LMFDB - Embedded newform 8007.2.a.c.1.14

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:	$39$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.03615 q^{2} -1.00000 q^{3} -0.926391 q^{4} -2.19284 q^{5} +1.03615 q^{6} +0.525649 q^{7} +3.03218 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.03615 q^{2} -1.00000 q^{3} -0.926391 q^{4} -2.19284 q^{5} +1.03615 q^{6} +0.525649 q^{7} +3.03218 q^{8} +1.00000 q^{9} +2.27211 q^{10} +3.25038 q^{11} +0.926391 q^{12} -6.70084 q^{13} -0.544652 q^{14} +2.19284 q^{15} -1.28902 q^{16} +1.00000 q^{17} -1.03615 q^{18} +3.24959 q^{19} +2.03143 q^{20} -0.525649 q^{21} -3.36788 q^{22} -3.92914 q^{23} -3.03218 q^{24} -0.191449 q^{25} +6.94308 q^{26} -1.00000 q^{27} -0.486957 q^{28} -0.274463 q^{29} -2.27211 q^{30} +7.90295 q^{31} -4.72875 q^{32} -3.25038 q^{33} -1.03615 q^{34} -1.15266 q^{35} -0.926391 q^{36} -2.01267 q^{37} -3.36707 q^{38} +6.70084 q^{39} -6.64909 q^{40} -5.79285 q^{41} +0.544652 q^{42} +11.3622 q^{43} -3.01112 q^{44} -2.19284 q^{45} +4.07118 q^{46} -1.64748 q^{47} +1.28902 q^{48} -6.72369 q^{49} +0.198370 q^{50} -1.00000 q^{51} +6.20760 q^{52} +3.44449 q^{53} +1.03615 q^{54} -7.12756 q^{55} +1.59386 q^{56} -3.24959 q^{57} +0.284385 q^{58} -4.12979 q^{59} -2.03143 q^{60} +3.70472 q^{61} -8.18865 q^{62} +0.525649 q^{63} +7.47773 q^{64} +14.6939 q^{65} +3.36788 q^{66} -9.87028 q^{67} -0.926391 q^{68} +3.92914 q^{69} +1.19433 q^{70} -1.84283 q^{71} +3.03218 q^{72} -5.57621 q^{73} +2.08543 q^{74} +0.191449 q^{75} -3.01039 q^{76} +1.70856 q^{77} -6.94308 q^{78} -2.77548 q^{79} +2.82661 q^{80} +1.00000 q^{81} +6.00226 q^{82} -5.77307 q^{83} +0.486957 q^{84} -2.19284 q^{85} -11.7730 q^{86} +0.274463 q^{87} +9.85574 q^{88} +11.5892 q^{89} +2.27211 q^{90} -3.52229 q^{91} +3.63992 q^{92} -7.90295 q^{93} +1.70704 q^{94} -7.12583 q^{95} +4.72875 q^{96} +13.5680 q^{97} +6.96676 q^{98} +3.25038 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9}+O(q^{10}) $ 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9	\( 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9} + 4 q^{10} + q^{11} - 30 q^{12} - 26 q^{13} - 4 q^{14} + 3 q^{15} + 8 q^{16} + 39 q^{17} - 4 q^{18} - 14 q^{19} - 14 q^{20} + 5 q^{21} - 17 q^{22} + 2 q^{23} + 3 q^{24} - 6 q^{25} - 17 q^{26} - 39 q^{27} - 14 q^{28} - 7 q^{29} - 4 q^{30} - q^{31} - 30 q^{32} - q^{33} - 4 q^{34} + q^{35} + 30 q^{36} - 24 q^{37} - 20 q^{38} + 26 q^{39} + 12 q^{40} + q^{41} + 4 q^{42} - 41 q^{43} - 2 q^{44} - 3 q^{45} - 6 q^{46} - 9 q^{47} - 8 q^{48} - 10 q^{49} - 9 q^{50} - 39 q^{51} - 37 q^{52} - 47 q^{53} + 4 q^{54} - 39 q^{55} + 8 q^{56} + 14 q^{57} - 27 q^{58} + 41 q^{59} + 14 q^{60} - 41 q^{61} + 36 q^{62} - 5 q^{63} - 47 q^{64} - 39 q^{65} + 17 q^{66} - 36 q^{67} + 30 q^{68} - 2 q^{69} - 52 q^{70} - 2 q^{71} - 3 q^{72} - 63 q^{73} - 6 q^{74} + 6 q^{75} - 34 q^{76} - 64 q^{77} + 17 q^{78} + 20 q^{79} - 28 q^{80} + 39 q^{81} - 37 q^{82} + 45 q^{83} + 14 q^{84} - 3 q^{85} + 32 q^{86} + 7 q^{87} + 6 q^{88} - 32 q^{89} + 4 q^{90} - 11 q^{91} + 28 q^{92} + q^{93} - 44 q^{94} + 22 q^{95} + 30 q^{96} - 20 q^{97} + 63 q^{98} + q^{99}+O(q^{100}) \) 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9 + 4 * q^10 + q^11 - 30 * q^12 - 26 * q^13 - 4 * q^14 + 3 * q^15 + 8 * q^16 + 39 * q^17 - 4 * q^18 - 14 * q^19 - 14 * q^20 + 5 * q^21 - 17 * q^22 + 2 * q^23 + 3 * q^24 - 6 * q^25 - 17 * q^26 - 39 * q^27 - 14 * q^28 - 7 * q^29 - 4 * q^30 - q^31 - 30 * q^32 - q^33 - 4 * q^34 + q^35 + 30 * q^36 - 24 * q^37 - 20 * q^38 + 26 * q^39 + 12 * q^40 + q^41 + 4 * q^42 - 41 * q^43 - 2 * q^44 - 3 * q^45 - 6 * q^46 - 9 * q^47 - 8 * q^48 - 10 * q^49 - 9 * q^50 - 39 * q^51 - 37 * q^52 - 47 * q^53 + 4 * q^54 - 39 * q^55 + 8 * q^56 + 14 * q^57 - 27 * q^58 + 41 * q^59 + 14 * q^60 - 41 * q^61 + 36 * q^62 - 5 * q^63 - 47 * q^64 - 39 * q^65 + 17 * q^66 - 36 * q^67 + 30 * q^68 - 2 * q^69 - 52 * q^70 - 2 * q^71 - 3 * q^72 - 63 * q^73 - 6 * q^74 + 6 * q^75 - 34 * q^76 - 64 * q^77 + 17 * q^78 + 20 * q^79 - 28 * q^80 + 39 * q^81 - 37 * q^82 + 45 * q^83 + 14 * q^84 - 3 * q^85 + 32 * q^86 + 7 * q^87 + 6 * q^88 - 32 * q^89 + 4 * q^90 - 11 * q^91 + 28 * q^92 + q^93 - 44 * q^94 + 22 * q^95 + 30 * q^96 - 20 * q^97 + 63 * q^98 + 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 $

