LMFDB - Embedded newform 8002.2.a.e.1.52

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8002,2,Mod(1,8002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8002, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8002 = 2 \cdot 4001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8002.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:	$63.8962916974$
Analytic rank:	$0$
Dimension:	$77$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.52
Character	$\chi$	$=$	8002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.25254 q^{3} +1.00000 q^{4} +3.78927 q^{5} -1.25254 q^{6} -0.301847 q^{7} -1.00000 q^{8} -1.43115 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.25254 q^{3} +1.00000 q^{4} +3.78927 q^{5} -1.25254 q^{6} -0.301847 q^{7} -1.00000 q^{8} -1.43115 q^{9} -3.78927 q^{10} -2.38376 q^{11} +1.25254 q^{12} -0.101009 q^{13} +0.301847 q^{14} +4.74621 q^{15} +1.00000 q^{16} +0.673322 q^{17} +1.43115 q^{18} -6.01720 q^{19} +3.78927 q^{20} -0.378075 q^{21} +2.38376 q^{22} +2.18685 q^{23} -1.25254 q^{24} +9.35858 q^{25} +0.101009 q^{26} -5.55018 q^{27} -0.301847 q^{28} +1.21872 q^{29} -4.74621 q^{30} +0.941940 q^{31} -1.00000 q^{32} -2.98575 q^{33} -0.673322 q^{34} -1.14378 q^{35} -1.43115 q^{36} +6.27420 q^{37} +6.01720 q^{38} -0.126518 q^{39} -3.78927 q^{40} +1.34283 q^{41} +0.378075 q^{42} +7.72190 q^{43} -2.38376 q^{44} -5.42302 q^{45} -2.18685 q^{46} +10.1353 q^{47} +1.25254 q^{48} -6.90889 q^{49} -9.35858 q^{50} +0.843362 q^{51} -0.101009 q^{52} +0.118920 q^{53} +5.55018 q^{54} -9.03271 q^{55} +0.301847 q^{56} -7.53677 q^{57} -1.21872 q^{58} +9.00032 q^{59} +4.74621 q^{60} +4.76267 q^{61} -0.941940 q^{62} +0.431988 q^{63} +1.00000 q^{64} -0.382752 q^{65} +2.98575 q^{66} +13.3882 q^{67} +0.673322 q^{68} +2.73912 q^{69} +1.14378 q^{70} -4.72336 q^{71} +1.43115 q^{72} +3.34711 q^{73} -6.27420 q^{74} +11.7220 q^{75} -6.01720 q^{76} +0.719531 q^{77} +0.126518 q^{78} +6.96333 q^{79} +3.78927 q^{80} -2.65836 q^{81} -1.34283 q^{82} -1.88085 q^{83} -0.378075 q^{84} +2.55140 q^{85} -7.72190 q^{86} +1.52649 q^{87} +2.38376 q^{88} -12.8656 q^{89} +5.42302 q^{90} +0.0304894 q^{91} +2.18685 q^{92} +1.17982 q^{93} -10.1353 q^{94} -22.8008 q^{95} -1.25254 q^{96} -11.0599 q^{97} +6.90889 q^{98} +3.41152 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9}+O(q^{10}) $ 77 * q - 77 * q^2 + 10 * q^3 + 77 * q^4 + 18 * q^5 - 10 * q^6 + 21 * q^7 - 77 * q^8 + 71 * q^9	\( 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9} - 18 q^{10} + 30 q^{11} + 10 q^{12} - 2 q^{13} - 21 q^{14} + 21 q^{15} + 77 q^{16} + 60 q^{17} - 71 q^{18} - 3 q^{19} + 18 q^{20} + 10 q^{21} - 30 q^{22} + 53 q^{23} - 10 q^{24} + 59 q^{25} + 2 q^{26} + 43 q^{27} + 21 q^{28} + 30 q^{29} - 21 q^{30} + 22 q^{31} - 77 q^{32} + 31 q^{33} - 60 q^{34} + 41 q^{35} + 71 q^{36} - 3 q^{37} + 3 q^{38} + 44 q^{39} - 18 q^{40} + 48 q^{41} - 10 q^{42} + 21 q^{43} + 30 q^{44} + 33 q^{45} - 53 q^{46} + 107 q^{47} + 10 q^{48} + 24 q^{49} - 59 q^{50} + 18 q^{51} - 2 q^{52} + 42 q^{53} - 43 q^{54} + 49 q^{55} - 21 q^{56} + 32 q^{57} - 30 q^{58} + 42 q^{59} + 21 q^{60} - 31 q^{61} - 22 q^{62} + 109 q^{63} + 77 q^{64} + 39 q^{65} - 31 q^{66} - q^{67} + 60 q^{68} - 33 q^{69} - 41 q^{70} + 58 q^{71} - 71 q^{72} + 35 q^{73} + 3 q^{74} + 34 q^{75} - 3 q^{76} + 86 q^{77} - 44 q^{78} + 25 q^{79} + 18 q^{80} + 53 q^{81} - 48 q^{82} + 107 q^{83} + 10 q^{84} + 21 q^{85} - 21 q^{86} + 100 q^{87} - 30 q^{88} + 34 q^{89} - 33 q^{90} - 51 q^{91} + 53 q^{92} + 48 q^{93} - 107 q^{94} + 118 q^{95} - 10 q^{96} - 13 q^{97} - 24 q^{98} + 63 q^{99}+O(q^{100}) \) 77 * q - 77 * q^2 + 10 * q^3 + 77 * q^4 + 18 * q^5 - 10 * q^6 + 21 * q^7 - 77 * q^8 + 71 * q^9 - 18 * q^10 + 30 * q^11 + 10 * q^12 - 2 * q^13 - 21 * q^14 + 21 * q^15 + 77 * q^16 + 60 * q^17 - 71 * q^18 - 3 * q^19 + 18 * q^20 + 10 * q^21 - 30 * q^22 + 53 * q^23 - 10 * q^24 + 59 * q^25 + 2 * q^26 + 43 * q^27 + 21 * q^28 + 30 * q^29 - 21 * q^30 + 22 * q^31 - 77 * q^32 + 31 * q^33 - 60 * q^34 + 41 * q^35 + 71 * q^36 - 3 * q^37 + 3 * q^38 + 44 * q^39 - 18 * q^40 + 48 * q^41 - 10 * q^42 + 21 * q^43 + 30 * q^44 + 33 * q^45 - 53 * q^46 + 107 * q^47 + 10 * q^48 + 24 * q^49 - 59 * q^50 + 18 * q^51 - 2 * q^52 + 42 * q^53 - 43 * q^54 + 49 * q^55 - 21 * q^56 + 32 * q^57 - 30 * q^58 + 42 * q^59 + 21 * q^60 - 31 * q^61 - 22 * q^62 + 109 * q^63 + 77 * q^64 + 39 * q^65 - 31 * q^66 - q^67 + 60 * q^68 - 33 * q^69 - 41 * q^70 + 58 * q^71 - 71 * q^72 + 35 * q^73 + 3 * q^74 + 34 * q^75 - 3 * q^76 + 86 * q^77 - 44 * q^78 + 25 * q^79 + 18 * q^80 + 53 * q^81 - 48 * q^82 + 107 * q^83 + 10 * q^84 + 21 * q^85 - 21 * q^86 + 100 * q^87 - 30 * q^88 + 34 * q^89 - 33 * q^90 - 51 * q^91 + 53 * q^92 + 48 * q^93 - 107 * q^94 + 118 * q^95 - 10 * q^96 - 13 * q^97 - 24 * q^98 + 63 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.25254	0.723153	0.361576	−	0.932342i	$-0.382239\pi$
$3$	1.25254	0.723153	0.361576	+	0.932342i	$0.382239\pi$
$4$	1.00000	0.500000
$5$	3.78927	1.69461	0.847307	−	0.531104i	$-0.178222\pi$
$5$	3.78927	1.69461	0.847307	+	0.531104i	$0.178222\pi$
$6$	−1.25254	−0.511346
$7$	−0.301847	−0.114087	−0.0570437	−	0.998372i	$-0.518167\pi$
$7$	−0.301847	−0.114087	−0.0570437	+	0.998372i	$0.518167\pi$
$8$	−1.00000	−0.353553
$9$	−1.43115	−0.477050
$10$	−3.78927	−1.19827
$11$	−2.38376	−0.718731	−0.359365	−	0.933197i	$-0.617007\pi$
$11$	−2.38376	−0.718731	−0.359365	+	0.933197i	$0.617007\pi$
$12$	1.25254	0.361576
$13$	−0.101009	−0.0280150	−0.0140075	−	0.999902i	$-0.504459\pi$
$13$	−0.101009	−0.0280150	−0.0140075	+	0.999902i	$0.504459\pi$
$14$	0.301847	0.0806720
$15$	4.74621	1.22546
$16$	1.00000	0.250000
$17$	0.673322	0.163305	0.0816523	−	0.996661i	$-0.473980\pi$
$17$	0.673322	0.163305	0.0816523	+	0.996661i	$0.473980\pi$
$18$	1.43115	0.337325
$19$	−6.01720	−1.38044	−0.690220	−	0.723599i	$-0.742486\pi$
$19$	−6.01720	−1.38044	−0.690220	+	0.723599i	$0.742486\pi$
$20$	3.78927	0.847307
$21$	−0.378075	−0.0825026
$22$	2.38376	0.508219
$23$	2.18685	0.455991	0.227995	−	0.973662i	$-0.426783\pi$
$23$	2.18685	0.455991	0.227995	+	0.973662i	$0.426783\pi$
$24$	−1.25254	−0.255673
$25$	9.35858	1.87172
$26$	0.101009	0.0198096
$27$	−5.55018	−1.06813
$28$	−0.301847	−0.0570437
$29$	1.21872	0.226311	0.113155	−	0.993577i	$-0.463904\pi$
