015i	−0.0690435	−	0.997614i	$-0.521995\pi$
$389$	−16.2377	−	6.72587i	−0.823284	−	0.341015i	−0.754240	+	0.656598i	$0.771995\pi$
$390$		0			0
$391$	16.1508	−	0.475081i	0.816783	−	0.0240259i
$392$	30.8119	−	40.7962i	1.55624	−	2.06052i
$393$		0			0
$394$	7.64607	+	7.94659i	0.385203	+	0.400344i
$395$	5.19204	−	5.19204i	0.261240	−	0.261240i
$396$		0			0
$397$	10.6669	+	15.9641i	0.535354	+	0.801214i	0.996276	−	0.0862268i	$-0.0274810\pi$
$397$	10.6669	+	15.9641i	0.535354	+	0.801214i	−0.460921	+	0.887441i	$0.652481\pi$
$398$	−3.76079	+	8.60641i	−0.188511	+	0.431400i
$399$		0			0
$400$	18.0602	−	35.5731i	0.903011	−	1.77865i
$401$	12.6594	+	2.51811i	0.632181	+	0.125749i	0.500771	−	0.865580i	$-0.333050\pi$
$401$	12.6594	+	2.51811i	0.632181	+	0.125749i	0.131409	+	0.991328i	$0.458050\pi$
$402$		0			0
$403$	0.797535	+	4.00948i	0.0397280	+	0.199726i
$404$	0.336732	−	0.124505i	0.0167530	−	0.00619437i
$405$		0			0
$406$	18.7035	+	13.0255i	0.928237	+	0.646444i
$407$	−8.11924			−0.402456
$408$		0			0
$409$	18.3979			0.909715			0.454858	−	0.890564i	$-0.349690\pi$
$409$	18.3979			0.909715			0.454858	+	0.890564i	$0.349690\pi$
$410$	−11.6717	−	8.12841i	−0.576424	−	0.401434i
$411$		0			0
$412$	−19.8469	+	7.33833i	−0.977788	+	0.361534i
$413$	−1.06475	−	5.35287i	−0.0523930	−	0.263398i
$414$		0			0
$415$	−36.9508	−	7.34998i	−1.81384	−	0.360796i
$416$	2.96771	−	3.62961i	0.145504	−	0.177956i
$417$		0			0
$418$	1.54910	−	3.54504i	0.0757688	−	0.173394i
$419$	14.5182	+	21.7280i	0.709260	+	1.06148i	0.994673	+	0.103079i	$0.0328693\pi$
$419$	14.5182	+	21.7280i	0.709260	+	1.06148i	−0.285413	+	0.958405i	$0.592131\pi$
$420$		0			0
$421$	4.31997	−	4.31997i	0.210543	−	0.210543i	−0.593955	−	0.804498i	$-0.702434\pi$
$421$	4.31997	−	4.31997i	0.210543	−	0.210543i	0.804498	+	0.593955i	$0.202434\pi$
$422$	12.5889	+	13.0837i	0.612817	+	0.636904i
$423$		0			0
$424$	−19.9891	−	15.0971i	−0.970758	−	0.733179i
$425$	−40.5512	−	6.83332i	−1.96702	−	0.331465i
$426$		0			0
$427$	−34.4816	−	14.2828i	−1.66868	−	0.691191i
$428$	−8.51436	−	13.8715i	−0.411557	−	0.670504i
$429$		0			0
$430$	−0.829854	+	43.0568i	−0.0400191	+	2.07638i
$431$	−20.1409	+	13.4577i	−0.970153	+	0.648235i	−0.936304	−	0.351192i	$-0.885777\pi$
$431$	−20.1409	+	13.4577i	−0.970153	+	0.648235i	−0.0338490	+	0.999427i	$0.510777\pi$
$432$		0			0
$433$	0.485480	−	0.201092i	0.0233307	−	0.00966388i	−0.370988	−	0.928638i	$-0.620981\pi$
$433$	0.485480	−	0.201092i	0.0233307	−	0.00966388i	0.394318	+	0.918974i	$0.370981\pi$
$434$	34.3838	−	6.15307i	1.65047	−	0.295357i
$435$		0			0
$436$	11.2145	−	1.78458i	0.537079	−	0.0854657i
$437$	−8.19028	+	1.62915i	−0.391794	+	0.0779327i
$438$		0			0
$439$	−11.4571	+	17.1467i	−0.546817	+	0.818369i	−0.997224	−	0.0744537i	$-0.976279\pi$
$439$	−11.4571	+	17.1467i	−0.546817	+	0.818369i	0.450408	+	0.892823i	$0.351279\pi$
$440$	−7.11805	−	12.1142i	−0.339340	−	0.577523i
$441$		0			0
$442$	−4.48337	−	1.80406i	−0.213252	−	0.0858101i
$443$			36.5774i			1.73784i	0.494950	+	0.868922i	$0.335187\pi$
$443$			36.5774i			1.73784i	−0.494950	+	0.868922i	$0.664813\pi$
$444$		0			0
$445$	−25.5141	+	38.1845i	−1.20948	+	1.81012i
$446$	−17.0140	−	26.5572i	−0.805637	−	1.25752i
$447$		0			0
$448$	−30.5187	−	25.9504i	−1.44187	−	1.22604i
$449$	3.08521	−	15.5104i	0.145600	−	0.731982i	−0.837140	−	0.546989i	$-0.815774\pi$
$449$	3.08521	−	15.5104i	0.145600	−	0.731982i	0.982740	−	0.184993i	$-0.0592262\pi$
$450$		0			0
$451$	−3.08261	+	1.27686i	−0.145154	+	0.0601249i
$452$	−19.7543	−	14.3304i	−0.929164	−	0.674044i
$453$		0			0
$454$	−11.4068	−	0.219848i	−0.535345	−	0.0103180i
$455$	11.3560	+	11.3560i	0.532377	+	0.532377i
$456$		0			0
$457$	−11.2208	−	4.64779i	−0.524885	−	0.217414i	0.104476	−	0.994527i	$-0.466683\pi$
$457$	−11.2208	−	4.64779i	−0.524885	−	0.217414i	−0.629361	+	0.777113i	$0.716683\pi$
$458$	0.104784	+	0.0229504i	0.00489624	+	0.00107240i
$459$		0			0
$460$	−12.6774	+	27.5520i	−0.591085	+	1.28462i
$461$	7.05651	−	17.0359i	0.328654	−	0.793442i	−0.670038	−	0.742326i	$-0.733722\pi$
$461$	7.05651	−	17.0359i	0.328654	−	0.793442i	0.998693	−	0.0511153i	$-0.0162776\pi$
$462$		0			0
$463$	−1.11187	+	1.11187i	−0.0516730	+	0.0516730i	−0.732471	−	0.680798i	$-0.761633\pi$
$463$	−1.11187	+	1.11187i	−0.0516730	+	0.0516730i	0.680798	+	0.732471i	$0.261633\pi$
$464$	7.95540	−	10.1216i	0.369320	−	0.469885i
$465$		0			0
$466$	10.2435	+	4.47617i	0.474523	+	0.207355i
$467$	−9.50916	−	22.9572i	−0.440032	−	1.06233i	−0.975937	−	0.218052i	$-0.930030\pi$
