LMFDB - Embedded newform 6002.2.a.a.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6002,2,Mod(1,6002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6002, 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("6002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6002 = 2 \cdot 3001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6002.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:	$47.9262112932$
Analytic rank:	$1$
Dimension:	$47$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	6002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.879988 q^{3} +1.00000 q^{4} -1.86923 q^{5} -0.879988 q^{6} +3.94056 q^{7} +1.00000 q^{8} -2.22562 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.879988 q^{3} +1.00000 q^{4} -1.86923 q^{5} -0.879988 q^{6} +3.94056 q^{7} +1.00000 q^{8} -2.22562 q^{9} -1.86923 q^{10} +4.65962 q^{11} -0.879988 q^{12} -0.219910 q^{13} +3.94056 q^{14} +1.64490 q^{15} +1.00000 q^{16} -5.06940 q^{17} -2.22562 q^{18} +1.38375 q^{19} -1.86923 q^{20} -3.46765 q^{21} +4.65962 q^{22} -6.27325 q^{23} -0.879988 q^{24} -1.50598 q^{25} -0.219910 q^{26} +4.59848 q^{27} +3.94056 q^{28} -2.83165 q^{29} +1.64490 q^{30} -8.21578 q^{31} +1.00000 q^{32} -4.10041 q^{33} -5.06940 q^{34} -7.36582 q^{35} -2.22562 q^{36} -6.28699 q^{37} +1.38375 q^{38} +0.193518 q^{39} -1.86923 q^{40} -3.26521 q^{41} -3.46765 q^{42} +1.35867 q^{43} +4.65962 q^{44} +4.16020 q^{45} -6.27325 q^{46} -7.82397 q^{47} -0.879988 q^{48} +8.52805 q^{49} -1.50598 q^{50} +4.46101 q^{51} -0.219910 q^{52} -0.433602 q^{53} +4.59848 q^{54} -8.70989 q^{55} +3.94056 q^{56} -1.21768 q^{57} -2.83165 q^{58} +15.2378 q^{59} +1.64490 q^{60} +8.74847 q^{61} -8.21578 q^{62} -8.77020 q^{63} +1.00000 q^{64} +0.411062 q^{65} -4.10041 q^{66} -12.4924 q^{67} -5.06940 q^{68} +5.52039 q^{69} -7.36582 q^{70} +9.27985 q^{71} -2.22562 q^{72} -3.82110 q^{73} -6.28699 q^{74} +1.32524 q^{75} +1.38375 q^{76} +18.3615 q^{77} +0.193518 q^{78} -4.32275 q^{79} -1.86923 q^{80} +2.63025 q^{81} -3.26521 q^{82} -9.42865 q^{83} -3.46765 q^{84} +9.47587 q^{85} +1.35867 q^{86} +2.49182 q^{87} +4.65962 q^{88} +7.66858 q^{89} +4.16020 q^{90} -0.866568 q^{91} -6.27325 q^{92} +7.22979 q^{93} -7.82397 q^{94} -2.58655 q^{95} -0.879988 q^{96} -8.84095 q^{97} +8.52805 q^{98} -10.3705 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 47 q + 47 q^{2} - 13 q^{3} + 47 q^{4} - 14 q^{5} - 13 q^{6} - 17 q^{7} + 47 q^{8} + 12 q^{9}+O(q^{10}) $ 47 * q + 47 * q^2 - 13 * q^3 + 47 * q^4 - 14 * q^5 - 13 * q^6 - 17 * q^7 + 47 * q^8 + 12 * q^9	\( 47 q + 47 q^{2} - 13 q^{3} + 47 q^{4} - 14 q^{5} - 13 q^{6} - 17 q^{7} + 47 q^{8} + 12 q^{9} - 14 q^{10} - 30 q^{11} - 13 q^{12} - 39 q^{13} - 17 q^{14} - 18 q^{15} + 47 q^{16} - 26 q^{17} + 12 q^{18} - 23 q^{19} - 14 q^{20} - 39 q^{21} - 30 q^{22} - 25 q^{23} - 13 q^{24} - 19 q^{25} - 39 q^{26} - 46 q^{27} - 17 q^{28} - 53 q^{29} - 18 q^{30} - 23 q^{31} + 47 q^{32} - 26 q^{33} - 26 q^{34} - 31 q^{35} + 12 q^{36} - 83 q^{37} - 23 q^{38} - 9 q^{39} - 14 q^{40} - 48 q^{41} - 39 q^{42} - 78 q^{43} - 30 q^{44} - 27 q^{45} - 25 q^{46} - 15 q^{47} - 13 q^{48} - 12 q^{49} - 19 q^{50} - 47 q^{51} - 39 q^{52} - 76 q^{53} - 46 q^{54} - 39 q^{55} - 17 q^{56} - 44 q^{57} - 53 q^{58} - 33 q^{59} - 18 q^{60} - 33 q^{61} - 23 q^{62} - 7 q^{63} + 47 q^{64} - 67 q^{65} - 26 q^{66} - 85 q^{67} - 26 q^{68} - 33 q^{69} - 31 q^{70} - 17 q^{71} + 12 q^{72} - 59 q^{73} - 83 q^{74} - 21 q^{75} - 23 q^{76} - 59 q^{77} - 9 q^{78} - 49 q^{79} - 14 q^{80} - 41 q^{81} - 48 q^{82} - 30 q^{83} - 39 q^{84} - 84 q^{85} - 78 q^{86} + 9 q^{87} - 30 q^{88} - 50 q^{89} - 27 q^{90} - 42 q^{91} - 25 q^{92} - 43 q^{93} - 15 q^{94} + 8 q^{95} - 13 q^{96} - 49 q^{97} - 12 q^{98} - 49 q^{99}+O(q^{100}) \) 47 * q + 47 * q^2 - 13 * q^3 + 47 * q^4 - 14 * q^5 - 13 * q^6 - 17 * q^7 + 47 * q^8 + 12 * q^9 - 14 * q^10 - 30 * q^11 - 13 * q^12 - 39 * q^13 - 17 * q^14 - 18 * q^15 + 47 * q^16 - 26 * q^17 + 12 * q^18 - 23 * q^19 - 14 * q^20 - 39 * q^21 - 30 * q^22 - 25 * q^23 - 13 * q^24 - 19 * q^25 - 39 * q^26 - 46 * q^27 - 17 * q^28 - 53 * q^29 - 18 * q^30 - 23 * q^31 + 47 * q^32 - 26 * q^33 - 26 * q^34 - 31 * q^35 + 12 * q^36 - 83 * q^37 - 23 * q^38 - 9 * q^39 - 14 * q^40 - 48 * q^41 - 39 * q^42 - 78 * q^43 - 30 * q^44 - 27 * q^45 - 25 * q^46 - 15 * q^47 - 13 * q^48 - 12 * q^49 - 19 * q^50 - 47 * q^51 - 39 * q^52 - 76 * q^53 - 46 * q^54 - 39 * q^55 - 17 * q^56 - 44 * q^57 - 53 * q^58 - 33 * q^59 - 18 * q^60 - 33 * q^61 - 23 * q^62 - 7 * q^63 + 47 * q^64 - 67 * q^65 - 26 * q^66 - 85 * q^67 - 26 * q^68 - 33 * q^69 - 31 * q^70 - 17 * q^71 + 12 * q^72 - 59 * q^73 - 83 * q^74 - 21 * q^75 - 23 * q^76 - 59 * q^77 - 9 * q^78 - 49 * q^79 - 14 * q^80 - 41 * q^81 - 48 * q^82 - 30 * q^83 - 39 * q^84 - 84 * q^85 - 78 * q^86 + 9 * q^87 - 30 * q^88 - 50 * q^89 - 27 * q^90 - 42 * q^91 - 25 * q^92 - 43 * q^93 - 15 * q^94 + 8 * q^95 - 13 * q^96 - 49 * q^97 - 12 * q^98 - 49 * 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
$3$	−0.879988	−0.508061	−0.254031	−	0.967196i	$-0.581756\pi$
$3$	−0.879988	−0.508061	−0.254031	+	0.967196i	$0.581756\pi$
$4$	1.00000	0.500000
$5$	−1.86923	−0.835945	−0.417973	−	0.908460i	$-0.637259\pi$
$5$	−1.86923	−0.835945	−0.417973	+	0.908460i	$0.637259\pi$
$6$	−0.879988	−0.359254
$7$	3.94056	1.48939	0.744697	−	0.667403i	$-0.232594\pi$
$7$	3.94056	1.48939	0.744697	+	0.667403i	$0.232594\pi$
$8$	1.00000	0.353553
$9$	−2.22562	−0.741874
$10$	−1.86923	−0.591102
$11$	4.65962	1.40493	0.702463	−	0.711720i	$-0.252083\pi$
$11$	4.65962	1.40493	0.702463	+	0.711720i	$0.252083\pi$
$12$	−0.879988	−0.254031
$13$	−0.219910	−0.0609920	−0.0304960	−	0.999535i	$-0.509709\pi$
$13$	−0.219910	−0.0609920	−0.0304960	+	0.999535i	$0.509709\pi$
$14$	3.94056	1.05316
$15$	1.64490	0.424712
$16$	1.00000	0.250000
$17$	−5.06940	−1.22951	−0.614755	−	0.788718i	$-0.710745\pi$
$17$	−5.06940	−1.22951	−0.614755	+	0.788718i	$0.710745\pi$
$18$	−2.22562	−0.524584
$19$	1.38375	0.317454	0.158727	−	0.987323i	$-0.449261\pi$
$19$	1.38375	0.317454	0.158727	+	0.987323i	$0.449261\pi$
$20$	−1.86923	−0.417973
$21$	−3.46765	−0.756703
$22$	4.65962	0.993433
$23$	−6.27325	−1.30806	−0.654031	−	0.756467i	$-0.726924\pi$
$23$	−6.27325	−1.30806	−0.654031	+	0.756467i	$0.726924\pi$
$24$	−0.879988	−0.179627
