LMFDB - Embedded newform 297.2.a.c.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)

$f(q)$

$=$

$q+1.00000 q^{2} -1.00000 q^{4} -2.00000 q^{5} -5.00000 q^{7} -3.00000 q^{8} +O(q^{10})$

$q+1.00000 q^{2} -1.00000 q^{4} -2.00000 q^{5} -5.00000 q^{7} -3.00000 q^{8} -2.00000 q^{10} +1.00000 q^{11} -2.00000 q^{13} -5.00000 q^{14} -1.00000 q^{16} +7.00000 q^{17} +2.00000 q^{20} +1.00000 q^{22} -1.00000 q^{23} -1.00000 q^{25} -2.00000 q^{26} +5.00000 q^{28} +3.00000 q^{29} -8.00000 q^{31} +5.00000 q^{32} +7.00000 q^{34} +10.0000 q^{35} -3.00000 q^{37} +6.00000 q^{40} -11.0000 q^{41} -9.00000 q^{43} -1.00000 q^{44} -1.00000 q^{46} -1.00000 q^{47} +18.0000 q^{49} -1.00000 q^{50} +2.00000 q^{52} -12.0000 q^{53} -2.00000 q^{55} +15.0000 q^{56} +3.00000 q^{58} +5.00000 q^{59} +6.00000 q^{61} -8.00000 q^{62} +7.00000 q^{64} +4.00000 q^{65} -4.00000 q^{67} -7.00000 q^{68} +10.0000 q^{70} +4.00000 q^{73} -3.00000 q^{74} -5.00000 q^{77} +5.00000 q^{79} +2.00000 q^{80} -11.0000 q^{82} -6.00000 q^{83} -14.0000 q^{85} -9.00000 q^{86} -3.00000 q^{88} -6.00000 q^{89} +10.0000 q^{91} +1.00000 q^{92} -1.00000 q^{94} +11.0000 q^{97} +18.0000 q^{98} +O(q^{100})$

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 $

$2$	1.00000	0.707107	0.353553	−	0.935414i	$-0.384973\pi$
$2$	1.00000	0.707107	0.353553	+	0.935414i	$0.384973\pi$
$3$	0	0
$3$	0	0
$4$	−1.00000	−0.500000
$5$	−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
$7$	−5.00000	−1.88982	−0.944911	−	0.327327i	$-0.893852\pi$
$7$	−5.00000	−1.88982	−0.944911	+	0.327327i	$0.893852\pi$
$8$	−3.00000	−1.06066
$9$	0	0
$10$	−2.00000	−0.632456
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0	0
$13$	−2.00000	−0.554700	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000	−0.554700	−0.277350	+	0.960769i	$0.589456\pi$
$14$	−5.00000	−1.33631
$15$	0	0
$16$	−1.00000	−0.250000
$17$	7.00000	1.69775	0.848875	−	0.528594i	$-0.177281\pi$
$17$	7.00000	1.69775	0.848875	+	0.528594i	$0.177281\pi$
$18$	0	0
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	2.00000	0.447214
$21$	0	0
$22$	1.00000	0.213201
$23$	−1.00000	−0.208514	−0.104257	−	0.994550i	$-0.533247\pi$
$23$	−1.00000	−0.208514	−0.104257	+	0.994550i	$0.533247\pi$
$24$	0	0
$25$	−1.00000	−0.200000
$26$	−2.00000	−0.392232
$27$	0	0
$28$	5.00000	0.944911
$29$	3.00000	0.557086	0.278543	−	0.960424i	$-0.410149\pi$
$29$	3.00000	0.557086	0.278543	+	0.960424i	$0.410149\pi$
$30$	0	0
$31$	−8.00000	−1.43684	−0.718421	−	0.695608i	$-0.755135\pi$
$31$	−8.00000	−1.43684	−0.718421	+	0.695608i	$0.755135\pi$
$32$	5.00000	0.883883
$33$	0	0
$34$	7.00000	1.20049
$35$	10.0000	1.69031
$36$	0	0
$37$	−3.00000	−0.493197	−0.246598	−	0.969118i	$-0.579313\pi$
$37$	−3.00000	−0.493197	−0.246598	+	0.969118i	$0.579313\pi$
$38$	0	0
$39$	0	0
$40$	6.00000	0.948683
$41$	−11.0000	−1.71791	−0.858956	−	0.512050i	$-0.828886\pi$
$41$	−11.0000	−1.71791	−0.858956	+	0.512050i	$0.828886\pi$
$42$	0	0
$43$	−9.00000	−1.37249	−0.686244	−	0.727372i	$-0.740742\pi$
$43$	−9.00000	−1.37249	−0.686244	+	0.727372i	$0.740742\pi$
$44$	−1.00000	−0.150756
$45$	0	0
$46$	−1.00000	−0.147442
$47$	−1.00000	−0.145865	−0.0729325	−	0.997337i	$-0.523236\pi$
$47$	−1.00000	−0.145865	−0.0729325	+	0.997337i	$0.523236\pi$
$48$	0	0
$49$	18.0000	2.57143
$50$	−1.00000	−0.141421
$51$	0	0
$52$	2.00000	0.277350
$53$	−12.0000	−1.64833	−0.824163	−	0.566352i	$-0.808354\pi$
$53$	−12.0000	−1.64833	−0.824163	+	0.566352i	$0.808354\pi$
$54$	0	0
$55$	−2.00000	−0.269680
$56$	15.0000	2.00446
$57$	0	0
$58$	3.00000	0.393919
$59$	5.00000	0.650945	0.325472	−	0.945552i	$-0.394477\pi$
$59$	5.00000	0.650945	0.325472	+	0.945552i	$0.394477\pi$
$60$	0	0
$61$	6.00000	0.768221	0.384111	−	0.923287i	$-0.374508\pi$
$61$	6.00000	0.768221	0.384111	+	0.923287i	$0.374508\pi$
$62$	−8.00000	−1.01600
$63$	0	0
$64$	7.00000	0.875000
$65$	4.00000	0.496139
$66$	0	0
$67$	−4.00000	−0.488678	−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000	−0.488678	−0.244339	+	0.969690i	$0.578571\pi$
$68$	−7.00000	−0.848875
$69$	0	0
$70$	10.0000	1.19523
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	0	0
$73$	4.00000	0.468165	0.234082	−	0.972217i	$-0.424791\pi$
$73$	4.00000	0.468165	0.234082	+	0.972217i	$0.424791\pi$
$74$	−3.00000	−0.348743
$75$	0	0
$76$	0	0
$77$	−5.00000	−0.569803
$78$	0	0
$79$	5.00000	0.562544	0.281272	−	0.959628i	$-0.409244\pi$
$79$	5.00000	0.562544	0.281272	+	0.959628i	$0.409244\pi$
$80$	2.00000	0.223607
