LMFDB - Embedded newform 8034.2.a.r.1.6

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:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 4x^{8} - 9x^{7} + 45x^{6} + 7x^{5} - 123x^{4} + 37x^{3} + 87x^{2} - 54x + 8 $ x^9 - 4x^8 - 9x^7 + 45x^6 + 7x^5 - 123x^4 + 37x^3 + 87x^2 - 54x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$0.254984$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.254984 q^{5} -1.00000 q^{6} +2.89551 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.254984 q^{5} -1.00000 q^{6} +2.89551 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.254984 q^{10} -3.38356 q^{11} -1.00000 q^{12} +1.00000 q^{13} +2.89551 q^{14} +0.254984 q^{15} +1.00000 q^{16} -2.25200 q^{17} +1.00000 q^{18} -4.71627 q^{19} -0.254984 q^{20} -2.89551 q^{21} -3.38356 q^{22} +7.05744 q^{23} -1.00000 q^{24} -4.93498 q^{25} +1.00000 q^{26} -1.00000 q^{27} +2.89551 q^{28} -6.73841 q^{29} +0.254984 q^{30} -3.07476 q^{31} +1.00000 q^{32} +3.38356 q^{33} -2.25200 q^{34} -0.738308 q^{35} +1.00000 q^{36} +10.5322 q^{37} -4.71627 q^{38} -1.00000 q^{39} -0.254984 q^{40} -4.02956 q^{41} -2.89551 q^{42} -9.59458 q^{43} -3.38356 q^{44} -0.254984 q^{45} +7.05744 q^{46} +8.51301 q^{47} -1.00000 q^{48} +1.38400 q^{49} -4.93498 q^{50} +2.25200 q^{51} +1.00000 q^{52} -0.171782 q^{53} -1.00000 q^{54} +0.862751 q^{55} +2.89551 q^{56} +4.71627 q^{57} -6.73841 q^{58} +7.58569 q^{59} +0.254984 q^{60} -1.83433 q^{61} -3.07476 q^{62} +2.89551 q^{63} +1.00000 q^{64} -0.254984 q^{65} +3.38356 q^{66} -5.17828 q^{67} -2.25200 q^{68} -7.05744 q^{69} -0.738308 q^{70} -11.3062 q^{71} +1.00000 q^{72} -13.5449 q^{73} +10.5322 q^{74} +4.93498 q^{75} -4.71627 q^{76} -9.79714 q^{77} -1.00000 q^{78} -8.40168 q^{79} -0.254984 q^{80} +1.00000 q^{81} -4.02956 q^{82} -15.9010 q^{83} -2.89551 q^{84} +0.574222 q^{85} -9.59458 q^{86} +6.73841 q^{87} -3.38356 q^{88} +3.35007 q^{89} -0.254984 q^{90} +2.89551 q^{91} +7.05744 q^{92} +3.07476 q^{93} +8.51301 q^{94} +1.20257 q^{95} -1.00000 q^{96} -8.53741 q^{97} +1.38400 q^{98} -3.38356 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} - 4 q^{5} - 9 q^{6} - 4 q^{7} + 9 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 - 4 * q^5 - 9 * q^6 - 4 * q^7 + 9 * q^8 + 9 * q^9	\( 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} - 4 q^{5} - 9 q^{6} - 4 q^{7} + 9 q^{8} + 9 q^{9} - 4 q^{10} - 5 q^{11} - 9 q^{12} + 9 q^{13} - 4 q^{14} + 4 q^{15} + 9 q^{16} - 6 q^{17} + 9 q^{18} - 4 q^{19} - 4 q^{20} + 4 q^{21} - 5 q^{22} - 6 q^{23} - 9 q^{24} - 11 q^{25} + 9 q^{26} - 9 q^{27} - 4 q^{28} - 19 q^{29} + 4 q^{30} - 6 q^{31} + 9 q^{32} + 5 q^{33} - 6 q^{34} + 10 q^{35} + 9 q^{36} - 13 q^{37} - 4 q^{38} - 9 q^{39} - 4 q^{40} - 18 q^{41} + 4 q^{42} - 20 q^{43} - 5 q^{44} - 4 q^{45} - 6 q^{46} + 14 q^{47} - 9 q^{48} - 3 q^{49} - 11 q^{50} + 6 q^{51} + 9 q^{52} - 3 q^{53} - 9 q^{54} - 4 q^{55} - 4 q^{56} + 4 q^{57} - 19 q^{58} - 9 q^{59} + 4 q^{60} - 24 q^{61} - 6 q^{62} - 4 q^{63} + 9 q^{64} - 4 q^{65} + 5 q^{66} - 4 q^{67} - 6 q^{68} + 6 q^{69} + 10 q^{70} - 9 q^{71} + 9 q^{72} - 24 q^{73} - 13 q^{74} + 11 q^{75} - 4 q^{76} + 3 q^{77} - 9 q^{78} - 15 q^{79} - 4 q^{80} + 9 q^{81} - 18 q^{82} + 20 q^{83} + 4 q^{84} - 31 q^{85} - 20 q^{86} + 19 q^{87} - 5 q^{88} + 3 q^{89} - 4 q^{90} - 4 q^{91} - 6 q^{92} + 6 q^{93} + 14 q^{94} - 4 q^{95} - 9 q^{96} - 19 q^{97} - 3 q^{98} - 5 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 - 4 * q^5 - 9 * q^6 - 4 * q^7 + 9 * q^8 + 9 * q^9 - 4 * q^10 - 5 * q^11 - 9 * q^12 + 9 * q^13 - 4 * q^14 + 4 * q^15 + 9 * q^16 - 6 * q^17 + 9 * q^18 - 4 * q^19 - 4 * q^20 + 4 * q^21 - 5 * q^22 - 6 * q^23 - 9 * q^24 - 11 * q^25 + 9 * q^26 - 9 * q^27 - 4 * q^28 - 19 * q^29 + 4 * q^30 - 6 * q^31 + 9 * q^32 + 5 * q^33 - 6 * q^34 + 10 * q^35 + 9 * q^36 - 13 * q^37 - 4 * q^38 - 9 * q^39 - 4 * q^40 - 18 * q^41 + 4 * q^42 - 20 * q^43 - 5 * q^44 - 4 * q^45 - 6 * q^46 + 14 * q^47 - 9 * q^48 - 3 * q^49 - 11 * q^50 + 6 * q^51 + 9 * q^52 - 3 * q^53 - 9 * q^54 - 4 * q^55 - 4 * q^56 + 4 * q^57 - 19 * q^58 - 9 * q^59 + 4 * q^60 - 24 * q^61 - 6 * q^62 - 4 * q^63 + 9 * q^64 - 4 * q^65 + 5 * q^66 - 4 * q^67 - 6 * q^68 + 6 * q^69 + 10 * q^70 - 9 * q^71 + 9 * q^72 - 24 * q^73 - 13 * q^74 + 11 * q^75 - 4 * q^76 + 3 * q^77 - 9 * q^78 - 15 * q^79 - 4 * q^80 + 9 * q^81 - 18 * q^82 + 20 * q^83 + 4 * q^84 - 31 * q^85 - 20 * q^86 + 19 * q^87 - 5 * q^88 + 3 * q^89 - 4 * q^90 - 4 * q^91 - 6 * q^92 + 6 * q^93 + 14 * q^94 - 4 * q^95 - 9 * q^96 - 19 * q^97 - 3 * q^98 - 5 * 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
$5$	−0.254984	−0.114032	−0.0570161	−	0.998373i	$-0.518159\pi$
$5$	−0.254984	−0.114032	−0.0570161	+	0.998373i	$0.518159\pi$
$6$	−1.00000	−0.408248
$7$	2.89551	1.09440	0.547201	−	0.837002i	$-0.315693\pi$
$7$	2.89551	1.09440	0.547201	+	0.837002i	$0.315693\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−0.254984	−0.0806329
$11$	−3.38356	−1.02018	−0.510090	−	0.860121i	$-0.670388\pi$
$11$	−3.38356	−1.02018	−0.510090	+	0.860121i	$0.670388\pi$
$12$	−1.00000	−0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	2.89551	0.773858
$15$	0.254984	0.0658365
$16$	1.00000	0.250000
$17$	−2.25200	−0.546189	−0.273095	−	0.961987i	$-0.588047\pi$
$17$	−2.25200	−0.546189	−0.273095	+	0.961987i	$0.588047\pi$
$18$	1.00000	0.235702
$19$	−4.71627	−1.08199	−0.540993	−	0.841027i	$-0.681951\pi$
$19$	−4.71627	−1.08199	−0.540993	+	0.841027i	$0.681951\pi$
$20$	−0.254984	−0.0570161
$21$	−2.89551	−0.631853
$22$	−3.38356	−0.721377
$23$	7.05744	1.47158	0.735789	−	0.677210i	$-0.236811\pi$
$23$	7.05744	1.47158	0.735789	+	0.677210i	$0.236811\pi$
$24$	−1.00000	−0.204124
$25$	−4.93498	−0.986997
$26$	1.00000	0.196116
$27$	−1.00000	−0.192450
$28$	2.89551	0.547201
$29$	−6.73841	−1.25129	−0.625645	−	0.780108i	$-0.715164\pi$
$29$	−6.73841	−1.25129	−0.625645	+	0.780108i	$0.715164\pi$
$30$	0.254984	0.0465534
$31$	−3.07476	−0.552243	−0.276122	−	0.961123i	$-0.589049\pi$
$31$	−3.07476	−0.552243	−0.276122	+	0.961123i	$0.589049\pi$
$32$	1.00000	0.176777
$33$	3.38356	0.589002
$34$	−2.25200	−0.386214
$35$	−0.738308	−0.124797
$36$	1.00000	0.166667
$37$	10.5322	1.73149	0.865745	−	0.500486i	$-0.166845\pi$