$29$	1.21872	0.226311	0.113155	+	0.993577i	$0.463904\pi$
$30$	−4.74621	−0.866535
$31$	0.941940	0.169177	0.0845887	−	0.996416i	$-0.473042\pi$
$31$	0.941940	0.169177	0.0845887	+	0.996416i	$0.473042\pi$
$32$	−1.00000	−0.176777
$33$	−2.98575	−0.519752
$34$	−0.673322	−0.115474
$35$	−1.14378	−0.193334
$36$	−1.43115	−0.238525
$37$	6.27420	1.03147	0.515736	−	0.856747i	$-0.327518\pi$
$37$	6.27420	1.03147	0.515736	+	0.856747i	$0.327518\pi$
$38$	6.01720	0.976119
$39$	−0.126518	−0.0202591
$40$	−3.78927	−0.599136
$41$	1.34283	0.209715	0.104857	−	0.994487i	$-0.466561\pi$
$41$	1.34283	0.209715	0.104857	+	0.994487i	$0.466561\pi$
$42$	0.378075	0.0583382
$43$	7.72190	1.17758	0.588789	−	0.808287i	$-0.299605\pi$
$43$	7.72190	1.17758	0.588789	+	0.808287i	$0.299605\pi$
$44$	−2.38376	−0.359365
$45$	−5.42302	−0.808415
$46$	−2.18685	−0.322434
$47$	10.1353	1.47838	0.739191	−	0.673496i	$-0.235208\pi$
$47$	10.1353	1.47838	0.739191	+	0.673496i	$0.235208\pi$
$48$	1.25254	0.180788
$49$	−6.90889	−0.986984
$50$	−9.35858	−1.32350
$51$	0.843362	0.118094
$52$	−0.101009	−0.0140075
$53$	0.118920	0.0163349	0.00816747	−	0.999967i	$-0.497400\pi$
$53$	0.118920	0.0163349	0.00816747	+	0.999967i	$0.497400\pi$
$54$	5.55018	0.755284
$55$	−9.03271	−1.21797
$56$	0.301847	0.0403360
$57$	−7.53677	−0.998269
$58$	−1.21872	−0.160026
$59$	9.00032	1.17174	0.585871	−	0.810404i	$-0.300752\pi$
$59$	9.00032	1.17174	0.585871	+	0.810404i	$0.300752\pi$
$60$	4.74621	0.612732
$61$	4.76267	0.609798	0.304899	−	0.952385i	$-0.401377\pi$
$61$	4.76267	0.609798	0.304899	+	0.952385i	$0.401377\pi$
$62$	−0.941940	−0.119627
$63$	0.431988	0.0544254
$64$	1.00000	0.125000
$65$	−0.382752	−0.0474745
$66$	2.98575	0.367520
$67$	13.3882	1.63563	0.817817	−	0.575478i	$-0.195184\pi$
$67$	13.3882	1.63563	0.817817	+	0.575478i	$0.195184\pi$
$68$	0.673322	0.0816523
$69$	2.73912	0.329751
$70$	1.14378	0.136708
$71$	−4.72336	−0.560559	−0.280280	−	0.959918i	$-0.590427\pi$
$71$	−4.72336	−0.560559	−0.280280	+	0.959918i	$0.590427\pi$
$72$	1.43115	0.168663
$73$	3.34711	0.391750	0.195875	−	0.980629i	$-0.437245\pi$
$73$	3.34711	0.391750	0.195875	+	0.980629i	$0.437245\pi$
$74$	−6.27420	−0.729361
$75$	11.7220	1.35354
$76$	−6.01720	−0.690220
$77$	0.719531	0.0819981
$78$	0.126518	0.0143253
$79$	6.96333	0.783436	0.391718	−	0.920085i	$-0.371881\pi$
$79$	6.96333	0.783436	0.391718	+	0.920085i	$0.371881\pi$
$80$	3.78927	0.423653
$81$	−2.65836	−0.295374
$82$	−1.34283	−0.148291
$83$	−1.88085	−0.206450	−0.103225	−	0.994658i	$-0.532916\pi$
$83$	−1.88085	−0.206450	−0.103225	+	0.994658i	$0.532916\pi$
$84$	−0.378075	−0.0412513
$85$	2.55140	0.276738
$86$	−7.72190	−0.832674
$87$	1.52649	0.163657
$88$	2.38376	0.254110
$89$	−12.8656	−1.36375	−0.681876	−	0.731467i	$-0.738836\pi$
$89$	−12.8656	−1.36375	−0.681876	+	0.731467i	$0.738836\pi$
$90$	5.42302	0.571636
$91$	0.0304894	0.00319615
$92$	2.18685	0.227995
$93$	1.17982	0.122341
$94$	−10.1353	−1.04537
$95$	−22.8008	−2.33931
$96$	−1.25254	−0.127837
$97$	−11.0599	−1.12297	−0.561483	−	0.827488i	$-0.689769\pi$
$97$	−11.0599	−1.12297	−0.561483	+	0.827488i	$0.689769\pi$
$98$	6.90889	0.697903
$99$	3.41152	0.342870
$100$	9.35858	0.935858
$101$	12.4856	1.24237	0.621183	−	0.783666i	$-0.286652\pi$
$101$	12.4856	1.24237	0.621183	+	0.783666i	$0.286652\pi$
$102$	−0.843362	−0.0835052
$103$	−8.99028	−0.885838	−0.442919	−	0.896562i	$-0.646057\pi$
$103$	−8.99028	−0.885838	−0.442919	+	0.896562i	$0.646057\pi$
$104$	0.101009	0.00990478
$105$	−1.43263	−0.139810
$106$	−0.118920	−0.0115505
$107$	9.59723	0.927799	0.463900	−	0.885888i	$-0.346450\pi$
$107$	9.59723	0.927799	0.463900	+	0.885888i	$0.346450\pi$
$108$	−5.55018	−0.534066
$109$	18.2131	1.74450	0.872251	−	0.489058i	$-0.162659\pi$
$109$	18.2131	1.74450	0.872251	+	0.489058i	$0.162659\pi$
$110$	9.03271	0.861235
$111$	7.85867	0.745912
$112$	−0.301847	−0.0285219
$113$	0.343024	0.0322690	0.0161345	−	0.999870i	$-0.494864\pi$
$113$	0.343024	0.0322690	0.0161345	+	0.999870i	$0.494864\pi$
$114$	7.53677	0.705883
$115$	8.28659	0.772728
$116$	1.21872	0.113155
$117$	0.144559	0.0133645
$118$	−9.00032	−0.828547
$119$	−0.203240	−0.0186310
$120$	−4.74621	−0.433267
$121$	−5.31769	−0.483426
$122$	−4.76267	−0.431192
$123$	1.68195	0.151656
$124$	0.941940	0.0845887
$125$	16.5158	1.47722
$126$	−0.431988	−0.0384846
$127$	−6.57707	−0.583621	−0.291810	−	0.956476i	$-0.594258\pi$
$127$	−6.57707	−0.583621	−0.291810	+	0.956476i	$0.594258\pi$
$128$	−1.00000	−0.0883883
$129$	9.67197	0.851569
$130$	0.382752	0.0335696
$131$	14.0836	1.23049	0.615243	−	0.788338i	$-0.289058\pi$
$131$	14.0836	1.23049	0.615243	+	0.788338i	$0.289058\pi$
$132$	−2.98575	−0.259876
$133$	1.81627	0.157491
$134$	−13.3882	−1.15657
$135$	−21.0311	−1.81007
$136$	−0.673322	−0.0577369
$137$	−2.99479	−0.255862	−0.127931	−	0.991783i	$-0.540834\pi$
$137$	−2.99479	−0.255862	−0.127931	+	0.991783i	$0.540834\pi$
$138$	−2.73912	−0.233169
$139$	19.2233	1.63050	0.815249	−	0.579111i	$-0.196600\pi$
$139$	19.2233	1.63050	0.815249	+	0.579111i	$0.196600\pi$
$140$	−1.14378	−0.0966670
$141$	12.6948	1.06910
$142$	4.72336	0.396375
$143$	0.240782	0.0201352
$144$	−1.43115	−0.119262
$145$	4.61806	0.383509
$146$	−3.34711	−0.277009
$147$	−8.65364	−0.713740
$148$	6.27420	0.515736
$149$	6.62826	0.543008	0.271504	−	0.962437i	$-0.412479\pi$
$149$	6.62826	0.543008	0.271504	+	0.962437i	$0.412479\pi$
$150$	−11.7220	−0.957095
$151$	22.6752	1.84528	0.922641	−	0.385660i	$-0.126026\pi$
$151$	22.6752	1.84528	0.922641	+	0.385660i	$0.126026\pi$
$152$	6.01720	0.488059
$153$	−0.963625	−0.0779045
$154$	−0.719531	−0.0579814
$155$	3.56927	0.286690
$156$	−0.126518	−0.0101295
$157$	−6.92807	−0.552920	−0.276460	−	0.961025i	$-0.589161\pi$
$157$	−6.92807	−0.552920	−0.276460	+	0.961025i	$0.589161\pi$
$158$	−6.96333	−0.553973
$159$	0.148952	0.0118127
$160$	−3.78927	−0.299568
$161$	−0.660095	−0.0520228
$162$	2.65836	0.208861
$163$	17.9150	1.40321	0.701606	−	0.712565i	$-0.252467\pi$
$163$	17.9150	1.40321	0.701606	+	0.712565i	$0.252467\pi$
$164$	1.34283	0.104857
$165$	−11.3138	−0.880779
$166$	1.88085	0.145982
$167$	−0.934745	−0.0723328	−0.0361664	−	0.999346i	$-0.511515\pi$
$167$	−0.934745	−0.0723328	−0.0361664	+	0.999346i	$0.511515\pi$
$168$	0.378075	0.0291691
$169$	−12.9898	−0.999215
$170$	−2.55140	−0.195684
$171$	8.61151	0.658539
