LMFDB - Embedded newform 9016.2.a.bo.1.9

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			1.9
Root			$1.66463$ 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)

$f(q)$	$=$	$q+1.66463 q^{3} -0.919906 q^{5} -0.229023 q^{9} +O(q^{10})$	$q+1.66463 q^{3} -0.919906 q^{5} -0.229023 q^{9} -3.45253 q^{11} +6.19741 q^{13} -1.53130 q^{15} +3.12889 q^{17} -3.03139 q^{19} -1.00000 q^{23} -4.15377 q^{25} -5.37511 q^{27} -1.77678 q^{29} +6.66624 q^{31} -5.74716 q^{33} -3.93255 q^{37} +10.3164 q^{39} -2.20337 q^{41} -7.45869 q^{43} +0.210680 q^{45} +7.81898 q^{47} +5.20843 q^{51} -2.52810 q^{53} +3.17600 q^{55} -5.04613 q^{57} -0.778173 q^{59} -11.2801 q^{61} -5.70103 q^{65} -0.0459864 q^{67} -1.66463 q^{69} -4.20473 q^{71} +8.68118 q^{73} -6.91447 q^{75} +2.05132 q^{79} -8.26048 q^{81} +12.3994 q^{83} -2.87828 q^{85} -2.95768 q^{87} -12.7320 q^{89} +11.0968 q^{93} +2.78860 q^{95} -13.0618 q^{97} +0.790708 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	1.66463	0.961072	0.480536	−	0.876975i	$-0.340442\pi$
$3$	1.66463	0.961072	0.480536	+	0.876975i	$0.340442\pi$
$4$	0	0
$5$	−0.919906	−0.411394	−0.205697	−	0.978616i	$-0.565946\pi$
$5$	−0.919906	−0.411394	−0.205697	+	0.978616i	$0.565946\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	0	0
$9$	−0.229023	−0.0763411
$10$	0	0
$11$	−3.45253	−1.04098	−0.520488	−	0.853869i	$-0.674250\pi$
$11$	−3.45253	−1.04098	−0.520488	+	0.853869i	$0.674250\pi$
$12$	0	0
$13$	6.19741	1.71885	0.859426	−	0.511261i	$-0.170821\pi$
$13$	6.19741	1.71885	0.859426	+	0.511261i	$0.170821\pi$
$14$	0	0
$15$	−1.53130	−0.395380
$16$	0	0
$17$	3.12889	0.758867	0.379433	−	0.925219i	$-0.376119\pi$
$17$	3.12889	0.758867	0.379433	+	0.925219i	$0.376119\pi$
$18$	0	0
$19$	−3.03139	−0.695449	−0.347725	−	0.937597i	$-0.613046\pi$
$19$	−3.03139	−0.695449	−0.347725	+	0.937597i	$0.613046\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	0	0
$25$	−4.15377	−0.830755
$26$	0	0
$27$	−5.37511	−1.03444
$28$	0	0
$29$	−1.77678	−0.329940	−0.164970	−	0.986299i	$-0.552753\pi$
$29$	−1.77678	−0.329940	−0.164970	+	0.986299i	$0.552753\pi$
$30$	0	0
$31$	6.66624	1.19729	0.598646	−	0.801014i	$-0.295706\pi$
$31$	6.66624	1.19729	0.598646	+	0.801014i	$0.295706\pi$
$32$	0	0
$33$	−5.74716	−1.00045
$34$	0	0
$35$	0	0
$36$	0	0
$37$	−3.93255	−0.646508	−0.323254	−	0.946312i	$-0.604777\pi$
$37$	−3.93255	−0.646508	−0.323254	+	0.946312i	$0.604777\pi$
$38$	0	0
$39$	10.3164	1.65194
$40$	0	0
$41$	−2.20337	−0.344108	−0.172054	−	0.985087i	$-0.555040\pi$
$41$	−2.20337	−0.344108	−0.172054	+	0.985087i	$0.555040\pi$
$42$	0	0
$43$	−7.45869	−1.13744	−0.568719	−	0.822532i	$-0.692561\pi$
$43$	−7.45869	−1.13744	−0.568719	+	0.822532i	$0.692561\pi$
$44$	0	0
$45$	0.210680	0.0314063
$46$	0	0
$47$	7.81898	1.14052	0.570258	−	0.821466i	$-0.306843\pi$
$47$	7.81898	1.14052	0.570258	+	0.821466i	$0.306843\pi$
$48$	0	0
$49$	0	0
$50$	0	0
$51$	5.20843	0.729325
$52$	0	0
$53$	−2.52810	−0.347262	−0.173631	−	0.984811i	$-0.555550\pi$
$53$	−2.52810	−0.347262	−0.173631	+	0.984811i	$0.555550\pi$
$54$	0	0
$55$	3.17600	0.428252
$56$	0	0
$57$	−5.04613	−0.668376
$58$	0	0
$59$	−0.778173	−0.101310	−0.0506548	−	0.998716i	$-0.516131\pi$
$59$	−0.778173	−0.101310	−0.0506548	+	0.998716i	$0.516131\pi$
$60$	0	0
$61$	−11.2801	−1.44427	−0.722137	−	0.691751i	$-0.756840\pi$
$61$	−11.2801	−1.44427	−0.722137	+	0.691751i	$0.756840\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	−5.70103	−0.707126
$66$	0	0
$67$	−0.0459864	−0.00561813	−0.00280906	−	0.999996i	$-0.500894\pi$
$67$	−0.0459864	−0.00561813	−0.00280906	+	0.999996i	$0.500894\pi$
$68$	0	0
$69$	−1.66463	−0.200397
$70$	0	0
$71$	−4.20473	−0.499009	−0.249505	−	0.968374i	$-0.580268\pi$
$71$	−4.20473	−0.499009	−0.249505	+	0.968374i	$0.580268\pi$
$72$	0	0
$73$	8.68118	1.01606	0.508028	−	0.861341i	$-0.330375\pi$
$73$	8.68118	1.01606	0.508028	+	0.861341i	$0.330375\pi$
$74$	0	0
$75$	−6.91447	−0.798415
$76$	0	0
$77$	0	0
$78$	0	0
$79$	2.05132	0.230791	0.115396	−	0.993320i	$-0.463186\pi$
$79$	2.05132	0.230791	0.115396	+	0.993320i	$0.463186\pi$
$80$	0	0
$81$	−8.26048	−0.917831
$82$	0	0
$83$	12.3994	1.36101	0.680504	−	0.732744i	$-0.261761\pi$
$83$	12.3994	1.36101	0.680504	+	0.732744i	$0.261761\pi$
$84$	0	0
$85$	−2.87828	−0.312194
$86$	0	0
$87$	−2.95768	−0.317096
$88$	0	0
$89$	−12.7320	−1.34959	−0.674794	−	0.738006i	$-0.735768\pi$
