LMFDB - Embedded newform 396.2.j.b.181.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [396,2,Mod(37,396)] 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("396.37"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(396, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 396 = 2^{2} \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	396.j (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,0,-3,0,7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$3.16207592004$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 132)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			181.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	396.181
Dual form			396.2.j.b.361.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.190983 + 0.587785i) q^{5} +(3.42705 - 2.48990i) q^{7} +(-0.309017 + 3.30220i) q^{11} +(0.0729490 + 0.224514i) q^{13} +(2.11803 - 6.51864i) q^{17} +(0.118034 + 0.0857567i) q^{19} +5.00000 q^{23} +(3.73607 + 2.71441i) q^{25} +(1.61803 - 1.17557i) q^{29} +(1.73607 + 5.34307i) q^{31} +(0.809017 + 2.48990i) q^{35} +(1.80902 - 1.31433i) q^{37} +(3.80902 + 2.76741i) q^{41} -11.4721 q^{43} +(-8.54508 - 6.20837i) q^{47} +(3.38197 - 10.4086i) q^{49} +(-1.35410 - 4.16750i) q^{53} +(-1.88197 - 0.812299i) q^{55} +(-10.3541 + 7.52270i) q^{59} +(-1.28115 + 3.94298i) q^{61} -0.145898 q^{65} -6.61803 q^{67} +(-1.71885 + 5.29007i) q^{71} +(1.85410 - 1.34708i) q^{73} +(7.16312 + 12.0862i) q^{77} +(1.45492 + 4.47777i) q^{79} +(1.92705 - 5.93085i) q^{83} +(3.42705 + 2.48990i) q^{85} -17.1803 q^{89} +(0.809017 + 0.587785i) q^{91} +(-0.0729490 + 0.0530006i) q^{95} +(-4.33688 - 13.3475i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3 q^{5} + 7 q^{7} + q^{11} + 7 q^{13} + 4 q^{17} - 4 q^{19} + 20 q^{23} + 6 q^{25} + 2 q^{29} - 2 q^{31} + q^{35} + 5 q^{37} + 13 q^{41} - 28 q^{43} - 23 q^{47} + 18 q^{49} + 8 q^{53} - 12 q^{55}+ \cdots - 33 q^{97}+O(q^{100}) $ 4 * q - 3 * q^5 + 7 * q^7 + q^11 + 7 * q^13 + 4 * q^17 - 4 * q^19 + 20 * q^23 + 6 * q^25 + 2 * q^29 - 2 * q^31 + q^35 + 5 * q^37 + 13 * q^41 - 28 * q^43 - 23 * q^47 + 18 * q^49 + 8 * q^53 - 12 * q^55 - 28 * q^59 + 15 * q^61 - 14 * q^65 - 22 * q^67 - 27 * q^71 - 6 * q^73 + 13 * q^77 + 17 * q^79 + q^83 + 7 * q^85 - 24 * q^89 + q^91 - 7 * q^95 - 33 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/396\mathbb{Z}\right)^\times$.

$n$	$145$	$199$	$353$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.190983	+	0.587785i	−0.0854102	+	0.262866i	−0.984636	−	0.174619i	$-0.944131\pi$
$5$	−0.190983	+	0.587785i	−0.0854102	+	0.262866i	0.899226	+	0.437485i	$0.144131\pi$
$6$		0			0
$7$	3.42705	−	2.48990i	1.29530	−	0.941093i	0.295405	−	0.955372i	$-0.404545\pi$
$7$	3.42705	−	2.48990i	1.29530	−	0.941093i	0.999898	+	0.0142789i	$0.00454526\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.309017	+	3.30220i	−0.0931721	+	0.995650i
$11$	−0.309017	+	3.30220i	−0.0931721	+	0.995650i
$12$		0			0
$13$	0.0729490	+	0.224514i	0.0202324	+	0.0622690i	0.960663	−	0.277717i	$-0.0895777\pi$
$13$	0.0729490	+	0.224514i	0.0202324	+	0.0622690i	−0.940431	+	0.339986i	$0.889578\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.11803	−	6.51864i	0.513699	−	1.58100i	−0.271939	−	0.962315i	$-0.587665\pi$
$17$	2.11803	−	6.51864i	0.513699	−	1.58100i	0.785637	−	0.618687i	$-0.212335\pi$
$18$		0			0
$19$	0.118034	+	0.0857567i	0.0270789	+	0.0196739i	0.601242	−	0.799067i	$-0.294673\pi$
$19$	0.118034	+	0.0857567i	0.0270789	+	0.0196739i	−0.574164	+	0.818741i	$0.694673\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	5.00000			1.04257			0.521286	−	0.853382i	$-0.325452\pi$
$23$	5.00000			1.04257			0.521286	+	0.853382i	$0.325452\pi$
$24$		0			0
$25$	3.73607	+	2.71441i	0.747214	+	0.542882i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.61803	−	1.17557i	0.300461	−	0.218298i	−0.427331	−	0.904095i	$-0.640546\pi$
$29$	1.61803	−	1.17557i	0.300461	−	0.218298i	0.727793	+	0.685797i	$0.240546\pi$
$30$		0			0
$31$	1.73607	+	5.34307i	0.311807	+	0.959643i	0.977049	+	0.213015i	$0.0683284\pi$
$31$	1.73607	+	5.34307i	0.311807	+	0.959643i	−0.665242	+	0.746628i	$0.731672\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.809017	+	2.48990i	0.136749	+	0.420870i
$36$		0			0
$37$	1.80902	−	1.31433i	0.297401	−	0.216074i	−0.429071	−	0.903271i	$-0.641159\pi$
$37$	1.80902	−	1.31433i	0.297401	−	0.216074i	0.726471	+	0.687197i	$0.241159\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.80902	+	2.76741i	0.594869	+	0.432197i	0.844054	−	0.536259i	$-0.180163\pi$
$41$	3.80902	+	2.76741i	0.594869	+	0.432197i	−0.249185	+	0.968456i	$0.580163\pi$
$42$		0			0
$43$	−11.4721			−1.74948			−0.874742	−	0.484589i	$-0.838969\pi$
$43$	−11.4721			−1.74948			−0.874742	+	0.484589i	$0.838969\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−8.54508	−	6.20837i	−1.24643	−	0.905583i	−0.248420	−	0.968653i	$-0.579911\pi$
$47$	−8.54508	−	6.20837i	−1.24643	−	0.905583i	−0.998009	+	0.0630690i	$0.979911\pi$
$48$		0			0
$49$	3.38197	−	10.4086i	0.483138	−	1.48695i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−1.35410	−	4.16750i	−0.186000	−	0.572450i	0.813964	−	0.580915i	$-0.197305\pi$
$53$	−1.35410	−	4.16750i	−0.186000	−	0.572450i	−0.999964	+	0.00846560i	$0.997305\pi$
$54$		0			0
$55$	−1.88197	−	0.812299i	−0.253764	−	0.109530i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−10.3541	+	7.52270i	−1.34799	+	0.979372i	−0.348880	+	0.937167i	$0.613438\pi$
$59$	−10.3541	+	7.52270i	−1.34799	+	0.979372i	−0.999109	+	0.0422042i	$0.986562\pi$
$60$		0			0
$61$	−1.28115	+	3.94298i	−0.164035	+	0.504847i	−0.998964	−	0.0455103i	$-0.985509\pi$
$61$	−1.28115	+	3.94298i	−0.164035	+	0.504847i	0.834929	+	0.550358i	$0.185509\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.145898			−0.0180964
$66$		0			0
$67$	−6.61803			−0.808522			−0.404261	−	0.914644i	$-0.632471\pi$
$67$	−6.61803			−0.808522			−0.404261	+	0.914644i	$0.632471\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−1.71885	+	5.29007i	−0.203990	+	0.627815i	0.795764	+	0.605607i	$0.207070\pi$
$71$	−1.71885	+	5.29007i	−0.203990	+	0.627815i	−0.999753	+	0.0222083i	$0.992930\pi$
$72$		0			0
