LMFDB - Embedded newform 2646.2.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(1,2646)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2646, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2646.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.a (trivial)

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:	yes
Analytic conductor:	$21.1284163748$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 378)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	2646.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{8} +O(q^{10})$

$q-1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{8} +6.00000 q^{11} -5.00000 q^{13} +1.00000 q^{16} -6.00000 q^{17} +4.00000 q^{19} -6.00000 q^{22} +6.00000 q^{23} -5.00000 q^{25} +5.00000 q^{26} +6.00000 q^{29} +1.00000 q^{31} -1.00000 q^{32} +6.00000 q^{34} -1.00000 q^{37} -4.00000 q^{38} +6.00000 q^{41} -1.00000 q^{43} +6.00000 q^{44} -6.00000 q^{46} +6.00000 q^{47} +5.00000 q^{50} -5.00000 q^{52} -6.00000 q^{53} -6.00000 q^{58} +6.00000 q^{59} +1.00000 q^{61} -1.00000 q^{62} +1.00000 q^{64} -1.00000 q^{67} -6.00000 q^{68} +12.0000 q^{71} -2.00000 q^{73} +1.00000 q^{74} +4.00000 q^{76} -1.00000 q^{79} -6.00000 q^{82} -6.00000 q^{83} +1.00000 q^{86} -6.00000 q^{88} +6.00000 q^{92} -6.00000 q^{94} -17.0000 q^{97} +O(q^{100})$

Display 100 coefficients 10 coefficients

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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0	0
$3$	0	0
$4$	1.00000	0.500000
$5$	0	0		−	1.00000i	$-0.5\pi$
$5$	0	0			1.00000i	$0.5\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	0	0
$10$	0	0
$11$	6.00000	1.80907	0.904534	−	0.426401i	$-0.140219\pi$
$11$	6.00000	1.80907	0.904534	+	0.426401i	$0.140219\pi$
$12$	0	0
$13$	−5.00000	−1.38675	−0.693375	−	0.720577i	$-0.743877\pi$
$13$	−5.00000	−1.38675	−0.693375	+	0.720577i	$0.743877\pi$
$14$	0	0
$15$	0	0
$16$	1.00000	0.250000
$17$	−6.00000	−1.45521	−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000	−1.45521	−0.727607	+	0.685994i	$0.759367\pi$
$18$	0	0
$19$	4.00000	0.917663	0.458831	−	0.888523i	$-0.348268\pi$
$19$	4.00000	0.917663	0.458831	+	0.888523i	$0.348268\pi$
$20$	0	0
$21$	0	0
$22$	−6.00000	−1.27920
$23$	6.00000	1.25109	0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000	1.25109	0.625543	+	0.780189i	$0.284877\pi$
$24$	0	0
$25$	−5.00000	−1.00000
$26$	5.00000	0.980581
$27$	0	0
$28$	0	0
$29$	6.00000	1.11417	0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000	1.11417	0.557086	+	0.830455i	$0.311919\pi$
$30$	0	0
$31$	1.00000	0.179605	0.0898027	−	0.995960i	$-0.471376\pi$
$31$	1.00000	0.179605	0.0898027	+	0.995960i	$0.471376\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	6.00000	1.02899
$35$	0	0
$36$	0	0
$37$	−1.00000	−0.164399	−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	−1.00000	−0.164399	−0.0821995	+	0.996616i	$0.526194\pi$
$38$	−4.00000	−0.648886
$39$	0	0
$40$	0	0
$41$	6.00000	0.937043	0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000	0.937043	0.468521	+	0.883452i	$0.344787\pi$
$42$	0	0
$43$	−1.00000	−0.152499	−0.0762493	−	0.997089i	$-0.524294\pi$
$43$	−1.00000	−0.152499	−0.0762493	+	0.997089i	$0.524294\pi$
$44$	6.00000	0.904534
$45$	0	0
$46$	−6.00000	−0.884652
$47$	6.00000	0.875190	0.437595	−	0.899172i	$-0.355830\pi$
$47$	6.00000	0.875190	0.437595	+	0.899172i	$0.355830\pi$
$48$	0	0
$49$	0	0
$50$	5.00000	0.707107
$51$	0	0
$52$	−5.00000	−0.693375
$53$	−6.00000	−0.824163	−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000	−0.824163	−0.412082	+	0.911147i	$0.635198\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	0	0
$58$	−6.00000	−0.787839
$59$	6.00000	0.781133	0.390567	−	0.920575i	$-0.372279\pi$
$59$	6.00000	0.781133	0.390567	+	0.920575i	$0.372279\pi$
$60$	0	0
$61$	1.00000	0.128037	0.0640184	−	0.997949i	$-0.479608\pi$
$61$	1.00000	0.128037	0.0640184	+	0.997949i	$0.479608\pi$
$62$	−1.00000	−0.127000
$63$	0	0
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	−1.00000	−0.122169	−0.0610847	−	0.998133i	$-0.519456\pi$
$67$	−1.00000	−0.122169	−0.0610847	+	0.998133i	$0.519456\pi$
$68$	−6.00000	−0.727607
$69$	0	0
$70$	0	0
$71$	12.0000	1.42414	0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000	1.42414	0.712069	+	0.702109i	$0.247758\pi$
$72$	0	0
$73$	−2.00000	−0.234082	−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000	−0.234082	−0.117041	+	0.993127i	$0.537341\pi$
