LMFDB - Embedded newform 8007.2.a.e.1.41

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$63.9362168984$
Analytic rank:	$1$
Dimension:	$46$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.41
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)

$f(q)$	$=$	$q+2.22406 q^{2} +1.00000 q^{3} +2.94644 q^{4} -1.48578 q^{5} +2.22406 q^{6} +3.09673 q^{7} +2.10494 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.22406 q^{2} +1.00000 q^{3} +2.94644 q^{4} -1.48578 q^{5} +2.22406 q^{6} +3.09673 q^{7} +2.10494 q^{8} +1.00000 q^{9} -3.30447 q^{10} -5.38754 q^{11} +2.94644 q^{12} -2.35958 q^{13} +6.88731 q^{14} -1.48578 q^{15} -1.21137 q^{16} -1.00000 q^{17} +2.22406 q^{18} -3.03370 q^{19} -4.37777 q^{20} +3.09673 q^{21} -11.9822 q^{22} -4.35972 q^{23} +2.10494 q^{24} -2.79245 q^{25} -5.24784 q^{26} +1.00000 q^{27} +9.12433 q^{28} +7.85913 q^{29} -3.30447 q^{30} -9.03897 q^{31} -6.90404 q^{32} -5.38754 q^{33} -2.22406 q^{34} -4.60107 q^{35} +2.94644 q^{36} +9.47790 q^{37} -6.74713 q^{38} -2.35958 q^{39} -3.12748 q^{40} -8.20710 q^{41} +6.88731 q^{42} +2.13514 q^{43} -15.8741 q^{44} -1.48578 q^{45} -9.69629 q^{46} +2.22766 q^{47} -1.21137 q^{48} +2.58974 q^{49} -6.21057 q^{50} -1.00000 q^{51} -6.95235 q^{52} -11.2271 q^{53} +2.22406 q^{54} +8.00472 q^{55} +6.51843 q^{56} -3.03370 q^{57} +17.4792 q^{58} -5.67894 q^{59} -4.37777 q^{60} +5.05001 q^{61} -20.1032 q^{62} +3.09673 q^{63} -12.9323 q^{64} +3.50582 q^{65} -11.9822 q^{66} +1.62152 q^{67} -2.94644 q^{68} -4.35972 q^{69} -10.2330 q^{70} -4.40914 q^{71} +2.10494 q^{72} -4.39000 q^{73} +21.0794 q^{74} -2.79245 q^{75} -8.93862 q^{76} -16.6838 q^{77} -5.24784 q^{78} -1.04912 q^{79} +1.79984 q^{80} +1.00000 q^{81} -18.2531 q^{82} +3.94602 q^{83} +9.12433 q^{84} +1.48578 q^{85} +4.74869 q^{86} +7.85913 q^{87} -11.3404 q^{88} +16.2851 q^{89} -3.30447 q^{90} -7.30697 q^{91} -12.8457 q^{92} -9.03897 q^{93} +4.95444 q^{94} +4.50742 q^{95} -6.90404 q^{96} +5.65061 q^{97} +5.75974 q^{98} -5.38754 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9}+O(q^{10}) $ 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9} - 10 q^{10} - 25 q^{11} + 43 q^{12} - 8 q^{13} - 28 q^{14} - 19 q^{15} + 33 q^{16} - 46 q^{17} - 5 q^{18} - 2 q^{19} - 56 q^{20} + q^{21} - 19 q^{22} - 64 q^{23} - 18 q^{24} + 11 q^{25} - 13 q^{26} + 46 q^{27} - 38 q^{28} - 51 q^{29} - 10 q^{30} - 19 q^{31} - 61 q^{32} - 25 q^{33} + 5 q^{34} - 39 q^{35} + 43 q^{36} - 46 q^{37} - 48 q^{38} - 8 q^{39} - 10 q^{40} - 53 q^{41} - 28 q^{42} - 33 q^{43} - 62 q^{44} - 19 q^{45} + 2 q^{46} - 45 q^{47} + 33 q^{48} + 21 q^{49} - 60 q^{50} - 46 q^{51} - 63 q^{52} - 47 q^{53} - 5 q^{54} + 5 q^{55} - 82 q^{56} - 2 q^{57} - 21 q^{58} - 65 q^{59} - 56 q^{60} - 37 q^{61} - 46 q^{62} + q^{63} + 74 q^{64} - 85 q^{65} - 19 q^{66} - 52 q^{67} - 43 q^{68} - 64 q^{69} - 20 q^{70} - 48 q^{71} - 18 q^{72} - 39 q^{73} - 16 q^{74} + 11 q^{75} + 42 q^{76} - 78 q^{77} - 13 q^{78} - 26 q^{79} - 78 q^{80} + 46 q^{81} + 3 q^{82} - 47 q^{83} - 38 q^{84} + 19 q^{85} - 6 q^{86} - 51 q^{87} - 58 q^{88} - 58 q^{89} - 10 q^{90} - 43 q^{91} - 68 q^{92} - 19 q^{93} - 78 q^{95} - 61 q^{96} - 44 q^{97} - 4 q^{98} - 25 q^{99}+O(q^{100}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9 - 10 * q^10 - 25 * q^11 + 43 * q^12 - 8 * q^13 - 28 * q^14 - 19 * q^15 + 33 * q^16 - 46 * q^17 - 5 * q^18 - 2 * q^19 - 56 * q^20 + q^21 - 19 * q^22 - 64 * q^23 - 18 * q^24 + 11 * q^25 - 13 * q^26 + 46 * q^27 - 38 * q^28 - 51 * q^29 - 10 * q^30 - 19 * q^31 - 61 * q^32 - 25 * q^33 + 5 * q^34 - 39 * q^35 + 43 * q^36 - 46 * q^37 - 48 * q^38 - 8 * q^39 - 10 * q^40 - 53 * q^41 - 28 * q^42 - 33 * q^43 - 62 * q^44 - 19 * q^45 + 2 * q^46 - 45 * q^47 + 33 * q^48 + 21 * q^49 - 60 * q^50 - 46 * q^51 - 63 * q^52 - 47 * q^53 - 5 * q^54 + 5 * q^55 - 82 * q^56 - 2 * q^57 - 21 * q^58 - 65 * q^59 - 56 * q^60 - 37 * q^61 - 46 * q^62 + q^63 + 74 * q^64 - 85 * q^65 - 19 * q^66 - 52 * q^67 - 43 * q^68 - 64 * q^69 - 20 * q^70 - 48 * q^71 - 18 * q^72 - 39 * q^73 - 16 * q^74 + 11 * q^75 + 42 * q^76 - 78 * q^77 - 13 * q^78 - 26 * q^79 - 78 * q^80 + 46 * q^81 + 3 * q^82 - 47 * q^83 - 38 * q^84 + 19 * q^85 - 6 * q^86 - 51 * q^87 - 58 * q^88 - 58 * q^89 - 10 * q^90 - 43 * q^91 - 68 * q^92 - 19 * q^93 - 78 * q^95 - 61 * q^96 - 44 * q^97 - 4 * q^98 - 25 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.22406	1.57265	0.786324	−	0.617815i	$-0.211982\pi$
$2$	2.22406	1.57265	0.786324	+	0.617815i	$0.211982\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.94644	1.47322
$5$	−1.48578	−0.664462	−0.332231	−	0.943198i	$-0.607801\pi$
$5$	−1.48578	−0.664462	−0.332231	+	0.943198i	$0.607801\pi$
$6$	2.22406	0.907968
$7$	3.09673	1.17045	0.585227	−	0.810869i	$-0.301005\pi$
$7$	3.09673	1.17045	0.585227	+	0.810869i	$0.301005\pi$
$8$	2.10494	0.744208
$9$	1.00000	0.333333
$10$	−3.30447	−1.04496
$11$	−5.38754	−1.62441	−0.812203	−	0.583375i	$-0.801732\pi$
$11$	−5.38754	−1.62441	−0.812203	+	0.583375i	$0.801732\pi$
$12$	2.94644	0.850564
$13$	−2.35958	−0.654429	−0.327214	−	0.944950i	$-0.606110\pi$
$13$	−2.35958	−0.654429	−0.327214	+	0.944950i	$0.606110\pi$
$14$	6.88731	1.84071
$15$	−1.48578	−0.383627
$16$	−1.21137	−0.302843
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	2.22406	0.524216
$19$	−3.03370	−0.695979	−0.347989	−	0.937498i	$-0.613136\pi$
$19$	−3.03370	−0.695979	−0.347989	+	0.937498i	$0.613136\pi$
$20$	−4.37777	−0.978899
$21$	3.09673	0.675762
$22$	−11.9822	−2.55462
$23$	−4.35972	−0.909065	−0.454533	−	0.890730i	$-0.650194\pi$
$23$	−4.35972	−0.909065	−0.454533	+	0.890730i	$0.650194\pi$
$24$	2.10494	0.429669
$25$	−2.79245	−0.558490
$26$	−5.24784	−1.02919
$27$	1.00000	0.192450
$28$	9.12433	1.72434
$29$	7.85913	1.45940	0.729702	−	0.683765i	$-0.239659\pi$
$29$	7.85913	1.45940	0.729702	+	0.683765i	$0.239659\pi$
$30$	−3.30447	−0.603311
$31$	−9.03897	−1.62345	−0.811724	−	0.584042i	$-0.801470\pi$
$31$	−9.03897	−1.62345	−0.811724	+	0.584042i	$0.801470\pi$
$32$	−6.90404	−1.22047
$33$	−5.38754	−0.937851
$34$	−2.22406	−0.381423
$35$	−4.60107	−0.777723
$36$	2.94644	0.491073
