LMFDB - Embedded newform 297.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [297,2,Mod(1,297)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(297, 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("297.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.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:	$2.37155694003$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	297.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-2.00000 q^{2} +2.00000 q^{4} -2.00000 q^{5} +1.00000 q^{7} +O(q^{10})$

$q-2.00000 q^{2} +2.00000 q^{4} -2.00000 q^{5} +1.00000 q^{7} +4.00000 q^{10} +1.00000 q^{11} -5.00000 q^{13} -2.00000 q^{14} -4.00000 q^{16} -2.00000 q^{17} +3.00000 q^{19} -4.00000 q^{20} -2.00000 q^{22} -4.00000 q^{23} -1.00000 q^{25} +10.0000 q^{26} +2.00000 q^{28} -6.00000 q^{29} -8.00000 q^{31} +8.00000 q^{32} +4.00000 q^{34} -2.00000 q^{35} -9.00000 q^{37} -6.00000 q^{38} +4.00000 q^{41} +2.00000 q^{44} +8.00000 q^{46} -10.0000 q^{47} -6.00000 q^{49} +2.00000 q^{50} -10.0000 q^{52} +6.00000 q^{53} -2.00000 q^{55} +12.0000 q^{58} +14.0000 q^{59} +9.00000 q^{61} +16.0000 q^{62} -8.00000 q^{64} +10.0000 q^{65} +5.00000 q^{67} -4.00000 q^{68} +4.00000 q^{70} -12.0000 q^{71} +7.00000 q^{73} +18.0000 q^{74} +6.00000 q^{76} +1.00000 q^{77} +11.0000 q^{79} +8.00000 q^{80} -8.00000 q^{82} -12.0000 q^{83} +4.00000 q^{85} -6.00000 q^{89} -5.00000 q^{91} -8.00000 q^{92} +20.0000 q^{94} -6.00000 q^{95} -7.00000 q^{97} +12.0000 q^{98} +O(q^{100})$

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 $

$2$	−2.00000	−1.41421	−0.707107	−	0.707107i	$-0.750000\pi$
$2$	−2.00000	−1.41421	−0.707107	+	0.707107i	$0.750000\pi$
$3$	0	0
$3$	0	0
$4$	2.00000	1.00000
$5$	−2.00000	−0.894427	−0.447214	−	0.894427i	$-0.647584\pi$
$5$	−2.00000	−0.894427	−0.447214	+	0.894427i	$0.647584\pi$
$6$	0	0
$7$	1.00000	0.377964	0.188982	−	0.981981i	$-0.439481\pi$
$7$	1.00000	0.377964	0.188982	+	0.981981i	$0.439481\pi$
$8$	0	0
$9$	0	0
$10$	4.00000	1.26491
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0	0
$13$	−5.00000	−1.38675	−0.693375	−	0.720577i	$-0.743877\pi$
$13$	−5.00000	−1.38675	−0.693375	+	0.720577i	$0.743877\pi$
$14$	−2.00000	−0.534522
$15$	0	0
$16$	−4.00000	−1.00000
$17$	−2.00000	−0.485071	−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000	−0.485071	−0.242536	+	0.970143i	$0.577979\pi$
$18$	0	0
$19$	3.00000	0.688247	0.344124	−	0.938924i	$-0.388176\pi$
$19$	3.00000	0.688247	0.344124	+	0.938924i	$0.388176\pi$
$20$	−4.00000	−0.894427
$21$	0	0
$22$	−2.00000	−0.426401
$23$	−4.00000	−0.834058	−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000	−0.834058	−0.417029	+	0.908893i	$0.636929\pi$
$24$	0	0
$25$	−1.00000	−0.200000
$26$	10.0000	1.96116
$27$	0	0
$28$	2.00000	0.377964
$29$	−6.00000	−1.11417	−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000	−1.11417	−0.557086	+	0.830455i	$0.688081\pi$
$30$	0	0
$31$	−8.00000	−1.43684	−0.718421	−	0.695608i	$-0.755135\pi$
$31$	−8.00000	−1.43684	−0.718421	+	0.695608i	$0.755135\pi$
$32$	8.00000	1.41421
$33$	0	0
$34$	4.00000	0.685994
$35$	−2.00000	−0.338062
$36$	0	0
$37$	−9.00000	−1.47959	−0.739795	−	0.672832i	$-0.765078\pi$
$37$	−9.00000	−1.47959	−0.739795	+	0.672832i	$0.765078\pi$
$38$	−6.00000	−0.973329
$39$	0	0
$40$	0	0
$41$	4.00000	0.624695	0.312348	−	0.949968i	$-0.398885\pi$
$41$	4.00000	0.624695	0.312348	+	0.949968i	$0.398885\pi$
$42$	0	0
$43$	0	0		−	1.00000i	$-0.5\pi$
$43$	0	0			1.00000i	$0.5\pi$
$44$	2.00000	0.301511
$45$	0	0
$46$	8.00000	1.17954
$47$	−10.0000	−1.45865	−0.729325	−	0.684167i	$-0.760166\pi$
$47$	−10.0000	−1.45865	−0.729325	+	0.684167i	$0.760166\pi$
$48$	0	0
$49$	−6.00000	−0.857143
$50$	2.00000	0.282843
$51$	0	0
$52$	−10.0000	−1.38675
$53$	6.00000	0.824163	0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000	0.824163	0.412082	+	0.911147i	$0.364802\pi$
$54$	0	0
$55$	−2.00000	−0.269680
$56$	0	0
$57$	0	0
$58$	12.0000	1.57568
$59$	14.0000	1.82264	0.911322	−	0.411693i	$-0.135063\pi$
$59$	14.0000	1.82264	0.911322	+	0.411693i	$0.135063\pi$
$60$	0	0
$61$	9.00000	1.15233	0.576166	−	0.817333i	$-0.304548\pi$
$61$	9.00000	1.15233	0.576166	+	0.817333i	$0.304548\pi$
$62$	16.0000	2.03200
$63$	0	0
$64$	−8.00000	−1.00000
$65$	10.0000	1.24035
$66$	0	0
$67$	5.00000	0.610847	0.305424	−	0.952217i	$-0.401202\pi$
$67$	5.00000	0.610847	0.305424	+	0.952217i	$0.401202\pi$
$68$	−4.00000	−0.485071
$69$	0	0
$70$	4.00000	0.478091
$71$	−12.0000	−1.42414	−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000	−1.42414	−0.712069	+	0.702109i	$0.752242\pi$
$72$	0	0
$73$	7.00000	0.819288	0.409644	−	0.912245i	$-0.365653\pi$
