LMFDB - Embedded newform 1584.2.cd.c.161.4

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			161.4
Root			$0.752864 + 0.902863i$ of defining polynomial
Character	$\chi$	$=$	1584.161
Dual form			1584.2.cd.c.305.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.23109 + 3.07083i) q^{5} +(0.349790 - 0.113654i) q^{7} +O(q^{10})$	$q+(2.23109 + 3.07083i) q^{5} +(0.349790 - 0.113654i) q^{7} +(-2.97756 + 1.46086i) q^{11} +(-0.557375 + 0.767161i) q^{13} +(-2.77873 + 2.01886i) q^{17} +(-4.05368 - 1.31712i) q^{19} +4.96800i q^{23} +(-2.90717 + 8.94734i) q^{25} +(0.767418 + 2.36187i) q^{29} +(2.84281 + 2.06543i) q^{31} +(1.12943 + 0.820576i) q^{35} +(-2.21947 - 6.83082i) q^{37} +(0.840249 - 2.58602i) q^{41} +1.88749i q^{43} +(0.0195991 + 0.00636813i) q^{47} +(-5.55368 + 4.03499i) q^{49} +(3.25941 - 4.48619i) q^{53} +(-11.1293 - 5.88428i) q^{55} +(6.29998 - 2.04699i) q^{59} +(-5.73238 - 7.88994i) q^{61} -3.59938 q^{65} -4.46351 q^{67} +(6.06985 + 8.35443i) q^{71} +(-4.18072 + 1.35840i) q^{73} +(-0.875490 + 0.849407i) q^{77} +(-6.42867 + 8.84831i) q^{79} +(7.42940 - 5.39778i) q^{83} +(-12.3992 - 4.02874i) q^{85} +3.04837i q^{89} +(-0.107774 + 0.331693i) q^{91} +(-4.99948 - 15.3868i) q^{95} +(12.2055 + 8.86782i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * 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

Display 100 coefficients 10 coefficients

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	$0.122649\pi$
$5$	2.23109	+	3.07083i	0.997774	+	1.37332i	0.0710932	+	0.997470i	$0.477351\pi$
$6$		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	−0.871342	−	0.490676i	$-0.836750\pi$
$17$	−2.77873	+	2.01886i	−0.673940	+	0.489646i	0.197402	+	0.980323i	$0.436750\pi$
$18$		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	$0.173305\pi$
$23$			4.96800i			1.03590i	−0.855411	+	0.517950i	$0.826695\pi$
$24$		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	0.996682	−	0.0813958i	$-0.0259378\pi$
$29$	0.767418	+	2.36187i	0.142506	+	0.438588i	−0.854176	+	0.519984i	$0.825938\pi$
$30$		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	−0.863759	−	0.503905i	$-0.831896\pi$
$41$	0.840249	−	2.58602i	0.131225	−	0.403869i	0.994984	+	0.100037i	$0.0318960\pi$
$42$		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	0.310446	−	0.950591i	$-0.399522\pi$
$47$	0.0195991	+	0.00636813i	0.00285882	+	0.000928888i	−0.307587	+	0.951520i	$0.599522\pi$
$48$		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	−0.524190	−	0.851601i	$-0.675632\pi$
$53$	3.25941	−	4.48619i	0.447714	−	0.616226i	0.971905	+	0.235375i	$0.0756319\pi$
$54$		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	0.131281	−	0.991345i	$-0.458091\pi$
$59$	6.29998	−	2.04699i	0.820187	−	0.266495i	0.688906	+	0.724850i	$0.258091\pi$
$60$		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	$0.00994626\pi$
$71$	6.06985	+	8.35443i	0.720359	+	0.991489i	−0.279153	+	0.960247i	$0.590054\pi$
$72$		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	−0.0999323	−	0.994994i	$-0.531863\pi$
$83$	7.42940	−	5.39778i	0.815483	−	0.592483i	0.915415	+	0.402511i	$0.131863\pi$
$84$		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	$0.0516536\pi$
$89$			3.04837i			0.323127i	−0.986862	+	0.161563i	$0.948346\pi$
$90$		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	$0.0350168\pi$
$101$	14.1253	+	10.2626i	1.40552	+	1.02117i	0.411562	+	0.911382i	$0.364983\pi$
$102$		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	$0.367847\pi$
$107$	−4.76675	+	14.6705i	−0.460819	+	1.41825i	−0.864166	+	0.503207i	$0.832153\pi$
