LMFDB - Embedded newform 2016.2.cp.b.593.12

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			593.12
Character	$\chi$	$=$	2016.593
Dual form			2016.2.cp.b.17.12

$q$-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 $\left(\mathbb{Z}/2016\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$1765$	$1793$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$

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	$-0.398321\pi$
$5$	−0.785247	−	0.453362i	−0.351173	−	0.202750i	−0.665202	+	0.746664i	$0.731654\pi$
$6$		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	$-0.159666\pi$
$11$	0.0729337	+	0.126325i	0.0219903	+	0.0380884i	−0.854821	+	0.518923i	$0.826333\pi$
$12$		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	0.957454	+	0.288587i	$0.0931856\pi$
$17$	3.00430	+	5.20361i	0.728651	+	1.26206i	−0.228803	+	0.973473i	$0.573481\pi$
$18$		0			0
$19$	2.10516	−	3.64625i	0.482957	−	0.836506i	−0.516851	−	0.856075i	$-0.672896\pi$
$19$	2.10516	−	3.64625i	0.482957	−	0.836506i	0.999809	+	0.0195688i	$0.00622934\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.20566	+	1.85079i	0.668426	+	0.385916i	0.795480	−	0.605980i	$-0.207219\pi$
$23$	3.20566	+	1.85079i	0.668426	+	0.385916i	−0.127054	+	0.991896i	$0.540552\pi$
$24$		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	$-0.0994973\pi$
$29$	10.2484			1.90309			0.951543	+	0.307515i	$0.0994973\pi$
$30$		0			0
$31$	3.54741	−	2.04810i	0.637134	−	0.367849i	−0.146376	−	0.989229i	$-0.546761\pi$
$31$	3.54741	−	2.04810i	0.637134	−	0.367849i	0.783510	+	0.621380i	$0.213428\pi$
$32$		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	0.692609	−	0.721313i	$-0.256461\pi$
$37$	2.51971	+	1.45475i	0.414238	+	0.239160i	−0.278371	+	0.960474i	$0.589795\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−2.26244			−0.353334			−0.176667	−	0.984271i	$-0.556532\pi$
$41$	−2.26244			−0.353334			−0.176667	+	0.984271i	$0.556532\pi$
$42$		0			0
$43$		−	8.73882i		−	1.33266i	−0.745658	−	0.666329i	$-0.767865\pi$
$43$		−	8.73882i		−	1.33266i	0.745658	−	0.666329i	$-0.232135\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.58285	−	6.20567i	0.522612	−	0.905190i	−0.477042	−	0.878881i	$-0.658291\pi$
$47$	3.58285	−	6.20567i	0.522612	−	0.905190i	0.999654	−	0.0263098i	$-0.00837564\pi$
$48$		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	$-0.249288\pi$
$53$	−1.86849	−	3.23632i	−0.256657	−	0.444543i	−0.965344	+	0.260980i	$0.915954\pi$
$54$		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	$-0.825077\pi$
$59$	−6.35100	+	3.66675i	−0.826829	+	0.477370i	0.0259364	+	0.999664i	$0.491743\pi$
$60$		0			0
$61$	−3.41070	+	5.90751i	−0.436696	+	0.756379i	−0.997432	−	0.0716150i	$-0.977185\pi$
$61$	−3.41070	+	5.90751i	−0.436696	+	0.756379i	0.560737	+	0.827994i	$0.310518\pi$
$62$		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	−0.654138	−	0.756376i	$-0.726968\pi$
$67$	−2.66978	+	1.54140i	−0.326166	+	0.188312i	0.327972	+	0.944688i	$0.393635\pi$
$68$		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	−0.334999	−	0.942218i	$-0.608736\pi$
$73$	2.67843	−	1.54639i	0.313486	−	0.180991i	0.648485	+	0.761227i	$0.275403\pi$
