LMFDB - Embedded newform 1584.2.cd.c.161.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1584,2,Mod(17,1584)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1584, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 5, 9]))

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

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

chi := DirichletCharacter("1584.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1584 = 2^{4} \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1584.cd (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$12.6483036802$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 2x^{14} - 16x^{12} - 72x^{10} + 26x^{8} + 360x^{6} + 725x^{4} + 1000x^{2} + 625 $ x^16 + 2x^14 - 16x^12 - 72x^10 + 26x^8 + 360x^6 + 725x^4 + 1000*x^2 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			161.1
Root			$-0.752864 - 0.902863i$ of defining polynomial
Character	$\chi$	$=$	1584.161
Dual form			1584.2.cd.c.305.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.23109 - 3.07083i) q^{5} +(0.349790 - 0.113654i) q^{7} +(2.97756 - 1.46086i) q^{11} +(-0.557375 + 0.767161i) q^{13} +(2.77873 - 2.01886i) q^{17} +(-4.05368 - 1.31712i) q^{19} -4.96800i q^{23} +(-2.90717 + 8.94734i) q^{25} +(-0.767418 - 2.36187i) q^{29} +(2.84281 + 2.06543i) q^{31} +(-1.12943 - 0.820576i) q^{35} +(-2.21947 - 6.83082i) q^{37} +(-0.840249 + 2.58602i) q^{41} +1.88749i q^{43} +(-0.0195991 - 0.00636813i) q^{47} +(-5.55368 + 4.03499i) q^{49} +(-3.25941 + 4.48619i) q^{53} +(-11.1293 - 5.88428i) q^{55} +(-6.29998 + 2.04699i) q^{59} +(-5.73238 - 7.88994i) q^{61} +3.59938 q^{65} -4.46351 q^{67} +(-6.06985 - 8.35443i) q^{71} +(-4.18072 + 1.35840i) q^{73} +(0.875490 - 0.849407i) q^{77} +(-6.42867 + 8.84831i) q^{79} +(-7.42940 + 5.39778i) q^{83} +(-12.3992 - 4.02874i) q^{85} -3.04837i q^{89} +(-0.107774 + 0.331693i) q^{91} +(4.99948 + 15.3868i) q^{95} +(12.2055 + 8.86782i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 32 q^{25} - 16 q^{31} - 12 q^{37} - 24 q^{49} - 16 q^{55} - 96 q^{67} - 20 q^{73} - 100 q^{85} + 72 q^{91} + 60 q^{97}+O(q^{100}) $ 16 * q - 32 * q^25 - 16 * q^31 - 12 * q^37 - 24 * q^49 - 16 * q^55 - 96 * q^67 - 20 * q^73 - 100 * q^85 + 72 * q^91 + 60 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1584\mathbb{Z}\right)^\times$.

$n$	$145$	$353$	$991$	$1189$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$	$1$	$1$

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
$5$	−2.23109	−	3.07083i	−0.997774	−	1.37332i	−0.926681	−	0.375849i	$-0.877351\pi$
$5$	−2.23109	−	3.07083i	−0.997774	−	1.37332i	−0.0710932	−	0.997470i	$-0.522649\pi$
$6$		0			0
$7$	0.349790	−	0.113654i	0.132208	−	0.0429571i	−0.242165	−	0.970235i	$-0.577858\pi$
$7$	0.349790	−	0.113654i	0.132208	−	0.0429571i	0.374374	+	0.927278i	$0.377858\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	2.97756	−	1.46086i	0.897769	−	0.440467i
$11$	2.97756	−	1.46086i	0.897769	−	0.440467i
$12$		0			0
$13$	−0.557375	+	0.767161i	−0.154588	+	0.212772i	−0.879286	−	0.476295i	$-0.841979\pi$
$13$	−0.557375	+	0.767161i	−0.154588	+	0.212772i	0.724698	+	0.689067i	$0.241979\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.77873	−	2.01886i	0.673940	−	0.489646i	−0.197402	−	0.980323i	$-0.563250\pi$
$17$	2.77873	−	2.01886i	0.673940	−	0.489646i	0.871342	+	0.490676i	$0.163250\pi$
$18$		0			0
$19$	−4.05368	−	1.31712i	−0.929979	−	0.302168i	−0.195425	−	0.980719i	$-0.562609\pi$
$19$	−4.05368	−	1.31712i	−0.929979	−	0.302168i	−0.734554	+	0.678550i	$0.762609\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$		−	4.96800i		−	1.03590i	−0.855411	−	0.517950i	$-0.826695\pi$
$23$		−	4.96800i		−	1.03590i	0.855411	−	0.517950i	$-0.173305\pi$
$24$		0			0
$25$	−2.90717	+	8.94734i	−0.581433	+	1.78947i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.767418	−	2.36187i	−0.142506	−	0.438588i	0.854176	−	0.519984i	$-0.174062\pi$
$29$	−0.767418	−	2.36187i	−0.142506	−	0.438588i	−0.996682	+	0.0813958i	$0.974062\pi$
$30$		0			0
$31$	2.84281	+	2.06543i	0.510585	+	0.370961i	0.813045	−	0.582200i	$-0.197808\pi$
$31$	2.84281	+	2.06543i	0.510585	+	0.370961i	−0.302461	+	0.953162i	$0.597808\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−1.12943	−	0.820576i	−0.190908	−	0.138703i
$36$		0			0
$37$	−2.21947	−	6.83082i	−0.364878	−	1.12298i	−0.950057	−	0.312075i	$-0.898976\pi$
$37$	−2.21947	−	6.83082i	−0.364878	−	1.12298i	0.585179	−	0.810904i	$-0.301024\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−0.840249	+	2.58602i	−0.131225	+	0.403869i	−0.994984	−	0.100037i	$-0.968104\pi$
$41$	−0.840249	+	2.58602i	−0.131225	+	0.403869i	0.863759	+	0.503905i	$0.168104\pi$
$42$		0			0
$43$			1.88749i			0.287839i	0.989589	+	0.143919i	$0.0459706\pi$
$43$			1.88749i			0.287839i	−0.989589	+	0.143919i	$0.954029\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.0195991	−	0.00636813i	−0.00285882	−	0.000928888i	0.307587	−	0.951520i	$-0.400478\pi$
$47$	−0.0195991	−	0.00636813i	−0.00285882	−	0.000928888i	−0.310446	+	0.950591i	$0.600478\pi$
$48$		0			0
$49$	−5.55368	+	4.03499i	−0.793383	+	0.576427i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−3.25941	+	4.48619i	−0.447714	+	0.616226i	−0.971905	−	0.235375i	$-0.924368\pi$
$53$	−3.25941	+	4.48619i	−0.447714	+	0.616226i	0.524190	+	0.851601i	$0.324368\pi$
$54$		0			0
$55$	−11.1293	−	5.88428i	−1.50067	−	0.793436i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−6.29998	+	2.04699i	−0.820187	+	0.266495i	−0.688906	−	0.724850i	$-0.741909\pi$
$59$	−6.29998	+	2.04699i	−0.820187	+	0.266495i	−0.131281	+	0.991345i	$0.541909\pi$
$60$		0			0
$61$	−5.73238	−	7.88994i	−0.733956	−	1.01020i	−0.998944	−	0.0459514i	$-0.985368\pi$
$61$	−5.73238	−	7.88994i	−0.733956	−	1.01020i	0.264988	−	0.964252i	$-0.414632\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	3.59938			0.446448
$66$		0			0
$67$	−4.46351			−0.545305			−0.272652	−	0.962113i	$-0.587901\pi$
$67$	−4.46351			−0.545305			−0.272652	+	0.962113i	$0.587901\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−6.06985	−	8.35443i	−0.720359	−	0.991489i	−0.999512	−	0.0312420i	$-0.990054\pi$
$71$	−6.06985	−	8.35443i	−0.720359	−	0.991489i	0.279153	−	0.960247i	$-0.409946\pi$
