LMFDB - Embedded newform 8036.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8036,2,Mod(1,8036)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8036, 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("8036.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8036 = 2^{2} \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8036.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:	$64.1677830643$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1148)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	8036.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

$q-1.00000 q^{3} +3.00000 q^{5} -2.00000 q^{9} +3.00000 q^{11} +4.00000 q^{13} -3.00000 q^{15} +7.00000 q^{19} +6.00000 q^{23} +4.00000 q^{25} +5.00000 q^{27} +6.00000 q^{29} +10.0000 q^{31} -3.00000 q^{33} +2.00000 q^{37} -4.00000 q^{39} +1.00000 q^{41} -4.00000 q^{43} -6.00000 q^{45} -12.0000 q^{47} -6.00000 q^{53} +9.00000 q^{55} -7.00000 q^{57} -6.00000 q^{59} +13.0000 q^{61} +12.0000 q^{65} -4.00000 q^{67} -6.00000 q^{69} -9.00000 q^{71} -14.0000 q^{73} -4.00000 q^{75} -1.00000 q^{79} +1.00000 q^{81} -12.0000 q^{83} -6.00000 q^{87} +12.0000 q^{89} -10.0000 q^{93} +21.0000 q^{95} -2.00000 q^{97} -6.00000 q^{99} +O(q^{100})$

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	$-0.593215\pi$
$3$	−1.00000	−0.577350	−0.288675	+	0.957427i	$0.593215\pi$
$4$	0	0
$5$	3.00000	1.34164	0.670820	−	0.741620i	$-0.265942\pi$
$5$	3.00000	1.34164	0.670820	+	0.741620i	$0.265942\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	0	0
$9$	−2.00000	−0.666667
$10$	0	0
$11$	3.00000	0.904534	0.452267	−	0.891883i	$-0.350615\pi$
$11$	3.00000	0.904534	0.452267	+	0.891883i	$0.350615\pi$
$12$	0	0
$13$	4.00000	1.10940	0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000	1.10940	0.554700	+	0.832050i	$0.312833\pi$
$14$	0	0
$15$	−3.00000	−0.774597
$16$	0	0
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	0	0
$19$	7.00000	1.60591	0.802955	−	0.596040i	$-0.203260\pi$
$19$	7.00000	1.60591	0.802955	+	0.596040i	$0.203260\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	6.00000	1.25109	0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000	1.25109	0.625543	+	0.780189i	$0.284877\pi$
$24$	0	0
$25$	4.00000	0.800000
$26$	0	0
$27$	5.00000	0.962250
$28$	0	0
$29$	6.00000	1.11417	0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000	1.11417	0.557086	+	0.830455i	$0.311919\pi$
$30$	0	0
$31$	10.0000	1.79605	0.898027	−	0.439941i	$-0.145001\pi$
$31$	10.0000	1.79605	0.898027	+	0.439941i	$0.145001\pi$
$32$	0	0
$33$	−3.00000	−0.522233
$34$	0	0
$35$	0	0
$36$	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
$39$	−4.00000	−0.640513
$40$	0	0
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	−4.00000	−0.609994	−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000	−0.609994	−0.304997	+	0.952353i	$0.598656\pi$
$44$	0	0
$45$	−6.00000	−0.894427
$46$	0	0
$47$	−12.0000	−1.75038	−0.875190	−	0.483779i	$-0.839264\pi$
$47$	−12.0000	−1.75038	−0.875190	+	0.483779i	$0.839264\pi$
$48$	0	0
$49$	0	0
$50$	0	0
$51$	0	0
$52$	0	0
$53$	−6.00000	−0.824163	−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000	−0.824163	−0.412082	+	0.911147i	$0.635198\pi$
$54$	0	0
$55$	9.00000	1.21356
$56$	0	0
$57$	−7.00000	−0.927173
$58$	0	0
$59$	−6.00000	−0.781133	−0.390567	−	0.920575i	$-0.627721\pi$
$59$	−6.00000	−0.781133	−0.390567	+	0.920575i	$0.627721\pi$
$60$	0	0
$61$	13.0000	1.66448	0.832240	−	0.554416i	$-0.187058\pi$
$61$	13.0000	1.66448	0.832240	+	0.554416i	$0.187058\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	12.0000	1.48842
$66$	0	0
$67$	−4.00000	−0.488678	−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000	−0.488678	−0.244339	+	0.969690i	$0.578571\pi$
$68$	0	0
$69$	−6.00000	−0.722315
$70$	0	0
$71$	−9.00000	−1.06810	−0.534052	−	0.845452i	$-0.679331\pi$
$71$	−9.00000	−1.06810	−0.534052	+	0.845452i	$0.679331\pi$
$72$	0	0
$73$	−14.0000	−1.63858	−0.819288	−	0.573382i	$-0.805631\pi$
$73$	−14.0000	−1.63858	−0.819288	+	0.573382i	$0.805631\pi$
$74$	0	0
$75$	−4.00000	−0.461880
$76$	0	0
$77$	0	0
$78$	0	0
$79$	−1.00000	−0.112509	−0.0562544	−	0.998416i	$-0.517916\pi$
