LMFDB - Embedded newform 3248.2.a.k.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3248,2,Mod(1,3248)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3248, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("3248.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3248 = 2^{4} \cdot 7 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3248.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:	$25.9354105765$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 406)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	3248.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{3} -3.00000 q^{5} +1.00000 q^{7} -2.00000 q^{9} +O(q^{10})$

$q+1.00000 q^{3} -3.00000 q^{5} +1.00000 q^{7} -2.00000 q^{9} +1.00000 q^{11} -1.00000 q^{13} -3.00000 q^{15} -4.00000 q^{17} +4.00000 q^{19} +1.00000 q^{21} +2.00000 q^{23} +4.00000 q^{25} -5.00000 q^{27} +1.00000 q^{29} +1.00000 q^{31} +1.00000 q^{33} -3.00000 q^{35} +6.00000 q^{37} -1.00000 q^{39} -3.00000 q^{43} +6.00000 q^{45} +9.00000 q^{47} +1.00000 q^{49} -4.00000 q^{51} +3.00000 q^{53} -3.00000 q^{55} +4.00000 q^{57} +6.00000 q^{61} -2.00000 q^{63} +3.00000 q^{65} -2.00000 q^{67} +2.00000 q^{69} +8.00000 q^{71} +4.00000 q^{75} +1.00000 q^{77} +13.0000 q^{79} +1.00000 q^{81} +12.0000 q^{85} +1.00000 q^{87} -14.0000 q^{89} -1.00000 q^{91} +1.00000 q^{93} -12.0000 q^{95} +16.0000 q^{97} -2.00000 q^{99} +O(q^{100})$

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 $

$2$	0	0
$2$	0	0
$3$	1.00000	0.577350	0.288675	−	0.957427i	$-0.406785\pi$
$3$	1.00000	0.577350	0.288675	+	0.957427i	$0.406785\pi$
$4$	0	0
$5$	−3.00000	−1.34164	−0.670820	−	0.741620i	$-0.734058\pi$
$5$	−3.00000	−1.34164	−0.670820	+	0.741620i	$0.734058\pi$
$6$	0	0
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	0	0
$9$	−2.00000	−0.666667
$10$	0	0
$11$	1.00000	0.301511	0.150756	−	0.988571i	$-0.451829\pi$
$11$	1.00000	0.301511	0.150756	+	0.988571i	$0.451829\pi$
$12$	0	0
$13$	−1.00000	−0.277350	−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000	−0.277350	−0.138675	+	0.990338i	$0.544284\pi$
$14$	0	0
$15$	−3.00000	−0.774597
$16$	0	0
$17$	−4.00000	−0.970143	−0.485071	−	0.874475i	$-0.661206\pi$
$17$	−4.00000	−0.970143	−0.485071	+	0.874475i	$0.661206\pi$
$18$	0	0
$19$	4.00000	0.917663	0.458831	−	0.888523i	$-0.348268\pi$
$19$	4.00000	0.917663	0.458831	+	0.888523i	$0.348268\pi$
$20$	0	0
$21$	1.00000	0.218218
$22$	0	0
$23$	2.00000	0.417029	0.208514	−	0.978019i	$-0.433137\pi$
$23$	2.00000	0.417029	0.208514	+	0.978019i	$0.433137\pi$
$24$	0	0
$25$	4.00000	0.800000
$26$	0	0
$27$	−5.00000	−0.962250
$28$	0	0
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	0	0
$31$	1.00000	0.179605	0.0898027	−	0.995960i	$-0.471376\pi$
$31$	1.00000	0.179605	0.0898027	+	0.995960i	$0.471376\pi$
$32$	0	0
$33$	1.00000	0.174078
$34$	0	0
$35$	−3.00000	−0.507093
$36$	0	0
$37$	6.00000	0.986394	0.493197	−	0.869918i	$-0.335828\pi$
$37$	6.00000	0.986394	0.493197	+	0.869918i	$0.335828\pi$
$38$	0	0
$39$	−1.00000	−0.160128
$40$	0	0
$41$	0	0		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	0	0
$43$	−3.00000	−0.457496	−0.228748	−	0.973486i	$-0.573463\pi$
$43$	−3.00000	−0.457496	−0.228748	+	0.973486i	$0.573463\pi$
$44$	0	0
$45$	6.00000	0.894427
$46$	0	0
$47$	9.00000	1.31278	0.656392	−	0.754420i	$-0.272082\pi$
$47$	9.00000	1.31278	0.656392	+	0.754420i	$0.272082\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	0	0
$51$	−4.00000	−0.560112
$52$	0	0
$53$	3.00000	0.412082	0.206041	−	0.978543i	$-0.433942\pi$
$53$	3.00000	0.412082	0.206041	+	0.978543i	$0.433942\pi$
$54$	0	0
$55$	−3.00000	−0.404520
$56$	0	0
$57$	4.00000	0.529813
$58$	0	0
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	0	0
$61$	6.00000	0.768221	0.384111	−	0.923287i	$-0.374508\pi$
$61$	6.00000	0.768221	0.384111	+	0.923287i	$0.374508\pi$
$62$	0	0
$63$	−2.00000	−0.251976
$64$	0	0
$65$	3.00000	0.372104
$66$	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
$69$	2.00000	0.240772
$70$	0	0
$71$	8.00000	0.949425	0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000	0.949425	0.474713	+	0.880141i	$0.342552\pi$
$72$	0	0
$73$	0	0		−	1.00000i	$-0.5\pi$
$73$	0	0			1.00000i	$0.5\pi$
$74$	0	0
$75$	4.00000	0.461880
$76$	0	0
$77$	1.00000	0.113961
$78$	0	0
$79$	13.0000	1.46261	0.731307	−	0.682048i	$-0.238911\pi$