$37$	9.47790	1.55816	0.779078	−	0.626926i	$-0.215687\pi$
$37$	9.47790	1.55816	0.779078	+	0.626926i	$0.215687\pi$
$38$	−6.74713	−1.09453
$39$	−2.35958	−0.377835
$40$	−3.12748	−0.494498
$41$	−8.20710	−1.28173	−0.640867	−	0.767652i	$-0.721425\pi$
$41$	−8.20710	−1.28173	−0.640867	+	0.767652i	$0.721425\pi$
$42$	6.88731	1.06274
$43$	2.13514	0.325606	0.162803	−	0.986659i	$-0.447946\pi$
$43$	2.13514	0.325606	0.162803	+	0.986659i	$0.447946\pi$
$44$	−15.8741	−2.39311
$45$	−1.48578	−0.221487
$46$	−9.69629	−1.42964
$47$	2.22766	0.324937	0.162469	−	0.986714i	$-0.448054\pi$
$47$	2.22766	0.324937	0.162469	+	0.986714i	$0.448054\pi$
$48$	−1.21137	−0.174846
$49$	2.58974	0.369963
$50$	−6.21057	−0.878308
$51$	−1.00000	−0.140028
$52$	−6.95235	−0.964117
$53$	−11.2271	−1.54216	−0.771082	−	0.636735i	$-0.780284\pi$
$53$	−11.2271	−1.54216	−0.771082	+	0.636735i	$0.780284\pi$
$54$	2.22406	0.302656
$55$	8.00472	1.07936
$56$	6.51843	0.871062
$57$	−3.03370	−0.401824
$58$	17.4792	2.29513
$59$	−5.67894	−0.739335	−0.369667	−	0.929164i	$-0.620528\pi$
$59$	−5.67894	−0.739335	−0.369667	+	0.929164i	$0.620528\pi$
$60$	−4.37777	−0.565168
$61$	5.05001	0.646588	0.323294	−	0.946299i	$-0.395210\pi$
$61$	5.05001	0.646588	0.323294	+	0.946299i	$0.395210\pi$
$62$	−20.1032	−2.55311
$63$	3.09673	0.390151
$64$	−12.9323	−1.61653
$65$	3.50582	0.434843
$66$	−11.9822	−1.47491
$67$	1.62152	0.198100	0.0990499	−	0.995082i	$-0.468420\pi$
$67$	1.62152	0.198100	0.0990499	+	0.995082i	$0.468420\pi$
$68$	−2.94644	−0.357308
$69$	−4.35972	−0.524849
$70$	−10.2330	−1.22308
$71$	−4.40914	−0.523268	−0.261634	−	0.965167i	$-0.584261\pi$
$71$	−4.40914	−0.523268	−0.261634	+	0.965167i	$0.584261\pi$
$72$	2.10494	0.248069
$73$	−4.39000	−0.513810	−0.256905	−	0.966437i	$-0.582703\pi$
$73$	−4.39000	−0.513810	−0.256905	+	0.966437i	$0.582703\pi$
$74$	21.0794	2.45043
$75$	−2.79245	−0.322444
$76$	−8.93862	−1.02533
$77$	−16.6838	−1.90129
$78$	−5.24784	−0.594201
$79$	−1.04912	−0.118035	−0.0590176	−	0.998257i	$-0.518797\pi$
$79$	−1.04912	−0.118035	−0.0590176	+	0.998257i	$0.518797\pi$
$80$	1.79984	0.201228
$81$	1.00000	0.111111
$82$	−18.2531	−2.01572
$83$	3.94602	0.433132	0.216566	−	0.976268i	$-0.430514\pi$
$83$	3.94602	0.433132	0.216566	+	0.976268i	$0.430514\pi$
$84$	9.12433	0.995546
$85$	1.48578	0.161156
$86$	4.74869	0.512064
$87$	7.85913	0.842587
$88$	−11.3404	−1.20890
$89$	16.2851	1.72621	0.863106	−	0.505023i	$-0.168516\pi$
$89$	16.2851	1.72621	0.863106	+	0.505023i	$0.168516\pi$
$90$	−3.30447	−0.348322
$91$	−7.30697	−0.765979
$92$	−12.8457	−1.33925
$93$	−9.03897	−0.937298
$94$	4.95444	0.511012
$95$	4.50742	0.462452
$96$	−6.90404	−0.704641
$97$	5.65061	0.573733	0.286866	−	0.957971i	$-0.407386\pi$
$97$	5.65061	0.573733	0.286866	+	0.957971i	$0.407386\pi$
$98$	5.75974	0.581821
$99$	−5.38754	−0.541469
$100$	−8.22779	−0.822779
$101$	−4.45536	−0.443325	−0.221663	−	0.975123i	$-0.571148\pi$
$101$	−4.45536	−0.443325	−0.221663	+	0.975123i	$0.571148\pi$
$102$	−2.22406	−0.220215
$103$	4.40377	0.433916	0.216958	−	0.976181i	$-0.430387\pi$
$103$	4.40377	0.433916	0.216958	+	0.976181i	$0.430387\pi$
$104$	−4.96676	−0.487031
$105$	−4.60107	−0.449018
$106$	−24.9698	−2.42528
$107$	−5.70095	−0.551132	−0.275566	−	0.961282i	$-0.588865\pi$
$107$	−5.70095	−0.551132	−0.275566	+	0.961282i	$0.588865\pi$
$108$	2.94644	0.283521
$109$	−17.9124	−1.71570	−0.857849	−	0.513902i	$-0.828200\pi$
$109$	−17.9124	−1.71570	−0.857849	+	0.513902i	$0.828200\pi$
$110$	17.8030	1.69745
$111$	9.47790	0.899602
$112$	−3.75129	−0.354464
$113$	−0.669117	−0.0629452	−0.0314726	−	0.999505i	$-0.510020\pi$
$113$	−0.669117	−0.0629452	−0.0314726	+	0.999505i	$0.510020\pi$
$114$	−6.74713	−0.631927
$115$	6.47760	0.604040
$116$	23.1565	2.15002
$117$	−2.35958	−0.218143
$118$	−12.6303	−1.16271
$119$	−3.09673	−0.283877
$120$	−3.12748	−0.285499
$121$	18.0256	1.63869
$122$	11.2315	1.01685
$123$	−8.20710	−0.740009
$124$	−26.6328	−2.39169
$125$	11.5779	1.03556
$126$	6.88731	0.613571
$127$	−15.1782	−1.34685	−0.673424	−	0.739257i	$-0.735177\pi$
$127$	−15.1782	−1.34685	−0.673424	+	0.739257i	$0.735177\pi$
$128$	−14.9540	−1.32176
$129$	2.13514	0.187989
$130$	7.79714	0.683855
$131$	0.362197	0.0316453	0.0158226	−	0.999875i	$-0.494963\pi$
$131$	0.362197	0.0316453	0.0158226	+	0.999875i	$0.494963\pi$
$132$	−15.8741	−1.38166
$133$	−9.39456	−0.814611
$134$	3.60635	0.311541
$135$	−1.48578	−0.127876
$136$	−2.10494	−0.180497
$137$	11.9601	1.02182	0.510911	−	0.859633i	$-0.329308\pi$
$137$	11.9601	1.02182	0.510911	+	0.859633i	$0.329308\pi$
$138$	−9.69629	−0.825403
$139$	−0.192267	−0.0163078	−0.00815392	−	0.999967i	$-0.502596\pi$
$139$	−0.192267	−0.0163078	−0.00815392	+	0.999967i	$0.502596\pi$
$140$	−13.5568	−1.14576
$141$	2.22766	0.187603
$142$	−9.80618	−0.822916
$143$	12.7123	1.06306
$144$	−1.21137	−0.100948
$145$	−11.6770	−0.969719
$146$	−9.76362	−0.808043
$147$	2.58974	0.213598
$148$	27.9261	2.29551
$149$	−11.3935	−0.933390	−0.466695	−	0.884418i	$-0.654555\pi$
$149$	−11.3935	−0.933390	−0.466695	+	0.884418i	$0.654555\pi$
$150$	−6.21057	−0.507091
$151$	20.9554	1.70533	0.852663	−	0.522462i	$-0.174986\pi$
$151$	20.9554	1.70533	0.852663	+	0.522462i	$0.174986\pi$
$152$	−6.38576	−0.517953
$153$	−1.00000	−0.0808452
$154$	−37.1057	−2.99006
$155$	13.4299	1.07872
$156$	−6.95235	−0.556633
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	−2.33331	−0.185628
$159$	−11.2271	−0.890369
$160$	10.2579	0.810958
$161$	−13.5009	−1.06402
$162$	2.22406	0.174739
$163$	25.2298	1.97615	0.988075	−	0.153971i	$-0.0492061\pi$
$163$	25.2298	1.97615	0.988075	+	0.153971i	$0.0492061\pi$
$164$	−24.1817	−1.88828
$165$	8.00472	0.623167
$166$	8.77619	0.681164
$167$	−3.05611	−0.236489	−0.118244	−	0.992985i	$-0.537727\pi$
$167$	−3.05611	−0.236489	−0.118244	+	0.992985i	$0.537727\pi$
$168$	6.51843	0.502908
$169$	−7.43240	−0.571723
$170$	3.30447	0.253441
$171$	−3.03370	−0.231993
$172$	6.29107	0.479690
$173$	−0.299755	−0.0227899	−0.0113950	−	0.999935i	$-0.503627\pi$
$173$	−0.299755	−0.0227899	−0.0113950	+	0.999935i	$0.503627\pi$
$174$	17.4792	1.32509
$175$	−8.64747	−0.653687
$176$	6.52632	0.491940
$177$	−5.67894	−0.426855
$178$	36.2189	2.71472