$74$		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	−0.381829	−	0.924233i	$-0.624706\pi$
$79$	5.41731	−	9.38305i	0.609495	−	1.05568i	0.991324	−	0.131443i	$-0.0419610\pi$
$80$		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	$-0.886112\pi$
$89$	−1.55708	+	2.69694i	−0.165050	+	0.285875i	0.771623	+	0.636080i	$0.219445\pi$
$90$		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	$0.00959715\pi$
$97$			0.593803i			0.0602915i	−0.999546	+	0.0301458i	$0.990403\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	9.65297	−	5.57314i	0.960506	−	0.554549i	0.0641776	−	0.997938i	$-0.479558\pi$
$101$	9.65297	−	5.57314i	0.960506	−	0.554549i	0.896329	+	0.443390i	$0.146224\pi$
$102$		0			0
$103$	1.41603	+	0.817548i	0.139526	+	0.0805554i	0.568138	−	0.822933i	$-0.307664\pi$
$103$	1.41603	+	0.817548i	0.139526	+	0.0805554i	−0.428612	+	0.903489i	$0.640997\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	7.12074	−	12.3335i	0.688387	−	1.19232i	−0.283972	−	0.958833i	$-0.591652\pi$
$107$	7.12074	−	12.3335i	0.688387	−	1.19232i	0.972359	−	0.233489i	$-0.0750144\pi$
$108$		0			0
$109$	5.88150	−	3.39568i	0.563345	−	0.325247i	−0.191142	−	0.981562i	$-0.561219\pi$
$109$	5.88150	−	3.39568i	0.563345	−	0.325247i	0.754487	+	0.656315i	$0.227886\pi$
$110$		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	$-0.194329\pi$
$131$	8.38458	+	4.84084i	0.732564	+	0.422946i	−0.0867954	+	0.996226i	$0.527663\pi$
$132$		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	$-0.518224\pi$
$137$	9.11532	−	5.26273i	0.778774	−	0.449625i	0.835996	+	0.548736i	$0.184891\pi$
$138$		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	$-0.990896\pi$
$149$	−5.79849	+	10.0433i	−0.475031	+	0.822777i	0.524560	+	0.851373i	$0.324230\pi$
$150$		0			0
$151$	−7.79321	−	13.4982i	−0.634202	−	1.09847i	−0.986684	−	0.162652i	$-0.947995\pi$
$151$	−7.79321	−	13.4982i	−0.634202	−	1.09847i	0.352481	−	0.935819i	$-0.385338\pi$
$152$		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	−0.999297	−	0.0374841i	$-0.988066\pi$
$157$	−6.66733	−	11.5482i	−0.532111	−	0.921643i	0.467186	−	0.884159i	$-0.345268\pi$
$158$		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	−0.207439	−	0.978248i	$-0.566513\pi$
$163$	−14.7888	−	8.53830i	−1.15835	−	0.668771i	−0.950907	+	0.309477i	$0.899846\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−1.64523			−0.127312			−0.0636558	−	0.997972i	$-0.520276\pi$
$167$	−1.64523			−0.127312			−0.0636558	+	0.997972i	$0.520276\pi$
$168$		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	$-0.444694\pi$
$173$	−7.80851	−	4.50825i	−0.593670	−	0.342756i	−0.766547	+	0.642188i	$0.778027\pi$
$174$		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	0.998534	+	0.0541368i	$0.0172407\pi$
$179$	7.30700	+	12.6561i	0.546151	+	0.945961i	−0.452383	+	0.891824i	$0.649426\pi$
$180$		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	$-0.335589\pi$
$191$	−0.169619	−	0.0979296i	−0.0122732	−	0.00708594i	−0.506124	+	0.862461i	$0.668922\pi$
$192$		0			0
$193$	5.03614	+	8.72285i	0.362509	+	0.627884i	0.988373	−	0.152048i	$-0.0485868\pi$
$193$	5.03614	+	8.72285i	0.362509	+	0.627884i	−0.625864	+	0.779932i	$0.715254\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−0.981430			−0.0699240			−0.0349620	−	0.999389i	$-0.511131\pi$
