LMFDB - Embedded newform 3549.2.a.bf.1.5

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			1.5
Root			$0.146218$ 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)

$f(q)$	$=$	$q+0.146218 q^{2} -1.00000 q^{3} -1.97862 q^{4} +1.04369 q^{5} -0.146218 q^{6} -1.00000 q^{7} -0.581745 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.146218 q^{2} -1.00000 q^{3} -1.97862 q^{4} +1.04369 q^{5} -0.146218 q^{6} -1.00000 q^{7} -0.581745 q^{8} +1.00000 q^{9} +0.152606 q^{10} -3.53195 q^{11} +1.97862 q^{12} -0.146218 q^{14} -1.04369 q^{15} +3.87218 q^{16} +6.85108 q^{17} +0.146218 q^{18} +3.55174 q^{19} -2.06507 q^{20} +1.00000 q^{21} -0.516433 q^{22} +0.0937939 q^{23} +0.581745 q^{24} -3.91070 q^{25} -1.00000 q^{27} +1.97862 q^{28} -10.5871 q^{29} -0.152606 q^{30} -4.44756 q^{31} +1.72967 q^{32} +3.53195 q^{33} +1.00175 q^{34} -1.04369 q^{35} -1.97862 q^{36} -12.0790 q^{37} +0.519327 q^{38} -0.607163 q^{40} -1.37186 q^{41} +0.146218 q^{42} +6.68018 q^{43} +6.98839 q^{44} +1.04369 q^{45} +0.0137143 q^{46} +9.55298 q^{47} -3.87218 q^{48} +1.00000 q^{49} -0.571814 q^{50} -6.85108 q^{51} -3.01527 q^{53} -0.146218 q^{54} -3.68627 q^{55} +0.581745 q^{56} -3.55174 q^{57} -1.54803 q^{58} -0.747537 q^{59} +2.06507 q^{60} +5.72344 q^{61} -0.650312 q^{62} -1.00000 q^{63} -7.49145 q^{64} +0.516433 q^{66} +9.38048 q^{67} -13.5557 q^{68} -0.0937939 q^{69} -0.152606 q^{70} -4.41098 q^{71} -0.581745 q^{72} +10.4079 q^{73} -1.76616 q^{74} +3.91070 q^{75} -7.02754 q^{76} +3.53195 q^{77} -11.4527 q^{79} +4.04137 q^{80} +1.00000 q^{81} -0.200591 q^{82} +0.520292 q^{83} -1.97862 q^{84} +7.15043 q^{85} +0.976761 q^{86} +10.5871 q^{87} +2.05469 q^{88} +4.78217 q^{89} +0.152606 q^{90} -0.185582 q^{92} +4.44756 q^{93} +1.39681 q^{94} +3.70692 q^{95} -1.72967 q^{96} -5.89081 q^{97} +0.146218 q^{98} -3.53195 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.146218	0.103392	0.0516958	−	0.998663i	$-0.483537\pi$
$2$	0.146218	0.103392	0.0516958	+	0.998663i	$0.483537\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.97862	−0.989310
$5$	1.04369	0.466754	0.233377	−	0.972386i	$-0.425022\pi$
$5$	1.04369	0.466754	0.233377	+	0.972386i	$0.425022\pi$
$6$	−0.146218	−0.0596931
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−0.581745	−0.205678
$9$	1.00000	0.333333
$10$	0.152606	0.0482584
$11$	−3.53195	−1.06492	−0.532461	−	0.846454i	$-0.678733\pi$
$11$	−3.53195	−1.06492	−0.532461	+	0.846454i	$0.678733\pi$
$12$	1.97862	0.571179
$13$	0	0
$13$	0	0
$14$	−0.146218	−0.0390783
$15$	−1.04369	−0.269480
$16$	3.87218	0.968045
$17$	6.85108	1.66163	0.830816	−	0.556547i	$-0.187874\pi$
$17$	6.85108	1.66163	0.830816	+	0.556547i	$0.187874\pi$
$18$	0.146218	0.0344638
$19$	3.55174	0.814824	0.407412	−	0.913244i	$-0.366431\pi$
$19$	3.55174	0.814824	0.407412	+	0.913244i	$0.366431\pi$
$20$	−2.06507	−0.461764
$21$	1.00000	0.218218
$22$	−0.516433	−0.110104
$23$	0.0937939	0.0195574	0.00977869	−	0.999952i	$-0.496887\pi$
$23$	0.0937939	0.0195574	0.00977869	+	0.999952i	$0.496887\pi$
$24$	0.581745	0.118748
$25$	−3.91070	−0.782141
$26$	0	0
$27$	−1.00000	−0.192450
$28$	1.97862	0.373924
$29$	−10.5871	−1.96598	−0.982991	−	0.183653i	$-0.941208\pi$
$29$	−10.5871	−1.96598	−0.982991	+	0.183653i	$0.941208\pi$
$30$	−0.152606	−0.0278620
$31$	−4.44756	−0.798805	−0.399402	−	0.916776i	$-0.630782\pi$
$31$	−4.44756	−0.798805	−0.399402	+	0.916776i	$0.630782\pi$
$32$	1.72967	0.305765
$33$	3.53195	0.614833
$34$	1.00175	0.171799
$35$	−1.04369	−0.176416
$36$	−1.97862	−0.329770
$37$	−12.0790	−1.98577	−0.992885	−	0.119075i	$-0.962007\pi$
$37$	−12.0790	−1.98577	−0.992885	+	0.119075i	$0.962007\pi$
$38$	0.519327	0.0842459
$39$	0	0
$40$	−0.607163	−0.0960009
$41$	−1.37186	−0.214249	−0.107125	−	0.994246i	$-0.534164\pi$
$41$	−1.37186	−0.214249	−0.107125	+	0.994246i	$0.534164\pi$
$42$	0.146218	0.0225619
$43$	6.68018	1.01872	0.509359	−	0.860554i	$-0.329883\pi$
$43$	6.68018	1.01872	0.509359	+	0.860554i	$0.329883\pi$
$44$	6.98839	1.05354
$45$	1.04369	0.155585
$46$	0.0137143	0.00202207
$47$	9.55298	1.39345	0.696723	−	0.717341i	$-0.254641\pi$
$47$	9.55298	1.39345	0.696723	+	0.717341i	$0.254641\pi$
$48$	−3.87218	−0.558901
$49$	1.00000	0.142857
$50$	−0.571814	−0.0808667
$51$	−6.85108	−0.959344
$52$	0	0
$53$	−3.01527	−0.414179	−0.207090	−	0.978322i	$-0.566399\pi$
$53$	−3.01527	−0.414179	−0.207090	+	0.978322i	$0.566399\pi$
$54$	−0.146218	−0.0198977
$55$	−3.68627	−0.497057
$56$	0.581745	0.0777389
$57$	−3.55174	−0.470439
$58$	−1.54803	−0.203266
$59$	−0.747537	−0.0973210	−0.0486605	−	0.998815i	$-0.515495\pi$
$59$	−0.747537	−0.0973210	−0.0486605	+	0.998815i	$0.515495\pi$
$60$	2.06507	0.266600
$61$	5.72344	0.732812	0.366406	−	0.930455i	$-0.380588\pi$
$61$	5.72344	0.732812	0.366406	+	0.930455i	$0.380588\pi$
$62$	−0.650312	−0.0825896
$63$	−1.00000	−0.125988
$64$	−7.49145	−0.936431
$65$	0	0
$66$	0.516433	0.0635686
$67$	9.38048	1.14601	0.573004	−	0.819553i	$-0.305778\pi$
$67$	9.38048	1.14601	0.573004	+	0.819553i	$0.305778\pi$
$68$	−13.5557	−1.64387
$69$	−0.0937939	−0.0112915
$70$	−0.152606	−0.0182400
$71$	−4.41098	−0.523487	−0.261744	−	0.965137i	$-0.584297\pi$
$71$	−4.41098	−0.523487	−0.261744	+	0.965137i	$0.584297\pi$
$72$	−0.581745	−0.0685593
$73$	10.4079	1.21816	0.609078	−	0.793110i	$-0.291540\pi$
$73$	10.4079	1.21816	0.609078	+	0.793110i	$0.291540\pi$
$74$	−1.76616	−0.205312
$75$	3.91070	0.451569
$76$	−7.02754	−0.806114
$77$	3.53195	0.402503
$78$	0	0
$79$	−11.4527	−1.28853	−0.644267	−	0.764801i	$-0.722837\pi$