$179$	−23.7625	−1.77609	−0.888044	−	0.459758i	$-0.847936\pi$
$179$	−23.7625	−1.77609	−0.888044	+	0.459758i	$0.847936\pi$
$180$	−4.37777	−0.326300
$181$	9.36043	0.695755	0.347878	−	0.937540i	$-0.386902\pi$
$181$	9.36043	0.695755	0.347878	+	0.937540i	$0.386902\pi$
$182$	−16.2511	−1.20461
$183$	5.05001	0.373308
$184$	−9.17695	−0.676534
$185$	−14.0821	−1.03534
$186$	−20.1032	−1.47404
$187$	5.38754	0.393976
$188$	6.56366	0.478704
$189$	3.09673	0.225254
$190$	10.0248	0.727273
$191$	19.1837	1.38808	0.694042	−	0.719934i	$-0.255828\pi$
$191$	19.1837	1.38808	0.694042	+	0.719934i	$0.255828\pi$
$192$	−12.9323	−0.933305
$193$	−4.55079	−0.327573	−0.163787	−	0.986496i	$-0.552371\pi$
$193$	−4.55079	−0.327573	−0.163787	+	0.986496i	$0.552371\pi$
$194$	12.5673	0.902279
$195$	3.50582	0.251057
$196$	7.63052	0.545037
$197$	0.661992	0.0471650	0.0235825	−	0.999722i	$-0.492493\pi$
$197$	0.661992	0.0471650	0.0235825	+	0.999722i	$0.492493\pi$
$198$	−11.9822	−0.851539
$199$	5.92778	0.420209	0.210105	−	0.977679i	$-0.432619\pi$
$199$	5.92778	0.420209	0.210105	+	0.977679i	$0.432619\pi$
$200$	−5.87794	−0.415633
$201$	1.62152	0.114373
$202$	−9.90899	−0.697194
$203$	24.3376	1.70817
$204$	−2.94644	−0.206292
$205$	12.1940	0.851664
$206$	9.79424	0.682397
$207$	−4.35972	−0.303022
$208$	2.85832	0.198189
$209$	16.3442	1.13055
$210$	−10.2330	−0.706148
$211$	−6.97687	−0.480308	−0.240154	−	0.970735i	$-0.577198\pi$
$211$	−6.97687	−0.480308	−0.240154	+	0.970735i	$0.577198\pi$
$212$	−33.0801	−2.27195
$213$	−4.40914	−0.302109
$214$	−12.6793	−0.866736
$215$	−3.17236	−0.216353
$216$	2.10494	0.143223
$217$	−27.9913	−1.90017
$218$	−39.8383	−2.69819
$219$	−4.39000	−0.296649
$220$	23.5854	1.59013
$221$	2.35958	0.158722
$222$	21.0794	1.41476
$223$	10.5109	0.703864	0.351932	−	0.936026i	$-0.385525\pi$
$223$	10.5109	0.703864	0.351932	+	0.936026i	$0.385525\pi$
$224$	−21.3800	−1.42851
$225$	−2.79245	−0.186163
$226$	−1.48816	−0.0989906
$227$	−2.66436	−0.176840	−0.0884199	−	0.996083i	$-0.528182\pi$
$227$	−2.66436	−0.176840	−0.0884199	+	0.996083i	$0.528182\pi$
$228$	−8.93862	−0.591975
$229$	−22.1892	−1.46630	−0.733152	−	0.680065i	$-0.761952\pi$
$229$	−22.1892	−1.46630	−0.733152	+	0.680065i	$0.761952\pi$
$230$	14.4066	0.949941
$231$	−16.6838	−1.09771
$232$	16.5430	1.08610
$233$	−24.1902	−1.58475	−0.792376	−	0.610034i	$-0.791156\pi$
$233$	−24.1902	−1.58475	−0.792376	+	0.610034i	$0.791156\pi$
$234$	−5.24784	−0.343062
$235$	−3.30982	−0.215909
$236$	−16.7327	−1.08920
$237$	−1.04912	−0.0681477
$238$	−6.88731	−0.446438
$239$	12.8397	0.830533	0.415266	−	0.909700i	$-0.363688\pi$
$239$	12.8397	0.830533	0.415266	+	0.909700i	$0.363688\pi$
$240$	1.79984	0.116179
$241$	20.0177	1.28945	0.644727	−	0.764413i	$-0.276971\pi$
$241$	20.0177	1.28945	0.644727	+	0.764413i	$0.276971\pi$
$242$	40.0901	2.57709
$243$	1.00000	0.0641500
$244$	14.8796	0.952566
$245$	−3.84779	−0.245826
$246$	−18.2531	−1.16377
$247$	7.15825	0.455469
$248$	−19.0265	−1.20818
$249$	3.94602	0.250069
$250$	25.7499	1.62857
$251$	8.32166	0.525259	0.262629	−	0.964897i	$-0.415410\pi$
$251$	8.32166	0.525259	0.262629	+	0.964897i	$0.415410\pi$
$252$	9.12433	0.574779
$253$	23.4882	1.47669
$254$	−33.7572	−2.11812
$255$	1.48578	0.0930433
$256$	−7.39411	−0.462132
$257$	−27.4424	−1.71181	−0.855905	−	0.517133i	$-0.826999\pi$
$257$	−27.4424	−1.71181	−0.855905	+	0.517133i	$0.826999\pi$
$258$	4.74869	0.295640
$259$	29.3505	1.82375
$260$	10.3297	0.640619
$261$	7.85913	0.486468
$262$	0.805547	0.0497668
$263$	−9.83411	−0.606397	−0.303199	−	0.952927i	$-0.598055\pi$
$263$	−9.83411	−0.606397	−0.303199	+	0.952927i	$0.598055\pi$
$264$	−11.3404	−0.697956
$265$	16.6811	1.02471
$266$	−20.8941	−1.28110
$267$	16.2851	0.996629
$268$	4.77770	0.291845
$269$	−13.3851	−0.816105	−0.408053	−	0.912958i	$-0.633792\pi$
$269$	−13.3851	−0.816105	−0.408053	+	0.912958i	$0.633792\pi$
$270$	−3.30447	−0.201104
$271$	0.589286	0.0357966	0.0178983	−	0.999840i	$-0.494302\pi$
$271$	0.589286	0.0357966	0.0178983	+	0.999840i	$0.494302\pi$
$272$	1.21137	0.0734502
$273$	−7.30697	−0.442238
$274$	26.6000	1.60697
$275$	15.0444	0.907214
$276$	−12.8457	−0.773218
$277$	−4.88708	−0.293636	−0.146818	−	0.989164i	$-0.546903\pi$
$277$	−4.88708	−0.293636	−0.146818	+	0.989164i	$0.546903\pi$
$278$	−0.427613	−0.0256465
$279$	−9.03897	−0.541149
$280$	−9.68497	−0.578787
$281$	1.20895	0.0721199	0.0360599	−	0.999350i	$-0.488519\pi$
$281$	1.20895	0.0721199	0.0360599	+	0.999350i	$0.488519\pi$
$282$	4.95444	0.295033
$283$	28.3981	1.68809	0.844045	−	0.536273i	$-0.180168\pi$
$283$	28.3981	1.68809	0.844045	+	0.536273i	$0.180168\pi$
$284$	−12.9913	−0.770889
$285$	4.50742	0.266997
$286$	28.2730	1.67181
$287$	−25.4152	−1.50021
$288$	−6.90404	−0.406824
$289$	1.00000	0.0588235
$290$	−25.9703	−1.52503
$291$	5.65061	0.331245
$292$	−12.9349	−0.756956
$293$	8.15265	0.476283	0.238141	−	0.971230i	$-0.423462\pi$
$293$	8.15265	0.476283	0.238141	+	0.971230i	$0.423462\pi$
$294$	5.75974	0.335915
$295$	8.43767	0.491260
$296$	19.9504	1.15959
$297$	−5.38754	−0.312617
$298$	−25.3398	−1.46789
$299$	10.2871	0.594918
$300$	−8.22779	−0.475031
$301$	6.61196	0.381107
$302$	46.6060	2.68188
$303$	−4.45536	−0.255954
$304$	3.67494	0.210772
$305$	−7.50322	−0.429633
$306$	−2.22406	−0.127141
$307$	−4.17711	−0.238400	−0.119200	−	0.992870i	$-0.538033\pi$
$307$	−4.17711	−0.238400	−0.119200	+	0.992870i	$0.538033\pi$
$308$	−49.1577	−2.80102
$309$	4.40377	0.250522
$310$	29.8690	1.69644
$311$	−22.0807	−1.25208	−0.626041	−	0.779790i	$-0.715326\pi$
$311$	−22.0807	−1.25208	−0.626041	+	0.779790i	$0.715326\pi$
$312$	−4.96676	−0.281188
$313$	19.1492	1.08238	0.541188	−	0.840902i	$-0.317975\pi$
$313$	19.1492	1.08238	0.541188	+	0.840902i	$0.317975\pi$
$314$	2.22406	0.125511
$315$	−4.60107	−0.259241
$316$	−3.09117	−0.173892
$317$	−8.18106	−0.459494	−0.229747	−	0.973250i	$-0.573790\pi$
$317$	−8.18106	−0.459494	−0.229747	+	0.973250i	$0.573790\pi$
$318$	−24.9698	−1.40024
$319$	−42.3414	−2.37066
$320$	19.2145	1.07412
$321$	−5.70095	−0.318196
$322$	−30.0268	−1.67333
$323$	3.03370	0.168800
$324$	2.94644	0.163691
$325$	6.58900	0.365492