$37$	10.5322	1.73149	0.865745	+	0.500486i	$0.166845\pi$
$38$	−4.71627	−0.765079
$39$	−1.00000	−0.160128
$40$	−0.254984	−0.0403164
$41$	−4.02956	−0.629311	−0.314656	−	0.949206i	$-0.601889\pi$
$41$	−4.02956	−0.629311	−0.314656	+	0.949206i	$0.601889\pi$
$42$	−2.89551	−0.446787
$43$	−9.59458	−1.46316	−0.731580	−	0.681756i	$-0.761217\pi$
$43$	−9.59458	−1.46316	−0.731580	+	0.681756i	$0.761217\pi$
$44$	−3.38356	−0.510090
$45$	−0.254984	−0.0380107
$46$	7.05744	1.04056
$47$	8.51301	1.24175	0.620875	−	0.783910i	$-0.286777\pi$
$47$	8.51301	1.24175	0.620875	+	0.783910i	$0.286777\pi$
$48$	−1.00000	−0.144338
$49$	1.38400	0.197714
$50$	−4.93498	−0.697912
$51$	2.25200	0.315343
$52$	1.00000	0.138675
$53$	−0.171782	−0.0235961	−0.0117981	−	0.999930i	$-0.503756\pi$
$53$	−0.171782	−0.0235961	−0.0117981	+	0.999930i	$0.503756\pi$
$54$	−1.00000	−0.136083
$55$	0.862751	0.116333
$56$	2.89551	0.386929
$57$	4.71627	0.624685
$58$	−6.73841	−0.884796
$59$	7.58569	0.987573	0.493786	−	0.869583i	$-0.335612\pi$
$59$	7.58569	0.987573	0.493786	+	0.869583i	$0.335612\pi$
$60$	0.254984	0.0329182
$61$	−1.83433	−0.234862	−0.117431	−	0.993081i	$-0.537466\pi$
$61$	−1.83433	−0.234862	−0.117431	+	0.993081i	$0.537466\pi$
$62$	−3.07476	−0.390495
$63$	2.89551	0.364800
$64$	1.00000	0.125000
$65$	−0.254984	−0.0316268
$66$	3.38356	0.416487
$67$	−5.17828	−0.632628	−0.316314	−	0.948655i	$-0.602445\pi$
$67$	−5.17828	−0.632628	−0.316314	+	0.948655i	$0.602445\pi$
$68$	−2.25200	−0.273095
$69$	−7.05744	−0.849616
$70$	−0.738308	−0.0882447
$71$	−11.3062	−1.34180	−0.670900	−	0.741547i	$-0.734092\pi$
$71$	−11.3062	−1.34180	−0.670900	+	0.741547i	$0.734092\pi$
$72$	1.00000	0.117851
$73$	−13.5449	−1.58531	−0.792657	−	0.609668i	$-0.791303\pi$
$73$	−13.5449	−1.58531	−0.792657	+	0.609668i	$0.791303\pi$
$74$	10.5322	1.22435
$75$	4.93498	0.569843
$76$	−4.71627	−0.540993
$77$	−9.79714	−1.11649
$78$	−1.00000	−0.113228
$79$	−8.40168	−0.945263	−0.472631	−	0.881260i	$-0.656696\pi$
$79$	−8.40168	−0.945263	−0.472631	+	0.881260i	$0.656696\pi$
$80$	−0.254984	−0.0285080
$81$	1.00000	0.111111
$82$	−4.02956	−0.444990
$83$	−15.9010	−1.74536	−0.872680	−	0.488293i	$-0.837620\pi$
$83$	−15.9010	−1.74536	−0.872680	+	0.488293i	$0.837620\pi$
$84$	−2.89551	−0.315926
$85$	0.574222	0.0622831
$86$	−9.59458	−1.03461
$87$	6.73841	0.722433
$88$	−3.38356	−0.360688
$89$	3.35007	0.355106	0.177553	−	0.984111i	$-0.443182\pi$
$89$	3.35007	0.355106	0.177553	+	0.984111i	$0.443182\pi$
$90$	−0.254984	−0.0268776
$91$	2.89551	0.303532
$92$	7.05744	0.735789
$93$	3.07476	0.318838
$94$	8.51301	0.878050
$95$	1.20257	0.123381
$96$	−1.00000	−0.102062
$97$	−8.53741	−0.866843	−0.433421	−	0.901191i	$-0.642694\pi$
$97$	−8.53741	−0.866843	−0.433421	+	0.901191i	$0.642694\pi$
$98$	1.38400	0.139805
$99$	−3.38356	−0.340060
$100$	−4.93498	−0.493498
$101$	−1.61474	−0.160672	−0.0803362	−	0.996768i	$-0.525599\pi$
$101$	−1.61474	−0.160672	−0.0803362	+	0.996768i	$0.525599\pi$
$102$	2.25200	0.222981
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	1.00000	0.0980581
$105$	0.738308	0.0720515
$106$	−0.171782	−0.0166850
$107$	−16.0107	−1.54782	−0.773908	−	0.633298i	$-0.781701\pi$
$107$	−16.0107	−1.54782	−0.773908	+	0.633298i	$0.781701\pi$
$108$	−1.00000	−0.0962250
$109$	−10.3194	−0.988416	−0.494208	−	0.869344i	$-0.664542\pi$
$109$	−10.3194	−0.988416	−0.494208	+	0.869344i	$0.664542\pi$
$110$	0.862751	0.0822601
$111$	−10.5322	−0.999676
$112$	2.89551	0.273600
$113$	15.6040	1.46790	0.733951	−	0.679202i	$-0.237674\pi$
$113$	15.6040	1.46790	0.733951	+	0.679202i	$0.237674\pi$
$114$	4.71627	0.441719
$115$	−1.79953	−0.167807
$116$	−6.73841	−0.625645
$117$	1.00000	0.0924500
$118$	7.58569	0.698320
$119$	−6.52069	−0.597750
$120$	0.254984	0.0232767
$121$	0.448461	0.0407692
$122$	−1.83433	−0.166073
$123$	4.02956	0.363333
$124$	−3.07476	−0.276122
$125$	2.53326	0.226581
$126$	2.89551	0.257953
$127$	−2.99485	−0.265750	−0.132875	−	0.991133i	$-0.542421\pi$
$127$	−2.99485	−0.265750	−0.132875	+	0.991133i	$0.542421\pi$
$128$	1.00000	0.0883883
$129$	9.59458	0.844756
$130$	−0.254984	−0.0223635
$131$	6.55354	0.572586	0.286293	−	0.958142i	$-0.407577\pi$
$131$	6.55354	0.572586	0.286293	+	0.958142i	$0.407577\pi$
$132$	3.38356	0.294501
$133$	−13.6560	−1.18413
$134$	−5.17828	−0.447336
$135$	0.254984	0.0219455
$136$	−2.25200	−0.193107
$137$	13.6219	1.16380	0.581900	−	0.813260i	$-0.302309\pi$
$137$	13.6219	1.16380	0.581900	+	0.813260i	$0.302309\pi$
$138$	−7.05744	−0.600769
$139$	21.3393	1.80998	0.904988	−	0.425436i	$-0.139879\pi$
$139$	21.3393	1.80998	0.904988	+	0.425436i	$0.139879\pi$
$140$	−0.738308	−0.0623984
$141$	−8.51301	−0.716925
$142$	−11.3062	−0.948797
$143$	−3.38356	−0.282947
$144$	1.00000	0.0833333
$145$	1.71818	0.142687
$146$	−13.5449	−1.12099
$147$	−1.38400	−0.114150
$148$	10.5322	0.865745
$149$	18.3249	1.50123	0.750617	−	0.660737i	$-0.229756\pi$
$149$	18.3249	1.50123	0.750617	+	0.660737i	$0.229756\pi$
$150$	4.93498	0.402940
$151$	17.4718	1.42184	0.710919	−	0.703274i	$-0.248279\pi$
$151$	17.4718	1.42184	0.710919	+	0.703274i	$0.248279\pi$
$152$	−4.71627	−0.382540
$153$	−2.25200	−0.182063
$154$	−9.79714	−0.789476
$155$	0.784013	0.0629735
$156$	−1.00000	−0.0800641
$157$	3.12465	0.249374	0.124687	−	0.992196i	$-0.460207\pi$
$157$	3.12465	0.249374	0.124687	+	0.992196i	$0.460207\pi$
$158$	−8.40168	−0.668402
$159$	0.171782	0.0136232
$160$	−0.254984	−0.0201582
$161$	20.4349	1.61050
$162$	1.00000	0.0785674
$163$	−3.74948	−0.293682	−0.146841	−	0.989160i	$-0.546911\pi$
$163$	−3.74948	−0.293682	−0.146841	+	0.989160i	$0.546911\pi$
$164$	−4.02956	−0.314656
$165$	−0.862751	−0.0671651
$166$	−15.9010	−1.23416
$167$	10.0758	0.779687	0.389844	−	0.920881i	$-0.372529\pi$
$167$	10.0758	0.779687	0.389844	+	0.920881i	$0.372529\pi$
$168$	−2.89551	−0.223394
$169$	1.00000	0.0769231
$170$	0.574222	0.0440408
$171$	−4.71627	−0.360662
$172$	−9.59458	−0.731580
$173$	7.15151	0.543719	0.271860	−	0.962337i	$-0.412361\pi$
$173$	7.15151	0.543719	0.271860	+	0.962337i	$0.412361\pi$
$174$	6.73841	0.510837
$175$	−14.2893	−1.08017
$176$	−3.38356	−0.255045
$177$	−7.58569	−0.570176
$178$	3.35007	0.251098
$179$	−8.02696	−0.599963	−0.299982	−	0.953945i	$-0.596981\pi$
