LMFDB - Embedded newform 2790.2.a.w.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2790,2,Mod(1,2790)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2790, 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("2790.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2790 = 2 \cdot 3^{2} \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2790.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:	$22.2782621639$
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	$\chi$	$=$	2790.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

$q+1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{5} +4.00000 q^{7} +1.00000 q^{8} -1.00000 q^{10} +4.00000 q^{11} +2.00000 q^{13} +4.00000 q^{14} +1.00000 q^{16} -1.00000 q^{20} +4.00000 q^{22} -2.00000 q^{23} +1.00000 q^{25} +2.00000 q^{26} +4.00000 q^{28} -2.00000 q^{29} -1.00000 q^{31} +1.00000 q^{32} -4.00000 q^{35} +2.00000 q^{37} -1.00000 q^{40} +4.00000 q^{43} +4.00000 q^{44} -2.00000 q^{46} +9.00000 q^{49} +1.00000 q^{50} +2.00000 q^{52} -10.0000 q^{53} -4.00000 q^{55} +4.00000 q^{56} -2.00000 q^{58} -4.00000 q^{59} +8.00000 q^{61} -1.00000 q^{62} +1.00000 q^{64} -2.00000 q^{65} -2.00000 q^{67} -4.00000 q^{70} -6.00000 q^{71} +2.00000 q^{73} +2.00000 q^{74} +16.0000 q^{77} -1.00000 q^{80} -4.00000 q^{83} +4.00000 q^{86} +4.00000 q^{88} +6.00000 q^{89} +8.00000 q^{91} -2.00000 q^{92} +10.0000 q^{97} +9.00000 q^{98} +O(q^{100})$

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
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0	0
$7$	4.00000	1.51186	0.755929	−	0.654654i	$-0.227186\pi$
$7$	4.00000	1.51186	0.755929	+	0.654654i	$0.227186\pi$
$8$	1.00000	0.353553
$9$	0	0
$10$	−1.00000	−0.316228
$11$	4.00000	1.20605	0.603023	−	0.797724i	$-0.293963\pi$
$11$	4.00000	1.20605	0.603023	+	0.797724i	$0.293963\pi$
$12$	0	0
$13$	2.00000	0.554700	0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000	0.554700	0.277350	+	0.960769i	$0.410544\pi$
$14$	4.00000	1.06904
$15$	0	0
$16$	1.00000	0.250000
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	0	0
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	−1.00000	−0.223607
$21$	0	0
$22$	4.00000	0.852803
$23$	−2.00000	−0.417029	−0.208514	−	0.978019i	$-0.566863\pi$
$23$	−2.00000	−0.417029	−0.208514	+	0.978019i	$0.566863\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	2.00000	0.392232
$27$	0	0
$28$	4.00000	0.755929
$29$	−2.00000	−0.371391	−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000	−0.371391	−0.185695	+	0.982607i	$0.559454\pi$
$30$	0	0
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	1.00000	0.176777
$33$	0	0
$34$	0	0
$35$	−4.00000	−0.676123
$36$	0	0
$37$	2.00000	0.328798	0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000	0.328798	0.164399	+	0.986394i	$0.447432\pi$
$38$	0	0
$39$	0	0
$40$	−1.00000	−0.158114
$41$	0	0		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	0	0
$43$	4.00000	0.609994	0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000	0.609994	0.304997	+	0.952353i	$0.401344\pi$
$44$	4.00000	0.603023
$45$	0	0
$46$	−2.00000	−0.294884
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	0	0
$49$	9.00000	1.28571
$50$	1.00000	0.141421
$51$	0	0
$52$	2.00000	0.277350
$53$	−10.0000	−1.37361	−0.686803	−	0.726844i	$-0.740986\pi$
$53$	−10.0000	−1.37361	−0.686803	+	0.726844i	$0.740986\pi$
$54$	0	0
$55$	−4.00000	−0.539360
$56$	4.00000	0.534522
$57$	0	0
$58$	−2.00000	−0.262613
$59$	−4.00000	−0.520756	−0.260378	−	0.965507i	$-0.583847\pi$
$59$	−4.00000	−0.520756	−0.260378	+	0.965507i	$0.583847\pi$
$60$	0	0
$61$	8.00000	1.02430	0.512148	−	0.858898i	$-0.328850\pi$
$61$	8.00000	1.02430	0.512148	+	0.858898i	$0.328850\pi$
$62$	−1.00000	−0.127000
$63$	0	0
$64$	1.00000	0.125000
$65$	−2.00000	−0.248069
$66$	0	0
$67$	−2.00000	−0.244339	−0.122169	−	0.992509i	$-0.538985\pi$
$67$	−2.00000	−0.244339	−0.122169	+	0.992509i	$0.538985\pi$
$68$	0	0
$69$	0	0
$70$	−4.00000	−0.478091
$71$	−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
$73$	2.00000	0.234082	0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000	0.234082	0.117041	+	0.993127i	$0.462659\pi$
$74$	2.00000	0.232495
$75$	0	0
$76$	0	0
$77$	16.0000	1.82337
$78$	0	0
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	−1.00000	−0.111803
$81$	0	0
$82$	0	0
$83$	−4.00000	−0.439057	−0.219529	−	0.975606i	$-0.570452\pi$