$172$	7.72190	0.588789
$173$	−21.4692	−1.63227	−0.816135	−	0.577861i	$-0.803888\pi$
$173$	−21.4692	−1.63227	−0.816135	+	0.577861i	$0.803888\pi$
$174$	−1.52649	−0.115723
$175$	−2.82486	−0.213539
$176$	−2.38376	−0.179683
$177$	11.2732	0.847349
$178$	12.8656	0.964319
$179$	21.4636	1.60426	0.802132	−	0.597147i	$-0.203699\pi$
$179$	21.4636	1.60426	0.802132	+	0.597147i	$0.203699\pi$
$180$	−5.42302	−0.404208
$181$	0.273850	0.0203551	0.0101776	−	0.999948i	$-0.496760\pi$
$181$	0.273850	0.0203551	0.0101776	+	0.999948i	$0.496760\pi$
$182$	−0.0304894	−0.00226002
$183$	5.96543	0.440977
$184$	−2.18685	−0.161217
$185$	23.7747	1.74795
$186$	−1.17982	−0.0865083
$187$	−1.60504	−0.117372
$188$	10.1353	0.739191
$189$	1.67531	0.121861
$190$	22.8008	1.65414
$191$	12.0251	0.870104	0.435052	−	0.900405i	$-0.356730\pi$
$191$	12.0251	0.870104	0.435052	+	0.900405i	$0.356730\pi$
$192$	1.25254	0.0903941
$193$	5.11030	0.367847	0.183924	−	0.982941i	$-0.441120\pi$
$193$	5.11030	0.367847	0.183924	+	0.982941i	$0.441120\pi$
$194$	11.0599	0.794057
$195$	−0.479411	−0.0343313
$196$	−6.90889	−0.493492
$197$	7.59270	0.540958	0.270479	−	0.962726i	$-0.412818\pi$
$197$	7.59270	0.540958	0.270479	+	0.962726i	$0.412818\pi$
$198$	−3.41152	−0.242446
$199$	7.67898	0.544349	0.272174	−	0.962248i	$-0.412257\pi$
$199$	7.67898	0.544349	0.272174	+	0.962248i	$0.412257\pi$
$200$	−9.35858	−0.661752
$201$	16.7693	1.18281
$202$	−12.4856	−0.878485
$203$	−0.367867	−0.0258192
$204$	0.843362	0.0590471
$205$	5.08835	0.355386
$206$	8.99028	0.626382
$207$	−3.12972	−0.217530
$208$	−0.101009	−0.00700374
$209$	14.3436	0.992165
$210$	1.43263	0.0988607
$211$	19.0068	1.30848	0.654241	−	0.756286i	$-0.272988\pi$
$211$	19.0068	1.30848	0.654241	+	0.756286i	$0.272988\pi$
$212$	0.118920	0.00816747
$213$	−5.91618	−0.405370
$214$	−9.59723	−0.656053
$215$	29.2604	1.99554
$216$	5.55018	0.377642
$217$	−0.284322	−0.0193010
$218$	−18.2131	−1.23355
$219$	4.19238	0.283295
$220$	−9.03271	−0.608985
$221$	−0.0680119	−0.00457497
$222$	−7.85867	−0.527440
$223$	−27.1266	−1.81653	−0.908264	−	0.418397i	$-0.862592\pi$
$223$	−27.1266	−1.81653	−0.908264	+	0.418397i	$0.862592\pi$
$224$	0.301847	0.0201680
$225$	−13.3935	−0.892902
$226$	−0.343024	−0.0228176
$227$	−3.07106	−0.203833	−0.101917	−	0.994793i	$-0.532498\pi$
$227$	−3.07106	−0.203833	−0.101917	+	0.994793i	$0.532498\pi$
$228$	−7.53677	−0.499135
$229$	10.1829	0.672907	0.336454	−	0.941700i	$-0.390772\pi$
$229$	10.1829	0.672907	0.336454	+	0.941700i	$0.390772\pi$
$230$	−8.28659	−0.546401
$231$	0.901239	0.0592972
$232$	−1.21872	−0.0800129
$233$	−28.8902	−1.89266	−0.946330	−	0.323202i	$-0.895241\pi$
$233$	−28.8902	−1.89266	−0.946330	+	0.323202i	$0.895241\pi$
$234$	−0.144559	−0.00945015
$235$	38.4053	2.50529
$236$	9.00032	0.585871
$237$	8.72184	0.566544
$238$	0.203240	0.0131741
$239$	4.34693	0.281179	0.140590	−	0.990068i	$-0.455100\pi$
$239$	4.34693	0.281179	0.140590	+	0.990068i	$0.455100\pi$
$240$	4.74621	0.306366
$241$	3.59199	0.231380	0.115690	−	0.993285i	$-0.463092\pi$
$241$	3.59199	0.231380	0.115690	+	0.993285i	$0.463092\pi$
$242$	5.31769	0.341834
$243$	13.3208	0.854533
$244$	4.76267	0.304899
$245$	−26.1797	−1.67256
$246$	−1.68195	−0.107237
$247$	0.607793	0.0386730
$248$	−0.941940	−0.0598133
$249$	−2.35584	−0.149295
$250$	−16.5158	−1.04455
$251$	−2.81681	−0.177795	−0.0888977	−	0.996041i	$-0.528334\pi$
$251$	−2.81681	−0.177795	−0.0888977	+	0.996041i	$0.528334\pi$
$252$	0.431988	0.0272127
$253$	−5.21294	−0.327735
$254$	6.57707	0.412682
$255$	3.19573	0.200124
$256$	1.00000	0.0625000
$257$	−25.5496	−1.59374	−0.796870	−	0.604151i	$-0.793512\pi$
$257$	−25.5496	−1.59374	−0.796870	+	0.604151i	$0.793512\pi$
$258$	−9.67197	−0.602150
$259$	−1.89385	−0.117678
$260$	−0.382752	−0.0237373
$261$	−1.74417	−0.107961
$262$	−14.0836	−0.870085
$263$	9.98727	0.615841	0.307921	−	0.951412i	$-0.400367\pi$
$263$	9.98727	0.615841	0.307921	+	0.951412i	$0.400367\pi$
$264$	2.98575	0.183760
$265$	0.450621	0.0276814
$266$	−1.81627	−0.111363
$267$	−16.1147	−0.986202
$268$	13.3882	0.817817
$269$	24.1292	1.47118	0.735592	−	0.677425i	$-0.236904\pi$
$269$	24.1292	1.47118	0.735592	+	0.677425i	$0.236904\pi$
$270$	21.0311	1.27991
$271$	−1.18766	−0.0721453	−0.0360727	−	0.999349i	$-0.511485\pi$
$271$	−1.18766	−0.0721453	−0.0360727	+	0.999349i	$0.511485\pi$
$272$	0.673322	0.0408262
$273$	0.0381891	0.00231131
$274$	2.99479	0.180922
$275$	−22.3086	−1.34526
$276$	2.73912	0.164876
$277$	6.20983	0.373113	0.186556	−	0.982444i	$-0.440267\pi$
$277$	6.20983	0.373113	0.186556	+	0.982444i	$0.440267\pi$
$278$	−19.2233	−1.15294
$279$	−1.34806	−0.0807061
$280$	1.14378	0.0683539
$281$	3.25504	0.194180	0.0970898	−	0.995276i	$-0.469047\pi$
$281$	3.25504	0.194180	0.0970898	+	0.995276i	$0.469047\pi$
$282$	−12.6948	−0.755965
$283$	4.23678	0.251850	0.125925	−	0.992040i	$-0.459810\pi$
$283$	4.23678	0.251850	0.125925	+	0.992040i	$0.459810\pi$
$284$	−4.72336	−0.280280
$285$	−28.5589	−1.69168
$286$	−0.240782	−0.0142377
$287$	−0.405329	−0.0239258
$288$	1.43115	0.0843313
$289$	−16.5466	−0.973332
$290$	−4.61806	−0.271182
$291$	−13.8530	−0.812077
$292$	3.34711	0.195875
$293$	−1.41385	−0.0825981	−0.0412990	−	0.999147i	$-0.513150\pi$
$293$	−1.41385	−0.0825981	−0.0412990	+	0.999147i	$0.513150\pi$
$294$	8.65364	0.504691
$295$	34.1047	1.98565
$296$	−6.27420	−0.364680
$297$	13.2303	0.767700
$298$	−6.62826	−0.383965
$299$	−0.220893	−0.0127746
$300$	11.7220	0.676768
$301$	−2.33083	−0.134347
$302$	−22.6752	−1.30481
$303$	15.6387	0.898420
$304$	−6.01720	−0.345110
$305$	18.0471	1.03337
$306$	0.963625	0.0550868
$307$	25.4063	1.45002	0.725008	−	0.688740i	$-0.241836\pi$
$307$	25.4063	1.45002	0.725008	+	0.688740i	$0.241836\pi$
$308$	0.719531	0.0409991
$309$	−11.2607	−0.640596
$310$	−3.56927	−0.202721
$311$	1.14644	0.0650088	0.0325044	−	0.999472i	$-0.489652\pi$
$311$	1.14644	0.0650088	0.0325044	+	0.999472i	$0.489652\pi$
$312$	0.126518	0.00716267
$313$	−6.21308	−0.351184	−0.175592	−	0.984463i	$-0.556184\pi$
$313$	−6.21308	−0.351184	−0.175592	+	0.984463i	$0.556184\pi$
$314$	6.92807	0.390974
$315$	1.63692	0.0922300
$316$	6.96333	0.391718
$317$	−28.2845	−1.58862	−0.794308	−	0.607515i	$-0.792167\pi$
$317$	−28.2845	−1.58862	−0.794308	+	0.607515i	$0.792167\pi$
$318$	−0.148952	−0.00835281
$319$	−2.90514	−0.162656
