LMFDB - Embedded newform 3381.2.a.bb.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3381,2,Mod(1,3381)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3381, 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("3381.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3381 = 3 \cdot 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3381.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:	$26.9974209234$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.62622704.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 5x^{4} + 13x^{3} + 9x^{2} - 5x - 2 $ x^6 - 3x^5 - 5x^4 + 13x^3 + 9x^2 - 5*x - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.311423$ of defining polynomial
Character	$\chi$	$=$	3381.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.31142 q^{2} +1.00000 q^{3} -0.280171 q^{4} -1.11850 q^{5} -1.31142 q^{6} +2.99027 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.31142 q^{2} +1.00000 q^{3} -0.280171 q^{4} -1.11850 q^{5} -1.31142 q^{6} +2.99027 q^{8} +1.00000 q^{9} +1.46683 q^{10} +2.92406 q^{11} -0.280171 q^{12} +0.149755 q^{13} -1.11850 q^{15} -3.36116 q^{16} -0.809030 q^{17} -1.31142 q^{18} -7.67167 q^{19} +0.313372 q^{20} -3.83468 q^{22} -1.00000 q^{23} +2.99027 q^{24} -3.74895 q^{25} -0.196392 q^{26} +1.00000 q^{27} +9.97665 q^{29} +1.46683 q^{30} -1.00760 q^{31} -1.57263 q^{32} +2.92406 q^{33} +1.06098 q^{34} -0.280171 q^{36} +4.97683 q^{37} +10.0608 q^{38} +0.149755 q^{39} -3.34462 q^{40} -10.2856 q^{41} -0.722617 q^{43} -0.819237 q^{44} -1.11850 q^{45} +1.31142 q^{46} -11.1260 q^{47} -3.36116 q^{48} +4.91646 q^{50} -0.809030 q^{51} -0.0419569 q^{52} -8.38177 q^{53} -1.31142 q^{54} -3.27057 q^{55} -7.67167 q^{57} -13.0836 q^{58} +6.45557 q^{59} +0.313372 q^{60} +8.06585 q^{61} +1.32139 q^{62} +8.78471 q^{64} -0.167501 q^{65} -3.83468 q^{66} +5.48069 q^{67} +0.226667 q^{68} -1.00000 q^{69} -15.6594 q^{71} +2.99027 q^{72} +14.3384 q^{73} -6.52673 q^{74} -3.74895 q^{75} +2.14938 q^{76} -0.196392 q^{78} +3.61793 q^{79} +3.75947 q^{80} +1.00000 q^{81} +13.4888 q^{82} +11.7089 q^{83} +0.904903 q^{85} +0.947656 q^{86} +9.97665 q^{87} +8.74372 q^{88} -12.2939 q^{89} +1.46683 q^{90} +0.280171 q^{92} -1.00760 q^{93} +14.5909 q^{94} +8.58079 q^{95} -1.57263 q^{96} +3.14045 q^{97} +2.92406 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} + 6 q^{3} + 7 q^{4} - 2 q^{5} - 3 q^{6} - 9 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 + 6 * q^3 + 7 * q^4 - 2 * q^5 - 3 * q^6 - 9 * q^8 + 6 * q^9	$ 6 q - 3 q^{2} + 6 q^{3} + 7 q^{4} - 2 q^{5} - 3 q^{6} - 9 q^{8} + 6 q^{9} - 8 q^{10} - 3 q^{11} + 7 q^{12} - 2 q^{15} + 5 q^{16} - 8 q^{17} - 3 q^{18} - 19 q^{19} + 24 q^{22} - 6 q^{23} - 9 q^{24} - 20 q^{26} + 6 q^{27} - 12 q^{29} - 8 q^{30} + 2 q^{31} - 41 q^{32} - 3 q^{33} - 2 q^{34} + 7 q^{36} - 10 q^{37} + 20 q^{38} - 22 q^{40} - 3 q^{41} - 2 q^{43} - 14 q^{44} - 2 q^{45} + 3 q^{46} - 7 q^{47} + 5 q^{48} + 17 q^{50} - 8 q^{51} + 44 q^{52} - 5 q^{53} - 3 q^{54} - 24 q^{55} - 19 q^{57} - 12 q^{58} - 21 q^{59} - 29 q^{61} - 10 q^{62} + 59 q^{64} - 18 q^{65} + 24 q^{66} + 16 q^{67} - 54 q^{68} - 6 q^{69} - 6 q^{71} - 9 q^{72} + 8 q^{73} - 16 q^{74} - 40 q^{76} - 20 q^{78} - 12 q^{79} + 78 q^{80} + 6 q^{81} - 44 q^{82} - 24 q^{83} + 10 q^{85} + 12 q^{86} - 12 q^{87} + 28 q^{88} - 18 q^{89} - 8 q^{90} - 7 q^{92} + 2 q^{93} + 8 q^{94} + 6 q^{95} - 41 q^{96} - 22 q^{97} - 3 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 + 6 * q^3 + 7 * q^4 - 2 * q^5 - 3 * q^6 - 9 * q^8 + 6 * q^9 - 8 * q^10 - 3 * q^11 + 7 * q^12 - 2 * q^15 + 5 * q^16 - 8 * q^17 - 3 * q^18 - 19 * q^19 + 24 * q^22 - 6 * q^23 - 9 * q^24 - 20 * q^26 + 6 * q^27 - 12 * q^29 - 8 * q^30 + 2 * q^31 - 41 * q^32 - 3 * q^33 - 2 * q^34 + 7 * q^36 - 10 * q^37 + 20 * q^38 - 22 * q^40 - 3 * q^41 - 2 * q^43 - 14 * q^44 - 2 * q^45 + 3 * q^46 - 7 * q^47 + 5 * q^48 + 17 * q^50 - 8 * q^51 + 44 * q^52 - 5 * q^53 - 3 * q^54 - 24 * q^55 - 19 * q^57 - 12 * q^58 - 21 * q^59 - 29 * q^61 - 10 * q^62 + 59 * q^64 - 18 * q^65 + 24 * q^66 + 16 * q^67 - 54 * q^68 - 6 * q^69 - 6 * q^71 - 9 * q^72 + 8 * q^73 - 16 * q^74 - 40 * q^76 - 20 * q^78 - 12 * q^79 + 78 * q^80 + 6 * q^81 - 44 * q^82 - 24 * q^83 + 10 * q^85 + 12 * q^86 - 12 * q^87 + 28 * q^88 - 18 * q^89 - 8 * q^90 - 7 * q^92 + 2 * q^93 + 8 * q^94 + 6 * q^95 - 41 * q^96 - 22 * q^97 - 3 * 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 $

$2$	−1.31142	−0.927316	−0.463658	−	0.886014i	$-0.653463\pi$
$2$	−1.31142	−0.927316	−0.463658	+	0.886014i	$0.653463\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.280171	−0.140085
$5$	−1.11850	−0.500210	−0.250105	−	0.968219i	$-0.580465\pi$
$5$	−1.11850	−0.500210	−0.250105	+	0.968219i	$0.580465\pi$
$6$	−1.31142	−0.535386
$7$	0	0
$7$	0	0
$8$	2.99027	1.05722
$9$	1.00000	0.333333
$10$	1.46683	0.463852
$11$	2.92406	0.881638	0.440819	−	0.897596i	$-0.354688\pi$
$11$	2.92406	0.881638	0.440819	+	0.897596i	$0.354688\pi$
$12$	−0.280171	−0.0808784
$13$	0.149755	0.0415345	0.0207672	−	0.999784i	$-0.493389\pi$
$13$	0.149755	0.0415345	0.0207672	+	0.999784i	$0.493389\pi$
$14$	0	0
$15$	−1.11850	−0.288796
$16$	−3.36116	−0.840291
$17$	−0.809030	−0.196219	−0.0981093	−	0.995176i	$-0.531279\pi$
$17$	−0.809030	−0.196219	−0.0981093	+	0.995176i	$0.531279\pi$
$18$	−1.31142	−0.309105
$19$	−7.67167	−1.76000	−0.880001	−	0.474972i	$-0.842458\pi$
$19$	−7.67167	−1.76000	−0.880001	+	0.474972i	$0.842458\pi$
$20$	0.313372	0.0700721
$21$	0	0
$22$	−3.83468	−0.817556
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	2.99027	0.610386
$25$	−3.74895	−0.749790
$26$	−0.196392	−0.0385156
$27$	1.00000	0.192450
$28$	0	0
$29$	9.97665	1.85262	0.926309	−	0.376765i	$-0.122964\pi$
$29$	9.97665	1.85262	0.926309	+	0.376765i	$0.122964\pi$
$30$	1.46683	0.267805
$31$	−1.00760	−0.180971	−0.0904854	−	0.995898i	$-0.528842\pi$
$31$	−1.00760	−0.180971	−0.0904854	+	0.995898i	$0.528842\pi$