$79$	−1.00000	−0.112509	−0.0562544	+	0.998416i	$0.517916\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	0	0
$83$	−12.0000	−1.31717	−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000	−1.31717	−0.658586	+	0.752506i	$0.728845\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	−6.00000	−0.643268
$88$	0	0
$89$	12.0000	1.27200	0.635999	−	0.771690i	$-0.280588\pi$
$89$	12.0000	1.27200	0.635999	+	0.771690i	$0.280588\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	−10.0000	−1.03695
$94$	0	0
$95$	21.0000	2.15455
$96$	0	0
$97$	−2.00000	−0.203069	−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000	−0.203069	−0.101535	+	0.994832i	$0.532375\pi$
$98$	0	0
$99$	−6.00000	−0.603023
$100$	0	0
$101$	0	0		−	1.00000i	$-0.5\pi$
$101$	0	0			1.00000i	$0.5\pi$
$102$	0	0
$103$	4.00000	0.394132	0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000	0.394132	0.197066	+	0.980390i	$0.436859\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	6.00000	0.580042	0.290021	−	0.957020i	$-0.406338\pi$
$107$	6.00000	0.580042	0.290021	+	0.957020i	$0.406338\pi$
$108$	0	0
$109$	8.00000	0.766261	0.383131	−	0.923694i	$-0.374846\pi$
$109$	8.00000	0.766261	0.383131	+	0.923694i	$0.374846\pi$
$110$	0	0
$111$	−2.00000	−0.189832
$112$	0	0
$113$	−3.00000	−0.282216	−0.141108	−	0.989994i	$-0.545067\pi$
$113$	−3.00000	−0.282216	−0.141108	+	0.989994i	$0.545067\pi$
$114$	0	0
$115$	18.0000	1.67851
$116$	0	0
$117$	−8.00000	−0.739600
$118$	0	0
$119$	0	0
$120$	0	0
$121$	−2.00000	−0.181818
$122$	0	0
$123$	−1.00000	−0.0901670
$124$	0	0
$125$	−3.00000	−0.268328
$126$	0	0
$127$	14.0000	1.24230	0.621150	−	0.783692i	$-0.286666\pi$
$127$	14.0000	1.24230	0.621150	+	0.783692i	$0.286666\pi$
$128$	0	0
$129$	4.00000	0.352180
$130$	0	0
$131$	−18.0000	−1.57267	−0.786334	−	0.617802i	$-0.788023\pi$
$131$	−18.0000	−1.57267	−0.786334	+	0.617802i	$0.788023\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	15.0000	1.29099
$136$	0	0
$137$	−12.0000	−1.02523	−0.512615	−	0.858619i	$-0.671323\pi$
$137$	−12.0000	−1.02523	−0.512615	+	0.858619i	$0.671323\pi$
$138$	0	0
$139$	−14.0000	−1.18746	−0.593732	−	0.804663i	$-0.702346\pi$
$139$	−14.0000	−1.18746	−0.593732	+	0.804663i	$0.702346\pi$
$140$	0	0
$141$	12.0000	1.01058
$142$	0	0
$143$	12.0000	1.00349
$144$	0	0
$145$	18.0000	1.49482
$146$	0	0
$147$	0	0
$148$	0	0
$149$	18.0000	1.47462	0.737309	−	0.675556i	$-0.236096\pi$
$149$	18.0000	1.47462	0.737309	+	0.675556i	$0.236096\pi$
$150$	0	0
$151$	−4.00000	−0.325515	−0.162758	−	0.986666i	$-0.552039\pi$
$151$	−4.00000	−0.325515	−0.162758	+	0.986666i	$0.552039\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	30.0000	2.40966
$156$	0	0
$157$	−14.0000	−1.11732	−0.558661	−	0.829396i	$-0.688685\pi$
$157$	−14.0000	−1.11732	−0.558661	+	0.829396i	$0.688685\pi$
$158$	0	0
$159$	6.00000	0.475831
$160$	0	0
$161$	0	0
$162$	0	0
$163$	14.0000	1.09656	0.548282	−	0.836293i	$-0.315282\pi$
$163$	14.0000	1.09656	0.548282	+	0.836293i	$0.315282\pi$
$164$	0	0
$165$	−9.00000	−0.700649
$166$	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
$169$	3.00000	0.230769
$170$	0	0
$171$	−14.0000	−1.07061
$172$	0	0
$173$	21.0000	1.59660	0.798300	−	0.602260i	$-0.205733\pi$
$173$	21.0000	1.59660	0.798300	+	0.602260i	$0.205733\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	6.00000	0.450988
$178$	0	0
$179$	3.00000	0.224231	0.112115	−	0.993695i	$-0.464237\pi$
$179$	3.00000	0.224231	0.112115	+	0.993695i	$0.464237\pi$
$180$	0	0
$181$	4.00000	0.297318	0.148659	−	0.988889i	$-0.452504\pi$
$181$	4.00000	0.297318	0.148659	+	0.988889i	$0.452504\pi$
$182$	0	0
$183$	−13.0000	−0.960988
$184$	0	0
$185$	6.00000	0.441129
$186$	0	0
$187$	0	0
$188$	0	0
$189$	0	0
$190$	0	0
$191$	0	0		−	1.00000i	$-0.5\pi$
$191$	0	0			1.00000i	$0.5\pi$
$192$	0	0
$193$	14.0000	1.00774	0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000	1.00774	0.503871	+	0.863779i	$0.331909\pi$
$194$	0	0
$195$	−12.0000	−0.859338
$196$	0	0
$197$	3.00000	0.213741	0.106871	−	0.994273i	$-0.465917\pi$
$197$	3.00000	0.213741	0.106871	+	0.994273i	$0.465917\pi$
$198$	0	0
$199$	16.0000	1.13421	0.567105	−	0.823646i	$-0.308063\pi$