$2$	−1.03615	−0.732669	−0.366335	−	0.930483i	$-0.619387\pi$
$2$	−1.03615	−0.732669	−0.366335	+	0.930483i	$0.619387\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.926391	−0.463196
$5$	−2.19284	−0.980668	−0.490334	−	0.871535i	$-0.663125\pi$
$5$	−2.19284	−0.980668	−0.490334	+	0.871535i	$0.663125\pi$
$6$	1.03615	0.423007
$7$	0.525649	0.198677	0.0993383	−	0.995054i	$-0.468327\pi$
$7$	0.525649	0.198677	0.0993383	+	0.995054i	$0.468327\pi$
$8$	3.03218	1.07204
$9$	1.00000	0.333333
$10$	2.27211	0.718506
$11$	3.25038	0.980025	0.490013	−	0.871715i	$-0.336992\pi$
$11$	3.25038	0.980025	0.490013	+	0.871715i	$0.336992\pi$
$12$	0.926391	0.267426
$13$	−6.70084	−1.85848	−0.929239	−	0.369479i	$-0.879536\pi$
$13$	−6.70084	−1.85848	−0.929239	+	0.369479i	$0.879536\pi$
$14$	−0.544652	−0.145564
$15$	2.19284	0.566189
$16$	−1.28902	−0.322254
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.03615	−0.244223
$19$	3.24959	0.745507	0.372754	−	0.927930i	$-0.378414\pi$
$19$	3.24959	0.745507	0.372754	+	0.927930i	$0.378414\pi$
$20$	2.03143	0.454241
$21$	−0.525649	−0.114706
$22$	−3.36788	−0.718034
$23$	−3.92914	−0.819282	−0.409641	−	0.912247i	$-0.634346\pi$
$23$	−3.92914	−0.819282	−0.409641	+	0.912247i	$0.634346\pi$
$24$	−3.03218	−0.618942
$25$	−0.191449	−0.0382897
$26$	6.94308	1.36165
$27$	−1.00000	−0.192450
$28$	−0.486957	−0.0920262
$29$	−0.274463	−0.0509665	−0.0254833	−	0.999675i	$-0.508112\pi$
$29$	−0.274463	−0.0509665	−0.0254833	+	0.999675i	$0.508112\pi$
$30$	−2.27211	−0.414829
$31$	7.90295	1.41941	0.709706	−	0.704498i	$-0.248828\pi$
$31$	7.90295	1.41941	0.709706	+	0.704498i	$0.248828\pi$
$32$	−4.72875	−0.835933
$33$	−3.25038	−0.565818
$34$	−1.03615	−0.177698
$35$	−1.15266	−0.194836
$36$	−0.926391	−0.154399
$37$	−2.01267	−0.330881	−0.165440	−	0.986220i	$-0.552905\pi$
$37$	−2.01267	−0.330881	−0.165440	+	0.986220i	$0.552905\pi$
$38$	−3.36707	−0.546210
$39$	6.70084	1.07299
$40$	−6.64909	−1.05131
$41$	−5.79285	−0.904691	−0.452345	−	0.891843i	$-0.649413\pi$
$41$	−5.79285	−0.904691	−0.452345	+	0.891843i	$0.649413\pi$
$42$	0.544652	0.0840416
$43$	11.3622	1.73273	0.866363	−	0.499415i	$-0.166452\pi$
$43$	11.3622	1.73273	0.866363	+	0.499415i	$0.166452\pi$
$44$	−3.01112	−0.453944
$45$	−2.19284	−0.326889
$46$	4.07118	0.600263
$47$	−1.64748	−0.240310	−0.120155	−	0.992755i	$-0.538339\pi$
$47$	−1.64748	−0.240310	−0.120155	+	0.992755i	$0.538339\pi$
$48$	1.28902	0.186053
$49$	−6.72369	−0.960528
$50$	0.198370	0.0280537
$51$	−1.00000	−0.140028
$52$	6.20760	0.860839
$53$	3.44449	0.473137	0.236568	−	0.971615i	$-0.423977\pi$
$53$	3.44449	0.473137	0.236568	+	0.971615i	$0.423977\pi$
$54$	1.03615	0.141002
$55$	−7.12756	−0.961080
$56$	1.59386	0.212989
$57$	−3.24959	−0.430419
$58$	0.284385	0.0373416
$59$	−4.12979	−0.537653	−0.268827	−	0.963189i	$-0.586636\pi$
$59$	−4.12979	−0.537653	−0.268827	+	0.963189i	$0.586636\pi$
$60$	−2.03143	−0.262256
$61$	3.70472	0.474341	0.237171	−	0.971468i	$-0.423780\pi$
$61$	3.70472	0.474341	0.237171	+	0.971468i	$0.423780\pi$
$62$	−8.18865	−1.03996
$63$	0.525649	0.0662255
$64$	7.47773	0.934716
$65$	14.6939	1.82255
$66$	3.36788	0.414557
$67$	−9.87028	−1.20585	−0.602924	−	0.797799i	$-0.705998\pi$
$67$	−9.87028	−1.20585	−0.602924	+	0.797799i	$0.705998\pi$
$68$	−0.926391	−0.112341