$179$	−8.02696	−0.599963	−0.299982	+	0.953945i	$0.596981\pi$
$180$	−0.254984	−0.0190054
$181$	1.09033	0.0810432	0.0405216	−	0.999179i	$-0.487098\pi$
$181$	1.09033	0.0810432	0.0405216	+	0.999179i	$0.487098\pi$
$182$	2.89551	0.214630
$183$	1.83433	0.135598
$184$	7.05744	0.520282
$185$	−2.68555	−0.197445
$186$	3.07476	0.225452
$187$	7.61976	0.557212
$188$	8.51301	0.620875
$189$	−2.89551	−0.210618
$190$	1.20257	0.0872436
$191$	21.3379	1.54395	0.771977	−	0.635651i	$-0.219268\pi$
$191$	21.3379	1.54395	0.771977	+	0.635651i	$0.219268\pi$
$192$	−1.00000	−0.0721688
$193$	−6.16320	−0.443637	−0.221819	−	0.975088i	$-0.571199\pi$
$193$	−6.16320	−0.443637	−0.221819	+	0.975088i	$0.571199\pi$
$194$	−8.53741	−0.612950
$195$	0.254984	0.0182598
$196$	1.38400	0.0988570
$197$	−20.9313	−1.49130	−0.745648	−	0.666340i	$-0.767860\pi$
$197$	−20.9313	−1.49130	−0.745648	+	0.666340i	$0.767860\pi$
$198$	−3.38356	−0.240459
$199$	−3.53167	−0.250354	−0.125177	−	0.992134i	$-0.539950\pi$
$199$	−3.53167	−0.250354	−0.125177	+	0.992134i	$0.539950\pi$
$200$	−4.93498	−0.348956
$201$	5.17828	0.365248
$202$	−1.61474	−0.113613
$203$	−19.5111	−1.36941
$204$	2.25200	0.157671
$205$	1.02747	0.0717617
$206$	−1.00000	−0.0696733
$207$	7.05744	0.490526
$208$	1.00000	0.0693375
$209$	15.9578	1.10382
$210$	0.738308	0.0509481
$211$	1.80935	0.124561	0.0622805	−	0.998059i	$-0.480163\pi$
$211$	1.80935	0.124561	0.0622805	+	0.998059i	$0.480163\pi$
$212$	−0.171782	−0.0117981
$213$	11.3062	0.774689
$214$	−16.0107	−1.09447
$215$	2.44646	0.166847
$216$	−1.00000	−0.0680414
$217$	−8.90301	−0.604376
$218$	−10.3194	−0.698915
$219$	13.5449	0.915282
$220$	0.862751	0.0581667
$221$	−2.25200	−0.151486
$222$	−10.5322	−0.706878
$223$	−28.0025	−1.87519	−0.937593	−	0.347734i	$-0.886951\pi$
$223$	−28.0025	−1.87519	−0.937593	+	0.347734i	$0.886951\pi$
$224$	2.89551	0.193465
$225$	−4.93498	−0.328999
$226$	15.6040	1.03796
$227$	12.3664	0.820790	0.410395	−	0.911908i	$-0.365391\pi$
$227$	12.3664	0.820790	0.410395	+	0.911908i	$0.365391\pi$
$228$	4.71627	0.312342
$229$	−12.7890	−0.845119	−0.422559	−	0.906335i	$-0.638868\pi$
$229$	−12.7890	−0.845119	−0.422559	+	0.906335i	$0.638868\pi$
$230$	−1.79953	−0.118658
$231$	9.79714	0.644604
$232$	−6.73841	−0.442398
$233$	−21.7764	−1.42662	−0.713309	−	0.700849i	$-0.752805\pi$
$233$	−21.7764	−1.42662	−0.713309	+	0.700849i	$0.752805\pi$
$234$	1.00000	0.0653720
$235$	−2.17068	−0.141599
$236$	7.58569	0.493786
$237$	8.40168	0.545748
$238$	−6.52069	−0.422673
$239$	−21.5769	−1.39570	−0.697848	−	0.716246i	$-0.745859\pi$
$239$	−21.5769	−1.39570	−0.697848	+	0.716246i	$0.745859\pi$
$240$	0.254984	0.0164591
$241$	−15.8803	−1.02294	−0.511470	−	0.859301i	$-0.670899\pi$
$241$	−15.8803	−1.02294	−0.511470	+	0.859301i	$0.670899\pi$
$242$	0.448461	0.0288282
$243$	−1.00000	−0.0641500
$244$	−1.83433	−0.117431
$245$	−0.352897	−0.0225457
$246$	4.02956	0.256915
$247$	−4.71627	−0.300089
$248$	−3.07476	−0.195247
$249$	15.9010	1.00768
$250$	2.53326	0.160217
$251$	3.47281	0.219202	0.109601	−	0.993976i	$-0.465043\pi$
$251$	3.47281	0.219202	0.109601	+	0.993976i	$0.465043\pi$
$252$	2.89551	0.182400
$253$	−23.8793	−1.50128
$254$	−2.99485	−0.187914
$255$	−0.574222	−0.0359592
$256$	1.00000	0.0625000
$257$	12.0932	0.754355	0.377177	−	0.926141i	$-0.376895\pi$
$257$	12.0932	0.754355	0.377177	+	0.926141i	$0.376895\pi$
$258$	9.59458	0.597332
$259$	30.4962	1.89494
$260$	−0.254984	−0.0158134
$261$	−6.73841	−0.417097
$262$	6.55354	0.404879
$263$	1.22342	0.0754396	0.0377198	−	0.999288i	$-0.487991\pi$
$263$	1.22342	0.0754396	0.0377198	+	0.999288i	$0.487991\pi$
$264$	3.38356	0.208244
$265$	0.0438017	0.00269072
$266$	−13.6560	−0.837304
$267$	−3.35007	−0.205021
$268$	−5.17828	−0.316314
$269$	−15.1485	−0.923621	−0.461811	−	0.886979i	$-0.652800\pi$
$269$	−15.1485	−0.923621	−0.461811	+	0.886979i	$0.652800\pi$
$270$	0.254984	0.0155178
$271$	−10.5614	−0.641561	−0.320780	−	0.947154i	$-0.603945\pi$
$271$	−10.5614	−0.641561	−0.320780	+	0.947154i	$0.603945\pi$
$272$	−2.25200	−0.136547
$273$	−2.89551	−0.175244
$274$	13.6219	0.822931
$275$	16.6978	1.00692
$276$	−7.05744	−0.424808
$277$	−26.0641	−1.56604	−0.783019	−	0.621998i	$-0.786321\pi$
$277$	−26.0641	−1.56604	−0.783019	+	0.621998i	$0.786321\pi$
$278$	21.3393	1.27985
$279$	−3.07476	−0.184081
$280$	−0.738308	−0.0441224
$281$	19.6014	1.16932	0.584659	−	0.811279i	$-0.301228\pi$
$281$	19.6014	1.16932	0.584659	+	0.811279i	$0.301228\pi$
$282$	−8.51301	−0.506942
$283$	16.9805	1.00939	0.504694	−	0.863298i	$-0.331605\pi$
$283$	16.9805	1.00939	0.504694	+	0.863298i	$0.331605\pi$
$284$	−11.3062	−0.670900
$285$	−1.20257	−0.0712341
$286$	−3.38356	−0.200074
$287$	−11.6676	−0.688719
$288$	1.00000	0.0589256
$289$	−11.9285	−0.701677
$290$	1.71818	0.100895
$291$	8.53741	0.500472
$292$	−13.5449	−0.792657
$293$	−11.8657	−0.693201	−0.346600	−	0.938013i	$-0.612664\pi$
$293$	−11.8657	−0.693201	−0.346600	+	0.938013i	$0.612664\pi$
$294$	−1.38400	−0.0807164
$295$	−1.93423	−0.112615
$296$	10.5322	0.612174
$297$	3.38356	0.196334
$298$	18.3249	1.06153
$299$	7.05744	0.408142
$300$	4.93498	0.284921
$301$	−27.7812	−1.60128
$302$	17.4718	1.00539
$303$	1.61474	0.0927643
$304$	−4.71627	−0.270496
$305$	0.467724	0.0267818
$306$	−2.25200	−0.128738
$307$	−30.2796	−1.72815	−0.864074	−	0.503364i	$-0.832095\pi$
$307$	−30.2796	−1.72815	−0.864074	+	0.503364i	$0.832095\pi$
$308$	−9.79714	−0.558244
$309$	1.00000	0.0568880
$310$	0.784013	0.0445290
$311$	19.4366	1.10215	0.551075	−	0.834456i	$-0.314218\pi$
$311$	19.4366	1.10215	0.551075	+	0.834456i	$0.314218\pi$
$312$	−1.00000	−0.0566139
$313$	−9.90265	−0.559731	−0.279865	−	0.960039i	$-0.590290\pi$
$313$	−9.90265	−0.559731	−0.279865	+	0.960039i	$0.590290\pi$
$314$	3.12465	0.176334
$315$	−0.738308	−0.0415990
$316$	−8.40168	−0.472631
$317$	−14.7302	−0.827329	−0.413665	−	0.910429i	$-0.635751\pi$
$317$	−14.7302	−0.827329	−0.413665	+	0.910429i	$0.635751\pi$
$318$	0.171782	0.00963308
$319$	22.7998	1.27654
$320$	−0.254984	−0.0142540
$321$	16.0107	0.893632
$322$	20.4349	1.13879
$323$	10.6210	0.590969
$324$	1.00000	0.0555556
$325$	−4.93498	−0.273744
$326$	−3.74948	−0.207664
$327$	10.3194	0.570662