$79$	13.0000	1.46261	0.731307	+	0.682048i	$0.238911\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	0	0
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	0	0
$85$	12.0000	1.30158
$86$	0	0
$87$	1.00000	0.107211
$88$	0	0
$89$	−14.0000	−1.48400	−0.741999	−	0.670402i	$-0.766122\pi$
$89$	−14.0000	−1.48400	−0.741999	+	0.670402i	$0.766122\pi$
$90$	0	0
$91$	−1.00000	−0.104828
$92$	0	0
$93$	1.00000	0.103695
$94$	0	0
$95$	−12.0000	−1.23117
$96$	0	0
$97$	16.0000	1.62455	0.812277	−	0.583272i	$-0.198228\pi$
$97$	16.0000	1.62455	0.812277	+	0.583272i	$0.198228\pi$
$98$	0	0
$99$	−2.00000	−0.201008
$100$	0	0
$101$	−4.00000	−0.398015	−0.199007	−	0.979998i	$-0.563772\pi$
$101$	−4.00000	−0.398015	−0.199007	+	0.979998i	$0.563772\pi$
$102$	0	0
$103$	−4.00000	−0.394132	−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000	−0.394132	−0.197066	+	0.980390i	$0.563141\pi$
$104$	0	0
$105$	−3.00000	−0.292770
$106$	0	0
$107$	14.0000	1.35343	0.676716	−	0.736245i	$-0.263403\pi$
$107$	14.0000	1.35343	0.676716	+	0.736245i	$0.263403\pi$
$108$	0	0
$109$	15.0000	1.43674	0.718370	−	0.695662i	$-0.244889\pi$
$109$	15.0000	1.43674	0.718370	+	0.695662i	$0.244889\pi$
$110$	0	0
$111$	6.00000	0.569495
$112$	0	0
$113$	0	0		−	1.00000i	$-0.5\pi$
$113$	0	0			1.00000i	$0.5\pi$
$114$	0	0
$115$	−6.00000	−0.559503
$116$	0	0
$117$	2.00000	0.184900
$118$	0	0
$119$	−4.00000	−0.366679
$120$	0	0
$121$	−10.0000	−0.909091
$122$	0	0
$123$	0	0
$124$	0	0
$125$	3.00000	0.268328
$126$	0	0
$127$	16.0000	1.41977	0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000	1.41977	0.709885	+	0.704317i	$0.248747\pi$
$128$	0	0
$129$	−3.00000	−0.264135
$130$	0	0
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	0	0
$133$	4.00000	0.346844
$134$	0	0
$135$	15.0000	1.29099
$136$	0	0
$137$	−10.0000	−0.854358	−0.427179	−	0.904167i	$-0.640493\pi$
$137$	−10.0000	−0.854358	−0.427179	+	0.904167i	$0.640493\pi$
$138$	0	0
$139$	14.0000	1.18746	0.593732	−	0.804663i	$-0.297654\pi$
$139$	14.0000	1.18746	0.593732	+	0.804663i	$0.297654\pi$
$140$	0	0
$141$	9.00000	0.757937
$142$	0	0
$143$	−1.00000	−0.0836242
$144$	0	0
$145$	−3.00000	−0.249136
$146$	0	0
$147$	1.00000	0.0824786
$148$	0	0
$149$	−11.0000	−0.901155	−0.450578	−	0.892737i	$-0.648782\pi$
$149$	−11.0000	−0.901155	−0.450578	+	0.892737i	$0.648782\pi$
$150$	0	0
$151$	−14.0000	−1.13930	−0.569652	−	0.821886i	$-0.692922\pi$
$151$	−14.0000	−1.13930	−0.569652	+	0.821886i	$0.692922\pi$
$152$	0	0
$153$	8.00000	0.646762
$154$	0	0
$155$	−3.00000	−0.240966
$156$	0	0
$157$	−12.0000	−0.957704	−0.478852	−	0.877896i	$-0.658947\pi$
$157$	−12.0000	−0.957704	−0.478852	+	0.877896i	$0.658947\pi$
$158$	0	0
$159$	3.00000	0.237915
$160$	0	0
$161$	2.00000	0.157622
$162$	0	0
$163$	21.0000	1.64485	0.822423	−	0.568876i	$-0.192621\pi$
$163$	21.0000	1.64485	0.822423	+	0.568876i	$0.192621\pi$
$164$	0	0
$165$	−3.00000	−0.233550
$166$	0	0
$167$	−12.0000	−0.928588	−0.464294	−	0.885681i	$-0.653692\pi$
$167$	−12.0000	−0.928588	−0.464294	+	0.885681i	$0.653692\pi$
$168$	0	0
$169$	−12.0000	−0.923077
$170$	0	0
$171$	−8.00000	−0.611775
$172$	0	0
$173$	14.0000	1.06440	0.532200	−	0.846619i	$-0.321365\pi$
$173$	14.0000	1.06440	0.532200	+	0.846619i	$0.321365\pi$
$174$	0	0
$175$	4.00000	0.302372
$176$	0	0
$177$	0	0
$178$	0	0
$179$	24.0000	1.79384	0.896922	−	0.442189i	$-0.145798\pi$
$179$	24.0000	1.79384	0.896922	+	0.442189i	$0.145798\pi$
$180$	0	0
$181$	23.0000	1.70958	0.854788	−	0.518977i	$-0.173687\pi$
$181$	23.0000	1.70958	0.854788	+	0.518977i	$0.173687\pi$
$182$	0	0
$183$	6.00000	0.443533
$184$	0	0
$185$	−18.0000	−1.32339
$186$	0	0
$187$	−4.00000	−0.292509
$188$	0	0
$189$	−5.00000	−0.363696
$190$	0	0
$191$	−8.00000	−0.578860	−0.289430	−	0.957199i	$-0.593466\pi$
$191$	−8.00000	−0.578860	−0.289430	+	0.957199i	$0.593466\pi$
$192$	0	0
$193$	12.0000	0.863779	0.431889	−	0.901927i	$-0.357847\pi$
$193$	12.0000	0.863779	0.431889	+	0.901927i	$0.357847\pi$
$194$	0	0
$195$	3.00000	0.214834
$196$	0	0
$197$	−2.00000	−0.142494	−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000	−0.142494	−0.0712470	+	0.997459i	$0.522698\pi$
$198$	0	0
$199$	20.0000	1.41776	0.708881	−	0.705328i	$-0.249200\pi$
$199$	20.0000	1.41776	0.708881	+	0.705328i	$0.249200\pi$
$200$	0	0
$201$	−2.00000	−0.141069
$202$	0	0
$203$	1.00000	0.0701862