$73$	7.00000	0.819288	0.409644	+	0.912245i	$0.365653\pi$
$74$	18.0000	2.09246
$75$	0	0
$76$	6.00000	0.688247
$77$	1.00000	0.113961
$78$	0	0
$79$	11.0000	1.23760	0.618798	−	0.785550i	$-0.287620\pi$
$79$	11.0000	1.23760	0.618798	+	0.785550i	$0.287620\pi$
$80$	8.00000	0.894427
$81$	0	0
$82$	−8.00000	−0.883452
$83$	−12.0000	−1.31717	−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000	−1.31717	−0.658586	+	0.752506i	$0.728845\pi$
$84$	0	0
$85$	4.00000	0.433861
$86$	0	0
$87$	0	0
$88$	0	0
$89$	−6.00000	−0.635999	−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000	−0.635999	−0.317999	+	0.948091i	$0.603011\pi$
$90$	0	0
$91$	−5.00000	−0.524142
$92$	−8.00000	−0.834058
$93$	0	0
$94$	20.0000	2.06284
$95$	−6.00000	−0.615587
$96$	0	0
$97$	−7.00000	−0.710742	−0.355371	−	0.934725i	$-0.615646\pi$
$97$	−7.00000	−0.710742	−0.355371	+	0.934725i	$0.615646\pi$
$98$	12.0000	1.21218
$99$	0	0
$100$	−2.00000	−0.200000
$101$	14.0000	1.39305	0.696526	−	0.717532i	$-0.254728\pi$
$101$	14.0000	1.39305	0.696526	+	0.717532i	$0.254728\pi$
$102$	0	0
$103$	11.0000	1.08386	0.541931	−	0.840423i	$-0.317693\pi$
$103$	11.0000	1.08386	0.541931	+	0.840423i	$0.317693\pi$
$104$	0	0
$105$	0	0
$106$	−12.0000	−1.16554
$107$	−18.0000	−1.74013	−0.870063	−	0.492941i	$-0.835922\pi$
$107$	−18.0000	−1.74013	−0.870063	+	0.492941i	$0.835922\pi$
$108$	0	0
$109$	10.0000	0.957826	0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000	0.957826	0.478913	+	0.877862i	$0.341031\pi$
$110$	4.00000	0.381385
$111$	0	0
$112$	−4.00000	−0.377964
$113$	−6.00000	−0.564433	−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000	−0.564433	−0.282216	+	0.959351i	$0.591070\pi$
$114$	0	0
$115$	8.00000	0.746004
$116$	−12.0000	−1.11417
$117$	0	0
$118$	−28.0000	−2.57761
$119$	−2.00000	−0.183340
$120$	0	0
$121$	1.00000	0.0909091
$122$	−18.0000	−1.62964
$123$	0	0
$124$	−16.0000	−1.43684
$125$	12.0000	1.07331
$126$	0	0
$127$	−16.0000	−1.41977	−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000	−1.41977	−0.709885	+	0.704317i	$0.751253\pi$
$128$	0	0
$129$	0	0
$130$	−20.0000	−1.75412
$131$	6.00000	0.524222	0.262111	−	0.965038i	$-0.415581\pi$
$131$	6.00000	0.524222	0.262111	+	0.965038i	$0.415581\pi$
$132$	0	0
$133$	3.00000	0.260133
$134$	−10.0000	−0.863868
$135$	0	0
$136$	0	0
$137$	−4.00000	−0.341743	−0.170872	−	0.985293i	$-0.554658\pi$
$137$	−4.00000	−0.341743	−0.170872	+	0.985293i	$0.554658\pi$
$138$	0	0
$139$	1.00000	0.0848189	0.0424094	−	0.999100i	$-0.486497\pi$
$139$	1.00000	0.0848189	0.0424094	+	0.999100i	$0.486497\pi$
$140$	−4.00000	−0.338062
$141$	0	0
$142$	24.0000	2.01404
$143$	−5.00000	−0.418121
$144$	0	0
$145$	12.0000	0.996546
$146$	−14.0000	−1.15865
$147$	0	0
$148$	−18.0000	−1.47959
$149$	−4.00000	−0.327693	−0.163846	−	0.986486i	$-0.552390\pi$
$149$	−4.00000	−0.327693	−0.163846	+	0.986486i	$0.552390\pi$
$150$	0	0
$151$	−13.0000	−1.05792	−0.528962	−	0.848645i	$-0.677419\pi$
$151$	−13.0000	−1.05792	−0.528962	+	0.848645i	$0.677419\pi$
$152$	0	0
$153$	0	0
$154$	−2.00000	−0.161165
$155$	16.0000	1.28515
$156$	0	0
$157$	−22.0000	−1.75579	−0.877896	−	0.478852i	$-0.841053\pi$
$157$	−22.0000	−1.75579	−0.877896	+	0.478852i	$0.841053\pi$
$158$	−22.0000	−1.75023
$159$	0	0
$160$	−16.0000	−1.26491
$161$	−4.00000	−0.315244
$162$	0	0
$163$	7.00000	0.548282	0.274141	−	0.961689i	$-0.411606\pi$
$163$	7.00000	0.548282	0.274141	+	0.961689i	$0.411606\pi$
$164$	8.00000	0.624695
$165$	0	0
$166$	24.0000	1.86276
$167$	6.00000	0.464294	0.232147	−	0.972681i	$-0.425425\pi$
$167$	6.00000	0.464294	0.232147	+	0.972681i	$0.425425\pi$
$168$	0	0
$169$	12.0000	0.923077
$170$	−8.00000	−0.613572
$171$	0	0
$172$	0	0
$173$	24.0000	1.82469	0.912343	−	0.409426i	$-0.134271\pi$
$173$	24.0000	1.82469	0.912343	+	0.409426i	$0.134271\pi$
$174$	0	0
$175$	−1.00000	−0.0755929
$176$	−4.00000	−0.301511
$177$	0	0
$178$	12.0000	0.899438
$179$	6.00000	0.448461	0.224231	−	0.974536i	$-0.428013\pi$
$179$	6.00000	0.448461	0.224231	+	0.974536i	$0.428013\pi$
$180$	0	0
$181$	13.0000	0.966282	0.483141	−	0.875542i	$-0.339496\pi$
$181$	13.0000	0.966282	0.483141	+	0.875542i	$0.339496\pi$
$182$	10.0000	0.741249
$183$	0	0
$184$	0	0
$185$	18.0000	1.32339
$186$	0	0
$187$	−2.00000	−0.146254
$188$	−20.0000	−1.45865
$189$	0	0
$190$	12.0000	0.870572
$191$	−16.0000	−1.15772	−0.578860	−	0.815427i	$-0.696502\pi$
$191$	−16.0000	−1.15772	−0.578860	+	0.815427i	$0.696502\pi$
$192$	0	0
$193$	13.0000	0.935760	0.467880	−	0.883792i	$-0.345018\pi$
$193$	13.0000	0.935760	0.467880	+	0.883792i	$0.345018\pi$
$194$	14.0000	1.00514
$195$	0	0
$196$	−12.0000	−0.857143