$25$	−1.50598	−0.301196
$26$	−0.219910	−0.0431278
$27$	4.59848	0.884979
$28$	3.94056	0.744697
$29$	−2.83165	−0.525824	−0.262912	−	0.964820i	$-0.584683\pi$
$29$	−2.83165	−0.525824	−0.262912	+	0.964820i	$0.584683\pi$
$30$	1.64490	0.300316
$31$	−8.21578	−1.47560	−0.737799	−	0.675021i	$-0.764135\pi$
$31$	−8.21578	−1.47560	−0.737799	+	0.675021i	$0.764135\pi$
$32$	1.00000	0.176777
$33$	−4.10041	−0.713789
$34$	−5.06940	−0.869394
$35$	−7.36582	−1.24505
$36$	−2.22562	−0.370937
$37$	−6.28699	−1.03357	−0.516787	−	0.856114i	$-0.672872\pi$
$37$	−6.28699	−1.03357	−0.516787	+	0.856114i	$0.672872\pi$
$38$	1.38375	0.224474
$39$	0.193518	0.0309877
$40$	−1.86923	−0.295551
$41$	−3.26521	−0.509940	−0.254970	−	0.966949i	$-0.582066\pi$
$41$	−3.26521	−0.509940	−0.254970	+	0.966949i	$0.582066\pi$
$42$	−3.46765	−0.535070
$43$	1.35867	0.207196	0.103598	−	0.994619i	$-0.466964\pi$
$43$	1.35867	0.207196	0.103598	+	0.994619i	$0.466964\pi$
$44$	4.65962	0.702463
$45$	4.16020	0.620166
$46$	−6.27325	−0.924940
$47$	−7.82397	−1.14124	−0.570622	−	0.821213i	$-0.693298\pi$
$47$	−7.82397	−1.14124	−0.570622	+	0.821213i	$0.693298\pi$
$48$	−0.879988	−0.127015
$49$	8.52805	1.21829
$50$	−1.50598	−0.212978
$51$	4.46101	0.624666
$52$	−0.219910	−0.0304960
$53$	−0.433602	−0.0595598	−0.0297799	−	0.999556i	$-0.509481\pi$
$53$	−0.433602	−0.0595598	−0.0297799	+	0.999556i	$0.509481\pi$
$54$	4.59848	0.625775
$55$	−8.70989	−1.17444
$56$	3.94056	0.526580
$57$	−1.21768	−0.161286
$58$	−2.83165	−0.371813
$59$	15.2378	1.98379	0.991896	−	0.127055i	$-0.0405525\pi$
$59$	15.2378	1.98379	0.991896	+	0.127055i	$0.0405525\pi$
$60$	1.64490	0.212356
$61$	8.74847	1.12013	0.560063	−	0.828450i	$-0.310777\pi$
$61$	8.74847	1.12013	0.560063	+	0.828450i	$0.310777\pi$
$62$	−8.21578	−1.04340
$63$	−8.77020	−1.10494
$64$	1.00000	0.125000
$65$	0.411062	0.0509859
$66$	−4.10041	−0.504725
$67$	−12.4924	−1.52619	−0.763097	−	0.646284i	$-0.776322\pi$
$67$	−12.4924	−1.52619	−0.763097	+	0.646284i	$0.776322\pi$
$68$	−5.06940	−0.614755
$69$	5.52039	0.664576
$70$	−7.36582	−0.880384
$71$	9.27985	1.10132	0.550658	−	0.834731i	$-0.314377\pi$
$71$	9.27985	1.10132	0.550658	+	0.834731i	$0.314377\pi$
$72$	−2.22562	−0.262292
$73$	−3.82110	−0.447226	−0.223613	−	0.974678i	$-0.571785\pi$
$73$	−3.82110	−0.447226	−0.223613	+	0.974678i	$0.571785\pi$
$74$	−6.28699	−0.730848
$75$	1.32524	0.153026
$76$	1.38375	0.158727
$77$	18.3615	2.09249
$78$	0.193518	0.0219116
$79$	−4.32275	−0.486347	−0.243173	−	0.969983i	$-0.578188\pi$
$79$	−4.32275	−0.486347	−0.243173	+	0.969983i	$0.578188\pi$
$80$	−1.86923	−0.208986
$81$	2.63025	0.292250
$82$	−3.26521	−0.360582
$83$	−9.42865	−1.03493	−0.517464	−	0.855705i	$-0.673124\pi$
$83$	−9.42865	−1.03493	−0.517464	+	0.855705i	$0.673124\pi$
$84$	−3.46765	−0.378352
$85$	9.47587	1.02780
$86$	1.35867	0.146510
$87$	2.49182	0.267151
$88$	4.65962	0.496717
$89$	7.66858	0.812868	0.406434	−	0.913680i	$-0.366772\pi$
$89$	7.66858	0.812868	0.406434	+	0.913680i	$0.366772\pi$
$90$	4.16020	0.438523
$91$	−0.866568	−0.0908410
$92$	−6.27325	−0.654031
$93$	7.22979	0.749694
$94$	−7.82397	−0.806981
$95$	−2.58655	−0.265374
$96$	−0.879988	−0.0898134
$97$	−8.84095	−0.897662	−0.448831	−	0.893617i	$-0.648160\pi$
$97$	−8.84095	−0.897662	−0.448831	+	0.893617i	$0.648160\pi$
$98$	8.52805	0.861463
$99$	−10.3705	−1.04228
$100$	−1.50598	−0.150598
$101$	7.70885	0.767059	0.383530	−	0.923529i	$-0.374708\pi$
$101$	7.70885	0.767059	0.383530	+	0.923529i	$0.374708\pi$
$102$	4.46101	0.441706
$103$	−11.8001	−1.16270	−0.581349	−	0.813655i	$-0.697475\pi$
$103$	−11.8001	−1.16270	−0.581349	+	0.813655i	$0.697475\pi$
$104$	−0.219910	−0.0215639
$105$	6.48184	0.632563
$106$	−0.433602	−0.0421152
$107$	2.89473	0.279844	0.139922	−	0.990163i	$-0.455315\pi$
$107$	2.89473	0.279844	0.139922	+	0.990163i	$0.455315\pi$
$108$	4.59848	0.442489
$109$	16.9959	1.62791	0.813957	−	0.580925i	$-0.197309\pi$
$109$	16.9959	1.62791	0.813957	+	0.580925i	$0.197309\pi$
$110$	−8.70989	−0.830456
$111$	5.53248	0.525119
$112$	3.94056	0.372348
$113$	−13.2848	−1.24973	−0.624864	−	0.780733i	$-0.714846\pi$
$113$	−13.2848	−1.24973	−0.624864	+	0.780733i	$0.714846\pi$
$114$	−1.21768	−0.114046
$115$	11.7261	1.09347
$116$	−2.83165	−0.262912
$117$	0.489435	0.0452483
$118$	15.2378	1.40275
$119$	−19.9763	−1.83122
$120$	1.64490	0.150158
$121$	10.7120	0.973820
$122$	8.74847	0.792049
$123$	2.87334	0.259081
$124$	−8.21578	−0.737799
$125$	12.1612	1.08773
$126$	−8.77020	−0.781312
$127$	−8.92382	−0.791861	−0.395931	−	0.918280i	$-0.629578\pi$
$127$	−8.92382	−0.791861	−0.395931	+	0.918280i	$0.629578\pi$
$128$	1.00000	0.0883883
$129$	−1.19562	−0.105268
$130$	0.411062	0.0360525
$131$	13.7075	1.19763	0.598814	−	0.800888i	$-0.295639\pi$
$131$	13.7075	1.19763	0.598814	+	0.800888i	$0.295639\pi$
$132$	−4.10041	−0.356895
$133$	5.45276	0.472814
$134$	−12.4924	−1.07918
$135$	−8.59563	−0.739794
$136$	−5.06940	−0.434697
$137$	−0.210910	−0.0180193	−0.00900965	−	0.999959i	$-0.502868\pi$
$137$	−0.210910	−0.0180193	−0.00900965	+	0.999959i	$0.502868\pi$
$138$	5.52039	0.469926
$139$	−18.3736	−1.55843	−0.779214	−	0.626758i	$-0.784381\pi$
$139$	−18.3736	−1.55843	−0.779214	+	0.626758i	$0.784381\pi$
$140$	−7.36582	−0.622526
$141$	6.88500	0.579822
$142$	9.27985	0.778748
$143$	−1.02469	−0.0856893
$144$	−2.22562	−0.185468
$145$	5.29300	0.439560
$146$	−3.82110	−0.316236
$147$	−7.50459	−0.618968
$148$	−6.28699	−0.516787
$149$	−15.0737	−1.23489	−0.617443	−	0.786615i	$-0.711832\pi$
$149$	−15.0737	−1.23489	−0.617443	+	0.786615i	$0.711832\pi$
$150$	1.32524	0.108206
$151$	−15.2489	−1.24094	−0.620468	−	0.784232i	$-0.713057\pi$
$151$	−15.2489	−1.24094	−0.620468	+	0.784232i	$0.713057\pi$
$152$	1.38375	0.112237
$153$	11.2826	0.912140
$154$	18.3615	1.47961
$155$	15.3572	1.23352
$156$	0.193518	0.0154938
$157$	−18.0682	−1.44200	−0.721000	−	0.692935i	$-0.756317\pi$
$157$	−18.0682	−1.44200	−0.721000	+	0.692935i	$0.756317\pi$
$158$	−4.32275	−0.343899
$159$	0.381565	0.0302601
$160$	−1.86923	−0.147776
$161$	−24.7201	−1.94822
$162$	2.63025	0.206652
$163$	−12.4609	−0.976017	−0.488008	−	0.872839i	$-0.662276\pi$
$163$	−12.4609	−0.976017	−0.488008	+	0.872839i	$0.662276\pi$
$164$	−3.26521	−0.254970
$165$	7.66460	0.596689
$166$	−9.42865	−0.731805
$167$	−0.380585	−0.0294505	−0.0147253	−	0.999892i	$-0.504687\pi$
