LMFDB - Embedded newform 8034.2.a.r.1.9

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			1.9
Root			$-2.74988$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.74988 q^{5} -1.00000 q^{6} -2.39902 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.74988 q^{5} -1.00000 q^{6} -2.39902 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.74988 q^{10} -1.84857 q^{11} -1.00000 q^{12} +1.00000 q^{13} -2.39902 q^{14} -2.74988 q^{15} +1.00000 q^{16} -7.09886 q^{17} +1.00000 q^{18} +7.61788 q^{19} +2.74988 q^{20} +2.39902 q^{21} -1.84857 q^{22} -0.525313 q^{23} -1.00000 q^{24} +2.56184 q^{25} +1.00000 q^{26} -1.00000 q^{27} -2.39902 q^{28} -3.74958 q^{29} -2.74988 q^{30} -4.81984 q^{31} +1.00000 q^{32} +1.84857 q^{33} -7.09886 q^{34} -6.59703 q^{35} +1.00000 q^{36} -3.48085 q^{37} +7.61788 q^{38} -1.00000 q^{39} +2.74988 q^{40} +0.958773 q^{41} +2.39902 q^{42} -11.7448 q^{43} -1.84857 q^{44} +2.74988 q^{45} -0.525313 q^{46} +3.33059 q^{47} -1.00000 q^{48} -1.24468 q^{49} +2.56184 q^{50} +7.09886 q^{51} +1.00000 q^{52} +4.47200 q^{53} -1.00000 q^{54} -5.08335 q^{55} -2.39902 q^{56} -7.61788 q^{57} -3.74958 q^{58} -1.08272 q^{59} -2.74988 q^{60} -8.03392 q^{61} -4.81984 q^{62} -2.39902 q^{63} +1.00000 q^{64} +2.74988 q^{65} +1.84857 q^{66} +8.95832 q^{67} -7.09886 q^{68} +0.525313 q^{69} -6.59703 q^{70} -1.24278 q^{71} +1.00000 q^{72} -2.09283 q^{73} -3.48085 q^{74} -2.56184 q^{75} +7.61788 q^{76} +4.43477 q^{77} -1.00000 q^{78} +2.18222 q^{79} +2.74988 q^{80} +1.00000 q^{81} +0.958773 q^{82} +6.22219 q^{83} +2.39902 q^{84} -19.5210 q^{85} -11.7448 q^{86} +3.74958 q^{87} -1.84857 q^{88} -9.80734 q^{89} +2.74988 q^{90} -2.39902 q^{91} -0.525313 q^{92} +4.81984 q^{93} +3.33059 q^{94} +20.9483 q^{95} -1.00000 q^{96} -1.02696 q^{97} -1.24468 q^{98} -1.84857 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	2.74988	1.22978	0.614892	−	0.788611i	$-0.289200\pi$
$5$	2.74988	1.22978	0.614892	+	0.788611i	$0.289200\pi$
$6$	−1.00000	−0.408248
$7$	−2.39902	−0.906746	−0.453373	−	0.891321i	$-0.649779\pi$
$7$	−2.39902	−0.906746	−0.453373	+	0.891321i	$0.649779\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	2.74988	0.869589
$11$	−1.84857	−0.557366	−0.278683	−	0.960383i	$-0.589898\pi$
$11$	−1.84857	−0.557366	−0.278683	+	0.960383i	$0.589898\pi$
$12$	−1.00000	−0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−2.39902	−0.641166
$15$	−2.74988	−0.710016
$16$	1.00000	0.250000
$17$	−7.09886	−1.72173	−0.860864	−	0.508836i	$-0.830076\pi$
$17$	−7.09886	−1.72173	−0.860864	+	0.508836i	$0.830076\pi$
$18$	1.00000	0.235702
$19$	7.61788	1.74766	0.873831	−	0.486230i	$-0.161628\pi$
$19$	7.61788	1.74766	0.873831	+	0.486230i	$0.161628\pi$
$20$	2.74988	0.614892
$21$	2.39902	0.523510
$22$	−1.84857	−0.394117
$23$	−0.525313	−0.109535	−0.0547677	−	0.998499i	$-0.517442\pi$
$23$	−0.525313	−0.109535	−0.0547677	+	0.998499i	$0.517442\pi$
$24$	−1.00000	−0.204124
$25$	2.56184	0.512368
$26$	1.00000	0.196116
$27$	−1.00000	−0.192450
$28$	−2.39902	−0.453373
$29$	−3.74958	−0.696279	−0.348140	−	0.937443i	$-0.613187\pi$
$29$	−3.74958	−0.696279	−0.348140	+	0.937443i	$0.613187\pi$
$30$	−2.74988	−0.502057
$31$	−4.81984	−0.865668	−0.432834	−	0.901474i	$-0.642486\pi$
$31$	−4.81984	−0.865668	−0.432834	+	0.901474i	$0.642486\pi$
$32$	1.00000	0.176777
$33$	1.84857	0.321795
$34$	−7.09886	−1.21744
$35$	−6.59703	−1.11510
$36$	1.00000	0.166667
$37$	−3.48085	−0.572247	−0.286124	−	0.958193i	$-0.592367\pi$
$37$	−3.48085	−0.572247	−0.286124	+	0.958193i	$0.592367\pi$
$38$	7.61788	1.23578
$39$	−1.00000	−0.160128
$40$	2.74988	0.434794
$41$	0.958773	0.149735	0.0748676	−	0.997193i	$-0.476147\pi$
$41$	0.958773	0.149735	0.0748676	+	0.997193i	$0.476147\pi$
$42$	2.39902	0.370177
$43$	−11.7448	−1.79106	−0.895532	−	0.444997i	$-0.853205\pi$
$43$	−11.7448	−1.79106	−0.895532	+	0.444997i	$0.853205\pi$
$44$	−1.84857	−0.278683
$45$	2.74988	0.409928
$46$	−0.525313	−0.0774532
$47$	3.33059	0.485816	0.242908	−	0.970049i	$-0.421899\pi$
$47$	3.33059	0.485816	0.242908	+	0.970049i	$0.421899\pi$
$48$	−1.00000	−0.144338
$49$	−1.24468	−0.177812
$50$	2.56184	0.362299
$51$	7.09886	0.994040
$52$	1.00000	0.138675
$53$	4.47200	0.614276	0.307138	−	0.951665i	$-0.400629\pi$
$53$	4.47200	0.614276	0.307138	+	0.951665i	$0.400629\pi$
$54$	−1.00000	−0.136083
$55$	−5.08335	−0.685439
$56$	−2.39902	−0.320583
$57$	−7.61788	−1.00901
$58$	−3.74958	−0.492344
$59$	−1.08272	−0.140958	−0.0704788	−	0.997513i	$-0.522453\pi$
$59$	−1.08272	−0.140958	−0.0704788	+	0.997513i	$0.522453\pi$
$60$	−2.74988	−0.355008
$61$	−8.03392	−1.02864	−0.514319	−	0.857599i	$-0.671955\pi$
$61$	−8.03392	−1.02864	−0.514319	+	0.857599i	$0.671955\pi$
$62$	−4.81984	−0.612120
$63$	−2.39902	−0.302249
$64$	1.00000	0.125000
$65$	2.74988	0.341081
$66$	1.84857	0.227544
$67$	8.95832	1.09443	0.547216	−	0.836991i	$-0.315688\pi$
$67$	8.95832	1.09443	0.547216	+	0.836991i	$0.315688\pi$
$68$	−7.09886	−0.860864
$69$	0.525313	0.0632402
$70$	−6.59703	−0.788496
$71$	−1.24278	−0.147491	−0.0737454	−	0.997277i	$-0.523495\pi$
$71$	−1.24278	−0.147491	−0.0737454	+	0.997277i	$0.523495\pi$
$72$	1.00000	0.117851
$73$	−2.09283	−0.244948	−0.122474	−	0.992472i	$-0.539083\pi$
$73$	−2.09283	−0.244948	−0.122474	+	0.992472i	$0.539083\pi$
$74$	−3.48085	−0.404640
$75$	−2.56184	−0.295816
$76$	7.61788	0.873831
$77$	4.43477	0.505389
$78$	−1.00000	−0.113228
$79$	2.18222	0.245519	0.122760	−	0.992436i	$-0.460826\pi$
$79$	2.18222	0.245519	0.122760	+	0.992436i	$0.460826\pi$
$80$	2.74988	0.307446
$81$	1.00000	0.111111
