LMFDB - Embedded newform 8007.2.a.h.1.10

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:	$56$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
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)

$f(q)$	$=$	$q-1.87368 q^{2} +1.00000 q^{3} +1.51068 q^{4} -1.39015 q^{5} -1.87368 q^{6} +0.634123 q^{7} +0.916837 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.87368 q^{2} +1.00000 q^{3} +1.51068 q^{4} -1.39015 q^{5} -1.87368 q^{6} +0.634123 q^{7} +0.916837 q^{8} +1.00000 q^{9} +2.60469 q^{10} -2.45618 q^{11} +1.51068 q^{12} +1.99183 q^{13} -1.18814 q^{14} -1.39015 q^{15} -4.73921 q^{16} -1.00000 q^{17} -1.87368 q^{18} +1.59884 q^{19} -2.10006 q^{20} +0.634123 q^{21} +4.60210 q^{22} +3.23694 q^{23} +0.916837 q^{24} -3.06750 q^{25} -3.73206 q^{26} +1.00000 q^{27} +0.957954 q^{28} -3.89007 q^{29} +2.60469 q^{30} -9.32086 q^{31} +7.04609 q^{32} -2.45618 q^{33} +1.87368 q^{34} -0.881523 q^{35} +1.51068 q^{36} -6.63914 q^{37} -2.99572 q^{38} +1.99183 q^{39} -1.27454 q^{40} +7.34627 q^{41} -1.18814 q^{42} +1.27335 q^{43} -3.71050 q^{44} -1.39015 q^{45} -6.06499 q^{46} +3.36503 q^{47} -4.73921 q^{48} -6.59789 q^{49} +5.74750 q^{50} -1.00000 q^{51} +3.00902 q^{52} +10.2659 q^{53} -1.87368 q^{54} +3.41445 q^{55} +0.581387 q^{56} +1.59884 q^{57} +7.28874 q^{58} +8.71911 q^{59} -2.10006 q^{60} +4.29955 q^{61} +17.4643 q^{62} +0.634123 q^{63} -3.72369 q^{64} -2.76894 q^{65} +4.60210 q^{66} -3.96312 q^{67} -1.51068 q^{68} +3.23694 q^{69} +1.65169 q^{70} -10.4112 q^{71} +0.916837 q^{72} -1.23227 q^{73} +12.4396 q^{74} -3.06750 q^{75} +2.41533 q^{76} -1.55752 q^{77} -3.73206 q^{78} +12.0657 q^{79} +6.58819 q^{80} +1.00000 q^{81} -13.7646 q^{82} -3.28038 q^{83} +0.957954 q^{84} +1.39015 q^{85} -2.38585 q^{86} -3.89007 q^{87} -2.25192 q^{88} +7.03647 q^{89} +2.60469 q^{90} +1.26307 q^{91} +4.88997 q^{92} -9.32086 q^{93} -6.30499 q^{94} -2.22263 q^{95} +7.04609 q^{96} -9.63010 q^{97} +12.3623 q^{98} -2.45618 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 7 q^{2} + 56 q^{3} + 61 q^{4} + 17 q^{5} + 7 q^{6} + 5 q^{7} + 18 q^{8} + 56 q^{9}+O(q^{10}) $ 56 * q + 7 * q^2 + 56 * q^3 + 61 * q^4 + 17 * q^5 + 7 * q^6 + 5 * q^7 + 18 * q^8 + 56 * q^9	\( 56 q + 7 q^{2} + 56 q^{3} + 61 q^{4} + 17 q^{5} + 7 q^{6} + 5 q^{7} + 18 q^{8} + 56 q^{9} - 2 q^{10} + 35 q^{11} + 61 q^{12} + 8 q^{13} + 36 q^{14} + 17 q^{15} + 71 q^{16} - 56 q^{17} + 7 q^{18} - 2 q^{19} + 58 q^{20} + 5 q^{21} + 27 q^{22} + 40 q^{23} + 18 q^{24} + 85 q^{25} + 15 q^{26} + 56 q^{27} - 4 q^{28} + 41 q^{29} - 2 q^{30} + q^{31} + 43 q^{32} + 35 q^{33} - 7 q^{34} + 57 q^{35} + 61 q^{36} + 34 q^{37} + 52 q^{38} + 8 q^{39} + 14 q^{40} + 49 q^{41} + 36 q^{42} + 27 q^{43} + 66 q^{44} + 17 q^{45} + 10 q^{46} + 43 q^{47} + 71 q^{48} + 51 q^{49} + 30 q^{50} - 56 q^{51} - 7 q^{52} + 73 q^{53} + 7 q^{54} + 15 q^{55} + 118 q^{56} - 2 q^{57} - q^{58} + 53 q^{59} + 58 q^{60} + 15 q^{61} + 16 q^{62} + 5 q^{63} + 124 q^{64} + 107 q^{65} + 27 q^{66} + 20 q^{67} - 61 q^{68} + 40 q^{69} + 16 q^{70} + 56 q^{71} + 18 q^{72} + 49 q^{73} + 28 q^{74} + 85 q^{75} - 38 q^{76} + 50 q^{77} + 15 q^{78} - 4 q^{79} + 74 q^{80} + 56 q^{81} + 59 q^{82} + 35 q^{83} - 4 q^{84} - 17 q^{85} + 38 q^{86} + 41 q^{87} + 64 q^{88} + 66 q^{89} - 2 q^{90} + 5 q^{91} + 96 q^{92} + q^{93} - 12 q^{94} + 70 q^{95} + 43 q^{96} + 60 q^{97} + 26 q^{98} + 35 q^{99}+O(q^{100}) \) 56 * q + 7 * q^2 + 56 * q^3 + 61 * q^4 + 17 * q^5 + 7 * q^6 + 5 * q^7 + 18 * q^8 + 56 * q^9 - 2 * q^10 + 35 * q^11 + 61 * q^12 + 8 * q^13 + 36 * q^14 + 17 * q^15 + 71 * q^16 - 56 * q^17 + 7 * q^18 - 2 * q^19 + 58 * q^20 + 5 * q^21 + 27 * q^22 + 40 * q^23 + 18 * q^24 + 85 * q^25 + 15 * q^26 + 56 * q^27 - 4 * q^28 + 41 * q^29 - 2 * q^30 + q^31 + 43 * q^32 + 35 * q^33 - 7 * q^34 + 57 * q^35 + 61 * q^36 + 34 * q^37 + 52 * q^38 + 8 * q^39 + 14 * q^40 + 49 * q^41 + 36 * q^42 + 27 * q^43 + 66 * q^44 + 17 * q^45 + 10 * q^46 + 43 * q^47 + 71 * q^48 + 51 * q^49 + 30 * q^50 - 56 * q^51 - 7 * q^52 + 73 * q^53 + 7 * q^54 + 15 * q^55 + 118 * q^56 - 2 * q^57 - q^58 + 53 * q^59 + 58 * q^60 + 15 * q^61 + 16 * q^62 + 5 * q^63 + 124 * q^64 + 107 * q^65 + 27 * q^66 + 20 * q^67 - 61 * q^68 + 40 * q^69 + 16 * q^70 + 56 * q^71 + 18 * q^72 + 49 * q^73 + 28 * q^74 + 85 * q^75 - 38 * q^76 + 50 * q^77 + 15 * q^78 - 4 * q^79 + 74 * q^80 + 56 * q^81 + 59 * q^82 + 35 * q^83 - 4 * q^84 - 17 * q^85 + 38 * q^86 + 41 * q^87 + 64 * q^88 + 66 * q^89 - 2 * q^90 + 5 * q^91 + 96 * q^92 + q^93 - 12 * q^94 + 70 * q^95 + 43 * q^96 + 60 * q^97 + 26 * q^98 + 35 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.87368	−1.32489	−0.662446	−	0.749110i	$-0.730482\pi$
$2$	−1.87368	−1.32489	−0.662446	+	0.749110i	$0.730482\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.51068	0.755338
$5$	−1.39015	−0.621692	−0.310846	−	0.950460i	$-0.600612\pi$
$5$	−1.39015	−0.621692	−0.310846	+	0.950460i	$0.600612\pi$
$6$	−1.87368	−0.764927
$7$	0.634123	0.239676	0.119838	−	0.992793i	$-0.461763\pi$
$7$	0.634123	0.239676	0.119838	+	0.992793i	$0.461763\pi$
$8$	0.916837	0.324151
$9$	1.00000	0.333333
$10$	2.60469	0.823674
$11$	−2.45618	−0.740567	−0.370284	−	0.928919i	$-0.620739\pi$
$11$	−2.45618	−0.740567	−0.370284	+	0.928919i	$0.620739\pi$
$12$	1.51068	0.436094
$13$	1.99183	0.552436	0.276218	−	0.961095i	$-0.410919\pi$
$13$	1.99183	0.552436	0.276218	+	0.961095i	$0.410919\pi$
$14$	−1.18814	−0.317545
$15$	−1.39015	−0.358934
$16$	−4.73921	−1.18480
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.87368	−0.441631
$19$	1.59884	0.366800	0.183400	−	0.983038i	$-0.441290\pi$
$19$	1.59884	0.366800	0.183400	+	0.983038i	$0.441290\pi$
$20$	−2.10006	−0.469587
$21$	0.634123	0.138377
$22$	4.60210	0.981171
$23$	3.23694	0.674949	0.337474	−	0.941335i	$-0.390427\pi$
$23$	3.23694	0.674949	0.337474	+	0.941335i	$0.390427\pi$
$24$	0.916837	0.187149
$25$	−3.06750	−0.613499
$26$	−3.73206	−0.731917
$27$	1.00000	0.192450
$28$	0.957954	0.181036
$29$	−3.89007	−0.722368	−0.361184	−	0.932495i	$-0.617627\pi$
$29$	−3.89007	−0.722368	−0.361184	+	0.932495i	$0.617627\pi$
$30$	2.60469	0.475549
$31$	−9.32086	−1.67408	−0.837038	−	0.547145i	$-0.815715\pi$
$31$	−9.32086	−1.67408	−0.837038	+	0.547145i	$0.815715\pi$
