LMFDB - Embedded newform 8030.2.a.l.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8030,2,Mod(1,8030)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8030, 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("8030.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8030 = 2 \cdot 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8030.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:	$64.1198728231$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{13}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 3 $ x^2 - x - 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.30278$ of defining polynomial
Character	$\chi$	$=$	8030.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.30278 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.30278 q^{6} -3.30278 q^{7} -1.00000 q^{8} -1.30278 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.30278 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.30278 q^{6} -3.30278 q^{7} -1.00000 q^{8} -1.30278 q^{9} +1.00000 q^{10} +1.00000 q^{11} -1.30278 q^{12} -4.90833 q^{13} +3.30278 q^{14} +1.30278 q^{15} +1.00000 q^{16} +6.90833 q^{17} +1.30278 q^{18} -4.00000 q^{19} -1.00000 q^{20} +4.30278 q^{21} -1.00000 q^{22} -2.30278 q^{23} +1.30278 q^{24} +1.00000 q^{25} +4.90833 q^{26} +5.60555 q^{27} -3.30278 q^{28} -5.30278 q^{29} -1.30278 q^{30} +0.605551 q^{31} -1.00000 q^{32} -1.30278 q^{33} -6.90833 q^{34} +3.30278 q^{35} -1.30278 q^{36} +8.90833 q^{37} +4.00000 q^{38} +6.39445 q^{39} +1.00000 q^{40} -6.00000 q^{41} -4.30278 q^{42} +5.21110 q^{43} +1.00000 q^{44} +1.30278 q^{45} +2.30278 q^{46} +3.21110 q^{47} -1.30278 q^{48} +3.90833 q^{49} -1.00000 q^{50} -9.00000 q^{51} -4.90833 q^{52} -5.60555 q^{54} -1.00000 q^{55} +3.30278 q^{56} +5.21110 q^{57} +5.30278 q^{58} -13.8167 q^{59} +1.30278 q^{60} +6.60555 q^{61} -0.605551 q^{62} +4.30278 q^{63} +1.00000 q^{64} +4.90833 q^{65} +1.30278 q^{66} +1.30278 q^{67} +6.90833 q^{68} +3.00000 q^{69} -3.30278 q^{70} +14.5139 q^{71} +1.30278 q^{72} +1.00000 q^{73} -8.90833 q^{74} -1.30278 q^{75} -4.00000 q^{76} -3.30278 q^{77} -6.39445 q^{78} +11.2111 q^{79} -1.00000 q^{80} -3.39445 q^{81} +6.00000 q^{82} +6.69722 q^{83} +4.30278 q^{84} -6.90833 q^{85} -5.21110 q^{86} +6.90833 q^{87} -1.00000 q^{88} -14.7250 q^{89} -1.30278 q^{90} +16.2111 q^{91} -2.30278 q^{92} -0.788897 q^{93} -3.21110 q^{94} +4.00000 q^{95} +1.30278 q^{96} -1.48612 q^{97} -3.90833 q^{98} -1.30278 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + q^{3} + 2 q^{4} - 2 q^{5} - q^{6} - 3 q^{7} - 2 q^{8} + q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + q^3 + 2 * q^4 - 2 * q^5 - q^6 - 3 * q^7 - 2 * q^8 + q^9	\( 2 q - 2 q^{2} + q^{3} + 2 q^{4} - 2 q^{5} - q^{6} - 3 q^{7} - 2 q^{8} + q^{9} + 2 q^{10} + 2 q^{11} + q^{12} + q^{13} + 3 q^{14} - q^{15} + 2 q^{16} + 3 q^{17} - q^{18} - 8 q^{19} - 2 q^{20} + 5 q^{21} - 2 q^{22} - q^{23} - q^{24} + 2 q^{25} - q^{26} + 4 q^{27} - 3 q^{28} - 7 q^{29} + q^{30} - 6 q^{31} - 2 q^{32} + q^{33} - 3 q^{34} + 3 q^{35} + q^{36} + 7 q^{37} + 8 q^{38} + 20 q^{39} + 2 q^{40} - 12 q^{41} - 5 q^{42} - 4 q^{43} + 2 q^{44} - q^{45} + q^{46} - 8 q^{47} + q^{48} - 3 q^{49} - 2 q^{50} - 18 q^{51} + q^{52} - 4 q^{54} - 2 q^{55} + 3 q^{56} - 4 q^{57} + 7 q^{58} - 6 q^{59} - q^{60} + 6 q^{61} + 6 q^{62} + 5 q^{63} + 2 q^{64} - q^{65} - q^{66} - q^{67} + 3 q^{68} + 6 q^{69} - 3 q^{70} + 11 q^{71} - q^{72} + 2 q^{73} - 7 q^{74} + q^{75} - 8 q^{76} - 3 q^{77} - 20 q^{78} + 8 q^{79} - 2 q^{80} - 14 q^{81} + 12 q^{82} + 17 q^{83} + 5 q^{84} - 3 q^{85} + 4 q^{86} + 3 q^{87} - 2 q^{88} + 3 q^{89} + q^{90} + 18 q^{91} - q^{92} - 16 q^{93} + 8 q^{94} + 8 q^{95} - q^{96} - 21 q^{97} + 3 q^{98} + q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + q^3 + 2 * q^4 - 2 * q^5 - q^6 - 3 * q^7 - 2 * q^8 + q^9 + 2 * q^10 + 2 * q^11 + q^12 + q^13 + 3 * q^14 - q^15 + 2 * q^16 + 3 * q^17 - q^18 - 8 * q^19 - 2 * q^20 + 5 * q^21 - 2 * q^22 - q^23 - q^24 + 2 * q^25 - q^26 + 4 * q^27 - 3 * q^28 - 7 * q^29 + q^30 - 6 * q^31 - 2 * q^32 + q^33 - 3 * q^34 + 3 * q^35 + q^36 + 7 * q^37 + 8 * q^38 + 20 * q^39 + 2 * q^40 - 12 * q^41 - 5 * q^42 - 4 * q^43 + 2 * q^44 - q^45 + q^46 - 8 * q^47 + q^48 - 3 * q^49 - 2 * q^50 - 18 * q^51 + q^52 - 4 * q^54 - 2 * q^55 + 3 * q^56 - 4 * q^57 + 7 * q^58 - 6 * q^59 - q^60 + 6 * q^61 + 6 * q^62 + 5 * q^63 + 2 * q^64 - q^65 - q^66 - q^67 + 3 * q^68 + 6 * q^69 - 3 * q^70 + 11 * q^71 - q^72 + 2 * q^73 - 7 * q^74 + q^75 - 8 * q^76 - 3 * q^77 - 20 * q^78 + 8 * q^79 - 2 * q^80 - 14 * q^81 + 12 * q^82 + 17 * q^83 + 5 * q^84 - 3 * q^85 + 4 * q^86 + 3 * q^87 - 2 * q^88 + 3 * q^89 + q^90 + 18 * q^91 - q^92 - 16 * q^93 + 8 * q^94 + 8 * q^95 - q^96 - 21 * q^97 + 3 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.30278	−0.752158	−0.376079	−	0.926588i	$-0.622728\pi$
$3$	−1.30278	−0.752158	−0.376079	+	0.926588i	$0.622728\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.30278	0.531856
$7$	−3.30278	−1.24833	−0.624166	−	0.781292i	$-0.714561\pi$
$7$	−3.30278	−1.24833	−0.624166	+	0.781292i	$0.714561\pi$
$8$	−1.00000	−0.353553
$9$	−1.30278	−0.434259
$10$	1.00000	0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.30278	−0.376079
$13$	−4.90833	−1.36132	−0.680662	−	0.732597i	$-0.738308\pi$
$13$	−4.90833	−1.36132	−0.680662	+	0.732597i	$0.738308\pi$
$14$	3.30278	0.882704
$15$	1.30278	0.336375
$16$	1.00000	0.250000
$17$	6.90833	1.67552	0.837758	−	0.546042i	$-0.183866\pi$
$17$	6.90833	1.67552	0.837758	+	0.546042i	$0.183866\pi$
$18$	1.30278	0.307067
$19$	−4.00000	−0.917663	−0.458831	−	0.888523i	$-0.651732\pi$
$19$	−4.00000	−0.917663	−0.458831	+	0.888523i	$0.651732\pi$
$20$	−1.00000	−0.223607
$21$	4.30278	0.938943
$22$	−1.00000	−0.213201
$23$	−2.30278	−0.480162	−0.240081	−	0.970753i	$-0.577174\pi$
$23$	−2.30278	−0.480162	−0.240081	+	0.970753i	$0.577174\pi$
$24$	1.30278	0.265928
$25$	1.00000	0.200000
$26$	4.90833	0.962602
$27$	5.60555	1.07879
$28$	−3.30278	−0.624166
$29$	−5.30278	−0.984701	−0.492350	−	0.870397i	$-0.663862\pi$
$29$	−5.30278	−0.984701	−0.492350	+	0.870397i	$0.663862\pi$
$30$	−1.30278	−0.237853
$31$	0.605551	0.108760	0.0543801	−	0.998520i	$-0.482682\pi$
