LMFDB - Embedded newform 8030.2.a.bf.1.12

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:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 4 x^{14} - 23 x^{13} + 99 x^{12} + 191 x^{11} - 922 x^{10} - 702 x^{9} + 4108 x^{8} + 957 x^{7} + \cdots + 8 $ x^15 - 4x^14 - 23x^13 + 99x^12 + 191x^11 - 922x^10 - 702x^9 + 4108x^8 + 957x^7 - 8875x^6 + 479x^5 + 7698x^4 - 1731x^3 - 626x^2 + 46x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$-1.82374$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.82374 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.82374 q^{6} -3.76421 q^{7} +1.00000 q^{8} +0.326027 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.82374 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.82374 q^{6} -3.76421 q^{7} +1.00000 q^{8} +0.326027 q^{9} -1.00000 q^{10} -1.00000 q^{11} +1.82374 q^{12} +6.64935 q^{13} -3.76421 q^{14} -1.82374 q^{15} +1.00000 q^{16} +1.83011 q^{17} +0.326027 q^{18} -2.41659 q^{19} -1.00000 q^{20} -6.86493 q^{21} -1.00000 q^{22} -7.65045 q^{23} +1.82374 q^{24} +1.00000 q^{25} +6.64935 q^{26} -4.87663 q^{27} -3.76421 q^{28} +5.16147 q^{29} -1.82374 q^{30} -8.41223 q^{31} +1.00000 q^{32} -1.82374 q^{33} +1.83011 q^{34} +3.76421 q^{35} +0.326027 q^{36} -6.78545 q^{37} -2.41659 q^{38} +12.1267 q^{39} -1.00000 q^{40} +0.709927 q^{41} -6.86493 q^{42} +10.5220 q^{43} -1.00000 q^{44} -0.326027 q^{45} -7.65045 q^{46} -3.00893 q^{47} +1.82374 q^{48} +7.16925 q^{49} +1.00000 q^{50} +3.33764 q^{51} +6.64935 q^{52} -12.6394 q^{53} -4.87663 q^{54} +1.00000 q^{55} -3.76421 q^{56} -4.40723 q^{57} +5.16147 q^{58} +13.7046 q^{59} -1.82374 q^{60} -9.81435 q^{61} -8.41223 q^{62} -1.22723 q^{63} +1.00000 q^{64} -6.64935 q^{65} -1.82374 q^{66} +5.05512 q^{67} +1.83011 q^{68} -13.9524 q^{69} +3.76421 q^{70} -5.65528 q^{71} +0.326027 q^{72} +1.00000 q^{73} -6.78545 q^{74} +1.82374 q^{75} -2.41659 q^{76} +3.76421 q^{77} +12.1267 q^{78} -6.93684 q^{79} -1.00000 q^{80} -9.87179 q^{81} +0.709927 q^{82} -17.6868 q^{83} -6.86493 q^{84} -1.83011 q^{85} +10.5220 q^{86} +9.41318 q^{87} -1.00000 q^{88} -12.0648 q^{89} -0.326027 q^{90} -25.0295 q^{91} -7.65045 q^{92} -15.3417 q^{93} -3.00893 q^{94} +2.41659 q^{95} +1.82374 q^{96} +7.69197 q^{97} +7.16925 q^{98} -0.326027 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q + 15 q^{2} - 4 q^{3} + 15 q^{4} - 15 q^{5} - 4 q^{6} - 6 q^{7} + 15 q^{8} + 17 q^{9}+O(q^{10}) $ 15 * q + 15 * q^2 - 4 * q^3 + 15 * q^4 - 15 * q^5 - 4 * q^6 - 6 * q^7 + 15 * q^8 + 17 * q^9	\( 15 q + 15 q^{2} - 4 q^{3} + 15 q^{4} - 15 q^{5} - 4 q^{6} - 6 q^{7} + 15 q^{8} + 17 q^{9} - 15 q^{10} - 15 q^{11} - 4 q^{12} - 6 q^{13} - 6 q^{14} + 4 q^{15} + 15 q^{16} + 2 q^{17} + 17 q^{18} - 8 q^{19} - 15 q^{20} - 17 q^{21} - 15 q^{22} - 4 q^{23} - 4 q^{24} + 15 q^{25} - 6 q^{26} - 19 q^{27} - 6 q^{28} - 13 q^{29} + 4 q^{30} - 20 q^{31} + 15 q^{32} + 4 q^{33} + 2 q^{34} + 6 q^{35} + 17 q^{36} - 15 q^{37} - 8 q^{38} - 11 q^{39} - 15 q^{40} + 2 q^{41} - 17 q^{42} - 26 q^{43} - 15 q^{44} - 17 q^{45} - 4 q^{46} - 14 q^{47} - 4 q^{48} + 11 q^{49} + 15 q^{50} - 39 q^{51} - 6 q^{52} - 21 q^{53} - 19 q^{54} + 15 q^{55} - 6 q^{56} + q^{57} - 13 q^{58} - 14 q^{59} + 4 q^{60} - 45 q^{61} - 20 q^{62} - 17 q^{63} + 15 q^{64} + 6 q^{65} + 4 q^{66} - 10 q^{67} + 2 q^{68} - 23 q^{69} + 6 q^{70} - 9 q^{71} + 17 q^{72} + 15 q^{73} - 15 q^{74} - 4 q^{75} - 8 q^{76} + 6 q^{77} - 11 q^{78} - 26 q^{79} - 15 q^{80} + 15 q^{81} + 2 q^{82} - 30 q^{83} - 17 q^{84} - 2 q^{85} - 26 q^{86} - 14 q^{87} - 15 q^{88} + 10 q^{89} - 17 q^{90} - 17 q^{91} - 4 q^{92} - 8 q^{93} - 14 q^{94} + 8 q^{95} - 4 q^{96} - 27 q^{97} + 11 q^{98} - 17 q^{99}+O(q^{100}) \) 15 * q + 15 * q^2 - 4 * q^3 + 15 * q^4 - 15 * q^5 - 4 * q^6 - 6 * q^7 + 15 * q^8 + 17 * q^9 - 15 * q^10 - 15 * q^11 - 4 * q^12 - 6 * q^13 - 6 * q^14 + 4 * q^15 + 15 * q^16 + 2 * q^17 + 17 * q^18 - 8 * q^19 - 15 * q^20 - 17 * q^21 - 15 * q^22 - 4 * q^23 - 4 * q^24 + 15 * q^25 - 6 * q^26 - 19 * q^27 - 6 * q^28 - 13 * q^29 + 4 * q^30 - 20 * q^31 + 15 * q^32 + 4 * q^33 + 2 * q^34 + 6 * q^35 + 17 * q^36 - 15 * q^37 - 8 * q^38 - 11 * q^39 - 15 * q^40 + 2 * q^41 - 17 * q^42 - 26 * q^43 - 15 * q^44 - 17 * q^45 - 4 * q^46 - 14 * q^47 - 4 * q^48 + 11 * q^49 + 15 * q^50 - 39 * q^51 - 6 * q^52 - 21 * q^53 - 19 * q^54 + 15 * q^55 - 6 * q^56 + q^57 - 13 * q^58 - 14 * q^59 + 4 * q^60 - 45 * q^61 - 20 * q^62 - 17 * q^63 + 15 * q^64 + 6 * q^65 + 4 * q^66 - 10 * q^67 + 2 * q^68 - 23 * q^69 + 6 * q^70 - 9 * q^71 + 17 * q^72 + 15 * q^73 - 15 * q^74 - 4 * q^75 - 8 * q^76 + 6 * q^77 - 11 * q^78 - 26 * q^79 - 15 * q^80 + 15 * q^81 + 2 * q^82 - 30 * q^83 - 17 * q^84 - 2 * q^85 - 26 * q^86 - 14 * q^87 - 15 * q^88 + 10 * q^89 - 17 * q^90 - 17 * q^91 - 4 * q^92 - 8 * q^93 - 14 * q^94 + 8 * q^95 - 4 * q^96 - 27 * q^97 + 11 * q^98 - 17 * 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
$3$	1.82374	1.05294	0.526468	−	0.850195i	$-0.323516\pi$
$3$	1.82374	1.05294	0.526468	+	0.850195i	$0.323516\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.82374	0.744539
$7$	−3.76421	−1.42274	−0.711368	−	0.702820i	$-0.751924\pi$
$7$	−3.76421	−1.42274	−0.711368	+	0.702820i	$0.751924\pi$
$8$	1.00000	0.353553
$9$	0.326027	0.108676
$10$	−1.00000	−0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.82374	0.526468
$13$	6.64935	1.84420	0.922099	−	0.386954i	$-0.126473\pi$
$13$	6.64935	1.84420	0.922099	+	0.386954i	$0.126473\pi$
$14$	−3.76421	−1.00603
$15$	−1.82374	−0.470888
$16$	1.00000	0.250000
$17$	1.83011	0.443866	0.221933	−	0.975062i	$-0.428763\pi$
$17$	1.83011	0.443866	0.221933	+	0.975062i	$0.428763\pi$
$18$	0.326027	0.0768453
$19$	−2.41659	−0.554403	−0.277202	−	0.960812i	$-0.589407\pi$
$19$	−2.41659	−0.554403	−0.277202	+	0.960812i	$0.589407\pi$
$20$	−1.00000	−0.223607
$21$	−6.86493	−1.49805
$22$	−1.00000	−0.213201
$23$	−7.65045	−1.59523	−0.797615	−	0.603168i	$-0.793905\pi$
$23$	−7.65045	−1.59523	−0.797615	+	0.603168i	$0.793905\pi$
$24$	1.82374	0.372269
$25$	1.00000	0.200000
$26$	6.64935	1.30405
$27$	−4.87663	−0.938508
$28$	−3.76421	−0.711368
$29$	5.16147	0.958462	0.479231	−	0.877689i	$-0.340916\pi$
$29$	5.16147	0.958462	0.479231	+	0.877689i	$0.340916\pi$
$30$	−1.82374	−0.332968