$74$	1.00000	0.116248
$75$	0	0
$76$	4.00000	0.458831
$77$	0	0
$78$	0	0
$79$	−1.00000	−0.112509	−0.0562544	−	0.998416i	$-0.517916\pi$
$79$	−1.00000	−0.112509	−0.0562544	+	0.998416i	$0.517916\pi$
$80$	0	0
$81$	0	0
$82$	−6.00000	−0.662589
$83$	−6.00000	−0.658586	−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000	−0.658586	−0.329293	+	0.944228i	$0.606810\pi$
$84$	0	0
$85$	0	0
$86$	1.00000	0.107833
$87$	0	0
$88$	−6.00000	−0.639602
$89$	0	0		−	1.00000i	$-0.5\pi$
$89$	0	0			1.00000i	$0.5\pi$
$90$	0	0
$91$	0	0
$92$	6.00000	0.625543
$93$	0	0
$94$	−6.00000	−0.618853
$95$	0	0
$96$	0	0
$97$	−17.0000	−1.72609	−0.863044	−	0.505128i	$-0.831445\pi$
$97$	−17.0000	−1.72609	−0.863044	+	0.505128i	$0.831445\pi$
$98$	0	0
$99$	0	0
$100$	−5.00000	−0.500000
$101$	−12.0000	−1.19404	−0.597022	−	0.802225i	$-0.703650\pi$
$101$	−12.0000	−1.19404	−0.597022	+	0.802225i	$0.703650\pi$
$102$	0	0
$103$	19.0000	1.87213	0.936063	−	0.351833i	$-0.114441\pi$
$103$	19.0000	1.87213	0.936063	+	0.351833i	$0.114441\pi$
$104$	5.00000	0.490290
$105$	0	0
$106$	6.00000	0.582772
$107$	18.0000	1.74013	0.870063	−	0.492941i	$-0.164078\pi$
$107$	18.0000	1.74013	0.870063	+	0.492941i	$0.164078\pi$
$108$	0	0
$109$	5.00000	0.478913	0.239457	−	0.970907i	$-0.423031\pi$
$109$	5.00000	0.478913	0.239457	+	0.970907i	$0.423031\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	12.0000	1.12887	0.564433	−	0.825479i	$-0.309095\pi$
$113$	12.0000	1.12887	0.564433	+	0.825479i	$0.309095\pi$
$114$	0	0
$115$	0	0
$116$	6.00000	0.557086
$117$	0	0
$118$	−6.00000	−0.552345
$119$	0	0
$120$	0	0
$121$	25.0000	2.27273
$122$	−1.00000	−0.0905357
$123$	0	0
$124$	1.00000	0.0898027
$125$	0	0
$126$	0	0
$127$	−13.0000	−1.15356	−0.576782	−	0.816898i	$-0.695692\pi$
$127$	−13.0000	−1.15356	−0.576782	+	0.816898i	$0.695692\pi$
$128$	−1.00000	−0.0883883
$129$	0	0
$130$	0	0
$131$	12.0000	1.04844	0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000	1.04844	0.524222	+	0.851581i	$0.324356\pi$
$132$	0	0
$133$	0	0
$134$	1.00000	0.0863868
$135$	0	0
$136$	6.00000	0.514496
$137$	−6.00000	−0.512615	−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−6.00000	−0.512615	−0.256307	+	0.966595i	$0.582506\pi$
$138$	0	0
$139$	7.00000	0.593732	0.296866	−	0.954919i	$-0.404058\pi$
$139$	7.00000	0.593732	0.296866	+	0.954919i	$0.404058\pi$
$140$	0	0
$141$	0	0
$142$	−12.0000	−1.00702
$143$	−30.0000	−2.50873
$144$	0	0
$145$	0	0
$146$	2.00000	0.165521
$147$	0	0
$148$	−1.00000	−0.0821995
$149$	−12.0000	−0.983078	−0.491539	−	0.870855i	$-0.663566\pi$
$149$	−12.0000	−0.983078	−0.491539	+	0.870855i	$0.663566\pi$
$150$	0	0
$151$	17.0000	1.38344	0.691720	−	0.722166i	$-0.256853\pi$
$151$	17.0000	1.38344	0.691720	+	0.722166i	$0.256853\pi$
$152$	−4.00000	−0.324443
$153$	0	0
$154$	0	0
$155$	0	0
$156$	0	0
$157$	22.0000	1.75579	0.877896	−	0.478852i	$-0.158947\pi$
$157$	22.0000	1.75579	0.877896	+	0.478852i	$0.158947\pi$
$158$	1.00000	0.0795557
$159$	0	0
$160$	0	0
$161$	0	0
$162$	0	0
$163$	11.0000	0.861586	0.430793	−	0.902451i	$-0.358234\pi$
$163$	11.0000	0.861586	0.430793	+	0.902451i	$0.358234\pi$
$164$	6.00000	0.468521
$165$	0	0
$166$	6.00000	0.465690
$167$	18.0000	1.39288	0.696441	−	0.717614i	$-0.254766\pi$
$167$	18.0000	1.39288	0.696441	+	0.717614i	$0.254766\pi$
$168$	0	0
$169$	12.0000	0.923077
$170$	0	0
$171$	0	0
$172$	−1.00000	−0.0762493
$173$	0	0		−	1.00000i	$-0.5\pi$
$173$	0	0			1.00000i	$0.5\pi$
$174$	0	0
$175$	0	0
$176$	6.00000	0.452267
$177$	0	0
$178$	0	0
$179$	0	0		−	1.00000i	$-0.5\pi$
$179$	0	0			1.00000i	$0.5\pi$
$180$	0	0
$181$	10.0000	0.743294	0.371647	−	0.928374i	$-0.378793\pi$
$181$	10.0000	0.743294	0.371647	+	0.928374i	$0.378793\pi$
$182$	0	0
$183$	0	0
$184$	−6.00000	−0.442326
$185$	0	0
$186$	0	0
$187$	−36.0000	−2.63258
$188$	6.00000	0.437595
$189$	0	0
$190$	0	0
$191$	0	0		−	1.00000i	$-0.5\pi$
$191$	0	0			1.00000i	$0.5\pi$
$192$	0	0
$193$	−1.00000	−0.0719816	−0.0359908	−	0.999352i	$-0.511459\pi$
$193$	−1.00000	−0.0719816	−0.0359908	+	0.999352i	$0.511459\pi$
$194$	17.0000	1.22053
$195$	0	0
$196$	0	0
$197$	−12.0000	−0.854965	−0.427482	−	0.904024i	$-0.640599\pi$
$197$	−12.0000	−0.854965	−0.427482	+	0.904024i	$0.640599\pi$
$198$	0	0
$199$	−11.0000	−0.779769	−0.389885	−	0.920864i	$-0.627485\pi$
$199$	−11.0000	−0.779769	−0.389885	+	0.920864i	$0.627485\pi$
$200$	5.00000	0.353553
$201$	0	0
$202$	12.0000	0.844317
$203$	0	0
$204$	0	0
