LMFDB - Embedded newform 2016.2.cp.b.17.18

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			17.18
Character	$\chi$	$=$	2016.17
Dual form			2016.2.cp.b.593.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.785247 - 0.453362i) q^{5} +(2.47043 + 0.947077i) q^{7} +O(q^{10})$	$q+(0.785247 - 0.453362i) q^{5} +(2.47043 + 0.947077i) q^{7} +(-0.0729337 + 0.126325i) q^{11} -6.12830 q^{13} +(-3.00430 + 5.20361i) q^{17} +(2.10516 + 3.64625i) q^{19} +(-3.20566 + 1.85079i) q^{23} +(-2.08893 + 3.61812i) q^{25} -10.2484 q^{29} +(3.54741 + 2.04810i) q^{31} +(2.36927 - 0.376312i) q^{35} +(2.51971 - 1.45475i) q^{37} +2.26244 q^{41} +8.73882i q^{43} +(-3.58285 - 6.20567i) q^{47} +(5.20609 + 4.67938i) q^{49} +(1.86849 - 3.23632i) q^{53} +0.132262i q^{55} +(6.35100 + 3.66675i) q^{59} +(-3.41070 - 5.90751i) q^{61} +(-4.81223 + 2.77834i) q^{65} +(-2.66978 - 1.54140i) q^{67} +4.91850i q^{71} +(2.67843 + 1.54639i) q^{73} +(-0.299817 + 0.243004i) q^{77} +(5.41731 + 9.38305i) q^{79} -12.8534i q^{83} +5.44815i q^{85} +(1.55708 + 2.69694i) q^{89} +(-15.1396 - 5.80397i) q^{91} +(3.30614 + 1.90880i) q^{95} -0.593803i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	0.785247	−	0.453362i	0.351173	−	0.202750i	−0.314029	−	0.949413i	$-0.601679\pi$
$5$	0.785247	−	0.453362i	0.351173	−	0.202750i	0.665202	+	0.746664i	$0.268346\pi$
$6$		0			0
$7$	2.47043	+	0.947077i	0.933736	+	0.357962i
$7$	2.47043	+	0.947077i	0.933736	+	0.357962i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.0729337	+	0.126325i	−0.0219903	+	0.0380884i	−0.876811	−	0.480835i	$-0.840334\pi$
$11$	−0.0729337	+	0.126325i	−0.0219903	+	0.0380884i	0.854821	+	0.518923i	$0.173667\pi$
$12$		0			0
$13$	−6.12830			−1.69968			−0.849842	−	0.527037i	$-0.823303\pi$
$13$	−6.12830			−1.69968			−0.849842	+	0.527037i	$0.823303\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.00430	+	5.20361i	−0.728651	+	1.26206i	0.228803	+	0.973473i	$0.426519\pi$
$17$	−3.00430	+	5.20361i	−0.728651	+	1.26206i	−0.957454	+	0.288587i	$0.906814\pi$
$18$		0			0
$19$	2.10516	+	3.64625i	0.482957	+	0.836506i	0.999809	−	0.0195688i	$-0.00622934\pi$
$19$	2.10516	+	3.64625i	0.482957	+	0.836506i	−0.516851	+	0.856075i	$0.672896\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.20566	+	1.85079i	−0.668426	+	0.385916i	−0.795480	−	0.605980i	$-0.792781\pi$
$23$	−3.20566	+	1.85079i	−0.668426	+	0.385916i	0.127054	+	0.991896i	$0.459448\pi$
$24$		0			0
$25$	−2.08893	+	3.61812i	−0.417785	+	0.723625i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−10.2484			−1.90309			−0.951543	−	0.307515i	$-0.900503\pi$
$29$	−10.2484			−1.90309			−0.951543	+	0.307515i	$0.900503\pi$
$30$		0			0
$31$	3.54741	+	2.04810i	0.637134	+	0.367849i	0.783510	−	0.621380i	$-0.213428\pi$
$31$	3.54741	+	2.04810i	0.637134	+	0.367849i	−0.146376	+	0.989229i	$0.546761\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	2.36927	−	0.376312i	0.400480	−	0.0636084i
$36$		0			0
$37$	2.51971	−	1.45475i	0.414238	−	0.239160i	−0.278371	−	0.960474i	$-0.589795\pi$
$37$	2.51971	−	1.45475i	0.414238	−	0.239160i	0.692609	+	0.721313i	$0.256461\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	2.26244			0.353334			0.176667	−	0.984271i	$-0.443468\pi$
$41$	2.26244			0.353334			0.176667	+	0.984271i	$0.443468\pi$
$42$		0			0
$43$			8.73882i			1.33266i	0.745658	+	0.666329i	$0.232135\pi$
$43$			8.73882i			1.33266i	−0.745658	+	0.666329i	$0.767865\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.58285	−	6.20567i	−0.522612	−	0.905190i	−0.999654	−	0.0263098i	$-0.991624\pi$
$47$	−3.58285	−	6.20567i	−0.522612	−	0.905190i	0.477042	−	0.878881i	$-0.341709\pi$
$48$		0			0
$49$	5.20609	+	4.67938i	0.743727	+	0.668483i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	1.86849	−	3.23632i	0.256657	−	0.444543i	−0.708687	−	0.705523i	$-0.750712\pi$
$53$	1.86849	−	3.23632i	0.256657	−	0.444543i	0.965344	+	0.260980i	$0.0840455\pi$
$54$		0			0
$55$			0.132262i			0.0178342i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	6.35100	+	3.66675i	0.826829	+	0.477370i	0.852766	−	0.522293i	$-0.174923\pi$
$59$	6.35100	+	3.66675i	0.826829	+	0.477370i	−0.0259364	+	0.999664i	$0.508257\pi$
$60$		0			0
$61$	−3.41070	−	5.90751i	−0.436696	−	0.756379i	0.560737	−	0.827994i	$-0.310518\pi$
$61$	−3.41070	−	5.90751i	−0.436696	−	0.756379i	−0.997432	+	0.0716150i	$0.977185\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−4.81223	+	2.77834i	−0.596883	+	0.344611i
$66$		0			0
$67$	−2.66978	−	1.54140i	−0.326166	−	0.188312i	0.327972	−	0.944688i	$-0.393635\pi$
$67$	−2.66978	−	1.54140i	−0.326166	−	0.188312i	−0.654138	+	0.756376i	$0.726968\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			4.91850i			0.583719i	0.956461	+	0.291859i	$0.0942739\pi$
$71$			4.91850i			0.583719i	−0.956461	+	0.291859i	$0.905726\pi$
$72$		0			0
$73$	2.67843	+	1.54639i	0.313486	+	0.180991i	0.648485	−	0.761227i	$-0.275403\pi$
$73$	2.67843	+	1.54639i	0.313486	+	0.180991i	−0.334999	+	0.942218i	$0.608736\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.299817	+	0.243004i	−0.0341674	+	0.0276928i
$78$		0			0
$79$	5.41731	+	9.38305i	0.609495	+	1.05568i	0.991324	+	0.131443i	$0.0419610\pi$
$79$	5.41731	+	9.38305i	0.609495	+	1.05568i	−0.381829	+	0.924233i	$0.624706\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$		−	12.8534i		−	1.41085i	−0.708785	−	0.705424i	$-0.750756\pi$
$83$		−	12.8534i		−	1.41085i	0.708785	−	0.705424i	$-0.249244\pi$
$84$		0			0
$85$			5.44815i			0.590935i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	1.55708	+	2.69694i	0.165050	+	0.285875i	0.936673	−	0.350205i	$-0.113888\pi$
$89$	1.55708	+	2.69694i	0.165050	+	0.285875i	−0.771623	+	0.636080i	$0.780555\pi$
$90$		0			0
$91$	−15.1396	−	5.80397i	−1.58706	−	0.608422i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	3.30614	+	1.90880i	0.339203	+	0.195839i
