LMFDB - Embedded newform 8007.2.a.j.1.8

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:	$0$
Dimension:	$64$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
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)

$f(q)$	$=$	$q-2.37098 q^{2} -1.00000 q^{3} +3.62156 q^{4} -2.47104 q^{5} +2.37098 q^{6} +5.22837 q^{7} -3.84468 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.37098 q^{2} -1.00000 q^{3} +3.62156 q^{4} -2.47104 q^{5} +2.37098 q^{6} +5.22837 q^{7} -3.84468 q^{8} +1.00000 q^{9} +5.85879 q^{10} -2.69830 q^{11} -3.62156 q^{12} -4.61025 q^{13} -12.3964 q^{14} +2.47104 q^{15} +1.87256 q^{16} +1.00000 q^{17} -2.37098 q^{18} +3.89560 q^{19} -8.94902 q^{20} -5.22837 q^{21} +6.39763 q^{22} -1.31247 q^{23} +3.84468 q^{24} +1.10604 q^{25} +10.9308 q^{26} -1.00000 q^{27} +18.9348 q^{28} -6.14894 q^{29} -5.85879 q^{30} -6.63171 q^{31} +3.24955 q^{32} +2.69830 q^{33} -2.37098 q^{34} -12.9195 q^{35} +3.62156 q^{36} -3.63240 q^{37} -9.23639 q^{38} +4.61025 q^{39} +9.50037 q^{40} -7.09471 q^{41} +12.3964 q^{42} +4.62347 q^{43} -9.77206 q^{44} -2.47104 q^{45} +3.11185 q^{46} -10.0238 q^{47} -1.87256 q^{48} +20.3358 q^{49} -2.62241 q^{50} -1.00000 q^{51} -16.6963 q^{52} -6.19366 q^{53} +2.37098 q^{54} +6.66762 q^{55} -20.1014 q^{56} -3.89560 q^{57} +14.5790 q^{58} +2.92971 q^{59} +8.94902 q^{60} -6.46956 q^{61} +15.7237 q^{62} +5.22837 q^{63} -11.4498 q^{64} +11.3921 q^{65} -6.39763 q^{66} -11.2487 q^{67} +3.62156 q^{68} +1.31247 q^{69} +30.6319 q^{70} +4.39922 q^{71} -3.84468 q^{72} +0.488239 q^{73} +8.61235 q^{74} -1.10604 q^{75} +14.1081 q^{76} -14.1077 q^{77} -10.9308 q^{78} -2.57608 q^{79} -4.62718 q^{80} +1.00000 q^{81} +16.8214 q^{82} -2.95749 q^{83} -18.9348 q^{84} -2.47104 q^{85} -10.9622 q^{86} +6.14894 q^{87} +10.3741 q^{88} +11.7140 q^{89} +5.85879 q^{90} -24.1041 q^{91} -4.75319 q^{92} +6.63171 q^{93} +23.7663 q^{94} -9.62618 q^{95} -3.24955 q^{96} -3.40745 q^{97} -48.2159 q^{98} -2.69830 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) $ 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * 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 $

$2$	−2.37098	−1.67654	−0.838269	−	0.545257i	$-0.816432\pi$
$2$	−2.37098	−1.67654	−0.838269	+	0.545257i	$0.816432\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.62156	1.81078
$5$	−2.47104	−1.10508	−0.552542	−	0.833485i	$-0.686342\pi$
$5$	−2.47104	−1.10508	−0.552542	+	0.833485i	$0.686342\pi$
$6$	2.37098	0.967950
$7$	5.22837	1.97614	0.988069	−	0.154013i	$-0.0492197\pi$
$7$	5.22837	1.97614	0.988069	+	0.154013i	$0.0492197\pi$
$8$	−3.84468	−1.35930
$9$	1.00000	0.333333
$10$	5.85879	1.85271
$11$	−2.69830	−0.813569	−0.406784	−	0.913524i	$-0.633350\pi$
$11$	−2.69830	−0.813569	−0.406784	+	0.913524i	$0.633350\pi$
$12$	−3.62156	−1.04545
$13$	−4.61025	−1.27865	−0.639326	−	0.768936i	$-0.720787\pi$
$13$	−4.61025	−1.27865	−0.639326	+	0.768936i	$0.720787\pi$
$14$	−12.3964	−3.31307
$15$	2.47104	0.638020
$16$	1.87256	0.468141
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.37098	−0.558846
$19$	3.89560	0.893711	0.446856	−	0.894606i	$-0.352544\pi$
$19$	3.89560	0.893711	0.446856	+	0.894606i	$0.352544\pi$
$20$	−8.94902	−2.00106
$21$	−5.22837	−1.14092
$22$	6.39763	1.36398
$23$	−1.31247	−0.273669	−0.136835	−	0.990594i	$-0.543693\pi$
$23$	−1.31247	−0.273669	−0.136835	+	0.990594i	$0.543693\pi$
$24$	3.84468	0.784793
$25$	1.10604	0.221209
$26$	10.9308	2.14371
$27$	−1.00000	−0.192450
$28$	18.9348	3.57835
$29$	−6.14894	−1.14183	−0.570914	−	0.821010i	$-0.693411\pi$
$29$	−6.14894	−1.14183	−0.570914	+	0.821010i	$0.693411\pi$
$30$	−5.85879	−1.06966
$31$	−6.63171	−1.19109	−0.595545	−	0.803322i	$-0.703064\pi$
$31$	−6.63171	−1.19109	−0.595545	+	0.803322i	$0.703064\pi$
$32$	3.24955	0.574445
$33$	2.69830	0.469714
$34$	−2.37098	−0.406620
$35$	−12.9195	−2.18380
$36$	3.62156	0.603593
$37$	−3.63240	−0.597162	−0.298581	−	0.954384i	$-0.596513\pi$
$37$	−3.63240	−0.597162	−0.298581	+	0.954384i	$0.596513\pi$
$38$	−9.23639	−1.49834
$39$	4.61025	0.738230
$40$	9.50037	1.50214
$41$	−7.09471	−1.10801	−0.554004	−	0.832514i	$-0.686901\pi$
$41$	−7.09471	−1.10801	−0.554004	+	0.832514i	$0.686901\pi$
$42$	12.3964	1.91280
$43$	4.62347	0.705072	0.352536	−	0.935798i	$-0.385319\pi$
$43$	4.62347	0.705072	0.352536	+	0.935798i	$0.385319\pi$
$44$	−9.77206	−1.47319
$45$	−2.47104	−0.368361
$46$	3.11185	0.458817
$47$	−10.0238	−1.46212	−0.731062	−	0.682311i	$-0.760975\pi$
$47$	−10.0238	−1.46212	−0.731062	+	0.682311i	$0.760975\pi$
$48$	−1.87256	−0.270281
$49$	20.3358	2.90512
$50$	−2.62241	−0.370865
$51$	−1.00000	−0.140028
$52$	−16.6963	−2.31536
$53$	−6.19366	−0.850764	−0.425382	−	0.905014i	$-0.639860\pi$
$53$	−6.19366	−0.850764	−0.425382	+	0.905014i	$0.639860\pi$
$54$	2.37098	0.322650
$55$	6.66762	0.899061
$56$	−20.1014	−2.68617
$57$	−3.89560	−0.515984
$58$	14.5790	1.91432
$59$	2.92971	0.381415	0.190708	−	0.981647i	$-0.438922\pi$
$59$	2.92971	0.381415	0.190708	+	0.981647i	$0.438922\pi$
$60$	8.94902	1.15531
$61$	−6.46956	−0.828342	−0.414171	−	0.910199i	$-0.635929\pi$
$61$	−6.46956	−0.828342	−0.414171	+	0.910199i	$0.635929\pi$
$62$	15.7237	1.99691
$63$	5.22837	0.658713
$64$	−11.4498	−1.43122
$65$	11.3921	1.41302
$66$	−6.39763	−0.787494
$67$	−11.2487	−1.37424	−0.687121	−	0.726543i	$-0.741126\pi$
$67$	−11.2487	−1.37424	−0.687121	+	0.726543i	$0.741126\pi$
$68$	3.62156	0.439178
$69$	1.31247	0.158003
$70$	30.6319	3.66122
$71$	4.39922	0.522092	0.261046	−	0.965326i	$-0.415933\pi$
$71$	4.39922	0.522092	0.261046	+	0.965326i	$0.415933\pi$