$197$	−0.981430			−0.0699240			−0.0349620	+	0.999389i	$0.511131\pi$
$198$		0			0
$199$	1.90703	−	1.10102i	0.135185	−	0.0780494i	−0.430882	−	0.902408i	$-0.641797\pi$
$199$	1.90703	−	1.10102i	0.135185	−	0.0780494i	0.566067	+	0.824359i	$0.308464\pi$
$200$		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	$0.209496\pi$
$211$			17.7696i			1.22331i	−0.791125	+	0.611654i	$0.790504\pi$
$212$		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	$0.244017\pi$
$223$			20.7181i			1.38738i	−0.720271	+	0.693692i	$0.755983\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−17.3954	+	10.0432i	−1.15457	+	0.666593i	−0.949997	−	0.312258i	$-0.898915\pi$
$227$	−17.3954	+	10.0432i	−1.15457	+	0.666593i	−0.204575	+	0.978851i	$0.565581\pi$
$228$		0			0
$229$	−9.68640	+	16.7773i	−0.640095	+	1.10868i	0.345316	+	0.938487i	$0.387772\pi$
$229$	−9.68640	+	16.7773i	−0.640095	+	1.10868i	−0.985411	+	0.170191i	$0.945562\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−22.4100	−	12.9384i	−1.46813	−	0.847625i	−0.468768	−	0.883322i	$-0.655302\pi$
$233$	−22.4100	−	12.9384i	−1.46813	−	0.847625i	−0.999363	+	0.0356961i	$0.988635\pi$
$234$		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	−0.526096	+	0.850425i	$0.676345\pi$
$241$	−23.6842	+	13.6741i	−1.52563	+	0.880825i	−0.999538	+	0.0303997i	$0.990322\pi$
$242$		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	$-0.710680\pi$
$257$	6.02554	−	10.4365i	0.375863	−	0.651014i	0.990456	+	0.137831i	$0.0440130\pi$
$258$		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	$-0.639800\pi$
$263$	2.36800	−	1.36716i	0.146017	−	0.0843029i	0.571229	+	0.820791i	$0.306467\pi$
$264$		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	$-0.616498\pi$
$269$	4.45879	−	2.57428i	0.271857	−	0.156957i	0.629731	+	0.776813i	$0.283165\pi$
$270$		0			0
$271$	−21.0489	−	12.1526i	−1.27863	−	0.738216i	−0.302031	−	0.953298i	$-0.597665\pi$
$271$	−21.0489	−	12.1526i	−1.27863	−	0.738216i	−0.976596	+	0.215082i	$0.930998\pi$
$272$		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	−0.521056	−	0.853523i	$-0.674462\pi$
$277$	−0.705869	+	0.407533i	−0.0424115	+	0.0244863i	0.478644	+	0.878009i	$0.341128\pi$
$278$		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	0.944265	−	0.329187i	$-0.106775\pi$
$283$	3.14663	+	5.45012i	0.187048	+	0.323976i	−0.757217	+	0.653164i	$0.773441\pi$
$284$		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	−0.958703	−	0.284410i	$-0.908202\pi$
$311$	−12.7971	−	22.1653i	−0.725658	−	1.25688i	0.233045	−	0.972466i	$-0.425131\pi$
$312$		0			0
$313$	−14.9541	−	8.63375i	−0.845255	−	0.488008i	0.0137920	−	0.999905i	$-0.495610\pi$
$313$	−14.9541	−	8.63375i	−0.845255	−	0.488008i	−0.859047	+	0.511897i	$0.828943\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−2.17346	+	3.76454i	−0.122074	+	0.211438i	−0.920585	−	0.390542i	$-0.872288\pi$
$317$	−2.17346	+	3.76454i	−0.122074	+	0.211438i	0.798512	+	0.601979i	$0.205621\pi$
$318$		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	0.852166	−	0.523271i	$-0.175288\pi$
$331$	15.0111	+	8.66665i	0.825084	+	0.476362i	−0.0270828	+	0.999633i	$0.508622\pi$