$82$	0.958773	0.105879
$83$	6.22219	0.682974	0.341487	−	0.939887i	$-0.389070\pi$
$83$	6.22219	0.682974	0.341487	+	0.939887i	$0.389070\pi$
$84$	2.39902	0.261755
$85$	−19.5210	−2.11735
$86$	−11.7448	−1.26647
$87$	3.74958	0.401997
$88$	−1.84857	−0.197059
$89$	−9.80734	−1.03958	−0.519788	−	0.854295i	$-0.673989\pi$
$89$	−9.80734	−1.03958	−0.519788	+	0.854295i	$0.673989\pi$
$90$	2.74988	0.289863
$91$	−2.39902	−0.251486
$92$	−0.525313	−0.0547677
$93$	4.81984	0.499794
$94$	3.33059	0.343524
$95$	20.9483	2.14925
$96$	−1.00000	−0.102062
$97$	−1.02696	−0.104272	−0.0521359	−	0.998640i	$-0.516603\pi$
$97$	−1.02696	−0.104272	−0.0521359	+	0.998640i	$0.516603\pi$
$98$	−1.24468	−0.125732
$99$	−1.84857	−0.185789
$100$	2.56184	0.256184
$101$	−11.1376	−1.10824	−0.554118	−	0.832438i	$-0.686944\pi$
$101$	−11.1376	−1.10824	−0.554118	+	0.832438i	$0.686944\pi$
$102$	7.09886	0.702892
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	1.00000	0.0980581
$105$	6.59703	0.643804
$106$	4.47200	0.434359
$107$	−3.30454	−0.319462	−0.159731	−	0.987161i	$-0.551063\pi$
$107$	−3.30454	−0.319462	−0.159731	+	0.987161i	$0.551063\pi$
$108$	−1.00000	−0.0962250
$109$	−13.7158	−1.31374	−0.656870	−	0.754004i	$-0.728120\pi$
$109$	−13.7158	−1.31374	−0.656870	+	0.754004i	$0.728120\pi$
$110$	−5.08335	−0.484679
$111$	3.48085	0.330387
$112$	−2.39902	−0.226686
$113$	6.96842	0.655534	0.327767	−	0.944759i	$-0.393704\pi$
$113$	6.96842	0.655534	0.327767	+	0.944759i	$0.393704\pi$
$114$	−7.61788	−0.713480
$115$	−1.44455	−0.134705
$116$	−3.74958	−0.348140
$117$	1.00000	0.0924500
$118$	−1.08272	−0.0996721
$119$	17.0303	1.56117
$120$	−2.74988	−0.251029
$121$	−7.58278	−0.689344
$122$	−8.03392	−0.727357
$123$	−0.958773	−0.0864497
$124$	−4.81984	−0.432834
$125$	−6.70464	−0.599682
$126$	−2.39902	−0.213722
$127$	−1.58206	−0.140385	−0.0701927	−	0.997533i	$-0.522361\pi$
$127$	−1.58206	−0.140385	−0.0701927	+	0.997533i	$0.522361\pi$
$128$	1.00000	0.0883883
$129$	11.7448	1.03407
$130$	2.74988	0.241180
$131$	10.0938	0.881903	0.440951	−	0.897531i	$-0.354641\pi$
$131$	10.0938	0.881903	0.440951	+	0.897531i	$0.354641\pi$
$132$	1.84857	0.160898
$133$	−18.2755	−1.58469
$134$	8.95832	0.773881
$135$	−2.74988	−0.236672
$136$	−7.09886	−0.608722
$137$	−19.5238	−1.66803	−0.834017	−	0.551739i	$-0.813964\pi$
$137$	−19.5238	−1.66803	−0.834017	+	0.551739i	$0.813964\pi$
$138$	0.525313	0.0447176
$139$	−9.19954	−0.780295	−0.390148	−	0.920752i	$-0.627576\pi$
$139$	−9.19954	−0.780295	−0.390148	+	0.920752i	$0.627576\pi$
$140$	−6.59703	−0.557551
$141$	−3.33059	−0.280486
$142$	−1.24278	−0.104292
$143$	−1.84857	−0.154585
$144$	1.00000	0.0833333
$145$	−10.3109	−0.856273
$146$	−2.09283	−0.173204
$147$	1.24468	0.102660
$148$	−3.48085	−0.286124
$149$	−7.16230	−0.586759	−0.293379	−	0.955996i	$-0.594780\pi$
$149$	−7.16230	−0.586759	−0.293379	+	0.955996i	$0.594780\pi$
$150$	−2.56184	−0.209173
$151$	8.61468	0.701053	0.350526	−	0.936553i	$-0.386003\pi$
$151$	8.61468	0.701053	0.350526	+	0.936553i	$0.386003\pi$
$152$	7.61788	0.617892
$153$	−7.09886	−0.573909
$154$	4.43477	0.357364
$155$	−13.2540	−1.06458
$156$	−1.00000	−0.0800641
$157$	12.1972	0.973446	0.486723	−	0.873556i	$-0.338192\pi$
$157$	12.1972	0.973446	0.486723	+	0.873556i	$0.338192\pi$
$158$	2.18222	0.173608
$159$	−4.47200	−0.354653
$160$	2.74988	0.217397
$161$	1.26024	0.0993207
$162$	1.00000	0.0785674
$163$	20.5550	1.60999	0.804997	−	0.593279i	$-0.202167\pi$
$163$	20.5550	1.60999	0.804997	+	0.593279i	$0.202167\pi$
$164$	0.958773	0.0748676
$165$	5.08335	0.395739
$166$	6.22219	0.482935
$167$	−7.03334	−0.544256	−0.272128	−	0.962261i	$-0.587727\pi$
$167$	−7.03334	−0.544256	−0.272128	+	0.962261i	$0.587727\pi$
$168$	2.39902	0.185089
$169$	1.00000	0.0769231
$170$	−19.5210	−1.49719
$171$	7.61788	0.582554
$172$	−11.7448	−0.895532
$173$	14.8424	1.12845	0.564224	−	0.825622i	$-0.309175\pi$
$173$	14.8424	1.12845	0.564224	+	0.825622i	$0.309175\pi$
$174$	3.74958	0.284255
$175$	−6.14592	−0.464588
$176$	−1.84857	−0.139341
$177$	1.08272	0.0813819
$178$	−9.80734	−0.735091
$179$	8.92436	0.667038	0.333519	−	0.942743i	$-0.391764\pi$
$179$	8.92436	0.667038	0.333519	+	0.942743i	$0.391764\pi$
$180$	2.74988	0.204964
$181$	0.631471	0.0469369	0.0234684	−	0.999725i	$-0.492529\pi$
$181$	0.631471	0.0469369	0.0234684	+	0.999725i	$0.492529\pi$
$182$	−2.39902	−0.177827
$183$	8.03392	0.593885
$184$	−0.525313	−0.0387266
$185$	−9.57191	−0.703741
$186$	4.81984	0.353407
$187$	13.1228	0.959632
$188$	3.33059	0.242908
$189$	2.39902	0.174503
$190$	20.9483	1.51975
$191$	15.8786	1.14893	0.574466	−	0.818528i	$-0.305210\pi$
$191$	15.8786	1.14893	0.574466	+	0.818528i	$0.305210\pi$
$192$	−1.00000	−0.0721688
$193$	−24.1334	−1.73716	−0.868581	−	0.495548i	$-0.834967\pi$
$193$	−24.1334	−1.73716	−0.868581	+	0.495548i	$0.834967\pi$
$194$	−1.02696	−0.0737312
$195$	−2.74988	−0.196923
$196$	−1.24468	−0.0889061
$197$	−1.91505	−0.136442	−0.0682209	−	0.997670i	$-0.521732\pi$
$197$	−1.91505	−0.136442	−0.0682209	+	0.997670i	$0.521732\pi$
$198$	−1.84857	−0.131372
$199$	−20.7332	−1.46974	−0.734868	−	0.678210i	$-0.762756\pi$
$199$	−20.7332	−1.46974	−0.734868	+	0.678210i	$0.762756\pi$
$200$	2.56184	0.181150
$201$	−8.95832	−0.631871
$202$	−11.1376	−0.783642
$203$	8.99533	0.631348
$204$	7.09886	0.497020
$205$	2.63651	0.184142
$206$	−1.00000	−0.0696733
$207$	−0.525313	−0.0365118
$208$	1.00000	0.0693375
$209$	−14.0822	−0.974087
$210$	6.59703	0.455238
$211$	−8.93942	−0.615415	−0.307708	−	0.951481i	$-0.599562\pi$
$211$	−8.93942	−0.615415	−0.307708	+	0.951481i	$0.599562\pi$
