LMFDB - Embedded newform 1008.2.bt.c.17.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1008,2,Mod(17,1008)] 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("1008.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1008, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 3, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.bt (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,0,0,-4] 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:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.1
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	1008.17
Dual form			1008.2.bt.c.593.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.09077 - 3.62132i) q^{5} +(1.62132 + 2.09077i) q^{7} +(-2.59808 - 1.50000i) q^{11} -2.44949i q^{13} +(0.507306 - 0.878680i) q^{17} +(0.878680 - 0.507306i) q^{19} +(-3.67423 + 2.12132i) q^{23} +(-6.24264 + 10.8126i) q^{25} +1.24264i q^{29} +(-4.86396 - 2.80821i) q^{31} +(4.18154 - 10.2426i) q^{35} +(-4.12132 - 7.13834i) q^{37} -2.02922 q^{41} -8.24264 q^{43} +(-0.507306 - 0.878680i) q^{47} +(-1.74264 + 6.77962i) q^{49} +(-1.07616 - 0.621320i) q^{53} +12.5446i q^{55} +(-5.76500 + 9.98528i) q^{59} +(5.12132 - 2.95680i) q^{61} +(-8.87039 + 5.12132i) q^{65} +(-5.00000 + 8.66025i) q^{67} -10.2426i q^{71} +(7.24264 + 4.18154i) q^{73} +(-1.07616 - 7.86396i) q^{77} +(-5.62132 - 9.73641i) q^{79} -3.16693 q^{83} -4.24264 q^{85} +(-5.19615 - 9.00000i) q^{89} +(5.12132 - 3.97141i) q^{91} +(-3.67423 - 2.12132i) q^{95} -3.76127i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{7} + 24 q^{19} - 16 q^{25} + 12 q^{31} - 16 q^{37} - 32 q^{43} + 20 q^{49} + 24 q^{61} - 40 q^{67} + 24 q^{73} - 28 q^{79} + 24 q^{91}+O(q^{100}) $ 8 * q - 4 * q^7 + 24 * q^19 - 16 * q^25 + 12 * q^31 - 16 * q^37 - 32 * q^43 + 20 * q^49 + 24 * q^61 - 40 * q^67 + 24 * q^73 - 28 * q^79 + 24 * q^91

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−2.09077	−	3.62132i	−0.935021	−	1.61950i	−0.774597	−	0.632456i	$-0.782047\pi$
$5$	−2.09077	−	3.62132i	−0.935021	−	1.61950i	−0.160424	−	0.987048i	$-0.551286\pi$
$6$		0			0
$7$	1.62132	+	2.09077i	0.612801	+	0.790237i
$7$	1.62132	+	2.09077i	0.612801	+	0.790237i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.59808	−	1.50000i	−0.783349	−	0.452267i	0.0542666	−	0.998526i	$-0.482718\pi$
$11$	−2.59808	−	1.50000i	−0.783349	−	0.452267i	−0.837616	+	0.546259i	$0.816051\pi$
$12$		0			0
$13$		−	2.44949i		−	0.679366i	−0.940540	−	0.339683i	$-0.889680\pi$
$13$		−	2.44949i		−	0.679366i	0.940540	−	0.339683i	$-0.110320\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.507306	−	0.878680i	0.123040	−	0.213111i	−0.797925	−	0.602756i	$-0.794069\pi$
$17$	0.507306	−	0.878680i	0.123040	−	0.213111i	0.920965	+	0.389645i	$0.127402\pi$
$18$		0			0
$19$	0.878680	−	0.507306i	0.201583	−	0.116384i	−0.395811	−	0.918332i	$-0.629536\pi$
$19$	0.878680	−	0.507306i	0.201583	−	0.116384i	0.597394	+	0.801948i	$0.296203\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.67423	+	2.12132i	−0.766131	+	0.442326i	−0.831493	−	0.555536i	$-0.812513\pi$
$23$	−3.67423	+	2.12132i	−0.766131	+	0.442326i	0.0653618	+	0.997862i	$0.479180\pi$
$24$		0			0
$25$	−6.24264	+	10.8126i	−1.24853	+	2.16251i
$26$		0			0
$27$		0			0
$28$		0			0
$29$			1.24264i			0.230753i	0.993322	+	0.115376i	$0.0368074\pi$
$29$			1.24264i			0.230753i	−0.993322	+	0.115376i	$0.963193\pi$
$30$		0			0
$31$	−4.86396	−	2.80821i	−0.873593	−	0.504369i	−0.00505256	−	0.999987i	$-0.501608\pi$
$31$	−4.86396	−	2.80821i	−0.873593	−	0.504369i	−0.868541	+	0.495618i	$0.834942\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	4.18154	−	10.2426i	0.706809	−	1.73132i
$36$		0			0
$37$	−4.12132	−	7.13834i	−0.677541	−	1.17354i	−0.975719	−	0.219025i	$-0.929712\pi$
$37$	−4.12132	−	7.13834i	−0.677541	−	1.17354i	0.298178	−	0.954510i	$-0.403621\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−2.02922			−0.316912			−0.158456	−	0.987366i	$-0.550652\pi$
$41$	−2.02922			−0.316912			−0.158456	+	0.987366i	$0.550652\pi$
$42$		0			0
$43$	−8.24264			−1.25699			−0.628495	−	0.777813i	$-0.716329\pi$
$43$	−8.24264			−1.25699			−0.628495	+	0.777813i	$0.716329\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.507306	−	0.878680i	−0.0739982	−	0.128169i	0.826652	−	0.562713i	$-0.190243\pi$
$47$	−0.507306	−	0.878680i	−0.0739982	−	0.128169i	−0.900650	+	0.434545i	$0.856909\pi$
$48$		0			0
$49$	−1.74264	+	6.77962i	−0.248949	+	0.968517i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−1.07616	−	0.621320i	−0.147822	−	0.0853449i	0.424265	−	0.905538i	$-0.360533\pi$
$53$	−1.07616	−	0.621320i	−0.147822	−	0.0853449i	−0.572087	+	0.820193i	$0.693866\pi$
$54$		0			0
$55$			12.5446i			1.69152i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−5.76500	+	9.98528i	−0.750540	+	1.29997i	0.197022	+	0.980399i	$0.436873\pi$
$59$	−5.76500	+	9.98528i	−0.750540	+	1.29997i	−0.947561	+	0.319574i	$0.896460\pi$
$60$		0			0
$61$	5.12132	−	2.95680i	0.655718	−	0.378579i	−0.134926	−	0.990856i	$-0.543080\pi$
$61$	5.12132	−	2.95680i	0.655718	−	0.378579i	0.790643	+	0.612277i	$0.209746\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−8.87039	+	5.12132i	−1.10024	+	0.635222i
$66$		0			0
$67$	−5.00000	+	8.66025i	−0.610847	+	1.05802i	0.380251	+	0.924883i	$0.375838\pi$
$67$	−5.00000	+	8.66025i	−0.610847	+	1.05802i	−0.991098	+	0.133135i	$0.957496\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	10.2426i		−	1.21558i	−0.794099	−	0.607789i	$-0.792057\pi$
$71$		−	10.2426i		−	1.21558i	0.794099	−	0.607789i	$-0.207943\pi$
$72$		0			0
$73$	7.24264	+	4.18154i	0.847687	+	0.489412i	0.859870	−	0.510513i	$-0.170545\pi$
$73$	7.24264	+	4.18154i	0.847687	+	0.489412i	−0.0121828	+	0.999926i	$0.503878\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.07616	−	7.86396i	−0.122640	−	0.896182i
$78$		0			0
$79$	−5.62132	−	9.73641i	−0.632448	−	1.09543i	−0.987050	−	0.160415i	$-0.948717\pi$
$79$	−5.62132	−	9.73641i	−0.632448	−	1.09543i	0.354602	−	0.935017i	$-0.384616\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−3.16693			−0.347616			−0.173808	−	0.984780i	$-0.555607\pi$
