LMFDB - Embedded newform 2016.2.cp.b.17.8

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			17.8
Character	$\chi$	$=$	2016.17
Dual form			2016.2.cp.b.593.8

$q$-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	−0.802790	−	0.596262i	$-0.796652\pi$
$5$	−1.53798	+	0.887954i	−0.687806	+	0.397105i	0.114983	+	0.993367i	$0.463319\pi$
$6$		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	$-0.615972\pi$
$11$	2.09284	−	3.62490i	0.631015	−	1.09295i	0.987345	−	0.158589i	$-0.0506945\pi$
$12$		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	$-0.642634\pi$
$17$	2.32502	−	4.02705i	0.563899	−	0.976702i	0.997151	−	0.0754291i	$-0.0240327\pi$
$18$		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	−0.859050	−	0.511891i	$-0.828945\pi$
$23$	−4.05375	+	2.34043i	−0.845265	+	0.488014i	0.0137854	+	0.999905i	$0.495612\pi$
$24$		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	$-0.294762\pi$
$29$	6.47316			1.20204			0.601018	+	0.799235i	$0.294762\pi$
$30$		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	$-0.283216\pi$
$41$	8.06290			1.25921			0.629606	+	0.776914i	$0.283216\pi$
$42$		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	0.840259	−	0.542186i	$-0.182403\pi$
$47$	−0.338788	−	0.586799i	−0.0494174	−	0.0855934i	−0.889676	+	0.456592i	$0.849070\pi$
$48$		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	−0.656958	−	0.753927i	$-0.728157\pi$
$53$	2.36197	−	4.09104i	0.324441	−	0.561948i	0.981399	+	0.191979i	$0.0614905\pi$
$54$		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	0.860789	−	0.508963i	$-0.169971\pi$
$59$	6.53211	+	3.77132i	0.850408	+	0.490983i	−0.0103803	+	0.999946i	$0.503304\pi$
$60$		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	$0.0979846\pi$
$71$			5.10606i			0.605978i	−0.952994	+	0.302989i	$0.902015\pi$
$72$		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	$-0.862085\pi$
$83$		−	7.64992i		−	0.839688i	0.907596	−	0.419844i	$-0.137915\pi$
$84$		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	$0.233640\pi$
$89$	8.97506	+	15.5453i	0.951354	+	1.64779i	0.208855	+	0.977947i	$0.433026\pi$
$90$		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	0.308042	−	0.951373i	$-0.400326\pi$
$101$	−3.63654	−	2.09956i	−0.361849	−	0.208914i	−0.669892	+	0.742459i	$0.733659\pi$
$102$		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	$-0.997187\pi$
$107$	−5.25101	−	9.09502i	−0.507635	−	0.879249i	0.492326	−	0.870411i	$-0.336147\pi$
$108$		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	$0.0688838\pi$
$113$			4.56501i			0.429440i	−0.976676	+	0.214720i	$0.931116\pi$
$114$		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	−0.242191	−	0.970229i	$-0.577866\pi$
$131$	5.45901	−	3.15176i	0.476956	−	0.275371i	0.719147	+	0.694858i	$0.244533\pi$
$132$		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	−0.0703639	−	0.997521i	$-0.522416\pi$
$137$	−11.3468	−	6.55109i	−0.969425	−	0.559698i	−0.899061	+	0.437824i	$0.855749\pi$
$138$		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	0.762048	−	0.647520i	$-0.224194\pi$
$149$	−2.19406	−	3.80023i	−0.179745	−	0.311327i	−0.941793	+	0.336193i	$0.890860\pi$
$150$		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	$-0.590607\pi$
$167$	−7.25804			−0.561644			−0.280822	+	0.959760i	$0.590607\pi$
$168$		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	−0.458728	−	0.888577i	$-0.651695\pi$
$173$	1.07114	−	0.618425i	0.0814375	−	0.0470180i	0.540166	+	0.841559i	$0.318362\pi$
$174$		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	$0.395216\pi$
$179$	−8.80192	+	15.2454i	−0.657886	+	1.13949i	−0.981162	+	0.193188i	$0.938117\pi$
$180$		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	0.112038	−	0.993704i	$-0.464262\pi$
$191$	14.2159	−	8.20758i	1.02863	−	0.593880i	0.916592	+	0.399824i	$0.130929\pi$