$31$	−8.41223	−1.51088	−0.755441	−	0.655217i	$-0.772577\pi$
$31$	−8.41223	−1.51088	−0.755441	+	0.655217i	$0.772577\pi$
$32$	1.00000	0.176777
$33$	−1.82374	−0.317472
$34$	1.83011	0.313861
$35$	3.76421	0.636267
$36$	0.326027	0.0543378
$37$	−6.78545	−1.11552	−0.557760	−	0.830002i	$-0.688339\pi$
$37$	−6.78545	−1.11552	−0.557760	+	0.830002i	$0.688339\pi$
$38$	−2.41659	−0.392022
$39$	12.1267	1.94182
$40$	−1.00000	−0.158114
$41$	0.709927	0.110872	0.0554360	−	0.998462i	$-0.482345\pi$
$41$	0.709927	0.110872	0.0554360	+	0.998462i	$0.482345\pi$
$42$	−6.86493	−1.05928
$43$	10.5220	1.60458	0.802292	−	0.596931i	$-0.203613\pi$
$43$	10.5220	1.60458	0.802292	+	0.596931i	$0.203613\pi$
$44$	−1.00000	−0.150756
$45$	−0.326027	−0.0486012
$46$	−7.65045	−1.12800
$47$	−3.00893	−0.438898	−0.219449	−	0.975624i	$-0.570426\pi$
$47$	−3.00893	−0.438898	−0.219449	+	0.975624i	$0.570426\pi$
$48$	1.82374	0.263234
$49$	7.16925	1.02418
$50$	1.00000	0.141421
$51$	3.33764	0.467363
$52$	6.64935	0.922099
$53$	−12.6394	−1.73615	−0.868076	−	0.496431i	$-0.834644\pi$
$53$	−12.6394	−1.73615	−0.868076	+	0.496431i	$0.834644\pi$
$54$	−4.87663	−0.663625
$55$	1.00000	0.134840
$56$	−3.76421	−0.503013
$57$	−4.40723	−0.583752
$58$	5.16147	0.677735
$59$	13.7046	1.78418	0.892092	−	0.451854i	$-0.149237\pi$
$59$	13.7046	1.78418	0.892092	+	0.451854i	$0.149237\pi$
$60$	−1.82374	−0.235444
$61$	−9.81435	−1.25660	−0.628300	−	0.777971i	$-0.716249\pi$
$61$	−9.81435	−1.25660	−0.628300	+	0.777971i	$0.716249\pi$
$62$	−8.41223	−1.06835
$63$	−1.22723	−0.154617
$64$	1.00000	0.125000
$65$	−6.64935	−0.824750
$66$	−1.82374	−0.224487
$67$	5.05512	0.617582	0.308791	−	0.951130i	$-0.400076\pi$
$67$	5.05512	0.617582	0.308791	+	0.951130i	$0.400076\pi$
$68$	1.83011	0.221933
$69$	−13.9524	−1.67968
$70$	3.76421	0.449909
$71$	−5.65528	−0.671159	−0.335579	−	0.942012i	$-0.608932\pi$
$71$	−5.65528	−0.671159	−0.335579	+	0.942012i	$0.608932\pi$
$72$	0.326027	0.0384227
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	−6.78545	−0.788792
$75$	1.82374	0.210587
$76$	−2.41659	−0.277202
$77$	3.76421	0.428971
$78$	12.1267	1.37308
$79$	−6.93684	−0.780456	−0.390228	−	0.920718i	$-0.627604\pi$
$79$	−6.93684	−0.780456	−0.390228	+	0.920718i	$0.627604\pi$
$80$	−1.00000	−0.111803
$81$	−9.87179	−1.09687
$82$	0.709927	0.0783983
$83$	−17.6868	−1.94138	−0.970692	−	0.240329i	$-0.922745\pi$
$83$	−17.6868	−1.94138	−0.970692	+	0.240329i	$0.922745\pi$
$84$	−6.86493	−0.749026
$85$	−1.83011	−0.198503
$86$	10.5220	1.13461
$87$	9.41318	1.00920
$88$	−1.00000	−0.106600
$89$	−12.0648	−1.27887	−0.639435	−	0.768845i	$-0.720832\pi$
$89$	−12.0648	−1.27887	−0.639435	+	0.768845i	$0.720832\pi$
$90$	−0.326027	−0.0343663
$91$	−25.0295	−2.62381
$92$	−7.65045	−0.797615
$93$	−15.3417	−1.59086
$94$	−3.00893	−0.310348
$95$	2.41659	0.247937
$96$	1.82374	0.186135
$97$	7.69197	0.781002	0.390501	−	0.920603i	$-0.372302\pi$
$97$	7.69197	0.781002	0.390501	+	0.920603i	$0.372302\pi$
$98$	7.16925	0.724203
$99$	−0.326027	−0.0327670
$100$	1.00000	0.100000
$101$	−4.38552	−0.436375	−0.218188	−	0.975907i	$-0.570014\pi$
$101$	−4.38552	−0.436375	−0.218188	+	0.975907i	$0.570014\pi$
$102$	3.33764	0.330476
$103$	−10.5627	−1.04077	−0.520384	−	0.853932i	$-0.674211\pi$
$103$	−10.5627	−1.04077	−0.520384	+	0.853932i	$0.674211\pi$
$104$	6.64935	0.652023
$105$	6.86493	0.669949
$106$	−12.6394	−1.22765
$107$	5.93321	0.573585	0.286793	−	0.957993i	$-0.407411\pi$
$107$	5.93321	0.573585	0.286793	+	0.957993i	$0.407411\pi$
$108$	−4.87663	−0.469254
$109$	−13.5687	−1.29964	−0.649822	−	0.760087i	$-0.725156\pi$
$109$	−13.5687	−1.29964	−0.649822	+	0.760087i	$0.725156\pi$
$110$	1.00000	0.0953463
$111$	−12.3749	−1.17457
$112$	−3.76421	−0.355684
$113$	8.73292	0.821524	0.410762	−	0.911743i	$-0.365263\pi$
$113$	8.73292	0.821524	0.410762	+	0.911743i	$0.365263\pi$
$114$	−4.40723	−0.412775
$115$	7.65045	0.713408
$116$	5.16147	0.479231
$117$	2.16787	0.200420
$118$	13.7046	1.26161
$119$	−6.88890	−0.631505
$120$	−1.82374	−0.166484
$121$	1.00000	0.0909091
$122$	−9.81435	−0.888550
$123$	1.29472	0.116741
$124$	−8.41223	−0.755441
$125$	−1.00000	−0.0894427
$126$	−1.22723	−0.109331
$127$	2.59647	0.230400	0.115200	−	0.993342i	$-0.463249\pi$
$127$	2.59647	0.230400	0.115200	+	0.993342i	$0.463249\pi$
$128$	1.00000	0.0883883
$129$	19.1893	1.68953
$130$	−6.64935	−0.583187
$131$	−4.26136	−0.372316	−0.186158	−	0.982520i	$-0.559604\pi$
$131$	−4.26136	−0.372316	−0.186158	+	0.982520i	$0.559604\pi$
$132$	−1.82374	−0.158736
$133$	9.09654	0.788770
$134$	5.05512	0.436696
$135$	4.87663	0.419714
$136$	1.83011	0.156930
$137$	13.1769	1.12578	0.562888	−	0.826533i	$-0.309690\pi$
$137$	13.1769	1.12578	0.562888	+	0.826533i	$0.309690\pi$
$138$	−13.9524	−1.18771
$139$	−16.7124	−1.41752	−0.708762	−	0.705448i	$-0.750746\pi$
$139$	−16.7124	−1.41752	−0.708762	+	0.705448i	$0.750746\pi$
$140$	3.76421	0.318133
$141$	−5.48751	−0.462131
$142$	−5.65528	−0.474581
$143$	−6.64935	−0.556047
$144$	0.326027	0.0271689
$145$	−5.16147	−0.428637
$146$	1.00000	0.0827606
$147$	13.0748	1.07839
$148$	−6.78545	−0.557760
$149$	9.46392	0.775314	0.387657	−	0.921804i	$-0.373284\pi$
$149$	9.46392	0.775314	0.387657	+	0.921804i	$0.373284\pi$
$150$	1.82374	0.148908
$151$	20.6353	1.67928	0.839638	−	0.543147i	$-0.182767\pi$
$151$	20.6353	1.67928	0.839638	+	0.543147i	$0.182767\pi$
$152$	−2.41659	−0.196011
$153$	0.596665	0.0482375
$154$	3.76421	0.303328
$155$	8.41223	0.675687
$156$	12.1267	0.970912
$157$	−22.3588	−1.78443	−0.892214	−	0.451613i	$-0.850849\pi$
$157$	−22.3588	−1.78443	−0.892214	+	0.451613i	$0.850849\pi$
$158$	−6.93684	−0.551865
$159$	−23.0509	−1.82806
$160$	−1.00000	−0.0790569
$161$	28.7979	2.26959
$162$	−9.87179	−0.775601
$163$	−21.1915	−1.65984	−0.829922	−	0.557879i	$-0.811615\pi$
$163$	−21.1915	−1.65984	−0.829922	+	0.557879i	$0.811615\pi$
$164$	0.709927	0.0554360
$165$	1.82374	0.141978
$166$	−17.6868	−1.37277
$167$	−0.605516	−0.0468562	−0.0234281	−	0.999726i	$-0.507458\pi$
$167$	−0.605516	−0.0468562	−0.0234281	+	0.999726i	$0.507458\pi$
$168$	−6.86493	−0.529641
$169$	31.2139	2.40107
$170$	−1.83011	−0.140363
$171$	−0.787873	−0.0602502
$172$	10.5220	0.802292
$173$	0.312273	0.0237417	0.0118709	−	0.999930i	$-0.496221\pi$