$89$	−12.7320	−1.34959	−0.674794	+	0.738006i	$0.735768\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	11.0968	1.15068
$94$	0	0
$95$	2.78860	0.286104
$96$	0	0
$97$	−13.0618	−1.32622	−0.663110	−	0.748522i	$-0.730764\pi$
$97$	−13.0618	−1.32622	−0.663110	+	0.748522i	$0.730764\pi$
$98$	0	0
$99$	0.790708	0.0794692
$100$	0	0
$101$	−16.0233	−1.59438	−0.797189	−	0.603730i	$-0.793681\pi$
$101$	−16.0233	−1.59438	−0.797189	+	0.603730i	$0.793681\pi$
$102$	0	0
$103$	3.26543	0.321753	0.160876	−	0.986975i	$-0.448568\pi$
$103$	3.26543	0.321753	0.160876	+	0.986975i	$0.448568\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	−16.7942	−1.62356	−0.811779	−	0.583964i	$-0.801501\pi$
$107$	−16.7942	−1.62356	−0.811779	+	0.583964i	$0.801501\pi$
$108$	0	0
$109$	−0.857194	−0.0821043	−0.0410522	−	0.999157i	$-0.513071\pi$
$109$	−0.857194	−0.0821043	−0.0410522	+	0.999157i	$0.513071\pi$
$110$	0	0
$111$	−6.54623	−0.621341
$112$	0	0
$113$	5.21625	0.490704	0.245352	−	0.969434i	$-0.421096\pi$
$113$	5.21625	0.490704	0.245352	+	0.969434i	$0.421096\pi$
$114$	0	0
$115$	0.919906	0.0857817
$116$	0	0
$117$	−1.41935	−0.131219
$118$	0	0
$119$	0	0
$120$	0	0
$121$	0.919932	0.0836301
$122$	0	0
$123$	−3.66778	−0.330713
$124$	0	0
$125$	8.42061	0.753162
$126$	0	0
$127$	8.65614	0.768108	0.384054	−	0.923311i	$-0.374528\pi$
$127$	8.65614	0.768108	0.384054	+	0.923311i	$0.374528\pi$
$128$	0	0
$129$	−12.4159	−1.09316
$130$	0	0
$131$	0.144460	0.0126216	0.00631078	−	0.999980i	$-0.497991\pi$
$131$	0.144460	0.0126216	0.00631078	+	0.999980i	$0.497991\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	4.94460	0.425563
$136$	0	0
$137$	7.98952	0.682591	0.341296	−	0.939956i	$-0.389134\pi$
$137$	7.98952	0.682591	0.341296	+	0.939956i	$0.389134\pi$
$138$	0	0
$139$	0.126678	0.0107447	0.00537236	−	0.999986i	$-0.498290\pi$
$139$	0.126678	0.0107447	0.00537236	+	0.999986i	$0.498290\pi$
$140$	0	0
$141$	13.0157	1.09612
$142$	0	0
$143$	−21.3967	−1.78928
$144$	0	0
$145$	1.63447	0.135736
$146$	0	0
$147$	0	0
$148$	0	0
$149$	−10.4999	−0.860187	−0.430094	−	0.902784i	$-0.641519\pi$
$149$	−10.4999	−0.860187	−0.430094	+	0.902784i	$0.641519\pi$
$150$	0	0
$151$	15.4769	1.25949	0.629747	−	0.776800i	$-0.283158\pi$
$151$	15.4769	1.25949	0.629747	+	0.776800i	$0.283158\pi$
$152$	0	0
$153$	−0.716588	−0.0579327
$154$	0	0
$155$	−6.13231	−0.492559
$156$	0	0
$157$	−0.976787	−0.0779561	−0.0389780	−	0.999240i	$-0.512410\pi$
$157$	−0.976787	−0.0779561	−0.0389780	+	0.999240i	$0.512410\pi$
$158$	0	0
$159$	−4.20834	−0.333743
$160$	0	0
$161$	0	0
$162$	0	0
$163$	−20.4705	−1.60338	−0.801688	−	0.597742i	$-0.796065\pi$
$163$	−20.4705	−1.60338	−0.801688	+	0.597742i	$0.796065\pi$
$164$	0	0
$165$	5.28685	0.411580
$166$	0	0
$167$	15.5940	1.20670	0.603349	−	0.797477i	$-0.293833\pi$
$167$	15.5940	1.20670	0.603349	+	0.797477i	$0.293833\pi$
$168$	0	0
$169$	25.4079	1.95445
$170$	0	0
$171$	0.694259	0.0530913
$172$	0	0
$173$	−5.04516	−0.383576	−0.191788	−	0.981436i	$-0.561429\pi$
$173$	−5.04516	−0.383576	−0.191788	+	0.981436i	$0.561429\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	−1.29537	−0.0973657
$178$	0	0
$179$	6.26923	0.468584	0.234292	−	0.972166i	$-0.424723\pi$
$179$	6.26923	0.468584	0.234292	+	0.972166i	$0.424723\pi$
$180$	0	0
$181$	−22.6103	−1.68061	−0.840303	−	0.542116i	$-0.817623\pi$
$181$	−22.6103	−1.68061	−0.840303	+	0.542116i	$0.817623\pi$
$182$	0	0
$183$	−18.7772	−1.38805
$184$	0	0
$185$	3.61758	0.265970
$186$	0	0
$187$	−10.8026	−0.789962
$188$	0	0
$189$	0	0
$190$	0	0
$191$	−11.1085	−0.803780	−0.401890	−	0.915688i	$-0.631647\pi$
$191$	−11.1085	−0.803780	−0.401890	+	0.915688i	$0.631647\pi$
$192$	0	0
$193$	−11.8720	−0.854565	−0.427282	−	0.904118i	$-0.640529\pi$
$193$	−11.8720	−0.854565	−0.427282	+	0.904118i	$0.640529\pi$
$194$	0	0
$195$	−9.49008	−0.679599
$196$	0	0
$197$	18.9226	1.34818	0.674090	−	0.738649i	$-0.264536\pi$
$197$	18.9226	1.34818	0.674090	+	0.738649i	$0.264536\pi$
$198$	0	0
$199$	8.96913	0.635805	0.317902	−	0.948123i	$-0.397022\pi$
$199$	8.96913	0.635805	0.317902	+	0.948123i	$0.397022\pi$
$200$	0	0
$201$	−0.0765501	−0.00539943
$202$	0	0
$203$	0	0
$204$	0	0
$205$	2.02689	0.141564
$206$	0	0
$207$	0.229023	0.0159182
$208$	0	0
$209$	10.4660	0.723946
$210$	0	0
$211$	−9.40798	−0.647672	−0.323836	−	0.946113i	$-0.604973\pi$
$211$	−9.40798	−0.647672	−0.323836	+	0.946113i	$0.604973\pi$
$212$	0	0
$213$	−6.99930	−0.479584
$214$	0	0