$167$	−0.380585	−0.0294505	−0.0147253	+	0.999892i	$0.504687\pi$
$168$	−3.46765	−0.267535
$169$	−12.9516	−0.996280
$170$	9.47587	0.726766
$171$	−3.07970	−0.235511
$172$	1.35867	0.103598
$173$	17.2593	1.31220	0.656101	−	0.754674i	$-0.272205\pi$
$173$	17.2593	1.31220	0.656101	+	0.754674i	$0.272205\pi$
$174$	2.49182	0.188904
$175$	−5.93441	−0.448599
$176$	4.65962	0.351232
$177$	−13.4091	−1.00789
$178$	7.66858	0.574784
$179$	−14.4538	−1.08032	−0.540162	−	0.841561i	$-0.681637\pi$
$179$	−14.4538	−1.08032	−0.540162	+	0.841561i	$0.681637\pi$
$180$	4.16020	0.310083
$181$	2.78115	0.206721	0.103361	−	0.994644i	$-0.467040\pi$
$181$	2.78115	0.206721	0.103361	+	0.994644i	$0.467040\pi$
$182$	−0.866568	−0.0642343
$183$	−7.69855	−0.569093
$184$	−6.27325	−0.462470
$185$	11.7518	0.864012
$186$	7.22979	0.530114
$187$	−23.6214	−1.72737
$188$	−7.82397	−0.570622
$189$	18.1206	1.31808
$190$	−2.58655	−0.187648
$191$	14.5502	1.05281	0.526406	−	0.850233i	$-0.323539\pi$
$191$	14.5502	1.05281	0.526406	+	0.850233i	$0.323539\pi$
$192$	−0.879988	−0.0635077
$193$	−11.7757	−0.847634	−0.423817	−	0.905748i	$-0.639310\pi$
$193$	−11.7757	−0.847634	−0.423817	+	0.905748i	$0.639310\pi$
$194$	−8.84095	−0.634743
$195$	−0.361730	−0.0259040
$196$	8.52805	0.609147
$197$	−8.97484	−0.639431	−0.319715	−	0.947514i	$-0.603587\pi$
$197$	−8.97484	−0.639431	−0.319715	+	0.947514i	$0.603587\pi$
$198$	−10.3705	−0.737002
$199$	−7.63160	−0.540990	−0.270495	−	0.962721i	$-0.587187\pi$
$199$	−7.63160	−0.540990	−0.270495	+	0.962721i	$0.587187\pi$
$200$	−1.50598	−0.106489
$201$	10.9932	0.775400
$202$	7.70885	0.542393
$203$	−11.1583	−0.783158
$204$	4.46101	0.312333
$205$	6.10343	0.426282
$206$	−11.8001	−0.822151
$207$	13.9619	0.970417
$208$	−0.219910	−0.0152480
$209$	6.44774	0.446000
$210$	6.48184	0.447289
$211$	−20.7726	−1.43005	−0.715023	−	0.699101i	$-0.753584\pi$
$211$	−20.7726	−1.43005	−0.715023	+	0.699101i	$0.753584\pi$
$212$	−0.433602	−0.0297799
$213$	−8.16616	−0.559536
$214$	2.89473	0.197880
$215$	−2.53968	−0.173204
$216$	4.59848	0.312887
$217$	−32.3748	−2.19775
$218$	16.9959	1.15111
$219$	3.36252	0.227218
$220$	−8.70989	−0.587221
$221$	1.11481	0.0749902
$222$	5.53248	0.371315
$223$	−5.68465	−0.380672	−0.190336	−	0.981719i	$-0.560958\pi$
$223$	−5.68465	−0.380672	−0.190336	+	0.981719i	$0.560958\pi$
$224$	3.94056	0.263290
$225$	3.35174	0.223449
$226$	−13.2848	−0.883692
$227$	11.7648	0.780856	0.390428	−	0.920633i	$-0.372327\pi$
$227$	11.7648	0.780856	0.390428	+	0.920633i	$0.372327\pi$
$228$	−1.21768	−0.0806431
$229$	8.39983	0.555077	0.277538	−	0.960715i	$-0.410481\pi$
$229$	8.39983	0.555077	0.277538	+	0.960715i	$0.410481\pi$
$230$	11.7261	0.773199
$231$	−16.1579	−1.06311
$232$	−2.83165	−0.185907
$233$	8.73248	0.572083	0.286042	−	0.958217i	$-0.407660\pi$
$233$	8.73248	0.572083	0.286042	+	0.958217i	$0.407660\pi$
$234$	0.489435	0.0319954
$235$	14.6248	0.954017
$236$	15.2378	0.991896
$237$	3.80397	0.247094
$238$	−19.9763	−1.29487
$239$	−5.79014	−0.374533	−0.187267	−	0.982309i	$-0.559963\pi$
$239$	−5.79014	−0.374533	−0.187267	+	0.982309i	$0.559963\pi$
$240$	1.64490	0.106178
$241$	1.51389	0.0975179	0.0487590	−	0.998811i	$-0.484473\pi$
$241$	1.51389	0.0975179	0.0487590	+	0.998811i	$0.484473\pi$
$242$	10.7120	0.688594
$243$	−16.1100	−1.03346
$244$	8.74847	0.560063
$245$	−15.9409	−1.01843
$246$	2.87334	0.183198
$247$	−0.304300	−0.0193621
$248$	−8.21578	−0.521702
$249$	8.29710	0.525807
$250$	12.1612	0.769140
$251$	18.5067	1.16814	0.584068	−	0.811705i	$-0.301460\pi$
$251$	18.5067	1.16814	0.584068	+	0.811705i	$0.301460\pi$
$252$	−8.77020	−0.552471
$253$	−29.2309	−1.83773
$254$	−8.92382	−0.559931
$255$	−8.33865	−0.522187
$256$	1.00000	0.0625000
$257$	15.4842	0.965875	0.482937	−	0.875655i	$-0.339570\pi$
$257$	15.4842	0.965875	0.482937	+	0.875655i	$0.339570\pi$
$258$	−1.19562	−0.0744359
$259$	−24.7743	−1.53940
$260$	0.411062	0.0254930
$261$	6.30217	0.390095
$262$	13.7075	0.846851
$263$	4.23264	0.260996	0.130498	−	0.991449i	$-0.458342\pi$
$263$	4.23264	0.260996	0.130498	+	0.991449i	$0.458342\pi$
$264$	−4.10041	−0.252363
$265$	0.810502	0.0497888
$266$	5.45276	0.334330
$267$	−6.74826	−0.412987
$268$	−12.4924	−0.763097
$269$	−18.1487	−1.10654	−0.553272	−	0.833000i	$-0.686621\pi$
$269$	−18.1487	−1.10654	−0.553272	+	0.833000i	$0.686621\pi$
$270$	−8.59563	−0.523113
$271$	25.2885	1.53616	0.768082	−	0.640351i	$-0.221211\pi$
$271$	25.2885	1.53616	0.768082	+	0.640351i	$0.221211\pi$
$272$	−5.06940	−0.307377
$273$	0.762570	0.0461528
$274$	−0.210910	−0.0127416
$275$	−7.01728	−0.423158
$276$	5.52039	0.332288
$277$	−8.67604	−0.521293	−0.260646	−	0.965434i	$-0.583936\pi$
$277$	−8.67604	−0.521293	−0.260646	+	0.965434i	$0.583936\pi$
$278$	−18.3736	−1.10197
$279$	18.2852	1.09471
$280$	−7.36582	−0.440192
$281$	9.46018	0.564347	0.282173	−	0.959363i	$-0.408945\pi$
$281$	9.46018	0.564347	0.282173	+	0.959363i	$0.408945\pi$
$282$	6.88500	0.409996
$283$	−9.71161	−0.577295	−0.288648	−	0.957435i	$-0.593206\pi$
$283$	−9.71161	−0.577295	−0.288648	+	0.957435i	$0.593206\pi$
$284$	9.27985	0.550658
$285$	2.27613	0.134826
$286$	−1.02469	−0.0605915
$287$	−12.8668	−0.759501
$288$	−2.22562	−0.131146
$289$	8.69878	0.511693
$290$	5.29300	0.310816
$291$	7.77993	0.456068
$292$	−3.82110	−0.223613
$293$	8.76871	0.512274	0.256137	−	0.966641i	$-0.417550\pi$
$293$	8.76871	0.512274	0.256137	+	0.966641i	$0.417550\pi$
$294$	−7.50459	−0.437676
$295$	−28.4829	−1.65834
$296$	−6.28699	−0.365424
$297$	21.4272	1.24333
$298$	−15.0737	−0.873197
$299$	1.37955	0.0797813
$300$	1.32524	0.0765130
$301$	5.35394	0.308596
$302$	−15.2489	−0.877475
$303$	−6.78370	−0.389713
$304$	1.38375	0.0793635
$305$	−16.3529	−0.936364
$306$	11.2826	0.644981
$307$	17.8380	1.01807	0.509035	−	0.860746i	$-0.330003\pi$
$307$	17.8380	1.01807	0.509035	+	0.860746i	$0.330003\pi$
$308$	18.3615	1.04624
$309$	10.3839	0.590722
$310$	15.3572	0.872229
$311$	11.4113	0.647074	0.323537	−	0.946215i	$-0.395128\pi$
$311$	11.4113	0.647074	0.323537	+	0.946215i	$0.395128\pi$
$312$	0.193518	0.0109558
$313$	−17.3955	−0.983250	−0.491625	−	0.870807i	$-0.663597\pi$
$313$	−17.3955	−0.983250	−0.491625	+	0.870807i	$0.663597\pi$
$314$	−18.0682	−1.01965
$315$	16.3935	0.923671
$316$	−4.32275	−0.243173
$317$	−28.6003	−1.60635	−0.803176	−	0.595741i	$-0.796858\pi$
