LMFDB - Embedded newform 1521.4.a.h.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1521,4,Mod(1,1521)] 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("1521.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1521, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 1521 = 3^{2} \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1521.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,1,0,-7,-7,0,-10,-15,0,-7,22,0,0,-10,0,41,-37] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(17)] == traces)

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

Self dual:	yes
Analytic conductor:	$89.7419051187$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 39)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1521.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} -7.00000 q^{4} -7.00000 q^{5} -10.0000 q^{7} -15.0000 q^{8} -7.00000 q^{10} +22.0000 q^{11} -10.0000 q^{14} +41.0000 q^{16} -37.0000 q^{17} +30.0000 q^{19} +49.0000 q^{20} +22.0000 q^{22} +162.000 q^{23} -76.0000 q^{25} +70.0000 q^{28} +113.000 q^{29} +196.000 q^{31} +161.000 q^{32} -37.0000 q^{34} +70.0000 q^{35} +13.0000 q^{37} +30.0000 q^{38} +105.000 q^{40} -285.000 q^{41} -246.000 q^{43} -154.000 q^{44} +162.000 q^{46} +462.000 q^{47} -243.000 q^{49} -76.0000 q^{50} +537.000 q^{53} -154.000 q^{55} +150.000 q^{56} +113.000 q^{58} -576.000 q^{59} -635.000 q^{61} +196.000 q^{62} -167.000 q^{64} +202.000 q^{67} +259.000 q^{68} +70.0000 q^{70} +1086.00 q^{71} -805.000 q^{73} +13.0000 q^{74} -210.000 q^{76} -220.000 q^{77} +884.000 q^{79} -287.000 q^{80} -285.000 q^{82} -518.000 q^{83} +259.000 q^{85} -246.000 q^{86} -330.000 q^{88} -194.000 q^{89} -1134.00 q^{92} +462.000 q^{94} -210.000 q^{95} -1202.00 q^{97} -243.000 q^{98} +O(q^{100})$

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	0.353553	0.176777	−	0.984251i	$-0.443433\pi$
$2$	1.00000	0.353553	0.176777	+	0.984251i	$0.443433\pi$
$3$	0	0
$3$	0	0
$4$	−7.00000	−0.875000
$5$	−7.00000	−0.626099	−0.313050	−	0.949737i	$-0.601351\pi$
$5$	−7.00000	−0.626099	−0.313050	+	0.949737i	$0.601351\pi$
$6$	0	0
$7$	−10.0000	−0.539949	−0.269975	−	0.962867i	$-0.587015\pi$
$7$	−10.0000	−0.539949	−0.269975	+	0.962867i	$0.587015\pi$
$8$	−15.0000	−0.662913
$9$	0	0
$10$	−7.00000	−0.221359
$11$	22.0000	0.603023	0.301511	−	0.953463i	$-0.402509\pi$
$11$	22.0000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	0	0
$13$	0	0
$13$	0	0
$14$	−10.0000	−0.190901
$15$	0	0
$16$	41.0000	0.640625
$17$	−37.0000	−0.527872	−0.263936	−	0.964540i	$-0.585021\pi$
$17$	−37.0000	−0.527872	−0.263936	+	0.964540i	$0.585021\pi$
$18$	0	0
$19$	30.0000	0.362235	0.181118	−	0.983461i	$-0.442029\pi$
$19$	30.0000	0.362235	0.181118	+	0.983461i	$0.442029\pi$
$20$	49.0000	0.547837
$21$	0	0
$22$	22.0000	0.213201
$23$	162.000	1.46867	0.734333	−	0.678789i	$-0.237495\pi$
$23$	162.000	1.46867	0.734333	+	0.678789i	$0.237495\pi$
$24$	0	0
$25$	−76.0000	−0.608000
$26$	0	0
$27$	0	0
$28$	70.0000	0.472456
$29$	113.000	0.723571	0.361786	−	0.932261i	$-0.382167\pi$
$29$	113.000	0.723571	0.361786	+	0.932261i	$0.382167\pi$
$30$	0	0
$31$	196.000	1.13557	0.567785	−	0.823177i	$-0.307801\pi$
$31$	196.000	1.13557	0.567785	+	0.823177i	$0.307801\pi$
$32$	161.000	0.889408
$33$	0	0
$34$	−37.0000	−0.186631
$35$	70.0000	0.338062
$36$	0	0
$37$	13.0000	0.0577618	0.0288809	−	0.999583i	$-0.490806\pi$
$37$	13.0000	0.0577618	0.0288809	+	0.999583i	$0.490806\pi$
$38$	30.0000	0.128070
$39$	0	0
$40$	105.000	0.415049
$41$	−285.000	−1.08560	−0.542799	−	0.839863i	$-0.682635\pi$
$41$	−285.000	−1.08560	−0.542799	+	0.839863i	$0.682635\pi$
$42$	0	0
$43$	−246.000	−0.872434	−0.436217	−	0.899842i	$-0.643682\pi$
$43$	−246.000	−0.872434	−0.436217	+	0.899842i	$0.643682\pi$
$44$	−154.000	−0.527645
$45$	0	0
$46$	162.000	0.519252
$47$	462.000	1.43382	0.716911	−	0.697165i	$-0.245555\pi$
$47$	462.000	1.43382	0.716911	+	0.697165i	$0.245555\pi$
$48$	0	0
$49$	−243.000	−0.708455
$50$	−76.0000	−0.214960
$51$	0	0
$52$	0	0
$53$	537.000	1.39175	0.695874	−	0.718164i	$-0.255017\pi$
$53$	537.000	1.39175	0.695874	+	0.718164i	$0.255017\pi$
$54$	0	0
$55$	−154.000	−0.377552
$56$	150.000	0.357939
$57$	0	0
$58$	113.000	0.255821
$59$	−576.000	−1.27100	−0.635498	−	0.772102i	$-0.719205\pi$
$59$	−576.000	−1.27100	−0.635498	+	0.772102i	$0.719205\pi$
$60$	0	0
$61$	−635.000	−1.33284	−0.666421	−	0.745575i	$-0.732175\pi$
$61$	−635.000	−1.33284	−0.666421	+	0.745575i	$0.732175\pi$
$62$	196.000	0.401484
$63$	0	0
$64$	−167.000	−0.326172
$65$	0	0
$66$	0	0
$67$	202.000	0.368332	0.184166	−	0.982895i	$-0.441042\pi$
$67$	202.000	0.368332	0.184166	+	0.982895i	$0.441042\pi$
$68$	259.000	0.461888
$69$	0	0
$70$	70.0000	0.119523
$71$	1086.00	1.81527	0.907637	−	0.419755i	$-0.137884\pi$