$73$	1.85410	−	1.34708i	0.217006	−	0.157664i	−0.473972	−	0.880540i	$-0.657180\pi$
$73$	1.85410	−	1.34708i	0.217006	−	0.157664i	0.690978	+	0.722876i	$0.257180\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	7.16312	+	12.0862i	0.816313	+	1.37735i
$78$		0			0
$79$	1.45492	+	4.47777i	0.163691	+	0.503788i	0.998937	−	0.0460871i	$-0.0146752\pi$
$79$	1.45492	+	4.47777i	0.163691	+	0.503788i	−0.835247	+	0.549875i	$0.814675\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	1.92705	−	5.93085i	0.211521	−	0.650996i	−0.787861	−	0.615853i	$-0.788811\pi$
$83$	1.92705	−	5.93085i	0.211521	−	0.650996i	0.999382	−	0.0351426i	$-0.0111885\pi$
$84$		0			0
$85$	3.42705	+	2.48990i	0.371716	+	0.270067i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−17.1803			−1.82111			−0.910556	−	0.413385i	$-0.864346\pi$
$89$	−17.1803			−1.82111			−0.910556	+	0.413385i	$0.864346\pi$
$90$		0			0
$91$	0.809017	+	0.587785i	0.0848080	+	0.0616166i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.0729490	+	0.0530006i	−0.00748441	+	0.00543774i
$96$		0			0
$97$	−4.33688	−	13.3475i	−0.440344	−	1.35524i	−0.887510	−	0.460788i	$-0.847567\pi$
$97$	−4.33688	−	13.3475i	−0.440344	−	1.35524i	0.447167	−	0.894451i	$-0.352433\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−3.63525	−	11.1882i	−0.361721	−	1.11326i	−0.952009	−	0.306071i	$-0.900986\pi$
$101$	−3.63525	−	11.1882i	−0.361721	−	1.11326i	0.590287	−	0.807193i	$-0.299014\pi$
$102$		0			0
$103$	−14.0902	+	10.2371i	−1.38835	+	1.00869i	−0.392301	+	0.919837i	$0.628321\pi$
$103$	−14.0902	+	10.2371i	−1.38835	+	1.00869i	−0.996045	+	0.0888554i	$0.971679\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	12.6631	+	9.20029i	1.22419	+	0.889426i	0.996441	−	0.0842938i	$-0.0268634\pi$
$107$	12.6631	+	9.20029i	1.22419	+	0.889426i	0.227749	+	0.973720i	$0.426863\pi$
$108$		0			0
$109$	−8.94427			−0.856706			−0.428353	−	0.903612i	$-0.640906\pi$
$109$	−8.94427			−0.856706			−0.428353	+	0.903612i	$0.640906\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	8.04508	+	5.84510i	0.756818	+	0.549860i	0.897933	−	0.440133i	$-0.145069\pi$
$113$	8.04508	+	5.84510i	0.756818	+	0.549860i	−0.141115	+	0.989993i	$0.545069\pi$
$114$		0			0
$115$	−0.954915	+	2.93893i	−0.0890463	+	0.274056i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−8.97214	−	27.6134i	−0.822474	−	2.53132i
$120$		0			0
$121$	−10.8090	−	2.04087i	−0.982638	−	0.185534i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−4.80902	+	3.49396i	−0.430132	+	0.312509i
$126$		0			0
$127$	−3.61803	+	11.1352i	−0.321049	+	0.988086i	0.652144	+	0.758095i	$0.273870\pi$
$127$	−3.61803	+	11.1352i	−0.321049	+	0.988086i	−0.973193	+	0.229991i	$0.926130\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	8.85410			0.773586			0.386793	−	0.922166i	$-0.373583\pi$
$131$	8.85410			0.773586			0.386793	+	0.922166i	$0.373583\pi$
$132$		0			0
$133$	0.618034			0.0535903
$134$		0			0
$135$		0			0
$136$		0			0
$137$	3.01722	−	9.28605i	0.257779	−	0.793361i	−0.735491	−	0.677535i	$-0.763048\pi$
$137$	3.01722	−	9.28605i	0.257779	−	0.793361i	0.993269	−	0.115826i	$-0.0369516\pi$
$138$		0			0
$139$	6.92705	−	5.03280i	0.587545	−	0.426876i	−0.253891	−	0.967233i	$-0.581711\pi$
$139$	6.92705	−	5.03280i	0.587545	−	0.426876i	0.841436	+	0.540356i	$0.181711\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.763932	+	0.171513i	−0.0638832	+	0.0143427i
$144$		0			0
$145$	0.381966	+	1.17557i	0.0317206	+	0.0976258i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−5.48936	+	16.8945i	−0.449706	+	1.38405i	0.427534	+	0.903999i	$0.359382\pi$
$149$	−5.48936	+	16.8945i	−0.449706	+	1.38405i	−0.877240	+	0.480052i	$0.840618\pi$
$150$		0			0
$151$	3.61803	+	2.62866i	0.294431	+	0.213917i	0.725188	−	0.688551i	$-0.241753\pi$
$151$	3.61803	+	2.62866i	0.294431	+	0.213917i	−0.430756	+	0.902468i	$0.641753\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−3.47214			−0.278889
$156$		0			0
$157$	12.7082	+	9.23305i	1.01423	+	0.736878i	0.965091	−	0.261915i	$-0.0843539\pi$
$157$	12.7082	+	9.23305i	1.01423	+	0.736878i	0.0491340	+	0.998792i	$0.484354\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	17.1353	−	12.4495i	1.35045	−	0.981157i
$162$		0			0
$163$	−3.20820	−	9.87384i	−0.251286	−	0.773379i	−0.994539	−	0.104368i	$-0.966718\pi$
$163$	−3.20820	−	9.87384i	−0.251286	−	0.773379i	0.743253	−	0.669011i	$-0.233282\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	4.80902	+	14.8006i	0.372133	+	1.14531i	0.945393	+	0.325934i	$0.105679\pi$
$167$	4.80902	+	14.8006i	0.372133	+	1.14531i	−0.573260	+	0.819374i	$0.694321\pi$
$168$		0			0
$169$	10.4721	−	7.60845i	0.805549	−	0.585266i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	7.82624	+	5.68609i	0.595018	+	0.432306i	0.844107	−	0.536175i	$-0.180131\pi$
$173$	7.82624	+	5.68609i	0.595018	+	0.432306i	−0.249089	+	0.968481i	$0.580131\pi$
$174$		0			0
$175$	19.5623			1.47877
$176$		0			0
$177$		0			0
$178$		0			0
$179$	1.04508	+	0.759299i	0.0781133	+	0.0567526i	0.626157	−	0.779697i	$-0.284627\pi$
$179$	1.04508	+	0.759299i	0.0781133	+	0.0567526i	−0.548043	+	0.836450i	$0.684627\pi$
$180$		0			0
$181$	1.54508	−	4.75528i	0.114845	−	0.353457i	−0.877069	−	0.480364i	$-0.840505\pi$
$181$	1.54508	−	4.75528i	0.114845	−	0.353457i	0.991915	+	0.126906i	$0.0405047\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.427051	+	1.31433i	0.0313974	+	0.0966313i
$186$		0			0
$187$	20.8713	+	9.00854i	1.52626	+	0.658769i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−10.8992	+	7.91872i	−0.788637	+	0.572979i	−0.907559	−	0.419925i	$-0.862056\pi$
$191$	−10.8992	+	7.91872i	−0.788637	+	0.572979i	0.118921	+	0.992904i	$0.462056\pi$
$192$		0			0
$193$	5.50000	−	16.9273i	0.395899	−	1.21845i	−0.532361	−	0.846518i	$-0.678695\pi$
$193$	5.50000	−	16.9273i	0.395899	−	1.21845i	0.928259	−	0.371933i	$-0.121305\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−19.3262			−1.37694			−0.688469	−	0.725266i	$-0.741717\pi$
$197$	−19.3262			−1.37694			−0.688469	+	0.725266i	$0.741717\pi$
$198$		0			0
$199$	0.0557281			0.00395046			0.00197523	−	0.999998i	$-0.499371\pi$
$199$	0.0557281			0.00395046			0.00197523	+	0.999998i	$0.499371\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	2.61803	−	8.05748i	0.183750	−	0.565524i