$320$	3.78927	0.211827
$321$	12.0209	0.670941
$322$	0.660095	0.0367857
$323$	−4.05152	−0.225432
$324$	−2.65836	−0.147687
$325$	−0.945304	−0.0524360
$326$	−17.9150	−0.992221
$327$	22.8126	1.26154
$328$	−1.34283	−0.0741454
$329$	−3.05930	−0.168665
$330$	11.3138	0.622805
$331$	−31.3593	−1.72366	−0.861831	−	0.507195i	$-0.830682\pi$
$331$	−31.3593	−1.72366	−0.861831	+	0.507195i	$0.830682\pi$
$332$	−1.88085	−0.103225
$333$	−8.97932	−0.492064
$334$	0.934745	0.0511470
$335$	50.7317	2.77177
$336$	−0.378075	−0.0206257
$337$	21.5043	1.17141	0.585706	−	0.810523i	$-0.300817\pi$
$337$	21.5043	1.17141	0.585706	+	0.810523i	$0.300817\pi$
$338$	12.9898	0.706552
$339$	0.429650	0.0233354
$340$	2.55140	0.138369
$341$	−2.24536	−0.121593
$342$	−8.61151	−0.465657
$343$	4.19835	0.226690
$344$	−7.72190	−0.416337
$345$	10.3793	0.558801
$346$	21.4692	1.15419
$347$	12.1422	0.651827	0.325914	−	0.945400i	$-0.394328\pi$
$347$	12.1422	0.651827	0.325914	+	0.945400i	$0.394328\pi$
$348$	1.52649	0.0818286
$349$	−20.7361	−1.10998	−0.554990	−	0.831857i	$-0.687278\pi$
$349$	−20.7361	−1.10998	−0.554990	+	0.831857i	$0.687278\pi$
$350$	2.82486	0.150995
$351$	0.560620	0.0299237
$352$	2.38376	0.127055
$353$	20.1486	1.07240	0.536201	−	0.844090i	$-0.319859\pi$
$353$	20.1486	1.07240	0.536201	+	0.844090i	$0.319859\pi$
$354$	−11.2732	−0.599166
$355$	−17.8981	−0.949932
$356$	−12.8656	−0.681876
$357$	−0.254566	−0.0134731
$358$	−21.4636	−1.13439
$359$	6.02663	0.318073	0.159037	−	0.987273i	$-0.449161\pi$
$359$	6.02663	0.318073	0.159037	+	0.987273i	$0.449161\pi$
$360$	5.42302	0.285818
$361$	17.2067	0.905616
$362$	−0.273850	−0.0143933
$363$	−6.66060	−0.349591
$364$	0.0304894	0.00159808
$365$	12.6831	0.663865
$366$	−5.96543	−0.311818
$367$	−37.2404	−1.94393	−0.971967	−	0.235117i	$-0.924453\pi$
$367$	−37.2404	−1.94393	−0.971967	+	0.235117i	$0.924453\pi$
$368$	2.18685	0.113998
$369$	−1.92179	−0.100044
$370$	−23.7747	−1.23599
$371$	−0.0358957	−0.00186361
$372$	1.17982	0.0611706
$373$	−12.0067	−0.621683	−0.310842	−	0.950462i	$-0.600611\pi$
$373$	−12.0067	−0.621683	−0.310842	+	0.950462i	$0.600611\pi$
$374$	1.60504	0.0829946
$375$	20.6867	1.06826
$376$	−10.1353	−0.522687
$377$	−0.123102	−0.00634008
$378$	−1.67531	−0.0861684
$379$	−20.1779	−1.03647	−0.518234	−	0.855239i	$-0.673410\pi$
$379$	−20.1779	−1.03647	−0.518234	+	0.855239i	$0.673410\pi$
$380$	−22.8008	−1.16966
$381$	−8.23803	−0.422047
$382$	−12.0251	−0.615257
$383$	−34.0881	−1.74182	−0.870910	−	0.491442i	$-0.836470\pi$
$383$	−34.0881	−1.74182	−0.870910	+	0.491442i	$0.836470\pi$
$384$	−1.25254	−0.0639183
$385$	2.72650	0.138955
$386$	−5.11030	−0.260107
$387$	−11.0512	−0.561764
$388$	−11.0599	−0.561483
$389$	−25.9348	−1.31495	−0.657474	−	0.753477i	$-0.728375\pi$
$389$	−25.9348	−1.31495	−0.657474	+	0.753477i	$0.728375\pi$
$390$	0.479411	0.0242759
$391$	1.47246	0.0744654
$392$	6.90889	0.348952
$393$	17.6402	0.889829
$394$	−7.59270	−0.382515
$395$	26.3860	1.32762
$396$	3.41152	0.171435
$397$	33.3217	1.67237	0.836184	−	0.548449i	$-0.184782\pi$
$397$	33.3217	1.67237	0.836184	+	0.548449i	$0.184782\pi$
$398$	−7.67898	−0.384913
$399$	2.27495	0.113890
$400$	9.35858	0.467929
$401$	17.9086	0.894310	0.447155	−	0.894456i	$-0.352437\pi$
$401$	17.9086	0.894310	0.447155	+	0.894456i	$0.352437\pi$
$402$	−16.7693	−0.836375
$403$	−0.0951448	−0.00473950
$404$	12.4856	0.621183
$405$	−10.0733	−0.500544
$406$	0.367867	0.0182569
$407$	−14.9562	−0.741351
$408$	−0.843362	−0.0417526
$409$	−2.25499	−0.111502	−0.0557510	−	0.998445i	$-0.517755\pi$
$409$	−2.25499	−0.111502	−0.0557510	+	0.998445i	$0.517755\pi$
$410$	−5.08835	−0.251296
$411$	−3.75109	−0.185028
$412$	−8.99028	−0.442919
$413$	−2.71672	−0.133681
$414$	3.12972	0.153817
$415$	−7.12706	−0.349853
$416$	0.101009	0.00495239
$417$	24.0779	1.17910
$418$	−14.3436	−0.701566
$419$	−0.269839	−0.0131825	−0.00659126	−	0.999978i	$-0.502098\pi$
$419$	−0.269839	−0.0131825	−0.00659126	+	0.999978i	$0.502098\pi$
$420$	−1.43263	−0.0699051
$421$	−17.4723	−0.851549	−0.425775	−	0.904829i	$-0.639998\pi$
$421$	−17.4723	−0.851549	−0.425775	+	0.904829i	$0.639998\pi$
$422$	−19.0068	−0.925237
$423$	−14.5051	−0.705262
$424$	−0.118920	−0.00577527
$425$	6.30134	0.305660
$426$	5.91618	0.286640
$427$	−1.43760	−0.0695703
$428$	9.59723	0.463900
$429$	0.301589	0.0145608
$430$	−29.2604	−1.41106
$431$	−22.0384	−1.06155	−0.530776	−	0.847512i	$-0.678100\pi$
$431$	−22.0384	−1.06155	−0.530776	+	0.847512i	$0.678100\pi$
$432$	−5.55018	−0.267033
$433$	−7.90819	−0.380043	−0.190022	−	0.981780i	$-0.560856\pi$
$433$	−7.90819	−0.380043	−0.190022	+	0.981780i	$0.560856\pi$
$434$	0.284322	0.0136479
$435$	5.78429	0.277336
$436$	18.2131	0.872251
$437$	−13.1587	−0.629468
$438$	−4.19238	−0.200320
$439$	−13.4070	−0.639881	−0.319941	−	0.947438i	$-0.603663\pi$
$439$	−13.4070	−0.639881	−0.319941	+	0.947438i	$0.603663\pi$
$440$	9.03271	0.430618
$441$	9.88765	0.470841
$442$	0.0680119	0.00323499
$443$	−0.583546	−0.0277251	−0.0138626	−	0.999904i	$-0.504413\pi$
$443$	−0.583546	−0.0277251	−0.0138626	+	0.999904i	$0.504413\pi$
$444$	7.85867	0.372956
$445$	−48.7513	−2.31103
$446$	27.1266	1.28448
$447$	8.30215	0.392678
$448$	−0.301847	−0.0142609
$449$	−40.3340	−1.90348	−0.951739	−	0.306910i	$-0.900705\pi$
$449$	−40.3340	−1.90348	−0.951739	+	0.306910i	$0.900705\pi$
$450$	13.3935	0.631377
$451$	−3.20098	−0.150728
$452$	0.343024	0.0161345
$453$	28.4015	1.33442
$454$	3.07106	0.144132
$455$	0.115532	0.00541625
$456$	7.53677	0.352942
$457$	−32.6633	−1.52793	−0.763963	−	0.645260i	$-0.776749\pi$
$457$	−32.6633	−1.52793	−0.763963	+	0.645260i	$0.776749\pi$
$458$	−10.1829	−0.475817
$459$	−3.73706	−0.174431
$460$	8.28659	0.386364
$461$	−30.1479	−1.40413	−0.702064	−	0.712114i	$-0.747738\pi$
$461$	−30.1479	−1.40413	−0.702064	+	0.712114i	$0.747738\pi$
$462$	−0.901239	−0.0419294
$463$	22.1188	1.02795	0.513974	−	0.857806i	$-0.328173\pi$
$463$	22.1188	1.02795	0.513974	+	0.857806i	$0.328173\pi$
$464$	1.21872	0.0565776
$465$	4.47064	0.207321
$466$	28.8902	1.33831
$467$	−0.107359	−0.00496796	−0.00248398	−	0.999997i	$-0.500791\pi$
$467$	−0.107359	−0.00496796	−0.00248398	+	0.999997i	$0.500791\pi$
$468$	0.144559	0.00668227
$469$	−4.04120	−0.186605
$470$	−38.4053	−1.77151
$471$	−8.67767	−0.399846
$472$	−9.00032	−0.414273
$473$	−18.4071	−0.846362