$32$	−1.57263	−0.278005
$33$	2.92406	0.509014
$34$	1.06098	0.181957
$35$	0	0
$36$	−0.280171	−0.0466952
$37$	4.97683	0.818186	0.409093	−	0.912493i	$-0.365845\pi$
$37$	4.97683	0.818186	0.409093	+	0.912493i	$0.365845\pi$
$38$	10.0608	1.63208
$39$	0.149755	0.0239800
$40$	−3.34462	−0.528831
$41$	−10.2856	−1.60635	−0.803174	−	0.595744i	$-0.796857\pi$
$41$	−10.2856	−1.60635	−0.803174	+	0.595744i	$0.796857\pi$
$42$	0	0
$43$	−0.722617	−0.110198	−0.0550990	−	0.998481i	$-0.517547\pi$
$43$	−0.722617	−0.110198	−0.0550990	+	0.998481i	$0.517547\pi$
$44$	−0.819237	−0.123505
$45$	−1.11850	−0.166737
$46$	1.31142	0.193359
$47$	−11.1260	−1.62289	−0.811445	−	0.584428i	$-0.801319\pi$
$47$	−11.1260	−1.62289	−0.811445	+	0.584428i	$0.801319\pi$
$48$	−3.36116	−0.485142
$49$	0	0
$50$	4.91646	0.695292
$51$	−0.809030	−0.113287
$52$	−0.0419569	−0.00581838
$53$	−8.38177	−1.15132	−0.575662	−	0.817688i	$-0.695256\pi$
$53$	−8.38177	−1.15132	−0.575662	+	0.817688i	$0.695256\pi$
$54$	−1.31142	−0.178462
$55$	−3.27057	−0.441004
$56$	0	0
$57$	−7.67167	−1.01614
$58$	−13.0836	−1.71796
$59$	6.45557	0.840444	0.420222	−	0.907421i	$-0.361952\pi$
$59$	6.45557	0.840444	0.420222	+	0.907421i	$0.361952\pi$
$60$	0.313372	0.0404562
$61$	8.06585	1.03273	0.516363	−	0.856370i	$-0.327285\pi$
$61$	8.06585	1.03273	0.516363	+	0.856370i	$0.327285\pi$
$62$	1.32139	0.167817
$63$	0	0
$64$	8.78471	1.09809
$65$	−0.167501	−0.0207760
$66$	−3.83468	−0.472016
$67$	5.48069	0.669573	0.334787	−	0.942294i	$-0.391336\pi$
$67$	5.48069	0.669573	0.334787	+	0.942294i	$0.391336\pi$
$68$	0.226667	0.0274874
$69$	−1.00000	−0.120386
$70$	0	0
$71$	−15.6594	−1.85843	−0.929214	−	0.369542i	$-0.879515\pi$
$71$	−15.6594	−1.85843	−0.929214	+	0.369542i	$0.879515\pi$
$72$	2.99027	0.352406
$73$	14.3384	1.67819	0.839093	−	0.543989i	$-0.183087\pi$
$73$	14.3384	1.67819	0.839093	+	0.543989i	$0.183087\pi$
$74$	−6.52673	−0.758717
$75$	−3.74895	−0.432892
$76$	2.14938	0.246551
$77$	0	0
$78$	−0.196392	−0.0222370
$79$	3.61793	0.407049	0.203524	−	0.979070i	$-0.434760\pi$
$79$	3.61793	0.407049	0.203524	+	0.979070i	$0.434760\pi$
$80$	3.75947	0.420322
$81$	1.00000	0.111111
$82$	13.4888	1.48959
$83$	11.7089	1.28522	0.642608	−	0.766195i	$-0.277852\pi$
$83$	11.7089	1.28522	0.642608	+	0.766195i	$0.277852\pi$
$84$	0	0
$85$	0.904903	0.0981505
$86$	0.947656	0.102188
$87$	9.97665	1.06961
$88$	8.74372	0.932084
$89$	−12.2939	−1.30315	−0.651576	−	0.758584i	$-0.725892\pi$
$89$	−12.2939	−1.30315	−0.651576	+	0.758584i	$0.725892\pi$
$90$	1.46683	0.154617
$91$	0	0
$92$	0.280171	0.0292098
$93$	−1.00760	−0.104484
$94$	14.5909	1.50493
$95$	8.58079	0.880370
$96$	−1.57263	−0.160506
$97$	3.14045	0.318864	0.159432	−	0.987209i	$-0.449034\pi$
$97$	3.14045	0.318864	0.159432	+	0.987209i	$0.449034\pi$
$98$	0	0
$99$	2.92406	0.293879
$100$	1.05035	0.105035
$101$	−5.76282	−0.573422	−0.286711	−	0.958017i	$-0.592562\pi$
$101$	−5.76282	−0.573422	−0.286711	+	0.958017i	$0.592562\pi$
$102$	1.06098	0.105053
$103$	−16.5778	−1.63346	−0.816729	−	0.577021i	$-0.804215\pi$
$103$	−16.5778	−1.63346	−0.816729	+	0.577021i	$0.804215\pi$
$104$	0.447807	0.0439111
$105$	0	0
$106$	10.9920	1.06764
$107$	−13.8280	−1.33680	−0.668401	−	0.743802i	$-0.733021\pi$
$107$	−13.8280	−1.33680	−0.668401	+	0.743802i	$0.733021\pi$
$108$	−0.280171	−0.0269595
$109$	9.99774	0.957610	0.478805	−	0.877921i	$-0.341070\pi$
$109$	9.99774	0.957610	0.478805	+	0.877921i	$0.341070\pi$
$110$	4.28910	0.408950
$111$	4.97683	0.472380
$112$	0	0
$113$	10.9837	1.03326	0.516632	−	0.856207i	$-0.327185\pi$
$113$	10.9837	1.03326	0.516632	+	0.856207i	$0.327185\pi$
$114$	10.0608	0.942280
$115$	1.11850	0.104301
$116$	−2.79517	−0.259525
$117$	0.149755	0.0138448
$118$	−8.46599	−0.779357
$119$	0	0
$120$	−3.34462	−0.305321
$121$	−2.44987	−0.222715
$122$	−10.5777	−0.957664
$123$	−10.2856	−0.927426
$124$	0.282301	0.0253514
$125$	9.78573	0.875262
$126$	0	0
$127$	−12.7559	−1.13191	−0.565953	−	0.824438i	$-0.691491\pi$
$127$	−12.7559	−1.13191	−0.565953	+	0.824438i	$0.691491\pi$
$128$	−8.37520	−0.740270
$129$	−0.722617	−0.0636229
$130$	0.219665	0.0192659
$131$	0.615930	0.0538141	0.0269070	−	0.999638i	$-0.491434\pi$
$131$	0.615930	0.0538141	0.0269070	+	0.999638i	$0.491434\pi$
$132$	−0.819237	−0.0713054
$133$	0	0
$134$	−7.18750	−0.620906
$135$	−1.11850	−0.0962654
$136$	−2.41922	−0.207446
$137$	−16.2310	−1.38671	−0.693356	−	0.720596i	$-0.743868\pi$
$137$	−16.2310	−1.38671	−0.693356	+	0.720596i	$0.743868\pi$
$138$	1.31142	0.111636
$139$	−8.90783	−0.755552	−0.377776	−	0.925897i	$-0.623311\pi$
$139$	−8.90783	−0.755552	−0.377776	+	0.925897i	$0.623311\pi$
$140$	0	0
$141$	−11.1260	−0.936976
$142$	20.5361	1.72335
$143$	0.437892	0.0366184
$144$	−3.36116	−0.280097
$145$	−11.1589	−0.926698
$146$	−18.8037	−1.55621
$147$	0	0
$148$	−1.39436	−0.114616
$149$	−3.61251	−0.295949	−0.147974	−	0.988991i	$-0.547275\pi$
$149$	−3.61251	−0.295949	−0.147974	+	0.988991i	$0.547275\pi$
$150$	4.91646	0.401427
$151$	5.04852	0.410843	0.205422	−	0.978674i	$-0.434143\pi$
$151$	5.04852	0.410843	0.205422	+	0.978674i	$0.434143\pi$
$152$	−22.9403	−1.86071
$153$	−0.809030	−0.0654062
$154$	0	0
$155$	1.12701	0.0905233
$156$	−0.0419569	−0.00335924
$157$	0.291168	0.0232378	0.0116189	−	0.999932i	$-0.496302\pi$
$157$	0.291168	0.0232378	0.0116189	+	0.999932i	$0.496302\pi$
$158$	−4.74463	−0.377463
$159$	−8.38177	−0.664717
$160$	1.75899	0.139061
$161$	0	0
$162$	−1.31142	−0.103035
$163$	−0.121471	−0.00951437	−0.00475718	−	0.999989i	$-0.501514\pi$
$163$	−0.121471	−0.00951437	−0.00475718	+	0.999989i	$0.501514\pi$
$164$	2.88174	0.225026
$165$	−3.27057	−0.254614
$166$	−15.3553	−1.19180
$167$	−9.05647	−0.700811	−0.350406	−	0.936598i	$-0.613956\pi$
$167$	−9.05647	−0.700811	−0.350406	+	0.936598i	$0.613956\pi$
$168$	0	0
$169$	−12.9776	−0.998275
$170$	−1.18671	−0.0910165
$171$	−7.67167	−0.586667
$172$	0.202456	0.0154371