$31$	0.605551	0.108760	0.0543801	+	0.998520i	$0.482682\pi$
$32$	−1.00000	−0.176777
$33$	−1.30278	−0.226784
$34$	−6.90833	−1.18477
$35$	3.30278	0.558271
$36$	−1.30278	−0.217129
$37$	8.90833	1.46452	0.732260	−	0.681025i	$-0.238466\pi$
$37$	8.90833	1.46452	0.732260	+	0.681025i	$0.238466\pi$
$38$	4.00000	0.648886
$39$	6.39445	1.02393
$40$	1.00000	0.158114
$41$	−6.00000	−0.937043	−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000	−0.937043	−0.468521	+	0.883452i	$0.655213\pi$
$42$	−4.30278	−0.663933
$43$	5.21110	0.794686	0.397343	−	0.917670i	$-0.369932\pi$
$43$	5.21110	0.794686	0.397343	+	0.917670i	$0.369932\pi$
$44$	1.00000	0.150756
$45$	1.30278	0.194206
$46$	2.30278	0.339526
$47$	3.21110	0.468387	0.234194	−	0.972190i	$-0.424755\pi$
$47$	3.21110	0.468387	0.234194	+	0.972190i	$0.424755\pi$
$48$	−1.30278	−0.188039
$49$	3.90833	0.558332
$50$	−1.00000	−0.141421
$51$	−9.00000	−1.26025
$52$	−4.90833	−0.680662
$53$	0	0		−	1.00000i	$-0.5\pi$
$53$	0	0			1.00000i	$0.5\pi$
$54$	−5.60555	−0.762819
$55$	−1.00000	−0.134840
$56$	3.30278	0.441352
$57$	5.21110	0.690227
$58$	5.30278	0.696289
$59$	−13.8167	−1.79878	−0.899388	−	0.437152i	$-0.855987\pi$
$59$	−13.8167	−1.79878	−0.899388	+	0.437152i	$0.855987\pi$
$60$	1.30278	0.168188
$61$	6.60555	0.845754	0.422877	−	0.906187i	$-0.361020\pi$
$61$	6.60555	0.845754	0.422877	+	0.906187i	$0.361020\pi$
$62$	−0.605551	−0.0769051
$63$	4.30278	0.542099
$64$	1.00000	0.125000
$65$	4.90833	0.608803
$66$	1.30278	0.160361
$67$	1.30278	0.159159	0.0795797	−	0.996829i	$-0.474642\pi$
$67$	1.30278	0.159159	0.0795797	+	0.996829i	$0.474642\pi$
$68$	6.90833	0.837758
$69$	3.00000	0.361158
$70$	−3.30278	−0.394757
$71$	14.5139	1.72248	0.861240	−	0.508198i	$-0.169688\pi$
$71$	14.5139	1.72248	0.861240	+	0.508198i	$0.169688\pi$
$72$	1.30278	0.153534
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	−8.90833	−1.03557
$75$	−1.30278	−0.150432
$76$	−4.00000	−0.458831
$77$	−3.30278	−0.376386
$78$	−6.39445	−0.724029
$79$	11.2111	1.26135	0.630674	−	0.776048i	$-0.282779\pi$
$79$	11.2111	1.26135	0.630674	+	0.776048i	$0.282779\pi$
$80$	−1.00000	−0.111803
$81$	−3.39445	−0.377161
$82$	6.00000	0.662589
$83$	6.69722	0.735116	0.367558	−	0.930001i	$-0.380194\pi$
$83$	6.69722	0.735116	0.367558	+	0.930001i	$0.380194\pi$
$84$	4.30278	0.469471
$85$	−6.90833	−0.749313
$86$	−5.21110	−0.561928
$87$	6.90833	0.740650
$88$	−1.00000	−0.106600
$89$	−14.7250	−1.56084	−0.780422	−	0.625253i	$-0.784996\pi$
$89$	−14.7250	−1.56084	−0.780422	+	0.625253i	$0.784996\pi$
$90$	−1.30278	−0.137325
$91$	16.2111	1.69939
$92$	−2.30278	−0.240081
$93$	−0.788897	−0.0818049
$94$	−3.21110	−0.331200
$95$	4.00000	0.410391
$96$	1.30278	0.132964
$97$	−1.48612	−0.150893	−0.0754464	−	0.997150i	$-0.524038\pi$
$97$	−1.48612	−0.150893	−0.0754464	+	0.997150i	$0.524038\pi$
$98$	−3.90833	−0.394801
$99$	−1.30278	−0.130934
$100$	1.00000	0.100000
$101$	5.30278	0.527646	0.263823	−	0.964571i	$-0.415017\pi$
$101$	5.30278	0.527646	0.263823	+	0.964571i	$0.415017\pi$
$102$	9.00000	0.891133
$103$	−11.3944	−1.12273	−0.561364	−	0.827569i	$-0.689723\pi$
$103$	−11.3944	−1.12273	−0.561364	+	0.827569i	$0.689723\pi$
$104$	4.90833	0.481301
$105$	−4.30278	−0.419908
$106$	0	0
$107$	17.5139	1.69313	0.846565	−	0.532285i	$-0.178667\pi$
$107$	17.5139	1.69313	0.846565	+	0.532285i	$0.178667\pi$
$108$	5.60555	0.539394
$109$	14.4222	1.38140	0.690698	−	0.723143i	$-0.257303\pi$
$109$	14.4222	1.38140	0.690698	+	0.723143i	$0.257303\pi$
$110$	1.00000	0.0953463
$111$	−11.6056	−1.10155
$112$	−3.30278	−0.312083
$113$	6.00000	0.564433	0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000	0.564433	0.282216	+	0.959351i	$0.408930\pi$
$114$	−5.21110	−0.488064
$115$	2.30278	0.214735
$116$	−5.30278	−0.492350
$117$	6.39445	0.591167
$118$	13.8167	1.27193
$119$	−22.8167	−2.09160
$120$	−1.30278	−0.118927
$121$	1.00000	0.0909091
$122$	−6.60555	−0.598039
$123$	7.81665	0.704804
$124$	0.605551	0.0543801
$125$	−1.00000	−0.0894427
$126$	−4.30278	−0.383322
$127$	12.6056	1.11856	0.559281	−	0.828978i	$-0.311077\pi$
$127$	12.6056	1.11856	0.559281	+	0.828978i	$0.311077\pi$
$128$	−1.00000	−0.0883883
$129$	−6.78890	−0.597729
$130$	−4.90833	−0.430489
$131$	0.486122	0.0424727	0.0212363	−	0.999774i	$-0.493240\pi$
$131$	0.486122	0.0424727	0.0212363	+	0.999774i	$0.493240\pi$
$132$	−1.30278	−0.113392
$133$	13.2111	1.14555
$134$	−1.30278	−0.112543
$135$	−5.60555	−0.482449
$136$	−6.90833	−0.592384
$137$	−3.90833	−0.333911	−0.166955	−	0.985964i	$-0.553394\pi$
$137$	−3.90833	−0.333911	−0.166955	+	0.985964i	$0.553394\pi$
$138$	−3.00000	−0.255377
$139$	−10.9083	−0.925232	−0.462616	−	0.886559i	$-0.653089\pi$
$139$	−10.9083	−0.925232	−0.462616	+	0.886559i	$0.653089\pi$
$140$	3.30278	0.279135
$141$	−4.18335	−0.352301
$142$	−14.5139	−1.21798
$143$	−4.90833	−0.410455
$144$	−1.30278	−0.108565
$145$	5.30278	0.440372
$146$	−1.00000	−0.0827606
$147$	−5.09167	−0.419954
$148$	8.90833	0.732260
$149$	−1.39445	−0.114238	−0.0571188	−	0.998367i	$-0.518191\pi$
$149$	−1.39445	−0.114238	−0.0571188	+	0.998367i	$0.518191\pi$
$150$	1.30278	0.106371
$151$	−4.90833	−0.399434	−0.199717	−	0.979854i	$-0.564002\pi$
$151$	−4.90833	−0.399434	−0.199717	+	0.979854i	$0.564002\pi$
$152$	4.00000	0.324443
$153$	−9.00000	−0.727607
$154$	3.30278	0.266145
$155$	−0.605551	−0.0486390
$156$	6.39445	0.511966
$157$	−6.78890	−0.541813	−0.270907	−	0.962606i	$-0.587323\pi$
$157$	−6.78890	−0.541813	−0.270907	+	0.962606i	$0.587323\pi$
$158$	−11.2111	−0.891907
$159$	0	0
$160$	1.00000	0.0790569
$161$	7.60555	0.599401
$162$	3.39445	0.266693
$163$	8.00000	0.626608	0.313304	−	0.949653i	$-0.398564\pi$
$163$	8.00000	0.626608	0.313304	+	0.949653i	$0.398564\pi$
$164$	−6.00000	−0.468521
$165$	1.30278	0.101421
$166$	−6.69722	−0.519805
$167$	12.0000	0.928588	0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000	0.928588	0.464294	+	0.885681i	$0.346308\pi$
$168$	−4.30278	−0.331966
$169$	11.0917	0.853206
$170$	6.90833	0.529844
$171$	5.21110	0.398503
$172$	5.21110	0.397343
$173$	−3.21110	−0.244136	−0.122068	−	0.992522i	$-0.538953\pi$
$173$	−3.21110	−0.244136	−0.122068	+	0.992522i	$0.538953\pi$