$83$	−4.00000	−0.439057	−0.219529	+	0.975606i	$0.570452\pi$
$84$	0	0
$85$	0	0
$86$	4.00000	0.431331
$87$	0	0
$88$	4.00000	0.426401
$89$	6.00000	0.635999	0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000	0.635999	0.317999	+	0.948091i	$0.396989\pi$
$90$	0	0
$91$	8.00000	0.838628
$92$	−2.00000	−0.208514
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	10.0000	1.01535	0.507673	−	0.861550i	$-0.330506\pi$
$97$	10.0000	1.01535	0.507673	+	0.861550i	$0.330506\pi$
$98$	9.00000	0.909137
$99$	0	0
$100$	1.00000	0.100000
$101$	6.00000	0.597022	0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000	0.597022	0.298511	+	0.954406i	$0.403510\pi$
$102$	0	0
$103$	−8.00000	−0.788263	−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000	−0.788263	−0.394132	+	0.919054i	$0.628955\pi$
$104$	2.00000	0.196116
$105$	0	0
$106$	−10.0000	−0.971286
$107$	12.0000	1.16008	0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000	1.16008	0.580042	+	0.814587i	$0.303036\pi$
$108$	0	0
$109$	−6.00000	−0.574696	−0.287348	−	0.957826i	$-0.592774\pi$
$109$	−6.00000	−0.574696	−0.287348	+	0.957826i	$0.592774\pi$
$110$	−4.00000	−0.381385
$111$	0	0
$112$	4.00000	0.377964
$113$	6.00000	0.564433	0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000	0.564433	0.282216	+	0.959351i	$0.408930\pi$
$114$	0	0
$115$	2.00000	0.186501
$116$	−2.00000	−0.185695
$117$	0	0
$118$	−4.00000	−0.368230
$119$	0	0
$120$	0	0
$121$	5.00000	0.454545
$122$	8.00000	0.724286
$123$	0	0
$124$	−1.00000	−0.0898027
$125$	−1.00000	−0.0894427
$126$	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
$130$	−2.00000	−0.175412
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	0	0
$133$	0	0
$134$	−2.00000	−0.172774
$135$	0	0
$136$	0	0
$137$	4.00000	0.341743	0.170872	−	0.985293i	$-0.445342\pi$
$137$	4.00000	0.341743	0.170872	+	0.985293i	$0.445342\pi$
$138$	0	0
$139$	14.0000	1.18746	0.593732	−	0.804663i	$-0.297654\pi$
$139$	14.0000	1.18746	0.593732	+	0.804663i	$0.297654\pi$
$140$	−4.00000	−0.338062
$141$	0	0
$142$	−6.00000	−0.503509
$143$	8.00000	0.668994
$144$	0	0
$145$	2.00000	0.166091
$146$	2.00000	0.165521
$147$	0	0
$148$	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
$151$	20.0000	1.62758	0.813788	−	0.581161i	$-0.197401\pi$
$151$	20.0000	1.62758	0.813788	+	0.581161i	$0.197401\pi$
$152$	0	0
$153$	0	0
$154$	16.0000	1.28932
$155$	1.00000	0.0803219
$156$	0	0
$157$	12.0000	0.957704	0.478852	−	0.877896i	$-0.341053\pi$
$157$	12.0000	0.957704	0.478852	+	0.877896i	$0.341053\pi$
$158$	0	0
$159$	0	0
$160$	−1.00000	−0.0790569
$161$	−8.00000	−0.630488
$162$	0	0
$163$	−14.0000	−1.09656	−0.548282	−	0.836293i	$-0.684718\pi$
$163$	−14.0000	−1.09656	−0.548282	+	0.836293i	$0.684718\pi$
$164$	0	0
$165$	0	0
$166$	−4.00000	−0.310460
$167$	6.00000	0.464294	0.232147	−	0.972681i	$-0.425425\pi$
$167$	6.00000	0.464294	0.232147	+	0.972681i	$0.425425\pi$
$168$	0	0
$169$	−9.00000	−0.692308
$170$	0	0
$171$	0	0
$172$	4.00000	0.304997
$173$	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
$175$	4.00000	0.302372
$176$	4.00000	0.301511
$177$	0	0
$178$	6.00000	0.449719
$179$	−20.0000	−1.49487	−0.747435	−	0.664335i	$-0.768715\pi$
$179$	−20.0000	−1.49487	−0.747435	+	0.664335i	$0.768715\pi$
$180$	0	0
$181$	4.00000	0.297318	0.148659	−	0.988889i	$-0.452504\pi$
$181$	4.00000	0.297318	0.148659	+	0.988889i	$0.452504\pi$
$182$	8.00000	0.592999
$183$	0	0
$184$	−2.00000	−0.147442
$185$	−2.00000	−0.147043
$186$	0	0
$187$	0	0
$188$	0	0
$189$	0	0
$190$	0	0
$191$	−2.00000	−0.144715	−0.0723575	−	0.997379i	$-0.523052\pi$
$191$	−2.00000	−0.144715	−0.0723575	+	0.997379i	$0.523052\pi$
$192$	0	0
$193$	14.0000	1.00774	0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000	1.00774	0.503871	+	0.863779i	$0.331909\pi$
$194$	10.0000	0.717958
$195$	0	0
$196$	9.00000	0.642857
$197$	−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
$199$	4.00000	0.283552	0.141776	−	0.989899i	$-0.454719\pi$
$199$	4.00000	0.283552	0.141776	+	0.989899i	$0.454719\pi$
$200$	1.00000	0.0707107
$201$	0	0
$202$	6.00000	0.422159
$203$	−8.00000	−0.561490
$204$	0	0
$205$	0	0
$206$	−8.00000	−0.557386
$207$	0	0
$208$	2.00000	0.138675
$209$	0	0
$210$	0	0
$211$	0	0		−	1.00000i	$-0.5\pi$
$211$	0	0			1.00000i	$0.5\pi$
$212$	−10.0000	−0.686803
$213$	0	0
$214$	12.0000	0.820303
$215$	−4.00000	−0.272798
$216$	0	0