$173$	0.111943	0.00851085	0.00425542	−	0.999991i	$-0.498645\pi$
$173$	0.111943	0.00851085	0.00425542	+	0.999991i	$0.498645\pi$
$174$	−13.0836	−0.991866
$175$	0	0
$176$	−9.82824	−0.740832
$177$	6.45557	0.485231
$178$	16.1225	1.20843
$179$	−9.54348	−0.713313	−0.356657	−	0.934236i	$-0.616083\pi$
$179$	−9.54348	−0.713313	−0.356657	+	0.934236i	$0.616083\pi$
$180$	0.313372	0.0233574
$181$	−22.8003	−1.69474	−0.847368	−	0.531007i	$-0.821814\pi$
$181$	−22.8003	−1.69474	−0.847368	+	0.531007i	$0.821814\pi$
$182$	0	0
$183$	8.06585	0.596245
$184$	−2.99027	−0.220445
$185$	−5.56660	−0.409265
$186$	1.32139	0.0968892
$187$	−2.36565	−0.172994
$188$	3.11718	0.227343
$189$	0	0
$190$	−11.2530	−0.816381
$191$	−2.09857	−0.151847	−0.0759236	−	0.997114i	$-0.524191\pi$
$191$	−2.09857	−0.151847	−0.0759236	+	0.997114i	$0.524191\pi$
$192$	8.78471	0.633982
$193$	11.3334	0.815797	0.407899	−	0.913027i	$-0.366262\pi$
$193$	11.3334	0.815797	0.407899	+	0.913027i	$0.366262\pi$
$194$	−4.11846	−0.295688
$195$	−0.167501	−0.0119950
$196$	0	0
$197$	−2.20393	−0.157024	−0.0785118	−	0.996913i	$-0.525017\pi$
$197$	−2.20393	−0.157024	−0.0785118	+	0.996913i	$0.525017\pi$
$198$	−3.83468	−0.272519
$199$	−13.1021	−0.928781	−0.464391	−	0.885631i	$-0.653727\pi$
$199$	−13.1021	−0.928781	−0.464391	+	0.885631i	$0.653727\pi$
$200$	−11.2104	−0.792693
$201$	5.48069	0.386578
$202$	7.55749	0.531743
$203$	0	0
$204$	0.226667	0.0158698
$205$	11.5045	0.803511
$206$	21.7405	1.51473
$207$	−1.00000	−0.0695048
$208$	−0.503350	−0.0349010
$209$	−22.4324	−1.55168
$210$	0	0
$211$	22.4409	1.54490	0.772449	−	0.635077i	$-0.219032\pi$
$211$	22.4409	1.54490	0.772449	+	0.635077i	$0.219032\pi$
$212$	2.34833	0.161284
$213$	−15.6594	−1.07296
$214$	18.1343	1.23964
$215$	0.808249	0.0551221
$216$	2.99027	0.203462
$217$	0	0
$218$	−13.1113	−0.888007
$219$	14.3384	0.968901
$220$	0.916319	0.0617782
$221$	−0.121156	−0.00814984
$222$	−6.52673	−0.438045
$223$	−27.1627	−1.81895	−0.909474	−	0.415761i	$-0.863515\pi$
$223$	−27.1627	−1.81895	−0.909474	+	0.415761i	$0.863515\pi$
$224$	0	0
$225$	−3.74895	−0.249930
$226$	−14.4043	−0.958162
$227$	−6.31421	−0.419089	−0.209544	−	0.977799i	$-0.567198\pi$
$227$	−6.31421	−0.419089	−0.209544	+	0.977799i	$0.567198\pi$
$228$	2.14938	0.142346
$229$	11.3408	0.749422	0.374711	−	0.927142i	$-0.377742\pi$
$229$	11.3408	0.749422	0.374711	+	0.927142i	$0.377742\pi$
$230$	−1.46683	−0.0967199
$231$	0	0
$232$	29.8329	1.95862
$233$	−10.6796	−0.699646	−0.349823	−	0.936816i	$-0.613758\pi$
$233$	−10.6796	−0.699646	−0.349823	+	0.936816i	$0.613758\pi$
$234$	−0.196392	−0.0128385
$235$	12.4444	0.811786
$236$	−1.80866	−0.117734
$237$	3.61793	0.235010
$238$	0	0
$239$	12.0283	0.778048	0.389024	−	0.921228i	$-0.372812\pi$
$239$	12.0283	0.778048	0.389024	+	0.921228i	$0.372812\pi$
$240$	3.75947	0.242673
$241$	−16.8323	−1.08427	−0.542133	−	0.840292i	$-0.682383\pi$
$241$	−16.8323	−1.08427	−0.542133	+	0.840292i	$0.682383\pi$
$242$	3.21281	0.206527
$243$	1.00000	0.0641500
$244$	−2.25982	−0.144670
$245$	0	0
$246$	13.4888	0.860017
$247$	−1.14887	−0.0731008
$248$	−3.01300	−0.191326
$249$	11.7089	0.742020
$250$	−12.8332	−0.811644
$251$	2.02747	0.127973	0.0639865	−	0.997951i	$-0.479619\pi$
$251$	2.02747	0.127973	0.0639865	+	0.997951i	$0.479619\pi$
$252$	0	0
$253$	−2.92406	−0.183834
$254$	16.7284	1.04963
$255$	0.904903	0.0566672
$256$	−6.58599	−0.411624
$257$	9.43969	0.588831	0.294416	−	0.955677i	$-0.404875\pi$
$257$	9.43969	0.588831	0.294416	+	0.955677i	$0.404875\pi$
$258$	0.947656	0.0589985
$259$	0	0
$260$	0.0469290	0.00291041
$261$	9.97665	0.617539
$262$	−0.807745	−0.0499026
$263$	−13.9815	−0.862137	−0.431069	−	0.902319i	$-0.641863\pi$
$263$	−13.9815	−0.862137	−0.431069	+	0.902319i	$0.641863\pi$
$264$	8.74372	0.538139
$265$	9.37503	0.575904
$266$	0	0
$267$	−12.2939	−0.752375
$268$	−1.53553	−0.0937975
$269$	18.3054	1.11610	0.558050	−	0.829807i	$-0.311550\pi$
$269$	18.3054	1.11610	0.558050	+	0.829807i	$0.311550\pi$
$270$	1.46683	0.0892684
$271$	−9.70426	−0.589492	−0.294746	−	0.955576i	$-0.595235\pi$
$271$	−9.70426	−0.589492	−0.294746	+	0.955576i	$0.595235\pi$
$272$	2.71928	0.164881
$273$	0	0
$274$	21.2858	1.28592
$275$	−10.9622	−0.661043
$276$	0.280171	0.0168643
$277$	4.90295	0.294590	0.147295	−	0.989093i	$-0.452943\pi$
$277$	4.90295	0.294590	0.147295	+	0.989093i	$0.452943\pi$
$278$	11.6819	0.700636
$279$	−1.00760	−0.0603236
$280$	0	0
$281$	−12.9632	−0.773321	−0.386661	−	0.922222i	$-0.626372\pi$
$281$	−12.9632	−0.773321	−0.386661	+	0.922222i	$0.626372\pi$
$282$	14.5909	0.868873
$283$	−31.6829	−1.88335	−0.941677	−	0.336519i	$-0.890750\pi$
$283$	−31.6829	−1.88335	−0.941677	+	0.336519i	$0.890750\pi$
$284$	4.38731	0.260339
$285$	8.58079	0.508282
$286$	−0.574262	−0.0339568
$287$	0	0
$288$	−1.57263	−0.0926682
$289$	−16.3455	−0.961498
$290$	14.6341	0.859341
$291$	3.14045	0.184096
$292$	−4.01721	−0.235089
$293$	−27.6472	−1.61517	−0.807584	−	0.589753i	$-0.799225\pi$
$293$	−27.6472	−1.61517	−0.807584	+	0.589753i	$0.799225\pi$
$294$	0	0
$295$	−7.22058	−0.420398
$296$	14.8821	0.865002
$297$	2.92406	0.169671
$298$	4.73753	0.274438
$299$	−0.149755	−0.00866054
$300$	1.05035	0.0606418
$301$	0	0
$302$	−6.62075	−0.380981
$303$	−5.76282	−0.331065
$304$	25.7857	1.47891
$305$	−9.02168	−0.516580
$306$	1.06098	0.0606522
$307$	10.2624	0.585709	0.292854	−	0.956157i	$-0.405395\pi$
$307$	10.2624	0.585709	0.292854	+	0.956157i	$0.405395\pi$
$308$	0	0
$309$	−16.5778	−0.943078
$310$	−1.47798	−0.0839437
$311$	−17.9118	−1.01569	−0.507843	−	0.861450i	$-0.669557\pi$
$311$	−17.9118	−1.01569	−0.507843	+	0.861450i	$0.669557\pi$
$312$	0.447807	0.0253521
$313$	−1.11809	−0.0631980	−0.0315990	−	0.999501i	$-0.510060\pi$
$313$	−1.11809	−0.0631980	−0.0315990	+	0.999501i	$0.510060\pi$
$314$	−0.381845	−0.0215487
$315$	0	0
$316$	−1.01364	−0.0570216
$317$	2.59719	0.145873	0.0729364	−	0.997337i	$-0.476763\pi$