$69$	3.92914	0.473013
$70$	1.19433	0.142750
$71$	−1.84283	−0.218704	−0.109352	−	0.994003i	$-0.534878\pi$
$71$	−1.84283	−0.218704	−0.109352	+	0.994003i	$0.534878\pi$
$72$	3.03218	0.357346
$73$	−5.57621	−0.652646	−0.326323	−	0.945258i	$-0.605810\pi$
$73$	−5.57621	−0.652646	−0.326323	+	0.945258i	$0.605810\pi$
$74$	2.08543	0.242426
$75$	0.191449	0.0221066
$76$	−3.01039	−0.345316
$77$	1.70856	0.194708
$78$	−6.94308	−0.786149
$79$	−2.77548	−0.312266	−0.156133	−	0.987736i	$-0.549903\pi$
$79$	−2.77548	−0.312266	−0.156133	+	0.987736i	$0.549903\pi$
$80$	2.82661	0.316024
$81$	1.00000	0.111111
$82$	6.00226	0.662839
$83$	−5.77307	−0.633677	−0.316838	−	0.948480i	$-0.602621\pi$
$83$	−5.77307	−0.633677	−0.316838	+	0.948480i	$0.602621\pi$
$84$	0.486957	0.0531313
$85$	−2.19284	−0.237847
$86$	−11.7730	−1.26952
$87$	0.274463	0.0294256
$88$	9.85574	1.05062
$89$	11.5892	1.22846	0.614229	−	0.789128i	$-0.289467\pi$
$89$	11.5892	1.22846	0.614229	+	0.789128i	$0.289467\pi$
$90$	2.27211	0.239502
$91$	−3.52229	−0.369236
$92$	3.63992	0.379488
$93$	−7.90295	−0.819497
$94$	1.70704	0.176068
$95$	−7.12583	−0.731095
$96$	4.72875	0.482626
$97$	13.5680	1.37763	0.688813	−	0.724939i	$-0.258132\pi$
$97$	13.5680	1.37763	0.688813	+	0.724939i	$0.258132\pi$
$98$	6.96676	0.703749
$99$	3.25038	0.326675
$100$	0.177356	0.0177356
$101$	9.18705	0.914146	0.457073	−	0.889429i	$-0.348898\pi$
$101$	9.18705	0.914146	0.457073	+	0.889429i	$0.348898\pi$
$102$	1.03615	0.102594
$103$	1.39001	0.136962	0.0684811	−	0.997652i	$-0.478185\pi$
$103$	1.39001	0.136962	0.0684811	+	0.997652i	$0.478185\pi$
$104$	−20.3182	−1.99236
$105$	1.15266	0.112489
$106$	−3.56901	−0.346653
$107$	−1.61719	−0.156340	−0.0781699	−	0.996940i	$-0.524908\pi$
$107$	−1.61719	−0.156340	−0.0781699	+	0.996940i	$0.524908\pi$
$108$	0.926391	0.0891421
$109$	6.22861	0.596593	0.298296	−	0.954473i	$-0.403582\pi$
$109$	6.22861	0.596593	0.298296	+	0.954473i	$0.403582\pi$
$110$	7.38522	0.704154
$111$	2.01267	0.191034
$112$	−0.677570	−0.0640243
$113$	2.56162	0.240977	0.120488	−	0.992715i	$-0.461554\pi$
$113$	2.56162	0.240977	0.120488	+	0.992715i	$0.461554\pi$
$114$	3.36707	0.315355
$115$	8.61598	0.803444
$116$	0.254260	0.0236075
$117$	−6.70084	−0.619493
$118$	4.27909	0.393922
$119$	0.525649	0.0481862
$120$	6.64909	0.606977
$121$	−0.435055	−0.0395505
$122$	−3.83865	−0.347535
$123$	5.79285	0.522323
$124$	−7.32122	−0.657465
$125$	11.3840	1.01822
$126$	−0.544652	−0.0485214
$127$	6.16614	0.547156	0.273578	−	0.961850i	$-0.411793\pi$
$127$	6.16614	0.547156	0.273578	+	0.961850i	$0.411793\pi$
$128$	1.70944	0.151095
$129$	−11.3622	−1.00039
$130$	−15.2251	−1.33533
$131$	−12.8625	−1.12380	−0.561902	−	0.827204i	$-0.689930\pi$
$131$	−12.8625	−1.12380	−0.561902	+	0.827204i	$0.689930\pi$
$132$	3.01112	0.262084
$133$	1.70814	0.148115
$134$	10.2271	0.883487
$135$	2.19284	0.188730
$136$	3.03218	0.260008
$137$	−8.10907	−0.692805	−0.346402	−	0.938086i	$-0.612597\pi$
$137$	−8.10907	−0.692805	−0.346402	+	0.938086i	$0.612597\pi$
$138$	−4.07118	−0.346562
$139$	2.61470	0.221776	0.110888	−	0.993833i	$-0.464631\pi$
$139$	2.61470	0.221776	0.110888	+	0.993833i	$0.464631\pi$
$140$	1.06782	0.0902471
$141$	1.64748	0.138743
$142$	1.90945	0.160238
$143$	−21.7802	−1.82136
$144$	−1.28902	−0.107418
$145$	0.601854	0.0499813
$146$	5.77780	0.478174
$147$	6.72369	0.554561
$148$	1.86452	0.153263
$149$	19.5318	1.60010	0.800052	−	0.599930i	$-0.204805\pi$
$149$	19.5318	1.60010	0.800052	+	0.599930i	$0.204805\pi$
$150$	−0.198370	−0.0161968
$151$	5.16171	0.420054	0.210027	−	0.977696i	$-0.432645\pi$
$151$	5.16171	0.420054	0.210027	+	0.977696i	$0.432645\pi$
$152$	9.85335	0.799212
$153$	1.00000	0.0808452
$154$	−1.77032	−0.142657
$155$	−17.3299	−1.39197
$156$	−6.20760	−0.497006
