LMFDB - Embedded newform 3024.2.df.c.17.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3024,2,Mod(17,3024)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3024.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3024, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.df (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$24.1467615712$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} - 8 x^{15} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + \cdots + 6561 $ x^16 - 8x^15 + 23x^14 - 8x^13 - 131x^12 + 380x^11 - 289x^10 - 880x^9 + 2785x^8 - 2640x^7 - 2601x^6 + 10260x^5 - 10611x^4 - 1944x^3 + 16767x^2 - 17496*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3^{6} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.7
Root			$1.71298 + 0.256290i$ of defining polynomial
Character	$\chi$	$=$	3024.17
Dual form			3024.2.df.c.1601.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+3.61932 q^{5} +(-0.266972 + 2.63225i) q^{7} +2.00379i q^{11} +(-2.95206 - 1.70437i) q^{13} +(-3.08709 + 5.34700i) q^{17} +(-0.877353 + 0.506540i) q^{19} -3.02799i q^{23} +8.09945 q^{25} +(-5.04560 + 2.91308i) q^{29} +(-0.787812 + 0.454844i) q^{31} +(-0.966257 + 9.52693i) q^{35} +(3.66825 + 6.35359i) q^{37} +(-2.85045 + 4.93712i) q^{41} +(2.39949 + 4.15605i) q^{43} +(-1.11511 + 1.93143i) q^{47} +(-6.85745 - 1.40547i) q^{49} +(7.58088 + 4.37683i) q^{53} +7.25237i q^{55} +(4.49313 + 7.78233i) q^{59} +(-12.7410 - 7.35603i) q^{61} +(-10.6844 - 6.16866i) q^{65} +(-4.15821 - 7.20222i) q^{67} +0.466287i q^{71} +(-3.65022 - 2.10746i) q^{73} +(-5.27448 - 0.534957i) q^{77} +(1.91267 - 3.31284i) q^{79} +(4.00481 + 6.93654i) q^{83} +(-11.1732 + 19.3525i) q^{85} +(-2.39324 - 4.14521i) q^{89} +(5.27445 - 7.31553i) q^{91} +(-3.17542 + 1.83333i) q^{95} +(10.1835 - 5.87944i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{7} - 6 q^{13} - 18 q^{17} + 16 q^{25} - 6 q^{29} - 6 q^{31} - 30 q^{35} - 2 q^{37} - 6 q^{41} + 2 q^{43} - 18 q^{47} + 10 q^{49} - 36 q^{53} + 30 q^{59} - 60 q^{61} - 42 q^{65} - 14 q^{67} + 18 q^{77}+ \cdots - 6 q^{97}+O(q^{100}) $ 16 * q - 2 * q^7 - 6 * q^13 - 18 * q^17 + 16 * q^25 - 6 * q^29 - 6 * q^31 - 30 * q^35 - 2 * q^37 - 6 * q^41 + 2 * q^43 - 18 * q^47 + 10 * q^49 - 36 * q^53 + 30 * q^59 - 60 * q^61 - 42 * q^65 - 14 * q^67 + 18 * q^77 + 16 * q^79 - 12 * q^85 - 24 * q^89 + 12 * q^91 - 66 * q^95 - 6 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	3.61932			1.61861			0.809304	−	0.587391i	$-0.199845\pi$
$5$	3.61932			1.61861			0.809304	+	0.587391i	$0.199845\pi$
$6$		0			0
$7$	−0.266972	+	2.63225i	−0.100906	+	0.994896i
$7$	−0.266972	+	2.63225i	−0.100906	+	0.994896i
$8$		0			0
$9$		0			0
$10$		0			0
$11$			2.00379i			0.604167i	0.953281	+	0.302083i	$0.0976821\pi$
$11$			2.00379i			0.604167i	−0.953281	+	0.302083i	$0.902318\pi$
$12$		0			0
$13$	−2.95206	−	1.70437i	−0.818754	−	0.472708i	0.0312328	−	0.999512i	$-0.490057\pi$
$13$	−2.95206	−	1.70437i	−0.818754	−	0.472708i	−0.849987	+	0.526804i	$0.823390\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.08709	+	5.34700i	−0.748730	+	1.29684i	0.199702	+	0.979857i	$0.436002\pi$
$17$	−3.08709	+	5.34700i	−0.748730	+	1.29684i	−0.948432	+	0.316981i	$0.897331\pi$
$18$		0			0
$19$	−0.877353	+	0.506540i	−0.201279	+	0.116208i	−0.597252	−	0.802054i	$-0.703741\pi$
$19$	−0.877353	+	0.506540i	−0.201279	+	0.116208i	0.395973	+	0.918262i	$0.370407\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$		−	3.02799i		−	0.631380i	−0.948862	−	0.315690i	$-0.897764\pi$
$23$		−	3.02799i		−	0.631380i	0.948862	−	0.315690i	$-0.102236\pi$
$24$		0			0
$25$	8.09945			1.61989
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−5.04560	+	2.91308i	−0.936945	+	0.540945i	−0.889001	−	0.457905i	$-0.848600\pi$
$29$	−5.04560	+	2.91308i	−0.936945	+	0.540945i	−0.0479434	+	0.998850i	$0.515267\pi$
$30$		0			0
$31$	−0.787812	+	0.454844i	−0.141495	+	0.0816923i	−0.569076	−	0.822285i	$-0.692699\pi$
$31$	−0.787812	+	0.454844i	−0.141495	+	0.0816923i	0.427581	+	0.903977i	$0.359366\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.966257	+	9.52693i	−0.163327	+	1.61035i
$36$		0			0
$37$	3.66825	+	6.35359i	0.603056	+	1.04452i	0.992355	+	0.123413i	$0.0393839\pi$
$37$	3.66825	+	6.35359i	0.603056	+	1.04452i	−0.389299	+	0.921111i	$0.627283\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−2.85045	+	4.93712i	−0.445165	+	0.771048i	−0.998064	−	0.0622002i	$-0.980188\pi$
$41$	−2.85045	+	4.93712i	−0.445165	+	0.771048i	0.552899	+	0.833248i	$0.313522\pi$
$42$		0			0
$43$	2.39949	+	4.15605i	0.365919	+	0.633791i	0.988923	−	0.148428i	$-0.0474212\pi$
$43$	2.39949	+	4.15605i	0.365919	+	0.633791i	−0.623004	+	0.782219i	$0.714088\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.11511	+	1.93143i	−0.162655	+	0.281727i	−0.935820	−	0.352478i	$-0.885339\pi$
$47$	−1.11511	+	1.93143i	−0.162655	+	0.281727i	0.773165	+	0.634205i	$0.218673\pi$
$48$		0			0
$49$	−6.85745	−	1.40547i	−0.979636	−	0.200782i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	7.58088	+	4.37683i	1.04131	+	0.601203i	0.920205	−	0.391436i	$-0.128022\pi$
$53$	7.58088	+	4.37683i	1.04131	+	0.601203i	0.121109	+	0.992639i	$0.461355\pi$
$54$		0			0
$55$			7.25237i			0.977909i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	4.49313	+	7.78233i	0.584956	+	1.01317i	0.994881	+	0.101054i	$0.0322216\pi$
$59$	4.49313	+	7.78233i	0.584956	+	1.01317i	−0.409925	+	0.912119i	$0.634445\pi$
$60$		0			0
$61$	−12.7410	−	7.35603i	−1.63132	−	0.941843i	−0.983686	−	0.179892i	$-0.942425\pi$
$61$	−12.7410	−	7.35603i	−1.63132	−	0.941843i	−0.647634	−	0.761952i	$-0.724241\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−10.6844	−	6.16866i	−1.32524	−	0.765128i
$66$		0			0
$67$	−4.15821	−	7.20222i	−0.508006	−	0.879892i	−0.999957	−	0.00926908i	$-0.997050\pi$
$67$	−4.15821	−	7.20222i	−0.508006	−	0.879892i	0.491951	−	0.870623i	$-0.336284\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			0.466287i			0.0553381i	0.999617	+	0.0276691i	$0.00880846\pi$
$71$			0.466287i			0.0553381i	−0.999617	+	0.0276691i	$0.991192\pi$
$72$		0			0
$73$	−3.65022	−	2.10746i	−0.427226	−	0.246659i	0.270938	−	0.962597i	$-0.412666\pi$