$317$	−28.6003	−1.60635	−0.803176	+	0.595741i	$0.796858\pi$
$318$	0.381565	0.0213971
$319$	−13.1944	−0.738744
$320$	−1.86923	−0.104493
$321$	−2.54733	−0.142178
$322$	−24.7201	−1.37760
$323$	−7.01477	−0.390313
$324$	2.63025	0.146125
$325$	0.331179	0.0183705
$326$	−12.4609	−0.690148
$327$	−14.9562	−0.827081
$328$	−3.26521	−0.180291
$329$	−30.8309	−1.69976
$330$	7.66460	0.421923
$331$	3.75502	0.206395	0.103197	−	0.994661i	$-0.467093\pi$
$331$	3.75502	0.206395	0.103197	+	0.994661i	$0.467093\pi$
$332$	−9.42865	−0.517464
$333$	13.9925	0.766782
$334$	−0.380585	−0.0208247
$335$	23.3512	1.27581
$336$	−3.46765	−0.189176
$337$	11.2643	0.613606	0.306803	−	0.951773i	$-0.400741\pi$
$337$	11.2643	0.613606	0.306803	+	0.951773i	$0.400741\pi$
$338$	−12.9516	−0.704476
$339$	11.6905	0.634939
$340$	9.47587	0.513901
$341$	−38.2824	−2.07311
$342$	−3.07970	−0.166531
$343$	6.02139	0.325124
$344$	1.35867	0.0732548
$345$	−10.3189	−0.555549
$346$	17.2593	0.927866
$347$	−20.4644	−1.09859	−0.549294	−	0.835629i	$-0.685103\pi$
$347$	−20.4644	−1.09859	−0.549294	+	0.835629i	$0.685103\pi$
$348$	2.49182	0.133575
$349$	22.0619	1.18095	0.590473	−	0.807057i	$-0.298941\pi$
$349$	22.0619	1.18095	0.590473	+	0.807057i	$0.298941\pi$
$350$	−5.93441	−0.317207
$351$	−1.01125	−0.0539766
$352$	4.65962	0.248358
$353$	−32.4941	−1.72949	−0.864744	−	0.502212i	$-0.832520\pi$
$353$	−32.4941	−1.72949	−0.864744	+	0.502212i	$0.832520\pi$
$354$	−13.4091	−0.712684
$355$	−17.3462	−0.920640
$356$	7.66858	0.406434
$357$	17.5789	0.930374
$358$	−14.4538	−0.763905
$359$	−3.61652	−0.190873	−0.0954363	−	0.995436i	$-0.530425\pi$
$359$	−3.61652	−0.190873	−0.0954363	+	0.995436i	$0.530425\pi$
$360$	4.16020	0.219262
$361$	−17.0852	−0.899223
$362$	2.78115	0.146174
$363$	−9.42645	−0.494760
$364$	−0.866568	−0.0454205
$365$	7.14251	0.373856
$366$	−7.69855	−0.402410
$367$	2.69071	0.140454	0.0702269	−	0.997531i	$-0.477628\pi$
$367$	2.69071	0.140454	0.0702269	+	0.997531i	$0.477628\pi$
$368$	−6.27325	−0.327016
$369$	7.26711	0.378311
$370$	11.7518	0.610948
$371$	−1.70864	−0.0887081
$372$	7.22979	0.374847
$373$	−3.97788	−0.205967	−0.102984	−	0.994683i	$-0.532839\pi$
$373$	−3.97788	−0.205967	−0.102984	+	0.994683i	$0.532839\pi$
$374$	−23.6214	−1.22144
$375$	−10.7017	−0.552633
$376$	−7.82397	−0.403491
$377$	0.622706	0.0320710
$378$	18.1206	0.932025
$379$	−27.7244	−1.42411	−0.712054	−	0.702125i	$-0.752235\pi$
$379$	−27.7244	−1.42411	−0.712054	+	0.702125i	$0.752235\pi$
$380$	−2.58655	−0.132687
$381$	7.85286	0.402314
$382$	14.5502	0.744451
$383$	5.57037	0.284632	0.142316	−	0.989821i	$-0.454545\pi$
$383$	5.57037	0.284632	0.142316	+	0.989821i	$0.454545\pi$
$384$	−0.879988	−0.0449067
$385$	−34.3219	−1.74921
$386$	−11.7757	−0.599368
$387$	−3.02389	−0.153713
$388$	−8.84095	−0.448831
$389$	−11.4474	−0.580406	−0.290203	−	0.956965i	$-0.593723\pi$
$389$	−11.4474	−0.580406	−0.290203	+	0.956965i	$0.593723\pi$
$390$	−0.361730	−0.0183169
$391$	31.8016	1.60828
$392$	8.52805	0.430732
$393$	−12.0624	−0.608469
$394$	−8.97484	−0.452146
$395$	8.08021	0.406559
$396$	−10.3705	−0.521139
$397$	25.7030	1.29000	0.644998	−	0.764185i	$-0.276858\pi$
$397$	25.7030	1.29000	0.644998	+	0.764185i	$0.276858\pi$
$398$	−7.63160	−0.382538
$399$	−4.79836	−0.240218
$400$	−1.50598	−0.0752989
$401$	25.5873	1.27777	0.638884	−	0.769303i	$-0.279396\pi$
$401$	25.5873	1.27777	0.638884	+	0.769303i	$0.279396\pi$
$402$	10.9932	0.548291
$403$	1.80673	0.0899996
$404$	7.70885	0.383530
$405$	−4.91654	−0.244305
$406$	−11.1583	−0.553777
$407$	−29.2949	−1.45210
$408$	4.46101	0.220853
$409$	−15.0686	−0.745096	−0.372548	−	0.928013i	$-0.621516\pi$
$409$	−15.0686	−0.745096	−0.372548	+	0.928013i	$0.621516\pi$
$410$	6.10343	0.301427
$411$	0.185599	0.00915491
$412$	−11.8001	−0.581349
$413$	60.0455	2.95465
$414$	13.9619	0.686189
$415$	17.6243	0.865144
$416$	−0.219910	−0.0107820
$417$	16.1685	0.791777
$418$	6.44774	0.315369
$419$	−36.8933	−1.80235	−0.901177	−	0.433451i	$-0.857296\pi$
$419$	−36.8933	−1.80235	−0.901177	+	0.433451i	$0.857296\pi$
$420$	6.48184	0.316281
$421$	0.969108	0.0472314	0.0236157	−	0.999721i	$-0.492482\pi$
$421$	0.969108	0.0472314	0.0236157	+	0.999721i	$0.492482\pi$
$422$	−20.7726	−1.01119
$423$	17.4132	0.846659
$424$	−0.433602	−0.0210576
$425$	7.63440	0.370323
$426$	−8.16616	−0.395652
$427$	34.4739	1.66831
$428$	2.89473	0.139922
$429$	0.901719	0.0435354
$430$	−2.53968	−0.122474
$431$	30.0151	1.44578	0.722889	−	0.690964i	$-0.242814\pi$
$431$	30.0151	1.44578	0.722889	+	0.690964i	$0.242814\pi$
$432$	4.59848	0.221245
$433$	22.7991	1.09566	0.547828	−	0.836591i	$-0.315455\pi$
$433$	22.7991	1.09566	0.547828	+	0.836591i	$0.315455\pi$
$434$	−32.3748	−1.55404
$435$	−4.65778	−0.223323
$436$	16.9959	0.813957
$437$	−8.68061	−0.415250
$438$	3.36252	0.160667
$439$	19.7700	0.943570	0.471785	−	0.881714i	$-0.343610\pi$
$439$	19.7700	0.943570	0.471785	+	0.881714i	$0.343610\pi$
$440$	−8.70989	−0.415228
$441$	−18.9802	−0.903820
$442$	1.11481	0.0530261
$443$	16.6970	0.793297	0.396649	−	0.917971i	$-0.370173\pi$
$443$	16.6970	0.793297	0.396649	+	0.917971i	$0.370173\pi$
$444$	5.53248	0.262560
$445$	−14.3343	−0.679513
$446$	−5.68465	−0.269176
$447$	13.2647	0.627398
$448$	3.94056	0.186174
$449$	19.0964	0.901213	0.450606	−	0.892723i	$-0.351208\pi$
$449$	19.0964	0.901213	0.450606	+	0.892723i	$0.351208\pi$
$450$	3.35174	0.158002
$451$	−15.2146	−0.716428
$452$	−13.2848	−0.624864
$453$	13.4188	0.630472
$454$	11.7648	0.552149
$455$	1.61982	0.0759381
$456$	−1.21768	−0.0570232
$457$	20.9760	0.981215	0.490607	−	0.871381i	$-0.336775\pi$
$457$	20.9760	0.981215	0.490607	+	0.871381i	$0.336775\pi$
$458$	8.39983	0.392499
$459$	−23.3115	−1.08809
$460$	11.7261	0.546734
$461$	−5.39464	−0.251253	−0.125627	−	0.992078i	$-0.540094\pi$
$461$	−5.39464	−0.251253	−0.125627	+	0.992078i	$0.540094\pi$
$462$	−16.1579	−0.751734
$463$	15.3749	0.714533	0.357266	−	0.934003i	$-0.383709\pi$
$463$	15.3749	0.714533	0.357266	+	0.934003i	$0.383709\pi$
$464$	−2.83165	−0.131456
$465$	−13.5141	−0.626703
$466$	8.73248	0.404524
$467$	−4.87313	−0.225501	−0.112751	−	0.993623i	$-0.535966\pi$
$467$	−4.87313	−0.225501	−0.112751	+	0.993623i	$0.535966\pi$
$468$	0.489435	0.0226242
$469$	−49.2272	−2.27310
$470$	14.6248	0.674592
$471$	15.8998	0.732625
$472$	15.2378	0.701376
