LMFDB - Embedded newform 8038.2.a.d.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8038,2,Mod(1,8038)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8038, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8038.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8038 = 2 \cdot 4019 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8038.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:	$64.1837531447$
Analytic rank:	$0$
Dimension:	$92$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	8038.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.58627 q^{3} +1.00000 q^{4} -0.666816 q^{5} -2.58627 q^{6} -1.51739 q^{7} +1.00000 q^{8} +3.68880 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.58627 q^{3} +1.00000 q^{4} -0.666816 q^{5} -2.58627 q^{6} -1.51739 q^{7} +1.00000 q^{8} +3.68880 q^{9} -0.666816 q^{10} +1.37541 q^{11} -2.58627 q^{12} +6.11611 q^{13} -1.51739 q^{14} +1.72457 q^{15} +1.00000 q^{16} -3.47105 q^{17} +3.68880 q^{18} +0.884056 q^{19} -0.666816 q^{20} +3.92439 q^{21} +1.37541 q^{22} +3.20287 q^{23} -2.58627 q^{24} -4.55536 q^{25} +6.11611 q^{26} -1.78142 q^{27} -1.51739 q^{28} -2.08647 q^{29} +1.72457 q^{30} -1.57471 q^{31} +1.00000 q^{32} -3.55717 q^{33} -3.47105 q^{34} +1.01182 q^{35} +3.68880 q^{36} +4.82447 q^{37} +0.884056 q^{38} -15.8179 q^{39} -0.666816 q^{40} +10.3067 q^{41} +3.92439 q^{42} +0.297180 q^{43} +1.37541 q^{44} -2.45975 q^{45} +3.20287 q^{46} -0.903999 q^{47} -2.58627 q^{48} -4.69751 q^{49} -4.55536 q^{50} +8.97709 q^{51} +6.11611 q^{52} -1.15112 q^{53} -1.78142 q^{54} -0.917143 q^{55} -1.51739 q^{56} -2.28641 q^{57} -2.08647 q^{58} +3.44799 q^{59} +1.72457 q^{60} +1.14764 q^{61} -1.57471 q^{62} -5.59736 q^{63} +1.00000 q^{64} -4.07832 q^{65} -3.55717 q^{66} +6.49408 q^{67} -3.47105 q^{68} -8.28348 q^{69} +1.01182 q^{70} +5.93835 q^{71} +3.68880 q^{72} -12.4349 q^{73} +4.82447 q^{74} +11.7814 q^{75} +0.884056 q^{76} -2.08703 q^{77} -15.8179 q^{78} +6.58098 q^{79} -0.666816 q^{80} -6.45916 q^{81} +10.3067 q^{82} -9.94322 q^{83} +3.92439 q^{84} +2.31455 q^{85} +0.297180 q^{86} +5.39617 q^{87} +1.37541 q^{88} -15.3511 q^{89} -2.45975 q^{90} -9.28056 q^{91} +3.20287 q^{92} +4.07262 q^{93} -0.903999 q^{94} -0.589503 q^{95} -2.58627 q^{96} +1.23871 q^{97} -4.69751 q^{98} +5.07360 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 92 q + 92 q^{2} + 31 q^{3} + 92 q^{4} + 28 q^{5} + 31 q^{6} + 29 q^{7} + 92 q^{8} + 113 q^{9}+O(q^{10}) $ 92 * q + 92 * q^2 + 31 * q^3 + 92 * q^4 + 28 * q^5 + 31 * q^6 + 29 * q^7 + 92 * q^8 + 113 * q^9	\( 92 q + 92 q^{2} + 31 q^{3} + 92 q^{4} + 28 q^{5} + 31 q^{6} + 29 q^{7} + 92 q^{8} + 113 q^{9} + 28 q^{10} + 37 q^{11} + 31 q^{12} + 20 q^{13} + 29 q^{14} + 30 q^{15} + 92 q^{16} + 52 q^{17} + 113 q^{18} + 61 q^{19} + 28 q^{20} + 5 q^{21} + 37 q^{22} + 71 q^{23} + 31 q^{24} + 118 q^{25} + 20 q^{26} + 112 q^{27} + 29 q^{28} + 30 q^{29} + 30 q^{30} + 89 q^{31} + 92 q^{32} + 52 q^{33} + 52 q^{34} + 58 q^{35} + 113 q^{36} + 15 q^{37} + 61 q^{38} + 43 q^{39} + 28 q^{40} + 75 q^{41} + 5 q^{42} + 46 q^{43} + 37 q^{44} + 63 q^{45} + 71 q^{46} + 92 q^{47} + 31 q^{48} + 131 q^{49} + 118 q^{50} + 45 q^{51} + 20 q^{52} + 72 q^{53} + 112 q^{54} + 86 q^{55} + 29 q^{56} + 44 q^{57} + 30 q^{58} + 95 q^{59} + 30 q^{60} - 4 q^{61} + 89 q^{62} + 67 q^{63} + 92 q^{64} + 55 q^{65} + 52 q^{66} + 40 q^{67} + 52 q^{68} + 25 q^{69} + 58 q^{70} + 84 q^{71} + 113 q^{72} + 87 q^{73} + 15 q^{74} + 132 q^{75} + 61 q^{76} + 96 q^{77} + 43 q^{78} + 68 q^{79} + 28 q^{80} + 156 q^{81} + 75 q^{82} + 120 q^{83} + 5 q^{84} - 14 q^{85} + 46 q^{86} + 73 q^{87} + 37 q^{88} + 86 q^{89} + 63 q^{90} + 93 q^{91} + 71 q^{92} + 29 q^{93} + 92 q^{94} + 67 q^{95} + 31 q^{96} + 65 q^{97} + 131 q^{98} + 94 q^{99}+O(q^{100}) \) 92 * q + 92 * q^2 + 31 * q^3 + 92 * q^4 + 28 * q^5 + 31 * q^6 + 29 * q^7 + 92 * q^8 + 113 * q^9 + 28 * q^10 + 37 * q^11 + 31 * q^12 + 20 * q^13 + 29 * q^14 + 30 * q^15 + 92 * q^16 + 52 * q^17 + 113 * q^18 + 61 * q^19 + 28 * q^20 + 5 * q^21 + 37 * q^22 + 71 * q^23 + 31 * q^24 + 118 * q^25 + 20 * q^26 + 112 * q^27 + 29 * q^28 + 30 * q^29 + 30 * q^30 + 89 * q^31 + 92 * q^32 + 52 * q^33 + 52 * q^34 + 58 * q^35 + 113 * q^36 + 15 * q^37 + 61 * q^38 + 43 * q^39 + 28 * q^40 + 75 * q^41 + 5 * q^42 + 46 * q^43 + 37 * q^44 + 63 * q^45 + 71 * q^46 + 92 * q^47 + 31 * q^48 + 131 * q^49 + 118 * q^50 + 45 * q^51 + 20 * q^52 + 72 * q^53 + 112 * q^54 + 86 * q^55 + 29 * q^56 + 44 * q^57 + 30 * q^58 + 95 * q^59 + 30 * q^60 - 4 * q^61 + 89 * q^62 + 67 * q^63 + 92 * q^64 + 55 * q^65 + 52 * q^66 + 40 * q^67 + 52 * q^68 + 25 * q^69 + 58 * q^70 + 84 * q^71 + 113 * q^72 + 87 * q^73 + 15 * q^74 + 132 * q^75 + 61 * q^76 + 96 * q^77 + 43 * q^78 + 68 * q^79 + 28 * q^80 + 156 * q^81 + 75 * q^82 + 120 * q^83 + 5 * q^84 - 14 * q^85 + 46 * q^86 + 73 * q^87 + 37 * q^88 + 86 * q^89 + 63 * q^90 + 93 * q^91 + 71 * q^92 + 29 * q^93 + 92 * q^94 + 67 * q^95 + 31 * q^96 + 65 * q^97 + 131 * q^98 + 94 * 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
$3$	−2.58627	−1.49318	−0.746592	−	0.665282i	$-0.768311\pi$
$3$	−2.58627	−1.49318	−0.746592	+	0.665282i	$0.768311\pi$
$4$	1.00000	0.500000
$5$	−0.666816	−0.298209	−0.149105	−	0.988821i	$-0.547639\pi$
$5$	−0.666816	−0.298209	−0.149105	+	0.988821i	$0.547639\pi$
$6$	−2.58627	−1.05584
$7$	−1.51739	−0.573521	−0.286761	−	0.958002i	$-0.592578\pi$
$7$	−1.51739	−0.573521	−0.286761	+	0.958002i	$0.592578\pi$
$8$	1.00000	0.353553
$9$	3.68880	1.22960
$10$	−0.666816	−0.210866
$11$	1.37541	0.414700	0.207350	−	0.978267i	$-0.433516\pi$
$11$	1.37541	0.414700	0.207350	+	0.978267i	$0.433516\pi$
$12$	−2.58627	−0.746592
$13$	6.11611	1.69630	0.848152	−	0.529752i	$-0.177715\pi$
$13$	6.11611	1.69630	0.848152	+	0.529752i	$0.177715\pi$
$14$	−1.51739	−0.405541
$15$	1.72457	0.445281
$16$	1.00000	0.250000
$17$	−3.47105	−0.841854	−0.420927	−	0.907094i	$-0.638295\pi$
$17$	−3.47105	−0.841854	−0.420927	+	0.907094i	$0.638295\pi$
$18$	3.68880	0.869458
$19$	0.884056	0.202816	0.101408	−	0.994845i	$-0.467665\pi$
$19$	0.884056	0.202816	0.101408	+	0.994845i	$0.467665\pi$
$20$	−0.666816	−0.149105
$21$	3.92439	0.856373
$22$	1.37541	0.293238
$23$	3.20287	0.667844	0.333922	−	0.942601i	$-0.391628\pi$
$23$	3.20287	0.667844	0.333922	+	0.942601i	$0.391628\pi$