$173$	0.312273	0.0237417	0.0118709	+	0.999930i	$0.496221\pi$
$174$	9.41318	0.713612
$175$	−3.76421	−0.284547
$176$	−1.00000	−0.0753778
$177$	24.9936	1.87863
$178$	−12.0648	−0.904297
$179$	−10.1394	−0.757857	−0.378929	−	0.925426i	$-0.623707\pi$
$179$	−10.1394	−0.757857	−0.378929	+	0.925426i	$0.623707\pi$
$180$	−0.326027	−0.0243006
$181$	2.84748	0.211652	0.105826	−	0.994385i	$-0.466251\pi$
$181$	2.84748	0.211652	0.105826	+	0.994385i	$0.466251\pi$
$182$	−25.0295	−1.85531
$183$	−17.8988	−1.32312
$184$	−7.65045	−0.563999
$185$	6.78545	0.498876
$186$	−15.3417	−1.12491
$187$	−1.83011	−0.133831
$188$	−3.00893	−0.219449
$189$	18.3566	1.33525
$190$	2.41659	0.175318
$191$	6.34991	0.459463	0.229732	−	0.973254i	$-0.426215\pi$
$191$	6.34991	0.459463	0.229732	+	0.973254i	$0.426215\pi$
$192$	1.82374	0.131617
$193$	−12.7539	−0.918045	−0.459022	−	0.888425i	$-0.651800\pi$
$193$	−12.7539	−0.918045	−0.459022	+	0.888425i	$0.651800\pi$
$194$	7.69197	0.552252
$195$	−12.1267	−0.868410
$196$	7.16925	0.512089
$197$	18.3809	1.30958	0.654792	−	0.755809i	$-0.272756\pi$
$197$	18.3809	1.30958	0.654792	+	0.755809i	$0.272756\pi$
$198$	−0.326027	−0.0231697
$199$	−8.33443	−0.590812	−0.295406	−	0.955372i	$-0.595455\pi$
$199$	−8.33443	−0.590812	−0.295406	+	0.955372i	$0.595455\pi$
$200$	1.00000	0.0707107
$201$	9.21923	0.650274
$202$	−4.38552	−0.308564
$203$	−19.4288	−1.36364
$204$	3.33764	0.233682
$205$	−0.709927	−0.0495835
$206$	−10.5627	−0.735935
$207$	−2.49425	−0.173363
$208$	6.64935	0.461050
$209$	2.41659	0.167159
$210$	6.86493	0.473725
$211$	−10.1243	−0.696988	−0.348494	−	0.937311i	$-0.613307\pi$
$211$	−10.1243	−0.696988	−0.348494	+	0.937311i	$0.613307\pi$
$212$	−12.6394	−0.868076
$213$	−10.3138	−0.706688
$214$	5.93321	0.405586
$215$	−10.5220	−0.717592
$216$	−4.87663	−0.331813
$217$	31.6654	2.14959
$218$	−13.5687	−0.918986
$219$	1.82374	0.123237
$220$	1.00000	0.0674200
$221$	12.1690	0.818577
$222$	−12.3749	−0.830548
$223$	−11.4204	−0.764766	−0.382383	−	0.924004i	$-0.624896\pi$
$223$	−11.4204	−0.764766	−0.382383	+	0.924004i	$0.624896\pi$
$224$	−3.76421	−0.251507
$225$	0.326027	0.0217351
$226$	8.73292	0.580905
$227$	−17.0667	−1.13275	−0.566377	−	0.824146i	$-0.691655\pi$
$227$	−17.0667	−1.13275	−0.566377	+	0.824146i	$0.691655\pi$
$228$	−4.40723	−0.291876
$229$	23.3396	1.54233	0.771164	−	0.636637i	$-0.219675\pi$
$229$	23.3396	1.54233	0.771164	+	0.636637i	$0.219675\pi$
$230$	7.65045	0.504456
$231$	6.86493	0.451679
$232$	5.16147	0.338867
$233$	−9.59083	−0.628316	−0.314158	−	0.949371i	$-0.601722\pi$
$233$	−9.59083	−0.628316	−0.314158	+	0.949371i	$0.601722\pi$
$234$	2.16787	0.141718
$235$	3.00893	0.196281
$236$	13.7046	0.892092
$237$	−12.6510	−0.821770
$238$	−6.88890	−0.446541
$239$	−7.07236	−0.457473	−0.228737	−	0.973488i	$-0.573459\pi$
$239$	−7.07236	−0.457473	−0.228737	+	0.973488i	$0.573459\pi$
$240$	−1.82374	−0.117722
$241$	8.01377	0.516213	0.258106	−	0.966117i	$-0.416902\pi$
$241$	8.01377	0.516213	0.258106	+	0.966117i	$0.416902\pi$
$242$	1.00000	0.0642824
$243$	−3.37368	−0.216422
$244$	−9.81435	−0.628300
$245$	−7.16925	−0.458026
$246$	1.29472	0.0825485
$247$	−16.0687	−1.02243
$248$	−8.41223	−0.534177
$249$	−32.2562	−2.04415
$250$	−1.00000	−0.0632456
$251$	3.43702	0.216943	0.108471	−	0.994100i	$-0.465404\pi$
$251$	3.43702	0.216943	0.108471	+	0.994100i	$0.465404\pi$
$252$	−1.22723	−0.0773084
$253$	7.65045	0.480980
$254$	2.59647	0.162917
$255$	−3.33764	−0.209011
$256$	1.00000	0.0625000
$257$	−19.1475	−1.19439	−0.597193	−	0.802098i	$-0.703717\pi$
$257$	−19.1475	−1.19439	−0.597193	+	0.802098i	$0.703717\pi$
$258$	19.1893	1.19468
$259$	25.5418	1.58709
$260$	−6.64935	−0.412375
$261$	1.68278	0.104161
$262$	−4.26136	−0.263267
$263$	−23.7926	−1.46712	−0.733558	−	0.679627i	$-0.762142\pi$
$263$	−23.7926	−1.46712	−0.733558	+	0.679627i	$0.762142\pi$
$264$	−1.82374	−0.112243
$265$	12.6394	0.776431
$266$	9.09654	0.557745
$267$	−22.0031	−1.34657
$268$	5.05512	0.308791
$269$	13.2301	0.806652	0.403326	−	0.915056i	$-0.367854\pi$
$269$	13.2301	0.806652	0.403326	+	0.915056i	$0.367854\pi$
$270$	4.87663	0.296782
$271$	−11.5981	−0.704534	−0.352267	−	0.935899i	$-0.614589\pi$
$271$	−11.5981	−0.704534	−0.352267	+	0.935899i	$0.614589\pi$
$272$	1.83011	0.110967
$273$	−45.6473	−2.76270
$274$	13.1769	0.796043
$275$	−1.00000	−0.0603023
$276$	−13.9524	−0.839838
$277$	31.0970	1.86844	0.934218	−	0.356704i	$-0.116099\pi$
$277$	31.0970	1.86844	0.934218	+	0.356704i	$0.116099\pi$
$278$	−16.7124	−1.00234
$279$	−2.74262	−0.164196
$280$	3.76421	0.224954
$281$	−6.11899	−0.365028	−0.182514	−	0.983203i	$-0.558423\pi$
$281$	−6.11899	−0.365028	−0.182514	+	0.983203i	$0.558423\pi$
$282$	−5.48751	−0.326776
$283$	31.1435	1.85129	0.925644	−	0.378396i	$-0.123524\pi$
$283$	31.1435	1.85129	0.925644	+	0.378396i	$0.123524\pi$
$284$	−5.65528	−0.335579
$285$	4.40723	0.261062
$286$	−6.64935	−0.393184
$287$	−2.67231	−0.157742
$288$	0.326027	0.0192113
$289$	−13.6507	−0.802983
$290$	−5.16147	−0.303092
$291$	14.0282	0.822345
$292$	1.00000	0.0585206
$293$	10.2092	0.596426	0.298213	−	0.954499i	$-0.403609\pi$
$293$	10.2092	0.596426	0.298213	+	0.954499i	$0.403609\pi$
$294$	13.0748	0.762540
$295$	−13.7046	−0.797911
$296$	−6.78545	−0.394396
$297$	4.87663	0.282971
$298$	9.46392	0.548230
$299$	−50.8705	−2.94192
$300$	1.82374	0.105294
$301$	−39.6069	−2.28290
$302$	20.6353	1.18743
$303$	−7.99804	−0.459475
$304$	−2.41659	−0.138601
$305$	9.81435	0.561968
$306$	0.596665	0.0341090
$307$	23.1448	1.32095	0.660473	−	0.750850i	$-0.270356\pi$
$307$	23.1448	1.32095	0.660473	+	0.750850i	$0.270356\pi$
$308$	3.76421	0.214486
$309$	−19.2635	−1.09586
$310$	8.41223	0.477783
$311$	7.68854	0.435977	0.217989	−	0.975951i	$-0.430050\pi$
$311$	7.68854	0.435977	0.217989	+	0.975951i	$0.430050\pi$
$312$	12.1267	0.686538
$313$	−25.4413	−1.43803	−0.719015	−	0.694995i	$-0.755407\pi$
$313$	−25.4413	−1.43803	−0.719015	+	0.694995i	$0.755407\pi$
$314$	−22.3588	−1.26178
$315$	1.22723	0.0691468
$316$	−6.93684	−0.390228
$317$	−14.8434	−0.833689	−0.416845	−	0.908978i	$-0.636864\pi$
$317$	−14.8434	−0.833689	−0.416845	+	0.908978i	$0.636864\pi$
$318$	−23.0509	−1.29263
$319$	−5.16147	−0.288987
$320$	−1.00000	−0.0559017
$321$	10.8206	0.603949
$322$	28.7979	1.60484
