LMFDB - Embedded newform 9016.2.a.u.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9016,2,Mod(1,9016)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9016, 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("9016.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9016 = 2^{3} \cdot 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9016.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:	$71.9931224624$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.41421$ of defining polynomial
Character	$\chi$	$=$	9016.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.82843 q^{3} -1.41421 q^{5} +5.00000 q^{9} +O(q^{10})$	$q-2.82843 q^{3} -1.41421 q^{5} +5.00000 q^{9} -4.00000 q^{11} +5.65685 q^{13} +4.00000 q^{15} -5.65685 q^{17} +7.07107 q^{19} +1.00000 q^{23} -3.00000 q^{25} -5.65685 q^{27} -6.00000 q^{29} +4.24264 q^{31} +11.3137 q^{33} -4.00000 q^{37} -16.0000 q^{39} -1.41421 q^{41} -6.00000 q^{43} -7.07107 q^{45} -4.24264 q^{47} +16.0000 q^{51} -8.00000 q^{53} +5.65685 q^{55} -20.0000 q^{57} +8.48528 q^{59} +1.41421 q^{61} -8.00000 q^{65} +10.0000 q^{67} -2.82843 q^{69} +2.00000 q^{71} +7.07107 q^{73} +8.48528 q^{75} +8.00000 q^{79} +1.00000 q^{81} +7.07107 q^{83} +8.00000 q^{85} +16.9706 q^{87} -2.82843 q^{89} -12.0000 q^{93} -10.0000 q^{95} +8.48528 q^{97} -20.0000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 10 q^{9}+O(q^{10}) $ 2 * q + 10 * q^9	$ 2 q + 10 q^{9} - 8 q^{11} + 8 q^{15} + 2 q^{23} - 6 q^{25} - 12 q^{29} - 8 q^{37} - 32 q^{39} - 12 q^{43} + 32 q^{51} - 16 q^{53} - 40 q^{57} - 16 q^{65} + 20 q^{67} + 4 q^{71} + 16 q^{79} + 2 q^{81} + 16 q^{85} - 24 q^{93} - 20 q^{95} - 40 q^{99}+O(q^{100}) $ 2 * q + 10 * q^9 - 8 * q^11 + 8 * q^15 + 2 * q^23 - 6 * q^25 - 12 * q^29 - 8 * q^37 - 32 * q^39 - 12 * q^43 + 32 * q^51 - 16 * q^53 - 40 * q^57 - 16 * q^65 + 20 * q^67 + 4 * q^71 + 16 * q^79 + 2 * q^81 + 16 * q^85 - 24 * q^93 - 20 * q^95 - 40 * q^99

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
$3$	−2.82843	−1.63299	−0.816497	−	0.577350i	$-0.804087\pi$
$3$	−2.82843	−1.63299	−0.816497	+	0.577350i	$0.804087\pi$
$4$	0	0
$5$	−1.41421	−0.632456	−0.316228	−	0.948683i	$-0.602416\pi$
$5$	−1.41421	−0.632456	−0.316228	+	0.948683i	$0.602416\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	0	0
$9$	5.00000	1.66667
$10$	0	0
$11$	−4.00000	−1.20605	−0.603023	−	0.797724i	$-0.706037\pi$
$11$	−4.00000	−1.20605	−0.603023	+	0.797724i	$0.706037\pi$
$12$	0	0
$13$	5.65685	1.56893	0.784465	−	0.620174i	$-0.212938\pi$
$13$	5.65685	1.56893	0.784465	+	0.620174i	$0.212938\pi$
$14$	0	0
$15$	4.00000	1.03280
$16$	0	0
$17$	−5.65685	−1.37199	−0.685994	−	0.727607i	$-0.740633\pi$
$17$	−5.65685	−1.37199	−0.685994	+	0.727607i	$0.740633\pi$
$18$	0	0
$19$	7.07107	1.62221	0.811107	−	0.584898i	$-0.198865\pi$
$19$	7.07107	1.62221	0.811107	+	0.584898i	$0.198865\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	0	0
$25$	−3.00000	−0.600000
$26$	0	0
$27$	−5.65685	−1.08866
$28$	0	0
$29$	−6.00000	−1.11417	−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000	−1.11417	−0.557086	+	0.830455i	$0.688081\pi$
$30$	0	0
$31$	4.24264	0.762001	0.381000	−	0.924575i	$-0.375580\pi$
$31$	4.24264	0.762001	0.381000	+	0.924575i	$0.375580\pi$
$32$	0	0
$33$	11.3137	1.96946
$34$	0	0
$35$	0	0
$36$	0	0
$37$	−4.00000	−0.657596	−0.328798	−	0.944400i	$-0.606644\pi$
$37$	−4.00000	−0.657596	−0.328798	+	0.944400i	$0.606644\pi$
$38$	0	0
$39$	−16.0000	−2.56205
$40$	0	0
$41$	−1.41421	−0.220863	−0.110432	−	0.993884i	$-0.535223\pi$
$41$	−1.41421	−0.220863	−0.110432	+	0.993884i	$0.535223\pi$
$42$	0	0
$43$	−6.00000	−0.914991	−0.457496	−	0.889212i	$-0.651253\pi$
$43$	−6.00000	−0.914991	−0.457496	+	0.889212i	$0.651253\pi$
$44$	0	0
$45$	−7.07107	−1.05409
$46$	0	0
$47$	−4.24264	−0.618853	−0.309426	−	0.950923i	$-0.600137\pi$
$47$	−4.24264	−0.618853	−0.309426	+	0.950923i	$0.600137\pi$
$48$	0	0
$49$	0	0
$50$	0	0
$51$	16.0000	2.24045
$52$	0	0
$53$	−8.00000	−1.09888	−0.549442	−	0.835532i	$-0.685160\pi$
$53$	−8.00000	−1.09888	−0.549442	+	0.835532i	$0.685160\pi$
$54$	0	0
$55$	5.65685	0.762770
$56$	0	0
$57$	−20.0000	−2.64906
$58$	0	0
$59$	8.48528	1.10469	0.552345	−	0.833616i	$-0.313733\pi$
$59$	8.48528	1.10469	0.552345	+	0.833616i	$0.313733\pi$
$60$	0	0
$61$	1.41421	0.181071	0.0905357	−	0.995893i	$-0.471142\pi$
$61$	1.41421	0.181071	0.0905357	+	0.995893i	$0.471142\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	−8.00000	−0.992278
$66$	0	0