$24$	−2.58627	−0.527920
$25$	−4.55536	−0.911071
$26$	6.11611	1.19947
$27$	−1.78142	−0.342835
$28$	−1.51739	−0.286761
$29$	−2.08647	−0.387447	−0.193724	−	0.981056i	$-0.562057\pi$
$29$	−2.08647	−0.387447	−0.193724	+	0.981056i	$0.562057\pi$
$30$	1.72457	0.314861
$31$	−1.57471	−0.282826	−0.141413	−	0.989951i	$-0.545165\pi$
$31$	−1.57471	−0.282826	−0.141413	+	0.989951i	$0.545165\pi$
$32$	1.00000	0.176777
$33$	−3.55717	−0.619224
$34$	−3.47105	−0.595281
$35$	1.01182	0.171029
$36$	3.68880	0.614800
$37$	4.82447	0.793138	0.396569	−	0.918005i	$-0.370201\pi$
$37$	4.82447	0.793138	0.396569	+	0.918005i	$0.370201\pi$
$38$	0.884056	0.143413
$39$	−15.8179	−2.53290
$40$	−0.666816	−0.105433
$41$	10.3067	1.60963	0.804817	−	0.593524i	$-0.202264\pi$
$41$	10.3067	1.60963	0.804817	+	0.593524i	$0.202264\pi$
$42$	3.92439	0.605547
$43$	0.297180	0.0453195	0.0226597	−	0.999743i	$-0.492787\pi$
$43$	0.297180	0.0453195	0.0226597	+	0.999743i	$0.492787\pi$
$44$	1.37541	0.207350
$45$	−2.45975	−0.366678
$46$	3.20287	0.472237
$47$	−0.903999	−0.131862	−0.0659309	−	0.997824i	$-0.521002\pi$
$47$	−0.903999	−0.131862	−0.0659309	+	0.997824i	$0.521002\pi$
$48$	−2.58627	−0.373296
$49$	−4.69751	−0.671073
$50$	−4.55536	−0.644225
$51$	8.97709	1.25704
$52$	6.11611	0.848152
$53$	−1.15112	−0.158118	−0.0790591	−	0.996870i	$-0.525192\pi$
$53$	−1.15112	−0.158118	−0.0790591	+	0.996870i	$0.525192\pi$
$54$	−1.78142	−0.242421
$55$	−0.917143	−0.123667
$56$	−1.51739	−0.202770
$57$	−2.28641	−0.302842
$58$	−2.08647	−0.273967
$59$	3.44799	0.448891	0.224445	−	0.974487i	$-0.427943\pi$
$59$	3.44799	0.448891	0.224445	+	0.974487i	$0.427943\pi$
$60$	1.72457	0.222641
$61$	1.14764	0.146940	0.0734702	−	0.997297i	$-0.476593\pi$
$61$	1.14764	0.146940	0.0734702	+	0.997297i	$0.476593\pi$
$62$	−1.57471	−0.199988
$63$	−5.59736	−0.705202
$64$	1.00000	0.125000
$65$	−4.07832	−0.505854
$66$	−3.55717	−0.437858
$67$	6.49408	0.793378	0.396689	−	0.917953i	$-0.370159\pi$
$67$	6.49408	0.793378	0.396689	+	0.917953i	$0.370159\pi$
$68$	−3.47105	−0.420927
$69$	−8.28348	−0.997214
$70$	1.01182	0.120936
$71$	5.93835	0.704753	0.352377	−	0.935858i	$-0.385374\pi$
$71$	5.93835	0.704753	0.352377	+	0.935858i	$0.385374\pi$
$72$	3.68880	0.434729
$73$	−12.4349	−1.45539	−0.727696	−	0.685899i	$-0.759409\pi$
$73$	−12.4349	−1.45539	−0.727696	+	0.685899i	$0.759409\pi$
$74$	4.82447	0.560833
$75$	11.7814	1.36040
$76$	0.884056	0.101408
$77$	−2.08703	−0.237840
$78$	−15.8179	−1.79103
$79$	6.58098	0.740418	0.370209	−	0.928948i	$-0.379286\pi$
$79$	6.58098	0.740418	0.370209	+	0.928948i	$0.379286\pi$
$80$	−0.666816	−0.0745523
$81$	−6.45916	−0.717684
$82$	10.3067	1.13818
$83$	−9.94322	−1.09141	−0.545705	−	0.837977i	$-0.683738\pi$
$83$	−9.94322	−1.09141	−0.545705	+	0.837977i	$0.683738\pi$
$84$	3.92439	0.428187
$85$	2.31455	0.251049
$86$	0.297180	0.0320457
$87$	5.39617	0.578530
$88$	1.37541	0.146619
$89$	−15.3511	−1.62721	−0.813607	−	0.581416i	$-0.802499\pi$
$89$	−15.3511	−1.62721	−0.813607	+	0.581416i	$0.802499\pi$
$90$	−2.45975	−0.259280
$91$	−9.28056	−0.972867
$92$	3.20287	0.333922
$93$	4.07262	0.422311
$94$	−0.903999	−0.0932404
$95$	−0.589503	−0.0604817
$96$	−2.58627	−0.263960
$97$	1.23871	0.125772	0.0628859	−	0.998021i	$-0.479970\pi$
$97$	1.23871	0.125772	0.0628859	+	0.998021i	$0.479970\pi$
$98$	−4.69751	−0.474521
$99$	5.07360	0.509916
$100$	−4.55536	−0.455536
$101$	12.5473	1.24851	0.624254	−	0.781222i	$-0.285403\pi$
$101$	12.5473	1.24851	0.624254	+	0.781222i	$0.285403\pi$
$102$	8.97709	0.888864
$103$	8.74169	0.861345	0.430672	−	0.902508i	$-0.358276\pi$
$103$	8.74169	0.861345	0.430672	+	0.902508i	$0.358276\pi$
$104$	6.11611	0.599734
$105$	−2.61685	−0.255378
$106$	−1.15112	−0.111807
$107$	−5.61455	−0.542779	−0.271390	−	0.962470i	$-0.587483\pi$
$107$	−5.61455	−0.542779	−0.271390	+	0.962470i	$0.587483\pi$
$108$	−1.78142	−0.171417
$109$	−14.1445	−1.35479	−0.677397	−	0.735618i	$-0.736892\pi$
$109$	−14.1445	−1.35479	−0.677397	+	0.735618i	$0.736892\pi$
$110$	−0.917143	−0.0874461
$111$	−12.4774	−1.18430
$112$	−1.51739	−0.143380
$113$	−2.98737	−0.281028	−0.140514	−	0.990079i	$-0.544875\pi$
$113$	−2.98737	−0.281028	−0.140514	+	0.990079i	$0.544875\pi$
$114$	−2.28641	−0.214142
$115$	−2.13572	−0.199157
$116$	−2.08647	−0.193724
$117$	22.5611	2.08578
$118$	3.44799	0.317414
$119$	5.26696	0.482821
$120$	1.72457	0.157431
$121$	−9.10826	−0.828024
$122$	1.14764	0.103903
$123$	−26.6559	−2.40348
$124$	−1.57471	−0.141413
$125$	6.37166	0.569899
$126$	−5.59736	−0.498653
$127$	16.8901	1.49875	0.749377	−	0.662143i	$-0.230353\pi$
$127$	16.8901	1.49875	0.749377	+	0.662143i	$0.230353\pi$
$128$	1.00000	0.0883883
$129$	−0.768588	−0.0676704
$130$	−4.07832	−0.357693
$131$	4.00538	0.349952	0.174976	−	0.984573i	$-0.444015\pi$
$131$	4.00538	0.349952	0.174976	+	0.984573i	$0.444015\pi$
$132$	−3.55717	−0.309612
$133$	−1.34146	−0.116319
$134$	6.49408	0.561003
$135$	1.18788	0.102236
$136$	−3.47105	−0.297640
$137$	−11.9776	−1.02331	−0.511656	−	0.859190i	$-0.670968\pi$
$137$	−11.9776	−1.02331	−0.511656	+	0.859190i	$0.670968\pi$
$138$	−8.28348	−0.705137
$139$	2.90853	0.246698	0.123349	−	0.992363i	$-0.460636\pi$
$139$	2.90853	0.246698	0.123349	+	0.992363i	$0.460636\pi$
$140$	1.01182	0.0855146
$141$	2.33799	0.196894
$142$	5.93835	0.498336
$143$	8.41214	0.703458
$144$	3.68880	0.307400
$145$	1.39129	0.115540
$146$	−12.4349	−1.02912
$147$	12.1490	1.00204
$148$	4.82447	0.396569
$149$	−7.20543	−0.590292	−0.295146	−	0.955452i	$-0.595368\pi$
$149$	−7.20543	−0.590292	−0.295146	+	0.955452i	$0.595368\pi$
$150$	11.7814	0.961946
$151$	−16.7875	−1.36614	−0.683072	−	0.730351i	$-0.739357\pi$
$151$	−16.7875	−1.36614	−0.683072	+	0.730351i	$0.739357\pi$
$152$	0.884056	0.0717064
$153$	−12.8040	−1.03514
$154$	−2.08703	−0.168178
$155$	1.05004	0.0843412
$156$	−15.8179	−1.26645
$157$	23.4069	1.86807	0.934037	−	0.357176i	$-0.116260\pi$
$157$	23.4069	1.86807	0.934037	+	0.357176i	$0.116260\pi$
$158$	6.58098	0.523555
$159$	2.97710	0.236100
$160$	−0.666816	−0.0527164
$161$	−4.86001	−0.383023
$162$	−6.45916	−0.507479
$163$	−11.7800	−0.922683	−0.461341	−	0.887223i	$-0.652632\pi$
$163$	−11.7800	−0.922683	−0.461341	+	0.887223i	$0.652632\pi$
$164$	10.3067	0.804817
$165$	2.37198	0.184658
$166$	−9.94322	−0.771743
$167$	−3.35513	−0.259628	−0.129814	−	0.991538i	$-0.541438\pi$
