LMFDB - Embedded newform 9163.2.a.j.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9163,2,Mod(1,9163)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9163, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("9163.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9163 = 7^{2} \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9163.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:	$73.1669233721$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 187)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.311108$ of defining polynomial
Character	$\chi$	$=$	9163.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.688892 q^{2} -1.21432 q^{3} -1.52543 q^{4} +2.31111 q^{5} +0.836535 q^{6} +2.42864 q^{8} -1.52543 q^{9} +O(q^{10})$	\(q-0.688892 q^{2} -1.21432 q^{3} -1.52543 q^{4} +2.31111 q^{5} +0.836535 q^{6} +2.42864 q^{8} -1.52543 q^{9} -1.59210 q^{10} -1.00000 q^{11} +1.85236 q^{12} +0.0666765 q^{13} -2.80642 q^{15} +1.37778 q^{16} +1.00000 q^{17} +1.05086 q^{18} -6.49532 q^{19} -3.52543 q^{20} +0.688892 q^{22} -2.78568 q^{23} -2.94914 q^{24} +0.341219 q^{25} -0.0459330 q^{26} +5.49532 q^{27} -2.40790 q^{29} +1.93332 q^{30} +7.49532 q^{31} -5.80642 q^{32} +1.21432 q^{33} -0.688892 q^{34} +2.32693 q^{36} +7.44938 q^{37} +4.47457 q^{38} -0.0809666 q^{39} +5.61285 q^{40} +4.42864 q^{41} +11.6128 q^{43} +1.52543 q^{44} -3.52543 q^{45} +1.91903 q^{46} +1.33185 q^{47} -1.67307 q^{48} -0.235063 q^{50} -1.21432 q^{51} -0.101710 q^{52} -12.2810 q^{53} -3.78568 q^{54} -2.31111 q^{55} +7.88739 q^{57} +1.65878 q^{58} -1.76986 q^{59} +4.28100 q^{60} -2.42864 q^{61} -5.16346 q^{62} +1.24443 q^{64} +0.154097 q^{65} -0.836535 q^{66} -13.2351 q^{67} -1.52543 q^{68} +3.38271 q^{69} -1.06668 q^{71} -3.70471 q^{72} +1.78568 q^{73} -5.13182 q^{74} -0.414349 q^{75} +9.90813 q^{76} +0.0557773 q^{78} +6.83654 q^{79} +3.18421 q^{80} -2.09679 q^{81} -3.05086 q^{82} -2.75557 q^{83} +2.31111 q^{85} -8.00000 q^{86} +2.92396 q^{87} -2.42864 q^{88} +8.47949 q^{89} +2.42864 q^{90} +4.24935 q^{92} -9.10171 q^{93} -0.917502 q^{94} -15.0114 q^{95} +7.05086 q^{96} +7.83654 q^{97} +1.52543 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 2 q^{2} + 3 q^{3} + 2 q^{4} + 7 q^{5} - 4 q^{6} - 6 q^{8} + 2 q^{9}+O(q^{10}) $ 3 * q - 2 * q^2 + 3 * q^3 + 2 * q^4 + 7 * q^5 - 4 * q^6 - 6 * q^8 + 2 * q^9	$ 3 q - 2 q^{2} + 3 q^{3} + 2 q^{4} + 7 q^{5} - 4 q^{6} - 6 q^{8} + 2 q^{9} + 2 q^{10} - 3 q^{11} + 12 q^{12} + 5 q^{15} + 4 q^{16} + 3 q^{17} - 10 q^{18} - 6 q^{19} - 4 q^{20} + 2 q^{22} - 15 q^{23} - 22 q^{24} + 8 q^{25} - 20 q^{26} + 3 q^{27} - 14 q^{29} + 6 q^{30} + 9 q^{31} - 4 q^{32} - 3 q^{33} - 2 q^{34} + 20 q^{36} - 11 q^{37} + 20 q^{38} + 6 q^{39} - 10 q^{40} + 8 q^{43} - 2 q^{44} - 4 q^{45} + 12 q^{46} - 16 q^{47} + 8 q^{48} + 26 q^{50} + 3 q^{51} + 26 q^{52} - 30 q^{53} - 18 q^{54} - 7 q^{55} + 4 q^{57} - 2 q^{58} + q^{59} + 6 q^{60} + 6 q^{61} - 22 q^{62} + 4 q^{64} - 20 q^{65} + 4 q^{66} - 13 q^{67} + 2 q^{68} - 23 q^{69} - 3 q^{71} - 24 q^{72} + 12 q^{73} + 4 q^{74} + 6 q^{75} - 10 q^{76} - 46 q^{78} + 14 q^{79} - 4 q^{80} - 13 q^{81} + 4 q^{82} - 8 q^{83} + 7 q^{85} - 24 q^{86} - 18 q^{87} + 6 q^{88} - q^{89} - 6 q^{90} - 20 q^{92} - q^{93} + 10 q^{94} + 2 q^{95} + 8 q^{96} + 17 q^{97} - 2 q^{99}+O(q^{100}) $ 3 * q - 2 * q^2 + 3 * q^3 + 2 * q^4 + 7 * q^5 - 4 * q^6 - 6 * q^8 + 2 * q^9 + 2 * q^10 - 3 * q^11 + 12 * q^12 + 5 * q^15 + 4 * q^16 + 3 * q^17 - 10 * q^18 - 6 * q^19 - 4 * q^20 + 2 * q^22 - 15 * q^23 - 22 * q^24 + 8 * q^25 - 20 * q^26 + 3 * q^27 - 14 * q^29 + 6 * q^30 + 9 * q^31 - 4 * q^32 - 3 * q^33 - 2 * q^34 + 20 * q^36 - 11 * q^37 + 20 * q^38 + 6 * q^39 - 10 * q^40 + 8 * q^43 - 2 * q^44 - 4 * q^45 + 12 * q^46 - 16 * q^47 + 8 * q^48 + 26 * q^50 + 3 * q^51 + 26 * q^52 - 30 * q^53 - 18 * q^54 - 7 * q^55 + 4 * q^57 - 2 * q^58 + q^59 + 6 * q^60 + 6 * q^61 - 22 * q^62 + 4 * q^64 - 20 * q^65 + 4 * q^66 - 13 * q^67 + 2 * q^68 - 23 * q^69 - 3 * q^71 - 24 * q^72 + 12 * q^73 + 4 * q^74 + 6 * q^75 - 10 * q^76 - 46 * q^78 + 14 * q^79 - 4 * q^80 - 13 * q^81 + 4 * q^82 - 8 * q^83 + 7 * q^85 - 24 * q^86 - 18 * q^87 + 6 * q^88 - q^89 - 6 * q^90 - 20 * q^92 - q^93 + 10 * q^94 + 2 * q^95 + 8 * q^96 + 17 * q^97 - 2 * 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 $

$2$	−0.688892	−0.487120	−0.243560	−	0.969886i	$-0.578315\pi$
$2$	−0.688892	−0.487120	−0.243560	+	0.969886i	$0.578315\pi$
$3$	−1.21432	−0.701088	−0.350544	−	0.936546i	$-0.614003\pi$
$3$	−1.21432	−0.701088	−0.350544	+	0.936546i	$0.614003\pi$
$4$	−1.52543	−0.762714
$5$	2.31111	1.03356	0.516779	−	0.856119i	$-0.327131\pi$
$5$	2.31111	1.03356	0.516779	+	0.856119i	$0.327131\pi$
$6$	0.836535	0.341514
$7$	0	0
$7$	0	0
$8$	2.42864	0.858654
$9$	−1.52543	−0.508476
$10$	−1.59210	−0.503468
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.85236	0.534729
$13$	0.0666765	0.0184927	0.00924637	−	0.999957i	$-0.497057\pi$
$13$	0.0666765	0.0184927	0.00924637	+	0.999957i	$0.497057\pi$
$14$	0	0
$15$	−2.80642	−0.724616
$16$	1.37778	0.344446
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.05086	0.247689
$19$	−6.49532	−1.49013	−0.745064	−	0.666993i	$-0.767581\pi$
$19$	−6.49532	−1.49013	−0.745064	+	0.666993i	$0.767581\pi$
$20$	−3.52543	−0.788310
$21$	0	0
$22$	0.688892	0.146872
$23$	−2.78568	−0.580854	−0.290427	−	0.956897i	$-0.593797\pi$
$23$	−2.78568	−0.580854	−0.290427	+	0.956897i	$0.593797\pi$
$24$	−2.94914	−0.601992
$25$	0.341219	0.0682439
$26$	−0.0459330	−0.00900819
$27$	5.49532	1.05757
$28$	0	0
$29$	−2.40790	−0.447135	−0.223568	−	0.974688i	$-0.571770\pi$
$29$	−2.40790	−0.447135	−0.223568	+	0.974688i	$0.571770\pi$
$30$	1.93332	0.352975
$31$	7.49532	1.34620	0.673099	−	0.739552i	$-0.264963\pi$
$31$	7.49532	1.34620	0.673099	+	0.739552i	$0.264963\pi$
$32$	−5.80642	−1.02644
$33$	1.21432	0.211386
$34$	−0.688892	−0.118144
$35$	0	0
$36$	2.32693	0.387822