$328$	−4.02956	−0.222495
$329$	24.6495	1.35897
$330$	−0.862751	−0.0474929
$331$	−17.5713	−0.965807	−0.482903	−	0.875674i	$-0.660418\pi$
$331$	−17.5713	−0.965807	−0.482903	+	0.875674i	$0.660418\pi$
$332$	−15.9010	−0.872680
$333$	10.5322	0.577163
$334$	10.0758	0.551322
$335$	1.32038	0.0721399
$336$	−2.89551	−0.157963
$337$	−12.1564	−0.662199	−0.331099	−	0.943596i	$-0.607420\pi$
$337$	−12.1564	−0.662199	−0.331099	+	0.943596i	$0.607420\pi$
$338$	1.00000	0.0543928
$339$	−15.6040	−0.847494
$340$	0.574222	0.0311416
$341$	10.4036	0.563388
$342$	−4.71627	−0.255026
$343$	−16.2612	−0.878023
$344$	−9.59458	−0.517305
$345$	1.79953	0.0968835
$346$	7.15151	0.384467
$347$	−23.2701	−1.24921	−0.624603	−	0.780942i	$-0.714739\pi$
$347$	−23.2701	−1.24921	−0.624603	+	0.780942i	$0.714739\pi$
$348$	6.73841	0.361217
$349$	4.86759	0.260556	0.130278	−	0.991477i	$-0.458413\pi$
$349$	4.86759	0.260556	0.130278	+	0.991477i	$0.458413\pi$
$350$	−14.2893	−0.763796
$351$	−1.00000	−0.0533761
$352$	−3.38356	−0.180344
$353$	35.4302	1.88576	0.942879	−	0.333137i	$-0.108107\pi$
$353$	35.4302	1.88576	0.942879	+	0.333137i	$0.108107\pi$
$354$	−7.58569	−0.403175
$355$	2.88290	0.153008
$356$	3.35007	0.177553
$357$	6.52069	0.345111
$358$	−8.02696	−0.424238
$359$	−13.5402	−0.714626	−0.357313	−	0.933985i	$-0.616307\pi$
$359$	−13.5402	−0.714626	−0.357313	+	0.933985i	$0.616307\pi$
$360$	−0.254984	−0.0134388
$361$	3.24317	0.170693
$362$	1.09033	0.0573062
$363$	−0.448461	−0.0235381
$364$	2.89551	0.151766
$365$	3.45373	0.180777
$366$	1.83433	0.0958820
$367$	29.8828	1.55987	0.779934	−	0.625862i	$-0.215253\pi$
$367$	29.8828	1.55987	0.779934	+	0.625862i	$0.215253\pi$
$368$	7.05744	0.367895
$369$	−4.02956	−0.209770
$370$	−2.68555	−0.139615
$371$	−0.497398	−0.0258236
$372$	3.07476	0.159419
$373$	−35.8607	−1.85680	−0.928400	−	0.371583i	$-0.878815\pi$
$373$	−35.8607	−1.85680	−0.928400	+	0.371583i	$0.878815\pi$
$374$	7.61976	0.394008
$375$	−2.53326	−0.130817
$376$	8.51301	0.439025
$377$	−6.73841	−0.347046
$378$	−2.89551	−0.148929
$379$	−15.6036	−0.801502	−0.400751	−	0.916187i	$-0.631251\pi$
$379$	−15.6036	−0.801502	−0.400751	+	0.916187i	$0.631251\pi$
$380$	1.20257	0.0616906
$381$	2.99485	0.153431
$382$	21.3379	1.09174
$383$	−26.2174	−1.33964	−0.669822	−	0.742522i	$-0.733630\pi$
$383$	−26.2174	−1.33964	−0.669822	+	0.742522i	$0.733630\pi$
$384$	−1.00000	−0.0510310
$385$	2.49811	0.127315
$386$	−6.16320	−0.313699
$387$	−9.59458	−0.487720
$388$	−8.53741	−0.433421
$389$	−13.7430	−0.696799	−0.348400	−	0.937346i	$-0.613275\pi$
$389$	−13.7430	−0.696799	−0.348400	+	0.937346i	$0.613275\pi$
$390$	0.254984	0.0129116
$391$	−15.8933	−0.803761
$392$	1.38400	0.0699024
$393$	−6.55354	−0.330582
$394$	−20.9313	−1.05450
$395$	2.14229	0.107790
$396$	−3.38356	−0.170030
$397$	11.9454	0.599523	0.299762	−	0.954014i	$-0.403093\pi$
$397$	11.9454	0.599523	0.299762	+	0.954014i	$0.403093\pi$
$398$	−3.53167	−0.177027
$399$	13.6560	0.683656
$400$	−4.93498	−0.246749
$401$	19.7209	0.984813	0.492407	−	0.870365i	$-0.336117\pi$
$401$	19.7209	0.984813	0.492407	+	0.870365i	$0.336117\pi$
$402$	5.17828	0.258269
$403$	−3.07476	−0.153165
$404$	−1.61474	−0.0803362
$405$	−0.254984	−0.0126702
$406$	−19.5111	−0.968322
$407$	−35.6364	−1.76643
$408$	2.25200	0.111490
$409$	27.2189	1.34589	0.672945	−	0.739692i	$-0.265029\pi$
$409$	27.2189	1.34589	0.672945	+	0.739692i	$0.265029\pi$
$410$	1.02747	0.0507432
$411$	−13.6219	−0.671920
$412$	−1.00000	−0.0492665
$413$	21.9645	1.08080
$414$	7.05744	0.346854
$415$	4.05449	0.199027
$416$	1.00000	0.0490290
$417$	−21.3393	−1.04499
$418$	15.9578	0.780519
$419$	−33.9553	−1.65882	−0.829412	−	0.558638i	$-0.811324\pi$
$419$	−33.9553	−1.65882	−0.829412	+	0.558638i	$0.811324\pi$
$420$	0.738308	0.0360258
$421$	−28.7260	−1.40002	−0.700011	−	0.714132i	$-0.746822\pi$
$421$	−28.7260	−1.40002	−0.700011	+	0.714132i	$0.746822\pi$
$422$	1.80935	0.0880779
$423$	8.51301	0.413917
$424$	−0.171782	−0.00834249
$425$	11.1136	0.539087
$426$	11.3062	0.547788
$427$	−5.31133	−0.257033
$428$	−16.0107	−0.773908
$429$	3.38356	0.163360
$430$	2.44646	0.117979
$431$	−5.30622	−0.255592	−0.127796	−	0.991801i	$-0.540790\pi$
$431$	−5.30622	−0.255592	−0.127796	+	0.991801i	$0.540790\pi$
$432$	−1.00000	−0.0481125
$433$	−39.0299	−1.87565	−0.937827	−	0.347102i	$-0.887166\pi$
$433$	−39.0299	−1.87565	−0.937827	+	0.347102i	$0.887166\pi$
$434$	−8.90301	−0.427358
$435$	−1.71818	−0.0823806
$436$	−10.3194	−0.494208
$437$	−33.2848	−1.59223
$438$	13.5449	0.647202
$439$	6.95768	0.332072	0.166036	−	0.986120i	$-0.446903\pi$
$439$	6.95768	0.332072	0.166036	+	0.986120i	$0.446903\pi$
$440$	0.862751	0.0411301
$441$	1.38400	0.0659046
$442$	−2.25200	−0.107117
$443$	15.2869	0.726305	0.363152	−	0.931730i	$-0.381700\pi$
$443$	15.2869	0.726305	0.363152	+	0.931730i	$0.381700\pi$
$444$	−10.5322	−0.499838
$445$	−0.854212	−0.0404935
$446$	−28.0025	−1.32596
$447$	−18.3249	−0.866738
$448$	2.89551	0.136800
$449$	−25.1056	−1.18480	−0.592402	−	0.805642i	$-0.701820\pi$
$449$	−25.1056	−1.18480	−0.592402	+	0.805642i	$0.701820\pi$
$450$	−4.93498	−0.232637
$451$	13.6342	0.642011
$452$	15.6040	0.733951
$453$	−17.4718	−0.820898
$454$	12.3664	0.580386
$455$	−0.738308	−0.0346124
$456$	4.71627	0.220859
$457$	−12.8275	−0.600047	−0.300024	−	0.953932i	$-0.596995\pi$
$457$	−12.8275	−0.600047	−0.300024	+	0.953932i	$0.596995\pi$
$458$	−12.7890	−0.597589
$459$	2.25200	0.105114
$460$	−1.79953	−0.0839036
$461$	28.4754	1.32623	0.663115	−	0.748517i	$-0.269234\pi$
$461$	28.4754	1.32623	0.663115	+	0.748517i	$0.269234\pi$
$462$	9.79714	0.455804
$463$	21.8937	1.01749	0.508744	−	0.860918i	$-0.330110\pi$
$463$	21.8937	1.01749	0.508744	+	0.860918i	$0.330110\pi$
$464$	−6.73841	−0.312823
$465$	−0.784013	−0.0363577
$466$	−21.7764	−1.00877
$467$	23.6835	1.09594	0.547971	−	0.836497i	$-0.315400\pi$
$467$	23.6835	1.09594	0.547971	+	0.836497i	$0.315400\pi$
$468$	1.00000	0.0462250
$469$	−14.9938	−0.692349
$470$	−2.17068	−0.100126
$471$	−3.12465	−0.143976
$472$	7.58569	0.349160
$473$	32.4638	1.49269
$474$	8.40168	0.385902
$475$	23.2747	1.06792
$476$	−6.52069	−0.298875
$477$	−0.171782	−0.00786537
$478$	−21.5769	−0.986906