$217$	−4.00000	−0.271538
$218$	−6.00000	−0.406371
$219$	0	0
$220$	−4.00000	−0.269680
$221$	0	0
$222$	0	0
$223$	−24.0000	−1.60716	−0.803579	−	0.595198i	$-0.797074\pi$
$223$	−24.0000	−1.60716	−0.803579	+	0.595198i	$0.797074\pi$
$224$	4.00000	0.267261
$225$	0	0
$226$	6.00000	0.399114
$227$	−12.0000	−0.796468	−0.398234	−	0.917284i	$-0.630377\pi$
$227$	−12.0000	−0.796468	−0.398234	+	0.917284i	$0.630377\pi$
$228$	0	0
$229$	4.00000	0.264327	0.132164	−	0.991228i	$-0.457808\pi$
$229$	4.00000	0.264327	0.132164	+	0.991228i	$0.457808\pi$
$230$	2.00000	0.131876
$231$	0	0
$232$	−2.00000	−0.131306
$233$	−30.0000	−1.96537	−0.982683	−	0.185296i	$-0.940675\pi$
$233$	−30.0000	−1.96537	−0.982683	+	0.185296i	$0.940675\pi$
$234$	0	0
$235$	0	0
$236$	−4.00000	−0.260378
$237$	0	0
$238$	0	0
$239$	8.00000	0.517477	0.258738	−	0.965947i	$-0.416693\pi$
$239$	8.00000	0.517477	0.258738	+	0.965947i	$0.416693\pi$
$240$	0	0
$241$	26.0000	1.67481	0.837404	−	0.546585i	$-0.184072\pi$
$241$	26.0000	1.67481	0.837404	+	0.546585i	$0.184072\pi$
$242$	5.00000	0.321412
$243$	0	0
$244$	8.00000	0.512148
$245$	−9.00000	−0.574989
$246$	0	0
$247$	0	0
$248$	−1.00000	−0.0635001
$249$	0	0
$250$	−1.00000	−0.0632456
$251$	−28.0000	−1.76734	−0.883672	−	0.468106i	$-0.844936\pi$
$251$	−28.0000	−1.76734	−0.883672	+	0.468106i	$0.844936\pi$
$252$	0	0
$253$	−8.00000	−0.502956
$254$	−8.00000	−0.501965
$255$	0	0
$256$	1.00000	0.0625000
$257$	14.0000	0.873296	0.436648	−	0.899632i	$-0.356166\pi$
$257$	14.0000	0.873296	0.436648	+	0.899632i	$0.356166\pi$
$258$	0	0
$259$	8.00000	0.497096
$260$	−2.00000	−0.124035
$261$	0	0
$262$	0	0
$263$	18.0000	1.10993	0.554964	−	0.831875i	$-0.312732\pi$
$263$	18.0000	1.10993	0.554964	+	0.831875i	$0.312732\pi$
$264$	0	0
$265$	10.0000	0.614295
$266$	0	0
$267$	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
$271$	−4.00000	−0.242983	−0.121491	−	0.992592i	$-0.538768\pi$
$271$	−4.00000	−0.242983	−0.121491	+	0.992592i	$0.538768\pi$
$272$	0	0
$273$	0	0
$274$	4.00000	0.241649
$275$	4.00000	0.241209
$276$	0	0
$277$	−10.0000	−0.600842	−0.300421	−	0.953807i	$-0.597127\pi$
$277$	−10.0000	−0.600842	−0.300421	+	0.953807i	$0.597127\pi$
$278$	14.0000	0.839664
$279$	0	0
$280$	−4.00000	−0.239046
$281$	−24.0000	−1.43172	−0.715860	−	0.698244i	$-0.753965\pi$
$281$	−24.0000	−1.43172	−0.715860	+	0.698244i	$0.753965\pi$
$282$	0	0
$283$	−22.0000	−1.30776	−0.653882	−	0.756596i	$-0.726861\pi$
$283$	−22.0000	−1.30776	−0.653882	+	0.756596i	$0.726861\pi$
$284$	−6.00000	−0.356034
$285$	0	0
$286$	8.00000	0.473050
$287$	0	0
$288$	0	0
$289$	−17.0000	−1.00000
$290$	2.00000	0.117444
$291$	0	0
$292$	2.00000	0.117041
$293$	6.00000	0.350524	0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000	0.350524	0.175262	+	0.984522i	$0.443923\pi$
$294$	0	0
$295$	4.00000	0.232889
$296$	2.00000	0.116248
$297$	0	0
$298$	−6.00000	−0.347571
$299$	−4.00000	−0.231326
$300$	0	0
$301$	16.0000	0.922225
$302$	20.0000	1.15087
$303$	0	0
$304$	0	0
$305$	−8.00000	−0.458079
$306$	0	0
$307$	30.0000	1.71219	0.856095	−	0.516818i	$-0.172884\pi$
$307$	30.0000	1.71219	0.856095	+	0.516818i	$0.172884\pi$
$308$	16.0000	0.911685
$309$	0	0
$310$	1.00000	0.0567962
$311$	−22.0000	−1.24751	−0.623753	−	0.781622i	$-0.714393\pi$
$311$	−22.0000	−1.24751	−0.623753	+	0.781622i	$0.714393\pi$
$312$	0	0
$313$	6.00000	0.339140	0.169570	−	0.985518i	$-0.445762\pi$
$313$	6.00000	0.339140	0.169570	+	0.985518i	$0.445762\pi$
$314$	12.0000	0.677199
$315$	0	0
$316$	0	0
$317$	−6.00000	−0.336994	−0.168497	−	0.985702i	$-0.553891\pi$
$317$	−6.00000	−0.336994	−0.168497	+	0.985702i	$0.553891\pi$
$318$	0	0
$319$	−8.00000	−0.447914
$320$	−1.00000	−0.0559017
$321$	0	0
$322$	−8.00000	−0.445823
$323$	0	0
$324$	0	0
$325$	2.00000	0.110940
$326$	−14.0000	−0.775388
$327$	0	0
$328$	0	0
$329$	0	0
$330$	0	0
$331$	−2.00000	−0.109930	−0.0549650	−	0.998488i	$-0.517505\pi$
$331$	−2.00000	−0.109930	−0.0549650	+	0.998488i	$0.517505\pi$
$332$	−4.00000	−0.219529
$333$	0	0
$334$	6.00000	0.328305
$335$	2.00000	0.109272
$336$	0	0
$337$	−2.00000	−0.108947	−0.0544735	−	0.998515i	$-0.517348\pi$
$337$	−2.00000	−0.108947	−0.0544735	+	0.998515i	$0.517348\pi$
$338$	−9.00000	−0.489535
$339$	0	0
$340$	0	0
$341$	−4.00000	−0.216612
$342$	0	0
$343$	8.00000	0.431959
$344$	4.00000	0.215666
$345$	0	0
$346$	2.00000	0.107521
$347$	12.0000	0.644194	0.322097	−	0.946707i	$-0.395612\pi$