$79$	−11.4527	−1.28853	−0.644267	+	0.764801i	$0.722837\pi$
$80$	4.04137	0.451839
$81$	1.00000	0.111111
$82$	−0.200591	−0.0221515
$83$	0.520292	0.0571094	0.0285547	−	0.999592i	$-0.490910\pi$
$83$	0.520292	0.0571094	0.0285547	+	0.999592i	$0.490910\pi$
$84$	−1.97862	−0.215885
$85$	7.15043	0.775573
$86$	0.976761	0.105327
$87$	10.5871	1.13506
$88$	2.05469	0.219031
$89$	4.78217	0.506909	0.253455	−	0.967347i	$-0.418433\pi$
$89$	4.78217	0.506909	0.253455	+	0.967347i	$0.418433\pi$
$90$	0.152606	0.0160861
$91$	0	0
$92$	−0.185582	−0.0193483
$93$	4.44756	0.461190
$94$	1.39681	0.144070
$95$	3.70692	0.380322
$96$	−1.72967	−0.176534
$97$	−5.89081	−0.598121	−0.299060	−	0.954234i	$-0.596673\pi$
$97$	−5.89081	−0.598121	−0.299060	+	0.954234i	$0.596673\pi$
$98$	0.146218	0.0147702
$99$	−3.53195	−0.354974
$100$	7.73780	0.773780
$101$	6.24161	0.621063	0.310532	−	0.950563i	$-0.399493\pi$
$101$	6.24161	0.621063	0.310532	+	0.950563i	$0.399493\pi$
$102$	−1.00175	−0.0991880
$103$	16.3514	1.61115	0.805575	−	0.592494i	$-0.201857\pi$
$103$	16.3514	1.61115	0.805575	+	0.592494i	$0.201857\pi$
$104$	0	0
$105$	1.04369	0.101854
$106$	−0.440886	−0.0428226
$107$	12.5824	1.21639	0.608194	−	0.793789i	$-0.291894\pi$
$107$	12.5824	1.21639	0.608194	+	0.793789i	$0.291894\pi$
$108$	1.97862	0.190393
$109$	16.5546	1.58564	0.792820	−	0.609456i	$-0.208612\pi$
$109$	16.5546	1.58564	0.792820	+	0.609456i	$0.208612\pi$
$110$	−0.538998	−0.0513915
$111$	12.0790	1.14649
$112$	−3.87218	−0.365887
$113$	4.24986	0.399793	0.199897	−	0.979817i	$-0.435939\pi$
$113$	4.24986	0.399793	0.199897	+	0.979817i	$0.435939\pi$
$114$	−0.519327	−0.0486394
$115$	0.0978920	0.00912848
$116$	20.9479	1.94497
$117$	0	0
$118$	−0.109303	−0.0100622
$119$	−6.85108	−0.628038
$120$	0.607163	0.0554262
$121$	1.47466	0.134060
$122$	0.836869	0.0757665
$123$	1.37186	0.123697
$124$	8.80003	0.790266
$125$	−9.30004	−0.831821
$126$	−0.146218	−0.0130261
$127$	13.1132	1.16361	0.581803	−	0.813330i	$-0.302347\pi$
$127$	13.1132	1.16361	0.581803	+	0.813330i	$0.302347\pi$
$128$	−4.55472	−0.402585
$129$	−6.68018	−0.588157
$130$	0	0
$131$	16.3145	1.42541	0.712704	−	0.701465i	$-0.247470\pi$
$131$	16.3145	1.42541	0.712704	+	0.701465i	$0.247470\pi$
$132$	−6.98839	−0.608261
$133$	−3.55174	−0.307975
$134$	1.37159	0.118487
$135$	−1.04369	−0.0898268
$136$	−3.98558	−0.341761
$137$	−13.8001	−1.17902	−0.589511	−	0.807760i	$-0.700680\pi$
$137$	−13.8001	−1.17902	−0.589511	+	0.807760i	$0.700680\pi$
$138$	−0.0137143	−0.00116744
$139$	10.6210	0.900863	0.450432	−	0.892811i	$-0.351270\pi$
$139$	10.6210	0.900863	0.450432	+	0.892811i	$0.351270\pi$
$140$	2.06507	0.174531
$141$	−9.55298	−0.804506
$142$	−0.644964	−0.0541242
$143$	0	0
$144$	3.87218	0.322682
$145$	−11.0497	−0.917630
$146$	1.52182	0.125947
$147$	−1.00000	−0.0824786
$148$	23.8997	1.96454
$149$	−17.4093	−1.42622	−0.713112	−	0.701050i	$-0.752715\pi$
$149$	−17.4093	−1.42622	−0.713112	+	0.701050i	$0.752715\pi$
$150$	0.571814	0.0466884
$151$	8.14197	0.662584	0.331292	−	0.943528i	$-0.392515\pi$
$151$	8.14197	0.662584	0.331292	+	0.943528i	$0.392515\pi$
$152$	−2.06620	−0.167591
$153$	6.85108	0.553877
$154$	0.516433	0.0416154
$155$	−4.64189	−0.372845
$156$	0	0
$157$	6.68582	0.533587	0.266793	−	0.963754i	$-0.414036\pi$
$157$	6.68582	0.533587	0.266793	+	0.963754i	$0.414036\pi$
$158$	−1.67459	−0.133223
$159$	3.01527	0.239127
$160$	1.80525	0.142717
$161$	−0.0937939	−0.00739199
$162$	0.146218	0.0114879
$163$	−1.38383	−0.108390	−0.0541951	−	0.998530i	$-0.517259\pi$
$163$	−1.38383	−0.108390	−0.0541951	+	0.998530i	$0.517259\pi$
$164$	2.71440	0.211959
$165$	3.68627	0.286976
$166$	0.0760759	0.00590463
$167$	−9.73351	−0.753201	−0.376601	−	0.926376i	$-0.622907\pi$
$167$	−9.73351	−0.753201	−0.376601	+	0.926376i	$0.622907\pi$
$168$	−0.581745	−0.0448826
$169$	0	0
$170$	1.04552	0.0801877
$171$	3.55174	0.271608
$172$	−13.2175	−1.00783
$173$	21.8671	1.66253	0.831263	−	0.555880i	$-0.187619\pi$
$173$	21.8671	1.66253	0.831263	+	0.555880i	$0.187619\pi$
$174$	1.54803	0.117356
$175$	3.91070	0.295621
$176$	−13.6763	−1.03089
$177$	0.747537	0.0561883
$178$	0.699238	0.0524101
$179$	9.76241	0.729677	0.364838	−	0.931071i	$-0.381124\pi$
$179$	9.76241	0.729677	0.364838	+	0.931071i	$0.381124\pi$
$180$	−2.06507	−0.153921
$181$	−6.12994	−0.455635	−0.227818	−	0.973704i	$-0.573159\pi$
$181$	−6.12994	−0.455635	−0.227818	+	0.973704i	$0.573159\pi$
$182$	0	0
$183$	−5.72344	−0.423089
$184$	−0.0545641	−0.00402252
$185$	−12.6067	−0.926866
$186$	0.650312	0.0476832
$187$	−24.1977	−1.76951
$188$	−18.9017	−1.37855
$189$	1.00000	0.0727393
$190$	0.542018	0.0393221
$191$	−6.99754	−0.506324	−0.253162	−	0.967424i	$-0.581471\pi$
$191$	−6.99754	−0.506324	−0.253162	+	0.967424i	$0.581471\pi$
$192$	7.49145	0.540649
$193$	−0.616731	−0.0443933	−0.0221966	−	0.999754i	$-0.507066\pi$
$193$	−0.616731	−0.0443933	−0.0221966	+	0.999754i	$0.507066\pi$
$194$	−0.861340	−0.0618406
$195$	0	0
$196$	−1.97862	−0.141330
$197$	16.1657	1.15176	0.575881	−	0.817534i	$-0.304659\pi$
$197$	16.1657	1.15176	0.575881	+	0.817534i	$0.304659\pi$
$198$	−0.516433	−0.0367013
$199$	−12.2086	−0.865444	−0.432722	−	0.901527i	$-0.642447\pi$
$199$	−12.2086	−0.865444	−0.432722	+	0.901527i	$0.642447\pi$
$200$	2.27503	0.160869
$201$	−9.38048	−0.661648
$202$	0.912634	0.0642127
$203$	10.5871	0.743071
$204$	13.5557	0.949088
$205$	−1.43181	−0.100002
$206$	2.39086	0.166579
$207$	0.0937939	0.00651912
$208$	0	0
$209$	−12.5445	−0.867725