$204$		0			0
$205$	−2.35410	+	1.71036i	−0.164418	+	0.119456i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.319660	+	0.363271i	−0.0221114	+	0.0251280i
$210$		0			0
$211$	−6.20820	−	19.1069i	−0.427390	−	1.31537i	−0.900687	−	0.434469i	$-0.856936\pi$
$211$	−6.20820	−	19.1069i	−0.427390	−	1.31537i	0.473296	−	0.880903i	$-0.343064\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	2.19098	−	6.74315i	0.149424	−	0.459879i
$216$		0			0
$217$	19.2533	+	13.9883i	1.30700	+	0.949590i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	1.61803			0.108841
$222$		0			0
$223$	−16.1353	−	11.7229i	−1.08050	−	0.785027i	−0.102727	−	0.994710i	$-0.532757\pi$
$223$	−16.1353	−	11.7229i	−1.08050	−	0.785027i	−0.977769	+	0.209683i	$0.932757\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	4.42705	−	3.21644i	0.293834	−	0.213483i	−0.431095	−	0.902307i	$-0.641873\pi$
$227$	4.42705	−	3.21644i	0.293834	−	0.213483i	0.724929	+	0.688824i	$0.241873\pi$
$228$		0			0
$229$	2.90983	+	8.95554i	0.192287	+	0.591798i	0.999998	+	0.00221926i	$0.000706412\pi$
$229$	2.90983	+	8.95554i	0.192287	+	0.591798i	−0.807711	+	0.589579i	$0.799294\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.246711	+	0.759299i	0.0161626	+	0.0497433i	0.958813	−	0.284040i	$-0.0916747\pi$
$233$	0.246711	+	0.759299i	0.0161626	+	0.0497433i	−0.942650	+	0.333783i	$0.891675\pi$
$234$		0			0
$235$	5.28115	−	3.83698i	0.344504	−	0.250297i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	18.3992	+	13.3678i	1.19014	+	0.864691i	0.993280	−	0.115740i	$-0.0369240\pi$
$239$	18.3992	+	13.3678i	1.19014	+	0.864691i	0.196865	+	0.980431i	$0.436924\pi$
$240$		0			0
$241$	−5.23607			−0.337285			−0.168642	−	0.985677i	$-0.553938\pi$
$241$	−5.23607			−0.337285			−0.168642	+	0.985677i	$0.553938\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	5.47214	+	3.97574i	0.349602	+	0.254001i
$246$		0			0
$247$	−0.0106431	+	0.0327561i	−0.000677205	+	0.00208422i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−2.88197	−	8.86978i	−0.181908	−	0.559856i	0.817973	−	0.575256i	$-0.195098\pi$
$251$	−2.88197	−	8.86978i	−0.181908	−	0.559856i	−0.999881	+	0.0154006i	$0.995098\pi$
$252$		0			0
$253$	−1.54508	+	16.5110i	−0.0971387	+	1.03804i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	3.35410	−	2.43690i	0.209223	−	0.152010i	−0.478239	−	0.878230i	$-0.658725\pi$
$257$	3.35410	−	2.43690i	0.209223	−	0.152010i	0.687462	+	0.726220i	$0.258725\pi$
$258$		0			0
$259$	2.92705	−	9.00854i	0.181878	−	0.559763i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−19.7426			−1.21738			−0.608692	−	0.793407i	$-0.708305\pi$
$263$	−19.7426			−1.21738			−0.608692	+	0.793407i	$0.708305\pi$
$264$		0			0
$265$	2.70820			0.166364
$266$		0			0
$267$		0			0
$268$		0			0
$269$	7.85410	−	24.1724i	0.478873	−	1.47382i	−0.361789	−	0.932260i	$-0.617834\pi$
$269$	7.85410	−	24.1724i	0.478873	−	1.47382i	0.840662	−	0.541560i	$-0.182166\pi$
$270$		0			0
$271$	9.20820	−	6.69015i	0.559359	−	0.406398i	−0.271866	−	0.962335i	$-0.587641\pi$
$271$	9.20820	−	6.69015i	0.559359	−	0.406398i	0.831224	+	0.555937i	$0.187641\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−10.1180	+	11.4984i	−0.610140	+	0.693382i
$276$		0			0
$277$	8.20820	+	25.2623i	0.493183	+	1.51786i	0.819769	+	0.572694i	$0.194102\pi$
$277$	8.20820	+	25.2623i	0.493183	+	1.51786i	−0.326586	+	0.945168i	$0.605898\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	1.29180	−	3.97574i	0.0770621	−	0.237173i	−0.905103	−	0.425192i	$-0.860207\pi$
$281$	1.29180	−	3.97574i	0.0770621	−	0.237173i	0.982165	+	0.188019i	$0.0602067\pi$
$282$		0			0
$283$	5.38197	+	3.91023i	0.319925	+	0.232439i	0.736143	−	0.676826i	$-0.236645\pi$
$283$	5.38197	+	3.91023i	0.319925	+	0.232439i	−0.416219	+	0.909265i	$0.636645\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	19.9443			1.17727
$288$		0			0
$289$	−24.2533	−	17.6210i	−1.42666	−	1.03653i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	17.9894	−	13.0700i	1.05095	−	0.763559i	0.0785567	−	0.996910i	$-0.474969\pi$
$293$	17.9894	−	13.0700i	1.05095	−	0.763559i	0.972393	+	0.233350i	$0.0749688\pi$
$294$		0			0
$295$	−2.44427	−	7.52270i	−0.142311	−	0.437988i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	0.364745	+	1.12257i	0.0210938	+	0.0649199i
$300$		0			0
$301$	−39.3156	+	28.5645i	−2.26611	+	1.64643i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−2.07295	−	1.50609i	−0.118697	−	0.0862382i
$306$		0			0
$307$	10.7426			0.613115			0.306558	−	0.951852i	$-0.400823\pi$
$307$	10.7426			0.613115			0.306558	+	0.951852i	$0.400823\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	10.8992	+	7.91872i	0.618036	+	0.449030i	0.852235	−	0.523159i	$-0.175247\pi$
$311$	10.8992	+	7.91872i	0.618036	+	0.449030i	−0.234199	+	0.972189i	$0.575247\pi$
$312$		0			0
$313$	−5.07295	+	15.6129i	−0.286740	+	0.882495i	0.699132	+	0.714993i	$0.253570\pi$
$313$	−5.07295	+	15.6129i	−0.286740	+	0.882495i	−0.985872	+	0.167502i	$0.946430\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	6.72542	+	20.6987i	0.377737	+	1.16256i	0.941613	+	0.336697i	$0.109310\pi$
$317$	6.72542	+	20.6987i	0.377737	+	1.16256i	−0.563876	+	0.825860i	$0.690690\pi$
$318$		0			0
$319$	3.38197	+	5.70634i	0.189354	+	0.319494i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	0.809017	−	0.587785i	0.0450149	−	0.0327052i
$324$		0			0
$325$	−0.336881	+	1.03681i	−0.0186868	+	0.0575121i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−44.7426			−2.46674
$330$		0			0
$331$	−5.94427			−0.326727			−0.163363	−	0.986566i	$-0.552234\pi$
$331$	−5.94427			−0.326727			−0.163363	+	0.986566i	$0.552234\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	1.26393	−	3.88998i	0.0690560	−	0.212532i
$336$		0			0
$337$	−8.23607	+	5.98385i	−0.448647	+	0.325961i	−0.789061	−	0.614314i	$-0.789433\pi$
$337$	−8.23607	+	5.98385i	−0.448647	+	0.325961i	0.340414	+	0.940276i	$0.389433\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−18.1803	+	4.08174i	−0.984521	+	0.221039i
$342$		0			0
$343$	−5.16312	−	15.8904i	−0.278782	−	0.858003i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	4.47214	−	13.7638i	0.240077	−	0.738881i	−0.756330	−	0.654190i	$-0.773010\pi$
