LMFDB - Embedded newform 2016.2.cp.b.17.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2016,2,Mod(17,2016)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2016, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 3, 1]))

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

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

chi := DirichletCharacter("2016.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2016 = 2^{5} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2016.cp (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$16.0978410475$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.22
Character	$\chi$	$=$	2016.17
Dual form			2016.2.cp.b.593.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.53798 - 0.887954i) q^{5} +(-0.843933 + 2.50754i) q^{7} +O(q^{10})$	$q+(1.53798 - 0.887954i) q^{5} +(-0.843933 + 2.50754i) q^{7} +(-2.09284 + 3.62490i) q^{11} +3.76443 q^{13} +(-2.32502 + 4.02705i) q^{17} +(0.0315203 + 0.0545948i) q^{19} +(4.05375 - 2.34043i) q^{23} +(-0.923074 + 1.59881i) q^{25} -6.47316 q^{29} +(-6.64896 - 3.83878i) q^{31} +(0.928631 + 4.60593i) q^{35} +(2.91602 - 1.68357i) q^{37} -8.06290 q^{41} +9.94628i q^{43} +(0.338788 + 0.586799i) q^{47} +(-5.57556 - 4.23240i) q^{49} +(-2.36197 + 4.09104i) q^{53} +7.43338i q^{55} +(-6.53211 - 3.77132i) q^{59} +(7.23104 + 12.5245i) q^{61} +(5.78962 - 3.34264i) q^{65} +(5.67866 + 3.27857i) q^{67} -5.10606i q^{71} +(1.29332 + 0.746696i) q^{73} +(-7.32339 - 8.30706i) q^{77} +(5.99485 + 10.3834i) q^{79} +7.64992i q^{83} +8.25803i q^{85} +(-8.97506 - 15.5453i) q^{89} +(-3.17692 + 9.43947i) q^{91} +(0.0969554 + 0.0559773i) q^{95} +4.24586i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 20 q^{7}+O(q^{10}) $ 56 * q + 20 * q^7	$ 56 q + 20 q^{7} + 8 q^{25} + 36 q^{31} - 28 q^{49} + 72 q^{73} + 12 q^{79}+O(q^{100}) $ 56 * q + 20 * q^7 + 8 * q^25 + 36 * q^31 - 28 * q^49 + 72 * q^73 + 12 * q^79

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2016\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$1765$	$1793$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$

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
$5$	1.53798	−	0.887954i	0.687806	−	0.397105i	−0.114983	−	0.993367i	$-0.536681\pi$
$5$	1.53798	−	0.887954i	0.687806	−	0.397105i	0.802790	+	0.596262i	$0.203348\pi$
$6$		0			0
$7$	−0.843933	+	2.50754i	−0.318977	+	0.947763i
$7$	−0.843933	+	2.50754i	−0.318977	+	0.947763i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.09284	+	3.62490i	−0.631015	+	1.09295i	0.356330	+	0.934360i	$0.384028\pi$
$11$	−2.09284	+	3.62490i	−0.631015	+	1.09295i	−0.987345	+	0.158589i	$0.949305\pi$
$12$		0			0
$13$	3.76443			1.04406			0.522032	−	0.852926i	$-0.325174\pi$
$13$	3.76443			1.04406			0.522032	+	0.852926i	$0.325174\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.32502	+	4.02705i	−0.563899	+	0.976702i	0.433252	+	0.901273i	$0.357366\pi$
$17$	−2.32502	+	4.02705i	−0.563899	+	0.976702i	−0.997151	+	0.0754291i	$0.975967\pi$
$18$		0			0
$19$	0.0315203	+	0.0545948i	0.00723126	+	0.0125249i	0.869618	−	0.493724i	$-0.164365\pi$
$19$	0.0315203	+	0.0545948i	0.00723126	+	0.0125249i	−0.862387	+	0.506249i	$0.831032\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	4.05375	−	2.34043i	0.845265	−	0.488014i	−0.0137854	−	0.999905i	$-0.504388\pi$
$23$	4.05375	−	2.34043i	0.845265	−	0.488014i	0.859050	+	0.511891i	$0.171055\pi$
$24$		0			0
$25$	−0.923074	+	1.59881i	−0.184615	+	0.319762i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−6.47316			−1.20204			−0.601018	−	0.799235i	$-0.705238\pi$
$29$	−6.47316			−1.20204			−0.601018	+	0.799235i	$0.705238\pi$
$30$		0			0
$31$	−6.64896	−	3.83878i	−1.19419	−	0.689465i	−0.234935	−	0.972011i	$-0.575488\pi$
$31$	−6.64896	−	3.83878i	−1.19419	−	0.689465i	−0.959254	+	0.282546i	$0.908821\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.928631	+	4.60593i	0.156967	+	0.778544i
$36$		0			0
$37$	2.91602	−	1.68357i	0.479391	−	0.276777i	−0.240772	−	0.970582i	$-0.577400\pi$
$37$	2.91602	−	1.68357i	0.479391	−	0.276777i	0.720163	+	0.693805i	$0.244067\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−8.06290			−1.25921			−0.629606	−	0.776914i	$-0.716784\pi$
$41$	−8.06290			−1.25921			−0.629606	+	0.776914i	$0.716784\pi$
$42$		0			0
$43$			9.94628i			1.51679i	0.651793	+	0.758397i	$0.274017\pi$
$43$			9.94628i			1.51679i	−0.651793	+	0.758397i	$0.725983\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.338788	+	0.586799i	0.0494174	+	0.0855934i	0.889676	−	0.456592i	$-0.150930\pi$
$47$	0.338788	+	0.586799i	0.0494174	+	0.0855934i	−0.840259	+	0.542186i	$0.817597\pi$
$48$		0			0
$49$	−5.57556	−	4.23240i	−0.796508	−	0.604628i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−2.36197	+	4.09104i	−0.324441	+	0.561948i	−0.981399	−	0.191979i	$-0.938509\pi$
$53$	−2.36197	+	4.09104i	−0.324441	+	0.561948i	0.656958	+	0.753927i	$0.271843\pi$
$54$		0			0
$55$			7.43338i			1.00232i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−6.53211	−	3.77132i	−0.850408	−	0.490983i	0.0103803	−	0.999946i	$-0.496696\pi$
$59$	−6.53211	−	3.77132i	−0.850408	−	0.490983i	−0.860789	+	0.508963i	$0.830029\pi$
$60$		0			0
$61$	7.23104	+	12.5245i	0.925840	+	1.60360i	0.790204	+	0.612844i	$0.209975\pi$
$61$	7.23104	+	12.5245i	0.925840	+	1.60360i	0.135636	+	0.990759i	$0.456692\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	5.78962	−	3.34264i	0.718115	−	0.414604i
$66$		0			0
$67$	5.67866	+	3.27857i	0.693758	+	0.400542i	0.805018	−	0.593250i	$-0.202155\pi$
$67$	5.67866	+	3.27857i	0.693758	+	0.400542i	−0.111260	+	0.993791i	$0.535489\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	5.10606i		−	0.605978i	−0.952994	−	0.302989i	$-0.902015\pi$
$71$		−	5.10606i		−	0.605978i	0.952994	−	0.302989i	$-0.0979846\pi$
$72$		0			0
$73$	1.29332	+	0.746696i	0.151371	+	0.0873942i	0.573772	−	0.819015i	$-0.305479\pi$