$347$	12.0000	0.644194	0.322097	+	0.946707i	$0.395612\pi$
$348$	0	0
$349$	−26.0000	−1.39175	−0.695874	−	0.718164i	$-0.744983\pi$
$349$	−26.0000	−1.39175	−0.695874	+	0.718164i	$0.744983\pi$
$350$	4.00000	0.213809
$351$	0	0
$352$	4.00000	0.213201
$353$	4.00000	0.212899	0.106449	−	0.994318i	$-0.466052\pi$
$353$	4.00000	0.212899	0.106449	+	0.994318i	$0.466052\pi$
$354$	0	0
$355$	6.00000	0.318447
$356$	6.00000	0.317999
$357$	0	0
$358$	−20.0000	−1.05703
$359$	14.0000	0.738892	0.369446	−	0.929252i	$-0.379548\pi$
$359$	14.0000	0.738892	0.369446	+	0.929252i	$0.379548\pi$
$360$	0	0
$361$	−19.0000	−1.00000
$362$	4.00000	0.210235
$363$	0	0
$364$	8.00000	0.419314
$365$	−2.00000	−0.104685
$366$	0	0
$367$	−24.0000	−1.25279	−0.626395	−	0.779506i	$-0.715470\pi$
$367$	−24.0000	−1.25279	−0.626395	+	0.779506i	$0.715470\pi$
$368$	−2.00000	−0.104257
$369$	0	0
$370$	−2.00000	−0.103975
$371$	−40.0000	−2.07670
$372$	0	0
$373$	−36.0000	−1.86401	−0.932005	−	0.362446i	$-0.881942\pi$
$373$	−36.0000	−1.86401	−0.932005	+	0.362446i	$0.881942\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	−4.00000	−0.206010
$378$	0	0
$379$	12.0000	0.616399	0.308199	−	0.951322i	$-0.400274\pi$
$379$	12.0000	0.616399	0.308199	+	0.951322i	$0.400274\pi$
$380$	0	0
$381$	0	0
$382$	−2.00000	−0.102329
$383$	6.00000	0.306586	0.153293	−	0.988181i	$-0.451012\pi$
$383$	6.00000	0.306586	0.153293	+	0.988181i	$0.451012\pi$
$384$	0	0
$385$	−16.0000	−0.815436
$386$	14.0000	0.712581
$387$	0	0
$388$	10.0000	0.507673
$389$	−26.0000	−1.31825	−0.659126	−	0.752032i	$-0.729074\pi$
$389$	−26.0000	−1.31825	−0.659126	+	0.752032i	$0.729074\pi$
$390$	0	0
$391$	0	0
$392$	9.00000	0.454569
$393$	0	0
$394$	−10.0000	−0.503793
$395$	0	0
$396$	0	0
$397$	4.00000	0.200754	0.100377	−	0.994949i	$-0.467995\pi$
$397$	4.00000	0.200754	0.100377	+	0.994949i	$0.467995\pi$
$398$	4.00000	0.200502
$399$	0	0
$400$	1.00000	0.0500000
$401$	−14.0000	−0.699127	−0.349563	−	0.936913i	$-0.613670\pi$
$401$	−14.0000	−0.699127	−0.349563	+	0.936913i	$0.613670\pi$
$402$	0	0
$403$	−2.00000	−0.0996271
$404$	6.00000	0.298511
$405$	0	0
$406$	−8.00000	−0.397033
$407$	8.00000	0.396545
$408$	0	0
$409$	−14.0000	−0.692255	−0.346128	−	0.938187i	$-0.612504\pi$
$409$	−14.0000	−0.692255	−0.346128	+	0.938187i	$0.612504\pi$
$410$	0	0
$411$	0	0
$412$	−8.00000	−0.394132
$413$	−16.0000	−0.787309
$414$	0	0
$415$	4.00000	0.196352
$416$	2.00000	0.0980581
$417$	0	0
$418$	0	0
$419$	−4.00000	−0.195413	−0.0977064	−	0.995215i	$-0.531151\pi$
$419$	−4.00000	−0.195413	−0.0977064	+	0.995215i	$0.531151\pi$
$420$	0	0
$421$	10.0000	0.487370	0.243685	−	0.969854i	$-0.421644\pi$
$421$	10.0000	0.487370	0.243685	+	0.969854i	$0.421644\pi$
$422$	0	0
$423$	0	0
$424$	−10.0000	−0.485643
$425$	0	0
$426$	0	0
$427$	32.0000	1.54859
$428$	12.0000	0.580042
$429$	0	0
$430$	−4.00000	−0.192897
$431$	−18.0000	−0.867029	−0.433515	−	0.901146i	$-0.642727\pi$
$431$	−18.0000	−0.867029	−0.433515	+	0.901146i	$0.642727\pi$
$432$	0	0
$433$	10.0000	0.480569	0.240285	−	0.970702i	$-0.422759\pi$
$433$	10.0000	0.480569	0.240285	+	0.970702i	$0.422759\pi$
$434$	−4.00000	−0.192006
$435$	0	0
$436$	−6.00000	−0.287348
$437$	0	0
$438$	0	0
$439$	−40.0000	−1.90910	−0.954548	−	0.298057i	$-0.903661\pi$
$439$	−40.0000	−1.90910	−0.954548	+	0.298057i	$0.903661\pi$
$440$	−4.00000	−0.190693
$441$	0	0
$442$	0	0
$443$	4.00000	0.190046	0.0950229	−	0.995475i	$-0.469708\pi$
$443$	4.00000	0.190046	0.0950229	+	0.995475i	$0.469708\pi$
$444$	0	0
$445$	−6.00000	−0.284427
$446$	−24.0000	−1.13643
$447$	0	0
$448$	4.00000	0.188982
$449$	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
$451$	0	0
$452$	6.00000	0.282216
$453$	0	0
$454$	−12.0000	−0.563188
$455$	−8.00000	−0.375046
$456$	0	0
$457$	−22.0000	−1.02912	−0.514558	−	0.857455i	$-0.672044\pi$
$457$	−22.0000	−1.02912	−0.514558	+	0.857455i	$0.672044\pi$
$458$	4.00000	0.186908
$459$	0	0
$460$	2.00000	0.0932505
$461$	6.00000	0.279448	0.139724	−	0.990190i	$-0.455378\pi$
$461$	6.00000	0.279448	0.139724	+	0.990190i	$0.455378\pi$
$462$	0	0
$463$	−8.00000	−0.371792	−0.185896	−	0.982569i	$-0.559519\pi$
$463$	−8.00000	−0.371792	−0.185896	+	0.982569i	$0.559519\pi$
$464$	−2.00000	−0.0928477
$465$	0	0
$466$	−30.0000	−1.38972
$467$	12.0000	0.555294	0.277647	−	0.960683i	$-0.410445\pi$
$467$	12.0000	0.555294	0.277647	+	0.960683i	$0.410445\pi$