$174$	−6.90833	−0.523719
$175$	−3.30278	−0.249666
$176$	1.00000	0.0753778
$177$	18.0000	1.35296
$178$	14.7250	1.10368
$179$	−3.21110	−0.240009	−0.120005	−	0.992773i	$-0.538291\pi$
$179$	−3.21110	−0.240009	−0.120005	+	0.992773i	$0.538291\pi$
$180$	1.30278	0.0971032
$181$	−7.90833	−0.587821	−0.293911	−	0.955833i	$-0.594957\pi$
$181$	−7.90833	−0.587821	−0.293911	+	0.955833i	$0.594957\pi$
$182$	−16.2111	−1.20165
$183$	−8.60555	−0.636141
$184$	2.30278	0.169763
$185$	−8.90833	−0.654953
$186$	0.788897	0.0578448
$187$	6.90833	0.505187
$188$	3.21110	0.234194
$189$	−18.5139	−1.34669
$190$	−4.00000	−0.290191
$191$	−17.0278	−1.23209	−0.616043	−	0.787713i	$-0.711265\pi$
$191$	−17.0278	−1.23209	−0.616043	+	0.787713i	$0.711265\pi$
$192$	−1.30278	−0.0940197
$193$	1.09167	0.0785803	0.0392902	−	0.999228i	$-0.487490\pi$
$193$	1.09167	0.0785803	0.0392902	+	0.999228i	$0.487490\pi$
$194$	1.48612	0.106697
$195$	−6.39445	−0.457916
$196$	3.90833	0.279166
$197$	12.6972	0.904640	0.452320	−	0.891856i	$-0.350597\pi$
$197$	12.6972	0.904640	0.452320	+	0.891856i	$0.350597\pi$
$198$	1.30278	0.0925842
$199$	3.81665	0.270555	0.135278	−	0.990808i	$-0.456807\pi$
$199$	3.81665	0.270555	0.135278	+	0.990808i	$0.456807\pi$
$200$	−1.00000	−0.0707107
$201$	−1.69722	−0.119713
$202$	−5.30278	−0.373102
$203$	17.5139	1.22923
$204$	−9.00000	−0.630126
$205$	6.00000	0.419058
$206$	11.3944	0.793889
$207$	3.00000	0.208514
$208$	−4.90833	−0.340331
$209$	−4.00000	−0.276686
$210$	4.30278	0.296920
$211$	−13.2111	−0.909490	−0.454745	−	0.890622i	$-0.650270\pi$
$211$	−13.2111	−0.909490	−0.454745	+	0.890622i	$0.650270\pi$
$212$	0	0
$213$	−18.9083	−1.29558
$214$	−17.5139	−1.19722
$215$	−5.21110	−0.355394
$216$	−5.60555	−0.381409
$217$	−2.00000	−0.135769
$218$	−14.4222	−0.976795
$219$	−1.30278	−0.0880334
$220$	−1.00000	−0.0674200
$221$	−33.9083	−2.28092
$222$	11.6056	0.778914
$223$	13.0917	0.876683	0.438342	−	0.898808i	$-0.355566\pi$
$223$	13.0917	0.876683	0.438342	+	0.898808i	$0.355566\pi$
$224$	3.30278	0.220676
$225$	−1.30278	−0.0868517
$226$	−6.00000	−0.399114
$227$	−4.18335	−0.277658	−0.138829	−	0.990316i	$-0.544334\pi$
$227$	−4.18335	−0.277658	−0.138829	+	0.990316i	$0.544334\pi$
$228$	5.21110	0.345114
$229$	−20.6056	−1.36165	−0.680827	−	0.732445i	$-0.738379\pi$
$229$	−20.6056	−1.36165	−0.680827	+	0.732445i	$0.738379\pi$
$230$	−2.30278	−0.151841
$231$	4.30278	0.283102
$232$	5.30278	0.348144
$233$	0.422205	0.0276596	0.0138298	−	0.999904i	$-0.495598\pi$
$233$	0.422205	0.0276596	0.0138298	+	0.999904i	$0.495598\pi$
$234$	−6.39445	−0.418018
$235$	−3.21110	−0.209469
$236$	−13.8167	−0.899388
$237$	−14.6056	−0.948733
$238$	22.8167	1.47898
$239$	20.3028	1.31328	0.656639	−	0.754205i	$-0.271978\pi$
$239$	20.3028	1.31328	0.656639	+	0.754205i	$0.271978\pi$
$240$	1.30278	0.0840938
$241$	14.0000	0.901819	0.450910	−	0.892570i	$-0.351100\pi$
$241$	14.0000	0.901819	0.450910	+	0.892570i	$0.351100\pi$
$242$	−1.00000	−0.0642824
$243$	−12.3944	−0.795104
$244$	6.60555	0.422877
$245$	−3.90833	−0.249694
$246$	−7.81665	−0.498372
$247$	19.6333	1.24924
$248$	−0.605551	−0.0384525
$249$	−8.72498	−0.552923
$250$	1.00000	0.0632456
$251$	25.5416	1.61217	0.806087	−	0.591797i	$-0.201581\pi$
$251$	25.5416	1.61217	0.806087	+	0.591797i	$0.201581\pi$
$252$	4.30278	0.271049
$253$	−2.30278	−0.144774
$254$	−12.6056	−0.790943
$255$	9.00000	0.563602
$256$	1.00000	0.0625000
$257$	−21.6333	−1.34945	−0.674724	−	0.738070i	$-0.735737\pi$
$257$	−21.6333	−1.34945	−0.674724	+	0.738070i	$0.735737\pi$
$258$	6.78890	0.422658
$259$	−29.4222	−1.82821
$260$	4.90833	0.304402
$261$	6.90833	0.427615
$262$	−0.486122	−0.0300327
$263$	−0.697224	−0.0429927	−0.0214963	−	0.999769i	$-0.506843\pi$
$263$	−0.697224	−0.0429927	−0.0214963	+	0.999769i	$0.506843\pi$
$264$	1.30278	0.0801803
$265$	0	0
$266$	−13.2111	−0.810025
$267$	19.1833	1.17400
$268$	1.30278	0.0795797
$269$	−26.5139	−1.61658	−0.808290	−	0.588785i	$-0.799607\pi$
$269$	−26.5139	−1.61658	−0.808290	+	0.588785i	$0.799607\pi$
$270$	5.60555	0.341143
$271$	−21.3028	−1.29405	−0.647026	−	0.762468i	$-0.723987\pi$
$271$	−21.3028	−1.29405	−0.647026	+	0.762468i	$0.723987\pi$
$272$	6.90833	0.418879
$273$	−21.1194	−1.27821
$274$	3.90833	0.236111
$275$	1.00000	0.0603023
$276$	3.00000	0.180579
$277$	−6.09167	−0.366013	−0.183007	−	0.983112i	$-0.558583\pi$
$277$	−6.09167	−0.366013	−0.183007	+	0.983112i	$0.558583\pi$
$278$	10.9083	0.654238
$279$	−0.788897	−0.0472301
$280$	−3.30278	−0.197379
$281$	−24.9083	−1.48591	−0.742953	−	0.669343i	$-0.766575\pi$
$281$	−24.9083	−1.48591	−0.742953	+	0.669343i	$0.766575\pi$
$282$	4.18335	0.249115
$283$	−16.4222	−0.976199	−0.488099	−	0.872788i	$-0.662310\pi$
$283$	−16.4222	−0.976199	−0.488099	+	0.872788i	$0.662310\pi$
$284$	14.5139	0.861240
$285$	−5.21110	−0.308679
$286$	4.90833	0.290235
$287$	19.8167	1.16974
$288$	1.30278	0.0767668
$289$	30.7250	1.80735
$290$	−5.30278	−0.311390
$291$	1.93608	0.113495
$292$	1.00000	0.0585206
$293$	27.6333	1.61436	0.807178	−	0.590309i	$-0.200994\pi$
$293$	27.6333	1.61436	0.807178	+	0.590309i	$0.200994\pi$
$294$	5.09167	0.296952
$295$	13.8167	0.804437
$296$	−8.90833	−0.517786
$297$	5.60555	0.325267
$298$	1.39445	0.0807782
$299$	11.3028	0.653656
$300$	−1.30278	−0.0752158
$301$	−17.2111	−0.992031
$302$	4.90833	0.282442
$303$	−6.90833	−0.396873
$304$	−4.00000	−0.229416
$305$	−6.60555	−0.378233
$306$	9.00000	0.514496
$307$	1.30278	0.0743533	0.0371767	−	0.999309i	$-0.488164\pi$
$307$	1.30278	0.0743533	0.0371767	+	0.999309i	$0.488164\pi$
$308$	−3.30278	−0.188193
$309$	14.8444	0.844469
$310$	0.605551	0.0343930
$311$	−24.0000	−1.36092	−0.680458	−	0.732787i	$-0.738219\pi$
$311$	−24.0000	−1.36092	−0.680458	+	0.732787i	$0.738219\pi$
$312$	−6.39445	−0.362014
$313$	2.42221	0.136911	0.0684556	−	0.997654i	$-0.478193\pi$
$313$	2.42221	0.136911	0.0684556	+	0.997654i	$0.478193\pi$
$314$	6.78890	0.383120
$315$	−4.30278	−0.242434
$316$	11.2111	0.630674
$317$	2.72498	0.153050	0.0765251	−	0.997068i	$-0.475617\pi$
$317$	2.72498	0.153050	0.0765251	+	0.997068i	$0.475617\pi$
$318$	0	0
$319$	−5.30278	−0.296898
$320$	−1.00000	−0.0559017
$321$	−22.8167	−1.27350
$322$	−7.60555	−0.423841