$210$	0.152606	0.0105308
$211$	3.69598	0.254442	0.127221	−	0.991874i	$-0.459394\pi$
$211$	3.69598	0.254442	0.127221	+	0.991874i	$0.459394\pi$
$212$	5.96608	0.409752
$213$	4.41098	0.302236
$214$	1.83977	0.125764
$215$	6.97206	0.475491
$216$	0.581745	0.0395827
$217$	4.44756	0.301920
$218$	2.42057	0.163942
$219$	−10.4079	−0.703303
$220$	7.29373	0.491743
$221$	0	0
$222$	1.76616	0.118537
$223$	2.45236	0.164222	0.0821112	−	0.996623i	$-0.473834\pi$
$223$	2.45236	0.164222	0.0821112	+	0.996623i	$0.473834\pi$
$224$	−1.72967	−0.115568
$225$	−3.91070	−0.260714
$226$	0.621405	0.0413352
$227$	26.2329	1.74114	0.870568	−	0.492048i	$-0.163752\pi$
$227$	26.2329	1.74114	0.870568	+	0.492048i	$0.163752\pi$
$228$	7.02754	0.465410
$229$	−17.0027	−1.12357	−0.561786	−	0.827282i	$-0.689886\pi$
$229$	−17.0027	−1.12357	−0.561786	+	0.827282i	$0.689886\pi$
$230$	0.0143135	0.000943807 0
$231$	−3.53195	−0.232385
$232$	6.15901	0.404359
$233$	17.2121	1.12760	0.563802	−	0.825910i	$-0.309338\pi$
$233$	17.2121	1.12760	0.563802	+	0.825910i	$0.309338\pi$
$234$	0	0
$235$	9.97038	0.650396
$236$	1.47909	0.0962807
$237$	11.4527	0.743935
$238$	−1.00175	−0.0649338
$239$	9.39453	0.607681	0.303841	−	0.952723i	$-0.401731\pi$
$239$	9.39453	0.607681	0.303841	+	0.952723i	$0.401731\pi$
$240$	−4.04137	−0.260869
$241$	17.6662	1.13798	0.568991	−	0.822344i	$-0.307334\pi$
$241$	17.6662	1.13798	0.568991	+	0.822344i	$0.307334\pi$
$242$	0.215621	0.0138607
$243$	−1.00000	−0.0641500
$244$	−11.3245	−0.724978
$245$	1.04369	0.0666791
$246$	0.200591	0.0127892
$247$	0	0
$248$	2.58734	0.164296
$249$	−0.520292	−0.0329721
$250$	−1.35983	−0.0860033
$251$	21.3529	1.34778	0.673892	−	0.738830i	$-0.264621\pi$
$251$	21.3529	1.34778	0.673892	+	0.738830i	$0.264621\pi$
$252$	1.97862	0.124641
$253$	−0.331275	−0.0208271
$254$	1.91738	0.120307
$255$	−7.15043	−0.447777
$256$	14.3169	0.894807
$257$	6.07035	0.378658	0.189329	−	0.981914i	$-0.439369\pi$
$257$	6.07035	0.378658	0.189329	+	0.981914i	$0.439369\pi$
$258$	−0.976761	−0.0608105
$259$	12.0790	0.750551
$260$	0	0
$261$	−10.5871	−0.655327
$262$	2.38548	0.147375
$263$	−11.3627	−0.700652	−0.350326	−	0.936628i	$-0.613929\pi$
$263$	−11.3627	−0.700652	−0.350326	+	0.936628i	$0.613929\pi$
$264$	−2.05469	−0.126458
$265$	−3.14702	−0.193320
$266$	−0.519327	−0.0318420
$267$	−4.78217	−0.292664
$268$	−18.5604	−1.13376
$269$	12.4693	0.760266	0.380133	−	0.924932i	$-0.375878\pi$
$269$	12.4693	0.760266	0.380133	+	0.924932i	$0.375878\pi$
$270$	−0.152606	−0.00928733
$271$	−23.4805	−1.42634	−0.713170	−	0.700991i	$-0.752741\pi$
$271$	−23.4805	−1.42634	−0.713170	+	0.700991i	$0.752741\pi$
$272$	26.5286	1.60853
$273$	0	0
$274$	−2.01782	−0.121901
$275$	13.8124	0.832919
$276$	0.185582	0.0111707
$277$	−4.47714	−0.269005	−0.134503	−	0.990913i	$-0.542944\pi$
$277$	−4.47714	−0.269005	−0.134503	+	0.990913i	$0.542944\pi$
$278$	1.55298	0.0931416
$279$	−4.44756	−0.266268
$280$	0.607163	0.0362849
$281$	−3.45840	−0.206311	−0.103156	−	0.994665i	$-0.532894\pi$
$281$	−3.45840	−0.206311	−0.103156	+	0.994665i	$0.532894\pi$
$282$	−1.39681	−0.0831791
$283$	28.4306	1.69002	0.845011	−	0.534748i	$-0.179594\pi$
$283$	28.4306	1.69002	0.845011	+	0.534748i	$0.179594\pi$
$284$	8.72766	0.517891
$285$	−3.70692	−0.219579
$286$	0	0
$287$	1.37186	0.0809786
$288$	1.72967	0.101922
$289$	29.9373	1.76102
$290$	−1.61567	−0.0948752
$291$	5.89081	0.345325
$292$	−20.5933	−1.20513
$293$	−27.7150	−1.61913	−0.809563	−	0.587033i	$-0.800296\pi$
$293$	−27.7150	−1.61913	−0.809563	+	0.587033i	$0.800296\pi$
$294$	−0.146218	−0.00852759
$295$	−0.780199	−0.0454250
$296$	7.02688	0.408429
$297$	3.53195	0.204944
$298$	−2.54555	−0.147459
$299$	0	0
$300$	−7.73780	−0.446742
$301$	−6.68018	−0.385039
$302$	1.19050	0.0685056
$303$	−6.24161	−0.358571
$304$	13.7530	0.788786
$305$	5.97352	0.342043
$306$	1.00175	0.0572662
$307$	18.9470	1.08136	0.540681	−	0.841227i	$-0.318166\pi$
$307$	18.9470	1.08136	0.540681	+	0.841227i	$0.318166\pi$
$308$	−6.98839	−0.398200
$309$	−16.3514	−0.930198
$310$	−0.678726	−0.0385490
$311$	19.1810	1.08766	0.543828	−	0.839197i	$-0.316974\pi$
$311$	19.1810	1.08766	0.543828	+	0.839197i	$0.316974\pi$
$312$	0	0
$313$	−8.34389	−0.471624	−0.235812	−	0.971799i	$-0.575775\pi$
$313$	−8.34389	−0.471624	−0.235812	+	0.971799i	$0.575775\pi$
$314$	0.977585	0.0551683
$315$	−1.04369	−0.0588055
$316$	22.6606	1.27476
$317$	−10.5961	−0.595136	−0.297568	−	0.954701i	$-0.596175\pi$
$317$	−10.5961	−0.595136	−0.297568	+	0.954701i	$0.596175\pi$
$318$	0.440886	0.0247237
$319$	37.3932	2.09362
$320$	−7.81878	−0.437083
$321$	−12.5824	−0.702282
$322$	−0.0137143	−0.000764269 0
$323$	24.3332	1.35394
$324$	−1.97862	−0.109923
$325$	0	0
$326$	−0.202341	−0.0112066
$327$	−16.5546	−0.915469
$328$	0.798075	0.0440663
$329$	−9.55298	−0.526673
$330$	0.538998	0.0296709
$331$	14.6461	0.805023	0.402512	−	0.915415i	$-0.368137\pi$
$331$	14.6461	0.805023	0.402512	+	0.915415i	$0.368137\pi$
$332$	−1.02946	−0.0564989
$333$	−12.0790	−0.661923
$334$	−1.42321	−0.0778747
$335$	9.79034	0.534904
$336$	3.87218	0.211245
$337$	−16.4037	−0.893567	−0.446783	−	0.894642i	$-0.647431\pi$
$337$	−16.4037	−0.893567	−0.446783	+	0.894642i	$0.647431\pi$
$338$	0	0
$339$	−4.24986	−0.230821
$340$	−14.1480	−0.767282
$341$	15.7085	0.850665
$342$	0.519327	0.0280820
$343$	−1.00000	−0.0539949
$344$	−3.88616	−0.209528
$345$	−0.0978920	−0.00527033
$346$	3.19736	0.171891
$347$	16.6360	0.893068	0.446534	−	0.894767i	$-0.352658\pi$
$347$	16.6360	0.893068	0.446534	+	0.894767i	$0.352658\pi$
