LMFDB - Embedded newform 2775.2.a.i.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2775,2,Mod(1,2775)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2775, 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("2775.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2775 = 3 \cdot 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2775.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:	$22.1584865609$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	2775.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+2.00000 q^{2} -1.00000 q^{3} +2.00000 q^{4} -2.00000 q^{6} -1.00000 q^{7} +1.00000 q^{9} +O(q^{10})$

\(q+2.00000 q^{2} -1.00000 q^{3} +2.00000 q^{4} -2.00000 q^{6} -1.00000 q^{7} +1.00000 q^{9} -2.00000 q^{12} +5.00000 q^{13} -2.00000 q^{14} -4.00000 q^{16} +4.00000 q^{17} +2.00000 q^{18} +5.00000 q^{19} +1.00000 q^{21} -4.00000 q^{23} +10.0000 q^{26} -1.00000 q^{27} -2.00000 q^{28} +2.00000 q^{29} -9.00000 q^{31} -8.00000 q^{32} +8.00000 q^{34} +2.00000 q^{36} +1.00000 q^{37} +10.0000 q^{38} -5.00000 q^{39} +4.00000 q^{41} +2.00000 q^{42} +13.0000 q^{43} -8.00000 q^{46} +4.00000 q^{47} +4.00000 q^{48} -6.00000 q^{49} -4.00000 q^{51} +10.0000 q^{52} +12.0000 q^{53} -2.00000 q^{54} -5.00000 q^{57} +4.00000 q^{58} +12.0000 q^{59} +5.00000 q^{61} -18.0000 q^{62} -1.00000 q^{63} -8.00000 q^{64} -1.00000 q^{67} +8.00000 q^{68} +4.00000 q^{69} -6.00000 q^{71} +10.0000 q^{73} +2.00000 q^{74} +10.0000 q^{76} -10.0000 q^{78} +1.00000 q^{81} +8.00000 q^{82} +18.0000 q^{83} +2.00000 q^{84} +26.0000 q^{86} -2.00000 q^{87} +8.00000 q^{89} -5.00000 q^{91} -8.00000 q^{92} +9.00000 q^{93} +8.00000 q^{94} +8.00000 q^{96} +1.00000 q^{97} -12.0000 q^{98} +O(q^{100})\)

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 $

$2$	2.00000	1.41421	0.707107	−	0.707107i	$-0.250000\pi$
$2$	2.00000	1.41421	0.707107	+	0.707107i	$0.250000\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.00000	1.00000
$5$	0	0
$5$	0	0
$6$	−2.00000	−0.816497
$7$	−1.00000	−0.377964	−0.188982	−	0.981981i	$-0.560519\pi$
$7$	−1.00000	−0.377964	−0.188982	+	0.981981i	$0.560519\pi$
$8$	0	0
$9$	1.00000	0.333333
$10$	0	0
$11$	0	0		−	1.00000i	$-0.5\pi$
$11$	0	0			1.00000i	$0.5\pi$
$12$	−2.00000	−0.577350
$13$	5.00000	1.38675	0.693375	−	0.720577i	$-0.256123\pi$
$13$	5.00000	1.38675	0.693375	+	0.720577i	$0.256123\pi$
$14$	−2.00000	−0.534522
$15$	0	0
$16$	−4.00000	−1.00000
$17$	4.00000	0.970143	0.485071	−	0.874475i	$-0.338794\pi$
$17$	4.00000	0.970143	0.485071	+	0.874475i	$0.338794\pi$
$18$	2.00000	0.471405
$19$	5.00000	1.14708	0.573539	−	0.819178i	$-0.305570\pi$
$19$	5.00000	1.14708	0.573539	+	0.819178i	$0.305570\pi$
$20$	0	0
$21$	1.00000	0.218218
$22$	0	0
$23$	−4.00000	−0.834058	−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000	−0.834058	−0.417029	+	0.908893i	$0.636929\pi$
$24$	0	0
$25$	0	0
$26$	10.0000	1.96116
$27$	−1.00000	−0.192450
$28$	−2.00000	−0.377964
$29$	2.00000	0.371391	0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000	0.371391	0.185695	+	0.982607i	$0.440546\pi$
$30$	0	0
$31$	−9.00000	−1.61645	−0.808224	−	0.588875i	$-0.799571\pi$
$31$	−9.00000	−1.61645	−0.808224	+	0.588875i	$0.799571\pi$
$32$	−8.00000	−1.41421
$33$	0	0
$34$	8.00000	1.37199
$35$	0	0
$36$	2.00000	0.333333
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	10.0000	1.62221
$39$	−5.00000	−0.800641
$40$	0	0
$41$	4.00000	0.624695	0.312348	−	0.949968i	$-0.398885\pi$
$41$	4.00000	0.624695	0.312348	+	0.949968i	$0.398885\pi$
$42$	2.00000	0.308607
$43$	13.0000	1.98248	0.991241	−	0.132068i	$-0.0421616\pi$
$43$	13.0000	1.98248	0.991241	+	0.132068i	$0.0421616\pi$
$44$	0	0
$45$	0	0
$46$	−8.00000	−1.17954
$47$	4.00000	0.583460	0.291730	−	0.956501i	$-0.405769\pi$
$47$	4.00000	0.583460	0.291730	+	0.956501i	$0.405769\pi$
$48$	4.00000	0.577350
$49$	−6.00000	−0.857143
$50$	0	0
$51$	−4.00000	−0.560112
$52$	10.0000	1.38675
$53$	12.0000	1.64833	0.824163	−	0.566352i	$-0.191646\pi$
$53$	12.0000	1.64833	0.824163	+	0.566352i	$0.191646\pi$
$54$	−2.00000	−0.272166
$55$	0	0
$56$	0	0
$57$	−5.00000	−0.662266
$58$	4.00000	0.525226
$59$	12.0000	1.56227	0.781133	−	0.624364i	$-0.214642\pi$
$59$	12.0000	1.56227	0.781133	+	0.624364i	$0.214642\pi$
$60$	0	0
$61$	5.00000	0.640184	0.320092	−	0.947386i	$-0.396286\pi$
$61$	5.00000	0.640184	0.320092	+	0.947386i	$0.396286\pi$
$62$	−18.0000	−2.28600
$63$	−1.00000	−0.125988
$64$	−8.00000	−1.00000
$65$	0	0
$66$	0	0
$67$	−1.00000	−0.122169	−0.0610847	−	0.998133i	$-0.519456\pi$
$67$	−1.00000	−0.122169	−0.0610847	+	0.998133i	$0.519456\pi$
$68$	8.00000	0.970143
$69$	4.00000	0.481543
$70$	0	0
$71$	−6.00000	−0.712069	−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000	−0.712069	−0.356034	+	0.934473i	$0.615871\pi$
