LMFDB - Embedded newform 8038.2.a.d.1.6

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			1.6
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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.70157 q^{3} +1.00000 q^{4} +0.143003 q^{5} -2.70157 q^{6} -2.92792 q^{7} +1.00000 q^{8} +4.29850 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.70157 q^{3} +1.00000 q^{4} +0.143003 q^{5} -2.70157 q^{6} -2.92792 q^{7} +1.00000 q^{8} +4.29850 q^{9} +0.143003 q^{10} +6.07110 q^{11} -2.70157 q^{12} +1.15954 q^{13} -2.92792 q^{14} -0.386334 q^{15} +1.00000 q^{16} +6.99137 q^{17} +4.29850 q^{18} +2.23064 q^{19} +0.143003 q^{20} +7.90999 q^{21} +6.07110 q^{22} +2.21391 q^{23} -2.70157 q^{24} -4.97955 q^{25} +1.15954 q^{26} -3.50800 q^{27} -2.92792 q^{28} +7.90755 q^{29} -0.386334 q^{30} +2.13106 q^{31} +1.00000 q^{32} -16.4015 q^{33} +6.99137 q^{34} -0.418702 q^{35} +4.29850 q^{36} -2.65427 q^{37} +2.23064 q^{38} -3.13258 q^{39} +0.143003 q^{40} -1.40140 q^{41} +7.90999 q^{42} +0.837498 q^{43} +6.07110 q^{44} +0.614700 q^{45} +2.21391 q^{46} +6.25503 q^{47} -2.70157 q^{48} +1.57270 q^{49} -4.97955 q^{50} -18.8877 q^{51} +1.15954 q^{52} +0.170293 q^{53} -3.50800 q^{54} +0.868187 q^{55} -2.92792 q^{56} -6.02624 q^{57} +7.90755 q^{58} -4.29663 q^{59} -0.386334 q^{60} -0.828855 q^{61} +2.13106 q^{62} -12.5857 q^{63} +1.00000 q^{64} +0.165818 q^{65} -16.4015 q^{66} +8.19496 q^{67} +6.99137 q^{68} -5.98104 q^{69} -0.418702 q^{70} -13.1234 q^{71} +4.29850 q^{72} +3.34062 q^{73} -2.65427 q^{74} +13.4526 q^{75} +2.23064 q^{76} -17.7757 q^{77} -3.13258 q^{78} -1.10006 q^{79} +0.143003 q^{80} -3.41838 q^{81} -1.40140 q^{82} +16.6199 q^{83} +7.90999 q^{84} +0.999789 q^{85} +0.837498 q^{86} -21.3628 q^{87} +6.07110 q^{88} -14.2210 q^{89} +0.614700 q^{90} -3.39503 q^{91} +2.21391 q^{92} -5.75720 q^{93} +6.25503 q^{94} +0.318989 q^{95} -2.70157 q^{96} -9.50109 q^{97} +1.57270 q^{98} +26.0966 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.70157	−1.55975	−0.779877	−	0.625932i	$-0.784719\pi$
$3$	−2.70157	−1.55975	−0.779877	+	0.625932i	$0.784719\pi$
$4$	1.00000	0.500000
$5$	0.143003	0.0639530	0.0319765	−	0.999489i	$-0.489820\pi$
$5$	0.143003	0.0639530	0.0319765	+	0.999489i	$0.489820\pi$
$6$	−2.70157	−1.10291
$7$	−2.92792	−1.10665	−0.553324	−	0.832966i	$-0.686641\pi$
$7$	−2.92792	−1.10665	−0.553324	+	0.832966i	$0.686641\pi$
$8$	1.00000	0.353553
$9$	4.29850	1.43283
$10$	0.143003	0.0452216
$11$	6.07110	1.83051	0.915253	−	0.402880i	$-0.131991\pi$
$11$	6.07110	1.83051	0.915253	+	0.402880i	$0.131991\pi$
$12$	−2.70157	−0.779877
$13$	1.15954	0.321598	0.160799	−	0.986987i	$-0.448593\pi$
$13$	1.15954	0.321598	0.160799	+	0.986987i	$0.448593\pi$
$14$	−2.92792	−0.782519
$15$	−0.386334	−0.0997510
$16$	1.00000	0.250000
$17$	6.99137	1.69566	0.847829	−	0.530270i	$-0.177910\pi$
$17$	6.99137	1.69566	0.847829	+	0.530270i	$0.177910\pi$
$18$	4.29850	1.01317
$19$	2.23064	0.511744	0.255872	−	0.966711i	$-0.417637\pi$
$19$	2.23064	0.511744	0.255872	+	0.966711i	$0.417637\pi$
$20$	0.143003	0.0319765
$21$	7.90999	1.72610
$22$	6.07110	1.29436
$23$	2.21391	0.461632	0.230816	−	0.972997i	$-0.425860\pi$
$23$	2.21391	0.461632	0.230816	+	0.972997i	$0.425860\pi$
$24$	−2.70157	−0.551457
$25$	−4.97955	−0.995910
$26$	1.15954	0.227404
$27$	−3.50800	−0.675115
$28$	−2.92792	−0.553324
$29$	7.90755	1.46840	0.734198	−	0.678936i	$-0.237558\pi$
$29$	7.90755	1.46840	0.734198	+	0.678936i	$0.237558\pi$
$30$	−0.386334	−0.0705346
$31$	2.13106	0.382749	0.191374	−	0.981517i	$-0.438706\pi$
$31$	2.13106	0.382749	0.191374	+	0.981517i	$0.438706\pi$
$32$	1.00000	0.176777
$33$	−16.4015	−2.85514
$34$	6.99137	1.19901
$35$	−0.418702	−0.0707735
$36$	4.29850	0.716417
$37$	−2.65427	−0.436360	−0.218180	−	0.975909i	$-0.570012\pi$
$37$	−2.65427	−0.436360	−0.218180	+	0.975909i	$0.570012\pi$
$38$	2.23064	0.361858
$39$	−3.13258	−0.501614
$40$	0.143003	0.0226108
$41$	−1.40140	−0.218861	−0.109431	−	0.993994i	$-0.534903\pi$
$41$	−1.40140	−0.218861	−0.109431	+	0.993994i	$0.534903\pi$
$42$	7.90999	1.22054
$43$	0.837498	0.127717	0.0638586	−	0.997959i	$-0.479659\pi$
$43$	0.837498	0.127717	0.0638586	+	0.997959i	$0.479659\pi$
$44$	6.07110	0.915253
$45$	0.614700	0.0916340
$46$	2.21391	0.326423
$47$	6.25503	0.912390	0.456195	−	0.889880i	$-0.349212\pi$
$47$	6.25503	0.912390	0.456195	+	0.889880i	$0.349212\pi$
$48$	−2.70157	−0.389939
$49$	1.57270	0.224671
$50$	−4.97955	−0.704215
$51$	−18.8877	−2.64481
$52$	1.15954	0.160799
$53$	0.170293	0.0233915	0.0116958	−	0.999932i	$-0.496277\pi$
$53$	0.170293	0.0233915	0.0116958	+	0.999932i	$0.496277\pi$
$54$	−3.50800	−0.477379
$55$	0.868187	0.117066
$56$	−2.92792	−0.391259
$57$	−6.02624	−0.798195
$58$	7.90755	1.03831
$59$	−4.29663	−0.559374	−0.279687	−	0.960091i	$-0.590231\pi$
$59$	−4.29663	−0.559374	−0.279687	+	0.960091i	$0.590231\pi$
$60$	−0.386334	−0.0498755
$61$	−0.828855	−0.106124	−0.0530620	−	0.998591i	$-0.516898\pi$
$61$	−0.828855	−0.106124	−0.0530620	+	0.998591i	$0.516898\pi$
$62$	2.13106	0.270644
$63$	−12.5857	−1.58564
$64$	1.00000	0.125000
$65$	0.165818	0.0205671
$66$	−16.4015	−2.01889
$67$	8.19496	1.00117	0.500587	−	0.865686i	$-0.333118\pi$
$67$	8.19496	1.00117	0.500587	+	0.865686i	$0.333118\pi$
$68$	6.99137	0.847829
$69$	−5.98104	−0.720033
$70$	−0.418702	−0.0500444
$71$	−13.1234	−1.55747	−0.778733	−	0.627356i	$-0.784137\pi$
$71$	−13.1234	−1.55747	−0.778733	+	0.627356i	$0.784137\pi$
$72$	4.29850	0.506583
$73$	3.34062	0.390990	0.195495	−	0.980705i	$-0.437369\pi$
$73$	3.34062	0.390990	0.195495	+	0.980705i	$0.437369\pi$
$74$	−2.65427	−0.308553
$75$	13.4526	1.55338