$332$		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	$-0.106520\pi$
$347$	3.49897	+	6.06039i	0.187834	+	0.325339i	−0.756694	+	0.653770i	$0.773187\pi$
$348$		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	$-0.0776738\pi$
$353$	5.18465	+	8.98008i	0.275951	+	0.477962i	−0.694423	+	0.719567i	$0.744341\pi$
$354$		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	$-0.513156\pi$
$359$	−17.5691	−	10.1436i	−0.927264	−	0.535356i	−0.885945	+	0.463790i	$0.846489\pi$
$360$		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	−0.943340	−	0.331829i	$-0.892334\pi$
$367$	−21.6024	+	12.4722i	−1.12764	+	0.651042i	−0.184298	+	0.982870i	$0.559001\pi$
$368$		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	0.606429	−	0.795138i	$-0.292602\pi$
$373$	4.26886	+	2.46463i	0.221033	+	0.127614i	−0.385395	+	0.922752i	$0.625935\pi$
$374$		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	$-0.776995\pi$
$379$		−	25.1007i		−	1.28934i	0.764462	−	0.644669i	$-0.223005\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	14.0619	−	24.3560i	0.718531	−	1.24453i	−0.243051	−	0.970014i	$-0.578148\pi$
$383$	14.0619	−	24.3560i	0.718531	−	1.24453i	0.961582	−	0.274519i	$-0.0885185\pi$
$384$		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	$-0.104512\pi$
$389$	3.82681	+	6.62822i	0.194027	+	0.336064i	−0.752554	+	0.658530i	$0.771178\pi$
$390$		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	−0.978913	−	0.204276i	$-0.934516\pi$
$397$	−6.22748	+	10.7863i	−0.312548	+	0.541350i	0.666365	+	0.745626i	$0.267849\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	18.1682	+	10.4894i	0.907279	+	0.523818i	0.879555	−	0.475798i	$-0.157841\pi$
$401$	18.1682	+	10.4894i	0.907279	+	0.523818i	0.0277241	+	0.999616i	$0.491174\pi$
$402$		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	−0.488662	−	0.872473i	$-0.662515\pi$
$409$	0.456865	−	0.263771i	0.0225905	−	0.0130426i	0.511253	+	0.859430i	$0.329182\pi$
$410$		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	$-0.853422\pi$
$421$		−	18.2360i		−	0.888771i	0.895836	−	0.444385i	$-0.146578\pi$
$422$		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	$-0.909432\pi$
$431$	−24.8419	+	14.3425i	−1.19659	+	0.690854i	−0.236799	+	0.971559i	$0.576098\pi$
$432$		0			0
$433$			37.7023i			1.81186i	0.423429	+	0.905929i	$0.360826\pi$
$433$			37.7023i			1.81186i	−0.423429	+	0.905929i	$0.639174\pi$
$434$		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	0.672114	−	0.740448i	$-0.265387\pi$
$439$	7.68790	+	4.43861i	0.366924	+	0.211843i	−0.305190	+	0.952291i	$0.598720\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−0.209480	+	0.362830i	−0.00995270	+	0.0172386i	−0.870959	−	0.491356i	$-0.836501\pi$
$443$	−0.209480	+	0.362830i	−0.00995270	+	0.0172386i	0.861006	+	0.508595i	$0.169835\pi$
$444$		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	−0.970909	−	0.239449i	$-0.923033\pi$
$457$	−5.94479	+	10.2967i	−0.278085	+	0.481658i	0.692823	+	0.721107i	$0.256367\pi$
$458$		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	$-0.548508\pi$
$467$	−23.4188	−	13.5208i	−1.08369	−	0.625670i	−0.931890	+	0.362741i	$0.881841\pi$