$83$	−3.16693			−0.347616			−0.173808	+	0.984780i	$0.555607\pi$
$84$		0			0
$85$	−4.24264			−0.460179
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−5.19615	−	9.00000i	−0.550791	−	0.953998i	−0.998218	−	0.0596775i	$-0.980993\pi$
$89$	−5.19615	−	9.00000i	−0.550791	−	0.953998i	0.447427	−	0.894321i	$-0.352341\pi$
$90$		0			0
$91$	5.12132	−	3.97141i	0.536860	−	0.416317i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−3.67423	−	2.12132i	−0.376969	−	0.217643i
$96$		0			0
$97$		−	3.76127i		−	0.381900i	−0.981600	−	0.190950i	$-0.938843\pi$
$97$		−	3.76127i		−	0.381900i	0.981600	−	0.190950i	$-0.0611568\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$101$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$102$		0			0
$103$	13.2426	−	7.64564i	1.30484	−	0.753348i	0.323607	−	0.946192i	$-0.395105\pi$
$103$	13.2426	−	7.64564i	1.30484	−	0.753348i	0.981229	+	0.192844i	$0.0617712\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.75039	−	2.74264i	0.459238	−	0.265141i	−0.252486	−	0.967601i	$-0.581248\pi$
$107$	4.75039	−	2.74264i	0.459238	−	0.265141i	0.711724	+	0.702459i	$0.247915\pi$
$108$		0			0
$109$	−0.757359	+	1.31178i	−0.0725419	+	0.125646i	−0.900015	−	0.435860i	$-0.856444\pi$
$109$	−0.757359	+	1.31178i	−0.0725419	+	0.125646i	0.827473	+	0.561506i	$0.189778\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$			8.48528i			0.798228i	0.916901	+	0.399114i	$0.130682\pi$
$113$			8.48528i			0.798228i	−0.916901	+	0.399114i	$0.869318\pi$
$114$		0			0
$115$	15.3640	+	8.87039i	1.43270	+	0.827168i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	2.65962	−	0.363961i	0.243807	−	0.0333643i
$120$		0			0
$121$	−1.00000	−	1.73205i	−0.0909091	−	0.157459i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	31.3000			2.79956
$126$		0			0
$127$	5.24264			0.465209			0.232605	−	0.972571i	$-0.425275\pi$
$127$	5.24264			0.465209			0.232605	+	0.972571i	$0.425275\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−2.59808	−	4.50000i	−0.226995	−	0.393167i	0.729921	−	0.683531i	$-0.239557\pi$
$131$	−2.59808	−	4.50000i	−0.226995	−	0.393167i	−0.956916	+	0.290365i	$0.906223\pi$
$132$		0			0
$133$	2.48528	+	1.01461i	0.215501	+	0.0879780i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−12.5446	−	7.24264i	−1.07176	−	0.618781i	−0.143098	−	0.989709i	$-0.545706\pi$
$137$	−12.5446	−	7.24264i	−1.07176	−	0.618781i	−0.928662	+	0.370928i	$0.879040\pi$
$138$		0			0
$139$		−	20.1903i		−	1.71252i	−0.516549	−	0.856258i	$-0.672783\pi$
$139$		−	20.1903i		−	1.71252i	0.516549	−	0.856258i	$-0.327217\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−3.67423	+	6.36396i	−0.307255	+	0.532181i
$144$		0			0
$145$	4.50000	−	2.59808i	0.373705	−	0.215758i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	17.7408	−	10.2426i	1.45338	−	0.839110i	0.454709	−	0.890640i	$-0.349743\pi$
$149$	17.7408	−	10.2426i	1.45338	−	0.839110i	0.998671	+	0.0515300i	$0.0164098\pi$
$150$		0			0
$151$	−1.62132	+	2.80821i	−0.131941	+	0.228529i	−0.924425	−	0.381364i	$-0.875454\pi$
$151$	−1.62132	+	2.80821i	−0.131941	+	0.228529i	0.792484	+	0.609893i	$0.208788\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$			23.4853i			1.88638i
$156$		0			0
$157$	−12.7279	−	7.34847i	−1.01580	−	0.586472i	−0.102915	−	0.994690i	$-0.532817\pi$
$157$	−12.7279	−	7.34847i	−1.01580	−	0.586472i	−0.912884	+	0.408219i	$0.866150\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−10.3923	−	4.24264i	−0.819028	−	0.334367i
$162$		0			0
$163$	3.12132	+	5.40629i	0.244481	+	0.423453i	0.961985	−	0.273101i	$-0.0880492\pi$
$163$	3.12132	+	5.40629i	0.244481	+	0.423453i	−0.717505	+	0.696554i	$0.754716\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	23.0600			1.78444			0.892219	−	0.451603i	$-0.149148\pi$
$167$	23.0600			1.78444			0.892219	+	0.451603i	$0.149148\pi$
$168$		0			0
$169$	7.00000			0.538462
$170$		0			0
$171$		0			0
$172$		0			0
$173$	10.3923	+	18.0000i	0.790112	+	1.36851i	0.925897	+	0.377776i	$0.123311\pi$
$173$	10.3923	+	18.0000i	0.790112	+	1.36851i	−0.135785	+	0.990738i	$0.543356\pi$
$174$		0			0
$175$	−32.7279	+	4.47871i	−2.47400	+	0.338559i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	8.23999	+	4.75736i	0.615886	+	0.355582i	0.775265	−	0.631636i	$-0.217616\pi$
$179$	8.23999	+	4.75736i	0.615886	+	0.355582i	−0.159380	+	0.987217i	$0.550949\pi$
$180$		0			0
$181$		−	2.02922i		−	0.150831i	−0.997152	−	0.0754155i	$-0.975972\pi$
$181$		−	2.02922i		−	0.150831i	0.997152	−	0.0754155i	$-0.0240283\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−17.2335	+	29.8492i	−1.26703	+	2.19456i
$186$		0			0
$187$	−2.63604	+	1.52192i	−0.192766	+	0.111294i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−7.34847	+	4.24264i	−0.531717	+	0.306987i	−0.741715	−	0.670715i	$-0.765987\pi$
$191$	−7.34847	+	4.24264i	−0.531717	+	0.306987i	0.209999	+	0.977702i	$0.432654\pi$
$192$		0			0
$193$	3.74264	−	6.48244i	0.269401	−	0.466617i	−0.699306	−	0.714822i	$-0.746508\pi$
$193$	3.74264	−	6.48244i	0.269401	−	0.466617i	0.968707	+	0.248206i	$0.0798409\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			9.51472i			0.677896i	0.940805	+	0.338948i	$0.110071\pi$
$197$			9.51472i			0.677896i	−0.940805	+	0.338948i	$0.889929\pi$
$198$		0			0
$199$	13.9706	+	8.06591i	0.990347	+	0.571777i	0.905378	−	0.424607i	$-0.139588\pi$
$199$	13.9706	+	8.06591i	0.990347	+	0.571777i	0.0849690	+	0.996384i	$0.472921\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−2.59808	+	2.01472i	−0.182349	+	0.141406i
$204$		0			0
$205$	4.24264	+	7.34847i	0.296319	+	0.513239i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−3.04384			−0.210547
$210$		0			0
$211$	−8.24264			−0.567447			−0.283723	−	0.958906i	$-0.591570\pi$
$211$	−8.24264			−0.567447			−0.283723	+	0.958906i	$0.591570\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	17.2335	+	29.8492i	1.17531	+	2.03570i
$216$		0			0
$217$	−2.01472	−	14.7224i	−0.136768	−	0.999424i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−2.15232	−	1.24264i	−0.144780	−	0.0835891i
$222$		0			0
$223$		−	12.5446i		−	0.840050i	−0.907513	−	0.420025i	$-0.862021\pi$