$467$	−9.50916	−	22.9572i	−0.440032	−	1.06233i	0.535905	−	0.844278i	$-0.319970\pi$
$468$		0			0
$469$	8.65432	+	1.72145i	0.399619	+	0.0794892i
$470$	−6.74654	+	2.64337i	−0.311195	+	0.121930i
$471$		0			0
$472$	−3.05320	+	0.425705i	−0.140535	+	0.0195947i
$473$	8.39990	+	5.61263i	0.386228	+	0.258069i
$474$		0			0
$475$	21.2533			0.975167
$476$	−16.1500	+	38.0038i	−0.740234	+	1.74190i
$477$		0			0
$478$	−10.7094	+	15.3778i	−0.489836	+	0.703363i
$479$	19.2975	+	12.8942i	0.881726	+	0.589151i	0.911908	−	0.410394i	$-0.134609\pi$
$479$	19.2975	+	12.8942i	0.881726	+	0.589151i	−0.0301821	+	0.999544i	$0.509609\pi$
$480$		0			0
$481$	−1.02263	−	5.14110i	−0.0466278	−	0.234414i
$482$	−24.7046	+	9.67955i	−1.12526	+	0.440892i
$483$		0			0
$484$	18.6900	+	0.720710i	0.849545	+	0.0327595i
$485$	17.2811	+	41.7203i	0.784694	+	1.89442i
$486$		0			0
$487$	−9.42335	−	14.1030i	−0.427013	−	0.639070i	0.554113	−	0.832442i	$-0.313058\pi$
$487$	−9.42335	−	14.1030i	−0.427013	−	0.639070i	−0.981126	+	0.193372i	$0.938058\pi$
$488$	−9.17932	+	18.9778i	−0.415528	+	0.859085i
$489$		0			0
$490$	71.2785	−	68.5829i	3.22003	−	3.09826i
$491$	1.60448	−	3.87356i	0.0724092	−	0.174811i	−0.883531	−	0.468373i	$-0.844840\pi$
$491$	1.60448	−	3.87356i	0.0724092	−	0.174811i	0.955940	+	0.293561i	$0.0948405\pi$
$492$		0			0
$493$	−12.4039	−	4.71556i	−0.558646	−	0.212378i
$494$	2.43983	+	0.534385i	0.109773	+	0.0240431i
$495$		0			0
$496$	−2.34750	−	19.5896i	−0.105406	−	0.879598i
$497$	3.22523	+	3.22523i	0.144671	+	0.144671i
$498$		0			0
$499$	−25.8497	+	17.2722i	−1.15719	+	0.773211i	−0.977588	−	0.210528i	$-0.932482\pi$
$499$	−25.8497	+	17.2722i	−1.15719	+	0.773211i	−0.179604	+	0.983739i	$0.557482\pi$
$500$	22.6029	−	31.1579i	1.01083	−	1.39342i
$501$		0			0
$502$	−4.15126	−	23.1975i	−0.185280	−	1.03536i
$503$	3.68471	−	18.5243i	0.164293	−	0.825958i	−0.807453	−	0.589931i	$-0.799155\pi$
$503$	3.68471	−	18.5243i	0.164293	−	0.825958i	0.971747	−	0.236027i	$-0.0758453\pi$
$504$		0			0
$505$	0.681269	−	0.135513i	0.0303161	−	0.00603024i
$506$	3.83801	+	5.99077i	0.170620	+	0.266322i
$507$		0			0
$508$	−9.42995	+	8.72969i	−0.418386	+	0.387318i
$509$			6.16276i			0.273159i	0.990629	+	0.136580i	$0.0436110\pi$
$509$			6.16276i			0.273159i	−0.990629	+	0.136580i	$0.956389\pi$
$510$		0			0
$511$		−	3.67461i		−	0.162555i
$512$	−15.6293	+	16.3623i	−0.690723	+	0.723119i
$513$		0			0
$514$	−15.2690	+	9.78215i	−0.673486	+	0.431472i
$515$	−40.1539	+	7.98712i	−1.76939	+	0.351954i
$516$		0			0
$517$	−0.331615	+	1.66714i	−0.0145844	+	0.0733208i
$518$	−44.0881	+	7.88970i	−1.93712	+	0.346653i
$519$		0			0
$520$	6.77419	−	6.03294i	0.297068	−	0.264562i
$521$	−23.1725	+	15.4834i	−1.01521	+	0.678339i	−0.947629	−	0.319375i	$-0.896527\pi$
$521$	−23.1725	+	15.4834i	−1.01521	+	0.678339i	−0.0675781	+	0.997714i	$0.521527\pi$
$522$		0			0
$523$	−1.57600	−	1.57600i	−0.0689135	−	0.0689135i	0.671810	−	0.740724i	$-0.265517\pi$
$523$	−1.57600	−	1.57600i	−0.0689135	−	0.0689135i	−0.740724	+	0.671810i	$0.765517\pi$
$524$	17.3774	−	10.6663i	0.759137	−	0.465960i
$525$		0			0
$526$	2.47002	−	11.2773i	0.107698	−	0.491715i
$527$	−18.5519	+	8.33169i	−0.808135	+	0.362934i
$528$		0			0
$529$	−2.92471	+	7.06088i	−0.127161	+	0.306995i
$530$	−33.6039	−	34.9247i	−1.45966	−	1.51703i
$531$		0			0
$532$	4.96690	−	20.7552i	0.215343	−	0.899851i
$533$	−1.19676	−	1.79108i	−0.0518376	−	0.0775805i
$534$		0			0
$535$	−12.0511	−	29.0939i	−0.521014	−	1.25784i
$536$	1.25316	−	4.82393i	0.0541284	−	0.208362i
$537$		0			0
$538$	−11.5891	−	29.5781i	−0.499639	−	1.27520i
$539$	−4.52694	−	22.7585i	−0.194989	−	0.980277i
$540$		0			0
$541$	−14.3386	−	9.58077i	−0.616466	−	0.411909i	0.207752	−	0.978181i	$-0.433385\pi$
$541$	−14.3386	−	9.58077i	−0.616466	−	0.411909i	−0.824218	+	0.566272i	$0.808385\pi$
$542$	28.5970	+	19.9156i	1.22835	+	0.855446i
$543$		0			0
$544$	20.9030	+	10.3472i	0.896209	+	0.443632i
$545$	21.9709			0.941129
$546$		0			0
$547$	4.52518	+	3.02363i	0.193483	+	0.129281i	0.648538	−	0.761182i	$-0.275381\pi$
$547$	4.52518	+	3.02363i	0.193483	+	0.129281i	−0.455056	+	0.890463i	$0.650381\pi$
$548$	−15.4401	−	41.7586i	−0.659569	−	1.78384i
$549$		0			0
$550$	−6.60581	−	16.8596i	−0.281673	−	0.718898i
$551$	6.72650	+	1.33798i	0.286558	+	0.0570000i
$552$		0			0
$553$	−3.63621	−	8.77860i	−0.154628	−	0.373304i
$554$	14.3693	−	32.8835i	0.610493	−	1.39709i
$555$		0			0
$556$	−0.546891	+	2.28529i	−0.0231934	+	0.0969179i
$557$	−16.0879	+	16.0879i	−0.681667	+	0.681667i	−0.960376	−	0.278709i	$-0.910094\pi$