$212$	4.47200	0.307138
$213$	1.24278	0.0851539
$214$	−3.30454	−0.225894
$215$	−32.2968	−2.20262
$216$	−1.00000	−0.0680414
$217$	11.5629	0.784941
$218$	−13.7158	−0.928954
$219$	2.09283	0.141421
$220$	−5.08335	−0.342720
$221$	−7.09886	−0.477521
$222$	3.48085	0.233619
$223$	−11.7404	−0.786193	−0.393096	−	0.919497i	$-0.628596\pi$
$223$	−11.7404	−0.786193	−0.393096	+	0.919497i	$0.628596\pi$
$224$	−2.39902	−0.160292
$225$	2.56184	0.170789
$226$	6.96842	0.463532
$227$	−28.6607	−1.90227	−0.951137	−	0.308768i	$-0.900083\pi$
$227$	−28.6607	−1.90227	−0.951137	+	0.308768i	$0.900083\pi$
$228$	−7.61788	−0.504507
$229$	7.61836	0.503435	0.251718	−	0.967801i	$-0.419005\pi$
$229$	7.61836	0.503435	0.251718	+	0.967801i	$0.419005\pi$
$230$	−1.44455	−0.0952507
$231$	−4.43477	−0.291786
$232$	−3.74958	−0.246172
$233$	1.83307	0.120088	0.0600441	−	0.998196i	$-0.480876\pi$
$233$	1.83307	0.120088	0.0600441	+	0.998196i	$0.480876\pi$
$234$	1.00000	0.0653720
$235$	9.15871	0.597449
$236$	−1.08272	−0.0704788
$237$	−2.18222	−0.141751
$238$	17.0303	1.10391
$239$	−18.9339	−1.22473	−0.612365	−	0.790575i	$-0.709782\pi$
$239$	−18.9339	−1.22473	−0.612365	+	0.790575i	$0.709782\pi$
$240$	−2.74988	−0.177504
$241$	−27.9303	−1.79915	−0.899574	−	0.436769i	$-0.856123\pi$
$241$	−27.9303	−1.79915	−0.899574	+	0.436769i	$0.856123\pi$
$242$	−7.58278	−0.487439
$243$	−1.00000	−0.0641500
$244$	−8.03392	−0.514319
$245$	−3.42273	−0.218670
$246$	−0.958773	−0.0611292
$247$	7.61788	0.484714
$248$	−4.81984	−0.306060
$249$	−6.22219	−0.394315
$250$	−6.70464	−0.424039
$251$	−8.95192	−0.565040	−0.282520	−	0.959261i	$-0.591170\pi$
$251$	−8.95192	−0.565040	−0.282520	+	0.959261i	$0.591170\pi$
$252$	−2.39902	−0.151124
$253$	0.971079	0.0610512
$254$	−1.58206	−0.0992675
$255$	19.5210	1.22245
$256$	1.00000	0.0625000
$257$	8.76617	0.546819	0.273409	−	0.961898i	$-0.411849\pi$
$257$	8.76617	0.546819	0.273409	+	0.961898i	$0.411849\pi$
$258$	11.7448	0.731199
$259$	8.35063	0.518883
$260$	2.74988	0.170540
$261$	−3.74958	−0.232093
$262$	10.0938	0.623599
$263$	26.0103	1.60387	0.801933	−	0.597413i	$-0.203805\pi$
$263$	26.0103	1.60387	0.801933	+	0.597413i	$0.203805\pi$
$264$	1.84857	0.113772
$265$	12.2975	0.755427
$266$	−18.2755	−1.12054
$267$	9.80734	0.600200
$268$	8.95832	0.547216
$269$	−2.85076	−0.173814	−0.0869070	−	0.996216i	$-0.527698\pi$
$269$	−2.85076	−0.173814	−0.0869070	+	0.996216i	$0.527698\pi$
$270$	−2.74988	−0.167352
$271$	9.18978	0.558239	0.279120	−	0.960256i	$-0.409957\pi$
$271$	9.18978	0.558239	0.279120	+	0.960256i	$0.409957\pi$
$272$	−7.09886	−0.430432
$273$	2.39902	0.145196
$274$	−19.5238	−1.17948
$275$	−4.73575	−0.285577
$276$	0.525313	0.0316201
$277$	−1.42425	−0.0855746	−0.0427873	−	0.999084i	$-0.513624\pi$
$277$	−1.42425	−0.0855746	−0.0427873	+	0.999084i	$0.513624\pi$
$278$	−9.19954	−0.551752
$279$	−4.81984	−0.288556
$280$	−6.59703	−0.394248
$281$	−9.53145	−0.568599	−0.284299	−	0.958736i	$-0.591761\pi$
$281$	−9.53145	−0.568599	−0.284299	+	0.958736i	$0.591761\pi$
$282$	−3.33059	−0.198334
$283$	13.7858	0.819483	0.409741	−	0.912202i	$-0.365619\pi$
$283$	13.7858	0.819483	0.409741	+	0.912202i	$0.365619\pi$
$284$	−1.24278	−0.0737454
$285$	−20.9483	−1.24087
$286$	−1.84857	−0.109308
$287$	−2.30012	−0.135772
$288$	1.00000	0.0589256
$289$	33.3939	1.96434
$290$	−10.3109	−0.605477
$291$	1.02696	0.0602013
$292$	−2.09283	−0.122474
$293$	13.8788	0.810808	0.405404	−	0.914138i	$-0.367131\pi$
$293$	13.8788	0.810808	0.405404	+	0.914138i	$0.367131\pi$
$294$	1.24468	0.0725915
$295$	−2.97734	−0.173347
$296$	−3.48085	−0.202320
$297$	1.84857	0.107265
$298$	−7.16230	−0.414901
$299$	−0.525313	−0.0303796
$300$	−2.56184	−0.147908
$301$	28.1760	1.62404
$302$	8.61468	0.495719
$303$	11.1376	0.639841
$304$	7.61788	0.436916
$305$	−22.0923	−1.26500
$306$	−7.09886	−0.405815
$307$	5.08604	0.290276	0.145138	−	0.989411i	$-0.453637\pi$
$307$	5.08604	0.290276	0.145138	+	0.989411i	$0.453637\pi$
$308$	4.43477	0.252694
$309$	1.00000	0.0568880
$310$	−13.2540	−0.752775
$311$	−10.6452	−0.603632	−0.301816	−	0.953366i	$-0.597593\pi$
$311$	−10.6452	−0.603632	−0.301816	+	0.953366i	$0.597593\pi$
$312$	−1.00000	−0.0566139
$313$	3.39492	0.191892	0.0959461	−	0.995387i	$-0.469412\pi$
$313$	3.39492	0.191892	0.0959461	+	0.995387i	$0.469412\pi$
$314$	12.1972	0.688331
$315$	−6.59703	−0.371700
$316$	2.18222	0.122760
$317$	−18.6327	−1.04652	−0.523258	−	0.852174i	$-0.675284\pi$
$317$	−18.6327	−1.04652	−0.523258	+	0.852174i	$0.675284\pi$
$318$	−4.47200	−0.250777
$319$	6.93137	0.388082
$320$	2.74988	0.153723
$321$	3.30454	0.184442
$322$	1.26024	0.0702303
$323$	−54.0783	−3.00900
$324$	1.00000	0.0555556
$325$	2.56184	0.142105
$326$	20.5550	1.13844
$327$	13.7158	0.758488
$328$	0.958773	0.0529394
$329$	−7.99016	−0.440512
$330$	5.08335	0.279829
$331$	18.3071	1.00625	0.503124	−	0.864214i	$-0.332184\pi$
$331$	18.3071	1.00625	0.503124	+	0.864214i	$0.332184\pi$
$332$	6.22219	0.341487
$333$	−3.48085	−0.190749
$334$	−7.03334	−0.384847
$335$	24.6343	1.34592
$336$	2.39902	0.130877
$337$	8.00650	0.436142	0.218071	−	0.975933i	$-0.430024\pi$
$337$	8.00650	0.436142	0.218071	+	0.975933i	$0.430024\pi$
$338$	1.00000	0.0543928
$339$	−6.96842	−0.378473
$340$	−19.5210	−1.05868
$341$	8.90982	0.482494
$342$	7.61788	0.411928
$343$	19.7792	1.06798
$344$	−11.7448	−0.633237
$345$	1.44455	0.0777718
$346$	14.8424	0.797934
$347$	1.65776	0.0889934	0.0444967	−	0.999010i	$-0.485832\pi$
$347$	1.65776	0.0889934	0.0444967	+	0.999010i	$0.485832\pi$
$348$	3.74958	0.200999