$223$		−	12.5446i		−	0.840050i	0.907513	−	0.420025i	$-0.137979\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	7.79423	−	13.5000i	0.517321	−	0.896026i	−0.482476	−	0.875909i	$-0.660263\pi$
$227$	7.79423	−	13.5000i	0.517321	−	0.896026i	0.999798	−	0.0201176i	$-0.00640405\pi$
$228$		0			0
$229$	−12.0000	+	6.92820i	−0.792982	+	0.457829i	−0.841011	−	0.541017i	$-0.818039\pi$
$229$	−12.0000	+	6.92820i	−0.792982	+	0.457829i	0.0480291	+	0.998846i	$0.484706\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	5.82655	−	3.36396i	0.381710	−	0.220380i	−0.296852	−	0.954924i	$-0.595937\pi$
$233$	5.82655	−	3.36396i	0.381710	−	0.220380i	0.678562	+	0.734543i	$0.262603\pi$
$234$		0			0
$235$	−2.12132	+	3.67423i	−0.138380	+	0.239681i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		−	12.7279i		−	0.823301i	−0.911342	−	0.411650i	$-0.864952\pi$
$239$		−	12.7279i		−	0.823301i	0.911342	−	0.411650i	$-0.135048\pi$
$240$		0			0
$241$	14.7426	+	8.51167i	0.949657	+	0.548285i	0.892974	−	0.450108i	$-0.148614\pi$
$241$	14.7426	+	8.51167i	0.949657	+	0.548285i	0.0566826	+	0.998392i	$0.481948\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	28.1946	−	7.86396i	1.80129	−	0.502410i
$246$		0			0
$247$	−1.24264	−	2.15232i	−0.0790673	−	0.136949i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−17.6177			−1.11202			−0.556009	−	0.831176i	$-0.687668\pi$
$251$	−17.6177			−1.11202			−0.556009	+	0.831176i	$0.687668\pi$
$252$		0			0
$253$	12.7279			0.800198
$254$		0			0
$255$		0			0
$256$		0			0
$257$	12.5446	+	21.7279i	0.782512	+	1.35535i	0.930474	+	0.366358i	$0.119395\pi$
$257$	12.5446	+	21.7279i	0.782512	+	1.35535i	−0.147962	+	0.988993i	$0.547271\pi$
$258$		0			0
$259$	8.24264	−	20.1903i	0.512173	−	1.25456i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−23.5673	−	13.6066i	−1.45322	−	0.839019i	−0.454561	−	0.890716i	$-0.650204\pi$
$263$	−23.5673	−	13.6066i	−1.45322	−	0.839019i	−0.998663	+	0.0516967i	$0.983537\pi$
$264$		0			0
$265$			5.19615i			0.319197i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−5.25770	+	9.10660i	−0.320568	+	0.555239i	−0.980605	−	0.195993i	$-0.937207\pi$
$269$	−5.25770	+	9.10660i	−0.320568	+	0.555239i	0.660038	+	0.751232i	$0.270540\pi$
$270$		0			0
$271$	9.62132	−	5.55487i	0.584454	−	0.337434i	−0.178448	−	0.983949i	$-0.557108\pi$
$271$	9.62132	−	5.55487i	0.584454	−	0.337434i	0.762901	+	0.646515i	$0.223774\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	32.4377	−	18.7279i	1.95607	−	1.12934i
$276$		0			0
$277$	10.4853	−	18.1610i	0.630000	−	1.09119i	−0.357552	−	0.933893i	$-0.616388\pi$
$277$	10.4853	−	18.1610i	0.630000	−	1.09119i	0.987551	−	0.157298i	$-0.0502783\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		−	6.00000i		−	0.357930i	−0.983855	−	0.178965i	$-0.942725\pi$
$281$		−	6.00000i		−	0.357930i	0.983855	−	0.178965i	$-0.0572749\pi$
$282$		0			0
$283$	5.63604	+	3.25397i	0.335028	+	0.193428i	0.658071	−	0.752956i	$-0.271373\pi$
$283$	5.63604	+	3.25397i	0.335028	+	0.193428i	−0.323043	+	0.946384i	$0.604706\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−3.29002	−	4.24264i	−0.194204	−	0.250435i
$288$		0			0
$289$	7.98528	+	13.8309i	0.469722	+	0.813583i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−4.18154			−0.244288			−0.122144	−	0.992512i	$-0.538977\pi$
$293$	−4.18154			−0.244288			−0.122144	+	0.992512i	$0.538977\pi$
$294$		0			0
$295$	48.2132			2.80708
$296$		0			0
$297$		0			0
$298$		0			0
$299$	5.19615	+	9.00000i	0.300501	+	0.520483i
$300$		0			0
$301$	−13.3640	−	17.2335i	−0.770286	−	0.993321i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−21.4150	−	12.3640i	−1.22622	−	0.707958i
$306$		0			0
$307$		−	24.6690i		−	1.40793i	−0.710233	−	0.703966i	$-0.751411\pi$
$307$		−	24.6690i		−	1.40793i	0.710233	−	0.703966i	$-0.248589\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−9.37769	+	16.2426i	−0.531760	+	0.921036i	0.467552	+	0.883965i	$0.345136\pi$
$311$	−9.37769	+	16.2426i	−0.531760	+	0.921036i	−0.999313	+	0.0370703i	$0.988197\pi$
$312$		0			0
$313$	−0.985281	+	0.568852i	−0.0556914	+	0.0321534i	−0.527587	−	0.849501i	$-0.676903\pi$
$313$	−0.985281	+	0.568852i	−0.0556914	+	0.0321534i	0.471896	+	0.881654i	$0.343570\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	6.27231	−	3.62132i	0.352288	−	0.203394i	−0.313404	−	0.949620i	$-0.601470\pi$
$317$	6.27231	−	3.62132i	0.352288	−	0.203394i	0.665693	+	0.746226i	$0.268136\pi$
$318$		0			0
$319$	1.86396	−	3.22848i	0.104362	−	0.180760i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	1.02944i		−	0.0572794i
$324$		0			0
$325$	26.4853	+	15.2913i	1.46914	+	0.848208i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	1.01461	−	2.48528i	0.0559374	−	0.137018i
$330$		0			0
$331$	8.72792	+	15.1172i	0.479730	+	0.830917i	0.999730	−	0.0232497i	$-0.00740129\pi$
$331$	8.72792	+	15.1172i	0.479730	+	0.830917i	−0.520000	+	0.854166i	$0.674068\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	41.8154			2.28462
$336$		0			0
$337$	−5.00000			−0.272367			−0.136184	−	0.990684i	$-0.543484\pi$
$337$	−5.00000			−0.272367			−0.136184	+	0.990684i	$0.543484\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	8.42463	+	14.5919i	0.456219	+	0.790195i
$342$		0			0
$343$	−17.0000	+	7.34847i	−0.917914	+	0.396780i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−12.5446	−	7.24264i	−0.673431	−	0.388805i	0.123945	−	0.992289i	$-0.460445\pi$
$347$	−12.5446	−	7.24264i	−0.673431	−	0.388805i	−0.797375	+	0.603484i	$0.793779\pi$
$348$		0			0
$349$		−	36.9164i		−	1.97609i	−0.154163	−	0.988045i	$-0.549268\pi$
$349$		−	36.9164i		−	1.97609i	0.154163	−	0.988045i	$-0.450732\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	9.37769	−	16.2426i	0.499124	−	0.864509i	−0.500875	−	0.865519i	$-0.666988\pi$
$353$	9.37769	−	16.2426i	0.499124	−	0.864509i	0.999999	+	0.00101095i	$0.000321796\pi$
$354$		0			0
$355$	−37.0919	+	21.4150i	−1.96863	+	1.13659i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−15.5885	+	9.00000i	−0.822727	+	0.475002i	−0.851356	−	0.524588i	$-0.824219\pi$