$197$	−26.0000	−1.85242	−0.926212	−	0.377004i	$-0.876954\pi$
$197$	−26.0000	−1.85242	−0.926212	+	0.377004i	$0.876954\pi$
$198$	0	0
$199$	3.00000	0.212664	0.106332	−	0.994331i	$-0.466089\pi$
$199$	3.00000	0.212664	0.106332	+	0.994331i	$0.466089\pi$
$200$	0	0
$201$	0	0
$202$	−28.0000	−1.97007
$203$	−6.00000	−0.421117
$204$	0	0
$205$	−8.00000	−0.558744
$206$	−22.0000	−1.53281
$207$	0	0
$208$	20.0000	1.38675
$209$	3.00000	0.207514
$210$	0	0
$211$	−3.00000	−0.206529	−0.103264	−	0.994654i	$-0.532929\pi$
$211$	−3.00000	−0.206529	−0.103264	+	0.994654i	$0.532929\pi$
$212$	12.0000	0.824163
$213$	0	0
$214$	36.0000	2.46091
$215$	0	0
$216$	0	0
$217$	−8.00000	−0.543075
$218$	−20.0000	−1.35457
$219$	0	0
$220$	−4.00000	−0.269680
$221$	10.0000	0.672673
$222$	0	0
$223$	4.00000	0.267860	0.133930	−	0.990991i	$-0.457240\pi$
$223$	4.00000	0.267860	0.133930	+	0.990991i	$0.457240\pi$
$224$	8.00000	0.534522
$225$	0	0
$226$	12.0000	0.798228
$227$	−18.0000	−1.19470	−0.597351	−	0.801980i	$-0.703780\pi$
$227$	−18.0000	−1.19470	−0.597351	+	0.801980i	$0.703780\pi$
$228$	0	0
$229$	6.00000	0.396491	0.198246	−	0.980152i	$-0.436476\pi$
$229$	6.00000	0.396491	0.198246	+	0.980152i	$0.436476\pi$
$230$	−16.0000	−1.05501
$231$	0	0
$232$	0	0
$233$	6.00000	0.393073	0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000	0.393073	0.196537	+	0.980497i	$0.437031\pi$
$234$	0	0
$235$	20.0000	1.30466
$236$	28.0000	1.82264
$237$	0	0
$238$	4.00000	0.259281
$239$	0	0		−	1.00000i	$-0.5\pi$
$239$	0	0			1.00000i	$0.5\pi$
$240$	0	0
$241$	−17.0000	−1.09507	−0.547533	−	0.836784i	$-0.684433\pi$
$241$	−17.0000	−1.09507	−0.547533	+	0.836784i	$0.684433\pi$
$242$	−2.00000	−0.128565
$243$	0	0
$244$	18.0000	1.15233
$245$	12.0000	0.766652
$246$	0	0
$247$	−15.0000	−0.954427
$248$	0	0
$249$	0	0
$250$	−24.0000	−1.51789
$251$	10.0000	0.631194	0.315597	−	0.948893i	$-0.397795\pi$
$251$	10.0000	0.631194	0.315597	+	0.948893i	$0.397795\pi$
$252$	0	0
$253$	−4.00000	−0.251478
$254$	32.0000	2.00786
$255$	0	0
$256$	16.0000	1.00000
$257$	22.0000	1.37232	0.686161	−	0.727450i	$-0.259294\pi$
$257$	22.0000	1.37232	0.686161	+	0.727450i	$0.259294\pi$
$258$	0	0
$259$	−9.00000	−0.559233
$260$	20.0000	1.24035
$261$	0	0
$262$	−12.0000	−0.741362
$263$	−10.0000	−0.616626	−0.308313	−	0.951285i	$-0.599764\pi$
$263$	−10.0000	−0.616626	−0.308313	+	0.951285i	$0.599764\pi$
$264$	0	0
$265$	−12.0000	−0.737154
$266$	−6.00000	−0.367884
$267$	0	0
$268$	10.0000	0.610847
$269$	28.0000	1.70719	0.853595	−	0.520937i	$-0.174417\pi$
$269$	28.0000	1.70719	0.853595	+	0.520937i	$0.174417\pi$
$270$	0	0
$271$	−1.00000	−0.0607457	−0.0303728	−	0.999539i	$-0.509669\pi$
$271$	−1.00000	−0.0607457	−0.0303728	+	0.999539i	$0.509669\pi$
$272$	8.00000	0.485071
$273$	0	0
$274$	8.00000	0.483298
$275$	−1.00000	−0.0603023
$276$	0	0
$277$	22.0000	1.32185	0.660926	−	0.750451i	$-0.270164\pi$
$277$	22.0000	1.32185	0.660926	+	0.750451i	$0.270164\pi$
$278$	−2.00000	−0.119952
$279$	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
$283$	4.00000	0.237775	0.118888	−	0.992908i	$-0.462067\pi$
$283$	4.00000	0.237775	0.118888	+	0.992908i	$0.462067\pi$
$284$	−24.0000	−1.42414
$285$	0	0
$286$	10.0000	0.591312
$287$	4.00000	0.236113
$288$	0	0
$289$	−13.0000	−0.764706
$290$	−24.0000	−1.40933
$291$	0	0
$292$	14.0000	0.819288
$293$	−6.00000	−0.350524	−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000	−0.350524	−0.175262	+	0.984522i	$0.556077\pi$
$294$	0	0
$295$	−28.0000	−1.63022
$296$	0	0
$297$	0	0
$298$	8.00000	0.463428
$299$	20.0000	1.15663
$300$	0	0
$301$	0	0
$302$	26.0000	1.49613
$303$	0	0
$304$	−12.0000	−0.688247
$305$	−18.0000	−1.03068
$306$	0	0
$307$	−28.0000	−1.59804	−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000	−1.59804	−0.799022	+	0.601302i	$0.794649\pi$
$308$	2.00000	0.113961
$309$	0	0
$310$	−32.0000	−1.81748
$311$	6.00000	0.340229	0.170114	−	0.985424i	$-0.445586\pi$
$311$	6.00000	0.340229	0.170114	+	0.985424i	$0.445586\pi$
$312$	0	0
$313$	−13.0000	−0.734803	−0.367402	−	0.930062i	$-0.619753\pi$
$313$	−13.0000	−0.734803	−0.367402	+	0.930062i	$0.619753\pi$
$314$	44.0000	2.48306
$315$	0	0
$316$	22.0000	1.23760
$317$	22.0000	1.23564	0.617822	−	0.786318i	$-0.288015\pi$
$317$	22.0000	1.23564	0.617822	+	0.786318i	$0.288015\pi$
$318$	0	0
$319$	−6.00000	−0.335936
$320$	16.0000	0.894427
$321$	0	0
$322$	8.00000	0.445823
$323$	−6.00000	−0.333849
$324$	0	0
$325$	5.00000	0.277350
$326$	−14.0000	−0.775388
$327$	0	0
$328$	0	0
$329$	−10.0000	−0.551318
$330$	0	0
$331$	−5.00000	−0.274825	−0.137412	−	0.990514i	$-0.543879\pi$
$331$	−5.00000	−0.274825	−0.137412	+	0.990514i	$0.543879\pi$