$348$	−20.9479	−1.12293
$349$	−22.3603	−1.19692	−0.598459	−	0.801154i	$-0.704220\pi$
$349$	−22.3603	−1.19692	−0.598459	+	0.801154i	$0.704220\pi$
$350$	0.571814	0.0305648
$351$	0	0
$352$	−6.10911	−0.325617
$353$	16.2683	0.865874	0.432937	−	0.901424i	$-0.357477\pi$
$353$	16.2683	0.865874	0.432937	+	0.901424i	$0.357477\pi$
$354$	0.109303	0.00580940
$355$	−4.60371	−0.244340
$356$	−9.46210	−0.501490
$357$	6.85108	0.362598
$358$	1.42744	0.0754424
$359$	30.0297	1.58491	0.792454	−	0.609931i	$-0.208803\pi$
$359$	30.0297	1.58491	0.792454	+	0.609931i	$0.208803\pi$
$360$	−0.607163	−0.0320003
$361$	−6.38517	−0.336062
$362$	−0.896306	−0.0471088
$363$	−1.47466	−0.0773995
$364$	0	0
$365$	10.8627	0.568579
$366$	−0.836869	−0.0437438
$367$	−20.6436	−1.07758	−0.538792	−	0.842439i	$-0.681119\pi$
$367$	−20.6436	−1.07758	−0.538792	+	0.842439i	$0.681119\pi$
$368$	0.363187	0.0189324
$369$	−1.37186	−0.0714164
$370$	−1.84333	−0.0958301
$371$	3.01527	0.156545
$372$	−8.80003	−0.456260
$373$	1.02353	0.0529966	0.0264983	−	0.999649i	$-0.491564\pi$
$373$	1.02353	0.0529966	0.0264983	+	0.999649i	$0.491564\pi$
$374$	−3.53813	−0.182952
$375$	9.30004	0.480252
$376$	−5.55740	−0.286601
$377$	0	0
$378$	0.146218	0.00752063
$379$	16.0762	0.825779	0.412890	−	0.910781i	$-0.364519\pi$
$379$	16.0762	0.825779	0.412890	+	0.910781i	$0.364519\pi$
$380$	−7.33459	−0.376257
$381$	−13.1132	−0.671809
$382$	−1.02316	−0.0523496
$383$	−3.72843	−0.190514	−0.0952571	−	0.995453i	$-0.530367\pi$
$383$	−3.72843	−0.190514	−0.0952571	+	0.995453i	$0.530367\pi$
$384$	4.55472	0.232432
$385$	3.68627	0.187870
$386$	−0.0901770	−0.00458989
$387$	6.68018	0.339573
$388$	11.6557	0.591727
$389$	−13.9725	−0.708435	−0.354218	−	0.935163i	$-0.615253\pi$
$389$	−13.9725	−0.708435	−0.354218	+	0.935163i	$0.615253\pi$
$390$	0	0
$391$	0.642589	0.0324971
$392$	−0.581745	−0.0293825
$393$	−16.3145	−0.822960
$394$	2.36372	0.119082
$395$	−11.9531	−0.601428
$396$	6.98839	0.351180
$397$	15.6076	0.783321	0.391660	−	0.920110i	$-0.371901\pi$
$397$	15.6076	0.783321	0.391660	+	0.920110i	$0.371901\pi$
$398$	−1.78511	−0.0894796
$399$	3.55174	0.177809
$400$	−15.1429	−0.757147
$401$	−20.6443	−1.03093	−0.515463	−	0.856912i	$-0.672380\pi$
$401$	−20.6443	−1.03093	−0.515463	+	0.856912i	$0.672380\pi$
$402$	−1.37159	−0.0684088
$403$	0	0
$404$	−12.3498	−0.614424
$405$	1.04369	0.0518615
$406$	1.54803	0.0768273
$407$	42.6623	2.11469
$408$	3.98558	0.197316
$409$	12.4181	0.614034	0.307017	−	0.951704i	$-0.400669\pi$
$409$	12.4181	0.614034	0.307017	+	0.951704i	$0.400669\pi$
$410$	−0.209355	−0.0103393
$411$	13.8001	0.680709
$412$	−32.3532	−1.59393
$413$	0.747537	0.0367839
$414$	0.0137143	0.000674022 0
$415$	0.543025	0.0266560
$416$	0	0
$417$	−10.6210	−0.520114
$418$	−1.83424	−0.0897154
$419$	14.0864	0.688165	0.344082	−	0.938939i	$-0.388190\pi$
$419$	14.0864	0.688165	0.344082	+	0.938939i	$0.388190\pi$
$420$	−2.06507	−0.100765
$421$	−8.37137	−0.407995	−0.203998	−	0.978971i	$-0.565394\pi$
$421$	−8.37137	−0.407995	−0.203998	+	0.978971i	$0.565394\pi$
$422$	0.540418	0.0263072
$423$	9.55298	0.464482
$424$	1.75412	0.0851875
$425$	−26.7926	−1.29963
$426$	0.644964	0.0312486
$427$	−5.72344	−0.276977
$428$	−24.8958	−1.20338
$429$	0	0
$430$	1.01944	0.0491617
$431$	0.617158	0.0297274	0.0148637	−	0.999890i	$-0.495269\pi$
$431$	0.617158	0.0297274	0.0148637	+	0.999890i	$0.495269\pi$
$432$	−3.87218	−0.186300
$433$	−5.24759	−0.252183	−0.126092	−	0.992019i	$-0.540243\pi$
$433$	−5.24759	−0.252183	−0.126092	+	0.992019i	$0.540243\pi$
$434$	0.650312	0.0312160
$435$	11.0497	0.529794
$436$	−32.7552	−1.56869
$437$	0.333131	0.0159358
$438$	−1.52182	−0.0727155
$439$	−15.2408	−0.727405	−0.363702	−	0.931515i	$-0.618488\pi$
$439$	−15.2408	−0.727405	−0.363702	+	0.931515i	$0.618488\pi$
$440$	2.14447	0.102234
$441$	1.00000	0.0476190
$442$	0	0
$443$	31.8306	1.51232	0.756159	−	0.654388i	$-0.227074\pi$
$443$	31.8306	1.51232	0.756159	+	0.654388i	$0.227074\pi$
$444$	−23.8997	−1.13423
$445$	4.99112	0.236602
$446$	0.358579	0.0169792
$447$	17.4093	0.823431
$448$	7.49145	0.353938
$449$	−11.8827	−0.560778	−0.280389	−	0.959886i	$-0.590463\pi$
$449$	−11.8827	−0.560778	−0.280389	+	0.959886i	$0.590463\pi$
$450$	−0.571814	−0.0269556
$451$	4.84535	0.228159
$452$	−8.40886	−0.395520
$453$	−8.14197	−0.382543
$454$	3.83571	0.180019
$455$	0	0
$456$	2.06620	0.0967589
$457$	−29.8436	−1.39602	−0.698012	−	0.716086i	$-0.745932\pi$
$457$	−29.8436	−1.39602	−0.698012	+	0.716086i	$0.745932\pi$
$458$	−2.48610	−0.116168
$459$	−6.85108	−0.319781
$460$	−0.193691	−0.00903090
$461$	37.9731	1.76858	0.884291	−	0.466936i	$-0.154642\pi$
$461$	37.9731	1.76858	0.884291	+	0.466936i	$0.154642\pi$
$462$	−0.516433	−0.0240267
$463$	−40.1068	−1.86392	−0.931961	−	0.362559i	$-0.881903\pi$
$463$	−40.1068	−1.86392	−0.931961	+	0.362559i	$0.881903\pi$
$464$	−40.9953	−1.90316
$465$	4.64189	0.215262
$466$	2.51672	0.116585
$467$	21.2918	0.985268	0.492634	−	0.870236i	$-0.336034\pi$
$467$	21.2918	0.985268	0.492634	+	0.870236i	$0.336034\pi$
$468$	0	0
$469$	−9.38048	−0.433150
$470$	1.45785	0.0672454
$471$	−6.68582	−0.308066
$472$	0.434876	0.0200168
$473$	−23.5941	−1.08486
$474$	1.67459	0.0769166
$475$	−13.8898	−0.637307
$476$	13.5557	0.621324
$477$	−3.01527	−0.138060
$478$	1.37365	0.0628291
$479$	−22.7366	−1.03886	−0.519430	−	0.854513i	$-0.673856\pi$
$479$	−22.7366	−1.03886	−0.519430	+	0.854513i	$0.673856\pi$
$480$	−1.80525	−0.0823978
$481$	0	0
$482$	2.58311	0.117658
$483$	0.0937939	0.00426777