$32$	7.04609	1.24558
$33$	−2.45618	−0.427567
$34$	1.87368	0.321333
$35$	−0.881523	−0.149005
$36$	1.51068	0.251779
$37$	−6.63914	−1.09147	−0.545734	−	0.837958i	$-0.683749\pi$
$37$	−6.63914	−1.09147	−0.545734	+	0.837958i	$0.683749\pi$
$38$	−2.99572	−0.485970
$39$	1.99183	0.318949
$40$	−1.27454	−0.201522
$41$	7.34627	1.14730	0.573648	−	0.819102i	$-0.305528\pi$
$41$	7.34627	1.14730	0.573648	+	0.819102i	$0.305528\pi$
$42$	−1.18814	−0.183334
$43$	1.27335	0.194184	0.0970921	−	0.995275i	$-0.469046\pi$
$43$	1.27335	0.194184	0.0970921	+	0.995275i	$0.469046\pi$
$44$	−3.71050	−0.559378
$45$	−1.39015	−0.207231
$46$	−6.06499	−0.894234
$47$	3.36503	0.490840	0.245420	−	0.969417i	$-0.421074\pi$
$47$	3.36503	0.490840	0.245420	+	0.969417i	$0.421074\pi$
$48$	−4.73921	−0.684046
$49$	−6.59789	−0.942555
$50$	5.74750	0.812820
$51$	−1.00000	−0.140028
$52$	3.00902	0.417275
$53$	10.2659	1.41013	0.705066	−	0.709141i	$-0.250917\pi$
$53$	10.2659	1.41013	0.705066	+	0.709141i	$0.250917\pi$
$54$	−1.87368	−0.254976
$55$	3.41445	0.460405
$56$	0.581387	0.0776912
$57$	1.59884	0.211772
$58$	7.28874	0.957059
$59$	8.71911	1.13513	0.567566	−	0.823328i	$-0.307885\pi$
$59$	8.71911	1.13513	0.567566	+	0.823328i	$0.307885\pi$
$60$	−2.10006	−0.271116
$61$	4.29955	0.550501	0.275250	−	0.961373i	$-0.411239\pi$
$61$	4.29955	0.550501	0.275250	+	0.961373i	$0.411239\pi$
$62$	17.4643	2.21797
$63$	0.634123	0.0798920
$64$	−3.72369	−0.465461
$65$	−2.76894	−0.343445
$66$	4.60210	0.566479
$67$	−3.96312	−0.484173	−0.242086	−	0.970255i	$-0.577832\pi$
$67$	−3.96312	−0.484173	−0.242086	+	0.970255i	$0.577832\pi$
$68$	−1.51068	−0.183196
$69$	3.23694	0.389682
$70$	1.65169	0.197415
$71$	−10.4112	−1.23558	−0.617792	−	0.786342i	$-0.711972\pi$
$71$	−10.4112	−1.23558	−0.617792	+	0.786342i	$0.711972\pi$
$72$	0.916837	0.108050
$73$	−1.23227	−0.144227	−0.0721134	−	0.997396i	$-0.522974\pi$
$73$	−1.23227	−0.144227	−0.0721134	+	0.997396i	$0.522974\pi$
$74$	12.4396	1.44608
$75$	−3.06750	−0.354204
$76$	2.41533	0.277058
$77$	−1.55752	−0.177496
$78$	−3.73206	−0.422573
$79$	12.0657	1.35750	0.678748	−	0.734371i	$-0.262523\pi$
$79$	12.0657	1.35750	0.678748	+	0.734371i	$0.262523\pi$
$80$	6.58819	0.736582
$81$	1.00000	0.111111
$82$	−13.7646	−1.52004
$83$	−3.28038	−0.360069	−0.180034	−	0.983660i	$-0.557621\pi$
$83$	−3.28038	−0.360069	−0.180034	+	0.983660i	$0.557621\pi$
$84$	0.957954	0.104521
$85$	1.39015	0.150782
$86$	−2.38585	−0.257273
$87$	−3.89007	−0.417059
$88$	−2.25192	−0.240056
$89$	7.03647	0.745864	0.372932	−	0.927859i	$-0.378352\pi$
$89$	7.03647	0.745864	0.372932	+	0.927859i	$0.378352\pi$
$90$	2.60469	0.274558
$91$	1.26307	0.132405
$92$	4.88997	0.509814
$93$	−9.32086	−0.966528
$94$	−6.30499	−0.650310
$95$	−2.22263	−0.228037
$96$	7.04609	0.719138
$97$	−9.63010	−0.977789	−0.488894	−	0.872343i	$-0.662600\pi$
$97$	−9.63010	−0.977789	−0.488894	+	0.872343i	$0.662600\pi$
$98$	12.3623	1.24878
$99$	−2.45618	−0.246856
$100$	−4.63399	−0.463399
$101$	12.4946	1.24325	0.621627	−	0.783313i	$-0.286472\pi$
$101$	12.4946	1.24325	0.621627	+	0.783313i	$0.286472\pi$
$102$	1.87368	0.185522
$103$	5.39297	0.531385	0.265693	−	0.964058i	$-0.414399\pi$
$103$	5.39297	0.531385	0.265693	+	0.964058i	$0.414399\pi$
$104$	1.82619	0.179073
$105$	−0.881523	−0.0860278
$106$	−19.2350	−1.86827
$107$	5.01557	0.484874	0.242437	−	0.970167i	$-0.422053\pi$
$107$	5.01557	0.484874	0.242437	+	0.970167i	$0.422053\pi$
$108$	1.51068	0.145365
$109$	−4.21886	−0.404094	−0.202047	−	0.979376i	$-0.564759\pi$
$109$	−4.21886	−0.404094	−0.202047	+	0.979376i	$0.564759\pi$
$110$	−6.39759	−0.609986
$111$	−6.63914	−0.630160
$112$	−3.00524	−0.283969
$113$	3.89083	0.366018	0.183009	−	0.983111i	$-0.441416\pi$
$113$	3.89083	0.366018	0.183009	+	0.983111i	$0.441416\pi$
$114$	−2.99572	−0.280575
$115$	−4.49982	−0.419610
$116$	−5.87663	−0.545632
$117$	1.99183	0.184145
$118$	−16.3368	−1.50393
$119$	−0.634123	−0.0581299
$120$	−1.27454	−0.116349
$121$	−4.96717	−0.451560
$122$	−8.05597	−0.729354
$123$	7.34627	0.662391
$124$	−14.0808	−1.26449
$125$	11.2150	1.00310
$126$	−1.18814	−0.105848
$127$	−7.91981	−0.702769	−0.351385	−	0.936231i	$-0.614289\pi$
$127$	−7.91981	−0.702769	−0.351385	+	0.936231i	$0.614289\pi$
$128$	−7.11517	−0.628898
$129$	1.27335	0.112112
$130$	5.18811	0.455027
$131$	10.5096	0.918227	0.459113	−	0.888378i	$-0.348167\pi$
$131$	10.5096	0.918227	0.459113	+	0.888378i	$0.348167\pi$
$132$	−3.71050	−0.322957
$133$	1.01386	0.0879131
$134$	7.42563	0.641476
$135$	−1.39015	−0.119645
$136$	−0.916837	−0.0786182
$137$	−10.5862	−0.904443	−0.452221	−	0.891906i	$-0.649368\pi$
$137$	−10.5862	−0.904443	−0.452221	+	0.891906i	$0.649368\pi$
$138$	−6.06499	−0.516286
$139$	11.5240	0.977451	0.488726	−	0.872438i	$-0.337462\pi$
$139$	11.5240	0.977451	0.488726	+	0.872438i	$0.337462\pi$
$140$	−1.33169	−0.112549
$141$	3.36503	0.283387
$142$	19.5073	1.63701
$143$	−4.89231	−0.409116
$144$	−4.73921	−0.394934
$145$	5.40776	0.449090
$146$	2.30889	0.191085
$147$	−6.59789	−0.544185
$148$	−10.0296	−0.824427
$149$	2.82957	0.231807	0.115904	−	0.993260i	$-0.463024\pi$
$149$	2.82957	0.231807	0.115904	+	0.993260i	$0.463024\pi$
$150$	5.74750	0.469282
$151$	21.9737	1.78819	0.894097	−	0.447873i	$-0.147818\pi$
$151$	21.9737	1.78819	0.894097	+	0.447873i	$0.147818\pi$
$152$	1.46588	0.118899
$153$	−1.00000	−0.0808452
$154$	2.91830	0.235163
$155$	12.9574	1.04076
$156$	3.00902	0.240914
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	−22.6072	−1.79854
$159$	10.2659	0.814140
$160$	−9.79509	−0.774370
$161$	2.05262	0.161769
$162$	−1.87368	−0.147210
$163$	−4.03439	−0.315998	−0.157999	−	0.987439i	$-0.550504\pi$
$163$	−4.03439	−0.315998	−0.157999	+	0.987439i	$0.550504\pi$
$164$	11.0978	0.866595
$165$	3.41445	0.265815
$166$	6.14639	0.477052
$167$	−4.93590	−0.381951	−0.190976	−	0.981595i	$-0.561165\pi$
$167$	−4.93590	−0.381951	−0.190976	+	0.981595i	$0.561165\pi$
$168$	0.581387	0.0448550
$169$	−9.03259	−0.694815
$170$	−2.60469	−0.199770
$171$	1.59884	0.122267
$172$	1.92362	0.146675
$173$	19.0748	1.45023	0.725116	−	0.688627i	$-0.241786\pi$
$173$	19.0748	1.45023	0.725116	+	0.688627i	$0.241786\pi$
$174$	7.28874	0.552558
$175$	−1.94517	−0.147041
$176$	11.6404	0.877426
