LMFDB - Embedded newform 3549.2.a.k.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3549,2,Mod(1,3549)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3549, 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("3549.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3549 = 3 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3549.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:	$28.3389076774$
Analytic rank:	$0$
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 273)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.48119$ of defining polynomial
Character	$\chi$	$=$	3549.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.48119 q^{2} +1.00000 q^{3} +0.193937 q^{4} -4.15633 q^{5} +1.48119 q^{6} +1.00000 q^{7} -2.67513 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.48119 q^{2} +1.00000 q^{3} +0.193937 q^{4} -4.15633 q^{5} +1.48119 q^{6} +1.00000 q^{7} -2.67513 q^{8} +1.00000 q^{9} -6.15633 q^{10} +3.19394 q^{11} +0.193937 q^{12} +1.48119 q^{14} -4.15633 q^{15} -4.35026 q^{16} -3.35026 q^{17} +1.48119 q^{18} +2.38787 q^{19} -0.806063 q^{20} +1.00000 q^{21} +4.73084 q^{22} -0.387873 q^{23} -2.67513 q^{24} +12.2750 q^{25} +1.00000 q^{27} +0.193937 q^{28} -7.92478 q^{29} -6.15633 q^{30} +10.7005 q^{31} -1.09332 q^{32} +3.19394 q^{33} -4.96239 q^{34} -4.15633 q^{35} +0.193937 q^{36} +1.61213 q^{37} +3.53690 q^{38} +11.1187 q^{40} +1.45580 q^{41} +1.48119 q^{42} -1.92478 q^{43} +0.619421 q^{44} -4.15633 q^{45} -0.574515 q^{46} +3.76845 q^{47} -4.35026 q^{48} +1.00000 q^{49} +18.1817 q^{50} -3.35026 q^{51} -6.00000 q^{53} +1.48119 q^{54} -13.2750 q^{55} -2.67513 q^{56} +2.38787 q^{57} -11.7381 q^{58} +6.15633 q^{59} -0.806063 q^{60} +14.4387 q^{61} +15.8496 q^{62} +1.00000 q^{63} +7.08110 q^{64} +4.73084 q^{66} +5.61213 q^{67} -0.649738 q^{68} -0.387873 q^{69} -6.15633 q^{70} +11.8192 q^{71} -2.67513 q^{72} +15.6629 q^{73} +2.38787 q^{74} +12.2750 q^{75} +0.463096 q^{76} +3.19394 q^{77} -8.96239 q^{79} +18.0811 q^{80} +1.00000 q^{81} +2.15633 q^{82} +6.99271 q^{83} +0.193937 q^{84} +13.9248 q^{85} -2.85097 q^{86} -7.92478 q^{87} -8.54420 q^{88} -0.932071 q^{89} -6.15633 q^{90} -0.0752228 q^{92} +10.7005 q^{93} +5.58181 q^{94} -9.92478 q^{95} -1.09332 q^{96} -3.35026 q^{97} +1.48119 q^{98} +3.19394 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - q^{2} + 3 q^{3} + q^{4} - 2 q^{5} - q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - q^2 + 3 * q^3 + q^4 - 2 * q^5 - q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9	$ 3 q - q^{2} + 3 q^{3} + q^{4} - 2 q^{5} - q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9} - 8 q^{10} + 10 q^{11} + q^{12} - q^{14} - 2 q^{15} - 3 q^{16} - q^{18} + 8 q^{19} - 2 q^{20} + 3 q^{21} - 8 q^{22} - 2 q^{23} - 3 q^{24} + 5 q^{25} + 3 q^{27} + q^{28} - 2 q^{29} - 8 q^{30} + 12 q^{31} + 3 q^{32} + 10 q^{33} - 4 q^{34} - 2 q^{35} + q^{36} + 4 q^{37} - 12 q^{38} + 12 q^{40} + 14 q^{41} - q^{42} + 16 q^{43} + 14 q^{44} - 2 q^{45} + 10 q^{46} - 3 q^{48} + 3 q^{49} + 29 q^{50} - 18 q^{53} - q^{54} - 8 q^{55} - 3 q^{56} + 8 q^{57} - 26 q^{58} + 8 q^{59} - 2 q^{60} + 14 q^{61} + 4 q^{62} + 3 q^{63} - 11 q^{64} - 8 q^{66} + 16 q^{67} - 12 q^{68} - 2 q^{69} - 8 q^{70} - 6 q^{71} - 3 q^{72} + 16 q^{73} + 8 q^{74} + 5 q^{75} + 24 q^{76} + 10 q^{77} - 16 q^{79} + 22 q^{80} + 3 q^{81} - 4 q^{82} + 8 q^{83} + q^{84} + 20 q^{85} - 32 q^{86} - 2 q^{87} - 16 q^{88} + 6 q^{89} - 8 q^{90} - 22 q^{92} + 12 q^{93} + 18 q^{94} - 8 q^{95} + 3 q^{96} - q^{98} + 10 q^{99}+O(q^{100}) $ 3 * q - q^2 + 3 * q^3 + q^4 - 2 * q^5 - q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9 - 8 * q^10 + 10 * q^11 + q^12 - q^14 - 2 * q^15 - 3 * q^16 - q^18 + 8 * q^19 - 2 * q^20 + 3 * q^21 - 8 * q^22 - 2 * q^23 - 3 * q^24 + 5 * q^25 + 3 * q^27 + q^28 - 2 * q^29 - 8 * q^30 + 12 * q^31 + 3 * q^32 + 10 * q^33 - 4 * q^34 - 2 * q^35 + q^36 + 4 * q^37 - 12 * q^38 + 12 * q^40 + 14 * q^41 - q^42 + 16 * q^43 + 14 * q^44 - 2 * q^45 + 10 * q^46 - 3 * q^48 + 3 * q^49 + 29 * q^50 - 18 * q^53 - q^54 - 8 * q^55 - 3 * q^56 + 8 * q^57 - 26 * q^58 + 8 * q^59 - 2 * q^60 + 14 * q^61 + 4 * q^62 + 3 * q^63 - 11 * q^64 - 8 * q^66 + 16 * q^67 - 12 * q^68 - 2 * q^69 - 8 * q^70 - 6 * q^71 - 3 * q^72 + 16 * q^73 + 8 * q^74 + 5 * q^75 + 24 * q^76 + 10 * q^77 - 16 * q^79 + 22 * q^80 + 3 * q^81 - 4 * q^82 + 8 * q^83 + q^84 + 20 * q^85 - 32 * q^86 - 2 * q^87 - 16 * q^88 + 6 * q^89 - 8 * q^90 - 22 * q^92 + 12 * q^93 + 18 * q^94 - 8 * q^95 + 3 * q^96 - q^98 + 10 * 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 $

$2$	1.48119	1.04736	0.523681	−	0.851914i	$-0.324558\pi$
$2$	1.48119	1.04736	0.523681	+	0.851914i	$0.324558\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.193937	0.0969683
$5$	−4.15633	−1.85877	−0.929383	−	0.369118i	$-0.879660\pi$
$5$	−4.15633	−1.85877	−0.929383	+	0.369118i	$0.879660\pi$
$6$	1.48119	0.604695
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.67513	−0.945802
$9$	1.00000	0.333333
$10$	−6.15633	−1.94680
$11$	3.19394	0.963008	0.481504	−	0.876444i	$-0.340091\pi$
$11$	3.19394	0.963008	0.481504	+	0.876444i	$0.340091\pi$
$12$	0.193937	0.0559847
$13$	0	0
$13$	0	0
$14$	1.48119	0.395866
$15$	−4.15633	−1.07316
$16$	−4.35026	−1.08757
$17$	−3.35026	−0.812558	−0.406279	−	0.913749i	$-0.633174\pi$
$17$	−3.35026	−0.812558	−0.406279	+	0.913749i	$0.633174\pi$
$18$	1.48119	0.349121
$19$	2.38787	0.547816	0.273908	−	0.961756i	$-0.411684\pi$
$19$	2.38787	0.547816	0.273908	+	0.961756i	$0.411684\pi$
$20$	−0.806063	−0.180241
$21$	1.00000	0.218218
$22$	4.73084	1.00862
$23$	−0.387873	−0.0808771	−0.0404386	−	0.999182i	$-0.512876\pi$
$23$	−0.387873	−0.0808771	−0.0404386	+	0.999182i	$0.512876\pi$
$24$	−2.67513	−0.546059
$25$	12.2750	2.45501
$26$	0	0
$27$	1.00000	0.192450
$28$	0.193937	0.0366506
$29$	−7.92478	−1.47159	−0.735797	−	0.677202i	$-0.763192\pi$
$29$	−7.92478	−1.47159	−0.735797	+	0.677202i	$0.763192\pi$
$30$	−6.15633	−1.12399
$31$	10.7005	1.92187	0.960935	−	0.276773i	$-0.0892650\pi$
$31$	10.7005	1.92187	0.960935	+	0.276773i	$0.0892650\pi$
$32$	−1.09332	−0.193274