$73$	1.29332	+	0.746696i	0.151371	+	0.0873942i	−0.422401	+	0.906409i	$0.638813\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−7.32339	−	8.30706i	−0.834578	−	0.946677i
$78$		0			0
$79$	5.99485	+	10.3834i	0.674473	+	1.16822i	0.976623	+	0.214961i	$0.0689624\pi$
$79$	5.99485	+	10.3834i	0.674473	+	1.16822i	−0.302150	+	0.953260i	$0.597704\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$			7.64992i			0.839688i	0.907596	+	0.419844i	$0.137915\pi$
$83$			7.64992i			0.839688i	−0.907596	+	0.419844i	$0.862085\pi$
$84$		0			0
$85$			8.25803i			0.895709i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−8.97506	−	15.5453i	−0.951354	−	1.64779i	−0.742499	−	0.669847i	$-0.766360\pi$
$89$	−8.97506	−	15.5453i	−0.951354	−	1.64779i	−0.208855	−	0.977947i	$-0.566974\pi$
$90$		0			0
$91$	−3.17692	+	9.43947i	−0.333032	+	0.989526i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.0969554	+	0.0559773i	0.00994742	+	0.00574315i
$96$		0			0
$97$			4.24586i			0.431102i	0.976493	+	0.215551i	$0.0691547\pi$
$97$			4.24586i			0.431102i	−0.976493	+	0.215551i	$0.930845\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	3.63654	+	2.09956i	0.361849	+	0.208914i	0.669892	−	0.742459i	$-0.266341\pi$
$101$	3.63654	+	2.09956i	0.361849	+	0.208914i	−0.308042	+	0.951373i	$0.599674\pi$
$102$		0			0
$103$	11.3144	−	6.53235i	1.11484	−	0.643652i	0.174759	−	0.984611i	$-0.444085\pi$
$103$	11.3144	−	6.53235i	1.11484	−	0.643652i	0.940078	+	0.340959i	$0.110752\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	5.25101	+	9.09502i	0.507635	+	0.879249i	0.999961	+	0.00883827i	$0.00281335\pi$
$107$	5.25101	+	9.09502i	0.507635	+	0.879249i	−0.492326	+	0.870411i	$0.663853\pi$
$108$		0			0
$109$	2.19797	+	1.26900i	0.210528	+	0.121548i	0.601557	−	0.798830i	$-0.294547\pi$
$109$	2.19797	+	1.26900i	0.210528	+	0.121548i	−0.391029	+	0.920378i	$0.627881\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		−	4.56501i		−	0.429440i	−0.976676	−	0.214720i	$-0.931116\pi$
$113$		−	4.56501i		−	0.429440i	0.976676	−	0.214720i	$-0.0688838\pi$
$114$		0			0
$115$	4.15639	−	7.19909i	0.387586	−	0.671318i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−8.13584	−	9.22863i	−0.745811	−	0.845988i
$120$		0			0
$121$	−3.25995	−	5.64639i	−0.296359	−	0.513308i
$122$		0			0
$123$		0			0
$124$		0			0
$125$			12.1581i			1.08746i
$126$		0			0
$127$	−8.36161			−0.741973			−0.370986	−	0.928638i	$-0.620980\pi$
$127$	−8.36161			−0.741973			−0.370986	+	0.928638i	$0.620980\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−5.45901	+	3.15176i	−0.476956	+	0.275371i	−0.719147	−	0.694858i	$-0.755467\pi$
$131$	−5.45901	+	3.15176i	−0.476956	+	0.275371i	0.242191	+	0.970229i	$0.422134\pi$
$132$		0			0
$133$	−0.163500	+	0.0329643i	−0.0141772	+	0.00285837i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	11.3468	+	6.55109i	0.969425	+	0.559698i	0.899061	−	0.437824i	$-0.144251\pi$
$137$	11.3468	+	6.55109i	0.969425	+	0.559698i	0.0703639	+	0.997521i	$0.477584\pi$
$138$		0			0
$139$	19.1125			1.62110			0.810549	−	0.585671i	$-0.199169\pi$
$139$	19.1125			1.62110			0.810549	+	0.585671i	$0.199169\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−7.87834	+	13.6457i	−0.658820	+	1.14111i
$144$		0			0
$145$	−9.95561	+	5.74787i	−0.826768	+	0.477335i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	2.19406	+	3.80023i	0.179745	+	0.311327i	0.941793	−	0.336193i	$-0.109140\pi$
$149$	2.19406	+	3.80023i	0.179745	+	0.311327i	−0.762048	+	0.647520i	$0.775806\pi$
$150$		0			0
$151$	−1.37428	+	2.38033i	−0.111838	+	0.193708i	−0.916511	−	0.400009i	$-0.869007\pi$
$151$	−1.37428	+	2.38033i	−0.111838	+	0.193708i	0.804674	+	0.593717i	$0.202340\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−13.6346			−1.09516
$156$		0			0
$157$	0.669124	−	1.15896i	0.0534019	−	0.0924948i	−0.838089	−	0.545534i	$-0.816327\pi$
$157$	0.669124	−	1.15896i	0.0534019	−	0.0924948i	0.891491	+	0.453039i	$0.149660\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	2.44765	+	12.1401i	0.192902	+	0.956776i
$162$		0			0
$163$	3.30942	−	1.91070i	0.259214	−	0.149657i	−0.364762	−	0.931101i	$-0.618850\pi$
$163$	3.30942	−	1.91070i	0.259214	−	0.149657i	0.623976	+	0.781444i	$0.285516\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	7.25804			0.561644			0.280822	−	0.959760i	$-0.409393\pi$
$167$	7.25804			0.561644			0.280822	+	0.959760i	$0.409393\pi$
$168$		0			0
$169$	1.17093			0.0900713
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−1.07114	+	0.618425i	−0.0814375	+	0.0470180i	−0.540166	−	0.841559i	$-0.681638\pi$
$173$	−1.07114	+	0.618425i	−0.0814375	+	0.0470180i	0.458728	+	0.888577i	$0.348305\pi$
$174$		0			0
$175$	−3.23008	−	3.66394i	−0.244171	−	0.276968i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	8.80192	−	15.2454i	0.657886	−	1.13949i	−0.323275	−	0.946305i	$-0.604784\pi$
$179$	8.80192	−	15.2454i	0.657886	−	1.13949i	0.981162	−	0.193188i	$-0.0618826\pi$
$180$		0			0
$181$	16.4773			1.22475			0.612376	−	0.790567i	$-0.290214\pi$
$181$	16.4773			1.22475			0.612376	+	0.790567i	$0.290214\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	2.98986	−	5.17859i	0.219819	−	0.380737i
$186$		0			0
$187$	−9.73176	−	16.8559i	−0.711657	−	1.23263i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−14.2159	+	8.20758i	−1.02863	+	0.593880i	−0.916592	−	0.399824i	$-0.869071\pi$
$191$	−14.2159	+	8.20758i	−1.02863	+	0.593880i	−0.112038	+	0.993704i	$0.535738\pi$
$192$		0			0
$193$	−11.7627	+	20.3736i	−0.846696	+	1.46652i	0.0374435	+	0.999299i	$0.488079\pi$
$193$	−11.7627	+	20.3736i	−0.846696	+	1.46652i	−0.884140	+	0.467222i	$0.845255\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	0.792724			0.0564792			0.0282396	−	0.999601i	$-0.491010\pi$
$197$	0.792724			0.0564792			0.0282396	+	0.999601i	$0.491010\pi$
$198$		0			0
$199$	−10.9922	−	6.34632i	−0.779213	−	0.449879i	0.0569382	−	0.998378i	$-0.481866\pi$
$199$	−10.9922	−	6.34632i	−0.779213	−	0.449879i	−0.836151	+	0.548499i	$0.815200\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	5.46292	−	16.2317i	0.383421	−	1.13925i
