LMFDB - Embedded newform 8034.2.a.ba.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("8034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.1518129839$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} - 44 x^{12} + 36 x^{11} + 722 x^{10} - 451 x^{9} - 5438 x^{8} + 2268 x^{7} + 18441 x^{6} + \cdots - 1492 $ x^14 - x^13 - 44x^12 + 36x^11 + 722x^10 - 451x^9 - 5438x^8 + 2268x^7 + 18441x^6 - 4126x^5 - 22759x^4 + 2997x^3 + 10504x^2 - 506x - 1492
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			1.1
Root			$4.07159$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.07159 q^{5} +1.00000 q^{6} +2.58120 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.07159 q^{5} +1.00000 q^{6} +2.58120 q^{7} -1.00000 q^{8} +1.00000 q^{9} +4.07159 q^{10} +3.75053 q^{11} -1.00000 q^{12} -1.00000 q^{13} -2.58120 q^{14} +4.07159 q^{15} +1.00000 q^{16} -4.96826 q^{17} -1.00000 q^{18} +3.27578 q^{19} -4.07159 q^{20} -2.58120 q^{21} -3.75053 q^{22} +6.21258 q^{23} +1.00000 q^{24} +11.5778 q^{25} +1.00000 q^{26} -1.00000 q^{27} +2.58120 q^{28} -3.00244 q^{29} -4.07159 q^{30} +0.515556 q^{31} -1.00000 q^{32} -3.75053 q^{33} +4.96826 q^{34} -10.5096 q^{35} +1.00000 q^{36} -0.169601 q^{37} -3.27578 q^{38} +1.00000 q^{39} +4.07159 q^{40} +9.14732 q^{41} +2.58120 q^{42} +5.16760 q^{43} +3.75053 q^{44} -4.07159 q^{45} -6.21258 q^{46} +9.19458 q^{47} -1.00000 q^{48} -0.337386 q^{49} -11.5778 q^{50} +4.96826 q^{51} -1.00000 q^{52} -1.36025 q^{53} +1.00000 q^{54} -15.2706 q^{55} -2.58120 q^{56} -3.27578 q^{57} +3.00244 q^{58} -7.18773 q^{59} +4.07159 q^{60} +8.72968 q^{61} -0.515556 q^{62} +2.58120 q^{63} +1.00000 q^{64} +4.07159 q^{65} +3.75053 q^{66} +5.57898 q^{67} -4.96826 q^{68} -6.21258 q^{69} +10.5096 q^{70} -8.81509 q^{71} -1.00000 q^{72} -6.75816 q^{73} +0.169601 q^{74} -11.5778 q^{75} +3.27578 q^{76} +9.68087 q^{77} -1.00000 q^{78} +11.5740 q^{79} -4.07159 q^{80} +1.00000 q^{81} -9.14732 q^{82} -12.6995 q^{83} -2.58120 q^{84} +20.2287 q^{85} -5.16760 q^{86} +3.00244 q^{87} -3.75053 q^{88} +1.52673 q^{89} +4.07159 q^{90} -2.58120 q^{91} +6.21258 q^{92} -0.515556 q^{93} -9.19458 q^{94} -13.3376 q^{95} +1.00000 q^{96} -1.76201 q^{97} +0.337386 q^{98} +3.75053 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - q^{5} + 14 q^{6} + 5 q^{7} - 14 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - q^5 + 14 * q^6 + 5 * q^7 - 14 * q^8 + 14 * q^9	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - q^{5} + 14 q^{6} + 5 q^{7} - 14 q^{8} + 14 q^{9} + q^{10} - q^{11} - 14 q^{12} - 14 q^{13} - 5 q^{14} + q^{15} + 14 q^{16} - 12 q^{17} - 14 q^{18} + 10 q^{19} - q^{20} - 5 q^{21} + q^{22} - q^{23} + 14 q^{24} + 19 q^{25} + 14 q^{26} - 14 q^{27} + 5 q^{28} + 6 q^{29} - q^{30} + 20 q^{31} - 14 q^{32} + q^{33} + 12 q^{34} - 16 q^{35} + 14 q^{36} - 3 q^{37} - 10 q^{38} + 14 q^{39} + q^{40} + q^{41} + 5 q^{42} + 6 q^{43} - q^{44} - q^{45} + q^{46} - 13 q^{47} - 14 q^{48} + 9 q^{49} - 19 q^{50} + 12 q^{51} - 14 q^{52} - 27 q^{53} + 14 q^{54} + 10 q^{55} - 5 q^{56} - 10 q^{57} - 6 q^{58} - 6 q^{59} + q^{60} - 4 q^{61} - 20 q^{62} + 5 q^{63} + 14 q^{64} + q^{65} - q^{66} + 13 q^{67} - 12 q^{68} + q^{69} + 16 q^{70} + 18 q^{71} - 14 q^{72} + 11 q^{73} + 3 q^{74} - 19 q^{75} + 10 q^{76} - 15 q^{77} - 14 q^{78} + 33 q^{79} - q^{80} + 14 q^{81} - q^{82} - 25 q^{83} - 5 q^{84} + 25 q^{85} - 6 q^{86} - 6 q^{87} + q^{88} + 3 q^{89} + q^{90} - 5 q^{91} - q^{92} - 20 q^{93} + 13 q^{94} + 30 q^{95} + 14 q^{96} + 11 q^{97} - 9 q^{98} - q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - q^5 + 14 * q^6 + 5 * q^7 - 14 * q^8 + 14 * q^9 + q^10 - q^11 - 14 * q^12 - 14 * q^13 - 5 * q^14 + q^15 + 14 * q^16 - 12 * q^17 - 14 * q^18 + 10 * q^19 - q^20 - 5 * q^21 + q^22 - q^23 + 14 * q^24 + 19 * q^25 + 14 * q^26 - 14 * q^27 + 5 * q^28 + 6 * q^29 - q^30 + 20 * q^31 - 14 * q^32 + q^33 + 12 * q^34 - 16 * q^35 + 14 * q^36 - 3 * q^37 - 10 * q^38 + 14 * q^39 + q^40 + q^41 + 5 * q^42 + 6 * q^43 - q^44 - q^45 + q^46 - 13 * q^47 - 14 * q^48 + 9 * q^49 - 19 * q^50 + 12 * q^51 - 14 * q^52 - 27 * q^53 + 14 * q^54 + 10 * q^55 - 5 * q^56 - 10 * q^57 - 6 * q^58 - 6 * q^59 + q^60 - 4 * q^61 - 20 * q^62 + 5 * q^63 + 14 * q^64 + q^65 - q^66 + 13 * q^67 - 12 * q^68 + q^69 + 16 * q^70 + 18 * q^71 - 14 * q^72 + 11 * q^73 + 3 * q^74 - 19 * q^75 + 10 * q^76 - 15 * q^77 - 14 * q^78 + 33 * q^79 - q^80 + 14 * q^81 - q^82 - 25 * q^83 - 5 * q^84 + 25 * q^85 - 6 * q^86 - 6 * q^87 + q^88 + 3 * q^89 + q^90 - 5 * q^91 - q^92 - 20 * q^93 + 13 * q^94 + 30 * q^95 + 14 * q^96 + 11 * q^97 - 9 * q^98 - 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
$5$	−4.07159	−1.82087	−0.910434	−	0.413653i	$-0.864253\pi$
$5$	−4.07159	−1.82087	−0.910434	+	0.413653i	$0.864253\pi$
$6$	1.00000	0.408248
$7$	2.58120	0.975603	0.487802	−	0.872954i	$-0.337799\pi$
$7$	2.58120	0.975603	0.487802	+	0.872954i	$0.337799\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	4.07159	1.28755
$11$	3.75053	1.13083	0.565413	−	0.824808i	$-0.308717\pi$
$11$	3.75053	1.13083	0.565413	+	0.824808i	$0.308717\pi$
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−2.58120	−0.689856
$15$	4.07159	1.05128
$16$	1.00000	0.250000
$17$	−4.96826	−1.20498	−0.602490	−	0.798127i	$-0.705825\pi$
$17$	−4.96826	−1.20498	−0.602490	+	0.798127i	$0.705825\pi$
$18$	−1.00000	−0.235702
$19$	3.27578	0.751516	0.375758	−	0.926718i	$-0.377382\pi$
$19$	3.27578	0.751516	0.375758	+	0.926718i	$0.377382\pi$
$20$	−4.07159	−0.910434
$21$	−2.58120	−0.563265
$22$	−3.75053	−0.799615
$23$	6.21258	1.29541	0.647706	−	0.761890i	$-0.275728\pi$
$23$	6.21258	1.29541	0.647706	+	0.761890i	$0.275728\pi$
$24$	1.00000	0.204124
$25$	11.5778	2.31556
$26$	1.00000	0.196116
$27$	−1.00000	−0.192450
$28$	2.58120	0.487802
$29$	−3.00244	−0.557538	−0.278769	−	0.960358i	$-0.589926\pi$
$29$	−3.00244	−0.557538	−0.278769	+	0.960358i	$0.589926\pi$
$30$	−4.07159	−0.743367
$31$	0.515556	0.0925966	0.0462983	−	0.998928i	$-0.485258\pi$
$31$	0.515556	0.0925966	0.0462983	+	0.998928i	$0.485258\pi$
$32$	−1.00000	−0.176777
$33$	−3.75053	−0.652883
$34$	4.96826	0.852049
$35$	−10.5096	−1.77645
$36$	1.00000	0.166667