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	2.87582	0.228788
$159$	−3.44449	−0.273166
$160$	10.3694	0.819773
$161$	−2.06535	−0.162772
$162$	−1.03615	−0.0814077
$163$	−11.1839	−0.875990	−0.437995	−	0.898977i	$-0.644311\pi$
$163$	−11.1839	−0.875990	−0.437995	+	0.898977i	$0.644311\pi$
$164$	5.36644	0.419049
$165$	7.12756	0.554880
$166$	5.98177	0.464275
$167$	6.47106	0.500745	0.250373	−	0.968150i	$-0.419447\pi$
$167$	6.47106	0.500745	0.250373	+	0.968150i	$0.419447\pi$
$168$	−1.59386	−0.122969
$169$	31.9012	2.45394
$170$	2.27211	0.174263
$171$	3.24959	0.248502
$172$	−10.5259	−0.802591
$173$	21.4932	1.63410	0.817048	−	0.576570i	$-0.195609\pi$
$173$	21.4932	1.63410	0.817048	+	0.576570i	$0.195609\pi$
$174$	−0.284385	−0.0215592
$175$	−0.100635	−0.00760728
$176$	−4.18979	−0.315817
$177$	4.12979	0.310414
$178$	−12.0082	−0.900053
$179$	16.9738	1.26868	0.634342	−	0.773053i	$-0.281271\pi$
$179$	16.9738	1.26868	0.634342	+	0.773053i	$0.281271\pi$
$180$	2.03143	0.151414
$181$	−12.7985	−0.951305	−0.475652	−	0.879633i	$-0.657788\pi$
$181$	−12.7985	−0.951305	−0.475652	+	0.879633i	$0.657788\pi$
$182$	3.64962	0.270528
$183$	−3.70472	−0.273861
$184$	−11.9139	−0.878302
$185$	4.41346	0.324484
$186$	8.18865	0.600421
$187$	3.25038	0.237691
$188$	1.52621	0.111311
$189$	−0.525649	−0.0382353
$190$	7.38344	0.535651
$191$	−11.7695	−0.851613	−0.425806	−	0.904814i	$-0.640010\pi$
$191$	−11.7695	−0.851613	−0.425806	+	0.904814i	$0.640010\pi$
$192$	−7.47773	−0.539659
$193$	6.46146	0.465106	0.232553	−	0.972584i	$-0.425292\pi$
$193$	6.46146	0.465106	0.232553	+	0.972584i	$0.425292\pi$
$194$	−14.0585	−1.00934
$195$	−14.6939	−1.05225
$196$	6.22877	0.444912
$197$	14.8268	1.05637	0.528183	−	0.849131i	$-0.322874\pi$
$197$	14.8268	1.05637	0.528183	+	0.849131i	$0.322874\pi$
$198$	−3.36788	−0.239345
$199$	7.38720	0.523665	0.261832	−	0.965113i	$-0.415673\pi$
$199$	7.38720	0.523665	0.261832	+	0.965113i	$0.415673\pi$
$200$	−0.580508	−0.0410481
$201$	9.87028	0.696196
$202$	−9.51917	−0.669767
$203$	−0.144271	−0.0101259
$204$	0.926391	0.0648604
$205$	12.7028	0.887201
$206$	−1.44026	−0.100348
$207$	−3.92914	−0.273094
$208$	8.63749	0.598902
$209$	10.5624	0.730616
$210$	−1.19433	−0.0824169
$211$	−11.7092	−0.806096	−0.403048	−	0.915179i	$-0.632049\pi$
$211$	−11.7092	−0.806096	−0.403048	+	0.915179i	$0.632049\pi$
$212$	−3.19094	−0.219155
$213$	1.84283	0.126269
$214$	1.67565	0.114545
$215$	−24.9156	−1.69923
$216$	−3.03218	−0.206314
$217$	4.15418	0.282004
$218$	−6.45378	−0.437105
$219$	5.57621	0.376805
$220$	6.60291	0.445168
$221$	−6.70084	−0.450747
$222$	−2.08543	−0.139965
$223$	−11.8870	−0.796010	−0.398005	−	0.917383i	$-0.630297\pi$
$223$	−11.8870	−0.796010	−0.398005	+	0.917383i	$0.630297\pi$
$224$	−2.48566	−0.166080
$225$	−0.191449	−0.0127632
$226$	−2.65422	−0.176556
$227$	8.46311	0.561717	0.280858	−	0.959749i	$-0.409381\pi$
$227$	8.46311	0.561717	0.280858	+	0.959749i	$0.409381\pi$
$228$	3.01039	0.199368
$229$	−5.95032	−0.393208	−0.196604	−	0.980483i	$-0.562991\pi$
$229$	−5.95032	−0.393208	−0.196604	+	0.980483i	$0.562991\pi$
$230$	−8.92746	−0.588659
$231$	−1.70856	−0.112415
$232$	−0.832223	−0.0546381
$233$	−9.09805	−0.596033	−0.298016	−	0.954561i	$-0.596325\pi$
$233$	−9.09805	−0.596033	−0.298016	+	0.954561i	$0.596325\pi$
$234$	6.94308	0.453883
$235$	3.61267	0.235664
$236$	3.82580	0.249039
$237$	2.77548	0.180287
$238$	−0.544652	−0.0353045
$239$	13.6718	0.884358	0.442179	−	0.896927i	$-0.354206\pi$
$239$	13.6718	0.884358	0.442179	+	0.896927i	$0.354206\pi$
$240$	−2.82661	−0.182457
$241$	−16.8681	−1.08657	−0.543284	−	0.839549i	$-0.682819\pi$
$241$	−16.8681	−1.08657	−0.543284	+	0.839549i	$0.682819\pi$
$242$	0.450783	0.0289774
$243$	−1.00000	−0.0641500
$244$	−3.43203	−0.219713
$245$	14.7440	0.941959
$246$	−6.00226	−0.382690