$167$	−3.35513	−0.259628	−0.129814	+	0.991538i	$0.541438\pi$
$168$	3.92439	0.302774
$169$	24.4068	1.87745
$170$	2.31455	0.177518
$171$	3.26110	0.249383
$172$	0.297180	0.0226597
$173$	14.0038	1.06469	0.532344	−	0.846528i	$-0.321311\pi$
$173$	14.0038	1.06469	0.532344	+	0.846528i	$0.321311\pi$
$174$	5.39617	0.409083
$175$	6.91227	0.522519
$176$	1.37541	0.103675
$177$	−8.91745	−0.670276
$178$	−15.3511	−1.15061
$179$	3.86111	0.288593	0.144297	−	0.989534i	$-0.453908\pi$
$179$	3.86111	0.288593	0.144297	+	0.989534i	$0.453908\pi$
$180$	−2.45975	−0.183339
$181$	−16.8587	−1.25310	−0.626550	−	0.779381i	$-0.715534\pi$
$181$	−16.8587	−1.25310	−0.626550	+	0.779381i	$0.715534\pi$
$182$	−9.28056	−0.687921
$183$	−2.96811	−0.219409
$184$	3.20287	0.236118
$185$	−3.21703	−0.236521
$186$	4.07262	0.298619
$187$	−4.77411	−0.349117
$188$	−0.903999	−0.0659309
$189$	2.70312	0.196623
$190$	−0.589503	−0.0427670
$191$	17.7595	1.28503	0.642517	−	0.766271i	$-0.277890\pi$
$191$	17.7595	1.28503	0.642517	+	0.766271i	$0.277890\pi$
$192$	−2.58627	−0.186648
$193$	−20.7886	−1.49639	−0.748197	−	0.663476i	$-0.769080\pi$
$193$	−20.7886	−1.49639	−0.748197	+	0.663476i	$0.769080\pi$
$194$	1.23871	0.0889341
$195$	10.5476	0.755333
$196$	−4.69751	−0.335537
$197$	21.7684	1.55093	0.775466	−	0.631389i	$-0.217515\pi$
$197$	21.7684	1.55093	0.775466	+	0.631389i	$0.217515\pi$
$198$	5.07360	0.360565
$199$	16.7255	1.18564	0.592821	−	0.805334i	$-0.298014\pi$
$199$	16.7255	1.18564	0.592821	+	0.805334i	$0.298014\pi$
$200$	−4.55536	−0.322112
$201$	−16.7955	−1.18466
$202$	12.5473	0.882828
$203$	3.16599	0.222209
$204$	8.97709	0.628522
$205$	−6.87266	−0.480007
$206$	8.74169	0.609063
$207$	11.8147	0.821180
$208$	6.11611	0.424076
$209$	1.21594	0.0841080
$210$	−2.61685	−0.180580
$211$	17.8955	1.23198	0.615990	−	0.787754i	$-0.288756\pi$
$211$	17.8955	1.23198	0.615990	+	0.787754i	$0.288756\pi$
$212$	−1.15112	−0.0790591
$213$	−15.3582	−1.05233
$214$	−5.61455	−0.383803
$215$	−0.198164	−0.0135147
$216$	−1.78142	−0.121210
$217$	2.38945	0.162207
$218$	−14.1445	−0.957984
$219$	32.1600	2.17317
$220$	−0.917143	−0.0618337
$221$	−21.2294	−1.42804
$222$	−12.4774	−0.837427
$223$	18.8404	1.26164	0.630822	−	0.775927i	$-0.282718\pi$
$223$	18.8404	1.26164	0.630822	+	0.775927i	$0.282718\pi$
$224$	−1.51739	−0.101385
$225$	−16.8038	−1.12025
$226$	−2.98737	−0.198717
$227$	−3.36575	−0.223393	−0.111696	−	0.993742i	$-0.535628\pi$
$227$	−3.36575	−0.223393	−0.111696	+	0.993742i	$0.535628\pi$
$228$	−2.28641	−0.151421
$229$	21.9141	1.44812	0.724061	−	0.689736i	$-0.242273\pi$
$229$	21.9141	1.44812	0.724061	+	0.689736i	$0.242273\pi$
$230$	−2.13572	−0.140825
$231$	5.39764	0.355138
$232$	−2.08647	−0.136983
$233$	4.83450	0.316718	0.158359	−	0.987382i	$-0.449380\pi$
$233$	4.83450	0.316718	0.158359	+	0.987382i	$0.449380\pi$
$234$	22.5611	1.47487
$235$	0.602801	0.0393224
$236$	3.44799	0.224445
$237$	−17.0202	−1.10558
$238$	5.26696	0.341406
$239$	19.8070	1.28121	0.640605	−	0.767870i	$-0.278684\pi$
$239$	19.8070	1.28121	0.640605	+	0.767870i	$0.278684\pi$
$240$	1.72457	0.111320
$241$	15.4339	0.994184	0.497092	−	0.867698i	$-0.334401\pi$
$241$	15.4339	0.994184	0.497092	+	0.867698i	$0.334401\pi$
$242$	−9.10826	−0.585501
$243$	22.0494	1.41447
$244$	1.14764	0.0734702
$245$	3.13238	0.200120
$246$	−26.6559	−1.69952
$247$	5.40699	0.344038
$248$	−1.57471	−0.0999940
$249$	25.7159	1.62968
$250$	6.37166	0.402979
$251$	5.06208	0.319516	0.159758	−	0.987156i	$-0.448929\pi$
$251$	5.06208	0.319516	0.159758	+	0.987156i	$0.448929\pi$
$252$	−5.59736	−0.352601
$253$	4.40524	0.276955
$254$	16.8901	1.05978
$255$	−5.98607	−0.374862
$256$	1.00000	0.0625000
$257$	−12.1761	−0.759523	−0.379761	−	0.925084i	$-0.623994\pi$
$257$	−12.1761	−0.759523	−0.379761	+	0.925084i	$0.623994\pi$
$258$	−0.768588	−0.0478502
$259$	−7.32062	−0.454881
$260$	−4.07832	−0.252927
$261$	−7.69656	−0.476405
$262$	4.00538	0.247453
$263$	1.57414	0.0970654	0.0485327	−	0.998822i	$-0.484545\pi$
$263$	1.57414	0.0970654	0.0485327	+	0.998822i	$0.484545\pi$
$264$	−3.55717	−0.218929
$265$	0.767584	0.0471523
$266$	−1.34146	−0.0822503
$267$	39.7021	2.42973
$268$	6.49408	0.396689
$269$	12.0978	0.737615	0.368808	−	0.929506i	$-0.379766\pi$
$269$	12.0978	0.737615	0.368808	+	0.929506i	$0.379766\pi$
$270$	1.18788	0.0722921
$271$	−2.59550	−0.157665	−0.0788327	−	0.996888i	$-0.525119\pi$
$271$	−2.59550	−0.157665	−0.0788327	+	0.996888i	$0.525119\pi$
$272$	−3.47105	−0.210464
$273$	24.0020	1.45267
$274$	−11.9776	−0.723591
$275$	−6.26546	−0.377822
$276$	−8.28348	−0.498607
$277$	15.7201	0.944531	0.472265	−	0.881456i	$-0.343436\pi$
$277$	15.7201	0.944531	0.472265	+	0.881456i	$0.343436\pi$
$278$	2.90853	0.174442
$279$	−5.80878	−0.347762
$280$	1.01182	0.0604680
$281$	8.24757	0.492009	0.246004	−	0.969269i	$-0.420882\pi$
$281$	8.24757	0.492009	0.246004	+	0.969269i	$0.420882\pi$
$282$	2.33799	0.139225
$283$	15.9491	0.948075	0.474037	−	0.880505i	$-0.342796\pi$
$283$	15.9491	0.948075	0.474037	+	0.880505i	$0.342796\pi$
$284$	5.93835	0.352377
$285$	1.52461	0.0903103
$286$	8.41214	0.497420
$287$	−15.6393	−0.923159
$288$	3.68880	0.217365
$289$	−4.95178	−0.291281
$290$	1.39129	0.0816993
$291$	−3.20364	−0.187801
$292$	−12.4349	−0.727696
$293$	11.1176	0.649495	0.324748	−	0.945801i	$-0.394721\pi$
$293$	11.1176	0.649495	0.324748	+	0.945801i	$0.394721\pi$
$294$	12.1490	0.708547
$295$	−2.29918	−0.133863
$296$	4.82447	0.280417
$297$	−2.45018	−0.142174
$298$	−7.20543	−0.417399
$299$	19.5891	1.13287
$300$	11.7814	0.680199
$301$	−0.450939	−0.0259917
$302$	−16.7875	−0.966010
$303$	−32.4508	−1.86425
$304$	0.884056	0.0507041
$305$	−0.765265	−0.0438190
$306$	−12.8040	−0.731957
$307$	21.3446	1.21820	0.609099	−	0.793094i	$-0.291531\pi$
$307$	21.3446	1.21820	0.609099	+	0.793094i	$0.291531\pi$
$308$	−2.08703	−0.118920
$309$	−22.6084	−1.28615
$310$	1.05004	0.0596382
$311$	5.47448	0.310429	0.155215	−	0.987881i	$-0.450393\pi$
$311$	5.47448	0.310429	0.155215	+	0.987881i	$0.450393\pi$
$312$	−15.8179	−0.895514
$313$	1.18606	0.0670402	0.0335201	−	0.999438i	$-0.489328\pi$
$313$	1.18606	0.0670402	0.0335201	+	0.999438i	$0.489328\pi$
$314$	23.4069	1.32093
$315$	3.73241	0.210298
$316$	6.58098	0.370209
$317$	23.9450	1.34488	0.672441	−	0.740150i	$-0.265246\pi$
$317$	23.9450	1.34488	0.672441	+	0.740150i	$0.265246\pi$