$33$	3.19394	0.555993
$34$	−4.96239	−0.851043
$35$	−4.15633	−0.702547
$36$	0.193937	0.0323228
$37$	1.61213	0.265032	0.132516	−	0.991181i	$-0.457694\pi$
$37$	1.61213	0.265032	0.132516	+	0.991181i	$0.457694\pi$
$38$	3.53690	0.573762
$39$	0	0
$40$	11.1187	1.75802
$41$	1.45580	0.227358	0.113679	−	0.993518i	$-0.463736\pi$
$41$	1.45580	0.227358	0.113679	+	0.993518i	$0.463736\pi$
$42$	1.48119	0.228553
$43$	−1.92478	−0.293526	−0.146763	−	0.989172i	$-0.546885\pi$
$43$	−1.92478	−0.293526	−0.146763	+	0.989172i	$0.546885\pi$
$44$	0.619421	0.0933812
$45$	−4.15633	−0.619588
$46$	−0.574515	−0.0847077
$47$	3.76845	0.549685	0.274843	−	0.961489i	$-0.411374\pi$
$47$	3.76845	0.549685	0.274843	+	0.961489i	$0.411374\pi$
$48$	−4.35026	−0.627906
$49$	1.00000	0.142857
$50$	18.1817	2.57128
$51$	−3.35026	−0.469130
$52$	0	0
$53$	−6.00000	−0.824163	−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000	−0.824163	−0.412082	+	0.911147i	$0.635198\pi$
$54$	1.48119	0.201565
$55$	−13.2750	−1.79001
$56$	−2.67513	−0.357479
$57$	2.38787	0.316282
$58$	−11.7381	−1.54129
$59$	6.15633	0.801485	0.400743	−	0.916191i	$-0.368752\pi$
$59$	6.15633	0.801485	0.400743	+	0.916191i	$0.368752\pi$
$60$	−0.806063	−0.104062
$61$	14.4387	1.84868	0.924340	−	0.381569i	$-0.124616\pi$
$61$	14.4387	1.84868	0.924340	+	0.381569i	$0.124616\pi$
$62$	15.8496	2.01290
$63$	1.00000	0.125988
$64$	7.08110	0.885138
$65$	0	0
$66$	4.73084	0.582326
$67$	5.61213	0.685630	0.342815	−	0.939403i	$-0.388620\pi$
$67$	5.61213	0.685630	0.342815	+	0.939403i	$0.388620\pi$
$68$	−0.649738	−0.0787923
$69$	−0.387873	−0.0466944
$70$	−6.15633	−0.735822
$71$	11.8192	1.40269	0.701343	−	0.712824i	$-0.252584\pi$
$71$	11.8192	1.40269	0.701343	+	0.712824i	$0.252584\pi$
$72$	−2.67513	−0.315267
$73$	15.6629	1.83321	0.916603	−	0.399800i	$-0.130920\pi$
$73$	15.6629	1.83321	0.916603	+	0.399800i	$0.130920\pi$
$74$	2.38787	0.277585
$75$	12.2750	1.41740
$76$	0.463096	0.0531207
$77$	3.19394	0.363983
$78$	0	0
$79$	−8.96239	−1.00835	−0.504174	−	0.863602i	$-0.668203\pi$
$79$	−8.96239	−1.00835	−0.504174	+	0.863602i	$0.668203\pi$
$80$	18.0811	2.02153
$81$	1.00000	0.111111
$82$	2.15633	0.238126
$83$	6.99271	0.767549	0.383775	−	0.923427i	$-0.374624\pi$
$83$	6.99271	0.767549	0.383775	+	0.923427i	$0.374624\pi$
$84$	0.193937	0.0211602
$85$	13.9248	1.51035
$86$	−2.85097	−0.307428
$87$	−7.92478	−0.849625
$88$	−8.54420	−0.910815
$89$	−0.932071	−0.0987994	−0.0493997	−	0.998779i	$-0.515731\pi$
$89$	−0.932071	−0.0987994	−0.0493997	+	0.998779i	$0.515731\pi$
$90$	−6.15633	−0.648934
$91$	0	0
$92$	−0.0752228	−0.00784252
$93$	10.7005	1.10959
$94$	5.58181	0.575720
$95$	−9.92478	−1.01826
$96$	−1.09332	−0.111587
$97$	−3.35026	−0.340168	−0.170084	−	0.985430i	$-0.554404\pi$
$97$	−3.35026	−0.340168	−0.170084	+	0.985430i	$0.554404\pi$
$98$	1.48119	0.149623
$99$	3.19394	0.321003
$100$	2.38058	0.238058
$101$	14.0508	1.39811	0.699053	−	0.715070i	$-0.253605\pi$
$101$	14.0508	1.39811	0.699053	+	0.715070i	$0.253605\pi$
$102$	−4.96239	−0.491350
$103$	−1.42548	−0.140457	−0.0702286	−	0.997531i	$-0.522373\pi$
$103$	−1.42548	−0.140457	−0.0702286	+	0.997531i	$0.522373\pi$
$104$	0	0
$105$	−4.15633	−0.405616
$106$	−8.88717	−0.863198
$107$	9.53690	0.921967	0.460984	−	0.887409i	$-0.347497\pi$
$107$	9.53690	0.921967	0.460984	+	0.887409i	$0.347497\pi$
$108$	0.193937	0.0186616
$109$	−6.23743	−0.597437	−0.298719	−	0.954341i	$-0.596559\pi$
$109$	−6.23743	−0.597437	−0.298719	+	0.954341i	$0.596559\pi$
$110$	−19.6629	−1.87479
$111$	1.61213	0.153016
$112$	−4.35026	−0.411061
$113$	−3.92478	−0.369212	−0.184606	−	0.982813i	$-0.559101\pi$
$113$	−3.92478	−0.369212	−0.184606	+	0.982813i	$0.559101\pi$
$114$	3.53690	0.331261
$115$	1.61213	0.150332
$116$	−1.53690	−0.142698
$117$	0	0
$118$	9.11871	0.839446
$119$	−3.35026	−0.307118
$120$	11.1187	1.01500
$121$	−0.798769	−0.0726154
$122$	21.3865	1.93624
$123$	1.45580	0.131265
$124$	2.07522	0.186361
$125$	−30.2374	−2.70452
$126$	1.48119	0.131955
$127$	0.962389	0.0853982	0.0426991	−	0.999088i	$-0.486404\pi$
$127$	0.962389	0.0853982	0.0426991	+	0.999088i	$0.486404\pi$
$128$	12.6751	1.12033
$129$	−1.92478	−0.169467
$130$	0	0
$131$	17.1490	1.49832	0.749159	−	0.662390i	$-0.230458\pi$
$131$	17.1490	1.49832	0.749159	+	0.662390i	$0.230458\pi$
$132$	0.619421	0.0539137
$133$	2.38787	0.207055
$134$	8.31265	0.718104
$135$	−4.15633	−0.357720
$136$	8.96239	0.768518
$137$	−4.85685	−0.414949	−0.207474	−	0.978240i	$-0.566524\pi$
$137$	−4.85685	−0.414949	−0.207474	+	0.978240i	$0.566524\pi$
$138$	−0.574515	−0.0489060
$139$	2.57452	0.218368	0.109184	−	0.994022i	$-0.465176\pi$
$139$	2.57452	0.218368	0.109184	+	0.994022i	$0.465176\pi$
$140$	−0.806063	−0.0681248
$141$	3.76845	0.317361
$142$	17.5066	1.46912
$143$	0	0
$144$	−4.35026	−0.362522
$145$	32.9380	2.73535
$146$	23.1998	1.92003
$147$	1.00000	0.0824786
$148$	0.312650	0.0256997
$149$	−13.3806	−1.09618	−0.548090	−	0.836419i	$-0.684645\pi$
$149$	−13.3806	−1.09618	−0.548090	+	0.836419i	$0.684645\pi$
$150$	18.1817	1.48453
$151$	−15.8496	−1.28982	−0.644909	−	0.764259i	$-0.723105\pi$
$151$	−15.8496	−1.28982	−0.644909	+	0.764259i	$0.723105\pi$
$152$	−6.38787	−0.518125
$153$	−3.35026	−0.270853
$154$	4.73084	0.381222
$155$	−44.4749	−3.57231
$156$	0	0
$157$	−12.7005	−1.01361	−0.506806	−	0.862060i	$-0.669174\pi$
$157$	−12.7005	−1.01361	−0.506806	+	0.862060i	$0.669174\pi$
$158$	−13.2750	−1.05611
$159$	−6.00000	−0.475831
$160$	4.54420	0.359250
$161$	−0.387873	−0.0305687
$162$	1.48119	0.116374
$163$	9.61213	0.752880	0.376440	−	0.926441i	$-0.377148\pi$
$163$	9.61213	0.752880	0.376440	+	0.926441i	$0.377148\pi$
$164$	0.282333	0.0220465
$165$	−13.2750	−1.03346
$166$	10.3576	0.803902
$167$	−12.0811	−0.934864	−0.467432	−	0.884029i	$-0.654821\pi$
$167$	−12.0811	−0.934864	−0.467432	+	0.884029i	$0.654821\pi$
$168$	−2.67513	−0.206391
$169$	0	0
$170$	20.6253	1.58189
$171$	2.38787	0.182605
$172$	−0.373285	−0.0284627
$173$	9.27504	0.705168	0.352584	−	0.935780i	$-0.385303\pi$
$173$	9.27504	0.705168	0.352584	+	0.935780i	$0.385303\pi$
$174$	−11.7381	−0.889866
$175$	12.2750	0.927906
