LMFDB - Embedded newform 3549.2.a.be.1.6

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:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - x^{8} - 11x^{7} + 8x^{6} + 37x^{5} - 18x^{4} - 41x^{3} + 12x^{2} + 6x - 1 $ x^9 - x^8 - 11x^7 + 8x^6 + 37x^5 - 18x^4 - 41x^3 + 12x^2 + 6*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-0.374817$ 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)

$f(q)$	$=$	$q+0.374817 q^{2} -1.00000 q^{3} -1.85951 q^{4} -1.32690 q^{5} -0.374817 q^{6} +1.00000 q^{7} -1.44661 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.374817 q^{2} -1.00000 q^{3} -1.85951 q^{4} -1.32690 q^{5} -0.374817 q^{6} +1.00000 q^{7} -1.44661 q^{8} +1.00000 q^{9} -0.497345 q^{10} -5.82806 q^{11} +1.85951 q^{12} +0.374817 q^{14} +1.32690 q^{15} +3.17681 q^{16} -0.442994 q^{17} +0.374817 q^{18} -1.34585 q^{19} +2.46739 q^{20} -1.00000 q^{21} -2.18446 q^{22} -2.67807 q^{23} +1.44661 q^{24} -3.23933 q^{25} -1.00000 q^{27} -1.85951 q^{28} +3.35417 q^{29} +0.497345 q^{30} -8.32825 q^{31} +4.08395 q^{32} +5.82806 q^{33} -0.166042 q^{34} -1.32690 q^{35} -1.85951 q^{36} -7.93555 q^{37} -0.504446 q^{38} +1.91951 q^{40} +0.816015 q^{41} -0.374817 q^{42} +3.16166 q^{43} +10.8373 q^{44} -1.32690 q^{45} -1.00379 q^{46} -4.29060 q^{47} -3.17681 q^{48} +1.00000 q^{49} -1.21416 q^{50} +0.442994 q^{51} -1.85465 q^{53} -0.374817 q^{54} +7.73326 q^{55} -1.44661 q^{56} +1.34585 q^{57} +1.25720 q^{58} +6.16798 q^{59} -2.46739 q^{60} -11.0420 q^{61} -3.12157 q^{62} +1.00000 q^{63} -4.82289 q^{64} +2.18446 q^{66} +1.64442 q^{67} +0.823753 q^{68} +2.67807 q^{69} -0.497345 q^{70} +12.9896 q^{71} -1.44661 q^{72} -7.20060 q^{73} -2.97438 q^{74} +3.23933 q^{75} +2.50262 q^{76} -5.82806 q^{77} -2.54704 q^{79} -4.21531 q^{80} +1.00000 q^{81} +0.305856 q^{82} +16.2210 q^{83} +1.85951 q^{84} +0.587809 q^{85} +1.18504 q^{86} -3.35417 q^{87} +8.43094 q^{88} +0.249528 q^{89} -0.497345 q^{90} +4.97991 q^{92} +8.32825 q^{93} -1.60819 q^{94} +1.78580 q^{95} -4.08395 q^{96} +3.75470 q^{97} +0.374817 q^{98} -5.82806 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - q^{2} - 9 q^{3} + 5 q^{4} + 9 q^{5} + q^{6} + 9 q^{7} - 6 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q - q^2 - 9 * q^3 + 5 * q^4 + 9 * q^5 + q^6 + 9 * q^7 - 6 * q^8 + 9 * q^9	$ 9 q - q^{2} - 9 q^{3} + 5 q^{4} + 9 q^{5} + q^{6} + 9 q^{7} - 6 q^{8} + 9 q^{9} + q^{10} - q^{11} - 5 q^{12} - q^{14} - 9 q^{15} + 5 q^{16} + 11 q^{17} - q^{18} + 7 q^{19} + 23 q^{20} - 9 q^{21} - 3 q^{22} + 22 q^{23} + 6 q^{24} - 8 q^{25} - 9 q^{27} + 5 q^{28} + 11 q^{29} - q^{30} + 7 q^{31} - 18 q^{32} + q^{33} - 6 q^{34} + 9 q^{35} + 5 q^{36} - q^{37} - 6 q^{38} - 14 q^{40} + 16 q^{41} + q^{42} + 32 q^{43} + 18 q^{44} + 9 q^{45} - 9 q^{46} - 12 q^{47} - 5 q^{48} + 9 q^{49} + 10 q^{50} - 11 q^{51} + 13 q^{53} + q^{54} + 9 q^{55} - 6 q^{56} - 7 q^{57} + 4 q^{58} + 29 q^{59} - 23 q^{60} - 12 q^{61} + 30 q^{62} + 9 q^{63} + 6 q^{64} + 3 q^{66} - 20 q^{67} + 34 q^{68} - 22 q^{69} + q^{70} - 2 q^{71} - 6 q^{72} + q^{73} + 43 q^{74} + 8 q^{75} + 13 q^{76} - q^{77} + 3 q^{79} - 39 q^{80} + 9 q^{81} - 19 q^{82} + 24 q^{83} - 5 q^{84} + 15 q^{85} - 28 q^{86} - 11 q^{87} - 19 q^{88} + 11 q^{89} + q^{90} + 73 q^{92} - 7 q^{93} + 15 q^{94} + 39 q^{95} + 18 q^{96} + 20 q^{97} - q^{98} - q^{99}+O(q^{100}) $ 9 * q - q^2 - 9 * q^3 + 5 * q^4 + 9 * q^5 + q^6 + 9 * q^7 - 6 * q^8 + 9 * q^9 + q^10 - q^11 - 5 * q^12 - q^14 - 9 * q^15 + 5 * q^16 + 11 * q^17 - q^18 + 7 * q^19 + 23 * q^20 - 9 * q^21 - 3 * q^22 + 22 * q^23 + 6 * q^24 - 8 * q^25 - 9 * q^27 + 5 * q^28 + 11 * q^29 - q^30 + 7 * q^31 - 18 * q^32 + q^33 - 6 * q^34 + 9 * q^35 + 5 * q^36 - q^37 - 6 * q^38 - 14 * q^40 + 16 * q^41 + q^42 + 32 * q^43 + 18 * q^44 + 9 * q^45 - 9 * q^46 - 12 * q^47 - 5 * q^48 + 9 * q^49 + 10 * q^50 - 11 * q^51 + 13 * q^53 + q^54 + 9 * q^55 - 6 * q^56 - 7 * q^57 + 4 * q^58 + 29 * q^59 - 23 * q^60 - 12 * q^61 + 30 * q^62 + 9 * q^63 + 6 * q^64 + 3 * q^66 - 20 * q^67 + 34 * q^68 - 22 * q^69 + q^70 - 2 * q^71 - 6 * q^72 + q^73 + 43 * q^74 + 8 * q^75 + 13 * q^76 - q^77 + 3 * q^79 - 39 * q^80 + 9 * q^81 - 19 * q^82 + 24 * q^83 - 5 * q^84 + 15 * q^85 - 28 * q^86 - 11 * q^87 - 19 * q^88 + 11 * q^89 + q^90 + 73 * q^92 - 7 * q^93 + 15 * q^94 + 39 * q^95 + 18 * q^96 + 20 * q^97 - q^98 - q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0.374817	0.265036	0.132518	−	0.991181i	$-0.457694\pi$
$2$	0.374817	0.265036	0.132518	+	0.991181i	$0.457694\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.85951	−0.929756
$5$	−1.32690	−0.593408	−0.296704	−	0.954969i	$-0.595888\pi$
$5$	−1.32690	−0.593408	−0.296704	+	0.954969i	$0.595888\pi$
$6$	−0.374817	−0.153018
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.44661	−0.511454
$9$	1.00000	0.333333
$10$	−0.497345	−0.157274
$11$	−5.82806	−1.75723	−0.878613	−	0.477534i	$-0.841531\pi$
$11$	−5.82806	−1.75723	−0.878613	+	0.477534i	$0.841531\pi$
$12$	1.85951	0.536795
$13$	0	0
$13$	0	0
$14$	0.374817	0.100174
$15$	1.32690	0.342604
$16$	3.17681	0.794202
$17$	−0.442994	−0.107442	−0.0537209	−	0.998556i	$-0.517108\pi$
$17$	−0.442994	−0.107442	−0.0537209	+	0.998556i	$0.517108\pi$
$18$	0.374817	0.0883452
$19$	−1.34585	−0.308758	−0.154379	−	0.988012i	$-0.549338\pi$
$19$	−1.34585	−0.308758	−0.154379	+	0.988012i	$0.549338\pi$
$20$	2.46739	0.551725
$21$	−1.00000	−0.218218
$22$	−2.18446	−0.465728
$23$	−2.67807	−0.558417	−0.279209	−	0.960230i	$-0.590072\pi$
$23$	−2.67807	−0.558417	−0.279209	+	0.960230i	$0.590072\pi$
$24$	1.44661	0.295288
$25$	−3.23933	−0.647867
$26$	0	0
$27$	−1.00000	−0.192450
$28$	−1.85951	−0.351415
$29$	3.35417	0.622853	0.311427	−	0.950270i	$-0.399193\pi$
$29$	3.35417	0.622853	0.311427	+	0.950270i	$0.399193\pi$
$30$	0.497345	0.0908024
$31$	−8.32825	−1.49580	−0.747899	−	0.663813i	$-0.768937\pi$
$31$	−8.32825	−1.49580	−0.747899	+	0.663813i	$0.768937\pi$
$32$	4.08395	0.721946
$33$	5.82806	1.01454
$34$	−0.166042	−0.0284759
$35$	−1.32690	−0.224287
$36$	−1.85951	−0.309919