$557$	−16.0879	+	16.0879i	−0.681667	+	0.681667i	0.278709	+	0.960376i	$0.410094\pi$
$558$		0			0
$559$	−2.49594	+	6.02573i	−0.105567	+	0.254861i
$560$	−50.4233	−	58.8644i	−2.13077	−	2.48747i
$561$		0			0
$562$	0.908153	−	4.14633i	0.0383081	−	0.174903i
$563$	35.3917	+	14.6597i	1.49158	+	0.617834i	0.971661	−	0.236379i	$-0.0759608\pi$
$563$	35.3917	+	14.6597i	1.49158	+	0.617834i	0.519923	+	0.854213i	$0.325961\pi$
$564$		0			0
$565$	−33.3883	−	33.3883i	−1.40466	−	1.40466i
$566$	0.279797	−	14.5172i	0.0117607	−	0.610204i
$567$		0			0
$568$	1.92395	−	1.71342i	0.0807270	−	0.0718936i
$569$	42.1642	−	17.4650i	1.76762	−	0.732170i	0.772326	−	0.635227i	$-0.219093\pi$
$569$	42.1642	−	17.4650i	1.76762	−	0.732170i	0.995290	−	0.0969434i	$-0.0309066\pi$
$570$		0			0
$571$	−7.51967	+	37.8039i	−0.314688	+	1.58204i	0.422503	+	0.906361i	$0.361151\pi$
$571$	−7.51967	+	37.8039i	−0.314688	+	1.58204i	−0.737192	+	0.675684i	$0.763849\pi$
$572$	−0.334420	−	2.10154i	−0.0139828	−	0.0878700i
$573$		0			0
$574$	−15.4981	+	9.92890i	−0.646876	+	0.414424i
$575$	−21.7148	+	32.4985i	−0.905571	+	1.35528i
$576$		0			0
$577$		−	12.8306i		−	0.534147i	−0.963676	−	0.267073i	$-0.913943\pi$
$577$		−	12.8306i		−	0.534147i	0.963676	−	0.267073i	$-0.0860566\pi$
$578$	3.75447	−	23.7467i	0.156165	−	0.987731i
$579$		0			0
$580$	18.2784	−	16.9211i	0.758969	−	0.702609i
$581$	−27.0861	+	40.5371i	−1.12372	+	1.68176i
$582$		0			0
$583$	−11.1511	+	2.21809i	−0.461831	+	0.0918639i
$584$	−2.07208	−	0.119928i	−0.0857435	−	0.00496264i
$585$		0			0
$586$	7.90725	+	44.1862i	0.326645	+	1.82532i
$587$	−9.24274	+	3.82847i	−0.381489	+	0.158018i	−0.565183	−	0.824966i	$-0.691194\pi$
$587$	−9.24274	+	3.82847i	−0.381489	+	0.158018i	0.183694	+	0.982983i	$0.441194\pi$
$588$		0			0
$589$	8.73926	−	5.83938i	0.360095	−	0.240608i
$590$	−5.96335	−	0.114935i	−0.245507	−	0.00473178i
$591$		0			0
$592$	3.01005	+	25.1185i	0.123712	+	1.03236i
$593$	−17.9665	−	7.44197i	−0.737796	−	0.305605i	−0.0180445	−	0.999837i	$-0.505744\pi$
$593$	−17.9665	−	7.44197i	−0.737796	−	0.305605i	−0.719751	+	0.694232i	$0.755744\pi$
$594$		0			0
$595$	−42.4141	+	67.7055i	−1.73881	+	2.77565i
$596$	−0.862336	−	0.396782i	−0.0353227	−	0.0162528i
$597$		0			0
$598$	−3.30995	+	3.18477i	−0.135354	+	0.130235i
$599$	−5.59980	+	5.59980i	−0.228802	+	0.228802i	−0.812192	−	0.583390i	$-0.801726\pi$
$599$	−5.59980	+	5.59980i	−0.228802	+	0.228802i	0.583390	+	0.812192i	$0.301726\pi$
$600$		0			0
$601$	−13.7179	−	20.5302i	−0.559563	−	0.837445i	0.438559	−	0.898702i	$-0.355489\pi$
$601$	−13.7179	−	20.5302i	−0.559563	−	0.837445i	−0.998122	+	0.0612570i	$0.980489\pi$
$602$	51.0661	+	22.3146i	2.08130	+	0.909476i
$603$		0			0
$604$	26.7914	+	1.03311i	1.09012	+	0.0420366i
$605$	35.4929	+	7.05997i	1.44299	+	0.287029i
$606$		0			0
$607$	−6.64028	−	33.3829i	−0.269521	−	1.35497i	−0.843952	−	0.536419i	$-0.819777\pi$
$607$	−6.64028	−	33.3829i	−0.269521	−	1.35497i	0.574431	−	0.818553i	$-0.305223\pi$
$608$	−11.5416	−	3.47818i	−0.468073	−	0.141059i
$609$		0			0
$610$	−23.3098	+	33.4709i	−0.943787	+	1.35520i
$611$	−1.09740			−0.0443961
$612$		0			0
$613$	43.6516			1.76307			0.881536	−	0.472117i	$-0.156510\pi$
$613$	43.6516			1.76307			0.881536	+	0.472117i	$0.156510\pi$
$614$	6.21962	−	8.93084i	0.251004	−	0.360419i
$615$		0			0
$616$	−18.0083	+	2.51088i	−0.725575	+	0.101166i
$617$	−1.11593	−	5.61014i	−0.0449255	−	0.225856i	0.951800	−	0.306721i	$-0.0992318\pi$
$617$	−1.11593	−	5.61014i	−0.0449255	−	0.225856i	−0.996725	+	0.0808649i	$0.974232\pi$
$618$		0			0
$619$	12.6876	+	2.52372i	0.509958	+	0.101437i	0.443361	−	0.896343i	$-0.353786\pi$
$619$	12.6876	+	2.52372i	0.509958	+	0.101437i	0.0665968	+	0.997780i	$0.478786\pi$
$620$	1.47091	−	38.1447i	0.0590731	−	1.53193i
$621$		0			0
$622$	8.53588	+	3.72997i	0.342258	+	0.149558i
$623$	33.0169	+	49.4133i	1.32279	+	1.97970i
$624$		0			0
$625$	17.3999	−	17.3999i	0.695996	−	0.695996i
$626$	−27.1402	+	26.1138i	−1.08474	+	1.04372i
$627$		0			0
$628$	9.84818	−	21.4033i	0.392985	−	0.854085i
$629$	23.7880	−	10.6832i	0.948489	−	0.425967i
$630$		0			0
$631$	27.5646	+	11.4176i	1.09733	+	0.454529i	0.856557	−	0.516053i	$-0.172599\pi$
$631$	27.5646	+	11.4176i	1.09733	+	0.454529i	0.240773	+	0.970582i	$0.422599\pi$
$632$	−5.06886	+	1.76393i	−0.201629	+	0.0701653i
$633$		0			0
$634$	6.30926	+	0.121601i	0.250573	+	0.00482941i
$635$	−20.6727	+	13.8130i	−0.820371	+	0.548154i
$636$		0			0
$637$	13.8405	−	5.73291i	0.548380	−	0.227146i
$638$	−1.02930	−	5.75181i	−0.0407505	−	0.227716i
$639$		0			0
$640$	−34.8389	+	26.5122i	−1.37713	+	1.04799i