$176$	−13.8945	−1.04733
$177$	6.15633	0.462738
$178$	−1.38058	−0.103479
$179$	5.01317	0.374702	0.187351	−	0.982293i	$-0.440010\pi$
$179$	5.01317	0.374702	0.187351	+	0.982293i	$0.440010\pi$
$180$	−0.806063	−0.0600804
$181$	13.8496	1.02943	0.514715	−	0.857362i	$-0.327898\pi$
$181$	13.8496	1.02943	0.514715	+	0.857362i	$0.327898\pi$
$182$	0	0
$183$	14.4387	1.06734
$184$	1.03761	0.0764937
$185$	−6.70052	−0.492632
$186$	15.8496	1.16215
$187$	−10.7005	−0.782500
$188$	0.730841	0.0533020
$189$	1.00000	0.0727393
$190$	−14.7005	−1.06649
$191$	−18.5647	−1.34329	−0.671646	−	0.740872i	$-0.734412\pi$
$191$	−18.5647	−1.34329	−0.671646	+	0.740872i	$0.734412\pi$
$192$	7.08110	0.511035
$193$	13.0884	0.942123	0.471062	−	0.882100i	$-0.343871\pi$
$193$	13.0884	0.942123	0.471062	+	0.882100i	$0.343871\pi$
$194$	−4.96239	−0.356279
$195$	0	0
$196$	0.193937	0.0138526
$197$	−7.24472	−0.516165	−0.258083	−	0.966123i	$-0.583091\pi$
$197$	−7.24472	−0.516165	−0.258083	+	0.966123i	$0.583091\pi$
$198$	4.73084	0.336206
$199$	−8.62530	−0.611431	−0.305716	−	0.952123i	$-0.598896\pi$
$199$	−8.62530	−0.611431	−0.305716	+	0.952123i	$0.598896\pi$
$200$	−32.8373	−2.32195
$201$	5.61213	0.395849
$202$	20.8119	1.46432
$203$	−7.92478	−0.556210
$204$	−0.649738	−0.0454908
$205$	−6.05079	−0.422605
$206$	−2.11142	−0.147110
$207$	−0.387873	−0.0269590
$208$	0	0
$209$	7.62672	0.527551
$210$	−6.15633	−0.424827
$211$	18.8872	1.30025	0.650123	−	0.759829i	$-0.274717\pi$
$211$	18.8872	1.30025	0.650123	+	0.759829i	$0.274717\pi$
$212$	−1.16362	−0.0799177
$213$	11.8192	0.809841
$214$	14.1260	0.965634
$215$	8.00000	0.545595
$216$	−2.67513	−0.182020
$217$	10.7005	0.726399
$218$	−9.23884	−0.625733
$219$	15.6629	1.05840
$220$	−2.57452	−0.173574
$221$	0	0
$222$	2.38787	0.160264
$223$	−16.1622	−1.08230	−0.541151	−	0.840926i	$-0.682011\pi$
$223$	−16.1622	−1.08230	−0.541151	+	0.840926i	$0.682011\pi$
$224$	−1.09332	−0.0730506
$225$	12.2750	0.818336
$226$	−5.81336	−0.386699
$227$	−27.2447	−1.80830	−0.904148	−	0.427220i	$-0.859493\pi$
$227$	−27.2447	−1.80830	−0.904148	+	0.427220i	$0.859493\pi$
$228$	0.463096	0.0306693
$229$	19.5125	1.28942	0.644710	−	0.764427i	$-0.276978\pi$
$229$	19.5125	1.28942	0.644710	+	0.764427i	$0.276978\pi$
$230$	2.38787	0.157452
$231$	3.19394	0.210146
$232$	21.1998	1.39184
$233$	21.8496	1.43141	0.715706	−	0.698402i	$-0.246105\pi$
$233$	21.8496	1.43141	0.715706	+	0.698402i	$0.246105\pi$
$234$	0	0
$235$	−15.6629	−1.02174
$236$	1.19394	0.0777187
$237$	−8.96239	−0.582170
$238$	−4.96239	−0.321664
$239$	8.49341	0.549393	0.274697	−	0.961531i	$-0.411423\pi$
$239$	8.49341	0.549393	0.274697	+	0.961531i	$0.411423\pi$
$240$	18.0811	1.16713
$241$	5.48612	0.353392	0.176696	−	0.984265i	$-0.443459\pi$
$241$	5.48612	0.353392	0.176696	+	0.984265i	$0.443459\pi$
$242$	−1.18313	−0.0760546
$243$	1.00000	0.0641500
$244$	2.80018	0.179263
$245$	−4.15633	−0.265538
$246$	2.15633	0.137482
$247$	0	0
$248$	−28.6253	−1.81771
$249$	6.99271	0.443145
$250$	−44.7875	−2.83261
$251$	−6.44851	−0.407026	−0.203513	−	0.979072i	$-0.565236\pi$
$251$	−6.44851	−0.407026	−0.203513	+	0.979072i	$0.565236\pi$
$252$	0.193937	0.0122169
$253$	−1.23884	−0.0778853
$254$	1.42548	0.0894429
$255$	13.9248	0.872003
$256$	4.61213	0.288258
$257$	−9.90034	−0.617566	−0.308783	−	0.951132i	$-0.599922\pi$
$257$	−9.90034	−0.617566	−0.308783	+	0.951132i	$0.599922\pi$
$258$	−2.85097	−0.177494
$259$	1.61213	0.100173
$260$	0	0
$261$	−7.92478	−0.490531
$262$	25.4010	1.56928
$263$	3.46168	0.213456	0.106728	−	0.994288i	$-0.465963\pi$
$263$	3.46168	0.213456	0.106728	+	0.994288i	$0.465963\pi$
$264$	−8.54420	−0.525859
$265$	24.9380	1.53193
$266$	3.53690	0.216862
$267$	−0.932071	−0.0570418
$268$	1.08840	0.0664844
$269$	16.7513	1.02135	0.510673	−	0.859775i	$-0.329396\pi$
$269$	16.7513	1.02135	0.510673	+	0.859775i	$0.329396\pi$
$270$	−6.15633	−0.374662
$271$	−6.38787	−0.388036	−0.194018	−	0.980998i	$-0.562152\pi$
$271$	−6.38787	−0.388036	−0.194018	+	0.980998i	$0.562152\pi$
$272$	14.5745	0.883710
$273$	0	0
$274$	−7.19394	−0.434602
$275$	39.2057	2.36419
$276$	−0.0752228	−0.00452788
$277$	−12.1768	−0.731633	−0.365816	−	0.930687i	$-0.619210\pi$
$277$	−12.1768	−0.731633	−0.365816	+	0.930687i	$0.619210\pi$
$278$	3.81336	0.228710
$279$	10.7005	0.640624
$280$	11.1187	0.664470
$281$	−27.3054	−1.62890	−0.814450	−	0.580233i	$-0.802961\pi$
$281$	−27.3054	−1.62890	−0.814450	+	0.580233i	$0.802961\pi$
$282$	5.58181	0.332392
$283$	−27.0738	−1.60937	−0.804685	−	0.593701i	$-0.797666\pi$
$283$	−27.0738	−1.60937	−0.804685	+	0.593701i	$0.797666\pi$
$284$	2.29218	0.136016
$285$	−9.92478	−0.587893
$286$	0	0
$287$	1.45580	0.0859333
$288$	−1.09332	−0.0644246
$289$	−5.77575	−0.339750
$290$	48.7875	2.86490
$291$	−3.35026	−0.196396
$292$	3.03761	0.177763
$293$	16.7816	0.980393	0.490197	−	0.871612i	$-0.336925\pi$
$293$	16.7816	0.980393	0.490197	+	0.871612i	$0.336925\pi$
$294$	1.48119	0.0863850
$295$	−25.5877	−1.48977
$296$	−4.31265	−0.250668
$297$	3.19394	0.185331
$298$	−19.8192	−1.14810
$299$	0	0
$300$	2.38058	0.137443
$301$	−1.92478	−0.110942
$302$	−23.4763	−1.35091
$303$	14.0508	0.807197
$304$	−10.3879	−0.595785
$305$	−60.0118	−3.43626
$306$	−4.96239	−0.283681
$307$	17.2995	0.987333	0.493667	−	0.869651i	$-0.335656\pi$
$307$	17.2995	0.987333	0.493667	+	0.869651i	$0.335656\pi$
$308$	0.619421	0.0352948
$309$	−1.42548	−0.0810930
$310$	−65.8759	−3.74150
$311$	−17.1490	−0.972432	−0.486216	−	0.873839i	$-0.661623\pi$
$311$	−17.1490	−0.972432	−0.486216	+	0.873839i	$0.661623\pi$
$312$	0	0
$313$	−10.8119	−0.611127	−0.305564	−	0.952172i	$-0.598845\pi$
$313$	−10.8119	−0.611127	−0.305564	+	0.952172i	$0.598845\pi$
$314$	−18.8119	−1.06162
$315$	−4.15633	−0.234182
$316$	−1.73813	−0.0977777
$317$	14.1563	0.795098	0.397549	−	0.917581i	$-0.369861\pi$
$317$	14.1563	0.795098	0.397549	+	0.917581i	$0.369861\pi$
$318$	−8.88717	−0.498368
$319$	−25.3112	−1.41716
$320$	−29.4314	−1.64526
$321$	9.53690	0.532298
$322$	−0.574515	−0.0320165
$323$	−8.00000	−0.445132
$324$	0.193937	0.0107743
$325$	0	0
$326$	14.2374	0.788538
$327$	−6.23743	−0.344931