$72$		0			0
$73$	−4.18072	+	1.35840i	−0.489317	+	0.158989i	−0.543275	−	0.839555i	$-0.682816\pi$
$73$	−4.18072	+	1.35840i	−0.489317	+	0.158989i	0.0539588	+	0.998543i	$0.482816\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.875490	−	0.849407i	0.0997714	−	0.0967989i
$78$		0			0
$79$	−6.42867	+	8.84831i	−0.723282	+	0.995513i	0.276126	+	0.961121i	$0.410949\pi$
$79$	−6.42867	+	8.84831i	−0.723282	+	0.995513i	−0.999408	+	0.0343911i	$0.989051\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−7.42940	+	5.39778i	−0.815483	+	0.592483i	−0.915415	−	0.402511i	$-0.868137\pi$
$83$	−7.42940	+	5.39778i	−0.815483	+	0.592483i	0.0999323	+	0.994994i	$0.468137\pi$
$84$		0			0
$85$	−12.3992	−	4.02874i	−1.34488	−	0.436978i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	3.04837i		−	0.323127i	−0.986862	−	0.161563i	$-0.948346\pi$
$89$		−	3.04837i		−	0.323127i	0.986862	−	0.161563i	$-0.0516536\pi$
$90$		0			0
$91$	−0.107774	+	0.331693i	−0.0112978	+	0.0347709i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	4.99948	+	15.3868i	0.512935	+	1.57865i
$96$		0			0
$97$	12.2055	+	8.86782i	1.23928	+	0.900391i	0.997550	−	0.0699519i	$-0.0222846\pi$
$97$	12.2055	+	8.86782i	1.23928	+	0.900391i	0.241732	+	0.970343i	$0.422285\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−14.1253	−	10.2626i	−1.40552	−	1.02117i	−0.993955	−	0.109787i	$-0.964983\pi$
$101$	−14.1253	−	10.2626i	−1.40552	−	1.02117i	−0.411562	−	0.911382i	$-0.635017\pi$
$102$		0			0
$103$	2.87868	+	8.85967i	0.283645	+	0.872969i	0.986802	+	0.161934i	$0.0517733\pi$
$103$	2.87868	+	8.85967i	0.283645	+	0.872969i	−0.703157	+	0.711035i	$0.748227\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.76675	−	14.6705i	0.460819	−	1.41825i	−0.403347	−	0.915047i	$-0.632153\pi$
$107$	4.76675	−	14.6705i	0.460819	−	1.41825i	0.864166	−	0.503207i	$-0.167847\pi$
$108$		0			0
$109$		−	10.6286i		−	1.01803i	−0.860757	−	0.509016i	$-0.830009\pi$
$109$		−	10.6286i		−	1.01803i	0.860757	−	0.509016i	$-0.169991\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.995774	−	0.323547i	−0.0936746	−	0.0304367i	0.261805	−	0.965121i	$-0.415682\pi$
$113$	−0.995774	−	0.323547i	−0.0936746	−	0.0304367i	−0.355479	+	0.934684i	$0.615682\pi$
$114$		0			0
$115$	−15.2559	+	11.0841i	−1.42262	+	1.03359i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	0.742521	−	1.02199i	0.0680668	−	0.0936859i
$120$		0			0
$121$	6.73176	−	8.69962i	0.611978	−	0.790875i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	15.9120	−	5.17013i	1.42321	−	0.462430i
$126$		0			0
$127$	−10.3127	−	14.1942i	−0.915101	−	1.25953i	−0.965394	−	0.260794i	$-0.916016\pi$
$127$	−10.3127	−	14.1942i	−0.915101	−	1.25953i	0.0502930	−	0.998735i	$-0.483984\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	13.8890			1.21349			0.606744	−	0.794897i	$-0.292475\pi$
$131$	13.8890			1.21349			0.606744	+	0.794897i	$0.292475\pi$
$132$		0			0
$133$	−1.56764			−0.135931
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−0.609963	−	0.839541i	−0.0521126	−	0.0717269i	0.782165	−	0.623071i	$-0.214115\pi$
$137$	−0.609963	−	0.839541i	−0.0521126	−	0.0717269i	−0.834278	+	0.551344i	$0.814115\pi$
$138$		0			0
$139$	18.8643	−	6.12938i	1.60005	−	0.519887i	0.632928	−	0.774210i	$-0.281853\pi$
$139$	18.8643	−	6.12938i	1.60005	−	0.519887i	0.967119	+	0.254324i	$0.0818528\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.538902	+	3.09852i	−0.0450652	+	0.259111i
$144$		0			0
$145$	−5.54073	+	7.62616i	−0.460133	+	0.633318i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	6.50125	−	4.72344i	0.532603	−	0.386959i	−0.288727	−	0.957411i	$-0.593232\pi$
$149$	6.50125	−	4.72344i	0.532603	−	0.386959i	0.821331	+	0.570452i	$0.193232\pi$
$150$		0			0
$151$	9.58050	+	3.11289i	0.779650	+	0.253324i	0.671691	−	0.740832i	$-0.265568\pi$
$151$	9.58050	+	3.11289i	0.779650	+	0.253324i	0.107959	+	0.994155i	$0.465568\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		−	13.3380i		−	1.07133i
$156$		0			0
$157$	−5.00062	+	15.3903i	−0.399093	+	1.22828i	0.526635	+	0.850091i	$0.323453\pi$
$157$	−5.00062	+	15.3903i	−0.399093	+	1.22828i	−0.925728	+	0.378190i	$0.876547\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−0.564633	−	1.73776i	−0.0444993	−	0.136955i
$162$		0			0
$163$	3.45923	+	2.51328i	0.270948	+	0.196855i	0.714959	−	0.699166i	$-0.246445\pi$
$163$	3.45923	+	2.51328i	0.270948	+	0.196855i	−0.444012	+	0.896021i	$0.646445\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−14.8478	−	10.7875i	−1.14896	−	0.834765i	−0.160614	−	0.987017i	$-0.551347\pi$
$167$	−14.8478	−	10.7875i	−1.14896	−	0.834765i	−0.988342	+	0.152252i	$0.951347\pi$
$168$		0			0
$169$	3.73935	+	11.5085i	0.287642	+	0.885272i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1.91046	−	5.87980i	0.145250	−	0.447033i	−0.851793	−	0.523878i	$-0.824485\pi$
$173$	1.91046	−	5.87980i	0.145250	−	0.447033i	0.997043	+	0.0768452i	$0.0244847\pi$
$174$		0			0
$175$			3.46010i			0.261559i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−8.77414	−	2.85089i	−0.655810	−	0.213086i	−0.0378357	−	0.999284i	$-0.512046\pi$
$179$	−8.77414	−	2.85089i	−0.655810	−	0.213086i	−0.617974	+	0.786198i	$0.712046\pi$
$180$		0			0
$181$	3.38790	−	2.46145i	0.251821	−	0.182958i	−0.454713	−	0.890638i	$-0.650258\pi$
$181$	3.38790	−	2.46145i	0.251821	−	0.182958i	0.706533	+	0.707680i	$0.250258\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−16.0245	+	22.0558i	−1.17814	+	1.62157i
$186$		0			0
$187$	5.32455	−	10.0706i	0.389370	−	0.736438i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	19.1951	−	6.23688i	1.38891	−	0.451285i	0.483323	−	0.875442i	$-0.339430\pi$
$191$	19.1951	−	6.23688i	1.38891	−	0.451285i	0.905589	+	0.424157i	$0.139430\pi$
$192$		0			0
$193$	4.71049	+	6.48343i	0.339068	+	0.466687i	0.944169	−	0.329462i	$-0.106867\pi$
$193$	4.71049	+	6.48343i	0.339068	+	0.466687i	−0.605101	+	0.796149i	$0.706867\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	21.1710			1.50837			0.754187	−	0.656659i	$-0.228031\pi$
$197$	21.1710			1.50837			0.754187	+	0.656659i	$0.228031\pi$
$198$		0			0
$199$	10.5160			0.745457			0.372729	−	0.927940i	$-0.378422\pi$