$359$	−15.5885	+	9.00000i	−0.822727	+	0.475002i	0.0286287	+	0.999590i	$0.490886\pi$
$360$		0			0
$361$	−8.98528	+	15.5630i	−0.472910	+	0.819103i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		−	34.9706i		−	1.83044i
$366$		0			0
$367$	−16.3492	−	9.43924i	−0.853424	−	0.492724i	0.00838099	−	0.999965i	$-0.497332\pi$
$367$	−16.3492	−	9.43924i	−0.853424	−	0.492724i	−0.861804	+	0.507241i	$0.830666\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.445759	−	3.25736i	−0.0231427	−	0.169114i
$372$		0			0
$373$	−10.7279	−	18.5813i	−0.555471	−	0.962104i	−0.997867	−	0.0652837i	$-0.979205\pi$
$373$	−10.7279	−	18.5813i	−0.555471	−	0.962104i	0.442396	−	0.896820i	$-0.354129\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	3.04384			0.156766
$378$		0			0
$379$	4.48528			0.230393			0.115197	−	0.993343i	$-0.463250\pi$
$379$	4.48528			0.230393			0.115197	+	0.993343i	$0.463250\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−6.21076	−	10.7574i	−0.317355	−	0.549675i	0.662580	−	0.748991i	$-0.269461\pi$
$383$	−6.21076	−	10.7574i	−0.317355	−	0.549675i	−0.979935	+	0.199316i	$0.936128\pi$
$384$		0			0
$385$	−26.2279	+	20.3389i	−1.33670	+	1.03656i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−16.8493	−	9.72792i	−0.854291	−	0.493225i	0.00780525	−	0.999970i	$-0.497515\pi$
$389$	−16.8493	−	9.72792i	−0.854291	−	0.493225i	−0.862096	+	0.506744i	$0.830849\pi$
$390$		0			0
$391$			4.30463i			0.217695i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−23.5058	+	40.7132i	−1.18270	+	2.04850i
$396$		0			0
$397$	12.0000	−	6.92820i	0.602263	−	0.347717i	−0.167668	−	0.985843i	$-0.553624\pi$
$397$	12.0000	−	6.92820i	0.602263	−	0.347717i	0.769931	+	0.638127i	$0.220290\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$401$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$402$		0			0
$403$	−6.87868	+	11.9142i	−0.342651	+	0.593490i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			24.7279i			1.22572i
$408$		0			0
$409$	−3.98528	−	2.30090i	−0.197059	−	0.113772i	0.398224	−	0.917288i	$-0.369627\pi$
$409$	−3.98528	−	2.30090i	−0.197059	−	0.113772i	−0.595283	+	0.803516i	$0.702960\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−30.2238	+	4.13604i	−1.48722	+	0.203521i
$414$		0			0
$415$	6.62132	+	11.4685i	0.325028	+	0.562965i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	4.05845			0.198268			0.0991341	−	0.995074i	$-0.468393\pi$
$419$	4.05845			0.198268			0.0991341	+	0.995074i	$0.468393\pi$
$420$		0			0
$421$	−5.75736			−0.280597			−0.140298	−	0.990109i	$-0.544806\pi$
$421$	−5.75736			−0.280597			−0.140298	+	0.990109i	$0.544806\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	6.33386	+	10.9706i	0.307237	+	0.532150i
$426$		0			0
$427$	14.4853	+	5.91359i	0.700992	+	0.286179i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−17.7408	−	10.2426i	−0.854543	−	0.493371i	0.00763808	−	0.999971i	$-0.497569\pi$
$431$	−17.7408	−	10.2426i	−0.854543	−	0.493371i	−0.862181	+	0.506600i	$0.830902\pi$
$432$		0			0
$433$			3.46410i			0.166474i	0.996530	+	0.0832370i	$0.0265259\pi$
$433$			3.46410i			0.166474i	−0.996530	+	0.0832370i	$0.973474\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−2.15232	+	3.72792i	−0.102959	+	0.178331i
$438$		0			0
$439$	−23.5919	+	13.6208i	−1.12598	+	0.650084i	−0.942921	−	0.333018i	$-0.891933\pi$
$439$	−23.5919	+	13.6208i	−1.12598	+	0.650084i	−0.183059	+	0.983102i	$0.558600\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	29.8396	−	17.2279i	1.41772	−	0.818523i	0.421625	−	0.906770i	$-0.361460\pi$
$443$	29.8396	−	17.2279i	1.41772	−	0.818523i	0.996099	+	0.0882469i	$0.0281264\pi$
$444$		0			0
$445$	−21.7279	+	37.6339i	−1.03000	+	1.78402i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			10.2426i			0.483380i	0.970354	+	0.241690i	$0.0777017\pi$
$449$			10.2426i			0.483380i	−0.970354	+	0.241690i	$0.922298\pi$
$450$		0			0
$451$	5.27208	+	3.04384i	0.248252	+	0.143329i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−25.0892	−	10.2426i	−1.17620	−	0.480182i
$456$		0			0
$457$	11.5000	+	19.9186i	0.537947	+	0.931752i	0.999014	+	0.0443868i	$0.0141334\pi$
$457$	11.5000	+	19.9186i	0.537947	+	0.931752i	−0.461067	+	0.887365i	$0.652533\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−22.8138			−1.06255			−0.531273	−	0.847201i	$-0.678286\pi$
$461$	−22.8138			−1.06255			−0.531273	+	0.847201i	$0.678286\pi$
$462$		0			0
$463$	−21.4558			−0.997138			−0.498569	−	0.866850i	$-0.666141\pi$
$463$	−21.4558			−0.997138			−0.498569	+	0.866850i	$0.666141\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−9.50079	−	16.4558i	−0.439644	−	0.761486i	0.558018	−	0.829829i	$-0.311562\pi$
$467$	−9.50079	−	16.4558i	−0.439644	−	0.761486i	−0.997662	+	0.0683432i	$0.978229\pi$
$468$		0			0
$469$	−26.2132	+	3.58719i	−1.21041	+	0.165641i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	21.4150	+	12.3640i	0.984663	+	0.568496i
$474$		0			0
$475$			12.6677i			0.581235i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	18.2481	−	31.6066i	0.833776	−	1.44414i	−0.0612470	−	0.998123i	$-0.519508\pi$
$479$	18.2481	−	31.6066i	0.833776	−	1.44414i	0.895023	−	0.446020i	$-0.147159\pi$
$480$		0			0
$481$	−17.4853	+	10.0951i	−0.797260	+	0.460298i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−13.6208	+	7.86396i	−0.618488	+	0.357084i
$486$		0			0
$487$	14.1066	−	24.4334i	0.639231	−	1.10718i	−0.346371	−	0.938098i	$-0.612586\pi$
$487$	14.1066	−	24.4334i	0.639231	−	1.10718i	0.985602	−	0.169083i	$-0.0540806\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$			19.9706i			0.901259i	0.892711	+	0.450629i	$0.148800\pi$
$491$			19.9706i			0.901259i	−0.892711	+	0.450629i	$0.851200\pi$
$492$		0			0
$493$	1.09188	+	0.630399i	0.0491759	+	0.0283917i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	21.4150	−	16.6066i	0.960594	−	0.744908i
$498$		0			0
$499$	−17.9706	−	31.1259i	−0.804473	−	1.39339i	−0.916646	−	0.399699i	$-0.869115\pi$
$499$	−17.9706	−	31.1259i	−0.804473	−	1.39339i	0.112173	−	0.993689i	$-0.464219\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	3.29002			0.146695			0.0733474	−	0.997306i	$-0.476632\pi$
