LMFDB - Embedded newform 9016.2.a.br.1.7

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:	$0$
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} - 4 x^{10} - 14 x^{9} + 61 x^{8} + 71 x^{7} - 343 x^{6} - 152 x^{5} + 867 x^{4} + 102 x^{3} + \cdots + 243 $ x^11 - 4x^10 - 14x^9 + 61x^8 + 71x^7 - 343x^6 - 152x^5 + 867x^4 + 102x^3 - 918x^2 + 35x + 243
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			1.7
Root			$1.59106$ 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)

$f(q)$	$=$	$q+1.59106 q^{3} -2.83508 q^{5} -0.468513 q^{9} +O(q^{10})$	$q+1.59106 q^{3} -2.83508 q^{5} -0.468513 q^{9} +5.68688 q^{11} -5.47160 q^{13} -4.51079 q^{15} +0.927480 q^{17} +7.70110 q^{19} -1.00000 q^{23} +3.03766 q^{25} -5.51863 q^{27} -0.155642 q^{29} +6.19318 q^{31} +9.04819 q^{33} -4.13469 q^{37} -8.70567 q^{39} +5.77277 q^{41} -8.58237 q^{43} +1.32827 q^{45} +1.52968 q^{47} +1.47568 q^{51} -3.51278 q^{53} -16.1227 q^{55} +12.2530 q^{57} -0.0446442 q^{59} +9.01884 q^{61} +15.5124 q^{65} -13.6206 q^{67} -1.59106 q^{69} -1.38742 q^{71} +13.9422 q^{73} +4.83312 q^{75} -9.51114 q^{79} -7.37496 q^{81} +8.29488 q^{83} -2.62948 q^{85} -0.247637 q^{87} -9.13979 q^{89} +9.85375 q^{93} -21.8332 q^{95} +3.16127 q^{97} -2.66437 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 4 q^{3} + 3 q^{5} + 11 q^{9}+O(q^{10}) $ 11 * q + 4 * q^3 + 3 * q^5 + 11 * q^9	$ 11 q + 4 q^{3} + 3 q^{5} + 11 q^{9} - 13 q^{13} + 7 q^{17} + 8 q^{19} - 11 q^{23} + 6 q^{25} + 25 q^{27} - 3 q^{29} + 12 q^{31} - 2 q^{33} - q^{37} - 21 q^{39} + 12 q^{41} + 9 q^{43} + 19 q^{45} + 17 q^{47} + 19 q^{51} - 5 q^{53} + 21 q^{55} + 11 q^{57} + 33 q^{59} - 15 q^{61} - 9 q^{65} - 5 q^{67} - 4 q^{69} - 9 q^{71} + 5 q^{73} + 44 q^{75} + 11 q^{79} - 13 q^{81} + 51 q^{83} + 33 q^{85} + 4 q^{87} + 26 q^{89} + 6 q^{93} - 19 q^{95} + 21 q^{97} + 15 q^{99}+O(q^{100}) $ 11 * q + 4 * q^3 + 3 * q^5 + 11 * q^9 - 13 * q^13 + 7 * q^17 + 8 * q^19 - 11 * q^23 + 6 * q^25 + 25 * q^27 - 3 * q^29 + 12 * q^31 - 2 * q^33 - q^37 - 21 * q^39 + 12 * q^41 + 9 * q^43 + 19 * q^45 + 17 * q^47 + 19 * q^51 - 5 * q^53 + 21 * q^55 + 11 * q^57 + 33 * q^59 - 15 * q^61 - 9 * q^65 - 5 * q^67 - 4 * q^69 - 9 * q^71 + 5 * q^73 + 44 * q^75 + 11 * q^79 - 13 * q^81 + 51 * q^83 + 33 * q^85 + 4 * q^87 + 26 * q^89 + 6 * q^93 - 19 * q^95 + 21 * q^97 + 15 * 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
$3$	1.59106	0.918602	0.459301	−	0.888281i	$-0.348100\pi$
$3$	1.59106	0.918602	0.459301	+	0.888281i	$0.348100\pi$
$4$	0	0
$5$	−2.83508	−1.26788	−0.633942	−	0.773380i	$-0.718564\pi$
$5$	−2.83508	−1.26788	−0.633942	+	0.773380i	$0.718564\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	0	0
$9$	−0.468513	−0.156171
$10$	0	0
$11$	5.68688	1.71466	0.857329	−	0.514769i	$-0.172122\pi$
$11$	5.68688	1.71466	0.857329	+	0.514769i	$0.172122\pi$
$12$	0	0
$13$	−5.47160	−1.51755	−0.758775	−	0.651353i	$-0.774202\pi$
$13$	−5.47160	−1.51755	−0.758775	+	0.651353i	$0.774202\pi$
$14$	0	0
$15$	−4.51079	−1.16468
$16$	0	0
$17$	0.927480	0.224947	0.112473	−	0.993655i	$-0.464123\pi$
$17$	0.927480	0.224947	0.112473	+	0.993655i	$0.464123\pi$
$18$	0	0
$19$	7.70110	1.76675	0.883377	−	0.468663i	$-0.155264\pi$
$19$	7.70110	1.76675	0.883377	+	0.468663i	$0.155264\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	0	0
$25$	3.03766	0.607532
$26$	0	0
$27$	−5.51863	−1.06206
$28$	0	0
$29$	−0.155642	−0.0289021	−0.0144510	−	0.999896i	$-0.504600\pi$
$29$	−0.155642	−0.0289021	−0.0144510	+	0.999896i	$0.504600\pi$
$30$	0	0
$31$	6.19318	1.11233	0.556164	−	0.831072i	$-0.312273\pi$
$31$	6.19318	1.11233	0.556164	+	0.831072i	$0.312273\pi$
$32$	0	0
$33$	9.04819	1.57509
$34$	0	0
$35$	0	0
$36$	0	0
$37$	−4.13469	−0.679739	−0.339870	−	0.940473i	$-0.610383\pi$
$37$	−4.13469	−0.679739	−0.339870	+	0.940473i	$0.610383\pi$
$38$	0	0
$39$	−8.70567	−1.39402
$40$	0	0
$41$	5.77277	0.901556	0.450778	−	0.892636i	$-0.351147\pi$
$41$	5.77277	0.901556	0.450778	+	0.892636i	$0.351147\pi$
$42$	0	0
$43$	−8.58237	−1.30880	−0.654399	−	0.756149i	$-0.727078\pi$
$43$	−8.58237	−1.30880	−0.654399	+	0.756149i	$0.727078\pi$
$44$	0	0
$45$	1.32827	0.198007
$46$	0	0
$47$	1.52968	0.223127	0.111563	−	0.993757i	$-0.464414\pi$
$47$	1.52968	0.223127	0.111563	+	0.993757i	$0.464414\pi$
$48$	0	0
$49$	0	0
$50$	0	0
$51$	1.47568	0.206637
$52$	0	0
$53$	−3.51278	−0.482517	−0.241258	−	0.970461i	$-0.577560\pi$
$53$	−3.51278	−0.482517	−0.241258	+	0.970461i	$0.577560\pi$
$54$	0	0
$55$	−16.1227	−2.17399
$56$	0	0
$57$	12.2530	1.62294
$58$	0	0
$59$	−0.0446442	−0.00581218	−0.00290609	−	0.999996i	$-0.500925\pi$
$59$	−0.0446442	−0.00581218	−0.00290609	+	0.999996i	$0.500925\pi$
$60$	0	0