$484$	−2.91779	−0.132627
$485$	−6.14820	−0.279175
$486$	−0.146218	−0.00663257
$487$	−7.35639	−0.333350	−0.166675	−	0.986012i	$-0.553303\pi$
$487$	−7.35639	−0.333350	−0.166675	+	0.986012i	$0.553303\pi$
$488$	−3.32958	−0.150723
$489$	1.38383	0.0625791
$490$	0.152606	0.00689406
$491$	40.6568	1.83482	0.917408	−	0.397948i	$-0.130278\pi$
$491$	40.6568	1.83482	0.917408	+	0.397948i	$0.130278\pi$
$492$	−2.71440	−0.122374
$493$	−72.5334	−3.26674
$494$	0	0
$495$	−3.68627	−0.165686
$496$	−17.2217	−0.773279
$497$	4.41098	0.197860
$498$	−0.0760759	−0.00340904
$499$	0.0721207	0.00322856	0.00161428	−	0.999999i	$-0.499486\pi$
$499$	0.0721207	0.00322856	0.00161428	+	0.999999i	$0.499486\pi$
$500$	18.4013	0.822929
$501$	9.73351	0.434861
$502$	3.12217	0.139349
$503$	5.61475	0.250349	0.125175	−	0.992135i	$-0.460051\pi$
$503$	5.61475	0.250349	0.125175	+	0.992135i	$0.460051\pi$
$504$	0.581745	0.0259130
$505$	6.51432	0.289884
$506$	−0.0484383	−0.00215334
$507$	0	0
$508$	−25.9460	−1.15117
$509$	−29.8050	−1.32108	−0.660541	−	0.750790i	$-0.729673\pi$
$509$	−29.8050	−1.32108	−0.660541	+	0.750790i	$0.729673\pi$
$510$	−1.04552	−0.0462964
$511$	−10.4079	−0.460420
$512$	11.2028	0.495100
$513$	−3.55174	−0.156813
$514$	0.887592	0.0391500
$515$	17.0658	0.752010
$516$	13.2175	0.581870
$517$	−33.7406	−1.48391
$518$	1.76616	0.0776006
$519$	−21.8671	−0.959860
$520$	0	0
$521$	35.8915	1.57243	0.786217	−	0.617951i	$-0.212037\pi$
$521$	35.8915	1.57243	0.786217	+	0.617951i	$0.212037\pi$
$522$	−1.54803	−0.0677553
$523$	−21.9498	−0.959800	−0.479900	−	0.877323i	$-0.659327\pi$
$523$	−21.9498	−0.959800	−0.479900	+	0.877323i	$0.659327\pi$
$524$	−32.2803	−1.41017
$525$	−3.91070	−0.170677
$526$	−1.66142	−0.0724415
$527$	−30.4706	−1.32732
$528$	13.6763	0.595186
$529$	−22.9912	−0.999618
$530$	−0.460150	−0.0199876
$531$	−0.747537	−0.0324403
$532$	7.02754	0.304682
$533$	0	0
$534$	−0.699238	−0.0302590
$535$	13.1322	0.567754
$536$	−5.45704	−0.235708
$537$	−9.76241	−0.421279
$538$	1.82323	0.0786051
$539$	−3.53195	−0.152132
$540$	2.06507	0.0888666
$541$	8.34399	0.358736	0.179368	−	0.983782i	$-0.442595\pi$
$541$	8.34399	0.358736	0.179368	+	0.983782i	$0.442595\pi$
$542$	−3.43327	−0.147472
$543$	6.12994	0.263061
$544$	11.8501	0.508070
$545$	17.2779	0.740103
$546$	0	0
$547$	−2.88177	−0.123216	−0.0616078	−	0.998100i	$-0.519623\pi$
$547$	−2.88177	−0.123216	−0.0616078	+	0.998100i	$0.519623\pi$
$548$	27.3052	1.16642
$549$	5.72344	0.244271
$550$	2.01962	0.0861168
$551$	−37.6027	−1.60193
$552$	0.0545641	0.00232240
$553$	11.4527	0.487020
$554$	−0.654637	−0.0278129
$555$	12.6067	0.535126
$556$	−21.0150	−0.891233
$557$	27.3118	1.15724	0.578620	−	0.815597i	$-0.303592\pi$
$557$	27.3118	1.15724	0.578620	+	0.815597i	$0.303592\pi$
$558$	−0.650312	−0.0275299
$559$	0	0
$560$	−4.04137	−0.170779
$561$	24.1977	1.02163
$562$	−0.505680	−0.0213308
$563$	7.36528	0.310410	0.155205	−	0.987882i	$-0.450396\pi$
$563$	7.36528	0.310410	0.155205	+	0.987882i	$0.450396\pi$
$564$	18.9017	0.795906
$565$	4.43555	0.186605
$566$	4.15705	0.174734
$567$	−1.00000	−0.0419961
$568$	2.56607	0.107670
$569$	−8.04377	−0.337212	−0.168606	−	0.985683i	$-0.553927\pi$
$569$	−8.04377	−0.337212	−0.168606	+	0.985683i	$0.553927\pi$
$570$	−0.542018	−0.0227026
$571$	−0.677399	−0.0283482	−0.0141741	−	0.999900i	$-0.504512\pi$
$571$	−0.677399	−0.0283482	−0.0141741	+	0.999900i	$0.504512\pi$
$572$	0	0
$573$	6.99754	0.292326
$574$	0.200591	0.00837250
$575$	−0.366800	−0.0152966
$576$	−7.49145	−0.312144
$577$	19.9767	0.831642	0.415821	−	0.909446i	$-0.363494\pi$
$577$	19.9767	0.831642	0.415821	+	0.909446i	$0.363494\pi$
$578$	4.37737	0.182075
$579$	0.616731	0.0256305
$580$	21.8632	0.907821
$581$	−0.520292	−0.0215853
$582$	0.861340	0.0357037
$583$	10.6498	0.441069
$584$	−6.05476	−0.250548
$585$	0	0
$586$	−4.05242	−0.167404
$587$	3.89654	0.160828	0.0804138	−	0.996762i	$-0.474376\pi$
$587$	3.89654	0.160828	0.0804138	+	0.996762i	$0.474376\pi$
$588$	1.97862	0.0815969
$589$	−15.7965	−0.650885
$590$	−0.114079	−0.00469656
$591$	−16.1657	−0.664970
$592$	−46.7719	−1.92231
$593$	19.7898	0.812668	0.406334	−	0.913725i	$-0.366807\pi$
$593$	19.7898	0.812668	0.406334	+	0.913725i	$0.366807\pi$
$594$	0.516433	0.0211895
$595$	−7.15043	−0.293139
$596$	34.4464	1.41098
$597$	12.2086	0.499664
$598$	0	0
$599$	18.1661	0.742247	0.371123	−	0.928584i	$-0.378973\pi$
$599$	18.1661	0.742247	0.371123	+	0.928584i	$0.378973\pi$
$600$	−2.27503	−0.0928778
$601$	28.3757	1.15747	0.578735	−	0.815516i	$-0.303547\pi$
$601$	28.3757	1.15747	0.578735	+	0.815516i	$0.303547\pi$
$602$	−0.976761	−0.0398098
$603$	9.38048	0.382003
$604$	−16.1099	−0.655501
$605$	1.53909	0.0625730
$606$	−0.912634	−0.0370732
$607$	−3.81922	−0.155017	−0.0775087	−	0.996992i	$-0.524697\pi$
$607$	−3.81922	−0.155017	−0.0775087	+	0.996992i	$0.524697\pi$
$608$	6.14333	0.249145
$609$	−10.5871	−0.429012
$610$	0.873434	0.0353643
$611$	0	0
$612$	−13.5557	−0.547956
$613$	25.9181	1.04682	0.523411	−	0.852080i	$-0.324659\pi$
$613$	25.9181	1.04682	0.523411	+	0.852080i	$0.324659\pi$
$614$	2.77039	0.111804
$615$	1.43181	0.0577360
$616$	−2.05469	−0.0827859
$617$	10.8734	0.437747	0.218873	−	0.975753i	$-0.429762\pi$
$617$	10.8734	0.437747	0.218873	+	0.975753i	$0.429762\pi$
$618$	−2.39086	−0.0961746
$619$	−46.0428	−1.85062	−0.925308	−	0.379216i	$-0.876194\pi$
$619$	−46.0428	−1.85062	−0.925308	+	0.379216i	$0.876194\pi$
$620$	9.18453	0.368860
$621$	−0.0937939	−0.00376382
$622$	2.80461	0.112454