$328$	−3.89446	−0.215036
$329$	3.76845	0.207761
$330$	−19.6629	−1.08241
$331$	−17.2506	−0.948179	−0.474089	−	0.880477i	$-0.657223\pi$
$331$	−17.2506	−0.948179	−0.474089	+	0.880477i	$0.657223\pi$
$332$	1.35614	0.0744279
$333$	1.61213	0.0883440
$334$	−17.8945	−0.979141
$335$	−23.3258	−1.27443
$336$	−4.35026	−0.237326
$337$	5.97556	0.325510	0.162755	−	0.986667i	$-0.447962\pi$
$337$	5.97556	0.325510	0.162755	+	0.986667i	$0.447962\pi$
$338$	0	0
$339$	−3.92478	−0.213165
$340$	2.70052	0.146456
$341$	34.1768	1.85078
$342$	3.53690	0.191254
$343$	1.00000	0.0539949
$344$	5.14903	0.277617
$345$	1.61213	0.0867940
$346$	13.7381	0.738567
$347$	25.7889	1.38442	0.692211	−	0.721695i	$-0.256637\pi$
$347$	25.7889	1.38442	0.692211	+	0.721695i	$0.256637\pi$
$348$	−1.53690	−0.0823867
$349$	12.9624	0.693861	0.346930	−	0.937891i	$-0.387224\pi$
$349$	12.9624	0.693861	0.346930	+	0.937891i	$0.387224\pi$
$350$	18.1817	0.971854
$351$	0	0
$352$	−3.49200	−0.186124
$353$	3.78304	0.201351	0.100675	−	0.994919i	$-0.467900\pi$
$353$	3.78304	0.201351	0.100675	+	0.994919i	$0.467900\pi$
$354$	9.11871	0.484654
$355$	−49.1246	−2.60726
$356$	−0.180763	−0.00958041
$357$	−3.35026	−0.177315
$358$	7.42548	0.392449
$359$	10.6702	0.563152	0.281576	−	0.959539i	$-0.409143\pi$
$359$	10.6702	0.563152	0.281576	+	0.959539i	$0.409143\pi$
$360$	11.1187	0.586008
$361$	−13.2981	−0.699898
$362$	20.5139	1.07819
$363$	−0.798769	−0.0419245
$364$	0	0
$365$	−65.1002	−3.40750
$366$	21.3865	1.11789
$367$	6.82653	0.356342	0.178171	−	0.984000i	$-0.442982\pi$
$367$	6.82653	0.356342	0.178171	+	0.984000i	$0.442982\pi$
$368$	1.68735	0.0879592
$369$	1.45580	0.0757860
$370$	−9.92478	−0.515965
$371$	−6.00000	−0.311504
$372$	2.07522	0.107595
$373$	16.5745	0.858196	0.429098	−	0.903258i	$-0.358832\pi$
$373$	16.5745	0.858196	0.429098	+	0.903258i	$0.358832\pi$
$374$	−15.8496	−0.819561
$375$	−30.2374	−1.56145
$376$	−10.0811	−0.519893
$377$	0	0
$378$	1.48119	0.0761844
$379$	19.0738	0.979756	0.489878	−	0.871791i	$-0.337041\pi$
$379$	19.0738	0.979756	0.489878	+	0.871791i	$0.337041\pi$
$380$	−1.92478	−0.0987390
$381$	0.962389	0.0493047
$382$	−27.4979	−1.40691
$383$	−8.29218	−0.423711	−0.211855	−	0.977301i	$-0.567951\pi$
$383$	−8.29218	−0.423711	−0.211855	+	0.977301i	$0.567951\pi$
$384$	12.6751	0.646825
$385$	−13.2750	−0.676559
$386$	19.3865	0.986745
$387$	−1.92478	−0.0978419
$388$	−0.649738	−0.0329855
$389$	−0.700523	−0.0355180	−0.0177590	−	0.999842i	$-0.505653\pi$
$389$	−0.700523	−0.0355180	−0.0177590	+	0.999842i	$0.505653\pi$
$390$	0	0
$391$	1.29948	0.0657174
$392$	−2.67513	−0.135115
$393$	17.1490	0.865054
$394$	−10.7308	−0.540612
$395$	37.2506	1.87428
$396$	0.619421	0.0311271
$397$	−12.4993	−0.627322	−0.313661	−	0.949535i	$-0.601555\pi$
$397$	−12.4993	−0.627322	−0.313661	+	0.949535i	$0.601555\pi$
$398$	−12.7757	−0.640390
$399$	2.38787	0.119543
$400$	−53.3996	−2.66998
$401$	28.7064	1.43353	0.716765	−	0.697315i	$-0.245622\pi$
$401$	28.7064	1.43353	0.716765	+	0.697315i	$0.245622\pi$
$402$	8.31265	0.414597
$403$	0	0
$404$	2.72496	0.135572
$405$	−4.15633	−0.206529
$406$	−11.7381	−0.582554
$407$	5.14903	0.255228
$408$	8.96239	0.443704
$409$	23.4518	1.15962	0.579809	−	0.814752i	$-0.303127\pi$
$409$	23.4518	1.15962	0.579809	+	0.814752i	$0.303127\pi$
$410$	−8.96239	−0.442621
$411$	−4.85685	−0.239571
$412$	−0.276454	−0.0136199
$413$	6.15633	0.302933
$414$	−0.574515	−0.0282359
$415$	−29.0640	−1.42669
$416$	0	0
$417$	2.57452	0.126075
$418$	11.2966	0.552537
$419$	−34.1768	−1.66965	−0.834823	−	0.550519i	$-0.814430\pi$
$419$	−34.1768	−1.66965	−0.834823	+	0.550519i	$0.814430\pi$
$420$	−0.806063	−0.0393319
$421$	−5.55149	−0.270563	−0.135282	−	0.990807i	$-0.543194\pi$
$421$	−5.55149	−0.270563	−0.135282	+	0.990807i	$0.543194\pi$
$422$	27.9756	1.36183
$423$	3.76845	0.183228
$424$	16.0508	0.779495
$425$	−41.1246	−1.99484
$426$	17.5066	0.848197
$427$	14.4387	0.698736
$428$	1.84955	0.0894016
$429$	0	0
$430$	11.8496	0.571436
$431$	5.43136	0.261620	0.130810	−	0.991407i	$-0.458242\pi$
$431$	5.43136	0.261620	0.130810	+	0.991407i	$0.458242\pi$
$432$	−4.35026	−0.209302
$433$	−40.2130	−1.93251	−0.966256	−	0.257582i	$-0.917074\pi$
$433$	−40.2130	−1.93251	−0.966256	+	0.257582i	$0.917074\pi$
$434$	15.8496	0.760803
$435$	32.9380	1.57925
$436$	−1.20967	−0.0579325
$437$	−0.926192	−0.0443058
$438$	23.1998	1.10853
$439$	22.5745	1.07742	0.538711	−	0.842490i	$-0.318911\pi$
$439$	22.5745	1.07742	0.538711	+	0.842490i	$0.318911\pi$
$440$	35.5125	1.69299
$441$	1.00000	0.0476190
$442$	0	0
$443$	−8.23743	−0.391372	−0.195686	−	0.980667i	$-0.562693\pi$
$443$	−8.23743	−0.391372	−0.195686	+	0.980667i	$0.562693\pi$
$444$	0.312650	0.0148377
$445$	3.87399	0.183645
$446$	−23.9394	−1.13356
$447$	−13.3806	−0.632880
$448$	7.08110	0.334551
$449$	2.40834	0.113657	0.0568283	−	0.998384i	$-0.481901\pi$
$449$	2.40834	0.113657	0.0568283	+	0.998384i	$0.481901\pi$
$450$	18.1817	0.857094
$451$	4.64974	0.218948
$452$	−0.761158	−0.0358019
$453$	−15.8496	−0.744677
$454$	−40.3547	−1.89394
$455$	0	0
$456$	−6.38787	−0.299140
$457$	−29.5633	−1.38291	−0.691455	−	0.722419i	$-0.743030\pi$
$457$	−29.5633	−1.38291	−0.691455	+	0.722419i	$0.743030\pi$
$458$	28.9018	1.35049
$459$	−3.35026	−0.156377
$460$	0.312650	0.0145774
$461$	33.7196	1.57048	0.785239	−	0.619193i	$-0.212540\pi$
$461$	33.7196	1.57048	0.785239	+	0.619193i	$0.212540\pi$
$462$	4.73084	0.220099
$463$	16.8364	0.782453	0.391226	−	0.920294i	$-0.372051\pi$
$463$	16.8364	0.782453	0.391226	+	0.920294i	$0.372051\pi$
$464$	34.4749	1.60045
$465$	−44.4749	−2.06247
$466$	32.3634	1.49921
$467$	22.7005	1.05045	0.525227	−	0.850962i	$-0.323980\pi$
$467$	22.7005	1.05045	0.525227	+	0.850962i	$0.323980\pi$
$468$	0	0
$469$	5.61213	0.259144
$470$	−23.1998	−1.07013
$471$	−12.7005	−0.585209
$472$	−16.4690	−0.758046
$473$	−6.14762	−0.282668
$474$	−13.2750	−0.609743
$475$	29.3112	1.34489
$476$	−0.649738	−0.0297807
$477$	−6.00000	−0.274721
$478$	12.5804	0.575414
$479$	−10.0957	−0.461284	−0.230642	−	0.973039i	$-0.574083\pi$
$479$	−10.0957	−0.461284	−0.230642	+	0.973039i	$0.574083\pi$
$480$	4.54420	0.207413