$37$	−7.93555	−1.30460	−0.652298	−	0.757962i	$-0.726195\pi$
$37$	−7.93555	−1.30460	−0.652298	+	0.757962i	$0.726195\pi$
$38$	−0.504446	−0.0818319
$39$	0	0
$40$	1.91951	0.303501
$41$	0.816015	0.127440	0.0637201	−	0.997968i	$-0.479704\pi$
$41$	0.816015	0.127440	0.0637201	+	0.997968i	$0.479704\pi$
$42$	−0.374817	−0.0578355
$43$	3.16166	0.482149	0.241074	−	0.970507i	$-0.422500\pi$
$43$	3.16166	0.482149	0.241074	+	0.970507i	$0.422500\pi$
$44$	10.8373	1.63379
$45$	−1.32690	−0.197803
$46$	−1.00379	−0.148000
$47$	−4.29060	−0.625848	−0.312924	−	0.949778i	$-0.601308\pi$
$47$	−4.29060	−0.625848	−0.312924	+	0.949778i	$0.601308\pi$
$48$	−3.17681	−0.458533
$49$	1.00000	0.142857
$50$	−1.21416	−0.171708
$51$	0.442994	0.0620316
$52$	0	0
$53$	−1.85465	−0.254756	−0.127378	−	0.991854i	$-0.540656\pi$
$53$	−1.85465	−0.254756	−0.127378	+	0.991854i	$0.540656\pi$
$54$	−0.374817	−0.0510061
$55$	7.73326	1.04275
$56$	−1.44661	−0.193312
$57$	1.34585	0.178262
$58$	1.25720	0.165078
$59$	6.16798	0.803002	0.401501	−	0.915858i	$-0.368489\pi$
$59$	6.16798	0.803002	0.401501	+	0.915858i	$0.368489\pi$
$60$	−2.46739	−0.318539
$61$	−11.0420	−1.41379	−0.706893	−	0.707320i	$-0.749904\pi$
$61$	−11.0420	−1.41379	−0.706893	+	0.707320i	$0.749904\pi$
$62$	−3.12157	−0.396440
$63$	1.00000	0.125988
$64$	−4.82289	−0.602861
$65$	0	0
$66$	2.18446	0.268888
$67$	1.64442	0.200898	0.100449	−	0.994942i	$-0.467972\pi$
$67$	1.64442	0.200898	0.100449	+	0.994942i	$0.467972\pi$
$68$	0.823753	0.0998947
$69$	2.67807	0.322402
$70$	−0.497345	−0.0594441
$71$	12.9896	1.54158	0.770792	−	0.637087i	$-0.219861\pi$
$71$	12.9896	1.54158	0.770792	+	0.637087i	$0.219861\pi$
$72$	−1.44661	−0.170485
$73$	−7.20060	−0.842767	−0.421384	−	0.906883i	$-0.638455\pi$
$73$	−7.20060	−0.842767	−0.421384	+	0.906883i	$0.638455\pi$
$74$	−2.97438	−0.345765
$75$	3.23933	0.374046
$76$	2.50262	0.287070
$77$	−5.82806	−0.664169
$78$	0	0
$79$	−2.54704	−0.286565	−0.143282	−	0.989682i	$-0.545766\pi$
$79$	−2.54704	−0.286565	−0.143282	+	0.989682i	$0.545766\pi$
$80$	−4.21531	−0.471286
$81$	1.00000	0.111111
$82$	0.305856	0.0337762
$83$	16.2210	1.78049	0.890243	−	0.455486i	$-0.150535\pi$
$83$	16.2210	1.78049	0.890243	+	0.455486i	$0.150535\pi$
$84$	1.85951	0.202889
$85$	0.587809	0.0637569
$86$	1.18504	0.127787
$87$	−3.35417	−0.359604
$88$	8.43094	0.898741
$89$	0.249528	0.0264499	0.0132249	−	0.999913i	$-0.495790\pi$
$89$	0.249528	0.0264499	0.0132249	+	0.999913i	$0.495790\pi$
$90$	−0.497345	−0.0524248
$91$	0	0
$92$	4.97991	0.519192
$93$	8.32825	0.863599
$94$	−1.60819	−0.165872
$95$	1.78580	0.183220
$96$	−4.08395	−0.416816
$97$	3.75470	0.381232	0.190616	−	0.981665i	$-0.438952\pi$
$97$	3.75470	0.381232	0.190616	+	0.981665i	$0.438952\pi$
$98$	0.374817	0.0378622
$99$	−5.82806	−0.585742
$100$	6.02358	0.602358
$101$	2.83930	0.282521	0.141261	−	0.989972i	$-0.454884\pi$
$101$	2.83930	0.282521	0.141261	+	0.989972i	$0.454884\pi$
$102$	0.166042	0.0164406
$103$	−13.0189	−1.28279	−0.641395	−	0.767211i	$-0.721644\pi$
$103$	−13.0189	−1.28279	−0.641395	+	0.767211i	$0.721644\pi$
$104$	0	0
$105$	1.32690	0.129492
$106$	−0.695154	−0.0675194
$107$	14.5111	1.40284	0.701421	−	0.712748i	$-0.252550\pi$
$107$	14.5111	1.40284	0.701421	+	0.712748i	$0.252550\pi$
$108$	1.85951	0.178932
$109$	−13.5778	−1.30051	−0.650257	−	0.759714i	$-0.725339\pi$
$109$	−13.5778	−1.30051	−0.650257	+	0.759714i	$0.725339\pi$
$110$	2.89856	0.276367
$111$	7.93555	0.753209
$112$	3.17681	0.300180
$113$	15.8715	1.49306	0.746532	−	0.665349i	$-0.231717\pi$
$113$	15.8715	1.49306	0.746532	+	0.665349i	$0.231717\pi$
$114$	0.504446	0.0472457
$115$	3.55354	0.331369
$116$	−6.23711	−0.579101
$117$	0	0
$118$	2.31186	0.212824
$119$	−0.442994	−0.0406092
$120$	−1.91951	−0.175227
$121$	22.9663	2.08784
$122$	−4.13874	−0.374704
$123$	−0.816015	−0.0735776
$124$	15.4865	1.39073
$125$	10.9328	0.977858
$126$	0.374817	0.0333914
$127$	−6.24679	−0.554313	−0.277157	−	0.960825i	$-0.589392\pi$
$127$	−6.24679	−0.554313	−0.277157	+	0.960825i	$0.589392\pi$
$128$	−9.97559	−0.881726
$129$	−3.16166	−0.278369
$130$	0	0
$131$	14.6868	1.28319	0.641596	−	0.767043i	$-0.278273\pi$
$131$	14.6868	1.28319	0.641596	+	0.767043i	$0.278273\pi$
$132$	−10.8373	−0.943270
$133$	−1.34585	−0.116700
$134$	0.616356	0.0532451
$135$	1.32690	0.114201
$136$	0.640840	0.0549516
$137$	0.933243	0.0797323	0.0398662	−	0.999205i	$-0.487307\pi$
$137$	0.933243	0.0797323	0.0398662	+	0.999205i	$0.487307\pi$
$138$	1.00379	0.0854481
$139$	20.0765	1.70287	0.851435	−	0.524461i	$-0.175733\pi$
$139$	20.0765	1.70287	0.851435	+	0.524461i	$0.175733\pi$
$140$	2.46739	0.208532
$141$	4.29060	0.361333
$142$	4.86873	0.408575
$143$	0	0
$144$	3.17681	0.264734
$145$	−4.45065	−0.369606
$146$	−2.69891	−0.223363
$147$	−1.00000	−0.0824786
$148$	14.7563	1.21296
$149$	−12.2978	−1.00748	−0.503739	−	0.863856i	$-0.668043\pi$
$149$	−12.2978	−1.00748	−0.503739	+	0.863856i	$0.668043\pi$
$150$	1.21416	0.0991355
$151$	−18.6796	−1.52013	−0.760064	−	0.649849i	$-0.774832\pi$
$151$	−18.6796	−1.52013	−0.760064	+	0.649849i	$0.774832\pi$
$152$	1.94692	0.157916
$153$	−0.442994	−0.0358139
$154$	−2.18446	−0.176029
$155$	11.0508	0.887619
$156$	0	0
$157$	24.3864	1.94624	0.973122	−	0.230288i	$-0.0739669\pi$
$157$	24.3864	1.94624	0.973122	+	0.230288i	$0.0739669\pi$
$158$	−0.954675	−0.0759499
$159$	1.85465	0.147083
$160$	−5.41899	−0.428409
$161$	−2.67807	−0.211062
$162$	0.374817	0.0294484
$163$	22.2649	1.74392	0.871962	−	0.489574i	$-0.162848\pi$
$163$	22.2649	1.74392	0.871962	+	0.489574i	$0.162848\pi$
$164$	−1.51739	−0.118488
$165$	−7.73326	−0.602034
$166$	6.07991	0.471892
$167$	−18.3284	−1.41829	−0.709146	−	0.705062i	$-0.750919\pi$
$167$	−18.3284	−1.41829	−0.709146	+	0.705062i	$0.750919\pi$
$168$	1.44661	0.111608
$169$	0	0
$170$	0.220321	0.0168979
$171$	−1.34585	−0.102919
$172$	−5.87914	−0.448281
$173$	−12.7444	−0.968940	−0.484470	−	0.874808i	$-0.660988\pi$
$173$	−12.7444	−0.968940	−0.484470	+	0.874808i	$0.660988\pi$
$174$	−1.25720	−0.0953080
$175$	−3.23933	−0.244871
$176$	−18.5146	−1.39559
$177$	−6.16798	−0.463614