$96$		0			0
$97$		−	0.593803i		−	0.0602915i	−0.999546	−	0.0301458i	$-0.990403\pi$
$97$		−	0.593803i		−	0.0602915i	0.999546	−	0.0301458i	$-0.00959715\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−9.65297	−	5.57314i	−0.960506	−	0.554549i	−0.0641776	−	0.997938i	$-0.520442\pi$
$101$	−9.65297	−	5.57314i	−0.960506	−	0.554549i	−0.896329	+	0.443390i	$0.853776\pi$
$102$		0			0
$103$	1.41603	−	0.817548i	0.139526	−	0.0805554i	−0.428612	−	0.903489i	$-0.640997\pi$
$103$	1.41603	−	0.817548i	0.139526	−	0.0805554i	0.568138	+	0.822933i	$0.307664\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−7.12074	−	12.3335i	−0.688387	−	1.19232i	−0.972359	−	0.233489i	$-0.924986\pi$
$107$	−7.12074	−	12.3335i	−0.688387	−	1.19232i	0.283972	−	0.958833i	$-0.408348\pi$
$108$		0			0
$109$	5.88150	+	3.39568i	0.563345	+	0.325247i	0.754487	−	0.656315i	$-0.227886\pi$
$109$	5.88150	+	3.39568i	0.563345	+	0.325247i	−0.191142	+	0.981562i	$0.561219\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$			8.54183i			0.803548i	0.915739	+	0.401774i	$0.131606\pi$
$113$			8.54183i			0.803548i	−0.915739	+	0.401774i	$0.868394\pi$
$114$		0			0
$115$	−1.67816	+	2.90665i	−0.156489	+	0.271046i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−12.3502	+	10.0099i	−1.13214	+	0.917602i
$120$		0			0
$121$	5.48936	+	9.50785i	0.499033	+	0.864350i
$122$		0			0
$123$		0			0
$124$		0			0
$125$			8.32178i			0.744323i
$126$		0			0
$127$	18.0974			1.60589			0.802944	−	0.596054i	$-0.203266\pi$
$127$	18.0974			1.60589			0.802944	+	0.596054i	$0.203266\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−8.38458	+	4.84084i	−0.732564	+	0.422946i	−0.819359	−	0.573280i	$-0.805671\pi$
$131$	−8.38458	+	4.84084i	−0.732564	+	0.422946i	0.0867954	+	0.996226i	$0.472337\pi$
$132$		0			0
$133$	1.74739	+	11.0016i	0.151518	+	0.953957i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−9.11532	−	5.26273i	−0.778774	−	0.449625i	0.0572215	−	0.998362i	$-0.481776\pi$
$137$	−9.11532	−	5.26273i	−0.778774	−	0.449625i	−0.835996	+	0.548736i	$0.815109\pi$
$138$		0			0
$139$	15.8152			1.34143			0.670715	−	0.741715i	$-0.265987\pi$
$139$	15.8152			1.34143			0.670715	+	0.741715i	$0.265987\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.446960	−	0.774157i	0.0373767	−	0.0647383i
$144$		0			0
$145$	−8.04755	+	4.64625i	−0.668312	+	0.385850i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	5.79849	+	10.0433i	0.475031	+	0.822777i	0.999591	−	0.0285960i	$-0.00910364\pi$
$149$	5.79849	+	10.0433i	0.475031	+	0.822777i	−0.524560	+	0.851373i	$0.675770\pi$
$150$		0			0
$151$	−7.79321	+	13.4982i	−0.634202	+	1.09847i	0.352481	+	0.935819i	$0.385338\pi$
$151$	−7.79321	+	13.4982i	−0.634202	+	1.09847i	−0.986684	+	0.162652i	$0.947995\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	3.71412			0.298326
$156$		0			0
$157$	−6.66733	+	11.5482i	−0.532111	+	0.921643i	0.467186	+	0.884159i	$0.345268\pi$
$157$	−6.66733	+	11.5482i	−0.532111	+	0.921643i	−0.999297	+	0.0374841i	$0.988066\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−9.67221	+	1.53624i	−0.762277	+	0.121073i
$162$		0			0
$163$	−14.7888	+	8.53830i	−1.15835	+	0.668771i	−0.950907	−	0.309477i	$-0.899846\pi$
$163$	−14.7888	+	8.53830i	−1.15835	+	0.668771i	−0.207439	+	0.978248i	$0.566513\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	1.64523			0.127312			0.0636558	−	0.997972i	$-0.479724\pi$
$167$	1.64523			0.127312			0.0636558	+	0.997972i	$0.479724\pi$
$168$		0			0
$169$	24.5561			1.88893
$170$		0			0
$171$		0			0
$172$		0			0
$173$	7.80851	−	4.50825i	0.593670	−	0.342756i	−0.172877	−	0.984943i	$-0.555306\pi$
$173$	7.80851	−	4.50825i	0.593670	−	0.342756i	0.766547	+	0.642188i	$0.221973\pi$
$174$		0			0
$175$	−8.58720	+	6.95996i	−0.649131	+	0.526124i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−7.30700	+	12.6561i	−0.546151	+	0.945961i	0.452383	+	0.891824i	$0.350574\pi$
$179$	−7.30700	+	12.6561i	−0.546151	+	0.945961i	−0.998534	+	0.0541368i	$0.982759\pi$
$180$		0			0
$181$	−0.198456			−0.0147511			−0.00737556	−	0.999973i	$-0.502348\pi$
$181$	−0.198456			−0.0147511			−0.00737556	+	0.999973i	$0.502348\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1.31906	−	2.28468i	0.0969793	−	0.167973i
$186$		0			0
$187$	−0.438230	−	0.759037i	−0.0320466	−	0.0555063i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	0.169619	−	0.0979296i	0.0122732	−	0.00708594i	−0.493851	−	0.869547i	$-0.664411\pi$
$191$	0.169619	−	0.0979296i	0.0122732	−	0.00708594i	0.506124	+	0.862461i	$0.331078\pi$
$192$		0			0
$193$	5.03614	−	8.72285i	0.362509	−	0.627884i	−0.625864	−	0.779932i	$-0.715254\pi$
$193$	5.03614	−	8.72285i	0.362509	−	0.627884i	0.988373	+	0.152048i	$0.0485868\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	0.981430			0.0699240			0.0349620	−	0.999389i	$-0.488869\pi$
$197$	0.981430			0.0699240			0.0349620	+	0.999389i	$0.488869\pi$
$198$		0			0
$199$	1.90703	+	1.10102i	0.135185	+	0.0780494i	0.566067	−	0.824359i	$-0.308464\pi$
$199$	1.90703	+	1.10102i	0.135185	+	0.0780494i	−0.430882	+	0.902408i	$0.641797\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−25.3181	−	9.70606i	−1.77698	−	0.681232i
$204$		0			0
$205$	1.77658	−	1.02571i	0.124081	−	0.0716385i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.614149			−0.0424816
$210$		0			0
$211$		−	17.7696i		−	1.22331i	−0.791125	−	0.611654i	$-0.790504\pi$
$211$		−	17.7696i		−	1.22331i	0.791125	−	0.611654i	$-0.209496\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	3.96185	+	6.86213i	0.270196	+	0.467993i
$216$		0			0
$217$	6.82394	+	8.41937i	0.463239	+	0.571544i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	18.4113	−	31.8893i	1.23848	−	2.14510i
$222$		0			0
$223$		−	20.7181i		−	1.38738i	−0.720271	−	0.693692i	$-0.755983\pi$