$317$	2.59719	0.145873	0.0729364	+	0.997337i	$0.476763\pi$
$318$	10.9920	0.616403
$319$	29.1723	1.63334
$320$	−9.82572	−0.549275
$321$	−13.8280	−0.771802
$322$	0	0
$323$	6.20661	0.345345
$324$	−0.280171	−0.0155651
$325$	−0.561423	−0.0311422
$326$	0.159300	0.00882282
$327$	9.99774	0.552876
$328$	−30.7568	−1.69826
$329$	0	0
$330$	4.28910	0.236107
$331$	26.7533	1.47049	0.735246	−	0.677800i	$-0.237067\pi$
$331$	26.7533	1.47049	0.735246	+	0.677800i	$0.237067\pi$
$332$	−3.28049	−0.180040
$333$	4.97683	0.272729
$334$	11.8769	0.649873
$335$	−6.13017	−0.334927
$336$	0	0
$337$	14.4459	0.786916	0.393458	−	0.919343i	$-0.371279\pi$
$337$	14.4459	0.786916	0.393458	+	0.919343i	$0.371279\pi$
$338$	17.0191	0.925716
$339$	10.9837	0.596555
$340$	−0.253527	−0.0137495
$341$	−2.94629	−0.159551
$342$	10.0608	0.544026
$343$	0	0
$344$	−2.16082	−0.116503
$345$	1.11850	0.0602182
$346$	−0.146804	−0.00789224
$347$	−14.0787	−0.755782	−0.377891	−	0.925850i	$-0.623351\pi$
$347$	−14.0787	−0.755782	−0.377891	+	0.925850i	$0.623351\pi$
$348$	−2.79517	−0.149837
$349$	13.6631	0.731369	0.365685	−	0.930739i	$-0.380835\pi$
$349$	13.6631	0.731369	0.365685	+	0.930739i	$0.380835\pi$
$350$	0	0
$351$	0.149755	0.00799332
$352$	−4.59847	−0.245099
$353$	−31.3365	−1.66787	−0.833935	−	0.551862i	$-0.813918\pi$
$353$	−31.3365	−1.66787	−0.833935	+	0.551862i	$0.813918\pi$
$354$	−8.46599	−0.449962
$355$	17.5151	0.929604
$356$	3.44440	0.182553
$357$	0	0
$358$	12.5155	0.661467
$359$	−6.34281	−0.334761	−0.167380	−	0.985892i	$-0.553531\pi$
$359$	−6.34281	−0.334761	−0.167380	+	0.985892i	$0.553531\pi$
$360$	−3.34462	−0.176277
$361$	39.8545	2.09761
$362$	29.9009	1.57155
$363$	−2.44987	−0.128585
$364$	0	0
$365$	−16.0376	−0.839445
$366$	−10.5777	−0.552907
$367$	4.68480	0.244544	0.122272	−	0.992497i	$-0.460982\pi$
$367$	4.68480	0.244544	0.122272	+	0.992497i	$0.460982\pi$
$368$	3.36116	0.175213
$369$	−10.2856	−0.535450
$370$	7.30017	0.379518
$371$	0	0
$372$	0.282301	0.0146366
$373$	4.83005	0.250091	0.125045	−	0.992151i	$-0.460092\pi$
$373$	4.83005	0.250091	0.125045	+	0.992151i	$0.460092\pi$
$374$	3.10237	0.160420
$375$	9.78573	0.505333
$376$	−33.2697	−1.71575
$377$	1.49405	0.0769475
$378$	0	0
$379$	4.67624	0.240202	0.120101	−	0.992762i	$-0.461678\pi$
$379$	4.67624	0.240202	0.120101	+	0.992762i	$0.461678\pi$
$380$	−2.40409	−0.123327
$381$	−12.7559	−0.653506
$382$	2.75211	0.140810
$383$	1.71617	0.0876920	0.0438460	−	0.999038i	$-0.486039\pi$
$383$	1.71617	0.0876920	0.0438460	+	0.999038i	$0.486039\pi$
$384$	−8.37520	−0.427395
$385$	0	0
$386$	−14.8629	−0.756502
$387$	−0.722617	−0.0367327
$388$	−0.879862	−0.0446683
$389$	−36.1973	−1.83528	−0.917638	−	0.397417i	$-0.869907\pi$
$389$	−36.1973	−1.83528	−0.917638	+	0.397417i	$0.869907\pi$
$390$	0.219665	0.0111232
$391$	0.809030	0.0409144
$392$	0	0
$393$	0.615930	0.0310696
$394$	2.89029	0.145610
$395$	−4.04666	−0.203610
$396$	−0.819237	−0.0411682
$397$	2.36543	0.118717	0.0593586	−	0.998237i	$-0.481094\pi$
$397$	2.36543	0.118717	0.0593586	+	0.998237i	$0.481094\pi$
$398$	17.1823	0.861273
$399$	0	0
$400$	12.6008	0.630042
$401$	12.3451	0.616485	0.308243	−	0.951308i	$-0.400259\pi$
$401$	12.3451	0.616485	0.308243	+	0.951308i	$0.400259\pi$
$402$	−7.18750	−0.358480
$403$	−0.150893	−0.00751653
$404$	1.61457	0.0803281
$405$	−1.11850	−0.0555789
$406$	0	0
$407$	14.5526	0.721344
$408$	−2.41922	−0.119769
$409$	−31.9909	−1.58185	−0.790924	−	0.611914i	$-0.790400\pi$
$409$	−31.9909	−1.58185	−0.790924	+	0.611914i	$0.790400\pi$
$410$	−15.0873	−0.745109
$411$	−16.2310	−0.800618
$412$	4.64462	0.228824
$413$	0	0
$414$	1.31142	0.0644529
$415$	−13.0964	−0.642878
$416$	−0.235509	−0.0115468
$417$	−8.90783	−0.436218
$418$	29.4184	1.43890
$419$	2.72267	0.133011	0.0665057	−	0.997786i	$-0.478815\pi$
$419$	2.72267	0.133011	0.0665057	+	0.997786i	$0.478815\pi$
$420$	0	0
$421$	−9.61420	−0.468567	−0.234284	−	0.972168i	$-0.575274\pi$
$421$	−9.61420	−0.468567	−0.234284	+	0.972168i	$0.575274\pi$
$422$	−29.4295	−1.43261
$423$	−11.1260	−0.540964
$424$	−25.0637	−1.21720
$425$	3.03301	0.147123
$426$	20.5361	0.994977
$427$	0	0
$428$	3.87420	0.187266
$429$	0.437892	0.0211416
$430$	−1.05996	−0.0511156
$431$	−12.2996	−0.592453	−0.296227	−	0.955118i	$-0.595728\pi$
$431$	−12.2996	−0.592453	−0.296227	+	0.955118i	$0.595728\pi$
$432$	−3.36116	−0.161714
$433$	10.6477	0.511697	0.255848	−	0.966717i	$-0.417645\pi$
$433$	10.6477	0.511697	0.255848	+	0.966717i	$0.417645\pi$
$434$	0	0
$435$	−11.1589	−0.535029
$436$	−2.80108	−0.134147
$437$	7.67167	0.366986
$438$	−18.8037	−0.898477
$439$	30.2468	1.44360	0.721801	−	0.692101i	$-0.243315\pi$
$439$	30.2468	1.44360	0.721801	+	0.692101i	$0.243315\pi$
$440$	−9.77988	−0.466238
$441$	0	0
$442$	0.158887	0.00755748
$443$	29.0358	1.37953	0.689766	−	0.724032i	$-0.257713\pi$
$443$	29.0358	1.37953	0.689766	+	0.724032i	$0.257713\pi$
$444$	−1.39436	−0.0661736
$445$	13.7508	0.651849
$446$	35.6218	1.68674
$447$	−3.61251	−0.170866
$448$	0	0
$449$	4.58989	0.216610	0.108305	−	0.994118i	$-0.465458\pi$
$449$	4.58989	0.216610	0.108305	+	0.994118i	$0.465458\pi$
$450$	4.91646	0.231764
$451$	−30.0759	−1.41622
$452$	−3.07733	−0.144745
$453$	5.04852	0.237200
$454$	8.28060	0.388628
$455$	0	0
$456$	−22.9403	−1.07428
$457$	−35.8225	−1.67571	−0.837854	−	0.545895i	$-0.816190\pi$
$457$	−35.8225	−1.67571	−0.837854	+	0.545895i	$0.816190\pi$
$458$	−14.8726	−0.694951
$459$	−0.809030	−0.0377623
$460$	−0.313372	−0.0146110
$461$	9.28315	0.432359	0.216180	−	0.976354i	$-0.430640\pi$
$461$	9.28315	0.432359	0.216180	+	0.976354i	$0.430640\pi$
$462$	0	0
$463$	36.7668	1.70870	0.854349	−	0.519700i	$-0.173956\pi$
$463$	36.7668	1.70870	0.854349	+	0.519700i	$0.173956\pi$
$464$	−33.5331	−1.55674
$465$	1.12701	0.0522637
$466$	14.0055	0.648793
$467$	10.0974	0.467252	0.233626	−	0.972327i	$-0.424941\pi$
$467$	10.0974	0.467252	0.233626	+	0.972327i	$0.424941\pi$
$468$	−0.0419569	−0.00193946