$481$	0	0
$482$	8.12601	0.370130
$483$	−0.387873	−0.0176488
$484$	−0.154911	−0.00704139
$485$	13.9248	0.632292
$486$	1.48119	0.0671883
$487$	−9.40105	−0.426002	−0.213001	−	0.977052i	$-0.568324\pi$
$487$	−9.40105	−0.426002	−0.213001	+	0.977052i	$0.568324\pi$
$488$	−38.6253	−1.74849
$489$	9.61213	0.434675
$490$	−6.15633	−0.278114
$491$	−20.7612	−0.936938	−0.468469	−	0.883480i	$-0.655194\pi$
$491$	−20.7612	−0.936938	−0.468469	+	0.883480i	$0.655194\pi$
$492$	0.282333	0.0127286
$493$	26.5501	1.19576
$494$	0	0
$495$	−13.2750	−0.596669
$496$	−46.5501	−2.09016
$497$	11.8192	0.530165
$498$	10.3576	0.464133
$499$	22.9525	1.02750	0.513748	−	0.857941i	$-0.328256\pi$
$499$	22.9525	1.02750	0.513748	+	0.857941i	$0.328256\pi$
$500$	−5.86414	−0.262252
$501$	−12.0811	−0.539744
$502$	−9.55149	−0.426304
$503$	−34.9234	−1.55716	−0.778578	−	0.627548i	$-0.784059\pi$
$503$	−34.9234	−1.55716	−0.778578	+	0.627548i	$0.784059\pi$
$504$	−2.67513	−0.119160
$505$	−58.3996	−2.59875
$506$	−1.83497	−0.0815742
$507$	0	0
$508$	0.186642	0.00828091
$509$	−19.2301	−0.852361	−0.426180	−	0.904638i	$-0.640141\pi$
$509$	−19.2301	−0.852361	−0.426180	+	0.904638i	$0.640141\pi$
$510$	20.6253	0.913304
$511$	15.6629	0.692886
$512$	−18.5188	−0.818423
$513$	2.38787	0.105427
$514$	−14.6643	−0.646816
$515$	5.92478	0.261077
$516$	−0.373285	−0.0164329
$517$	12.0362	0.529351
$518$	2.38787	0.104917
$519$	9.27504	0.407129
$520$	0	0
$521$	21.5271	0.943117	0.471559	−	0.881835i	$-0.343692\pi$
$521$	21.5271	0.943117	0.471559	+	0.881835i	$0.343692\pi$
$522$	−11.7381	−0.513764
$523$	39.6747	1.73485	0.867426	−	0.497566i	$-0.165773\pi$
$523$	39.6747	1.73485	0.867426	+	0.497566i	$0.165773\pi$
$524$	3.32582	0.145289
$525$	12.2750	0.535727
$526$	5.12742	0.223566
$527$	−35.8496	−1.56163
$528$	−13.8945	−0.604679
$529$	−22.8496	−0.993459
$530$	36.9380	1.60448
$531$	6.15633	0.267162
$532$	0.463096	0.0200778
$533$	0	0
$534$	−1.38058	−0.0597435
$535$	−39.6385	−1.71372
$536$	−15.0132	−0.648470
$537$	5.01317	0.216334
$538$	24.8119	1.06972
$539$	3.19394	0.137573
$540$	−0.806063	−0.0346874
$541$	−10.0263	−0.431066	−0.215533	−	0.976497i	$-0.569149\pi$
$541$	−10.0263	−0.431066	−0.215533	+	0.976497i	$0.569149\pi$
$542$	−9.46168	−0.406414
$543$	13.8496	0.594341
$544$	3.66291	0.157046
$545$	25.9248	1.11050
$546$	0	0
$547$	−26.4485	−1.13086	−0.565428	−	0.824797i	$-0.691289\pi$
$547$	−26.4485	−1.13086	−0.565428	+	0.824797i	$0.691289\pi$
$548$	−0.941921	−0.0402369
$549$	14.4387	0.616227
$550$	58.0713	2.47617
$551$	−18.9234	−0.806162
$552$	1.03761	0.0441637
$553$	−8.96239	−0.381120
$554$	−18.0362	−0.766285
$555$	−6.70052	−0.284421
$556$	0.499293	0.0211747
$557$	5.84367	0.247604	0.123802	−	0.992307i	$-0.460491\pi$
$557$	5.84367	0.247604	0.123802	+	0.992307i	$0.460491\pi$
$558$	15.8496	0.670965
$559$	0	0
$560$	18.0811	0.764066
$561$	−10.7005	−0.451776
$562$	−40.4445	−1.70605
$563$	−1.25060	−0.0527066	−0.0263533	−	0.999653i	$-0.508389\pi$
$563$	−1.25060	−0.0527066	−0.0263533	+	0.999653i	$0.508389\pi$
$564$	0.730841	0.0307739
$565$	16.3127	0.686278
$566$	−40.1016	−1.68559
$567$	1.00000	0.0419961
$568$	−31.6180	−1.32666
$569$	38.2228	1.60238	0.801192	−	0.598407i	$-0.204199\pi$
$569$	38.2228	1.60238	0.801192	+	0.598407i	$0.204199\pi$
$570$	−14.7005	−0.615737
$571$	9.73813	0.407528	0.203764	−	0.979020i	$-0.434682\pi$
$571$	9.73813	0.407528	0.203764	+	0.979020i	$0.434682\pi$
$572$	0	0
$573$	−18.5647	−0.775550
$574$	2.15633	0.0900033
$575$	−4.76116	−0.198554
$576$	7.08110	0.295046
$577$	3.87399	0.161276	0.0806382	−	0.996743i	$-0.474304\pi$
$577$	3.87399	0.161276	0.0806382	+	0.996743i	$0.474304\pi$
$578$	−8.55500	−0.355841
$579$	13.0884	0.543935
$580$	6.38787	0.265242
$581$	6.99271	0.290106
$582$	−4.96239	−0.205698
$583$	−19.1636	−0.793676
$584$	−41.9003	−1.73385
$585$	0	0
$586$	24.8568	1.02683
$587$	11.2447	0.464119	0.232060	−	0.972702i	$-0.425454\pi$
$587$	11.2447	0.464119	0.232060	+	0.972702i	$0.425454\pi$
$588$	0.193937	0.00799781
$589$	25.5515	1.05283
$590$	−37.9003	−1.56033
$591$	−7.24472	−0.298008
$592$	−7.01317	−0.288240
$593$	28.7210	1.17943	0.589715	−	0.807612i	$-0.299240\pi$
$593$	28.7210	1.17943	0.589715	+	0.807612i	$0.299240\pi$
$594$	4.73084	0.194109
$595$	13.9248	0.570860
$596$	−2.59498	−0.106295
$597$	−8.62530	−0.353010
$598$	0	0
$599$	−21.1344	−0.863530	−0.431765	−	0.901986i	$-0.642109\pi$
$599$	−21.1344	−0.863530	−0.431765	+	0.901986i	$0.642109\pi$
$600$	−32.8373	−1.34058
$601$	18.9135	0.771498	0.385749	−	0.922604i	$-0.373943\pi$
$601$	18.9135	0.771498	0.385749	+	0.922604i	$0.373943\pi$
$602$	−2.85097	−0.116197
$603$	5.61213	0.228543
$604$	−3.07381	−0.125071
$605$	3.31994	0.134975
$606$	20.8119	0.845427
$607$	−41.1246	−1.66920	−0.834598	−	0.550860i	$-0.814300\pi$
$607$	−41.1246	−1.66920	−0.834598	+	0.550860i	$0.814300\pi$
$608$	−2.61071	−0.105878
$609$	−7.92478	−0.321128
$610$	−88.8891	−3.59901
$611$	0	0
$612$	−0.649738	−0.0262641
$613$	23.3258	0.942121	0.471061	−	0.882101i	$-0.343871\pi$
$613$	23.3258	0.942121	0.471061	+	0.882101i	$0.343871\pi$
$614$	25.6239	1.03410
$615$	−6.05079	−0.243991
$616$	−8.54420	−0.344256
$617$	−17.7830	−0.715918	−0.357959	−	0.933737i	$-0.616527\pi$
$617$	−17.7830	−0.715918	−0.357959	+	0.933737i	$0.616527\pi$
$618$	−2.11142	−0.0849338
$619$	−8.93795	−0.359247	−0.179623	−	0.983735i	$-0.557488\pi$
$619$	−8.93795	−0.359247	−0.179623	+	0.983735i	$0.557488\pi$
$620$	−8.62530	−0.346400
$621$	−0.387873	−0.0155648
$622$	−25.4010	−1.01849
$623$	−0.932071	−0.0373427
$624$	0	0
$625$	64.3014	2.57206
$626$	−16.0146	−0.640072
$627$	7.62672	0.304582
$628$	−2.46310	−0.0982882
$629$	−5.40105	−0.215354
$630$	−6.15633	−0.245274
$631$	32.2638	1.28440	0.642200	−	0.766537i	$-0.278022\pi$
$631$	32.2638	1.28440	0.642200	+	0.766537i	$0.278022\pi$
$632$	23.9756	0.953697
$633$	18.8872	0.750697
$634$	20.9683	0.832756
$635$	−4.00000	−0.158735
$636$	−1.16362	−0.0461405
$637$	0	0
$638$	−37.4909	−1.48428
$639$	11.8192	0.467562
$640$	−52.6820	−2.08244
$641$	49.4274	1.95226	0.976132	−	0.217176i	$-0.0696847\pi$
$641$	49.4274	1.95226	0.976132	+	0.217176i	$0.0696847\pi$