$37$	−0.169601	−0.0278822	−0.0139411	−	0.999903i	$-0.504438\pi$
$37$	−0.169601	−0.0278822	−0.0139411	+	0.999903i	$0.504438\pi$
$38$	−3.27578	−0.531402
$39$	1.00000	0.160128
$40$	4.07159	0.643774
$41$	9.14732	1.42857	0.714285	−	0.699854i	$-0.246752\pi$
$41$	9.14732	1.42857	0.714285	+	0.699854i	$0.246752\pi$
$42$	2.58120	0.398288
$43$	5.16760	0.788052	0.394026	−	0.919099i	$-0.371082\pi$
$43$	5.16760	0.788052	0.394026	+	0.919099i	$0.371082\pi$
$44$	3.75053	0.565413
$45$	−4.07159	−0.606956
$46$	−6.21258	−0.915995
$47$	9.19458	1.34117	0.670584	−	0.741834i	$-0.266044\pi$
$47$	9.19458	1.34117	0.670584	+	0.741834i	$0.266044\pi$
$48$	−1.00000	−0.144338
$49$	−0.337386	−0.0481980
$50$	−11.5778	−1.63735
$51$	4.96826	0.695695
$52$	−1.00000	−0.138675
$53$	−1.36025	−0.186845	−0.0934223	−	0.995627i	$-0.529781\pi$
$53$	−1.36025	−0.186845	−0.0934223	+	0.995627i	$0.529781\pi$
$54$	1.00000	0.136083
$55$	−15.2706	−2.05909
$56$	−2.58120	−0.344928
$57$	−3.27578	−0.433888
$58$	3.00244	0.394239
$59$	−7.18773	−0.935763	−0.467881	−	0.883791i	$-0.654983\pi$
$59$	−7.18773	−0.935763	−0.467881	+	0.883791i	$0.654983\pi$
$60$	4.07159	0.525640
$61$	8.72968	1.11772	0.558860	−	0.829262i	$-0.311239\pi$
$61$	8.72968	1.11772	0.558860	+	0.829262i	$0.311239\pi$
$62$	−0.515556	−0.0654757
$63$	2.58120	0.325201
$64$	1.00000	0.125000
$65$	4.07159	0.505018
$66$	3.75053	0.461658
$67$	5.57898	0.681581	0.340790	−	0.940139i	$-0.389305\pi$
$67$	5.57898	0.681581	0.340790	+	0.940139i	$0.389305\pi$
$68$	−4.96826	−0.602490
$69$	−6.21258	−0.747907
$70$	10.5096	1.25614
$71$	−8.81509	−1.04616	−0.523079	−	0.852284i	$-0.675217\pi$
$71$	−8.81509	−1.04616	−0.523079	+	0.852284i	$0.675217\pi$
$72$	−1.00000	−0.117851
$73$	−6.75816	−0.790983	−0.395491	−	0.918470i	$-0.629426\pi$
$73$	−6.75816	−0.790983	−0.395491	+	0.918470i	$0.629426\pi$
$74$	0.169601	0.0197157
$75$	−11.5778	−1.33689
$76$	3.27578	0.375758
$77$	9.68087	1.10324
$78$	−1.00000	−0.113228
$79$	11.5740	1.30218	0.651089	−	0.759001i	$-0.274312\pi$
$79$	11.5740	1.30218	0.651089	+	0.759001i	$0.274312\pi$
$80$	−4.07159	−0.455217
$81$	1.00000	0.111111
$82$	−9.14732	−1.01015
$83$	−12.6995	−1.39395	−0.696975	−	0.717096i	$-0.745471\pi$
$83$	−12.6995	−1.39395	−0.696975	+	0.717096i	$0.745471\pi$
$84$	−2.58120	−0.281632
$85$	20.2287	2.19411
$86$	−5.16760	−0.557237
$87$	3.00244	0.321895
$88$	−3.75053	−0.399807
$89$	1.52673	0.161833	0.0809165	−	0.996721i	$-0.474215\pi$
$89$	1.52673	0.161833	0.0809165	+	0.996721i	$0.474215\pi$
$90$	4.07159	0.429183
$91$	−2.58120	−0.270584
$92$	6.21258	0.647706
$93$	−0.515556	−0.0534607
$94$	−9.19458	−0.948349
$95$	−13.3376	−1.36841
$96$	1.00000	0.102062
$97$	−1.76201	−0.178905	−0.0894524	−	0.995991i	$-0.528512\pi$
$97$	−1.76201	−0.178905	−0.0894524	+	0.995991i	$0.528512\pi$
$98$	0.337386	0.0340811
$99$	3.75053	0.376942
$100$	11.5778	1.15778
$101$	−9.92757	−0.987830	−0.493915	−	0.869510i	$-0.664435\pi$
$101$	−9.92757	−0.987830	−0.493915	+	0.869510i	$0.664435\pi$
$102$	−4.96826	−0.491931
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	1.00000	0.0980581
$105$	10.5096	1.02563
$106$	1.36025	0.132119
$107$	−12.6827	−1.22608	−0.613041	−	0.790051i	$-0.710054\pi$
$107$	−12.6827	−1.22608	−0.613041	+	0.790051i	$0.710054\pi$
$108$	−1.00000	−0.0962250
$109$	6.63187	0.635218	0.317609	−	0.948222i	$-0.397120\pi$
$109$	6.63187	0.635218	0.317609	+	0.948222i	$0.397120\pi$
$110$	15.2706	1.45599
$111$	0.169601	0.0160978
$112$	2.58120	0.243901
$113$	16.1053	1.51506	0.757528	−	0.652802i	$-0.226407\pi$
$113$	16.1053	1.51506	0.757528	+	0.652802i	$0.226407\pi$
$114$	3.27578	0.306805
$115$	−25.2951	−2.35878
$116$	−3.00244	−0.278769
$117$	−1.00000	−0.0924500
$118$	7.18773	0.661684
$119$	−12.8241	−1.17558
$120$	−4.07159	−0.371683
$121$	3.06644	0.278767
$122$	−8.72968	−0.790348
$123$	−9.14732	−0.824786
$124$	0.515556	0.0462983
$125$	−26.7822	−2.39547
$126$	−2.58120	−0.229952
$127$	14.4538	1.28257	0.641283	−	0.767305i	$-0.278403\pi$
$127$	14.4538	1.28257	0.641283	+	0.767305i	$0.278403\pi$
$128$	−1.00000	−0.0883883
$129$	−5.16760	−0.454982
$130$	−4.07159	−0.357102
$131$	7.73157	0.675511	0.337755	−	0.941234i	$-0.390332\pi$
$131$	7.73157	0.675511	0.337755	+	0.941234i	$0.390332\pi$
$132$	−3.75053	−0.326441
$133$	8.45546	0.733181
$134$	−5.57898	−0.481950
$135$	4.07159	0.350426
$136$	4.96826	0.426024
$137$	9.54400	0.815399	0.407699	−	0.913116i	$-0.366331\pi$
$137$	9.54400	0.815399	0.407699	+	0.913116i	$0.366331\pi$
$138$	6.21258	0.528850
$139$	−8.60003	−0.729445	−0.364722	−	0.931116i	$-0.618836\pi$
$139$	−8.60003	−0.729445	−0.364722	+	0.931116i	$0.618836\pi$
$140$	−10.5096	−0.888223
$141$	−9.19458	−0.774323
$142$	8.81509	0.739746
$143$	−3.75053	−0.313635
$144$	1.00000	0.0833333
$145$	12.2247	1.01520
$146$	6.75816	0.559309
$147$	0.337386	0.0278271
$148$	−0.169601	−0.0139411
$149$	12.1260	0.993402	0.496701	−	0.867922i	$-0.334545\pi$
$149$	12.1260	0.993402	0.496701	+	0.867922i	$0.334545\pi$
$150$	11.5778	0.945325
$151$	−9.15082	−0.744683	−0.372341	−	0.928096i	$-0.621445\pi$
$151$	−9.15082	−0.744683	−0.372341	+	0.928096i	$0.621445\pi$
$152$	−3.27578	−0.265701
$153$	−4.96826	−0.401660
$154$	−9.68087	−0.780107
$155$	−2.09913	−0.168606
$156$	1.00000	0.0800641
$157$	7.49283	0.597993	0.298997	−	0.954254i	$-0.403348\pi$
$157$	7.49283	0.597993	0.298997	+	0.954254i	$0.403348\pi$
$158$	−11.5740	−0.920779
$159$	1.36025	0.107875
$160$	4.07159	0.321887
$161$	16.0359	1.26381
$162$	−1.00000	−0.0785674
$163$	−24.8572	−1.94696	−0.973482	−	0.228762i	$-0.926532\pi$
$163$	−24.8572	−1.94696	−0.973482	+	0.228762i	$0.926532\pi$
$164$	9.14732	0.714285
$165$	15.2706	1.18881
$166$	12.6995	0.985671
$167$	−24.7241	−1.91321	−0.956606	−	0.291385i	$-0.905884\pi$
$167$	−24.7241	−1.91321	−0.956606	+	0.291385i	$0.905884\pi$
$168$	2.58120	0.199144
$169$	1.00000	0.0769231
$170$	−20.2287	−1.55147
$171$	3.27578	0.250505
$172$	5.16760	0.394026
$173$	−4.49671	−0.341878	−0.170939	−	0.985282i	$-0.554680\pi$
$173$	−4.49671	−0.341878	−0.170939	+	0.985282i	$0.554680\pi$
$174$	−3.00244	−0.227614
$175$	29.8847	2.25907
$176$	3.75053	0.282707
$177$	7.18773	0.540263
$178$	−1.52673	−0.114433