$473$	6.33090	0.291095
$474$	3.80397	0.174722
$475$	−2.08390	−0.0956158
$476$	−19.9763	−0.915612
$477$	0.965034	0.0441859
$478$	−5.79014	−0.264835
$479$	14.5702	0.665729	0.332865	−	0.942975i	$-0.391985\pi$
$479$	14.5702	0.665729	0.332865	+	0.942975i	$0.391985\pi$
$480$	1.64490	0.0750791
$481$	1.38257	0.0630397
$482$	1.51389	0.0689556
$483$	21.7534	0.989816
$484$	10.7120	0.486910
$485$	16.5258	0.750396
$486$	−16.1100	−0.730766
$487$	3.24681	0.147127	0.0735636	−	0.997291i	$-0.476563\pi$
$487$	3.24681	0.147127	0.0735636	+	0.997291i	$0.476563\pi$
$488$	8.74847	0.396024
$489$	10.9655	0.495877
$490$	−15.9409	−0.720136
$491$	−15.1452	−0.683495	−0.341748	−	0.939792i	$-0.611019\pi$
$491$	−15.1452	−0.683495	−0.341748	+	0.939792i	$0.611019\pi$
$492$	2.87334	0.129540
$493$	14.3547	0.646505
$494$	−0.304300	−0.0136911
$495$	19.3849	0.871287
$496$	−8.21578	−0.368899
$497$	36.5679	1.64029
$498$	8.29710	0.371802
$499$	20.6115	0.922698	0.461349	−	0.887219i	$-0.347366\pi$
$499$	20.6115	0.922698	0.461349	+	0.887219i	$0.347366\pi$
$500$	12.1612	0.543864
$501$	0.334910	0.0149627
$502$	18.5067	0.825996
$503$	−7.57328	−0.337676	−0.168838	−	0.985644i	$-0.554001\pi$
$503$	−7.57328	−0.337676	−0.168838	+	0.985644i	$0.554001\pi$
$504$	−8.77020	−0.390656
$505$	−14.4096	−0.641219
$506$	−29.2309	−1.29947
$507$	11.3973	0.506171
$508$	−8.92382	−0.395931
$509$	15.1619	0.672040	0.336020	−	0.941855i	$-0.390919\pi$
$509$	15.1619	0.672040	0.336020	+	0.941855i	$0.390919\pi$
$510$	−8.33865	−0.369242
$511$	−15.0573	−0.666095
$512$	1.00000	0.0441942
$513$	6.36315	0.280940
$514$	15.4842	0.682977
$515$	22.0571	0.971951
$516$	−1.19562	−0.0526341
$517$	−36.4567	−1.60336
$518$	−24.7743	−1.08852
$519$	−15.1880	−0.666679
$520$	0.411062	0.0180263
$521$	11.5965	0.508050	0.254025	−	0.967198i	$-0.418245\pi$
$521$	11.5965	0.508050	0.254025	+	0.967198i	$0.418245\pi$
$522$	6.30217	0.275839
$523$	−34.5441	−1.51051	−0.755254	−	0.655432i	$-0.772487\pi$
$523$	−34.5441	−1.51051	−0.755254	+	0.655432i	$0.772487\pi$
$524$	13.7075	0.598814
$525$	5.22221	0.227916
$526$	4.23264	0.184552
$527$	41.6490	1.81426
$528$	−4.10041	−0.178447
$529$	16.3537	0.711029
$530$	0.810502	0.0352060
$531$	−33.9135	−1.47172
$532$	5.45276	0.236407
$533$	0.718051	0.0311022
$534$	−6.74826	−0.292026
$535$	−5.41091	−0.233934
$536$	−12.4924	−0.539591
$537$	12.7191	0.548871
$538$	−18.1487	−0.782445
$539$	39.7374	1.71161
$540$	−8.59563	−0.369897
$541$	−3.57007	−0.153489	−0.0767447	−	0.997051i	$-0.524453\pi$
$541$	−3.57007	−0.153489	−0.0767447	+	0.997051i	$0.524453\pi$
$542$	25.2885	1.08623
$543$	−2.44738	−0.105027
$544$	−5.06940	−0.217349
$545$	−31.7693	−1.36085
$546$	0.762570	0.0326350
$547$	−0.165701	−0.00708485	−0.00354242	−	0.999994i	$-0.501128\pi$
$547$	−0.165701	−0.00708485	−0.00354242	+	0.999994i	$0.501128\pi$
$548$	−0.210910	−0.00900965
$549$	−19.4708	−0.830992
$550$	−7.01728	−0.299218
$551$	−3.91829	−0.166925
$552$	5.52039	0.234963
$553$	−17.0341	−0.724362
$554$	−8.67604	−0.368610
$555$	−10.3415	−0.438971
$556$	−18.3736	−0.779214
$557$	8.55918	0.362664	0.181332	−	0.983422i	$-0.441959\pi$
$557$	8.55918	0.362664	0.181332	+	0.983422i	$0.441959\pi$
$558$	18.2852	0.774074
$559$	−0.298786	−0.0126373
$560$	−7.36582	−0.311263
$561$	20.7866	0.877610
$562$	9.46018	0.399053
$563$	−44.3333	−1.86843	−0.934214	−	0.356714i	$-0.883897\pi$
$563$	−44.3333	−1.86843	−0.934214	+	0.356714i	$0.883897\pi$
$564$	6.88500	0.289911
$565$	24.8323	1.04470
$566$	−9.71161	−0.408209
$567$	10.3647	0.435275
$568$	9.27985	0.389374
$569$	−23.9513	−1.00409	−0.502045	−	0.864842i	$-0.667419\pi$
$569$	−23.9513	−1.00409	−0.502045	+	0.864842i	$0.667419\pi$
$570$	2.27613	0.0953366
$571$	−19.2951	−0.807477	−0.403738	−	0.914875i	$-0.632289\pi$
$571$	−19.2951	−0.807477	−0.403738	+	0.914875i	$0.632289\pi$
$572$	−1.02469	−0.0428446
$573$	−12.8040	−0.534894
$574$	−12.8668	−0.537048
$575$	9.44738	0.393983
$576$	−2.22562	−0.0927342
$577$	16.5128	0.687436	0.343718	−	0.939073i	$-0.388314\pi$
$577$	16.5128	0.687436	0.343718	+	0.939073i	$0.388314\pi$
$578$	8.69878	0.361821
$579$	10.3625	0.430650
$580$	5.29300	0.219780
$581$	−37.1542	−1.54142
$582$	7.77993	0.322489
$583$	−2.02042	−0.0836772
$584$	−3.82110	−0.158118
$585$	−0.914868	−0.0378251
$586$	8.76871	0.362232
$587$	−25.2179	−1.04086	−0.520428	−	0.853906i	$-0.674228\pi$
$587$	−25.2179	−1.04086	−0.520428	+	0.853906i	$0.674228\pi$
$588$	−7.50459	−0.309484
$589$	−11.3686	−0.468434
$590$	−28.4829	−1.17262
$591$	7.89775	0.324870
$592$	−6.28699	−0.258394
$593$	17.1475	0.704163	0.352081	−	0.935969i	$-0.385474\pi$
$593$	17.1475	0.704163	0.352081	+	0.935969i	$0.385474\pi$
$594$	21.4272	0.879167
$595$	37.3403	1.53080
$596$	−15.0737	−0.617443
$597$	6.71572	0.274856
$598$	1.37955	0.0564139
$599$	1.81276	0.0740675	0.0370338	−	0.999314i	$-0.488209\pi$
$599$	1.81276	0.0740675	0.0370338	+	0.999314i	$0.488209\pi$
$600$	1.32524	0.0541028
$601$	−28.6289	−1.16780	−0.583898	−	0.811827i	$-0.698473\pi$
$601$	−28.6289	−1.16780	−0.583898	+	0.811827i	$0.698473\pi$
$602$	5.35394	0.218210
$603$	27.8034	1.13224
$604$	−15.2489	−0.620468
$605$	−20.0232	−0.814060
$606$	−6.78370	−0.275569
$607$	29.6544	1.20363	0.601817	−	0.798634i	$-0.294444\pi$
$607$	29.6544	1.20363	0.601817	+	0.798634i	$0.294444\pi$
$608$	1.38375	0.0561185
$609$	9.81916	0.397893
$610$	−16.3529	−0.662109
$611$	1.72057	0.0696067
$612$	11.2826	0.456070
$613$	16.9257	0.683623	0.341811	−	0.939769i	$-0.388960\pi$
$613$	16.9257	0.683623	0.341811	+	0.939769i	$0.388960\pi$
$614$	17.8380	0.719884
$615$	−5.37094	−0.216577
$616$	18.3615	0.739807
$617$	−7.79369	−0.313762	−0.156881	−	0.987617i	$-0.550144\pi$
$617$	−7.79369	−0.313762	−0.156881	+	0.987617i	$0.550144\pi$
$618$	10.3839	0.417703
$619$	1.77995	0.0715421	0.0357710	−	0.999360i	$-0.488611\pi$
$619$	1.77995	0.0715421	0.0357710	+	0.999360i	$0.488611\pi$
$620$	15.3572	0.616759
$621$	−28.8474	−1.15761
$622$	11.4113	0.457551
$623$	30.2185	1.21068
$624$	0.193518	0.00774692
$625$	−15.2021	−0.608085
$626$	−17.3955	−0.695263
$627$	−5.67394	−0.226595
$628$	−18.0682	−0.721000
$629$	31.8712	1.27079
$630$	16.3935	0.653134
$631$	5.70364	0.227058	0.113529	−	0.993535i	$-0.463784\pi$
$631$	5.70364	0.227058	0.113529	+	0.993535i	$0.463784\pi$
$632$	−4.32275	−0.171950
$633$	18.2797	0.726551
$634$	−28.6003	−1.13586