$61$	9.01884	1.15474	0.577372	−	0.816481i	$-0.304078\pi$
$61$	9.01884	1.15474	0.577372	+	0.816481i	$0.304078\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	15.5124	1.92408
$66$	0	0
$67$	−13.6206	−1.66402	−0.832012	−	0.554757i	$-0.812811\pi$
$67$	−13.6206	−1.66402	−0.832012	+	0.554757i	$0.812811\pi$
$68$	0	0
$69$	−1.59106	−0.191542
$70$	0	0
$71$	−1.38742	−0.164656	−0.0823280	−	0.996605i	$-0.526236\pi$
$71$	−1.38742	−0.164656	−0.0823280	+	0.996605i	$0.526236\pi$
$72$	0	0
$73$	13.9422	1.63182	0.815908	−	0.578182i	$-0.196237\pi$
$73$	13.9422	1.63182	0.815908	+	0.578182i	$0.196237\pi$
$74$	0	0
$75$	4.83312	0.558080
$76$	0	0
$77$	0	0
$78$	0	0
$79$	−9.51114	−1.07009	−0.535043	−	0.844825i	$-0.679705\pi$
$79$	−9.51114	−1.07009	−0.535043	+	0.844825i	$0.679705\pi$
$80$	0	0
$81$	−7.37496	−0.819440
$82$	0	0
$83$	8.29488	0.910481	0.455241	−	0.890368i	$-0.349553\pi$
$83$	8.29488	0.910481	0.455241	+	0.890368i	$0.349553\pi$
$84$	0	0
$85$	−2.62948	−0.285207
$86$	0	0
$87$	−0.247637	−0.0265495
$88$	0	0
$89$	−9.13979	−0.968816	−0.484408	−	0.874842i	$-0.660965\pi$
$89$	−9.13979	−0.968816	−0.484408	+	0.874842i	$0.660965\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	9.85375	1.02179
$94$	0	0
$95$	−21.8332	−2.24004
$96$	0	0
$97$	3.16127	0.320979	0.160489	−	0.987038i	$-0.448693\pi$
$97$	3.16127	0.320979	0.160489	+	0.987038i	$0.448693\pi$
$98$	0	0
$99$	−2.66437	−0.267780
$100$	0	0
$101$	−9.04967	−0.900476	−0.450238	−	0.892909i	$-0.648661\pi$
$101$	−9.04967	−0.900476	−0.450238	+	0.892909i	$0.648661\pi$
$102$	0	0
$103$	17.0747	1.68242	0.841210	−	0.540708i	$-0.181844\pi$
$103$	17.0747	1.68242	0.841210	+	0.540708i	$0.181844\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	−12.6947	−1.22725	−0.613623	−	0.789599i	$-0.710288\pi$
$107$	−12.6947	−1.22725	−0.613623	+	0.789599i	$0.710288\pi$
$108$	0	0
$109$	4.99507	0.478441	0.239221	−	0.970965i	$-0.423108\pi$
$109$	4.99507	0.478441	0.239221	+	0.970965i	$0.423108\pi$
$110$	0	0
$111$	−6.57856	−0.624410
$112$	0	0
$113$	12.9019	1.21371	0.606856	−	0.794812i	$-0.292431\pi$
$113$	12.9019	1.21371	0.606856	+	0.794812i	$0.292431\pi$
$114$	0	0
$115$	2.83508	0.264372
$116$	0	0
$117$	2.56351	0.236997
$118$	0	0
$119$	0	0
$120$	0	0
$121$	21.3406	1.94005
$122$	0	0
$123$	9.18486	0.828171
$124$	0	0
$125$	5.56338	0.497604
$126$	0	0
$127$	13.8162	1.22599	0.612993	−	0.790088i	$-0.289965\pi$
$127$	13.8162	1.22599	0.612993	+	0.790088i	$0.289965\pi$
$128$	0	0
$129$	−13.6551	−1.20226
$130$	0	0
$131$	11.0502	0.965459	0.482730	−	0.875769i	$-0.339645\pi$
$131$	11.0502	0.965459	0.482730	+	0.875769i	$0.339645\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	15.6457	1.34657
$136$	0	0
$137$	1.69956	0.145203	0.0726017	−	0.997361i	$-0.476870\pi$
$137$	1.69956	0.145203	0.0726017	+	0.997361i	$0.476870\pi$
$138$	0	0
$139$	12.0798	1.02460	0.512298	−	0.858808i	$-0.328794\pi$
$139$	12.0798	1.02460	0.512298	+	0.858808i	$0.328794\pi$
$140$	0	0
$141$	2.43382	0.204965
$142$	0	0
$143$	−31.1163	−2.60208
$144$	0	0
$145$	0.441258	0.0366445
$146$	0	0
$147$	0	0
$148$	0	0
$149$	−6.12978	−0.502171	−0.251085	−	0.967965i	$-0.580788\pi$
$149$	−6.12978	−0.502171	−0.251085	+	0.967965i	$0.580788\pi$
$150$	0	0
$151$	0.190212	0.0154792	0.00773960	−	0.999970i	$-0.497536\pi$
$151$	0.190212	0.0154792	0.00773960	+	0.999970i	$0.497536\pi$
$152$	0	0
$153$	−0.434536	−0.0351301
$154$	0	0
$155$	−17.5581	−1.41030
$156$	0	0
$157$	5.02361	0.400927	0.200464	−	0.979701i	$-0.435755\pi$
$157$	5.02361	0.400927	0.200464	+	0.979701i	$0.435755\pi$
$158$	0	0
$159$	−5.58906	−0.443241
$160$	0	0
$161$	0	0
$162$	0	0
$163$	11.7623	0.921292	0.460646	−	0.887584i	$-0.347618\pi$
$163$	11.7623	0.921292	0.460646	+	0.887584i	$0.347618\pi$
$164$	0	0
$165$	−25.6523	−1.99703
$166$	0	0
$167$	−22.7283	−1.75877	−0.879386	−	0.476109i	$-0.842047\pi$
$167$	−22.7283	−1.75877	−0.879386	+	0.476109i	$0.842047\pi$
$168$	0	0
$169$	16.9384	1.30296
$170$	0	0
$171$	−3.60806	−0.275915
$172$	0	0
$173$	1.64265	0.124888	0.0624442	−	0.998048i	$-0.480110\pi$
$173$	1.64265	0.124888	0.0624442	+	0.998048i	$0.480110\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	−0.0710319	−0.00533908
$178$	0	0
$179$	22.0732	1.64983	0.824913	−	0.565259i	$-0.191224\pi$
$179$	22.0732	1.64983	0.824913	+	0.565259i	$0.191224\pi$
$180$	0	0
$181$	−3.85689	−0.286680	−0.143340	−	0.989673i	$-0.545784\pi$
$181$	−3.85689	−0.286680	−0.143340	+	0.989673i	$0.545784\pi$
$182$	0	0
$183$	14.3496	1.06075
$184$	0	0
$185$	11.7222	0.861831
$186$	0	0
$187$	5.27446	0.385707
$188$	0	0
$189$	0	0
$190$	0	0
$191$	6.86103	0.496447	0.248223	−	0.968703i	$-0.420153\pi$
$191$	6.86103	0.496447	0.248223	+	0.968703i	$0.420153\pi$