$67$	10.0000	1.22169	0.610847	−	0.791748i	$-0.290829\pi$
$67$	10.0000	1.22169	0.610847	+	0.791748i	$0.290829\pi$
$68$	0	0
$69$	−2.82843	−0.340503
$70$	0	0
$71$	2.00000	0.237356	0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000	0.237356	0.118678	+	0.992933i	$0.462134\pi$
$72$	0	0
$73$	7.07107	0.827606	0.413803	−	0.910366i	$-0.364200\pi$
$73$	7.07107	0.827606	0.413803	+	0.910366i	$0.364200\pi$
$74$	0	0
$75$	8.48528	0.979796
$76$	0	0
$77$	0	0
$78$	0	0
$79$	8.00000	0.900070	0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000	0.900070	0.450035	+	0.893011i	$0.351411\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	0	0
$83$	7.07107	0.776151	0.388075	−	0.921628i	$-0.373140\pi$
$83$	7.07107	0.776151	0.388075	+	0.921628i	$0.373140\pi$
$84$	0	0
$85$	8.00000	0.867722
$86$	0	0
$87$	16.9706	1.81944
$88$	0	0
$89$	−2.82843	−0.299813	−0.149906	−	0.988700i	$-0.547897\pi$
$89$	−2.82843	−0.299813	−0.149906	+	0.988700i	$0.547897\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	−12.0000	−1.24434
$94$	0	0
$95$	−10.0000	−1.02598
$96$	0	0
$97$	8.48528	0.861550	0.430775	−	0.902459i	$-0.358240\pi$
$97$	8.48528	0.861550	0.430775	+	0.902459i	$0.358240\pi$
$98$	0	0
$99$	−20.0000	−2.01008
$100$	0	0
$101$	−8.48528	−0.844317	−0.422159	−	0.906522i	$-0.638727\pi$
$101$	−8.48528	−0.844317	−0.422159	+	0.906522i	$0.638727\pi$
$102$	0	0
$103$	8.48528	0.836080	0.418040	−	0.908429i	$-0.362717\pi$
$103$	8.48528	0.836080	0.418040	+	0.908429i	$0.362717\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	20.0000	1.93347	0.966736	−	0.255774i	$-0.0823304\pi$
$107$	20.0000	1.93347	0.966736	+	0.255774i	$0.0823304\pi$
$108$	0	0
$109$	−14.0000	−1.34096	−0.670478	−	0.741929i	$-0.733911\pi$
$109$	−14.0000	−1.34096	−0.670478	+	0.741929i	$0.733911\pi$
$110$	0	0
$111$	11.3137	1.07385
$112$	0	0
$113$	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
$115$	−1.41421	−0.131876
$116$	0	0
$117$	28.2843	2.61488
$118$	0	0
$119$	0	0
$120$	0	0
$121$	5.00000	0.454545
$122$	0	0
$123$	4.00000	0.360668
$124$	0	0
$125$	11.3137	1.01193
$126$	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
$129$	16.9706	1.49417
$130$	0	0
$131$	−19.7990	−1.72985	−0.864923	−	0.501905i	$-0.832633\pi$
$131$	−19.7990	−1.72985	−0.864923	+	0.501905i	$0.832633\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	8.00000	0.688530
$136$	0	0
$137$	18.0000	1.53784	0.768922	−	0.639343i	$-0.220793\pi$
$137$	18.0000	1.53784	0.768922	+	0.639343i	$0.220793\pi$
$138$	0	0
$139$	−5.65685	−0.479808	−0.239904	−	0.970797i	$-0.577116\pi$
$139$	−5.65685	−0.479808	−0.239904	+	0.970797i	$0.577116\pi$
$140$	0	0
$141$	12.0000	1.01058
$142$	0	0
$143$	−22.6274	−1.89220
$144$	0	0
$145$	8.48528	0.704664
$146$	0	0
$147$	0	0
$148$	0	0
$149$	−18.0000	−1.47462	−0.737309	−	0.675556i	$-0.763904\pi$
$149$	−18.0000	−1.47462	−0.737309	+	0.675556i	$0.763904\pi$
$150$	0	0
$151$	18.0000	1.46482	0.732410	−	0.680864i	$-0.238396\pi$
$151$	18.0000	1.46482	0.732410	+	0.680864i	$0.238396\pi$
$152$	0	0
$153$	−28.2843	−2.28665
$154$	0	0
$155$	−6.00000	−0.481932
$156$	0	0
$157$	−4.24264	−0.338600	−0.169300	−	0.985565i	$-0.554151\pi$
$157$	−4.24264	−0.338600	−0.169300	+	0.985565i	$0.554151\pi$
$158$	0	0
$159$	22.6274	1.79447
$160$	0	0
$161$	0	0
$162$	0	0
$163$	−24.0000	−1.87983	−0.939913	−	0.341415i	$-0.889094\pi$
$163$	−24.0000	−1.87983	−0.939913	+	0.341415i	$0.889094\pi$
$164$	0	0
$165$	−16.0000	−1.24560
$166$	0	0
$167$	−15.5563	−1.20379	−0.601893	−	0.798577i	$-0.705587\pi$
$167$	−15.5563	−1.20379	−0.601893	+	0.798577i	$0.705587\pi$
$168$	0	0
$169$	19.0000	1.46154
$170$	0	0
$171$	35.3553	2.70369
$172$	0	0
$173$	14.1421	1.07521	0.537603	−	0.843198i	$-0.319330\pi$
$173$	14.1421	1.07521	0.537603	+	0.843198i	$0.319330\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	−24.0000	−1.80395
$178$	0	0
$179$	8.00000	0.597948	0.298974	−	0.954261i	$-0.403356\pi$
$179$	8.00000	0.597948	0.298974	+	0.954261i	$0.403356\pi$
$180$	0	0
$181$	−4.24264	−0.315353	−0.157676	−	0.987491i	$-0.550400\pi$
$181$	−4.24264	−0.315353	−0.157676	+	0.987491i	$0.550400\pi$
$182$	0	0
$183$	−4.00000	−0.295689
$184$	0	0
$185$	5.65685	0.415900
$186$	0	0
$187$	22.6274	1.65468
$188$	0	0
$189$	0	0
$190$	0	0
$191$	−16.0000	−1.15772	−0.578860	−	0.815427i	$-0.696502\pi$
$191$	−16.0000	−1.15772	−0.578860	+	0.815427i	$0.696502\pi$
$192$	0	0
$193$	−20.0000	−1.43963	−0.719816	−	0.694165i	$-0.755774\pi$
$193$	−20.0000	−1.43963	−0.719816	+	0.694165i	$0.755774\pi$
$194$	0	0