$72$	−3.84468	−0.453100
$73$	0.488239	0.0571441	0.0285720	−	0.999592i	$-0.490904\pi$
$73$	0.488239	0.0571441	0.0285720	+	0.999592i	$0.490904\pi$
$74$	8.61235	1.00117
$75$	−1.10604	−0.127715
$76$	14.1081	1.61831
$77$	−14.1077	−1.60772
$78$	−10.9308	−1.23767
$79$	−2.57608	−0.289832	−0.144916	−	0.989444i	$-0.546291\pi$
$79$	−2.57608	−0.289832	−0.144916	+	0.989444i	$0.546291\pi$
$80$	−4.62718	−0.517335
$81$	1.00000	0.111111
$82$	16.8214	1.85762
$83$	−2.95749	−0.324627	−0.162313	−	0.986739i	$-0.551896\pi$
$83$	−2.95749	−0.324627	−0.162313	+	0.986739i	$0.551896\pi$
$84$	−18.9348	−2.06596
$85$	−2.47104	−0.268022
$86$	−10.9622	−1.18208
$87$	6.14894	0.659235
$88$	10.3741	1.10589
$89$	11.7140	1.24168	0.620841	−	0.783937i	$-0.286791\pi$
$89$	11.7140	1.24168	0.620841	+	0.783937i	$0.286791\pi$
$90$	5.85879	0.617571
$91$	−24.1041	−2.52679
$92$	−4.75319	−0.495555
$93$	6.63171	0.687677
$94$	23.7663	2.45131
$95$	−9.62618	−0.987625
$96$	−3.24955	−0.331656
$97$	−3.40745	−0.345974	−0.172987	−	0.984924i	$-0.555342\pi$
$97$	−3.40745	−0.345974	−0.172987	+	0.984924i	$0.555342\pi$
$98$	−48.2159	−4.87054
$99$	−2.69830	−0.271190
$100$	4.00560	0.400560
$101$	12.9375	1.28733	0.643663	−	0.765309i	$-0.277414\pi$
$101$	12.9375	1.28733	0.643663	+	0.765309i	$0.277414\pi$
$102$	2.37098	0.234762
$103$	15.3394	1.51144	0.755719	−	0.654896i	$-0.227287\pi$
$103$	15.3394	1.51144	0.755719	+	0.654896i	$0.227287\pi$
$104$	17.7249	1.73807
$105$	12.9195	1.26082
$106$	14.6851	1.42634
$107$	10.4852	1.01364	0.506820	−	0.862052i	$-0.330821\pi$
$107$	10.4852	1.01364	0.506820	+	0.862052i	$0.330821\pi$
$108$	−3.62156	−0.348485
$109$	−0.790168	−0.0756843	−0.0378422	−	0.999284i	$-0.512048\pi$
$109$	−0.790168	−0.0756843	−0.0378422	+	0.999284i	$0.512048\pi$
$110$	−15.8088	−1.50731
$111$	3.63240	0.344772
$112$	9.79045	0.925111
$113$	−14.4514	−1.35947	−0.679735	−	0.733457i	$-0.737905\pi$
$113$	−14.4514	−1.35947	−0.679735	+	0.733457i	$0.737905\pi$
$114$	9.23639	0.865067
$115$	3.24317	0.302427
$116$	−22.2687	−2.06760
$117$	−4.61025	−0.426217
$118$	−6.94629	−0.639457
$119$	5.22837	0.479284
$120$	−9.50037	−0.867261
$121$	−3.71916	−0.338106
$122$	15.3392	1.38875
$123$	7.09471	0.639708
$124$	−24.0171	−2.15680
$125$	9.62213	0.860629
$126$	−12.3964	−1.10436
$127$	7.69943	0.683214	0.341607	−	0.939843i	$-0.389029\pi$
$127$	7.69943	0.683214	0.341607	+	0.939843i	$0.389029\pi$
$128$	20.6481	1.82505
$129$	−4.62347	−0.407074
$130$	−27.0105	−2.36898
$131$	−6.33756	−0.553715	−0.276858	−	0.960911i	$-0.589293\pi$
$131$	−6.33756	−0.553715	−0.276858	+	0.960911i	$0.589293\pi$
$132$	9.77206	0.850549
$133$	20.3676	1.76610
$134$	26.6704	2.30397
$135$	2.47104	0.212673
$136$	−3.84468	−0.329679
$137$	21.4514	1.83272	0.916360	−	0.400356i	$-0.131113\pi$
$137$	21.4514	1.83272	0.916360	+	0.400356i	$0.131113\pi$
$138$	−3.11185	−0.264898
$139$	20.5715	1.74485	0.872426	−	0.488746i	$-0.162546\pi$
$139$	20.5715	1.74485	0.872426	+	0.488746i	$0.162546\pi$
$140$	−46.7888	−3.95437
$141$	10.0238	0.844157
$142$	−10.4305	−0.875307
$143$	12.4398	1.04027
$144$	1.87256	0.156047
$145$	15.1943	1.26182
$146$	−1.15761	−0.0958042
$147$	−20.3358	−1.67727
$148$	−13.1549	−1.08133
$149$	−6.85932	−0.561937	−0.280968	−	0.959717i	$-0.590656\pi$
$149$	−6.85932	−0.561937	−0.280968	+	0.959717i	$0.590656\pi$
$150$	2.62241	0.214119
$151$	10.7211	0.872471	0.436236	−	0.899832i	$-0.356311\pi$
$151$	10.7211	0.872471	0.436236	+	0.899832i	$0.356311\pi$
$152$	−14.9773	−1.21482
$153$	1.00000	0.0808452
$154$	33.4492	2.69541
$155$	16.3872	1.31625
$156$	16.6963	1.33677
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	6.10784	0.485914
$159$	6.19366	0.491189
$160$	−8.02978	−0.634810
$161$	−6.86209	−0.540808
$162$	−2.37098	−0.186282
$163$	11.9402	0.935229	0.467615	−	0.883932i	$-0.345114\pi$
$163$	11.9402	0.935229	0.467615	+	0.883932i	$0.345114\pi$
$164$	−25.6939	−2.00636
$165$	−6.66762	−0.519073
$166$	7.01216	0.544249
$167$	−11.3402	−0.877528	−0.438764	−	0.898602i	$-0.644584\pi$
$167$	−11.3402	−0.877528	−0.438764	+	0.898602i	$0.644584\pi$
$168$	20.1014	1.55086
$169$	8.25437	0.634951
$170$	5.85879	0.449349
$171$	3.89560	0.297904
$172$	16.7442	1.27673
$173$	−22.8280	−1.73558	−0.867791	−	0.496929i	$-0.834461\pi$
$173$	−22.8280	−1.73558	−0.867791	+	0.496929i	$0.834461\pi$
$174$	−14.5790	−1.10523
$175$	5.78280	0.437139
$176$	−5.05274	−0.380865
$177$	−2.92971	−0.220210
$178$	−27.7737	−2.08173
$179$	22.2811	1.66537	0.832684	−	0.553748i	$-0.186803\pi$
$179$	22.2811	1.66537	0.832684	+	0.553748i	$0.186803\pi$
$180$	−8.94902	−0.667020
$181$	−8.52326	−0.633529	−0.316764	−	0.948504i	$-0.602596\pi$
$181$	−8.52326	−0.633529	−0.316764	+	0.948504i	$0.602596\pi$
$182$	57.1503	4.23626
$183$	6.46956	0.478244
$184$	5.04604	0.371999
$185$	8.97580	0.659914
$186$	−15.7237	−1.15292
$187$	−2.69830	−0.197319
$188$	−36.3018	−2.64758
$189$	−5.22837	−0.380308
$190$	22.8235	1.65579
$191$	−16.8920	−1.22226	−0.611129	−	0.791531i	$-0.709285\pi$
$191$	−16.8920	−1.22226	−0.611129	+	0.791531i	$0.709285\pi$
$192$	11.4498	0.826315
$193$	18.4292	1.32657	0.663283	−	0.748369i	$-0.269163\pi$
$193$	18.4292	1.32657	0.663283	+	0.748369i	$0.269163\pi$
$194$	8.07901	0.580039
$195$	−11.3921	−0.815806
$196$	73.6474	5.26053
$197$	−5.02015	−0.357671	−0.178835	−	0.983879i	$-0.557233\pi$
$197$	−5.02015	−0.357671	−0.178835	+	0.983879i	$0.557233\pi$
$198$	6.39763	0.454660
$199$	−2.23856	−0.158687	−0.0793436	−	0.996847i	$-0.525282\pi$
$199$	−2.23856	−0.158687	−0.0793436	+	0.996847i	$0.525282\pi$
$200$	−4.25239	−0.300689