$349$	−15.9832	−0.855562	−0.427781	−	0.903882i	$-0.640704\pi$
$349$	−15.9832	−0.855562	−0.427781	+	0.903882i	$0.640704\pi$
$350$	−6.14592	−0.328513
$351$	−1.00000	−0.0533761
$352$	−1.84857	−0.0985293
$353$	7.79964	0.415133	0.207566	−	0.978221i	$-0.433446\pi$
$353$	7.79964	0.415133	0.207566	+	0.978221i	$0.433446\pi$
$354$	1.08272	0.0575457
$355$	−3.41750	−0.181382
$356$	−9.80734	−0.519788
$357$	−17.0303	−0.901341
$358$	8.92436	0.471667
$359$	−35.4461	−1.87078	−0.935388	−	0.353623i	$-0.884950\pi$
$359$	−35.4461	−1.87078	−0.935388	+	0.353623i	$0.884950\pi$
$360$	2.74988	0.144931
$361$	39.0321	2.05432
$362$	0.631471	0.0331894
$363$	7.58278	0.397993
$364$	−2.39902	−0.125743
$365$	−5.75504	−0.301233
$366$	8.03392	0.419940
$367$	−31.6019	−1.64961	−0.824804	−	0.565419i	$-0.808715\pi$
$367$	−31.6019	−1.64961	−0.824804	+	0.565419i	$0.808715\pi$
$368$	−0.525313	−0.0273838
$369$	0.958773	0.0499117
$370$	−9.57191	−0.497620
$371$	−10.7284	−0.556992
$372$	4.81984	0.249897
$373$	17.2187	0.891551	0.445775	−	0.895145i	$-0.352928\pi$
$373$	17.2187	0.891551	0.445775	+	0.895145i	$0.352928\pi$
$374$	13.1228	0.678562
$375$	6.70464	0.346226
$376$	3.33059	0.171762
$377$	−3.74958	−0.193113
$378$	2.39902	0.123392
$379$	13.8709	0.712502	0.356251	−	0.934390i	$-0.384055\pi$
$379$	13.8709	0.712502	0.356251	+	0.934390i	$0.384055\pi$
$380$	20.9483	1.07462
$381$	1.58206	0.0810516
$382$	15.8786	0.812418
$383$	38.2368	1.95381	0.976905	−	0.213674i	$-0.0685429\pi$
$383$	38.2368	1.95381	0.976905	+	0.213674i	$0.0685429\pi$
$384$	−1.00000	−0.0510310
$385$	12.1951	0.621519
$386$	−24.1334	−1.22836
$387$	−11.7448	−0.597021
$388$	−1.02696	−0.0521359
$389$	12.2268	0.619925	0.309962	−	0.950749i	$-0.399684\pi$
$389$	12.2268	0.619925	0.309962	+	0.950749i	$0.399684\pi$
$390$	−2.74988	−0.139246
$391$	3.72912	0.188590
$392$	−1.24468	−0.0628661
$393$	−10.0938	−0.509167
$394$	−1.91505	−0.0964789
$395$	6.00085	0.301936
$396$	−1.84857	−0.0928943
$397$	5.14188	0.258064	0.129032	−	0.991640i	$-0.458813\pi$
$397$	5.14188	0.258064	0.129032	+	0.991640i	$0.458813\pi$
$398$	−20.7332	−1.03926
$399$	18.2755	0.914918
$400$	2.56184	0.128092
$401$	13.0778	0.653072	0.326536	−	0.945185i	$-0.394119\pi$
$401$	13.0778	0.653072	0.326536	+	0.945185i	$0.394119\pi$
$402$	−8.95832	−0.446800
$403$	−4.81984	−0.240093
$404$	−11.1376	−0.554118
$405$	2.74988	0.136643
$406$	8.99533	0.446431
$407$	6.43460	0.318951
$408$	7.09886	0.351446
$409$	−23.4215	−1.15812	−0.579059	−	0.815285i	$-0.696580\pi$
$409$	−23.4215	−1.15812	−0.579059	+	0.815285i	$0.696580\pi$
$410$	2.63651	0.130208
$411$	19.5238	0.963039
$412$	−1.00000	−0.0492665
$413$	2.59746	0.127813
$414$	−0.525313	−0.0258177
$415$	17.1103	0.839910
$416$	1.00000	0.0490290
$417$	9.19954	0.450504
$418$	−14.0822	−0.688783
$419$	3.23799	0.158186	0.0790931	−	0.996867i	$-0.474798\pi$
$419$	3.23799	0.158186	0.0790931	+	0.996867i	$0.474798\pi$
$420$	6.59703	0.321902
$421$	13.3026	0.648330	0.324165	−	0.946001i	$-0.394917\pi$
$421$	13.3026	0.648330	0.324165	+	0.946001i	$0.394917\pi$
$422$	−8.93942	−0.435164
$423$	3.33059	0.161939
$424$	4.47200	0.217179
$425$	−18.1862	−0.882158
$426$	1.24278	0.0602129
$427$	19.2736	0.932714
$428$	−3.30454	−0.159731
$429$	1.84857	0.0892499
$430$	−32.2968	−1.55749
$431$	−21.4746	−1.03440	−0.517198	−	0.855866i	$-0.673025\pi$
$431$	−21.4746	−1.03440	−0.517198	+	0.855866i	$0.673025\pi$
$432$	−1.00000	−0.0481125
$433$	−8.56079	−0.411405	−0.205703	−	0.978615i	$-0.565948\pi$
$433$	−8.56079	−0.411405	−0.205703	+	0.978615i	$0.565948\pi$
$434$	11.5629	0.555037
$435$	10.3109	0.494370
$436$	−13.7158	−0.656870
$437$	−4.00177	−0.191431
$438$	2.09283	0.0999994
$439$	−1.29475	−0.0617953	−0.0308976	−	0.999523i	$-0.509837\pi$
$439$	−1.29475	−0.0617953	−0.0308976	+	0.999523i	$0.509837\pi$
$440$	−5.08335	−0.242339
$441$	−1.24468	−0.0592707
$442$	−7.09886	−0.337658
$443$	33.4116	1.58743	0.793715	−	0.608289i	$-0.208144\pi$
$443$	33.4116	1.58743	0.793715	+	0.608289i	$0.208144\pi$
$444$	3.48085	0.165194
$445$	−26.9690	−1.27845
$446$	−11.7404	−0.555922
$447$	7.16230	0.338765
$448$	−2.39902	−0.113343
$449$	−11.6236	−0.548550	−0.274275	−	0.961651i	$-0.588438\pi$
$449$	−11.6236	−0.548550	−0.274275	+	0.961651i	$0.588438\pi$
$450$	2.56184	0.120766
$451$	−1.77236	−0.0834573
$452$	6.96842	0.327767
$453$	−8.61468	−0.404753
$454$	−28.6607	−1.34511
$455$	−6.59703	−0.309273
$456$	−7.61788	−0.356740
$457$	−6.01911	−0.281562	−0.140781	−	0.990041i	$-0.544961\pi$
$457$	−6.01911	−0.281562	−0.140781	+	0.990041i	$0.544961\pi$
$458$	7.61836	0.355983
$459$	7.09886	0.331347
$460$	−1.44455	−0.0673524
$461$	12.3731	0.576272	0.288136	−	0.957589i	$-0.406964\pi$
$461$	12.3731	0.576272	0.288136	+	0.957589i	$0.406964\pi$
$462$	−4.43477	−0.206324
$463$	−19.6719	−0.914231	−0.457116	−	0.889407i	$-0.651117\pi$
$463$	−19.6719	−0.914231	−0.457116	+	0.889407i	$0.651117\pi$
$464$	−3.74958	−0.174070
$465$	13.2540	0.614638
$466$	1.83307	0.0849152
$467$	15.0412	0.696025	0.348012	−	0.937490i	$-0.386857\pi$
$467$	15.0412	0.696025	0.348012	+	0.937490i	$0.386857\pi$
$468$	1.00000	0.0462250
$469$	−21.4912	−0.992372
$470$	9.15871	0.422460
$471$	−12.1972	−0.562020
$472$	−1.08272	−0.0498361
$473$	21.7111	0.998278
$474$	−2.18222	−0.100233
$475$	19.5158	0.895447
$476$	17.0303	0.780584
$477$	4.47200	0.204759
$478$	−18.9339	−0.866015
$479$	−2.23839	−0.102275	−0.0511373	−	0.998692i	$-0.516285\pi$
$479$	−2.23839	−0.102275	−0.0511373	+	0.998692i	$0.516285\pi$
$480$	−2.74988	−0.125514
$481$	−3.48085	−0.158713
$482$	−27.9303	−1.27219
$483$	−1.26024	−0.0573428