$635$	16.6807	0.661953
$636$	0.381565	0.0151300
$637$	−1.87540	−0.0743061
$638$	−13.1944	−0.522371
$639$	−20.6534	−0.817037
$640$	−1.86923	−0.0738878
$641$	−1.44540	−0.0570899	−0.0285450	−	0.999593i	$-0.509087\pi$
$641$	−1.44540	−0.0570899	−0.0285450	+	0.999593i	$0.509087\pi$
$642$	−2.54733	−0.100535
$643$	38.6055	1.52245	0.761227	−	0.648486i	$-0.224598\pi$
$643$	38.6055	1.52245	0.761227	+	0.648486i	$0.224598\pi$
$644$	−24.7201	−0.974110
$645$	2.23488	0.0879985
$646$	−7.01477	−0.275993
$647$	−29.4533	−1.15793	−0.578965	−	0.815352i	$-0.696543\pi$
$647$	−29.4533	−1.15793	−0.578965	+	0.815352i	$0.696543\pi$
$648$	2.63025	0.103326
$649$	71.0022	2.78708
$650$	0.331179	0.0129899
$651$	28.4894	1.11659
$652$	−12.4609	−0.488008
$653$	−38.5262	−1.50765	−0.753824	−	0.657076i	$-0.771793\pi$
$653$	−38.5262	−1.50765	−0.753824	+	0.657076i	$0.771793\pi$
$654$	−14.9562	−0.584834
$655$	−25.6224	−1.00115
$656$	−3.26521	−0.127485
$657$	8.50431	0.331785
$658$	−30.8309	−1.20191
$659$	14.4226	0.561825	0.280912	−	0.959733i	$-0.409363\pi$
$659$	14.4226	0.561825	0.280912	+	0.959733i	$0.409363\pi$
$660$	7.66460	0.298344
$661$	−44.2835	−1.72243	−0.861214	−	0.508242i	$-0.830296\pi$
$661$	−44.2835	−1.72243	−0.861214	+	0.508242i	$0.830296\pi$
$662$	3.75502	0.145943
$663$	−0.981019	−0.0380996
$664$	−9.42865	−0.365903
$665$	−10.1925	−0.395246
$666$	13.9925	0.542196
$667$	17.7636	0.687810
$668$	−0.380585	−0.0147253
$669$	5.00242	0.193405
$670$	23.3512	0.902137
$671$	40.7645	1.57370
$672$	−3.46765	−0.133768
$673$	−12.2553	−0.472406	−0.236203	−	0.971704i	$-0.575903\pi$
$673$	−12.2553	−0.472406	−0.236203	+	0.971704i	$0.575903\pi$
$674$	11.2643	0.433885
$675$	−6.92522	−0.266552
$676$	−12.9516	−0.498140
$677$	14.2132	0.546258	0.273129	−	0.961977i	$-0.411941\pi$
$677$	14.2132	0.546258	0.273129	+	0.961977i	$0.411941\pi$
$678$	11.6905	0.448970
$679$	−34.8383	−1.33697
$680$	9.47587	0.363383
$681$	−10.3529	−0.396723
$682$	−38.2824	−1.46591
$683$	24.8839	0.952158	0.476079	−	0.879403i	$-0.342058\pi$
$683$	24.8839	0.952158	0.476079	+	0.879403i	$0.342058\pi$
$684$	−3.07970	−0.117755
$685$	0.394240	0.0150631
$686$	6.02139	0.229898
$687$	−7.39176	−0.282013
$688$	1.35867	0.0517990
$689$	0.0953533	0.00363267
$690$	−10.3189	−0.392833
$691$	−0.859420	−0.0326939	−0.0163469	−	0.999866i	$-0.505204\pi$
$691$	−0.859420	−0.0326939	−0.0163469	+	0.999866i	$0.505204\pi$
$692$	17.2593	0.656101
$693$	−40.8658	−1.55236
$694$	−20.4644	−0.776818
$695$	34.3445	1.30276
$696$	2.49182	0.0944520
$697$	16.5526	0.626976
$698$	22.0619	0.835055
$699$	−7.68448	−0.290654
$700$	−5.93441	−0.224299
$701$	24.4391	0.923053	0.461526	−	0.887127i	$-0.347302\pi$
$701$	24.4391	0.923053	0.461526	+	0.887127i	$0.347302\pi$
$702$	−1.01125	−0.0381672
$703$	−8.69962	−0.328112
$704$	4.65962	0.175616
$705$	−12.8697	−0.484699
$706$	−32.4941	−1.22293
$707$	30.3772	1.14245
$708$	−13.4091	−0.503944
$709$	20.8579	0.783335	0.391668	−	0.920107i	$-0.371898\pi$
$709$	20.8579	0.783335	0.391668	+	0.920107i	$0.371898\pi$
$710$	−17.3462	−0.650991
$711$	9.62079	0.360808
$712$	7.66858	0.287392
$713$	51.5396	1.93017
$714$	17.5789	0.657874
$715$	1.91539	0.0716315
$716$	−14.4538	−0.540162
$717$	5.09526	0.190286
$718$	−3.61652	−0.134967
$719$	12.4234	0.463315	0.231657	−	0.972797i	$-0.425585\pi$
$719$	12.4234	0.463315	0.231657	+	0.972797i	$0.425585\pi$
$720$	4.16020	0.155041
$721$	−46.4990	−1.73171
$722$	−17.0852	−0.635847
$723$	−1.33220	−0.0495451
$724$	2.78115	0.103361
$725$	4.26440	0.158376
$726$	−9.42645	−0.349848
$727$	−31.4454	−1.16624	−0.583122	−	0.812385i	$-0.698169\pi$
$727$	−31.4454	−1.16624	−0.583122	+	0.812385i	$0.698169\pi$
$728$	−0.866568	−0.0321172
$729$	6.28590	0.232811
$730$	7.14251	0.264356
$731$	−6.88766	−0.254749
$732$	−7.69855	−0.284547
$733$	−34.9778	−1.29193	−0.645966	−	0.763366i	$-0.723545\pi$
$733$	−34.9778	−1.29193	−0.645966	+	0.763366i	$0.723545\pi$
$734$	2.69071	0.0993158
$735$	14.0278	0.517423
$736$	−6.27325	−0.231235
$737$	−58.2099	−2.14419
$738$	7.26711	0.267506
$739$	−15.1921	−0.558851	−0.279426	−	0.960167i	$-0.590144\pi$
$739$	−15.1921	−0.558851	−0.279426	+	0.960167i	$0.590144\pi$
$740$	11.7518	0.432006
$741$	0.267780	0.00983716
$742$	−1.70864	−0.0627261
$743$	−19.4057	−0.711926	−0.355963	−	0.934500i	$-0.615847\pi$
$743$	−19.4057	−0.711926	−0.355963	+	0.934500i	$0.615847\pi$
$744$	7.22979	0.265057
$745$	28.1762	1.03230
$746$	−3.97788	−0.145641
$747$	20.9846	0.767786
$748$	−23.6214	−0.863685
$749$	11.4069	0.416798
$750$	−10.7017	−0.390770
$751$	−2.31953	−0.0846407	−0.0423204	−	0.999104i	$-0.513475\pi$
$751$	−2.31953	−0.0846407	−0.0423204	+	0.999104i	$0.513475\pi$
$752$	−7.82397	−0.285311
$753$	−16.2857	−0.593485
$754$	0.622706	0.0226776
$755$	28.5037	1.03735
$756$	18.1206	0.659041
$757$	50.1440	1.82251	0.911257	−	0.411839i	$-0.135113\pi$
$757$	50.1440	1.82251	0.911257	+	0.411839i	$0.135113\pi$
$758$	−27.7244	−1.00700
$759$	25.7229	0.933681
$760$	−2.58655	−0.0938239
$761$	47.8635	1.73505	0.867525	−	0.497393i	$-0.165709\pi$
$761$	47.8635	1.73505	0.867525	+	0.497393i	$0.165709\pi$
$762$	7.85286	0.284479
$763$	66.9736	2.42461
$764$	14.5502	0.526406
$765$	−21.0897	−0.762499
$766$	5.57037	0.201266
$767$	−3.35094	−0.120995
$768$	−0.879988	−0.0317538
$769$	−51.9509	−1.87340	−0.936698	−	0.350137i	$-0.886135\pi$
$769$	−51.9509	−1.87340	−0.936698	+	0.350137i	$0.886135\pi$
$770$	−34.3219	−1.23688
$771$	−13.6259	−0.490724
$772$	−11.7757	−0.423817
$773$	−46.4099	−1.66925	−0.834624	−	0.550820i	$-0.814315\pi$
$773$	−46.4099	−1.66925	−0.834624	+	0.550820i	$0.814315\pi$
$774$	−3.02389	−0.108692
$775$	12.3728	0.444444
$776$	−8.84095	−0.317372
$777$	21.8011	0.782109
$778$	−11.4474	−0.410409
$779$	−4.51823	−0.161882
$780$	−0.361730	−0.0129520
$781$	43.2406	1.54727
$782$	31.8016	1.13722
$783$	−13.0213	−0.465343
$784$	8.52805	0.304573
$785$	33.7737	1.20543
$786$	−12.0624	−0.430252
$787$	53.7084	1.91450	0.957249	−	0.289266i	$-0.0934111\pi$
$787$	53.7084	1.91450	0.957249	+	0.289266i	$0.0934111\pi$
$788$	−8.97484	−0.319715
$789$	−3.72468	−0.132602
$790$	8.08021	0.287481
$791$	−52.3496	−1.86134
$792$	−10.3705	−0.368501
$793$	−1.92387	−0.0683187
$794$	25.7030	0.912164
$795$	−0.713233	−0.0252958
$796$	−7.63160	−0.270495
$797$	17.1702	0.608200	0.304100	−	0.952640i	$-0.401644\pi$
