LMFDB - Embedded newform 8034.2.a.v.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8034,2,Mod(1,8034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8034, 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("8034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8034 = 2 \cdot 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8034.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:	$64.1518129839$
Analytic rank:	$0$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 5 x^{10} - 31 x^{9} + 168 x^{8} + 300 x^{7} - 1928 x^{6} - 736 x^{5} + 8532 x^{4} - 2065 x^{3} + \cdots + 576 $ x^11 - 5x^10 - 31x^9 + 168x^8 + 300x^7 - 1928x^6 - 736x^5 + 8532x^4 - 2065x^3 - 10494x^2 + 4024x + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-3.73039$ of defining polynomial
Character	$\chi$	$=$	8034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.73039 q^{5} +1.00000 q^{6} -3.81724 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.73039 q^{5} +1.00000 q^{6} -3.81724 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.73039 q^{10} -2.78739 q^{11} +1.00000 q^{12} +1.00000 q^{13} -3.81724 q^{14} -3.73039 q^{15} +1.00000 q^{16} -1.82947 q^{17} +1.00000 q^{18} -4.81724 q^{19} -3.73039 q^{20} -3.81724 q^{21} -2.78739 q^{22} -7.96106 q^{23} +1.00000 q^{24} +8.91584 q^{25} +1.00000 q^{26} +1.00000 q^{27} -3.81724 q^{28} +1.52088 q^{29} -3.73039 q^{30} +4.81724 q^{31} +1.00000 q^{32} -2.78739 q^{33} -1.82947 q^{34} +14.2398 q^{35} +1.00000 q^{36} -2.06613 q^{37} -4.81724 q^{38} +1.00000 q^{39} -3.73039 q^{40} +9.25760 q^{41} -3.81724 q^{42} -12.4337 q^{43} -2.78739 q^{44} -3.73039 q^{45} -7.96106 q^{46} +7.09597 q^{47} +1.00000 q^{48} +7.57129 q^{49} +8.91584 q^{50} -1.82947 q^{51} +1.00000 q^{52} +8.32162 q^{53} +1.00000 q^{54} +10.3981 q^{55} -3.81724 q^{56} -4.81724 q^{57} +1.52088 q^{58} -11.8102 q^{59} -3.73039 q^{60} +7.08018 q^{61} +4.81724 q^{62} -3.81724 q^{63} +1.00000 q^{64} -3.73039 q^{65} -2.78739 q^{66} +0.370914 q^{67} -1.82947 q^{68} -7.96106 q^{69} +14.2398 q^{70} -5.96079 q^{71} +1.00000 q^{72} -8.16895 q^{73} -2.06613 q^{74} +8.91584 q^{75} -4.81724 q^{76} +10.6401 q^{77} +1.00000 q^{78} -0.128451 q^{79} -3.73039 q^{80} +1.00000 q^{81} +9.25760 q^{82} -0.0889117 q^{83} -3.81724 q^{84} +6.82463 q^{85} -12.4337 q^{86} +1.52088 q^{87} -2.78739 q^{88} +16.1743 q^{89} -3.73039 q^{90} -3.81724 q^{91} -7.96106 q^{92} +4.81724 q^{93} +7.09597 q^{94} +17.9702 q^{95} +1.00000 q^{96} -5.41994 q^{97} +7.57129 q^{98} -2.78739 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 11 q^{2} + 11 q^{3} + 11 q^{4} + 5 q^{5} + 11 q^{6} + 4 q^{7} + 11 q^{8} + 11 q^{9}+O(q^{10}) $ 11 * q + 11 * q^2 + 11 * q^3 + 11 * q^4 + 5 * q^5 + 11 * q^6 + 4 * q^7 + 11 * q^8 + 11 * q^9	\( 11 q + 11 q^{2} + 11 q^{3} + 11 q^{4} + 5 q^{5} + 11 q^{6} + 4 q^{7} + 11 q^{8} + 11 q^{9} + 5 q^{10} - 7 q^{11} + 11 q^{12} + 11 q^{13} + 4 q^{14} + 5 q^{15} + 11 q^{16} + 10 q^{17} + 11 q^{18} - 7 q^{19} + 5 q^{20} + 4 q^{21} - 7 q^{22} + 18 q^{23} + 11 q^{24} + 32 q^{25} + 11 q^{26} + 11 q^{27} + 4 q^{28} + 29 q^{29} + 5 q^{30} + 7 q^{31} + 11 q^{32} - 7 q^{33} + 10 q^{34} + 31 q^{35} + 11 q^{36} + 21 q^{37} - 7 q^{38} + 11 q^{39} + 5 q^{40} - 3 q^{41} + 4 q^{42} - 17 q^{43} - 7 q^{44} + 5 q^{45} + 18 q^{46} + 12 q^{47} + 11 q^{48} + 21 q^{49} + 32 q^{50} + 10 q^{51} + 11 q^{52} + 11 q^{53} + 11 q^{54} + 4 q^{55} + 4 q^{56} - 7 q^{57} + 29 q^{58} - 48 q^{59} + 5 q^{60} - q^{61} + 7 q^{62} + 4 q^{63} + 11 q^{64} + 5 q^{65} - 7 q^{66} - 9 q^{67} + 10 q^{68} + 18 q^{69} + 31 q^{70} + 17 q^{71} + 11 q^{72} - 23 q^{73} + 21 q^{74} + 32 q^{75} - 7 q^{76} + 26 q^{77} + 11 q^{78} + 41 q^{79} + 5 q^{80} + 11 q^{81} - 3 q^{82} + 19 q^{83} + 4 q^{84} + 17 q^{85} - 17 q^{86} + 29 q^{87} - 7 q^{88} + 32 q^{89} + 5 q^{90} + 4 q^{91} + 18 q^{92} + 7 q^{93} + 12 q^{94} + 26 q^{95} + 11 q^{96} - 16 q^{97} + 21 q^{98} - 7 q^{99}+O(q^{100}) \) 11 * q + 11 * q^2 + 11 * q^3 + 11 * q^4 + 5 * q^5 + 11 * q^6 + 4 * q^7 + 11 * q^8 + 11 * q^9 + 5 * q^10 - 7 * q^11 + 11 * q^12 + 11 * q^13 + 4 * q^14 + 5 * q^15 + 11 * q^16 + 10 * q^17 + 11 * q^18 - 7 * q^19 + 5 * q^20 + 4 * q^21 - 7 * q^22 + 18 * q^23 + 11 * q^24 + 32 * q^25 + 11 * q^26 + 11 * q^27 + 4 * q^28 + 29 * q^29 + 5 * q^30 + 7 * q^31 + 11 * q^32 - 7 * q^33 + 10 * q^34 + 31 * q^35 + 11 * q^36 + 21 * q^37 - 7 * q^38 + 11 * q^39 + 5 * q^40 - 3 * q^41 + 4 * q^42 - 17 * q^43 - 7 * q^44 + 5 * q^45 + 18 * q^46 + 12 * q^47 + 11 * q^48 + 21 * q^49 + 32 * q^50 + 10 * q^51 + 11 * q^52 + 11 * q^53 + 11 * q^54 + 4 * q^55 + 4 * q^56 - 7 * q^57 + 29 * q^58 - 48 * q^59 + 5 * q^60 - q^61 + 7 * q^62 + 4 * q^63 + 11 * q^64 + 5 * q^65 - 7 * q^66 - 9 * q^67 + 10 * q^68 + 18 * q^69 + 31 * q^70 + 17 * q^71 + 11 * q^72 - 23 * q^73 + 21 * q^74 + 32 * q^75 - 7 * q^76 + 26 * q^77 + 11 * q^78 + 41 * q^79 + 5 * q^80 + 11 * q^81 - 3 * q^82 + 19 * q^83 + 4 * q^84 + 17 * q^85 - 17 * q^86 + 29 * q^87 - 7 * q^88 + 32 * q^89 + 5 * q^90 + 4 * q^91 + 18 * q^92 + 7 * q^93 + 12 * q^94 + 26 * q^95 + 11 * q^96 - 16 * q^97 + 21 * q^98 - 7 * 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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−3.73039	−1.66828	−0.834142	−	0.551550i	$-0.814036\pi$
$5$	−3.73039	−1.66828	−0.834142	+	0.551550i	$0.814036\pi$
$6$	1.00000	0.408248
$7$	−3.81724	−1.44278	−0.721390	−	0.692529i	$-0.756496\pi$
$7$	−3.81724	−1.44278	−0.721390	+	0.692529i	$0.756496\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−3.73039	−1.17965
$11$	−2.78739	−0.840430	−0.420215	−	0.907425i	$-0.638045\pi$
$11$	−2.78739	−0.840430	−0.420215	+	0.907425i	$0.638045\pi$
$12$	1.00000	0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−3.81724	−1.02020
$15$	−3.73039	−0.963184
$16$	1.00000	0.250000
$17$	−1.82947	−0.443711	−0.221855	−	0.975080i	$-0.571211\pi$
$17$	−1.82947	−0.443711	−0.221855	+	0.975080i	$0.571211\pi$
$18$	1.00000	0.235702
$19$	−4.81724	−1.10515	−0.552575	−	0.833463i	$-0.686355\pi$
$19$	−4.81724	−1.10515	−0.552575	+	0.833463i	$0.686355\pi$
$20$	−3.73039	−0.834142
$21$	−3.81724	−0.832989
$22$	−2.78739	−0.594274
$23$	−7.96106	−1.66000	−0.829998	−	0.557767i	$-0.811658\pi$
$23$	−7.96106	−1.66000	−0.829998	+	0.557767i	$0.811658\pi$