$204$		0			0
$205$	−12.4006	+	7.15948i	−0.866095	+	0.500040i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.263868			−0.0182521
$210$		0			0
$211$			18.9821i			1.30678i	0.757020	+	0.653392i	$0.226655\pi$
$211$			18.9821i			1.30678i	−0.757020	+	0.653392i	$0.773345\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	8.83184	+	15.2972i	0.602326	+	1.04326i
$216$		0			0
$217$	15.2372	−	13.4329i	1.03437	−	0.911884i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−8.75236	+	15.1595i	−0.588747	+	1.01974i
$222$		0			0
$223$		−	8.56676i		−	0.573673i	−0.957980	−	0.286836i	$-0.907396\pi$
$223$		−	8.56676i		−	0.573673i	0.957980	−	0.286836i	$-0.0926036\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−12.3870	−	7.15164i	−0.822155	−	0.474671i	0.0290044	−	0.999579i	$-0.490766\pi$
$227$	−12.3870	−	7.15164i	−0.822155	−	0.474671i	−0.851159	+	0.524908i	$0.824100\pi$
$228$		0			0
$229$	−14.0246	−	24.2914i	−0.926774	−	1.60522i	−0.788683	−	0.614800i	$-0.789237\pi$
$229$	−14.0246	−	24.2914i	−0.926774	−	1.60522i	−0.138091	−	0.990420i	$-0.544097\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−7.52792	+	4.34625i	−0.493170	+	0.284732i	−0.725889	−	0.687812i	$-0.758571\pi$
$233$	−7.52792	+	4.34625i	−0.493170	+	0.284732i	0.232718	+	0.972544i	$0.425238\pi$
$234$		0			0
$235$	1.04210	+	0.601657i	0.0679792	+	0.0392478i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		−	12.4878i		−	0.807772i	−0.914809	−	0.403886i	$-0.867659\pi$
$239$		−	12.4878i		−	0.807772i	0.914809	−	0.403886i	$-0.132341\pi$
$240$		0			0
$241$	20.0923	+	11.6003i	1.29426	+	0.747240i	0.979406	−	0.201900i	$-0.0647117\pi$
$241$	20.0923	+	11.6003i	1.29426	+	0.747240i	0.314852	+	0.949141i	$0.398045\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−12.3333	−	1.55851i	−0.787944	−	0.0995697i
$246$		0			0
$247$	0.118656	+	0.205518i	0.00754991	+	0.0130768i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			13.9698i			0.881768i	0.897564	+	0.440884i	$0.145335\pi$
$251$			13.9698i			0.881768i	−0.897564	+	0.440884i	$0.854665\pi$
$252$		0			0
$253$			19.5926i			1.23178i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	11.8457	+	20.5174i	0.738915	+	1.27984i	0.952984	+	0.303020i	$0.0979950\pi$
$257$	11.8457	+	20.5174i	0.738915	+	1.27984i	−0.214069	+	0.976819i	$0.568672\pi$
$258$		0			0
$259$	1.76069	+	8.73287i	0.109404	+	0.542634i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−13.5097	−	7.79983i	−0.833044	−	0.480958i	0.0218497	−	0.999761i	$-0.493044\pi$
$263$	−13.5097	−	7.79983i	−0.833044	−	0.480958i	−0.854894	+	0.518803i	$0.826378\pi$
$264$		0			0
$265$			8.38927i			0.515349i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	27.5546	+	15.9086i	1.68003	+	0.969966i	0.961635	+	0.274332i	$0.0884566\pi$
$269$	27.5546	+	15.9086i	1.68003	+	0.969966i	0.718396	+	0.695635i	$0.244877\pi$
$270$		0			0
$271$	−8.16789	+	4.71573i	−0.496164	+	0.286460i	−0.727128	−	0.686502i	$-0.759145\pi$
$271$	−8.16789	+	4.71573i	−0.496164	+	0.286460i	0.230964	+	0.972962i	$0.425812\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−3.86369	−	6.69211i	−0.232989	−	0.403549i
$276$		0			0
$277$	−23.1275	−	13.3527i	−1.38960	−	0.802284i	−0.396327	−	0.918109i	$-0.629715\pi$
$277$	−23.1275	−	13.3527i	−1.38960	−	0.802284i	−0.993270	+	0.115825i	$0.963049\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		−	26.1930i		−	1.56254i	−0.624193	−	0.781271i	$-0.714572\pi$
$281$		−	26.1930i		−	1.56254i	0.624193	−	0.781271i	$-0.285428\pi$
$282$		0			0
$283$	2.62071	−	4.53920i	0.155785	−	0.269827i	−0.777560	−	0.628809i	$-0.783543\pi$
$283$	2.62071	−	4.53920i	0.155785	−	0.269827i	0.933345	+	0.358982i	$0.116876\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	6.80454	−	20.2181i	0.401659	−	1.19343i
$288$		0			0
$289$	−2.31140	−	4.00346i	−0.135964	−	0.235497i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		−	8.29435i		−	0.484561i	−0.970206	−	0.242280i	$-0.922105\pi$
$293$		−	8.29435i		−	0.484561i	0.970206	−	0.242280i	$-0.0778954\pi$
$294$		0			0
$295$	−13.3950			−0.779888
$296$		0			0
$297$		0			0
$298$		0			0
$299$	15.2600	−	8.81039i	0.882511	−	0.509518i
$300$		0			0
$301$	−24.9407	−	8.39399i	−1.43756	−	0.483821i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	22.2424	+	12.8417i	1.27360	+	0.735312i
$306$		0			0
$307$	−17.8873			−1.02088			−0.510442	−	0.859912i	$-0.670518\pi$
$307$	−17.8873			−1.02088			−0.510442	+	0.859912i	$0.670518\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	0.257495	−	0.445994i	0.0146012	−	0.0252900i	−0.858632	−	0.512592i	$-0.828685\pi$
$311$	0.257495	−	0.445994i	0.0146012	−	0.0252900i	0.873234	+	0.487302i	$0.162019\pi$
$312$		0			0
$313$	20.1970	−	11.6607i	1.14160	−	0.659104i	0.194775	−	0.980848i	$-0.437602\pi$
$313$	20.1970	−	11.6607i	1.14160	−	0.659104i	0.946827	+	0.321744i	$0.104269\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−10.4926	−	18.1736i	−0.589321	−	1.02073i	−0.994322	−	0.106417i	$-0.966062\pi$
$317$	−10.4926	−	18.1736i	−0.589321	−	1.02073i	0.405001	−	0.914316i	$-0.367271\pi$
$318$		0			0
$319$	13.5473	−	23.4646i	0.758503	−	1.31376i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−0.293141			−0.0163108
$324$		0			0
$325$	−3.47485	+	6.01861i	−0.192750	+	0.333853i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−1.75734	+	0.354308i	−0.0968852	+	0.0195336i
$330$		0			0
$331$	8.16441	−	4.71372i	0.448756	−	0.259090i	−0.258548	−	0.965998i	$-0.583244\pi$
$331$	8.16441	−	4.71372i	0.448756	−	0.259090i	0.707305	+	0.706909i	$0.249911\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	11.6449			0.636229
$336$		0			0
$337$	−14.8141			−0.806977			−0.403488	−	0.914985i	$-0.632202\pi$
$337$	−14.8141			−0.806977			−0.403488	+	0.914985i	$0.632202\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	27.8304	−	16.0679i	1.50710	−	0.870125i
$342$		0			0
$343$	15.3183	−	10.4091i	0.827111	−	0.562038i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	10.9642	−	18.9905i	0.588587	−	1.01946i	−0.405830	−	0.913948i	$-0.633018\pi$
