LMFDB - Embedded newform 3229.2.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3229,2,Mod(1,3229)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3229, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3229.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3229.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:	$25.7836948127$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	3229.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.618034 q^{2} -2.00000 q^{3} -1.61803 q^{4} +1.61803 q^{5} -1.23607 q^{6} -1.00000 q^{7} -2.23607 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.618034 q^{2} -2.00000 q^{3} -1.61803 q^{4} +1.61803 q^{5} -1.23607 q^{6} -1.00000 q^{7} -2.23607 q^{8} +1.00000 q^{9} +1.00000 q^{10} +0.763932 q^{11} +3.23607 q^{12} -2.38197 q^{13} -0.618034 q^{14} -3.23607 q^{15} +1.85410 q^{16} +5.23607 q^{17} +0.618034 q^{18} +2.85410 q^{19} -2.61803 q^{20} +2.00000 q^{21} +0.472136 q^{22} -4.47214 q^{23} +4.47214 q^{24} -2.38197 q^{25} -1.47214 q^{26} +4.00000 q^{27} +1.61803 q^{28} +7.61803 q^{29} -2.00000 q^{30} -9.61803 q^{31} +5.61803 q^{32} -1.52786 q^{33} +3.23607 q^{34} -1.61803 q^{35} -1.61803 q^{36} +8.09017 q^{37} +1.76393 q^{38} +4.76393 q^{39} -3.61803 q^{40} +10.0902 q^{41} +1.23607 q^{42} -6.09017 q^{43} -1.23607 q^{44} +1.61803 q^{45} -2.76393 q^{46} -2.23607 q^{47} -3.70820 q^{48} -6.00000 q^{49} -1.47214 q^{50} -10.4721 q^{51} +3.85410 q^{52} -7.47214 q^{53} +2.47214 q^{54} +1.23607 q^{55} +2.23607 q^{56} -5.70820 q^{57} +4.70820 q^{58} +2.23607 q^{59} +5.23607 q^{60} +2.00000 q^{61} -5.94427 q^{62} -1.00000 q^{63} -0.236068 q^{64} -3.85410 q^{65} -0.944272 q^{66} +12.7082 q^{67} -8.47214 q^{68} +8.94427 q^{69} -1.00000 q^{70} -0.708204 q^{71} -2.23607 q^{72} -12.4164 q^{73} +5.00000 q^{74} +4.76393 q^{75} -4.61803 q^{76} -0.763932 q^{77} +2.94427 q^{78} -15.7082 q^{79} +3.00000 q^{80} -11.0000 q^{81} +6.23607 q^{82} +8.61803 q^{83} -3.23607 q^{84} +8.47214 q^{85} -3.76393 q^{86} -15.2361 q^{87} -1.70820 q^{88} -16.7984 q^{89} +1.00000 q^{90} +2.38197 q^{91} +7.23607 q^{92} +19.2361 q^{93} -1.38197 q^{94} +4.61803 q^{95} -11.2361 q^{96} +2.85410 q^{97} -3.70820 q^{98} +0.763932 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - 4 q^{3} - q^{4} + q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{9}+O(q^{10}) $ 2 * q - q^2 - 4 * q^3 - q^4 + q^5 + 2 * q^6 - 2 * q^7 + 2 * q^9	$ 2 q - q^{2} - 4 q^{3} - q^{4} + q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{9} + 2 q^{10} + 6 q^{11} + 2 q^{12} - 7 q^{13} + q^{14} - 2 q^{15} - 3 q^{16} + 6 q^{17} - q^{18} - q^{19} - 3 q^{20} + 4 q^{21} - 8 q^{22} - 7 q^{25} + 6 q^{26} + 8 q^{27} + q^{28} + 13 q^{29} - 4 q^{30} - 17 q^{31} + 9 q^{32} - 12 q^{33} + 2 q^{34} - q^{35} - q^{36} + 5 q^{37} + 8 q^{38} + 14 q^{39} - 5 q^{40} + 9 q^{41} - 2 q^{42} - q^{43} + 2 q^{44} + q^{45} - 10 q^{46} + 6 q^{48} - 12 q^{49} + 6 q^{50} - 12 q^{51} + q^{52} - 6 q^{53} - 4 q^{54} - 2 q^{55} + 2 q^{57} - 4 q^{58} + 6 q^{60} + 4 q^{61} + 6 q^{62} - 2 q^{63} + 4 q^{64} - q^{65} + 16 q^{66} + 12 q^{67} - 8 q^{68} - 2 q^{70} + 12 q^{71} + 2 q^{73} + 10 q^{74} + 14 q^{75} - 7 q^{76} - 6 q^{77} - 12 q^{78} - 18 q^{79} + 6 q^{80} - 22 q^{81} + 8 q^{82} + 15 q^{83} - 2 q^{84} + 8 q^{85} - 12 q^{86} - 26 q^{87} + 10 q^{88} - 9 q^{89} + 2 q^{90} + 7 q^{91} + 10 q^{92} + 34 q^{93} - 5 q^{94} + 7 q^{95} - 18 q^{96} - q^{97} + 6 q^{98} + 6 q^{99}+O(q^{100}) $ 2 * q - q^2 - 4 * q^3 - q^4 + q^5 + 2 * q^6 - 2 * q^7 + 2 * q^9 + 2 * q^10 + 6 * q^11 + 2 * q^12 - 7 * q^13 + q^14 - 2 * q^15 - 3 * q^16 + 6 * q^17 - q^18 - q^19 - 3 * q^20 + 4 * q^21 - 8 * q^22 - 7 * q^25 + 6 * q^26 + 8 * q^27 + q^28 + 13 * q^29 - 4 * q^30 - 17 * q^31 + 9 * q^32 - 12 * q^33 + 2 * q^34 - q^35 - q^36 + 5 * q^37 + 8 * q^38 + 14 * q^39 - 5 * q^40 + 9 * q^41 - 2 * q^42 - q^43 + 2 * q^44 + q^45 - 10 * q^46 + 6 * q^48 - 12 * q^49 + 6 * q^50 - 12 * q^51 + q^52 - 6 * q^53 - 4 * q^54 - 2 * q^55 + 2 * q^57 - 4 * q^58 + 6 * q^60 + 4 * q^61 + 6 * q^62 - 2 * q^63 + 4 * q^64 - q^65 + 16 * q^66 + 12 * q^67 - 8 * q^68 - 2 * q^70 + 12 * q^71 + 2 * q^73 + 10 * q^74 + 14 * q^75 - 7 * q^76 - 6 * q^77 - 12 * q^78 - 18 * q^79 + 6 * q^80 - 22 * q^81 + 8 * q^82 + 15 * q^83 - 2 * q^84 + 8 * q^85 - 12 * q^86 - 26 * q^87 + 10 * q^88 - 9 * q^89 + 2 * q^90 + 7 * q^91 + 10 * q^92 + 34 * q^93 - 5 * q^94 + 7 * q^95 - 18 * q^96 - q^97 + 6 * q^98 + 6 * 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 $

$2$	0.618034	0.437016	0.218508	−	0.975835i	$-0.429881\pi$
$2$	0.618034	0.437016	0.218508	+	0.975835i	$0.429881\pi$
$3$	−2.00000	−1.15470	−0.577350	−	0.816497i	$-0.695913\pi$
$3$	−2.00000	−1.15470	−0.577350	+	0.816497i	$0.695913\pi$
$4$	−1.61803	−0.809017
$5$	1.61803	0.723607	0.361803	−	0.932254i	$-0.382161\pi$
$5$	1.61803	0.723607	0.361803	+	0.932254i	$0.382161\pi$
$6$	−1.23607	−0.504623
$7$	−1.00000	−0.377964	−0.188982	−	0.981981i	$-0.560519\pi$
$7$	−1.00000	−0.377964	−0.188982	+	0.981981i	$0.560519\pi$
$8$	−2.23607	−0.790569
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	0.763932	0.230334	0.115167	−	0.993346i	$-0.463260\pi$
$11$	0.763932	0.230334	0.115167	+	0.993346i	$0.463260\pi$
$12$	3.23607	0.934172
$13$	−2.38197	−0.660639	−0.330319	−	0.943869i	$-0.607156\pi$
$13$	−2.38197	−0.660639	−0.330319	+	0.943869i	$0.607156\pi$
$14$	−0.618034	−0.165177
$15$	−3.23607	−0.835549
$16$	1.85410	0.463525
$17$	5.23607	1.26993	0.634967	−	0.772540i	$-0.281014\pi$
$17$	5.23607	1.26993	0.634967	+	0.772540i	$0.281014\pi$
$18$	0.618034	0.145672
$19$	2.85410	0.654776	0.327388	−	0.944890i	$-0.393832\pi$
$19$	2.85410	0.654776	0.327388	+	0.944890i	$0.393832\pi$
$20$	−2.61803	−0.585410
$21$	2.00000	0.436436
$22$	0.472136	0.100660
$23$	−4.47214	−0.932505	−0.466252	−	0.884652i	$-0.654396\pi$
$23$	−4.47214	−0.932505	−0.466252	+	0.884652i	$0.654396\pi$
$24$	4.47214	0.912871
$25$	−2.38197	−0.476393
$26$	−1.47214	−0.288710
$27$	4.00000	0.769800
$28$	1.61803	0.305780
$29$	7.61803	1.41463	0.707317	−	0.706897i	$-0.249905\pi$
$29$	7.61803	1.41463	0.707317	+	0.706897i	$0.249905\pi$
$30$	−2.00000	−0.365148
$31$	−9.61803	−1.72745	−0.863725	−	0.503964i	$-0.831875\pi$
