LMFDB - Embedded newform 9016.2.a.bo.1.10

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:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 2 x^{10} - 20 x^{9} + 37 x^{8} + 125 x^{7} - 215 x^{6} - 278 x^{5} + 443 x^{4} + 256 x^{3} + \cdots + 99 $ x^11 - 2x^10 - 20x^9 + 37x^8 + 125x^7 - 215x^6 - 278x^5 + 443x^4 + 256x^3 - 362x^2 - 85x + 99
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1288)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$2.66192$ 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)

$f(q)$	$=$	$q+2.66192 q^{3} +0.382846 q^{5} +4.08581 q^{9} +O(q^{10})$	$q+2.66192 q^{3} +0.382846 q^{5} +4.08581 q^{9} -1.76420 q^{11} -6.63543 q^{13} +1.01910 q^{15} -3.28890 q^{17} +8.14914 q^{19} -1.00000 q^{23} -4.85343 q^{25} +2.89033 q^{27} -6.27547 q^{29} -3.65509 q^{31} -4.69615 q^{33} +9.39951 q^{37} -17.6630 q^{39} +0.176793 q^{41} -3.46133 q^{43} +1.56423 q^{45} -5.54190 q^{47} -8.75477 q^{51} +12.2398 q^{53} -0.675416 q^{55} +21.6923 q^{57} -9.10036 q^{59} -7.35066 q^{61} -2.54035 q^{65} +2.21998 q^{67} -2.66192 q^{69} -10.5757 q^{71} +0.979879 q^{73} -12.9194 q^{75} -13.3030 q^{79} -4.56360 q^{81} -4.35606 q^{83} -1.25914 q^{85} -16.7048 q^{87} -2.49594 q^{89} -9.72956 q^{93} +3.11987 q^{95} +4.82460 q^{97} -7.20817 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 2 q^{3} - 9 q^{5} + 11 q^{9}+O(q^{10}) $ 11 * q + 2 * q^3 - 9 * q^5 + 11 * q^9	$ 11 q + 2 q^{3} - 9 q^{5} + 11 q^{9} - 15 q^{13} - 2 q^{15} - 5 q^{17} - 11 q^{23} + 22 q^{25} + 5 q^{27} + 5 q^{29} - 6 q^{31} - 14 q^{33} - q^{37} + 11 q^{39} - 20 q^{41} - 7 q^{43} - 41 q^{45} + 3 q^{47} - 13 q^{51} + 19 q^{53} + 3 q^{55} - 5 q^{57} - 7 q^{59} - 39 q^{61} + 5 q^{65} + 7 q^{67} - 2 q^{69} - 19 q^{71} + 5 q^{73} - 16 q^{75} + 11 q^{79} + 43 q^{81} - 33 q^{83} - 13 q^{85} + 30 q^{87} - 34 q^{89} - 12 q^{93} + 37 q^{95} - 17 q^{97} - 49 q^{99}+O(q^{100}) $ 11 * q + 2 * q^3 - 9 * q^5 + 11 * q^9 - 15 * q^13 - 2 * q^15 - 5 * q^17 - 11 * q^23 + 22 * q^25 + 5 * q^27 + 5 * q^29 - 6 * q^31 - 14 * q^33 - q^37 + 11 * q^39 - 20 * q^41 - 7 * q^43 - 41 * q^45 + 3 * q^47 - 13 * q^51 + 19 * q^53 + 3 * q^55 - 5 * q^57 - 7 * q^59 - 39 * q^61 + 5 * q^65 + 7 * q^67 - 2 * q^69 - 19 * q^71 + 5 * q^73 - 16 * q^75 + 11 * q^79 + 43 * q^81 - 33 * q^83 - 13 * q^85 + 30 * q^87 - 34 * q^89 - 12 * q^93 + 37 * q^95 - 17 * q^97 - 49 * 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
$3$	2.66192	1.53686	0.768430	−	0.639934i	$-0.221039\pi$
$3$	2.66192	1.53686	0.768430	+	0.639934i	$0.221039\pi$
$4$	0	0
$5$	0.382846	0.171214	0.0856070	−	0.996329i	$-0.472717\pi$
$5$	0.382846	0.171214	0.0856070	+	0.996329i	$0.472717\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	0	0
$9$	4.08581	1.36194
$10$	0	0
$11$	−1.76420	−0.531925	−0.265963	−	0.963983i	$-0.585690\pi$
$11$	−1.76420	−0.531925	−0.265963	+	0.963983i	$0.585690\pi$
$12$	0	0
$13$	−6.63543	−1.84034	−0.920169	−	0.391522i	$-0.871949\pi$
$13$	−6.63543	−1.84034	−0.920169	+	0.391522i	$0.871949\pi$
$14$	0	0
$15$	1.01910	0.263132
$16$	0	0
$17$	−3.28890	−0.797675	−0.398837	−	0.917022i	$-0.630586\pi$
$17$	−3.28890	−0.797675	−0.398837	+	0.917022i	$0.630586\pi$
$18$	0	0
$19$	8.14914	1.86954	0.934770	−	0.355252i	$-0.115605\pi$
$19$	8.14914	1.86954	0.934770	+	0.355252i	$0.115605\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	0	0
$25$	−4.85343	−0.970686
$26$	0	0
$27$	2.89033	0.556244
$28$	0	0
$29$	−6.27547	−1.16532	−0.582662	−	0.812714i	$-0.697989\pi$
$29$	−6.27547	−1.16532	−0.582662	+	0.812714i	$0.697989\pi$
$30$	0	0
$31$	−3.65509	−0.656474	−0.328237	−	0.944595i	$-0.606455\pi$
$31$	−3.65509	−0.656474	−0.328237	+	0.944595i	$0.606455\pi$
$32$	0	0
$33$	−4.69615	−0.817494
$34$	0	0
$35$	0	0
$36$	0	0
$37$	9.39951	1.54527	0.772635	−	0.634851i	$-0.218938\pi$
$37$	9.39951	1.54527	0.772635	+	0.634851i	$0.218938\pi$
$38$	0	0
$39$	−17.6630	−2.82834
$40$	0	0
$41$	0.176793	0.0276104	0.0138052	−	0.999905i	$-0.495606\pi$
$41$	0.176793	0.0276104	0.0138052	+	0.999905i	$0.495606\pi$
$42$	0	0
$43$	−3.46133	−0.527847	−0.263924	−	0.964544i	$-0.585017\pi$
$43$	−3.46133	−0.527847	−0.263924	+	0.964544i	$0.585017\pi$
$44$	0	0
$45$	1.56423	0.233182
$46$	0	0
$47$	−5.54190	−0.808369	−0.404184	−	0.914678i	$-0.632445\pi$
$47$	−5.54190	−0.808369	−0.404184	+	0.914678i	$0.632445\pi$
$48$	0	0
$49$	0	0
$50$	0	0
$51$	−8.75477	−1.22591
$52$	0	0
$53$	12.2398	1.68126	0.840631	−	0.541608i	$-0.182184\pi$
$53$	12.2398	1.68126	0.840631	+	0.541608i	$0.182184\pi$
$54$	0	0
$55$	−0.675416	−0.0910730
$56$	0	0
$57$	21.6923	2.87322
$58$	0	0
$59$	−9.10036	−1.18477	−0.592383	−	0.805656i	$-0.701813\pi$
$59$	−9.10036	−1.18477	−0.592383	+	0.805656i	$0.701813\pi$
