LMFDB - Embedded newform 297.2.a.b.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} -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})

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	$-0.615027\pi$
$2$	−1.00000	−0.707107	−0.353553	+	0.935414i	$0.615027\pi$
$3$	0	0
$3$	0	0
$4$	−1.00000	−0.500000
$5$	2.00000	0.894427	0.447214	−	0.894427i	$-0.352416\pi$
$5$	2.00000	0.894427	0.447214	+	0.894427i	$0.352416\pi$
$6$	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	$-0.822719\pi$
$17$	−7.00000	−1.69775	−0.848875	+	0.528594i	$0.822719\pi$
$18$	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	$-0.466753\pi$
$23$	1.00000	0.208514	0.104257	+	0.994550i	$0.466753\pi$
$24$	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	$-0.589851\pi$
$29$	−3.00000	−0.557086	−0.278543	+	0.960424i	$0.589851\pi$
$30$	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	$-0.171114\pi$
$41$	11.0000	1.71791	0.858956	+	0.512050i	$0.171114\pi$
$42$	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	$-0.476764\pi$
$47$	1.00000	0.145865	0.0729325	+	0.997337i	$0.476764\pi$
$48$	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	$-0.191646\pi$
$53$	12.0000	1.64833	0.824163	+	0.566352i	$0.191646\pi$
$54$	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	$-0.605523\pi$
$59$	−5.00000	−0.650945	−0.325472	+	0.945552i	$0.605523\pi$
$60$	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	$-0.393190\pi$
$83$	6.00000	0.658586	0.329293	+	0.944228i	$0.393190\pi$
$84$	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	$-0.396989\pi$
$89$	6.00000	0.635999	0.317999	+	0.948091i	$0.396989\pi$
$90$	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	$-0.684333\pi$
$101$	−11.0000	−1.09454	−0.547270	+	0.836956i	$0.684333\pi$
$102$	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	$-0.593662\pi$
$107$	−6.00000	−0.580042	−0.290021	+	0.957020i	$0.593662\pi$
$108$	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	$-0.690905\pi$
$113$	−12.0000	−1.12887	−0.564433	+	0.825479i	$0.690905\pi$
$114$	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	$-0.584419\pi$
$131$	−6.00000	−0.524222	−0.262111	+	0.965038i	$0.584419\pi$
$132$	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	$-0.260463\pi$
$137$	16.0000	1.36697	0.683486	+	0.729964i	$0.260463\pi$
$138$	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	$-0.694400\pi$
$149$	−14.0000	−1.14692	−0.573462	+	0.819232i	$0.694400\pi$
$150$	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	$-0.745234\pi$
$167$	−18.0000	−1.39288	−0.696441	+	0.717614i	$0.745234\pi$
$168$	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	$-0.426753\pi$
$173$	6.00000	0.456172	0.228086	+	0.973641i	$0.426753\pi$
$174$	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	$-0.310580\pi$
$179$	15.0000	1.12115	0.560576	+	0.828103i	$0.310580\pi$
$180$	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	$-0.258754\pi$
$191$	19.0000	1.37479	0.687396	+	0.726283i	$0.258754\pi$
$192$	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	$-0.442999\pi$
$197$	5.00000	0.356235	0.178118	+	0.984009i	$0.442999\pi$
$198$	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	$-0.436193\pi$
$227$	6.00000	0.398234	0.199117	+	0.979976i	$0.436193\pi$
$228$	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	$-0.437031\pi$
$233$	6.00000	0.393073	0.196537	+	0.980497i	$0.437031\pi$
$234$	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	$-0.373129\pi$
$239$	12.0000	0.776215	0.388108	+	0.921614i	$0.373129\pi$
$240$	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	$-0.449560\pi$
$251$	5.00000	0.315597	0.157799	+	0.987471i	$0.449560\pi$
$252$	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	$-0.740706\pi$
$257$	−22.0000	−1.37232	−0.686161	+	0.727450i	$0.740706\pi$
$258$	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	$-0.519640\pi$
$263$	−2.00000	−0.123325	−0.0616626	+	0.998097i	$0.519640\pi$
$264$	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	$-0.662189\pi$
$269$	−16.0000	−0.975537	−0.487769	+	0.872973i	$0.662189\pi$