$347$	10.9642	−	18.9905i	0.588587	−	1.01946i	0.994418	−	0.105515i	$-0.0336491\pi$
$348$		0			0
$349$	34.9301			1.86977			0.934884	−	0.354954i	$-0.115503\pi$
$349$	34.9301			1.86977			0.934884	+	0.354954i	$0.115503\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	3.71324	−	6.43152i	0.197636	−	0.342315i	−0.750126	−	0.661295i	$-0.770007\pi$
$353$	3.71324	−	6.43152i	0.197636	−	0.342315i	0.947761	+	0.318980i	$0.103340\pi$
$354$		0			0
$355$	−4.53395	−	7.85303i	−0.240637	−	0.416796i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−6.73364	+	3.88767i	−0.355388	+	0.205183i	−0.667056	−	0.745008i	$-0.732446\pi$
$359$	−6.73364	+	3.88767i	−0.355388	+	0.205183i	0.311668	+	0.950191i	$0.399112\pi$
$360$		0			0
$361$	9.49801	−	16.4510i	0.499895	−	0.865844i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	2.65213			0.138819
$366$		0			0
$367$	6.99509	+	4.03862i	0.365141	+	0.210814i	0.671333	−	0.741155i	$-0.265722\pi$
$367$	6.99509	+	4.03862i	0.365141	+	0.210814i	−0.306193	+	0.951970i	$0.599055\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−8.26513	−	9.37530i	−0.429104	−	0.486741i
$372$		0			0
$373$	24.1708	−	13.9550i	1.25152	−	0.722563i	0.280105	−	0.959969i	$-0.409631\pi$
$373$	24.1708	−	13.9550i	1.25152	−	0.722563i	0.971410	+	0.237407i	$0.0762974\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−24.3678			−1.25500
$378$		0			0
$379$		−	29.0460i		−	1.49199i	−0.665949	−	0.745997i	$-0.731973\pi$
$379$		−	29.0460i		−	1.49199i	0.665949	−	0.745997i	$-0.268027\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	5.63040	+	9.75214i	0.287700	+	0.498311i	0.973260	−	0.229705i	$-0.0737760\pi$
$383$	5.63040	+	9.75214i	0.287700	+	0.498311i	−0.685560	+	0.728016i	$0.740443\pi$
$384$		0			0
$385$	−18.6395	−	6.27327i	−0.949958	−	0.319716i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	2.51811	−	4.36149i	0.127673	−	0.221136i	−0.795102	−	0.606476i	$-0.792583\pi$
$389$	2.51811	−	4.36149i	0.127673	−	0.221136i	0.922775	+	0.385340i	$0.125916\pi$
$390$		0			0
$391$			21.7662i			1.10076i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	18.4399	+	10.6463i	0.927814	+	0.535674i
$396$		0			0
$397$	−13.8771	−	24.0358i	−0.696471	−	1.20632i	−0.969682	−	0.244369i	$-0.921419\pi$
$397$	−13.8771	−	24.0358i	−0.696471	−	1.20632i	0.273211	−	0.961954i	$-0.411914\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	3.70394	−	2.13847i	0.184966	−	0.106790i	−0.404658	−	0.914468i	$-0.632609\pi$
$401$	3.70394	−	2.13847i	0.184966	−	0.106790i	0.589624	+	0.807678i	$0.299276\pi$
$402$		0			0
$403$	−25.0295	−	14.4508i	−1.24681	−	0.719846i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			14.0937i			0.698600i
$408$		0			0
$409$	13.6093	+	7.85734i	0.672937	+	0.388521i	0.797189	−	0.603730i	$-0.206320\pi$
$409$	13.6093	+	7.85734i	0.672937	+	0.388521i	−0.124251	+	0.992251i	$0.539653\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	14.9694	−	13.1968i	0.736596	−	0.649373i
$414$		0			0
$415$	6.79278	+	11.7654i	0.333444	+	0.577543i
$416$		0			0
$417$		0			0
$418$		0			0
$419$			38.0838i			1.86052i	0.366904	+	0.930259i	$0.380418\pi$
$419$			38.0838i			1.86052i	−0.366904	+	0.930259i	$0.619582\pi$
$420$		0			0
$421$			15.7506i			0.767635i	0.923409	+	0.383818i	$0.125391\pi$
$421$			15.7506i			0.767635i	−0.923409	+	0.383818i	$0.874609\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−4.29232	−	7.43452i	−0.208208	−	0.360627i
$426$		0			0
$427$	−37.5083	+	7.56230i	−1.81516	+	0.365965i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	6.36898	+	3.67713i	0.306783	+	0.177121i	0.645486	−	0.763772i	$-0.276655\pi$
$431$	6.36898	+	3.67713i	0.306783	+	0.177121i	−0.338703	+	0.940893i	$0.609988\pi$
$432$		0			0
$433$		−	8.06468i		−	0.387564i	−0.981045	−	0.193782i	$-0.937925\pi$
$433$		−	8.06468i		−	0.387564i	0.981045	−	0.193782i	$-0.0620754\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	0.255551	+	0.147542i	0.0122247	+	0.00705791i
$438$		0			0
$439$	5.02415	−	2.90069i	0.239790	−	0.138443i	−0.375290	−	0.926907i	$-0.622457\pi$
$439$	5.02415	−	2.90069i	0.239790	−	0.138443i	0.615080	+	0.788465i	$0.289124\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	7.82446	+	13.5524i	0.371751	+	0.643892i	0.989835	−	0.142220i	$-0.0454241\pi$
$443$	7.82446	+	13.5524i	0.371751	+	0.643892i	−0.618084	+	0.786112i	$0.712091\pi$
$444$		0			0
$445$	−27.6069	−	15.9389i	−1.30869	−	0.755575i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			34.7839i			1.64155i	0.571250	+	0.820776i	$0.306459\pi$
$449$			34.7839i			1.64155i	−0.571250	+	0.820776i	$0.693541\pi$
$450$		0			0
$451$	16.8743	−	29.2272i	0.794582	−	1.37626i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	3.49577	+	17.3387i	0.163884	+	0.812851i
$456$		0			0
$457$	−5.38911	−	9.33422i	−0.252092	−	0.436636i	0.712010	−	0.702170i	$-0.247785\pi$
$457$	−5.38911	−	9.33422i	−0.252092	−	0.436636i	−0.964102	+	0.265533i	$0.914452\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		−	19.5062i		−	0.908494i	−0.890876	−	0.454247i	$-0.849908\pi$
$461$		−	19.5062i		−	0.908494i	0.890876	−	0.454247i	$-0.150092\pi$
$462$		0			0
$463$	27.2099			1.26455			0.632275	−	0.774744i	$-0.282121\pi$
$463$	27.2099			1.26455			0.632275	+	0.774744i	$0.282121\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	29.3243	−	16.9304i	1.35697	−	0.783445i	0.367752	−	0.929924i	$-0.380128\pi$
$467$	29.3243	−	16.9304i	1.35697	−	0.783445i	0.989214	+	0.146479i	$0.0467942\pi$
$468$		0			0
$469$	−13.0136	+	11.4726i	−0.600911	+	0.529755i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−36.0543	−	20.8160i	−1.65778	−	0.957118i
$474$		0			0
$475$	−0.116382			−0.00533999
$476$		0			0
$477$		0			0
$478$		0			0
$479$	0.640883	−	1.11004i	0.0292827	−	0.0507191i	−0.851013	−	0.525145i	$-0.824011\pi$
$479$	0.640883	−	1.11004i	0.0292827	−	0.0507191i	0.880295	+	0.474426i	$0.157344\pi$
$480$		0			0