$178$	0.0935273	0.00701016
$179$	3.10502	0.232080	0.116040	−	0.993245i	$-0.462980\pi$
$179$	3.10502	0.232080	0.116040	+	0.993245i	$0.462980\pi$
$180$	2.46739	0.183908
$181$	−0.670686	−0.0498517	−0.0249259	−	0.999689i	$-0.507935\pi$
$181$	−0.670686	−0.0498517	−0.0249259	+	0.999689i	$0.507935\pi$
$182$	0	0
$183$	11.0420	0.816250
$184$	3.87413	0.285605
$185$	10.5297	0.774158
$186$	3.12157	0.228885
$187$	2.58180	0.188800
$188$	7.97841	0.581886
$189$	−1.00000	−0.0727393
$190$	0.669350	0.0485598
$191$	17.8728	1.29323	0.646614	−	0.762817i	$-0.276184\pi$
$191$	17.8728	1.29323	0.646614	+	0.762817i	$0.276184\pi$
$192$	4.82289	0.348062
$193$	5.62386	0.404814	0.202407	−	0.979301i	$-0.435124\pi$
$193$	5.62386	0.404814	0.202407	+	0.979301i	$0.435124\pi$
$194$	1.40732	0.101040
$195$	0	0
$196$	−1.85951	−0.132822
$197$	−16.5783	−1.18116	−0.590579	−	0.806980i	$-0.701100\pi$
$197$	−16.5783	−1.18116	−0.590579	+	0.806980i	$0.701100\pi$
$198$	−2.18446	−0.155243
$199$	24.4240	1.73137	0.865687	−	0.500585i	$-0.166882\pi$
$199$	24.4240	1.73137	0.865687	+	0.500585i	$0.166882\pi$
$200$	4.68605	0.331354
$201$	−1.64442	−0.115988
$202$	1.06422	0.0748782
$203$	3.35417	0.235416
$204$	−0.823753	−0.0576742
$205$	−1.08277	−0.0756240
$206$	−4.87970	−0.339985
$207$	−2.67807	−0.186139
$208$	0	0
$209$	7.84367	0.542558
$210$	0.497345	0.0343201
$211$	−10.9881	−0.756454	−0.378227	−	0.925713i	$-0.623466\pi$
$211$	−10.9881	−0.756454	−0.378227	+	0.925713i	$0.623466\pi$
$212$	3.44874	0.236861
$213$	−12.9896	−0.890033
$214$	5.43901	0.371803
$215$	−4.19521	−0.286111
$216$	1.44661	0.0984294
$217$	−8.32825	−0.565358
$218$	−5.08918	−0.344683
$219$	7.20060	0.486572
$220$	−14.3801	−0.969506
$221$	0	0
$222$	2.97438	0.199627
$223$	14.6782	0.982922	0.491461	−	0.870900i	$-0.336463\pi$
$223$	14.6782	0.982922	0.491461	+	0.870900i	$0.336463\pi$
$224$	4.08395	0.272870
$225$	−3.23933	−0.215956
$226$	5.94891	0.395715
$227$	0.615870	0.0408767	0.0204384	−	0.999791i	$-0.493494\pi$
$227$	0.615870	0.0408767	0.0204384	+	0.999791i	$0.493494\pi$
$228$	−2.50262	−0.165740
$229$	9.47389	0.626053	0.313026	−	0.949744i	$-0.398657\pi$
$229$	9.47389	0.626053	0.313026	+	0.949744i	$0.398657\pi$
$230$	1.33193	0.0878247
$231$	5.82806	0.383458
$232$	−4.85218	−0.318561
$233$	−8.35195	−0.547154	−0.273577	−	0.961850i	$-0.588207\pi$
$233$	−8.35195	−0.547154	−0.273577	+	0.961850i	$0.588207\pi$
$234$	0	0
$235$	5.69320	0.371383
$236$	−11.4694	−0.746596
$237$	2.54704	0.165448
$238$	−0.166042	−0.0107629
$239$	3.25440	0.210510	0.105255	−	0.994445i	$-0.466434\pi$
$239$	3.25440	0.210510	0.105255	+	0.994445i	$0.466434\pi$
$240$	4.21531	0.272097
$241$	−16.1085	−1.03764	−0.518819	−	0.854884i	$-0.673628\pi$
$241$	−16.1085	−1.03764	−0.518819	+	0.854884i	$0.673628\pi$
$242$	8.60816	0.553353
$243$	−1.00000	−0.0641500
$244$	20.5328	1.31448
$245$	−1.32690	−0.0847726
$246$	−0.305856	−0.0195007
$247$	0	0
$248$	12.0477	0.765032
$249$	−16.2210	−1.02796
$250$	4.09779	0.259167
$251$	20.4332	1.28973	0.644866	−	0.764296i	$-0.276913\pi$
$251$	20.4332	1.28973	0.644866	+	0.764296i	$0.276913\pi$
$252$	−1.85951	−0.117138
$253$	15.6080	0.981265
$254$	−2.34141	−0.146913
$255$	−0.587809	−0.0368101
$256$	5.90675	0.369172
$257$	−15.8411	−0.988142	−0.494071	−	0.869422i	$-0.664492\pi$
$257$	−15.8411	−0.988142	−0.494071	+	0.869422i	$0.664492\pi$
$258$	−1.18504	−0.0737776
$259$	−7.93555	−0.493091
$260$	0	0
$261$	3.35417	0.207618
$262$	5.50487	0.340092
$263$	17.0251	1.04982	0.524908	−	0.851159i	$-0.324100\pi$
$263$	17.0251	1.04982	0.524908	+	0.851159i	$0.324100\pi$
$264$	−8.43094	−0.518888
$265$	2.46094	0.151174
$266$	−0.504446	−0.0309296
$267$	−0.249528	−0.0152708
$268$	−3.05782	−0.186786
$269$	−16.0150	−0.976454	−0.488227	−	0.872717i	$-0.662356\pi$
$269$	−16.0150	−0.976454	−0.488227	+	0.872717i	$0.662356\pi$
$270$	0.497345	0.0302675
$271$	10.3553	0.629040	0.314520	−	0.949251i	$-0.398156\pi$
$271$	10.3553	0.629040	0.314520	+	0.949251i	$0.398156\pi$
$272$	−1.40731	−0.0853306
$273$	0	0
$274$	0.349795	0.0211319
$275$	18.8790	1.13845
$276$	−4.97991	−0.299755
$277$	−8.83806	−0.531027	−0.265514	−	0.964107i	$-0.585542\pi$
$277$	−8.83806	−0.531027	−0.265514	+	0.964107i	$0.585542\pi$
$278$	7.52503	0.451321
$279$	−8.32825	−0.498599
$280$	1.91951	0.114713
$281$	−14.3408	−0.855503	−0.427752	−	0.903896i	$-0.640694\pi$
$281$	−14.3408	−0.855503	−0.427752	+	0.903896i	$0.640694\pi$
$282$	1.60819	0.0957662
$283$	13.9259	0.827808	0.413904	−	0.910321i	$-0.364165\pi$
$283$	13.9259	0.827808	0.413904	+	0.910321i	$0.364165\pi$
$284$	−24.1543	−1.43330
$285$	−1.78580	−0.105782
$286$	0	0
$287$	0.816015	0.0481678
$288$	4.08395	0.240649
$289$	−16.8038	−0.988456
$290$	−1.66818	−0.0979589
$291$	−3.75470	−0.220104
$292$	13.3896	0.783568
$293$	24.0035	1.40230	0.701149	−	0.713015i	$-0.252671\pi$
$293$	24.0035	1.40230	0.701149	+	0.713015i	$0.252671\pi$
$294$	−0.374817	−0.0218598
$295$	−8.18430	−0.476508
$296$	11.4797	0.667241
$297$	5.82806	0.338178
$298$	−4.60944	−0.267018
$299$	0	0
$300$	−6.02358	−0.347771
$301$	3.16166	0.182235
$302$	−7.00145	−0.402888
$303$	−2.83930	−0.163114
$304$	−4.27550	−0.245216
$305$	14.6517	0.838953
$306$	−0.166042	−0.00949197
$307$	−20.6185	−1.17676	−0.588381	−	0.808584i	$-0.700235\pi$
$307$	−20.6185	−1.17676	−0.588381	+	0.808584i	$0.700235\pi$
$308$	10.8373	0.617515
$309$	13.0189	0.740619
$310$	4.14202	0.235251
$311$	33.6435	1.90775	0.953873	−	0.300210i	$-0.0970566\pi$
$311$	33.6435	1.90775	0.953873	+	0.300210i	$0.0970566\pi$
$312$	0	0
$313$	9.87809	0.558342	0.279171	−	0.960241i	$-0.409940\pi$
$313$	9.87809	0.558342	0.279171	+	0.960241i	$0.409940\pi$
$314$	9.14043	0.515824
$315$	−1.32690	−0.0747624
$316$	4.73626	0.266435
$317$	13.6053	0.764151	0.382075	−	0.924131i	$-0.375209\pi$
$317$	13.6053	0.764151	0.382075	+	0.924131i	$0.375209\pi$
$318$	0.695154	0.0389823
$319$	−19.5483	−1.09449
$320$	6.39950	0.357743
$321$	−14.5111	−0.809931
$322$	−1.00379	−0.0559389
$323$	0.596202	0.0331735
$324$	−1.85951	−0.103306
$325$	0	0
$326$	8.34527	0.462202