$192$	0	0
$193$	6.81022	0.490210	0.245105	−	0.969496i	$-0.421177\pi$
$193$	6.81022	0.490210	0.245105	+	0.969496i	$0.421177\pi$
$194$	0	0
$195$	24.6813	1.76746
$196$	0	0
$197$	11.2767	0.803435	0.401717	−	0.915764i	$-0.368413\pi$
$197$	11.2767	0.803435	0.401717	+	0.915764i	$0.368413\pi$
$198$	0	0
$199$	23.4941	1.66545	0.832725	−	0.553687i	$-0.186780\pi$
$199$	23.4941	1.66545	0.832725	+	0.553687i	$0.186780\pi$
$200$	0	0
$201$	−21.6713	−1.52858
$202$	0	0
$203$	0	0
$204$	0	0
$205$	−16.3663	−1.14307
$206$	0	0
$207$	0.468513	0.0325639
$208$	0	0
$209$	43.7952	3.02938
$210$	0	0
$211$	−2.71973	−0.187234	−0.0936170	−	0.995608i	$-0.529843\pi$
$211$	−2.71973	−0.187234	−0.0936170	+	0.995608i	$0.529843\pi$
$212$	0	0
$213$	−2.20747	−0.151253
$214$	0	0
$215$	24.3317	1.65941
$216$	0	0
$217$	0	0
$218$	0	0
$219$	22.1830	1.49899
$220$	0	0
$221$	−5.07480	−0.341368
$222$	0	0
$223$	17.8482	1.19520	0.597602	−	0.801793i	$-0.296120\pi$
$223$	17.8482	1.19520	0.597602	+	0.801793i	$0.296120\pi$
$224$	0	0
$225$	−1.42318	−0.0948788
$226$	0	0
$227$	13.6572	0.906457	0.453229	−	0.891394i	$-0.350272\pi$
$227$	13.6572	0.906457	0.453229	+	0.891394i	$0.350272\pi$
$228$	0	0
$229$	1.75676	0.116090	0.0580451	−	0.998314i	$-0.481513\pi$
$229$	1.75676	0.116090	0.0580451	+	0.998314i	$0.481513\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	25.9297	1.69871	0.849354	−	0.527823i	$-0.176992\pi$
$233$	25.9297	1.69871	0.849354	+	0.527823i	$0.176992\pi$
$234$	0	0
$235$	−4.33676	−0.282899
$236$	0	0
$237$	−15.1328	−0.982983
$238$	0	0
$239$	−8.01201	−0.518254	−0.259127	−	0.965843i	$-0.583435\pi$
$239$	−8.01201	−0.518254	−0.259127	+	0.965843i	$0.583435\pi$
$240$	0	0
$241$	3.83084	0.246766	0.123383	−	0.992359i	$-0.460626\pi$
$241$	3.83084	0.246766	0.123383	+	0.992359i	$0.460626\pi$
$242$	0	0
$243$	4.82185	0.309322
$244$	0	0
$245$	0	0
$246$	0	0
$247$	−42.1374	−2.68114
$248$	0	0
$249$	13.1977	0.836369
$250$	0	0
$251$	−2.15527	−0.136040	−0.0680198	−	0.997684i	$-0.521668\pi$
$251$	−2.15527	−0.136040	−0.0680198	+	0.997684i	$0.521668\pi$
$252$	0	0
$253$	−5.68688	−0.357531
$254$	0	0
$255$	−4.18367	−0.261991
$256$	0	0
$257$	−3.70356	−0.231022	−0.115511	−	0.993306i	$-0.536851\pi$
$257$	−3.70356	−0.231022	−0.115511	+	0.993306i	$0.536851\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	0.0729204	0.00451366
$262$	0	0
$263$	−7.35262	−0.453382	−0.226691	−	0.973967i	$-0.572791\pi$
$263$	−7.35262	−0.453382	−0.226691	+	0.973967i	$0.572791\pi$
$264$	0	0
$265$	9.95899	0.611776
$266$	0	0
$267$	−14.5420	−0.889956
$268$	0	0
$269$	14.4244	0.879473	0.439737	−	0.898127i	$-0.355072\pi$
$269$	14.4244	0.879473	0.439737	+	0.898127i	$0.355072\pi$
$270$	0	0
$271$	−21.1101	−1.28235	−0.641175	−	0.767395i	$-0.721553\pi$
$271$	−21.1101	−1.28235	−0.641175	+	0.767395i	$0.721553\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	17.2748	1.04171
$276$	0	0
$277$	9.23187	0.554689	0.277345	−	0.960771i	$-0.410546\pi$
$277$	9.23187	0.554689	0.277345	+	0.960771i	$0.410546\pi$
$278$	0	0
$279$	−2.90158	−0.173713
$280$	0	0
$281$	5.53493	0.330186	0.165093	−	0.986278i	$-0.447208\pi$
$281$	5.53493	0.330186	0.165093	+	0.986278i	$0.447208\pi$
$282$	0	0
$283$	8.89184	0.528565	0.264283	−	0.964445i	$-0.414865\pi$
$283$	8.89184	0.528565	0.264283	+	0.964445i	$0.414865\pi$
$284$	0	0
$285$	−34.7381	−2.05771
$286$	0	0
$287$	0	0
$288$	0	0
$289$	−16.1398	−0.949399
$290$	0	0
$291$	5.02979	0.294852
$292$	0	0
$293$	22.3380	1.30500	0.652499	−	0.757790i	$-0.273721\pi$
$293$	22.3380	1.30500	0.652499	+	0.757790i	$0.273721\pi$
$294$	0	0
$295$	0.126570	0.00736918
$296$	0	0
$297$	−31.3838	−1.82107
$298$	0	0
$299$	5.47160	0.316431
$300$	0	0
$301$	0	0
$302$	0	0
$303$	−14.3986	−0.827179
$304$	0	0
$305$	−25.5691	−1.46408
$306$	0	0
$307$	−24.4507	−1.39547	−0.697737	−	0.716354i	$-0.745810\pi$
$307$	−24.4507	−1.39547	−0.697737	+	0.716354i	$0.745810\pi$
$308$	0	0
$309$	27.1670	1.54547
$310$	0	0
$311$	−17.8294	−1.01101	−0.505507	−	0.862822i	$-0.668695\pi$
$311$	−17.8294	−1.01101	−0.505507	+	0.862822i	$0.668695\pi$
$312$	0	0
$313$	−19.0265	−1.07544	−0.537722	−	0.843122i	$-0.680715\pi$
$313$	−19.0265	−1.07544	−0.537722	+	0.843122i	$0.680715\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	24.9421	1.40089	0.700443	−	0.713708i	$-0.252986\pi$
$317$	24.9421	1.40089	0.700443	+	0.713708i	$0.252986\pi$
$318$	0	0
$319$	−0.885119	−0.0495571
$320$	0	0
$321$	−20.1981	−1.12735
$322$	0	0
$323$	7.14262	0.397426
$324$	0	0
$325$	−16.6209	−0.921960
$326$	0	0
$327$	7.94749	0.439497
$328$	0	0
$329$	0	0
$330$	0	0
$331$	21.4302	1.17791	0.588954	−	0.808166i	$-0.299540\pi$
$331$	21.4302	1.17791	0.588954	+	0.808166i	$0.299540\pi$