$318$	2.97710	0.166948
$319$	−2.86974	−0.160675
$320$	−0.666816	−0.0372761
$321$	14.5208	0.810469
$322$	−4.86001	−0.270838
$323$	−3.06861	−0.170742
$324$	−6.45916	−0.358842
$325$	−27.8611	−1.54545
$326$	−11.7800	−0.652435
$327$	36.5814	2.02296
$328$	10.3067	0.569091
$329$	1.37172	0.0756256
$330$	2.37198	0.130573
$331$	5.89640	0.324095	0.162048	−	0.986783i	$-0.448190\pi$
$331$	5.89640	0.324095	0.162048	+	0.986783i	$0.448190\pi$
$332$	−9.94322	−0.545705
$333$	17.7965	0.975242
$334$	−3.35513	−0.183585
$335$	−4.33036	−0.236593
$336$	3.92439	0.214093
$337$	8.83563	0.481307	0.240654	−	0.970611i	$-0.422638\pi$
$337$	8.83563	0.481307	0.240654	+	0.970611i	$0.422638\pi$
$338$	24.4068	1.32756
$339$	7.72614	0.419626
$340$	2.31455	0.125524
$341$	−2.16586	−0.117288
$342$	3.26110	0.176340
$343$	17.7497	0.958396
$344$	0.297180	0.0160229
$345$	5.52356	0.297378
$346$	14.0038	0.752848
$347$	9.92597	0.532854	0.266427	−	0.963855i	$-0.414157\pi$
$347$	9.92597	0.532854	0.266427	+	0.963855i	$0.414157\pi$
$348$	5.39617	0.289265
$349$	−13.0108	−0.696454	−0.348227	−	0.937410i	$-0.613216\pi$
$349$	−13.0108	−0.696454	−0.348227	+	0.937410i	$0.613216\pi$
$350$	6.91227	0.369477
$351$	−10.8954	−0.581552
$352$	1.37541	0.0733094
$353$	−2.42345	−0.128987	−0.0644937	−	0.997918i	$-0.520543\pi$
$353$	−2.42345	−0.128987	−0.0644937	+	0.997918i	$0.520543\pi$
$354$	−8.91745	−0.473957
$355$	−3.95979	−0.210164
$356$	−15.3511	−0.813607
$357$	−13.6218	−0.720941
$358$	3.86111	0.204066
$359$	1.03022	0.0543727	0.0271864	−	0.999630i	$-0.491345\pi$
$359$	1.03022	0.0543727	0.0271864	+	0.999630i	$0.491345\pi$
$360$	−2.45975	−0.129640
$361$	−18.2184	−0.958866
$362$	−16.8587	−0.886075
$363$	23.5564	1.23639
$364$	−9.28056	−0.486433
$365$	8.29178	0.434011
$366$	−2.96811	−0.155146
$367$	−11.5245	−0.601576	−0.300788	−	0.953691i	$-0.597250\pi$
$367$	−11.5245	−0.601576	−0.300788	+	0.953691i	$0.597250\pi$
$368$	3.20287	0.166961
$369$	38.0193	1.97920
$370$	−3.21703	−0.167246
$371$	1.74670	0.0906842
$372$	4.07262	0.211155
$373$	−9.74925	−0.504797	−0.252398	−	0.967623i	$-0.581219\pi$
$373$	−9.74925	−0.504797	−0.252398	+	0.967623i	$0.581219\pi$
$374$	−4.77411	−0.246863
$375$	−16.4789	−0.850964
$376$	−0.903999	−0.0466202
$377$	−12.7611	−0.657229
$378$	2.70312	0.139033
$379$	−8.16575	−0.419446	−0.209723	−	0.977761i	$-0.567256\pi$
$379$	−8.16575	−0.419446	−0.209723	+	0.977761i	$0.567256\pi$
$380$	−0.589503	−0.0302408
$381$	−43.6824	−2.23792
$382$	17.7595	0.908657
$383$	32.6246	1.66704	0.833520	−	0.552489i	$-0.186322\pi$
$383$	32.6246	1.66704	0.833520	+	0.552489i	$0.186322\pi$
$384$	−2.58627	−0.131980
$385$	1.39167	0.0709259
$386$	−20.7886	−1.05811
$387$	1.09624	0.0557248
$388$	1.23871	0.0628859
$389$	34.5838	1.75347	0.876735	−	0.480974i	$-0.159717\pi$
$389$	34.5838	1.75347	0.876735	+	0.480974i	$0.159717\pi$
$390$	10.5476	0.534101
$391$	−11.1173	−0.562227
$392$	−4.69751	−0.237260
$393$	−10.3590	−0.522543
$394$	21.7684	1.09668
$395$	−4.38830	−0.220799
$396$	5.07360	0.254958
$397$	−0.387078	−0.0194269	−0.00971344	−	0.999953i	$-0.503092\pi$
$397$	−0.387078	−0.0194269	−0.00971344	+	0.999953i	$0.503092\pi$
$398$	16.7255	0.838375
$399$	3.46938	0.173686
$400$	−4.55536	−0.227768
$401$	20.5140	1.02442	0.512211	−	0.858860i	$-0.328827\pi$
$401$	20.5140	1.02442	0.512211	+	0.858860i	$0.328827\pi$
$402$	−16.7955	−0.837681
$403$	−9.63109	−0.479759
$404$	12.5473	0.624254
$405$	4.30707	0.214020
$406$	3.16599	0.157126
$407$	6.63560	0.328915
$408$	8.97709	0.444432
$409$	−1.48439	−0.0733986	−0.0366993	−	0.999326i	$-0.511684\pi$
$409$	−1.48439	−0.0733986	−0.0366993	+	0.999326i	$0.511684\pi$
$410$	−6.87266	−0.339416
$411$	30.9772	1.52799
$412$	8.74169	0.430672
$413$	−5.23197	−0.257448
$414$	11.8147	0.580662
$415$	6.63030	0.325468
$416$	6.11611	0.299867
$417$	−7.52225	−0.368366
$418$	1.21594	0.0594734
$419$	34.4721	1.68407	0.842036	−	0.539421i	$-0.181357\pi$
$419$	34.4721	1.68407	0.842036	+	0.539421i	$0.181357\pi$
$420$	−2.61685	−0.127689
$421$	−27.2112	−1.32619	−0.663097	−	0.748533i	$-0.730758\pi$
$421$	−27.2112	−1.32619	−0.663097	+	0.748533i	$0.730758\pi$
$422$	17.8955	0.871141
$423$	−3.33467	−0.162137
$424$	−1.15112	−0.0559033
$425$	15.8119	0.766989
$426$	−15.3582	−0.744107
$427$	−1.74142	−0.0842734
$428$	−5.61455	−0.271390
$429$	−21.7561	−1.05039
$430$	−0.198164	−0.00955633
$431$	−13.3673	−0.643878	−0.321939	−	0.946760i	$-0.604335\pi$
$431$	−13.3673	−0.643878	−0.321939	+	0.946760i	$0.604335\pi$
$432$	−1.78142	−0.0857087
$433$	14.2652	0.685542	0.342771	−	0.939419i	$-0.388634\pi$
$433$	14.2652	0.685542	0.342771	+	0.939419i	$0.388634\pi$
$434$	2.38945	0.114697
$435$	−3.59825	−0.172523
$436$	−14.1445	−0.677397
$437$	2.83151	0.135450
$438$	32.1600	1.53666
$439$	−26.3005	−1.25526	−0.627628	−	0.778513i	$-0.715974\pi$
$439$	−26.3005	−1.25526	−0.627628	+	0.778513i	$0.715974\pi$
$440$	−0.917143	−0.0437231
$441$	−17.3282	−0.825152
$442$	−21.2294	−1.00978
$443$	−7.64307	−0.363133	−0.181567	−	0.983379i	$-0.558117\pi$
$443$	−7.64307	−0.363133	−0.181567	+	0.983379i	$0.558117\pi$
$444$	−12.4774	−0.592151
$445$	10.2364	0.485250
$446$	18.8404	0.892118
$447$	18.6352	0.881414
$448$	−1.51739	−0.0716902
$449$	20.8772	0.985254	0.492627	−	0.870240i	$-0.336037\pi$
$449$	20.8772	0.985254	0.492627	+	0.870240i	$0.336037\pi$
$450$	−16.8038	−0.792138
$451$	14.1759	0.667516
$452$	−2.98737	−0.140514
$453$	43.4169	2.03991
$454$	−3.36575	−0.157962
$455$	6.18842	0.290118
$456$	−2.28641	−0.107071
$457$	24.0023	1.12278	0.561389	−	0.827552i	$-0.310267\pi$
$457$	24.0023	1.12278	0.561389	+	0.827552i	$0.310267\pi$
$458$	21.9141	1.02398
$459$	6.18341	0.288617
$460$	−2.13572	−0.0995786
$461$	−0.197333	−0.00919070	−0.00459535	−	0.999989i	$-0.501463\pi$
$461$	−0.197333	−0.00919070	−0.00459535	+	0.999989i	$0.501463\pi$
$462$	5.39764	0.251121
$463$	−41.8546	−1.94515	−0.972575	−	0.232590i	$-0.925280\pi$
$463$	−41.8546	−1.94515	−0.972575	+	0.232590i	$0.925280\pi$
$464$	−2.08647	−0.0968618
$465$	−2.71569	−0.125937
$466$	4.83450	0.223954
$467$	−0.459201	−0.0212493	−0.0106247	−	0.999944i	$-0.503382\pi$
$467$	−0.459201	−0.0212493	−0.0106247	+	0.999944i	$0.503382\pi$
$468$	22.5611	1.04289
$469$	−9.85408	−0.455019
$470$	0.602801	0.0278051
$471$	−60.5366	−2.78938
$472$	3.44799	0.158707
$473$	0.408743	0.0187940
$474$	−17.0202	−0.781764