$73$	−3.65022	−	2.10746i	−0.427226	−	0.246659i	−0.698164	+	0.715938i	$0.746000\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−5.27448	−	0.534957i	−0.601083	−	0.0609641i
$78$		0			0
$79$	1.91267	−	3.31284i	0.215192	−	0.372723i	−0.738140	−	0.674648i	$-0.764296\pi$
$79$	1.91267	−	3.31284i	0.215192	−	0.372723i	0.953332	+	0.301924i	$0.0976290\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	4.00481	+	6.93654i	0.439585	+	0.761384i	0.997657	−	0.0684084i	$-0.0217921\pi$
$83$	4.00481	+	6.93654i	0.439585	+	0.761384i	−0.558072	+	0.829792i	$0.688459\pi$
$84$		0			0
$85$	−11.1732	+	19.3525i	−1.21190	+	2.09907i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−2.39324	−	4.14521i	−0.253683	−	0.439391i	0.710854	−	0.703339i	$-0.248309\pi$
$89$	−2.39324	−	4.14521i	−0.253683	−	0.439391i	−0.964537	+	0.263948i	$0.914975\pi$
$90$		0			0
$91$	5.27445	−	7.31553i	0.552912	−	0.766876i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−3.17542	+	1.83333i	−0.325791	+	0.188096i
$96$		0			0
$97$	10.1835	−	5.87944i	1.03398	−	0.596967i	0.115856	−	0.993266i	$-0.463039\pi$
$97$	10.1835	−	5.87944i	1.03398	−	0.596967i	0.918121	+	0.396299i	$0.129706\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	12.8922			1.28282			0.641411	−	0.767197i	$-0.278349\pi$
$101$	12.8922			1.28282			0.641411	+	0.767197i	$0.278349\pi$
$102$		0			0
$103$			10.7588i			1.06010i	0.847968	+	0.530048i	$0.177826\pi$
$103$			10.7588i			1.06010i	−0.847968	+	0.530048i	$0.822174\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.28602	−	1.31983i	0.220998	−	0.127593i	−0.385414	−	0.922744i	$-0.625942\pi$
$107$	2.28602	−	1.31983i	0.220998	−	0.127593i	0.606412	+	0.795151i	$0.292608\pi$
$108$		0			0
$109$	4.51768	−	7.82484i	0.432715	−	0.749484i	−0.564391	−	0.825507i	$-0.690889\pi$
$109$	4.51768	−	7.82484i	0.432715	−	0.749484i	0.997106	+	0.0760233i	$0.0242224\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.46411	+	0.845306i	0.137732	+	0.0795197i	0.567283	−	0.823523i	$-0.307995\pi$
$113$	1.46411	+	0.845306i	0.137732	+	0.0795197i	−0.429551	+	0.903043i	$0.641328\pi$
$114$		0			0
$115$		−	10.9593i		−	1.02196i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−13.2505	−	9.55349i	−1.21467	−	0.875767i
$120$		0			0
$121$	6.98481			0.634982
$122$		0			0
$123$		0			0
$124$		0			0
$125$	11.2179			1.00336
$126$		0			0
$127$	−17.9292			−1.59096			−0.795478	−	0.605983i	$-0.792780\pi$
$127$	−17.9292			−1.59096			−0.795478	+	0.605983i	$0.792780\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	17.3313			1.51425			0.757123	−	0.653272i	$-0.226604\pi$
$131$	17.3313			1.51425			0.757123	+	0.653272i	$0.226604\pi$
$132$		0			0
$133$	−1.09911	−	2.44464i	−0.0953049	−	0.211977i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0	0.000645123i		0	5.51166e-5i	1.00000		2.75583e-5i	$8.77208e-6\pi$
$137$		0	0.000645123i		0	5.51166e-5i	−1.00000		2.75583e-5i	$0.999991\pi$
$138$		0			0
$139$	−8.73273	−	5.04185i	−0.740701	−	0.427644i	0.0816233	−	0.996663i	$-0.473990\pi$
$139$	−8.73273	−	5.04185i	−0.740701	−	0.427644i	−0.822324	+	0.569019i	$0.807323\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	3.41521	−	5.91532i	0.285594	−	0.494664i
$144$		0			0
$145$	−18.2616	+	10.5434i	−1.51655	+	0.875578i
$146$		0			0
$147$		0			0
$148$		0			0
$149$			11.2475i			0.921433i	0.887547	+	0.460716i	$0.152407\pi$
$149$			11.2475i			0.921433i	−0.887547	+	0.460716i	$0.847593\pi$
$150$		0			0
$151$	4.72379			0.384417			0.192208	−	0.981354i	$-0.438435\pi$
$151$	4.72379			0.384417			0.192208	+	0.981354i	$0.438435\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−2.85134	+	1.64622i	−0.229025	+	0.132228i
$156$		0			0
$157$	2.65845	−	1.53486i	0.212168	−	0.122495i	−0.390151	−	0.920751i	$-0.627577\pi$
$157$	2.65845	−	1.53486i	0.212168	−	0.122495i	0.602318	+	0.798256i	$0.294244\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	7.97043	+	0.808390i	0.628158	+	0.0637101i
$162$		0			0
$163$	1.43687	+	2.48873i	0.112544	+	0.194932i	0.916795	−	0.399357i	$-0.130767\pi$
$163$	1.43687	+	2.48873i	0.112544	+	0.194932i	−0.804251	+	0.594289i	$0.797433\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−0.730517	+	1.26529i	−0.0565291	+	0.0979113i	−0.892905	−	0.450245i	$-0.851337\pi$
$167$	−0.730517	+	1.26529i	−0.0565291	+	0.0979113i	0.836376	+	0.548156i	$0.184670\pi$
$168$		0			0
$169$	−0.690233	−	1.19552i	−0.0530948	−	0.0919630i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1.53541	−	2.65940i	0.116735	−	0.202191i	−0.801737	−	0.597677i	$-0.796091\pi$
$173$	1.53541	−	2.65940i	0.116735	−	0.202191i	0.918472	+	0.395486i	$0.129424\pi$
$174$		0			0
$175$	−2.16233	+	21.3197i	−0.163457	+	1.61162i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−16.7310	−	9.65966i	−1.25054	−	0.721997i	−0.279320	−	0.960198i	$-0.590109\pi$
$179$	−16.7310	−	9.65966i	−1.25054	−	0.721997i	−0.971216	+	0.238201i	$0.923442\pi$
$180$		0			0
$181$			7.89318i			0.586695i	0.956006	+	0.293348i	$0.0947693\pi$
$181$			7.89318i			0.586695i	−0.956006	+	0.293348i	$0.905231\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	13.2765	+	22.9957i	0.976111	+	1.69067i
$186$		0			0
$187$	−10.7143	−	6.18590i	−0.783506	−	0.452358i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	11.5218	+	6.65211i	0.833688	+	0.481330i	0.855114	−	0.518441i	$-0.173487\pi$
$191$	11.5218	+	6.65211i	0.833688	+	0.481330i	−0.0214259	+	0.999770i	$0.506821\pi$
$192$		0			0
$193$	−3.26786	−	5.66011i	−0.235226	−	0.407423i	0.724112	−	0.689682i	$-0.242250\pi$
$193$	−3.26786	−	5.66011i	−0.235226	−	0.407423i	−0.959338	+	0.282259i	$0.908916\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			4.44250i			0.316515i	0.987398	+	0.158258i	$0.0505876\pi$
$197$			4.44250i			0.316515i	−0.987398	+	0.158258i	$0.949412\pi$
$198$		0			0
$199$	−9.96868	−	5.75542i	−0.706661	−	0.407991i	0.103163	−	0.994665i	$-0.467104\pi$
$199$	−9.96868	−	5.75542i	−0.706661	−	0.407991i	−0.809823	+	0.586674i	$0.800437\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−6.32091	−	14.0590i	−0.443641	−	0.986747i
$204$		0			0
$205$	−10.3167	+	17.8690i	−0.720547	+	1.24802i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−1.01500	−	1.75804i	−0.0702092	−	0.121606i
