LMFDB - Embedded newform 8034.2.a.bd.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8034, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.1518129839$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} - 36 x^{14} + 196 x^{13} + 498 x^{12} - 3101 x^{11} - 3150 x^{10} + 25368 x^{9} + \cdots - 66432 $ x^16 - 5x^15 - 36x^14 + 196x^13 + 498x^12 - 3101x^11 - 3150x^10 + 25368x^9 + 6763x^8 - 113788x^7 + 19731x^6 + 270913x^5 - 122680x^4 - 296326x^3 + 185524x^2 + 94528*x - 66432
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-2.44876$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.44876 q^{5} +1.00000 q^{6} -1.82729 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.44876 q^{5} +1.00000 q^{6} -1.82729 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.44876 q^{10} +0.163827 q^{11} +1.00000 q^{12} -1.00000 q^{13} -1.82729 q^{14} -2.44876 q^{15} +1.00000 q^{16} +6.53476 q^{17} +1.00000 q^{18} +3.88193 q^{19} -2.44876 q^{20} -1.82729 q^{21} +0.163827 q^{22} -0.103683 q^{23} +1.00000 q^{24} +0.996443 q^{25} -1.00000 q^{26} +1.00000 q^{27} -1.82729 q^{28} -7.07183 q^{29} -2.44876 q^{30} +5.07047 q^{31} +1.00000 q^{32} +0.163827 q^{33} +6.53476 q^{34} +4.47459 q^{35} +1.00000 q^{36} -11.2304 q^{37} +3.88193 q^{38} -1.00000 q^{39} -2.44876 q^{40} +1.24437 q^{41} -1.82729 q^{42} -0.424033 q^{43} +0.163827 q^{44} -2.44876 q^{45} -0.103683 q^{46} +7.02979 q^{47} +1.00000 q^{48} -3.66103 q^{49} +0.996443 q^{50} +6.53476 q^{51} -1.00000 q^{52} -5.21386 q^{53} +1.00000 q^{54} -0.401174 q^{55} -1.82729 q^{56} +3.88193 q^{57} -7.07183 q^{58} -7.00193 q^{59} -2.44876 q^{60} +12.6542 q^{61} +5.07047 q^{62} -1.82729 q^{63} +1.00000 q^{64} +2.44876 q^{65} +0.163827 q^{66} +16.1486 q^{67} +6.53476 q^{68} -0.103683 q^{69} +4.47459 q^{70} +10.8140 q^{71} +1.00000 q^{72} +11.1135 q^{73} -11.2304 q^{74} +0.996443 q^{75} +3.88193 q^{76} -0.299359 q^{77} -1.00000 q^{78} -5.61903 q^{79} -2.44876 q^{80} +1.00000 q^{81} +1.24437 q^{82} +15.3660 q^{83} -1.82729 q^{84} -16.0021 q^{85} -0.424033 q^{86} -7.07183 q^{87} +0.163827 q^{88} -14.2700 q^{89} -2.44876 q^{90} +1.82729 q^{91} -0.103683 q^{92} +5.07047 q^{93} +7.02979 q^{94} -9.50592 q^{95} +1.00000 q^{96} +9.39168 q^{97} -3.66103 q^{98} +0.163827 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 5 q^{5} + 16 q^{6} + 4 q^{7} + 16 q^{8} + 16 q^{9}+O(q^{10}) $ 16 * q + 16 * q^2 + 16 * q^3 + 16 * q^4 + 5 * q^5 + 16 * q^6 + 4 * q^7 + 16 * q^8 + 16 * q^9	\( 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 5 q^{5} + 16 q^{6} + 4 q^{7} + 16 q^{8} + 16 q^{9} + 5 q^{10} + 18 q^{11} + 16 q^{12} - 16 q^{13} + 4 q^{14} + 5 q^{15} + 16 q^{16} + 17 q^{17} + 16 q^{18} + 8 q^{19} + 5 q^{20} + 4 q^{21} + 18 q^{22} + 9 q^{23} + 16 q^{24} + 17 q^{25} - 16 q^{26} + 16 q^{27} + 4 q^{28} + 14 q^{29} + 5 q^{30} + 12 q^{31} + 16 q^{32} + 18 q^{33} + 17 q^{34} + 16 q^{35} + 16 q^{36} + 31 q^{37} + 8 q^{38} - 16 q^{39} + 5 q^{40} + 29 q^{41} + 4 q^{42} + 30 q^{43} + 18 q^{44} + 5 q^{45} + 9 q^{46} - q^{47} + 16 q^{48} + 36 q^{49} + 17 q^{50} + 17 q^{51} - 16 q^{52} + 12 q^{53} + 16 q^{54} + 30 q^{55} + 4 q^{56} + 8 q^{57} + 14 q^{58} + 38 q^{59} + 5 q^{60} + 12 q^{62} + 4 q^{63} + 16 q^{64} - 5 q^{65} + 18 q^{66} + 28 q^{67} + 17 q^{68} + 9 q^{69} + 16 q^{70} + 32 q^{71} + 16 q^{72} + 20 q^{73} + 31 q^{74} + 17 q^{75} + 8 q^{76} + 26 q^{77} - 16 q^{78} + 13 q^{79} + 5 q^{80} + 16 q^{81} + 29 q^{82} + 39 q^{83} + 4 q^{84} + 31 q^{85} + 30 q^{86} + 14 q^{87} + 18 q^{88} + 9 q^{89} + 5 q^{90} - 4 q^{91} + 9 q^{92} + 12 q^{93} - q^{94} - 20 q^{95} + 16 q^{96} + 35 q^{97} + 36 q^{98} + 18 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 + 16 * q^3 + 16 * q^4 + 5 * q^5 + 16 * q^6 + 4 * q^7 + 16 * q^8 + 16 * q^9 + 5 * q^10 + 18 * q^11 + 16 * q^12 - 16 * q^13 + 4 * q^14 + 5 * q^15 + 16 * q^16 + 17 * q^17 + 16 * q^18 + 8 * q^19 + 5 * q^20 + 4 * q^21 + 18 * q^22 + 9 * q^23 + 16 * q^24 + 17 * q^25 - 16 * q^26 + 16 * q^27 + 4 * q^28 + 14 * q^29 + 5 * q^30 + 12 * q^31 + 16 * q^32 + 18 * q^33 + 17 * q^34 + 16 * q^35 + 16 * q^36 + 31 * q^37 + 8 * q^38 - 16 * q^39 + 5 * q^40 + 29 * q^41 + 4 * q^42 + 30 * q^43 + 18 * q^44 + 5 * q^45 + 9 * q^46 - q^47 + 16 * q^48 + 36 * q^49 + 17 * q^50 + 17 * q^51 - 16 * q^52 + 12 * q^53 + 16 * q^54 + 30 * q^55 + 4 * q^56 + 8 * q^57 + 14 * q^58 + 38 * q^59 + 5 * q^60 + 12 * q^62 + 4 * q^63 + 16 * q^64 - 5 * q^65 + 18 * q^66 + 28 * q^67 + 17 * q^68 + 9 * q^69 + 16 * q^70 + 32 * q^71 + 16 * q^72 + 20 * q^73 + 31 * q^74 + 17 * q^75 + 8 * q^76 + 26 * q^77 - 16 * q^78 + 13 * q^79 + 5 * q^80 + 16 * q^81 + 29 * q^82 + 39 * q^83 + 4 * q^84 + 31 * q^85 + 30 * q^86 + 14 * q^87 + 18 * q^88 + 9 * q^89 + 5 * q^90 - 4 * q^91 + 9 * q^92 + 12 * q^93 - q^94 - 20 * q^95 + 16 * q^96 + 35 * q^97 + 36 * q^98 + 18 * 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
$5$	−2.44876	−1.09512	−0.547560	−	0.836766i	$-0.684443\pi$
$5$	−2.44876	−1.09512	−0.547560	+	0.836766i	$0.684443\pi$
$6$	1.00000	0.408248
$7$	−1.82729	−0.690649	−0.345325	−	0.938483i	$-0.612231\pi$
$7$	−1.82729	−0.690649	−0.345325	+	0.938483i	$0.612231\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−2.44876	−0.774367
$11$	0.163827	0.0493958	0.0246979	−	0.999695i	$-0.492138\pi$
$11$	0.163827	0.0493958	0.0246979	+	0.999695i	$0.492138\pi$
$12$	1.00000	0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−1.82729	−0.488363
$15$	−2.44876	−0.632268
$16$	1.00000	0.250000
$17$	6.53476	1.58491	0.792456	−	0.609929i	$-0.208802\pi$
$17$	6.53476	1.58491	0.792456	+	0.609929i	$0.208802\pi$
$18$	1.00000	0.235702
$19$	3.88193	0.890575	0.445287	−	0.895388i	$-0.353101\pi$
$19$	3.88193	0.890575	0.445287	+	0.895388i	$0.353101\pi$
$20$	−2.44876	−0.547560
$21$	−1.82729	−0.398747
$22$	0.163827	0.0349281
$23$	−0.103683	−0.0216194	−0.0108097	−	0.999942i	$-0.503441\pi$
$23$	−0.103683	−0.0216194	−0.0108097	+	0.999942i	$0.503441\pi$
$24$	1.00000	0.204124
$25$	0.996443	0.199289
$26$	−1.00000	−0.196116
$27$	1.00000	0.192450
$28$	−1.82729	−0.345325
$29$	−7.07183	−1.31321	−0.656603	−	0.754236i	$-0.728007\pi$
$29$	−7.07183	−1.31321	−0.656603	+	0.754236i	$0.728007\pi$
$30$	−2.44876	−0.447081
$31$	5.07047	0.910684	0.455342	−	0.890317i	$-0.349517\pi$