$484$	−7.58278	−0.344672
$485$	−2.82401	−0.128232
$486$	−1.00000	−0.0453609
$487$	−2.13282	−0.0966472	−0.0483236	−	0.998832i	$-0.515388\pi$
$487$	−2.13282	−0.0966472	−0.0483236	+	0.998832i	$0.515388\pi$
$488$	−8.03392	−0.363679
$489$	−20.5550	−0.929531
$490$	−3.42273	−0.154623
$491$	2.37971	0.107395	0.0536975	−	0.998557i	$-0.482899\pi$
$491$	2.37971	0.107395	0.0536975	+	0.998557i	$0.482899\pi$
$492$	−0.958773	−0.0432248
$493$	26.6177	1.19880
$494$	7.61788	0.342745
$495$	−5.08335	−0.228480
$496$	−4.81984	−0.216417
$497$	2.98146	0.133737
$498$	−6.22219	−0.278823
$499$	0.814165	0.0364470	0.0182235	−	0.999834i	$-0.494199\pi$
$499$	0.814165	0.0364470	0.0182235	+	0.999834i	$0.494199\pi$
$500$	−6.70464	−0.299841
$501$	7.03334	0.314226
$502$	−8.95192	−0.399544
$503$	−20.2427	−0.902577	−0.451289	−	0.892378i	$-0.649035\pi$
$503$	−20.2427	−0.902577	−0.451289	+	0.892378i	$0.649035\pi$
$504$	−2.39902	−0.106861
$505$	−30.6272	−1.36289
$506$	0.971079	0.0431697
$507$	−1.00000	−0.0444116
$508$	−1.58206	−0.0701927
$509$	−31.2309	−1.38428	−0.692142	−	0.721761i	$-0.743333\pi$
$509$	−31.2309	−1.38428	−0.692142	+	0.721761i	$0.743333\pi$
$510$	19.5210	0.864405
$511$	5.02076	0.222105
$512$	1.00000	0.0441942
$513$	−7.61788	−0.336338
$514$	8.76617	0.386659
$515$	−2.74988	−0.121174
$516$	11.7448	0.517036
$517$	−6.15683	−0.270777
$518$	8.35063	0.366906
$519$	−14.8424	−0.651510
$520$	2.74988	0.120590
$521$	−35.3542	−1.54889	−0.774447	−	0.632639i	$-0.781972\pi$
$521$	−35.3542	−1.54889	−0.774447	+	0.632639i	$0.781972\pi$
$522$	−3.74958	−0.164115
$523$	−28.2084	−1.23347	−0.616734	−	0.787172i	$-0.711545\pi$
$523$	−28.2084	−1.23347	−0.616734	+	0.787172i	$0.711545\pi$
$524$	10.0938	0.440951
$525$	6.14592	0.268230
$526$	26.0103	1.13411
$527$	34.2153	1.49044
$528$	1.84857	0.0804488
$529$	−22.7240	−0.988002
$530$	12.2975	0.534168
$531$	−1.08272	−0.0469859
$532$	−18.2755	−0.792343
$533$	0.958773	0.0415291
$534$	9.80734	0.424405
$535$	−9.08709	−0.392869
$536$	8.95832	0.386940
$537$	−8.92436	−0.385115
$538$	−2.85076	−0.122905
$539$	2.30089	0.0991064
$540$	−2.74988	−0.118336
$541$	−19.1096	−0.821585	−0.410792	−	0.911729i	$-0.634748\pi$
$541$	−19.1096	−0.821585	−0.410792	+	0.911729i	$0.634748\pi$
$542$	9.18978	0.394735
$543$	−0.631471	−0.0270990
$544$	−7.09886	−0.304361
$545$	−37.7169	−1.61562
$546$	2.39902	0.102669
$547$	−33.7131	−1.44147	−0.720733	−	0.693212i	$-0.756195\pi$
$547$	−33.7131	−1.44147	−0.720733	+	0.693212i	$0.756195\pi$
$548$	−19.5238	−0.834017
$549$	−8.03392	−0.342879
$550$	−4.73575	−0.201933
$551$	−28.5639	−1.21686
$552$	0.525313	0.0223588
$553$	−5.23521	−0.222624
$554$	−1.42425	−0.0605104
$555$	9.57191	0.406305
$556$	−9.19954	−0.390148
$557$	26.3990	1.11856	0.559281	−	0.828978i	$-0.311077\pi$
$557$	26.3990	1.11856	0.559281	+	0.828978i	$0.311077\pi$
$558$	−4.81984	−0.204040
$559$	−11.7448	−0.496752
$560$	−6.59703	−0.278775
$561$	−13.1228	−0.554044
$562$	−9.53145	−0.402060
$563$	1.39511	0.0587971	0.0293985	−	0.999568i	$-0.490641\pi$
$563$	1.39511	0.0587971	0.0293985	+	0.999568i	$0.490641\pi$
$564$	−3.33059	−0.140243
$565$	19.1623	0.806165
$566$	13.7858	0.579462
$567$	−2.39902	−0.100750
$568$	−1.24278	−0.0521459
$569$	−12.2486	−0.513489	−0.256744	−	0.966479i	$-0.582650\pi$
$569$	−12.2486	−0.513489	−0.256744	+	0.966479i	$0.582650\pi$
$570$	−20.9483	−0.877426
$571$	8.99869	0.376583	0.188292	−	0.982113i	$-0.439705\pi$
$571$	8.99869	0.376583	0.188292	+	0.982113i	$0.439705\pi$
$572$	−1.84857	−0.0772927
$573$	−15.8786	−0.663337
$574$	−2.30012	−0.0960051
$575$	−1.34577	−0.0561224
$576$	1.00000	0.0416667
$577$	−5.80834	−0.241804	−0.120902	−	0.992664i	$-0.538579\pi$
$577$	−5.80834	−0.241804	−0.120902	+	0.992664i	$0.538579\pi$
$578$	33.3939	1.38900
$579$	24.1334	1.00295
$580$	−10.3109	−0.428137
$581$	−14.9272	−0.619283
$582$	1.02696	0.0425688
$583$	−8.26682	−0.342377
$584$	−2.09283	−0.0866021
$585$	2.74988	0.113694
$586$	13.8788	0.573328
$587$	1.90842	0.0787688	0.0393844	−	0.999224i	$-0.487460\pi$
$587$	1.90842	0.0787688	0.0393844	+	0.999224i	$0.487460\pi$
$588$	1.24468	0.0513299
$589$	−36.7169	−1.51290
$590$	−2.97734	−0.122575
$591$	1.91505	0.0787747
$592$	−3.48085	−0.143062
$593$	−7.32701	−0.300884	−0.150442	−	0.988619i	$-0.548070\pi$
$593$	−7.32701	−0.300884	−0.150442	+	0.988619i	$0.548070\pi$
$594$	1.84857	0.0758479
$595$	46.8314	1.91990
$596$	−7.16230	−0.293379
$597$	20.7332	0.848552
$598$	−0.525313	−0.0214816
$599$	−4.63687	−0.189457	−0.0947286	−	0.995503i	$-0.530198\pi$
$599$	−4.63687	−0.189457	−0.0947286	+	0.995503i	$0.530198\pi$
$600$	−2.56184	−0.104587
$601$	12.2129	0.498174	0.249087	−	0.968481i	$-0.419870\pi$
$601$	12.2129	0.498174	0.249087	+	0.968481i	$0.419870\pi$
$602$	28.1760	1.14837
$603$	8.95832	0.364811
$604$	8.61468	0.350526
$605$	−20.8517	−0.847744
$606$	11.1376	0.452436
$607$	29.6888	1.20503	0.602515	−	0.798108i	$-0.294165\pi$
$607$	29.6888	1.20503	0.602515	+	0.798108i	$0.294165\pi$
$608$	7.61788	0.308946
$609$	−8.99533	−0.364509
$610$	−22.0923	−0.894492
$611$	3.33059	0.134741
$612$	−7.09886	−0.286955
$613$	−20.2901	−0.819509	−0.409755	−	0.912196i	$-0.634386\pi$
$613$	−20.2901	−0.819509	−0.409755	+	0.912196i	$0.634386\pi$
$614$	5.08604	0.205256
$615$	−2.63651	−0.106314
$616$	4.43477	0.178682
$617$	−41.0626	−1.65312	−0.826558	−	0.562851i	$-0.809704\pi$
$617$	−41.0626	−1.65312	−0.826558	+	0.562851i	$0.809704\pi$
$618$	1.00000	0.0402259
$619$	21.2710	0.854953	0.427476	−	0.904026i	$-0.359403\pi$
$619$	21.2710	0.854953	0.427476	+	0.904026i	$0.359403\pi$