$205$	0	0
$206$	−19.0000	−1.32379
$207$	0	0
$208$	−5.00000	−0.346688
$209$	24.0000	1.66011
$210$	0	0
$211$	−13.0000	−0.894957	−0.447478	−	0.894295i	$-0.647678\pi$
$211$	−13.0000	−0.894957	−0.447478	+	0.894295i	$0.647678\pi$
$212$	−6.00000	−0.412082
$213$	0	0
$214$	−18.0000	−1.23045
$215$	0	0
$216$	0	0
$217$	0	0
$218$	−5.00000	−0.338643
$219$	0	0
$220$	0	0
$221$	30.0000	2.01802
$222$	0	0
$223$	−8.00000	−0.535720	−0.267860	−	0.963458i	$-0.586316\pi$
$223$	−8.00000	−0.535720	−0.267860	+	0.963458i	$0.586316\pi$
$224$	0	0
$225$	0	0
$226$	−12.0000	−0.798228
$227$	6.00000	0.398234	0.199117	−	0.979976i	$-0.436193\pi$
$227$	6.00000	0.398234	0.199117	+	0.979976i	$0.436193\pi$
$228$	0	0
$229$	−5.00000	−0.330409	−0.165205	−	0.986259i	$-0.552828\pi$
$229$	−5.00000	−0.330409	−0.165205	+	0.986259i	$0.552828\pi$
$230$	0	0
$231$	0	0
$232$	−6.00000	−0.393919
$233$	24.0000	1.57229	0.786146	−	0.618041i	$-0.212073\pi$
$233$	24.0000	1.57229	0.786146	+	0.618041i	$0.212073\pi$
$234$	0	0
$235$	0	0
$236$	6.00000	0.390567
$237$	0	0
$238$	0	0
$239$	24.0000	1.55243	0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000	1.55243	0.776215	+	0.630468i	$0.217137\pi$
$240$	0	0
$241$	−17.0000	−1.09507	−0.547533	−	0.836784i	$-0.684433\pi$
$241$	−17.0000	−1.09507	−0.547533	+	0.836784i	$0.684433\pi$
$242$	−25.0000	−1.60706
$243$	0	0
$244$	1.00000	0.0640184
$245$	0	0
$246$	0	0
$247$	−20.0000	−1.27257
$248$	−1.00000	−0.0635001
$249$	0	0
$250$	0	0
$251$	−18.0000	−1.13615	−0.568075	−	0.822977i	$-0.692312\pi$
$251$	−18.0000	−1.13615	−0.568075	+	0.822977i	$0.692312\pi$
$252$	0	0
$253$	36.0000	2.26330
$254$	13.0000	0.815693
$255$	0	0
$256$	1.00000	0.0625000
$257$	6.00000	0.374270	0.187135	−	0.982334i	$-0.440080\pi$
$257$	6.00000	0.374270	0.187135	+	0.982334i	$0.440080\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	0	0
$262$	−12.0000	−0.741362
$263$	6.00000	0.369976	0.184988	−	0.982741i	$-0.440775\pi$
$263$	6.00000	0.369976	0.184988	+	0.982741i	$0.440775\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	−1.00000	−0.0610847
$269$	0	0		−	1.00000i	$-0.5\pi$
$269$	0	0			1.00000i	$0.5\pi$
$270$	0	0
$271$	7.00000	0.425220	0.212610	−	0.977137i	$-0.431804\pi$
$271$	7.00000	0.425220	0.212610	+	0.977137i	$0.431804\pi$
$272$	−6.00000	−0.363803
$273$	0	0
$274$	6.00000	0.362473
$275$	−30.0000	−1.80907
$276$	0	0
$277$	17.0000	1.02143	0.510716	−	0.859750i	$-0.329381\pi$
$277$	17.0000	1.02143	0.510716	+	0.859750i	$0.329381\pi$
$278$	−7.00000	−0.419832
$279$	0	0
$280$	0	0
$281$	12.0000	0.715860	0.357930	−	0.933748i	$-0.383483\pi$
$281$	12.0000	0.715860	0.357930	+	0.933748i	$0.383483\pi$
$282$	0	0
$283$	13.0000	0.772770	0.386385	−	0.922338i	$-0.373724\pi$
$283$	13.0000	0.772770	0.386385	+	0.922338i	$0.373724\pi$
$284$	12.0000	0.712069
$285$	0	0
$286$	30.0000	1.77394
$287$	0	0
$288$	0	0
$289$	19.0000	1.11765
$290$	0	0
$291$	0	0
$292$	−2.00000	−0.117041
$293$	−18.0000	−1.05157	−0.525786	−	0.850617i	$-0.676229\pi$
$293$	−18.0000	−1.05157	−0.525786	+	0.850617i	$0.676229\pi$
$294$	0	0
$295$	0	0
$296$	1.00000	0.0581238
$297$	0	0
$298$	12.0000	0.695141
$299$	−30.0000	−1.73494
$300$	0	0
$301$	0	0
$302$	−17.0000	−0.978240
$303$	0	0
$304$	4.00000	0.229416
$305$	0	0
$306$	0	0
$307$	−17.0000	−0.970241	−0.485121	−	0.874447i	$-0.661224\pi$
$307$	−17.0000	−0.970241	−0.485121	+	0.874447i	$0.661224\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	12.0000	0.680458	0.340229	−	0.940343i	$-0.389495\pi$
$311$	12.0000	0.680458	0.340229	+	0.940343i	$0.389495\pi$
$312$	0	0
$313$	22.0000	1.24351	0.621757	−	0.783210i	$-0.286419\pi$
$313$	22.0000	1.24351	0.621757	+	0.783210i	$0.286419\pi$
$314$	−22.0000	−1.24153
$315$	0	0
$316$	−1.00000	−0.0562544
$317$	18.0000	1.01098	0.505490	−	0.862832i	$-0.331312\pi$
$317$	18.0000	1.01098	0.505490	+	0.862832i	$0.331312\pi$
$318$	0	0
$319$	36.0000	2.01561
$320$	0	0
$321$	0	0
$322$	0	0
$323$	−24.0000	−1.33540
$324$	0	0
$325$	25.0000	1.38675
$326$	−11.0000	−0.609234
$327$	0	0
$328$	−6.00000	−0.331295
$329$	0	0
$330$	0	0
$331$	20.0000	1.09930	0.549650	−	0.835395i	$-0.314761\pi$
$331$	20.0000	1.09930	0.549650	+	0.835395i	$0.314761\pi$
$332$	−6.00000	−0.329293
$333$	0	0
$334$	−18.0000	−0.984916
$335$	0	0
$336$	0	0
$337$	2.00000	0.108947	0.0544735	−	0.998515i	$-0.482652\pi$
$337$	2.00000	0.108947	0.0544735	+	0.998515i	$0.482652\pi$
$338$	−12.0000	−0.652714
$339$	0	0
$340$	0	0