$223$		−	20.7181i		−	1.38738i	0.720271	−	0.693692i	$-0.244017\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	17.3954	+	10.0432i	1.15457	+	0.666593i	0.949997	−	0.312258i	$-0.101085\pi$
$227$	17.3954	+	10.0432i	1.15457	+	0.666593i	0.204575	+	0.978851i	$0.434419\pi$
$228$		0			0
$229$	−9.68640	−	16.7773i	−0.640095	−	1.10868i	−0.985411	−	0.170191i	$-0.945562\pi$
$229$	−9.68640	−	16.7773i	−0.640095	−	1.10868i	0.345316	−	0.938487i	$-0.387772\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	22.4100	−	12.9384i	1.46813	−	0.847625i	0.468768	−	0.883322i	$-0.344698\pi$
$233$	22.4100	−	12.9384i	1.46813	−	0.847625i	0.999363	+	0.0356961i	$0.0113649\pi$
$234$		0			0
$235$	−5.62684	−	3.24866i	−0.367054	−	0.211919i
$236$		0			0
$237$		0			0
$238$		0			0
$239$			11.2007i			0.724512i	0.932079	+	0.362256i	$0.117993\pi$
$239$			11.2007i			0.724512i	−0.932079	+	0.362256i	$0.882007\pi$
$240$		0			0
$241$	−23.6842	−	13.6741i	−1.52563	−	0.880825i	−0.999538	−	0.0303997i	$-0.990322\pi$
$241$	−23.6842	−	13.6741i	−1.52563	−	0.880825i	−0.526096	−	0.850425i	$-0.676345\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	6.20952	+	1.31423i	0.396712	+	0.0839628i
$246$		0			0
$247$	−12.9011	−	22.3453i	−0.820875	−	1.42180i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			29.0073i			1.83092i	0.402407	+	0.915461i	$0.368174\pi$
$251$			29.0073i			1.83092i	−0.402407	+	0.915461i	$0.631826\pi$
$252$		0			0
$253$		−	0.539939i		−	0.0339457i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−6.02554	−	10.4365i	−0.375863	−	0.651014i	0.614593	−	0.788845i	$-0.289320\pi$
$257$	−6.02554	−	10.4365i	−0.375863	−	0.651014i	−0.990456	+	0.137831i	$0.955987\pi$
$258$		0			0
$259$	7.60254	−	1.20752i	0.472399	−	0.0750314i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−2.36800	−	1.36716i	−0.146017	−	0.0843029i	0.425212	−	0.905094i	$-0.360200\pi$
$263$	−2.36800	−	1.36716i	−0.146017	−	0.0843029i	−0.571229	+	0.820791i	$0.693533\pi$
$264$		0			0
$265$		−	3.38842i		−	0.208149i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−4.45879	−	2.57428i	−0.271857	−	0.156957i	0.357874	−	0.933770i	$-0.383502\pi$
$269$	−4.45879	−	2.57428i	−0.271857	−	0.156957i	−0.629731	+	0.776813i	$0.716835\pi$
$270$		0			0
$271$	−21.0489	+	12.1526i	−1.27863	+	0.738216i	−0.976596	−	0.215082i	$-0.930998\pi$
$271$	−21.0489	+	12.1526i	−1.27863	+	0.738216i	−0.302031	+	0.953298i	$0.597665\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.304706	−	0.527767i	−0.0183745	−	0.0318255i
$276$		0			0
$277$	−0.705869	−	0.407533i	−0.0424115	−	0.0244863i	0.478644	−	0.878009i	$-0.341128\pi$
$277$	−0.705869	−	0.407533i	−0.0424115	−	0.0244863i	−0.521056	+	0.853523i	$0.674462\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$			1.06599i			0.0635918i	0.999494	+	0.0317959i	$0.0101227\pi$
$281$			1.06599i			0.0635918i	−0.999494	+	0.0317959i	$0.989877\pi$
$282$		0			0
$283$	3.14663	−	5.45012i	0.187048	−	0.323976i	−0.757217	−	0.653164i	$-0.773441\pi$
$283$	3.14663	−	5.45012i	0.187048	−	0.323976i	0.944265	+	0.329187i	$0.106775\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	5.58922	+	2.14271i	0.329921	+	0.126480i
$288$		0			0
$289$	−9.55169	−	16.5440i	−0.561864	−	0.973177i
$290$		0			0
$291$		0			0
$292$		0			0
$293$			17.9687i			1.04974i	0.851181	+	0.524872i	$0.175887\pi$
$293$			17.9687i			1.04974i	−0.851181	+	0.524872i	$0.824113\pi$
$294$		0			0
$295$	6.64946			0.387147
$296$		0			0
$297$		0			0
$298$		0			0
$299$	19.6452	−	11.3422i	1.13611	−	0.655936i
$300$		0			0
$301$	−8.27634	+	21.5887i	−0.477040	+	1.24435i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−5.35648	−	3.09257i	−0.306711	−	0.177080i
$306$		0			0
$307$	27.7008			1.58097			0.790485	−	0.612481i	$-0.209829\pi$
$307$	27.7008			1.58097			0.790485	+	0.612481i	$0.209829\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	12.7971	−	22.1653i	0.725658	−	1.25688i	−0.233045	−	0.972466i	$-0.574869\pi$
$311$	12.7971	−	22.1653i	0.725658	−	1.25688i	0.958703	−	0.284410i	$-0.0917977\pi$
$312$		0			0
$313$	−14.9541	+	8.63375i	−0.845255	+	0.488008i	−0.859047	−	0.511897i	$-0.828943\pi$
$313$	−14.9541	+	8.63375i	−0.845255	+	0.488008i	0.0137920	+	0.999905i	$0.495610\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	2.17346	+	3.76454i	0.122074	+	0.211438i	0.920585	−	0.390542i	$-0.127712\pi$
$317$	2.17346	+	3.76454i	0.122074	+	0.211438i	−0.798512	+	0.601979i	$0.794379\pi$
$318$		0			0
$319$	0.747457	−	1.29463i	0.0418495	−	0.0724855i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−25.2982			−1.40763
$324$		0			0
$325$	12.8016	−	22.1730i	0.710103	−	1.22993i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−2.97393	−	18.7239i	−0.163958	−	1.03228i
$330$		0			0
$331$	15.0111	−	8.66665i	0.825084	−	0.476362i	−0.0270828	−	0.999633i	$-0.508622\pi$
$331$	15.0111	−	8.66665i	0.825084	−	0.476362i	0.852166	+	0.523271i	$0.175288\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−2.79525			−0.152721
$336$		0			0
$337$	−0.659592			−0.0359303			−0.0179651	−	0.999839i	$-0.505719\pi$
$337$	−0.659592			−0.0359303			−0.0179651	+	0.999839i	$0.505719\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−0.517452	+	0.298751i	−0.0280216	+	0.0161783i
$342$		0			0
$343$	8.42956	+	16.4907i	0.455154	+	0.890413i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−3.49897	+	6.06039i	−0.187834	+	0.325339i	−0.944528	−	0.328431i	$-0.893480\pi$
$347$	−3.49897	+	6.06039i	−0.187834	+	0.325339i	0.756694	+	0.653770i	$0.226813\pi$
$348$		0			0
$349$	20.2632			1.08467			0.542333	−	0.840164i	$-0.317541\pi$
$349$	20.2632			1.08467			0.542333	+	0.840164i	$0.317541\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−5.18465	+	8.98008i	−0.275951	+	0.477962i	−0.970375	−	0.241605i	$-0.922326\pi$
$353$	−5.18465	+	8.98008i	−0.275951	+	0.477962i	0.694423	+	0.719567i	$0.255659\pi$
$354$		0			0