$327$	13.5778	0.750853
$328$	−1.18046	−0.0651798
$329$	−4.29060	−0.236548
$330$	−2.89856	−0.159560
$331$	1.35950	0.0747251	0.0373625	−	0.999302i	$-0.488104\pi$
$331$	1.35950	0.0747251	0.0373625	+	0.999302i	$0.488104\pi$
$332$	−30.1631	−1.65542
$333$	−7.93555	−0.434865
$334$	−6.86979	−0.375898
$335$	−2.18198	−0.119214
$336$	−3.17681	−0.173309
$337$	31.6542	1.72432	0.862158	−	0.506640i	$-0.169113\pi$
$337$	31.6542	1.72432	0.862158	+	0.506640i	$0.169113\pi$
$338$	0	0
$339$	−15.8715	−0.862021
$340$	−1.09304	−0.0592783
$341$	48.5375	2.62846
$342$	−0.504446	−0.0272773
$343$	1.00000	0.0539949
$344$	−4.57369	−0.246597
$345$	−3.55354	−0.191316
$346$	−4.77683	−0.256804
$347$	18.5368	0.995108	0.497554	−	0.867433i	$-0.334232\pi$
$347$	18.5368	0.995108	0.497554	+	0.867433i	$0.334232\pi$
$348$	6.23711	0.334344
$349$	31.9333	1.70935	0.854674	−	0.519165i	$-0.173757\pi$
$349$	31.9333	1.70935	0.854674	+	0.519165i	$0.173757\pi$
$350$	−1.21416	−0.0648994
$351$	0	0
$352$	−23.8015	−1.26862
$353$	1.62631	0.0865598	0.0432799	−	0.999063i	$-0.486219\pi$
$353$	1.62631	0.0865598	0.0432799	+	0.999063i	$0.486219\pi$
$354$	−2.31186	−0.122874
$355$	−17.2359	−0.914788
$356$	−0.464000	−0.0245919
$357$	0.442994	0.0234457
$358$	1.16381	0.0615095
$359$	−24.7731	−1.30747	−0.653736	−	0.756722i	$-0.726799\pi$
$359$	−24.7731	−1.30747	−0.653736	+	0.756722i	$0.726799\pi$
$360$	1.91951	0.101167
$361$	−17.1887	−0.904668
$362$	−0.251385	−0.0132125
$363$	−22.9663	−1.20542
$364$	0	0
$365$	9.55449	0.500105
$366$	4.13874	0.216335
$367$	5.26649	0.274909	0.137454	−	0.990508i	$-0.456108\pi$
$367$	5.26649	0.274909	0.137454	+	0.990508i	$0.456108\pi$
$368$	−8.50773	−0.443496
$369$	0.816015	0.0424800
$370$	3.94671	0.205180
$371$	−1.85465	−0.0962886
$372$	−15.4865	−0.802937
$373$	−27.3669	−1.41701	−0.708503	−	0.705708i	$-0.750629\pi$
$373$	−27.3669	−1.41701	−0.708503	+	0.705708i	$0.750629\pi$
$374$	0.967701	0.0500386
$375$	−10.9328	−0.564566
$376$	6.20682	0.320092
$377$	0	0
$378$	−0.374817	−0.0192785
$379$	−25.4725	−1.30844	−0.654218	−	0.756306i	$-0.727002\pi$
$379$	−25.4725	−1.30844	−0.654218	+	0.756306i	$0.727002\pi$
$380$	−3.32073	−0.170350
$381$	6.24679	0.320033
$382$	6.69902	0.342752
$383$	−22.9476	−1.17257	−0.586283	−	0.810106i	$-0.699409\pi$
$383$	−22.9476	−1.17257	−0.586283	+	0.810106i	$0.699409\pi$
$384$	9.97559	0.509065
$385$	7.73326	0.394123
$386$	2.10792	0.107290
$387$	3.16166	0.160716
$388$	−6.98190	−0.354452
$389$	15.0422	0.762671	0.381335	−	0.924437i	$-0.375464\pi$
$389$	15.0422	0.762671	0.381335	+	0.924437i	$0.375464\pi$
$390$	0	0
$391$	1.18637	0.0599974
$392$	−1.44661	−0.0730649
$393$	−14.6868	−0.740851
$394$	−6.21384	−0.313049
$395$	3.37967	0.170050
$396$	10.8373	0.544597
$397$	16.4236	0.824278	0.412139	−	0.911121i	$-0.364782\pi$
$397$	16.4236	0.824278	0.412139	+	0.911121i	$0.364782\pi$
$398$	9.15455	0.458876
$399$	1.34585	0.0673766
$400$	−10.2907	−0.514537
$401$	17.7054	0.884168	0.442084	−	0.896974i	$-0.354239\pi$
$401$	17.7054	0.884168	0.442084	+	0.896974i	$0.354239\pi$
$402$	−0.616356	−0.0307411
$403$	0	0
$404$	−5.27972	−0.262676
$405$	−1.32690	−0.0659343
$406$	1.25720	0.0623937
$407$	46.2489	2.29247
$408$	−0.640840	−0.0317263
$409$	4.05274	0.200395	0.100198	−	0.994968i	$-0.468053\pi$
$409$	4.05274	0.200395	0.100198	+	0.994968i	$0.468053\pi$
$410$	−0.405841	−0.0200431
$411$	−0.933243	−0.0460335
$412$	24.2088	1.19268
$413$	6.16798	0.303506
$414$	−1.00379	−0.0493335
$415$	−21.5237	−1.05655
$416$	0	0
$417$	−20.0765	−0.983152
$418$	2.93994	0.143797
$419$	−7.13923	−0.348774	−0.174387	−	0.984677i	$-0.555794\pi$
$419$	−7.13923	−0.348774	−0.174387	+	0.984677i	$0.555794\pi$
$420$	−2.46739	−0.120396
$421$	−32.2979	−1.57410	−0.787052	−	0.616887i	$-0.788394\pi$
$421$	−32.2979	−1.57410	−0.787052	+	0.616887i	$0.788394\pi$
$422$	−4.11854	−0.200487
$423$	−4.29060	−0.208616
$424$	2.68296	0.130296
$425$	1.43501	0.0696080
$426$	−4.86873	−0.235891
$427$	−11.0420	−0.534361
$428$	−26.9836	−1.30430
$429$	0	0
$430$	−1.57244	−0.0758296
$431$	13.3707	0.644046	0.322023	−	0.946732i	$-0.395637\pi$
$431$	13.3707	0.644046	0.322023	+	0.946732i	$0.395637\pi$
$432$	−3.17681	−0.152844
$433$	−30.7437	−1.47745	−0.738723	−	0.674009i	$-0.764571\pi$
$433$	−30.7437	−1.47745	−0.738723	+	0.674009i	$0.764571\pi$
$434$	−3.12157	−0.149840
$435$	4.45065	0.213392
$436$	25.2480	1.20916
$437$	3.60427	0.172416
$438$	2.69891	0.128959
$439$	−22.4974	−1.07374	−0.536871	−	0.843664i	$-0.680394\pi$
$439$	−22.4974	−1.07374	−0.536871	+	0.843664i	$0.680394\pi$
$440$	−11.1870	−0.533320
$441$	1.00000	0.0476190
$442$	0	0
$443$	−26.6355	−1.26549	−0.632746	−	0.774359i	$-0.718072\pi$
$443$	−26.6355	−1.26549	−0.632746	+	0.774359i	$0.718072\pi$
$444$	−14.7563	−0.700301
$445$	−0.331099	−0.0156956
$446$	5.50162	0.260509
$447$	12.2978	0.581668
$448$	−4.82289	−0.227860
$449$	−30.2908	−1.42951	−0.714757	−	0.699373i	$-0.753463\pi$
$449$	−30.2908	−1.42951	−0.714757	+	0.699373i	$0.753463\pi$
$450$	−1.21416	−0.0572359
$451$	−4.75578	−0.223941
$452$	−29.5132	−1.38819
$453$	18.6796	0.877646
$454$	0.230839	0.0108338
$455$	0	0
$456$	−1.94692	−0.0911727
$457$	7.92047	0.370504	0.185252	−	0.982691i	$-0.440690\pi$
$457$	7.92047	0.370504	0.185252	+	0.982691i	$0.440690\pi$
$458$	3.55098	0.165926
$459$	0.442994	0.0206772
$460$	−6.60785	−0.308093
$461$	−10.9884	−0.511783	−0.255891	−	0.966706i	$-0.582369\pi$
$461$	−10.9884	−0.511783	−0.255891	+	0.966706i	$0.582369\pi$
$462$	2.18446	0.101630
$463$	−8.71786	−0.405153	−0.202577	−	0.979266i	$-0.564932\pi$
$463$	−8.71786	−0.405153	−0.202577	+	0.979266i	$0.564932\pi$
$464$	10.6555	0.494671
$465$	−11.0508	−0.512467
$466$	−3.13045	−0.145015
$467$	33.7907	1.56365	0.781824	−	0.623499i	$-0.214289\pi$
$467$	33.7907	1.56365	0.781824	+	0.623499i	$0.214289\pi$
$468$	0	0
$469$	1.64442	0.0759322
$470$	2.13391	0.0984298
$471$	−24.3864	−1.12367
$472$	−8.92267	−0.410699
$473$	−18.4263	−0.847244
$474$	0.954675	0.0438497
$475$	4.35964	0.200034
$476$	0.823753	0.0377566
$477$	−1.85465	−0.0849186
$478$	1.21981	0.0557926