$642$	14.1260	0.557509
$643$	6.07522	0.239583	0.119792	−	0.992799i	$-0.461777\pi$
$643$	6.07522	0.239583	0.119792	+	0.992799i	$0.461777\pi$
$644$	−0.0752228	−0.00296419
$645$	8.00000	0.315000
$646$	−11.8496	−0.466214
$647$	12.9986	0.511027	0.255514	−	0.966805i	$-0.417755\pi$
$647$	12.9986	0.511027	0.255514	+	0.966805i	$0.417755\pi$
$648$	−2.67513	−0.105089
$649$	19.6629	0.771837
$650$	0	0
$651$	10.7005	0.419387
$652$	1.86414	0.0730055
$653$	15.4010	0.602690	0.301345	−	0.953515i	$-0.402564\pi$
$653$	15.4010	0.602690	0.301345	+	0.953515i	$0.402564\pi$
$654$	−9.23884	−0.361267
$655$	−71.2769	−2.78502
$656$	−6.33312	−0.247267
$657$	15.6629	0.611068
$658$	5.58181	0.217602
$659$	8.76116	0.341286	0.170643	−	0.985333i	$-0.445415\pi$
$659$	8.76116	0.341286	0.170643	+	0.985333i	$0.445415\pi$
$660$	−2.57452	−0.100213
$661$	33.4372	1.30056	0.650279	−	0.759695i	$-0.274652\pi$
$661$	33.4372	1.30056	0.650279	+	0.759695i	$0.274652\pi$
$662$	−25.5515	−0.993087
$663$	0	0
$664$	−18.7064	−0.725949
$665$	−9.92478	−0.384866
$666$	2.38787	0.0925282
$667$	3.07381	0.119018
$668$	−2.34297	−0.0906521
$669$	−16.1622	−0.624867
$670$	−34.5501	−1.33479
$671$	46.1162	1.78029
$672$	−1.09332	−0.0421758
$673$	0.176793	0.00681488	0.00340744	−	0.999994i	$-0.498915\pi$
$673$	0.176793	0.00681488	0.00340744	+	0.999994i	$0.498915\pi$
$674$	8.85097	0.340927
$675$	12.2750	0.472466
$676$	0	0
$677$	−5.67750	−0.218204	−0.109102	−	0.994031i	$-0.534798\pi$
$677$	−5.67750	−0.218204	−0.109102	+	0.994031i	$0.534798\pi$
$678$	−5.81336	−0.223261
$679$	−3.35026	−0.128571
$680$	−37.2506	−1.42850
$681$	−27.2447	−1.04402
$682$	50.6225	1.93843
$683$	−50.4299	−1.92965	−0.964824	−	0.262896i	$-0.915322\pi$
$683$	−50.4299	−1.92965	−0.964824	+	0.262896i	$0.915322\pi$
$684$	0.463096	0.0177069
$685$	20.1866	0.771292
$686$	1.48119	0.0565523
$687$	19.5125	0.744447
$688$	8.37328	0.319228
$689$	0	0
$690$	2.38787	0.0909048
$691$	41.5633	1.58114	0.790570	−	0.612371i	$-0.209784\pi$
$691$	41.5633	1.58114	0.790570	+	0.612371i	$0.209784\pi$
$692$	1.79877	0.0683789
$693$	3.19394	0.121328
$694$	38.1984	1.44999
$695$	−10.7005	−0.405894
$696$	21.1998	0.803577
$697$	−4.87732	−0.184742
$698$	19.1998	0.726724
$699$	21.8496	0.826426
$700$	2.38058	0.0899774
$701$	2.47486	0.0934740	0.0467370	−	0.998907i	$-0.485118\pi$
$701$	2.47486	0.0934740	0.0467370	+	0.998907i	$0.485118\pi$
$702$	0	0
$703$	3.84955	0.145189
$704$	22.6166	0.852395
$705$	−15.6629	−0.589899
$706$	5.60342	0.210887
$707$	14.0508	0.528434
$708$	1.19394	0.0448709
$709$	7.91019	0.297073	0.148537	−	0.988907i	$-0.452544\pi$
$709$	7.91019	0.297073	0.148537	+	0.988907i	$0.452544\pi$
$710$	−72.7631	−2.73075
$711$	−8.96239	−0.336116
$712$	2.49341	0.0934446
$713$	−4.15045	−0.155435
$714$	−4.96239	−0.185713
$715$	0	0
$716$	0.972238	0.0363342
$717$	8.49341	0.317192
$718$	15.8046	0.589824
$719$	−26.5501	−0.990151	−0.495075	−	0.868850i	$-0.664860\pi$
$719$	−26.5501	−0.990151	−0.495075	+	0.868850i	$0.664860\pi$
$720$	18.0811	0.673843
$721$	−1.42548	−0.0530878
$722$	−19.6970	−0.733047
$723$	5.48612	0.204031
$724$	2.68594	0.0998220
$725$	−97.2769	−3.61278
$726$	−1.18313	−0.0439102
$727$	6.44851	0.239162	0.119581	−	0.992824i	$-0.461845\pi$
$727$	6.44851	0.239162	0.119581	+	0.992824i	$0.461845\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−96.4260	−3.56889
$731$	6.44851	0.238507
$732$	2.80018	0.103498
$733$	28.8119	1.06419	0.532097	−	0.846684i	$-0.321404\pi$
$733$	28.8119	1.06419	0.532097	+	0.846684i	$0.321404\pi$
$734$	10.1114	0.373219
$735$	−4.15633	−0.153308
$736$	0.424070	0.0156314
$737$	17.9248	0.660268
$738$	2.15633	0.0793754
$739$	−29.6121	−1.08930	−0.544650	−	0.838664i	$-0.683337\pi$
$739$	−29.6121	−1.08930	−0.544650	+	0.838664i	$0.683337\pi$
$740$	−1.29948	−0.0477697
$741$	0	0
$742$	−8.88717	−0.326258
$743$	−3.77830	−0.138612	−0.0693062	−	0.997595i	$-0.522079\pi$
$743$	−3.77830	−0.138612	−0.0693062	+	0.997595i	$0.522079\pi$
$744$	−28.6253	−1.04945
$745$	55.6140	2.03754
$746$	24.5501	0.898842
$747$	6.99271	0.255850
$748$	−2.07522	−0.0758777
$749$	9.53690	0.348471
$750$	−44.7875	−1.63541
$751$	10.0752	0.367650	0.183825	−	0.982959i	$-0.441152\pi$
$751$	10.0752	0.367650	0.183825	+	0.982959i	$0.441152\pi$
$752$	−16.3938	−0.597819
$753$	−6.44851	−0.234997
$754$	0	0
$755$	65.8759	2.39747
$756$	0.193937	0.00705340
$757$	39.4979	1.43557	0.717787	−	0.696262i	$-0.245155\pi$
$757$	39.4979	1.43557	0.717787	+	0.696262i	$0.245155\pi$
$758$	28.2520	1.02616
$759$	−1.23884	−0.0449671
$760$	26.5501	0.963073
$761$	−25.7685	−0.934106	−0.467053	−	0.884229i	$-0.654684\pi$
$761$	−25.7685	−0.934106	−0.467053	+	0.884229i	$0.654684\pi$
$762$	1.42548	0.0516399
$763$	−6.23743	−0.225810
$764$	−3.60037	−0.130257
$765$	13.9248	0.503451
$766$	−12.2823	−0.443779
$767$	0	0
$768$	4.61213	0.166426
$769$	49.4372	1.78275	0.891376	−	0.453264i	$-0.149741\pi$
$769$	49.4372	1.78275	0.891376	+	0.453264i	$0.149741\pi$
$770$	−19.6629	−0.708602
$771$	−9.90034	−0.356552
$772$	2.53832	0.0913561
$773$	−15.2184	−0.547367	−0.273683	−	0.961820i	$-0.588242\pi$
$773$	−15.2184	−0.547367	−0.273683	+	0.961820i	$0.588242\pi$
$774$	−2.85097	−0.102476
$775$	131.349	4.71821
$776$	8.96239	0.321731
$777$	1.61213	0.0578347
$778$	−1.03761	−0.0372002
$779$	3.47627	0.124550
$780$	0	0
$781$	37.7499	1.35080
$782$	1.92478	0.0688299
$783$	−7.92478	−0.283208
$784$	−4.35026	−0.155366
$785$	52.7875	1.88407
$786$	25.4010	0.906025
$787$	−26.6107	−0.948569	−0.474285	−	0.880372i	$-0.657293\pi$
$787$	−26.6107	−0.948569	−0.474285	+	0.880372i	$0.657293\pi$
$788$	−1.40502	−0.0500516
$789$	3.46168	0.123239
$790$	55.1754	1.96305
$791$	−3.92478	−0.139549
$792$	−8.54420	−0.303605
$793$	0	0
$794$	−18.5139	−0.657033
$795$	24.9380	0.884458
$796$	−1.67276	−0.0592894
$797$	−12.2473	−0.433821	−0.216910	−	0.976192i	$-0.569598\pi$
$797$	−12.2473	−0.433821	−0.216910	+	0.976192i	$0.569598\pi$
$798$	3.53690	0.125205
$799$	−12.6253	−0.446651
$800$	−13.4206	−0.474488
$801$	−0.932071	−0.0329331
$802$	42.5198	1.50142
$803$	50.0263	1.76539
$804$	1.08840	0.0383848
$805$	1.61213	0.0568200