$72$	0	0
$73$	10.0000	1.17041	0.585206	−	0.810885i	$-0.301014\pi$
$73$	10.0000	1.17041	0.585206	+	0.810885i	$0.301014\pi$
$74$	2.00000	0.232495
$75$	0	0
$76$	10.0000	1.14708
$77$	0	0
$78$	−10.0000	−1.13228
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	8.00000	0.883452
$83$	18.0000	1.97576	0.987878	−	0.155230i	$-0.0496119\pi$
$83$	18.0000	1.97576	0.987878	+	0.155230i	$0.0496119\pi$
$84$	2.00000	0.218218
$85$	0	0
$86$	26.0000	2.80365
$87$	−2.00000	−0.214423
$88$	0	0
$89$	8.00000	0.847998	0.423999	−	0.905663i	$-0.360626\pi$
$89$	8.00000	0.847998	0.423999	+	0.905663i	$0.360626\pi$
$90$	0	0
$91$	−5.00000	−0.524142
$92$	−8.00000	−0.834058
$93$	9.00000	0.933257
$94$	8.00000	0.825137
$95$	0	0
$96$	8.00000	0.816497
$97$	1.00000	0.101535	0.0507673	−	0.998711i	$-0.483833\pi$
$97$	1.00000	0.101535	0.0507673	+	0.998711i	$0.483833\pi$
$98$	−12.0000	−1.21218
$99$	0	0
$100$	0	0
$101$	10.0000	0.995037	0.497519	−	0.867453i	$-0.334245\pi$
$101$	10.0000	0.995037	0.497519	+	0.867453i	$0.334245\pi$
$102$	−8.00000	−0.792118
$103$	−8.00000	−0.788263	−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000	−0.788263	−0.394132	+	0.919054i	$0.628955\pi$
$104$	0	0
$105$	0	0
$106$	24.0000	2.33109
$107$	−6.00000	−0.580042	−0.290021	−	0.957020i	$-0.593662\pi$
$107$	−6.00000	−0.580042	−0.290021	+	0.957020i	$0.593662\pi$
$108$	−2.00000	−0.192450
$109$	11.0000	1.05361	0.526804	−	0.849987i	$-0.323390\pi$
$109$	11.0000	1.05361	0.526804	+	0.849987i	$0.323390\pi$
$110$	0	0
$111$	−1.00000	−0.0949158
$112$	4.00000	0.377964
$113$	−14.0000	−1.31701	−0.658505	−	0.752577i	$-0.728811\pi$
$113$	−14.0000	−1.31701	−0.658505	+	0.752577i	$0.728811\pi$
$114$	−10.0000	−0.936586
$115$	0	0
$116$	4.00000	0.371391
$117$	5.00000	0.462250
$118$	24.0000	2.20938
$119$	−4.00000	−0.366679
$120$	0	0
$121$	−11.0000	−1.00000
$122$	10.0000	0.905357
$123$	−4.00000	−0.360668
$124$	−18.0000	−1.61645
$125$	0	0
$126$	−2.00000	−0.178174
$127$	8.00000	0.709885	0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000	0.709885	0.354943	+	0.934888i	$0.384500\pi$
$128$	0	0
$129$	−13.0000	−1.14459
$130$	0	0
$131$	−6.00000	−0.524222	−0.262111	−	0.965038i	$-0.584419\pi$
$131$	−6.00000	−0.524222	−0.262111	+	0.965038i	$0.584419\pi$
$132$	0	0
$133$	−5.00000	−0.433555
$134$	−2.00000	−0.172774
$135$	0	0
$136$	0	0
$137$	12.0000	1.02523	0.512615	−	0.858619i	$-0.328677\pi$
$137$	12.0000	1.02523	0.512615	+	0.858619i	$0.328677\pi$
$138$	8.00000	0.681005
$139$	−16.0000	−1.35710	−0.678551	−	0.734553i	$-0.737392\pi$
$139$	−16.0000	−1.35710	−0.678551	+	0.734553i	$0.737392\pi$
$140$	0	0
$141$	−4.00000	−0.336861
$142$	−12.0000	−1.00702
$143$	0	0
$144$	−4.00000	−0.333333
$145$	0	0
$146$	20.0000	1.65521
$147$	6.00000	0.494872
$148$	2.00000	0.164399
$149$	−6.00000	−0.491539	−0.245770	−	0.969328i	$-0.579041\pi$
$149$	−6.00000	−0.491539	−0.245770	+	0.969328i	$0.579041\pi$
$150$	0	0
$151$	−17.0000	−1.38344	−0.691720	−	0.722166i	$-0.743147\pi$
$151$	−17.0000	−1.38344	−0.691720	+	0.722166i	$0.743147\pi$
$152$	0	0
$153$	4.00000	0.323381
$154$	0	0
$155$	0	0
$156$	−10.0000	−0.800641
$157$	−3.00000	−0.239426	−0.119713	−	0.992809i	$-0.538197\pi$
$157$	−3.00000	−0.239426	−0.119713	+	0.992809i	$0.538197\pi$
$158$	0	0
$159$	−12.0000	−0.951662
$160$	0	0
$161$	4.00000	0.315244
$162$	2.00000	0.157135
$163$	11.0000	0.861586	0.430793	−	0.902451i	$-0.358234\pi$
$163$	11.0000	0.861586	0.430793	+	0.902451i	$0.358234\pi$
$164$	8.00000	0.624695
$165$	0	0
$166$	36.0000	2.79414
$167$	−24.0000	−1.85718	−0.928588	−	0.371113i	$-0.878976\pi$
$167$	−24.0000	−1.85718	−0.928588	+	0.371113i	$0.878976\pi$
$168$	0	0
$169$	12.0000	0.923077
$170$	0	0
$171$	5.00000	0.382360
$172$	26.0000	1.98248
$173$	−2.00000	−0.152057	−0.0760286	−	0.997106i	$-0.524224\pi$
$173$	−2.00000	−0.152057	−0.0760286	+	0.997106i	$0.524224\pi$
$174$	−4.00000	−0.303239
$175$	0	0
$176$	0	0
$177$	−12.0000	−0.901975
$178$	16.0000	1.19925
$179$	−10.0000	−0.747435	−0.373718	−	0.927543i	$-0.621917\pi$
$179$	−10.0000	−0.747435	−0.373718	+	0.927543i	$0.621917\pi$
$180$	0	0
$181$	−11.0000	−0.817624	−0.408812	−	0.912619i	$-0.634057\pi$
$181$	−11.0000	−0.817624	−0.408812	+	0.912619i	$0.634057\pi$
$182$	−10.0000	−0.741249
$183$	−5.00000	−0.369611
$184$	0	0
$185$	0	0
$186$	18.0000	1.31982
$187$	0	0
$188$	8.00000	0.583460
$189$	1.00000	0.0727393
$190$	0	0
$191$	−2.00000	−0.144715	−0.0723575	−	0.997379i	$-0.523052\pi$
$191$	−2.00000	−0.144715	−0.0723575	+	0.997379i	$0.523052\pi$
$192$	8.00000	0.577350
$193$	−5.00000	−0.359908	−0.179954	−	0.983675i	$-0.557595\pi$
$193$	−5.00000	−0.359908	−0.179954	+	0.983675i	$0.557595\pi$
$194$	2.00000	0.143592
$195$	0	0
$196$	−12.0000	−0.857143