$620$	−13.2540	−0.532292
$621$	0.525313	0.0210801
$622$	−10.6452	−0.426832
$623$	23.5280	0.942631
$624$	−1.00000	−0.0400320
$625$	−31.2462	−1.24985
$626$	3.39492	0.135688
$627$	14.0822	0.562389
$628$	12.1972	0.486723
$629$	24.7100	0.985254
$630$	−6.59703	−0.262832
$631$	−23.4290	−0.932692	−0.466346	−	0.884602i	$-0.654430\pi$
$631$	−23.4290	−0.932692	−0.466346	+	0.884602i	$0.654430\pi$
$632$	2.18222	0.0868042
$633$	8.93942	0.355310
$634$	−18.6327	−0.739999
$635$	−4.35048	−0.172644
$636$	−4.47200	−0.177326
$637$	−1.24468	−0.0493162
$638$	6.93137	0.274416
$639$	−1.24278	−0.0491636
$640$	2.74988	0.108699
$641$	9.41484	0.371864	0.185932	−	0.982563i	$-0.440470\pi$
$641$	9.41484	0.371864	0.185932	+	0.982563i	$0.440470\pi$
$642$	3.30454	0.130420
$643$	18.0928	0.713509	0.356754	−	0.934198i	$-0.383883\pi$
$643$	18.0928	0.713509	0.356754	+	0.934198i	$0.383883\pi$
$644$	1.26024	0.0496603
$645$	32.2968	1.27168
$646$	−54.0783	−2.12768
$647$	−5.54538	−0.218011	−0.109006	−	0.994041i	$-0.534767\pi$
$647$	−5.54538	−0.218011	−0.109006	+	0.994041i	$0.534767\pi$
$648$	1.00000	0.0392837
$649$	2.00148	0.0785650
$650$	2.56184	0.100484
$651$	−11.5629	−0.453186
$652$	20.5550	0.804997
$653$	29.4314	1.15174	0.575870	−	0.817541i	$-0.304663\pi$
$653$	29.4314	1.15174	0.575870	+	0.817541i	$0.304663\pi$
$654$	13.7158	0.536332
$655$	27.7568	1.08455
$656$	0.958773	0.0374338
$657$	−2.09283	−0.0816492
$658$	−7.99016	−0.311489
$659$	−32.3986	−1.26207	−0.631035	−	0.775754i	$-0.717370\pi$
$659$	−32.3986	−1.26207	−0.631035	+	0.775754i	$0.717370\pi$
$660$	5.08335	0.197869
$661$	−46.2422	−1.79861	−0.899306	−	0.437319i	$-0.855928\pi$
$661$	−46.2422	−1.79861	−0.899306	+	0.437319i	$0.855928\pi$
$662$	18.3071	0.711525
$663$	7.09886	0.275697
$664$	6.22219	0.241468
$665$	−50.2554	−1.94882
$666$	−3.48085	−0.134880
$667$	1.96970	0.0762672
$668$	−7.03334	−0.272128
$669$	11.7404	0.453909
$670$	24.6343	0.951706
$671$	14.8513	0.573328
$672$	2.39902	0.0925444
$673$	39.7318	1.53155	0.765775	−	0.643109i	$-0.222356\pi$
$673$	39.7318	1.53155	0.765775	+	0.643109i	$0.222356\pi$
$674$	8.00650	0.308399
$675$	−2.56184	−0.0986053
$676$	1.00000	0.0384615
$677$	36.7131	1.41100	0.705499	−	0.708711i	$-0.250723\pi$
$677$	36.7131	1.41100	0.705499	+	0.708711i	$0.250723\pi$
$678$	−6.96842	−0.267621
$679$	2.46370	0.0945479
$680$	−19.5210	−0.748597
$681$	28.6607	1.09828
$682$	8.90982	0.341174
$683$	29.0191	1.11038	0.555192	−	0.831722i	$-0.312645\pi$
$683$	29.0191	1.11038	0.555192	+	0.831722i	$0.312645\pi$
$684$	7.61788	0.291277
$685$	−53.6882	−2.05132
$686$	19.7792	0.755173
$687$	−7.61836	−0.290659
$688$	−11.7448	−0.447766
$689$	4.47200	0.170370
$690$	1.44455	0.0549930
$691$	−5.11500	−0.194584	−0.0972918	−	0.995256i	$-0.531018\pi$
$691$	−5.11500	−0.194584	−0.0972918	+	0.995256i	$0.531018\pi$
$692$	14.8424	0.564224
$693$	4.43477	0.168463
$694$	1.65776	0.0629278
$695$	−25.2976	−0.959594
$696$	3.74958	0.142127
$697$	−6.80620	−0.257803
$698$	−15.9832	−0.604973
$699$	−1.83307	−0.0693330
$700$	−6.14592	−0.232294
$701$	32.7732	1.23783	0.618914	−	0.785459i	$-0.287573\pi$
$701$	32.7732	1.23783	0.618914	+	0.785459i	$0.287573\pi$
$702$	−1.00000	−0.0377426
$703$	−26.5167	−1.00010
$704$	−1.84857	−0.0696707
$705$	−9.15871	−0.344937
$706$	7.79964	0.293543
$707$	26.7195	1.00489
$708$	1.08272	0.0406910
$709$	−19.4102	−0.728966	−0.364483	−	0.931210i	$-0.618754\pi$
$709$	−19.4102	−0.728966	−0.364483	+	0.931210i	$0.618754\pi$
$710$	−3.41750	−0.128256
$711$	2.18222	0.0818398
$712$	−9.80734	−0.367546
$713$	2.53192	0.0948212
$714$	−17.0303	−0.637345
$715$	−5.08335	−0.190107
$716$	8.92436	0.333519
$717$	18.9339	0.707098
$718$	−35.4461	−1.32284
$719$	−29.3774	−1.09559	−0.547796	−	0.836612i	$-0.684533\pi$
$719$	−29.3774	−1.09559	−0.547796	+	0.836612i	$0.684533\pi$
$720$	2.74988	0.102482
$721$	2.39902	0.0893443
$722$	39.0321	1.45263
$723$	27.9303	1.03874
$724$	0.631471	0.0234684
$725$	−9.60583	−0.356752
$726$	7.58278	0.281423
$727$	5.60550	0.207897	0.103948	−	0.994583i	$-0.466852\pi$
$727$	5.60550	0.207897	0.103948	+	0.994583i	$0.466852\pi$
$728$	−2.39902	−0.0889137
$729$	1.00000	0.0370370
$730$	−5.75504	−0.213004
$731$	83.3747	3.08372
$732$	8.03392	0.296942
$733$	29.1976	1.07844	0.539219	−	0.842165i	$-0.318719\pi$
$733$	29.1976	1.07844	0.539219	+	0.842165i	$0.318719\pi$
$734$	−31.6019	−1.16645
$735$	3.42273	0.126249
$736$	−0.525313	−0.0193633
$737$	−16.5601	−0.609999
$738$	0.958773	0.0352929
$739$	−0.563896	−0.0207433	−0.0103716	−	0.999946i	$-0.503301\pi$
$739$	−0.563896	−0.0207433	−0.0103716	+	0.999946i	$0.503301\pi$
$740$	−9.57191	−0.351870
$741$	−7.61788	−0.279850
$742$	−10.7284	−0.393853
$743$	16.3686	0.600507	0.300253	−	0.953859i	$-0.402929\pi$
$743$	16.3686	0.600507	0.300253	+	0.953859i	$0.402929\pi$
$744$	4.81984	0.176704
$745$	−19.6955	−0.721586
$746$	17.2187	0.630421
$747$	6.22219	0.227658
$748$	13.1228	0.479816
$749$	7.92767	0.289671
$750$	6.70464	0.244819
$751$	12.2446	0.446810	0.223405	−	0.974726i	$-0.428283\pi$
$751$	12.2446	0.446810	0.223405	+	0.974726i	$0.428283\pi$
$752$	3.33059	0.121454
$753$	8.95192	0.326226
$754$	−3.74958	−0.136552
$755$	23.6893	0.862143
$756$	2.39902	0.0872517
$757$	−10.9420	−0.397695	−0.198847	−	0.980030i	$-0.563720\pi$
$757$	−10.9420	−0.397695	−0.198847	+	0.980030i	$0.563720\pi$
$758$	13.8709	0.503815
$759$	−0.971079	−0.0352479
$760$	20.9483	0.759873
$761$	−42.1392	−1.52754	−0.763772	−	0.645486i	$-0.776655\pi$
$761$	−42.1392	−1.52754	−0.763772	+	0.645486i	$0.776655\pi$
$762$	1.58206	0.0573121
$763$	32.9046	1.19123