$37$	7.44938	1.22467	0.612336	−	0.790598i	$-0.290230\pi$
$37$	7.44938	1.22467	0.612336	+	0.790598i	$0.290230\pi$
$38$	4.47457	0.725872
$39$	−0.0809666	−0.0129650
$40$	5.61285	0.887469
$41$	4.42864	0.691637	0.345819	−	0.938301i	$-0.387601\pi$
$41$	4.42864	0.691637	0.345819	+	0.938301i	$0.387601\pi$
$42$	0	0
$43$	11.6128	1.77094	0.885471	−	0.464694i	$-0.153836\pi$
$43$	11.6128	1.77094	0.885471	+	0.464694i	$0.153836\pi$
$44$	1.52543	0.229967
$45$	−3.52543	−0.525540
$46$	1.91903	0.282946
$47$	1.33185	0.194270	0.0971352	−	0.995271i	$-0.469032\pi$
$47$	1.33185	0.194270	0.0971352	+	0.995271i	$0.469032\pi$
$48$	−1.67307	−0.241487
$49$	0	0
$50$	−0.235063	−0.0332430
$51$	−1.21432	−0.170039
$52$	−0.101710	−0.0141047
$53$	−12.2810	−1.68692	−0.843462	−	0.537188i	$-0.819486\pi$
$53$	−12.2810	−1.68692	−0.843462	+	0.537188i	$0.819486\pi$
$54$	−3.78568	−0.515166
$55$	−2.31111	−0.311630
$56$	0	0
$57$	7.88739	1.04471
$58$	1.65878	0.217809
$59$	−1.76986	−0.230416	−0.115208	−	0.993341i	$-0.536753\pi$
$59$	−1.76986	−0.230416	−0.115208	+	0.993341i	$0.536753\pi$
$60$	4.28100	0.552674
$61$	−2.42864	−0.310955	−0.155478	−	0.987839i	$-0.549692\pi$
$61$	−2.42864	−0.310955	−0.155478	+	0.987839i	$0.549692\pi$
$62$	−5.16346	−0.655761
$63$	0	0
$64$	1.24443	0.155554
$65$	0.154097	0.0191133
$66$	−0.836535	−0.102970
$67$	−13.2351	−1.61692	−0.808460	−	0.588551i	$-0.799699\pi$
$67$	−13.2351	−1.61692	−0.808460	+	0.588551i	$0.799699\pi$
$68$	−1.52543	−0.184985
$69$	3.38271	0.407230
$70$	0	0
$71$	−1.06668	−0.126591	−0.0632956	−	0.997995i	$-0.520161\pi$
$71$	−1.06668	−0.126591	−0.0632956	+	0.997995i	$0.520161\pi$
$72$	−3.70471	−0.436605
$73$	1.78568	0.208998	0.104499	−	0.994525i	$-0.466676\pi$
$73$	1.78568	0.208998	0.104499	+	0.994525i	$0.466676\pi$
$74$	−5.13182	−0.596562
$75$	−0.414349	−0.0478449
$76$	9.90813	1.13654
$77$	0	0
$78$	0.0557773	0.00631553
$79$	6.83654	0.769170	0.384585	−	0.923090i	$-0.374345\pi$
$79$	6.83654	0.769170	0.384585	+	0.923090i	$0.374345\pi$
$80$	3.18421	0.356005
$81$	−2.09679	−0.232976
$82$	−3.05086	−0.336911
$83$	−2.75557	−0.302463	−0.151231	−	0.988498i	$-0.548324\pi$
$83$	−2.75557	−0.302463	−0.151231	+	0.988498i	$0.548324\pi$
$84$	0	0
$85$	2.31111	0.250675
$86$	−8.00000	−0.862662
$87$	2.92396	0.313481
$88$	−2.42864	−0.258894
$89$	8.47949	0.898825	0.449412	−	0.893324i	$-0.351633\pi$
$89$	8.47949	0.898825	0.449412	+	0.893324i	$0.351633\pi$
$90$	2.42864	0.256001
$91$	0	0
$92$	4.24935	0.443026
$93$	−9.10171	−0.943803
$94$	−0.917502	−0.0946331
$95$	−15.0114	−1.54013
$96$	7.05086	0.719625
$97$	7.83654	0.795680	0.397840	−	0.917455i	$-0.369760\pi$
$97$	7.83654	0.795680	0.397840	+	0.917455i	$0.369760\pi$
$98$	0	0
$99$	1.52543	0.153311
$100$	−0.520505	−0.0520505
$101$	4.36196	0.434032	0.217016	−	0.976168i	$-0.430368\pi$
$101$	4.36196	0.434032	0.217016	+	0.976168i	$0.430368\pi$
$102$	0.836535	0.0828293
$103$	12.2494	1.20696	0.603482	−	0.797376i	$-0.293779\pi$
$103$	12.2494	1.20696	0.603482	+	0.797376i	$0.293779\pi$
$104$	0.161933	0.0158789
$105$	0	0
$106$	8.46028	0.821735
$107$	−12.0207	−1.16209	−0.581045	−	0.813872i	$-0.697356\pi$
$107$	−12.0207	−1.16209	−0.581045	+	0.813872i	$0.697356\pi$
$108$	−8.38271	−0.806626
$109$	−14.1541	−1.35572	−0.677858	−	0.735193i	$-0.737092\pi$
$109$	−14.1541	−1.35572	−0.677858	+	0.735193i	$0.737092\pi$
$110$	1.59210	0.151801
$111$	−9.04593	−0.858602
$112$	0	0
$113$	4.44446	0.418100	0.209050	−	0.977905i	$-0.432963\pi$
$113$	4.44446	0.418100	0.209050	+	0.977905i	$0.432963\pi$
$114$	−5.43356	−0.508900
$115$	−6.43801	−0.600347
$116$	3.67307	0.341036
$117$	−0.101710	−0.00940312
$118$	1.21924	0.112240
$119$	0	0
$120$	−6.81579	−0.622194
$121$	1.00000	0.0909091
$122$	1.67307	0.151473
$123$	−5.37778	−0.484898
$124$	−11.4336	−1.02676
$125$	−10.7669	−0.963025
$126$	0	0
$127$	13.6128	1.20794	0.603972	−	0.797005i	$-0.293584\pi$
$127$	13.6128	1.20794	0.603972	+	0.797005i	$0.293584\pi$
$128$	10.7556	0.950667
$129$	−14.1017	−1.24159
$130$	−0.106156	−0.00931050
$131$	−20.9590	−1.83120	−0.915598	−	0.402096i	$-0.868282\pi$
$131$	−20.9590	−1.83120	−0.915598	+	0.402096i	$0.868282\pi$
$132$	−1.85236	−0.161227
$133$	0	0
$134$	9.11753	0.787635
$135$	12.7003	1.09307
$136$	2.42864	0.208254
$137$	−17.2351	−1.47249	−0.736245	−	0.676715i	$-0.763403\pi$
$137$	−17.2351	−1.47249	−0.736245	+	0.676715i	$0.763403\pi$
$138$	−2.33032	−0.198370
$139$	−6.96989	−0.591178	−0.295589	−	0.955315i	$-0.595516\pi$
$139$	−6.96989	−0.591178	−0.295589	+	0.955315i	$0.595516\pi$
$140$	0	0
$141$	−1.61729	−0.136201
$142$	0.734825	0.0616652
$143$	−0.0666765	−0.00557577
$144$	−2.10171	−0.175143
$145$	−5.56491	−0.462140
$146$	−1.23014	−0.101807
$147$	0	0
$148$	−11.3635	−0.934073
$149$	−12.3620	−1.01273	−0.506366	−	0.862319i	$-0.669011\pi$
$149$	−12.3620	−1.01273	−0.506366	+	0.862319i	$0.669011\pi$
$150$	0.285442	0.0233062
$151$	14.4953	1.17961	0.589806	−	0.807545i	$-0.299204\pi$
$151$	14.4953	1.17961	0.589806	+	0.807545i	$0.299204\pi$
$152$	−15.7748	−1.27950
$153$	−1.52543	−0.123324
$154$	0	0
$155$	17.3225	1.39138
$156$	0.123509	0.00988861
$157$	−14.2859	−1.14014	−0.570070	−	0.821596i	$-0.693084\pi$
$157$	−14.2859	−1.14014	−0.570070	+	0.821596i	$0.693084\pi$
$158$	−4.70964	−0.374679
$159$	14.9131	1.18268
$160$	−13.4193	−1.06089
$161$	0	0
$162$	1.44446	0.113488
$163$	8.29529	0.649737	0.324868	−	0.945759i	$-0.394680\pi$
$163$	8.29529	0.649737	0.324868	+	0.945759i	$0.394680\pi$
$164$	−6.75557	−0.527521
$165$	2.80642	0.218480
$166$	1.89829	0.147336
$167$	11.2050	0.867065	0.433533	−	0.901138i	$-0.357267\pi$
$167$	11.2050	0.867065	0.433533	+	0.901138i	$0.357267\pi$
$168$	0	0
$169$	−12.9956	−0.999658
$170$	−1.59210	−0.122109
$171$	9.90813	0.757694
$172$	−17.7146	−1.35072
$173$	19.0923	1.45156	0.725782	−	0.687925i	$-0.241478\pi$
$173$	19.0923	1.45156	0.725782	+	0.687925i	$0.241478\pi$
$174$	−2.01429	−0.152703
$175$	0	0
$176$	−1.37778	−0.103854
$177$	2.14917	0.161542
$178$	−5.84146	−0.437836