$179$	−0.474184	−0.0354421	−0.0177211	−	0.999843i	$-0.505641\pi$
$179$	−0.474184	−0.0354421	−0.0177211	+	0.999843i	$0.505641\pi$
$180$	−4.07159	−0.303478
$181$	−6.40924	−0.476395	−0.238198	−	0.971217i	$-0.576557\pi$
$181$	−6.40924	−0.476395	−0.238198	+	0.971217i	$0.576557\pi$
$182$	2.58120	0.191332
$183$	−8.72968	−0.645316
$184$	−6.21258	−0.457997
$185$	0.690546	0.0507699
$186$	0.515556	0.0378024
$187$	−18.6336	−1.36262
$188$	9.19458	0.670584
$189$	−2.58120	−0.187755
$190$	13.3376	0.967613
$191$	−14.6130	−1.05736	−0.528681	−	0.848820i	$-0.677313\pi$
$191$	−14.6130	−1.05736	−0.528681	+	0.848820i	$0.677313\pi$
$192$	−1.00000	−0.0721688
$193$	−9.13430	−0.657501	−0.328751	−	0.944417i	$-0.606628\pi$
$193$	−9.13430	−0.657501	−0.328751	+	0.944417i	$0.606628\pi$
$194$	1.76201	0.126505
$195$	−4.07159	−0.291572
$196$	−0.337386	−0.0240990
$197$	−20.0325	−1.42726	−0.713629	−	0.700524i	$-0.752950\pi$
$197$	−20.0325	−1.42726	−0.713629	+	0.700524i	$0.752950\pi$
$198$	−3.75053	−0.266538
$199$	1.01631	0.0720440	0.0360220	−	0.999351i	$-0.488531\pi$
$199$	1.01631	0.0720440	0.0360220	+	0.999351i	$0.488531\pi$
$200$	−11.5778	−0.818675
$201$	−5.57898	−0.393511
$202$	9.92757	0.698501
$203$	−7.74990	−0.543936
$204$	4.96826	0.347848
$205$	−37.2441	−2.60124
$206$	−1.00000	−0.0696733
$207$	6.21258	0.431804
$208$	−1.00000	−0.0693375
$209$	12.2859	0.849834
$210$	−10.5096	−0.725231
$211$	17.7043	1.21882	0.609408	−	0.792857i	$-0.291407\pi$
$211$	17.7043	1.21882	0.609408	+	0.792857i	$0.291407\pi$
$212$	−1.36025	−0.0934223
$213$	8.81509	0.604000
$214$	12.6827	0.866970
$215$	−21.0403	−1.43494
$216$	1.00000	0.0680414
$217$	1.33076	0.0903376
$218$	−6.63187	−0.449167
$219$	6.75816	0.456674
$220$	−15.2706	−1.02954
$221$	4.96826	0.334201
$222$	−0.169601	−0.0113829
$223$	23.8931	1.60000	0.799999	−	0.600002i	$-0.204833\pi$
$223$	23.8931	1.60000	0.799999	+	0.600002i	$0.204833\pi$
$224$	−2.58120	−0.172464
$225$	11.5778	0.771854
$226$	−16.1053	−1.07131
$227$	11.5062	0.763692	0.381846	−	0.924226i	$-0.375288\pi$
$227$	11.5062	0.763692	0.381846	+	0.924226i	$0.375288\pi$
$228$	−3.27578	−0.216944
$229$	−5.01532	−0.331422	−0.165711	−	0.986174i	$-0.552992\pi$
$229$	−5.01532	−0.331422	−0.165711	+	0.986174i	$0.552992\pi$
$230$	25.2951	1.66791
$231$	−9.68087	−0.636955
$232$	3.00244	0.197120
$233$	25.1837	1.64984	0.824921	−	0.565249i	$-0.191220\pi$
$233$	25.1837	1.64984	0.824921	+	0.565249i	$0.191220\pi$
$234$	1.00000	0.0653720
$235$	−37.4365	−2.44209
$236$	−7.18773	−0.467881
$237$	−11.5740	−0.751813
$238$	12.8241	0.831262
$239$	8.78476	0.568239	0.284119	−	0.958789i	$-0.408299\pi$
$239$	8.78476	0.568239	0.284119	+	0.958789i	$0.408299\pi$
$240$	4.07159	0.262820
$241$	5.11482	0.329475	0.164737	−	0.986337i	$-0.447322\pi$
$241$	5.11482	0.329475	0.164737	+	0.986337i	$0.447322\pi$
$242$	−3.06644	−0.197118
$243$	−1.00000	−0.0641500
$244$	8.72968	0.558860
$245$	1.37370	0.0877622
$246$	9.14732	0.583212
$247$	−3.27578	−0.208433
$248$	−0.515556	−0.0327378
$249$	12.6995	0.804797
$250$	26.7822	1.69385
$251$	−2.96547	−0.187179	−0.0935895	−	0.995611i	$-0.529834\pi$
$251$	−2.96547	−0.187179	−0.0935895	+	0.995611i	$0.529834\pi$
$252$	2.58120	0.162601
$253$	23.3004	1.46489
$254$	−14.4538	−0.906911
$255$	−20.2287	−1.26677
$256$	1.00000	0.0625000
$257$	−19.7234	−1.23031	−0.615156	−	0.788406i	$-0.710907\pi$
$257$	−19.7234	−1.23031	−0.615156	+	0.788406i	$0.710907\pi$
$258$	5.16760	0.321721
$259$	−0.437775	−0.0272020
$260$	4.07159	0.252509
$261$	−3.00244	−0.185846
$262$	−7.73157	−0.477658
$263$	−27.6687	−1.70613	−0.853063	−	0.521809i	$-0.825258\pi$
$263$	−27.6687	−1.70613	−0.853063	+	0.521809i	$0.825258\pi$
$264$	3.75053	0.230829
$265$	5.53838	0.340220
$266$	−8.45546	−0.518438
$267$	−1.52673	−0.0934343
$268$	5.57898	0.340790
$269$	−7.45176	−0.454342	−0.227171	−	0.973855i	$-0.572948\pi$
$269$	−7.45176	−0.454342	−0.227171	+	0.973855i	$0.572948\pi$
$270$	−4.07159	−0.247789
$271$	−1.58452	−0.0962527	−0.0481264	−	0.998841i	$-0.515325\pi$
$271$	−1.58452	−0.0962527	−0.0481264	+	0.998841i	$0.515325\pi$
$272$	−4.96826	−0.301245
$273$	2.58120	0.156222
$274$	−9.54400	−0.576574
$275$	43.4229	2.61850
$276$	−6.21258	−0.373953
$277$	1.30007	0.0781135	0.0390568	−	0.999237i	$-0.487565\pi$
$277$	1.30007	0.0781135	0.0390568	+	0.999237i	$0.487565\pi$
$278$	8.60003	0.515795
$279$	0.515556	0.0308655
$280$	10.5096	0.628068
$281$	13.8619	0.826934	0.413467	−	0.910519i	$-0.364318\pi$
$281$	13.8619	0.826934	0.413467	+	0.910519i	$0.364318\pi$
$282$	9.19458	0.547529
$283$	−23.0435	−1.36979	−0.684897	−	0.728639i	$-0.740153\pi$
$283$	−23.0435	−1.36979	−0.684897	+	0.728639i	$0.740153\pi$
$284$	−8.81509	−0.523079
$285$	13.3376	0.790053
$286$	3.75053	0.221773
$287$	23.6111	1.39372
$288$	−1.00000	−0.0589256
$289$	7.68357	0.451975
$290$	−12.2247	−0.717858
$291$	1.76201	0.103291
$292$	−6.75816	−0.395491
$293$	−8.97969	−0.524599	−0.262300	−	0.964986i	$-0.584481\pi$
$293$	−8.97969	−0.524599	−0.262300	+	0.964986i	$0.584481\pi$
$294$	−0.337386	−0.0196767
$295$	29.2655	1.70390
$296$	0.169601	0.00985786
$297$	−3.75053	−0.217628
$298$	−12.1260	−0.702441
$299$	−6.21258	−0.359283
$300$	−11.5778	−0.668446
$301$	13.3386	0.768826
$302$	9.15082	0.526570
$303$	9.92757	0.570324
$304$	3.27578	0.187879
$305$	−35.5436	−2.03522
$306$	4.96826	0.284016
$307$	6.96717	0.397637	0.198819	−	0.980036i	$-0.436290\pi$
$307$	6.96717	0.397637	0.198819	+	0.980036i	$0.436290\pi$
$308$	9.68087	0.551619
$309$	−1.00000	−0.0568880
$310$	2.09913	0.119223
$311$	12.9719	0.735570	0.367785	−	0.929911i	$-0.380116\pi$
$311$	12.9719	0.735570	0.367785	+	0.929911i	$0.380116\pi$
$312$	−1.00000	−0.0566139
$313$	−5.37301	−0.303700	−0.151850	−	0.988404i	$-0.548523\pi$
$313$	−5.37301	−0.303700	−0.151850	+	0.988404i	$0.548523\pi$
$314$	−7.49283	−0.422845
$315$	−10.5096	−0.592149
$316$	11.5740	0.651089
$317$	6.85531	0.385032	0.192516	−	0.981294i	$-0.438335\pi$
$317$	6.85531	0.385032	0.192516	+	0.981294i	$0.438335\pi$
$318$	−1.36025	−0.0762790
$319$	−11.2607	−0.630479
$320$	−4.07159	−0.227609
$321$	12.6827	0.707878
$322$	−16.0359	−0.893648
$323$	−16.2749	−0.905561
$324$	1.00000	0.0555556