$60$	0	0
$61$	−7.35066	−0.941156	−0.470578	−	0.882359i	$-0.655954\pi$
$61$	−7.35066	−0.941156	−0.470578	+	0.882359i	$0.655954\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	−2.54035	−0.315092
$66$	0	0
$67$	2.21998	0.271214	0.135607	−	0.990763i	$-0.456702\pi$
$67$	2.21998	0.271214	0.135607	+	0.990763i	$0.456702\pi$
$68$	0	0
$69$	−2.66192	−0.320457
$70$	0	0
$71$	−10.5757	−1.25510	−0.627551	−	0.778576i	$-0.715943\pi$
$71$	−10.5757	−1.25510	−0.627551	+	0.778576i	$0.715943\pi$
$72$	0	0
$73$	0.979879	0.114686	0.0573431	−	0.998355i	$-0.481737\pi$
$73$	0.979879	0.114686	0.0573431	+	0.998355i	$0.481737\pi$
$74$	0	0
$75$	−12.9194	−1.49181
$76$	0	0
$77$	0	0
$78$	0	0
$79$	−13.3030	−1.49671	−0.748353	−	0.663301i	$-0.769155\pi$
$79$	−13.3030	−1.49671	−0.748353	+	0.663301i	$0.769155\pi$
$80$	0	0
$81$	−4.56360	−0.507067
$82$	0	0
$83$	−4.35606	−0.478140	−0.239070	−	0.971002i	$-0.576842\pi$
$83$	−4.35606	−0.478140	−0.239070	+	0.971002i	$0.576842\pi$
$84$	0	0
$85$	−1.25914	−0.136573
$86$	0	0
$87$	−16.7048	−1.79094
$88$	0	0
$89$	−2.49594	−0.264569	−0.132285	−	0.991212i	$-0.542231\pi$
$89$	−2.49594	−0.264569	−0.132285	+	0.991212i	$0.542231\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	−9.72956	−1.00891
$94$	0	0
$95$	3.11987	0.320091
$96$	0	0
$97$	4.82460	0.489864	0.244932	−	0.969540i	$-0.421234\pi$
$97$	4.82460	0.489864	0.244932	+	0.969540i	$0.421234\pi$
$98$	0	0
$99$	−7.20817	−0.724448
$100$	0	0
$101$	15.8650	1.57862	0.789312	−	0.613993i	$-0.210438\pi$
$101$	15.8650	1.57862	0.789312	+	0.613993i	$0.210438\pi$
$102$	0	0
$103$	−3.88718	−0.383015	−0.191508	−	0.981491i	$-0.561338\pi$
$103$	−3.88718	−0.383015	−0.191508	+	0.981491i	$0.561338\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	14.3028	1.38271	0.691353	−	0.722517i	$-0.257015\pi$
$107$	14.3028	1.38271	0.691353	+	0.722517i	$0.257015\pi$
$108$	0	0
$109$	6.83887	0.655045	0.327523	−	0.944843i	$-0.393786\pi$
$109$	6.83887	0.655045	0.327523	+	0.944843i	$0.393786\pi$
$110$	0	0
$111$	25.0207	2.37486
$112$	0	0
$113$	−8.08622	−0.760687	−0.380344	−	0.924845i	$-0.624194\pi$
$113$	−8.08622	−0.760687	−0.380344	+	0.924845i	$0.624194\pi$
$114$	0	0
$115$	−0.382846	−0.0357006
$116$	0	0
$117$	−27.1111	−2.50642
$118$	0	0
$119$	0	0
$120$	0	0
$121$	−7.88761	−0.717055
$122$	0	0
$123$	0.470608	0.0424333
$124$	0	0
$125$	−3.77235	−0.337409
$126$	0	0
$127$	−19.1019	−1.69502	−0.847509	−	0.530782i	$-0.821898\pi$
$127$	−19.1019	−1.69502	−0.847509	+	0.530782i	$0.821898\pi$
$128$	0	0
$129$	−9.21377	−0.811227
$130$	0	0
$131$	−1.17940	−0.103045	−0.0515223	−	0.998672i	$-0.516407\pi$
$131$	−1.17940	−0.103045	−0.0515223	+	0.998672i	$0.516407\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	1.10655	0.0952367
$136$	0	0
$137$	−11.7449	−1.00343	−0.501716	−	0.865032i	$-0.667298\pi$
$137$	−11.7449	−1.00343	−0.501716	+	0.865032i	$0.667298\pi$
$138$	0	0
$139$	11.3696	0.964357	0.482179	−	0.876073i	$-0.339846\pi$
$139$	11.3696	0.964357	0.482179	+	0.876073i	$0.339846\pi$
$140$	0	0
$141$	−14.7521	−1.24235
$142$	0	0
$143$	11.7062	0.978922
$144$	0	0
$145$	−2.40254	−0.199520
$146$	0	0
$147$	0	0
$148$	0	0
$149$	−24.0139	−1.96730	−0.983648	−	0.180101i	$-0.942358\pi$
$149$	−24.0139	−1.96730	−0.983648	+	0.180101i	$0.942358\pi$
$150$	0	0
$151$	−7.93558	−0.645788	−0.322894	−	0.946435i	$-0.604656\pi$
$151$	−7.93558	−0.645788	−0.322894	+	0.946435i	$0.604656\pi$
$152$	0	0
$153$	−13.4378	−1.08638
$154$	0	0
$155$	−1.39934	−0.112398
$156$	0	0
$157$	−5.58963	−0.446101	−0.223050	−	0.974807i	$-0.571601\pi$
$157$	−5.58963	−0.446101	−0.223050	+	0.974807i	$0.571601\pi$
$158$	0	0
$159$	32.5813	2.58386
$160$	0	0
$161$	0	0
$162$	0	0
$163$	5.75195	0.450527	0.225264	−	0.974298i	$-0.427676\pi$
$163$	5.75195	0.450527	0.225264	+	0.974298i	$0.427676\pi$
$164$	0	0
$165$	−1.79790	−0.139966
$166$	0	0
$167$	−3.91905	−0.303265	−0.151633	−	0.988437i	$-0.548453\pi$
$167$	−3.91905	−0.303265	−0.151633	+	0.988437i	$0.548453\pi$
$168$	0	0
$169$	31.0290	2.38684
$170$	0	0
$171$	33.2958	2.54619
$172$	0	0
$173$	−13.0515	−0.992286	−0.496143	−	0.868241i	$-0.665251\pi$
$173$	−13.0515	−0.992286	−0.496143	+	0.868241i	$0.665251\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	−24.2244	−1.82082
$178$	0	0
$179$	3.79598	0.283725	0.141863	−	0.989886i	$-0.454691\pi$
$179$	3.79598	0.283725	0.141863	+	0.989886i	$0.454691\pi$
$180$	0	0
$181$	16.2852	1.21047	0.605233	−	0.796048i	$-0.293080\pi$
$181$	16.2852	1.21047	0.605233	+	0.796048i	$0.293080\pi$
$182$	0	0
$183$	−19.5669	−1.44642
$184$	0	0
$185$	3.59857	0.264572
$186$	0	0
$187$	5.80226	0.424303
$188$	0	0
$189$	0	0
$190$	0	0
$191$	−25.2927	−1.83011	−0.915057	−	0.403325i	$-0.867854\pi$