$108$		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	0.355479	−	0.934684i	$-0.384318\pi$
$113$	0.995774	+	0.323547i	0.0936746	+	0.0304367i	−0.261805	+	0.965121i	$0.584318\pi$
$114$		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	$-0.707525\pi$
$131$	−13.8890			−1.21349			−0.606744	+	0.794897i	$0.707525\pi$
$132$		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	0.834278	−	0.551344i	$-0.185885\pi$
$137$	0.609963	+	0.839541i	0.0521126	+	0.0717269i	−0.782165	+	0.623071i	$0.785885\pi$
$138$		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	−0.821331	−	0.570452i	$-0.806768\pi$
$149$	−6.50125	+	4.72344i	−0.532603	+	0.386959i	0.288727	+	0.957411i	$0.406768\pi$
$150$		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	0.988342	−	0.152252i	$-0.0486526\pi$
$167$	14.8478	+	10.7875i	1.14896	+	0.834765i	0.160614	+	0.987017i	$0.448653\pi$
$168$		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	−0.997043	−	0.0768452i	$-0.975515\pi$
$173$	−1.91046	+	5.87980i	−0.145250	+	0.447033i	0.851793	+	0.523878i	$0.175515\pi$
$174$		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	0.617974	−	0.786198i	$-0.287954\pi$
$179$	8.77414	+	2.85089i	0.655810	+	0.213086i	0.0378357	+	0.999284i	$0.487954\pi$
$180$		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	−0.905589	−	0.424157i	$-0.860570\pi$
$191$	−19.1951	+	6.23688i	−1.38891	+	0.451285i	−0.483323	+	0.875442i	$0.660570\pi$
$192$		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	$-0.771969\pi$
$197$	−21.1710			−1.50837			−0.754187	+	0.656659i	$0.771969\pi$
$198$		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	$-0.904332\pi$
$227$	−5.37022	−	16.5278i	−0.356434	−	1.09699i	0.598740	−	0.800944i	$-0.295668\pi$
$228$		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	0.997552	−	0.0699355i	$-0.0222793\pi$
$233$	18.9171	+	13.7441i	1.23930	+	0.900404i	0.241748	+	0.970339i	$0.422279\pi$
$234$		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	$-0.676145\pi$
$239$	6.17902	−	19.0171i	0.399687	−	1.23011i	0.925251	−	0.379356i	$-0.123855\pi$
$240$		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	−0.745307	−	0.666721i	$-0.767697\pi$
$251$	1.88681	−	2.59698i	0.119095	−	0.163920i	0.864402	+	0.502801i	$0.167697\pi$
$252$		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	0.279752	−	0.960072i	$-0.409748\pi$
$257$	17.1597	−	5.57552i	1.07039	−	0.347792i	0.790641	+	0.612281i	$0.209748\pi$
$258$		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	$-0.479773\pi$
$263$	2.05966			0.127004			0.0635019	+	0.997982i	$0.479773\pi$
$264$		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	0.754287	−	0.656545i	$-0.227983\pi$
$269$	−1.69280	−	2.32994i	−0.103212	−	0.142059i	−0.857499	+	0.514486i	$0.827983\pi$
$270$		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	−0.530762	−	0.847521i	$-0.678094\pi$
$281$	1.86513	−	1.35510i	0.111264	−	0.0808384i	0.642026	+	0.766683i	$0.278094\pi$
$282$		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	$-0.999194\pi$
$293$	−3.29456	−	10.1396i	−0.192470	−	0.592362i	0.807527	−	0.589831i	$-0.200806\pi$
$294$		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	0.0448944	−	0.998992i	$-0.485705\pi$
$311$	−8.92302	−	2.89926i	−0.505978	−	0.164402i	−0.550872	+	0.834590i	$0.685705\pi$
$312$		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	−0.957023	−	0.290011i	$-0.906341\pi$
$317$	−6.86310	+	9.44624i	−0.385470	+	0.530554i	0.571553	+	0.820565i	$0.306341\pi$
$318$		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	0.00813801	−	0.999967i	$-0.497410\pi$
$347$	17.9141	−	13.0153i	0.961678	−	0.698700i	0.953540	+	0.301267i	$0.0974096\pi$