$641$	−1.06921	+	0.212680i	−0.0422314	+	0.00840035i	−0.216161	−	0.976358i	$-0.569354\pi$
$641$	−1.06921	+	0.212680i	−0.0422314	+	0.00840035i	0.173929	+	0.984758i	$0.444354\pi$
$642$		0			0
$643$	−14.5290	+	21.7442i	−0.572968	+	0.857506i	−0.998883	−	0.0472566i	$-0.984952\pi$
$643$	−14.5290	+	21.7442i	−0.572968	+	0.857506i	0.425915	+	0.904763i	$0.359952\pi$
$644$	26.6621	+	28.8008i	1.05063	+	1.13491i
$645$		0			0
$646$	0.125937	+	12.4246i	0.00495493	+	0.488841i
$647$		−	29.1409i		−	1.14565i	−0.819679	−	0.572824i	$-0.805848\pi$
$647$		−	29.1409i		−	1.14565i	0.819679	−	0.572824i	$-0.194152\pi$
$648$		0			0
$649$	−0.777349	+	1.16338i	−0.0305136	+	0.0456668i
$650$	9.84350	−	6.30629i	0.386094	−	0.247353i
$651$		0			0
$652$	42.3720	−	6.74268i	1.65942	−	0.264064i
$653$	6.12474	−	30.7912i	0.239680	−	1.20495i	−0.654087	−	0.756419i	$-0.726947\pi$
$653$	6.12474	−	30.7912i	0.239680	−	1.20495i	0.893767	−	0.448532i	$-0.148053\pi$
$654$		0			0
$655$	36.4472	−	15.0969i	1.42411	−	0.589886i
$656$	5.09303	+	9.06329i	0.198849	+	0.353862i
$657$		0			0
$658$	−0.180688	+	9.37495i	−0.00704394	+	0.365474i
$659$	−13.3117	−	13.3117i	−0.518550	−	0.518550i	0.398582	−	0.917133i	$-0.369502\pi$
$659$	−13.3117	−	13.3117i	−0.518550	−	0.518550i	−0.917133	+	0.398582i	$0.869502\pi$
$660$		0			0
$661$	−28.8920	−	11.9675i	−1.12377	−	0.465480i	−0.258110	−	0.966115i	$-0.583100\pi$
$661$	−28.8920	−	11.9675i	−1.12377	−	0.465480i	−0.865658	+	0.500635i	$0.833100\pi$
$662$	−7.19018	+	32.8280i	−0.279454	+	1.27590i
$663$		0			0
$664$	21.9746	+	16.5966i	0.852780	+	0.644075i
$665$	15.8013	−	38.1478i	0.612750	−	1.47931i
$666$		0			0
$667$	−8.91849	+	8.91849i	−0.345325	+	0.345325i
$668$	−16.0126	−	3.83196i	−0.619545	−	0.148263i
$669$		0			0
$670$	3.86125	−	8.83631i	0.149173	−	0.341376i
$671$	3.66164	+	8.83999i	0.141356	+	0.341264i
$672$		0			0
$673$	10.1166	+	2.01231i	0.389965	+	0.0775689i	0.386179	−	0.922424i	$-0.373795\pi$
$673$	10.1166	+	2.01231i	0.389965	+	0.0775689i	0.00378638	+	0.999993i	$0.498795\pi$
$674$	−7.74978	−	19.7793i	−0.298510	−	0.761871i
$675$		0			0
$676$	−23.0978	+	8.54035i	−0.888379	+	0.328475i
$677$	0.107942	+	0.0721244i	0.00414854	+	0.00277197i	0.557643	−	0.830081i	$-0.311706\pi$
$677$	0.107942	+	0.0721244i	0.00414854	+	0.00277197i	−0.553494	+	0.832853i	$0.686706\pi$
$678$		0			0
$679$	58.4370			2.24261
$680$	36.7944	+	26.1267i	1.41100	+	1.00191i
$681$		0			0
$682$	−7.34850	−	5.11765i	−0.281389	−	0.195965i
$683$	17.7485	+	11.8592i	0.679128	+	0.453779i	0.846692	−	0.532083i	$-0.178590\pi$
$683$	17.7485	+	11.8592i	0.679128	+	0.453779i	−0.167565	+	0.985861i	$0.553590\pi$
$684$		0			0
$685$	−16.8052	−	84.4853i	−0.642093	−	3.22802i
$686$	−28.6124	−	73.0258i	−1.09243	−	2.78814i
$687$		0			0
$688$	14.2497	−	28.0675i	0.543264	−	1.07006i
$689$	−2.80899	−	6.78149i	−0.107014	−	0.258354i
$690$		0			0
$691$	20.4317	+	30.5782i	0.777258	+	1.16325i	0.982813	+	0.184603i	$0.0590998\pi$
$691$	20.4317	+	30.5782i	0.777258	+	1.16325i	−0.205556	+	0.978645i	$0.565900\pi$
$692$	20.8292	+	4.98463i	0.791809	+	0.189487i
$693$		0			0
$694$	5.48691	+	5.70257i	0.208280	+	0.216467i
$695$	−1.73984	+	4.20035i	−0.0659959	+	0.159328i
$696$		0			0
$697$	7.35144	−	7.79703i	0.278456	−	0.295334i
$698$	2.86720	−	13.0907i	0.108525	−	0.495491i
$699$		0			0
$700$	−52.2531	−	85.1301i	−1.97498	−	3.21762i
$701$	2.70012	+	2.70012i	0.101982	+	0.101982i	0.756257	−	0.654275i	$-0.227026\pi$
$701$	2.70012	+	2.70012i	0.101982	+	0.101982i	−0.654275	+	0.756257i	$0.727026\pi$
$702$		0			0
$703$	−11.2058	+	7.48747i	−0.422634	+	0.282395i
$704$	0.828136	+	10.2367i	0.0312116	+	0.385810i
$705$		0			0
$706$	−26.0320	+	4.65849i	−0.979726	+	0.175325i
$707$	0.175363	−	0.881607i	0.00659519	−	0.0331563i
$708$		0			0
$709$	−37.2926	+	7.41796i	−1.40055	+	0.278587i	−0.836869	−	0.547403i	$-0.815616\pi$
$709$	−37.2926	+	7.41796i	−1.40055	+	0.278587i	−0.563684	+	0.825991i	$0.690616\pi$
$710$	4.19717	−	2.68894i	0.157517	−	0.100914i
$711$		0			0
$712$	28.9414	−	17.0053i	1.08462	−	0.637301i
$713$			19.3295i			0.723894i
$714$		0			0
$715$		−	4.11722i		−	0.153975i
$716$	26.7843	+	28.9328i	1.00098	+	1.08127i
$717$		0			0
$718$	14.0826	+	21.9816i	0.525559	+	0.820347i
$719$	33.9272	−	6.74854i	1.26527	−	0.251678i	0.483556	−	0.875313i	$-0.339345\pi$
$719$	33.9272	−	6.74854i	1.26527	−	0.251678i	0.781715	+	0.623635i	$0.214345\pi$
$720$		0			0
$721$	−10.3359	+	51.9619i	−0.384928	+	1.93516i
$722$	3.60207	+	20.1286i	0.134055	+	0.749110i
$723$		0			0
$724$	−6.41759	−	4.65552i	−0.238508	−	0.173021i