$355$	2.22986	+	3.86224i	0.118349	+	0.204986i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	17.5691	−	10.1436i	0.927264	−	0.535356i	0.0413188	−	0.999146i	$-0.486844\pi$
$359$	17.5691	−	10.1436i	0.927264	−	0.535356i	0.885945	+	0.463790i	$0.153511\pi$
$360$		0			0
$361$	0.636589	−	1.10261i	0.0335047	−	0.0580319i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	2.80430			0.146784
$366$		0			0
$367$	−21.6024	−	12.4722i	−1.12764	−	0.651042i	−0.184298	−	0.982870i	$-0.559001\pi$
$367$	−21.6024	−	12.4722i	−1.12764	−	0.651042i	−0.943340	+	0.331829i	$0.892334\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	7.68104	−	6.22552i	0.398780	−	0.323213i
$372$		0			0
$373$	4.26886	−	2.46463i	0.221033	−	0.127614i	−0.385395	−	0.922752i	$-0.625935\pi$
$373$	4.26886	−	2.46463i	0.221033	−	0.127614i	0.606429	+	0.795138i	$0.292602\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	62.8055			3.23465
$378$		0			0
$379$			25.1007i			1.28934i	0.764462	+	0.644669i	$0.223005\pi$
$379$			25.1007i			1.28934i	−0.764462	+	0.644669i	$0.776995\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−14.0619	−	24.3560i	−0.718531	−	1.24453i	−0.961582	−	0.274519i	$-0.911482\pi$
$383$	−14.0619	−	24.3560i	−0.718531	−	1.24453i	0.243051	−	0.970014i	$-0.421852\pi$
$384$		0			0
$385$	−0.125262	+	0.326744i	−0.00638394	+	0.0166524i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−3.82681	+	6.62822i	−0.194027	+	0.336064i	−0.946581	−	0.322466i	$-0.895488\pi$
$389$	−3.82681	+	6.62822i	−0.194027	+	0.336064i	0.752554	+	0.658530i	$0.228822\pi$
$390$		0			0
$391$		−	22.2413i		−	1.12479i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	8.50785	+	4.91201i	0.428076	+	0.247150i
$396$		0			0
$397$	−6.22748	−	10.7863i	−0.312548	−	0.541350i	0.666365	−	0.745626i	$-0.267849\pi$
$397$	−6.22748	−	10.7863i	−0.312548	−	0.541350i	−0.978913	+	0.204276i	$0.934516\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−18.1682	+	10.4894i	−0.907279	+	0.523818i	−0.879555	−	0.475798i	$-0.842159\pi$
$401$	−18.1682	+	10.4894i	−0.907279	+	0.523818i	−0.0277241	+	0.999616i	$0.508826\pi$
$402$		0			0
$403$	−21.7396	−	12.5514i	−1.08293	−	0.625228i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			0.424403i			0.0210369i
$408$		0			0
$409$	0.456865	+	0.263771i	0.0225905	+	0.0130426i	0.511253	−	0.859430i	$-0.329182\pi$
$409$	0.456865	+	0.263771i	0.0225905	+	0.0130426i	−0.488662	+	0.872473i	$0.662515\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	12.2170	+	15.0733i	0.601160	+	0.741711i
$414$		0			0
$415$	−5.82727	−	10.0931i	−0.286049	−	0.495452i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		−	22.0482i		−	1.07713i	−0.842585	−	0.538564i	$-0.818967\pi$
$419$		−	22.0482i		−	1.07713i	0.842585	−	0.538564i	$-0.181033\pi$
$420$		0			0
$421$			18.2360i			0.888771i	0.895836	+	0.444385i	$0.146578\pi$
$421$			18.2360i			0.888771i	−0.895836	+	0.444385i	$0.853422\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−12.5515	−	21.7399i	−0.608839	−	1.05454i
$426$		0			0
$427$	−2.83105	−	17.8243i	−0.137004	−	0.862579i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	24.8419	+	14.3425i	1.19659	+	0.690854i	0.959794	−	0.280705i	$-0.0905683\pi$
$431$	24.8419	+	14.3425i	1.19659	+	0.690854i	0.236799	+	0.971559i	$0.423902\pi$
$432$		0			0
$433$		−	37.7023i		−	1.81186i	−0.423429	−	0.905929i	$-0.639174\pi$
$433$		−	37.7023i		−	1.81186i	0.423429	−	0.905929i	$-0.360826\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−13.4969	−	7.79242i	−0.645642	−	0.372762i
$438$		0			0
$439$	7.68790	−	4.43861i	0.366924	−	0.211843i	−0.305190	−	0.952291i	$-0.598720\pi$
$439$	7.68790	−	4.43861i	0.366924	−	0.211843i	0.672114	+	0.740448i	$0.265387\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	0.209480	+	0.362830i	0.00995270	+	0.0172386i	0.870959	−	0.491356i	$-0.163499\pi$
$443$	0.209480	+	0.362830i	0.00995270	+	0.0172386i	−0.861006	+	0.508595i	$0.830165\pi$
$444$		0			0
$445$	2.44538	+	1.41184i	0.115922	+	0.0669278i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			39.4411i			1.86134i	0.365861	+	0.930670i	$0.380775\pi$
$449$			39.4411i			1.86134i	−0.365861	+	0.930670i	$0.619225\pi$
$450$		0			0
$451$	−0.165008	+	0.285803i	−0.00776994	+	0.0134579i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−14.5196	+	2.30616i	−0.680689	+	0.108114i
$456$		0			0
$457$	−5.94479	−	10.2967i	−0.278085	−	0.481658i	0.692823	−	0.721107i	$-0.256367\pi$
$457$	−5.94479	−	10.2967i	−0.278085	−	0.481658i	−0.970909	+	0.239449i	$0.923033\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$			0.217896i			0.0101484i	0.999987	+	0.00507422i	$0.00161518\pi$
$461$			0.217896i			0.0101484i	−0.999987	+	0.00507422i	$0.998385\pi$
$462$		0			0
$463$	9.13271			0.424433			0.212216	−	0.977223i	$-0.431932\pi$
$463$	9.13271			0.424433			0.212216	+	0.977223i	$0.431932\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	23.4188	−	13.5208i	1.08369	−	0.625670i	0.151802	−	0.988411i	$-0.451492\pi$
$467$	23.4188	−	13.5208i	1.08369	−	0.625670i	0.931890	+	0.362741i	$0.118159\pi$
$468$		0			0
$469$	−5.13570	−	6.33642i	−0.237145	−	0.292589i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−1.10393	−	0.637355i	−0.0507588	−	0.0293056i
$474$		0			0
$475$	−17.5901			−0.807089
$476$		0			0
$477$		0			0
$478$		0			0
$479$	5.06539	−	8.77352i	0.231444	−	0.400872i	−0.726789	−	0.686860i	$-0.758988\pi$
$479$	5.06539	−	8.77352i	0.231444	−	0.400872i	0.958233	+	0.285988i	$0.0923218\pi$
$480$		0			0
$481$	−15.4415	+	8.91517i	−0.704073	+	0.406497i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−0.269208	−	0.466281i	−0.0122241	−	0.0211728i
$486$		0			0
$487$	−5.08735	+	8.81155i	−0.230530	+	0.399290i	−0.957964	−	0.286888i	$-0.907379\pi$
$487$	−5.08735	+	8.81155i	−0.230530	+	0.399290i	0.727434	+	0.686177i	$0.240713\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	24.6642			1.11308			0.556540	−	0.830821i	$-0.312129\pi$