$191$	−25.2927	−1.83011	−0.915057	+	0.403325i	$0.867854\pi$
$192$	0	0
$193$	15.7678	1.13499	0.567495	−	0.823377i	$-0.307912\pi$
$193$	15.7678	1.13499	0.567495	+	0.823377i	$0.307912\pi$
$194$	0	0
$195$	−6.76220	−0.484251
$196$	0	0
$197$	2.26359	0.161274	0.0806370	−	0.996744i	$-0.474305\pi$
$197$	2.26359	0.161274	0.0806370	+	0.996744i	$0.474305\pi$
$198$	0	0
$199$	−17.5945	−1.24724	−0.623622	−	0.781726i	$-0.714339\pi$
$199$	−17.5945	−1.24724	−0.623622	+	0.781726i	$0.714339\pi$
$200$	0	0
$201$	5.90942	0.416818
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0.0676845	0.00472729
$206$	0	0
$207$	−4.08581	−0.283983
$208$	0	0
$209$	−14.3767	−0.994456
$210$	0	0
$211$	21.4724	1.47822	0.739111	−	0.673584i	$-0.235246\pi$
$211$	21.4724	1.47822	0.739111	+	0.673584i	$0.235246\pi$
$212$	0	0
$213$	−28.1516	−1.92891
$214$	0	0
$215$	−1.32516	−0.0903748
$216$	0	0
$217$	0	0
$218$	0	0
$219$	2.60836	0.176257
$220$	0	0
$221$	21.8233	1.46799
$222$	0	0
$223$	−3.17427	−0.212565	−0.106283	−	0.994336i	$-0.533895\pi$
$223$	−3.17427	−0.212565	−0.106283	+	0.994336i	$0.533895\pi$
$224$	0	0
$225$	−19.8302	−1.32201
$226$	0	0
$227$	−1.75321	−0.116365	−0.0581823	−	0.998306i	$-0.518530\pi$
$227$	−1.75321	−0.116365	−0.0581823	+	0.998306i	$0.518530\pi$
$228$	0	0
$229$	−3.78062	−0.249830	−0.124915	−	0.992167i	$-0.539866\pi$
$229$	−3.78062	−0.249830	−0.124915	+	0.992167i	$0.539866\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	−15.9785	−1.04679	−0.523394	−	0.852091i	$-0.675334\pi$
$233$	−15.9785	−1.04679	−0.523394	+	0.852091i	$0.675334\pi$
$234$	0	0
$235$	−2.12169	−0.138404
$236$	0	0
$237$	−35.4115	−2.30023
$238$	0	0
$239$	13.3633	0.864403	0.432201	−	0.901777i	$-0.357737\pi$
$239$	13.3633	0.864403	0.432201	+	0.901777i	$0.357737\pi$
$240$	0	0
$241$	20.5145	1.32146	0.660728	−	0.750626i	$-0.270248\pi$
$241$	20.5145	1.32146	0.660728	+	0.750626i	$0.270248\pi$
$242$	0	0
$243$	−20.8189	−1.33553
$244$	0	0
$245$	0	0
$246$	0	0
$247$	−54.0731	−3.44059
$248$	0	0
$249$	−11.5955	−0.734833
$250$	0	0
$251$	−4.95583	−0.312809	−0.156405	−	0.987693i	$-0.549990\pi$
$251$	−4.95583	−0.312809	−0.156405	+	0.987693i	$0.549990\pi$
$252$	0	0
$253$	1.76420	0.110914
$254$	0	0
$255$	−3.35173	−0.209893
$256$	0	0
$257$	−27.5709	−1.71982	−0.859912	−	0.510443i	$-0.829481\pi$
$257$	−27.5709	−1.71982	−0.859912	+	0.510443i	$0.829481\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	−25.6403	−1.58710
$262$	0	0
$263$	29.2621	1.80438	0.902188	−	0.431342i	$-0.141960\pi$
$263$	29.2621	1.80438	0.902188	+	0.431342i	$0.141960\pi$
$264$	0	0
$265$	4.68595	0.287856
$266$	0	0
$267$	−6.64399	−0.406606
$268$	0	0
$269$	−12.6135	−0.769061	−0.384531	−	0.923112i	$-0.625637\pi$
$269$	−12.6135	−0.769061	−0.384531	+	0.923112i	$0.625637\pi$
$270$	0	0
$271$	19.8009	1.20282	0.601408	−	0.798942i	$-0.294606\pi$
$271$	19.8009	1.20282	0.601408	+	0.798942i	$0.294606\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	8.56240	0.516332
$276$	0	0
$277$	−33.0089	−1.98331	−0.991655	−	0.128918i	$-0.958850\pi$
$277$	−33.0089	−1.98331	−0.991655	+	0.128918i	$0.958850\pi$
$278$	0	0
$279$	−14.9340	−0.894076
$280$	0	0
$281$	23.0732	1.37643	0.688215	−	0.725507i	$-0.258395\pi$
$281$	23.0732	1.37643	0.688215	+	0.725507i	$0.258395\pi$
$282$	0	0
$283$	−3.03758	−0.180565	−0.0902826	−	0.995916i	$-0.528777\pi$
$283$	−3.03758	−0.180565	−0.0902826	+	0.995916i	$0.528777\pi$
$284$	0	0
$285$	8.30483	0.491935
$286$	0	0
$287$	0	0
$288$	0	0
$289$	−6.18316	−0.363715
$290$	0	0
$291$	12.8427	0.752852
$292$	0	0
$293$	−8.01177	−0.468053	−0.234026	−	0.972230i	$-0.575190\pi$
$293$	−8.01177	−0.468053	−0.234026	+	0.972230i	$0.575190\pi$
$294$	0	0
$295$	−3.48404	−0.202849
$296$	0	0
$297$	−5.09911	−0.295880
$298$	0	0
$299$	6.63543	0.383737
$300$	0	0
$301$	0	0
$302$	0	0
$303$	42.2312	2.42612
$304$	0	0
$305$	−2.81417	−0.161139
$306$	0	0
$307$	−17.2671	−0.985485	−0.492742	−	0.870175i	$-0.664006\pi$
$307$	−17.2671	−0.985485	−0.492742	+	0.870175i	$0.664006\pi$
$308$	0	0
$309$	−10.3474	−0.588640
$310$	0	0
$311$	−23.2158	−1.31645	−0.658224	−	0.752822i	$-0.728692\pi$
$311$	−23.2158	−1.31645	−0.658224	+	0.752822i	$0.728692\pi$
$312$	0	0
$313$	7.44257	0.420679	0.210339	−	0.977628i	$-0.432543\pi$
$313$	7.44257	0.420679	0.210339	+	0.977628i	$0.432543\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	27.3511	1.53619	0.768096	−	0.640335i	$-0.221204\pi$
$317$	27.3511	1.53619	0.768096	+	0.640335i	$0.221204\pi$
$318$	0	0
$319$	11.0712	0.619866
$320$	0	0
$321$	38.0730	2.12503
$322$	0	0
$323$	−26.8017	−1.49129
$324$	0	0
$325$	32.2046	1.78639
$326$	0	0
$327$	18.2045	1.00671
$328$	0	0
$329$	0	0
$330$	0	0