$323$	−27.6333	−1.53756
$324$	−3.39445	−0.188580
$325$	−4.90833	−0.272265
$326$	−8.00000	−0.443079
$327$	−18.7889	−1.03903
$328$	6.00000	0.331295
$329$	−10.6056	−0.584703
$330$	−1.30278	−0.0717154
$331$	17.6333	0.969214	0.484607	−	0.874732i	$-0.338963\pi$
$331$	17.6333	0.969214	0.484607	+	0.874732i	$0.338963\pi$
$332$	6.69722	0.367558
$333$	−11.6056	−0.635980
$334$	−12.0000	−0.656611
$335$	−1.30278	−0.0711782
$336$	4.30278	0.234736
$337$	−3.72498	−0.202913	−0.101456	−	0.994840i	$-0.532350\pi$
$337$	−3.72498	−0.202913	−0.101456	+	0.994840i	$0.532350\pi$
$338$	−11.0917	−0.603307
$339$	−7.81665	−0.424542
$340$	−6.90833	−0.374657
$341$	0.605551	0.0327924
$342$	−5.21110	−0.281784
$343$	10.2111	0.551348
$344$	−5.21110	−0.280964
$345$	−3.00000	−0.161515
$346$	3.21110	0.172630
$347$	21.6333	1.16134	0.580668	−	0.814140i	$-0.302791\pi$
$347$	21.6333	1.16134	0.580668	+	0.814140i	$0.302791\pi$
$348$	6.90833	0.370325
$349$	4.78890	0.256344	0.128172	−	0.991752i	$-0.459089\pi$
$349$	4.78890	0.256344	0.128172	+	0.991752i	$0.459089\pi$
$350$	3.30278	0.176541
$351$	−27.5139	−1.46858
$352$	−1.00000	−0.0533002
$353$	15.9083	0.846715	0.423357	−	0.905963i	$-0.360851\pi$
$353$	15.9083	0.846715	0.423357	+	0.905963i	$0.360851\pi$
$354$	−18.0000	−0.956689
$355$	−14.5139	−0.770317
$356$	−14.7250	−0.780422
$357$	29.7250	1.57321
$358$	3.21110	0.169712
$359$	−17.0278	−0.898691	−0.449345	−	0.893358i	$-0.648343\pi$
$359$	−17.0278	−0.898691	−0.449345	+	0.893358i	$0.648343\pi$
$360$	−1.30278	−0.0686623
$361$	−3.00000	−0.157895
$362$	7.90833	0.415652
$363$	−1.30278	−0.0683780
$364$	16.2111	0.849693
$365$	−1.00000	−0.0523424
$366$	8.60555	0.449819
$367$	−35.7527	−1.86628	−0.933139	−	0.359516i	$-0.882942\pi$
$367$	−35.7527	−1.86628	−0.933139	+	0.359516i	$0.882942\pi$
$368$	−2.30278	−0.120040
$369$	7.81665	0.406919
$370$	8.90833	0.463122
$371$	0	0
$372$	−0.788897	−0.0409024
$373$	−17.3944	−0.900650	−0.450325	−	0.892865i	$-0.648692\pi$
$373$	−17.3944	−0.900650	−0.450325	+	0.892865i	$0.648692\pi$
$374$	−6.90833	−0.357221
$375$	1.30278	0.0672750
$376$	−3.21110	−0.165600
$377$	26.0278	1.34050
$378$	18.5139	0.952251
$379$	14.4222	0.740819	0.370409	−	0.928869i	$-0.379217\pi$
$379$	14.4222	0.740819	0.370409	+	0.928869i	$0.379217\pi$
$380$	4.00000	0.205196
$381$	−16.4222	−0.841335
$382$	17.0278	0.871216
$383$	−9.21110	−0.470665	−0.235333	−	0.971915i	$-0.575618\pi$
$383$	−9.21110	−0.470665	−0.235333	+	0.971915i	$0.575618\pi$
$384$	1.30278	0.0664820
$385$	3.30278	0.168325
$386$	−1.09167	−0.0555647
$387$	−6.78890	−0.345099
$388$	−1.48612	−0.0754464
$389$	18.9083	0.958690	0.479345	−	0.877626i	$-0.340874\pi$
$389$	18.9083	0.958690	0.479345	+	0.877626i	$0.340874\pi$
$390$	6.39445	0.323795
$391$	−15.9083	−0.804519
$392$	−3.90833	−0.197400
$393$	−0.633308	−0.0319461
$394$	−12.6972	−0.639677
$395$	−11.2111	−0.564092
$396$	−1.30278	−0.0654669
$397$	−3.09167	−0.155167	−0.0775833	−	0.996986i	$-0.524720\pi$
$397$	−3.09167	−0.155167	−0.0775833	+	0.996986i	$0.524720\pi$
$398$	−3.81665	−0.191312
$399$	−17.2111	−0.861633
$400$	1.00000	0.0500000
$401$	−24.6972	−1.23332	−0.616660	−	0.787229i	$-0.711515\pi$
$401$	−24.6972	−1.23332	−0.616660	+	0.787229i	$0.711515\pi$
$402$	1.69722	0.0846499
$403$	−2.97224	−0.148058
$404$	5.30278	0.263823
$405$	3.39445	0.168672
$406$	−17.5139	−0.869199
$407$	8.90833	0.441569
$408$	9.00000	0.445566
$409$	12.3305	0.609706	0.304853	−	0.952399i	$-0.401393\pi$
$409$	12.3305	0.609706	0.304853	+	0.952399i	$0.401393\pi$
$410$	−6.00000	−0.296319
$411$	5.09167	0.251154
$412$	−11.3944	−0.561364
$413$	45.6333	2.24547
$414$	−3.00000	−0.147442
$415$	−6.69722	−0.328754
$416$	4.90833	0.240651
$417$	14.2111	0.695921
$418$	4.00000	0.195646
$419$	23.3028	1.13842	0.569208	−	0.822194i	$-0.307250\pi$
$419$	23.3028	1.13842	0.569208	+	0.822194i	$0.307250\pi$
$420$	−4.30278	−0.209954
$421$	8.00000	0.389896	0.194948	−	0.980814i	$-0.437546\pi$
$421$	8.00000	0.389896	0.194948	+	0.980814i	$0.437546\pi$
$422$	13.2111	0.643106
$423$	−4.18335	−0.203401
$424$	0	0
$425$	6.90833	0.335103
$426$	18.9083	0.916111
$427$	−21.8167	−1.05578
$428$	17.5139	0.846565
$429$	6.39445	0.308727
$430$	5.21110	0.251302
$431$	−8.30278	−0.399931	−0.199965	−	0.979803i	$-0.564083\pi$
$431$	−8.30278	−0.399931	−0.199965	+	0.979803i	$0.564083\pi$
$432$	5.60555	0.269697
$433$	21.8167	1.04844	0.524221	−	0.851582i	$-0.324357\pi$
$433$	21.8167	1.04844	0.524221	+	0.851582i	$0.324357\pi$
$434$	2.00000	0.0960031
$435$	−6.90833	−0.331229
$436$	14.4222	0.690698
$437$	9.21110	0.440627
$438$	1.30278	0.0622490
$439$	41.2111	1.96690	0.983449	−	0.181184i	$-0.0579928\pi$
$439$	41.2111	1.96690	0.983449	+	0.181184i	$0.0579928\pi$
$440$	1.00000	0.0476731
$441$	−5.09167	−0.242461
$442$	33.9083	1.61285
$443$	−29.0278	−1.37915	−0.689575	−	0.724214i	$-0.742203\pi$
$443$	−29.0278	−1.37915	−0.689575	+	0.724214i	$0.742203\pi$
$444$	−11.6056	−0.550775
$445$	14.7250	0.698031
$446$	−13.0917	−0.619909
$447$	1.81665	0.0859248
$448$	−3.30278	−0.156041
$449$	−12.0000	−0.566315	−0.283158	−	0.959073i	$-0.591382\pi$
$449$	−12.0000	−0.566315	−0.283158	+	0.959073i	$0.591382\pi$
$450$	1.30278	0.0614134
$451$	−6.00000	−0.282529
$452$	6.00000	0.282216
$453$	6.39445	0.300437
$454$	4.18335	0.196334
$455$	−16.2111	−0.759988
$456$	−5.21110	−0.244032
$457$	−37.6333	−1.76041	−0.880206	−	0.474592i	$-0.842596\pi$
$457$	−37.6333	−1.76041	−0.880206	+	0.474592i	$0.842596\pi$
$458$	20.6056	0.962834
$459$	38.7250	1.80753
$460$	2.30278	0.107367
$461$	6.00000	0.279448	0.139724	−	0.990190i	$-0.455378\pi$
$461$	6.00000	0.279448	0.139724	+	0.990190i	$0.455378\pi$
$462$	−4.30278	−0.200183
$463$	−9.93608	−0.461769	−0.230884	−	0.972981i	$-0.574162\pi$
$463$	−9.93608	−0.461769	−0.230884	+	0.972981i	$0.574162\pi$
$464$	−5.30278	−0.246175
$465$	0.788897	0.0365842
$466$	−0.422205	−0.0195583
$467$	12.0000	0.555294	0.277647	−	0.960683i	$-0.410445\pi$
$467$	12.0000	0.555294	0.277647	+	0.960683i	$0.410445\pi$
$468$	6.39445	0.295583
$469$	−4.30278	−0.198684
$470$	3.21110	0.148117
$471$	8.84441	0.407529
$472$	13.8167	0.635963
$473$	5.21110	0.239607
$474$	14.6056	0.670855
$475$	−4.00000	−0.183533
$476$	−22.8167	−1.04580