$31$	5.07047	0.910684	0.455342	+	0.890317i	$0.349517\pi$
$32$	1.00000	0.176777
$33$	0.163827	0.0285187
$34$	6.53476	1.12070
$35$	4.47459	0.756344
$36$	1.00000	0.166667
$37$	−11.2304	−1.84626	−0.923130	−	0.384487i	$-0.874378\pi$
$37$	−11.2304	−1.84626	−0.923130	+	0.384487i	$0.874378\pi$
$38$	3.88193	0.629732
$39$	−1.00000	−0.160128
$40$	−2.44876	−0.387184
$41$	1.24437	0.194338	0.0971692	−	0.995268i	$-0.469021\pi$
$41$	1.24437	0.194338	0.0971692	+	0.995268i	$0.469021\pi$
$42$	−1.82729	−0.281956
$43$	−0.424033	−0.0646645	−0.0323322	−	0.999477i	$-0.510293\pi$
$43$	−0.424033	−0.0646645	−0.0323322	+	0.999477i	$0.510293\pi$
$44$	0.163827	0.0246979
$45$	−2.44876	−0.365040
$46$	−0.103683	−0.0152872
$47$	7.02979	1.02540	0.512700	−	0.858568i	$-0.328645\pi$
$47$	7.02979	1.02540	0.512700	+	0.858568i	$0.328645\pi$
$48$	1.00000	0.144338
$49$	−3.66103	−0.523004
$50$	0.996443	0.140918
$51$	6.53476	0.915050
$52$	−1.00000	−0.138675
$53$	−5.21386	−0.716178	−0.358089	−	0.933687i	$-0.616572\pi$
$53$	−5.21386	−0.716178	−0.358089	+	0.933687i	$0.616572\pi$
$54$	1.00000	0.136083
$55$	−0.401174	−0.0540943
$56$	−1.82729	−0.244181
$57$	3.88193	0.514174
$58$	−7.07183	−0.928577
$59$	−7.00193	−0.911573	−0.455787	−	0.890089i	$-0.650642\pi$
$59$	−7.00193	−0.911573	−0.455787	+	0.890089i	$0.650642\pi$
$60$	−2.44876	−0.316134
$61$	12.6542	1.62021	0.810105	−	0.586285i	$-0.199410\pi$
$61$	12.6542	1.62021	0.810105	+	0.586285i	$0.199410\pi$
$62$	5.07047	0.643951
$63$	−1.82729	−0.230216
$64$	1.00000	0.125000
$65$	2.44876	0.303732
$66$	0.163827	0.0201657
$67$	16.1486	1.97286	0.986431	−	0.164177i	$-0.0524969\pi$
$67$	16.1486	1.97286	0.986431	+	0.164177i	$0.0524969\pi$
$68$	6.53476	0.792456
$69$	−0.103683	−0.0124820
$70$	4.47459	0.534816
$71$	10.8140	1.28339	0.641694	−	0.766961i	$-0.278232\pi$
$71$	10.8140	1.28339	0.641694	+	0.766961i	$0.278232\pi$
$72$	1.00000	0.117851
$73$	11.1135	1.30074	0.650370	−	0.759617i	$-0.274614\pi$
$73$	11.1135	1.30074	0.650370	+	0.759617i	$0.274614\pi$
$74$	−11.2304	−1.30550
$75$	0.996443	0.115059
$76$	3.88193	0.445287
$77$	−0.299359	−0.0341152
$78$	−1.00000	−0.113228
$79$	−5.61903	−0.632190	−0.316095	−	0.948727i	$-0.602372\pi$
$79$	−5.61903	−0.632190	−0.316095	+	0.948727i	$0.602372\pi$
$80$	−2.44876	−0.273780
$81$	1.00000	0.111111
$82$	1.24437	0.137418
$83$	15.3660	1.68664	0.843321	−	0.537410i	$-0.180597\pi$
$83$	15.3660	1.68664	0.843321	+	0.537410i	$0.180597\pi$
$84$	−1.82729	−0.199373
$85$	−16.0021	−1.73567
$86$	−0.424033	−0.0457247
$87$	−7.07183	−0.758180
$88$	0.163827	0.0174640
$89$	−14.2700	−1.51262	−0.756309	−	0.654215i	$-0.772999\pi$
$89$	−14.2700	−1.51262	−0.756309	+	0.654215i	$0.772999\pi$
$90$	−2.44876	−0.258122
$91$	1.82729	0.191552
$92$	−0.103683	−0.0108097
$93$	5.07047	0.525783
$94$	7.02979	0.725068
$95$	−9.50592	−0.975287
$96$	1.00000	0.102062
$97$	9.39168	0.953580	0.476790	−	0.879017i	$-0.341800\pi$
$97$	9.39168	0.953580	0.476790	+	0.879017i	$0.341800\pi$
$98$	−3.66103	−0.369819
$99$	0.163827	0.0164653
$100$	0.996443	0.0996443
$101$	9.72990	0.968161	0.484080	−	0.875024i	$-0.339154\pi$
$101$	9.72990	0.968161	0.484080	+	0.875024i	$0.339154\pi$
$102$	6.53476	0.647038
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−1.00000	−0.0980581
$105$	4.47459	0.436675
$106$	−5.21386	−0.506414
$107$	17.2973	1.67219	0.836095	−	0.548585i	$-0.184833\pi$
$107$	17.2973	1.67219	0.836095	+	0.548585i	$0.184833\pi$
$108$	1.00000	0.0962250
$109$	−14.0955	−1.35011	−0.675054	−	0.737769i	$-0.735879\pi$
$109$	−14.0955	−1.35011	−0.675054	+	0.737769i	$0.735879\pi$
$110$	−0.401174	−0.0382505
$111$	−11.2304	−1.06594
$112$	−1.82729	−0.172662
$113$	−7.84932	−0.738402	−0.369201	−	0.929350i	$-0.620369\pi$
$113$	−7.84932	−0.738402	−0.369201	+	0.929350i	$0.620369\pi$
$114$	3.88193	0.363576
$115$	0.253896	0.0236759
$116$	−7.07183	−0.656603
$117$	−1.00000	−0.0924500
$118$	−7.00193	−0.644579
$119$	−11.9409	−1.09462
$120$	−2.44876	−0.223541
$121$	−10.9732	−0.997560
$122$	12.6542	1.14566
$123$	1.24437	0.112201
$124$	5.07047	0.455342
$125$	9.80376	0.876875
$126$	−1.82729	−0.162788
$127$	7.65716	0.679463	0.339732	−	0.940522i	$-0.389664\pi$
$127$	7.65716	0.679463	0.339732	+	0.940522i	$0.389664\pi$
$128$	1.00000	0.0883883
$129$	−0.424033	−0.0373340
$130$	2.44876	0.214771
$131$	5.54049	0.484075	0.242037	−	0.970267i	$-0.422184\pi$
$131$	5.54049	0.484075	0.242037	+	0.970267i	$0.422184\pi$
$132$	0.163827	0.0142593
$133$	−7.09339	−0.615075
$134$	16.1486	1.39502
$135$	−2.44876	−0.210756
$136$	6.53476	0.560351
$137$	7.99646	0.683184	0.341592	−	0.939848i	$-0.389034\pi$
$137$	7.99646	0.683184	0.341592	+	0.939848i	$0.389034\pi$
$138$	−0.103683	−0.00882610
$139$	−14.8549	−1.25998	−0.629990	−	0.776603i	$-0.716941\pi$
$139$	−14.8549	−1.25998	−0.629990	+	0.776603i	$0.716941\pi$
$140$	4.47459	0.378172
$141$	7.02979	0.592015
$142$	10.8140	0.907492
$143$	−0.163827	−0.0136999
$144$	1.00000	0.0833333
$145$	17.3173	1.43812
$146$	11.1135	0.919763
$147$	−3.66103	−0.301956
$148$	−11.2304	−0.923130
$149$	−11.0069	−0.901723	−0.450861	−	0.892594i	$-0.648883\pi$
$149$	−11.0069	−0.901723	−0.450861	+	0.892594i	$0.648883\pi$
$150$	0.996443	0.0813592
$151$	18.6686	1.51923	0.759614	−	0.650374i	$-0.225388\pi$
$151$	18.6686	1.51923	0.759614	+	0.650374i	$0.225388\pi$
$152$	3.88193	0.314866
$153$	6.53476	0.528304
$154$	−0.299359	−0.0241231
$155$	−12.4164	−0.997308
$156$	−1.00000	−0.0800641
$157$	13.4297	1.07181	0.535905	−	0.844278i	$-0.319971\pi$
$157$	13.4297	1.07181	0.535905	+	0.844278i	$0.319971\pi$
$158$	−5.61903	−0.447026
$159$	−5.21386	−0.413486
$160$	−2.44876	−0.193592
$161$	0.189459	0.0149314
$162$	1.00000	0.0785674
$163$	11.1277	0.871587	0.435794	−	0.900047i	$-0.356468\pi$
$163$	11.1277	0.871587	0.435794	+	0.900047i	$0.356468\pi$
$164$	1.24437	0.0971692
$165$	−0.401174	−0.0312314
$166$	15.3660	1.19264
$167$	10.8057	0.836171	0.418085	−	0.908408i	$-0.362701\pi$
$167$	10.8057	0.836171	0.418085	+	0.908408i	$0.362701\pi$
$168$	−1.82729	−0.140978
$169$	1.00000	0.0769231
$170$	−16.0021	−1.22730
$171$	3.88193	0.296858
$172$	−0.424033	−0.0323322
$173$	0.391889	0.0297948	0.0148974	−	0.999889i	$-0.495258\pi$
$173$	0.391889	0.0297948	0.0148974	+	0.999889i	$0.495258\pi$
$174$	−7.07183	−0.536114