$474$	−8.72184	−0.400607
$475$	−56.3125	−2.58379
$476$	−0.203240	−0.00931550
$477$	−0.170193	−0.00779258
$478$	−4.34693	−0.198824
$479$	−2.67121	−0.122051	−0.0610255	−	0.998136i	$-0.519437\pi$
$479$	−2.67121	−0.122051	−0.0610255	+	0.998136i	$0.519437\pi$
$480$	−4.74621	−0.216634
$481$	−0.633753	−0.0288966
$482$	−3.59199	−0.163610
$483$	−0.826794	−0.0376204
$484$	−5.31769	−0.241713
$485$	−41.9091	−1.90299
$486$	−13.3208	−0.604246
$487$	−28.9817	−1.31329	−0.656643	−	0.754201i	$-0.728024\pi$
$487$	−28.9817	−1.31329	−0.656643	+	0.754201i	$0.728024\pi$
$488$	−4.76267	−0.215596
$489$	22.4392	1.01474
$490$	26.1797	1.18268
$491$	19.5271	0.881247	0.440623	−	0.897692i	$-0.354757\pi$
$491$	19.5271	0.881247	0.440623	+	0.897692i	$0.354757\pi$
$492$	1.68195	0.0758279
$493$	0.820591	0.0369576
$494$	−0.607793	−0.0273459
$495$	12.9272	0.581033
$496$	0.941940	0.0422944
$497$	1.42573	0.0639528
$498$	2.35584	0.105568
$499$	19.8419	0.888248	0.444124	−	0.895965i	$-0.353515\pi$
$499$	19.8419	0.888248	0.444124	+	0.895965i	$0.353515\pi$
$500$	16.5158	0.738611
$501$	−1.17080	−0.0523076
$502$	2.81681	0.125720
$503$	−24.1042	−1.07475	−0.537376	−	0.843343i	$-0.680584\pi$
$503$	−24.1042	−1.07475	−0.537376	+	0.843343i	$0.680584\pi$
$504$	−0.431988	−0.0192423
$505$	47.3114	2.10533
$506$	5.21294	0.231743
$507$	−16.2702	−0.722585
$508$	−6.57707	−0.291810
$509$	12.4563	0.552117	0.276059	−	0.961141i	$-0.410972\pi$
$509$	12.4563	0.552117	0.276059	+	0.961141i	$0.410972\pi$
$510$	−3.19573	−0.141509
$511$	−1.01032	−0.0446937
$512$	−1.00000	−0.0441942
$513$	33.3966	1.47449
$514$	25.5496	1.12694
$515$	−34.0666	−1.50115
$516$	9.67197	0.425785
$517$	−24.1601	−1.06256
$518$	1.89385	0.0832109
$519$	−26.8909	−1.18038
$520$	0.382752	0.0167848
$521$	0.278623	0.0122067	0.00610334	−	0.999981i	$-0.498057\pi$
$521$	0.278623	0.0122067	0.00610334	+	0.999981i	$0.498057\pi$
$522$	1.74417	0.0763403
$523$	−9.98001	−0.436395	−0.218198	−	0.975905i	$-0.570018\pi$
$523$	−9.98001	−0.436395	−0.218198	+	0.975905i	$0.570018\pi$
$524$	14.0836	0.615243
$525$	−3.53824	−0.154422
$526$	−9.98727	−0.435465
$527$	0.634230	0.0276275
$528$	−2.98575	−0.129938
$529$	−18.2177	−0.792072
$530$	−0.450621	−0.0195737
$531$	−12.8808	−0.558979
$532$	1.81627	0.0787454
$533$	−0.135638	−0.00587515
$534$	16.1147	0.697350
$535$	36.3665	1.57226
$536$	−13.3882	−0.578284
$537$	26.8839	1.16013
$538$	−24.1292	−1.04028
$539$	16.4691	0.709376
$540$	−21.0311	−0.905036
$541$	−16.3140	−0.701396	−0.350698	−	0.936489i	$-0.614056\pi$
$541$	−16.3140	−0.701396	−0.350698	+	0.936489i	$0.614056\pi$
$542$	1.18766	0.0510145
$543$	0.343008	0.0147199
$544$	−0.673322	−0.0288685
$545$	69.0145	2.95626
$546$	−0.0381891	−0.00163434
$547$	31.9872	1.36767	0.683837	−	0.729635i	$-0.260310\pi$
$547$	31.9872	1.36767	0.683837	+	0.729635i	$0.260310\pi$
$548$	−2.99479	−0.127931
$549$	−6.81610	−0.290904
$550$	22.3086	0.951242
$551$	−7.33328	−0.312408
$552$	−2.73912	−0.116585
$553$	−2.10186	−0.0893802
$554$	−6.20983	−0.263830
$555$	29.7786	1.26403
$556$	19.2233	0.815249
$557$	16.4062	0.695155	0.347577	−	0.937651i	$-0.387004\pi$
$557$	16.4062	0.695155	0.347577	+	0.937651i	$0.387004\pi$
$558$	1.34806	0.0570678
$559$	−0.779984	−0.0329898
$560$	−1.14378	−0.0483335
$561$	−2.01037	−0.0848780
$562$	−3.25504	−0.137306
$563$	37.7637	1.59155	0.795774	−	0.605594i	$-0.207064\pi$
$563$	37.7637	1.59155	0.795774	+	0.605594i	$0.207064\pi$
$564$	12.6948	0.534548
$565$	1.29981	0.0546834
$566$	−4.23678	−0.178085
$567$	0.802418	0.0336984
$568$	4.72336	0.198188
$569$	41.5432	1.74158	0.870790	−	0.491654i	$-0.163608\pi$
$569$	41.5432	1.74158	0.870790	+	0.491654i	$0.163608\pi$
$570$	28.5589	1.19620
$571$	−33.2003	−1.38939	−0.694695	−	0.719304i	$-0.744461\pi$
$571$	−33.2003	−1.38939	−0.694695	+	0.719304i	$0.744461\pi$
$572$	0.240782	0.0100676
$573$	15.0619	0.629218
$574$	0.405329	0.0169181
$575$	20.4659	0.853485
$576$	−1.43115	−0.0596312
$577$	21.6225	0.900156	0.450078	−	0.892989i	$-0.351396\pi$
$577$	21.6225	0.900156	0.450078	+	0.892989i	$0.351396\pi$
$578$	16.5466	0.688249
$579$	6.40084	0.266010
$580$	4.61806	0.191755
$581$	0.567729	0.0235534
$582$	13.8530	0.574225
$583$	−0.283477	−0.0117404
$584$	−3.34711	−0.138504
$585$	0.547775	0.0226477
$586$	1.41385	0.0584057
$587$	−31.6549	−1.30654	−0.653270	−	0.757125i	$-0.726603\pi$
$587$	−31.6549	−1.30654	−0.653270	+	0.757125i	$0.726603\pi$
$588$	−8.65364	−0.356870
$589$	−5.66784	−0.233539
$590$	−34.1047	−1.40407
$591$	9.51015	0.391195
$592$	6.27420	0.257868
$593$	−2.82286	−0.115921	−0.0579605	−	0.998319i	$-0.518460\pi$
$593$	−2.82286	−0.115921	−0.0579605	+	0.998319i	$0.518460\pi$
$594$	−13.2303	−0.542846
$595$	−0.770133	−0.0315724
$596$	6.62826	0.271504
$597$	9.61821	0.393647
$598$	0.220893	0.00903298
$599$	−32.2983	−1.31967	−0.659836	−	0.751409i	$-0.729374\pi$
$599$	−32.2983	−1.31967	−0.659836	+	0.751409i	$0.729374\pi$
$600$	−11.7220	−0.478548
$601$	−0.117476	−0.00479196	−0.00239598	−	0.999997i	$-0.500763\pi$
$601$	−0.117476	−0.00479196	−0.00239598	+	0.999997i	$0.500763\pi$
$602$	2.33083	0.0949976
$603$	−19.1606	−0.780279
$604$	22.6752	0.922641
$605$	−20.1502	−0.819221
$606$	−15.6387	−0.635279
$607$	41.6275	1.68961	0.844804	−	0.535075i	$-0.179717\pi$
$607$	41.6275	1.68961	0.844804	+	0.535075i	$0.179717\pi$
$608$	6.01720	0.244030
$609$	−0.460767	−0.0186712
$610$	−18.0471	−0.730704
$611$	−1.02376	−0.0414168
$612$	−0.963625	−0.0389522
$613$	17.7117	0.715369	0.357684	−	0.933843i	$-0.383566\pi$
$613$	17.7117	0.715369	0.357684	+	0.933843i	$0.383566\pi$
$614$	−25.4063	−1.02532
$615$	6.37335	0.256998
$616$	−0.719531	−0.0289907
$617$	43.4719	1.75011	0.875057	−	0.484020i	$-0.160824\pi$
$617$	43.4719	1.75011	0.875057	+	0.484020i	$0.160824\pi$
$618$	11.2607	0.452970
$619$	−31.0800	−1.24921	−0.624606	−	0.780940i	$-0.714740\pi$
$619$	−31.0800	−1.24921	−0.624606	+	0.780940i	$0.714740\pi$
$620$	3.56927	0.143345
$621$	−12.1374	−0.487059
$622$	−1.14644	−0.0459681
$623$	3.88345	0.155587
$624$	−0.126518	−0.00506477
$625$	15.7901	0.631605
$626$	6.21308	0.248325
$627$	17.9658	0.717487
$628$	−6.92807	−0.276460
$629$	4.22456	0.168444
$630$	−1.63692	−0.0652165
$631$	−2.01801	−0.0803358	−0.0401679	−	0.999193i	$-0.512789\pi$
$631$	−2.01801	−0.0803358	−0.0401679	+	0.999193i	$0.512789\pi$
$632$	−6.96333	−0.276987