$199$	10.5160			0.745457			0.372729	+	0.927940i	$0.378422\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−0.536871	−	0.738940i	−0.0376810	−	0.0518634i
$204$		0			0
$205$	9.81591	−	3.18938i	0.685573	−	0.222756i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−13.9942	+	2.00007i	−0.968001	+	0.138347i
$210$		0			0
$211$	2.17376	−	2.99193i	0.149648	−	0.205973i	−0.727611	−	0.685990i	$-0.759369\pi$
$211$	2.17376	−	2.99193i	0.149648	−	0.205973i	0.877259	+	0.480017i	$0.159369\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	5.79615	−	4.21115i	0.395294	−	0.287198i
$216$		0			0
$217$	1.22913	+	0.399369i	0.0834390	+	0.0271110i
$218$		0			0
$219$		0			0
$220$		0			0
$221$			3.25699i			0.219089i
$222$		0			0
$223$	5.53051	−	17.0212i	0.370351	−	1.13982i	−0.576212	−	0.817301i	$-0.695470\pi$
$223$	5.53051	−	17.0212i	0.370351	−	1.13982i	0.946562	−	0.322521i	$-0.104530\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	5.37022	+	16.5278i	0.356434	+	1.09699i	0.955173	+	0.296047i	$0.0956684\pi$
$227$	5.37022	+	16.5278i	0.356434	+	1.09699i	−0.598740	+	0.800944i	$0.704332\pi$
$228$		0			0
$229$	−3.45989	−	2.51375i	−0.228636	−	0.166114i	0.467570	−	0.883956i	$-0.345130\pi$
$229$	−3.45989	−	2.51375i	−0.228636	−	0.166114i	−0.696205	+	0.717843i	$0.745130\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−18.9171	−	13.7441i	−1.23930	−	0.900404i	−0.241748	−	0.970339i	$-0.577721\pi$
$233$	−18.9171	−	13.7441i	−1.23930	−	0.900404i	−0.997552	+	0.0699355i	$0.977721\pi$
$234$		0			0
$235$	0.0241719	+	0.0743935i	0.00157680	+	0.00485289i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−6.17902	+	19.0171i	−0.399687	+	1.23011i	0.525563	+	0.850754i	$0.323855\pi$
$239$	−6.17902	+	19.0171i	−0.399687	+	1.23011i	−0.925251	+	0.379356i	$0.876145\pi$
$240$		0			0
$241$		−	2.32570i		−	0.149811i	−0.997191	−	0.0749057i	$-0.976134\pi$
$241$		−	2.32570i		−	0.149811i	0.997191	−	0.0749057i	$-0.0238656\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	24.7815	+	8.05201i	1.58323	+	0.514424i
$246$		0			0
$247$	3.26987	−	2.37570i	0.208057	−	0.151162i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−1.88681	+	2.59698i	−0.119095	+	0.163920i	−0.864402	−	0.502801i	$-0.832303\pi$
$251$	−1.88681	+	2.59698i	−0.119095	+	0.163920i	0.745307	+	0.666721i	$0.232303\pi$
$252$		0			0
$253$	−7.25758	−	14.7925i	−0.456280	−	0.929999i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−17.1597	+	5.57552i	−1.07039	+	0.347792i	−0.790641	−	0.612281i	$-0.790252\pi$
$257$	−17.1597	+	5.57552i	−1.07039	+	0.347792i	−0.279752	+	0.960072i	$0.590252\pi$
$258$		0			0
$259$	−1.55270	−	2.13710i	−0.0964798	−	0.132793i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−2.05966			−0.127004			−0.0635019	−	0.997982i	$-0.520227\pi$
$263$	−2.05966			−0.127004			−0.0635019	+	0.997982i	$0.520227\pi$
$264$		0			0
$265$	21.0484			1.29299
$266$		0			0
$267$		0			0
$268$		0			0
$269$	1.69280	+	2.32994i	0.103212	+	0.142059i	0.857499	−	0.514486i	$-0.172017\pi$
$269$	1.69280	+	2.32994i	0.103212	+	0.142059i	−0.754287	+	0.656545i	$0.772017\pi$
$270$		0			0
$271$	−9.67272	+	3.14286i	−0.587576	+	0.190915i	−0.587692	−	0.809085i	$-0.699963\pi$
$271$	−9.67272	+	3.14286i	−0.587576	+	0.190915i	0.000115761		1.00000i	$0.499963\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	4.41457	+	30.8882i	0.266208	+	1.86263i
$276$		0			0
$277$	4.29714	−	5.91450i	0.258190	−	0.355368i	−0.660169	−	0.751117i	$-0.729515\pi$
$277$	4.29714	−	5.91450i	0.258190	−	0.355368i	0.918358	+	0.395750i	$0.129515\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−1.86513	+	1.35510i	−0.111264	+	0.0808384i	−0.642026	−	0.766683i	$-0.721906\pi$
$281$	−1.86513	+	1.35510i	−0.111264	+	0.0808384i	0.530762	+	0.847521i	$0.321906\pi$
$282$		0			0
$283$	−23.2370	−	7.55016i	−1.38130	−	0.448810i	−0.478200	−	0.878251i	$-0.658711\pi$
$283$	−23.2370	−	7.55016i	−1.38130	−	0.448810i	−0.903095	+	0.429441i	$0.858711\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			1.00006i			0.0590318i
$288$		0			0
$289$	−1.60777	+	4.94822i	−0.0945749	+	0.291072i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	3.29456	+	10.1396i	0.192470	+	0.592362i	0.999997	+	0.00253112i	$0.000805683\pi$
$293$	3.29456	+	10.1396i	0.192470	+	0.592362i	−0.807527	+	0.589831i	$0.799194\pi$
$294$		0			0
$295$	20.3418	+	14.7792i	1.18434	+	0.860476i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	3.81126	+	2.76904i	0.220411	+	0.160138i
$300$		0			0
$301$	0.214520	+	0.660224i	0.0123647	+	0.0380547i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−11.4392	+	35.2063i	−0.655009	+	2.01591i
$306$		0			0
$307$			4.56848i			0.260737i	0.991466	+	0.130369i	$0.0416160\pi$
$307$			4.56848i			0.260737i	−0.991466	+	0.130369i	$0.958384\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	8.92302	+	2.89926i	0.505978	+	0.164402i	0.550872	−	0.834590i	$-0.314295\pi$
$311$	8.92302	+	2.89926i	0.505978	+	0.164402i	−0.0448944	+	0.998992i	$0.514295\pi$
$312$		0			0
$313$	4.05804	−	2.94834i	0.229374	−	0.166650i	−0.467162	−	0.884172i	$-0.654724\pi$
$313$	4.05804	−	2.94834i	0.229374	−	0.166650i	0.696536	+	0.717522i	$0.254724\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	6.86310	−	9.44624i	0.385470	−	0.530554i	−0.571553	−	0.820565i	$-0.693659\pi$
$317$	6.86310	−	9.44624i	0.385470	−	0.530554i	0.957023	+	0.290011i	$0.0936590\pi$
$318$		0			0
$319$	−5.73541	−	5.91153i	−0.321121	−	0.330982i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−13.9232	+	4.52391i	−0.774706	+	0.251717i
$324$		0			0
$325$	−5.24366	−	7.21728i	−0.290866	−	0.400343i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−0.00757934			−0.000417863
$330$		0			0
$331$	29.0516			1.59682			0.798411	−	0.602113i	$-0.205674\pi$
$331$	29.0516			1.59682			0.798411	+	0.602113i	$0.205674\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	9.95850	+	13.7067i	0.544091	+	0.748877i
$336$		0			0
$337$	27.4668	−	8.92451i	1.49621	−	0.486149i	0.557302	−	0.830310i	$-0.311837\pi$
$337$	27.4668	−	8.92451i	1.49621	−	0.486149i	0.938911	+	0.344161i	$0.111837\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	11.4820	+	1.99697i	0.621783	+	0.108142i
$342$		0			0