$469$	0	0
$470$	−16.3199	−0.752782
$471$	0.291168	0.0134163
$472$	19.3039	0.888534
$473$	−2.11298	−0.0971547
$474$	−4.74463	−0.217928
$475$	28.7607	1.31963
$476$	0	0
$477$	−8.38177	−0.383775
$478$	−15.7742	−0.721497
$479$	−12.2248	−0.558568	−0.279284	−	0.960209i	$-0.590097\pi$
$479$	−12.2248	−0.558568	−0.279284	+	0.960209i	$0.590097\pi$
$480$	1.75899	0.0802867
$481$	0.745304	0.0339829
$482$	22.0743	1.00546
$483$	0	0
$484$	0.686382	0.0311992
$485$	−3.51260	−0.159499
$486$	−1.31142	−0.0594873
$487$	28.3896	1.28645	0.643227	−	0.765676i	$-0.277595\pi$
$487$	28.3896	1.28645	0.643227	+	0.765676i	$0.277595\pi$
$488$	24.1191	1.09182
$489$	−0.121471	−0.00549312
$490$	0	0
$491$	17.6134	0.794882	0.397441	−	0.917628i	$-0.369898\pi$
$491$	17.6134	0.794882	0.397441	+	0.917628i	$0.369898\pi$
$492$	2.88174	0.129919
$493$	−8.07141	−0.363518
$494$	1.50665	0.0677875
$495$	−3.27057	−0.147001
$496$	3.38672	0.152068
$497$	0	0
$498$	−15.3553	−0.688087
$499$	−9.83089	−0.440091	−0.220046	−	0.975490i	$-0.570621\pi$
$499$	−9.83089	−0.440091	−0.220046	+	0.975490i	$0.570621\pi$
$500$	−2.74168	−0.122612
$501$	−9.05647	−0.404613
$502$	−2.65887	−0.118671
$503$	−21.6468	−0.965184	−0.482592	−	0.875845i	$-0.660305\pi$
$503$	−21.6468	−0.965184	−0.482592	+	0.875845i	$0.660305\pi$
$504$	0	0
$505$	6.44573	0.286831
$506$	3.83468	0.170472
$507$	−12.9776	−0.576354
$508$	3.57384	0.158563
$509$	9.25571	0.410252	0.205126	−	0.978736i	$-0.434240\pi$
$509$	9.25571	0.410252	0.205126	+	0.978736i	$0.434240\pi$
$510$	−1.18671	−0.0525484
$511$	0	0
$512$	25.3874	1.12198
$513$	−7.67167	−0.338712
$514$	−12.3794	−0.546033
$515$	18.5423	0.817072
$516$	0.202456	0.00891264
$517$	−32.5330	−1.43080
$518$	0	0
$519$	0.111943	0.00491374
$520$	−0.500873	−0.0219647
$521$	−45.0902	−1.97544	−0.987718	−	0.156249i	$-0.950060\pi$
$521$	−45.0902	−1.97544	−0.987718	+	0.156249i	$0.950060\pi$
$522$	−13.0836	−0.572654
$523$	10.9454	0.478610	0.239305	−	0.970945i	$-0.423080\pi$
$523$	10.9454	0.478610	0.239305	+	0.970945i	$0.423080\pi$
$524$	−0.172566	−0.00753857
$525$	0	0
$526$	18.3357	0.799473
$527$	0.815181	0.0355098
$528$	−9.82824	−0.427719
$529$	1.00000	0.0434783
$530$	−12.2946	−0.534044
$531$	6.45557	0.280148
$532$	0	0
$533$	−1.54033	−0.0667189
$534$	16.1225	0.697689
$535$	15.4666	0.668681
$536$	16.3887	0.707886
$537$	−9.54348	−0.411832
$538$	−24.0061	−1.03498
$539$	0	0
$540$	0.313372	0.0134854
$541$	8.72410	0.375078	0.187539	−	0.982257i	$-0.439949\pi$
$541$	8.72410	0.375078	0.187539	+	0.982257i	$0.439949\pi$
$542$	12.7264	0.546645
$543$	−22.8003	−0.978456
$544$	1.27231	0.0545497
$545$	−11.1825	−0.479006
$546$	0	0
$547$	−36.9222	−1.57868	−0.789339	−	0.613957i	$-0.789577\pi$
$547$	−36.9222	−1.57868	−0.789339	+	0.613957i	$0.789577\pi$
$548$	4.54747	0.194258
$549$	8.06585	0.344242
$550$	14.3760	0.612996
$551$	−76.5376	−3.26061
$552$	−2.99027	−0.127274
$553$	0	0
$554$	−6.42984	−0.273178
$555$	−5.56660	−0.236289
$556$	2.49572	0.105842
$557$	29.3344	1.24294	0.621468	−	0.783439i	$-0.286536\pi$
$557$	29.3344	1.24294	0.621468	+	0.783439i	$0.286536\pi$
$558$	1.32139	0.0559390
$559$	−0.108215	−0.00457702
$560$	0	0
$561$	−2.36565	−0.0998780
$562$	17.0003	0.717113
$563$	33.1964	1.39906	0.699532	−	0.714602i	$-0.253392\pi$
$563$	33.1964	1.39906	0.699532	+	0.714602i	$0.253392\pi$
$564$	3.11718	0.131257
$565$	−12.2854	−0.516849
$566$	41.5497	1.74646
$567$	0	0
$568$	−46.8258	−1.96477
$569$	−20.2844	−0.850366	−0.425183	−	0.905107i	$-0.639790\pi$
$569$	−20.2844	−0.850366	−0.425183	+	0.905107i	$0.639790\pi$
$570$	−11.2530	−0.471338
$571$	−28.9567	−1.21180	−0.605899	−	0.795541i	$-0.707187\pi$
$571$	−28.9567	−1.21180	−0.605899	+	0.795541i	$0.707187\pi$
$572$	−0.122685	−0.00512970
$573$	−2.09857	−0.0876690
$574$	0	0
$575$	3.74895	0.156342
$576$	8.78471	0.366030
$577$	9.62800	0.400819	0.200409	−	0.979712i	$-0.435773\pi$
$577$	9.62800	0.400819	0.200409	+	0.979712i	$0.435773\pi$
$578$	21.4358	0.891612
$579$	11.3334	0.471001
$580$	3.12640	0.129817
$581$	0	0
$582$	−4.11846	−0.170715
$583$	−24.5088	−1.01505
$584$	42.8757	1.77421
$585$	−0.167501	−0.00692532
$586$	36.2572	1.49777
$587$	−16.5572	−0.683387	−0.341694	−	0.939811i	$-0.611001\pi$
$587$	−16.5572	−0.683387	−0.341694	+	0.939811i	$0.611001\pi$
$588$	0	0
$589$	7.72999	0.318509
$590$	9.46923	0.389842
$591$	−2.20393	−0.0906576
$592$	−16.7279	−0.687514
$593$	−5.55190	−0.227989	−0.113995	−	0.993481i	$-0.536365\pi$
$593$	−5.55190	−0.227989	−0.113995	+	0.993481i	$0.536365\pi$
$594$	−3.83468	−0.157339
$595$	0	0
$596$	1.01212	0.0414581
$597$	−13.1021	−0.536232
$598$	0.196392	0.00803106
$599$	−13.2040	−0.539501	−0.269750	−	0.962930i	$-0.586941\pi$
$599$	−13.2040	−0.539501	−0.269750	+	0.962930i	$0.586941\pi$
$600$	−11.2104	−0.457661
$601$	9.21681	0.375962	0.187981	−	0.982173i	$-0.439806\pi$
$601$	9.21681	0.375962	0.187981	+	0.982173i	$0.439806\pi$
$602$	0	0
$603$	5.48069	0.223191
$604$	−1.41445	−0.0575531
$605$	2.74018	0.111404
$606$	7.55749	0.307002
$607$	30.1828	1.22508	0.612541	−	0.790439i	$-0.290147\pi$
$607$	30.1828	1.22508	0.612541	+	0.790439i	$0.290147\pi$
$608$	12.0647	0.489288
$609$	0	0
$610$	11.8312	0.479033
$611$	−1.66617	−0.0674060
$612$	0.226667	0.00916246
$613$	−21.9188	−0.885291	−0.442645	−	0.896697i	$-0.645960\pi$
$613$	−21.9188	−0.885291	−0.442645	+	0.896697i	$0.645960\pi$
$614$	−13.4584	−0.543137
$615$	11.5045	0.463908
$616$	0	0
$617$	36.6476	1.47538	0.737688	−	0.675142i	$-0.235917\pi$
$617$	36.6476	1.47538	0.737688	+	0.675142i	$0.235917\pi$
$618$	21.7405	0.874531
$619$	−6.45623	−0.259498	−0.129749	−	0.991547i	$-0.541417\pi$
$619$	−6.45623	−0.259498	−0.129749	+	0.991547i	$0.541417\pi$
$620$	−0.315754	−0.0126810
$621$	−1.00000	−0.0401286
$622$	23.4899	0.941861
$623$	0	0
$624$	−0.503350	−0.0201501
$625$	7.79938	0.311975
$626$	1.46628	0.0586045
$627$	−22.4324	−0.895865
$628$	−0.0815769	−0.00325527
$629$	−4.02641	−0.160543