$76$	2.23064	0.255872
$77$	−17.7757	−2.02573
$78$	−3.13258	−0.354694
$79$	−1.10006	−0.123767	−0.0618834	−	0.998083i	$-0.519711\pi$
$79$	−1.10006	−0.123767	−0.0618834	+	0.998083i	$0.519711\pi$
$80$	0.143003	0.0159882
$81$	−3.41838	−0.379820
$82$	−1.40140	−0.154758
$83$	16.6199	1.82428	0.912138	−	0.409883i	$-0.134430\pi$
$83$	16.6199	1.82428	0.912138	+	0.409883i	$0.134430\pi$
$84$	7.90999	0.863050
$85$	0.999789	0.108442
$86$	0.837498	0.0903097
$87$	−21.3628	−2.29034
$88$	6.07110	0.647182
$89$	−14.2210	−1.50742	−0.753712	−	0.657204i	$-0.771739\pi$
$89$	−14.2210	−1.50742	−0.753712	+	0.657204i	$0.771739\pi$
$90$	0.614700	0.0647951
$91$	−3.39503	−0.355896
$92$	2.21391	0.230816
$93$	−5.75720	−0.596994
$94$	6.25503	0.645157
$95$	0.318989	0.0327276
$96$	−2.70157	−0.275728
$97$	−9.50109	−0.964690	−0.482345	−	0.875981i	$-0.660215\pi$
$97$	−9.50109	−0.964690	−0.482345	+	0.875981i	$0.660215\pi$
$98$	1.57270	0.158867
$99$	26.0966	2.62281
$100$	−4.97955	−0.497955
$101$	−13.7218	−1.36537	−0.682683	−	0.730715i	$-0.739187\pi$
$101$	−13.7218	−1.36537	−0.682683	+	0.730715i	$0.739187\pi$
$102$	−18.8877	−1.87016
$103$	8.98180	0.885003	0.442501	−	0.896768i	$-0.354091\pi$
$103$	8.98180	0.885003	0.442501	+	0.896768i	$0.354091\pi$
$104$	1.15954	0.113702
$105$	1.13115	0.110389
$106$	0.170293	0.0165403
$107$	9.59988	0.928055	0.464027	−	0.885821i	$-0.346404\pi$
$107$	9.59988	0.928055	0.464027	+	0.885821i	$0.346404\pi$
$108$	−3.50800	−0.337558
$109$	−7.13551	−0.683458	−0.341729	−	0.939799i	$-0.611012\pi$
$109$	−7.13551	−0.683458	−0.341729	+	0.939799i	$0.611012\pi$
$110$	0.868187	0.0827784
$111$	7.17072	0.680615
$112$	−2.92792	−0.276662
$113$	−3.97433	−0.373874	−0.186937	−	0.982372i	$-0.559856\pi$
$113$	−3.97433	−0.373874	−0.186937	+	0.982372i	$0.559856\pi$
$114$	−6.02624	−0.564409
$115$	0.316596	0.0295228
$116$	7.90755	0.734198
$117$	4.98428	0.460796
$118$	−4.29663	−0.395537
$119$	−20.4702	−1.87650
$120$	−0.386334	−0.0352673
$121$	25.8583	2.35075
$122$	−0.828855	−0.0750410
$123$	3.78598	0.341370
$124$	2.13106	0.191374
$125$	−1.42711	−0.127644
$126$	−12.5857	−1.12122
$127$	6.27373	0.556703	0.278352	−	0.960479i	$-0.410212\pi$
$127$	6.27373	0.556703	0.278352	+	0.960479i	$0.410212\pi$
$128$	1.00000	0.0883883
$129$	−2.26256	−0.199208
$130$	0.165818	0.0145432
$131$	13.9425	1.21816	0.609082	−	0.793107i	$-0.291538\pi$
$131$	13.9425	1.21816	0.609082	+	0.793107i	$0.291538\pi$
$132$	−16.4015	−1.42757
$133$	−6.53113	−0.566321
$134$	8.19496	0.707937
$135$	−0.501656	−0.0431756
$136$	6.99137	0.599505
$137$	5.22187	0.446134	0.223067	−	0.974803i	$-0.428393\pi$
$137$	5.22187	0.446134	0.223067	+	0.974803i	$0.428393\pi$
$138$	−5.98104	−0.509140
$139$	0.107441	0.00911304	0.00455652	−	0.999990i	$-0.498550\pi$
$139$	0.107441	0.00911304	0.00455652	+	0.999990i	$0.498550\pi$
$140$	−0.418702	−0.0353867
$141$	−16.8984	−1.42311
$142$	−13.1234	−1.10129
$143$	7.03967	0.588687
$144$	4.29850	0.358209
$145$	1.13081	0.0939083
$146$	3.34062	0.276472
$147$	−4.24876	−0.350432
$148$	−2.65427	−0.218180
$149$	−12.9916	−1.06431	−0.532157	−	0.846646i	$-0.678618\pi$
$149$	−12.9916	−1.06431	−0.532157	+	0.846646i	$0.678618\pi$
$150$	13.4526	1.09840
$151$	4.43634	0.361024	0.180512	−	0.983573i	$-0.442224\pi$
$151$	4.43634	0.361024	0.180512	+	0.983573i	$0.442224\pi$
$152$	2.23064	0.180929
$153$	30.0524	2.42960
$154$	−17.7757	−1.43241
$155$	0.304748	0.0244779
$156$	−3.13258	−0.250807
$157$	9.34704	0.745975	0.372988	−	0.927836i	$-0.378333\pi$
$157$	9.34704	0.745975	0.372988	+	0.927836i	$0.378333\pi$
$158$	−1.10006	−0.0875164
$159$	−0.460059	−0.0364850
$160$	0.143003	0.0113054
$161$	−6.48215	−0.510865
$162$	−3.41838	−0.268573
$163$	−3.89511	−0.305089	−0.152544	−	0.988297i	$-0.548747\pi$
$163$	−3.89511	−0.305089	−0.152544	+	0.988297i	$0.548747\pi$
$164$	−1.40140	−0.109431
$165$	−2.34547	−0.182595
$166$	16.6199	1.28996
$167$	0.882823	0.0683149	0.0341575	−	0.999416i	$-0.489125\pi$
$167$	0.882823	0.0683149	0.0341575	+	0.999416i	$0.489125\pi$
$168$	7.90999	0.610269
$169$	−11.6555	−0.896575
$170$	0.999789	0.0766803
$171$	9.58841	0.733244
$172$	0.837498	0.0638586
$173$	−18.9250	−1.43884	−0.719421	−	0.694575i	$-0.755593\pi$
$173$	−18.9250	−1.43884	−0.719421	+	0.694575i	$0.755593\pi$
$174$	−21.3628	−1.61951
$175$	14.5797	1.10212
$176$	6.07110	0.457626
$177$	11.6077	0.872486
$178$	−14.2210	−1.06591
$179$	11.3848	0.850937	0.425469	−	0.904973i	$-0.360109\pi$
$179$	11.3848	0.850937	0.425469	+	0.904973i	$0.360109\pi$
$180$	0.614700	0.0458170
$181$	22.4049	1.66534	0.832671	−	0.553768i	$-0.186810\pi$
$181$	22.4049	1.66534	0.832671	+	0.553768i	$0.186810\pi$
$182$	−3.39503	−0.251656
$183$	2.23921	0.165527
$184$	2.21391	0.163212
$185$	−0.379570	−0.0279065
$186$	−5.75720	−0.422139
$187$	42.4453	3.10391
$188$	6.25503	0.456195
$189$	10.2711	0.747116
$190$	0.318989	0.0231419
$191$	−6.11109	−0.442183	−0.221091	−	0.975253i	$-0.570962\pi$
$191$	−6.11109	−0.442183	−0.221091	+	0.975253i	$0.570962\pi$
$192$	−2.70157	−0.194969
$193$	−15.8470	−1.14069	−0.570346	−	0.821404i	$-0.693191\pi$
$193$	−15.8470	−1.14069	−0.570346	+	0.821404i	$0.693191\pi$
$194$	−9.50109	−0.682139
$195$	−0.447969	−0.0320797
$196$	1.57270	0.112336
$197$	−14.9167	−1.06277	−0.531387	−	0.847129i	$-0.678329\pi$
$197$	−14.9167	−1.06277	−0.531387	+	0.847129i	$0.678329\pi$
$198$	26.0966	1.85461
$199$	−5.14486	−0.364709	−0.182355	−	0.983233i	$-0.558372\pi$
$199$	−5.14486	−0.364709	−0.182355	+	0.983233i	$0.558372\pi$
$200$	−4.97955	−0.352107
$201$	−22.1393	−1.56159
$202$	−13.7218	−0.965460
$203$	−23.1527	−1.62500
$204$	−18.8877	−1.32240
