LMFDB - Embedded newform 2898.2.a.n.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:	$1$
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)

$f(q)$

$=$

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

$q+1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{7} +1.00000 q^{8} +2.00000 q^{11} -6.00000 q^{13} -1.00000 q^{14} +1.00000 q^{16} -2.00000 q^{17} -6.00000 q^{19} +2.00000 q^{22} -1.00000 q^{23} -5.00000 q^{25} -6.00000 q^{26} -1.00000 q^{28} +6.00000 q^{29} +1.00000 q^{32} -2.00000 q^{34} -6.00000 q^{38} -6.00000 q^{41} -6.00000 q^{43} +2.00000 q^{44} -1.00000 q^{46} -8.00000 q^{47} +1.00000 q^{49} -5.00000 q^{50} -6.00000 q^{52} +4.00000 q^{53} -1.00000 q^{56} +6.00000 q^{58} -8.00000 q^{61} +1.00000 q^{64} -2.00000 q^{67} -2.00000 q^{68} -2.00000 q^{73} -6.00000 q^{76} -2.00000 q^{77} +8.00000 q^{79} -6.00000 q^{82} +2.00000 q^{83} -6.00000 q^{86} +2.00000 q^{88} +2.00000 q^{89} +6.00000 q^{91} -1.00000 q^{92} -8.00000 q^{94} +14.0000 q^{97} +1.00000 q^{98} +O(q^{100})$

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
$5$	0	0		−	1.00000i	$-0.5\pi$
$5$	0	0			1.00000i	$0.5\pi$
$6$	0	0
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	0	0
$10$	0	0
$11$	2.00000	0.603023	0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	0	0
$13$	−6.00000	−1.66410	−0.832050	−	0.554700i	$-0.812833\pi$
$13$	−6.00000	−1.66410	−0.832050	+	0.554700i	$0.812833\pi$
$14$	−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
$19$	−6.00000	−1.37649	−0.688247	−	0.725476i	$-0.741620\pi$
$19$	−6.00000	−1.37649	−0.688247	+	0.725476i	$0.741620\pi$
$20$	0	0
$21$	0	0
$22$	2.00000	0.426401
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	0	0
$25$	−5.00000	−1.00000
$26$	−6.00000	−1.17670
$27$	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
$35$	0	0
$36$	0	0
$37$	0	0		−	1.00000i	$-0.5\pi$
$37$	0	0			1.00000i	$0.5\pi$
$38$	−6.00000	−0.973329
$39$	0	0
$40$	0	0
$41$	−6.00000	−0.937043	−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000	−0.937043	−0.468521	+	0.883452i	$0.655213\pi$
$42$	0	0
$43$	−6.00000	−0.914991	−0.457496	−	0.889212i	$-0.651253\pi$
$43$	−6.00000	−0.914991	−0.457496	+	0.889212i	$0.651253\pi$
$44$	2.00000	0.301511
$45$	0	0
$46$	−1.00000	−0.147442
$47$	−8.00000	−1.16692	−0.583460	−	0.812142i	$-0.698301\pi$
$47$	−8.00000	−1.16692	−0.583460	+	0.812142i	$0.698301\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	−5.00000	−0.707107
$51$	0	0
$52$	−6.00000	−0.832050
$53$	4.00000	0.549442	0.274721	−	0.961524i	$-0.411414\pi$
$53$	4.00000	0.549442	0.274721	+	0.961524i	$0.411414\pi$
$54$	0	0
$55$	0	0
$56$	−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
$61$	−8.00000	−1.02430	−0.512148	−	0.858898i	$-0.671150\pi$
$61$	−8.00000	−1.02430	−0.512148	+	0.858898i	$0.671150\pi$
$62$	0	0
$63$	0	0
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	−2.00000	−0.244339	−0.122169	−	0.992509i	$-0.538985\pi$
$67$	−2.00000	−0.244339	−0.122169	+	0.992509i	$0.538985\pi$
$68$	−2.00000	−0.242536
$69$	0	0
$70$	0	0
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	0	0
$73$	−2.00000	−0.234082	−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000	−0.234082	−0.117041	+	0.993127i	$0.537341\pi$
$74$	0	0
$75$	0	0
$76$	−6.00000	−0.688247
$77$	−2.00000	−0.227921
$78$	0	0
$79$	8.00000	0.900070	0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000	0.900070	0.450035	+	0.893011i	$0.351411\pi$
$80$	0	0
$81$	0	0
$82$	−6.00000	−0.662589
$83$	2.00000	0.219529	0.109764	−	0.993958i	$-0.464990\pi$
$83$	2.00000	0.219529	0.109764	+	0.993958i	$0.464990\pi$
$84$	0	0
$85$	0	0
$86$	−6.00000	−0.646997
$87$	0	0
$88$	2.00000	0.213201
$89$	2.00000	0.212000	0.106000	−	0.994366i	$-0.466196\pi$
$89$	2.00000	0.212000	0.106000	+	0.994366i	$0.466196\pi$
$90$	0	0
$91$	6.00000	0.628971
$92$	−1.00000	−0.104257
$93$	0	0
$94$	−8.00000	−0.825137
$95$	0	0
$96$	0	0
$97$	14.0000	1.42148	0.710742	−	0.703452i	$-0.248359\pi$
$97$	14.0000	1.42148	0.710742	+	0.703452i	$0.248359\pi$
$98$	1.00000	0.101015
$99$	0	0
$100$	−5.00000	−0.500000
$101$	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