$71$	1086.00	1.81527	0.907637	+	0.419755i	$0.137884\pi$
$72$	0	0
$73$	−805.000	−1.29066	−0.645330	−	0.763904i	$-0.723280\pi$
$73$	−805.000	−1.29066	−0.645330	+	0.763904i	$0.723280\pi$
$74$	13.0000	0.0204219
$75$	0	0
$76$	−210.000	−0.316956
$77$	−220.000	−0.325602
$78$	0	0
$79$	884.000	1.25896	0.629480	−	0.777017i	$-0.283268\pi$
$79$	884.000	1.25896	0.629480	+	0.777017i	$0.283268\pi$
$80$	−287.000	−0.401095
$81$	0	0
$82$	−285.000	−0.383817
$83$	−518.000	−0.685035	−0.342517	−	0.939511i	$-0.611280\pi$
$83$	−518.000	−0.685035	−0.342517	+	0.939511i	$0.611280\pi$
$84$	0	0
$85$	259.000	0.330500
$86$	−246.000	−0.308452
$87$	0	0
$88$	−330.000	−0.399751
$89$	−194.000	−0.231056	−0.115528	−	0.993304i	$-0.536856\pi$
$89$	−194.000	−0.231056	−0.115528	+	0.993304i	$0.536856\pi$
$90$	0	0
$91$	0	0
$92$	−1134.00	−1.28508
$93$	0	0
$94$	462.000	0.506933
$95$	−210.000	−0.226795
$96$	0	0
$97$	−1202.00	−1.25819	−0.629096	−	0.777328i	$-0.716575\pi$
$97$	−1202.00	−1.25819	−0.629096	+	0.777328i	$0.716575\pi$
$98$	−243.000	−0.250477
$99$	0	0
$100$	532.000	0.532000
$101$	429.000	0.422645	0.211322	−	0.977416i	$-0.432223\pi$
$101$	429.000	0.422645	0.211322	+	0.977416i	$0.432223\pi$
$102$	0	0
$103$	−1302.00	−1.24553	−0.622766	−	0.782408i	$-0.713991\pi$
$103$	−1302.00	−1.24553	−0.622766	+	0.782408i	$0.713991\pi$
$104$	0	0
$105$	0	0
$106$	537.000	0.492057
$107$	1338.00	1.20887	0.604436	−	0.796654i	$-0.293398\pi$
$107$	1338.00	1.20887	0.604436	+	0.796654i	$0.293398\pi$
$108$	0	0
$109$	−1034.00	−0.908617	−0.454308	−	0.890844i	$-0.650114\pi$
$109$	−1034.00	−0.908617	−0.454308	+	0.890844i	$0.650114\pi$
$110$	−154.000	−0.133485
$111$	0	0
$112$	−410.000	−0.345905
$113$	−1077.00	−0.896599	−0.448299	−	0.893884i	$-0.647970\pi$
$113$	−1077.00	−0.896599	−0.448299	+	0.893884i	$0.647970\pi$
$114$	0	0
$115$	−1134.00	−0.919531
$116$	−791.000	−0.633125
$117$	0	0
$118$	−576.000	−0.449365
$119$	370.000	0.285024
$120$	0	0
$121$	−847.000	−0.636364
$122$	−635.000	−0.471231
$123$	0	0
$124$	−1372.00	−0.993623
$125$	1407.00	1.00677
$126$	0	0
$127$	−988.000	−0.690321	−0.345161	−	0.938544i	$-0.612176\pi$
$127$	−988.000	−0.690321	−0.345161	+	0.938544i	$0.612176\pi$
$128$	−1455.00	−1.00473
$129$	0	0
$130$	0	0
$131$	−560.000	−0.373492	−0.186746	−	0.982408i	$-0.559794\pi$
$131$	−560.000	−0.373492	−0.186746	+	0.982408i	$0.559794\pi$
$132$	0	0
$133$	−300.000	−0.195589
$134$	202.000	0.130225
$135$	0	0
$136$	555.000	0.349933
$137$	519.000	0.323658	0.161829	−	0.986819i	$-0.448261\pi$
$137$	519.000	0.323658	0.161829	+	0.986819i	$0.448261\pi$
$138$	0	0
$139$	−348.000	−0.212352	−0.106176	−	0.994347i	$-0.533861\pi$
$139$	−348.000	−0.212352	−0.106176	+	0.994347i	$0.533861\pi$
$140$	−490.000	−0.295804
$141$	0	0
$142$	1086.00	0.641796
$143$	0	0
$144$	0	0
$145$	−791.000	−0.453027
$146$	−805.000	−0.456317
$147$	0	0
$148$	−91.0000	−0.0505416
$149$	645.000	0.354634	0.177317	−	0.984154i	$-0.443258\pi$
$149$	645.000	0.354634	0.177317	+	0.984154i	$0.443258\pi$
$150$	0	0
$151$	2914.00	1.57045	0.785225	−	0.619211i	$-0.212547\pi$
$151$	2914.00	1.57045	0.785225	+	0.619211i	$0.212547\pi$
$152$	−450.000	−0.240130
$153$	0	0
$154$	−220.000	−0.115118
$155$	−1372.00	−0.710979
$156$	0	0
$157$	−2079.00	−1.05683	−0.528415	−	0.848986i	$-0.677213\pi$
$157$	−2079.00	−1.05683	−0.528415	+	0.848986i	$0.677213\pi$
$158$	884.000	0.445109
$159$	0	0
$160$	−1127.00	−0.556857
$161$	−1620.00	−0.793006
$162$	0	0
$163$	1700.00	0.816897	0.408449	−	0.912781i	$-0.366070\pi$
$163$	1700.00	0.816897	0.408449	+	0.912781i	$0.366070\pi$
$164$	1995.00	0.949898
$165$	0	0
$166$	−518.000	−0.242196
$167$	−3680.00	−1.70519	−0.852596	−	0.522571i	$-0.824973\pi$
$167$	−3680.00	−1.70519	−0.852596	+	0.522571i	$0.824973\pi$
$168$	0	0
$169$	0	0
$170$	259.000	0.116849
$171$	0	0
$172$	1722.00	0.763379
$173$	−4146.00	−1.82205	−0.911025	−	0.412352i	$-0.864707\pi$
$173$	−4146.00	−1.82205	−0.911025	+	0.412352i	$0.864707\pi$
$174$	0	0
$175$	760.000	0.328289
$176$	902.000	0.386311
$177$	0	0
$178$	−194.000	−0.0816905
$179$	−3674.00	−1.53412	−0.767060	−	0.641575i	$-0.778281\pi$
$179$	−3674.00	−1.53412	−0.767060	+	0.641575i	$0.778281\pi$
$180$	0	0
$181$	−3283.00	−1.34820	−0.674098	−	0.738642i	$-0.735467\pi$
$181$	−3283.00	−1.34820	−0.674098	+	0.738642i	$0.735467\pi$
$182$	0	0
$183$	0	0
$184$	−2430.00	−0.973598
$185$	−91.0000	−0.0361646
$186$	0	0
$187$	−814.000	−0.318319
$188$	−3234.00	−1.25459
$189$	0	0
$190$	−210.000	−0.0801842
$191$	596.000	0.225786	0.112893	−	0.993607i	$-0.463988\pi$
$191$	596.000	0.225786	0.112893	+	0.993607i	$0.463988\pi$
$192$	0	0
$193$	−393.000	−0.146574	−0.0732869	−	0.997311i	$-0.523349\pi$
$193$	−393.000	−0.146574	−0.0732869	+	0.997311i	$0.523349\pi$
$194$	−1202.00	−0.444838