$215$	6.86129	0.467936
$216$	0	0
$217$	0	0
$218$	0	0
$219$	14.4509	0.976502
$220$	0	0
$221$	19.3910	1.30438
$222$	0	0
$223$	−17.7025	−1.18545	−0.592724	−	0.805406i	$-0.701947\pi$
$223$	−17.7025	−1.18545	−0.592724	+	0.805406i	$0.701947\pi$
$224$	0	0
$225$	0.951310	0.0634207
$226$	0	0
$227$	−10.7356	−0.712544	−0.356272	−	0.934382i	$-0.615952\pi$
$227$	−10.7356	−0.712544	−0.356272	+	0.934382i	$0.615952\pi$
$228$	0	0
$229$	5.03782	0.332909	0.166454	−	0.986049i	$-0.446768\pi$
$229$	5.03782	0.332909	0.166454	+	0.986049i	$0.446768\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	−13.5859	−0.890042	−0.445021	−	0.895520i	$-0.646804\pi$
$233$	−13.5859	−0.890042	−0.445021	+	0.895520i	$0.646804\pi$
$234$	0	0
$235$	−7.19272	−0.469202
$236$	0	0
$237$	3.41467	0.221807
$238$	0	0
$239$	−18.5960	−1.20287	−0.601437	−	0.798920i	$-0.705405\pi$
$239$	−18.5960	−1.20287	−0.601437	+	0.798920i	$0.705405\pi$
$240$	0	0
$241$	5.10880	0.329087	0.164543	−	0.986370i	$-0.447385\pi$
$241$	5.10880	0.329087	0.164543	+	0.986370i	$0.447385\pi$
$242$	0	0
$243$	2.37474	0.152340
$244$	0	0
$245$	0	0
$246$	0	0
$247$	−18.7868	−1.19537
$248$	0	0
$249$	20.6403	1.30803
$250$	0	0
$251$	−1.94799	−0.122956	−0.0614779	−	0.998108i	$-0.519581\pi$
$251$	−1.94799	−0.122956	−0.0614779	+	0.998108i	$0.519581\pi$
$252$	0	0
$253$	3.45253	0.217058
$254$	0	0
$255$	−4.79126	−0.300040
$256$	0	0
$257$	−28.7889	−1.79580	−0.897902	−	0.440196i	$-0.854909\pi$
$257$	−28.7889	−1.79580	−0.897902	+	0.440196i	$0.854909\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	0.406924	0.0251880
$262$	0	0
$263$	−22.5899	−1.39295	−0.696477	−	0.717579i	$-0.745250\pi$
$263$	−22.5899	−1.39295	−0.696477	+	0.717579i	$0.745250\pi$
$264$	0	0
$265$	2.32562	0.142862
$266$	0	0
$267$	−21.1940	−1.29705
$268$	0	0
$269$	−9.86411	−0.601426	−0.300713	−	0.953715i	$-0.597225\pi$
$269$	−9.86411	−0.601426	−0.300713	+	0.953715i	$0.597225\pi$
$270$	0	0
$271$	24.7923	1.50602	0.753012	−	0.658007i	$-0.228600\pi$
$271$	24.7923	1.50602	0.753012	+	0.658007i	$0.228600\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	14.3410	0.864795
$276$	0	0
$277$	22.5133	1.35269	0.676347	−	0.736583i	$-0.263562\pi$
$277$	22.5133	1.35269	0.676347	+	0.736583i	$0.263562\pi$
$278$	0	0
$279$	−1.52672	−0.0914025
$280$	0	0
$281$	1.01020	0.0602635	0.0301317	−	0.999546i	$-0.490407\pi$
$281$	1.01020	0.0602635	0.0301317	+	0.999546i	$0.490407\pi$
$282$	0	0
$283$	1.53324	0.0911419	0.0455709	−	0.998961i	$-0.485489\pi$
$283$	1.53324	0.0911419	0.0455709	+	0.998961i	$0.485489\pi$
$284$	0	0
$285$	4.64197	0.274966
$286$	0	0
$287$	0	0
$288$	0	0
$289$	−7.21006	−0.424121
$290$	0	0
$291$	−21.7429	−1.27459
$292$	0	0
$293$	−25.1317	−1.46821	−0.734105	−	0.679036i	$-0.762398\pi$
$293$	−25.1317	−1.46821	−0.734105	+	0.679036i	$0.762398\pi$
$294$	0	0
$295$	0.715846	0.0416782
$296$	0	0
$297$	18.5577	1.07683
$298$	0	0
$299$	−6.19741	−0.358405
$300$	0	0
$301$	0	0
$302$	0	0
$303$	−26.6728	−1.53231
$304$	0	0
$305$	10.3767	0.594166
$306$	0	0
$307$	−29.2429	−1.66898	−0.834491	−	0.551021i	$-0.814238\pi$
$307$	−29.2429	−1.66898	−0.834491	+	0.551021i	$0.814238\pi$
$308$	0	0
$309$	5.43572	0.309227
$310$	0	0
$311$	−26.2498	−1.48849	−0.744244	−	0.667908i	$-0.767190\pi$
$311$	−26.2498	−1.48849	−0.744244	+	0.667908i	$0.767190\pi$
$312$	0	0
$313$	5.33619	0.301619	0.150810	−	0.988563i	$-0.451812\pi$
$313$	5.33619	0.301619	0.150810	+	0.988563i	$0.451812\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	−20.4284	−1.14737	−0.573686	−	0.819075i	$-0.694487\pi$
$317$	−20.4284	−1.14737	−0.573686	+	0.819075i	$0.694487\pi$
$318$	0	0
$319$	6.13439	0.343460
$320$	0	0
$321$	−27.9561	−1.56036
$322$	0	0
$323$	−9.48489	−0.527753
$324$	0	0
$325$	−25.7426	−1.42794
$326$	0	0
$327$	−1.42691	−0.0789082
$328$	0	0
$329$	0	0
$330$	0	0
$331$	11.4610	0.629953	0.314976	−	0.949100i	$-0.398003\pi$
$331$	11.4610	0.629953	0.314976	+	0.949100i	$0.398003\pi$
$332$	0	0
$333$	0.900646	0.0493551
$334$	0	0
$335$	0.0423031	0.00231127
$336$	0	0
$337$	−22.6485	−1.23374	−0.616870	−	0.787065i	$-0.711600\pi$
$337$	−22.6485	−1.23374	−0.616870	+	0.787065i	$0.711600\pi$
$338$	0	0
$339$	8.68311	0.471602
$340$	0	0
$341$	−23.0153	−1.24635
$342$	0	0
$343$	0	0
$344$	0	0
$345$	1.53130	0.0824423
$346$	0	0
$347$	−3.98045	−0.213682	−0.106841	−	0.994276i	$-0.534074\pi$
$347$	−3.98045	−0.213682	−0.106841	+	0.994276i	$0.534074\pi$
$348$	0	0