$175$	−1.82079	−0.137639
$176$	0.163827	0.0123489
$177$	−7.00193	−0.526297
$178$	−14.2700	−1.06958
$179$	21.1449	1.58045	0.790223	−	0.612820i	$-0.209965\pi$
$179$	21.1449	1.58045	0.790223	+	0.612820i	$0.209965\pi$
$180$	−2.44876	−0.182520
$181$	6.21449	0.461919	0.230960	−	0.972963i	$-0.425813\pi$
$181$	6.21449	0.461919	0.230960	+	0.972963i	$0.425813\pi$
$182$	1.82729	0.135447
$183$	12.6542	0.935429
$184$	−0.103683	−0.00764362
$185$	27.5005	2.02188
$186$	5.07047	0.371785
$187$	1.07057	0.0782880
$188$	7.02979	0.512700
$189$	−1.82729	−0.132916
$190$	−9.50592	−0.689632
$191$	−10.7736	−0.779553	−0.389777	−	0.920909i	$-0.627448\pi$
$191$	−10.7736	−0.779553	−0.389777	+	0.920909i	$0.627448\pi$
$192$	1.00000	0.0721688
$193$	9.98698	0.718879	0.359439	−	0.933168i	$-0.382968\pi$
$193$	9.98698	0.718879	0.359439	+	0.933168i	$0.382968\pi$
$194$	9.39168	0.674283
$195$	2.44876	0.175360
$196$	−3.66103	−0.261502
$197$	15.5369	1.10696	0.553480	−	0.832862i	$-0.313299\pi$
$197$	15.5369	1.10696	0.553480	+	0.832862i	$0.313299\pi$
$198$	0.163827	0.0116427
$199$	−10.7123	−0.759378	−0.379689	−	0.925114i	$-0.623969\pi$
$199$	−10.7123	−0.759378	−0.379689	+	0.925114i	$0.623969\pi$
$200$	0.996443	0.0704592
$201$	16.1486	1.13903
$202$	9.72990	0.684593
$203$	12.9223	0.906965
$204$	6.53476	0.457525
$205$	−3.04718	−0.212824
$206$	1.00000	0.0696733
$207$	−0.103683	−0.00720648
$208$	−1.00000	−0.0693375
$209$	0.635965	0.0439906
$210$	4.47459	0.308776
$211$	22.2540	1.53203	0.766014	−	0.642824i	$-0.222237\pi$
$211$	22.2540	1.53203	0.766014	+	0.642824i	$0.222237\pi$
$212$	−5.21386	−0.358089
$213$	10.8140	0.740964
$214$	17.2973	1.18242
$215$	1.03836	0.0708154
$216$	1.00000	0.0680414
$217$	−9.26520	−0.628963
$218$	−14.0955	−0.954670
$219$	11.1135	0.750983
$220$	−0.401174	−0.0270472
$221$	−6.53476	−0.439576
$222$	−11.2304	−0.753733
$223$	6.44775	0.431774	0.215887	−	0.976418i	$-0.430736\pi$
$223$	6.44775	0.431774	0.215887	+	0.976418i	$0.430736\pi$
$224$	−1.82729	−0.122091
$225$	0.996443	0.0664295
$226$	−7.84932	−0.522129
$227$	22.8556	1.51698	0.758490	−	0.651685i	$-0.225937\pi$
$227$	22.8556	1.51698	0.758490	+	0.651685i	$0.225937\pi$
$228$	3.88193	0.257087
$229$	−9.49593	−0.627508	−0.313754	−	0.949504i	$-0.601587\pi$
$229$	−9.49593	−0.627508	−0.313754	+	0.949504i	$0.601587\pi$
$230$	0.253896	0.0167414
$231$	−0.299359	−0.0196964
$232$	−7.07183	−0.464289
$233$	−1.87538	−0.122860	−0.0614301	−	0.998111i	$-0.519566\pi$
$233$	−1.87538	−0.122860	−0.0614301	+	0.998111i	$0.519566\pi$
$234$	−1.00000	−0.0653720
$235$	−17.2143	−1.12294
$236$	−7.00193	−0.455787
$237$	−5.61903	−0.364995
$238$	−11.9409	−0.774012
$239$	−20.5294	−1.32793	−0.663967	−	0.747762i	$-0.731128\pi$
$239$	−20.5294	−1.32793	−0.663967	+	0.747762i	$0.731128\pi$
$240$	−2.44876	−0.158067
$241$	−14.1025	−0.908425	−0.454212	−	0.890893i	$-0.650079\pi$
$241$	−14.1025	−0.908425	−0.454212	+	0.890893i	$0.650079\pi$
$242$	−10.9732	−0.705381
$243$	1.00000	0.0641500
$244$	12.6542	0.810105
$245$	8.96499	0.572752
$246$	1.24437	0.0793383
$247$	−3.88193	−0.247001
$248$	5.07047	0.321975
$249$	15.3660	0.973783
$250$	9.80376	0.620045
$251$	−3.79844	−0.239755	−0.119878	−	0.992789i	$-0.538250\pi$
$251$	−3.79844	−0.239755	−0.119878	+	0.992789i	$0.538250\pi$
$252$	−1.82729	−0.115108
$253$	−0.0169861	−0.00106791
$254$	7.65716	0.480453
$255$	−16.0021	−1.00209
$256$	1.00000	0.0625000
$257$	7.33213	0.457365	0.228683	−	0.973501i	$-0.426558\pi$
$257$	7.33213	0.457365	0.228683	+	0.973501i	$0.426558\pi$
$258$	−0.424033	−0.0263992
$259$	20.5211	1.27512
$260$	2.44876	0.151866
$261$	−7.07183	−0.437736
$262$	5.54049	0.342293
$263$	−21.4838	−1.32475	−0.662375	−	0.749172i	$-0.730452\pi$
$263$	−21.4838	−1.32475	−0.662375	+	0.749172i	$0.730452\pi$
$264$	0.163827	0.0100829
$265$	12.7675	0.784301
$266$	−7.09339	−0.434924
$267$	−14.2700	−0.873310
$268$	16.1486	0.986431
$269$	20.0289	1.22118	0.610591	−	0.791946i	$-0.290932\pi$
$269$	20.0289	1.22118	0.610591	+	0.791946i	$0.290932\pi$
$270$	−2.44876	−0.149027
$271$	−4.14433	−0.251750	−0.125875	−	0.992046i	$-0.540174\pi$
$271$	−4.14433	−0.251750	−0.125875	+	0.992046i	$0.540174\pi$
$272$	6.53476	0.396228
$273$	1.82729	0.110592
$274$	7.99646	0.483084
$275$	0.163245	0.00984402
$276$	−0.103683	−0.00624099
$277$	6.29476	0.378216	0.189108	−	0.981956i	$-0.439440\pi$
$277$	6.29476	0.378216	0.189108	+	0.981956i	$0.439440\pi$
$278$	−14.8549	−0.890940
$279$	5.07047	0.303561
$280$	4.47459	0.267408
$281$	3.26127	0.194551	0.0972754	−	0.995258i	$-0.468987\pi$
$281$	3.26127	0.194551	0.0972754	+	0.995258i	$0.468987\pi$
$282$	7.02979	0.418618
$283$	−23.7653	−1.41270	−0.706350	−	0.707862i	$-0.749660\pi$
$283$	−23.7653	−1.41270	−0.706350	+	0.707862i	$0.749660\pi$
$284$	10.8140	0.641694
$285$	−9.50592	−0.563082
$286$	−0.163827	−0.00968731
$287$	−2.27383	−0.134220
$288$	1.00000	0.0589256
$289$	25.7031	1.51195
$290$	17.3173	1.01690
$291$	9.39168	0.550550
$292$	11.1135	0.650370
$293$	14.6422	0.855406	0.427703	−	0.903919i	$-0.359323\pi$
$293$	14.6422	0.855406	0.427703	+	0.903919i	$0.359323\pi$
$294$	−3.66103	−0.213515
$295$	17.1461	0.998282
$296$	−11.2304	−0.652752
$297$	0.163827	0.00950622
$298$	−11.0069	−0.637614
$299$	0.103683	0.00599615
$300$	0.996443	0.0575297
$301$	0.774830	0.0446605
$302$	18.6686	1.07426
$303$	9.72990	0.558968
$304$	3.88193	0.222644
$305$	−30.9872	−1.77432
$306$	6.53476	0.373567
$307$	−10.8005	−0.616417	−0.308209	−	0.951319i	$-0.599729\pi$
$307$	−10.8005	−0.616417	−0.308209	+	0.951319i	$0.599729\pi$
$308$	−0.299359	−0.0170576
$309$	1.00000	0.0568880
$310$	−12.4164	−0.705203
$311$	2.38123	0.135027	0.0675135	−	0.997718i	$-0.478493\pi$
$311$	2.38123	0.135027	0.0675135	+	0.997718i	$0.478493\pi$
$312$	−1.00000	−0.0566139
$313$	20.0756	1.13474	0.567370	−	0.823463i	$-0.307961\pi$
$313$	20.0756	1.13474	0.567370	+	0.823463i	$0.307961\pi$
$314$	13.4297	0.757884
$315$	4.47459	0.252115
$316$	−5.61903	−0.316095
$317$	−1.05684	−0.0593583	−0.0296792	−	0.999559i	$-0.509449\pi$
$317$	−1.05684	−0.0593583	−0.0296792	+	0.999559i	$0.509449\pi$
$318$	−5.21386	−0.292378
$319$	−1.15856	−0.0648669
$320$	−2.44876	−0.136890
$321$	17.2973	0.965439
$322$	0.189459	0.0105581
$323$	25.3675	1.41148
$324$	1.00000	0.0555556
