LMFDB - Embedded newform 2898.2.a.u.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2898,2,Mod(1,2898)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2898, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2898.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2898 = 2 \cdot 3^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2898.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:	$23.1406465058$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 966)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	2898.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} +1.00000 q^{4} +4.00000 q^{5} +1.00000 q^{7} +1.00000 q^{8} +O(q^{10})$

$q+1.00000 q^{2} +1.00000 q^{4} +4.00000 q^{5} +1.00000 q^{7} +1.00000 q^{8} +4.00000 q^{10} -2.00000 q^{11} +2.00000 q^{13} +1.00000 q^{14} +1.00000 q^{16} -2.00000 q^{17} -2.00000 q^{19} +4.00000 q^{20} -2.00000 q^{22} -1.00000 q^{23} +11.0000 q^{25} +2.00000 q^{26} +1.00000 q^{28} +6.00000 q^{29} +1.00000 q^{32} -2.00000 q^{34} +4.00000 q^{35} +4.00000 q^{37} -2.00000 q^{38} +4.00000 q^{40} +10.0000 q^{41} -10.0000 q^{43} -2.00000 q^{44} -1.00000 q^{46} +8.00000 q^{47} +1.00000 q^{49} +11.0000 q^{50} +2.00000 q^{52} -8.00000 q^{55} +1.00000 q^{56} +6.00000 q^{58} -4.00000 q^{61} +1.00000 q^{64} +8.00000 q^{65} +2.00000 q^{67} -2.00000 q^{68} +4.00000 q^{70} -8.00000 q^{71} -2.00000 q^{73} +4.00000 q^{74} -2.00000 q^{76} -2.00000 q^{77} -8.00000 q^{79} +4.00000 q^{80} +10.0000 q^{82} +6.00000 q^{83} -8.00000 q^{85} -10.0000 q^{86} -2.00000 q^{88} -6.00000 q^{89} +2.00000 q^{91} -1.00000 q^{92} +8.00000 q^{94} -8.00000 q^{95} -2.00000 q^{97} +1.00000 q^{98} +O(q^{100})$

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0	0
$3$	0	0
$4$	1.00000	0.500000
$5$	4.00000	1.78885	0.894427	−	0.447214i	$-0.147584\pi$
$5$	4.00000	1.78885	0.894427	+	0.447214i	$0.147584\pi$
$6$	0	0
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	0	0
$10$	4.00000	1.26491
$11$	−2.00000	−0.603023	−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000	−0.603023	−0.301511	+	0.953463i	$0.597491\pi$
$12$	0	0
$13$	2.00000	0.554700	0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000	0.554700	0.277350	+	0.960769i	$0.410544\pi$
$14$	1.00000	0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	−2.00000	−0.485071	−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000	−0.485071	−0.242536	+	0.970143i	$0.577979\pi$
$18$	0	0
$19$	−2.00000	−0.458831	−0.229416	−	0.973329i	$-0.573682\pi$
$19$	−2.00000	−0.458831	−0.229416	+	0.973329i	$0.573682\pi$
$20$	4.00000	0.894427
$21$	0	0
$22$	−2.00000	−0.426401
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	0	0
$25$	11.0000	2.20000
$26$	2.00000	0.392232
$27$	0	0
$28$	1.00000	0.188982
$29$	6.00000	1.11417	0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000	1.11417	0.557086	+	0.830455i	$0.311919\pi$
$30$	0	0
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−2.00000	−0.342997
$35$	4.00000	0.676123
$36$	0	0
$37$	4.00000	0.657596	0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000	0.657596	0.328798	+	0.944400i	$0.393356\pi$
$38$	−2.00000	−0.324443
$39$	0	0
$40$	4.00000	0.632456
$41$	10.0000	1.56174	0.780869	−	0.624695i	$-0.214777\pi$
$41$	10.0000	1.56174	0.780869	+	0.624695i	$0.214777\pi$
$42$	0	0
$43$	−10.0000	−1.52499	−0.762493	−	0.646997i	$-0.776025\pi$
$43$	−10.0000	−1.52499	−0.762493	+	0.646997i	$0.776025\pi$
$44$	−2.00000	−0.301511
$45$	0	0
$46$	−1.00000	−0.147442
$47$	8.00000	1.16692	0.583460	−	0.812142i	$-0.301699\pi$
$47$	8.00000	1.16692	0.583460	+	0.812142i	$0.301699\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	11.0000	1.55563
$51$	0	0
$52$	2.00000	0.277350
$53$	0	0		−	1.00000i	$-0.5\pi$
$53$	0	0			1.00000i	$0.5\pi$
$54$	0	0
$55$	−8.00000	−1.07872
$56$	1.00000	0.133631
$57$	0	0
$58$	6.00000	0.787839
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	0	0
$61$	−4.00000	−0.512148	−0.256074	−	0.966657i	$-0.582429\pi$
$61$	−4.00000	−0.512148	−0.256074	+	0.966657i	$0.582429\pi$
$62$	0	0
$63$	0	0
$64$	1.00000	0.125000
$65$	8.00000	0.992278
$66$	0	0
$67$	2.00000	0.244339	0.122169	−	0.992509i	$-0.461015\pi$
$67$	2.00000	0.244339	0.122169	+	0.992509i	$0.461015\pi$
$68$	−2.00000	−0.242536
$69$	0	0
$70$	4.00000	0.478091
$71$	−8.00000	−0.949425	−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000	−0.949425	−0.474713	+	0.880141i	$0.657448\pi$
$72$	0	0
$73$	−2.00000	−0.234082	−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000	−0.234082	−0.117041	+	0.993127i	$0.537341\pi$