$199$	16.0000	1.13421	0.567105	+	0.823646i	$0.308063\pi$
$200$	0	0
$201$	4.00000	0.282138
$202$	0	0
$203$	0	0
$204$	0	0
$205$	3.00000	0.209529
$206$	0	0
$207$	−12.0000	−0.834058
$208$	0	0
$209$	21.0000	1.45260
$210$	0	0
$211$	23.0000	1.58339	0.791693	−	0.610920i	$-0.209200\pi$
$211$	23.0000	1.58339	0.791693	+	0.610920i	$0.209200\pi$
$212$	0	0
$213$	9.00000	0.616670
$214$	0	0
$215$	−12.0000	−0.818393
$216$	0	0
$217$	0	0
$218$	0	0
$219$	14.0000	0.946032
$220$	0	0
$221$	0	0
$222$	0	0
$223$	−8.00000	−0.535720	−0.267860	−	0.963458i	$-0.586316\pi$
$223$	−8.00000	−0.535720	−0.267860	+	0.963458i	$0.586316\pi$
$224$	0	0
$225$	−8.00000	−0.533333
$226$	0	0
$227$	−21.0000	−1.39382	−0.696909	−	0.717159i	$-0.745442\pi$
$227$	−21.0000	−1.39382	−0.696909	+	0.717159i	$0.745442\pi$
$228$	0	0
$229$	4.00000	0.264327	0.132164	−	0.991228i	$-0.457808\pi$
$229$	4.00000	0.264327	0.132164	+	0.991228i	$0.457808\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	6.00000	0.393073	0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000	0.393073	0.196537	+	0.980497i	$0.437031\pi$
$234$	0	0
$235$	−36.0000	−2.34838
$236$	0	0
$237$	1.00000	0.0649570
$238$	0	0
$239$	−27.0000	−1.74648	−0.873242	−	0.487286i	$-0.837987\pi$
$239$	−27.0000	−1.74648	−0.873242	+	0.487286i	$0.837987\pi$
$240$	0	0
$241$	22.0000	1.41714	0.708572	−	0.705638i	$-0.249340\pi$
$241$	22.0000	1.41714	0.708572	+	0.705638i	$0.249340\pi$
$242$	0	0
$243$	−16.0000	−1.02640
$244$	0	0
$245$	0	0
$246$	0	0
$247$	28.0000	1.78160
$248$	0	0
$249$	12.0000	0.760469
$250$	0	0
$251$	−12.0000	−0.757433	−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000	−0.757433	−0.378717	+	0.925513i	$0.623635\pi$
$252$	0	0
$253$	18.0000	1.13165
$254$	0	0
$255$	0	0
$256$	0	0
$257$	6.00000	0.374270	0.187135	−	0.982334i	$-0.440080\pi$
$257$	6.00000	0.374270	0.187135	+	0.982334i	$0.440080\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	−12.0000	−0.742781
$262$	0	0
$263$	12.0000	0.739952	0.369976	−	0.929041i	$-0.379366\pi$
$263$	12.0000	0.739952	0.369976	+	0.929041i	$0.379366\pi$
$264$	0	0
$265$	−18.0000	−1.10573
$266$	0	0
$267$	−12.0000	−0.734388
$268$	0	0
$269$	15.0000	0.914566	0.457283	−	0.889321i	$-0.348823\pi$
$269$	15.0000	0.914566	0.457283	+	0.889321i	$0.348823\pi$
$270$	0	0
$271$	−8.00000	−0.485965	−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000	−0.485965	−0.242983	+	0.970031i	$0.578126\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	12.0000	0.723627
$276$	0	0
$277$	−13.0000	−0.781094	−0.390547	−	0.920583i	$-0.627714\pi$
$277$	−13.0000	−0.781094	−0.390547	+	0.920583i	$0.627714\pi$
$278$	0	0
$279$	−20.0000	−1.19737
$280$	0	0
$281$	6.00000	0.357930	0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000	0.357930	0.178965	+	0.983855i	$0.442725\pi$
$282$	0	0
$283$	−26.0000	−1.54554	−0.772770	−	0.634686i	$-0.781129\pi$
$283$	−26.0000	−1.54554	−0.772770	+	0.634686i	$0.781129\pi$
$284$	0	0
$285$	−21.0000	−1.24393
$286$	0	0
$287$	0	0
$288$	0	0
$289$	−17.0000	−1.00000
$290$	0	0
$291$	2.00000	0.117242
$292$	0	0
$293$	−12.0000	−0.701047	−0.350524	−	0.936554i	$-0.613996\pi$
$293$	−12.0000	−0.701047	−0.350524	+	0.936554i	$0.613996\pi$
$294$	0	0
$295$	−18.0000	−1.04800
$296$	0	0
$297$	15.0000	0.870388
$298$	0	0
$299$	24.0000	1.38796
$300$	0	0
$301$	0	0
$302$	0	0
$303$	0	0
$304$	0	0
$305$	39.0000	2.23313
$306$	0	0
$307$	−20.0000	−1.14146	−0.570730	−	0.821138i	$-0.693340\pi$
$307$	−20.0000	−1.14146	−0.570730	+	0.821138i	$0.693340\pi$
$308$	0	0
$309$	−4.00000	−0.227552
$310$	0	0
$311$	−12.0000	−0.680458	−0.340229	−	0.940343i	$-0.610505\pi$
$311$	−12.0000	−0.680458	−0.340229	+	0.940343i	$0.610505\pi$
$312$	0	0
$313$	−20.0000	−1.13047	−0.565233	−	0.824931i	$-0.691214\pi$
$313$	−20.0000	−1.13047	−0.565233	+	0.824931i	$0.691214\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	−18.0000	−1.01098	−0.505490	−	0.862832i	$-0.668688\pi$
$317$	−18.0000	−1.01098	−0.505490	+	0.862832i	$0.668688\pi$
$318$	0	0
$319$	18.0000	1.00781
$320$	0	0
$321$	−6.00000	−0.334887
$322$	0	0
$323$	0	0
$324$	0	0
$325$	16.0000	0.887520
$326$	0	0
$327$	−8.00000	−0.442401
$328$	0	0
$329$	0	0