$195$	0	0
$196$	1701.00	0.619898
$197$	3522.00	1.27377	0.636884	−	0.770960i	$-0.280223\pi$
$197$	3522.00	1.27377	0.636884	+	0.770960i	$0.280223\pi$
$198$	0	0
$199$	2018.00	0.718855	0.359428	−	0.933173i	$-0.382972\pi$
$199$	2018.00	0.718855	0.359428	+	0.933173i	$0.382972\pi$
$200$	1140.00	0.403051
$201$	0	0
$202$	429.000	0.149427
$203$	−1130.00	−0.390692
$204$	0	0
$205$	1995.00	0.679692
$206$	−1302.00	−0.440362
$207$	0	0
$208$	0	0
$209$	660.000	0.218436
$210$	0	0
$211$	160.000	0.0522031	0.0261016	−	0.999659i	$-0.491691\pi$
$211$	160.000	0.0522031	0.0261016	+	0.999659i	$0.491691\pi$
$212$	−3759.00	−1.21778
$213$	0	0
$214$	1338.00	0.427401
$215$	1722.00	0.546230
$216$	0	0
$217$	−1960.00	−0.613150
$218$	−1034.00	−0.321245
$219$	0	0
$220$	1078.00	0.330358
$221$	0	0
$222$	0	0
$223$	4072.00	1.22279	0.611393	−	0.791327i	$-0.290609\pi$
$223$	4072.00	1.22279	0.611393	+	0.791327i	$0.290609\pi$
$224$	−1610.00	−0.480235
$225$	0	0
$226$	−1077.00	−0.316995
$227$	5794.00	1.69410	0.847051	−	0.531511i	$-0.178376\pi$
$227$	5794.00	1.69410	0.847051	+	0.531511i	$0.178376\pi$
$228$	0	0
$229$	6482.00	1.87049	0.935246	−	0.353999i	$-0.115178\pi$
$229$	6482.00	1.87049	0.935246	+	0.353999i	$0.115178\pi$
$230$	−1134.00	−0.325103
$231$	0	0
$232$	−1695.00	−0.479665
$233$	−6890.00	−1.93725	−0.968624	−	0.248530i	$-0.920053\pi$
$233$	−6890.00	−1.93725	−0.968624	+	0.248530i	$0.920053\pi$
$234$	0	0
$235$	−3234.00	−0.897714
$236$	4032.00	1.11212
$237$	0	0
$238$	370.000	0.100771
$239$	−2466.00	−0.667415	−0.333708	−	0.942677i	$-0.608300\pi$
$239$	−2466.00	−0.667415	−0.333708	+	0.942677i	$0.608300\pi$
$240$	0	0
$241$	−3617.00	−0.966770	−0.483385	−	0.875408i	$-0.660593\pi$
$241$	−3617.00	−0.966770	−0.483385	+	0.875408i	$0.660593\pi$
$242$	−847.000	−0.224989
$243$	0	0
$244$	4445.00	1.16624
$245$	1701.00	0.443563
$246$	0	0
$247$	0	0
$248$	−2940.00	−0.752783
$249$	0	0
$250$	1407.00	0.355946
$251$	−4860.00	−1.22215	−0.611077	−	0.791571i	$-0.709263\pi$
$251$	−4860.00	−1.22215	−0.611077	+	0.791571i	$0.709263\pi$
$252$	0	0
$253$	3564.00	0.885639
$254$	−988.000	−0.244065
$255$	0	0
$256$	−119.000	−0.0290527
$257$	−565.000	−0.137135	−0.0685676	−	0.997646i	$-0.521843\pi$
$257$	−565.000	−0.137135	−0.0685676	+	0.997646i	$0.521843\pi$
$258$	0	0
$259$	−130.000	−0.0311884
$260$	0	0
$261$	0	0
$262$	−560.000	−0.132049
$263$	498.000	0.116760	0.0583802	−	0.998294i	$-0.481406\pi$
$263$	498.000	0.116760	0.0583802	+	0.998294i	$0.481406\pi$
$264$	0	0
$265$	−3759.00	−0.871372
$266$	−300.000	−0.0691511
$267$	0	0
$268$	−1414.00	−0.322290
$269$	−5546.00	−1.25705	−0.628523	−	0.777791i	$-0.716340\pi$
$269$	−5546.00	−1.25705	−0.628523	+	0.777791i	$0.716340\pi$
$270$	0	0
$271$	−2256.00	−0.505691	−0.252845	−	0.967507i	$-0.581366\pi$
$271$	−2256.00	−0.505691	−0.252845	+	0.967507i	$0.581366\pi$
$272$	−1517.00	−0.338168
$273$	0	0
$274$	519.000	0.114430
$275$	−1672.00	−0.366638
$276$	0	0
$277$	2309.00	0.500846	0.250423	−	0.968137i	$-0.419430\pi$
$277$	2309.00	0.500846	0.250423	+	0.968137i	$0.419430\pi$
$278$	−348.000	−0.0750779
$279$	0	0
$280$	−1050.00	−0.224105
$281$	−5833.00	−1.23832	−0.619159	−	0.785265i	$-0.712527\pi$
$281$	−5833.00	−1.23832	−0.619159	+	0.785265i	$0.712527\pi$
$282$	0	0
$283$	1650.00	0.346581	0.173290	−	0.984871i	$-0.444560\pi$
$283$	1650.00	0.346581	0.173290	+	0.984871i	$0.444560\pi$
$284$	−7602.00	−1.58837
$285$	0	0
$286$	0	0
$287$	2850.00	0.586168
$288$	0	0
$289$	−3544.00	−0.721352
$290$	−791.000	−0.160169
$291$	0	0
$292$	5635.00	1.12933
$293$	−2991.00	−0.596369	−0.298184	−	0.954508i	$-0.596381\pi$
$293$	−2991.00	−0.596369	−0.298184	+	0.954508i	$0.596381\pi$
$294$	0	0
$295$	4032.00	0.795770
$296$	−195.000	−0.0382910
$297$	0	0
$298$	645.000	0.125382
$299$	0	0
$300$	0	0
$301$	2460.00	0.471070
$302$	2914.00	0.555238
$303$	0	0
$304$	1230.00	0.232057
$305$	4445.00	0.834492
$306$	0	0
$307$	−2422.00	−0.450263	−0.225132	−	0.974328i	$-0.572281\pi$
$307$	−2422.00	−0.450263	−0.225132	+	0.974328i	$0.572281\pi$
$308$	1540.00	0.284901
$309$	0	0
$310$	−1372.00	−0.251369
$311$	3402.00	0.620288	0.310144	−	0.950690i	$-0.399623\pi$
$311$	3402.00	0.620288	0.310144	+	0.950690i	$0.399623\pi$
$312$	0	0
$313$	2310.00	0.417153	0.208577	−	0.978006i	$-0.433117\pi$
$313$	2310.00	0.417153	0.208577	+	0.978006i	$0.433117\pi$
$314$	−2079.00	−0.373646
$315$	0	0
$316$	−6188.00	−1.10159
$317$	257.000	0.0455349	0.0227674	−	0.999741i	$-0.492752\pi$
$317$	257.000	0.0455349	0.0227674	+	0.999741i	$0.492752\pi$
$318$	0	0
$319$	2486.00	0.436330
$320$	1169.00	0.204216
$321$	0	0
$322$	−1620.00	−0.280370
$323$	−1110.00	−0.191214
$324$	0	0
$325$	0	0
$326$	1700.00	0.288817
$327$	0	0
$328$	4275.00	0.719657
$329$	−4620.00	−0.774191
$330$	0	0