$31$	−9.61803	−1.72745	−0.863725	+	0.503964i	$0.831875\pi$
$32$	5.61803	0.993137
$33$	−1.52786	−0.265967
$34$	3.23607	0.554981
$35$	−1.61803	−0.273498
$36$	−1.61803	−0.269672
$37$	8.09017	1.33002	0.665008	−	0.746836i	$-0.268428\pi$
$37$	8.09017	1.33002	0.665008	+	0.746836i	$0.268428\pi$
$38$	1.76393	0.286148
$39$	4.76393	0.762840
$40$	−3.61803	−0.572061
$41$	10.0902	1.57582	0.787910	−	0.615791i	$-0.211163\pi$
$41$	10.0902	1.57582	0.787910	+	0.615791i	$0.211163\pi$
$42$	1.23607	0.190729
$43$	−6.09017	−0.928742	−0.464371	−	0.885641i	$-0.653720\pi$
$43$	−6.09017	−0.928742	−0.464371	+	0.885641i	$0.653720\pi$
$44$	−1.23607	−0.186344
$45$	1.61803	0.241202
$46$	−2.76393	−0.407520
$47$	−2.23607	−0.326164	−0.163082	−	0.986613i	$-0.552144\pi$
$47$	−2.23607	−0.326164	−0.163082	+	0.986613i	$0.552144\pi$
$48$	−3.70820	−0.535233
$49$	−6.00000	−0.857143
$50$	−1.47214	−0.208191
$51$	−10.4721	−1.46639
$52$	3.85410	0.534468
$53$	−7.47214	−1.02638	−0.513188	−	0.858276i	$-0.671536\pi$
$53$	−7.47214	−1.02638	−0.513188	+	0.858276i	$0.671536\pi$
$54$	2.47214	0.336415
$55$	1.23607	0.166671
$56$	2.23607	0.298807
$57$	−5.70820	−0.756070
$58$	4.70820	0.618217
$59$	2.23607	0.291111	0.145556	−	0.989350i	$-0.453503\pi$
$59$	2.23607	0.291111	0.145556	+	0.989350i	$0.453503\pi$
$60$	5.23607	0.675973
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	−5.94427	−0.754923
$63$	−1.00000	−0.125988
$64$	−0.236068	−0.0295085
$65$	−3.85410	−0.478043
$66$	−0.944272	−0.116232
$67$	12.7082	1.55255	0.776277	−	0.630392i	$-0.217106\pi$
$67$	12.7082	1.55255	0.776277	+	0.630392i	$0.217106\pi$
$68$	−8.47214	−1.02740
$69$	8.94427	1.07676
$70$	−1.00000	−0.119523
$71$	−0.708204	−0.0840483	−0.0420242	−	0.999117i	$-0.513381\pi$
$71$	−0.708204	−0.0840483	−0.0420242	+	0.999117i	$0.513381\pi$
$72$	−2.23607	−0.263523
$73$	−12.4164	−1.45323	−0.726615	−	0.687045i	$-0.758908\pi$
$73$	−12.4164	−1.45323	−0.726615	+	0.687045i	$0.758908\pi$
$74$	5.00000	0.581238
$75$	4.76393	0.550091
$76$	−4.61803	−0.529725
$77$	−0.763932	−0.0870581
$78$	2.94427	0.333373
$79$	−15.7082	−1.76731	−0.883656	−	0.468138i	$-0.844925\pi$
$79$	−15.7082	−1.76731	−0.883656	+	0.468138i	$0.844925\pi$
$80$	3.00000	0.335410
$81$	−11.0000	−1.22222
$82$	6.23607	0.688659
$83$	8.61803	0.945952	0.472976	−	0.881075i	$-0.343180\pi$
$83$	8.61803	0.945952	0.472976	+	0.881075i	$0.343180\pi$
$84$	−3.23607	−0.353084
$85$	8.47214	0.918932
$86$	−3.76393	−0.405875
$87$	−15.2361	−1.63348
$88$	−1.70820	−0.182095
$89$	−16.7984	−1.78062	−0.890312	−	0.455351i	$-0.849514\pi$
$89$	−16.7984	−1.78062	−0.890312	+	0.455351i	$0.849514\pi$
$90$	1.00000	0.105409
$91$	2.38197	0.249698
$92$	7.23607	0.754412
$93$	19.2361	1.99469
$94$	−1.38197	−0.142539
$95$	4.61803	0.473800
$96$	−11.2361	−1.14678
$97$	2.85410	0.289790	0.144895	−	0.989447i	$-0.453716\pi$
$97$	2.85410	0.289790	0.144895	+	0.989447i	$0.453716\pi$
$98$	−3.70820	−0.374585
$99$	0.763932	0.0767781
$100$	3.85410	0.385410
$101$	16.7984	1.67150	0.835750	−	0.549110i	$-0.185033\pi$
$101$	16.7984	1.67150	0.835750	+	0.549110i	$0.185033\pi$
$102$	−6.47214	−0.640837
$103$	−2.09017	−0.205951	−0.102975	−	0.994684i	$-0.532836\pi$
$103$	−2.09017	−0.205951	−0.102975	+	0.994684i	$0.532836\pi$
$104$	5.32624	0.522281
$105$	3.23607	0.315808
$106$	−4.61803	−0.448543
$107$	−1.47214	−0.142317	−0.0711584	−	0.997465i	$-0.522670\pi$
$107$	−1.47214	−0.142317	−0.0711584	+	0.997465i	$0.522670\pi$
$108$	−6.47214	−0.622782
$109$	−6.70820	−0.642529	−0.321265	−	0.946989i	$-0.604108\pi$
$109$	−6.70820	−0.642529	−0.321265	+	0.946989i	$0.604108\pi$
$110$	0.763932	0.0728381
$111$	−16.1803	−1.53577
$112$	−1.85410	−0.175196
$113$	5.47214	0.514775	0.257388	−	0.966308i	$-0.417138\pi$
$113$	5.47214	0.514775	0.257388	+	0.966308i	$0.417138\pi$
$114$	−3.52786	−0.330415
$115$	−7.23607	−0.674767
$116$	−12.3262	−1.14446
$117$	−2.38197	−0.220213
$118$	1.38197	0.127220
$119$	−5.23607	−0.479990
$120$	7.23607	0.660560
$121$	−10.4164	−0.946946
$122$	1.23607	0.111908
$123$	−20.1803	−1.81960
$124$	15.5623	1.39754
$125$	−11.9443	−1.06833
$126$	−0.618034	−0.0550588
$127$	−7.18034	−0.637152	−0.318576	−	0.947897i	$-0.603205\pi$
$127$	−7.18034	−0.637152	−0.318576	+	0.947897i	$0.603205\pi$
$128$	−11.3820	−1.00603
$129$	12.1803	1.07242
$130$	−2.38197	−0.208912
$131$	9.70820	0.848210	0.424105	−	0.905613i	$-0.360589\pi$
$131$	9.70820	0.848210	0.424105	+	0.905613i	$0.360589\pi$
$132$	2.47214	0.215172
$133$	−2.85410	−0.247482
$134$	7.85410	0.678491
$135$	6.47214	0.557033
$136$	−11.7082	−1.00397
$137$	−1.90983	−0.163168	−0.0815839	−	0.996666i	$-0.525998\pi$
$137$	−1.90983	−0.163168	−0.0815839	+	0.996666i	$0.525998\pi$
$138$	5.52786	0.470563
$139$	−18.0000	−1.52674	−0.763370	−	0.645961i	$-0.776457\pi$
$139$	−18.0000	−1.52674	−0.763370	+	0.645961i	$0.776457\pi$
$140$	2.61803	0.221264
$141$	4.47214	0.376622
$142$	−0.437694	−0.0367305
$143$	−1.81966	−0.152168
$144$	1.85410	0.154508
$145$	12.3262	1.02364
$146$	−7.67376	−0.635085
$147$	12.0000	0.989743
$148$	−13.0902	−1.07601
$149$	4.14590	0.339645	0.169823	−	0.985475i	$-0.445681\pi$
$149$	4.14590	0.339645	0.169823	+	0.985475i	$0.445681\pi$
$150$	2.94427	0.240399
$151$	−21.6180	−1.75925	−0.879625	−	0.475667i	$-0.842207\pi$
$151$	−21.6180	−1.75925	−0.879625	+	0.475667i	$0.842207\pi$
$152$	−6.38197	−0.517646
$153$	5.23607	0.423311
$154$	−0.472136	−0.0380458
$155$	−15.5623	−1.24999
$156$	−7.70820	−0.617150
$157$	5.00000	0.399043	0.199522	−	0.979893i	$-0.436061\pi$
$157$	5.00000	0.399043	0.199522	+	0.979893i	$0.436061\pi$
$158$	−9.70820	−0.772343
$159$	14.9443	1.18516
$160$	9.09017	0.718641
$161$	4.47214	0.352454
$162$	−6.79837	−0.534131
$163$	−13.5623	−1.06228	−0.531141	−	0.847284i	$-0.678237\pi$
$163$	−13.5623	−1.06228	−0.531141	+	0.847284i	$0.678237\pi$
$164$	−16.3262	−1.27486
$165$	−2.47214	−0.192456
$166$	5.32624	0.413396
$167$	−19.0902	−1.47724	−0.738621	−	0.674121i	$-0.764523\pi$
$167$	−19.0902	−1.47724	−0.738621	+	0.674121i	$0.764523\pi$
$168$	−4.47214	−0.345033
$169$	−7.32624	−0.563557
$170$	5.23607	0.401588
$171$	2.85410	0.218259
$172$	9.85410	0.751368
$173$	−12.7082	−0.966187	−0.483093	−	0.875569i	$-0.660487\pi$