$323$	−4.42262	−0.246081
$324$	−9.87179	−0.548433
$325$	6.64935	0.368840
$326$	−21.1915	−1.17369
$327$	−24.7457	−1.36844
$328$	0.709927	0.0391992
$329$	11.3262	0.624436
$330$	1.82374	0.100394
$331$	−9.77665	−0.537373	−0.268687	−	0.963228i	$-0.586590\pi$
$331$	−9.77665	−0.537373	−0.268687	+	0.963228i	$0.586590\pi$
$332$	−17.6868	−0.970692
$333$	−2.21224	−0.121230
$334$	−0.605516	−0.0331324
$335$	−5.05512	−0.276191
$336$	−6.86493	−0.374513
$337$	−29.4228	−1.60276	−0.801381	−	0.598155i	$-0.795901\pi$
$337$	−29.4228	−1.60276	−0.801381	+	0.598155i	$0.795901\pi$
$338$	31.2139	1.69781
$339$	15.9266	0.865013
$340$	−1.83011	−0.0992515
$341$	8.41223	0.455548
$342$	−0.787873	−0.0426033
$343$	−0.637086	−0.0343994
$344$	10.5220	0.567306
$345$	13.9524	0.751174
$346$	0.312273	0.0167879
$347$	19.6132	1.05289	0.526447	−	0.850208i	$-0.323524\pi$
$347$	19.6132	1.05289	0.526447	+	0.850208i	$0.323524\pi$
$348$	9.41318	0.504600
$349$	11.9808	0.641317	0.320659	−	0.947195i	$-0.396096\pi$
$349$	11.9808	0.641317	0.320659	+	0.947195i	$0.396096\pi$
$350$	−3.76421	−0.201205
$351$	−32.4264	−1.73079
$352$	−1.00000	−0.0533002
$353$	13.7635	0.732559	0.366279	−	0.930505i	$-0.380631\pi$
$353$	13.7635	0.732559	0.366279	+	0.930505i	$0.380631\pi$
$354$	24.9936	1.32839
$355$	5.65528	0.300151
$356$	−12.0648	−0.639435
$357$	−12.5636	−0.664934
$358$	−10.1394	−0.535886
$359$	−9.09155	−0.479834	−0.239917	−	0.970793i	$-0.577120\pi$
$359$	−9.09155	−0.479834	−0.239917	+	0.970793i	$0.577120\pi$
$360$	−0.326027	−0.0171831
$361$	−13.1601	−0.692637
$362$	2.84748	0.149660
$363$	1.82374	0.0957215
$364$	−25.0295	−1.31190
$365$	−1.00000	−0.0523424
$366$	−17.8988	−0.935587
$367$	−17.5410	−0.915635	−0.457818	−	0.889046i	$-0.651369\pi$
$367$	−17.5410	−0.915635	−0.457818	+	0.889046i	$0.651369\pi$
$368$	−7.65045	−0.398807
$369$	0.231455	0.0120491
$370$	6.78545	0.352759
$371$	47.5772	2.47009
$372$	−15.3417	−0.795431
$373$	13.1874	0.682816	0.341408	−	0.939915i	$-0.389096\pi$
$373$	13.1874	0.682816	0.341408	+	0.939915i	$0.389096\pi$
$374$	−1.83011	−0.0946326
$375$	−1.82374	−0.0941775
$376$	−3.00893	−0.155174
$377$	34.3204	1.76759
$378$	18.3566	0.944164
$379$	−20.2936	−1.04241	−0.521205	−	0.853431i	$-0.674517\pi$
$379$	−20.2936	−1.04241	−0.521205	+	0.853431i	$0.674517\pi$
$380$	2.41659	0.123968
$381$	4.73529	0.242596
$382$	6.34991	0.324889
$383$	−0.413563	−0.0211321	−0.0105660	−	0.999944i	$-0.503363\pi$
$383$	−0.413563	−0.0211321	−0.0105660	+	0.999944i	$0.503363\pi$
$384$	1.82374	0.0930673
$385$	−3.76421	−0.191842
$386$	−12.7539	−0.649156
$387$	3.43045	0.174379
$388$	7.69197	0.390501
$389$	−5.53519	−0.280645	−0.140323	−	0.990106i	$-0.544814\pi$
$389$	−5.53519	−0.280645	−0.140323	+	0.990106i	$0.544814\pi$
$390$	−12.1267	−0.614059
$391$	−14.0011	−0.708068
$392$	7.16925	0.362102
$393$	−7.77160	−0.392026
$394$	18.3809	0.926016
$395$	6.93684	0.349030
$396$	−0.326027	−0.0163835
$397$	−3.00816	−0.150975	−0.0754876	−	0.997147i	$-0.524051\pi$
$397$	−3.00816	−0.150975	−0.0754876	+	0.997147i	$0.524051\pi$
$398$	−8.33443	−0.417767
$399$	16.5897	0.830525
$400$	1.00000	0.0500000
$401$	−17.6916	−0.883478	−0.441739	−	0.897144i	$-0.645638\pi$
$401$	−17.6916	−0.883478	−0.441739	+	0.897144i	$0.645638\pi$
$402$	9.21923	0.459813
$403$	−55.9359	−2.78636
$404$	−4.38552	−0.218188
$405$	9.87179	0.490533
$406$	−19.4288	−0.964238
$407$	6.78545	0.336342
$408$	3.33764	0.165238
$409$	37.0741	1.83320	0.916599	−	0.399807i	$-0.130923\pi$
$409$	37.0741	1.83320	0.916599	+	0.399807i	$0.130923\pi$
$410$	−0.709927	−0.0350608
$411$	24.0312	1.18537
$412$	−10.5627	−0.520384
$413$	−51.5868	−2.53842
$414$	−2.49425	−0.122586
$415$	17.6868	0.868213
$416$	6.64935	0.326011
$417$	−30.4790	−1.49256
$418$	2.41659	0.118199
$419$	16.4757	0.804892	0.402446	−	0.915444i	$-0.368160\pi$
$419$	16.4757	0.804892	0.402446	+	0.915444i	$0.368160\pi$
$420$	6.86493	0.334974
$421$	10.5179	0.512611	0.256305	−	0.966596i	$-0.417495\pi$
$421$	10.5179	0.512611	0.256305	+	0.966596i	$0.417495\pi$
$422$	−10.1243	−0.492845
$423$	−0.980993	−0.0476975
$424$	−12.6394	−0.613823
$425$	1.83011	0.0887733
$426$	−10.3138	−0.499704
$427$	36.9433	1.78781
$428$	5.93321	0.286793
$429$	−12.1267	−0.585482
$430$	−10.5220	−0.507414
$431$	2.31003	0.111270	0.0556352	−	0.998451i	$-0.482282\pi$
$431$	2.31003	0.111270	0.0556352	+	0.998451i	$0.482282\pi$
$432$	−4.87663	−0.234627
$433$	−22.6997	−1.09088	−0.545440	−	0.838150i	$-0.683637\pi$
$433$	−22.6997	−1.09088	−0.545440	+	0.838150i	$0.683637\pi$
$434$	31.6654	1.51999
$435$	−9.41318	−0.451328
$436$	−13.5687	−0.649822
$437$	18.4880	0.884400
$438$	1.82374	0.0871417
$439$	11.4354	0.545784	0.272892	−	0.962045i	$-0.412020\pi$
$439$	11.4354	0.545784	0.272892	+	0.962045i	$0.412020\pi$
$440$	1.00000	0.0476731
$441$	2.33737	0.111303
$442$	12.1690	0.578822
$443$	36.9085	1.75358	0.876789	−	0.480875i	$-0.159681\pi$
$443$	36.9085	1.75358	0.876789	+	0.480875i	$0.159681\pi$
$444$	−12.3749	−0.587286
$445$	12.0648	0.571928
$446$	−11.4204	−0.540771
$447$	17.2597	0.816357
$448$	−3.76421	−0.177842
$449$	35.5505	1.67773	0.838866	−	0.544337i	$-0.183219\pi$
$449$	35.5505	1.67773	0.838866	+	0.544337i	$0.183219\pi$
$450$	0.326027	0.0153691
$451$	−0.709927	−0.0334292
$452$	8.73292	0.410762
$453$	37.6334	1.76817
$454$	−17.0667	−0.800978
$455$	25.0295	1.17340
$456$	−4.40723	−0.206387
$457$	15.7243	0.735551	0.367775	−	0.929915i	$-0.380120\pi$
$457$	15.7243	0.735551	0.367775	+	0.929915i	$0.380120\pi$
$458$	23.3396	1.09059
$459$	−8.92476	−0.416572
$460$	7.65045	0.356704
$461$	22.9722	1.06992	0.534962	−	0.844876i	$-0.320326\pi$
$461$	22.9722	1.06992	0.534962	+	0.844876i	$0.320326\pi$
$462$	6.86493	0.319386
$463$	18.4747	0.858594	0.429297	−	0.903163i	$-0.358761\pi$
$463$	18.4747	0.858594	0.429297	+	0.903163i	$0.358761\pi$
$464$	5.16147	0.239615
$465$	15.3417	0.711455
$466$	−9.59083	−0.444287
$467$	−5.08642	−0.235372	−0.117686	−	0.993051i	$-0.537548\pi$
$467$	−5.08642	−0.235372	−0.117686	+	0.993051i	$0.537548\pi$
$468$	2.16787	0.100210
$469$	−19.0285	−0.878656
$470$	3.00893	0.138792
$471$	−40.7767	−1.87889
$472$	13.7046	0.630804
$473$	−10.5220	−0.483801
$474$	−12.6510	−0.581079
$475$	−2.41659	−0.110881
$476$	−6.88890	−0.315752