$347$	4.47214	−	13.7638i	0.240077	−	0.738881i	0.996407	−	0.0846908i	$-0.0269902\pi$
$348$		0			0
$349$	−26.4615	−	19.2254i	−1.41645	−	1.02911i	−0.992345	−	0.123500i	$-0.960588\pi$
$349$	−26.4615	−	19.2254i	−1.41645	−	1.02911i	−0.424107	−	0.905612i	$-0.639412\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−15.0557			−0.801336			−0.400668	−	0.916223i	$-0.631222\pi$
$353$	−15.0557			−0.801336			−0.400668	+	0.916223i	$0.631222\pi$
$354$		0			0
$355$	−2.78115	−	2.02063i	−0.147608	−	0.107244i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−3.38197	+	2.45714i	−0.178493	+	0.129683i	−0.673444	−	0.739238i	$-0.735186\pi$
$359$	−3.38197	+	2.45714i	−0.178493	+	0.129683i	0.494951	+	0.868921i	$0.335186\pi$
$360$		0			0
$361$	−5.86475	−	18.0498i	−0.308671	−	0.949991i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	0.437694	+	1.34708i	0.0229100	+	0.0705096i
$366$		0			0
$367$	8.82624	−	6.41264i	0.460726	−	0.334737i	−0.333090	−	0.942895i	$-0.608091\pi$
$367$	8.82624	−	6.41264i	0.460726	−	0.334737i	0.793816	+	0.608158i	$0.208091\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−15.0172	−	10.9106i	−0.779655	−	0.566453i
$372$		0			0
$373$	−4.41641			−0.228673			−0.114336	−	0.993442i	$-0.536474\pi$
$373$	−4.41641			−0.228673			−0.114336	+	0.993442i	$0.536474\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	0.381966	+	0.277515i	0.0196723	+	0.0142927i
$378$		0			0
$379$	−8.10739	+	24.9520i	−0.416449	+	1.28170i	0.494500	+	0.869178i	$0.335351\pi$
$379$	−8.10739	+	24.9520i	−0.416449	+	1.28170i	−0.910949	+	0.412520i	$0.864649\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	1.54508	+	4.75528i	0.0789502	+	0.242984i	0.982740	−	0.184993i	$-0.0592264\pi$
$383$	1.54508	+	4.75528i	0.0789502	+	0.242984i	−0.903790	+	0.427977i	$0.859226\pi$
$384$		0			0
$385$	−8.47214	+	1.90211i	−0.431780	+	0.0969407i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−6.16312	+	4.47777i	−0.312483	+	0.227032i	−0.732961	−	0.680271i	$-0.761862\pi$
$389$	−6.16312	+	4.47777i	−0.312483	+	0.227032i	0.420478	+	0.907303i	$0.361862\pi$
$390$		0			0
$391$	10.5902	−	32.5932i	0.535568	−	1.64831i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−2.90983			−0.146409
$396$		0			0
$397$	10.2361			0.513734			0.256867	−	0.966447i	$-0.417310\pi$
$397$	10.2361			0.513734			0.256867	+	0.966447i	$0.417310\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−3.97214	+	12.2250i	−0.198359	+	0.610486i	0.801562	+	0.597912i	$0.204003\pi$
$401$	−3.97214	+	12.2250i	−0.198359	+	0.610486i	−0.999921	+	0.0125745i	$0.995997\pi$
$402$		0			0
$403$	−1.07295	+	0.779543i	−0.0534474	+	0.0388318i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	3.78115	+	6.37988i	0.187425	+	0.316239i
$408$		0			0
$409$	−1.05573	−	3.24920i	−0.0522024	−	0.160662i	0.921557	−	0.388244i	$-0.126918\pi$
$409$	−1.05573	−	3.24920i	−0.0522024	−	0.160662i	−0.973759	+	0.227581i	$0.926918\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−16.7533	+	51.5613i	−0.824375	+	2.53717i
$414$		0			0
$415$	3.11803	+	2.26538i	0.153058	+	0.111203i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−12.7984			−0.625241			−0.312621	−	0.949878i	$-0.601207\pi$
$419$	−12.7984			−0.625241			−0.312621	+	0.949878i	$0.601207\pi$
$420$		0			0
$421$	19.6803	+	14.2986i	0.959161	+	0.696871i	0.952956	−	0.303109i	$-0.0980248\pi$
$421$	19.6803	+	14.2986i	0.959161	+	0.696871i	0.00620532	+	0.999981i	$0.498025\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	25.6074	−	18.6049i	1.24214	−	0.902468i
$426$		0			0
$427$	5.42705	+	16.7027i	0.262633	+	0.808303i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−2.31966	−	7.13918i	−0.111734	−	0.343882i	0.879518	−	0.475866i	$-0.157865\pi$
$431$	−2.31966	−	7.13918i	−0.111734	−	0.343882i	−0.991252	+	0.131984i	$0.957865\pi$
$432$		0			0
$433$	10.0902	−	7.33094i	0.484903	−	0.352302i	−0.318318	−	0.947984i	$-0.603118\pi$
$433$	10.0902	−	7.33094i	0.484903	−	0.352302i	0.803221	+	0.595682i	$0.203118\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	0.590170	+	0.428784i	0.0282317	+	0.0205115i
$438$		0			0
$439$	−5.47214			−0.261171			−0.130585	−	0.991437i	$-0.541686\pi$
$439$	−5.47214			−0.261171			−0.130585	+	0.991437i	$0.541686\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−5.09017	−	3.69822i	−0.241841	−	0.175708i	0.460262	−	0.887783i	$-0.347755\pi$
$443$	−5.09017	−	3.69822i	−0.241841	−	0.175708i	−0.702103	+	0.712075i	$0.747755\pi$
$444$		0			0
$445$	3.28115	−	10.0984i	0.155542	−	0.478708i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	2.14590	+	6.60440i	0.101271	+	0.311681i	0.988837	−	0.149000i	$-0.0476054\pi$
$449$	2.14590	+	6.60440i	0.101271	+	0.311681i	−0.887566	+	0.460681i	$0.847605\pi$
$450$		0			0
$451$	−10.3156	+	11.7229i	−0.485742	+	0.552012i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.500000	+	0.363271i	−0.0234404	+	0.0170304i
$456$		0			0
$457$	−2.40983	+	7.41669i	−0.112727	+	0.346938i	−0.991466	−	0.130364i	$-0.958385\pi$
$457$	−2.40983	+	7.41669i	−0.112727	+	0.346938i	0.878739	+	0.477302i	$0.158385\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	17.2705			0.804368			0.402184	−	0.915559i	$-0.368251\pi$
$461$	17.2705			0.804368			0.402184	+	0.915559i	$0.368251\pi$
$462$		0			0
$463$	−13.0344			−0.605762			−0.302881	−	0.953028i	$-0.597948\pi$
$463$	−13.0344			−0.605762			−0.302881	+	0.953028i	$0.597948\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	2.39919	−	7.38394i	0.111021	−	0.341688i	−0.880075	−	0.474834i	$-0.842508\pi$
$467$	2.39919	−	7.38394i	0.111021	−	0.341688i	0.991096	+	0.133146i	$0.0425080\pi$
$468$		0			0
$469$	−22.6803	+	16.4782i	−1.04728	+	0.760894i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	3.54508	−	37.8833i	0.163003	−	1.74187i
$474$		0			0
$475$	0.208204	+	0.640786i	0.00955305	+	0.0294013i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	7.79180	−	23.9807i	0.356016	−	1.09571i	−0.599402	−	0.800448i	$-0.704595\pi$
$479$	7.79180	−	23.9807i	0.356016	−	1.09571i	0.955418	−	0.295257i	$-0.0954052\pi$
$480$		0			0
$481$	0.427051	+	0.310271i	0.0194718	+	0.0141471i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	8.67376			0.393855
