LMFDB - Embedded newform 9522.2.a.o.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [9522,2,Mod(1,9522)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("9522.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9522, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 9522 = 2 \cdot 3^{2} \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9522.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,1,0,1,3,0,-2,1,0,3,6,0,-1,-2,0,1,6,0,-2,3,0,6,0,0,4,-1,0,-2, 9] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(29)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$76.0335528047$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1058)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	9522.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} +1.00000 q^{4} +3.00000 q^{5} -2.00000 q^{7} +1.00000 q^{8} +3.00000 q^{10} +6.00000 q^{11} -1.00000 q^{13} -2.00000 q^{14} +1.00000 q^{16} +6.00000 q^{17} -2.00000 q^{19} +3.00000 q^{20} +6.00000 q^{22} +4.00000 q^{25} -1.00000 q^{26} -2.00000 q^{28} +9.00000 q^{29} -4.00000 q^{31} +1.00000 q^{32} +6.00000 q^{34} -6.00000 q^{35} -2.00000 q^{37} -2.00000 q^{38} +3.00000 q^{40} +9.00000 q^{41} +4.00000 q^{43} +6.00000 q^{44} -6.00000 q^{47} -3.00000 q^{49} +4.00000 q^{50} -1.00000 q^{52} +3.00000 q^{53} +18.0000 q^{55} -2.00000 q^{56} +9.00000 q^{58} -6.00000 q^{59} +1.00000 q^{61} -4.00000 q^{62} +1.00000 q^{64} -3.00000 q^{65} -8.00000 q^{67} +6.00000 q^{68} -6.00000 q^{70} -6.00000 q^{71} +11.0000 q^{73} -2.00000 q^{74} -2.00000 q^{76} -12.0000 q^{77} -8.00000 q^{79} +3.00000 q^{80} +9.00000 q^{82} +18.0000 q^{85} +4.00000 q^{86} +6.00000 q^{88} -9.00000 q^{89} +2.00000 q^{91} -6.00000 q^{94} -6.00000 q^{95} +1.00000 q^{97} -3.00000 q^{98} +O(q^{100})$

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
$2$	1.00000	0.707107
$3$	0	0
$3$	0	0
$4$	1.00000	0.500000
$5$	3.00000	1.34164	0.670820	−	0.741620i	$-0.265942\pi$
$5$	3.00000	1.34164	0.670820	+	0.741620i	$0.265942\pi$
$6$	0	0
$7$	−2.00000	−0.755929	−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000	−0.755929	−0.377964	+	0.925820i	$0.623376\pi$
$8$	1.00000	0.353553
$9$	0	0
$10$	3.00000	0.948683
$11$	6.00000	1.80907	0.904534	−	0.426401i	$-0.140219\pi$
$11$	6.00000	1.80907	0.904534	+	0.426401i	$0.140219\pi$
$12$	0	0
$13$	−1.00000	−0.277350	−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000	−0.277350	−0.138675	+	0.990338i	$0.544284\pi$
$14$	−2.00000	−0.534522
$15$	0	0
$16$	1.00000	0.250000
$17$	6.00000	1.45521	0.727607	−	0.685994i	$-0.240633\pi$
$17$	6.00000	1.45521	0.727607	+	0.685994i	$0.240633\pi$
$18$	0	0
$19$	−2.00000	−0.458831	−0.229416	−	0.973329i	$-0.573682\pi$
$19$	−2.00000	−0.458831	−0.229416	+	0.973329i	$0.573682\pi$
$20$	3.00000	0.670820
$21$	0	0
$22$	6.00000	1.27920
$23$	0	0
$23$	0	0
$24$	0	0
$25$	4.00000	0.800000
$26$	−1.00000	−0.196116
$27$	0	0
$28$	−2.00000	−0.377964
$29$	9.00000	1.67126	0.835629	−	0.549294i	$-0.185103\pi$
$29$	9.00000	1.67126	0.835629	+	0.549294i	$0.185103\pi$
$30$	0	0
$31$	−4.00000	−0.718421	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000	−0.718421	−0.359211	+	0.933257i	$0.616954\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	6.00000	1.02899
$35$	−6.00000	−1.01419
$36$	0	0
$37$	−2.00000	−0.328798	−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000	−0.328798	−0.164399	+	0.986394i	$0.552568\pi$
$38$	−2.00000	−0.324443
$39$	0	0
$40$	3.00000	0.474342
$41$	9.00000	1.40556	0.702782	−	0.711405i	$-0.251941\pi$
$41$	9.00000	1.40556	0.702782	+	0.711405i	$0.251941\pi$
$42$	0	0
$43$	4.00000	0.609994	0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000	0.609994	0.304997	+	0.952353i	$0.401344\pi$
$44$	6.00000	0.904534
$45$	0	0
$46$	0	0
$47$	−6.00000	−0.875190	−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000	−0.875190	−0.437595	+	0.899172i	$0.644170\pi$
$48$	0	0
$49$	−3.00000	−0.428571
$50$	4.00000	0.565685
$51$	0	0
$52$	−1.00000	−0.138675
$53$	3.00000	0.412082	0.206041	−	0.978543i	$-0.433942\pi$
$53$	3.00000	0.412082	0.206041	+	0.978543i	$0.433942\pi$
$54$	0	0
$55$	18.0000	2.42712
$56$	−2.00000	−0.267261
$57$	0	0
$58$	9.00000	1.18176
$59$	−6.00000	−0.781133	−0.390567	−	0.920575i	$-0.627721\pi$
$59$	−6.00000	−0.781133	−0.390567	+	0.920575i	$0.627721\pi$
$60$	0	0
$61$	1.00000	0.128037	0.0640184	−	0.997949i	$-0.479608\pi$
$61$	1.00000	0.128037	0.0640184	+	0.997949i	$0.479608\pi$
$62$	−4.00000	−0.508001
$63$	0	0
$64$	1.00000	0.125000
$65$	−3.00000	−0.372104
$66$	0	0
$67$	−8.00000	−0.977356	−0.488678	−	0.872464i	$-0.662521\pi$