$177$	8.71911	0.655368
$178$	−13.1841	−0.988189
$179$	−12.3095	−0.920055	−0.460027	−	0.887905i	$-0.652160\pi$
$179$	−12.3095	−0.920055	−0.460027	+	0.887905i	$0.652160\pi$
$180$	−2.10006	−0.156529
$181$	−22.3294	−1.65973	−0.829867	−	0.557962i	$-0.811584\pi$
$181$	−22.3294	−1.65973	−0.829867	+	0.557962i	$0.811584\pi$
$182$	−2.36658	−0.175423
$183$	4.29955	0.317832
$184$	2.96775	0.218785
$185$	9.22938	0.678557
$186$	17.4643	1.28055
$187$	2.45618	0.179614
$188$	5.08347	0.370750
$189$	0.634123	0.0461256
$190$	4.16449	0.302124
$191$	−11.7047	−0.846920	−0.423460	−	0.905915i	$-0.639185\pi$
$191$	−11.7047	−0.846920	−0.423460	+	0.905915i	$0.639185\pi$
$192$	−3.72369	−0.268734
$193$	0.608452	0.0437973	0.0218987	−	0.999760i	$-0.493029\pi$
$193$	0.608452	0.0437973	0.0218987	+	0.999760i	$0.493029\pi$
$194$	18.0437	1.29546
$195$	−2.76894	−0.198288
$196$	−9.96727	−0.711948
$197$	−4.63697	−0.330371	−0.165185	−	0.986263i	$-0.552822\pi$
$197$	−4.63697	−0.330371	−0.165185	+	0.986263i	$0.552822\pi$
$198$	4.60210	0.327057
$199$	17.7795	1.26036	0.630178	−	0.776450i	$-0.282982\pi$
$199$	17.7795	1.26036	0.630178	+	0.776450i	$0.282982\pi$
$200$	−2.81239	−0.198866
$201$	−3.96312	−0.279537
$202$	−23.4108	−1.64718
$203$	−2.46678	−0.173134
$204$	−1.51068	−0.105768
$205$	−10.2124	−0.713264
$206$	−10.1047	−0.704028
$207$	3.23694	0.224983
$208$	−9.43973	−0.654527
$209$	−3.92705	−0.271640
$210$	1.65169	0.113978
$211$	6.57533	0.452665	0.226332	−	0.974050i	$-0.427326\pi$
$211$	6.57533	0.452665	0.226332	+	0.974050i	$0.427326\pi$
$212$	15.5085	1.06513
$213$	−10.4112	−0.713364
$214$	−9.39758	−0.642405
$215$	−1.77014	−0.120723
$216$	0.916837	0.0623829
$217$	−5.91057	−0.401236
$218$	7.90480	0.535381
$219$	−1.23227	−0.0832694
$220$	5.15813	0.347761
$221$	−1.99183	−0.133985
$222$	12.4396	0.834893
$223$	−17.3118	−1.15928	−0.579641	−	0.814872i	$-0.696807\pi$
$223$	−17.3118	−1.15928	−0.579641	+	0.814872i	$0.696807\pi$
$224$	4.46808	0.298536
$225$	−3.06750	−0.204500
$226$	−7.29017	−0.484935
$227$	5.14601	0.341553	0.170776	−	0.985310i	$-0.445372\pi$
$227$	5.14601	0.341553	0.170776	+	0.985310i	$0.445372\pi$
$228$	2.41533	0.159959
$229$	14.7923	0.977502	0.488751	−	0.872423i	$-0.337453\pi$
$229$	14.7923	0.977502	0.488751	+	0.872423i	$0.337453\pi$
$230$	8.43122	0.555938
$231$	−1.55752	−0.102477
$232$	−3.56656	−0.234156
$233$	8.56155	0.560886	0.280443	−	0.959871i	$-0.409519\pi$
$233$	8.56155	0.560886	0.280443	+	0.959871i	$0.409519\pi$
$234$	−3.73206	−0.243972
$235$	−4.67788	−0.305151
$236$	13.1717	0.857408
$237$	12.0657	0.783751
$238$	1.18814	0.0770159
$239$	−8.34208	−0.539604	−0.269802	−	0.962916i	$-0.586958\pi$
$239$	−8.34208	−0.539604	−0.269802	+	0.962916i	$0.586958\pi$
$240$	6.58819	0.425266
$241$	17.9947	1.15914	0.579569	−	0.814923i	$-0.303221\pi$
$241$	17.9947	1.15914	0.579569	+	0.814923i	$0.303221\pi$
$242$	9.30688	0.598269
$243$	1.00000	0.0641500
$244$	6.49522	0.415814
$245$	9.17202	0.585979
$246$	−13.7646	−0.877597
$247$	3.18463	0.202633
$248$	−8.54572	−0.542653
$249$	−3.28038	−0.207886
$250$	−21.0133	−1.32900
$251$	5.65320	0.356827	0.178413	−	0.983956i	$-0.442904\pi$
$251$	5.65320	0.356827	0.178413	+	0.983956i	$0.442904\pi$
$252$	0.957954	0.0603454
$253$	−7.95052	−0.499845
$254$	14.8392	0.931093
$255$	1.39015	0.0870543
$256$	20.7789	1.29868
$257$	−2.12336	−0.132452	−0.0662259	−	0.997805i	$-0.521096\pi$
$257$	−2.12336	−0.132452	−0.0662259	+	0.997805i	$0.521096\pi$
$258$	−2.38585	−0.148537
$259$	−4.21003	−0.261599
$260$	−4.18297	−0.259417
$261$	−3.89007	−0.240789
$262$	−19.6916	−1.21655
$263$	−0.236397	−0.0145768	−0.00728842	−	0.999973i	$-0.502320\pi$
$263$	−0.236397	−0.0145768	−0.00728842	+	0.999973i	$0.502320\pi$
$264$	−2.25192	−0.138596
$265$	−14.2711	−0.876668
$266$	−1.89965	−0.116475
$267$	7.03647	0.430625
$268$	−5.98700	−0.365714
$269$	21.9024	1.33541	0.667707	−	0.744424i	$-0.267276\pi$
$269$	21.9024	1.33541	0.667707	+	0.744424i	$0.267276\pi$
$270$	2.60469	0.158516
$271$	−25.8623	−1.57102	−0.785510	−	0.618849i	$-0.787599\pi$
$271$	−25.8623	−1.57102	−0.785510	+	0.618849i	$0.787599\pi$
$272$	4.73921	0.287357
$273$	1.26307	0.0764443
$274$	19.8352	1.19829
$275$	7.53433	0.454337
$276$	4.88997	0.294341
$277$	4.45474	0.267660	0.133830	−	0.991004i	$-0.457272\pi$
$277$	4.45474	0.267660	0.133830	+	0.991004i	$0.457272\pi$
$278$	−21.5922	−1.29502
$279$	−9.32086	−0.558025
$280$	−0.808213	−0.0483000
$281$	−4.92164	−0.293600	−0.146800	−	0.989166i	$-0.546897\pi$
$281$	−4.92164	−0.293600	−0.146800	+	0.989166i	$0.546897\pi$
$282$	−6.30499	−0.375457
$283$	24.8385	1.47650	0.738248	−	0.674529i	$-0.235653\pi$
$283$	24.8385	1.47650	0.738248	+	0.674529i	$0.235653\pi$
$284$	−15.7280	−0.933283
$285$	−2.22263	−0.131657
$286$	9.16662	0.542034
$287$	4.65844	0.274979
$288$	7.04609	0.415195
$289$	1.00000	0.0588235
$290$	−10.1324	−0.594996
$291$	−9.63010	−0.564527
$292$	−1.86157	−0.108940
$293$	−3.11302	−0.181865	−0.0909323	−	0.995857i	$-0.528985\pi$
$293$	−3.11302	−0.181865	−0.0909323	+	0.995857i	$0.528985\pi$
$294$	12.3623	0.720986
$295$	−12.1208	−0.705702
$296$	−6.08701	−0.353801
$297$	−2.45618	−0.142522
$298$	−5.30170	−0.307119
$299$	6.44745	0.372866
$300$	−4.63399	−0.267544
$301$	0.807461	0.0465413
$302$	−41.1717	−2.36916
$303$	12.4946	0.717793
$304$	−7.57726	−0.434586
$305$	−5.97700	−0.342242
$306$	1.87368	0.107111
$307$	11.3561	0.648127	0.324063	−	0.946035i	$-0.394951\pi$
$307$	11.3561	0.648127	0.324063	+	0.946035i	$0.394951\pi$
$308$	−2.35291	−0.134069
$309$	5.39297	0.306795
$310$	−24.2779	−1.37889
$311$	1.77755	0.100796	0.0503978	−	0.998729i	$-0.483951\pi$
$311$	1.77755	0.100796	0.0503978	+	0.998729i	$0.483951\pi$
$312$	1.82619	0.103388
$313$	5.14107	0.290591	0.145295	−	0.989388i	$-0.453587\pi$
$313$	5.14107	0.290591	0.145295	+	0.989388i	$0.453587\pi$
$314$	1.87368	0.105738
$315$	−0.881523	−0.0496682
$316$	18.2273	1.02537
$317$	−34.5478	−1.94040	−0.970199	−	0.242310i	$-0.922095\pi$
$317$	−34.5478	−1.94040	−0.970199	+	0.242310i	$0.922095\pi$
$318$	−19.2350	−1.07865
$319$	9.55472	0.534962
$320$	5.17647	0.289374
$321$	5.01557	0.279942
$322$	−3.84595	−0.214326
$323$	−1.59884	−0.0889621
$324$	1.51068	0.0839264
$325$	−6.10994	−0.338919