$349$	32.5779	1.74385	0.871927	−	0.489636i	$-0.162870\pi$
$349$	32.5779	1.74385	0.871927	+	0.489636i	$0.162870\pi$
$350$	0	0
$351$	−33.3118	−1.77805
$352$	0	0
$353$	24.2415	1.29025	0.645123	−	0.764079i	$-0.276806\pi$
$353$	24.2415	1.29025	0.645123	+	0.764079i	$0.276806\pi$
$354$	0	0
$355$	3.86795	0.205290
$356$	0	0
$357$	0	0
$358$	0	0
$359$	−36.9205	−1.94859	−0.974296	−	0.225273i	$-0.927673\pi$
$359$	−36.9205	−1.94859	−0.974296	+	0.225273i	$0.927673\pi$
$360$	0	0
$361$	−9.81066	−0.516351
$362$	0	0
$363$	1.53134	0.0803746
$364$	0	0
$365$	−7.98587	−0.417999
$366$	0	0
$367$	11.8670	0.619453	0.309726	−	0.950826i	$-0.399763\pi$
$367$	11.8670	0.619453	0.309726	+	0.950826i	$0.399763\pi$
$368$	0	0
$369$	0.504623	0.0262696
$370$	0	0
$371$	0	0
$372$	0	0
$373$	−3.44837	−0.178550	−0.0892750	−	0.996007i	$-0.528455\pi$
$373$	−3.44837	−0.178550	−0.0892750	+	0.996007i	$0.528455\pi$
$374$	0	0
$375$	14.0172	0.723843
$376$	0	0
$377$	−11.0114	−0.567118
$378$	0	0
$379$	34.1466	1.75400	0.876998	−	0.480495i	$-0.159543\pi$
$379$	34.1466	1.75400	0.876998	+	0.480495i	$0.159543\pi$
$380$	0	0
$381$	14.4092	0.738207
$382$	0	0
$383$	−2.00535	−0.102468	−0.0512342	−	0.998687i	$-0.516316\pi$
$383$	−2.00535	−0.102468	−0.0512342	+	0.998687i	$0.516316\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	1.70821	0.0868333
$388$	0	0
$389$	9.44288	0.478773	0.239386	−	0.970924i	$-0.423054\pi$
$389$	9.44288	0.478773	0.239386	+	0.970924i	$0.423054\pi$
$390$	0	0
$391$	−3.12889	−0.158235
$392$	0	0
$393$	0.240472	0.0121302
$394$	0	0
$395$	−1.88702	−0.0949462
$396$	0	0
$397$	−10.6634	−0.535182	−0.267591	−	0.963533i	$-0.586228\pi$
$397$	−10.6634	−0.535182	−0.267591	+	0.963533i	$0.586228\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	−13.9735	−0.697805	−0.348902	−	0.937159i	$-0.613446\pi$
$401$	−13.9735	−0.697805	−0.348902	+	0.937159i	$0.613446\pi$
$402$	0	0
$403$	41.3134	2.05797
$404$	0	0
$405$	7.59886	0.377591
$406$	0	0
$407$	13.5772	0.672999
$408$	0	0
$409$	−21.0721	−1.04195	−0.520974	−	0.853573i	$-0.674431\pi$
$409$	−21.0721	−1.04195	−0.520974	+	0.853573i	$0.674431\pi$
$410$	0	0
$411$	13.2996	0.656019
$412$	0	0
$413$	0	0
$414$	0	0
$415$	−11.4063	−0.559911
$416$	0	0
$417$	0.210872	0.0103264
$418$	0	0
$419$	−28.5948	−1.39695	−0.698474	−	0.715636i	$-0.746137\pi$
$419$	−28.5948	−1.39695	−0.698474	+	0.715636i	$0.746137\pi$
$420$	0	0
$421$	−9.42425	−0.459310	−0.229655	−	0.973272i	$-0.573760\pi$
$421$	−9.42425	−0.459310	−0.229655	+	0.973272i	$0.573760\pi$
$422$	0	0
$423$	−1.79073	−0.0870681
$424$	0	0
$425$	−12.9967	−0.630432
$426$	0	0
$427$	0	0
$428$	0	0
$429$	−35.6175	−1.71963
$430$	0	0
$431$	18.8165	0.906360	0.453180	−	0.891419i	$-0.350290\pi$
$431$	18.8165	0.906360	0.453180	+	0.891419i	$0.350290\pi$
$432$	0	0
$433$	27.1071	1.30269	0.651343	−	0.758784i	$-0.274206\pi$
$433$	27.1071	1.30269	0.651343	+	0.758784i	$0.274206\pi$
$434$	0	0
$435$	2.72079	0.130452
$436$	0	0
$437$	3.03139	0.145011
$438$	0	0
$439$	14.9482	0.713438	0.356719	−	0.934212i	$-0.383895\pi$
$439$	14.9482	0.713438	0.356719	+	0.934212i	$0.383895\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	36.6145	1.73961	0.869803	−	0.493399i	$-0.164246\pi$
$443$	36.6145	1.73961	0.869803	+	0.493399i	$0.164246\pi$
$444$	0	0
$445$	11.7122	0.555213
$446$	0	0
$447$	−17.4784	−0.826702
$448$	0	0
$449$	−30.4906	−1.43894	−0.719470	−	0.694523i	$-0.755615\pi$
$449$	−30.4906	−1.43894	−0.719470	+	0.694523i	$0.755615\pi$
$450$	0	0
$451$	7.60719	0.358208
$452$	0	0
$453$	25.7633	1.21046
$454$	0	0
$455$	0	0
$456$	0	0
$457$	41.8566	1.95797	0.978984	−	0.203939i	$-0.0653746\pi$
$457$	41.8566	1.95797	0.978984	+	0.203939i	$0.0653746\pi$
$458$	0	0
$459$	−16.8181	−0.785003
$460$	0	0
$461$	−18.7895	−0.875115	−0.437557	−	0.899190i	$-0.644156\pi$
$461$	−18.7895	−0.875115	−0.437557	+	0.899190i	$0.644156\pi$
$462$	0	0
$463$	−24.2203	−1.12561	−0.562805	−	0.826589i	$-0.690278\pi$
$463$	−24.2203	−1.12561	−0.562805	+	0.826589i	$0.690278\pi$
$464$	0	0
$465$	−10.2080	−0.473384
$466$	0	0
$467$	14.4547	0.668882	0.334441	−	0.942417i	$-0.391453\pi$
$467$	14.4547	0.668882	0.334441	+	0.942417i	$0.391453\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	−1.62598	−0.0749214
$472$	0	0
$473$	25.7513	1.18405
$474$	0	0
$475$	12.5917	0.577748
$476$	0	0
$477$	0.578994	0.0265103
$478$	0	0
$479$	−16.7500	−0.765325	−0.382663	−	0.923888i	$-0.624993\pi$