$247$	−21.7750	−1.38551
$248$	23.9632	1.52166
$249$	5.77307	0.365853
$250$	−11.7956	−0.746017
$251$	15.7722	0.995534	0.497767	−	0.867311i	$-0.334154\pi$
$251$	15.7722	0.995534	0.497767	+	0.867311i	$0.334154\pi$
$252$	−0.486957	−0.0306754
$253$	−12.7712	−0.802917
$254$	−6.38905	−0.400885
$255$	2.19284	0.137321
$256$	−16.7267	−1.04542
$257$	8.25281	0.514796	0.257398	−	0.966305i	$-0.417135\pi$
$257$	8.25281	0.514796	0.257398	+	0.966305i	$0.417135\pi$
$258$	11.7730	0.732955
$259$	−1.05796	−0.0657383
$260$	−13.6123	−0.844198
$261$	−0.274463	−0.0169888
$262$	13.3275	0.823376
$263$	−9.74789	−0.601081	−0.300540	−	0.953769i	$-0.597167\pi$
$263$	−9.74789	−0.601081	−0.300540	+	0.953769i	$0.597167\pi$
$264$	−9.85574	−0.606579
$265$	−7.55321	−0.463990
$266$	−1.76989	−0.108519
$267$	−11.5892	−0.709251
$268$	9.14375	0.558543
$269$	29.6145	1.80563	0.902815	−	0.430030i	$-0.141497\pi$
$269$	29.6145	1.80563	0.902815	+	0.430030i	$0.141497\pi$
$270$	−2.27211	−0.138276
$271$	22.5063	1.36716	0.683579	−	0.729876i	$-0.260422\pi$
$271$	22.5063	1.36716	0.683579	+	0.729876i	$0.260422\pi$
$272$	−1.28902	−0.0781581
$273$	3.52229	0.213179
$274$	8.40222	0.507597
$275$	−0.622280	−0.0375249
$276$	−3.63992	−0.219098
$277$	−23.6687	−1.42212	−0.711058	−	0.703133i	$-0.751784\pi$
$277$	−23.6687	−1.42212	−0.711058	+	0.703133i	$0.751784\pi$
$278$	−2.70922	−0.162488
$279$	7.90295	0.473137
$280$	−3.49509	−0.208872
$281$	24.2468	1.44644	0.723222	−	0.690615i	$-0.242660\pi$
$281$	24.2468	1.44644	0.723222	+	0.690615i	$0.242660\pi$
$282$	−1.70704	−0.101653
$283$	−27.2743	−1.62129	−0.810644	−	0.585539i	$-0.800883\pi$
$283$	−27.2743	−1.62129	−0.810644	+	0.585539i	$0.800883\pi$
$284$	1.70718	0.101303
$285$	7.12583	0.422098
$286$	22.5676	1.33445
$287$	−3.04500	−0.179741
$288$	−4.72875	−0.278644
$289$	1.00000	0.0588235
$290$	−0.623612	−0.0366197
$291$	−13.5680	−0.795372
$292$	5.16575	0.302303
$293$	10.2125	0.596618	0.298309	−	0.954469i	$-0.403577\pi$
$293$	10.2125	0.596618	0.298309	+	0.954469i	$0.403577\pi$
$294$	−6.96676	−0.406310
$295$	9.05598	0.527259
$296$	−6.10278	−0.354717
$297$	−3.25038	−0.188606
$298$	−20.2379	−1.17235
$299$	26.3285	1.52262
$300$	−0.177356	−0.0102397
$301$	5.97255	0.344252
$302$	−5.34831	−0.307761
$303$	−9.18705	−0.527782
$304$	−4.18877	−0.240243
$305$	−8.12387	−0.465172
$306$	−1.03615	−0.0592328
$307$	−25.0091	−1.42734	−0.713671	−	0.700481i	$-0.752969\pi$
$307$	−25.0091	−1.42734	−0.713671	+	0.700481i	$0.752969\pi$
$308$	−1.58279	−0.0901880
$309$	−1.39001	−0.0790752
$310$	17.9564	1.01985
$311$	9.05936	0.513709	0.256855	−	0.966450i	$-0.417314\pi$
$311$	9.05936	0.513709	0.256855	+	0.966450i	$0.417314\pi$
$312$	20.3182	1.15029
$313$	9.01553	0.509588	0.254794	−	0.966995i	$-0.417992\pi$
$313$	9.01553	0.509588	0.254794	+	0.966995i	$0.417992\pi$
$314$	−1.03615	−0.0584734
$315$	−1.15266	−0.0649453
$316$	2.57118	0.144640
$317$	−4.03825	−0.226811	−0.113405	−	0.993549i	$-0.536176\pi$
$317$	−4.03825	−0.226811	−0.113405	+	0.993549i	$0.536176\pi$
$318$	3.56901	0.200140
$319$	−0.892109	−0.0499485
$320$	−16.3975	−0.916647
$321$	1.61719	0.0902628
$322$	2.14001	0.119258
$323$	3.24959	0.180812
$324$	−0.926391	−0.0514662
$325$	1.28287	0.0711607
$326$	11.5882	0.641811
$327$	−6.22861	−0.344443
$328$	−17.5650	−0.969863
$329$	−0.865997	−0.0477440
$330$	−7.38522	−0.406543
$331$	−30.1696	−1.65827	−0.829135	−	0.559048i	$-0.811167\pi$
$331$	−30.1696	−1.65827	−0.829135	+	0.559048i	$0.811167\pi$
$332$	5.34812	0.293516
$333$	−2.01267	−0.110294
$334$	−6.70499	−0.366881
$335$	21.6440	1.18254
$336$	0.677570	0.0369645
$337$	−23.1082	−1.25879	−0.629393	−	0.777087i	$-0.716696\pi$
$337$	−23.1082	−1.25879	−0.629393	+	0.777087i	$0.716696\pi$
$338$	−33.0545	−1.79793
$339$	−2.56162	−0.139128
$340$	2.03143	0.110170
$341$	25.6876	1.39106