$103$	−4.00000	−0.394132	−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000	−0.394132	−0.197066	+	0.980390i	$0.563141\pi$
$104$	−6.00000	−0.588348
$105$	0	0
$106$	4.00000	0.388514
$107$	−2.00000	−0.193347	−0.0966736	−	0.995316i	$-0.530820\pi$
$107$	−2.00000	−0.193347	−0.0966736	+	0.995316i	$0.530820\pi$
$108$	0	0
$109$	−12.0000	−1.14939	−0.574696	−	0.818367i	$-0.694880\pi$
$109$	−12.0000	−1.14939	−0.574696	+	0.818367i	$0.694880\pi$
$110$	0	0
$111$	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
$115$	0	0
$116$	6.00000	0.557086
$117$	0	0
$118$	0	0
$119$	2.00000	0.183340
$120$	0	0
$121$	−7.00000	−0.636364
$122$	−8.00000	−0.724286
$123$	0	0
$124$	0	0
$125$	0	0
$126$	0	0
$127$	−8.00000	−0.709885	−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000	−0.709885	−0.354943	+	0.934888i	$0.615500\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	0	0
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	0	0
$133$	6.00000	0.520266
$134$	−2.00000	−0.172774
$135$	0	0
$136$	−2.00000	−0.171499
$137$	6.00000	0.512615	0.256307	−	0.966595i	$-0.417494\pi$
$137$	6.00000	0.512615	0.256307	+	0.966595i	$0.417494\pi$
$138$	0	0
$139$	0	0		−	1.00000i	$-0.5\pi$
$139$	0	0			1.00000i	$0.5\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	−12.0000	−1.00349
$144$	0	0
$145$	0	0
$146$	−2.00000	−0.165521
$147$	0	0
$148$	0	0
$149$	−4.00000	−0.327693	−0.163846	−	0.986486i	$-0.552390\pi$
$149$	−4.00000	−0.327693	−0.163846	+	0.986486i	$0.552390\pi$
$150$	0	0
$151$	−24.0000	−1.95309	−0.976546	−	0.215308i	$-0.930924\pi$
$151$	−24.0000	−1.95309	−0.976546	+	0.215308i	$0.930924\pi$
$152$	−6.00000	−0.486664
$153$	0	0
$154$	−2.00000	−0.161165
$155$	0	0
$156$	0	0
$157$	−20.0000	−1.59617	−0.798087	−	0.602542i	$-0.794154\pi$
$157$	−20.0000	−1.59617	−0.798087	+	0.602542i	$0.794154\pi$
$158$	8.00000	0.636446
$159$	0	0
$160$	0	0
$161$	1.00000	0.0788110
$162$	0	0
$163$	16.0000	1.25322	0.626608	−	0.779334i	$-0.284443\pi$
$163$	16.0000	1.25322	0.626608	+	0.779334i	$0.284443\pi$
$164$	−6.00000	−0.468521
$165$	0	0
$166$	2.00000	0.155230
$167$	−16.0000	−1.23812	−0.619059	−	0.785345i	$-0.712486\pi$
$167$	−16.0000	−1.23812	−0.619059	+	0.785345i	$0.712486\pi$
$168$	0	0
$169$	23.0000	1.76923
$170$	0	0
$171$	0	0
$172$	−6.00000	−0.457496
$173$	−6.00000	−0.456172	−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000	−0.456172	−0.228086	+	0.973641i	$0.573247\pi$
$174$	0	0
$175$	5.00000	0.377964
$176$	2.00000	0.150756
$177$	0	0
$178$	2.00000	0.149906
$179$	8.00000	0.597948	0.298974	−	0.954261i	$-0.403356\pi$
$179$	8.00000	0.597948	0.298974	+	0.954261i	$0.403356\pi$
$180$	0	0
$181$	−8.00000	−0.594635	−0.297318	−	0.954779i	$-0.596092\pi$
$181$	−8.00000	−0.594635	−0.297318	+	0.954779i	$0.596092\pi$
$182$	6.00000	0.444750
$183$	0	0
$184$	−1.00000	−0.0737210
$185$	0	0
$186$	0	0
$187$	−4.00000	−0.292509
$188$	−8.00000	−0.583460
$189$	0	0
$190$	0	0
$191$	12.0000	0.868290	0.434145	−	0.900843i	$-0.357051\pi$
$191$	12.0000	0.868290	0.434145	+	0.900843i	$0.357051\pi$
$192$	0	0
$193$	10.0000	0.719816	0.359908	−	0.932988i	$-0.382808\pi$
$193$	10.0000	0.719816	0.359908	+	0.932988i	$0.382808\pi$
$194$	14.0000	1.00514
$195$	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
$199$	16.0000	1.13421	0.567105	−	0.823646i	$-0.308063\pi$
$199$	16.0000	1.13421	0.567105	+	0.823646i	$0.308063\pi$
$200$	−5.00000	−0.353553
$201$	0	0
$202$	14.0000	0.985037
$203$	−6.00000	−0.421117
$204$	0	0
$205$	0	0
$206$	−4.00000	−0.278693
$207$	0	0
$208$	−6.00000	−0.416025
$209$	−12.0000	−0.830057
$210$	0	0
$211$	12.0000	0.826114	0.413057	−	0.910705i	$-0.364461\pi$
$211$	12.0000	0.826114	0.413057	+	0.910705i	$0.364461\pi$
$212$	4.00000	0.274721
$213$	0	0
$214$	−2.00000	−0.136717
$215$	0	0
$216$	0	0
$217$	0	0
$218$	−12.0000	−0.812743
$219$	0	0
$220$	0	0
$221$	12.0000	0.807207
$222$	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
$227$	−26.0000	−1.72568	−0.862840	−	0.505477i	$-0.831317\pi$
$227$	−26.0000	−1.72568	−0.862840	+	0.505477i	$0.831317\pi$
$228$	0	0
$229$	24.0000	1.58596	0.792982	−	0.609245i	$-0.208527\pi$