$332$	−24.0000	−1.31717
$333$	0	0
$334$	−12.0000	−0.656611
$335$	−10.0000	−0.546358
$336$	0	0
$337$	23.0000	1.25289	0.626445	−	0.779466i	$-0.284509\pi$
$337$	23.0000	1.25289	0.626445	+	0.779466i	$0.284509\pi$
$338$	−24.0000	−1.30543
$339$	0	0
$340$	8.00000	0.433861
$341$	−8.00000	−0.433224
$342$	0	0
$343$	−13.0000	−0.701934
$344$	0	0
$345$	0	0
$346$	−48.0000	−2.58050
$347$	22.0000	1.18102	0.590511	−	0.807030i	$-0.298926\pi$
$347$	22.0000	1.18102	0.590511	+	0.807030i	$0.298926\pi$
$348$	0	0
$349$	−3.00000	−0.160586	−0.0802932	−	0.996771i	$-0.525586\pi$
$349$	−3.00000	−0.160586	−0.0802932	+	0.996771i	$0.525586\pi$
$350$	2.00000	0.106904
$351$	0	0
$352$	8.00000	0.426401
$353$	18.0000	0.958043	0.479022	−	0.877803i	$-0.340992\pi$
$353$	18.0000	0.958043	0.479022	+	0.877803i	$0.340992\pi$
$354$	0	0
$355$	24.0000	1.27379
$356$	−12.0000	−0.635999
$357$	0	0
$358$	−12.0000	−0.634220
$359$	−20.0000	−1.05556	−0.527780	−	0.849381i	$-0.676975\pi$
$359$	−20.0000	−1.05556	−0.527780	+	0.849381i	$0.676975\pi$
$360$	0	0
$361$	−10.0000	−0.526316
$362$	−26.0000	−1.36653
$363$	0	0
$364$	−10.0000	−0.524142
$365$	−14.0000	−0.732793
$366$	0	0
$367$	−5.00000	−0.260998	−0.130499	−	0.991448i	$-0.541658\pi$
$367$	−5.00000	−0.260998	−0.130499	+	0.991448i	$0.541658\pi$
$368$	16.0000	0.834058
$369$	0	0
$370$	−36.0000	−1.87155
$371$	6.00000	0.311504
$372$	0	0
$373$	1.00000	0.0517780	0.0258890	−	0.999665i	$-0.491758\pi$
$373$	1.00000	0.0517780	0.0258890	+	0.999665i	$0.491758\pi$
$374$	4.00000	0.206835
$375$	0	0
$376$	0	0
$377$	30.0000	1.54508
$378$	0	0
$379$	−11.0000	−0.565032	−0.282516	−	0.959263i	$-0.591169\pi$
$379$	−11.0000	−0.565032	−0.282516	+	0.959263i	$0.591169\pi$
$380$	−12.0000	−0.615587
$381$	0	0
$382$	32.0000	1.63726
$383$	−10.0000	−0.510976	−0.255488	−	0.966812i	$-0.582236\pi$
$383$	−10.0000	−0.510976	−0.255488	+	0.966812i	$0.582236\pi$
$384$	0	0
$385$	−2.00000	−0.101929
$386$	−26.0000	−1.32337
$387$	0	0
$388$	−14.0000	−0.710742
$389$	−24.0000	−1.21685	−0.608424	−	0.793612i	$-0.708198\pi$
$389$	−24.0000	−1.21685	−0.608424	+	0.793612i	$0.708198\pi$
$390$	0	0
$391$	8.00000	0.404577
$392$	0	0
$393$	0	0
$394$	52.0000	2.61972
$395$	−22.0000	−1.10694
$396$	0	0
$397$	−14.0000	−0.702640	−0.351320	−	0.936255i	$-0.614267\pi$
$397$	−14.0000	−0.702640	−0.351320	+	0.936255i	$0.614267\pi$
$398$	−6.00000	−0.300753
$399$	0	0
$400$	4.00000	0.200000
$401$	−16.0000	−0.799002	−0.399501	−	0.916733i	$-0.630817\pi$
$401$	−16.0000	−0.799002	−0.399501	+	0.916733i	$0.630817\pi$
$402$	0	0
$403$	40.0000	1.99254
$404$	28.0000	1.39305
$405$	0	0
$406$	12.0000	0.595550
$407$	−9.00000	−0.446113
$408$	0	0
$409$	3.00000	0.148340	0.0741702	−	0.997246i	$-0.476369\pi$
$409$	3.00000	0.148340	0.0741702	+	0.997246i	$0.476369\pi$
$410$	16.0000	0.790184
$411$	0	0
$412$	22.0000	1.08386
$413$	14.0000	0.688895
$414$	0	0
$415$	24.0000	1.17811
$416$	−40.0000	−1.96116
$417$	0	0
$418$	−6.00000	−0.293470
$419$	20.0000	0.977064	0.488532	−	0.872546i	$-0.337533\pi$
$419$	20.0000	0.977064	0.488532	+	0.872546i	$0.337533\pi$
$420$	0	0
$421$	−35.0000	−1.70580	−0.852898	−	0.522078i	$-0.825157\pi$
$421$	−35.0000	−1.70580	−0.852898	+	0.522078i	$0.825157\pi$
$422$	6.00000	0.292075
$423$	0	0
$424$	0	0
$425$	2.00000	0.0970143
$426$	0	0
$427$	9.00000	0.435541
$428$	−36.0000	−1.74013
$429$	0	0
$430$	0	0
$431$	0	0		−	1.00000i	$-0.5\pi$
$431$	0	0			1.00000i	$0.5\pi$
$432$	0	0
$433$	−2.00000	−0.0961139	−0.0480569	−	0.998845i	$-0.515303\pi$
$433$	−2.00000	−0.0961139	−0.0480569	+	0.998845i	$0.515303\pi$
$434$	16.0000	0.768025
$435$	0	0
$436$	20.0000	0.957826
$437$	−12.0000	−0.574038
$438$	0	0
$439$	16.0000	0.763638	0.381819	−	0.924237i	$-0.375298\pi$
$439$	16.0000	0.763638	0.381819	+	0.924237i	$0.375298\pi$
$440$	0	0
$441$	0	0
$442$	−20.0000	−0.951303
$443$	−26.0000	−1.23530	−0.617649	−	0.786454i	$-0.711915\pi$
$443$	−26.0000	−1.23530	−0.617649	+	0.786454i	$0.711915\pi$
$444$	0	0
$445$	12.0000	0.568855
$446$	−8.00000	−0.378811
$447$	0	0
$448$	−8.00000	−0.377964
$449$	20.0000	0.943858	0.471929	−	0.881636i	$-0.343558\pi$
$449$	20.0000	0.943858	0.471929	+	0.881636i	$0.343558\pi$
$450$	0	0
$451$	4.00000	0.188353
$452$	−12.0000	−0.564433
$453$	0	0
$454$	36.0000	1.68956
$455$	10.0000	0.468807
$456$	0	0
$457$	6.00000	0.280668	0.140334	−	0.990104i	$-0.455182\pi$
$457$	6.00000	0.280668	0.140334	+	0.990104i	$0.455182\pi$
$458$	−12.0000	−0.560723
$459$	0	0
$460$	16.0000	0.746004
$461$	−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
$463$	7.00000	0.325318	0.162659	−	0.986682i	$-0.447993\pi$
$463$	7.00000	0.325318	0.162659	+	0.986682i	$0.447993\pi$