$330$	0	0
$331$	−28.0000	−1.53902	−0.769510	−	0.638635i	$-0.779499\pi$
$331$	−28.0000	−1.53902	−0.769510	+	0.638635i	$0.779499\pi$
$332$	0	0
$333$	−4.00000	−0.219199
$334$	0	0
$335$	−12.0000	−0.655630
$336$	0	0
$337$	23.0000	1.25289	0.626445	−	0.779466i	$-0.284509\pi$
$337$	23.0000	1.25289	0.626445	+	0.779466i	$0.284509\pi$
$338$	0	0
$339$	3.00000	0.162938
$340$	0	0
$341$	30.0000	1.62459
$342$	0	0
$343$	0	0
$344$	0	0
$345$	−18.0000	−0.969087
$346$	0	0
$347$	−15.0000	−0.805242	−0.402621	−	0.915367i	$-0.631901\pi$
$347$	−15.0000	−0.805242	−0.402621	+	0.915367i	$0.631901\pi$
$348$	0	0
$349$	−14.0000	−0.749403	−0.374701	−	0.927146i	$-0.622255\pi$
$349$	−14.0000	−0.749403	−0.374701	+	0.927146i	$0.622255\pi$
$350$	0	0
$351$	20.0000	1.06752
$352$	0	0
$353$	15.0000	0.798369	0.399185	−	0.916871i	$-0.369293\pi$
$353$	15.0000	0.798369	0.399185	+	0.916871i	$0.369293\pi$
$354$	0	0
$355$	−27.0000	−1.43301
$356$	0	0
$357$	0	0
$358$	0	0
$359$	36.0000	1.90001	0.950004	−	0.312239i	$-0.101079\pi$
$359$	36.0000	1.90001	0.950004	+	0.312239i	$0.101079\pi$
$360$	0	0
$361$	30.0000	1.57895
$362$	0	0
$363$	2.00000	0.104973
$364$	0	0
$365$	−42.0000	−2.19838
$366$	0	0
$367$	28.0000	1.46159	0.730794	−	0.682598i	$-0.239150\pi$
$367$	28.0000	1.46159	0.730794	+	0.682598i	$0.239150\pi$
$368$	0	0
$369$	−2.00000	−0.104116
$370$	0	0
$371$	0	0
$372$	0	0
$373$	29.0000	1.50156	0.750782	−	0.660551i	$-0.229677\pi$
$373$	29.0000	1.50156	0.750782	+	0.660551i	$0.229677\pi$
$374$	0	0
$375$	3.00000	0.154919
$376$	0	0
$377$	24.0000	1.23606
$378$	0	0
$379$	−16.0000	−0.821865	−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000	−0.821865	−0.410932	+	0.911666i	$0.634797\pi$
$380$	0	0
$381$	−14.0000	−0.717242
$382$	0	0
$383$	27.0000	1.37964	0.689818	−	0.723983i	$-0.257691\pi$
$383$	27.0000	1.37964	0.689818	+	0.723983i	$0.257691\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	8.00000	0.406663
$388$	0	0
$389$	15.0000	0.760530	0.380265	−	0.924878i	$-0.375833\pi$
$389$	15.0000	0.760530	0.380265	+	0.924878i	$0.375833\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	18.0000	0.907980
$394$	0	0
$395$	−3.00000	−0.150946
$396$	0	0
$397$	−14.0000	−0.702640	−0.351320	−	0.936255i	$-0.614267\pi$
$397$	−14.0000	−0.702640	−0.351320	+	0.936255i	$0.614267\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	27.0000	1.34832	0.674158	−	0.738587i	$-0.264507\pi$
$401$	27.0000	1.34832	0.674158	+	0.738587i	$0.264507\pi$
$402$	0	0
$403$	40.0000	1.99254
$404$	0	0
$405$	3.00000	0.149071
$406$	0	0
$407$	6.00000	0.297409
$408$	0	0
$409$	31.0000	1.53285	0.766426	−	0.642333i	$-0.222033\pi$
$409$	31.0000	1.53285	0.766426	+	0.642333i	$0.222033\pi$
$410$	0	0
$411$	12.0000	0.591916
$412$	0	0
$413$	0	0
$414$	0	0
$415$	−36.0000	−1.76717
$416$	0	0
$417$	14.0000	0.685583
$418$	0	0
$419$	6.00000	0.293119	0.146560	−	0.989202i	$-0.453180\pi$
$419$	6.00000	0.293119	0.146560	+	0.989202i	$0.453180\pi$
$420$	0	0
$421$	8.00000	0.389896	0.194948	−	0.980814i	$-0.437546\pi$
$421$	8.00000	0.389896	0.194948	+	0.980814i	$0.437546\pi$
$422$	0	0
$423$	24.0000	1.16692
$424$	0	0
$425$	0	0
$426$	0	0
$427$	0	0
$428$	0	0
$429$	−12.0000	−0.579365
$430$	0	0
$431$	18.0000	0.867029	0.433515	−	0.901146i	$-0.357273\pi$
$431$	18.0000	0.867029	0.433515	+	0.901146i	$0.357273\pi$
$432$	0	0
$433$	−23.0000	−1.10531	−0.552655	−	0.833410i	$-0.686385\pi$
$433$	−23.0000	−1.10531	−0.552655	+	0.833410i	$0.686385\pi$
$434$	0	0
$435$	−18.0000	−0.863034
$436$	0	0
$437$	42.0000	2.00913
$438$	0	0
$439$	1.00000	0.0477274	0.0238637	−	0.999715i	$-0.492403\pi$
$439$	1.00000	0.0477274	0.0238637	+	0.999715i	$0.492403\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	18.0000	0.855206	0.427603	−	0.903967i	$-0.359358\pi$
$443$	18.0000	0.855206	0.427603	+	0.903967i	$0.359358\pi$
$444$	0	0
$445$	36.0000	1.70656
$446$	0	0
$447$	−18.0000	−0.851371
$448$	0	0
$449$	9.00000	0.424736	0.212368	−	0.977190i	$-0.431882\pi$
$449$	9.00000	0.424736	0.212368	+	0.977190i	$0.431882\pi$
$450$	0	0
$451$	3.00000	0.141264
$452$	0	0
$453$	4.00000	0.187936
$454$	0	0
$455$	0	0
$456$	0	0
$457$	−16.0000	−0.748448	−0.374224	−	0.927338i	$-0.622091\pi$