$475$	−4.02719	−0.184780
$476$	5.26696	0.241411
$477$	−4.24624	−0.194422
$478$	19.8070	0.905952
$479$	−36.8063	−1.68172	−0.840861	−	0.541252i	$-0.817951\pi$
$479$	−36.8063	−1.68172	−0.840861	+	0.541252i	$0.817951\pi$
$480$	1.72457	0.0787153
$481$	29.5070	1.34540
$482$	15.4339	0.702994
$483$	12.5693	0.571923
$484$	−9.10826	−0.414012
$485$	−0.825991	−0.0375063
$486$	22.0494	1.00018
$487$	14.4908	0.656639	0.328319	−	0.944567i	$-0.393518\pi$
$487$	14.4908	0.656639	0.328319	+	0.944567i	$0.393518\pi$
$488$	1.14764	0.0519513
$489$	30.4663	1.37774
$490$	3.13238	0.141506
$491$	−15.9682	−0.720637	−0.360318	−	0.932829i	$-0.617332\pi$
$491$	−15.9682	−0.720637	−0.360318	+	0.932829i	$0.617332\pi$
$492$	−26.6559	−1.20174
$493$	7.24224	0.326174
$494$	5.40699	0.243272
$495$	−3.38315	−0.152061
$496$	−1.57471	−0.0707064
$497$	−9.01083	−0.404191
$498$	25.7159	1.15236
$499$	−23.7040	−1.06114	−0.530568	−	0.847642i	$-0.678021\pi$
$499$	−23.7040	−1.06114	−0.530568	+	0.847642i	$0.678021\pi$
$500$	6.37166	0.284949
$501$	8.67728	0.387672
$502$	5.06208	0.225932
$503$	32.4019	1.44473	0.722365	−	0.691512i	$-0.243055\pi$
$503$	32.4019	1.44473	0.722365	+	0.691512i	$0.243055\pi$
$504$	−5.59736	−0.249326
$505$	−8.36677	−0.372316
$506$	4.40524	0.195837
$507$	−63.1227	−2.80338
$508$	16.8901	0.749377
$509$	1.93399	0.0857225	0.0428613	−	0.999081i	$-0.486353\pi$
$509$	1.93399	0.0857225	0.0428613	+	0.999081i	$0.486353\pi$
$510$	−5.98607	−0.265067
$511$	18.8686	0.834699
$512$	1.00000	0.0441942
$513$	−1.57488	−0.0695325
$514$	−12.1761	−0.537064
$515$	−5.82910	−0.256861
$516$	−0.768588	−0.0338352
$517$	−1.24337	−0.0546832
$518$	−7.32062	−0.321650
$519$	−36.2176	−1.58978
$520$	−4.07832	−0.178846
$521$	−14.6440	−0.641565	−0.320783	−	0.947153i	$-0.603946\pi$
$521$	−14.6440	−0.641565	−0.320783	+	0.947153i	$0.603946\pi$
$522$	−7.69656	−0.336869
$523$	5.84510	0.255588	0.127794	−	0.991801i	$-0.459210\pi$
$523$	5.84510	0.255588	0.127794	+	0.991801i	$0.459210\pi$
$524$	4.00538	0.174976
$525$	−17.8770	−0.780217
$526$	1.57414	0.0686356
$527$	5.46589	0.238098
$528$	−3.55717	−0.154806
$529$	−12.7416	−0.553985
$530$	0.767584	0.0333417
$531$	12.7190	0.551956
$532$	−1.34146	−0.0581597
$533$	63.0368	2.73043
$534$	39.7021	1.71808
$535$	3.74387	0.161862
$536$	6.49408	0.280502
$537$	−9.98588	−0.430923
$538$	12.0978	0.521573
$539$	−6.46099	−0.278294
$540$	1.18788	0.0511182
$541$	16.7531	0.720271	0.360135	−	0.932900i	$-0.382730\pi$
$541$	16.7531	0.720271	0.360135	+	0.932900i	$0.382730\pi$
$542$	−2.59550	−0.111486
$543$	43.6013	1.87111
$544$	−3.47105	−0.148820
$545$	9.43175	0.404012
$546$	24.0020	1.02719
$547$	36.0084	1.53961	0.769803	−	0.638281i	$-0.220354\pi$
$547$	36.0084	1.53961	0.769803	+	0.638281i	$0.220354\pi$
$548$	−11.9776	−0.511656
$549$	4.23342	0.180678
$550$	−6.26546	−0.267160
$551$	−1.84455	−0.0785806
$552$	−8.28348	−0.352568
$553$	−9.98594	−0.424646
$554$	15.7201	0.667884
$555$	8.32012	0.353169
$556$	2.90853	0.123349
$557$	−7.65403	−0.324312	−0.162156	−	0.986765i	$-0.551845\pi$
$557$	−7.65403	−0.324312	−0.162156	+	0.986765i	$0.551845\pi$
$558$	−5.80878	−0.245905
$559$	1.81759	0.0768757
$560$	1.01182	0.0427573
$561$	12.3471	0.521297
$562$	8.24757	0.347903
$563$	−5.78749	−0.243914	−0.121957	−	0.992535i	$-0.538917\pi$
$563$	−5.78749	−0.243914	−0.121957	+	0.992535i	$0.538917\pi$
$564$	2.33799	0.0984470
$565$	1.99202	0.0838051
$566$	15.9491	0.670390
$567$	9.80109	0.411607
$568$	5.93835	0.249168
$569$	−9.12818	−0.382673	−0.191337	−	0.981524i	$-0.561282\pi$
$569$	−9.12818	−0.382673	−0.191337	+	0.981524i	$0.561282\pi$
$570$	1.52461	0.0638590
$571$	−23.1688	−0.969585	−0.484792	−	0.874629i	$-0.661105\pi$
$571$	−23.1688	−0.969585	−0.484792	+	0.874629i	$0.661105\pi$
$572$	8.41214	0.351729
$573$	−45.9310	−1.91879
$574$	−15.6393	−0.652772
$575$	−14.5902	−0.608453
$576$	3.68880	0.153700
$577$	−13.3748	−0.556801	−0.278400	−	0.960465i	$-0.589804\pi$
$577$	−13.3748	−0.556801	−0.278400	+	0.960465i	$0.589804\pi$
$578$	−4.95178	−0.205967
$579$	53.7649	2.23439
$580$	1.39129	0.0577702
$581$	15.0878	0.625947
$582$	−3.20364	−0.132795
$583$	−1.58326	−0.0655717
$584$	−12.4349	−0.514559
$585$	−15.0441	−0.621997
$586$	11.1176	0.459263
$587$	8.24071	0.340130	0.170065	−	0.985433i	$-0.445602\pi$
$587$	8.24071	0.340130	0.170065	+	0.985433i	$0.445602\pi$
$588$	12.1490	0.501018
$589$	−1.39213	−0.0573617
$590$	−2.29918	−0.0946556
$591$	−56.2989	−2.31583
$592$	4.82447	0.198284
$593$	−41.6712	−1.71123	−0.855615	−	0.517612i	$-0.826821\pi$
$593$	−41.6712	−1.71123	−0.855615	+	0.517612i	$0.826821\pi$
$594$	−2.45018	−0.100532
$595$	−3.51209	−0.143982
$596$	−7.20543	−0.295146
$597$	−43.2568	−1.77038
$598$	19.5891	0.801058
$599$	17.0512	0.696692	0.348346	−	0.937366i	$-0.386743\pi$
$599$	17.0512	0.696692	0.348346	+	0.937366i	$0.386743\pi$
$600$	11.7814	0.480973
$601$	37.1326	1.51467	0.757335	−	0.653027i	$-0.226501\pi$
$601$	37.1326	1.51467	0.757335	+	0.653027i	$0.226501\pi$
$602$	−0.450939	−0.0183789
$603$	23.9554	0.975538
$604$	−16.7875	−0.683072
$605$	6.07353	0.246924
$606$	−32.4508	−1.31823
$607$	23.0340	0.934920	0.467460	−	0.884014i	$-0.345169\pi$
$607$	23.0340	0.934920	0.467460	+	0.884014i	$0.345169\pi$
$608$	0.884056	0.0358532
$609$	−8.18812	−0.331799
$610$	−0.765265	−0.0309847
$611$	−5.52896	−0.223678
$612$	−12.8040	−0.517572
$613$	−17.9071	−0.723260	−0.361630	−	0.932322i	$-0.617780\pi$
$613$	−17.9071	−0.723260	−0.361630	+	0.932322i	$0.617780\pi$
$614$	21.3446	0.861396
$615$	17.7746	0.716739
$616$	−2.08703	−0.0840890
$617$	0.564020	0.0227066	0.0113533	−	0.999936i	$-0.496386\pi$
$617$	0.564020	0.0227066	0.0113533	+	0.999936i	$0.496386\pi$
$618$	−22.6084	−0.909443
$619$	−15.5837	−0.626363	−0.313181	−	0.949693i	$-0.601395\pi$
$619$	−15.5837	−0.626363	−0.313181	+	0.949693i	$0.601395\pi$
$620$	1.05004	0.0421706
$621$	−5.70565	−0.228960
$622$	5.47448	0.219507
$623$	23.2937	0.933241
$624$	−15.8179	−0.633224
$625$	18.5281	0.741122
$626$	1.18606	0.0474045
$627$	−3.14474	−0.125589
$628$	23.4069	0.934037
$629$	−16.7460	−0.667707
$630$	3.73241	0.148703
$631$	5.75300	0.229023	0.114512	−	0.993422i	$-0.463470\pi$
$631$	5.75300	0.229023	0.114512	+	0.993422i	$0.463470\pi$
$632$	6.58098	0.261777
$633$	−46.2827	−1.83957
$634$	23.9450	0.950976
$635$	−11.2626	−0.446942
$636$	2.97710	0.118050