$503$	3.29002			0.146695			0.0733474	+	0.997306i	$0.476632\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−20.8462	−	36.1066i	−0.923990	−	1.60040i	−0.793178	−	0.608990i	$-0.791575\pi$
$509$	−20.8462	−	36.1066i	−0.923990	−	1.60040i	−0.130812	−	0.991407i	$-0.541758\pi$
$510$		0			0
$511$	3.00000	+	21.9223i	0.132712	+	0.969786i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−55.3746	−	31.9706i	−2.44010	−	1.40879i
$516$		0			0
$517$			3.04384i			0.133868i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−10.0081	+	17.3345i	−0.438462	+	0.759439i	−0.997571	−	0.0696551i	$-0.977810\pi$
$521$	−10.0081	+	17.3345i	−0.438462	+	0.759439i	0.559109	+	0.829094i	$0.311143\pi$
$522$		0			0
$523$	23.8492	−	13.7694i	1.04285	−	0.602092i	0.122214	−	0.992504i	$-0.461001\pi$
$523$	23.8492	−	13.7694i	1.04285	−	0.602092i	0.920641	+	0.390411i	$0.127667\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−4.93503	+	2.84924i	−0.214973	+	0.124115i
$528$		0			0
$529$	−2.50000	+	4.33013i	−0.108696	+	0.188266i
$530$		0			0
$531$		0			0
$532$		0			0
$533$			4.97056i			0.215299i
$534$		0			0
$535$	−19.8640	−	11.4685i	−0.858794	−	0.495825i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	14.6969	−	15.0000i	0.633042	−	0.646096i
$540$		0			0
$541$	5.36396	+	9.29065i	0.230615	+	0.399436i	0.957989	−	0.286804i	$-0.0925930\pi$
$541$	5.36396	+	9.29065i	0.230615	+	0.399436i	−0.727374	+	0.686241i	$0.759260\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	6.33386			0.271313
$546$		0			0
$547$	−19.6985			−0.842246			−0.421123	−	0.907003i	$-0.638364\pi$
$547$	−19.6985			−0.842246			−0.421123	+	0.907003i	$0.638364\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	0.630399	+	1.09188i	0.0268559	+	0.0465158i
$552$		0			0
$553$	11.2426	−	27.5387i	0.478086	−	1.17107i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	13.6208	+	7.86396i	0.577131	+	0.333207i	0.759992	−	0.649932i	$-0.225203\pi$
$557$	13.6208	+	7.86396i	0.577131	+	0.333207i	−0.182861	+	0.983139i	$0.558536\pi$
$558$		0			0
$559$			20.1903i			0.853957i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−12.0989	+	20.9558i	−0.509906	+	0.883184i	0.490028	+	0.871707i	$0.336987\pi$
$563$	−12.0989	+	20.9558i	−0.509906	+	0.883184i	−0.999934	+	0.0114768i	$0.996347\pi$
$564$		0			0
$565$	30.7279	−	17.7408i	1.29273	−	0.746360i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	1.52192	−	0.878680i	0.0638021	−	0.0368362i	−0.467760	−	0.883856i	$-0.654939\pi$
$569$	1.52192	−	0.878680i	0.0638021	−	0.0368362i	0.531562	+	0.847020i	$0.321605\pi$
$570$		0			0
$571$	−8.36396	+	14.4868i	−0.350021	+	0.606254i	−0.986253	−	0.165244i	$-0.947159\pi$
$571$	−8.36396	+	14.4868i	−0.350021	+	0.606254i	0.636232	+	0.771498i	$0.280492\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	52.9706i		−	2.20903i
$576$		0			0
$577$	17.7426	+	10.2437i	0.738636	+	0.426452i	0.821573	−	0.570103i	$-0.193097\pi$
$577$	17.7426	+	10.2437i	0.738636	+	0.426452i	−0.0829373	+	0.996555i	$0.526430\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−5.13461	−	6.62132i	−0.213019	−	0.274699i
$582$		0			0
$583$	1.86396	+	3.22848i	0.0771974	+	0.133710i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	5.19615			0.214468			0.107234	−	0.994234i	$-0.465801\pi$
$587$	5.19615			0.214468			0.107234	+	0.994234i	$0.465801\pi$
$588$		0			0
$589$	−5.69848			−0.234802
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−15.2042	−	26.3345i	−0.624363	−	1.08143i	−0.988664	−	0.150148i	$-0.952025\pi$
$593$	−15.2042	−	26.3345i	−0.624363	−	1.08143i	0.364300	−	0.931282i	$-0.381308\pi$
$594$		0			0
$595$	−6.87868	−	8.87039i	−0.281998	−	0.363650i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	37.6339	+	21.7279i	1.53768	+	0.887779i	0.998974	+	0.0452836i	$0.0144192\pi$
$599$	37.6339	+	21.7279i	1.53768	+	0.887779i	0.538704	+	0.842495i	$0.318914\pi$
$600$		0			0
$601$			6.03668i			0.246241i	0.992392	+	0.123121i	$0.0392902\pi$
$601$			6.03668i			0.246241i	−0.992392	+	0.123121i	$0.960710\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−4.18154	+	7.24264i	−0.170004	+	0.294455i
$606$		0			0
$607$	21.6213	−	12.4831i	0.877582	−	0.506672i	0.00772182	−	0.999970i	$-0.497542\pi$
$607$	21.6213	−	12.4831i	0.877582	−	0.506672i	0.869860	+	0.493298i	$0.164209\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−2.15232	+	1.24264i	−0.0870734	+	0.0502719i
$612$		0			0
$613$	−2.60660	+	4.51477i	−0.105280	+	0.182350i	−0.913852	−	0.406046i	$-0.866907\pi$
$613$	−2.60660	+	4.51477i	−0.105280	+	0.182350i	0.808573	+	0.588396i	$0.200240\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	41.6985i		−	1.67872i	−0.543578	−	0.839359i	$-0.682931\pi$
$617$		−	41.6985i		−	1.67872i	0.543578	−	0.839359i	$-0.317069\pi$
$618$		0			0
$619$	41.3345	+	23.8645i	1.66137	+	0.959195i	0.972060	+	0.234733i	$0.0754217\pi$
$619$	41.3345	+	23.8645i	1.66137	+	0.959195i	0.689315	+	0.724462i	$0.257912\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	10.3923	−	25.4558i	0.416359	−	1.01987i
$624$		0			0
$625$	−34.2279	−	59.2845i	−1.36912	−	2.37138i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−8.36308			−0.333458
$630$		0			0
$631$	−33.2426			−1.32337			−0.661684	−	0.749783i	$-0.730158\pi$
$631$	−33.2426			−1.32337			−0.661684	+	0.749783i	$0.730158\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−10.9612	−	18.9853i	−0.434980	−	0.753408i
$636$		0			0
$637$	16.6066	+	4.26858i	0.657978	+	0.169127i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−36.1119	−	20.8492i	−1.42634	−	0.823496i	−0.429507	−	0.903064i	$-0.641313\pi$
$641$	−36.1119	−	20.8492i	−1.42634	−	0.823496i	−0.996829	+	0.0795681i	$0.974646\pi$
$642$		0			0
$643$			2.62357i			0.103463i	0.998661	+	0.0517317i	$0.0164741\pi$
$643$			2.62357i			0.103463i	−0.998661	+	0.0517317i	$0.983526\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	5.82655	−	10.0919i	0.229065	−	0.396753i	−0.728466	−	0.685082i	$-0.759766\pi$
$647$	5.82655	−	10.0919i	0.229065	−	0.396753i	0.957531	+	0.288329i	$0.0930997\pi$
$648$		0			0