$348$		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	$0.0960161\pi$
$353$			11.1636i			0.594180i	−0.954850	+	0.297090i	$0.903984\pi$
$354$		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	$0.0440002\pi$
$359$	5.11867	+	15.7536i	0.270153	+	0.831445i	−0.720308	+	0.693654i	$0.756000\pi$
$360$		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	−0.321539	−	0.946896i	$-0.604200\pi$
$383$	13.2760	−	18.2729i	0.678374	−	0.933701i	0.999913	+	0.0131951i	$0.00420024\pi$
$384$		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	−0.481015	−	0.876712i	$-0.659732\pi$
$389$	−6.99867	+	2.27401i	−0.354847	+	0.115297i	0.126169	+	0.992009i	$0.459732\pi$
$390$		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	0.876959	−	0.480566i	$-0.159569\pi$
$401$	2.98209	+	4.10449i	0.148918	+	0.204968i	−0.728040	+	0.685534i	$0.759569\pi$
$402$		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	$0.238753\pi$
$419$			27.9075i			1.36337i	−0.731645	+	0.681686i	$0.761247\pi$
$420$		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	0.573735	−	0.819041i	$-0.305494\pi$
$431$	−0.579760	−	0.421220i	−0.0279260	−	0.0202895i	−0.601661	+	0.798752i	$0.705494\pi$
$432$		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	0.607267	−	0.794498i	$-0.292266\pi$
$443$	13.2928	+	4.31910i	0.631561	+	0.205207i	0.0242947	+	0.999705i	$0.492266\pi$
$444$		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	−0.995652	−	0.0931501i	$-0.970306\pi$
$449$	−12.7008	+	17.4811i	−0.599388	+	0.824986i	0.396264	+	0.918136i	$0.370306\pi$
$450$		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	$-0.407077\pi$
$461$	12.3585			0.575595			0.287797	+	0.957691i	$0.407077\pi$
$462$		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	0.967501	−	0.252867i	$-0.0813734\pi$
$467$	9.24994	+	12.7315i	0.428036	+	0.589142i	−0.539465	+	0.842008i	$0.681373\pi$
$468$		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	−0.332973	−	0.942936i	$-0.608052\pi$
$479$	10.0877	−	7.32913i	0.460918	−	0.334877i	0.793891	+	0.608060i	$0.208052\pi$
$480$		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	0.953140	−	0.302531i	$-0.0978314\pi$
$491$	0.0932984	+	0.287143i	0.00421050	+	0.0129586i	−0.948929	+	0.315489i	$0.897831\pi$
$492$		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	−0.996657	−	0.0817056i	$-0.973963\pi$
$503$	−3.19188	+	9.82361i	−0.142319	+	0.438013i	0.854337	+	0.519719i	$0.173963\pi$
$504$		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	−0.152507	−	0.988302i	$-0.548735\pi$
$509$	−19.3302	−	6.28078i	−0.856798	−	0.278390i	−0.704291	+	0.709912i	$0.748735\pi$
$510$		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	−0.548115	−	0.836403i	$-0.684654\pi$
$521$	−11.4110	+	3.70764i	−0.499923	+	0.162435i	0.0481915	+	0.998838i	$0.484654\pi$
$522$		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	0.987968	−	0.154660i	$-0.0494281\pi$
$557$	2.30765	+	7.10223i	0.0977784	+	0.300931i	−0.890189	+	0.455591i	$0.849428\pi$
$558$		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	0.652521	−	0.757770i	$-0.273711\pi$
$563$	3.16715	+	2.30107i	0.133479	+	0.0969784i	−0.519042	+	0.854749i	$0.673711\pi$
$564$		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	$0.389727\pi$
$569$	−11.6410	+	35.8274i	−0.488017	+	1.50196i	−0.827563	+	0.561373i	$0.810273\pi$
$570$		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	−0.968531	−	0.248893i	$-0.919933\pi$
$587$	−38.9053	+	12.6411i	−1.60579	+	0.521754i	−0.637263	+	0.770647i	$0.719933\pi$
$588$		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	$-0.530301\pi$