$74$	4.00000	0.464991
$75$	0	0
$76$	−2.00000	−0.229416
$77$	−2.00000	−0.227921
$78$	0	0
$79$	−8.00000	−0.900070	−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000	−0.900070	−0.450035	+	0.893011i	$0.648589\pi$
$80$	4.00000	0.447214
$81$	0	0
$82$	10.0000	1.10432
$83$	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
$85$	−8.00000	−0.867722
$86$	−10.0000	−1.07833
$87$	0	0
$88$	−2.00000	−0.213201
$89$	−6.00000	−0.635999	−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000	−0.635999	−0.317999	+	0.948091i	$0.603011\pi$
$90$	0	0
$91$	2.00000	0.209657
$92$	−1.00000	−0.104257
$93$	0	0
$94$	8.00000	0.825137
$95$	−8.00000	−0.820783
$96$	0	0
$97$	−2.00000	−0.203069	−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000	−0.203069	−0.101535	+	0.994832i	$0.532375\pi$
$98$	1.00000	0.101015
$99$	0	0
$100$	11.0000	1.10000
$101$	14.0000	1.39305	0.696526	−	0.717532i	$-0.254728\pi$
$101$	14.0000	1.39305	0.696526	+	0.717532i	$0.254728\pi$
$102$	0	0
$103$	−12.0000	−1.18240	−0.591198	−	0.806527i	$-0.701345\pi$
$103$	−12.0000	−1.18240	−0.591198	+	0.806527i	$0.701345\pi$
$104$	2.00000	0.196116
$105$	0	0
$106$	0	0
$107$	2.00000	0.193347	0.0966736	−	0.995316i	$-0.469180\pi$
$107$	2.00000	0.193347	0.0966736	+	0.995316i	$0.469180\pi$
$108$	0	0
$109$	−16.0000	−1.53252	−0.766261	−	0.642529i	$-0.777885\pi$
$109$	−16.0000	−1.53252	−0.766261	+	0.642529i	$0.777885\pi$
$110$	−8.00000	−0.762770
$111$	0	0
$112$	1.00000	0.0944911
$113$	−6.00000	−0.564433	−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000	−0.564433	−0.282216	+	0.959351i	$0.591070\pi$
$114$	0	0
$115$	−4.00000	−0.373002
$116$	6.00000	0.557086
$117$	0	0
$118$	0	0
$119$	−2.00000	−0.183340
$120$	0	0
$121$	−7.00000	−0.636364
$122$	−4.00000	−0.362143
$123$	0	0
$124$	0	0
$125$	24.0000	2.14663
$126$	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
$130$	8.00000	0.701646
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	0	0
$133$	−2.00000	−0.173422
$134$	2.00000	0.172774
$135$	0	0
$136$	−2.00000	−0.171499
$137$	−18.0000	−1.53784	−0.768922	−	0.639343i	$-0.779207\pi$
$137$	−18.0000	−1.53784	−0.768922	+	0.639343i	$0.779207\pi$
$138$	0	0
$139$	−16.0000	−1.35710	−0.678551	−	0.734553i	$-0.737392\pi$
$139$	−16.0000	−1.35710	−0.678551	+	0.734553i	$0.737392\pi$
$140$	4.00000	0.338062
$141$	0	0
$142$	−8.00000	−0.671345
$143$	−4.00000	−0.334497
$144$	0	0
$145$	24.0000	1.99309
$146$	−2.00000	−0.165521
$147$	0	0
$148$	4.00000	0.328798
$149$	24.0000	1.96616	0.983078	−	0.183186i	$-0.0586410\pi$
$149$	24.0000	1.96616	0.983078	+	0.183186i	$0.0586410\pi$
$150$	0	0
$151$	16.0000	1.30206	0.651031	−	0.759051i	$-0.274337\pi$
$151$	16.0000	1.30206	0.651031	+	0.759051i	$0.274337\pi$
$152$	−2.00000	−0.162221
$153$	0	0
$154$	−2.00000	−0.161165
$155$	0	0
$156$	0	0
$157$	−8.00000	−0.638470	−0.319235	−	0.947676i	$-0.603426\pi$
$157$	−8.00000	−0.638470	−0.319235	+	0.947676i	$0.603426\pi$
$158$	−8.00000	−0.636446
$159$	0	0
$160$	4.00000	0.316228
$161$	−1.00000	−0.0788110
$162$	0	0
$163$	24.0000	1.87983	0.939913	−	0.341415i	$-0.110906\pi$
$163$	24.0000	1.87983	0.939913	+	0.341415i	$0.110906\pi$
$164$	10.0000	0.780869
$165$	0	0
$166$	6.00000	0.465690
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	0	0
$169$	−9.00000	−0.692308
$170$	−8.00000	−0.613572
$171$	0	0
$172$	−10.0000	−0.762493
$173$	2.00000	0.152057	0.0760286	−	0.997106i	$-0.475776\pi$
$173$	2.00000	0.152057	0.0760286	+	0.997106i	$0.475776\pi$
$174$	0	0
$175$	11.0000	0.831522
$176$	−2.00000	−0.150756
$177$	0	0
$178$	−6.00000	−0.449719
$179$	−16.0000	−1.19590	−0.597948	−	0.801535i	$-0.704017\pi$
$179$	−16.0000	−1.19590	−0.597948	+	0.801535i	$0.704017\pi$
$180$	0	0
$181$	−20.0000	−1.48659	−0.743294	−	0.668965i	$-0.766738\pi$
$181$	−20.0000	−1.48659	−0.743294	+	0.668965i	$0.766738\pi$
$182$	2.00000	0.148250
$183$	0	0
$184$	−1.00000	−0.0737210
$185$	16.0000	1.17634
$186$	0	0
$187$	4.00000	0.292509
$188$	8.00000	0.583460
$189$	0	0
$190$	−8.00000	−0.580381
$191$	20.0000	1.44715	0.723575	−	0.690246i	$-0.242498\pi$
$191$	20.0000	1.44715	0.723575	+	0.690246i	$0.242498\pi$
$192$	0	0
$193$	−6.00000	−0.431889	−0.215945	−	0.976406i	$-0.569283\pi$
$193$	−6.00000	−0.431889	−0.215945	+	0.976406i	$0.569283\pi$
$194$	−2.00000	−0.143592
$195$	0	0
$196$	1.00000	0.0714286
$197$	−10.0000	−0.712470	−0.356235	−	0.934396i	$-0.615940\pi$
$197$	−10.0000	−0.712470	−0.356235	+	0.934396i	$0.615940\pi$
$198$	0	0
$199$	0	0		−	1.00000i	$-0.5\pi$