$229$	24.0000	1.58596	0.792982	+	0.609245i	$0.208527\pi$
$230$	0	0
$231$	0	0
$232$	6.00000	0.393919
$233$	−26.0000	−1.70332	−0.851658	−	0.524097i	$-0.824403\pi$
$233$	−26.0000	−1.70332	−0.851658	+	0.524097i	$0.824403\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	0	0
$238$	2.00000	0.129641
$239$	−24.0000	−1.55243	−0.776215	−	0.630468i	$-0.782863\pi$
$239$	−24.0000	−1.55243	−0.776215	+	0.630468i	$0.782863\pi$
$240$	0	0
$241$	−2.00000	−0.128831	−0.0644157	−	0.997923i	$-0.520518\pi$
$241$	−2.00000	−0.128831	−0.0644157	+	0.997923i	$0.520518\pi$
$242$	−7.00000	−0.449977
$243$	0	0
$244$	−8.00000	−0.512148
$245$	0	0
$246$	0	0
$247$	36.0000	2.29063
$248$	0	0
$249$	0	0
$250$	0	0
$251$	2.00000	0.126239	0.0631194	−	0.998006i	$-0.479895\pi$
$251$	2.00000	0.126239	0.0631194	+	0.998006i	$0.479895\pi$
$252$	0	0
$253$	−2.00000	−0.125739
$254$	−8.00000	−0.501965
$255$	0	0
$256$	1.00000	0.0625000
$257$	2.00000	0.124757	0.0623783	−	0.998053i	$-0.480131\pi$
$257$	2.00000	0.124757	0.0623783	+	0.998053i	$0.480131\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	0	0
$262$	0	0
$263$	24.0000	1.47990	0.739952	−	0.672660i	$-0.234848\pi$
$263$	24.0000	1.47990	0.739952	+	0.672660i	$0.234848\pi$
$264$	0	0
$265$	0	0
$266$	6.00000	0.367884
$267$	0	0
$268$	−2.00000	−0.122169
$269$	−6.00000	−0.365826	−0.182913	−	0.983129i	$-0.558553\pi$
$269$	−6.00000	−0.365826	−0.182913	+	0.983129i	$0.558553\pi$
$270$	0	0
$271$	8.00000	0.485965	0.242983	−	0.970031i	$-0.421874\pi$
$271$	8.00000	0.485965	0.242983	+	0.970031i	$0.421874\pi$
$272$	−2.00000	−0.121268
$273$	0	0
$274$	6.00000	0.362473
$275$	−10.0000	−0.603023
$276$	0	0
$277$	−22.0000	−1.32185	−0.660926	−	0.750451i	$-0.729836\pi$
$277$	−22.0000	−1.32185	−0.660926	+	0.750451i	$0.729836\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	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
$283$	30.0000	1.78331	0.891657	−	0.452711i	$-0.149543\pi$
$283$	30.0000	1.78331	0.891657	+	0.452711i	$0.149543\pi$
$284$	0	0
$285$	0	0
$286$	−12.0000	−0.709575
$287$	6.00000	0.354169
$288$	0	0
$289$	−13.0000	−0.764706
$290$	0	0
$291$	0	0
$292$	−2.00000	−0.117041
$293$	24.0000	1.40209	0.701047	−	0.713115i	$-0.252716\pi$
$293$	24.0000	1.40209	0.701047	+	0.713115i	$0.252716\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	0	0
$298$	−4.00000	−0.231714
$299$	6.00000	0.346989
$300$	0	0
$301$	6.00000	0.345834
$302$	−24.0000	−1.38104
$303$	0	0
$304$	−6.00000	−0.344124
$305$	0	0
$306$	0	0
$307$	12.0000	0.684876	0.342438	−	0.939540i	$-0.388747\pi$
$307$	12.0000	0.684876	0.342438	+	0.939540i	$0.388747\pi$
$308$	−2.00000	−0.113961
$309$	0	0
$310$	0	0
$311$	16.0000	0.907277	0.453638	−	0.891186i	$-0.350126\pi$
$311$	16.0000	0.907277	0.453638	+	0.891186i	$0.350126\pi$
$312$	0	0
$313$	−26.0000	−1.46961	−0.734803	−	0.678280i	$-0.762726\pi$
$313$	−26.0000	−1.46961	−0.734803	+	0.678280i	$0.762726\pi$
$314$	−20.0000	−1.12867
$315$	0	0
$316$	8.00000	0.450035
$317$	−2.00000	−0.112331	−0.0561656	−	0.998421i	$-0.517887\pi$
$317$	−2.00000	−0.112331	−0.0561656	+	0.998421i	$0.517887\pi$
$318$	0	0
$319$	12.0000	0.671871
$320$	0	0
$321$	0	0
$322$	1.00000	0.0557278
$323$	12.0000	0.667698
$324$	0	0
$325$	30.0000	1.66410
$326$	16.0000	0.886158
$327$	0	0
$328$	−6.00000	−0.331295
$329$	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	$0.314761\pi$
$332$	2.00000	0.109764
$333$	0	0
$334$	−16.0000	−0.875481
$335$	0	0
$336$	0	0
$337$	−6.00000	−0.326841	−0.163420	−	0.986557i	$-0.552253\pi$
$337$	−6.00000	−0.326841	−0.163420	+	0.986557i	$0.552253\pi$
$338$	23.0000	1.25104
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	−6.00000	−0.323498
$345$	0	0
$346$	−6.00000	−0.322562
$347$	−8.00000	−0.429463	−0.214731	−	0.976673i	$-0.568888\pi$
$347$	−8.00000	−0.429463	−0.214731	+	0.976673i	$0.568888\pi$
$348$	0	0
$349$	−2.00000	−0.107058	−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000	−0.107058	−0.0535288	+	0.998566i	$0.517047\pi$
$350$	5.00000	0.267261
$351$	0	0
$352$	2.00000	0.106600
$353$	14.0000	0.745145	0.372572	−	0.928003i	$-0.378476\pi$