$332$	0	0
$333$	1.93715	0.106155
$334$	0	0
$335$	38.6155	2.10979
$336$	0	0
$337$	−25.1959	−1.37251	−0.686255	−	0.727361i	$-0.740746\pi$
$337$	−25.1959	−1.37251	−0.686255	+	0.727361i	$0.740746\pi$
$338$	0	0
$339$	20.5278	1.11492
$340$	0	0
$341$	35.2199	1.90726
$342$	0	0
$343$	0	0
$344$	0	0
$345$	4.51079	0.242853
$346$	0	0
$347$	20.1561	1.08203	0.541017	−	0.841012i	$-0.318040\pi$
$347$	20.1561	1.08203	0.541017	+	0.841012i	$0.318040\pi$
$348$	0	0
$349$	4.12556	0.220836	0.110418	−	0.993885i	$-0.464781\pi$
$349$	4.12556	0.220836	0.110418	+	0.993885i	$0.464781\pi$
$350$	0	0
$351$	30.1957	1.61173
$352$	0	0
$353$	−2.77923	−0.147923	−0.0739617	−	0.997261i	$-0.523564\pi$
$353$	−2.77923	−0.147923	−0.0739617	+	0.997261i	$0.523564\pi$
$354$	0	0
$355$	3.93343	0.208765
$356$	0	0
$357$	0	0
$358$	0	0
$359$	24.2275	1.27868	0.639340	−	0.768925i	$-0.279208\pi$
$359$	24.2275	1.27868	0.639340	+	0.768925i	$0.279208\pi$
$360$	0	0
$361$	40.3070	2.12142
$362$	0	0
$363$	33.9542	1.78213
$364$	0	0
$365$	−39.5273	−2.06896
$366$	0	0
$367$	7.14581	0.373008	0.186504	−	0.982454i	$-0.440284\pi$
$367$	7.14581	0.373008	0.186504	+	0.982454i	$0.440284\pi$
$368$	0	0
$369$	−2.70462	−0.140797
$370$	0	0
$371$	0	0
$372$	0	0
$373$	12.6183	0.653353	0.326676	−	0.945136i	$-0.394071\pi$
$373$	12.6183	0.653353	0.326676	+	0.945136i	$0.394071\pi$
$374$	0	0
$375$	8.85170	0.457100
$376$	0	0
$377$	0.851613	0.0438603
$378$	0	0
$379$	−30.4112	−1.56212	−0.781060	−	0.624456i	$-0.785321\pi$
$379$	−30.4112	−1.56212	−0.781060	+	0.624456i	$0.785321\pi$
$380$	0	0
$381$	21.9824	1.12619
$382$	0	0
$383$	−28.7852	−1.47086	−0.735428	−	0.677603i	$-0.763019\pi$
$383$	−28.7852	−1.47086	−0.735428	+	0.677603i	$0.763019\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	4.02095	0.204396
$388$	0	0
$389$	−8.54256	−0.433125	−0.216562	−	0.976269i	$-0.569484\pi$
$389$	−8.54256	−0.433125	−0.216562	+	0.976269i	$0.569484\pi$
$390$	0	0
$391$	−0.927480	−0.0469047
$392$	0	0
$393$	17.5816	0.886873
$394$	0	0
$395$	26.9648	1.35675
$396$	0	0
$397$	−14.8368	−0.744640	−0.372320	−	0.928104i	$-0.621438\pi$
$397$	−14.8368	−0.744640	−0.372320	+	0.928104i	$0.621438\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	1.67987	0.0838888	0.0419444	−	0.999120i	$-0.486645\pi$
$401$	1.67987	0.0838888	0.0419444	+	0.999120i	$0.486645\pi$
$402$	0	0
$403$	−33.8866	−1.68801
$404$	0	0
$405$	20.9086	1.03896
$406$	0	0
$407$	−23.5135	−1.16552
$408$	0	0
$409$	−20.4362	−1.01051	−0.505254	−	0.862971i	$-0.668601\pi$
$409$	−20.4362	−1.01051	−0.505254	+	0.862971i	$0.668601\pi$
$410$	0	0
$411$	2.70411	0.133384
$412$	0	0
$413$	0	0
$414$	0	0
$415$	−23.5166	−1.15439
$416$	0	0
$417$	19.2198	0.941196
$418$	0	0
$419$	22.2285	1.08594	0.542968	−	0.839754i	$-0.317301\pi$
$419$	22.2285	1.08594	0.542968	+	0.839754i	$0.317301\pi$
$420$	0	0
$421$	−7.27042	−0.354338	−0.177169	−	0.984180i	$-0.556694\pi$
$421$	−7.27042	−0.354338	−0.177169	+	0.984180i	$0.556694\pi$
$422$	0	0
$423$	−0.716675	−0.0348459
$424$	0	0
$425$	2.81737	0.136663
$426$	0	0
$427$	0	0
$428$	0	0
$429$	−49.5081	−2.39027
$430$	0	0
$431$	9.78849	0.471495	0.235747	−	0.971814i	$-0.424246\pi$
$431$	9.78849	0.471495	0.235747	+	0.971814i	$0.424246\pi$
$432$	0	0
$433$	27.7236	1.33231	0.666156	−	0.745812i	$-0.267939\pi$
$433$	27.7236	1.33231	0.666156	+	0.745812i	$0.267939\pi$
$434$	0	0
$435$	0.702070	0.0336617
$436$	0	0
$437$	−7.70110	−0.368394
$438$	0	0
$439$	30.9337	1.47639	0.738193	−	0.674590i	$-0.235679\pi$
$439$	30.9337	1.47639	0.738193	+	0.674590i	$0.235679\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	25.0736	1.19128	0.595642	−	0.803250i	$-0.296898\pi$
$443$	25.0736	1.19128	0.595642	+	0.803250i	$0.296898\pi$
$444$	0	0
$445$	25.9120	1.22835
$446$	0	0
$447$	−9.75287	−0.461295
$448$	0	0
$449$	26.5576	1.25333	0.626665	−	0.779289i	$-0.284420\pi$
$449$	26.5576	1.25333	0.626665	+	0.779289i	$0.284420\pi$
$450$	0	0
$451$	32.8290	1.54586
$452$	0	0
$453$	0.302639	0.0142192
$454$	0	0
$455$	0	0
$456$	0	0
$457$	5.97324	0.279416	0.139708	−	0.990193i	$-0.455384\pi$
$457$	5.97324	0.279416	0.139708	+	0.990193i	$0.455384\pi$
$458$	0	0
$459$	−5.11842	−0.238907
$460$	0	0
$461$	−10.7132	−0.498961	−0.249481	−	0.968380i	$-0.580260\pi$
$461$	−10.7132	−0.498961	−0.249481	+	0.968380i	$0.580260\pi$
$462$	0	0
$463$	−38.5686	−1.79243	−0.896217	−	0.443616i	$-0.853695\pi$
$463$	−38.5686	−1.79243	−0.896217	+	0.443616i	$0.853695\pi$
$464$	0	0
$465$	−27.9362	−1.29551
$466$	0	0
$467$	21.8471	1.01096	0.505482	−	0.862837i	$-0.331315\pi$
$467$	21.8471	1.01096	0.505482	+	0.862837i	$0.331315\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	7.99288	0.368293
$472$	0	0