$201$	11.2487	0.793419
$202$	−30.6745	−2.15825
$203$	−32.1489	−2.25641
$204$	−3.62156	−0.253560
$205$	17.5313	1.22444
$206$	−36.3695	−2.53398
$207$	−1.31247	−0.0912231
$208$	−8.63298	−0.598589
$209$	−10.5115	−0.727096
$210$	−30.6319	−2.11380
$211$	14.7607	1.01617	0.508083	−	0.861308i	$-0.330354\pi$
$211$	14.7607	1.01617	0.508083	+	0.861308i	$0.330354\pi$
$212$	−22.4307	−1.54055
$213$	−4.39922	−0.301430
$214$	−24.8601	−1.69940
$215$	−11.4248	−0.779163
$216$	3.84468	0.261598
$217$	−34.6730	−2.35376
$218$	1.87347	0.126888
$219$	−0.488239	−0.0329921
$220$	24.1472	1.62800
$221$	−4.61025	−0.310119
$222$	−8.61235	−0.578023
$223$	−6.47232	−0.433418	−0.216709	−	0.976236i	$-0.569532\pi$
$223$	−6.47232	−0.433418	−0.216709	+	0.976236i	$0.569532\pi$
$224$	16.9899	1.13518
$225$	1.10604	0.0737362
$226$	34.2640	2.27920
$227$	−10.3529	−0.687148	−0.343574	−	0.939126i	$-0.611638\pi$
$227$	−10.3529	−0.687148	−0.343574	+	0.939126i	$0.611638\pi$
$228$	−14.1081	−0.934334
$229$	−28.5081	−1.88387	−0.941933	−	0.335800i	$-0.890993\pi$
$229$	−28.5081	−1.88387	−0.941933	+	0.335800i	$0.890993\pi$
$230$	−7.68950	−0.507031
$231$	14.1077	0.928220
$232$	23.6407	1.55209
$233$	2.47644	0.162237	0.0811184	−	0.996704i	$-0.474151\pi$
$233$	2.47644	0.162237	0.0811184	+	0.996704i	$0.474151\pi$
$234$	10.9308	0.714569
$235$	24.7693	1.61577
$236$	10.6101	0.690659
$237$	2.57608	0.167334
$238$	−12.3964	−0.803537
$239$	21.5273	1.39249	0.696243	−	0.717807i	$-0.254854\pi$
$239$	21.5273	1.39249	0.696243	+	0.717807i	$0.254854\pi$
$240$	4.62718	0.298683
$241$	−15.8335	−1.01992	−0.509961	−	0.860197i	$-0.670340\pi$
$241$	−15.8335	−1.01992	−0.509961	+	0.860197i	$0.670340\pi$
$242$	8.81806	0.566847
$243$	−1.00000	−0.0641500
$244$	−23.4299	−1.49994
$245$	−50.2507	−3.21040
$246$	−16.8214	−1.07250
$247$	−17.9597	−1.14275
$248$	25.4968	1.61905
$249$	2.95749	0.187423
$250$	−22.8139	−1.44288
$251$	17.3138	1.09284	0.546420	−	0.837512i	$-0.315990\pi$
$251$	17.3138	1.09284	0.546420	+	0.837512i	$0.315990\pi$
$252$	18.9348	1.19278
$253$	3.54145	0.222649
$254$	−18.2552	−1.14543
$255$	2.47104	0.154743
$256$	−26.0567	−1.62854
$257$	0.945145	0.0589565	0.0294783	−	0.999565i	$-0.490615\pi$
$257$	0.945145	0.0589565	0.0294783	+	0.999565i	$0.490615\pi$
$258$	10.9622	0.682474
$259$	−18.9915	−1.18008
$260$	41.2572	2.55866
$261$	−6.14894	−0.380610
$262$	15.0262	0.928324
$263$	20.0507	1.23638	0.618190	−	0.786029i	$-0.287866\pi$
$263$	20.0507	1.23638	0.618190	+	0.786029i	$0.287866\pi$
$264$	−10.3741	−0.638483
$265$	15.3048	0.940165
$266$	−48.2913	−2.96093
$267$	−11.7140	−0.716885
$268$	−40.7377	−2.48845
$269$	−25.0222	−1.52563	−0.762816	−	0.646615i	$-0.776184\pi$
$269$	−25.0222	−1.52563	−0.762816	+	0.646615i	$0.776184\pi$
$270$	−5.85879	−0.356555
$271$	−12.0829	−0.733986	−0.366993	−	0.930224i	$-0.619613\pi$
$271$	−12.0829	−0.733986	−0.366993	+	0.930224i	$0.619613\pi$
$272$	1.87256	0.113541
$273$	24.1041	1.45884
$274$	−50.8610	−3.07262
$275$	−2.98444	−0.179968
$276$	4.75319	0.286109
$277$	−11.9900	−0.720411	−0.360206	−	0.932873i	$-0.617294\pi$
$277$	−11.9900	−0.720411	−0.360206	+	0.932873i	$0.617294\pi$
$278$	−48.7747	−2.92531
$279$	−6.63171	−0.397030
$280$	49.6714	2.96844
$281$	−3.78720	−0.225925	−0.112963	−	0.993599i	$-0.536034\pi$
$281$	−3.78720	−0.225925	−0.112963	+	0.993599i	$0.536034\pi$
$282$	−23.7663	−1.41526
$283$	−19.6833	−1.17005	−0.585025	−	0.811015i	$-0.698915\pi$
$283$	−19.6833	−1.17005	−0.585025	+	0.811015i	$0.698915\pi$
$284$	15.9320	0.945393
$285$	9.62618	0.570206
$286$	−29.4946	−1.74405
$287$	−37.0938	−2.18958
$288$	3.24955	0.191482
$289$	1.00000	0.0588235
$290$	−36.0253	−2.11548
$291$	3.40745	0.199748
$292$	1.76819	0.103475
$293$	−5.42312	−0.316822	−0.158411	−	0.987373i	$-0.550637\pi$
$293$	−5.42312	−0.316822	−0.158411	+	0.987373i	$0.550637\pi$
$294$	48.2159	2.81201
$295$	−7.23943	−0.421496
$296$	13.9654	0.811724
$297$	2.69830	0.156571
$298$	16.2633	0.942109
$299$	6.05082	0.349928
$300$	−4.00560	−0.231263
$301$	24.1732	1.39332
$302$	−25.4196	−1.46273
$303$	−12.9375	−0.743238
$304$	7.29475	0.418383
$305$	15.9865	0.915387
$306$	−2.37098	−0.135540
$307$	11.6524	0.665039	0.332520	−	0.943096i	$-0.392101\pi$
$307$	11.6524	0.665039	0.332520	+	0.943096i	$0.392101\pi$
$308$	−51.0919	−2.91123
$309$	−15.3394	−0.872630
$310$	−38.8538	−2.20675
$311$	6.91745	0.392252	0.196126	−	0.980579i	$-0.437164\pi$
$311$	6.91745	0.392252	0.196126	+	0.980579i	$0.437164\pi$
$312$	−17.7249	−1.00348
$313$	7.62009	0.430713	0.215357	−	0.976535i	$-0.430909\pi$
$313$	7.62009	0.430713	0.215357	+	0.976535i	$0.430909\pi$
$314$	2.37098	0.133802
$315$	−12.9195	−0.727932
$316$	−9.32942	−0.524821
$317$	−17.2337	−0.967940	−0.483970	−	0.875085i	$-0.660806\pi$
$317$	−17.2337	−0.967940	−0.483970	+	0.875085i	$0.660806\pi$
$318$	−14.6851	−0.823497
$319$	16.5917	0.928956
$320$	28.2928	1.58162
$321$	−10.4852	−0.585225
$322$	16.2699	0.906685
$323$	3.89560	0.216757
$324$	3.62156	0.201198
$325$	−5.09913	−0.282849
$326$	−28.3100	−1.56795
$327$	0.790168	0.0436964
$328$	27.2769	1.50612
$329$	−52.4082	−2.88936
$330$	15.8088	0.870246
$331$	−3.41851	−0.187898	−0.0939492	−	0.995577i	$-0.529949\pi$
$331$	−3.41851	−0.187898	−0.0939492	+	0.995577i	$0.529949\pi$
$332$	−10.7107	−0.587828
$333$	−3.63240	−0.199054
$334$	26.8873	1.47121
$335$	27.7959	1.51865
$336$	−9.79045	−0.534113
$337$	8.67559	0.472589	0.236295	−	0.971681i	$-0.424067\pi$
$337$	8.67559	0.472589	0.236295	+	0.971681i	$0.424067\pi$
$338$	−19.5710	−1.06452
$339$	14.4514	0.784891
$340$	−8.94902	−0.485329