$630$	0	0
$631$	27.5595	1.09712	0.548562	−	0.836110i	$-0.315175\pi$
$631$	27.5595	1.09712	0.548562	+	0.836110i	$0.315175\pi$
$632$	10.8186	0.430340
$633$	22.4409	0.891947
$634$	−3.40602	−0.135270
$635$	14.2675	0.566190
$636$	2.34833	0.0931172
$637$	0	0
$638$	−38.2573	−1.51462
$639$	−15.6594	−0.619476
$640$	9.36769	0.370290
$641$	−24.0087	−0.948285	−0.474143	−	0.880448i	$-0.657242\pi$
$641$	−24.0087	−0.948285	−0.474143	+	0.880448i	$0.657242\pi$
$642$	18.1343	0.715705
$643$	−30.4129	−1.19937	−0.599683	−	0.800237i	$-0.704707\pi$
$643$	−30.4129	−1.19937	−0.599683	+	0.800237i	$0.704707\pi$
$644$	0	0
$645$	0.808249	0.0318248
$646$	−8.13949	−0.320244
$647$	−23.4125	−0.920442	−0.460221	−	0.887804i	$-0.652230\pi$
$647$	−23.4125	−0.920442	−0.460221	+	0.887804i	$0.652230\pi$
$648$	2.99027	0.117469
$649$	18.8765	0.740967
$650$	0.736263	0.0288786
$651$	0	0
$652$	0.0340327	0.00133282
$653$	−16.2406	−0.635543	−0.317771	−	0.948167i	$-0.602934\pi$
$653$	−16.2406	−0.635543	−0.317771	+	0.948167i	$0.602934\pi$
$654$	−13.1113	−0.512691
$655$	−0.688920	−0.0269183
$656$	34.5717	1.34980
$657$	14.3384	0.559395
$658$	0	0
$659$	31.3642	1.22177	0.610887	−	0.791718i	$-0.290813\pi$
$659$	31.3642	1.22177	0.610887	+	0.791718i	$0.290813\pi$
$660$	0.916319	0.0356677
$661$	24.0789	0.936561	0.468281	−	0.883580i	$-0.344874\pi$
$661$	24.0789	0.936561	0.468281	+	0.883580i	$0.344874\pi$
$662$	−35.0848	−1.36361
$663$	−0.121156	−0.00470531
$664$	35.0127	1.35875
$665$	0	0
$666$	−6.52673	−0.252906
$667$	−9.97665	−0.386297
$668$	2.53736	0.0981734
$669$	−27.1627	−1.05017
$670$	8.03925	0.310583
$671$	23.5850	0.910490
$672$	0	0
$673$	−35.8442	−1.38169	−0.690846	−	0.723002i	$-0.742762\pi$
$673$	−35.8442	−1.38169	−0.690846	+	0.723002i	$0.742762\pi$
$674$	−18.9446	−0.729720
$675$	−3.74895	−0.144297
$676$	3.63594	0.139844
$677$	45.3563	1.74319	0.871593	−	0.490231i	$-0.163087\pi$
$677$	45.3563	1.74319	0.871593	+	0.490231i	$0.163087\pi$
$678$	−14.4043	−0.553195
$679$	0	0
$680$	2.70590	0.103767
$681$	−6.31421	−0.241961
$682$	3.86383	0.147954
$683$	0.498576	0.0190775	0.00953873	−	0.999955i	$-0.496964\pi$
$683$	0.498576	0.0190775	0.00953873	+	0.999955i	$0.496964\pi$
$684$	2.14938	0.0821835
$685$	18.1545	0.693647
$686$	0	0
$687$	11.3408	0.432679
$688$	2.42883	0.0925984
$689$	−1.25521	−0.0478197
$690$	−1.46683	−0.0558413
$691$	−35.6442	−1.35597	−0.677985	−	0.735076i	$-0.737146\pi$
$691$	−35.6442	−1.35597	−0.677985	+	0.735076i	$0.737146\pi$
$692$	−0.0313631	−0.00119225
$693$	0	0
$694$	18.4631	0.700848
$695$	9.96344	0.377935
$696$	29.8329	1.13081
$697$	8.32140	0.315196
$698$	−17.9181	−0.678210
$699$	−10.6796	−0.403941
$700$	0	0
$701$	−37.3720	−1.41152	−0.705761	−	0.708450i	$-0.749395\pi$
$701$	−37.3720	−1.41152	−0.705761	+	0.708450i	$0.749395\pi$
$702$	−0.196392	−0.00741233
$703$	−38.1806	−1.44001
$704$	25.6870	0.968116
$705$	12.4444	0.468685
$706$	41.0953	1.54664
$707$	0	0
$708$	−1.80866	−0.0679738
$709$	39.0146	1.46522	0.732611	−	0.680647i	$-0.238301\pi$
$709$	39.0146	1.46522	0.732611	+	0.680647i	$0.238301\pi$
$710$	−22.9697	−0.862037
$711$	3.61793	0.135683
$712$	−36.7621	−1.37772
$713$	1.00760	0.0377350
$714$	0	0
$715$	−0.489784	−0.0183169
$716$	2.67381	0.0999248
$717$	12.0283	0.449207
$718$	8.31810	0.310429
$719$	−4.04650	−0.150909	−0.0754545	−	0.997149i	$-0.524041\pi$
$719$	−4.04650	−0.150909	−0.0754545	+	0.997149i	$0.524041\pi$
$720$	3.75947	0.140107
$721$	0	0
$722$	−52.2661	−1.94514
$723$	−16.8323	−0.626002
$724$	6.38799	0.237408
$725$	−37.4020	−1.38907
$726$	3.21281	0.119239
$727$	23.5206	0.872331	0.436166	−	0.899866i	$-0.356336\pi$
$727$	23.5206	0.872331	0.436166	+	0.899866i	$0.356336\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	21.0320	0.778430
$731$	0.584619	0.0216229
$732$	−2.25982	−0.0835253
$733$	−7.02956	−0.259643	−0.129821	−	0.991537i	$-0.541440\pi$
$733$	−7.02956	−0.259643	−0.129821	+	0.991537i	$0.541440\pi$
$734$	−6.14375	−0.226770
$735$	0	0
$736$	1.57263	0.0579679
$737$	16.0259	0.590321
$738$	13.4888	0.496531
$739$	25.1430	0.924899	0.462450	−	0.886646i	$-0.346971\pi$
$739$	25.1430	0.924899	0.462450	+	0.886646i	$0.346971\pi$
$740$	1.55960	0.0573320
$741$	−1.14887	−0.0422048
$742$	0	0
$743$	1.31141	0.0481111	0.0240555	−	0.999711i	$-0.492342\pi$
$743$	1.31141	0.0481111	0.0240555	+	0.999711i	$0.492342\pi$
$744$	−3.01300	−0.110462
$745$	4.04061	0.148036
$746$	−6.33424	−0.231913
$747$	11.7089	0.428405
$748$	0.662787	0.0242339
$749$	0	0
$750$	−12.8332	−0.468603
$751$	−27.2473	−0.994270	−0.497135	−	0.867673i	$-0.665615\pi$
$751$	−27.2473	−0.994270	−0.497135	+	0.867673i	$0.665615\pi$
$752$	37.3962	1.36370
$753$	2.02747	0.0738852
$754$	−1.95933	−0.0713547
$755$	−5.64679	−0.205508
$756$	0	0
$757$	−28.8354	−1.04804	−0.524020	−	0.851706i	$-0.675568\pi$
$757$	−28.8354	−1.04804	−0.524020	+	0.851706i	$0.675568\pi$
$758$	−6.13253	−0.222743
$759$	−2.92406	−0.106137
$760$	25.6588	0.930744
$761$	49.0933	1.77963	0.889815	−	0.456322i	$-0.150833\pi$
$761$	49.0933	1.77963	0.889815	+	0.456322i	$0.150833\pi$
$762$	16.7284	0.606006
$763$	0	0
$764$	0.587958	0.0212716
$765$	0.904903	0.0327168
$766$	−2.25062	−0.0813182
$767$	0.966753	0.0349074
$768$	−6.58599	−0.237651
$769$	47.7521	1.72199	0.860993	−	0.508617i	$-0.169843\pi$
$769$	47.7521	1.72199	0.860993	+	0.508617i	$0.169843\pi$
$770$	0	0
$771$	9.43969	0.339962
$772$	−3.17529	−0.114281
$773$	−23.3453	−0.839671	−0.419836	−	0.907600i	$-0.637912\pi$
$773$	−23.3453	−0.839671	−0.419836	+	0.907600i	$0.637912\pi$
$774$	0.947656	0.0340628
$775$	3.77745	0.135690
$776$	9.39078	0.337109
$777$	0	0
$778$	47.4700	1.70188
$779$	78.9081	2.82718
$780$	0.0469290	0.00168033
$781$	−45.7890	−1.63846
$782$	−1.06098	−0.0379406
$783$	9.97665	0.356536
$784$	0	0
$785$	−0.325673	−0.0116238
$786$	−0.807745	−0.0288113
$787$	−26.7531	−0.953645	−0.476823	−	0.878999i	$-0.658212\pi$
$787$	−26.7531	−0.953645	−0.476823	+	0.878999i	$0.658212\pi$