$341$	6.00000	0.324918
$342$	0	0
$343$	0	0
$344$	1.00000	0.0539164
$345$	0	0
$346$	0	0
$347$	−24.0000	−1.28839	−0.644194	−	0.764862i	$-0.722807\pi$
$347$	−24.0000	−1.28839	−0.644194	+	0.764862i	$0.722807\pi$
$348$	0	0
$349$	1.00000	0.0535288	0.0267644	−	0.999642i	$-0.491480\pi$
$349$	1.00000	0.0535288	0.0267644	+	0.999642i	$0.491480\pi$
$350$	0	0
$351$	0	0
$352$	−6.00000	−0.319801
$353$	36.0000	1.91609	0.958043	−	0.286623i	$-0.0925328\pi$
$353$	36.0000	1.91609	0.958043	+	0.286623i	$0.0925328\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	0	0
$359$	6.00000	0.316668	0.158334	−	0.987386i	$-0.449388\pi$
$359$	6.00000	0.316668	0.158334	+	0.987386i	$0.449388\pi$
$360$	0	0
$361$	−3.00000	−0.157895
$362$	−10.0000	−0.525588
$363$	0	0
$364$	0	0
$365$	0	0
$366$	0	0
$367$	28.0000	1.46159	0.730794	−	0.682598i	$-0.239150\pi$
$367$	28.0000	1.46159	0.730794	+	0.682598i	$0.239150\pi$
$368$	6.00000	0.312772
$369$	0	0
$370$	0	0
$371$	0	0
$372$	0	0
$373$	26.0000	1.34623	0.673114	−	0.739538i	$-0.264956\pi$
$373$	26.0000	1.34623	0.673114	+	0.739538i	$0.264956\pi$
$374$	36.0000	1.86152
$375$	0	0
$376$	−6.00000	−0.309426
$377$	−30.0000	−1.54508
$378$	0	0
$379$	−1.00000	−0.0513665	−0.0256833	−	0.999670i	$-0.508176\pi$
$379$	−1.00000	−0.0513665	−0.0256833	+	0.999670i	$0.508176\pi$
$380$	0	0
$381$	0	0
$382$	0	0
$383$	−6.00000	−0.306586	−0.153293	−	0.988181i	$-0.548988\pi$
$383$	−6.00000	−0.306586	−0.153293	+	0.988181i	$0.548988\pi$
$384$	0	0
$385$	0	0
$386$	1.00000	0.0508987
$387$	0	0
$388$	−17.0000	−0.863044
$389$	−12.0000	−0.608424	−0.304212	−	0.952604i	$-0.598393\pi$
$389$	−12.0000	−0.608424	−0.304212	+	0.952604i	$0.598393\pi$
$390$	0	0
$391$	−36.0000	−1.82060
$392$	0	0
$393$	0	0
$394$	12.0000	0.604551
$395$	0	0
$396$	0	0
$397$	13.0000	0.652451	0.326226	−	0.945292i	$-0.394223\pi$
$397$	13.0000	0.652451	0.326226	+	0.945292i	$0.394223\pi$
$398$	11.0000	0.551380
$399$	0	0
$400$	−5.00000	−0.250000
$401$	−6.00000	−0.299626	−0.149813	−	0.988714i	$-0.547867\pi$
$401$	−6.00000	−0.299626	−0.149813	+	0.988714i	$0.547867\pi$
$402$	0	0
$403$	−5.00000	−0.249068
$404$	−12.0000	−0.597022
$405$	0	0
$406$	0	0
$407$	−6.00000	−0.297409
$408$	0	0
$409$	−29.0000	−1.43396	−0.716979	−	0.697095i	$-0.754476\pi$
$409$	−29.0000	−1.43396	−0.716979	+	0.697095i	$0.754476\pi$
$410$	0	0
$411$	0	0
$412$	19.0000	0.936063
$413$	0	0
$414$	0	0
$415$	0	0
$416$	5.00000	0.245145
$417$	0	0
$418$	−24.0000	−1.17388
$419$	24.0000	1.17248	0.586238	−	0.810139i	$-0.300608\pi$
$419$	24.0000	1.17248	0.586238	+	0.810139i	$0.300608\pi$
$420$	0	0
$421$	14.0000	0.682318	0.341159	−	0.940006i	$-0.389181\pi$
$421$	14.0000	0.682318	0.341159	+	0.940006i	$0.389181\pi$
$422$	13.0000	0.632830
$423$	0	0
$424$	6.00000	0.291386
$425$	30.0000	1.45521
$426$	0	0
$427$	0	0
$428$	18.0000	0.870063
$429$	0	0
$430$	0	0
$431$	−18.0000	−0.867029	−0.433515	−	0.901146i	$-0.642727\pi$
$431$	−18.0000	−0.867029	−0.433515	+	0.901146i	$0.642727\pi$
$432$	0	0
$433$	25.0000	1.20142	0.600712	−	0.799466i	$-0.294884\pi$
$433$	25.0000	1.20142	0.600712	+	0.799466i	$0.294884\pi$
$434$	0	0
$435$	0	0
$436$	5.00000	0.239457
$437$	24.0000	1.14808
$438$	0	0
$439$	−8.00000	−0.381819	−0.190910	−	0.981608i	$-0.561144\pi$
$439$	−8.00000	−0.381819	−0.190910	+	0.981608i	$0.561144\pi$
$440$	0	0
$441$	0	0
$442$	−30.0000	−1.42695
$443$	−24.0000	−1.14027	−0.570137	−	0.821549i	$-0.693110\pi$
$443$	−24.0000	−1.14027	−0.570137	+	0.821549i	$0.693110\pi$
$444$	0	0
$445$	0	0
$446$	8.00000	0.378811
$447$	0	0
$448$	0	0
$449$	−24.0000	−1.13263	−0.566315	−	0.824189i	$-0.691631\pi$
$449$	−24.0000	−1.13263	−0.566315	+	0.824189i	$0.691631\pi$
$450$	0	0
$451$	36.0000	1.69517
$452$	12.0000	0.564433
$453$	0	0
$454$	−6.00000	−0.281594
$455$	0	0
$456$	0	0
$457$	−19.0000	−0.888783	−0.444391	−	0.895833i	$-0.646580\pi$
$457$	−19.0000	−0.888783	−0.444391	+	0.895833i	$0.646580\pi$
$458$	5.00000	0.233635
$459$	0	0
$460$	0	0
$461$	−18.0000	−0.838344	−0.419172	−	0.907907i	$-0.637680\pi$
$461$	−18.0000	−0.838344	−0.419172	+	0.907907i	$0.637680\pi$
$462$	0	0
$463$	8.00000	0.371792	0.185896	−	0.982569i	$-0.440481\pi$
$463$	8.00000	0.371792	0.185896	+	0.982569i	$0.440481\pi$
$464$	6.00000	0.278543
$465$	0	0
$466$	−24.0000	−1.11178
$467$	−12.0000	−0.555294	−0.277647	−	0.960683i	$-0.589555\pi$
$467$	−12.0000	−0.555294	−0.277647	+	0.960683i	$0.589555\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	0	0