$637$	−28.7305	−1.13834
$638$	−2.86974	−0.113614
$639$	21.9054	0.866564
$640$	−0.666816	−0.0263582
$641$	−4.65171	−0.183732	−0.0918658	−	0.995771i	$-0.529283\pi$
$641$	−4.65171	−0.183732	−0.0918658	+	0.995771i	$0.529283\pi$
$642$	14.5208	0.573088
$643$	17.4666	0.688817	0.344408	−	0.938820i	$-0.388079\pi$
$643$	17.4666	0.688817	0.344408	+	0.938820i	$0.388079\pi$
$644$	−4.86001	−0.191511
$645$	0.512506	0.0201799
$646$	−3.06861	−0.120733
$647$	39.4886	1.55246	0.776228	−	0.630452i	$-0.217131\pi$
$647$	39.4886	1.55246	0.776228	+	0.630452i	$0.217131\pi$
$648$	−6.45916	−0.253740
$649$	4.74239	0.186155
$650$	−27.8611	−1.09280
$651$	−6.17977	−0.242204
$652$	−11.7800	−0.461341
$653$	−7.63960	−0.298961	−0.149480	−	0.988765i	$-0.547760\pi$
$653$	−7.63960	−0.298961	−0.149480	+	0.988765i	$0.547760\pi$
$654$	36.5814	1.43045
$655$	−2.67085	−0.104359
$656$	10.3067	0.402408
$657$	−45.8698	−1.78955
$658$	1.37172	0.0534753
$659$	20.4107	0.795089	0.397544	−	0.917583i	$-0.369863\pi$
$659$	20.4107	0.795089	0.397544	+	0.917583i	$0.369863\pi$
$660$	2.37198	0.0923292
$661$	−18.6573	−0.725684	−0.362842	−	0.931851i	$-0.618194\pi$
$661$	−18.6573	−0.725684	−0.362842	+	0.931851i	$0.618194\pi$
$662$	5.89640	0.229170
$663$	54.9049	2.13233
$664$	−9.94322	−0.385872
$665$	0.894508	0.0346875
$666$	17.7965	0.689600
$667$	−6.68268	−0.258754
$668$	−3.35513	−0.129814
$669$	−48.7263	−1.88387
$670$	−4.33036	−0.167296
$671$	1.57847	0.0609362
$672$	3.92439	0.151387
$673$	−45.4841	−1.75328	−0.876641	−	0.481144i	$-0.840221\pi$
$673$	−45.4841	−1.75328	−0.876641	+	0.481144i	$0.840221\pi$
$674$	8.83563	0.340336
$675$	8.11501	0.312347
$676$	24.4068	0.938725
$677$	11.6704	0.448530	0.224265	−	0.974528i	$-0.428002\pi$
$677$	11.6704	0.448530	0.224265	+	0.974528i	$0.428002\pi$
$678$	7.72614	0.296721
$679$	−1.87961	−0.0721328
$680$	2.31455	0.0887591
$681$	8.70474	0.333566
$682$	−2.16586	−0.0829351
$683$	17.6241	0.674368	0.337184	−	0.941439i	$-0.390526\pi$
$683$	17.6241	0.674368	0.337184	+	0.941439i	$0.390526\pi$
$684$	3.26110	0.124691
$685$	7.98683	0.305161
$686$	17.7497	0.677688
$687$	−56.6757	−2.16231
$688$	0.297180	0.0113299
$689$	−7.04037	−0.268217
$690$	5.52356	0.210278
$691$	1.92284	0.0731481	0.0365740	−	0.999331i	$-0.488356\pi$
$691$	1.92284	0.0731481	0.0365740	+	0.999331i	$0.488356\pi$
$692$	14.0038	0.532344
$693$	−7.69865	−0.292447
$694$	9.92597	0.376784
$695$	−1.93946	−0.0735677
$696$	5.39617	0.204541
$697$	−35.7751	−1.35508
$698$	−13.0108	−0.492467
$699$	−12.5033	−0.472919
$700$	6.91227	0.261259
$701$	−1.85245	−0.0699662	−0.0349831	−	0.999388i	$-0.511138\pi$
$701$	−1.85245	−0.0699662	−0.0349831	+	0.999388i	$0.511138\pi$
$702$	−10.8954	−0.411219
$703$	4.26510	0.160861
$704$	1.37541	0.0518376
$705$	−1.55901	−0.0587156
$706$	−2.42345	−0.0912079
$707$	−19.0393	−0.716046
$708$	−8.91745	−0.335138
$709$	14.0872	0.529056	0.264528	−	0.964378i	$-0.414784\pi$
$709$	14.0872	0.529056	0.264528	+	0.964378i	$0.414784\pi$
$710$	−3.95979	−0.148608
$711$	24.2759	0.910418
$712$	−15.3511	−0.575307
$713$	−5.04358	−0.188883
$714$	−13.6218	−0.509783
$715$	−5.60935	−0.209778
$716$	3.86111	0.144297
$717$	−51.2264	−1.91308
$718$	1.03022	0.0384473
$719$	−0.501094	−0.0186876	−0.00934382	−	0.999956i	$-0.502974\pi$
$719$	−0.501094	−0.0186876	−0.00934382	+	0.999956i	$0.502974\pi$
$720$	−2.45975	−0.0916695
$721$	−13.2646	−0.494000
$722$	−18.2184	−0.678020
$723$	−39.9162	−1.48450
$724$	−16.8587	−0.626550
$725$	9.50460	0.352992
$726$	23.5564	0.874261
$727$	40.0353	1.48483	0.742413	−	0.669942i	$-0.233681\pi$
$727$	40.0353	1.48483	0.742413	+	0.669942i	$0.233681\pi$
$728$	−9.28056	−0.343960
$729$	−37.6483	−1.39438
$730$	8.29178	0.306892
$731$	−1.03153	−0.0381524
$732$	−2.96811	−0.109705
$733$	3.74506	0.138327	0.0691634	−	0.997605i	$-0.477967\pi$
$733$	3.74506	0.138327	0.0691634	+	0.997605i	$0.477967\pi$
$734$	−11.5245	−0.425379
$735$	−8.10118	−0.298816
$736$	3.20287	0.118059
$737$	8.93200	0.329014
$738$	38.0193	1.39951
$739$	−12.9429	−0.476111	−0.238056	−	0.971252i	$-0.576510\pi$
$739$	−12.9429	−0.476111	−0.238056	+	0.971252i	$0.576510\pi$
$740$	−3.21703	−0.118260
$741$	−13.9839	−0.513713
$742$	1.74670	0.0641234
$743$	−7.55436	−0.277142	−0.138571	−	0.990352i	$-0.544251\pi$
$743$	−7.55436	−0.277142	−0.138571	+	0.990352i	$0.544251\pi$
$744$	4.07262	0.149309
$745$	4.80469	0.176030
$746$	−9.74925	−0.356945
$747$	−36.6785	−1.34200
$748$	−4.77411	−0.174559
$749$	8.51949	0.311295
$750$	−16.4789	−0.601723
$751$	27.3382	0.997585	0.498792	−	0.866721i	$-0.333777\pi$
$751$	27.3382	0.997585	0.498792	+	0.866721i	$0.333777\pi$
$752$	−0.903999	−0.0329655
$753$	−13.0919	−0.477096
$754$	−12.7611	−0.464731
$755$	11.1941	0.407397
$756$	2.70312	0.0983115
$757$	−10.4183	−0.378659	−0.189330	−	0.981914i	$-0.560631\pi$
$757$	−10.4183	−0.378659	−0.189330	+	0.981914i	$0.560631\pi$
$758$	−8.16575	−0.296593
$759$	−11.3931	−0.413545
$760$	−0.589503	−0.0213835
$761$	19.0308	0.689867	0.344933	−	0.938627i	$-0.387901\pi$
$761$	19.0308	0.689867	0.344933	+	0.938627i	$0.387901\pi$
$762$	−43.6824	−1.58245
$763$	21.4627	0.777003
$764$	17.7595	0.642517
$765$	8.53793	0.308689
$766$	32.6246	1.17878
$767$	21.0883	0.761455
$768$	−2.58627	−0.0933240
$769$	−24.6785	−0.889930	−0.444965	−	0.895548i	$-0.646784\pi$
$769$	−24.6785	−0.889930	−0.444965	+	0.895548i	$0.646784\pi$
$770$	1.39167	0.0501522
$771$	31.4906	1.13411
$772$	−20.7886	−0.748197
$773$	11.3179	0.407076	0.203538	−	0.979067i	$-0.434756\pi$
$773$	11.3179	0.407076	0.203538	+	0.979067i	$0.434756\pi$
$774$	1.09624	0.0394034
$775$	7.17335	0.257674
$776$	1.23871	0.0444671
$777$	18.9331	0.679222
$778$	34.5838	1.23989
$779$	9.11168	0.326460
$780$	10.5476	0.377666
$781$	8.16765	0.292261
$782$	−11.1173	−0.397555
$783$	3.71688	0.132830
$784$	−4.69751	−0.167768
$785$	−15.6081	−0.557077
$786$	−10.3590	−0.369494
$787$	15.3273	0.546358	0.273179	−	0.961963i	$-0.411925\pi$
$787$	15.3273	0.546358	0.273179	+	0.961963i	$0.411925\pi$
$788$	21.7684	0.775466
$789$	−4.07114	−0.144937
$790$	−4.38830	−0.156129
$791$	4.53302	0.161175
$792$	5.07360	0.180282
$793$	7.01910	0.249256
$794$	−0.387078	−0.0137369
$795$	−1.98518	−0.0704071
$796$	16.7255	0.592821
$797$	−50.2995	−1.78170	−0.890849	−	0.454299i	$-0.849890\pi$
$797$	−50.2995	−1.78170	−0.890849	+	0.454299i	$0.849890\pi$