$477$	0	0
$478$	−20.3028	−0.928627
$479$	33.2111	1.51745	0.758727	−	0.651409i	$-0.225822\pi$
$479$	33.2111	1.51745	0.758727	+	0.651409i	$0.225822\pi$
$480$	−1.30278	−0.0594633
$481$	−43.7250	−1.99369
$482$	−14.0000	−0.637683
$483$	−9.90833	−0.450844
$484$	1.00000	0.0454545
$485$	1.48612	0.0674813
$486$	12.3944	0.562224
$487$	36.3305	1.64629	0.823147	−	0.567829i	$-0.192216\pi$
$487$	36.3305	1.64629	0.823147	+	0.567829i	$0.192216\pi$
$488$	−6.60555	−0.299019
$489$	−10.4222	−0.471308
$490$	3.90833	0.176560
$491$	17.7250	0.799917	0.399959	−	0.916533i	$-0.369025\pi$
$491$	17.7250	0.799917	0.399959	+	0.916533i	$0.369025\pi$
$492$	7.81665	0.352402
$493$	−36.6333	−1.64988
$494$	−19.6333	−0.883344
$495$	1.30278	0.0585554
$496$	0.605551	0.0271901
$497$	−47.9361	−2.15023
$498$	8.72498	0.390976
$499$	33.3305	1.49208	0.746040	−	0.665901i	$-0.231953\pi$
$499$	33.3305	1.49208	0.746040	+	0.665901i	$0.231953\pi$
$500$	−1.00000	−0.0447214
$501$	−15.6333	−0.698445
$502$	−25.5416	−1.13998
$503$	−30.0000	−1.33763	−0.668817	−	0.743427i	$-0.733199\pi$
$503$	−30.0000	−1.33763	−0.668817	+	0.743427i	$0.733199\pi$
$504$	−4.30278	−0.191661
$505$	−5.30278	−0.235970
$506$	2.30278	0.102371
$507$	−14.4500	−0.641745
$508$	12.6056	0.559281
$509$	9.69722	0.429822	0.214911	−	0.976634i	$-0.431054\pi$
$509$	9.69722	0.429822	0.214911	+	0.976634i	$0.431054\pi$
$510$	−9.00000	−0.398527
$511$	−3.30278	−0.146106
$512$	−1.00000	−0.0441942
$513$	−22.4222	−0.989965
$514$	21.6333	0.954204
$515$	11.3944	0.502099
$516$	−6.78890	−0.298865
$517$	3.21110	0.141224
$518$	29.4222	1.29274
$519$	4.18335	0.183629
$520$	−4.90833	−0.215244
$521$	10.1833	0.446140	0.223070	−	0.974802i	$-0.428392\pi$
$521$	10.1833	0.446140	0.223070	+	0.974802i	$0.428392\pi$
$522$	−6.90833	−0.302369
$523$	−25.6333	−1.12087	−0.560433	−	0.828200i	$-0.689365\pi$
$523$	−25.6333	−1.12087	−0.560433	+	0.828200i	$0.689365\pi$
$524$	0.486122	0.0212363
$525$	4.30278	0.187789
$526$	0.697224	0.0304004
$527$	4.18335	0.182229
$528$	−1.30278	−0.0566960
$529$	−17.6972	−0.769445
$530$	0	0
$531$	18.0000	0.781133
$532$	13.2111	0.572774
$533$	29.4500	1.27562
$534$	−19.1833	−0.830145
$535$	−17.5139	−0.757191
$536$	−1.30278	−0.0562713
$537$	4.18335	0.180525
$538$	26.5139	1.14309
$539$	3.90833	0.168344
$540$	−5.60555	−0.241225
$541$	17.4861	0.751787	0.375894	−	0.926663i	$-0.377336\pi$
$541$	17.4861	0.751787	0.375894	+	0.926663i	$0.377336\pi$
$542$	21.3028	0.915033
$543$	10.3028	0.442134
$544$	−6.90833	−0.296192
$545$	−14.4222	−0.617779
$546$	21.1194	0.903828
$547$	−19.6333	−0.839460	−0.419730	−	0.907649i	$-0.637875\pi$
$547$	−19.6333	−0.839460	−0.419730	+	0.907649i	$0.637875\pi$
$548$	−3.90833	−0.166955
$549$	−8.60555	−0.367276
$550$	−1.00000	−0.0426401
$551$	21.2111	0.903623
$552$	−3.00000	−0.127688
$553$	−37.0278	−1.57458
$554$	6.09167	0.258810
$555$	11.6056	0.492628
$556$	−10.9083	−0.462616
$557$	−33.6333	−1.42509	−0.712544	−	0.701627i	$-0.752457\pi$
$557$	−33.6333	−1.42509	−0.712544	+	0.701627i	$0.752457\pi$
$558$	0.788897	0.0333967
$559$	−25.5778	−1.08183
$560$	3.30278	0.139568
$561$	−9.00000	−0.379980
$562$	24.9083	1.05069
$563$	−13.1194	−0.552918	−0.276459	−	0.961026i	$-0.589161\pi$
$563$	−13.1194	−0.552918	−0.276459	+	0.961026i	$0.589161\pi$
$564$	−4.18335	−0.176151
$565$	−6.00000	−0.252422
$566$	16.4222	0.690277
$567$	11.2111	0.470822
$568$	−14.5139	−0.608989
$569$	−20.5139	−0.859987	−0.429993	−	0.902832i	$-0.641484\pi$
$569$	−20.5139	−0.859987	−0.429993	+	0.902832i	$0.641484\pi$
$570$	5.21110	0.218269
$571$	7.51388	0.314446	0.157223	−	0.987563i	$-0.449746\pi$
$571$	7.51388	0.314446	0.157223	+	0.987563i	$0.449746\pi$
$572$	−4.90833	−0.205227
$573$	22.1833	0.926723
$574$	−19.8167	−0.827131
$575$	−2.30278	−0.0960324
$576$	−1.30278	−0.0542823
$577$	−16.4222	−0.683665	−0.341833	−	0.939761i	$-0.611048\pi$
$577$	−16.4222	−0.683665	−0.341833	+	0.939761i	$0.611048\pi$
$578$	−30.7250	−1.27799
$579$	−1.42221	−0.0591048
$580$	5.30278	0.220186
$581$	−22.1194	−0.917669
$582$	−1.93608	−0.0802532
$583$	0	0
$584$	−1.00000	−0.0413803
$585$	−6.39445	−0.264378
$586$	−27.6333	−1.14152
$587$	2.51388	0.103759	0.0518794	−	0.998653i	$-0.483479\pi$
$587$	2.51388	0.103759	0.0518794	+	0.998653i	$0.483479\pi$
$588$	−5.09167	−0.209977
$589$	−2.42221	−0.0998052
$590$	−13.8167	−0.568823
$591$	−16.5416	−0.680432
$592$	8.90833	0.366130
$593$	10.1833	0.418180	0.209090	−	0.977896i	$-0.432950\pi$
$593$	10.1833	0.418180	0.209090	+	0.977896i	$0.432950\pi$
$594$	−5.60555	−0.229999
$595$	22.8167	0.935392
$596$	−1.39445	−0.0571188
$597$	−4.97224	−0.203500
$598$	−11.3028	−0.462205
$599$	−25.8167	−1.05484	−0.527420	−	0.849605i	$-0.676841\pi$
$599$	−25.8167	−1.05484	−0.527420	+	0.849605i	$0.676841\pi$
$600$	1.30278	0.0531856
$601$	−16.9083	−0.689705	−0.344853	−	0.938657i	$-0.612071\pi$
$601$	−16.9083	−0.689705	−0.344853	+	0.938657i	$0.612071\pi$
$602$	17.2111	0.701472
$603$	−1.69722	−0.0691163
$604$	−4.90833	−0.199717
$605$	−1.00000	−0.0406558
$606$	6.90833	0.280632
$607$	−22.0000	−0.892952	−0.446476	−	0.894795i	$-0.647321\pi$
$607$	−22.0000	−0.892952	−0.446476	+	0.894795i	$0.647321\pi$
$608$	4.00000	0.162221
$609$	−22.8167	−0.924577
$610$	6.60555	0.267451
$611$	−15.7611	−0.637628
$612$	−9.00000	−0.363803
$613$	−18.7250	−0.756295	−0.378147	−	0.925745i	$-0.623439\pi$
$613$	−18.7250	−0.756295	−0.378147	+	0.925745i	$0.623439\pi$
$614$	−1.30278	−0.0525757
$615$	−7.81665	−0.315198
$616$	3.30278	0.133073
$617$	−28.6056	−1.15162	−0.575808	−	0.817585i	$-0.695312\pi$
$617$	−28.6056	−1.15162	−0.575808	+	0.817585i	$0.695312\pi$
$618$	−14.8444	−0.597130
$619$	−30.3028	−1.21797	−0.608986	−	0.793181i	$-0.708423\pi$
$619$	−30.3028	−1.21797	−0.608986	+	0.793181i	$0.708423\pi$
$620$	−0.605551	−0.0243195
$621$	−12.9083	−0.517993
$622$	24.0000	0.962312
$623$	48.6333	1.94845
$624$	6.39445	0.255983
$625$	1.00000	0.0400000
$626$	−2.42221	−0.0968108
$627$	5.21110	0.208111
$628$	−6.78890	−0.270907
$629$	61.5416	2.45383
$630$	4.30278	0.171427
$631$	−26.1833	−1.04234	−0.521171	−	0.853452i	$-0.674505\pi$
$631$	−26.1833	−1.04234	−0.521171	+	0.853452i	$0.674505\pi$
$632$	−11.2111	−0.445954