$472$	−6.00000	−0.276172
$473$	−6.00000	−0.275880
$474$	0	0
$475$	−20.0000	−0.917663
$476$	0	0
$477$	0	0
$478$	−24.0000	−1.09773
$479$	−12.0000	−0.548294	−0.274147	−	0.961688i	$-0.588395\pi$
$479$	−12.0000	−0.548294	−0.274147	+	0.961688i	$0.588395\pi$
$480$	0	0
$481$	5.00000	0.227980
$482$	17.0000	0.774329
$483$	0	0
$484$	25.0000	1.13636
$485$	0	0
$486$	0	0
$487$	−40.0000	−1.81257	−0.906287	−	0.422664i	$-0.861095\pi$
$487$	−40.0000	−1.81257	−0.906287	+	0.422664i	$0.861095\pi$
$488$	−1.00000	−0.0452679
$489$	0	0
$490$	0	0
$491$	−30.0000	−1.35388	−0.676941	−	0.736038i	$-0.736695\pi$
$491$	−30.0000	−1.35388	−0.676941	+	0.736038i	$0.736695\pi$
$492$	0	0
$493$	−36.0000	−1.62136
$494$	20.0000	0.899843
$495$	0	0
$496$	1.00000	0.0449013
$497$	0	0
$498$	0	0
$499$	−25.0000	−1.11915	−0.559577	−	0.828778i	$-0.689036\pi$
$499$	−25.0000	−1.11915	−0.559577	+	0.828778i	$0.689036\pi$
$500$	0	0
$501$	0	0
$502$	18.0000	0.803379
$503$	−6.00000	−0.267527	−0.133763	−	0.991013i	$-0.542706\pi$
$503$	−6.00000	−0.267527	−0.133763	+	0.991013i	$0.542706\pi$
$504$	0	0
$505$	0	0
$506$	−36.0000	−1.60040
$507$	0	0
$508$	−13.0000	−0.576782
$509$	−30.0000	−1.32973	−0.664863	−	0.746965i	$-0.731510\pi$
$509$	−30.0000	−1.32973	−0.664863	+	0.746965i	$0.731510\pi$
$510$	0	0
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−6.00000	−0.264649
$515$	0	0
$516$	0	0
$517$	36.0000	1.58328
$518$	0	0
$519$	0	0
$520$	0	0
$521$	−42.0000	−1.84005	−0.920027	−	0.391856i	$-0.871833\pi$
$521$	−42.0000	−1.84005	−0.920027	+	0.391856i	$0.871833\pi$
$522$	0	0
$523$	−23.0000	−1.00572	−0.502860	−	0.864368i	$-0.667719\pi$
$523$	−23.0000	−1.00572	−0.502860	+	0.864368i	$0.667719\pi$
$524$	12.0000	0.524222
$525$	0	0
$526$	−6.00000	−0.261612
$527$	−6.00000	−0.261364
$528$	0	0
$529$	13.0000	0.565217
$530$	0	0
$531$	0	0
$532$	0	0
$533$	−30.0000	−1.29944
$534$	0	0
$535$	0	0
$536$	1.00000	0.0431934
$537$	0	0
$538$	0	0
$539$	0	0
$540$	0	0
$541$	−10.0000	−0.429934	−0.214967	−	0.976621i	$-0.568964\pi$
$541$	−10.0000	−0.429934	−0.214967	+	0.976621i	$0.568964\pi$
$542$	−7.00000	−0.300676
$543$	0	0
$544$	6.00000	0.257248
$545$	0	0
$546$	0	0
$547$	−37.0000	−1.58201	−0.791003	−	0.611812i	$-0.790441\pi$
$547$	−37.0000	−1.58201	−0.791003	+	0.611812i	$0.790441\pi$
$548$	−6.00000	−0.256307
$549$	0	0
$550$	30.0000	1.27920
$551$	24.0000	1.02243
$552$	0	0
$553$	0	0
$554$	−17.0000	−0.722261
$555$	0	0
$556$	7.00000	0.296866
$557$	0	0		−	1.00000i	$-0.5\pi$
$557$	0	0			1.00000i	$0.5\pi$
$558$	0	0
$559$	5.00000	0.211477
$560$	0	0
$561$	0	0
$562$	−12.0000	−0.506189
$563$	42.0000	1.77009	0.885044	−	0.465506i	$-0.154128\pi$
$563$	42.0000	1.77009	0.885044	+	0.465506i	$0.154128\pi$
$564$	0	0
$565$	0	0
$566$	−13.0000	−0.546431
$567$	0	0
$568$	−12.0000	−0.503509
$569$	−36.0000	−1.50920	−0.754599	−	0.656186i	$-0.772169\pi$
$569$	−36.0000	−1.50920	−0.754599	+	0.656186i	$0.772169\pi$
$570$	0	0
$571$	−16.0000	−0.669579	−0.334790	−	0.942293i	$-0.608665\pi$
$571$	−16.0000	−0.669579	−0.334790	+	0.942293i	$0.608665\pi$
$572$	−30.0000	−1.25436
$573$	0	0
$574$	0	0
$575$	−30.0000	−1.25109
$576$	0	0
$577$	−23.0000	−0.957503	−0.478751	−	0.877951i	$-0.658910\pi$
$577$	−23.0000	−0.957503	−0.478751	+	0.877951i	$0.658910\pi$
$578$	−19.0000	−0.790296
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	−36.0000	−1.49097
$584$	2.00000	0.0827606
$585$	0	0
$586$	18.0000	0.743573
$587$	0	0		−	1.00000i	$-0.5\pi$
$587$	0	0			1.00000i	$0.5\pi$
$588$	0	0
$589$	4.00000	0.164817
$590$	0	0
$591$	0	0
$592$	−1.00000	−0.0410997
$593$	−36.0000	−1.47834	−0.739171	−	0.673517i	$-0.764783\pi$
$593$	−36.0000	−1.47834	−0.739171	+	0.673517i	$0.764783\pi$
$594$	0	0
$595$	0	0
$596$	−12.0000	−0.491539
$597$	0	0
$598$	30.0000	1.22679
$599$	36.0000	1.47092	0.735460	−	0.677568i	$-0.236966\pi$
$599$	36.0000	1.47092	0.735460	+	0.677568i	$0.236966\pi$
$600$	0	0
$601$	−47.0000	−1.91717	−0.958585	−	0.284807i	$-0.908071\pi$
$601$	−47.0000	−1.91717	−0.958585	+	0.284807i	$0.908071\pi$
$602$	0	0
$603$	0	0
$604$	17.0000	0.691720
$605$	0	0
$606$	0	0
$607$	16.0000	0.649420	0.324710	−	0.945814i	$-0.394733\pi$
$607$	16.0000	0.649420	0.324710	+	0.945814i	$0.394733\pi$
$608$	−4.00000	−0.162221
$609$	0	0
$610$	0	0
$611$	−30.0000	−1.21367
$612$	0	0
$613$	11.0000	0.444286	0.222143	−	0.975014i	$-0.428695\pi$
$613$	11.0000	0.444286	0.222143	+	0.975014i	$0.428695\pi$
$614$	17.0000	0.686064
