LMFDB - Embedded newform 8007.2.a.e.1.40

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.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:	$63.9362168984$
Analytic rank:	$1$
Dimension:	$46$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.40
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.05372 q^{2} +1.00000 q^{3} +2.21777 q^{4} +2.38650 q^{5} +2.05372 q^{6} -5.11130 q^{7} +0.447239 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.05372 q^{2} +1.00000 q^{3} +2.21777 q^{4} +2.38650 q^{5} +2.05372 q^{6} -5.11130 q^{7} +0.447239 q^{8} +1.00000 q^{9} +4.90121 q^{10} +1.96292 q^{11} +2.21777 q^{12} -2.07863 q^{13} -10.4972 q^{14} +2.38650 q^{15} -3.51704 q^{16} -1.00000 q^{17} +2.05372 q^{18} -2.46590 q^{19} +5.29272 q^{20} -5.11130 q^{21} +4.03128 q^{22} -8.81159 q^{23} +0.447239 q^{24} +0.695400 q^{25} -4.26892 q^{26} +1.00000 q^{27} -11.3357 q^{28} +5.45372 q^{29} +4.90121 q^{30} +5.62706 q^{31} -8.11749 q^{32} +1.96292 q^{33} -2.05372 q^{34} -12.1981 q^{35} +2.21777 q^{36} -8.11399 q^{37} -5.06427 q^{38} -2.07863 q^{39} +1.06734 q^{40} -0.208278 q^{41} -10.4972 q^{42} -5.51276 q^{43} +4.35330 q^{44} +2.38650 q^{45} -18.0965 q^{46} +7.50680 q^{47} -3.51704 q^{48} +19.1254 q^{49} +1.42816 q^{50} -1.00000 q^{51} -4.60992 q^{52} -12.2599 q^{53} +2.05372 q^{54} +4.68451 q^{55} -2.28597 q^{56} -2.46590 q^{57} +11.2004 q^{58} -5.74314 q^{59} +5.29272 q^{60} -0.000881582 q^{61} +11.5564 q^{62} -5.11130 q^{63} -9.63698 q^{64} -4.96066 q^{65} +4.03128 q^{66} -5.07294 q^{67} -2.21777 q^{68} -8.81159 q^{69} -25.0516 q^{70} +7.80376 q^{71} +0.447239 q^{72} -15.1223 q^{73} -16.6639 q^{74} +0.695400 q^{75} -5.46880 q^{76} -10.0330 q^{77} -4.26892 q^{78} +2.62696 q^{79} -8.39342 q^{80} +1.00000 q^{81} -0.427745 q^{82} +15.0001 q^{83} -11.3357 q^{84} -2.38650 q^{85} -11.3217 q^{86} +5.45372 q^{87} +0.877892 q^{88} -13.4040 q^{89} +4.90121 q^{90} +10.6245 q^{91} -19.5421 q^{92} +5.62706 q^{93} +15.4169 q^{94} -5.88488 q^{95} -8.11749 q^{96} +3.16365 q^{97} +39.2782 q^{98} +1.96292 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9}+O(q^{10}) $ 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9} - 10 q^{10} - 25 q^{11} + 43 q^{12} - 8 q^{13} - 28 q^{14} - 19 q^{15} + 33 q^{16} - 46 q^{17} - 5 q^{18} - 2 q^{19} - 56 q^{20} + q^{21} - 19 q^{22} - 64 q^{23} - 18 q^{24} + 11 q^{25} - 13 q^{26} + 46 q^{27} - 38 q^{28} - 51 q^{29} - 10 q^{30} - 19 q^{31} - 61 q^{32} - 25 q^{33} + 5 q^{34} - 39 q^{35} + 43 q^{36} - 46 q^{37} - 48 q^{38} - 8 q^{39} - 10 q^{40} - 53 q^{41} - 28 q^{42} - 33 q^{43} - 62 q^{44} - 19 q^{45} + 2 q^{46} - 45 q^{47} + 33 q^{48} + 21 q^{49} - 60 q^{50} - 46 q^{51} - 63 q^{52} - 47 q^{53} - 5 q^{54} + 5 q^{55} - 82 q^{56} - 2 q^{57} - 21 q^{58} - 65 q^{59} - 56 q^{60} - 37 q^{61} - 46 q^{62} + q^{63} + 74 q^{64} - 85 q^{65} - 19 q^{66} - 52 q^{67} - 43 q^{68} - 64 q^{69} - 20 q^{70} - 48 q^{71} - 18 q^{72} - 39 q^{73} - 16 q^{74} + 11 q^{75} + 42 q^{76} - 78 q^{77} - 13 q^{78} - 26 q^{79} - 78 q^{80} + 46 q^{81} + 3 q^{82} - 47 q^{83} - 38 q^{84} + 19 q^{85} - 6 q^{86} - 51 q^{87} - 58 q^{88} - 58 q^{89} - 10 q^{90} - 43 q^{91} - 68 q^{92} - 19 q^{93} - 78 q^{95} - 61 q^{96} - 44 q^{97} - 4 q^{98} - 25 q^{99}+O(q^{100}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9 - 10 * q^10 - 25 * q^11 + 43 * q^12 - 8 * q^13 - 28 * q^14 - 19 * q^15 + 33 * q^16 - 46 * q^17 - 5 * q^18 - 2 * q^19 - 56 * q^20 + q^21 - 19 * q^22 - 64 * q^23 - 18 * q^24 + 11 * q^25 - 13 * q^26 + 46 * q^27 - 38 * q^28 - 51 * q^29 - 10 * q^30 - 19 * q^31 - 61 * q^32 - 25 * q^33 + 5 * q^34 - 39 * q^35 + 43 * q^36 - 46 * q^37 - 48 * q^38 - 8 * q^39 - 10 * q^40 - 53 * q^41 - 28 * q^42 - 33 * q^43 - 62 * q^44 - 19 * q^45 + 2 * q^46 - 45 * q^47 + 33 * q^48 + 21 * q^49 - 60 * q^50 - 46 * q^51 - 63 * q^52 - 47 * q^53 - 5 * q^54 + 5 * q^55 - 82 * q^56 - 2 * q^57 - 21 * q^58 - 65 * q^59 - 56 * q^60 - 37 * q^61 - 46 * q^62 + q^63 + 74 * q^64 - 85 * q^65 - 19 * q^66 - 52 * q^67 - 43 * q^68 - 64 * q^69 - 20 * q^70 - 48 * q^71 - 18 * q^72 - 39 * q^73 - 16 * q^74 + 11 * q^75 + 42 * q^76 - 78 * q^77 - 13 * q^78 - 26 * q^79 - 78 * q^80 + 46 * q^81 + 3 * q^82 - 47 * q^83 - 38 * q^84 + 19 * q^85 - 6 * q^86 - 51 * q^87 - 58 * q^88 - 58 * q^89 - 10 * q^90 - 43 * q^91 - 68 * q^92 - 19 * q^93 - 78 * q^95 - 61 * q^96 - 44 * q^97 - 4 * q^98 - 25 * 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 $

$2$	2.05372	1.45220	0.726100	−	0.687589i	$-0.241331\pi$
$2$	2.05372	1.45220	0.726100	+	0.687589i	$0.241331\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.21777	1.10888
$5$	2.38650	1.06728	0.533638	−	0.845713i	$-0.320824\pi$
$5$	2.38650	1.06728	0.533638	+	0.845713i	$0.320824\pi$
$6$	2.05372	0.838428
$7$	−5.11130	−1.93189	−0.965945	−	0.258749i	$-0.916690\pi$
$7$	−5.11130	−1.93189	−0.965945	+	0.258749i	$0.916690\pi$
$8$	0.447239	0.158123
$9$	1.00000	0.333333
$10$	4.90121	1.54990
$11$	1.96292	0.591841	0.295921	−	0.955213i	$-0.404374\pi$
$11$	1.96292	0.591841	0.295921	+	0.955213i	$0.404374\pi$
$12$	2.21777	0.640215
$13$	−2.07863	−0.576508	−0.288254	−	0.957554i	$-0.593075\pi$
$13$	−2.07863	−0.576508	−0.288254	+	0.957554i	$0.593075\pi$
$14$	−10.4972	−2.80549
$15$	2.38650	0.616193
$16$	−3.51704	−0.879259
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	2.05372	0.484067
$19$	−2.46590	−0.565716	−0.282858	−	0.959162i	$-0.591283\pi$
$19$	−2.46590	−0.565716	−0.282858	+	0.959162i	$0.591283\pi$
$20$	5.29272	1.18349
$21$	−5.11130	−1.11538
$22$	4.03128	0.859472
$23$	−8.81159	−1.83734	−0.918671	−	0.395023i	$-0.870737\pi$
$23$	−8.81159	−1.83734	−0.918671	+	0.395023i	$0.870737\pi$
$24$	0.447239	0.0912922
$25$	0.695400	0.139080
$26$	−4.26892	−0.837205
$27$	1.00000	0.192450
$28$	−11.3357	−2.14224
$29$	5.45372	1.01273	0.506365	−	0.862319i	$-0.330989\pi$
$29$	5.45372	1.01273	0.506365	+	0.862319i	$0.330989\pi$
$30$	4.90121	0.894835
$31$	5.62706	1.01065	0.505325	−	0.862929i	$-0.331373\pi$
$31$	5.62706	1.01065	0.505325	+	0.862929i	$0.331373\pi$
$32$	−8.11749	−1.43498
$33$	1.96292	0.341700
$34$	−2.05372	−0.352210
$35$	−12.1981	−2.06186
$36$	2.21777	0.369628