$486$		0			0
$487$	−7.57295	−	5.50207i	−0.343163	−	0.249323i	0.402832	−	0.915274i	$-0.368026\pi$
$487$	−7.57295	−	5.50207i	−0.343163	−	0.249323i	−0.745995	+	0.665951i	$0.768026\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−9.63525	+	7.00042i	−0.434833	+	0.315925i	−0.783578	−	0.621293i	$-0.786608\pi$
$491$	−9.63525	+	7.00042i	−0.434833	+	0.315925i	0.348746	+	0.937217i	$0.386608\pi$
$492$		0			0
$493$	−4.23607	−	13.0373i	−0.190783	−	0.587169i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	7.28115	+	22.4091i	0.326604	+	1.00518i
$498$		0			0
$499$	−8.82624	+	6.41264i	−0.395117	+	0.287069i	−0.767549	−	0.640990i	$-0.778524\pi$
$499$	−8.82624	+	6.41264i	−0.395117	+	0.287069i	0.372432	+	0.928059i	$0.378524\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−6.70820	−	4.87380i	−0.299104	−	0.217312i	0.428103	−	0.903730i	$-0.359182\pi$
$503$	−6.70820	−	4.87380i	−0.299104	−	0.217312i	−0.727207	+	0.686418i	$0.759182\pi$
$504$		0			0
$505$	7.27051			0.323533
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−13.1631	−	9.56357i	−0.583445	−	0.423898i	0.256519	−	0.966539i	$-0.417424\pi$
$509$	−13.1631	−	9.56357i	−0.583445	−	0.423898i	−0.839964	+	0.542641i	$0.817424\pi$
$510$		0			0
$511$	3.00000	−	9.23305i	0.132712	−	0.408446i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−3.32624	−	10.2371i	−0.146572	−	0.451101i
$516$		0			0
$517$	23.1418	−	26.2991i	1.01778	−	1.15663i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−3.23607	+	2.35114i	−0.141775	+	0.103005i	−0.656412	−	0.754403i	$-0.727927\pi$
$521$	−3.23607	+	2.35114i	−0.141775	+	0.103005i	0.514637	+	0.857408i	$0.327927\pi$
$522$		0			0
$523$	−5.97214	+	18.3803i	−0.261143	+	0.803716i	0.731414	+	0.681934i	$0.238861\pi$
$523$	−5.97214	+	18.3803i	−0.261143	+	0.803716i	−0.992557	+	0.121782i	$0.961139\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	38.5066			1.67737
$528$		0			0
$529$	2.00000			0.0869565
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−0.343459	+	1.05706i	−0.0148769	+	0.0457862i
$534$		0			0
$535$	−7.82624	+	5.68609i	−0.338358	+	0.245831i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	33.3262	+	14.3844i	1.43546	+	0.619578i
$540$		0			0
$541$	2.62868	+	8.09024i	0.113016	+	0.347826i	0.991528	−	0.129893i	$-0.0414635\pi$
$541$	2.62868	+	8.09024i	0.113016	+	0.347826i	−0.878512	+	0.477720i	$0.841463\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	1.70820	−	5.25731i	0.0731714	−	0.225198i
$546$		0			0
$547$	17.1074	+	12.4292i	0.731459	+	0.531436i	0.890025	−	0.455912i	$-0.150687\pi$
$547$	17.1074	+	12.4292i	0.731459	+	0.531436i	−0.158566	+	0.987348i	$0.550687\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	0.291796			0.0124309
$552$		0			0
$553$	16.1353	+	11.7229i	0.686141	+	0.498510i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−16.4443	+	11.9475i	−0.696766	+	0.506230i	−0.878877	−	0.477048i	$-0.841707\pi$
$557$	−16.4443	+	11.9475i	−0.696766	+	0.506230i	0.182111	+	0.983278i	$0.441707\pi$
$558$		0			0
$559$	−0.836881	−	2.57565i	−0.0353963	−	0.108939i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−7.98278	−	24.5685i	−0.336434	−	1.03544i	−0.966011	−	0.258500i	$-0.916772\pi$
$563$	−7.98278	−	24.5685i	−0.336434	−	1.03544i	0.629577	−	0.776938i	$-0.283228\pi$
$564$		0			0
$565$	−4.97214	+	3.61247i	−0.209179	+	0.151978i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	21.1803	+	15.3884i	0.887926	+	0.645116i	0.935336	−	0.353759i	$-0.115097\pi$
$569$	21.1803	+	15.3884i	0.887926	+	0.645116i	−0.0474104	+	0.998875i	$0.515097\pi$
$570$		0			0
$571$	11.3820			0.476320			0.238160	−	0.971226i	$-0.423456\pi$
$571$	11.3820			0.476320			0.238160	+	0.971226i	$0.423456\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	18.6803	+	13.5721i	0.779024	+	0.565994i
$576$		0			0
$577$	8.67376	−	26.6951i	0.361093	−	1.11133i	−0.591298	−	0.806453i	$-0.701384\pi$
$577$	8.67376	−	26.6951i	0.361093	−	1.11133i	0.952391	−	0.304878i	$-0.0986157\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−8.16312	−	25.1235i	−0.338663	−	1.04230i
$582$		0			0
$583$	14.1803	−	3.18368i	0.587290	−	0.131855i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	18.9894	−	13.7966i	0.783775	−	0.569446i	−0.122335	−	0.992489i	$-0.539038\pi$
$587$	18.9894	−	13.7966i	0.783775	−	0.569446i	0.906109	+	0.423043i	$0.139038\pi$
$588$		0			0
$589$	−0.253289	+	0.779543i	−0.0104366	+	0.0321205i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	17.3820			0.713792			0.356896	−	0.934144i	$-0.383835\pi$
$593$	17.3820			0.713792			0.356896	+	0.934144i	$0.383835\pi$
$594$		0			0
$595$	17.9443			0.735643
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−4.20163	+	12.9313i	−0.171674	+	0.528358i	−0.999466	−	0.0326773i	$-0.989597\pi$
$599$	−4.20163	+	12.9313i	−0.171674	+	0.528358i	0.827792	+	0.561035i	$0.189597\pi$
$600$		0			0
$601$	34.6976	−	25.2093i	1.41534	−	1.02831i	0.422825	−	0.906212i	$-0.361039\pi$
$601$	34.6976	−	25.2093i	1.41534	−	1.02831i	0.992518	−	0.122095i	$-0.0389614\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	3.26393	−	5.96361i	0.132698	−	0.242455i
$606$		0			0
$607$	10.9721	+	33.7688i	0.445345	+	1.37063i	0.882105	+	0.471053i	$0.156126\pi$
$607$	10.9721	+	33.7688i	0.445345	+	1.37063i	−0.436759	+	0.899578i	$0.643874\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	0.770510	−	2.37139i	0.0311715	−	0.0959360i
$612$		0			0
$613$	16.7984	+	12.2047i	0.678480	+	0.492945i	0.872853	−	0.487983i	$-0.162267\pi$
$613$	16.7984	+	12.2047i	0.678480	+	0.492945i	−0.194373	+	0.980928i	$0.562267\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−26.7082			−1.07523			−0.537616	−	0.843190i	$-0.680675\pi$
$617$	−26.7082			−1.07523			−0.537616	+	0.843190i	$0.680675\pi$
$618$		0			0
$619$	0.336881	+	0.244758i	0.0135404	+	0.00983767i	0.594535	−	0.804070i	$-0.297336\pi$
$619$	0.336881	+	0.244758i	0.0135404	+	0.00983767i	−0.580994	+	0.813908i	$0.697336\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−58.8779	+	42.7773i	−2.35889	+	1.71384i
$624$		0			0
$625$	6.00000	+	18.4661i	0.240000	+	0.738644i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−4.73607	−	14.5761i	−0.188839	−	0.581188i
$630$		0			0