$353$	14.0000	0.745145	0.372572	+	0.928003i	$0.378476\pi$
$354$	0	0
$355$	0	0
$356$	2.00000	0.106000
$357$	0	0
$358$	8.00000	0.422813
$359$	28.0000	1.47778	0.738892	−	0.673824i	$-0.235349\pi$
$359$	28.0000	1.47778	0.738892	+	0.673824i	$0.235349\pi$
$360$	0	0
$361$	17.0000	0.894737
$362$	−8.00000	−0.420471
$363$	0	0
$364$	6.00000	0.314485
$365$	0	0
$366$	0	0
$367$	16.0000	0.835193	0.417597	−	0.908633i	$-0.362873\pi$
$367$	16.0000	0.835193	0.417597	+	0.908633i	$0.362873\pi$
$368$	−1.00000	−0.0521286
$369$	0	0
$370$	0	0
$371$	−4.00000	−0.207670
$372$	0	0
$373$	−8.00000	−0.414224	−0.207112	−	0.978317i	$-0.566407\pi$
$373$	−8.00000	−0.414224	−0.207112	+	0.978317i	$0.566407\pi$
$374$	−4.00000	−0.206835
$375$	0	0
$376$	−8.00000	−0.412568
$377$	−36.0000	−1.85409
$378$	0	0
$379$	−34.0000	−1.74646	−0.873231	−	0.487306i	$-0.837980\pi$
$379$	−34.0000	−1.74646	−0.873231	+	0.487306i	$0.837980\pi$
$380$	0	0
$381$	0	0
$382$	12.0000	0.613973
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	0	0
$385$	0	0
$386$	10.0000	0.508987
$387$	0	0
$388$	14.0000	0.710742
$389$	0	0		−	1.00000i	$-0.5\pi$
$389$	0	0			1.00000i	$0.5\pi$
$390$	0	0
$391$	2.00000	0.101144
$392$	1.00000	0.0505076
$393$	0	0
$394$	−10.0000	−0.503793
$395$	0	0
$396$	0	0
$397$	−14.0000	−0.702640	−0.351320	−	0.936255i	$-0.614267\pi$
$397$	−14.0000	−0.702640	−0.351320	+	0.936255i	$0.614267\pi$
$398$	16.0000	0.802008
$399$	0	0
$400$	−5.00000	−0.250000
$401$	−2.00000	−0.0998752	−0.0499376	−	0.998752i	$-0.515902\pi$
$401$	−2.00000	−0.0998752	−0.0499376	+	0.998752i	$0.515902\pi$
$402$	0	0
$403$	0	0
$404$	14.0000	0.696526
$405$	0	0
$406$	−6.00000	−0.297775
$407$	0	0
$408$	0	0
$409$	10.0000	0.494468	0.247234	−	0.968956i	$-0.420478\pi$
$409$	10.0000	0.494468	0.247234	+	0.968956i	$0.420478\pi$
$410$	0	0
$411$	0	0
$412$	−4.00000	−0.197066
$413$	0	0
$414$	0	0
$415$	0	0
$416$	−6.00000	−0.294174
$417$	0	0
$418$	−12.0000	−0.586939
$419$	−38.0000	−1.85642	−0.928211	−	0.372055i	$-0.878653\pi$
$419$	−38.0000	−1.85642	−0.928211	+	0.372055i	$0.878653\pi$
$420$	0	0
$421$	0	0		−	1.00000i	$-0.5\pi$
$421$	0	0			1.00000i	$0.5\pi$
$422$	12.0000	0.584151
$423$	0	0
$424$	4.00000	0.194257
$425$	10.0000	0.485071
$426$	0	0
$427$	8.00000	0.387147
$428$	−2.00000	−0.0966736
$429$	0	0
$430$	0	0
$431$	36.0000	1.73406	0.867029	−	0.498257i	$-0.166026\pi$
$431$	36.0000	1.73406	0.867029	+	0.498257i	$0.166026\pi$
$432$	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
$436$	−12.0000	−0.574696
$437$	6.00000	0.287019
$438$	0	0
$439$	−16.0000	−0.763638	−0.381819	−	0.924237i	$-0.624702\pi$
$439$	−16.0000	−0.763638	−0.381819	+	0.924237i	$0.624702\pi$
$440$	0	0
$441$	0	0
$442$	12.0000	0.570782
$443$	32.0000	1.52037	0.760183	−	0.649709i	$-0.225109\pi$
$443$	32.0000	1.52037	0.760183	+	0.649709i	$0.225109\pi$
$444$	0	0
$445$	0	0
$446$	16.0000	0.757622
$447$	0	0
$448$	−1.00000	−0.0472456
$449$	−6.00000	−0.283158	−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000	−0.283158	−0.141579	+	0.989927i	$0.545218\pi$
$450$	0	0
$451$	−12.0000	−0.565058
$452$	−6.00000	−0.282216
$453$	0	0
$454$	−26.0000	−1.22024
$455$	0	0
$456$	0	0
$457$	−18.0000	−0.842004	−0.421002	−	0.907060i	$-0.638322\pi$
$457$	−18.0000	−0.842004	−0.421002	+	0.907060i	$0.638322\pi$
$458$	24.0000	1.12145
$459$	0	0
$460$	0	0
$461$	10.0000	0.465746	0.232873	−	0.972507i	$-0.425187\pi$
$461$	10.0000	0.465746	0.232873	+	0.972507i	$0.425187\pi$
$462$	0	0
$463$	16.0000	0.743583	0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000	0.743583	0.371792	+	0.928316i	$0.378744\pi$
$464$	6.00000	0.278543
$465$	0	0
$466$	−26.0000	−1.20443
$467$	−22.0000	−1.01804	−0.509019	−	0.860755i	$-0.669992\pi$
$467$	−22.0000	−1.01804	−0.509019	+	0.860755i	$0.669992\pi$
$468$	0	0
$469$	2.00000	0.0923514
$470$	0	0
$471$	0	0
$472$	0	0
$473$	−12.0000	−0.551761
$474$	0	0
$475$	30.0000	1.37649
$476$	2.00000	0.0916698
$477$	0	0
$478$	−24.0000	−1.09773
$479$	24.0000	1.09659	0.548294	−	0.836286i	$-0.315277\pi$
$479$	24.0000	1.09659	0.548294	+	0.836286i	$0.315277\pi$
$480$	0	0
$481$	0	0
$482$	−2.00000	−0.0910975