$331$	1028.00	0.170707	0.0853535	−	0.996351i	$-0.472798\pi$
$331$	1028.00	0.170707	0.0853535	+	0.996351i	$0.472798\pi$
$332$	3626.00	0.599405
$333$	0	0
$334$	−3680.00	−0.602876
$335$	−1414.00	−0.230612
$336$	0	0
$337$	2487.00	0.402005	0.201002	−	0.979591i	$-0.435580\pi$
$337$	2487.00	0.402005	0.201002	+	0.979591i	$0.435580\pi$
$338$	0	0
$339$	0	0
$340$	−1813.00	−0.289187
$341$	4312.00	0.684774
$342$	0	0
$343$	5860.00	0.922479
$344$	3690.00	0.578347
$345$	0	0
$346$	−4146.00	−0.644192
$347$	2850.00	0.440911	0.220455	−	0.975397i	$-0.429246\pi$
$347$	2850.00	0.440911	0.220455	+	0.975397i	$0.429246\pi$
$348$	0	0
$349$	−2018.00	−0.309516	−0.154758	−	0.987952i	$-0.549460\pi$
$349$	−2018.00	−0.309516	−0.154758	+	0.987952i	$0.549460\pi$
$350$	760.000	0.116068
$351$	0	0
$352$	3542.00	0.536333
$353$	5287.00	0.797163	0.398582	−	0.917133i	$-0.369503\pi$
$353$	5287.00	0.797163	0.398582	+	0.917133i	$0.369503\pi$
$354$	0	0
$355$	−7602.00	−1.13654
$356$	1358.00	0.202174
$357$	0	0
$358$	−3674.00	−0.542394
$359$	7278.00	1.06997	0.534983	−	0.844863i	$-0.320318\pi$
$359$	7278.00	1.06997	0.534983	+	0.844863i	$0.320318\pi$
$360$	0	0
$361$	−5959.00	−0.868786
$362$	−3283.00	−0.476659
$363$	0	0
$364$	0	0
$365$	5635.00	0.808080
$366$	0	0
$367$	−4202.00	−0.597664	−0.298832	−	0.954306i	$-0.596597\pi$
$367$	−4202.00	−0.597664	−0.298832	+	0.954306i	$0.596597\pi$
$368$	6642.00	0.940865
$369$	0	0
$370$	−91.0000	−0.0127861
$371$	−5370.00	−0.751473
$372$	0	0
$373$	−1583.00	−0.219744	−0.109872	−	0.993946i	$-0.535044\pi$
$373$	−1583.00	−0.219744	−0.109872	+	0.993946i	$0.535044\pi$
$374$	−814.000	−0.112543
$375$	0	0
$376$	−6930.00	−0.950499
$377$	0	0
$378$	0	0
$379$	−2052.00	−0.278111	−0.139056	−	0.990285i	$-0.544407\pi$
$379$	−2052.00	−0.278111	−0.139056	+	0.990285i	$0.544407\pi$
$380$	1470.00	0.198446
$381$	0	0
$382$	596.000	0.0798273
$383$	6872.00	0.916822	0.458411	−	0.888740i	$-0.348419\pi$
$383$	6872.00	0.916822	0.458411	+	0.888740i	$0.348419\pi$
$384$	0	0
$385$	1540.00	0.203859
$386$	−393.000	−0.0518217
$387$	0	0
$388$	8414.00	1.10092
$389$	11653.0	1.51884	0.759422	−	0.650598i	$-0.225482\pi$
$389$	11653.0	1.51884	0.759422	+	0.650598i	$0.225482\pi$
$390$	0	0
$391$	−5994.00	−0.775268
$392$	3645.00	0.469644
$393$	0	0
$394$	3522.00	0.450345
$395$	−6188.00	−0.788233
$396$	0	0
$397$	6134.00	0.775458	0.387729	−	0.921774i	$-0.373260\pi$
$397$	6134.00	0.775458	0.387729	+	0.921774i	$0.373260\pi$
$398$	2018.00	0.254154
$399$	0	0
$400$	−3116.00	−0.389500
$401$	10795.0	1.34433	0.672165	−	0.740401i	$-0.265364\pi$
$401$	10795.0	1.34433	0.672165	+	0.740401i	$0.265364\pi$
$402$	0	0
$403$	0	0
$404$	−3003.00	−0.369814
$405$	0	0
$406$	−1130.00	−0.138130
$407$	286.000	0.0348317
$408$	0	0
$409$	−8489.00	−1.02629	−0.513147	−	0.858301i	$-0.671520\pi$
$409$	−8489.00	−1.02629	−0.513147	+	0.858301i	$0.671520\pi$
$410$	1995.00	0.240307
$411$	0	0
$412$	9114.00	1.08984
$413$	5760.00	0.686274
$414$	0	0
$415$	3626.00	0.428900
$416$	0	0
$417$	0	0
$418$	660.000	0.0772288
$419$	−1496.00	−0.174426	−0.0872129	−	0.996190i	$-0.527796\pi$
$419$	−1496.00	−0.174426	−0.0872129	+	0.996190i	$0.527796\pi$
$420$	0	0
$421$	−11695.0	−1.35387	−0.676935	−	0.736043i	$-0.736692\pi$
$421$	−11695.0	−1.35387	−0.676935	+	0.736043i	$0.736692\pi$
$422$	160.000	0.0184566
$423$	0	0
$424$	−8055.00	−0.922607
$425$	2812.00	0.320946
$426$	0	0
$427$	6350.00	0.719668
$428$	−9366.00	−1.05776
$429$	0	0
$430$	1722.00	0.193121
$431$	−10590.0	−1.18353	−0.591766	−	0.806110i	$-0.701569\pi$
$431$	−10590.0	−1.18353	−0.591766	+	0.806110i	$0.701569\pi$
$432$	0	0
$433$	−13949.0	−1.54814	−0.774072	−	0.633098i	$-0.781783\pi$
$433$	−13949.0	−1.54814	−0.774072	+	0.633098i	$0.781783\pi$
$434$	−1960.00	−0.216781
$435$	0	0
$436$	7238.00	0.795040
$437$	4860.00	0.532003
$438$	0	0
$439$	−10726.0	−1.16611	−0.583057	−	0.812431i	$-0.698144\pi$
$439$	−10726.0	−1.16611	−0.583057	+	0.812431i	$0.698144\pi$
$440$	2310.00	0.250284
$441$	0	0
$442$	0	0
$443$	−16228.0	−1.74044	−0.870221	−	0.492662i	$-0.836024\pi$
$443$	−16228.0	−1.74044	−0.870221	+	0.492662i	$0.836024\pi$
$444$	0	0
$445$	1358.00	0.144664
$446$	4072.00	0.432320
$447$	0	0
$448$	1670.00	0.176116
$449$	−7538.00	−0.792294	−0.396147	−	0.918187i	$-0.629653\pi$
$449$	−7538.00	−0.792294	−0.396147	+	0.918187i	$0.629653\pi$
$450$	0	0
$451$	−6270.00	−0.654640
$452$	7539.00	0.784524
$453$	0	0
$454$	5794.00	0.598956
$455$	0	0
$456$	0	0
$457$	15539.0	1.59056	0.795278	−	0.606245i	$-0.207325\pi$
$457$	15539.0	1.59056	0.795278	+	0.606245i	$0.207325\pi$
$458$	6482.00	0.661319
$459$	0	0
$460$	7938.00	0.804589
$461$	−4811.00	−0.486053	−0.243027	−	0.970020i	$-0.578140\pi$
$461$	−4811.00	−0.486053	−0.243027	+	0.970020i	$0.578140\pi$
$462$	0	0
$463$	562.000	0.0564111	0.0282056	−	0.999602i	$-0.491021\pi$