$204$	0	0
$205$	0	0
$206$	0	0
$207$	−4.00000	−0.278019
$208$	0	0
$209$	4.00000	0.276686
$210$	0	0
$211$	9.00000	0.619586	0.309793	−	0.950804i	$-0.399740\pi$
$211$	9.00000	0.619586	0.309793	+	0.950804i	$0.399740\pi$
$212$	0	0
$213$	8.00000	0.548151
$214$	0	0
$215$	9.00000	0.613795
$216$	0	0
$217$	1.00000	0.0678844
$218$	0	0
$219$	0	0
$220$	0	0
$221$	4.00000	0.269069
$222$	0	0
$223$	4.00000	0.267860	0.133930	−	0.990991i	$-0.457240\pi$
$223$	4.00000	0.267860	0.133930	+	0.990991i	$0.457240\pi$
$224$	0	0
$225$	−8.00000	−0.533333
$226$	0	0
$227$	−14.0000	−0.929213	−0.464606	−	0.885517i	$-0.653804\pi$
$227$	−14.0000	−0.929213	−0.464606	+	0.885517i	$0.653804\pi$
$228$	0	0
$229$	14.0000	0.925146	0.462573	−	0.886581i	$-0.346926\pi$
$229$	14.0000	0.925146	0.462573	+	0.886581i	$0.346926\pi$
$230$	0	0
$231$	1.00000	0.0657952
$232$	0	0
$233$	11.0000	0.720634	0.360317	−	0.932830i	$-0.382669\pi$
$233$	11.0000	0.720634	0.360317	+	0.932830i	$0.382669\pi$
$234$	0	0
$235$	−27.0000	−1.76129
$236$	0	0
$237$	13.0000	0.844441
$238$	0	0
$239$	12.0000	0.776215	0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000	0.776215	0.388108	+	0.921614i	$0.373129\pi$
$240$	0	0
$241$	−29.0000	−1.86805	−0.934027	−	0.357202i	$-0.883731\pi$
$241$	−29.0000	−1.86805	−0.934027	+	0.357202i	$0.883731\pi$
$242$	0	0
$243$	16.0000	1.02640
$244$	0	0
$245$	−3.00000	−0.191663
$246$	0	0
$247$	−4.00000	−0.254514
$248$	0	0
$249$	0	0
$250$	0	0
$251$	17.0000	1.07303	0.536515	−	0.843891i	$-0.319740\pi$
$251$	17.0000	1.07303	0.536515	+	0.843891i	$0.319740\pi$
$252$	0	0
$253$	2.00000	0.125739
$254$	0	0
$255$	12.0000	0.751469
$256$	0	0
$257$	−9.00000	−0.561405	−0.280702	−	0.959795i	$-0.590567\pi$
$257$	−9.00000	−0.561405	−0.280702	+	0.959795i	$0.590567\pi$
$258$	0	0
$259$	6.00000	0.372822
$260$	0	0
$261$	−2.00000	−0.123797
$262$	0	0
$263$	−5.00000	−0.308313	−0.154157	−	0.988046i	$-0.549266\pi$
$263$	−5.00000	−0.308313	−0.154157	+	0.988046i	$0.549266\pi$
$264$	0	0
$265$	−9.00000	−0.552866
$266$	0	0
$267$	−14.0000	−0.856786
$268$	0	0
$269$	−28.0000	−1.70719	−0.853595	−	0.520937i	$-0.825583\pi$
$269$	−28.0000	−1.70719	−0.853595	+	0.520937i	$0.825583\pi$
$270$	0	0
$271$	−25.0000	−1.51864	−0.759321	−	0.650716i	$-0.774469\pi$
$271$	−25.0000	−1.51864	−0.759321	+	0.650716i	$0.774469\pi$
$272$	0	0
$273$	−1.00000	−0.0605228
$274$	0	0
$275$	4.00000	0.241209
$276$	0	0
$277$	10.0000	0.600842	0.300421	−	0.953807i	$-0.402873\pi$
$277$	10.0000	0.600842	0.300421	+	0.953807i	$0.402873\pi$
$278$	0	0
$279$	−2.00000	−0.119737
$280$	0	0
$281$	−21.0000	−1.25275	−0.626377	−	0.779520i	$-0.715463\pi$
$281$	−21.0000	−1.25275	−0.626377	+	0.779520i	$0.715463\pi$
$282$	0	0
$283$	2.00000	0.118888	0.0594438	−	0.998232i	$-0.481067\pi$
$283$	2.00000	0.118888	0.0594438	+	0.998232i	$0.481067\pi$
$284$	0	0
$285$	−12.0000	−0.710819
$286$	0	0
$287$	0	0
$288$	0	0
$289$	−1.00000	−0.0588235
$290$	0	0
$291$	16.0000	0.937937
$292$	0	0
$293$	18.0000	1.05157	0.525786	−	0.850617i	$-0.323771\pi$
$293$	18.0000	1.05157	0.525786	+	0.850617i	$0.323771\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	−5.00000	−0.290129
$298$	0	0
$299$	−2.00000	−0.115663
$300$	0	0
$301$	−3.00000	−0.172917
$302$	0	0
$303$	−4.00000	−0.229794
$304$	0	0
$305$	−18.0000	−1.03068
$306$	0	0
$307$	−9.00000	−0.513657	−0.256829	−	0.966457i	$-0.582678\pi$
$307$	−9.00000	−0.513657	−0.256829	+	0.966457i	$0.582678\pi$
$308$	0	0
$309$	−4.00000	−0.227552
$310$	0	0
$311$	−20.0000	−1.13410	−0.567048	−	0.823685i	$-0.691915\pi$
$311$	−20.0000	−1.13410	−0.567048	+	0.823685i	$0.691915\pi$
$312$	0	0
$313$	−5.00000	−0.282617	−0.141308	−	0.989966i	$-0.545131\pi$
$313$	−5.00000	−0.282617	−0.141308	+	0.989966i	$0.545131\pi$
$314$	0	0
$315$	6.00000	0.338062
$316$	0	0
$317$	22.0000	1.23564	0.617822	−	0.786318i	$-0.288015\pi$
$317$	22.0000	1.23564	0.617822	+	0.786318i	$0.288015\pi$
$318$	0	0
$319$	1.00000	0.0559893
$320$	0	0
$321$	14.0000	0.781404
$322$	0	0
$323$	−16.0000	−0.890264
$324$	0	0
$325$	−4.00000	−0.221880
$326$	0	0
$327$	15.0000	0.829502
$328$	0	0
$329$	9.00000	0.496186
$330$	0	0
$331$	−27.0000	−1.48405	−0.742027	−	0.670370i	$-0.766135\pi$
$331$	−27.0000	−1.48405	−0.742027	+	0.670370i	$0.766135\pi$
$332$	0	0
$333$	−12.0000	−0.657596
$334$	0	0
$335$	6.00000	0.327815
$336$	0	0