$633$	17.2111	0.684080
$634$	−2.72498	−0.108223
$635$	−12.6056	−0.500236
$636$	0	0
$637$	−19.1833	−0.760072
$638$	5.30278	0.209939
$639$	−18.9083	−0.748002
$640$	1.00000	0.0395285
$641$	−11.3028	−0.446433	−0.223216	−	0.974769i	$-0.571656\pi$
$641$	−11.3028	−0.446433	−0.223216	+	0.974769i	$0.571656\pi$
$642$	22.8167	0.900501
$643$	3.39445	0.133864	0.0669320	−	0.997758i	$-0.478679\pi$
$643$	3.39445	0.133864	0.0669320	+	0.997758i	$0.478679\pi$
$644$	7.60555	0.299701
$645$	6.78890	0.267313
$646$	27.6333	1.08722
$647$	−16.6056	−0.652832	−0.326416	−	0.945226i	$-0.605841\pi$
$647$	−16.6056	−0.652832	−0.326416	+	0.945226i	$0.605841\pi$
$648$	3.39445	0.133347
$649$	−13.8167	−0.542351
$650$	4.90833	0.192520
$651$	2.60555	0.102120
$652$	8.00000	0.313304
$653$	0.697224	0.0272845	0.0136422	−	0.999907i	$-0.495657\pi$
$653$	0.697224	0.0272845	0.0136422	+	0.999907i	$0.495657\pi$
$654$	18.7889	0.734704
$655$	−0.486122	−0.0189944
$656$	−6.00000	−0.234261
$657$	−1.30278	−0.0508261
$658$	10.6056	0.413447
$659$	−32.2389	−1.25585	−0.627924	−	0.778275i	$-0.716095\pi$
$659$	−32.2389	−1.25585	−0.627924	+	0.778275i	$0.716095\pi$
$660$	1.30278	0.0507105
$661$	−11.8806	−0.462101	−0.231050	−	0.972942i	$-0.574216\pi$
$661$	−11.8806	−0.462101	−0.231050	+	0.972942i	$0.574216\pi$
$662$	−17.6333	−0.685338
$663$	44.1749	1.71561
$664$	−6.69722	−0.259903
$665$	−13.2111	−0.512305
$666$	11.6056	0.449706
$667$	12.2111	0.472816
$668$	12.0000	0.464294
$669$	−17.0555	−0.659404
$670$	1.30278	0.0503306
$671$	6.60555	0.255004
$672$	−4.30278	−0.165983
$673$	−48.2389	−1.85947	−0.929736	−	0.368228i	$-0.879965\pi$
$673$	−48.2389	−1.85947	−0.929736	+	0.368228i	$0.879965\pi$
$674$	3.72498	0.143481
$675$	5.60555	0.215758
$676$	11.0917	0.426603
$677$	11.9361	0.458741	0.229370	−	0.973339i	$-0.426333\pi$
$677$	11.9361	0.458741	0.229370	+	0.973339i	$0.426333\pi$
$678$	7.81665	0.300197
$679$	4.90833	0.188364
$680$	6.90833	0.264922
$681$	5.44996	0.208843
$682$	−0.605551	−0.0231878
$683$	21.2111	0.811620	0.405810	−	0.913957i	$-0.366989\pi$
$683$	21.2111	0.811620	0.405810	+	0.913957i	$0.366989\pi$
$684$	5.21110	0.199251
$685$	3.90833	0.149329
$686$	−10.2111	−0.389862
$687$	26.8444	1.02418
$688$	5.21110	0.198671
$689$	0	0
$690$	3.00000	0.114208
$691$	−17.3944	−0.661716	−0.330858	−	0.943681i	$-0.607338\pi$
$691$	−17.3944	−0.661716	−0.330858	+	0.943681i	$0.607338\pi$
$692$	−3.21110	−0.122068
$693$	4.30278	0.163449
$694$	−21.6333	−0.821189
$695$	10.9083	0.413776
$696$	−6.90833	−0.261859
$697$	−41.4500	−1.57003
$698$	−4.78890	−0.181262
$699$	−0.550039	−0.0208044
$700$	−3.30278	−0.124833
$701$	30.0000	1.13308	0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000	1.13308	0.566542	+	0.824033i	$0.308281\pi$
$702$	27.5139	1.03844
$703$	−35.6333	−1.34394
$704$	1.00000	0.0376889
$705$	4.18335	0.157554
$706$	−15.9083	−0.598718
$707$	−17.5139	−0.658677
$708$	18.0000	0.676481
$709$	−28.8444	−1.08327	−0.541637	−	0.840612i	$-0.682195\pi$
$709$	−28.8444	−1.08327	−0.541637	+	0.840612i	$0.682195\pi$
$710$	14.5139	0.544696
$711$	−14.6056	−0.547751
$712$	14.7250	0.551842
$713$	−1.39445	−0.0522225
$714$	−29.7250	−1.11243
$715$	4.90833	0.183561
$716$	−3.21110	−0.120005
$717$	−26.4500	−0.987792
$718$	17.0278	0.635470
$719$	−21.6333	−0.806786	−0.403393	−	0.915027i	$-0.632169\pi$
$719$	−21.6333	−0.806786	−0.403393	+	0.915027i	$0.632169\pi$
$720$	1.30278	0.0485516
$721$	37.6333	1.40154
$722$	3.00000	0.111648
$723$	−18.2389	−0.678310
$724$	−7.90833	−0.293911
$725$	−5.30278	−0.196940
$726$	1.30278	0.0483505
$727$	7.30278	0.270845	0.135422	−	0.990788i	$-0.456761\pi$
$727$	7.30278	0.270845	0.135422	+	0.990788i	$0.456761\pi$
$728$	−16.2111	−0.600823
$729$	26.3305	0.975205
$730$	1.00000	0.0370117
$731$	36.0000	1.33151
$732$	−8.60555	−0.318070
$733$	18.1833	0.671617	0.335809	−	0.941930i	$-0.390990\pi$
$733$	18.1833	0.671617	0.335809	+	0.941930i	$0.390990\pi$
$734$	35.7527	1.31966
$735$	5.09167	0.187809
$736$	2.30278	0.0848814
$737$	1.30278	0.0479884
$738$	−7.81665	−0.287735
$739$	−26.6056	−0.978701	−0.489351	−	0.872087i	$-0.662766\pi$
$739$	−26.6056	−0.978701	−0.489351	+	0.872087i	$0.662766\pi$
$740$	−8.90833	−0.327477
$741$	−25.5778	−0.939624
$742$	0	0
$743$	21.9083	0.803739	0.401869	−	0.915697i	$-0.368361\pi$
$743$	21.9083	0.803739	0.401869	+	0.915697i	$0.368361\pi$
$744$	0.788897	0.0289224
$745$	1.39445	0.0510886
$746$	17.3944	0.636856
$747$	−8.72498	−0.319230
$748$	6.90833	0.252593
$749$	−57.8444	−2.11359
$750$	−1.30278	−0.0475706
$751$	−0.788897	−0.0287873	−0.0143936	−	0.999896i	$-0.504582\pi$
$751$	−0.788897	−0.0287873	−0.0143936	+	0.999896i	$0.504582\pi$
$752$	3.21110	0.117097
$753$	−33.2750	−1.21261
$754$	−26.0278	−0.947875
$755$	4.90833	0.178632
$756$	−18.5139	−0.673343
$757$	17.9083	0.650889	0.325445	−	0.945561i	$-0.394486\pi$
$757$	17.9083	0.650889	0.325445	+	0.945561i	$0.394486\pi$
$758$	−14.4222	−0.523838
$759$	3.00000	0.108893
$760$	−4.00000	−0.145095
$761$	−21.1472	−0.766585	−0.383292	−	0.923627i	$-0.625210\pi$
$761$	−21.1472	−0.766585	−0.383292	+	0.923627i	$0.625210\pi$
$762$	16.4222	0.594914
$763$	−47.6333	−1.72444
$764$	−17.0278	−0.616043
$765$	9.00000	0.325396
$766$	9.21110	0.332811
$767$	67.8167	2.44872
$768$	−1.30278	−0.0470099
$769$	−39.9361	−1.44013	−0.720066	−	0.693906i	$-0.755888\pi$
$769$	−39.9361	−1.44013	−0.720066	+	0.693906i	$0.755888\pi$
$770$	−3.30278	−0.119024
$771$	28.1833	1.01500
$772$	1.09167	0.0392902
$773$	29.4500	1.05924	0.529621	−	0.848235i	$-0.322334\pi$
$773$	29.4500	1.05924	0.529621	+	0.848235i	$0.322334\pi$
$774$	6.78890	0.244022
$775$	0.605551	0.0217520
$776$	1.48612	0.0533487
$777$	38.3305	1.37510
$778$	−18.9083	−0.677896
$779$	24.0000	0.859889
$780$	−6.39445	−0.228958
$781$	14.5139	0.519347
$782$	15.9083	0.568881
$783$	−29.7250	−1.06228
$784$	3.90833	0.139583
$785$	6.78890	0.242306
$786$	0.633308	0.0225893
$787$	53.6333	1.91182	0.955910	−	0.293658i	$-0.0948728\pi$
$787$	53.6333	1.91182	0.955910	+	0.293658i	$0.0948728\pi$
$788$	12.6972	0.452320
$789$	0.908327	0.0323373
$790$	11.2111	0.398873
$791$	−19.8167	−0.704599
$792$	1.30278	0.0462921
$793$	−32.4222	−1.15135
$794$	3.09167	0.109719