$331$	13.1155	0.720891	0.360445	−	0.932780i	$-0.382625\pi$
$331$	13.1155	0.720891	0.360445	+	0.932780i	$0.382625\pi$
$332$	0	0
$333$	38.4046	2.10456
$334$	0	0
$335$	0.849912	0.0464357
$336$	0	0
$337$	22.2681	1.21302	0.606511	−	0.795075i	$-0.292568\pi$
$337$	22.2681	1.21302	0.606511	+	0.795075i	$0.292568\pi$
$338$	0	0
$339$	−21.5248	−1.16907
$340$	0	0
$341$	6.44831	0.349195
$342$	0	0
$343$	0	0
$344$	0	0
$345$	−1.01910	−0.0548668
$346$	0	0
$347$	6.27104	0.336647	0.168324	−	0.985732i	$-0.446165\pi$
$347$	6.27104	0.336647	0.168324	+	0.985732i	$0.446165\pi$
$348$	0	0
$349$	15.6251	0.836392	0.418196	−	0.908357i	$-0.362662\pi$
$349$	15.6251	0.836392	0.418196	+	0.908357i	$0.362662\pi$
$350$	0	0
$351$	−19.1786	−1.02368
$352$	0	0
$353$	3.03077	0.161311	0.0806557	−	0.996742i	$-0.474299\pi$
$353$	3.03077	0.161311	0.0806557	+	0.996742i	$0.474299\pi$
$354$	0	0
$355$	−4.04885	−0.214891
$356$	0	0
$357$	0	0
$358$	0	0
$359$	18.6933	0.986597	0.493298	−	0.869860i	$-0.335791\pi$
$359$	18.6933	0.986597	0.493298	+	0.869860i	$0.335791\pi$
$360$	0	0
$361$	47.4085	2.49518
$362$	0	0
$363$	−20.9962	−1.10201
$364$	0	0
$365$	0.375143	0.0196359
$366$	0	0
$367$	3.47655	0.181474	0.0907372	−	0.995875i	$-0.471078\pi$
$367$	3.47655	0.181474	0.0907372	+	0.995875i	$0.471078\pi$
$368$	0	0
$369$	0.722342	0.0376036
$370$	0	0
$371$	0	0
$372$	0	0
$373$	−0.885153	−0.0458315	−0.0229157	−	0.999737i	$-0.507295\pi$
$373$	−0.885153	−0.0458315	−0.0229157	+	0.999737i	$0.507295\pi$
$374$	0	0
$375$	−10.0417	−0.518550
$376$	0	0
$377$	41.6404	2.14459
$378$	0	0
$379$	14.9636	0.768626	0.384313	−	0.923203i	$-0.374438\pi$
$379$	14.9636	0.768626	0.384313	+	0.923203i	$0.374438\pi$
$380$	0	0
$381$	−50.8476	−2.60500
$382$	0	0
$383$	13.4336	0.686425	0.343212	−	0.939258i	$-0.388485\pi$
$383$	13.4336	0.686425	0.343212	+	0.939258i	$0.388485\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	−14.1423	−0.718894
$388$	0	0
$389$	11.8982	0.603264	0.301632	−	0.953424i	$-0.402469\pi$
$389$	11.8982	0.603264	0.301632	+	0.953424i	$0.402469\pi$
$390$	0	0
$391$	3.28890	0.166327
$392$	0	0
$393$	−3.13946	−0.158365
$394$	0	0
$395$	−5.09301	−0.256257
$396$	0	0
$397$	−28.7180	−1.44131	−0.720657	−	0.693292i	$-0.756160\pi$
$397$	−28.7180	−1.44131	−0.720657	+	0.693292i	$0.756160\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	3.03043	0.151332	0.0756662	−	0.997133i	$-0.475892\pi$
$401$	3.03043	0.151332	0.0756662	+	0.997133i	$0.475892\pi$
$402$	0	0
$403$	24.2531	1.20813
$404$	0	0
$405$	−1.74716	−0.0868170
$406$	0	0
$407$	−16.5826	−0.821968
$408$	0	0
$409$	−17.9009	−0.885143	−0.442571	−	0.896733i	$-0.645934\pi$
$409$	−17.9009	−0.885143	−0.442571	+	0.896733i	$0.645934\pi$
$410$	0	0
$411$	−31.2639	−1.54213
$412$	0	0
$413$	0	0
$414$	0	0
$415$	−1.66770	−0.0818642
$416$	0	0
$417$	30.2649	1.48208
$418$	0	0
$419$	−24.3009	−1.18718	−0.593589	−	0.804768i	$-0.702290\pi$
$419$	−24.3009	−1.18718	−0.593589	+	0.804768i	$0.702290\pi$
$420$	0	0
$421$	−28.1915	−1.37397	−0.686986	−	0.726671i	$-0.741066\pi$
$421$	−28.1915	−1.37397	−0.686986	+	0.726671i	$0.741066\pi$
$422$	0	0
$423$	−22.6431	−1.10095
$424$	0	0
$425$	15.9624	0.774291
$426$	0	0
$427$	0	0
$428$	0	0
$429$	31.1610	1.50447
$430$	0	0
$431$	10.2257	0.492552	0.246276	−	0.969200i	$-0.420793\pi$
$431$	10.2257	0.492552	0.246276	+	0.969200i	$0.420793\pi$
$432$	0	0
$433$	−30.2318	−1.45285	−0.726424	−	0.687246i	$-0.758819\pi$
$433$	−30.2318	−1.45285	−0.726424	+	0.687246i	$0.758819\pi$
$434$	0	0
$435$	−6.39536	−0.306634
$436$	0	0
$437$	−8.14914	−0.389826
$438$	0	0
$439$	10.1296	0.483461	0.241731	−	0.970343i	$-0.422285\pi$
$439$	10.1296	0.483461	0.241731	+	0.970343i	$0.422285\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	16.0381	0.761991	0.380995	−	0.924577i	$-0.375581\pi$
$443$	16.0381	0.761991	0.380995	+	0.924577i	$0.375581\pi$
$444$	0	0
$445$	−0.955561	−0.0452980
$446$	0	0
$447$	−63.9231	−3.02346
$448$	0	0
$449$	16.3513	0.771666	0.385833	−	0.922569i	$-0.373914\pi$
$449$	16.3513	0.771666	0.385833	+	0.922569i	$0.373914\pi$
$450$	0	0
$451$	−0.311898	−0.0146867
$452$	0	0
$453$	−21.1239	−0.992485
$454$	0	0
$455$	0	0
$456$	0	0
$457$	8.37826	0.391919	0.195959	−	0.980612i	$-0.437218\pi$
$457$	8.37826	0.391919	0.195959	+	0.980612i	$0.437218\pi$
$458$	0	0
$459$	−9.50599	−0.443702
$460$	0	0
$461$	22.6148	1.05328	0.526638	−	0.850090i	$-0.323452\pi$
$461$	22.6148	1.05328	0.526638	+	0.850090i	$0.323452\pi$
$462$	0	0
$463$	−8.79592	−0.408781	−0.204391	−	0.978889i	$-0.565521\pi$
$463$	−8.79592	−0.408781	−0.204391	+	0.978889i	$0.565521\pi$
$464$	0	0
$465$	−3.72492	−0.172739
$466$	0	0
$467$	32.9508	1.52478	0.762391	−	0.647116i	$-0.224025\pi$