$195$	22.6274	1.62038
$196$	0	0
$197$	14.0000	0.997459	0.498729	−	0.866758i	$-0.333800\pi$
$197$	14.0000	0.997459	0.498729	+	0.866758i	$0.333800\pi$
$198$	0	0
$199$	25.4558	1.80452	0.902258	−	0.431196i	$-0.141908\pi$
$199$	25.4558	1.80452	0.902258	+	0.431196i	$0.141908\pi$
$200$	0	0
$201$	−28.2843	−1.99502
$202$	0	0
$203$	0	0
$204$	0	0
$205$	2.00000	0.139686
$206$	0	0
$207$	5.00000	0.347524
$208$	0	0
$209$	−28.2843	−1.95646
$210$	0	0
$211$	−16.0000	−1.10149	−0.550743	−	0.834675i	$-0.685655\pi$
$211$	−16.0000	−1.10149	−0.550743	+	0.834675i	$0.685655\pi$
$212$	0	0
$213$	−5.65685	−0.387601
$214$	0	0
$215$	8.48528	0.578691
$216$	0	0
$217$	0	0
$218$	0	0
$219$	−20.0000	−1.35147
$220$	0	0
$221$	−32.0000	−2.15255
$222$	0	0
$223$	4.24264	0.284108	0.142054	−	0.989859i	$-0.454629\pi$
$223$	4.24264	0.284108	0.142054	+	0.989859i	$0.454629\pi$
$224$	0	0
$225$	−15.0000	−1.00000
$226$	0	0
$227$	−9.89949	−0.657053	−0.328526	−	0.944495i	$-0.606552\pi$
$227$	−9.89949	−0.657053	−0.328526	+	0.944495i	$0.606552\pi$
$228$	0	0
$229$	9.89949	0.654177	0.327089	−	0.944994i	$-0.393932\pi$
$229$	9.89949	0.654177	0.327089	+	0.944994i	$0.393932\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	26.0000	1.70332	0.851658	−	0.524097i	$-0.175597\pi$
$233$	26.0000	1.70332	0.851658	+	0.524097i	$0.175597\pi$
$234$	0	0
$235$	6.00000	0.391397
$236$	0	0
$237$	−22.6274	−1.46981
$238$	0	0
$239$	6.00000	0.388108	0.194054	−	0.980991i	$-0.437836\pi$
$239$	6.00000	0.388108	0.194054	+	0.980991i	$0.437836\pi$
$240$	0	0
$241$	−5.65685	−0.364390	−0.182195	−	0.983262i	$-0.558320\pi$
$241$	−5.65685	−0.364390	−0.182195	+	0.983262i	$0.558320\pi$
$242$	0	0
$243$	14.1421	0.907218
$244$	0	0
$245$	0	0
$246$	0	0
$247$	40.0000	2.54514
$248$	0	0
$249$	−20.0000	−1.26745
$250$	0	0
$251$	−24.0416	−1.51749	−0.758747	−	0.651385i	$-0.774188\pi$
$251$	−24.0416	−1.51749	−0.758747	+	0.651385i	$0.774188\pi$
$252$	0	0
$253$	−4.00000	−0.251478
$254$	0	0
$255$	−22.6274	−1.41698
$256$	0	0
$257$	−9.89949	−0.617514	−0.308757	−	0.951141i	$-0.599913\pi$
$257$	−9.89949	−0.617514	−0.308757	+	0.951141i	$0.599913\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	−30.0000	−1.85695
$262$	0	0
$263$	8.00000	0.493301	0.246651	−	0.969104i	$-0.420670\pi$
$263$	8.00000	0.493301	0.246651	+	0.969104i	$0.420670\pi$
$264$	0	0
$265$	11.3137	0.694996
$266$	0	0
$267$	8.00000	0.489592
$268$	0	0
$269$	19.7990	1.20717	0.603583	−	0.797300i	$-0.293739\pi$
$269$	19.7990	1.20717	0.603583	+	0.797300i	$0.293739\pi$
$270$	0	0
$271$	26.8701	1.63224	0.816120	−	0.577883i	$-0.196121\pi$
$271$	26.8701	1.63224	0.816120	+	0.577883i	$0.196121\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	12.0000	0.723627
$276$	0	0
$277$	−14.0000	−0.841178	−0.420589	−	0.907251i	$-0.638177\pi$
$277$	−14.0000	−0.841178	−0.420589	+	0.907251i	$0.638177\pi$
$278$	0	0
$279$	21.2132	1.27000
$280$	0	0
$281$	22.0000	1.31241	0.656205	−	0.754583i	$-0.272161\pi$
$281$	22.0000	1.31241	0.656205	+	0.754583i	$0.272161\pi$
$282$	0	0
$283$	−15.5563	−0.924729	−0.462364	−	0.886690i	$-0.652999\pi$
$283$	−15.5563	−0.924729	−0.462364	+	0.886690i	$0.652999\pi$
$284$	0	0
$285$	28.2843	1.67542
$286$	0	0
$287$	0	0
$288$	0	0
$289$	15.0000	0.882353
$290$	0	0
$291$	−24.0000	−1.40690
$292$	0	0
$293$	7.07107	0.413096	0.206548	−	0.978436i	$-0.433777\pi$
$293$	7.07107	0.413096	0.206548	+	0.978436i	$0.433777\pi$
$294$	0	0
$295$	−12.0000	−0.698667
$296$	0	0
$297$	22.6274	1.31298
$298$	0	0
$299$	5.65685	0.327144
$300$	0	0
$301$	0	0
$302$	0	0
$303$	24.0000	1.37876
$304$	0	0
$305$	−2.00000	−0.114520
$306$	0	0
$307$	−11.3137	−0.645707	−0.322854	−	0.946449i	$-0.604642\pi$
$307$	−11.3137	−0.645707	−0.322854	+	0.946449i	$0.604642\pi$
$308$	0	0
$309$	−24.0000	−1.36531
$310$	0	0
$311$	−9.89949	−0.561349	−0.280674	−	0.959803i	$-0.590558\pi$
$311$	−9.89949	−0.561349	−0.280674	+	0.959803i	$0.590558\pi$
$312$	0	0
$313$	16.9706	0.959233	0.479616	−	0.877478i	$-0.340776\pi$
$313$	16.9706	0.959233	0.479616	+	0.877478i	$0.340776\pi$
$314$	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
$319$	24.0000	1.34374
$320$	0	0
$321$	−56.5685	−3.15735
$322$	0	0
$323$	−40.0000	−2.22566
$324$	0	0
$325$	−16.9706	−0.941357
$326$	0	0
$327$	39.5980	2.18977
$328$	0	0
$329$	0	0
$330$	0	0
$331$	−16.0000	−0.879440	−0.439720	−	0.898135i	$-0.644922\pi$
$331$	−16.0000	−0.879440	−0.439720	+	0.898135i	$0.644922\pi$
$332$	0	0
$333$	−20.0000	−1.09599
$334$	0	0
$335$	−14.1421	−0.772667
$336$	0	0