$337$	26.0000	1.41631	0.708155	−	0.706057i	$-0.249528\pi$
$337$	26.0000	1.41631	0.708155	+	0.706057i	$0.249528\pi$
$338$	0	0
$339$	0	0
$340$	0	0
$341$	1.00000	0.0541530
$342$	0	0
$343$	1.00000	0.0539949
$344$	0	0
$345$	−6.00000	−0.323029
$346$	0	0
$347$	−10.0000	−0.536828	−0.268414	−	0.963304i	$-0.586500\pi$
$347$	−10.0000	−0.536828	−0.268414	+	0.963304i	$0.586500\pi$
$348$	0	0
$349$	−3.00000	−0.160586	−0.0802932	−	0.996771i	$-0.525586\pi$
$349$	−3.00000	−0.160586	−0.0802932	+	0.996771i	$0.525586\pi$
$350$	0	0
$351$	5.00000	0.266880
$352$	0	0
$353$	−34.0000	−1.80964	−0.904819	−	0.425797i	$-0.859994\pi$
$353$	−34.0000	−1.80964	−0.904819	+	0.425797i	$0.859994\pi$
$354$	0	0
$355$	−24.0000	−1.27379
$356$	0	0
$357$	−4.00000	−0.211702
$358$	0	0
$359$	21.0000	1.10834	0.554169	−	0.832404i	$-0.313036\pi$
$359$	21.0000	1.10834	0.554169	+	0.832404i	$0.313036\pi$
$360$	0	0
$361$	−3.00000	−0.157895
$362$	0	0
$363$	−10.0000	−0.524864
$364$	0	0
$365$	0	0
$366$	0	0
$367$	−16.0000	−0.835193	−0.417597	−	0.908633i	$-0.637127\pi$
$367$	−16.0000	−0.835193	−0.417597	+	0.908633i	$0.637127\pi$
$368$	0	0
$369$	0	0
$370$	0	0
$371$	3.00000	0.155752
$372$	0	0
$373$	17.0000	0.880227	0.440113	−	0.897942i	$-0.354938\pi$
$373$	17.0000	0.880227	0.440113	+	0.897942i	$0.354938\pi$
$374$	0	0
$375$	3.00000	0.154919
$376$	0	0
$377$	−1.00000	−0.0515026
$378$	0	0
$379$	−36.0000	−1.84920	−0.924598	−	0.380945i	$-0.875599\pi$
$379$	−36.0000	−1.84920	−0.924598	+	0.380945i	$0.875599\pi$
$380$	0	0
$381$	16.0000	0.819705
$382$	0	0
$383$	−30.0000	−1.53293	−0.766464	−	0.642287i	$-0.777986\pi$
$383$	−30.0000	−1.53293	−0.766464	+	0.642287i	$0.777986\pi$
$384$	0	0
$385$	−3.00000	−0.152894
$386$	0	0
$387$	6.00000	0.304997
$388$	0	0
$389$	−4.00000	−0.202808	−0.101404	−	0.994845i	$-0.532333\pi$
$389$	−4.00000	−0.202808	−0.101404	+	0.994845i	$0.532333\pi$
$390$	0	0
$391$	−8.00000	−0.404577
$392$	0	0
$393$	0	0
$394$	0	0
$395$	−39.0000	−1.96230
$396$	0	0
$397$	11.0000	0.552074	0.276037	−	0.961147i	$-0.410979\pi$
$397$	11.0000	0.552074	0.276037	+	0.961147i	$0.410979\pi$
$398$	0	0
$399$	4.00000	0.200250
$400$	0	0
$401$	39.0000	1.94757	0.973784	−	0.227477i	$-0.0730475\pi$
$401$	39.0000	1.94757	0.973784	+	0.227477i	$0.0730475\pi$
$402$	0	0
$403$	−1.00000	−0.0498135
$404$	0	0
$405$	−3.00000	−0.149071
$406$	0	0
$407$	6.00000	0.297409
$408$	0	0
$409$	28.0000	1.38451	0.692255	−	0.721653i	$-0.256617\pi$
$409$	28.0000	1.38451	0.692255	+	0.721653i	$0.256617\pi$
$410$	0	0
$411$	−10.0000	−0.493264
$412$	0	0
$413$	0	0
$414$	0	0
$415$	0	0
$416$	0	0
$417$	14.0000	0.685583
$418$	0	0
$419$	16.0000	0.781651	0.390826	−	0.920465i	$-0.372190\pi$
$419$	16.0000	0.781651	0.390826	+	0.920465i	$0.372190\pi$
$420$	0	0
$421$	26.0000	1.26716	0.633581	−	0.773676i	$-0.281584\pi$
$421$	26.0000	1.26716	0.633581	+	0.773676i	$0.281584\pi$
$422$	0	0
$423$	−18.0000	−0.875190
$424$	0	0
$425$	−16.0000	−0.776114
$426$	0	0
$427$	6.00000	0.290360
$428$	0	0
$429$	−1.00000	−0.0482805
$430$	0	0
$431$	24.0000	1.15604	0.578020	−	0.816023i	$-0.303826\pi$
$431$	24.0000	1.15604	0.578020	+	0.816023i	$0.303826\pi$
$432$	0	0
$433$	34.0000	1.63394	0.816968	−	0.576683i	$-0.195653\pi$
$433$	34.0000	1.63394	0.816968	+	0.576683i	$0.195653\pi$
$434$	0	0
$435$	−3.00000	−0.143839
$436$	0	0
$437$	8.00000	0.382692
$438$	0	0
$439$	−2.00000	−0.0954548	−0.0477274	−	0.998860i	$-0.515198\pi$
$439$	−2.00000	−0.0954548	−0.0477274	+	0.998860i	$0.515198\pi$
$440$	0	0
$441$	−2.00000	−0.0952381
$442$	0	0
$443$	−20.0000	−0.950229	−0.475114	−	0.879924i	$-0.657593\pi$
$443$	−20.0000	−0.950229	−0.475114	+	0.879924i	$0.657593\pi$
$444$	0	0
$445$	42.0000	1.99099
$446$	0	0
$447$	−11.0000	−0.520282
$448$	0	0
$449$	−16.0000	−0.755087	−0.377543	−	0.925992i	$-0.623231\pi$
$449$	−16.0000	−0.755087	−0.377543	+	0.925992i	$0.623231\pi$
$450$	0	0
$451$	0	0
$452$	0	0
$453$	−14.0000	−0.657777
$454$	0	0
$455$	3.00000	0.140642
$456$	0	0
$457$	−26.0000	−1.21623	−0.608114	−	0.793849i	$-0.708074\pi$
$457$	−26.0000	−1.21623	−0.608114	+	0.793849i	$0.708074\pi$
$458$	0	0
$459$	20.0000	0.933520
$460$	0	0
$461$	−28.0000	−1.30409	−0.652045	−	0.758180i	$-0.726089\pi$
$461$	−28.0000	−1.30409	−0.652045	+	0.758180i	$0.726089\pi$
$462$	0	0
$463$	20.0000	0.929479	0.464739	−	0.885448i	$-0.346148\pi$