$24$	1.00000	0.204124
$25$	8.91584	1.78317
$26$	1.00000	0.196116
$27$	1.00000	0.192450
$28$	−3.81724	−0.721390
$29$	1.52088	0.282421	0.141211	−	0.989980i	$-0.454901\pi$
$29$	1.52088	0.282421	0.141211	+	0.989980i	$0.454901\pi$
$30$	−3.73039	−0.681074
$31$	4.81724	0.865201	0.432601	−	0.901586i	$-0.357596\pi$
$31$	4.81724	0.865201	0.432601	+	0.901586i	$0.357596\pi$
$32$	1.00000	0.176777
$33$	−2.78739	−0.485222
$34$	−1.82947	−0.313751
$35$	14.2398	2.40696
$36$	1.00000	0.166667
$37$	−2.06613	−0.339669	−0.169835	−	0.985473i	$-0.554323\pi$
$37$	−2.06613	−0.339669	−0.169835	+	0.985473i	$0.554323\pi$
$38$	−4.81724	−0.781459
$39$	1.00000	0.160128
$40$	−3.73039	−0.589827
$41$	9.25760	1.44579	0.722897	−	0.690955i	$-0.242810\pi$
$41$	9.25760	1.44579	0.722897	+	0.690955i	$0.242810\pi$
$42$	−3.81724	−0.589012
$43$	−12.4337	−1.89612	−0.948060	−	0.318092i	$-0.896958\pi$
$43$	−12.4337	−1.89612	−0.948060	+	0.318092i	$0.896958\pi$
$44$	−2.78739	−0.420215
$45$	−3.73039	−0.556094
$46$	−7.96106	−1.17379
$47$	7.09597	1.03505	0.517527	−	0.855667i	$-0.326853\pi$
$47$	7.09597	1.03505	0.517527	+	0.855667i	$0.326853\pi$
$48$	1.00000	0.144338
$49$	7.57129	1.08161
$50$	8.91584	1.26089
$51$	−1.82947	−0.256177
$52$	1.00000	0.138675
$53$	8.32162	1.14306	0.571531	−	0.820580i	$-0.306350\pi$
$53$	8.32162	1.14306	0.571531	+	0.820580i	$0.306350\pi$
$54$	1.00000	0.136083
$55$	10.3981	1.40208
$56$	−3.81724	−0.510100
$57$	−4.81724	−0.638059
$58$	1.52088	0.199702
$59$	−11.8102	−1.53755	−0.768776	−	0.639518i	$-0.779134\pi$
$59$	−11.8102	−1.53755	−0.768776	+	0.639518i	$0.779134\pi$
$60$	−3.73039	−0.481592
$61$	7.08018	0.906524	0.453262	−	0.891377i	$-0.350260\pi$
$61$	7.08018	0.906524	0.453262	+	0.891377i	$0.350260\pi$
$62$	4.81724	0.611790
$63$	−3.81724	−0.480927
$64$	1.00000	0.125000
$65$	−3.73039	−0.462698
$66$	−2.78739	−0.343104
$67$	0.370914	0.0453143	0.0226572	−	0.999743i	$-0.492787\pi$
$67$	0.370914	0.0453143	0.0226572	+	0.999743i	$0.492787\pi$
$68$	−1.82947	−0.221855
$69$	−7.96106	−0.958399
$70$	14.2398	1.70198
$71$	−5.96079	−0.707415	−0.353708	−	0.935356i	$-0.615079\pi$
$71$	−5.96079	−0.707415	−0.353708	+	0.935356i	$0.615079\pi$
$72$	1.00000	0.117851
$73$	−8.16895	−0.956103	−0.478051	−	0.878332i	$-0.658657\pi$
$73$	−8.16895	−0.956103	−0.478051	+	0.878332i	$0.658657\pi$
$74$	−2.06613	−0.240182
$75$	8.91584	1.02951
$76$	−4.81724	−0.552575
$77$	10.6401	1.21256
$78$	1.00000	0.113228
$79$	−0.128451	−0.0144519	−0.00722595	−	0.999974i	$-0.502300\pi$
$79$	−0.128451	−0.0144519	−0.00722595	+	0.999974i	$0.502300\pi$
$80$	−3.73039	−0.417071
$81$	1.00000	0.111111
$82$	9.25760	1.02233
$83$	−0.0889117	−0.00975933	−0.00487966	−	0.999988i	$-0.501553\pi$
$83$	−0.0889117	−0.00975933	−0.00487966	+	0.999988i	$0.501553\pi$
$84$	−3.81724	−0.416495
$85$	6.82463	0.740235
$86$	−12.4337	−1.34076
$87$	1.52088	0.163056
$88$	−2.78739	−0.297137
$89$	16.1743	1.71447	0.857236	−	0.514923i	$-0.172180\pi$
$89$	16.1743	1.71447	0.857236	+	0.514923i	$0.172180\pi$
$90$	−3.73039	−0.393218
$91$	−3.81724	−0.400155
$92$	−7.96106	−0.829998
$93$	4.81724	0.499524
$94$	7.09597	0.731894
$95$	17.9702	1.84370
$96$	1.00000	0.102062
$97$	−5.41994	−0.550312	−0.275156	−	0.961400i	$-0.588729\pi$
$97$	−5.41994	−0.550312	−0.275156	+	0.961400i	$0.588729\pi$
$98$	7.57129	0.764816
$99$	−2.78739	−0.280143
$100$	8.91584	0.891584
$101$	11.8049	1.17463	0.587316	−	0.809358i	$-0.300185\pi$
$101$	11.8049	1.17463	0.587316	+	0.809358i	$0.300185\pi$
$102$	−1.82947	−0.181144
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	1.00000	0.0980581
$105$	14.2398	1.38966
$106$	8.32162	0.808267
$107$	10.8880	1.05258	0.526292	−	0.850304i	$-0.323582\pi$
$107$	10.8880	1.05258	0.526292	+	0.850304i	$0.323582\pi$
$108$	1.00000	0.0962250
$109$	−3.84577	−0.368358	−0.184179	−	0.982893i	$-0.558963\pi$
$109$	−3.84577	−0.368358	−0.184179	+	0.982893i	$0.558963\pi$
$110$	10.3981	0.991417
$111$	−2.06613	−0.196108
$112$	−3.81724	−0.360695
$113$	16.4690	1.54927	0.774637	−	0.632406i	$-0.217933\pi$
$113$	16.4690	1.54927	0.774637	+	0.632406i	$0.217933\pi$
$114$	−4.81724	−0.451176
$115$	29.6979	2.76934
$116$	1.52088	0.141211
$117$	1.00000	0.0924500
$118$	−11.8102	−1.08721
$119$	6.98350	0.640177
$120$	−3.73039	−0.340537
$121$	−3.23045	−0.293677
$122$	7.08018	0.641009
$123$	9.25760	0.834730
$124$	4.81724	0.432601
$125$	−14.6076	−1.30655
$126$	−3.81724	−0.340066
$127$	−2.03375	−0.180466	−0.0902331	−	0.995921i	$-0.528761\pi$
$127$	−2.03375	−0.180466	−0.0902331	+	0.995921i	$0.528761\pi$
$128$	1.00000	0.0883883
$129$	−12.4337	−1.09473
$130$	−3.73039	−0.327177
$131$	20.0652	1.75311	0.876554	−	0.481303i	$-0.159836\pi$
$131$	20.0652	1.75311	0.876554	+	0.481303i	$0.159836\pi$
$132$	−2.78739	−0.242611
$133$	18.3885	1.59449
$134$	0.370914	0.0320421
$135$	−3.73039	−0.321061
$136$	−1.82947	−0.156875
$137$	14.9760	1.27948	0.639742	−	0.768590i	$-0.279041\pi$
$137$	14.9760	1.27948	0.639742	+	0.768590i	$0.279041\pi$
$138$	−7.96106	−0.677690
$139$	7.38106	0.626054	0.313027	−	0.949744i	$-0.398657\pi$
$139$	7.38106	0.626054	0.313027	+	0.949744i	$0.398657\pi$
$140$	14.2398	1.20348
$141$	7.09597	0.597589
$142$	−5.96079	−0.500218
$143$	−2.78739	−0.233093
$144$	1.00000	0.0833333
$145$	−5.67350	−0.471158
$146$	−8.16895	−0.676067
$147$	7.57129	0.624470
$148$	−2.06613	−0.169835
$149$	−11.1664	−0.914786	−0.457393	−	0.889265i	$-0.651217\pi$
$149$	−11.1664	−0.914786	−0.457393	+	0.889265i	$0.651217\pi$
$150$	8.91584	0.727975
$151$	−22.5400	−1.83428	−0.917141	−	0.398563i	$-0.869509\pi$
$151$	−22.5400	−1.83428	−0.917141	+	0.398563i	$0.869509\pi$
$152$	−4.81724	−0.390729
$153$	−1.82947	−0.147904
$154$	10.6401	0.857406
$155$	−17.9702	−1.44340
$156$	1.00000	0.0800641
$157$	4.08972	0.326395	0.163198	−	0.986593i	$-0.447819\pi$
$157$	4.08972	0.326395	0.163198	+	0.986593i	$0.447819\pi$
$158$	−0.128451	−0.0102190
$159$	8.32162	0.659947
$160$	−3.73039	−0.294914
$161$	30.3892	2.39501
$162$	1.00000	0.0785674
$163$	1.05188	0.0823894	0.0411947	−	0.999151i	$-0.486884\pi$
$163$	1.05188	0.0823894	0.0411947	+	0.999151i	$0.486884\pi$
$164$	9.25760	0.722897
$165$	10.3981	0.809488
$166$	−0.0889117	−0.00690089
$167$	−17.9339	−1.38777	−0.693885	−	0.720086i	$-0.744102\pi$
$167$	−17.9339	−1.38777	−0.693885	+	0.720086i	$0.744102\pi$