$337$	−2.00000	−0.108947	−0.0544735	−	0.998515i	$-0.517348\pi$
$337$	−2.00000	−0.108947	−0.0544735	+	0.998515i	$0.517348\pi$
$338$	0	0
$339$	−16.9706	−0.921714
$340$	0	0
$341$	−16.9706	−0.919007
$342$	0	0
$343$	0	0
$344$	0	0
$345$	4.00000	0.215353
$346$	0	0
$347$	0	0		−	1.00000i	$-0.5\pi$
$347$	0	0			1.00000i	$0.5\pi$
$348$	0	0
$349$	2.82843	0.151402	0.0757011	−	0.997131i	$-0.475881\pi$
$349$	2.82843	0.151402	0.0757011	+	0.997131i	$0.475881\pi$
$350$	0	0
$351$	−32.0000	−1.70803
$352$	0	0
$353$	−18.3848	−0.978523	−0.489261	−	0.872137i	$-0.662734\pi$
$353$	−18.3848	−0.978523	−0.489261	+	0.872137i	$0.662734\pi$
$354$	0	0
$355$	−2.82843	−0.150117
$356$	0	0
$357$	0	0
$358$	0	0
$359$	24.0000	1.26667	0.633336	−	0.773877i	$-0.281685\pi$
$359$	24.0000	1.26667	0.633336	+	0.773877i	$0.281685\pi$
$360$	0	0
$361$	31.0000	1.63158
$362$	0	0
$363$	−14.1421	−0.742270
$364$	0	0
$365$	−10.0000	−0.523424
$366$	0	0
$367$	−8.48528	−0.442928	−0.221464	−	0.975169i	$-0.571084\pi$
$367$	−8.48528	−0.442928	−0.221464	+	0.975169i	$0.571084\pi$
$368$	0	0
$369$	−7.07107	−0.368105
$370$	0	0
$371$	0	0
$372$	0	0
$373$	−22.0000	−1.13912	−0.569558	−	0.821951i	$-0.692886\pi$
$373$	−22.0000	−1.13912	−0.569558	+	0.821951i	$0.692886\pi$
$374$	0	0
$375$	−32.0000	−1.65247
$376$	0	0
$377$	−33.9411	−1.74806
$378$	0	0
$379$	−28.0000	−1.43826	−0.719132	−	0.694874i	$-0.755460\pi$
$379$	−28.0000	−1.43826	−0.719132	+	0.694874i	$0.755460\pi$
$380$	0	0
$381$	−39.5980	−2.02867
$382$	0	0
$383$	5.65685	0.289052	0.144526	−	0.989501i	$-0.453834\pi$
$383$	5.65685	0.289052	0.144526	+	0.989501i	$0.453834\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	−30.0000	−1.52499
$388$	0	0
$389$	6.00000	0.304212	0.152106	−	0.988364i	$-0.451394\pi$
$389$	6.00000	0.304212	0.152106	+	0.988364i	$0.451394\pi$
$390$	0	0
$391$	−5.65685	−0.286079
$392$	0	0
$393$	56.0000	2.82483
$394$	0	0
$395$	−11.3137	−0.569254
$396$	0	0
$397$	28.2843	1.41955	0.709773	−	0.704430i	$-0.248797\pi$
$397$	28.2843	1.41955	0.709773	+	0.704430i	$0.248797\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	−30.0000	−1.49813	−0.749064	−	0.662497i	$-0.769497\pi$
$401$	−30.0000	−1.49813	−0.749064	+	0.662497i	$0.769497\pi$
$402$	0	0
$403$	24.0000	1.19553
$404$	0	0
$405$	−1.41421	−0.0702728
$406$	0	0
$407$	16.0000	0.793091
$408$	0	0
$409$	−21.2132	−1.04893	−0.524463	−	0.851433i	$-0.675734\pi$
$409$	−21.2132	−1.04893	−0.524463	+	0.851433i	$0.675734\pi$
$410$	0	0
$411$	−50.9117	−2.51129
$412$	0	0
$413$	0	0
$414$	0	0
$415$	−10.0000	−0.490881
$416$	0	0
$417$	16.0000	0.783523
$418$	0	0
$419$	21.2132	1.03633	0.518166	−	0.855280i	$-0.326615\pi$
$419$	21.2132	1.03633	0.518166	+	0.855280i	$0.326615\pi$
$420$	0	0
$421$	40.0000	1.94948	0.974740	−	0.223341i	$-0.0716964\pi$
$421$	40.0000	1.94948	0.974740	+	0.223341i	$0.0716964\pi$
$422$	0	0
$423$	−21.2132	−1.03142
$424$	0	0
$425$	16.9706	0.823193
$426$	0	0
$427$	0	0
$428$	0	0
$429$	64.0000	3.08995
$430$	0	0
$431$	−8.00000	−0.385346	−0.192673	−	0.981263i	$-0.561716\pi$
$431$	−8.00000	−0.385346	−0.192673	+	0.981263i	$0.561716\pi$
$432$	0	0
$433$	−8.48528	−0.407777	−0.203888	−	0.978994i	$-0.565358\pi$
$433$	−8.48528	−0.407777	−0.203888	+	0.978994i	$0.565358\pi$
$434$	0	0
$435$	−24.0000	−1.15071
$436$	0	0
$437$	7.07107	0.338255
$438$	0	0
$439$	−18.3848	−0.877457	−0.438729	−	0.898620i	$-0.644571\pi$
$439$	−18.3848	−0.877457	−0.438729	+	0.898620i	$0.644571\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	−12.0000	−0.570137	−0.285069	−	0.958507i	$-0.592016\pi$
$443$	−12.0000	−0.570137	−0.285069	+	0.958507i	$0.592016\pi$
$444$	0	0
$445$	4.00000	0.189618
$446$	0	0
$447$	50.9117	2.40804
$448$	0	0
$449$	−24.0000	−1.13263	−0.566315	−	0.824189i	$-0.691631\pi$
$449$	−24.0000	−1.13263	−0.566315	+	0.824189i	$0.691631\pi$
$450$	0	0
$451$	5.65685	0.266371
$452$	0	0
$453$	−50.9117	−2.39204
$454$	0	0
$455$	0	0
$456$	0	0
$457$	−18.0000	−0.842004	−0.421002	−	0.907060i	$-0.638322\pi$
$457$	−18.0000	−0.842004	−0.421002	+	0.907060i	$0.638322\pi$
$458$	0	0
$459$	32.0000	1.49363
$460$	0	0
$461$	−19.7990	−0.922131	−0.461065	−	0.887366i	$-0.652533\pi$
$461$	−19.7990	−0.922131	−0.461065	+	0.887366i	$0.652533\pi$
$462$	0	0
$463$	−8.00000	−0.371792	−0.185896	−	0.982569i	$-0.559519\pi$
$463$	−8.00000	−0.371792	−0.185896	+	0.982569i	$0.559519\pi$
$464$	0	0
$465$	16.9706	0.786991
$466$	0	0
$467$	−7.07107	−0.327210	−0.163605	−	0.986526i	$-0.552312\pi$
$467$	−7.07107	−0.327210	−0.163605	+	0.986526i	$0.552312\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	12.0000	0.552931