$341$	17.8944	0.969035
$342$	−9.23639	−0.499447
$343$	69.7247	3.76478
$344$	−17.7758	−0.958405
$345$	−3.24317	−0.174606
$346$	54.1249	2.90977
$347$	36.6289	1.96634	0.983172	−	0.182684i	$-0.0584784\pi$
$347$	36.6289	1.96634	0.983172	+	0.182684i	$0.0584784\pi$
$348$	22.2687	1.19373
$349$	0.392277	0.0209981	0.0104991	−	0.999945i	$-0.496658\pi$
$349$	0.392277	0.0209981	0.0104991	+	0.999945i	$0.496658\pi$
$350$	−13.7109	−0.732879
$351$	4.61025	0.246077
$352$	−8.76828	−0.467351
$353$	10.1166	0.538453	0.269227	−	0.963077i	$-0.413232\pi$
$353$	10.1166	0.538453	0.269227	+	0.963077i	$0.413232\pi$
$354$	6.94629	0.369191
$355$	−10.8707	−0.576955
$356$	42.4229	2.24841
$357$	−5.22837	−0.276715
$358$	−52.8281	−2.79205
$359$	13.6110	0.718362	0.359181	−	0.933268i	$-0.383056\pi$
$359$	13.6110	0.718362	0.359181	+	0.933268i	$0.383056\pi$
$360$	9.50037	0.500714
$361$	−3.82432	−0.201280
$362$	20.2085	1.06214
$363$	3.71916	0.195205
$364$	−87.2943	−4.57546
$365$	−1.20646	−0.0631490
$366$	−15.3392	−0.801794
$367$	−5.45469	−0.284732	−0.142366	−	0.989814i	$-0.545471\pi$
$367$	−5.45469	−0.284732	−0.142366	+	0.989814i	$0.545471\pi$
$368$	−2.45769	−0.128116
$369$	−7.09471	−0.369336
$370$	−21.2815	−1.10637
$371$	−32.3827	−1.68123
$372$	24.0171	1.24523
$373$	20.4238	1.05751	0.528753	−	0.848776i	$-0.322660\pi$
$373$	20.4238	1.05751	0.528753	+	0.848776i	$0.322660\pi$
$374$	6.39763	0.330814
$375$	−9.62213	−0.496885
$376$	38.5384	1.98747
$377$	28.3481	1.46000
$378$	12.3964	0.637600
$379$	−2.81061	−0.144371	−0.0721857	−	0.997391i	$-0.522997\pi$
$379$	−2.81061	−0.144371	−0.0721857	+	0.997391i	$0.522997\pi$
$380$	−34.8618	−1.78837
$381$	−7.69943	−0.394454
$382$	40.0505	2.04916
$383$	−3.61760	−0.184851	−0.0924253	−	0.995720i	$-0.529462\pi$
$383$	−3.61760	−0.184851	−0.0924253	+	0.995720i	$0.529462\pi$
$384$	−20.6481	−1.05369
$385$	34.8608	1.77667
$386$	−43.6954	−2.22404
$387$	4.62347	0.235024
$388$	−12.3403	−0.626483
$389$	−33.0758	−1.67701	−0.838504	−	0.544896i	$-0.816569\pi$
$389$	−33.0758	−1.67701	−0.838504	+	0.544896i	$0.816569\pi$
$390$	27.0105	1.36773
$391$	−1.31247	−0.0663746
$392$	−78.1849	−3.94893
$393$	6.33756	0.319688
$394$	11.9027	0.599649
$395$	6.36560	0.320288
$396$	−9.77206	−0.491064
$397$	−12.0119	−0.602858	−0.301429	−	0.953489i	$-0.597464\pi$
$397$	−12.0119	−0.602858	−0.301429	+	0.953489i	$0.597464\pi$
$398$	5.30758	0.266045
$399$	−20.3676	−1.01966
$400$	2.07114	0.103557
$401$	4.09414	0.204451	0.102226	−	0.994761i	$-0.467404\pi$
$401$	4.09414	0.204451	0.102226	+	0.994761i	$0.467404\pi$
$402$	−26.6704	−1.33020
$403$	30.5738	1.52299
$404$	46.8538	2.33106
$405$	−2.47104	−0.122787
$406$	76.2245	3.78296
$407$	9.80131	0.485833
$408$	3.84468	0.190340
$409$	−28.8685	−1.42746	−0.713728	−	0.700423i	$-0.752995\pi$
$409$	−28.8685	−1.42746	−0.713728	+	0.700423i	$0.752995\pi$
$410$	−41.5664	−2.05282
$411$	−21.4514	−1.05812
$412$	55.5526	2.73688
$413$	15.3176	0.753729
$414$	3.11185	0.152939
$415$	7.30809	0.358740
$416$	−14.9812	−0.734516
$417$	−20.5715	−1.00739
$418$	24.9226	1.21900
$419$	−3.10891	−0.151880	−0.0759402	−	0.997112i	$-0.524196\pi$
$419$	−3.10891	−0.151880	−0.0759402	+	0.997112i	$0.524196\pi$
$420$	46.7888	2.28306
$421$	−13.0424	−0.635647	−0.317824	−	0.948150i	$-0.602952\pi$
$421$	−13.0424	−0.635647	−0.317824	+	0.948150i	$0.602952\pi$
$422$	−34.9973	−1.70364
$423$	−10.0238	−0.487375
$424$	23.8127	1.15644
$425$	1.10604	0.0536510
$426$	10.4305	0.505358
$427$	−33.8253	−1.63692
$428$	37.9726	1.83548
$429$	−12.4398	−0.600601
$430$	27.0879	1.30630
$431$	23.4130	1.12777	0.563883	−	0.825855i	$-0.309307\pi$
$431$	23.4130	1.12777	0.563883	+	0.825855i	$0.309307\pi$
$432$	−1.87256	−0.0900938
$433$	39.3613	1.89158	0.945792	−	0.324772i	$-0.105288\pi$
$433$	39.3613	1.89158	0.945792	+	0.324772i	$0.105288\pi$
$434$	82.2092	3.94617
$435$	−15.1943	−0.728510
$436$	−2.86164	−0.137048
$437$	−5.11286	−0.244581
$438$	1.15761	0.0553126
$439$	−1.79667	−0.0857506	−0.0428753	−	0.999080i	$-0.513652\pi$
$439$	−1.79667	−0.0857506	−0.0428753	+	0.999080i	$0.513652\pi$
$440$	−25.6349	−1.22210
$441$	20.3358	0.968373
$442$	10.9308	0.519926
$443$	−1.79144	−0.0851138	−0.0425569	−	0.999094i	$-0.513550\pi$
$443$	−1.79144	−0.0851138	−0.0425569	+	0.999094i	$0.513550\pi$
$444$	13.1549	0.624306
$445$	−28.9458	−1.37216
$446$	15.3458	0.726642
$447$	6.85932	0.324434
$448$	−59.8636	−2.82829
$449$	12.7484	0.601632	0.300816	−	0.953682i	$-0.402741\pi$
$449$	12.7484	0.601632	0.300816	+	0.953682i	$0.402741\pi$
$450$	−2.62241	−0.123622
$451$	19.1437	0.901440
$452$	−52.3365	−2.46170
$453$	−10.7211	−0.503722
$454$	24.5466	1.15203
$455$	59.5621	2.79232
$456$	14.9773	0.701378
$457$	−15.1845	−0.710300	−0.355150	−	0.934809i	$-0.615570\pi$
$457$	−15.1845	−0.710300	−0.355150	+	0.934809i	$0.615570\pi$
$458$	67.5921	3.15837
$459$	−1.00000	−0.0466760
$460$	11.7453	0.547629
$461$	10.2843	0.478987	0.239493	−	0.970898i	$-0.423019\pi$
$461$	10.2843	0.478987	0.239493	+	0.970898i	$0.423019\pi$
$462$	−33.4492	−1.55620
$463$	−28.9102	−1.34357	−0.671786	−	0.740745i	$-0.734473\pi$
$463$	−28.9102	−1.34357	−0.671786	+	0.740745i	$0.734473\pi$
$464$	−11.5143	−0.534537
$465$	−16.3872	−0.759940
$466$	−5.87159	−0.271996
$467$	31.6556	1.46485	0.732424	−	0.680849i	$-0.238389\pi$
$467$	31.6556	1.46485	0.732424	+	0.680849i	$0.238389\pi$
$468$	−16.6963	−0.771785
$469$	−58.8121	−2.71569
$470$	−58.7275	−2.70890
$471$	1.00000	0.0460776
$472$	−11.2638	−0.518458
$473$	−12.4755	−0.573625
$474$	−6.10784	−0.280542
$475$	4.30870	0.197697
$476$	18.9348	0.867877