$179$	23.6637	1.76871	0.884354	−	0.466817i	$-0.154599\pi$
$179$	23.6637	1.76871	0.884354	+	0.466817i	$0.154599\pi$
$180$	5.37778	0.400836
$181$	3.21432	0.238919	0.119459	−	0.992839i	$-0.461884\pi$
$181$	3.21432	0.238919	0.119459	+	0.992839i	$0.461884\pi$
$182$	0	0
$183$	2.94914	0.218007
$184$	−6.76541	−0.498753
$185$	17.2163	1.26577
$186$	6.27010	0.459746
$187$	−1.00000	−0.0731272
$188$	−2.03164	−0.148173
$189$	0	0
$190$	10.3412	0.750231
$191$	12.6128	0.912634	0.456317	−	0.889817i	$-0.349168\pi$
$191$	12.6128	0.912634	0.456317	+	0.889817i	$0.349168\pi$
$192$	−1.51114	−0.109057
$193$	5.03011	0.362075	0.181038	−	0.983476i	$-0.442054\pi$
$193$	5.03011	0.362075	0.181038	+	0.983476i	$0.442054\pi$
$194$	−5.39853	−0.387592
$195$	−0.187123	−0.0134001
$196$	0	0
$197$	−21.8874	−1.55941	−0.779706	−	0.626146i	$-0.784631\pi$
$197$	−21.8874	−1.55941	−0.779706	+	0.626146i	$0.784631\pi$
$198$	−1.05086	−0.0746810
$199$	−15.7748	−1.11824	−0.559122	−	0.829085i	$-0.688862\pi$
$199$	−15.7748	−1.11824	−0.559122	+	0.829085i	$0.688862\pi$
$200$	0.828699	0.0585979
$201$	16.0716	1.13360
$202$	−3.00492	−0.211426
$203$	0	0
$204$	1.85236	0.129691
$205$	10.2351	0.714848
$206$	−8.43848	−0.587937
$207$	4.24935	0.295350
$208$	0.0918659	0.00636975
$209$	6.49532	0.449290
$210$	0	0
$211$	−7.51114	−0.517088	−0.258544	−	0.965999i	$-0.583243\pi$
$211$	−7.51114	−0.517088	−0.258544	+	0.965999i	$0.583243\pi$
$212$	18.7338	1.28664
$213$	1.29529	0.0887516
$214$	8.28100	0.566077
$215$	26.8385	1.83037
$216$	13.3461	0.908090
$217$	0	0
$218$	9.75065	0.660397
$219$	−2.16839	−0.146526
$220$	3.52543	0.237684
$221$	0.0666765	0.00448515
$222$	6.23167	0.418242
$223$	19.1476	1.28222	0.641111	−	0.767449i	$-0.278474\pi$
$223$	19.1476	1.28222	0.641111	+	0.767449i	$0.278474\pi$
$224$	0	0
$225$	−0.520505	−0.0347004
$226$	−3.06175	−0.203665
$227$	15.1318	1.00433	0.502167	−	0.864771i	$-0.332536\pi$
$227$	15.1318	1.00433	0.502167	+	0.864771i	$0.332536\pi$
$228$	−12.0316	−0.796815
$229$	−2.79213	−0.184509	−0.0922547	−	0.995735i	$-0.529407\pi$
$229$	−2.79213	−0.184509	−0.0922547	+	0.995735i	$0.529407\pi$
$230$	4.43509	0.292441
$231$	0	0
$232$	−5.84791	−0.383934
$233$	4.32693	0.283467	0.141733	−	0.989905i	$-0.454732\pi$
$233$	4.32693	0.283467	0.141733	+	0.989905i	$0.454732\pi$
$234$	0.0700674	0.00458045
$235$	3.07805	0.200790
$236$	2.69979	0.175741
$237$	−8.30174	−0.539256
$238$	0	0
$239$	11.9748	0.774586	0.387293	−	0.921957i	$-0.373410\pi$
$239$	11.9748	0.774586	0.387293	+	0.921957i	$0.373410\pi$
$240$	−3.86665	−0.249591
$241$	7.31756	0.471366	0.235683	−	0.971830i	$-0.424267\pi$
$241$	7.31756	0.471366	0.235683	+	0.971830i	$0.424267\pi$
$242$	−0.688892	−0.0442837
$243$	−13.9398	−0.894237
$244$	3.70471	0.237170
$245$	0	0
$246$	3.70471	0.236204
$247$	−0.433085	−0.0275566
$248$	18.2034	1.15592
$249$	3.34614	0.212053
$250$	7.41726	0.469109
$251$	−22.6731	−1.43111	−0.715556	−	0.698556i	$-0.753826\pi$
$251$	−22.6731	−1.43111	−0.715556	+	0.698556i	$0.753826\pi$
$252$	0	0
$253$	2.78568	0.175134
$254$	−9.37778	−0.588415
$255$	−2.80642	−0.175745
$256$	−9.89829	−0.618643
$257$	6.22077	0.388041	0.194021	−	0.980997i	$-0.437847\pi$
$257$	6.22077	0.388041	0.194021	+	0.980997i	$0.437847\pi$
$258$	9.71456	0.604802
$259$	0	0
$260$	−0.235063	−0.0145780
$261$	3.67307	0.227357
$262$	14.4385	0.892013
$263$	9.78123	0.603137	0.301568	−	0.953445i	$-0.402490\pi$
$263$	9.78123	0.603137	0.301568	+	0.953445i	$0.402490\pi$
$264$	2.94914	0.181507
$265$	−28.3827	−1.74354
$266$	0	0
$267$	−10.2968	−0.630155
$268$	20.1891	1.23325
$269$	−13.5714	−0.827460	−0.413730	−	0.910400i	$-0.635774\pi$
$269$	−13.5714	−0.827460	−0.413730	+	0.910400i	$0.635774\pi$
$270$	−8.74912	−0.532454
$271$	−7.41927	−0.450689	−0.225344	−	0.974279i	$-0.572351\pi$
$271$	−7.41927	−0.450689	−0.225344	+	0.974279i	$0.572351\pi$
$272$	1.37778	0.0835404
$273$	0	0
$274$	11.8731	0.717280
$275$	−0.341219	−0.0205763
$276$	−5.16007	−0.310600
$277$	−20.8256	−1.25129	−0.625646	−	0.780107i	$-0.715164\pi$
$277$	−20.8256	−1.25129	−0.625646	+	0.780107i	$0.715164\pi$
$278$	4.80150	0.287975
$279$	−11.4336	−0.684509
$280$	0	0
$281$	11.5462	0.688787	0.344393	−	0.938825i	$-0.388085\pi$
$281$	11.5462	0.688787	0.344393	+	0.938825i	$0.388085\pi$
$282$	1.11414	0.0663461
$283$	23.6938	1.40845	0.704226	−	0.709976i	$-0.251294\pi$
$283$	23.6938	1.40845	0.704226	+	0.709976i	$0.251294\pi$
$284$	1.62714	0.0965529
$285$	18.2286	1.07977
$286$	0.0459330	0.00271607
$287$	0	0
$288$	8.85728	0.521920
$289$	1.00000	0.0588235
$290$	3.83362	0.225118
$291$	−9.51606	−0.557841
$292$	−2.72393	−0.159406
$293$	4.94914	0.289132	0.144566	−	0.989495i	$-0.453821\pi$
$293$	4.94914	0.289132	0.144566	+	0.989495i	$0.453821\pi$
$294$	0	0
$295$	−4.09033	−0.238148
$296$	18.0919	1.05157
$297$	−5.49532	−0.318871
$298$	8.51606	0.493322
$299$	−0.185740	−0.0107416
$300$	0.632060	0.0364920
$301$	0	0
$302$	−9.98571	−0.574613
$303$	−5.29682	−0.304294
$304$	−8.94914	−0.513269
$305$	−5.61285	−0.321391
$306$	1.05086	0.0600734
$307$	−6.45383	−0.368339	−0.184170	−	0.982894i	$-0.558960\pi$
$307$	−6.45383	−0.368339	−0.184170	+	0.982894i	$0.558960\pi$
$308$	0	0
$309$	−14.8746	−0.846188
$310$	−11.9333	−0.677767
$311$	−9.41927	−0.534118	−0.267059	−	0.963680i	$-0.586052\pi$
$311$	−9.41927	−0.534118	−0.267059	+	0.963680i	$0.586052\pi$
$312$	−0.196639	−0.0111325
$313$	−14.7812	−0.835485	−0.417742	−	0.908566i	$-0.637179\pi$
$313$	−14.7812	−0.835485	−0.417742	+	0.908566i	$0.637179\pi$
$314$	9.84146	0.555386
$315$	0	0
$316$	−10.4286	−0.586657
$317$	−13.8825	−0.779717	−0.389859	−	0.920875i	$-0.627476\pi$
$317$	−13.8825	−0.779717	−0.389859	+	0.920875i	$0.627476\pi$
$318$	−10.2735	−0.576109
$319$	2.40790	0.134816
$320$	2.87601	0.160774
$321$	14.5970	0.814727
$322$	0	0
$323$	−6.49532	−0.361409
$324$	3.19850	0.177694
$325$	0.0227513	0.00126202
$326$	−5.71456	−0.316500
$327$	17.1876	0.950476
$328$	10.7556	0.593877