$205$	−0.200404	−0.0139968
$206$	8.98180	0.625791
$207$	9.51650	0.661443
$208$	1.15954	0.0803995
$209$	13.5424	0.936750
$210$	1.13115	0.0780570
$211$	6.72091	0.462687	0.231343	−	0.972872i	$-0.425688\pi$
$211$	6.72091	0.462687	0.231343	+	0.972872i	$0.425688\pi$
$212$	0.170293	0.0116958
$213$	35.4539	2.42926
$214$	9.59988	0.656234
$215$	0.119765	0.00816790
$216$	−3.50800	−0.238689
$217$	−6.23955	−0.423569
$218$	−7.13551	−0.483278
$219$	−9.02494	−0.609849
$220$	0.868187	0.0585332
$221$	8.10676	0.545320
$222$	7.17072	0.481267
$223$	13.8619	0.928261	0.464131	−	0.885767i	$-0.346367\pi$
$223$	13.8619	0.928261	0.464131	+	0.885767i	$0.346367\pi$
$224$	−2.92792	−0.195630
$225$	−21.4046	−1.42697
$226$	−3.97433	−0.264369
$227$	24.3204	1.61420	0.807101	−	0.590414i	$-0.201035\pi$
$227$	24.3204	1.61420	0.807101	+	0.590414i	$0.201035\pi$
$228$	−6.02624	−0.399097
$229$	10.5866	0.699579	0.349790	−	0.936828i	$-0.386253\pi$
$229$	10.5866	0.699579	0.349790	+	0.936828i	$0.386253\pi$
$230$	0.316596	0.0208757
$231$	48.0223	3.15964
$232$	7.90755	0.519156
$233$	13.0208	0.853022	0.426511	−	0.904482i	$-0.359742\pi$
$233$	13.0208	0.853022	0.426511	+	0.904482i	$0.359742\pi$
$234$	4.98428	0.325832
$235$	0.894490	0.0583501
$236$	−4.29663	−0.279687
$237$	2.97190	0.193046
$238$	−20.4702	−1.32688
$239$	−23.8410	−1.54215	−0.771074	−	0.636745i	$-0.780280\pi$
$239$	−23.8410	−1.54215	−0.771074	+	0.636745i	$0.780280\pi$
$240$	−0.386334	−0.0249377
$241$	30.0654	1.93668	0.968342	−	0.249627i	$-0.0803078\pi$
$241$	30.0654	1.93668	0.968342	+	0.249627i	$0.0803078\pi$
$242$	25.8583	1.66223
$243$	19.7590	1.26754
$244$	−0.828855	−0.0530620
$245$	0.224901	0.0143684
$246$	3.78598	0.241385
$247$	2.58651	0.164576
$248$	2.13106	0.135322
$249$	−44.9000	−2.84542
$250$	−1.42711	−0.0902582
$251$	−2.35176	−0.148442	−0.0742209	−	0.997242i	$-0.523647\pi$
$251$	−2.35176	−0.148442	−0.0742209	+	0.997242i	$0.523647\pi$
$252$	−12.5857	−0.792822
$253$	13.4409	0.845021
$254$	6.27373	0.393649
$255$	−2.70100	−0.169143
$256$	1.00000	0.0625000
$257$	17.1209	1.06797	0.533986	−	0.845493i	$-0.320693\pi$
$257$	17.1209	1.06797	0.533986	+	0.845493i	$0.320693\pi$
$258$	−2.26256	−0.140861
$259$	7.77150	0.482897
$260$	0.165818	0.0102836
$261$	33.9906	2.10397
$262$	13.9425	0.861372
$263$	−14.5707	−0.898466	−0.449233	−	0.893415i	$-0.648303\pi$
$263$	−14.5707	−0.898466	−0.449233	+	0.893415i	$0.648303\pi$
$264$	−16.4015	−1.00944
$265$	0.0243524	0.00149596
$266$	−6.53113	−0.400449
$267$	38.4191	2.35121
$268$	8.19496	0.500587
$269$	−10.4087	−0.634630	−0.317315	−	0.948320i	$-0.602781\pi$
$269$	−10.4087	−0.634630	−0.317315	+	0.948320i	$0.602781\pi$
$270$	−0.501656	−0.0305298
$271$	4.28064	0.260031	0.130015	−	0.991512i	$-0.458497\pi$
$271$	4.28064	0.260031	0.130015	+	0.991512i	$0.458497\pi$
$272$	6.99137	0.423914
$273$	9.17192	0.555110
$274$	5.22187	0.315465
$275$	−30.2314	−1.82302
$276$	−5.98104	−0.360017
$277$	−1.61707	−0.0971606	−0.0485803	−	0.998819i	$-0.515470\pi$
$277$	−1.61707	−0.0971606	−0.0485803	+	0.998819i	$0.515470\pi$
$278$	0.107441	0.00644389
$279$	9.16035	0.548416
$280$	−0.418702	−0.0250222
$281$	−1.67878	−0.100148	−0.0500740	−	0.998746i	$-0.515946\pi$
$281$	−1.67878	−0.100148	−0.0500740	+	0.998746i	$0.515946\pi$
$282$	−16.8984	−1.00629
$283$	11.8332	0.703409	0.351705	−	0.936111i	$-0.385602\pi$
$283$	11.8332	0.703409	0.351705	+	0.936111i	$0.385602\pi$
$284$	−13.1234	−0.778733
$285$	−0.861772	−0.0510469
$286$	7.03967	0.416264
$287$	4.10317	0.242203
$288$	4.29850	0.253292
$289$	31.8793	1.87525
$290$	1.13081	0.0664032
$291$	25.6679	1.50468
$292$	3.34062	0.195495
$293$	31.1774	1.82140	0.910702	−	0.413063i	$-0.135541\pi$
$293$	31.1774	1.82140	0.910702	+	0.413063i	$0.135541\pi$
$294$	−4.24876	−0.247793
$295$	−0.614432	−0.0357736
$296$	−2.65427	−0.154277
$297$	−21.2974	−1.23580
$298$	−12.9916	−0.752583
$299$	2.56711	0.148460
$300$	13.4526	0.776688
$301$	−2.45212	−0.141338
$302$	4.43634	0.255283
$303$	37.0703	2.12964
$304$	2.23064	0.127936
$305$	−0.118529	−0.00678695
$306$	30.0524	1.71798
$307$	−26.3214	−1.50224	−0.751122	−	0.660164i	$-0.770487\pi$
$307$	−26.3214	−1.50224	−0.751122	+	0.660164i	$0.770487\pi$
$308$	−17.7757	−1.01286
$309$	−24.2650	−1.38039
$310$	0.304748	0.0173085
$311$	−12.1906	−0.691263	−0.345631	−	0.938370i	$-0.612335\pi$
$311$	−12.1906	−0.691263	−0.345631	+	0.938370i	$0.612335\pi$
$312$	−3.13258	−0.177347
$313$	15.1100	0.854065	0.427033	−	0.904236i	$-0.359559\pi$
$313$	15.1100	0.854065	0.427033	+	0.904236i	$0.359559\pi$
$314$	9.34704	0.527484
$315$	−1.79979	−0.101407
$316$	−1.10006	−0.0618834
$317$	−6.44833	−0.362174	−0.181087	−	0.983467i	$-0.557962\pi$
$317$	−6.44833	−0.362174	−0.181087	+	0.983467i	$0.557962\pi$
$318$	−0.460059	−0.0257988
$319$	48.0076	2.68791
$320$	0.143003	0.00799412
$321$	−25.9348	−1.44754
$322$	−6.48215	−0.361236
$323$	15.5952	0.867742
$324$	−3.41838	−0.189910
$325$	−5.77397	−0.320282
$326$	−3.89511	−0.215730
$327$	19.2771	1.06603
$328$	−1.40140	−0.0773792
$329$	−18.3142	−1.00970
$330$	−2.34547	−0.129114
$331$	−8.50927	−0.467712	−0.233856	−	0.972271i	$-0.575134\pi$
$331$	−8.50927	−0.467712	−0.233856	+	0.972271i	$0.575134\pi$
$332$	16.6199	0.912138
$333$	−11.4094	−0.625232
$334$	0.882823	0.0483059
$335$	1.17191	0.0640281
$336$	7.90999	0.431525
$337$	6.14168	0.334559	0.167279	−	0.985910i	$-0.446502\pi$
$337$	6.14168	0.334559	0.167279	+	0.985910i	$0.446502\pi$
$338$	−11.6555	−0.633974
$339$	10.7369	0.583151
$340$	0.999789	0.0542212
$341$	12.9379	0.700624
$342$	9.58841	0.518482
$343$	15.8907	0.858016
$344$	0.837498	0.0451549
$345$	−0.855309	−0.0460483
$346$	−18.9250	−1.01741