$67$	−8.00000	−0.977356	−0.488678	+	0.872464i	$0.662521\pi$
$68$	6.00000	0.727607
$69$	0	0
$70$	−6.00000	−0.717137
$71$	−6.00000	−0.712069	−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000	−0.712069	−0.356034	+	0.934473i	$0.615871\pi$
$72$	0	0
$73$	11.0000	1.28745	0.643726	−	0.765256i	$-0.277388\pi$
$73$	11.0000	1.28745	0.643726	+	0.765256i	$0.277388\pi$
$74$	−2.00000	−0.232495
$75$	0	0
$76$	−2.00000	−0.229416
$77$	−12.0000	−1.36753
$78$	0	0
$79$	−8.00000	−0.900070	−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000	−0.900070	−0.450035	+	0.893011i	$0.648589\pi$
$80$	3.00000	0.335410
$81$	0	0
$82$	9.00000	0.993884
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	0	0
$85$	18.0000	1.95237
$86$	4.00000	0.431331
$87$	0	0
$88$	6.00000	0.639602
$89$	−9.00000	−0.953998	−0.476999	−	0.878904i	$-0.658275\pi$
$89$	−9.00000	−0.953998	−0.476999	+	0.878904i	$0.658275\pi$
$90$	0	0
$91$	2.00000	0.209657
$92$	0	0
$93$	0	0
$94$	−6.00000	−0.618853
$95$	−6.00000	−0.615587
$96$	0	0
$97$	1.00000	0.101535	0.0507673	−	0.998711i	$-0.483833\pi$
$97$	1.00000	0.101535	0.0507673	+	0.998711i	$0.483833\pi$
$98$	−3.00000	−0.303046
$99$	0	0
$100$	4.00000	0.400000
$101$	9.00000	0.895533	0.447767	−	0.894150i	$-0.352219\pi$
$101$	9.00000	0.895533	0.447767	+	0.894150i	$0.352219\pi$
$102$	0	0
$103$	4.00000	0.394132	0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000	0.394132	0.197066	+	0.980390i	$0.436859\pi$
$104$	−1.00000	−0.0980581
$105$	0	0
$106$	3.00000	0.291386
$107$	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
$109$	−11.0000	−1.05361	−0.526804	−	0.849987i	$-0.676610\pi$
$109$	−11.0000	−1.05361	−0.526804	+	0.849987i	$0.676610\pi$
$110$	18.0000	1.71623
$111$	0	0
$112$	−2.00000	−0.188982
$113$	3.00000	0.282216	0.141108	−	0.989994i	$-0.454933\pi$
$113$	3.00000	0.282216	0.141108	+	0.989994i	$0.454933\pi$
$114$	0	0
$115$	0	0
$116$	9.00000	0.835629
$117$	0	0
$118$	−6.00000	−0.552345
$119$	−12.0000	−1.10004
$120$	0	0
$121$	25.0000	2.27273
$122$	1.00000	0.0905357
$123$	0	0
$124$	−4.00000	−0.359211
$125$	−3.00000	−0.268328
$126$	0	0
$127$	8.00000	0.709885	0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000	0.709885	0.354943	+	0.934888i	$0.384500\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	−3.00000	−0.263117
$131$	18.0000	1.57267	0.786334	−	0.617802i	$-0.211977\pi$
$131$	18.0000	1.57267	0.786334	+	0.617802i	$0.211977\pi$
$132$	0	0
$133$	4.00000	0.346844
$134$	−8.00000	−0.691095
$135$	0	0
$136$	6.00000	0.514496
$137$	−9.00000	−0.768922	−0.384461	−	0.923141i	$-0.625613\pi$
$137$	−9.00000	−0.768922	−0.384461	+	0.923141i	$0.625613\pi$
$138$	0	0
$139$	−4.00000	−0.339276	−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000	−0.339276	−0.169638	+	0.985506i	$0.554260\pi$
$140$	−6.00000	−0.507093
$141$	0	0
$142$	−6.00000	−0.503509
$143$	−6.00000	−0.501745
$144$	0	0
$145$	27.0000	2.24223
$146$	11.0000	0.910366
$147$	0	0
$148$	−2.00000	−0.164399
$149$	15.0000	1.22885	0.614424	−	0.788976i	$-0.289388\pi$
$149$	15.0000	1.22885	0.614424	+	0.788976i	$0.289388\pi$
$150$	0	0
$151$	2.00000	0.162758	0.0813788	−	0.996683i	$-0.474068\pi$
$151$	2.00000	0.162758	0.0813788	+	0.996683i	$0.474068\pi$
$152$	−2.00000	−0.162221
$153$	0	0
$154$	−12.0000	−0.966988
$155$	−12.0000	−0.963863
$156$	0	0
$157$	−23.0000	−1.83560	−0.917800	−	0.397043i	$-0.870036\pi$
$157$	−23.0000	−1.83560	−0.917800	+	0.397043i	$0.870036\pi$
$158$	−8.00000	−0.636446
$159$	0	0
$160$	3.00000	0.237171
$161$	0	0
$162$	0	0
$163$	2.00000	0.156652	0.0783260	−	0.996928i	$-0.475042\pi$
$163$	2.00000	0.156652	0.0783260	+	0.996928i	$0.475042\pi$
$164$	9.00000	0.702782
$165$	0	0
$166$	0	0
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	0	0
$169$	−12.0000	−0.923077
$170$	18.0000	1.38054
$171$	0	0
$172$	4.00000	0.304997
$173$	9.00000	0.684257	0.342129	−	0.939653i	$-0.388852\pi$
$173$	9.00000	0.684257	0.342129	+	0.939653i	$0.388852\pi$
$174$	0	0
$175$	−8.00000	−0.604743
$176$	6.00000	0.452267
$177$	0	0
$178$	−9.00000	−0.674579
$179$	0	0		−	1.00000i	$-0.5\pi$
$179$	0	0			1.00000i	$0.5\pi$
$180$	0	0
$181$	−2.00000	−0.148659	−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000	−0.148659	−0.0743294	+	0.997234i	$0.523682\pi$
$182$	2.00000	0.148250
$183$	0	0
$184$	0	0
$185$	−6.00000	−0.441129
$186$	0	0
$187$	36.0000	2.63258
$188$	−6.00000	−0.437595
$189$	0	0
$190$	−6.00000	−0.435286
$191$	−12.0000	−0.868290	−0.434145	−	0.900843i	$-0.642949\pi$
$191$	−12.0000	−0.868290	−0.434145	+	0.900843i	$0.642949\pi$
$192$	0	0
$193$	−13.0000	−0.935760	−0.467880	−	0.883792i	$-0.654982\pi$