$479$	−16.7500	−0.765325	−0.382663	+	0.923888i	$0.624993\pi$
$480$	0	0
$481$	−24.3716	−1.11125
$482$	0	0
$483$	0	0
$484$	0	0
$485$	12.0156	0.545600
$486$	0	0
$487$	23.2203	1.05221	0.526105	−	0.850419i	$-0.323652\pi$
$487$	23.2203	1.05221	0.526105	+	0.850419i	$0.323652\pi$
$488$	0	0
$489$	−34.0758	−1.54096
$490$	0	0
$491$	−13.2143	−0.596352	−0.298176	−	0.954511i	$-0.596378\pi$
$491$	−13.2143	−0.596352	−0.298176	+	0.954511i	$0.596378\pi$
$492$	0	0
$493$	−5.55935	−0.250381
$494$	0	0
$495$	−0.727377	−0.0326932
$496$	0	0
$497$	0	0
$498$	0	0
$499$	26.4177	1.18262	0.591308	−	0.806445i	$-0.298612\pi$
$499$	26.4177	1.18262	0.591308	+	0.806445i	$0.298612\pi$
$500$	0	0
$501$	25.9581	1.15972
$502$	0	0
$503$	0.709608	0.0316399	0.0158199	−	0.999875i	$-0.494964\pi$
$503$	0.709608	0.0316399	0.0158199	+	0.999875i	$0.494964\pi$
$504$	0	0
$505$	14.7399	0.655918
$506$	0	0
$507$	42.2946	1.87837
$508$	0	0
$509$	−13.5428	−0.600276	−0.300138	−	0.953896i	$-0.597033\pi$
$509$	−13.5428	−0.600276	−0.300138	+	0.953896i	$0.597033\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	16.2941	0.719401
$514$	0	0
$515$	−3.00389	−0.132367
$516$	0	0
$517$	−26.9952	−1.18725
$518$	0	0
$519$	−8.39829	−0.368644
$520$	0	0
$521$	−18.8551	−0.826056	−0.413028	−	0.910718i	$-0.635529\pi$
$521$	−18.8551	−0.826056	−0.413028	+	0.910718i	$0.635529\pi$
$522$	0	0
$523$	30.6207	1.33895	0.669476	−	0.742834i	$-0.266519\pi$
$523$	30.6207	1.33895	0.669476	+	0.742834i	$0.266519\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	20.8579	0.908584
$528$	0	0
$529$	1.00000	0.0434783
$530$	0	0
$531$	0.178220	0.00773407
$532$	0	0
$533$	−13.6552	−0.591471
$534$	0	0
$535$	15.4491	0.667923
$536$	0	0
$537$	10.4359	0.450343
$538$	0	0
$539$	0	0
$540$	0	0
$541$	−0.748408	−0.0321766	−0.0160883	−	0.999871i	$-0.505121\pi$
$541$	−0.748408	−0.0321766	−0.0160883	+	0.999871i	$0.505121\pi$
$542$	0	0
$543$	−37.6376	−1.61518
$544$	0	0
$545$	0.788538	0.0337773
$546$	0	0
$547$	2.36972	0.101322	0.0506611	−	0.998716i	$-0.483867\pi$
$547$	2.36972	0.101322	0.0506611	+	0.998716i	$0.483867\pi$
$548$	0	0
$549$	2.58341	0.110257
$550$	0	0
$551$	5.38613	0.229457
$552$	0	0
$553$	0	0
$554$	0	0
$555$	6.02192	0.255616
$556$	0	0
$557$	−31.3025	−1.32633	−0.663164	−	0.748474i	$-0.730787\pi$
$557$	−31.3025	−1.32633	−0.663164	+	0.748474i	$0.730787\pi$
$558$	0	0
$559$	−46.2245	−1.95509
$560$	0	0
$561$	−17.9822	−0.759210
$562$	0	0
$563$	19.4129	0.818156	0.409078	−	0.912499i	$-0.365850\pi$
$563$	19.4129	0.818156	0.409078	+	0.912499i	$0.365850\pi$
$564$	0	0
$565$	−4.79846	−0.201873
$566$	0	0
$567$	0	0
$568$	0	0
$569$	−6.57939	−0.275823	−0.137911	−	0.990445i	$-0.544039\pi$
$569$	−6.57939	−0.275823	−0.137911	+	0.990445i	$0.544039\pi$
$570$	0	0
$571$	−20.1417	−0.842903	−0.421451	−	0.906851i	$-0.638479\pi$
$571$	−20.1417	−0.842903	−0.421451	+	0.906851i	$0.638479\pi$
$572$	0	0
$573$	−18.4914	−0.772490
$574$	0	0
$575$	4.15377	0.173224
$576$	0	0
$577$	1.77220	0.0737775	0.0368887	−	0.999319i	$-0.488255\pi$
$577$	1.77220	0.0737775	0.0368887	+	0.999319i	$0.488255\pi$
$578$	0	0
$579$	−19.7624	−0.821298
$580$	0	0
$581$	0	0
$582$	0	0
$583$	8.72834	0.361491
$584$	0	0
$585$	1.30567	0.0539827
$586$	0	0
$587$	3.03541	0.125285	0.0626424	−	0.998036i	$-0.480047\pi$
$587$	3.03541	0.125285	0.0626424	+	0.998036i	$0.480047\pi$
$588$	0	0
$589$	−20.2080	−0.832655
$590$	0	0
$591$	31.4991	1.29570
$592$	0	0
$593$	−21.2091	−0.870951	−0.435476	−	0.900200i	$-0.643420\pi$
$593$	−21.2091	−0.870951	−0.435476	+	0.900200i	$0.643420\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	14.9302	0.611054
$598$	0	0
$599$	16.8810	0.689739	0.344869	−	0.938651i	$-0.387923\pi$
$599$	16.8810	0.689739	0.344869	+	0.938651i	$0.387923\pi$
$600$	0	0
$601$	42.3556	1.72772	0.863860	−	0.503732i	$-0.168040\pi$
$601$	42.3556	1.72772	0.863860	+	0.503732i	$0.168040\pi$
$602$	0	0
$603$	0.0105319	0.000428894 0
$604$	0	0
$605$	−0.846250	−0.0344050
$606$	0	0
$607$	−18.7124	−0.759512	−0.379756	−	0.925087i	$-0.623992\pi$
$607$	−18.7124	−0.759512	−0.379756	+	0.925087i	$0.623992\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	48.4574	1.96038
$612$	0	0
$613$	−40.2431	−1.62541	−0.812703	−	0.582679i	$-0.802005\pi$
$613$	−40.2431	−1.62541	−0.812703	+	0.582679i	$0.802005\pi$
$614$	0	0
$615$	3.37402	0.136053
$616$	0	0
$617$	34.9722	1.40793	0.703964	−	0.710236i	$-0.251412\pi$
$617$	34.9722	1.40793	0.703964	+	0.710236i	$0.251412\pi$