$481$	10.9772	−	6.33766i	0.500515	−	0.288973i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	3.77013	+	6.53005i	0.171193	+	0.296515i
$486$		0			0
$487$	11.5313	−	19.9728i	0.522534	−	0.905055i	−0.477122	−	0.878837i	$-0.658320\pi$
$487$	11.5313	−	19.9728i	0.522534	−	0.905055i	0.999656	−	0.0262185i	$-0.00834656\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−33.6759			−1.51977			−0.759886	−	0.650057i	$-0.774745\pi$
$491$	−33.6759			−1.51977			−0.759886	+	0.650057i	$0.774745\pi$
$492$		0			0
$493$	15.0502	−	26.0677i	0.677827	−	1.17403i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	12.8037	+	4.30917i	0.574323	+	0.193293i
$498$		0			0
$499$	−5.15436	+	2.97587i	−0.230741	+	0.133218i	−0.610914	−	0.791697i	$-0.709198\pi$
$499$	−5.15436	+	2.97587i	−0.230741	+	0.133218i	0.380173	+	0.924915i	$0.375865\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	1.41791			0.0632214			0.0316107	−	0.999500i	$-0.489936\pi$
$503$	1.41791			0.0632214			0.0316107	+	0.999500i	$0.489936\pi$
$504$		0			0
$505$	7.45725			0.331843
$506$		0			0
$507$		0			0
$508$		0			0
$509$	7.25269	−	4.18734i	0.321470	−	0.185601i	−0.330578	−	0.943779i	$-0.607244\pi$
$509$	7.25269	−	4.18734i	0.321470	−	0.185601i	0.652048	+	0.758178i	$0.273910\pi$
$510$		0			0
$511$	−2.96385	+	2.61289i	−0.131113	+	0.115587i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	11.6009	−	20.0933i	0.511195	−	0.885416i
$516$		0			0
$517$	−2.83612			−0.124732
$518$		0			0
$519$		0			0
$520$		0			0
$521$	11.7714	−	20.3887i	0.515715	−	0.893244i	−0.484119	−	0.875002i	$-0.660860\pi$
$521$	11.7714	−	20.3887i	0.515715	−	0.893244i	0.999834	−	0.0182421i	$-0.00580695\pi$
$522$		0			0
$523$	−14.4448	−	25.0191i	−0.631626	−	1.09401i	−0.987219	−	0.159368i	$-0.949054\pi$
$523$	−14.4448	−	25.0191i	−0.631626	−	1.09401i	0.355593	−	0.934641i	$-0.384279\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	30.9179	−	17.8504i	1.34680	−	0.777577i
$528$		0			0
$529$	−0.544750	+	0.943535i	−0.0236848	+	0.0410233i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−30.3522			−1.31470
$534$		0			0
$535$	16.1519	+	9.32532i	0.698309	+	0.403169i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	27.0108	−	11.3531i	1.16344	−	0.489014i
$540$		0			0
$541$	1.78575	−	1.03100i	0.0767754	−	0.0443263i	−0.461121	−	0.887337i	$-0.652553\pi$
$541$	1.78575	−	1.03100i	0.0767754	−	0.0443263i	0.537896	+	0.843011i	$0.319219\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	4.50726			0.193070
$546$		0			0
$547$			35.7819i			1.52992i	0.644076	+	0.764962i	$0.277242\pi$
$547$			35.7819i			1.52992i	−0.644076	+	0.764962i	$0.722758\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−0.204036	−	0.353401i	−0.00869224	−	0.0150554i
$552$		0			0
$553$	−31.0960	+	6.26947i	−1.32234	+	0.266605i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	11.9748	−	20.7409i	0.507388	−	0.878821i	−0.492576	−	0.870270i	$-0.663945\pi$
$557$	11.9748	−	20.7409i	0.507388	−	0.878821i	0.999963	−	0.00855174i	$-0.00272214\pi$
$558$		0			0
$559$			37.4421i			1.58363i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	22.4987	+	12.9896i	0.948206	+	0.547447i	0.892523	−	0.451001i	$-0.148933\pi$
$563$	22.4987	+	12.9896i	0.948206	+	0.547447i	0.0556830	+	0.998448i	$0.482266\pi$
$564$		0			0
$565$	−4.05352	−	7.02090i	−0.170533	−	0.295371i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−15.4525	+	8.92150i	−0.647802	+	0.374009i	−0.787614	−	0.616169i	$-0.788684\pi$
$569$	−15.4525	+	8.92150i	−0.647802	+	0.374009i	0.139812	+	0.990178i	$0.455350\pi$
$570$		0			0
$571$	15.9523	+	9.21009i	0.667585	+	0.385430i	0.795161	−	0.606398i	$-0.207386\pi$
$571$	15.9523	+	9.21009i	0.667585	+	0.385430i	−0.127576	+	0.991829i	$0.540720\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			8.64157i			0.360378i
$576$		0			0
$577$	−17.5485	−	10.1317i	−0.730556	−	0.421786i	0.0880698	−	0.996114i	$-0.471930\pi$
$577$	−17.5485	−	10.1317i	−0.730556	−	0.421786i	−0.818625	+	0.574328i	$0.805263\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−19.1825	−	6.45602i	−0.795825	−	0.267841i
$582$		0			0
$583$	−9.88642	−	17.1238i	−0.409454	−	0.709195i
$584$		0			0
$585$		0			0
$586$		0			0
$587$			3.63501i			0.150033i	0.997182	+	0.0750164i	$0.0239009\pi$
$587$			3.63501i			0.150033i	−0.997182	+	0.0750164i	$0.976099\pi$
$588$		0			0
$589$		−	0.483999i		−	0.0199428i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	10.4731	+	18.1399i	0.430078	+	0.744918i	0.996880	−	0.0789370i	$-0.0251526\pi$
$593$	10.4731	+	18.1399i	0.430078	+	0.744918i	−0.566801	+	0.823855i	$0.691819\pi$
$594$		0			0
$595$	−20.7074	−	6.96922i	−0.848920	−	0.285710i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−1.58346	−	0.914209i	−0.0646983	−	0.0373536i	0.467302	−	0.884098i	$-0.345226\pi$
$599$	−1.58346	−	0.914209i	−0.0646983	−	0.0373536i	−0.532000	+	0.846744i	$0.678559\pi$
$600$		0			0
$601$		−	29.7207i		−	1.21233i	−0.795338	−	0.606166i	$-0.792707\pi$
$601$		−	29.7207i		−	1.21233i	0.795338	−	0.606166i	$-0.207293\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−10.0275	−	5.78937i	−0.407675	−	0.235371i
$606$		0			0
$607$	5.04013	−	2.90992i	0.204573	−	0.118110i	−0.394214	−	0.919019i	$-0.628983\pi$
$607$	5.04013	−	2.90992i	0.204573	−	0.118110i	0.598787	+	0.800909i	$0.295650\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	1.27534	+	2.20896i	0.0515949	+	0.0893650i
$612$		0			0
$613$	6.81649	+	3.93550i	0.275316	+	0.158954i	0.631301	−	0.775538i	$-0.282521\pi$
$613$	6.81649	+	3.93550i	0.275316	+	0.158954i	−0.355985	+	0.934492i	$0.615855\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	8.93676i		−	0.359781i	−0.983687	−	0.179890i	$-0.942426\pi$
$617$		−	8.93676i		−	0.359781i	0.983687	−	0.179890i	$-0.0575743\pi$
$618$		0			0
$619$	−3.80163	+	6.58462i	−0.152801	+	0.264658i	−0.932256	−	0.361799i	$-0.882163\pi$
$619$	−3.80163	+	6.58462i	−0.152801	+	0.264658i	0.779455	+	0.626458i	$0.215496\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	46.5547	−	9.38620i	1.86518	−	0.376050i