$193$	−13.0000	−0.935760	−0.467880	+	0.883792i	$0.654982\pi$
$194$	1.00000	0.0717958
$195$	0	0
$196$	−3.00000	−0.214286
$197$	21.0000	1.49619	0.748094	−	0.663593i	$-0.230969\pi$
$197$	21.0000	1.49619	0.748094	+	0.663593i	$0.230969\pi$
$198$	0	0
$199$	−14.0000	−0.992434	−0.496217	−	0.868199i	$-0.665278\pi$
$199$	−14.0000	−0.992434	−0.496217	+	0.868199i	$0.665278\pi$
$200$	4.00000	0.282843
$201$	0	0
$202$	9.00000	0.633238
$203$	−18.0000	−1.26335
$204$	0	0
$205$	27.0000	1.88576
$206$	4.00000	0.278693
$207$	0	0
$208$	−1.00000	−0.0693375
$209$	−12.0000	−0.830057
$210$	0	0
$211$	−22.0000	−1.51454	−0.757271	−	0.653101i	$-0.773468\pi$
$211$	−22.0000	−1.51454	−0.757271	+	0.653101i	$0.773468\pi$
$212$	3.00000	0.206041
$213$	0	0
$214$	6.00000	0.410152
$215$	12.0000	0.818393
$216$	0	0
$217$	8.00000	0.543075
$218$	−11.0000	−0.745014
$219$	0	0
$220$	18.0000	1.21356
$221$	−6.00000	−0.403604
$222$	0	0
$223$	14.0000	0.937509	0.468755	−	0.883328i	$-0.344703\pi$
$223$	14.0000	0.937509	0.468755	+	0.883328i	$0.344703\pi$
$224$	−2.00000	−0.133631
$225$	0	0
$226$	3.00000	0.199557
$227$	−12.0000	−0.796468	−0.398234	−	0.917284i	$-0.630377\pi$
$227$	−12.0000	−0.796468	−0.398234	+	0.917284i	$0.630377\pi$
$228$	0	0
$229$	−2.00000	−0.132164	−0.0660819	−	0.997814i	$-0.521050\pi$
$229$	−2.00000	−0.132164	−0.0660819	+	0.997814i	$0.521050\pi$
$230$	0	0
$231$	0	0
$232$	9.00000	0.590879
$233$	9.00000	0.589610	0.294805	−	0.955557i	$-0.404745\pi$
$233$	9.00000	0.589610	0.294805	+	0.955557i	$0.404745\pi$
$234$	0	0
$235$	−18.0000	−1.17419
$236$	−6.00000	−0.390567
$237$	0	0
$238$	−12.0000	−0.777844
$239$	0	0		−	1.00000i	$-0.5\pi$
$239$	0	0			1.00000i	$0.5\pi$
$240$	0	0
$241$	1.00000	0.0644157	0.0322078	−	0.999481i	$-0.489746\pi$
$241$	1.00000	0.0644157	0.0322078	+	0.999481i	$0.489746\pi$
$242$	25.0000	1.60706
$243$	0	0
$244$	1.00000	0.0640184
$245$	−9.00000	−0.574989
$246$	0	0
$247$	2.00000	0.127257
$248$	−4.00000	−0.254000
$249$	0	0
$250$	−3.00000	−0.189737
$251$	18.0000	1.13615	0.568075	−	0.822977i	$-0.307688\pi$
$251$	18.0000	1.13615	0.568075	+	0.822977i	$0.307688\pi$
$252$	0	0
$253$	0	0
$254$	8.00000	0.501965
$255$	0	0
$256$	1.00000	0.0625000
$257$	−3.00000	−0.187135	−0.0935674	−	0.995613i	$-0.529827\pi$
$257$	−3.00000	−0.187135	−0.0935674	+	0.995613i	$0.529827\pi$
$258$	0	0
$259$	4.00000	0.248548
$260$	−3.00000	−0.186052
$261$	0	0
$262$	18.0000	1.11204
$263$	30.0000	1.84988	0.924940	−	0.380114i	$-0.124115\pi$
$263$	30.0000	1.84988	0.924940	+	0.380114i	$0.124115\pi$
$264$	0	0
$265$	9.00000	0.552866
$266$	4.00000	0.245256
$267$	0	0
$268$	−8.00000	−0.488678
$269$	30.0000	1.82913	0.914566	−	0.404436i	$-0.132532\pi$
$269$	30.0000	1.82913	0.914566	+	0.404436i	$0.132532\pi$
$270$	0	0
$271$	2.00000	0.121491	0.0607457	−	0.998153i	$-0.480652\pi$
$271$	2.00000	0.121491	0.0607457	+	0.998153i	$0.480652\pi$
$272$	6.00000	0.363803
$273$	0	0
$274$	−9.00000	−0.543710
$275$	24.0000	1.44725
$276$	0	0
$277$	−22.0000	−1.32185	−0.660926	−	0.750451i	$-0.729836\pi$
$277$	−22.0000	−1.32185	−0.660926	+	0.750451i	$0.729836\pi$
$278$	−4.00000	−0.239904
$279$	0	0
$280$	−6.00000	−0.358569
$281$	30.0000	1.78965	0.894825	−	0.446417i	$-0.147300\pi$
$281$	30.0000	1.78965	0.894825	+	0.446417i	$0.147300\pi$
$282$	0	0
$283$	−20.0000	−1.18888	−0.594438	−	0.804141i	$-0.702626\pi$
$283$	−20.0000	−1.18888	−0.594438	+	0.804141i	$0.702626\pi$
$284$	−6.00000	−0.356034
$285$	0	0
$286$	−6.00000	−0.354787
$287$	−18.0000	−1.06251
$288$	0	0
$289$	19.0000	1.11765
$290$	27.0000	1.58549
$291$	0	0
$292$	11.0000	0.643726
$293$	−9.00000	−0.525786	−0.262893	−	0.964825i	$-0.584677\pi$
$293$	−9.00000	−0.525786	−0.262893	+	0.964825i	$0.584677\pi$
$294$	0	0
$295$	−18.0000	−1.04800
$296$	−2.00000	−0.116248
$297$	0	0
$298$	15.0000	0.868927
$299$	0	0
$300$	0	0
$301$	−8.00000	−0.461112
$302$	2.00000	0.115087
$303$	0	0
$304$	−2.00000	−0.114708
$305$	3.00000	0.171780
$306$	0	0
$307$	26.0000	1.48390	0.741949	−	0.670456i	$-0.233902\pi$
$307$	26.0000	1.48390	0.741949	+	0.670456i	$0.233902\pi$
$308$	−12.0000	−0.683763
$309$	0	0
$310$	−12.0000	−0.681554
$311$	−18.0000	−1.02069	−0.510343	−	0.859971i	$-0.670482\pi$
$311$	−18.0000	−1.02069	−0.510343	+	0.859971i	$0.670482\pi$
$312$	0	0
$313$	1.00000	0.0565233	0.0282617	−	0.999601i	$-0.491003\pi$
$313$	1.00000	0.0565233	0.0282617	+	0.999601i	$0.491003\pi$
$314$	−23.0000	−1.29797
$315$	0	0
$316$	−8.00000	−0.450035
$317$	−15.0000	−0.842484	−0.421242	−	0.906948i	$-0.638406\pi$
$317$	−15.0000	−0.842484	−0.421242	+	0.906948i	$0.638406\pi$
$318$	0	0
$319$	54.0000	3.02342
$320$	3.00000	0.167705
$321$	0	0
$322$	0	0