$479$	−39.0440	−1.78396	−0.891982	−	0.452071i	$-0.850685\pi$
$479$	−39.0440	−1.78396	−0.891982	+	0.452071i	$0.850685\pi$
$480$	5.41899	0.247342
$481$	0	0
$482$	−6.03773	−0.275011
$483$	2.67807	0.121857
$484$	−42.7061	−1.94119
$485$	−4.98211	−0.226226
$486$	−0.374817	−0.0170020
$487$	−12.0804	−0.547416	−0.273708	−	0.961813i	$-0.588250\pi$
$487$	−12.0804	−0.547416	−0.273708	+	0.961813i	$0.588250\pi$
$488$	15.9735	0.723087
$489$	−22.2649	−1.00685
$490$	−0.497345	−0.0224678
$491$	−42.4080	−1.91385	−0.956923	−	0.290343i	$-0.906231\pi$
$491$	−42.4080	−1.91385	−0.956923	+	0.290343i	$0.906231\pi$
$492$	1.51739	0.0684092
$493$	−1.48588	−0.0669205
$494$	0	0
$495$	7.73326	0.347584
$496$	−26.4573	−1.18797
$497$	12.9896	0.582664
$498$	−6.07991	−0.272447
$499$	−23.7535	−1.06335	−0.531677	−	0.846947i	$-0.678438\pi$
$499$	−23.7535	−1.06335	−0.531677	+	0.846947i	$0.678438\pi$
$500$	−20.3296	−0.909169
$501$	18.3284	0.818851
$502$	7.65871	0.341825
$503$	−18.4558	−0.822905	−0.411453	−	0.911431i	$-0.634978\pi$
$503$	−18.4558	−0.822905	−0.411453	+	0.911431i	$0.634978\pi$
$504$	−1.44661	−0.0644372
$505$	−3.76747	−0.167650
$506$	5.85014	0.260070
$507$	0	0
$508$	11.6160	0.515376
$509$	12.5610	0.556755	0.278378	−	0.960472i	$-0.410203\pi$
$509$	12.5610	0.556755	0.278378	+	0.960472i	$0.410203\pi$
$510$	−0.220321	−0.00975598
$511$	−7.20060	−0.318536
$512$	22.1651	0.979570
$513$	1.34585	0.0594205
$514$	−5.93752	−0.261893
$515$	17.2748	0.761218
$516$	5.87914	0.258815
$517$	25.0058	1.09976
$518$	−2.97438	−0.130687
$519$	12.7444	0.559418
$520$	0	0
$521$	−23.8796	−1.04618	−0.523092	−	0.852276i	$-0.675221\pi$
$521$	−23.8796	−1.04618	−0.523092	+	0.852276i	$0.675221\pi$
$522$	1.25720	0.0550261
$523$	27.5520	1.20476	0.602382	−	0.798208i	$-0.294218\pi$
$523$	27.5520	1.20476	0.602382	+	0.798208i	$0.294218\pi$
$524$	−27.3103	−1.19306
$525$	3.23933	0.141376
$526$	6.38132	0.278239
$527$	3.68937	0.160711
$528$	18.5146	0.805746
$529$	−15.8279	−0.688170
$530$	0.922401	0.0400666
$531$	6.16798	0.267667
$532$	2.50262	0.108502
$533$	0	0
$534$	−0.0935273	−0.00404732
$535$	−19.2548	−0.832458
$536$	−2.37884	−0.102750
$537$	−3.10502	−0.133992
$538$	−6.00271	−0.258795
$539$	−5.82806	−0.251032
$540$	−2.46739	−0.106180
$541$	8.30651	0.357125	0.178562	−	0.983929i	$-0.442855\pi$
$541$	8.30651	0.357125	0.178562	+	0.983929i	$0.442855\pi$
$542$	3.88134	0.166718
$543$	0.670686	0.0287819
$544$	−1.80916	−0.0775672
$545$	18.0164	0.771736
$546$	0	0
$547$	−19.1011	−0.816705	−0.408353	−	0.912824i	$-0.633897\pi$
$547$	−19.1011	−0.816705	−0.408353	+	0.912824i	$0.633897\pi$
$548$	−1.73538	−0.0741316
$549$	−11.0420	−0.471262
$550$	7.07618	0.301729
$551$	−4.51419	−0.192311
$552$	−3.87413	−0.164894
$553$	−2.54704	−0.108311
$554$	−3.31266	−0.140741
$555$	−10.5297	−0.446961
$556$	−37.3326	−1.58325
$557$	−0.238603	−0.0101099	−0.00505496	−	0.999987i	$-0.501609\pi$
$557$	−0.238603	−0.0101099	−0.00505496	+	0.999987i	$0.501609\pi$
$558$	−3.12157	−0.132147
$559$	0	0
$560$	−4.21531	−0.178129
$561$	−2.58180	−0.109004
$562$	−5.37519	−0.226739
$563$	20.7512	0.874559	0.437279	−	0.899326i	$-0.355942\pi$
$563$	20.7512	0.874559	0.437279	+	0.899326i	$0.355942\pi$
$564$	−7.97841	−0.335952
$565$	−21.0599	−0.885997
$566$	5.21966	0.219399
$567$	1.00000	0.0419961
$568$	−18.7909	−0.788449
$569$	6.55284	0.274709	0.137355	−	0.990522i	$-0.456140\pi$
$569$	6.55284	0.274709	0.137355	+	0.990522i	$0.456140\pi$
$570$	−0.669350	−0.0280360
$571$	1.75392	0.0733995	0.0366997	−	0.999326i	$-0.488315\pi$
$571$	1.75392	0.0733995	0.0366997	+	0.999326i	$0.488315\pi$
$572$	0	0
$573$	−17.8728	−0.746646
$574$	0.305856	0.0127662
$575$	8.67517	0.361780
$576$	−4.82289	−0.200954
$577$	−3.46646	−0.144311	−0.0721553	−	0.997393i	$-0.522988\pi$
$577$	−3.46646	−0.144311	−0.0721553	+	0.997393i	$0.522988\pi$
$578$	−6.29834	−0.261976
$579$	−5.62386	−0.233720
$580$	8.27603	0.343644
$581$	16.2210	0.672960
$582$	−1.40732	−0.0583355
$583$	10.8090	0.447663
$584$	10.4165	0.431037
$585$	0	0
$586$	8.99692	0.371659
$587$	38.9101	1.60599	0.802997	−	0.595984i	$-0.203238\pi$
$587$	38.9101	1.60599	0.802997	+	0.595984i	$0.203238\pi$
$588$	1.85951	0.0766850
$589$	11.2085	0.461840
$590$	−3.06762	−0.126292
$591$	16.5783	0.681941
$592$	−25.2097	−1.03611
$593$	25.4135	1.04361	0.521803	−	0.853066i	$-0.325260\pi$
$593$	25.4135	1.04361	0.521803	+	0.853066i	$0.325260\pi$
$594$	2.18446	0.0896293
$595$	0.587809	0.0240978
$596$	22.8680	0.936709
$597$	−24.4240	−0.999610
$598$	0	0
$599$	−7.40004	−0.302357	−0.151179	−	0.988506i	$-0.548307\pi$
$599$	−7.40004	−0.302357	−0.151179	+	0.988506i	$0.548307\pi$
$600$	−4.68605	−0.191307
$601$	−14.4392	−0.588988	−0.294494	−	0.955653i	$-0.595151\pi$
$601$	−14.4392	−0.588988	−0.294494	+	0.955653i	$0.595151\pi$
$602$	1.18504	0.0482988
$603$	1.64442	0.0669659
$604$	34.7350	1.41335
$605$	−30.4740	−1.23894
$606$	−1.06422	−0.0432309
$607$	6.40534	0.259985	0.129992	−	0.991515i	$-0.458505\pi$
$607$	6.40534	0.259985	0.129992	+	0.991515i	$0.458505\pi$
$608$	−5.49636	−0.222907
$609$	−3.35417	−0.135918
$610$	5.49170	0.222352
$611$	0	0
$612$	0.823753	0.0332982
$613$	9.33764	0.377144	0.188572	−	0.982059i	$-0.439614\pi$
$613$	9.33764	0.377144	0.188572	+	0.982059i	$0.439614\pi$
$614$	−7.72818	−0.311884
$615$	1.08277	0.0436616
$616$	8.43094	0.339692
$617$	4.02033	0.161852	0.0809262	−	0.996720i	$-0.474212\pi$
$617$	4.02033	0.161852	0.0809262	+	0.996720i	$0.474212\pi$
$618$	4.87970	0.196290
$619$	22.6258	0.909408	0.454704	−	0.890643i	$-0.349745\pi$
$619$	22.6258	0.909408	0.454704	+	0.890643i	$0.349745\pi$
$620$	−20.5490	−0.825269
$621$	2.67807	0.107467
$622$	12.6102	0.505621
$623$	0.249528	0.00999712
$624$	0	0
$625$	1.68994	0.0675975
$626$	3.70248	0.147981
$627$	−7.84367	−0.313246
$628$	−45.3468	−1.80953
$629$	3.51540	0.140168
$630$	−0.497345	−0.0198147
$631$	−24.6591	−0.981665	−0.490832	−	0.871254i	$-0.663307\pi$
$631$	−24.6591	−0.981665	−0.490832	+	0.871254i	$0.663307\pi$
$632$	3.68458	0.146565
$633$	10.9881	0.436739
$634$	5.09951	0.202527