$325$	−11.5778	−0.642222
$326$	24.8572	1.37671
$327$	−6.63187	−0.366743
$328$	−9.14732	−0.505076
$329$	23.7331	1.30845
$330$	−15.2706	−0.840618
$331$	28.8357	1.58495	0.792477	−	0.609902i	$-0.208791\pi$
$331$	28.8357	1.58495	0.792477	+	0.609902i	$0.208791\pi$
$332$	−12.6995	−0.696975
$333$	−0.169601	−0.00929408
$334$	24.7241	1.35284
$335$	−22.7153	−1.24107
$336$	−2.58120	−0.140816
$337$	−30.7712	−1.67621	−0.838106	−	0.545507i	$-0.816337\pi$
$337$	−30.7712	−1.67621	−0.838106	+	0.545507i	$0.816337\pi$
$338$	−1.00000	−0.0543928
$339$	−16.1053	−0.874718
$340$	20.2287	1.09705
$341$	1.93361	0.104711
$342$	−3.27578	−0.177134
$343$	−18.9393	−1.02263
$344$	−5.16760	−0.278619
$345$	25.2951	1.36184
$346$	4.49671	0.241744
$347$	37.0016	1.98635	0.993175	−	0.116637i	$-0.0372115\pi$
$347$	37.0016	1.98635	0.993175	+	0.116637i	$0.0372115\pi$
$348$	3.00244	0.160947
$349$	19.4923	1.04340	0.521700	−	0.853129i	$-0.325298\pi$
$349$	19.4923	1.04340	0.521700	+	0.853129i	$0.325298\pi$
$350$	−29.8847	−1.59740
$351$	1.00000	0.0533761
$352$	−3.75053	−0.199904
$353$	19.9930	1.06412	0.532061	−	0.846706i	$-0.321418\pi$
$353$	19.9930	1.06412	0.532061	+	0.846706i	$0.321418\pi$
$354$	−7.18773	−0.382023
$355$	35.8914	1.90492
$356$	1.52673	0.0809165
$357$	12.8241	0.678722
$358$	0.474184	0.0250614
$359$	−16.0667	−0.847970	−0.423985	−	0.905669i	$-0.639369\pi$
$359$	−16.0667	−0.847970	−0.423985	+	0.905669i	$0.639369\pi$
$360$	4.07159	0.214591
$361$	−8.26925	−0.435224
$362$	6.40924	0.336862
$363$	−3.06644	−0.160946
$364$	−2.58120	−0.135292
$365$	27.5164	1.44028
$366$	8.72968	0.456307
$367$	24.4433	1.27593	0.637964	−	0.770066i	$-0.279777\pi$
$367$	24.4433	1.27593	0.637964	+	0.770066i	$0.279777\pi$
$368$	6.21258	0.323853
$369$	9.14732	0.476190
$370$	−0.690546	−0.0358998
$371$	−3.51108	−0.182286
$372$	−0.515556	−0.0267303
$373$	10.1846	0.527338	0.263669	−	0.964613i	$-0.415067\pi$
$373$	10.1846	0.527338	0.263669	+	0.964613i	$0.415067\pi$
$374$	18.6336	0.963519
$375$	26.7822	1.38302
$376$	−9.19458	−0.474174
$377$	3.00244	0.154633
$378$	2.58120	0.132763
$379$	35.1348	1.80475	0.902376	−	0.430950i	$-0.141822\pi$
$379$	35.1348	1.80475	0.902376	+	0.430950i	$0.141822\pi$
$380$	−13.3376	−0.684206
$381$	−14.4538	−0.740490
$382$	14.6130	0.747668
$383$	−4.80554	−0.245552	−0.122776	−	0.992434i	$-0.539180\pi$
$383$	−4.80554	−0.245552	−0.122776	+	0.992434i	$0.539180\pi$
$384$	1.00000	0.0510310
$385$	−39.4165	−2.00885
$386$	9.13430	0.464924
$387$	5.16760	0.262684
$388$	−1.76201	−0.0894524
$389$	11.0101	0.558236	0.279118	−	0.960257i	$-0.409958\pi$
$389$	11.0101	0.558236	0.279118	+	0.960257i	$0.409958\pi$
$390$	4.07159	0.206173
$391$	−30.8657	−1.56094
$392$	0.337386	0.0170406
$393$	−7.73157	−0.390006
$394$	20.0325	1.00922
$395$	−47.1246	−2.37110
$396$	3.75053	0.188471
$397$	35.9964	1.80661	0.903303	−	0.429004i	$-0.141135\pi$
$397$	35.9964	1.80661	0.903303	+	0.429004i	$0.141135\pi$
$398$	−1.01631	−0.0509428
$399$	−8.45546	−0.423303
$400$	11.5778	0.578891
$401$	26.5560	1.32614	0.663071	−	0.748557i	$-0.269253\pi$
$401$	26.5560	1.32614	0.663071	+	0.748557i	$0.269253\pi$
$402$	5.57898	0.278254
$403$	−0.515556	−0.0256817
$404$	−9.92757	−0.493915
$405$	−4.07159	−0.202319
$406$	7.74990	0.384621
$407$	−0.636093	−0.0315300
$408$	−4.96826	−0.245965
$409$	13.5214	0.668592	0.334296	−	0.942468i	$-0.391501\pi$
$409$	13.5214	0.668592	0.334296	+	0.942468i	$0.391501\pi$
$410$	37.2441	1.83935
$411$	−9.54400	−0.470771
$412$	1.00000	0.0492665
$413$	−18.5530	−0.912933
$414$	−6.21258	−0.305332
$415$	51.7071	2.53820
$416$	1.00000	0.0490290
$417$	8.60003	0.421145
$418$	−12.2859	−0.600923
$419$	−3.26115	−0.159318	−0.0796588	−	0.996822i	$-0.525383\pi$
$419$	−3.26115	−0.159318	−0.0796588	+	0.996822i	$0.525383\pi$
$420$	10.5096	0.512816
$421$	10.8036	0.526536	0.263268	−	0.964723i	$-0.415200\pi$
$421$	10.8036	0.526536	0.263268	+	0.964723i	$0.415200\pi$
$422$	−17.7043	−0.861834
$423$	9.19458	0.447056
$424$	1.36025	0.0660596
$425$	−57.5216	−2.79021
$426$	−8.81509	−0.427093
$427$	22.5331	1.09045
$428$	−12.6827	−0.613041
$429$	3.75053	0.181077
$430$	21.0403	1.01466
$431$	9.42187	0.453836	0.226918	−	0.973914i	$-0.427135\pi$
$431$	9.42187	0.453836	0.226918	+	0.973914i	$0.427135\pi$
$432$	−1.00000	−0.0481125
$433$	−14.6310	−0.703121	−0.351560	−	0.936165i	$-0.614349\pi$
$433$	−14.6310	−0.703121	−0.351560	+	0.936165i	$0.614349\pi$
$434$	−1.33076	−0.0638783
$435$	−12.2247	−0.586129
$436$	6.63187	0.317609
$437$	20.3511	0.973523
$438$	−6.75816	−0.322917
$439$	0.578539	0.0276122	0.0138061	−	0.999905i	$-0.495605\pi$
$439$	0.578539	0.0276122	0.0138061	+	0.999905i	$0.495605\pi$
$440$	15.2706	0.727997
$441$	−0.337386	−0.0160660
$442$	−4.96826	−0.236316
$443$	−16.9554	−0.805575	−0.402787	−	0.915294i	$-0.631959\pi$
$443$	−16.9554	−0.805575	−0.402787	+	0.915294i	$0.631959\pi$
$444$	0.169601	0.00804891
$445$	−6.21621	−0.294677
$446$	−23.8931	−1.13137
$447$	−12.1260	−0.573541
$448$	2.58120	0.121950
$449$	16.6918	0.787735	0.393867	−	0.919167i	$-0.371137\pi$
$449$	16.6918	0.787735	0.393867	+	0.919167i	$0.371137\pi$
$450$	−11.5778	−0.545784
$451$	34.3072	1.61547
$452$	16.1053	0.757528
$453$	9.15082	0.429943
$454$	−11.5062	−0.540012
$455$	10.5096	0.492697
$456$	3.27578	0.153403
$457$	−0.498348	−0.0233117	−0.0116559	−	0.999932i	$-0.503710\pi$
$457$	−0.498348	−0.0233117	−0.0116559	+	0.999932i	$0.503710\pi$
$458$	5.01532	0.234350
$459$	4.96826	0.231898
$460$	−25.2951	−1.17939
$461$	2.29262	0.106778	0.0533889	−	0.998574i	$-0.482998\pi$
$461$	2.29262	0.106778	0.0533889	+	0.998574i	$0.482998\pi$
$462$	9.68087	0.450395
$463$	7.76040	0.360657	0.180328	−	0.983606i	$-0.442284\pi$
$463$	7.76040	0.360657	0.180328	+	0.983606i	$0.442284\pi$
$464$	−3.00244	−0.139385
$465$	2.09913	0.0973449
$466$	−25.1837	−1.16661
$467$	−35.3243	−1.63461	−0.817307	−	0.576202i	$-0.804534\pi$
$467$	−35.3243	−1.63461	−0.817307	+	0.576202i	$0.804534\pi$
$468$	−1.00000	−0.0462250
$469$	14.4005	0.664953
$470$	37.4365	1.72682
$471$	−7.49283	−0.345252
$472$	7.18773	0.330842
$473$	19.3812	0.891150
$474$	11.5740	0.531612
$475$	37.9264	1.74018
$476$	−12.8241	−0.587791