$199$	0	0			1.00000i	$0.5\pi$
$200$	11.0000	0.777817
$201$	0	0
$202$	14.0000	0.985037
$203$	6.00000	0.421117
$204$	0	0
$205$	40.0000	2.79372
$206$	−12.0000	−0.836080
$207$	0	0
$208$	2.00000	0.138675
$209$	4.00000	0.276686
$210$	0	0
$211$	−20.0000	−1.37686	−0.688428	−	0.725304i	$-0.741699\pi$
$211$	−20.0000	−1.37686	−0.688428	+	0.725304i	$0.741699\pi$
$212$	0	0
$213$	0	0
$214$	2.00000	0.136717
$215$	−40.0000	−2.72798
$216$	0	0
$217$	0	0
$218$	−16.0000	−1.08366
$219$	0	0
$220$	−8.00000	−0.539360
$221$	−4.00000	−0.269069
$222$	0	0
$223$	16.0000	1.07144	0.535720	−	0.844396i	$-0.320040\pi$
$223$	16.0000	1.07144	0.535720	+	0.844396i	$0.320040\pi$
$224$	1.00000	0.0668153
$225$	0	0
$226$	−6.00000	−0.399114
$227$	−14.0000	−0.929213	−0.464606	−	0.885517i	$-0.653804\pi$
$227$	−14.0000	−0.929213	−0.464606	+	0.885517i	$0.653804\pi$
$228$	0	0
$229$	12.0000	0.792982	0.396491	−	0.918039i	$-0.370228\pi$
$229$	12.0000	0.792982	0.396491	+	0.918039i	$0.370228\pi$
$230$	−4.00000	−0.263752
$231$	0	0
$232$	6.00000	0.393919
$233$	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
$235$	32.0000	2.08745
$236$	0	0
$237$	0	0
$238$	−2.00000	−0.129641
$239$	−8.00000	−0.517477	−0.258738	−	0.965947i	$-0.583307\pi$
$239$	−8.00000	−0.517477	−0.258738	+	0.965947i	$0.583307\pi$
$240$	0	0
$241$	−18.0000	−1.15948	−0.579741	−	0.814801i	$-0.696846\pi$
$241$	−18.0000	−1.15948	−0.579741	+	0.814801i	$0.696846\pi$
$242$	−7.00000	−0.449977
$243$	0	0
$244$	−4.00000	−0.256074
$245$	4.00000	0.255551
$246$	0	0
$247$	−4.00000	−0.254514
$248$	0	0
$249$	0	0
$250$	24.0000	1.51789
$251$	−26.0000	−1.64111	−0.820553	−	0.571571i	$-0.806334\pi$
$251$	−26.0000	−1.64111	−0.820553	+	0.571571i	$0.806334\pi$
$252$	0	0
$253$	2.00000	0.125739
$254$	8.00000	0.501965
$255$	0	0
$256$	1.00000	0.0625000
$257$	−14.0000	−0.873296	−0.436648	−	0.899632i	$-0.643834\pi$
$257$	−14.0000	−0.873296	−0.436648	+	0.899632i	$0.643834\pi$
$258$	0	0
$259$	4.00000	0.248548
$260$	8.00000	0.496139
$261$	0	0
$262$	0	0
$263$	8.00000	0.493301	0.246651	−	0.969104i	$-0.420670\pi$
$263$	8.00000	0.493301	0.246651	+	0.969104i	$0.420670\pi$
$264$	0	0
$265$	0	0
$266$	−2.00000	−0.122628
$267$	0	0
$268$	2.00000	0.122169
$269$	18.0000	1.09748	0.548740	−	0.835993i	$-0.315108\pi$
$269$	18.0000	1.09748	0.548740	+	0.835993i	$0.315108\pi$
$270$	0	0
$271$	16.0000	0.971931	0.485965	−	0.873978i	$-0.338468\pi$
$271$	16.0000	0.971931	0.485965	+	0.873978i	$0.338468\pi$
$272$	−2.00000	−0.121268
$273$	0	0
$274$	−18.0000	−1.08742
$275$	−22.0000	−1.32665
$276$	0	0
$277$	2.00000	0.120168	0.0600842	−	0.998193i	$-0.480863\pi$
$277$	2.00000	0.120168	0.0600842	+	0.998193i	$0.480863\pi$
$278$	−16.0000	−0.959616
$279$	0	0
$280$	4.00000	0.239046
$281$	10.0000	0.596550	0.298275	−	0.954480i	$-0.403589\pi$
$281$	10.0000	0.596550	0.298275	+	0.954480i	$0.403589\pi$
$282$	0	0
$283$	−6.00000	−0.356663	−0.178331	−	0.983970i	$-0.557070\pi$
$283$	−6.00000	−0.356663	−0.178331	+	0.983970i	$0.557070\pi$
$284$	−8.00000	−0.474713
$285$	0	0
$286$	−4.00000	−0.236525
$287$	10.0000	0.590281
$288$	0	0
$289$	−13.0000	−0.764706
$290$	24.0000	1.40933
$291$	0	0
$292$	−2.00000	−0.117041
$293$	12.0000	0.701047	0.350524	−	0.936554i	$-0.386004\pi$
$293$	12.0000	0.701047	0.350524	+	0.936554i	$0.386004\pi$
$294$	0	0
$295$	0	0
$296$	4.00000	0.232495
$297$	0	0
$298$	24.0000	1.39028
$299$	−2.00000	−0.115663
$300$	0	0
$301$	−10.0000	−0.576390
$302$	16.0000	0.920697
$303$	0	0
$304$	−2.00000	−0.114708
$305$	−16.0000	−0.916157
$306$	0	0
$307$	−12.0000	−0.684876	−0.342438	−	0.939540i	$-0.611253\pi$
$307$	−12.0000	−0.684876	−0.342438	+	0.939540i	$0.611253\pi$
$308$	−2.00000	−0.113961
$309$	0	0
$310$	0	0
$311$	−24.0000	−1.36092	−0.680458	−	0.732787i	$-0.738219\pi$
$311$	−24.0000	−1.36092	−0.680458	+	0.732787i	$0.738219\pi$
$312$	0	0
$313$	22.0000	1.24351	0.621757	−	0.783210i	$-0.286419\pi$
$313$	22.0000	1.24351	0.621757	+	0.783210i	$0.286419\pi$
$314$	−8.00000	−0.451466
$315$	0	0
$316$	−8.00000	−0.450035
$317$	30.0000	1.68497	0.842484	−	0.538721i	$-0.181092\pi$
$317$	30.0000	1.68497	0.842484	+	0.538721i	$0.181092\pi$
$318$	0	0
$319$	−12.0000	−0.671871
$320$	4.00000	0.223607
$321$	0	0
$322$	−1.00000	−0.0557278
$323$	4.00000	0.222566
$324$	0	0
$325$	22.0000	1.22034
$326$	24.0000	1.32924
$327$	0	0
$328$	10.0000	0.552158
$329$	8.00000	0.441054
$330$	0	0
$331$	20.0000	1.09930	0.549650	−	0.835395i	$-0.314761\pi$
$331$	20.0000	1.09930	0.549650	+	0.835395i	$0.314761\pi$
$332$	6.00000	0.329293
$333$	0	0