$81$	0	0
$82$	−11.0000	−1.21475
$83$	−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
$85$	−14.0000	−1.51851
$86$	−9.00000	−0.970495
$87$	0	0
$88$	−3.00000	−0.319801
$89$	−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
$91$	10.0000	1.04828
$92$	1.00000	0.104257
$93$	0	0
$94$	−1.00000	−0.103142
$95$	0	0
$96$	0	0
$97$	11.0000	1.11688	0.558440	−	0.829545i	$-0.311400\pi$
$97$	11.0000	1.11688	0.558440	+	0.829545i	$0.311400\pi$
$98$	18.0000	1.81827
$99$	0	0
$100$	1.00000	0.100000
$101$	11.0000	1.09454	0.547270	−	0.836956i	$-0.315667\pi$
$101$	11.0000	1.09454	0.547270	+	0.836956i	$0.315667\pi$
$102$	0	0
$103$	−10.0000	−0.985329	−0.492665	−	0.870219i	$-0.663977\pi$
$103$	−10.0000	−0.985329	−0.492665	+	0.870219i	$0.663977\pi$
$104$	6.00000	0.588348
$105$	0	0
$106$	−12.0000	−1.16554
$107$	6.00000	0.580042	0.290021	−	0.957020i	$-0.406338\pi$
$107$	6.00000	0.580042	0.290021	+	0.957020i	$0.406338\pi$
$108$	0	0
$109$	−2.00000	−0.191565	−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000	−0.191565	−0.0957826	+	0.995402i	$0.530535\pi$
$110$	−2.00000	−0.190693
$111$	0	0
$112$	5.00000	0.472456
$113$	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
$115$	2.00000	0.186501
$116$	−3.00000	−0.278543
$117$	0	0
$118$	5.00000	0.460287
$119$	−35.0000	−3.20844
$120$	0	0
$121$	1.00000	0.0909091
$122$	6.00000	0.543214
$123$	0	0
$124$	8.00000	0.718421
$125$	12.0000	1.07331
$126$	0	0
$127$	−4.00000	−0.354943	−0.177471	−	0.984126i	$-0.556792\pi$
$127$	−4.00000	−0.354943	−0.177471	+	0.984126i	$0.556792\pi$
$128$	−3.00000	−0.265165
$129$	0	0
$130$	4.00000	0.350823
$131$	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
$133$	0	0
$134$	−4.00000	−0.345547
$135$	0	0
$136$	−21.0000	−1.80074
$137$	−16.0000	−1.36697	−0.683486	−	0.729964i	$-0.739537\pi$
$137$	−16.0000	−1.36697	−0.683486	+	0.729964i	$0.739537\pi$
$138$	0	0
$139$	1.00000	0.0848189	0.0424094	−	0.999100i	$-0.486497\pi$
$139$	1.00000	0.0848189	0.0424094	+	0.999100i	$0.486497\pi$
$140$	−10.0000	−0.845154
$141$	0	0
$142$	0	0
$143$	−2.00000	−0.167248
$144$	0	0
$145$	−6.00000	−0.498273
$146$	4.00000	0.331042
$147$	0	0
$148$	3.00000	0.246598
$149$	14.0000	1.14692	0.573462	−	0.819232i	$-0.305600\pi$
$149$	14.0000	1.14692	0.573462	+	0.819232i	$0.305600\pi$
$150$	0	0
$151$	−16.0000	−1.30206	−0.651031	−	0.759051i	$-0.725663\pi$
$151$	−16.0000	−1.30206	−0.651031	+	0.759051i	$0.725663\pi$
$152$	0	0
$153$	0	0
$154$	−5.00000	−0.402911
$155$	16.0000	1.28515
$156$	0	0
$157$	−13.0000	−1.03751	−0.518756	−	0.854922i	$-0.673605\pi$
$157$	−13.0000	−1.03751	−0.518756	+	0.854922i	$0.673605\pi$
$158$	5.00000	0.397779
$159$	0	0
$160$	−10.0000	−0.790569
$161$	5.00000	0.394055
$162$	0	0
$163$	−14.0000	−1.09656	−0.548282	−	0.836293i	$-0.684718\pi$
$163$	−14.0000	−1.09656	−0.548282	+	0.836293i	$0.684718\pi$
$164$	11.0000	0.858956
$165$	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
$169$	−9.00000	−0.692308
$170$	−14.0000	−1.07375
$171$	0	0
$172$	9.00000	0.686244
$173$	−6.00000	−0.456172	−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000	−0.456172	−0.228086	+	0.973641i	$0.573247\pi$
$174$	0	0
$175$	5.00000	0.377964
$176$	−1.00000	−0.0753778
$177$	0	0
$178$	−6.00000	−0.449719
$179$	−15.0000	−1.12115	−0.560576	−	0.828103i	$-0.689420\pi$
$179$	−15.0000	−1.12115	−0.560576	+	0.828103i	$0.689420\pi$
$180$	0	0
$181$	−5.00000	−0.371647	−0.185824	−	0.982583i	$-0.559495\pi$
$181$	−5.00000	−0.371647	−0.185824	+	0.982583i	$0.559495\pi$
$182$	10.0000	0.741249
$183$	0	0
$184$	3.00000	0.221163
$185$	6.00000	0.441129
$186$	0	0
$187$	7.00000	0.511891
$188$	1.00000	0.0729325
$189$	0	0
$190$	0	0
$191$	−19.0000	−1.37479	−0.687396	−	0.726283i	$-0.741246\pi$
$191$	−19.0000	−1.37479	−0.687396	+	0.726283i	$0.741246\pi$
$192$	0	0
$193$	−14.0000	−1.00774	−0.503871	−	0.863779i	$-0.668091\pi$
$193$	−14.0000	−1.00774	−0.503871	+	0.863779i	$0.668091\pi$
$194$	11.0000	0.789754
$195$	0	0
$196$	−18.0000	−1.28571
$197$	−5.00000	−0.356235	−0.178118	−	0.984009i	$-0.557001\pi$
$197$	−5.00000	−0.356235	−0.178118	+	0.984009i	$0.557001\pi$
$198$	0	0
$199$	0	0		−	1.00000i	$-0.5\pi$
$199$	0	0			1.00000i	$0.5\pi$
$200$	3.00000	0.212132
$201$	0	0
$202$	11.0000	0.773957
$203$	−15.0000	−1.05279
$204$	0	0
$205$	22.0000	1.53655
$206$	−10.0000	−0.696733
$207$	0	0
$208$	2.00000	0.138675
$209$	0	0
$210$	0	0
$211$	27.0000	1.85876	0.929378	−	0.369129i	$-0.120344\pi$
$211$	27.0000	1.85876	0.929378	+	0.369129i	$0.120344\pi$