$479$	8.98472	0.410522	0.205261	−	0.978707i	$-0.434196\pi$
$479$	8.98472	0.410522	0.205261	+	0.978707i	$0.434196\pi$
$480$	0.254984	0.0116384
$481$	10.5322	0.480229
$482$	−15.8803	−0.723327
$483$	−20.4349	−0.929821
$484$	0.448461	0.0203846
$485$	2.17690	0.0988479
$486$	−1.00000	−0.0453609
$487$	33.2828	1.50819	0.754093	−	0.656767i	$-0.228077\pi$
$487$	33.2828	1.50819	0.754093	+	0.656767i	$0.228077\pi$
$488$	−1.83433	−0.0830363
$489$	3.74948	0.169557
$490$	−0.352897	−0.0159422
$491$	−4.81059	−0.217099	−0.108550	−	0.994091i	$-0.534621\pi$
$491$	−4.81059	−0.217099	−0.108550	+	0.994091i	$0.534621\pi$
$492$	4.02956	0.181667
$493$	15.1749	0.683442
$494$	−4.71627	−0.212195
$495$	0.862751	0.0387778
$496$	−3.07476	−0.138061
$497$	−32.7373	−1.46847
$498$	15.9010	0.712540
$499$	39.0904	1.74993	0.874963	−	0.484190i	$-0.160886\pi$
$499$	39.0904	1.74993	0.874963	+	0.484190i	$0.160886\pi$
$500$	2.53326	0.113291
$501$	−10.0758	−0.450153
$502$	3.47281	0.154999
$503$	12.6397	0.563574	0.281787	−	0.959477i	$-0.409073\pi$
$503$	12.6397	0.563574	0.281787	+	0.959477i	$0.409073\pi$
$504$	2.89551	0.128976
$505$	0.411732	0.0183218
$506$	−23.8793	−1.06156
$507$	−1.00000	−0.0444116
$508$	−2.99485	−0.132875
$509$	−16.7289	−0.741497	−0.370748	−	0.928733i	$-0.620899\pi$
$509$	−16.7289	−0.741497	−0.370748	+	0.928733i	$0.620899\pi$
$510$	−0.574222	−0.0254270
$511$	−39.2195	−1.73497
$512$	1.00000	0.0441942
$513$	4.71627	0.208228
$514$	12.0932	0.533409
$515$	0.254984	0.0112359
$516$	9.59458	0.422378
$517$	−28.8043	−1.26681
$518$	30.4962	1.33993
$519$	−7.15151	−0.313916
$520$	−0.254984	−0.0111818
$521$	1.17490	0.0514735	0.0257368	−	0.999669i	$-0.491807\pi$
$521$	1.17490	0.0514735	0.0257368	+	0.999669i	$0.491807\pi$
$522$	−6.73841	−0.294932
$523$	24.3124	1.06311	0.531553	−	0.847025i	$-0.321609\pi$
$523$	24.3124	1.06311	0.531553	+	0.847025i	$0.321609\pi$
$524$	6.55354	0.286293
$525$	14.2893	0.623637
$526$	1.22342	0.0533438
$527$	6.92435	0.301629
$528$	3.38356	0.147250
$529$	26.8075	1.16554
$530$	0.0438017	0.00190262
$531$	7.58569	0.329191
$532$	−13.6560	−0.592063
$533$	−4.02956	−0.174540
$534$	−3.35007	−0.144972
$535$	4.08248	0.176501
$536$	−5.17828	−0.223668
$537$	8.02696	0.346389
$538$	−15.1485	−0.653099
$539$	−4.68283	−0.201704
$540$	0.254984	0.0109727
$541$	43.8457	1.88507	0.942537	−	0.334102i	$-0.108433\pi$
$541$	43.8457	1.88507	0.942537	+	0.334102i	$0.108433\pi$
$542$	−10.5614	−0.453652
$543$	−1.09033	−0.0467903
$544$	−2.25200	−0.0965536
$545$	2.63127	0.112711
$546$	−2.89551	−0.123917
$547$	19.7810	0.845773	0.422887	−	0.906183i	$-0.361017\pi$
$547$	19.7810	0.845773	0.422887	+	0.906183i	$0.361017\pi$
$548$	13.6219	0.581900
$549$	−1.83433	−0.0782874
$550$	16.6978	0.711997
$551$	31.7801	1.35388
$552$	−7.05744	−0.300385
$553$	−24.3272	−1.03450
$554$	−26.0641	−1.10736
$555$	2.68555	0.113995
$556$	21.3393	0.904988
$557$	−2.72785	−0.115583	−0.0577913	−	0.998329i	$-0.518406\pi$
$557$	−2.72785	−0.115583	−0.0577913	+	0.998329i	$0.518406\pi$
$558$	−3.07476	−0.130165
$559$	−9.59458	−0.405808
$560$	−0.738308	−0.0311992
$561$	−7.61976	−0.321707
$562$	19.6014	0.826833
$563$	−33.7815	−1.42372	−0.711860	−	0.702322i	$-0.752147\pi$
$563$	−33.7815	−1.42372	−0.711860	+	0.702322i	$0.752147\pi$
$564$	−8.51301	−0.358462
$565$	−3.97877	−0.167388
$566$	16.9805	0.713746
$567$	2.89551	0.121600
$568$	−11.3062	−0.474398
$569$	14.1617	0.593687	0.296844	−	0.954926i	$-0.404066\pi$
$569$	14.1617	0.593687	0.296844	+	0.954926i	$0.404066\pi$
$570$	−1.20257	−0.0503701
$571$	10.0196	0.419307	0.209653	−	0.977776i	$-0.432766\pi$
$571$	10.0196	0.419307	0.209653	+	0.977776i	$0.432766\pi$
$572$	−3.38356	−0.141474
$573$	−21.3379	−0.891402
$574$	−11.6676	−0.486998
$575$	−34.8284	−1.45244
$576$	1.00000	0.0416667
$577$	−4.31051	−0.179449	−0.0897244	−	0.995967i	$-0.528599\pi$
$577$	−4.31051	−0.179449	−0.0897244	+	0.995967i	$0.528599\pi$
$578$	−11.9285	−0.496161
$579$	6.16320	0.256134
$580$	1.71818	0.0713437
$581$	−46.0415	−1.91012
$582$	8.53741	0.353887
$583$	0.581235	0.0240723
$584$	−13.5449	−0.560493
$585$	−0.254984	−0.0105423
$586$	−11.8657	−0.490167
$587$	18.2322	0.752525	0.376263	−	0.926513i	$-0.377209\pi$
$587$	18.2322	0.752525	0.376263	+	0.926513i	$0.377209\pi$
$588$	−1.38400	−0.0570751
$589$	14.5014	0.597519
$590$	−1.93423	−0.0796309
$591$	20.9313	0.861000
$592$	10.5322	0.432872
$593$	−4.34494	−0.178425	−0.0892126	−	0.996013i	$-0.528435\pi$
$593$	−4.34494	−0.178425	−0.0892126	+	0.996013i	$0.528435\pi$
$594$	3.38356	0.138829
$595$	1.66267	0.0681627
$596$	18.3249	0.750617
$597$	3.53167	0.144542
$598$	7.05744	0.288600
$599$	30.9622	1.26508	0.632541	−	0.774527i	$-0.282012\pi$
$599$	30.9622	1.26508	0.632541	+	0.774527i	$0.282012\pi$
$600$	4.93498	0.201470
$601$	20.4211	0.832992	0.416496	−	0.909137i	$-0.363258\pi$
$601$	20.4211	0.832992	0.416496	+	0.909137i	$0.363258\pi$
$602$	−27.7812	−1.13228
$603$	−5.17828	−0.210876
$604$	17.4718	0.710919
$605$	−0.114350	−0.00464900
$606$	1.61474	0.0655943
$607$	−35.8712	−1.45597	−0.727983	−	0.685595i	$-0.759542\pi$
$607$	−35.8712	−1.45597	−0.727983	+	0.685595i	$0.759542\pi$
$608$	−4.71627	−0.191270
$609$	19.5111	0.790632
$610$	0.467724	0.0189376
$611$	8.51301	0.344400
$612$	−2.25200	−0.0910316
$613$	−0.00616926	−0.000249174 0	−0.000124587	−	1.00000i	$-0.500040\pi$
$613$	−0.00616926	−0.000249174 0	−0.000124587		1.00000i	$0.500040\pi$
$614$	−30.2796	−1.22199
$615$	−1.02747	−0.0414316
$616$	−9.79714	−0.394738
$617$	21.1793	0.852646	0.426323	−	0.904571i	$-0.359809\pi$
$617$	21.1793	0.852646	0.426323	+	0.904571i	$0.359809\pi$
$618$	1.00000	0.0402259
$619$	−7.61247	−0.305971	−0.152985	−	0.988228i	$-0.548889\pi$
$619$	−7.61247	−0.305971	−0.152985	+	0.988228i	$0.548889\pi$
$620$	0.784013	0.0314867
$621$	−7.05744	−0.283205
$622$	19.4366	0.779337
$623$	9.70017	0.388629
$624$	−1.00000	−0.0400320
$625$	24.0290	0.961159
$626$	−9.90265	−0.395789
$627$	−15.9578	−0.637291
$628$	3.12465	0.124687
$629$	−23.7186	−0.945721
$630$	−0.738308	−0.0294149
$631$	16.5868	0.660309	0.330155	−	0.943927i	$-0.392899\pi$
$631$	16.5868	0.660309	0.330155	+	0.943927i	$0.392899\pi$
$632$	−8.40168	−0.334201
$633$	−1.80935	−0.0719153
$634$	−14.7302	−0.585010