$37$	−8.11399	−1.33393	−0.666966	−	0.745088i	$-0.732407\pi$
$37$	−8.11399	−1.33393	−0.666966	+	0.745088i	$0.732407\pi$
$38$	−5.06427	−0.821533
$39$	−2.07863	−0.332847
$40$	1.06734	0.168761
$41$	−0.208278	−0.0325276	−0.0162638	−	0.999868i	$-0.505177\pi$
$41$	−0.208278	−0.0325276	−0.0162638	+	0.999868i	$0.505177\pi$
$42$	−10.4972	−1.61975
$43$	−5.51276	−0.840687	−0.420344	−	0.907365i	$-0.638090\pi$
$43$	−5.51276	−0.840687	−0.420344	+	0.907365i	$0.638090\pi$
$44$	4.35330	0.656284
$45$	2.38650	0.355759
$46$	−18.0965	−2.66819
$47$	7.50680	1.09498	0.547489	−	0.836813i	$-0.315584\pi$
$47$	7.50680	1.09498	0.547489	+	0.836813i	$0.315584\pi$
$48$	−3.51704	−0.507640
$49$	19.1254	2.73220
$50$	1.42816	0.201972
$51$	−1.00000	−0.140028
$52$	−4.60992	−0.639281
$53$	−12.2599	−1.68402	−0.842012	−	0.539459i	$-0.818629\pi$
$53$	−12.2599	−1.68402	−0.842012	+	0.539459i	$0.818629\pi$
$54$	2.05372	0.279476
$55$	4.68451	0.631659
$56$	−2.28597	−0.305476
$57$	−2.46590	−0.326616
$58$	11.2004	1.47069
$59$	−5.74314	−0.747693	−0.373847	−	0.927491i	$-0.621961\pi$
$59$	−5.74314	−0.747693	−0.373847	+	0.927491i	$0.621961\pi$
$60$	5.29272	0.683287
$61$	−0.000881582 0	−0.000112875 0	−5.64375e−5	−	1.00000i	$-0.500018\pi$
$61$	−0.000881582 0	−0.000112875 0	−5.64375e−5		1.00000i	$0.500018\pi$
$62$	11.5564	1.46767
$63$	−5.11130	−0.643963
$64$	−9.63698	−1.20462
$65$	−4.96066	−0.615294
$66$	4.03128	0.496216
$67$	−5.07294	−0.619758	−0.309879	−	0.950776i	$-0.600289\pi$
$67$	−5.07294	−0.619758	−0.309879	+	0.950776i	$0.600289\pi$
$68$	−2.21777	−0.268944
$69$	−8.81159	−1.06079
$70$	−25.0516	−2.99423
$71$	7.80376	0.926136	0.463068	−	0.886323i	$-0.346749\pi$
$71$	7.80376	0.926136	0.463068	+	0.886323i	$0.346749\pi$
$72$	0.447239	0.0527076
$73$	−15.1223	−1.76993	−0.884965	−	0.465658i	$-0.845818\pi$
$73$	−15.1223	−1.76993	−0.884965	+	0.465658i	$0.845818\pi$
$74$	−16.6639	−1.93714
$75$	0.695400	0.0802979
$76$	−5.46880	−0.627314
$77$	−10.0330	−1.14337
$78$	−4.26892	−0.483360
$79$	2.62696	0.295556	0.147778	−	0.989021i	$-0.452788\pi$
$79$	2.62696	0.295556	0.147778	+	0.989021i	$0.452788\pi$
$80$	−8.39342	−0.938413
$81$	1.00000	0.111111
$82$	−0.427745	−0.0472365
$83$	15.0001	1.64647	0.823237	−	0.567698i	$-0.192166\pi$
$83$	15.0001	1.64647	0.823237	+	0.567698i	$0.192166\pi$
$84$	−11.3357	−1.23682
$85$	−2.38650	−0.258853
$86$	−11.3217	−1.22085
$87$	5.45372	0.584700
$88$	0.877892	0.0935836
$89$	−13.4040	−1.42082	−0.710409	−	0.703789i	$-0.751490\pi$
$89$	−13.4040	−1.42082	−0.710409	+	0.703789i	$0.751490\pi$
$90$	4.90121	0.516633
$91$	10.6245	1.11375
$92$	−19.5421	−2.03740
$93$	5.62706	0.583499
$94$	15.4169	1.59013
$95$	−5.88488	−0.603776
$96$	−8.11749	−0.828488
$97$	3.16365	0.321220	0.160610	−	0.987018i	$-0.448654\pi$
$97$	3.16365	0.321220	0.160610	+	0.987018i	$0.448654\pi$
$98$	39.2782	3.96769
$99$	1.96292	0.197280
$100$	1.54224	0.154224
$101$	−0.766851	−0.0763045	−0.0381523	−	0.999272i	$-0.512147\pi$
$101$	−0.766851	−0.0763045	−0.0381523	+	0.999272i	$0.512147\pi$
$102$	−2.05372	−0.203349
$103$	−17.4373	−1.71814	−0.859072	−	0.511855i	$-0.828958\pi$
$103$	−17.4373	−1.71814	−0.859072	+	0.511855i	$0.828958\pi$
$104$	−0.929643	−0.0911590
$105$	−12.1981	−1.19042
$106$	−25.1784	−2.44554
$107$	−18.3862	−1.77747	−0.888733	−	0.458426i	$-0.848413\pi$
$107$	−18.3862	−1.77747	−0.888733	+	0.458426i	$0.848413\pi$
$108$	2.21777	0.213405
$109$	7.08530	0.678648	0.339324	−	0.940669i	$-0.389802\pi$
$109$	7.08530	0.678648	0.339324	+	0.940669i	$0.389802\pi$
$110$	9.62067	0.917295
$111$	−8.11399	−0.770146
$112$	17.9766	1.69863
$113$	3.45623	0.325135	0.162567	−	0.986697i	$-0.448023\pi$
$113$	3.45623	0.325135	0.162567	+	0.986697i	$0.448023\pi$
$114$	−5.06427	−0.474312
$115$	−21.0289	−1.96095
$116$	12.0951	1.12300
$117$	−2.07863	−0.192169
$118$	−11.7948	−1.08580
$119$	5.11130	0.468552
$120$	1.06734	0.0974341
$121$	−7.14696	−0.649724
$122$	−0.00181052	−0.000163917 0
$123$	−0.208278	−0.0187798
$124$	12.4795	1.12069
$125$	−10.2729	−0.918840
$126$	−10.4972	−0.935163
$127$	4.68003	0.415286	0.207643	−	0.978205i	$-0.433421\pi$
$127$	4.68003	0.415286	0.207643	+	0.978205i	$0.433421\pi$
$128$	−3.55670	−0.314371
$129$	−5.51276	−0.485371
$130$	−10.1878	−0.893529
$131$	11.3925	0.995363	0.497682	−	0.867360i	$-0.334185\pi$
$131$	11.3925	0.995363	0.497682	+	0.867360i	$0.334185\pi$
$132$	4.35330	0.378906
$133$	12.6039	1.09290
$134$	−10.4184	−0.900013
$135$	2.38650	0.205398
$136$	−0.447239	−0.0383504
$137$	9.92735	0.848150	0.424075	−	0.905627i	$-0.360599\pi$
$137$	9.92735	0.848150	0.424075	+	0.905627i	$0.360599\pi$
$138$	−18.0965	−1.54048
$139$	−10.1394	−0.860016	−0.430008	−	0.902825i	$-0.641489\pi$
$139$	−10.1394	−0.860016	−0.430008	+	0.902825i	$0.641489\pi$
$140$	−27.0526	−2.28637
$141$	7.50680	0.632186
$142$	16.0267	1.34493
$143$	−4.08017	−0.341201
$144$	−3.51704	−0.293086
$145$	13.0153	1.08086
$146$	−31.0570	−2.57029
$147$	19.1254	1.57743
$148$	−17.9950	−1.47918
$149$	−8.57132	−0.702190	−0.351095	−	0.936340i	$-0.614191\pi$
$149$	−8.57132	−0.702190	−0.351095	+	0.936340i	$0.614191\pi$
$150$	1.42816	0.116609
$151$	5.96822	0.485687	0.242843	−	0.970066i	$-0.421920\pi$
$151$	5.96822	0.485687	0.242843	+	0.970066i	$0.421920\pi$
$152$	−1.10285	−0.0894526
$153$	−1.00000	−0.0808452
$154$	−20.6051	−1.66040
$155$	13.4290	1.07864
$156$	−4.60992	−0.369089
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	5.39503	0.429206
$159$	−12.2599	−0.972271
$160$	−19.3724	−1.53152
$161$	45.0386	3.54954
$162$	2.05372	0.161356
$163$	15.1518	1.18678	0.593389	−	0.804916i	$-0.297790\pi$
$163$	15.1518	1.18678	0.593389	+	0.804916i	$0.297790\pi$
$164$	−0.461913	−0.0360693
$165$	4.68451	0.364688
$166$	30.8060	2.39101
$167$	−1.94995	−0.150892	−0.0754458	−	0.997150i	$-0.524038\pi$
$167$	−1.94995	−0.150892	−0.0754458	+	0.997150i	$0.524038\pi$
$168$	−2.28597	−0.176366
$169$	−8.67930	−0.667639
$170$	−4.90121	−0.375906
$171$	−2.46590	−0.188572
$172$	−12.2260	−0.932226
$173$	10.4175	0.792026	0.396013	−	0.918245i	$-0.370394\pi$
$173$	10.4175	0.792026	0.396013	+	0.918245i	$0.370394\pi$
$174$	11.2004	0.849102
$175$	−3.55440	−0.268687
$176$	−6.90365	−0.520382
$177$	−5.74314	−0.431681
$178$	−27.5280	−2.06331