$797$	17.1702	0.608200	0.304100	+	0.952640i	$0.401644\pi$
$798$	−4.79836	−0.169860
$799$	39.6628	1.40317
$800$	−1.50598	−0.0532444
$801$	−17.0674	−0.603045
$802$	25.5873	0.903519
$803$	−17.8048	−0.628319
$804$	10.9932	0.387700
$805$	46.2076	1.62861
$806$	1.80673	0.0636393
$807$	15.9706	0.562193
$808$	7.70885	0.271196
$809$	3.88824	0.136703	0.0683516	−	0.997661i	$-0.478226\pi$
$809$	3.88824	0.136703	0.0683516	+	0.997661i	$0.478226\pi$
$810$	−4.91654	−0.172750
$811$	−21.6950	−0.761815	−0.380908	−	0.924613i	$-0.624388\pi$
$811$	−21.6950	−0.761815	−0.380908	+	0.924613i	$0.624388\pi$
$812$	−11.1583	−0.391579
$813$	−22.2535	−0.780466
$814$	−29.2949	−1.02679
$815$	23.2924	0.815897
$816$	4.46101	0.156167
$817$	1.88007	0.0657752
$818$	−15.0686	−0.526863
$819$	1.92865	0.0673926
$820$	6.10343	0.213141
$821$	18.3261	0.639586	0.319793	−	0.947487i	$-0.396387\pi$
$821$	18.3261	0.639586	0.319793	+	0.947487i	$0.396387\pi$
$822$	0.185599	0.00647350
$823$	−12.3076	−0.429017	−0.214509	−	0.976722i	$-0.568815\pi$
$823$	−12.3076	−0.429017	−0.214509	+	0.976722i	$0.568815\pi$
$824$	−11.8001	−0.411076
$825$	6.17512	0.214990
$826$	60.0455	2.08925
$827$	20.3866	0.708913	0.354456	−	0.935073i	$-0.384666\pi$
$827$	20.3866	0.708913	0.354456	+	0.935073i	$0.384666\pi$
$828$	13.9619	0.485209
$829$	7.46715	0.259345	0.129672	−	0.991557i	$-0.458607\pi$
$829$	7.46715	0.259345	0.129672	+	0.991557i	$0.458607\pi$
$830$	17.6243	0.611749
$831$	7.63482	0.264849
$832$	−0.219910	−0.00762400
$833$	−43.2321	−1.49790
$834$	16.1685	0.559871
$835$	0.711400	0.0246190
$836$	6.44774	0.223000
$837$	−37.7801	−1.30587
$838$	−36.8933	−1.27446
$839$	14.9852	0.517347	0.258673	−	0.965965i	$-0.416715\pi$
$839$	14.9852	0.517347	0.258673	+	0.965965i	$0.416715\pi$
$840$	6.48184	0.223645
$841$	−20.9818	−0.723510
$842$	0.969108	0.0333977
$843$	−8.32484	−0.286723
$844$	−20.7726	−0.715023
$845$	24.2096	0.832835
$846$	17.4132	0.598678
$847$	42.2114	1.45040
$848$	−0.433602	−0.0148900
$849$	8.54610	0.293302
$850$	7.63440	0.261858
$851$	39.4398	1.35198
$852$	−8.16616	−0.279768
$853$	15.8633	0.543149	0.271575	−	0.962417i	$-0.412456\pi$
$853$	15.8633	0.543149	0.271575	+	0.962417i	$0.412456\pi$
$854$	34.4739	1.17967
$855$	5.75667	0.196874
$856$	2.89473	0.0989398
$857$	2.89715	0.0989647	0.0494823	−	0.998775i	$-0.484243\pi$
$857$	2.89715	0.0989647	0.0494823	+	0.998775i	$0.484243\pi$
$858$	0.901719	0.0307842
$859$	45.9662	1.56835	0.784174	−	0.620541i	$-0.213087\pi$
$859$	45.9662	1.56835	0.784174	+	0.620541i	$0.213087\pi$
$860$	−2.53968	−0.0866022
$861$	11.3226	0.385873
$862$	30.0151	1.02232
$863$	−14.3140	−0.487253	−0.243626	−	0.969869i	$-0.578337\pi$
$863$	−14.3140	−0.487253	−0.243626	+	0.969869i	$0.578337\pi$
$864$	4.59848	0.156444
$865$	−32.2616	−1.09693
$866$	22.7991	0.774745
$867$	−7.65482	−0.259971
$868$	−32.3748	−1.09887
$869$	−20.1423	−0.683282
$870$	−4.65778	−0.157913
$871$	2.74721	0.0930855
$872$	16.9959	0.575555
$873$	19.6766	0.665952
$874$	−8.68061	−0.293626
$875$	47.9219	1.62006
$876$	3.36252	0.113609
$877$	−7.13031	−0.240773	−0.120387	−	0.992727i	$-0.538413\pi$
$877$	−7.13031	−0.240773	−0.120387	+	0.992727i	$0.538413\pi$
$878$	19.7700	0.667205
$879$	−7.71637	−0.260267
$880$	−8.70989	−0.293610
$881$	32.0856	1.08099	0.540496	−	0.841346i	$-0.318236\pi$
$881$	32.0856	1.08099	0.540496	+	0.841346i	$0.318236\pi$
$882$	−18.9802	−0.639097
$883$	−27.9931	−0.942044	−0.471022	−	0.882121i	$-0.656115\pi$
$883$	−27.9931	−0.942044	−0.471022	+	0.882121i	$0.656115\pi$
$884$	1.11481	0.0374951
$885$	25.0647	0.842539
$886$	16.6970	0.560946
$887$	43.5494	1.46224	0.731122	−	0.682246i	$-0.238997\pi$
$887$	43.5494	1.46224	0.731122	+	0.682246i	$0.238997\pi$
$888$	5.53248	0.185658
$889$	−35.1649	−1.17939
$890$	−14.3343	−0.480488
$891$	12.2560	0.410590
$892$	−5.68465	−0.190336
$893$	−10.8264	−0.362292
$894$	13.2647	0.443638
$895$	27.0174	0.903092
$896$	3.94056	0.131645
$897$	−1.21399	−0.0405338
$898$	19.0964	0.637254
$899$	23.2642	0.775904
$900$	3.35174	0.111725
$901$	2.19810	0.0732294
$902$	−15.2146	−0.506591
$903$	−4.71141	−0.156786
$904$	−13.2848	−0.441846
$905$	−5.19861	−0.172808
$906$	13.4188	0.445811
$907$	10.3978	0.345255	0.172627	−	0.984987i	$-0.444774\pi$
$907$	10.3978	0.345255	0.172627	+	0.984987i	$0.444774\pi$
$908$	11.7648	0.390428
$909$	−17.1570	−0.569061
$910$	1.61982	0.0536964
$911$	−16.2144	−0.537207	−0.268603	−	0.963251i	$-0.586562\pi$
$911$	−16.2144	−0.537207	−0.268603	+	0.963251i	$0.586562\pi$
$912$	−1.21768	−0.0403215
$913$	−43.9339	−1.45400
$914$	20.9760	0.693824
$915$	14.3904	0.475731
$916$	8.39983	0.277538
$917$	54.0152	1.78374
$918$	−23.3115	−0.769396
$919$	−38.1033	−1.25691	−0.628456	−	0.777845i	$-0.716313\pi$
$919$	−38.1033	−1.25691	−0.628456	+	0.777845i	$0.716313\pi$
$920$	11.7261	0.386600
$921$	−15.6972	−0.517242
$922$	−5.39464	−0.177663
$923$	−2.04073	−0.0671714
$924$	−16.1579	−0.531557
$925$	9.46807	0.311308
$926$	15.3749	0.505251
$927$	26.2625	0.862574
$928$	−2.83165	−0.0929534
$929$	45.7373	1.50059	0.750296	−	0.661102i	$-0.229911\pi$
$929$	45.7373	1.50059	0.750296	+	0.661102i	$0.229911\pi$
$930$	−13.5141	−0.443146
$931$	11.8007	0.386752
$932$	8.73248	0.286042
$933$	−10.0418	−0.328754
$934$	−4.87313	−0.159454
$935$	44.1539	1.44399
$936$	0.489435	0.0159977
$937$	42.2921	1.38162	0.690812	−	0.723035i	$-0.257253\pi$
$937$	42.2921	1.38162	0.690812	+	0.723035i	$0.257253\pi$
$938$	−49.2272	−1.60733
$939$	15.3078	0.499551
$940$	14.6248	0.477009
$941$	−20.7781	−0.677347	−0.338674	−	0.940904i	$-0.609978\pi$
$941$	−20.7781	−0.677347	−0.338674	+	0.940904i	$0.609978\pi$
$942$	15.8998	0.518044
$943$	20.4835	0.667033
$944$	15.2378	0.495948
$945$	−33.8716	−1.10184
$946$	6.33090	0.205835
$947$	−38.3621	−1.24660	−0.623301	−	0.781982i	$-0.714209\pi$
$947$	−38.3621	−1.24660	−0.623301	+	0.781982i	$0.714209\pi$
$948$	3.80397	0.123547
$949$	0.840296	0.0272772
$950$	−2.08390	−0.0676106
$951$	25.1679	0.816126
$952$	−19.9763	−0.647435
$953$	24.3557	0.788959	0.394479	−	0.918905i	$-0.370925\pi$
$953$	24.3557	0.788959	0.394479	+	0.918905i	$0.370925\pi$
$954$	0.965034	0.0312441
$955$	−27.1976	−0.880094
$956$	−5.79014	−0.187267
$957$	11.6109	0.375327
$958$	14.5702	0.470742
$959$	−0.831106	−0.0268378
$960$	1.64490	0.0530889
$961$	36.4990	1.17739
$962$	1.38257	0.0445758