$623$	−4.78217	−0.191594
$624$	0	0
$625$	9.84713	0.393885
$626$	−1.22002	−0.0487620
$627$	12.5445	0.500981
$628$	−13.2287	−0.527883
$629$	−82.7540	−3.29962
$630$	−0.152606	−0.00607999
$631$	0.673777	0.0268226	0.0134113	−	0.999910i	$-0.495731\pi$
$631$	0.673777	0.0268226	0.0134113	+	0.999910i	$0.495731\pi$
$632$	6.66257	0.265023
$633$	−3.69598	−0.146902
$634$	−1.54934	−0.0615320
$635$	13.6861	0.543118
$636$	−5.96608	−0.236570
$637$	0	0
$638$	5.46755	0.216462
$639$	−4.41098	−0.174496
$640$	−4.75374	−0.187908
$641$	−25.8132	−1.01956	−0.509780	−	0.860305i	$-0.670273\pi$
$641$	−25.8132	−1.01956	−0.509780	+	0.860305i	$0.670273\pi$
$642$	−1.83977	−0.0726100
$643$	−45.2454	−1.78430	−0.892152	−	0.451736i	$-0.850805\pi$
$643$	−45.2454	−1.78430	−0.892152	+	0.451736i	$0.850805\pi$
$644$	0.185582	0.00731297
$645$	−6.97206	−0.274525
$646$	3.55795	0.139986
$647$	−35.7822	−1.40674	−0.703372	−	0.710821i	$-0.748323\pi$
$647$	−35.7822	−1.40674	−0.703372	+	0.710821i	$0.748323\pi$
$648$	−0.581745	−0.0228531
$649$	2.64026	0.103639
$650$	0	0
$651$	−4.44756	−0.174313
$652$	2.73808	0.107231
$653$	42.0570	1.64582	0.822908	−	0.568174i	$-0.192350\pi$
$653$	42.0570	1.64582	0.822908	+	0.568174i	$0.192350\pi$
$654$	−2.42057	−0.0946518
$655$	17.0274	0.665315
$656$	−5.31210	−0.207403
$657$	10.4079	0.406052
$658$	−1.39681	−0.0544535
$659$	−4.31664	−0.168152	−0.0840761	−	0.996459i	$-0.526794\pi$
$659$	−4.31664	−0.168152	−0.0840761	+	0.996459i	$0.526794\pi$
$660$	−7.29373	−0.283908
$661$	38.3032	1.48982	0.744910	−	0.667165i	$-0.232492\pi$
$661$	38.3032	1.48982	0.744910	+	0.667165i	$0.232492\pi$
$662$	2.14152	0.0832326
$663$	0	0
$664$	−0.302677	−0.0117461
$665$	−3.70692	−0.143748
$666$	−1.76616	−0.0684373
$667$	−0.993008	−0.0384494
$668$	19.2589	0.745150
$669$	−2.45236	−0.0948138
$670$	1.43152	0.0553045
$671$	−20.2149	−0.780388
$672$	1.72967	0.0667235
$673$	−6.22782	−0.240065	−0.120032	−	0.992770i	$-0.538300\pi$
$673$	−6.22782	−0.240065	−0.120032	+	0.992770i	$0.538300\pi$
$674$	−2.39851	−0.0923872
$675$	3.91070	0.150523
$676$	0	0
$677$	42.5387	1.63489	0.817447	−	0.576004i	$-0.195389\pi$
$677$	42.5387	1.63489	0.817447	+	0.576004i	$0.195389\pi$
$678$	−0.621405	−0.0238649
$679$	5.89081	0.226068
$680$	−4.15973	−0.159518
$681$	−26.2329	−1.00525
$682$	2.29687	0.0879516
$683$	−42.7618	−1.63624	−0.818118	−	0.575051i	$-0.804982\pi$
$683$	−42.7618	−1.63624	−0.818118	+	0.575051i	$0.804982\pi$
$684$	−7.02754	−0.268705
$685$	−14.4031	−0.550313
$686$	−0.146218	−0.00558262
$687$	17.0027	0.648695
$688$	25.8669	0.986165
$689$	0	0
$690$	−0.0143135	−0.000544907 0
$691$	−19.5828	−0.744967	−0.372483	−	0.928039i	$-0.621494\pi$
$691$	−19.5828	−0.744967	−0.372483	+	0.928039i	$0.621494\pi$
$692$	−43.2667	−1.64475
$693$	3.53195	0.134168
$694$	2.43248	0.0923356
$695$	11.0851	0.420481
$696$	−6.15901	−0.233457
$697$	−9.39875	−0.356003
$698$	−3.26947	−0.123751
$699$	−17.2121	−0.651023
$700$	−7.73780	−0.292461
$701$	−49.5279	−1.87064	−0.935322	−	0.353799i	$-0.884890\pi$
$701$	−49.5279	−1.87064	−0.935322	+	0.353799i	$0.884890\pi$
$702$	0	0
$703$	−42.9013	−1.61805
$704$	26.4594	0.997227
$705$	−9.97038	−0.375506
$706$	2.37871	0.0895241
$707$	−6.24161	−0.234740
$708$	−1.47909	−0.0555877
$709$	12.7801	0.479968	0.239984	−	0.970777i	$-0.422858\pi$
$709$	12.7801	0.479968	0.239984	+	0.970777i	$0.422858\pi$
$710$	−0.673144	−0.0252627
$711$	−11.4527	−0.429511
$712$	−2.78200	−0.104260
$713$	−0.417153	−0.0156225
$714$	1.00175	0.0374895
$715$	0	0
$716$	−19.3161	−0.721877
$717$	−9.39453	−0.350845
$718$	4.39088	0.163866
$719$	−21.8912	−0.816405	−0.408203	−	0.912891i	$-0.633844\pi$
$719$	−21.8912	−0.816405	−0.408203	+	0.912891i	$0.633844\pi$
$720$	4.04137	0.150613
$721$	−16.3514	−0.608957
$722$	−0.933625	−0.0347459
$723$	−17.6662	−0.657014
$724$	12.1288	0.450764
$725$	41.4032	1.53767
$726$	−0.215621	−0.00800246
$727$	−2.99931	−0.111238	−0.0556191	−	0.998452i	$-0.517713\pi$
$727$	−2.99931	−0.111238	−0.0556191	+	0.998452i	$0.517713\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	1.58832	0.0587863
$731$	45.7665	1.69273
$732$	11.3245	0.418566
$733$	−24.7708	−0.914931	−0.457465	−	0.889227i	$-0.651243\pi$
$733$	−24.7708	−0.914931	−0.457465	+	0.889227i	$0.651243\pi$
$734$	−3.01845	−0.111413
$735$	−1.04369	−0.0384972
$736$	0.162232	0.00597997
$737$	−33.1314	−1.22041
$738$	−0.200591	−0.00738385
$739$	3.77938	0.139027	0.0695133	−	0.997581i	$-0.477855\pi$
$739$	3.77938	0.139027	0.0695133	+	0.997581i	$0.477855\pi$
$740$	24.9440	0.916958
$741$	0	0
$742$	0.440886	0.0161854
$743$	28.1339	1.03213	0.516066	−	0.856549i	$-0.327396\pi$
$743$	28.1339	1.03213	0.516066	+	0.856549i	$0.327396\pi$
$744$	−2.58734	−0.0948566
$745$	−18.1700	−0.665695
$746$	0.149659	0.00547940
$747$	0.520292	0.0190365
$748$	47.8780	1.75059
$749$	−12.5824	−0.459751
$750$	1.35983	0.0496540
$751$	−16.3083	−0.595097	−0.297548	−	0.954707i	$-0.596169\pi$
$751$	−16.3083	−0.595097	−0.297548	+	0.954707i	$0.596169\pi$
$752$	36.9909	1.34892
$753$	−21.3529	−0.778144
$754$	0	0
$755$	8.49772	0.309264
$756$	−1.97862	−0.0719617
$757$	−33.3205	−1.21105	−0.605526	−	0.795825i	$-0.707037\pi$
$757$	−33.3205	−1.21105	−0.605526	+	0.795825i	$0.707037\pi$
$758$	2.35063	0.0853786
$759$	0.331275	0.0120245
$760$	−2.15648	−0.0782239
$761$	21.2851	0.771586	0.385793	−	0.922585i	$-0.373928\pi$
$761$	21.2851	0.771586	0.385793	+	0.922585i	$0.373928\pi$
$762$	−1.91738	−0.0694593
$763$	−16.5546	−0.599315
$764$	13.8455	0.500911
$765$	7.15043	0.258524