$179$	17.7029	1.32318	0.661590	−	0.749866i	$-0.269882\pi$
$179$	17.7029	1.32318	0.661590	+	0.749866i	$0.269882\pi$
$180$	5.29272	0.394496
$181$	−13.2742	−0.986667	−0.493334	−	0.869840i	$-0.664222\pi$
$181$	−13.2742	−0.986667	−0.493334	+	0.869840i	$0.664222\pi$
$182$	21.8197	1.61739
$183$	−0.000881582 0	−6.51684e−5 0
$184$	−3.94088	−0.290526
$185$	−19.3641	−1.42367
$186$	11.5564	0.847357
$187$	−1.96292	−0.143543
$188$	16.6483	1.21421
$189$	−5.11130	−0.371792
$190$	−12.0859	−0.876803
$191$	27.0592	1.95793	0.978967	−	0.204018i	$-0.0654000\pi$
$191$	27.0592	1.95793	0.978967	+	0.204018i	$0.0654000\pi$
$192$	−9.63698	−0.695489
$193$	−5.69108	−0.409653	−0.204826	−	0.978798i	$-0.565663\pi$
$193$	−5.69108	−0.409653	−0.204826	+	0.978798i	$0.565663\pi$
$194$	6.49726	0.466476
$195$	−4.96066	−0.355240
$196$	42.4157	3.02969
$197$	6.37348	0.454092	0.227046	−	0.973884i	$-0.427093\pi$
$197$	6.37348	0.454092	0.227046	+	0.973884i	$0.427093\pi$
$198$	4.03128	0.286491
$199$	15.8923	1.12657	0.563286	−	0.826262i	$-0.309537\pi$
$199$	15.8923	1.12657	0.563286	+	0.826262i	$0.309537\pi$
$200$	0.311010	0.0219917
$201$	−5.07294	−0.357817
$202$	−1.57490	−0.110809
$203$	−27.8756	−1.95648
$204$	−2.21777	−0.155275
$205$	−0.497056	−0.0347159
$206$	−35.8113	−2.49509
$207$	−8.81159	−0.612448
$208$	7.31061	0.506900
$209$	−4.84035	−0.334814
$210$	−25.0516	−1.72872
$211$	−9.22586	−0.635134	−0.317567	−	0.948236i	$-0.602866\pi$
$211$	−9.22586	−0.635134	−0.317567	+	0.948236i	$0.602866\pi$
$212$	−27.1896	−1.86739
$213$	7.80376	0.534705
$214$	−37.7602	−2.58123
$215$	−13.1562	−0.897246
$216$	0.447239	0.0304307
$217$	−28.7616	−1.95246
$218$	14.5512	0.985533
$219$	−15.1223	−1.02187
$220$	10.3892	0.700437
$221$	2.07863	0.139824
$222$	−16.6639	−1.11841
$223$	7.33250	0.491021	0.245510	−	0.969394i	$-0.421044\pi$
$223$	7.33250	0.491021	0.245510	+	0.969394i	$0.421044\pi$
$224$	41.4909	2.77223
$225$	0.695400	0.0463600
$226$	7.09813	0.472160
$227$	4.61050	0.306009	0.153005	−	0.988225i	$-0.451105\pi$
$227$	4.61050	0.306009	0.153005	+	0.988225i	$0.451105\pi$
$228$	−5.46880	−0.362180
$229$	−25.4603	−1.68246	−0.841232	−	0.540675i	$-0.818169\pi$
$229$	−25.4603	−1.68246	−0.841232	+	0.540675i	$0.818169\pi$
$230$	−43.1875	−2.84770
$231$	−10.0330	−0.660126
$232$	2.43911	0.160136
$233$	9.05618	0.593290	0.296645	−	0.954988i	$-0.404132\pi$
$233$	9.05618	0.593290	0.296645	+	0.954988i	$0.404132\pi$
$234$	−4.26892	−0.279068
$235$	17.9150	1.16865
$236$	−12.7370	−0.829106
$237$	2.62696	0.170639
$238$	10.4972	0.680431
$239$	8.43282	0.545474	0.272737	−	0.962089i	$-0.412071\pi$
$239$	8.43282	0.545474	0.272737	+	0.962089i	$0.412071\pi$
$240$	−8.39342	−0.541793
$241$	−22.7774	−1.46722	−0.733610	−	0.679570i	$-0.762166\pi$
$241$	−22.7774	−1.46722	−0.733610	+	0.679570i	$0.762166\pi$
$242$	−14.6779	−0.943529
$243$	1.00000	0.0641500
$244$	−0.00195515	−0.000125165 0
$245$	45.6428	2.91601
$246$	−0.427745	−0.0272720
$247$	5.12569	0.326140
$248$	2.51664	0.159807
$249$	15.0001	0.950592
$250$	−21.0978	−1.33434
$251$	−18.6018	−1.17414	−0.587068	−	0.809538i	$-0.699718\pi$
$251$	−18.6018	−1.17414	−0.587068	+	0.809538i	$0.699718\pi$
$252$	−11.3357	−0.714081
$253$	−17.2964	−1.08742
$254$	9.61148	0.603078
$255$	−2.38650	−0.149449
$256$	11.9695	0.748094
$257$	−18.7466	−1.16938	−0.584691	−	0.811256i	$-0.698784\pi$
$257$	−18.7466	−1.16938	−0.584691	+	0.811256i	$0.698784\pi$
$258$	−11.3217	−0.704856
$259$	41.4730	2.57701
$260$	−11.0016	−0.682290
$261$	5.45372	0.337577
$262$	23.3969	1.44547
$263$	15.3752	0.948075	0.474038	−	0.880505i	$-0.342796\pi$
$263$	15.3752	0.948075	0.474038	+	0.880505i	$0.342796\pi$
$264$	0.877892	0.0540305
$265$	−29.2582	−1.79732
$266$	25.8850	1.58711
$267$	−13.4040	−0.820310
$268$	−11.2506	−0.687240
$269$	−5.53471	−0.337457	−0.168729	−	0.985663i	$-0.553966\pi$
$269$	−5.53471	−0.337457	−0.168729	+	0.985663i	$0.553966\pi$
$270$	4.90121	0.298278
$271$	−4.09513	−0.248762	−0.124381	−	0.992235i	$-0.539694\pi$
$271$	−4.09513	−0.248762	−0.124381	+	0.992235i	$0.539694\pi$
$272$	3.51704	0.213252
$273$	10.6245	0.643023
$274$	20.3880	1.23168
$275$	1.36501	0.0823133
$276$	−19.5421	−1.17629
$277$	−0.518286	−0.0311408	−0.0155704	−	0.999879i	$-0.504956\pi$
$277$	−0.518286	−0.0311408	−0.0155704	+	0.999879i	$0.504956\pi$
$278$	−20.8236	−1.24892
$279$	5.62706	0.336883
$280$	−5.45548	−0.326027
$281$	19.0745	1.13789	0.568945	−	0.822375i	$-0.307352\pi$
$281$	19.0745	1.13789	0.568945	+	0.822375i	$0.307352\pi$
$282$	15.4169	0.918061
$283$	−2.61434	−0.155406	−0.0777031	−	0.996977i	$-0.524759\pi$
$283$	−2.61434	−0.155406	−0.0777031	+	0.996977i	$0.524759\pi$
$284$	17.3069	1.02698
$285$	−5.88488	−0.348590
$286$	−8.37954	−0.495492
$287$	1.06457	0.0628396
$288$	−8.11749	−0.478328
$289$	1.00000	0.0588235
$290$	26.7298	1.56963
$291$	3.16365	0.185457
$292$	−33.5378	−1.96265
$293$	25.0031	1.46070	0.730348	−	0.683075i	$-0.239358\pi$
$293$	25.0031	1.46070	0.730348	+	0.683075i	$0.239358\pi$
$294$	39.2782	2.29075
$295$	−13.7060	−0.797996
$296$	−3.62889	−0.210925
$297$	1.96292	0.113900
$298$	−17.6031	−1.01972
$299$	18.3160	1.05924
$300$	1.54224	0.0890411
$301$	28.1773	1.62411
$302$	12.2571	0.705314
$303$	−0.766851	−0.0440544
$304$	8.67266	0.497411
$305$	−0.00210390	−0.000120469 0
$306$	−2.05372	−0.117403
$307$	−4.74071	−0.270567	−0.135283	−	0.990807i	$-0.543194\pi$
$307$	−4.74071	−0.270567	−0.135283	+	0.990807i	$0.543194\pi$
$308$	−22.2510	−1.26787
$309$	−17.4373	−0.991971
$310$	27.5794	1.56641
$311$	1.87989	0.106599	0.0532994	−	0.998579i	$-0.483026\pi$
$311$	1.87989	0.106599	0.0532994	+	0.998579i	$0.483026\pi$
$312$	−0.929643	−0.0526307
$313$	−1.70160	−0.0961799	−0.0480900	−	0.998843i	$-0.515313\pi$
$313$	−1.70160	−0.0961799	−0.0480900	+	0.998843i	$0.515313\pi$
$314$	2.05372	0.115898
$315$	−12.1981	−0.687287
$316$	5.82598	0.327737
$317$	9.54172	0.535916	0.267958	−	0.963431i	$-0.413651\pi$
$317$	9.54172	0.535916	0.267958	+	0.963431i	$0.413651\pi$
$318$	−25.1784	−1.41193
$319$	10.7052	0.599376
$320$	−22.9987	−1.28567
$321$	−18.3862	−1.02622
$322$	92.4968	5.15465
$323$	2.46590	0.137206
$324$	2.21777	0.123209
$325$	−1.44548	−0.0801807
$326$	31.1175	1.72344