$463$	20.0000	0.929479	0.464739	+	0.885448i	$0.346148\pi$
$464$	0	0
$465$	−3.00000	−0.139122
$466$	0	0
$467$	−13.0000	−0.601568	−0.300784	−	0.953692i	$-0.597248\pi$
$467$	−13.0000	−0.601568	−0.300784	+	0.953692i	$0.597248\pi$
$468$	0	0
$469$	−2.00000	−0.0923514
$470$	0	0
$471$	−12.0000	−0.552931
$472$	0	0
$473$	−3.00000	−0.137940
$474$	0	0
$475$	16.0000	0.734130
$476$	0	0
$477$	−6.00000	−0.274721
$478$	0	0
$479$	−21.0000	−0.959514	−0.479757	−	0.877401i	$-0.659275\pi$
$479$	−21.0000	−0.959514	−0.479757	+	0.877401i	$0.659275\pi$
$480$	0	0
$481$	−6.00000	−0.273576
$482$	0	0
$483$	2.00000	0.0910032
$484$	0	0
$485$	−48.0000	−2.17957
$486$	0	0
$487$	20.0000	0.906287	0.453143	−	0.891438i	$-0.350303\pi$
$487$	20.0000	0.906287	0.453143	+	0.891438i	$0.350303\pi$
$488$	0	0
$489$	21.0000	0.949653
$490$	0	0
$491$	−9.00000	−0.406164	−0.203082	−	0.979162i	$-0.565096\pi$
$491$	−9.00000	−0.406164	−0.203082	+	0.979162i	$0.565096\pi$
$492$	0	0
$493$	−4.00000	−0.180151
$494$	0	0
$495$	6.00000	0.269680
$496$	0	0
$497$	8.00000	0.358849
$498$	0	0
$499$	38.0000	1.70111	0.850557	−	0.525883i	$-0.176265\pi$
$499$	38.0000	1.70111	0.850557	+	0.525883i	$0.176265\pi$
$500$	0	0
$501$	−12.0000	−0.536120
$502$	0	0
$503$	11.0000	0.490466	0.245233	−	0.969464i	$-0.421136\pi$
$503$	11.0000	0.490466	0.245233	+	0.969464i	$0.421136\pi$
$504$	0	0
$505$	12.0000	0.533993
$506$	0	0
$507$	−12.0000	−0.532939
$508$	0	0
$509$	−7.00000	−0.310270	−0.155135	−	0.987893i	$-0.549581\pi$
$509$	−7.00000	−0.310270	−0.155135	+	0.987893i	$0.549581\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	−20.0000	−0.883022
$514$	0	0
$515$	12.0000	0.528783
$516$	0	0
$517$	9.00000	0.395820
$518$	0	0
$519$	14.0000	0.614532
$520$	0	0
$521$	25.0000	1.09527	0.547635	−	0.836717i	$-0.315528\pi$
$521$	25.0000	1.09527	0.547635	+	0.836717i	$0.315528\pi$
$522$	0	0
$523$	34.0000	1.48672	0.743358	−	0.668894i	$-0.233232\pi$
$523$	34.0000	1.48672	0.743358	+	0.668894i	$0.233232\pi$
$524$	0	0
$525$	4.00000	0.174574
$526$	0	0
$527$	−4.00000	−0.174243
$528$	0	0
$529$	−19.0000	−0.826087
$530$	0	0
$531$	0	0
$532$	0	0
$533$	0	0
$534$	0	0
$535$	−42.0000	−1.81582
$536$	0	0
$537$	24.0000	1.03568
$538$	0	0
$539$	1.00000	0.0430730
$540$	0	0
$541$	−20.0000	−0.859867	−0.429934	−	0.902861i	$-0.641463\pi$
$541$	−20.0000	−0.859867	−0.429934	+	0.902861i	$0.641463\pi$
$542$	0	0
$543$	23.0000	0.987024
$544$	0	0
$545$	−45.0000	−1.92759
$546$	0	0
$547$	14.0000	0.598597	0.299298	−	0.954160i	$-0.403247\pi$
$547$	14.0000	0.598597	0.299298	+	0.954160i	$0.403247\pi$
$548$	0	0
$549$	−12.0000	−0.512148
$550$	0	0
$551$	4.00000	0.170406
$552$	0	0
$553$	13.0000	0.552816
$554$	0	0
$555$	−18.0000	−0.764057
$556$	0	0
$557$	18.0000	0.762684	0.381342	−	0.924434i	$-0.375462\pi$
$557$	18.0000	0.762684	0.381342	+	0.924434i	$0.375462\pi$
$558$	0	0
$559$	3.00000	0.126886
$560$	0	0
$561$	−4.00000	−0.168880
$562$	0	0
$563$	−9.00000	−0.379305	−0.189652	−	0.981851i	$-0.560736\pi$
$563$	−9.00000	−0.379305	−0.189652	+	0.981851i	$0.560736\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	1.00000	0.0419961
$568$	0	0
$569$	10.0000	0.419222	0.209611	−	0.977785i	$-0.432780\pi$
$569$	10.0000	0.419222	0.209611	+	0.977785i	$0.432780\pi$
$570$	0	0
$571$	−18.0000	−0.753277	−0.376638	−	0.926360i	$-0.622920\pi$
$571$	−18.0000	−0.753277	−0.376638	+	0.926360i	$0.622920\pi$
$572$	0	0
$573$	−8.00000	−0.334205
$574$	0	0
$575$	8.00000	0.333623
$576$	0	0
$577$	−2.00000	−0.0832611	−0.0416305	−	0.999133i	$-0.513255\pi$
$577$	−2.00000	−0.0832611	−0.0416305	+	0.999133i	$0.513255\pi$
$578$	0	0
$579$	12.0000	0.498703
$580$	0	0
$581$	0	0
$582$	0	0
$583$	3.00000	0.124247
$584$	0	0
$585$	−6.00000	−0.248069
$586$	0	0
$587$	−30.0000	−1.23823	−0.619116	−	0.785299i	$-0.712509\pi$
$587$	−30.0000	−1.23823	−0.619116	+	0.785299i	$0.712509\pi$
$588$	0	0
$589$	4.00000	0.164817
$590$	0	0
$591$	−2.00000	−0.0822690
$592$	0	0
$593$	−3.00000	−0.123195	−0.0615976	−	0.998101i	$-0.519620\pi$
$593$	−3.00000	−0.123195	−0.0615976	+	0.998101i	$0.519620\pi$
$594$	0	0
$595$	12.0000	0.491952
$596$	0	0
$597$	20.0000	0.818546
$598$	0	0
$599$	−15.0000	−0.612883	−0.306442	−	0.951889i	$-0.599138\pi$
$599$	−15.0000	−0.612883	−0.306442	+	0.951889i	$0.599138\pi$
$600$	0	0
$601$	−28.0000	−1.14214	−0.571072	−	0.820900i	$-0.693472\pi$