$624$		0			0
$625$	6.18050	+	10.7049i	0.247220	+	0.428197i
$626$		0			0
$627$		0			0
$628$		0			0
$629$			15.6573i			0.624296i
$630$		0			0
$631$	−49.9909			−1.99010			−0.995052	−	0.0993517i	$-0.968323\pi$
$631$	−49.9909			−1.99010			−0.995052	+	0.0993517i	$0.968323\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−12.8600	+	7.42473i	−0.510334	+	0.294641i
$636$		0			0
$637$	−20.9888	−	15.9326i	−0.831606	−	0.631271i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	34.4319	+	19.8793i	1.35998	+	0.785184i	0.989621	−	0.143705i	$-0.0459016\pi$
$641$	34.4319	+	19.8793i	1.35998	+	0.785184i	0.370358	+	0.928889i	$0.379235\pi$
$642$		0			0
$643$	28.7989			1.13572			0.567858	−	0.823126i	$-0.307772\pi$
$643$	28.7989			1.13572			0.567858	+	0.823126i	$0.307772\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−13.1134	+	22.7130i	−0.515540	+	0.892941i	0.484298	+	0.874903i	$0.339075\pi$
$647$	−13.1134	+	22.7130i	−0.515540	+	0.892941i	−0.999837	+	0.0180376i	$0.994258\pi$
$648$		0			0
$649$	27.3413	−	15.7855i	1.07324	−	0.619635i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−3.12639	−	5.41506i	−0.122345	−	0.211908i	0.798347	−	0.602198i	$-0.205708\pi$
$653$	−3.12639	−	5.41506i	−0.122345	−	0.211908i	−0.920692	+	0.390290i	$0.872375\pi$
$654$		0			0
$655$	−5.59724	+	9.69470i	−0.218702	+	0.378803i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−32.2081			−1.25465			−0.627326	−	0.778757i	$-0.715850\pi$
$659$	−32.2081			−1.25465			−0.627326	+	0.778757i	$0.715850\pi$
$660$		0			0
$661$	−8.81544	+	15.2688i	−0.342881	+	0.593887i	−0.984966	−	0.172746i	$-0.944736\pi$
$661$	−8.81544	+	15.2688i	−0.342881	+	0.593887i	0.642085	+	0.766633i	$0.278069\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−0.222189	+	0.195879i	−0.00861613	+	0.00759586i
$666$		0			0
$667$	−26.2406	+	15.1500i	−1.01604	+	0.586611i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−60.5336			−2.33687
$672$		0			0
$673$	−32.0260			−1.23451			−0.617256	−	0.786762i	$-0.711756\pi$
$673$	−32.0260			−1.23451			−0.617256	+	0.786762i	$0.711756\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	20.5345	−	11.8556i	0.789205	−	0.455648i	−0.0504774	−	0.998725i	$-0.516074\pi$
$677$	20.5345	−	11.8556i	0.789205	−	0.455648i	0.839683	+	0.543077i	$0.182741\pi$
$678$		0			0
$679$	−10.6467	−	3.58322i	−0.408582	−	0.137511i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−9.16325	+	15.8712i	−0.350622	+	0.607295i	−0.986359	−	0.164611i	$-0.947363\pi$
$683$	−9.16325	+	15.8712i	−0.350622	+	0.607295i	0.635737	+	0.771906i	$0.280696\pi$
$684$		0			0
$685$	23.2683			0.889035
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−8.89145	+	15.4004i	−0.338737	+	0.586710i
$690$		0			0
$691$	−20.3501	−	35.2473i	−0.774153	−	1.34087i	−0.935269	−	0.353937i	$-0.884843\pi$
$691$	−20.3501	−	35.2473i	−0.774153	−	1.34087i	0.161116	−	0.986935i	$-0.448491\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	29.3946	−	16.9710i	1.11500	−	0.643746i
$696$		0			0
$697$	18.7464	−	32.4697i	0.710069	−	1.22988i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	12.2653			0.463255			0.231628	−	0.972805i	$-0.425595\pi$
$701$	12.2653			0.463255			0.231628	+	0.972805i	$0.425595\pi$
$702$		0			0
$703$	0.183828	+	0.106133i	0.00693321	+	0.00400289i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−8.33373	+	7.34690i	−0.313422	+	0.276309i
$708$		0			0
$709$	5.83014	−	3.36604i	0.218956	−	0.126414i	−0.386511	−	0.922285i	$-0.626320\pi$
$709$	5.83014	−	3.36604i	0.218956	−	0.126414i	0.605467	+	0.795871i	$0.292987\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−35.9376			−1.34587
$714$		0			0
$715$			27.9824i			1.04648i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	1.45947	+	2.52788i	0.0544291	+	0.0942739i	0.891956	−	0.452122i	$-0.149333\pi$
$719$	1.45947	+	2.52788i	0.0544291	+	0.0942739i	−0.837527	+	0.546396i	$0.815999\pi$
$720$		0			0
$721$	6.83160	+	33.8841i	0.254422	+	1.26191i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	5.97521	−	10.3494i	0.221914	−	0.384366i
$726$		0			0
$727$		−	3.12734i		−	0.115987i	−0.998317	−	0.0579933i	$-0.981530\pi$
$727$		−	3.12734i		−	0.115987i	0.998317	−	0.0579933i	$-0.0184702\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−40.0541	−	23.1252i	−1.48145	−	0.855318i
$732$		0			0
$733$	−3.93077	−	6.80830i	−0.145186	−	0.251470i	0.784256	−	0.620437i	$-0.213045\pi$
$733$	−3.93077	−	6.80830i	−0.145186	−	0.251470i	−0.929442	+	0.368967i	$0.879712\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−23.7690	+	13.7231i	−0.875543	+	0.505495i
$738$		0			0
$739$	−1.01186	−	0.584195i	−0.0372217	−	0.0214900i	0.481274	−	0.876570i	$-0.340174\pi$
$739$	−1.01186	−	0.584195i	−0.0372217	−	0.0214900i	−0.518495	+	0.855080i	$0.673508\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$			6.12199i			0.224594i	0.993675	+	0.112297i	$0.0358208\pi$
$743$			6.12199i			0.224594i	−0.993675	+	0.112297i	$0.964179\pi$
$744$		0			0
$745$	6.74886	+	3.89645i	0.247259	+	0.142755i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−27.2377	+	5.49156i	−0.995243	+	0.200657i
$750$		0			0
$751$	−20.8430	−	36.1012i	−0.760573	−	1.31735i	−0.942556	−	0.334049i	$-0.891585\pi$
$751$	−20.8430	−	36.1012i	−0.760573	−	1.31735i	0.181983	−	0.983302i	$-0.441748\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			4.88120i			0.177645i
$756$		0			0
$757$			35.8599i			1.30335i	0.758498	+	0.651676i	$0.225934\pi$
$757$			35.8599i			1.30335i	−0.758498	+	0.651676i	$0.774066\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−4.88971	−	8.46923i	−0.177252	−	0.307009i	0.763686	−	0.645587i	$-0.223387\pi$
$761$	−4.88971	−	8.46923i	−0.177252	−	0.307009i	−0.940938	+	0.338578i	$0.890054\pi$
$762$		0			0
$763$	−5.03702	+	4.44056i	−0.182352	+	0.160759i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−24.5897	−	14.1968i	−0.887881	−	0.512619i
$768$		0			0