$173$	−12.7082	−0.966187	−0.483093	+	0.875569i	$0.660487\pi$
$174$	−9.41641	−0.713856
$175$	2.38197	0.180060
$176$	1.41641	0.106766
$177$	−4.47214	−0.336146
$178$	−10.3820	−0.778161
$179$	12.3262	0.921306	0.460653	−	0.887580i	$-0.347615\pi$
$179$	12.3262	0.921306	0.460653	+	0.887580i	$0.347615\pi$
$180$	−2.61803	−0.195137
$181$	−12.7082	−0.944593	−0.472297	−	0.881440i	$-0.656575\pi$
$181$	−12.7082	−0.944593	−0.472297	+	0.881440i	$0.656575\pi$
$182$	1.47214	0.109122
$183$	−4.00000	−0.295689
$184$	10.0000	0.737210
$185$	13.0902	0.962408
$186$	11.8885	0.871710
$187$	4.00000	0.292509
$188$	3.61803	0.263872
$189$	−4.00000	−0.290957
$190$	2.85410	0.207058
$191$	−9.70820	−0.702461	−0.351230	−	0.936289i	$-0.614237\pi$
$191$	−9.70820	−0.702461	−0.351230	+	0.936289i	$0.614237\pi$
$192$	0.472136	0.0340735
$193$	5.56231	0.400384	0.200192	−	0.979757i	$-0.435843\pi$
$193$	5.56231	0.400384	0.200192	+	0.979757i	$0.435843\pi$
$194$	1.76393	0.126643
$195$	7.70820	0.551996
$196$	9.70820	0.693443
$197$	21.6525	1.54268	0.771338	−	0.636426i	$-0.219588\pi$
$197$	21.6525	1.54268	0.771338	+	0.636426i	$0.219588\pi$
$198$	0.472136	0.0335532
$199$	21.1803	1.50143	0.750717	−	0.660624i	$-0.229708\pi$
$199$	21.1803	1.50143	0.750717	+	0.660624i	$0.229708\pi$
$200$	5.32624	0.376622
$201$	−25.4164	−1.79274
$202$	10.3820	0.730473
$203$	−7.61803	−0.534681
$204$	16.9443	1.18634
$205$	16.3262	1.14027
$206$	−1.29180	−0.0900037
$207$	−4.47214	−0.310835
$208$	−4.41641	−0.306223
$209$	2.18034	0.150817
$210$	2.00000	0.138013
$211$	−22.5623	−1.55325	−0.776627	−	0.629961i	$-0.783071\pi$
$211$	−22.5623	−1.55325	−0.776627	+	0.629961i	$0.783071\pi$
$212$	12.0902	0.830356
$213$	1.41641	0.0970507
$214$	−0.909830	−0.0621947
$215$	−9.85410	−0.672044
$216$	−8.94427	−0.608581
$217$	9.61803	0.652915
$218$	−4.14590	−0.280796
$219$	24.8328	1.67805
$220$	−2.00000	−0.134840
$221$	−12.4721	−0.838967
$222$	−10.0000	−0.671156
$223$	−9.70820	−0.650109	−0.325055	−	0.945695i	$-0.605383\pi$
$223$	−9.70820	−0.650109	−0.325055	+	0.945695i	$0.605383\pi$
$224$	−5.61803	−0.375371
$225$	−2.38197	−0.158798
$226$	3.38197	0.224965
$227$	−17.0902	−1.13431	−0.567157	−	0.823610i	$-0.691957\pi$
$227$	−17.0902	−1.13431	−0.567157	+	0.823610i	$0.691957\pi$
$228$	9.23607	0.611674
$229$	−16.0000	−1.05731	−0.528655	−	0.848837i	$-0.677303\pi$
$229$	−16.0000	−1.05731	−0.528655	+	0.848837i	$0.677303\pi$
$230$	−4.47214	−0.294884
$231$	1.52786	0.100526
$232$	−17.0344	−1.11837
$233$	−6.88854	−0.451284	−0.225642	−	0.974210i	$-0.572448\pi$
$233$	−6.88854	−0.451284	−0.225642	+	0.974210i	$0.572448\pi$
$234$	−1.47214	−0.0962365
$235$	−3.61803	−0.236015
$236$	−3.61803	−0.235514
$237$	31.4164	2.04071
$238$	−3.23607	−0.209763
$239$	−21.4721	−1.38892	−0.694459	−	0.719533i	$-0.744356\pi$
$239$	−21.4721	−1.38892	−0.694459	+	0.719533i	$0.744356\pi$
$240$	−6.00000	−0.387298
$241$	−0.583592	−0.0375925	−0.0187962	−	0.999823i	$-0.505983\pi$
$241$	−0.583592	−0.0375925	−0.0187962	+	0.999823i	$0.505983\pi$
$242$	−6.43769	−0.413831
$243$	10.0000	0.641500
$244$	−3.23607	−0.207168
$245$	−9.70820	−0.620234
$246$	−12.4721	−0.795194
$247$	−6.79837	−0.432570
$248$	21.5066	1.36567
$249$	−17.2361	−1.09229
$250$	−7.38197	−0.466877
$251$	−18.4721	−1.16595	−0.582975	−	0.812490i	$-0.698112\pi$
$251$	−18.4721	−1.16595	−0.582975	+	0.812490i	$0.698112\pi$
$252$	1.61803	0.101927
$253$	−3.41641	−0.214788
$254$	−4.43769	−0.278446
$255$	−16.9443	−1.06109
$256$	−6.56231	−0.410144
$257$	11.4721	0.715612	0.357806	−	0.933796i	$-0.383525\pi$
$257$	11.4721	0.715612	0.357806	+	0.933796i	$0.383525\pi$
$258$	7.52786	0.468664
$259$	−8.09017	−0.502699
$260$	6.23607	0.386745
$261$	7.61803	0.471544
$262$	6.00000	0.370681
$263$	−6.52786	−0.402525	−0.201263	−	0.979537i	$-0.564504\pi$
$263$	−6.52786	−0.402525	−0.201263	+	0.979537i	$0.564504\pi$
$264$	3.41641	0.210265
$265$	−12.0902	−0.742693
$266$	−1.76393	−0.108154
$267$	33.5967	2.05609
$268$	−20.5623	−1.25604
$269$	−6.27051	−0.382320	−0.191160	−	0.981559i	$-0.561225\pi$
$269$	−6.27051	−0.382320	−0.191160	+	0.981559i	$0.561225\pi$
$270$	4.00000	0.243432
$271$	11.2705	0.684635	0.342317	−	0.939584i	$-0.388788\pi$
$271$	11.2705	0.684635	0.342317	+	0.939584i	$0.388788\pi$
$272$	9.70820	0.588646
$273$	−4.76393	−0.288326
$274$	−1.18034	−0.0713069
$275$	−1.81966	−0.109730
$276$	−14.4721	−0.871120
$277$	8.65248	0.519877	0.259938	−	0.965625i	$-0.416298\pi$
$277$	8.65248	0.519877	0.259938	+	0.965625i	$0.416298\pi$
$278$	−11.1246	−0.667210
$279$	−9.61803	−0.575817
$280$	3.61803	0.216219
$281$	7.14590	0.426289	0.213144	−	0.977021i	$-0.431630\pi$
$281$	7.14590	0.426289	0.213144	+	0.977021i	$0.431630\pi$
$282$	2.76393	0.164590
$283$	28.5623	1.69785	0.848926	−	0.528511i	$-0.177249\pi$
$283$	28.5623	1.69785	0.848926	+	0.528511i	$0.177249\pi$
$284$	1.14590	0.0679965
$285$	−9.23607	−0.547097
$286$	−1.12461	−0.0664997
$287$	−10.0902	−0.595604
$288$	5.61803	0.331046
$289$	10.4164	0.612730
$290$	7.61803	0.447346
$291$	−5.70820	−0.334621
$292$	20.0902	1.17569
$293$	23.4721	1.37126	0.685628	−	0.727952i	$-0.259528\pi$
$293$	23.4721	1.37126	0.685628	+	0.727952i	$0.259528\pi$
$294$	7.41641	0.432534
$295$	3.61803	0.210650
$296$	−18.0902	−1.05147
$297$	3.05573	0.177311
$298$	2.56231	0.148430
$299$	10.6525	0.616049
$300$	−7.70820	−0.445033
$301$	6.09017	0.351032
$302$	−13.3607	−0.768821
$303$	−33.5967	−1.93008
$304$	5.29180	0.303505
$305$	3.23607	0.185297
$306$	3.23607	0.184994
$307$	−13.8541	−0.790695	−0.395348	−	0.918532i	$-0.629376\pi$
$307$	−13.8541	−0.790695	−0.395348	+	0.918532i	$0.629376\pi$
$308$	1.23607	0.0704315
$309$	4.18034	0.237811
$310$	−9.61803	−0.546268
$311$	30.7426	1.74326	0.871628	−	0.490168i	$-0.163065\pi$
$311$	30.7426	1.74326	0.871628	+	0.490168i	$0.163065\pi$
$312$	−10.6525	−0.603078
$313$	−3.18034	−0.179763	−0.0898817	−	0.995952i	$-0.528649\pi$
$313$	−3.18034	−0.179763	−0.0898817	+	0.995952i	$0.528649\pi$
$314$	3.09017	0.174388
$315$	−1.61803	−0.0911659
$316$	25.4164	1.42978
$317$	6.76393	0.379900	0.189950	−	0.981794i	$-0.439167\pi$
$317$	6.76393	0.379900	0.189950	+	0.981794i	$0.439167\pi$
$318$	9.23607	0.517933
$319$	5.81966	0.325838
$320$	−0.381966	−0.0213525