$197$	−16.0000	−1.13995	−0.569976	−	0.821661i	$-0.693048\pi$
$197$	−16.0000	−1.13995	−0.569976	+	0.821661i	$0.693048\pi$
$198$	0	0
$199$	−11.0000	−0.779769	−0.389885	−	0.920864i	$-0.627485\pi$
$199$	−11.0000	−0.779769	−0.389885	+	0.920864i	$0.627485\pi$
$200$	0	0
$201$	1.00000	0.0705346
$202$	20.0000	1.40720
$203$	−2.00000	−0.140372
$204$	−8.00000	−0.560112
$205$	0	0
$206$	−16.0000	−1.11477
$207$	−4.00000	−0.278019
$208$	−20.0000	−1.38675
$209$	0	0
$210$	0	0
$211$	−1.00000	−0.0688428	−0.0344214	−	0.999407i	$-0.510959\pi$
$211$	−1.00000	−0.0688428	−0.0344214	+	0.999407i	$0.510959\pi$
$212$	24.0000	1.64833
$213$	6.00000	0.411113
$214$	−12.0000	−0.820303
$215$	0	0
$216$	0	0
$217$	9.00000	0.610960
$218$	22.0000	1.49003
$219$	−10.0000	−0.675737
$220$	0	0
$221$	20.0000	1.34535
$222$	−2.00000	−0.134231
$223$	−25.0000	−1.67412	−0.837062	−	0.547108i	$-0.815729\pi$
$223$	−25.0000	−1.67412	−0.837062	+	0.547108i	$0.815729\pi$
$224$	8.00000	0.534522
$225$	0	0
$226$	−28.0000	−1.86253
$227$	14.0000	0.929213	0.464606	−	0.885517i	$-0.346196\pi$
$227$	14.0000	0.929213	0.464606	+	0.885517i	$0.346196\pi$
$228$	−10.0000	−0.662266
$229$	9.00000	0.594737	0.297368	−	0.954763i	$-0.403891\pi$
$229$	9.00000	0.594737	0.297368	+	0.954763i	$0.403891\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	−10.0000	−0.655122	−0.327561	−	0.944830i	$-0.606227\pi$
$233$	−10.0000	−0.655122	−0.327561	+	0.944830i	$0.606227\pi$
$234$	10.0000	0.653720
$235$	0	0
$236$	24.0000	1.56227
$237$	0	0
$238$	−8.00000	−0.518563
$239$	6.00000	0.388108	0.194054	−	0.980991i	$-0.437836\pi$
$239$	6.00000	0.388108	0.194054	+	0.980991i	$0.437836\pi$
$240$	0	0
$241$	−17.0000	−1.09507	−0.547533	−	0.836784i	$-0.684433\pi$
$241$	−17.0000	−1.09507	−0.547533	+	0.836784i	$0.684433\pi$
$242$	−22.0000	−1.41421
$243$	−1.00000	−0.0641500
$244$	10.0000	0.640184
$245$	0	0
$246$	−8.00000	−0.510061
$247$	25.0000	1.59071
$248$	0	0
$249$	−18.0000	−1.14070
$250$	0	0
$251$	−20.0000	−1.26239	−0.631194	−	0.775625i	$-0.717435\pi$
$251$	−20.0000	−1.26239	−0.631194	+	0.775625i	$0.717435\pi$
$252$	−2.00000	−0.125988
$253$	0	0
$254$	16.0000	1.00393
$255$	0	0
$256$	16.0000	1.00000
$257$	24.0000	1.49708	0.748539	−	0.663090i	$-0.230755\pi$
$257$	24.0000	1.49708	0.748539	+	0.663090i	$0.230755\pi$
$258$	−26.0000	−1.61869
$259$	−1.00000	−0.0621370
$260$	0	0
$261$	2.00000	0.123797
$262$	−12.0000	−0.741362
$263$	−4.00000	−0.246651	−0.123325	−	0.992366i	$-0.539356\pi$
$263$	−4.00000	−0.246651	−0.123325	+	0.992366i	$0.539356\pi$
$264$	0	0
$265$	0	0
$266$	−10.0000	−0.613139
$267$	−8.00000	−0.489592
$268$	−2.00000	−0.122169
$269$	−12.0000	−0.731653	−0.365826	−	0.930683i	$-0.619214\pi$
$269$	−12.0000	−0.731653	−0.365826	+	0.930683i	$0.619214\pi$
$270$	0	0
$271$	−24.0000	−1.45790	−0.728948	−	0.684569i	$-0.759990\pi$
$271$	−24.0000	−1.45790	−0.728948	+	0.684569i	$0.759990\pi$
$272$	−16.0000	−0.970143
$273$	5.00000	0.302614
$274$	24.0000	1.44989
$275$	0	0
$276$	8.00000	0.481543
$277$	13.0000	0.781094	0.390547	−	0.920583i	$-0.372286\pi$
$277$	13.0000	0.781094	0.390547	+	0.920583i	$0.372286\pi$
$278$	−32.0000	−1.91923
$279$	−9.00000	−0.538816
$280$	0	0
$281$	8.00000	0.477240	0.238620	−	0.971113i	$-0.423305\pi$
$281$	8.00000	0.477240	0.238620	+	0.971113i	$0.423305\pi$
$282$	−8.00000	−0.476393
$283$	31.0000	1.84276	0.921379	−	0.388664i	$-0.127063\pi$
$283$	31.0000	1.84276	0.921379	+	0.388664i	$0.127063\pi$
$284$	−12.0000	−0.712069
$285$	0	0
$286$	0	0
$287$	−4.00000	−0.236113
$288$	−8.00000	−0.471405
$289$	−1.00000	−0.0588235
$290$	0	0
$291$	−1.00000	−0.0586210
$292$	20.0000	1.17041
$293$	−4.00000	−0.233682	−0.116841	−	0.993151i	$-0.537277\pi$
$293$	−4.00000	−0.233682	−0.116841	+	0.993151i	$0.537277\pi$
$294$	12.0000	0.699854
$295$	0	0
$296$	0	0
$297$	0	0
$298$	−12.0000	−0.695141
$299$	−20.0000	−1.15663
$300$	0	0
$301$	−13.0000	−0.749308
$302$	−34.0000	−1.95648
$303$	−10.0000	−0.574485
$304$	−20.0000	−1.14708
$305$	0	0
$306$	8.00000	0.457330
$307$	5.00000	0.285365	0.142683	−	0.989769i	$-0.454427\pi$
$307$	5.00000	0.285365	0.142683	+	0.989769i	$0.454427\pi$
$308$	0	0
$309$	8.00000	0.455104
$310$	0	0
$311$	0	0		−	1.00000i	$-0.5\pi$
$311$	0	0			1.00000i	$0.5\pi$
$312$	0	0
$313$	−25.0000	−1.41308	−0.706542	−	0.707671i	$-0.749746\pi$
$313$	−25.0000	−1.41308	−0.706542	+	0.707671i	$0.749746\pi$
$314$	−6.00000	−0.338600
$315$	0	0
$316$	0	0
$317$	20.0000	1.12331	0.561656	−	0.827371i	$-0.310164\pi$
$317$	20.0000	1.12331	0.561656	+	0.827371i	$0.310164\pi$
$318$	−24.0000	−1.34585
$319$	0	0
$320$	0	0
$321$	6.00000	0.334887
$322$	8.00000	0.445823
$323$	20.0000	1.11283
$324$	2.00000	0.111111
$325$	0	0
$326$	22.0000	1.21847
$327$	−11.0000	−0.608301
$328$	0	0
$329$	−4.00000	−0.220527
$330$	0	0