$615$	0	0
$616$	0	0
$617$	−30.0000	−1.20775	−0.603877	−	0.797077i	$-0.706378\pi$
$617$	−30.0000	−1.20775	−0.603877	+	0.797077i	$0.706378\pi$
$618$	0	0
$619$	25.0000	1.00483	0.502417	−	0.864625i	$-0.332444\pi$
$619$	25.0000	1.00483	0.502417	+	0.864625i	$0.332444\pi$
$620$	0	0
$621$	0	0
$622$	−12.0000	−0.481156
$623$	0	0
$624$	0	0
$625$	25.0000	1.00000
$626$	−22.0000	−0.879297
$627$	0	0
$628$	22.0000	0.877896
$629$	6.00000	0.239236
$630$	0	0
$631$	−7.00000	−0.278666	−0.139333	−	0.990246i	$-0.544496\pi$
$631$	−7.00000	−0.278666	−0.139333	+	0.990246i	$0.544496\pi$
$632$	1.00000	0.0397779
$633$	0	0
$634$	−18.0000	−0.714871
$635$	0	0
$636$	0	0
$637$	0	0
$638$	−36.0000	−1.42525
$639$	0	0
$640$	0	0
$641$	18.0000	0.710957	0.355479	−	0.934684i	$-0.384318\pi$
$641$	18.0000	0.710957	0.355479	+	0.934684i	$0.384318\pi$
$642$	0	0
$643$	25.0000	0.985904	0.492952	−	0.870057i	$-0.335918\pi$
$643$	25.0000	0.985904	0.492952	+	0.870057i	$0.335918\pi$
$644$	0	0
$645$	0	0
$646$	24.0000	0.944267
$647$	12.0000	0.471769	0.235884	−	0.971781i	$-0.424201\pi$
$647$	12.0000	0.471769	0.235884	+	0.971781i	$0.424201\pi$
$648$	0	0
$649$	36.0000	1.41312
$650$	−25.0000	−0.980581
$651$	0	0
$652$	11.0000	0.430793
$653$	−18.0000	−0.704394	−0.352197	−	0.935926i	$-0.614565\pi$
$653$	−18.0000	−0.704394	−0.352197	+	0.935926i	$0.614565\pi$
$654$	0	0
$655$	0	0
$656$	6.00000	0.234261
$657$	0	0
$658$	0	0
$659$	0	0		−	1.00000i	$-0.5\pi$
$659$	0	0			1.00000i	$0.5\pi$
$660$	0	0
$661$	−50.0000	−1.94477	−0.972387	−	0.233373i	$-0.925024\pi$
$661$	−50.0000	−1.94477	−0.972387	+	0.233373i	$0.925024\pi$
$662$	−20.0000	−0.777322
$663$	0	0
$664$	6.00000	0.232845
$665$	0	0
$666$	0	0
$667$	36.0000	1.39393
$668$	18.0000	0.696441
$669$	0	0
$670$	0	0
$671$	6.00000	0.231627
$672$	0	0
$673$	−34.0000	−1.31060	−0.655302	−	0.755367i	$-0.727459\pi$
$673$	−34.0000	−1.31060	−0.655302	+	0.755367i	$0.727459\pi$
$674$	−2.00000	−0.0770371
$675$	0	0
$676$	12.0000	0.461538
$677$	−12.0000	−0.461197	−0.230599	−	0.973049i	$-0.574068\pi$
$677$	−12.0000	−0.461197	−0.230599	+	0.973049i	$0.574068\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	0	0
$682$	−6.00000	−0.229752
$683$	12.0000	0.459167	0.229584	−	0.973289i	$-0.426264\pi$
$683$	12.0000	0.459167	0.229584	+	0.973289i	$0.426264\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	0	0
$688$	−1.00000	−0.0381246
$689$	30.0000	1.14291
$690$	0	0
$691$	−17.0000	−0.646710	−0.323355	−	0.946278i	$-0.604811\pi$
$691$	−17.0000	−0.646710	−0.323355	+	0.946278i	$0.604811\pi$
$692$	0	0
$693$	0	0
$694$	24.0000	0.911028
$695$	0	0
$696$	0	0
$697$	−36.0000	−1.36360
$698$	−1.00000	−0.0378506
$699$	0	0
$700$	0	0
$701$	48.0000	1.81293	0.906467	−	0.422276i	$-0.138769\pi$
$701$	48.0000	1.81293	0.906467	+	0.422276i	$0.138769\pi$
$702$	0	0
$703$	−4.00000	−0.150863
$704$	6.00000	0.226134
$705$	0	0
$706$	−36.0000	−1.35488
$707$	0	0
$708$	0	0
$709$	17.0000	0.638448	0.319224	−	0.947679i	$-0.396578\pi$
$709$	17.0000	0.638448	0.319224	+	0.947679i	$0.396578\pi$
$710$	0	0
$711$	0	0
$712$	0	0
$713$	6.00000	0.224702
$714$	0	0
$715$	0	0
$716$	0	0
$717$	0	0
$718$	−6.00000	−0.223918
$719$	−12.0000	−0.447524	−0.223762	−	0.974644i	$-0.571834\pi$
$719$	−12.0000	−0.447524	−0.223762	+	0.974644i	$0.571834\pi$
$720$	0	0
$721$	0	0
$722$	3.00000	0.111648
$723$	0	0
$724$	10.0000	0.371647
$725$	−30.0000	−1.11417
$726$	0	0
$727$	−5.00000	−0.185440	−0.0927199	−	0.995692i	$-0.529556\pi$
$727$	−5.00000	−0.185440	−0.0927199	+	0.995692i	$0.529556\pi$
$728$	0	0
$729$	0	0
$730$	0	0
$731$	6.00000	0.221918
$732$	0	0
$733$	−17.0000	−0.627909	−0.313955	−	0.949438i	$-0.601654\pi$
$733$	−17.0000	−0.627909	−0.313955	+	0.949438i	$0.601654\pi$
$734$	−28.0000	−1.03350
$735$	0	0
$736$	−6.00000	−0.221163
$737$	−6.00000	−0.221013
$738$	0	0
$739$	−49.0000	−1.80249	−0.901247	−	0.433306i	$-0.857347\pi$
$739$	−49.0000	−1.80249	−0.901247	+	0.433306i	$0.857347\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	18.0000	0.660356	0.330178	−	0.943919i	$-0.392891\pi$
$743$	18.0000	0.660356	0.330178	+	0.943919i	$0.392891\pi$
$744$	0	0
$745$	0	0
$746$	−26.0000	−0.951928
$747$	0	0
$748$	−36.0000	−1.31629
$749$	0	0
$750$	0	0
$751$	−16.0000	−0.583848	−0.291924	−	0.956441i	$-0.594295\pi$
$751$	−16.0000	−0.583848	−0.291924	+	0.956441i	$0.594295\pi$
$752$	6.00000	0.218797
$753$	0	0
$754$	30.0000	1.09254
$755$	0	0
$756$	0	0