$477$	−1.36025	−0.0622816
$478$	−8.78476	−0.401805
$479$	37.0768	1.69408	0.847042	−	0.531526i	$-0.178381\pi$
$479$	37.0768	1.69408	0.847042	+	0.531526i	$0.178381\pi$
$480$	−4.07159	−0.185842
$481$	0.169601	0.00773314
$482$	−5.11482	−0.232974
$483$	−16.0359	−0.729660
$484$	3.06644	0.139384
$485$	7.17417	0.325762
$486$	1.00000	0.0453609
$487$	14.8710	0.673868	0.336934	−	0.941528i	$-0.390610\pi$
$487$	14.8710	0.673868	0.336934	+	0.941528i	$0.390610\pi$
$488$	−8.72968	−0.395174
$489$	24.8572	1.12408
$490$	−1.37370	−0.0620572
$491$	16.8665	0.761176	0.380588	−	0.924745i	$-0.375722\pi$
$491$	16.8665	0.761176	0.380588	+	0.924745i	$0.375722\pi$
$492$	−9.14732	−0.412393
$493$	14.9169	0.671822
$494$	3.27578	0.147384
$495$	−15.2706	−0.686362
$496$	0.515556	0.0231491
$497$	−22.7536	−1.02064
$498$	−12.6995	−0.569078
$499$	16.9371	0.758210	0.379105	−	0.925354i	$-0.376232\pi$
$499$	16.9371	0.758210	0.379105	+	0.925354i	$0.376232\pi$
$500$	−26.7822	−1.19773
$501$	24.7241	1.10459
$502$	2.96547	0.132356
$503$	24.5868	1.09627	0.548135	−	0.836390i	$-0.315338\pi$
$503$	24.5868	1.09627	0.548135	+	0.836390i	$0.315338\pi$
$504$	−2.58120	−0.114976
$505$	40.4209	1.79871
$506$	−23.3004	−1.03583
$507$	−1.00000	−0.0444116
$508$	14.4538	0.641283
$509$	27.8995	1.23662	0.618311	−	0.785934i	$-0.287817\pi$
$509$	27.8995	1.23662	0.618311	+	0.785934i	$0.287817\pi$
$510$	20.2287	0.895741
$511$	−17.4442	−0.771685
$512$	−1.00000	−0.0441942
$513$	−3.27578	−0.144629
$514$	19.7234	0.869962
$515$	−4.07159	−0.179416
$516$	−5.16760	−0.227491
$517$	34.4845	1.51663
$518$	0.437775	0.0192347
$519$	4.49671	0.197383
$520$	−4.07159	−0.178551
$521$	21.3868	0.936974	0.468487	−	0.883470i	$-0.344799\pi$
$521$	21.3868	0.936974	0.468487	+	0.883470i	$0.344799\pi$
$522$	3.00244	0.131413
$523$	−19.9409	−0.871956	−0.435978	−	0.899957i	$-0.643597\pi$
$523$	−19.9409	−0.871956	−0.435978	+	0.899957i	$0.643597\pi$
$524$	7.73157	0.337755
$525$	−29.8847	−1.30428
$526$	27.6687	1.20641
$527$	−2.56141	−0.111577
$528$	−3.75053	−0.163221
$529$	15.5961	0.678093
$530$	−5.53838	−0.240572
$531$	−7.18773	−0.311921
$532$	8.45546	0.366591
$533$	−9.14732	−0.396214
$534$	1.52673	0.0660681
$535$	51.6386	2.23253
$536$	−5.57898	−0.240975
$537$	0.474184	0.0204625
$538$	7.45176	0.321268
$539$	−1.26537	−0.0545035
$540$	4.07159	0.175213
$541$	−12.8726	−0.553437	−0.276719	−	0.960951i	$-0.589247\pi$
$541$	−12.8726	−0.553437	−0.276719	+	0.960951i	$0.589247\pi$
$542$	1.58452	0.0680610
$543$	6.40924	0.275047
$544$	4.96826	0.213012
$545$	−27.0022	−1.15665
$546$	−2.58120	−0.110465
$547$	−3.66737	−0.156806	−0.0784028	−	0.996922i	$-0.524982\pi$
$547$	−3.66737	−0.156806	−0.0784028	+	0.996922i	$0.524982\pi$
$548$	9.54400	0.407699
$549$	8.72968	0.372573
$550$	−43.4229	−1.85156
$551$	−9.83533	−0.418999
$552$	6.21258	0.264425
$553$	29.8749	1.27041
$554$	−1.30007	−0.0552346
$555$	−0.690546	−0.0293120
$556$	−8.60003	−0.364722
$557$	40.3235	1.70856	0.854280	−	0.519813i	$-0.173998\pi$
$557$	40.3235	1.70856	0.854280	+	0.519813i	$0.173998\pi$
$558$	−0.515556	−0.0218252
$559$	−5.16760	−0.218566
$560$	−10.5096	−0.444111
$561$	18.6336	0.786710
$562$	−13.8619	−0.584731
$563$	14.1289	0.595462	0.297731	−	0.954650i	$-0.403770\pi$
$563$	14.1289	0.595462	0.297731	+	0.954650i	$0.403770\pi$
$564$	−9.19458	−0.387162
$565$	−65.5740	−2.75872
$566$	23.0435	0.968591
$567$	2.58120	0.108400
$568$	8.81509	0.369873
$569$	36.8899	1.54651	0.773253	−	0.634097i	$-0.218628\pi$
$569$	36.8899	1.54651	0.773253	+	0.634097i	$0.218628\pi$
$570$	−13.3376	−0.558652
$571$	−18.4187	−0.770797	−0.385399	−	0.922750i	$-0.625936\pi$
$571$	−18.4187	−0.770797	−0.385399	+	0.922750i	$0.625936\pi$
$572$	−3.75053	−0.156817
$573$	14.6130	0.610469
$574$	−23.6111	−0.985508
$575$	71.9281	2.99961
$576$	1.00000	0.0416667
$577$	2.14056	0.0891128	0.0445564	−	0.999007i	$-0.485813\pi$
$577$	2.14056	0.0891128	0.0445564	+	0.999007i	$0.485813\pi$
$578$	−7.68357	−0.319595
$579$	9.13430	0.379608
$580$	12.2247	0.507602
$581$	−32.7800	−1.35994
$582$	−1.76201	−0.0730376
$583$	−5.10165	−0.211289
$584$	6.75816	0.279655
$585$	4.07159	0.168339
$586$	8.97969	0.370948
$587$	−20.2440	−0.835559	−0.417780	−	0.908548i	$-0.637192\pi$
$587$	−20.2440	−0.835559	−0.417780	+	0.908548i	$0.637192\pi$
$588$	0.337386	0.0139136
$589$	1.68885	0.0695878
$590$	−29.2655	−1.20484
$591$	20.0325	0.824028
$592$	−0.169601	−0.00697056
$593$	17.7664	0.729580	0.364790	−	0.931090i	$-0.381141\pi$
$593$	17.7664	0.729580	0.364790	+	0.931090i	$0.381141\pi$
$594$	3.75053	0.153886
$595$	52.2144	2.14058
$596$	12.1260	0.496701
$597$	−1.01631	−0.0415946
$598$	6.21258	0.254051
$599$	13.4618	0.550035	0.275018	−	0.961439i	$-0.411316\pi$
$599$	13.4618	0.550035	0.275018	+	0.961439i	$0.411316\pi$
$600$	11.5778	0.472662
$601$	−10.8488	−0.442531	−0.221266	−	0.975214i	$-0.571019\pi$
$601$	−10.8488	−0.442531	−0.221266	+	0.975214i	$0.571019\pi$
$602$	−13.3386	−0.543642
$603$	5.57898	0.227194
$604$	−9.15082	−0.372341
$605$	−12.4853	−0.507599
$606$	−9.92757	−0.403280
$607$	23.0492	0.935539	0.467770	−	0.883850i	$-0.345058\pi$
$607$	23.0492	0.935539	0.467770	+	0.883850i	$0.345058\pi$
$608$	−3.27578	−0.132850
$609$	7.74990	0.314042
$610$	35.5436	1.43912
$611$	−9.19458	−0.371973
$612$	−4.96826	−0.200830
$613$	−1.28093	−0.0517362	−0.0258681	−	0.999665i	$-0.508235\pi$
$613$	−1.28093	−0.0517362	−0.0258681	+	0.999665i	$0.508235\pi$
$614$	−6.96717	−0.281172
$615$	37.2441	1.50183
$616$	−9.68087	−0.390053
$617$	17.0369	0.685881	0.342941	−	0.939357i	$-0.388577\pi$
$617$	17.0369	0.685881	0.342941	+	0.939357i	$0.388577\pi$
$618$	1.00000	0.0402259
$619$	−1.79480	−0.0721390	−0.0360695	−	0.999349i	$-0.511484\pi$
$619$	−1.79480	−0.0721390	−0.0360695	+	0.999349i	$0.511484\pi$
$620$	−2.09913	−0.0843031
$621$	−6.21258	−0.249302
$622$	−12.9719	−0.520127
$623$	3.94080	0.157885
$624$	1.00000	0.0400320
$625$	51.1568	2.04627
$626$	5.37301	0.214749
$627$	−12.2859	−0.490652
$628$	7.49283	0.298997
$629$	0.842622	0.0335975
$630$	10.5096	0.418712
$631$	39.1444	1.55831	0.779157	−	0.626829i	$-0.215648\pi$
$631$	39.1444	1.55831	0.779157	+	0.626829i	$0.215648\pi$
$632$	−11.5740	−0.460390