$326$	7.55915	0.418663
$327$	−4.21886	−0.233304
$328$	6.73534	0.371897
$329$	2.13384	0.117643
$330$	−6.39759	−0.352176
$331$	−6.97356	−0.383302	−0.191651	−	0.981463i	$-0.561384\pi$
$331$	−6.97356	−0.383302	−0.191651	+	0.981463i	$0.561384\pi$
$332$	−4.95560	−0.271974
$333$	−6.63914	−0.363823
$334$	9.24829	0.506044
$335$	5.50932	0.301006
$336$	−3.00524	−0.163949
$337$	35.4121	1.92902	0.964511	−	0.264044i	$-0.0850565\pi$
$337$	35.4121	1.92902	0.964511	+	0.264044i	$0.0850565\pi$
$338$	16.9242	0.920554
$339$	3.89083	0.211321
$340$	2.10006	0.113892
$341$	22.8937	1.23977
$342$	−2.99572	−0.161990
$343$	−8.62273	−0.465584
$344$	1.16746	0.0629450
$345$	−4.49982	−0.242262
$346$	−35.7401	−1.92140
$347$	−8.72502	−0.468384	−0.234192	−	0.972190i	$-0.575244\pi$
$347$	−8.72502	−0.468384	−0.234192	+	0.972190i	$0.575244\pi$
$348$	−5.87663	−0.315021
$349$	36.7481	1.96708	0.983541	−	0.180686i	$-0.0578317\pi$
$349$	36.7481	1.96708	0.983541	+	0.180686i	$0.0578317\pi$
$350$	3.64462	0.194813
$351$	1.99183	0.106316
$352$	−17.3065	−0.922439
$353$	−8.59919	−0.457689	−0.228844	−	0.973463i	$-0.573495\pi$
$353$	−8.59919	−0.457689	−0.228844	+	0.973463i	$0.573495\pi$
$354$	−16.3368	−0.868292
$355$	14.4731	0.768152
$356$	10.6298	0.563379
$357$	−0.634123	−0.0335613
$358$	23.0641	1.21897
$359$	19.2467	1.01580	0.507901	−	0.861416i	$-0.330422\pi$
$359$	19.2467	1.01580	0.507901	+	0.861416i	$0.330422\pi$
$360$	−1.27454	−0.0671740
$361$	−16.4437	−0.865458
$362$	41.8382	2.19897
$363$	−4.96717	−0.260709
$364$	1.90809	0.100011
$365$	1.71304	0.0896647
$366$	−8.05597	−0.421092
$367$	8.09819	0.422722	0.211361	−	0.977408i	$-0.432210\pi$
$367$	8.09819	0.422722	0.211361	+	0.977408i	$0.432210\pi$
$368$	−15.3405	−0.799681
$369$	7.34627	0.382432
$370$	−17.2929	−0.899015
$371$	6.50985	0.337975
$372$	−14.0808	−0.730055
$373$	−7.77894	−0.402778	−0.201389	−	0.979511i	$-0.564546\pi$
$373$	−7.77894	−0.402778	−0.201389	+	0.979511i	$0.564546\pi$
$374$	−4.60210	−0.237969
$375$	11.2150	0.579140
$376$	3.08519	0.159106
$377$	−7.74838	−0.399062
$378$	−1.18814	−0.0611115
$379$	19.0659	0.979349	0.489674	−	0.871905i	$-0.337116\pi$
$379$	19.0659	0.979349	0.489674	+	0.871905i	$0.337116\pi$
$380$	−3.35767	−0.172245
$381$	−7.91981	−0.405744
$382$	21.9308	1.12208
$383$	17.7684	0.907925	0.453962	−	0.891021i	$-0.350010\pi$
$383$	17.7684	0.907925	0.453962	+	0.891021i	$0.350010\pi$
$384$	−7.11517	−0.363095
$385$	2.16518	0.110348
$386$	−1.14004	−0.0580267
$387$	1.27335	0.0647281
$388$	−14.5480	−0.738561
$389$	−14.7108	−0.745866	−0.372933	−	0.927858i	$-0.621648\pi$
$389$	−14.7108	−0.745866	−0.372933	+	0.927858i	$0.621648\pi$
$390$	5.18811	0.262710
$391$	−3.23694	−0.163699
$392$	−6.04919	−0.305530
$393$	10.5096	0.530138
$394$	8.68820	0.437705
$395$	−16.7731	−0.843944
$396$	−3.71050	−0.186459
$397$	27.6381	1.38711	0.693557	−	0.720402i	$-0.256043\pi$
$397$	27.6381	1.38711	0.693557	+	0.720402i	$0.256043\pi$
$398$	−33.3131	−1.66984
$399$	1.01386	0.0507566
$400$	14.5375	0.726875
$401$	31.7588	1.58596	0.792979	−	0.609248i	$-0.208529\pi$
$401$	31.7588	1.58596	0.792979	+	0.609248i	$0.208529\pi$
$402$	7.42563	0.370357
$403$	−18.5656	−0.924819
$404$	18.8752	0.939077
$405$	−1.39015	−0.0690769
$406$	4.62196	0.229384
$407$	16.3070	0.808306
$408$	−0.916837	−0.0453902
$409$	7.24317	0.358152	0.179076	−	0.983835i	$-0.442689\pi$
$409$	7.24317	0.358152	0.179076	+	0.983835i	$0.442689\pi$
$410$	19.1347	0.944998
$411$	−10.5862	−0.522180
$412$	8.14703	0.401375
$413$	5.52899	0.272064
$414$	−6.06499	−0.298078
$415$	4.56021	0.223852
$416$	14.0346	0.688105
$417$	11.5240	0.564332
$418$	7.35804	0.359893
$419$	25.4438	1.24301	0.621505	−	0.783410i	$-0.286522\pi$
$419$	25.4438	1.24301	0.621505	+	0.783410i	$0.286522\pi$
$420$	−1.33169	−0.0649801
$421$	−21.8554	−1.06517	−0.532583	−	0.846378i	$-0.678779\pi$
$421$	−21.8554	−1.06517	−0.532583	+	0.846378i	$0.678779\pi$
$422$	−12.3201	−0.599731
$423$	3.36503	0.163613
$424$	9.41218	0.457096
$425$	3.06750	0.148795
$426$	19.5073	0.945130
$427$	2.72644	0.131942
$428$	7.57690	0.366243
$429$	−4.89231	−0.236203
$430$	3.31668	0.159945
$431$	37.0793	1.78605	0.893023	−	0.450011i	$-0.148580\pi$
$431$	37.0793	1.78605	0.893023	+	0.450011i	$0.148580\pi$
$432$	−4.73921	−0.228015
$433$	−16.4029	−0.788273	−0.394137	−	0.919052i	$-0.628956\pi$
$433$	−16.4029	−0.788273	−0.394137	+	0.919052i	$0.628956\pi$
$434$	11.0745	0.531594
$435$	5.40776	0.259282
$436$	−6.37333	−0.305227
$437$	5.17536	0.247571
$438$	2.30889	0.110323
$439$	−1.21303	−0.0578949	−0.0289475	−	0.999581i	$-0.509216\pi$
$439$	−1.21303	−0.0578949	−0.0289475	+	0.999581i	$0.509216\pi$
$440$	3.13050	0.149241
$441$	−6.59789	−0.314185
$442$	3.73206	0.177516
$443$	10.9284	0.519225	0.259612	−	0.965713i	$-0.416405\pi$
$443$	10.9284	0.519225	0.259612	+	0.965713i	$0.416405\pi$
$444$	−10.0296	−0.475983
$445$	−9.78172	−0.463698
$446$	32.4367	1.53592
$447$	2.82957	0.133834
$448$	−2.36128	−0.111560
$449$	15.6444	0.738305	0.369153	−	0.929369i	$-0.379648\pi$
$449$	15.6444	0.738305	0.369153	+	0.929369i	$0.379648\pi$
$450$	5.74750	0.270940
$451$	−18.0438	−0.849649
$452$	5.87778	0.276467
$453$	21.9737	1.03241
$454$	−9.64198	−0.452520
$455$	−1.75585	−0.0823154
$456$	1.46588	0.0686461
$457$	−14.6241	−0.684087	−0.342044	−	0.939684i	$-0.611119\pi$
$457$	−14.6241	−0.684087	−0.342044	+	0.939684i	$0.611119\pi$
$458$	−27.7160	−1.29508
$459$	−1.00000	−0.0466760
$460$	−6.79777	−0.316947
$461$	19.8450	0.924273	0.462137	−	0.886809i	$-0.347083\pi$
$461$	19.8450	0.924273	0.462137	+	0.886809i	$0.347083\pi$
$462$	2.91830	0.135771
$463$	5.63419	0.261843	0.130921	−	0.991393i	$-0.458206\pi$
$463$	5.63419	0.261843	0.130921	+	0.991393i	$0.458206\pi$
$464$	18.4359	0.855863
$465$	12.9574	0.600883
$466$	−16.0416	−0.743113
$467$	−20.8269	−0.963755	−0.481877	−	0.876239i	$-0.660045\pi$
$467$	−20.8269	−0.963755	−0.481877	+	0.876239i	$0.660045\pi$
$468$	3.00902	0.139092
$469$	−2.51311	−0.116045
$470$	8.76485	0.404293
$471$	−1.00000	−0.0460776
$472$	7.99401	0.367954
$473$	−3.12758	−0.143806
$474$	−22.6072	−1.03838
$475$	−4.90445	−0.225031
$476$	−0.957954	−0.0439077
$477$	10.2659	0.470044
$478$	15.6304	0.714917
$479$	−14.9814	−0.684518	−0.342259	−	0.939606i	$-0.611192\pi$