$325$	−0.996443	−0.0552727
$326$	11.1277	0.616305
$327$	−14.0955	−0.779485
$328$	1.24437	0.0687090
$329$	−12.8454	−0.708192
$330$	−0.401174	−0.0220839
$331$	10.3676	0.569857	0.284928	−	0.958549i	$-0.408030\pi$
$331$	10.3676	0.569857	0.284928	+	0.958549i	$0.408030\pi$
$332$	15.3660	0.843321
$333$	−11.2304	−0.615420
$334$	10.8057	0.591262
$335$	−39.5440	−2.16052
$336$	−1.82729	−0.0996866
$337$	−2.68861	−0.146458	−0.0732290	−	0.997315i	$-0.523330\pi$
$337$	−2.68861	−0.146458	−0.0732290	+	0.997315i	$0.523330\pi$
$338$	1.00000	0.0543928
$339$	−7.84932	−0.426316
$340$	−16.0021	−0.867835
$341$	0.830682	0.0449839
$342$	3.88193	0.209911
$343$	19.4807	1.05186
$344$	−0.424033	−0.0228623
$345$	0.253896	0.0136693
$346$	0.391889	0.0210681
$347$	−17.1702	−0.921745	−0.460872	−	0.887466i	$-0.652463\pi$
$347$	−17.1702	−0.921745	−0.460872	+	0.887466i	$0.652463\pi$
$348$	−7.07183	−0.379090
$349$	22.1554	1.18595	0.592977	−	0.805220i	$-0.297953\pi$
$349$	22.1554	1.18595	0.592977	+	0.805220i	$0.297953\pi$
$350$	−1.82079	−0.0973251
$351$	−1.00000	−0.0533761
$352$	0.163827	0.00873202
$353$	22.0100	1.17147	0.585737	−	0.810501i	$-0.300805\pi$
$353$	22.0100	1.17147	0.585737	+	0.810501i	$0.300805\pi$
$354$	−7.00193	−0.372148
$355$	−26.4810	−1.40546
$356$	−14.2700	−0.756309
$357$	−11.9409	−0.631978
$358$	21.1449	1.11754
$359$	10.7530	0.567520	0.283760	−	0.958895i	$-0.408418\pi$
$359$	10.7530	0.567520	0.283760	+	0.958895i	$0.408418\pi$
$360$	−2.44876	−0.129061
$361$	−3.93065	−0.206876
$362$	6.21449	0.326626
$363$	−10.9732	−0.575942
$364$	1.82729	0.0957758
$365$	−27.2144	−1.42447
$366$	12.6542	0.661448
$367$	−15.2404	−0.795545	−0.397772	−	0.917484i	$-0.630217\pi$
$367$	−15.2404	−0.795545	−0.397772	+	0.917484i	$0.630217\pi$
$368$	−0.103683	−0.00540486
$369$	1.24437	0.0647795
$370$	27.5005	1.42968
$371$	9.52721	0.494628
$372$	5.07047	0.262892
$373$	−13.2238	−0.684701	−0.342351	−	0.939572i	$-0.611223\pi$
$373$	−13.2238	−0.684701	−0.342351	+	0.939572i	$0.611223\pi$
$374$	1.07057	0.0553580
$375$	9.80376	0.506264
$376$	7.02979	0.362534
$377$	7.07183	0.364218
$378$	−1.82729	−0.0939855
$379$	0.623159	0.0320095	0.0160048	−	0.999872i	$-0.494905\pi$
$379$	0.623159	0.0320095	0.0160048	+	0.999872i	$0.494905\pi$
$380$	−9.50592	−0.487643
$381$	7.65716	0.392288
$382$	−10.7736	−0.551227
$383$	1.82865	0.0934395	0.0467198	−	0.998908i	$-0.485123\pi$
$383$	1.82865	0.0934395	0.0467198	+	0.998908i	$0.485123\pi$
$384$	1.00000	0.0510310
$385$	0.733060	0.0373602
$386$	9.98698	0.508324
$387$	−0.424033	−0.0215548
$388$	9.39168	0.476790
$389$	29.0430	1.47254	0.736269	−	0.676688i	$-0.236586\pi$
$389$	29.0430	1.47254	0.736269	+	0.676688i	$0.236586\pi$
$390$	2.44876	0.123998
$391$	−0.677545	−0.0342649
$392$	−3.66103	−0.184910
$393$	5.54049	0.279481
$394$	15.5369	0.782739
$395$	13.7597	0.692325
$396$	0.163827	0.00823263
$397$	−21.5471	−1.08142	−0.540710	−	0.841209i	$-0.681844\pi$
$397$	−21.5471	−1.08142	−0.540710	+	0.841209i	$0.681844\pi$
$398$	−10.7123	−0.536961
$399$	−7.09339	−0.355114
$400$	0.996443	0.0498222
$401$	−11.5811	−0.578335	−0.289167	−	0.957279i	$-0.593378\pi$
$401$	−11.5811	−0.578335	−0.289167	+	0.957279i	$0.593378\pi$
$402$	16.1486	0.805417
$403$	−5.07047	−0.252578
$404$	9.72990	0.484080
$405$	−2.44876	−0.121680
$406$	12.9223	0.641321
$407$	−1.83984	−0.0911975
$408$	6.53476	0.323519
$409$	−18.4137	−0.910499	−0.455249	−	0.890364i	$-0.650450\pi$
$409$	−18.4137	−0.910499	−0.455249	+	0.890364i	$0.650450\pi$
$410$	−3.04718	−0.150489
$411$	7.99646	0.394436
$412$	1.00000	0.0492665
$413$	12.7945	0.629577
$414$	−0.103683	−0.00509575
$415$	−37.6278	−1.84708
$416$	−1.00000	−0.0490290
$417$	−14.8549	−0.727450
$418$	0.635965	0.0311061
$419$	19.8661	0.970524	0.485262	−	0.874369i	$-0.338724\pi$
$419$	19.8661	0.970524	0.485262	+	0.874369i	$0.338724\pi$
$420$	4.47459	0.218338
$421$	−1.78317	−0.0869063	−0.0434531	−	0.999055i	$-0.513836\pi$
$421$	−1.78317	−0.0869063	−0.0434531	+	0.999055i	$0.513836\pi$
$422$	22.2540	1.08331
$423$	7.02979	0.341800
$424$	−5.21386	−0.253207
$425$	6.51152	0.315855
$426$	10.8140	0.523941
$427$	−23.1229	−1.11900
$428$	17.2973	0.836095
$429$	−0.163827	−0.00790966
$430$	1.03836	0.0500740
$431$	−1.26086	−0.0607333	−0.0303667	−	0.999539i	$-0.509667\pi$
$431$	−1.26086	−0.0607333	−0.0303667	+	0.999539i	$0.509667\pi$
$432$	1.00000	0.0481125
$433$	−27.5023	−1.32168	−0.660838	−	0.750529i	$-0.729799\pi$
$433$	−27.5023	−1.32168	−0.660838	+	0.750529i	$0.729799\pi$
$434$	−9.26520	−0.444744
$435$	17.3173	0.830299
$436$	−14.0955	−0.675054
$437$	−0.402490	−0.0192537
$438$	11.1135	0.531025
$439$	−39.2426	−1.87295	−0.936474	−	0.350738i	$-0.885931\pi$
$439$	−39.2426	−1.87295	−0.936474	+	0.350738i	$0.885931\pi$
$440$	−0.401174	−0.0191252
$441$	−3.66103	−0.174335
$442$	−6.53476	−0.310827
$443$	−23.7997	−1.13076	−0.565379	−	0.824831i	$-0.691270\pi$
$443$	−23.7997	−1.13076	−0.565379	+	0.824831i	$0.691270\pi$
$444$	−11.2304	−0.532969
$445$	34.9439	1.65650
$446$	6.44775	0.305310
$447$	−11.0069	−0.520610
$448$	−1.82729	−0.0863312
$449$	18.6740	0.881282	0.440641	−	0.897683i	$-0.354751\pi$
$449$	18.6740	0.881282	0.440641	+	0.897683i	$0.354751\pi$
$450$	0.996443	0.0469728
$451$	0.203862	0.00959950
$452$	−7.84932	−0.369201
$453$	18.6686	0.877127
$454$	22.8556	1.07267
$455$	−4.47459	−0.209772
$456$	3.88193	0.181788
$457$	−25.3722	−1.18686	−0.593430	−	0.804885i	$-0.702227\pi$
$457$	−25.3722	−1.18686	−0.593430	+	0.804885i	$0.702227\pi$
$458$	−9.49593	−0.443715
$459$	6.53476	0.305017
$460$	0.253896	0.0118379
$461$	−17.4833	−0.814277	−0.407139	−	0.913366i	$-0.633473\pi$
$461$	−17.4833	−0.814277	−0.407139	+	0.913366i	$0.633473\pi$
$462$	−0.299359	−0.0139275
$463$	−30.3195	−1.40907	−0.704533	−	0.709671i	$-0.748843\pi$
$463$	−30.3195	−1.40907	−0.704533	+	0.709671i	$0.748843\pi$
$464$	−7.07183	−0.328302
$465$	−12.4164	−0.575796
$466$	−1.87538	−0.0868752
$467$	33.5087	1.55060	0.775299	−	0.631594i	$-0.217599\pi$
$467$	33.5087	1.55060	0.775299	+	0.631594i	$0.217599\pi$
$468$	−1.00000	−0.0462250
$469$	−29.5081	−1.36256
$470$	−17.2143	−0.794037
$471$	13.4297	0.618809
$472$	−7.00193	−0.322290
$473$	−0.0694682	−0.00319415
$474$	−5.61903	−0.258091
$475$	3.86812	0.177481
$476$	−11.9409	−0.547309