$343$	−2.99731	+	4.12544i	−0.161840	+	0.222753i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−17.9141	+	13.0153i	−0.961678	+	0.698700i	−0.953540	−	0.301267i	$-0.902590\pi$
$347$	−17.9141	+	13.0153i	−0.961678	+	0.698700i	−0.00813801	+	0.999967i	$0.502590\pi$
$348$		0			0
$349$	−14.8959	−	4.83997i	−0.797359	−	0.259078i	−0.118125	−	0.992999i	$-0.537688\pi$
$349$	−14.8959	−	4.83997i	−0.797359	−	0.259078i	−0.679235	+	0.733921i	$0.737688\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$		−	11.1636i		−	0.594180i	−0.954850	−	0.297090i	$-0.903984\pi$
$353$		−	11.1636i		−	0.594180i	0.954850	−	0.297090i	$-0.0960161\pi$
$354$		0			0
$355$	−12.1127	+	37.2790i	−0.642874	+	1.97856i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−5.11867	−	15.7536i	−0.270153	−	0.831445i	−0.990461	−	0.137791i	$-0.956000\pi$
$359$	−5.11867	−	15.7536i	−0.270153	−	0.831445i	0.720308	−	0.693654i	$-0.244000\pi$
$360$		0			0
$361$	−0.673787	−	0.489535i	−0.0354625	−	0.0257650i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	13.4990	+	9.80759i	0.706569	+	0.513353i
$366$		0			0
$367$	−3.03154	−	9.33012i	−0.158245	−	0.487028i	0.840230	−	0.542230i	$-0.182420\pi$
$367$	−3.03154	−	9.33012i	−0.158245	−	0.487028i	−0.998475	+	0.0552016i	$0.982420\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.630238	+	1.93967i	−0.0327203	+	0.100703i
$372$		0			0
$373$			12.6350i			0.654216i	0.944987	+	0.327108i	$0.106074\pi$
$373$			12.6350i			0.654216i	−0.944987	+	0.327108i	$0.893926\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	2.23967	+	0.727714i	0.115349	+	0.0374792i
$378$		0			0
$379$	28.3981	−	20.6325i	1.45871	−	1.05982i	0.475019	−	0.879975i	$-0.342441\pi$
$379$	28.3981	−	20.6325i	1.45871	−	1.05982i	0.983695	−	0.179843i	$-0.0575589\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−13.2760	+	18.2729i	−0.678374	+	0.933701i	−0.999913	−	0.0131951i	$-0.995800\pi$
$383$	−13.2760	+	18.2729i	−0.678374	+	0.933701i	0.321539	+	0.946896i	$0.395800\pi$
$384$		0			0
$385$	−4.56169	−	0.793379i	−0.232485	−	0.0404344i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	6.99867	−	2.27401i	0.354847	−	0.115297i	−0.126169	−	0.992009i	$-0.540268\pi$
$389$	6.99867	−	2.27401i	0.354847	−	0.115297i	0.481015	+	0.876712i	$0.340268\pi$
$390$		0			0
$391$	−10.0297	−	13.8047i	−0.507225	−	0.698135i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	41.5146			2.08883
$396$		0			0
$397$	16.7327			0.839790			0.419895	−	0.907573i	$-0.362067\pi$
$397$	16.7327			0.839790			0.419895	+	0.907573i	$0.362067\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−2.98209	−	4.10449i	−0.148918	−	0.204968i	0.728040	−	0.685534i	$-0.240431\pi$
$401$	−2.98209	−	4.10449i	−0.148918	−	0.204968i	−0.876959	+	0.480566i	$0.840431\pi$
$402$		0			0
$403$	−3.16903	+	1.02968i	−0.157860	+	0.0512920i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−16.5875	−	17.0968i	−0.822211	−	0.847459i
$408$		0			0
$409$	19.0135	−	26.1698i	0.940156	−	1.29401i	−0.0156071	−	0.999878i	$-0.504968\pi$
$409$	19.0135	−	26.1698i	0.940156	−	1.29401i	0.955764	−	0.294136i	$-0.0950319\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−1.97102	+	1.43203i	−0.0969877	+	0.0704657i
$414$		0			0
$415$	33.1513	+	10.7715i	1.62734	+	0.528753i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		−	27.9075i		−	1.36337i	−0.731645	−	0.681686i	$-0.761247\pi$
$419$		−	27.9075i		−	1.36337i	0.731645	−	0.681686i	$-0.238753\pi$
$420$		0			0
$421$	8.25960	−	25.4204i	0.402549	−	1.23892i	−0.520376	−	0.853937i	$-0.674208\pi$
$421$	8.25960	−	25.4204i	0.402549	−	1.23892i	0.922925	−	0.384980i	$-0.125792\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	9.98523	+	30.7314i	0.484355	+	1.49069i
$426$		0			0
$427$	−2.90185	−	2.10832i	−0.140430	−	0.102029i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	0.579760	+	0.421220i	0.0279260	+	0.0202895i	0.601661	−	0.798752i	$-0.294506\pi$
$431$	0.579760	+	0.421220i	0.0279260	+	0.0202895i	−0.573735	+	0.819041i	$0.694506\pi$
$432$		0			0
$433$	3.53281	+	10.8729i	0.169776	+	0.522517i	0.999356	−	0.0358703i	$-0.0114203\pi$
$433$	3.53281	+	10.8729i	0.169776	+	0.522517i	−0.829580	+	0.558387i	$0.811420\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−6.54346	+	20.1387i	−0.313016	+	0.963365i
$438$		0			0
$439$			8.57525i			0.409274i	0.978838	+	0.204637i	$0.0656015\pi$
$439$			8.57525i			0.409274i	−0.978838	+	0.204637i	$0.934399\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−13.2928	−	4.31910i	−0.631561	−	0.205207i	−0.0242947	−	0.999705i	$-0.507734\pi$
$443$	−13.2928	−	4.31910i	−0.631561	−	0.205207i	−0.607267	+	0.794498i	$0.707734\pi$
$444$		0			0
$445$	−9.36104	+	6.80119i	−0.443756	+	0.322407i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	12.7008	−	17.4811i	0.599388	−	0.824986i	−0.396264	−	0.918136i	$-0.629694\pi$
$449$	12.7008	−	17.4811i	0.599388	−	0.824986i	0.995652	+	0.0931501i	$0.0296936\pi$
$450$		0			0
$451$	1.27593	+	8.92753i	0.0600811	+	0.420381i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	1.25903	−	0.409083i	0.0590241	−	0.0191781i
$456$		0			0
$457$	5.76327	+	7.93246i	0.269594	+	0.371065i	0.922253	−	0.386587i	$-0.126346\pi$
$457$	5.76327	+	7.93246i	0.269594	+	0.371065i	−0.652658	+	0.757652i	$0.726346\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−12.3585			−0.575595			−0.287797	−	0.957691i	$-0.592923\pi$
$461$	−12.3585			−0.575595			−0.287797	+	0.957691i	$0.592923\pi$
$462$		0			0
$463$	33.8717			1.57415			0.787076	−	0.616856i	$-0.211594\pi$
$463$	33.8717			1.57415			0.787076	+	0.616856i	$0.211594\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−9.24994	−	12.7315i	−0.428036	−	0.589142i	0.539465	−	0.842008i	$-0.318627\pi$
$467$	−9.24994	−	12.7315i	−0.428036	−	0.589142i	−0.967501	+	0.252867i	$0.918627\pi$
$468$		0			0
$469$	−1.56129	+	0.507295i	−0.0720939	+	0.0234247i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	2.75736	+	5.62011i	0.126783	+	0.258413i
$474$		0			0
$475$	23.5695	−	32.4406i	1.08144	−	1.48848i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−10.0877	+	7.32913i	−0.460918	+	0.334877i	−0.793891	−	0.608060i	$-0.791948\pi$
$479$	−10.0877	+	7.32913i	−0.460918	+	0.334877i	0.332973	+	0.942936i	$0.391948\pi$
$480$		0			0