$323$	−12.0000	−0.667698
$324$	0	0
$325$	−4.00000	−0.221880
$326$	2.00000	0.110770
$327$	0	0
$328$	9.00000	0.496942
$329$	12.0000	0.661581
$330$	0	0
$331$	−16.0000	−0.879440	−0.439720	−	0.898135i	$-0.644922\pi$
$331$	−16.0000	−0.879440	−0.439720	+	0.898135i	$0.644922\pi$
$332$	0	0
$333$	0	0
$334$	0	0
$335$	−24.0000	−1.31126
$336$	0	0
$337$	1.00000	0.0544735	0.0272367	−	0.999629i	$-0.491329\pi$
$337$	1.00000	0.0544735	0.0272367	+	0.999629i	$0.491329\pi$
$338$	−12.0000	−0.652714
$339$	0	0
$340$	18.0000	0.976187
$341$	−24.0000	−1.29967
$342$	0	0
$343$	20.0000	1.07990
$344$	4.00000	0.215666
$345$	0	0
$346$	9.00000	0.483843
$347$	30.0000	1.61048	0.805242	−	0.592946i	$-0.202035\pi$
$347$	30.0000	1.61048	0.805242	+	0.592946i	$0.202035\pi$
$348$	0	0
$349$	2.00000	0.107058	0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000	0.107058	0.0535288	+	0.998566i	$0.482953\pi$
$350$	−8.00000	−0.427618
$351$	0	0
$352$	6.00000	0.319801
$353$	21.0000	1.11772	0.558859	−	0.829263i	$-0.311239\pi$
$353$	21.0000	1.11772	0.558859	+	0.829263i	$0.311239\pi$
$354$	0	0
$355$	−18.0000	−0.955341
$356$	−9.00000	−0.476999
$357$	0	0
$358$	0	0
$359$	−6.00000	−0.316668	−0.158334	−	0.987386i	$-0.550612\pi$
$359$	−6.00000	−0.316668	−0.158334	+	0.987386i	$0.550612\pi$
$360$	0	0
$361$	−15.0000	−0.789474
$362$	−2.00000	−0.105118
$363$	0	0
$364$	2.00000	0.104828
$365$	33.0000	1.72730
$366$	0	0
$367$	10.0000	0.521996	0.260998	−	0.965339i	$-0.415948\pi$
$367$	10.0000	0.521996	0.260998	+	0.965339i	$0.415948\pi$
$368$	0	0
$369$	0	0
$370$	−6.00000	−0.311925
$371$	−6.00000	−0.311504
$372$	0	0
$373$	22.0000	1.13912	0.569558	−	0.821951i	$-0.307114\pi$
$373$	22.0000	1.13912	0.569558	+	0.821951i	$0.307114\pi$
$374$	36.0000	1.86152
$375$	0	0
$376$	−6.00000	−0.309426
$377$	−9.00000	−0.463524
$378$	0	0
$379$	34.0000	1.74646	0.873231	−	0.487306i	$-0.162020\pi$
$379$	34.0000	1.74646	0.873231	+	0.487306i	$0.162020\pi$
$380$	−6.00000	−0.307794
$381$	0	0
$382$	−12.0000	−0.613973
$383$	−24.0000	−1.22634	−0.613171	−	0.789950i	$-0.710106\pi$
$383$	−24.0000	−1.22634	−0.613171	+	0.789950i	$0.710106\pi$
$384$	0	0
$385$	−36.0000	−1.83473
$386$	−13.0000	−0.661683
$387$	0	0
$388$	1.00000	0.0507673
$389$	−30.0000	−1.52106	−0.760530	−	0.649303i	$-0.775061\pi$
$389$	−30.0000	−1.52106	−0.760530	+	0.649303i	$0.775061\pi$
$390$	0	0
$391$	0	0
$392$	−3.00000	−0.151523
$393$	0	0
$394$	21.0000	1.05796
$395$	−24.0000	−1.20757
$396$	0	0
$397$	35.0000	1.75660	0.878300	−	0.478110i	$-0.158678\pi$
$397$	35.0000	1.75660	0.878300	+	0.478110i	$0.158678\pi$
$398$	−14.0000	−0.701757
$399$	0	0
$400$	4.00000	0.200000
$401$	15.0000	0.749064	0.374532	−	0.927214i	$-0.377803\pi$
$401$	15.0000	0.749064	0.374532	+	0.927214i	$0.377803\pi$
$402$	0	0
$403$	4.00000	0.199254
$404$	9.00000	0.447767
$405$	0	0
$406$	−18.0000	−0.893325
$407$	−12.0000	−0.594818
$408$	0	0
$409$	−10.0000	−0.494468	−0.247234	−	0.968956i	$-0.579522\pi$
$409$	−10.0000	−0.494468	−0.247234	+	0.968956i	$0.579522\pi$
$410$	27.0000	1.33343
$411$	0	0
$412$	4.00000	0.197066
$413$	12.0000	0.590481
$414$	0	0
$415$	0	0
$416$	−1.00000	−0.0490290
$417$	0	0
$418$	−12.0000	−0.586939
$419$	−24.0000	−1.17248	−0.586238	−	0.810139i	$-0.699392\pi$
$419$	−24.0000	−1.17248	−0.586238	+	0.810139i	$0.699392\pi$
$420$	0	0
$421$	−38.0000	−1.85201	−0.926003	−	0.377515i	$-0.876779\pi$
$421$	−38.0000	−1.85201	−0.926003	+	0.377515i	$0.876779\pi$
$422$	−22.0000	−1.07094
$423$	0	0
$424$	3.00000	0.145693
$425$	24.0000	1.16417
$426$	0	0
$427$	−2.00000	−0.0967868
$428$	6.00000	0.290021
$429$	0	0
$430$	12.0000	0.578691
$431$	−30.0000	−1.44505	−0.722525	−	0.691345i	$-0.757018\pi$
$431$	−30.0000	−1.44505	−0.722525	+	0.691345i	$0.757018\pi$
$432$	0	0
$433$	1.00000	0.0480569	0.0240285	−	0.999711i	$-0.492351\pi$
$433$	1.00000	0.0480569	0.0240285	+	0.999711i	$0.492351\pi$
$434$	8.00000	0.384012
$435$	0	0
$436$	−11.0000	−0.526804
$437$	0	0
$438$	0	0
$439$	32.0000	1.52728	0.763638	−	0.645644i	$-0.223411\pi$
$439$	32.0000	1.52728	0.763638	+	0.645644i	$0.223411\pi$
$440$	18.0000	0.858116
$441$	0	0
$442$	−6.00000	−0.285391
$443$	24.0000	1.14027	0.570137	−	0.821549i	$-0.306890\pi$
$443$	24.0000	1.14027	0.570137	+	0.821549i	$0.306890\pi$
$444$	0	0
$445$	−27.0000	−1.27992
$446$	14.0000	0.662919
$447$	0	0
$448$	−2.00000	−0.0944911
$449$	−39.0000	−1.84052	−0.920262	−	0.391303i	$-0.872024\pi$
$449$	−39.0000	−1.84052	−0.920262	+	0.391303i	$0.872024\pi$
$450$	0	0
$451$	54.0000	2.54276
$452$	3.00000	0.141108
$453$	0	0
$454$	−12.0000	−0.563188
$455$	6.00000	0.281284
$456$	0	0