$491$	24.6642			1.11308			0.556540	+	0.830821i	$0.312129\pi$
$492$		0			0
$493$	30.7894	−	53.3288i	1.38669	−	2.40181i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−4.65820	+	12.1508i	−0.208949	+	0.545039i
$498$		0			0
$499$	12.8103	−	7.39603i	0.573468	−	0.331092i	−0.185065	−	0.982726i	$-0.559250\pi$
$499$	12.8103	−	7.39603i	0.573468	−	0.331092i	0.758533	+	0.651634i	$0.225916\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	34.7978			1.55156			0.775778	−	0.631006i	$-0.217358\pi$
$503$	34.7978			1.55156			0.775778	+	0.631006i	$0.217358\pi$
$504$		0			0
$505$	−10.1066			−0.449738
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−30.0509	+	17.3499i	−1.33198	+	0.769021i	−0.985604	−	0.169073i	$-0.945923\pi$
$509$	−30.0509	+	17.3499i	−1.33198	+	0.769021i	−0.346381	+	0.938094i	$0.612589\pi$
$510$		0			0
$511$	5.15233	+	6.35693i	0.227926	+	0.281214i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	0.741291	−	1.28395i	0.0326652	−	0.0565778i
$516$		0			0
$517$	1.04524			0.0459697
$518$		0			0
$519$		0			0
$520$		0			0
$521$	19.9658	−	34.5818i	0.874718	−	1.51506i	0.0176549	−	0.999844i	$-0.494380\pi$
$521$	19.9658	−	34.5818i	0.874718	−	1.51506i	0.857063	−	0.515212i	$-0.172287\pi$
$522$		0			0
$523$	−3.77245	−	6.53407i	−0.164958	−	0.285715i	0.771683	−	0.636008i	$-0.219415\pi$
$523$	−3.77245	−	6.53407i	−0.164958	−	0.285715i	−0.936640	+	0.350293i	$0.886082\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−21.3150	+	12.3062i	−0.928496	+	0.536068i
$528$		0			0
$529$	−4.64917	+	8.05259i	−0.202138	+	0.350113i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−13.8649			−0.600557
$534$		0			0
$535$	−11.1831	−	6.45655i	−0.483486	−	0.279141i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−0.970822	+	0.316374i	−0.0418163	+	0.0136272i
$540$		0			0
$541$	14.8073	−	8.54900i	0.636616	−	0.367550i	−0.146694	−	0.989182i	$-0.546863\pi$
$541$	14.8073	−	8.54900i	0.636616	−	0.367550i	0.783310	+	0.621632i	$0.213530\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	6.15790			0.263775
$546$		0			0
$547$			26.4723i			1.13187i	0.824449	+	0.565936i	$0.191485\pi$
$547$			26.4723i			1.13187i	−0.824449	+	0.565936i	$0.808515\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−21.5746	−	37.3683i	−0.919109	−	1.59194i
$552$		0			0
$553$	4.49663	+	28.3108i	0.191216	+	1.20390i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−21.9010	+	37.9337i	−0.927976	+	1.60730i	−0.141273	+	0.989971i	$0.545119\pi$
$557$	−21.9010	+	37.9337i	−0.927976	+	1.60730i	−0.786703	+	0.617331i	$0.788214\pi$
$558$		0			0
$559$		−	53.5541i		−	2.26510i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	30.7646	+	17.7620i	1.29657	+	0.748578i	0.979811	−	0.199927i	$-0.0640705\pi$
$563$	30.7646	+	17.7620i	1.29657	+	0.748578i	0.316764	+	0.948505i	$0.397404\pi$
$564$		0			0
$565$	3.87254	+	6.70744i	0.162919	+	0.282184i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	22.4782	−	12.9778i	0.942334	−	0.544057i	0.0516428	−	0.998666i	$-0.483554\pi$
$569$	22.4782	−	12.9778i	0.942334	−	0.544057i	0.890691	+	0.454609i	$0.150221\pi$
$570$		0			0
$571$	13.6202	+	7.86364i	0.569989	+	0.329083i	0.757145	−	0.653247i	$-0.226594\pi$
$571$	13.6202	+	7.86364i	0.569989	+	0.329083i	−0.187156	+	0.982330i	$0.559927\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	15.4646i		−	0.644920i
$576$		0			0
$577$	−31.0772	−	17.9424i	−1.29376	−	0.746953i	−0.314441	−	0.949277i	$-0.601817\pi$
$577$	−31.0772	−	17.9424i	−1.29376	−	0.746953i	−0.979319	+	0.202324i	$0.935150\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	12.1732	−	31.7536i	0.505030	−	1.31736i
$582$		0			0
$583$	0.272552	+	0.472074i	0.0112880	+	0.0195513i
$584$		0			0
$585$		0			0
$586$		0			0
$587$			3.78446i			0.156201i	0.996945	+	0.0781007i	$0.0248856\pi$
$587$			3.78446i			0.156201i	−0.996945	+	0.0781007i	$0.975114\pi$
$588$		0			0
$589$			17.2463i			0.710622i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	11.6115	+	20.1117i	0.476826	+	0.825887i	0.999647	−	0.0265552i	$-0.00845376\pi$
$593$	11.6115	+	20.1117i	0.476826	+	0.825887i	−0.522821	+	0.852442i	$0.675120\pi$
$594$		0			0
$595$	−5.15982	+	13.4593i	−0.211532	+	0.551778i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−13.4585	−	7.77024i	−0.549898	−	0.317484i	0.199183	−	0.979962i	$-0.436171\pi$
$599$	−13.4585	−	7.77024i	−0.549898	−	0.317484i	−0.749081	+	0.662479i	$0.769504\pi$
$600$		0			0
$601$		−	23.5188i		−	0.959354i	−0.877445	−	0.479677i	$-0.840754\pi$
$601$		−	23.5188i		−	0.959354i	0.877445	−	0.479677i	$-0.159246\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	8.62100	+	4.97734i	0.350494	+	0.202358i
$606$		0			0
$607$	−29.9332	+	17.2819i	−1.21495	+	0.701452i	−0.963834	−	0.266505i	$-0.914131\pi$
$607$	−29.9332	+	17.2819i	−1.21495	+	0.701452i	−0.251117	+	0.967957i	$0.580798\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	21.9568	+	38.0302i	0.888275	+	1.53854i
$612$		0			0
$613$	7.20869	+	4.16194i	0.291156	+	0.168099i	0.638463	−	0.769652i	$-0.279570\pi$
$613$	7.20869	+	4.16194i	0.291156	+	0.168099i	−0.347307	+	0.937752i	$0.612904\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	9.28453i		−	0.373781i	−0.982381	−	0.186891i	$-0.940159\pi$
$617$		−	9.28453i		−	0.373781i	0.982381	−	0.186891i	$-0.0598410\pi$
$618$		0			0
$619$	−12.0804	+	20.9238i	−0.485551	+	0.840999i	−0.999862	−	0.0166047i	$-0.994714\pi$
$619$	−12.0804	+	20.9238i	−0.485551	+	0.840999i	0.514311	+	0.857604i	$0.328048\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	1.29245	+	8.13729i	0.0517810	+	0.326014i
$624$		0			0
$625$	−6.67184	−	11.5560i	−0.266874	−	0.462239i
$626$		0			0
$627$		0			0
$628$		0			0
$629$			17.4821i			0.697057i
$630$		0			0
$631$	10.8391			0.431498			0.215749	−	0.976449i	$-0.430781\pi$