$457$	−16.0000	−0.748448	−0.374224	+	0.927338i	$0.622091\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	−27.0000	−1.25752	−0.628758	−	0.777601i	$-0.716436\pi$
$461$	−27.0000	−1.25752	−0.628758	+	0.777601i	$0.716436\pi$
$462$	0	0
$463$	−1.00000	−0.0464739	−0.0232370	−	0.999730i	$-0.507397\pi$
$463$	−1.00000	−0.0464739	−0.0232370	+	0.999730i	$0.507397\pi$
$464$	0	0
$465$	−30.0000	−1.39122
$466$	0	0
$467$	−30.0000	−1.38823	−0.694117	−	0.719862i	$-0.744205\pi$
$467$	−30.0000	−1.38823	−0.694117	+	0.719862i	$0.744205\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	14.0000	0.645086
$472$	0	0
$473$	−12.0000	−0.551761
$474$	0	0
$475$	28.0000	1.28473
$476$	0	0
$477$	12.0000	0.549442
$478$	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
$481$	8.00000	0.364769
$482$	0	0
$483$	0	0
$484$	0	0
$485$	−6.00000	−0.272446
$486$	0	0
$487$	8.00000	0.362515	0.181257	−	0.983436i	$-0.441983\pi$
$487$	8.00000	0.362515	0.181257	+	0.983436i	$0.441983\pi$
$488$	0	0
$489$	−14.0000	−0.633102
$490$	0	0
$491$	−42.0000	−1.89543	−0.947717	−	0.319113i	$-0.896615\pi$
$491$	−42.0000	−1.89543	−0.947717	+	0.319113i	$0.896615\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	−18.0000	−0.809040
$496$	0	0
$497$	0	0
$498$	0	0
$499$	−4.00000	−0.179065	−0.0895323	−	0.995984i	$-0.528537\pi$
$499$	−4.00000	−0.179065	−0.0895323	+	0.995984i	$0.528537\pi$
$500$	0	0
$501$	12.0000	0.536120
$502$	0	0
$503$	−9.00000	−0.401290	−0.200645	−	0.979664i	$-0.564304\pi$
$503$	−9.00000	−0.401290	−0.200645	+	0.979664i	$0.564304\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	−3.00000	−0.133235
$508$	0	0
$509$	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
$511$	0	0
$512$	0	0
$513$	35.0000	1.54529
$514$	0	0
$515$	12.0000	0.528783
$516$	0	0
$517$	−36.0000	−1.58328
$518$	0	0
$519$	−21.0000	−0.921798
$520$	0	0
$521$	−30.0000	−1.31432	−0.657162	−	0.753749i	$-0.728243\pi$
$521$	−30.0000	−1.31432	−0.657162	+	0.753749i	$0.728243\pi$
$522$	0	0
$523$	−38.0000	−1.66162	−0.830812	−	0.556553i	$-0.812124\pi$
$523$	−38.0000	−1.66162	−0.830812	+	0.556553i	$0.812124\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	0	0
$528$	0	0
$529$	13.0000	0.565217
$530$	0	0
$531$	12.0000	0.520756
$532$	0	0
$533$	4.00000	0.173259
$534$	0	0
$535$	18.0000	0.778208
$536$	0	0
$537$	−3.00000	−0.129460
$538$	0	0
$539$	0	0
$540$	0	0
$541$	14.0000	0.601907	0.300954	−	0.953639i	$-0.402695\pi$
$541$	14.0000	0.601907	0.300954	+	0.953639i	$0.402695\pi$
$542$	0	0
$543$	−4.00000	−0.171656
$544$	0	0
$545$	24.0000	1.02805
$546$	0	0
$547$	20.0000	0.855138	0.427569	−	0.903983i	$-0.359370\pi$
$547$	20.0000	0.855138	0.427569	+	0.903983i	$0.359370\pi$
$548$	0	0
$549$	−26.0000	−1.10965
$550$	0	0
$551$	42.0000	1.78926
$552$	0	0
$553$	0	0
$554$	0	0
$555$	−6.00000	−0.254686
$556$	0	0
$557$	−12.0000	−0.508456	−0.254228	−	0.967144i	$-0.581821\pi$
$557$	−12.0000	−0.508456	−0.254228	+	0.967144i	$0.581821\pi$
$558$	0	0
$559$	−16.0000	−0.676728
$560$	0	0
$561$	0	0
$562$	0	0
$563$	15.0000	0.632175	0.316087	−	0.948730i	$-0.397631\pi$
$563$	15.0000	0.632175	0.316087	+	0.948730i	$0.397631\pi$
$564$	0	0
$565$	−9.00000	−0.378633
$566$	0	0
$567$	0	0
$568$	0	0
$569$	30.0000	1.25767	0.628833	−	0.777541i	$-0.283533\pi$
$569$	30.0000	1.25767	0.628833	+	0.777541i	$0.283533\pi$
$570$	0	0
$571$	5.00000	0.209243	0.104622	−	0.994512i	$-0.466637\pi$
$571$	5.00000	0.209243	0.104622	+	0.994512i	$0.466637\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	24.0000	1.00087
$576$	0	0
$577$	−20.0000	−0.832611	−0.416305	−	0.909225i	$-0.636675\pi$
$577$	−20.0000	−0.832611	−0.416305	+	0.909225i	$0.636675\pi$
$578$	0	0
$579$	−14.0000	−0.581820
$580$	0	0
$581$	0	0
$582$	0	0
$583$	−18.0000	−0.745484
$584$	0	0
$585$	−24.0000	−0.992278
$586$	0	0
$587$	33.0000	1.36206	0.681028	−	0.732257i	$-0.261533\pi$
$587$	33.0000	1.36206	0.681028	+	0.732257i	$0.261533\pi$
$588$	0	0
$589$	70.0000	2.88430
$590$	0	0
$591$	−3.00000	−0.123404
$592$	0	0
$593$	6.00000	0.246390	0.123195	−	0.992382i	$-0.460686\pi$
$593$	6.00000	0.246390	0.123195	+	0.992382i	$0.460686\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	−16.0000	−0.654836