$192$		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	$-0.508990\pi$
$197$	−0.792724			−0.0564792			−0.0282396	+	0.999601i	$0.508990\pi$
$198$		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	0.851159	−	0.524908i	$-0.175900\pi$
$227$	12.3870	+	7.15164i	0.822155	+	0.474671i	−0.0290044	+	0.999579i	$0.509234\pi$
$228$		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	−0.232718	−	0.972544i	$-0.574762\pi$
$233$	7.52792	−	4.34625i	0.493170	−	0.284732i	0.725889	+	0.687812i	$0.241429\pi$
$234$		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	$0.132341\pi$
$239$			12.4878i			0.807772i	−0.914809	+	0.403886i	$0.867659\pi$
$240$		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	$-0.854665\pi$
$251$		−	13.9698i		−	0.881768i	0.897564	−	0.440884i	$-0.145335\pi$
$252$		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	$-0.902005\pi$
$257$	−11.8457	−	20.5174i	−0.738915	−	1.27984i	0.214069	−	0.976819i	$-0.431328\pi$
$258$		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	0.854894	−	0.518803i	$-0.173622\pi$
$263$	13.5097	+	7.79983i	0.833044	+	0.480958i	−0.0218497	+	0.999761i	$0.506956\pi$
$264$		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	$-0.911543\pi$
$269$	−27.5546	−	15.9086i	−1.68003	−	0.969966i	−0.718396	−	0.695635i	$-0.755123\pi$
$270$		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	$0.285428\pi$
$281$			26.1930i			1.56254i	−0.624193	+	0.781271i	$0.714572\pi$
$282$		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	$0.0778954\pi$
$293$			8.29435i			0.484561i	−0.970206	+	0.242280i	$0.922105\pi$
$294$		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	−0.873234	−	0.487302i	$-0.837981\pi$
$311$	−0.257495	+	0.445994i	−0.0146012	+	0.0252900i	0.858632	+	0.512592i	$0.171315\pi$
$312$		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	$0.0339379\pi$
$317$	10.4926	+	18.1736i	0.589321	+	1.02073i	−0.405001	+	0.914316i	$0.632729\pi$
$318$		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	$0.366982\pi$
$347$	−10.9642	+	18.9905i	−0.588587	+	1.01946i	−0.994418	+	0.105515i	$0.966351\pi$
$348$		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	−0.947761	−	0.318980i	$-0.896660\pi$
$353$	−3.71324	+	6.43152i	−0.197636	+	0.342315i	0.750126	+	0.661295i	$0.229993\pi$
$354$		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	−0.311668	−	0.950191i	$-0.600888\pi$
$359$	6.73364	−	3.88767i	0.355388	−	0.205183i	0.667056	+	0.745008i	$0.267554\pi$
$360$		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	0.685560	−	0.728016i	$-0.259557\pi$
$383$	−5.63040	−	9.75214i	−0.287700	−	0.498311i	−0.973260	+	0.229705i	$0.926224\pi$
$384$		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	−0.922775	−	0.385340i	$-0.874084\pi$
$389$	−2.51811	+	4.36149i	−0.127673	+	0.221136i	0.795102	+	0.606476i	$0.207417\pi$
$390$		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	−0.589624	−	0.807678i	$-0.700724\pi$
$401$	−3.70394	+	2.13847i	−0.184966	+	0.106790i	0.404658	+	0.914468i	$0.367391\pi$
$402$		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	$-0.619582\pi$
$419$		−	38.0838i		−	1.86052i	0.366904	−	0.930259i	$-0.380418\pi$
$420$		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	0.338703	−	0.940893i	$-0.390012\pi$
$431$	−6.36898	−	3.67713i	−0.306783	−	0.177121i	−0.645486	+	0.763772i	$0.723345\pi$
$432$		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	0.618084	−	0.786112i	$-0.287909\pi$
$443$	−7.82446	−	13.5524i	−0.371751	−	0.643892i	−0.989835	+	0.142220i	$0.954576\pi$
$444$		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	$-0.693541\pi$
$449$		−	34.7839i		−	1.64155i	0.571250	−	0.820776i	$-0.306459\pi$
$450$		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	$0.150092\pi$
$461$			19.5062i			0.908494i	−0.890876	+	0.454247i	$0.849908\pi$