$635$	8.28888	0.328934
$636$	−3.44874	−0.136752
$637$	0	0
$638$	−7.32703	−0.290080
$639$	12.9896	0.513861
$640$	13.2366	0.523224
$641$	39.3652	1.55483	0.777416	−	0.628987i	$-0.216530\pi$
$641$	39.3652	1.55483	0.777416	+	0.628987i	$0.216530\pi$
$642$	−5.43901	−0.214661
$643$	−40.6170	−1.60178	−0.800889	−	0.598812i	$-0.795639\pi$
$643$	−40.6170	−1.60178	−0.800889	+	0.598812i	$0.795639\pi$
$644$	4.97991	0.196236
$645$	4.19521	0.165186
$646$	0.223467	0.00879217
$647$	4.38181	0.172267	0.0861333	−	0.996284i	$-0.472549\pi$
$647$	4.38181	0.172267	0.0861333	+	0.996284i	$0.472549\pi$
$648$	−1.44661	−0.0568283
$649$	−35.9473	−1.41106
$650$	0	0
$651$	8.32825	0.326410
$652$	−41.4019	−1.62142
$653$	18.0074	0.704683	0.352342	−	0.935871i	$-0.385386\pi$
$653$	18.0074	0.704683	0.352342	+	0.935871i	$0.385386\pi$
$654$	5.08918	0.199003
$655$	−19.4879	−0.761457
$656$	2.59232	0.101213
$657$	−7.20060	−0.280922
$658$	−1.60819	−0.0626937
$659$	−9.85306	−0.383821	−0.191910	−	0.981412i	$-0.561468\pi$
$659$	−9.85306	−0.383821	−0.191910	+	0.981412i	$0.561468\pi$
$660$	14.3801	0.559744
$661$	27.3954	1.06556	0.532779	−	0.846254i	$-0.321148\pi$
$661$	27.3954	1.06556	0.532779	+	0.846254i	$0.321148\pi$
$662$	0.509565	0.0198048
$663$	0	0
$664$	−23.4655	−0.910637
$665$	1.78580	0.0692505
$666$	−2.97438	−0.115255
$667$	−8.98271	−0.347812
$668$	34.0818	1.31867
$669$	−14.6782	−0.567490
$670$	−0.817844	−0.0315961
$671$	64.3536	2.48434
$672$	−4.08395	−0.157542
$673$	−17.8948	−0.689796	−0.344898	−	0.938640i	$-0.612086\pi$
$673$	−17.8948	−0.689796	−0.344898	+	0.938640i	$0.612086\pi$
$674$	11.8645	0.457005
$675$	3.23933	0.124682
$676$	0	0
$677$	−37.6226	−1.44595	−0.722977	−	0.690872i	$-0.757227\pi$
$677$	−37.6226	−1.44595	−0.722977	+	0.690872i	$0.757227\pi$
$678$	−5.94891	−0.228466
$679$	3.75470	0.144092
$680$	−0.850332	−0.0326087
$681$	−0.615870	−0.0236002
$682$	18.1927	0.696635
$683$	−37.2441	−1.42511	−0.712553	−	0.701618i	$-0.752461\pi$
$683$	−37.2441	−1.42511	−0.712553	+	0.701618i	$0.752461\pi$
$684$	2.50262	0.0956899
$685$	−1.23832	−0.0473138
$686$	0.374817	0.0143106
$687$	−9.47389	−0.361452
$688$	10.0440	0.382924
$689$	0	0
$690$	−1.33193	−0.0507056
$691$	13.3126	0.506437	0.253218	−	0.967409i	$-0.418511\pi$
$691$	13.3126	0.506437	0.253218	+	0.967409i	$0.418511\pi$
$692$	23.6984	0.900878
$693$	−5.82806	−0.221390
$694$	6.94791	0.263739
$695$	−26.6396	−1.01050
$696$	4.85218	0.183921
$697$	−0.361490	−0.0136924
$698$	11.9691	0.453038
$699$	8.35195	0.315900
$700$	6.02358	0.227670
$701$	40.6477	1.53524	0.767622	−	0.640903i	$-0.221440\pi$
$701$	40.6477	1.53524	0.767622	+	0.640903i	$0.221440\pi$
$702$	0	0
$703$	10.6800	0.402805
$704$	28.1081	1.05936
$705$	−5.69320	−0.214418
$706$	0.609570	0.0229415
$707$	2.83930	0.106783
$708$	11.4694	0.431048
$709$	22.3533	0.839497	0.419748	−	0.907641i	$-0.362118\pi$
$709$	22.3533	0.839497	0.419748	+	0.907641i	$0.362118\pi$
$710$	−6.46032	−0.242452
$711$	−2.54704	−0.0955215
$712$	−0.360970	−0.0135279
$713$	22.3037	0.835279
$714$	0.166042	0.00621396
$715$	0	0
$716$	−5.77382	−0.215778
$717$	−3.25440	−0.121538
$718$	−9.28537	−0.346527
$719$	−13.6829	−0.510288	−0.255144	−	0.966903i	$-0.582123\pi$
$719$	−13.6829	−0.510288	−0.255144	+	0.966903i	$0.582123\pi$
$720$	−4.21531	−0.157095
$721$	−13.0189	−0.484849
$722$	−6.44262	−0.239769
$723$	16.1085	0.599080
$724$	1.24715	0.0463499
$725$	−10.8653	−0.403526
$726$	−8.60816	−0.319479
$727$	−9.65059	−0.357920	−0.178960	−	0.983856i	$-0.557273\pi$
$727$	−9.65059	−0.357920	−0.178960	+	0.983856i	$0.557273\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	3.58119	0.132546
$731$	−1.40060	−0.0518029
$732$	−20.5328	−0.758914
$733$	42.0579	1.55344	0.776722	−	0.629844i	$-0.216881\pi$
$733$	42.0579	1.55344	0.776722	+	0.629844i	$0.216881\pi$
$734$	1.97397	0.0728606
$735$	1.32690	0.0489435
$736$	−10.9371	−0.403147
$737$	−9.58377	−0.353023
$738$	0.305856	0.0112587
$739$	19.4048	0.713818	0.356909	−	0.934139i	$-0.383831\pi$
$739$	19.4048	0.713818	0.356909	+	0.934139i	$0.383831\pi$
$740$	−19.5801	−0.719778
$741$	0	0
$742$	−0.695154	−0.0255199
$743$	−35.6920	−1.30941	−0.654706	−	0.755884i	$-0.727207\pi$
$743$	−35.6920	−1.30941	−0.654706	+	0.755884i	$0.727207\pi$
$744$	−12.0477	−0.441692
$745$	16.3180	0.597846
$746$	−10.2576	−0.375557
$747$	16.2210	0.593495
$748$	−4.80088	−0.175538
$749$	14.5111	0.530224
$750$	−4.09779	−0.149630
$751$	51.8856	1.89333	0.946666	−	0.322217i	$-0.104428\pi$
$751$	51.8856	1.89333	0.946666	+	0.322217i	$0.104428\pi$
$752$	−13.6304	−0.497050
$753$	−20.4332	−0.744627
$754$	0	0
$755$	24.7860	0.902056
$756$	1.85951	0.0676298
$757$	−29.7035	−1.07959	−0.539796	−	0.841796i	$-0.681499\pi$
$757$	−29.7035	−1.07959	−0.539796	+	0.841796i	$0.681499\pi$
$758$	−9.54754	−0.346782
$759$	−15.6080	−0.566534
$760$	−2.58336	−0.0937085
$761$	11.5829	0.419879	0.209940	−	0.977714i	$-0.432673\pi$
$761$	11.5829	0.419879	0.209940	+	0.977714i	$0.432673\pi$
$762$	2.34141	0.0848202
$763$	−13.5778	−0.491548
$764$	−33.2346	−1.20239
$765$	0.587809	0.0212523
$766$	−8.60114	−0.310772
$767$	0	0
$768$	−5.90675	−0.213142
$769$	7.72447	0.278551	0.139276	−	0.990254i	$-0.455523\pi$
$769$	7.72447	0.278551	0.139276	+	0.990254i	$0.455523\pi$
$770$	2.89856	0.104457
$771$	15.8411	0.570504
$772$	−10.4576	−0.376378
$773$	−5.56390	−0.200120	−0.100060	−	0.994981i	$-0.531903\pi$
$773$	−5.56390	−0.200120	−0.100060	+	0.994981i	$0.531903\pi$
$774$	1.18504	0.0425955
$775$	26.9780	0.969077
$776$	−5.43158	−0.194983
$777$	7.93555	0.284686
$778$	5.63808	0.202135
$779$	−1.09823	−0.0393482
$780$	0	0
$781$	−75.7042	−2.70891
$782$	0.444672	0.0159014
$783$	−3.35417	−0.119868
$784$	3.17681	0.113457
$785$	−32.3583	−1.15492
$786$	−5.50487	−0.196352
$787$	−1.31894	−0.0470150	−0.0235075	−	0.999724i	$-0.507483\pi$
$787$	−1.31894	−0.0470150	−0.0235075	+	0.999724i	$0.507483\pi$
$788$	30.8276	1.09819
$789$	−17.0251	−0.606111
$790$	1.26676	0.0450693
$791$	15.8715	0.564325
$792$	8.43094	0.299580
$793$	0	0
$794$	6.15586	0.218463
$795$	−2.46094	−0.0872805