$457$	−23.0000	−1.07589	−0.537947	−	0.842978i	$-0.680800\pi$
$457$	−23.0000	−1.07589	−0.537947	+	0.842978i	$0.680800\pi$
$458$	−2.00000	−0.0934539
$459$	0	0
$460$	0	0
$461$	−15.0000	−0.698620	−0.349310	−	0.937007i	$-0.613584\pi$
$461$	−15.0000	−0.698620	−0.349310	+	0.937007i	$0.613584\pi$
$462$	0	0
$463$	−40.0000	−1.85896	−0.929479	−	0.368875i	$-0.879743\pi$
$463$	−40.0000	−1.85896	−0.929479	+	0.368875i	$0.879743\pi$
$464$	9.00000	0.417815
$465$	0	0
$466$	9.00000	0.416917
$467$	−24.0000	−1.11059	−0.555294	−	0.831654i	$-0.687394\pi$
$467$	−24.0000	−1.11059	−0.555294	+	0.831654i	$0.687394\pi$
$468$	0	0
$469$	16.0000	0.738811
$470$	−18.0000	−0.830278
$471$	0	0
$472$	−6.00000	−0.276172
$473$	24.0000	1.10352
$474$	0	0
$475$	−8.00000	−0.367065
$476$	−12.0000	−0.550019
$477$	0	0
$478$	0	0
$479$	0	0		−	1.00000i	$-0.5\pi$
$479$	0	0			1.00000i	$0.5\pi$
$480$	0	0
$481$	2.00000	0.0911922
$482$	1.00000	0.0455488
$483$	0	0
$484$	25.0000	1.13636
$485$	3.00000	0.136223
$486$	0	0
$487$	−22.0000	−0.996915	−0.498458	−	0.866914i	$-0.666100\pi$
$487$	−22.0000	−0.996915	−0.498458	+	0.866914i	$0.666100\pi$
$488$	1.00000	0.0452679
$489$	0	0
$490$	−9.00000	−0.406579
$491$	0	0		−	1.00000i	$-0.5\pi$
$491$	0	0			1.00000i	$0.5\pi$
$492$	0	0
$493$	54.0000	2.43204
$494$	2.00000	0.0899843
$495$	0	0
$496$	−4.00000	−0.179605
$497$	12.0000	0.538274
$498$	0	0
$499$	20.0000	0.895323	0.447661	−	0.894203i	$-0.352257\pi$
$499$	20.0000	0.895323	0.447661	+	0.894203i	$0.352257\pi$
$500$	−3.00000	−0.134164
$501$	0	0
$502$	18.0000	0.803379
$503$	30.0000	1.33763	0.668817	−	0.743427i	$-0.266801\pi$
$503$	30.0000	1.33763	0.668817	+	0.743427i	$0.266801\pi$
$504$	0	0
$505$	27.0000	1.20148
$506$	0	0
$507$	0	0
$508$	8.00000	0.354943
$509$	21.0000	0.930809	0.465404	−	0.885098i	$-0.345909\pi$
$509$	21.0000	0.930809	0.465404	+	0.885098i	$0.345909\pi$
$510$	0	0
$511$	−22.0000	−0.973223
$512$	1.00000	0.0441942
$513$	0	0
$514$	−3.00000	−0.132324
$515$	12.0000	0.528783
$516$	0	0
$517$	−36.0000	−1.58328
$518$	4.00000	0.175750
$519$	0	0
$520$	−3.00000	−0.131559
$521$	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
$523$	−20.0000	−0.874539	−0.437269	−	0.899331i	$-0.644054\pi$
$523$	−20.0000	−0.874539	−0.437269	+	0.899331i	$0.644054\pi$
$524$	18.0000	0.786334
$525$	0	0
$526$	30.0000	1.30806
$527$	−24.0000	−1.04546
$528$	0	0
$529$	0	0
$530$	9.00000	0.390935
$531$	0	0
$532$	4.00000	0.173422
$533$	−9.00000	−0.389833
$534$	0	0
$535$	18.0000	0.778208
$536$	−8.00000	−0.345547
$537$	0	0
$538$	30.0000	1.29339
$539$	−18.0000	−0.775315
$540$	0	0
$541$	11.0000	0.472927	0.236463	−	0.971640i	$-0.424012\pi$
$541$	11.0000	0.472927	0.236463	+	0.971640i	$0.424012\pi$
$542$	2.00000	0.0859074
$543$	0	0
$544$	6.00000	0.257248
$545$	−33.0000	−1.41356
$546$	0	0
$547$	8.00000	0.342055	0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000	0.342055	0.171028	+	0.985266i	$0.445291\pi$
$548$	−9.00000	−0.384461
$549$	0	0
$550$	24.0000	1.02336
$551$	−18.0000	−0.766826
$552$	0	0
$553$	16.0000	0.680389
$554$	−22.0000	−0.934690
$555$	0	0
$556$	−4.00000	−0.169638
$557$	−33.0000	−1.39825	−0.699127	−	0.714997i	$-0.746428\pi$
$557$	−33.0000	−1.39825	−0.699127	+	0.714997i	$0.746428\pi$
$558$	0	0
$559$	−4.00000	−0.169182
$560$	−6.00000	−0.253546
$561$	0	0
$562$	30.0000	1.26547
$563$	24.0000	1.01148	0.505740	−	0.862686i	$-0.331220\pi$
$563$	24.0000	1.01148	0.505740	+	0.862686i	$0.331220\pi$
$564$	0	0
$565$	9.00000	0.378633
$566$	−20.0000	−0.840663
$567$	0	0
$568$	−6.00000	−0.251754
$569$	−9.00000	−0.377300	−0.188650	−	0.982044i	$-0.560411\pi$
$569$	−9.00000	−0.377300	−0.188650	+	0.982044i	$0.560411\pi$
$570$	0	0
$571$	−14.0000	−0.585882	−0.292941	−	0.956131i	$-0.594634\pi$
$571$	−14.0000	−0.585882	−0.292941	+	0.956131i	$0.594634\pi$
$572$	−6.00000	−0.250873
$573$	0	0
$574$	−18.0000	−0.751305
$575$	0	0
$576$	0	0
$577$	2.00000	0.0832611	0.0416305	−	0.999133i	$-0.486745\pi$
$577$	2.00000	0.0832611	0.0416305	+	0.999133i	$0.486745\pi$
$578$	19.0000	0.790296
$579$	0	0
$580$	27.0000	1.12111
$581$	0	0
$582$	0	0
$583$	18.0000	0.745484
$584$	11.0000	0.455183
$585$	0	0
$586$	−9.00000	−0.371787
$587$	24.0000	0.990586	0.495293	−	0.868726i	$-0.335061\pi$
$587$	24.0000	0.990586	0.495293	+	0.868726i	$0.335061\pi$
$588$	0	0
$589$	8.00000	0.329634
$590$	−18.0000	−0.741048
$591$	0	0
$592$	−2.00000	−0.0821995
$593$	−6.00000	−0.246390	−0.123195	−	0.992382i	$-0.539314\pi$
$593$	−6.00000	−0.246390	−0.123195	+	0.992382i	$0.539314\pi$
$594$	0	0
$595$	−36.0000	−1.47586
$596$	15.0000	0.614424
$597$	0	0
$598$	0	0
$599$	30.0000	1.22577	0.612883	−	0.790173i	$-0.290010\pi$