$334$	0	0
$335$	8.00000	0.437087
$336$	0	0
$337$	26.0000	1.41631	0.708155	−	0.706057i	$-0.249528\pi$
$337$	26.0000	1.41631	0.708155	+	0.706057i	$0.249528\pi$
$338$	−9.00000	−0.489535
$339$	0	0
$340$	−8.00000	−0.433861
$341$	0	0
$342$	0	0
$343$	1.00000	0.0539949
$344$	−10.0000	−0.539164
$345$	0	0
$346$	2.00000	0.107521
$347$	−16.0000	−0.858925	−0.429463	−	0.903085i	$-0.641297\pi$
$347$	−16.0000	−0.858925	−0.429463	+	0.903085i	$0.641297\pi$
$348$	0	0
$349$	14.0000	0.749403	0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000	0.749403	0.374701	+	0.927146i	$0.377745\pi$
$350$	11.0000	0.587975
$351$	0	0
$352$	−2.00000	−0.106600
$353$	−34.0000	−1.80964	−0.904819	−	0.425797i	$-0.859994\pi$
$353$	−34.0000	−1.80964	−0.904819	+	0.425797i	$0.859994\pi$
$354$	0	0
$355$	−32.0000	−1.69838
$356$	−6.00000	−0.317999
$357$	0	0
$358$	−16.0000	−0.845626
$359$	20.0000	1.05556	0.527780	−	0.849381i	$-0.323025\pi$
$359$	20.0000	1.05556	0.527780	+	0.849381i	$0.323025\pi$
$360$	0	0
$361$	−15.0000	−0.789474
$362$	−20.0000	−1.05118
$363$	0	0
$364$	2.00000	0.104828
$365$	−8.00000	−0.418739
$366$	0	0
$367$	−32.0000	−1.67039	−0.835193	−	0.549957i	$-0.814644\pi$
$367$	−32.0000	−1.67039	−0.835193	+	0.549957i	$0.814644\pi$
$368$	−1.00000	−0.0521286
$369$	0	0
$370$	16.0000	0.831800
$371$	0	0
$372$	0	0
$373$	−36.0000	−1.86401	−0.932005	−	0.362446i	$-0.881942\pi$
$373$	−36.0000	−1.86401	−0.932005	+	0.362446i	$0.881942\pi$
$374$	4.00000	0.206835
$375$	0	0
$376$	8.00000	0.412568
$377$	12.0000	0.618031
$378$	0	0
$379$	2.00000	0.102733	0.0513665	−	0.998680i	$-0.483642\pi$
$379$	2.00000	0.102733	0.0513665	+	0.998680i	$0.483642\pi$
$380$	−8.00000	−0.410391
$381$	0	0
$382$	20.0000	1.02329
$383$	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
$385$	−8.00000	−0.407718
$386$	−6.00000	−0.305392
$387$	0	0
$388$	−2.00000	−0.101535
$389$	36.0000	1.82527	0.912636	−	0.408773i	$-0.134043\pi$
$389$	36.0000	1.82527	0.912636	+	0.408773i	$0.134043\pi$
$390$	0	0
$391$	2.00000	0.101144
$392$	1.00000	0.0505076
$393$	0	0
$394$	−10.0000	−0.503793
$395$	−32.0000	−1.61009
$396$	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
$400$	11.0000	0.550000
$401$	38.0000	1.89763	0.948815	−	0.315833i	$-0.102284\pi$
$401$	38.0000	1.89763	0.948815	+	0.315833i	$0.102284\pi$
$402$	0	0
$403$	0	0
$404$	14.0000	0.696526
$405$	0	0
$406$	6.00000	0.297775
$407$	−8.00000	−0.396545
$408$	0	0
$409$	−6.00000	−0.296681	−0.148340	−	0.988936i	$-0.547393\pi$
$409$	−6.00000	−0.296681	−0.148340	+	0.988936i	$0.547393\pi$
$410$	40.0000	1.97546
$411$	0	0
$412$	−12.0000	−0.591198
$413$	0	0
$414$	0	0
$415$	24.0000	1.17811
$416$	2.00000	0.0980581
$417$	0	0
$418$	4.00000	0.195646
$419$	−2.00000	−0.0977064	−0.0488532	−	0.998806i	$-0.515557\pi$
$419$	−2.00000	−0.0977064	−0.0488532	+	0.998806i	$0.515557\pi$
$420$	0	0
$421$	4.00000	0.194948	0.0974740	−	0.995238i	$-0.468924\pi$
$421$	4.00000	0.194948	0.0974740	+	0.995238i	$0.468924\pi$
$422$	−20.0000	−0.973585
$423$	0	0
$424$	0	0
$425$	−22.0000	−1.06716
$426$	0	0
$427$	−4.00000	−0.193574
$428$	2.00000	0.0966736
$429$	0	0
$430$	−40.0000	−1.92897
$431$	28.0000	1.34871	0.674356	−	0.738406i	$-0.264421\pi$
$431$	28.0000	1.34871	0.674356	+	0.738406i	$0.264421\pi$
$432$	0	0
$433$	−34.0000	−1.63394	−0.816968	−	0.576683i	$-0.804347\pi$
$433$	−34.0000	−1.63394	−0.816968	+	0.576683i	$0.804347\pi$
$434$	0	0
$435$	0	0
$436$	−16.0000	−0.766261
$437$	2.00000	0.0956730
$438$	0	0
$439$	−8.00000	−0.381819	−0.190910	−	0.981608i	$-0.561144\pi$
$439$	−8.00000	−0.381819	−0.190910	+	0.981608i	$0.561144\pi$
$440$	−8.00000	−0.381385
$441$	0	0
$442$	−4.00000	−0.190261
$443$	−8.00000	−0.380091	−0.190046	−	0.981775i	$-0.560864\pi$
$443$	−8.00000	−0.380091	−0.190046	+	0.981775i	$0.560864\pi$
$444$	0	0
$445$	−24.0000	−1.13771
$446$	16.0000	0.757622
$447$	0	0
$448$	1.00000	0.0472456
$449$	10.0000	0.471929	0.235965	−	0.971762i	$-0.424175\pi$
$449$	10.0000	0.471929	0.235965	+	0.971762i	$0.424175\pi$
$450$	0	0
$451$	−20.0000	−0.941763
$452$	−6.00000	−0.282216
$453$	0	0
$454$	−14.0000	−0.657053
$455$	8.00000	0.375046
$456$	0	0
$457$	6.00000	0.280668	0.140334	−	0.990104i	$-0.455182\pi$
$457$	6.00000	0.280668	0.140334	+	0.990104i	$0.455182\pi$
$458$	12.0000	0.560723
$459$	0	0
$460$	−4.00000	−0.186501
$461$	−30.0000	−1.39724	−0.698620	−	0.715493i	$-0.746202\pi$
$461$	−30.0000	−1.39724	−0.698620	+	0.715493i	$0.746202\pi$
$462$	0	0
$463$	−32.0000	−1.48717	−0.743583	−	0.668644i	$-0.766875\pi$