$347$	6.67864	0.358528	0.179264	−	0.983801i	$-0.442628\pi$
$347$	6.67864	0.358528	0.179264	+	0.983801i	$0.442628\pi$
$348$	−21.3628	−1.14517
$349$	23.0510	1.23389	0.616947	−	0.787005i	$-0.288369\pi$
$349$	23.0510	1.23389	0.616947	+	0.787005i	$0.288369\pi$
$350$	14.5797	0.779318
$351$	−4.06766	−0.217116
$352$	6.07110	0.323591
$353$	17.5252	0.932774	0.466387	−	0.884581i	$-0.345555\pi$
$353$	17.5252	0.932774	0.466387	+	0.884581i	$0.345555\pi$
$354$	11.6077	0.616941
$355$	−1.87669	−0.0996046
$356$	−14.2210	−0.753712
$357$	55.3017	2.92687
$358$	11.3848	0.601704
$359$	−23.1411	−1.22134	−0.610669	−	0.791886i	$-0.709099\pi$
$359$	−23.1411	−1.22134	−0.610669	+	0.791886i	$0.709099\pi$
$360$	0.614700	0.0323975
$361$	−14.0242	−0.738118
$362$	22.4049	1.17757
$363$	−69.8580	−3.66660
$364$	−3.39503	−0.177948
$365$	0.477720	0.0250050
$366$	2.23921	0.117046
$367$	−19.0449	−0.994136	−0.497068	−	0.867712i	$-0.665590\pi$
$367$	−19.0449	−0.994136	−0.497068	+	0.867712i	$0.665590\pi$
$368$	2.21391	0.115408
$369$	−6.02391	−0.313592
$370$	−0.379570	−0.0197329
$371$	−0.498603	−0.0258862
$372$	−5.75720	−0.298497
$373$	6.53952	0.338604	0.169302	−	0.985564i	$-0.445849\pi$
$373$	6.53952	0.338604	0.169302	+	0.985564i	$0.445849\pi$
$374$	42.4453	2.19480
$375$	3.85544	0.199094
$376$	6.25503	0.322579
$377$	9.16910	0.472233
$378$	10.2711	0.528290
$379$	−4.93791	−0.253644	−0.126822	−	0.991926i	$-0.540478\pi$
$379$	−4.93791	−0.253644	−0.126822	+	0.991926i	$0.540478\pi$
$380$	0.318989	0.0163638
$381$	−16.9489	−0.868321
$382$	−6.11109	−0.312671
$383$	−8.44046	−0.431287	−0.215644	−	0.976472i	$-0.569185\pi$
$383$	−8.44046	−0.431287	−0.215644	+	0.976472i	$0.569185\pi$
$384$	−2.70157	−0.137864
$385$	−2.54198	−0.129551
$386$	−15.8470	−0.806592
$387$	3.59999	0.182998
$388$	−9.50109	−0.482345
$389$	10.3352	0.524014	0.262007	−	0.965066i	$-0.415616\pi$
$389$	10.3352	0.524014	0.262007	+	0.965066i	$0.415616\pi$
$390$	−0.447969	−0.0226838
$391$	15.4783	0.782770
$392$	1.57270	0.0794333
$393$	−37.6668	−1.90004
$394$	−14.9167	−0.751494
$395$	−0.157313	−0.00791526
$396$	26.0966	1.31141
$397$	−30.4737	−1.52943	−0.764715	−	0.644369i	$-0.777120\pi$
$397$	−30.4737	−1.52943	−0.764715	+	0.644369i	$0.777120\pi$
$398$	−5.14486	−0.257888
$399$	17.6443	0.883321
$400$	−4.97955	−0.248978
$401$	8.30499	0.414732	0.207366	−	0.978263i	$-0.433511\pi$
$401$	8.30499	0.414732	0.207366	+	0.978263i	$0.433511\pi$
$402$	−22.1393	−1.10421
$403$	2.47104	0.123091
$404$	−13.7218	−0.682683
$405$	−0.488839	−0.0242906
$406$	−23.1527	−1.14905
$407$	−16.1144	−0.798760
$408$	−18.8877	−0.935081
$409$	−6.71514	−0.332042	−0.166021	−	0.986122i	$-0.553092\pi$
$409$	−6.71514	−0.332042	−0.166021	+	0.986122i	$0.553092\pi$
$410$	−0.200404	−0.00989726
$411$	−14.1073	−0.695860
$412$	8.98180	0.442501
$413$	12.5802	0.619030
$414$	9.51650	0.467711
$415$	2.37671	0.116668
$416$	1.15954	0.0568510
$417$	−0.290260	−0.0142141
$418$	13.5424	0.662382
$419$	2.20109	0.107530	0.0537652	−	0.998554i	$-0.482878\pi$
$419$	2.20109	0.107530	0.0537652	+	0.998554i	$0.482878\pi$
$420$	1.13115	0.0551946
$421$	2.11978	0.103312	0.0516559	−	0.998665i	$-0.483550\pi$
$421$	2.11978	0.103312	0.0516559	+	0.998665i	$0.483550\pi$
$422$	6.72091	0.327169
$423$	26.8873	1.30730
$424$	0.170293	0.00827015
$425$	−34.8139	−1.68872
$426$	35.4539	1.71775
$427$	2.42682	0.117442
$428$	9.59988	0.464027
$429$	−19.0182	−0.918207
$430$	0.119765	0.00577558
$431$	2.83602	0.136606	0.0683032	−	0.997665i	$-0.478241\pi$
$431$	2.83602	0.136606	0.0683032	+	0.997665i	$0.478241\pi$
$432$	−3.50800	−0.168779
$433$	−31.2827	−1.50335	−0.751675	−	0.659534i	$-0.770754\pi$
$433$	−31.2827	−1.50335	−0.751675	+	0.659534i	$0.770754\pi$
$434$	−6.23955	−0.299508
$435$	−3.05496	−0.146474
$436$	−7.13551	−0.341729
$437$	4.93844	0.236237
$438$	−9.02494	−0.431228
$439$	24.8600	1.18650	0.593251	−	0.805018i	$-0.297844\pi$
$439$	24.8600	1.18650	0.593251	+	0.805018i	$0.297844\pi$
$440$	0.868187	0.0413892
$441$	6.76025	0.321917
$442$	8.10676	0.385599
$443$	−11.5394	−0.548252	−0.274126	−	0.961694i	$-0.588389\pi$
$443$	−11.5394	−0.548252	−0.274126	+	0.961694i	$0.588389\pi$
$444$	7.17072	0.340307
$445$	−2.03365	−0.0964043
$446$	13.8619	0.656380
$447$	35.0978	1.66007
$448$	−2.92792	−0.138331
$449$	−12.0885	−0.570492	−0.285246	−	0.958454i	$-0.592075\pi$
$449$	−12.0885	−0.570492	−0.285246	+	0.958454i	$0.592075\pi$
$450$	−21.4046	−1.00902
$451$	−8.50802	−0.400627
$452$	−3.97433	−0.186937
$453$	−11.9851	−0.563109
$454$	24.3204	1.14141
$455$	−0.485500	−0.0227606
$456$	−6.02624	−0.282204
$457$	1.07378	0.0502294	0.0251147	−	0.999685i	$-0.492005\pi$
$457$	1.07378	0.0502294	0.0251147	+	0.999685i	$0.492005\pi$
$458$	10.5866	0.494677
$459$	−24.5258	−1.14476
$460$	0.316596	0.0147614
$461$	−34.4227	−1.60323	−0.801614	−	0.597843i	$-0.796025\pi$
$461$	−34.4227	−1.60323	−0.801614	+	0.597843i	$0.796025\pi$
$462$	48.0223	2.23420
$463$	−1.44601	−0.0672018	−0.0336009	−	0.999435i	$-0.510698\pi$
$463$	−1.44601	−0.0672018	−0.0336009	+	0.999435i	$0.510698\pi$
$464$	7.90755	0.367099
$465$	−0.823299	−0.0381796
$466$	13.0208	0.603178
$467$	33.4066	1.54587	0.772936	−	0.634484i	$-0.218788\pi$
$467$	33.4066	1.54587	0.772936	+	0.634484i	$0.218788\pi$
$468$	4.98428	0.230398
$469$	−23.9942	−1.10795
$470$	0.894490	0.0412597
$471$	−25.2517	−1.16354
$472$	−4.29663	−0.197769
$473$	5.08453	0.233787
$474$	2.97190	0.136504
$475$	−11.1076	−0.509651
$476$	−20.4702	−0.938248
$477$	0.732004	0.0335162
$478$	−23.8410	−1.09046
$479$	−13.1373	−0.600258	−0.300129	−	0.953899i	$-0.597030\pi$
$479$	−13.1373	−0.600258	−0.300129	+	0.953899i	$0.597030\pi$