$327$	7.08530	0.391818
$328$	−0.0931500	−0.00514335
$329$	−38.3695	−2.11538
$330$	9.62067	0.529600
$331$	35.3307	1.94195	0.970974	−	0.239184i	$-0.0768800\pi$
$331$	35.3307	1.94195	0.970974	+	0.239184i	$0.0768800\pi$
$332$	33.2667	1.82575
$333$	−8.11399	−0.444644
$334$	−4.00465	−0.219125
$335$	−12.1066	−0.661453
$336$	17.9766	0.980705
$337$	0.475011	0.0258755	0.0129378	−	0.999916i	$-0.495882\pi$
$337$	0.475011	0.0258755	0.0129378	+	0.999916i	$0.495882\pi$
$338$	−17.8249	−0.969545
$339$	3.45623	0.187717
$340$	−5.29272	−0.287038
$341$	11.0454	0.598144
$342$	−5.06427	−0.273844
$343$	−61.9764	−3.34641
$344$	−2.46552	−0.132932
$345$	−21.0289	−1.13216
$346$	21.3946	1.15018
$347$	36.8747	1.97954	0.989769	−	0.142678i	$-0.0455713\pi$
$347$	36.8747	1.97954	0.989769	+	0.142678i	$0.0455713\pi$
$348$	12.0951	0.648365
$349$	−11.9781	−0.641173	−0.320586	−	0.947219i	$-0.603880\pi$
$349$	−11.9781	−0.641173	−0.320586	+	0.947219i	$0.603880\pi$
$350$	−7.29974	−0.390188
$351$	−2.07863	−0.110949
$352$	−15.9339	−0.849282
$353$	1.92889	0.102664	0.0513321	−	0.998682i	$-0.483653\pi$
$353$	1.92889	0.102664	0.0513321	+	0.998682i	$0.483653\pi$
$354$	−11.7948	−0.626887
$355$	18.6237	0.988443
$356$	−29.7269	−1.57552
$357$	5.11130	0.270519
$358$	36.3569	1.92152
$359$	−8.72869	−0.460683	−0.230341	−	0.973110i	$-0.573984\pi$
$359$	−8.72869	−0.460683	−0.230341	+	0.973110i	$0.573984\pi$
$360$	1.06734	0.0562536
$361$	−12.9193	−0.679965
$362$	−27.2616	−1.43284
$363$	−7.14696	−0.375118
$364$	23.5627	1.23502
$365$	−36.0894	−1.88901
$366$	−0.00181052	−9.46376e−5 0
$367$	−17.1475	−0.895092	−0.447546	−	0.894261i	$-0.647702\pi$
$367$	−17.1475	−0.895092	−0.447546	+	0.894261i	$0.647702\pi$
$368$	30.9907	1.61550
$369$	−0.208278	−0.0108425
$370$	−39.7684	−2.06746
$371$	62.6639	3.25335
$372$	12.4795	0.647033
$373$	−13.5066	−0.699348	−0.349674	−	0.936872i	$-0.613708\pi$
$373$	−13.5066	−0.699348	−0.349674	+	0.936872i	$0.613708\pi$
$374$	−4.03128	−0.208453
$375$	−10.2729	−0.530493
$376$	3.35733	0.173141
$377$	−11.3363	−0.583847
$378$	−10.4972	−0.539917
$379$	−16.2890	−0.836711	−0.418356	−	0.908283i	$-0.637393\pi$
$379$	−16.2890	−0.836711	−0.418356	+	0.908283i	$0.637393\pi$
$380$	−13.0513	−0.669518
$381$	4.68003	0.239765
$382$	55.5720	2.84331
$383$	4.75739	0.243091	0.121546	−	0.992586i	$-0.461215\pi$
$383$	4.75739	0.243091	0.121546	+	0.992586i	$0.461215\pi$
$384$	−3.55670	−0.181502
$385$	−23.9439	−1.22029
$386$	−11.6879	−0.594897
$387$	−5.51276	−0.280229
$388$	7.01626	0.356197
$389$	11.3768	0.576829	0.288415	−	0.957506i	$-0.406872\pi$
$389$	11.3768	0.576829	0.288415	+	0.957506i	$0.406872\pi$
$390$	−10.1878	−0.515879
$391$	8.81159	0.445621
$392$	8.55360	0.432022
$393$	11.3925	0.574673
$394$	13.0893	0.659432
$395$	6.26924	0.315440
$396$	4.35330	0.218761
$397$	−0.00201406	−0.000101083 0	−5.05415e−5	−	1.00000i	$-0.500016\pi$
$397$	−0.00201406	−0.000101083 0	−5.05415e−5		1.00000i	$0.500016\pi$
$398$	32.6383	1.63601
$399$	12.6039	0.630986
$400$	−2.44575	−0.122287
$401$	11.0650	0.552561	0.276281	−	0.961077i	$-0.410898\pi$
$401$	11.0650	0.552561	0.276281	+	0.961077i	$0.410898\pi$
$402$	−10.4184	−0.519622
$403$	−11.6966	−0.582647
$404$	−1.70070	−0.0846130
$405$	2.38650	0.118586
$406$	−57.2487	−2.84120
$407$	−15.9271	−0.789476
$408$	−0.447239	−0.0221416
$409$	24.6562	1.21917	0.609586	−	0.792720i	$-0.291336\pi$
$409$	24.6562	1.21917	0.609586	+	0.792720i	$0.291336\pi$
$410$	−1.02082	−0.0504145
$411$	9.92735	0.489680
$412$	−38.6718	−1.90522
$413$	29.3549	1.44446
$414$	−18.0965	−0.889396
$415$	35.7978	1.75724
$416$	16.8732	0.827279
$417$	−10.1394	−0.496531
$418$	−9.94073	−0.486217
$419$	−1.34498	−0.0657066	−0.0328533	−	0.999460i	$-0.510459\pi$
$419$	−1.34498	−0.0657066	−0.0328533	+	0.999460i	$0.510459\pi$
$420$	−27.0526	−1.32003
$421$	−23.9486	−1.16718	−0.583591	−	0.812048i	$-0.698353\pi$
$421$	−23.9486	−1.16718	−0.583591	+	0.812048i	$0.698353\pi$
$422$	−18.9473	−0.922342
$423$	7.50680	0.364993
$424$	−5.48309	−0.266282
$425$	−0.695400	−0.0337319
$426$	16.0267	0.776498
$427$	0.00450603	0.000218062 0
$428$	−40.7765	−1.97100
$429$	−4.08017	−0.196993
$430$	−27.0192	−1.30298
$431$	9.93672	0.478635	0.239318	−	0.970941i	$-0.423076\pi$
$431$	9.93672	0.478635	0.239318	+	0.970941i	$0.423076\pi$
$432$	−3.51704	−0.169213
$433$	−29.1923	−1.40289	−0.701446	−	0.712723i	$-0.747462\pi$
$433$	−29.1923	−1.40289	−0.701446	+	0.712723i	$0.747462\pi$
$434$	−59.0683	−2.83537
$435$	13.0153	0.624037
$436$	15.7136	0.752543
$437$	21.7285	1.03941
$438$	−31.0570	−1.48396
$439$	−2.11350	−0.100872	−0.0504359	−	0.998727i	$-0.516061\pi$
$439$	−2.11350	−0.100872	−0.0504359	+	0.998727i	$0.516061\pi$
$440$	2.09509	0.0998796
$441$	19.1254	0.910732
$442$	4.26892	0.203052
$443$	−39.5365	−1.87844	−0.939218	−	0.343323i	$-0.888448\pi$
$443$	−39.5365	−1.87844	−0.939218	+	0.343323i	$0.888448\pi$
$444$	−17.9950	−0.854003
$445$	−31.9886	−1.51641
$446$	15.0589	0.713060
$447$	−8.57132	−0.405410
$448$	49.2575	2.32720
$449$	−21.0495	−0.993387	−0.496693	−	0.867926i	$-0.665453\pi$
$449$	−21.0495	−0.993387	−0.496693	+	0.867926i	$0.665453\pi$
$450$	1.42816	0.0673240
$451$	−0.408832	−0.0192512
$452$	7.66512	0.360537
$453$	5.96822	0.280411
$454$	9.46867	0.444387
$455$	25.3554	1.18868
$456$	−1.10285	−0.0516455
$457$	−31.7419	−1.48482	−0.742412	−	0.669944i	$-0.766318\pi$
$457$	−31.7419	−1.48482	−0.742412	+	0.669944i	$0.766318\pi$
$458$	−52.2883	−2.44327
$459$	−1.00000	−0.0466760
$460$	−46.6372	−2.17447
$461$	−9.34796	−0.435378	−0.217689	−	0.976018i	$-0.569852\pi$
$461$	−9.34796	−0.435378	−0.217689	+	0.976018i	$0.569852\pi$
$462$	−20.6051	−0.958635
$463$	−38.5734	−1.79266	−0.896328	−	0.443392i	$-0.853775\pi$
$463$	−38.5734	−1.79266	−0.896328	+	0.443392i	$0.853775\pi$
$464$	−19.1809	−0.890452
$465$	13.4290	0.622755
$466$	18.5989	0.861576
$467$	13.9785	0.646846	0.323423	−	0.946254i	$-0.395166\pi$
$467$	13.9785	0.646846	0.323423	+	0.946254i	$0.395166\pi$
$468$	−4.60992	−0.213094
$469$	25.9293	1.19730
$470$	36.7924	1.69711
$471$	1.00000	0.0460776
$472$	−2.56855	−0.118227
$473$	−10.8211	−0.497554
$474$	5.39503	0.247802
$475$	−1.71479	−0.0786798
$476$	11.3357	0.519570
$477$	−12.2599	−0.561341