$468$	0	0
$469$	−8.00000	−0.369406
$470$	0	0
$471$	0	0
$472$	−4.00000	−0.184115
$473$	16.0000	0.735681
$474$	0	0
$475$	0	0
$476$	0	0
$477$	0	0
$478$	8.00000	0.365911
$479$	30.0000	1.37073	0.685367	−	0.728197i	$-0.259642\pi$
$479$	30.0000	1.37073	0.685367	+	0.728197i	$0.259642\pi$
$480$	0	0
$481$	4.00000	0.182384
$482$	26.0000	1.18427
$483$	0	0
$484$	5.00000	0.227273
$485$	−10.0000	−0.454077
$486$	0	0
$487$	24.0000	1.08754	0.543772	−	0.839233i	$-0.316996\pi$
$487$	24.0000	1.08754	0.543772	+	0.839233i	$0.316996\pi$
$488$	8.00000	0.362143
$489$	0	0
$490$	−9.00000	−0.406579
$491$	−12.0000	−0.541552	−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000	−0.541552	−0.270776	+	0.962642i	$0.587280\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	0	0
$496$	−1.00000	−0.0449013
$497$	−24.0000	−1.07655
$498$	0	0
$499$	−10.0000	−0.447661	−0.223831	−	0.974628i	$-0.571856\pi$
$499$	−10.0000	−0.447661	−0.223831	+	0.974628i	$0.571856\pi$
$500$	−1.00000	−0.0447214
$501$	0	0
$502$	−28.0000	−1.24970
$503$	44.0000	1.96186	0.980932	−	0.194354i	$-0.0622609\pi$
$503$	44.0000	1.96186	0.980932	+	0.194354i	$0.0622609\pi$
$504$	0	0
$505$	−6.00000	−0.266996
$506$	−8.00000	−0.355643
$507$	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
$511$	8.00000	0.353899
$512$	1.00000	0.0441942
$513$	0	0
$514$	14.0000	0.617514
$515$	8.00000	0.352522
$516$	0	0
$517$	0	0
$518$	8.00000	0.351500
$519$	0	0
$520$	−2.00000	−0.0877058
$521$	−28.0000	−1.22670	−0.613351	−	0.789810i	$-0.710179\pi$
$521$	−28.0000	−1.22670	−0.613351	+	0.789810i	$0.710179\pi$
$522$	0	0
$523$	16.0000	0.699631	0.349816	−	0.936819i	$-0.386244\pi$
$523$	16.0000	0.699631	0.349816	+	0.936819i	$0.386244\pi$
$524$	0	0
$525$	0	0
$526$	18.0000	0.784837
$527$	0	0
$528$	0	0
$529$	−19.0000	−0.826087
$530$	10.0000	0.434372
$531$	0	0
$532$	0	0
$533$	0	0
$534$	0	0
$535$	−12.0000	−0.518805
$536$	−2.00000	−0.0863868
$537$	0	0
$538$	−6.00000	−0.258678
$539$	36.0000	1.55063
$540$	0	0
$541$	10.0000	0.429934	0.214967	−	0.976621i	$-0.431036\pi$
$541$	10.0000	0.429934	0.214967	+	0.976621i	$0.431036\pi$
$542$	−4.00000	−0.171815
$543$	0	0
$544$	0	0
$545$	6.00000	0.257012
$546$	0	0
$547$	14.0000	0.598597	0.299298	−	0.954160i	$-0.403247\pi$
$547$	14.0000	0.598597	0.299298	+	0.954160i	$0.403247\pi$
$548$	4.00000	0.170872
$549$	0	0
$550$	4.00000	0.170561
$551$	0	0
$552$	0	0
$553$	0	0
$554$	−10.0000	−0.424859
$555$	0	0
$556$	14.0000	0.593732
$557$	−38.0000	−1.61011	−0.805056	−	0.593199i	$-0.797865\pi$
$557$	−38.0000	−1.61011	−0.805056	+	0.593199i	$0.797865\pi$
$558$	0	0
$559$	8.00000	0.338364
$560$	−4.00000	−0.169031
$561$	0	0
$562$	−24.0000	−1.01238
$563$	20.0000	0.842900	0.421450	−	0.906852i	$-0.361521\pi$
$563$	20.0000	0.842900	0.421450	+	0.906852i	$0.361521\pi$
$564$	0	0
$565$	−6.00000	−0.252422
$566$	−22.0000	−0.924729
$567$	0	0
$568$	−6.00000	−0.251754
$569$	42.0000	1.76073	0.880366	−	0.474295i	$-0.157297\pi$
$569$	42.0000	1.76073	0.880366	+	0.474295i	$0.157297\pi$
$570$	0	0
$571$	−18.0000	−0.753277	−0.376638	−	0.926360i	$-0.622920\pi$
$571$	−18.0000	−0.753277	−0.376638	+	0.926360i	$0.622920\pi$
$572$	8.00000	0.334497
$573$	0	0
$574$	0	0
$575$	−2.00000	−0.0834058
$576$	0	0
$577$	10.0000	0.416305	0.208153	−	0.978096i	$-0.433255\pi$
$577$	10.0000	0.416305	0.208153	+	0.978096i	$0.433255\pi$
$578$	−17.0000	−0.707107
$579$	0	0
$580$	2.00000	0.0830455
$581$	−16.0000	−0.663792
$582$	0	0
$583$	−40.0000	−1.65663
$584$	2.00000	0.0827606
$585$	0	0
$586$	6.00000	0.247858
$587$	0	0		−	1.00000i	$-0.5\pi$
$587$	0	0			1.00000i	$0.5\pi$
$588$	0	0
$589$	0	0
$590$	4.00000	0.164677
$591$	0	0
$592$	2.00000	0.0821995
$593$	−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
$595$	0	0
$596$	−6.00000	−0.245770
$597$	0	0
$598$	−4.00000	−0.163572
$599$	14.0000	0.572024	0.286012	−	0.958226i	$-0.407670\pi$
$599$	14.0000	0.572024	0.286012	+	0.958226i	$0.407670\pi$
$600$	0	0
$601$	2.00000	0.0815817	0.0407909	−	0.999168i	$-0.487012\pi$
$601$	2.00000	0.0815817	0.0407909	+	0.999168i	$0.487012\pi$
$602$	16.0000	0.652111
$603$	0	0
$604$	20.0000	0.813788
$605$	−5.00000	−0.203279
$606$	0	0
$607$	16.0000	0.649420	0.324710	−	0.945814i	$-0.394733\pi$
$607$	16.0000	0.649420	0.324710	+	0.945814i	$0.394733\pi$
$608$	0	0
$609$	0	0
$610$	−8.00000	−0.323911
$611$	0	0
$612$	0	0