$477$	−5.21386	−0.238726
$478$	−20.5294	−0.938991
$479$	20.0670	0.916886	0.458443	−	0.888724i	$-0.348407\pi$
$479$	20.0670	0.916886	0.458443	+	0.888724i	$0.348407\pi$
$480$	−2.44876	−0.111770
$481$	11.2304	0.512061
$482$	−14.1025	−0.642353
$483$	0.189459	0.00862067
$484$	−10.9732	−0.498780
$485$	−22.9980	−1.04429
$486$	1.00000	0.0453609
$487$	−31.1034	−1.40943	−0.704716	−	0.709490i	$-0.748925\pi$
$487$	−31.1034	−1.40943	−0.704716	+	0.709490i	$0.748925\pi$
$488$	12.6542	0.572831
$489$	11.1277	0.503211
$490$	8.96499	0.404997
$491$	−12.8407	−0.579493	−0.289746	−	0.957103i	$-0.593571\pi$
$491$	−12.8407	−0.579493	−0.289746	+	0.957103i	$0.593571\pi$
$492$	1.24437	0.0561007
$493$	−46.2128	−2.08132
$494$	−3.88193	−0.174656
$495$	−0.401174	−0.0180314
$496$	5.07047	0.227671
$497$	−19.7603	−0.886371
$498$	15.3660	0.688569
$499$	9.71936	0.435098	0.217549	−	0.976049i	$-0.430194\pi$
$499$	9.71936	0.435098	0.217549	+	0.976049i	$0.430194\pi$
$500$	9.80376	0.438438
$501$	10.8057	0.482763
$502$	−3.79844	−0.169533
$503$	−9.11094	−0.406237	−0.203118	−	0.979154i	$-0.565108\pi$
$503$	−9.11094	−0.406237	−0.203118	+	0.979154i	$0.565108\pi$
$504$	−1.82729	−0.0813938
$505$	−23.8262	−1.06025
$506$	−0.0169861	−0.000755126 0
$507$	1.00000	0.0444116
$508$	7.65716	0.339732
$509$	42.4720	1.88254	0.941269	−	0.337657i	$-0.109634\pi$
$509$	42.4720	1.88254	0.941269	+	0.337657i	$0.109634\pi$
$510$	−16.0021	−0.708584
$511$	−20.3076	−0.898356
$512$	1.00000	0.0441942
$513$	3.88193	0.171391
$514$	7.33213	0.323406
$515$	−2.44876	−0.107905
$516$	−0.424033	−0.0186670
$517$	1.15167	0.0506505
$518$	20.5211	0.901645
$519$	0.391889	0.0172020
$520$	2.44876	0.107385
$521$	−22.7199	−0.995375	−0.497688	−	0.867356i	$-0.665817\pi$
$521$	−22.7199	−0.995375	−0.497688	+	0.867356i	$0.665817\pi$
$522$	−7.07183	−0.309526
$523$	−8.94646	−0.391201	−0.195601	−	0.980684i	$-0.562666\pi$
$523$	−8.94646	−0.391201	−0.195601	+	0.980684i	$0.562666\pi$
$524$	5.54049	0.242037
$525$	−1.82079	−0.0794656
$526$	−21.4838	−0.936740
$527$	33.1343	1.44335
$528$	0.163827	0.00712967
$529$	−22.9892	−0.999533
$530$	12.7675	0.554585
$531$	−7.00193	−0.303858
$532$	−7.09339	−0.307537
$533$	−1.24437	−0.0538998
$534$	−14.2700	−0.617523
$535$	−42.3569	−1.83125
$536$	16.1486	0.697512
$537$	21.1449	0.912471
$538$	20.0289	0.863506
$539$	−0.599776	−0.0258342
$540$	−2.44876	−0.105378
$541$	14.0523	0.604154	0.302077	−	0.953283i	$-0.402320\pi$
$541$	14.0523	0.604154	0.302077	+	0.953283i	$0.402320\pi$
$542$	−4.14433	−0.178014
$543$	6.21449	0.266689
$544$	6.53476	0.280176
$545$	34.5166	1.47853
$546$	1.82729	0.0782006
$547$	−4.34995	−0.185990	−0.0929952	−	0.995667i	$-0.529644\pi$
$547$	−4.34995	−0.185990	−0.0929952	+	0.995667i	$0.529644\pi$
$548$	7.99646	0.341592
$549$	12.6542	0.540070
$550$	0.163245	0.00696077
$551$	−27.4523	−1.16951
$552$	−0.103683	−0.00441305
$553$	10.2676	0.436622
$554$	6.29476	0.267439
$555$	27.5005	1.16733
$556$	−14.8549	−0.629990
$557$	28.5051	1.20780	0.603900	−	0.797060i	$-0.293612\pi$
$557$	28.5051	1.20780	0.603900	+	0.797060i	$0.293612\pi$
$558$	5.07047	0.214650
$559$	0.424033	0.0179347
$560$	4.47459	0.189086
$561$	1.07057	0.0451996
$562$	3.26127	0.137568
$563$	15.2823	0.644071	0.322035	−	0.946728i	$-0.395633\pi$
$563$	15.2823	0.644071	0.322035	+	0.946728i	$0.395633\pi$
$564$	7.02979	0.296008
$565$	19.2211	0.808639
$566$	−23.7653	−0.998930
$567$	−1.82729	−0.0767388
$568$	10.8140	0.453746
$569$	−13.7293	−0.575562	−0.287781	−	0.957696i	$-0.592917\pi$
$569$	−13.7293	−0.575562	−0.287781	+	0.957696i	$0.592917\pi$
$570$	−9.50592	−0.398159
$571$	42.2517	1.76818	0.884089	−	0.467319i	$-0.154780\pi$
$571$	42.2517	1.76818	0.884089	+	0.467319i	$0.154780\pi$
$572$	−0.163827	−0.00684996
$573$	−10.7736	−0.450075
$574$	−2.27383	−0.0949077
$575$	−0.103314	−0.00430851
$576$	1.00000	0.0416667
$577$	7.28596	0.303318	0.151659	−	0.988433i	$-0.451538\pi$
$577$	7.28596	0.303318	0.151659	+	0.988433i	$0.451538\pi$
$578$	25.7031	1.06911
$579$	9.98698	0.415045
$580$	17.3173	0.719060
$581$	−28.0782	−1.16488
$582$	9.39168	0.389298
$583$	−0.854172	−0.0353762
$584$	11.1135	0.459881
$585$	2.44876	0.101244
$586$	14.6422	0.604863
$587$	−20.2751	−0.836844	−0.418422	−	0.908253i	$-0.637417\pi$
$587$	−20.2751	−0.836844	−0.418422	+	0.908253i	$0.637417\pi$
$588$	−3.66103	−0.150978
$589$	19.6832	0.811032
$590$	17.1461	0.705892
$591$	15.5369	0.639104
$592$	−11.2304	−0.461565
$593$	−21.1167	−0.867158	−0.433579	−	0.901116i	$-0.642750\pi$
$593$	−21.1167	−0.867158	−0.433579	+	0.901116i	$0.642750\pi$
$594$	0.163827	0.00672191
$595$	29.2404	1.19874
$596$	−11.0069	−0.450861
$597$	−10.7123	−0.438427
$598$	0.103683	0.00423992
$599$	−4.04269	−0.165180	−0.0825899	−	0.996584i	$-0.526319\pi$
$599$	−4.04269	−0.165180	−0.0825899	+	0.996584i	$0.526319\pi$
$600$	0.996443	0.0406796
$601$	10.7726	0.439422	0.219711	−	0.975565i	$-0.429489\pi$
$601$	10.7726	0.439422	0.219711	+	0.975565i	$0.429489\pi$
$602$	0.774830	0.0315797
$603$	16.1486	0.657621
$604$	18.6686	0.759614
$605$	26.8707	1.09245
$606$	9.72990	0.395250
$607$	−48.0953	−1.95213	−0.976065	−	0.217481i	$-0.930216\pi$
$607$	−48.0953	−1.95213	−0.976065	+	0.217481i	$0.930216\pi$
$608$	3.88193	0.157433
$609$	12.9223	0.523637
$610$	−30.9872	−1.25464
$611$	−7.02979	−0.284395
$612$	6.53476	0.264152
$613$	−33.9980	−1.37317	−0.686584	−	0.727051i	$-0.740891\pi$
$613$	−33.9980	−1.37317	−0.686584	+	0.727051i	$0.740891\pi$
$614$	−10.8005	−0.435873
$615$	−3.04718	−0.122874
$616$	−0.299359	−0.0120615
$617$	10.7469	0.432653	0.216327	−	0.976321i	$-0.430592\pi$
$617$	10.7469	0.432653	0.216327	+	0.976321i	$0.430592\pi$
$618$	1.00000	0.0402259
$619$	43.5818	1.75170	0.875849	−	0.482585i	$-0.160302\pi$
$619$	43.5818	1.75170	0.875849	+	0.482585i	$0.160302\pi$
$620$	−12.4164	−0.498654
$621$	−0.103683	−0.00416066
$622$	2.38123	0.0954785
$623$	26.0754	1.04469
$624$	−1.00000	−0.0400320
$625$	−28.9893	−1.15957
$626$	20.0756	0.802383
$627$	0.635965	0.0253980
$628$	13.4297	0.535905
$629$	−73.3877	−2.92616
$630$	4.47459	0.178272
$631$	−25.2237	−1.00414	−0.502071	−	0.864827i	$-0.667428\pi$
$631$	−25.2237	−1.00414	−0.502071	+	0.864827i	$0.667428\pi$
$632$	−5.61903	−0.223513
$633$	22.2540	0.884517
$634$	−1.05684	−0.0419727