$210$		0			0
$211$	−11.3005	+	19.5731i	−0.777961	+	1.34747i	0.155155	+	0.987890i	$0.450412\pi$
$211$	−11.3005	+	19.5731i	−0.777961	+	1.34747i	−0.933115	+	0.359577i	$0.882921\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	8.68453	+	15.0420i	0.592280	+	1.02586i
$216$		0			0
$217$	−0.986937	−	2.19515i	−0.0669976	−	0.149016i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	18.2265	−	10.5231i	1.22605	−	0.707860i
$222$		0			0
$223$	16.2994	−	9.41045i	1.09149	−	0.630170i	0.157515	−	0.987517i	$-0.449652\pi$
$223$	16.2994	−	9.41045i	1.09149	−	0.630170i	0.933972	+	0.357346i	$0.116318\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−14.6133			−0.969919			−0.484960	−	0.874537i	$-0.661166\pi$
$227$	−14.6133			−0.969919			−0.484960	+	0.874537i	$0.661166\pi$
$228$		0			0
$229$		−	2.37919i		−	0.157221i	−0.996905	−	0.0786106i	$-0.974952\pi$
$229$		−	2.37919i		−	0.157221i	0.996905	−	0.0786106i	$-0.0250484\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	9.03470	−	5.21619i	0.591883	−	0.341724i	−0.173959	−	0.984753i	$-0.555656\pi$
$233$	9.03470	−	5.21619i	0.591883	−	0.341724i	0.765842	+	0.643029i	$0.222323\pi$
$234$		0			0
$235$	−4.03593	+	6.99044i	−0.263275	+	0.456006i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	20.5971	+	11.8917i	1.33232	+	0.769213i	0.985654	−	0.168777i	$-0.0539818\pi$
$239$	20.5971	+	11.8917i	1.33232	+	0.769213i	0.346662	+	0.937990i	$0.387315\pi$
$240$		0			0
$241$			28.6487i			1.84542i	0.385489	+	0.922712i	$0.374033\pi$
$241$			28.6487i			1.84542i	−0.385489	+	0.922712i	$0.625967\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−24.8193	−	5.08685i	−1.58565	−	0.324987i
$246$		0			0
$247$	3.45333			0.219730
$248$		0			0
$249$		0			0
$250$		0			0
$251$	11.0301			0.696216			0.348108	−	0.937454i	$-0.386824\pi$
$251$	11.0301			0.696216			0.348108	+	0.937454i	$0.386824\pi$
$252$		0			0
$253$	6.06748			0.381459
$254$		0			0
$255$		0			0
$256$		0			0
$257$	15.0978			0.941775			0.470888	−	0.882193i	$-0.343934\pi$
$257$	15.0978			0.941775			0.470888	+	0.882193i	$0.343934\pi$
$258$		0			0
$259$	−17.7035	+	7.95950i	−1.10004	+	0.494579i
$260$		0			0
$261$		0			0
$262$		0			0
$263$		−	19.6385i		−	1.21096i	−0.795859	−	0.605482i	$-0.792980\pi$
$263$		−	19.6385i		−	1.21096i	0.795859	−	0.605482i	$-0.207020\pi$
$264$		0			0
$265$	27.4376	+	15.8411i	1.68548	+	0.973112i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	0.245503	−	0.425223i	0.0149686	−	0.0259263i	−0.858444	−	0.512907i	$-0.828569\pi$
$269$	0.245503	−	0.425223i	0.0149686	−	0.0259263i	0.873413	+	0.486981i	$0.161902\pi$
$270$		0			0
$271$	12.1927	−	7.03945i	0.740653	−	0.427616i	−0.0816537	−	0.996661i	$-0.526020\pi$
$271$	12.1927	−	7.03945i	0.740653	−	0.427616i	0.822307	+	0.569045i	$0.192687\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$			16.2296i			0.978683i
$276$		0			0
$277$	30.7200			1.84579			0.922894	−	0.385054i	$-0.125817\pi$
$277$	30.7200			1.84579			0.922894	+	0.385054i	$0.125817\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−6.86286	+	3.96227i	−0.409404	+	0.236369i	−0.690534	−	0.723300i	$-0.742624\pi$
$281$	−6.86286	+	3.96227i	−0.409404	+	0.236369i	0.281130	+	0.959670i	$0.409291\pi$
$282$		0			0
$283$	9.97303	−	5.75793i	0.592835	−	0.342273i	−0.173383	−	0.984855i	$-0.555470\pi$
$283$	9.97303	−	5.75793i	0.592835	−	0.342273i	0.766218	+	0.642581i	$0.222136\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−12.2347	−	8.82115i	−0.722193	−	0.520696i
$288$		0			0
$289$	−10.5603	−	18.2909i	−0.621192	−	1.07594i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−2.50937	+	4.34636i	−0.146599	+	0.253917i	−0.929968	−	0.367639i	$-0.880166\pi$
$293$	−2.50937	+	4.34636i	−0.146599	+	0.253917i	0.783369	+	0.621557i	$0.213499\pi$
$294$		0			0
$295$	16.2621	+	28.1667i	0.946814	+	1.63993i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−5.16083	+	8.93882i	−0.298458	+	0.516945i
$300$		0			0
$301$	−11.5803	+	5.20651i	−0.667480	+	0.300098i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−46.1138	−	26.6238i	−2.64047	−	1.52447i
$306$		0			0
$307$			17.5309i			1.00054i	0.865869	+	0.500271i	$0.166766\pi$
$307$			17.5309i			1.00054i	−0.865869	+	0.500271i	$0.833234\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	8.64759	+	14.9781i	0.490360	+	0.849328i	0.999938	−	0.0110959i	$-0.00353200\pi$
$311$	8.64759	+	14.9781i	0.490360	+	0.849328i	−0.509579	+	0.860424i	$0.670199\pi$
$312$		0			0
$313$	7.78988	+	4.49749i	0.440310	+	0.254213i	0.703729	−	0.710468i	$-0.251517\pi$
$313$	7.78988	+	4.49749i	0.440310	+	0.254213i	−0.263419	+	0.964681i	$0.584850\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	5.82002	+	3.36019i	0.326885	+	0.188727i	0.654457	−	0.756099i	$-0.272897\pi$
$317$	5.82002	+	3.36019i	0.326885	+	0.188727i	−0.327572	+	0.944826i	$0.606230\pi$
$318$		0			0
$319$	−5.83721	−	10.1103i	−0.326821	−	0.566071i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	6.25494i		−	0.348034i
$324$		0			0
$325$	−23.9100	−	13.8045i	−1.32629	−	0.765734i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−4.78629	−	3.45088i	−0.263876	−	0.190253i
$330$		0			0
$331$	−9.38725	+	16.2592i	−0.515970	+	0.893686i	0.483858	+	0.875146i	$0.339235\pi$
$331$	−9.38725	+	16.2592i	−0.515970	+	0.893686i	−0.999828	+	0.0185396i	$0.994098\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−15.0499	−	26.0671i	−0.822262	−	1.42420i
$336$		0			0
$337$	2.42287	−	4.19654i	0.131982	−	0.228600i	−0.792458	−	0.609926i	$-0.791199\pi$
$337$	2.42287	−	4.19654i	0.131982	−	0.228600i	0.924441	+	0.381326i	$0.124532\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−0.911413	−	1.57861i	−0.0493558	−	0.0854868i
$342$		0			0
$343$	5.53030	−	17.6753i	0.298608	−	0.954376i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−15.1305	+	8.73559i	−0.812247	+	0.468951i	−0.847736	−	0.530419i	$-0.822035\pi$
$347$	−15.1305	+	8.73559i	−0.812247	+	0.468951i	0.0354887	+	0.999370i	$0.488701\pi$
$348$		0			0
$349$	−20.6338	+	11.9129i	−1.10450	+	0.637683i	−0.937399	−	0.348257i	$-0.886774\pi$
$349$	−20.6338	+	11.9129i	−1.10450	+	0.637683i	−0.167101	+	0.985940i	$0.553440\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−10.0412			−0.534441			−0.267220	−	0.963635i	$-0.586105\pi$