$766$	−0.545163	−0.0196975
$767$	0	0
$768$	−14.3169	−0.516617
$769$	−35.2935	−1.27272	−0.636358	−	0.771394i	$-0.719560\pi$
$769$	−35.2935	−1.27272	−0.636358	+	0.771394i	$0.719560\pi$
$770$	0.538998	0.0194241
$771$	−6.07035	−0.218618
$772$	1.22028	0.0439187
$773$	19.4548	0.699741	0.349871	−	0.936798i	$-0.386226\pi$
$773$	19.4548	0.699741	0.349871	+	0.936798i	$0.386226\pi$
$774$	0.976761	0.0351089
$775$	17.3931	0.624778
$776$	3.42695	0.123020
$777$	−12.0790	−0.433331
$778$	−2.04303	−0.0732462
$779$	−4.87250	−0.174575
$780$	0	0
$781$	15.5794	0.557473
$782$	0.0939580	0.00335993
$783$	10.5871	0.378353
$784$	3.87218	0.138292
$785$	6.97795	0.249054
$786$	−2.38548	−0.0850871
$787$	−49.1398	−1.75164	−0.875822	−	0.482635i	$-0.839680\pi$
$787$	−49.1398	−1.75164	−0.875822	+	0.482635i	$0.839680\pi$
$788$	−31.9859	−1.13945
$789$	11.3627	0.404522
$790$	−1.74776	−0.0621826
$791$	−4.24986	−0.151108
$792$	2.05469	0.0730103
$793$	0	0
$794$	2.28210	0.0809887
$795$	3.14702	0.111613
$796$	24.1562	0.856193
$797$	−2.13400	−0.0755902	−0.0377951	−	0.999286i	$-0.512033\pi$
$797$	−2.13400	−0.0755902	−0.0377951	+	0.999286i	$0.512033\pi$
$798$	0.519327	0.0183840
$799$	65.4483	2.31539
$800$	−6.76423	−0.239152
$801$	4.78217	0.168970
$802$	−3.01856	−0.106589
$803$	−36.7603	−1.29724
$804$	18.5604	0.654575
$805$	−0.0978920	−0.00345024
$806$	0	0
$807$	−12.4693	−0.438940
$808$	−3.63102	−0.127739
$809$	25.4023	0.893096	0.446548	−	0.894760i	$-0.352653\pi$
$809$	25.4023	0.893096	0.446548	+	0.894760i	$0.352653\pi$
$810$	0.152606	0.00536204
$811$	−15.6885	−0.550899	−0.275450	−	0.961316i	$-0.588827\pi$
$811$	−15.6885	−0.550899	−0.275450	+	0.961316i	$0.588827\pi$
$812$	−20.9479	−0.735128
$813$	23.4805	0.823498
$814$	6.23798	0.218641
$815$	−1.44430	−0.0505915
$816$	−26.5286	−0.928688
$817$	23.7262	0.830076
$818$	1.81574	0.0634859
$819$	0	0
$820$	2.83300	0.0989326
$821$	−29.7835	−1.03945	−0.519725	−	0.854334i	$-0.673966\pi$
$821$	−29.7835	−1.03945	−0.519725	+	0.854334i	$0.673966\pi$
$822$	2.01782	0.0703795
$823$	−38.8845	−1.35543	−0.677714	−	0.735326i	$-0.737029\pi$
$823$	−38.8845	−1.35543	−0.677714	+	0.735326i	$0.737029\pi$
$824$	−9.51233	−0.331378
$825$	−13.8124	−0.480886
$826$	0.109303	0.00380314
$827$	18.0200	0.626615	0.313308	−	0.949652i	$-0.398563\pi$
$827$	18.0200	0.626615	0.313308	+	0.949652i	$0.398563\pi$
$828$	−0.185582	−0.00644944
$829$	16.6753	0.579158	0.289579	−	0.957154i	$-0.406485\pi$
$829$	16.6753	0.579158	0.289579	+	0.957154i	$0.406485\pi$
$830$	0.0793999	0.00275601
$831$	4.47714	0.155310
$832$	0	0
$833$	6.85108	0.237376
$834$	−1.55298	−0.0537753
$835$	−10.1588	−0.351560
$836$	24.8209	0.858449
$837$	4.44756	0.153730
$838$	2.05968	0.0711504
$839$	−47.1236	−1.62689	−0.813444	−	0.581643i	$-0.802410\pi$
$839$	−47.1236	−1.62689	−0.813444	+	0.581643i	$0.802410\pi$
$840$	−0.607163	−0.0209491
$841$	83.0875	2.86509
$842$	−1.22404	−0.0421833
$843$	3.45840	0.119114
$844$	−7.31295	−0.251722
$845$	0	0
$846$	1.39681	0.0480235
$847$	−1.47466	−0.0506699
$848$	−11.6757	−0.400944
$849$	−28.4306	−0.975735
$850$	−3.91755	−0.134371
$851$	−1.13293	−0.0388364
$852$	−8.72766	−0.299005
$853$	4.30839	0.147517	0.0737583	−	0.997276i	$-0.476501\pi$
$853$	4.30839	0.147517	0.0737583	+	0.997276i	$0.476501\pi$
$854$	−0.836869	−0.0286371
$855$	3.70692	0.126774
$856$	−7.31975	−0.250184
$857$	−6.11232	−0.208793	−0.104396	−	0.994536i	$-0.533291\pi$
$857$	−6.11232	−0.208793	−0.104396	+	0.994536i	$0.533291\pi$
$858$	0	0
$859$	34.4693	1.17608	0.588039	−	0.808832i	$-0.299900\pi$
$859$	34.4693	1.17608	0.588039	+	0.808832i	$0.299900\pi$
$860$	−13.7951	−0.470408
$861$	−1.37186	−0.0467530
$862$	0.0902394	0.00307357
$863$	6.39934	0.217836	0.108918	−	0.994051i	$-0.465261\pi$
$863$	6.39934	0.217836	0.108918	+	0.994051i	$0.465261\pi$
$864$	−1.72967	−0.0588446
$865$	22.8226	0.775990
$866$	−0.767291	−0.0260736
$867$	−29.9373	−1.01673
$868$	−8.80003	−0.298692
$869$	40.4505	1.37219
$870$	1.61567	0.0547762
$871$	0	0
$872$	−9.63053	−0.326131
$873$	−5.89081	−0.199374
$874$	0.0487097	0.00164763
$875$	9.30004	0.314399
$876$	20.5933	0.695784
$877$	−14.7519	−0.498137	−0.249069	−	0.968486i	$-0.580124\pi$
$877$	−14.7519	−0.498137	−0.249069	+	0.968486i	$0.580124\pi$
$878$	−2.22848	−0.0752075
$879$	27.7150	0.934803
$880$	−14.2739	−0.481173
$881$	−51.9538	−1.75037	−0.875184	−	0.483791i	$-0.839260\pi$
$881$	−51.9538	−1.75037	−0.875184	+	0.483791i	$0.839260\pi$
$882$	0.146218	0.00492341
$883$	−22.7151	−0.764426	−0.382213	−	0.924074i	$-0.624838\pi$
$883$	−22.7151	−0.764426	−0.382213	+	0.924074i	$0.624838\pi$
$884$	0	0
$885$	0.780199	0.0262261
$886$	4.65420	0.156361
$887$	14.6854	0.493089	0.246544	−	0.969132i	$-0.420705\pi$
$887$	14.6854	0.493089	0.246544	+	0.969132i	$0.420705\pi$
$888$	−7.02688	−0.235807
$889$	−13.1132	−0.439802
$890$	0.729790	0.0244626
$891$	−3.53195	−0.118325
$892$	−4.85229	−0.162467
$893$	33.9297	1.13541
$894$	2.54555	0.0851358
$895$	10.1890	0.340580
$896$	4.55472	0.152163
$897$	0	0
$898$	−1.73746	−0.0579797
$899$	47.0869	1.57044
$900$	7.73780	0.257927
$901$	−20.6579	−0.688214
$902$	0.708476	0.0235897
$903$	6.68018	0.222303
$904$	−2.47233	−0.0822286
$905$	−6.39778	−0.212669
$906$	−1.19050	−0.0395517
$907$	−3.21863	−0.106873	−0.0534364	−	0.998571i	$-0.517017\pi$
$907$	−3.21863	−0.106873	−0.0534364	+	0.998571i	$0.517017\pi$
$908$	−51.9049	−1.72252
$909$	6.24161	0.207021
$910$	0	0
$911$	30.7915	1.02017	0.510083	−	0.860125i	$-0.329615\pi$
$911$	30.7915	1.02017	0.510083	+	0.860125i	$0.329615\pi$