$483$	0	0
$484$	−7.00000	−0.318182
$485$	0	0
$486$	0	0
$487$	−8.00000	−0.362515	−0.181257	−	0.983436i	$-0.558017\pi$
$487$	−8.00000	−0.362515	−0.181257	+	0.983436i	$0.558017\pi$
$488$	−8.00000	−0.362143
$489$	0	0
$490$	0	0
$491$	0	0		−	1.00000i	$-0.5\pi$
$491$	0	0			1.00000i	$0.5\pi$
$492$	0	0
$493$	−12.0000	−0.540453
$494$	36.0000	1.61972
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	16.0000	0.716258	0.358129	−	0.933672i	$-0.383415\pi$
$499$	16.0000	0.716258	0.358129	+	0.933672i	$0.383415\pi$
$500$	0	0
$501$	0	0
$502$	2.00000	0.0892644
$503$	−12.0000	−0.535054	−0.267527	−	0.963550i	$-0.586206\pi$
$503$	−12.0000	−0.535054	−0.267527	+	0.963550i	$0.586206\pi$
$504$	0	0
$505$	0	0
$506$	−2.00000	−0.0889108
$507$	0	0
$508$	−8.00000	−0.354943
$509$	−14.0000	−0.620539	−0.310270	−	0.950649i	$-0.600419\pi$
$509$	−14.0000	−0.620539	−0.310270	+	0.950649i	$0.600419\pi$
$510$	0	0
$511$	2.00000	0.0884748
$512$	1.00000	0.0441942
$513$	0	0
$514$	2.00000	0.0882162
$515$	0	0
$516$	0	0
$517$	−16.0000	−0.703679
$518$	0	0
$519$	0	0
$520$	0	0
$521$	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
$523$	18.0000	0.787085	0.393543	−	0.919306i	$-0.371249\pi$
$523$	18.0000	0.787085	0.393543	+	0.919306i	$0.371249\pi$
$524$	0	0
$525$	0	0
$526$	24.0000	1.04645
$527$	0	0
$528$	0	0
$529$	1.00000	0.0434783
$530$	0	0
$531$	0	0
$532$	6.00000	0.260133
$533$	36.0000	1.55933
$534$	0	0
$535$	0	0
$536$	−2.00000	−0.0863868
$537$	0	0
$538$	−6.00000	−0.258678
$539$	2.00000	0.0861461
$540$	0	0
$541$	−22.0000	−0.945854	−0.472927	−	0.881102i	$-0.656803\pi$
$541$	−22.0000	−0.945854	−0.472927	+	0.881102i	$0.656803\pi$
$542$	8.00000	0.343629
$543$	0	0
$544$	−2.00000	−0.0857493
$545$	0	0
$546$	0	0
$547$	4.00000	0.171028	0.0855138	−	0.996337i	$-0.472747\pi$
$547$	4.00000	0.171028	0.0855138	+	0.996337i	$0.472747\pi$
$548$	6.00000	0.256307
$549$	0	0
$550$	−10.0000	−0.426401
$551$	−36.0000	−1.53365
$552$	0	0
$553$	−8.00000	−0.340195
$554$	−22.0000	−0.934690
$555$	0	0
$556$	0	0
$557$	24.0000	1.01691	0.508456	−	0.861088i	$-0.330216\pi$
$557$	24.0000	1.01691	0.508456	+	0.861088i	$0.330216\pi$
$558$	0	0
$559$	36.0000	1.52264
$560$	0	0
$561$	0	0
$562$	10.0000	0.421825
$563$	6.00000	0.252870	0.126435	−	0.991975i	$-0.459647\pi$
$563$	6.00000	0.252870	0.126435	+	0.991975i	$0.459647\pi$
$564$	0	0
$565$	0	0
$566$	30.0000	1.26099
$567$	0	0
$568$	0	0
$569$	46.0000	1.92842	0.964210	−	0.265139i	$-0.0854179\pi$
$569$	46.0000	1.92842	0.964210	+	0.265139i	$0.0854179\pi$
$570$	0	0
$571$	−2.00000	−0.0836974	−0.0418487	−	0.999124i	$-0.513325\pi$
$571$	−2.00000	−0.0836974	−0.0418487	+	0.999124i	$0.513325\pi$
$572$	−12.0000	−0.501745
$573$	0	0
$574$	6.00000	0.250435
$575$	5.00000	0.208514
$576$	0	0
$577$	6.00000	0.249783	0.124892	−	0.992170i	$-0.460142\pi$
$577$	6.00000	0.249783	0.124892	+	0.992170i	$0.460142\pi$
$578$	−13.0000	−0.540729
$579$	0	0
$580$	0	0
$581$	−2.00000	−0.0829740
$582$	0	0
$583$	8.00000	0.331326
$584$	−2.00000	−0.0827606
$585$	0	0
$586$	24.0000	0.991431
$587$	−48.0000	−1.98117	−0.990586	−	0.136892i	$-0.956289\pi$
$587$	−48.0000	−1.98117	−0.990586	+	0.136892i	$0.956289\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	0	0
$592$	0	0
$593$	−14.0000	−0.574911	−0.287456	−	0.957794i	$-0.592809\pi$
$593$	−14.0000	−0.574911	−0.287456	+	0.957794i	$0.592809\pi$
$594$	0	0
$595$	0	0
$596$	−4.00000	−0.163846
$597$	0	0
$598$	6.00000	0.245358
$599$	40.0000	1.63436	0.817178	−	0.576386i	$-0.195537\pi$
$599$	40.0000	1.63436	0.817178	+	0.576386i	$0.195537\pi$
$600$	0	0
$601$	−34.0000	−1.38689	−0.693444	−	0.720510i	$-0.743908\pi$
$601$	−34.0000	−1.38689	−0.693444	+	0.720510i	$0.743908\pi$
$602$	6.00000	0.244542
$603$	0	0
$604$	−24.0000	−0.976546
$605$	0	0
$606$	0	0
$607$	48.0000	1.94826	0.974130	−	0.225989i	$-0.0725612\pi$
$607$	48.0000	1.94826	0.974130	+	0.225989i	$0.0725612\pi$
$608$	−6.00000	−0.243332
$609$	0	0
$610$	0	0
$611$	48.0000	1.94187
$612$	0	0
$613$	−20.0000	−0.807792	−0.403896	−	0.914805i	$-0.632344\pi$
$613$	−20.0000	−0.807792	−0.403896	+	0.914805i	$0.632344\pi$
$614$	12.0000	0.484281