$769$			54.2218i			1.95529i	0.210269	+	0.977644i	$0.432566\pi$
$769$			54.2218i			1.95529i	−0.210269	+	0.977644i	$0.567434\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	20.8017	+	12.0099i	0.748185	+	0.431965i	0.825038	−	0.565078i	$-0.191154\pi$
$773$	20.8017	+	12.0099i	0.748185	+	0.431965i	−0.0768527	+	0.997042i	$0.524487\pi$
$774$		0			0
$775$	12.2750	−	7.08696i	0.440930	−	0.254571i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−0.254145	−	0.440193i	−0.00910570	−	0.0157715i
$780$		0			0
$781$	18.5090	+	10.6862i	0.662303	+	0.382381i
$782$		0			0
$783$		0			0
$784$		0			0
$785$		−	2.37661i		−	0.0848247i
$786$		0			0
$787$	13.5019	−	23.3859i	0.481290	−	0.833619i	−0.518479	−	0.855090i	$-0.673502\pi$
$787$	13.5019	−	23.3859i	0.481290	−	0.833619i	0.999769	+	0.0214714i	$0.00683508\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	11.4470	+	3.85256i	0.407007	+	0.136981i
$792$		0			0
$793$	27.2208	+	47.1477i	0.966637	+	1.67426i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			30.6501i			1.08568i	0.839835	+	0.542841i	$0.182651\pi$
$797$			30.6501i			1.08568i	−0.839835	+	0.542841i	$0.817349\pi$
$798$		0			0
$799$	−3.15075			−0.111466
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−5.41340	+	3.12543i	−0.191035	+	0.110294i
$804$		0			0
$805$	14.5443	+	16.4979i	0.512620	+	0.581474i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−10.5996	−	6.11967i	−0.372661	−	0.215156i	0.301959	−	0.953321i	$-0.402359\pi$
$809$	−10.5996	−	6.11967i	−0.372661	−	0.215156i	−0.674620	+	0.738165i	$0.735693\pi$
$810$		0			0
$811$	51.5601			1.81052			0.905260	−	0.424858i	$-0.139676\pi$
$811$	51.5601			1.81052			0.905260	+	0.424858i	$0.139676\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	3.39322	−	5.87723i	0.118859	−	0.205870i
$816$		0			0
$817$	−0.543015	+	0.313510i	−0.0189977	+	0.0109683i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	22.3477	+	38.7073i	0.779940	+	1.35090i	0.931976	+	0.362520i	$0.118084\pi$
$821$	22.3477	+	38.7073i	0.779940	+	1.35090i	−0.152036	+	0.988375i	$0.548583\pi$
$822$		0			0
$823$	−8.91299	+	15.4378i	−0.310687	+	0.538126i	−0.978511	−	0.206193i	$-0.933893\pi$
$823$	−8.91299	+	15.4378i	−0.310687	+	0.538126i	0.667824	+	0.744319i	$0.267226\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	44.4781			1.54665			0.773327	−	0.634007i	$-0.218591\pi$
$827$	44.4781			1.54665			0.773327	+	0.634007i	$0.218591\pi$
$828$		0			0
$829$	6.86797	−	11.8957i	0.238534	−	0.413154i	−0.721760	−	0.692144i	$-0.756666\pi$
$829$	6.86797	−	11.8957i	0.238534	−	0.413154i	0.960294	+	0.278990i	$0.0899997\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	30.0073	−	12.6126i	1.03969	−	0.437002i
$834$		0			0
$835$	11.1627	−	6.44481i	0.386303	−	0.223032i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	18.7998			0.649040			0.324520	−	0.945879i	$-0.394797\pi$
$839$	18.7998			0.649040			0.324520	+	0.945879i	$0.394797\pi$
$840$		0			0
$841$	12.9019			0.444892
$842$		0			0
$843$		0			0
$844$		0			0
$845$	1.80086	−	1.03973i	0.0619516	−	0.0357678i
$846$		0			0
$847$	16.9098	−	3.40928i	0.581026	−	0.117144i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	7.88055	−	13.6495i	0.270142	−	0.467899i
$852$		0			0
$853$	4.23719			0.145079			0.0725393	−	0.997366i	$-0.476890\pi$
$853$	4.23719			0.145079			0.0725393	+	0.997366i	$0.476890\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	6.78696	−	11.7554i	0.231838	−	0.401556i	−0.726511	−	0.687155i	$-0.758859\pi$
$857$	6.78696	−	11.7554i	0.231838	−	0.401556i	0.958349	+	0.285599i	$0.0921927\pi$
$858$		0			0
$859$	14.8653	+	25.7475i	0.507198	+	0.878494i	0.999965	+	0.00833211i	$0.00265222\pi$
$859$	14.8653	+	25.7475i	0.507198	+	0.878494i	−0.492767	+	0.870161i	$0.664014\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−26.7055	+	15.4184i	−0.909066	+	0.524849i	−0.880130	−	0.474732i	$-0.842545\pi$
$863$	−26.7055	+	15.4184i	−0.909066	+	0.524849i	−0.0289352	+	0.999581i	$0.509212\pi$
$864$		0			0
$865$	−1.09827	+	1.90225i	−0.0373422	+	0.0646785i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−50.1850			−1.70241
$870$		0			0
$871$	21.3769	+	12.3420i	0.724329	+	0.418191i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−30.4871	−	10.2606i	−1.03065	−	0.346873i
$876$		0			0
$877$	10.0815	−	5.82055i	0.340428	−	0.196546i	−0.320033	−	0.947406i	$-0.603694\pi$
$877$	10.0815	−	5.82055i	0.340428	−	0.196546i	0.660461	+	0.750860i	$0.270361\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	23.5879			0.794698			0.397349	−	0.917668i	$-0.369930\pi$
$881$	23.5879			0.794698			0.397349	+	0.917668i	$0.369930\pi$
$882$		0			0
$883$			39.4950i			1.32911i	0.747239	+	0.664556i	$0.231379\pi$
$883$			39.4950i			1.32911i	−0.747239	+	0.664556i	$0.768621\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−27.3283	−	47.3340i	−0.917595	−	1.58932i	−0.803058	−	0.595901i	$-0.796795\pi$
$887$	−27.3283	−	47.3340i	−0.917595	−	1.58932i	−0.114537	−	0.993419i	$-0.536538\pi$
$888$		0			0
$889$	7.05664	−	20.9671i	0.236672	−	0.703214i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−0.0213575	+	0.0369922i	−0.000714700	+	0.00123790i
$894$		0			0
$895$		−	31.2628i		−	1.04500i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	43.0398	+	24.8490i	1.43546	+	0.828762i
$900$		0			0
$901$	−10.9832	−	19.0235i	−0.365904	−	0.633764i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	25.3419	−	14.6311i	0.842392	−	0.486355i
$906$		0			0
$907$	7.80208	+	4.50453i	0.259064	+	0.149571i	0.623907	−	0.781498i	$-0.285544\pi$
$907$	7.80208	+	4.50453i	0.259064	+	0.149571i	−0.364844	+	0.931069i	$0.618878\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		−	35.3463i		−	1.17107i	−0.810646	−	0.585537i	$-0.800884\pi$
$911$		−	35.3463i		−	1.17107i	0.810646	−	0.585537i	$-0.199116\pi$
$912$		0			0
$913$	−27.7302	−	16.0100i	−0.917736	−	0.529855i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−3.29614	−	16.3486i	−0.108848	−	0.539878i
$918$		0			0