$329$	0	0
$330$	−1.93332	−0.106426
$331$	−26.5812	−1.46104	−0.730518	−	0.682894i	$-0.760721\pi$
$331$	−26.5812	−1.46104	−0.730518	+	0.682894i	$0.760721\pi$
$332$	4.20342	0.230693
$333$	−11.3635	−0.622716
$334$	−7.71900	−0.422365
$335$	−30.5877	−1.67118
$336$	0	0
$337$	−10.6637	−0.580889	−0.290444	−	0.956892i	$-0.593803\pi$
$337$	−10.6637	−0.580889	−0.290444	+	0.956892i	$0.593803\pi$
$338$	8.95254	0.486954
$339$	−5.39700	−0.293125
$340$	−3.52543	−0.191193
$341$	−7.49532	−0.405894
$342$	−6.82564	−0.369088
$343$	0	0
$344$	28.2034	1.52063
$345$	7.81780	0.420896
$346$	−13.1526	−0.707086
$347$	27.0321	1.45116	0.725580	−	0.688138i	$-0.241572\pi$
$347$	27.0321	1.45116	0.725580	+	0.688138i	$0.241572\pi$
$348$	−4.46028	−0.239096
$349$	−2.79706	−0.149723	−0.0748615	−	0.997194i	$-0.523851\pi$
$349$	−2.79706	−0.149723	−0.0748615	+	0.997194i	$0.523851\pi$
$350$	0	0
$351$	0.366409	0.0195574
$352$	5.80642	0.309483
$353$	−18.7003	−0.995315	−0.497657	−	0.867374i	$-0.665806\pi$
$353$	−18.7003	−0.995315	−0.497657	+	0.867374i	$0.665806\pi$
$354$	−1.48055	−0.0786903
$355$	−2.46520	−0.130839
$356$	−12.9349	−0.685546
$357$	0	0
$358$	−16.3017	−0.861574
$359$	−26.0163	−1.37309	−0.686544	−	0.727088i	$-0.740873\pi$
$359$	−26.0163	−1.37309	−0.686544	+	0.727088i	$0.740873\pi$
$360$	−8.56199	−0.451257
$361$	23.1891	1.22048
$362$	−2.21432	−0.116382
$363$	−1.21432	−0.0637353
$364$	0	0
$365$	4.12690	0.216012
$366$	−2.03164	−0.106196
$367$	16.6479	0.869012	0.434506	−	0.900669i	$-0.356923\pi$
$367$	16.6479	0.869012	0.434506	+	0.900669i	$0.356923\pi$
$368$	−3.83807	−0.200073
$369$	−6.75557	−0.351681
$370$	−11.8602	−0.616582
$371$	0	0
$372$	13.8840	0.719852
$373$	5.77139	0.298831	0.149416	−	0.988774i	$-0.452261\pi$
$373$	5.77139	0.298831	0.149416	+	0.988774i	$0.452261\pi$
$374$	0.688892	0.0356218
$375$	13.0745	0.675165
$376$	3.23459	0.166811
$377$	−0.160550	−0.00826876
$378$	0	0
$379$	−17.2099	−0.884012	−0.442006	−	0.897012i	$-0.645733\pi$
$379$	−17.2099	−0.884012	−0.442006	+	0.897012i	$0.645733\pi$
$380$	22.8988	1.17468
$381$	−16.5303	−0.846875
$382$	−8.68889	−0.444562
$383$	18.5526	0.947995	0.473997	−	0.880526i	$-0.342811\pi$
$383$	18.5526	0.947995	0.473997	+	0.880526i	$0.342811\pi$
$384$	−13.0607	−0.666501
$385$	0	0
$386$	−3.46520	−0.176374
$387$	−17.7146	−0.900482
$388$	−11.9541	−0.606876
$389$	2.03657	0.103258	0.0516290	−	0.998666i	$-0.483559\pi$
$389$	2.03657	0.103258	0.0516290	+	0.998666i	$0.483559\pi$
$390$	0.128907	0.00652748
$391$	−2.78568	−0.140878
$392$	0	0
$393$	25.4509	1.28383
$394$	15.0781	0.759621
$395$	15.8000	0.794983
$396$	−2.32693	−0.116933
$397$	−25.9353	−1.30166	−0.650828	−	0.759225i	$-0.725578\pi$
$397$	−25.9353	−1.30166	−0.650828	+	0.759225i	$0.725578\pi$
$398$	10.8671	0.544720
$399$	0	0
$400$	0.470127	0.0235063
$401$	−1.55707	−0.0777564	−0.0388782	−	0.999244i	$-0.512378\pi$
$401$	−1.55707	−0.0777564	−0.0388782	+	0.999244i	$0.512378\pi$
$402$	−11.0716	−0.552201
$403$	0.499762	0.0248949
$404$	−6.65386	−0.331042
$405$	−4.84590	−0.240795
$406$	0	0
$407$	−7.44938	−0.369252
$408$	−2.94914	−0.146004
$409$	−12.4351	−0.614876	−0.307438	−	0.951568i	$-0.599472\pi$
$409$	−12.4351	−0.614876	−0.307438	+	0.951568i	$0.599472\pi$
$410$	−7.05086	−0.348217
$411$	20.9289	1.03235
$412$	−18.6855	−0.920569
$413$	0	0
$414$	−2.92735	−0.143871
$415$	−6.36842	−0.312613
$416$	−0.387152	−0.0189817
$417$	8.46367	0.414468
$418$	−4.47457	−0.218858
$419$	−23.8666	−1.16596	−0.582981	−	0.812486i	$-0.698114\pi$
$419$	−23.8666	−1.16596	−0.582981	+	0.812486i	$0.698114\pi$
$420$	0	0
$421$	4.54770	0.221641	0.110821	−	0.993840i	$-0.464652\pi$
$421$	4.54770	0.221641	0.110821	+	0.993840i	$0.464652\pi$
$422$	5.17436	0.251884
$423$	−2.03164	−0.0987819
$424$	−29.8261	−1.44848
$425$	0.341219	0.0165516
$426$	−0.892313	−0.0432327
$427$	0	0
$428$	18.3368	0.886341
$429$	0.0809666	0.00390911
$430$	−18.4889	−0.891612
$431$	−28.1225	−1.35461	−0.677305	−	0.735702i	$-0.736852\pi$
$431$	−28.1225	−1.35461	−0.677305	+	0.735702i	$0.736852\pi$
$432$	7.57136	0.364277
$433$	23.2623	1.11791	0.558956	−	0.829197i	$-0.311202\pi$
$433$	23.2623	1.11791	0.558956	+	0.829197i	$0.311202\pi$
$434$	0	0
$435$	6.75758	0.324001
$436$	21.5910	1.03402
$437$	18.0939	0.865547
$438$	1.49378	0.0713758
$439$	−25.8557	−1.23403	−0.617014	−	0.786952i	$-0.711658\pi$
$439$	−25.8557	−1.23403	−0.617014	+	0.786952i	$0.711658\pi$
$440$	−5.61285	−0.267582
$441$	0	0
$442$	−0.0459330	−0.00218481
$443$	−36.7101	−1.74415	−0.872075	−	0.489372i	$-0.837226\pi$
$443$	−36.7101	−1.74415	−0.872075	+	0.489372i	$0.837226\pi$
$444$	13.7989	0.654868
$445$	19.5970	0.928988
$446$	−13.1907	−0.624596
$447$	15.0114	0.710014
$448$	0	0
$449$	−25.1541	−1.18710	−0.593548	−	0.804799i	$-0.702273\pi$
$449$	−25.1541	−1.18710	−0.593548	+	0.804799i	$0.702273\pi$
$450$	0.358572	0.0169033
$451$	−4.42864	−0.208536
$452$	−6.77970	−0.318890
$453$	−17.6019	−0.827012
$454$	−10.4242	−0.489232
$455$	0	0
$456$	19.1556	0.897044
$457$	12.2701	0.573971	0.286985	−	0.957935i	$-0.407347\pi$
$457$	12.2701	0.573971	0.286985	+	0.957935i	$0.407347\pi$
$458$	1.92348	0.0898783
$459$	5.49532	0.256499
$460$	9.82071	0.457893
$461$	−26.1017	−1.21568	−0.607839	−	0.794060i	$-0.707963\pi$
$461$	−26.1017	−1.21568	−0.607839	+	0.794060i	$0.707963\pi$
$462$	0	0
$463$	20.4336	0.949628	0.474814	−	0.880086i	$-0.342515\pi$
$463$	20.4336	0.949628	0.474814	+	0.880086i	$0.342515\pi$
$464$	−3.31756	−0.154014
$465$	−21.0350	−0.975476
$466$	−2.98079	−0.138082
$467$	41.5259	1.92159	0.960795	−	0.277260i	$-0.0894264\pi$
$467$	41.5259	1.92159	0.960795	+	0.277260i	$0.0894264\pi$
$468$	0.155152	0.00717189
$469$	0	0
$470$	−2.12045	−0.0978089
$471$	17.3477	0.799339
$472$	−4.29835	−0.197848
$473$	−11.6128	−0.533959
$474$	5.71900	0.262683
$475$	−2.21633	−0.101692
$476$	0	0
$477$	18.7338	0.857760
$478$	−8.24935	−0.377317
$479$	−14.9304	−0.682188	−0.341094	−	0.940029i	$-0.610797\pi$