$270$	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	$-0.586511\pi$
$281$	−9.00000	−0.536895	−0.268447	+	0.963294i	$0.586511\pi$
$282$	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	$-0.840002\pi$
$293$	−30.0000	−1.75262	−0.876309	+	0.481749i	$0.840002\pi$
$294$	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	$-0.360174\pi$
$311$	15.0000	0.850572	0.425286	+	0.905059i	$0.360174\pi$
$312$	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	$-0.711985\pi$
$317$	−22.0000	−1.23564	−0.617822	+	0.786318i	$0.711985\pi$
$318$	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	$-0.171133\pi$
$347$	32.0000	1.71785	0.858925	+	0.512101i	$0.171133\pi$
$348$	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	$-0.340992\pi$
$353$	18.0000	0.958043	0.479022	+	0.877803i	$0.340992\pi$
$354$	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	$-0.585006\pi$
$359$	−10.0000	−0.527780	−0.263890	+	0.964553i	$0.585006\pi$
$360$	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	$-0.365954\pi$
$383$	16.0000	0.817562	0.408781	+	0.912633i	$0.365954\pi$
$384$	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	$-0.650832\pi$
$389$	−18.0000	−0.912636	−0.456318	+	0.889817i	$0.650832\pi$
$390$	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	$-0.724892\pi$
$401$	−26.0000	−1.29838	−0.649189	+	0.760627i	$0.724892\pi$
$402$	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	$-0.468849\pi$
$419$	4.00000	0.195413	0.0977064	+	0.995215i	$0.468849\pi$
$420$	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	$-0.453841\pi$
$431$	6.00000	0.289010	0.144505	+	0.989504i	$0.453841\pi$
$432$	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	$-0.439136\pi$
$443$	8.00000	0.380091	0.190046	+	0.981775i	$0.439136\pi$
$444$	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	$-0.376769\pi$
$449$	16.0000	0.755087	0.377543	+	0.925992i	$0.376769\pi$
$450$	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	$-0.544622\pi$
$461$	−6.00000	−0.279448	−0.139724	+	0.990190i	$0.544622\pi$
$462$	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	$-0.477888\pi$
$467$	3.00000	0.138823	0.0694117	+	0.997588i	$0.477888\pi$
$468$	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	$-0.279068\pi$
$479$	28.0000	1.27935	0.639676	+	0.768644i	$0.279068\pi$
$480$	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	$-0.665354\pi$
$491$	−22.0000	−0.992846	−0.496423	+	0.868081i	$0.665354\pi$
$492$	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	$-0.663173\pi$
$503$	−22.0000	−0.980932	−0.490466	+	0.871460i	$0.663173\pi$
$504$	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	$-0.457548\pi$
$509$	6.00000	0.265945	0.132973	+	0.991120i	$0.457548\pi$
$510$	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	$-0.541958\pi$
$521$	−6.00000	−0.262865	−0.131432	+	0.991325i	$0.541958\pi$
$522$	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	$-0.337993\pi$
$557$	23.0000	0.974541	0.487271	+	0.873251i	$0.337993\pi$
$558$	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	$-0.315433\pi$
$563$	26.0000	1.09577	0.547885	+	0.836554i	$0.315433\pi$
$564$	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	$-0.459861\pi$
$569$	6.00000	0.251533	0.125767	+	0.992060i	$0.459861\pi$
$570$	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	$-0.776559\pi$
$587$	−37.0000	−1.52715	−0.763577	+	0.645717i	$0.776559\pi$
$588$	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	$-0.155588\pi$
$593$	43.0000	1.76580	0.882899	+	0.469563i	$0.155588\pi$
$594$	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	$-0.772795\pi$
$599$	−37.0000	−1.51178	−0.755890	+	0.654699i	$0.772795\pi$
$600$	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	$-0.422344\pi$
$617$	12.0000	0.483102	0.241551	+	0.970388i	$0.422344\pi$
$618$	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	$-0.384318\pi$
$641$	18.0000	0.710957	0.355479	+	0.934684i	$0.384318\pi$
$642$	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	$-0.832624\pi$
$647$	−44.0000	−1.72982	−0.864909	+	0.501928i	$0.832624\pi$