$477$	−6.19366	−0.283588
$478$	−51.0408	−2.33455
$479$	17.1393	0.783115	0.391558	−	0.920154i	$-0.371936\pi$
$479$	17.1393	0.783115	0.391558	+	0.920154i	$0.371936\pi$
$480$	8.02978	0.366508
$481$	16.7462	0.763563
$482$	37.5408	1.70994
$483$	6.86209	0.312236
$484$	−13.4692	−0.612234
$485$	8.41995	0.382330
$486$	2.37098	0.107550
$487$	40.0408	1.81442	0.907210	−	0.420678i	$-0.138208\pi$
$487$	40.0408	1.81442	0.907210	+	0.420678i	$0.138208\pi$
$488$	24.8734	1.12597
$489$	−11.9402	−0.539955
$490$	119.144	5.38236
$491$	16.8237	0.759244	0.379622	−	0.925142i	$-0.376054\pi$
$491$	16.8237	0.759244	0.379622	+	0.925142i	$0.376054\pi$
$492$	25.6939	1.15837
$493$	−6.14894	−0.276934
$494$	42.5820	1.91586
$495$	6.66762	0.299687
$496$	−12.4183	−0.557598
$497$	23.0008	1.03173
$498$	−7.01216	−0.314223
$499$	−18.0131	−0.806376	−0.403188	−	0.915117i	$-0.632098\pi$
$499$	−18.0131	−0.806376	−0.403188	+	0.915117i	$0.632098\pi$
$500$	34.8471	1.55841
$501$	11.3402	0.506641
$502$	−41.0508	−1.83219
$503$	27.5885	1.23011	0.615055	−	0.788485i	$-0.289134\pi$
$503$	27.5885	1.23011	0.615055	+	0.788485i	$0.289134\pi$
$504$	−20.1014	−0.895389
$505$	−31.9690	−1.42260
$506$	−8.39671	−0.373279
$507$	−8.25437	−0.366589
$508$	27.8839	1.23715
$509$	16.1843	0.717354	0.358677	−	0.933462i	$-0.383228\pi$
$509$	16.1843	0.717354	0.358677	+	0.933462i	$0.383228\pi$
$510$	−5.85879	−0.259432
$511$	2.55269	0.112925
$512$	20.4838	0.905266
$513$	−3.89560	−0.171995
$514$	−2.24092	−0.0988428
$515$	−37.9044	−1.67027
$516$	−16.7442	−0.737120
$517$	27.0473	1.18954
$518$	45.0285	1.97844
$519$	22.8280	1.00204
$520$	−43.7990	−1.92072
$521$	−1.87747	−0.0822534	−0.0411267	−	0.999154i	$-0.513095\pi$
$521$	−1.87747	−0.0822534	−0.0411267	+	0.999154i	$0.513095\pi$
$522$	14.5790	0.638106
$523$	−5.56844	−0.243491	−0.121746	−	0.992561i	$-0.538849\pi$
$523$	−5.56844	−0.243491	−0.121746	+	0.992561i	$0.538849\pi$
$524$	−22.9518	−1.00266
$525$	−5.78280	−0.252382
$526$	−47.5399	−2.07284
$527$	−6.63171	−0.288882
$528$	5.05274	0.219892
$529$	−21.2774	−0.925105
$530$	−36.2874	−1.57622
$531$	2.92971	0.127138
$532$	73.7625	3.19801
$533$	32.7084	1.41676
$534$	27.7737	1.20188
$535$	−25.9093	−1.12016
$536$	43.2475	1.86801
$537$	−22.2811	−0.961501
$538$	59.3273	2.55778
$539$	−54.8723	−2.36352
$540$	8.94902	0.385104
$541$	14.1546	0.608556	0.304278	−	0.952583i	$-0.401585\pi$
$541$	14.1546	0.608556	0.304278	+	0.952583i	$0.401585\pi$
$542$	28.6484	1.23055
$543$	8.52326	0.365768
$544$	3.24955	0.139323
$545$	1.95254	0.0836375
$546$	−57.1503	−2.44581
$547$	−37.4452	−1.60104	−0.800521	−	0.599305i	$-0.795444\pi$
$547$	−37.4452	−1.60104	−0.800521	+	0.599305i	$0.795444\pi$
$548$	77.6876	3.31865
$549$	−6.46956	−0.276114
$550$	7.07605	0.301724
$551$	−23.9538	−1.02047
$552$	−5.04604	−0.214774
$553$	−13.4687	−0.572747
$554$	28.4282	1.20780
$555$	−8.97580	−0.381002
$556$	74.5009	3.15954
$557$	−2.38070	−0.100873	−0.0504367	−	0.998727i	$-0.516061\pi$
$557$	−2.38070	−0.100873	−0.0504367	+	0.998727i	$0.516061\pi$
$558$	15.7237	0.665636
$559$	−21.3153	−0.901542
$560$	−24.1926	−1.02232
$561$	2.69830	0.113922
$562$	8.97937	0.378772
$563$	39.6280	1.67012	0.835060	−	0.550159i	$-0.185433\pi$
$563$	39.6280	1.67012	0.835060	+	0.550159i	$0.185433\pi$
$564$	36.3018	1.52858
$565$	35.7099	1.50233
$566$	46.6687	1.96163
$567$	5.22837	0.219571
$568$	−16.9136	−0.709680
$569$	12.5126	0.524556	0.262278	−	0.964992i	$-0.415526\pi$
$569$	12.5126	0.524556	0.262278	+	0.964992i	$0.415526\pi$
$570$	−22.8235	−0.955971
$571$	−41.6648	−1.74362	−0.871809	−	0.489846i	$-0.837053\pi$
$571$	−41.6648	−1.74362	−0.871809	+	0.489846i	$0.837053\pi$
$572$	45.0516	1.88370
$573$	16.8920	0.705672
$574$	87.9486	3.67091
$575$	−1.45165	−0.0605380
$576$	−11.4498	−0.477073
$577$	24.6149	1.02473	0.512366	−	0.858767i	$-0.328769\pi$
$577$	24.6149	1.02473	0.512366	+	0.858767i	$0.328769\pi$
$578$	−2.37098	−0.0986199
$579$	−18.4292	−0.765893
$580$	55.0269	2.28487
$581$	−15.4629	−0.641508
$582$	−8.07901	−0.334886
$583$	16.7124	0.692155
$584$	−1.87713	−0.0776760
$585$	11.3921	0.471006
$586$	12.8581	0.531164
$587$	27.3401	1.12845	0.564223	−	0.825622i	$-0.309176\pi$
$587$	27.3401	1.12845	0.564223	+	0.825622i	$0.309176\pi$
$588$	−73.6474	−3.03717
$589$	−25.8345	−1.06449
$590$	17.1646	0.706654
$591$	5.02015	0.206501
$592$	−6.80190	−0.279556
$593$	34.9444	1.43499	0.717497	−	0.696562i	$-0.245288\pi$
$593$	34.9444	1.43499	0.717497	+	0.696562i	$0.245288\pi$
$594$	−6.39763	−0.262498
$595$	−12.9195	−0.529648
$596$	−24.8414	−1.01754
$597$	2.23856	0.0916181
$598$	−14.3464	−0.586667
$599$	−15.9735	−0.652658	−0.326329	−	0.945256i	$-0.605812\pi$
$599$	−15.9735	−0.652658	−0.326329	+	0.945256i	$0.605812\pi$
$600$	4.25239	0.173603
$601$	−17.4472	−0.711686	−0.355843	−	0.934546i	$-0.615806\pi$
$601$	−17.4472	−0.711686	−0.355843	+	0.934546i	$0.615806\pi$
$602$	−57.3142	−2.33595
$603$	−11.2487	−0.458081
$604$	38.8271	1.57985
$605$	9.19020	0.373635
$606$	30.6745	1.24607
$607$	43.8396	1.77939	0.889697	−	0.456551i	$-0.150915\pi$
$607$	43.8396	1.77939	0.889697	+	0.456551i	$0.150915\pi$
$608$	12.6589	0.513388
$609$	32.1489	1.30274
$610$	−37.9038	−1.53468
$611$	46.2122	1.86955
$612$	3.62156	0.146393
$613$	18.4040	0.743332	0.371666	−	0.928367i	$-0.378787\pi$
$613$	18.4040	0.743332	0.371666	+	0.928367i	$0.378787\pi$
$614$	−27.6277	−1.11496
$615$	−17.5313	−0.706931
$616$	54.2397	2.18538
$617$	−20.7757	−0.836399	−0.418200	−	0.908355i	$-0.637339\pi$
$617$	−20.7757	−0.836399	−0.418200	+	0.908355i	$0.637339\pi$
$618$	36.3695	1.46300