$615$	0	0
$616$	−2.00000	−0.0805823
$617$	42.0000	1.69086	0.845428	−	0.534089i	$-0.179345\pi$
$617$	42.0000	1.69086	0.845428	+	0.534089i	$0.179345\pi$
$618$	0	0
$619$	14.0000	0.562708	0.281354	−	0.959604i	$-0.409217\pi$
$619$	14.0000	0.562708	0.281354	+	0.959604i	$0.409217\pi$
$620$	0	0
$621$	0	0
$622$	16.0000	0.641542
$623$	−2.00000	−0.0801283
$624$	0	0
$625$	25.0000	1.00000
$626$	−26.0000	−1.03917
$627$	0	0
$628$	−20.0000	−0.798087
$629$	0	0
$630$	0	0
$631$	4.00000	0.159237	0.0796187	−	0.996825i	$-0.474630\pi$
$631$	4.00000	0.159237	0.0796187	+	0.996825i	$0.474630\pi$
$632$	8.00000	0.318223
$633$	0	0
$634$	−2.00000	−0.0794301
$635$	0	0
$636$	0	0
$637$	−6.00000	−0.237729
$638$	12.0000	0.475085
$639$	0	0
$640$	0	0
$641$	30.0000	1.18493	0.592464	−	0.805597i	$-0.298155\pi$
$641$	30.0000	1.18493	0.592464	+	0.805597i	$0.298155\pi$
$642$	0	0
$643$	−26.0000	−1.02534	−0.512670	−	0.858586i	$-0.671344\pi$
$643$	−26.0000	−1.02534	−0.512670	+	0.858586i	$0.671344\pi$
$644$	1.00000	0.0394055
$645$	0	0
$646$	12.0000	0.472134
$647$	0	0		−	1.00000i	$-0.5\pi$
$647$	0	0			1.00000i	$0.5\pi$
$648$	0	0
$649$	0	0
$650$	30.0000	1.17670
$651$	0	0
$652$	16.0000	0.626608
$653$	−22.0000	−0.860927	−0.430463	−	0.902608i	$-0.641650\pi$
$653$	−22.0000	−0.860927	−0.430463	+	0.902608i	$0.641650\pi$
$654$	0	0
$655$	0	0
$656$	−6.00000	−0.234261
$657$	0	0
$658$	8.00000	0.311872
$659$	6.00000	0.233727	0.116863	−	0.993148i	$-0.462716\pi$
$659$	6.00000	0.233727	0.116863	+	0.993148i	$0.462716\pi$
$660$	0	0
$661$	−8.00000	−0.311164	−0.155582	−	0.987823i	$-0.549725\pi$
$661$	−8.00000	−0.311164	−0.155582	+	0.987823i	$0.549725\pi$
$662$	20.0000	0.777322
$663$	0	0
$664$	2.00000	0.0776151
$665$	0	0
$666$	0	0
$667$	−6.00000	−0.232321
$668$	−16.0000	−0.619059
$669$	0	0
$670$	0	0
$671$	−16.0000	−0.617673
$672$	0	0
$673$	−50.0000	−1.92736	−0.963679	−	0.267063i	$-0.913947\pi$
$673$	−50.0000	−1.92736	−0.963679	+	0.267063i	$0.913947\pi$
$674$	−6.00000	−0.231111
$675$	0	0
$676$	23.0000	0.884615
$677$	8.00000	0.307465	0.153732	−	0.988113i	$-0.450871\pi$
$677$	8.00000	0.307465	0.153732	+	0.988113i	$0.450871\pi$
$678$	0	0
$679$	−14.0000	−0.537271
$680$	0	0
$681$	0	0
$682$	0	0
$683$	−44.0000	−1.68361	−0.841807	−	0.539779i	$-0.818508\pi$
$683$	−44.0000	−1.68361	−0.841807	+	0.539779i	$0.818508\pi$
$684$	0	0
$685$	0	0
$686$	−1.00000	−0.0381802
$687$	0	0
$688$	−6.00000	−0.228748
$689$	−24.0000	−0.914327
$690$	0	0
$691$	−8.00000	−0.304334	−0.152167	−	0.988355i	$-0.548625\pi$
$691$	−8.00000	−0.304334	−0.152167	+	0.988355i	$0.548625\pi$
$692$	−6.00000	−0.228086
$693$	0	0
$694$	−8.00000	−0.303676
$695$	0	0
$696$	0	0
$697$	12.0000	0.454532
$698$	−2.00000	−0.0757011
$699$	0	0
$700$	5.00000	0.188982
$701$	−24.0000	−0.906467	−0.453234	−	0.891392i	$-0.649730\pi$
$701$	−24.0000	−0.906467	−0.453234	+	0.891392i	$0.649730\pi$
$702$	0	0
$703$	0	0
$704$	2.00000	0.0753778
$705$	0	0
$706$	14.0000	0.526897
$707$	−14.0000	−0.526524
$708$	0	0
$709$	32.0000	1.20179	0.600893	−	0.799330i	$-0.294812\pi$
$709$	32.0000	1.20179	0.600893	+	0.799330i	$0.294812\pi$
$710$	0	0
$711$	0	0
$712$	2.00000	0.0749532
$713$	0	0
$714$	0	0
$715$	0	0
$716$	8.00000	0.298974
$717$	0	0
$718$	28.0000	1.04495
$719$	40.0000	1.49175	0.745874	−	0.666087i	$-0.232032\pi$
$719$	40.0000	1.49175	0.745874	+	0.666087i	$0.232032\pi$
$720$	0	0
$721$	4.00000	0.148968
$722$	17.0000	0.632674
$723$	0	0
$724$	−8.00000	−0.297318
$725$	−30.0000	−1.11417
$726$	0	0
$727$	40.0000	1.48352	0.741759	−	0.670667i	$-0.233992\pi$
$727$	40.0000	1.48352	0.741759	+	0.670667i	$0.233992\pi$
$728$	6.00000	0.222375
$729$	0	0
$730$	0	0
$731$	12.0000	0.443836
$732$	0	0
$733$	20.0000	0.738717	0.369358	−	0.929287i	$-0.379577\pi$
$733$	20.0000	0.738717	0.369358	+	0.929287i	$0.379577\pi$
$734$	16.0000	0.590571
$735$	0	0
$736$	−1.00000	−0.0368605
$737$	−4.00000	−0.147342
$738$	0	0
$739$	8.00000	0.294285	0.147142	−	0.989115i	$-0.452992\pi$
$739$	8.00000	0.294285	0.147142	+	0.989115i	$0.452992\pi$
$740$	0	0
$741$	0	0
$742$	−4.00000	−0.146845
$743$	32.0000	1.17397	0.586983	−	0.809599i	$-0.300316\pi$