$477$	−4.12078	−0.188678
$478$	−7.07236	−0.323482
$479$	−10.9358	−0.499668	−0.249834	−	0.968289i	$-0.580376\pi$
$479$	−10.9358	−0.499668	−0.249834	+	0.968289i	$0.580376\pi$
$480$	−1.82374	−0.0832420
$481$	−45.1188	−2.05724
$482$	8.01377	0.365017
$483$	52.5198	2.38973
$484$	1.00000	0.0454545
$485$	−7.69197	−0.349275
$486$	−3.37368	−0.153033
$487$	−27.6336	−1.25220	−0.626100	−	0.779743i	$-0.715350\pi$
$487$	−27.6336	−1.25220	−0.626100	+	0.779743i	$0.715350\pi$
$488$	−9.81435	−0.444275
$489$	−38.6477	−1.74771
$490$	−7.16925	−0.323874
$491$	−27.4673	−1.23958	−0.619790	−	0.784768i	$-0.712782\pi$
$491$	−27.4673	−1.23958	−0.619790	+	0.784768i	$0.712782\pi$
$492$	1.29472	0.0583706
$493$	9.44605	0.425429
$494$	−16.0687	−0.722967
$495$	0.326027	0.0146538
$496$	−8.41223	−0.377720
$497$	21.2877	0.954882
$498$	−32.2562	−1.44543
$499$	15.3268	0.686123	0.343062	−	0.939313i	$-0.388536\pi$
$499$	15.3268	0.686123	0.343062	+	0.939313i	$0.388536\pi$
$500$	−1.00000	−0.0447214
$501$	−1.10430	−0.0493367
$502$	3.43702	0.153402
$503$	−5.84687	−0.260699	−0.130350	−	0.991468i	$-0.541610\pi$
$503$	−5.84687	−0.260699	−0.130350	+	0.991468i	$0.541610\pi$
$504$	−1.22723	−0.0546653
$505$	4.38552	0.195153
$506$	7.65045	0.340104
$507$	56.9260	2.52817
$508$	2.59647	0.115200
$509$	21.8293	0.967567	0.483784	−	0.875188i	$-0.339262\pi$
$509$	21.8293	0.967567	0.483784	+	0.875188i	$0.339262\pi$
$510$	−3.33764	−0.147793
$511$	−3.76421	−0.166519
$512$	1.00000	0.0441942
$513$	11.7848	0.520312
$514$	−19.1475	−0.844558
$515$	10.5627	0.465446
$516$	19.1893	0.844763
$517$	3.00893	0.132333
$518$	25.5418	1.12224
$519$	0.569505	0.0249985
$520$	−6.64935	−0.291593
$521$	13.2465	0.580341	0.290170	−	0.956975i	$-0.406288\pi$
$521$	13.2465	0.580341	0.290170	+	0.956975i	$0.406288\pi$
$522$	1.68278	0.0736533
$523$	33.6872	1.47304	0.736520	−	0.676416i	$-0.236468\pi$
$523$	33.6872	1.47304	0.736520	+	0.676416i	$0.236468\pi$
$524$	−4.26136	−0.186158
$525$	−6.86493	−0.299610
$526$	−23.7926	−1.03741
$527$	−15.3953	−0.670629
$528$	−1.82374	−0.0793681
$529$	35.5294	1.54476
$530$	12.6394	0.549020
$531$	4.46806	0.193897
$532$	9.09654	0.394385
$533$	4.72055	0.204470
$534$	−22.0031	−0.952168
$535$	−5.93321	−0.256515
$536$	5.05512	0.218348
$537$	−18.4917	−0.797976
$538$	13.2301	0.570389
$539$	−7.16925	−0.308801
$540$	4.87663	0.209857
$541$	−2.53520	−0.108997	−0.0544984	−	0.998514i	$-0.517356\pi$
$541$	−2.53520	−0.108997	−0.0544984	+	0.998514i	$0.517356\pi$
$542$	−11.5981	−0.498181
$543$	5.19307	0.222856
$544$	1.83011	0.0784652
$545$	13.5687	0.581218
$546$	−45.6473	−1.95353
$547$	−31.8324	−1.36106	−0.680528	−	0.732722i	$-0.738249\pi$
$547$	−31.8324	−1.36106	−0.680528	+	0.732722i	$0.738249\pi$
$548$	13.1769	0.562888
$549$	−3.19975	−0.136562
$550$	−1.00000	−0.0426401
$551$	−12.4732	−0.531374
$552$	−13.9524	−0.593855
$553$	26.1117	1.11038
$554$	31.0970	1.32118
$555$	12.3749	0.525285
$556$	−16.7124	−0.708762
$557$	15.6171	0.661716	0.330858	−	0.943681i	$-0.392662\pi$
$557$	15.6171	0.661716	0.330858	+	0.943681i	$0.392662\pi$
$558$	−2.74262	−0.116104
$559$	69.9643	2.95917
$560$	3.76421	0.159067
$561$	−3.33764	−0.140915
$562$	−6.11899	−0.258114
$563$	7.16497	0.301967	0.150984	−	0.988536i	$-0.451756\pi$
$563$	7.16497	0.301967	0.150984	+	0.988536i	$0.451756\pi$
$564$	−5.48751	−0.231066
$565$	−8.73292	−0.367397
$566$	31.1435	1.30906
$567$	37.1594	1.56055
$568$	−5.65528	−0.237290
$569$	−16.5429	−0.693513	−0.346756	−	0.937955i	$-0.612717\pi$
$569$	−16.5429	−0.693513	−0.346756	+	0.937955i	$0.612717\pi$
$570$	4.40723	0.184599
$571$	−14.4976	−0.606705	−0.303353	−	0.952878i	$-0.598106\pi$
$571$	−14.4976	−0.606705	−0.303353	+	0.952878i	$0.598106\pi$
$572$	−6.64935	−0.278023
$573$	11.5806	0.483786
$574$	−2.67231	−0.111540
$575$	−7.65045	−0.319046
$576$	0.326027	0.0135845
$577$	−17.3382	−0.721799	−0.360900	−	0.932605i	$-0.617530\pi$
$577$	−17.3382	−0.721799	−0.360900	+	0.932605i	$0.617530\pi$
$578$	−13.6507	−0.567795
$579$	−23.2598	−0.966643
$580$	−5.16147	−0.214319
$581$	66.5769	2.76208
$582$	14.0282	0.581486
$583$	12.6394	0.523470
$584$	1.00000	0.0413803
$585$	−2.16787	−0.0896303
$586$	10.2092	0.421737
$587$	6.45240	0.266319	0.133159	−	0.991095i	$-0.457488\pi$
$587$	6.45240	0.266319	0.133159	+	0.991095i	$0.457488\pi$
$588$	13.0748	0.539197
$589$	20.3289	0.837638
$590$	−13.7046	−0.564208
$591$	33.5220	1.37891
$592$	−6.78545	−0.278880
$593$	−20.8754	−0.857251	−0.428626	−	0.903482i	$-0.641002\pi$
$593$	−20.8754	−0.857251	−0.428626	+	0.903482i	$0.641002\pi$
$594$	4.87663	0.200091
$595$	6.88890	0.282417
$596$	9.46392	0.387657
$597$	−15.1998	−0.622088
$598$	−50.8705	−2.08025
$599$	−17.5372	−0.716550	−0.358275	−	0.933616i	$-0.616635\pi$
$599$	−17.5372	−0.716550	−0.358275	+	0.933616i	$0.616635\pi$
$600$	1.82374	0.0744539
$601$	−35.6666	−1.45487	−0.727435	−	0.686177i	$-0.759288\pi$
$601$	−35.6666	−1.45487	−0.727435	+	0.686177i	$0.759288\pi$
$602$	−39.6069	−1.61425
$603$	1.64811	0.0671161
$604$	20.6353	0.839638
$605$	−1.00000	−0.0406558
$606$	−7.99804	−0.324898
$607$	17.2121	0.698618	0.349309	−	0.937008i	$-0.386416\pi$
$607$	17.2121	0.698618	0.349309	+	0.937008i	$0.386416\pi$
$608$	−2.41659	−0.0980056
$609$	−35.4332	−1.43582
$610$	9.81435	0.397372
$611$	−20.0074	−0.809414
$612$	0.596665	0.0241187
$613$	6.05314	0.244484	0.122242	−	0.992500i	$-0.460992\pi$
$613$	6.05314	0.244484	0.122242	+	0.992500i	$0.460992\pi$
$614$	23.1448	0.934050
$615$	−1.29472	−0.0522082
$616$	3.76421	0.151664
$617$	17.7828	0.715908	0.357954	−	0.933739i	$-0.383475\pi$
$617$	17.7828	0.715908	0.357954	+	0.933739i	$0.383475\pi$
$618$	−19.2635	−0.774893
$619$	46.7532	1.87917	0.939586	−	0.342314i	$-0.111211\pi$
$619$	46.7532	1.87917	0.939586	+	0.342314i	$0.111211\pi$
$620$	8.41223	0.337843
$621$	37.3084	1.49714
$622$	7.68854	0.308282
$623$	45.4145	1.81949
$624$	12.1267	0.485456
$625$	1.00000	0.0400000
$626$	−25.4413	−1.01684
$627$	4.40723	0.176008
$628$	−22.3588	−0.892214
$629$	−12.4181	−0.495142
$630$	1.22723	0.0488941
$631$	23.8891	0.951008	0.475504	−	0.879713i	$-0.342266\pi$
$631$	23.8891	0.951008	0.475504	+	0.879713i	$0.342266\pi$
$632$	−6.93684	−0.275933
$633$	−18.4642	−0.733885
$634$	−14.8434	−0.589507
$635$	−2.59647	−0.103038