$353$	−10.0412			−0.534441			−0.267220	+	0.963635i	$0.586105\pi$
$354$		0			0
$355$			1.68764i			0.0895707i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	10.5353	−	6.08254i	0.556030	−	0.321024i	−0.195521	−	0.980700i	$-0.562640\pi$
$359$	10.5353	−	6.08254i	0.556030	−	0.321024i	0.751550	+	0.659676i	$0.229306\pi$
$360$		0			0
$361$	−8.98683	+	15.5657i	−0.472991	+	0.819245i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−13.2113	−	7.62756i	−0.691512	−	0.399245i
$366$		0			0
$367$		−	3.63061i		−	0.189516i	−0.995500	−	0.0947582i	$-0.969792\pi$
$367$		−	3.63061i		−	0.189516i	0.995500	−	0.0947582i	$-0.0302078\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−13.5448	+	18.7863i	−0.703210	+	0.975335i
$372$		0			0
$373$	5.49231			0.284381			0.142191	−	0.989839i	$-0.454585\pi$
$373$	5.49231			0.284381			0.142191	+	0.989839i	$0.454585\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	19.8599			1.02284
$378$		0			0
$379$	15.5960			0.801112			0.400556	−	0.916272i	$-0.368817\pi$
$379$	15.5960			0.801112			0.400556	+	0.916272i	$0.368817\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	9.43067			0.481885			0.240942	−	0.970539i	$-0.422544\pi$
$383$	9.43067			0.481885			0.240942	+	0.970539i	$0.422544\pi$
$384$		0			0
$385$	−19.0900	−	1.93618i	−0.972918	−	0.0986769i
$386$		0			0
$387$		0			0
$388$		0			0
$389$			6.42177i			0.325597i	0.986659	+	0.162798i	$0.0520520\pi$
$389$			6.42177i			0.325597i	−0.986659	+	0.162798i	$0.947948\pi$
$390$		0			0
$391$	16.1907	+	9.34769i	0.818798	+	0.472733i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	6.92255	−	11.9902i	0.348311	−	0.603293i
$396$		0			0
$397$	5.99750	−	3.46266i	0.301006	−	0.173786i	−0.341889	−	0.939740i	$-0.611067\pi$
$397$	5.99750	−	3.46266i	0.301006	−	0.173786i	0.642895	+	0.765955i	$0.277733\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			10.5869i			0.528682i	0.964429	+	0.264341i	$0.0851545\pi$
$401$			10.5869i			0.528682i	−0.964429	+	0.264341i	$0.914846\pi$
$402$		0			0
$403$	3.10089			0.154466
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−12.7313	+	7.35042i	−0.631067	+	0.364347i
$408$		0			0
$409$	7.72792	−	4.46172i	0.382121	−	0.220618i	−0.296620	−	0.954996i	$-0.595859\pi$
$409$	7.72792	−	4.46172i	0.382121	−	0.220618i	0.678741	+	0.734378i	$0.262526\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−21.6846	+	9.74937i	−1.06703	+	0.479735i
$414$		0			0
$415$	14.4947	+	25.1055i	0.711516	+	1.23238i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−17.1924	+	29.7781i	−0.839903	+	1.45475i	0.0500724	+	0.998746i	$0.484055\pi$
$419$	−17.1924	+	29.7781i	−0.839903	+	1.45475i	−0.889975	+	0.456009i	$0.849279\pi$
$420$		0			0
$421$	−17.7840	−	30.8028i	−0.866739	−	1.50124i	−0.865310	−	0.501237i	$-0.832879\pi$
$421$	−17.7840	−	30.8028i	−0.866739	−	1.50124i	−0.00142877	−	0.999999i	$-0.500455\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−25.0037	+	43.3077i	−1.21286	+	2.10073i
$426$		0			0
$427$	22.7644	−	31.5737i	1.10165	−	1.52796i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	26.7338	+	15.4348i	1.28772	+	0.743466i	0.978247	−	0.207442i	$-0.0665138\pi$
$431$	26.7338	+	15.4348i	1.28772	+	0.743466i	0.309474	+	0.950908i	$0.399847\pi$
$432$		0			0
$433$		−	23.2463i		−	1.11715i	−0.829455	−	0.558574i	$-0.811349\pi$
$433$		−	23.2463i		−	1.11715i	0.829455	−	0.558574i	$-0.188651\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1.53380	+	2.65662i	0.0733716	+	0.127083i
$438$		0			0
$439$	−19.2887	−	11.1364i	−0.920601	−	0.531509i	−0.0367744	−	0.999324i	$-0.511708\pi$
$439$	−19.2887	−	11.1364i	−0.920601	−	0.531509i	−0.883827	+	0.467814i	$0.845042\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	15.5756	+	8.99259i	0.740020	+	0.427251i	0.822077	−	0.569377i	$-0.192815\pi$
$443$	15.5756	+	8.99259i	0.740020	+	0.427251i	−0.0820566	+	0.996628i	$0.526149\pi$
$444$		0			0
$445$	−8.66188	−	15.0028i	−0.410612	−	0.711202i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	9.44363i		−	0.445673i	−0.974856	−	0.222836i	$-0.928468\pi$
$449$		−	9.44363i		−	0.445673i	0.974856	−	0.222836i	$-0.0715315\pi$
$450$		0			0
$451$	−9.89297	−	5.71171i	−0.465842	−	0.268954i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	19.0899	−	26.4772i	0.894948	−	1.24127i
$456$		0			0
$457$	0.922251	−	1.59739i	0.0431411	−	0.0747225i	−0.843649	−	0.536896i	$-0.819597\pi$
$457$	0.922251	−	1.59739i	0.0431411	−	0.0747225i	0.886790	+	0.462173i	$0.152930\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−18.1869	−	31.5007i	−0.847050	−	1.46713i	−0.883829	−	0.467810i	$-0.845043\pi$
$461$	−18.1869	−	31.5007i	−0.847050	−	1.46713i	0.0367790	−	0.999323i	$-0.488290\pi$
$462$		0			0
$463$	15.9830	−	27.6834i	0.742794	−	1.28656i	−0.208425	−	0.978038i	$-0.566834\pi$
$463$	15.9830	−	27.6834i	0.742794	−	1.28656i	0.951219	−	0.308518i	$-0.0998330\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−12.2206	−	21.1666i	−0.565500	−	0.979475i	−0.997003	−	0.0773632i	$-0.975350\pi$
$467$	−12.2206	−	21.1666i	−0.565500	−	0.979475i	0.431503	−	0.902112i	$-0.357983\pi$
$468$		0			0
$469$	20.0682	−	9.02263i	0.926662	−	0.416627i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−8.32786	+	4.80809i	−0.382916	+	0.221076i
$474$		0			0
$475$	−7.10607	+	4.10269i	−0.326049	+	0.188245i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	10.9606			0.500805			0.250402	−	0.968142i	$-0.419437\pi$
$479$	10.9606			0.500805			0.250402	+	0.968142i	$0.419437\pi$
$480$		0			0
$481$		−	25.0082i		−	1.14028i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	36.8573	−	21.2796i	1.67360	−	0.966255i
$486$		0			0
$487$	16.8087	−	29.1136i	0.761677	−	1.31926i	−0.180309	−	0.983610i	$-0.557710\pi$
$487$	16.8087	−	29.1136i	0.761677	−	1.31926i	0.941986	−	0.335653i	$-0.108957\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−19.6893	−	11.3676i	−0.888568	−	0.513015i	−0.0150939	−	0.999886i	$-0.504805\pi$
$491$	−19.6893	−	11.3676i	−0.888568	−	0.513015i	−0.873474	+	0.486871i	$0.838138\pi$
$492$		0			0
$493$		−	35.9718i		−	1.62009i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.22738	−	0.124486i	−0.0550557	−	0.00558395i