$212$	12.0000	0.824163
$213$	0	0
$214$	6.00000	0.410152
$215$	18.0000	1.22759
$216$	0	0
$217$	40.0000	2.71538
$218$	−2.00000	−0.135457
$219$	0	0
$220$	2.00000	0.134840
$221$	−14.0000	−0.941742
$222$	0	0
$223$	−20.0000	−1.33930	−0.669650	−	0.742677i	$-0.733556\pi$
$223$	−20.0000	−1.33930	−0.669650	+	0.742677i	$0.733556\pi$
$224$	−25.0000	−1.67038
$225$	0	0
$226$	12.0000	0.798228
$227$	−6.00000	−0.398234	−0.199117	−	0.979976i	$-0.563807\pi$
$227$	−6.00000	−0.398234	−0.199117	+	0.979976i	$0.563807\pi$
$228$	0	0
$229$	15.0000	0.991228	0.495614	−	0.868543i	$-0.334943\pi$
$229$	15.0000	0.991228	0.495614	+	0.868543i	$0.334943\pi$
$230$	2.00000	0.131876
$231$	0	0
$232$	−9.00000	−0.590879
$233$	−6.00000	−0.393073	−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000	−0.393073	−0.196537	+	0.980497i	$0.562969\pi$
$234$	0	0
$235$	2.00000	0.130466
$236$	−5.00000	−0.325472
$237$	0	0
$238$	−35.0000	−2.26871
$239$	−12.0000	−0.776215	−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000	−0.776215	−0.388108	+	0.921614i	$0.626871\pi$
$240$	0	0
$241$	10.0000	0.644157	0.322078	−	0.946713i	$-0.395619\pi$
$241$	10.0000	0.644157	0.322078	+	0.946713i	$0.395619\pi$
$242$	1.00000	0.0642824
$243$	0	0
$244$	−6.00000	−0.384111
$245$	−36.0000	−2.29996
$246$	0	0
$247$	0	0
$248$	24.0000	1.52400
$249$	0	0
$250$	12.0000	0.758947
$251$	−5.00000	−0.315597	−0.157799	−	0.987471i	$-0.550440\pi$
$251$	−5.00000	−0.315597	−0.157799	+	0.987471i	$0.550440\pi$
$252$	0	0
$253$	−1.00000	−0.0628695
$254$	−4.00000	−0.250982
$255$	0	0
$256$	−17.0000	−1.06250
$257$	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
$259$	15.0000	0.932055
$260$	−4.00000	−0.248069
$261$	0	0
$262$	6.00000	0.370681
$263$	2.00000	0.123325	0.0616626	−	0.998097i	$-0.480360\pi$
$263$	2.00000	0.123325	0.0616626	+	0.998097i	$0.480360\pi$
$264$	0	0
$265$	24.0000	1.47431
$266$	0	0
$267$	0	0
$268$	4.00000	0.244339
$269$	16.0000	0.975537	0.487769	−	0.872973i	$-0.337811\pi$
$269$	16.0000	0.975537	0.487769	+	0.872973i	$0.337811\pi$
$270$	0	0
$271$	11.0000	0.668202	0.334101	−	0.942537i	$-0.391567\pi$
$271$	11.0000	0.668202	0.334101	+	0.942537i	$0.391567\pi$
$272$	−7.00000	−0.424437
$273$	0	0
$274$	−16.0000	−0.966595
$275$	−1.00000	−0.0603023
$276$	0	0
$277$	−8.00000	−0.480673	−0.240337	−	0.970690i	$-0.577258\pi$
$277$	−8.00000	−0.480673	−0.240337	+	0.970690i	$0.577258\pi$
$278$	1.00000	0.0599760
$279$	0	0
$280$	−30.0000	−1.79284
$281$	9.00000	0.536895	0.268447	−	0.963294i	$-0.413489\pi$
$281$	9.00000	0.536895	0.268447	+	0.963294i	$0.413489\pi$
$282$	0	0
$283$	−20.0000	−1.18888	−0.594438	−	0.804141i	$-0.702626\pi$
$283$	−20.0000	−1.18888	−0.594438	+	0.804141i	$0.702626\pi$
$284$	0	0
$285$	0	0
$286$	−2.00000	−0.118262
$287$	55.0000	3.24655
$288$	0	0
$289$	32.0000	1.88235
$290$	−6.00000	−0.352332
$291$	0	0
$292$	−4.00000	−0.234082
$293$	30.0000	1.75262	0.876309	−	0.481749i	$-0.159998\pi$
$293$	30.0000	1.75262	0.876309	+	0.481749i	$0.159998\pi$
$294$	0	0
$295$	−10.0000	−0.582223
$296$	9.00000	0.523114
$297$	0	0
$298$	14.0000	0.810998
$299$	2.00000	0.115663
$300$	0	0
$301$	45.0000	2.59376
$302$	−16.0000	−0.920697
$303$	0	0
$304$	0	0
$305$	−12.0000	−0.687118
$306$	0	0
$307$	23.0000	1.31268	0.656340	−	0.754466i	$-0.272104\pi$
$307$	23.0000	1.31268	0.656340	+	0.754466i	$0.272104\pi$
$308$	5.00000	0.284901
$309$	0	0
$310$	16.0000	0.908739
$311$	−15.0000	−0.850572	−0.425286	−	0.905059i	$-0.639826\pi$
$311$	−15.0000	−0.850572	−0.425286	+	0.905059i	$0.639826\pi$
$312$	0	0
$313$	14.0000	0.791327	0.395663	−	0.918396i	$-0.370515\pi$
$313$	14.0000	0.791327	0.395663	+	0.918396i	$0.370515\pi$
$314$	−13.0000	−0.733632
$315$	0	0
$316$	−5.00000	−0.281272
$317$	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
$319$	3.00000	0.167968
$320$	−14.0000	−0.782624
$321$	0	0
$322$	5.00000	0.278639
$323$	0	0
$324$	0	0
$325$	2.00000	0.110940
$326$	−14.0000	−0.775388
$327$	0	0
$328$	33.0000	1.82212
$329$	5.00000	0.275659
$330$	0	0
$331$	−20.0000	−1.09930	−0.549650	−	0.835395i	$-0.685239\pi$
$331$	−20.0000	−1.09930	−0.549650	+	0.835395i	$0.685239\pi$
$332$	6.00000	0.329293
$333$	0	0
$334$	18.0000	0.984916
$335$	8.00000	0.437087
$336$	0	0
$337$	−22.0000	−1.19842	−0.599208	−	0.800593i	$-0.704518\pi$
$337$	−22.0000	−1.19842	−0.599208	+	0.800593i	$0.704518\pi$
$338$	−9.00000	−0.489535
$339$	0	0
$340$	14.0000	0.759257
$341$	−8.00000	−0.433224
$342$	0	0
$343$	−55.0000	−2.96972
$344$	27.0000	1.45574