$478$	17.3187	0.792137
$479$	−3.97555	−0.181648	−0.0908238	−	0.995867i	$-0.528950\pi$
$479$	−3.97555	−0.181648	−0.0908238	+	0.995867i	$0.528950\pi$
$480$	−19.3724	−0.884226
$481$	16.8660	0.769022
$482$	−46.7784	−2.13070
$483$	45.0386	2.04933
$484$	−15.8503	−0.720469
$485$	7.55007	0.342831
$486$	2.05372	0.0931587
$487$	−15.6657	−0.709879	−0.354940	−	0.934889i	$-0.615499\pi$
$487$	−15.6657	−0.709879	−0.354940	+	0.934889i	$0.615499\pi$
$488$	−0.000394278 0	−1.78481e−5 0
$489$	15.1518	0.685186
$490$	93.7375	4.23463
$491$	27.9680	1.26218	0.631089	−	0.775711i	$-0.282608\pi$
$491$	27.9680	1.26218	0.631089	+	0.775711i	$0.282608\pi$
$492$	−0.461913	−0.0208246
$493$	−5.45372	−0.245623
$494$	10.5267	0.473620
$495$	4.68451	0.210553
$496$	−19.7906	−0.888623
$497$	−39.8873	−1.78919
$498$	30.8060	1.38045
$499$	8.32845	0.372833	0.186416	−	0.982471i	$-0.440313\pi$
$499$	8.32845	0.372833	0.186416	+	0.982471i	$0.440313\pi$
$500$	−22.7830	−1.01889
$501$	−1.94995	−0.0871173
$502$	−38.2029	−1.70508
$503$	−3.81118	−0.169932	−0.0849660	−	0.996384i	$-0.527078\pi$
$503$	−3.81118	−0.169932	−0.0849660	+	0.996384i	$0.527078\pi$
$504$	−2.28597	−0.101825
$505$	−1.83009	−0.0814381
$506$	−35.5220	−1.57914
$507$	−8.67930	−0.385461
$508$	10.3792	0.460504
$509$	35.6864	1.58177	0.790887	−	0.611962i	$-0.209620\pi$
$509$	35.6864	1.58177	0.790887	+	0.611962i	$0.209620\pi$
$510$	−4.90121	−0.217029
$511$	77.2945	3.41931
$512$	31.6954	1.40075
$513$	−2.46590	−0.108872
$514$	−38.5003	−1.69818
$515$	−41.6141	−1.83374
$516$	−12.2260	−0.538221
$517$	14.7352	0.648054
$518$	85.1740	3.74233
$519$	10.4175	0.457276
$520$	−2.21860	−0.0972919
$521$	19.4256	0.851050	0.425525	−	0.904947i	$-0.360089\pi$
$521$	19.4256	0.851050	0.425525	+	0.904947i	$0.360089\pi$
$522$	11.2004	0.490229
$523$	28.1945	1.23286	0.616429	−	0.787410i	$-0.288579\pi$
$523$	28.1945	1.23286	0.616429	+	0.787410i	$0.288579\pi$
$524$	25.2658	1.10374
$525$	−3.55440	−0.155127
$526$	31.5764	1.37679
$527$	−5.62706	−0.245119
$528$	−6.90365	−0.300443
$529$	54.6441	2.37583
$530$	−60.0883	−2.61007
$531$	−5.74314	−0.249231
$532$	27.9526	1.21190
$533$	0.432933	0.0187524
$534$	−27.5280	−1.19125
$535$	−43.8788	−1.89705
$536$	−2.26881	−0.0979978
$537$	17.7029	0.763938
$538$	−11.3668	−0.490056
$539$	37.5415	1.61703
$540$	5.29272	0.227762
$541$	−8.58385	−0.369048	−0.184524	−	0.982828i	$-0.559074\pi$
$541$	−8.58385	−0.369048	−0.184524	+	0.982828i	$0.559074\pi$
$542$	−8.41026	−0.361251
$543$	−13.2742	−0.569652
$544$	8.11749	0.348034
$545$	16.9091	0.724306
$546$	21.8197	0.933799
$547$	13.6337	0.582937	0.291469	−	0.956580i	$-0.405856\pi$
$547$	13.6337	0.582937	0.291469	+	0.956580i	$0.405856\pi$
$548$	22.0166	0.940501
$549$	−0.000881582 0	−3.76250e−5 0
$550$	2.80335	0.119535
$551$	−13.4483	−0.572918
$552$	−3.94088	−0.167735
$553$	−13.4272	−0.570981
$554$	−1.06441	−0.0452226
$555$	−19.3641	−0.821959
$556$	−22.4869	−0.953659
$557$	0.585496	0.0248083	0.0124041	−	0.999923i	$-0.496052\pi$
$557$	0.585496	0.0248083	0.0124041	+	0.999923i	$0.496052\pi$
$558$	11.5564	0.489222
$559$	11.4590	0.484663
$560$	42.9013	1.81291
$561$	−1.96292	−0.0828744
$562$	39.1737	1.65244
$563$	−36.8999	−1.55515	−0.777573	−	0.628792i	$-0.783550\pi$
$563$	−36.8999	−1.55515	−0.777573	+	0.628792i	$0.783550\pi$
$564$	16.6483	0.701022
$565$	8.24830	0.347009
$566$	−5.36912	−0.225681
$567$	−5.11130	−0.214654
$568$	3.49014	0.146443
$569$	16.4778	0.690786	0.345393	−	0.938458i	$-0.387746\pi$
$569$	16.4778	0.690786	0.345393	+	0.938458i	$0.387746\pi$
$570$	−12.0859	−0.506222
$571$	−3.53102	−0.147769	−0.0738843	−	0.997267i	$-0.523540\pi$
$571$	−3.53102	−0.147769	−0.0738843	+	0.997267i	$0.523540\pi$
$572$	−9.04889	−0.378353
$573$	27.0592	1.13041
$574$	2.18633	0.0912557
$575$	−6.12758	−0.255538
$576$	−9.63698	−0.401541
$577$	−24.2170	−1.00817	−0.504084	−	0.863655i	$-0.668170\pi$
$577$	−24.2170	−1.00817	−0.504084	+	0.863655i	$0.668170\pi$
$578$	2.05372	0.0854235
$579$	−5.69108	−0.236513
$580$	28.8650	1.19855
$581$	−76.6699	−3.18080
$582$	6.49726	0.269320
$583$	−24.0651	−0.996675
$584$	−6.76327	−0.279866
$585$	−4.96066	−0.205098
$586$	51.3494	2.12122
$587$	39.3719	1.62505	0.812526	−	0.582924i	$-0.198092\pi$
$587$	39.3719	1.62505	0.812526	+	0.582924i	$0.198092\pi$
$588$	42.4157	1.74919
$589$	−13.8758	−0.571741
$590$	−28.1484	−1.15885
$591$	6.37348	0.262170
$592$	28.5372	1.17287
$593$	9.98868	0.410186	0.205093	−	0.978743i	$-0.434250\pi$
$593$	9.98868	0.410186	0.205093	+	0.978743i	$0.434250\pi$
$594$	4.03128	0.165405
$595$	12.1981	0.500075
$596$	−19.0092	−0.778648
$597$	15.8923	0.650427
$598$	37.6160	1.53823
$599$	21.6958	0.886466	0.443233	−	0.896406i	$-0.353831\pi$
$599$	21.6958	0.886466	0.443233	+	0.896406i	$0.353831\pi$
$600$	0.311010	0.0126969
$601$	−30.9272	−1.26155	−0.630773	−	0.775967i	$-0.717262\pi$
$601$	−30.9272	−1.26155	−0.630773	+	0.775967i	$0.717262\pi$
$602$	57.8684	2.35854
$603$	−5.07294	−0.206586
$604$	13.2361	0.538571
$605$	−17.0562	−0.693435
$606$	−1.57490	−0.0639759
$607$	28.4397	1.15433	0.577167	−	0.816626i	$-0.304158\pi$
$607$	28.4397	1.15433	0.577167	+	0.816626i	$0.304158\pi$
$608$	20.0169	0.811793
$609$	−27.8756	−1.12958
$610$	−0.00432082	−0.000174945 0
$611$	−15.6038	−0.631264
$612$	−2.21777	−0.0896480
$613$	30.9698	1.25086	0.625428	−	0.780282i	$-0.284924\pi$
$613$	30.9698	1.25086	0.625428	+	0.780282i	$0.284924\pi$
$614$	−9.73610	−0.392917
$615$	−0.497056	−0.0200432
$616$	−4.48717	−0.180793
$617$	−47.2731	−1.90314	−0.951571	−	0.307428i	$-0.900532\pi$
$617$	−47.2731	−1.90314	−0.951571	+	0.307428i	$0.900532\pi$
$618$	−35.8113	−1.44054
$619$	−15.2296	−0.612128	−0.306064	−	0.952011i	$-0.599012\pi$
$619$	−15.2296	−0.612128	−0.306064	+	0.952011i	$0.599012\pi$
$620$	29.7824	1.19609
$621$	−8.81159	−0.353597
$622$	3.86077	0.154803
$623$	68.5117	2.74486
$624$	7.31061	0.292659
$625$	−27.9934	−1.11974
$626$	−3.49460	−0.139672
$627$	−4.84035	−0.193305
$628$	2.21777	0.0884987
$629$	8.11399	0.323526
$630$	−25.0516	−0.998078
$631$	−43.8700	−1.74644	−0.873218	−	0.487329i	$-0.837971\pi$
$631$	−43.8700	−1.74644	−0.873218	+	0.487329i	$0.837971\pi$
$632$	1.17488	0.0467341
$633$	−9.22586	−0.366695