$635$	0.763638	0.0303040
$636$	0.171782	0.00681161
$637$	1.38400	0.0548360
$638$	22.7998	0.902652
$639$	−11.3062	−0.447267
$640$	−0.254984	−0.0100791
$641$	0.155658	0.00614811	0.00307405	−	0.999995i	$-0.499021\pi$
$641$	0.155658	0.00614811	0.00307405	+	0.999995i	$0.499021\pi$
$642$	16.0107	0.631894
$643$	−37.3290	−1.47211	−0.736056	−	0.676921i	$-0.763314\pi$
$643$	−37.3290	−1.47211	−0.736056	+	0.676921i	$0.763314\pi$
$644$	20.4349	0.805249
$645$	−2.44646	−0.0963293
$646$	10.6210	0.417878
$647$	−27.1971	−1.06923	−0.534614	−	0.845097i	$-0.679543\pi$
$647$	−27.1971	−1.06923	−0.534614	+	0.845097i	$0.679543\pi$
$648$	1.00000	0.0392837
$649$	−25.6666	−1.00750
$650$	−4.93498	−0.193566
$651$	8.90301	0.348936
$652$	−3.74948	−0.146841
$653$	−39.3037	−1.53807	−0.769036	−	0.639206i	$-0.779263\pi$
$653$	−39.3037	−1.53807	−0.769036	+	0.639206i	$0.779263\pi$
$654$	10.3194	0.403519
$655$	−1.67105	−0.0652931
$656$	−4.02956	−0.157328
$657$	−13.5449	−0.528438
$658$	24.6495	0.960939
$659$	−30.6947	−1.19570	−0.597848	−	0.801609i	$-0.703977\pi$
$659$	−30.6947	−1.19570	−0.597848	+	0.801609i	$0.703977\pi$
$660$	−0.862751	−0.0335826
$661$	29.2323	1.13700	0.568502	−	0.822682i	$-0.307523\pi$
$661$	29.2323	1.13700	0.568502	+	0.822682i	$0.307523\pi$
$662$	−17.5713	−0.682928
$663$	2.25200	0.0874603
$664$	−15.9010	−0.617078
$665$	3.48206	0.135028
$666$	10.5322	0.408116
$667$	−47.5559	−1.84137
$668$	10.0758	0.389844
$669$	28.0025	1.08264
$670$	1.32038	0.0510106
$671$	6.20657	0.239602
$672$	−2.89551	−0.111697
$673$	6.20231	0.239081	0.119541	−	0.992829i	$-0.461858\pi$
$673$	6.20231	0.239081	0.119541	+	0.992829i	$0.461858\pi$
$674$	−12.1564	−0.468245
$675$	4.93498	0.189948
$676$	1.00000	0.0384615
$677$	−38.7223	−1.48822	−0.744109	−	0.668058i	$-0.767126\pi$
$677$	−38.7223	−1.48822	−0.744109	+	0.668058i	$0.767126\pi$
$678$	−15.6040	−0.599268
$679$	−24.7202	−0.948674
$680$	0.574222	0.0220204
$681$	−12.3664	−0.473883
$682$	10.4036	0.398375
$683$	10.9473	0.418886	0.209443	−	0.977821i	$-0.432835\pi$
$683$	10.9473	0.418886	0.209443	+	0.977821i	$0.432835\pi$
$684$	−4.71627	−0.180331
$685$	−3.47337	−0.132711
$686$	−16.2612	−0.620856
$687$	12.7890	0.487929
$688$	−9.59458	−0.365790
$689$	−0.171782	−0.00654439
$690$	1.79953	0.0685070
$691$	27.4808	1.04542	0.522709	−	0.852511i	$-0.324921\pi$
$691$	27.4808	1.04542	0.522709	+	0.852511i	$0.324921\pi$
$692$	7.15151	0.271860
$693$	−9.79714	−0.372162
$694$	−23.2701	−0.883322
$695$	−5.44117	−0.206395
$696$	6.73841	0.255419
$697$	9.07455	0.343723
$698$	4.86759	0.184241
$699$	21.7764	0.823659
$700$	−14.2893	−0.540085
$701$	−14.7635	−0.557608	−0.278804	−	0.960348i	$-0.589938\pi$
$701$	−14.7635	−0.557608	−0.278804	+	0.960348i	$0.589938\pi$
$702$	−1.00000	−0.0377426
$703$	−49.6729	−1.87345
$704$	−3.38356	−0.127523
$705$	2.17068	0.0817524
$706$	35.4302	1.33343
$707$	−4.67550	−0.175840
$708$	−7.58569	−0.285088
$709$	−48.7731	−1.83171	−0.915856	−	0.401508i	$-0.868486\pi$
$709$	−48.7731	−1.83171	−0.915856	+	0.401508i	$0.868486\pi$
$710$	2.88290	0.108193
$711$	−8.40168	−0.315088
$712$	3.35007	0.125549
$713$	−21.6999	−0.812669
$714$	6.52069	0.244031
$715$	0.862751	0.0322651
$716$	−8.02696	−0.299982
$717$	21.5769	0.805805
$718$	−13.5402	−0.505317
$719$	25.3702	0.946147	0.473074	−	0.881023i	$-0.343144\pi$
$719$	25.3702	0.946147	0.473074	+	0.881023i	$0.343144\pi$
$720$	−0.254984	−0.00950268
$721$	−2.89551	−0.107835
$722$	3.24317	0.120698
$723$	15.8803	0.590594
$724$	1.09033	0.0405216
$725$	33.2539	1.23502
$726$	−0.448461	−0.0166439
$727$	−7.48795	−0.277713	−0.138856	−	0.990313i	$-0.544343\pi$
$727$	−7.48795	−0.277713	−0.138856	+	0.990313i	$0.544343\pi$
$728$	2.89551	0.107315
$729$	1.00000	0.0370370
$730$	3.45373	0.127828
$731$	21.6070	0.799162
$732$	1.83433	0.0677988
$733$	42.1337	1.55624	0.778121	−	0.628114i	$-0.216173\pi$
$733$	42.1337	1.55624	0.778121	+	0.628114i	$0.216173\pi$
$734$	29.8828	1.10299
$735$	0.352897	0.0130168
$736$	7.05744	0.260141
$737$	17.5210	0.645395
$738$	−4.02956	−0.148330
$739$	10.9448	0.402609	0.201305	−	0.979529i	$-0.435482\pi$
$739$	10.9448	0.402609	0.201305	+	0.979529i	$0.435482\pi$
$740$	−2.68555	−0.0987227
$741$	4.71627	0.173256
$742$	−0.497398	−0.0182601
$743$	−14.0538	−0.515585	−0.257792	−	0.966200i	$-0.582995\pi$
$743$	−14.0538	−0.515585	−0.257792	+	0.966200i	$0.582995\pi$
$744$	3.07476	0.112726
$745$	−4.67255	−0.171189
$746$	−35.8607	−1.31296
$747$	−15.9010	−0.581787
$748$	7.61976	0.278606
$749$	−46.3593	−1.69393
$750$	−2.53326	−0.0925015
$751$	27.0381	0.986634	0.493317	−	0.869849i	$-0.335784\pi$
$751$	27.0381	0.986634	0.493317	+	0.869849i	$0.335784\pi$
$752$	8.51301	0.310438
$753$	−3.47281	−0.126556
$754$	−6.73841	−0.245398
$755$	−4.45503	−0.162135
$756$	−2.89551	−0.105309
$757$	−0.245699	−0.00893008	−0.00446504	−	0.999990i	$-0.501421\pi$
$757$	−0.245699	−0.00893008	−0.00446504	+	0.999990i	$0.501421\pi$
$758$	−15.6036	−0.566747
$759$	23.8793	0.866762
$760$	1.20257	0.0436218
$761$	−22.3481	−0.810117	−0.405059	−	0.914291i	$-0.632749\pi$
$761$	−22.3481	−0.810117	−0.405059	+	0.914291i	$0.632749\pi$
$762$	2.99485	0.108492
$763$	−29.8799	−1.08172
$764$	21.3379	0.771977
$765$	0.574222	0.0207610
$766$	−26.2174	−0.947272
$767$	7.58569	0.273903
$768$	−1.00000	−0.0360844
$769$	0.0178361	0.000643186 0	0.000321593	−	1.00000i	$-0.499898\pi$
$769$	0.0178361	0.000643186 0	0.000321593		1.00000i	$0.499898\pi$
$770$	2.49811	0.0900256
$771$	−12.0932	−0.435527
$772$	−6.16320	−0.221819
$773$	8.24675	0.296615	0.148308	−	0.988941i	$-0.452617\pi$
$773$	8.24675	0.296615	0.148308	+	0.988941i	$0.452617\pi$
$774$	−9.59458	−0.344870
$775$	15.1739	0.545062
$776$	−8.53741	−0.306475
$777$	−30.4962	−1.09405
$778$	−13.7430	−0.492712
$779$	19.0045	0.680906
$780$	0.254984	0.00912988
$781$	38.2552	1.36888
$782$	−15.8933	−0.568345
$783$	6.73841	0.240811
$784$	1.38400	0.0494285
$785$	−0.796734	−0.0284367
$786$	−6.55354	−0.233757
$787$	30.5798	1.09005	0.545026	−	0.838419i	$-0.316520\pi$
$787$	30.5798	1.09005	0.545026	+	0.838419i	$0.316520\pi$
$788$	−20.9313	−0.745648
$789$	−1.22342	−0.0435551
$790$	2.14229	0.0762193
$791$	45.1816	1.60647
$792$	−3.38356	−0.120229
$793$	−1.83433	−0.0651390