$479$	−14.9304	−0.682188	−0.341094	+	0.940029i	$0.610797\pi$
$480$	16.2953	0.743775
$481$	0.496699	0.0226475
$482$	−5.04101	−0.229612
$483$	0	0
$484$	−1.52543	−0.0693376
$485$	18.1111	0.822382
$486$	9.60300	0.435601
$487$	−22.9476	−1.03986	−0.519928	−	0.854210i	$-0.674041\pi$
$487$	−22.9476	−1.03986	−0.519928	+	0.854210i	$0.674041\pi$
$488$	−5.89829	−0.267003
$489$	−10.0731	−0.455523
$490$	0	0
$491$	−19.7527	−0.891425	−0.445712	−	0.895176i	$-0.647050\pi$
$491$	−19.7527	−0.891425	−0.445712	+	0.895176i	$0.647050\pi$
$492$	8.20342	0.369839
$493$	−2.40790	−0.108446
$494$	0.298349	0.0134234
$495$	3.52543	0.158456
$496$	10.3269	0.463693
$497$	0	0
$498$	−2.30513	−0.103295
$499$	−9.43356	−0.422304	−0.211152	−	0.977453i	$-0.567722\pi$
$499$	−9.43356	−0.422304	−0.211152	+	0.977453i	$0.567722\pi$
$500$	16.4242	0.734512
$501$	−13.6064	−0.607889
$502$	15.6193	0.697124
$503$	−14.3763	−0.641005	−0.320503	−	0.947248i	$-0.603852\pi$
$503$	−14.3763	−0.641005	−0.320503	+	0.947248i	$0.603852\pi$
$504$	0	0
$505$	10.0810	0.448597
$506$	−1.91903	−0.0853114
$507$	15.7808	0.700848
$508$	−20.7654	−0.921316
$509$	31.6766	1.40404	0.702021	−	0.712157i	$-0.252281\pi$
$509$	31.6766	1.40404	0.702021	+	0.712157i	$0.252281\pi$
$510$	1.93332	0.0856090
$511$	0	0
$512$	−14.6923	−0.649313
$513$	−35.6938	−1.57592
$514$	−4.28544	−0.189023
$515$	28.3096	1.24747
$516$	21.5111	0.946975
$517$	−1.33185	−0.0585748
$518$	0	0
$519$	−23.1842	−1.01767
$520$	0.374245	0.0164117
$521$	20.9748	0.918923	0.459462	−	0.888198i	$-0.348042\pi$
$521$	20.9748	0.918923	0.459462	+	0.888198i	$0.348042\pi$
$522$	−2.53035	−0.110750
$523$	6.91750	0.302481	0.151241	−	0.988497i	$-0.451673\pi$
$523$	6.91750	0.302481	0.151241	+	0.988497i	$0.451673\pi$
$524$	31.9714	1.39668
$525$	0	0
$526$	−6.73822	−0.293800
$527$	7.49532	0.326501
$528$	1.67307	0.0728111
$529$	−15.2400	−0.662608
$530$	19.5526	0.849312
$531$	2.69979	0.117161
$532$	0	0
$533$	0.295286	0.0127903
$534$	7.09340	0.306961
$535$	−27.7812	−1.20109
$536$	−32.1432	−1.38837
$537$	−28.7353	−1.24002
$538$	9.34920	0.403073
$539$	0	0
$540$	−19.3733	−0.833696
$541$	12.5096	0.537830	0.268915	−	0.963164i	$-0.413335\pi$
$541$	12.5096	0.537830	0.268915	+	0.963164i	$0.413335\pi$
$542$	5.11108	0.219540
$543$	−3.90321	−0.167503
$544$	−5.80642	−0.248948
$545$	−32.7116	−1.40121
$546$	0	0
$547$	−8.35752	−0.357342	−0.178671	−	0.983909i	$-0.557180\pi$
$547$	−8.35752	−0.357342	−0.178671	+	0.983909i	$0.557180\pi$
$548$	26.2908	1.12309
$549$	3.70471	0.158113
$550$	0.235063	0.0100231
$551$	15.6400	0.666288
$552$	8.21537	0.349670
$553$	0	0
$554$	14.3466	0.609529
$555$	−20.9061	−0.887416
$556$	10.6321	0.450900
$557$	−27.1427	−1.15007	−0.575037	−	0.818127i	$-0.695012\pi$
$557$	−27.1427	−1.15007	−0.575037	+	0.818127i	$0.695012\pi$
$558$	7.87649	0.333438
$559$	0.774305	0.0327496
$560$	0	0
$561$	1.21432	0.0512686
$562$	−7.95407	−0.335522
$563$	−12.5239	−0.527819	−0.263910	−	0.964547i	$-0.585012\pi$
$563$	−12.5239	−0.527819	−0.263910	+	0.964547i	$0.585012\pi$
$564$	2.46706	0.103882
$565$	10.2716	0.432131
$566$	−16.3225	−0.686085
$567$	0	0
$568$	−2.59057	−0.108698
$569$	−3.14272	−0.131750	−0.0658749	−	0.997828i	$-0.520984\pi$
$569$	−3.14272	−0.131750	−0.0658749	+	0.997828i	$0.520984\pi$
$570$	−12.5575	−0.525978
$571$	−26.9195	−1.12655	−0.563273	−	0.826271i	$-0.690458\pi$
$571$	−26.9195	−1.12655	−0.563273	+	0.826271i	$0.690458\pi$
$572$	0.101710	0.00425272
$573$	−15.3160	−0.639836
$574$	0	0
$575$	−0.950528	−0.0396398
$576$	−1.89829	−0.0790954
$577$	−34.0607	−1.41797	−0.708983	−	0.705226i	$-0.750846\pi$
$577$	−34.0607	−1.41797	−0.708983	+	0.705226i	$0.750846\pi$
$578$	−0.688892	−0.0286541
$579$	−6.10816	−0.253847
$580$	8.48886	0.352481
$581$	0	0
$582$	6.55554	0.271736
$583$	12.2810	0.508627
$584$	4.33677	0.179457
$585$	−0.235063	−0.00971867
$586$	−3.40943	−0.140842
$587$	−23.0464	−0.951227	−0.475614	−	0.879654i	$-0.657774\pi$
$587$	−23.0464	−0.951227	−0.475614	+	0.879654i	$0.657774\pi$
$588$	0	0
$589$	−48.6844	−2.00601
$590$	2.81780	0.116007
$591$	26.5783	1.09328
$592$	10.2636	0.421833
$593$	16.9427	0.695753	0.347876	−	0.937540i	$-0.386903\pi$
$593$	16.9427	0.695753	0.347876	+	0.937540i	$0.386903\pi$
$594$	3.78568	0.155328
$595$	0	0
$596$	18.8573	0.772424
$597$	19.1556	0.783988
$598$	0.127955	0.00523245
$599$	−32.8528	−1.34233	−0.671165	−	0.741308i	$-0.734206\pi$
$599$	−32.8528	−1.34233	−0.671165	+	0.741308i	$0.734206\pi$
$600$	−1.00631	−0.0410822
$601$	13.9496	0.569017	0.284508	−	0.958674i	$-0.408170\pi$
$601$	13.9496	0.569017	0.284508	+	0.958674i	$0.408170\pi$
$602$	0	0
$603$	20.1891	0.822165
$604$	−22.1116	−0.899706
$605$	2.31111	0.0939599
$606$	3.64894	0.148228
$607$	−31.3274	−1.27154	−0.635770	−	0.771878i	$-0.719317\pi$
$607$	−31.3274	−1.27154	−0.635770	+	0.771878i	$0.719317\pi$
$608$	37.7146	1.52953
$609$	0	0
$610$	3.86665	0.156556
$611$	0.0888033	0.00359260
$612$	2.32693	0.0940605
$613$	−39.2355	−1.58471	−0.792354	−	0.610061i	$-0.791145\pi$
$613$	−39.2355	−1.58471	−0.792354	+	0.610061i	$0.791145\pi$
$614$	4.44599	0.179426
$615$	−12.4286	−0.501171
$616$	0	0
$617$	−10.1748	−0.409624	−0.204812	−	0.978801i	$-0.565658\pi$
$617$	−10.1748	−0.409624	−0.204812	+	0.978801i	$0.565658\pi$
$618$	10.2470	0.412195
$619$	23.6702	0.951384	0.475692	−	0.879612i	$-0.342198\pi$
$619$	23.6702	0.951384	0.475692	+	0.879612i	$0.342198\pi$
$620$	−26.4242	−1.06122
$621$	−15.3082	−0.614297
$622$	6.48886	0.260180
$623$	0	0
$624$	−0.111555	−0.00446576
$625$	−26.5897	−1.06359
$626$	10.1827	0.406982
$627$	−7.88739	−0.314992
$628$	21.7921	0.869601
$629$	7.44938	0.297026
$630$	0	0
$631$	35.6450	1.41900	0.709502	−	0.704704i	$-0.248920\pi$
$631$	35.6450	1.41900	0.709502	+	0.704704i	$0.248920\pi$
$632$	16.6035	0.660451
$633$	9.12092	0.362524
$634$	9.56352	0.379816
$635$	31.4608	1.24848
$636$	−22.7488	−0.902048
$637$	0	0
$638$	−1.65878	−0.0656718
$639$	1.62714	0.0643686
$640$	24.8573	0.982570