$463$	−32.0000	−1.48717	−0.743583	+	0.668644i	$0.766875\pi$
$464$	6.00000	0.278543
$465$	0	0
$466$	6.00000	0.277945
$467$	−34.0000	−1.57333	−0.786666	−	0.617379i	$-0.788195\pi$
$467$	−34.0000	−1.57333	−0.786666	+	0.617379i	$0.788195\pi$
$468$	0	0
$469$	2.00000	0.0923514
$470$	32.0000	1.47605
$471$	0	0
$472$	0	0
$473$	20.0000	0.919601
$474$	0	0
$475$	−22.0000	−1.00943
$476$	−2.00000	−0.0916698
$477$	0	0
$478$	−8.00000	−0.365911
$479$	−40.0000	−1.82765	−0.913823	−	0.406112i	$-0.866884\pi$
$479$	−40.0000	−1.82765	−0.913823	+	0.406112i	$0.866884\pi$
$480$	0	0
$481$	8.00000	0.364769
$482$	−18.0000	−0.819878
$483$	0	0
$484$	−7.00000	−0.318182
$485$	−8.00000	−0.363261
$486$	0	0
$487$	40.0000	1.81257	0.906287	−	0.422664i	$-0.138905\pi$
$487$	40.0000	1.81257	0.906287	+	0.422664i	$0.138905\pi$
$488$	−4.00000	−0.181071
$489$	0	0
$490$	4.00000	0.180702
$491$	−8.00000	−0.361035	−0.180517	−	0.983572i	$-0.557777\pi$
$491$	−8.00000	−0.361035	−0.180517	+	0.983572i	$0.557777\pi$
$492$	0	0
$493$	−12.0000	−0.540453
$494$	−4.00000	−0.179969
$495$	0	0
$496$	0	0
$497$	−8.00000	−0.358849
$498$	0	0
$499$	−8.00000	−0.358129	−0.179065	−	0.983837i	$-0.557307\pi$
$499$	−8.00000	−0.358129	−0.179065	+	0.983837i	$0.557307\pi$
$500$	24.0000	1.07331
$501$	0	0
$502$	−26.0000	−1.16044
$503$	12.0000	0.535054	0.267527	−	0.963550i	$-0.413794\pi$
$503$	12.0000	0.535054	0.267527	+	0.963550i	$0.413794\pi$
$504$	0	0
$505$	56.0000	2.49197
$506$	2.00000	0.0889108
$507$	0	0
$508$	8.00000	0.354943
$509$	−6.00000	−0.265945	−0.132973	−	0.991120i	$-0.542452\pi$
$509$	−6.00000	−0.265945	−0.132973	+	0.991120i	$0.542452\pi$
$510$	0	0
$511$	−2.00000	−0.0884748
$512$	1.00000	0.0441942
$513$	0	0
$514$	−14.0000	−0.617514
$515$	−48.0000	−2.11513
$516$	0	0
$517$	−16.0000	−0.703679
$518$	4.00000	0.175750
$519$	0	0
$520$	8.00000	0.350823
$521$	30.0000	1.31432	0.657162	−	0.753749i	$-0.271757\pi$
$521$	30.0000	1.31432	0.657162	+	0.753749i	$0.271757\pi$
$522$	0	0
$523$	−10.0000	−0.437269	−0.218635	−	0.975807i	$-0.570160\pi$
$523$	−10.0000	−0.437269	−0.218635	+	0.975807i	$0.570160\pi$
$524$	0	0
$525$	0	0
$526$	8.00000	0.348817
$527$	0	0
$528$	0	0
$529$	1.00000	0.0434783
$530$	0	0
$531$	0	0
$532$	−2.00000	−0.0867110
$533$	20.0000	0.866296
$534$	0	0
$535$	8.00000	0.345870
$536$	2.00000	0.0863868
$537$	0	0
$538$	18.0000	0.776035
$539$	−2.00000	−0.0861461
$540$	0	0
$541$	18.0000	0.773880	0.386940	−	0.922105i	$-0.373532\pi$
$541$	18.0000	0.773880	0.386940	+	0.922105i	$0.373532\pi$
$542$	16.0000	0.687259
$543$	0	0
$544$	−2.00000	−0.0857493
$545$	−64.0000	−2.74146
$546$	0	0
$547$	−28.0000	−1.19719	−0.598597	−	0.801050i	$-0.704275\pi$
$547$	−28.0000	−1.19719	−0.598597	+	0.801050i	$0.704275\pi$
$548$	−18.0000	−0.768922
$549$	0	0
$550$	−22.0000	−0.938083
$551$	−12.0000	−0.511217
$552$	0	0
$553$	−8.00000	−0.340195
$554$	2.00000	0.0849719
$555$	0	0
$556$	−16.0000	−0.678551
$557$	28.0000	1.18640	0.593199	−	0.805056i	$-0.297865\pi$
$557$	28.0000	1.18640	0.593199	+	0.805056i	$0.297865\pi$
$558$	0	0
$559$	−20.0000	−0.845910
$560$	4.00000	0.169031
$561$	0	0
$562$	10.0000	0.421825
$563$	34.0000	1.43293	0.716465	−	0.697623i	$-0.245759\pi$
$563$	34.0000	1.43293	0.716465	+	0.697623i	$0.245759\pi$
$564$	0	0
$565$	−24.0000	−1.00969
$566$	−6.00000	−0.252199
$567$	0	0
$568$	−8.00000	−0.335673
$569$	−26.0000	−1.08998	−0.544988	−	0.838444i	$-0.683466\pi$
$569$	−26.0000	−1.08998	−0.544988	+	0.838444i	$0.683466\pi$
$570$	0	0
$571$	2.00000	0.0836974	0.0418487	−	0.999124i	$-0.486675\pi$
$571$	2.00000	0.0836974	0.0418487	+	0.999124i	$0.486675\pi$
$572$	−4.00000	−0.167248
$573$	0	0
$574$	10.0000	0.417392
$575$	−11.0000	−0.458732
$576$	0	0
$577$	38.0000	1.58196	0.790980	−	0.611842i	$-0.209571\pi$
$577$	38.0000	1.58196	0.790980	+	0.611842i	$0.209571\pi$
$578$	−13.0000	−0.540729
$579$	0	0
$580$	24.0000	0.996546
$581$	6.00000	0.248922
$582$	0	0
$583$	0	0
$584$	−2.00000	−0.0827606
$585$	0	0
$586$	12.0000	0.495715
$587$	−16.0000	−0.660391	−0.330195	−	0.943913i	$-0.607115\pi$
$587$	−16.0000	−0.660391	−0.330195	+	0.943913i	$0.607115\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	0	0
$592$	4.00000	0.164399
$593$	−30.0000	−1.23195	−0.615976	−	0.787765i	$-0.711238\pi$
$593$	−30.0000	−1.23195	−0.615976	+	0.787765i	$0.711238\pi$
$594$	0	0
$595$	−8.00000	−0.327968
$596$	24.0000	0.983078
$597$	0	0
$598$	−2.00000	−0.0817861
$599$	−24.0000	−0.980613	−0.490307	−	0.871550i	$-0.663115\pi$
$599$	−24.0000	−0.980613	−0.490307	+	0.871550i	$0.663115\pi$
$600$	0	0