$498$		0			0
$499$	−19.5235			−0.873992			−0.436996	−	0.899463i	$-0.643958\pi$
$499$	−19.5235			−0.873992			−0.436996	+	0.899463i	$0.643958\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	13.6867			0.610262			0.305131	−	0.952310i	$-0.401300\pi$
$503$	13.6867			0.610262			0.305131	+	0.952310i	$0.401300\pi$
$504$		0			0
$505$	46.6609			2.07638
$506$		0			0
$507$		0			0
$508$		0			0
$509$	2.29166			0.101576			0.0507881	−	0.998709i	$-0.483827\pi$
$509$	2.29166			0.101576			0.0507881	+	0.998709i	$0.483827\pi$
$510$		0			0
$511$	6.52186	−	9.04566i	0.288510	−	0.400156i
$512$		0			0
$513$		0			0
$514$		0			0
$515$			38.9395i			1.71588i
$516$		0			0
$517$	−3.87018	−	2.23445i	−0.170210	−	0.0982710i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	8.54102	−	14.7935i	0.374189	−	0.648114i	−0.616017	−	0.787733i	$-0.711255\pi$
$521$	8.54102	−	14.7935i	0.374189	−	0.648114i	0.990205	+	0.139619i	$0.0445879\pi$
$522$		0			0
$523$	−35.7462	+	20.6381i	−1.56307	+	0.902440i	−0.566128	+	0.824317i	$0.691559\pi$
$523$	−35.7462	+	20.6381i	−1.56307	+	0.902440i	−0.996944	+	0.0781229i	$0.975107\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	5.61657i		−	0.244662i
$528$		0			0
$529$	13.8313			0.601359
$530$		0			0
$531$		0			0
$532$		0			0
$533$	16.8294	−	9.71644i	0.728961	−	0.420866i
$534$		0			0
$535$	8.27382	−	4.77689i	0.357708	−	0.206523i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	2.81628	−	13.7409i	0.121306	−	0.591864i
$540$		0			0
$541$	22.7197	+	39.3516i	0.976795	+	1.69186i	0.673880	+	0.738841i	$0.264627\pi$
$541$	22.7197	+	39.3516i	0.976795	+	1.69186i	0.302915	+	0.953018i	$0.402040\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	16.3509	−	28.3206i	0.700395	−	1.21312i
$546$		0			0
$547$	−15.1095	−	26.1705i	−0.646037	−	1.11897i	−0.984061	−	0.177832i	$-0.943092\pi$
$547$	−15.1095	−	26.1705i	−0.646037	−	1.11897i	0.338024	−	0.941138i	$-0.390242\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	2.95118	−	5.11160i	0.125725	−	0.217761i
$552$		0			0
$553$	8.20958	+	5.91905i	0.349107	+	0.251704i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	22.0154	+	12.7106i	0.932822	+	0.538565i	0.887703	−	0.460417i	$-0.152300\pi$
$557$	22.0154	+	12.7106i	0.932822	+	0.538565i	0.0451189	+	0.998982i	$0.485633\pi$
$558$		0			0
$559$		−	16.3585i		−	0.691892i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	1.44346	+	2.50015i	0.0608346	+	0.105369i	0.894839	−	0.446390i	$-0.147290\pi$
$563$	1.44346	+	2.50015i	0.0608346	+	0.105369i	−0.834004	+	0.551758i	$0.813957\pi$
$564$		0			0
$565$	5.29909	+	3.05943i	0.222934	+	0.128711i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	38.5945	+	22.2826i	1.61797	+	0.934134i	0.987445	+	0.157963i	$0.0504927\pi$
$569$	38.5945	+	22.2826i	1.61797	+	0.934134i	0.630523	+	0.776171i	$0.282841\pi$
$570$		0			0
$571$	−3.26470	−	5.65462i	−0.136623	−	0.236638i	0.789593	−	0.613631i	$-0.210292\pi$
$571$	−3.26470	−	5.65462i	−0.136623	−	0.236638i	−0.926216	+	0.376992i	$0.876958\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	24.5251i		−	1.02277i
$576$		0			0
$577$	1.17720	+	0.679658i	0.0490076	+	0.0282945i	0.524304	−	0.851531i	$-0.324326\pi$
$577$	1.17720	+	0.679658i	0.0490076	+	0.0282945i	−0.475296	+	0.879826i	$0.657659\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−19.3279	+	8.68979i	−0.801855	+	0.360513i
$582$		0			0
$583$	−8.77026	+	15.1905i	−0.363227	+	0.629128i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−22.2025	−	38.4559i	−0.916397	−	1.58725i	−0.804843	−	0.593488i	$-0.797750\pi$
$587$	−22.2025	−	38.4559i	−0.916397	−	1.58725i	−0.111555	−	0.993758i	$-0.535583\pi$
$588$		0			0
$589$	0.460793	−	0.798117i	0.0189866	−	0.0328858i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	7.17564	+	12.4286i	0.294668	+	0.510380i	0.974908	−	0.222610i	$-0.0714576\pi$
$593$	7.17564	+	12.4286i	0.294668	+	0.510380i	−0.680240	+	0.732990i	$0.738124\pi$
$594$		0			0
$595$	−47.9576	−	34.5771i	−1.96607	−	1.41752i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−3.03349	+	1.75139i	−0.123945	+	0.0715597i	−0.560691	−	0.828025i	$-0.689464\pi$
$599$	−3.03349	+	1.75139i	−0.123945	+	0.0715597i	0.436746	+	0.899585i	$0.356131\pi$
$600$		0			0
$601$	−15.1846	+	8.76685i	−0.619394	+	0.357607i	−0.776633	−	0.629953i	$-0.783074\pi$
$601$	−15.1846	+	8.76685i	−0.619394	+	0.357607i	0.157239	+	0.987561i	$0.449741\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	25.2802			1.02779
$606$		0			0
$607$			0.0872864i			0.00354285i	0.999998	+	0.00177142i	$0.000563862\pi$
$607$			0.0872864i			0.00354285i	−0.999998	+	0.00177142i	$0.999436\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	6.58373	−	3.80112i	0.266349	−	0.153777i
$612$		0			0
$613$	12.5352	−	21.7116i	0.506292	−	0.876924i	−0.493681	−	0.869643i	$-0.664349\pi$
$613$	12.5352	−	21.7116i	0.506292	−	0.876924i	0.999973	−	0.00728071i	$-0.00231754\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	10.6365	+	6.14101i	0.428211	+	0.247228i	0.698584	−	0.715528i	$-0.253814\pi$
$617$	10.6365	+	6.14101i	0.428211	+	0.247228i	−0.270373	+	0.962756i	$0.587147\pi$
$618$		0			0
$619$			20.3076i			0.816229i	0.912931	+	0.408115i	$0.133814\pi$
$619$			20.3076i			0.816229i	−0.912931	+	0.408115i	$0.866186\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	11.5501	−	5.19294i	0.462747	−	0.208051i
$624$		0			0
$625$	0.103794			0.00415176
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−45.2969			−1.80610
$630$		0			0
$631$	45.9665			1.82990			0.914950	−	0.403568i	$-0.132230\pi$
$631$	45.9665			1.82990			0.914950	+	0.403568i	$0.132230\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−64.8913			−2.57513
$636$		0			0
$637$	17.8482	+	15.8367i	0.707169	+	0.627472i
$638$		0			0
$639$		0			0
$640$		0			0
$641$		−	31.6509i		−	1.25013i	−0.780571	−	0.625067i	$-0.785072\pi$
$641$		−	31.6509i		−	1.25013i	0.780571	−	0.625067i	$-0.214928\pi$
$642$		0			0
$643$	−10.0106	−	5.77960i	−0.394778	−	0.227925i	0.289450	−	0.957193i	$-0.406528\pi$
$643$	−10.0106	−	5.77960i	−0.394778	−	0.227925i	−0.684228	+	0.729268i	$0.739861\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	13.0365	−	22.5799i	0.512519	−	0.887708i	−0.487376	−	0.873192i	$-0.662046\pi$