$168$	−3.81724	−0.294506
$169$	1.00000	0.0769231
$170$	6.82463	0.523425
$171$	−4.81724	−0.368383
$172$	−12.4337	−0.948060
$173$	20.6373	1.56902	0.784512	−	0.620113i	$-0.212913\pi$
$173$	20.6373	1.56902	0.784512	+	0.620113i	$0.212913\pi$
$174$	1.52088	0.115298
$175$	−34.0339	−2.57272
$176$	−2.78739	−0.210107
$177$	−11.8102	−0.887706
$178$	16.1743	1.21232
$179$	−7.03790	−0.526037	−0.263019	−	0.964791i	$-0.584718\pi$
$179$	−7.03790	−0.526037	−0.263019	+	0.964791i	$0.584718\pi$
$180$	−3.73039	−0.278047
$181$	21.1121	1.56925	0.784626	−	0.619969i	$-0.212855\pi$
$181$	21.1121	1.56925	0.784626	+	0.619969i	$0.212855\pi$
$182$	−3.81724	−0.282952
$183$	7.08018	0.523382
$184$	−7.96106	−0.586897
$185$	7.70747	0.566665
$186$	4.81724	0.353217
$187$	5.09944	0.372908
$188$	7.09597	0.517527
$189$	−3.81724	−0.277663
$190$	17.9702	1.30369
$191$	−14.5164	−1.05037	−0.525185	−	0.850988i	$-0.676004\pi$
$191$	−14.5164	−1.05037	−0.525185	+	0.850988i	$0.676004\pi$
$192$	1.00000	0.0721688
$193$	21.4780	1.54602	0.773012	−	0.634392i	$-0.218749\pi$
$193$	21.4780	1.54602	0.773012	+	0.634392i	$0.218749\pi$
$194$	−5.41994	−0.389129
$195$	−3.73039	−0.267139
$196$	7.57129	0.540807
$197$	−3.80287	−0.270943	−0.135472	−	0.990781i	$-0.543255\pi$
$197$	−3.80287	−0.270943	−0.135472	+	0.990781i	$0.543255\pi$
$198$	−2.78739	−0.198091
$199$	−15.4692	−1.09659	−0.548293	−	0.836286i	$-0.684722\pi$
$199$	−15.4692	−1.09659	−0.548293	+	0.836286i	$0.684722\pi$
$200$	8.91584	0.630445
$201$	0.370914	0.0261622
$202$	11.8049	0.830590
$203$	−5.80557	−0.407471
$204$	−1.82947	−0.128088
$205$	−34.5345	−2.41200
$206$	−1.00000	−0.0696733
$207$	−7.96106	−0.553332
$208$	1.00000	0.0693375
$209$	13.4275	0.928801
$210$	14.2398	0.982639
$211$	19.3357	1.33112	0.665561	−	0.746344i	$-0.268192\pi$
$211$	19.3357	1.33112	0.665561	+	0.746344i	$0.268192\pi$
$212$	8.32162	0.571531
$213$	−5.96079	−0.408426
$214$	10.8880	0.744289
$215$	46.3826	3.16326
$216$	1.00000	0.0680414
$217$	−18.3885	−1.24829
$218$	−3.84577	−0.260468
$219$	−8.16895	−0.552006
$220$	10.3981	0.701038
$221$	−1.82947	−0.123063
$222$	−2.06613	−0.138669
$223$	9.66464	0.647192	0.323596	−	0.946195i	$-0.395108\pi$
$223$	9.66464	0.647192	0.323596	+	0.946195i	$0.395108\pi$
$224$	−3.81724	−0.255050
$225$	8.91584	0.594389
$226$	16.4690	1.09550
$227$	−14.7387	−0.978240	−0.489120	−	0.872216i	$-0.662682\pi$
$227$	−14.7387	−0.978240	−0.489120	+	0.872216i	$0.662682\pi$
$228$	−4.81724	−0.319029
$229$	−25.0490	−1.65529	−0.827643	−	0.561255i	$-0.810319\pi$
$229$	−25.0490	−1.65529	−0.827643	+	0.561255i	$0.810319\pi$
$230$	29.6979	1.95822
$231$	10.6401	0.700069
$232$	1.52088	0.0998509
$233$	0.594073	0.0389190	0.0194595	−	0.999811i	$-0.493805\pi$
$233$	0.594073	0.0389190	0.0194595	+	0.999811i	$0.493805\pi$
$234$	1.00000	0.0653720
$235$	−26.4708	−1.72676
$236$	−11.8102	−0.768776
$237$	−0.128451	−0.00834381
$238$	6.98350	0.452673
$239$	11.6810	0.755580	0.377790	−	0.925891i	$-0.376684\pi$
$239$	11.6810	0.755580	0.377790	+	0.925891i	$0.376684\pi$
$240$	−3.73039	−0.240796
$241$	15.5781	1.00348	0.501738	−	0.865020i	$-0.332694\pi$
$241$	15.5781	1.00348	0.501738	+	0.865020i	$0.332694\pi$
$242$	−3.23045	−0.207661
$243$	1.00000	0.0641500
$244$	7.08018	0.453262
$245$	−28.2439	−1.80444
$246$	9.25760	0.590243
$247$	−4.81724	−0.306513
$248$	4.81724	0.305895
$249$	−0.0889117	−0.00563455
$250$	−14.6076	−0.923868
$251$	7.11665	0.449199	0.224600	−	0.974451i	$-0.427893\pi$
$251$	7.11665	0.449199	0.224600	+	0.974451i	$0.427893\pi$
$252$	−3.81724	−0.240463
$253$	22.1906	1.39511
$254$	−2.03375	−0.127609
$255$	6.82463	0.427375
$256$	1.00000	0.0625000
$257$	11.6819	0.728696	0.364348	−	0.931263i	$-0.381292\pi$
$257$	11.6819	0.728696	0.364348	+	0.931263i	$0.381292\pi$
$258$	−12.4337	−0.774088
$259$	7.88690	0.490068
$260$	−3.73039	−0.231349
$261$	1.52088	0.0941404
$262$	20.0652	1.23963
$263$	−17.8452	−1.10038	−0.550190	−	0.835039i	$-0.685445\pi$
$263$	−17.8452	−1.10038	−0.550190	+	0.835039i	$0.685445\pi$
$264$	−2.78739	−0.171552
$265$	−31.0429	−1.90695
$266$	18.3885	1.12747
$267$	16.1743	0.989851
$268$	0.370914	0.0226572
$269$	3.55344	0.216657	0.108328	−	0.994115i	$-0.465450\pi$
$269$	3.55344	0.216657	0.108328	+	0.994115i	$0.465450\pi$
$270$	−3.73039	−0.227025
$271$	−20.3787	−1.23792	−0.618958	−	0.785424i	$-0.712445\pi$
$271$	−20.3787	−1.23792	−0.618958	+	0.785424i	$0.712445\pi$
$272$	−1.82947	−0.110928
$273$	−3.81724	−0.231030
$274$	14.9760	0.904732
$275$	−24.8519	−1.49863
$276$	−7.96106	−0.479199
$277$	28.3979	1.70626	0.853131	−	0.521697i	$-0.174701\pi$
$277$	28.3979	1.70626	0.853131	+	0.521697i	$0.174701\pi$
$278$	7.38106	0.442687
$279$	4.81724	0.288400
$280$	14.2398	0.850991
$281$	11.9777	0.714527	0.357263	−	0.934004i	$-0.383710\pi$
$281$	11.9777	0.714527	0.357263	+	0.934004i	$0.383710\pi$
$282$	7.09597	0.422559
$283$	3.74997	0.222912	0.111456	−	0.993769i	$-0.464449\pi$
$283$	3.74997	0.222912	0.111456	+	0.993769i	$0.464449\pi$
$284$	−5.96079	−0.353708
$285$	17.9702	1.06446
$286$	−2.78739	−0.164822
$287$	−35.3385	−2.08596
$288$	1.00000	0.0589256
$289$	−13.6531	−0.803121
$290$	−5.67350	−0.333159
$291$	−5.41994	−0.317723
$292$	−8.16895	−0.478051
$293$	−21.7349	−1.26977	−0.634883	−	0.772609i	$-0.718952\pi$
$293$	−21.7349	−1.26977	−0.634883	+	0.772609i	$0.718952\pi$
$294$	7.57129	0.441567
$295$	44.0566	2.56507
$296$	−2.06613	−0.120091
$297$	−2.78739	−0.161741
$298$	−11.1664	−0.646851
$299$	−7.96106	−0.460400
$300$	8.91584	0.514756
$301$	47.4623	2.73568
$302$	−22.5400	−1.29703
$303$	11.8049	0.678174
$304$	−4.81724	−0.276287
$305$	−26.4119	−1.51234
$306$	−1.82947	−0.104584
$307$	−7.34713	−0.419323	−0.209661	−	0.977774i	$-0.567236\pi$
$307$	−7.34713	−0.419323	−0.209661	+	0.977774i	$0.567236\pi$
$308$	10.6401	0.606278
$309$	−1.00000	−0.0568880
$310$	−17.9702	−1.02064
$311$	−10.6301	−0.602779	−0.301389	−	0.953501i	$-0.597450\pi$
$311$	−10.6301	−0.602779	−0.301389	+	0.953501i	$0.597450\pi$
$312$	1.00000	0.0566139
$313$	−25.5229	−1.44264	−0.721320	−	0.692602i	$-0.756464\pi$
$313$	−25.5229	−1.44264	−0.721320	+	0.692602i	$0.756464\pi$
$314$	4.08972	0.230796
$315$	14.2398	0.802322
$316$	−0.128451	−0.00722595
$317$	1.54530	0.0867924	0.0433962	−	0.999058i	$-0.486182\pi$