$481$	6.47741	+	2.10464i	0.295344	+	0.0959632i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		−	57.2660i		−	2.60032i
$486$		0			0
$487$	2.14955	−	6.61563i	0.0974054	−	0.299783i	−0.890468	−	0.455046i	$-0.849623\pi$
$487$	2.14955	−	6.61563i	0.0974054	−	0.299783i	0.987873	+	0.155263i	$0.0496227\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−0.0932984	−	0.287143i	−0.00421050	−	0.0129586i	0.948929	−	0.315489i	$-0.102169\pi$
$491$	−0.0932984	−	0.287143i	−0.00421050	−	0.0129586i	−0.953140	+	0.302531i	$0.902169\pi$
$492$		0			0
$493$	−6.90074	−	5.01368i	−0.310794	−	0.225805i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−3.07269	−	2.23244i	−0.137829	−	0.100139i
$498$		0			0
$499$	−2.04468	−	6.29287i	−0.0915323	−	0.281707i	0.894802	−	0.446463i	$-0.147317\pi$
$499$	−2.04468	−	6.29287i	−0.0915323	−	0.281707i	−0.986334	+	0.164755i	$0.947317\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	3.19188	−	9.82361i	0.142319	−	0.438013i	−0.854337	−	0.519719i	$-0.826037\pi$
$503$	3.19188	−	9.82361i	0.142319	−	0.438013i	0.996657	+	0.0817056i	$0.0260367\pi$
$504$		0			0
$505$			66.2732i			2.94912i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	19.3302	+	6.28078i	0.856798	+	0.278390i	0.704291	−	0.709912i	$-0.251265\pi$
$509$	19.3302	+	6.28078i	0.856798	+	0.278390i	0.152507	+	0.988302i	$0.451265\pi$
$510$		0			0
$511$	−1.30799	+	0.950310i	−0.0578621	+	0.0420392i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	20.7840	−	28.6067i	0.915851	−	1.26056i
$516$		0			0
$517$	−0.0676605	+	0.00967009i	−0.00297571	+	0.000425290i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	11.4110	−	3.70764i	0.499923	−	0.162435i	−0.0481915	−	0.998838i	$-0.515346\pi$
$521$	11.4110	−	3.70764i	0.499923	−	0.162435i	0.548115	+	0.836403i	$0.315346\pi$
$522$		0			0
$523$	22.2395	+	30.6101i	0.972466	+	1.33848i	0.940791	+	0.338986i	$0.110084\pi$
$523$	22.2395	+	30.6101i	0.972466	+	1.33848i	0.0316743	+	0.999498i	$0.489916\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	12.0692			0.525743
$528$		0			0
$529$	−1.68106			−0.0730898
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−1.51556	−	2.08599i	−0.0656462	−	0.0903542i
$534$		0			0
$535$	−55.6858	+	18.0934i	−2.40751	+	0.782247i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−10.6419	+	20.1276i	−0.458378	+	0.866957i
$540$		0			0
$541$	21.6491	−	29.7975i	0.930769	−	1.28109i	−0.0287904	−	0.999585i	$-0.509166\pi$
$541$	21.6491	−	29.7975i	0.930769	−	1.28109i	0.959559	−	0.281508i	$-0.0908345\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−32.6386	+	23.7133i	−1.39808	+	1.01577i
$546$		0			0
$547$	−34.8795	−	11.3330i	−1.49134	−	0.484565i	−0.553860	−	0.832610i	$-0.686846\pi$
$547$	−34.8795	−	11.3330i	−1.49134	−	0.484565i	−0.937478	+	0.348044i	$0.886846\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$			10.5851i			0.450939i
$552$		0			0
$553$	−1.24304	+	3.82570i	−0.0528596	+	0.162685i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−2.30765	−	7.10223i	−0.0977784	−	0.300931i	0.890189	−	0.455591i	$-0.150572\pi$
$557$	−2.30765	−	7.10223i	−0.0977784	−	0.300931i	−0.987968	+	0.154660i	$0.950572\pi$
$558$		0			0
$559$	−1.44800	−	1.05204i	−0.0612441	−	0.0444964i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−3.16715	−	2.30107i	−0.133479	−	0.0969784i	0.519042	−	0.854749i	$-0.326289\pi$
$563$	−3.16715	−	2.30107i	−0.133479	−	0.0969784i	−0.652521	+	0.757770i	$0.726289\pi$
$564$		0			0
$565$	1.22811	+	3.77972i	0.0516668	+	0.159014i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	11.6410	−	35.8274i	0.488017	−	1.50196i	−0.339546	−	0.940590i	$-0.610273\pi$
$569$	11.6410	−	35.8274i	0.488017	−	1.50196i	0.827563	−	0.561373i	$-0.189727\pi$
$570$		0			0
$571$		−	30.3411i		−	1.26974i	−0.772621	−	0.634868i	$-0.781054\pi$
$571$		−	30.3411i		−	1.26974i	0.772621	−	0.634868i	$-0.218946\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	44.4504	+	14.4428i	1.85371	+	0.602307i
$576$		0			0
$577$	2.68563	−	1.95122i	0.111804	−	0.0812305i	−0.530478	−	0.847699i	$-0.677988\pi$
$577$	2.68563	−	1.95122i	0.111804	−	0.0812305i	0.642282	+	0.766468i	$0.277988\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−1.98526	+	2.73247i	−0.0823623	+	0.113362i
$582$		0			0
$583$	−3.15138	+	18.1195i	−0.130517	+	0.750432i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	38.9053	−	12.6411i	1.60579	−	0.521754i	0.637263	−	0.770647i	$-0.280067\pi$
$587$	38.9053	−	12.6411i	1.60579	−	0.521754i	0.968531	+	0.248893i	$0.0800666\pi$
$588$		0			0
$589$	−8.80345	−	12.1169i	−0.362740	−	0.499269i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	4.62924			0.190100			0.0950500	−	0.995472i	$-0.469699\pi$
$593$	4.62924			0.190100			0.0950500	+	0.995472i	$0.469699\pi$
$594$		0			0
$595$	−4.79500			−0.196576
$596$		0			0
$597$		0			0
$598$		0			0
$599$	17.9738	+	24.7388i	0.734390	+	1.01080i	0.998922	+	0.0464237i	$0.0147824\pi$
$599$	17.9738	+	24.7388i	0.734390	+	1.01080i	−0.264532	+	0.964377i	$0.585218\pi$
$600$		0			0
$601$	−29.7015	+	9.65061i	−1.21155	+	0.393657i	−0.843998	−	0.536346i	$-0.819804\pi$
$601$	−29.7015	+	9.65061i	−1.21155	+	0.393657i	−0.367552	+	0.930003i	$0.619804\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−41.7343	−	1.26245i	−1.69674	−	0.0513259i
$606$		0			0
$607$	18.0842	−	24.8908i	0.734016	−	1.01029i	−0.264925	−	0.964269i	$-0.585347\pi$
$607$	18.0842	−	24.8908i	0.734016	−	1.01029i	0.998941	−	0.0460167i	$-0.0146527\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	0.0158094	−	0.0114862i	0.000639581	−	0.000464683i
$612$		0			0
$613$	24.2244	+	7.87097i	0.978413	+	0.317906i	0.754207	−	0.656636i	$-0.228021\pi$
$613$	24.2244	+	7.87097i	0.978413	+	0.317906i	0.224205	+	0.974542i	$0.428021\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			4.20930i			0.169460i	0.996404	+	0.0847300i	$0.0270028\pi$
$617$			4.20930i			0.169460i	−0.996404	+	0.0847300i	$0.972997\pi$
$618$		0			0
$619$	−11.8981	+	36.6187i	−0.478227	+	1.47183i	0.363329	+	0.931661i	$0.381640\pi$
$619$	−11.8981	+	36.6187i	−0.478227	+	1.47183i	−0.841556	+	0.540170i	$0.818360\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−0.346459	−	1.06629i	−0.0138806	−	0.0427200i
$624$		0			0