$631$	10.8391			0.431498			0.215749	+	0.976449i	$0.430781\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	14.2110	−	8.20470i	0.563944	−	0.325593i
$636$		0			0
$637$	−31.9045	−	28.6767i	−1.26410	−	1.13621i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−32.0492	−	18.5036i	−1.26587	−	0.730849i	−0.291664	−	0.956521i	$-0.594209\pi$
$641$	−32.0492	−	18.5036i	−1.26587	−	0.730849i	−0.974203	+	0.225672i	$0.927542\pi$
$642$		0			0
$643$	24.9620			0.984405			0.492203	−	0.870481i	$-0.336192\pi$
$643$	24.9620			0.984405			0.492203	+	0.870481i	$0.336192\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	15.6875	−	27.1715i	0.616738	−	1.06822i	−0.373339	−	0.927695i	$-0.621787\pi$
$647$	15.6875	−	27.1715i	0.616738	−	1.06822i	0.990077	−	0.140527i	$-0.0448797\pi$
$648$		0			0
$649$	−0.926404	+	0.534859i	−0.0363645	+	0.0209951i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	3.95300	+	6.84679i	0.154693	+	0.267936i	0.932947	−	0.360014i	$-0.117228\pi$
$653$	3.95300	+	6.84679i	0.154693	+	0.267936i	−0.778254	+	0.627949i	$0.783895\pi$
$654$		0			0
$655$	−4.38931	+	7.60250i	−0.171504	+	0.297054i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−32.9121			−1.28207			−0.641036	−	0.767510i	$-0.721495\pi$
$659$	−32.9121			−1.28207			−0.641036	+	0.767510i	$0.721495\pi$
$660$		0			0
$661$	−2.37104	+	4.10677i	−0.0922230	+	0.159735i	−0.908446	−	0.418002i	$-0.862731\pi$
$661$	−2.37104	+	4.10677i	−0.0922230	+	0.159735i	0.816223	+	0.577737i	$0.196064\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	6.35982	+	7.84674i	0.246623	+	0.304284i
$666$		0			0
$667$	32.8530	−	18.9677i	1.27207	−	0.734432i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	0.995021			0.0384124
$672$		0			0
$673$	12.7891			0.492983			0.246492	−	0.969145i	$-0.420722\pi$
$673$	12.7891			0.492983			0.246492	+	0.969145i	$0.420722\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	19.9765	−	11.5334i	0.767759	−	0.443266i	−0.0643155	−	0.997930i	$-0.520486\pi$
$677$	19.9765	−	11.5334i	0.767759	−	0.443266i	0.832075	+	0.554664i	$0.187153\pi$
$678$		0			0
$679$	0.562377	−	1.46695i	0.0215820	−	0.0562964i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−3.40643	+	5.90011i	−0.130343	+	0.225761i	−0.923809	−	0.382854i	$-0.874941\pi$
$683$	−3.40643	+	5.90011i	−0.130343	+	0.225761i	0.793466	+	0.608615i	$0.208275\pi$
$684$		0			0
$685$	−9.54370			−0.364646
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−11.4507	+	19.8332i	−0.436236	+	0.755583i
$690$		0			0
$691$	−14.9637	−	25.9178i	−0.569245	−	0.985961i	−0.996641	−	0.0818962i	$-0.973902\pi$
$691$	−14.9637	−	25.9178i	−0.569245	−	0.985961i	0.427396	−	0.904064i	$-0.359431\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	12.4188	−	7.17002i	0.471074	−	0.271975i
$696$		0			0
$697$	−6.79707	+	11.7729i	−0.257457	+	0.445929i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−18.0414			−0.681415			−0.340707	−	0.940169i	$-0.610667\pi$
$701$	−18.0414			−0.681415			−0.340707	+	0.940169i	$0.610667\pi$
$702$		0			0
$703$	10.6088	+	6.12499i	0.400118	+	0.231008i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−18.5688	−	22.9102i	−0.698353	−	0.861627i
$708$		0			0
$709$	−29.1885	+	16.8520i	−1.09620	+	0.632889i	−0.935219	−	0.354069i	$-0.884798\pi$
$709$	−29.1885	+	16.8520i	−1.09620	+	0.632889i	−0.160977	+	0.986958i	$0.551464\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−15.1624			−0.567836
$714$		0			0
$715$		−	0.810539i		−	0.0303124i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	24.8458	+	43.0342i	0.926592	+	1.60490i	0.788981	+	0.614418i	$0.210609\pi$
$719$	24.8458	+	43.0342i	0.926592	+	1.60490i	0.137611	+	0.990486i	$0.456058\pi$
$720$		0			0
$721$	4.27250	−	0.678604i	0.159116	−	0.0252725i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	21.4082	−	37.0801i	0.795081	−	1.37712i
$726$		0			0
$727$			5.49208i			0.203690i	0.994800	+	0.101845i	$0.0324746\pi$
$727$			5.49208i			0.203690i	−0.994800	+	0.101845i	$0.967525\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−45.4734	−	26.2541i	−1.68189	−	0.971042i
$732$		0			0
$733$	−0.176068	−	0.304959i	−0.00650322	−	0.0112639i	0.862755	−	0.505621i	$-0.168737\pi$
$733$	−0.176068	−	0.304959i	−0.00650322	−	0.0112639i	−0.869259	+	0.494357i	$0.835403\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.389435	−	0.224840i	0.0143450	−	0.00828209i
$738$		0			0
$739$	−13.2521	−	7.65108i	−0.487485	−	0.281450i	0.236045	−	0.971742i	$-0.424149\pi$
$739$	−13.2521	−	7.65108i	−0.487485	−	0.281450i	−0.723531	+	0.690292i	$0.757482\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$			41.8196i			1.53421i	0.641520	+	0.767106i	$0.278304\pi$
$743$			41.8196i			1.53421i	−0.641520	+	0.767106i	$0.721696\pi$
$744$		0			0
$745$	9.10648	+	5.25763i	0.333636	+	0.192625i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−5.91055	−	37.2129i	−0.215967	−	1.35973i
$750$		0			0
$751$	−0.457654	−	0.792680i	−0.0167000	−	0.0289253i	0.857555	−	0.514393i	$-0.171983\pi$
$751$	−0.457654	−	0.792680i	−0.0167000	−	0.0289253i	−0.874255	+	0.485468i	$0.838649\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			14.1326i			0.514338i
$756$		0			0
$757$		−	20.2296i		−	0.735257i	−0.929973	−	0.367628i	$-0.880170\pi$
$757$		−	20.2296i		−	0.735257i	0.929973	−	0.367628i	$-0.119830\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−5.53329	−	9.58394i	−0.200582	−	0.347417i	0.748134	−	0.663547i	$-0.230950\pi$
$761$	−5.53329	−	9.58394i	−0.200582	−	0.347417i	−0.948716	+	0.316130i	$0.897616\pi$
$762$		0			0
$763$	11.3139	+	13.9590i	0.409590	+	0.505351i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−38.9208	−	22.4709i	−1.40535	−	0.811379i
$768$		0			0
$769$		−	20.8715i		−	0.752646i	−0.926489	−	0.376323i	$-0.877188\pi$