$480$	−0.386334	−0.0176336
$481$	−3.07773	−0.140332
$482$	30.0654	1.36944
$483$	17.5120	0.796824
$484$	25.8583	1.17538
$485$	−1.35869	−0.0616948
$486$	19.7590	0.896287
$487$	−1.54010	−0.0697888	−0.0348944	−	0.999391i	$-0.511109\pi$
$487$	−1.54010	−0.0697888	−0.0348944	+	0.999391i	$0.511109\pi$
$488$	−0.828855	−0.0375205
$489$	10.5229	0.475863
$490$	0.224901	0.0101600
$491$	−21.7459	−0.981379	−0.490690	−	0.871334i	$-0.663255\pi$
$491$	−21.7459	−0.981379	−0.490690	+	0.871334i	$0.663255\pi$
$492$	3.78598	0.170685
$493$	55.2847	2.48990
$494$	2.58651	0.116373
$495$	3.73190	0.167737
$496$	2.13106	0.0956872
$497$	38.4243	1.72357
$498$	−44.9000	−2.01202
$499$	3.28934	0.147251	0.0736255	−	0.997286i	$-0.476543\pi$
$499$	3.28934	0.147251	0.0736255	+	0.997286i	$0.476543\pi$
$500$	−1.42711	−0.0638222
$501$	−2.38501	−0.106555
$502$	−2.35176	−0.104964
$503$	23.3857	1.04272	0.521358	−	0.853338i	$-0.325426\pi$
$503$	23.3857	1.04272	0.521358	+	0.853338i	$0.325426\pi$
$504$	−12.5857	−0.560610
$505$	−1.96226	−0.0873192
$506$	13.4409	0.597520
$507$	31.4881	1.39844
$508$	6.27373	0.278352
$509$	37.0967	1.64428	0.822141	−	0.569284i	$-0.192779\pi$
$509$	37.0967	1.64428	0.822141	+	0.569284i	$0.192779\pi$
$510$	−2.70100	−0.119602
$511$	−9.78106	−0.432689
$512$	1.00000	0.0441942
$513$	−7.82509	−0.345486
$514$	17.1209	0.755171
$515$	1.28443	0.0565986
$516$	−2.26256	−0.0996038
$517$	37.9749	1.67014
$518$	7.77150	0.341460
$519$	51.1273	2.24424
$520$	0.165818	0.00727158
$521$	20.3379	0.891017	0.445509	−	0.895278i	$-0.353023\pi$
$521$	20.3379	0.891017	0.445509	+	0.895278i	$0.353023\pi$
$522$	33.9906	1.48773
$523$	−2.52360	−0.110349	−0.0551746	−	0.998477i	$-0.517572\pi$
$523$	−2.52360	−0.110349	−0.0551746	+	0.998477i	$0.517572\pi$
$524$	13.9425	0.609082
$525$	−39.3882	−1.71904
$526$	−14.5707	−0.635311
$527$	14.8990	0.649011
$528$	−16.4015	−0.713785
$529$	−18.0986	−0.786896
$530$	0.0243524	0.00105780
$531$	−18.4691	−0.801490
$532$	−6.53113	−0.283160
$533$	−1.62497	−0.0703853
$534$	38.4191	1.66256
$535$	1.37281	0.0593519
$536$	8.19496	0.353969
$537$	−30.7568	−1.32725
$538$	−10.4087	−0.448751
$539$	9.54802	0.411262
$540$	−0.501656	−0.0215878
$541$	11.6513	0.500931	0.250465	−	0.968126i	$-0.419416\pi$
$541$	11.6513	0.500931	0.250465	+	0.968126i	$0.419416\pi$
$542$	4.28064	0.183869
$543$	−60.5285	−2.59753
$544$	6.99137	0.299753
$545$	−1.02040	−0.0437092
$546$	9.17192	0.392522
$547$	31.0669	1.32832	0.664162	−	0.747588i	$-0.268788\pi$
$547$	31.0669	1.32832	0.664162	+	0.747588i	$0.268788\pi$
$548$	5.22187	0.223067
$549$	−3.56283	−0.152058
$550$	−30.2314	−1.28907
$551$	17.6389	0.751443
$552$	−5.98104	−0.254570
$553$	3.22090	0.136966
$554$	−1.61707	−0.0687029
$555$	1.02544	0.0435273
$556$	0.107441	0.00455652
$557$	30.0472	1.27314	0.636571	−	0.771218i	$-0.280352\pi$
$557$	30.0472	1.27314	0.636571	+	0.771218i	$0.280352\pi$
$558$	9.16035	0.387788
$559$	0.971110	0.0410736
$560$	−0.418702	−0.0176934
$561$	−114.669	−4.84134
$562$	−1.67878	−0.0708153
$563$	14.1798	0.597608	0.298804	−	0.954315i	$-0.403412\pi$
$563$	14.1798	0.597608	0.298804	+	0.954315i	$0.403412\pi$
$564$	−16.8984	−0.711553
$565$	−0.568342	−0.0239103
$566$	11.8332	0.497385
$567$	10.0087	0.420327
$568$	−13.1234	−0.550647
$569$	−31.2151	−1.30860	−0.654302	−	0.756234i	$-0.727037\pi$
$569$	−31.2151	−1.30860	−0.654302	+	0.756234i	$0.727037\pi$
$570$	−0.861772	−0.0360956
$571$	6.05227	0.253280	0.126640	−	0.991949i	$-0.459581\pi$
$571$	6.05227	0.253280	0.126640	+	0.991949i	$0.459581\pi$
$572$	7.03967	0.294343
$573$	16.5096	0.689697
$574$	4.10317	0.171263
$575$	−11.0243	−0.459744
$576$	4.29850	0.179104
$577$	−3.43588	−0.143038	−0.0715188	−	0.997439i	$-0.522785\pi$
$577$	−3.43588	−0.143038	−0.0715188	+	0.997439i	$0.522785\pi$
$578$	31.8793	1.32600
$579$	42.8119	1.77920
$580$	1.13081	0.0469542
$581$	−48.6618	−2.01883
$582$	25.6679	1.06397
$583$	1.03387	0.0428183
$584$	3.34062	0.138236
$585$	0.712767	0.0294693
$586$	31.1774	1.28793
$587$	−16.1245	−0.665528	−0.332764	−	0.943010i	$-0.607981\pi$
$587$	−16.1245	−0.665528	−0.332764	+	0.943010i	$0.607981\pi$
$588$	−4.24876	−0.175216
$589$	4.75362	0.195869
$590$	−0.614432	−0.0252958
$591$	40.2987	1.65767
$592$	−2.65427	−0.109090
$593$	−1.93996	−0.0796646	−0.0398323	−	0.999206i	$-0.512682\pi$
$593$	−1.93996	−0.0796646	−0.0398323	+	0.999206i	$0.512682\pi$
$594$	−21.2974	−0.873844
$595$	−2.92730	−0.120008
$596$	−12.9916	−0.532157
$597$	13.8992	0.568857
$598$	2.56711	0.104977
$599$	21.8918	0.894475	0.447238	−	0.894415i	$-0.352408\pi$
$599$	21.8918	0.894475	0.447238	+	0.894415i	$0.352408\pi$
$600$	13.4526	0.549201
$601$	14.7275	0.600748	0.300374	−	0.953822i	$-0.402889\pi$
$601$	14.7275	0.600748	0.300374	+	0.953822i	$0.402889\pi$
$602$	−2.45212	−0.0999411
$603$	35.2261	1.43452
$604$	4.43634	0.180512
$605$	3.69782	0.150338
$606$	37.0703	1.50588
$607$	6.36462	0.258332	0.129166	−	0.991623i	$-0.458770\pi$
$607$	6.36462	0.258332	0.129166	+	0.991623i	$0.458770\pi$
$608$	2.23064	0.0904644
$609$	62.5486	2.53460
$610$	−0.118529	−0.00479909
$611$	7.25295	0.293423
$612$	30.0524	1.21480
$613$	22.9912	0.928607	0.464303	−	0.885676i	$-0.346305\pi$
$613$	22.9912	0.928607	0.464303	+	0.885676i	$0.346305\pi$
$614$	−26.3214	−1.06225
$615$	0.541407	0.0218316
$616$	−17.7757	−0.716203
$617$	−41.5889	−1.67430	−0.837152	−	0.546970i	$-0.815781\pi$
$617$	−41.5889	−1.67430	−0.837152	+	0.546970i	$0.815781\pi$
$618$	−24.2650	−0.976081
$619$	−30.6069	−1.23019	−0.615097	−	0.788451i	$-0.710883\pi$
$619$	−30.6069	−1.23019	−0.615097	+	0.788451i	$0.710883\pi$
$620$	0.304748	0.0122390