$326$	56.1126	3.10779
$327$	−17.9124	−0.990559
$328$	−17.2754	−0.953877
$329$	6.89846	0.380324
$330$	17.8030	0.980021
$331$	5.05041	0.277595	0.138798	−	0.990321i	$-0.455676\pi$
$331$	5.05041	0.277595	0.138798	+	0.990321i	$0.455676\pi$
$332$	11.6267	0.638099
$333$	9.47790	0.519386
$334$	−6.79696	−0.371913
$335$	−2.40922	−0.131630
$336$	−3.75129	−0.204650
$337$	−8.27191	−0.450599	−0.225300	−	0.974289i	$-0.572336\pi$
$337$	−8.27191	−0.450599	−0.225300	+	0.974289i	$0.572336\pi$
$338$	−16.5301	−0.899119
$339$	−0.669117	−0.0363414
$340$	4.37777	0.237418
$341$	48.6979	2.63714
$342$	−6.74713	−0.364843
$343$	−13.6574	−0.737429
$344$	4.49434	0.242319
$345$	6.47760	0.348742
$346$	−0.666672	−0.0358405
$347$	−10.2787	−0.551789	−0.275895	−	0.961188i	$-0.588974\pi$
$347$	−10.2787	−0.551789	−0.275895	+	0.961188i	$0.588974\pi$
$348$	23.1565	1.24132
$349$	−19.7558	−1.05750	−0.528752	−	0.848776i	$-0.677340\pi$
$349$	−19.7558	−1.05750	−0.528752	+	0.848776i	$0.677340\pi$
$350$	−19.2325	−1.02802
$351$	−2.35958	−0.125945
$352$	37.1958	1.98254
$353$	−33.0027	−1.75655	−0.878277	−	0.478152i	$-0.841307\pi$
$353$	−33.0027	−1.75655	−0.878277	+	0.478152i	$0.841307\pi$
$354$	−12.6303	−0.671293
$355$	6.55102	0.347692
$356$	47.9829	2.54309
$357$	−3.09673	−0.163896
$358$	−52.8491	−2.79316
$359$	24.2419	1.27944	0.639719	−	0.768609i	$-0.279051\pi$
$359$	24.2419	1.27944	0.639719	+	0.768609i	$0.279051\pi$
$360$	−3.12748	−0.164833
$361$	−9.79665	−0.515613
$362$	20.8182	1.09418
$363$	18.0256	0.946101
$364$	−21.5296	−1.12846
$365$	6.52258	0.341408
$366$	11.2315	0.587081
$367$	−11.3249	−0.591154	−0.295577	−	0.955319i	$-0.595512\pi$
$367$	−11.3249	−0.591154	−0.295577	+	0.955319i	$0.595512\pi$
$368$	5.28125	0.275304
$369$	−8.20710	−0.427245
$370$	−31.3194	−1.62822
$371$	−34.7674	−1.80503
$372$	−26.6328	−1.38085
$373$	24.6989	1.27886	0.639429	−	0.768850i	$-0.279171\pi$
$373$	24.6989	1.27886	0.639429	+	0.768850i	$0.279171\pi$
$374$	11.9822	0.619586
$375$	11.5779	0.597879
$376$	4.68908	0.241821
$377$	−18.5442	−0.955076
$378$	6.88731	0.354245
$379$	−24.8336	−1.27562	−0.637808	−	0.770196i	$-0.720159\pi$
$379$	−24.8336	−1.27562	−0.637808	+	0.770196i	$0.720159\pi$
$380$	13.2808	0.681293
$381$	−15.1782	−0.777603
$382$	42.6657	2.18297
$383$	20.5227	1.04866	0.524331	−	0.851514i	$-0.324315\pi$
$383$	20.5227	1.04866	0.524331	+	0.851514i	$0.324315\pi$
$384$	−14.9540	−0.763119
$385$	24.7885	1.26334
$386$	−10.1212	−0.515157
$387$	2.13514	0.108535
$388$	16.6492	0.845234
$389$	−12.8309	−0.650553	−0.325276	−	0.945619i	$-0.605457\pi$
$389$	−12.8309	−0.650553	−0.325276	+	0.945619i	$0.605457\pi$
$390$	7.79714	0.394824
$391$	4.35972	0.220481
$392$	5.45125	0.275330
$393$	0.362197	0.0182704
$394$	1.47231	0.0741739
$395$	1.55876	0.0784300
$396$	−15.8741	−0.797702
$397$	−3.48268	−0.174791	−0.0873953	−	0.996174i	$-0.527854\pi$
$397$	−3.48268	−0.174791	−0.0873953	+	0.996174i	$0.527854\pi$
$398$	13.1837	0.660841
$399$	−9.39456	−0.470316
$400$	3.38270	0.169135
$401$	7.72553	0.385795	0.192897	−	0.981219i	$-0.438212\pi$
$401$	7.72553	0.385795	0.192897	+	0.981219i	$0.438212\pi$
$402$	3.60635	0.179868
$403$	21.3281	1.06243
$404$	−13.1275	−0.653115
$405$	−1.48578	−0.0738291
$406$	54.1283	2.68634
$407$	−51.0626	−2.53108
$408$	−2.10494	−0.104210
$409$	2.75085	0.136021	0.0680105	−	0.997685i	$-0.478335\pi$
$409$	2.75085	0.136021	0.0680105	+	0.997685i	$0.478335\pi$
$410$	27.1201	1.33937
$411$	11.9601	0.589949
$412$	12.9754	0.639254
$413$	−17.5861	−0.865358
$414$	−9.69629	−0.476546
$415$	−5.86293	−0.287800
$416$	16.2906	0.798713
$417$	−0.192267	−0.00941534
$418$	36.3505	1.77796
$419$	−16.9565	−0.828381	−0.414190	−	0.910190i	$-0.635935\pi$
$419$	−16.9565	−0.828381	−0.414190	+	0.910190i	$0.635935\pi$
$420$	−13.5568	−0.661503
$421$	7.67753	0.374180	0.187090	−	0.982343i	$-0.440094\pi$
$421$	7.67753	0.374180	0.187090	+	0.982343i	$0.440094\pi$
$422$	−15.5170	−0.755355
$423$	2.22766	0.108312
$424$	−23.6324	−1.14769
$425$	2.79245	0.135454
$426$	−9.80618	−0.475111
$427$	15.6385	0.756802
$428$	−16.7975	−0.811938
$429$	12.7123	0.613757
$430$	−7.05551	−0.340247
$431$	−30.2346	−1.45635	−0.728175	−	0.685392i	$-0.759631\pi$
$431$	−30.2346	−1.45635	−0.728175	+	0.685392i	$0.759631\pi$
$432$	−1.21137	−0.0582822
$433$	−3.00624	−0.144470	−0.0722352	−	0.997388i	$-0.523013\pi$
$433$	−3.00624	−0.144470	−0.0722352	+	0.997388i	$0.523013\pi$
$434$	−62.2542	−2.98830
$435$	−11.6770	−0.559867
$436$	−52.7778	−2.52760
$437$	13.2261	0.632690
$438$	−9.76362	−0.466524
$439$	0.676690	0.0322967	0.0161483	−	0.999870i	$-0.494860\pi$
$439$	0.676690	0.0322967	0.0161483	+	0.999870i	$0.494860\pi$
$440$	16.8494	0.803266
$441$	2.58974	0.123321
$442$	5.24784	0.249614
$443$	34.6509	1.64632	0.823158	−	0.567813i	$-0.192210\pi$
$443$	34.6509	1.64632	0.823158	+	0.567813i	$0.192210\pi$
$444$	27.9261	1.32531
$445$	−24.1960	−1.14700
$446$	23.3769	1.10693
$447$	−11.3935	−0.538893
$448$	−40.0477	−1.89208
$449$	−17.5696	−0.829161	−0.414580	−	0.910013i	$-0.636072\pi$
$449$	−17.5696	−0.829161	−0.414580	+	0.910013i	$0.636072\pi$
$450$	−6.21057	−0.292769
$451$	44.2161	2.08206
$452$	−1.97151	−0.0927321
$453$	20.9554	0.984570
$454$	−5.92570	−0.278107
$455$	10.8566	0.508964
$456$	−6.38576	−0.299040
$457$	28.8984	1.35181	0.675905	−	0.736989i	$-0.263753\pi$
$457$	28.8984	1.35181	0.675905	+	0.736989i	$0.263753\pi$
$458$	−49.3501	−2.30598
$459$	−1.00000	−0.0466760
$460$	19.0859	0.889883
$461$	−11.6610	−0.543107	−0.271553	−	0.962423i	$-0.587537\pi$
$461$	−11.6610	−0.543107	−0.271553	+	0.962423i	$0.587537\pi$
$462$	−37.1057	−1.72631
$463$	2.94554	0.136891	0.0684455	−	0.997655i	$-0.478196\pi$
$463$	2.94554	0.136891	0.0684455	+	0.997655i	$0.478196\pi$
$464$	−9.52033	−0.441970
$465$	13.4299	0.622799
$466$	−53.8004	−2.49225
$467$	34.4909	1.59605	0.798025	−	0.602625i	$-0.205878\pi$
$467$	34.4909	1.59605	0.798025	+	0.602625i	$0.205878\pi$
$468$	−6.95235	−0.321372
$469$	5.02140	0.231867
$470$	−7.36123	−0.339548
$471$	1.00000	0.0460776
$472$	−11.9538	−0.550219
$473$	−11.5032	−0.528917
$474$	−2.33331	−0.107172
$475$	8.47146	0.388697
$476$	−9.12433	−0.418213
$477$	−11.2271	−0.514055