$598$	0	0
$599$	−30.0000	−1.22577	−0.612883	−	0.790173i	$-0.709990\pi$
$599$	−30.0000	−1.22577	−0.612883	+	0.790173i	$0.709990\pi$
$600$	0	0
$601$	34.0000	1.38689	0.693444	−	0.720510i	$-0.256092\pi$
$601$	34.0000	1.38689	0.693444	+	0.720510i	$0.256092\pi$
$602$	0	0
$603$	8.00000	0.325785
$604$	0	0
$605$	−6.00000	−0.243935
$606$	0	0
$607$	28.0000	1.13648	0.568242	−	0.822861i	$-0.307624\pi$
$607$	28.0000	1.13648	0.568242	+	0.822861i	$0.307624\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	−48.0000	−1.94187
$612$	0	0
$613$	−7.00000	−0.282727	−0.141364	−	0.989958i	$-0.545149\pi$
$613$	−7.00000	−0.282727	−0.141364	+	0.989958i	$0.545149\pi$
$614$	0	0
$615$	−3.00000	−0.120972
$616$	0	0
$617$	−27.0000	−1.08698	−0.543490	−	0.839416i	$-0.682897\pi$
$617$	−27.0000	−1.08698	−0.543490	+	0.839416i	$0.682897\pi$
$618$	0	0
$619$	−44.0000	−1.76851	−0.884255	−	0.467005i	$-0.845333\pi$
$619$	−44.0000	−1.76851	−0.884255	+	0.467005i	$0.845333\pi$
$620$	0	0
$621$	30.0000	1.20386
$622$	0	0
$623$	0	0
$624$	0	0
$625$	−29.0000	−1.16000
$626$	0	0
$627$	−21.0000	−0.838659
$628$	0	0
$629$	0	0
$630$	0	0
$631$	20.0000	0.796187	0.398094	−	0.917345i	$-0.369672\pi$
$631$	20.0000	0.796187	0.398094	+	0.917345i	$0.369672\pi$
$632$	0	0
$633$	−23.0000	−0.914168
$634$	0	0
$635$	42.0000	1.66672
$636$	0	0
$637$	0	0
$638$	0	0
$639$	18.0000	0.712069
$640$	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
$643$	−5.00000	−0.197181	−0.0985904	−	0.995128i	$-0.531433\pi$
$643$	−5.00000	−0.197181	−0.0985904	+	0.995128i	$0.531433\pi$
$644$	0	0
$645$	12.0000	0.472500
$646$	0	0
$647$	12.0000	0.471769	0.235884	−	0.971781i	$-0.424201\pi$
$647$	12.0000	0.471769	0.235884	+	0.971781i	$0.424201\pi$
$648$	0	0
$649$	−18.0000	−0.706562
$650$	0	0
$651$	0	0
$652$	0	0
$653$	36.0000	1.40879	0.704394	−	0.709809i	$-0.251219\pi$
$653$	36.0000	1.40879	0.704394	+	0.709809i	$0.251219\pi$
$654$	0	0
$655$	−54.0000	−2.10995
$656$	0	0
$657$	28.0000	1.09238
$658$	0	0
$659$	−48.0000	−1.86981	−0.934907	−	0.354892i	$-0.884518\pi$
$659$	−48.0000	−1.86981	−0.934907	+	0.354892i	$0.884518\pi$
$660$	0	0
$661$	31.0000	1.20576	0.602880	−	0.797832i	$-0.294020\pi$
$661$	31.0000	1.20576	0.602880	+	0.797832i	$0.294020\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	0	0
$666$	0	0
$667$	36.0000	1.39393
$668$	0	0
$669$	8.00000	0.309298
$670$	0	0
$671$	39.0000	1.50558
$672$	0	0
$673$	−22.0000	−0.848038	−0.424019	−	0.905653i	$-0.639381\pi$
$673$	−22.0000	−0.848038	−0.424019	+	0.905653i	$0.639381\pi$
$674$	0	0
$675$	20.0000	0.769800
$676$	0	0
$677$	15.0000	0.576497	0.288248	−	0.957556i	$-0.406927\pi$
$677$	15.0000	0.576497	0.288248	+	0.957556i	$0.406927\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	21.0000	0.804722
$682$	0	0
$683$	12.0000	0.459167	0.229584	−	0.973289i	$-0.426264\pi$
$683$	12.0000	0.459167	0.229584	+	0.973289i	$0.426264\pi$
$684$	0	0
$685$	−36.0000	−1.37549
$686$	0	0
$687$	−4.00000	−0.152610
$688$	0	0
$689$	−24.0000	−0.914327
$690$	0	0
$691$	1.00000	0.0380418	0.0190209	−	0.999819i	$-0.493945\pi$
$691$	1.00000	0.0380418	0.0190209	+	0.999819i	$0.493945\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	−42.0000	−1.59315
$696$	0	0
$697$	0	0
$698$	0	0
$699$	−6.00000	−0.226941
$700$	0	0
$701$	15.0000	0.566542	0.283271	−	0.959040i	$-0.408580\pi$
$701$	15.0000	0.566542	0.283271	+	0.959040i	$0.408580\pi$
$702$	0	0
$703$	14.0000	0.528020
$704$	0	0
$705$	36.0000	1.35584
$706$	0	0
$707$	0	0
$708$	0	0
$709$	−10.0000	−0.375558	−0.187779	−	0.982211i	$-0.560129\pi$
$709$	−10.0000	−0.375558	−0.187779	+	0.982211i	$0.560129\pi$
$710$	0	0
$711$	2.00000	0.0750059
$712$	0	0
$713$	60.0000	2.24702
$714$	0	0
$715$	36.0000	1.34632
$716$	0	0
$717$	27.0000	1.00833
$718$	0	0
$719$	−3.00000	−0.111881	−0.0559406	−	0.998434i	$-0.517816\pi$
$719$	−3.00000	−0.111881	−0.0559406	+	0.998434i	$0.517816\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	−22.0000	−0.818189
$724$	0	0
$725$	24.0000	0.891338
$726$	0	0
$727$	40.0000	1.48352	0.741759	−	0.670667i	$-0.233992\pi$
$727$	40.0000	1.48352	0.741759	+	0.670667i	$0.233992\pi$
$728$	0	0
$729$	13.0000	0.481481