$621$	−7.76640	−0.311655
$622$	−12.1906	−0.488797
$623$	41.6380	1.66819
$624$	−3.13258	−0.125403
$625$	24.6937	0.987747
$626$	15.1100	0.603915
$627$	−36.5859	−1.46110
$628$	9.34704	0.372988
$629$	−18.5570	−0.739917
$630$	−1.79979	−0.0717054
$631$	33.7741	1.34453	0.672263	−	0.740312i	$-0.265322\pi$
$631$	33.7741	1.34453	0.672263	+	0.740312i	$0.265322\pi$
$632$	−1.10006	−0.0437582
$633$	−18.1570	−0.721678
$634$	−6.44833	−0.256096
$635$	0.897163	0.0356028
$636$	−0.460059	−0.0182425
$637$	1.82360	0.0722538
$638$	48.0076	1.90064
$639$	−56.4111	−2.23159
$640$	0.143003	0.00565270
$641$	23.1902	0.915956	0.457978	−	0.888963i	$-0.348574\pi$
$641$	23.1902	0.915956	0.457978	+	0.888963i	$0.348574\pi$
$642$	−25.9348	−1.02356
$643$	4.61827	0.182127	0.0910635	−	0.995845i	$-0.470973\pi$
$643$	4.61827	0.182127	0.0910635	+	0.995845i	$0.470973\pi$
$644$	−6.48215	−0.255432
$645$	−0.323554	−0.0127399
$646$	15.5952	0.613586
$647$	−4.78992	−0.188311	−0.0941557	−	0.995557i	$-0.530015\pi$
$647$	−4.78992	−0.188311	−0.0941557	+	0.995557i	$0.530015\pi$
$648$	−3.41838	−0.134287
$649$	−26.0853	−1.02394
$650$	−5.77397	−0.226474
$651$	16.8566	0.660663
$652$	−3.89511	−0.152544
$653$	21.8948	0.856811	0.428405	−	0.903587i	$-0.359076\pi$
$653$	21.8948	0.856811	0.428405	+	0.903587i	$0.359076\pi$
$654$	19.2771	0.753795
$655$	1.99383	0.0779052
$656$	−1.40140	−0.0547153
$657$	14.3597	0.560224
$658$	−18.3142	−0.713963
$659$	5.86848	0.228603	0.114302	−	0.993446i	$-0.463537\pi$
$659$	5.86848	0.228603	0.114302	+	0.993446i	$0.463537\pi$
$660$	−2.34547	−0.0912974
$661$	−19.8420	−0.771764	−0.385882	−	0.922548i	$-0.626103\pi$
$661$	−19.8420	−0.771764	−0.385882	+	0.922548i	$0.626103\pi$
$662$	−8.50927	−0.330722
$663$	−21.9010	−0.850565
$664$	16.6199	0.644979
$665$	−0.933973	−0.0362179
$666$	−11.4094	−0.442106
$667$	17.5066	0.677859
$668$	0.882823	0.0341575
$669$	−37.4490	−1.44786
$670$	1.17191	0.0452747
$671$	−5.03206	−0.194261
$672$	7.90999	0.305134
$673$	−13.2378	−0.510281	−0.255140	−	0.966904i	$-0.582122\pi$
$673$	−13.2378	−0.510281	−0.255140	+	0.966904i	$0.582122\pi$
$674$	6.14168	0.236569
$675$	17.4683	0.672354
$676$	−11.6555	−0.448287
$677$	−20.6082	−0.792037	−0.396019	−	0.918242i	$-0.629608\pi$
$677$	−20.6082	−0.792037	−0.396019	+	0.918242i	$0.629608\pi$
$678$	10.7369	0.412350
$679$	27.8184	1.06757
$680$	0.999789	0.0383402
$681$	−65.7033	−2.51776
$682$	12.9379	0.495416
$683$	5.12315	0.196032	0.0980159	−	0.995185i	$-0.468750\pi$
$683$	5.12315	0.196032	0.0980159	+	0.995185i	$0.468750\pi$
$684$	9.58841	0.366622
$685$	0.746744	0.0285316
$686$	15.8907	0.606709
$687$	−28.6004	−1.09117
$688$	0.837498	0.0319293
$689$	0.197461	0.00752266
$690$	−0.855309	−0.0325610
$691$	−45.7102	−1.73890	−0.869450	−	0.494021i	$-0.835527\pi$
$691$	−45.7102	−1.73890	−0.869450	+	0.494021i	$0.835527\pi$
$692$	−18.9250	−0.719421
$693$	−76.4088	−2.90253
$694$	6.67864	0.253518
$695$	0.0153644	0.000582806 0
$696$	−21.3628	−0.809756
$697$	−9.79769	−0.371114
$698$	23.0510	0.872495
$699$	−35.1767	−1.33051
$700$	14.5797	0.551061
$701$	28.6378	1.08164	0.540818	−	0.841139i	$-0.318115\pi$
$701$	28.6378	1.08164	0.540818	+	0.841139i	$0.318115\pi$
$702$	−4.06766	−0.153524
$703$	−5.92073	−0.223305
$704$	6.07110	0.228813
$705$	−2.41653	−0.0910118
$706$	17.5252	0.659571
$707$	40.1762	1.51098
$708$	11.6077	0.436243
$709$	−17.3905	−0.653114	−0.326557	−	0.945178i	$-0.605888\pi$
$709$	−17.3905	−0.653114	−0.326557	+	0.945178i	$0.605888\pi$
$710$	−1.87669	−0.0704311
$711$	−4.72863	−0.177337
$712$	−14.2210	−0.532955
$713$	4.71797	0.176689
$714$	55.3017	2.06961
$715$	1.00670	0.0376483
$716$	11.3848	0.425469
$717$	64.4083	2.40537
$718$	−23.1411	−0.863617
$719$	−4.26850	−0.159188	−0.0795941	−	0.996827i	$-0.525362\pi$
$719$	−4.26850	−0.159188	−0.0795941	+	0.996827i	$0.525362\pi$
$720$	0.614700	0.0229085
$721$	−26.2980	−0.979387
$722$	−14.0242	−0.521928
$723$	−81.2240	−3.02075
$724$	22.4049	0.832671
$725$	−39.3761	−1.46239
$726$	−69.8580	−2.59267
$727$	6.76129	0.250762	0.125381	−	0.992109i	$-0.459985\pi$
$727$	6.76129	0.250762	0.125381	+	0.992109i	$0.459985\pi$
$728$	−3.39503	−0.125828
$729$	−43.1253	−1.59723
$730$	0.477720	0.0176812
$731$	5.85526	0.216565
$732$	2.23921	0.0827637
$733$	26.8758	0.992682	0.496341	−	0.868128i	$-0.334677\pi$
$733$	26.8758	0.992682	0.496341	+	0.868128i	$0.334677\pi$
$734$	−19.0449	−0.702960
$735$	−0.607587	−0.0224112
$736$	2.21391	0.0816058
$737$	49.7525	1.83266
$738$	−6.02391	−0.221743
$739$	−17.1849	−0.632155	−0.316078	−	0.948733i	$-0.602366\pi$
$739$	−17.1849	−0.632155	−0.316078	+	0.948733i	$0.602366\pi$
$740$	−0.379570	−0.0139533
$741$	−6.98765	−0.256698
$742$	−0.498603	−0.0183043
$743$	19.9597	0.732250	0.366125	−	0.930566i	$-0.380684\pi$
$743$	19.9597	0.732250	0.366125	+	0.930566i	$0.380684\pi$
$744$	−5.75720	−0.211069
$745$	−1.85784	−0.0680660
$746$	6.53952	0.239429
$747$	71.4409	2.61389
$748$	42.4453	1.55196
$749$	−28.1076	−1.02703
$750$	3.85544	0.140781
$751$	−2.32529	−0.0848512	−0.0424256	−	0.999100i	$-0.513509\pi$
$751$	−2.32529	−0.0848512	−0.0424256	+	0.999100i	$0.513509\pi$
$752$	6.25503	0.228098
$753$	6.35345	0.231533
$754$	9.16910	0.333919
$755$	0.634411	0.0230886
$756$	10.2711	0.373558
$757$	20.2987	0.737768	0.368884	−	0.929475i	$-0.379740\pi$
$757$	20.2987	0.737768	0.368884	+	0.929475i	$0.379740\pi$
$758$	−4.93791	−0.179353
$759$	−36.3115	−1.31802
$760$	0.318989	0.0115709
$761$	−7.53441	−0.273122	−0.136561	−	0.990632i	$-0.543605\pi$
$761$	−7.53441	−0.273122	−0.136561	+	0.990632i	$0.543605\pi$
$762$	−16.9489	−0.613995
$763$	20.8922	0.756348
$764$	−6.11109	−0.221091