$769$		−	20.8715i		−	0.752646i	0.926489	−	0.376323i	$-0.122812\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	25.3570	+	14.6399i	0.912030	+	0.526561i	0.881084	−	0.472961i	$-0.156815\pi$
$773$	25.3570	+	14.6399i	0.912030	+	0.526561i	0.0309460	+	0.999521i	$0.490148\pi$
$774$		0			0
$775$	−14.8206	+	8.55665i	−0.532370	+	0.307364i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	4.76281	+	8.24943i	0.170645	+	0.295566i
$780$		0			0
$781$	−0.621329	−	0.358725i	−0.0222329	−	0.0128362i
$782$		0			0
$783$		0			0
$784$		0			0
$785$			12.0909i			0.431541i
$786$		0			0
$787$	10.4134	−	18.0366i	0.371199	−	0.642935i	−0.618551	−	0.785744i	$-0.712280\pi$
$787$	10.4134	−	18.0366i	0.371199	−	0.642935i	0.989750	+	0.142809i	$0.0456135\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−8.08977	+	21.1020i	−0.287639	+	0.750302i
$792$		0			0
$793$	20.9018	+	36.2030i	0.742245	+	1.28561i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			28.8543i			1.02207i	0.859559	+	0.511036i	$0.170738\pi$
$797$			28.8543i			1.02207i	−0.859559	+	0.511036i	$0.829262\pi$
$798$		0			0
$799$	43.0558			1.52321
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−0.390695	+	0.225568i	−0.0137873	+	0.00796013i
$804$		0			0
$805$	−6.89859	+	5.59134i	−0.243143	+	0.197069i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	32.6025	+	18.8231i	1.14624	+	0.661784i	0.947969	−	0.318362i	$-0.103133\pi$
$809$	32.6025	+	18.8231i	1.14624	+	0.661784i	0.198275	+	0.980146i	$0.436466\pi$
$810$		0			0
$811$	−11.3863			−0.399827			−0.199913	−	0.979814i	$-0.564066\pi$
$811$	−11.3863			−0.399827			−0.199913	+	0.979814i	$0.564066\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−7.74189	+	13.4093i	−0.271186	+	0.469709i
$816$		0			0
$817$	−31.8639	+	18.3966i	−1.11478	+	0.643617i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−6.92169	−	11.9887i	−0.241569	−	0.418409i	0.719593	−	0.694396i	$-0.244329\pi$
$821$	−6.92169	−	11.9887i	−0.241569	−	0.418409i	−0.961161	+	0.275987i	$0.910995\pi$
$822$		0			0
$823$	6.60648	−	11.4428i	0.230287	−	0.398869i	−0.727605	−	0.685996i	$-0.759367\pi$
$823$	6.60648	−	11.4428i	0.230287	−	0.398869i	0.957893	+	0.287127i	$0.0927000\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	12.2445			0.425784			0.212892	−	0.977076i	$-0.431712\pi$
$827$	12.2445			0.425784			0.212892	+	0.977076i	$0.431712\pi$
$828$		0			0
$829$	−21.1084	+	36.5609i	−0.733126	+	1.26981i	0.222415	+	0.974952i	$0.428606\pi$
$829$	−21.1084	+	36.5609i	−0.733126	+	1.26981i	−0.955541	+	0.294859i	$0.904727\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−39.9904	+	13.0322i	−1.38558	+	0.451537i
$834$		0			0
$835$	1.29191	−	0.745885i	0.0447084	−	0.0258124i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	4.30094			0.148485			0.0742424	−	0.997240i	$-0.476346\pi$
$839$	4.30094			0.148485			0.0742424	+	0.997240i	$0.476346\pi$
$840$		0			0
$841$	76.0304			2.62174
$842$		0			0
$843$		0			0
$844$		0			0
$845$	19.2826	−	11.1328i	0.663340	−	0.382980i
$846$		0			0
$847$	4.55643	+	28.6874i	0.156561	+	0.985710i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−5.38488	+	9.32689i	−0.184591	+	0.319722i
$852$		0			0
$853$	28.0209			0.959416			0.479708	−	0.877428i	$-0.340743\pi$
$853$	28.0209			0.959416			0.479708	+	0.877428i	$0.340743\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	6.76275	−	11.7134i	0.231011	−	0.400123i	−0.727095	−	0.686537i	$-0.759130\pi$
$857$	6.76275	−	11.7134i	0.231011	−	0.400123i	0.958106	+	0.286414i	$0.0924632\pi$
$858$		0			0
$859$	−9.51823	−	16.4861i	−0.324758	−	0.562497i	0.656705	−	0.754147i	$-0.271950\pi$
$859$	−9.51823	−	16.4861i	−0.324758	−	0.562497i	−0.981463	+	0.191650i	$0.938616\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	14.7548	−	8.51871i	0.502260	−	0.289980i	−0.227386	−	0.973805i	$-0.573018\pi$
$863$	14.7548	−	8.51871i	0.502260	−	0.289980i	0.729646	+	0.683825i	$0.239685\pi$
$864$		0			0
$865$	4.08774	−	7.08017i	0.138987	−	0.240733i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−1.58042			−0.0536120
$870$		0			0
$871$	16.3612	+	9.44617i	0.554379	+	0.320071i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−7.88137	+	20.5584i	−0.266439	+	0.695001i
$876$		0			0
$877$	−39.7587	+	22.9547i	−1.34255	+	0.775124i	−0.987182	−	0.159600i	$-0.948980\pi$
$877$	−39.7587	+	22.9547i	−1.34255	+	0.775124i	−0.355373	+	0.934725i	$0.615646\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−12.9601			−0.436638			−0.218319	−	0.975877i	$-0.570057\pi$
$881$	−12.9601			−0.436638			−0.218319	+	0.975877i	$0.570057\pi$
$882$		0			0
$883$			53.9117i			1.81427i	0.420835	+	0.907137i	$0.361737\pi$
$883$			53.9117i			1.81427i	−0.420835	+	0.907137i	$0.638263\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−8.11124	−	14.0491i	−0.272349	−	0.471722i	0.697114	−	0.716960i	$-0.254467\pi$
$887$	−8.11124	−	14.0491i	−0.272349	−	0.471722i	−0.969463	+	0.245238i	$0.921134\pi$
$888$		0			0
$889$	44.7085	+	17.1397i	1.49948	+	0.574846i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	15.0849	−	26.1279i	0.504798	−	0.874336i
$894$		0			0
$895$			13.2509i			0.442928i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−36.3554	−	20.9898i	−1.21252	−	0.700049i
$900$		0			0
$901$	11.2270	+	19.4458i	0.374027	+	0.647834i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−0.155837	+	0.0899725i	−0.00518019	+	0.00299079i
$906$		0			0
$907$	6.60352	+	3.81255i	0.219266	+	0.126594i	0.605611	−	0.795761i	$-0.292929\pi$
$907$	6.60352	+	3.81255i	0.219266	+	0.126594i	−0.386344	+	0.922355i	$0.626262\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			33.1109i			1.09701i	0.836146	+	0.548507i	$0.184804\pi$
$911$			33.1109i			1.09701i	−0.836146	+	0.548507i	$0.815196\pi$
$912$		0			0
$913$	1.62371	+	0.937450i	0.0537370	+	0.0310251i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−25.2982	+	4.01813i	−0.835420	+	0.132690i
$918$		0			0