$317$	1.54530	0.0867924	0.0433962	+	0.999058i	$0.486182\pi$
$318$	8.32162	0.466653
$319$	−4.23930	−0.237355
$320$	−3.73039	−0.208535
$321$	10.8880	0.607710
$322$	30.3892	1.69353
$323$	8.81297	0.490367
$324$	1.00000	0.0555556
$325$	8.91584	0.494562
$326$	1.05188	0.0582581
$327$	−3.84577	−0.212671
$328$	9.25760	0.511166
$329$	−27.0870	−1.49335
$330$	10.3981	0.572395
$331$	19.0229	1.04559	0.522797	−	0.852457i	$-0.324888\pi$
$331$	19.0229	1.04559	0.522797	+	0.852457i	$0.324888\pi$
$332$	−0.0889117	−0.00487966
$333$	−2.06613	−0.113223
$334$	−17.9339	−0.981302
$335$	−1.38365	−0.0755971
$336$	−3.81724	−0.208247
$337$	−26.2691	−1.43097	−0.715484	−	0.698629i	$-0.753794\pi$
$337$	−26.2691	−1.43097	−0.715484	+	0.698629i	$0.753794\pi$
$338$	1.00000	0.0543928
$339$	16.4690	0.894474
$340$	6.82463	0.370118
$341$	−13.4275	−0.727141
$342$	−4.81724	−0.260486
$343$	−2.18075	−0.117750
$344$	−12.4337	−0.670379
$345$	29.6979	1.59888
$346$	20.6373	1.10947
$347$	35.7052	1.91676	0.958378	−	0.285501i	$-0.0921600\pi$
$347$	35.7052	1.91676	0.958378	+	0.285501i	$0.0921600\pi$
$348$	1.52088	0.0815279
$349$	3.62434	0.194006	0.0970031	−	0.995284i	$-0.469074\pi$
$349$	3.62434	0.194006	0.0970031	+	0.995284i	$0.469074\pi$
$350$	−34.0339	−1.81919
$351$	1.00000	0.0533761
$352$	−2.78739	−0.148568
$353$	−12.8869	−0.685900	−0.342950	−	0.939354i	$-0.611426\pi$
$353$	−12.8869	−0.685900	−0.342950	+	0.939354i	$0.611426\pi$
$354$	−11.8102	−0.627703
$355$	22.2361	1.18017
$356$	16.1743	0.857236
$357$	6.98350	0.369606
$358$	−7.03790	−0.371964
$359$	29.0019	1.53066	0.765330	−	0.643638i	$-0.222576\pi$
$359$	29.0019	1.53066	0.765330	+	0.643638i	$0.222576\pi$
$360$	−3.73039	−0.196609
$361$	4.20576	0.221356
$362$	21.1121	1.10963
$363$	−3.23045	−0.169555
$364$	−3.81724	−0.200078
$365$	30.4734	1.59505
$366$	7.08018	0.370087
$367$	14.9919	0.782572	0.391286	−	0.920269i	$-0.372030\pi$
$367$	14.9919	0.782572	0.391286	+	0.920269i	$0.372030\pi$
$368$	−7.96106	−0.414999
$369$	9.25760	0.481932
$370$	7.70747	0.400692
$371$	−31.7656	−1.64919
$372$	4.81724	0.249762
$373$	−19.7058	−1.02033	−0.510165	−	0.860077i	$-0.670416\pi$
$373$	−19.7058	−1.02033	−0.510165	+	0.860077i	$0.670416\pi$
$374$	5.09944	0.263686
$375$	−14.6076	−0.754335
$376$	7.09597	0.365947
$377$	1.52088	0.0783295
$378$	−3.81724	−0.196337
$379$	31.3027	1.60791	0.803956	−	0.594689i	$-0.202725\pi$
$379$	31.3027	1.60791	0.803956	+	0.594689i	$0.202725\pi$
$380$	17.9702	0.921851
$381$	−2.03375	−0.104192
$382$	−14.5164	−0.742724
$383$	−38.8196	−1.98359	−0.991796	−	0.127833i	$-0.959198\pi$
$383$	−38.8196	−1.98359	−0.991796	+	0.127833i	$0.959198\pi$
$384$	1.00000	0.0510310
$385$	−39.6919	−2.02289
$386$	21.4780	1.09320
$387$	−12.4337	−0.632040
$388$	−5.41994	−0.275156
$389$	11.8863	0.602660	0.301330	−	0.953520i	$-0.402569\pi$
$389$	11.8863	0.602660	0.301330	+	0.953520i	$0.402569\pi$
$390$	−3.73039	−0.188896
$391$	14.5645	0.736558
$392$	7.57129	0.382408
$393$	20.0652	1.01216
$394$	−3.80287	−0.191586
$395$	0.479174	0.0241099
$396$	−2.78739	−0.140072
$397$	0.194384	0.00975585	0.00487793	−	0.999988i	$-0.498447\pi$
$397$	0.194384	0.00975585	0.00487793	+	0.999988i	$0.498447\pi$
$398$	−15.4692	−0.775403
$399$	18.3885	0.920578
$400$	8.91584	0.445792
$401$	27.8375	1.39014	0.695068	−	0.718944i	$-0.255374\pi$
$401$	27.8375	1.39014	0.695068	+	0.718944i	$0.255374\pi$
$402$	0.370914	0.0184995
$403$	4.81724	0.239964
$404$	11.8049	0.587316
$405$	−3.73039	−0.185365
$406$	−5.80557	−0.288126
$407$	5.75911	0.285468
$408$	−1.82947	−0.0905721
$409$	23.5882	1.16636	0.583180	−	0.812343i	$-0.301808\pi$
$409$	23.5882	1.16636	0.583180	+	0.812343i	$0.301808\pi$
$410$	−34.5345	−1.70554
$411$	14.9760	0.738711
$412$	−1.00000	−0.0492665
$413$	45.0822	2.21835
$414$	−7.96106	−0.391265
$415$	0.331676	0.0162813
$416$	1.00000	0.0490290
$417$	7.38106	0.361452
$418$	13.4275	0.656761
$419$	17.6651	0.862998	0.431499	−	0.902113i	$-0.357985\pi$
$419$	17.6651	0.862998	0.431499	+	0.902113i	$0.357985\pi$
$420$	14.2398	0.694831
$421$	12.8435	0.625954	0.312977	−	0.949761i	$-0.398674\pi$
$421$	12.8435	0.625954	0.312977	+	0.949761i	$0.398674\pi$
$422$	19.3357	0.941245
$423$	7.09597	0.345018
$424$	8.32162	0.404134
$425$	−16.3112	−0.791211
$426$	−5.96079	−0.288801
$427$	−27.0267	−1.30791
$428$	10.8880	0.526292
$429$	−2.78739	−0.134576
$430$	46.3826	2.23677
$431$	−31.2742	−1.50642	−0.753212	−	0.657778i	$-0.771496\pi$
$431$	−31.2742	−1.50642	−0.753212	+	0.657778i	$0.771496\pi$
$432$	1.00000	0.0481125
$433$	−39.9789	−1.92126	−0.960631	−	0.277827i	$-0.910386\pi$
$433$	−39.9789	−1.92126	−0.960631	+	0.277827i	$0.910386\pi$
$434$	−18.3885	−0.882678
$435$	−5.67350	−0.272023
$436$	−3.84577	−0.184179
$437$	38.3503	1.83454
$438$	−8.16895	−0.390327
$439$	21.1632	1.01006	0.505031	−	0.863101i	$-0.331481\pi$
$439$	21.1632	1.01006	0.505031	+	0.863101i	$0.331481\pi$
$440$	10.3981	0.495708
$441$	7.57129	0.360538
$442$	−1.82947	−0.0870188
$443$	6.17581	0.293422	0.146711	−	0.989179i	$-0.453131\pi$
$443$	6.17581	0.293422	0.146711	+	0.989179i	$0.453131\pi$
$444$	−2.06613	−0.0980541
$445$	−60.3365	−2.86023
$446$	9.66464	0.457634
$447$	−11.1664	−0.528152
$448$	−3.81724	−0.180347
$449$	16.0216	0.756105	0.378052	−	0.925784i	$-0.376594\pi$
$449$	16.0216	0.756105	0.378052	+	0.925784i	$0.376594\pi$
$450$	8.91584	0.420297
$451$	−25.8046	−1.21509
$452$	16.4690	0.774637
$453$	−22.5400	−1.05902
$454$	−14.7387	−0.691720
$455$	14.2398	0.667572
$456$	−4.81724	−0.225588
$457$	27.8214	1.30143	0.650716	−	0.759322i	$-0.274469\pi$
$457$	27.8214	1.30143	0.650716	+	0.759322i	$0.274469\pi$
$458$	−25.0490	−1.17046
$459$	−1.82947	−0.0853922
$460$	29.6979	1.38467
$461$	−2.60939	−0.121532	−0.0607658	−	0.998152i	$-0.519354\pi$
$461$	−2.60939	−0.121532	−0.0607658	+	0.998152i	$0.519354\pi$
$462$	10.6401	0.495024
$463$	−23.8969	−1.11058	−0.555292	−	0.831655i	$-0.687394\pi$
$463$	−23.8969	−1.11058	−0.555292	+	0.831655i	$0.687394\pi$
$464$	1.52088	0.0706053
$465$	−17.9702	−0.833348
$466$	0.594073	0.0275199
$467$	4.16228	0.192607	0.0963036	−	0.995352i	$-0.469298\pi$
$467$	4.16228	0.192607	0.0963036	+	0.995352i	$0.469298\pi$
$468$	1.00000	0.0462250
$469$	−1.41587	−0.0653786
$470$	−26.4708	−1.22101
$471$	4.08972	0.188444
$472$	−11.8102	−0.543607