$473$	−48.8069	−2.24414
$474$	0	0
$475$	23.3933	1.07336
$476$	0	0
$477$	1.64578	0.0753551
$478$	0	0
$479$	40.1702	1.83542	0.917711	−	0.397248i	$-0.130035\pi$
$479$	40.1702	1.83542	0.917711	+	0.397248i	$0.130035\pi$
$480$	0	0
$481$	22.6234	1.03154
$482$	0	0
$483$	0	0
$484$	0	0
$485$	−8.96245	−0.406964
$486$	0	0
$487$	−33.8525	−1.53400	−0.767002	−	0.641645i	$-0.778252\pi$
$487$	−33.8525	−1.53400	−0.767002	+	0.641645i	$0.778252\pi$
$488$	0	0
$489$	18.7145	0.846301
$490$	0	0
$491$	30.6167	1.38171	0.690856	−	0.722992i	$-0.257234\pi$
$491$	30.6167	1.38171	0.690856	+	0.722992i	$0.257234\pi$
$492$	0	0
$493$	−0.144355	−0.00650143
$494$	0	0
$495$	7.55370	0.339514
$496$	0	0
$497$	0	0
$498$	0	0
$499$	4.58820	0.205396	0.102698	−	0.994713i	$-0.467252\pi$
$499$	4.58820	0.205396	0.102698	+	0.994713i	$0.467252\pi$
$500$	0	0
$501$	−36.1623	−1.61561
$502$	0	0
$503$	−24.4041	−1.08813	−0.544063	−	0.839044i	$-0.683115\pi$
$503$	−24.4041	−1.08813	−0.544063	+	0.839044i	$0.683115\pi$
$504$	0	0
$505$	25.6565	1.14170
$506$	0	0
$507$	26.9501	1.19690
$508$	0	0
$509$	−19.0047	−0.842367	−0.421184	−	0.906975i	$-0.638385\pi$
$509$	−19.0047	−0.842367	−0.421184	+	0.906975i	$0.638385\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	−42.4995	−1.87640
$514$	0	0
$515$	−48.4081	−2.13312
$516$	0	0
$517$	8.69911	0.382586
$518$	0	0
$519$	2.61356	0.114723
$520$	0	0
$521$	31.0560	1.36059	0.680293	−	0.732940i	$-0.261853\pi$
$521$	31.0560	1.36059	0.680293	+	0.732940i	$0.261853\pi$
$522$	0	0
$523$	35.6108	1.55715	0.778576	−	0.627551i	$-0.215942\pi$
$523$	35.6108	1.55715	0.778576	+	0.627551i	$0.215942\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	5.74405	0.250215
$528$	0	0
$529$	1.00000	0.0434783
$530$	0	0
$531$	0.0209164	0.000907694 0
$532$	0	0
$533$	−31.5863	−1.36815
$534$	0	0
$535$	35.9905	1.55601
$536$	0	0
$537$	35.1199	1.51553
$538$	0	0
$539$	0	0
$540$	0	0
$541$	1.53695	0.0660788	0.0330394	−	0.999454i	$-0.489481\pi$
$541$	1.53695	0.0660788	0.0330394	+	0.999454i	$0.489481\pi$
$542$	0	0
$543$	−6.13656	−0.263345
$544$	0	0
$545$	−14.1614	−0.606609
$546$	0	0
$547$	−26.7557	−1.14399	−0.571995	−	0.820257i	$-0.693830\pi$
$547$	−26.7557	−1.14399	−0.571995	+	0.820257i	$0.693830\pi$
$548$	0	0
$549$	−4.22544	−0.180337
$550$	0	0
$551$	−1.19862	−0.0510628
$552$	0	0
$553$	0	0
$554$	0	0
$555$	18.6507	0.791679
$556$	0	0
$557$	0.305154	0.0129298	0.00646490	−	0.999979i	$-0.497942\pi$
$557$	0.305154	0.0129298	0.00646490	+	0.999979i	$0.497942\pi$
$558$	0	0
$559$	46.9593	1.98617
$560$	0	0
$561$	8.39201	0.354311
$562$	0	0
$563$	−34.3537	−1.44784	−0.723918	−	0.689886i	$-0.757661\pi$
$563$	−34.3537	−1.44784	−0.723918	+	0.689886i	$0.757661\pi$
$564$	0	0
$565$	−36.5780	−1.53885
$566$	0	0
$567$	0	0
$568$	0	0
$569$	47.3530	1.98514	0.992571	−	0.121666i	$-0.0388236\pi$
$569$	47.3530	1.98514	0.992571	+	0.121666i	$0.0388236\pi$
$570$	0	0
$571$	8.15337	0.341208	0.170604	−	0.985340i	$-0.445428\pi$
$571$	8.15337	0.341208	0.170604	+	0.985340i	$0.445428\pi$
$572$	0	0
$573$	10.9163	0.456037
$574$	0	0
$575$	−3.03766	−0.126679
$576$	0	0
$577$	−6.74738	−0.280897	−0.140449	−	0.990088i	$-0.544854\pi$
$577$	−6.74738	−0.280897	−0.140449	+	0.990088i	$0.544854\pi$
$578$	0	0
$579$	10.8355	0.450308
$580$	0	0
$581$	0	0
$582$	0	0
$583$	−19.9767	−0.827351
$584$	0	0
$585$	−7.26776	−0.300485
$586$	0	0
$587$	−11.9654	−0.493863	−0.246932	−	0.969033i	$-0.579422\pi$
$587$	−11.9654	−0.493863	−0.246932	+	0.969033i	$0.579422\pi$
$588$	0	0
$589$	47.6943	1.96521
$590$	0	0
$591$	17.9420	0.738037
$592$	0	0
$593$	14.0872	0.578493	0.289247	−	0.957255i	$-0.406595\pi$
$593$	14.0872	0.578493	0.289247	+	0.957255i	$0.406595\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	37.3806	1.52988
$598$	0	0
$599$	−3.80253	−0.155367	−0.0776835	−	0.996978i	$-0.524752\pi$
$599$	−3.80253	−0.155367	−0.0776835	+	0.996978i	$0.524752\pi$
$600$	0	0
$601$	−15.3123	−0.624602	−0.312301	−	0.949983i	$-0.601100\pi$
$601$	−15.3123	−0.624602	−0.312301	+	0.949983i	$0.601100\pi$
$602$	0	0
$603$	6.38143	0.259872
$604$	0	0
$605$	−60.5021	−2.45976
$606$	0	0
$607$	14.8863	0.604217	0.302108	−	0.953274i	$-0.402310\pi$
$607$	14.8863	0.604217	0.302108	+	0.953274i	$0.402310\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	−8.36980	−0.338606
$612$	0	0
$613$	−28.3843	−1.14643	−0.573216	−	0.819404i	$-0.694304\pi$
$613$	−28.3843	−1.14643	−0.573216	+	0.819404i	$0.694304\pi$
$614$	0	0
$615$	−26.0398	−1.05002
$616$	0	0
$617$	28.3540	1.14149	0.570745	−	0.821127i	$-0.306654\pi$
$617$	28.3540	1.14149	0.570745	+	0.821127i	$0.306654\pi$
$618$	0	0
$619$	−49.1169	−1.97417	−0.987087	−	0.160184i	$-0.948791\pi$
$619$	−49.1169	−1.97417	−0.987087	+	0.160184i	$0.948791\pi$