$593$	−4.62924			−0.190100			−0.0950500	+	0.995472i	$0.530301\pi$
$594$		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	$-0.985218\pi$
$599$	−17.9738	−	24.7388i	−0.734390	−	1.01080i	0.264532	−	0.964377i	$-0.414782\pi$
$600$		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	$-0.972997\pi$
$617$		−	4.20930i		−	0.169460i	0.996404	−	0.0847300i	$-0.0270028\pi$
$618$		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	−0.457354	−	0.889285i	$-0.651203\pi$
$641$	−34.1810	−	11.1061i	−1.35007	−	0.438664i	−0.892716	+	0.450620i	$0.851203\pi$
$642$		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	−0.645145	−	0.764060i	$-0.723203\pi$
$647$	7.14454	−	9.83361i	0.280881	−	0.386599i	0.926025	+	0.377461i	$0.123203\pi$
$648$		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	0.207172	−	0.978305i	$-0.433574\pi$
$653$	24.2713	−	7.88623i	0.949811	−	0.308612i	0.742639	+	0.669692i	$0.233574\pi$
$654$		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	$-0.316806\pi$
$659$	27.9441			1.08855			0.544273	+	0.838908i	$0.316806\pi$
$660$		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	0.153760	−	0.988108i	$-0.450862\pi$
$677$	29.6885	−	21.5700i	1.14102	−	0.829001i	0.987261	+	0.159107i	$0.0508616\pi$
$678$		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	$0.200844\pi$
$683$			30.8347i			1.17986i	−0.807455	+	0.589929i	$0.799156\pi$
$684$		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	−0.834799	−	0.550555i	$-0.814416\pi$
$701$	4.34678	−	13.3780i	0.164176	−	0.505281i	0.998975	+	0.0452742i	$0.0144162\pi$
$702$		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	−0.841176	−	0.540761i	$-0.818136\pi$
$719$	−32.2802	+	10.4885i	−1.20385	+	0.391155i	−0.362674	+	0.931916i	$0.618136\pi$
$720$		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	−0.370373	−	0.928883i	$-0.620770\pi$
$743$	10.8649	−	7.89384i	0.398596	−	0.289597i	0.768969	+	0.639286i	$0.220770\pi$
$744$		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	0.536657	−	0.843801i	$-0.319687\pi$
$761$	−2.75887	−	2.00443i	−0.100009	−	0.0726607i	−0.636666	+	0.771140i	$0.719687\pi$
$762$		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	0.849836	−	0.527048i	$-0.176701\pi$
$773$	34.1302	+	11.0896i	1.22758	+	0.398864i	0.377741	+	0.925911i	$0.376701\pi$
$774$		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	0.741428	−	0.671033i	$-0.234149\pi$
$797$	−3.55363	−	4.89115i	−0.125876	−	0.173253i	−0.867304	+	0.497779i	$0.834149\pi$
$798$		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	−0.477016	−	0.878895i	$-0.658282\pi$
$809$	6.01444	−	4.36974i	0.211456	−	0.153632i	0.688472	+	0.725263i	$0.258282\pi$
$810$		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	0.956673	−	0.291165i	$-0.0940430\pi$
$821$	0.331389	+	1.01991i	0.0115656	+	0.0355952i	−0.945107	+	0.326760i	$0.894043\pi$
$822$		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	−0.0325471	−	0.999470i	$-0.510362\pi$
$827$	−28.5608	−	20.7507i	−0.993157	−	0.721571i	−0.960610	+	0.277899i	$0.910362\pi$
$828$		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	−0.374515	−	0.927221i	$-0.622191\pi$
$839$	−35.4106	−	11.5056i	−1.22251	−	0.397218i	−0.847996	+	0.530003i	$0.822191\pi$
$840$		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	$-0.671010\pi$
$857$	−29.9637			−1.02354			−0.511770	+	0.859122i	$0.671010\pi$
$858$		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	$0.00188178\pi$
$863$	20.4637	+	28.1659i	0.696593	+	0.958778i	−0.303389	+	0.952867i	$0.598118\pi$
$864$		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	$0.308658\pi$