$473$	34.6575	1.59356
$474$	−0.128451	−0.00589997
$475$	−42.9497	−1.97067
$476$	6.98350	0.320088
$477$	8.32162	0.381021
$478$	11.6810	0.534276
$479$	−10.8745	−0.496867	−0.248434	−	0.968649i	$-0.579916\pi$
$479$	−10.8745	−0.496867	−0.248434	+	0.968649i	$0.579916\pi$
$480$	−3.73039	−0.170268
$481$	−2.06613	−0.0942073
$482$	15.5781	0.709564
$483$	30.3892	1.38276
$484$	−3.23045	−0.146839
$485$	20.2185	0.918076
$486$	1.00000	0.0453609
$487$	−12.8951	−0.584333	−0.292166	−	0.956367i	$-0.594376\pi$
$487$	−12.8951	−0.584333	−0.292166	+	0.956367i	$0.594376\pi$
$488$	7.08018	0.320505
$489$	1.05188	0.0475676
$490$	−28.2439	−1.27593
$491$	−18.7583	−0.846550	−0.423275	−	0.906001i	$-0.639120\pi$
$491$	−18.7583	−0.846550	−0.423275	+	0.906001i	$0.639120\pi$
$492$	9.25760	0.417365
$493$	−2.78241	−0.125313
$494$	−4.81724	−0.216738
$495$	10.3981	0.467358
$496$	4.81724	0.216300
$497$	22.7537	1.02064
$498$	−0.0889117	−0.00398423
$499$	11.8267	0.529438	0.264719	−	0.964326i	$-0.414721\pi$
$499$	11.8267	0.529438	0.264719	+	0.964326i	$0.414721\pi$
$500$	−14.6076	−0.653273
$501$	−17.9339	−0.801229
$502$	7.11665	0.317632
$503$	−5.18477	−0.231177	−0.115589	−	0.993297i	$-0.536875\pi$
$503$	−5.18477	−0.231177	−0.115589	+	0.993297i	$0.536875\pi$
$504$	−3.81724	−0.170033
$505$	−44.0369	−1.95962
$506$	22.1906	0.986492
$507$	1.00000	0.0444116
$508$	−2.03375	−0.0902331
$509$	−15.2130	−0.674306	−0.337153	−	0.941450i	$-0.609464\pi$
$509$	−15.2130	−0.674306	−0.337153	+	0.941450i	$0.609464\pi$
$510$	6.82463	0.302200
$511$	31.1828	1.37945
$512$	1.00000	0.0441942
$513$	−4.81724	−0.212686
$514$	11.6819	0.515266
$515$	3.73039	0.164381
$516$	−12.4337	−0.547363
$517$	−19.7793	−0.869890
$518$	7.88690	0.346530
$519$	20.6373	0.905877
$520$	−3.73039	−0.163589
$521$	−8.28142	−0.362815	−0.181408	−	0.983408i	$-0.558065\pi$
$521$	−8.28142	−0.362815	−0.181408	+	0.983408i	$0.558065\pi$
$522$	1.52088	0.0665673
$523$	−22.2347	−0.972257	−0.486128	−	0.873887i	$-0.661591\pi$
$523$	−22.2347	−0.972257	−0.486128	+	0.873887i	$0.661591\pi$
$524$	20.0652	0.876554
$525$	−34.0339	−1.48536
$526$	−17.8452	−0.778086
$527$	−8.81297	−0.383899
$528$	−2.78739	−0.121306
$529$	40.3785	1.75559
$530$	−31.0429	−1.34842
$531$	−11.8102	−0.512517
$532$	18.3885	0.797244
$533$	9.25760	0.400991
$534$	16.1743	0.699931
$535$	−40.6166	−1.75601
$536$	0.370914	0.0160210
$537$	−7.03790	−0.303708
$538$	3.55344	0.153199
$539$	−21.1041	−0.909020
$540$	−3.73039	−0.160531
$541$	2.74010	0.117806	0.0589030	−	0.998264i	$-0.481240\pi$
$541$	2.74010	0.117806	0.0589030	+	0.998264i	$0.481240\pi$
$542$	−20.3787	−0.875339
$543$	21.1121	0.906008
$544$	−1.82947	−0.0784377
$545$	14.3462	0.614525
$546$	−3.81724	−0.163363
$547$	−23.4272	−1.00167	−0.500836	−	0.865542i	$-0.666974\pi$
$547$	−23.4272	−1.00167	−0.500836	+	0.865542i	$0.666974\pi$
$548$	14.9760	0.639742
$549$	7.08018	0.302175
$550$	−24.8519	−1.05969
$551$	−7.32646	−0.312118
$552$	−7.96106	−0.338845
$553$	0.490329	0.0208509
$554$	28.3979	1.20651
$555$	7.70747	0.327164
$556$	7.38106	0.313027
$557$	37.7843	1.60097	0.800486	−	0.599351i	$-0.204575\pi$
$557$	37.7843	1.60097	0.800486	+	0.599351i	$0.204575\pi$
$558$	4.81724	0.203930
$559$	−12.4337	−0.525889
$560$	14.2398	0.601741
$561$	5.09944	0.215298
$562$	11.9777	0.505247
$563$	10.7857	0.454561	0.227281	−	0.973829i	$-0.427017\pi$
$563$	10.7857	0.454561	0.227281	+	0.973829i	$0.427017\pi$
$564$	7.09597	0.298794
$565$	−61.4359	−2.58463
$566$	3.74997	0.157623
$567$	−3.81724	−0.160309
$568$	−5.96079	−0.250109
$569$	6.03987	0.253204	0.126602	−	0.991954i	$-0.459593\pi$
$569$	6.03987	0.253204	0.126602	+	0.991954i	$0.459593\pi$
$570$	17.9702	0.752688
$571$	−7.62352	−0.319034	−0.159517	−	0.987195i	$-0.550994\pi$
$571$	−7.62352	−0.319034	−0.159517	+	0.987195i	$0.550994\pi$
$572$	−2.78739	−0.116547
$573$	−14.5164	−0.606432
$574$	−35.3385	−1.47500
$575$	−70.9795	−2.96005
$576$	1.00000	0.0416667
$577$	−16.7035	−0.695376	−0.347688	−	0.937610i	$-0.613033\pi$
$577$	−16.7035	−0.695376	−0.347688	+	0.937610i	$0.613033\pi$
$578$	−13.6531	−0.567892
$579$	21.4780	0.892597
$580$	−5.67350	−0.235579
$581$	0.339397	0.0140806
$582$	−5.41994	−0.224664
$583$	−23.1956	−0.960664
$584$	−8.16895	−0.338033
$585$	−3.73039	−0.154233
$586$	−21.7349	−0.897860
$587$	25.3613	1.04677	0.523387	−	0.852095i	$-0.324668\pi$
$587$	25.3613	1.04677	0.523387	+	0.852095i	$0.324668\pi$
$588$	7.57129	0.312235
$589$	−23.2058	−0.956177
$590$	44.0566	1.81378
$591$	−3.80287	−0.156429
$592$	−2.06613	−0.0849173
$593$	−32.6380	−1.34028	−0.670142	−	0.742233i	$-0.733767\pi$
$593$	−32.6380	−1.34028	−0.670142	+	0.742233i	$0.733767\pi$
$594$	−2.78739	−0.114368
$595$	−26.0512	−1.06800
$596$	−11.1664	−0.457393
$597$	−15.4692	−0.633114
$598$	−7.96106	−0.325552
$599$	21.9840	0.898242	0.449121	−	0.893471i	$-0.351737\pi$
$599$	21.9840	0.898242	0.449121	+	0.893471i	$0.351737\pi$
$600$	8.91584	0.363988
$601$	−14.2291	−0.580416	−0.290208	−	0.956964i	$-0.593724\pi$
$601$	−14.2291	−0.580416	−0.290208	+	0.956964i	$0.593724\pi$
$602$	47.4623	1.93442
$603$	0.370914	0.0151048
$604$	−22.5400	−0.917141
$605$	12.0509	0.489937
$606$	11.8049	0.479541
$607$	−17.1936	−0.697865	−0.348933	−	0.937148i	$-0.613456\pi$
$607$	−17.1936	−0.697865	−0.348933	+	0.937148i	$0.613456\pi$
$608$	−4.81724	−0.195365
$609$	−5.80557	−0.235254
$610$	−26.4119	−1.06939
$611$	7.09597	0.287072
$612$	−1.82947	−0.0739518
$613$	−14.0586	−0.567821	−0.283910	−	0.958851i	$-0.591632\pi$
$613$	−14.0586	−0.567821	−0.283910	+	0.958851i	$0.591632\pi$
$614$	−7.34713	−0.296506
$615$	−34.5345	−1.39257
$616$	10.6401	0.428703
$617$	−36.8543	−1.48370	−0.741849	−	0.670567i	$-0.766051\pi$
$617$	−36.8543	−1.48370	−0.741849	+	0.670567i	$0.766051\pi$
$618$	−1.00000	−0.0402259
$619$	33.7962	1.35838	0.679191	−	0.733961i	$-0.262331\pi$
$619$	33.7962	1.35838	0.679191	+	0.733961i	$0.262331\pi$
$620$	−17.9702	−0.721700
$621$	−7.96106	−0.319466
$622$	−10.6301	−0.426229
$623$	−61.7411	−2.47361
$624$	1.00000	0.0400320
$625$	9.91303	0.396521
$626$	−25.5229	−1.02010
$627$	13.4275	0.536243
$628$	4.08972	0.163198
$629$	3.77991	0.150715
$630$	14.2398	0.567327
$631$	17.4751	0.695675	0.347837	−	0.937555i	$-0.386916\pi$
$631$	17.4751	0.695675	0.347837	+	0.937555i	$0.386916\pi$