$796$	−45.4168	−1.60976
$797$	−15.5957	−0.552429	−0.276215	−	0.961096i	$-0.589080\pi$
$797$	−15.5957	−0.552429	−0.276215	+	0.961096i	$0.589080\pi$
$798$	0.504446	0.0178572
$799$	1.90071	0.0672422
$800$	−13.2293	−0.467725
$801$	0.249528	0.00881663
$802$	6.63631	0.234336
$803$	41.9656	1.48093
$804$	3.05782	0.107841
$805$	3.55354	0.125246
$806$	0	0
$807$	16.0150	0.563756
$808$	−4.10737	−0.144497
$809$	−37.9340	−1.33369	−0.666844	−	0.745197i	$-0.732355\pi$
$809$	−37.9340	−1.33369	−0.666844	+	0.745197i	$0.732355\pi$
$810$	−0.497345	−0.0174749
$811$	23.0022	0.807718	0.403859	−	0.914821i	$-0.367669\pi$
$811$	23.0022	0.807718	0.403859	+	0.914821i	$0.367669\pi$
$812$	−6.23711	−0.218880
$813$	−10.3553	−0.363176
$814$	17.3349	0.607587
$815$	−29.5434	−1.03486
$816$	1.40731	0.0492656
$817$	−4.25511	−0.148867
$818$	1.51904	0.0531118
$819$	0	0
$820$	2.01343	0.0703119
$821$	−16.9276	−0.590778	−0.295389	−	0.955377i	$-0.595449\pi$
$821$	−16.9276	−0.590778	−0.295389	+	0.955377i	$0.595449\pi$
$822$	−0.349795	−0.0122005
$823$	7.69045	0.268072	0.134036	−	0.990976i	$-0.457206\pi$
$823$	7.69045	0.268072	0.134036	+	0.990976i	$0.457206\pi$
$824$	18.8333	0.656088
$825$	−18.8790	−0.657283
$826$	2.31186	0.0804400
$827$	42.2818	1.47028	0.735140	−	0.677915i	$-0.237116\pi$
$827$	42.2818	1.47028	0.735140	+	0.677915i	$0.237116\pi$
$828$	4.97991	0.173064
$829$	9.67366	0.335980	0.167990	−	0.985789i	$-0.446272\pi$
$829$	9.67366	0.335980	0.167990	+	0.985789i	$0.446272\pi$
$830$	−8.06744	−0.280025
$831$	8.83806	0.306589
$832$	0	0
$833$	−0.442994	−0.0153488
$834$	−7.52503	−0.260570
$835$	24.3199	0.841626
$836$	−14.5854	−0.504447
$837$	8.32825	0.287866
$838$	−2.67591	−0.0924377
$839$	12.2804	0.423967	0.211983	−	0.977273i	$-0.432008\pi$
$839$	12.2804	0.423967	0.211983	+	0.977273i	$0.432008\pi$
$840$	−1.91951	−0.0662294
$841$	−17.7496	−0.612054
$842$	−12.1058	−0.417194
$843$	14.3408	0.493925
$844$	20.4326	0.703318
$845$	0	0
$846$	−1.60819	−0.0552907
$847$	22.9663	0.789131
$848$	−5.89187	−0.202328
$849$	−13.9259	−0.477935
$850$	0.537864	0.0184486
$851$	21.2520	0.728509
$852$	24.1543	0.827514
$853$	−0.0616267	−0.00211006	−0.00105503	−	0.999999i	$-0.500336\pi$
$853$	−0.0616267	−0.00211006	−0.00105503	+	0.999999i	$0.500336\pi$
$854$	−4.13874	−0.141625
$855$	1.78580	0.0610732
$856$	−20.9919	−0.717489
$857$	56.0433	1.91440	0.957202	−	0.289421i	$-0.0934629\pi$
$857$	56.0433	1.91440	0.957202	+	0.289421i	$0.0934629\pi$
$858$	0	0
$859$	−16.0721	−0.548372	−0.274186	−	0.961677i	$-0.588408\pi$
$859$	−16.0721	−0.548372	−0.274186	+	0.961677i	$0.588408\pi$
$860$	7.80104	0.266013
$861$	−0.816015	−0.0278097
$862$	5.01158	0.170695
$863$	−5.29127	−0.180117	−0.0900585	−	0.995936i	$-0.528705\pi$
$863$	−5.29127	−0.180117	−0.0900585	+	0.995936i	$0.528705\pi$
$864$	−4.08395	−0.138939
$865$	16.9106	0.574977
$866$	−11.5233	−0.391576
$867$	16.8038	0.570685
$868$	15.4865	0.525645
$869$	14.8443	0.503559
$870$	1.66818	0.0565566
$871$	0	0
$872$	19.6418	0.665154
$873$	3.75470	0.127077
$874$	1.35094	0.0456964
$875$	10.9328	0.369595
$876$	−13.3896	−0.452393
$877$	−33.2558	−1.12297	−0.561484	−	0.827487i	$-0.689770\pi$
$877$	−33.2558	−1.12297	−0.561484	+	0.827487i	$0.689770\pi$
$878$	−8.43241	−0.284580
$879$	−24.0035	−0.809617
$880$	24.5671	0.828157
$881$	35.0421	1.18060	0.590299	−	0.807185i	$-0.299010\pi$
$881$	35.0421	1.18060	0.590299	+	0.807185i	$0.299010\pi$
$882$	0.374817	0.0126207
$883$	31.8305	1.07118	0.535590	−	0.844478i	$-0.320089\pi$
$883$	31.8305	1.07118	0.535590	+	0.844478i	$0.320089\pi$
$884$	0	0
$885$	8.18430	0.275112
$886$	−9.98346	−0.335401
$887$	49.6809	1.66812	0.834060	−	0.551673i	$-0.186010\pi$
$887$	49.6809	1.66812	0.834060	+	0.551673i	$0.186010\pi$
$888$	−11.4797	−0.385232
$889$	−6.24679	−0.209511
$890$	−0.124101	−0.00415989
$891$	−5.82806	−0.195247
$892$	−27.2942	−0.913878
$893$	5.77448	0.193236
$894$	4.60944	0.154163
$895$	−4.12006	−0.137718
$896$	−9.97559	−0.333261
$897$	0	0
$898$	−11.3535	−0.378872
$899$	−27.9343	−0.931662
$900$	6.02358	0.200786
$901$	0.821599	0.0273714
$902$	−1.78255	−0.0593524
$903$	−3.16166	−0.105213
$904$	−22.9599	−0.763634
$905$	0.889935	0.0295824
$906$	7.00145	0.232607
$907$	−8.42301	−0.279681	−0.139841	−	0.990174i	$-0.544659\pi$
$907$	−8.42301	−0.279681	−0.139841	+	0.990174i	$0.544659\pi$
$908$	−1.14522	−0.0380054
$909$	2.83930	0.0941737
$910$	0	0
$911$	1.84825	0.0612351	0.0306176	−	0.999531i	$-0.490253\pi$
$911$	1.84825	0.0612351	0.0306176	+	0.999531i	$0.490253\pi$
$912$	4.27550	0.141576
$913$	−94.5369	−3.12872
$914$	2.96873	0.0981968
$915$	−14.6517	−0.484370
$916$	−17.6168	−0.582076
$917$	14.6868	0.485001
$918$	0.166042	0.00548019
$919$	55.6552	1.83590	0.917948	−	0.396700i	$-0.129845\pi$
$919$	55.6552	1.83590	0.917948	+	0.396700i	$0.129845\pi$
$920$	−5.14059	−0.169480
$921$	20.6185	0.679404
$922$	−4.11866	−0.135641
$923$	0	0
$924$	−10.8373	−0.356523
$925$	25.7059	0.845204
$926$	−3.26760	−0.107380
$927$	−13.0189	−0.427596
$928$	13.6982	0.449667
$929$	−39.2038	−1.28624	−0.643118	−	0.765767i	$-0.722359\pi$
$929$	−39.2038	−1.28624	−0.643118	+	0.765767i	$0.722359\pi$
$930$	−4.14202	−0.135822
$931$	−1.34585	−0.0441083
$932$	15.5306	0.508720
$933$	−33.6435	−1.10144
$934$	12.6653	0.414423
$935$	−3.42579	−0.112035
$936$	0	0
$937$	−12.6724	−0.413989	−0.206995	−	0.978342i	$-0.566368\pi$
$937$	−12.6724	−0.413989	−0.206995	+	0.978342i	$0.566368\pi$
$938$	0.616356	0.0201248
$939$	−9.87809	−0.322359
$940$	−10.5866	−0.345296
$941$	−7.81644	−0.254809	−0.127404	−	0.991851i	$-0.540665\pi$
$941$	−7.81644	−0.254809	−0.127404	+	0.991851i	$0.540665\pi$
$942$	−9.14043	−0.297811
$943$	−2.18535	−0.0711648
$944$	19.5945	0.637746
$945$	1.32690	0.0431641
$946$	−6.90651	−0.224550
$947$	−48.1824	−1.56572	−0.782859	−	0.622199i	$-0.786240\pi$
$947$	−48.1824	−1.56572	−0.782859	+	0.622199i	$0.786240\pi$
$948$	−4.73626	−0.153826
$949$	0	0
$950$	1.63407	0.0530162
$951$	−13.6053	−0.441183
$952$	0.640840	0.0207697
$953$	51.8052	1.67813	0.839067	−	0.544028i	$-0.183101\pi$