$620$	0	0
$621$	5.51863	0.221455
$622$	0	0
$623$	0	0
$624$	0	0
$625$	−30.9609	−1.23844
$626$	0	0
$627$	69.6810	2.78279
$628$	0	0
$629$	−3.83484	−0.152905
$630$	0	0
$631$	6.85076	0.272725	0.136362	−	0.990659i	$-0.456459\pi$
$631$	6.85076	0.272725	0.136362	+	0.990659i	$0.456459\pi$
$632$	0	0
$633$	−4.32727	−0.171994
$634$	0	0
$635$	−39.1699	−1.55441
$636$	0	0
$637$	0	0
$638$	0	0
$639$	0.650022	0.0257145
$640$	0	0
$641$	−43.2455	−1.70809	−0.854046	−	0.520197i	$-0.825859\pi$
$641$	−43.2455	−1.70809	−0.854046	+	0.520197i	$0.825859\pi$
$642$	0	0
$643$	−5.48698	−0.216385	−0.108193	−	0.994130i	$-0.534506\pi$
$643$	−5.48698	−0.216385	−0.108193	+	0.994130i	$0.534506\pi$
$644$	0	0
$645$	38.7133	1.52433
$646$	0	0
$647$	−39.3140	−1.54559	−0.772796	−	0.634655i	$-0.781142\pi$
$647$	−39.3140	−1.54559	−0.772796	+	0.634655i	$0.781142\pi$
$648$	0	0
$649$	−0.253886	−0.00996591
$650$	0	0
$651$	0	0
$652$	0	0
$653$	−40.5433	−1.58658	−0.793290	−	0.608843i	$-0.791634\pi$
$653$	−40.5433	−1.58658	−0.793290	+	0.608843i	$0.791634\pi$
$654$	0	0
$655$	−31.3281	−1.22409
$656$	0	0
$657$	−6.53212	−0.254842
$658$	0	0
$659$	−14.3289	−0.558173	−0.279087	−	0.960266i	$-0.590032\pi$
$659$	−14.3289	−0.558173	−0.279087	+	0.960266i	$0.590032\pi$
$660$	0	0
$661$	21.8444	0.849649	0.424824	−	0.905276i	$-0.360336\pi$
$661$	21.8444	0.849649	0.424824	+	0.905276i	$0.360336\pi$
$662$	0	0
$663$	−8.07434	−0.313581
$664$	0	0
$665$	0	0
$666$	0	0
$667$	0.155642	0.00602650
$668$	0	0
$669$	28.3977	1.09792
$670$	0	0
$671$	51.2890	1.97999
$672$	0	0
$673$	38.3350	1.47770	0.738852	−	0.673867i	$-0.235368\pi$
$673$	38.3350	1.47770	0.738852	+	0.673867i	$0.235368\pi$
$674$	0	0
$675$	−16.7637	−0.645236
$676$	0	0
$677$	27.3871	1.05257	0.526286	−	0.850308i	$-0.323584\pi$
$677$	27.3871	1.05257	0.526286	+	0.850308i	$0.323584\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	21.7294	0.832673
$682$	0	0
$683$	−15.7233	−0.601634	−0.300817	−	0.953682i	$-0.597259\pi$
$683$	−15.7233	−0.601634	−0.300817	+	0.953682i	$0.597259\pi$
$684$	0	0
$685$	−4.81839	−0.184101
$686$	0	0
$687$	2.79513	0.106641
$688$	0	0
$689$	19.2205	0.732243
$690$	0	0
$691$	−18.2850	−0.695596	−0.347798	−	0.937570i	$-0.613070\pi$
$691$	−18.2850	−0.695596	−0.347798	+	0.937570i	$0.613070\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	−34.2472	−1.29907
$696$	0	0
$697$	5.35413	0.202802
$698$	0	0
$699$	41.2558	1.56044
$700$	0	0
$701$	35.9195	1.35666	0.678330	−	0.734757i	$-0.262704\pi$
$701$	35.9195	1.35666	0.678330	+	0.734757i	$0.262704\pi$
$702$	0	0
$703$	−31.8417	−1.20093
$704$	0	0
$705$	−6.90007	−0.259872
$706$	0	0
$707$	0	0
$708$	0	0
$709$	−30.7979	−1.15664	−0.578320	−	0.815810i	$-0.696291\pi$
$709$	−30.7979	−1.15664	−0.578320	+	0.815810i	$0.696291\pi$
$710$	0	0
$711$	4.45609	0.167116
$712$	0	0
$713$	−6.19318	−0.231936
$714$	0	0
$715$	88.2172	3.29913
$716$	0	0
$717$	−12.7476	−0.476069
$718$	0	0
$719$	1.05369	0.0392959	0.0196480	−	0.999807i	$-0.493745\pi$
$719$	1.05369	0.0392959	0.0196480	+	0.999807i	$0.493745\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	6.09512	0.226680
$724$	0	0
$725$	−0.472789	−0.0175589
$726$	0	0
$727$	50.0566	1.85650	0.928248	−	0.371961i	$-0.121315\pi$
$727$	50.0566	1.85650	0.928248	+	0.371961i	$0.121315\pi$
$728$	0	0
$729$	29.7967	1.10358
$730$	0	0
$731$	−7.95997	−0.294410
$732$	0	0
$733$	32.4632	1.19905	0.599527	−	0.800354i	$-0.295355\pi$
$733$	32.4632	1.19905	0.599527	+	0.800354i	$0.295355\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−77.4588	−2.85323
$738$	0	0
$739$	−14.1789	−0.521581	−0.260790	−	0.965395i	$-0.583983\pi$
$739$	−14.1789	−0.521581	−0.260790	+	0.965395i	$0.583983\pi$
$740$	0	0
$741$	−67.0433	−2.46290
$742$	0	0
$743$	29.4829	1.08162	0.540811	−	0.841144i	$-0.318117\pi$
$743$	29.4829	1.08162	0.540811	+	0.841144i	$0.318117\pi$
$744$	0	0
$745$	17.3784	0.636695
$746$	0	0
$747$	−3.88625	−0.142191
$748$	0	0
$749$	0	0
$750$	0	0
$751$	−35.3614	−1.29036	−0.645178	−	0.764032i	$-0.723217\pi$
$751$	−35.3614	−1.29036	−0.645178	+	0.764032i	$0.723217\pi$
$752$	0	0
$753$	−3.42918	−0.124966
$754$	0	0
$755$	−0.539265	−0.0196258
$756$	0	0
$757$	−15.9396	−0.579333	−0.289666	−	0.957128i	$-0.593544\pi$
$757$	−15.9396	−0.579333	−0.289666	+	0.957128i	$0.593544\pi$
$758$	0	0
$759$	−9.04819	−0.328428
$760$	0	0
$761$	−22.9947	−0.833558	−0.416779	−	0.909008i	$-0.636841\pi$
$761$	−22.9947	−0.833558	−0.416779	+	0.909008i	$0.636841\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	1.23194	0.0445410
$766$	0	0
$767$	0.244275	0.00882027
$768$	0	0
$769$	28.7874	1.03810	0.519050	−	0.854744i	$-0.326286\pi$
$769$	28.7874	1.03810	0.519050	+	0.854744i	$0.326286\pi$