$479$	−14.9814	−0.684518	−0.342259	+	0.939606i	$0.611192\pi$
$480$	−9.79509	−0.447083
$481$	−13.2241	−0.602966
$482$	−33.7162	−1.53573
$483$	2.05262	0.0933974
$484$	−7.50377	−0.341081
$485$	13.3872	0.607883
$486$	−1.87368	−0.0849918
$487$	−21.9180	−0.993198	−0.496599	−	0.867980i	$-0.665418\pi$
$487$	−21.9180	−0.993198	−0.496599	+	0.867980i	$0.665418\pi$
$488$	3.94199	0.178445
$489$	−4.03439	−0.182441
$490$	−17.1854	−0.776359
$491$	−6.72471	−0.303482	−0.151741	−	0.988420i	$-0.548488\pi$
$491$	−6.72471	−0.303482	−0.151741	+	0.988420i	$0.548488\pi$
$492$	11.0978	0.500329
$493$	3.89007	0.175200
$494$	−5.96698	−0.268467
$495$	3.41445	0.153468
$496$	44.1735	1.98345
$497$	−6.60198	−0.296139
$498$	6.14639	0.275426
$499$	37.3672	1.67279	0.836393	−	0.548130i	$-0.184660\pi$
$499$	37.3672	1.67279	0.836393	+	0.548130i	$0.184660\pi$
$500$	16.9422	0.757679
$501$	−4.93590	−0.220520
$502$	−10.5923	−0.472757
$503$	29.6193	1.32066	0.660329	−	0.750976i	$-0.270417\pi$
$503$	29.6193	1.32066	0.660329	+	0.750976i	$0.270417\pi$
$504$	0.581387	0.0258971
$505$	−17.3693	−0.772922
$506$	14.8967	0.662240
$507$	−9.03259	−0.401152
$508$	−11.9643	−0.530828
$509$	8.91889	0.395323	0.197661	−	0.980270i	$-0.436665\pi$
$509$	8.91889	0.395323	0.197661	+	0.980270i	$0.436665\pi$
$510$	−2.60469	−0.115337
$511$	−0.781413	−0.0345677
$512$	−24.7027	−1.09172
$513$	1.59884	0.0705907
$514$	3.97850	0.175484
$515$	−7.49702	−0.330358
$516$	1.92362	0.0846827
$517$	−8.26513	−0.363500
$518$	7.88825	0.346590
$519$	19.0748	0.837292
$520$	−2.53867	−0.111328
$521$	−21.9202	−0.960342	−0.480171	−	0.877175i	$-0.659425\pi$
$521$	−21.9202	−0.960342	−0.480171	+	0.877175i	$0.659425\pi$
$522$	7.28874	0.319020
$523$	−37.6643	−1.64694	−0.823472	−	0.567357i	$-0.807966\pi$
$523$	−37.6643	−1.64694	−0.823472	+	0.567357i	$0.807966\pi$
$524$	15.8766	0.693571
$525$	−1.94517	−0.0848941
$526$	0.442932	0.0193127
$527$	9.32086	0.406023
$528$	11.6404	0.506582
$529$	−12.5222	−0.544444
$530$	26.7395	1.16149
$531$	8.71911	0.378377
$532$	1.53162	0.0664041
$533$	14.6326	0.633807
$534$	−13.1841	−0.570531
$535$	−6.97238	−0.301442
$536$	−3.63354	−0.156945
$537$	−12.3095	−0.531194
$538$	−41.0381	−1.76928
$539$	16.2056	0.698026
$540$	−2.10006	−0.0903721
$541$	4.44006	0.190893	0.0954465	−	0.995435i	$-0.469572\pi$
$541$	4.44006	0.190893	0.0954465	+	0.995435i	$0.469572\pi$
$542$	48.4576	2.08143
$543$	−22.3294	−0.958247
$544$	−7.04609	−0.302099
$545$	5.86483	0.251222
$546$	−2.36658	−0.101280
$547$	−32.2103	−1.37721	−0.688606	−	0.725136i	$-0.741777\pi$
$547$	−32.2103	−1.37721	−0.688606	+	0.725136i	$0.741777\pi$
$548$	−15.9924	−0.683160
$549$	4.29955	0.183500
$550$	−14.1169	−0.601948
$551$	−6.21961	−0.264964
$552$	2.96775	0.126316
$553$	7.65113	0.325359
$554$	−8.34676	−0.354620
$555$	9.22938	0.391765
$556$	17.4090	0.738306
$557$	−39.4739	−1.67256	−0.836282	−	0.548300i	$-0.815275\pi$
$557$	−39.4739	−1.67256	−0.836282	+	0.548300i	$0.815275\pi$
$558$	17.4643	0.739323
$559$	2.53631	0.107274
$560$	4.17772	0.176541
$561$	2.45618	0.103700
$562$	9.22157	0.388988
$563$	33.6542	1.41836	0.709178	−	0.705029i	$-0.249066\pi$
$563$	33.6542	1.41836	0.709178	+	0.705029i	$0.249066\pi$
$564$	5.08347	0.214053
$565$	−5.40882	−0.227551
$566$	−46.5394	−1.95620
$567$	0.634123	0.0266307
$568$	−9.54539	−0.400516
$569$	−0.850011	−0.0356343	−0.0178172	−	0.999841i	$-0.505672\pi$
$569$	−0.850011	−0.0356343	−0.0178172	+	0.999841i	$0.505672\pi$
$570$	4.16449	0.174431
$571$	−16.7791	−0.702185	−0.351093	−	0.936341i	$-0.614190\pi$
$571$	−16.7791	−0.702185	−0.351093	+	0.936341i	$0.614190\pi$
$572$	−7.39069	−0.309020
$573$	−11.7047	−0.488970
$574$	−8.72842	−0.364317
$575$	−9.92930	−0.414081
$576$	−3.72369	−0.155154
$577$	27.8845	1.16085	0.580423	−	0.814315i	$-0.302887\pi$
$577$	27.8845	1.16085	0.580423	+	0.814315i	$0.302887\pi$
$578$	−1.87368	−0.0779348
$579$	0.608452	0.0252864
$580$	8.16937	0.339215
$581$	−2.08017	−0.0862998
$582$	18.0437	0.747936
$583$	−25.2150	−1.04430
$584$	−1.12980	−0.0467513
$585$	−2.76894	−0.114482
$586$	5.83280	0.240951
$587$	26.2847	1.08489	0.542444	−	0.840092i	$-0.317499\pi$
$587$	26.2847	1.08489	0.542444	+	0.840092i	$0.317499\pi$
$588$	−9.96727	−0.411043
$589$	−14.9026	−0.614051
$590$	22.7106	0.934979
$591$	−4.63697	−0.190740
$592$	31.4643	1.29317
$593$	13.9054	0.571028	0.285514	−	0.958375i	$-0.407836\pi$
$593$	13.9054	0.571028	0.285514	+	0.958375i	$0.407836\pi$
$594$	4.60210	0.188826
$595$	0.881523	0.0361389
$596$	4.27456	0.175093
$597$	17.7795	0.727667
$598$	−12.0805	−0.494007
$599$	33.5455	1.37063	0.685316	−	0.728245i	$-0.259664\pi$
$599$	33.5455	1.37063	0.685316	+	0.728245i	$0.259664\pi$
$600$	−2.81239	−0.114816
$601$	36.3245	1.48171	0.740853	−	0.671667i	$-0.234421\pi$
$601$	36.3245	1.48171	0.740853	+	0.671667i	$0.234421\pi$
$602$	−1.51292	−0.0616621
$603$	−3.96312	−0.161391
$604$	33.1951	1.35069
$605$	6.90508	0.280732
$606$	−23.4108	−0.950999
$607$	9.48911	0.385151	0.192576	−	0.981282i	$-0.438316\pi$
$607$	9.48911	0.385151	0.192576	+	0.981282i	$0.438316\pi$
$608$	11.2656	0.456880
$609$	−2.46678	−0.0999590
$610$	11.1990	0.453433
$611$	6.70259	0.271158
$612$	−1.51068	−0.0610654
$613$	31.4440	1.27001	0.635005	−	0.772508i	$-0.280998\pi$
$613$	31.4440	1.27001	0.635005	+	0.772508i	$0.280998\pi$
$614$	−21.2777	−0.858698
$615$	−10.2124	−0.411803
$616$	−1.42799	−0.0575355
$617$	2.53578	0.102087	0.0510433	−	0.998696i	$-0.483745\pi$
$617$	2.53578	0.102087	0.0510433	+	0.998696i	$0.483745\pi$
$618$	−10.1047	−0.406471
$619$	−21.9469	−0.882120	−0.441060	−	0.897478i	$-0.645397\pi$
$619$	−21.9469	−0.882120	−0.441060	+	0.897478i	$0.645397\pi$
$620$	19.5744	0.786125
$621$	3.23694	0.129894
$622$	−3.33056	−0.133543
$623$	4.46199	0.178766
$624$	−9.43973	−0.377891
$625$	−0.252993	−0.0101197
$626$	−9.63273	−0.385001
$627$	−3.92705	−0.156831
$628$	−1.51068	−0.0602825
$629$	6.63914	0.264720
$630$	1.65169	0.0658050
$631$	−5.07594	−0.202070	−0.101035	−	0.994883i	$-0.532215\pi$
$631$	−5.07594	−0.202070	−0.101035	+	0.994883i	$0.532215\pi$
$632$	11.0623	0.440034
$633$	6.57533	0.261346
$634$	64.7315	2.57082
$635$	11.0097	0.436906
$636$	15.5085	0.614951
$637$	−13.1419	−0.520701
$638$	−17.9025	−0.708766