$631$	34.1074	−	24.7805i	1.35779	−	0.986495i	0.359212	−	0.933256i	$-0.383046\pi$
$631$	34.1074	−	24.7805i	1.35779	−	0.986495i	0.998582	−	0.0532389i	$-0.0169545\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−5.85410	−	4.25325i	−0.232313	−	0.168785i
$636$		0			0
$637$	2.58359			0.102366
$638$		0			0
$639$		0			0
$640$		0			0
$641$	23.8262	+	17.3108i	0.941080	+	0.683735i	0.948680	−	0.316237i	$-0.102419\pi$
$641$	23.8262	+	17.3108i	0.941080	+	0.683735i	−0.00760053	+	0.999971i	$0.502419\pi$
$642$		0			0
$643$	4.06231	−	12.5025i	0.160202	−	0.493050i	−0.838449	−	0.544980i	$-0.816537\pi$
$643$	4.06231	−	12.5025i	0.160202	−	0.493050i	0.998651	+	0.0519299i	$0.0165372\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	0.409830	+	1.26133i	0.0161121	+	0.0495879i	0.958789	−	0.284118i	$-0.0917008\pi$
$647$	0.409830	+	1.26133i	0.0161121	+	0.0495879i	−0.942677	+	0.333706i	$0.891701\pi$
$648$		0			0
$649$	−21.6418	−	36.5159i	−0.849516	−	1.43338i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	20.5451	−	14.9269i	0.803991	−	0.584134i	−0.108091	−	0.994141i	$-0.534474\pi$
$653$	20.5451	−	14.9269i	0.803991	−	0.584134i	0.912082	+	0.410007i	$0.134474\pi$
$654$		0			0
$655$	−1.69098	+	5.20431i	−0.0660722	+	0.203349i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	30.6525			1.19405			0.597025	−	0.802222i	$-0.296349\pi$
$659$	30.6525			1.19405			0.597025	+	0.802222i	$0.296349\pi$
$660$		0			0
$661$	−12.9656			−0.504302			−0.252151	−	0.967688i	$-0.581138\pi$
$661$	−12.9656			−0.504302			−0.252151	+	0.967688i	$0.581138\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−0.118034	+	0.363271i	−0.00457716	+	0.0140871i
$666$		0			0
$667$	8.09017	−	5.87785i	0.313253	−	0.227591i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−12.6246	−	5.44907i	−0.487368	−	0.210359i
$672$		0			0
$673$	−5.57953	−	17.1720i	−0.215075	−	0.661933i	−0.999148	−	0.0412644i	$-0.986861\pi$
$673$	−5.57953	−	17.1720i	−0.215075	−	0.661933i	0.784073	−	0.620668i	$-0.213139\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−11.8197	+	36.3772i	−0.454266	+	1.39809i	0.417728	+	0.908572i	$0.362827\pi$
$677$	−11.8197	+	36.3772i	−0.454266	+	1.39809i	−0.871994	+	0.489516i	$0.837173\pi$
$678$		0			0
$679$	−48.0967	−	34.9443i	−1.84578	−	1.34104i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−0.0557281			−0.00213238			−0.00106619	−	0.999999i	$-0.500339\pi$
$683$	−0.0557281			−0.00213238			−0.00106619	+	0.999999i	$0.500339\pi$
$684$		0			0
$685$	4.88197	+	3.54696i	0.186530	+	0.135522i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	0.836881	−	0.608030i	0.0318826	−	0.0231641i
$690$		0			0
$691$	5.29180	+	16.2865i	0.201309	+	0.619567i	0.999845	+	0.0176188i	$0.00560852\pi$
$691$	5.29180	+	16.2865i	0.201309	+	0.619567i	−0.798535	+	0.601948i	$0.794391\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	1.63525	+	5.03280i	0.0620288	+	0.190905i
$696$		0			0
$697$	26.1074	−	18.9681i	0.988888	−	0.718469i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−31.6246	−	22.9766i	−1.19445	−	0.867815i	−0.200718	−	0.979649i	$-0.564328\pi$
$701$	−31.6246	−	22.9766i	−1.19445	−	0.867815i	−0.993727	+	0.111834i	$0.964328\pi$
$702$		0			0
$703$	0.326238			0.0123043
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−40.3156	−	29.2910i	−1.51622	−	1.10160i
$708$		0			0
$709$	−0.534442	+	1.64484i	−0.0200714	+	0.0617734i	−0.960591	−	0.277967i	$-0.910339\pi$
$709$	−0.534442	+	1.64484i	−0.0200714	+	0.0617734i	0.940519	+	0.339741i	$0.110339\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	8.68034	+	26.7153i	0.325081	+	1.00050i
$714$		0			0
$715$	0.0450850	−	0.481784i	0.00168608	−	0.0180177i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−7.66312	+	5.56758i	−0.285786	+	0.207636i	−0.721437	−	0.692480i	$-0.756518\pi$
$719$	−7.66312	+	5.56758i	−0.285786	+	0.207636i	0.435651	+	0.900116i	$0.356518\pi$
$720$		0			0
$721$	−22.7984	+	70.1662i	−0.849056	+	2.61313i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	9.23607			0.343019
$726$		0			0
$727$	−2.02129			−0.0749654			−0.0374827	−	0.999297i	$-0.511934\pi$
$727$	−2.02129			−0.0749654			−0.0374827	+	0.999297i	$0.511934\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−24.2984	+	74.7827i	−0.898708	+	2.76594i
$732$		0			0
$733$	27.0902	−	19.6822i	1.00060	−	0.726977i	0.0383819	−	0.999263i	$-0.487780\pi$
$733$	27.0902	−	19.6822i	1.00060	−	0.726977i	0.962216	+	0.272286i	$0.0877797\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	2.04508	−	21.8541i	0.0753317	−	0.805004i
$738$		0			0
$739$	−14.3647	−	44.2101i	−0.528416	−	1.62630i	−0.757461	−	0.652880i	$-0.773560\pi$
$739$	−14.3647	−	44.2101i	−0.528416	−	1.62630i	0.229045	−	0.973416i	$-0.426440\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	13.0517	−	40.1689i	0.478819	−	1.47365i	−0.361918	−	0.932210i	$-0.617878\pi$
$743$	13.0517	−	40.1689i	0.478819	−	1.47365i	0.840737	−	0.541444i	$-0.182122\pi$
$744$		0			0
$745$	−8.88197	−	6.45313i	−0.325410	−	0.236424i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	66.3050			2.42273
$750$		0			0
$751$	36.1525	+	26.2663i	1.31922	+	0.958471i	0.999942	+	0.0108112i	$0.00344139\pi$
$751$	36.1525	+	26.2663i	1.31922	+	0.958471i	0.319281	+	0.947660i	$0.396559\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−2.23607	+	1.62460i	−0.0813788	+	0.0591252i
$756$		0			0
$757$	10.6697	+	32.8380i	0.387797	+	1.19352i	0.934431	+	0.356144i	$0.115909\pi$
$757$	10.6697	+	32.8380i	0.387797	+	1.19352i	−0.546634	+	0.837371i	$0.684091\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	1.34346	+	4.13474i	0.0487003	+	0.149884i	0.972449	−	0.233114i	$-0.0748915\pi$
$761$	1.34346	+	4.13474i	0.0487003	+	0.149884i	−0.923749	+	0.382998i	$0.874892\pi$
$762$		0			0
$763$	−30.6525	+	22.2703i	−1.10969	+	0.806240i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−2.44427	−	1.77587i	−0.0882575	−	0.0641229i
$768$		0			0
$769$	−36.9787			−1.33349			−0.666743	−	0.745287i	$-0.732312\pi$
$769$	−36.9787			−1.33349			−0.666743	+	0.745287i	$0.732312\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−15.9894	−	11.6169i	−0.575097	−	0.417833i	0.261856	−	0.965107i	$-0.415665\pi$