$725$	26.6903	−	17.8339i	0.991254	−	0.662335i
$726$		0			0
$727$	29.5184	+	29.5184i	1.09478	+	1.09478i	0.995011	+	0.0997645i	$0.0318089\pi$
$727$	29.5184	+	29.5184i	1.09478	+	1.09478i	0.0997645	+	0.995011i	$0.468191\pi$
$728$	−3.85805	−	11.0866i	−0.142989	−	0.410896i
$729$		0			0
$730$	−3.92278	−	0.859190i	−0.145189	−	0.0318000i
$731$	−31.9953	−	5.39156i	−1.18339	−	0.199414i
$732$		0			0
$733$	−0.260935	+	0.629952i	−0.00963785	+	0.0232678i	−0.928625	−	0.371019i	$-0.879008\pi$
$733$	−0.260935	+	0.629952i	−0.00963785	+	0.0232678i	0.918987	+	0.394287i	$0.129008\pi$
$734$	−19.3904	+	18.6571i	−0.715712	+	0.688645i
$735$		0			0
$736$	17.1107	−	14.0946i	0.630710	−	0.519534i
$737$	−1.25679	−	1.88092i	−0.0462944	−	0.0692844i
$738$		0			0
$739$	−2.52910	−	6.10579i	−0.0930344	−	0.224605i	0.870511	−	0.492148i	$-0.163788\pi$
$739$	−2.52910	−	6.10579i	−0.0930344	−	0.224605i	−0.963546	+	0.267543i	$0.913788\pi$
$740$	−1.88605	+	48.9105i	−0.0693327	+	1.79799i
$741$		0			0
$742$	−58.3959	+	22.8802i	−2.14378	+	0.839960i
$743$	8.03838	+	40.4117i	0.294900	+	1.48256i	0.789667	+	0.613535i	$0.210253\pi$
$743$	8.03838	+	40.4117i	0.294900	+	1.48256i	−0.494768	+	0.869025i	$0.664747\pi$
$744$		0			0
$745$	−1.52707	−	1.02035i	−0.0559475	−	0.0373829i
$746$	3.09157	−	4.43923i	0.113191	−	0.162532i
$747$		0			0
$748$	9.81699	−	3.96165i	0.358945	−	0.144852i
$749$	−40.7515			−1.48903
$750$		0			0
$751$	−10.1417	−	6.77649i	−0.370077	−	0.247277i	0.356600	−	0.934257i	$-0.383936\pi$
$751$	−10.1417	−	6.77649i	−0.370077	−	0.247277i	−0.726676	+	0.686980i	$0.758936\pi$
$752$	5.28057	+	0.407857i	0.192563	+	0.0148730i
$753$		0			0
$754$	3.51240	−	1.37620i	0.127914	−	0.0501183i
$755$	50.8776	+	10.1202i	1.85163	+	0.368311i
$756$		0			0
$757$	17.3893	+	41.9815i	0.632025	+	1.52584i	0.837073	+	0.547091i	$0.184265\pi$
$757$	17.3893	+	41.9815i	0.632025	+	1.52584i	−0.205048	+	0.978752i	$0.565735\pi$
$758$	−49.2548	−	21.5231i	−1.78901	−	0.781756i
$759$		0			0
$760$	−20.9956	−	10.1553i	−0.761590	−	0.368371i
$761$	−12.6449	+	12.6449i	−0.458376	+	0.458376i	−0.898122	−	0.439746i	$-0.855068\pi$
$761$	−12.6449	+	12.6449i	−0.458376	+	0.458376i	0.439746	+	0.898122i	$0.355068\pi$
$762$		0			0
$763$	10.8804	−	26.2675i	0.393896	−	0.950949i
$764$	33.6695	+	15.4922i	1.21812	+	0.560487i
$765$		0			0
$766$	2.50048	+	0.547670i	0.0903462	+	0.0197881i
$767$	−0.834562	−	0.345687i	−0.0301343	−	0.0124820i
$768$		0			0
$769$	17.0165	+	17.0165i	0.613631	+	0.613631i	0.943890	−	0.330259i	$-0.107136\pi$
$769$	17.0165	+	17.0165i	0.613631	+	0.613631i	−0.330259	+	0.943890i	$0.607136\pi$
$770$	−35.1729	−	0.677904i	−1.26754	−	0.0244300i
$771$		0			0
$772$	24.8384	−	34.2395i	0.893952	−	1.23230i
$773$	−31.1288	+	12.8940i	−1.11962	+	0.463763i	−0.864242	−	0.503077i	$-0.832201\pi$
$773$	−31.1288	+	12.8940i	−1.11962	+	0.463763i	−0.255382	+	0.966840i	$0.582201\pi$
$774$		0			0
$775$	9.59746	−	48.2497i	0.344751	−	1.73318i
$776$	1.90720	−	32.9522i	0.0684646	−	1.18292i
$777$		0			0
$778$	13.4082	+	20.9289i	0.480708	+	0.750339i
$779$	−3.07697	+	4.60501i	−0.110244	+	0.164991i
$780$		0			0
$781$		−	1.16934i		−	0.0418422i
$782$	−19.1273	−	12.5019i	−0.683990	−	0.447067i
$783$		0			0
$784$	−68.7295	+	22.4422i	−2.45463	+	0.801508i
$785$	25.3254	−	37.9021i	0.903901	−	1.35278i
$786$		0			0
$787$	−27.1178	+	5.39406i	−0.966644	+	0.192277i	−0.653079	−	0.757289i	$-0.726523\pi$
$787$	−27.1178	+	5.39406i	−0.966644	+	0.192277i	−0.313565	+	0.949567i	$0.601523\pi$
$788$	−2.45089	−	15.4018i	−0.0873094	−	0.548665i
$789$		0			0
$790$	−10.2217	+	1.82920i	−0.363672	+	0.0650801i
$791$	−56.4523	+	23.3833i	−2.00721	+	0.831415i
$792$		0			0
$793$	−5.13629	+	3.43196i	−0.182395	+	0.121872i
$794$	0.523229	−	27.1476i	0.0185687	−	0.963433i
$795$		0			0
$796$	11.3202	−	6.94838i	0.401235	−	0.246279i
$797$	−7.40672	−	3.06796i	−0.262359	−	0.108673i	0.247627	−	0.968856i	$-0.420349\pi$
$797$	−7.40672	−	3.06796i	−0.262359	−	0.108673i	−0.509986	+	0.860183i	$0.670349\pi$
$798$		0			0
$799$	−1.22203	−	5.32077i	−0.0432323	−	0.188235i
$800$	−49.7097	+	26.6868i	−1.75750	+	0.943519i
$801$		0			0
$802$	−12.6563	−	13.1537i	−0.446909	−	0.464475i
$803$	−0.666131	+	0.666131i	−0.0235073	+	0.0235073i
$804$		0			0
$805$	42.1876	+	63.1382i	1.48692	+	2.22533i
$806$	2.31494	−	5.29764i	0.0815403	−	0.186601i
$807$		0			0
$808$	−0.491409	−	0.127659i	−0.0172877	−	0.00449102i
$809$	−16.1461	−	3.21167i	−0.567668	−	0.112916i	−0.0970917	−	0.995275i	$-0.530954\pi$
$809$	−16.1461	−	3.21167i	−0.567668	−	0.112916i	−0.470576	+	0.882359i	$0.655954\pi$