$635$	−18.7506	−0.744094
$636$	−5.21386	−0.206743
$637$	3.66103	0.145055
$638$	−1.15856	−0.0458678
$639$	10.8140	0.427796
$640$	−2.44876	−0.0967959
$641$	22.5606	0.891090	0.445545	−	0.895260i	$-0.353010\pi$
$641$	22.5606	0.891090	0.445545	+	0.895260i	$0.353010\pi$
$642$	17.2973	0.682669
$643$	26.0001	1.02535	0.512673	−	0.858584i	$-0.328655\pi$
$643$	26.0001	1.02535	0.512673	+	0.858584i	$0.328655\pi$
$644$	0.189459	0.00746572
$645$	1.03836	0.0408853
$646$	25.3675	0.998069
$647$	−16.4548	−0.646905	−0.323453	−	0.946244i	$-0.604844\pi$
$647$	−16.4548	−0.646905	−0.323453	+	0.946244i	$0.604844\pi$
$648$	1.00000	0.0392837
$649$	−1.14711	−0.0450279
$650$	−0.996443	−0.0390837
$651$	−9.26520	−0.363132
$652$	11.1277	0.435794
$653$	3.06046	0.119765	0.0598825	−	0.998205i	$-0.480927\pi$
$653$	3.06046	0.119765	0.0598825	+	0.998205i	$0.480927\pi$
$654$	−14.0955	−0.551179
$655$	−13.5673	−0.530120
$656$	1.24437	0.0485846
$657$	11.1135	0.433580
$658$	−12.8454	−0.500768
$659$	−27.1581	−1.05793	−0.528966	−	0.848643i	$-0.677420\pi$
$659$	−27.1581	−1.05793	−0.528966	+	0.848643i	$0.677420\pi$
$660$	−0.401174	−0.0156157
$661$	22.4363	0.872673	0.436336	−	0.899784i	$-0.356276\pi$
$661$	22.4363	0.872673	0.436336	+	0.899784i	$0.356276\pi$
$662$	10.3676	0.402950
$663$	−6.53476	−0.253789
$664$	15.3660	0.596318
$665$	17.3700	0.673581
$666$	−11.2304	−0.435168
$667$	0.733230	0.0283908
$668$	10.8057	0.418085
$669$	6.44775	0.249285
$670$	−39.5440	−1.52772
$671$	2.07311	0.0800315
$672$	−1.82729	−0.0704891
$673$	−35.4406	−1.36614	−0.683068	−	0.730355i	$-0.739355\pi$
$673$	−35.4406	−1.36614	−0.683068	+	0.730355i	$0.739355\pi$
$674$	−2.68861	−0.103562
$675$	0.996443	0.0383531
$676$	1.00000	0.0384615
$677$	−27.2318	−1.04660	−0.523302	−	0.852147i	$-0.675300\pi$
$677$	−27.2318	−1.04660	−0.523302	+	0.852147i	$0.675300\pi$
$678$	−7.84932	−0.301451
$679$	−17.1613	−0.658590
$680$	−16.0021	−0.613652
$681$	22.8556	0.875829
$682$	0.830682	0.0318084
$683$	−13.3465	−0.510690	−0.255345	−	0.966850i	$-0.582189\pi$
$683$	−13.3465	−0.510690	−0.255345	+	0.966850i	$0.582189\pi$
$684$	3.88193	0.148429
$685$	−19.5814	−0.748168
$686$	19.4807	0.743778
$687$	−9.49593	−0.362292
$688$	−0.424033	−0.0161661
$689$	5.21386	0.198632
$690$	0.253896	0.00966564
$691$	−0.955569	−0.0363516	−0.0181758	−	0.999835i	$-0.505786\pi$
$691$	−0.955569	−0.0363516	−0.0181758	+	0.999835i	$0.505786\pi$
$692$	0.391889	0.0148974
$693$	−0.299359	−0.0113717
$694$	−17.1702	−0.651772
$695$	36.3762	1.37983
$696$	−7.07183	−0.268057
$697$	8.13168	0.308009
$698$	22.1554	0.838596
$699$	−1.87538	−0.0709333
$700$	−1.82079	−0.0688193
$701$	17.1322	0.647075	0.323537	−	0.946215i	$-0.395128\pi$
$701$	17.1322	0.647075	0.323537	+	0.946215i	$0.395128\pi$
$702$	−1.00000	−0.0377426
$703$	−43.5954	−1.64423
$704$	0.163827	0.00617447
$705$	−17.2143	−0.648328
$706$	22.0100	0.828358
$707$	−17.7793	−0.668660
$708$	−7.00193	−0.263148
$709$	20.5254	0.770846	0.385423	−	0.922740i	$-0.374055\pi$
$709$	20.5254	0.770846	0.385423	+	0.922740i	$0.374055\pi$
$710$	−26.4810	−0.993813
$711$	−5.61903	−0.210730
$712$	−14.2700	−0.534791
$713$	−0.525723	−0.0196885
$714$	−11.9409	−0.446876
$715$	0.401174	0.0150031
$716$	21.1449	0.790223
$717$	−20.5294	−0.766683
$718$	10.7530	0.401297
$719$	−1.12798	−0.0420665	−0.0210333	−	0.999779i	$-0.506696\pi$
$719$	−1.12798	−0.0420665	−0.0210333	+	0.999779i	$0.506696\pi$
$720$	−2.44876	−0.0912600
$721$	−1.82729	−0.0680517
$722$	−3.93065	−0.146284
$723$	−14.1025	−0.524479
$724$	6.21449	0.230960
$725$	−7.04668	−0.261707
$726$	−10.9732	−0.407252
$727$	15.0853	0.559484	0.279742	−	0.960075i	$-0.409751\pi$
$727$	15.0853	0.559484	0.279742	+	0.960075i	$0.409751\pi$
$728$	1.82729	0.0677237
$729$	1.00000	0.0370370
$730$	−27.2144	−1.00725
$731$	−2.77096	−0.102488
$732$	12.6542	0.467714
$733$	−16.3050	−0.602239	−0.301120	−	0.953586i	$-0.597360\pi$
$733$	−16.3050	−0.602239	−0.301120	+	0.953586i	$0.597360\pi$
$734$	−15.2404	−0.562535
$735$	8.96499	0.330678
$736$	−0.103683	−0.00382181
$737$	2.64558	0.0974510
$738$	1.24437	0.0458060
$739$	−37.0043	−1.36123	−0.680613	−	0.732644i	$-0.738286\pi$
$739$	−37.0043	−1.36123	−0.680613	+	0.732644i	$0.738286\pi$
$740$	27.5005	1.01094
$741$	−3.88193	−0.142606
$742$	9.52721	0.349755
$743$	4.81656	0.176702	0.0883511	−	0.996089i	$-0.471840\pi$
$743$	4.81656	0.176702	0.0883511	+	0.996089i	$0.471840\pi$
$744$	5.07047	0.185893
$745$	26.9534	0.987495
$746$	−13.2238	−0.484157
$747$	15.3660	0.562214
$748$	1.07057	0.0391440
$749$	−31.6071	−1.15490
$750$	9.80376	0.357983
$751$	−42.6398	−1.55595	−0.777973	−	0.628297i	$-0.783752\pi$
$751$	−42.6398	−1.55595	−0.777973	+	0.628297i	$0.783752\pi$
$752$	7.02979	0.256350
$753$	−3.79844	−0.138423
$754$	7.07183	0.257541
$755$	−45.7150	−1.66374
$756$	−1.82729	−0.0664578
$757$	−39.9172	−1.45082	−0.725409	−	0.688319i	$-0.758349\pi$
$757$	−39.9172	−1.45082	−0.725409	+	0.688319i	$0.758349\pi$
$758$	0.623159	0.0226342
$759$	−0.0169861	−0.000616557 0
$760$	−9.50592	−0.344816
$761$	−9.06915	−0.328756	−0.164378	−	0.986397i	$-0.552562\pi$
$761$	−9.06915	−0.328756	−0.164378	+	0.986397i	$0.552562\pi$
$762$	7.65716	0.277390
$763$	25.7566	0.932450
$764$	−10.7736	−0.389777
$765$	−16.0021	−0.578557
$766$	1.82865	0.0660717
$767$	7.00193	0.252825
$768$	1.00000	0.0360844
$769$	−39.8392	−1.43664	−0.718320	−	0.695713i	$-0.755089\pi$
$769$	−39.8392	−1.43664	−0.718320	+	0.695713i	$0.755089\pi$
$770$	0.733060	0.0264177
$771$	7.33213	0.264060
$772$	9.98698	0.359439
$773$	10.5839	0.380677	0.190338	−	0.981719i	$-0.439041\pi$
$773$	10.5839	0.380677	0.190338	+	0.981719i	$0.439041\pi$
$774$	−0.424033	−0.0152416
$775$	5.05244	0.181489
$776$	9.39168	0.337142
$777$	20.5211	0.736190
$778$	29.0430	1.04124
$779$	4.83057	0.173073
$780$	2.44876	0.0876798
$781$	1.77163	0.0633940
$782$	−0.677545	−0.0242289
$783$	−7.07183	−0.252727
$784$	−3.66103	−0.130751
$785$	−32.8862	−1.17376
$786$	5.54049	0.197623
$787$	−15.9277	−0.567761	−0.283880	−	0.958860i	$-0.591622\pi$
$787$	−15.9277	−0.567761	−0.283880	+	0.958860i	$0.591622\pi$
$788$	15.5369	0.553480
$789$	−21.4838	−0.764845
$790$	13.7597	0.489547
$791$	14.3429	0.509977
$792$	0.163827	0.00582135
$793$	−12.6542	−0.449365
$794$	−21.5471	−0.764679