$634$	19.5960	0.778258
$635$	11.1689	0.443225
$636$	−27.1896	−1.07814
$637$	−39.7545	−1.57513
$638$	21.9855	0.870414
$639$	7.80376	0.308712
$640$	−8.48808	−0.335521
$641$	−32.5356	−1.28508	−0.642539	−	0.766253i	$-0.722119\pi$
$641$	−32.5356	−1.28508	−0.642539	+	0.766253i	$0.722119\pi$
$642$	−37.7602	−1.49028
$643$	−38.6428	−1.52393	−0.761963	−	0.647621i	$-0.775764\pi$
$643$	−38.6428	−1.52393	−0.761963	+	0.647621i	$0.775764\pi$
$644$	99.8854	3.93603
$645$	−13.1562	−0.518025
$646$	5.06427	0.199251
$647$	26.2191	1.03078	0.515390	−	0.856956i	$-0.327647\pi$
$647$	26.2191	1.03078	0.515390	+	0.856956i	$0.327647\pi$
$648$	0.447239	0.0175692
$649$	−11.2733	−0.442516
$650$	−2.96861	−0.116438
$651$	−28.7616	−1.12726
$652$	33.6031	1.31600
$653$	24.4541	0.956963	0.478481	−	0.878098i	$-0.341187\pi$
$653$	24.4541	0.956963	0.478481	+	0.878098i	$0.341187\pi$
$654$	14.5512	0.568998
$655$	27.1881	1.06233
$656$	0.732521	0.0286002
$657$	−15.1223	−0.589977
$658$	−78.8002	−3.07195
$659$	3.68300	0.143469	0.0717347	−	0.997424i	$-0.477147\pi$
$659$	3.68300	0.143469	0.0717347	+	0.997424i	$0.477147\pi$
$660$	10.3892	0.404397
$661$	28.6772	1.11542	0.557708	−	0.830037i	$-0.311681\pi$
$661$	28.6772	1.11542	0.557708	+	0.830037i	$0.311681\pi$
$662$	72.5593	2.82010
$663$	2.07863	0.0807272
$664$	6.70862	0.260345
$665$	30.0794	1.16643
$666$	−16.6639	−0.645712
$667$	−48.0559	−1.86073
$668$	−4.32454	−0.167321
$669$	7.33250	0.283491
$670$	−24.8635	−0.960563
$671$	−0.00173047	−6.68041e−5 0
$672$	41.4909	1.60055
$673$	−12.4203	−0.478766	−0.239383	−	0.970925i	$-0.576945\pi$
$673$	−12.4203	−0.478766	−0.239383	+	0.970925i	$0.576945\pi$
$674$	0.975541	0.0375764
$675$	0.695400	0.0267660
$676$	−19.2487	−0.740334
$677$	17.6157	0.677026	0.338513	−	0.940962i	$-0.390076\pi$
$677$	17.6157	0.677026	0.338513	+	0.940962i	$0.390076\pi$
$678$	7.09813	0.272602
$679$	−16.1704	−0.620562
$680$	−1.06734	−0.0409305
$681$	4.61050	0.176675
$682$	22.6843	0.868625
$683$	1.18311	0.0452704	0.0226352	−	0.999744i	$-0.492794\pi$
$683$	1.18311	0.0452704	0.0226352	+	0.999744i	$0.492794\pi$
$684$	−5.46880	−0.209105
$685$	23.6916	0.905211
$686$	−127.282	−4.85966
$687$	−25.4603	−0.971371
$688$	19.3886	0.739182
$689$	25.4837	0.970853
$690$	−43.1875	−1.64412
$691$	−1.41953	−0.0540016	−0.0270008	−	0.999635i	$-0.508596\pi$
$691$	−1.41953	−0.0540016	−0.0270008	+	0.999635i	$0.508596\pi$
$692$	23.1036	0.878265
$693$	−10.0330	−0.381124
$694$	75.7304	2.87469
$695$	−24.1978	−0.917876
$696$	2.43911	0.0924544
$697$	0.208278	0.00788909
$698$	−24.5997	−0.931111
$699$	9.05618	0.342536
$700$	−7.88284	−0.297943
$701$	−19.2685	−0.727762	−0.363881	−	0.931445i	$-0.618549\pi$
$701$	−19.2685	−0.727762	−0.363881	+	0.931445i	$0.618549\pi$
$702$	−4.26892	−0.161120
$703$	20.0083	0.754626
$704$	−18.9166	−0.712946
$705$	17.9150	0.674718
$706$	3.96139	0.149089
$707$	3.91960	0.147412
$708$	−12.7370	−0.478684
$709$	17.5598	0.659471	0.329736	−	0.944073i	$-0.393040\pi$
$709$	17.5598	0.659471	0.329736	+	0.944073i	$0.393040\pi$
$710$	38.2479	1.43542
$711$	2.62696	0.0985185
$712$	−5.99477	−0.224664
$713$	−49.5833	−1.85691
$714$	10.4972	0.392847
$715$	−9.73735	−0.364156
$716$	39.2610	1.46725
$717$	8.43282	0.314929
$718$	−17.9263	−0.669004
$719$	−13.9228	−0.519233	−0.259616	−	0.965712i	$-0.583596\pi$
$719$	−13.9228	−0.519233	−0.259616	+	0.965712i	$0.583596\pi$
$720$	−8.39342	−0.312804
$721$	89.1270	3.31926
$722$	−26.5327	−0.987446
$723$	−22.7774	−0.847100
$724$	−29.4392	−1.09410
$725$	3.79252	0.140851
$726$	−14.6779	−0.544747
$727$	32.9951	1.22372	0.611861	−	0.790966i	$-0.290421\pi$
$727$	32.9951	1.22372	0.611861	+	0.790966i	$0.290421\pi$
$728$	4.75168	0.176109
$729$	1.00000	0.0370370
$730$	−74.1175	−2.74321
$731$	5.51276	0.203897
$732$	−0.00195515	−7.22643e−5 0
$733$	−25.3618	−0.936759	−0.468380	−	0.883527i	$-0.655162\pi$
$733$	−25.3618	−0.936759	−0.468380	+	0.883527i	$0.655162\pi$
$734$	−35.2162	−1.29985
$735$	45.6428	1.68356
$736$	71.5280	2.63656
$737$	−9.95775	−0.366798
$738$	−0.427745	−0.0157455
$739$	13.2304	0.486689	0.243344	−	0.969940i	$-0.421755\pi$
$739$	13.2304	0.486689	0.243344	+	0.969940i	$0.421755\pi$
$740$	−42.9450	−1.57869
$741$	5.12569	0.188297
$742$	128.694	4.72451
$743$	8.23304	0.302041	0.151020	−	0.988531i	$-0.451744\pi$
$743$	8.23304	0.302041	0.151020	+	0.988531i	$0.451744\pi$
$744$	2.51664	0.0922644
$745$	−20.4555	−0.749431
$746$	−27.7389	−1.01559
$747$	15.0001	0.548824
$748$	−4.35330	−0.159172
$749$	93.9776	3.43387
$750$	−21.0978	−0.770381
$751$	24.0085	0.876084	0.438042	−	0.898955i	$-0.355672\pi$
$751$	24.0085	0.876084	0.438042	+	0.898955i	$0.355672\pi$
$752$	−26.4017	−0.962770
$753$	−18.6018	−0.677887
$754$	−23.2815	−0.847863
$755$	14.2432	0.518362
$756$	−11.3357	−0.412275
$757$	33.9577	1.23421	0.617107	−	0.786879i	$-0.288304\pi$
$757$	33.9577	1.23421	0.617107	+	0.786879i	$0.288304\pi$
$758$	−33.4531	−1.21507
$759$	−17.2964	−0.627820
$760$	−2.63194	−0.0954706
$761$	8.28849	0.300458	0.150229	−	0.988651i	$-0.451999\pi$
$761$	8.28849	0.300458	0.150229	+	0.988651i	$0.451999\pi$
$762$	9.61148	0.348187
$763$	−36.2151	−1.31107
$764$	60.0111	2.17112
$765$	−2.38650	−0.0862842
$766$	9.77035	0.353017
$767$	11.9379	0.431051
$768$	11.9695	0.431912
$769$	24.7492	0.892481	0.446240	−	0.894913i	$-0.352763\pi$
$769$	24.7492	0.892481	0.446240	+	0.894913i	$0.352763\pi$
$770$	−49.1741	−1.77211
$771$	−18.7466	−0.675143
$772$	−12.6215	−0.454258
$773$	2.04383	0.0735114	0.0367557	−	0.999324i	$-0.488298\pi$
$773$	2.04383	0.0735114	0.0367557	+	0.999324i	$0.488298\pi$
$774$	−11.3217	−0.406949
$775$	3.91306	0.140561
$776$	1.41491	0.0507923
$777$	41.4730	1.48784
$778$	23.3649	0.837671
$779$	0.513593	0.0184014
$780$	−11.0016	−0.393920
$781$	15.3181	0.548125
$782$	18.0965	0.647131
$783$	5.45372	0.194900
$784$	−67.2646	−2.40231
$785$	2.38650	0.0851780
$786$	23.3969	0.834540
$787$	−13.1967	−0.470410	−0.235205	−	0.971946i	$-0.575576\pi$
$787$	−13.1967	−0.470410	−0.235205	+	0.971946i	$0.575576\pi$
$788$	14.1349	0.503535
$789$	15.3752	0.547372
$790$	12.8753	0.458082
$791$	−17.6658	−0.628124
$792$	0.877892	0.0311945
$793$	0.00183248	6.50733e−5 0
$794$	−0.00413633	−0.000146793 0