$613$	38.0000	1.53481	0.767403	−	0.641165i	$-0.221549\pi$
$613$	38.0000	1.53481	0.767403	+	0.641165i	$0.221549\pi$
$614$	30.0000	1.21070
$615$	0	0
$616$	16.0000	0.644658
$617$	30.0000	1.20775	0.603877	−	0.797077i	$-0.293622\pi$
$617$	30.0000	1.20775	0.603877	+	0.797077i	$0.293622\pi$
$618$	0	0
$619$	18.0000	0.723481	0.361741	−	0.932279i	$-0.382183\pi$
$619$	18.0000	0.723481	0.361741	+	0.932279i	$0.382183\pi$
$620$	1.00000	0.0401610
$621$	0	0
$622$	−22.0000	−0.882120
$623$	24.0000	0.961540
$624$	0	0
$625$	1.00000	0.0400000
$626$	6.00000	0.239808
$627$	0	0
$628$	12.0000	0.478852
$629$	0	0
$630$	0	0
$631$	−8.00000	−0.318475	−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000	−0.318475	−0.159237	+	0.987240i	$0.550904\pi$
$632$	0	0
$633$	0	0
$634$	−6.00000	−0.238290
$635$	8.00000	0.317470
$636$	0	0
$637$	18.0000	0.713186
$638$	−8.00000	−0.316723
$639$	0	0
$640$	−1.00000	−0.0395285
$641$	−30.0000	−1.18493	−0.592464	−	0.805597i	$-0.701845\pi$
$641$	−30.0000	−1.18493	−0.592464	+	0.805597i	$0.701845\pi$
$642$	0	0
$643$	−40.0000	−1.57745	−0.788723	−	0.614749i	$-0.789257\pi$
$643$	−40.0000	−1.57745	−0.788723	+	0.614749i	$0.789257\pi$
$644$	−8.00000	−0.315244
$645$	0	0
$646$	0	0
$647$	42.0000	1.65119	0.825595	−	0.564263i	$-0.190840\pi$
$647$	42.0000	1.65119	0.825595	+	0.564263i	$0.190840\pi$
$648$	0	0
$649$	−16.0000	−0.628055
$650$	2.00000	0.0784465
$651$	0	0
$652$	−14.0000	−0.548282
$653$	−2.00000	−0.0782660	−0.0391330	−	0.999234i	$-0.512460\pi$
$653$	−2.00000	−0.0782660	−0.0391330	+	0.999234i	$0.512460\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	0	0
$658$	0	0
$659$	4.00000	0.155818	0.0779089	−	0.996960i	$-0.475176\pi$
$659$	4.00000	0.155818	0.0779089	+	0.996960i	$0.475176\pi$
$660$	0	0
$661$	−38.0000	−1.47803	−0.739014	−	0.673690i	$-0.764708\pi$
$661$	−38.0000	−1.47803	−0.739014	+	0.673690i	$0.764708\pi$
$662$	−2.00000	−0.0777322
$663$	0	0
$664$	−4.00000	−0.155230
$665$	0	0
$666$	0	0
$667$	4.00000	0.154881
$668$	6.00000	0.232147
$669$	0	0
$670$	2.00000	0.0772667
$671$	32.0000	1.23535
$672$	0	0
$673$	18.0000	0.693849	0.346925	−	0.937893i	$-0.387226\pi$
$673$	18.0000	0.693849	0.346925	+	0.937893i	$0.387226\pi$
$674$	−2.00000	−0.0770371
$675$	0	0
$676$	−9.00000	−0.346154
$677$	18.0000	0.691796	0.345898	−	0.938272i	$-0.387574\pi$
$677$	18.0000	0.691796	0.345898	+	0.938272i	$0.387574\pi$
$678$	0	0
$679$	40.0000	1.53506
$680$	0	0
$681$	0	0
$682$	−4.00000	−0.153168
$683$	−4.00000	−0.153056	−0.0765279	−	0.997067i	$-0.524383\pi$
$683$	−4.00000	−0.153056	−0.0765279	+	0.997067i	$0.524383\pi$
$684$	0	0
$685$	−4.00000	−0.152832
$686$	8.00000	0.305441
$687$	0	0
$688$	4.00000	0.152499
$689$	−20.0000	−0.761939
$690$	0	0
$691$	−48.0000	−1.82601	−0.913003	−	0.407953i	$-0.866243\pi$
$691$	−48.0000	−1.82601	−0.913003	+	0.407953i	$0.866243\pi$
$692$	2.00000	0.0760286
$693$	0	0
$694$	12.0000	0.455514
$695$	−14.0000	−0.531050
$696$	0	0
$697$	0	0
$698$	−26.0000	−0.984115
$699$	0	0
$700$	4.00000	0.151186
$701$	−26.0000	−0.982006	−0.491003	−	0.871158i	$-0.663370\pi$
$701$	−26.0000	−0.982006	−0.491003	+	0.871158i	$0.663370\pi$
$702$	0	0
$703$	0	0
$704$	4.00000	0.150756
$705$	0	0
$706$	4.00000	0.150542
$707$	24.0000	0.902613
$708$	0	0
$709$	−32.0000	−1.20179	−0.600893	−	0.799330i	$-0.705188\pi$
$709$	−32.0000	−1.20179	−0.600893	+	0.799330i	$0.705188\pi$
$710$	6.00000	0.225176
$711$	0	0
$712$	6.00000	0.224860
$713$	2.00000	0.0749006
$714$	0	0
$715$	−8.00000	−0.299183
$716$	−20.0000	−0.747435
$717$	0	0
$718$	14.0000	0.522475
$719$	44.0000	1.64092	0.820462	−	0.571702i	$-0.193717\pi$
$719$	44.0000	1.64092	0.820462	+	0.571702i	$0.193717\pi$
$720$	0	0
$721$	−32.0000	−1.19174
$722$	−19.0000	−0.707107
$723$	0	0
$724$	4.00000	0.148659
$725$	−2.00000	−0.0742781
$726$	0	0
$727$	−28.0000	−1.03846	−0.519231	−	0.854634i	$-0.673782\pi$
$727$	−28.0000	−1.03846	−0.519231	+	0.854634i	$0.673782\pi$
$728$	8.00000	0.296500
$729$	0	0
$730$	−2.00000	−0.0740233
$731$	0	0
$732$	0	0
$733$	−20.0000	−0.738717	−0.369358	−	0.929287i	$-0.620423\pi$
$733$	−20.0000	−0.738717	−0.369358	+	0.929287i	$0.620423\pi$
$734$	−24.0000	−0.885856
$735$	0	0
$736$	−2.00000	−0.0737210
$737$	−8.00000	−0.294684
$738$	0	0
$739$	−2.00000	−0.0735712	−0.0367856	−	0.999323i	$-0.511712\pi$
$739$	−2.00000	−0.0735712	−0.0367856	+	0.999323i	$0.511712\pi$
$740$	−2.00000	−0.0735215
$741$	0	0