$625$	−13.3225	−	9.67935i	−0.532899	−	0.387174i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−19.9578	−	14.5002i	−0.795769	−	0.578160i
$630$		0			0
$631$	3.65655	+	11.2537i	0.145565	+	0.448003i	0.997083	−	0.0763220i	$-0.0243177\pi$
$631$	3.65655	+	11.2537i	0.145565	+	0.448003i	−0.851518	+	0.524325i	$0.824318\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−20.5794	+	63.3370i	−0.816670	+	2.51345i
$636$		0			0
$637$		−	6.50957i		−	0.257918i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	34.1810	+	11.1061i	1.35007	+	0.438664i	0.892716	−	0.450620i	$-0.148797\pi$
$641$	34.1810	+	11.1061i	1.35007	+	0.438664i	0.457354	+	0.889285i	$0.348797\pi$
$642$		0			0
$643$	2.63357	−	1.91340i	0.103858	−	0.0754571i	−0.534644	−	0.845077i	$-0.679554\pi$
$643$	2.63357	−	1.91340i	0.103858	−	0.0754571i	0.638502	+	0.769620i	$0.279554\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−7.14454	+	9.83361i	−0.280881	+	0.386599i	−0.926025	−	0.377461i	$-0.876797\pi$
$647$	−7.14454	+	9.83361i	−0.280881	+	0.386599i	0.645145	+	0.764060i	$0.276797\pi$
$648$		0			0
$649$	−15.7682	+	15.2984i	−0.618956	+	0.600516i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−24.2713	+	7.88623i	−0.949811	+	0.308612i	−0.742639	−	0.669692i	$-0.766426\pi$
$653$	−24.2713	+	7.88623i	−0.949811	+	0.308612i	−0.207172	+	0.978305i	$0.566426\pi$
$654$		0			0
$655$	−30.9877	−	42.6508i	−1.21079	−	1.66651i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−27.9441			−1.08855			−0.544273	−	0.838908i	$-0.683194\pi$
$659$	−27.9441			−1.08855			−0.544273	+	0.838908i	$0.683194\pi$
$660$		0			0
$661$	−27.3798			−1.06495			−0.532475	−	0.846446i	$-0.678738\pi$
$661$	−27.3798			−1.06495			−0.532475	+	0.846446i	$0.678738\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	3.49754	+	4.81395i	0.135629	+	0.186677i
$666$		0			0
$667$	−11.7338	+	3.81254i	−0.454334	+	0.147622i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−28.5946	−	15.1186i	−1.10388	−	0.583646i
$672$		0			0
$673$	−7.96377	+	10.9612i	−0.306981	+	0.422523i	−0.934437	−	0.356129i	$-0.884096\pi$
$673$	−7.96377	+	10.9612i	−0.306981	+	0.422523i	0.627456	+	0.778652i	$0.284096\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−29.6885	+	21.5700i	−1.14102	+	0.829001i	−0.987261	−	0.159107i	$-0.949138\pi$
$677$	−29.6885	+	21.5700i	−1.14102	+	0.829001i	−0.153760	+	0.988108i	$0.549138\pi$
$678$		0			0
$679$	5.27723	+	1.71468i	0.202522	+	0.0658033i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	30.8347i		−	1.17986i	−0.807455	−	0.589929i	$-0.799156\pi$
$683$		−	30.8347i		−	1.17986i	0.807455	−	0.589929i	$-0.200844\pi$
$684$		0			0
$685$	−1.21721	+	3.74619i	−0.0465072	+	0.143134i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−1.62492	−	5.00098i	−0.0619045	−	0.190522i
$690$		0			0
$691$	−38.6062	−	28.0491i	−1.46865	−	1.06704i	−0.981002	−	0.193997i	$-0.937855\pi$
$691$	−38.6062	−	28.0491i	−1.46865	−	1.06704i	−0.487649	−	0.873040i	$-0.662145\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−60.9102	−	44.2539i	−2.31046	−	1.67864i
$696$		0			0
$697$	2.88600	+	8.88220i	0.109315	+	0.336437i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−4.34678	+	13.3780i	−0.164176	+	0.505281i	−0.998975	−	0.0452742i	$-0.985584\pi$
$701$	−4.34678	+	13.3780i	−0.164176	+	0.505281i	0.834799	+	0.550555i	$0.185584\pi$
$702$		0			0
$703$			30.6133i			1.15460i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−6.10727	−	1.98437i	−0.229688	−	0.0746300i
$708$		0			0
$709$	7.34115	−	5.33366i	0.275703	−	0.200310i	−0.441338	−	0.897341i	$-0.645496\pi$
$709$	7.34115	−	5.33366i	0.275703	−	0.200310i	0.717041	+	0.697031i	$0.245496\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	10.2610	−	14.1231i	0.384279	−	0.528915i
$714$		0			0
$715$	10.7174	−	5.25820i	0.400807	−	0.196645i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	32.2802	−	10.4885i	1.20385	−	0.391155i	0.362674	−	0.931916i	$-0.381864\pi$
$719$	32.2802	−	10.4885i	1.20385	−	0.391155i	0.841176	+	0.540761i	$0.181864\pi$
$720$		0			0
$721$	2.01387	+	2.77186i	0.0750005	+	0.103229i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	23.3635			0.867697
$726$		0			0
$727$	−30.8992			−1.14599			−0.572993	−	0.819560i	$-0.694218\pi$
$727$	−30.8992			−1.14599			−0.572993	+	0.819560i	$0.694218\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	3.81058	+	5.24481i	0.140939	+	0.193986i
$732$		0			0
$733$	−39.5648	+	12.8554i	−1.46136	+	0.474825i	−0.928485	−	0.371369i	$-0.878889\pi$
$733$	−39.5648	+	12.8554i	−1.46136	+	0.474825i	−0.532876	+	0.846194i	$0.678889\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−13.2904	+	6.52058i	−0.489558	+	0.240189i
$738$		0			0
$739$	8.44687	−	11.6261i	0.310723	−	0.427674i	−0.624883	−	0.780718i	$-0.714854\pi$
$739$	8.44687	−	11.6261i	0.310723	−	0.427674i	0.935607	+	0.353044i	$0.114854\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−10.8649	+	7.89384i	−0.398596	+	0.289597i	−0.768969	−	0.639286i	$-0.779230\pi$
$743$	−10.8649	+	7.89384i	−0.398596	+	0.289597i	0.370373	+	0.928883i	$0.379230\pi$
$744$		0			0
$745$	−29.0098	−	9.42585i	−1.06284	−	0.345336i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		−	5.67337i		−	0.207301i
$750$		0			0
$751$	11.2373	−	34.5847i	0.410054	−	1.26202i	−0.506547	−	0.862212i	$-0.669078\pi$
$751$	11.2373	−	34.5847i	0.410054	−	1.26202i	0.916601	−	0.399803i	$-0.130922\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−11.8158	−	36.3653i	−0.430021	−	1.32347i
$756$		0			0
$757$	−32.2811	−	23.4536i	−1.17328	−	0.852435i	−0.181878	−	0.983321i	$-0.558218\pi$
$757$	−32.2811	−	23.4536i	−1.17328	−	0.852435i	−0.991397	+	0.130887i	$0.958218\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	2.75887	+	2.00443i	0.100009	+	0.0726607i	0.636666	−	0.771140i	$-0.280313\pi$
$761$	2.75887	+	2.00443i	0.100009	+	0.0726607i	−0.536657	+	0.843801i	$0.680313\pi$
$762$		0			0
$763$	−1.20798	−	3.71777i	−0.0437317	−	0.134592i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	1.94108	−	5.97403i	0.0700884	−	0.215710i
$768$		0			0
$769$		−	21.4154i		−	0.772260i	−0.922444	−	0.386130i	$-0.873812\pi$
$769$		−	21.4154i		−	0.772260i	0.922444	−	0.386130i	$-0.126188\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−34.1302	−	11.0896i	−1.22758	−	0.398864i	−0.377741	−	0.925911i	$-0.623299\pi$