$468$		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	$-0.241012\pi$
$479$	−5.06539	−	8.77352i	−0.231444	−	0.400872i	−0.958233	+	0.285988i	$0.907678\pi$
$480$		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	0.727434	−	0.686177i	$-0.240713\pi$
$487$	−5.08735	−	8.81155i	−0.230530	−	0.399290i	−0.957964	+	0.286888i	$0.907379\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−24.6642			−1.11308			−0.556540	−	0.830821i	$-0.687871\pi$
$491$	−24.6642			−1.11308			−0.556540	+	0.830821i	$0.687871\pi$
$492$		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	0.758533	−	0.651634i	$-0.225916\pi$
$499$	12.8103	+	7.39603i	0.573468	+	0.331092i	−0.185065	+	0.982726i	$0.559250\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−34.7978			−1.55156			−0.775778	−	0.631006i	$-0.782642\pi$
$503$	−34.7978			−1.55156			−0.775778	+	0.631006i	$0.782642\pi$
$504$		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	$-0.0540772\pi$
$509$	30.0509	+	17.3499i	1.33198	+	0.769021i	0.346381	+	0.938094i	$0.387411\pi$
$510$		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	−0.857063	−	0.515212i	$-0.827713\pi$
$521$	−19.9658	−	34.5818i	−0.874718	−	1.51506i	−0.0176549	−	0.999844i	$-0.505620\pi$
$522$		0			0
$523$	−3.77245	+	6.53407i	−0.164958	+	0.285715i	−0.936640	−	0.350293i	$-0.886082\pi$
$523$	−3.77245	+	6.53407i	−0.164958	+	0.285715i	0.771683	+	0.636008i	$0.219415\pi$
$524$		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	0.783310	−	0.621632i	$-0.213530\pi$
$541$	14.8073	+	8.54900i	0.636616	+	0.367550i	−0.146694	+	0.989182i	$0.546863\pi$
$542$		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	$-0.808515\pi$
$547$		−	26.4723i		−	1.13187i	0.824449	−	0.565936i	$-0.191485\pi$
$548$		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	0.786703	+	0.617331i	$0.211786\pi$
$557$	21.9010	+	37.9337i	0.927976	+	1.60730i	0.141273	+	0.989971i	$0.454881\pi$
$558$		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	$-0.935930\pi$
$563$	−30.7646	+	17.7620i	−1.29657	+	0.748578i	−0.316764	+	0.948505i	$0.602596\pi$
$564$		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	$-0.516446\pi$
$569$	−22.4782	−	12.9778i	−0.942334	−	0.544057i	−0.890691	+	0.454609i	$0.849779\pi$
$570$		0			0
$571$	13.6202	−	7.86364i	0.569989	−	0.329083i	−0.187156	−	0.982330i	$-0.559927\pi$
$571$	13.6202	−	7.86364i	0.569989	−	0.329083i	0.757145	+	0.653247i	$0.226594\pi$
$572$		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	−0.979319	−	0.202324i	$-0.935150\pi$
$577$	−31.0772	+	17.9424i	−1.29376	+	0.746953i	−0.314441	+	0.949277i	$0.601817\pi$
$578$		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	$-0.991546\pi$
$593$	−11.6115	+	20.1117i	−0.476826	+	0.825887i	0.522821	+	0.852442i	$0.324880\pi$
$594$		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	$-0.563829\pi$
$599$	13.4585	−	7.77024i	0.549898	−	0.317484i	0.749081	+	0.662479i	$0.230496\pi$
$600$		0			0
$601$			23.5188i			0.959354i	0.877445	+	0.479677i	$0.159246\pi$
$601$			23.5188i			0.959354i	−0.877445	+	0.479677i	$0.840754\pi$
$602$		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	−0.251117	−	0.967957i	$-0.580798\pi$
$607$	−29.9332	−	17.2819i	−1.21495	−	0.701452i	−0.963834	+	0.266505i	$0.914131\pi$