$649$	29.9558	−	17.2950i	1.17587	−	0.678889i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−9.31615	+	5.37868i	−0.364569	+	0.210484i	−0.671083	−	0.741382i	$-0.734171\pi$
$653$	−9.31615	+	5.37868i	−0.364569	+	0.210484i	0.306514	+	0.951866i	$0.400837\pi$
$654$		0			0
$655$	−10.8640	+	18.8169i	−0.424490	+	0.735238i
$656$		0			0
$657$		0			0
$658$		0			0
$659$			6.00000i			0.233727i	0.993148	+	0.116863i	$0.0372840\pi$
$659$			6.00000i			0.233727i	−0.993148	+	0.116863i	$0.962716\pi$
$660$		0			0
$661$	35.1213	+	20.2773i	1.36606	+	0.788696i	0.990422	−	0.138071i	$-0.0440901\pi$
$661$	35.1213	+	20.2773i	1.36606	+	0.788696i	0.375639	+	0.926766i	$0.377423\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−1.52192	−	11.1213i	−0.0590174	−	0.431266i
$666$		0			0
$667$	−2.63604	−	4.56575i	−0.102068	−	0.176787i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−17.7408			−0.684875
$672$		0			0
$673$	−15.9706			−0.615620			−0.307810	−	0.951448i	$-0.599596\pi$
$673$	−15.9706			−0.615620			−0.307810	+	0.951448i	$0.599596\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	6.27231	+	10.8640i	0.241064	+	0.417536i	0.961018	−	0.276487i	$-0.0891701\pi$
$677$	6.27231	+	10.8640i	0.241064	+	0.417536i	−0.719953	+	0.694023i	$0.755837\pi$
$678$		0			0
$679$	7.86396	−	6.09823i	0.301791	−	0.234029i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	22.4912	+	12.9853i	0.860601	+	0.496868i	0.864213	−	0.503125i	$-0.167817\pi$
$683$	22.4912	+	12.9853i	0.860601	+	0.496868i	−0.00361277	+	0.999993i	$0.501150\pi$
$684$		0			0
$685$			60.5708i			2.31429i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−1.52192	+	2.63604i	−0.0579805	+	0.100425i
$690$		0			0
$691$	0.727922	−	0.420266i	0.0276915	−	0.0159877i	−0.486090	−	0.873909i	$-0.661577\pi$
$691$	0.727922	−	0.420266i	0.0276915	−	0.0159877i	0.513782	+	0.857921i	$0.328244\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−73.1154	+	42.2132i	−2.77343	+	1.60124i
$696$		0			0
$697$	−1.02944	+	1.78304i	−0.0389927	+	0.0675374i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			38.6985i			1.46162i	0.682580	+	0.730811i	$0.260858\pi$
$701$			38.6985i			1.46162i	−0.682580	+	0.730811i	$0.739142\pi$
$702$		0			0
$703$	−7.24264	−	4.18154i	−0.273161	−	0.157710i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	3.48528	+	6.03668i	0.130892	+	0.226712i	0.924021	−	0.382342i	$-0.124882\pi$
$709$	3.48528	+	6.03668i	0.130892	+	0.226712i	−0.793128	+	0.609055i	$0.791549\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	23.8284			0.892382
$714$		0			0
$715$	30.7279			1.14916
$716$		0			0
$717$		0			0
$718$		0			0
$719$	11.5300	+	19.9706i	0.429997	+	0.744776i	0.996872	−	0.0790270i	$-0.0251813\pi$
$719$	11.5300	+	19.9706i	0.429997	+	0.744776i	−0.566876	+	0.823803i	$0.691848\pi$
$720$		0			0
$721$	37.4558	+	15.2913i	1.39493	+	0.569477i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−13.4361	−	7.75736i	−0.499006	−	0.288101i
$726$		0			0
$727$		−	26.4010i		−	0.979160i	−0.871958	−	0.489580i	$-0.837150\pi$
$727$		−	26.4010i		−	0.979160i	0.871958	−	0.489580i	$-0.162850\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−4.18154	+	7.24264i	−0.154660	+	0.267879i
$732$		0			0
$733$	−34.0919	+	19.6830i	−1.25921	+	0.727007i	−0.972921	−	0.231136i	$-0.925756\pi$
$733$	−34.0919	+	19.6830i	−1.25921	+	0.727007i	−0.286291	+	0.958143i	$0.592422\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	25.9808	−	15.0000i	0.957014	−	0.552532i
$738$		0			0
$739$	−17.7279	+	30.7057i	−0.652132	+	1.12953i	0.330472	+	0.943816i	$0.392792\pi$
$739$	−17.7279	+	30.7057i	−0.652132	+	1.12953i	−0.982605	+	0.185710i	$0.940541\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$			21.5147i			0.789298i	0.918832	+	0.394649i	$0.129134\pi$
$743$			21.5147i			0.789298i	−0.918832	+	0.394649i	$0.870866\pi$
$744$		0			0
$745$	−74.1838	−	42.8300i	−2.71788	−	1.56917i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	13.4361	+	5.48528i	0.490946	+	0.200428i
$750$		0			0
$751$	13.3787	+	23.1726i	0.488195	+	0.845578i	0.999908	−	0.0135781i	$-0.00432217\pi$
$751$	13.3787	+	23.1726i	0.488195	+	0.845578i	−0.511713	+	0.859157i	$0.670989\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	13.5592			0.493471
$756$		0			0
$757$	−42.2426			−1.53533			−0.767667	−	0.640848i	$-0.778583\pi$
$757$	−42.2426			−1.53533			−0.767667	+	0.640848i	$0.778583\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	2.53653	+	4.39340i	0.0919491	+	0.159261i	0.908331	−	0.418252i	$-0.137357\pi$
$761$	2.53653	+	4.39340i	0.0919491	+	0.159261i	−0.816382	+	0.577512i	$0.804024\pi$
$762$		0			0
$763$	−3.97056	+	0.543359i	−0.143744	+	0.0196709i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	24.4588	+	14.1213i	0.883158	+	0.509891i
$768$		0			0
$769$		−	49.0408i		−	1.76846i	−0.467056	−	0.884228i	$-0.654685\pi$
$769$		−	49.0408i		−	1.76846i	0.467056	−	0.884228i	$-0.345315\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	11.5300	−	19.9706i	0.414706	−	0.718291i	−0.580692	−	0.814123i	$-0.697218\pi$
$773$	11.5300	−	19.9706i	0.414706	−	0.718291i	0.995398	+	0.0958322i	$0.0305512\pi$
$774$		0			0
$775$	60.7279	−	35.0613i	2.18141	−	1.25944i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−1.78304	+	1.02944i	−0.0638840	+	0.0368834i
$780$		0			0
$781$	−15.3640	+	26.6112i	−0.549766	+	0.952222i
$782$		0			0
$783$		0			0
$784$		0			0
$785$			61.4558i			2.19345i
$786$		0			0
$787$	−32.1213	−	18.5453i	−1.14500	−	0.661067i	−0.197337	−	0.980336i	$-0.563229\pi$
$787$	−32.1213	−	18.5453i	−1.14500	−	0.661067i	−0.947664	+	0.319269i	$0.896563\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−17.7408	+	13.7574i	−0.630789	+	0.489155i
$792$		0			0
$793$	−7.24264	−	12.5446i	−0.257194	−	0.445473i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	37.6339			1.33306			0.666530	−	0.745478i	$-0.267779\pi$
$797$	37.6339			1.33306			0.666530	+	0.745478i	$0.267779\pi$
$798$		0			0
$799$	−1.02944			−0.0364189
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−12.5446	−	21.7279i	−0.442690	−	0.766762i
$804$		0			0