$798$	3.46938	0.122815
$799$	3.13783	0.111008
$800$	−4.55536	−0.161056
$801$	−56.6271	−2.00082
$802$	20.5140	0.724375
$803$	−17.1030	−0.603552
$804$	−16.7955	−0.592330
$805$	3.24073	0.114221
$806$	−9.63109	−0.339241
$807$	−31.2882	−1.10140
$808$	12.5473	0.441414
$809$	6.05309	0.212815	0.106408	−	0.994323i	$-0.466065\pi$
$809$	6.05309	0.212815	0.106408	+	0.994323i	$0.466065\pi$
$810$	4.30707	0.151335
$811$	−8.79213	−0.308734	−0.154367	−	0.988014i	$-0.549334\pi$
$811$	−8.79213	−0.308734	−0.154367	+	0.988014i	$0.549334\pi$
$812$	3.16599	0.111105
$813$	6.71267	0.235423
$814$	6.63560	0.232578
$815$	7.85511	0.275152
$816$	8.97709	0.314261
$817$	0.262724	0.00919153
$818$	−1.48439	−0.0519007
$819$	−34.2341	−1.19624
$820$	−6.87266	−0.240004
$821$	−51.8089	−1.80814	−0.904071	−	0.427382i	$-0.859436\pi$
$821$	−51.8089	−1.80814	−0.904071	+	0.427382i	$0.859436\pi$
$822$	30.9772	1.08045
$823$	−16.3436	−0.569703	−0.284851	−	0.958572i	$-0.591944\pi$
$823$	−16.3436	−0.569703	−0.284851	+	0.958572i	$0.591944\pi$
$824$	8.74169	0.304531
$825$	16.2042	0.564157
$826$	−5.23197	−0.182043
$827$	−17.9442	−0.623980	−0.311990	−	0.950085i	$-0.600996\pi$
$827$	−17.9442	−0.623980	−0.311990	+	0.950085i	$0.600996\pi$
$828$	11.8147	0.410590
$829$	−19.6922	−0.683938	−0.341969	−	0.939711i	$-0.611094\pi$
$829$	−19.6922	−0.683938	−0.341969	+	0.939711i	$0.611094\pi$
$830$	6.63030	0.230141
$831$	−40.6565	−1.41036
$832$	6.11611	0.212038
$833$	16.3053	0.564946
$834$	−7.52225	−0.260474
$835$	2.23726	0.0774234
$836$	1.21594	0.0420540
$837$	2.80522	0.0969624
$838$	34.4721	1.19082
$839$	−4.59393	−0.158600	−0.0793001	−	0.996851i	$-0.525269\pi$
$839$	−4.59393	−0.158600	−0.0793001	+	0.996851i	$0.525269\pi$
$840$	−2.61685	−0.0902899
$841$	−24.6467	−0.849885
$842$	−27.2112	−0.937761
$843$	−21.3305	−0.734660
$844$	17.8955	0.615990
$845$	−16.2749	−0.559873
$846$	−3.33467	−0.114648
$847$	13.8208	0.474889
$848$	−1.15112	−0.0395296
$849$	−41.2487	−1.41565
$850$	15.8119	0.542343
$851$	15.4521	0.529692
$852$	−15.3582	−0.526163
$853$	40.1291	1.37399	0.686997	−	0.726660i	$-0.258929\pi$
$853$	40.1291	1.37399	0.686997	+	0.726660i	$0.258929\pi$
$854$	−1.74142	−0.0595903
$855$	−2.17456	−0.0743683
$856$	−5.61455	−0.191901
$857$	10.4714	0.357697	0.178849	−	0.983877i	$-0.442763\pi$
$857$	10.4714	0.357697	0.178849	+	0.983877i	$0.442763\pi$
$858$	−21.7561	−0.742740
$859$	17.0056	0.580223	0.290111	−	0.956993i	$-0.406308\pi$
$859$	17.0056	0.580223	0.290111	+	0.956993i	$0.406308\pi$
$860$	−0.198164	−0.00675734
$861$	40.4475	1.37845
$862$	−13.3673	−0.455291
$863$	−34.1719	−1.16323	−0.581613	−	0.813465i	$-0.697578\pi$
$863$	−34.1719	−1.16323	−0.581613	+	0.813465i	$0.697578\pi$
$864$	−1.78142	−0.0606052
$865$	−9.33795	−0.317500
$866$	14.2652	0.484752
$867$	12.8066	0.434937
$868$	2.38945	0.0811033
$869$	9.05152	0.307052
$870$	−3.59825	−0.121992
$871$	39.7185	1.34581
$872$	−14.1445	−0.478992
$873$	4.56935	0.154649
$874$	2.83151	0.0957774
$875$	−9.66833	−0.326849
$876$	32.1600	1.08658
$877$	6.32942	0.213729	0.106865	−	0.994274i	$-0.465919\pi$
$877$	6.32942	0.213729	0.106865	+	0.994274i	$0.465919\pi$
$878$	−26.3005	−0.887600
$879$	−28.7531	−0.969816
$880$	−0.917143	−0.0309169
$881$	30.1245	1.01492	0.507461	−	0.861675i	$-0.330584\pi$
$881$	30.1245	1.01492	0.507461	+	0.861675i	$0.330584\pi$
$882$	−17.3282	−0.583470
$883$	−22.3707	−0.752833	−0.376417	−	0.926450i	$-0.622844\pi$
$883$	−22.3707	−0.752833	−0.376417	+	0.926450i	$0.622844\pi$
$884$	−21.2294	−0.714021
$885$	5.94630	0.199883
$886$	−7.64307	−0.256774
$887$	36.6531	1.23069	0.615345	−	0.788258i	$-0.289017\pi$
$887$	36.6531	1.23069	0.615345	+	0.788258i	$0.289017\pi$
$888$	−12.4774	−0.418714
$889$	−25.6290	−0.859568
$890$	10.2364	0.343123
$891$	−8.88397	−0.297624
$892$	18.8404	0.630822
$893$	−0.799186	−0.0267437
$894$	18.6352	0.623254
$895$	−2.57465	−0.0860611
$896$	−1.51739	−0.0506926
$897$	−50.6627	−1.69158
$898$	20.8772	0.696680
$899$	3.28557	0.109580
$900$	−16.8038	−0.560126
$901$	3.99560	0.133113
$902$	14.1759	0.472005
$903$	1.16625	0.0388104
$904$	−2.98737	−0.0993584
$905$	11.2417	0.373686
$906$	43.4169	1.44243
$907$	−15.4220	−0.512080	−0.256040	−	0.966666i	$-0.582418\pi$
$907$	−15.4220	−0.512080	−0.256040	+	0.966666i	$0.582418\pi$
$908$	−3.36575	−0.111696
$909$	46.2846	1.53516
$910$	6.18842	0.205144
$911$	42.4966	1.40797	0.703987	−	0.710213i	$-0.251401\pi$
$911$	42.4966	1.40797	0.703987	+	0.710213i	$0.251401\pi$
$912$	−2.28641	−0.0757106
$913$	−13.6760	−0.452608
$914$	24.0023	0.793924
$915$	1.97918	0.0654298
$916$	21.9141	0.724061
$917$	−6.07775	−0.200705
$918$	6.18341	0.204083
$919$	−25.5421	−0.842557	−0.421278	−	0.906931i	$-0.638418\pi$
$919$	−25.5421	−0.842557	−0.421278	+	0.906931i	$0.638418\pi$
$920$	−2.13572	−0.0704127
$921$	−55.2028	−1.81899
$922$	−0.197333	−0.00649880
$923$	36.3197	1.19548
$924$	5.39764	0.177569
$925$	−21.9772	−0.722605
$926$	−41.8546	−1.37543
$927$	32.2464	1.05911
$928$	−2.08647	−0.0684916
$929$	43.7368	1.43496	0.717479	−	0.696580i	$-0.245296\pi$
$929$	43.7368	1.43496	0.717479	+	0.696580i	$0.245296\pi$
$930$	−2.71569	−0.0890509
$931$	−4.15286	−0.136105
$932$	4.83450	0.158359
$933$	−14.1585	−0.463528
$934$	−0.459201	−0.0150255
$935$	3.18345	0.104110
$936$	22.5611	0.737433
$937$	−20.0621	−0.655399	−0.327700	−	0.944782i	$-0.606273\pi$
$937$	−20.0621	−0.655399	−0.327700	+	0.944782i	$0.606273\pi$
$938$	−9.85408	−0.321747
$939$	−3.06748	−0.100103
$940$	0.602801	0.0196612
$941$	−15.8658	−0.517209	−0.258604	−	0.965983i	$-0.583263\pi$
$941$	−15.8658	−0.517209	−0.258604	+	0.965983i	$0.583263\pi$
$942$	−60.5366	−1.97239
$943$	33.0109	1.07498
$944$	3.44799	0.112223
$945$	−1.80248	−0.0586348
$946$	0.408743	0.0132894
$947$	−36.2486	−1.17792	−0.588961	−	0.808161i	$-0.700463\pi$
$947$	−36.2486	−1.17792	−0.588961	+	0.808161i	$0.700463\pi$
$948$	−17.0202	−0.552790
$949$	−76.0531	−2.46879
$950$	−4.02719	−0.130659
$951$	−61.9281	−2.00816
$952$	5.26696	0.170703
$953$	5.20581	0.168633	0.0843164	−	0.996439i	$-0.473129\pi$
$953$	5.20581	0.168633	0.0843164	+	0.996439i	$0.473129\pi$
$954$	−4.24624	−0.137477
$955$	−11.8423	−0.383209
$956$	19.8070	0.640605
$957$	7.42192	0.239917
$958$	−36.8063	−1.18916
$959$	18.1747	0.586891
$960$	1.72457	0.0556602
$961$	−28.5203	−0.920010
$962$	29.5070	0.951344