$881$			48.9571i			1.64941i	−0.565566	+	0.824703i	$0.691342\pi$
$882$		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	0.997663	−	0.0683244i	$-0.0217653\pi$
$887$	4.47860	+	13.7837i	0.150377	+	0.462812i	−0.847287	+	0.531136i	$0.821765\pi$
$888$		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	−0.970645	−	0.240515i	$-0.922684\pi$
$911$	−13.3395	+	18.3602i	−0.441956	+	0.608300i	0.528689	+	0.848815i	$0.322684\pi$
$912$		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	0.835839	−	0.548974i	$-0.184981\pi$
$929$	1.68995	+	2.32602i	0.0554456	+	0.0763143i	−0.780394	+	0.625288i	$0.784981\pi$
$930$		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	−0.670687	−	0.741741i	$-0.734001\pi$
$941$	−5.29167	+	3.84462i	−0.172503	+	0.125331i	0.498184	+	0.867072i	$0.334001\pi$
$942$		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	$0.181715\pi$
$947$			33.2579i			1.08074i	−0.841429	+	0.540368i	$0.818285\pi$
$948$		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	$0.249352\pi$
$953$	16.9820	+	52.2651i	0.550100	+	1.69303i	−0.158445	+	0.987368i	$0.550648\pi$
$954$		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	−0.336186	−	0.941796i	$-0.609137\pi$
$971$	−36.2008	−	11.7624i	−1.16174	−	0.377472i	−0.825554	+	0.564323i	$0.809137\pi$
$972$		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	−0.996036	−	0.0889499i	$-0.971649\pi$
$977$	−18.8682	+	25.9699i	−0.603648	+	0.830850i	0.392388	+	0.919800i	$0.371649\pi$
$978$		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	−0.615446	−	0.788179i	$-0.711024\pi$
$983$	−20.3816	+	6.62238i	−0.650071	+	0.211221i	−0.0346258	+	0.999400i	$0.511024\pi$
$984$		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.161.4		16
3.2	odd	2	inner	1584.2.cd.c.161.1		16
4.3	odd	2		99.2.j.a.62.1	yes	16
11.8	odd	10	inner	1584.2.cd.c.305.1		16
12.11	even	2		99.2.j.a.62.4	yes	16
33.8	even	10	inner	1584.2.cd.c.305.4		16
36.7	odd	6		891.2.u.c.458.1		32
36.11	even	6		891.2.u.c.458.4		32
36.23	even	6		891.2.u.c.755.1		32
36.31	odd	6		891.2.u.c.755.4		32
44.19	even	10		99.2.j.a.8.4	yes	16
44.27	odd	10		1089.2.d.g.1088.15		16
44.39	even	10		1089.2.d.g.1088.1		16
132.71	even	10		1089.2.d.g.1088.2		16
132.83	odd	10		1089.2.d.g.1088.16		16
132.107	odd	10		99.2.j.a.8.1	✓	16
396.151	even	30		891.2.u.c.701.1		32
396.239	odd	30		891.2.u.c.107.1		32
396.283	even	30		891.2.u.c.107.4		32
396.371	odd	30		891.2.u.c.701.4		32

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

\(f(q)\)	\(=\)	\(q+(2.23109 + 3.07083i) q^{5} +(0.349790 - 0.113654i) q^{7} +O(q^{10})\)	\(q+(2.23109 + 3.07083i) q^{5} +(0.349790 - 0.113654i) q^{7} +(-2.97756 + 1.46086i) q^{11} +(-0.557375 + 0.767161i) q^{13} +(-2.77873 + 2.01886i) q^{17} +(-4.05368 - 1.31712i) q^{19} +4.96800i q^{23} +(-2.90717 + 8.94734i) q^{25} +(0.767418 + 2.36187i) q^{29} +(2.84281 + 2.06543i) q^{31} +(1.12943 + 0.820576i) q^{35} +(-2.21947 - 6.83082i) q^{37} +(0.840249 - 2.58602i) q^{41} +1.88749i q^{43} +(0.0195991 + 0.00636813i) q^{47} +(-5.55368 + 4.03499i) q^{49} +(3.25941 - 4.48619i) q^{53} +(-11.1293 - 5.88428i) q^{55} +(6.29998 - 2.04699i) q^{59} +(-5.73238 - 7.88994i) q^{61} -3.59938 q^{65} -4.46351 q^{67} +(6.06985 + 8.35443i) q^{71} +(-4.18072 + 1.35840i) q^{73} +(-0.875490 + 0.849407i) q^{77} +(-6.42867 + 8.84831i) q^{79} +(7.42940 - 5.39778i) q^{83} +(-12.3992 - 4.02874i) q^{85} +3.04837i q^{89} +(-0.107774 + 0.331693i) q^{91} +(-4.99948 - 15.3868i) q^{95} +(12.2055 + 8.86782i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * 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

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