$464$	24.0000	1.11417
$465$	0	0
$466$	−12.0000	−0.555889
$467$	12.0000	0.555294	0.277647	−	0.960683i	$-0.410445\pi$
$467$	12.0000	0.555294	0.277647	+	0.960683i	$0.410445\pi$
$468$	0	0
$469$	5.00000	0.230879
$470$	−40.0000	−1.84506
$471$	0	0
$472$	0	0
$473$	0	0
$474$	0	0
$475$	−3.00000	−0.137649
$476$	−4.00000	−0.183340
$477$	0	0
$478$	0	0
$479$	−10.0000	−0.456912	−0.228456	−	0.973554i	$-0.573368\pi$
$479$	−10.0000	−0.456912	−0.228456	+	0.973554i	$0.573368\pi$
$480$	0	0
$481$	45.0000	2.05182
$482$	34.0000	1.54866
$483$	0	0
$484$	2.00000	0.0909091
$485$	14.0000	0.635707
$486$	0	0
$487$	−1.00000	−0.0453143	−0.0226572	−	0.999743i	$-0.507213\pi$
$487$	−1.00000	−0.0453143	−0.0226572	+	0.999743i	$0.507213\pi$
$488$	0	0
$489$	0	0
$490$	−24.0000	−1.08421
$491$	−2.00000	−0.0902587	−0.0451294	−	0.998981i	$-0.514370\pi$
$491$	−2.00000	−0.0902587	−0.0451294	+	0.998981i	$0.514370\pi$
$492$	0	0
$493$	12.0000	0.540453
$494$	30.0000	1.34976
$495$	0	0
$496$	32.0000	1.43684
$497$	−12.0000	−0.538274
$498$	0	0
$499$	−28.0000	−1.25345	−0.626726	−	0.779240i	$-0.715605\pi$
$499$	−28.0000	−1.25345	−0.626726	+	0.779240i	$0.715605\pi$
$500$	24.0000	1.07331
$501$	0	0
$502$	−20.0000	−0.892644
$503$	−8.00000	−0.356702	−0.178351	−	0.983967i	$-0.557076\pi$
$503$	−8.00000	−0.356702	−0.178351	+	0.983967i	$0.557076\pi$
$504$	0	0
$505$	−28.0000	−1.24598
$506$	8.00000	0.355643
$507$	0	0
$508$	−32.0000	−1.41977
$509$	−18.0000	−0.797836	−0.398918	−	0.916987i	$-0.630614\pi$
$509$	−18.0000	−0.797836	−0.398918	+	0.916987i	$0.630614\pi$
$510$	0	0
$511$	7.00000	0.309662
$512$	−32.0000	−1.41421
$513$	0	0
$514$	−44.0000	−1.94076
$515$	−22.0000	−0.969436
$516$	0	0
$517$	−10.0000	−0.439799
$518$	18.0000	0.790875
$519$	0	0
$520$	0	0
$521$	−24.0000	−1.05146	−0.525730	−	0.850652i	$-0.676208\pi$
$521$	−24.0000	−1.05146	−0.525730	+	0.850652i	$0.676208\pi$
$522$	0	0
$523$	11.0000	0.480996	0.240498	−	0.970650i	$-0.422689\pi$
$523$	11.0000	0.480996	0.240498	+	0.970650i	$0.422689\pi$
$524$	12.0000	0.524222
$525$	0	0
$526$	20.0000	0.872041
$527$	16.0000	0.696971
$528$	0	0
$529$	−7.00000	−0.304348
$530$	24.0000	1.04249
$531$	0	0
$532$	6.00000	0.260133
$533$	−20.0000	−0.866296
$534$	0	0
$535$	36.0000	1.55642
$536$	0	0
$537$	0	0
$538$	−56.0000	−2.41433
$539$	−6.00000	−0.258438
$540$	0	0
$541$	−41.0000	−1.76273	−0.881364	−	0.472438i	$-0.843374\pi$
$541$	−41.0000	−1.76273	−0.881364	+	0.472438i	$0.843374\pi$
$542$	2.00000	0.0859074
$543$	0	0
$544$	−16.0000	−0.685994
$545$	−20.0000	−0.856706
$546$	0	0
$547$	−7.00000	−0.299298	−0.149649	−	0.988739i	$-0.547814\pi$
$547$	−7.00000	−0.299298	−0.149649	+	0.988739i	$0.547814\pi$
$548$	−8.00000	−0.341743
$549$	0	0
$550$	2.00000	0.0852803
$551$	−18.0000	−0.766826
$552$	0	0
$553$	11.0000	0.467768
$554$	−44.0000	−1.86938
$555$	0	0
$556$	2.00000	0.0848189
$557$	10.0000	0.423714	0.211857	−	0.977301i	$-0.432049\pi$
$557$	10.0000	0.423714	0.211857	+	0.977301i	$0.432049\pi$
$558$	0	0
$559$	0	0
$560$	8.00000	0.338062
$561$	0	0
$562$	−24.0000	−1.01238
$563$	4.00000	0.168580	0.0842900	−	0.996441i	$-0.473138\pi$
$563$	4.00000	0.168580	0.0842900	+	0.996441i	$0.473138\pi$
$564$	0	0
$565$	12.0000	0.504844
$566$	−8.00000	−0.336265
$567$	0	0
$568$	0	0
$569$	24.0000	1.00613	0.503066	−	0.864248i	$-0.332205\pi$
$569$	24.0000	1.00613	0.503066	+	0.864248i	$0.332205\pi$
$570$	0	0
$571$	−37.0000	−1.54840	−0.774201	−	0.632940i	$-0.781848\pi$
$571$	−37.0000	−1.54840	−0.774201	+	0.632940i	$0.781848\pi$
$572$	−10.0000	−0.418121
$573$	0	0
$574$	−8.00000	−0.333914
$575$	4.00000	0.166812
$576$	0	0
$577$	27.0000	1.12402	0.562012	−	0.827129i	$-0.310027\pi$
$577$	27.0000	1.12402	0.562012	+	0.827129i	$0.310027\pi$
$578$	26.0000	1.08146
$579$	0	0
$580$	24.0000	0.996546
$581$	−12.0000	−0.497844
$582$	0	0
$583$	6.00000	0.248495
$584$	0	0
$585$	0	0
$586$	12.0000	0.495715
$587$	22.0000	0.908037	0.454019	−	0.890992i	$-0.349990\pi$
$587$	22.0000	0.908037	0.454019	+	0.890992i	$0.349990\pi$
$588$	0	0
$589$	−24.0000	−0.988903
$590$	56.0000	2.30548
$591$	0	0
$592$	36.0000	1.47959
$593$	−4.00000	−0.164260	−0.0821302	−	0.996622i	$-0.526172\pi$
$593$	−4.00000	−0.164260	−0.0821302	+	0.996622i	$0.526172\pi$
$594$	0	0
$595$	4.00000	0.163984
$596$	−8.00000	−0.327693
$597$	0	0
$598$	−40.0000	−1.63572
$599$	−32.0000	−1.30748	−0.653742	−	0.756717i	$-0.726802\pi$
$599$	−32.0000	−1.30748	−0.653742	+	0.756717i	$0.726802\pi$
$600$	0	0
$601$	−46.0000	−1.87638	−0.938190	−	0.346122i	$-0.887498\pi$
$601$	−46.0000	−1.87638	−0.938190	+	0.346122i	$0.887498\pi$
$602$	0	0
$603$	0	0
$604$	−26.0000	−1.05792