$462$		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	−0.989214	−	0.146479i	$-0.953206\pi$
$467$	−29.3243	+	16.9304i	−1.35697	+	0.783445i	−0.367752	+	0.929924i	$0.619872\pi$
$468$		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	−0.880295	−	0.474426i	$-0.842656\pi$
$479$	−0.640883	+	1.11004i	−0.0292827	+	0.0507191i	0.851013	+	0.525145i	$0.175989\pi$
$480$		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	$-0.225255\pi$
$491$	33.6759			1.51977			0.759886	+	0.650057i	$0.225255\pi$
$492$		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	$-0.510064\pi$
$503$	−1.41791			−0.0632214			−0.0316107	+	0.999500i	$0.510064\pi$
$504$		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	−0.652048	−	0.758178i	$-0.726090\pi$
$509$	−7.25269	+	4.18734i	−0.321470	+	0.185601i	0.330578	+	0.943779i	$0.392756\pi$
$510$		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	$0.339140\pi$
$521$	−11.7714	+	20.3887i	−0.515715	+	0.893244i	−0.999834	+	0.0182421i	$0.994193\pi$
$522$		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	$0.336055\pi$
$557$	−11.9748	+	20.7409i	−0.507388	+	0.878821i	−0.999963	+	0.00855174i	$0.997278\pi$
$558$		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	−0.0556830	−	0.998448i	$-0.517734\pi$
$563$	−22.4987	−	12.9896i	−0.948206	−	0.547447i	−0.892523	+	0.451001i	$0.851067\pi$
$564$		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	−0.139812	−	0.990178i	$-0.544650\pi$
$569$	15.4525	−	8.92150i	0.647802	−	0.374009i	0.787614	+	0.616169i	$0.211316\pi$
$570$		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	$-0.976099\pi$
$587$		−	3.63501i		−	0.150033i	0.997182	−	0.0750164i	$-0.0239009\pi$
$588$		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	0.566801	−	0.823855i	$-0.308181\pi$
$593$	−10.4731	−	18.1399i	−0.430078	−	0.744918i	−0.996880	+	0.0789370i	$0.974847\pi$
$594$		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	0.532000	−	0.846744i	$-0.321441\pi$
$599$	1.58346	+	0.914209i	0.0646983	+	0.0373536i	−0.467302	+	0.884098i	$0.654774\pi$
$600$		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	$0.0575743\pi$
$617$			8.93676i			0.359781i	−0.983687	+	0.179890i	$0.942426\pi$
$618$		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	−0.370358	−	0.928889i	$-0.620765\pi$
$641$	−34.4319	−	19.8793i	−1.35998	−	0.785184i	−0.989621	+	0.143705i	$0.954098\pi$
$642$		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	$-0.660925\pi$
$647$	13.1134	−	22.7130i	0.515540	−	0.892941i	0.999837	−	0.0180376i	$-0.00574185\pi$
$648$		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	0.920692	−	0.390290i	$-0.127625\pi$
$653$	3.12639	+	5.41506i	0.122345	+	0.211908i	−0.798347	+	0.602198i	$0.794292\pi$
$654$		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	$-0.284150\pi$
$659$	32.2081			1.25465			0.627326	+	0.778757i	$0.284150\pi$
$660$		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	−0.839683	−	0.543077i	$-0.817259\pi$
$677$	−20.5345	+	11.8556i	−0.789205	+	0.455648i	0.0504774	+	0.998725i	$0.483926\pi$
$678$		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	−0.635737	−	0.771906i	$-0.719304\pi$
$683$	9.16325	−	15.8712i	0.350622	−	0.607295i	0.986359	+	0.164611i	$0.0526369\pi$
$684$		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	$-0.574405\pi$
$701$	−12.2653			−0.463255			−0.231628	+	0.972805i	$0.574405\pi$
$702$		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	0.837527	−	0.546396i	$-0.184001\pi$
$719$	−1.45947	−	2.52788i	−0.0544291	−	0.0942739i	−0.891956	+	0.452122i	$0.850667\pi$
$720$		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	$-0.964179\pi$
$743$		−	6.12199i		−	0.224594i	0.993675	−	0.112297i	$-0.0358208\pi$
$744$		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	0.940938	−	0.338578i	$-0.109946\pi$