$599$	30.0000	1.22577	0.612883	+	0.790173i	$0.290010\pi$
$600$	0	0
$601$	−13.0000	−0.530281	−0.265141	−	0.964210i	$-0.585418\pi$
$601$	−13.0000	−0.530281	−0.265141	+	0.964210i	$0.585418\pi$
$602$	−8.00000	−0.326056
$603$	0	0
$604$	2.00000	0.0813788
$605$	75.0000	3.04918
$606$	0	0
$607$	26.0000	1.05531	0.527654	−	0.849460i	$-0.323072\pi$
$607$	26.0000	1.05531	0.527654	+	0.849460i	$0.323072\pi$
$608$	−2.00000	−0.0811107
$609$	0	0
$610$	3.00000	0.121466
$611$	6.00000	0.242734
$612$	0	0
$613$	−11.0000	−0.444286	−0.222143	−	0.975014i	$-0.571305\pi$
$613$	−11.0000	−0.444286	−0.222143	+	0.975014i	$0.571305\pi$
$614$	26.0000	1.04927
$615$	0	0
$616$	−12.0000	−0.483494
$617$	−6.00000	−0.241551	−0.120775	−	0.992680i	$-0.538538\pi$
$617$	−6.00000	−0.241551	−0.120775	+	0.992680i	$0.538538\pi$
$618$	0	0
$619$	16.0000	0.643094	0.321547	−	0.946894i	$-0.395797\pi$
$619$	16.0000	0.643094	0.321547	+	0.946894i	$0.395797\pi$
$620$	−12.0000	−0.481932
$621$	0	0
$622$	−18.0000	−0.721734
$623$	18.0000	0.721155
$624$	0	0
$625$	−29.0000	−1.16000
$626$	1.00000	0.0399680
$627$	0	0
$628$	−23.0000	−0.917800
$629$	−12.0000	−0.478471
$630$	0	0
$631$	−32.0000	−1.27390	−0.636950	−	0.770905i	$-0.719804\pi$
$631$	−32.0000	−1.27390	−0.636950	+	0.770905i	$0.719804\pi$
$632$	−8.00000	−0.318223
$633$	0	0
$634$	−15.0000	−0.595726
$635$	24.0000	0.952411
$636$	0	0
$637$	3.00000	0.118864
$638$	54.0000	2.13788
$639$	0	0
$640$	3.00000	0.118585
$641$	27.0000	1.06644	0.533218	−	0.845978i	$-0.320983\pi$
$641$	27.0000	1.06644	0.533218	+	0.845978i	$0.320983\pi$
$642$	0	0
$643$	−2.00000	−0.0788723	−0.0394362	−	0.999222i	$-0.512556\pi$
$643$	−2.00000	−0.0788723	−0.0394362	+	0.999222i	$0.512556\pi$
$644$	0	0
$645$	0	0
$646$	−12.0000	−0.472134
$647$	−30.0000	−1.17942	−0.589711	−	0.807614i	$-0.700758\pi$
$647$	−30.0000	−1.17942	−0.589711	+	0.807614i	$0.700758\pi$
$648$	0	0
$649$	−36.0000	−1.41312
$650$	−4.00000	−0.156893
$651$	0	0
$652$	2.00000	0.0783260
$653$	−39.0000	−1.52619	−0.763094	−	0.646288i	$-0.776321\pi$
$653$	−39.0000	−1.52619	−0.763094	+	0.646288i	$0.776321\pi$
$654$	0	0
$655$	54.0000	2.10995
$656$	9.00000	0.351391
$657$	0	0
$658$	12.0000	0.467809
$659$	−36.0000	−1.40236	−0.701180	−	0.712984i	$-0.747343\pi$
$659$	−36.0000	−1.40236	−0.701180	+	0.712984i	$0.747343\pi$
$660$	0	0
$661$	13.0000	0.505641	0.252821	−	0.967513i	$-0.418642\pi$
$661$	13.0000	0.505641	0.252821	+	0.967513i	$0.418642\pi$
$662$	−16.0000	−0.621858
$663$	0	0
$664$	0	0
$665$	12.0000	0.465340
$666$	0	0
$667$	0	0
$668$	0	0
$669$	0	0
$670$	−24.0000	−0.927201
$671$	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	$0.561736\pi$
$674$	1.00000	0.0385186
$675$	0	0
$676$	−12.0000	−0.461538
$677$	−21.0000	−0.807096	−0.403548	−	0.914959i	$-0.632223\pi$
$677$	−21.0000	−0.807096	−0.403548	+	0.914959i	$0.632223\pi$
$678$	0	0
$679$	−2.00000	−0.0767530
$680$	18.0000	0.690268
$681$	0	0
$682$	−24.0000	−0.919007
$683$	12.0000	0.459167	0.229584	−	0.973289i	$-0.426264\pi$
$683$	12.0000	0.459167	0.229584	+	0.973289i	$0.426264\pi$
$684$	0	0
$685$	−27.0000	−1.03162
$686$	20.0000	0.763604
$687$	0	0
$688$	4.00000	0.152499
$689$	−3.00000	−0.114291
$690$	0	0
$691$	−40.0000	−1.52167	−0.760836	−	0.648944i	$-0.775211\pi$
$691$	−40.0000	−1.52167	−0.760836	+	0.648944i	$0.775211\pi$
$692$	9.00000	0.342129
$693$	0	0
$694$	30.0000	1.13878
$695$	−12.0000	−0.455186
$696$	0	0
$697$	54.0000	2.04540
$698$	2.00000	0.0757011
$699$	0	0
$700$	−8.00000	−0.302372
$701$	−30.0000	−1.13308	−0.566542	−	0.824033i	$-0.691719\pi$
$701$	−30.0000	−1.13308	−0.566542	+	0.824033i	$0.691719\pi$
$702$	0	0
$703$	4.00000	0.150863
$704$	6.00000	0.226134
$705$	0	0
$706$	21.0000	0.790345
$707$	−18.0000	−0.676960
$708$	0	0
$709$	−11.0000	−0.413114	−0.206557	−	0.978435i	$-0.566226\pi$
$709$	−11.0000	−0.413114	−0.206557	+	0.978435i	$0.566226\pi$
$710$	−18.0000	−0.675528
$711$	0	0
$712$	−9.00000	−0.337289
$713$	0	0
$714$	0	0
$715$	−18.0000	−0.673162
$716$	0	0
$717$	0	0
$718$	−6.00000	−0.223918
$719$	−36.0000	−1.34257	−0.671287	−	0.741198i	$-0.734258\pi$
$719$	−36.0000	−1.34257	−0.671287	+	0.741198i	$0.734258\pi$
$720$	0	0
$721$	−8.00000	−0.297936
$722$	−15.0000	−0.558242
$723$	0	0
$724$	−2.00000	−0.0743294
$725$	36.0000	1.33701
$726$	0	0
$727$	−26.0000	−0.964287	−0.482143	−	0.876092i	$-0.660142\pi$
$727$	−26.0000	−0.964287	−0.482143	+	0.876092i	$0.660142\pi$
$728$	2.00000	0.0741249
$729$	0	0
$730$	33.0000	1.22138
$731$	24.0000	0.887672
$732$	0	0
$733$	25.0000	0.923396	0.461698	−	0.887037i	$-0.347240\pi$
$733$	25.0000	0.923396	0.461698	+	0.887037i	$0.347240\pi$