$633$	23.8067	0.946233
$634$	28.2845	1.12332
$635$	−24.9223	−0.989012
$636$	0.148952	0.00590633
$637$	0.697862	0.0276503
$638$	2.90514	0.115015
$639$	6.75983	0.267415
$640$	−3.78927	−0.149784
$641$	−15.6817	−0.619389	−0.309694	−	0.950836i	$-0.600227\pi$
$641$	−15.6817	−0.619389	−0.309694	+	0.950836i	$0.600227\pi$
$642$	−12.0209	−0.474427
$643$	18.7144	0.738023	0.369012	−	0.929425i	$-0.379696\pi$
$643$	18.7144	0.738023	0.369012	+	0.929425i	$0.379696\pi$
$644$	−0.660095	−0.0260114
$645$	36.6497	1.44308
$646$	4.05152	0.159405
$647$	−1.36842	−0.0537980	−0.0268990	−	0.999638i	$-0.508563\pi$
$647$	−1.36842	−0.0537980	−0.0268990	+	0.999638i	$0.508563\pi$
$648$	2.65836	0.104430
$649$	−21.4546	−0.842167
$650$	0.945304	0.0370779
$651$	−0.356124	−0.0139576
$652$	17.9150	0.701606
$653$	−8.03491	−0.314430	−0.157215	−	0.987564i	$-0.550252\pi$
$653$	−8.03491	−0.314430	−0.157215	+	0.987564i	$0.550252\pi$
$654$	−22.8126	−0.892045
$655$	53.3664	2.08520
$656$	1.34283	0.0524287
$657$	−4.79022	−0.186884
$658$	3.05930	0.119264
$659$	−8.39970	−0.327206	−0.163603	−	0.986526i	$-0.552312\pi$
$659$	−8.39970	−0.327206	−0.163603	+	0.986526i	$0.552312\pi$
$660$	−11.3138	−0.440390
$661$	−33.6287	−1.30800	−0.654001	−	0.756493i	$-0.726911\pi$
$661$	−33.6287	−1.30800	−0.654001	+	0.756493i	$0.726911\pi$
$662$	31.3593	1.21881
$663$	−0.0851874	−0.00330840
$664$	1.88085	0.0729912
$665$	6.88235	0.266886
$666$	8.97932	0.347942
$667$	2.66516	0.103196
$668$	−0.934745	−0.0361664
$669$	−33.9770	−1.31363
$670$	−50.7317	−1.95994
$671$	−11.3531	−0.438280
$672$	0.378075	0.0145845
$673$	−26.1643	−1.00856	−0.504280	−	0.863540i	$-0.668242\pi$
$673$	−26.1643	−1.00856	−0.504280	+	0.863540i	$0.668242\pi$
$674$	−21.5043	−0.828314
$675$	−51.9418	−1.99924
$676$	−12.9898	−0.499608
$677$	9.91517	0.381071	0.190535	−	0.981680i	$-0.438978\pi$
$677$	9.91517	0.381071	0.190535	+	0.981680i	$0.438978\pi$
$678$	−0.429650	−0.0165006
$679$	3.33841	0.128116
$680$	−2.55140	−0.0978418
$681$	−3.84662	−0.147403
$682$	2.24536	0.0859793
$683$	5.50113	0.210495	0.105247	−	0.994446i	$-0.466437\pi$
$683$	5.50113	0.210495	0.105247	+	0.994446i	$0.466437\pi$
$684$	8.61151	0.329269
$685$	−11.3481	−0.433588
$686$	−4.19835	−0.160294
$687$	12.7545	0.486615
$688$	7.72190	0.294395
$689$	−0.0120120	−0.000457622 0
$690$	−10.3793	−0.395132
$691$	45.8476	1.74412	0.872062	−	0.489396i	$-0.162783\pi$
$691$	45.8476	1.74412	0.872062	+	0.489396i	$0.162783\pi$
$692$	−21.4692	−0.816135
$693$	−1.02976	−0.0391172
$694$	−12.1422	−0.460912
$695$	72.8422	2.76306
$696$	−1.52649	−0.0578615
$697$	0.904158	0.0342474
$698$	20.7361	0.784874
$699$	−36.1861	−1.36868
$700$	−2.82486	−0.106770
$701$	39.2078	1.48086	0.740430	−	0.672134i	$-0.234622\pi$
$701$	39.2078	1.48086	0.740430	+	0.672134i	$0.234622\pi$
$702$	−0.560620	−0.0211592
$703$	−37.7531	−1.42389
$704$	−2.38376	−0.0898413
$705$	48.1041	1.81171
$706$	−20.1486	−0.758303
$707$	−3.76875	−0.141738
$708$	11.2732	0.423674
$709$	−36.8716	−1.38474	−0.692371	−	0.721542i	$-0.743434\pi$
$709$	−36.8716	−1.38474	−0.692371	+	0.721542i	$0.743434\pi$
$710$	17.8981	0.671703
$711$	−9.96557	−0.373738
$712$	12.8656	0.482159
$713$	2.05989	0.0771434
$714$	0.254566	0.00952690
$715$	0.912389	0.0341214
$716$	21.4636	0.802132
$717$	5.44469	0.203336
$718$	−6.02663	−0.224912
$719$	1.31447	0.0490216	0.0245108	−	0.999700i	$-0.492197\pi$
$719$	1.31447	0.0490216	0.0245108	+	0.999700i	$0.492197\pi$
$720$	−5.42302	−0.202104
$721$	2.71369	0.101063
$722$	−17.2067	−0.640367
$723$	4.49910	0.167323
$724$	0.273850	0.0101776
$725$	11.4055	0.423589
$726$	6.66060	0.247198
$727$	7.96065	0.295244	0.147622	−	0.989044i	$-0.452838\pi$
$727$	7.96065	0.295244	0.147622	+	0.989044i	$0.452838\pi$
$728$	−0.0304894	−0.00113001
$729$	24.6599	0.913331
$730$	−12.6831	−0.469423
$731$	5.19933	0.192304
$732$	5.96543	0.220489
$733$	49.1106	1.81394	0.906971	−	0.421193i	$-0.138388\pi$
$733$	49.1106	1.81394	0.906971	+	0.421193i	$0.138388\pi$
$734$	37.2404	1.37457
$735$	−32.7910	−1.20951
$736$	−2.18685	−0.0806085
$737$	−31.9144	−1.17558
$738$	1.92179	0.0707421
$739$	−12.1642	−0.447467	−0.223733	−	0.974650i	$-0.571824\pi$
$739$	−12.1642	−0.447467	−0.223733	+	0.974650i	$0.571824\pi$
$740$	23.7747	0.873974
$741$	0.761284	0.0279665
$742$	0.0358957	0.00131777
$743$	−51.4087	−1.88600	−0.943001	−	0.332790i	$-0.892010\pi$
$743$	−51.4087	−1.88600	−0.943001	+	0.332790i	$0.892010\pi$
$744$	−1.17982	−0.0432541
$745$	25.1163	0.920190
$746$	12.0067	0.439596
$747$	2.69178	0.0984871
$748$	−1.60504	−0.0586860
$749$	−2.89689	−0.105850
$750$	−20.6867	−0.755372
$751$	32.4158	1.18287	0.591434	−	0.806353i	$-0.298562\pi$
$751$	32.4158	1.18287	0.591434	+	0.806353i	$0.298562\pi$
$752$	10.1353	0.369595
$753$	−3.52816	−0.128573
$754$	0.123102	0.00448311
$755$	85.9225	3.12704
$756$	1.67531	0.0609303
$757$	26.9478	0.979433	0.489717	−	0.871882i	$-0.337100\pi$
$757$	26.9478	0.979433	0.489717	+	0.871882i	$0.337100\pi$
$758$	20.1779	0.732893
$759$	−6.52940	−0.237002
$760$	22.8008	0.827072
$761$	31.2611	1.13321	0.566607	−	0.823988i	$-0.308256\pi$
$761$	31.2611	1.13321	0.566607	+	0.823988i	$0.308256\pi$
$762$	8.23803	0.298432
$763$	−5.49758	−0.199026
$764$	12.0251	0.435052
$765$	−3.65144	−0.132018
$766$	34.0881	1.23165
$767$	−0.909117	−0.0328263
$768$	1.25254	0.0451971
$769$	−26.4651	−0.954355	−0.477177	−	0.878807i	$-0.658340\pi$
$769$	−26.4651	−0.954355	−0.477177	+	0.878807i	$0.658340\pi$
$770$	−2.72650	−0.0982561
$771$	−32.0018	−1.15252
$772$	5.11030	0.183924
$773$	25.1166	0.903381	0.451691	−	0.892175i	$-0.350821\pi$
$773$	25.1166	0.903381	0.451691	+	0.892175i	$0.350821\pi$
$774$	11.0512	0.397227
$775$	8.81522	0.316652
$776$	11.0599	0.397029
$777$	−2.37212	−0.0850992
$778$	25.9348	0.929809
$779$	−8.08008	−0.289499
$780$	−0.479411	−0.0171657
$781$	11.2593	0.402891
$782$	−1.47246	−0.0526550
$783$	−6.76412	−0.241730
$784$	−6.90889	−0.246746
$785$	−26.2523	−0.936986
$786$	−17.6402	−0.629204
$787$	−20.9994	−0.748549	−0.374274	−	0.927318i	$-0.622108\pi$
$787$	−20.9994	−0.748549	−0.374274	+	0.927318i	$0.622108\pi$
$788$	7.59270	0.270479
$789$	12.5094	0.445347
$790$	−26.3860	−0.938771
$791$	−0.103541	−0.00368148
$792$	−3.41152	−0.121223
$793$	−0.481075	−0.0170835
$794$	−33.3217	−1.18254
$795$	0.564419	0.0200179
$796$	7.67898	0.272174