$345$	0	0
$346$	−6.00000	−0.322562
$347$	−32.0000	−1.71785	−0.858925	−	0.512101i	$-0.828867\pi$
$347$	−32.0000	−1.71785	−0.858925	+	0.512101i	$0.828867\pi$
$348$	0	0
$349$	6.00000	0.321173	0.160586	−	0.987022i	$-0.448662\pi$
$349$	6.00000	0.321173	0.160586	+	0.987022i	$0.448662\pi$
$350$	5.00000	0.267261
$351$	0	0
$352$	5.00000	0.266501
$353$	−18.0000	−0.958043	−0.479022	−	0.877803i	$-0.659008\pi$
$353$	−18.0000	−0.958043	−0.479022	+	0.877803i	$0.659008\pi$
$354$	0	0
$355$	0	0
$356$	6.00000	0.317999
$357$	0	0
$358$	−15.0000	−0.792775
$359$	10.0000	0.527780	0.263890	−	0.964553i	$-0.414994\pi$
$359$	10.0000	0.527780	0.263890	+	0.964553i	$0.414994\pi$
$360$	0	0
$361$	−19.0000	−1.00000
$362$	−5.00000	−0.262794
$363$	0	0
$364$	−10.0000	−0.524142
$365$	−8.00000	−0.418739
$366$	0	0
$367$	4.00000	0.208798	0.104399	−	0.994535i	$-0.466708\pi$
$367$	4.00000	0.208798	0.104399	+	0.994535i	$0.466708\pi$
$368$	1.00000	0.0521286
$369$	0	0
$370$	6.00000	0.311925
$371$	60.0000	3.11504
$372$	0	0
$373$	16.0000	0.828449	0.414224	−	0.910175i	$-0.364053\pi$
$373$	16.0000	0.828449	0.414224	+	0.910175i	$0.364053\pi$
$374$	7.00000	0.361961
$375$	0	0
$376$	3.00000	0.154713
$377$	−6.00000	−0.309016
$378$	0	0
$379$	−26.0000	−1.33553	−0.667765	−	0.744372i	$-0.732749\pi$
$379$	−26.0000	−1.33553	−0.667765	+	0.744372i	$0.732749\pi$
$380$	0	0
$381$	0	0
$382$	−19.0000	−0.972125
$383$	−16.0000	−0.817562	−0.408781	−	0.912633i	$-0.634046\pi$
$383$	−16.0000	−0.817562	−0.408781	+	0.912633i	$0.634046\pi$
$384$	0	0
$385$	10.0000	0.509647
$386$	−14.0000	−0.712581
$387$	0	0
$388$	−11.0000	−0.558440
$389$	18.0000	0.912636	0.456318	−	0.889817i	$-0.349168\pi$
$389$	18.0000	0.912636	0.456318	+	0.889817i	$0.349168\pi$
$390$	0	0
$391$	−7.00000	−0.354005
$392$	−54.0000	−2.72741
$393$	0	0
$394$	−5.00000	−0.251896
$395$	−10.0000	−0.503155
$396$	0	0
$397$	−38.0000	−1.90717	−0.953583	−	0.301131i	$-0.902636\pi$
$397$	−38.0000	−1.90717	−0.953583	+	0.301131i	$0.902636\pi$
$398$	0	0
$399$	0	0
$400$	1.00000	0.0500000
$401$	26.0000	1.29838	0.649189	−	0.760627i	$-0.275108\pi$
$401$	26.0000	1.29838	0.649189	+	0.760627i	$0.275108\pi$
$402$	0	0
$403$	16.0000	0.797017
$404$	−11.0000	−0.547270
$405$	0	0
$406$	−15.0000	−0.744438
$407$	−3.00000	−0.148704
$408$	0	0
$409$	0	0		−	1.00000i	$-0.5\pi$
$409$	0	0			1.00000i	$0.5\pi$
$410$	22.0000	1.08650
$411$	0	0
$412$	10.0000	0.492665
$413$	−25.0000	−1.23017
$414$	0	0
$415$	12.0000	0.589057
$416$	−10.0000	−0.490290
$417$	0	0
$418$	0	0
$419$	−4.00000	−0.195413	−0.0977064	−	0.995215i	$-0.531151\pi$
$419$	−4.00000	−0.195413	−0.0977064	+	0.995215i	$0.531151\pi$
$420$	0	0
$421$	1.00000	0.0487370	0.0243685	−	0.999703i	$-0.492242\pi$
$421$	1.00000	0.0487370	0.0243685	+	0.999703i	$0.492242\pi$
$422$	27.0000	1.31434
$423$	0	0
$424$	36.0000	1.74831
$425$	−7.00000	−0.339550
$426$	0	0
$427$	−30.0000	−1.45180
$428$	−6.00000	−0.290021
$429$	0	0
$430$	18.0000	0.868037
$431$	−6.00000	−0.289010	−0.144505	−	0.989504i	$-0.546159\pi$
$431$	−6.00000	−0.289010	−0.144505	+	0.989504i	$0.546159\pi$
$432$	0	0
$433$	−11.0000	−0.528626	−0.264313	−	0.964437i	$-0.585145\pi$
$433$	−11.0000	−0.528626	−0.264313	+	0.964437i	$0.585145\pi$
$434$	40.0000	1.92006
$435$	0	0
$436$	2.00000	0.0957826
$437$	0	0
$438$	0	0
$439$	7.00000	0.334092	0.167046	−	0.985949i	$-0.446577\pi$
$439$	7.00000	0.334092	0.167046	+	0.985949i	$0.446577\pi$
$440$	6.00000	0.286039
$441$	0	0
$442$	−14.0000	−0.665912
$443$	−8.00000	−0.380091	−0.190046	−	0.981775i	$-0.560864\pi$
$443$	−8.00000	−0.380091	−0.190046	+	0.981775i	$0.560864\pi$
$444$	0	0
$445$	12.0000	0.568855
$446$	−20.0000	−0.947027
$447$	0	0
$448$	−35.0000	−1.65359
$449$	−16.0000	−0.755087	−0.377543	−	0.925992i	$-0.623231\pi$
$449$	−16.0000	−0.755087	−0.377543	+	0.925992i	$0.623231\pi$
$450$	0	0
$451$	−11.0000	−0.517970
$452$	−12.0000	−0.564433
$453$	0	0
$454$	−6.00000	−0.281594
$455$	−20.0000	−0.937614
$456$	0	0
$457$	−18.0000	−0.842004	−0.421002	−	0.907060i	$-0.638322\pi$
$457$	−18.0000	−0.842004	−0.421002	+	0.907060i	$0.638322\pi$
$458$	15.0000	0.700904
$459$	0	0
$460$	−2.00000	−0.0932505
$461$	6.00000	0.279448	0.139724	−	0.990190i	$-0.455378\pi$
$461$	6.00000	0.279448	0.139724	+	0.990190i	$0.455378\pi$
$462$	0	0
$463$	−20.0000	−0.929479	−0.464739	−	0.885448i	$-0.653852\pi$
$463$	−20.0000	−0.929479	−0.464739	+	0.885448i	$0.653852\pi$
$464$	−3.00000	−0.139272
$465$	0	0
$466$	−6.00000	−0.277945