$463$	562.000	0.0564111	0.0282056	+	0.999602i	$0.491021\pi$
$464$	4633.00	0.463538
$465$	0	0
$466$	−6890.00	−0.684921
$467$	−4914.00	−0.486922	−0.243461	−	0.969911i	$-0.578283\pi$
$467$	−4914.00	−0.486922	−0.243461	+	0.969911i	$0.578283\pi$
$468$	0	0
$469$	−2020.00	−0.198880
$470$	−3234.00	−0.317390
$471$	0	0
$472$	8640.00	0.842560
$473$	−5412.00	−0.526097
$474$	0	0
$475$	−2280.00	−0.220239
$476$	−2590.00	−0.249396
$477$	0	0
$478$	−2466.00	−0.235967
$479$	3600.00	0.343399	0.171700	−	0.985149i	$-0.445074\pi$
$479$	3600.00	0.343399	0.171700	+	0.985149i	$0.445074\pi$
$480$	0	0
$481$	0	0
$482$	−3617.00	−0.341805
$483$	0	0
$484$	5929.00	0.556818
$485$	8414.00	0.787753
$486$	0	0
$487$	−17130.0	−1.59391	−0.796955	−	0.604038i	$-0.793557\pi$
$487$	−17130.0	−1.59391	−0.796955	+	0.604038i	$0.793557\pi$
$488$	9525.00	0.883558
$489$	0	0
$490$	1701.00	0.156823
$491$	11838.0	1.08807	0.544034	−	0.839063i	$-0.316896\pi$
$491$	11838.0	1.08807	0.544034	+	0.839063i	$0.316896\pi$
$492$	0	0
$493$	−4181.00	−0.381953
$494$	0	0
$495$	0	0
$496$	8036.00	0.727474
$497$	−10860.0	−0.980156
$498$	0	0
$499$	8976.00	0.805252	0.402626	−	0.915364i	$-0.368097\pi$
$499$	8976.00	0.805252	0.402626	+	0.915364i	$0.368097\pi$
$500$	−9849.00	−0.880921
$501$	0	0
$502$	−4860.00	−0.432096
$503$	−1682.00	−0.149099	−0.0745494	−	0.997217i	$-0.523752\pi$
$503$	−1682.00	−0.149099	−0.0745494	+	0.997217i	$0.523752\pi$
$504$	0	0
$505$	−3003.00	−0.264617
$506$	3564.00	0.313121
$507$	0	0
$508$	6916.00	0.604031
$509$	−15167.0	−1.32076	−0.660379	−	0.750933i	$-0.729604\pi$
$509$	−15167.0	−1.32076	−0.660379	+	0.750933i	$0.729604\pi$
$510$	0	0
$511$	8050.00	0.696890
$512$	11521.0	0.994455
$513$	0	0
$514$	−565.000	−0.0484846
$515$	9114.00	0.779827
$516$	0	0
$517$	10164.0	0.864627
$518$	−130.000	−0.0110268
$519$	0	0
$520$	0	0
$521$	6783.00	0.570381	0.285191	−	0.958471i	$-0.407943\pi$
$521$	6783.00	0.570381	0.285191	+	0.958471i	$0.407943\pi$
$522$	0	0
$523$	−13918.0	−1.16366	−0.581828	−	0.813312i	$-0.697662\pi$
$523$	−13918.0	−1.16366	−0.581828	+	0.813312i	$0.697662\pi$
$524$	3920.00	0.326805
$525$	0	0
$526$	498.000	0.0412810
$527$	−7252.00	−0.599435
$528$	0	0
$529$	14077.0	1.15698
$530$	−3759.00	−0.308076
$531$	0	0
$532$	2100.00	0.171140
$533$	0	0
$534$	0	0
$535$	−9366.00	−0.756874
$536$	−3030.00	−0.244172
$537$	0	0
$538$	−5546.00	−0.444433
$539$	−5346.00	−0.427214
$540$	0	0
$541$	−1335.00	−0.106093	−0.0530463	−	0.998592i	$-0.516893\pi$
$541$	−1335.00	−0.106093	−0.0530463	+	0.998592i	$0.516893\pi$
$542$	−2256.00	−0.178789
$543$	0	0
$544$	−5957.00	−0.469493
$545$	7238.00	0.568884
$546$	0	0
$547$	−3806.00	−0.297501	−0.148750	−	0.988875i	$-0.547525\pi$
$547$	−3806.00	−0.297501	−0.148750	+	0.988875i	$0.547525\pi$
$548$	−3633.00	−0.283201
$549$	0	0
$550$	−1672.00	−0.129626
$551$	3390.00	0.262103
$552$	0	0
$553$	−8840.00	−0.679774
$554$	2309.00	0.177076
$555$	0	0
$556$	2436.00	0.185808
$557$	1905.00	0.144915	0.0724573	−	0.997372i	$-0.476916\pi$
$557$	1905.00	0.144915	0.0724573	+	0.997372i	$0.476916\pi$
$558$	0	0
$559$	0	0
$560$	2870.00	0.216571
$561$	0	0
$562$	−5833.00	−0.437812
$563$	4800.00	0.359318	0.179659	−	0.983729i	$-0.442501\pi$
$563$	4800.00	0.359318	0.179659	+	0.983729i	$0.442501\pi$
$564$	0	0
$565$	7539.00	0.561359
$566$	1650.00	0.122535
$567$	0	0
$568$	−16290.0	−1.20337
$569$	−14678.0	−1.08143	−0.540715	−	0.841206i	$-0.681846\pi$
$569$	−14678.0	−1.08143	−0.540715	+	0.841206i	$0.681846\pi$
$570$	0	0
$571$	−586.000	−0.0429481	−0.0214740	−	0.999769i	$-0.506836\pi$
$571$	−586.000	−0.0429481	−0.0214740	+	0.999769i	$0.506836\pi$
$572$	0	0
$573$	0	0
$574$	2850.00	0.207242
$575$	−12312.0	−0.892949
$576$	0	0
$577$	8939.00	0.644949	0.322474	−	0.946578i	$-0.395485\pi$
$577$	8939.00	0.644949	0.322474	+	0.946578i	$0.395485\pi$
$578$	−3544.00	−0.255036
$579$	0	0
$580$	5537.00	0.396399
$581$	5180.00	0.369884
$582$	0	0
$583$	11814.0	0.839255
$584$	12075.0	0.855594
$585$	0	0
$586$	−2991.00	−0.210848
$587$	13792.0	0.969773	0.484887	−	0.874577i	$-0.338861\pi$
$587$	13792.0	0.969773	0.484887	+	0.874577i	$0.338861\pi$
$588$	0	0
$589$	5880.00	0.411343
$590$	4032.00	0.281347
$591$	0	0
$592$	533.000	0.0370037
$593$	−9569.00	−0.662650	−0.331325	−	0.943517i	$-0.607496\pi$
$593$	−9569.00	−0.662650	−0.331325	+	0.943517i	$0.607496\pi$
$594$	0	0
$595$	−2590.00	−0.178453
$596$	−4515.00	−0.310305
$597$	0	0
$598$	0	0
$599$	5192.00	0.354156	0.177078	−	0.984197i	$-0.443336\pi$
$599$	5192.00	0.354156	0.177078	+	0.984197i	$0.443336\pi$
$600$	0	0
$601$	−3677.00	−0.249564	−0.124782	−	0.992184i	$-0.539823\pi$
$601$	−3677.00	−0.249564	−0.124782	+	0.992184i	$0.539823\pi$
$602$	2460.00	0.166548
$603$	0	0
$604$	−20398.0	−1.37414