$963$	−20.7109	−0.667401
$964$	15.4339	0.497092
$965$	13.8622	0.446238
$966$	12.5693	0.404411
$967$	13.8612	0.445745	0.222873	−	0.974848i	$-0.428457\pi$
$967$	13.8612	0.445745	0.222873	+	0.974848i	$0.428457\pi$
$968$	−9.10826	−0.292751
$969$	7.93625	0.254949
$970$	−0.825991	−0.0265210
$971$	−44.2741	−1.42082	−0.710411	−	0.703787i	$-0.751491\pi$
$971$	−44.2741	−1.42082	−0.710411	+	0.703787i	$0.751491\pi$
$972$	22.0494	0.707235
$973$	−4.41339	−0.141487
$974$	14.4908	0.464314
$975$	72.0563	2.30765
$976$	1.14764	0.0367351
$977$	−15.3062	−0.489689	−0.244845	−	0.969562i	$-0.578737\pi$
$977$	−15.3062	−0.489689	−0.244845	+	0.969562i	$0.578737\pi$
$978$	30.4663	0.974206
$979$	−21.1140	−0.674806
$980$	3.13238	0.100060
$981$	−52.1761	−1.66585
$982$	−15.9682	−0.509567
$983$	−27.1158	−0.864859	−0.432430	−	0.901668i	$-0.642344\pi$
$983$	−27.1158	−0.864859	−0.432430	+	0.901668i	$0.642344\pi$
$984$	−26.6559	−0.849758
$985$	−14.5155	−0.462502
$986$	7.24224	0.230640
$987$	−3.54765	−0.112923
$988$	5.40699	0.172019
$989$	0.951827	0.0302663
$990$	−3.38315	−0.107524
$991$	43.2116	1.37266	0.686330	−	0.727290i	$-0.259220\pi$
$991$	43.2116	1.37266	0.686330	+	0.727290i	$0.259220\pi$
$992$	−1.57471	−0.0499970
$993$	−15.2497	−0.483934
$994$	−9.01083	−0.285806
$995$	−11.1528	−0.353569
$996$	25.7159	0.814838
$997$	44.2008	1.39985	0.699926	−	0.714215i	$-0.253216\pi$
$997$	44.2008	1.39985	0.699926	+	0.714215i	$0.253216\pi$
$998$	−23.7040	−0.750337
$999$	−8.59441	−0.271915

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8038.2.a.d.1.9	✓	92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8038.2.a.d.1.9	✓	92	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:	\( N \)	\(=\)	\( 8038 = 2 \cdot 4019 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8038.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.58627 q^{3} +1.00000 q^{4} -0.666816 q^{5} -2.58627 q^{6} -1.51739 q^{7} +1.00000 q^{8} +3.68880 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.58627 q^{3} +1.00000 q^{4} -0.666816 q^{5} -2.58627 q^{6} -1.51739 q^{7} +1.00000 q^{8} +3.68880 q^{9} -0.666816 q^{10} +1.37541 q^{11} -2.58627 q^{12} +6.11611 q^{13} -1.51739 q^{14} +1.72457 q^{15} +1.00000 q^{16} -3.47105 q^{17} +3.68880 q^{18} +0.884056 q^{19} -0.666816 q^{20} +3.92439 q^{21} +1.37541 q^{22} +3.20287 q^{23} -2.58627 q^{24} -4.55536 q^{25} +6.11611 q^{26} -1.78142 q^{27} -1.51739 q^{28} -2.08647 q^{29} +1.72457 q^{30} -1.57471 q^{31} +1.00000 q^{32} -3.55717 q^{33} -3.47105 q^{34} +1.01182 q^{35} +3.68880 q^{36} +4.82447 q^{37} +0.884056 q^{38} -15.8179 q^{39} -0.666816 q^{40} +10.3067 q^{41} +3.92439 q^{42} +0.297180 q^{43} +1.37541 q^{44} -2.45975 q^{45} +3.20287 q^{46} -0.903999 q^{47} -2.58627 q^{48} -4.69751 q^{49} -4.55536 q^{50} +8.97709 q^{51} +6.11611 q^{52} -1.15112 q^{53} -1.78142 q^{54} -0.917143 q^{55} -1.51739 q^{56} -2.28641 q^{57} -2.08647 q^{58} +3.44799 q^{59} +1.72457 q^{60} +1.14764 q^{61} -1.57471 q^{62} -5.59736 q^{63} +1.00000 q^{64} -4.07832 q^{65} -3.55717 q^{66} +6.49408 q^{67} -3.47105 q^{68} -8.28348 q^{69} +1.01182 q^{70} +5.93835 q^{71} +3.68880 q^{72} -12.4349 q^{73} +4.82447 q^{74} +11.7814 q^{75} +0.884056 q^{76} -2.08703 q^{77} -15.8179 q^{78} +6.58098 q^{79} -0.666816 q^{80} -6.45916 q^{81} +10.3067 q^{82} -9.94322 q^{83} +3.92439 q^{84} +2.31455 q^{85} +0.297180 q^{86} +5.39617 q^{87} +1.37541 q^{88} -15.3511 q^{89} -2.45975 q^{90} -9.28056 q^{91} +3.20287 q^{92} +4.07262 q^{93} -0.903999 q^{94} -0.589503 q^{95} -2.58627 q^{96} +1.23871 q^{97} -4.69751 q^{98} +5.07360 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 92 q + 92 q^{2} + 31 q^{3} + 92 q^{4} + 28 q^{5} + 31 q^{6} + 29 q^{7} + 92 q^{8} + 113 q^{9}+O(q^{10}) \) 92 * q + 92 * q^2 + 31 * q^3 + 92 * q^4 + 28 * q^5 + 31 * q^6 + 29 * q^7 + 92 * q^8 + 113 * q^9	\( 92 q + 92 q^{2} + 31 q^{3} + 92 q^{4} + 28 q^{5} + 31 q^{6} + 29 q^{7} + 92 q^{8} + 113 q^{9} + 28 q^{10} + 37 q^{11} + 31 q^{12} + 20 q^{13} + 29 q^{14} + 30 q^{15} + 92 q^{16} + 52 q^{17} + 113 q^{18} + 61 q^{19} + 28 q^{20} + 5 q^{21} + 37 q^{22} + 71 q^{23} + 31 q^{24} + 118 q^{25} + 20 q^{26} + 112 q^{27} + 29 q^{28} + 30 q^{29} + 30 q^{30} + 89 q^{31} + 92 q^{32} + 52 q^{33} + 52 q^{34} + 58 q^{35} + 113 q^{36} + 15 q^{37} + 61 q^{38} + 43 q^{39} + 28 q^{40} + 75 q^{41} + 5 q^{42} + 46 q^{43} + 37 q^{44} + 63 q^{45} + 71 q^{46} + 92 q^{47} + 31 q^{48} + 131 q^{49} + 118 q^{50} + 45 q^{51} + 20 q^{52} + 72 q^{53} + 112 q^{54} + 86 q^{55} + 29 q^{56} + 44 q^{57} + 30 q^{58} + 95 q^{59} + 30 q^{60} - 4 q^{61} + 89 q^{62} + 67 q^{63} + 92 q^{64} + 55 q^{65} + 52 q^{66} + 40 q^{67} + 52 q^{68} + 25 q^{69} + 58 q^{70} + 84 q^{71} + 113 q^{72} + 87 q^{73} + 15 q^{74} + 132 q^{75} + 61 q^{76} + 96 q^{77} + 43 q^{78} + 68 q^{79} + 28 q^{80} + 156 q^{81} + 75 q^{82} + 120 q^{83} + 5 q^{84} - 14 q^{85} + 46 q^{86} + 73 q^{87} + 37 q^{88} + 86 q^{89} + 63 q^{90} + 93 q^{91} + 71 q^{92} + 29 q^{93} + 92 q^{94} + 67 q^{95} + 31 q^{96} + 65 q^{97} + 131 q^{98} + 94 q^{99}+O(q^{100}) \) 92 * q + 92 * q^2 + 31 * q^3 + 92 * q^4 + 28 * q^5 + 31 * q^6 + 29 * q^7 + 92 * q^8 + 113 * q^9 + 28 * q^10 + 37 * q^11 + 31 * q^12 + 20 * q^13 + 29 * q^14 + 30 * q^15 + 92 * q^16 + 52 * q^17 + 113 * q^18 + 61 * q^19 + 28 * q^20 + 5 * q^21 + 37 * q^22 + 71 * q^23 + 31 * q^24 + 118 * q^25 + 20 * q^26 + 112 * q^27 + 29 * q^28 + 30 * q^29 + 30 * q^30 + 89 * q^31 + 92 * q^32 + 52 * q^33 + 52 * q^34 + 58 * q^35 + 113 * q^36 + 15 * q^37 + 61 * q^38 + 43 * q^39 + 28 * q^40 + 75 * q^41 + 5 * q^42 + 46 * q^43 + 37 * q^44 + 63 * q^45 + 71 * q^46 + 92 * q^47 + 31 * q^48 + 131 * q^49 + 118 * q^50 + 45 * q^51 + 20 * q^52 + 72 * q^53 + 112 * q^54 + 86 * q^55 + 29 * q^56 + 44 * q^57 + 30 * q^58 + 95 * q^59 + 30 * q^60 - 4 * q^61 + 89 * q^62 + 67 * q^63 + 92 * q^64 + 55 * q^65 + 52 * q^66 + 40 * q^67 + 52 * q^68 + 25 * q^69 + 58 * q^70 + 84 * q^71 + 113 * q^72 + 87 * q^73 + 15 * q^74 + 132 * q^75 + 61 * q^76 + 96 * q^77 + 43 * q^78 + 68 * q^79 + 28 * q^80 + 156 * q^81 + 75 * q^82 + 120 * q^83 + 5 * q^84 - 14 * q^85 + 46 * q^86 + 73 * q^87 + 37 * q^88 + 86 * q^89 + 63 * q^90 + 93 * q^91 + 71 * q^92 + 29 * q^93 + 92 * q^94 + 67 * q^95 + 31 * q^96 + 65 * q^97 + 131 * q^98 + 94 * q^99

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