$618$	0	0
$619$	12.3376	0.495891	0.247946	−	0.968774i	$-0.420245\pi$
$619$	12.3376	0.495891	0.247946	+	0.968774i	$0.420245\pi$
$620$	0	0
$621$	5.37511	0.215696
$622$	0	0
$623$	0	0
$624$	0	0
$625$	13.0227	0.520908
$626$	0	0
$627$	17.4219	0.695764
$628$	0	0
$629$	−12.3045	−0.490613
$630$	0	0
$631$	42.1997	1.67994	0.839971	−	0.542632i	$-0.182572\pi$
$631$	42.1997	1.67994	0.839971	+	0.542632i	$0.182572\pi$
$632$	0	0
$633$	−15.6608	−0.622459
$634$	0	0
$635$	−7.96284	−0.315995
$636$	0	0
$637$	0	0
$638$	0	0
$639$	0.962980	0.0380949
$640$	0	0
$641$	40.1095	1.58423	0.792114	−	0.610373i	$-0.208980\pi$
$641$	40.1095	1.58423	0.792114	+	0.610373i	$0.208980\pi$
$642$	0	0
$643$	−44.8359	−1.76816	−0.884078	−	0.467339i	$-0.845213\pi$
$643$	−44.8359	−1.76816	−0.884078	+	0.467339i	$0.845213\pi$
$644$	0	0
$645$	11.4215	0.449720
$646$	0	0
$647$	−22.8294	−0.897517	−0.448759	−	0.893653i	$-0.648134\pi$
$647$	−22.8294	−0.897517	−0.448759	+	0.893653i	$0.648134\pi$
$648$	0	0
$649$	2.68666	0.105461
$650$	0	0
$651$	0	0
$652$	0	0
$653$	−1.02233	−0.0400067	−0.0200034	−	0.999800i	$-0.506368\pi$
$653$	−1.02233	−0.0400067	−0.0200034	+	0.999800i	$0.506368\pi$
$654$	0	0
$655$	−0.132890	−0.00519244
$656$	0	0
$657$	−1.98819	−0.0775667
$658$	0	0
$659$	37.6561	1.46687	0.733437	−	0.679757i	$-0.237915\pi$
$659$	37.6561	1.46687	0.733437	+	0.679757i	$0.237915\pi$
$660$	0	0
$661$	5.06310	0.196932	0.0984658	−	0.995140i	$-0.468606\pi$
$661$	5.06310	0.196932	0.0984658	+	0.995140i	$0.468606\pi$
$662$	0	0
$663$	32.2787	1.25360
$664$	0	0
$665$	0	0
$666$	0	0
$667$	1.77678	0.0687973
$668$	0	0
$669$	−29.4680	−1.13930
$670$	0	0
$671$	38.9449	1.50345
$672$	0	0
$673$	28.9235	1.11492	0.557459	−	0.830204i	$-0.311776\pi$
$673$	28.9235	1.11492	0.557459	+	0.830204i	$0.311776\pi$
$674$	0	0
$675$	22.3270	0.859367
$676$	0	0
$677$	−40.7928	−1.56779	−0.783897	−	0.620890i	$-0.786771\pi$
$677$	−40.7928	−1.56779	−0.783897	+	0.620890i	$0.786771\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	−17.8707	−0.684806
$682$	0	0
$683$	40.0253	1.53153	0.765763	−	0.643123i	$-0.222362\pi$
$683$	40.0253	1.53153	0.765763	+	0.643123i	$0.222362\pi$
$684$	0	0
$685$	−7.34961	−0.280814
$686$	0	0
$687$	8.38608	0.319949
$688$	0	0
$689$	−15.6677	−0.596891
$690$	0	0
$691$	−13.8245	−0.525908	−0.262954	−	0.964808i	$-0.584697\pi$
$691$	−13.8245	−0.525908	−0.262954	+	0.964808i	$0.584697\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	−0.116532	−0.00442032
$696$	0	0
$697$	−6.89409	−0.261132
$698$	0	0
$699$	−22.6154	−0.855394
$700$	0	0
$701$	28.7529	1.08598	0.542992	−	0.839738i	$-0.317291\pi$
$701$	28.7529	1.08598	0.542992	+	0.839738i	$0.317291\pi$
$702$	0	0
$703$	11.9211	0.449613
$704$	0	0
$705$	−11.9732	−0.450936
$706$	0	0
$707$	0	0
$708$	0	0
$709$	0.813500	0.0305517	0.0152758	−	0.999883i	$-0.495137\pi$
$709$	0.813500	0.0305517	0.0152758	+	0.999883i	$0.495137\pi$
$710$	0	0
$711$	−0.469799	−0.0176188
$712$	0	0
$713$	−6.66624	−0.249652
$714$	0	0
$715$	19.6830	0.736101
$716$	0	0
$717$	−30.9553	−1.15605
$718$	0	0
$719$	−7.38937	−0.275577	−0.137788	−	0.990462i	$-0.543999\pi$
$719$	−7.38937	−0.275577	−0.137788	+	0.990462i	$0.543999\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	8.50424	0.316276
$724$	0	0
$725$	7.38035	0.274099
$726$	0	0
$727$	2.82894	0.104920	0.0524598	−	0.998623i	$-0.483294\pi$
$727$	2.82894	0.104920	0.0524598	+	0.998623i	$0.483294\pi$
$728$	0	0
$729$	28.7345	1.06424
$730$	0	0
$731$	−23.3374	−0.863164
$732$	0	0
$733$	−30.6871	−1.13346	−0.566728	−	0.823905i	$-0.691791\pi$
$733$	−30.6871	−1.13346	−0.566728	+	0.823905i	$0.691791\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	0.158769	0.00584834
$738$	0	0
$739$	52.3108	1.92428	0.962142	−	0.272548i	$-0.0878664\pi$
$739$	52.3108	1.92428	0.962142	+	0.272548i	$0.0878664\pi$
$740$	0	0
$741$	−31.2729	−1.14884
$742$	0	0
$743$	−31.8312	−1.16777	−0.583887	−	0.811835i	$-0.698469\pi$
$743$	−31.8312	−1.16777	−0.583887	+	0.811835i	$0.698469\pi$
$744$	0	0
$745$	9.65894	0.353876
$746$	0	0
$747$	−2.83974	−0.103901
$748$	0	0
$749$	0	0
$750$	0	0
$751$	22.1290	0.807498	0.403749	−	0.914870i	$-0.367707\pi$
$751$	22.1290	0.807498	0.403749	+	0.914870i	$0.367707\pi$
$752$	0	0
$753$	−3.24267	−0.118169
$754$	0	0
$755$	−14.2373	−0.518149
$756$	0	0
$757$	−21.3850	−0.777252	−0.388626	−	0.921396i	$-0.627050\pi$
$757$	−21.3850	−0.777252	−0.388626	+	0.921396i	$0.627050\pi$