$331$	4.00000	0.219860	0.109930	−	0.993939i	$-0.464937\pi$
$331$	4.00000	0.219860	0.109930	+	0.993939i	$0.464937\pi$
$332$	36.0000	1.97576
$333$	1.00000	0.0547997
$334$	−48.0000	−2.62644
$335$	0	0
$336$	−4.00000	−0.218218
$337$	19.0000	1.03500	0.517498	−	0.855684i	$-0.326864\pi$
$337$	19.0000	1.03500	0.517498	+	0.855684i	$0.326864\pi$
$338$	24.0000	1.30543
$339$	14.0000	0.760376
$340$	0	0
$341$	0	0
$342$	10.0000	0.540738
$343$	13.0000	0.701934
$344$	0	0
$345$	0	0
$346$	−4.00000	−0.215041
$347$	−2.00000	−0.107366	−0.0536828	−	0.998558i	$-0.517096\pi$
$347$	−2.00000	−0.107366	−0.0536828	+	0.998558i	$0.517096\pi$
$348$	−4.00000	−0.214423
$349$	−22.0000	−1.17763	−0.588817	−	0.808267i	$-0.700406\pi$
$349$	−22.0000	−1.17763	−0.588817	+	0.808267i	$0.700406\pi$
$350$	0	0
$351$	−5.00000	−0.266880
$352$	0	0
$353$	26.0000	1.38384	0.691920	−	0.721974i	$-0.256765\pi$
$353$	26.0000	1.38384	0.691920	+	0.721974i	$0.256765\pi$
$354$	−24.0000	−1.27559
$355$	0	0
$356$	16.0000	0.847998
$357$	4.00000	0.211702
$358$	−20.0000	−1.05703
$359$	6.00000	0.316668	0.158334	−	0.987386i	$-0.449388\pi$
$359$	6.00000	0.316668	0.158334	+	0.987386i	$0.449388\pi$
$360$	0	0
$361$	6.00000	0.315789
$362$	−22.0000	−1.15629
$363$	11.0000	0.577350
$364$	−10.0000	−0.524142
$365$	0	0
$366$	−10.0000	−0.522708
$367$	17.0000	0.887393	0.443696	−	0.896177i	$-0.353667\pi$
$367$	17.0000	0.887393	0.443696	+	0.896177i	$0.353667\pi$
$368$	16.0000	0.834058
$369$	4.00000	0.208232
$370$	0	0
$371$	−12.0000	−0.623009
$372$	18.0000	0.933257
$373$	9.00000	0.466002	0.233001	−	0.972476i	$-0.425145\pi$
$373$	9.00000	0.466002	0.233001	+	0.972476i	$0.425145\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	10.0000	0.515026
$378$	2.00000	0.102869
$379$	25.0000	1.28416	0.642082	−	0.766636i	$-0.278071\pi$
$379$	25.0000	1.28416	0.642082	+	0.766636i	$0.278071\pi$
$380$	0	0
$381$	−8.00000	−0.409852
$382$	−4.00000	−0.204658
$383$	12.0000	0.613171	0.306586	−	0.951843i	$-0.400813\pi$
$383$	12.0000	0.613171	0.306586	+	0.951843i	$0.400813\pi$
$384$	0	0
$385$	0	0
$386$	−10.0000	−0.508987
$387$	13.0000	0.660827
$388$	2.00000	0.101535
$389$	18.0000	0.912636	0.456318	−	0.889817i	$-0.349168\pi$
$389$	18.0000	0.912636	0.456318	+	0.889817i	$0.349168\pi$
$390$	0	0
$391$	−16.0000	−0.809155
$392$	0	0
$393$	6.00000	0.302660
$394$	−32.0000	−1.61214
$395$	0	0
$396$	0	0
$397$	−27.0000	−1.35509	−0.677546	−	0.735481i	$-0.736956\pi$
$397$	−27.0000	−1.35509	−0.677546	+	0.735481i	$0.736956\pi$
$398$	−22.0000	−1.10276
$399$	5.00000	0.250313
$400$	0	0
$401$	−30.0000	−1.49813	−0.749064	−	0.662497i	$-0.769497\pi$
$401$	−30.0000	−1.49813	−0.749064	+	0.662497i	$0.769497\pi$
$402$	2.00000	0.0997509
$403$	−45.0000	−2.24161
$404$	20.0000	0.995037
$405$	0	0
$406$	−4.00000	−0.198517
$407$	0	0
$408$	0	0
$409$	35.0000	1.73064	0.865319	−	0.501221i	$-0.167116\pi$
$409$	35.0000	1.73064	0.865319	+	0.501221i	$0.167116\pi$
$410$	0	0
$411$	−12.0000	−0.591916
$412$	−16.0000	−0.788263
$413$	−12.0000	−0.590481
$414$	−8.00000	−0.393179
$415$	0	0
$416$	−40.0000	−1.96116
$417$	16.0000	0.783523
$418$	0	0
$419$	30.0000	1.46560	0.732798	−	0.680446i	$-0.238214\pi$
$419$	30.0000	1.46560	0.732798	+	0.680446i	$0.238214\pi$
$420$	0	0
$421$	2.00000	0.0974740	0.0487370	−	0.998812i	$-0.484480\pi$
$421$	2.00000	0.0974740	0.0487370	+	0.998812i	$0.484480\pi$
$422$	−2.00000	−0.0973585
$423$	4.00000	0.194487
$424$	0	0
$425$	0	0
$426$	12.0000	0.581402
$427$	−5.00000	−0.241967
$428$	−12.0000	−0.580042
$429$	0	0
$430$	0	0
$431$	12.0000	0.578020	0.289010	−	0.957326i	$-0.406674\pi$
$431$	12.0000	0.578020	0.289010	+	0.957326i	$0.406674\pi$
$432$	4.00000	0.192450
$433$	5.00000	0.240285	0.120142	−	0.992757i	$-0.461665\pi$
$433$	5.00000	0.240285	0.120142	+	0.992757i	$0.461665\pi$
$434$	18.0000	0.864028
$435$	0	0
$436$	22.0000	1.05361
$437$	−20.0000	−0.956730
$438$	−20.0000	−0.955637
$439$	7.00000	0.334092	0.167046	−	0.985949i	$-0.446577\pi$
$439$	7.00000	0.334092	0.167046	+	0.985949i	$0.446577\pi$
$440$	0	0
$441$	−6.00000	−0.285714
$442$	40.0000	1.90261
$443$	6.00000	0.285069	0.142534	−	0.989790i	$-0.454475\pi$
$443$	6.00000	0.285069	0.142534	+	0.989790i	$0.454475\pi$
$444$	−2.00000	−0.0949158
$445$	0	0
$446$	−50.0000	−2.36757
$447$	6.00000	0.283790
$448$	8.00000	0.377964
$449$	−34.0000	−1.60456	−0.802280	−	0.596948i	$-0.796380\pi$
$449$	−34.0000	−1.60456	−0.802280	+	0.596948i	$0.796380\pi$
$450$	0	0
$451$	0	0
$452$	−28.0000	−1.31701
$453$	17.0000	0.798730
$454$	28.0000	1.31411
$455$	0	0
$456$	0	0
$457$	6.00000	0.280668	0.140334	−	0.990104i	$-0.455182\pi$
$457$	6.00000	0.280668	0.140334	+	0.990104i	$0.455182\pi$
$458$	18.0000	0.841085
$459$	−4.00000	−0.186704
$460$	0	0
$461$	−42.0000	−1.95614	−0.978068	−	0.208288i	$-0.933211\pi$