$641$	32.0114	1.26437	0.632187	−	0.774816i	$-0.282158\pi$
$641$	32.0114	1.26437	0.632187	+	0.774816i	$0.282158\pi$
$642$	−10.0558	−0.396870
$643$	−14.2652	−0.562564	−0.281282	−	0.959625i	$-0.590760\pi$
$643$	−14.2652	−0.562564	−0.281282	+	0.959625i	$0.590760\pi$
$644$	0	0
$645$	−32.5906	−1.28325
$646$	4.47457	0.176050
$647$	−21.1704	−0.832294	−0.416147	−	0.909297i	$-0.636620\pi$
$647$	−21.1704	−0.832294	−0.416147	+	0.909297i	$0.636620\pi$
$648$	−5.09234	−0.200046
$649$	1.76986	0.0694730
$650$	−0.0156732	−0.000614754 0
$651$	0	0
$652$	−12.6539	−0.495563
$653$	0.882945	0.0345523	0.0172761	−	0.999851i	$-0.494501\pi$
$653$	0.882945	0.0345523	0.0172761	+	0.999851i	$0.494501\pi$
$654$	−11.8404	−0.462996
$655$	−48.4385	−1.89265
$656$	6.10171	0.238232
$657$	−2.72393	−0.106270
$658$	0	0
$659$	−21.4958	−0.837357	−0.418679	−	0.908134i	$-0.637507\pi$
$659$	−21.4958	−0.837357	−0.418679	+	0.908134i	$0.637507\pi$
$660$	−4.28100	−0.166638
$661$	−13.9951	−0.544345	−0.272173	−	0.962248i	$-0.587742\pi$
$661$	−13.9951	−0.544345	−0.272173	+	0.962248i	$0.587742\pi$
$662$	18.3116	0.711700
$663$	−0.0809666	−0.00314448
$664$	−6.69228	−0.259711
$665$	0	0
$666$	7.82822	0.303337
$667$	6.70763	0.259720
$668$	−17.0923	−0.661323
$669$	−23.2514	−0.898950
$670$	21.0716	0.814067
$671$	2.42864	0.0937566
$672$	0	0
$673$	−16.2973	−0.628215	−0.314107	−	0.949388i	$-0.601705\pi$
$673$	−16.2973	−0.628215	−0.314107	+	0.949388i	$0.601705\pi$
$674$	7.34614	0.282963
$675$	1.87511	0.0721729
$676$	19.8238	0.762453
$677$	−10.4681	−0.402322	−0.201161	−	0.979558i	$-0.564472\pi$
$677$	−10.4681	−0.402322	−0.201161	+	0.979558i	$0.564472\pi$
$678$	3.71795	0.142787
$679$	0	0
$680$	5.61285	0.215243
$681$	−18.3749	−0.704127
$682$	5.16346	0.197719
$683$	15.5625	0.595481	0.297741	−	0.954647i	$-0.403767\pi$
$683$	15.5625	0.595481	0.297741	+	0.954647i	$0.403767\pi$
$684$	−15.1141	−0.577904
$685$	−39.8321	−1.52191
$686$	0	0
$687$	3.39054	0.129357
$688$	16.0000	0.609994
$689$	−0.818854	−0.0311959
$690$	−5.38562	−0.205027
$691$	25.9940	0.988859	0.494430	−	0.869218i	$-0.335377\pi$
$691$	25.9940	0.988859	0.494430	+	0.869218i	$0.335377\pi$
$692$	−29.1240	−1.10713
$693$	0	0
$694$	−18.6222	−0.706890
$695$	−16.1082	−0.611017
$696$	7.10123	0.269172
$697$	4.42864	0.167747
$698$	1.92687	0.0729331
$699$	−5.25428	−0.198735
$700$	0	0
$701$	9.24443	0.349157	0.174579	−	0.984643i	$-0.444144\pi$
$701$	9.24443	0.349157	0.174579	+	0.984643i	$0.444144\pi$
$702$	−0.252416	−0.00952683
$703$	−48.3861	−1.82492
$704$	−1.24443	−0.0469013
$705$	−3.73774	−0.140771
$706$	12.8825	0.484838
$707$	0	0
$708$	−3.27841	−0.123210
$709$	−22.0114	−0.826655	−0.413327	−	0.910583i	$-0.635633\pi$
$709$	−22.0114	−0.826655	−0.413327	+	0.910583i	$0.635633\pi$
$710$	1.69826	0.0637346
$711$	−10.4286	−0.391105
$712$	20.5936	0.771779
$713$	−20.8796	−0.781945
$714$	0	0
$715$	−0.154097	−0.00576289
$716$	−36.0973	−1.34902
$717$	−14.5412	−0.543053
$718$	17.9224	0.668859
$719$	10.0618	0.375240	0.187620	−	0.982242i	$-0.439923\pi$
$719$	10.0618	0.375240	0.187620	+	0.982242i	$0.439923\pi$
$720$	−4.85728	−0.181020
$721$	0	0
$722$	−15.9748	−0.594521
$723$	−8.88586	−0.330469
$724$	−4.90321	−0.182226
$725$	−0.821621	−0.0305142
$726$	0.836535	0.0310467
$727$	−12.0607	−0.447307	−0.223653	−	0.974669i	$-0.571798\pi$
$727$	−12.0607	−0.447307	−0.223653	+	0.974669i	$0.571798\pi$
$728$	0	0
$729$	23.2177	0.859915
$730$	−2.84299	−0.105224
$731$	11.6128	0.429517
$732$	−4.49871	−0.166277
$733$	−22.2449	−0.821634	−0.410817	−	0.911718i	$-0.634757\pi$
$733$	−22.2449	−0.821634	−0.410817	+	0.911718i	$0.634757\pi$
$734$	−11.4686	−0.423314
$735$	0	0
$736$	16.1748	0.596213
$737$	13.2351	0.487520
$738$	4.65386	0.171311
$739$	15.2924	0.562539	0.281269	−	0.959629i	$-0.409245\pi$
$739$	15.2924	0.562539	0.281269	+	0.959629i	$0.409245\pi$
$740$	−26.2623	−0.965420
$741$	0.525904	0.0193196
$742$	0	0
$743$	49.4893	1.81559	0.907794	−	0.419417i	$-0.137765\pi$
$743$	49.4893	1.81559	0.907794	+	0.419417i	$0.137765\pi$
$744$	−22.1048	−0.810400
$745$	−28.5698	−1.04672
$746$	−3.97587	−0.145567
$747$	4.20342	0.153795
$748$	1.52543	0.0557752
$749$	0	0
$750$	−9.00693	−0.328887
$751$	−48.2005	−1.75886	−0.879431	−	0.476027i	$-0.842076\pi$
$751$	−48.2005	−1.75886	−0.879431	+	0.476027i	$0.842076\pi$
$752$	1.83500	0.0669157
$753$	27.5324	1.00333
$754$	0.110602	0.00402788
$755$	33.5002	1.21920
$756$	0	0
$757$	−21.1842	−0.769953	−0.384977	−	0.922926i	$-0.625790\pi$
$757$	−21.1842	−0.769953	−0.384977	+	0.922926i	$0.625790\pi$
$758$	11.8557	0.430620
$759$	−3.38271	−0.122784
$760$	−36.4572	−1.32244
$761$	−12.0350	−0.436270	−0.218135	−	0.975919i	$-0.569997\pi$
$761$	−12.0350	−0.436270	−0.218135	+	0.975919i	$0.569997\pi$
$762$	11.3876	0.412530
$763$	0	0
$764$	−19.2400	−0.696078
$765$	−3.52543	−0.127462
$766$	−12.7808	−0.461788
$767$	−0.118008	−0.00426102
$768$	12.0197	0.433723
$769$	−32.7467	−1.18088	−0.590438	−	0.807083i	$-0.701045\pi$
$769$	−32.7467	−1.18088	−0.590438	+	0.807083i	$0.701045\pi$
$770$	0	0
$771$	−7.55401	−0.272051
$772$	−7.67307	−0.276160
$773$	−6.60793	−0.237671	−0.118835	−	0.992914i	$-0.537916\pi$
$773$	−6.60793	−0.237671	−0.118835	+	0.992914i	$0.537916\pi$
$774$	12.2034	0.438643
$775$	2.55755	0.0918698
$776$	19.0321	0.683213
$777$	0	0
$778$	−1.40297	−0.0502990
$779$	−28.7654	−1.03063
$780$	0.285442	0.0102205
$781$	1.06668	0.0381687
$782$	1.91903	0.0686245
$783$	−13.2321	−0.472878
$784$	0	0
$785$	−33.0163	−1.17840
$786$	−17.5329	−0.625379
$787$	23.8084	0.848679	0.424339	−	0.905503i	$-0.360506\pi$
$787$	23.8084	0.848679	0.424339	+	0.905503i	$0.360506\pi$
$788$	33.3876	1.18939
$789$	−11.8775	−0.422852
$790$	−10.8845	−0.387252
$791$	0	0
$792$	3.70471	0.131641
$793$	−0.161933	−0.00575042
$794$	17.8666	0.634064
$795$	34.4657	1.22237
$796$	24.0633	0.852901
$797$	31.7783	1.12565	0.562823	−	0.826577i	$-0.309715\pi$
$797$	31.7783	1.12565	0.562823	+	0.826577i	$0.309715\pi$