$632$	−0.128451	−0.00510952
$633$	19.3357	0.768523
$634$	1.54530	0.0613715
$635$	7.58669	0.301069
$636$	8.32162	0.329974
$637$	7.57129	0.299985
$638$	−4.23930	−0.167835
$639$	−5.96079	−0.235805
$640$	−3.73039	−0.147457
$641$	28.4738	1.12465	0.562323	−	0.826918i	$-0.309908\pi$
$641$	28.4738	1.12465	0.562323	+	0.826918i	$0.309908\pi$
$642$	10.8880	0.429716
$643$	−16.8499	−0.664495	−0.332247	−	0.943192i	$-0.607807\pi$
$643$	−16.8499	−0.664495	−0.332247	+	0.943192i	$0.607807\pi$
$644$	30.3892	1.19750
$645$	46.3826	1.82631
$646$	8.81297	0.346742
$647$	38.6850	1.52086	0.760432	−	0.649417i	$-0.224987\pi$
$647$	38.6850	1.52086	0.760432	+	0.649417i	$0.224987\pi$
$648$	1.00000	0.0392837
$649$	32.9195	1.29220
$650$	8.91584	0.349708
$651$	−18.3885	−0.720703
$652$	1.05188	0.0411947
$653$	−21.5460	−0.843159	−0.421579	−	0.906792i	$-0.638524\pi$
$653$	−21.5460	−0.843159	−0.421579	+	0.906792i	$0.638524\pi$
$654$	−3.84577	−0.150381
$655$	−74.8513	−2.92468
$656$	9.25760	0.361449
$657$	−8.16895	−0.318701
$658$	−27.0870	−1.05596
$659$	6.25967	0.243842	0.121921	−	0.992540i	$-0.461095\pi$
$659$	6.25967	0.243842	0.121921	+	0.992540i	$0.461095\pi$
$660$	10.3981	0.404744
$661$	−18.3348	−0.713140	−0.356570	−	0.934269i	$-0.616054\pi$
$661$	−18.3348	−0.713140	−0.356570	+	0.934269i	$0.616054\pi$
$662$	19.0229	0.739347
$663$	−1.82947	−0.0710506
$664$	−0.0889117	−0.00345044
$665$	−68.5965	−2.66006
$666$	−2.06613	−0.0800608
$667$	−12.1078	−0.468818
$668$	−17.9339	−0.693885
$669$	9.66464	0.373657
$670$	−1.38365	−0.0534553
$671$	−19.7352	−0.761870
$672$	−3.81724	−0.147253
$673$	19.4710	0.750551	0.375276	−	0.926913i	$-0.377548\pi$
$673$	19.4710	0.750551	0.375276	+	0.926913i	$0.377548\pi$
$674$	−26.2691	−1.01185
$675$	8.91584	0.343171
$676$	1.00000	0.0384615
$677$	17.4527	0.670761	0.335381	−	0.942083i	$-0.391135\pi$
$677$	17.4527	0.670761	0.335381	+	0.942083i	$0.391135\pi$
$678$	16.4690	0.632488
$679$	20.6892	0.793979
$680$	6.82463	0.261713
$681$	−14.7387	−0.564787
$682$	−13.4275	−0.514166
$683$	51.1105	1.95569	0.977845	−	0.209329i	$-0.0671281\pi$
$683$	51.1105	1.95569	0.977845	+	0.209329i	$0.0671281\pi$
$684$	−4.81724	−0.184192
$685$	−55.8663	−2.13454
$686$	−2.18075	−0.0832616
$687$	−25.0490	−0.955680
$688$	−12.4337	−0.474030
$689$	8.32162	0.317028
$690$	29.6979	1.13058
$691$	13.7032	0.521295	0.260647	−	0.965434i	$-0.416064\pi$
$691$	13.7032	0.521295	0.260647	+	0.965434i	$0.416064\pi$
$692$	20.6373	0.784512
$693$	10.6401	0.404185
$694$	35.7052	1.35535
$695$	−27.5343	−1.04443
$696$	1.52088	0.0576490
$697$	−16.9365	−0.641515
$698$	3.62434	0.137183
$699$	0.594073	0.0224699
$700$	−34.0339	−1.28636
$701$	−20.5188	−0.774985	−0.387493	−	0.921873i	$-0.626659\pi$
$701$	−20.5188	−0.774985	−0.387493	+	0.921873i	$0.626659\pi$
$702$	1.00000	0.0377426
$703$	9.95303	0.375385
$704$	−2.78739	−0.105054
$705$	−26.4708	−0.996947
$706$	−12.8869	−0.485004
$707$	−45.0621	−1.69473
$708$	−11.8102	−0.443853
$709$	−31.2068	−1.17199	−0.585997	−	0.810313i	$-0.699297\pi$
$709$	−31.2068	−1.17199	−0.585997	+	0.810313i	$0.699297\pi$
$710$	22.2361	0.834505
$711$	−0.128451	−0.00481730
$712$	16.1743	0.606158
$713$	−38.3503	−1.43623
$714$	6.98350	0.261351
$715$	10.3981	0.388866
$716$	−7.03790	−0.263019
$717$	11.6810	0.436234
$718$	29.0019	1.08234
$719$	−0.0607422	−0.00226530	−0.00113265	−	0.999999i	$-0.500361\pi$
$719$	−0.0607422	−0.00226530	−0.00113265	+	0.999999i	$0.500361\pi$
$720$	−3.73039	−0.139024
$721$	3.81724	0.142161
$722$	4.20576	0.156522
$723$	15.5781	0.579357
$724$	21.1121	0.784626
$725$	13.5600	0.503604
$726$	−3.23045	−0.119893
$727$	−13.3691	−0.495833	−0.247917	−	0.968781i	$-0.579746\pi$
$727$	−13.3691	−0.495833	−0.247917	+	0.968781i	$0.579746\pi$
$728$	−3.81724	−0.141476
$729$	1.00000	0.0370370
$730$	30.4734	1.12787
$731$	22.7470	0.841329
$732$	7.08018	0.261691
$733$	−6.32904	−0.233769	−0.116884	−	0.993146i	$-0.537291\pi$
$733$	−6.32904	−0.233769	−0.116884	+	0.993146i	$0.537291\pi$
$734$	14.9919	0.553362
$735$	−28.2439	−1.04179
$736$	−7.96106	−0.293449
$737$	−1.03388	−0.0380835
$738$	9.25760	0.340777
$739$	47.7107	1.75507	0.877534	−	0.479515i	$-0.159187\pi$
$739$	47.7107	1.75507	0.877534	+	0.479515i	$0.159187\pi$
$740$	7.70747	0.283332
$741$	−4.81724	−0.176966
$742$	−31.7656	−1.16615
$743$	−16.1107	−0.591045	−0.295523	−	0.955336i	$-0.595494\pi$
$743$	−16.1107	−0.591045	−0.295523	+	0.955336i	$0.595494\pi$
$744$	4.81724	0.176608
$745$	41.6550	1.52612
$746$	−19.7058	−0.721482
$747$	−0.0889117	−0.00325311
$748$	5.09944	0.186454
$749$	−41.5621	−1.51865
$750$	−14.6076	−0.533395
$751$	29.6824	1.08313	0.541563	−	0.840660i	$-0.317833\pi$
$751$	29.6824	1.08313	0.541563	+	0.840660i	$0.317833\pi$
$752$	7.09597	0.258764
$753$	7.11665	0.259345
$754$	1.52088	0.0553873
$755$	84.0832	3.06010
$756$	−3.81724	−0.138832
$757$	21.9207	0.796722	0.398361	−	0.917229i	$-0.369579\pi$
$757$	21.9207	0.796722	0.398361	+	0.917229i	$0.369579\pi$
$758$	31.3027	1.13697
$759$	22.1906	0.805467
$760$	17.9702	0.651847
$761$	−19.8987	−0.721329	−0.360664	−	0.932696i	$-0.617450\pi$
$761$	−19.8987	−0.721329	−0.360664	+	0.932696i	$0.617450\pi$
$762$	−2.03375	−0.0736750
$763$	14.6802	0.531459
$764$	−14.5164	−0.525185
$765$	6.82463	0.246745
$766$	−38.8196	−1.40261
$767$	−11.8102	−0.426440
$768$	1.00000	0.0360844
$769$	8.94794	0.322671	0.161335	−	0.986900i	$-0.448420\pi$
$769$	8.94794	0.322671	0.161335	+	0.986900i	$0.448420\pi$
$770$	−39.6919	−1.43040
$771$	11.6819	0.420713
$772$	21.4780	0.773012
$773$	30.1153	1.08317	0.541586	−	0.840645i	$-0.317824\pi$
$773$	30.1153	1.08317	0.541586	+	0.840645i	$0.317824\pi$
$774$	−12.4337	−0.446920
$775$	42.9497	1.54280
$776$	−5.41994	−0.194565
$777$	7.88690	0.282941
$778$	11.8863	0.426145
$779$	−44.5961	−1.59782
$780$	−3.73039	−0.133570
$781$	16.6150	0.594533
$782$	14.5645	0.520825
$783$	1.52088	0.0543520
$784$	7.57129	0.270403
$785$	−15.2563	−0.544520
$786$	20.0652	0.715704
$787$	30.5382	1.08857	0.544285	−	0.838900i	$-0.316801\pi$
$787$	30.5382	1.08857	0.544285	+	0.838900i	$0.316801\pi$
$788$	−3.80287	−0.135472
$789$	−17.8452	−0.635305
$790$	0.479174	0.0170483
$791$	−62.8661	−2.23526
$792$	−2.78739	−0.0990456
$793$	7.08018	0.251425
$794$	0.194384	0.00689843
$795$	−31.0429	−1.10098