$919$	16.2880	+	28.2116i	0.537291	+	0.930616i	0.999049	+	0.0436094i	$0.0138857\pi$
$919$	16.2880	+	28.2116i	0.537291	+	0.930616i	−0.461758	+	0.887006i	$0.652781\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		−	30.1421i		−	0.992138i
$924$		0			0
$925$			12.1555i			0.399670i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−7.81822	−	13.5416i	−0.256507	−	0.444284i	0.708796	−	0.705413i	$-0.249238\pi$
$929$	−7.81822	−	13.5416i	−0.256507	−	0.444284i	−0.965304	+	0.261129i	$0.915905\pi$
$930$		0			0
$931$	−6.10253	+	28.8335i	−0.200002	+	0.944981i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−0.688237	−	0.397354i	−0.0225078	−	0.0129949i
$936$		0			0
$937$			49.5708i			1.61941i	0.586839	+	0.809704i	$0.300372\pi$
$937$			49.5708i			1.61941i	−0.586839	+	0.809704i	$0.699628\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−10.5801	−	6.10840i	−0.344900	−	0.199128i	0.317537	−	0.948246i	$-0.397144\pi$
$941$	−10.5801	−	6.10840i	−0.344900	−	0.199128i	−0.662437	+	0.749118i	$0.730478\pi$
$942$		0			0
$943$	−7.25262	+	4.18730i	−0.236178	+	0.136357i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−11.4761	−	19.8772i	−0.372923	−	0.645921i	0.617091	−	0.786892i	$-0.288311\pi$
$947$	−11.4761	−	19.8772i	−0.372923	−	0.645921i	−0.990014	+	0.140971i	$0.954978\pi$
$948$		0			0
$949$	−16.4142	−	9.47675i	−0.532828	−	0.307628i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	10.7450i		−	0.348063i	−0.984740	−	0.174032i	$-0.944321\pi$
$953$		−	10.7450i		−	0.348063i	0.984740	−	0.174032i	$-0.0556795\pi$
$954$		0			0
$955$	0.0887952	−	0.153798i	0.00287334	−	0.00497678i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−17.5346	−	21.6341i	−0.566221	−	0.698603i
$960$		0			0
$961$	−7.11058	−	12.3159i	−0.229374	−	0.397287i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		−	9.13278i		−	0.293995i
$966$		0			0
$967$	7.48832			0.240808			0.120404	−	0.992725i	$-0.461581\pi$
$967$	7.48832			0.240808			0.120404	+	0.992725i	$0.461581\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−45.0252	+	25.9953i	−1.44493	+	0.834229i	−0.998173	−	0.0604275i	$-0.980754\pi$
$971$	−45.0252	+	25.9953i	−1.44493	+	0.834229i	−0.446755	+	0.894657i	$0.647420\pi$
$972$		0			0
$973$	39.0705	+	14.9782i	1.25254	+	0.480180i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−17.3850	−	10.0372i	−0.556196	−	0.321120i	0.195421	−	0.980719i	$-0.437393\pi$
$977$	−17.3850	−	10.0372i	−0.556196	−	0.321120i	−0.751617	+	0.659600i	$0.770726\pi$
$978$		0			0
$979$	−0.454255			−0.0145180
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−30.7294	+	53.2249i	−0.980115	+	1.69761i	−0.318214	+	0.948019i	$0.603083\pi$
$983$	−30.7294	+	53.2249i	−0.980115	+	1.69761i	−0.661902	+	0.749591i	$0.730250\pi$
$984$		0			0
$985$	0.770664	−	0.444943i	0.0245554	−	0.0141771i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−16.1737	−	28.0137i	−0.514294	−	0.890783i
$990$		0			0
$991$	−9.87483	+	17.1037i	−0.313684	+	0.543317i	−0.979157	−	0.203105i	$-0.934897\pi$
$991$	−9.87483	+	17.1037i	−0.313684	+	0.543317i	0.665473	+	0.746422i	$0.268230\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	1.99665			0.0632980
$996$		0			0
$997$	−1.94579	+	3.37021i	−0.0616239	+	0.106736i	−0.895191	−	0.445682i	$-0.852961\pi$
$997$	−1.94579	+	3.37021i	−0.0616239	+	0.106736i	0.833568	+	0.552418i	$0.186295\pi$
$998$		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.17.18		56
3.2	odd	2	inner	2016.2.cp.b.17.12		56
4.3	odd	2		504.2.ch.b.269.9	yes	56
7.5	odd	6	inner	2016.2.cp.b.593.17		56
8.3	odd	2		504.2.ch.b.269.1	✓	56
8.5	even	2	inner	2016.2.cp.b.17.11		56
12.11	even	2		504.2.ch.b.269.20	yes	56
21.5	even	6	inner	2016.2.cp.b.593.11		56
24.5	odd	2	inner	2016.2.cp.b.17.17		56
24.11	even	2		504.2.ch.b.269.28	yes	56
28.19	even	6		504.2.ch.b.341.28	yes	56
56.5	odd	6	inner	2016.2.cp.b.593.12		56
56.19	even	6		504.2.ch.b.341.20	yes	56
84.47	odd	6		504.2.ch.b.341.1	yes	56
168.5	even	6	inner	2016.2.cp.b.593.18		56
168.131	odd	6		504.2.ch.b.341.9	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.ch.b.269.1	✓	56	8.3	odd	2
504.2.ch.b.269.9	yes	56	4.3	odd	2
504.2.ch.b.269.20	yes	56	12.11	even	2
504.2.ch.b.269.28	yes	56	24.11	even	2
504.2.ch.b.341.1	yes	56	84.47	odd	6
504.2.ch.b.341.9	yes	56	168.131	odd	6
504.2.ch.b.341.20	yes	56	56.19	even	6
504.2.ch.b.341.28	yes	56	28.19	even	6
2016.2.cp.b.17.11		56	8.5	even	2	inner
2016.2.cp.b.17.12		56	3.2	odd	2	inner
2016.2.cp.b.17.17		56	24.5	odd	2	inner
2016.2.cp.b.17.18		56	1.1	even	1	trivial
2016.2.cp.b.593.11		56	21.5	even	6	inner
2016.2.cp.b.593.12		56	56.5	odd	6	inner
2016.2.cp.b.593.17		56	7.5	odd	6	inner
2016.2.cp.b.593.18		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)

\(f(q)\)	\(=\)	\(q+(0.785247 - 0.453362i) q^{5} +(2.47043 + 0.947077i) q^{7} +O(q^{10})\)	\(q+(0.785247 - 0.453362i) q^{5} +(2.47043 + 0.947077i) q^{7} +(-0.0729337 + 0.126325i) q^{11} -6.12830 q^{13} +(-3.00430 + 5.20361i) q^{17} +(2.10516 + 3.64625i) q^{19} +(-3.20566 + 1.85079i) q^{23} +(-2.08893 + 3.61812i) q^{25} -10.2484 q^{29} +(3.54741 + 2.04810i) q^{31} +(2.36927 - 0.376312i) q^{35} +(2.51971 - 1.45475i) q^{37} +2.26244 q^{41} +8.73882i q^{43} +(-3.58285 - 6.20567i) q^{47} +(5.20609 + 4.67938i) q^{49} +(1.86849 - 3.23632i) q^{53} +0.132262i q^{55} +(6.35100 + 3.66675i) q^{59} +(-3.41070 - 5.90751i) q^{61} +(-4.81223 + 2.77834i) q^{65} +(-2.66978 - 1.54140i) q^{67} +4.91850i q^{71} +(2.67843 + 1.54639i) q^{73} +(-0.299817 + 0.243004i) q^{77} +(5.41731 + 9.38305i) q^{79} -12.8534i q^{83} +5.44815i q^{85} +(1.55708 + 2.69694i) q^{89} +(-15.1396 - 5.80397i) q^{91} +(3.30614 + 1.90880i) q^{95} -0.593803i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 20 q^{7}+O(q^{10}) \) 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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