$743$	32.0000	1.17397	0.586983	+	0.809599i	$0.300316\pi$
$744$	0	0
$745$	0	0
$746$	−8.00000	−0.292901
$747$	0	0
$748$	−4.00000	−0.146254
$749$	2.00000	0.0730784
$750$	0	0
$751$	20.0000	0.729810	0.364905	−	0.931045i	$-0.381101\pi$
$751$	20.0000	0.729810	0.364905	+	0.931045i	$0.381101\pi$
$752$	−8.00000	−0.291730
$753$	0	0
$754$	−36.0000	−1.31104
$755$	0	0
$756$	0	0
$757$	−28.0000	−1.01768	−0.508839	−	0.860862i	$-0.669925\pi$
$757$	−28.0000	−1.01768	−0.508839	+	0.860862i	$0.669925\pi$
$758$	−34.0000	−1.23494
$759$	0	0
$760$	0	0
$761$	−42.0000	−1.52250	−0.761249	−	0.648459i	$-0.775414\pi$
$761$	−42.0000	−1.52250	−0.761249	+	0.648459i	$0.775414\pi$
$762$	0	0
$763$	12.0000	0.434429
$764$	12.0000	0.434145
$765$	0	0
$766$	0	0
$767$	0	0
$768$	0	0
$769$	−34.0000	−1.22607	−0.613036	−	0.790055i	$-0.710052\pi$
$769$	−34.0000	−1.22607	−0.613036	+	0.790055i	$0.710052\pi$
$770$	0	0
$771$	0	0
$772$	10.0000	0.359908
$773$	−28.0000	−1.00709	−0.503545	−	0.863969i	$-0.667971\pi$
$773$	−28.0000	−1.00709	−0.503545	+	0.863969i	$0.667971\pi$
$774$	0	0
$775$	0	0
$776$	14.0000	0.502571
$777$	0	0
$778$	0	0
$779$	36.0000	1.28983
$780$	0	0
$781$	0	0
$782$	2.00000	0.0715199
$783$	0	0
$784$	1.00000	0.0357143
$785$	0	0
$786$	0	0
$787$	−10.0000	−0.356462	−0.178231	−	0.983989i	$-0.557037\pi$
$787$	−10.0000	−0.356462	−0.178231	+	0.983989i	$0.557037\pi$
$788$	−10.0000	−0.356235
$789$	0	0
$790$	0	0
$791$	6.00000	0.213335
$792$	0	0
$793$	48.0000	1.70453
$794$	−14.0000	−0.496841
$795$	0	0
$796$	16.0000	0.567105
$797$	52.0000	1.84193	0.920967	−	0.389640i	$-0.127401\pi$
$797$	52.0000	1.84193	0.920967	+	0.389640i	$0.127401\pi$
$798$	0	0
$799$	16.0000	0.566039
$800$	−5.00000	−0.176777
$801$	0	0
$802$	−2.00000	−0.0706225
$803$	−4.00000	−0.141157
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	14.0000	0.492518
$809$	−26.0000	−0.914111	−0.457056	−	0.889438i	$-0.651096\pi$
$809$	−26.0000	−0.914111	−0.457056	+	0.889438i	$0.651096\pi$
$810$	0	0
$811$	−48.0000	−1.68551	−0.842754	−	0.538299i	$-0.819067\pi$
$811$	−48.0000	−1.68551	−0.842754	+	0.538299i	$0.819067\pi$
$812$	−6.00000	−0.210559
$813$	0	0
$814$	0	0
$815$	0	0
$816$	0	0
$817$	36.0000	1.25948
$818$	10.0000	0.349642
$819$	0	0
$820$	0	0
$821$	42.0000	1.46581	0.732905	−	0.680331i	$-0.238164\pi$
$821$	42.0000	1.46581	0.732905	+	0.680331i	$0.238164\pi$
$822$	0	0
$823$	−8.00000	−0.278862	−0.139431	−	0.990232i	$-0.544527\pi$
$823$	−8.00000	−0.278862	−0.139431	+	0.990232i	$0.544527\pi$
$824$	−4.00000	−0.139347
$825$	0	0
$826$	0	0
$827$	−42.0000	−1.46048	−0.730242	−	0.683189i	$-0.760592\pi$
$827$	−42.0000	−1.46048	−0.730242	+	0.683189i	$0.760592\pi$
$828$	0	0
$829$	−34.0000	−1.18087	−0.590434	−	0.807086i	$-0.701044\pi$
$829$	−34.0000	−1.18087	−0.590434	+	0.807086i	$0.701044\pi$
$830$	0	0
$831$	0	0
$832$	−6.00000	−0.208013
$833$	−2.00000	−0.0692959
$834$	0	0
$835$	0	0
$836$	−12.0000	−0.415029
$837$	0	0
$838$	−38.0000	−1.31269
$839$	0	0		−	1.00000i	$-0.5\pi$
$839$	0	0			1.00000i	$0.5\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	0	0
$843$	0	0
$844$	12.0000	0.413057
$845$	0	0
$846$	0	0
$847$	7.00000	0.240523
$848$	4.00000	0.137361
$849$	0	0
$850$	10.0000	0.342997
$851$	0	0
$852$	0	0
$853$	34.0000	1.16414	0.582069	−	0.813139i	$-0.302243\pi$
$853$	34.0000	1.16414	0.582069	+	0.813139i	$0.302243\pi$
$854$	8.00000	0.273754
$855$	0	0
$856$	−2.00000	−0.0683586
$857$	−42.0000	−1.43469	−0.717346	−	0.696717i	$-0.754643\pi$
$857$	−42.0000	−1.43469	−0.717346	+	0.696717i	$0.754643\pi$
$858$	0	0
$859$	−20.0000	−0.682391	−0.341196	−	0.939992i	$-0.610832\pi$
$859$	−20.0000	−0.682391	−0.341196	+	0.939992i	$0.610832\pi$
$860$	0	0
$861$	0	0
$862$	36.0000	1.22616
$863$	56.0000	1.90626	0.953131	−	0.302558i	$-0.0978405\pi$
$863$	56.0000	1.90626	0.953131	+	0.302558i	$0.0978405\pi$
$864$	0	0
$865$	0	0
$866$	−34.0000	−1.15537
$867$	0	0
$868$	0	0
$869$	16.0000	0.542763
$870$	0	0
$871$	12.0000	0.406604
$872$	−12.0000	−0.406371
$873$	0	0
$874$	6.00000	0.202953
$875$	0	0
$876$	0	0
$877$	18.0000	0.607817	0.303908	−	0.952701i	$-0.401708\pi$