$953$	51.8052	1.67813	0.839067	+	0.544028i	$0.183101\pi$
$954$	−0.695154	−0.0225065
$955$	−23.7154	−0.767412
$956$	−6.05160	−0.195723
$957$	19.5483	0.631906
$958$	−14.6343	−0.472814
$959$	0.933243	0.0301360
$960$	−6.39950	−0.206543
$961$	38.3598	1.23741
$962$	0	0
$963$	14.5111	0.467614
$964$	29.9539	0.964750
$965$	−7.46231	−0.240220
$966$	1.00379	0.0322964
$967$	5.87478	0.188920	0.0944602	−	0.995529i	$-0.469887\pi$
$967$	5.87478	0.188920	0.0944602	+	0.995529i	$0.469887\pi$
$968$	−33.2233	−1.06784
$969$	−0.596202	−0.0191528
$970$	−1.86738	−0.0599580
$971$	53.1421	1.70541	0.852705	−	0.522392i	$-0.174960\pi$
$971$	53.1421	1.70541	0.852705	+	0.522392i	$0.174960\pi$
$972$	1.85951	0.0596439
$973$	20.0765	0.643624
$974$	−4.52795	−0.145085
$975$	0	0
$976$	−35.0784	−1.12283
$977$	−16.9292	−0.541612	−0.270806	−	0.962634i	$-0.587290\pi$
$977$	−16.9292	−0.541612	−0.270806	+	0.962634i	$0.587290\pi$
$978$	−8.34527	−0.266852
$979$	−1.45426	−0.0464784
$980$	2.46739	0.0788179
$981$	−13.5778	−0.433505
$982$	−15.8952	−0.507237
$983$	−34.7612	−1.10871	−0.554355	−	0.832281i	$-0.687035\pi$
$983$	−34.7612	−1.10871	−0.554355	+	0.832281i	$0.687035\pi$
$984$	1.18046	0.0376316
$985$	21.9978	0.700908
$986$	−0.556932	−0.0177363
$987$	4.29060	0.136571
$988$	0	0
$989$	−8.46716	−0.269240
$990$	2.89856	0.0921222
$991$	33.6843	1.07002	0.535009	−	0.844846i	$-0.320308\pi$
$991$	33.6843	1.07002	0.535009	+	0.844846i	$0.320308\pi$
$992$	−34.0121	−1.07989
$993$	−1.35950	−0.0431426
$994$	4.86873	0.154427
$995$	−32.4083	−1.02741
$996$	30.1631	0.955756
$997$	9.21153	0.291732	0.145866	−	0.989304i	$-0.453403\pi$
$997$	9.21153	0.291732	0.145866	+	0.989304i	$0.453403\pi$
$998$	−8.90322	−0.281827
$999$	7.93555	0.251070

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.be.1.6	✓	9
13.12	even	2		3549.2.a.bf.1.4	yes	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3549.2.a.be.1.6	✓	9	1.1	even	1	trivial
3549.2.a.bf.1.4	yes	9	13.12	even	2

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)

\(f(q)\)	\(=\)	\(q+0.374817 q^{2} -1.00000 q^{3} -1.85951 q^{4} -1.32690 q^{5} -0.374817 q^{6} +1.00000 q^{7} -1.44661 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.374817 q^{2} -1.00000 q^{3} -1.85951 q^{4} -1.32690 q^{5} -0.374817 q^{6} +1.00000 q^{7} -1.44661 q^{8} +1.00000 q^{9} -0.497345 q^{10} -5.82806 q^{11} +1.85951 q^{12} +0.374817 q^{14} +1.32690 q^{15} +3.17681 q^{16} -0.442994 q^{17} +0.374817 q^{18} -1.34585 q^{19} +2.46739 q^{20} -1.00000 q^{21} -2.18446 q^{22} -2.67807 q^{23} +1.44661 q^{24} -3.23933 q^{25} -1.00000 q^{27} -1.85951 q^{28} +3.35417 q^{29} +0.497345 q^{30} -8.32825 q^{31} +4.08395 q^{32} +5.82806 q^{33} -0.166042 q^{34} -1.32690 q^{35} -1.85951 q^{36} -7.93555 q^{37} -0.504446 q^{38} +1.91951 q^{40} +0.816015 q^{41} -0.374817 q^{42} +3.16166 q^{43} +10.8373 q^{44} -1.32690 q^{45} -1.00379 q^{46} -4.29060 q^{47} -3.17681 q^{48} +1.00000 q^{49} -1.21416 q^{50} +0.442994 q^{51} -1.85465 q^{53} -0.374817 q^{54} +7.73326 q^{55} -1.44661 q^{56} +1.34585 q^{57} +1.25720 q^{58} +6.16798 q^{59} -2.46739 q^{60} -11.0420 q^{61} -3.12157 q^{62} +1.00000 q^{63} -4.82289 q^{64} +2.18446 q^{66} +1.64442 q^{67} +0.823753 q^{68} +2.67807 q^{69} -0.497345 q^{70} +12.9896 q^{71} -1.44661 q^{72} -7.20060 q^{73} -2.97438 q^{74} +3.23933 q^{75} +2.50262 q^{76} -5.82806 q^{77} -2.54704 q^{79} -4.21531 q^{80} +1.00000 q^{81} +0.305856 q^{82} +16.2210 q^{83} +1.85951 q^{84} +0.587809 q^{85} +1.18504 q^{86} -3.35417 q^{87} +8.43094 q^{88} +0.249528 q^{89} -0.497345 q^{90} +4.97991 q^{92} +8.32825 q^{93} -1.60819 q^{94} +1.78580 q^{95} -4.08395 q^{96} +3.75470 q^{97} +0.374817 q^{98} -5.82806 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - q^{2} - 9 q^{3} + 5 q^{4} + 9 q^{5} + q^{6} + 9 q^{7} - 6 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q - q^2 - 9 * q^3 + 5 * q^4 + 9 * q^5 + q^6 + 9 * q^7 - 6 * q^8 + 9 * q^9	\( 9 q - q^{2} - 9 q^{3} + 5 q^{4} + 9 q^{5} + q^{6} + 9 q^{7} - 6 q^{8} + 9 q^{9} + q^{10} - q^{11} - 5 q^{12} - q^{14} - 9 q^{15} + 5 q^{16} + 11 q^{17} - q^{18} + 7 q^{19} + 23 q^{20} - 9 q^{21} - 3 q^{22} + 22 q^{23} + 6 q^{24} - 8 q^{25} - 9 q^{27} + 5 q^{28} + 11 q^{29} - q^{30} + 7 q^{31} - 18 q^{32} + q^{33} - 6 q^{34} + 9 q^{35} + 5 q^{36} - q^{37} - 6 q^{38} - 14 q^{40} + 16 q^{41} + q^{42} + 32 q^{43} + 18 q^{44} + 9 q^{45} - 9 q^{46} - 12 q^{47} - 5 q^{48} + 9 q^{49} + 10 q^{50} - 11 q^{51} + 13 q^{53} + q^{54} + 9 q^{55} - 6 q^{56} - 7 q^{57} + 4 q^{58} + 29 q^{59} - 23 q^{60} - 12 q^{61} + 30 q^{62} + 9 q^{63} + 6 q^{64} + 3 q^{66} - 20 q^{67} + 34 q^{68} - 22 q^{69} + q^{70} - 2 q^{71} - 6 q^{72} + q^{73} + 43 q^{74} + 8 q^{75} + 13 q^{76} - q^{77} + 3 q^{79} - 39 q^{80} + 9 q^{81} - 19 q^{82} + 24 q^{83} - 5 q^{84} + 15 q^{85} - 28 q^{86} - 11 q^{87} - 19 q^{88} + 11 q^{89} + q^{90} + 73 q^{92} - 7 q^{93} + 15 q^{94} + 39 q^{95} + 18 q^{96} + 20 q^{97} - q^{98} - q^{99}+O(q^{100}) \) 9 * q - q^2 - 9 * q^3 + 5 * q^4 + 9 * q^5 + q^6 + 9 * q^7 - 6 * q^8 + 9 * q^9 + q^10 - q^11 - 5 * q^12 - q^14 - 9 * q^15 + 5 * q^16 + 11 * q^17 - q^18 + 7 * q^19 + 23 * q^20 - 9 * q^21 - 3 * q^22 + 22 * q^23 + 6 * q^24 - 8 * q^25 - 9 * q^27 + 5 * q^28 + 11 * q^29 - q^30 + 7 * q^31 - 18 * q^32 + q^33 - 6 * q^34 + 9 * q^35 + 5 * q^36 - q^37 - 6 * q^38 - 14 * q^40 + 16 * q^41 + q^42 + 32 * q^43 + 18 * q^44 + 9 * q^45 - 9 * q^46 - 12 * q^47 - 5 * q^48 + 9 * q^49 + 10 * q^50 - 11 * q^51 + 13 * q^53 + q^54 + 9 * q^55 - 6 * q^56 - 7 * q^57 + 4 * q^58 + 29 * q^59 - 23 * q^60 - 12 * q^61 + 30 * q^62 + 9 * q^63 + 6 * q^64 + 3 * q^66 - 20 * q^67 + 34 * q^68 - 22 * q^69 + q^70 - 2 * q^71 - 6 * q^72 + q^73 + 43 * q^74 + 8 * q^75 + 13 * q^76 - q^77 + 3 * q^79 - 39 * q^80 + 9 * q^81 - 19 * q^82 + 24 * q^83 - 5 * q^84 + 15 * q^85 - 28 * q^86 - 11 * q^87 - 19 * q^88 + 11 * q^89 + q^90 + 73 * q^92 - 7 * q^93 + 15 * q^94 + 39 * q^95 + 18 * q^96 + 20 * q^97 - q^98 - q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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