$342$	−3.36707	−0.182070
$343$	−7.21384	−0.389511
$344$	34.4524	1.85755
$345$	−8.61598	−0.463869
$346$	−22.2702	−1.19725
$347$	−14.5982	−0.783671	−0.391835	−	0.920035i	$-0.628160\pi$
$347$	−14.5982	−0.783671	−0.391835	+	0.920035i	$0.628160\pi$
$348$	−0.254260	−0.0136298
$349$	6.60256	0.353427	0.176714	−	0.984262i	$-0.443453\pi$
$349$	6.60256	0.353427	0.176714	+	0.984262i	$0.443453\pi$
$350$	0.104273	0.00557362
$351$	6.70084	0.357664
$352$	−15.3702	−0.819235
$353$	−5.74959	−0.306020	−0.153010	−	0.988225i	$-0.548897\pi$
$353$	−5.74959	−0.306020	−0.153010	+	0.988225i	$0.548897\pi$
$354$	−4.27909	−0.227431
$355$	4.04104	0.214476
$356$	−10.7362	−0.569016
$357$	−0.525649	−0.0278203
$358$	−17.5875	−0.929526
$359$	−3.06002	−0.161501	−0.0807507	−	0.996734i	$-0.525732\pi$
$359$	−3.06002	−0.161501	−0.0807507	+	0.996734i	$0.525732\pi$
$360$	−6.64909	−0.350438
$361$	−8.44016	−0.444219
$362$	13.2612	0.696992
$363$	0.435055	0.0228345
$364$	3.26302	0.171029
$365$	12.2277	0.640029
$366$	3.83865	0.200650
$367$	9.51030	0.496434	0.248217	−	0.968704i	$-0.420155\pi$
$367$	9.51030	0.496434	0.248217	+	0.968704i	$0.420155\pi$
$368$	5.06473	0.264017
$369$	−5.79285	−0.301564
$370$	−4.57301	−0.237740
$371$	1.81059	0.0940012
$372$	7.32122	0.379588
$373$	−35.7889	−1.85308	−0.926539	−	0.376199i	$-0.877231\pi$
$373$	−35.7889	−1.85308	−0.926539	+	0.376199i	$0.877231\pi$
$374$	−3.36788	−0.174149
$375$	−11.3840	−0.587868
$376$	−4.99547	−0.257622
$377$	1.83913	0.0947202
$378$	0.544652	0.0280139
$379$	−12.6606	−0.650330	−0.325165	−	0.945657i	$-0.605420\pi$
$379$	−12.6606	−0.650330	−0.325165	+	0.945657i	$0.605420\pi$
$380$	6.60131	0.338640
$381$	−6.16614	−0.315901
$382$	12.1950	0.623950
$383$	−7.03360	−0.359400	−0.179700	−	0.983721i	$-0.557513\pi$
$383$	−7.03360	−0.359400	−0.179700	+	0.983721i	$0.557513\pi$
$384$	−1.70944	−0.0872347
$385$	−3.74659	−0.190944
$386$	−6.69505	−0.340769
$387$	11.3622	0.577575
$388$	−12.5693	−0.638110
$389$	−14.1558	−0.717729	−0.358865	−	0.933390i	$-0.616836\pi$
$389$	−14.1558	−0.717729	−0.358865	+	0.933390i	$0.616836\pi$
$390$	15.2251	0.770951
$391$	−3.92914	−0.198705
$392$	−20.3875	−1.02972
$393$	12.8625	0.648828
$394$	−15.3628	−0.773966
$395$	6.08619	0.306229
$396$	−3.01112	−0.151315
$397$	−14.1031	−0.707812	−0.353906	−	0.935281i	$-0.615147\pi$
$397$	−14.1031	−0.707812	−0.353906	+	0.935281i	$0.615147\pi$
$398$	−7.65425	−0.383673
$399$	−1.70814	−0.0855141
$400$	0.246780	0.0123390
$401$	13.4742	0.672871	0.336435	−	0.941707i	$-0.390779\pi$
$401$	13.4742	0.672871	0.336435	+	0.941707i	$0.390779\pi$
$402$	−10.2271	−0.510082
$403$	−52.9564	−2.63795
$404$	−8.51081	−0.423428
$405$	−2.19284	−0.108963
$406$	0.149487	0.00741891
$407$	−6.54193	−0.324272
$408$	−3.03218	−0.150115
$409$	−10.1636	−0.502560	−0.251280	−	0.967914i	$-0.580851\pi$
$409$	−10.1636	−0.502560	−0.251280	+	0.967914i	$0.580851\pi$
$410$	−13.1620	−0.650025
$411$	8.10907	0.399991
$412$	−1.28770	−0.0634403
$413$	−2.17082	−0.106819
$414$	4.07118	0.200088
$415$	12.6594	0.621426
$416$	31.6866	1.55356
$417$	−2.61470	−0.128042
$418$	−10.9442	−0.535300
$419$	25.3750	1.23965	0.619824	−	0.784741i	$-0.287204\pi$
$419$	25.3750	1.23965	0.619824	+	0.784741i	$0.287204\pi$
$420$	−1.06782	−0.0521042
$421$	−24.6165	−1.19973	−0.599867	−	0.800099i	$-0.704780\pi$
$421$	−24.6165	−1.19973	−0.599867	+	0.800099i	$0.704780\pi$
$422$	12.1325	0.590602
$423$	−1.64748	−0.0801033
$424$	10.4443	0.507221
$425$	−0.191449	−0.00928663
$426$	−1.90945	−0.0925133
$427$	1.94738	0.0942405
$428$	1.49815	0.0724159
$429$	21.7802	1.05156
$430$	25.8163	1.24497
$431$	−36.5701	−1.76152	−0.880759	−	0.473565i	$-0.842967\pi$
$431$	−36.5701	−1.76152	−0.880759	+	0.473565i	$0.842967\pi$
$432$	1.28902	0.0620178
$433$	8.22225	0.395136	0.197568	−	0.980289i	$-0.436696\pi$