$467$	−3.00000	−0.138823	−0.0694117	−	0.997588i	$-0.522112\pi$
$467$	−3.00000	−0.138823	−0.0694117	+	0.997588i	$0.522112\pi$
$468$	0	0
$469$	20.0000	0.923514
$470$	2.00000	0.0922531
$471$	0	0
$472$	−15.0000	−0.690431
$473$	−9.00000	−0.413820
$474$	0	0
$475$	0	0
$476$	35.0000	1.60422
$477$	0	0
$478$	−12.0000	−0.548867
$479$	−28.0000	−1.27935	−0.639676	−	0.768644i	$-0.720932\pi$
$479$	−28.0000	−1.27935	−0.639676	+	0.768644i	$0.720932\pi$
$480$	0	0
$481$	6.00000	0.273576
$482$	10.0000	0.455488
$483$	0	0
$484$	−1.00000	−0.0454545
$485$	−22.0000	−0.998969
$486$	0	0
$487$	−16.0000	−0.725029	−0.362515	−	0.931978i	$-0.618082\pi$
$487$	−16.0000	−0.725029	−0.362515	+	0.931978i	$0.618082\pi$
$488$	−18.0000	−0.814822
$489$	0	0
$490$	−36.0000	−1.62631
$491$	22.0000	0.992846	0.496423	−	0.868081i	$-0.334646\pi$
$491$	22.0000	0.992846	0.496423	+	0.868081i	$0.334646\pi$
$492$	0	0
$493$	21.0000	0.945792
$494$	0	0
$495$	0	0
$496$	8.00000	0.359211
$497$	0	0
$498$	0	0
$499$	14.0000	0.626726	0.313363	−	0.949633i	$-0.398544\pi$
$499$	14.0000	0.626726	0.313363	+	0.949633i	$0.398544\pi$
$500$	−12.0000	−0.536656
$501$	0	0
$502$	−5.00000	−0.223161
$503$	22.0000	0.980932	0.490466	−	0.871460i	$-0.336827\pi$
$503$	22.0000	0.980932	0.490466	+	0.871460i	$0.336827\pi$
$504$	0	0
$505$	−22.0000	−0.978987
$506$	−1.00000	−0.0444554
$507$	0	0
$508$	4.00000	0.177471
$509$	−6.00000	−0.265945	−0.132973	−	0.991120i	$-0.542452\pi$
$509$	−6.00000	−0.265945	−0.132973	+	0.991120i	$0.542452\pi$
$510$	0	0
$511$	−20.0000	−0.884748
$512$	−11.0000	−0.486136
$513$	0	0
$514$	22.0000	0.970378
$515$	20.0000	0.881305
$516$	0	0
$517$	−1.00000	−0.0439799
$518$	15.0000	0.659062
$519$	0	0
$520$	−12.0000	−0.526235
$521$	6.00000	0.262865	0.131432	−	0.991325i	$-0.458042\pi$
$521$	6.00000	0.262865	0.131432	+	0.991325i	$0.458042\pi$
$522$	0	0
$523$	11.0000	0.480996	0.240498	−	0.970650i	$-0.422689\pi$
$523$	11.0000	0.480996	0.240498	+	0.970650i	$0.422689\pi$
$524$	−6.00000	−0.262111
$525$	0	0
$526$	2.00000	0.0872041
$527$	−56.0000	−2.43940
$528$	0	0
$529$	−22.0000	−0.956522
$530$	24.0000	1.04249
$531$	0	0
$532$	0	0
$533$	22.0000	0.952926
$534$	0	0
$535$	−12.0000	−0.518805
$536$	12.0000	0.518321
$537$	0	0
$538$	16.0000	0.689809
$539$	18.0000	0.775315
$540$	0	0
$541$	10.0000	0.429934	0.214967	−	0.976621i	$-0.431036\pi$
$541$	10.0000	0.429934	0.214967	+	0.976621i	$0.431036\pi$
$542$	11.0000	0.472490
$543$	0	0
$544$	35.0000	1.50061
$545$	4.00000	0.171341
$546$	0	0
$547$	35.0000	1.49649	0.748246	−	0.663421i	$-0.230896\pi$
$547$	35.0000	1.49649	0.748246	+	0.663421i	$0.230896\pi$
$548$	16.0000	0.683486
$549$	0	0
$550$	−1.00000	−0.0426401
$551$	0	0
$552$	0	0
$553$	−25.0000	−1.06311
$554$	−8.00000	−0.339887
$555$	0	0
$556$	−1.00000	−0.0424094
$557$	−23.0000	−0.974541	−0.487271	−	0.873251i	$-0.662007\pi$
$557$	−23.0000	−0.974541	−0.487271	+	0.873251i	$0.662007\pi$
$558$	0	0
$559$	18.0000	0.761319
$560$	−10.0000	−0.422577
$561$	0	0
$562$	9.00000	0.379642
$563$	−26.0000	−1.09577	−0.547885	−	0.836554i	$-0.684567\pi$
$563$	−26.0000	−1.09577	−0.547885	+	0.836554i	$0.684567\pi$
$564$	0	0
$565$	−24.0000	−1.00969
$566$	−20.0000	−0.840663
$567$	0	0
$568$	0	0
$569$	−6.00000	−0.251533	−0.125767	−	0.992060i	$-0.540139\pi$
$569$	−6.00000	−0.251533	−0.125767	+	0.992060i	$0.540139\pi$
$570$	0	0
$571$	29.0000	1.21361	0.606806	−	0.794850i	$-0.292450\pi$
$571$	29.0000	1.21361	0.606806	+	0.794850i	$0.292450\pi$
$572$	2.00000	0.0836242
$573$	0	0
$574$	55.0000	2.29566
$575$	1.00000	0.0417029
$576$	0	0
$577$	−39.0000	−1.62359	−0.811796	−	0.583942i	$-0.801510\pi$
$577$	−39.0000	−1.62359	−0.811796	+	0.583942i	$0.801510\pi$
$578$	32.0000	1.33102
$579$	0	0
$580$	6.00000	0.249136
$581$	30.0000	1.24461
$582$	0	0
$583$	−12.0000	−0.496989
$584$	−12.0000	−0.496564
$585$	0	0
$586$	30.0000	1.23929
$587$	37.0000	1.52715	0.763577	−	0.645717i	$-0.223441\pi$
$587$	37.0000	1.52715	0.763577	+	0.645717i	$0.223441\pi$
$588$	0	0
$589$	0	0
$590$	−10.0000	−0.411693
$591$	0	0
$592$	3.00000	0.123299
$593$	−43.0000	−1.76580	−0.882899	−	0.469563i	$-0.844412\pi$
$593$	−43.0000	−1.76580	−0.882899	+	0.469563i	$0.844412\pi$
$594$	0	0
$595$	70.0000	2.86972
$596$	−14.0000	−0.573462
$597$	0	0
$598$	2.00000	0.0817861
$599$	37.0000	1.51178	0.755890	−	0.654699i	$-0.227205\pi$
$599$	37.0000	1.51178	0.755890	+	0.654699i	$0.227205\pi$
$600$	0	0
$601$	−28.0000	−1.14214	−0.571072	−	0.820900i	$-0.693472\pi$
$601$	−28.0000	−1.14214	−0.571072	+	0.820900i	$0.693472\pi$