$605$	−2.00000	−0.0813116
$606$	0	0
$607$	17.0000	0.690009	0.345004	−	0.938601i	$-0.387877\pi$
$607$	17.0000	0.690009	0.345004	+	0.938601i	$0.387877\pi$
$608$	24.0000	0.973329
$609$	0	0
$610$	36.0000	1.45760
$611$	50.0000	2.02278
$612$	0	0
$613$	41.0000	1.65597	0.827987	−	0.560747i	$-0.189486\pi$
$613$	41.0000	1.65597	0.827987	+	0.560747i	$0.189486\pi$
$614$	56.0000	2.25998
$615$	0	0
$616$	0	0
$617$	−48.0000	−1.93241	−0.966204	−	0.257780i	$-0.917009\pi$
$617$	−48.0000	−1.93241	−0.966204	+	0.257780i	$0.917009\pi$
$618$	0	0
$619$	−43.0000	−1.72832	−0.864158	−	0.503221i	$-0.832148\pi$
$619$	−43.0000	−1.72832	−0.864158	+	0.503221i	$0.832148\pi$
$620$	32.0000	1.28515
$621$	0	0
$622$	−12.0000	−0.481156
$623$	−6.00000	−0.240385
$624$	0	0
$625$	−19.0000	−0.760000
$626$	26.0000	1.03917
$627$	0	0
$628$	−44.0000	−1.75579
$629$	18.0000	0.717707
$630$	0	0
$631$	49.0000	1.95066	0.975330	−	0.220754i	$-0.0708517\pi$
$631$	49.0000	1.95066	0.975330	+	0.220754i	$0.0708517\pi$
$632$	0	0
$633$	0	0
$634$	−44.0000	−1.74746
$635$	32.0000	1.26988
$636$	0	0
$637$	30.0000	1.18864
$638$	12.0000	0.475085
$639$	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
$643$	−4.00000	−0.157745	−0.0788723	−	0.996885i	$-0.525132\pi$
$643$	−4.00000	−0.157745	−0.0788723	+	0.996885i	$0.525132\pi$
$644$	−8.00000	−0.315244
$645$	0	0
$646$	12.0000	0.472134
$647$	−16.0000	−0.629025	−0.314512	−	0.949253i	$-0.601841\pi$
$647$	−16.0000	−0.629025	−0.314512	+	0.949253i	$0.601841\pi$
$648$	0	0
$649$	14.0000	0.549548
$650$	−10.0000	−0.392232
$651$	0	0
$652$	14.0000	0.548282
$653$	4.00000	0.156532	0.0782660	−	0.996933i	$-0.475062\pi$
$653$	4.00000	0.156532	0.0782660	+	0.996933i	$0.475062\pi$
$654$	0	0
$655$	−12.0000	−0.468879
$656$	−16.0000	−0.624695
$657$	0	0
$658$	20.0000	0.779681
$659$	34.0000	1.32445	0.662226	−	0.749304i	$-0.269612\pi$
$659$	34.0000	1.32445	0.662226	+	0.749304i	$0.269612\pi$
$660$	0	0
$661$	−5.00000	−0.194477	−0.0972387	−	0.995261i	$-0.531001\pi$
$661$	−5.00000	−0.194477	−0.0972387	+	0.995261i	$0.531001\pi$
$662$	10.0000	0.388661
$663$	0	0
$664$	0	0
$665$	−6.00000	−0.232670
$666$	0	0
$667$	24.0000	0.929284
$668$	12.0000	0.464294
$669$	0	0
$670$	20.0000	0.772667
$671$	9.00000	0.347441
$672$	0	0
$673$	41.0000	1.58043	0.790217	−	0.612827i	$-0.209968\pi$
$673$	41.0000	1.58043	0.790217	+	0.612827i	$0.209968\pi$
$674$	−46.0000	−1.77185
$675$	0	0
$676$	24.0000	0.923077
$677$	−36.0000	−1.38359	−0.691796	−	0.722093i	$-0.743180\pi$
$677$	−36.0000	−1.38359	−0.691796	+	0.722093i	$0.743180\pi$
$678$	0	0
$679$	−7.00000	−0.268635
$680$	0	0
$681$	0	0
$682$	16.0000	0.612672
$683$	14.0000	0.535695	0.267848	−	0.963461i	$-0.413688\pi$
$683$	14.0000	0.535695	0.267848	+	0.963461i	$0.413688\pi$
$684$	0	0
$685$	8.00000	0.305664
$686$	26.0000	0.992685
$687$	0	0
$688$	0	0
$689$	−30.0000	−1.14291
$690$	0	0
$691$	−16.0000	−0.608669	−0.304334	−	0.952565i	$-0.598434\pi$
$691$	−16.0000	−0.608669	−0.304334	+	0.952565i	$0.598434\pi$
$692$	48.0000	1.82469
$693$	0	0
$694$	−44.0000	−1.67022
$695$	−2.00000	−0.0758643
$696$	0	0
$697$	−8.00000	−0.303022
$698$	6.00000	0.227103
$699$	0	0
$700$	−2.00000	−0.0755929
$701$	38.0000	1.43524	0.717620	−	0.696435i	$-0.245231\pi$
$701$	38.0000	1.43524	0.717620	+	0.696435i	$0.245231\pi$
$702$	0	0
$703$	−27.0000	−1.01832
$704$	−8.00000	−0.301511
$705$	0	0
$706$	−36.0000	−1.35488
$707$	14.0000	0.526524
$708$	0	0
$709$	17.0000	0.638448	0.319224	−	0.947679i	$-0.396578\pi$
$709$	17.0000	0.638448	0.319224	+	0.947679i	$0.396578\pi$
$710$	−48.0000	−1.80141
$711$	0	0
$712$	0	0
$713$	32.0000	1.19841
$714$	0	0
$715$	10.0000	0.373979
$716$	12.0000	0.448461
$717$	0	0
$718$	40.0000	1.49279
$719$	−42.0000	−1.56634	−0.783168	−	0.621810i	$-0.786397\pi$
$719$	−42.0000	−1.56634	−0.783168	+	0.621810i	$0.786397\pi$
$720$	0	0
$721$	11.0000	0.409661
$722$	20.0000	0.744323
$723$	0	0
$724$	26.0000	0.966282
$725$	6.00000	0.222834
$726$	0	0
$727$	24.0000	0.890111	0.445055	−	0.895503i	$-0.353184\pi$
$727$	24.0000	0.890111	0.445055	+	0.895503i	$0.353184\pi$
$728$	0	0
$729$	0	0
$730$	28.0000	1.03633
$731$	0	0
$732$	0	0
$733$	−6.00000	−0.221615	−0.110808	−	0.993842i	$-0.535344\pi$
$733$	−6.00000	−0.221615	−0.110808	+	0.993842i	$0.535344\pi$
$734$	10.0000	0.369107
$735$	0	0
$736$	−32.0000	−1.17954
$737$	5.00000	0.184177
$738$	0	0
$739$	44.0000	1.61857	0.809283	−	0.587419i	$-0.199856\pi$
$739$	44.0000	1.61857	0.809283	+	0.587419i	$0.199856\pi$
$740$	36.0000	1.32339
$741$	0	0
$742$	−12.0000	−0.440534
$743$	−38.0000	−1.39408	−0.697042	−	0.717030i	$-0.745501\pi$
$743$	−38.0000	−1.39408	−0.697042	+	0.717030i	$0.745501\pi$