$797$	−6.68410	−0.236763	−0.118382	−	0.992968i	$-0.537771\pi$
$797$	−6.68410	−0.236763	−0.118382	+	0.992968i	$0.537771\pi$
$798$	−2.27495	−0.0805324
$799$	6.82431	0.241427
$800$	−9.35858	−0.330876
$801$	18.4126	0.650578
$802$	−17.9086	−0.632373
$803$	−7.97871	−0.281563
$804$	16.7693	0.591407
$805$	−2.50128	−0.0881586
$806$	0.0951448	0.00335133
$807$	30.2227	1.06389
$808$	−12.4856	−0.439243
$809$	−51.3474	−1.80528	−0.902639	−	0.430398i	$-0.858373\pi$
$809$	−51.3474	−1.80528	−0.902639	+	0.430398i	$0.858373\pi$
$810$	10.0733	0.353938
$811$	51.3456	1.80299	0.901494	−	0.432793i	$-0.142472\pi$
$811$	51.3456	1.80299	0.901494	+	0.432793i	$0.142472\pi$
$812$	−0.367867	−0.0129096
$813$	−1.48759	−0.0521721
$814$	14.9562	0.524214
$815$	67.8849	2.37790
$816$	0.843362	0.0295236
$817$	−46.4642	−1.62558
$818$	2.25499	0.0788438
$819$	−0.0436348	−0.00152472
$820$	5.08835	0.177693
$821$	−6.06572	−0.211695	−0.105848	−	0.994382i	$-0.533756\pi$
$821$	−6.06572	−0.211695	−0.105848	+	0.994382i	$0.533756\pi$
$822$	3.75109	0.130834
$823$	−34.0006	−1.18519	−0.592594	−	0.805502i	$-0.701896\pi$
$823$	−34.0006	−1.18519	−0.592594	+	0.805502i	$0.701896\pi$
$824$	8.99028	0.313191
$825$	−27.9424	−0.972828
$826$	2.71672	0.0945268
$827$	−17.6010	−0.612045	−0.306023	−	0.952024i	$-0.598998\pi$
$827$	−17.6010	−0.612045	−0.306023	+	0.952024i	$0.598998\pi$
$828$	−3.12972	−0.108765
$829$	21.9010	0.760652	0.380326	−	0.924853i	$-0.375812\pi$
$829$	21.9010	0.760652	0.380326	+	0.924853i	$0.375812\pi$
$830$	7.12706	0.247384
$831$	7.77805	0.269817
$832$	−0.101009	−0.00350187
$833$	−4.65191	−0.161179
$834$	−24.0779	−0.833749
$835$	−3.54200	−0.122576
$836$	14.3436	0.496082
$837$	−5.22794	−0.180704
$838$	0.269839	0.00932144
$839$	6.99058	0.241342	0.120671	−	0.992693i	$-0.461495\pi$
$839$	6.99058	0.241342	0.120671	+	0.992693i	$0.461495\pi$
$840$	1.43263	0.0494303
$841$	−27.5147	−0.948784
$842$	17.4723	0.602136
$843$	4.07706	0.140422
$844$	19.0068	0.654241
$845$	−49.2219	−1.69328
$846$	14.5051	0.498695
$847$	1.60513	0.0551528
$848$	0.118920	0.00408373
$849$	5.30672	0.182126
$850$	−6.30134	−0.216134
$851$	13.7208	0.470342
$852$	−5.91618	−0.202685
$853$	−39.4619	−1.35115	−0.675575	−	0.737292i	$-0.736104\pi$
$853$	−39.4619	−1.35115	−0.675575	+	0.737292i	$0.736104\pi$
$854$	1.43760	0.0491936
$855$	32.6314	1.11597
$856$	−9.59723	−0.328027
$857$	46.4832	1.58784	0.793918	−	0.608025i	$-0.208038\pi$
$857$	46.4832	1.58784	0.793918	+	0.608025i	$0.208038\pi$
$858$	−0.301589	−0.0102961
$859$	27.3972	0.934781	0.467390	−	0.884051i	$-0.345194\pi$
$859$	27.3972	0.934781	0.467390	+	0.884051i	$0.345194\pi$
$860$	29.2604	0.997770
$861$	−0.507690	−0.0173020
$862$	22.0384	0.750631
$863$	51.3560	1.74818	0.874090	−	0.485765i	$-0.161459\pi$
$863$	51.3560	1.74818	0.874090	+	0.485765i	$0.161459\pi$
$864$	5.55018	0.188821
$865$	−81.3525	−2.76607
$866$	7.90819	0.268731
$867$	−20.7253	−0.703868
$868$	−0.284322	−0.00965051
$869$	−16.5989	−0.563080
$870$	−5.78429	−0.196106
$871$	−1.35234	−0.0458222
$872$	−18.2131	−0.616775
$873$	15.8284	0.535711
$874$	13.1587	0.445101
$875$	−4.98526	−0.168532
$876$	4.19238	0.141648
$877$	−10.1791	−0.343722	−0.171861	−	0.985121i	$-0.554978\pi$
$877$	−10.1791	−0.343722	−0.171861	+	0.985121i	$0.554978\pi$
$878$	13.4070	0.452464
$879$	−1.77090	−0.0597310
$880$	−9.03271	−0.304493
$881$	24.9526	0.840674	0.420337	−	0.907368i	$-0.361912\pi$
$881$	24.9526	0.840674	0.420337	+	0.907368i	$0.361912\pi$
$882$	−9.88765	−0.332935
$883$	18.3795	0.618520	0.309260	−	0.950978i	$-0.399919\pi$
$883$	18.3795	0.618520	0.309260	+	0.950978i	$0.399919\pi$
$884$	−0.0680119	−0.00228749
$885$	42.7174	1.43593
$886$	0.583546	0.0196046
$887$	−12.6015	−0.423116	−0.211558	−	0.977365i	$-0.567854\pi$
$887$	−12.6015	−0.423116	−0.211558	+	0.977365i	$0.567854\pi$
$888$	−7.85867	−0.263720
$889$	1.98527	0.0665838
$890$	48.7513	1.63415
$891$	6.33690	0.212294
$892$	−27.1266	−0.908264
$893$	−60.9860	−2.04082
$894$	−8.30215	−0.277665
$895$	81.3313	2.71861
$896$	0.301847	0.0100840
$897$	−0.276676	−0.00923796
$898$	40.3340	1.34596
$899$	1.14796	0.0382866
$900$	−13.3935	−0.446451
$901$	0.0800716	0.00266757
$902$	3.20098	0.106581
$903$	−2.91945	−0.0971533
$904$	−0.343024	−0.0114088
$905$	1.03769	0.0344941
$906$	−28.4015	−0.943578
$907$	−21.9038	−0.727303	−0.363651	−	0.931535i	$-0.618470\pi$
$907$	−21.9038	−0.727303	−0.363651	+	0.931535i	$0.618470\pi$
$908$	−3.07106	−0.101917
$909$	−17.8688	−0.592670
$910$	−0.115532	−0.00382986
$911$	−45.7531	−1.51587	−0.757934	−	0.652332i	$-0.773791\pi$
$911$	−45.7531	−1.51587	−0.757934	+	0.652332i	$0.773791\pi$
$912$	−7.53677	−0.249567
$913$	4.48350	0.148382
$914$	32.6633	1.08041
$915$	22.6046	0.747286
$916$	10.1829	0.336454
$917$	−4.25108	−0.140383
$918$	3.73706	0.123341
$919$	23.6137	0.778945	0.389472	−	0.921038i	$-0.372657\pi$
$919$	23.6137	0.778945	0.389472	+	0.921038i	$0.372657\pi$
$920$	−8.28659	−0.273201
$921$	31.8224	1.04858
$922$	30.1479	0.992869
$923$	0.477103	0.0157040
$924$	0.901239	0.0296486
$925$	58.7176	1.93062
$926$	−22.1188	−0.726869
$927$	12.8664	0.422589
$928$	−1.21872	−0.0400064
$929$	20.5111	0.672947	0.336474	−	0.941693i	$-0.390766\pi$
$929$	20.5111	0.672947	0.336474	+	0.941693i	$0.390766\pi$
$930$	−4.47064	−0.146598
$931$	41.5722	1.36247
$932$	−28.8902	−0.946330
$933$	1.43596	0.0470113
$934$	0.107359	0.00351288
$935$	−6.08193	−0.198900
$936$	−0.144559	−0.00472507
$937$	−2.96810	−0.0969635	−0.0484818	−	0.998824i	$-0.515438\pi$
$937$	−2.96810	−0.0969635	−0.0484818	+	0.998824i	$0.515438\pi$
$938$	4.04120	0.131950
$939$	−7.78211	−0.253960
$940$	38.4053	1.25264
$941$	−30.4200	−0.991663	−0.495832	−	0.868419i	$-0.665137\pi$
$941$	−30.4200	−0.991663	−0.495832	+	0.868419i	$0.665137\pi$
$942$	8.67767	0.282734
$943$	2.93657	0.0956280
$944$	9.00032	0.292936
$945$	6.34819	0.206507
$946$	18.4071	0.598468
$947$	−6.93156	−0.225245	−0.112623	−	0.993638i	$-0.535925\pi$
$947$	−6.93156	−0.225245	−0.112623	+	0.993638i	$0.535925\pi$
$948$	8.72184	0.283272
$949$	−0.338090	−0.0109749
$950$	56.3125	1.82702
$951$	−35.4274	−1.14881
$952$	0.203240	0.00658706
$953$	15.2955	0.495469	0.247734	−	0.968828i	$-0.420314\pi$
$953$	15.2955	0.495469	0.247734	+	0.968828i	$0.420314\pi$
$954$	0.170193	0.00551019
$955$	45.5663	1.47449
$956$	4.34693	0.140590