$608$		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	−0.347307	−	0.937752i	$-0.612904\pi$
$613$	7.20869	−	4.16194i	0.291156	−	0.168099i	0.638463	+	0.769652i	$0.279570\pi$
$614$		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	0.514311	−	0.857604i	$-0.328048\pi$
$619$	−12.0804	−	20.9238i	−0.485551	−	0.840999i	−0.999862	+	0.0166047i	$0.994714\pi$
$620$		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	$-0.405791\pi$
$641$	32.0492	−	18.5036i	1.26587	−	0.730849i	0.974203	+	0.225672i	$0.0724576\pi$
$642$		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	−0.990077	−	0.140527i	$-0.955120\pi$
$647$	−15.6875	−	27.1715i	−0.616738	−	1.06822i	0.373339	−	0.927695i	$-0.378213\pi$
$648$		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	$-0.882772\pi$
$653$	−3.95300	+	6.84679i	−0.154693	+	0.267936i	0.778254	+	0.627949i	$0.216105\pi$
$654$		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	$-0.278505\pi$
$659$	32.9121			1.28207			0.641036	+	0.767510i	$0.278505\pi$
$660$		0			0
$661$	−2.37104	−	4.10677i	−0.0922230	−	0.159735i	0.816223	−	0.577737i	$-0.196064\pi$
$661$	−2.37104	−	4.10677i	−0.0922230	−	0.159735i	−0.908446	+	0.418002i	$0.862731\pi$
$662$		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	$-0.479514\pi$
$677$	−19.9765	−	11.5334i	−0.767759	−	0.443266i	−0.832075	+	0.554664i	$0.812847\pi$
$678$		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	$-0.125059\pi$
$683$	3.40643	+	5.90011i	0.130343	+	0.225761i	−0.793466	+	0.608615i	$0.791725\pi$
$684$		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	0.427396	+	0.904064i	$0.359431\pi$
$691$	−14.9637	+	25.9178i	−0.569245	+	0.985961i	−0.996641	+	0.0818962i	$0.973902\pi$
$692$		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	$-0.389333\pi$
$701$	18.0414			0.681415			0.340707	+	0.940169i	$0.389333\pi$
$702$		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	−0.160977	−	0.986958i	$-0.551464\pi$
$709$	−29.1885	−	16.8520i	−1.09620	−	0.632889i	−0.935219	+	0.354069i	$0.884798\pi$
$710$		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	−0.137611	+	0.990486i	$0.543942\pi$
$719$	−24.8458	+	43.0342i	−0.926592	+	1.60490i	−0.788981	+	0.614418i	$0.789391\pi$
$720$		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	$-0.967525\pi$
$727$		−	5.49208i		−	0.203690i	0.994800	−	0.101845i	$-0.0324746\pi$
$728$		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	−0.869259	−	0.494357i	$-0.835403\pi$
$733$	−0.176068	+	0.304959i	−0.00650322	+	0.0112639i	0.862755	+	0.505621i	$0.168737\pi$
$734$		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	−0.723531	−	0.690292i	$-0.757482\pi$
$739$	−13.2521	+	7.65108i	−0.487485	+	0.281450i	0.236045	+	0.971742i	$0.424149\pi$
$740$		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	−0.874255	−	0.485468i	$-0.838649\pi$
$751$	−0.457654	+	0.792680i	−0.0167000	+	0.0289253i	0.857555	+	0.514393i	$0.171983\pi$
$752$		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	$0.119830\pi$
$757$			20.2296i			0.735257i	−0.929973	+	0.367628i	$0.880170\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	5.53329	−	9.58394i	0.200582	−	0.347417i	−0.748134	−	0.663547i	$-0.769050\pi$