$639$	−10.4112	−0.411861
$640$	9.89113	0.390981
$641$	−7.71472	−0.304713	−0.152357	−	0.988326i	$-0.548686\pi$
$641$	−7.71472	−0.304713	−0.152357	+	0.988326i	$0.548686\pi$
$642$	−9.39758	−0.370893
$643$	24.4928	0.965902	0.482951	−	0.875647i	$-0.339565\pi$
$643$	24.4928	0.965902	0.482951	+	0.875647i	$0.339565\pi$
$644$	3.10084	0.122190
$645$	−1.77014	−0.0696993
$646$	2.99572	0.117865
$647$	−21.4328	−0.842611	−0.421305	−	0.906919i	$-0.638428\pi$
$647$	−21.4328	−0.842611	−0.421305	+	0.906919i	$0.638428\pi$
$648$	0.916837	0.0360168
$649$	−21.4157	−0.840641
$650$	11.4481	0.449031
$651$	−5.91057	−0.231654
$652$	−6.09465	−0.238685
$653$	−0.0739333	−0.00289323	−0.00144662	−	0.999999i	$-0.500460\pi$
$653$	−0.0739333	−0.00289323	−0.00144662	+	0.999999i	$0.500460\pi$
$654$	7.90480	0.309102
$655$	−14.6099	−0.570854
$656$	−34.8155	−1.35932
$657$	−1.23227	−0.0480756
$658$	−3.99814	−0.155864
$659$	18.7856	0.731783	0.365892	−	0.930658i	$-0.380764\pi$
$659$	18.7856	0.731783	0.365892	+	0.930658i	$0.380764\pi$
$660$	5.15813	0.200780
$661$	−22.9702	−0.893437	−0.446719	−	0.894675i	$-0.647407\pi$
$661$	−22.9702	−0.893437	−0.446719	+	0.894675i	$0.647407\pi$
$662$	13.0662	0.507833
$663$	−1.99183	−0.0773565
$664$	−3.00758	−0.116717
$665$	−1.40942	−0.0546549
$666$	12.4396	0.482026
$667$	−12.5919	−0.487561
$668$	−7.45654	−0.288502
$669$	−17.3118	−0.669311
$670$	−10.3227	−0.398801
$671$	−10.5605	−0.407683
$672$	4.46808	0.172360
$673$	43.6371	1.68209	0.841043	−	0.540968i	$-0.181942\pi$
$673$	43.6371	1.68209	0.841043	+	0.540968i	$0.181942\pi$
$674$	−66.3510	−2.55574
$675$	−3.06750	−0.118068
$676$	−13.6453	−0.524820
$677$	30.9388	1.18907	0.594537	−	0.804068i	$-0.297335\pi$
$677$	30.9388	1.18907	0.594537	+	0.804068i	$0.297335\pi$
$678$	−7.29017	−0.279977
$679$	−6.10667	−0.234352
$680$	1.27454	0.0488763
$681$	5.14601	0.197196
$682$	−42.8955	−1.64256
$683$	12.7056	0.486165	0.243083	−	0.970006i	$-0.421841\pi$
$683$	12.7056	0.486165	0.243083	+	0.970006i	$0.421841\pi$
$684$	2.41533	0.0923526
$685$	14.7164	0.562285
$686$	16.1562	0.616848
$687$	14.7923	0.564361
$688$	−6.03468	−0.230070
$689$	20.4480	0.779007
$690$	8.43122	0.320971
$691$	−5.91607	−0.225058	−0.112529	−	0.993648i	$-0.535895\pi$
$691$	−5.91607	−0.225058	−0.112529	+	0.993648i	$0.535895\pi$
$692$	28.8159	1.09541
$693$	−1.55752	−0.0591653
$694$	16.3479	0.620558
$695$	−16.0200	−0.607674
$696$	−3.56656	−0.135190
$697$	−7.34627	−0.278260
$698$	−68.8542	−2.60617
$699$	8.56155	0.323828
$700$	−2.93852	−0.111066
$701$	−33.7797	−1.27584	−0.637921	−	0.770102i	$-0.720205\pi$
$701$	−33.7797	−1.27584	−0.637921	+	0.770102i	$0.720205\pi$
$702$	−3.73206	−0.140858
$703$	−10.6150	−0.400351
$704$	9.14606	0.344705
$705$	−4.67788	−0.176179
$706$	16.1121	0.606388
$707$	7.92308	0.297978
$708$	13.1717	0.495025
$709$	−19.7534	−0.741853	−0.370927	−	0.928662i	$-0.620960\pi$
$709$	−19.7534	−0.741853	−0.370927	+	0.928662i	$0.620960\pi$
$710$	−27.1179	−1.01772
$711$	12.0657	0.452499
$712$	6.45130	0.241773
$713$	−30.1711	−1.12992
$714$	1.18814	0.0444651
$715$	6.80102	0.254344
$716$	−18.5957	−0.694952
$717$	−8.34208	−0.311541
$718$	−36.0621	−1.34583
$719$	−0.878213	−0.0327518	−0.0163759	−	0.999866i	$-0.505213\pi$
$719$	−0.878213	−0.0327518	−0.0163759	+	0.999866i	$0.505213\pi$
$720$	6.58819	0.245527
$721$	3.41981	0.127360
$722$	30.8102	1.14664
$723$	17.9947	0.669228
$724$	−33.7325	−1.25366
$725$	11.9328	0.443172
$726$	9.30688	0.345411
$727$	10.7419	0.398395	0.199198	−	0.979959i	$-0.436166\pi$
$727$	10.7419	0.398395	0.199198	+	0.979959i	$0.436166\pi$
$728$	1.15803	0.0429194
$729$	1.00000	0.0370370
$730$	−3.20969	−0.118796
$731$	−1.27335	−0.0470966
$732$	6.49522	0.240070
$733$	44.2308	1.63370	0.816850	−	0.576850i	$-0.195718\pi$
$733$	44.2308	1.63370	0.816850	+	0.576850i	$0.195718\pi$
$734$	−15.1734	−0.560061
$735$	9.17202	0.338315
$736$	22.8078	0.840706
$737$	9.73416	0.358562
$738$	−13.7646	−0.506681
$739$	−19.7025	−0.724768	−0.362384	−	0.932029i	$-0.618037\pi$
$739$	−19.7025	−0.724768	−0.362384	+	0.932029i	$0.618037\pi$
$740$	13.9426	0.512540
$741$	3.18463	0.116990
$742$	−12.1974	−0.447780
$743$	−1.59002	−0.0583323	−0.0291661	−	0.999575i	$-0.509285\pi$
$743$	−1.59002	−0.0583323	−0.0291661	+	0.999575i	$0.509285\pi$
$744$	−8.54572	−0.313301
$745$	−3.93351	−0.144113
$746$	14.5752	0.533638
$747$	−3.28038	−0.120023
$748$	3.71050	0.135669
$749$	3.18049	0.116213
$750$	−21.0133	−0.767297
$751$	1.17844	0.0430018	0.0215009	−	0.999769i	$-0.493156\pi$
$751$	1.17844	0.0430018	0.0215009	+	0.999769i	$0.493156\pi$
$752$	−15.9476	−0.581549
$753$	5.65320	0.206014
$754$	14.5180	0.528713
$755$	−30.5466	−1.11171
$756$	0.957954	0.0348404
$757$	−35.6808	−1.29684	−0.648421	−	0.761282i	$-0.724570\pi$
$757$	−35.6808	−1.29684	−0.648421	+	0.761282i	$0.724570\pi$
$758$	−35.7234	−1.29753
$759$	−7.95052	−0.288586
$760$	−2.03779	−0.0739183
$761$	15.7976	0.572663	0.286331	−	0.958131i	$-0.407564\pi$
$761$	15.7976	0.572663	0.286331	+	0.958131i	$0.407564\pi$
$762$	14.8392	0.537567
$763$	−2.67528	−0.0968515
$764$	−17.6820	−0.639711
$765$	1.39015	0.0502608
$766$	−33.2924	−1.20290
$767$	17.3670	0.627087
$768$	20.7789	0.749795
$769$	10.6389	0.383649	0.191824	−	0.981429i	$-0.438560\pi$
$769$	10.6389	0.383649	0.191824	+	0.981429i	$0.438560\pi$
$770$	−4.05686	−0.146199
$771$	−2.12336	−0.0764711
$772$	0.919173	0.0330818
$773$	38.6280	1.38935	0.694676	−	0.719323i	$-0.255548\pi$
$773$	38.6280	1.38935	0.694676	+	0.719323i	$0.255548\pi$
$774$	−2.38585	−0.0857577
$775$	28.5917	1.02704
$776$	−8.82924	−0.316951
$777$	−4.21003	−0.151034
$778$	27.5633	0.988191
$779$	11.7455	0.420828
$780$	−4.18297	−0.149774
$781$	25.5718	0.915032
$782$	6.06499	0.216884
$783$	−3.89007	−0.139020
$784$	31.2688	1.11674
$785$	1.39015	0.0496164
$786$	−19.6916	−0.702376
$787$	−32.4097	−1.15528	−0.577641	−	0.816291i	$-0.696027\pi$
$787$	−32.4097	−1.15528	−0.577641	+	0.816291i	$0.696027\pi$
$788$	−7.00496	−0.249541
$789$	−0.236397	−0.00841595
$790$	31.4273	1.11813
$791$	2.46726	0.0877258
$792$	−2.25192	−0.0800185
$793$	8.56399	0.304116
$794$	−51.7849	−1.83778
$795$	−14.2711	−0.506145
$796$	26.8591	0.951995
$797$	13.7407	0.486721	0.243361	−	0.969936i	$-0.421750\pi$