$957$	−3.63879	−0.117625
$958$	2.67121	0.0863030
$959$	0.903969	0.0291907
$960$	4.74621	0.153183
$961$	−30.1127	−0.971379
$962$	0.633753	0.0204330
$963$	−13.7351	−0.442606
$964$	3.59199	0.115690
$965$	19.3643	0.623359
$966$	0.826794	0.0266017
$967$	18.6465	0.599632	0.299816	−	0.953997i	$-0.403075\pi$
$967$	18.6465	0.599632	0.299816	+	0.953997i	$0.403075\pi$
$968$	5.31769	0.170917
$969$	−5.07468	−0.163022
$970$	41.9091	1.34562
$971$	11.0606	0.354951	0.177475	−	0.984125i	$-0.443207\pi$
$971$	11.0606	0.354951	0.177475	+	0.984125i	$0.443207\pi$
$972$	13.3208	0.427266
$973$	−5.80249	−0.186019
$974$	28.9817	0.928634
$975$	−1.18403	−0.0379193
$976$	4.76267	0.152449
$977$	31.0080	0.992033	0.496016	−	0.868313i	$-0.334796\pi$
$977$	31.0080	0.992033	0.496016	+	0.868313i	$0.334796\pi$
$978$	−22.4392	−0.717527
$979$	30.6685	0.980171
$980$	−26.1797	−0.836278
$981$	−26.0657	−0.832215
$982$	−19.5271	−0.623135
$983$	17.8163	0.568252	0.284126	−	0.958787i	$-0.408297\pi$
$983$	17.8163	0.568252	0.284126	+	0.958787i	$0.408297\pi$
$984$	−1.68195	−0.0536185
$985$	28.7708	0.916714
$986$	−0.820591	−0.0261330
$987$	−3.83189	−0.121970
$988$	0.607793	0.0193365
$989$	16.8867	0.536965
$990$	−12.9272	−0.410852
$991$	−14.8610	−0.472075	−0.236038	−	0.971744i	$-0.575849\pi$
$991$	−14.8610	−0.472075	−0.236038	+	0.971744i	$0.575849\pi$
$992$	−0.941940	−0.0299066
$993$	−39.2787	−1.24647
$994$	−1.42573	−0.0452214
$995$	29.0978	0.922461
$996$	−2.35584	−0.0746476
$997$	−21.9242	−0.694345	−0.347173	−	0.937801i	$-0.612858\pi$
$997$	−21.9242	−0.694345	−0.347173	+	0.937801i	$0.612858\pi$
$998$	−19.8419	−0.628086
$999$	−34.8230	−1.10175

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.e.1.52	✓	77

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.e.1.52	✓	77	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:	\( N \)	\(=\)	\( 8002 = 2 \cdot 4001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8002.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.25254 q^{3} +1.00000 q^{4} +3.78927 q^{5} -1.25254 q^{6} -0.301847 q^{7} -1.00000 q^{8} -1.43115 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.25254 q^{3} +1.00000 q^{4} +3.78927 q^{5} -1.25254 q^{6} -0.301847 q^{7} -1.00000 q^{8} -1.43115 q^{9} -3.78927 q^{10} -2.38376 q^{11} +1.25254 q^{12} -0.101009 q^{13} +0.301847 q^{14} +4.74621 q^{15} +1.00000 q^{16} +0.673322 q^{17} +1.43115 q^{18} -6.01720 q^{19} +3.78927 q^{20} -0.378075 q^{21} +2.38376 q^{22} +2.18685 q^{23} -1.25254 q^{24} +9.35858 q^{25} +0.101009 q^{26} -5.55018 q^{27} -0.301847 q^{28} +1.21872 q^{29} -4.74621 q^{30} +0.941940 q^{31} -1.00000 q^{32} -2.98575 q^{33} -0.673322 q^{34} -1.14378 q^{35} -1.43115 q^{36} +6.27420 q^{37} +6.01720 q^{38} -0.126518 q^{39} -3.78927 q^{40} +1.34283 q^{41} +0.378075 q^{42} +7.72190 q^{43} -2.38376 q^{44} -5.42302 q^{45} -2.18685 q^{46} +10.1353 q^{47} +1.25254 q^{48} -6.90889 q^{49} -9.35858 q^{50} +0.843362 q^{51} -0.101009 q^{52} +0.118920 q^{53} +5.55018 q^{54} -9.03271 q^{55} +0.301847 q^{56} -7.53677 q^{57} -1.21872 q^{58} +9.00032 q^{59} +4.74621 q^{60} +4.76267 q^{61} -0.941940 q^{62} +0.431988 q^{63} +1.00000 q^{64} -0.382752 q^{65} +2.98575 q^{66} +13.3882 q^{67} +0.673322 q^{68} +2.73912 q^{69} +1.14378 q^{70} -4.72336 q^{71} +1.43115 q^{72} +3.34711 q^{73} -6.27420 q^{74} +11.7220 q^{75} -6.01720 q^{76} +0.719531 q^{77} +0.126518 q^{78} +6.96333 q^{79} +3.78927 q^{80} -2.65836 q^{81} -1.34283 q^{82} -1.88085 q^{83} -0.378075 q^{84} +2.55140 q^{85} -7.72190 q^{86} +1.52649 q^{87} +2.38376 q^{88} -12.8656 q^{89} +5.42302 q^{90} +0.0304894 q^{91} +2.18685 q^{92} +1.17982 q^{93} -10.1353 q^{94} -22.8008 q^{95} -1.25254 q^{96} -11.0599 q^{97} +6.90889 q^{98} +3.41152 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9}+O(q^{10}) \) 77 * q - 77 * q^2 + 10 * q^3 + 77 * q^4 + 18 * q^5 - 10 * q^6 + 21 * q^7 - 77 * q^8 + 71 * q^9	\( 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9} - 18 q^{10} + 30 q^{11} + 10 q^{12} - 2 q^{13} - 21 q^{14} + 21 q^{15} + 77 q^{16} + 60 q^{17} - 71 q^{18} - 3 q^{19} + 18 q^{20} + 10 q^{21} - 30 q^{22} + 53 q^{23} - 10 q^{24} + 59 q^{25} + 2 q^{26} + 43 q^{27} + 21 q^{28} + 30 q^{29} - 21 q^{30} + 22 q^{31} - 77 q^{32} + 31 q^{33} - 60 q^{34} + 41 q^{35} + 71 q^{36} - 3 q^{37} + 3 q^{38} + 44 q^{39} - 18 q^{40} + 48 q^{41} - 10 q^{42} + 21 q^{43} + 30 q^{44} + 33 q^{45} - 53 q^{46} + 107 q^{47} + 10 q^{48} + 24 q^{49} - 59 q^{50} + 18 q^{51} - 2 q^{52} + 42 q^{53} - 43 q^{54} + 49 q^{55} - 21 q^{56} + 32 q^{57} - 30 q^{58} + 42 q^{59} + 21 q^{60} - 31 q^{61} - 22 q^{62} + 109 q^{63} + 77 q^{64} + 39 q^{65} - 31 q^{66} - q^{67} + 60 q^{68} - 33 q^{69} - 41 q^{70} + 58 q^{71} - 71 q^{72} + 35 q^{73} + 3 q^{74} + 34 q^{75} - 3 q^{76} + 86 q^{77} - 44 q^{78} + 25 q^{79} + 18 q^{80} + 53 q^{81} - 48 q^{82} + 107 q^{83} + 10 q^{84} + 21 q^{85} - 21 q^{86} + 100 q^{87} - 30 q^{88} + 34 q^{89} - 33 q^{90} - 51 q^{91} + 53 q^{92} + 48 q^{93} - 107 q^{94} + 118 q^{95} - 10 q^{96} - 13 q^{97} - 24 q^{98} + 63 q^{99}+O(q^{100}) \) 77 * q - 77 * q^2 + 10 * q^3 + 77 * q^4 + 18 * q^5 - 10 * q^6 + 21 * q^7 - 77 * q^8 + 71 * q^9 - 18 * q^10 + 30 * q^11 + 10 * q^12 - 2 * q^13 - 21 * q^14 + 21 * q^15 + 77 * q^16 + 60 * q^17 - 71 * q^18 - 3 * q^19 + 18 * q^20 + 10 * q^21 - 30 * q^22 + 53 * q^23 - 10 * q^24 + 59 * q^25 + 2 * q^26 + 43 * q^27 + 21 * q^28 + 30 * q^29 - 21 * q^30 + 22 * q^31 - 77 * q^32 + 31 * q^33 - 60 * q^34 + 41 * q^35 + 71 * q^36 - 3 * q^37 + 3 * q^38 + 44 * q^39 - 18 * q^40 + 48 * q^41 - 10 * q^42 + 21 * q^43 + 30 * q^44 + 33 * q^45 - 53 * q^46 + 107 * q^47 + 10 * q^48 + 24 * q^49 - 59 * q^50 + 18 * q^51 - 2 * q^52 + 42 * q^53 - 43 * q^54 + 49 * q^55 - 21 * q^56 + 32 * q^57 - 30 * q^58 + 42 * q^59 + 21 * q^60 - 31 * q^61 - 22 * q^62 + 109 * q^63 + 77 * q^64 + 39 * q^65 - 31 * q^66 - q^67 + 60 * q^68 - 33 * q^69 - 41 * q^70 + 58 * q^71 - 71 * q^72 + 35 * q^73 + 3 * q^74 + 34 * q^75 - 3 * q^76 + 86 * q^77 - 44 * q^78 + 25 * q^79 + 18 * q^80 + 53 * q^81 - 48 * q^82 + 107 * q^83 + 10 * q^84 + 21 * q^85 - 21 * q^86 + 100 * q^87 - 30 * q^88 + 34 * q^89 - 33 * q^90 - 51 * q^91 + 53 * q^92 + 48 * q^93 - 107 * q^94 + 118 * q^95 - 10 * q^96 - 13 * q^97 - 24 * q^98 + 63 * q^99

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