$795$	12.7675	0.452817
$796$	−10.7123	−0.379689
$797$	8.58677	0.304159	0.152080	−	0.988368i	$-0.451403\pi$
$797$	8.58677	0.304159	0.152080	+	0.988368i	$0.451403\pi$
$798$	−7.09339	−0.251103
$799$	45.9380	1.62517
$800$	0.996443	0.0352296
$801$	−14.2700	−0.504206
$802$	−11.5811	−0.408945
$803$	1.82070	0.0642511
$804$	16.1486	0.569516
$805$	−0.463940	−0.0163517
$806$	−5.07047	−0.178600
$807$	20.0289	0.705050
$808$	9.72990	0.342297
$809$	17.7498	0.624048	0.312024	−	0.950074i	$-0.398993\pi$
$809$	17.7498	0.624048	0.312024	+	0.950074i	$0.398993\pi$
$810$	−2.44876	−0.0860408
$811$	48.7291	1.71111	0.855554	−	0.517713i	$-0.173217\pi$
$811$	48.7291	1.71111	0.855554	+	0.517713i	$0.173217\pi$
$812$	12.9223	0.453483
$813$	−4.14433	−0.145348
$814$	−1.83984	−0.0644864
$815$	−27.2491	−0.954493
$816$	6.53476	0.228762
$817$	−1.64607	−0.0575885
$818$	−18.4137	−0.643820
$819$	1.82729	0.0638505
$820$	−3.04718	−0.106412
$821$	−21.4360	−0.748120	−0.374060	−	0.927404i	$-0.622035\pi$
$821$	−21.4360	−0.748120	−0.374060	+	0.927404i	$0.622035\pi$
$822$	7.99646	0.278909
$823$	22.6044	0.787939	0.393970	−	0.919123i	$-0.371101\pi$
$823$	22.6044	0.787939	0.393970	+	0.919123i	$0.371101\pi$
$824$	1.00000	0.0348367
$825$	0.163245	0.00568345
$826$	12.7945	0.445178
$827$	26.8179	0.932551	0.466275	−	0.884640i	$-0.345596\pi$
$827$	26.8179	0.932551	0.466275	+	0.884640i	$0.345596\pi$
$828$	−0.103683	−0.00360324
$829$	8.32695	0.289207	0.144604	−	0.989490i	$-0.453809\pi$
$829$	8.32695	0.289207	0.144604	+	0.989490i	$0.453809\pi$
$830$	−37.6278	−1.30608
$831$	6.29476	0.218363
$832$	−1.00000	−0.0346688
$833$	−23.9239	−0.828915
$834$	−14.8549	−0.514385
$835$	−26.4606	−0.915708
$836$	0.635965	0.0219953
$837$	5.07047	0.175261
$838$	19.8661	0.686264
$839$	45.0249	1.55443	0.777217	−	0.629233i	$-0.216631\pi$
$839$	45.0249	1.55443	0.777217	+	0.629233i	$0.216631\pi$
$840$	4.47459	0.154388
$841$	21.0108	0.724512
$842$	−1.78317	−0.0614520
$843$	3.26127	0.112324
$844$	22.2540	0.766014
$845$	−2.44876	−0.0842400
$846$	7.02979	0.241689
$847$	20.0511	0.688964
$848$	−5.21386	−0.179045
$849$	−23.7653	−0.815623
$850$	6.51152	0.223343
$851$	1.16440	0.0399151
$852$	10.8140	0.370482
$853$	34.4818	1.18063	0.590317	−	0.807171i	$-0.299003\pi$
$853$	34.4818	1.18063	0.590317	+	0.807171i	$0.299003\pi$
$854$	−23.1229	−0.791250
$855$	−9.50592	−0.325096
$856$	17.2973	0.591208
$857$	51.5946	1.76244	0.881218	−	0.472710i	$-0.156724\pi$
$857$	51.5946	1.76244	0.881218	+	0.472710i	$0.156724\pi$
$858$	−0.163827	−0.00559297
$859$	32.1998	1.09864	0.549322	−	0.835611i	$-0.314886\pi$
$859$	32.1998	1.09864	0.549322	+	0.835611i	$0.314886\pi$
$860$	1.03836	0.0354077
$861$	−2.27383	−0.0774918
$862$	−1.26086	−0.0429449
$863$	−21.6221	−0.736026	−0.368013	−	0.929821i	$-0.619962\pi$
$863$	−21.6221	−0.736026	−0.368013	+	0.929821i	$0.619962\pi$
$864$	1.00000	0.0340207
$865$	−0.959643	−0.0326288
$866$	−27.5023	−0.934565
$867$	25.7031	0.872923
$868$	−9.26520	−0.314482
$869$	−0.920551	−0.0312275
$870$	17.3173	0.587110
$871$	−16.1486	−0.547173
$872$	−14.0955	−0.477335
$873$	9.39168	0.317860
$874$	−0.402490	−0.0136144
$875$	−17.9143	−0.605613
$876$	11.1135	0.375492
$877$	−45.8463	−1.54812	−0.774060	−	0.633113i	$-0.781777\pi$
$877$	−45.8463	−1.54812	−0.774060	+	0.633113i	$0.781777\pi$
$878$	−39.2426	−1.32437
$879$	14.6422	0.493869
$880$	−0.401174	−0.0135236
$881$	5.13903	0.173138	0.0865691	−	0.996246i	$-0.472410\pi$
$881$	5.13903	0.173138	0.0865691	+	0.996246i	$0.472410\pi$
$882$	−3.66103	−0.123273
$883$	3.82878	0.128849	0.0644243	−	0.997923i	$-0.479479\pi$
$883$	3.82878	0.128849	0.0644243	+	0.997923i	$0.479479\pi$
$884$	−6.53476	−0.219788
$885$	17.1461	0.576358
$886$	−23.7997	−0.799567
$887$	−22.3363	−0.749978	−0.374989	−	0.927029i	$-0.622354\pi$
$887$	−22.3363	−0.749978	−0.374989	+	0.927029i	$0.622354\pi$
$888$	−11.2304	−0.376866
$889$	−13.9918	−0.469271
$890$	34.9439	1.17132
$891$	0.163827	0.00548842
$892$	6.44775	0.215887
$893$	27.2891	0.913196
$894$	−11.0069	−0.368127
$895$	−51.7789	−1.73078
$896$	−1.82729	−0.0610453
$897$	0.103683	0.00346188
$898$	18.6740	0.623161
$899$	−35.8575	−1.19592
$900$	0.996443	0.0332148
$901$	−34.0713	−1.13508
$902$	0.203862	0.00678787
$903$	0.774830	0.0257847
$904$	−7.84932	−0.261064
$905$	−15.2178	−0.505857
$906$	18.6686	0.620223
$907$	16.1043	0.534736	0.267368	−	0.963595i	$-0.413846\pi$
$907$	16.1043	0.534736	0.267368	+	0.963595i	$0.413846\pi$
$908$	22.8556	0.758490
$909$	9.72990	0.322720
$910$	−4.47459	−0.148331
$911$	29.2247	0.968256	0.484128	−	0.874997i	$-0.339137\pi$
$911$	29.2247	0.968256	0.484128	+	0.874997i	$0.339137\pi$
$912$	3.88193	0.128543
$913$	2.51738	0.0833130
$914$	−25.3722	−0.839237
$915$	−30.9872	−1.02441
$916$	−9.49593	−0.313754
$917$	−10.1241	−0.334326
$918$	6.53476	0.215679
$919$	27.5495	0.908776	0.454388	−	0.890804i	$-0.349858\pi$
$919$	27.5495	0.908776	0.454388	+	0.890804i	$0.349858\pi$
$920$	0.253896	0.00837069
$921$	−10.8005	−0.355889
$922$	−17.4833	−0.575781
$923$	−10.8140	−0.355948
$924$	−0.299359	−0.00984820
$925$	−11.1904	−0.367939
$926$	−30.3195	−0.996360
$927$	1.00000	0.0328443
$928$	−7.07183	−0.232144
$929$	−26.0664	−0.855212	−0.427606	−	0.903965i	$-0.640643\pi$
$929$	−26.0664	−0.855212	−0.427606	+	0.903965i	$0.640643\pi$
$930$	−12.4164	−0.407149
$931$	−14.2118	−0.465774
$932$	−1.87538	−0.0614301
$933$	2.38123	0.0779578
$934$	33.5087	1.09644
$935$	−2.62158	−0.0857348
$936$	−1.00000	−0.0326860
$937$	−41.1767	−1.34518	−0.672592	−	0.740014i	$-0.734819\pi$
$937$	−41.1767	−1.34518	−0.672592	+	0.740014i	$0.734819\pi$
$938$	−29.5081	−0.963472
$939$	20.0756	0.655143
$940$	−17.2143	−0.561469
$941$	−38.0764	−1.24126	−0.620628	−	0.784105i	$-0.713122\pi$
$941$	−38.0764	−1.24126	−0.620628	+	0.784105i	$0.713122\pi$
$942$	13.4297	0.437564
$943$	−0.129021	−0.00420149
$944$	−7.00193	−0.227893
$945$	4.47459	0.145558
$946$	−0.0694682	−0.00225861
$947$	27.6725	0.899236	0.449618	−	0.893221i	$-0.351560\pi$
$947$	27.6725	0.899236	0.449618	+	0.893221i	$0.351560\pi$
$948$	−5.61903	−0.182498
$949$	−11.1135	−0.360761
$950$	3.86812	0.125498
$951$	−1.05684	−0.0342705
$952$	−11.9409	−0.387006
$953$	−61.7142	−1.99912	−0.999560	−	0.0296691i	$-0.990555\pi$