$619$	22.0025	0.884354	0.442177	−	0.896928i	$-0.354206\pi$
$619$	22.0025	0.884354	0.442177	+	0.896928i	$0.354206\pi$
$620$	59.3473	2.38345
$621$	1.31247	0.0526677
$622$	−16.4011	−0.657626
$623$	61.2451	2.45373
$624$	8.63298	0.345596
$625$	−29.3069	−1.17228
$626$	−18.0671	−0.722107
$627$	10.5115	0.419789
$628$	−3.62156	−0.144516
$629$	−3.63240	−0.144833
$630$	30.6319	1.22041
$631$	−12.4476	−0.495532	−0.247766	−	0.968820i	$-0.579696\pi$
$631$	−12.4476	−0.495532	−0.247766	+	0.968820i	$0.579696\pi$
$632$	9.90422	0.393969
$633$	−14.7607	−0.586683
$634$	40.8608	1.62279
$635$	−19.0256	−0.755008
$636$	22.4307	0.889435
$637$	−93.7532	−3.71464
$638$	−39.3386	−1.55743
$639$	4.39922	0.174031
$640$	−51.0222	−2.01683
$641$	35.9584	1.42027	0.710135	−	0.704065i	$-0.248634\pi$
$641$	35.9584	1.42027	0.710135	+	0.704065i	$0.248634\pi$
$642$	24.8601	0.981152
$643$	27.8508	1.09833	0.549163	−	0.835715i	$-0.314947\pi$
$643$	27.8508	1.09833	0.549163	+	0.835715i	$0.314947\pi$
$644$	−24.8514	−0.979284
$645$	11.4248	0.449850
$646$	−9.23639	−0.363401
$647$	−39.8037	−1.56484	−0.782422	−	0.622748i	$-0.786016\pi$
$647$	−39.8037	−1.56484	−0.782422	+	0.622748i	$0.786016\pi$
$648$	−3.84468	−0.151033
$649$	−7.90524	−0.310308
$650$	12.0899	0.474207
$651$	34.6730	1.35894
$652$	43.2422	1.69349
$653$	−8.51179	−0.333092	−0.166546	−	0.986034i	$-0.553261\pi$
$653$	−8.51179	−0.333092	−0.166546	+	0.986034i	$0.553261\pi$
$654$	−1.87347	−0.0732586
$655$	15.6604	0.611901
$656$	−13.2853	−0.518704
$657$	0.488239	0.0190480
$658$	124.259	4.84412
$659$	−11.1397	−0.433943	−0.216971	−	0.976178i	$-0.569618\pi$
$659$	−11.1397	−0.433943	−0.216971	+	0.976178i	$0.569618\pi$
$660$	−24.1472	−0.939927
$661$	−19.7188	−0.766974	−0.383487	−	0.923546i	$-0.625277\pi$
$661$	−19.7188	−0.766974	−0.383487	+	0.923546i	$0.625277\pi$
$662$	8.10523	0.315019
$663$	4.61025	0.179047
$664$	11.3706	0.441266
$665$	−50.3292	−1.95168
$666$	8.61235	0.333722
$667$	8.07030	0.312483
$668$	−41.0690	−1.58901
$669$	6.47232	0.250234
$670$	−65.9036	−2.54608
$671$	17.4568	0.673914
$672$	−16.9899	−0.655398
$673$	−14.4367	−0.556494	−0.278247	−	0.960510i	$-0.589753\pi$
$673$	−14.4367	−0.556494	−0.278247	+	0.960510i	$0.589753\pi$
$674$	−20.5697	−0.792314
$675$	−1.10604	−0.0425716
$676$	29.8937	1.14976
$677$	−41.6253	−1.59979	−0.799894	−	0.600141i	$-0.795111\pi$
$677$	−41.6253	−1.59979	−0.799894	+	0.600141i	$0.795111\pi$
$678$	−34.2640	−1.31590
$679$	−17.8154	−0.683693
$680$	9.50037	0.364323
$681$	10.3529	0.396725
$682$	−42.4272	−1.62462
$683$	−35.9057	−1.37389	−0.686947	−	0.726708i	$-0.741049\pi$
$683$	−35.9057	−1.37389	−0.686947	+	0.726708i	$0.741049\pi$
$684$	14.1081	0.539438
$685$	−53.0074	−2.02531
$686$	−165.316	−6.31180
$687$	28.5081	1.08765
$688$	8.65774	0.330073
$689$	28.5543	1.08783
$690$	7.68950	0.292734
$691$	−28.0004	−1.06519	−0.532593	−	0.846372i	$-0.678782\pi$
$691$	−28.0004	−1.06519	−0.532593	+	0.846372i	$0.678782\pi$
$692$	−82.6730	−3.14276
$693$	−14.1077	−0.535908
$694$	−86.8465	−3.29665
$695$	−50.8330	−1.92821
$696$	−23.6407	−0.896099
$697$	−7.09471	−0.268731
$698$	−0.930082	−0.0352041
$699$	−2.47644	−0.0936674
$700$	20.9427	0.791561
$701$	20.1014	0.759218	0.379609	−	0.925147i	$-0.376059\pi$
$701$	20.1014	0.759218	0.379609	+	0.925147i	$0.376059\pi$
$702$	−10.9308	−0.412557
$703$	−14.1504	−0.533691
$704$	30.8949	1.16440
$705$	−24.7693	−0.932864
$706$	−23.9863	−0.902737
$707$	67.6418	2.54393
$708$	−10.6101	−0.398752
$709$	9.96787	0.374351	0.187176	−	0.982326i	$-0.440067\pi$
$709$	9.96787	0.374351	0.187176	+	0.982326i	$0.440067\pi$
$710$	25.7741	0.967286
$711$	−2.57608	−0.0966106
$712$	−45.0366	−1.68782
$713$	8.70394	0.325965
$714$	12.3964	0.463923
$715$	−30.7394	−1.14959
$716$	80.6923	3.01561
$717$	−21.5273	−0.803952
$718$	−32.2715	−1.20436
$719$	16.6736	0.621821	0.310911	−	0.950439i	$-0.399366\pi$
$719$	16.6736	0.621821	0.310911	+	0.950439i	$0.399366\pi$
$720$	−4.62718	−0.172445
$721$	80.2002	2.98681
$722$	9.06740	0.337454
$723$	15.8335	0.588852
$724$	−30.8675	−1.14718
$725$	−6.80099	−0.252582
$726$	−8.81806	−0.327269
$727$	19.3536	0.717785	0.358893	−	0.933379i	$-0.383154\pi$
$727$	19.3536	0.717785	0.358893	+	0.933379i	$0.383154\pi$
$728$	92.6725	3.43467
$729$	1.00000	0.0370370
$730$	2.86049	0.105872
$731$	4.62347	0.171005
$732$	23.4299	0.865994
$733$	37.6818	1.39181	0.695904	−	0.718135i	$-0.255004\pi$
$733$	37.6818	1.39181	0.695904	+	0.718135i	$0.255004\pi$
$734$	12.9330	0.477365
$735$	50.2507	1.85352
$736$	−4.26495	−0.157208
$737$	30.3523	1.11804
$738$	16.8214	0.619205
$739$	−35.0246	−1.28840	−0.644201	−	0.764856i	$-0.722810\pi$
$739$	−35.0246	−1.28840	−0.644201	+	0.764856i	$0.722810\pi$
$740$	32.5064	1.19496
$741$	17.9597	0.659765
$742$	76.7789	2.81864
$743$	10.7145	0.393076	0.196538	−	0.980496i	$-0.437030\pi$
$743$	10.7145	0.393076	0.196538	+	0.980496i	$0.437030\pi$
$744$	−25.4968	−0.934760
$745$	16.9496	0.620987
$746$	−48.4245	−1.77295
$747$	−2.95749	−0.108209
$748$	−9.77206	−0.357302
$749$	54.8203	2.00309
$750$	22.8139	0.833046
$751$	8.76531	0.319851	0.159925	−	0.987129i	$-0.448875\pi$
$751$	8.76531	0.319851	0.159925	+	0.987129i	$0.448875\pi$
$752$	−18.7702	−0.684480
$753$	−17.3138	−0.630951
$754$	−67.2129	−2.44775
$755$	−26.4923	−0.964153
$756$	−18.9348	−0.688653
$757$	7.09252	0.257782	0.128891	−	0.991659i	$-0.458858\pi$
$757$	7.09252	0.257782	0.128891	+	0.991659i	$0.458858\pi$
$758$	6.66391	0.242044
$759$	−3.54145	−0.128546
$760$	37.0096	1.34248
$761$	19.7331	0.715326	0.357663	−	0.933851i	$-0.383574\pi$