$761$	4.88971	+	8.46923i	0.177252	+	0.307009i	−0.763686	+	0.645587i	$0.776613\pi$
$762$		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	0.0768527	−	0.997042i	$-0.475513\pi$
$773$	−20.8017	−	12.0099i	−0.748185	−	0.431965i	−0.825038	+	0.565078i	$0.808846\pi$
$774$		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	$-0.817349\pi$
$797$		−	30.6501i		−	1.08568i	0.839835	−	0.542841i	$-0.182651\pi$
$798$		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	0.674620	−	0.738165i	$-0.264307\pi$
$809$	10.5996	+	6.11967i	0.372661	+	0.215156i	−0.301959	+	0.953321i	$0.597641\pi$
$810$		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	$-0.881916\pi$
$821$	−22.3477	−	38.7073i	−0.779940	−	1.35090i	0.152036	−	0.988375i	$-0.451417\pi$
$822$		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	$-0.781409\pi$
$827$	−44.4781			−1.54665			−0.773327	+	0.634007i	$0.781409\pi$
$828$		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	$-0.605203\pi$
$839$	−18.7998			−0.649040			−0.324520	+	0.945879i	$0.605203\pi$
$840$		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	−0.958349	−	0.285599i	$-0.907807\pi$
$857$	−6.78696	+	11.7554i	−0.231838	+	0.401556i	0.726511	+	0.687155i	$0.241141\pi$
$858$		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	0.0289352	−	0.999581i	$-0.490788\pi$
$863$	26.7055	−	15.4184i	0.909066	−	0.524849i	0.880130	+	0.474732i	$0.157455\pi$
$864$		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	$-0.630070\pi$
$881$	−23.5879			−0.794698			−0.397349	+	0.917668i	$0.630070\pi$
$882$		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	$0.203205\pi$
$887$	27.3283	+	47.3340i	0.917595	+	1.58932i	0.114537	+	0.993419i	$0.463462\pi$
$888$		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	$0.199116\pi$
$911$			35.3463i			1.17107i	−0.810646	+	0.585537i	$0.800884\pi$
$912$		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	0.779235	−	0.626731i	$-0.215608\pi$
$929$	−4.66786	−	8.08497i	−0.153148	−	0.265259i	−0.932383	+	0.361472i	$0.882274\pi$
$930$		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	−0.182481	−	0.983209i	$-0.558413\pi$
$941$	−34.5165	−	19.9281i	−1.12521	−	0.649638i	−0.942725	+	0.333571i	$0.891746\pi$
$942$		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	0.983525	−	0.180773i	$-0.0578600\pi$
$947$	10.3155	+	17.8669i	0.335208	+	0.580598i	−0.648317	+	0.761371i	$0.724527\pi$
$948$		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	$0.202061\pi$
$953$			36.6133i			1.18602i	−0.805194	+	0.593011i	$0.797939\pi$
$954$		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	−0.543653	−	0.839310i	$-0.682959\pi$
$971$	−2.76132	+	1.59425i	−0.0886149	+	0.0511618i	0.455038	+	0.890472i	$0.349626\pi$
$972$		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	0.441264	−	0.897377i	$-0.354530\pi$
$977$	−3.60255	−	2.07994i	−0.115256	−	0.0665430i	−0.556520	+	0.830834i	$0.687864\pi$
$978$		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	−0.983080	−	0.183179i	$-0.941361\pi$
$983$	−10.4374	+	18.0782i	−0.332902	+	0.576604i	0.650177	+	0.759783i	$0.274695\pi$
$984$		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.17.8		56
3.2	odd	2	inner	2016.2.cp.b.17.22		56
4.3	odd	2		504.2.ch.b.269.5	✓	56
7.5	odd	6	inner	2016.2.cp.b.593.7		56
8.3	odd	2		504.2.ch.b.269.15	yes	56
8.5	even	2	inner	2016.2.cp.b.17.21		56
12.11	even	2		504.2.ch.b.269.24	yes	56
21.5	even	6	inner	2016.2.cp.b.593.21		56
24.5	odd	2	inner	2016.2.cp.b.17.7		56
24.11	even	2		504.2.ch.b.269.14	yes	56
28.19	even	6		504.2.ch.b.341.14	yes	56
56.5	odd	6	inner	2016.2.cp.b.593.22		56
56.19	even	6		504.2.ch.b.341.24	yes	56
84.47	odd	6		504.2.ch.b.341.15	yes	56
168.5	even	6	inner	2016.2.cp.b.593.8		56
168.131	odd	6		504.2.ch.b.341.5	yes	56

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