$794$	11.9454	0.423927
$795$	−0.0438017	−0.00155349
$796$	−3.53167	−0.125177
$797$	13.7622	0.487482	0.243741	−	0.969840i	$-0.421625\pi$
$797$	13.7622	0.487482	0.243741	+	0.969840i	$0.421625\pi$
$798$	13.6560	0.483418
$799$	−19.1713	−0.678231
$800$	−4.93498	−0.174478
$801$	3.35007	0.118369
$802$	19.7209	0.696368
$803$	45.8301	1.61731
$804$	5.17828	0.182624
$805$	−5.21057	−0.183648
$806$	−3.07476	−0.108304
$807$	15.1485	0.533253
$808$	−1.61474	−0.0568063
$809$	35.3767	1.24378	0.621888	−	0.783106i	$-0.286366\pi$
$809$	35.3767	1.24378	0.621888	+	0.783106i	$0.286366\pi$
$810$	−0.254984	−0.00895921
$811$	−24.3174	−0.853900	−0.426950	−	0.904275i	$-0.640412\pi$
$811$	−24.3174	−0.853900	−0.426950	+	0.904275i	$0.640412\pi$
$812$	−19.5111	−0.684707
$813$	10.5614	0.370405
$814$	−35.6364	−1.24906
$815$	0.956055	0.0334892
$816$	2.25200	0.0788357
$817$	45.2506	1.58312
$818$	27.2189	0.951688
$819$	2.89551	0.101177
$820$	1.02747	0.0358808
$821$	−49.1162	−1.71417	−0.857084	−	0.515177i	$-0.827726\pi$
$821$	−49.1162	−1.71417	−0.857084	+	0.515177i	$0.827726\pi$
$822$	−13.6219	−0.475120
$823$	18.4671	0.643723	0.321861	−	0.946787i	$-0.395692\pi$
$823$	18.4671	0.643723	0.321861	+	0.946787i	$0.395692\pi$
$824$	−1.00000	−0.0348367
$825$	−16.6978	−0.581343
$826$	21.9645	0.764242
$827$	47.5426	1.65322	0.826609	−	0.562777i	$-0.190267\pi$
$827$	47.5426	1.65322	0.826609	+	0.562777i	$0.190267\pi$
$828$	7.05744	0.245263
$829$	−28.7525	−0.998617	−0.499308	−	0.866424i	$-0.666413\pi$
$829$	−28.7525	−0.998617	−0.499308	+	0.866424i	$0.666413\pi$
$830$	4.05449	0.140733
$831$	26.0641	0.904152
$832$	1.00000	0.0346688
$833$	−3.11676	−0.107989
$834$	−21.3393	−0.738920
$835$	−2.56916	−0.0889094
$836$	15.9578	0.551911
$837$	3.07476	0.106279
$838$	−33.9553	−1.17297
$839$	−29.0167	−1.00177	−0.500885	−	0.865514i	$-0.666992\pi$
$839$	−29.0167	−1.00177	−0.500885	+	0.865514i	$0.666992\pi$
$840$	0.738308	0.0254741
$841$	16.4061	0.565728
$842$	−28.7260	−0.989965
$843$	−19.6014	−0.675107
$844$	1.80935	0.0622805
$845$	−0.254984	−0.00877170
$846$	8.51301	0.292683
$847$	1.29852	0.0446178
$848$	−0.171782	−0.00589903
$849$	−16.9805	−0.582771
$850$	11.1136	0.381192
$851$	74.3307	2.54802
$852$	11.3062	0.387345
$853$	−6.66594	−0.228237	−0.114119	−	0.993467i	$-0.536404\pi$
$853$	−6.66594	−0.228237	−0.114119	+	0.993467i	$0.536404\pi$
$854$	−5.31133	−0.181750
$855$	1.20257	0.0411270
$856$	−16.0107	−0.547236
$857$	−11.3801	−0.388738	−0.194369	−	0.980928i	$-0.562266\pi$
$857$	−11.3801	−0.388738	−0.194369	+	0.980928i	$0.562266\pi$
$858$	3.38356	0.115513
$859$	43.4855	1.48371	0.741854	−	0.670562i	$-0.233947\pi$
$859$	43.4855	1.48371	0.741854	+	0.670562i	$0.233947\pi$
$860$	2.44646	0.0834236
$861$	11.6676	0.397632
$862$	−5.30622	−0.180730
$863$	−13.1850	−0.448822	−0.224411	−	0.974495i	$-0.572046\pi$
$863$	−13.1850	−0.448822	−0.224411	+	0.974495i	$0.572046\pi$
$864$	−1.00000	−0.0340207
$865$	−1.82352	−0.0620014
$866$	−39.0299	−1.32629
$867$	11.9285	0.405113
$868$	−8.90301	−0.302188
$869$	28.4276	0.964339
$870$	−1.71818	−0.0582519
$871$	−5.17828	−0.175459
$872$	−10.3194	−0.349458
$873$	−8.53741	−0.288948
$874$	−33.2848	−1.12587
$875$	7.33508	0.247971
$876$	13.5449	0.457641
$877$	−38.7418	−1.30822	−0.654109	−	0.756400i	$-0.726956\pi$
$877$	−38.7418	−1.30822	−0.654109	+	0.756400i	$0.726956\pi$
$878$	6.95768	0.234810
$879$	11.8657	0.400220
$880$	0.862751	0.0290833
$881$	37.2763	1.25587	0.627935	−	0.778266i	$-0.283900\pi$
$881$	37.2763	1.25587	0.627935	+	0.778266i	$0.283900\pi$
$882$	1.38400	0.0466016
$883$	−36.9499	−1.24346	−0.621732	−	0.783230i	$-0.713571\pi$
$883$	−36.9499	−1.24346	−0.621732	+	0.783230i	$0.713571\pi$
$884$	−2.25200	−0.0757429
$885$	1.93423	0.0650183
$886$	15.2869	0.513575
$887$	26.3461	0.884614	0.442307	−	0.896864i	$-0.354160\pi$
$887$	26.3461	0.884614	0.442307	+	0.896864i	$0.354160\pi$
$888$	−10.5322	−0.353439
$889$	−8.67163	−0.290837
$890$	−0.854212	−0.0286333
$891$	−3.38356	−0.113353
$892$	−28.0025	−0.937593
$893$	−40.1496	−1.34356
$894$	−18.3249	−0.612877
$895$	2.04674	0.0684150
$896$	2.89551	0.0967323
$897$	−7.05744	−0.235641
$898$	−25.1056	−0.837783
$899$	20.7190	0.691017
$900$	−4.93498	−0.164499
$901$	0.386853	0.0128880
$902$	13.6342	0.453971
$903$	27.7812	0.924502
$904$	15.6040	0.518982
$905$	−0.278015	−0.00924153
$906$	−17.4718	−0.580463
$907$	6.41065	0.212862	0.106431	−	0.994320i	$-0.466058\pi$
$907$	6.41065	0.212862	0.106431	+	0.994320i	$0.466058\pi$
$908$	12.3664	0.410395
$909$	−1.61474	−0.0535575
$910$	−0.738308	−0.0244747
$911$	49.8179	1.65054	0.825271	−	0.564737i	$-0.191023\pi$
$911$	49.8179	1.65054	0.825271	+	0.564737i	$0.191023\pi$
$912$	4.71627	0.156171
$913$	53.8019	1.78058
$914$	−12.8275	−0.424298
$915$	−0.467724	−0.0154625
$916$	−12.7890	−0.422559
$917$	18.9759	0.626638
$918$	2.25200	0.0743270
$919$	−19.0081	−0.627021	−0.313510	−	0.949585i	$-0.601505\pi$
$919$	−19.0081	−0.627021	−0.313510	+	0.949585i	$0.601505\pi$
$920$	−1.79953	−0.0593288
$921$	30.2796	0.997747
$922$	28.4754	0.937786
$923$	−11.3062	−0.372149
$924$	9.79714	0.322302
$925$	−51.9764	−1.70897
$926$	21.8937	0.719473
$927$	−1.00000	−0.0328443
$928$	−6.73841	−0.221199
$929$	9.43875	0.309675	0.154838	−	0.987940i	$-0.450515\pi$
$929$	9.43875	0.309675	0.154838	+	0.987940i	$0.450515\pi$
$930$	−0.784013	−0.0257088
$931$	−6.52730	−0.213924
$932$	−21.7764	−0.713309
$933$	−19.4366	−0.636326
$934$	23.6835	0.774948
$935$	−1.94291	−0.0635401
$936$	1.00000	0.0326860
$937$	11.4855	0.375214	0.187607	−	0.982244i	$-0.439927\pi$
$937$	11.4855	0.375214	0.187607	+	0.982244i	$0.439927\pi$
$938$	−14.9938	−0.489565
$939$	9.90265	0.323161
$940$	−2.17068	−0.0707997
$941$	−17.5742	−0.572902	−0.286451	−	0.958095i	$-0.592476\pi$
$941$	−17.5742	−0.572902	−0.286451	+	0.958095i	$0.592476\pi$
$942$	−3.12465	−0.101807
$943$	−28.4384	−0.926081
$944$	7.58569	0.246893
$945$	0.738308	0.0240172
$946$	32.4638	1.05549
$947$	−16.6698	−0.541695	−0.270847	−	0.962622i	$-0.587304\pi$
$947$	−16.6698	−0.541695	−0.270847	+	0.962622i	$0.587304\pi$
$948$	8.40168	0.272874
$949$	−13.5449	−0.439687
$950$	23.2747	0.755131
$951$	14.7302	0.477659
$952$	−6.52069	−0.211337