$797$	13.7407	0.486721	0.243361	+	0.969936i	$0.421750\pi$
$798$	−1.89965	−0.0672471
$799$	−3.36503	−0.119046
$800$	−21.6138	−0.764165
$801$	7.03647	0.248621
$802$	−59.5058	−2.10122
$803$	3.02669	0.106810
$804$	−5.98700	−0.211145
$805$	−2.85344	−0.100570
$806$	34.7860	1.22529
$807$	21.9024	0.771002
$808$	11.4555	0.403002
$809$	44.3525	1.55935	0.779676	−	0.626184i	$-0.215384\pi$
$809$	44.3525	1.55935	0.779676	+	0.626184i	$0.215384\pi$
$810$	2.60469	0.0915194
$811$	−46.3543	−1.62772	−0.813860	−	0.581061i	$-0.802638\pi$
$811$	−46.3543	−1.62772	−0.813860	+	0.581061i	$0.802638\pi$
$812$	−3.72651	−0.130775
$813$	−25.8623	−0.907029
$814$	−30.5540	−1.07092
$815$	5.60839	0.196453
$816$	4.73921	0.165906
$817$	2.03589	0.0712268
$818$	−13.5714	−0.474512
$819$	1.26307	0.0441352
$820$	−15.4276	−0.538755
$821$	45.4491	1.58619	0.793093	−	0.609101i	$-0.208470\pi$
$821$	45.4491	1.58619	0.793093	+	0.609101i	$0.208470\pi$
$822$	19.8352	0.691832
$823$	−31.1548	−1.08599	−0.542994	−	0.839737i	$-0.682709\pi$
$823$	−31.1548	−1.08599	−0.542994	+	0.839737i	$0.682709\pi$
$824$	4.94448	0.172249
$825$	7.53433	0.262312
$826$	−10.3595	−0.360455
$827$	9.14748	0.318089	0.159045	−	0.987271i	$-0.449159\pi$
$827$	9.14748	0.318089	0.159045	+	0.987271i	$0.449159\pi$
$828$	4.88997	0.169938
$829$	−51.9722	−1.80507	−0.902534	−	0.430619i	$-0.858295\pi$
$829$	−51.9722	−1.80507	−0.902534	+	0.430619i	$0.858295\pi$
$830$	−8.54437	−0.296580
$831$	4.45474	0.154533
$832$	−7.41698	−0.257137
$833$	6.59789	0.228603
$834$	−21.5922	−0.747678
$835$	6.86161	0.237456
$836$	−5.93250	−0.205180
$837$	−9.32086	−0.322176
$838$	−47.6735	−1.64685
$839$	−19.4738	−0.672309	−0.336155	−	0.941807i	$-0.609126\pi$
$839$	−19.4738	−0.672309	−0.336155	+	0.941807i	$0.609126\pi$
$840$	−0.808213	−0.0278860
$841$	−13.8674	−0.478185
$842$	40.9500	1.41123
$843$	−4.92164	−0.169510
$844$	9.93319	0.341915
$845$	12.5566	0.431961
$846$	−6.30499	−0.216770
$847$	−3.14979	−0.108228
$848$	−48.6524	−1.67073
$849$	24.8385	0.852456
$850$	−5.74750	−0.197138
$851$	−21.4905	−0.736685
$852$	−15.7280	−0.538831
$853$	31.6129	1.08241	0.541203	−	0.840892i	$-0.317969\pi$
$853$	31.6129	1.08241	0.541203	+	0.840892i	$0.317969\pi$
$854$	−5.10848	−0.174808
$855$	−2.22263	−0.0760122
$856$	4.59846	0.157172
$857$	1.76488	0.0602872	0.0301436	−	0.999546i	$-0.490404\pi$
$857$	1.76488	0.0602872	0.0301436	+	0.999546i	$0.490404\pi$
$858$	9.16662	0.312943
$859$	37.8699	1.29210	0.646052	−	0.763294i	$-0.276419\pi$
$859$	37.8699	1.29210	0.646052	+	0.763294i	$0.276419\pi$
$860$	−2.67411	−0.0911865
$861$	4.65844	0.158759
$862$	−69.4747	−2.36632
$863$	50.0950	1.70525	0.852627	−	0.522520i	$-0.175008\pi$
$863$	50.0950	1.70525	0.852627	+	0.522520i	$0.175008\pi$
$864$	7.04609	0.239713
$865$	−26.5168	−0.901597
$866$	30.7338	1.04438
$867$	1.00000	0.0339618
$868$	−8.92895	−0.303068
$869$	−29.6355	−1.00532
$870$	−10.1324	−0.343521
$871$	−7.89389	−0.267474
$872$	−3.86801	−0.130987
$873$	−9.63010	−0.325930
$874$	−9.69697	−0.328005
$875$	7.11168	0.240419
$876$	−1.86157	−0.0628965
$877$	20.0685	0.677666	0.338833	−	0.940846i	$-0.389968\pi$
$877$	20.0685	0.677666	0.338833	+	0.940846i	$0.389968\pi$
$878$	2.27284	0.0767045
$879$	−3.11302	−0.105000
$880$	−16.1818	−0.545489
$881$	−18.6483	−0.628279	−0.314139	−	0.949377i	$-0.601716\pi$
$881$	−18.6483	−0.628279	−0.314139	+	0.949377i	$0.601716\pi$
$882$	12.3623	0.416261
$883$	0.508297	0.0171056	0.00855278	−	0.999963i	$-0.497278\pi$
$883$	0.508297	0.0171056	0.00855278	+	0.999963i	$0.497278\pi$
$884$	−3.00902	−0.101204
$885$	−12.1208	−0.407437
$886$	−20.4764	−0.687917
$887$	26.2224	0.880463	0.440232	−	0.897884i	$-0.354896\pi$
$887$	26.2224	0.880463	0.440232	+	0.897884i	$0.354896\pi$
$888$	−6.08701	−0.204267
$889$	−5.02213	−0.168437
$890$	18.3278	0.614349
$891$	−2.45618	−0.0822852
$892$	−26.1524	−0.875649
$893$	5.38016	0.180040
$894$	−5.30170	−0.177315
$895$	17.1120	0.571991
$896$	−4.51189	−0.150732
$897$	6.44745	0.215274
$898$	−29.3126	−0.978174
$899$	36.2588	1.20930
$900$	−4.63399	−0.154466
$901$	−10.2659	−0.342007
$902$	33.8083	1.12569
$903$	0.807461	0.0268706
$904$	3.56726	0.118645
$905$	31.0412	1.03184
$906$	−41.1717	−1.36784
$907$	36.2094	1.20231	0.601157	−	0.799131i	$-0.294707\pi$
$907$	36.2094	1.20231	0.601157	+	0.799131i	$0.294707\pi$
$908$	7.77395	0.257988
$909$	12.4946	0.414418
$910$	3.28990	0.109059
$911$	−37.7972	−1.25228	−0.626138	−	0.779712i	$-0.715365\pi$
$911$	−37.7972	−1.25228	−0.626138	+	0.779712i	$0.715365\pi$
$912$	−7.57726	−0.250908
$913$	8.05722	0.266655
$914$	27.4009	0.906341
$915$	−5.97700	−0.197593
$916$	22.3463	0.738344
$917$	6.66437	0.220077
$918$	1.87368	0.0618406
$919$	25.9541	0.856148	0.428074	−	0.903744i	$-0.359192\pi$
$919$	25.9541	0.856148	0.428074	+	0.903744i	$0.359192\pi$
$920$	−4.12560	−0.136017
$921$	11.3561	0.374196
$922$	−37.1832	−1.22456
$923$	−20.7374	−0.682580
$924$	−2.35291	−0.0774050
$925$	20.3655	0.669615
$926$	−10.5567	−0.346913
$927$	5.39297	0.177128
$928$	−27.4098	−0.899770
$929$	−31.9609	−1.04860	−0.524302	−	0.851532i	$-0.675674\pi$
$929$	−31.9609	−1.04860	−0.524302	+	0.851532i	$0.675674\pi$
$930$	−24.2779	−0.796105
$931$	−10.5490	−0.345729
$932$	12.9337	0.423658
$933$	1.77755	0.0581944
$934$	39.0230	1.27687
$935$	−3.41445	−0.111665
$936$	1.82619	0.0596908
$937$	59.1404	1.93203	0.966016	−	0.258482i	$-0.0832224\pi$
$937$	59.1404	1.93203	0.966016	+	0.258482i	$0.0832224\pi$
$938$	4.70876	0.153746
$939$	5.14107	0.167773
$940$	−7.06676	−0.230492
$941$	19.3609	0.631149	0.315574	−	0.948901i	$-0.397803\pi$
$941$	19.3609	0.631149	0.315574	+	0.948901i	$0.397803\pi$
$942$	1.87368	0.0610478
$943$	23.7795	0.774366
$944$	−41.3217	−1.34491
$945$	−0.881523	−0.0286759
$946$	5.86009	0.190528
$947$	38.9179	1.26466	0.632330	−	0.774699i	$-0.282099\pi$
$947$	38.9179	1.26466	0.632330	+	0.774699i	$0.282099\pi$
$948$	18.2273	0.591996
$949$	−2.45449	−0.0796761
$950$	9.18936	0.298142
$951$	−34.5478	−1.12029
$952$	−0.581387	−0.0188429
$953$	−37.8988	−1.22766	−0.613831	−	0.789438i	$-0.710372\pi$
$953$	−37.8988	−1.22766	−0.613831	+	0.789438i	$0.710372\pi$
$954$	−19.2350	−0.622758
$955$	16.2712	0.526524
$956$	−12.6022	−0.407583
$957$	9.55472	0.308860