$633$	−17.7043	−0.703684
$634$	−6.85531	−0.272259
$635$	−58.8498	−2.33538
$636$	1.36025	0.0539374
$637$	0.337386	0.0133677
$638$	11.2607	0.445816
$639$	−8.81509	−0.348720
$640$	4.07159	0.160944
$641$	−3.41253	−0.134787	−0.0673934	−	0.997726i	$-0.521468\pi$
$641$	−3.41253	−0.134787	−0.0673934	+	0.997726i	$0.521468\pi$
$642$	−12.6827	−0.500546
$643$	−31.8411	−1.25569	−0.627845	−	0.778338i	$-0.716063\pi$
$643$	−31.8411	−1.25569	−0.627845	+	0.778338i	$0.716063\pi$
$644$	16.0359	0.631904
$645$	21.0403	0.828463
$646$	16.2749	0.640328
$647$	−1.53527	−0.0603576	−0.0301788	−	0.999545i	$-0.509608\pi$
$647$	−1.53527	−0.0603576	−0.0301788	+	0.999545i	$0.509608\pi$
$648$	−1.00000	−0.0392837
$649$	−26.9578	−1.05818
$650$	11.5778	0.454119
$651$	−1.33076	−0.0521564
$652$	−24.8572	−0.973482
$653$	6.19853	0.242567	0.121284	−	0.992618i	$-0.461299\pi$
$653$	6.19853	0.242567	0.121284	+	0.992618i	$0.461299\pi$
$654$	6.63187	0.259327
$655$	−31.4798	−1.23002
$656$	9.14732	0.357143
$657$	−6.75816	−0.263661
$658$	−23.7331	−0.925212
$659$	−46.9403	−1.82853	−0.914267	−	0.405113i	$-0.867232\pi$
$659$	−46.9403	−1.82853	−0.914267	+	0.405113i	$0.867232\pi$
$660$	15.2706	0.594407
$661$	−17.3549	−0.675028	−0.337514	−	0.941321i	$-0.609586\pi$
$661$	−17.3549	−0.675028	−0.337514	+	0.941321i	$0.609586\pi$
$662$	−28.8357	−1.12073
$663$	−4.96826	−0.192951
$664$	12.6995	0.492836
$665$	−34.4271	−1.33503
$666$	0.169601	0.00657191
$667$	−18.6529	−0.722242
$668$	−24.7241	−0.956606
$669$	−23.8931	−0.923759
$670$	22.7153	0.877568
$671$	32.7409	1.26395
$672$	2.58120	0.0995721
$673$	−47.2284	−1.82052	−0.910261	−	0.414035i	$-0.864119\pi$
$673$	−47.2284	−1.82052	−0.910261	+	0.414035i	$0.864119\pi$
$674$	30.7712	1.18526
$675$	−11.5778	−0.445630
$676$	1.00000	0.0384615
$677$	−2.25869	−0.0868086	−0.0434043	−	0.999058i	$-0.513820\pi$
$677$	−2.25869	−0.0868086	−0.0434043	+	0.999058i	$0.513820\pi$
$678$	16.1053	0.618519
$679$	−4.54810	−0.174540
$680$	−20.2287	−0.775735
$681$	−11.5062	−0.440918
$682$	−1.93361	−0.0740416
$683$	−18.7360	−0.716915	−0.358457	−	0.933546i	$-0.616697\pi$
$683$	−18.7360	−0.716915	−0.358457	+	0.933546i	$0.616697\pi$
$684$	3.27578	0.125253
$685$	−38.8592	−1.48473
$686$	18.9393	0.723105
$687$	5.01532	0.191346
$688$	5.16760	0.197013
$689$	1.36025	0.0518214
$690$	−25.2951	−0.962966
$691$	−15.3009	−0.582074	−0.291037	−	0.956712i	$-0.594000\pi$
$691$	−15.3009	−0.582074	−0.291037	+	0.956712i	$0.594000\pi$
$692$	−4.49671	−0.170939
$693$	9.68087	0.367746
$694$	−37.0016	−1.40456
$695$	35.0158	1.32822
$696$	−3.00244	−0.113807
$697$	−45.4462	−1.72140
$698$	−19.4923	−0.737795
$699$	−25.1837	−0.952536
$700$	29.8847	1.12954
$701$	29.4589	1.11265	0.556323	−	0.830966i	$-0.312212\pi$
$701$	29.4589	1.11265	0.556323	+	0.830966i	$0.312212\pi$
$702$	−1.00000	−0.0377426
$703$	−0.555576	−0.0209540
$704$	3.75053	0.141353
$705$	37.4365	1.40994
$706$	−19.9930	−0.752448
$707$	−25.6251	−0.963730
$708$	7.18773	0.270131
$709$	7.78290	0.292293	0.146146	−	0.989263i	$-0.453313\pi$
$709$	7.78290	0.292293	0.146146	+	0.989263i	$0.453313\pi$
$710$	−35.8914	−1.34698
$711$	11.5740	0.434059
$712$	−1.52673	−0.0572166
$713$	3.20293	0.119951
$714$	−12.8241	−0.479929
$715$	15.2706	0.571088
$716$	−0.474184	−0.0177211
$717$	−8.78476	−0.328073
$718$	16.0667	0.599605
$719$	−0.207218	−0.00772794	−0.00386397	−	0.999993i	$-0.501230\pi$
$719$	−0.207218	−0.00772794	−0.00386397	+	0.999993i	$0.501230\pi$
$720$	−4.07159	−0.151739
$721$	2.58120	0.0961291
$722$	8.26925	0.307750
$723$	−5.11482	−0.190222
$724$	−6.40924	−0.238198
$725$	−34.7617	−1.29102
$726$	3.06644	0.113806
$727$	−30.8695	−1.14489	−0.572444	−	0.819944i	$-0.694005\pi$
$727$	−30.8695	−1.14489	−0.572444	+	0.819944i	$0.694005\pi$
$728$	2.58120	0.0956658
$729$	1.00000	0.0370370
$730$	−27.5164	−1.01843
$731$	−25.6740	−0.949587
$732$	−8.72968	−0.322658
$733$	−35.9740	−1.32873	−0.664366	−	0.747408i	$-0.731298\pi$
$733$	−35.9740	−1.32873	−0.664366	+	0.747408i	$0.731298\pi$
$734$	−24.4433	−0.902218
$735$	−1.37370	−0.0506695
$736$	−6.21258	−0.228999
$737$	20.9241	0.770749
$738$	−9.14732	−0.336717
$739$	25.9587	0.954907	0.477454	−	0.878657i	$-0.341560\pi$
$739$	25.9587	0.954907	0.477454	+	0.878657i	$0.341560\pi$
$740$	0.690546	0.0253850
$741$	3.27578	0.120339
$742$	3.51108	0.128896
$743$	36.4624	1.33768	0.668838	−	0.743408i	$-0.266792\pi$
$743$	36.4624	1.33768	0.668838	+	0.743408i	$0.266792\pi$
$744$	0.515556	0.0189012
$745$	−49.3721	−1.80886
$746$	−10.1846	−0.372884
$747$	−12.6995	−0.464650
$748$	−18.6336	−0.681311
$749$	−32.7366	−1.19617
$750$	−26.7822	−0.977946
$751$	−50.8823	−1.85672	−0.928361	−	0.371679i	$-0.878782\pi$
$751$	−50.8823	−1.85672	−0.928361	+	0.371679i	$0.878782\pi$
$752$	9.19458	0.335292
$753$	2.96547	0.108068
$754$	−3.00244	−0.109342
$755$	37.2583	1.35597
$756$	−2.58120	−0.0938775
$757$	9.23185	0.335537	0.167769	−	0.985826i	$-0.446344\pi$
$757$	9.23185	0.335537	0.167769	+	0.985826i	$0.446344\pi$
$758$	−35.1348	−1.27615
$759$	−23.3004	−0.845752
$760$	13.3376	0.483807
$761$	38.0894	1.38074	0.690370	−	0.723456i	$-0.257448\pi$
$761$	38.0894	1.38074	0.690370	+	0.723456i	$0.257448\pi$
$762$	14.4538	0.523605
$763$	17.1182	0.619721
$764$	−14.6130	−0.528681
$765$	20.2287	0.731370
$766$	4.80554	0.173631
$767$	7.18773	0.259534
$768$	−1.00000	−0.0360844
$769$	45.4423	1.63869	0.819345	−	0.573301i	$-0.194337\pi$
$769$	45.4423	1.63869	0.819345	+	0.573301i	$0.194337\pi$
$770$	39.4165	1.42047
$771$	19.7234	0.710321
$772$	−9.13430	−0.328751
$773$	8.18641	0.294445	0.147222	−	0.989103i	$-0.452967\pi$
$773$	8.18641	0.294445	0.147222	+	0.989103i	$0.452967\pi$
$774$	−5.16760	−0.185746
$775$	5.96901	0.214413
$776$	1.76201	0.0632524
$777$	0.437775	0.0157051
$778$	−11.0101	−0.394733
$779$	29.9646	1.07359
$780$	−4.07159	−0.145786
$781$	−33.0612	−1.18302
$782$	30.8657	1.10375
$783$	3.00244	0.107298
$784$	−0.337386	−0.0120495
$785$	−30.5077	−1.08887
$786$	7.73157	0.275776
$787$	−2.63487	−0.0939231	−0.0469615	−	0.998897i	$-0.514954\pi$
$787$	−2.63487	−0.0939231	−0.0469615	+	0.998897i	$0.514954\pi$
$788$	−20.0325	−0.713629
$789$	27.6687	0.985032
$790$	47.1246	1.67662