$601$	−2.00000	−0.0815817	−0.0407909	−	0.999168i	$-0.512988\pi$
$601$	−2.00000	−0.0815817	−0.0407909	+	0.999168i	$0.512988\pi$
$602$	−10.0000	−0.407570
$603$	0	0
$604$	16.0000	0.651031
$605$	−28.0000	−1.13836
$606$	0	0
$607$	16.0000	0.649420	0.324710	−	0.945814i	$-0.394733\pi$
$607$	16.0000	0.649420	0.324710	+	0.945814i	$0.394733\pi$
$608$	−2.00000	−0.0811107
$609$	0	0
$610$	−16.0000	−0.647821
$611$	16.0000	0.647291
$612$	0	0
$613$	−8.00000	−0.323117	−0.161558	−	0.986863i	$-0.551652\pi$
$613$	−8.00000	−0.323117	−0.161558	+	0.986863i	$0.551652\pi$
$614$	−12.0000	−0.484281
$615$	0	0
$616$	−2.00000	−0.0805823
$617$	−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
$619$	10.0000	0.401934	0.200967	−	0.979598i	$-0.435592\pi$
$619$	10.0000	0.401934	0.200967	+	0.979598i	$0.435592\pi$
$620$	0	0
$621$	0	0
$622$	−24.0000	−0.962312
$623$	−6.00000	−0.240385
$624$	0	0
$625$	41.0000	1.64000
$626$	22.0000	0.879297
$627$	0	0
$628$	−8.00000	−0.319235
$629$	−8.00000	−0.318981
$630$	0	0
$631$	−20.0000	−0.796187	−0.398094	−	0.917345i	$-0.630328\pi$
$631$	−20.0000	−0.796187	−0.398094	+	0.917345i	$0.630328\pi$
$632$	−8.00000	−0.318223
$633$	0	0
$634$	30.0000	1.19145
$635$	32.0000	1.26988
$636$	0	0
$637$	2.00000	0.0792429
$638$	−12.0000	−0.475085
$639$	0	0
$640$	4.00000	0.158114
$641$	−42.0000	−1.65890	−0.829450	−	0.558581i	$-0.811346\pi$
$641$	−42.0000	−1.65890	−0.829450	+	0.558581i	$0.811346\pi$
$642$	0	0
$643$	−14.0000	−0.552106	−0.276053	−	0.961142i	$-0.589027\pi$
$643$	−14.0000	−0.552106	−0.276053	+	0.961142i	$0.589027\pi$
$644$	−1.00000	−0.0394055
$645$	0	0
$646$	4.00000	0.157378
$647$	−8.00000	−0.314512	−0.157256	−	0.987558i	$-0.550265\pi$
$647$	−8.00000	−0.314512	−0.157256	+	0.987558i	$0.550265\pi$
$648$	0	0
$649$	0	0
$650$	22.0000	0.862911
$651$	0	0
$652$	24.0000	0.939913
$653$	−14.0000	−0.547862	−0.273931	−	0.961749i	$-0.588324\pi$
$653$	−14.0000	−0.547862	−0.273931	+	0.961749i	$0.588324\pi$
$654$	0	0
$655$	0	0
$656$	10.0000	0.390434
$657$	0	0
$658$	8.00000	0.311872
$659$	26.0000	1.01282	0.506408	−	0.862294i	$-0.330973\pi$
$659$	26.0000	1.01282	0.506408	+	0.862294i	$0.330973\pi$
$660$	0	0
$661$	28.0000	1.08907	0.544537	−	0.838737i	$-0.316705\pi$
$661$	28.0000	1.08907	0.544537	+	0.838737i	$0.316705\pi$
$662$	20.0000	0.777322
$663$	0	0
$664$	6.00000	0.232845
$665$	−8.00000	−0.310227
$666$	0	0
$667$	−6.00000	−0.232321
$668$	0	0
$669$	0	0
$670$	8.00000	0.309067
$671$	8.00000	0.308837
$672$	0	0
$673$	−18.0000	−0.693849	−0.346925	−	0.937893i	$-0.612774\pi$
$673$	−18.0000	−0.693849	−0.346925	+	0.937893i	$0.612774\pi$
$674$	26.0000	1.00148
$675$	0	0
$676$	−9.00000	−0.346154
$677$	−36.0000	−1.38359	−0.691796	−	0.722093i	$-0.743180\pi$
$677$	−36.0000	−1.38359	−0.691796	+	0.722093i	$0.743180\pi$
$678$	0	0
$679$	−2.00000	−0.0767530
$680$	−8.00000	−0.306786
$681$	0	0
$682$	0	0
$683$	−28.0000	−1.07139	−0.535695	−	0.844411i	$-0.679950\pi$
$683$	−28.0000	−1.07139	−0.535695	+	0.844411i	$0.679950\pi$
$684$	0	0
$685$	−72.0000	−2.75098
$686$	1.00000	0.0381802
$687$	0	0
$688$	−10.0000	−0.381246
$689$	0	0
$690$	0	0
$691$	−40.0000	−1.52167	−0.760836	−	0.648944i	$-0.775211\pi$
$691$	−40.0000	−1.52167	−0.760836	+	0.648944i	$0.775211\pi$
$692$	2.00000	0.0760286
$693$	0	0
$694$	−16.0000	−0.607352
$695$	−64.0000	−2.42766
$696$	0	0
$697$	−20.0000	−0.757554
$698$	14.0000	0.529908
$699$	0	0
$700$	11.0000	0.415761
$701$	−36.0000	−1.35970	−0.679851	−	0.733351i	$-0.737955\pi$
$701$	−36.0000	−1.35970	−0.679851	+	0.733351i	$0.737955\pi$
$702$	0	0
$703$	−8.00000	−0.301726
$704$	−2.00000	−0.0753778
$705$	0	0
$706$	−34.0000	−1.27961
$707$	14.0000	0.526524
$708$	0	0
$709$	−12.0000	−0.450669	−0.225335	−	0.974281i	$-0.572348\pi$
$709$	−12.0000	−0.450669	−0.225335	+	0.974281i	$0.572348\pi$
$710$	−32.0000	−1.20094
$711$	0	0
$712$	−6.00000	−0.224860
$713$	0	0
$714$	0	0
$715$	−16.0000	−0.598366
$716$	−16.0000	−0.597948
$717$	0	0
$718$	20.0000	0.746393
$719$	48.0000	1.79010	0.895049	−	0.445968i	$-0.147140\pi$
$719$	48.0000	1.79010	0.895049	+	0.445968i	$0.147140\pi$
$720$	0	0
$721$	−12.0000	−0.446903
$722$	−15.0000	−0.558242
$723$	0	0
$724$	−20.0000	−0.743294
$725$	66.0000	2.45118
$726$	0	0
$727$	8.00000	0.296704	0.148352	−	0.988935i	$-0.452603\pi$
$727$	8.00000	0.296704	0.148352	+	0.988935i	$0.452603\pi$
$728$	2.00000	0.0741249
$729$	0	0
$730$	−8.00000	−0.296093
$731$	20.0000	0.739727
$732$	0	0
$733$	−32.0000	−1.18195	−0.590973	−	0.806691i	$-0.701256\pi$
$733$	−32.0000	−1.18195	−0.590973	+	0.806691i	$0.701256\pi$