$805$	6.36396	+	46.5043i	0.224300	+	1.63906i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	35.4815	+	20.4853i	1.24746	+	0.720224i	0.970603	−	0.240686i	$-0.0773723\pi$
$809$	35.4815	+	20.4853i	1.24746	+	0.720224i	0.276862	+	0.960910i	$0.410706\pi$
$810$		0			0
$811$			31.1769i			1.09477i	0.836881	+	0.547385i	$0.184377\pi$
$811$			31.1769i			1.09477i	−0.836881	+	0.547385i	$0.815623\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	13.0519	−	22.6066i	0.457189	−	0.791875i
$816$		0			0
$817$	−7.24264	+	4.18154i	−0.253388	+	0.146294i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−42.6454	+	24.6213i	−1.48833	+	0.859290i	−0.999911	−	0.0133172i	$-0.995761\pi$
$821$	−42.6454	+	24.6213i	−1.48833	+	0.859290i	−0.488423	+	0.872607i	$0.662428\pi$
$822$		0			0
$823$	−18.9706	+	32.8580i	−0.661272	+	1.14536i	0.319009	+	0.947752i	$0.396650\pi$
$823$	−18.9706	+	32.8580i	−0.661272	+	1.14536i	−0.980282	+	0.197606i	$0.936683\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			4.02944i			0.140117i	0.997543	+	0.0700586i	$0.0223186\pi$
$827$			4.02944i			0.140117i	−0.997543	+	0.0700586i	$0.977681\pi$
$828$		0			0
$829$	−35.3345	−	20.4004i	−1.22722	−	0.708535i	−0.260772	−	0.965401i	$-0.583977\pi$
$829$	−35.3345	−	20.4004i	−1.22722	−	0.708535i	−0.966447	+	0.256865i	$0.917310\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	5.07306	+	4.97056i	0.175771	+	0.172220i
$834$		0			0
$835$	−48.2132	−	83.5077i	−1.66849	−	2.88990i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−24.0746			−0.831149			−0.415574	−	0.909559i	$-0.636419\pi$
$839$	−24.0746			−0.831149			−0.415574	+	0.909559i	$0.636419\pi$
$840$		0			0
$841$	27.4558			0.946753
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−14.6354	−	25.3492i	−0.503473	−	0.872040i
$846$		0			0
$847$	2.00000	−	4.89898i	0.0687208	−	0.168331i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	30.2854	+	17.4853i	1.03817	+	0.599388i
$852$		0			0
$853$			2.27541i			0.0779085i	0.999241	+	0.0389543i	$0.0124027\pi$
$853$			2.27541i			0.0779085i	−0.999241	+	0.0389543i	$0.987597\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	10.0081	−	17.3345i	0.341870	−	0.592136i	−0.642910	−	0.765942i	$-0.722273\pi$
$857$	10.0081	−	17.3345i	0.341870	−	0.592136i	0.984780	+	0.173806i	$0.0556064\pi$
$858$		0			0
$859$	−3.87868	+	2.23936i	−0.132339	+	0.0764059i	−0.564708	−	0.825291i	$-0.691011\pi$
$859$	−3.87868	+	2.23936i	−0.132339	+	0.0764059i	0.432369	+	0.901697i	$0.357678\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	43.7215	−	25.2426i	1.48830	−	0.859269i	0.488388	−	0.872627i	$-0.337585\pi$
$863$	43.7215	−	25.2426i	1.48830	−	0.859269i	0.999911	+	0.0133573i	$0.00425189\pi$
$864$		0			0
$865$	43.4558	−	75.2677i	1.47754	−	2.55918i
$866$		0			0
$867$		0			0
$868$		0			0
$869$			33.7279i			1.14414i
$870$		0			0
$871$	21.2132	+	12.2474i	0.718782	+	0.414989i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	50.7473	+	65.4411i	1.71557	+	2.21231i
$876$		0			0
$877$	6.24264	+	10.8126i	0.210799	+	0.365115i	0.951965	−	0.306207i	$-0.0990601\pi$
$877$	6.24264	+	10.8126i	0.210799	+	0.365115i	−0.741166	+	0.671322i	$0.765727\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	39.7862			1.34043			0.670215	−	0.742167i	$-0.266202\pi$
$881$	39.7862			1.34043			0.670215	+	0.742167i	$0.266202\pi$
$882$		0			0
$883$	9.45584			0.318214			0.159107	−	0.987261i	$-0.449138\pi$
$883$	9.45584			0.318214			0.159107	+	0.987261i	$0.449138\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	22.4296	+	38.8492i	0.753113	+	1.30443i	0.946307	+	0.323269i	$0.104782\pi$
$887$	22.4296	+	38.8492i	0.753113	+	1.30443i	−0.193194	+	0.981161i	$0.561885\pi$
$888$		0			0
$889$	8.50000	+	10.9612i	0.285081	+	0.367625i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−0.891519	−	0.514719i	−0.0298335	−	0.0172244i
$894$		0			0
$895$		−	39.7862i		−	1.32991i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	3.48960	−	6.04416i	0.116385	−	0.201584i
$900$		0			0
$901$	−1.09188	+	0.630399i	−0.0363759	+	0.0210016i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−7.34847	+	4.24264i	−0.244271	+	0.141030i
$906$		0			0
$907$	13.8492	−	23.9876i	0.459857	−	0.796495i	−0.539096	−	0.842244i	$-0.681234\pi$
$907$	13.8492	−	23.9876i	0.459857	−	0.796495i	0.998953	+	0.0457492i	$0.0145675\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			18.7279i			0.620484i	0.950658	+	0.310242i	$0.100410\pi$
$911$			18.7279i			0.620484i	−0.950658	+	0.310242i	$0.899590\pi$
$912$		0			0
$913$	8.22792	+	4.75039i	0.272304	+	0.157215i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	5.19615	−	12.7279i	0.171592	−	0.420313i
$918$		0			0
$919$	9.75736	+	16.9002i	0.321866	+	0.557488i	0.980873	−	0.194649i	$-0.0623567\pi$
$919$	9.75736	+	16.9002i	0.321866	+	0.557488i	−0.659007	+	0.752136i	$0.729023\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−25.0892			−0.825823
$924$		0			0
$925$	102.912			3.38372
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−1.64501	−	2.84924i	−0.0539711	−	0.0934806i	0.837778	−	0.546012i	$-0.183855\pi$
$929$	−1.64501	−	2.84924i	−0.0539711	−	0.0934806i	−0.891749	+	0.452531i	$0.850521\pi$
$930$		0			0
$931$	1.90812	+	6.84116i	0.0625360	+	0.224210i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	11.0227	+	6.36396i	0.360481	+	0.208124i
$936$		0			0
$937$		−	4.00746i		−	0.130918i	−0.997855	−	0.0654590i	$-0.979149\pi$
$937$		−	4.00746i		−	0.130918i	0.997855	−	0.0654590i	$-0.0208512\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−26.0423	+	45.1066i	−0.848955	+	1.47043i	0.0331867	+	0.999449i	$0.489434\pi$
$941$	−26.0423	+	45.1066i	−0.848955	+	1.47043i	−0.882142	+	0.470984i	$0.843899\pi$
$942$		0			0
$943$	7.45584	−	4.30463i	0.242796	−	0.140178i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	19.8931	−	11.4853i	0.646439	−	0.373221i	−0.140652	−	0.990059i	$-0.544920\pi$
$947$	19.8931	−	11.4853i	0.646439	−	0.373221i	0.787090	+	0.616838i	$0.211586\pi$
$948$		0			0
$949$	10.2426	−	17.7408i	0.332490	−	0.575890i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	41.6985i		−	1.35075i	−0.737476	−	0.675373i	$-0.763983\pi$