$472$	0	0
$473$	24.0000	1.10352
$474$	0	0
$475$	−21.2132	−0.973329
$476$	0	0
$477$	−40.0000	−1.83147
$478$	0	0
$479$	−8.48528	−0.387702	−0.193851	−	0.981031i	$-0.562098\pi$
$479$	−8.48528	−0.387702	−0.193851	+	0.981031i	$0.562098\pi$
$480$	0	0
$481$	−22.6274	−1.03172
$482$	0	0
$483$	0	0
$484$	0	0
$485$	−12.0000	−0.544892
$486$	0	0
$487$	−32.0000	−1.45006	−0.725029	−	0.688718i	$-0.758174\pi$
$487$	−32.0000	−1.45006	−0.725029	+	0.688718i	$0.758174\pi$
$488$	0	0
$489$	67.8823	3.06974
$490$	0	0
$491$	−32.0000	−1.44414	−0.722070	−	0.691820i	$-0.756809\pi$
$491$	−32.0000	−1.44414	−0.722070	+	0.691820i	$0.756809\pi$
$492$	0	0
$493$	33.9411	1.52863
$494$	0	0
$495$	28.2843	1.27128
$496$	0	0
$497$	0	0
$498$	0	0
$499$	4.00000	0.179065	0.0895323	−	0.995984i	$-0.471463\pi$
$499$	4.00000	0.179065	0.0895323	+	0.995984i	$0.471463\pi$
$500$	0	0
$501$	44.0000	1.96578
$502$	0	0
$503$	−22.6274	−1.00891	−0.504453	−	0.863439i	$-0.668306\pi$
$503$	−22.6274	−1.00891	−0.504453	+	0.863439i	$0.668306\pi$
$504$	0	0
$505$	12.0000	0.533993
$506$	0	0
$507$	−53.7401	−2.38668
$508$	0	0
$509$	−25.4558	−1.12831	−0.564155	−	0.825669i	$-0.690798\pi$
$509$	−25.4558	−1.12831	−0.564155	+	0.825669i	$0.690798\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	−40.0000	−1.76604
$514$	0	0
$515$	−12.0000	−0.528783
$516$	0	0
$517$	16.9706	0.746364
$518$	0	0
$519$	−40.0000	−1.75581
$520$	0	0
$521$	−19.7990	−0.867409	−0.433705	−	0.901055i	$-0.642794\pi$
$521$	−19.7990	−0.867409	−0.433705	+	0.901055i	$0.642794\pi$
$522$	0	0
$523$	−12.7279	−0.556553	−0.278277	−	0.960501i	$-0.589763\pi$
$523$	−12.7279	−0.556553	−0.278277	+	0.960501i	$0.589763\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	−24.0000	−1.04546
$528$	0	0
$529$	1.00000	0.0434783
$530$	0	0
$531$	42.4264	1.84115
$532$	0	0
$533$	−8.00000	−0.346518
$534$	0	0
$535$	−28.2843	−1.22284
$536$	0	0
$537$	−22.6274	−0.976445
$538$	0	0
$539$	0	0
$540$	0	0
$541$	−10.0000	−0.429934	−0.214967	−	0.976621i	$-0.568964\pi$
$541$	−10.0000	−0.429934	−0.214967	+	0.976621i	$0.568964\pi$
$542$	0	0
$543$	12.0000	0.514969
$544$	0	0
$545$	19.7990	0.848096
$546$	0	0
$547$	−12.0000	−0.513083	−0.256541	−	0.966533i	$-0.582583\pi$
$547$	−12.0000	−0.513083	−0.256541	+	0.966533i	$0.582583\pi$
$548$	0	0
$549$	7.07107	0.301786
$550$	0	0
$551$	−42.4264	−1.80743
$552$	0	0
$553$	0	0
$554$	0	0
$555$	−16.0000	−0.679162
$556$	0	0
$557$	14.0000	0.593199	0.296600	−	0.955002i	$-0.404147\pi$
$557$	14.0000	0.593199	0.296600	+	0.955002i	$0.404147\pi$
$558$	0	0
$559$	−33.9411	−1.43556
$560$	0	0
$561$	−64.0000	−2.70208
$562$	0	0
$563$	−35.3553	−1.49005	−0.745025	−	0.667037i	$-0.767562\pi$
$563$	−35.3553	−1.49005	−0.745025	+	0.667037i	$0.767562\pi$
$564$	0	0
$565$	−8.48528	−0.356978
$566$	0	0
$567$	0	0
$568$	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
$571$	2.00000	0.0836974	0.0418487	−	0.999124i	$-0.486675\pi$
$571$	2.00000	0.0836974	0.0418487	+	0.999124i	$0.486675\pi$
$572$	0	0
$573$	45.2548	1.89055
$574$	0	0
$575$	−3.00000	−0.125109
$576$	0	0
$577$	−1.41421	−0.0588745	−0.0294372	−	0.999567i	$-0.509372\pi$
$577$	−1.41421	−0.0588745	−0.0294372	+	0.999567i	$0.509372\pi$
$578$	0	0
$579$	56.5685	2.35091
$580$	0	0
$581$	0	0
$582$	0	0
$583$	32.0000	1.32530
$584$	0	0
$585$	−40.0000	−1.65380
$586$	0	0
$587$	22.6274	0.933933	0.466967	−	0.884275i	$-0.345347\pi$
$587$	22.6274	0.933933	0.466967	+	0.884275i	$0.345347\pi$
$588$	0	0
$589$	30.0000	1.23613
$590$	0	0
$591$	−39.5980	−1.62884
$592$	0	0
$593$	43.8406	1.80032	0.900159	−	0.435561i	$-0.143450\pi$
$593$	43.8406	1.80032	0.900159	+	0.435561i	$0.143450\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	−72.0000	−2.94676
$598$	0	0
$599$	−16.0000	−0.653742	−0.326871	−	0.945069i	$-0.605994\pi$
$599$	−16.0000	−0.653742	−0.326871	+	0.945069i	$0.605994\pi$
$600$	0	0
$601$	−46.6690	−1.90367	−0.951835	−	0.306610i	$-0.900805\pi$
$601$	−46.6690	−1.90367	−0.951835	+	0.306610i	$0.900805\pi$
$602$	0	0
$603$	50.0000	2.03616
$604$	0	0
$605$	−7.07107	−0.287480
$606$	0	0
$607$	21.2132	0.861017	0.430509	−	0.902586i	$-0.358334\pi$
$607$	21.2132	0.861017	0.430509	+	0.902586i	$0.358334\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	−24.0000	−0.970936
$612$	0	0
$613$	−26.0000	−1.05013	−0.525065	−	0.851062i	$-0.675959\pi$
$613$	−26.0000	−1.05013	−0.525065	+	0.851062i	$0.675959\pi$
$614$	0	0
$615$	−5.65685	−0.228106
$616$	0	0