$953$	−61.7142	−1.99912	−0.999560	+	0.0296691i	$0.990555\pi$
$954$	−5.21386	−0.168805
$955$	26.3821	0.853704
$956$	−20.5294	−0.663967
$957$	−1.15856	−0.0374509
$958$	20.0670	0.648336
$959$	−14.6118	−0.471840
$960$	−2.44876	−0.0790335
$961$	−5.29031	−0.170655
$962$	11.2304	0.362081
$963$	17.2973	0.557397
$964$	−14.1025	−0.454212
$965$	−24.4558	−0.787259
$966$	0.189459	0.00609574
$967$	23.4006	0.752514	0.376257	−	0.926515i	$-0.377211\pi$
$967$	23.4006	0.752514	0.376257	+	0.926515i	$0.377211\pi$
$968$	−10.9732	−0.352691
$969$	25.3675	0.814920
$970$	−22.9980	−0.738421
$971$	−19.6717	−0.631295	−0.315647	−	0.948877i	$-0.602222\pi$
$971$	−19.6717	−0.631295	−0.315647	+	0.948877i	$0.602222\pi$
$972$	1.00000	0.0320750
$973$	27.1442	0.870204
$974$	−31.1034	−0.996618
$975$	−0.996443	−0.0319117
$976$	12.6542	0.405052
$977$	−21.0477	−0.673375	−0.336687	−	0.941617i	$-0.609307\pi$
$977$	−21.0477	−0.673375	−0.336687	+	0.941617i	$0.609307\pi$
$978$	11.1277	0.355824
$979$	−2.33782	−0.0747169
$980$	8.96499	0.286376
$981$	−14.0955	−0.450036
$982$	−12.8407	−0.409763
$983$	−6.36153	−0.202901	−0.101451	−	0.994841i	$-0.532348\pi$
$983$	−6.36153	−0.202901	−0.101451	+	0.994841i	$0.532348\pi$
$984$	1.24437	0.0396692
$985$	−38.0463	−1.21226
$986$	−46.2128	−1.47171
$987$	−12.8454	−0.408875
$988$	−3.88193	−0.123501
$989$	0.0439651	0.00139801
$990$	−0.401174	−0.0127502
$991$	5.59086	0.177599	0.0887997	−	0.996050i	$-0.471697\pi$
$991$	5.59086	0.177599	0.0887997	+	0.996050i	$0.471697\pi$
$992$	5.07047	0.160988
$993$	10.3676	0.329007
$994$	−19.7603	−0.626759
$995$	26.2320	0.831610
$996$	15.3660	0.486892
$997$	−37.6167	−1.19133	−0.595667	−	0.803232i	$-0.703112\pi$
$997$	−37.6167	−1.19133	−0.595667	+	0.803232i	$0.703112\pi$
$998$	9.71936	0.307661
$999$	−11.2304	−0.355313

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.bd.1.4	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.bd.1.4	✓	16	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.44876 q^{5} +1.00000 q^{6} -1.82729 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.44876 q^{5} +1.00000 q^{6} -1.82729 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.44876 q^{10} +0.163827 q^{11} +1.00000 q^{12} -1.00000 q^{13} -1.82729 q^{14} -2.44876 q^{15} +1.00000 q^{16} +6.53476 q^{17} +1.00000 q^{18} +3.88193 q^{19} -2.44876 q^{20} -1.82729 q^{21} +0.163827 q^{22} -0.103683 q^{23} +1.00000 q^{24} +0.996443 q^{25} -1.00000 q^{26} +1.00000 q^{27} -1.82729 q^{28} -7.07183 q^{29} -2.44876 q^{30} +5.07047 q^{31} +1.00000 q^{32} +0.163827 q^{33} +6.53476 q^{34} +4.47459 q^{35} +1.00000 q^{36} -11.2304 q^{37} +3.88193 q^{38} -1.00000 q^{39} -2.44876 q^{40} +1.24437 q^{41} -1.82729 q^{42} -0.424033 q^{43} +0.163827 q^{44} -2.44876 q^{45} -0.103683 q^{46} +7.02979 q^{47} +1.00000 q^{48} -3.66103 q^{49} +0.996443 q^{50} +6.53476 q^{51} -1.00000 q^{52} -5.21386 q^{53} +1.00000 q^{54} -0.401174 q^{55} -1.82729 q^{56} +3.88193 q^{57} -7.07183 q^{58} -7.00193 q^{59} -2.44876 q^{60} +12.6542 q^{61} +5.07047 q^{62} -1.82729 q^{63} +1.00000 q^{64} +2.44876 q^{65} +0.163827 q^{66} +16.1486 q^{67} +6.53476 q^{68} -0.103683 q^{69} +4.47459 q^{70} +10.8140 q^{71} +1.00000 q^{72} +11.1135 q^{73} -11.2304 q^{74} +0.996443 q^{75} +3.88193 q^{76} -0.299359 q^{77} -1.00000 q^{78} -5.61903 q^{79} -2.44876 q^{80} +1.00000 q^{81} +1.24437 q^{82} +15.3660 q^{83} -1.82729 q^{84} -16.0021 q^{85} -0.424033 q^{86} -7.07183 q^{87} +0.163827 q^{88} -14.2700 q^{89} -2.44876 q^{90} +1.82729 q^{91} -0.103683 q^{92} +5.07047 q^{93} +7.02979 q^{94} -9.50592 q^{95} +1.00000 q^{96} +9.39168 q^{97} -3.66103 q^{98} +0.163827 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 5 q^{5} + 16 q^{6} + 4 q^{7} + 16 q^{8} + 16 q^{9}+O(q^{10}) \) 16 * q + 16 * q^2 + 16 * q^3 + 16 * q^4 + 5 * q^5 + 16 * q^6 + 4 * q^7 + 16 * q^8 + 16 * q^9	\( 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 5 q^{5} + 16 q^{6} + 4 q^{7} + 16 q^{8} + 16 q^{9} + 5 q^{10} + 18 q^{11} + 16 q^{12} - 16 q^{13} + 4 q^{14} + 5 q^{15} + 16 q^{16} + 17 q^{17} + 16 q^{18} + 8 q^{19} + 5 q^{20} + 4 q^{21} + 18 q^{22} + 9 q^{23} + 16 q^{24} + 17 q^{25} - 16 q^{26} + 16 q^{27} + 4 q^{28} + 14 q^{29} + 5 q^{30} + 12 q^{31} + 16 q^{32} + 18 q^{33} + 17 q^{34} + 16 q^{35} + 16 q^{36} + 31 q^{37} + 8 q^{38} - 16 q^{39} + 5 q^{40} + 29 q^{41} + 4 q^{42} + 30 q^{43} + 18 q^{44} + 5 q^{45} + 9 q^{46} - q^{47} + 16 q^{48} + 36 q^{49} + 17 q^{50} + 17 q^{51} - 16 q^{52} + 12 q^{53} + 16 q^{54} + 30 q^{55} + 4 q^{56} + 8 q^{57} + 14 q^{58} + 38 q^{59} + 5 q^{60} + 12 q^{62} + 4 q^{63} + 16 q^{64} - 5 q^{65} + 18 q^{66} + 28 q^{67} + 17 q^{68} + 9 q^{69} + 16 q^{70} + 32 q^{71} + 16 q^{72} + 20 q^{73} + 31 q^{74} + 17 q^{75} + 8 q^{76} + 26 q^{77} - 16 q^{78} + 13 q^{79} + 5 q^{80} + 16 q^{81} + 29 q^{82} + 39 q^{83} + 4 q^{84} + 31 q^{85} + 30 q^{86} + 14 q^{87} + 18 q^{88} + 9 q^{89} + 5 q^{90} - 4 q^{91} + 9 q^{92} + 12 q^{93} - q^{94} - 20 q^{95} + 16 q^{96} + 35 q^{97} + 36 q^{98} + 18 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 + 16 * q^3 + 16 * q^4 + 5 * q^5 + 16 * q^6 + 4 * q^7 + 16 * q^8 + 16 * q^9 + 5 * q^10 + 18 * q^11 + 16 * q^12 - 16 * q^13 + 4 * q^14 + 5 * q^15 + 16 * q^16 + 17 * q^17 + 16 * q^18 + 8 * q^19 + 5 * q^20 + 4 * q^21 + 18 * q^22 + 9 * q^23 + 16 * q^24 + 17 * q^25 - 16 * q^26 + 16 * q^27 + 4 * q^28 + 14 * q^29 + 5 * q^30 + 12 * q^31 + 16 * q^32 + 18 * q^33 + 17 * q^34 + 16 * q^35 + 16 * q^36 + 31 * q^37 + 8 * q^38 - 16 * q^39 + 5 * q^40 + 29 * q^41 + 4 * q^42 + 30 * q^43 + 18 * q^44 + 5 * q^45 + 9 * q^46 - q^47 + 16 * q^48 + 36 * q^49 + 17 * q^50 + 17 * q^51 - 16 * q^52 + 12 * q^53 + 16 * q^54 + 30 * q^55 + 4 * q^56 + 8 * q^57 + 14 * q^58 + 38 * q^59 + 5 * q^60 + 12 * q^62 + 4 * q^63 + 16 * q^64 - 5 * q^65 + 18 * q^66 + 28 * q^67 + 17 * q^68 + 9 * q^69 + 16 * q^70 + 32 * q^71 + 16 * q^72 + 20 * q^73 + 31 * q^74 + 17 * q^75 + 8 * q^76 + 26 * q^77 - 16 * q^78 + 13 * q^79 + 5 * q^80 + 16 * q^81 + 29 * q^82 + 39 * q^83 + 4 * q^84 + 31 * q^85 + 30 * q^86 + 14 * q^87 + 18 * q^88 + 9 * q^89 + 5 * q^90 - 4 * q^91 + 9 * q^92 + 12 * q^93 - q^94 - 20 * q^95 + 16 * q^96 + 35 * q^97 + 36 * q^98 + 18 * q^99

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