$806$	0	0
$807$	16.7513	0.589674
$808$	−37.5877	−1.32233
$809$	−28.9234	−1.01689	−0.508446	−	0.861094i	$-0.669780\pi$
$809$	−28.9234	−1.01689	−0.508446	+	0.861094i	$0.669780\pi$
$810$	−6.15633	−0.216311
$811$	33.1002	1.16230	0.581152	−	0.813795i	$-0.302602\pi$
$811$	33.1002	1.16230	0.581152	+	0.813795i	$0.302602\pi$
$812$	−1.53690	−0.0539348
$813$	−6.38787	−0.224032
$814$	7.62672	0.267316
$815$	−39.9511	−1.39943
$816$	14.5745	0.510210
$817$	−4.59612	−0.160798
$818$	34.7367	1.21454
$819$	0	0
$820$	−1.17347	−0.0409793
$821$	6.46898	0.225769	0.112884	−	0.993608i	$-0.463991\pi$
$821$	6.46898	0.225769	0.112884	+	0.993608i	$0.463991\pi$
$822$	−7.19394	−0.250917
$823$	−9.55149	−0.332944	−0.166472	−	0.986046i	$-0.553238\pi$
$823$	−9.55149	−0.332944	−0.166472	+	0.986046i	$0.553238\pi$
$824$	3.81336	0.132845
$825$	39.2057	1.36497
$826$	9.11871	0.317281
$827$	36.3430	1.26377	0.631884	−	0.775063i	$-0.282282\pi$
$827$	36.3430	1.26377	0.631884	+	0.775063i	$0.282282\pi$
$828$	−0.0752228	−0.00261417
$829$	21.7645	0.755912	0.377956	−	0.925824i	$-0.376627\pi$
$829$	21.7645	0.755912	0.377956	+	0.925824i	$0.376627\pi$
$830$	−43.0494	−1.49427
$831$	−12.1768	−0.422408
$832$	0	0
$833$	−3.35026	−0.116080
$834$	3.81336	0.132046
$835$	50.2130	1.73769
$836$	1.47910	0.0511557
$837$	10.7005	0.369864
$838$	−50.6225	−1.74872
$839$	−0.0693432	−0.00239399	−0.00119700	−	0.999999i	$-0.500381\pi$
$839$	−0.0693432	−0.00239399	−0.00119700	+	0.999999i	$0.500381\pi$
$840$	11.1187	0.383632
$841$	33.8021	1.16559
$842$	−8.22284	−0.283378
$843$	−27.3054	−0.940446
$844$	3.66291	0.126083
$845$	0	0
$846$	5.58181	0.191907
$847$	−0.798769	−0.0274460
$848$	26.1016	0.896332
$849$	−27.0738	−0.929171
$850$	−60.9135	−2.08932
$851$	−0.625301	−0.0214350
$852$	2.29218	0.0785289
$853$	−5.17347	−0.177136	−0.0885681	−	0.996070i	$-0.528229\pi$
$853$	−5.17347	−0.177136	−0.0885681	+	0.996070i	$0.528229\pi$
$854$	21.3865	0.731830
$855$	−9.92478	−0.339420
$856$	−25.5125	−0.871998
$857$	−41.2750	−1.40993	−0.704964	−	0.709243i	$-0.749037\pi$
$857$	−41.2750	−1.40993	−0.704964	+	0.709243i	$0.749037\pi$
$858$	0	0
$859$	−14.1768	−0.483706	−0.241853	−	0.970313i	$-0.577755\pi$
$859$	−14.1768	−0.483706	−0.241853	+	0.970313i	$0.577755\pi$
$860$	1.55149	0.0529055
$861$	1.45580	0.0496136
$862$	8.04491	0.274011
$863$	7.62786	0.259655	0.129828	−	0.991537i	$-0.458558\pi$
$863$	7.62786	0.259655	0.129828	+	0.991537i	$0.458558\pi$
$864$	−1.09332	−0.0371955
$865$	−38.5501	−1.31074
$866$	−59.5633	−2.02404
$867$	−5.77575	−0.196155
$868$	2.07522	0.0704377
$869$	−28.6253	−0.971047
$870$	48.7875	1.65405
$871$	0	0
$872$	16.6859	0.565057
$873$	−3.35026	−0.113389
$874$	−1.37187	−0.0464042
$875$	−30.2374	−1.02221
$876$	3.03761	0.102631
$877$	−43.1754	−1.45793	−0.728964	−	0.684552i	$-0.759998\pi$
$877$	−43.1754	−1.45793	−0.728964	+	0.684552i	$0.759998\pi$
$878$	33.4372	1.12845
$879$	16.7816	0.566030
$880$	57.7499	1.94675
$881$	29.9003	1.00737	0.503684	−	0.863888i	$-0.331978\pi$
$881$	29.9003	1.00737	0.503684	+	0.863888i	$0.331978\pi$
$882$	1.48119	0.0498744
$883$	9.83971	0.331132	0.165566	−	0.986199i	$-0.447055\pi$
$883$	9.83971	0.331132	0.165566	+	0.986199i	$0.447055\pi$
$884$	0	0
$885$	−25.5877	−0.860121
$886$	−12.2012	−0.409908
$887$	−43.0249	−1.44464	−0.722318	−	0.691561i	$-0.756923\pi$
$887$	−43.0249	−1.44464	−0.722318	+	0.691561i	$0.756923\pi$
$888$	−4.31265	−0.144723
$889$	0.962389	0.0322775
$890$	5.73813	0.192343
$891$	3.19394	0.107001
$892$	−3.13444	−0.104949
$893$	8.99859	0.301126
$894$	−19.8192	−0.662854
$895$	−20.8364	−0.696483
$896$	12.6751	0.423446
$897$	0	0
$898$	3.56722	0.119040
$899$	−84.7993	−2.82821
$900$	2.38058	0.0793526
$901$	20.1016	0.669680
$902$	6.88717	0.229318
$903$	−1.92478	−0.0640526
$904$	10.4993	0.349201
$905$	−57.5633	−1.91347
$906$	−23.4763	−0.779947
$907$	11.2605	0.373897	0.186949	−	0.982370i	$-0.440140\pi$
$907$	11.2605	0.373897	0.186949	+	0.982370i	$0.440140\pi$
$908$	−5.28375	−0.175347
$909$	14.0508	0.466035
$910$	0	0
$911$	23.5633	0.780685	0.390343	−	0.920670i	$-0.372357\pi$
$911$	23.5633	0.780685	0.390343	+	0.920670i	$0.372357\pi$
$912$	−10.3879	−0.343977
$913$	22.3343	0.739156
$914$	−43.7889	−1.44841
$915$	−60.0118	−1.98393
$916$	3.78418	0.125033
$917$	17.1490	0.566311
$918$	−4.96239	−0.163783
$919$	12.8411	0.423589	0.211795	−	0.977314i	$-0.432069\pi$
$919$	12.8411	0.423589	0.211795	+	0.977314i	$0.432069\pi$
$920$	−4.31265	−0.142184
$921$	17.2995	0.570037
$922$	49.9452	1.64486
$923$	0	0
$924$	0.619421	0.0203775
$925$	19.7889	0.650656
$926$	24.9380	0.819512
$927$	−1.42548	−0.0468191
$928$	8.66433	0.284420
$929$	−24.6194	−0.807737	−0.403869	−	0.914817i	$-0.632335\pi$
$929$	−24.6194	−0.807737	−0.403869	+	0.914817i	$0.632335\pi$
$930$	−65.8759	−2.16016
$931$	2.38787	0.0782594
$932$	4.23743	0.138802
$933$	−17.1490	−0.561434
$934$	33.6239	1.10021
$935$	44.4749	1.45448
$936$	0	0
$937$	44.4847	1.45325	0.726626	−	0.687033i	$-0.241087\pi$
$937$	44.4847	1.45325	0.726626	+	0.687033i	$0.241087\pi$
$938$	8.31265	0.271418
$939$	−10.8119	−0.352834
$940$	−3.03761	−0.0990760
$941$	−2.69464	−0.0878429	−0.0439214	−	0.999035i	$-0.513985\pi$
$941$	−2.69464	−0.0878429	−0.0439214	+	0.999035i	$0.513985\pi$
$942$	−18.8119	−0.612926
$943$	−0.564666	−0.0183881
$944$	−26.7816	−0.871668
$945$	−4.15633	−0.135205
$946$	−9.10581	−0.296056
$947$	−3.09237	−0.100488	−0.0502442	−	0.998737i	$-0.516000\pi$
$947$	−3.09237	−0.100488	−0.0502442	+	0.998737i	$0.516000\pi$
$948$	−1.73813	−0.0564520
$949$	0	0
$950$	43.4156	1.40859
$951$	14.1563	0.459050
$952$	8.96239	0.290473
$953$	−8.57925	−0.277909	−0.138955	−	0.990299i	$-0.544374\pi$
$953$	−8.57925	−0.277909	−0.138955	+	0.990299i	$0.544374\pi$
$954$	−8.88717	−0.287733
$955$	77.1608	2.49686
$956$	1.64718	0.0532737
$957$	−25.3112	−0.818196
$958$	−14.9537	−0.483131
$959$	−4.85685	−0.156836
$960$	−29.4314	−0.949893
$961$	83.5012	2.69359
$962$	0	0
$963$	9.53690	0.307322
$964$	1.06396	0.0342678
$965$	−54.3996	−1.75119
$966$	−0.574515	−0.0184847
$967$	−7.43533	−0.239104	−0.119552	−	0.992828i	$-0.538146\pi$