$770$	0	0
$771$	−5.89261	−0.212217
$772$	0	0
$773$	20.6826	0.743901	0.371951	−	0.928253i	$-0.378689\pi$
$773$	20.6826	0.743901	0.371951	+	0.928253i	$0.378689\pi$
$774$	0	0
$775$	18.8128	0.675775
$776$	0	0
$777$	0	0
$778$	0	0
$779$	44.4567	1.59283
$780$	0	0
$781$	−7.89006	−0.282329
$782$	0	0
$783$	0.858933	0.0306957
$784$	0	0
$785$	−14.2423	−0.508330
$786$	0	0
$787$	−41.1515	−1.46689	−0.733446	−	0.679748i	$-0.762089\pi$
$787$	−41.1515	−1.46689	−0.733446	+	0.679748i	$0.762089\pi$
$788$	0	0
$789$	−11.6985	−0.416477
$790$	0	0
$791$	0	0
$792$	0	0
$793$	−49.3475	−1.75238
$794$	0	0
$795$	15.8454	0.561979
$796$	0	0
$797$	−42.6780	−1.51173	−0.755865	−	0.654727i	$-0.772784\pi$
$797$	−42.6780	−1.51173	−0.755865	+	0.654727i	$0.772784\pi$
$798$	0	0
$799$	1.41875	0.0501917
$800$	0	0
$801$	4.28210	0.151301
$802$	0	0
$803$	79.2878	2.79801
$804$	0	0
$805$	0	0
$806$	0	0
$807$	22.9502	0.807885
$808$	0	0
$809$	4.11666	0.144734	0.0723671	−	0.997378i	$-0.476945\pi$
$809$	4.11666	0.144734	0.0723671	+	0.997378i	$0.476945\pi$
$810$	0	0
$811$	−36.1729	−1.27020	−0.635102	−	0.772428i	$-0.719042\pi$
$811$	−36.1729	−1.27020	−0.635102	+	0.772428i	$0.719042\pi$
$812$	0	0
$813$	−33.5876	−1.17797
$814$	0	0
$815$	−33.3469	−1.16809
$816$	0	0
$817$	−66.0937	−2.31233
$818$	0	0
$819$	0	0
$820$	0	0
$821$	36.8245	1.28518	0.642591	−	0.766209i	$-0.277859\pi$
$821$	36.8245	1.28518	0.642591	+	0.766209i	$0.277859\pi$
$822$	0	0
$823$	−47.0251	−1.63919	−0.819595	−	0.572943i	$-0.805802\pi$
$823$	−47.0251	−1.63919	−0.819595	+	0.572943i	$0.805802\pi$
$824$	0	0
$825$	27.4853	0.956917
$826$	0	0
$827$	−54.1850	−1.88420	−0.942098	−	0.335337i	$-0.891150\pi$
$827$	−54.1850	−1.88420	−0.942098	+	0.335337i	$0.891150\pi$
$828$	0	0
$829$	−24.7420	−0.859326	−0.429663	−	0.902989i	$-0.641368\pi$
$829$	−24.7420	−0.859326	−0.429663	+	0.902989i	$0.641368\pi$
$830$	0	0
$831$	14.6885	0.509539
$832$	0	0
$833$	0	0
$834$	0	0
$835$	64.4366	2.22992
$836$	0	0
$837$	−34.1779	−1.18136
$838$	0	0
$839$	32.6449	1.12703	0.563514	−	0.826107i	$-0.309449\pi$
$839$	32.6449	1.12703	0.563514	+	0.826107i	$0.309449\pi$
$840$	0	0
$841$	−28.9758	−0.999165
$842$	0	0
$843$	8.80644	0.303310
$844$	0	0
$845$	−48.0217	−1.65200
$846$	0	0
$847$	0	0
$848$	0	0
$849$	14.1475	0.485541
$850$	0	0
$851$	4.13469	0.141735
$852$	0	0
$853$	−20.7319	−0.709847	−0.354923	−	0.934895i	$-0.615493\pi$
$853$	−20.7319	−0.709847	−0.354923	+	0.934895i	$0.615493\pi$
$854$	0	0
$855$	10.2291	0.349829
$856$	0	0
$857$	14.5163	0.495867	0.247934	−	0.968777i	$-0.420248\pi$
$857$	14.5163	0.495867	0.247934	+	0.968777i	$0.420248\pi$
$858$	0	0
$859$	−4.61394	−0.157426	−0.0787128	−	0.996897i	$-0.525081\pi$
$859$	−4.61394	−0.157426	−0.0787128	+	0.996897i	$0.525081\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	16.7672	0.570761	0.285380	−	0.958414i	$-0.407880\pi$
$863$	16.7672	0.570761	0.285380	+	0.958414i	$0.407880\pi$
$864$	0	0
$865$	−4.65704	−0.158344
$866$	0	0
$867$	−25.6794	−0.872119
$868$	0	0
$869$	−54.0887	−1.83483
$870$	0	0
$871$	74.5266	2.52524
$872$	0	0
$873$	−1.48110	−0.0501275
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−6.26696	−0.211620	−0.105810	−	0.994386i	$-0.533744\pi$
$877$	−6.26696	−0.211620	−0.105810	+	0.994386i	$0.533744\pi$
$878$	0	0
$879$	35.5411	1.19877
$880$	0	0
$881$	40.4770	1.36370	0.681852	−	0.731490i	$-0.261175\pi$
$881$	40.4770	1.36370	0.681852	+	0.731490i	$0.261175\pi$
$882$	0	0
$883$	−16.3919	−0.551632	−0.275816	−	0.961210i	$-0.588948\pi$
$883$	−16.3919	−0.551632	−0.275816	+	0.961210i	$0.588948\pi$
$884$	0	0
$885$	0.201381	0.00676934
$886$	0	0
$887$	−14.7063	−0.493788	−0.246894	−	0.969043i	$-0.579410\pi$
$887$	−14.7063	−0.493788	−0.246894	+	0.969043i	$0.579410\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	−41.9405	−1.40506
$892$	0	0
$893$	11.7802	0.394210
$894$	0	0
$895$	−62.5792	−2.09179
$896$	0	0
$897$	8.70567	0.290674
$898$	0	0
$899$	−0.963922	−0.0321486
$900$	0	0
$901$	−3.25803	−0.108541
$902$	0	0
$903$	0	0
$904$	0	0
$905$	10.9346	0.363478
$906$	0	0
$907$	18.7404	0.622263	0.311132	−	0.950367i	$-0.399292\pi$
$907$	18.7404	0.622263	0.311132	+	0.950367i	$0.399292\pi$
$908$	0	0
$909$	4.23988	0.140628
$910$	0	0
$911$	−0.806797	−0.0267304	−0.0133652	−	0.999911i	$-0.504254\pi$
$911$	−0.806797	−0.0267304	−0.0133652	+	0.999911i	$0.504254\pi$
$912$	0	0
$913$	47.1719	1.56116
$914$	0	0
$915$	−40.6821	−1.34491
$916$	0	0
$917$	0	0
$918$	0	0
$919$	38.8606	1.28189	0.640946	−	0.767586i	$-0.278542\pi$
$919$	38.8606	1.28189	0.640946	+	0.767586i	$0.278542\pi$
$920$	0	0
$921$	−38.9026	−1.28189
$922$	0	0
$923$	7.59138	0.249873
$924$	0	0
$925$	−12.5598	−0.412963
$926$	0	0