$321$	2.94427	0.164333
$322$	2.76393	0.154028
$323$	14.9443	0.831522
$324$	17.7984	0.988799
$325$	5.67376	0.314724
$326$	−8.38197	−0.464234
$327$	13.4164	0.741929
$328$	−22.5623	−1.24579
$329$	2.23607	0.123278
$330$	−1.52786	−0.0841061
$331$	−12.0902	−0.664536	−0.332268	−	0.943185i	$-0.607814\pi$
$331$	−12.0902	−0.664536	−0.332268	+	0.943185i	$0.607814\pi$
$332$	−13.9443	−0.765291
$333$	8.09017	0.443339
$334$	−11.7984	−0.645578
$335$	20.5623	1.12344
$336$	3.70820	0.202299
$337$	−3.52786	−0.192175	−0.0960875	−	0.995373i	$-0.530633\pi$
$337$	−3.52786	−0.192175	−0.0960875	+	0.995373i	$0.530633\pi$
$338$	−4.52786	−0.246283
$339$	−10.9443	−0.594411
$340$	−13.7082	−0.743432
$341$	−7.34752	−0.397891
$342$	1.76393	0.0953825
$343$	13.0000	0.701934
$344$	13.6180	0.734235
$345$	14.4721	0.779154
$346$	−7.85410	−0.422239
$347$	−10.1459	−0.544660	−0.272330	−	0.962204i	$-0.587794\pi$
$347$	−10.1459	−0.544660	−0.272330	+	0.962204i	$0.587794\pi$
$348$	24.6525	1.32151
$349$	−34.0000	−1.81998	−0.909989	−	0.414632i	$-0.863910\pi$
$349$	−34.0000	−1.81998	−0.909989	+	0.414632i	$0.863910\pi$
$350$	1.47214	0.0786890
$351$	−9.52786	−0.508560
$352$	4.29180	0.228753
$353$	−13.4721	−0.717049	−0.358525	−	0.933520i	$-0.616720\pi$
$353$	−13.4721	−0.717049	−0.358525	+	0.933520i	$0.616720\pi$
$354$	−2.76393	−0.146901
$355$	−1.14590	−0.0608180
$356$	27.1803	1.44056
$357$	10.4721	0.554244
$358$	7.61803	0.402626
$359$	31.6869	1.67237	0.836186	−	0.548446i	$-0.184780\pi$
$359$	31.6869	1.67237	0.836186	+	0.548446i	$0.184780\pi$
$360$	−3.61803	−0.190687
$361$	−10.8541	−0.571269
$362$	−7.85410	−0.412802
$363$	20.8328	1.09344
$364$	−3.85410	−0.202010
$365$	−20.0902	−1.05157
$366$	−2.47214	−0.129221
$367$	−18.4721	−0.964238	−0.482119	−	0.876106i	$-0.660133\pi$
$367$	−18.4721	−0.964238	−0.482119	+	0.876106i	$0.660133\pi$
$368$	−8.29180	−0.432240
$369$	10.0902	0.525273
$370$	8.09017	0.420588
$371$	7.47214	0.387934
$372$	−31.1246	−1.61374
$373$	12.2361	0.633560	0.316780	−	0.948499i	$-0.397398\pi$
$373$	12.2361	0.633560	0.316780	+	0.948499i	$0.397398\pi$
$374$	2.47214	0.127831
$375$	23.8885	1.23360
$376$	5.00000	0.257855
$377$	−18.1459	−0.934561
$378$	−2.47214	−0.127153
$379$	−27.1803	−1.39616	−0.698080	−	0.716020i	$-0.745962\pi$
$379$	−27.1803	−1.39616	−0.698080	+	0.716020i	$0.745962\pi$
$380$	−7.47214	−0.383312
$381$	14.3607	0.735720
$382$	−6.00000	−0.306987
$383$	34.4164	1.75860	0.879298	−	0.476272i	$-0.158012\pi$
$383$	34.4164	1.75860	0.879298	+	0.476272i	$0.158012\pi$
$384$	22.7639	1.16167
$385$	−1.23607	−0.0629959
$386$	3.43769	0.174974
$387$	−6.09017	−0.309581
$388$	−4.61803	−0.234445
$389$	−0.472136	−0.0239382	−0.0119691	−	0.999928i	$-0.503810\pi$
$389$	−0.472136	−0.0239382	−0.0119691	+	0.999928i	$0.503810\pi$
$390$	4.76393	0.241231
$391$	−23.4164	−1.18422
$392$	13.4164	0.677631
$393$	−19.4164	−0.979428
$394$	13.3820	0.674174
$395$	−25.4164	−1.27884
$396$	−1.23607	−0.0621148
$397$	0.270510	0.0135765	0.00678825	−	0.999977i	$-0.497839\pi$
$397$	0.270510	0.0135765	0.00678825	+	0.999977i	$0.497839\pi$
$398$	13.0902	0.656151
$399$	5.70820	0.285768
$400$	−4.41641	−0.220820
$401$	5.76393	0.287837	0.143919	−	0.989590i	$-0.454030\pi$
$401$	5.76393	0.287837	0.143919	+	0.989590i	$0.454030\pi$
$402$	−15.7082	−0.783454
$403$	22.9098	1.14122
$404$	−27.1803	−1.35227
$405$	−17.7984	−0.884408
$406$	−4.70820	−0.233664
$407$	6.18034	0.306348
$408$	23.4164	1.15928
$409$	19.2361	0.951162	0.475581	−	0.879672i	$-0.342238\pi$
$409$	19.2361	0.951162	0.475581	+	0.879672i	$0.342238\pi$
$410$	10.0902	0.498318
$411$	3.81966	0.188410
$412$	3.38197	0.166618
$413$	−2.23607	−0.110030
$414$	−2.76393	−0.135840
$415$	13.9443	0.684497
$416$	−13.3820	−0.656105
$417$	36.0000	1.76293
$418$	1.34752	0.0659096
$419$	9.27051	0.452894	0.226447	−	0.974023i	$-0.427289\pi$
$419$	9.27051	0.452894	0.226447	+	0.974023i	$0.427289\pi$
$420$	−5.23607	−0.255494
$421$	−19.2918	−0.940225	−0.470112	−	0.882607i	$-0.655787\pi$
$421$	−19.2918	−0.940225	−0.470112	+	0.882607i	$0.655787\pi$
$422$	−13.9443	−0.678797
$423$	−2.23607	−0.108721
$424$	16.7082	0.811422
$425$	−12.4721	−0.604987
$426$	0.875388	0.0424127
$427$	−2.00000	−0.0967868
$428$	2.38197	0.115137
$429$	3.63932	0.175708
$430$	−6.09017	−0.293694
$431$	31.4508	1.51493	0.757467	−	0.652873i	$-0.226437\pi$
$431$	31.4508	1.51493	0.757467	+	0.652873i	$0.226437\pi$
$432$	7.41641	0.356822
$433$	−34.8885	−1.67664	−0.838318	−	0.545181i	$-0.816461\pi$
$433$	−34.8885	−1.67664	−0.838318	+	0.545181i	$0.816461\pi$
$434$	5.94427	0.285334
$435$	−24.6525	−1.18200
$436$	10.8541	0.519817
$437$	−12.7639	−0.610582
$438$	15.3475	0.733333
$439$	−22.8541	−1.09077	−0.545383	−	0.838187i	$-0.683616\pi$
$439$	−22.8541	−1.09077	−0.545383	+	0.838187i	$0.683616\pi$
$440$	−2.76393	−0.131765
$441$	−6.00000	−0.285714
$442$	−7.70820	−0.366642
$443$	12.2705	0.582990	0.291495	−	0.956572i	$-0.405847\pi$
$443$	12.2705	0.582990	0.291495	+	0.956572i	$0.405847\pi$
$444$	26.1803	1.24246
$445$	−27.1803	−1.28847
$446$	−6.00000	−0.284108
$447$	−8.29180	−0.392188
$448$	0.236068	0.0111532
$449$	−17.8885	−0.844213	−0.422106	−	0.906546i	$-0.638709\pi$
$449$	−17.8885	−0.844213	−0.422106	+	0.906546i	$0.638709\pi$
$450$	−1.47214	−0.0693972
$451$	7.70820	0.362965
$452$	−8.85410	−0.416462
$453$	43.2361	2.03141
$454$	−10.5623	−0.495714
$455$	3.85410	0.180683
$456$	12.7639	0.597726
$457$	−27.1803	−1.27144	−0.635721	−	0.771919i	$-0.719297\pi$
$457$	−27.1803	−1.27144	−0.635721	+	0.771919i	$0.719297\pi$
$458$	−9.88854	−0.462061
$459$	20.9443	0.977595
$460$	11.7082	0.545898
$461$	31.5066	1.46741	0.733704	−	0.679469i	$-0.237790\pi$
$461$	31.5066	1.46741	0.733704	+	0.679469i	$0.237790\pi$
$462$	0.944272	0.0439315
$463$	−9.41641	−0.437618	−0.218809	−	0.975768i	$-0.570217\pi$
$463$	−9.41641	−0.437618	−0.218809	+	0.975768i	$0.570217\pi$
$464$	14.1246	0.655719
$465$	31.1246	1.44337
$466$	−4.25735	−0.197218
$467$	13.8885	0.642685	0.321343	−	0.946963i	$-0.395866\pi$
$467$	13.8885	0.642685	0.321343	+	0.946963i	$0.395866\pi$
$468$	3.85410	0.178156
$469$	−12.7082	−0.586810
$470$	−2.23607	−0.103142
$471$	−10.0000	−0.460776
$472$	−5.00000	−0.230144