$963$	−6.44257	−0.207609
$964$	1.51389	0.0487590
$965$	22.0115	0.708576
$966$	21.7534	0.699905
$967$	−5.63101	−0.181081	−0.0905405	−	0.995893i	$-0.528859\pi$
$967$	−5.63101	−0.181081	−0.0905405	+	0.995893i	$0.528859\pi$
$968$	10.7120	0.344297
$969$	6.17292	0.198303
$970$	16.5258	0.530610
$971$	24.6991	0.792632	0.396316	−	0.918114i	$-0.370288\pi$
$971$	24.6991	0.792632	0.396316	+	0.918114i	$0.370288\pi$
$972$	−16.1100	−0.516730
$973$	−72.4023	−2.32111
$974$	3.24681	0.104035
$975$	−0.291434	−0.00933335
$976$	8.74847	0.280032
$977$	−56.2314	−1.79900	−0.899501	−	0.436919i	$-0.856070\pi$
$977$	−56.2314	−1.79900	−0.899501	+	0.436919i	$0.856070\pi$
$978$	10.9655	0.350638
$979$	35.7326	1.14202
$980$	−15.9409	−0.509213
$981$	−37.8265	−1.20771
$982$	−15.1452	−0.483304
$983$	−6.51269	−0.207723	−0.103861	−	0.994592i	$-0.533120\pi$
$983$	−6.51269	−0.207723	−0.103861	+	0.994592i	$0.533120\pi$
$984$	2.87334	0.0915989
$985$	16.7760	0.534529
$986$	14.3547	0.457148
$987$	27.1308	0.863583
$988$	−0.304300	−0.00968107
$989$	−8.52330	−0.271025
$990$	19.3849	0.616093
$991$	−2.04918	−0.0650943	−0.0325471	−	0.999470i	$-0.510362\pi$
$991$	−2.04918	−0.0650943	−0.0325471	+	0.999470i	$0.510362\pi$
$992$	−8.21578	−0.260851
$993$	−3.30438	−0.104861
$994$	36.5679	1.15986
$995$	14.2652	0.452238
$996$	8.29710	0.262904
$997$	37.0662	1.17390	0.586949	−	0.809624i	$-0.300329\pi$
$997$	37.0662	1.17390	0.586949	+	0.809624i	$0.300329\pi$
$998$	20.6115	0.652446
$999$	−28.9106	−0.914691

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6002.2.a.a.1.20	✓	47

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6002.2.a.a.1.20	✓	47	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:	\( N \)	\(=\)	\( 6002 = 2 \cdot 3001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6002.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.879988 q^{3} +1.00000 q^{4} -1.86923 q^{5} -0.879988 q^{6} +3.94056 q^{7} +1.00000 q^{8} -2.22562 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.879988 q^{3} +1.00000 q^{4} -1.86923 q^{5} -0.879988 q^{6} +3.94056 q^{7} +1.00000 q^{8} -2.22562 q^{9} -1.86923 q^{10} +4.65962 q^{11} -0.879988 q^{12} -0.219910 q^{13} +3.94056 q^{14} +1.64490 q^{15} +1.00000 q^{16} -5.06940 q^{17} -2.22562 q^{18} +1.38375 q^{19} -1.86923 q^{20} -3.46765 q^{21} +4.65962 q^{22} -6.27325 q^{23} -0.879988 q^{24} -1.50598 q^{25} -0.219910 q^{26} +4.59848 q^{27} +3.94056 q^{28} -2.83165 q^{29} +1.64490 q^{30} -8.21578 q^{31} +1.00000 q^{32} -4.10041 q^{33} -5.06940 q^{34} -7.36582 q^{35} -2.22562 q^{36} -6.28699 q^{37} +1.38375 q^{38} +0.193518 q^{39} -1.86923 q^{40} -3.26521 q^{41} -3.46765 q^{42} +1.35867 q^{43} +4.65962 q^{44} +4.16020 q^{45} -6.27325 q^{46} -7.82397 q^{47} -0.879988 q^{48} +8.52805 q^{49} -1.50598 q^{50} +4.46101 q^{51} -0.219910 q^{52} -0.433602 q^{53} +4.59848 q^{54} -8.70989 q^{55} +3.94056 q^{56} -1.21768 q^{57} -2.83165 q^{58} +15.2378 q^{59} +1.64490 q^{60} +8.74847 q^{61} -8.21578 q^{62} -8.77020 q^{63} +1.00000 q^{64} +0.411062 q^{65} -4.10041 q^{66} -12.4924 q^{67} -5.06940 q^{68} +5.52039 q^{69} -7.36582 q^{70} +9.27985 q^{71} -2.22562 q^{72} -3.82110 q^{73} -6.28699 q^{74} +1.32524 q^{75} +1.38375 q^{76} +18.3615 q^{77} +0.193518 q^{78} -4.32275 q^{79} -1.86923 q^{80} +2.63025 q^{81} -3.26521 q^{82} -9.42865 q^{83} -3.46765 q^{84} +9.47587 q^{85} +1.35867 q^{86} +2.49182 q^{87} +4.65962 q^{88} +7.66858 q^{89} +4.16020 q^{90} -0.866568 q^{91} -6.27325 q^{92} +7.22979 q^{93} -7.82397 q^{94} -2.58655 q^{95} -0.879988 q^{96} -8.84095 q^{97} +8.52805 q^{98} -10.3705 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 47 q + 47 q^{2} - 13 q^{3} + 47 q^{4} - 14 q^{5} - 13 q^{6} - 17 q^{7} + 47 q^{8} + 12 q^{9}+O(q^{10}) \) 47 * q + 47 * q^2 - 13 * q^3 + 47 * q^4 - 14 * q^5 - 13 * q^6 - 17 * q^7 + 47 * q^8 + 12 * q^9	\( 47 q + 47 q^{2} - 13 q^{3} + 47 q^{4} - 14 q^{5} - 13 q^{6} - 17 q^{7} + 47 q^{8} + 12 q^{9} - 14 q^{10} - 30 q^{11} - 13 q^{12} - 39 q^{13} - 17 q^{14} - 18 q^{15} + 47 q^{16} - 26 q^{17} + 12 q^{18} - 23 q^{19} - 14 q^{20} - 39 q^{21} - 30 q^{22} - 25 q^{23} - 13 q^{24} - 19 q^{25} - 39 q^{26} - 46 q^{27} - 17 q^{28} - 53 q^{29} - 18 q^{30} - 23 q^{31} + 47 q^{32} - 26 q^{33} - 26 q^{34} - 31 q^{35} + 12 q^{36} - 83 q^{37} - 23 q^{38} - 9 q^{39} - 14 q^{40} - 48 q^{41} - 39 q^{42} - 78 q^{43} - 30 q^{44} - 27 q^{45} - 25 q^{46} - 15 q^{47} - 13 q^{48} - 12 q^{49} - 19 q^{50} - 47 q^{51} - 39 q^{52} - 76 q^{53} - 46 q^{54} - 39 q^{55} - 17 q^{56} - 44 q^{57} - 53 q^{58} - 33 q^{59} - 18 q^{60} - 33 q^{61} - 23 q^{62} - 7 q^{63} + 47 q^{64} - 67 q^{65} - 26 q^{66} - 85 q^{67} - 26 q^{68} - 33 q^{69} - 31 q^{70} - 17 q^{71} + 12 q^{72} - 59 q^{73} - 83 q^{74} - 21 q^{75} - 23 q^{76} - 59 q^{77} - 9 q^{78} - 49 q^{79} - 14 q^{80} - 41 q^{81} - 48 q^{82} - 30 q^{83} - 39 q^{84} - 84 q^{85} - 78 q^{86} + 9 q^{87} - 30 q^{88} - 50 q^{89} - 27 q^{90} - 42 q^{91} - 25 q^{92} - 43 q^{93} - 15 q^{94} + 8 q^{95} - 13 q^{96} - 49 q^{97} - 12 q^{98} - 49 q^{99}+O(q^{100}) \) 47 * q + 47 * q^2 - 13 * q^3 + 47 * q^4 - 14 * q^5 - 13 * q^6 - 17 * q^7 + 47 * q^8 + 12 * q^9 - 14 * q^10 - 30 * q^11 - 13 * q^12 - 39 * q^13 - 17 * q^14 - 18 * q^15 + 47 * q^16 - 26 * q^17 + 12 * q^18 - 23 * q^19 - 14 * q^20 - 39 * q^21 - 30 * q^22 - 25 * q^23 - 13 * q^24 - 19 * q^25 - 39 * q^26 - 46 * q^27 - 17 * q^28 - 53 * q^29 - 18 * q^30 - 23 * q^31 + 47 * q^32 - 26 * q^33 - 26 * q^34 - 31 * q^35 + 12 * q^36 - 83 * q^37 - 23 * q^38 - 9 * q^39 - 14 * q^40 - 48 * q^41 - 39 * q^42 - 78 * q^43 - 30 * q^44 - 27 * q^45 - 25 * q^46 - 15 * q^47 - 13 * q^48 - 12 * q^49 - 19 * q^50 - 47 * q^51 - 39 * q^52 - 76 * q^53 - 46 * q^54 - 39 * q^55 - 17 * q^56 - 44 * q^57 - 53 * q^58 - 33 * q^59 - 18 * q^60 - 33 * q^61 - 23 * q^62 - 7 * q^63 + 47 * q^64 - 67 * q^65 - 26 * q^66 - 85 * q^67 - 26 * q^68 - 33 * q^69 - 31 * q^70 - 17 * q^71 + 12 * q^72 - 59 * q^73 - 83 * q^74 - 21 * q^75 - 23 * q^76 - 59 * q^77 - 9 * q^78 - 49 * q^79 - 14 * q^80 - 41 * q^81 - 48 * q^82 - 30 * q^83 - 39 * q^84 - 84 * q^85 - 78 * q^86 + 9 * q^87 - 30 * q^88 - 50 * q^89 - 27 * q^90 - 42 * q^91 - 25 * q^92 - 43 * q^93 - 15 * q^94 + 8 * q^95 - 13 * q^96 - 49 * q^97 - 12 * q^98 - 49 * q^99

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