$601$	−28.0000	−1.14214	−0.571072	+	0.820900i	$0.693472\pi$
$602$	0	0
$603$	4.00000	0.162893
$604$	0	0
$605$	30.0000	1.21967
$606$	0	0
$607$	7.00000	0.284121	0.142061	−	0.989858i	$-0.454627\pi$
$607$	7.00000	0.284121	0.142061	+	0.989858i	$0.454627\pi$
$608$	0	0
$609$	1.00000	0.0405220
$610$	0	0
$611$	−9.00000	−0.364101
$612$	0	0
$613$	−29.0000	−1.17130	−0.585649	−	0.810564i	$-0.699160\pi$
$613$	−29.0000	−1.17130	−0.585649	+	0.810564i	$0.699160\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−36.0000	−1.44931	−0.724653	−	0.689114i	$-0.758000\pi$
$617$	−36.0000	−1.44931	−0.724653	+	0.689114i	$0.758000\pi$
$618$	0	0
$619$	3.00000	0.120580	0.0602901	−	0.998181i	$-0.480797\pi$
$619$	3.00000	0.120580	0.0602901	+	0.998181i	$0.480797\pi$
$620$	0	0
$621$	−10.0000	−0.401286
$622$	0	0
$623$	−14.0000	−0.560898
$624$	0	0
$625$	−29.0000	−1.16000
$626$	0	0
$627$	4.00000	0.159745
$628$	0	0
$629$	−24.0000	−0.956943
$630$	0	0
$631$	12.0000	0.477712	0.238856	−	0.971055i	$-0.423228\pi$
$631$	12.0000	0.477712	0.238856	+	0.971055i	$0.423228\pi$
$632$	0	0
$633$	9.00000	0.357718
$634$	0	0
$635$	−48.0000	−1.90482
$636$	0	0
$637$	−1.00000	−0.0396214
$638$	0	0
$639$	−16.0000	−0.632950
$640$	0	0
$641$	12.0000	0.473972	0.236986	−	0.971513i	$-0.423841\pi$
$641$	12.0000	0.473972	0.236986	+	0.971513i	$0.423841\pi$
$642$	0	0
$643$	−12.0000	−0.473234	−0.236617	−	0.971603i	$-0.576039\pi$
$643$	−12.0000	−0.473234	−0.236617	+	0.971603i	$0.576039\pi$
$644$	0	0
$645$	9.00000	0.354375
$646$	0	0
$647$	20.0000	0.786281	0.393141	−	0.919478i	$-0.371389\pi$
$647$	20.0000	0.786281	0.393141	+	0.919478i	$0.371389\pi$
$648$	0	0
$649$	0	0
$650$	0	0
$651$	1.00000	0.0391931
$652$	0	0
$653$	20.0000	0.782660	0.391330	−	0.920250i	$-0.372015\pi$
$653$	20.0000	0.782660	0.391330	+	0.920250i	$0.372015\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	0	0
$658$	0	0
$659$	43.0000	1.67504	0.837521	−	0.546405i	$-0.184004\pi$
$659$	43.0000	1.67504	0.837521	+	0.546405i	$0.184004\pi$
$660$	0	0
$661$	−2.00000	−0.0777910	−0.0388955	−	0.999243i	$-0.512384\pi$
$661$	−2.00000	−0.0777910	−0.0388955	+	0.999243i	$0.512384\pi$
$662$	0	0
$663$	4.00000	0.155347
$664$	0	0
$665$	−12.0000	−0.465340
$666$	0	0
$667$	2.00000	0.0774403
$668$	0	0
$669$	4.00000	0.154649
$670$	0	0
$671$	6.00000	0.231627
$672$	0	0
$673$	−19.0000	−0.732396	−0.366198	−	0.930537i	$-0.619341\pi$
$673$	−19.0000	−0.732396	−0.366198	+	0.930537i	$0.619341\pi$
$674$	0	0
$675$	−20.0000	−0.769800
$676$	0	0
$677$	40.0000	1.53732	0.768662	−	0.639655i	$-0.220923\pi$
$677$	40.0000	1.53732	0.768662	+	0.639655i	$0.220923\pi$
$678$	0	0
$679$	16.0000	0.614024
$680$	0	0
$681$	−14.0000	−0.536481
$682$	0	0
$683$	24.0000	0.918334	0.459167	−	0.888350i	$-0.348148\pi$
$683$	24.0000	0.918334	0.459167	+	0.888350i	$0.348148\pi$
$684$	0	0
$685$	30.0000	1.14624
$686$	0	0
$687$	14.0000	0.534133
$688$	0	0
$689$	−3.00000	−0.114291
$690$	0	0
$691$	48.0000	1.82601	0.913003	−	0.407953i	$-0.133757\pi$
$691$	48.0000	1.82601	0.913003	+	0.407953i	$0.133757\pi$
$692$	0	0
$693$	−2.00000	−0.0759737
$694$	0	0
$695$	−42.0000	−1.59315
$696$	0	0
$697$	0	0
$698$	0	0
$699$	11.0000	0.416058
$700$	0	0
$701$	−35.0000	−1.32193	−0.660966	−	0.750416i	$-0.729853\pi$
$701$	−35.0000	−1.32193	−0.660966	+	0.750416i	$0.729853\pi$
$702$	0	0
$703$	24.0000	0.905177
$704$	0	0
$705$	−27.0000	−1.01688
$706$	0	0
$707$	−4.00000	−0.150435
$708$	0	0
$709$	9.00000	0.338002	0.169001	−	0.985616i	$-0.445946\pi$
$709$	9.00000	0.338002	0.169001	+	0.985616i	$0.445946\pi$
$710$	0	0
$711$	−26.0000	−0.975076
$712$	0	0
$713$	2.00000	0.0749006
$714$	0	0
$715$	3.00000	0.112194
$716$	0	0
$717$	12.0000	0.448148
$718$	0	0
$719$	2.00000	0.0745874	0.0372937	−	0.999304i	$-0.488126\pi$
$719$	2.00000	0.0745874	0.0372937	+	0.999304i	$0.488126\pi$
$720$	0	0
$721$	−4.00000	−0.148968
$722$	0	0
$723$	−29.0000	−1.07852
$724$	0	0
$725$	4.00000	0.148556
$726$	0	0
$727$	−12.0000	−0.445055	−0.222528	−	0.974926i	$-0.571431\pi$
$727$	−12.0000	−0.445055	−0.222528	+	0.974926i	$0.571431\pi$
$728$	0	0
$729$	13.0000	0.481481
$730$	0	0
$731$	12.0000	0.443836
$732$	0	0
$733$	−38.0000	−1.40356	−0.701781	−	0.712393i	$-0.747612\pi$
$733$	−38.0000	−1.40356	−0.701781	+	0.712393i	$0.747612\pi$
$734$	0	0
$735$	−3.00000	−0.110657
$736$	0	0
$737$	−2.00000	−0.0736709
$738$	0	0