$795$	0	0
$796$	3.81665	0.135278
$797$	−30.3583	−1.07535	−0.537673	−	0.843154i	$-0.680696\pi$
$797$	−30.3583	−1.07535	−0.537673	+	0.843154i	$0.680696\pi$
$798$	17.2111	0.609266
$799$	22.1833	0.784790
$800$	−1.00000	−0.0353553
$801$	19.1833	0.677810
$802$	24.6972	0.872089
$803$	1.00000	0.0352892
$804$	−1.69722	−0.0598565
$805$	−7.60555	−0.268060
$806$	2.97224	0.104693
$807$	34.5416	1.21592
$808$	−5.30278	−0.186551
$809$	20.2389	0.711560	0.355780	−	0.934570i	$-0.384215\pi$
$809$	20.2389	0.711560	0.355780	+	0.934570i	$0.384215\pi$
$810$	−3.39445	−0.119269
$811$	−1.21110	−0.0425276	−0.0212638	−	0.999774i	$-0.506769\pi$
$811$	−1.21110	−0.0425276	−0.0212638	+	0.999774i	$0.506769\pi$
$812$	17.5139	0.614617
$813$	27.7527	0.973331
$814$	−8.90833	−0.312237
$815$	−8.00000	−0.280228
$816$	−9.00000	−0.315063
$817$	−20.8444	−0.729254
$818$	−12.3305	−0.431127
$819$	−21.1194	−0.737973
$820$	6.00000	0.209529
$821$	26.7889	0.934939	0.467469	−	0.884009i	$-0.345166\pi$
$821$	26.7889	0.934939	0.467469	+	0.884009i	$0.345166\pi$
$822$	−5.09167	−0.177592
$823$	−27.0278	−0.942128	−0.471064	−	0.882099i	$-0.656130\pi$
$823$	−27.0278	−0.942128	−0.471064	+	0.882099i	$0.656130\pi$
$824$	11.3944	0.396944
$825$	−1.30278	−0.0453568
$826$	−45.6333	−1.58779
$827$	39.6333	1.37819	0.689093	−	0.724673i	$-0.258009\pi$
$827$	39.6333	1.37819	0.689093	+	0.724673i	$0.258009\pi$
$828$	3.00000	0.104257
$829$	−33.0278	−1.14710	−0.573551	−	0.819170i	$-0.694434\pi$
$829$	−33.0278	−1.14710	−0.573551	+	0.819170i	$0.694434\pi$
$830$	6.69722	0.232464
$831$	7.93608	0.275300
$832$	−4.90833	−0.170166
$833$	27.0000	0.935495
$834$	−14.2111	−0.492090
$835$	−12.0000	−0.415277
$836$	−4.00000	−0.138343
$837$	3.39445	0.117329
$838$	−23.3028	−0.804981
$839$	51.6333	1.78258	0.891290	−	0.453434i	$-0.149801\pi$
$839$	51.6333	1.78258	0.891290	+	0.453434i	$0.149801\pi$
$840$	4.30278	0.148460
$841$	−0.880571	−0.0303645
$842$	−8.00000	−0.275698
$843$	32.4500	1.11764
$844$	−13.2111	−0.454745
$845$	−11.0917	−0.381565
$846$	4.18335	0.143826
$847$	−3.30278	−0.113485
$848$	0	0
$849$	21.3944	0.734256
$850$	−6.90833	−0.236954
$851$	−20.5139	−0.703207
$852$	−18.9083	−0.647789
$853$	−16.8444	−0.576742	−0.288371	−	0.957519i	$-0.593114\pi$
$853$	−16.8444	−0.576742	−0.288371	+	0.957519i	$0.593114\pi$
$854$	21.8167	0.746551
$855$	−5.21110	−0.178216
$856$	−17.5139	−0.598612
$857$	−16.6056	−0.567235	−0.283617	−	0.958938i	$-0.591535\pi$
$857$	−16.6056	−0.567235	−0.283617	+	0.958938i	$0.591535\pi$
$858$	−6.39445	−0.218303
$859$	−4.97224	−0.169651	−0.0848254	−	0.996396i	$-0.527033\pi$
$859$	−4.97224	−0.169651	−0.0848254	+	0.996396i	$0.527033\pi$
$860$	−5.21110	−0.177697
$861$	−25.8167	−0.879829
$862$	8.30278	0.282794
$863$	−15.2111	−0.517792	−0.258896	−	0.965905i	$-0.583359\pi$
$863$	−15.2111	−0.517792	−0.258896	+	0.965905i	$0.583359\pi$
$864$	−5.60555	−0.190705
$865$	3.21110	0.109181
$866$	−21.8167	−0.741360
$867$	−40.0278	−1.35941
$868$	−2.00000	−0.0678844
$869$	11.2111	0.380311
$870$	6.90833	0.234214
$871$	−6.39445	−0.216668
$872$	−14.4222	−0.488397
$873$	1.93608	0.0655265
$874$	−9.21110	−0.311570
$875$	3.30278	0.111654
$876$	−1.30278	−0.0440167
$877$	44.4222	1.50003	0.750016	−	0.661420i	$-0.230046\pi$
$877$	44.4222	1.50003	0.750016	+	0.661420i	$0.230046\pi$
$878$	−41.2111	−1.39081
$879$	−36.0000	−1.21425
$880$	−1.00000	−0.0337100
$881$	−15.2111	−0.512475	−0.256238	−	0.966614i	$-0.582483\pi$
$881$	−15.2111	−0.512475	−0.256238	+	0.966614i	$0.582483\pi$
$882$	5.09167	0.171446
$883$	−48.2389	−1.62337	−0.811683	−	0.584098i	$-0.801449\pi$
$883$	−48.2389	−1.62337	−0.811683	+	0.584098i	$0.801449\pi$
$884$	−33.9083	−1.14046
$885$	−18.0000	−0.605063
$886$	29.0278	0.975207
$887$	−16.3305	−0.548326	−0.274163	−	0.961683i	$-0.588401\pi$
$887$	−16.3305	−0.548326	−0.274163	+	0.961683i	$0.588401\pi$
$888$	11.6056	0.389457
$889$	−41.6333	−1.39634
$890$	−14.7250	−0.493582
$891$	−3.39445	−0.113718
$892$	13.0917	0.438342
$893$	−12.8444	−0.429822
$894$	−1.81665	−0.0607580
$895$	3.21110	0.107335
$896$	3.30278	0.110338
$897$	−14.7250	−0.491653
$898$	12.0000	0.400445
$899$	−3.21110	−0.107096
$900$	−1.30278	−0.0434259
$901$	0	0
$902$	6.00000	0.199778
$903$	22.4222	0.746164
$904$	−6.00000	−0.199557
$905$	7.90833	0.262882
$906$	−6.39445	−0.212441
$907$	−28.0000	−0.929725	−0.464862	−	0.885383i	$-0.653896\pi$
$907$	−28.0000	−0.929725	−0.464862	+	0.885383i	$0.653896\pi$
$908$	−4.18335	−0.138829
$909$	−6.90833	−0.229135
$910$	16.2111	0.537393
$911$	47.9361	1.58819	0.794097	−	0.607792i	$-0.207944\pi$
$911$	47.9361	1.58819	0.794097	+	0.607792i	$0.207944\pi$
$912$	5.21110	0.172557
$913$	6.69722	0.221646
$914$	37.6333	1.24480
$915$	8.60555	0.284491
$916$	−20.6056	−0.680827
$917$	−1.60555	−0.0530200
$918$	−38.7250	−1.27811
$919$	−28.8444	−0.951489	−0.475745	−	0.879583i	$-0.657821\pi$
$919$	−28.8444	−0.951489	−0.475745	+	0.879583i	$0.657821\pi$
$920$	−2.30278	−0.0759203
$921$	−1.69722	−0.0559254
$922$	−6.00000	−0.197599
$923$	−71.2389	−2.34486
$924$	4.30278	0.141551
$925$	8.90833	0.292904
$926$	9.93608	0.326520
$927$	14.8444	0.487554
$928$	5.30278	0.174072
$929$	21.6333	0.709766	0.354883	−	0.934911i	$-0.384521\pi$
$929$	21.6333	0.709766	0.354883	+	0.934911i	$0.384521\pi$
$930$	−0.788897	−0.0258690
$931$	−15.6333	−0.512361
$932$	0.422205	0.0138298
$933$	31.2666	1.02362
$934$	−12.0000	−0.392652
$935$	−6.90833	−0.225926
$936$	−6.39445	−0.209009
$937$	−34.8444	−1.13832	−0.569159	−	0.822228i	$-0.692731\pi$
$937$	−34.8444	−1.13832	−0.569159	+	0.822228i	$0.692731\pi$
$938$	4.30278	0.140491
$939$	−3.15559	−0.102979
$940$	−3.21110	−0.104735
$941$	30.4222	0.991736	0.495868	−	0.868398i	$-0.334850\pi$
$941$	30.4222	0.991736	0.495868	+	0.868398i	$0.334850\pi$
$942$	−8.84441	−0.288166
$943$	13.8167	0.449932
$944$	−13.8167	−0.449694
$945$	18.5139	0.602257
$946$	−5.21110	−0.169428
$947$	−33.2111	−1.07922	−0.539608	−	0.841916i	$-0.681428\pi$
$947$	−33.2111	−1.07922	−0.539608	+	0.841916i	$0.681428\pi$
$948$	−14.6056	−0.474366
$949$	−4.90833	−0.159331
$950$	4.00000	0.129777
$951$	−3.55004	−0.115118
$952$	22.8167	0.739492
$953$	16.0555	0.520089	0.260045	−	0.965597i	$-0.416263\pi$