$788$	0.617478	0.0219967
$789$	−13.9815	−0.497755
$790$	5.30689	0.188811
$791$	0	0
$792$	8.74372	0.310695
$793$	1.20790	0.0428938
$794$	−3.10207	−0.110088
$795$	9.37503	0.332498
$796$	3.67082	0.130109
$797$	37.8014	1.33899	0.669497	−	0.742815i	$-0.266510\pi$
$797$	37.8014	1.33899	0.669497	+	0.742815i	$0.266510\pi$
$798$	0	0
$799$	9.00125	0.318441
$800$	5.89572	0.208445
$801$	−12.2939	−0.434384
$802$	−16.1897	−0.571676
$803$	41.9264	1.47955
$804$	−1.53553	−0.0541540
$805$	0	0
$806$	0.197885	0.00697020
$807$	18.3054	0.644381
$808$	−17.2324	−0.606233
$809$	7.49276	0.263431	0.131716	−	0.991288i	$-0.457951\pi$
$809$	7.49276	0.263431	0.131716	+	0.991288i	$0.457951\pi$
$810$	1.46683	0.0515392
$811$	−7.49072	−0.263035	−0.131517	−	0.991314i	$-0.541985\pi$
$811$	−7.49072	−0.263035	−0.131517	+	0.991314i	$0.541985\pi$
$812$	0	0
$813$	−9.70426	−0.340343
$814$	−19.0846	−0.668913
$815$	0.135866	0.00475918
$816$	2.71928	0.0951939
$817$	5.54368	0.193949
$818$	41.9536	1.46687
$819$	0	0
$820$	−3.22324	−0.112560
$821$	−36.8662	−1.28664	−0.643320	−	0.765598i	$-0.722443\pi$
$821$	−36.8662	−1.28664	−0.643320	+	0.765598i	$0.722443\pi$
$822$	21.2858	0.742426
$823$	44.8005	1.56165	0.780823	−	0.624752i	$-0.214800\pi$
$823$	44.8005	1.56165	0.780823	+	0.624752i	$0.214800\pi$
$824$	−49.5720	−1.72692
$825$	−10.9622	−0.381653
$826$	0	0
$827$	−25.7968	−0.897041	−0.448520	−	0.893773i	$-0.648049\pi$
$827$	−25.7968	−0.897041	−0.448520	+	0.893773i	$0.648049\pi$
$828$	0.280171	0.00973661
$829$	25.2848	0.878179	0.439089	−	0.898443i	$-0.355301\pi$
$829$	25.2848	0.878179	0.439089	+	0.898443i	$0.355301\pi$
$830$	17.1749	0.596151
$831$	4.90295	0.170082
$832$	1.31555	0.0456086
$833$	0	0
$834$	11.6819	0.404512
$835$	10.1297	0.350553
$836$	6.28491	0.217368
$837$	−1.00760	−0.0348278
$838$	−3.57058	−0.123343
$839$	49.9499	1.72446	0.862231	−	0.506516i	$-0.169067\pi$
$839$	49.9499	1.72446	0.862231	+	0.506516i	$0.169067\pi$
$840$	0	0
$841$	70.5336	2.43219
$842$	12.6083	0.434510
$843$	−12.9632	−0.446477
$844$	−6.28730	−0.216418
$845$	14.5155	0.499347
$846$	14.5909	0.501644
$847$	0	0
$848$	28.1725	0.967447
$849$	−31.6829	−1.08735
$850$	−3.97756	−0.136429
$851$	−4.97683	−0.170604
$852$	4.38731	0.150307
$853$	10.8482	0.371434	0.185717	−	0.982603i	$-0.440539\pi$
$853$	10.8482	0.371434	0.185717	+	0.982603i	$0.440539\pi$
$854$	0	0
$855$	8.58079	0.293457
$856$	−41.3494	−1.41329
$857$	38.1729	1.30396	0.651981	−	0.758235i	$-0.273938\pi$
$857$	38.1729	1.30396	0.651981	+	0.758235i	$0.273938\pi$
$858$	−0.574262	−0.0196050
$859$	−37.1313	−1.26690	−0.633451	−	0.773782i	$-0.718362\pi$
$859$	−37.1313	−1.26690	−0.633451	+	0.773782i	$0.718362\pi$
$860$	−0.226448	−0.00772181
$861$	0	0
$862$	16.1300	0.549391
$863$	37.7064	1.28354	0.641771	−	0.766897i	$-0.278200\pi$
$863$	37.7064	1.28354	0.641771	+	0.766897i	$0.278200\pi$
$864$	−1.57263	−0.0535020
$865$	−0.125208	−0.00425721
$866$	−13.9637	−0.474504
$867$	−16.3455	−0.555121
$868$	0	0
$869$	10.5790	0.358869
$870$	14.6341	0.496141
$871$	0.820760	0.0278104
$872$	29.8959	1.01240
$873$	3.14045	0.106288
$874$	−10.0608	−0.340312
$875$	0	0
$876$	−4.01721	−0.135729
$877$	8.05869	0.272123	0.136061	−	0.990700i	$-0.456556\pi$
$877$	8.05869	0.272123	0.136061	+	0.990700i	$0.456556\pi$
$878$	−39.6664	−1.33867
$879$	−27.6472	−0.932517
$880$	10.9929	0.370571
$881$	−6.75884	−0.227711	−0.113856	−	0.993497i	$-0.536320\pi$
$881$	−6.75884	−0.227711	−0.113856	+	0.993497i	$0.536320\pi$
$882$	0	0
$883$	−16.0173	−0.539023	−0.269512	−	0.962997i	$-0.586862\pi$
$883$	−16.0173	−0.539023	−0.269512	+	0.962997i	$0.586862\pi$
$884$	0.0339444	0.00114167
$885$	−7.22058	−0.242717
$886$	−38.0782	−1.27926
$887$	7.28247	0.244522	0.122261	−	0.992498i	$-0.460986\pi$
$887$	7.28247	0.244522	0.122261	+	0.992498i	$0.460986\pi$
$888$	14.8821	0.499409
$889$	0	0
$890$	−18.0331	−0.604470
$891$	2.92406	0.0979597
$892$	7.61019	0.254808
$893$	85.3548	2.85629
$894$	4.73753	0.158447
$895$	10.6744	0.356806
$896$	0	0
$897$	−0.149755	−0.00500017
$898$	−6.01929	−0.200866
$899$	−10.0525	−0.335270
$900$	1.05035	0.0350116
$901$	6.78110	0.225911
$902$	39.4422	1.31328
$903$	0	0
$904$	32.8443	1.09239
$905$	25.5022	0.847723
$906$	−6.62075	−0.219960
$907$	13.4821	0.447665	0.223833	−	0.974628i	$-0.428143\pi$
$907$	13.4821	0.447665	0.223833	+	0.974628i	$0.428143\pi$
$908$	1.76906	0.0587083
$909$	−5.76282	−0.191141
$910$	0	0
$911$	7.73932	0.256415	0.128208	−	0.991747i	$-0.459078\pi$
$911$	7.73932	0.256415	0.128208	+	0.991747i	$0.459078\pi$
$912$	25.7857	0.853851
$913$	34.2375	1.13309
$914$	46.9785	1.55391
$915$	−9.02168	−0.298248
$916$	−3.17737	−0.104983
$917$	0	0
$918$	1.06098	0.0350176
$919$	42.0047	1.38561	0.692804	−	0.721126i	$-0.256375\pi$
$919$	42.0047	1.38561	0.692804	+	0.721126i	$0.256375\pi$
$920$	3.34462	0.110269
$921$	10.2624	0.338159
$922$	−12.1741	−0.400934
$923$	−2.34507	−0.0771889
$924$	0	0
$925$	−18.6579	−0.613468
$926$	−48.2168	−1.58450
$927$	−16.5778	−0.544486
$928$	−15.6896	−0.515036
$929$	14.7403	0.483614	0.241807	−	0.970324i	$-0.422260\pi$
$929$	14.7403	0.483614	0.241807	+	0.970324i	$0.422260\pi$
$930$	−1.47798	−0.0484649
$931$	0	0
$932$	2.99212	0.0980103
$933$	−17.9118	−0.586406
$934$	−13.2420	−0.433290
$935$	2.64599	0.0865332
$936$	0.447807	0.0146370
$937$	−56.6040	−1.84917	−0.924586	−	0.380973i	$-0.875589\pi$
$937$	−56.6040	−1.84917	−0.924586	+	0.380973i	$0.875589\pi$
$938$	0	0
$939$	−1.11809	−0.0364874
$940$	−3.48657	−0.113719
$941$	−1.62085	−0.0528383	−0.0264192	−	0.999651i	$-0.508410\pi$
$941$	−1.62085	−0.0528383	−0.0264192	+	0.999651i	$0.508410\pi$
$942$	−0.381845	−0.0124412
$943$	10.2856	0.334947
$944$	−21.6982	−0.706217
$945$	0	0
$946$	2.77100	0.0900931
$947$	4.65821	0.151372	0.0756858	−	0.997132i	$-0.475885\pi$
$947$	4.65821	0.151372	0.0756858	+	0.997132i	$0.475885\pi$
$948$	−1.01364	−0.0329214
$949$	2.14725	0.0697026