$461$	−42.0000	−1.95614	−0.978068	+	0.208288i	$0.933211\pi$
$462$	0	0
$463$	−16.0000	−0.743583	−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000	−0.743583	−0.371792	+	0.928316i	$0.621256\pi$
$464$	−8.00000	−0.371391
$465$	0	0
$466$	−20.0000	−0.926482
$467$	28.0000	1.29569	0.647843	−	0.761774i	$-0.275671\pi$
$467$	28.0000	1.29569	0.647843	+	0.761774i	$0.275671\pi$
$468$	10.0000	0.462250
$469$	1.00000	0.0461757
$470$	0	0
$471$	3.00000	0.138233
$472$	0	0
$473$	0	0
$474$	0	0
$475$	0	0
$476$	−8.00000	−0.366679
$477$	12.0000	0.549442
$478$	12.0000	0.548867
$479$	−18.0000	−0.822441	−0.411220	−	0.911536i	$-0.634897\pi$
$479$	−18.0000	−0.822441	−0.411220	+	0.911536i	$0.634897\pi$
$480$	0	0
$481$	5.00000	0.227980
$482$	−34.0000	−1.54866
$483$	−4.00000	−0.182006
$484$	−22.0000	−1.00000
$485$	0	0
$486$	−2.00000	−0.0907218
$487$	−33.0000	−1.49537	−0.747686	−	0.664052i	$-0.768835\pi$
$487$	−33.0000	−1.49537	−0.747686	+	0.664052i	$0.768835\pi$
$488$	0	0
$489$	−11.0000	−0.497437
$490$	0	0
$491$	2.00000	0.0902587	0.0451294	−	0.998981i	$-0.485630\pi$
$491$	2.00000	0.0902587	0.0451294	+	0.998981i	$0.485630\pi$
$492$	−8.00000	−0.360668
$493$	8.00000	0.360302
$494$	50.0000	2.24961
$495$	0	0
$496$	36.0000	1.61645
$497$	6.00000	0.269137
$498$	−36.0000	−1.61320
$499$	5.00000	0.223831	0.111915	−	0.993718i	$-0.464301\pi$
$499$	5.00000	0.223831	0.111915	+	0.993718i	$0.464301\pi$
$500$	0	0
$501$	24.0000	1.07224
$502$	−40.0000	−1.78529
$503$	24.0000	1.07011	0.535054	−	0.844818i	$-0.320291\pi$
$503$	24.0000	1.07011	0.535054	+	0.844818i	$0.320291\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	−12.0000	−0.532939
$508$	16.0000	0.709885
$509$	18.0000	0.797836	0.398918	−	0.916987i	$-0.369386\pi$
$509$	18.0000	0.797836	0.398918	+	0.916987i	$0.369386\pi$
$510$	0	0
$511$	−10.0000	−0.442374
$512$	32.0000	1.41421
$513$	−5.00000	−0.220755
$514$	48.0000	2.11719
$515$	0	0
$516$	−26.0000	−1.14459
$517$	0	0
$518$	−2.00000	−0.0878750
$519$	2.00000	0.0877903
$520$	0	0
$521$	30.0000	1.31432	0.657162	−	0.753749i	$-0.271757\pi$
$521$	30.0000	1.31432	0.657162	+	0.753749i	$0.271757\pi$
$522$	4.00000	0.175075
$523$	−25.0000	−1.09317	−0.546587	−	0.837402i	$-0.684073\pi$
$523$	−25.0000	−1.09317	−0.546587	+	0.837402i	$0.684073\pi$
$524$	−12.0000	−0.524222
$525$	0	0
$526$	−8.00000	−0.348817
$527$	−36.0000	−1.56818
$528$	0	0
$529$	−7.00000	−0.304348
$530$	0	0
$531$	12.0000	0.520756
$532$	−10.0000	−0.433555
$533$	20.0000	0.866296
$534$	−16.0000	−0.692388
$535$	0	0
$536$	0	0
$537$	10.0000	0.431532
$538$	−24.0000	−1.03471
$539$	0	0
$540$	0	0
$541$	19.0000	0.816874	0.408437	−	0.912787i	$-0.366074\pi$
$541$	19.0000	0.816874	0.408437	+	0.912787i	$0.366074\pi$
$542$	−48.0000	−2.06178
$543$	11.0000	0.472055
$544$	−32.0000	−1.37199
$545$	0	0
$546$	10.0000	0.427960
$547$	36.0000	1.53925	0.769624	−	0.638497i	$-0.220443\pi$
$547$	36.0000	1.53925	0.769624	+	0.638497i	$0.220443\pi$
$548$	24.0000	1.02523
$549$	5.00000	0.213395
$550$	0	0
$551$	10.0000	0.426014
$552$	0	0
$553$	0	0
$554$	26.0000	1.10463
$555$	0	0
$556$	−32.0000	−1.35710
$557$	−36.0000	−1.52537	−0.762684	−	0.646771i	$-0.776119\pi$
$557$	−36.0000	−1.52537	−0.762684	+	0.646771i	$0.776119\pi$
$558$	−18.0000	−0.762001
$559$	65.0000	2.74921
$560$	0	0
$561$	0	0
$562$	16.0000	0.674919
$563$	−6.00000	−0.252870	−0.126435	−	0.991975i	$-0.540353\pi$
$563$	−6.00000	−0.252870	−0.126435	+	0.991975i	$0.540353\pi$
$564$	−8.00000	−0.336861
$565$	0	0
$566$	62.0000	2.60605
$567$	−1.00000	−0.0419961
$568$	0	0
$569$	0	0		−	1.00000i	$-0.5\pi$
$569$	0	0			1.00000i	$0.5\pi$
$570$	0	0
$571$	11.0000	0.460336	0.230168	−	0.973151i	$-0.426072\pi$
$571$	11.0000	0.460336	0.230168	+	0.973151i	$0.426072\pi$
$572$	0	0
$573$	2.00000	0.0835512
$574$	−8.00000	−0.333914
$575$	0	0
$576$	−8.00000	−0.333333
$577$	−37.0000	−1.54033	−0.770165	−	0.637845i	$-0.779826\pi$
$577$	−37.0000	−1.54033	−0.770165	+	0.637845i	$0.779826\pi$
$578$	−2.00000	−0.0831890
$579$	5.00000	0.207793
$580$	0	0
$581$	−18.0000	−0.746766
$582$	−2.00000	−0.0829027
$583$	0	0
$584$	0	0
$585$	0	0
$586$	−8.00000	−0.330477
$587$	−42.0000	−1.73353	−0.866763	−	0.498721i	$-0.833803\pi$
$587$	−42.0000	−1.73353	−0.866763	+	0.498721i	$0.833803\pi$
$588$	12.0000	0.494872
$589$	−45.0000	−1.85419
$590$	0	0
$591$	16.0000	0.658152
$592$	−4.00000	−0.164399
$593$	−16.0000	−0.657041	−0.328521	−	0.944497i	$-0.606550\pi$
$593$	−16.0000	−0.657041	−0.328521	+	0.944497i	$0.606550\pi$
$594$	0	0
$595$	0	0
$596$	−12.0000	−0.491539
$597$	11.0000	0.450200
$598$	−40.0000	−1.63572
$599$	24.0000	0.980613	0.490307	−	0.871550i	$-0.336885\pi$
$599$	24.0000	0.980613	0.490307	+	0.871550i	$0.336885\pi$
$600$	0	0