$919$	10.9416	+	18.9514i	0.360931	+	0.625150i	0.988114	−	0.153721i	$-0.0491257\pi$
$919$	10.9416	+	18.9514i	0.360931	+	0.625150i	−0.627184	+	0.778871i	$0.715792\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		−	19.2214i		−	0.632680i
$924$		0			0
$925$			6.21623i			0.204388i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	4.66786	+	8.08497i	0.153148	+	0.265259i	0.932383	−	0.361472i	$-0.117726\pi$
$929$	4.66786	+	8.08497i	0.153148	+	0.265259i	−0.779235	+	0.626731i	$0.784392\pi$
$930$		0			0
$931$	0.0553236	−	0.437803i	0.00181316	−	0.0143484i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−29.9346	−	17.2827i	−0.978965	−	0.565206i
$936$		0			0
$937$		−	14.0652i		−	0.459492i	−0.973251	−	0.229746i	$-0.926211\pi$
$937$		−	14.0652i		−	0.459492i	0.973251	−	0.229746i	$-0.0737895\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	34.5165	+	19.9281i	1.12521	+	0.649638i	0.942725	−	0.333571i	$-0.108254\pi$
$941$	34.5165	+	19.9281i	1.12521	+	0.649638i	0.182481	+	0.983209i	$0.441587\pi$
$942$		0			0
$943$	−32.6850	+	18.8707i	−1.06437	+	0.614513i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−10.3155	−	17.8669i	−0.335208	−	0.580598i	0.648317	−	0.761371i	$-0.275473\pi$
$947$	−10.3155	−	17.8669i	−0.335208	−	0.580598i	−0.983525	+	0.180773i	$0.942140\pi$
$948$		0			0
$949$	4.86860	+	2.81088i	0.158041	+	0.0912452i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	36.6133i		−	1.18602i	−0.805194	−	0.593011i	$-0.797939\pi$
$953$		−	36.6133i		−	1.18602i	0.805194	−	0.593011i	$-0.202061\pi$
$954$		0			0
$955$	−14.5759	+	25.2462i	−0.471665	+	0.816948i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−26.0031	+	22.9240i	−0.839684	+	0.740254i
$960$		0			0
$961$	13.9724	+	24.2010i	0.450724	+	0.780677i
$962$		0			0
$963$		0			0
$964$		0			0
$965$			41.7789i			1.34491i
$966$		0			0
$967$	10.0693			0.323808			0.161904	−	0.986806i	$-0.448236\pi$
$967$	10.0693			0.323808			0.161904	+	0.986806i	$0.448236\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	2.76132	−	1.59425i	0.0886149	−	0.0511618i	−0.455038	−	0.890472i	$-0.650374\pi$
$971$	2.76132	−	1.59425i	0.0886149	−	0.0511618i	0.543653	+	0.839310i	$0.317041\pi$
$972$		0			0
$973$	−16.1296	+	47.9253i	−0.517092	+	1.53642i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	3.60255	+	2.07994i	0.115256	+	0.0665430i	0.556520	−	0.830834i	$-0.312136\pi$
$977$	3.60255	+	2.07994i	0.115256	+	0.0665430i	−0.441264	+	0.897377i	$0.645470\pi$
$978$		0			0
$979$	75.1334			2.40127
$980$		0			0
$981$		0			0
$982$		0			0
$983$	10.4374	−	18.0782i	0.332902	−	0.576604i	−0.650177	−	0.759783i	$-0.725305\pi$
$983$	10.4374	−	18.0782i	0.332902	−	0.576604i	0.983080	+	0.183179i	$0.0586387\pi$
$984$		0			0
$985$	1.21919	−	0.703903i	0.0388468	−	0.0224282i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	23.2786	+	40.3197i	0.740216	+	1.28209i
$990$		0			0
$991$	−6.31063	+	10.9303i	−0.200464	+	0.347213i	−0.948678	−	0.316244i	$-0.897578\pi$
$991$	−6.31063	+	10.9303i	−0.200464	+	0.347213i	0.748214	+	0.663457i	$0.230912\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−22.5410			−0.714597
$996$		0			0
$997$	−9.23934	+	16.0030i	−0.292613	+	0.506820i	−0.974427	−	0.224705i	$-0.927858\pi$
$997$	−9.23934	+	16.0030i	−0.292613	+	0.506820i	0.681814	+	0.731526i	$0.261191\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2016.2.cp.b.17.22		56
3.2	odd	2	inner	2016.2.cp.b.17.8		56
4.3	odd	2		504.2.ch.b.269.24	yes	56
7.5	odd	6	inner	2016.2.cp.b.593.21		56
8.3	odd	2		504.2.ch.b.269.14	yes	56
8.5	even	2	inner	2016.2.cp.b.17.7		56
12.11	even	2		504.2.ch.b.269.5	✓	56
21.5	even	6	inner	2016.2.cp.b.593.7		56
24.5	odd	2	inner	2016.2.cp.b.17.21		56
24.11	even	2		504.2.ch.b.269.15	yes	56
28.19	even	6		504.2.ch.b.341.15	yes	56
56.5	odd	6	inner	2016.2.cp.b.593.8		56
56.19	even	6		504.2.ch.b.341.5	yes	56
84.47	odd	6		504.2.ch.b.341.14	yes	56
168.5	even	6	inner	2016.2.cp.b.593.22		56
168.131	odd	6		504.2.ch.b.341.24	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.ch.b.269.5	✓	56	12.11	even	2
504.2.ch.b.269.14	yes	56	8.3	odd	2
504.2.ch.b.269.15	yes	56	24.11	even	2
504.2.ch.b.269.24	yes	56	4.3	odd	2
504.2.ch.b.341.5	yes	56	56.19	even	6
504.2.ch.b.341.14	yes	56	84.47	odd	6
504.2.ch.b.341.15	yes	56	28.19	even	6
504.2.ch.b.341.24	yes	56	168.131	odd	6
2016.2.cp.b.17.7		56	8.5	even	2	inner
2016.2.cp.b.17.8		56	3.2	odd	2	inner
2016.2.cp.b.17.21		56	24.5	odd	2	inner
2016.2.cp.b.17.22		56	1.1	even	1	trivial
2016.2.cp.b.593.7		56	21.5	even	6	inner
2016.2.cp.b.593.8		56	56.5	odd	6	inner
2016.2.cp.b.593.21		56	7.5	odd	6	inner
2016.2.cp.b.593.22		56	168.5	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2016.cp (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.53798 - 0.887954i) q^{5} +(-0.843933 + 2.50754i) q^{7} +O(q^{10})\)	\(q+(1.53798 - 0.887954i) q^{5} +(-0.843933 + 2.50754i) q^{7} +(-2.09284 + 3.62490i) q^{11} +3.76443 q^{13} +(-2.32502 + 4.02705i) q^{17} +(0.0315203 + 0.0545948i) q^{19} +(4.05375 - 2.34043i) q^{23} +(-0.923074 + 1.59881i) q^{25} -6.47316 q^{29} +(-6.64896 - 3.83878i) q^{31} +(0.928631 + 4.60593i) q^{35} +(2.91602 - 1.68357i) q^{37} -8.06290 q^{41} +9.94628i q^{43} +(0.338788 + 0.586799i) q^{47} +(-5.57556 - 4.23240i) q^{49} +(-2.36197 + 4.09104i) q^{53} +7.43338i q^{55} +(-6.53211 - 3.77132i) q^{59} +(7.23104 + 12.5245i) q^{61} +(5.78962 - 3.34264i) q^{65} +(5.67866 + 3.27857i) q^{67} -5.10606i q^{71} +(1.29332 + 0.746696i) q^{73} +(-7.32339 - 8.30706i) q^{77} +(5.99485 + 10.3834i) q^{79} +7.64992i q^{83} +8.25803i q^{85} +(-8.97506 - 15.5453i) q^{89} +(-3.17692 + 9.43947i) q^{91} +(0.0969554 + 0.0559773i) q^{95} +4.24586i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 20 q^{7}+O(q^{10}) \) 56 * q + 20 * q^7	\( 56 q + 20 q^{7} + 8 q^{25} + 36 q^{31} - 28 q^{49} + 72 q^{73} + 12 q^{79}+O(q^{100}) \) 56 * q + 20 * q^7 + 8 * q^25 + 36 * q^31 - 28 * q^49 + 72 * q^73 + 12 * q^79

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