$478$	28.5563	1.30614
$479$	9.48069	0.433184	0.216592	−	0.976262i	$-0.430506\pi$
$479$	9.48069	0.433184	0.216592	+	0.976262i	$0.430506\pi$
$480$	10.2579	0.468207
$481$	−22.3638	−1.01970
$482$	44.5206	2.02786
$483$	−13.5009	−0.614312
$484$	53.1115	2.41416
$485$	−8.39558	−0.381224
$486$	2.22406	0.100885
$487$	39.1358	1.77341	0.886705	−	0.462335i	$-0.152988\pi$
$487$	39.1358	1.77341	0.886705	+	0.462335i	$0.152988\pi$
$488$	10.6300	0.481196
$489$	25.2298	1.14093
$490$	−8.55772	−0.386598
$491$	9.60913	0.433654	0.216827	−	0.976210i	$-0.430429\pi$
$491$	9.60913	0.433654	0.216827	+	0.976210i	$0.430429\pi$
$492$	−24.1817	−1.09020
$493$	−7.85913	−0.353958
$494$	15.9204	0.716291
$495$	8.00472	0.359785
$496$	10.9496	0.491650
$497$	−13.6539	−0.612462
$498$	8.77619	0.393270
$499$	−2.57053	−0.115073	−0.0575363	−	0.998343i	$-0.518324\pi$
$499$	−2.57053	−0.115073	−0.0575363	+	0.998343i	$0.518324\pi$
$500$	34.1135	1.52560
$501$	−3.05611	−0.136537
$502$	18.5079	0.826047
$503$	−32.9446	−1.46893	−0.734463	−	0.678649i	$-0.762566\pi$
$503$	−32.9446	−1.46893	−0.734463	+	0.678649i	$0.762566\pi$
$504$	6.51843	0.290354
$505$	6.61970	0.294573
$506$	52.2392	2.32231
$507$	−7.43240	−0.330085
$508$	−44.7216	−1.98420
$509$	−3.52500	−0.156243	−0.0781215	−	0.996944i	$-0.524892\pi$
$509$	−3.52500	−0.156243	−0.0781215	+	0.996944i	$0.524892\pi$
$510$	3.30447	0.146324
$511$	−13.5946	−0.601392
$512$	13.4631	0.594990
$513$	−3.03370	−0.133941
$514$	−61.0335	−2.69207
$515$	−6.54304	−0.288321
$516$	6.29107	0.276949
$517$	−12.0016	−0.527830
$518$	65.2773	2.86812
$519$	−0.299755	−0.0131578
$520$	7.37953	0.323614
$521$	−38.1233	−1.67021	−0.835106	−	0.550089i	$-0.814594\pi$
$521$	−38.1233	−1.67021	−0.835106	+	0.550089i	$0.814594\pi$
$522$	17.4792	0.765043
$523$	33.4572	1.46298	0.731490	−	0.681852i	$-0.238825\pi$
$523$	33.4572	1.46298	0.731490	+	0.681852i	$0.238825\pi$
$524$	1.06719	0.0466204
$525$	−8.64747	−0.377406
$526$	−21.8717	−0.953649
$527$	9.03897	0.393744
$528$	6.52632	0.284022
$529$	−3.99280	−0.173600
$530$	37.0997	1.61151
$531$	−5.67894	−0.246445
$532$	−27.6805	−1.20010
$533$	19.3653	0.838803
$534$	36.2189	1.56735
$535$	8.47037	0.366206
$536$	3.41319	0.147428
$537$	−23.7625	−1.02543
$538$	−29.7693	−1.28345
$539$	−13.9523	−0.600970
$540$	−4.37777	−0.188389
$541$	−17.6219	−0.757625	−0.378812	−	0.925474i	$-0.623667\pi$
$541$	−17.6219	−0.757625	−0.378812	+	0.925474i	$0.623667\pi$
$542$	1.31061	0.0562954
$543$	9.36043	0.401695
$544$	6.90404	0.296008
$545$	26.6140	1.14002
$546$	−16.2511	−0.695485
$547$	−10.5724	−0.452044	−0.226022	−	0.974122i	$-0.572572\pi$
$547$	−10.5724	−0.452044	−0.226022	+	0.974122i	$0.572572\pi$
$548$	35.2398	1.50537
$549$	5.05001	0.215529
$550$	33.4597	1.42673
$551$	−23.8423	−1.01571
$552$	−9.17695	−0.390597
$553$	−3.24884	−0.138155
$554$	−10.8692	−0.461786
$555$	−14.0821	−0.597752
$556$	−0.566502	−0.0240250
$557$	−17.6879	−0.749460	−0.374730	−	0.927134i	$-0.622265\pi$
$557$	−17.6879	−0.749460	−0.374730	+	0.927134i	$0.622265\pi$
$558$	−20.1032	−0.851037
$559$	−5.03803	−0.213086
$560$	5.57361	0.235528
$561$	5.38754	0.227462
$562$	2.68877	0.113419
$563$	32.1637	1.35554	0.677770	−	0.735274i	$-0.262947\pi$
$563$	32.1637	1.35554	0.677770	+	0.735274i	$0.262947\pi$
$564$	6.56366	0.276380
$565$	0.994162	0.0418247
$566$	63.1590	2.65477
$567$	3.09673	0.130050
$568$	−9.28096	−0.389420
$569$	−20.1786	−0.845932	−0.422966	−	0.906146i	$-0.639011\pi$
$569$	−20.1786	−0.845932	−0.422966	+	0.906146i	$0.639011\pi$
$570$	10.0248	0.419892
$571$	10.3479	0.433047	0.216524	−	0.976277i	$-0.430528\pi$
$571$	10.3479	0.433047	0.216524	+	0.976277i	$0.430528\pi$
$572$	37.4561	1.56612
$573$	19.1837	0.801411
$574$	−56.5249	−2.35930
$575$	12.1743	0.507704
$576$	−12.9323	−0.538844
$577$	4.54483	0.189204	0.0946018	−	0.995515i	$-0.469842\pi$
$577$	4.54483	0.189204	0.0946018	+	0.995515i	$0.469842\pi$
$578$	2.22406	0.0925087
$579$	−4.55079	−0.189124
$580$	−34.4055	−1.42861
$581$	12.2198	0.506961
$582$	12.5673	0.520931
$583$	60.4867	2.50510
$584$	−9.24068	−0.382382
$585$	3.50582	0.144948
$586$	18.1320	0.749025
$587$	−43.9967	−1.81594	−0.907969	−	0.419037i	$-0.862368\pi$
$587$	−43.9967	−1.81594	−0.907969	+	0.419037i	$0.862368\pi$
$588$	7.63052	0.314677
$589$	27.4215	1.12989
$590$	18.7659	0.772579
$591$	0.661992	0.0272307
$592$	−11.4813	−0.471877
$593$	14.7640	0.606284	0.303142	−	0.952945i	$-0.401964\pi$
$593$	14.7640	0.606284	0.303142	+	0.952945i	$0.401964\pi$
$594$	−11.9822	−0.491636
$595$	4.60107	0.188625
$596$	−33.5702	−1.37509
$597$	5.92778	0.242608
$598$	22.8791	0.935597
$599$	−0.565292	−0.0230972	−0.0115486	−	0.999933i	$-0.503676\pi$
$599$	−0.565292	−0.0230972	−0.0115486	+	0.999933i	$0.503676\pi$
$600$	−5.87794	−0.239966
$601$	45.6462	1.86195	0.930974	−	0.365085i	$-0.118960\pi$
$601$	45.6462	1.86195	0.930974	+	0.365085i	$0.118960\pi$
$602$	14.7054	0.599347
$603$	1.62152	0.0660333
$604$	61.7438	2.51232
$605$	−26.7822	−1.08885
$606$	−9.90899	−0.402525
$607$	20.3583	0.826316	0.413158	−	0.910659i	$-0.364426\pi$
$607$	20.3583	0.826316	0.413158	+	0.910659i	$0.364426\pi$
$608$	20.9448	0.849424
$609$	24.3376	0.986210
$610$	−16.6876	−0.675662
$611$	−5.25633	−0.212648
$612$	−2.94644	−0.119103
$613$	−16.9450	−0.684401	−0.342201	−	0.939627i	$-0.611172\pi$
$613$	−16.9450	−0.684401	−0.342201	+	0.939627i	$0.611172\pi$
$614$	−9.29015	−0.374920
$615$	12.1940	0.491708
$616$	−35.1183	−1.41496
$617$	−39.5803	−1.59344	−0.796722	−	0.604346i	$-0.793435\pi$
$617$	−39.5803	−1.59344	−0.796722	+	0.604346i	$0.793435\pi$
$618$	9.79424	0.393982
$619$	−17.3245	−0.696332	−0.348166	−	0.937433i	$-0.613195\pi$
$619$	−17.3245	−0.696332	−0.348166	+	0.937433i	$0.613195\pi$
$620$	39.5705	1.58919
$621$	−4.35972	−0.174950
$622$	−49.1088	−1.96908
$623$	50.4304	2.02045
$624$	2.85832	0.114425
$625$	−3.23997	−0.129599
$626$	42.5889	1.70220
$627$	16.3442	0.652725
$628$	2.94644	0.117576
$629$	−9.47790	−0.377909
$630$	−10.2330	−0.407694
$631$	6.41240	0.255274	0.127637	−	0.991821i	$-0.459261\pi$
$631$	6.41240	0.255274	0.127637	+	0.991821i	$0.459261\pi$
$632$	−2.20833	−0.0878428
$633$	−6.97687	−0.277306