$617$	−22.0000	−0.885687	−0.442843	−	0.896599i	$-0.646030\pi$
$617$	−22.0000	−0.885687	−0.442843	+	0.896599i	$0.646030\pi$
$618$	0	0
$619$	24.0416	0.966315	0.483157	−	0.875534i	$-0.339490\pi$
$619$	24.0416	0.966315	0.483157	+	0.875534i	$0.339490\pi$
$620$	0	0
$621$	−5.65685	−0.227002
$622$	0	0
$623$	0	0
$624$	0	0
$625$	−1.00000	−0.0400000
$626$	0	0
$627$	80.0000	3.19489
$628$	0	0
$629$	22.6274	0.902214
$630$	0	0
$631$	16.0000	0.636950	0.318475	−	0.947931i	$-0.396829\pi$
$631$	16.0000	0.636950	0.318475	+	0.947931i	$0.396829\pi$
$632$	0	0
$633$	45.2548	1.79872
$634$	0	0
$635$	−19.7990	−0.785699
$636$	0	0
$637$	0	0
$638$	0	0
$639$	10.0000	0.395594
$640$	0	0
$641$	−34.0000	−1.34292	−0.671460	−	0.741041i	$-0.734332\pi$
$641$	−34.0000	−1.34292	−0.671460	+	0.741041i	$0.734332\pi$
$642$	0	0
$643$	7.07107	0.278856	0.139428	−	0.990232i	$-0.455474\pi$
$643$	7.07107	0.278856	0.139428	+	0.990232i	$0.455474\pi$
$644$	0	0
$645$	−24.0000	−0.944999
$646$	0	0
$647$	41.0122	1.61236	0.806178	−	0.591673i	$-0.201532\pi$
$647$	41.0122	1.61236	0.806178	+	0.591673i	$0.201532\pi$
$648$	0	0
$649$	−33.9411	−1.33231
$650$	0	0
$651$	0	0
$652$	0	0
$653$	−30.0000	−1.17399	−0.586995	−	0.809590i	$-0.699689\pi$
$653$	−30.0000	−1.17399	−0.586995	+	0.809590i	$0.699689\pi$
$654$	0	0
$655$	28.0000	1.09405
$656$	0	0
$657$	35.3553	1.37934
$658$	0	0
$659$	30.0000	1.16863	0.584317	−	0.811525i	$-0.301362\pi$
$659$	30.0000	1.16863	0.584317	+	0.811525i	$0.301362\pi$
$660$	0	0
$661$	−7.07107	−0.275033	−0.137516	−	0.990499i	$-0.543912\pi$
$661$	−7.07107	−0.275033	−0.137516	+	0.990499i	$0.543912\pi$
$662$	0	0
$663$	90.5097	3.51510
$664$	0	0
$665$	0	0
$666$	0	0
$667$	−6.00000	−0.232321
$668$	0	0
$669$	−12.0000	−0.463947
$670$	0	0
$671$	−5.65685	−0.218380
$672$	0	0
$673$	22.0000	0.848038	0.424019	−	0.905653i	$-0.360619\pi$
$673$	22.0000	0.848038	0.424019	+	0.905653i	$0.360619\pi$
$674$	0	0
$675$	16.9706	0.653197
$676$	0	0
$677$	−15.5563	−0.597879	−0.298940	−	0.954272i	$-0.596633\pi$
$677$	−15.5563	−0.597879	−0.298940	+	0.954272i	$0.596633\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	28.0000	1.07296
$682$	0	0
$683$	−24.0000	−0.918334	−0.459167	−	0.888350i	$-0.651852\pi$
$683$	−24.0000	−0.918334	−0.459167	+	0.888350i	$0.651852\pi$
$684$	0	0
$685$	−25.4558	−0.972618
$686$	0	0
$687$	−28.0000	−1.06827
$688$	0	0
$689$	−45.2548	−1.72407
$690$	0	0
$691$	0	0		−	1.00000i	$-0.5\pi$
$691$	0	0			1.00000i	$0.5\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	8.00000	0.303457
$696$	0	0
$697$	8.00000	0.303022
$698$	0	0
$699$	−73.5391	−2.78150
$700$	0	0
$701$	−24.0000	−0.906467	−0.453234	−	0.891392i	$-0.649730\pi$
$701$	−24.0000	−0.906467	−0.453234	+	0.891392i	$0.649730\pi$
$702$	0	0
$703$	−28.2843	−1.06676
$704$	0	0
$705$	−16.9706	−0.639148
$706$	0	0
$707$	0	0
$708$	0	0
$709$	−28.0000	−1.05156	−0.525781	−	0.850620i	$-0.676227\pi$
$709$	−28.0000	−1.05156	−0.525781	+	0.850620i	$0.676227\pi$
$710$	0	0
$711$	40.0000	1.50012
$712$	0	0
$713$	4.24264	0.158888
$714$	0	0
$715$	32.0000	1.19673
$716$	0	0
$717$	−16.9706	−0.633777
$718$	0	0
$719$	−43.8406	−1.63498	−0.817490	−	0.575943i	$-0.804635\pi$
$719$	−43.8406	−1.63498	−0.817490	+	0.575943i	$0.804635\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	16.0000	0.595046
$724$	0	0
$725$	18.0000	0.668503
$726$	0	0
$727$	19.7990	0.734304	0.367152	−	0.930161i	$-0.380333\pi$
$727$	19.7990	0.734304	0.367152	+	0.930161i	$0.380333\pi$
$728$	0	0
$729$	−43.0000	−1.59259
$730$	0	0
$731$	33.9411	1.25536
$732$	0	0
$733$	−24.0416	−0.887998	−0.443999	−	0.896027i	$-0.646441\pi$
$733$	−24.0416	−0.887998	−0.443999	+	0.896027i	$0.646441\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−40.0000	−1.47342
$738$	0	0
$739$	28.0000	1.03000	0.514998	−	0.857191i	$-0.327793\pi$
$739$	28.0000	1.03000	0.514998	+	0.857191i	$0.327793\pi$
$740$	0	0
$741$	−113.137	−4.15619
$742$	0	0
$743$	24.0000	0.880475	0.440237	−	0.897881i	$-0.354894\pi$
$743$	24.0000	0.880475	0.440237	+	0.897881i	$0.354894\pi$
$744$	0	0
$745$	25.4558	0.932630
$746$	0	0
$747$	35.3553	1.29358
$748$	0	0
$749$	0	0
$750$	0	0
$751$	−44.0000	−1.60558	−0.802791	−	0.596260i	$-0.796653\pi$
$751$	−44.0000	−1.60558	−0.802791	+	0.596260i	$0.796653\pi$
$752$	0	0
$753$	68.0000	2.47806
$754$	0	0
$755$	−25.4558	−0.926433
$756$	0	0
$757$	10.0000	0.363456	0.181728	−	0.983349i	$-0.441831\pi$
$757$	10.0000	0.363456	0.181728	+	0.983349i	$0.441831\pi$
$758$	0	0
$759$	11.3137	0.410662
$760$	0	0