$730$	0	0
$731$	0	0
$732$	0	0
$733$	22.0000	0.812589	0.406294	−	0.913742i	$-0.366821\pi$
$733$	22.0000	0.812589	0.406294	+	0.913742i	$0.366821\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−12.0000	−0.442026
$738$	0	0
$739$	−16.0000	−0.588570	−0.294285	−	0.955718i	$-0.595081\pi$
$739$	−16.0000	−0.588570	−0.294285	+	0.955718i	$0.595081\pi$
$740$	0	0
$741$	−28.0000	−1.02861
$742$	0	0
$743$	6.00000	0.220119	0.110059	−	0.993925i	$-0.464896\pi$
$743$	6.00000	0.220119	0.110059	+	0.993925i	$0.464896\pi$
$744$	0	0
$745$	54.0000	1.97841
$746$	0	0
$747$	24.0000	0.878114
$748$	0	0
$749$	0	0
$750$	0	0
$751$	−43.0000	−1.56909	−0.784546	−	0.620070i	$-0.787104\pi$
$751$	−43.0000	−1.56909	−0.784546	+	0.620070i	$0.787104\pi$
$752$	0	0
$753$	12.0000	0.437304
$754$	0	0
$755$	−12.0000	−0.436725
$756$	0	0
$757$	−40.0000	−1.45382	−0.726912	−	0.686730i	$-0.759045\pi$
$757$	−40.0000	−1.45382	−0.726912	+	0.686730i	$0.759045\pi$
$758$	0	0
$759$	−18.0000	−0.653359
$760$	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
$763$	0	0
$764$	0	0
$765$	0	0
$766$	0	0
$767$	−24.0000	−0.866590
$768$	0	0
$769$	−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
$771$	−6.00000	−0.216085
$772$	0	0
$773$	−36.0000	−1.29483	−0.647415	−	0.762138i	$-0.724150\pi$
$773$	−36.0000	−1.29483	−0.647415	+	0.762138i	$0.724150\pi$
$774$	0	0
$775$	40.0000	1.43684
$776$	0	0
$777$	0	0
$778$	0	0
$779$	7.00000	0.250801
$780$	0	0
$781$	−27.0000	−0.966136
$782$	0	0
$783$	30.0000	1.07211
$784$	0	0
$785$	−42.0000	−1.49904
$786$	0	0
$787$	28.0000	0.998092	0.499046	−	0.866575i	$-0.333684\pi$
$787$	28.0000	0.998092	0.499046	+	0.866575i	$0.333684\pi$
$788$	0	0
$789$	−12.0000	−0.427211
$790$	0	0
$791$	0	0
$792$	0	0
$793$	52.0000	1.84657
$794$	0	0
$795$	18.0000	0.638394
$796$	0	0
$797$	30.0000	1.06265	0.531327	−	0.847167i	$-0.321693\pi$
$797$	30.0000	1.06265	0.531327	+	0.847167i	$0.321693\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	−24.0000	−0.847998
$802$	0	0
$803$	−42.0000	−1.48215
$804$	0	0
$805$	0	0
$806$	0	0
$807$	−15.0000	−0.528025
$808$	0	0
$809$	−12.0000	−0.421898	−0.210949	−	0.977497i	$-0.567655\pi$
$809$	−12.0000	−0.421898	−0.210949	+	0.977497i	$0.567655\pi$
$810$	0	0
$811$	−38.0000	−1.33436	−0.667180	−	0.744896i	$-0.732499\pi$
$811$	−38.0000	−1.33436	−0.667180	+	0.744896i	$0.732499\pi$
$812$	0	0
$813$	8.00000	0.280572
$814$	0	0
$815$	42.0000	1.47120
$816$	0	0
$817$	−28.0000	−0.979596
$818$	0	0
$819$	0	0
$820$	0	0
$821$	−9.00000	−0.314102	−0.157051	−	0.987590i	$-0.550199\pi$
$821$	−9.00000	−0.314102	−0.157051	+	0.987590i	$0.550199\pi$
$822$	0	0
$823$	5.00000	0.174289	0.0871445	−	0.996196i	$-0.472226\pi$
$823$	5.00000	0.174289	0.0871445	+	0.996196i	$0.472226\pi$
$824$	0	0
$825$	−12.0000	−0.417786
$826$	0	0
$827$	12.0000	0.417281	0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000	0.417281	0.208640	+	0.977992i	$0.433096\pi$
$828$	0	0
$829$	−38.0000	−1.31979	−0.659897	−	0.751356i	$-0.729400\pi$
$829$	−38.0000	−1.31979	−0.659897	+	0.751356i	$0.729400\pi$
$830$	0	0
$831$	13.0000	0.450965
$832$	0	0
$833$	0	0
$834$	0	0
$835$	−36.0000	−1.24583
$836$	0	0
$837$	50.0000	1.72825
$838$	0	0
$839$	3.00000	0.103572	0.0517858	−	0.998658i	$-0.483509\pi$
$839$	3.00000	0.103572	0.0517858	+	0.998658i	$0.483509\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	0	0
$843$	−6.00000	−0.206651
$844$	0	0
$845$	9.00000	0.309609
$846$	0	0
$847$	0	0
$848$	0	0
$849$	26.0000	0.892318
$850$	0	0
$851$	12.0000	0.411355
$852$	0	0
$853$	49.0000	1.67773	0.838864	−	0.544341i	$-0.183220\pi$
$853$	49.0000	1.67773	0.838864	+	0.544341i	$0.183220\pi$
$854$	0	0
$855$	−42.0000	−1.43637
$856$	0	0
$857$	3.00000	0.102478	0.0512390	−	0.998686i	$-0.483683\pi$
$857$	3.00000	0.102478	0.0512390	+	0.998686i	$0.483683\pi$
$858$	0	0
$859$	−8.00000	−0.272956	−0.136478	−	0.990643i	$-0.543578\pi$
$859$	−8.00000	−0.272956	−0.136478	+	0.990643i	$0.543578\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	24.0000	0.816970	0.408485	−	0.912765i	$-0.366057\pi$
$863$	24.0000	0.816970	0.408485	+	0.912765i	$0.366057\pi$
$864$	0	0
$865$	63.0000	2.14206
$866$	0	0
$867$	17.0000	0.577350