$601$	−17.0000	−0.693444	−0.346722	−	0.937968i	$-0.612705\pi$
$601$	−17.0000	−0.693444	−0.346722	+	0.937968i	$0.612705\pi$
$602$	−26.0000	−1.05968
$603$	−1.00000	−0.0407231
$604$	−34.0000	−1.38344
$605$	0	0
$606$	−20.0000	−0.812444
$607$	−40.0000	−1.62355	−0.811775	−	0.583970i	$-0.801498\pi$
$607$	−40.0000	−1.62355	−0.811775	+	0.583970i	$0.801498\pi$
$608$	−40.0000	−1.62221
$609$	2.00000	0.0810441
$610$	0	0
$611$	20.0000	0.809113
$612$	8.00000	0.323381
$613$	−2.00000	−0.0807792	−0.0403896	−	0.999184i	$-0.512860\pi$
$613$	−2.00000	−0.0807792	−0.0403896	+	0.999184i	$0.512860\pi$
$614$	10.0000	0.403567
$615$	0	0
$616$	0	0
$617$	16.0000	0.644136	0.322068	−	0.946717i	$-0.395622\pi$
$617$	16.0000	0.644136	0.322068	+	0.946717i	$0.395622\pi$
$618$	16.0000	0.643614
$619$	−21.0000	−0.844061	−0.422031	−	0.906582i	$-0.638683\pi$
$619$	−21.0000	−0.844061	−0.422031	+	0.906582i	$0.638683\pi$
$620$	0	0
$621$	4.00000	0.160514
$622$	0	0
$623$	−8.00000	−0.320513
$624$	20.0000	0.800641
$625$	0	0
$626$	−50.0000	−1.99840
$627$	0	0
$628$	−6.00000	−0.239426
$629$	4.00000	0.159490
$630$	0	0
$631$	−25.0000	−0.995234	−0.497617	−	0.867397i	$-0.665792\pi$
$631$	−25.0000	−0.995234	−0.497617	+	0.867397i	$0.665792\pi$
$632$	0	0
$633$	1.00000	0.0397464
$634$	40.0000	1.58860
$635$	0	0
$636$	−24.0000	−0.951662
$637$	−30.0000	−1.18864
$638$	0	0
$639$	−6.00000	−0.237356
$640$	0	0
$641$	18.0000	0.710957	0.355479	−	0.934684i	$-0.384318\pi$
$641$	18.0000	0.710957	0.355479	+	0.934684i	$0.384318\pi$
$642$	12.0000	0.473602
$643$	−44.0000	−1.73519	−0.867595	−	0.497271i	$-0.834335\pi$
$643$	−44.0000	−1.73519	−0.867595	+	0.497271i	$0.834335\pi$
$644$	8.00000	0.315244
$645$	0	0
$646$	40.0000	1.57378
$647$	−2.00000	−0.0786281	−0.0393141	−	0.999227i	$-0.512517\pi$
$647$	−2.00000	−0.0786281	−0.0393141	+	0.999227i	$0.512517\pi$
$648$	0	0
$649$	0	0
$650$	0	0
$651$	−9.00000	−0.352738
$652$	22.0000	0.861586
$653$	10.0000	0.391330	0.195665	−	0.980671i	$-0.437313\pi$
$653$	10.0000	0.391330	0.195665	+	0.980671i	$0.437313\pi$
$654$	−22.0000	−0.860268
$655$	0	0
$656$	−16.0000	−0.624695
$657$	10.0000	0.390137
$658$	−8.00000	−0.311872
$659$	−22.0000	−0.856998	−0.428499	−	0.903542i	$-0.640958\pi$
$659$	−22.0000	−0.856998	−0.428499	+	0.903542i	$0.640958\pi$
$660$	0	0
$661$	−18.0000	−0.700119	−0.350059	−	0.936727i	$-0.613839\pi$
$661$	−18.0000	−0.700119	−0.350059	+	0.936727i	$0.613839\pi$
$662$	8.00000	0.310929
$663$	−20.0000	−0.776736
$664$	0	0
$665$	0	0
$666$	2.00000	0.0774984
$667$	−8.00000	−0.309761
$668$	−48.0000	−1.85718
$669$	25.0000	0.966556
$670$	0	0
$671$	0	0
$672$	−8.00000	−0.308607
$673$	34.0000	1.31060	0.655302	−	0.755367i	$-0.272541\pi$
$673$	34.0000	1.31060	0.655302	+	0.755367i	$0.272541\pi$
$674$	38.0000	1.46371
$675$	0	0
$676$	24.0000	0.923077
$677$	22.0000	0.845529	0.422764	−	0.906240i	$-0.361060\pi$
$677$	22.0000	0.845529	0.422764	+	0.906240i	$0.361060\pi$
$678$	28.0000	1.07533
$679$	−1.00000	−0.0383765
$680$	0	0
$681$	−14.0000	−0.536481
$682$	0	0
$683$	−22.0000	−0.841807	−0.420903	−	0.907106i	$-0.638287\pi$
$683$	−22.0000	−0.841807	−0.420903	+	0.907106i	$0.638287\pi$
$684$	10.0000	0.382360
$685$	0	0
$686$	26.0000	0.992685
$687$	−9.00000	−0.343371
$688$	−52.0000	−1.98248
$689$	60.0000	2.28582
$690$	0	0
$691$	−20.0000	−0.760836	−0.380418	−	0.924815i	$-0.624220\pi$
$691$	−20.0000	−0.760836	−0.380418	+	0.924815i	$0.624220\pi$
$692$	−4.00000	−0.152057
$693$	0	0
$694$	−4.00000	−0.151838
$695$	0	0
$696$	0	0
$697$	16.0000	0.606043
$698$	−44.0000	−1.66542
$699$	10.0000	0.378235
$700$	0	0
$701$	−24.0000	−0.906467	−0.453234	−	0.891392i	$-0.649730\pi$
$701$	−24.0000	−0.906467	−0.453234	+	0.891392i	$0.649730\pi$
$702$	−10.0000	−0.377426
$703$	5.00000	0.188579
$704$	0	0
$705$	0	0
$706$	52.0000	1.95705
$707$	−10.0000	−0.376089
$708$	−24.0000	−0.901975
$709$	−1.00000	−0.0375558	−0.0187779	−	0.999824i	$-0.505978\pi$
$709$	−1.00000	−0.0375558	−0.0187779	+	0.999824i	$0.505978\pi$
$710$	0	0
$711$	0	0
$712$	0	0
$713$	36.0000	1.34821
$714$	8.00000	0.299392
$715$	0	0
$716$	−20.0000	−0.747435
$717$	−6.00000	−0.224074
$718$	12.0000	0.447836
$719$	12.0000	0.447524	0.223762	−	0.974644i	$-0.428166\pi$
$719$	12.0000	0.447524	0.223762	+	0.974644i	$0.428166\pi$
$720$	0	0
$721$	8.00000	0.297936
$722$	12.0000	0.446594
$723$	17.0000	0.632237
$724$	−22.0000	−0.817624
$725$	0	0
$726$	22.0000	0.816497
$727$	−43.0000	−1.59478	−0.797391	−	0.603463i	$-0.793787\pi$
$727$	−43.0000	−1.59478	−0.797391	+	0.603463i	$0.793787\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	0	0
$731$	52.0000	1.92329
$732$	−10.0000	−0.369611
$733$	34.0000	1.25582	0.627909	−	0.778287i	$-0.283911\pi$
$733$	34.0000	1.25582	0.627909	+	0.778287i	$0.283911\pi$
$734$	34.0000	1.25496
$735$	0	0