$950$	−37.7174	−1.22372
$951$	2.59719	0.0842197
$952$	0	0
$953$	−14.7592	−0.478096	−0.239048	−	0.971008i	$-0.576835\pi$
$953$	−14.7592	−0.478096	−0.239048	+	0.971008i	$0.576835\pi$
$954$	10.9920	0.355880
$955$	2.34726	0.0759554
$956$	−3.36999	−0.108993
$957$	29.1723	0.943008
$958$	16.0319	0.517969
$959$	0	0
$960$	−9.82572	−0.317124
$961$	−29.9847	−0.967250
$962$	−0.977409	−0.0315129
$963$	−13.8280	−0.445600
$964$	4.71593	0.151890
$965$	−12.6765	−0.408070
$966$	0	0
$967$	17.7781	0.571704	0.285852	−	0.958274i	$-0.407723\pi$
$967$	17.7781	0.571704	0.285852	+	0.958274i	$0.407723\pi$
$968$	−7.32576	−0.235459
$969$	6.20661	0.199385
$970$	4.60651	0.147906
$971$	−56.8306	−1.82378	−0.911890	−	0.410435i	$-0.865377\pi$
$971$	−56.8306	−1.82378	−0.911890	+	0.410435i	$0.865377\pi$
$972$	−0.280171	−0.00898649
$973$	0	0
$974$	−37.2307	−1.19295
$975$	−0.561423	−0.0179799
$976$	−27.1106	−0.867790
$977$	−43.0212	−1.37637	−0.688185	−	0.725535i	$-0.741592\pi$
$977$	−43.0212	−1.37637	−0.688185	+	0.725535i	$0.741592\pi$
$978$	0.159300	0.00509386
$979$	−35.9481	−1.14891
$980$	0	0
$981$	9.99774	0.319203
$982$	−23.0986	−0.737107
$983$	25.5484	0.814866	0.407433	−	0.913235i	$-0.366424\pi$
$983$	25.5484	0.814866	0.407433	+	0.913235i	$0.366424\pi$
$984$	−30.7568	−0.980492
$985$	2.46510	0.0785448
$986$	10.5850	0.337096
$987$	0	0
$988$	0.321880	0.0102404
$989$	0.722617	0.0229779
$990$	4.28910	0.136317
$991$	−2.79912	−0.0889169	−0.0444585	−	0.999011i	$-0.514156\pi$
$991$	−2.79912	−0.0889169	−0.0444585	+	0.999011i	$0.514156\pi$
$992$	1.58459	0.0503107
$993$	26.7533	0.848989
$994$	0	0
$995$	14.6547	0.464585
$996$	−3.28049	−0.103946
$997$	44.2277	1.40070	0.700352	−	0.713798i	$-0.253026\pi$
$997$	44.2277	1.40070	0.700352	+	0.713798i	$0.253026\pi$
$998$	12.8925	0.408103
$999$	4.97683	0.157460

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3381.2.a.bb.1.3	yes	6
7.6	odd	2		3381.2.a.ba.1.3	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3381.2.a.ba.1.3	✓	6	7.6	odd	2
3381.2.a.bb.1.3	yes	6	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:	\( N \)	\(=\)	\( 3381 = 3 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3381.a (trivial)

\(f(q)\)	\(=\)	\(q-1.31142 q^{2} +1.00000 q^{3} -0.280171 q^{4} -1.11850 q^{5} -1.31142 q^{6} +2.99027 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.31142 q^{2} +1.00000 q^{3} -0.280171 q^{4} -1.11850 q^{5} -1.31142 q^{6} +2.99027 q^{8} +1.00000 q^{9} +1.46683 q^{10} +2.92406 q^{11} -0.280171 q^{12} +0.149755 q^{13} -1.11850 q^{15} -3.36116 q^{16} -0.809030 q^{17} -1.31142 q^{18} -7.67167 q^{19} +0.313372 q^{20} -3.83468 q^{22} -1.00000 q^{23} +2.99027 q^{24} -3.74895 q^{25} -0.196392 q^{26} +1.00000 q^{27} +9.97665 q^{29} +1.46683 q^{30} -1.00760 q^{31} -1.57263 q^{32} +2.92406 q^{33} +1.06098 q^{34} -0.280171 q^{36} +4.97683 q^{37} +10.0608 q^{38} +0.149755 q^{39} -3.34462 q^{40} -10.2856 q^{41} -0.722617 q^{43} -0.819237 q^{44} -1.11850 q^{45} +1.31142 q^{46} -11.1260 q^{47} -3.36116 q^{48} +4.91646 q^{50} -0.809030 q^{51} -0.0419569 q^{52} -8.38177 q^{53} -1.31142 q^{54} -3.27057 q^{55} -7.67167 q^{57} -13.0836 q^{58} +6.45557 q^{59} +0.313372 q^{60} +8.06585 q^{61} +1.32139 q^{62} +8.78471 q^{64} -0.167501 q^{65} -3.83468 q^{66} +5.48069 q^{67} +0.226667 q^{68} -1.00000 q^{69} -15.6594 q^{71} +2.99027 q^{72} +14.3384 q^{73} -6.52673 q^{74} -3.74895 q^{75} +2.14938 q^{76} -0.196392 q^{78} +3.61793 q^{79} +3.75947 q^{80} +1.00000 q^{81} +13.4888 q^{82} +11.7089 q^{83} +0.904903 q^{85} +0.947656 q^{86} +9.97665 q^{87} +8.74372 q^{88} -12.2939 q^{89} +1.46683 q^{90} +0.280171 q^{92} -1.00760 q^{93} +14.5909 q^{94} +8.58079 q^{95} -1.57263 q^{96} +3.14045 q^{97} +2.92406 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} + 6 q^{3} + 7 q^{4} - 2 q^{5} - 3 q^{6} - 9 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 + 6 * q^3 + 7 * q^4 - 2 * q^5 - 3 * q^6 - 9 * q^8 + 6 * q^9	\( 6 q - 3 q^{2} + 6 q^{3} + 7 q^{4} - 2 q^{5} - 3 q^{6} - 9 q^{8} + 6 q^{9} - 8 q^{10} - 3 q^{11} + 7 q^{12} - 2 q^{15} + 5 q^{16} - 8 q^{17} - 3 q^{18} - 19 q^{19} + 24 q^{22} - 6 q^{23} - 9 q^{24} - 20 q^{26} + 6 q^{27} - 12 q^{29} - 8 q^{30} + 2 q^{31} - 41 q^{32} - 3 q^{33} - 2 q^{34} + 7 q^{36} - 10 q^{37} + 20 q^{38} - 22 q^{40} - 3 q^{41} - 2 q^{43} - 14 q^{44} - 2 q^{45} + 3 q^{46} - 7 q^{47} + 5 q^{48} + 17 q^{50} - 8 q^{51} + 44 q^{52} - 5 q^{53} - 3 q^{54} - 24 q^{55} - 19 q^{57} - 12 q^{58} - 21 q^{59} - 29 q^{61} - 10 q^{62} + 59 q^{64} - 18 q^{65} + 24 q^{66} + 16 q^{67} - 54 q^{68} - 6 q^{69} - 6 q^{71} - 9 q^{72} + 8 q^{73} - 16 q^{74} - 40 q^{76} - 20 q^{78} - 12 q^{79} + 78 q^{80} + 6 q^{81} - 44 q^{82} - 24 q^{83} + 10 q^{85} + 12 q^{86} - 12 q^{87} + 28 q^{88} - 18 q^{89} - 8 q^{90} - 7 q^{92} + 2 q^{93} + 8 q^{94} + 6 q^{95} - 41 q^{96} - 22 q^{97} - 3 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 + 6 * q^3 + 7 * q^4 - 2 * q^5 - 3 * q^6 - 9 * q^8 + 6 * q^9 - 8 * q^10 - 3 * q^11 + 7 * q^12 - 2 * q^15 + 5 * q^16 - 8 * q^17 - 3 * q^18 - 19 * q^19 + 24 * q^22 - 6 * q^23 - 9 * q^24 - 20 * q^26 + 6 * q^27 - 12 * q^29 - 8 * q^30 + 2 * q^31 - 41 * q^32 - 3 * q^33 - 2 * q^34 + 7 * q^36 - 10 * q^37 + 20 * q^38 - 22 * q^40 - 3 * q^41 - 2 * q^43 - 14 * q^44 - 2 * q^45 + 3 * q^46 - 7 * q^47 + 5 * q^48 + 17 * q^50 - 8 * q^51 + 44 * q^52 - 5 * q^53 - 3 * q^54 - 24 * q^55 - 19 * q^57 - 12 * q^58 - 21 * q^59 - 29 * q^61 - 10 * q^62 + 59 * q^64 - 18 * q^65 + 24 * q^66 + 16 * q^67 - 54 * q^68 - 6 * q^69 - 6 * q^71 - 9 * q^72 + 8 * q^73 - 16 * q^74 - 40 * q^76 - 20 * q^78 - 12 * q^79 + 78 * q^80 + 6 * q^81 - 44 * q^82 - 24 * q^83 + 10 * q^85 + 12 * q^86 - 12 * q^87 + 28 * q^88 - 18 * q^89 - 8 * q^90 - 7 * q^92 + 2 * q^93 + 8 * q^94 + 6 * q^95 - 41 * q^96 - 22 * q^97 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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