$868$	0	0
$869$	−3.00000	−0.101768
$870$	0	0
$871$	−16.0000	−0.542139
$872$	0	0
$873$	4.00000	0.135379
$874$	0	0
$875$	0	0
$876$	0	0
$877$	17.0000	0.574049	0.287025	−	0.957923i	$-0.407334\pi$
$877$	17.0000	0.574049	0.287025	+	0.957923i	$0.407334\pi$
$878$	0	0
$879$	12.0000	0.404750
$880$	0	0
$881$	−45.0000	−1.51609	−0.758044	−	0.652203i	$-0.773845\pi$
$881$	−45.0000	−1.51609	−0.758044	+	0.652203i	$0.773845\pi$
$882$	0	0
$883$	32.0000	1.07689	0.538443	−	0.842662i	$-0.319013\pi$
$883$	32.0000	1.07689	0.538443	+	0.842662i	$0.319013\pi$
$884$	0	0
$885$	18.0000	0.605063
$886$	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
$889$	0	0
$890$	0	0
$891$	3.00000	0.100504
$892$	0	0
$893$	−84.0000	−2.81095
$894$	0	0
$895$	9.00000	0.300837
$896$	0	0
$897$	−24.0000	−0.801337
$898$	0	0
$899$	60.0000	2.00111
$900$	0	0
$901$	0	0
$902$	0	0
$903$	0	0
$904$	0	0
$905$	12.0000	0.398893
$906$	0	0
$907$	−10.0000	−0.332045	−0.166022	−	0.986122i	$-0.553092\pi$
$907$	−10.0000	−0.332045	−0.166022	+	0.986122i	$0.553092\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	0	0		−	1.00000i	$-0.5\pi$
$911$	0	0			1.00000i	$0.5\pi$
$912$	0	0
$913$	−36.0000	−1.19143
$914$	0	0
$915$	−39.0000	−1.28930
$916$	0	0
$917$	0	0
$918$	0	0
$919$	59.0000	1.94623	0.973115	−	0.230319i	$-0.0739769\pi$
$919$	59.0000	1.94623	0.973115	+	0.230319i	$0.0739769\pi$
$920$	0	0
$921$	20.0000	0.659022
$922$	0	0
$923$	−36.0000	−1.18495
$924$	0	0
$925$	8.00000	0.263038
$926$	0	0
$927$	−8.00000	−0.262754
$928$	0	0
$929$	0	0		−	1.00000i	$-0.5\pi$
$929$	0	0			1.00000i	$0.5\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	12.0000	0.392862
$934$	0	0
$935$	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	$0.312578\pi$
$938$	0	0
$939$	20.0000	0.652675
$940$	0	0
$941$	45.0000	1.46696	0.733479	−	0.679712i	$-0.237895\pi$
$941$	45.0000	1.46696	0.733479	+	0.679712i	$0.237895\pi$
$942$	0	0
$943$	6.00000	0.195387
$944$	0	0
$945$	0	0
$946$	0	0
$947$	−18.0000	−0.584921	−0.292461	−	0.956278i	$-0.594474\pi$
$947$	−18.0000	−0.584921	−0.292461	+	0.956278i	$0.594474\pi$
$948$	0	0
$949$	−56.0000	−1.81784
$950$	0	0
$951$	18.0000	0.583690
$952$	0	0
$953$	−6.00000	−0.194359	−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000	−0.194359	−0.0971795	+	0.995267i	$0.530982\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	−18.0000	−0.581857
$958$	0	0
$959$	0	0
$960$	0	0
$961$	69.0000	2.22581
$962$	0	0
$963$	−12.0000	−0.386695
$964$	0	0
$965$	42.0000	1.35203
$966$	0	0
$967$	23.0000	0.739630	0.369815	−	0.929105i	$-0.379421\pi$
$967$	23.0000	0.739630	0.369815	+	0.929105i	$0.379421\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	0	0		−	1.00000i	$-0.5\pi$
$971$	0	0			1.00000i	$0.5\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	−16.0000	−0.512410
$976$	0	0
$977$	−42.0000	−1.34370	−0.671850	−	0.740688i	$-0.734500\pi$
$977$	−42.0000	−1.34370	−0.671850	+	0.740688i	$0.734500\pi$
$978$	0	0
$979$	36.0000	1.15056
$980$	0	0
$981$	−16.0000	−0.510841
$982$	0	0
$983$	−12.0000	−0.382741	−0.191370	−	0.981518i	$-0.561293\pi$
$983$	−12.0000	−0.382741	−0.191370	+	0.981518i	$0.561293\pi$
$984$	0	0
$985$	9.00000	0.286764
$986$	0	0
$987$	0	0
$988$	0	0
$989$	−24.0000	−0.763156
$990$	0	0
$991$	−43.0000	−1.36594	−0.682970	−	0.730446i	$-0.739312\pi$
$991$	−43.0000	−1.36594	−0.682970	+	0.730446i	$0.739312\pi$
$992$	0	0
$993$	28.0000	0.888553
$994$	0	0
$995$	48.0000	1.52170
$996$	0	0
$997$	28.0000	0.886769	0.443384	−	0.896332i	$-0.353778\pi$
$997$	28.0000	0.886769	0.443384	+	0.896332i	$0.353778\pi$
$998$	0	0
$999$	10.0000	0.316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8036.2.a.c.1.1		1
7.3	odd	6		1148.2.i.a.821.1	yes	2
7.5	odd	6		1148.2.i.a.165.1	✓	2
7.6	odd	2		8036.2.a.d.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.i.a.165.1	✓	2	7.5	odd	6
1148.2.i.a.821.1	yes	2	7.3	odd	6
8036.2.a.c.1.1		1	1.1	even	1	trivial
8036.2.a.d.1.1		1	7.6	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:	\( N \)	\(=\)	\( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8036.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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