$473$	−4.65248	−0.213921
$474$	19.4164	0.891825
$475$	−6.79837	−0.311931
$476$	8.47214	0.388320
$477$	−7.47214	−0.342126
$478$	−13.2705	−0.606979
$479$	3.43769	0.157072	0.0785361	−	0.996911i	$-0.474975\pi$
$479$	3.43769	0.157072	0.0785361	+	0.996911i	$0.474975\pi$
$480$	−18.1803	−0.829815
$481$	−19.2705	−0.878660
$482$	−0.360680	−0.0164285
$483$	−8.94427	−0.406978
$484$	16.8541	0.766096
$485$	4.61803	0.209694
$486$	6.18034	0.280346
$487$	36.9787	1.67567	0.837833	−	0.545927i	$-0.183822\pi$
$487$	36.9787	1.67567	0.837833	+	0.545927i	$0.183822\pi$
$488$	−4.47214	−0.202444
$489$	27.1246	1.22662
$490$	−6.00000	−0.271052
$491$	−11.5967	−0.523354	−0.261677	−	0.965156i	$-0.584275\pi$
$491$	−11.5967	−0.523354	−0.261677	+	0.965156i	$0.584275\pi$
$492$	32.6525	1.47209
$493$	39.8885	1.79649
$494$	−4.20163	−0.189040
$495$	1.23607	0.0555571
$496$	−17.8328	−0.800717
$497$	0.708204	0.0317673
$498$	−10.6525	−0.477349
$499$	−23.4721	−1.05076	−0.525379	−	0.850869i	$-0.676076\pi$
$499$	−23.4721	−1.05076	−0.525379	+	0.850869i	$0.676076\pi$
$500$	19.3262	0.864296
$501$	38.1803	1.70577
$502$	−11.4164	−0.509539
$503$	−21.0344	−0.937879	−0.468940	−	0.883230i	$-0.655364\pi$
$503$	−21.0344	−0.937879	−0.468940	+	0.883230i	$0.655364\pi$
$504$	2.23607	0.0996024
$505$	27.1803	1.20951
$506$	−2.11146	−0.0938657
$507$	14.6525	0.650739
$508$	11.6180	0.515467
$509$	27.7426	1.22967	0.614836	−	0.788655i	$-0.289222\pi$
$509$	27.7426	1.22967	0.614836	+	0.788655i	$0.289222\pi$
$510$	−10.4721	−0.463714
$511$	12.4164	0.549270
$512$	18.7082	0.826794
$513$	11.4164	0.504047
$514$	7.09017	0.312734
$515$	−3.38197	−0.149027
$516$	−19.7082	−0.867605
$517$	−1.70820	−0.0751267
$518$	−5.00000	−0.219687
$519$	25.4164	1.11566
$520$	8.61803	0.377926
$521$	31.3820	1.37487	0.687434	−	0.726246i	$-0.258737\pi$
$521$	31.3820	1.37487	0.687434	+	0.726246i	$0.258737\pi$
$522$	4.70820	0.206072
$523$	7.41641	0.324297	0.162148	−	0.986766i	$-0.448158\pi$
$523$	7.41641	0.324297	0.162148	+	0.986766i	$0.448158\pi$
$524$	−15.7082	−0.686216
$525$	−4.76393	−0.207915
$526$	−4.03444	−0.175910
$527$	−50.3607	−2.19375
$528$	−2.83282	−0.123282
$529$	−3.00000	−0.130435
$530$	−7.47214	−0.324569
$531$	2.23607	0.0970371
$532$	4.61803	0.200217
$533$	−24.0344	−1.04105
$534$	20.7639	0.898543
$535$	−2.38197	−0.102981
$536$	−28.4164	−1.22740
$537$	−24.6525	−1.06383
$538$	−3.87539	−0.167080
$539$	−4.58359	−0.197429
$540$	−10.4721	−0.450649
$541$	4.81966	0.207213	0.103607	−	0.994618i	$-0.466962\pi$
$541$	4.81966	0.207213	0.103607	+	0.994618i	$0.466962\pi$
$542$	6.96556	0.299196
$543$	25.4164	1.09072
$544$	29.4164	1.26122
$545$	−10.8541	−0.464939
$546$	−2.94427	−0.126003
$547$	−43.5410	−1.86168	−0.930840	−	0.365428i	$-0.880923\pi$
$547$	−43.5410	−1.86168	−0.930840	+	0.365428i	$0.880923\pi$
$548$	3.09017	0.132006
$549$	2.00000	0.0853579
$550$	−1.12461	−0.0479536
$551$	21.7426	0.926268
$552$	−20.0000	−0.851257
$553$	15.7082	0.667981
$554$	5.34752	0.227195
$555$	−26.1803	−1.11129
$556$	29.1246	1.23516
$557$	33.9787	1.43972	0.719862	−	0.694117i	$-0.244205\pi$
$557$	33.9787	1.43972	0.719862	+	0.694117i	$0.244205\pi$
$558$	−5.94427	−0.251641
$559$	14.5066	0.613563
$560$	−3.00000	−0.126773
$561$	−8.00000	−0.337760
$562$	4.41641	0.186295
$563$	1.79837	0.0757924	0.0378962	−	0.999282i	$-0.487934\pi$
$563$	1.79837	0.0757924	0.0378962	+	0.999282i	$0.487934\pi$
$564$	−7.23607	−0.304693
$565$	8.85410	0.372495
$566$	17.6525	0.741989
$567$	11.0000	0.461957
$568$	1.58359	0.0664460
$569$	−11.1803	−0.468704	−0.234352	−	0.972152i	$-0.575297\pi$
$569$	−11.1803	−0.468704	−0.234352	+	0.972152i	$0.575297\pi$
$570$	−5.70820	−0.239090
$571$	−12.7082	−0.531822	−0.265911	−	0.963998i	$-0.585673\pi$
$571$	−12.7082	−0.531822	−0.265911	+	0.963998i	$0.585673\pi$
$572$	2.94427	0.123106
$573$	19.4164	0.811132
$574$	−6.23607	−0.260288
$575$	10.6525	0.444239
$576$	−0.236068	−0.00983617
$577$	28.1803	1.17316	0.586581	−	0.809890i	$-0.300473\pi$
$577$	28.1803	1.17316	0.586581	+	0.809890i	$0.300473\pi$
$578$	6.43769	0.267773
$579$	−11.1246	−0.462323
$580$	−19.9443	−0.828141
$581$	−8.61803	−0.357536
$582$	−3.52786	−0.146235
$583$	−5.70820	−0.236410
$584$	27.7639	1.14888
$585$	−3.85410	−0.159348
$586$	14.5066	0.599261
$587$	−22.1803	−0.915481	−0.457740	−	0.889086i	$-0.651341\pi$
$587$	−22.1803	−0.915481	−0.457740	+	0.889086i	$0.651341\pi$
$588$	−19.4164	−0.800719
$589$	−27.4508	−1.13109
$590$	2.23607	0.0920575
$591$	−43.3050	−1.78133
$592$	15.0000	0.616496
$593$	11.4721	0.471104	0.235552	−	0.971862i	$-0.424310\pi$
$593$	11.4721	0.471104	0.235552	+	0.971862i	$0.424310\pi$
$594$	1.88854	0.0774879
$595$	−8.47214	−0.347324
$596$	−6.70820	−0.274779
$597$	−42.3607	−1.73371
$598$	6.58359	0.269223
$599$	17.2016	0.702839	0.351420	−	0.936218i	$-0.385699\pi$
$599$	17.2016	0.702839	0.351420	+	0.936218i	$0.385699\pi$
$600$	−10.6525	−0.434886
$601$	20.5623	0.838754	0.419377	−	0.907812i	$-0.362249\pi$
$601$	20.5623	0.838754	0.419377	+	0.907812i	$0.362249\pi$
$602$	3.76393	0.153406
$603$	12.7082	0.517518
$604$	34.9787	1.42326
$605$	−16.8541	−0.685217
$606$	−20.7639	−0.843477
$607$	7.83282	0.317924	0.158962	−	0.987285i	$-0.449185\pi$
$607$	7.83282	0.317924	0.158962	+	0.987285i	$0.449185\pi$
$608$	16.0344	0.650282
$609$	15.2361	0.617397
$610$	2.00000	0.0809776
$611$	5.32624	0.215477
$612$	−8.47214	−0.342466
$613$	44.8541	1.81164	0.905820	−	0.423663i	$-0.139256\pi$
$613$	44.8541	1.81164	0.905820	+	0.423663i	$0.139256\pi$
$614$	−8.56231	−0.345547
$615$	−32.6525	−1.31667
$616$	1.70820	0.0688255
$617$	−15.7639	−0.634632	−0.317316	−	0.948320i	$-0.602782\pi$
$617$	−15.7639	−0.634632	−0.317316	+	0.948320i	$0.602782\pi$
$618$	2.58359	0.103927
$619$	−48.2361	−1.93877	−0.969386	−	0.245543i	$-0.921034\pi$
$619$	−48.2361	−1.93877	−0.969386	+	0.245543i	$0.921034\pi$
$620$	25.1803	1.01127
$621$	−17.8885	−0.717843
$622$	19.0000	0.761831
$623$	16.7984	0.673013
$624$	8.83282	0.353596
$625$	−7.41641	−0.296656
$626$	−1.96556	−0.0785595
$627$	−4.36068	−0.174149
$628$	−8.09017	−0.322833
$629$	42.3607	1.68903
$630$	−1.00000	−0.0398410
$631$	44.5967	1.77537	0.887684	−	0.460453i	$-0.152313\pi$
$631$	44.5967	1.77537	0.887684	+	0.460453i	$0.152313\pi$