$791$	41.5710	1.47809
$792$	−3.75053	−0.133269
$793$	−8.72968	−0.310000
$794$	−35.9964	−1.27746
$795$	−5.53838	−0.196426
$796$	1.01631	0.0360220
$797$	−7.51714	−0.266271	−0.133135	−	0.991098i	$-0.542505\pi$
$797$	−7.51714	−0.266271	−0.133135	+	0.991098i	$0.542505\pi$
$798$	8.45546	0.299320
$799$	−45.6810	−1.61608
$800$	−11.5778	−0.409338
$801$	1.52673	0.0539443
$802$	−26.5560	−0.937723
$803$	−25.3466	−0.894464
$804$	−5.57898	−0.196755
$805$	−65.2917	−2.30123
$806$	0.515556	0.0181597
$807$	7.45176	0.262314
$808$	9.92757	0.349251
$809$	11.1468	0.391900	0.195950	−	0.980614i	$-0.437221\pi$
$809$	11.1468	0.391900	0.195950	+	0.980614i	$0.437221\pi$
$810$	4.07159	0.143061
$811$	−9.67856	−0.339860	−0.169930	−	0.985456i	$-0.554354\pi$
$811$	−9.67856	−0.339860	−0.169930	+	0.985456i	$0.554354\pi$
$812$	−7.74990	−0.271968
$813$	1.58452	0.0555715
$814$	0.636093	0.0222951
$815$	101.208	3.54517
$816$	4.96826	0.173924
$817$	16.9279	0.592234
$818$	−13.5214	−0.472766
$819$	−2.58120	−0.0901946
$820$	−37.2441	−1.30062
$821$	−3.72242	−0.129913	−0.0649567	−	0.997888i	$-0.520691\pi$
$821$	−3.72242	−0.129913	−0.0649567	+	0.997888i	$0.520691\pi$
$822$	9.54400	0.332885
$823$	−20.5031	−0.714694	−0.357347	−	0.933972i	$-0.616319\pi$
$823$	−20.5031	−0.714694	−0.357347	+	0.933972i	$0.616319\pi$
$824$	−1.00000	−0.0348367
$825$	−43.4229	−1.51179
$826$	18.5530	0.645541
$827$	3.08433	0.107253	0.0536263	−	0.998561i	$-0.482922\pi$
$827$	3.08433	0.107253	0.0536263	+	0.998561i	$0.482922\pi$
$828$	6.21258	0.215902
$829$	−30.7010	−1.06629	−0.533144	−	0.846024i	$-0.678990\pi$
$829$	−30.7010	−1.06629	−0.533144	+	0.846024i	$0.678990\pi$
$830$	−51.7071	−1.79478
$831$	−1.30007	−0.0450989
$832$	−1.00000	−0.0346688
$833$	1.67622	0.0580776
$834$	−8.60003	−0.297795
$835$	100.666	3.48371
$836$	12.2859	0.424917
$837$	−0.515556	−0.0178202
$838$	3.26115	0.112655
$839$	−33.1287	−1.14373	−0.571864	−	0.820348i	$-0.693780\pi$
$839$	−33.1287	−1.14373	−0.571864	+	0.820348i	$0.693780\pi$
$840$	−10.5096	−0.362615
$841$	−19.9854	−0.689151
$842$	−10.8036	−0.372317
$843$	−13.8619	−0.477431
$844$	17.7043	0.609408
$845$	−4.07159	−0.140067
$846$	−9.19458	−0.316116
$847$	7.91511	0.271966
$848$	−1.36025	−0.0467112
$849$	23.0435	0.790851
$850$	57.5216	1.97297
$851$	−1.05366	−0.0361190
$852$	8.81509	0.302000
$853$	6.39008	0.218792	0.109396	−	0.993998i	$-0.465108\pi$
$853$	6.39008	0.218792	0.109396	+	0.993998i	$0.465108\pi$
$854$	−22.5331	−0.771066
$855$	−13.3376	−0.456137
$856$	12.6827	0.433485
$857$	20.9962	0.717216	0.358608	−	0.933488i	$-0.383251\pi$
$857$	20.9962	0.717216	0.358608	+	0.933488i	$0.383251\pi$
$858$	−3.75053	−0.128041
$859$	5.21647	0.177984	0.0889919	−	0.996032i	$-0.471635\pi$
$859$	5.21647	0.177984	0.0889919	+	0.996032i	$0.471635\pi$
$860$	−21.0403	−0.717470
$861$	−23.6111	−0.804664
$862$	−9.42187	−0.320910
$863$	28.5164	0.970710	0.485355	−	0.874317i	$-0.338690\pi$
$863$	28.5164	0.970710	0.485355	+	0.874317i	$0.338690\pi$
$864$	1.00000	0.0340207
$865$	18.3087	0.622515
$866$	14.6310	0.497181
$867$	−7.68357	−0.260948
$868$	1.33076	0.0451688
$869$	43.4086	1.47254
$870$	12.2247	0.414455
$871$	−5.57898	−0.189037
$872$	−6.63187	−0.224583
$873$	−1.76201	−0.0596349
$874$	−20.3511	−0.688385
$875$	−69.1302	−2.33703
$876$	6.75816	0.228337
$877$	43.7797	1.47834	0.739168	−	0.673521i	$-0.235219\pi$
$877$	43.7797	1.47834	0.739168	+	0.673521i	$0.235219\pi$
$878$	−0.578539	−0.0195248
$879$	8.97969	0.302878
$880$	−15.2706	−0.514771
$881$	48.0897	1.62018	0.810092	−	0.586303i	$-0.199417\pi$
$881$	48.0897	1.62018	0.810092	+	0.586303i	$0.199417\pi$
$882$	0.337386	0.0113604
$883$	−35.3368	−1.18918	−0.594589	−	0.804030i	$-0.702685\pi$
$883$	−35.3368	−1.18918	−0.594589	+	0.804030i	$0.702685\pi$
$884$	4.96826	0.167101
$885$	−29.2655	−0.983748
$886$	16.9554	0.569627
$887$	−5.21276	−0.175027	−0.0875137	−	0.996163i	$-0.527892\pi$
$887$	−5.21276	−0.175027	−0.0875137	+	0.996163i	$0.527892\pi$
$888$	−0.169601	−0.00569144
$889$	37.3082	1.25128
$890$	6.21621	0.208368
$891$	3.75053	0.125647
$892$	23.8931	0.799999
$893$	30.1194	1.00791
$894$	12.1260	0.405555
$895$	1.93068	0.0645355
$896$	−2.58120	−0.0862320
$897$	6.21258	0.207432
$898$	−16.6918	−0.557013
$899$	−1.54792	−0.0516262
$900$	11.5778	0.385927
$901$	6.75807	0.225144
$902$	−34.3072	−1.14231
$903$	−13.3386	−0.443882
$904$	−16.1053	−0.535653
$905$	26.0958	0.867453
$906$	−9.15082	−0.304016
$907$	56.8488	1.88763	0.943816	−	0.330470i	$-0.107207\pi$
$907$	56.8488	1.88763	0.943816	+	0.330470i	$0.107207\pi$
$908$	11.5062	0.381846
$909$	−9.92757	−0.329277
$910$	−10.5096	−0.348390
$911$	−8.13961	−0.269677	−0.134839	−	0.990868i	$-0.543052\pi$
$911$	−8.13961	−0.269677	−0.134839	+	0.990868i	$0.543052\pi$
$912$	−3.27578	−0.108472
$913$	−47.6297	−1.57631
$914$	0.498348	0.0164839
$915$	35.5436	1.17504
$916$	−5.01532	−0.165711
$917$	19.9568	0.659030
$918$	−4.96826	−0.163977
$919$	−21.0280	−0.693649	−0.346824	−	0.937930i	$-0.612740\pi$
$919$	−21.0280	−0.693649	−0.346824	+	0.937930i	$0.612740\pi$
$920$	25.2951	0.833953
$921$	−6.96717	−0.229576
$922$	−2.29262	−0.0755034
$923$	8.81509	0.290152
$924$	−9.68087	−0.318477
$925$	−1.96361	−0.0645631
$926$	−7.76040	−0.255023
$927$	1.00000	0.0328443
$928$	3.00244	0.0985598
$929$	−52.0443	−1.70752	−0.853760	−	0.520667i	$-0.825683\pi$
$929$	−52.0443	−1.70752	−0.853760	+	0.520667i	$0.825683\pi$
$930$	−2.09913	−0.0688332
$931$	−1.10520	−0.0362215
$932$	25.1837	0.824921
$933$	−12.9719	−0.424682
$934$	35.3243	1.15585
$935$	75.8682	2.48116
$936$	1.00000	0.0326860
$937$	−10.5363	−0.344205	−0.172102	−	0.985079i	$-0.555056\pi$
$937$	−10.5363	−0.344205	−0.172102	+	0.985079i	$0.555056\pi$
$938$	−14.4005	−0.470192
$939$	5.37301	0.175342
$940$	−37.4365	−1.22105
$941$	6.00150	0.195643	0.0978217	−	0.995204i	$-0.468813\pi$
$941$	6.00150	0.195643	0.0978217	+	0.995204i	$0.468813\pi$
$942$	7.49283	0.244130
$943$	56.8284	1.85059
$944$	−7.18773	−0.233941
$945$	10.5096	0.341877
$946$	−19.3812	−0.630138
$947$	−33.8206	−1.09902	−0.549511	−	0.835487i	$-0.685186\pi$
$947$	−33.8206	−1.09902	−0.549511	+	0.835487i	$0.685186\pi$
$948$	−11.5740	−0.375907