$758$	0	0
$759$	5.74716	0.208609
$760$	0	0
$761$	−11.1203	−0.403110	−0.201555	−	0.979477i	$-0.564600\pi$
$761$	−11.1203	−0.403110	−0.201555	+	0.979477i	$0.564600\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	0.659193	0.0238332
$766$	0	0
$767$	−4.82266	−0.174136
$768$	0	0
$769$	15.6702	0.565081	0.282541	−	0.959255i	$-0.408823\pi$
$769$	15.6702	0.565081	0.282541	+	0.959255i	$0.408823\pi$
$770$	0	0
$771$	−47.9228	−1.72590
$772$	0	0
$773$	−18.6314	−0.670124	−0.335062	−	0.942196i	$-0.608757\pi$
$773$	−18.6314	−0.670124	−0.335062	+	0.942196i	$0.608757\pi$
$774$	0	0
$775$	−27.6900	−0.994655
$776$	0	0
$777$	0	0
$778$	0	0
$779$	6.67928	0.239310
$780$	0	0
$781$	14.5169	0.519457
$782$	0	0
$783$	9.55041	0.341304
$784$	0	0
$785$	0.898552	0.0320707
$786$	0	0
$787$	32.5153	1.15905	0.579523	−	0.814956i	$-0.303239\pi$
$787$	32.5153	1.15905	0.579523	+	0.814956i	$0.303239\pi$
$788$	0	0
$789$	−37.6037	−1.33873
$790$	0	0
$791$	0	0
$792$	0	0
$793$	−69.9076	−2.48249
$794$	0	0
$795$	3.87128	0.137300
$796$	0	0
$797$	−7.26112	−0.257202	−0.128601	−	0.991696i	$-0.541049\pi$
$797$	−7.26112	−0.257202	−0.128601	+	0.991696i	$0.541049\pi$
$798$	0	0
$799$	24.4647	0.865499
$800$	0	0
$801$	2.91592	0.103029
$802$	0	0
$803$	−29.9720	−1.05769
$804$	0	0
$805$	0	0
$806$	0	0
$807$	−16.4201	−0.578013
$808$	0	0
$809$	−9.70034	−0.341046	−0.170523	−	0.985354i	$-0.554546\pi$
$809$	−9.70034	−0.341046	−0.170523	+	0.985354i	$0.554546\pi$
$810$	0	0
$811$	22.3029	0.783161	0.391580	−	0.920144i	$-0.371929\pi$
$811$	22.3029	0.783161	0.391580	+	0.920144i	$0.371929\pi$
$812$	0	0
$813$	41.2699	1.44740
$814$	0	0
$815$	18.8310	0.659620
$816$	0	0
$817$	22.6102	0.791031
$818$	0	0
$819$	0	0
$820$	0	0
$821$	5.84245	0.203903	0.101951	−	0.994789i	$-0.467491\pi$
$821$	5.84245	0.203903	0.101951	+	0.994789i	$0.467491\pi$
$822$	0	0
$823$	10.8211	0.377200	0.188600	−	0.982054i	$-0.439605\pi$
$823$	10.8211	0.377200	0.188600	+	0.982054i	$0.439605\pi$
$824$	0	0
$825$	23.8724	0.831130
$826$	0	0
$827$	−9.84654	−0.342398	−0.171199	−	0.985236i	$-0.554764\pi$
$827$	−9.84654	−0.342398	−0.171199	+	0.985236i	$0.554764\pi$
$828$	0	0
$829$	54.5762	1.89551	0.947755	−	0.318999i	$-0.103347\pi$
$829$	54.5762	1.89551	0.947755	+	0.318999i	$0.103347\pi$
$830$	0	0
$831$	37.4763	1.30004
$832$	0	0
$833$	0	0
$834$	0	0
$835$	−14.3450	−0.496429
$836$	0	0
$837$	−35.8318	−1.23853
$838$	0	0
$839$	55.1860	1.90523	0.952616	−	0.304174i	$-0.0983805\pi$
$839$	55.1860	1.90523	0.952616	+	0.304174i	$0.0983805\pi$
$840$	0	0
$841$	−25.8430	−0.891139
$842$	0	0
$843$	1.68160	0.0579175
$844$	0	0
$845$	−23.3728	−0.804050
$846$	0	0
$847$	0	0
$848$	0	0
$849$	2.55228	0.0875939
$850$	0	0
$851$	3.93255	0.134806
$852$	0	0
$853$	−55.6017	−1.90377	−0.951883	−	0.306463i	$-0.900854\pi$
$853$	−55.6017	−1.90377	−0.951883	+	0.306463i	$0.900854\pi$
$854$	0	0
$855$	−0.638653	−0.0218415
$856$	0	0
$857$	−26.0932	−0.891328	−0.445664	−	0.895200i	$-0.647032\pi$
$857$	−26.0932	−0.891328	−0.445664	+	0.895200i	$0.647032\pi$
$858$	0	0
$859$	−2.20257	−0.0751506	−0.0375753	−	0.999294i	$-0.511963\pi$
$859$	−2.20257	−0.0751506	−0.0375753	+	0.999294i	$0.511963\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	4.78487	0.162879	0.0814394	−	0.996678i	$-0.474048\pi$
$863$	4.78487	0.162879	0.0814394	+	0.996678i	$0.474048\pi$
$864$	0	0
$865$	4.64107	0.157801
$866$	0	0
$867$	−12.0021	−0.407611
$868$	0	0
$869$	−7.08222	−0.240248
$870$	0	0
$871$	−0.284996	−0.00965673
$872$	0	0
$873$	2.99144	0.101245
$874$	0	0
$875$	0	0
$876$	0	0
$877$	47.2057	1.59402	0.797012	−	0.603964i	$-0.206413\pi$
$877$	47.2057	1.59402	0.797012	+	0.603964i	$0.206413\pi$
$878$	0	0
$879$	−41.8349	−1.41106
$880$	0	0
$881$	34.3740	1.15809	0.579045	−	0.815296i	$-0.303426\pi$
$881$	34.3740	1.15809	0.579045	+	0.815296i	$0.303426\pi$
$882$	0	0
$883$	−10.3267	−0.347520	−0.173760	−	0.984788i	$-0.555592\pi$
$883$	−10.3267	−0.347520	−0.173760	+	0.984788i	$0.555592\pi$
$884$	0	0
$885$	1.19162	0.0400557
$886$	0	0
$887$	−12.6374	−0.424323	−0.212161	−	0.977235i	$-0.568050\pi$
$887$	−12.6374	−0.424323	−0.212161	+	0.977235i	$0.568050\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	28.5195	0.955440
$892$	0	0
$893$	−23.7024	−0.793170
$894$	0	0
$895$	−5.76710	−0.192773
$896$	0	0
$897$	−10.3164	−0.344453
$898$	0	0
$899$	−11.8445	−0.395035
$900$	0	0
$901$	−7.91015	−0.263525
$902$	0	0
$903$	0	0
$904$	0	0