$734$	10.0000	0.369107
$735$	0	0
$736$	0	0
$737$	−48.0000	−1.76810
$738$	0	0
$739$	−10.0000	−0.367856	−0.183928	−	0.982940i	$-0.558881\pi$
$739$	−10.0000	−0.367856	−0.183928	+	0.982940i	$0.558881\pi$
$740$	−6.00000	−0.220564
$741$	0	0
$742$	−6.00000	−0.220267
$743$	6.00000	0.220119	0.110059	−	0.993925i	$-0.464896\pi$
$743$	6.00000	0.220119	0.110059	+	0.993925i	$0.464896\pi$
$744$	0	0
$745$	45.0000	1.64867
$746$	22.0000	0.805477
$747$	0	0
$748$	36.0000	1.31629
$749$	−12.0000	−0.438470
$750$	0	0
$751$	−14.0000	−0.510867	−0.255434	−	0.966827i	$-0.582218\pi$
$751$	−14.0000	−0.510867	−0.255434	+	0.966827i	$0.582218\pi$
$752$	−6.00000	−0.218797
$753$	0	0
$754$	−9.00000	−0.327761
$755$	6.00000	0.218362
$756$	0	0
$757$	25.0000	0.908640	0.454320	−	0.890838i	$-0.349882\pi$
$757$	25.0000	0.908640	0.454320	+	0.890838i	$0.349882\pi$
$758$	34.0000	1.23494
$759$	0	0
$760$	−6.00000	−0.217643
$761$	45.0000	1.63125	0.815624	−	0.578582i	$-0.196394\pi$
$761$	45.0000	1.63125	0.815624	+	0.578582i	$0.196394\pi$
$762$	0	0
$763$	22.0000	0.796453
$764$	−12.0000	−0.434145
$765$	0	0
$766$	−24.0000	−0.867155
$767$	6.00000	0.216647
$768$	0	0
$769$	10.0000	0.360609	0.180305	−	0.983611i	$-0.442292\pi$
$769$	10.0000	0.360609	0.180305	+	0.983611i	$0.442292\pi$
$770$	−36.0000	−1.29735
$771$	0	0
$772$	−13.0000	−0.467880
$773$	−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
$775$	−16.0000	−0.574737
$776$	1.00000	0.0358979
$777$	0	0
$778$	−30.0000	−1.07555
$779$	−18.0000	−0.644917
$780$	0	0
$781$	−36.0000	−1.28818
$782$	0	0
$783$	0	0
$784$	−3.00000	−0.107143
$785$	−69.0000	−2.46272
$786$	0	0
$787$	22.0000	0.784215	0.392108	−	0.919919i	$-0.371746\pi$
$787$	22.0000	0.784215	0.392108	+	0.919919i	$0.371746\pi$
$788$	21.0000	0.748094
$789$	0	0
$790$	−24.0000	−0.853882
$791$	−6.00000	−0.213335
$792$	0	0
$793$	−1.00000	−0.0355110
$794$	35.0000	1.24210
$795$	0	0
$796$	−14.0000	−0.496217
$797$	42.0000	1.48772	0.743858	−	0.668338i	$-0.232994\pi$
$797$	42.0000	1.48772	0.743858	+	0.668338i	$0.232994\pi$
$798$	0	0
$799$	−36.0000	−1.27359
$800$	4.00000	0.141421
$801$	0	0
$802$	15.0000	0.529668
$803$	66.0000	2.32909
$804$	0	0
$805$	0	0
$806$	4.00000	0.140894
$807$	0	0
$808$	9.00000	0.316619
$809$	6.00000	0.210949	0.105474	−	0.994422i	$-0.466364\pi$
$809$	6.00000	0.210949	0.105474	+	0.994422i	$0.466364\pi$
$810$	0	0
$811$	−46.0000	−1.61528	−0.807639	−	0.589677i	$-0.799255\pi$
$811$	−46.0000	−1.61528	−0.807639	+	0.589677i	$0.799255\pi$
$812$	−18.0000	−0.631676
$813$	0	0
$814$	−12.0000	−0.420600
$815$	6.00000	0.210171
$816$	0	0
$817$	−8.00000	−0.279885
$818$	−10.0000	−0.349642
$819$	0	0
$820$	27.0000	0.942881
$821$	33.0000	1.15171	0.575854	−	0.817553i	$-0.304670\pi$
$821$	33.0000	1.15171	0.575854	+	0.817553i	$0.304670\pi$
$822$	0	0
$823$	50.0000	1.74289	0.871445	−	0.490493i	$-0.163183\pi$
$823$	50.0000	1.74289	0.871445	+	0.490493i	$0.163183\pi$
$824$	4.00000	0.139347
$825$	0	0
$826$	12.0000	0.417533
$827$	−18.0000	−0.625921	−0.312961	−	0.949766i	$-0.601321\pi$
$827$	−18.0000	−0.625921	−0.312961	+	0.949766i	$0.601321\pi$
$828$	0	0
$829$	11.0000	0.382046	0.191023	−	0.981586i	$-0.438820\pi$
$829$	11.0000	0.382046	0.191023	+	0.981586i	$0.438820\pi$
$830$	0	0
$831$	0	0
$832$	−1.00000	−0.0346688
$833$	−18.0000	−0.623663
$834$	0	0
$835$	0	0
$836$	−12.0000	−0.415029
$837$	0	0
$838$	−24.0000	−0.829066
$839$	42.0000	1.45000	0.725001	−	0.688748i	$-0.241839\pi$
$839$	42.0000	1.45000	0.725001	+	0.688748i	$0.241839\pi$
$840$	0	0
$841$	52.0000	1.79310
$842$	−38.0000	−1.30957
$843$	0	0
$844$	−22.0000	−0.757271
$845$	−36.0000	−1.23844
$846$	0	0
$847$	−50.0000	−1.71802
$848$	3.00000	0.103020
$849$	0	0
$850$	24.0000	0.823193
$851$	0	0
$852$	0	0
$853$	2.00000	0.0684787	0.0342393	−	0.999414i	$-0.489099\pi$
$853$	2.00000	0.0684787	0.0342393	+	0.999414i	$0.489099\pi$
$854$	−2.00000	−0.0684386
$855$	0	0
$856$	6.00000	0.205076
$857$	33.0000	1.12726	0.563629	−	0.826028i	$-0.309405\pi$
$857$	33.0000	1.12726	0.563629	+	0.826028i	$0.309405\pi$
$858$	0	0
$859$	−10.0000	−0.341196	−0.170598	−	0.985341i	$-0.554570\pi$
$859$	−10.0000	−0.341196	−0.170598	+	0.985341i	$0.554570\pi$
$860$	12.0000	0.409197
$861$	0	0
$862$	−30.0000	−1.02180
$863$	18.0000	0.612727	0.306364	−	0.951915i	$-0.400888\pi$
$863$	18.0000	0.612727	0.306364	+	0.951915i	$0.400888\pi$
$864$	0	0
$865$	27.0000	0.918028
$866$	1.00000	0.0339814
$867$	0	0
$868$	8.00000	0.271538
$869$	−48.0000	−1.62829
$870$	0	0
$871$	8.00000	0.271070
$872$	−11.0000	−0.372507
$873$	0	0
$874$	0	0
$875$	6.00000	0.202837
$876$	0	0
$877$	−22.0000	−0.742887	−0.371444	−	0.928456i	$-0.621137\pi$