$433$	8.22225	0.395136	0.197568	+	0.980289i	$0.436696\pi$
$434$	−4.30435	−0.206616
$435$	−0.601854	−0.0288567
$436$	−5.77013	−0.276339
$437$	−12.7681	−0.610781
$438$	−5.77780	−0.276074
$439$	26.8224	1.28017	0.640083	−	0.768306i	$-0.278900\pi$
$439$	26.8224	1.28017	0.640083	+	0.768306i	$0.278900\pi$
$440$	−21.6121	−1.03031
$441$	−6.72369	−0.320176
$442$	6.94308	0.330249
$443$	−24.1556	−1.14767	−0.573834	−	0.818972i	$-0.694545\pi$
$443$	−24.1556	−1.14767	−0.573834	+	0.818972i	$0.694545\pi$
$444$	−1.86452	−0.0884862
$445$	−25.4134	−1.20471
$446$	12.3167	0.583212
$447$	−19.5318	−0.923821
$448$	3.93066	0.185706
$449$	−4.76845	−0.225037	−0.112519	−	0.993650i	$-0.535892\pi$
$449$	−4.76845	−0.225037	−0.112519	+	0.993650i	$0.535892\pi$
$450$	0.198370	0.00935124
$451$	−18.8289	−0.886620
$452$	−2.37306	−0.111619
$453$	−5.16171	−0.242518
$454$	−8.76906	−0.411552
$455$	7.72382	0.362098
$456$	−9.85335	−0.461425
$457$	−5.19202	−0.242872	−0.121436	−	0.992599i	$-0.538750\pi$
$457$	−5.19202	−0.242872	−0.121436	+	0.992599i	$0.538750\pi$
$458$	6.16543	0.288092
$459$	−1.00000	−0.0466760
$460$	−7.98177	−0.372152
$461$	−17.6997	−0.824358	−0.412179	−	0.911103i	$-0.635232\pi$
$461$	−17.6997	−0.824358	−0.412179	+	0.911103i	$0.635232\pi$
$462$	1.77032	0.0823628
$463$	5.24089	0.243565	0.121783	−	0.992557i	$-0.461139\pi$
$463$	5.24089	0.243565	0.121783	+	0.992557i	$0.461139\pi$
$464$	0.353788	0.0164242
$465$	17.3299	0.803655
$466$	9.42695	0.436695
$467$	−24.5009	−1.13376	−0.566882	−	0.823799i	$-0.691851\pi$
$467$	−24.5009	−1.13376	−0.566882	+	0.823799i	$0.691851\pi$
$468$	6.20760	0.286946
$469$	−5.18830	−0.239574
$470$	−3.74327	−0.172664
$471$	−1.00000	−0.0460776
$472$	−12.5223	−0.576385
$473$	36.9316	1.69812
$474$	−2.87582	−0.132091
$475$	−0.622130	−0.0285453
$476$	−0.486957	−0.0223196
$477$	3.44449	0.157712
$478$	−14.1661	−0.647942
$479$	−14.2276	−0.650074	−0.325037	−	0.945701i	$-0.605377\pi$
$479$	−14.2276	−0.650074	−0.325037	+	0.945701i	$0.605377\pi$
$480$	−10.3694	−0.473296
$481$	13.4866	0.614935
$482$	17.4779	0.796095
$483$	2.06535	0.0939766
$484$	0.403031	0.0183196
$485$	−29.7525	−1.35099
$486$	1.03615	0.0470008
$487$	3.24642	0.147109	0.0735546	−	0.997291i	$-0.476566\pi$
$487$	3.24642	0.147109	0.0735546	+	0.997291i	$0.476566\pi$
$488$	11.2334	0.508512
$489$	11.1839	0.505753
$490$	−15.2770	−0.690144
$491$	−7.35883	−0.332099	−0.166050	−	0.986117i	$-0.553101\pi$
$491$	−7.35883	−0.332099	−0.166050	+	0.986117i	$0.553101\pi$
$492$	−5.36644	−0.241938
$493$	−0.274463	−0.0123612
$494$	22.5622	1.01512
$495$	−7.12756	−0.320360
$496$	−10.1870	−0.457411
$497$	−0.968683	−0.0434514
$498$	−5.98177	−0.268049
$499$	17.9841	0.805079	0.402539	−	0.915403i	$-0.368128\pi$
$499$	17.9841	0.805079	0.402539	+	0.915403i	$0.368128\pi$
$500$	−10.5461	−0.471634
$501$	−6.47106	−0.289106
$502$	−16.3424	−0.729397
$503$	−43.4472	−1.93721	−0.968607	−	0.248597i	$-0.920031\pi$
$503$	−43.4472	−1.93721	−0.968607	+	0.248597i	$0.920031\pi$
$504$	1.59386	0.0709963
$505$	−20.1457	−0.896474
$506$	13.2329	0.588273
$507$	−31.9012	−1.41678
$508$	−5.71226	−0.253440
$509$	−39.0881	−1.73255	−0.866274	−	0.499569i	$-0.833492\pi$
$509$	−39.0881	−1.73255	−0.866274	+	0.499569i	$0.833492\pi$
$510$	−2.27211	−0.100611
$511$	−2.93113	−0.129666
$512$	13.9125	0.614851
$513$	−3.24959	−0.143473
$514$	−8.55115	−0.377175
$515$	−3.04808	−0.134315
$516$	10.5259	0.463376
$517$	−5.35494	−0.235510
$518$	1.09620	0.0481644
$519$	−21.4932	−0.943446
$520$	44.5545	1.95384
$521$	−22.3421	−0.978827	−0.489413	−	0.872052i	$-0.662789\pi$
$521$	−22.3421	−0.978827	−0.489413	+	0.872052i	$0.662789\pi$
$522$	0.284385	0.0124472
$523$	26.1553	1.14369	0.571845	−	0.820362i	$-0.306228\pi$
$523$	26.1553	1.14369	0.571845	+	0.820362i	$0.306228\pi$