$761$	19.7331	0.715326	0.357663	+	0.933851i	$0.383574\pi$
$762$	18.2552	0.661316
$763$	−4.13129	−0.149563
$764$	−61.1752	−2.21324
$765$	−2.47104	−0.0893407
$766$	8.57726	0.309909
$767$	−13.5067	−0.487698
$768$	26.0567	0.940240
$769$	45.2567	1.63200	0.815999	−	0.578053i	$-0.196187\pi$
$769$	45.2567	1.63200	0.815999	+	0.578053i	$0.196187\pi$
$770$	−82.6543	−2.97865
$771$	−0.945145	−0.0340386
$772$	66.7426	2.40212
$773$	−52.8290	−1.90013	−0.950063	−	0.312058i	$-0.898982\pi$
$773$	−52.8290	−1.90013	−0.950063	+	0.312058i	$0.898982\pi$
$774$	−10.9622	−0.394027
$775$	−7.33496	−0.263480
$776$	13.1006	0.470283
$777$	18.9915	0.681317
$778$	78.4220	2.81157
$779$	−27.6381	−0.990239
$780$	−41.2572	−1.47724
$781$	−11.8704	−0.424758
$782$	3.11185	0.111279
$783$	6.14894	0.219745
$784$	38.0802	1.36001
$785$	2.47104	0.0881952
$786$	−15.0262	−0.535968
$787$	52.4223	1.86865	0.934327	−	0.356417i	$-0.116002\pi$
$787$	52.4223	1.86865	0.934327	+	0.356417i	$0.116002\pi$
$788$	−18.1808	−0.647663
$789$	−20.0507	−0.713824
$790$	−15.0927	−0.536975
$791$	−75.5571	−2.68650
$792$	10.3741	0.368628
$793$	29.8263	1.05916
$794$	28.4799	1.01071
$795$	−15.3048	−0.542805
$796$	−8.10707	−0.287347
$797$	−45.7120	−1.61920	−0.809601	−	0.586980i	$-0.800317\pi$
$797$	−45.7120	−1.61920	−0.809601	+	0.586980i	$0.800317\pi$
$798$	48.2913	1.70949
$799$	−10.0238	−0.354617
$800$	3.59415	0.127072
$801$	11.7140	0.413894
$802$	−9.70713	−0.342771
$803$	−1.31742	−0.0464907
$804$	40.7377	1.43671
$805$	16.9565	0.597638
$806$	−72.4900	−2.55335
$807$	25.0222	0.880825
$808$	−49.7405	−1.74986
$809$	−14.0152	−0.492749	−0.246375	−	0.969175i	$-0.579239\pi$
$809$	−14.0152	−0.492749	−0.246375	+	0.969175i	$0.579239\pi$
$810$	5.85879	0.205857
$811$	−14.6650	−0.514957	−0.257478	−	0.966284i	$-0.582892\pi$
$811$	−14.6650	−0.514957	−0.257478	+	0.966284i	$0.582892\pi$
$812$	−116.429	−4.08586
$813$	12.0829	0.423767
$814$	−23.2387	−0.814517
$815$	−29.5047	−1.03351
$816$	−1.87256	−0.0655528
$817$	18.0112	0.630131
$818$	68.4467	2.39318
$819$	−24.1041	−0.842264
$820$	63.4907	2.21719
$821$	10.7239	0.374267	0.187134	−	0.982334i	$-0.440080\pi$
$821$	10.7239	0.374267	0.187134	+	0.982334i	$0.440080\pi$
$822$	50.8610	1.77398
$823$	47.2063	1.64551	0.822754	−	0.568397i	$-0.192436\pi$
$823$	47.2063	1.64551	0.822754	+	0.568397i	$0.192436\pi$
$824$	−58.9753	−2.05450
$825$	2.98444	0.103905
$826$	−36.3177	−1.26366
$827$	−12.1829	−0.423639	−0.211820	−	0.977309i	$-0.567939\pi$
$827$	−12.1829	−0.423639	−0.211820	+	0.977309i	$0.567939\pi$
$828$	−4.75319	−0.165185
$829$	8.53163	0.296316	0.148158	−	0.988964i	$-0.452666\pi$
$829$	8.53163	0.296316	0.148158	+	0.988964i	$0.452666\pi$
$830$	−17.3273	−0.601441
$831$	11.9900	0.415930
$832$	52.7862	1.83003
$833$	20.3358	0.704595
$834$	48.7747	1.68893
$835$	28.0220	0.969741
$836$	−38.0680	−1.31661
$837$	6.63171	0.229226
$838$	7.37118	0.254633
$839$	4.13492	0.142753	0.0713766	−	0.997449i	$-0.477261\pi$
$839$	4.13492	0.142753	0.0713766	+	0.997449i	$0.477261\pi$
$840$	−49.6714	−1.71383
$841$	8.80941	0.303773
$842$	30.9233	1.06569
$843$	3.78720	0.130438
$844$	53.4566	1.84005
$845$	−20.3969	−0.701674
$846$	23.7663	0.817102
$847$	−19.4451	−0.668143
$848$	−11.5980	−0.398278
$849$	19.6833	0.675529
$850$	−2.62241	−0.0899479
$851$	4.76742	0.163425
$852$	−15.9320	−0.545823
$853$	29.1229	0.997147	0.498574	−	0.866847i	$-0.333857\pi$
$853$	29.1229	0.997147	0.498574	+	0.866847i	$0.333857\pi$
$854$	80.1991	2.74436
$855$	−9.62618	−0.329208
$856$	−40.3122	−1.37784
$857$	−21.2480	−0.725818	−0.362909	−	0.931825i	$-0.618216\pi$
$857$	−21.2480	−0.725818	−0.362909	+	0.931825i	$0.618216\pi$
$858$	29.4946	1.00693
$859$	42.9267	1.46464	0.732321	−	0.680960i	$-0.238437\pi$
$859$	42.9267	1.46464	0.732321	+	0.680960i	$0.238437\pi$
$860$	−41.3755	−1.41089
$861$	37.0938	1.26415
$862$	−55.5119	−1.89074
$863$	42.7711	1.45594	0.727972	−	0.685606i	$-0.240463\pi$
$863$	42.7711	1.45594	0.727972	+	0.685606i	$0.240463\pi$
$864$	−3.24955	−0.110552
$865$	56.4090	1.91796
$866$	−93.3250	−3.17131
$867$	−1.00000	−0.0339618
$868$	−125.570	−4.26214
$869$	6.95105	0.235798
$870$	36.0253	1.22137
$871$	51.8591	1.75718
$872$	3.03794	0.102878
$873$	−3.40745	−0.115325
$874$	12.1225	0.410050
$875$	50.3080	1.70072
$876$	−1.76819	−0.0597415
$877$	3.09226	0.104418	0.0522091	−	0.998636i	$-0.483374\pi$
$877$	3.09226	0.104418	0.0522091	+	0.998636i	$0.483374\pi$
$878$	4.25988	0.143764
$879$	5.42312	0.182917
$880$	12.4855	0.420887
$881$	22.0756	0.743746	0.371873	−	0.928284i	$-0.378716\pi$
$881$	22.0756	0.743746	0.371873	+	0.928284i	$0.378716\pi$
$882$	−48.2159	−1.62351
$883$	0.933810	0.0314252	0.0157126	−	0.999877i	$-0.494998\pi$
$883$	0.933810	0.0314252	0.0157126	+	0.999877i	$0.494998\pi$
$884$	−16.6963	−0.561556
$885$	7.23943	0.243351
$886$	4.24747	0.142696
$887$	57.1959	1.92045	0.960226	−	0.279224i	$-0.0900773\pi$
$887$	57.1959	1.92045	0.960226	+	0.279224i	$0.0900773\pi$
$888$	−13.9654	−0.468649
$889$	40.2555	1.35012
$890$	68.6299	2.30048
$891$	−2.69830	−0.0903966
$892$	−23.4399	−0.784825
$893$	−39.0487	−1.30672
$894$	−16.2633	−0.543927
$895$	−55.0575	−1.84037
$896$	107.956	3.60655
$897$	−6.05082	−0.202031
$898$	−30.2261	−1.00866
$899$	40.7780	1.36002
$900$	4.00560	0.133520
$901$	−6.19366	−0.206341
$902$	−45.3893	−1.51130
$903$	−24.1732	−0.804434
$904$	55.5610	1.84793
$905$	21.0613	0.700102
$906$	25.4196	0.844508
$907$	47.0996	1.56392	0.781958	−	0.623331i	$-0.214221\pi$
$907$	47.0996	1.56392	0.781958	+	0.623331i	$0.214221\pi$
$908$	−37.4938	−1.24427