$761$	41.0122	1.48669	0.743345	−	0.668908i	$-0.233238\pi$
$761$	41.0122	1.48669	0.743345	+	0.668908i	$0.233238\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	40.0000	1.44620
$766$	0	0
$767$	48.0000	1.73318
$768$	0	0
$769$	−16.9706	−0.611974	−0.305987	−	0.952036i	$-0.598986\pi$
$769$	−16.9706	−0.611974	−0.305987	+	0.952036i	$0.598986\pi$
$770$	0	0
$771$	28.0000	1.00840
$772$	0	0
$773$	−7.07107	−0.254329	−0.127164	−	0.991882i	$-0.540588\pi$
$773$	−7.07107	−0.254329	−0.127164	+	0.991882i	$0.540588\pi$
$774$	0	0
$775$	−12.7279	−0.457200
$776$	0	0
$777$	0	0
$778$	0	0
$779$	−10.0000	−0.358287
$780$	0	0
$781$	−8.00000	−0.286263
$782$	0	0
$783$	33.9411	1.21296
$784$	0	0
$785$	6.00000	0.214149
$786$	0	0
$787$	−49.4975	−1.76439	−0.882197	−	0.470880i	$-0.843936\pi$
$787$	−49.4975	−1.76439	−0.882197	+	0.470880i	$0.843936\pi$
$788$	0	0
$789$	−22.6274	−0.805557
$790$	0	0
$791$	0	0
$792$	0	0
$793$	8.00000	0.284088
$794$	0	0
$795$	−32.0000	−1.13492
$796$	0	0
$797$	−4.24264	−0.150282	−0.0751410	−	0.997173i	$-0.523941\pi$
$797$	−4.24264	−0.150282	−0.0751410	+	0.997173i	$0.523941\pi$
$798$	0	0
$799$	24.0000	0.849059
$800$	0	0
$801$	−14.1421	−0.499688
$802$	0	0
$803$	−28.2843	−0.998130
$804$	0	0
$805$	0	0
$806$	0	0
$807$	−56.0000	−1.97129
$808$	0	0
$809$	−36.0000	−1.26569	−0.632846	−	0.774277i	$-0.718114\pi$
$809$	−36.0000	−1.26569	−0.632846	+	0.774277i	$0.718114\pi$
$810$	0	0
$811$	19.7990	0.695237	0.347618	−	0.937636i	$-0.386991\pi$
$811$	19.7990	0.695237	0.347618	+	0.937636i	$0.386991\pi$
$812$	0	0
$813$	−76.0000	−2.66544
$814$	0	0
$815$	33.9411	1.18891
$816$	0	0
$817$	−42.4264	−1.48431
$818$	0	0
$819$	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
$823$	−54.0000	−1.88232	−0.941161	−	0.337959i	$-0.890263\pi$
$823$	−54.0000	−1.88232	−0.941161	+	0.337959i	$0.890263\pi$
$824$	0	0
$825$	−33.9411	−1.18168
$826$	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
$829$	−50.9117	−1.76824	−0.884118	−	0.467264i	$-0.845240\pi$
$829$	−50.9117	−1.76824	−0.884118	+	0.467264i	$0.845240\pi$
$830$	0	0
$831$	39.5980	1.37364
$832$	0	0
$833$	0	0
$834$	0	0
$835$	22.0000	0.761341
$836$	0	0
$837$	−24.0000	−0.829561
$838$	0	0
$839$	22.6274	0.781185	0.390593	−	0.920564i	$-0.372270\pi$
$839$	22.6274	0.781185	0.390593	+	0.920564i	$0.372270\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	0	0
$843$	−62.2254	−2.14316
$844$	0	0
$845$	−26.8701	−0.924358
$846$	0	0
$847$	0	0
$848$	0	0
$849$	44.0000	1.51008
$850$	0	0
$851$	−4.00000	−0.137118
$852$	0	0
$853$	28.2843	0.968435	0.484218	−	0.874948i	$-0.339104\pi$
$853$	28.2843	0.968435	0.484218	+	0.874948i	$0.339104\pi$
$854$	0	0
$855$	−50.0000	−1.70996
$856$	0	0
$857$	46.6690	1.59418	0.797092	−	0.603858i	$-0.206370\pi$
$857$	46.6690	1.59418	0.797092	+	0.603858i	$0.206370\pi$
$858$	0	0
$859$	−39.5980	−1.35107	−0.675533	−	0.737330i	$-0.736086\pi$
$859$	−39.5980	−1.35107	−0.675533	+	0.737330i	$0.736086\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	14.0000	0.476566	0.238283	−	0.971196i	$-0.423415\pi$
$863$	14.0000	0.476566	0.238283	+	0.971196i	$0.423415\pi$
$864$	0	0
$865$	−20.0000	−0.680020
$866$	0	0
$867$	−42.4264	−1.44088
$868$	0	0
$869$	−32.0000	−1.08553
$870$	0	0
$871$	56.5685	1.91675
$872$	0	0
$873$	42.4264	1.43592
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−42.0000	−1.41824	−0.709120	−	0.705088i	$-0.750907\pi$
$877$	−42.0000	−1.41824	−0.709120	+	0.705088i	$0.750907\pi$
$878$	0	0
$879$	−20.0000	−0.674583
$880$	0	0
$881$	5.65685	0.190584	0.0952921	−	0.995449i	$-0.469621\pi$
$881$	5.65685	0.190584	0.0952921	+	0.995449i	$0.469621\pi$
$882$	0	0
$883$	40.0000	1.34611	0.673054	−	0.739594i	$-0.264982\pi$
$883$	40.0000	1.34611	0.673054	+	0.739594i	$0.264982\pi$
$884$	0	0
$885$	33.9411	1.14092
$886$	0	0
$887$	−7.07107	−0.237423	−0.118712	−	0.992929i	$-0.537876\pi$
$887$	−7.07107	−0.237423	−0.118712	+	0.992929i	$0.537876\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	−4.00000	−0.134005
$892$	0	0
$893$	−30.0000	−1.00391
$894$	0	0
$895$	−11.3137	−0.378176
$896$	0	0
$897$	−16.0000	−0.534224
$898$	0	0
$899$	−25.4558	−0.849000
$900$	0	0
$901$	45.2548	1.50766
$902$	0	0
$903$	0	0
$904$	0	0
$905$	6.00000	0.199447
$906$	0	0
$907$	28.0000	0.929725	0.464862	−	0.885383i	$-0.346104\pi$
$907$	28.0000	0.929725	0.464862	+	0.885383i	$0.346104\pi$
$908$	0	0
$909$	−42.4264	−1.40720
$910$	0	0
$911$	56.0000	1.85536	0.927681	−	0.373373i	$-0.121799\pi$
$911$	56.0000	1.85536	0.927681	+	0.373373i	$0.121799\pi$
$912$	0	0