$761$	5.53329	−	9.58394i	0.200582	−	0.347417i	0.948716	+	0.316130i	$0.102384\pi$
$762$		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	$0.122812\pi$
$769$			20.8715i			0.752646i	−0.926489	+	0.376323i	$0.877188\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−25.3570	+	14.6399i	−0.912030	+	0.526561i	−0.881084	−	0.472961i	$-0.843185\pi$
$773$	−25.3570	+	14.6399i	−0.912030	+	0.526561i	−0.0309460	+	0.999521i	$0.509852\pi$
$774$		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	0.989750	−	0.142809i	$-0.0456135\pi$
$787$	10.4134	+	18.0366i	0.371199	+	0.642935i	−0.618551	+	0.785744i	$0.712280\pi$
$788$		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	$-0.896867\pi$
$809$	−32.6025	+	18.8231i	−1.14624	+	0.661784i	−0.198275	+	0.980146i	$0.563534\pi$
$810$		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	$-0.755671\pi$
$821$	6.92169	−	11.9887i	0.241569	−	0.418409i	0.961161	+	0.275987i	$0.0890048\pi$
$822$		0			0
$823$	6.60648	+	11.4428i	0.230287	+	0.398869i	0.957893	−	0.287127i	$-0.0927000\pi$
$823$	6.60648	+	11.4428i	0.230287	+	0.398869i	−0.727605	+	0.685996i	$0.759367\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−12.2445			−0.425784			−0.212892	−	0.977076i	$-0.568288\pi$
$827$	−12.2445			−0.425784			−0.212892	+	0.977076i	$0.568288\pi$
$828$		0			0
$829$	−21.1084	−	36.5609i	−0.733126	−	1.26981i	−0.955541	−	0.294859i	$-0.904727\pi$
$829$	−21.1084	−	36.5609i	−0.733126	−	1.26981i	0.222415	−	0.974952i	$-0.428606\pi$
$830$		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	$-0.523654\pi$
$839$	−4.30094			−0.148485			−0.0742424	+	0.997240i	$0.523654\pi$
$840$		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	$-0.240870\pi$
$857$	−6.76275	−	11.7134i	−0.231011	−	0.400123i	−0.958106	+	0.286414i	$0.907537\pi$
$858$		0			0
$859$	−9.51823	+	16.4861i	−0.324758	+	0.562497i	−0.981463	−	0.191650i	$-0.938616\pi$
$859$	−9.51823	+	16.4861i	−0.324758	+	0.562497i	0.656705	+	0.754147i	$0.271950\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−14.7548	−	8.51871i	−0.502260	−	0.289980i	0.227386	−	0.973805i	$-0.426982\pi$
$863$	−14.7548	−	8.51871i	−0.502260	−	0.289980i	−0.729646	+	0.683825i	$0.760315\pi$
$864$		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	−0.355373	−	0.934725i	$-0.615646\pi$
$877$	−39.7587	−	22.9547i	−1.34255	−	0.775124i	−0.987182	+	0.159600i	$0.948980\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	12.9601			0.436638			0.218319	−	0.975877i	$-0.429943\pi$
$881$	12.9601			0.436638			0.218319	+	0.975877i	$0.429943\pi$
$882$		0			0
$883$		−	53.9117i		−	1.81427i	−0.420835	−	0.907137i	$-0.638263\pi$
$883$		−	53.9117i		−	1.81427i	0.420835	−	0.907137i	$-0.361737\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	8.11124	−	14.0491i	0.272349	−	0.471722i	−0.697114	−	0.716960i	$-0.745533\pi$
$887$	8.11124	−	14.0491i	0.272349	−	0.471722i	0.969463	+	0.245238i	$0.0788662\pi$
$888$		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	−0.386344	−	0.922355i	$-0.626262\pi$
$907$	6.60352	−	3.81255i	0.219266	−	0.126594i	0.605611	+	0.795761i	$0.292929\pi$
$908$		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	−0.461758	−	0.887006i	$-0.652781\pi$