$744$	0	0
$745$	8.00000	0.293097
$746$	−2.00000	−0.0732252
$747$	0	0
$748$	−4.00000	−0.146254
$749$	−18.0000	−0.657706
$750$	0	0
$751$	−35.0000	−1.27717	−0.638584	−	0.769552i	$-0.720480\pi$
$751$	−35.0000	−1.27717	−0.638584	+	0.769552i	$0.720480\pi$
$752$	40.0000	1.45865
$753$	0	0
$754$	−60.0000	−2.18507
$755$	26.0000	0.946237
$756$	0	0
$757$	17.0000	0.617876	0.308938	−	0.951082i	$-0.400027\pi$
$757$	17.0000	0.617876	0.308938	+	0.951082i	$0.400027\pi$
$758$	22.0000	0.799076
$759$	0	0
$760$	0	0
$761$	−36.0000	−1.30500	−0.652499	−	0.757789i	$-0.726280\pi$
$761$	−36.0000	−1.30500	−0.652499	+	0.757789i	$0.726280\pi$
$762$	0	0
$763$	10.0000	0.362024
$764$	−32.0000	−1.15772
$765$	0	0
$766$	20.0000	0.722629
$767$	−70.0000	−2.52755
$768$	0	0
$769$	−7.00000	−0.252426	−0.126213	−	0.992003i	$-0.540282\pi$
$769$	−7.00000	−0.252426	−0.126213	+	0.992003i	$0.540282\pi$
$770$	4.00000	0.144150
$771$	0	0
$772$	26.0000	0.935760
$773$	−42.0000	−1.51064	−0.755318	−	0.655359i	$-0.772517\pi$
$773$	−42.0000	−1.51064	−0.755318	+	0.655359i	$0.772517\pi$
$774$	0	0
$775$	8.00000	0.287368
$776$	0	0
$777$	0	0
$778$	48.0000	1.72088
$779$	12.0000	0.429945
$780$	0	0
$781$	−12.0000	−0.429394
$782$	−16.0000	−0.572159
$783$	0	0
$784$	24.0000	0.857143
$785$	44.0000	1.57043
$786$	0	0
$787$	−29.0000	−1.03374	−0.516869	−	0.856064i	$-0.672903\pi$
$787$	−29.0000	−1.03374	−0.516869	+	0.856064i	$0.672903\pi$
$788$	−52.0000	−1.85242
$789$	0	0
$790$	44.0000	1.56545
$791$	−6.00000	−0.213335
$792$	0	0
$793$	−45.0000	−1.59800
$794$	28.0000	0.993683
$795$	0	0
$796$	6.00000	0.212664
$797$	−28.0000	−0.991811	−0.495905	−	0.868377i	$-0.665164\pi$
$797$	−28.0000	−0.991811	−0.495905	+	0.868377i	$0.665164\pi$
$798$	0	0
$799$	20.0000	0.707549
$800$	−8.00000	−0.282843
$801$	0	0
$802$	32.0000	1.12996
$803$	7.00000	0.247025
$804$	0	0
$805$	8.00000	0.281963
$806$	−80.0000	−2.81788
$807$	0	0
$808$	0	0
$809$	−42.0000	−1.47664	−0.738321	−	0.674450i	$-0.764381\pi$
$809$	−42.0000	−1.47664	−0.738321	+	0.674450i	$0.764381\pi$
$810$	0	0
$811$	−20.0000	−0.702295	−0.351147	−	0.936320i	$-0.614208\pi$
$811$	−20.0000	−0.702295	−0.351147	+	0.936320i	$0.614208\pi$
$812$	−12.0000	−0.421117
$813$	0	0
$814$	18.0000	0.630900
$815$	−14.0000	−0.490399
$816$	0	0
$817$	0	0
$818$	−6.00000	−0.209785
$819$	0	0
$820$	−16.0000	−0.558744
$821$	40.0000	1.39601	0.698005	−	0.716093i	$-0.254071\pi$
$821$	40.0000	1.39601	0.698005	+	0.716093i	$0.254071\pi$
$822$	0	0
$823$	21.0000	0.732014	0.366007	−	0.930612i	$-0.380725\pi$
$823$	21.0000	0.732014	0.366007	+	0.930612i	$0.380725\pi$
$824$	0	0
$825$	0	0
$826$	−28.0000	−0.974245
$827$	−10.0000	−0.347734	−0.173867	−	0.984769i	$-0.555626\pi$
$827$	−10.0000	−0.347734	−0.173867	+	0.984769i	$0.555626\pi$
$828$	0	0
$829$	−11.0000	−0.382046	−0.191023	−	0.981586i	$-0.561180\pi$
$829$	−11.0000	−0.382046	−0.191023	+	0.981586i	$0.561180\pi$
$830$	−48.0000	−1.66610
$831$	0	0
$832$	40.0000	1.38675
$833$	12.0000	0.415775
$834$	0	0
$835$	−12.0000	−0.415277
$836$	6.00000	0.207514
$837$	0	0
$838$	−40.0000	−1.38178
$839$	4.00000	0.138095	0.0690477	−	0.997613i	$-0.478004\pi$
$839$	4.00000	0.138095	0.0690477	+	0.997613i	$0.478004\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	70.0000	2.41236
$843$	0	0
$844$	−6.00000	−0.206529
$845$	−24.0000	−0.825625
$846$	0	0
$847$	1.00000	0.0343604
$848$	−24.0000	−0.824163
$849$	0	0
$850$	−4.00000	−0.137199
$851$	36.0000	1.23406
$852$	0	0
$853$	−19.0000	−0.650548	−0.325274	−	0.945620i	$-0.605456\pi$
$853$	−19.0000	−0.650548	−0.325274	+	0.945620i	$0.605456\pi$
$854$	−18.0000	−0.615947
$855$	0	0
$856$	0	0
$857$	14.0000	0.478231	0.239115	−	0.970991i	$-0.423143\pi$
$857$	14.0000	0.478231	0.239115	+	0.970991i	$0.423143\pi$
$858$	0	0
$859$	3.00000	0.102359	0.0511793	−	0.998689i	$-0.483702\pi$
$859$	3.00000	0.102359	0.0511793	+	0.998689i	$0.483702\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	−6.00000	−0.204242	−0.102121	−	0.994772i	$-0.532563\pi$
$863$	−6.00000	−0.204242	−0.102121	+	0.994772i	$0.532563\pi$
$864$	0	0
$865$	−48.0000	−1.63205
$866$	4.00000	0.135926
$867$	0	0
$868$	−16.0000	−0.543075
$869$	11.0000	0.373149
$870$	0	0
$871$	−25.0000	−0.847093
$872$	0	0
$873$	0	0
$874$	24.0000	0.811812
$875$	12.0000	0.405674
$876$	0	0
$877$	−3.00000	−0.101303	−0.0506514	−	0.998716i	$-0.516130\pi$
$877$	−3.00000	−0.101303	−0.0506514	+	0.998716i	$0.516130\pi$
$878$	−32.0000	−1.07995
$879$	0	0
$880$	8.00000	0.269680
$881$	32.0000	1.07811	0.539054	−	0.842271i	$-0.318782\pi$
$881$	32.0000	1.07811	0.539054	+	0.842271i	$0.318782\pi$
$882$	0	0
$883$	−53.0000	−1.78359	−0.891796	−	0.452438i	$-0.850554\pi$