$757$	29.0000	1.05402	0.527011	−	0.849858i	$-0.323312\pi$
$757$	29.0000	1.05402	0.527011	+	0.849858i	$0.323312\pi$
$758$	1.00000	0.0363216
$759$	0	0
$760$	0	0
$761$	0	0		−	1.00000i	$-0.5\pi$
$761$	0	0			1.00000i	$0.5\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	0	0
$766$	6.00000	0.216789
$767$	−30.0000	−1.08324
$768$	0	0
$769$	10.0000	0.360609	0.180305	−	0.983611i	$-0.442292\pi$
$769$	10.0000	0.360609	0.180305	+	0.983611i	$0.442292\pi$
$770$	0	0
$771$	0	0
$772$	−1.00000	−0.0359908
$773$	24.0000	0.863220	0.431610	−	0.902060i	$-0.357946\pi$
$773$	24.0000	0.863220	0.431610	+	0.902060i	$0.357946\pi$
$774$	0	0
$775$	−5.00000	−0.179605
$776$	17.0000	0.610264
$777$	0	0
$778$	12.0000	0.430221
$779$	24.0000	0.859889
$780$	0	0
$781$	72.0000	2.57636
$782$	36.0000	1.28736
$783$	0	0
$784$	0	0
$785$	0	0
$786$	0	0
$787$	31.0000	1.10503	0.552515	−	0.833503i	$-0.313668\pi$
$787$	31.0000	1.10503	0.552515	+	0.833503i	$0.313668\pi$
$788$	−12.0000	−0.427482
$789$	0	0
$790$	0	0
$791$	0	0
$792$	0	0
$793$	−5.00000	−0.177555
$794$	−13.0000	−0.461353
$795$	0	0
$796$	−11.0000	−0.389885
$797$	30.0000	1.06265	0.531327	−	0.847167i	$-0.321693\pi$
$797$	30.0000	1.06265	0.531327	+	0.847167i	$0.321693\pi$
$798$	0	0
$799$	−36.0000	−1.27359
$800$	5.00000	0.176777
$801$	0	0
$802$	6.00000	0.211867
$803$	−12.0000	−0.423471
$804$	0	0
$805$	0	0
$806$	5.00000	0.176117
$807$	0	0
$808$	12.0000	0.422159
$809$	−30.0000	−1.05474	−0.527372	−	0.849635i	$-0.676823\pi$
$809$	−30.0000	−1.05474	−0.527372	+	0.849635i	$0.676823\pi$
$810$	0	0
$811$	16.0000	0.561836	0.280918	−	0.959732i	$-0.409361\pi$
$811$	16.0000	0.561836	0.280918	+	0.959732i	$0.409361\pi$
$812$	0	0
$813$	0	0
$814$	6.00000	0.210300
$815$	0	0
$816$	0	0
$817$	−4.00000	−0.139942
$818$	29.0000	1.01396
$819$	0	0
$820$	0	0
$821$	6.00000	0.209401	0.104701	−	0.994504i	$-0.466612\pi$
$821$	6.00000	0.209401	0.104701	+	0.994504i	$0.466612\pi$
$822$	0	0
$823$	−31.0000	−1.08059	−0.540296	−	0.841475i	$-0.681688\pi$
$823$	−31.0000	−1.08059	−0.540296	+	0.841475i	$0.681688\pi$
$824$	−19.0000	−0.661896
$825$	0	0
$826$	0	0
$827$	−12.0000	−0.417281	−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000	−0.417281	−0.208640	+	0.977992i	$0.566904\pi$
$828$	0	0
$829$	−14.0000	−0.486240	−0.243120	−	0.969996i	$-0.578171\pi$
$829$	−14.0000	−0.486240	−0.243120	+	0.969996i	$0.578171\pi$
$830$	0	0
$831$	0	0
$832$	−5.00000	−0.173344
$833$	0	0
$834$	0	0
$835$	0	0
$836$	24.0000	0.830057
$837$	0	0
$838$	−24.0000	−0.829066
$839$	−18.0000	−0.621429	−0.310715	−	0.950503i	$-0.600568\pi$
$839$	−18.0000	−0.621429	−0.310715	+	0.950503i	$0.600568\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	−14.0000	−0.482472
$843$	0	0
$844$	−13.0000	−0.447478
$845$	0	0
$846$	0	0
$847$	0	0
$848$	−6.00000	−0.206041
$849$	0	0
$850$	−30.0000	−1.02899
$851$	−6.00000	−0.205677
$852$	0	0
$853$	46.0000	1.57501	0.787505	−	0.616308i	$-0.211372\pi$
$853$	46.0000	1.57501	0.787505	+	0.616308i	$0.211372\pi$
$854$	0	0
$855$	0	0
$856$	−18.0000	−0.615227
$857$	12.0000	0.409912	0.204956	−	0.978771i	$-0.434295\pi$
$857$	12.0000	0.409912	0.204956	+	0.978771i	$0.434295\pi$
$858$	0	0
$859$	−23.0000	−0.784750	−0.392375	−	0.919805i	$-0.628346\pi$
$859$	−23.0000	−0.784750	−0.392375	+	0.919805i	$0.628346\pi$
$860$	0	0
$861$	0	0
$862$	18.0000	0.613082
$863$	36.0000	1.22545	0.612727	−	0.790295i	$-0.290072\pi$
$863$	36.0000	1.22545	0.612727	+	0.790295i	$0.290072\pi$
$864$	0	0
$865$	0	0
$866$	−25.0000	−0.849535
$867$	0	0
$868$	0	0
$869$	−6.00000	−0.203536
$870$	0	0
$871$	5.00000	0.169419
$872$	−5.00000	−0.169321
$873$	0	0
$874$	−24.0000	−0.811812
$875$	0	0
$876$	0	0
$877$	−13.0000	−0.438979	−0.219489	−	0.975615i	$-0.570439\pi$
$877$	−13.0000	−0.438979	−0.219489	+	0.975615i	$0.570439\pi$
$878$	8.00000	0.269987
$879$	0	0
$880$	0	0
$881$	−30.0000	−1.01073	−0.505363	−	0.862907i	$-0.668641\pi$
$881$	−30.0000	−1.01073	−0.505363	+	0.862907i	$0.668641\pi$
$882$	0	0
$883$	−40.0000	−1.34611	−0.673054	−	0.739594i	$-0.735018\pi$
$883$	−40.0000	−1.34611	−0.673054	+	0.739594i	$0.735018\pi$
$884$	30.0000	1.00901
$885$	0	0
$886$	24.0000	0.806296
$887$	18.0000	0.604381	0.302190	−	0.953248i	$-0.402282\pi$
$887$	18.0000	0.604381	0.302190	+	0.953248i	$0.402282\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	0	0
$892$	−8.00000	−0.267860
$893$	24.0000	0.803129
$894$	0	0
$895$	0	0
$896$	0	0
$897$	0	0
$898$	24.0000	0.800890
$899$	6.00000	0.200111