$953$	16.0555	0.520089	0.260045	+	0.965597i	$0.416263\pi$
$954$	0	0
$955$	17.0278	0.551005
$956$	20.3028	0.656639
$957$	6.90833	0.223314
$958$	−33.2111	−1.07300
$959$	12.9083	0.416832
$960$	1.30278	0.0420469
$961$	−30.6333	−0.988171
$962$	43.7250	1.40975
$963$	−22.8167	−0.735256
$964$	14.0000	0.450910
$965$	−1.09167	−0.0351422
$966$	9.90833	0.318795
$967$	46.7889	1.50463	0.752315	−	0.658804i	$-0.228937\pi$
$967$	46.7889	1.50463	0.752315	+	0.658804i	$0.228937\pi$
$968$	−1.00000	−0.0321412
$969$	36.0000	1.15649
$970$	−1.48612	−0.0477165
$971$	9.76114	0.313250	0.156625	−	0.987658i	$-0.449939\pi$
$971$	9.76114	0.313250	0.156625	+	0.987658i	$0.449939\pi$
$972$	−12.3944	−0.397552
$973$	36.0278	1.15500
$974$	−36.3305	−1.16411
$975$	6.39445	0.204786
$976$	6.60555	0.211439
$977$	−10.6056	−0.339302	−0.169651	−	0.985504i	$-0.554264\pi$
$977$	−10.6056	−0.339302	−0.169651	+	0.985504i	$0.554264\pi$
$978$	10.4222	0.333265
$979$	−14.7250	−0.470612
$980$	−3.90833	−0.124847
$981$	−18.7889	−0.599883
$982$	−17.7250	−0.565627
$983$	31.2666	0.997250	0.498625	−	0.866818i	$-0.333838\pi$
$983$	31.2666	0.997250	0.498625	+	0.866818i	$0.333838\pi$
$984$	−7.81665	−0.249186
$985$	−12.6972	−0.404567
$986$	36.6333	1.16664
$987$	13.8167	0.439789
$988$	19.6333	0.624619
$989$	−12.0000	−0.381578
$990$	−1.30278	−0.0414049
$991$	−26.0555	−0.827681	−0.413840	−	0.910349i	$-0.635813\pi$
$991$	−26.0555	−0.827681	−0.413840	+	0.910349i	$0.635813\pi$
$992$	−0.605551	−0.0192263
$993$	−22.9722	−0.729002
$994$	47.9361	1.52044
$995$	−3.81665	−0.120996
$996$	−8.72498	−0.276462
$997$	13.4500	0.425965	0.212982	−	0.977056i	$-0.431682\pi$
$997$	13.4500	0.425965	0.212982	+	0.977056i	$0.431682\pi$
$998$	−33.3305	−1.05506
$999$	49.9361	1.57991

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8030.2.a.l.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8030.2.a.l.1.1	✓	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:	\( N \)	\(=\)	\( 8030 = 2 \cdot 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8030.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.30278 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.30278 q^{6} -3.30278 q^{7} -1.00000 q^{8} -1.30278 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.30278 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.30278 q^{6} -3.30278 q^{7} -1.00000 q^{8} -1.30278 q^{9} +1.00000 q^{10} +1.00000 q^{11} -1.30278 q^{12} -4.90833 q^{13} +3.30278 q^{14} +1.30278 q^{15} +1.00000 q^{16} +6.90833 q^{17} +1.30278 q^{18} -4.00000 q^{19} -1.00000 q^{20} +4.30278 q^{21} -1.00000 q^{22} -2.30278 q^{23} +1.30278 q^{24} +1.00000 q^{25} +4.90833 q^{26} +5.60555 q^{27} -3.30278 q^{28} -5.30278 q^{29} -1.30278 q^{30} +0.605551 q^{31} -1.00000 q^{32} -1.30278 q^{33} -6.90833 q^{34} +3.30278 q^{35} -1.30278 q^{36} +8.90833 q^{37} +4.00000 q^{38} +6.39445 q^{39} +1.00000 q^{40} -6.00000 q^{41} -4.30278 q^{42} +5.21110 q^{43} +1.00000 q^{44} +1.30278 q^{45} +2.30278 q^{46} +3.21110 q^{47} -1.30278 q^{48} +3.90833 q^{49} -1.00000 q^{50} -9.00000 q^{51} -4.90833 q^{52} -5.60555 q^{54} -1.00000 q^{55} +3.30278 q^{56} +5.21110 q^{57} +5.30278 q^{58} -13.8167 q^{59} +1.30278 q^{60} +6.60555 q^{61} -0.605551 q^{62} +4.30278 q^{63} +1.00000 q^{64} +4.90833 q^{65} +1.30278 q^{66} +1.30278 q^{67} +6.90833 q^{68} +3.00000 q^{69} -3.30278 q^{70} +14.5139 q^{71} +1.30278 q^{72} +1.00000 q^{73} -8.90833 q^{74} -1.30278 q^{75} -4.00000 q^{76} -3.30278 q^{77} -6.39445 q^{78} +11.2111 q^{79} -1.00000 q^{80} -3.39445 q^{81} +6.00000 q^{82} +6.69722 q^{83} +4.30278 q^{84} -6.90833 q^{85} -5.21110 q^{86} +6.90833 q^{87} -1.00000 q^{88} -14.7250 q^{89} -1.30278 q^{90} +16.2111 q^{91} -2.30278 q^{92} -0.788897 q^{93} -3.21110 q^{94} +4.00000 q^{95} +1.30278 q^{96} -1.48612 q^{97} -3.90833 q^{98} -1.30278 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + q^{3} + 2 q^{4} - 2 q^{5} - q^{6} - 3 q^{7} - 2 q^{8} + q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + q^3 + 2 * q^4 - 2 * q^5 - q^6 - 3 * q^7 - 2 * q^8 + q^9	\( 2 q - 2 q^{2} + q^{3} + 2 q^{4} - 2 q^{5} - q^{6} - 3 q^{7} - 2 q^{8} + q^{9} + 2 q^{10} + 2 q^{11} + q^{12} + q^{13} + 3 q^{14} - q^{15} + 2 q^{16} + 3 q^{17} - q^{18} - 8 q^{19} - 2 q^{20} + 5 q^{21} - 2 q^{22} - q^{23} - q^{24} + 2 q^{25} - q^{26} + 4 q^{27} - 3 q^{28} - 7 q^{29} + q^{30} - 6 q^{31} - 2 q^{32} + q^{33} - 3 q^{34} + 3 q^{35} + q^{36} + 7 q^{37} + 8 q^{38} + 20 q^{39} + 2 q^{40} - 12 q^{41} - 5 q^{42} - 4 q^{43} + 2 q^{44} - q^{45} + q^{46} - 8 q^{47} + q^{48} - 3 q^{49} - 2 q^{50} - 18 q^{51} + q^{52} - 4 q^{54} - 2 q^{55} + 3 q^{56} - 4 q^{57} + 7 q^{58} - 6 q^{59} - q^{60} + 6 q^{61} + 6 q^{62} + 5 q^{63} + 2 q^{64} - q^{65} - q^{66} - q^{67} + 3 q^{68} + 6 q^{69} - 3 q^{70} + 11 q^{71} - q^{72} + 2 q^{73} - 7 q^{74} + q^{75} - 8 q^{76} - 3 q^{77} - 20 q^{78} + 8 q^{79} - 2 q^{80} - 14 q^{81} + 12 q^{82} + 17 q^{83} + 5 q^{84} - 3 q^{85} + 4 q^{86} + 3 q^{87} - 2 q^{88} + 3 q^{89} + q^{90} + 18 q^{91} - q^{92} - 16 q^{93} + 8 q^{94} + 8 q^{95} - q^{96} - 21 q^{97} + 3 q^{98} + q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + q^3 + 2 * q^4 - 2 * q^5 - q^6 - 3 * q^7 - 2 * q^8 + q^9 + 2 * q^10 + 2 * q^11 + q^12 + q^13 + 3 * q^14 - q^15 + 2 * q^16 + 3 * q^17 - q^18 - 8 * q^19 - 2 * q^20 + 5 * q^21 - 2 * q^22 - q^23 - q^24 + 2 * q^25 - q^26 + 4 * q^27 - 3 * q^28 - 7 * q^29 + q^30 - 6 * q^31 - 2 * q^32 + q^33 - 3 * q^34 + 3 * q^35 + q^36 + 7 * q^37 + 8 * q^38 + 20 * q^39 + 2 * q^40 - 12 * q^41 - 5 * q^42 - 4 * q^43 + 2 * q^44 - q^45 + q^46 - 8 * q^47 + q^48 - 3 * q^49 - 2 * q^50 - 18 * q^51 + q^52 - 4 * q^54 - 2 * q^55 + 3 * q^56 - 4 * q^57 + 7 * q^58 - 6 * q^59 - q^60 + 6 * q^61 + 6 * q^62 + 5 * q^63 + 2 * q^64 - q^65 - q^66 - q^67 + 3 * q^68 + 6 * q^69 - 3 * q^70 + 11 * q^71 - q^72 + 2 * q^73 - 7 * q^74 + q^75 - 8 * q^76 - 3 * q^77 - 20 * q^78 + 8 * q^79 - 2 * q^80 - 14 * q^81 + 12 * q^82 + 17 * q^83 + 5 * q^84 - 3 * q^85 + 4 * q^86 + 3 * q^87 - 2 * q^88 + 3 * q^89 + q^90 + 18 * q^91 - q^92 - 16 * q^93 + 8 * q^94 + 8 * q^95 - q^96 - 21 * q^97 + 3 * q^98 + q^99

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