$602$	45.0000	1.83406
$603$	0	0
$604$	16.0000	0.651031
$605$	−2.00000	−0.0813116
$606$	0	0
$607$	32.0000	1.29884	0.649420	−	0.760430i	$-0.275012\pi$
$607$	32.0000	1.29884	0.649420	+	0.760430i	$0.275012\pi$
$608$	0	0
$609$	0	0
$610$	−12.0000	−0.485866
$611$	2.00000	0.0809113
$612$	0	0
$613$	14.0000	0.565455	0.282727	−	0.959200i	$-0.408761\pi$
$613$	14.0000	0.565455	0.282727	+	0.959200i	$0.408761\pi$
$614$	23.0000	0.928204
$615$	0	0
$616$	15.0000	0.604367
$617$	−12.0000	−0.483102	−0.241551	−	0.970388i	$-0.577656\pi$
$617$	−12.0000	−0.483102	−0.241551	+	0.970388i	$0.577656\pi$
$618$	0	0
$619$	8.00000	0.321547	0.160774	−	0.986991i	$-0.448601\pi$
$619$	8.00000	0.321547	0.160774	+	0.986991i	$0.448601\pi$
$620$	−16.0000	−0.642575
$621$	0	0
$622$	−15.0000	−0.601445
$623$	30.0000	1.20192
$624$	0	0
$625$	−19.0000	−0.760000
$626$	14.0000	0.559553
$627$	0	0
$628$	13.0000	0.518756
$629$	−21.0000	−0.837325
$630$	0	0
$631$	−38.0000	−1.51276	−0.756378	−	0.654135i	$-0.773033\pi$
$631$	−38.0000	−1.51276	−0.756378	+	0.654135i	$0.773033\pi$
$632$	−15.0000	−0.596668
$633$	0	0
$634$	22.0000	0.873732
$635$	8.00000	0.317470
$636$	0	0
$637$	−36.0000	−1.42637
$638$	3.00000	0.118771
$639$	0	0
$640$	6.00000	0.237171
$641$	−18.0000	−0.710957	−0.355479	−	0.934684i	$-0.615682\pi$
$641$	−18.0000	−0.710957	−0.355479	+	0.934684i	$0.615682\pi$
$642$	0	0
$643$	38.0000	1.49857	0.749287	−	0.662246i	$-0.230396\pi$
$643$	38.0000	1.49857	0.749287	+	0.662246i	$0.230396\pi$
$644$	−5.00000	−0.197028
$645$	0	0
$646$	0	0
$647$	44.0000	1.72982	0.864909	−	0.501928i	$-0.167376\pi$
$647$	44.0000	1.72982	0.864909	+	0.501928i	$0.167376\pi$
$648$	0	0
$649$	5.00000	0.196267
$650$	2.00000	0.0784465
$651$	0	0
$652$	14.0000	0.548282
$653$	−20.0000	−0.782660	−0.391330	−	0.920250i	$-0.627985\pi$
$653$	−20.0000	−0.782660	−0.391330	+	0.920250i	$0.627985\pi$
$654$	0	0
$655$	−12.0000	−0.468879
$656$	11.0000	0.429478
$657$	0	0
$658$	5.00000	0.194920
$659$	4.00000	0.155818	0.0779089	−	0.996960i	$-0.475176\pi$
$659$	4.00000	0.155818	0.0779089	+	0.996960i	$0.475176\pi$
$660$	0	0
$661$	−17.0000	−0.661223	−0.330612	−	0.943767i	$-0.607255\pi$
$661$	−17.0000	−0.661223	−0.330612	+	0.943767i	$0.607255\pi$
$662$	−20.0000	−0.777322
$663$	0	0
$664$	18.0000	0.698535
$665$	0	0
$666$	0	0
$667$	−3.00000	−0.116160
$668$	−18.0000	−0.696441
$669$	0	0
$670$	8.00000	0.309067
$671$	6.00000	0.231627
$672$	0	0
$673$	−10.0000	−0.385472	−0.192736	−	0.981251i	$-0.561736\pi$
$673$	−10.0000	−0.385472	−0.192736	+	0.981251i	$0.561736\pi$
$674$	−22.0000	−0.847408
$675$	0	0
$676$	9.00000	0.346154
$677$	27.0000	1.03769	0.518847	−	0.854867i	$-0.326361\pi$
$677$	27.0000	1.03769	0.518847	+	0.854867i	$0.326361\pi$
$678$	0	0
$679$	−55.0000	−2.11071
$680$	42.0000	1.61063
$681$	0	0
$682$	−8.00000	−0.306336
$683$	−25.0000	−0.956598	−0.478299	−	0.878197i	$-0.658747\pi$
$683$	−25.0000	−0.956598	−0.478299	+	0.878197i	$0.658747\pi$
$684$	0	0
$685$	32.0000	1.22266
$686$	−55.0000	−2.09991
$687$	0	0
$688$	9.00000	0.343122
$689$	24.0000	0.914327
$690$	0	0
$691$	44.0000	1.67384	0.836919	−	0.547326i	$-0.184354\pi$
$691$	44.0000	1.67384	0.836919	+	0.547326i	$0.184354\pi$
$692$	6.00000	0.228086
$693$	0	0
$694$	−32.0000	−1.21470
$695$	−2.00000	−0.0758643
$696$	0	0
$697$	−77.0000	−2.91658
$698$	6.00000	0.227103
$699$	0	0
$700$	−5.00000	−0.188982
$701$	5.00000	0.188847	0.0944237	−	0.995532i	$-0.469899\pi$
$701$	5.00000	0.188847	0.0944237	+	0.995532i	$0.469899\pi$
$702$	0	0
$703$	0	0
$704$	7.00000	0.263822
$705$	0	0
$706$	−18.0000	−0.677439
$707$	−55.0000	−2.06849
$708$	0	0
$709$	11.0000	0.413114	0.206557	−	0.978435i	$-0.433774\pi$
$709$	11.0000	0.413114	0.206557	+	0.978435i	$0.433774\pi$
$710$	0	0
$711$	0	0
$712$	18.0000	0.674579
$713$	8.00000	0.299602
$714$	0	0
$715$	4.00000	0.149592
$716$	15.0000	0.560576
$717$	0	0
$718$	10.0000	0.373197
$719$	−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
$721$	50.0000	1.86210
$722$	−19.0000	−0.707107
$723$	0	0
$724$	5.00000	0.185824
$725$	−3.00000	−0.111417
$726$	0	0
$727$	36.0000	1.33517	0.667583	−	0.744535i	$-0.267329\pi$
$727$	36.0000	1.33517	0.667583	+	0.744535i	$0.267329\pi$
$728$	−30.0000	−1.11187
$729$	0	0
$730$	−8.00000	−0.296093
$731$	−63.0000	−2.33014
$732$	0	0
$733$	48.0000	1.77292	0.886460	−	0.462805i	$-0.153157\pi$
$733$	48.0000	1.77292	0.886460	+	0.462805i	$0.153157\pi$
$734$	4.00000	0.147643
$735$	0	0
$736$	−5.00000	−0.184302