$605$	5929.00	0.398427
$606$	0	0
$607$	−10960.0	−0.732871	−0.366435	−	0.930443i	$-0.619422\pi$
$607$	−10960.0	−0.732871	−0.366435	+	0.930443i	$0.619422\pi$
$608$	4830.00	0.322175
$609$	0	0
$610$	4445.00	0.295037
$611$	0	0
$612$	0	0
$613$	−26027.0	−1.71488	−0.857439	−	0.514585i	$-0.827946\pi$
$613$	−26027.0	−1.71488	−0.857439	+	0.514585i	$0.827946\pi$
$614$	−2422.00	−0.159192
$615$	0	0
$616$	3300.00	0.215845
$617$	−17681.0	−1.15366	−0.576832	−	0.816863i	$-0.695711\pi$
$617$	−17681.0	−1.15366	−0.576832	+	0.816863i	$0.695711\pi$
$618$	0	0
$619$	3192.00	0.207265	0.103633	−	0.994616i	$-0.466953\pi$
$619$	3192.00	0.207265	0.103633	+	0.994616i	$0.466953\pi$
$620$	9604.00	0.622106
$621$	0	0
$622$	3402.00	0.219305
$623$	1940.00	0.124758
$624$	0	0
$625$	−349.000	−0.0223360
$626$	2310.00	0.147486
$627$	0	0
$628$	14553.0	0.924726
$629$	−481.000	−0.0304908
$630$	0	0
$631$	7580.00	0.478217	0.239109	−	0.970993i	$-0.423145\pi$
$631$	7580.00	0.478217	0.239109	+	0.970993i	$0.423145\pi$
$632$	−13260.0	−0.834580
$633$	0	0
$634$	257.000	0.0160990
$635$	6916.00	0.432210
$636$	0	0
$637$	0	0
$638$	2486.00	0.154266
$639$	0	0
$640$	10185.0	0.629059
$641$	27707.0	1.70727	0.853635	−	0.520871i	$-0.174393\pi$
$641$	27707.0	1.70727	0.853635	+	0.520871i	$0.174393\pi$
$642$	0	0
$643$	11216.0	0.687894	0.343947	−	0.938989i	$-0.388236\pi$
$643$	11216.0	0.687894	0.343947	+	0.938989i	$0.388236\pi$
$644$	11340.0	0.693880
$645$	0	0
$646$	−1110.00	−0.0676043
$647$	2536.00	0.154097	0.0770483	−	0.997027i	$-0.475450\pi$
$647$	2536.00	0.154097	0.0770483	+	0.997027i	$0.475450\pi$
$648$	0	0
$649$	−12672.0	−0.766440
$650$	0	0
$651$	0	0
$652$	−11900.0	−0.714785
$653$	−17730.0	−1.06252	−0.531262	−	0.847207i	$-0.678282\pi$
$653$	−17730.0	−1.06252	−0.531262	+	0.847207i	$0.678282\pi$
$654$	0	0
$655$	3920.00	0.233843
$656$	−11685.0	−0.695461
$657$	0	0
$658$	−4620.00	−0.273718
$659$	−18920.0	−1.11839	−0.559195	−	0.829036i	$-0.688890\pi$
$659$	−18920.0	−1.11839	−0.559195	+	0.829036i	$0.688890\pi$
$660$	0	0
$661$	5241.00	0.308398	0.154199	−	0.988040i	$-0.450720\pi$
$661$	5241.00	0.308398	0.154199	+	0.988040i	$0.450720\pi$
$662$	1028.00	0.0603540
$663$	0	0
$664$	7770.00	0.454118
$665$	2100.00	0.122458
$666$	0	0
$667$	18306.0	1.06269
$668$	25760.0	1.49204
$669$	0	0
$670$	−1414.00	−0.0815337
$671$	−13970.0	−0.803735
$672$	0	0
$673$	20467.0	1.17228	0.586140	−	0.810210i	$-0.300647\pi$
$673$	20467.0	1.17228	0.586140	+	0.810210i	$0.300647\pi$
$674$	2487.00	0.142130
$675$	0	0
$676$	0	0
$677$	70.0000	0.00397388	0.00198694	−	0.999998i	$-0.499368\pi$
$677$	70.0000	0.00397388	0.00198694	+	0.999998i	$0.499368\pi$
$678$	0	0
$679$	12020.0	0.679360
$680$	−3885.00	−0.219093
$681$	0	0
$682$	4312.00	0.242104
$683$	−6432.00	−0.360342	−0.180171	−	0.983635i	$-0.557665\pi$
$683$	−6432.00	−0.360342	−0.180171	+	0.983635i	$0.557665\pi$
$684$	0	0
$685$	−3633.00	−0.202642
$686$	5860.00	0.326146
$687$	0	0
$688$	−10086.0	−0.558903
$689$	0	0
$690$	0	0
$691$	−6666.00	−0.366985	−0.183492	−	0.983021i	$-0.558740\pi$
$691$	−6666.00	−0.366985	−0.183492	+	0.983021i	$0.558740\pi$
$692$	29022.0	1.59429
$693$	0	0
$694$	2850.00	0.155885
$695$	2436.00	0.132954
$696$	0	0
$697$	10545.0	0.573056
$698$	−2018.00	−0.109430
$699$	0	0
$700$	−5320.00	−0.287253
$701$	14054.0	0.757221	0.378611	−	0.925556i	$-0.376402\pi$
$701$	14054.0	0.757221	0.378611	+	0.925556i	$0.376402\pi$
$702$	0	0
$703$	390.000	0.0209234
$704$	−3674.00	−0.196689
$705$	0	0
$706$	5287.00	0.281840
$707$	−4290.00	−0.228207
$708$	0	0
$709$	−71.0000	−0.00376088	−0.00188044	−	0.999998i	$-0.500599\pi$
$709$	−71.0000	−0.00376088	−0.00188044	+	0.999998i	$0.500599\pi$
$710$	−7602.00	−0.401828
$711$	0	0
$712$	2910.00	0.153170
$713$	31752.0	1.66777
$714$	0	0
$715$	0	0
$716$	25718.0	1.34236
$717$	0	0
$718$	7278.00	0.378290
$719$	−3936.00	−0.204156	−0.102078	−	0.994776i	$-0.532549\pi$
$719$	−3936.00	−0.204156	−0.102078	+	0.994776i	$0.532549\pi$
$720$	0	0
$721$	13020.0	0.672524
$722$	−5959.00	−0.307162
$723$	0	0
$724$	22981.0	1.17967
$725$	−8588.00	−0.439931
$726$	0	0
$727$	34202.0	1.74482	0.872409	−	0.488777i	$-0.162557\pi$
$727$	34202.0	1.74482	0.872409	+	0.488777i	$0.162557\pi$
$728$	0	0
$729$	0	0
$730$	5635.00	0.285700
$731$	9102.00	0.460533
$732$	0	0
$733$	−27363.0	−1.37882	−0.689410	−	0.724371i	$-0.742130\pi$
$733$	−27363.0	−1.37882	−0.689410	+	0.724371i	$0.742130\pi$
$734$	−4202.00	−0.211306
$735$	0	0
$736$	26082.0	1.30624
$737$	4444.00	0.222112
$738$	0	0
$739$	21776.0	1.08396	0.541978	−	0.840393i	$-0.317676\pi$
$739$	21776.0	1.08396	0.541978	+	0.840393i	$0.317676\pi$
$740$	637.000	0.0316440
$741$	0	0
$742$	−5370.00	−0.265686
$743$	−2484.00	−0.122650	−0.0613251	−	0.998118i	$-0.519533\pi$
$743$	−2484.00	−0.122650	−0.0613251	+	0.998118i	$0.519533\pi$