$467$	32.9508	1.52478	0.762391	+	0.647116i	$0.224025\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	−14.8791	−0.685594
$472$	0	0
$473$	6.10646	0.280775
$474$	0	0
$475$	−39.5513	−1.81474
$476$	0	0
$477$	50.0094	2.28977
$478$	0	0
$479$	18.7844	0.858283	0.429141	−	0.903237i	$-0.358816\pi$
$479$	18.7844	0.858283	0.429141	+	0.903237i	$0.358816\pi$
$480$	0	0
$481$	−62.3698	−2.84382
$482$	0	0
$483$	0	0
$484$	0	0
$485$	1.84708	0.0838716
$486$	0	0
$487$	11.0185	0.499294	0.249647	−	0.968337i	$-0.419685\pi$
$487$	11.0185	0.499294	0.249647	+	0.968337i	$0.419685\pi$
$488$	0	0
$489$	15.3112	0.692397
$490$	0	0
$491$	5.54412	0.250203	0.125101	−	0.992144i	$-0.460074\pi$
$491$	5.54412	0.250203	0.125101	+	0.992144i	$0.460074\pi$
$492$	0	0
$493$	20.6394	0.929550
$494$	0	0
$495$	−2.75962	−0.124036
$496$	0	0
$497$	0	0
$498$	0	0
$499$	−22.7575	−1.01877	−0.509383	−	0.860540i	$-0.670126\pi$
$499$	−22.7575	−1.01877	−0.509383	+	0.860540i	$0.670126\pi$
$500$	0	0
$501$	−10.4322	−0.466076
$502$	0	0
$503$	18.4830	0.824118	0.412059	−	0.911157i	$-0.364810\pi$
$503$	18.4830	0.824118	0.412059	+	0.911157i	$0.364810\pi$
$504$	0	0
$505$	6.07384	0.270282
$506$	0	0
$507$	82.5965	3.66824
$508$	0	0
$509$	−36.8972	−1.63544	−0.817719	−	0.575617i	$-0.804762\pi$
$509$	−36.8972	−1.63544	−0.817719	+	0.575617i	$0.804762\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	23.5537	1.03992
$514$	0	0
$515$	−1.48819	−0.0655776
$516$	0	0
$517$	9.77700	0.429992
$518$	0	0
$519$	−34.7420	−1.52500
$520$	0	0
$521$	2.53111	0.110890	0.0554450	−	0.998462i	$-0.482342\pi$
$521$	2.53111	0.110890	0.0554450	+	0.998462i	$0.482342\pi$
$522$	0	0
$523$	1.41659	0.0619433	0.0309716	−	0.999520i	$-0.490140\pi$
$523$	1.41659	0.0619433	0.0309716	+	0.999520i	$0.490140\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	12.0212	0.523653
$528$	0	0
$529$	1.00000	0.0434783
$530$	0	0
$531$	−37.1823	−1.61358
$532$	0	0
$533$	−1.17310	−0.0508125
$534$	0	0
$535$	5.47578	0.236739
$536$	0	0
$537$	10.1046	0.436045
$538$	0	0
$539$	0	0
$540$	0	0
$541$	28.9626	1.24520	0.622601	−	0.782540i	$-0.286076\pi$
$541$	28.9626	1.24520	0.622601	+	0.782540i	$0.286076\pi$
$542$	0	0
$543$	43.3498	1.86032
$544$	0	0
$545$	2.61824	0.112153
$546$	0	0
$547$	9.50026	0.406202	0.203101	−	0.979158i	$-0.434898\pi$
$547$	9.50026	0.406202	0.203101	+	0.979158i	$0.434898\pi$
$548$	0	0
$549$	−30.0334	−1.28179
$550$	0	0
$551$	−51.1396	−2.17862
$552$	0	0
$553$	0	0
$554$	0	0
$555$	9.57908	0.406609
$556$	0	0
$557$	−26.2476	−1.11215	−0.556073	−	0.831133i	$-0.687693\pi$
$557$	−26.2476	−1.11215	−0.556073	+	0.831133i	$0.687693\pi$
$558$	0	0
$559$	22.9674	0.971417
$560$	0	0
$561$	15.4451	0.652094
$562$	0	0
$563$	2.50348	0.105509	0.0527546	−	0.998608i	$-0.483200\pi$
$563$	2.50348	0.105509	0.0527546	+	0.998608i	$0.483200\pi$
$564$	0	0
$565$	−3.09578	−0.130240
$566$	0	0
$567$	0	0
$568$	0	0
$569$	15.1063	0.633288	0.316644	−	0.948544i	$-0.397444\pi$
$569$	15.1063	0.633288	0.316644	+	0.948544i	$0.397444\pi$
$570$	0	0
$571$	−41.0126	−1.71632	−0.858161	−	0.513380i	$-0.828393\pi$
$571$	−41.0126	−1.71632	−0.858161	+	0.513380i	$0.828393\pi$
$572$	0	0
$573$	−67.3270	−2.81263
$574$	0	0
$575$	4.85343	0.202402
$576$	0	0
$577$	25.6914	1.06955	0.534774	−	0.844995i	$-0.320397\pi$
$577$	25.6914	1.06955	0.534774	+	0.844995i	$0.320397\pi$
$578$	0	0
$579$	41.9726	1.74432
$580$	0	0
$581$	0	0
$582$	0	0
$583$	−21.5934	−0.894306
$584$	0	0
$585$	−10.3794	−0.429134
$586$	0	0
$587$	−11.2585	−0.464686	−0.232343	−	0.972634i	$-0.574639\pi$
$587$	−11.2585	−0.464686	−0.232343	+	0.972634i	$0.574639\pi$
$588$	0	0
$589$	−29.7859	−1.22731
$590$	0	0
$591$	6.02549	0.247856
$592$	0	0
$593$	21.2430	0.872346	0.436173	−	0.899863i	$-0.356334\pi$
$593$	21.2430	0.872346	0.436173	+	0.899863i	$0.356334\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	−46.8352	−1.91684
$598$	0	0
$599$	−2.48942	−0.101715	−0.0508574	−	0.998706i	$-0.516195\pi$
$599$	−2.48942	−0.101715	−0.0508574	+	0.998706i	$0.516195\pi$
$600$	0	0
$601$	−22.1995	−0.905536	−0.452768	−	0.891628i	$-0.649563\pi$
$601$	−22.1995	−0.905536	−0.452768	+	0.891628i	$0.649563\pi$
$602$	0	0
$603$	9.07043	0.369376
$604$	0	0
$605$	−3.01974	−0.122770
$606$	0	0
$607$	3.43477	0.139413	0.0697065	−	0.997568i	$-0.477794\pi$
$607$	3.43477	0.139413	0.0697065	+	0.997568i	$0.477794\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	36.7729	1.48767
$612$	0	0
$613$	13.2143	0.533721	0.266861	−	0.963735i	$-0.414014\pi$
$613$	13.2143	0.533721	0.266861	+	0.963735i	$0.414014\pi$
$614$	0	0
$615$	0.180171	0.00726518
$616$	0	0
$617$	−18.0191	−0.725421	−0.362710	−	0.931902i	$-0.618149\pi$
$617$	−18.0191	−0.725421	−0.362710	+	0.931902i	$0.618149\pi$
$618$	0	0