$773$	−15.9894	−	11.6169i	−0.575097	−	0.417833i	−0.836953	+	0.547274i	$0.815665\pi$
$774$		0			0
$775$	−8.01722	+	24.6745i	−0.287987	+	0.886333i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	0.212269	+	0.653298i	0.00760533	+	0.0234068i
$780$		0			0
$781$	−16.9377	−	7.31069i	−0.606078	−	0.261597i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−7.85410	+	5.70634i	−0.280325	+	0.203668i
$786$		0			0
$787$	0.708204	−	2.17963i	0.0252447	−	0.0776953i	−0.937640	−	0.347607i	$-0.886994\pi$
$787$	0.708204	−	2.17963i	0.0252447	−	0.0776953i	0.962885	+	0.269911i	$0.0869944\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	42.1246			1.49778
$792$		0			0
$793$	−0.978714			−0.0347551
$794$		0			0
$795$		0			0
$796$		0			0
$797$	9.90983	−	30.4993i	0.351024	−	1.08034i	−0.607255	−	0.794507i	$-0.707729\pi$
$797$	9.90983	−	30.4993i	0.351024	−	1.08034i	0.958279	−	0.285834i	$-0.0922707\pi$
$798$		0			0
$799$	−58.5689	+	42.5528i	−2.07202	+	1.50541i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	3.87539	+	6.53888i	0.136759	+	0.230752i
$804$		0			0
$805$	4.04508	+	12.4495i	0.142571	+	0.438787i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	16.4828	−	50.7288i	0.579504	−	1.78353i	−0.0408003	−	0.999167i	$-0.512991\pi$
$809$	16.4828	−	50.7288i	0.579504	−	1.78353i	0.620304	−	0.784362i	$-0.287009\pi$
$810$		0			0
$811$	−2.69098	−	1.95511i	−0.0944932	−	0.0686533i	0.539535	−	0.841963i	$-0.318600\pi$
$811$	−2.69098	−	1.95511i	−0.0944932	−	0.0686533i	−0.634029	+	0.773310i	$0.718600\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	6.41641			0.224757
$816$		0			0
$817$	−1.35410	−	0.983813i	−0.0473740	−	0.0344192i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−11.4271	+	8.30224i	−0.398807	+	0.289750i	−0.769055	−	0.639183i	$-0.779273\pi$
$821$	−11.4271	+	8.30224i	−0.398807	+	0.289750i	0.370248	+	0.928933i	$0.379273\pi$
$822$		0			0
$823$	−6.83688	−	21.0418i	−0.238319	−	0.733470i	−0.996664	−	0.0816163i	$-0.973992\pi$
$823$	−6.83688	−	21.0418i	−0.238319	−	0.733470i	0.758345	−	0.651853i	$-0.226008\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	5.36068	+	16.4985i	0.186409	+	0.573708i	0.999970	−	0.00777178i	$-0.00247386\pi$
$827$	5.36068	+	16.4985i	0.186409	+	0.573708i	−0.813561	+	0.581480i	$0.802474\pi$
$828$		0			0
$829$	34.3435	−	24.9520i	1.19280	−	0.866618i	0.199241	−	0.979951i	$-0.436153\pi$
$829$	34.3435	−	24.9520i	1.19280	−	0.866618i	0.993557	+	0.113332i	$0.0361525\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−60.6869	−	44.0916i	−2.10268	−	1.52768i
$834$		0			0
$835$	−9.61803			−0.332846
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−36.0795	−	26.2133i	−1.24560	−	0.904984i	−0.247645	−	0.968851i	$-0.579657\pi$
$839$	−36.0795	−	26.2133i	−1.24560	−	0.904984i	−0.997958	+	0.0638668i	$0.979657\pi$
$840$		0			0
$841$	−7.72542	+	23.7764i	−0.266394	+	0.819876i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	2.47214	+	7.60845i	0.0850441	+	0.261739i
$846$		0			0
$847$	−42.1246	+	19.9192i	−1.44742	+	0.684431i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	9.04508	−	6.57164i	0.310062	−	0.225273i
$852$		0			0
$853$	9.69098	−	29.8258i	0.331813	−	1.02122i	−0.636458	−	0.771312i	$-0.719601\pi$
$853$	9.69098	−	29.8258i	0.331813	−	1.02122i	0.968271	−	0.249904i	$-0.0803990\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	6.81966			0.232955			0.116478	−	0.993193i	$-0.462840\pi$
$857$	6.81966			0.232955			0.116478	+	0.993193i	$0.462840\pi$
$858$		0			0
$859$	−17.8754			−0.609900			−0.304950	−	0.952368i	$-0.598640\pi$
$859$	−17.8754			−0.609900			−0.304950	+	0.952368i	$0.598640\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−14.0344	+	43.1936i	−0.477738	+	1.47033i	0.364491	+	0.931207i	$0.381243\pi$
$863$	−14.0344	+	43.1936i	−0.477738	+	1.47033i	−0.842229	+	0.539119i	$0.818757\pi$
$864$		0			0
$865$	−4.83688	+	3.51420i	−0.164459	+	0.119486i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−15.2361	+	3.42071i	−0.516848	+	0.116040i
$870$		0			0
$871$	−0.482779	−	1.48584i	−0.0163583	−	0.0503458i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−7.78115	+	23.9479i	−0.263051	+	0.809588i
$876$		0			0
$877$	−40.7877	−	29.6340i	−1.37730	−	1.00067i	−0.997126	−	0.0757562i	$-0.975863\pi$
$877$	−40.7877	−	29.6340i	−1.37730	−	1.00067i	−0.380177	−	0.924914i	$-0.624137\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	15.5066			0.522430			0.261215	−	0.965281i	$-0.415877\pi$
$881$	15.5066			0.522430			0.261215	+	0.965281i	$0.415877\pi$
$882$		0			0
$883$	−35.7984	−	26.0090i	−1.20471	−	0.875274i	−0.209971	−	0.977708i	$-0.567337\pi$
$883$	−35.7984	−	26.0090i	−1.20471	−	0.875274i	−0.994740	+	0.102434i	$0.967337\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−30.3156	+	22.0256i	−1.01790	+	0.739546i	−0.965851	−	0.259098i	$-0.916575\pi$
$887$	−30.3156	+	22.0256i	−1.01790	+	0.739546i	−0.0520471	+	0.998645i	$0.516575\pi$
$888$		0			0
$889$	15.3262	+	47.1693i	0.514026	+	1.58201i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−0.476201	−	1.46560i	−0.0159355	−	0.0490443i
$894$		0			0
$895$	−0.645898	+	0.469272i	−0.0215900	+	0.0156860i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	9.09017	+	6.60440i	0.303174	+	0.220269i
$900$		0			0
$901$	−30.0344			−1.00059
$902$		0			0
$903$		0			0
$904$		0			0
$905$	2.50000	+	1.81636i	0.0831028	+	0.0603777i
$906$		0			0
$907$	9.04508	−	27.8379i	0.300337	−	0.924343i	−0.681039	−	0.732247i	$-0.738472\pi$
$907$	9.04508	−	27.8379i	0.300337	−	0.924343i	0.981376	−	0.192096i	$-0.0615284\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	10.4549	+	32.1769i	0.346387	+	1.06607i	0.960837	+	0.277113i	$0.0893778\pi$
$911$	10.4549	+	32.1769i	0.346387	+	1.06607i	−0.614450	+	0.788955i	$0.710622\pi$
$912$		0			0
$913$	18.9894	+	8.19624i	0.628456	+	0.271256i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	30.3435	−	22.0458i	1.00203	−	0.728017i
$918$		0			0
$919$	−8.78115	+	27.0256i	−0.289664	+	0.891493i	0.695298	+	0.718721i	$0.255272\pi$
$919$	−8.78115	+	27.0256i	−0.289664	+	0.891493i	−0.984962	+	0.172771i	$0.944728\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−1.31308			−0.0432206
$924$		0			0
$925$	10.3262			0.339525