$764$	15.8786	0.574466
$765$	−19.5210	−0.705784
$766$	38.2368	1.38155
$767$	−1.08272	−0.0390946
$768$	−1.00000	−0.0360844
$769$	−1.84043	−0.0663676	−0.0331838	−	0.999449i	$-0.510565\pi$
$769$	−1.84043	−0.0663676	−0.0331838	+	0.999449i	$0.510565\pi$
$770$	12.1951	0.439480
$771$	−8.76617	−0.315706
$772$	−24.1334	−0.868581
$773$	50.6095	1.82030	0.910149	−	0.414280i	$-0.135967\pi$
$773$	50.6095	1.82030	0.910149	+	0.414280i	$0.135967\pi$
$774$	−11.7448	−0.422158
$775$	−12.3477	−0.443541
$776$	−1.02696	−0.0368656
$777$	−8.35063	−0.299577
$778$	12.2268	0.438353
$779$	7.30382	0.261687
$780$	−2.74988	−0.0984615
$781$	2.29737	0.0822063
$782$	3.72912	0.133353
$783$	3.74958	0.133999
$784$	−1.24468	−0.0444530
$785$	33.5410	1.19713
$786$	−10.0938	−0.360035
$787$	11.8537	0.422539	0.211269	−	0.977428i	$-0.432240\pi$
$787$	11.8537	0.422539	0.211269	+	0.977428i	$0.432240\pi$
$788$	−1.91505	−0.0682209
$789$	−26.0103	−0.925993
$790$	6.00085	0.213501
$791$	−16.7174	−0.594402
$792$	−1.84857	−0.0656862
$793$	−8.03392	−0.285293
$794$	5.14188	0.182479
$795$	−12.2975	−0.436146
$796$	−20.7332	−0.734868
$797$	0.446239	0.0158066	0.00790329	−	0.999969i	$-0.497484\pi$
$797$	0.446239	0.0158066	0.00790329	+	0.999969i	$0.497484\pi$
$798$	18.2755	0.646945
$799$	−23.6434	−0.836443
$800$	2.56184	0.0905748
$801$	−9.80734	−0.346525
$802$	13.0778	0.461792
$803$	3.86875	0.136525
$804$	−8.95832	−0.315935
$805$	3.46550	0.122143
$806$	−4.81984	−0.169771
$807$	2.85076	0.100352
$808$	−11.1376	−0.391821
$809$	−26.9072	−0.946008	−0.473004	−	0.881060i	$-0.656830\pi$
$809$	−26.9072	−0.946008	−0.473004	+	0.881060i	$0.656830\pi$
$810$	2.74988	0.0966209
$811$	49.1760	1.72680	0.863402	−	0.504516i	$-0.168329\pi$
$811$	49.1760	1.72680	0.863402	+	0.504516i	$0.168329\pi$
$812$	8.99533	0.315674
$813$	−9.18978	−0.322300
$814$	6.43460	0.225532
$815$	56.5239	1.97994
$816$	7.09886	0.248510
$817$	−89.4705	−3.13017
$818$	−23.4215	−0.818914
$819$	−2.39902	−0.0838287
$820$	2.63651	0.0920710
$821$	17.4928	0.610504	0.305252	−	0.952272i	$-0.401259\pi$
$821$	17.4928	0.610504	0.305252	+	0.952272i	$0.401259\pi$
$822$	19.5238	0.680972
$823$	−44.5174	−1.55178	−0.775890	−	0.630869i	$-0.782699\pi$
$823$	−44.5174	−1.55178	−0.775890	+	0.630869i	$0.782699\pi$
$824$	−1.00000	−0.0348367
$825$	4.73575	0.164878
$826$	2.59746	0.0903773
$827$	−6.37892	−0.221817	−0.110908	−	0.993831i	$-0.535376\pi$
$827$	−6.37892	−0.221817	−0.110908	+	0.993831i	$0.535376\pi$
$828$	−0.525313	−0.0182559
$829$	−6.13786	−0.213177	−0.106588	−	0.994303i	$-0.533993\pi$
$829$	−6.13786	−0.213177	−0.106588	+	0.994303i	$0.533993\pi$
$830$	17.1103	0.593906
$831$	1.42425	0.0494065
$832$	1.00000	0.0346688
$833$	8.83585	0.306144
$834$	9.19954	0.318554
$835$	−19.3408	−0.669317
$836$	−14.0822	−0.487043
$837$	4.81984	0.166598
$838$	3.23799	0.111855
$839$	−9.81846	−0.338971	−0.169485	−	0.985533i	$-0.554211\pi$
$839$	−9.81846	−0.338971	−0.169485	+	0.985533i	$0.554211\pi$
$840$	6.59703	0.227619
$841$	−14.9407	−0.515195
$842$	13.3026	0.458439
$843$	9.53145	0.328281
$844$	−8.93942	−0.307708
$845$	2.74988	0.0945988
$846$	3.33059	0.114508
$847$	18.1913	0.625059
$848$	4.47200	0.153569
$849$	−13.7858	−0.473129
$850$	−18.1862	−0.623780
$851$	1.82853	0.0626813
$852$	1.24278	0.0425769
$853$	23.5380	0.805924	0.402962	−	0.915217i	$-0.367981\pi$
$853$	23.5380	0.805924	0.402962	+	0.915217i	$0.367981\pi$
$854$	19.2736	0.659528
$855$	20.9483	0.716416
$856$	−3.30454	−0.112947
$857$	29.7073	1.01478	0.507391	−	0.861716i	$-0.330610\pi$
$857$	29.7073	1.01478	0.507391	+	0.861716i	$0.330610\pi$
$858$	1.84857	0.0631092
$859$	4.75805	0.162343	0.0811714	−	0.996700i	$-0.474134\pi$
$859$	4.75805	0.162343	0.0811714	+	0.996700i	$0.474134\pi$
$860$	−32.2968	−1.10131
$861$	2.30012	0.0783879
$862$	−21.4746	−0.731428
$863$	44.9006	1.52843	0.764217	−	0.644959i	$-0.223126\pi$
$863$	44.9006	1.52843	0.764217	+	0.644959i	$0.223126\pi$
$864$	−1.00000	−0.0340207
$865$	40.8149	1.38775
$866$	−8.56079	−0.290907
$867$	−33.3939	−1.13411
$868$	11.5629	0.392470
$869$	−4.03400	−0.136844
$870$	10.3109	0.349572
$871$	8.95832	0.303541
$872$	−13.7158	−0.464477
$873$	−1.02696	−0.0347572
$874$	−4.00177	−0.135362
$875$	16.0846	0.543759
$876$	2.09283	0.0707103
$877$	−8.30275	−0.280364	−0.140182	−	0.990126i	$-0.544769\pi$
$877$	−8.30275	−0.280364	−0.140182	+	0.990126i	$0.544769\pi$
$878$	−1.29475	−0.0436959
$879$	−13.8788	−0.468120
$880$	−5.08335	−0.171360
$881$	−33.4605	−1.12731	−0.563656	−	0.826009i	$-0.690606\pi$
$881$	−33.4605	−1.12731	−0.563656	+	0.826009i	$0.690606\pi$
$882$	−1.24468	−0.0419107
$883$	−48.3483	−1.62705	−0.813524	−	0.581531i	$-0.802454\pi$
$883$	−48.3483	−1.62705	−0.813524	+	0.581531i	$0.802454\pi$
$884$	−7.09886	−0.238761
$885$	2.97734	0.100082
$886$	33.4116	1.12248
$887$	4.57364	0.153568	0.0767839	−	0.997048i	$-0.475535\pi$
$887$	4.57364	0.153568	0.0767839	+	0.997048i	$0.475535\pi$
$888$	3.48085	0.116810
$889$	3.79541	0.127294
$890$	−26.9690	−0.904004
$891$	−1.84857	−0.0619295
$892$	−11.7404	−0.393096
$893$	25.3720	0.849042
$894$	7.16230	0.239543
$895$	24.5409	0.820313
$896$	−2.39902	−0.0801458
$897$	0.525313	0.0175397
$898$	−11.6236	−0.387883
$899$	18.0724	0.602747
$900$	2.56184	0.0853947
$901$	−31.7461	−1.05762
$902$	−1.77236	−0.0590132
$903$	−28.1760	−0.937640
$904$	6.96842	0.231766
$905$	1.73647	0.0577222
$906$	−8.61468	−0.286204
$907$	44.2367	1.46886	0.734428	−	0.678687i	$-0.237451\pi$
$907$	44.2367	1.46886	0.734428	+	0.678687i	$0.237451\pi$
$908$	−28.6607	−0.951137
$909$	−11.1376	−0.369412