$742$	−40.0000	−1.46845
$743$	30.0000	1.10059	0.550297	−	0.834969i	$-0.314515\pi$
$743$	30.0000	1.10059	0.550297	+	0.834969i	$0.314515\pi$
$744$	0	0
$745$	6.00000	0.219823
$746$	−36.0000	−1.31805
$747$	0	0
$748$	0	0
$749$	48.0000	1.75388
$750$	0	0
$751$	−40.0000	−1.45962	−0.729810	−	0.683650i	$-0.760392\pi$
$751$	−40.0000	−1.45962	−0.729810	+	0.683650i	$0.760392\pi$
$752$	0	0
$753$	0	0
$754$	−4.00000	−0.145671
$755$	−20.0000	−0.727875
$756$	0	0
$757$	26.0000	0.944986	0.472493	−	0.881334i	$-0.343354\pi$
$757$	26.0000	0.944986	0.472493	+	0.881334i	$0.343354\pi$
$758$	12.0000	0.435860
$759$	0	0
$760$	0	0
$761$	26.0000	0.942499	0.471250	−	0.882000i	$-0.343803\pi$
$761$	26.0000	0.942499	0.471250	+	0.882000i	$0.343803\pi$
$762$	0	0
$763$	−24.0000	−0.868858
$764$	−2.00000	−0.0723575
$765$	0	0
$766$	6.00000	0.216789
$767$	−8.00000	−0.288863
$768$	0	0
$769$	−2.00000	−0.0721218	−0.0360609	−	0.999350i	$-0.511481\pi$
$769$	−2.00000	−0.0721218	−0.0360609	+	0.999350i	$0.511481\pi$
$770$	−16.0000	−0.576600
$771$	0	0
$772$	14.0000	0.503871
$773$	−26.0000	−0.935155	−0.467578	−	0.883952i	$-0.654873\pi$
$773$	−26.0000	−0.935155	−0.467578	+	0.883952i	$0.654873\pi$
$774$	0	0
$775$	−1.00000	−0.0359211
$776$	10.0000	0.358979
$777$	0	0
$778$	−26.0000	−0.932145
$779$	0	0
$780$	0	0
$781$	−24.0000	−0.858788
$782$	0	0
$783$	0	0
$784$	9.00000	0.321429
$785$	−12.0000	−0.428298
$786$	0	0
$787$	48.0000	1.71102	0.855508	−	0.517790i	$-0.173245\pi$
$787$	48.0000	1.71102	0.855508	+	0.517790i	$0.173245\pi$
$788$	−10.0000	−0.356235
$789$	0	0
$790$	0	0
$791$	24.0000	0.853342
$792$	0	0
$793$	16.0000	0.568177
$794$	4.00000	0.141955
$795$	0	0
$796$	4.00000	0.141776
$797$	26.0000	0.920967	0.460484	−	0.887668i	$-0.347676\pi$
$797$	26.0000	0.920967	0.460484	+	0.887668i	$0.347676\pi$
$798$	0	0
$799$	0	0
$800$	1.00000	0.0353553
$801$	0	0
$802$	−14.0000	−0.494357
$803$	8.00000	0.282314
$804$	0	0
$805$	8.00000	0.281963
$806$	−2.00000	−0.0704470
$807$	0	0
$808$	6.00000	0.211079
$809$	−6.00000	−0.210949	−0.105474	−	0.994422i	$-0.533636\pi$
$809$	−6.00000	−0.210949	−0.105474	+	0.994422i	$0.533636\pi$
$810$	0	0
$811$	12.0000	0.421377	0.210688	−	0.977553i	$-0.432429\pi$
$811$	12.0000	0.421377	0.210688	+	0.977553i	$0.432429\pi$
$812$	−8.00000	−0.280745
$813$	0	0
$814$	8.00000	0.280400
$815$	14.0000	0.490399
$816$	0	0
$817$	0	0
$818$	−14.0000	−0.489499
$819$	0	0
$820$	0	0
$821$	−30.0000	−1.04701	−0.523504	−	0.852023i	$-0.675375\pi$
$821$	−30.0000	−1.04701	−0.523504	+	0.852023i	$0.675375\pi$
$822$	0	0
$823$	−16.0000	−0.557725	−0.278862	−	0.960331i	$-0.589957\pi$
$823$	−16.0000	−0.557725	−0.278862	+	0.960331i	$0.589957\pi$
$824$	−8.00000	−0.278693
$825$	0	0
$826$	−16.0000	−0.556711
$827$	16.0000	0.556375	0.278187	−	0.960527i	$-0.410266\pi$
$827$	16.0000	0.556375	0.278187	+	0.960527i	$0.410266\pi$
$828$	0	0
$829$	−28.0000	−0.972480	−0.486240	−	0.873825i	$-0.661632\pi$
$829$	−28.0000	−0.972480	−0.486240	+	0.873825i	$0.661632\pi$
$830$	4.00000	0.138842
$831$	0	0
$832$	2.00000	0.0693375
$833$	0	0
$834$	0	0
$835$	−6.00000	−0.207639
$836$	0	0
$837$	0	0
$838$	−4.00000	−0.138178
$839$	−2.00000	−0.0690477	−0.0345238	−	0.999404i	$-0.510991\pi$
$839$	−2.00000	−0.0690477	−0.0345238	+	0.999404i	$0.510991\pi$
$840$	0	0
$841$	−25.0000	−0.862069
$842$	10.0000	0.344623
$843$	0	0
$844$	0	0
$845$	9.00000	0.309609
$846$	0	0
$847$	20.0000	0.687208
$848$	−10.0000	−0.343401
$849$	0	0
$850$	0	0
$851$	−4.00000	−0.137118
$852$	0	0
$853$	−36.0000	−1.23262	−0.616308	−	0.787505i	$-0.711372\pi$
$853$	−36.0000	−1.23262	−0.616308	+	0.787505i	$0.711372\pi$
$854$	32.0000	1.09502
$855$	0	0
$856$	12.0000	0.410152
$857$	18.0000	0.614868	0.307434	−	0.951569i	$-0.400530\pi$
$857$	18.0000	0.614868	0.307434	+	0.951569i	$0.400530\pi$
$858$	0	0
$859$	−22.0000	−0.750630	−0.375315	−	0.926897i	$-0.622466\pi$
$859$	−22.0000	−0.750630	−0.375315	+	0.926897i	$0.622466\pi$
$860$	−4.00000	−0.136399
$861$	0	0
$862$	−18.0000	−0.613082
$863$	−10.0000	−0.340404	−0.170202	−	0.985409i	$-0.554442\pi$
$863$	−10.0000	−0.340404	−0.170202	+	0.985409i	$0.554442\pi$
$864$	0	0
$865$	−2.00000	−0.0680020
$866$	10.0000	0.339814
$867$	0	0
$868$	−4.00000	−0.135769
$869$	0	0
$870$	0	0
$871$	−4.00000	−0.135535
$872$	−6.00000	−0.203186
$873$	0	0
$874$	0	0
$875$	−4.00000	−0.135225
$876$	0	0