$773$	−34.1302	−	11.0896i	−1.22758	−	0.398864i	−0.849836	+	0.527048i	$0.823299\pi$
$774$		0			0
$775$	−26.7446	+	19.4311i	−0.960694	+	0.697985i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	6.81221	−	9.37620i	0.244073	−	0.335937i
$780$		0			0
$781$	−30.2780	−	16.0086i	−1.08343	−	0.572833i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	58.4180	−	18.9811i	2.08503	−	0.677466i
$786$		0			0
$787$	28.2510	+	38.8842i	1.00704	+	1.38607i	0.920905	+	0.389787i	$0.127451\pi$
$787$	28.2510	+	38.8842i	1.00704	+	1.38607i	0.0861340	+	0.996284i	$0.472549\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−0.385085			−0.0136920
$792$		0			0
$793$	9.24793			0.328404
$794$		0			0
$795$		0			0
$796$		0			0
$797$	3.55363	+	4.89115i	0.125876	+	0.173253i	0.867304	−	0.497779i	$-0.165851\pi$
$797$	3.55363	+	4.89115i	0.125876	+	0.173253i	−0.741428	+	0.671033i	$0.765851\pi$
$798$		0			0
$799$	−0.0673169	+	0.0218726i	−0.00238150	+	0.000773797i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−10.4639	+	10.1522i	−0.369264	+	0.358263i
$804$		0			0
$805$	−4.07663	+	5.61099i	−0.143682	+	0.197762i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−6.01444	+	4.36974i	−0.211456	+	0.153632i	−0.688472	−	0.725263i	$-0.741718\pi$
$809$	−6.01444	+	4.36974i	−0.211456	+	0.153632i	0.477016	+	0.878895i	$0.341718\pi$
$810$		0			0
$811$	−27.7357	−	9.01188i	−0.973933	−	0.316450i	−0.221530	−	0.975154i	$-0.571105\pi$
$811$	−27.7357	−	9.01188i	−0.973933	−	0.316450i	−0.752402	+	0.658704i	$0.771105\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		−	16.2301i		−	0.568514i
$816$		0			0
$817$	2.48605	−	7.65127i	0.0869758	−	0.267684i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−0.331389	−	1.01991i	−0.0115656	−	0.0355952i	0.945107	−	0.326760i	$-0.105957\pi$
$821$	−0.331389	−	1.01991i	−0.0115656	−	0.0355952i	−0.956673	+	0.291165i	$0.905957\pi$
$822$		0			0
$823$	−7.23762	−	5.25844i	−0.252288	−	0.183298i	0.454452	−	0.890771i	$-0.349835\pi$
$823$	−7.23762	−	5.25844i	−0.252288	−	0.183298i	−0.706740	+	0.707473i	$0.749835\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	28.5608	+	20.7507i	0.993157	+	0.721571i	0.960610	−	0.277899i	$-0.0896381\pi$
$827$	28.5608	+	20.7507i	0.993157	+	0.721571i	0.0325471	+	0.999470i	$0.489638\pi$
$828$		0			0
$829$	8.36614	+	25.7483i	0.290568	+	0.894276i	0.984674	+	0.174404i	$0.0557998\pi$
$829$	8.36614	+	25.7483i	0.290568	+	0.894276i	−0.694106	+	0.719873i	$0.744200\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−7.28608	+	22.4243i	−0.252448	+	0.776954i
$834$		0			0
$835$			69.6630i			2.41079i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	35.4106	+	11.5056i	1.22251	+	0.397218i	0.847996	−	0.530003i	$-0.177809\pi$
$839$	35.4106	+	11.5056i	1.22251	+	0.397218i	0.374515	+	0.927221i	$0.377809\pi$
$840$		0			0
$841$	18.4720	−	13.4207i	0.636965	−	0.462782i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	26.9980	−	37.1595i	0.928759	−	1.27833i
$846$		0			0
$847$	1.36596	−	3.80813i	0.0469349	−	0.130849i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−33.9355	+	11.0263i	−1.16329	+	0.377977i
$852$		0			0
$853$	20.6424	+	28.4118i	0.706782	+	0.972802i	0.999860	+	0.0167139i	$0.00532045\pi$
$853$	20.6424	+	28.4118i	0.706782	+	0.972802i	−0.293078	+	0.956089i	$0.594680\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	29.9637			1.02354			0.511770	−	0.859122i	$-0.328990\pi$
$857$	29.9637			1.02354			0.511770	+	0.859122i	$0.328990\pi$
$858$		0			0
$859$	−17.2684			−0.589189			−0.294595	−	0.955622i	$-0.595185\pi$
$859$	−17.2684			−0.589189			−0.294595	+	0.955622i	$0.595185\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−20.4637	−	28.1659i	−0.696593	−	0.958778i	−0.999983	−	0.00591175i	$-0.998118\pi$
$863$	−20.4637	−	28.1659i	−0.696593	−	0.958778i	0.303389	−	0.952867i	$-0.401882\pi$
$864$		0			0
$865$	−22.3183	+	7.25166i	−0.758845	+	0.246564i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−6.21560	+	35.7378i	−0.210850	+	1.21232i
$870$		0			0
$871$	2.48785	−	3.42423i	0.0842976	−	0.116026i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	4.97827	−	3.61692i	0.168296	−	0.122274i
$876$		0			0
$877$	−1.88584	−	0.612748i	−0.0636804	−	0.0206910i	0.277004	−	0.960869i	$-0.410659\pi$
$877$	−1.88584	−	0.612748i	−0.0636804	−	0.0206910i	−0.340684	+	0.940178i	$0.610659\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	48.9571i		−	1.64941i	−0.565566	−	0.824703i	$-0.691342\pi$
$881$		−	48.9571i		−	1.64941i	0.565566	−	0.824703i	$-0.308658\pi$
$882$		0			0
$883$	−10.7400	+	33.0542i	−0.361429	+	1.11236i	0.590758	+	0.806848i	$0.298829\pi$
$883$	−10.7400	+	33.0542i	−0.361429	+	1.11236i	−0.952187	+	0.305515i	$0.901171\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−4.47860	−	13.7837i	−0.150377	−	0.462812i	0.847287	−	0.531136i	$-0.178235\pi$
$887$	−4.47860	−	13.7837i	−0.150377	−	0.462812i	−0.997663	+	0.0683244i	$0.978235\pi$
$888$		0			0
$889$	−5.22049	−	3.79291i	−0.175090	−	0.127210i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	0.0710609	+	0.0516288i	0.00237796	+	0.00172769i
$894$		0			0
$895$	10.8213	+	33.3045i	0.361716	+	1.11325i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	2.69664	−	8.29941i	0.0899380	−	0.276801i
$900$		0			0
$901$			19.0462i			0.634521i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−15.1174	−	4.91195i	−0.502520	−	0.163279i
$906$		0			0
$907$	18.4206	−	13.3834i	0.611647	−	0.444387i	−0.238347	−	0.971180i	$-0.576606\pi$
$907$	18.4206	−	13.3834i	0.611647	−	0.444387i	0.849994	+	0.526793i	$0.176606\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	13.3395	−	18.3602i	0.441956	−	0.608300i	−0.528689	−	0.848815i	$-0.677316\pi$
$911$	13.3395	−	18.3602i	0.441956	−	0.608300i	0.970645	+	0.240515i	$0.0773164\pi$
$912$		0			0
$913$	−14.2361	+	26.9256i	−0.471146	+	0.891106i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	4.85824	−	1.57854i	0.160433	−	0.0521280i
$918$		0			0
$919$	0.737746	+	1.01542i	0.0243360	+	0.0334956i	0.821012	−	0.570911i	$-0.193410\pi$
$919$	0.737746	+	1.01542i	0.0243360	+	0.0334956i	−0.796676	+	0.604407i	$0.793410\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	9.79237			0.322320