$795$	−29.2582	−1.03768
$796$	35.2454	1.24924
$797$	−20.5067	−0.726383	−0.363191	−	0.931715i	$-0.618313\pi$
$797$	−20.5067	−0.726383	−0.363191	+	0.931715i	$0.618313\pi$
$798$	25.8850	0.916318
$799$	−7.50680	−0.265571
$800$	−5.64490	−0.199577
$801$	−13.4040	−0.473606
$802$	22.7245	0.802429
$803$	−29.6838	−1.04752
$804$	−11.2506	−0.396778
$805$	107.485	3.78834
$806$	−24.0215	−0.846121
$807$	−5.53471	−0.194831
$808$	−0.342965	−0.0120655
$809$	3.29466	0.115834	0.0579170	−	0.998321i	$-0.481554\pi$
$809$	3.29466	0.115834	0.0579170	+	0.998321i	$0.481554\pi$
$810$	4.90121	0.172211
$811$	−1.59945	−0.0561644	−0.0280822	−	0.999606i	$-0.508940\pi$
$811$	−1.59945	−0.0561644	−0.0280822	+	0.999606i	$0.508940\pi$
$812$	−61.8216	−2.16951
$813$	−4.09513	−0.143623
$814$	−32.7098	−1.14648
$815$	36.1597	1.26662
$816$	3.51704	0.123121
$817$	13.5939	0.475590
$818$	50.6370	1.77048
$819$	10.6245	0.371250
$820$	−1.10236	−0.0384960
$821$	−16.2412	−0.566822	−0.283411	−	0.958999i	$-0.591466\pi$
$821$	−16.2412	−0.566822	−0.283411	+	0.958999i	$0.591466\pi$
$822$	20.3880	0.711113
$823$	20.7381	0.722886	0.361443	−	0.932394i	$-0.382284\pi$
$823$	20.7381	0.722886	0.361443	+	0.932394i	$0.382284\pi$
$824$	−7.79861	−0.271678
$825$	1.36501	0.0475236
$826$	60.2868	2.09765
$827$	−17.2964	−0.601455	−0.300727	−	0.953710i	$-0.597229\pi$
$827$	−17.2964	−0.601455	−0.300727	+	0.953710i	$0.597229\pi$
$828$	−19.5421	−0.679134
$829$	−19.8466	−0.689302	−0.344651	−	0.938731i	$-0.612003\pi$
$829$	−19.8466	−0.689302	−0.344651	+	0.938731i	$0.612003\pi$
$830$	73.5186	2.55187
$831$	−0.518286	−0.0179791
$832$	20.0317	0.694475
$833$	−19.1254	−0.662655
$834$	−20.8236	−0.721062
$835$	−4.65356	−0.161043
$836$	−10.7348	−0.371270
$837$	5.62706	0.194500
$838$	−2.76222	−0.0954192
$839$	−6.07416	−0.209703	−0.104852	−	0.994488i	$-0.533437\pi$
$839$	−6.07416	−0.209703	−0.104852	+	0.994488i	$0.533437\pi$
$840$	−5.45548	−0.188232
$841$	0.743065	0.0256229
$842$	−49.1837	−1.69498
$843$	19.0745	0.656961
$844$	−20.4608	−0.704291
$845$	−20.7132	−0.712555
$846$	15.4169	0.530043
$847$	36.5302	1.25519
$848$	43.1184	1.48069
$849$	−2.61434	−0.0897238
$850$	−1.42816	−0.0489854
$851$	71.4971	2.45089
$852$	17.3069	0.592926
$853$	11.0048	0.376799	0.188399	−	0.982092i	$-0.439670\pi$
$853$	11.0048	0.376799	0.188399	+	0.982092i	$0.439670\pi$
$854$	0.00925412	0.000316670 0
$855$	−5.88488	−0.201259
$856$	−8.22304	−0.281058
$857$	27.8294	0.950636	0.475318	−	0.879814i	$-0.342333\pi$
$857$	27.8294	0.950636	0.475318	+	0.879814i	$0.342333\pi$
$858$	−8.37954	−0.286073
$859$	39.7657	1.35679	0.678394	−	0.734698i	$-0.262676\pi$
$859$	39.7657	1.35679	0.678394	+	0.734698i	$0.262676\pi$
$860$	−29.1775	−0.994943
$861$	1.06457	0.0362805
$862$	20.4073	0.695074
$863$	−8.47187	−0.288386	−0.144193	−	0.989550i	$-0.546059\pi$
$863$	−8.47187	−0.288386	−0.144193	+	0.989550i	$0.546059\pi$
$864$	−8.11749	−0.276163
$865$	24.8613	0.845311
$866$	−59.9528	−2.03728
$867$	1.00000	0.0339618
$868$	−63.7866	−2.16506
$869$	5.15649	0.174922
$870$	26.7298	0.906227
$871$	10.5448	0.357295
$872$	3.16882	0.107310
$873$	3.16365	0.107073
$874$	44.6242	1.50944
$875$	52.5081	1.77510
$876$	−33.5378	−1.13314
$877$	−35.0264	−1.18276	−0.591380	−	0.806393i	$-0.701416\pi$
$877$	−35.0264	−1.18276	−0.591380	+	0.806393i	$0.701416\pi$
$878$	−4.34053	−0.146486
$879$	25.0031	0.843334
$880$	−16.4756	−0.555392
$881$	−49.6220	−1.67181	−0.835903	−	0.548877i	$-0.815056\pi$
$881$	−49.6220	−1.67181	−0.835903	+	0.548877i	$0.815056\pi$
$882$	39.2782	1.32256
$883$	0.540829	0.0182004	0.00910018	−	0.999959i	$-0.497103\pi$
$883$	0.540829	0.0182004	0.00910018	+	0.999959i	$0.497103\pi$
$884$	4.60992	0.155048
$885$	−13.7060	−0.460723
$886$	−81.1969	−2.72786
$887$	12.6782	0.425692	0.212846	−	0.977086i	$-0.431727\pi$
$887$	12.6782	0.425692	0.212846	+	0.977086i	$0.431727\pi$
$888$	−3.62889	−0.121778
$889$	−23.9210	−0.802286
$890$	−65.6957	−2.20213
$891$	1.96292	0.0657602
$892$	16.2618	0.544485
$893$	−18.5110	−0.619447
$894$	−17.6031	−0.588736
$895$	42.2481	1.41220
$896$	18.1793	0.607329
$897$	18.3160	0.611554
$898$	−43.2298	−1.44260
$899$	30.6884	1.02352
$900$	1.54224	0.0514079
$901$	12.2599	0.408436
$902$	−0.839627	−0.0279565
$903$	28.1773	0.937683
$904$	1.54576	0.0514112
$905$	−31.6790	−1.05305
$906$	12.2571	0.407213
$907$	−0.723937	−0.0240379	−0.0120190	−	0.999928i	$-0.503826\pi$
$907$	−0.723937	−0.0240379	−0.0120190	+	0.999928i	$0.503826\pi$
$908$	10.2250	0.339329
$909$	−0.766851	−0.0254348
$910$	52.0729	1.72620
$911$	−0.369526	−0.0122430	−0.00612148	−	0.999981i	$-0.501949\pi$
$911$	−0.369526	−0.0122430	−0.00612148	+	0.999981i	$0.501949\pi$
$912$	8.67266	0.287180
$913$	29.4439	0.974451
$914$	−65.1890	−2.15626
$915$	−0.00210390	−6.95527e−5 0
$916$	−56.4651	−1.86566
$917$	−58.2302	−1.92293
$918$	−2.05372	−0.0677829
$919$	−45.4407	−1.49895	−0.749476	−	0.662032i	$-0.769694\pi$
$919$	−45.4407	−1.49895	−0.749476	+	0.662032i	$0.769694\pi$
$920$	−9.40493	−0.310071
$921$	−4.74071	−0.156212
$922$	−19.1981	−0.632256
$923$	−16.2211	−0.533924
$924$	−22.2510	−0.732004
$925$	−5.64247	−0.185523
$926$	−79.2189	−2.60329
$927$	−17.4373	−0.572715
$928$	−44.2705	−1.45325
$929$	32.2343	1.05757	0.528786	−	0.848755i	$-0.322648\pi$
$929$	32.2343	1.05757	0.528786	+	0.848755i	$0.322648\pi$
$930$	27.5794	0.904365
$931$	−47.1612	−1.54565
$932$	20.0845	0.657891
$933$	1.87989	0.0615448
$934$	28.7079	0.939350
$935$	−4.68451	−0.153200
$936$	−0.929643	−0.0303863
$937$	24.0331	0.785126	0.392563	−	0.919725i	$-0.371589\pi$
$937$	24.0331	0.785126	0.392563	+	0.919725i	$0.371589\pi$
$938$	53.2515	1.73872
$939$	−1.70160	−0.0555295
$940$	39.7313	1.29589
$941$	−28.7578	−0.937478	−0.468739	−	0.883337i	$-0.655292\pi$
$941$	−28.7578	−0.937478	−0.468739	+	0.883337i	$0.655292\pi$
$942$	2.05372	0.0669138
$943$	1.83526	0.0597643
$944$	20.1988	0.657416
$945$	−12.1981	−0.396805
$946$	−22.2235	−0.722547
$947$	−57.3276	−1.86290	−0.931449	−	0.363873i	$-0.881454\pi$
$947$	−57.3276	−1.86290	−0.931449	+	0.363873i	$0.881454\pi$
$948$	5.82598	0.189219
$949$	31.4336	1.02038
$950$	−3.52169	−0.114259
$951$	9.54172	0.309411
$952$	2.28597	0.0740887