$883$	−53.0000	−1.78359	−0.891796	+	0.452438i	$0.850554\pi$
$884$	20.0000	0.672673
$885$	0	0
$886$	52.0000	1.74697
$887$	26.0000	0.872995	0.436497	−	0.899706i	$-0.356219\pi$
$887$	26.0000	0.872995	0.436497	+	0.899706i	$0.356219\pi$
$888$	0	0
$889$	−16.0000	−0.536623
$890$	−24.0000	−0.804482
$891$	0	0
$892$	8.00000	0.267860
$893$	−30.0000	−1.00391
$894$	0	0
$895$	−12.0000	−0.401116
$896$	0	0
$897$	0	0
$898$	−40.0000	−1.33482
$899$	48.0000	1.60089
$900$	0	0
$901$	−12.0000	−0.399778
$902$	−8.00000	−0.266371
$903$	0	0
$904$	0	0
$905$	−26.0000	−0.864269
$906$	0	0
$907$	9.00000	0.298840	0.149420	−	0.988774i	$-0.452259\pi$
$907$	9.00000	0.298840	0.149420	+	0.988774i	$0.452259\pi$
$908$	−36.0000	−1.19470
$909$	0	0
$910$	−20.0000	−0.662994
$911$	12.0000	0.397578	0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000	0.397578	0.198789	+	0.980042i	$0.436299\pi$
$912$	0	0
$913$	−12.0000	−0.397142
$914$	−12.0000	−0.396925
$915$	0	0
$916$	12.0000	0.396491
$917$	6.00000	0.198137
$918$	0	0
$919$	−56.0000	−1.84727	−0.923635	−	0.383274i	$-0.874797\pi$
$919$	−56.0000	−1.84727	−0.923635	+	0.383274i	$0.874797\pi$
$920$	0	0
$921$	0	0
$922$	36.0000	1.18560
$923$	60.0000	1.97492
$924$	0	0
$925$	9.00000	0.295918
$926$	−14.0000	−0.460069
$927$	0	0
$928$	−48.0000	−1.57568
$929$	6.00000	0.196854	0.0984268	−	0.995144i	$-0.468619\pi$
$929$	6.00000	0.196854	0.0984268	+	0.995144i	$0.468619\pi$
$930$	0	0
$931$	−18.0000	−0.589926
$932$	12.0000	0.393073
$933$	0	0
$934$	−24.0000	−0.785304
$935$	4.00000	0.130814
$936$	0	0
$937$	−7.00000	−0.228680	−0.114340	−	0.993442i	$-0.536475\pi$
$937$	−7.00000	−0.228680	−0.114340	+	0.993442i	$0.536475\pi$
$938$	−10.0000	−0.326512
$939$	0	0
$940$	40.0000	1.30466
$941$	0	0		−	1.00000i	$-0.5\pi$
$941$	0	0			1.00000i	$0.5\pi$
$942$	0	0
$943$	−16.0000	−0.521032
$944$	−56.0000	−1.82264
$945$	0	0
$946$	0	0
$947$	−54.0000	−1.75476	−0.877382	−	0.479792i	$-0.840712\pi$
$947$	−54.0000	−1.75476	−0.877382	+	0.479792i	$0.840712\pi$
$948$	0	0
$949$	−35.0000	−1.13615
$950$	6.00000	0.194666
$951$	0	0
$952$	0	0
$953$	−32.0000	−1.03658	−0.518291	−	0.855204i	$-0.673432\pi$
$953$	−32.0000	−1.03658	−0.518291	+	0.855204i	$0.673432\pi$
$954$	0	0
$955$	32.0000	1.03550
$956$	0	0
$957$	0	0
$958$	20.0000	0.646171
$959$	−4.00000	−0.129167
$960$	0	0
$961$	33.0000	1.06452
$962$	−90.0000	−2.90172
$963$	0	0
$964$	−34.0000	−1.09507
$965$	−26.0000	−0.836970
$966$	0	0
$967$	−41.0000	−1.31847	−0.659236	−	0.751936i	$-0.729120\pi$
$967$	−41.0000	−1.31847	−0.659236	+	0.751936i	$0.729120\pi$
$968$	0	0
$969$	0	0
$970$	−28.0000	−0.899026
$971$	50.0000	1.60458	0.802288	−	0.596937i	$-0.203616\pi$
$971$	50.0000	1.60458	0.802288	+	0.596937i	$0.203616\pi$
$972$	0	0
$973$	1.00000	0.0320585
$974$	2.00000	0.0640841
$975$	0	0
$976$	−36.0000	−1.15233
$977$	−30.0000	−0.959785	−0.479893	−	0.877327i	$-0.659324\pi$
$977$	−30.0000	−0.959785	−0.479893	+	0.877327i	$0.659324\pi$
$978$	0	0
$979$	−6.00000	−0.191761
$980$	24.0000	0.766652
$981$	0	0
$982$	4.00000	0.127645
$983$	42.0000	1.33959	0.669796	−	0.742545i	$-0.266382\pi$
$983$	42.0000	1.33959	0.669796	+	0.742545i	$0.266382\pi$
$984$	0	0
$985$	52.0000	1.65686
$986$	−24.0000	−0.764316
$987$	0	0
$988$	−30.0000	−0.954427
$989$	0	0
$990$	0	0
$991$	7.00000	0.222362	0.111181	−	0.993800i	$-0.464537\pi$
$991$	7.00000	0.222362	0.111181	+	0.993800i	$0.464537\pi$
$992$	−64.0000	−2.03200
$993$	0	0
$994$	24.0000	0.761234
$995$	−6.00000	−0.190213
$996$	0	0
$997$	38.0000	1.20347	0.601736	−	0.798695i	$-0.294476\pi$
$997$	38.0000	1.20347	0.601736	+	0.798695i	$0.294476\pi$
$998$	56.0000	1.77265
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.a.a.1.1	✓	1
3.2	odd	2		297.2.a.d.1.1	yes	1
4.3	odd	2		4752.2.a.c.1.1		1
5.4	even	2		7425.2.a.u.1.1		1
9.2	odd	6		891.2.e.a.595.1		2
9.4	even	3		891.2.e.l.298.1		2
9.5	odd	6		891.2.e.a.298.1		2
9.7	even	3		891.2.e.l.595.1		2
11.10	odd	2		3267.2.a.k.1.1		1
12.11	even	2		4752.2.a.o.1.1		1
15.14	odd	2		7425.2.a.b.1.1		1
33.32	even	2		3267.2.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
297.2.a.a.1.1	✓	1	1.1	even	1	trivial
297.2.a.d.1.1	yes	1	3.2	odd	2
891.2.e.a.298.1		2	9.5	odd	6
891.2.e.a.595.1		2	9.2	odd	6
891.2.e.l.298.1		2	9.4	even	3
891.2.e.l.595.1		2	9.7	even	3
3267.2.a.a.1.1		1	33.32	even	2
3267.2.a.k.1.1		1	11.10	odd	2
4752.2.a.c.1.1		1	4.3	odd	2
4752.2.a.o.1.1		1	12.11	even	2
7425.2.a.b.1.1		1	15.14	odd	2
7425.2.a.u.1.1		1	5.4	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:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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