$734$	−32.0000	−1.18114
$735$	0	0
$736$	−1.00000	−0.0368605
$737$	−4.00000	−0.147342
$738$	0	0
$739$	16.0000	0.588570	0.294285	−	0.955718i	$-0.404919\pi$
$739$	16.0000	0.588570	0.294285	+	0.955718i	$0.404919\pi$
$740$	16.0000	0.588172
$741$	0	0
$742$	0	0
$743$	−16.0000	−0.586983	−0.293492	−	0.955962i	$-0.594817\pi$
$743$	−16.0000	−0.586983	−0.293492	+	0.955962i	$0.594817\pi$
$744$	0	0
$745$	96.0000	3.51717
$746$	−36.0000	−1.31805
$747$	0	0
$748$	4.00000	0.146254
$749$	2.00000	0.0730784
$750$	0	0
$751$	12.0000	0.437886	0.218943	−	0.975738i	$-0.429739\pi$
$751$	12.0000	0.437886	0.218943	+	0.975738i	$0.429739\pi$
$752$	8.00000	0.291730
$753$	0	0
$754$	12.0000	0.437014
$755$	64.0000	2.32920
$756$	0	0
$757$	48.0000	1.74459	0.872295	−	0.488980i	$-0.162631\pi$
$757$	48.0000	1.74459	0.872295	+	0.488980i	$0.162631\pi$
$758$	2.00000	0.0726433
$759$	0	0
$760$	−8.00000	−0.290191
$761$	22.0000	0.797499	0.398750	−	0.917060i	$-0.369444\pi$
$761$	22.0000	0.797499	0.398750	+	0.917060i	$0.369444\pi$
$762$	0	0
$763$	−16.0000	−0.579239
$764$	20.0000	0.723575
$765$	0	0
$766$	16.0000	0.578103
$767$	0	0
$768$	0	0
$769$	14.0000	0.504853	0.252426	−	0.967616i	$-0.418771\pi$
$769$	14.0000	0.504853	0.252426	+	0.967616i	$0.418771\pi$
$770$	−8.00000	−0.288300
$771$	0	0
$772$	−6.00000	−0.215945
$773$	0	0		−	1.00000i	$-0.5\pi$
$773$	0	0			1.00000i	$0.5\pi$
$774$	0	0
$775$	0	0
$776$	−2.00000	−0.0717958
$777$	0	0
$778$	36.0000	1.29066
$779$	−20.0000	−0.716574
$780$	0	0
$781$	16.0000	0.572525
$782$	2.00000	0.0715199
$783$	0	0
$784$	1.00000	0.0357143
$785$	−32.0000	−1.14213
$786$	0	0
$787$	18.0000	0.641631	0.320815	−	0.947142i	$-0.396043\pi$
$787$	18.0000	0.641631	0.320815	+	0.947142i	$0.396043\pi$
$788$	−10.0000	−0.356235
$789$	0	0
$790$	−32.0000	−1.13851
$791$	−6.00000	−0.213335
$792$	0	0
$793$	−8.00000	−0.284088
$794$	−38.0000	−1.34857
$795$	0	0
$796$	0	0
$797$	0	0		−	1.00000i	$-0.5\pi$
$797$	0	0			1.00000i	$0.5\pi$
$798$	0	0
$799$	−16.0000	−0.566039
$800$	11.0000	0.388909
$801$	0	0
$802$	38.0000	1.34183
$803$	4.00000	0.141157
$804$	0	0
$805$	−4.00000	−0.140981
$806$	0	0
$807$	0	0
$808$	14.0000	0.492518
$809$	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
$811$	16.0000	0.561836	0.280918	−	0.959732i	$-0.409361\pi$
$811$	16.0000	0.561836	0.280918	+	0.959732i	$0.409361\pi$
$812$	6.00000	0.210559
$813$	0	0
$814$	−8.00000	−0.280400
$815$	96.0000	3.36273
$816$	0	0
$817$	20.0000	0.699711
$818$	−6.00000	−0.209785
$819$	0	0
$820$	40.0000	1.39686
$821$	50.0000	1.74501	0.872506	−	0.488603i	$-0.162493\pi$
$821$	50.0000	1.74501	0.872506	+	0.488603i	$0.162493\pi$
$822$	0	0
$823$	−32.0000	−1.11545	−0.557725	−	0.830026i	$-0.688326\pi$
$823$	−32.0000	−1.11545	−0.557725	+	0.830026i	$0.688326\pi$
$824$	−12.0000	−0.418040
$825$	0	0
$826$	0	0
$827$	−54.0000	−1.87776	−0.938882	−	0.344239i	$-0.888137\pi$
$827$	−54.0000	−1.87776	−0.938882	+	0.344239i	$0.888137\pi$
$828$	0	0
$829$	14.0000	0.486240	0.243120	−	0.969996i	$-0.421829\pi$
$829$	14.0000	0.486240	0.243120	+	0.969996i	$0.421829\pi$
$830$	24.0000	0.833052
$831$	0	0
$832$	2.00000	0.0693375
$833$	−2.00000	−0.0692959
$834$	0	0
$835$	0	0
$836$	4.00000	0.138343
$837$	0	0
$838$	−2.00000	−0.0690889
$839$	0	0		−	1.00000i	$-0.5\pi$
$839$	0	0			1.00000i	$0.5\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	4.00000	0.137849
$843$	0	0
$844$	−20.0000	−0.688428
$845$	−36.0000	−1.23844
$846$	0	0
$847$	−7.00000	−0.240523
$848$	0	0
$849$	0	0
$850$	−22.0000	−0.754594
$851$	−4.00000	−0.137118
$852$	0	0
$853$	42.0000	1.43805	0.719026	−	0.694983i	$-0.244588\pi$
$853$	42.0000	1.43805	0.719026	+	0.694983i	$0.244588\pi$
$854$	−4.00000	−0.136877
$855$	0	0
$856$	2.00000	0.0683586
$857$	22.0000	0.751506	0.375753	−	0.926720i	$-0.377384\pi$
$857$	22.0000	0.751506	0.375753	+	0.926720i	$0.377384\pi$
$858$	0	0
$859$	−28.0000	−0.955348	−0.477674	−	0.878537i	$-0.658520\pi$
$859$	−28.0000	−0.955348	−0.477674	+	0.878537i	$0.658520\pi$
$860$	−40.0000	−1.36399
$861$	0	0
$862$	28.0000	0.953684
$863$	40.0000	1.36162	0.680808	−	0.732462i	$-0.261629\pi$
$863$	40.0000	1.36162	0.680808	+	0.732462i	$0.261629\pi$
$864$	0	0
$865$	8.00000	0.272008
$866$	−34.0000	−1.15537
$867$	0	0
$868$	0	0
$869$	16.0000	0.542763
$870$	0	0
$871$	4.00000	0.135535
$872$	−16.0000	−0.541828
$873$	0	0
$874$	2.00000	0.0676510
$875$	24.0000	0.811348
$876$	0	0
$877$	58.0000	1.95852	0.979260	−	0.202606i	$-0.0649409\pi$
$877$	58.0000	1.95852	0.979260	+	0.202606i	$0.0649409\pi$