$810$		0			0
$811$	−2.12785	−	10.6974i	−0.0747190	−	0.375638i	0.925274	−	0.379299i	$-0.123835\pi$
$811$	−2.12785	−	10.6974i	−0.0747190	−	0.375638i	−0.999993	+	0.00366088i	$0.998835\pi$
$812$	−11.1784	−	30.2326i	−0.392284	−	1.06096i
$813$		0			0
$814$	9.42252	+	6.56204i	0.330259	+	0.229999i
$815$	83.0127			2.90781
$816$		0			0
$817$	16.7690			0.586675
$818$	−21.3510	−	14.8693i	−0.746521	−	0.519893i
$819$		0			0
$820$	6.97576	+	18.8663i	0.243604	+	0.658841i
$821$	−1.41641	−	7.12079i	−0.0494332	−	0.248517i	0.948166	−	0.317777i	$-0.102936\pi$
$821$	−1.41641	−	7.12079i	−0.0494332	−	0.248517i	−0.997599	+	0.0692597i	$0.977936\pi$
$822$		0			0
$823$	−47.6996	−	9.48803i	−1.66270	−	0.330732i	−0.727841	−	0.685746i	$-0.759476\pi$
$823$	−47.6996	−	9.48803i	−1.66270	−	0.330732i	−0.934861	+	0.355014i	$0.884476\pi$
$824$	28.9636	+	7.52419i	1.00899	+	0.262118i
$825$		0			0
$826$	−3.09057	+	7.07264i	−0.107535	+	0.246089i
$827$	27.1056	+	40.5664i	0.942554	+	1.41063i	0.911585	+	0.411112i	$0.134859\pi$
$827$	27.1056	+	40.5664i	0.942554	+	1.41063i	0.0309692	+	0.999520i	$0.490141\pi$
$828$		0			0
$829$	22.5577	−	22.5577i	0.783462	−	0.783462i	−0.196952	−	0.980413i	$-0.563104\pi$
$829$	22.5577	−	22.5577i	0.783462	−	0.783462i	0.980413	+	0.196952i	$0.0631042\pi$
$830$	36.9417	+	38.3937i	1.28227	+	1.33267i
$831$		0			0
$832$	−6.37756	+	1.81370i	−0.221102	+	0.0628787i
$833$	43.2085	+	60.7219i	1.49708	+	2.10389i
$834$		0			0
$835$	−29.4310	−	12.1907i	−1.01850	−	0.421877i
$836$	−4.66289	+	2.86209i	−0.161269	+	0.0989875i
$837$		0			0
$838$	0.712145	−	36.9495i	0.0246006	−	1.27640i
$839$	−25.2257	+	16.8553i	−0.870888	+	0.581908i	−0.908734	−	0.417375i	$-0.862950\pi$
$839$	−25.2257	+	16.8553i	−0.870888	+	0.581908i	0.0378468	+	0.999284i	$0.487950\pi$
$840$		0			0
$841$	−17.2225	+	7.13380i	−0.593880	+	0.245993i
$842$	−8.50484	+	1.52196i	−0.293096	+	0.0524504i
$843$		0			0
$844$	−4.03527	−	25.3583i	−0.138900	−	0.872868i
$845$	−46.7311	+	9.29540i	−1.60760	+	0.319771i
$846$		0			0
$847$	26.0173	−	38.9377i	0.893966	−	1.33792i
$848$	10.9961	+	33.6758i	0.377609	+	1.15643i
$849$		0			0
$850$	41.5376	+	40.7040i	1.42473	+	1.39613i
$851$		−	24.7849i		−	0.849616i
$852$		0			0
$853$	−24.6371	+	36.8721i	−0.843560	+	1.26248i	0.119404	+	0.992846i	$0.461902\pi$
$853$	−24.6371	+	36.8721i	−0.843560	+	1.26248i	−0.962964	+	0.269630i	$0.913098\pi$
$854$	28.4731	+	44.4437i	0.974329	+	1.52083i
$855$		0			0
$856$	−1.33000	+	22.9795i	−0.0454585	+	0.785422i
$857$	−3.64341	+	18.3167i	−0.124456	+	0.625685i	0.867325	+	0.497742i	$0.165837\pi$
$857$	−3.64341	+	18.3167i	−0.124456	+	0.625685i	−0.991782	+	0.127943i	$0.959163\pi$
$858$		0			0
$859$	1.42430	−	0.589964i	0.0485964	−	0.0201293i	−0.358253	−	0.933625i	$-0.616627\pi$
$859$	1.42430	−	0.589964i	0.0485964	−	0.0201293i	0.406849	+	0.913495i	$0.366627\pi$
$860$	35.7619	−	49.2974i	1.21947	−	1.68103i
$861$		0			0
$862$	34.2505	+	0.660126i	1.16658	+	0.0224840i
$863$	1.96301	+	1.96301i	0.0668217	+	0.0668217i	0.739728	−	0.672906i	$-0.234954\pi$
$863$	1.96301	+	1.96301i	0.0668217	+	0.0668217i	−0.672906	+	0.739728i	$0.734954\pi$
$864$		0			0
$865$	38.2840	+	15.8577i	1.30169	+	0.539179i
$866$	−0.725932	−	0.158998i	−0.0246682	−	0.00540296i
$867$		0			0
$868$	−44.8759	−	20.6485i	−1.52319	−	0.700856i
$869$	−0.932209	+	2.25055i	−0.0316230	+	0.0763448i
$870$		0			0
$871$	1.03270	−	1.03270i	0.0349917	−	0.0349917i
$872$	−14.4570	−	6.99265i	−0.489575	−	0.236801i
$873$		0			0
$874$	10.8217	+	4.72880i	0.366048	+	0.159954i
$875$	−36.8818	−	89.0407i	−1.24683	−	3.01012i
$876$		0			0
$877$	−38.8096	−	7.71972i	−1.31051	−	0.260676i	−0.510091	−	0.860120i	$-0.670388\pi$
$877$	−38.8096	−	7.71972i	−1.31051	−	0.260676i	−0.800417	+	0.599444i	$0.795388\pi$
$878$	27.1543	−	10.6394i	0.916413	−	0.359062i
$879$		0			0
$880$	−1.53020	+	19.8116i	−0.0515830	+	0.667850i
$881$	37.7574	+	25.2287i	1.27208	+	0.849977i	0.993871	−	0.110543i	$-0.0352591\pi$
$881$	37.7574	+	25.2287i	1.27208	+	0.849977i	0.278209	+	0.960520i	$0.410259\pi$
$882$		0			0
$883$	−17.3887			−0.585178			−0.292589	−	0.956238i	$-0.594517\pi$
$883$	−17.3887			−0.585178			−0.292589	+	0.956238i	$0.594517\pi$
$884$	3.74498	+	5.71713i	0.125957	+	0.192288i
$885$		0			0
$886$	29.5621	−	42.4487i	0.993159	−	1.42609i
$887$	−27.3364	−	18.2656i	−0.917866	−	0.613298i	0.00434299	−	0.999991i	$-0.498618\pi$
$887$	−27.3364	−	18.2656i	−0.917866	−	0.613298i	−0.922209	+	0.386692i	$0.873618\pi$
$888$		0			0
$889$	6.27687	+	31.5559i	0.210519	+	1.05835i