$953$		−	41.6985i		−	1.35075i	0.737476	−	0.675373i	$-0.236017\pi$
$954$		0			0
$955$	30.7279	+	17.7408i	0.994332	+	0.574078i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−5.19615	−	37.9706i	−0.167793	−	1.22613i
$960$		0			0
$961$	0.272078	+	0.471253i	0.00877671	+	0.0152017i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−31.3000			−1.00758
$966$		0			0
$967$	−22.2721			−0.716222			−0.358111	−	0.933679i	$-0.616579\pi$
$967$	−22.2721			−0.716222			−0.358111	+	0.933679i	$0.616579\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−25.6581	−	44.4411i	−0.823407	−	1.42618i	−0.903130	−	0.429367i	$-0.858737\pi$
$971$	−25.6581	−	44.4411i	−0.823407	−	1.42618i	0.0797229	−	0.996817i	$-0.474596\pi$
$972$		0			0
$973$	42.2132	−	32.7349i	1.35329	−	1.04943i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	27.5027	+	15.8787i	0.879889	+	0.508004i	0.870622	−	0.491953i	$-0.163717\pi$
$977$	27.5027	+	15.8787i	0.879889	+	0.508004i	0.00926698	+	0.999957i	$0.497050\pi$
$978$		0			0
$979$			31.1769i			0.996419i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−4.05845	+	7.02944i	−0.129444	+	0.224204i	−0.923461	−	0.383691i	$-0.874653\pi$
$983$	−4.05845	+	7.02944i	−0.129444	+	0.224204i	0.794017	+	0.607895i	$0.207986\pi$
$984$		0			0
$985$	34.4558	−	19.8931i	1.09785	−	0.633847i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	30.2854	−	17.4853i	0.963020	−	0.556000i
$990$		0			0
$991$	4.89340	−	8.47561i	0.155444	−	0.269237i	−0.777777	−	0.628541i	$-0.783653\pi$
$991$	4.89340	−	8.47561i	0.155444	−	0.269237i	0.933221	+	0.359304i	$0.116986\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		−	67.4558i		−	2.13849i
$996$		0			0
$997$	−8.27208	−	4.77589i	−0.261979	−	0.151254i	0.363258	−	0.931689i	$-0.381664\pi$
$997$	−8.27208	−	4.77589i	−0.261979	−	0.151254i	−0.625237	+	0.780435i	$0.714998\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.bt.c.17.1		8
3.2	odd	2	inner	1008.2.bt.c.17.4		8
4.3	odd	2		126.2.k.a.17.1	✓	8
7.3	odd	6		7056.2.k.f.881.2		8
7.4	even	3		7056.2.k.f.881.8		8
7.5	odd	6	inner	1008.2.bt.c.593.4		8
12.11	even	2		126.2.k.a.17.4	yes	8
20.3	even	4		3150.2.bp.e.899.1		8
20.7	even	4		3150.2.bp.b.899.4		8
20.19	odd	2		3150.2.bf.a.1151.4		8
21.5	even	6	inner	1008.2.bt.c.593.1		8
21.11	odd	6		7056.2.k.f.881.1		8
21.17	even	6		7056.2.k.f.881.7		8
28.3	even	6		882.2.d.a.881.1		8
28.11	odd	6		882.2.d.a.881.4		8
28.19	even	6		126.2.k.a.89.4	yes	8
28.23	odd	6		882.2.k.a.215.3		8
28.27	even	2		882.2.k.a.521.2		8
36.7	odd	6		1134.2.t.e.1025.4		8
36.11	even	6		1134.2.t.e.1025.1		8
36.23	even	6		1134.2.l.f.269.4		8
36.31	odd	6		1134.2.l.f.269.1		8
60.23	odd	4		3150.2.bp.b.899.1		8
60.47	odd	4		3150.2.bp.e.899.4		8
60.59	even	2		3150.2.bf.a.1151.2		8
84.11	even	6		882.2.d.a.881.5		8
84.23	even	6		882.2.k.a.215.2		8
84.47	odd	6		126.2.k.a.89.1	yes	8
84.59	odd	6		882.2.d.a.881.8		8
84.83	odd	2		882.2.k.a.521.3		8
140.19	even	6		3150.2.bf.a.1601.2		8
140.47	odd	12		3150.2.bp.b.1349.1		8
140.103	odd	12		3150.2.bp.e.1349.4		8
252.47	odd	6		1134.2.l.f.215.3		8
252.103	even	6		1134.2.t.e.593.1		8
252.131	odd	6		1134.2.t.e.593.4		8
252.187	even	6		1134.2.l.f.215.2		8
420.47	even	12		3150.2.bp.e.1349.1		8
420.299	odd	6		3150.2.bf.a.1601.4		8
420.383	even	12		3150.2.bp.b.1349.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.k.a.17.1	✓	8	4.3	odd	2
126.2.k.a.17.4	yes	8	12.11	even	2
126.2.k.a.89.1	yes	8	84.47	odd	6
126.2.k.a.89.4	yes	8	28.19	even	6
882.2.d.a.881.1		8	28.3	even	6
882.2.d.a.881.4		8	28.11	odd	6
882.2.d.a.881.5		8	84.11	even	6
882.2.d.a.881.8		8	84.59	odd	6
882.2.k.a.215.2		8	84.23	even	6
882.2.k.a.215.3		8	28.23	odd	6
882.2.k.a.521.2		8	28.27	even	2
882.2.k.a.521.3		8	84.83	odd	2
1008.2.bt.c.17.1		8	1.1	even	1	trivial
1008.2.bt.c.17.4		8	3.2	odd	2	inner
1008.2.bt.c.593.1		8	21.5	even	6	inner
1008.2.bt.c.593.4		8	7.5	odd	6	inner
1134.2.l.f.215.2		8	252.187	even	6
1134.2.l.f.215.3		8	252.47	odd	6
1134.2.l.f.269.1		8	36.31	odd	6
1134.2.l.f.269.4		8	36.23	even	6
1134.2.t.e.593.1		8	252.103	even	6
1134.2.t.e.593.4		8	252.131	odd	6
1134.2.t.e.1025.1		8	36.11	even	6
1134.2.t.e.1025.4		8	36.7	odd	6
3150.2.bf.a.1151.2		8	60.59	even	2
3150.2.bf.a.1151.4		8	20.19	odd	2
3150.2.bf.a.1601.2		8	140.19	even	6
3150.2.bf.a.1601.4		8	420.299	odd	6
3150.2.bp.b.899.1		8	60.23	odd	4
3150.2.bp.b.899.4		8	20.7	even	4
3150.2.bp.b.1349.1		8	140.47	odd	12
3150.2.bp.b.1349.4		8	420.383	even	12
3150.2.bp.e.899.1		8	20.3	even	4
3150.2.bp.e.899.4		8	60.47	odd	4
3150.2.bp.e.1349.1		8	420.47	even	12
3150.2.bp.e.1349.4		8	140.103	odd	12
7056.2.k.f.881.1		8	21.11	odd	6
7056.2.k.f.881.2		8	7.3	odd	6
7056.2.k.f.881.7		8	21.17	even	6
7056.2.k.f.881.8		8	7.4	even	3

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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.bt (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.09077 - 3.62132i) q^{5} +(1.62132 + 2.09077i) q^{7} +(-2.59808 - 1.50000i) q^{11} -2.44949i q^{13} +(0.507306 - 0.878680i) q^{17} +(0.878680 - 0.507306i) q^{19} +(-3.67423 + 2.12132i) q^{23} +(-6.24264 + 10.8126i) q^{25} +1.24264i q^{29} +(-4.86396 - 2.80821i) q^{31} +(4.18154 - 10.2426i) q^{35} +(-4.12132 - 7.13834i) q^{37} -2.02922 q^{41} -8.24264 q^{43} +(-0.507306 - 0.878680i) q^{47} +(-1.74264 + 6.77962i) q^{49} +(-1.07616 - 0.621320i) q^{53} +12.5446i q^{55} +(-5.76500 + 9.98528i) q^{59} +(5.12132 - 2.95680i) q^{61} +(-8.87039 + 5.12132i) q^{65} +(-5.00000 + 8.66025i) q^{67} -10.2426i q^{71} +(7.24264 + 4.18154i) q^{73} +(-1.07616 - 7.86396i) q^{77} +(-5.62132 - 9.73641i) q^{79} -3.16693 q^{83} -4.24264 q^{85} +(-5.19615 - 9.00000i) q^{89} +(5.12132 - 3.97141i) q^{91} +(-3.67423 - 2.12132i) q^{95} -3.76127i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{7} + 24 q^{19} - 16 q^{25} + 12 q^{31} - 16 q^{37} - 32 q^{43} + 20 q^{49} + 24 q^{61} - 40 q^{67} + 24 q^{73} - 28 q^{79} + 24 q^{91}+O(q^{100}) \) 8 * q - 4 * q^7 + 24 * q^19 - 16 * q^25 + 12 * q^31 - 16 * q^37 - 32 * q^43 + 20 * q^49 + 24 * q^61 - 40 * q^67 + 24 * q^73 - 28 * q^79 + 24 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more