$927$	−7.99971	−0.262745
$928$	0	0
$929$	1.72990	0.0567562	0.0283781	−	0.999597i	$-0.490966\pi$
$929$	1.72990	0.0567562	0.0283781	+	0.999597i	$0.490966\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	−28.3678	−0.928719
$934$	0	0
$935$	−14.9535	−0.489032
$936$	0	0
$937$	−16.5789	−0.541610	−0.270805	−	0.962634i	$-0.587290\pi$
$937$	−16.5789	−0.541610	−0.270805	+	0.962634i	$0.587290\pi$
$938$	0	0
$939$	−30.2725	−0.987904
$940$	0	0
$941$	32.9020	1.07257	0.536287	−	0.844036i	$-0.319826\pi$
$941$	32.9020	1.07257	0.536287	+	0.844036i	$0.319826\pi$
$942$	0	0
$943$	−5.77277	−0.187987
$944$	0	0
$945$	0	0
$946$	0	0
$947$	−30.7189	−0.998230	−0.499115	−	0.866536i	$-0.666341\pi$
$947$	−30.7189	−0.998230	−0.499115	+	0.866536i	$0.666341\pi$
$948$	0	0
$949$	−76.2864	−2.47636
$950$	0	0
$951$	39.6844	1.28686
$952$	0	0
$953$	−38.6042	−1.25051	−0.625256	−	0.780420i	$-0.715006\pi$
$953$	−38.6042	−1.25051	−0.625256	+	0.780420i	$0.715006\pi$
$954$	0	0
$955$	−19.4515	−0.629437
$956$	0	0
$957$	−1.40828	−0.0455233
$958$	0	0
$959$	0	0
$960$	0	0
$961$	7.35550	0.237274
$962$	0	0
$963$	5.94764	0.191660
$964$	0	0
$965$	−19.3075	−0.621530
$966$	0	0
$967$	54.3349	1.74729	0.873646	−	0.486563i	$-0.161750\pi$
$967$	54.3349	1.74729	0.873646	+	0.486563i	$0.161750\pi$
$968$	0	0
$969$	11.3644	0.365076
$970$	0	0
$971$	−12.0981	−0.388247	−0.194123	−	0.980977i	$-0.562186\pi$
$971$	−12.0981	−0.388247	−0.194123	+	0.980977i	$0.562186\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	−26.4449	−0.846914
$976$	0	0
$977$	15.4277	0.493574	0.246787	−	0.969070i	$-0.420625\pi$
$977$	15.4277	0.493574	0.246787	+	0.969070i	$0.420625\pi$
$978$	0	0
$979$	−51.9768	−1.66119
$980$	0	0
$981$	−2.34025	−0.0747186
$982$	0	0
$983$	−2.00301	−0.0638862	−0.0319431	−	0.999490i	$-0.510170\pi$
$983$	−2.00301	−0.0638862	−0.0319431	+	0.999490i	$0.510170\pi$
$984$	0	0
$985$	−31.9704	−1.01866
$986$	0	0
$987$	0	0
$988$	0	0
$989$	8.58237	0.272903
$990$	0	0
$991$	−38.4943	−1.22281	−0.611406	−	0.791317i	$-0.709396\pi$
$991$	−38.4943	−1.22281	−0.611406	+	0.791317i	$0.709396\pi$
$992$	0	0
$993$	34.0968	1.08203
$994$	0	0
$995$	−66.6075	−2.11160
$996$	0	0
$997$	−28.0730	−0.889081	−0.444541	−	0.895759i	$-0.646633\pi$
$997$	−28.0730	−0.889081	−0.444541	+	0.895759i	$0.646633\pi$
$998$	0	0
$999$	22.8178	0.721924

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9016.2.a.br.1.7		11
7.3	odd	6		1288.2.q.d.737.7	✓	22
7.5	odd	6		1288.2.q.d.921.7	yes	22
7.6	odd	2		9016.2.a.bk.1.5		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1288.2.q.d.737.7	✓	22	7.3	odd	6
1288.2.q.d.921.7	yes	22	7.5	odd	6
9016.2.a.bk.1.5		11	7.6	odd	2
9016.2.a.br.1.7		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)

\(f(q)\)	\(=\)	\(q+1.59106 q^{3} -2.83508 q^{5} -0.468513 q^{9} +O(q^{10})\)	\(q+1.59106 q^{3} -2.83508 q^{5} -0.468513 q^{9} +5.68688 q^{11} -5.47160 q^{13} -4.51079 q^{15} +0.927480 q^{17} +7.70110 q^{19} -1.00000 q^{23} +3.03766 q^{25} -5.51863 q^{27} -0.155642 q^{29} +6.19318 q^{31} +9.04819 q^{33} -4.13469 q^{37} -8.70567 q^{39} +5.77277 q^{41} -8.58237 q^{43} +1.32827 q^{45} +1.52968 q^{47} +1.47568 q^{51} -3.51278 q^{53} -16.1227 q^{55} +12.2530 q^{57} -0.0446442 q^{59} +9.01884 q^{61} +15.5124 q^{65} -13.6206 q^{67} -1.59106 q^{69} -1.38742 q^{71} +13.9422 q^{73} +4.83312 q^{75} -9.51114 q^{79} -7.37496 q^{81} +8.29488 q^{83} -2.62948 q^{85} -0.247637 q^{87} -9.13979 q^{89} +9.85375 q^{93} -21.8332 q^{95} +3.16127 q^{97} -2.66437 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 4 q^{3} + 3 q^{5} + 11 q^{9}+O(q^{10}) \) 11 * q + 4 * q^3 + 3 * q^5 + 11 * q^9	\( 11 q + 4 q^{3} + 3 q^{5} + 11 q^{9} - 13 q^{13} + 7 q^{17} + 8 q^{19} - 11 q^{23} + 6 q^{25} + 25 q^{27} - 3 q^{29} + 12 q^{31} - 2 q^{33} - q^{37} - 21 q^{39} + 12 q^{41} + 9 q^{43} + 19 q^{45} + 17 q^{47} + 19 q^{51} - 5 q^{53} + 21 q^{55} + 11 q^{57} + 33 q^{59} - 15 q^{61} - 9 q^{65} - 5 q^{67} - 4 q^{69} - 9 q^{71} + 5 q^{73} + 44 q^{75} + 11 q^{79} - 13 q^{81} + 51 q^{83} + 33 q^{85} + 4 q^{87} + 26 q^{89} + 6 q^{93} - 19 q^{95} + 21 q^{97} + 15 q^{99}+O(q^{100}) \) 11 * q + 4 * q^3 + 3 * q^5 + 11 * q^9 - 13 * q^13 + 7 * q^17 + 8 * q^19 - 11 * q^23 + 6 * q^25 + 25 * q^27 - 3 * q^29 + 12 * q^31 - 2 * q^33 - q^37 - 21 * q^39 + 12 * q^41 + 9 * q^43 + 19 * q^45 + 17 * q^47 + 19 * q^51 - 5 * q^53 + 21 * q^55 + 11 * q^57 + 33 * q^59 - 15 * q^61 - 9 * q^65 - 5 * q^67 - 4 * q^69 - 9 * q^71 + 5 * q^73 + 44 * q^75 + 11 * q^79 - 13 * q^81 + 51 * q^83 + 33 * q^85 + 4 * q^87 + 26 * q^89 + 6 * q^93 - 19 * q^95 + 21 * q^97 + 15 * q^99

Introduction

L-functions

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