$890$	60.4705	−	23.6931i	2.02698	−	0.794194i
$891$		0			0
$892$	−1.71871	+	44.5710i	−0.0575468	+	1.49235i
$893$	1.07974	+	2.60672i	0.0361321	+	0.0872306i
$894$		0			0
$895$	42.3809	+	63.4275i	1.41664	+	2.12015i
$896$	14.4441	+	54.7813i	0.482544	+	1.83012i
$897$		0			0
$898$	−16.1161	+	15.5066i	−0.537801	+	0.517462i
$899$	6.07504	−	14.6664i	0.202614	−	0.489153i
$900$		0			0
$901$	29.7522	−	21.1711i	0.991190	−	0.705311i
$902$	4.60939	+	1.00957i	0.153476	+	0.0336151i
$903$		0			0
$904$	11.3433	+	32.5962i	0.377271	+	1.08413i
$905$	−10.8469	−	10.8469i	−0.360563	−	0.360563i
$906$		0			0
$907$	−17.4738	+	11.6756i	−0.580207	+	0.387682i	−0.810761	−	0.585377i	$-0.800946\pi$
$907$	−17.4738	+	11.6756i	−0.580207	+	0.387682i	0.230553	+	0.973060i	$0.425946\pi$
$908$	13.0600	+	9.47417i	0.433413	+	0.314411i
$909$		0			0
$910$	−4.00082	−	22.3568i	−0.132626	−	0.741122i
$911$	10.6189	−	53.3847i	0.351819	−	1.76871i	−0.248182	−	0.968713i	$-0.579833\pi$
$911$	10.6189	−	53.3847i	0.351819	−	1.76871i	0.600001	−	0.799999i	$-0.295167\pi$
$912$		0			0
$913$	12.2587	−	2.43841i	0.405704	−	0.0806996i
$914$	9.26549	+	14.4625i	0.306475	+	0.478378i
$915$		0			0
$916$	−0.103055	−	0.111322i	−0.00340503	−	0.00367817i
$917$		−	51.0512i		−	1.68586i
$918$		0			0
$919$			13.0466i			0.430367i	0.976574	+	0.215184i	$0.0690350\pi$
$919$			13.0466i			0.430367i	−0.976574	+	0.215184i	$0.930965\pi$
$920$	36.9801	−	21.7287i	1.21920	−	0.716373i
$921$		0			0
$922$	−21.9578	+	14.0673i	−0.723140	+	0.463283i
$923$	0.740423	−	0.147279i	0.0243713	−	0.00484776i
$924$		0			0
$925$	−12.3062	+	61.8675i	−0.404626	+	2.03419i
$926$	2.18897	−	0.391722i	0.0719339	−	0.0128728i
$927$		0			0
$928$	−17.4128	+	5.31672i	−0.571602	+	0.174530i
$929$	−20.0886	+	13.4228i	−0.659087	+	0.440388i	−0.839615	−	0.543182i	$-0.817219\pi$
$929$	−20.0886	+	13.4228i	−0.659087	+	0.440388i	0.180528	+	0.983570i	$0.442219\pi$
$930$		0			0
$931$	−27.2355	−	27.2355i	−0.892606	−	0.892606i
$932$	−8.27012	−	13.4736i	−0.270897	−	0.441342i
$933$		0			0
$934$	−7.51861	+	34.3275i	−0.246016	+	1.12323i
$935$	19.9624	−	4.58480i	0.652842	−	0.149939i
$936$		0			0
$937$	8.49993	−	20.5206i	0.277681	−	0.670380i	−0.722090	−	0.691799i	$-0.756818\pi$
$937$	8.49993	−	20.5206i	0.277681	−	0.670380i	0.999771	+	0.0214188i	$0.00681834\pi$
$938$	−8.65219	−	8.99226i	−0.282504	−	0.293608i
$939$		0			0
$940$	9.96587	+	2.38492i	0.325051	+	0.0777876i
$941$	9.89431	+	14.8079i	0.322545	+	0.482723i	0.956940	−	0.290286i	$-0.0937505\pi$
$941$	9.89431	+	14.8079i	0.322545	+	0.482723i	−0.634394	+	0.773009i	$0.718750\pi$
$942$		0			0
$943$	−3.89776	−	9.41002i	−0.126929	−	0.306433i
$944$	3.88734	+	1.97358i	0.126522	+	0.0642345i
$945$		0			0
$946$	−5.21205	−	13.3024i	−0.169458	−	0.432499i
$947$	4.40160	+	22.1283i	0.143033	+	0.719074i	0.984026	+	0.178028i	$0.0569716\pi$
$947$	4.40160	+	22.1283i	0.143033	+	0.719074i	−0.840993	+	0.541046i	$0.818028\pi$
$948$		0			0
$949$	−0.505694	−	0.337894i	−0.0164155	−	0.0109685i
$950$	−24.6648	−	17.1771i	−0.800232	−	0.557298i
$951$		0			0
$952$	49.4573	−	31.0515i	1.60292	−	1.00639i
$953$	10.1093			0.327472			0.163736	−	0.986504i	$-0.447646\pi$
$953$	10.1093			0.327472			0.163736	+	0.986504i	$0.447646\pi$
$954$		0			0
$955$	59.6237	+	39.8393i	1.92938	+	1.28917i
$956$	24.8569	−	9.19074i	0.803929	−	0.297250i
$957$		0			0
$958$	−11.9739	−	30.5603i	−0.386860	−	0.987360i
$959$	−109.330	−	21.7470i	−3.53044	−	0.702248i
$960$		0			0
$961$	2.55292	+	6.16329i	0.0823522	+	0.198816i
$962$	−2.96830	+	6.79283i	−0.0957019	+	0.219010i
$963$		0			0
$964$	36.4932	+	8.73315i	1.17537	+	0.281276i
$965$	57.8709	−	57.8709i	1.86293	−	1.86293i
$966$		0			0
$967$	−3.77287	+	9.10852i	−0.121327	+	0.292910i	−0.972861	−	0.231389i	$-0.925673\pi$
$967$	−3.77287	+	9.10852i	−0.121327	+	0.292910i	0.851534	+	0.524300i	$0.175673\pi$
$968$	−21.1076	−	15.9418i	−0.678423	−	0.512389i
$969$		0			0
$970$	13.6636	−	62.3838i	0.438713	−	2.00302i
$971$	−8.21366	−	3.40221i	−0.263589	−	0.109182i	0.246975	−	0.969022i	$-0.420563\pi$
$971$	−8.21366	−	3.40221i	−0.263589	−	0.109182i	−0.510564	+	0.859840i	$0.670563\pi$
$972$		0			0
$973$	4.16017	+	4.16017i	0.133369	+	0.133369i
$974$	−0.462233	+	23.9828i	−0.0148109	+	0.768460i
$975$		0			0
$976$	25.9908	−	14.6053i	0.831944	−	0.467503i
$977$	−51.1302	+	21.1788i	−1.63580	+	0.677571i	−0.995864	−	0.0908572i	$-0.971039\pi$
$977$	−51.1302	+	21.1788i	−1.63580	+	0.677571i	−0.639936	+	0.768428i	$0.721039\pi$
$978$		0			0
$979$	2.97233	−	14.9429i	0.0949961	−	0.477578i