$900$	0	0
$901$	36.0000	1.19933
$902$	−36.0000	−1.19867
$903$	0	0
$904$	−12.0000	−0.399114
$905$	0	0
$906$	0	0
$907$	−37.0000	−1.22856	−0.614282	−	0.789086i	$-0.710554\pi$
$907$	−37.0000	−1.22856	−0.614282	+	0.789086i	$0.710554\pi$
$908$	6.00000	0.199117
$909$	0	0
$910$	0	0
$911$	−6.00000	−0.198789	−0.0993944	−	0.995048i	$-0.531691\pi$
$911$	−6.00000	−0.198789	−0.0993944	+	0.995048i	$0.531691\pi$
$912$	0	0
$913$	−36.0000	−1.19143
$914$	19.0000	0.628464
$915$	0	0
$916$	−5.00000	−0.165205
$917$	0	0
$918$	0	0
$919$	−55.0000	−1.81428	−0.907141	−	0.420826i	$-0.861740\pi$
$919$	−55.0000	−1.81428	−0.907141	+	0.420826i	$0.861740\pi$
$920$	0	0
$921$	0	0
$922$	18.0000	0.592798
$923$	−60.0000	−1.97492
$924$	0	0
$925$	5.00000	0.164399
$926$	−8.00000	−0.262896
$927$	0	0
$928$	−6.00000	−0.196960
$929$	−48.0000	−1.57483	−0.787414	−	0.616424i	$-0.788581\pi$
$929$	−48.0000	−1.57483	−0.787414	+	0.616424i	$0.788581\pi$
$930$	0	0
$931$	0	0
$932$	24.0000	0.786146
$933$	0	0
$934$	12.0000	0.392652
$935$	0	0
$936$	0	0
$937$	37.0000	1.20874	0.604369	−	0.796705i	$-0.293425\pi$
$937$	37.0000	1.20874	0.604369	+	0.796705i	$0.293425\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	−18.0000	−0.586783	−0.293392	−	0.955992i	$-0.594784\pi$
$941$	−18.0000	−0.586783	−0.293392	+	0.955992i	$0.594784\pi$
$942$	0	0
$943$	36.0000	1.17232
$944$	6.00000	0.195283
$945$	0	0
$946$	6.00000	0.195077
$947$	18.0000	0.584921	0.292461	−	0.956278i	$-0.405526\pi$
$947$	18.0000	0.584921	0.292461	+	0.956278i	$0.405526\pi$
$948$	0	0
$949$	10.0000	0.324614
$950$	20.0000	0.648886
$951$	0	0
$952$	0	0
$953$	−6.00000	−0.194359	−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000	−0.194359	−0.0971795	+	0.995267i	$0.530982\pi$
$954$	0	0
$955$	0	0
$956$	24.0000	0.776215
$957$	0	0
$958$	12.0000	0.387702
$959$	0	0
$960$	0	0
$961$	−30.0000	−0.967742
$962$	−5.00000	−0.161206
$963$	0	0
$964$	−17.0000	−0.547533
$965$	0	0
$966$	0	0
$967$	35.0000	1.12552	0.562762	−	0.826619i	$-0.309739\pi$
$967$	35.0000	1.12552	0.562762	+	0.826619i	$0.309739\pi$
$968$	−25.0000	−0.803530
$969$	0	0
$970$	0	0
$971$	36.0000	1.15529	0.577647	−	0.816286i	$-0.303971\pi$
$971$	36.0000	1.15529	0.577647	+	0.816286i	$0.303971\pi$
$972$	0	0
$973$	0	0
$974$	40.0000	1.28168
$975$	0	0
$976$	1.00000	0.0320092
$977$	6.00000	0.191957	0.0959785	−	0.995383i	$-0.469402\pi$
$977$	6.00000	0.191957	0.0959785	+	0.995383i	$0.469402\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	0	0
$982$	30.0000	0.957338
$983$	24.0000	0.765481	0.382741	−	0.923856i	$-0.374980\pi$
$983$	24.0000	0.765481	0.382741	+	0.923856i	$0.374980\pi$
$984$	0	0
$985$	0	0
$986$	36.0000	1.14647
$987$	0	0
$988$	−20.0000	−0.636285
$989$	−6.00000	−0.190789
$990$	0	0
$991$	5.00000	0.158830	0.0794151	−	0.996842i	$-0.474695\pi$
$991$	5.00000	0.158830	0.0794151	+	0.996842i	$0.474695\pi$
$992$	−1.00000	−0.0317500
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	−23.0000	−0.728417	−0.364209	−	0.931317i	$-0.618661\pi$
$997$	−23.0000	−0.728417	−0.364209	+	0.931317i	$0.618661\pi$
$998$	25.0000	0.791361
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.a.g.1.1		1
3.2	odd	2		2646.2.a.w.1.1		1
7.3	odd	6		378.2.g.e.163.1	yes	2
7.5	odd	6		378.2.g.e.109.1	yes	2
7.6	odd	2		2646.2.a.h.1.1		1
21.5	even	6		378.2.g.b.109.1	✓	2
21.17	even	6		378.2.g.b.163.1	yes	2
21.20	even	2		2646.2.a.x.1.1		1
63.5	even	6		1134.2.e.m.865.1		2
63.31	odd	6		1134.2.h.n.541.1		2
63.38	even	6		1134.2.e.m.919.1		2
63.40	odd	6		1134.2.e.c.865.1		2
63.47	even	6		1134.2.h.d.109.1		2
63.52	odd	6		1134.2.e.c.919.1		2
63.59	even	6		1134.2.h.d.541.1		2
63.61	odd	6		1134.2.h.n.109.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.g.b.109.1	✓	2	21.5	even	6
378.2.g.b.163.1	yes	2	21.17	even	6
378.2.g.e.109.1	yes	2	7.5	odd	6
378.2.g.e.163.1	yes	2	7.3	odd	6
1134.2.e.c.865.1		2	63.40	odd	6
1134.2.e.c.919.1		2	63.52	odd	6
1134.2.e.m.865.1		2	63.5	even	6
1134.2.e.m.919.1		2	63.38	even	6
1134.2.h.d.109.1		2	63.47	even	6
1134.2.h.d.541.1		2	63.59	even	6
1134.2.h.n.109.1		2	63.61	odd	6
1134.2.h.n.541.1		2	63.31	odd	6
2646.2.a.g.1.1		1	1.1	even	1	trivial
2646.2.a.h.1.1		1	7.6	odd	2
2646.2.a.w.1.1		1	3.2	odd	2
2646.2.a.x.1.1		1	21.20	even	2

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:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2646.a (trivial)

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