$877$	−22.0000	−0.742887	−0.371444	+	0.928456i	$0.621137\pi$
$878$	32.0000	1.07995
$879$	0	0
$880$	18.0000	0.606780
$881$	15.0000	0.505363	0.252681	−	0.967550i	$-0.418688\pi$
$881$	15.0000	0.505363	0.252681	+	0.967550i	$0.418688\pi$
$882$	0	0
$883$	−34.0000	−1.14419	−0.572096	−	0.820187i	$-0.693869\pi$
$883$	−34.0000	−1.14419	−0.572096	+	0.820187i	$0.693869\pi$
$884$	−6.00000	−0.201802
$885$	0	0
$886$	24.0000	0.806296
$887$	0	0		−	1.00000i	$-0.5\pi$
$887$	0	0			1.00000i	$0.5\pi$
$888$	0	0
$889$	−16.0000	−0.536623
$890$	−27.0000	−0.905042
$891$	0	0
$892$	14.0000	0.468755
$893$	12.0000	0.401565
$894$	0	0
$895$	0	0
$896$	−2.00000	−0.0668153
$897$	0	0
$898$	−39.0000	−1.30145
$899$	−36.0000	−1.20067
$900$	0	0
$901$	18.0000	0.599667
$902$	54.0000	1.79800
$903$	0	0
$904$	3.00000	0.0997785
$905$	−6.00000	−0.199447
$906$	0	0
$907$	−26.0000	−0.863316	−0.431658	−	0.902037i	$-0.642071\pi$
$907$	−26.0000	−0.863316	−0.431658	+	0.902037i	$0.642071\pi$
$908$	−12.0000	−0.398234
$909$	0	0
$910$	6.00000	0.198898
$911$	−12.0000	−0.397578	−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000	−0.397578	−0.198789	+	0.980042i	$0.563701\pi$
$912$	0	0
$913$	0	0
$914$	−23.0000	−0.760772
$915$	0	0
$916$	−2.00000	−0.0660819
$917$	−36.0000	−1.18882
$918$	0	0
$919$	−26.0000	−0.857661	−0.428830	−	0.903385i	$-0.641074\pi$
$919$	−26.0000	−0.857661	−0.428830	+	0.903385i	$0.641074\pi$
$920$	0	0
$921$	0	0
$922$	−15.0000	−0.493999
$923$	6.00000	0.197492
$924$	0	0
$925$	−8.00000	−0.263038
$926$	−40.0000	−1.31448
$927$	0	0
$928$	9.00000	0.295439
$929$	18.0000	0.590561	0.295280	−	0.955411i	$-0.404587\pi$
$929$	18.0000	0.590561	0.295280	+	0.955411i	$0.404587\pi$
$930$	0	0
$931$	6.00000	0.196642
$932$	9.00000	0.294805
$933$	0	0
$934$	−24.0000	−0.785304
$935$	108.000	3.53198
$936$	0	0
$937$	−38.0000	−1.24141	−0.620703	−	0.784046i	$-0.713153\pi$
$937$	−38.0000	−1.24141	−0.620703	+	0.784046i	$0.713153\pi$
$938$	16.0000	0.522419
$939$	0	0
$940$	−18.0000	−0.587095
$941$	−18.0000	−0.586783	−0.293392	−	0.955992i	$-0.594784\pi$
$941$	−18.0000	−0.586783	−0.293392	+	0.955992i	$0.594784\pi$
$942$	0	0
$943$	0	0
$944$	−6.00000	−0.195283
$945$	0	0
$946$	24.0000	0.780307
$947$	36.0000	1.16984	0.584921	−	0.811090i	$-0.301125\pi$
$947$	36.0000	1.16984	0.584921	+	0.811090i	$0.301125\pi$
$948$	0	0
$949$	−11.0000	−0.357075
$950$	−8.00000	−0.259554
$951$	0	0
$952$	−12.0000	−0.388922
$953$	−21.0000	−0.680257	−0.340128	−	0.940379i	$-0.610471\pi$
$953$	−21.0000	−0.680257	−0.340128	+	0.940379i	$0.610471\pi$
$954$	0	0
$955$	−36.0000	−1.16493
$956$	0	0
$957$	0	0
$958$	0	0
$959$	18.0000	0.581250
$960$	0	0
$961$	−15.0000	−0.483871
$962$	2.00000	0.0644826
$963$	0	0
$964$	1.00000	0.0322078
$965$	−39.0000	−1.25545
$966$	0	0
$967$	14.0000	0.450210	0.225105	−	0.974335i	$-0.427728\pi$
$967$	14.0000	0.450210	0.225105	+	0.974335i	$0.427728\pi$
$968$	25.0000	0.803530
$969$	0	0
$970$	3.00000	0.0963242
$971$	18.0000	0.577647	0.288824	−	0.957382i	$-0.406736\pi$
$971$	18.0000	0.577647	0.288824	+	0.957382i	$0.406736\pi$
$972$	0	0
$973$	8.00000	0.256468
$974$	−22.0000	−0.704925
$975$	0	0
$976$	1.00000	0.0320092
$977$	27.0000	0.863807	0.431903	−	0.901920i	$-0.357842\pi$
$977$	27.0000	0.863807	0.431903	+	0.901920i	$0.357842\pi$
$978$	0	0
$979$	−54.0000	−1.72585
$980$	−9.00000	−0.287494
$981$	0	0
$982$	0	0
$983$	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
$985$	63.0000	2.00735
$986$	54.0000	1.71971
$987$	0	0
$988$	2.00000	0.0636285
$989$	0	0
$990$	0	0
$991$	−52.0000	−1.65183	−0.825917	−	0.563791i	$-0.809342\pi$
$991$	−52.0000	−1.65183	−0.825917	+	0.563791i	$0.809342\pi$
$992$	−4.00000	−0.127000
$993$	0	0
$994$	12.0000	0.380617
$995$	−42.0000	−1.33149
$996$	0	0
$997$	23.0000	0.728417	0.364209	−	0.931317i	$-0.381339\pi$
$997$	23.0000	0.728417	0.364209	+	0.931317i	$0.381339\pi$
$998$	20.0000	0.633089
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9522.2.a.o.1.1		1
3.2	odd	2		1058.2.a.a.1.1	✓	1
12.11	even	2		8464.2.a.q.1.1		1
23.22	odd	2		9522.2.a.f.1.1		1
69.68	even	2		1058.2.a.b.1.1	yes	1
276.275	odd	2		8464.2.a.r.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1058.2.a.a.1.1	✓	1	3.2	odd	2
1058.2.a.b.1.1	yes	1	69.68	even	2
8464.2.a.q.1.1		1	12.11	even	2
8464.2.a.r.1.1		1	276.275	odd	2
9522.2.a.f.1.1		1	23.22	odd	2
9522.2.a.o.1.1		1	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 9522 = 2 \cdot 3^{2} \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9522.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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