$919$	16.2880	−	28.2116i	0.537291	−	0.930616i	0.999049	−	0.0436094i	$-0.0138857\pi$
$920$		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	$-0.750762\pi$
$929$	7.81822	−	13.5416i	0.256507	−	0.444284i	0.965304	+	0.261129i	$0.0840948\pi$
$930$		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	$-0.699628\pi$
$937$		−	49.5708i		−	1.61941i	0.586839	−	0.809704i	$-0.300372\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	10.5801	−	6.10840i	0.344900	−	0.199128i	−0.317537	−	0.948246i	$-0.602856\pi$
$941$	10.5801	−	6.10840i	0.344900	−	0.199128i	0.662437	+	0.749118i	$0.269522\pi$
$942$		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	$-0.711689\pi$
$947$	11.4761	−	19.8772i	0.372923	−	0.645921i	0.990014	+	0.140971i	$0.0450223\pi$
$948$		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	$-0.0192464\pi$
$971$	45.0252	+	25.9953i	1.44493	+	0.834229i	0.446755	+	0.894657i	$0.352580\pi$
$972$		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	$-0.562607\pi$
$977$	17.3850	−	10.0372i	0.556196	−	0.321120i	0.751617	+	0.659600i	$0.229274\pi$
$978$		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	0.661902	+	0.749591i	$0.269750\pi$
$983$	30.7294	+	53.2249i	0.980115	+	1.69761i	0.318214	+	0.948019i	$0.396917\pi$
$984$		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	0.665473	−	0.746422i	$-0.268230\pi$
$991$	−9.87483	−	17.1037i	−0.313684	−	0.543317i	−0.979157	+	0.203105i	$0.934897\pi$
$992$		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	0.833568	−	0.552418i	$-0.186295\pi$
$997$	−1.94579	−	3.37021i	−0.0616239	−	0.106736i	−0.895191	+	0.445682i	$0.852961\pi$
$998$		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.593.12		56
3.2	odd	2	inner	2016.2.cp.b.593.18		56
4.3	odd	2		504.2.ch.b.341.20	yes	56
7.3	odd	6	inner	2016.2.cp.b.17.11		56
8.3	odd	2		504.2.ch.b.341.28	yes	56
8.5	even	2	inner	2016.2.cp.b.593.17		56
12.11	even	2		504.2.ch.b.341.9	yes	56
21.17	even	6	inner	2016.2.cp.b.17.17		56
24.5	odd	2	inner	2016.2.cp.b.593.11		56
24.11	even	2		504.2.ch.b.341.1	yes	56
28.3	even	6		504.2.ch.b.269.1	✓	56
56.3	even	6		504.2.ch.b.269.9	yes	56
56.45	odd	6	inner	2016.2.cp.b.17.18		56
84.59	odd	6		504.2.ch.b.269.28	yes	56
168.59	odd	6		504.2.ch.b.269.20	yes	56
168.101	even	6	inner	2016.2.cp.b.17.12		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.ch.b.269.1	✓	56	28.3	even	6
504.2.ch.b.269.9	yes	56	56.3	even	6
504.2.ch.b.269.20	yes	56	168.59	odd	6
504.2.ch.b.269.28	yes	56	84.59	odd	6
504.2.ch.b.341.1	yes	56	24.11	even	2
504.2.ch.b.341.9	yes	56	12.11	even	2
504.2.ch.b.341.20	yes	56	4.3	odd	2
504.2.ch.b.341.28	yes	56	8.3	odd	2
2016.2.cp.b.17.11		56	7.3	odd	6	inner
2016.2.cp.b.17.12		56	168.101	even	6	inner
2016.2.cp.b.17.17		56	21.17	even	6	inner
2016.2.cp.b.17.18		56	56.45	odd	6	inner
2016.2.cp.b.593.11		56	24.5	odd	2	inner
2016.2.cp.b.593.12		56	1.1	even	1	trivial
2016.2.cp.b.593.17		56	8.5	even	2	inner
2016.2.cp.b.593.18		56	3.2	odd	2	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

Introduction

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Modular forms

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