$924$		0			0
$925$	67.5699			2.22169
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−1.68995	−	2.32602i	−0.0554456	−	0.0763143i	0.780394	−	0.625288i	$-0.215019\pi$
$929$	−1.68995	−	2.32602i	−0.0554456	−	0.0763143i	−0.835839	+	0.548974i	$0.815019\pi$
$930$		0			0
$931$	27.8274	−	9.04168i	0.912007	−	0.296329i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−42.8048	+	6.11769i	−1.39987	+	0.200070i
$936$		0			0
$937$	18.1303	−	24.9542i	0.592291	−	0.815219i	−0.402684	−	0.915339i	$-0.631923\pi$
$937$	18.1303	−	24.9542i	0.592291	−	0.815219i	0.994975	+	0.100120i	$0.0319227\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	5.29167	−	3.84462i	0.172503	−	0.125331i	−0.498184	−	0.867072i	$-0.665999\pi$
$941$	5.29167	−	3.84462i	0.172503	−	0.125331i	0.670687	+	0.741741i	$0.265999\pi$
$942$		0			0
$943$	12.8474	+	4.17436i	0.418368	+	0.135936i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	33.2579i		−	1.08074i	−0.841429	−	0.540368i	$-0.818285\pi$
$947$		−	33.2579i		−	1.08074i	0.841429	−	0.540368i	$-0.181715\pi$
$948$		0			0
$949$	1.28812	−	3.96442i	0.0418141	−	0.128691i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−16.9820	−	52.2651i	−0.550100	−	1.69303i	−0.708545	−	0.705666i	$-0.750648\pi$
$953$	−16.9820	−	52.2651i	−0.550100	−	1.69303i	0.158445	−	0.987368i	$-0.449352\pi$
$954$		0			0
$955$	−61.9785	−	45.0300i	−2.00558	−	1.45714i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−0.308776	−	0.224339i	−0.00997090	−	0.00724428i
$960$		0			0
$961$	−5.76392	−	17.7395i	−0.185933	−	0.572242i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	9.40000	−	28.9302i	0.302597	−	0.931297i
$966$		0			0
$967$			34.0395i			1.09464i	0.836925	+	0.547318i	$0.184351\pi$
$967$			34.0395i			1.09464i	−0.836925	+	0.547318i	$0.815649\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	36.2008	+	11.7624i	1.16174	+	0.377472i	0.825554	−	0.564323i	$-0.190863\pi$
$971$	36.2008	+	11.7624i	1.16174	+	0.377472i	0.336186	+	0.941796i	$0.390863\pi$
$972$		0			0
$973$	5.90192	−	4.28799i	0.189207	−	0.137467i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	18.8682	−	25.9699i	0.603648	−	0.830850i	−0.392388	−	0.919800i	$-0.628351\pi$
$977$	18.8682	−	25.9699i	0.603648	−	0.830850i	0.996036	+	0.0889499i	$0.0283511\pi$
$978$		0			0
$979$	−4.45325	−	9.07671i	−0.142327	−	0.290093i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	20.3816	−	6.62238i	0.650071	−	0.211221i	0.0346258	−	0.999400i	$-0.488976\pi$
$983$	20.3816	−	6.62238i	0.650071	−	0.211221i	0.615446	+	0.788179i	$0.288976\pi$
$984$		0			0
$985$	−47.2345	−	65.0128i	−1.50502	−	2.07148i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	9.37704			0.298172
$990$		0			0
$991$	29.3068			0.930962			0.465481	−	0.885058i	$-0.345881\pi$
$991$	29.3068			0.930962			0.465481	+	0.885058i	$0.345881\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−23.4621	−	32.2928i	−0.743798	−	1.02375i
$996$		0			0
$997$	−31.1587	+	10.1241i	−0.986807	+	0.320633i	−0.757582	−	0.652740i	$-0.773619\pi$
$997$	−31.1587	+	10.1241i	−0.986807	+	0.320633i	−0.229225	+	0.973373i	$0.573619\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1584.2.cd.c.161.1		16
3.2	odd	2	inner	1584.2.cd.c.161.4		16
4.3	odd	2		99.2.j.a.62.4	yes	16
11.8	odd	10	inner	1584.2.cd.c.305.4		16
12.11	even	2		99.2.j.a.62.1	yes	16
33.8	even	10	inner	1584.2.cd.c.305.1		16
36.7	odd	6		891.2.u.c.458.4		32
36.11	even	6		891.2.u.c.458.1		32
36.23	even	6		891.2.u.c.755.4		32
36.31	odd	6		891.2.u.c.755.1		32
44.19	even	10		99.2.j.a.8.1	✓	16
44.27	odd	10		1089.2.d.g.1088.2		16
44.39	even	10		1089.2.d.g.1088.16		16
132.71	even	10		1089.2.d.g.1088.15		16
132.83	odd	10		1089.2.d.g.1088.1		16
132.107	odd	10		99.2.j.a.8.4	yes	16
396.151	even	30		891.2.u.c.701.4		32
396.239	odd	30		891.2.u.c.107.4		32
396.283	even	30		891.2.u.c.107.1		32
396.371	odd	30		891.2.u.c.701.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.j.a.8.1	✓	16	44.19	even	10
99.2.j.a.8.4	yes	16	132.107	odd	10
99.2.j.a.62.1	yes	16	12.11	even	2
99.2.j.a.62.4	yes	16	4.3	odd	2
891.2.u.c.107.1		32	396.283	even	30
891.2.u.c.107.4		32	396.239	odd	30
891.2.u.c.458.1		32	36.11	even	6
891.2.u.c.458.4		32	36.7	odd	6
891.2.u.c.701.1		32	396.371	odd	30
891.2.u.c.701.4		32	396.151	even	30
891.2.u.c.755.1		32	36.31	odd	6
891.2.u.c.755.4		32	36.23	even	6
1089.2.d.g.1088.1		16	132.83	odd	10
1089.2.d.g.1088.2		16	44.27	odd	10
1089.2.d.g.1088.15		16	132.71	even	10
1089.2.d.g.1088.16		16	44.39	even	10
1584.2.cd.c.161.1		16	1.1	even	1	trivial
1584.2.cd.c.161.4		16	3.2	odd	2	inner
1584.2.cd.c.305.1		16	33.8	even	10	inner
1584.2.cd.c.305.4		16	11.8	odd	10	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1584 = 2^{4} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1584.cd (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.23109 - 3.07083i) q^{5} +(0.349790 - 0.113654i) q^{7} +(2.97756 - 1.46086i) q^{11} +(-0.557375 + 0.767161i) q^{13} +(2.77873 - 2.01886i) q^{17} +(-4.05368 - 1.31712i) q^{19} -4.96800i q^{23} +(-2.90717 + 8.94734i) q^{25} +(-0.767418 - 2.36187i) q^{29} +(2.84281 + 2.06543i) q^{31} +(-1.12943 - 0.820576i) q^{35} +(-2.21947 - 6.83082i) q^{37} +(-0.840249 + 2.58602i) q^{41} +1.88749i q^{43} +(-0.0195991 - 0.00636813i) q^{47} +(-5.55368 + 4.03499i) q^{49} +(-3.25941 + 4.48619i) q^{53} +(-11.1293 - 5.88428i) q^{55} +(-6.29998 + 2.04699i) q^{59} +(-5.73238 - 7.88994i) q^{61} +3.59938 q^{65} -4.46351 q^{67} +(-6.06985 - 8.35443i) q^{71} +(-4.18072 + 1.35840i) q^{73} +(0.875490 - 0.849407i) q^{77} +(-6.42867 + 8.84831i) q^{79} +(-7.42940 + 5.39778i) q^{83} +(-12.3992 - 4.02874i) q^{85} -3.04837i q^{89} +(-0.107774 + 0.331693i) q^{91} +(4.99948 + 15.3868i) q^{95} +(12.2055 + 8.86782i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 32 q^{25} - 16 q^{31} - 12 q^{37} - 24 q^{49} - 16 q^{55} - 96 q^{67} - 20 q^{73} - 100 q^{85} + 72 q^{91} + 60 q^{97}+O(q^{100}) \) 16 * q - 32 * q^25 - 16 * q^31 - 12 * q^37 - 24 * q^49 - 16 * q^55 - 96 * q^67 - 20 * q^73 - 100 * q^85 + 72 * q^91 + 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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