$739$	47.0000	1.72892	0.864461	−	0.502699i	$-0.167660\pi$
$739$	47.0000	1.72892	0.864461	+	0.502699i	$0.167660\pi$
$740$	0	0
$741$	−4.00000	−0.146944
$742$	0	0
$743$	20.0000	0.733729	0.366864	−	0.930274i	$-0.380431\pi$
$743$	20.0000	0.733729	0.366864	+	0.930274i	$0.380431\pi$
$744$	0	0
$745$	33.0000	1.20903
$746$	0	0
$747$	0	0
$748$	0	0
$749$	14.0000	0.511549
$750$	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
$753$	17.0000	0.619514
$754$	0	0
$755$	42.0000	1.52854
$756$	0	0
$757$	−28.0000	−1.01768	−0.508839	−	0.860862i	$-0.669925\pi$
$757$	−28.0000	−1.01768	−0.508839	+	0.860862i	$0.669925\pi$
$758$	0	0
$759$	2.00000	0.0725954
$760$	0	0
$761$	−18.0000	−0.652499	−0.326250	−	0.945284i	$-0.605785\pi$
$761$	−18.0000	−0.652499	−0.326250	+	0.945284i	$0.605785\pi$
$762$	0	0
$763$	15.0000	0.543036
$764$	0	0
$765$	−24.0000	−0.867722
$766$	0	0
$767$	0	0
$768$	0	0
$769$	4.00000	0.144244	0.0721218	−	0.997396i	$-0.477023\pi$
$769$	4.00000	0.144244	0.0721218	+	0.997396i	$0.477023\pi$
$770$	0	0
$771$	−9.00000	−0.324127
$772$	0	0
$773$	−20.0000	−0.719350	−0.359675	−	0.933078i	$-0.617112\pi$
$773$	−20.0000	−0.719350	−0.359675	+	0.933078i	$0.617112\pi$
$774$	0	0
$775$	4.00000	0.143684
$776$	0	0
$777$	6.00000	0.215249
$778$	0	0
$779$	0	0
$780$	0	0
$781$	8.00000	0.286263
$782$	0	0
$783$	−5.00000	−0.178685
$784$	0	0
$785$	36.0000	1.28490
$786$	0	0
$787$	12.0000	0.427754	0.213877	−	0.976861i	$-0.431391\pi$
$787$	12.0000	0.427754	0.213877	+	0.976861i	$0.431391\pi$
$788$	0	0
$789$	−5.00000	−0.178005
$790$	0	0
$791$	0	0
$792$	0	0
$793$	−6.00000	−0.213066
$794$	0	0
$795$	−9.00000	−0.319197
$796$	0	0
$797$	12.0000	0.425062	0.212531	−	0.977154i	$-0.431829\pi$
$797$	12.0000	0.425062	0.212531	+	0.977154i	$0.431829\pi$
$798$	0	0
$799$	−36.0000	−1.27359
$800$	0	0
$801$	28.0000	0.989331
$802$	0	0
$803$	0	0
$804$	0	0
$805$	−6.00000	−0.211472
$806$	0	0
$807$	−28.0000	−0.985647
$808$	0	0
$809$	−18.0000	−0.632846	−0.316423	−	0.948618i	$-0.602482\pi$
$809$	−18.0000	−0.632846	−0.316423	+	0.948618i	$0.602482\pi$
$810$	0	0
$811$	30.0000	1.05344	0.526721	−	0.850038i	$-0.323421\pi$
$811$	30.0000	1.05344	0.526721	+	0.850038i	$0.323421\pi$
$812$	0	0
$813$	−25.0000	−0.876788
$814$	0	0
$815$	−63.0000	−2.20679
$816$	0	0
$817$	−12.0000	−0.419827
$818$	0	0
$819$	2.00000	0.0698857
$820$	0	0
$821$	53.0000	1.84971	0.924856	−	0.380317i	$-0.124185\pi$
$821$	53.0000	1.84971	0.924856	+	0.380317i	$0.124185\pi$
$822$	0	0
$823$	8.00000	0.278862	0.139431	−	0.990232i	$-0.455473\pi$
$823$	8.00000	0.278862	0.139431	+	0.990232i	$0.455473\pi$
$824$	0	0
$825$	4.00000	0.139262
$826$	0	0
$827$	−47.0000	−1.63435	−0.817175	−	0.576390i	$-0.804461\pi$
$827$	−47.0000	−1.63435	−0.817175	+	0.576390i	$0.804461\pi$
$828$	0	0
$829$	−20.0000	−0.694629	−0.347314	−	0.937749i	$-0.612906\pi$
$829$	−20.0000	−0.694629	−0.347314	+	0.937749i	$0.612906\pi$
$830$	0	0
$831$	10.0000	0.346896
$832$	0	0
$833$	−4.00000	−0.138592
$834$	0	0
$835$	36.0000	1.24583
$836$	0	0
$837$	−5.00000	−0.172825
$838$	0	0
$839$	21.0000	0.725001	0.362500	−	0.931984i	$-0.381923\pi$
$839$	21.0000	0.725001	0.362500	+	0.931984i	$0.381923\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	0	0
$843$	−21.0000	−0.723278
$844$	0	0
$845$	36.0000	1.23844
$846$	0	0
$847$	−10.0000	−0.343604
$848$	0	0
$849$	2.00000	0.0686398
$850$	0	0
$851$	12.0000	0.411355
$852$	0	0
$853$	−26.0000	−0.890223	−0.445112	−	0.895475i	$-0.646836\pi$
$853$	−26.0000	−0.890223	−0.445112	+	0.895475i	$0.646836\pi$
$854$	0	0
$855$	24.0000	0.820783
$856$	0	0
$857$	−41.0000	−1.40053	−0.700267	−	0.713881i	$-0.746936\pi$
$857$	−41.0000	−1.40053	−0.700267	+	0.713881i	$0.746936\pi$
$858$	0	0
$859$	−31.0000	−1.05771	−0.528853	−	0.848713i	$-0.677378\pi$
$859$	−31.0000	−1.05771	−0.528853	+	0.848713i	$0.677378\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	−58.0000	−1.97434	−0.987171	−	0.159664i	$-0.948959\pi$
$863$	−58.0000	−1.97434	−0.987171	+	0.159664i	$0.948959\pi$
$864$	0	0
$865$	−42.0000	−1.42804
$866$	0	0
$867$	−1.00000	−0.0339618
$868$	0	0
$869$	13.0000	0.440995
$870$	0	0
$871$	2.00000	0.0677674
$872$	0	0
$873$	−32.0000	−1.08304
$874$	0	0
$875$	3.00000	0.101419
$876$	0	0
$877$	31.0000	1.04680	0.523398	−	0.852088i	$-0.324664\pi$
$877$	31.0000	1.04680	0.523398	+	0.852088i	$0.324664\pi$
$878$	0	0