$632$	35.1246	1.39718
$633$	45.1246	1.79354
$634$	4.18034	0.166023
$635$	−11.6180	−0.461048
$636$	−24.1803	−0.958813
$637$	14.2918	0.566262
$638$	3.59675	0.142397
$639$	−0.708204	−0.0280161
$640$	−18.4164	−0.727972
$641$	16.9098	0.667898	0.333949	−	0.942591i	$-0.391619\pi$
$641$	16.9098	0.667898	0.333949	+	0.942591i	$0.391619\pi$
$642$	1.81966	0.0718163
$643$	17.4721	0.689034	0.344517	−	0.938780i	$-0.388043\pi$
$643$	17.4721	0.689034	0.344517	+	0.938780i	$0.388043\pi$
$644$	−7.23607	−0.285141
$645$	19.7082	0.776010
$646$	9.23607	0.363388
$647$	−18.7984	−0.739040	−0.369520	−	0.929223i	$-0.620478\pi$
$647$	−18.7984	−0.739040	−0.369520	+	0.929223i	$0.620478\pi$
$648$	24.5967	0.966252
$649$	1.70820	0.0670529
$650$	3.50658	0.137539
$651$	−19.2361	−0.753921
$652$	21.9443	0.859404
$653$	−31.9443	−1.25008	−0.625038	−	0.780594i	$-0.714917\pi$
$653$	−31.9443	−1.25008	−0.625038	+	0.780594i	$0.714917\pi$
$654$	8.29180	0.324235
$655$	15.7082	0.613770
$656$	18.7082	0.730433
$657$	−12.4164	−0.484410
$658$	1.38197	0.0538746
$659$	−8.36068	−0.325686	−0.162843	−	0.986652i	$-0.552066\pi$
$659$	−8.36068	−0.325686	−0.162843	+	0.986652i	$0.552066\pi$
$660$	4.00000	0.155700
$661$	−7.76393	−0.301982	−0.150991	−	0.988535i	$-0.548246\pi$
$661$	−7.76393	−0.301982	−0.150991	+	0.988535i	$0.548246\pi$
$662$	−7.47214	−0.290413
$663$	24.9443	0.968755
$664$	−19.2705	−0.747841
$665$	−4.61803	−0.179080
$666$	5.00000	0.193746
$667$	−34.0689	−1.31915
$668$	30.8885	1.19511
$669$	19.4164	0.750682
$670$	12.7082	0.490961
$671$	1.52786	0.0589825
$672$	11.2361	0.433441
$673$	−19.1459	−0.738020	−0.369010	−	0.929425i	$-0.620303\pi$
$673$	−19.1459	−0.738020	−0.369010	+	0.929425i	$0.620303\pi$
$674$	−2.18034	−0.0839836
$675$	−9.52786	−0.366728
$676$	11.8541	0.455927
$677$	27.0000	1.03769	0.518847	−	0.854867i	$-0.326361\pi$
$677$	27.0000	1.03769	0.518847	+	0.854867i	$0.326361\pi$
$678$	−6.76393	−0.259767
$679$	−2.85410	−0.109530
$680$	−18.9443	−0.726480
$681$	34.1803	1.30979
$682$	−4.54102	−0.173885
$683$	26.1803	1.00176	0.500881	−	0.865516i	$-0.333009\pi$
$683$	26.1803	1.00176	0.500881	+	0.865516i	$0.333009\pi$
$684$	−4.61803	−0.176575
$685$	−3.09017	−0.118069
$686$	8.03444	0.306756
$687$	32.0000	1.22088
$688$	−11.2918	−0.430496
$689$	17.7984	0.678064
$690$	8.94427	0.340503
$691$	35.8328	1.36314	0.681572	−	0.731751i	$-0.261297\pi$
$691$	35.8328	1.36314	0.681572	+	0.731751i	$0.261297\pi$
$692$	20.5623	0.781662
$693$	−0.763932	−0.0290194
$694$	−6.27051	−0.238025
$695$	−29.1246	−1.10476
$696$	34.0689	1.29138
$697$	52.8328	2.00119
$698$	−21.0132	−0.795360
$699$	13.7771	0.521097
$700$	−3.85410	−0.145671
$701$	−22.6525	−0.855572	−0.427786	−	0.903880i	$-0.640706\pi$
$701$	−22.6525	−0.855572	−0.427786	+	0.903880i	$0.640706\pi$
$702$	−5.88854	−0.222249
$703$	23.0902	0.870862
$704$	−0.180340	−0.00679682
$705$	7.23607	0.272526
$706$	−8.32624	−0.313362
$707$	−16.7984	−0.631768
$708$	7.23607	0.271948
$709$	−31.4164	−1.17987	−0.589934	−	0.807451i	$-0.700846\pi$
$709$	−31.4164	−1.17987	−0.589934	+	0.807451i	$0.700846\pi$
$710$	−0.708204	−0.0265784
$711$	−15.7082	−0.589104
$712$	37.5623	1.40771
$713$	43.0132	1.61086
$714$	6.47214	0.242214
$715$	−2.94427	−0.110110
$716$	−19.9443	−0.745352
$717$	42.9443	1.60378
$718$	19.5836	0.730853
$719$	−37.8885	−1.41300	−0.706502	−	0.707711i	$-0.749728\pi$
$719$	−37.8885	−1.41300	−0.706502	+	0.707711i	$0.749728\pi$
$720$	3.00000	0.111803
$721$	2.09017	0.0778420
$722$	−6.70820	−0.249653
$723$	1.16718	0.0434081
$724$	20.5623	0.764192
$725$	−18.1459	−0.673922
$726$	12.8754	0.477850
$727$	−4.88854	−0.181306	−0.0906530	−	0.995883i	$-0.528895\pi$
$727$	−4.88854	−0.181306	−0.0906530	+	0.995883i	$0.528895\pi$
$728$	−5.32624	−0.197404
$729$	13.0000	0.481481
$730$	−12.4164	−0.459552
$731$	−31.8885	−1.17944
$732$	6.47214	0.239217
$733$	52.9574	1.95603	0.978014	−	0.208541i	$-0.0668715\pi$
$733$	52.9574	1.95603	0.978014	+	0.208541i	$0.0668715\pi$
$734$	−11.4164	−0.421387
$735$	19.4164	0.716185
$736$	−25.1246	−0.926105
$737$	9.70820	0.357606
$738$	6.23607	0.229553
$739$	33.3607	1.22719	0.613596	−	0.789620i	$-0.289722\pi$
$739$	33.3607	1.22719	0.613596	+	0.789620i	$0.289722\pi$
$740$	−21.1803	−0.778605
$741$	13.5967	0.499489
$742$	4.61803	0.169533
$743$	−44.0132	−1.61469	−0.807343	−	0.590082i	$-0.799095\pi$
$743$	−44.0132	−1.61469	−0.807343	+	0.590082i	$0.799095\pi$
$744$	−43.0132	−1.57694
$745$	6.70820	0.245770
$746$	7.56231	0.276876
$747$	8.61803	0.315317
$748$	−6.47214	−0.236645
$749$	1.47214	0.0537907
$750$	14.7639	0.539103
$751$	−16.8541	−0.615015	−0.307507	−	0.951546i	$-0.599495\pi$
$751$	−16.8541	−0.615015	−0.307507	+	0.951546i	$0.599495\pi$
$752$	−4.14590	−0.151185
$753$	36.9443	1.34632
$754$	−11.2148	−0.408418
$755$	−34.9787	−1.27301
$756$	6.47214	0.235389
$757$	28.5623	1.03811	0.519057	−	0.854739i	$-0.326283\pi$
$757$	28.5623	1.03811	0.519057	+	0.854739i	$0.326283\pi$
$758$	−16.7984	−0.610144
$759$	6.83282	0.248015
$760$	−10.3262	−0.374572
$761$	−50.0344	−1.81375	−0.906874	−	0.421403i	$-0.861538\pi$
$761$	−50.0344	−1.81375	−0.906874	+	0.421403i	$0.861538\pi$
$762$	8.87539	0.321521
$763$	6.70820	0.242853
$764$	15.7082	0.568303
$765$	8.47214	0.306311
$766$	21.2705	0.768535
$767$	−5.32624	−0.192319
$768$	13.1246	0.473594
$769$	24.1246	0.869956	0.434978	−	0.900441i	$-0.356756\pi$
$769$	24.1246	0.869956	0.434978	+	0.900441i	$0.356756\pi$
$770$	−0.763932	−0.0275302
$771$	−22.9443	−0.826318
$772$	−9.00000	−0.323917
$773$	−5.38197	−0.193576	−0.0967879	−	0.995305i	$-0.530857\pi$
$773$	−5.38197	−0.193576	−0.0967879	+	0.995305i	$0.530857\pi$
$774$	−3.76393	−0.135292
$775$	22.9098	0.822945
$776$	−6.38197	−0.229099
$777$	16.1803	0.580466
$778$	−0.291796	−0.0104614
$779$	28.7984	1.03181
$780$	−12.4721	−0.446574
$781$	−0.541020	−0.0193592
$782$	−14.4721	−0.517523
$783$	30.4721	1.08899
$784$	−11.1246	−0.397308
$785$	8.09017	0.288751
$786$	−12.0000	−0.428026
$787$	−51.0902	−1.82117	−0.910584	−	0.413324i	$-0.864368\pi$
$787$	−51.0902	−1.82117	−0.910584	+	0.413324i	$0.864368\pi$
$788$	−35.0344	−1.24805
$789$	13.0557	0.464796
$790$	−15.7082	−0.558873
$791$	−5.47214	−0.194567