$636$	−23.0509	−0.914029
$637$	47.6708	1.88879
$638$	−5.16147	−0.204345
$639$	−1.84378	−0.0729386
$640$	−1.00000	−0.0395285
$641$	41.6618	1.64554	0.822771	−	0.568373i	$-0.192427\pi$
$641$	41.6618	1.64554	0.822771	+	0.568373i	$0.192427\pi$
$642$	10.8206	0.427056
$643$	36.2485	1.42950	0.714750	−	0.699380i	$-0.246541\pi$
$643$	36.2485	1.42950	0.714750	+	0.699380i	$0.246541\pi$
$644$	28.7979	1.13480
$645$	−19.1893	−0.755579
$646$	−4.42262	−0.174006
$647$	17.2887	0.679687	0.339843	−	0.940482i	$-0.389626\pi$
$647$	17.2887	0.679687	0.339843	+	0.940482i	$0.389626\pi$
$648$	−9.87179	−0.387800
$649$	−13.7046	−0.537952
$650$	6.64935	0.260809
$651$	57.7494	2.26338
$652$	−21.1915	−0.829922
$653$	23.5485	0.921522	0.460761	−	0.887524i	$-0.347576\pi$
$653$	23.5485	0.921522	0.460761	+	0.887524i	$0.347576\pi$
$654$	−24.7457	−0.967635
$655$	4.26136	0.166505
$656$	0.709927	0.0277180
$657$	0.326027	0.0127195
$658$	11.3262	0.441543
$659$	19.0179	0.740833	0.370416	−	0.928866i	$-0.379215\pi$
$659$	19.0179	0.740833	0.370416	+	0.928866i	$0.379215\pi$
$660$	1.82374	0.0709890
$661$	7.47682	0.290814	0.145407	−	0.989372i	$-0.453551\pi$
$661$	7.47682	0.290814	0.145407	+	0.989372i	$0.453551\pi$
$662$	−9.77665	−0.379980
$663$	22.1931	0.861910
$664$	−17.6868	−0.686383
$665$	−9.09654	−0.352749
$666$	−2.21224	−0.0857225
$667$	−39.4876	−1.52897
$668$	−0.605516	−0.0234281
$669$	−20.8278	−0.805250
$670$	−5.05512	−0.195296
$671$	9.81435	0.378879
$672$	−6.86493	−0.264821
$673$	−17.7176	−0.682963	−0.341482	−	0.939888i	$-0.610929\pi$
$673$	−17.7176	−0.682963	−0.341482	+	0.939888i	$0.610929\pi$
$674$	−29.4228	−1.13332
$675$	−4.87663	−0.187702
$676$	31.2139	1.20053
$677$	−8.27775	−0.318140	−0.159070	−	0.987267i	$-0.550850\pi$
$677$	−8.27775	−0.318140	−0.159070	+	0.987267i	$0.550850\pi$
$678$	15.9266	0.611657
$679$	−28.9542	−1.11116
$680$	−1.83011	−0.0701814
$681$	−31.1252	−1.19272
$682$	8.41223	0.322121
$683$	45.8259	1.75348	0.876739	−	0.480966i	$-0.159714\pi$
$683$	45.8259	1.75348	0.876739	+	0.480966i	$0.159714\pi$
$684$	−0.787873	−0.0301251
$685$	−13.1769	−0.503462
$686$	−0.637086	−0.0243241
$687$	42.5654	1.62397
$688$	10.5220	0.401146
$689$	−84.0437	−3.20181
$690$	13.9524	0.531160
$691$	30.4948	1.16008	0.580038	−	0.814590i	$-0.303038\pi$
$691$	30.4948	1.16008	0.580038	+	0.814590i	$0.303038\pi$
$692$	0.312273	0.0118709
$693$	1.22723	0.0466187
$694$	19.6132	0.744509
$695$	16.7124	0.633936
$696$	9.41318	0.356806
$697$	1.29924	0.0492123
$698$	11.9808	0.453480
$699$	−17.4912	−0.661577
$700$	−3.76421	−0.142274
$701$	−4.40807	−0.166490	−0.0832452	−	0.996529i	$-0.526528\pi$
$701$	−4.40807	−0.166490	−0.0832452	+	0.996529i	$0.526528\pi$
$702$	−32.4264	−1.22386
$703$	16.3976	0.618449
$704$	−1.00000	−0.0376889
$705$	5.48751	0.206671
$706$	13.7635	0.517997
$707$	16.5080	0.620847
$708$	24.9936	0.939316
$709$	−6.85043	−0.257273	−0.128637	−	0.991692i	$-0.541060\pi$
$709$	−6.85043	−0.257273	−0.128637	+	0.991692i	$0.541060\pi$
$710$	5.65528	0.212239
$711$	−2.26160	−0.0848166
$712$	−12.0648	−0.452149
$713$	64.3573	2.41020
$714$	−12.5636	−0.470180
$715$	6.64935	0.248672
$716$	−10.1394	−0.378929
$717$	−12.8982	−0.481690
$718$	−9.09155	−0.339294
$719$	12.5135	0.466676	0.233338	−	0.972396i	$-0.425035\pi$
$719$	12.5135	0.466676	0.233338	+	0.972396i	$0.425035\pi$
$720$	−0.326027	−0.0121503
$721$	39.7600	1.48074
$722$	−13.1601	−0.489768
$723$	14.6150	0.543539
$724$	2.84748	0.105826
$725$	5.16147	0.191692
$726$	1.82374	0.0676853
$727$	−1.19389	−0.0442789	−0.0221395	−	0.999755i	$-0.507048\pi$
$727$	−1.19389	−0.0442789	−0.0221395	+	0.999755i	$0.507048\pi$
$728$	−25.0295	−0.927656
$729$	23.4626	0.868987
$730$	−1.00000	−0.0370117
$731$	19.2563	0.712221
$732$	−17.8988	−0.661560
$733$	−6.66636	−0.246228	−0.123114	−	0.992393i	$-0.539288\pi$
$733$	−6.66636	−0.246228	−0.123114	+	0.992393i	$0.539288\pi$
$734$	−17.5410	−0.647452
$735$	−13.0748	−0.482273
$736$	−7.65045	−0.281999
$737$	−5.05512	−0.186208
$738$	0.231455	0.00851999
$739$	−46.9039	−1.72539	−0.862694	−	0.505727i	$-0.831224\pi$
$739$	−46.9039	−1.72539	−0.862694	+	0.505727i	$0.831224\pi$
$740$	6.78545	0.249438
$741$	−29.3052	−1.07655
$742$	47.5772	1.74662
$743$	−25.7694	−0.945388	−0.472694	−	0.881227i	$-0.656718\pi$
$743$	−25.7694	−0.945388	−0.472694	+	0.881227i	$0.656718\pi$
$744$	−15.3417	−0.562455
$745$	−9.46392	−0.346731
$746$	13.1874	0.482824
$747$	−5.76639	−0.210981
$748$	−1.83011	−0.0669154
$749$	−22.3338	−0.816060
$750$	−1.82374	−0.0665936
$751$	−30.5663	−1.11538	−0.557691	−	0.830049i	$-0.688312\pi$
$751$	−30.5663	−1.11538	−0.557691	+	0.830049i	$0.688312\pi$
$752$	−3.00893	−0.109724
$753$	6.26823	0.228427
$754$	34.3204	1.24988
$755$	−20.6353	−0.750995
$756$	18.3566	0.667625
$757$	1.11708	0.0406010	0.0203005	−	0.999794i	$-0.493538\pi$
$757$	1.11708	0.0406010	0.0203005	+	0.999794i	$0.493538\pi$
$758$	−20.2936	−0.737096
$759$	13.9524	0.506441
$760$	2.41659	0.0876589
$761$	25.6047	0.928171	0.464085	−	0.885790i	$-0.346383\pi$
$761$	25.6047	0.928171	0.464085	+	0.885790i	$0.346383\pi$
$762$	4.73529	0.171541
$763$	51.0753	1.84905
$764$	6.34991	0.229732
$765$	−0.596665	−0.0215725
$766$	−0.413563	−0.0149426
$767$	91.1265	3.29039
$768$	1.82374	0.0658085
$769$	−8.64973	−0.311917	−0.155959	−	0.987764i	$-0.549847\pi$
$769$	−8.64973	−0.311917	−0.155959	+	0.987764i	$0.549847\pi$
$770$	−3.76421	−0.135653
$771$	−34.9200	−1.25761
$772$	−12.7539	−0.459022
$773$	−54.3877	−1.95619	−0.978095	−	0.208157i	$-0.933253\pi$
$773$	−54.3877	−1.95619	−0.978095	+	0.208157i	$0.933253\pi$
$774$	3.43045	0.123305
$775$	−8.41223	−0.302176
$776$	7.69197	0.276126
$777$	46.5816	1.67111
$778$	−5.53519	−0.198446
$779$	−1.71560	−0.0614678
$780$	−12.1267	−0.434205
$781$	5.65528	0.202362
$782$	−14.0011	−0.500680
$783$	−25.1706	−0.899524
$784$	7.16925	0.256045
$785$	22.3588	0.798020
$786$	−7.77160	−0.277204
$787$	28.5853	1.01895	0.509477	−	0.860484i	$-0.329839\pi$
$787$	28.5853	1.01895	0.509477	+	0.860484i	$0.329839\pi$
$788$	18.3809	0.654792
$789$	−43.3915	−1.54478
$790$	6.93684	0.246802
$791$	−32.8725	−1.16881
$792$	−0.326027	−0.0115849
$793$	−65.2591	−2.31742
$794$	−3.00816	−0.106756
$795$	23.0509	0.817533
$796$	−8.33443	−0.295406
$797$	8.87727	0.314449	0.157224	−	0.987563i	$-0.449745\pi$