$647$	13.0365	−	22.5799i	0.512519	−	0.887708i	0.999895	−	0.0145160i	$-0.00462076\pi$
$648$		0			0
$649$	−15.5942	+	9.00332i	−0.612126	+	0.353411i
$650$		0			0
$651$		0			0
$652$		0			0
$653$		−	18.9315i		−	0.740847i	−0.928863	−	0.370424i	$-0.879212\pi$
$653$		−	18.9315i		−	0.740847i	0.928863	−	0.370424i	$-0.120788\pi$
$654$		0			0
$655$	62.7276			2.45097
$656$		0			0
$657$		0			0
$658$		0			0
$659$	23.3508	−	13.4816i	0.909618	−	0.525168i	0.0293098	−	0.999570i	$-0.490669\pi$
$659$	23.3508	−	13.4816i	0.909618	−	0.525168i	0.880308	+	0.474402i	$0.157336\pi$
$660$		0			0
$661$	22.3201	−	12.8865i	0.868151	−	0.501227i	0.00141768	−	0.999999i	$-0.499549\pi$
$661$	22.3201	−	12.8865i	0.868151	−	0.501227i	0.866733	+	0.498772i	$0.166215\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−3.97803	−	8.84793i	−0.154261	−	0.343108i
$666$		0			0
$667$	8.82079	+	15.2780i	0.341542	+	0.591568i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	14.7400	−	25.5304i	0.569030	−	0.985590i
$672$		0			0
$673$	−12.9608	−	22.4487i	−0.499601	−	0.865335i	0.500398	−	0.865795i	$-0.333187\pi$
$673$	−12.9608	−	22.4487i	−0.499601	−	0.865335i	−1.00000		0.000460130i	$0.999854\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−6.55382	+	11.3515i	−0.251884	+	0.436275i	−0.964044	−	0.265741i	$-0.914383\pi$
$677$	−6.55382	+	11.3515i	−0.251884	+	0.436275i	0.712161	+	0.702016i	$0.247717\pi$
$678$		0			0
$679$	12.7574	+	28.3751i	0.489585	+	1.08894i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−25.6910	−	14.8327i	−0.983038	−	0.567557i	−0.0798523	−	0.996807i	$-0.525445\pi$
$683$	−25.6910	−	14.8327i	−0.983038	−	0.567557i	−0.903186	+	0.429249i	$0.858778\pi$
$684$		0			0
$685$			0.00233490i			8.92121e-5i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−14.9195	−	25.8413i	−0.568387	−	0.984475i
$690$		0			0
$691$	−40.9767	−	23.6579i	−1.55883	−	0.899990i	−0.997369	−	0.0724857i	$-0.976907\pi$
$691$	−40.9767	−	23.6579i	−1.55883	−	0.899990i	−0.561459	−	0.827504i	$-0.689760\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−31.6065	−	18.2480i	−1.19890	−	0.692187i
$696$		0			0
$697$	−17.5992	−	30.4827i	−0.666616	−	1.15461i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	13.7742i		−	0.520244i	−0.965576	−	0.260122i	$-0.916237\pi$
$701$		−	13.7742i		−	0.520244i	0.965576	−	0.260122i	$-0.0837627\pi$
$702$		0			0
$703$	−6.43670	−	3.71623i	−0.242765	−	0.140160i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−3.44186	+	33.9355i	−0.129444	+	1.27627i
$708$		0			0
$709$	21.9691	−	38.0517i	0.825069	−	1.42906i	−0.0767981	−	0.997047i	$-0.524470\pi$
$709$	21.9691	−	38.0517i	0.825069	−	1.42906i	0.901867	−	0.432014i	$-0.142197\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	1.37726	+	2.38549i	0.0515789	+	0.0893373i
$714$		0			0
$715$	12.3607	−	21.4094i	0.462265	−	0.800667i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	14.7930	+	25.6223i	0.551687	+	0.955549i	0.998153	+	0.0607489i	$0.0193489\pi$
$719$	14.7930	+	25.6223i	0.551687	+	0.955549i	−0.446466	+	0.894800i	$0.647318\pi$
$720$		0			0
$721$	−28.3198	−	2.87230i	−1.05469	−	0.106970i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−40.8666	+	23.5943i	−1.51775	+	0.876271i
$726$		0			0
$727$	10.1244	−	5.84534i	0.375494	−	0.216792i	−0.300362	−	0.953825i	$-0.597107\pi$
$727$	10.1244	−	5.84534i	0.375494	−	0.216792i	0.675856	+	0.737034i	$0.263774\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−29.6298			−1.09590
$732$		0			0
$733$			33.0733i			1.22159i	0.791789	+	0.610795i	$0.209150\pi$
$733$			33.0733i			1.22159i	−0.791789	+	0.610795i	$0.790850\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	14.4318	−	8.33219i	0.531601	−	0.306920i
$738$		0			0
$739$	21.7528	−	37.6770i	0.800190	−	1.38597i	−0.119301	−	0.992858i	$-0.538065\pi$
$739$	21.7528	−	37.6770i	0.800190	−	1.38597i	0.919491	−	0.393111i	$-0.128601\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	18.0206	+	10.4042i	0.661112	+	0.381693i	0.792701	−	0.609611i	$-0.208674\pi$
$743$	18.0206	+	10.4042i	0.661112	+	0.381693i	−0.131589	+	0.991304i	$0.542008\pi$
$744$		0			0
$745$			40.7083i			1.49144i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	2.86382	+	6.36972i	0.104642	+	0.232745i
$750$		0			0
$751$	39.8984			1.45591			0.727957	−	0.685623i	$-0.240470\pi$
$751$	39.8984			1.45591			0.727957	+	0.685623i	$0.240470\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	17.0969			0.622219
$756$		0			0
$757$	7.45545			0.270973			0.135486	−	0.990779i	$-0.456740\pi$
$757$	7.45545			0.270973			0.135486	+	0.990779i	$0.456740\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	8.64924			0.313535			0.156767	−	0.987636i	$-0.449893\pi$
$761$	8.64924			0.313535			0.156767	+	0.987636i	$0.449893\pi$
$762$		0			0
$763$	19.3908	+	13.9807i	0.701995	+	0.506134i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	30.6319i		−	1.10605i
$768$		0			0
$769$	−20.4818	−	11.8252i	−0.738592	−	0.426426i	0.0829652	−	0.996552i	$-0.473561\pi$
$769$	−20.4818	−	11.8252i	−0.738592	−	0.426426i	−0.821557	+	0.570126i	$0.806894\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	23.2849	−	40.3307i	0.837501	−	1.45059i	−0.0544774	−	0.998515i	$-0.517349\pi$
$773$	23.2849	−	40.3307i	0.837501	−	1.45059i	0.891978	−	0.452079i	$-0.149317\pi$
$774$		0			0
$775$	−6.38084	+	3.68398i	−0.229207	+	0.132333i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		−	5.77546i		−	0.206927i
$780$		0			0
$781$	−0.934344			−0.0334335
$782$		0			0
$783$		0			0
$784$		0			0
$785$	9.62178	−	5.55513i	0.343416	−	0.198271i
$786$		0			0
$787$	21.1657	−	12.2200i	0.754474	−	0.435596i	−0.0728341	−	0.997344i	$-0.523204\pi$
$787$	21.1657	−	12.2200i	0.754474	−	0.435596i	0.827308	+	0.561748i	$0.189871\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−2.61593	+	3.62823i	−0.0930118	+	0.129005i
$792$		0			0
$793$	25.0748	+	43.4309i	0.890433	+	1.54228i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−24.9202	+	43.1631i	−0.882719	+	1.52891i	−0.0344128	+	0.999408i	$0.510956\pi$
$797$	−24.9202	+	43.1631i	−0.882719	+	1.52891i	−0.848306	+	0.529506i	$0.822377\pi$
$798$		0			0