$737$	−4.00000	−0.147342
$738$	0	0
$739$	−37.0000	−1.36107	−0.680534	−	0.732717i	$-0.738252\pi$
$739$	−37.0000	−1.36107	−0.680534	+	0.732717i	$0.738252\pi$
$740$	−6.00000	−0.220564
$741$	0	0
$742$	60.0000	2.20267
$743$	4.00000	0.146746	0.0733729	−	0.997305i	$-0.476624\pi$
$743$	4.00000	0.146746	0.0733729	+	0.997305i	$0.476624\pi$
$744$	0	0
$745$	−28.0000	−1.02584
$746$	16.0000	0.585802
$747$	0	0
$748$	−7.00000	−0.255945
$749$	−30.0000	−1.09618
$750$	0	0
$751$	10.0000	0.364905	0.182453	−	0.983215i	$-0.441596\pi$
$751$	10.0000	0.364905	0.182453	+	0.983215i	$0.441596\pi$
$752$	1.00000	0.0364662
$753$	0	0
$754$	−6.00000	−0.218507
$755$	32.0000	1.16460
$756$	0	0
$757$	−19.0000	−0.690567	−0.345283	−	0.938498i	$-0.612217\pi$
$757$	−19.0000	−0.690567	−0.345283	+	0.938498i	$0.612217\pi$
$758$	−26.0000	−0.944363
$759$	0	0
$760$	0	0
$761$	6.00000	0.217500	0.108750	−	0.994069i	$-0.465315\pi$
$761$	6.00000	0.217500	0.108750	+	0.994069i	$0.465315\pi$
$762$	0	0
$763$	10.0000	0.362024
$764$	19.0000	0.687396
$765$	0	0
$766$	−16.0000	−0.578103
$767$	−10.0000	−0.361079
$768$	0	0
$769$	2.00000	0.0721218	0.0360609	−	0.999350i	$-0.488519\pi$
$769$	2.00000	0.0721218	0.0360609	+	0.999350i	$0.488519\pi$
$770$	10.0000	0.360375
$771$	0	0
$772$	14.0000	0.503871
$773$	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
$775$	8.00000	0.287368
$776$	−33.0000	−1.18463
$777$	0	0
$778$	18.0000	0.645331
$779$	0	0
$780$	0	0
$781$	0	0
$782$	−7.00000	−0.250319
$783$	0	0
$784$	−18.0000	−0.642857
$785$	26.0000	0.927980
$786$	0	0
$787$	28.0000	0.998092	0.499046	−	0.866575i	$-0.333684\pi$
$787$	28.0000	0.998092	0.499046	+	0.866575i	$0.333684\pi$
$788$	5.00000	0.178118
$789$	0	0
$790$	−10.0000	−0.355784
$791$	−60.0000	−2.13335
$792$	0	0
$793$	−12.0000	−0.426132
$794$	−38.0000	−1.34857
$795$	0	0
$796$	0	0
$797$	−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
$799$	−7.00000	−0.247642
$800$	−5.00000	−0.176777
$801$	0	0
$802$	26.0000	0.918092
$803$	4.00000	0.141157
$804$	0	0
$805$	−10.0000	−0.352454
$806$	16.0000	0.563576
$807$	0	0
$808$	−33.0000	−1.16094
$809$	27.0000	0.949269	0.474635	−	0.880183i	$-0.342580\pi$
$809$	27.0000	0.949269	0.474635	+	0.880183i	$0.342580\pi$
$810$	0	0
$811$	7.00000	0.245803	0.122902	−	0.992419i	$-0.460780\pi$
$811$	7.00000	0.245803	0.122902	+	0.992419i	$0.460780\pi$
$812$	15.0000	0.526397
$813$	0	0
$814$	−3.00000	−0.105150
$815$	28.0000	0.980797
$816$	0	0
$817$	0	0
$818$	0	0
$819$	0	0
$820$	−22.0000	−0.768273
$821$	31.0000	1.08191	0.540954	−	0.841052i	$-0.318063\pi$
$821$	31.0000	1.08191	0.540954	+	0.841052i	$0.318063\pi$
$822$	0	0
$823$	−48.0000	−1.67317	−0.836587	−	0.547833i	$-0.815453\pi$
$823$	−48.0000	−1.67317	−0.836587	+	0.547833i	$0.815453\pi$
$824$	30.0000	1.04510
$825$	0	0
$826$	−25.0000	−0.869861
$827$	20.0000	0.695468	0.347734	−	0.937593i	$-0.386951\pi$
$827$	20.0000	0.695468	0.347734	+	0.937593i	$0.386951\pi$
$828$	0	0
$829$	25.0000	0.868286	0.434143	−	0.900844i	$-0.357051\pi$
$829$	25.0000	0.868286	0.434143	+	0.900844i	$0.357051\pi$
$830$	12.0000	0.416526
$831$	0	0
$832$	−14.0000	−0.485363
$833$	126.000	4.36564
$834$	0	0
$835$	−36.0000	−1.24583
$836$	0	0
$837$	0	0
$838$	−4.00000	−0.138178
$839$	25.0000	0.863096	0.431548	−	0.902090i	$-0.357968\pi$
$839$	25.0000	0.863096	0.431548	+	0.902090i	$0.357968\pi$
$840$	0	0
$841$	−20.0000	−0.689655
$842$	1.00000	0.0344623
$843$	0	0
$844$	−27.0000	−0.929378
$845$	18.0000	0.619219
$846$	0	0
$847$	−5.00000	−0.171802
$848$	12.0000	0.412082
$849$	0	0
$850$	−7.00000	−0.240098
$851$	3.00000	0.102839
$852$	0	0
$853$	−16.0000	−0.547830	−0.273915	−	0.961754i	$-0.588319\pi$
$853$	−16.0000	−0.547830	−0.273915	+	0.961754i	$0.588319\pi$
$854$	−30.0000	−1.02658
$855$	0	0
$856$	−18.0000	−0.615227
$857$	−37.0000	−1.26390	−0.631948	−	0.775011i	$-0.717744\pi$
$857$	−37.0000	−1.26390	−0.631948	+	0.775011i	$0.717744\pi$
$858$	0	0
$859$	0	0		−	1.00000i	$-0.5\pi$
$859$	0	0			1.00000i	$0.5\pi$
$860$	−18.0000	−0.613795
$861$	0	0
$862$	−6.00000	−0.204361
$863$	21.0000	0.714848	0.357424	−	0.933942i	$-0.383655\pi$
$863$	21.0000	0.714848	0.357424	+	0.933942i	$0.383655\pi$
$864$	0	0
$865$	12.0000	0.408012
$866$	−11.0000	−0.373795
$867$	0	0
$868$	−40.0000	−1.35769
$869$	5.00000	0.169613
$870$	0	0
$871$	8.00000	0.271070
$872$	6.00000	0.203186
$873$	0	0
$874$	0	0
$875$	−60.0000	−2.02837
$876$	0	0
$877$	−30.0000	−1.01303	−0.506514	−	0.862232i	$-0.669066\pi$
$877$	−30.0000	−1.01303	−0.506514	+	0.862232i	$0.669066\pi$