$910$	−6.59703	−0.218689
$911$	−4.70702	−0.155950	−0.0779752	−	0.996955i	$-0.524845\pi$
$911$	−4.70702	−0.155950	−0.0779752	+	0.996955i	$0.524845\pi$
$912$	−7.61788	−0.252253
$913$	−11.5022	−0.380666
$914$	−6.01911	−0.199094
$915$	22.0923	0.730350
$916$	7.61836	0.251718
$917$	−24.2154	−0.799661
$918$	7.09886	0.234297
$919$	9.63062	0.317685	0.158842	−	0.987304i	$-0.449224\pi$
$919$	9.63062	0.317685	0.158842	+	0.987304i	$0.449224\pi$
$920$	−1.44455	−0.0476253
$921$	−5.08604	−0.167591
$922$	12.3731	0.407486
$923$	−1.24278	−0.0409066
$924$	−4.43477	−0.145893
$925$	−8.91737	−0.293201
$926$	−19.6719	−0.646459
$927$	−1.00000	−0.0328443
$928$	−3.74958	−0.123086
$929$	−23.3070	−0.764677	−0.382339	−	0.924022i	$-0.624881\pi$
$929$	−23.3070	−0.764677	−0.382339	+	0.924022i	$0.624881\pi$
$930$	13.2540	0.434615
$931$	−9.48186	−0.310756
$932$	1.83307	0.0600441
$933$	10.6452	0.348507
$934$	15.0412	0.492164
$935$	36.0860	1.18014
$936$	1.00000	0.0326860
$937$	4.59330	0.150056	0.0750282	−	0.997181i	$-0.476095\pi$
$937$	4.59330	0.150056	0.0750282	+	0.997181i	$0.476095\pi$
$938$	−21.4912	−0.701713
$939$	−3.39492	−0.110789
$940$	9.15871	0.298724
$941$	10.3365	0.336960	0.168480	−	0.985705i	$-0.446114\pi$
$941$	10.3365	0.336960	0.168480	+	0.985705i	$0.446114\pi$
$942$	−12.1972	−0.397408
$943$	−0.503656	−0.0164013
$944$	−1.08272	−0.0352394
$945$	6.59703	0.214601
$946$	21.7111	0.705889
$947$	44.8268	1.45668	0.728338	−	0.685218i	$-0.240293\pi$
$947$	44.8268	1.45668	0.728338	+	0.685218i	$0.240293\pi$
$948$	−2.18222	−0.0708753
$949$	−2.09283	−0.0679362
$950$	19.5158	0.633176
$951$	18.6327	0.604207
$952$	17.0303	0.551957
$953$	15.1527	0.490845	0.245422	−	0.969416i	$-0.421073\pi$
$953$	15.1527	0.490845	0.245422	+	0.969416i	$0.421073\pi$
$954$	4.47200	0.144786
$955$	43.6642	1.41294
$956$	−18.9339	−0.612365
$957$	−6.93137	−0.224059
$958$	−2.23839	−0.0723191
$959$	46.8381	1.51248
$960$	−2.74988	−0.0887520
$961$	−7.76919	−0.250619
$962$	−3.48085	−0.112227
$963$	−3.30454	−0.106487
$964$	−27.9303	−0.899574
$965$	−66.3640	−2.13633
$966$	−1.26024	−0.0405475
$967$	−7.11621	−0.228842	−0.114421	−	0.993432i	$-0.536501\pi$
$967$	−7.11621	−0.228842	−0.114421	+	0.993432i	$0.536501\pi$
$968$	−7.58278	−0.243720
$969$	54.0783	1.73725
$970$	−2.82401	−0.0906735
$971$	21.1369	0.678315	0.339157	−	0.940730i	$-0.389858\pi$
$971$	21.1369	0.678315	0.339157	+	0.940730i	$0.389858\pi$
$972$	−1.00000	−0.0320750
$973$	22.0699	0.707529
$974$	−2.13282	−0.0683399
$975$	−2.56184	−0.0820446
$976$	−8.03392	−0.257160
$977$	51.2240	1.63880	0.819401	−	0.573221i	$-0.194306\pi$
$977$	51.2240	1.63880	0.819401	+	0.573221i	$0.194306\pi$
$978$	−20.5550	−0.657277
$979$	18.1296	0.579424
$980$	−3.42273	−0.109335
$981$	−13.7158	−0.437913
$982$	2.37971	0.0759398
$983$	−16.9797	−0.541569	−0.270784	−	0.962640i	$-0.587283\pi$
$983$	−16.9797	−0.541569	−0.270784	+	0.962640i	$0.587283\pi$
$984$	−0.958773	−0.0305646
$985$	−5.26616	−0.167794
$986$	26.6177	0.847682
$987$	7.99016	0.254329
$988$	7.61788	0.242357
$989$	6.16969	0.196185
$990$	−5.08335	−0.161560
$991$	32.8951	1.04495	0.522474	−	0.852655i	$-0.325009\pi$
$991$	32.8951	1.04495	0.522474	+	0.852655i	$0.325009\pi$
$992$	−4.81984	−0.153030
$993$	−18.3071	−0.580957
$994$	2.98146	0.0945661
$995$	−57.0137	−1.80746
$996$	−6.22219	−0.197157
$997$	6.85686	0.217159	0.108579	−	0.994088i	$-0.465370\pi$
$997$	6.85686	0.217159	0.108579	+	0.994088i	$0.465370\pi$
$998$	0.814165	0.0257720
$999$	3.48085	0.110129

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.r.1.9	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.r.1.9	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.74988 q^{5} -1.00000 q^{6} -2.39902 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.74988 q^{5} -1.00000 q^{6} -2.39902 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.74988 q^{10} -1.84857 q^{11} -1.00000 q^{12} +1.00000 q^{13} -2.39902 q^{14} -2.74988 q^{15} +1.00000 q^{16} -7.09886 q^{17} +1.00000 q^{18} +7.61788 q^{19} +2.74988 q^{20} +2.39902 q^{21} -1.84857 q^{22} -0.525313 q^{23} -1.00000 q^{24} +2.56184 q^{25} +1.00000 q^{26} -1.00000 q^{27} -2.39902 q^{28} -3.74958 q^{29} -2.74988 q^{30} -4.81984 q^{31} +1.00000 q^{32} +1.84857 q^{33} -7.09886 q^{34} -6.59703 q^{35} +1.00000 q^{36} -3.48085 q^{37} +7.61788 q^{38} -1.00000 q^{39} +2.74988 q^{40} +0.958773 q^{41} +2.39902 q^{42} -11.7448 q^{43} -1.84857 q^{44} +2.74988 q^{45} -0.525313 q^{46} +3.33059 q^{47} -1.00000 q^{48} -1.24468 q^{49} +2.56184 q^{50} +7.09886 q^{51} +1.00000 q^{52} +4.47200 q^{53} -1.00000 q^{54} -5.08335 q^{55} -2.39902 q^{56} -7.61788 q^{57} -3.74958 q^{58} -1.08272 q^{59} -2.74988 q^{60} -8.03392 q^{61} -4.81984 q^{62} -2.39902 q^{63} +1.00000 q^{64} +2.74988 q^{65} +1.84857 q^{66} +8.95832 q^{67} -7.09886 q^{68} +0.525313 q^{69} -6.59703 q^{70} -1.24278 q^{71} +1.00000 q^{72} -2.09283 q^{73} -3.48085 q^{74} -2.56184 q^{75} +7.61788 q^{76} +4.43477 q^{77} -1.00000 q^{78} +2.18222 q^{79} +2.74988 q^{80} +1.00000 q^{81} +0.958773 q^{82} +6.22219 q^{83} +2.39902 q^{84} -19.5210 q^{85} -11.7448 q^{86} +3.74958 q^{87} -1.84857 q^{88} -9.80734 q^{89} +2.74988 q^{90} -2.39902 q^{91} -0.525313 q^{92} +4.81984 q^{93} +3.33059 q^{94} +20.9483 q^{95} -1.00000 q^{96} -1.02696 q^{97} -1.24468 q^{98} -1.84857 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} - 4 q^{5} - 9 q^{6} - 4 q^{7} + 9 q^{8} + 9 q^{9}+O(q^{10}) \) 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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