$796$	−15.4692	−0.548293
$797$	−36.7380	−1.30133	−0.650663	−	0.759367i	$-0.725509\pi$
$797$	−36.7380	−1.30133	−0.650663	+	0.759367i	$0.725509\pi$
$798$	18.3885	0.650947
$799$	−12.9818	−0.459265
$800$	8.91584	0.315223
$801$	16.1743	0.571491
$802$	27.8375	0.982975
$803$	22.7700	0.803537
$804$	0.370914	0.0130811
$805$	−113.364	−3.99555
$806$	4.81724	0.169680
$807$	3.55344	0.125087
$808$	11.8049	0.415295
$809$	26.3020	0.924730	0.462365	−	0.886690i	$-0.347001\pi$
$809$	26.3020	0.924730	0.462365	+	0.886690i	$0.347001\pi$
$810$	−3.73039	−0.131073
$811$	−4.87813	−0.171294	−0.0856471	−	0.996326i	$-0.527296\pi$
$811$	−4.87813	−0.171294	−0.0856471	+	0.996326i	$0.527296\pi$
$812$	−5.80557	−0.203736
$813$	−20.3787	−0.714711
$814$	5.75911	0.201857
$815$	−3.92392	−0.137449
$816$	−1.82947	−0.0640441
$817$	59.8960	2.09550
$818$	23.5882	0.824741
$819$	−3.81724	−0.133385
$820$	−34.5345	−1.20600
$821$	14.8445	0.518076	0.259038	−	0.965867i	$-0.416594\pi$
$821$	14.8445	0.518076	0.259038	+	0.965867i	$0.416594\pi$
$822$	14.9760	0.522347
$823$	−12.2833	−0.428168	−0.214084	−	0.976815i	$-0.568677\pi$
$823$	−12.2833	−0.428168	−0.214084	+	0.976815i	$0.568677\pi$
$824$	−1.00000	−0.0348367
$825$	−24.8519	−0.865233
$826$	45.0822	1.56861
$827$	15.3321	0.533148	0.266574	−	0.963814i	$-0.414108\pi$
$827$	15.3321	0.533148	0.266574	+	0.963814i	$0.414108\pi$
$828$	−7.96106	−0.276666
$829$	−28.9893	−1.00684	−0.503420	−	0.864042i	$-0.667925\pi$
$829$	−28.9893	−1.00684	−0.503420	+	0.864042i	$0.667925\pi$
$830$	0.331676	0.0115126
$831$	28.3979	0.985111
$832$	1.00000	0.0346688
$833$	−13.8514	−0.479923
$834$	7.38106	0.255585
$835$	66.9007	2.31519
$836$	13.4275	0.464400
$837$	4.81724	0.166508
$838$	17.6651	0.610232
$839$	−12.2096	−0.421522	−0.210761	−	0.977538i	$-0.567594\pi$
$839$	−12.2096	−0.421522	−0.210761	+	0.977538i	$0.567594\pi$
$840$	14.2398	0.491320
$841$	−26.6869	−0.920238
$842$	12.8435	0.442616
$843$	11.9777	0.412532
$844$	19.3357	0.665561
$845$	−3.73039	−0.128329
$846$	7.09597	0.243965
$847$	12.3314	0.423712
$848$	8.32162	0.285766
$849$	3.74997	0.128699
$850$	−16.3112	−0.559471
$851$	16.4486	0.563850
$852$	−5.96079	−0.204213
$853$	−44.3468	−1.51840	−0.759202	−	0.650855i	$-0.774411\pi$
$853$	−44.3468	−1.51840	−0.759202	+	0.650855i	$0.774411\pi$
$854$	−27.0267	−0.924835
$855$	17.9702	0.614568
$856$	10.8880	0.372145
$857$	50.5552	1.72693	0.863466	−	0.504407i	$-0.168289\pi$
$857$	50.5552	1.72693	0.863466	+	0.504407i	$0.168289\pi$
$858$	−2.78739	−0.0951600
$859$	−37.2008	−1.26927	−0.634637	−	0.772811i	$-0.718850\pi$
$859$	−37.2008	−1.26927	−0.634637	+	0.772811i	$0.718850\pi$
$860$	46.3826	1.58163
$861$	−35.3385	−1.20433
$862$	−31.2742	−1.06520
$863$	−6.36316	−0.216605	−0.108302	−	0.994118i	$-0.534541\pi$
$863$	−6.36316	−0.216605	−0.108302	+	0.994118i	$0.534541\pi$
$864$	1.00000	0.0340207
$865$	−76.9852	−2.61758
$866$	−39.9789	−1.35854
$867$	−13.6531	−0.463682
$868$	−18.3885	−0.624147
$869$	0.358044	0.0121458
$870$	−5.67350	−0.192350
$871$	0.370914	0.0125679
$872$	−3.84577	−0.130234
$873$	−5.41994	−0.183437
$874$	38.3503	1.29722
$875$	55.7608	1.88506
$876$	−8.16895	−0.276003
$877$	−24.5505	−0.829013	−0.414506	−	0.910046i	$-0.636046\pi$
$877$	−24.5505	−0.829013	−0.414506	+	0.910046i	$0.636046\pi$
$878$	21.1632	0.714222
$879$	−21.7349	−0.733099
$880$	10.3981	0.350519
$881$	−33.4171	−1.12585	−0.562925	−	0.826508i	$-0.690324\pi$
$881$	−33.4171	−1.12585	−0.562925	+	0.826508i	$0.690324\pi$
$882$	7.57129	0.254939
$883$	−9.57439	−0.322204	−0.161102	−	0.986938i	$-0.551505\pi$
$883$	−9.57439	−0.322204	−0.161102	+	0.986938i	$0.551505\pi$
$884$	−1.82947	−0.0615316
$885$	44.0566	1.48094
$886$	6.17581	0.207480
$887$	−0.473993	−0.0159151	−0.00795756	−	0.999968i	$-0.502533\pi$
$887$	−0.473993	−0.0159151	−0.00795756	+	0.999968i	$0.502533\pi$
$888$	−2.06613	−0.0693347
$889$	7.76330	0.260373
$890$	−60.3365	−2.02249
$891$	−2.78739	−0.0933811
$892$	9.66464	0.323596
$893$	−34.1830	−1.14389
$894$	−11.1664	−0.373460
$895$	26.2541	0.877579
$896$	−3.81724	−0.127525
$897$	−7.96106	−0.265812
$898$	16.0216	0.534647
$899$	7.32646	0.244351
$900$	8.91584	0.297195
$901$	−15.2241	−0.507189
$902$	−25.8046	−0.859198
$903$	47.4623	1.57945
$904$	16.4690	0.547751
$905$	−78.7566	−2.61796
$906$	−22.5400	−0.748842
$907$	0.916903	0.0304453	0.0152226	−	0.999884i	$-0.495154\pi$
$907$	0.916903	0.0304453	0.0152226	+	0.999884i	$0.495154\pi$
$908$	−14.7387	−0.489120
$909$	11.8049	0.391544
$910$	14.2398	0.472045
$911$	22.8535	0.757172	0.378586	−	0.925566i	$-0.376410\pi$
$911$	22.8535	0.757172	0.378586	+	0.925566i	$0.376410\pi$
$912$	−4.81724	−0.159515
$913$	0.247832	0.00820203
$914$	27.8214	0.920251
$915$	−26.4119	−0.873149
$916$	−25.0490	−0.827643
$917$	−76.5938	−2.52935
$918$	−1.82947	−0.0603814
$919$	56.8972	1.87687	0.938433	−	0.345462i	$-0.112278\pi$
$919$	56.8972	1.87687	0.938433	+	0.345462i	$0.112278\pi$
$920$	29.6979	0.979110
$921$	−7.34713	−0.242096
$922$	−2.60939	−0.0859358
$923$	−5.96079	−0.196202
$924$	10.6401	0.350035
$925$	−18.4213	−0.605688
$926$	−23.8969	−0.785302
$927$	−1.00000	−0.0328443
$928$	1.52088	0.0499255
$929$	−4.01742	−0.131807	−0.0659036	−	0.997826i	$-0.520993\pi$
$929$	−4.01742	−0.131807	−0.0659036	+	0.997826i	$0.520993\pi$
$930$	−17.9702	−0.589266
$931$	−36.4727	−1.19534
$932$	0.594073	0.0194595
$933$	−10.6301	−0.348014
$934$	4.16228	0.136194
$935$	−19.0229	−0.622116
$936$	1.00000	0.0326860
$937$	−17.3250	−0.565982	−0.282991	−	0.959123i	$-0.591327\pi$
$937$	−17.3250	−0.565982	−0.282991	+	0.959123i	$0.591327\pi$
$938$	−1.41587	−0.0462297
$939$	−25.5229	−0.832908
$940$	−26.4708	−0.863382
$941$	21.1195	0.688477	0.344239	−	0.938882i	$-0.388137\pi$
$941$	21.1195	0.688477	0.344239	+	0.938882i	$0.388137\pi$
$942$	4.08972	0.133250
$943$	−73.7003	−2.40001
$944$	−11.8102	−0.384388
$945$	14.2398	0.463221
$946$	34.6575	1.12681
$947$	−44.8177	−1.45638	−0.728190	−	0.685375i	$-0.759638\pi$
$947$	−44.8177	−1.45638	−0.728190	+	0.685375i	$0.759638\pi$
$948$	−0.128451	−0.00417191
$949$	−8.16895	−0.265175
$950$	−42.9497	−1.39347
$951$	1.54530	0.0501096
$952$	6.98350	0.226337
$953$	−2.74155	−0.0888074	−0.0444037	−	0.999014i	$-0.514139\pi$
$953$	−2.74155	−0.0888074	−0.0444037	+	0.999014i	$0.514139\pi$