$797$	8.87727	0.314449	0.157224	+	0.987563i	$0.449745\pi$
$798$	16.5897	0.587270
$799$	−5.50667	−0.194812
$800$	1.00000	0.0353553
$801$	−3.93346	−0.138982
$802$	−17.6916	−0.624713
$803$	−1.00000	−0.0352892
$804$	9.21923	0.325137
$805$	−28.7979	−1.01499
$806$	−55.9359	−1.97026
$807$	24.1282	0.849353
$808$	−4.38552	−0.154282
$809$	−30.2829	−1.06469	−0.532345	−	0.846528i	$-0.678689\pi$
$809$	−30.2829	−1.06469	−0.532345	+	0.846528i	$0.678689\pi$
$810$	9.87179	0.346859
$811$	−28.3478	−0.995426	−0.497713	−	0.867342i	$-0.665827\pi$
$811$	−28.3478	−0.995426	−0.497713	+	0.867342i	$0.665827\pi$
$812$	−19.4288	−0.681819
$813$	−21.1519	−0.741830
$814$	6.78545	0.237830
$815$	21.1915	0.742305
$816$	3.33764	0.116841
$817$	−25.4273	−0.889587
$818$	37.0741	1.29627
$819$	−8.16030	−0.285144
$820$	−0.709927	−0.0247917
$821$	23.3925	0.816403	0.408202	−	0.912892i	$-0.366156\pi$
$821$	23.3925	0.816403	0.408202	+	0.912892i	$0.366156\pi$
$822$	24.0312	0.838183
$823$	−33.6002	−1.17123	−0.585614	−	0.810590i	$-0.699147\pi$
$823$	−33.6002	−1.17123	−0.585614	+	0.810590i	$0.699147\pi$
$824$	−10.5627	−0.367967
$825$	−1.82374	−0.0634945
$826$	−51.5868	−1.79494
$827$	−11.0802	−0.385297	−0.192649	−	0.981268i	$-0.561708\pi$
$827$	−11.0802	−0.385297	−0.192649	+	0.981268i	$0.561708\pi$
$828$	−2.49425	−0.0866813
$829$	−21.4097	−0.743590	−0.371795	−	0.928315i	$-0.621258\pi$
$829$	−21.4097	−0.743590	−0.371795	+	0.928315i	$0.621258\pi$
$830$	17.6868	0.613919
$831$	56.7128	1.96734
$832$	6.64935	0.230525
$833$	13.1205	0.454598
$834$	−30.4790	−1.05540
$835$	0.605516	0.0209547
$836$	2.41659	0.0835795
$837$	41.0233	1.41797
$838$	16.4757	0.569144
$839$	−46.9019	−1.61923	−0.809617	−	0.586959i	$-0.800325\pi$
$839$	−46.9019	−1.61923	−0.809617	+	0.586959i	$0.800325\pi$
$840$	6.86493	0.236863
$841$	−2.35919	−0.0813515
$842$	10.5179	0.362471
$843$	−11.1594	−0.384351
$844$	−10.1243	−0.348494
$845$	−31.2139	−1.07379
$846$	−0.980993	−0.0337272
$847$	−3.76421	−0.129340
$848$	−12.6394	−0.434038
$849$	56.7976	1.94929
$850$	1.83011	0.0627722
$851$	51.9117	1.77951
$852$	−10.3138	−0.353344
$853$	−38.5074	−1.31847	−0.659234	−	0.751938i	$-0.729119\pi$
$853$	−38.5074	−1.31847	−0.659234	+	0.751938i	$0.729119\pi$
$854$	36.9433	1.26417
$855$	0.787873	0.0269447
$856$	5.93321	0.202793
$857$	23.5381	0.804045	0.402022	−	0.915630i	$-0.368307\pi$
$857$	23.5381	0.804045	0.402022	+	0.915630i	$0.368307\pi$
$858$	−12.1267	−0.413998
$859$	31.5901	1.07784	0.538920	−	0.842357i	$-0.318832\pi$
$859$	31.5901	1.07784	0.538920	+	0.842357i	$0.318832\pi$
$860$	−10.5220	−0.358796
$861$	−4.87360	−0.166092
$862$	2.31003	0.0786800
$863$	−18.6171	−0.633733	−0.316866	−	0.948470i	$-0.602631\pi$
$863$	−18.6171	−0.633733	−0.316866	+	0.948470i	$0.602631\pi$
$864$	−4.87663	−0.165906
$865$	−0.312273	−0.0106176
$866$	−22.6997	−0.771368
$867$	−24.8953	−0.845490
$868$	31.6654	1.07479
$869$	6.93684	0.235316
$870$	−9.41318	−0.319137
$871$	33.6133	1.13894
$872$	−13.5687	−0.459493
$873$	2.50779	0.0848759
$874$	18.4880	0.625366
$875$	3.76421	0.127253
$876$	1.82374	0.0616185
$877$	26.5549	0.896695	0.448348	−	0.893859i	$-0.352013\pi$
$877$	26.5549	0.896695	0.448348	+	0.893859i	$0.352013\pi$
$878$	11.4354	0.385928
$879$	18.6189	0.627999
$880$	1.00000	0.0337100
$881$	13.3075	0.448340	0.224170	−	0.974550i	$-0.428033\pi$
$881$	13.3075	0.448340	0.224170	+	0.974550i	$0.428033\pi$
$882$	2.33737	0.0787033
$883$	−4.72581	−0.159036	−0.0795181	−	0.996833i	$-0.525338\pi$
$883$	−4.72581	−0.159036	−0.0795181	+	0.996833i	$0.525338\pi$
$884$	12.1690	0.409289
$885$	−24.9936	−0.840150
$886$	36.9085	1.23997
$887$	−35.0258	−1.17605	−0.588026	−	0.808842i	$-0.700095\pi$
$887$	−35.0258	−1.17605	−0.588026	+	0.808842i	$0.700095\pi$
$888$	−12.3749	−0.415274
$889$	−9.77366	−0.327798
$890$	12.0648	0.404414
$891$	9.87179	0.330717
$892$	−11.4204	−0.382383
$893$	7.27135	0.243326
$894$	17.2597	0.577252
$895$	10.1394	0.338924
$896$	−3.76421	−0.125753
$897$	−92.7746	−3.09765
$898$	35.5505	1.18634
$899$	−43.4195	−1.44812
$900$	0.326027	0.0108676
$901$	−23.1314	−0.770620
$902$	−0.709927	−0.0236380
$903$	−72.2326	−2.40375
$904$	8.73292	0.290453
$905$	−2.84748	−0.0946536
$906$	37.6334	1.25029
$907$	−24.2632	−0.805646	−0.402823	−	0.915278i	$-0.631971\pi$
$907$	−24.2632	−0.805646	−0.402823	+	0.915278i	$0.631971\pi$
$908$	−17.0667	−0.566377
$909$	−1.42980	−0.0474234
$910$	25.0295	0.829721
$911$	−34.3104	−1.13676	−0.568378	−	0.822768i	$-0.692429\pi$
$911$	−34.3104	−1.13676	−0.568378	+	0.822768i	$0.692429\pi$
$912$	−4.40723	−0.145938
$913$	17.6868	0.585349
$914$	15.7243	0.520113
$915$	17.8988	0.591717
$916$	23.3396	0.771164
$917$	16.0406	0.529708
$918$	−8.92476	−0.294561
$919$	−43.5129	−1.43536	−0.717678	−	0.696375i	$-0.754795\pi$
$919$	−43.5129	−1.43536	−0.717678	+	0.696375i	$0.754795\pi$
$920$	7.65045	0.252228
$921$	42.2102	1.39087
$922$	22.9722	0.756551
$923$	−37.6040	−1.23775
$924$	6.86493	0.225840
$925$	−6.78545	−0.223104
$926$	18.4747	0.607117
$927$	−3.44371	−0.113106
$928$	5.16147	0.169434
$929$	−0.257313	−0.00844217	−0.00422108	−	0.999991i	$-0.501344\pi$
$929$	−0.257313	−0.00844217	−0.00422108	+	0.999991i	$0.501344\pi$
$930$	15.3417	0.503075
$931$	−17.3251	−0.567808
$932$	−9.59083	−0.314158
$933$	14.0219	0.459056
$934$	−5.08642	−0.166433
$935$	1.83011	0.0598509
$936$	2.16787	0.0708590
$937$	42.2482	1.38019	0.690094	−	0.723720i	$-0.257569\pi$
$937$	42.2482	1.38019	0.690094	+	0.723720i	$0.257569\pi$
$938$	−19.0285	−0.621304
$939$	−46.3984	−1.51415
$940$	3.00893	0.0981405
$941$	11.6552	0.379948	0.189974	−	0.981789i	$-0.439160\pi$
$941$	11.6552	0.379948	0.189974	+	0.981789i	$0.439160\pi$
$942$	−40.7767	−1.32858
$943$	−5.43126	−0.176866
$944$	13.7046	0.446046
$945$	−18.3566	−0.597142
$946$	−10.5220	−0.342099
$947$	25.1277	0.816540	0.408270	−	0.912861i	$-0.366132\pi$
$947$	25.1277	0.816540	0.408270	+	0.912861i	$0.366132\pi$
$948$	−12.6510	−0.410885
$949$	6.64935	0.215847
$950$	−2.41659	−0.0784045
$951$	−27.0705	−0.877822
$952$	−6.88890	−0.223271
$953$	44.2502	1.43340	0.716702	−	0.697380i	$-0.245651\pi$
$953$	44.2502	1.43340	0.716702	+	0.697380i	$0.245651\pi$
$954$	−4.12078	−0.133415
$955$	−6.34991	−0.205478
$956$	−7.07236	−0.228737