$619$	20.7186	0.832751	0.416375	−	0.909193i	$-0.363300\pi$
$619$	20.7186	0.832751	0.416375	+	0.909193i	$0.363300\pi$
$620$	0	0
$621$	−2.89033	−0.115985
$622$	0	0
$623$	0	0
$624$	0	0
$625$	22.8229	0.912917
$626$	0	0
$627$	−38.2696	−1.52834
$628$	0	0
$629$	−30.9140	−1.23262
$630$	0	0
$631$	6.60038	0.262757	0.131379	−	0.991332i	$-0.458060\pi$
$631$	6.60038	0.262757	0.131379	+	0.991332i	$0.458060\pi$
$632$	0	0
$633$	57.1578	2.27182
$634$	0	0
$635$	−7.31308	−0.290211
$636$	0	0
$637$	0	0
$638$	0	0
$639$	−43.2102	−1.70937
$640$	0	0
$641$	−16.6762	−0.658672	−0.329336	−	0.944213i	$-0.606825\pi$
$641$	−16.6762	−0.658672	−0.329336	+	0.944213i	$0.606825\pi$
$642$	0	0
$643$	−8.15501	−0.321602	−0.160801	−	0.986987i	$-0.551408\pi$
$643$	−8.15501	−0.321602	−0.160801	+	0.986987i	$0.551408\pi$
$644$	0	0
$645$	−3.52745	−0.138893
$646$	0	0
$647$	−10.1215	−0.397918	−0.198959	−	0.980008i	$-0.563756\pi$
$647$	−10.1215	−0.397918	−0.198959	+	0.980008i	$0.563756\pi$
$648$	0	0
$649$	16.0548	0.630207
$650$	0	0
$651$	0	0
$652$	0	0
$653$	16.4454	0.643557	0.321778	−	0.946815i	$-0.395719\pi$
$653$	16.4454	0.643557	0.321778	+	0.946815i	$0.395719\pi$
$654$	0	0
$655$	−0.451528	−0.0176427
$656$	0	0
$657$	4.00360	0.156195
$658$	0	0
$659$	−19.4636	−0.758195	−0.379098	−	0.925357i	$-0.623766\pi$
$659$	−19.4636	−0.758195	−0.379098	+	0.925357i	$0.623766\pi$
$660$	0	0
$661$	7.31702	0.284599	0.142299	−	0.989824i	$-0.454550\pi$
$661$	7.31702	0.284599	0.142299	+	0.989824i	$0.454550\pi$
$662$	0	0
$663$	58.0917	2.25609
$664$	0	0
$665$	0	0
$666$	0	0
$667$	6.27547	0.242987
$668$	0	0
$669$	−8.44965	−0.326683
$670$	0	0
$671$	12.9680	0.500625
$672$	0	0
$673$	−27.2545	−1.05058	−0.525291	−	0.850923i	$-0.676044\pi$
$673$	−27.2545	−1.05058	−0.525291	+	0.850923i	$0.676044\pi$
$674$	0	0
$675$	−14.0280	−0.539938
$676$	0	0
$677$	−23.8433	−0.916374	−0.458187	−	0.888856i	$-0.651501\pi$
$677$	−23.8433	−0.916374	−0.458187	+	0.888856i	$0.651501\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	−4.66690	−0.178836
$682$	0	0
$683$	−3.23560	−0.123807	−0.0619033	−	0.998082i	$-0.519717\pi$
$683$	−3.23560	−0.123807	−0.0619033	+	0.998082i	$0.519717\pi$
$684$	0	0
$685$	−4.49648	−0.171802
$686$	0	0
$687$	−10.0637	−0.383954
$688$	0	0
$689$	−81.2162	−3.09409
$690$	0	0
$691$	35.9697	1.36835	0.684176	−	0.729317i	$-0.260162\pi$
$691$	35.9697	1.36835	0.684176	+	0.729317i	$0.260162\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	4.35281	0.165111
$696$	0	0
$697$	−0.581454	−0.0220241
$698$	0	0
$699$	−42.5335	−1.60877
$700$	0	0
$701$	12.1374	0.458423	0.229212	−	0.973377i	$-0.426385\pi$
$701$	12.1374	0.458423	0.229212	+	0.973377i	$0.426385\pi$
$702$	0	0
$703$	76.5979	2.88895
$704$	0	0
$705$	−5.64777	−0.212707
$706$	0	0
$707$	0	0
$708$	0	0
$709$	22.4255	0.842206	0.421103	−	0.907013i	$-0.361643\pi$
$709$	22.4255	0.842206	0.421103	+	0.907013i	$0.361643\pi$
$710$	0	0
$711$	−54.3535	−2.03842
$712$	0	0
$713$	3.65509	0.136884
$714$	0	0
$715$	4.48168	0.167605
$716$	0	0
$717$	35.5721	1.32846
$718$	0	0
$719$	−35.6632	−1.33001	−0.665006	−	0.746838i	$-0.731571\pi$
$719$	−35.6632	−1.33001	−0.665006	+	0.746838i	$0.731571\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	54.6079	2.03089
$724$	0	0
$725$	30.4575	1.13116
$726$	0	0
$727$	−9.79850	−0.363406	−0.181703	−	0.983353i	$-0.558161\pi$
$727$	−9.79850	−0.363406	−0.181703	+	0.983353i	$0.558161\pi$
$728$	0	0
$729$	−41.7275	−1.54546
$730$	0	0
$731$	11.3839	0.421050
$732$	0	0
$733$	−35.8769	−1.32514	−0.662571	−	0.748999i	$-0.730535\pi$
$733$	−35.8769	−1.32514	−0.662571	+	0.748999i	$0.730535\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−3.91649	−0.144266
$738$	0	0
$739$	22.4125	0.824458	0.412229	−	0.911080i	$-0.364750\pi$
$739$	22.4125	0.824458	0.412229	+	0.911080i	$0.364750\pi$
$740$	0	0
$741$	−143.938	−5.28770
$742$	0	0
$743$	34.4028	1.26212	0.631058	−	0.775736i	$-0.282621\pi$
$743$	34.4028	1.26212	0.631058	+	0.775736i	$0.282621\pi$
$744$	0	0
$745$	−9.19363	−0.336829
$746$	0	0
$747$	−17.7980	−0.651196
$748$	0	0
$749$	0	0
$750$	0	0
$751$	19.6024	0.715303	0.357651	−	0.933855i	$-0.383578\pi$
$751$	19.6024	0.715303	0.357651	+	0.933855i	$0.383578\pi$
$752$	0	0
$753$	−13.1920	−0.480744
$754$	0	0
$755$	−3.03810	−0.110568
$756$	0	0
$757$	34.8833	1.26786	0.633928	−	0.773392i	$-0.281442\pi$
$757$	34.8833	1.26786	0.633928	+	0.773392i	$0.281442\pi$
$758$	0	0
$759$	4.69615	0.170459
$760$	0	0
$761$	−16.1856	−0.586726	−0.293363	−	0.956001i	$-0.594774\pi$
$761$	−16.1856	−0.586726	−0.293363	+	0.956001i	$0.594774\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	−5.14461	−0.186004
$766$	0	0
$767$	60.3848	2.18037
$768$	0	0