$879$	18.0000	0.607125
$880$	0	0
$881$	−26.0000	−0.875962	−0.437981	−	0.898984i	$-0.644306\pi$
$881$	−26.0000	−0.875962	−0.437981	+	0.898984i	$0.644306\pi$
$882$	0	0
$883$	6.00000	0.201916	0.100958	−	0.994891i	$-0.467809\pi$
$883$	6.00000	0.201916	0.100958	+	0.994891i	$0.467809\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	−3.00000	−0.100730	−0.0503651	−	0.998731i	$-0.516038\pi$
$887$	−3.00000	−0.100730	−0.0503651	+	0.998731i	$0.516038\pi$
$888$	0	0
$889$	16.0000	0.536623
$890$	0	0
$891$	1.00000	0.0335013
$892$	0	0
$893$	36.0000	1.20469
$894$	0	0
$895$	−72.0000	−2.40669
$896$	0	0
$897$	−2.00000	−0.0667781
$898$	0	0
$899$	1.00000	0.0333519
$900$	0	0
$901$	−12.0000	−0.399778
$902$	0	0
$903$	−3.00000	−0.0998337
$904$	0	0
$905$	−69.0000	−2.29364
$906$	0	0
$907$	−28.0000	−0.929725	−0.464862	−	0.885383i	$-0.653896\pi$
$907$	−28.0000	−0.929725	−0.464862	+	0.885383i	$0.653896\pi$
$908$	0	0
$909$	8.00000	0.265343
$910$	0	0
$911$	9.00000	0.298183	0.149092	−	0.988823i	$-0.452365\pi$
$911$	9.00000	0.298183	0.149092	+	0.988823i	$0.452365\pi$
$912$	0	0
$913$	0	0
$914$	0	0
$915$	−18.0000	−0.595062
$916$	0	0
$917$	0	0
$918$	0	0
$919$	−10.0000	−0.329870	−0.164935	−	0.986304i	$-0.552741\pi$
$919$	−10.0000	−0.329870	−0.164935	+	0.986304i	$0.552741\pi$
$920$	0	0
$921$	−9.00000	−0.296560
$922$	0	0
$923$	−8.00000	−0.263323
$924$	0	0
$925$	24.0000	0.789115
$926$	0	0
$927$	8.00000	0.262754
$928$	0	0
$929$	54.0000	1.77168	0.885841	−	0.463988i	$-0.153582\pi$
$929$	54.0000	1.77168	0.885841	+	0.463988i	$0.153582\pi$
$930$	0	0
$931$	4.00000	0.131095
$932$	0	0
$933$	−20.0000	−0.654771
$934$	0	0
$935$	12.0000	0.392442
$936$	0	0
$937$	2.00000	0.0653372	0.0326686	−	0.999466i	$-0.489599\pi$
$937$	2.00000	0.0653372	0.0326686	+	0.999466i	$0.489599\pi$
$938$	0	0
$939$	−5.00000	−0.163169
$940$	0	0
$941$	−27.0000	−0.880175	−0.440087	−	0.897955i	$-0.645053\pi$
$941$	−27.0000	−0.880175	−0.440087	+	0.897955i	$0.645053\pi$
$942$	0	0
$943$	0	0
$944$	0	0
$945$	15.0000	0.487950
$946$	0	0
$947$	−19.0000	−0.617417	−0.308709	−	0.951157i	$-0.599897\pi$
$947$	−19.0000	−0.617417	−0.308709	+	0.951157i	$0.599897\pi$
$948$	0	0
$949$	0	0
$950$	0	0
$951$	22.0000	0.713399
$952$	0	0
$953$	47.0000	1.52248	0.761240	−	0.648471i	$-0.224591\pi$
$953$	47.0000	1.52248	0.761240	+	0.648471i	$0.224591\pi$
$954$	0	0
$955$	24.0000	0.776622
$956$	0	0
$957$	1.00000	0.0323254
$958$	0	0
$959$	−10.0000	−0.322917
$960$	0	0
$961$	−30.0000	−0.967742
$962$	0	0
$963$	−28.0000	−0.902287
$964$	0	0
$965$	−36.0000	−1.15888
$966$	0	0
$967$	31.0000	0.996893	0.498446	−	0.866921i	$-0.333904\pi$
$967$	31.0000	0.996893	0.498446	+	0.866921i	$0.333904\pi$
$968$	0	0
$969$	−16.0000	−0.513994
$970$	0	0
$971$	−12.0000	−0.385098	−0.192549	−	0.981287i	$-0.561675\pi$
$971$	−12.0000	−0.385098	−0.192549	+	0.981287i	$0.561675\pi$
$972$	0	0
$973$	14.0000	0.448819
$974$	0	0
$975$	−4.00000	−0.128103
$976$	0	0
$977$	53.0000	1.69562	0.847810	−	0.530300i	$-0.177921\pi$
$977$	53.0000	1.69562	0.847810	+	0.530300i	$0.177921\pi$
$978$	0	0
$979$	−14.0000	−0.447442
$980$	0	0
$981$	−30.0000	−0.957826
$982$	0	0
$983$	−39.0000	−1.24391	−0.621953	−	0.783054i	$-0.713661\pi$
$983$	−39.0000	−1.24391	−0.621953	+	0.783054i	$0.713661\pi$
$984$	0	0
$985$	6.00000	0.191176
$986$	0	0
$987$	9.00000	0.286473
$988$	0	0
$989$	−6.00000	−0.190789
$990$	0	0
$991$	2.00000	0.0635321	0.0317660	−	0.999495i	$-0.489887\pi$
$991$	2.00000	0.0635321	0.0317660	+	0.999495i	$0.489887\pi$
$992$	0	0
$993$	−27.0000	−0.856819
$994$	0	0
$995$	−60.0000	−1.90213
$996$	0	0
$997$	−14.0000	−0.443384	−0.221692	−	0.975117i	$-0.571158\pi$
$997$	−14.0000	−0.443384	−0.221692	+	0.975117i	$0.571158\pi$
$998$	0	0
$999$	−30.0000	−0.949158

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3248.2.a.k.1.1		1
4.3	odd	2		406.2.a.d.1.1	✓	1
12.11	even	2		3654.2.a.l.1.1		1
28.27	even	2		2842.2.a.f.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
406.2.a.d.1.1	✓	1	4.3	odd	2
2842.2.a.f.1.1		1	28.27	even	2
3248.2.a.k.1.1		1	1.1	even	1	trivial
3654.2.a.l.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:	\( N \)	\(=\)	\( 3248 = 2^{4} \cdot 7 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3248.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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