$765$	4.29760	0.155380
$766$	−8.44046	−0.304966
$767$	−4.98211	−0.179893
$768$	−2.70157	−0.0974847
$769$	−20.2504	−0.730249	−0.365125	−	0.930959i	$-0.618974\pi$
$769$	−20.2504	−0.730249	−0.365125	+	0.930959i	$0.618974\pi$
$770$	−2.54198	−0.0916066
$771$	−46.2534	−1.66577
$772$	−15.8470	−0.570346
$773$	−39.2204	−1.41066	−0.705330	−	0.708879i	$-0.749201\pi$
$773$	−39.2204	−1.41066	−0.705330	+	0.708879i	$0.749201\pi$
$774$	3.59999	0.129399
$775$	−10.6117	−0.381183
$776$	−9.50109	−0.341069
$777$	−20.9953	−0.753201
$778$	10.3352	0.370534
$779$	−3.12601	−0.112001
$780$	−0.447969	−0.0160398
$781$	−79.6737	−2.85095
$782$	15.4783	0.553502
$783$	−27.7397	−0.991337
$784$	1.57270	0.0561678
$785$	1.33666	0.0477073
$786$	−37.6668	−1.34353
$787$	45.0111	1.60447	0.802236	−	0.597008i	$-0.203644\pi$
$787$	45.0111	1.60447	0.802236	+	0.597008i	$0.203644\pi$
$788$	−14.9167	−0.531387
$789$	39.3637	1.40139
$790$	−0.157313	−0.00559694
$791$	11.6365	0.413747
$792$	26.0966	0.927304
$793$	−0.961088	−0.0341292
$794$	−30.4737	−1.08147
$795$	−0.0657899	−0.00233333
$796$	−5.14486	−0.182355
$797$	9.05369	0.320698	0.160349	−	0.987060i	$-0.448738\pi$
$797$	9.05369	0.320698	0.160349	+	0.987060i	$0.448738\pi$
$798$	17.6443	0.624602
$799$	43.7313	1.54710
$800$	−4.97955	−0.176054
$801$	−61.1291	−2.15989
$802$	8.30499	0.293260
$803$	20.2813	0.715710
$804$	−22.1393	−0.780793
$805$	−0.926968	−0.0326713
$806$	2.47104	0.0870386
$807$	28.1199	0.989867
$808$	−13.7218	−0.482730
$809$	−7.74794	−0.272403	−0.136202	−	0.990681i	$-0.543489\pi$
$809$	−7.74794	−0.272403	−0.136202	+	0.990681i	$0.543489\pi$
$810$	−0.488839	−0.0171761
$811$	−19.0370	−0.668481	−0.334241	−	0.942488i	$-0.608480\pi$
$811$	−19.0370	−0.668481	−0.334241	+	0.942488i	$0.608480\pi$
$812$	−23.1527	−0.812499
$813$	−11.5645	−0.405584
$814$	−16.1144	−0.564808
$815$	−0.557013	−0.0195113
$816$	−18.8877	−0.661202
$817$	1.86816	0.0653585
$818$	−6.71514	−0.234789
$819$	−14.5935	−0.509940
$820$	−0.200404	−0.00699842
$821$	14.2201	0.496284	0.248142	−	0.968724i	$-0.420180\pi$
$821$	14.2201	0.496284	0.248142	+	0.968724i	$0.420180\pi$
$822$	−14.1073	−0.492047
$823$	19.8169	0.690772	0.345386	−	0.938461i	$-0.387748\pi$
$823$	19.8169	0.690772	0.345386	+	0.938461i	$0.387748\pi$
$824$	8.98180	0.312896
$825$	81.6722	2.84346
$826$	12.5802	0.437721
$827$	−23.4940	−0.816968	−0.408484	−	0.912766i	$-0.633942\pi$
$827$	−23.4940	−0.816968	−0.408484	+	0.912766i	$0.633942\pi$
$828$	9.51650	0.330721
$829$	−3.38975	−0.117731	−0.0588655	−	0.998266i	$-0.518748\pi$
$829$	−3.38975	−0.117731	−0.0588655	+	0.998266i	$0.518748\pi$
$830$	2.37671	0.0824967
$831$	4.36865	0.151547
$832$	1.15954	0.0401997
$833$	10.9953	0.380966
$834$	−0.290260	−0.0100509
$835$	0.126247	0.00436894
$836$	13.5424	0.468375
$837$	−7.47575	−0.258400
$838$	2.20109	0.0760355
$839$	16.3186	0.563380	0.281690	−	0.959505i	$-0.409105\pi$
$839$	16.3186	0.563380	0.281690	+	0.959505i	$0.409105\pi$
$840$	1.13115	0.0390285
$841$	33.5294	1.15619
$842$	2.11978	0.0730525
$843$	4.53536	0.156206
$844$	6.72091	0.231343
$845$	−1.66677	−0.0573386
$846$	26.8873	0.924404
$847$	−75.7109	−2.60146
$848$	0.170293	0.00584788
$849$	−31.9682	−1.09715
$850$	−34.8139	−1.19411
$851$	−5.87633	−0.201438
$852$	35.4539	1.21463
$853$	−55.1785	−1.88928	−0.944638	−	0.328115i	$-0.893587\pi$
$853$	−55.1785	−1.88928	−0.944638	+	0.328115i	$0.893587\pi$
$854$	2.42682	0.0830440
$855$	1.37117	0.0468932
$856$	9.59988	0.328117
$857$	−6.90404	−0.235838	−0.117919	−	0.993023i	$-0.537622\pi$
$857$	−6.90404	−0.235838	−0.117919	+	0.993023i	$0.537622\pi$
$858$	−19.0182	−0.649270
$859$	4.08910	0.139518	0.0697592	−	0.997564i	$-0.477777\pi$
$859$	4.08910	0.139518	0.0697592	+	0.997564i	$0.477777\pi$
$860$	0.119765	0.00408395
$861$	−11.0850	−0.377777
$862$	2.83602	0.0965954
$863$	−8.03720	−0.273590	−0.136795	−	0.990599i	$-0.543680\pi$
$863$	−8.03720	−0.273590	−0.136795	+	0.990599i	$0.543680\pi$
$864$	−3.50800	−0.119345
$865$	−2.70634	−0.0920182
$866$	−31.2827	−1.06303
$867$	−86.1243	−2.92493
$868$	−6.23955	−0.211784
$869$	−6.67860	−0.226556
$870$	−3.05496	−0.103573
$871$	9.50237	0.321975
$872$	−7.13551	−0.241639
$873$	−40.8405	−1.38224
$874$	4.93844	0.167045
$875$	4.17845	0.141258
$876$	−9.02494	−0.304924
$877$	−40.3129	−1.36127	−0.680635	−	0.732623i	$-0.738296\pi$
$877$	−40.3129	−1.36127	−0.680635	+	0.732623i	$0.738296\pi$
$878$	24.8600	0.838983
$879$	−84.2281	−2.84094
$880$	0.868187	0.0292666
$881$	−19.1036	−0.643615	−0.321808	−	0.946805i	$-0.604290\pi$
$881$	−19.1036	−0.643615	−0.321808	+	0.946805i	$0.604290\pi$
$882$	6.76025	0.227630
$883$	50.1642	1.68816	0.844079	−	0.536218i	$-0.180148\pi$
$883$	50.1642	1.68816	0.844079	+	0.536218i	$0.180148\pi$
$884$	8.10676	0.272660
$885$	1.65993	0.0557981
$886$	−11.5394	−0.387673
$887$	−31.6046	−1.06118	−0.530589	−	0.847629i	$-0.678029\pi$
$887$	−31.6046	−1.06118	−0.530589	+	0.847629i	$0.678029\pi$
$888$	7.17072	0.240634
$889$	−18.3690	−0.616075
$890$	−2.03365	−0.0681681
$891$	−20.7533	−0.695263
$892$	13.8619	0.464131
$893$	13.9527	0.466910
$894$	35.0978	1.17385
$895$	1.62806	0.0544200
$896$	−2.92792	−0.0978149
$897$	−6.93524	−0.231561
$898$	−12.0885	−0.403399
$899$	16.8514	0.562027
$900$	−21.4046	−0.713487
$901$	1.19058	0.0396640
$902$	−8.50802	−0.283286
$903$	6.62460	0.220453
$904$	−3.97433	−0.132184
$905$	3.20397	0.106504
$906$	−11.9851	−0.398178
$907$	20.3720	0.676443	0.338221	−	0.941067i	$-0.390175\pi$
$907$	20.3720	0.676443	0.338221	+	0.941067i	$0.390175\pi$
$908$	24.3204	0.807101
$909$	−58.9830	−1.95634
$910$	−0.485500	−0.0160942
$911$	11.9643	0.396393	0.198197	−	0.980162i	$-0.436492\pi$