$980$	−138.149	+	21.9837i	−4.41301	+	0.702245i
$981$		0			0
$982$	−4.99267	+	3.19858i	−0.159323	+	0.102071i
$983$	−29.5813	+	44.2716i	−0.943498	+	1.41204i	−0.0325739	+	0.999469i	$0.510370\pi$
$983$	−29.5813	+	44.2716i	−0.943498	+	1.41204i	−0.910924	+	0.412575i	$0.864630\pi$
$984$		0			0
$985$		−	30.1742i		−	0.961431i
$986$	10.5838	+	15.4975i	0.337058	+	0.493540i
$987$		0			0
$988$	−2.39957	−	2.59205i	−0.0763405	−	0.0824642i
$989$	−17.1332	+	25.6417i	−0.544804	+	0.815357i
$990$		0			0
$991$	28.2420	−	5.61768i	0.897137	−	0.178452i	0.275078	−	0.961422i	$-0.411296\pi$
$991$	28.2420	−	5.61768i	0.897137	−	0.178452i	0.622059	+	0.782970i	$0.286296\pi$
$992$	−13.1081	+	24.6313i	−0.416184	+	0.782045i
$993$		0			0
$994$	−1.13628	−	6.34959i	−0.0360405	−	0.201397i
$995$	23.7429	−	9.83464i	0.752701	−	0.311779i
$996$		0			0
$997$	−23.9891	+	16.0290i	−0.759742	+	0.507643i	−0.874070	−	0.485800i	$-0.838528\pi$
$997$	−23.9891	+	16.0290i	−0.759742	+	0.507643i	0.114329	+	0.993443i	$0.463528\pi$
$998$	43.9586	+	0.847234i	1.39148	+	0.0268187i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	612.2.bd.f.415.4		144
3.2	odd	2		204.2.r.a.7.15	yes	144
4.3	odd	2	inner	612.2.bd.f.415.17		144
12.11	even	2		204.2.r.a.7.2	✓	144
17.5	odd	16	inner	612.2.bd.f.379.17		144
51.5	even	16		204.2.r.a.175.2	yes	144
68.39	even	16	inner	612.2.bd.f.379.4		144
204.107	odd	16		204.2.r.a.175.15	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
204.2.r.a.7.2	✓	144	12.11	even	2
204.2.r.a.7.15	yes	144	3.2	odd	2
204.2.r.a.175.2	yes	144	51.5	even	16
204.2.r.a.175.15	yes	144	204.107	odd	16
612.2.bd.f.379.4		144	68.39	even	16	inner
612.2.bd.f.379.17		144	17.5	odd	16	inner
612.2.bd.f.415.4		144	1.1	even	1	trivial
612.2.bd.f.415.17		144	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 612 = 2^{2} \cdot 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	612.bd (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.16052 - 0.808208i) q^{2} +(0.693599 + 1.87588i) q^{4} +(0.754921 + 3.79524i) q^{5} +(4.91130 + 0.976917i) q^{7} +(0.711166 - 2.73756i) q^{8} +(2.19125 - 5.01458i) q^{10} +(-0.713223 - 1.06741i) q^{11} +(0.586054 - 0.586054i) q^{13} +(-4.91009 - 5.10308i) q^{14} +(-3.03784 + 2.60222i) q^{16} +(3.49411 + 2.18889i) q^{17} +(-1.96871 - 0.815467i) q^{19} +(-6.59580 + 4.04852i) q^{20} +(-0.0349849 + 1.81518i) q^{22} +(3.25840 - 2.17719i) q^{23} +(-9.21456 + 3.81680i) q^{25} +(-1.15378 + 0.206472i) q^{26} +(1.57389 + 9.89058i) q^{28} +(-3.15662 + 0.627891i) q^{29} +(-2.74031 + 4.10117i) q^{31} +(5.62860 - 0.564710i) q^{32} +(-2.28590 - 5.36420i) q^{34} +19.3771i q^{35} +(3.51373 - 5.25867i) q^{37} +(1.62566 + 2.53749i) q^{38} +(10.9266 + 0.632406i) q^{40} +(0.507052 - 2.54912i) q^{41} +(-7.27038 + 3.01149i) q^{43} +(1.50765 - 2.07828i) q^{44} +(-5.54106 - 0.106795i) q^{46} +(-0.936262 - 0.936262i) q^{47} +(16.6993 + 6.91708i) q^{49} +(13.7784 + 3.01782i) q^{50} +(1.50585 + 0.692879i) q^{52} +(3.38920 - 8.18225i) q^{53} +(3.51266 - 3.51266i) q^{55} +(6.16712 - 12.7502i) q^{56} +(4.17078 + 1.82253i) q^{58} +(-0.417091 - 1.00695i) q^{59} +(-7.31011 - 1.45407i) q^{61} +(6.49478 - 2.54473i) q^{62} +(-6.98849 - 3.89372i) q^{64} +(2.66664 + 1.78179i) q^{65} +1.76213 q^{67} +(-1.68257 + 8.07273i) q^{68} +(15.6607 - 22.4874i) q^{70} +(0.757356 + 0.506049i) q^{71} +(-0.143161 - 0.719719i) q^{73} +(-8.32784 + 3.26295i) q^{74} +(0.164220 - 4.25867i) q^{76} +(-2.46007 - 5.93914i) q^{77} +(-1.05421 - 1.57773i) q^{79} +(-12.1694 - 9.56487i) q^{80} +(-2.64867 + 2.54850i) q^{82} +(-3.72584 + 8.99498i) q^{83} +(-5.66958 + 14.9134i) q^{85} +(10.8713 + 2.38109i) q^{86} +(-3.42933 + 1.19338i) q^{88} +(8.39190 + 8.39190i) q^{89} +(3.45081 - 2.30576i) q^{91} +(6.34418 + 4.60226i) q^{92} +(0.329853 + 1.84324i) q^{94} +(1.60867 - 8.08735i) q^{95} +(11.4456 - 2.27668i) q^{97} +(-13.7894 - 21.5239i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 64 q^{26} - 48 q^{28} + 80 q^{32} - 16 q^{34} + 80 q^{38} - 64 q^{40} + 64 q^{44} - 16 q^{46} + 16 q^{53} - 80 q^{56} + 112 q^{58} - 64 q^{61} - 112 q^{62} + 96 q^{64} + 208 q^{65} - 176 q^{68}+ \cdots - 96 q^{94}+O(q^{100}) \) 144 * q + 64 * q^26 - 48 * q^28 + 80 * q^32 - 16 * q^34 + 80 * q^38 - 64 * q^40 + 64 * q^44 - 16 * q^46 + 16 * q^53 - 80 * q^56 + 112 * q^58 - 64 * q^61 - 112 * q^62 + 96 * q^64 + 208 * q^65 - 176 * q^68 + 176 * q^70 - 208 * q^73 - 96 * q^74 + 112 * q^76 + 64 * q^77 - 112 * q^80 + 80 * q^82 - 16 * q^85 - 64 * q^88 - 96 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more