$949$	6.75816	0.219379
$950$	−37.9264	−1.23050
$951$	−6.85531	−0.222299
$952$	12.8241	0.415631
$953$	−6.31648	−0.204611	−0.102305	−	0.994753i	$-0.532622\pi$
$953$	−6.31648	−0.204611	−0.102305	+	0.994753i	$0.532622\pi$
$954$	1.36025	0.0440397
$955$	59.4983	1.92532
$956$	8.78476	0.284119
$957$	11.2607	0.364007
$958$	−37.0768	−1.19790
$959$	24.6350	0.795506
$960$	4.07159	0.131410
$961$	−30.7342	−0.991426
$962$	−0.169601	−0.00546816
$963$	−12.6827	−0.408694
$964$	5.11482	0.164737
$965$	37.1911	1.19722
$966$	16.0359	0.515948
$967$	58.9751	1.89651	0.948256	−	0.317506i	$-0.102845\pi$
$967$	58.9751	1.89651	0.948256	+	0.317506i	$0.102845\pi$
$968$	−3.06644	−0.0985592
$969$	16.2749	0.522826
$970$	−7.17417	−0.230349
$971$	47.2237	1.51548	0.757741	−	0.652556i	$-0.226303\pi$
$971$	47.2237	1.51548	0.757741	+	0.652556i	$0.226303\pi$
$972$	−1.00000	−0.0320750
$973$	−22.1984	−0.711649
$974$	−14.8710	−0.476497
$975$	11.5778	0.370787
$976$	8.72968	0.279430
$977$	−47.3246	−1.51405	−0.757024	−	0.653387i	$-0.773348\pi$
$977$	−47.3246	−1.51405	−0.757024	+	0.653387i	$0.773348\pi$
$978$	−24.8572	−0.794845
$979$	5.72604	0.183005
$980$	1.37370	0.0438811
$981$	6.63187	0.211739
$982$	−16.8665	−0.538232
$983$	51.3562	1.63801	0.819004	−	0.573788i	$-0.194527\pi$
$983$	51.3562	1.63801	0.819004	+	0.573788i	$0.194527\pi$
$984$	9.14732	0.291606
$985$	81.5641	2.59885
$986$	−14.9169	−0.475050
$987$	−23.7331	−0.755433
$988$	−3.27578	−0.104217
$989$	32.1041	1.02085
$990$	15.2706	0.485331
$991$	31.3541	0.995997	0.497998	−	0.867178i	$-0.334069\pi$
$991$	31.3541	0.995997	0.497998	+	0.867178i	$0.334069\pi$
$992$	−0.515556	−0.0163689
$993$	−28.8357	−0.915073
$994$	22.7536	0.721699
$995$	−4.13798	−0.131183
$996$	12.6995	0.402399
$997$	49.2862	1.56091	0.780455	−	0.625212i	$-0.214987\pi$
$997$	49.2862	1.56091	0.780455	+	0.625212i	$0.214987\pi$
$998$	−16.9371	−0.536135
$999$	0.169601	0.00536594

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.ba.1.1	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.ba.1.1	✓	14	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.07159 q^{5} +1.00000 q^{6} +2.58120 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.07159 q^{5} +1.00000 q^{6} +2.58120 q^{7} -1.00000 q^{8} +1.00000 q^{9} +4.07159 q^{10} +3.75053 q^{11} -1.00000 q^{12} -1.00000 q^{13} -2.58120 q^{14} +4.07159 q^{15} +1.00000 q^{16} -4.96826 q^{17} -1.00000 q^{18} +3.27578 q^{19} -4.07159 q^{20} -2.58120 q^{21} -3.75053 q^{22} +6.21258 q^{23} +1.00000 q^{24} +11.5778 q^{25} +1.00000 q^{26} -1.00000 q^{27} +2.58120 q^{28} -3.00244 q^{29} -4.07159 q^{30} +0.515556 q^{31} -1.00000 q^{32} -3.75053 q^{33} +4.96826 q^{34} -10.5096 q^{35} +1.00000 q^{36} -0.169601 q^{37} -3.27578 q^{38} +1.00000 q^{39} +4.07159 q^{40} +9.14732 q^{41} +2.58120 q^{42} +5.16760 q^{43} +3.75053 q^{44} -4.07159 q^{45} -6.21258 q^{46} +9.19458 q^{47} -1.00000 q^{48} -0.337386 q^{49} -11.5778 q^{50} +4.96826 q^{51} -1.00000 q^{52} -1.36025 q^{53} +1.00000 q^{54} -15.2706 q^{55} -2.58120 q^{56} -3.27578 q^{57} +3.00244 q^{58} -7.18773 q^{59} +4.07159 q^{60} +8.72968 q^{61} -0.515556 q^{62} +2.58120 q^{63} +1.00000 q^{64} +4.07159 q^{65} +3.75053 q^{66} +5.57898 q^{67} -4.96826 q^{68} -6.21258 q^{69} +10.5096 q^{70} -8.81509 q^{71} -1.00000 q^{72} -6.75816 q^{73} +0.169601 q^{74} -11.5778 q^{75} +3.27578 q^{76} +9.68087 q^{77} -1.00000 q^{78} +11.5740 q^{79} -4.07159 q^{80} +1.00000 q^{81} -9.14732 q^{82} -12.6995 q^{83} -2.58120 q^{84} +20.2287 q^{85} -5.16760 q^{86} +3.00244 q^{87} -3.75053 q^{88} +1.52673 q^{89} +4.07159 q^{90} -2.58120 q^{91} +6.21258 q^{92} -0.515556 q^{93} -9.19458 q^{94} -13.3376 q^{95} +1.00000 q^{96} -1.76201 q^{97} +0.337386 q^{98} +3.75053 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - q^{5} + 14 q^{6} + 5 q^{7} - 14 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - q^5 + 14 * q^6 + 5 * q^7 - 14 * q^8 + 14 * q^9	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - q^{5} + 14 q^{6} + 5 q^{7} - 14 q^{8} + 14 q^{9} + q^{10} - q^{11} - 14 q^{12} - 14 q^{13} - 5 q^{14} + q^{15} + 14 q^{16} - 12 q^{17} - 14 q^{18} + 10 q^{19} - q^{20} - 5 q^{21} + q^{22} - q^{23} + 14 q^{24} + 19 q^{25} + 14 q^{26} - 14 q^{27} + 5 q^{28} + 6 q^{29} - q^{30} + 20 q^{31} - 14 q^{32} + q^{33} + 12 q^{34} - 16 q^{35} + 14 q^{36} - 3 q^{37} - 10 q^{38} + 14 q^{39} + q^{40} + q^{41} + 5 q^{42} + 6 q^{43} - q^{44} - q^{45} + q^{46} - 13 q^{47} - 14 q^{48} + 9 q^{49} - 19 q^{50} + 12 q^{51} - 14 q^{52} - 27 q^{53} + 14 q^{54} + 10 q^{55} - 5 q^{56} - 10 q^{57} - 6 q^{58} - 6 q^{59} + q^{60} - 4 q^{61} - 20 q^{62} + 5 q^{63} + 14 q^{64} + q^{65} - q^{66} + 13 q^{67} - 12 q^{68} + q^{69} + 16 q^{70} + 18 q^{71} - 14 q^{72} + 11 q^{73} + 3 q^{74} - 19 q^{75} + 10 q^{76} - 15 q^{77} - 14 q^{78} + 33 q^{79} - q^{80} + 14 q^{81} - q^{82} - 25 q^{83} - 5 q^{84} + 25 q^{85} - 6 q^{86} - 6 q^{87} + q^{88} + 3 q^{89} + q^{90} - 5 q^{91} - q^{92} - 20 q^{93} + 13 q^{94} + 30 q^{95} + 14 q^{96} + 11 q^{97} - 9 q^{98} - q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - q^5 + 14 * q^6 + 5 * q^7 - 14 * q^8 + 14 * q^9 + q^10 - q^11 - 14 * q^12 - 14 * q^13 - 5 * q^14 + q^15 + 14 * q^16 - 12 * q^17 - 14 * q^18 + 10 * q^19 - q^20 - 5 * q^21 + q^22 - q^23 + 14 * q^24 + 19 * q^25 + 14 * q^26 - 14 * q^27 + 5 * q^28 + 6 * q^29 - q^30 + 20 * q^31 - 14 * q^32 + q^33 + 12 * q^34 - 16 * q^35 + 14 * q^36 - 3 * q^37 - 10 * q^38 + 14 * q^39 + q^40 + q^41 + 5 * q^42 + 6 * q^43 - q^44 - q^45 + q^46 - 13 * q^47 - 14 * q^48 + 9 * q^49 - 19 * q^50 + 12 * q^51 - 14 * q^52 - 27 * q^53 + 14 * q^54 + 10 * q^55 - 5 * q^56 - 10 * q^57 - 6 * q^58 - 6 * q^59 + q^60 - 4 * q^61 - 20 * q^62 + 5 * q^63 + 14 * q^64 + q^65 - q^66 + 13 * q^67 - 12 * q^68 + q^69 + 16 * q^70 + 18 * q^71 - 14 * q^72 + 11 * q^73 + 3 * q^74 - 19 * q^75 + 10 * q^76 - 15 * q^77 - 14 * q^78 + 33 * q^79 - q^80 + 14 * q^81 - q^82 - 25 * q^83 - 5 * q^84 + 25 * q^85 - 6 * q^86 - 6 * q^87 + q^88 + 3 * q^89 + q^90 - 5 * q^91 - q^92 - 20 * q^93 + 13 * q^94 + 30 * q^95 + 14 * q^96 + 11 * q^97 - 9 * q^98 - q^99

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