$957$	−9.41318	−0.304285
$958$	−10.9358	−0.353319
$959$	−49.6004	−1.60168
$960$	−1.82374	−0.0588610
$961$	39.7656	1.28276
$962$	−45.1188	−1.45469
$963$	1.93439	0.0623347
$964$	8.01377	0.258106
$965$	12.7539	0.410562
$966$	52.5198	1.68980
$967$	−16.4826	−0.530046	−0.265023	−	0.964242i	$-0.585379\pi$
$967$	−16.4826	−0.530046	−0.265023	+	0.964242i	$0.585379\pi$
$968$	1.00000	0.0321412
$969$	−8.06570	−0.259108
$970$	−7.69197	−0.246974
$971$	−34.5175	−1.10772	−0.553860	−	0.832610i	$-0.686846\pi$
$971$	−34.5175	−1.10772	−0.553860	+	0.832610i	$0.686846\pi$
$972$	−3.37368	−0.108211
$973$	62.9088	2.01676
$974$	−27.6336	−0.885439
$975$	12.1267	0.388365
$976$	−9.81435	−0.314150
$977$	38.4598	1.23044	0.615219	−	0.788356i	$-0.289068\pi$
$977$	38.4598	1.23044	0.615219	+	0.788356i	$0.289068\pi$
$978$	−38.6477	−1.23582
$979$	12.0648	0.385594
$980$	−7.16925	−0.229013
$981$	−4.42375	−0.141240
$982$	−27.4673	−0.876515
$983$	44.4436	1.41753	0.708766	−	0.705444i	$-0.249252\pi$
$983$	44.4436	1.41753	0.708766	+	0.705444i	$0.249252\pi$
$984$	1.29472	0.0412742
$985$	−18.3809	−0.585664
$986$	9.44605	0.300824
$987$	20.6561	0.657491
$988$	−16.0687	−0.511215
$989$	−80.4978	−2.55968
$990$	0.326027	0.0103618
$991$	54.1205	1.71920	0.859598	−	0.510971i	$-0.170714\pi$
$991$	54.1205	1.71920	0.859598	+	0.510971i	$0.170714\pi$
$992$	−8.41223	−0.267089
$993$	−17.8301	−0.565820
$994$	21.2877	0.675203
$995$	8.33443	0.264219
$996$	−32.2562	−1.02208
$997$	−1.77895	−0.0563398	−0.0281699	−	0.999603i	$-0.508968\pi$
$997$	−1.77895	−0.0563398	−0.0281699	+	0.999603i	$0.508968\pi$
$998$	15.3268	0.485162
$999$	33.0901	1.04693

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8030.2.a.bf.1.12	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8030.2.a.bf.1.12	✓	15	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.82374 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.82374 q^{6} -3.76421 q^{7} +1.00000 q^{8} +0.326027 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.82374 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.82374 q^{6} -3.76421 q^{7} +1.00000 q^{8} +0.326027 q^{9} -1.00000 q^{10} -1.00000 q^{11} +1.82374 q^{12} +6.64935 q^{13} -3.76421 q^{14} -1.82374 q^{15} +1.00000 q^{16} +1.83011 q^{17} +0.326027 q^{18} -2.41659 q^{19} -1.00000 q^{20} -6.86493 q^{21} -1.00000 q^{22} -7.65045 q^{23} +1.82374 q^{24} +1.00000 q^{25} +6.64935 q^{26} -4.87663 q^{27} -3.76421 q^{28} +5.16147 q^{29} -1.82374 q^{30} -8.41223 q^{31} +1.00000 q^{32} -1.82374 q^{33} +1.83011 q^{34} +3.76421 q^{35} +0.326027 q^{36} -6.78545 q^{37} -2.41659 q^{38} +12.1267 q^{39} -1.00000 q^{40} +0.709927 q^{41} -6.86493 q^{42} +10.5220 q^{43} -1.00000 q^{44} -0.326027 q^{45} -7.65045 q^{46} -3.00893 q^{47} +1.82374 q^{48} +7.16925 q^{49} +1.00000 q^{50} +3.33764 q^{51} +6.64935 q^{52} -12.6394 q^{53} -4.87663 q^{54} +1.00000 q^{55} -3.76421 q^{56} -4.40723 q^{57} +5.16147 q^{58} +13.7046 q^{59} -1.82374 q^{60} -9.81435 q^{61} -8.41223 q^{62} -1.22723 q^{63} +1.00000 q^{64} -6.64935 q^{65} -1.82374 q^{66} +5.05512 q^{67} +1.83011 q^{68} -13.9524 q^{69} +3.76421 q^{70} -5.65528 q^{71} +0.326027 q^{72} +1.00000 q^{73} -6.78545 q^{74} +1.82374 q^{75} -2.41659 q^{76} +3.76421 q^{77} +12.1267 q^{78} -6.93684 q^{79} -1.00000 q^{80} -9.87179 q^{81} +0.709927 q^{82} -17.6868 q^{83} -6.86493 q^{84} -1.83011 q^{85} +10.5220 q^{86} +9.41318 q^{87} -1.00000 q^{88} -12.0648 q^{89} -0.326027 q^{90} -25.0295 q^{91} -7.65045 q^{92} -15.3417 q^{93} -3.00893 q^{94} +2.41659 q^{95} +1.82374 q^{96} +7.69197 q^{97} +7.16925 q^{98} -0.326027 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 15 q^{2} - 4 q^{3} + 15 q^{4} - 15 q^{5} - 4 q^{6} - 6 q^{7} + 15 q^{8} + 17 q^{9}+O(q^{10}) \) 15 * q + 15 * q^2 - 4 * q^3 + 15 * q^4 - 15 * q^5 - 4 * q^6 - 6 * q^7 + 15 * q^8 + 17 * q^9	\( 15 q + 15 q^{2} - 4 q^{3} + 15 q^{4} - 15 q^{5} - 4 q^{6} - 6 q^{7} + 15 q^{8} + 17 q^{9} - 15 q^{10} - 15 q^{11} - 4 q^{12} - 6 q^{13} - 6 q^{14} + 4 q^{15} + 15 q^{16} + 2 q^{17} + 17 q^{18} - 8 q^{19} - 15 q^{20} - 17 q^{21} - 15 q^{22} - 4 q^{23} - 4 q^{24} + 15 q^{25} - 6 q^{26} - 19 q^{27} - 6 q^{28} - 13 q^{29} + 4 q^{30} - 20 q^{31} + 15 q^{32} + 4 q^{33} + 2 q^{34} + 6 q^{35} + 17 q^{36} - 15 q^{37} - 8 q^{38} - 11 q^{39} - 15 q^{40} + 2 q^{41} - 17 q^{42} - 26 q^{43} - 15 q^{44} - 17 q^{45} - 4 q^{46} - 14 q^{47} - 4 q^{48} + 11 q^{49} + 15 q^{50} - 39 q^{51} - 6 q^{52} - 21 q^{53} - 19 q^{54} + 15 q^{55} - 6 q^{56} + q^{57} - 13 q^{58} - 14 q^{59} + 4 q^{60} - 45 q^{61} - 20 q^{62} - 17 q^{63} + 15 q^{64} + 6 q^{65} + 4 q^{66} - 10 q^{67} + 2 q^{68} - 23 q^{69} + 6 q^{70} - 9 q^{71} + 17 q^{72} + 15 q^{73} - 15 q^{74} - 4 q^{75} - 8 q^{76} + 6 q^{77} - 11 q^{78} - 26 q^{79} - 15 q^{80} + 15 q^{81} + 2 q^{82} - 30 q^{83} - 17 q^{84} - 2 q^{85} - 26 q^{86} - 14 q^{87} - 15 q^{88} + 10 q^{89} - 17 q^{90} - 17 q^{91} - 4 q^{92} - 8 q^{93} - 14 q^{94} + 8 q^{95} - 4 q^{96} - 27 q^{97} + 11 q^{98} - 17 q^{99}+O(q^{100}) \) 15 * q + 15 * q^2 - 4 * q^3 + 15 * q^4 - 15 * q^5 - 4 * q^6 - 6 * q^7 + 15 * q^8 + 17 * q^9 - 15 * q^10 - 15 * q^11 - 4 * q^12 - 6 * q^13 - 6 * q^14 + 4 * q^15 + 15 * q^16 + 2 * q^17 + 17 * q^18 - 8 * q^19 - 15 * q^20 - 17 * q^21 - 15 * q^22 - 4 * q^23 - 4 * q^24 + 15 * q^25 - 6 * q^26 - 19 * q^27 - 6 * q^28 - 13 * q^29 + 4 * q^30 - 20 * q^31 + 15 * q^32 + 4 * q^33 + 2 * q^34 + 6 * q^35 + 17 * q^36 - 15 * q^37 - 8 * q^38 - 11 * q^39 - 15 * q^40 + 2 * q^41 - 17 * q^42 - 26 * q^43 - 15 * q^44 - 17 * q^45 - 4 * q^46 - 14 * q^47 - 4 * q^48 + 11 * q^49 + 15 * q^50 - 39 * q^51 - 6 * q^52 - 21 * q^53 - 19 * q^54 + 15 * q^55 - 6 * q^56 + q^57 - 13 * q^58 - 14 * q^59 + 4 * q^60 - 45 * q^61 - 20 * q^62 - 17 * q^63 + 15 * q^64 + 6 * q^65 + 4 * q^66 - 10 * q^67 + 2 * q^68 - 23 * q^69 + 6 * q^70 - 9 * q^71 + 17 * q^72 + 15 * q^73 - 15 * q^74 - 4 * q^75 - 8 * q^76 + 6 * q^77 - 11 * q^78 - 26 * q^79 - 15 * q^80 + 15 * q^81 + 2 * q^82 - 30 * q^83 - 17 * q^84 - 2 * q^85 - 26 * q^86 - 14 * q^87 - 15 * q^88 + 10 * q^89 - 17 * q^90 - 17 * q^91 - 4 * q^92 - 8 * q^93 - 14 * q^94 + 8 * q^95 - 4 * q^96 - 27 * q^97 + 11 * q^98 - 17 * q^99

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