$905$	20.7993	0.691392
$906$	0	0
$907$	6.65059	0.220829	0.110415	−	0.993886i	$-0.464782\pi$
$907$	6.65059	0.220829	0.110415	+	0.993886i	$0.464782\pi$
$908$	0	0
$909$	3.66971	0.121717
$910$	0	0
$911$	−58.4181	−1.93548	−0.967739	−	0.251955i	$-0.918927\pi$
$911$	−58.4181	−1.93548	−0.967739	+	0.251955i	$0.918927\pi$
$912$	0	0
$913$	−42.8091	−1.41678
$914$	0	0
$915$	17.2733	0.571036
$916$	0	0
$917$	0	0
$918$	0	0
$919$	47.8620	1.57882	0.789411	−	0.613864i	$-0.210386\pi$
$919$	47.8620	1.57882	0.789411	+	0.613864i	$0.210386\pi$
$920$	0	0
$921$	−48.6785	−1.60401
$922$	0	0
$923$	−26.0584	−0.857723
$924$	0	0
$925$	16.3349	0.537089
$926$	0	0
$927$	−0.747860	−0.0245629
$928$	0	0
$929$	42.9107	1.40785	0.703927	−	0.710273i	$-0.251428\pi$
$929$	42.9107	1.40785	0.703927	+	0.710273i	$0.251428\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	−43.6960	−1.43054
$934$	0	0
$935$	9.93734	0.324986
$936$	0	0
$937$	−8.70212	−0.284286	−0.142143	−	0.989846i	$-0.545399\pi$
$937$	−8.70212	−0.284286	−0.142143	+	0.989846i	$0.545399\pi$
$938$	0	0
$939$	8.88276	0.289878
$940$	0	0
$941$	−43.8846	−1.43060	−0.715299	−	0.698819i	$-0.753709\pi$
$941$	−43.8846	−1.43060	−0.715299	+	0.698819i	$0.753709\pi$
$942$	0	0
$943$	2.20337	0.0717516
$944$	0	0
$945$	0	0
$946$	0	0
$947$	−42.9283	−1.39498	−0.697490	−	0.716594i	$-0.745700\pi$
$947$	−42.9283	−1.39498	−0.697490	+	0.716594i	$0.745700\pi$
$948$	0	0
$949$	53.8008	1.74645
$950$	0	0
$951$	−34.0056	−1.10271
$952$	0	0
$953$	5.49111	0.177874	0.0889372	−	0.996037i	$-0.471653\pi$
$953$	5.49111	0.177874	0.0889372	+	0.996037i	$0.471653\pi$
$954$	0	0
$955$	10.2187	0.330671
$956$	0	0
$957$	10.2115	0.330090
$958$	0	0
$959$	0	0
$960$	0	0
$961$	13.4387	0.433506
$962$	0	0
$963$	3.84627	0.123944
$964$	0	0
$965$	10.9211	0.351563
$966$	0	0
$967$	−7.91850	−0.254642	−0.127321	−	0.991862i	$-0.540638\pi$
$967$	−7.91850	−0.254642	−0.127321	+	0.991862i	$0.540638\pi$
$968$	0	0
$969$	−15.7888	−0.507209
$970$	0	0
$971$	5.65936	0.181617	0.0908087	−	0.995868i	$-0.471055\pi$
$971$	5.65936	0.181617	0.0908087	+	0.995868i	$0.471055\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	−42.8518	−1.37236
$976$	0	0
$977$	56.4480	1.80593	0.902966	−	0.429712i	$-0.141385\pi$
$977$	56.4480	1.80593	0.902966	+	0.429712i	$0.141385\pi$
$978$	0	0
$979$	43.9575	1.40489
$980$	0	0
$981$	0.196317	0.00626793
$982$	0	0
$983$	26.6658	0.850506	0.425253	−	0.905074i	$-0.360185\pi$
$983$	26.6658	0.850506	0.425253	+	0.905074i	$0.360185\pi$
$984$	0	0
$985$	−17.4070	−0.554634
$986$	0	0
$987$	0	0
$988$	0	0
$989$	7.45869	0.237172
$990$	0	0
$991$	−13.7119	−0.435573	−0.217786	−	0.975996i	$-0.569884\pi$
$991$	−13.7119	−0.435573	−0.217786	+	0.975996i	$0.569884\pi$
$992$	0	0
$993$	19.0782	0.605430
$994$	0	0
$995$	−8.25076	−0.261567
$996$	0	0
$997$	47.4742	1.50352	0.751762	−	0.659434i	$-0.229204\pi$
$997$	47.4742	1.50352	0.751762	+	0.659434i	$0.229204\pi$
$998$	0	0
$999$	21.1379	0.668774

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9016.2.a.bo.1.9		11
7.3	odd	6		1288.2.q.b.737.9	✓	22
7.5	odd	6		1288.2.q.b.921.9	yes	22
7.6	odd	2		9016.2.a.bn.1.3		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1288.2.q.b.737.9	✓	22	7.3	odd	6
1288.2.q.b.921.9	yes	22	7.5	odd	6
9016.2.a.bn.1.3		11	7.6	odd	2
9016.2.a.bo.1.9		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)

\(f(q)\)	\(=\)	\(q+1.66463 q^{3} -0.919906 q^{5} -0.229023 q^{9} +O(q^{10})\)	\(q+1.66463 q^{3} -0.919906 q^{5} -0.229023 q^{9} -3.45253 q^{11} +6.19741 q^{13} -1.53130 q^{15} +3.12889 q^{17} -3.03139 q^{19} -1.00000 q^{23} -4.15377 q^{25} -5.37511 q^{27} -1.77678 q^{29} +6.66624 q^{31} -5.74716 q^{33} -3.93255 q^{37} +10.3164 q^{39} -2.20337 q^{41} -7.45869 q^{43} +0.210680 q^{45} +7.81898 q^{47} +5.20843 q^{51} -2.52810 q^{53} +3.17600 q^{55} -5.04613 q^{57} -0.778173 q^{59} -11.2801 q^{61} -5.70103 q^{65} -0.0459864 q^{67} -1.66463 q^{69} -4.20473 q^{71} +8.68118 q^{73} -6.91447 q^{75} +2.05132 q^{79} -8.26048 q^{81} +12.3994 q^{83} -2.87828 q^{85} -2.95768 q^{87} -12.7320 q^{89} +11.0968 q^{93} +2.78860 q^{95} -13.0618 q^{97} +0.790708 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 2 q^{3} - 9 q^{5} + 11 q^{9}+O(q^{10}) \) 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

L-functions

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Database

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