$798$	0	0
$799$	1.33185	0.0471175
$800$	−1.98126	−0.0700483
$801$	−12.9349	−0.457031
$802$	1.07265	0.0378767
$803$	−1.78568	−0.0630153
$804$	−24.5161	−0.864615
$805$	0	0
$806$	−0.344282	−0.0121268
$807$	16.4800	0.580122
$808$	10.5936	0.372683
$809$	−32.2242	−1.13294	−0.566471	−	0.824082i	$-0.691692\pi$
$809$	−32.2242	−1.13294	−0.566471	+	0.824082i	$0.691692\pi$
$810$	3.33830	0.117296
$811$	1.36689	0.0479978	0.0239989	−	0.999712i	$-0.492360\pi$
$811$	1.36689	0.0479978	0.0239989	+	0.999712i	$0.492360\pi$
$812$	0	0
$813$	9.00937	0.315972
$814$	5.13182	0.179870
$815$	19.1713	0.671541
$816$	−1.67307	−0.0585692
$817$	−75.4291	−2.63893
$818$	8.56644	0.299518
$819$	0	0
$820$	−15.6128	−0.545224
$821$	20.4780	0.714686	0.357343	−	0.933973i	$-0.383683\pi$
$821$	20.4780	0.714686	0.357343	+	0.933973i	$0.383683\pi$
$822$	−14.4177	−0.502876
$823$	52.2835	1.82249	0.911244	−	0.411867i	$-0.135123\pi$
$823$	52.2835	1.82249	0.911244	+	0.411867i	$0.135123\pi$
$824$	29.7493	1.03636
$825$	0.414349	0.0144258
$826$	0	0
$827$	0.956981	0.0332775	0.0166388	−	0.999862i	$-0.494703\pi$
$827$	0.956981	0.0332775	0.0166388	+	0.999862i	$0.494703\pi$
$828$	−6.48208	−0.225268
$829$	40.8894	1.42015	0.710074	−	0.704127i	$-0.248662\pi$
$829$	40.8894	1.42015	0.710074	+	0.704127i	$0.248662\pi$
$830$	4.38715	0.152280
$831$	25.2890	0.877265
$832$	0.0829744	0.00287662
$833$	0	0
$834$	−5.83056	−0.201896
$835$	25.8959	0.896163
$836$	−9.90813	−0.342680
$837$	41.1891	1.42370
$838$	16.4415	0.567964
$839$	22.3067	0.770111	0.385056	−	0.922893i	$-0.374182\pi$
$839$	22.3067	0.770111	0.385056	+	0.922893i	$0.374182\pi$
$840$	0	0
$841$	−23.2020	−0.800070
$842$	−3.13288	−0.107966
$843$	−14.0207	−0.482900
$844$	11.4577	0.394390
$845$	−30.0341	−1.03321
$846$	1.39958	0.0481187
$847$	0	0
$848$	−16.9206	−0.581055
$849$	−28.7719	−0.987448
$850$	−0.235063	−0.00806261
$851$	−20.7516	−0.711356
$852$	−1.97587	−0.0676920
$853$	−24.6242	−0.843117	−0.421559	−	0.906801i	$-0.638517\pi$
$853$	−24.6242	−0.843117	−0.421559	+	0.906801i	$0.638517\pi$
$854$	0	0
$855$	22.8988	0.783121
$856$	−29.1941	−0.997832
$857$	5.50024	0.187885	0.0939423	−	0.995578i	$-0.470053\pi$
$857$	5.50024	0.187885	0.0939423	+	0.995578i	$0.470053\pi$
$858$	−0.0557773	−0.00190421
$859$	35.2208	1.20172	0.600859	−	0.799355i	$-0.294825\pi$
$859$	35.2208	1.20172	0.600859	+	0.799355i	$0.294825\pi$
$860$	−40.9403	−1.39605
$861$	0	0
$862$	19.3733	0.659859
$863$	3.17976	0.108240	0.0541202	−	0.998534i	$-0.482765\pi$
$863$	3.17976	0.108240	0.0541202	+	0.998534i	$0.482765\pi$
$864$	−31.9081	−1.08554
$865$	44.1245	1.50028
$866$	−16.0252	−0.544558
$867$	−1.21432	−0.0412405
$868$	0	0
$869$	−6.83654	−0.231914
$870$	−4.65524	−0.157827
$871$	−0.882468	−0.0299013
$872$	−34.3752	−1.16409
$873$	−11.9541	−0.404584
$874$	−12.4647	−0.421626
$875$	0	0
$876$	3.30772	0.111757
$877$	−50.4623	−1.70399	−0.851995	−	0.523550i	$-0.824607\pi$
$877$	−50.4623	−1.70399	−0.851995	+	0.523550i	$0.824607\pi$
$878$	17.8118	0.601120
$879$	−6.00984	−0.202707
$880$	−3.18421	−0.107340
$881$	18.3526	0.618315	0.309157	−	0.951011i	$-0.399953\pi$
$881$	18.3526	0.618315	0.309157	+	0.951011i	$0.399953\pi$
$882$	0	0
$883$	16.8573	0.567293	0.283646	−	0.958929i	$-0.408456\pi$
$883$	16.8573	0.567293	0.283646	+	0.958929i	$0.408456\pi$
$884$	−0.101710	−0.00342089
$885$	4.96697	0.166963
$886$	25.2893	0.849611
$887$	39.6829	1.33242	0.666211	−	0.745763i	$-0.267915\pi$
$887$	39.6829	1.33242	0.666211	+	0.745763i	$0.267915\pi$
$888$	−21.9693	−0.737242
$889$	0	0
$890$	−13.5002	−0.452529
$891$	2.09679	0.0702450
$892$	−29.2083	−0.977968
$893$	−8.65080	−0.289488
$894$	−10.3412	−0.345862
$895$	54.6894	1.82806
$896$	0	0
$897$	0.225547	0.00753080
$898$	17.3285	0.578258
$899$	−18.0479	−0.601933
$900$	0.793993	0.0264664
$901$	−12.2810	−0.409139
$902$	3.05086	0.101582
$903$	0	0
$904$	10.7940	0.359003
$905$	7.42864	0.246936
$906$	12.1258	0.402854
$907$	8.94025	0.296856	0.148428	−	0.988923i	$-0.452579\pi$
$907$	8.94025	0.296856	0.148428	+	0.988923i	$0.452579\pi$
$908$	−23.0825	−0.766020
$909$	−6.65386	−0.220695
$910$	0	0
$911$	−50.5861	−1.67599	−0.837997	−	0.545675i	$-0.816273\pi$
$911$	−50.5861	−1.67599	−0.837997	+	0.545675i	$0.816273\pi$
$912$	10.8671	0.359846
$913$	2.75557	0.0911960
$914$	−8.45277	−0.279593
$915$	6.81579	0.225323
$916$	4.25920	0.140728
$917$	0	0
$918$	−3.78568	−0.124946
$919$	−42.1718	−1.39112	−0.695559	−	0.718469i	$-0.744843\pi$
$919$	−42.1718	−1.39112	−0.695559	+	0.718469i	$0.744843\pi$
$920$	−15.6356	−0.515490
$921$	7.83701	0.258238
$922$	17.9813	0.592181
$923$	−0.0711223	−0.00234102
$924$	0	0
$925$	2.54187	0.0835763
$926$	−14.0765	−0.462583
$927$	−18.6855	−0.613712
$928$	13.9813	0.458957
$929$	−57.6040	−1.88992	−0.944962	−	0.327179i	$-0.893902\pi$
$929$	−57.6040	−1.88992	−0.944962	+	0.327179i	$0.893902\pi$
$930$	14.4909	0.475174
$931$	0	0
$932$	−6.60042	−0.216204
$933$	11.4380	0.374464
$934$	−28.6069	−0.936045
$935$	−2.31111	−0.0755813
$936$	−0.247018	−0.00807402
$937$	32.7273	1.06915	0.534577	−	0.845120i	$-0.320471\pi$
$937$	32.7273	1.06915	0.534577	+	0.845120i	$0.320471\pi$
$938$	0	0
$939$	17.9491	0.585748
$940$	−4.69535	−0.153145
$941$	−25.6543	−0.836307	−0.418154	−	0.908376i	$-0.637323\pi$
$941$	−25.6543	−0.836307	−0.418154	+	0.908376i	$0.637323\pi$
$942$	−11.9507	−0.389374
$943$	−12.3368	−0.401741
$944$	−2.43848	−0.0793659
$945$	0	0
$946$	8.00000	0.260102
$947$	−44.7782	−1.45510	−0.727548	−	0.686057i	$-0.759340\pi$
$947$	−44.7782	−1.45510	−0.727548	+	0.686057i	$0.759340\pi$
$948$	12.6637	0.411298
$949$	0.119063	0.00386495
$950$	1.52681	0.0495363
$951$	16.8578	0.546650
$952$	0	0
$953$	−9.22570	−0.298850	−0.149425	−	0.988773i	$-0.547742\pi$
$953$	−9.22570	−0.298850	−0.149425	+	0.988773i	$0.547742\pi$
$954$	−12.9055	−0.417833
$955$	29.1497	0.943261
$956$	−18.2667	−0.590787
$957$	−2.92396	−0.0945181
$958$	10.2854	0.332308
$959$	0	0