$958$	28.0703	0.906912
$959$	−6.71297	−0.216773
$960$	5.17647	0.167070
$961$	55.8785	1.80253
$962$	24.7777	0.798865
$963$	5.01557	0.161625
$964$	27.1841	0.875540
$965$	−0.845837	−0.0272284
$966$	−3.84595	−0.123741
$967$	−41.0577	−1.32033	−0.660164	−	0.751122i	$-0.729513\pi$
$967$	−41.0577	−1.32033	−0.660164	+	0.751122i	$0.729513\pi$
$968$	−4.55408	−0.146374
$969$	−1.59884	−0.0513623
$970$	−25.0834	−0.805379
$971$	−4.02189	−0.129068	−0.0645342	−	0.997915i	$-0.520556\pi$
$971$	−4.02189	−0.129068	−0.0645342	+	0.997915i	$0.520556\pi$
$972$	1.51068	0.0484549
$973$	7.30762	0.234271
$974$	41.0672	1.31588
$975$	−6.10994	−0.195675
$976$	−20.3765	−0.652234
$977$	49.7728	1.59237	0.796186	−	0.605052i	$-0.206848\pi$
$977$	49.7728	1.59237	0.796186	+	0.605052i	$0.206848\pi$
$978$	7.55915	0.241715
$979$	−17.2829	−0.552362
$980$	13.8560	0.442612
$981$	−4.21886	−0.134698
$982$	12.5999	0.402080
$983$	61.1854	1.95151	0.975755	−	0.218864i	$-0.0702352\pi$
$983$	61.1854	1.95151	0.975755	+	0.218864i	$0.0702352\pi$
$984$	6.73534	0.214715
$985$	6.44606	0.205389
$986$	−7.28874	−0.232121
$987$	2.13384	0.0679210
$988$	4.81095	0.153057
$989$	4.12176	0.131064
$990$	−6.39759	−0.203329
$991$	52.2823	1.66080	0.830401	−	0.557166i	$-0.188111\pi$
$991$	52.2823	1.66080	0.830401	+	0.557166i	$0.188111\pi$
$992$	−65.6756	−2.08520
$993$	−6.97356	−0.221299
$994$	12.3700	0.392353
$995$	−24.7161	−0.783554
$996$	−4.95560	−0.157024
$997$	59.6207	1.88821	0.944104	−	0.329648i	$-0.106930\pi$
$997$	59.6207	1.88821	0.944104	+	0.329648i	$0.106930\pi$
$998$	−70.0142	−2.21626
$999$	−6.63914	−0.210053

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.h.1.10	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.h.1.10	✓	56	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)

\(f(q)\)	\(=\)	\(q-1.87368 q^{2} +1.00000 q^{3} +1.51068 q^{4} -1.39015 q^{5} -1.87368 q^{6} +0.634123 q^{7} +0.916837 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.87368 q^{2} +1.00000 q^{3} +1.51068 q^{4} -1.39015 q^{5} -1.87368 q^{6} +0.634123 q^{7} +0.916837 q^{8} +1.00000 q^{9} +2.60469 q^{10} -2.45618 q^{11} +1.51068 q^{12} +1.99183 q^{13} -1.18814 q^{14} -1.39015 q^{15} -4.73921 q^{16} -1.00000 q^{17} -1.87368 q^{18} +1.59884 q^{19} -2.10006 q^{20} +0.634123 q^{21} +4.60210 q^{22} +3.23694 q^{23} +0.916837 q^{24} -3.06750 q^{25} -3.73206 q^{26} +1.00000 q^{27} +0.957954 q^{28} -3.89007 q^{29} +2.60469 q^{30} -9.32086 q^{31} +7.04609 q^{32} -2.45618 q^{33} +1.87368 q^{34} -0.881523 q^{35} +1.51068 q^{36} -6.63914 q^{37} -2.99572 q^{38} +1.99183 q^{39} -1.27454 q^{40} +7.34627 q^{41} -1.18814 q^{42} +1.27335 q^{43} -3.71050 q^{44} -1.39015 q^{45} -6.06499 q^{46} +3.36503 q^{47} -4.73921 q^{48} -6.59789 q^{49} +5.74750 q^{50} -1.00000 q^{51} +3.00902 q^{52} +10.2659 q^{53} -1.87368 q^{54} +3.41445 q^{55} +0.581387 q^{56} +1.59884 q^{57} +7.28874 q^{58} +8.71911 q^{59} -2.10006 q^{60} +4.29955 q^{61} +17.4643 q^{62} +0.634123 q^{63} -3.72369 q^{64} -2.76894 q^{65} +4.60210 q^{66} -3.96312 q^{67} -1.51068 q^{68} +3.23694 q^{69} +1.65169 q^{70} -10.4112 q^{71} +0.916837 q^{72} -1.23227 q^{73} +12.4396 q^{74} -3.06750 q^{75} +2.41533 q^{76} -1.55752 q^{77} -3.73206 q^{78} +12.0657 q^{79} +6.58819 q^{80} +1.00000 q^{81} -13.7646 q^{82} -3.28038 q^{83} +0.957954 q^{84} +1.39015 q^{85} -2.38585 q^{86} -3.89007 q^{87} -2.25192 q^{88} +7.03647 q^{89} +2.60469 q^{90} +1.26307 q^{91} +4.88997 q^{92} -9.32086 q^{93} -6.30499 q^{94} -2.22263 q^{95} +7.04609 q^{96} -9.63010 q^{97} +12.3623 q^{98} -2.45618 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 7 q^{2} + 56 q^{3} + 61 q^{4} + 17 q^{5} + 7 q^{6} + 5 q^{7} + 18 q^{8} + 56 q^{9}+O(q^{10}) \) 56 * q + 7 * q^2 + 56 * q^3 + 61 * q^4 + 17 * q^5 + 7 * q^6 + 5 * q^7 + 18 * q^8 + 56 * q^9	\( 56 q + 7 q^{2} + 56 q^{3} + 61 q^{4} + 17 q^{5} + 7 q^{6} + 5 q^{7} + 18 q^{8} + 56 q^{9} - 2 q^{10} + 35 q^{11} + 61 q^{12} + 8 q^{13} + 36 q^{14} + 17 q^{15} + 71 q^{16} - 56 q^{17} + 7 q^{18} - 2 q^{19} + 58 q^{20} + 5 q^{21} + 27 q^{22} + 40 q^{23} + 18 q^{24} + 85 q^{25} + 15 q^{26} + 56 q^{27} - 4 q^{28} + 41 q^{29} - 2 q^{30} + q^{31} + 43 q^{32} + 35 q^{33} - 7 q^{34} + 57 q^{35} + 61 q^{36} + 34 q^{37} + 52 q^{38} + 8 q^{39} + 14 q^{40} + 49 q^{41} + 36 q^{42} + 27 q^{43} + 66 q^{44} + 17 q^{45} + 10 q^{46} + 43 q^{47} + 71 q^{48} + 51 q^{49} + 30 q^{50} - 56 q^{51} - 7 q^{52} + 73 q^{53} + 7 q^{54} + 15 q^{55} + 118 q^{56} - 2 q^{57} - q^{58} + 53 q^{59} + 58 q^{60} + 15 q^{61} + 16 q^{62} + 5 q^{63} + 124 q^{64} + 107 q^{65} + 27 q^{66} + 20 q^{67} - 61 q^{68} + 40 q^{69} + 16 q^{70} + 56 q^{71} + 18 q^{72} + 49 q^{73} + 28 q^{74} + 85 q^{75} - 38 q^{76} + 50 q^{77} + 15 q^{78} - 4 q^{79} + 74 q^{80} + 56 q^{81} + 59 q^{82} + 35 q^{83} - 4 q^{84} - 17 q^{85} + 38 q^{86} + 41 q^{87} + 64 q^{88} + 66 q^{89} - 2 q^{90} + 5 q^{91} + 96 q^{92} + q^{93} - 12 q^{94} + 70 q^{95} + 43 q^{96} + 60 q^{97} + 26 q^{98} + 35 q^{99}+O(q^{100}) \) 56 * q + 7 * q^2 + 56 * q^3 + 61 * q^4 + 17 * q^5 + 7 * q^6 + 5 * q^7 + 18 * q^8 + 56 * q^9 - 2 * q^10 + 35 * q^11 + 61 * q^12 + 8 * q^13 + 36 * q^14 + 17 * q^15 + 71 * q^16 - 56 * q^17 + 7 * q^18 - 2 * q^19 + 58 * q^20 + 5 * q^21 + 27 * q^22 + 40 * q^23 + 18 * q^24 + 85 * q^25 + 15 * q^26 + 56 * q^27 - 4 * q^28 + 41 * q^29 - 2 * q^30 + q^31 + 43 * q^32 + 35 * q^33 - 7 * q^34 + 57 * q^35 + 61 * q^36 + 34 * q^37 + 52 * q^38 + 8 * q^39 + 14 * q^40 + 49 * q^41 + 36 * q^42 + 27 * q^43 + 66 * q^44 + 17 * q^45 + 10 * q^46 + 43 * q^47 + 71 * q^48 + 51 * q^49 + 30 * q^50 - 56 * q^51 - 7 * q^52 + 73 * q^53 + 7 * q^54 + 15 * q^55 + 118 * q^56 - 2 * q^57 - q^58 + 53 * q^59 + 58 * q^60 + 15 * q^61 + 16 * q^62 + 5 * q^63 + 124 * q^64 + 107 * q^65 + 27 * q^66 + 20 * q^67 - 61 * q^68 + 40 * q^69 + 16 * q^70 + 56 * q^71 + 18 * q^72 + 49 * q^73 + 28 * q^74 + 85 * q^75 - 38 * q^76 + 50 * q^77 + 15 * q^78 - 4 * q^79 + 74 * q^80 + 56 * q^81 + 59 * q^82 + 35 * q^83 - 4 * q^84 - 17 * q^85 + 38 * q^86 + 41 * q^87 + 64 * q^88 + 66 * q^89 - 2 * q^90 + 5 * q^91 + 96 * q^92 + q^93 - 12 * q^94 + 70 * q^95 + 43 * q^96 + 60 * q^97 + 26 * q^98 + 35 * q^99

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