$769$	−15.6997	−0.566147	−0.283073	−	0.959098i	$-0.591354\pi$
$769$	−15.6997	−0.566147	−0.283073	+	0.959098i	$0.591354\pi$
$770$	0	0
$771$	−73.3914	−2.64313
$772$	0	0
$773$	−11.1732	−0.401871	−0.200935	−	0.979604i	$-0.564398\pi$
$773$	−11.1732	−0.401871	−0.200935	+	0.979604i	$0.564398\pi$
$774$	0	0
$775$	17.7397	0.637230
$776$	0	0
$777$	0	0
$778$	0	0
$779$	1.44071	0.0516188
$780$	0	0
$781$	18.6576	0.667620
$782$	0	0
$783$	−18.1382	−0.648205
$784$	0	0
$785$	−2.13997	−0.0763787
$786$	0	0
$787$	−32.6225	−1.16287	−0.581433	−	0.813594i	$-0.697508\pi$
$787$	−32.6225	−1.16287	−0.581433	+	0.813594i	$0.697508\pi$
$788$	0	0
$789$	77.8932	2.77307
$790$	0	0
$791$	0	0
$792$	0	0
$793$	48.7748	1.73204
$794$	0	0
$795$	12.4736	0.442394
$796$	0	0
$797$	−34.7040	−1.22928	−0.614640	−	0.788808i	$-0.710699\pi$
$797$	−34.7040	−1.22928	−0.614640	+	0.788808i	$0.710699\pi$
$798$	0	0
$799$	18.2267	0.644815
$800$	0	0
$801$	−10.1979	−0.360326
$802$	0	0
$803$	−1.72870	−0.0610045
$804$	0	0
$805$	0	0
$806$	0	0
$807$	−33.5762	−1.18194
$808$	0	0
$809$	52.3566	1.84076	0.920380	−	0.391026i	$-0.127880\pi$
$809$	52.3566	1.84076	0.920380	+	0.391026i	$0.127880\pi$
$810$	0	0
$811$	48.3966	1.69943	0.849717	−	0.527239i	$-0.176773\pi$
$811$	48.3966	1.69943	0.849717	+	0.527239i	$0.176773\pi$
$812$	0	0
$813$	52.7083	1.84856
$814$	0	0
$815$	2.20211	0.0771366
$816$	0	0
$817$	−28.2068	−0.986832
$818$	0	0
$819$	0	0
$820$	0	0
$821$	−4.77451	−0.166632	−0.0833158	−	0.996523i	$-0.526551\pi$
$821$	−4.77451	−0.166632	−0.0833158	+	0.996523i	$0.526551\pi$
$822$	0	0
$823$	22.5682	0.786677	0.393339	−	0.919394i	$-0.371320\pi$
$823$	22.5682	0.786677	0.393339	+	0.919394i	$0.371320\pi$
$824$	0	0
$825$	22.7924	0.793530
$826$	0	0
$827$	8.36084	0.290735	0.145367	−	0.989378i	$-0.453564\pi$
$827$	8.36084	0.290735	0.145367	+	0.989378i	$0.453564\pi$
$828$	0	0
$829$	−18.1650	−0.630895	−0.315448	−	0.948943i	$-0.602155\pi$
$829$	−18.1650	−0.630895	−0.315448	+	0.948943i	$0.602155\pi$
$830$	0	0
$831$	−87.8669	−3.04807
$832$	0	0
$833$	0	0
$834$	0	0
$835$	−1.50039	−0.0519232
$836$	0	0
$837$	−10.5644	−0.365160
$838$	0	0
$839$	27.0165	0.932713	0.466357	−	0.884597i	$-0.345566\pi$
$839$	27.0165	0.932713	0.466357	+	0.884597i	$0.345566\pi$
$840$	0	0
$841$	10.3815	0.357982
$842$	0	0
$843$	61.4189	2.11538
$844$	0	0
$845$	11.8793	0.408661
$846$	0	0
$847$	0	0
$848$	0	0
$849$	−8.08578	−0.277503
$850$	0	0
$851$	−9.39951	−0.322211
$852$	0	0
$853$	24.6843	0.845174	0.422587	−	0.906322i	$-0.361122\pi$
$853$	24.6843	0.845174	0.422587	+	0.906322i	$0.361122\pi$
$854$	0	0
$855$	12.7472	0.435944
$856$	0	0
$857$	27.0590	0.924319	0.462159	−	0.886797i	$-0.347075\pi$
$857$	27.0590	0.924319	0.462159	+	0.886797i	$0.347075\pi$
$858$	0	0
$859$	−32.7904	−1.11879	−0.559396	−	0.828900i	$-0.688967\pi$
$859$	−32.7904	−1.11879	−0.559396	+	0.828900i	$0.688967\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	−16.6819	−0.567857	−0.283929	−	0.958845i	$-0.591638\pi$
$863$	−16.6819	−0.567857	−0.283929	+	0.958845i	$0.591638\pi$
$864$	0	0
$865$	−4.99671	−0.169893
$866$	0	0
$867$	−16.4591	−0.558979
$868$	0	0
$869$	23.4691	0.796136
$870$	0	0
$871$	−14.7306	−0.499126
$872$	0	0
$873$	19.7124	0.667164
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−23.6589	−0.798905	−0.399453	−	0.916754i	$-0.630800\pi$
$877$	−23.6589	−0.798905	−0.399453	+	0.916754i	$0.630800\pi$
$878$	0	0
$879$	−21.3267	−0.719331
$880$	0	0
$881$	−2.87101	−0.0967267	−0.0483633	−	0.998830i	$-0.515401\pi$
$881$	−2.87101	−0.0967267	−0.0483633	+	0.998830i	$0.515401\pi$
$882$	0	0
$883$	17.3780	0.584816	0.292408	−	0.956294i	$-0.405543\pi$
$883$	17.3780	0.584816	0.292408	+	0.956294i	$0.405543\pi$
$884$	0	0
$885$	−9.27422	−0.311750
$886$	0	0
$887$	15.5692	0.522762	0.261381	−	0.965236i	$-0.415822\pi$
$887$	15.5692	0.522762	0.261381	+	0.965236i	$0.415822\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	8.05109	0.269722
$892$	0	0
$893$	−45.1617	−1.51128
$894$	0	0
$895$	1.45328	0.0485777
$896$	0	0
$897$	17.6630	0.589750
$898$	0	0
$899$	22.9374	0.765006
$900$	0	0
$901$	−40.2554	−1.34110
$902$	0	0
$903$	0	0
$904$	0	0
$905$	6.23471	0.207249
$906$	0	0
$907$	11.8785	0.394420	0.197210	−	0.980361i	$-0.436812\pi$
$907$	11.8785	0.394420	0.197210	+	0.980361i	$0.436812\pi$
$908$	0	0
$909$	64.8212	2.14998
$910$	0	0
$911$	10.5681	0.350138	0.175069	−	0.984556i	$-0.443985\pi$
$911$	10.5681	0.350138	0.175069	+	0.984556i	$0.443985\pi$
$912$	0	0
$913$	7.68495	0.254335
$914$	0	0
$915$	−7.49109	−0.247648
$916$	0	0
$917$	0	0
$918$	0	0
$919$	−19.6161	−0.647076	−0.323538	−	0.946215i	$-0.604872\pi$
$919$	−19.6161	−0.647076	−0.323538	+	0.946215i	$0.604872\pi$
$920$	0	0
$921$	−45.9636	−1.51455
$922$	0	0