$912$	−13.7530	−0.455406
$913$	−1.83764	−0.0608171
$914$	−4.36366	−0.144337
$915$	−5.97352	−0.197478
$916$	33.6420	1.11156
$917$	−16.3145	−0.538754
$918$	−1.00175	−0.0330627
$919$	17.5053	0.577446	0.288723	−	0.957413i	$-0.406769\pi$
$919$	17.5053	0.577446	0.288723	+	0.957413i	$0.406769\pi$
$920$	−0.0569482	−0.00187753
$921$	−18.9470	−0.624325
$922$	5.55233	0.182856
$923$	0	0
$924$	6.98839	0.229901
$925$	47.2373	1.55315
$926$	−5.86433	−0.192714
$927$	16.3514	0.537050
$928$	−18.3123	−0.601129
$929$	−33.3753	−1.09501	−0.547505	−	0.836803i	$-0.684422\pi$
$929$	−33.3753	−1.09501	−0.547505	+	0.836803i	$0.684422\pi$
$930$	0.678726	0.0222563
$931$	3.55174	0.116403
$932$	−34.0563	−1.11555
$933$	−19.1810	−0.627959
$934$	3.11324	0.101868
$935$	−25.2550	−0.825925
$936$	0	0
$937$	28.0519	0.916416	0.458208	−	0.888845i	$-0.348491\pi$
$937$	28.0519	0.916416	0.458208	+	0.888845i	$0.348491\pi$
$938$	−1.37159	−0.0447841
$939$	8.34389	0.272292
$940$	−19.7276	−0.643443
$941$	54.9687	1.79193	0.895965	−	0.444125i	$-0.146485\pi$
$941$	54.9687	1.79193	0.895965	+	0.444125i	$0.146485\pi$
$942$	−0.977585	−0.0318515
$943$	−0.128672	−0.00419015
$944$	−2.89460	−0.0942111
$945$	1.04369	0.0339513
$946$	−3.44987	−0.112165
$947$	42.8342	1.39192	0.695962	−	0.718079i	$-0.254978\pi$
$947$	42.8342	1.39192	0.695962	+	0.718079i	$0.254978\pi$
$948$	−22.6606	−0.735983
$949$	0	0
$950$	−2.03093	−0.0658922
$951$	10.5961	0.343602
$952$	3.98558	0.129173
$953$	−24.9354	−0.807736	−0.403868	−	0.914817i	$-0.632335\pi$
$953$	−24.9354	−0.807736	−0.403868	+	0.914817i	$0.632335\pi$
$954$	−0.440886	−0.0142742
$955$	−7.30328	−0.236329
$956$	−18.5882	−0.601185
$957$	−37.3932	−1.20875
$958$	−3.32449	−0.107409
$959$	13.8001	0.445629
$960$	7.81878	0.252350
$961$	−11.2192	−0.361911
$962$	0	0
$963$	12.5824	0.405462
$964$	−34.9547	−1.12582
$965$	−0.643678	−0.0207207
$966$	0.0137143	0.000441251 0
$967$	20.0431	0.644543	0.322272	−	0.946647i	$-0.395554\pi$
$967$	20.0431	0.644543	0.322272	+	0.946647i	$0.395554\pi$
$968$	−0.857875	−0.0275732
$969$	−24.3332	−0.781696
$970$	−0.898975	−0.0288643
$971$	−19.2927	−0.619134	−0.309567	−	0.950878i	$-0.600184\pi$
$971$	−19.2927	−0.619134	−0.309567	+	0.950878i	$0.600184\pi$
$972$	1.97862	0.0634643
$973$	−10.6210	−0.340494
$974$	−1.07563	−0.0344655
$975$	0	0
$976$	22.1622	0.709395
$977$	−23.6469	−0.756533	−0.378266	−	0.925697i	$-0.623480\pi$
$977$	−23.6469	−0.756533	−0.378266	+	0.925697i	$0.623480\pi$
$978$	0.202341	0.00647015
$979$	−16.8904	−0.539819
$980$	−2.06507	−0.0659663
$981$	16.5546	0.528547
$982$	5.94474	0.189704
$983$	−42.0050	−1.33975	−0.669876	−	0.742473i	$-0.733653\pi$
$983$	−42.0050	−1.33975	−0.669876	+	0.742473i	$0.733653\pi$
$984$	−0.798075	−0.0254417
$985$	16.8721	0.537589
$986$	−10.6057	−0.337753
$987$	9.55298	0.304075
$988$	0	0
$989$	0.626560	0.0199234
$990$	−0.538998	−0.0171305
$991$	28.0000	0.889450	0.444725	−	0.895667i	$-0.353301\pi$
$991$	28.0000	0.889450	0.444725	+	0.895667i	$0.353301\pi$
$992$	−7.69281	−0.244247
$993$	−14.6461	−0.464780
$994$	0.644964	0.0204570
$995$	−12.7420	−0.403949
$996$	1.02946	0.0326197
$997$	−15.9033	−0.503664	−0.251832	−	0.967771i	$-0.581033\pi$
$997$	−15.9033	−0.503664	−0.251832	+	0.967771i	$0.581033\pi$
$998$	0.0105453	0.000333806 0
$999$	12.0790	0.382162

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.bf.1.5	yes	9
13.12	even	2		3549.2.a.be.1.5	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3549.2.a.be.1.5	✓	9	13.12	even	2
3549.2.a.bf.1.5	yes	9	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+0.146218 q^{2} -1.00000 q^{3} -1.97862 q^{4} +1.04369 q^{5} -0.146218 q^{6} -1.00000 q^{7} -0.581745 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.146218 q^{2} -1.00000 q^{3} -1.97862 q^{4} +1.04369 q^{5} -0.146218 q^{6} -1.00000 q^{7} -0.581745 q^{8} +1.00000 q^{9} +0.152606 q^{10} -3.53195 q^{11} +1.97862 q^{12} -0.146218 q^{14} -1.04369 q^{15} +3.87218 q^{16} +6.85108 q^{17} +0.146218 q^{18} +3.55174 q^{19} -2.06507 q^{20} +1.00000 q^{21} -0.516433 q^{22} +0.0937939 q^{23} +0.581745 q^{24} -3.91070 q^{25} -1.00000 q^{27} +1.97862 q^{28} -10.5871 q^{29} -0.152606 q^{30} -4.44756 q^{31} +1.72967 q^{32} +3.53195 q^{33} +1.00175 q^{34} -1.04369 q^{35} -1.97862 q^{36} -12.0790 q^{37} +0.519327 q^{38} -0.607163 q^{40} -1.37186 q^{41} +0.146218 q^{42} +6.68018 q^{43} +6.98839 q^{44} +1.04369 q^{45} +0.0137143 q^{46} +9.55298 q^{47} -3.87218 q^{48} +1.00000 q^{49} -0.571814 q^{50} -6.85108 q^{51} -3.01527 q^{53} -0.146218 q^{54} -3.68627 q^{55} +0.581745 q^{56} -3.55174 q^{57} -1.54803 q^{58} -0.747537 q^{59} +2.06507 q^{60} +5.72344 q^{61} -0.650312 q^{62} -1.00000 q^{63} -7.49145 q^{64} +0.516433 q^{66} +9.38048 q^{67} -13.5557 q^{68} -0.0937939 q^{69} -0.152606 q^{70} -4.41098 q^{71} -0.581745 q^{72} +10.4079 q^{73} -1.76616 q^{74} +3.91070 q^{75} -7.02754 q^{76} +3.53195 q^{77} -11.4527 q^{79} +4.04137 q^{80} +1.00000 q^{81} -0.200591 q^{82} +0.520292 q^{83} -1.97862 q^{84} +7.15043 q^{85} +0.976761 q^{86} +10.5871 q^{87} +2.05469 q^{88} +4.78217 q^{89} +0.152606 q^{90} -0.185582 q^{92} +4.44756 q^{93} +1.39681 q^{94} +3.70692 q^{95} -1.72967 q^{96} -5.89081 q^{97} +0.146218 q^{98} -3.53195 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + q^{2} - 9 q^{3} + 5 q^{4} - 9 q^{5} - q^{6} - 9 q^{7} + 6 q^{8} + 9 q^{9}+O(q^{10}) \) 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

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