$634$	−18.1952	−0.722623
$635$	22.5515	0.894929
$636$	−33.0801	−1.31171
$637$	−6.11069	−0.242114
$638$	−94.1698	−3.72822
$639$	−4.40914	−0.174423
$640$	22.2184	0.878260
$641$	−38.8684	−1.53521	−0.767604	−	0.640925i	$-0.778551\pi$
$641$	−38.8684	−1.53521	−0.767604	+	0.640925i	$0.778551\pi$
$642$	−12.6793	−0.500410
$643$	−20.1198	−0.793448	−0.396724	−	0.917938i	$-0.629853\pi$
$643$	−20.1198	−0.793448	−0.396724	+	0.917938i	$0.629853\pi$
$644$	−39.7796	−1.56753
$645$	−3.17236	−0.124911
$646$	6.74713	0.265462
$647$	11.3706	0.447025	0.223513	−	0.974701i	$-0.428248\pi$
$647$	11.3706	0.447025	0.223513	+	0.974701i	$0.428248\pi$
$648$	2.10494	0.0826898
$649$	30.5955	1.20098
$650$	14.6543	0.574790
$651$	−27.9913	−1.09706
$652$	74.3381	2.91130
$653$	44.7933	1.75290	0.876449	−	0.481494i	$-0.159906\pi$
$653$	44.7933	1.75290	0.876449	+	0.481494i	$0.159906\pi$
$654$	−39.8383	−1.55780
$655$	−0.538145	−0.0210271
$656$	9.94185	0.388164
$657$	−4.39000	−0.171270
$658$	15.3426	0.598116
$659$	28.4243	1.10725	0.553626	−	0.832765i	$-0.313244\pi$
$659$	28.4243	1.10725	0.553626	+	0.832765i	$0.313244\pi$
$660$	23.5854	0.918061
$661$	−26.4612	−1.02922	−0.514611	−	0.857424i	$-0.672064\pi$
$661$	−26.4612	−1.02922	−0.514611	+	0.857424i	$0.672064\pi$
$662$	11.2324	0.436560
$663$	2.35958	0.0916383
$664$	8.30613	0.322340
$665$	13.9583	0.541279
$666$	21.0794	0.816811
$667$	−34.2637	−1.32669
$668$	−9.00463	−0.348400
$669$	10.5109	0.406376
$670$	−5.35825	−0.207007
$671$	−27.2072	−1.05032
$672$	−21.3800	−0.824750
$673$	−16.6885	−0.643295	−0.321647	−	0.946859i	$-0.604237\pi$
$673$	−16.6885	−0.643295	−0.321647	+	0.946859i	$0.604237\pi$
$674$	−18.3972	−0.708634
$675$	−2.79245	−0.107481
$676$	−21.8991	−0.842274
$677$	−2.17242	−0.0834929	−0.0417464	−	0.999128i	$-0.513292\pi$
$677$	−2.17242	−0.0834929	−0.0417464	+	0.999128i	$0.513292\pi$
$678$	−1.48816	−0.0571522
$679$	17.4984	0.671528
$680$	3.12748	0.119933
$681$	−2.66436	−0.102099
$682$	108.307	4.14729
$683$	−29.4083	−1.12528	−0.562638	−	0.826704i	$-0.690213\pi$
$683$	−29.4083	−1.12528	−0.562638	+	0.826704i	$0.690213\pi$
$684$	−8.93862	−0.341777
$685$	−17.7701	−0.678962
$686$	−30.3748	−1.15972
$687$	−22.1892	−0.846571
$688$	−2.58645	−0.0986076
$689$	26.4913	1.00924
$690$	14.4066	0.548449
$691$	−39.3982	−1.49878	−0.749390	−	0.662129i	$-0.769653\pi$
$691$	−39.3982	−1.49878	−0.749390	+	0.662129i	$0.769653\pi$
$692$	−0.883210	−0.0335746
$693$	−16.6838	−0.633764
$694$	−22.8604	−0.867770
$695$	0.285667	0.0108359
$696$	16.5430	0.627060
$697$	8.20710	0.310866
$698$	−43.9381	−1.66308
$699$	−24.1902	−0.914957
$700$	−25.4792	−0.963025
$701$	−7.20638	−0.272181	−0.136091	−	0.990696i	$-0.543454\pi$
$701$	−7.20638	−0.272181	−0.136091	+	0.990696i	$0.543454\pi$
$702$	−5.24784	−0.198067
$703$	−28.7531	−1.08444
$704$	69.6731	2.62590
$705$	−3.30982	−0.124655
$706$	−73.3999	−2.76244
$707$	−13.7971	−0.518892
$708$	−16.7327	−0.628852
$709$	−37.0792	−1.39254	−0.696270	−	0.717780i	$-0.745158\pi$
$709$	−37.0792	−1.39254	−0.696270	+	0.717780i	$0.745158\pi$
$710$	14.5699	0.546797
$711$	−1.04912	−0.0393451
$712$	34.2790	1.28466
$713$	39.4074	1.47582
$714$	−6.88731	−0.257751
$715$	−18.8877	−0.706362
$716$	−70.0146	−2.61657
$717$	12.8397	0.479508
$718$	53.9154	2.01210
$719$	−15.1358	−0.564468	−0.282234	−	0.959346i	$-0.591076\pi$
$719$	−15.1358	−0.564468	−0.282234	+	0.959346i	$0.591076\pi$
$720$	1.79984	0.0670759
$721$	13.6373	0.507879
$722$	−21.7883	−0.810878
$723$	20.0177	0.744467
$724$	27.5799	1.02500
$725$	−21.9462	−0.815063
$726$	40.0901	1.48788
$727$	10.5647	0.391825	0.195912	−	0.980621i	$-0.437233\pi$
$727$	10.5647	0.391825	0.195912	+	0.980621i	$0.437233\pi$
$728$	−15.3807	−0.570048
$729$	1.00000	0.0370370
$730$	14.5066	0.536914
$731$	−2.13514	−0.0789711
$732$	14.8796	0.549964
$733$	8.78762	0.324578	0.162289	−	0.986743i	$-0.448112\pi$
$733$	8.78762	0.324578	0.162289	+	0.986743i	$0.448112\pi$
$734$	−25.1872	−0.929677
$735$	−3.84779	−0.141928
$736$	30.0997	1.10949
$737$	−8.73600	−0.321795
$738$	−18.2531	−0.671905
$739$	−1.99998	−0.0735705	−0.0367852	−	0.999323i	$-0.511712\pi$
$739$	−1.99998	−0.0735705	−0.0367852	+	0.999323i	$0.511712\pi$
$740$	−41.4921	−1.52528
$741$	7.15825	0.262965
$742$	−77.3247	−2.83868
$743$	−44.9718	−1.64986	−0.824928	−	0.565238i	$-0.808784\pi$
$743$	−44.9718	−1.64986	−0.824928	+	0.565238i	$0.808784\pi$
$744$	−19.0265	−0.697544
$745$	16.9282	0.620203
$746$	54.9317	2.01119
$747$	3.94602	0.144377
$748$	15.8741	0.580414
$749$	−17.6543	−0.645074
$750$	25.7499	0.940254
$751$	−40.0333	−1.46084	−0.730418	−	0.683000i	$-0.760675\pi$
$751$	−40.0333	−1.46084	−0.730418	+	0.683000i	$0.760675\pi$
$752$	−2.69852	−0.0984050
$753$	8.32166	0.303258
$754$	−41.2434	−1.50200
$755$	−31.1352	−1.13312
$756$	9.12433	0.331849
$757$	−28.8005	−1.04677	−0.523386	−	0.852096i	$-0.675331\pi$
$757$	−28.8005	−1.04677	−0.523386	+	0.852096i	$0.675331\pi$
$758$	−55.2314	−2.00609
$759$	23.4882	0.852568
$760$	9.48784	0.344160
$761$	−10.8833	−0.394521	−0.197260	−	0.980351i	$-0.563204\pi$
$761$	−10.8833	−0.394521	−0.197260	+	0.980351i	$0.563204\pi$
$762$	−33.7572	−1.22289
$763$	−55.4699	−2.00815
$764$	56.5236	2.04495
$765$	1.48578	0.0537186
$766$	45.6438	1.64918
$767$	13.3999	0.483842
$768$	−7.39411	−0.266812
$769$	27.0028	0.973747	0.486874	−	0.873472i	$-0.338137\pi$
$769$	27.0028	0.973747	0.486874	+	0.873472i	$0.338137\pi$
$770$	55.1310	1.98678
$771$	−27.4424	−0.988314
$772$	−13.4086	−0.482587
$773$	−40.9391	−1.47248	−0.736238	−	0.676723i	$-0.763400\pi$
$773$	−40.9391	−1.47248	−0.736238	+	0.676723i	$0.763400\pi$
$774$	4.74869	0.170688
$775$	25.2409	0.906679
$776$	11.8942	0.426976
$777$	29.3505	1.05294
$778$	−28.5367	−1.02309
$779$	24.8979	0.892060
$780$	10.3297	0.369862
$781$	23.7544	0.850000
$782$	9.69629	0.346738
$783$	7.85913	0.280862
$784$	−3.13714	−0.112041
$785$	−1.48578	−0.0530299
$786$	0.805547	0.0287329
$787$	−8.74257	−0.311639	−0.155819	−	0.987786i	$-0.549802\pi$
$787$	−8.74257	−0.311639	−0.155819	+	0.987786i	$0.549802\pi$
$788$	1.95052	0.0694844
$789$	−9.83411	−0.350104
$790$	3.46679	0.123343
$791$	−2.07207	−0.0736745