$877$	18.0000	0.607817	0.303908	+	0.952701i	$0.401708\pi$
$878$	−16.0000	−0.539974
$879$	0	0
$880$	0	0
$881$	−30.0000	−1.01073	−0.505363	−	0.862907i	$-0.668641\pi$
$881$	−30.0000	−1.01073	−0.505363	+	0.862907i	$0.668641\pi$
$882$	0	0
$883$	−36.0000	−1.21150	−0.605748	−	0.795656i	$-0.707126\pi$
$883$	−36.0000	−1.21150	−0.605748	+	0.795656i	$0.707126\pi$
$884$	12.0000	0.403604
$885$	0	0
$886$	32.0000	1.07506
$887$	−48.0000	−1.61168	−0.805841	−	0.592132i	$-0.798286\pi$
$887$	−48.0000	−1.61168	−0.805841	+	0.592132i	$0.798286\pi$
$888$	0	0
$889$	8.00000	0.268311
$890$	0	0
$891$	0	0
$892$	16.0000	0.535720
$893$	48.0000	1.60626
$894$	0	0
$895$	0	0
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	−6.00000	−0.200223
$899$	0	0
$900$	0	0
$901$	−8.00000	−0.266519
$902$	−12.0000	−0.399556
$903$	0	0
$904$	−6.00000	−0.199557
$905$	0	0
$906$	0	0
$907$	−38.0000	−1.26177	−0.630885	−	0.775877i	$-0.717308\pi$
$907$	−38.0000	−1.26177	−0.630885	+	0.775877i	$0.717308\pi$
$908$	−26.0000	−0.862840
$909$	0	0
$910$	0	0
$911$	−44.0000	−1.45779	−0.728893	−	0.684628i	$-0.759965\pi$
$911$	−44.0000	−1.45779	−0.728893	+	0.684628i	$0.759965\pi$
$912$	0	0
$913$	4.00000	0.132381
$914$	−18.0000	−0.595387
$915$	0	0
$916$	24.0000	0.792982
$917$	0	0
$918$	0	0
$919$	0	0		−	1.00000i	$-0.5\pi$
$919$	0	0			1.00000i	$0.5\pi$
$920$	0	0
$921$	0	0
$922$	10.0000	0.329332
$923$	0	0
$924$	0	0
$925$	0	0
$926$	16.0000	0.525793
$927$	0	0
$928$	6.00000	0.196960
$929$	−30.0000	−0.984268	−0.492134	−	0.870519i	$-0.663783\pi$
$929$	−30.0000	−0.984268	−0.492134	+	0.870519i	$0.663783\pi$
$930$	0	0
$931$	−6.00000	−0.196642
$932$	−26.0000	−0.851658
$933$	0	0
$934$	−22.0000	−0.719862
$935$	0	0
$936$	0	0
$937$	−38.0000	−1.24141	−0.620703	−	0.784046i	$-0.713153\pi$
$937$	−38.0000	−1.24141	−0.620703	+	0.784046i	$0.713153\pi$
$938$	2.00000	0.0653023
$939$	0	0
$940$	0	0
$941$	48.0000	1.56476	0.782378	−	0.622804i	$-0.214007\pi$
$941$	48.0000	1.56476	0.782378	+	0.622804i	$0.214007\pi$
$942$	0	0
$943$	6.00000	0.195387
$944$	0	0
$945$	0	0
$946$	−12.0000	−0.390154
$947$	−32.0000	−1.03986	−0.519930	−	0.854209i	$-0.674042\pi$
$947$	−32.0000	−1.03986	−0.519930	+	0.854209i	$0.674042\pi$
$948$	0	0
$949$	12.0000	0.389536
$950$	30.0000	0.973329
$951$	0	0
$952$	2.00000	0.0648204
$953$	−58.0000	−1.87880	−0.939402	−	0.342817i	$-0.888619\pi$
$953$	−58.0000	−1.87880	−0.939402	+	0.342817i	$0.888619\pi$
$954$	0	0
$955$	0	0
$956$	−24.0000	−0.776215
$957$	0	0
$958$	24.0000	0.775405
$959$	−6.00000	−0.193750
$960$	0	0
$961$	−31.0000	−1.00000
$962$	0	0
$963$	0	0
$964$	−2.00000	−0.0644157
$965$	0	0
$966$	0	0
$967$	−56.0000	−1.80084	−0.900419	−	0.435023i	$-0.856740\pi$
$967$	−56.0000	−1.80084	−0.900419	+	0.435023i	$0.856740\pi$
$968$	−7.00000	−0.224989
$969$	0	0
$970$	0	0
$971$	6.00000	0.192549	0.0962746	−	0.995355i	$-0.469307\pi$
$971$	6.00000	0.192549	0.0962746	+	0.995355i	$0.469307\pi$
$972$	0	0
$973$	0	0
$974$	−8.00000	−0.256337
$975$	0	0
$976$	−8.00000	−0.256074
$977$	−10.0000	−0.319928	−0.159964	−	0.987123i	$-0.551138\pi$
$977$	−10.0000	−0.319928	−0.159964	+	0.987123i	$0.551138\pi$
$978$	0	0
$979$	4.00000	0.127841
$980$	0	0
$981$	0	0
$982$	0	0
$983$	36.0000	1.14822	0.574111	−	0.818778i	$-0.305348\pi$
$983$	36.0000	1.14822	0.574111	+	0.818778i	$0.305348\pi$
$984$	0	0
$985$	0	0
$986$	−12.0000	−0.382158
$987$	0	0
$988$	36.0000	1.14531
$989$	6.00000	0.190789
$990$	0	0
$991$	−24.0000	−0.762385	−0.381193	−	0.924496i	$-0.624487\pi$
$991$	−24.0000	−0.762385	−0.381193	+	0.924496i	$0.624487\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	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	$0.294476\pi$
$998$	16.0000	0.506471
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2898.2.a.n.1.1		1
3.2	odd	2		966.2.a.e.1.1	✓	1
12.11	even	2		7728.2.a.g.1.1		1
21.20	even	2		6762.2.a.f.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.a.e.1.1	✓	1	3.2	odd	2
2898.2.a.n.1.1		1	1.1	even	1	trivial
6762.2.a.f.1.1		1	21.20	even	2
7728.2.a.g.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

Related objects

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