$792$	−1.70820	−0.0606984
$793$	−4.76393	−0.169172
$794$	0.167184	0.00593315
$795$	24.1803	0.857588
$796$	−34.2705	−1.21469
$797$	16.1803	0.573137	0.286569	−	0.958060i	$-0.407485\pi$
$797$	16.1803	0.573137	0.286569	+	0.958060i	$0.407485\pi$
$798$	3.52786	0.124885
$799$	−11.7082	−0.414206
$800$	−13.3820	−0.473124
$801$	−16.7984	−0.593541
$802$	3.56231	0.125789
$803$	−9.48529	−0.334729
$804$	41.1246	1.45035
$805$	7.23607	0.255038
$806$	14.1591	0.498731
$807$	12.5410	0.441465
$808$	−37.5623	−1.32144
$809$	14.8328	0.521494	0.260747	−	0.965407i	$-0.416031\pi$
$809$	14.8328	0.521494	0.260747	+	0.965407i	$0.416031\pi$
$810$	−11.0000	−0.386501
$811$	−52.1246	−1.83034	−0.915171	−	0.403065i	$-0.867945\pi$
$811$	−52.1246	−1.83034	−0.915171	+	0.403065i	$0.867945\pi$
$812$	12.3262	0.432566
$813$	−22.5410	−0.790548
$814$	3.81966	0.133879
$815$	−21.9443	−0.768674
$816$	−19.4164	−0.679710
$817$	−17.3820	−0.608118
$818$	11.8885	0.415673
$819$	2.38197	0.0832326
$820$	−26.4164	−0.922501
$821$	−23.3050	−0.813348	−0.406674	−	0.913573i	$-0.633312\pi$
$821$	−23.3050	−0.813348	−0.406674	+	0.913573i	$0.633312\pi$
$822$	2.36068	0.0823382
$823$	46.4296	1.61843	0.809216	−	0.587511i	$-0.199892\pi$
$823$	46.4296	1.61843	0.809216	+	0.587511i	$0.199892\pi$
$824$	4.67376	0.162818
$825$	3.63932	0.126705
$826$	−1.38197	−0.0480847
$827$	14.6525	0.509517	0.254758	−	0.967005i	$-0.418004\pi$
$827$	14.6525	0.509517	0.254758	+	0.967005i	$0.418004\pi$
$828$	7.23607	0.251471
$829$	46.9230	1.62970	0.814851	−	0.579670i	$-0.196819\pi$
$829$	46.9230	1.62970	0.814851	+	0.579670i	$0.196819\pi$
$830$	8.61803	0.299136
$831$	−17.3050	−0.600302
$832$	0.562306	0.0194944
$833$	−31.4164	−1.08851
$834$	22.2492	0.770428
$835$	−30.8885	−1.06894
$836$	−3.52786	−0.122014
$837$	−38.4721	−1.32979
$838$	5.72949	0.197922
$839$	−21.0000	−0.725001	−0.362500	−	0.931984i	$-0.618077\pi$
$839$	−21.0000	−0.725001	−0.362500	+	0.931984i	$0.618077\pi$
$840$	−7.23607	−0.249668
$841$	29.0344	1.00119
$842$	−11.9230	−0.410893
$843$	−14.2918	−0.492236
$844$	36.5066	1.25661
$845$	−11.8541	−0.407794
$846$	−1.38197	−0.0475130
$847$	10.4164	0.357912
$848$	−13.8541	−0.475752
$849$	−57.1246	−1.96051
$850$	−7.70820	−0.264389
$851$	−36.1803	−1.24025
$852$	−2.29180	−0.0785156
$853$	−19.8328	−0.679063	−0.339531	−	0.940595i	$-0.610268\pi$
$853$	−19.8328	−0.679063	−0.339531	+	0.940595i	$0.610268\pi$
$854$	−1.23607	−0.0422974
$855$	4.61803	0.157933
$856$	3.29180	0.112511
$857$	−33.0000	−1.12726	−0.563629	−	0.826028i	$-0.690595\pi$
$857$	−33.0000	−1.12726	−0.563629	+	0.826028i	$0.690595\pi$
$858$	2.24922	0.0767872
$859$	−38.4164	−1.31075	−0.655375	−	0.755303i	$-0.727490\pi$
$859$	−38.4164	−1.31075	−0.655375	+	0.755303i	$0.727490\pi$
$860$	15.9443	0.543695
$861$	20.1803	0.687744
$862$	19.4377	0.662050
$863$	34.4164	1.17155	0.585774	−	0.810474i	$-0.300791\pi$
$863$	34.4164	1.17155	0.585774	+	0.810474i	$0.300791\pi$
$864$	22.4721	0.764518
$865$	−20.5623	−0.699139
$866$	−21.5623	−0.732717
$867$	−20.8328	−0.707520
$868$	−15.5623	−0.528219
$869$	−12.0000	−0.407072
$870$	−15.2361	−0.516551
$871$	−30.2705	−1.02568
$872$	15.0000	0.507964
$873$	2.85410	0.0965967
$874$	−7.88854	−0.266834
$875$	11.9443	0.403790
$876$	−40.1803	−1.35757
$877$	−0.472136	−0.0159429	−0.00797145	−	0.999968i	$-0.502537\pi$
$877$	−0.472136	−0.0159429	−0.00797145	+	0.999968i	$0.502537\pi$
$878$	−14.1246	−0.476683
$879$	−46.9443	−1.58339
$880$	2.29180	0.0772564
$881$	−12.9787	−0.437264	−0.218632	−	0.975807i	$-0.570159\pi$
$881$	−12.9787	−0.437264	−0.218632	+	0.975807i	$0.570159\pi$
$882$	−3.70820	−0.124862
$883$	3.18034	0.107027	0.0535135	−	0.998567i	$-0.482958\pi$
$883$	3.18034	0.107027	0.0535135	+	0.998567i	$0.482958\pi$
$884$	20.1803	0.678738
$885$	−7.23607	−0.243238
$886$	7.58359	0.254776
$887$	26.8885	0.902829	0.451414	−	0.892314i	$-0.350920\pi$
$887$	26.8885	0.902829	0.451414	+	0.892314i	$0.350920\pi$
$888$	36.1803	1.21413
$889$	7.18034	0.240821
$890$	−16.7984	−0.563083
$891$	−8.40325	−0.281520
$892$	15.7082	0.525950
$893$	−6.38197	−0.213564
$894$	−5.12461	−0.171393
$895$	19.9443	0.666663
$896$	11.3820	0.380245
$897$	−21.3050	−0.711352
$898$	−11.0557	−0.368934
$899$	−73.2705	−2.44371
$900$	3.85410	0.128470
$901$	−39.1246	−1.30343
$902$	4.76393	0.158622
$903$	−12.1803	−0.405336
$904$	−12.2361	−0.406966
$905$	−20.5623	−0.683514
$906$	26.7214	0.887758
$907$	−34.0000	−1.12895	−0.564476	−	0.825450i	$-0.690922\pi$
$907$	−34.0000	−1.12895	−0.564476	+	0.825450i	$0.690922\pi$
$908$	27.6525	0.917680
$909$	16.7984	0.557167
$910$	2.38197	0.0789614
$911$	6.23607	0.206610	0.103305	−	0.994650i	$-0.467058\pi$
$911$	6.23607	0.206610	0.103305	+	0.994650i	$0.467058\pi$
$912$	−10.5836	−0.350458
$913$	6.58359	0.217885
$914$	−16.7984	−0.555641
$915$	−6.47214	−0.213962
$916$	25.8885	0.855382
$917$	−9.70820	−0.320593
$918$	12.9443	0.427225
$919$	−40.5066	−1.33619	−0.668094	−	0.744077i	$-0.732890\pi$
$919$	−40.5066	−1.33619	−0.668094	+	0.744077i	$0.732890\pi$
$920$	16.1803	0.533450
$921$	27.7082	0.913016
$922$	19.4721	0.641281
$923$	1.68692	0.0555256
$924$	−2.47214	−0.0813273
$925$	−19.2705	−0.633610
$926$	−5.81966	−0.191246
$927$	−2.09017	−0.0686502
$928$	42.7984	1.40493
$929$	18.5967	0.610140	0.305070	−	0.952330i	$-0.401320\pi$
$929$	18.5967	0.610140	0.305070	+	0.952330i	$0.401320\pi$
$930$	19.2361	0.630776
$931$	−17.1246	−0.561236
$932$	11.1459	0.365096
$933$	−61.4853	−2.01294
$934$	8.58359	0.280864
$935$	6.47214	0.211661
$936$	5.32624	0.174094
$937$	−32.1246	−1.04947	−0.524733	−	0.851267i	$-0.675835\pi$
$937$	−32.1246	−1.04947	−0.524733	+	0.851267i	$0.675835\pi$
$938$	−7.85410	−0.256446
$939$	6.36068	0.207573
$940$	5.85410	0.190940
$941$	−29.8328	−0.972522	−0.486261	−	0.873814i	$-0.661640\pi$
$941$	−29.8328	−0.972522	−0.486261	+	0.873814i	$0.661640\pi$
$942$	−6.18034	−0.201366
$943$	−45.1246	−1.46946
$944$	4.14590	0.134937
$945$	−6.47214	−0.210539
$946$	−2.87539	−0.0934869
$947$	0.0901699	0.00293013	0.00146506	−	0.999999i	$-0.499534\pi$
$947$	0.0901699	0.00293013	0.00146506	+	0.999999i	$0.499534\pi$
$948$	−50.8328	−1.65097
$949$	29.5755	0.960060
$950$	−4.20163	−0.136319
$951$	−13.5279	−0.438671