$953$	−10.2059	−0.330602	−0.165301	−	0.986243i	$-0.552860\pi$
$953$	−10.2059	−0.330602	−0.165301	+	0.986243i	$0.552860\pi$
$954$	−25.1784	−0.815180
$955$	64.5769	2.08966
$956$	18.7021	0.604868
$957$	10.7052	0.346050
$958$	−8.16467	−0.263789
$959$	−50.7416	−1.63853
$960$	−22.9987	−0.742280
$961$	0.663793	0.0214127
$962$	34.6380	1.11677
$963$	−18.3862	−0.592488
$964$	−50.5150	−1.62698
$965$	−13.5818	−0.437213
$966$	92.4968	2.97604
$967$	−46.1319	−1.48350	−0.741751	−	0.670675i	$-0.766004\pi$
$967$	−46.1319	−1.48350	−0.741751	+	0.670675i	$0.766004\pi$
$968$	−3.19640	−0.102736
$969$	2.46590	0.0792161
$970$	15.5057	0.497859
$971$	21.2795	0.682893	0.341446	−	0.939901i	$-0.389083\pi$
$971$	21.2795	0.682893	0.341446	+	0.939901i	$0.389083\pi$
$972$	2.21777	0.0711350
$973$	51.8257	1.66146
$974$	−32.1729	−1.03089
$975$	−1.44548	−0.0462924
$976$	0.00310056	9.92464e−5 0
$977$	53.9640	1.72646	0.863231	−	0.504808i	$-0.168437\pi$
$977$	53.9640	1.72646	0.863231	+	0.504808i	$0.168437\pi$
$978$	31.1175	0.995027
$979$	−26.3109	−0.840899
$980$	101.225	3.23352
$981$	7.08530	0.226216
$982$	57.4384	1.83293
$983$	−34.0247	−1.08522	−0.542609	−	0.839985i	$-0.682563\pi$
$983$	−34.0247	−1.08522	−0.542609	+	0.839985i	$0.682563\pi$
$984$	−0.0931500	−0.00296951
$985$	15.2103	0.484641
$986$	−11.2004	−0.356694
$987$	−38.3695	−1.22131
$988$	11.3676	0.361651
$989$	48.5761	1.54463
$990$	9.62067	0.305765
$991$	−39.9716	−1.26974	−0.634870	−	0.772619i	$-0.718946\pi$
$991$	−39.9716	−1.26974	−0.634870	+	0.772619i	$0.718946\pi$
$992$	−45.6776	−1.45026
$993$	35.3307	1.12118
$994$	−81.9174	−2.59826
$995$	37.9269	1.20236
$996$	33.2667	1.05410
$997$	38.3542	1.21469	0.607344	−	0.794439i	$-0.292235\pi$
$997$	38.3542	1.21469	0.607344	+	0.794439i	$0.292235\pi$
$998$	17.1043	0.541428
$999$	−8.11399	−0.256715

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.e.1.40	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.e.1.40	✓	46	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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q+2.05372 q^{2} +1.00000 q^{3} +2.21777 q^{4} +2.38650 q^{5} +2.05372 q^{6} -5.11130 q^{7} +0.447239 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.05372 q^{2} +1.00000 q^{3} +2.21777 q^{4} +2.38650 q^{5} +2.05372 q^{6} -5.11130 q^{7} +0.447239 q^{8} +1.00000 q^{9} +4.90121 q^{10} +1.96292 q^{11} +2.21777 q^{12} -2.07863 q^{13} -10.4972 q^{14} +2.38650 q^{15} -3.51704 q^{16} -1.00000 q^{17} +2.05372 q^{18} -2.46590 q^{19} +5.29272 q^{20} -5.11130 q^{21} +4.03128 q^{22} -8.81159 q^{23} +0.447239 q^{24} +0.695400 q^{25} -4.26892 q^{26} +1.00000 q^{27} -11.3357 q^{28} +5.45372 q^{29} +4.90121 q^{30} +5.62706 q^{31} -8.11749 q^{32} +1.96292 q^{33} -2.05372 q^{34} -12.1981 q^{35} +2.21777 q^{36} -8.11399 q^{37} -5.06427 q^{38} -2.07863 q^{39} +1.06734 q^{40} -0.208278 q^{41} -10.4972 q^{42} -5.51276 q^{43} +4.35330 q^{44} +2.38650 q^{45} -18.0965 q^{46} +7.50680 q^{47} -3.51704 q^{48} +19.1254 q^{49} +1.42816 q^{50} -1.00000 q^{51} -4.60992 q^{52} -12.2599 q^{53} +2.05372 q^{54} +4.68451 q^{55} -2.28597 q^{56} -2.46590 q^{57} +11.2004 q^{58} -5.74314 q^{59} +5.29272 q^{60} -0.000881582 q^{61} +11.5564 q^{62} -5.11130 q^{63} -9.63698 q^{64} -4.96066 q^{65} +4.03128 q^{66} -5.07294 q^{67} -2.21777 q^{68} -8.81159 q^{69} -25.0516 q^{70} +7.80376 q^{71} +0.447239 q^{72} -15.1223 q^{73} -16.6639 q^{74} +0.695400 q^{75} -5.46880 q^{76} -10.0330 q^{77} -4.26892 q^{78} +2.62696 q^{79} -8.39342 q^{80} +1.00000 q^{81} -0.427745 q^{82} +15.0001 q^{83} -11.3357 q^{84} -2.38650 q^{85} -11.3217 q^{86} +5.45372 q^{87} +0.877892 q^{88} -13.4040 q^{89} +4.90121 q^{90} +10.6245 q^{91} -19.5421 q^{92} +5.62706 q^{93} +15.4169 q^{94} -5.88488 q^{95} -8.11749 q^{96} +3.16365 q^{97} +39.2782 q^{98} +1.96292 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9}+O(q^{10}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9} - 10 q^{10} - 25 q^{11} + 43 q^{12} - 8 q^{13} - 28 q^{14} - 19 q^{15} + 33 q^{16} - 46 q^{17} - 5 q^{18} - 2 q^{19} - 56 q^{20} + q^{21} - 19 q^{22} - 64 q^{23} - 18 q^{24} + 11 q^{25} - 13 q^{26} + 46 q^{27} - 38 q^{28} - 51 q^{29} - 10 q^{30} - 19 q^{31} - 61 q^{32} - 25 q^{33} + 5 q^{34} - 39 q^{35} + 43 q^{36} - 46 q^{37} - 48 q^{38} - 8 q^{39} - 10 q^{40} - 53 q^{41} - 28 q^{42} - 33 q^{43} - 62 q^{44} - 19 q^{45} + 2 q^{46} - 45 q^{47} + 33 q^{48} + 21 q^{49} - 60 q^{50} - 46 q^{51} - 63 q^{52} - 47 q^{53} - 5 q^{54} + 5 q^{55} - 82 q^{56} - 2 q^{57} - 21 q^{58} - 65 q^{59} - 56 q^{60} - 37 q^{61} - 46 q^{62} + q^{63} + 74 q^{64} - 85 q^{65} - 19 q^{66} - 52 q^{67} - 43 q^{68} - 64 q^{69} - 20 q^{70} - 48 q^{71} - 18 q^{72} - 39 q^{73} - 16 q^{74} + 11 q^{75} + 42 q^{76} - 78 q^{77} - 13 q^{78} - 26 q^{79} - 78 q^{80} + 46 q^{81} + 3 q^{82} - 47 q^{83} - 38 q^{84} + 19 q^{85} - 6 q^{86} - 51 q^{87} - 58 q^{88} - 58 q^{89} - 10 q^{90} - 43 q^{91} - 68 q^{92} - 19 q^{93} - 78 q^{95} - 61 q^{96} - 44 q^{97} - 4 q^{98} - 25 q^{99}+O(q^{100}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9 - 10 * q^10 - 25 * q^11 + 43 * q^12 - 8 * q^13 - 28 * q^14 - 19 * q^15 + 33 * q^16 - 46 * q^17 - 5 * q^18 - 2 * q^19 - 56 * q^20 + q^21 - 19 * q^22 - 64 * q^23 - 18 * q^24 + 11 * q^25 - 13 * q^26 + 46 * q^27 - 38 * q^28 - 51 * q^29 - 10 * q^30 - 19 * q^31 - 61 * q^32 - 25 * q^33 + 5 * q^34 - 39 * q^35 + 43 * q^36 - 46 * q^37 - 48 * q^38 - 8 * q^39 - 10 * q^40 - 53 * q^41 - 28 * q^42 - 33 * q^43 - 62 * q^44 - 19 * q^45 + 2 * q^46 - 45 * q^47 + 33 * q^48 + 21 * q^49 - 60 * q^50 - 46 * q^51 - 63 * q^52 - 47 * q^53 - 5 * q^54 + 5 * q^55 - 82 * q^56 - 2 * q^57 - 21 * q^58 - 65 * q^59 - 56 * q^60 - 37 * q^61 - 46 * q^62 + q^63 + 74 * q^64 - 85 * q^65 - 19 * q^66 - 52 * q^67 - 43 * q^68 - 64 * q^69 - 20 * q^70 - 48 * q^71 - 18 * q^72 - 39 * q^73 - 16 * q^74 + 11 * q^75 + 42 * q^76 - 78 * q^77 - 13 * q^78 - 26 * q^79 - 78 * q^80 + 46 * q^81 + 3 * q^82 - 47 * q^83 - 38 * q^84 + 19 * q^85 - 6 * q^86 - 51 * q^87 - 58 * q^88 - 58 * q^89 - 10 * q^90 - 43 * q^91 - 68 * q^92 - 19 * q^93 - 78 * q^95 - 61 * q^96 - 44 * q^97 - 4 * q^98 - 25 * q^99

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