$923$	70.1742	2.30981
$924$	0	0
$925$	−45.6199	−1.49997
$926$	0	0
$927$	−15.8823	−0.521642
$928$	0	0
$929$	19.6169	0.643609	0.321805	−	0.946806i	$-0.395711\pi$
$929$	19.6169	0.643609	0.321805	+	0.946806i	$0.395711\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	−61.7986	−2.02320
$934$	0	0
$935$	2.22137	0.0726467
$936$	0	0
$937$	−36.1983	−1.18255	−0.591273	−	0.806472i	$-0.701374\pi$
$937$	−36.1983	−1.18255	−0.591273	+	0.806472i	$0.701374\pi$
$938$	0	0
$939$	19.8115	0.646524
$940$	0	0
$941$	16.9107	0.551274	0.275637	−	0.961262i	$-0.411111\pi$
$941$	16.9107	0.551274	0.275637	+	0.961262i	$0.411111\pi$
$942$	0	0
$943$	−0.176793	−0.00575717
$944$	0	0
$945$	0	0
$946$	0	0
$947$	54.6826	1.77695	0.888473	−	0.458929i	$-0.151767\pi$
$947$	54.6826	1.77695	0.888473	+	0.458929i	$0.151767\pi$
$948$	0	0
$949$	−6.50192	−0.211061
$950$	0	0
$951$	72.8064	2.36091
$952$	0	0
$953$	−15.8524	−0.513510	−0.256755	−	0.966477i	$-0.582653\pi$
$953$	−15.8524	−0.513510	−0.256755	+	0.966477i	$0.582653\pi$
$954$	0	0
$955$	−9.68320	−0.313341
$956$	0	0
$957$	29.4705	0.952646
$958$	0	0
$959$	0	0
$960$	0	0
$961$	−17.6403	−0.569041
$962$	0	0
$963$	58.4386	1.88316
$964$	0	0
$965$	6.03664	0.194326
$966$	0	0
$967$	4.44476	0.142934	0.0714669	−	0.997443i	$-0.477232\pi$
$967$	4.44476	0.142934	0.0714669	+	0.997443i	$0.477232\pi$
$968$	0	0
$969$	−71.3439	−2.29190
$970$	0	0
$971$	−53.2014	−1.70731	−0.853657	−	0.520836i	$-0.825620\pi$
$971$	−53.2014	−1.70731	−0.853657	+	0.520836i	$0.825620\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	85.7260	2.74543
$976$	0	0
$977$	35.6249	1.13974	0.569871	−	0.821735i	$-0.306993\pi$
$977$	35.6249	1.13974	0.569871	+	0.821735i	$0.306993\pi$
$978$	0	0
$979$	4.40333	0.140731
$980$	0	0
$981$	27.9423	0.892129
$982$	0	0
$983$	−43.8676	−1.39916	−0.699579	−	0.714555i	$-0.746629\pi$
$983$	−43.8676	−1.39916	−0.699579	+	0.714555i	$0.746629\pi$
$984$	0	0
$985$	0.866606	0.0276124
$986$	0	0
$987$	0	0
$988$	0	0
$989$	3.46133	0.110064
$990$	0	0
$991$	−2.83860	−0.0901710	−0.0450855	−	0.998983i	$-0.514356\pi$
$991$	−2.83860	−0.0901710	−0.0450855	+	0.998983i	$0.514356\pi$
$992$	0	0
$993$	34.9123	1.10791
$994$	0	0
$995$	−6.73600	−0.213546
$996$	0	0
$997$	26.4785	0.838582	0.419291	−	0.907852i	$-0.362279\pi$
$997$	26.4785	0.838582	0.419291	+	0.907852i	$0.362279\pi$
$998$	0	0
$999$	27.1677	0.859547

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9016.2.a.bo.1.10		11
7.3	odd	6		1288.2.q.b.737.10	✓	22
7.5	odd	6		1288.2.q.b.921.10	yes	22
7.6	odd	2		9016.2.a.bn.1.2		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1288.2.q.b.737.10	✓	22	7.3	odd	6
1288.2.q.b.921.10	yes	22	7.5	odd	6
9016.2.a.bn.1.2		11	7.6	odd	2
9016.2.a.bo.1.10		11	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+2.66192 q^{3} +0.382846 q^{5} +4.08581 q^{9} +O(q^{10})\)	\(q+2.66192 q^{3} +0.382846 q^{5} +4.08581 q^{9} -1.76420 q^{11} -6.63543 q^{13} +1.01910 q^{15} -3.28890 q^{17} +8.14914 q^{19} -1.00000 q^{23} -4.85343 q^{25} +2.89033 q^{27} -6.27547 q^{29} -3.65509 q^{31} -4.69615 q^{33} +9.39951 q^{37} -17.6630 q^{39} +0.176793 q^{41} -3.46133 q^{43} +1.56423 q^{45} -5.54190 q^{47} -8.75477 q^{51} +12.2398 q^{53} -0.675416 q^{55} +21.6923 q^{57} -9.10036 q^{59} -7.35066 q^{61} -2.54035 q^{65} +2.21998 q^{67} -2.66192 q^{69} -10.5757 q^{71} +0.979879 q^{73} -12.9194 q^{75} -13.3030 q^{79} -4.56360 q^{81} -4.35606 q^{83} -1.25914 q^{85} -16.7048 q^{87} -2.49594 q^{89} -9.72956 q^{93} +3.11987 q^{95} +4.82460 q^{97} -7.20817 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 2 q^{3} - 9 q^{5} + 11 q^{9}+O(q^{10}) \) 11 * q + 2 * q^3 - 9 * q^5 + 11 * q^9	\( 11 q + 2 q^{3} - 9 q^{5} + 11 q^{9} - 15 q^{13} - 2 q^{15} - 5 q^{17} - 11 q^{23} + 22 q^{25} + 5 q^{27} + 5 q^{29} - 6 q^{31} - 14 q^{33} - q^{37} + 11 q^{39} - 20 q^{41} - 7 q^{43} - 41 q^{45} + 3 q^{47} - 13 q^{51} + 19 q^{53} + 3 q^{55} - 5 q^{57} - 7 q^{59} - 39 q^{61} + 5 q^{65} + 7 q^{67} - 2 q^{69} - 19 q^{71} + 5 q^{73} - 16 q^{75} + 11 q^{79} + 43 q^{81} - 33 q^{83} - 13 q^{85} + 30 q^{87} - 34 q^{89} - 12 q^{93} + 37 q^{95} - 17 q^{97} - 49 q^{99}+O(q^{100}) \) 11 * q + 2 * q^3 - 9 * q^5 + 11 * q^9 - 15 * q^13 - 2 * q^15 - 5 * q^17 - 11 * q^23 + 22 * q^25 + 5 * q^27 + 5 * q^29 - 6 * q^31 - 14 * q^33 - q^37 + 11 * q^39 - 20 * q^41 - 7 * q^43 - 41 * q^45 + 3 * q^47 - 13 * q^51 + 19 * q^53 + 3 * q^55 - 5 * q^57 - 7 * q^59 - 39 * q^61 + 5 * q^65 + 7 * q^67 - 2 * q^69 - 19 * q^71 + 5 * q^73 - 16 * q^75 + 11 * q^79 + 43 * q^81 - 33 * q^83 - 13 * q^85 + 30 * q^87 - 34 * q^89 - 12 * q^93 + 37 * q^95 - 17 * q^97 - 49 * q^99

Introduction

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