$954$	8.32162	0.269422
$955$	54.1519	1.75232
$956$	11.6810	0.377790
$957$	−4.23930	−0.137037
$958$	−10.8745	−0.351338
$959$	−57.1669	−1.84601
$960$	−3.73039	−0.120398
$961$	−7.79424	−0.251427
$962$	−2.06613	−0.0666146
$963$	10.8880	0.350861
$964$	15.5781	0.501738
$965$	−80.1216	−2.57920
$966$	30.3892	0.977758
$967$	−7.76513	−0.249710	−0.124855	−	0.992175i	$-0.539847\pi$
$967$	−7.76513	−0.249710	−0.124855	+	0.992175i	$0.539847\pi$
$968$	−3.23045	−0.103831
$969$	8.81297	0.283113
$970$	20.2185	0.649178
$971$	30.6759	0.984438	0.492219	−	0.870471i	$-0.336186\pi$
$971$	30.6759	0.984438	0.492219	+	0.870471i	$0.336186\pi$
$972$	1.00000	0.0320750
$973$	−28.1753	−0.903258
$974$	−12.8951	−0.413186
$975$	8.91584	0.285535
$976$	7.08018	0.226631
$977$	59.9638	1.91841	0.959206	−	0.282709i	$-0.0912329\pi$
$977$	59.9638	1.91841	0.959206	+	0.282709i	$0.0912329\pi$
$978$	1.05188	0.0336353
$979$	−45.0841	−1.44089
$980$	−28.2439	−0.902218
$981$	−3.84577	−0.122786
$982$	−18.7583	−0.598601
$983$	−26.9882	−0.860790	−0.430395	−	0.902641i	$-0.641626\pi$
$983$	−26.9882	−0.860790	−0.430395	+	0.902641i	$0.641626\pi$
$984$	9.25760	0.295122
$985$	14.1862	0.452010
$986$	−2.78241	−0.0886099
$987$	−27.0870	−0.862189
$988$	−4.81724	−0.153257
$989$	98.9853	3.14755
$990$	10.3981	0.330472
$991$	15.9683	0.507251	0.253625	−	0.967303i	$-0.418377\pi$
$991$	15.9683	0.507251	0.253625	+	0.967303i	$0.418377\pi$
$992$	4.81724	0.152947
$993$	19.0229	0.603674
$994$	22.7537	0.721704
$995$	57.7064	1.82942
$996$	−0.0889117	−0.00281728
$997$	−38.8569	−1.23061	−0.615305	−	0.788289i	$-0.710967\pi$
$997$	−38.8569	−1.23061	−0.615305	+	0.788289i	$0.710967\pi$
$998$	11.8267	0.374369
$999$	−2.06613	−0.0653694

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.v.1.1	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.v.1.1	✓	11	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:	\( N \)	\(=\)	\( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.73039 q^{5} +1.00000 q^{6} -3.81724 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.73039 q^{5} +1.00000 q^{6} -3.81724 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.73039 q^{10} -2.78739 q^{11} +1.00000 q^{12} +1.00000 q^{13} -3.81724 q^{14} -3.73039 q^{15} +1.00000 q^{16} -1.82947 q^{17} +1.00000 q^{18} -4.81724 q^{19} -3.73039 q^{20} -3.81724 q^{21} -2.78739 q^{22} -7.96106 q^{23} +1.00000 q^{24} +8.91584 q^{25} +1.00000 q^{26} +1.00000 q^{27} -3.81724 q^{28} +1.52088 q^{29} -3.73039 q^{30} +4.81724 q^{31} +1.00000 q^{32} -2.78739 q^{33} -1.82947 q^{34} +14.2398 q^{35} +1.00000 q^{36} -2.06613 q^{37} -4.81724 q^{38} +1.00000 q^{39} -3.73039 q^{40} +9.25760 q^{41} -3.81724 q^{42} -12.4337 q^{43} -2.78739 q^{44} -3.73039 q^{45} -7.96106 q^{46} +7.09597 q^{47} +1.00000 q^{48} +7.57129 q^{49} +8.91584 q^{50} -1.82947 q^{51} +1.00000 q^{52} +8.32162 q^{53} +1.00000 q^{54} +10.3981 q^{55} -3.81724 q^{56} -4.81724 q^{57} +1.52088 q^{58} -11.8102 q^{59} -3.73039 q^{60} +7.08018 q^{61} +4.81724 q^{62} -3.81724 q^{63} +1.00000 q^{64} -3.73039 q^{65} -2.78739 q^{66} +0.370914 q^{67} -1.82947 q^{68} -7.96106 q^{69} +14.2398 q^{70} -5.96079 q^{71} +1.00000 q^{72} -8.16895 q^{73} -2.06613 q^{74} +8.91584 q^{75} -4.81724 q^{76} +10.6401 q^{77} +1.00000 q^{78} -0.128451 q^{79} -3.73039 q^{80} +1.00000 q^{81} +9.25760 q^{82} -0.0889117 q^{83} -3.81724 q^{84} +6.82463 q^{85} -12.4337 q^{86} +1.52088 q^{87} -2.78739 q^{88} +16.1743 q^{89} -3.73039 q^{90} -3.81724 q^{91} -7.96106 q^{92} +4.81724 q^{93} +7.09597 q^{94} +17.9702 q^{95} +1.00000 q^{96} -5.41994 q^{97} +7.57129 q^{98} -2.78739 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 11 q^{2} + 11 q^{3} + 11 q^{4} + 5 q^{5} + 11 q^{6} + 4 q^{7} + 11 q^{8} + 11 q^{9}+O(q^{10}) \) 11 * q + 11 * q^2 + 11 * q^3 + 11 * q^4 + 5 * q^5 + 11 * q^6 + 4 * q^7 + 11 * q^8 + 11 * q^9	\( 11 q + 11 q^{2} + 11 q^{3} + 11 q^{4} + 5 q^{5} + 11 q^{6} + 4 q^{7} + 11 q^{8} + 11 q^{9} + 5 q^{10} - 7 q^{11} + 11 q^{12} + 11 q^{13} + 4 q^{14} + 5 q^{15} + 11 q^{16} + 10 q^{17} + 11 q^{18} - 7 q^{19} + 5 q^{20} + 4 q^{21} - 7 q^{22} + 18 q^{23} + 11 q^{24} + 32 q^{25} + 11 q^{26} + 11 q^{27} + 4 q^{28} + 29 q^{29} + 5 q^{30} + 7 q^{31} + 11 q^{32} - 7 q^{33} + 10 q^{34} + 31 q^{35} + 11 q^{36} + 21 q^{37} - 7 q^{38} + 11 q^{39} + 5 q^{40} - 3 q^{41} + 4 q^{42} - 17 q^{43} - 7 q^{44} + 5 q^{45} + 18 q^{46} + 12 q^{47} + 11 q^{48} + 21 q^{49} + 32 q^{50} + 10 q^{51} + 11 q^{52} + 11 q^{53} + 11 q^{54} + 4 q^{55} + 4 q^{56} - 7 q^{57} + 29 q^{58} - 48 q^{59} + 5 q^{60} - q^{61} + 7 q^{62} + 4 q^{63} + 11 q^{64} + 5 q^{65} - 7 q^{66} - 9 q^{67} + 10 q^{68} + 18 q^{69} + 31 q^{70} + 17 q^{71} + 11 q^{72} - 23 q^{73} + 21 q^{74} + 32 q^{75} - 7 q^{76} + 26 q^{77} + 11 q^{78} + 41 q^{79} + 5 q^{80} + 11 q^{81} - 3 q^{82} + 19 q^{83} + 4 q^{84} + 17 q^{85} - 17 q^{86} + 29 q^{87} - 7 q^{88} + 32 q^{89} + 5 q^{90} + 4 q^{91} + 18 q^{92} + 7 q^{93} + 12 q^{94} + 26 q^{95} + 11 q^{96} - 16 q^{97} + 21 q^{98} - 7 q^{99}+O(q^{100}) \) 11 * q + 11 * q^2 + 11 * q^3 + 11 * q^4 + 5 * q^5 + 11 * q^6 + 4 * q^7 + 11 * q^8 + 11 * q^9 + 5 * q^10 - 7 * q^11 + 11 * q^12 + 11 * q^13 + 4 * q^14 + 5 * q^15 + 11 * q^16 + 10 * q^17 + 11 * q^18 - 7 * q^19 + 5 * q^20 + 4 * q^21 - 7 * q^22 + 18 * q^23 + 11 * q^24 + 32 * q^25 + 11 * q^26 + 11 * q^27 + 4 * q^28 + 29 * q^29 + 5 * q^30 + 7 * q^31 + 11 * q^32 - 7 * q^33 + 10 * q^34 + 31 * q^35 + 11 * q^36 + 21 * q^37 - 7 * q^38 + 11 * q^39 + 5 * q^40 - 3 * q^41 + 4 * q^42 - 17 * q^43 - 7 * q^44 + 5 * q^45 + 18 * q^46 + 12 * q^47 + 11 * q^48 + 21 * q^49 + 32 * q^50 + 10 * q^51 + 11 * q^52 + 11 * q^53 + 11 * q^54 + 4 * q^55 + 4 * q^56 - 7 * q^57 + 29 * q^58 - 48 * q^59 + 5 * q^60 - q^61 + 7 * q^62 + 4 * q^63 + 11 * q^64 + 5 * q^65 - 7 * q^66 - 9 * q^67 + 10 * q^68 + 18 * q^69 + 31 * q^70 + 17 * q^71 + 11 * q^72 - 23 * q^73 + 21 * q^74 + 32 * q^75 - 7 * q^76 + 26 * q^77 + 11 * q^78 + 41 * q^79 + 5 * q^80 + 11 * q^81 - 3 * q^82 + 19 * q^83 + 4 * q^84 + 17 * q^85 - 17 * q^86 + 29 * q^87 - 7 * q^88 + 32 * q^89 + 5 * q^90 + 4 * q^91 + 18 * q^92 + 7 * q^93 + 12 * q^94 + 26 * q^95 + 11 * q^96 - 16 * q^97 + 21 * q^98 - 7 * q^99

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