$648$	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	$-0.372015\pi$
$653$	20.0000	0.782660	0.391330	+	0.920250i	$0.372015\pi$
$654$	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	$-0.524824\pi$
$659$	−4.00000	−0.155818	−0.0779089	+	0.996960i	$0.524824\pi$
$660$	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	$-0.673639\pi$
$677$	−27.0000	−1.03769	−0.518847	+	0.854867i	$0.673639\pi$
$678$	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	$-0.341253\pi$
$683$	25.0000	0.956598	0.478299	+	0.878197i	$0.341253\pi$
$684$	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	$-0.530101\pi$
$701$	−5.00000	−0.188847	−0.0944237	+	0.995532i	$0.530101\pi$
$702$	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	$-0.428166\pi$
$719$	12.0000	0.447524	0.223762	+	0.974644i	$0.428166\pi$
$720$	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	$-0.523376\pi$
$743$	−4.00000	−0.146746	−0.0733729	+	0.997305i	$0.523376\pi$
$744$	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	$-0.534685\pi$
$761$	−6.00000	−0.217500	−0.108750	+	0.994069i	$0.534685\pi$
$762$	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	$-0.642054\pi$
$773$	−24.0000	−0.863220	−0.431610	+	0.902060i	$0.642054\pi$
$774$	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	$-0.334836\pi$
$797$	28.0000	0.991811	0.495905	+	0.868377i	$0.334836\pi$
$798$	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	$-0.657420\pi$
$809$	−27.0000	−0.949269	−0.474635	+	0.880183i	$0.657420\pi$
$810$	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	$-0.681937\pi$
$821$	−31.0000	−1.08191	−0.540954	+	0.841052i	$0.681937\pi$
$822$	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	$-0.613049\pi$
$827$	−20.0000	−0.695468	−0.347734	+	0.937593i	$0.613049\pi$
$828$	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	$-0.642032\pi$
$839$	−25.0000	−0.863096	−0.431548	+	0.902090i	$0.642032\pi$
$840$	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	$-0.282256\pi$
$857$	37.0000	1.26390	0.631948	+	0.775011i	$0.282256\pi$
$858$	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	$-0.616345\pi$
$863$	−21.0000	−0.714848	−0.357424	+	0.933942i	$0.616345\pi$
$864$	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	$-0.217805\pi$
$881$	46.0000	1.54978	0.774890	+	0.632096i	$0.217805\pi$
$882$	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	$-0.344227\pi$
$887$	28.0000	0.940148	0.470074	+	0.882627i	$0.344227\pi$
$888$	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	$-0.579933\pi$
$911$	−15.0000	−0.496972	−0.248486	+	0.968635i	$0.579933\pi$
$912$	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	$-0.788581\pi$
$929$	−48.0000	−1.57483	−0.787414	+	0.616424i	$0.788581\pi$
$930$	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	$-0.453136\pi$
$941$	9.00000	0.293392	0.146696	+	0.989182i	$0.453136\pi$
$942$	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	$-0.372493\pi$
$947$	24.0000	0.779895	0.389948	+	0.920837i	$0.372493\pi$
$948$	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	$-0.268832\pi$
$953$	41.0000	1.32812	0.664060	+	0.747679i	$0.268832\pi$
$954$	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	$-0.603990\pi$
$971$	−20.0000	−0.641831	−0.320915	+	0.947108i	$0.603990\pi$
$972$	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	$-0.265500\pi$
$977$	42.0000	1.34370	0.671850	+	0.740688i	$0.265500\pi$
$978$	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	$-0.625020\pi$
$983$	−24.0000	−0.765481	−0.382741	+	0.923856i	$0.625020\pi$
$984$	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

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

)

Twists

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

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

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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Newspace parameters

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	297.2.a.b.1.1

Level	$297$
Weight	$2$
Character	297.1
Self dual	yes
Analytic conductor	$2.372$
Analytic rank	$1$
Dimension	$1$
CM	no
Inner twists	$1$