$736$	32.0000	1.17954
$737$	0	0
$738$	8.00000	0.294484
$739$	12.0000	0.441427	0.220714	−	0.975339i	$-0.429161\pi$
$739$	12.0000	0.441427	0.220714	+	0.975339i	$0.429161\pi$
$740$	0	0
$741$	−25.0000	−0.918398
$742$	−24.0000	−0.881068
$743$	0	0		−	1.00000i	$-0.5\pi$
$743$	0	0			1.00000i	$0.5\pi$
$744$	0	0
$745$	0	0
$746$	18.0000	0.659027
$747$	18.0000	0.658586
$748$	0	0
$749$	6.00000	0.219235
$750$	0	0
$751$	40.0000	1.45962	0.729810	−	0.683650i	$-0.239608\pi$
$751$	40.0000	1.45962	0.729810	+	0.683650i	$0.239608\pi$
$752$	−16.0000	−0.583460
$753$	20.0000	0.728841
$754$	20.0000	0.728357
$755$	0	0
$756$	2.00000	0.0727393
$757$	−15.0000	−0.545184	−0.272592	−	0.962130i	$-0.587881\pi$
$757$	−15.0000	−0.545184	−0.272592	+	0.962130i	$0.587881\pi$
$758$	50.0000	1.81608
$759$	0	0
$760$	0	0
$761$	14.0000	0.507500	0.253750	−	0.967270i	$-0.418336\pi$
$761$	14.0000	0.507500	0.253750	+	0.967270i	$0.418336\pi$
$762$	−16.0000	−0.579619
$763$	−11.0000	−0.398227
$764$	−4.00000	−0.144715
$765$	0	0
$766$	24.0000	0.867155
$767$	60.0000	2.16647
$768$	−16.0000	−0.577350
$769$	−35.0000	−1.26213	−0.631066	−	0.775729i	$-0.717382\pi$
$769$	−35.0000	−1.26213	−0.631066	+	0.775729i	$0.717382\pi$
$770$	0	0
$771$	−24.0000	−0.864339
$772$	−10.0000	−0.359908
$773$	−48.0000	−1.72644	−0.863220	−	0.504828i	$-0.831556\pi$
$773$	−48.0000	−1.72644	−0.863220	+	0.504828i	$0.831556\pi$
$774$	26.0000	0.934551
$775$	0	0
$776$	0	0
$777$	1.00000	0.0358748
$778$	36.0000	1.29066
$779$	20.0000	0.716574
$780$	0	0
$781$	0	0
$782$	−32.0000	−1.14432
$783$	−2.00000	−0.0714742
$784$	24.0000	0.857143
$785$	0	0
$786$	12.0000	0.428026
$787$	−35.0000	−1.24762	−0.623808	−	0.781578i	$-0.714415\pi$
$787$	−35.0000	−1.24762	−0.623808	+	0.781578i	$0.714415\pi$
$788$	−32.0000	−1.13995
$789$	4.00000	0.142404
$790$	0	0
$791$	14.0000	0.497783
$792$	0	0
$793$	25.0000	0.887776
$794$	−54.0000	−1.91639
$795$	0	0
$796$	−22.0000	−0.779769
$797$	−2.00000	−0.0708436	−0.0354218	−	0.999372i	$-0.511277\pi$
$797$	−2.00000	−0.0708436	−0.0354218	+	0.999372i	$0.511277\pi$
$798$	10.0000	0.353996
$799$	16.0000	0.566039
$800$	0	0
$801$	8.00000	0.282666
$802$	−60.0000	−2.11867
$803$	0	0
$804$	2.00000	0.0705346
$805$	0	0
$806$	−90.0000	−3.17011
$807$	12.0000	0.422420
$808$	0	0
$809$	28.0000	0.984428	0.492214	−	0.870474i	$-0.336188\pi$
$809$	28.0000	0.984428	0.492214	+	0.870474i	$0.336188\pi$
$810$	0	0
$811$	−53.0000	−1.86108	−0.930541	−	0.366188i	$-0.880663\pi$
$811$	−53.0000	−1.86108	−0.930541	+	0.366188i	$0.880663\pi$
$812$	−4.00000	−0.140372
$813$	24.0000	0.841717
$814$	0	0
$815$	0	0
$816$	16.0000	0.560112
$817$	65.0000	2.27406
$818$	70.0000	2.44749
$819$	−5.00000	−0.174714
$820$	0	0
$821$	30.0000	1.04701	0.523504	−	0.852023i	$-0.324625\pi$
$821$	30.0000	1.04701	0.523504	+	0.852023i	$0.324625\pi$
$822$	−24.0000	−0.837096
$823$	−41.0000	−1.42917	−0.714585	−	0.699549i	$-0.753384\pi$
$823$	−41.0000	−1.42917	−0.714585	+	0.699549i	$0.753384\pi$
$824$	0	0
$825$	0	0
$826$	−24.0000	−0.835067
$827$	30.0000	1.04320	0.521601	−	0.853189i	$-0.325335\pi$
$827$	30.0000	1.04320	0.521601	+	0.853189i	$0.325335\pi$
$828$	−8.00000	−0.278019
$829$	26.0000	0.903017	0.451509	−	0.892267i	$-0.350886\pi$
$829$	26.0000	0.903017	0.451509	+	0.892267i	$0.350886\pi$
$830$	0	0
$831$	−13.0000	−0.450965
$832$	−40.0000	−1.38675
$833$	−24.0000	−0.831551
$834$	32.0000	1.10807
$835$	0	0
$836$	0	0
$837$	9.00000	0.311086
$838$	60.0000	2.07267
$839$	30.0000	1.03572	0.517858	−	0.855467i	$-0.326730\pi$
$839$	30.0000	1.03572	0.517858	+	0.855467i	$0.326730\pi$
$840$	0	0
$841$	−25.0000	−0.862069
$842$	4.00000	0.137849
$843$	−8.00000	−0.275535
$844$	−2.00000	−0.0688428
$845$	0	0
$846$	8.00000	0.275046
$847$	11.0000	0.377964
$848$	−48.0000	−1.64833
$849$	−31.0000	−1.06392
$850$	0	0
$851$	−4.00000	−0.137118
$852$	12.0000	0.411113
$853$	3.00000	0.102718	0.0513590	−	0.998680i	$-0.483645\pi$
$853$	3.00000	0.102718	0.0513590	+	0.998680i	$0.483645\pi$
$854$	−10.0000	−0.342193
$855$	0	0
$856$	0	0
$857$	−2.00000	−0.0683187	−0.0341593	−	0.999416i	$-0.510875\pi$
$857$	−2.00000	−0.0683187	−0.0341593	+	0.999416i	$0.510875\pi$
$858$	0	0
$859$	28.0000	0.955348	0.477674	−	0.878537i	$-0.341480\pi$
$859$	28.0000	0.955348	0.477674	+	0.878537i	$0.341480\pi$
$860$	0	0
$861$	4.00000	0.136320
$862$	24.0000	0.817443
$863$	54.0000	1.83818	0.919091	−	0.394046i	$-0.128925\pi$
$863$	54.0000	1.83818	0.919091	+	0.394046i	$0.128925\pi$
$864$	8.00000	0.272166
$865$	0	0
$866$	10.0000	0.339814
$867$	1.00000	0.0339618
$868$	18.0000	0.610960
$869$	0	0
$870$	0	0
$871$	−5.00000	−0.169419
$872$	0	0
$873$	1.00000	0.0338449
$874$	−40.0000	−1.35302
$875$	0	0
$876$	−20.0000	−0.675737
$877$	53.0000	1.78968	0.894841	−	0.446384i	$-0.147289\pi$