$967$	−7.43533	−0.239104	−0.119552	+	0.992828i	$0.538146\pi$
$968$	2.13681	0.0686797
$969$	−8.00000	−0.256997
$970$	20.6253	0.662238
$971$	52.3244	1.67917	0.839585	−	0.543228i	$-0.182798\pi$
$971$	52.3244	1.67917	0.839585	+	0.543228i	$0.182798\pi$
$972$	0.193937	0.00622052
$973$	2.57452	0.0825352
$974$	−13.9248	−0.446179
$975$	0	0
$976$	−62.8119	−2.01056
$977$	12.0811	0.386509	0.193254	−	0.981149i	$-0.438096\pi$
$977$	12.0811	0.386509	0.193254	+	0.981149i	$0.438096\pi$
$978$	14.2374	0.455263
$979$	−2.97698	−0.0951446
$980$	−0.806063	−0.0257488
$981$	−6.23743	−0.199146
$982$	−30.7513	−0.981314
$983$	16.7553	0.534410	0.267205	−	0.963640i	$-0.413900\pi$
$983$	16.7553	0.534410	0.267205	+	0.963640i	$0.413900\pi$
$984$	−3.89446	−0.124151
$985$	30.1114	0.959430
$986$	39.3258	1.25239
$987$	3.76845	0.119951
$988$	0	0
$989$	0.746569	0.0237395
$990$	−19.6629	−0.624928
$991$	−1.77433	−0.0563635	−0.0281818	−	0.999603i	$-0.508972\pi$
$991$	−1.77433	−0.0563635	−0.0281818	+	0.999603i	$0.508972\pi$
$992$	−11.6991	−0.371447
$993$	−17.2506	−0.547431
$994$	17.5066	0.555275
$995$	35.8496	1.13651
$996$	1.35614	0.0429710
$997$	24.5501	0.777509	0.388754	−	0.921341i	$-0.372905\pi$
$997$	24.5501	0.777509	0.388754	+	0.921341i	$0.372905\pi$
$998$	33.9972	1.07616
$999$	1.61213	0.0510054

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.k.1.3		3
13.5	odd	4		273.2.c.b.64.2	✓	6
13.8	odd	4		273.2.c.b.64.5	yes	6
13.12	even	2		3549.2.a.q.1.1		3
39.5	even	4		819.2.c.c.64.5		6
39.8	even	4		819.2.c.c.64.2		6
52.31	even	4		4368.2.h.o.337.6		6
52.47	even	4		4368.2.h.o.337.1		6
91.34	even	4		1911.2.c.h.883.5		6
91.83	even	4		1911.2.c.h.883.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.c.b.64.2	✓	6	13.5	odd	4
273.2.c.b.64.5	yes	6	13.8	odd	4
819.2.c.c.64.2		6	39.8	even	4
819.2.c.c.64.5		6	39.5	even	4
1911.2.c.h.883.2		6	91.83	even	4
1911.2.c.h.883.5		6	91.34	even	4
3549.2.a.k.1.3		3	1.1	even	1	trivial
3549.2.a.q.1.1		3	13.12	even	2
4368.2.h.o.337.1		6	52.47	even	4
4368.2.h.o.337.6		6	52.31	even	4

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:	\( N \)	\(=\)	\( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3549.a (trivial)

\(f(q)\)	\(=\)	\(q+1.48119 q^{2} +1.00000 q^{3} +0.193937 q^{4} -4.15633 q^{5} +1.48119 q^{6} +1.00000 q^{7} -2.67513 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.48119 q^{2} +1.00000 q^{3} +0.193937 q^{4} -4.15633 q^{5} +1.48119 q^{6} +1.00000 q^{7} -2.67513 q^{8} +1.00000 q^{9} -6.15633 q^{10} +3.19394 q^{11} +0.193937 q^{12} +1.48119 q^{14} -4.15633 q^{15} -4.35026 q^{16} -3.35026 q^{17} +1.48119 q^{18} +2.38787 q^{19} -0.806063 q^{20} +1.00000 q^{21} +4.73084 q^{22} -0.387873 q^{23} -2.67513 q^{24} +12.2750 q^{25} +1.00000 q^{27} +0.193937 q^{28} -7.92478 q^{29} -6.15633 q^{30} +10.7005 q^{31} -1.09332 q^{32} +3.19394 q^{33} -4.96239 q^{34} -4.15633 q^{35} +0.193937 q^{36} +1.61213 q^{37} +3.53690 q^{38} +11.1187 q^{40} +1.45580 q^{41} +1.48119 q^{42} -1.92478 q^{43} +0.619421 q^{44} -4.15633 q^{45} -0.574515 q^{46} +3.76845 q^{47} -4.35026 q^{48} +1.00000 q^{49} +18.1817 q^{50} -3.35026 q^{51} -6.00000 q^{53} +1.48119 q^{54} -13.2750 q^{55} -2.67513 q^{56} +2.38787 q^{57} -11.7381 q^{58} +6.15633 q^{59} -0.806063 q^{60} +14.4387 q^{61} +15.8496 q^{62} +1.00000 q^{63} +7.08110 q^{64} +4.73084 q^{66} +5.61213 q^{67} -0.649738 q^{68} -0.387873 q^{69} -6.15633 q^{70} +11.8192 q^{71} -2.67513 q^{72} +15.6629 q^{73} +2.38787 q^{74} +12.2750 q^{75} +0.463096 q^{76} +3.19394 q^{77} -8.96239 q^{79} +18.0811 q^{80} +1.00000 q^{81} +2.15633 q^{82} +6.99271 q^{83} +0.193937 q^{84} +13.9248 q^{85} -2.85097 q^{86} -7.92478 q^{87} -8.54420 q^{88} -0.932071 q^{89} -6.15633 q^{90} -0.0752228 q^{92} +10.7005 q^{93} +5.58181 q^{94} -9.92478 q^{95} -1.09332 q^{96} -3.35026 q^{97} +1.48119 q^{98} +3.19394 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - q^{2} + 3 q^{3} + q^{4} - 2 q^{5} - q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - q^2 + 3 * q^3 + q^4 - 2 * q^5 - q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - q^{2} + 3 q^{3} + q^{4} - 2 q^{5} - q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9} - 8 q^{10} + 10 q^{11} + q^{12} - q^{14} - 2 q^{15} - 3 q^{16} - q^{18} + 8 q^{19} - 2 q^{20} + 3 q^{21} - 8 q^{22} - 2 q^{23} - 3 q^{24} + 5 q^{25} + 3 q^{27} + q^{28} - 2 q^{29} - 8 q^{30} + 12 q^{31} + 3 q^{32} + 10 q^{33} - 4 q^{34} - 2 q^{35} + q^{36} + 4 q^{37} - 12 q^{38} + 12 q^{40} + 14 q^{41} - q^{42} + 16 q^{43} + 14 q^{44} - 2 q^{45} + 10 q^{46} - 3 q^{48} + 3 q^{49} + 29 q^{50} - 18 q^{53} - q^{54} - 8 q^{55} - 3 q^{56} + 8 q^{57} - 26 q^{58} + 8 q^{59} - 2 q^{60} + 14 q^{61} + 4 q^{62} + 3 q^{63} - 11 q^{64} - 8 q^{66} + 16 q^{67} - 12 q^{68} - 2 q^{69} - 8 q^{70} - 6 q^{71} - 3 q^{72} + 16 q^{73} + 8 q^{74} + 5 q^{75} + 24 q^{76} + 10 q^{77} - 16 q^{79} + 22 q^{80} + 3 q^{81} - 4 q^{82} + 8 q^{83} + q^{84} + 20 q^{85} - 32 q^{86} - 2 q^{87} - 16 q^{88} + 6 q^{89} - 8 q^{90} - 22 q^{92} + 12 q^{93} + 18 q^{94} - 8 q^{95} + 3 q^{96} - q^{98} + 10 q^{99}+O(q^{100}) \) 3 * q - q^2 + 3 * q^3 + q^4 - 2 * q^5 - q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9 - 8 * q^10 + 10 * q^11 + q^12 - q^14 - 2 * q^15 - 3 * q^16 - q^18 + 8 * q^19 - 2 * q^20 + 3 * q^21 - 8 * q^22 - 2 * q^23 - 3 * q^24 + 5 * q^25 + 3 * q^27 + q^28 - 2 * q^29 - 8 * q^30 + 12 * q^31 + 3 * q^32 + 10 * q^33 - 4 * q^34 - 2 * q^35 + q^36 + 4 * q^37 - 12 * q^38 + 12 * q^40 + 14 * q^41 - q^42 + 16 * q^43 + 14 * q^44 - 2 * q^45 + 10 * q^46 - 3 * q^48 + 3 * q^49 + 29 * q^50 - 18 * q^53 - q^54 - 8 * q^55 - 3 * q^56 + 8 * q^57 - 26 * q^58 + 8 * q^59 - 2 * q^60 + 14 * q^61 + 4 * q^62 + 3 * q^63 - 11 * q^64 - 8 * q^66 + 16 * q^67 - 12 * q^68 - 2 * q^69 - 8 * q^70 - 6 * q^71 - 3 * q^72 + 16 * q^73 + 8 * q^74 + 5 * q^75 + 24 * q^76 + 10 * q^77 - 16 * q^79 + 22 * q^80 + 3 * q^81 - 4 * q^82 + 8 * q^83 + q^84 + 20 * q^85 - 32 * q^86 - 2 * q^87 - 16 * q^88 + 6 * q^89 - 8 * q^90 - 22 * q^92 + 12 * q^93 + 18 * q^94 - 8 * q^95 + 3 * q^96 - q^98 + 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more