$799$	−6.88489	−	11.9250i	−0.243570	−	0.421875i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	4.22291	−	7.31430i	0.149023	−	0.258116i
$804$		0			0
$805$	28.8475	+	2.92582i	1.01674	+	0.103122i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−10.6735	−	6.16237i	−0.375262	−	0.216657i	0.300493	−	0.953784i	$-0.402849\pi$
$809$	−10.6735	−	6.16237i	−0.375262	−	0.216657i	−0.675755	+	0.737127i	$0.736182\pi$
$810$		0			0
$811$			24.8017i			0.870906i	0.900212	+	0.435453i	$0.143412\pi$
$811$			24.8017i			0.870906i	−0.900212	+	0.435453i	$0.856588\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	5.20047	+	9.00748i	0.182165	+	0.315518i
$816$		0			0
$817$	−4.21041	−	2.43088i	−0.147304	−	0.0850457i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−31.3573	−	18.1041i	−1.09438	−	0.631839i	−0.159639	−	0.987175i	$-0.551033\pi$
$821$	−31.3573	−	18.1041i	−1.09438	−	0.631839i	−0.934738	+	0.355336i	$0.884366\pi$
$822$		0			0
$823$	−9.54093	−	16.5254i	−0.332576	−	0.576038i	0.650440	−	0.759557i	$-0.274584\pi$
$823$	−9.54093	−	16.5254i	−0.332576	−	0.576038i	−0.983016	+	0.183519i	$0.941251\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			31.9013i			1.10932i	0.832079	+	0.554658i	$0.187151\pi$
$827$			31.9013i			1.10932i	−0.832079	+	0.554658i	$0.812849\pi$
$828$		0			0
$829$	13.0645	+	7.54278i	0.453748	+	0.261971i	0.709412	−	0.704794i	$-0.248961\pi$
$829$	13.0645	+	7.54278i	0.453748	+	0.261971i	−0.255664	+	0.966766i	$0.582294\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	28.6846	−	32.3280i	0.993864	−	1.12010i
$834$		0			0
$835$	−2.64397	+	4.57950i	−0.0914985	+	0.158480i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	8.19860	+	14.2004i	0.283047	+	0.490252i	0.972134	−	0.234427i	$-0.0753214\pi$
$839$	8.19860	+	14.2004i	0.283047	+	0.490252i	−0.689087	+	0.724679i	$0.741988\pi$
$840$		0			0
$841$	2.47206	−	4.28173i	0.0852434	−	0.147646i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−2.49817	−	4.32696i	−0.0859397	−	0.148852i
$846$		0			0
$847$	−1.86475	+	18.3857i	−0.0640735	+	0.631741i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	19.2386	−	11.1074i	0.659492	−	0.380758i
$852$		0			0
$853$	−16.5936	+	9.58030i	−0.568153	+	0.328023i	−0.756411	−	0.654096i	$-0.773049\pi$
$853$	−16.5936	+	9.58030i	−0.568153	+	0.328023i	0.188258	+	0.982120i	$0.439716\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−16.1145			−0.550460			−0.275230	−	0.961378i	$-0.588754\pi$
$857$	−16.1145			−0.550460			−0.275230	+	0.961378i	$0.588754\pi$
$858$		0			0
$859$			12.1048i			0.413009i	0.978446	+	0.206505i	$0.0662089\pi$
$859$			12.1048i			0.413009i	−0.978446	+	0.206505i	$0.933791\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−32.2728	+	18.6327i	−1.09858	+	0.634265i	−0.935848	−	0.352405i	$-0.885364\pi$
$863$	−32.2728	+	18.6327i	−1.09858	+	0.634265i	−0.162732	+	0.986670i	$0.552031\pi$
$864$		0			0
$865$	5.55712	−	9.62522i	0.188948	−	0.327267i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	6.63824	+	3.83259i	0.225187	+	0.130012i
$870$		0			0
$871$			28.3485i			0.960553i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−2.99486	+	29.5282i	−0.101245	+	0.998236i
$876$		0			0
$877$	−9.70948			−0.327866			−0.163933	−	0.986471i	$-0.552418\pi$
$877$	−9.70948			−0.327866			−0.163933	+	0.986471i	$0.552418\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−2.63241			−0.0886881			−0.0443440	−	0.999016i	$-0.514120\pi$
$881$	−2.63241			−0.0886881			−0.0443440	+	0.999016i	$0.514120\pi$
$882$		0			0
$883$	36.3181			1.22220			0.611101	−	0.791553i	$-0.290727\pi$
$883$	36.3181			1.22220			0.611101	+	0.791553i	$0.290727\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−16.3642			−0.549455			−0.274728	−	0.961522i	$-0.588588\pi$
$887$	−16.3642			−0.549455			−0.274728	+	0.961522i	$0.588588\pi$
$888$		0			0
$889$	4.78659	−	47.1940i	0.160537	−	1.58284i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		−	2.25939i		−	0.0756076i
$894$		0			0
$895$	−60.5549	−	34.9614i	−2.02413	−	1.16863i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	2.64999	−	4.58992i	0.0883822	−	0.153082i
$900$		0			0
$901$	−46.8058	+	27.0233i	−1.55933	+	0.900277i
$902$		0			0
$903$		0			0
$904$		0			0
$905$			28.5679i			0.949629i
$906$		0			0
$907$	−10.8333			−0.359714			−0.179857	−	0.983693i	$-0.557564\pi$
$907$	−10.8333			−0.359714			−0.179857	+	0.983693i	$0.557564\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	36.8512	−	21.2760i	1.22093	−	0.704907i	0.255817	−	0.966725i	$-0.417655\pi$
$911$	36.8512	−	21.2760i	1.22093	−	0.704907i	0.965117	+	0.261818i	$0.0843221\pi$
$912$		0			0
$913$	−13.8994	+	8.02482i	−0.460003	+	0.265583i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−4.62699	+	45.6204i	−0.152797	+	1.50652i
$918$		0			0
$919$	12.9697	+	22.4641i	0.427829	+	0.741022i	0.996680	−	0.0814187i	$-0.0259451\pi$
$919$	12.9697	+	22.4641i	0.427829	+	0.741022i	−0.568851	+	0.822441i	$0.692612\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	0.794727	−	1.37651i	0.0261588	−	0.0453083i
$924$		0			0
$925$	29.7108	+	51.4606i	0.976884	+	1.69201i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−23.4456	+	40.6089i	−0.769224	+	1.33234i	0.168760	+	0.985657i	$0.446024\pi$
$929$	−23.4456	+	40.6089i	−0.769224	+	1.33234i	−0.937984	+	0.346678i	$0.887310\pi$
$930$		0			0
$931$	6.72834	−	2.24048i	0.220512	−	0.0734287i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−38.7784	−	22.3887i	−1.26819	−	0.732189i
$936$		0			0
$937$		−	0.209357i		−	0.00683939i	−0.999994	−	0.00341969i	$-0.998911\pi$
$937$		−	0.209357i		−	0.00683939i	0.999994	−	0.00341969i	$-0.00108852\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	0.388565	+	0.673014i	0.0126669	+	0.0219396i	0.872289	−	0.488990i	$-0.162635\pi$
$941$	0.388565	+	0.673014i	0.0126669	+	0.0219396i	−0.859622	+	0.510930i	$0.829301\pi$
$942$		0			0
$943$	14.9496	+	8.63113i	0.486825	+	0.281068i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	43.1233	+	24.8972i	1.40132	+	0.809052i	0.994528	−	0.104470i	$-0.0333145\pi$
$947$	43.1233	+	24.8972i	1.40132	+	0.809052i	0.406791	+	0.913521i	$0.366648\pi$
$948$		0			0