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−1.16312	+	3.57971i	−0.0381607	+	0.117447i	−0.968322	−	0.249704i	$-0.919667\pi$
$929$	−1.16312	+	3.57971i	−0.0381607	+	0.117447i	0.930161	+	0.367151i	$0.119667\pi$
$930$		0			0
$931$	1.29180	−	0.938545i	0.0423369	−	0.0307596i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−9.28115	+	10.5474i	−0.303526	+	0.344936i
$936$		0			0
$937$	−7.30902	−	22.4948i	−0.238775	−	0.734874i	−0.996598	−	0.0824142i	$-0.973737\pi$
$937$	−7.30902	−	22.4948i	−0.238775	−	0.734874i	0.757823	−	0.652460i	$-0.226263\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	1.82624	−	5.62058i	0.0595337	−	0.183226i	−0.916867	−	0.399193i	$-0.869290\pi$
$941$	1.82624	−	5.62058i	0.0595337	−	0.183226i	0.976401	+	0.215967i	$0.0692904\pi$
$942$		0			0
$943$	19.0451	+	13.8371i	0.620193	+	0.450597i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−31.9230			−1.03736			−0.518679	−	0.854969i	$-0.673576\pi$
$947$	−31.9230			−1.03736			−0.518679	+	0.854969i	$0.673576\pi$
$948$		0			0
$949$	0.437694	+	0.318003i	0.0142082	+	0.0103228i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−30.5967	+	22.2298i	−0.991126	+	0.720095i	−0.960167	−	0.279426i	$-0.909856\pi$
$953$	−30.5967	+	22.2298i	−0.991126	+	0.720095i	−0.0309585	+	0.999521i	$0.509856\pi$
$954$		0			0
$955$	−2.57295	−	7.91872i	−0.0832587	−	0.256244i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−12.7812	−	39.3363i	−0.412725	−	1.27024i
$960$		0			0
$961$	−0.454915	+	0.330515i	−0.0146747	+	0.0106618i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	8.89919	+	6.46564i	0.286475	+	0.208136i
$966$		0			0
$967$	−23.1591			−0.744745			−0.372372	−	0.928083i	$-0.621456\pi$
$967$	−23.1591			−0.744745			−0.372372	+	0.928083i	$0.621456\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−28.7426	−	20.8828i	−0.922395	−	0.670159i	0.0217237	−	0.999764i	$-0.493085\pi$
$971$	−28.7426	−	20.8828i	−0.922395	−	0.670159i	−0.944119	+	0.329605i	$0.893085\pi$
$972$		0			0
$973$	11.2082	−	34.4953i	0.359319	−	1.10587i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	13.3435	+	41.0669i	0.426895	+	1.31385i	0.901168	+	0.433470i	$0.142711\pi$
$977$	13.3435	+	41.0669i	0.426895	+	1.31385i	−0.474273	+	0.880378i	$0.657289\pi$
$978$		0			0
$979$	5.30902	−	56.7329i	0.169677	−	1.81319i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	24.5623	−	17.8456i	0.783416	−	0.569185i	−0.122586	−	0.992458i	$-0.539119\pi$
$983$	24.5623	−	17.8456i	0.783416	−	0.569185i	0.906002	+	0.423273i	$0.139119\pi$
$984$		0			0
$985$	3.69098	−	11.3597i	0.117604	−	0.361949i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−57.3607			−1.82396
$990$		0			0
$991$	39.8541			1.26601			0.633004	−	0.774149i	$-0.281822\pi$
$991$	39.8541			1.26601			0.633004	+	0.774149i	$0.281822\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−0.0106431	+	0.0327561i	−0.000337410	+	0.00103844i
$996$		0			0
$997$	18.9721	−	13.7841i	0.600854	−	0.436546i	−0.245328	−	0.969440i	$-0.578896\pi$
$997$	18.9721	−	13.7841i	0.600854	−	0.436546i	0.846182	+	0.532894i	$0.178896\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	396.2.j.b.181.1		4
3.2	odd	2		132.2.i.a.49.1	✓	4
11.3	even	5		4356.2.a.r.1.1		2
11.8	odd	10		4356.2.a.w.1.1		2
11.9	even	5	inner	396.2.j.b.361.1		4
12.11	even	2		528.2.y.i.49.1		4
33.2	even	10		1452.2.i.g.493.1		4
33.5	odd	10		1452.2.i.c.565.1		4
33.8	even	10		1452.2.a.m.1.2		2
33.14	odd	10		1452.2.a.l.1.2		2
33.17	even	10		1452.2.i.f.565.1		4
33.20	odd	10		132.2.i.a.97.1	yes	4
33.26	odd	10		1452.2.i.c.1213.1		4
33.29	even	10		1452.2.i.f.1213.1		4
33.32	even	2		1452.2.i.g.1237.1		4
132.47	even	10		5808.2.a.bq.1.2		2
132.107	odd	10		5808.2.a.bn.1.2		2
132.119	even	10		528.2.y.i.97.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
132.2.i.a.49.1	✓	4	3.2	odd	2
132.2.i.a.97.1	yes	4	33.20	odd	10
396.2.j.b.181.1		4	1.1	even	1	trivial
396.2.j.b.361.1		4	11.9	even	5	inner
528.2.y.i.49.1		4	12.11	even	2
528.2.y.i.97.1		4	132.119	even	10
1452.2.a.l.1.2		2	33.14	odd	10
1452.2.a.m.1.2		2	33.8	even	10
1452.2.i.c.565.1		4	33.5	odd	10
1452.2.i.c.1213.1		4	33.26	odd	10
1452.2.i.f.565.1		4	33.17	even	10
1452.2.i.f.1213.1		4	33.29	even	10
1452.2.i.g.493.1		4	33.2	even	10
1452.2.i.g.1237.1		4	33.32	even	2
4356.2.a.r.1.1		2	11.3	even	5
4356.2.a.w.1.1		2	11.8	odd	10
5808.2.a.bn.1.2		2	132.107	odd	10
5808.2.a.bq.1.2		2	132.47	even	10

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:	\( N \)	\(=\)	\( 396 = 2^{2} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	396.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.190983 + 0.587785i) q^{5} +(3.42705 - 2.48990i) q^{7} +(-0.309017 + 3.30220i) q^{11} +(0.0729490 + 0.224514i) q^{13} +(2.11803 - 6.51864i) q^{17} +(0.118034 + 0.0857567i) q^{19} +5.00000 q^{23} +(3.73607 + 2.71441i) q^{25} +(1.61803 - 1.17557i) q^{29} +(1.73607 + 5.34307i) q^{31} +(0.809017 + 2.48990i) q^{35} +(1.80902 - 1.31433i) q^{37} +(3.80902 + 2.76741i) q^{41} -11.4721 q^{43} +(-8.54508 - 6.20837i) q^{47} +(3.38197 - 10.4086i) q^{49} +(-1.35410 - 4.16750i) q^{53} +(-1.88197 - 0.812299i) q^{55} +(-10.3541 + 7.52270i) q^{59} +(-1.28115 + 3.94298i) q^{61} -0.145898 q^{65} -6.61803 q^{67} +(-1.71885 + 5.29007i) q^{71} +(1.85410 - 1.34708i) q^{73} +(7.16312 + 12.0862i) q^{77} +(1.45492 + 4.47777i) q^{79} +(1.92705 - 5.93085i) q^{83} +(3.42705 + 2.48990i) q^{85} -17.1803 q^{89} +(0.809017 + 0.587785i) q^{91} +(-0.0729490 + 0.0530006i) q^{95} +(-4.33688 - 13.3475i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{5} + 7 q^{7} + q^{11} + 7 q^{13} + 4 q^{17} - 4 q^{19} + 20 q^{23} + 6 q^{25} + 2 q^{29} - 2 q^{31} + q^{35} + 5 q^{37} + 13 q^{41} - 28 q^{43} - 23 q^{47} + 18 q^{49} + 8 q^{53} - 12 q^{55}+ \cdots - 33 q^{97}+O(q^{100}) \) 4 * q - 3 * q^5 + 7 * q^7 + q^11 + 7 * q^13 + 4 * q^17 - 4 * q^19 + 20 * q^23 + 6 * q^25 + 2 * q^29 - 2 * q^31 + q^35 + 5 * q^37 + 13 * q^41 - 28 * q^43 - 23 * q^47 + 18 * q^49 + 8 * q^53 - 12 * q^55 - 28 * q^59 + 15 * q^61 - 14 * q^65 - 22 * q^67 - 27 * q^71 - 6 * q^73 + 13 * q^77 + 17 * q^79 + q^83 + 7 * q^85 - 24 * q^89 + q^91 - 7 * q^95 - 33 * q^97

Introduction

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