$878$	−8.00000	−0.269987
$879$	0	0
$880$	−8.00000	−0.269680
$881$	−38.0000	−1.28025	−0.640126	−	0.768270i	$-0.721118\pi$
$881$	−38.0000	−1.28025	−0.640126	+	0.768270i	$0.721118\pi$
$882$	0	0
$883$	44.0000	1.48072	0.740359	−	0.672212i	$-0.234656\pi$
$883$	44.0000	1.48072	0.740359	+	0.672212i	$0.234656\pi$
$884$	−4.00000	−0.134535
$885$	0	0
$886$	−8.00000	−0.268765
$887$	48.0000	1.61168	0.805841	−	0.592132i	$-0.201714\pi$
$887$	48.0000	1.61168	0.805841	+	0.592132i	$0.201714\pi$
$888$	0	0
$889$	8.00000	0.268311
$890$	−24.0000	−0.804482
$891$	0	0
$892$	16.0000	0.535720
$893$	−16.0000	−0.535420
$894$	0	0
$895$	−64.0000	−2.13928
$896$	1.00000	0.0334077
$897$	0	0
$898$	10.0000	0.333704
$899$	0	0
$900$	0	0
$901$	0	0
$902$	−20.0000	−0.665927
$903$	0	0
$904$	−6.00000	−0.199557
$905$	−80.0000	−2.65929
$906$	0	0
$907$	38.0000	1.26177	0.630885	−	0.775877i	$-0.282692\pi$
$907$	38.0000	1.26177	0.630885	+	0.775877i	$0.282692\pi$
$908$	−14.0000	−0.464606
$909$	0	0
$910$	8.00000	0.265197
$911$	−36.0000	−1.19273	−0.596367	−	0.802712i	$-0.703390\pi$
$911$	−36.0000	−1.19273	−0.596367	+	0.802712i	$0.703390\pi$
$912$	0	0
$913$	−12.0000	−0.397142
$914$	6.00000	0.198462
$915$	0	0
$916$	12.0000	0.396491
$917$	0	0
$918$	0	0
$919$	48.0000	1.58337	0.791687	−	0.610927i	$-0.209203\pi$
$919$	48.0000	1.58337	0.791687	+	0.610927i	$0.209203\pi$
$920$	−4.00000	−0.131876
$921$	0	0
$922$	−30.0000	−0.987997
$923$	−16.0000	−0.526646
$924$	0	0
$925$	44.0000	1.44671
$926$	−32.0000	−1.05159
$927$	0	0
$928$	6.00000	0.196960
$929$	−14.0000	−0.459325	−0.229663	−	0.973270i	$-0.573762\pi$
$929$	−14.0000	−0.459325	−0.229663	+	0.973270i	$0.573762\pi$
$930$	0	0
$931$	−2.00000	−0.0655474
$932$	6.00000	0.196537
$933$	0	0
$934$	−34.0000	−1.11251
$935$	16.0000	0.523256
$936$	0	0
$937$	34.0000	1.11073	0.555366	−	0.831606i	$-0.312578\pi$
$937$	34.0000	1.11073	0.555366	+	0.831606i	$0.312578\pi$
$938$	2.00000	0.0653023
$939$	0	0
$940$	32.0000	1.04372
$941$	20.0000	0.651981	0.325991	−	0.945373i	$-0.394302\pi$
$941$	20.0000	0.651981	0.325991	+	0.945373i	$0.394302\pi$
$942$	0	0
$943$	−10.0000	−0.325645
$944$	0	0
$945$	0	0
$946$	20.0000	0.650256
$947$	56.0000	1.81976	0.909878	−	0.414876i	$-0.136175\pi$
$947$	56.0000	1.81976	0.909878	+	0.414876i	$0.136175\pi$
$948$	0	0
$949$	−4.00000	−0.129845
$950$	−22.0000	−0.713774
$951$	0	0
$952$	−2.00000	−0.0648204
$953$	30.0000	0.971795	0.485898	−	0.874016i	$-0.338493\pi$
$953$	30.0000	0.971795	0.485898	+	0.874016i	$0.338493\pi$
$954$	0	0
$955$	80.0000	2.58874
$956$	−8.00000	−0.258738
$957$	0	0
$958$	−40.0000	−1.29234
$959$	−18.0000	−0.581250
$960$	0	0
$961$	−31.0000	−1.00000
$962$	8.00000	0.257930
$963$	0	0
$964$	−18.0000	−0.579741
$965$	−24.0000	−0.772587
$966$	0	0
$967$	48.0000	1.54358	0.771788	−	0.635880i	$-0.219363\pi$
$967$	48.0000	1.54358	0.771788	+	0.635880i	$0.219363\pi$
$968$	−7.00000	−0.224989
$969$	0	0
$970$	−8.00000	−0.256865
$971$	−30.0000	−0.962746	−0.481373	−	0.876516i	$-0.659862\pi$
$971$	−30.0000	−0.962746	−0.481373	+	0.876516i	$0.659862\pi$
$972$	0	0
$973$	−16.0000	−0.512936
$974$	40.0000	1.28168
$975$	0	0
$976$	−4.00000	−0.128037
$977$	−2.00000	−0.0639857	−0.0319928	−	0.999488i	$-0.510185\pi$
$977$	−2.00000	−0.0639857	−0.0319928	+	0.999488i	$0.510185\pi$
$978$	0	0
$979$	12.0000	0.383522
$980$	4.00000	0.127775
$981$	0	0
$982$	−8.00000	−0.255290
$983$	−36.0000	−1.14822	−0.574111	−	0.818778i	$-0.694652\pi$
$983$	−36.0000	−1.14822	−0.574111	+	0.818778i	$0.694652\pi$
$984$	0	0
$985$	−40.0000	−1.27451
$986$	−12.0000	−0.382158
$987$	0	0
$988$	−4.00000	−0.127257
$989$	10.0000	0.317982
$990$	0	0
$991$	16.0000	0.508257	0.254128	−	0.967170i	$-0.418211\pi$
$991$	16.0000	0.508257	0.254128	+	0.967170i	$0.418211\pi$
$992$	0	0
$993$	0	0
$994$	−8.00000	−0.253745
$995$	0	0
$996$	0	0
$997$	38.0000	1.20347	0.601736	−	0.798695i	$-0.294476\pi$
$997$	38.0000	1.20347	0.601736	+	0.798695i	$0.294476\pi$
$998$	−8.00000	−0.253236
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2898.2.a.u.1.1		1
3.2	odd	2		966.2.a.a.1.1	✓	1
12.11	even	2		7728.2.a.m.1.1		1
21.20	even	2		6762.2.a.v.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.a.a.1.1	✓	1	3.2	odd	2
2898.2.a.u.1.1		1	1.1	even	1	trivial
6762.2.a.v.1.1		1	21.20	even	2
7728.2.a.m.1.1		1	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2898 = 2 \cdot 3^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2898.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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