$877$	53.0000	1.78968	0.894841	+	0.446384i	$0.147289\pi$
$878$	14.0000	0.472477
$879$	4.00000	0.134917
$880$	0	0
$881$	20.0000	0.673817	0.336909	−	0.941537i	$-0.390619\pi$
$881$	20.0000	0.673817	0.336909	+	0.941537i	$0.390619\pi$
$882$	−12.0000	−0.404061
$883$	−43.0000	−1.44707	−0.723533	−	0.690290i	$-0.757483\pi$
$883$	−43.0000	−1.44707	−0.723533	+	0.690290i	$0.757483\pi$
$884$	40.0000	1.34535
$885$	0	0
$886$	12.0000	0.403148
$887$	20.0000	0.671534	0.335767	−	0.941945i	$-0.391004\pi$
$887$	20.0000	0.671534	0.335767	+	0.941945i	$0.391004\pi$
$888$	0	0
$889$	−8.00000	−0.268311
$890$	0	0
$891$	0	0
$892$	−50.0000	−1.67412
$893$	20.0000	0.669274
$894$	12.0000	0.401340
$895$	0	0
$896$	0	0
$897$	20.0000	0.667781
$898$	−68.0000	−2.26919
$899$	−18.0000	−0.600334
$900$	0	0
$901$	48.0000	1.59911
$902$	0	0
$903$	13.0000	0.432613
$904$	0	0
$905$	0	0
$906$	34.0000	1.12957
$907$	4.00000	0.132818	0.0664089	−	0.997792i	$-0.478846\pi$
$907$	4.00000	0.132818	0.0664089	+	0.997792i	$0.478846\pi$
$908$	28.0000	0.929213
$909$	10.0000	0.331679
$910$	0	0
$911$	−28.0000	−0.927681	−0.463841	−	0.885919i	$-0.653529\pi$
$911$	−28.0000	−0.927681	−0.463841	+	0.885919i	$0.653529\pi$
$912$	20.0000	0.662266
$913$	0	0
$914$	12.0000	0.396925
$915$	0	0
$916$	18.0000	0.594737
$917$	6.00000	0.198137
$918$	−8.00000	−0.264039
$919$	13.0000	0.428830	0.214415	−	0.976743i	$-0.431215\pi$
$919$	13.0000	0.428830	0.214415	+	0.976743i	$0.431215\pi$
$920$	0	0
$921$	−5.00000	−0.164756
$922$	−84.0000	−2.76639
$923$	−30.0000	−0.987462
$924$	0	0
$925$	0	0
$926$	−32.0000	−1.05159
$927$	−8.00000	−0.262754
$928$	−16.0000	−0.525226
$929$	−8.00000	−0.262471	−0.131236	−	0.991351i	$-0.541894\pi$
$929$	−8.00000	−0.262471	−0.131236	+	0.991351i	$0.541894\pi$
$930$	0	0
$931$	−30.0000	−0.983210
$932$	−20.0000	−0.655122
$933$	0	0
$934$	56.0000	1.83238
$935$	0	0
$936$	0	0
$937$	−39.0000	−1.27407	−0.637037	−	0.770833i	$-0.719840\pi$
$937$	−39.0000	−1.27407	−0.637037	+	0.770833i	$0.719840\pi$
$938$	2.00000	0.0653023
$939$	25.0000	0.815844
$940$	0	0
$941$	−2.00000	−0.0651981	−0.0325991	−	0.999469i	$-0.510378\pi$
$941$	−2.00000	−0.0651981	−0.0325991	+	0.999469i	$0.510378\pi$
$942$	6.00000	0.195491
$943$	−16.0000	−0.521032
$944$	−48.0000	−1.56227
$945$	0	0
$946$	0	0
$947$	22.0000	0.714904	0.357452	−	0.933932i	$-0.383646\pi$
$947$	22.0000	0.714904	0.357452	+	0.933932i	$0.383646\pi$
$948$	0	0
$949$	50.0000	1.62307
$950$	0	0
$951$	−20.0000	−0.648544
$952$	0	0
$953$	6.00000	0.194359	0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000	0.194359	0.0971795	+	0.995267i	$0.469018\pi$
$954$	24.0000	0.777029
$955$	0	0
$956$	12.0000	0.388108
$957$	0	0
$958$	−36.0000	−1.16311
$959$	−12.0000	−0.387500
$960$	0	0
$961$	50.0000	1.61290
$962$	10.0000	0.322413
$963$	−6.00000	−0.193347
$964$	−34.0000	−1.09507
$965$	0	0
$966$	−8.00000	−0.257396
$967$	−40.0000	−1.28631	−0.643157	−	0.765735i	$-0.722376\pi$
$967$	−40.0000	−1.28631	−0.643157	+	0.765735i	$0.722376\pi$
$968$	0	0
$969$	−20.0000	−0.642493
$970$	0	0
$971$	24.0000	0.770197	0.385098	−	0.922876i	$-0.374168\pi$
$971$	24.0000	0.770197	0.385098	+	0.922876i	$0.374168\pi$
$972$	−2.00000	−0.0641500
$973$	16.0000	0.512936
$974$	−66.0000	−2.11478
$975$	0	0
$976$	−20.0000	−0.640184
$977$	8.00000	0.255943	0.127971	−	0.991778i	$-0.459153\pi$
$977$	8.00000	0.255943	0.127971	+	0.991778i	$0.459153\pi$
$978$	−22.0000	−0.703482
$979$	0	0
$980$	0	0
$981$	11.0000	0.351203
$982$	4.00000	0.127645
$983$	22.0000	0.701691	0.350846	−	0.936433i	$-0.385894\pi$
$983$	22.0000	0.701691	0.350846	+	0.936433i	$0.385894\pi$
$984$	0	0
$985$	0	0
$986$	16.0000	0.509544
$987$	4.00000	0.127321
$988$	50.0000	1.59071
$989$	−52.0000	−1.65350
$990$	0	0
$991$	−25.0000	−0.794151	−0.397076	−	0.917786i	$-0.629975\pi$
$991$	−25.0000	−0.794151	−0.397076	+	0.917786i	$0.629975\pi$
$992$	72.0000	2.28600
$993$	−4.00000	−0.126936
$994$	12.0000	0.380617
$995$	0	0
$996$	−36.0000	−1.14070
$997$	−6.00000	−0.190022	−0.0950110	−	0.995476i	$-0.530289\pi$
$997$	−6.00000	−0.190022	−0.0950110	+	0.995476i	$0.530289\pi$
$998$	10.0000	0.316544
$999$	−1.00000	−0.0316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2775.2.a.i.1.1	yes	1
3.2	odd	2		8325.2.a.c.1.1		1
5.4	even	2		2775.2.a.b.1.1	✓	1
15.14	odd	2		8325.2.a.be.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2775.2.a.b.1.1	✓	1	5.4	even	2
2775.2.a.i.1.1	yes	1	1.1	even	1	trivial
8325.2.a.c.1.1		1	3.2	odd	2
8325.2.a.be.1.1		1	15.14	odd	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:	\( N \)	\(=\)	\( 2775 = 3 \cdot 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2775.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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