$744$	0	0
$745$	−4515.00	−0.222036
$746$	−1583.00	−0.0776914
$747$	0	0
$748$	5698.00	0.278529
$749$	−13380.0	−0.652730
$750$	0	0
$751$	32906.0	1.59888	0.799439	−	0.600748i	$-0.205130\pi$
$751$	32906.0	1.59888	0.799439	+	0.600748i	$0.205130\pi$
$752$	18942.0	0.918542
$753$	0	0
$754$	0	0
$755$	−20398.0	−0.983257
$756$	0	0
$757$	−3914.00	−0.187922	−0.0939609	−	0.995576i	$-0.529953\pi$
$757$	−3914.00	−0.187922	−0.0939609	+	0.995576i	$0.529953\pi$
$758$	−2052.00	−0.0983272
$759$	0	0
$760$	3150.00	0.150345
$761$	33038.0	1.57375	0.786877	−	0.617110i	$-0.211697\pi$
$761$	33038.0	1.57375	0.786877	+	0.617110i	$0.211697\pi$
$762$	0	0
$763$	10340.0	0.490607
$764$	−4172.00	−0.197562
$765$	0	0
$766$	6872.00	0.324145
$767$	0	0
$768$	0	0
$769$	−17586.0	−0.824665	−0.412332	−	0.911033i	$-0.635286\pi$
$769$	−17586.0	−0.824665	−0.412332	+	0.911033i	$0.635286\pi$
$770$	1540.00	0.0720750
$771$	0	0
$772$	2751.00	0.128252
$773$	−18314.0	−0.852146	−0.426073	−	0.904689i	$-0.640103\pi$
$773$	−18314.0	−0.852146	−0.426073	+	0.904689i	$0.640103\pi$
$774$	0	0
$775$	−14896.0	−0.690426
$776$	18030.0	0.834071
$777$	0	0
$778$	11653.0	0.536993
$779$	−8550.00	−0.393242
$780$	0	0
$781$	23892.0	1.09465
$782$	−5994.00	−0.274098
$783$	0	0
$784$	−9963.00	−0.453854
$785$	14553.0	0.661680
$786$	0	0
$787$	−42068.0	−1.90542	−0.952708	−	0.303888i	$-0.901715\pi$
$787$	−42068.0	−1.90542	−0.952708	+	0.303888i	$0.901715\pi$
$788$	−24654.0	−1.11455
$789$	0	0
$790$	−6188.00	−0.278682
$791$	10770.0	0.484118
$792$	0	0
$793$	0	0
$794$	6134.00	0.274166
$795$	0	0
$796$	−14126.0	−0.628998
$797$	4282.00	0.190309	0.0951545	−	0.995463i	$-0.469665\pi$
$797$	4282.00	0.190309	0.0951545	+	0.995463i	$0.469665\pi$
$798$	0	0
$799$	−17094.0	−0.756874
$800$	−12236.0	−0.540760
$801$	0	0
$802$	10795.0	0.475293
$803$	−17710.0	−0.778297
$804$	0	0
$805$	11340.0	0.496500
$806$	0	0
$807$	0	0
$808$	−6435.00	−0.280176
$809$	−40221.0	−1.74795	−0.873977	−	0.485967i	$-0.838468\pi$
$809$	−40221.0	−1.74795	−0.873977	+	0.485967i	$0.838468\pi$
$810$	0	0
$811$	−7084.00	−0.306724	−0.153362	−	0.988170i	$-0.549010\pi$
$811$	−7084.00	−0.306724	−0.153362	+	0.988170i	$0.549010\pi$
$812$	7910.00	0.341855
$813$	0	0
$814$	286.000	0.0123149
$815$	−11900.0	−0.511459
$816$	0	0
$817$	−7380.00	−0.316026
$818$	−8489.00	−0.362850
$819$	0	0
$820$	−13965.0	−0.594730
$821$	−17338.0	−0.737028	−0.368514	−	0.929622i	$-0.620133\pi$
$821$	−17338.0	−0.737028	−0.368514	+	0.929622i	$0.620133\pi$
$822$	0	0
$823$	35496.0	1.50342	0.751709	−	0.659495i	$-0.229230\pi$
$823$	35496.0	1.50342	0.751709	+	0.659495i	$0.229230\pi$
$824$	19530.0	0.825679
$825$	0	0
$826$	5760.00	0.242634
$827$	14992.0	0.630378	0.315189	−	0.949029i	$-0.397932\pi$
$827$	14992.0	0.630378	0.315189	+	0.949029i	$0.397932\pi$
$828$	0	0
$829$	−20659.0	−0.865521	−0.432760	−	0.901509i	$-0.642460\pi$
$829$	−20659.0	−0.865521	−0.432760	+	0.901509i	$0.642460\pi$
$830$	3626.00	0.151639
$831$	0	0
$832$	0	0
$833$	8991.00	0.373973
$834$	0	0
$835$	25760.0	1.06762
$836$	−4620.00	−0.191132
$837$	0	0
$838$	−1496.00	−0.0616688
$839$	−28716.0	−1.18163	−0.590814	−	0.806808i	$-0.701193\pi$
$839$	−28716.0	−1.18163	−0.590814	+	0.806808i	$0.701193\pi$
$840$	0	0
$841$	−11620.0	−0.476444
$842$	−11695.0	−0.478665
$843$	0	0
$844$	−1120.00	−0.0456777
$845$	0	0
$846$	0	0
$847$	8470.00	0.343604
$848$	22017.0	0.891588
$849$	0	0
$850$	2812.00	0.113472
$851$	2106.00	0.0848328
$852$	0	0
$853$	13377.0	0.536952	0.268476	−	0.963286i	$-0.413480\pi$
$853$	13377.0	0.536952	0.268476	+	0.963286i	$0.413480\pi$
$854$	6350.00	0.254441
$855$	0	0
$856$	−20070.0	−0.801377
$857$	27419.0	1.09290	0.546450	−	0.837492i	$-0.315979\pi$
$857$	27419.0	1.09290	0.546450	+	0.837492i	$0.315979\pi$
$858$	0	0
$859$	2422.00	0.0962021	0.0481010	−	0.998842i	$-0.484683\pi$
$859$	2422.00	0.0962021	0.0481010	+	0.998842i	$0.484683\pi$
$860$	−12054.0	−0.477951
$861$	0	0
$862$	−10590.0	−0.418442
$863$	34522.0	1.36169	0.680847	−	0.732425i	$-0.261612\pi$
$863$	34522.0	1.36169	0.680847	+	0.732425i	$0.261612\pi$
$864$	0	0
$865$	29022.0	1.14078
$866$	−13949.0	−0.547351
$867$	0	0
$868$	13720.0	0.536506
$869$	19448.0	0.759181
$870$	0	0
$871$	0	0
$872$	15510.0	0.602334
$873$	0	0
$874$	4860.00	0.188091
$875$	−14070.0	−0.543603
$876$	0	0
$877$	13733.0	0.528769	0.264385	−	0.964417i	$-0.414831\pi$
$877$	13733.0	0.528769	0.264385	+	0.964417i	$0.414831\pi$
$878$	−10726.0	−0.412284
$879$	0	0
$880$	−6314.00	−0.241869
$881$	22759.0	0.870341	0.435170	−	0.900348i	$-0.356688\pi$
$881$	22759.0	0.870341	0.435170	+	0.900348i	$0.356688\pi$
$882$	0	0
$883$	−2168.00	−0.0826263	−0.0413131	−	0.999146i	$-0.513154\pi$
$883$	−2168.00	−0.0826263	−0.0413131	+	0.999146i	$0.513154\pi$
$884$	0	0