$877$	−32.0000	−1.08056	−0.540282	−	0.841484i	$-0.681682\pi$
$877$	−32.0000	−1.08056	−0.540282	+	0.841484i	$0.681682\pi$
$878$	−40.0000	−1.34993
$879$	0	0
$880$	−4.00000	−0.134840
$881$	14.0000	0.471672	0.235836	−	0.971793i	$-0.424217\pi$
$881$	14.0000	0.471672	0.235836	+	0.971793i	$0.424217\pi$
$882$	0	0
$883$	−12.0000	−0.403832	−0.201916	−	0.979403i	$-0.564717\pi$
$883$	−12.0000	−0.403832	−0.201916	+	0.979403i	$0.564717\pi$
$884$	0	0
$885$	0	0
$886$	4.00000	0.134383
$887$	24.0000	0.805841	0.402921	−	0.915235i	$-0.367995\pi$
$887$	24.0000	0.805841	0.402921	+	0.915235i	$0.367995\pi$
$888$	0	0
$889$	−32.0000	−1.07325
$890$	−6.00000	−0.201120
$891$	0	0
$892$	−24.0000	−0.803579
$893$	0	0
$894$	0	0
$895$	20.0000	0.668526
$896$	4.00000	0.133631
$897$	0	0
$898$	10.0000	0.333704
$899$	2.00000	0.0667037
$900$	0	0
$901$	0	0
$902$	0	0
$903$	0	0
$904$	6.00000	0.199557
$905$	−4.00000	−0.132964
$906$	0	0
$907$	−18.0000	−0.597680	−0.298840	−	0.954303i	$-0.596600\pi$
$907$	−18.0000	−0.597680	−0.298840	+	0.954303i	$0.596600\pi$
$908$	−12.0000	−0.398234
$909$	0	0
$910$	−8.00000	−0.265197
$911$	48.0000	1.59031	0.795155	−	0.606406i	$-0.207389\pi$
$911$	48.0000	1.59031	0.795155	+	0.606406i	$0.207389\pi$
$912$	0	0
$913$	−16.0000	−0.529523
$914$	−22.0000	−0.727695
$915$	0	0
$916$	4.00000	0.132164
$917$	0	0
$918$	0	0
$919$	8.00000	0.263896	0.131948	−	0.991257i	$-0.457877\pi$
$919$	8.00000	0.263896	0.131948	+	0.991257i	$0.457877\pi$
$920$	2.00000	0.0659380
$921$	0	0
$922$	6.00000	0.197599
$923$	−12.0000	−0.394985
$924$	0	0
$925$	2.00000	0.0657596
$926$	−8.00000	−0.262896
$927$	0	0
$928$	−2.00000	−0.0656532
$929$	−34.0000	−1.11550	−0.557752	−	0.830008i	$-0.688336\pi$
$929$	−34.0000	−1.11550	−0.557752	+	0.830008i	$0.688336\pi$
$930$	0	0
$931$	0	0
$932$	−30.0000	−0.982683
$933$	0	0
$934$	12.0000	0.392652
$935$	0	0
$936$	0	0
$937$	34.0000	1.11073	0.555366	−	0.831606i	$-0.312578\pi$
$937$	34.0000	1.11073	0.555366	+	0.831606i	$0.312578\pi$
$938$	−8.00000	−0.261209
$939$	0	0
$940$	0	0
$941$	−18.0000	−0.586783	−0.293392	−	0.955992i	$-0.594784\pi$
$941$	−18.0000	−0.586783	−0.293392	+	0.955992i	$0.594784\pi$
$942$	0	0
$943$	0	0
$944$	−4.00000	−0.130189
$945$	0	0
$946$	16.0000	0.520205
$947$	4.00000	0.129983	0.0649913	−	0.997886i	$-0.479298\pi$
$947$	4.00000	0.129983	0.0649913	+	0.997886i	$0.479298\pi$
$948$	0	0
$949$	4.00000	0.129845
$950$	0	0
$951$	0	0
$952$	0	0
$953$	−44.0000	−1.42530	−0.712650	−	0.701520i	$-0.752505\pi$
$953$	−44.0000	−1.42530	−0.712650	+	0.701520i	$0.752505\pi$
$954$	0	0
$955$	2.00000	0.0647185
$956$	8.00000	0.258738
$957$	0	0
$958$	30.0000	0.969256
$959$	16.0000	0.516667
$960$	0	0
$961$	1.00000	0.0322581
$962$	4.00000	0.128965
$963$	0	0
$964$	26.0000	0.837404
$965$	−14.0000	−0.450676
$966$	0	0
$967$	−24.0000	−0.771788	−0.385894	−	0.922543i	$-0.626107\pi$
$967$	−24.0000	−0.771788	−0.385894	+	0.922543i	$0.626107\pi$
$968$	5.00000	0.160706
$969$	0	0
$970$	−10.0000	−0.321081
$971$	16.0000	0.513464	0.256732	−	0.966483i	$-0.417354\pi$
$971$	16.0000	0.513464	0.256732	+	0.966483i	$0.417354\pi$
$972$	0	0
$973$	56.0000	1.79528
$974$	24.0000	0.769010
$975$	0	0
$976$	8.00000	0.256074
$977$	38.0000	1.21573	0.607864	−	0.794041i	$-0.292027\pi$
$977$	38.0000	1.21573	0.607864	+	0.794041i	$0.292027\pi$
$978$	0	0
$979$	24.0000	0.767043
$980$	−9.00000	−0.287494
$981$	0	0
$982$	−12.0000	−0.382935
$983$	38.0000	1.21201	0.606006	−	0.795460i	$-0.292771\pi$
$983$	38.0000	1.21201	0.606006	+	0.795460i	$0.292771\pi$
$984$	0	0
$985$	10.0000	0.318626
$986$	0	0
$987$	0	0
$988$	0	0
$989$	−8.00000	−0.254385
$990$	0	0
$991$	40.0000	1.27064	0.635321	−	0.772248i	$-0.280868\pi$
$991$	40.0000	1.27064	0.635321	+	0.772248i	$0.280868\pi$
$992$	−1.00000	−0.0317500
$993$	0	0
$994$	−24.0000	−0.761234
$995$	−4.00000	−0.126809
$996$	0	0
$997$	−44.0000	−1.39349	−0.696747	−	0.717317i	$-0.745370\pi$
$997$	−44.0000	−1.39349	−0.696747	+	0.717317i	$0.745370\pi$
$998$	−10.0000	−0.316544
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2790.2.a.w.1.1	yes	1
3.2	odd	2		2790.2.a.m.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2790.2.a.m.1.1	✓	1	3.2	odd	2
2790.2.a.w.1.1	yes	1	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2790 = 2 \cdot 3^{2} \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2790.a (trivial)

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