$949$	7.18378	+	12.4427i	0.233196	+	0.403906i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	41.4104i		−	1.34141i	−0.741722	−	0.670707i	$-0.765991\pi$
$953$		−	41.4104i		−	1.34141i	0.741722	−	0.670707i	$-0.234009\pi$
$954$		0			0
$955$	41.7010	+	24.0761i	1.34941	+	0.779084i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−0.00169812		0.000172230i	−5.48353e−5		5.56160e-6i
$960$		0			0
$961$	−15.0862	+	26.1301i	−0.486653	+	0.842907i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−11.8274	−	20.4857i	−0.380739	−	0.659459i
$966$		0			0
$967$	−22.8028	+	39.4956i	−0.733289	+	1.27009i	0.222181	+	0.975005i	$0.428682\pi$
$967$	−22.8028	+	39.4956i	−0.733289	+	1.27009i	−0.955470	+	0.295088i	$0.904651\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	4.36733	+	7.56444i	0.140154	+	0.242754i	0.927555	−	0.373688i	$-0.121907\pi$
$971$	4.36733	+	7.56444i	0.140154	+	0.242754i	−0.787400	+	0.616442i	$0.788573\pi$
$972$		0			0
$973$	15.6028	−	21.6407i	0.500202	−	0.693768i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	12.9058	−	7.45114i	0.412892	−	0.238383i	−0.279140	−	0.960250i	$-0.590049\pi$
$977$	12.9058	−	7.45114i	0.412892	−	0.238383i	0.692031	+	0.721867i	$0.256716\pi$
$978$		0			0
$979$	8.30615	−	4.79556i	0.265466	−	0.153267i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−3.06917			−0.0978912			−0.0489456	−	0.998801i	$-0.515586\pi$
$983$	−3.06917			−0.0978912			−0.0489456	+	0.998801i	$0.515586\pi$
$984$		0			0
$985$			16.0788i			0.512314i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	12.5845	−	7.26565i	0.400163	−	0.231034i
$990$		0			0
$991$	−27.9075	+	48.3372i	−0.886510	+	1.53548i	−0.0425375	+	0.999095i	$0.513544\pi$
$991$	−27.9075	+	48.3372i	−0.886510	+	1.53548i	−0.843973	+	0.536386i	$0.819789\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−36.0798	−	20.8307i	−1.14381	−	0.660377i
$996$		0			0
$997$			6.12692i			0.194042i	0.995282	+	0.0970208i	$0.0309313\pi$
$997$			6.12692i			0.194042i	−0.995282	+	0.0970208i	$0.969069\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.df.c.17.7		16
3.2	odd	2		1008.2.df.c.689.5		16
4.3	odd	2		378.2.t.a.17.8		16
7.5	odd	6		3024.2.ca.c.2609.7		16
9.2	odd	6		3024.2.ca.c.2033.7		16
9.7	even	3		1008.2.ca.c.353.8		16
12.11	even	2		126.2.t.a.59.2	yes	16
21.5	even	6		1008.2.ca.c.257.8		16
28.3	even	6		2646.2.m.b.881.4		16
28.11	odd	6		2646.2.m.a.881.1		16
28.19	even	6		378.2.l.a.341.4		16
28.23	odd	6		2646.2.l.a.1097.1		16
28.27	even	2		2646.2.t.b.2285.5		16
36.7	odd	6		126.2.l.a.101.1	yes	16
36.11	even	6		378.2.l.a.143.8		16
36.23	even	6		1134.2.k.b.647.8		16
36.31	odd	6		1134.2.k.a.647.1		16
63.47	even	6	inner	3024.2.df.c.1601.7		16
63.61	odd	6		1008.2.df.c.929.5		16
84.11	even	6		882.2.m.a.293.6		16
84.23	even	6		882.2.l.b.509.8		16
84.47	odd	6		126.2.l.a.5.5	✓	16
84.59	odd	6		882.2.m.b.293.7		16
84.83	odd	2		882.2.t.a.815.3		16
252.11	even	6		2646.2.m.b.1763.4		16
252.47	odd	6		378.2.t.a.89.8		16
252.79	odd	6		882.2.t.a.803.3		16
252.83	odd	6		2646.2.l.a.521.5		16
252.103	even	6		1134.2.k.b.971.8		16
252.115	even	6		882.2.m.a.587.6		16
252.131	odd	6		1134.2.k.a.971.1		16
252.151	odd	6		882.2.m.b.587.7		16
252.187	even	6		126.2.t.a.47.2	yes	16
252.191	even	6		2646.2.t.b.1979.5		16
252.223	even	6		882.2.l.b.227.4		16
252.227	odd	6		2646.2.m.a.1763.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.5	✓	16	84.47	odd	6
126.2.l.a.101.1	yes	16	36.7	odd	6
126.2.t.a.47.2	yes	16	252.187	even	6
126.2.t.a.59.2	yes	16	12.11	even	2
378.2.l.a.143.8		16	36.11	even	6
378.2.l.a.341.4		16	28.19	even	6
378.2.t.a.17.8		16	4.3	odd	2
378.2.t.a.89.8		16	252.47	odd	6
882.2.l.b.227.4		16	252.223	even	6
882.2.l.b.509.8		16	84.23	even	6
882.2.m.a.293.6		16	84.11	even	6
882.2.m.a.587.6		16	252.115	even	6
882.2.m.b.293.7		16	84.59	odd	6
882.2.m.b.587.7		16	252.151	odd	6
882.2.t.a.803.3		16	252.79	odd	6
882.2.t.a.815.3		16	84.83	odd	2
1008.2.ca.c.257.8		16	21.5	even	6
1008.2.ca.c.353.8		16	9.7	even	3
1008.2.df.c.689.5		16	3.2	odd	2
1008.2.df.c.929.5		16	63.61	odd	6
1134.2.k.a.647.1		16	36.31	odd	6
1134.2.k.a.971.1		16	252.131	odd	6
1134.2.k.b.647.8		16	36.23	even	6
1134.2.k.b.971.8		16	252.103	even	6
2646.2.l.a.521.5		16	252.83	odd	6
2646.2.l.a.1097.1		16	28.23	odd	6
2646.2.m.a.881.1		16	28.11	odd	6
2646.2.m.a.1763.1		16	252.227	odd	6
2646.2.m.b.881.4		16	28.3	even	6
2646.2.m.b.1763.4		16	252.11	even	6
2646.2.t.b.1979.5		16	252.191	even	6
2646.2.t.b.2285.5		16	28.27	even	2
3024.2.ca.c.2033.7		16	9.2	odd	6
3024.2.ca.c.2609.7		16	7.5	odd	6
3024.2.df.c.17.7		16	1.1	even	1	trivial
3024.2.df.c.1601.7		16	63.47	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.df (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+3.61932 q^{5} +(-0.266972 + 2.63225i) q^{7} +2.00379i q^{11} +(-2.95206 - 1.70437i) q^{13} +(-3.08709 + 5.34700i) q^{17} +(-0.877353 + 0.506540i) q^{19} -3.02799i q^{23} +8.09945 q^{25} +(-5.04560 + 2.91308i) q^{29} +(-0.787812 + 0.454844i) q^{31} +(-0.966257 + 9.52693i) q^{35} +(3.66825 + 6.35359i) q^{37} +(-2.85045 + 4.93712i) q^{41} +(2.39949 + 4.15605i) q^{43} +(-1.11511 + 1.93143i) q^{47} +(-6.85745 - 1.40547i) q^{49} +(7.58088 + 4.37683i) q^{53} +7.25237i q^{55} +(4.49313 + 7.78233i) q^{59} +(-12.7410 - 7.35603i) q^{61} +(-10.6844 - 6.16866i) q^{65} +(-4.15821 - 7.20222i) q^{67} +0.466287i q^{71} +(-3.65022 - 2.10746i) q^{73} +(-5.27448 - 0.534957i) q^{77} +(1.91267 - 3.31284i) q^{79} +(4.00481 + 6.93654i) q^{83} +(-11.1732 + 19.3525i) q^{85} +(-2.39324 - 4.14521i) q^{89} +(5.27445 - 7.31553i) q^{91} +(-3.17542 + 1.83333i) q^{95} +(10.1835 - 5.87944i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{7} - 6 q^{13} - 18 q^{17} + 16 q^{25} - 6 q^{29} - 6 q^{31} - 30 q^{35} - 2 q^{37} - 6 q^{41} + 2 q^{43} - 18 q^{47} + 10 q^{49} - 36 q^{53} + 30 q^{59} - 60 q^{61} - 42 q^{65} - 14 q^{67} + 18 q^{77}+ \cdots - 6 q^{97}+O(q^{100}) \) 16 * q - 2 * q^7 - 6 * q^13 - 18 * q^17 + 16 * q^25 - 6 * q^29 - 6 * q^31 - 30 * q^35 - 2 * q^37 - 6 * q^41 + 2 * q^43 - 18 * q^47 + 10 * q^49 - 36 * q^53 + 30 * q^59 - 60 * q^61 - 42 * q^65 - 14 * q^67 + 18 * q^77 + 16 * q^79 - 12 * q^85 - 24 * q^89 + 12 * q^91 - 66 * q^95 - 6 * q^97

Introduction

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