$952$	11.7082	0.379465
$953$	−30.9443	−1.00238	−0.501192	−	0.865336i	$-0.667105\pi$
$953$	−30.9443	−1.00238	−0.501192	+	0.865336i	$0.667105\pi$
$954$	−4.61803	−0.149514
$955$	−15.7082	−0.508306
$956$	34.7426	1.12366
$957$	−11.6393	−0.376246
$958$	2.12461	0.0686431
$959$	1.90983	0.0616716
$960$	0.763932	0.0246558
$961$	61.5066	1.98408
$962$	−11.9098	−0.383988
$963$	−1.47214	−0.0474389
$964$	0.944272	0.0304130
$965$	9.00000	0.289720
$966$	−5.52786	−0.177856
$967$	−56.1591	−1.80595	−0.902977	−	0.429689i	$-0.858623\pi$
$967$	−56.1591	−1.80595	−0.902977	+	0.429689i	$0.858623\pi$
$968$	23.2918	0.748627
$969$	−29.8885	−0.960158
$970$	2.85410	0.0916397
$971$	−28.5279	−0.915503	−0.457751	−	0.889080i	$-0.651345\pi$
$971$	−28.5279	−0.915503	−0.457751	+	0.889080i	$0.651345\pi$
$972$	−16.1803	−0.518985
$973$	18.0000	0.577054
$974$	22.8541	0.732293
$975$	−11.3475	−0.363412
$976$	3.70820	0.118697
$977$	−61.6869	−1.97354	−0.986770	−	0.162128i	$-0.948164\pi$
$977$	−61.6869	−1.97354	−0.986770	+	0.162128i	$0.948164\pi$
$978$	16.7639	0.536051
$979$	−12.8328	−0.410139
$980$	15.7082	0.501780
$981$	−6.70820	−0.214176
$982$	−7.16718	−0.228714
$983$	−3.88854	−0.124025	−0.0620126	−	0.998075i	$-0.519752\pi$
$983$	−3.88854	−0.124025	−0.0620126	+	0.998075i	$0.519752\pi$
$984$	45.1246	1.43852
$985$	35.0344	1.11629
$986$	24.6525	0.785095
$987$	−4.47214	−0.142350
$988$	11.0000	0.349957
$989$	27.2361	0.866057
$990$	0.763932	0.0242794
$991$	−31.5410	−1.00193	−0.500967	−	0.865467i	$-0.667022\pi$
$991$	−31.5410	−1.00193	−0.500967	+	0.865467i	$0.667022\pi$
$992$	−54.0344	−1.71560
$993$	24.1803	0.767340
$994$	0.437694	0.0138828
$995$	34.2705	1.08645
$996$	27.8885	0.883682
$997$	28.4164	0.899957	0.449978	−	0.893039i	$-0.351432\pi$
$997$	28.4164	0.899957	0.449978	+	0.893039i	$0.351432\pi$
$998$	−14.5066	−0.459198
$999$	32.3607	1.02385

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3229.2.a.b.1.2	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3229.2.a.b.1.2	✓	2	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:	\( N \)	\(=\)	\( 3229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3229.a (trivial)

\(f(q)\)	\(=\)	\(q+0.618034 q^{2} -2.00000 q^{3} -1.61803 q^{4} +1.61803 q^{5} -1.23607 q^{6} -1.00000 q^{7} -2.23607 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.618034 q^{2} -2.00000 q^{3} -1.61803 q^{4} +1.61803 q^{5} -1.23607 q^{6} -1.00000 q^{7} -2.23607 q^{8} +1.00000 q^{9} +1.00000 q^{10} +0.763932 q^{11} +3.23607 q^{12} -2.38197 q^{13} -0.618034 q^{14} -3.23607 q^{15} +1.85410 q^{16} +5.23607 q^{17} +0.618034 q^{18} +2.85410 q^{19} -2.61803 q^{20} +2.00000 q^{21} +0.472136 q^{22} -4.47214 q^{23} +4.47214 q^{24} -2.38197 q^{25} -1.47214 q^{26} +4.00000 q^{27} +1.61803 q^{28} +7.61803 q^{29} -2.00000 q^{30} -9.61803 q^{31} +5.61803 q^{32} -1.52786 q^{33} +3.23607 q^{34} -1.61803 q^{35} -1.61803 q^{36} +8.09017 q^{37} +1.76393 q^{38} +4.76393 q^{39} -3.61803 q^{40} +10.0902 q^{41} +1.23607 q^{42} -6.09017 q^{43} -1.23607 q^{44} +1.61803 q^{45} -2.76393 q^{46} -2.23607 q^{47} -3.70820 q^{48} -6.00000 q^{49} -1.47214 q^{50} -10.4721 q^{51} +3.85410 q^{52} -7.47214 q^{53} +2.47214 q^{54} +1.23607 q^{55} +2.23607 q^{56} -5.70820 q^{57} +4.70820 q^{58} +2.23607 q^{59} +5.23607 q^{60} +2.00000 q^{61} -5.94427 q^{62} -1.00000 q^{63} -0.236068 q^{64} -3.85410 q^{65} -0.944272 q^{66} +12.7082 q^{67} -8.47214 q^{68} +8.94427 q^{69} -1.00000 q^{70} -0.708204 q^{71} -2.23607 q^{72} -12.4164 q^{73} +5.00000 q^{74} +4.76393 q^{75} -4.61803 q^{76} -0.763932 q^{77} +2.94427 q^{78} -15.7082 q^{79} +3.00000 q^{80} -11.0000 q^{81} +6.23607 q^{82} +8.61803 q^{83} -3.23607 q^{84} +8.47214 q^{85} -3.76393 q^{86} -15.2361 q^{87} -1.70820 q^{88} -16.7984 q^{89} +1.00000 q^{90} +2.38197 q^{91} +7.23607 q^{92} +19.2361 q^{93} -1.38197 q^{94} +4.61803 q^{95} -11.2361 q^{96} +2.85410 q^{97} -3.70820 q^{98} +0.763932 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - 4 q^{3} - q^{4} + q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q - q^2 - 4 * q^3 - q^4 + q^5 + 2 * q^6 - 2 * q^7 + 2 * q^9	\( 2 q - q^{2} - 4 q^{3} - q^{4} + q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{9} + 2 q^{10} + 6 q^{11} + 2 q^{12} - 7 q^{13} + q^{14} - 2 q^{15} - 3 q^{16} + 6 q^{17} - q^{18} - q^{19} - 3 q^{20} + 4 q^{21} - 8 q^{22} - 7 q^{25} + 6 q^{26} + 8 q^{27} + q^{28} + 13 q^{29} - 4 q^{30} - 17 q^{31} + 9 q^{32} - 12 q^{33} + 2 q^{34} - q^{35} - q^{36} + 5 q^{37} + 8 q^{38} + 14 q^{39} - 5 q^{40} + 9 q^{41} - 2 q^{42} - q^{43} + 2 q^{44} + q^{45} - 10 q^{46} + 6 q^{48} - 12 q^{49} + 6 q^{50} - 12 q^{51} + q^{52} - 6 q^{53} - 4 q^{54} - 2 q^{55} + 2 q^{57} - 4 q^{58} + 6 q^{60} + 4 q^{61} + 6 q^{62} - 2 q^{63} + 4 q^{64} - q^{65} + 16 q^{66} + 12 q^{67} - 8 q^{68} - 2 q^{70} + 12 q^{71} + 2 q^{73} + 10 q^{74} + 14 q^{75} - 7 q^{76} - 6 q^{77} - 12 q^{78} - 18 q^{79} + 6 q^{80} - 22 q^{81} + 8 q^{82} + 15 q^{83} - 2 q^{84} + 8 q^{85} - 12 q^{86} - 26 q^{87} + 10 q^{88} - 9 q^{89} + 2 q^{90} + 7 q^{91} + 10 q^{92} + 34 q^{93} - 5 q^{94} + 7 q^{95} - 18 q^{96} - q^{97} + 6 q^{98} + 6 q^{99}+O(q^{100}) \) 2 * q - q^2 - 4 * q^3 - q^4 + q^5 + 2 * q^6 - 2 * q^7 + 2 * q^9 + 2 * q^10 + 6 * q^11 + 2 * q^12 - 7 * q^13 + q^14 - 2 * q^15 - 3 * q^16 + 6 * q^17 - q^18 - q^19 - 3 * q^20 + 4 * q^21 - 8 * q^22 - 7 * q^25 + 6 * q^26 + 8 * q^27 + q^28 + 13 * q^29 - 4 * q^30 - 17 * q^31 + 9 * q^32 - 12 * q^33 + 2 * q^34 - q^35 - q^36 + 5 * q^37 + 8 * q^38 + 14 * q^39 - 5 * q^40 + 9 * q^41 - 2 * q^42 - q^43 + 2 * q^44 + q^45 - 10 * q^46 + 6 * q^48 - 12 * q^49 + 6 * q^50 - 12 * q^51 + q^52 - 6 * q^53 - 4 * q^54 - 2 * q^55 + 2 * q^57 - 4 * q^58 + 6 * q^60 + 4 * q^61 + 6 * q^62 - 2 * q^63 + 4 * q^64 - q^65 + 16 * q^66 + 12 * q^67 - 8 * q^68 - 2 * q^70 + 12 * q^71 + 2 * q^73 + 10 * q^74 + 14 * q^75 - 7 * q^76 - 6 * q^77 - 12 * q^78 - 18 * q^79 + 6 * q^80 - 22 * q^81 + 8 * q^82 + 15 * q^83 - 2 * q^84 + 8 * q^85 - 12 * q^86 - 26 * q^87 + 10 * q^88 - 9 * q^89 + 2 * q^90 + 7 * q^91 + 10 * q^92 + 34 * q^93 - 5 * q^94 + 7 * q^95 - 18 * q^96 - q^97 + 6 * q^98 + 6 * q^99

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