$878$	7.00000	0.236239
$879$	0	0
$880$	2.00000	0.0674200
$881$	−46.0000	−1.54978	−0.774890	−	0.632096i	$-0.782195\pi$
$881$	−46.0000	−1.54978	−0.774890	+	0.632096i	$0.782195\pi$
$882$	0	0
$883$	−2.00000	−0.0673054	−0.0336527	−	0.999434i	$-0.510714\pi$
$883$	−2.00000	−0.0673054	−0.0336527	+	0.999434i	$0.510714\pi$
$884$	14.0000	0.470871
$885$	0	0
$886$	−8.00000	−0.268765
$887$	−28.0000	−0.940148	−0.470074	−	0.882627i	$-0.655773\pi$
$887$	−28.0000	−0.940148	−0.470074	+	0.882627i	$0.655773\pi$
$888$	0	0
$889$	20.0000	0.670778
$890$	12.0000	0.402241
$891$	0	0
$892$	20.0000	0.669650
$893$	0	0
$894$	0	0
$895$	30.0000	1.00279
$896$	15.0000	0.501115
$897$	0	0
$898$	−16.0000	−0.533927
$899$	−24.0000	−0.800445
$900$	0	0
$901$	−84.0000	−2.79845
$902$	−11.0000	−0.366260
$903$	0	0
$904$	−36.0000	−1.19734
$905$	10.0000	0.332411
$906$	0	0
$907$	30.0000	0.996134	0.498067	−	0.867139i	$-0.334043\pi$
$907$	30.0000	0.996134	0.498067	+	0.867139i	$0.334043\pi$
$908$	6.00000	0.199117
$909$	0	0
$910$	−20.0000	−0.662994
$911$	15.0000	0.496972	0.248486	−	0.968635i	$-0.420067\pi$
$911$	15.0000	0.496972	0.248486	+	0.968635i	$0.420067\pi$
$912$	0	0
$913$	−6.00000	−0.198571
$914$	−18.0000	−0.595387
$915$	0	0
$916$	−15.0000	−0.495614
$917$	−30.0000	−0.990687
$918$	0	0
$919$	−11.0000	−0.362857	−0.181428	−	0.983404i	$-0.558072\pi$
$919$	−11.0000	−0.362857	−0.181428	+	0.983404i	$0.558072\pi$
$920$	−6.00000	−0.197814
$921$	0	0
$922$	6.00000	0.197599
$923$	0	0
$924$	0	0
$925$	3.00000	0.0986394
$926$	−20.0000	−0.657241
$927$	0	0
$928$	15.0000	0.492399
$929$	48.0000	1.57483	0.787414	−	0.616424i	$-0.211419\pi$
$929$	48.0000	1.57483	0.787414	+	0.616424i	$0.211419\pi$
$930$	0	0
$931$	0	0
$932$	6.00000	0.196537
$933$	0	0
$934$	−3.00000	−0.0981630
$935$	−14.0000	−0.457849
$936$	0	0
$937$	26.0000	0.849383	0.424691	−	0.905338i	$-0.360383\pi$
$937$	26.0000	0.849383	0.424691	+	0.905338i	$0.360383\pi$
$938$	20.0000	0.653023
$939$	0	0
$940$	−2.00000	−0.0652328
$941$	−9.00000	−0.293392	−0.146696	−	0.989182i	$-0.546864\pi$
$941$	−9.00000	−0.293392	−0.146696	+	0.989182i	$0.546864\pi$
$942$	0	0
$943$	11.0000	0.358209
$944$	−5.00000	−0.162736
$945$	0	0
$946$	−9.00000	−0.292615
$947$	−24.0000	−0.779895	−0.389948	−	0.920837i	$-0.627507\pi$
$947$	−24.0000	−0.779895	−0.389948	+	0.920837i	$0.627507\pi$
$948$	0	0
$949$	−8.00000	−0.259691
$950$	0	0
$951$	0	0
$952$	105.000	3.40307
$953$	−41.0000	−1.32812	−0.664060	−	0.747679i	$-0.731168\pi$
$953$	−41.0000	−1.32812	−0.664060	+	0.747679i	$0.731168\pi$
$954$	0	0
$955$	38.0000	1.22965
$956$	12.0000	0.388108
$957$	0	0
$958$	−28.0000	−0.904639
$959$	80.0000	2.58333
$960$	0	0
$961$	33.0000	1.06452
$962$	6.00000	0.193448
$963$	0	0
$964$	−10.0000	−0.322078
$965$	28.0000	0.901352
$966$	0	0
$967$	−23.0000	−0.739630	−0.369815	−	0.929105i	$-0.620579\pi$
$967$	−23.0000	−0.739630	−0.369815	+	0.929105i	$0.620579\pi$
$968$	−3.00000	−0.0964237
$969$	0	0
$970$	−22.0000	−0.706377
$971$	20.0000	0.641831	0.320915	−	0.947108i	$-0.396010\pi$
$971$	20.0000	0.641831	0.320915	+	0.947108i	$0.396010\pi$
$972$	0	0
$973$	−5.00000	−0.160293
$974$	−16.0000	−0.512673
$975$	0	0
$976$	−6.00000	−0.192055
$977$	−42.0000	−1.34370	−0.671850	−	0.740688i	$-0.734500\pi$
$977$	−42.0000	−1.34370	−0.671850	+	0.740688i	$0.734500\pi$
$978$	0	0
$979$	−6.00000	−0.191761
$980$	36.0000	1.14998
$981$	0	0
$982$	22.0000	0.702048
$983$	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
$985$	10.0000	0.318626
$986$	21.0000	0.668776
$987$	0	0
$988$	0	0
$989$	9.00000	0.286183
$990$	0	0
$991$	4.00000	0.127064	0.0635321	−	0.997980i	$-0.479763\pi$
$991$	4.00000	0.127064	0.0635321	+	0.997980i	$0.479763\pi$
$992$	−40.0000	−1.27000
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	−40.0000	−1.26681	−0.633406	−	0.773819i	$-0.718344\pi$
$997$	−40.0000	−1.26681	−0.633406	+	0.773819i	$0.718344\pi$
$998$	14.0000	0.443162
$999$	0	0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
297.2.a.b.1.1	✓	1	3.2	odd	2
297.2.a.c.1.1	yes	1	1.1	even	1	trivial
891.2.e.f.298.1		2	9.4	even	3
891.2.e.f.595.1		2	9.7	even	3
891.2.e.h.298.1		2	9.5	odd	6
891.2.e.h.595.1		2	9.2	odd	6
3267.2.a.c.1.1		1	11.10	odd	2
3267.2.a.j.1.1		1	33.32	even	2
4752.2.a.g.1.1		1	4.3	odd	2
4752.2.a.r.1.1		1	12.11	even	2
7425.2.a.k.1.1		1	5.4	even	2
7425.2.a.s.1.1		1	15.14	odd	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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