$911$	11.9643	0.396393	0.198197	+	0.980162i	$0.436492\pi$
$912$	−6.02624	−0.199549
$913$	100.901	3.33935
$914$	1.07378	0.0355175
$915$	0.320215	0.0105860
$916$	10.5866	0.349790
$917$	−40.8225	−1.34808
$918$	−24.5258	−0.809471
$919$	−17.2368	−0.568589	−0.284294	−	0.958737i	$-0.591759\pi$
$919$	−17.2368	−0.568589	−0.284294	+	0.958737i	$0.591759\pi$
$920$	0.316596	0.0104379
$921$	71.1093	2.34313
$922$	−34.4227	−1.13365
$923$	−15.2171	−0.500878
$924$	48.0223	1.57982
$925$	13.2171	0.434575
$926$	−1.44601	−0.0475188
$927$	38.6083	1.26806
$928$	7.90755	0.259578
$929$	43.9222	1.44104	0.720520	−	0.693435i	$-0.243903\pi$
$929$	43.9222	1.44104	0.720520	+	0.693435i	$0.243903\pi$
$930$	−0.823299	−0.0269970
$931$	3.50813	0.114974
$932$	13.0208	0.426511
$933$	32.9337	1.07820
$934$	33.4066	1.09310
$935$	6.06982	0.198504
$936$	4.98428	0.162916
$937$	60.3454	1.97140	0.985698	−	0.168519i	$-0.0538986\pi$
$937$	60.3454	1.97140	0.985698	+	0.168519i	$0.0538986\pi$
$938$	−23.9942	−0.783438
$939$	−40.8207	−1.33213
$940$	0.894490	0.0291750
$941$	−33.0602	−1.07773	−0.538866	−	0.842392i	$-0.681147\pi$
$941$	−33.0602	−1.07773	−0.538866	+	0.842392i	$0.681147\pi$
$942$	−25.2517	−0.822746
$943$	−3.10257	−0.101033
$944$	−4.29663	−0.139843
$945$	1.46881	0.0477803
$946$	5.08453	0.165312
$947$	−57.0573	−1.85411	−0.927057	−	0.374920i	$-0.877670\pi$
$947$	−57.0573	−1.85411	−0.927057	+	0.374920i	$0.877670\pi$
$948$	2.97190	0.0965230
$949$	3.87358	0.125742
$950$	−11.1076	−0.360378
$951$	17.4206	0.564903
$952$	−20.4702	−0.663442
$953$	45.8266	1.48447	0.742235	−	0.670139i	$-0.233766\pi$
$953$	45.8266	1.48447	0.742235	+	0.670139i	$0.233766\pi$
$954$	0.732004	0.0236995
$955$	−0.873906	−0.0282789
$956$	−23.8410	−0.771074
$957$	−129.696	−4.19248
$958$	−13.1373	−0.424446
$959$	−15.2892	−0.493714
$960$	−0.386334	−0.0124689
$961$	−26.4586	−0.853503
$962$	−3.07773	−0.0992300
$963$	41.2651	1.32975
$964$	30.0654	0.968342
$965$	−2.26617	−0.0729507
$966$	17.5120	0.563439
$967$	−2.63490	−0.0847328	−0.0423664	−	0.999102i	$-0.513490\pi$
$967$	−2.63490	−0.0847328	−0.0423664	+	0.999102i	$0.513490\pi$
$968$	25.8583	0.831116
$969$	−42.1317	−1.35346
$970$	−1.35869	−0.0436248
$971$	8.04854	0.258290	0.129145	−	0.991626i	$-0.458777\pi$
$971$	8.04854	0.258290	0.129145	+	0.991626i	$0.458777\pi$
$972$	19.7590	0.633771
$973$	−0.314579	−0.0100849
$974$	−1.54010	−0.0493481
$975$	15.5988	0.499562
$976$	−0.828855	−0.0265310
$977$	−37.9440	−1.21393	−0.606967	−	0.794727i	$-0.707614\pi$
$977$	−37.9440	−1.21393	−0.606967	+	0.794727i	$0.707614\pi$
$978$	10.5229	0.336486
$979$	−86.3372	−2.75935
$980$	0.224901	0.00718420
$981$	−30.6720	−0.979282
$982$	−21.7459	−0.693940
$983$	23.6056	0.752902	0.376451	−	0.926436i	$-0.377144\pi$
$983$	23.6056	0.752902	0.376451	+	0.926436i	$0.377144\pi$
$984$	3.78598	0.120693
$985$	−2.13314	−0.0679676
$986$	55.2847	1.76062
$987$	49.4772	1.57488
$988$	2.58651	0.0822879
$989$	1.85415	0.0589584
$990$	3.73190	0.118608
$991$	0.463054	0.0147094	0.00735469	−	0.999973i	$-0.497659\pi$
$991$	0.463054	0.0147094	0.00735469	+	0.999973i	$0.497659\pi$
$992$	2.13106	0.0676611
$993$	22.9884	0.729516
$994$	38.4243	1.21875
$995$	−0.735731	−0.0233243
$996$	−44.9000	−1.42271
$997$	61.6046	1.95104	0.975519	−	0.219916i	$-0.0705783\pi$
$997$	61.6046	1.95104	0.975519	+	0.219916i	$0.0705783\pi$
$998$	3.28934	0.104122
$999$	9.31120	0.294593

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8038.2.a.d.1.6	✓	92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8038.2.a.d.1.6	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.70157 q^{3} +1.00000 q^{4} +0.143003 q^{5} -2.70157 q^{6} -2.92792 q^{7} +1.00000 q^{8} +4.29850 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.70157 q^{3} +1.00000 q^{4} +0.143003 q^{5} -2.70157 q^{6} -2.92792 q^{7} +1.00000 q^{8} +4.29850 q^{9} +0.143003 q^{10} +6.07110 q^{11} -2.70157 q^{12} +1.15954 q^{13} -2.92792 q^{14} -0.386334 q^{15} +1.00000 q^{16} +6.99137 q^{17} +4.29850 q^{18} +2.23064 q^{19} +0.143003 q^{20} +7.90999 q^{21} +6.07110 q^{22} +2.21391 q^{23} -2.70157 q^{24} -4.97955 q^{25} +1.15954 q^{26} -3.50800 q^{27} -2.92792 q^{28} +7.90755 q^{29} -0.386334 q^{30} +2.13106 q^{31} +1.00000 q^{32} -16.4015 q^{33} +6.99137 q^{34} -0.418702 q^{35} +4.29850 q^{36} -2.65427 q^{37} +2.23064 q^{38} -3.13258 q^{39} +0.143003 q^{40} -1.40140 q^{41} +7.90999 q^{42} +0.837498 q^{43} +6.07110 q^{44} +0.614700 q^{45} +2.21391 q^{46} +6.25503 q^{47} -2.70157 q^{48} +1.57270 q^{49} -4.97955 q^{50} -18.8877 q^{51} +1.15954 q^{52} +0.170293 q^{53} -3.50800 q^{54} +0.868187 q^{55} -2.92792 q^{56} -6.02624 q^{57} +7.90755 q^{58} -4.29663 q^{59} -0.386334 q^{60} -0.828855 q^{61} +2.13106 q^{62} -12.5857 q^{63} +1.00000 q^{64} +0.165818 q^{65} -16.4015 q^{66} +8.19496 q^{67} +6.99137 q^{68} -5.98104 q^{69} -0.418702 q^{70} -13.1234 q^{71} +4.29850 q^{72} +3.34062 q^{73} -2.65427 q^{74} +13.4526 q^{75} +2.23064 q^{76} -17.7757 q^{77} -3.13258 q^{78} -1.10006 q^{79} +0.143003 q^{80} -3.41838 q^{81} -1.40140 q^{82} +16.6199 q^{83} +7.90999 q^{84} +0.999789 q^{85} +0.837498 q^{86} -21.3628 q^{87} +6.07110 q^{88} -14.2210 q^{89} +0.614700 q^{90} -3.39503 q^{91} +2.21391 q^{92} -5.75720 q^{93} +6.25503 q^{94} +0.318989 q^{95} -2.70157 q^{96} -9.50109 q^{97} +1.57270 q^{98} +26.0966 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 92 q + 92 q^{2} + 31 q^{3} + 92 q^{4} + 28 q^{5} + 31 q^{6} + 29 q^{7} + 92 q^{8} + 113 q^{9}+O(q^{10}) \) 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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