$885$	0	0
$886$	−16228.0	−0.615339
$887$	−15888.0	−0.601428	−0.300714	−	0.953714i	$-0.597225\pi$
$887$	−15888.0	−0.601428	−0.300714	+	0.953714i	$0.597225\pi$
$888$	0	0
$889$	9880.00	0.372739
$890$	1358.00	0.0511464
$891$	0	0
$892$	−28504.0	−1.06994
$893$	13860.0	0.519381
$894$	0	0
$895$	25718.0	0.960512
$896$	14550.0	0.542502
$897$	0	0
$898$	−7538.00	−0.280118
$899$	22148.0	0.821665
$900$	0	0
$901$	−19869.0	−0.734664
$902$	−6270.00	−0.231450
$903$	0	0
$904$	16155.0	0.594366
$905$	22981.0	0.844104
$906$	0	0
$907$	−11628.0	−0.425691	−0.212845	−	0.977086i	$-0.568273\pi$
$907$	−11628.0	−0.425691	−0.212845	+	0.977086i	$0.568273\pi$
$908$	−40558.0	−1.48234
$909$	0	0
$910$	0	0
$911$	12584.0	0.457658	0.228829	−	0.973467i	$-0.426510\pi$
$911$	12584.0	0.457658	0.228829	+	0.973467i	$0.426510\pi$
$912$	0	0
$913$	−11396.0	−0.413092
$914$	15539.0	0.562346
$915$	0	0
$916$	−45374.0	−1.63668
$917$	5600.00	0.201667
$918$	0	0
$919$	17184.0	0.616809	0.308405	−	0.951255i	$-0.400205\pi$
$919$	17184.0	0.616809	0.308405	+	0.951255i	$0.400205\pi$
$920$	17010.0	0.609569
$921$	0	0
$922$	−4811.00	−0.171846
$923$	0	0
$924$	0	0
$925$	−988.000	−0.0351192
$926$	562.000	0.0199443
$927$	0	0
$928$	18193.0	0.643550
$929$	−12777.0	−0.451238	−0.225619	−	0.974216i	$-0.572440\pi$
$929$	−12777.0	−0.451238	−0.225619	+	0.974216i	$0.572440\pi$
$930$	0	0
$931$	−7290.00	−0.256627
$932$	48230.0	1.69509
$933$	0	0
$934$	−4914.00	−0.172153
$935$	5698.00	0.199299
$936$	0	0
$937$	9191.00	0.320445	0.160222	−	0.987081i	$-0.448779\pi$
$937$	9191.00	0.320445	0.160222	+	0.987081i	$0.448779\pi$
$938$	−2020.00	−0.0703149
$939$	0	0
$940$	22638.0	0.785500
$941$	−50498.0	−1.74940	−0.874701	−	0.484662i	$-0.838942\pi$
$941$	−50498.0	−1.74940	−0.874701	+	0.484662i	$0.838942\pi$
$942$	0	0
$943$	−46170.0	−1.59438
$944$	−23616.0	−0.814232
$945$	0	0
$946$	−5412.00	−0.186003
$947$	−1560.00	−0.0535303	−0.0267651	−	0.999642i	$-0.508521\pi$
$947$	−1560.00	−0.0535303	−0.0267651	+	0.999642i	$0.508521\pi$
$948$	0	0
$949$	0	0
$950$	−2280.00	−0.0778663
$951$	0	0
$952$	−5550.00	−0.188946
$953$	21498.0	0.730733	0.365366	−	0.930864i	$-0.380944\pi$
$953$	21498.0	0.730733	0.365366	+	0.930864i	$0.380944\pi$
$954$	0	0
$955$	−4172.00	−0.141364
$956$	17262.0	0.583988
$957$	0	0
$958$	3600.00	0.121410
$959$	−5190.00	−0.174759
$960$	0	0
$961$	8625.00	0.289517
$962$	0	0
$963$	0	0
$964$	25319.0	0.845923
$965$	2751.00	0.0917698
$966$	0	0
$967$	−418.000	−0.0139007	−0.00695035	−	0.999976i	$-0.502212\pi$
$967$	−418.000	−0.0139007	−0.00695035	+	0.999976i	$0.502212\pi$
$968$	12705.0	0.421853
$969$	0	0
$970$	8414.00	0.278513
$971$	−18132.0	−0.599262	−0.299631	−	0.954055i	$-0.596864\pi$
$971$	−18132.0	−0.599262	−0.299631	+	0.954055i	$0.596864\pi$
$972$	0	0
$973$	3480.00	0.114659
$974$	−17130.0	−0.563532
$975$	0	0
$976$	−26035.0	−0.853853
$977$	−12501.0	−0.409358	−0.204679	−	0.978829i	$-0.565615\pi$
$977$	−12501.0	−0.409358	−0.204679	+	0.978829i	$0.565615\pi$
$978$	0	0
$979$	−4268.00	−0.139332
$980$	−11907.0	−0.388118
$981$	0	0
$982$	11838.0	0.384690
$983$	43708.0	1.41818	0.709089	−	0.705119i	$-0.249106\pi$
$983$	43708.0	1.41818	0.709089	+	0.705119i	$0.249106\pi$
$984$	0	0
$985$	−24654.0	−0.797504
$986$	−4181.00	−0.135041
$987$	0	0
$988$	0	0
$989$	−39852.0	−1.28131
$990$	0	0
$991$	−39614.0	−1.26981	−0.634904	−	0.772591i	$-0.718960\pi$
$991$	−39614.0	−1.26981	−0.634904	+	0.772591i	$0.718960\pi$
$992$	31556.0	1.00998
$993$	0	0
$994$	−10860.0	−0.346538
$995$	−14126.0	−0.450075
$996$	0	0
$997$	−36503.0	−1.15954	−0.579770	−	0.814780i	$-0.696858\pi$
$997$	−36503.0	−1.15954	−0.579770	+	0.814780i	$0.696858\pi$
$998$	8976.00	0.284700
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1521.4.a.h.1.1		1
3.2	odd	2		507.4.a.b.1.1		1
13.3	even	3		117.4.g.a.100.1		2
13.9	even	3		117.4.g.a.55.1		2
13.12	even	2		1521.4.a.e.1.1		1
39.5	even	4		507.4.b.d.337.2		2
39.8	even	4		507.4.b.d.337.1		2
39.29	odd	6		39.4.e.b.22.1	yes	2
39.35	odd	6		39.4.e.b.16.1	✓	2
39.38	odd	2		507.4.a.d.1.1		1
156.35	even	6		624.4.q.c.289.1		2
156.107	even	6		624.4.q.c.529.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.e.b.16.1	✓	2	39.35	odd	6
39.4.e.b.22.1	yes	2	39.29	odd	6
117.4.g.a.55.1		2	13.9	even	3
117.4.g.a.100.1		2	13.3	even	3
507.4.a.b.1.1		1	3.2	odd	2
507.4.a.d.1.1		1	39.38	odd	2
507.4.b.d.337.1		2	39.8	even	4
507.4.b.d.337.2		2	39.5	even	4
624.4.q.c.289.1		2	156.35	even	6
624.4.q.c.529.1		2	156.107	even	6
1521.4.a.e.1.1		1	13.12	even	2
1521.4.a.h.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:	\( N \)	\(=\)	\( 1521 = 3^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1521.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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