$953$	−5.52966	−0.179123	−0.0895617	−	0.995981i	$-0.528547\pi$
$953$	−5.52966	−0.179123	−0.0895617	+	0.995981i	$0.528547\pi$
$954$	−0.171782	−0.00556166
$955$	−5.44080	−0.176060
$956$	−21.5769	−0.697848
$957$	−22.7998	−0.737012
$958$	8.98472	0.290283
$959$	39.4425	1.27366
$960$	0.254984	0.00822956
$961$	−21.5459	−0.695027
$962$	10.5322	0.339573
$963$	−16.0107	−0.515939
$964$	−15.8803	−0.511470
$965$	1.57152	0.0505889
$966$	−20.4349	−0.657483
$967$	41.0461	1.31995	0.659976	−	0.751286i	$-0.270566\pi$
$967$	41.0461	1.31995	0.659976	+	0.751286i	$0.270566\pi$
$968$	0.448461	0.0144141
$969$	−10.6210	−0.341196
$970$	2.17690	0.0698960
$971$	27.2913	0.875819	0.437909	−	0.899019i	$-0.355719\pi$
$971$	27.2913	0.875819	0.437909	+	0.899019i	$0.355719\pi$
$972$	−1.00000	−0.0320750
$973$	61.7883	1.98084
$974$	33.2828	1.06645
$975$	4.93498	0.158046
$976$	−1.83433	−0.0587155
$977$	60.2284	1.92688	0.963439	−	0.267929i	$-0.0863392\pi$
$977$	60.2284	1.92688	0.963439	+	0.267929i	$0.0863392\pi$
$978$	3.74948	0.119895
$979$	−11.3351	−0.362273
$980$	−0.352897	−0.0112729
$981$	−10.3194	−0.329472
$982$	−4.81059	−0.153512
$983$	40.9882	1.30732	0.653661	−	0.756788i	$-0.273232\pi$
$983$	40.9882	1.30732	0.653661	+	0.756788i	$0.273232\pi$
$984$	4.02956	0.128458
$985$	5.33714	0.170056
$986$	15.1749	0.483266
$987$	−24.6495	−0.784603
$988$	−4.71627	−0.150044
$989$	−67.7132	−2.15315
$990$	0.862751	0.0274200
$991$	0.00822925	0.000261411 0	0.000130705	−	1.00000i	$-0.499958\pi$
$991$	0.00822925	0.000261411 0	0.000130705		1.00000i	$0.499958\pi$
$992$	−3.07476	−0.0976237
$993$	17.5713	0.557609
$994$	−32.7373	−1.03836
$995$	0.900518	0.0285483
$996$	15.9010	0.503842
$997$	4.70129	0.148891	0.0744457	−	0.997225i	$-0.476281\pi$
$997$	4.70129	0.148891	0.0744457	+	0.997225i	$0.476281\pi$
$998$	39.0904	1.23738
$999$	−10.5322	−0.333225

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.r.1.6	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.r.1.6	✓	9	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.254984 q^{5} -1.00000 q^{6} +2.89551 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.254984 q^{5} -1.00000 q^{6} +2.89551 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.254984 q^{10} -3.38356 q^{11} -1.00000 q^{12} +1.00000 q^{13} +2.89551 q^{14} +0.254984 q^{15} +1.00000 q^{16} -2.25200 q^{17} +1.00000 q^{18} -4.71627 q^{19} -0.254984 q^{20} -2.89551 q^{21} -3.38356 q^{22} +7.05744 q^{23} -1.00000 q^{24} -4.93498 q^{25} +1.00000 q^{26} -1.00000 q^{27} +2.89551 q^{28} -6.73841 q^{29} +0.254984 q^{30} -3.07476 q^{31} +1.00000 q^{32} +3.38356 q^{33} -2.25200 q^{34} -0.738308 q^{35} +1.00000 q^{36} +10.5322 q^{37} -4.71627 q^{38} -1.00000 q^{39} -0.254984 q^{40} -4.02956 q^{41} -2.89551 q^{42} -9.59458 q^{43} -3.38356 q^{44} -0.254984 q^{45} +7.05744 q^{46} +8.51301 q^{47} -1.00000 q^{48} +1.38400 q^{49} -4.93498 q^{50} +2.25200 q^{51} +1.00000 q^{52} -0.171782 q^{53} -1.00000 q^{54} +0.862751 q^{55} +2.89551 q^{56} +4.71627 q^{57} -6.73841 q^{58} +7.58569 q^{59} +0.254984 q^{60} -1.83433 q^{61} -3.07476 q^{62} +2.89551 q^{63} +1.00000 q^{64} -0.254984 q^{65} +3.38356 q^{66} -5.17828 q^{67} -2.25200 q^{68} -7.05744 q^{69} -0.738308 q^{70} -11.3062 q^{71} +1.00000 q^{72} -13.5449 q^{73} +10.5322 q^{74} +4.93498 q^{75} -4.71627 q^{76} -9.79714 q^{77} -1.00000 q^{78} -8.40168 q^{79} -0.254984 q^{80} +1.00000 q^{81} -4.02956 q^{82} -15.9010 q^{83} -2.89551 q^{84} +0.574222 q^{85} -9.59458 q^{86} +6.73841 q^{87} -3.38356 q^{88} +3.35007 q^{89} -0.254984 q^{90} +2.89551 q^{91} +7.05744 q^{92} +3.07476 q^{93} +8.51301 q^{94} +1.20257 q^{95} -1.00000 q^{96} -8.53741 q^{97} +1.38400 q^{98} -3.38356 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} - 4 q^{5} - 9 q^{6} - 4 q^{7} + 9 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 - 4 * q^5 - 9 * q^6 - 4 * q^7 + 9 * q^8 + 9 * q^9	\( 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} - 4 q^{5} - 9 q^{6} - 4 q^{7} + 9 q^{8} + 9 q^{9} - 4 q^{10} - 5 q^{11} - 9 q^{12} + 9 q^{13} - 4 q^{14} + 4 q^{15} + 9 q^{16} - 6 q^{17} + 9 q^{18} - 4 q^{19} - 4 q^{20} + 4 q^{21} - 5 q^{22} - 6 q^{23} - 9 q^{24} - 11 q^{25} + 9 q^{26} - 9 q^{27} - 4 q^{28} - 19 q^{29} + 4 q^{30} - 6 q^{31} + 9 q^{32} + 5 q^{33} - 6 q^{34} + 10 q^{35} + 9 q^{36} - 13 q^{37} - 4 q^{38} - 9 q^{39} - 4 q^{40} - 18 q^{41} + 4 q^{42} - 20 q^{43} - 5 q^{44} - 4 q^{45} - 6 q^{46} + 14 q^{47} - 9 q^{48} - 3 q^{49} - 11 q^{50} + 6 q^{51} + 9 q^{52} - 3 q^{53} - 9 q^{54} - 4 q^{55} - 4 q^{56} + 4 q^{57} - 19 q^{58} - 9 q^{59} + 4 q^{60} - 24 q^{61} - 6 q^{62} - 4 q^{63} + 9 q^{64} - 4 q^{65} + 5 q^{66} - 4 q^{67} - 6 q^{68} + 6 q^{69} + 10 q^{70} - 9 q^{71} + 9 q^{72} - 24 q^{73} - 13 q^{74} + 11 q^{75} - 4 q^{76} + 3 q^{77} - 9 q^{78} - 15 q^{79} - 4 q^{80} + 9 q^{81} - 18 q^{82} + 20 q^{83} + 4 q^{84} - 31 q^{85} - 20 q^{86} + 19 q^{87} - 5 q^{88} + 3 q^{89} - 4 q^{90} - 4 q^{91} - 6 q^{92} + 6 q^{93} + 14 q^{94} - 4 q^{95} - 9 q^{96} - 19 q^{97} - 3 q^{98} - 5 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 - 4 * q^5 - 9 * q^6 - 4 * q^7 + 9 * q^8 + 9 * q^9 - 4 * q^10 - 5 * q^11 - 9 * q^12 + 9 * q^13 - 4 * q^14 + 4 * q^15 + 9 * q^16 - 6 * q^17 + 9 * q^18 - 4 * q^19 - 4 * q^20 + 4 * q^21 - 5 * q^22 - 6 * q^23 - 9 * q^24 - 11 * q^25 + 9 * q^26 - 9 * q^27 - 4 * q^28 - 19 * q^29 + 4 * q^30 - 6 * q^31 + 9 * q^32 + 5 * q^33 - 6 * q^34 + 10 * q^35 + 9 * q^36 - 13 * q^37 - 4 * q^38 - 9 * q^39 - 4 * q^40 - 18 * q^41 + 4 * q^42 - 20 * q^43 - 5 * q^44 - 4 * q^45 - 6 * q^46 + 14 * q^47 - 9 * q^48 - 3 * q^49 - 11 * q^50 + 6 * q^51 + 9 * q^52 - 3 * q^53 - 9 * q^54 - 4 * q^55 - 4 * q^56 + 4 * q^57 - 19 * q^58 - 9 * q^59 + 4 * q^60 - 24 * q^61 - 6 * q^62 - 4 * q^63 + 9 * q^64 - 4 * q^65 + 5 * q^66 - 4 * q^67 - 6 * q^68 + 6 * q^69 + 10 * q^70 - 9 * q^71 + 9 * q^72 - 24 * q^73 - 13 * q^74 + 11 * q^75 - 4 * q^76 + 3 * q^77 - 9 * q^78 - 15 * q^79 - 4 * q^80 + 9 * q^81 - 18 * q^82 + 20 * q^83 + 4 * q^84 - 31 * q^85 - 20 * q^86 + 19 * q^87 - 5 * q^88 + 3 * q^89 - 4 * q^90 - 4 * q^91 - 6 * q^92 + 6 * q^93 + 14 * q^94 - 4 * q^95 - 9 * q^96 - 19 * q^97 - 3 * q^98 - 5 * q^99

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