$960$	−3.49240	−0.112717
$961$	25.1798	0.812250
$962$	−0.342172	−0.0110321
$963$	18.3368	0.590894
$964$	−11.1624	−0.359517
$965$	11.6251	0.374226
$966$	0	0
$967$	−0.0162978	−0.000524103 0	−0.000262051	−	1.00000i	$-0.500083\pi$
$967$	−0.0162978	−0.000524103 0	−0.000262051		1.00000i	$0.500083\pi$
$968$	2.42864	0.0780594
$969$	7.88739	0.253379
$970$	−12.4766	−0.400599
$971$	−29.3225	−0.941003	−0.470502	−	0.882399i	$-0.655927\pi$
$971$	−29.3225	−0.941003	−0.470502	+	0.882399i	$0.655927\pi$
$972$	21.2641	0.682047
$973$	0	0
$974$	15.8084	0.506535
$975$	−0.0276274	−0.000884784 0
$976$	−3.34614	−0.107107
$977$	−7.72837	−0.247253	−0.123626	−	0.992329i	$-0.539452\pi$
$977$	−7.72837	−0.247253	−0.123626	+	0.992329i	$0.539452\pi$
$978$	6.93930	0.221894
$979$	−8.47949	−0.271006
$980$	0	0
$981$	21.5910	0.689349
$982$	13.6074	0.434231
$983$	7.06668	0.225392	0.112696	−	0.993630i	$-0.464051\pi$
$983$	7.06668	0.225392	0.112696	+	0.993630i	$0.464051\pi$
$984$	−13.0607	−0.416360
$985$	−50.5841	−1.61174
$986$	1.65878	0.0528263
$987$	0	0
$988$	0.660640	0.0210178
$989$	−32.3497	−1.02866
$990$	−2.42864	−0.0771872
$991$	−6.06022	−0.192509	−0.0962547	−	0.995357i	$-0.530686\pi$
$991$	−6.06022	−0.192509	−0.0962547	+	0.995357i	$0.530686\pi$
$992$	−43.5210	−1.38179
$993$	32.2781	1.02431
$994$	0	0
$995$	−36.4572	−1.15577
$996$	−5.10430	−0.161736
$997$	−30.7447	−0.973693	−0.486847	−	0.873487i	$-0.661853\pi$
$997$	−30.7447	−0.973693	−0.486847	+	0.873487i	$0.661853\pi$
$998$	6.49871	0.205713
$999$	40.9367	1.29518

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9163.2.a.j.1.2		3
7.6	odd	2		187.2.a.e.1.2	✓	3
21.20	even	2		1683.2.a.v.1.2		3
28.27	even	2		2992.2.a.r.1.1		3
35.34	odd	2		4675.2.a.bc.1.2		3
77.76	even	2		2057.2.a.p.1.2		3
119.118	odd	2		3179.2.a.t.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.a.e.1.2	✓	3	7.6	odd	2
1683.2.a.v.1.2		3	21.20	even	2
2057.2.a.p.1.2		3	77.76	even	2
2992.2.a.r.1.1		3	28.27	even	2
3179.2.a.t.1.2		3	119.118	odd	2
4675.2.a.bc.1.2		3	35.34	odd	2
9163.2.a.j.1.2		3	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:	\( N \)	\(=\)	\( 9163 = 7^{2} \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9163.a (trivial)

\(f(q)\)	\(=\)	\(q-0.688892 q^{2} -1.21432 q^{3} -1.52543 q^{4} +2.31111 q^{5} +0.836535 q^{6} +2.42864 q^{8} -1.52543 q^{9} +O(q^{10})\)	\(q-0.688892 q^{2} -1.21432 q^{3} -1.52543 q^{4} +2.31111 q^{5} +0.836535 q^{6} +2.42864 q^{8} -1.52543 q^{9} -1.59210 q^{10} -1.00000 q^{11} +1.85236 q^{12} +0.0666765 q^{13} -2.80642 q^{15} +1.37778 q^{16} +1.00000 q^{17} +1.05086 q^{18} -6.49532 q^{19} -3.52543 q^{20} +0.688892 q^{22} -2.78568 q^{23} -2.94914 q^{24} +0.341219 q^{25} -0.0459330 q^{26} +5.49532 q^{27} -2.40790 q^{29} +1.93332 q^{30} +7.49532 q^{31} -5.80642 q^{32} +1.21432 q^{33} -0.688892 q^{34} +2.32693 q^{36} +7.44938 q^{37} +4.47457 q^{38} -0.0809666 q^{39} +5.61285 q^{40} +4.42864 q^{41} +11.6128 q^{43} +1.52543 q^{44} -3.52543 q^{45} +1.91903 q^{46} +1.33185 q^{47} -1.67307 q^{48} -0.235063 q^{50} -1.21432 q^{51} -0.101710 q^{52} -12.2810 q^{53} -3.78568 q^{54} -2.31111 q^{55} +7.88739 q^{57} +1.65878 q^{58} -1.76986 q^{59} +4.28100 q^{60} -2.42864 q^{61} -5.16346 q^{62} +1.24443 q^{64} +0.154097 q^{65} -0.836535 q^{66} -13.2351 q^{67} -1.52543 q^{68} +3.38271 q^{69} -1.06668 q^{71} -3.70471 q^{72} +1.78568 q^{73} -5.13182 q^{74} -0.414349 q^{75} +9.90813 q^{76} +0.0557773 q^{78} +6.83654 q^{79} +3.18421 q^{80} -2.09679 q^{81} -3.05086 q^{82} -2.75557 q^{83} +2.31111 q^{85} -8.00000 q^{86} +2.92396 q^{87} -2.42864 q^{88} +8.47949 q^{89} +2.42864 q^{90} +4.24935 q^{92} -9.10171 q^{93} -0.917502 q^{94} -15.0114 q^{95} +7.05086 q^{96} +7.83654 q^{97} +1.52543 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 2 q^{2} + 3 q^{3} + 2 q^{4} + 7 q^{5} - 4 q^{6} - 6 q^{8} + 2 q^{9}+O(q^{10}) \) 3 * q - 2 * q^2 + 3 * q^3 + 2 * q^4 + 7 * q^5 - 4 * q^6 - 6 * q^8 + 2 * q^9	\( 3 q - 2 q^{2} + 3 q^{3} + 2 q^{4} + 7 q^{5} - 4 q^{6} - 6 q^{8} + 2 q^{9} + 2 q^{10} - 3 q^{11} + 12 q^{12} + 5 q^{15} + 4 q^{16} + 3 q^{17} - 10 q^{18} - 6 q^{19} - 4 q^{20} + 2 q^{22} - 15 q^{23} - 22 q^{24} + 8 q^{25} - 20 q^{26} + 3 q^{27} - 14 q^{29} + 6 q^{30} + 9 q^{31} - 4 q^{32} - 3 q^{33} - 2 q^{34} + 20 q^{36} - 11 q^{37} + 20 q^{38} + 6 q^{39} - 10 q^{40} + 8 q^{43} - 2 q^{44} - 4 q^{45} + 12 q^{46} - 16 q^{47} + 8 q^{48} + 26 q^{50} + 3 q^{51} + 26 q^{52} - 30 q^{53} - 18 q^{54} - 7 q^{55} + 4 q^{57} - 2 q^{58} + q^{59} + 6 q^{60} + 6 q^{61} - 22 q^{62} + 4 q^{64} - 20 q^{65} + 4 q^{66} - 13 q^{67} + 2 q^{68} - 23 q^{69} - 3 q^{71} - 24 q^{72} + 12 q^{73} + 4 q^{74} + 6 q^{75} - 10 q^{76} - 46 q^{78} + 14 q^{79} - 4 q^{80} - 13 q^{81} + 4 q^{82} - 8 q^{83} + 7 q^{85} - 24 q^{86} - 18 q^{87} + 6 q^{88} - q^{89} - 6 q^{90} - 20 q^{92} - q^{93} + 10 q^{94} + 2 q^{95} + 8 q^{96} + 17 q^{97} - 2 q^{99}+O(q^{100}) \) 3 * q - 2 * q^2 + 3 * q^3 + 2 * q^4 + 7 * q^5 - 4 * q^6 - 6 * q^8 + 2 * q^9 + 2 * q^10 - 3 * q^11 + 12 * q^12 + 5 * q^15 + 4 * q^16 + 3 * q^17 - 10 * q^18 - 6 * q^19 - 4 * q^20 + 2 * q^22 - 15 * q^23 - 22 * q^24 + 8 * q^25 - 20 * q^26 + 3 * q^27 - 14 * q^29 + 6 * q^30 + 9 * q^31 - 4 * q^32 - 3 * q^33 - 2 * q^34 + 20 * q^36 - 11 * q^37 + 20 * q^38 + 6 * q^39 - 10 * q^40 + 8 * q^43 - 2 * q^44 - 4 * q^45 + 12 * q^46 - 16 * q^47 + 8 * q^48 + 26 * q^50 + 3 * q^51 + 26 * q^52 - 30 * q^53 - 18 * q^54 - 7 * q^55 + 4 * q^57 - 2 * q^58 + q^59 + 6 * q^60 + 6 * q^61 - 22 * q^62 + 4 * q^64 - 20 * q^65 + 4 * q^66 - 13 * q^67 + 2 * q^68 - 23 * q^69 - 3 * q^71 - 24 * q^72 + 12 * q^73 + 4 * q^74 + 6 * q^75 - 10 * q^76 - 46 * q^78 + 14 * q^79 - 4 * q^80 - 13 * q^81 + 4 * q^82 - 8 * q^83 + 7 * q^85 - 24 * q^86 - 18 * q^87 + 6 * q^88 - q^89 - 6 * q^90 - 20 * q^92 - q^93 + 10 * q^94 + 2 * q^95 + 8 * q^96 + 17 * q^97 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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