$909$	12.9375	0.429109
$910$	−141.221	−4.68142
$911$	−13.6451	−0.452083	−0.226041	−	0.974118i	$-0.572578\pi$
$911$	−13.6451	−0.452083	−0.226041	+	0.974118i	$0.572578\pi$
$912$	−7.29475	−0.241553
$913$	7.98021	0.264106
$914$	36.0021	1.19085
$915$	−15.9865	−0.528499
$916$	−103.244	−3.41127
$917$	−33.1351	−1.09422
$918$	2.37098	0.0782541
$919$	10.4768	0.345599	0.172799	−	0.984957i	$-0.444719\pi$
$919$	10.4768	0.345599	0.172799	+	0.984957i	$0.444719\pi$
$920$	−12.4690	−0.411090
$921$	−11.6524	−0.383961
$922$	−24.3839	−0.803040
$923$	−20.2815	−0.667574
$924$	51.0919	1.68080
$925$	−4.01759	−0.132097
$926$	68.5457	2.25255
$927$	15.3394	0.503813
$928$	−19.9813	−0.655918
$929$	36.3078	1.19122	0.595610	−	0.803274i	$-0.296911\pi$
$929$	36.3078	1.19122	0.595610	+	0.803274i	$0.296911\pi$
$930$	38.8538	1.27407
$931$	79.2202	2.59634
$932$	8.96856	0.293775
$933$	−6.91745	−0.226467
$934$	−75.0549	−2.45587
$935$	6.66762	0.218054
$936$	17.7249	0.579358
$937$	−23.8356	−0.778675	−0.389337	−	0.921095i	$-0.627296\pi$
$937$	−23.8356	−0.778675	−0.389337	+	0.921095i	$0.627296\pi$
$938$	139.443	4.55296
$939$	−7.62009	−0.248672
$940$	89.7033	2.92580
$941$	−55.4565	−1.80783	−0.903915	−	0.427711i	$-0.859320\pi$
$941$	−55.4565	−1.80783	−0.903915	+	0.427711i	$0.859320\pi$
$942$	−2.37098	−0.0772508
$943$	9.31161	0.303228
$944$	5.48606	0.178556
$945$	12.9195	0.420272
$946$	29.5792	0.961704
$947$	0.627943	0.0204054	0.0102027	−	0.999948i	$-0.496752\pi$
$947$	0.627943	0.0204054	0.0102027	+	0.999948i	$0.496752\pi$
$948$	9.32942	0.303006
$949$	−2.25090	−0.0730674
$950$	−10.2158	−0.331446
$951$	17.2337	0.558840
$952$	−20.1014	−0.651491
$953$	25.4306	0.823777	0.411888	−	0.911234i	$-0.364869\pi$
$953$	25.4306	0.823777	0.411888	+	0.911234i	$0.364869\pi$
$954$	14.6851	0.475446
$955$	41.7407	1.35070
$956$	77.9623	2.52148
$957$	−16.5917	−0.536333
$958$	−40.6370	−1.31292
$959$	112.156	3.62171
$960$	−28.2928	−0.913147
$961$	12.9796	0.418697
$962$	−39.7051	−1.28014
$963$	10.4852	0.337880
$964$	−57.3418	−1.84685
$965$	−45.5394	−1.46597
$966$	−16.2699	−0.523475
$967$	−19.8242	−0.637504	−0.318752	−	0.947838i	$-0.603264\pi$
$967$	−19.8242	−0.637504	−0.318752	+	0.947838i	$0.603264\pi$
$968$	14.2990	0.459587
$969$	−3.89560	−0.125145
$970$	−19.9636	−0.640991
$971$	37.3772	1.19949	0.599746	−	0.800191i	$-0.295268\pi$
$971$	37.3772	1.19949	0.599746	+	0.800191i	$0.295268\pi$
$972$	−3.62156	−0.116162
$973$	107.555	3.44807
$974$	−94.9359	−3.04194
$975$	5.09913	0.163303
$976$	−12.1147	−0.387781
$977$	−0.783683	−0.0250723	−0.0125361	−	0.999921i	$-0.503990\pi$
$977$	−0.783683	−0.0250723	−0.0125361	+	0.999921i	$0.503990\pi$
$978$	28.3100	0.905255
$979$	−31.6079	−1.01019
$980$	−181.986	−5.81332
$981$	−0.790168	−0.0252281
$982$	−39.8887	−1.27290
$983$	1.62564	0.0518500	0.0259250	−	0.999664i	$-0.491747\pi$
$983$	1.62564	0.0518500	0.0259250	+	0.999664i	$0.491747\pi$
$984$	−27.2769	−0.869556
$985$	12.4050	0.395256
$986$	14.5790	0.464291
$987$	52.4082	1.66817
$988$	−65.0419	−2.06926
$989$	−6.06817	−0.192957
$990$	−15.8088	−0.502437
$991$	−4.02362	−0.127815	−0.0639073	−	0.997956i	$-0.520356\pi$
$991$	−4.02362	−0.127815	−0.0639073	+	0.997956i	$0.520356\pi$
$992$	−21.5501	−0.684216
$993$	3.41851	0.108483
$994$	−54.5344	−1.72973
$995$	5.53157	0.175363
$996$	10.7107	0.339382
$997$	33.7232	1.06802	0.534012	−	0.845477i	$-0.320684\pi$
$997$	33.7232	1.06802	0.534012	+	0.845477i	$0.320684\pi$
$998$	42.7087	1.35192
$999$	3.63240	0.114924

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.j.1.8	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.j.1.8	✓	64	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)

\(f(q)\)	\(=\)	\(q-2.37098 q^{2} -1.00000 q^{3} +3.62156 q^{4} -2.47104 q^{5} +2.37098 q^{6} +5.22837 q^{7} -3.84468 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.37098 q^{2} -1.00000 q^{3} +3.62156 q^{4} -2.47104 q^{5} +2.37098 q^{6} +5.22837 q^{7} -3.84468 q^{8} +1.00000 q^{9} +5.85879 q^{10} -2.69830 q^{11} -3.62156 q^{12} -4.61025 q^{13} -12.3964 q^{14} +2.47104 q^{15} +1.87256 q^{16} +1.00000 q^{17} -2.37098 q^{18} +3.89560 q^{19} -8.94902 q^{20} -5.22837 q^{21} +6.39763 q^{22} -1.31247 q^{23} +3.84468 q^{24} +1.10604 q^{25} +10.9308 q^{26} -1.00000 q^{27} +18.9348 q^{28} -6.14894 q^{29} -5.85879 q^{30} -6.63171 q^{31} +3.24955 q^{32} +2.69830 q^{33} -2.37098 q^{34} -12.9195 q^{35} +3.62156 q^{36} -3.63240 q^{37} -9.23639 q^{38} +4.61025 q^{39} +9.50037 q^{40} -7.09471 q^{41} +12.3964 q^{42} +4.62347 q^{43} -9.77206 q^{44} -2.47104 q^{45} +3.11185 q^{46} -10.0238 q^{47} -1.87256 q^{48} +20.3358 q^{49} -2.62241 q^{50} -1.00000 q^{51} -16.6963 q^{52} -6.19366 q^{53} +2.37098 q^{54} +6.66762 q^{55} -20.1014 q^{56} -3.89560 q^{57} +14.5790 q^{58} +2.92971 q^{59} +8.94902 q^{60} -6.46956 q^{61} +15.7237 q^{62} +5.22837 q^{63} -11.4498 q^{64} +11.3921 q^{65} -6.39763 q^{66} -11.2487 q^{67} +3.62156 q^{68} +1.31247 q^{69} +30.6319 q^{70} +4.39922 q^{71} -3.84468 q^{72} +0.488239 q^{73} +8.61235 q^{74} -1.10604 q^{75} +14.1081 q^{76} -14.1077 q^{77} -10.9308 q^{78} -2.57608 q^{79} -4.62718 q^{80} +1.00000 q^{81} +16.8214 q^{82} -2.95749 q^{83} -18.9348 q^{84} -2.47104 q^{85} -10.9622 q^{86} +6.14894 q^{87} +10.3741 q^{88} +11.7140 q^{89} +5.85879 q^{90} -24.1041 q^{91} -4.75319 q^{92} +6.63171 q^{93} +23.7663 q^{94} -9.62618 q^{95} -3.24955 q^{96} -3.40745 q^{97} -48.2159 q^{98} -2.69830 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * q^99

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