$792$	−11.3404	−0.402965
$793$	−11.9159	−0.423146
$794$	−7.74568	−0.274884
$795$	16.6811	0.591617
$796$	17.4659	0.619061
$797$	−11.4084	−0.404105	−0.202053	−	0.979375i	$-0.564761\pi$
$797$	−11.4084	−0.404105	−0.202053	+	0.979375i	$0.564761\pi$
$798$	−20.8941	−0.739642
$799$	−2.22766	−0.0788089
$800$	19.2792	0.681622
$801$	16.2851	0.575404
$802$	17.1820	0.606719
$803$	23.6513	0.834637
$804$	4.77770	0.168497
$805$	20.0594	0.707001
$806$	47.4350	1.67083
$807$	−13.3851	−0.471178
$808$	−9.37826	−0.329926
$809$	53.4072	1.87770	0.938848	−	0.344331i	$-0.111894\pi$
$809$	53.4072	1.87770	0.938848	+	0.344331i	$0.111894\pi$
$810$	−3.30447	−0.116107
$811$	−28.0315	−0.984320	−0.492160	−	0.870505i	$-0.663793\pi$
$811$	−28.0315	−0.984320	−0.492160	+	0.870505i	$0.663793\pi$
$812$	71.7093	2.51650
$813$	0.589286	0.0206672
$814$	−113.566	−3.98050
$815$	−37.4860	−1.31308
$816$	1.21137	0.0424065
$817$	−6.47739	−0.226615
$818$	6.11806	0.213913
$819$	−7.30697	−0.255326
$820$	35.9288	1.25469
$821$	−7.31377	−0.255252	−0.127626	−	0.991822i	$-0.540736\pi$
$821$	−7.31377	−0.255252	−0.127626	+	0.991822i	$0.540736\pi$
$822$	26.6000	0.927782
$823$	15.2136	0.530312	0.265156	−	0.964206i	$-0.414577\pi$
$823$	15.2136	0.530312	0.265156	+	0.964206i	$0.414577\pi$
$824$	9.26966	0.322924
$825$	15.0444	0.523781
$826$	−39.1126	−1.36090
$827$	27.5279	0.957239	0.478619	−	0.878023i	$-0.341137\pi$
$827$	27.5279	0.957239	0.478619	+	0.878023i	$0.341137\pi$
$828$	−12.8457	−0.446418
$829$	47.1192	1.63652	0.818258	−	0.574851i	$-0.194940\pi$
$829$	47.1192	1.63652	0.818258	+	0.574851i	$0.194940\pi$
$830$	−13.0395	−0.452608
$831$	−4.88708	−0.169531
$832$	30.5146	1.05790
$833$	−2.58974	−0.0897292
$834$	−0.427613	−0.0148070
$835$	4.54071	0.157138
$836$	48.1572	1.66555
$837$	−9.03897	−0.312433
$838$	−37.7123	−1.30275
$839$	−18.1005	−0.624899	−0.312449	−	0.949934i	$-0.601149\pi$
$839$	−18.1005	−0.624899	−0.312449	+	0.949934i	$0.601149\pi$
$840$	−9.68497	−0.334163
$841$	32.7660	1.12986
$842$	17.0753	0.588453
$843$	1.20895	0.0416384
$844$	−20.5569	−0.707599
$845$	11.0429	0.379888
$846$	4.95444	0.170337
$847$	55.8206	1.91802
$848$	13.6002	0.467034
$849$	28.3981	0.974619
$850$	6.21057	0.213021
$851$	−41.3210	−1.41647
$852$	−12.9913	−0.445073
$853$	27.0153	0.924987	0.462493	−	0.886623i	$-0.346955\pi$
$853$	27.0153	0.924987	0.462493	+	0.886623i	$0.346955\pi$
$854$	34.7810	1.19018
$855$	4.50742	0.154151
$856$	−12.0001	−0.410157
$857$	25.4285	0.868622	0.434311	−	0.900763i	$-0.356992\pi$
$857$	25.4285	0.868622	0.434311	+	0.900763i	$0.356992\pi$
$858$	28.2730	0.965223
$859$	30.7889	1.05050	0.525252	−	0.850947i	$-0.323971\pi$
$859$	30.7889	1.05050	0.525252	+	0.850947i	$0.323971\pi$
$860$	−9.34716	−0.318736
$861$	−25.4152	−0.866147
$862$	−67.2435	−2.29032
$863$	−12.3704	−0.421092	−0.210546	−	0.977584i	$-0.567524\pi$
$863$	−12.3704	−0.421092	−0.210546	+	0.977584i	$0.567524\pi$
$864$	−6.90404	−0.234880
$865$	0.445370	0.0151431
$866$	−6.68605	−0.227201
$867$	1.00000	0.0339618
$868$	−82.4746	−2.79937
$869$	5.65218	0.191737
$870$	−25.9703	−0.880474
$871$	−3.82609	−0.129642
$872$	−37.7045	−1.27684
$873$	5.65061	0.191244
$874$	29.4156	0.994999
$875$	35.8536	1.21207
$876$	−12.9349	−0.437029
$877$	−9.68091	−0.326901	−0.163451	−	0.986552i	$-0.552262\pi$
$877$	−9.68091	−0.326901	−0.163451	+	0.986552i	$0.552262\pi$
$878$	1.50500	0.0507913
$879$	8.15265	0.274982
$880$	−9.69669	−0.326875
$881$	46.9955	1.58332	0.791659	−	0.610963i	$-0.209218\pi$
$881$	46.9955	1.58332	0.791659	+	0.610963i	$0.209218\pi$
$882$	5.75974	0.193940
$883$	33.2481	1.11889	0.559444	−	0.828868i	$-0.311015\pi$
$883$	33.2481	1.11889	0.559444	+	0.828868i	$0.311015\pi$
$884$	6.95235	0.233833
$885$	8.43767	0.283629
$886$	77.0657	2.58907
$887$	−42.3830	−1.42308	−0.711541	−	0.702645i	$-0.752002\pi$
$887$	−42.3830	−1.42308	−0.711541	+	0.702645i	$0.752002\pi$
$888$	19.9504	0.669491
$889$	−47.0028	−1.57642
$890$	−53.8134	−1.80383
$891$	−5.38754	−0.180490
$892$	30.9698	1.03695
$893$	−6.75805	−0.226150
$894$	−25.3398	−0.847489
$895$	35.3058	1.18014
$896$	−46.3085	−1.54706
$897$	10.2871	0.343476
$898$	−39.0758	−1.30398
$899$	−71.0385	−2.36927
$900$	−8.22779	−0.274260
$901$	11.2271	0.374030
$902$	98.3393	3.27434
$903$	6.61196	0.220032
$904$	−1.40845	−0.0468443
$905$	−13.9076	−0.462303
$906$	46.6060	1.54838
$907$	−31.9958	−1.06240	−0.531202	−	0.847245i	$-0.678260\pi$
$907$	−31.9958	−1.06240	−0.531202	+	0.847245i	$0.678260\pi$
$908$	−7.85038	−0.260524
$909$	−4.45536	−0.147775
$910$	24.1457	0.800421
$911$	−17.9249	−0.593879	−0.296940	−	0.954896i	$-0.595966\pi$
$911$	−17.9249	−0.593879	−0.296940	+	0.954896i	$0.595966\pi$
$912$	3.67494	0.121689
$913$	−21.2594	−0.703582
$914$	64.2717	2.12592
$915$	−7.50322	−0.248049
$916$	−65.3792	−2.16019
$917$	1.12163	0.0370393
$918$	−2.22406	−0.0734049
$919$	14.0593	0.463773	0.231887	−	0.972743i	$-0.425510\pi$
$919$	14.0593	0.463773	0.231887	+	0.972743i	$0.425510\pi$
$920$	13.6350	0.449531
$921$	−4.17711	−0.137641
$922$	−25.9347	−0.854115
$923$	10.4037	0.342442
$924$	−49.1577	−1.61717
$925$	−26.4666	−0.870215
$926$	6.55107	0.215281
$927$	4.40377	0.144639
$928$	−54.2598	−1.78116
$929$	10.1328	0.332446	0.166223	−	0.986088i	$-0.446843\pi$
$929$	10.1328	0.332446	0.166223	+	0.986088i	$0.446843\pi$
$930$	29.8690	0.979443
$931$	−7.85650	−0.257487
$932$	−71.2749	−2.33469
$933$	−22.0807	−0.722890
$934$	76.7098	2.51002
$935$	−8.00472	−0.261782
$936$	−4.96676	−0.162344
$937$	−43.5919	−1.42408	−0.712042	−	0.702137i	$-0.752229\pi$
$937$	−43.5919	−1.42408	−0.712042	+	0.702137i	$0.752229\pi$
$938$	11.1679	0.364645
$939$	19.1492	0.624910
$940$	−9.75217	−0.318081
$941$	41.5504	1.35450	0.677252	−	0.735751i	$-0.263171\pi$
$941$	41.5504	1.35450	0.677252	+	0.735751i	$0.263171\pi$
$942$	2.22406	0.0724638
$943$	35.7807	1.16518
$944$	6.87931	0.223902
$945$	−4.60107	−0.149673
$946$	−25.5838	−0.831800
$947$	58.8706	1.91304	0.956518	−	0.291672i	$-0.0942116\pi$
$947$	58.8706	1.91304	0.956518	+	0.291672i	$0.0942116\pi$
$948$	−3.09117	−0.100397
$949$	10.3585	0.336252
$950$	18.8410	0.611284
$951$	−8.18106	−0.265289
$952$	−6.51843	−0.211263