$913$	−28.2843	−0.936073
$914$	0	0
$915$	5.65685	0.187010
$916$	0	0
$917$	0	0
$918$	0	0
$919$	−16.0000	−0.527791	−0.263896	−	0.964551i	$-0.585007\pi$
$919$	−16.0000	−0.527791	−0.263896	+	0.964551i	$0.585007\pi$
$920$	0	0
$921$	32.0000	1.05444
$922$	0	0
$923$	11.3137	0.372395
$924$	0	0
$925$	12.0000	0.394558
$926$	0	0
$927$	42.4264	1.39347
$928$	0	0
$929$	9.89949	0.324792	0.162396	−	0.986726i	$-0.448078\pi$
$929$	9.89949	0.324792	0.162396	+	0.986726i	$0.448078\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	28.0000	0.916679
$934$	0	0
$935$	−32.0000	−1.04651
$936$	0	0
$937$	−11.3137	−0.369603	−0.184801	−	0.982776i	$-0.559164\pi$
$937$	−11.3137	−0.369603	−0.184801	+	0.982776i	$0.559164\pi$
$938$	0	0
$939$	−48.0000	−1.56642
$940$	0	0
$941$	52.3259	1.70578	0.852888	−	0.522094i	$-0.174849\pi$
$941$	52.3259	1.70578	0.852888	+	0.522094i	$0.174849\pi$
$942$	0	0
$943$	−1.41421	−0.0460531
$944$	0	0
$945$	0	0
$946$	0	0
$947$	12.0000	0.389948	0.194974	−	0.980808i	$-0.437538\pi$
$947$	12.0000	0.389948	0.194974	+	0.980808i	$0.437538\pi$
$948$	0	0
$949$	40.0000	1.29845
$950$	0	0
$951$	50.9117	1.65092
$952$	0	0
$953$	6.00000	0.194359	0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000	0.194359	0.0971795	+	0.995267i	$0.469018\pi$
$954$	0	0
$955$	22.6274	0.732206
$956$	0	0
$957$	−67.8823	−2.19432
$958$	0	0
$959$	0	0
$960$	0	0
$961$	−13.0000	−0.419355
$962$	0	0
$963$	100.000	3.22245
$964$	0	0
$965$	28.2843	0.910503
$966$	0	0
$967$	−40.0000	−1.28631	−0.643157	−	0.765735i	$-0.722376\pi$
$967$	−40.0000	−1.28631	−0.643157	+	0.765735i	$0.722376\pi$
$968$	0	0
$969$	113.137	3.63449
$970$	0	0
$971$	18.3848	0.589996	0.294998	−	0.955498i	$-0.404681\pi$
$971$	18.3848	0.589996	0.294998	+	0.955498i	$0.404681\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	48.0000	1.53723
$976$	0	0
$977$	22.0000	0.703842	0.351921	−	0.936030i	$-0.385529\pi$
$977$	22.0000	0.703842	0.351921	+	0.936030i	$0.385529\pi$
$978$	0	0
$979$	11.3137	0.361588
$980$	0	0
$981$	−70.0000	−2.23493
$982$	0	0
$983$	16.9706	0.541277	0.270638	−	0.962681i	$-0.412765\pi$
$983$	16.9706	0.541277	0.270638	+	0.962681i	$0.412765\pi$
$984$	0	0
$985$	−19.7990	−0.630848
$986$	0	0
$987$	0	0
$988$	0	0
$989$	−6.00000	−0.190789
$990$	0	0
$991$	−50.0000	−1.58830	−0.794151	−	0.607720i	$-0.792084\pi$
$991$	−50.0000	−1.58830	−0.794151	+	0.607720i	$0.792084\pi$
$992$	0	0
$993$	45.2548	1.43612
$994$	0	0
$995$	−36.0000	−1.14128
$996$	0	0
$997$	−45.2548	−1.43323	−0.716617	−	0.697466i	$-0.754311\pi$
$997$	−45.2548	−1.43323	−0.716617	+	0.697466i	$0.754311\pi$
$998$	0	0
$999$	22.6274	0.715900

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9016.2.a.u.1.1	✓	2
7.6	odd	2	inner	9016.2.a.u.1.2	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9016.2.a.u.1.1	✓	2	1.1	even	1	trivial
9016.2.a.u.1.2	yes	2	7.6	odd	2	inner

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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:	\( N \)	\(=\)	\( 9016 = 2^{3} \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9016.a (trivial)

\(f(q)\)	\(=\)	\(q-2.82843 q^{3} -1.41421 q^{5} +5.00000 q^{9} +O(q^{10})\)	\(q-2.82843 q^{3} -1.41421 q^{5} +5.00000 q^{9} -4.00000 q^{11} +5.65685 q^{13} +4.00000 q^{15} -5.65685 q^{17} +7.07107 q^{19} +1.00000 q^{23} -3.00000 q^{25} -5.65685 q^{27} -6.00000 q^{29} +4.24264 q^{31} +11.3137 q^{33} -4.00000 q^{37} -16.0000 q^{39} -1.41421 q^{41} -6.00000 q^{43} -7.07107 q^{45} -4.24264 q^{47} +16.0000 q^{51} -8.00000 q^{53} +5.65685 q^{55} -20.0000 q^{57} +8.48528 q^{59} +1.41421 q^{61} -8.00000 q^{65} +10.0000 q^{67} -2.82843 q^{69} +2.00000 q^{71} +7.07107 q^{73} +8.48528 q^{75} +8.00000 q^{79} +1.00000 q^{81} +7.07107 q^{83} +8.00000 q^{85} +16.9706 q^{87} -2.82843 q^{89} -12.0000 q^{93} -10.0000 q^{95} +8.48528 q^{97} -20.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 10 q^{9}+O(q^{10}) \) 2 * q + 10 * q^9	\( 2 q + 10 q^{9} - 8 q^{11} + 8 q^{15} + 2 q^{23} - 6 q^{25} - 12 q^{29} - 8 q^{37} - 32 q^{39} - 12 q^{43} + 32 q^{51} - 16 q^{53} - 40 q^{57} - 16 q^{65} + 20 q^{67} + 4 q^{71} + 16 q^{79} + 2 q^{81} + 16 q^{85} - 24 q^{93} - 20 q^{95} - 40 q^{99}+O(q^{100}) \) 2 * q + 10 * q^9 - 8 * q^11 + 8 * q^15 + 2 * q^23 - 6 * q^25 - 12 * q^29 - 8 * q^37 - 32 * q^39 - 12 * q^43 + 32 * q^51 - 16 * q^53 - 40 * q^57 - 16 * q^65 + 20 * q^67 + 4 * q^71 + 16 * q^79 + 2 * q^81 + 16 * q^85 - 24 * q^93 - 20 * q^95 - 40 * q^99

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