$953$	−4.94438	−0.160164	−0.0800822	−	0.996788i	$-0.525518\pi$
$953$	−4.94438	−0.160164	−0.0800822	+	0.996788i	$0.525518\pi$
$954$	−24.9698	−0.808427
$955$	−28.5028	−0.922329
$956$	37.8315	1.22356
$957$	−42.3414	−1.36870
$958$	21.0856	0.681245
$959$	37.0373	1.19600
$960$	19.2145	0.620146
$961$	50.7030	1.63558
$962$	−49.7385	−1.60363
$963$	−5.70095	−0.183711
$964$	58.9810	1.89965
$965$	6.76149	0.217660
$966$	−30.0268	−0.966096
$967$	−58.2081	−1.87185	−0.935923	−	0.352204i	$-0.885432\pi$
$967$	−58.2081	−1.87185	−0.935923	+	0.352204i	$0.885432\pi$
$968$	37.9429	1.21953
$969$	3.03370	0.0974565
$970$	−18.6723	−0.599530
$971$	37.2170	1.19435	0.597175	−	0.802111i	$-0.296290\pi$
$971$	37.2170	1.19435	0.597175	+	0.802111i	$0.296290\pi$
$972$	2.94644	0.0945071
$973$	−0.595398	−0.0190876
$974$	87.0403	2.78895
$975$	6.58900	0.211017
$976$	−6.11744	−0.195815
$977$	10.4581	0.334586	0.167293	−	0.985907i	$-0.446497\pi$
$977$	10.4581	0.334586	0.167293	+	0.985907i	$0.446497\pi$
$978$	56.1126	1.79428
$979$	−87.7364	−2.80407
$980$	−11.3373	−0.362156
$981$	−17.9124	−0.571899
$982$	21.3713	0.681985
$983$	−22.7156	−0.724514	−0.362257	−	0.932078i	$-0.617994\pi$
$983$	−22.7156	−0.724514	−0.362257	+	0.932078i	$0.617994\pi$
$984$	−17.2754	−0.550721
$985$	−0.983576	−0.0313393
$986$	−17.4792	−0.556650
$987$	6.89846	0.219580
$988$	21.0914	0.671005
$989$	−9.30864	−0.295997
$990$	17.8030	0.565816
$991$	39.9033	1.26757	0.633785	−	0.773509i	$-0.281500\pi$
$991$	39.9033	1.26757	0.633785	+	0.773509i	$0.281500\pi$
$992$	62.4054	1.98137
$993$	5.05041	0.160270
$994$	−30.3671	−0.963186
$995$	−8.80740	−0.279213
$996$	11.6267	0.368407
$997$	54.7738	1.73470	0.867352	−	0.497695i	$-0.165820\pi$
$997$	54.7738	1.73470	0.867352	+	0.497695i	$0.165820\pi$
$998$	−5.71701	−0.180969
$999$	9.47790	0.299867

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.e.1.41	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.e.1.41	✓	46	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q+2.22406 q^{2} +1.00000 q^{3} +2.94644 q^{4} -1.48578 q^{5} +2.22406 q^{6} +3.09673 q^{7} +2.10494 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.22406 q^{2} +1.00000 q^{3} +2.94644 q^{4} -1.48578 q^{5} +2.22406 q^{6} +3.09673 q^{7} +2.10494 q^{8} +1.00000 q^{9} -3.30447 q^{10} -5.38754 q^{11} +2.94644 q^{12} -2.35958 q^{13} +6.88731 q^{14} -1.48578 q^{15} -1.21137 q^{16} -1.00000 q^{17} +2.22406 q^{18} -3.03370 q^{19} -4.37777 q^{20} +3.09673 q^{21} -11.9822 q^{22} -4.35972 q^{23} +2.10494 q^{24} -2.79245 q^{25} -5.24784 q^{26} +1.00000 q^{27} +9.12433 q^{28} +7.85913 q^{29} -3.30447 q^{30} -9.03897 q^{31} -6.90404 q^{32} -5.38754 q^{33} -2.22406 q^{34} -4.60107 q^{35} +2.94644 q^{36} +9.47790 q^{37} -6.74713 q^{38} -2.35958 q^{39} -3.12748 q^{40} -8.20710 q^{41} +6.88731 q^{42} +2.13514 q^{43} -15.8741 q^{44} -1.48578 q^{45} -9.69629 q^{46} +2.22766 q^{47} -1.21137 q^{48} +2.58974 q^{49} -6.21057 q^{50} -1.00000 q^{51} -6.95235 q^{52} -11.2271 q^{53} +2.22406 q^{54} +8.00472 q^{55} +6.51843 q^{56} -3.03370 q^{57} +17.4792 q^{58} -5.67894 q^{59} -4.37777 q^{60} +5.05001 q^{61} -20.1032 q^{62} +3.09673 q^{63} -12.9323 q^{64} +3.50582 q^{65} -11.9822 q^{66} +1.62152 q^{67} -2.94644 q^{68} -4.35972 q^{69} -10.2330 q^{70} -4.40914 q^{71} +2.10494 q^{72} -4.39000 q^{73} +21.0794 q^{74} -2.79245 q^{75} -8.93862 q^{76} -16.6838 q^{77} -5.24784 q^{78} -1.04912 q^{79} +1.79984 q^{80} +1.00000 q^{81} -18.2531 q^{82} +3.94602 q^{83} +9.12433 q^{84} +1.48578 q^{85} +4.74869 q^{86} +7.85913 q^{87} -11.3404 q^{88} +16.2851 q^{89} -3.30447 q^{90} -7.30697 q^{91} -12.8457 q^{92} -9.03897 q^{93} +4.95444 q^{94} +4.50742 q^{95} -6.90404 q^{96} +5.65061 q^{97} +5.75974 q^{98} -5.38754 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9}+O(q^{10}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9} - 10 q^{10} - 25 q^{11} + 43 q^{12} - 8 q^{13} - 28 q^{14} - 19 q^{15} + 33 q^{16} - 46 q^{17} - 5 q^{18} - 2 q^{19} - 56 q^{20} + q^{21} - 19 q^{22} - 64 q^{23} - 18 q^{24} + 11 q^{25} - 13 q^{26} + 46 q^{27} - 38 q^{28} - 51 q^{29} - 10 q^{30} - 19 q^{31} - 61 q^{32} - 25 q^{33} + 5 q^{34} - 39 q^{35} + 43 q^{36} - 46 q^{37} - 48 q^{38} - 8 q^{39} - 10 q^{40} - 53 q^{41} - 28 q^{42} - 33 q^{43} - 62 q^{44} - 19 q^{45} + 2 q^{46} - 45 q^{47} + 33 q^{48} + 21 q^{49} - 60 q^{50} - 46 q^{51} - 63 q^{52} - 47 q^{53} - 5 q^{54} + 5 q^{55} - 82 q^{56} - 2 q^{57} - 21 q^{58} - 65 q^{59} - 56 q^{60} - 37 q^{61} - 46 q^{62} + q^{63} + 74 q^{64} - 85 q^{65} - 19 q^{66} - 52 q^{67} - 43 q^{68} - 64 q^{69} - 20 q^{70} - 48 q^{71} - 18 q^{72} - 39 q^{73} - 16 q^{74} + 11 q^{75} + 42 q^{76} - 78 q^{77} - 13 q^{78} - 26 q^{79} - 78 q^{80} + 46 q^{81} + 3 q^{82} - 47 q^{83} - 38 q^{84} + 19 q^{85} - 6 q^{86} - 51 q^{87} - 58 q^{88} - 58 q^{89} - 10 q^{90} - 43 q^{91} - 68 q^{92} - 19 q^{93} - 78 q^{95} - 61 q^{96} - 44 q^{97} - 4 q^{98} - 25 q^{99}+O(q^{100}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9 - 10 * q^10 - 25 * q^11 + 43 * q^12 - 8 * q^13 - 28 * q^14 - 19 * q^15 + 33 * q^16 - 46 * q^17 - 5 * q^18 - 2 * q^19 - 56 * q^20 + q^21 - 19 * q^22 - 64 * q^23 - 18 * q^24 + 11 * q^25 - 13 * q^26 + 46 * q^27 - 38 * q^28 - 51 * q^29 - 10 * q^30 - 19 * q^31 - 61 * q^32 - 25 * q^33 + 5 * q^34 - 39 * q^35 + 43 * q^36 - 46 * q^37 - 48 * q^38 - 8 * q^39 - 10 * q^40 - 53 * q^41 - 28 * q^42 - 33 * q^43 - 62 * q^44 - 19 * q^45 + 2 * q^46 - 45 * q^47 + 33 * q^48 + 21 * q^49 - 60 * q^50 - 46 * q^51 - 63 * q^52 - 47 * q^53 - 5 * q^54 + 5 * q^55 - 82 * q^56 - 2 * q^57 - 21 * q^58 - 65 * q^59 - 56 * q^60 - 37 * q^61 - 46 * q^62 + q^63 + 74 * q^64 - 85 * q^65 - 19 * q^66 - 52 * q^67 - 43 * q^68 - 64 * q^69 - 20 * q^70 - 48 * q^71 - 18 * q^72 - 39 * q^73 - 16 * q^74 + 11 * q^75 + 42 * q^76 - 78 * q^77 - 13 * q^78 - 26 * q^79 - 78 * q^80 + 46 * q^81 + 3 * q^82 - 47 * q^83 - 38 * q^84 + 19 * q^85 - 6 * q^86 - 51 * q^87 - 58 * q^88 - 58 * q^89 - 10 * q^90 - 43 * q^91 - 68 * q^92 - 19 * q^93 - 78 * q^95 - 61 * q^96 - 44 * q^97 - 4 * q^98 - 25 * q^99

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