$524$	11.9157	0.520541
$525$	0.100635	0.00439206
$526$	10.1003	0.440393
$527$	7.90295	0.344258
$528$	4.18979	0.182337
$529$	−7.56185	−0.328776
$530$	7.82627	0.339951
$531$	−4.12979	−0.179218
$532$	−1.58241	−0.0686062
$533$	38.8169	1.68135
$534$	12.0082	0.519646
$535$	3.54624	0.153317
$536$	−29.9285	−1.29271
$537$	−16.9738	−0.732475
$538$	−30.6851	−1.32293
$539$	−21.8545	−0.941341
$540$	−2.03143	−0.0874188
$541$	−14.3225	−0.615771	−0.307885	−	0.951423i	$-0.599621\pi$
$541$	−14.3225	−0.615771	−0.307885	+	0.951423i	$0.599621\pi$
$542$	−23.3199	−1.00168
$543$	12.7985	0.549236
$544$	−4.72875	−0.202744
$545$	−13.6583	−0.585059
$546$	−3.64962	−0.156189
$547$	−30.0410	−1.28446	−0.642230	−	0.766512i	$-0.721991\pi$
$547$	−30.0410	−1.28446	−0.642230	+	0.766512i	$0.721991\pi$
$548$	7.51217	0.320904
$549$	3.70472	0.158114
$550$	0.644776	0.0274934
$551$	−0.891893	−0.0379959
$552$	11.9139	0.507088
$553$	−1.45893	−0.0620399
$554$	24.5244	1.04194
$555$	−4.41346	−0.187341
$556$	−2.42224	−0.102726
$557$	30.5537	1.29460	0.647300	−	0.762235i	$-0.275898\pi$
$557$	30.5537	1.29460	0.647300	+	0.762235i	$0.275898\pi$
$558$	−8.18865	−0.346653
$559$	−76.1366	−3.22023
$560$	1.48580	0.0627866
$561$	−3.25038	−0.137231
$562$	−25.1234	−1.05977
$563$	−14.0198	−0.590862	−0.295431	−	0.955364i	$-0.595463\pi$
$563$	−14.0198	−0.590862	−0.295431	+	0.955364i	$0.595463\pi$
$564$	−1.52621	−0.0642652
$565$	−5.61722	−0.236318
$566$	28.2603	1.18787
$567$	0.525649	0.0220752
$568$	−5.58781	−0.234459
$569$	−13.6880	−0.573830	−0.286915	−	0.957956i	$-0.592630\pi$
$569$	−13.6880	−0.573830	−0.286915	+	0.957956i	$0.592630\pi$
$570$	−7.38344	−0.309258
$571$	35.4409	1.48315	0.741577	−	0.670867i	$-0.234078\pi$
$571$	35.4409	1.48315	0.741577	+	0.670867i	$0.234078\pi$
$572$	20.1770	0.843644
$573$	11.7695	0.491679
$574$	3.15508	0.131691
$575$	0.752229	0.0313701
$576$	7.47773	0.311572
$577$	14.7957	0.615953	0.307976	−	0.951394i	$-0.400348\pi$
$577$	14.7957	0.615953	0.307976	+	0.951394i	$0.400348\pi$
$578$	−1.03615	−0.0430982
$579$	−6.46146	−0.268529
$580$	−0.557553	−0.0231511
$581$	−3.03461	−0.125897
$582$	14.0585	0.582745
$583$	11.1959	0.463686
$584$	−16.9081	−0.699662
$585$	14.6939	0.607517
$586$	−10.5817	−0.437124
$587$	33.3815	1.37780	0.688900	−	0.724856i	$-0.258094\pi$
$587$	33.3815	1.37780	0.688900	+	0.724856i	$0.258094\pi$
$588$	−6.22877	−0.256870
$589$	25.6813	1.05818
$590$	−9.38336	−0.386307
$591$	−14.8268	−0.609893
$592$	2.59436	0.106628
$593$	−27.5306	−1.13055	−0.565273	−	0.824904i	$-0.691229\pi$
$593$	−27.5306	−1.13055	−0.565273	+	0.824904i	$0.691229\pi$
$594$	3.36788	0.138186
$595$	−1.15266	−0.0472546
$596$	−18.0941	−0.741162
$597$	−7.38720	−0.302338
$598$	−27.2803	−1.11558
$599$	4.41646	0.180452	0.0902259	−	0.995921i	$-0.471241\pi$
$599$	4.41646	0.180452	0.0902259	+	0.995921i	$0.471241\pi$
$600$	0.580508	0.0236991
$601$	−2.12997	−0.0868832	−0.0434416	−	0.999056i	$-0.513832\pi$
$601$	−2.12997	−0.0868832	−0.0434416	+	0.999056i	$0.513832\pi$
$602$	−6.18846	−0.252223
$603$	−9.87028	−0.401949
$604$	−4.78177	−0.194567
$605$	0.954007	0.0387859
$606$	9.51917	0.386690
$607$	−24.5646	−0.997047	−0.498524	−	0.866876i	$-0.666124\pi$
$607$	−24.5646	−0.997047	−0.498524	+	0.866876i	$0.666124\pi$
$608$	−15.3665	−0.623194
$609$	0.144271	0.00584617
$610$	8.41756	0.340817
$611$	11.0395	0.446611
$612$	−0.926391	−0.0374472
$613$	12.6636	0.511478	0.255739	−	0.966746i	$-0.417681\pi$
$613$	12.6636	0.511478	0.255739	+	0.966746i	$0.417681\pi$
$614$	25.9132	1.04577
$615$	−12.7028	−0.512226
$616$	5.18066	0.208735
$617$	−20.0735	−0.808130	−0.404065	−	0.914730i	$-0.632403\pi$
$617$	−20.0735	−0.808130	−0.404065	+	0.914730i	$0.632403\pi$
$618$	1.44026	0.0579360
$619$	−0.483805	−0.0194458	−0.00972288	−	0.999953i	$-0.503095\pi$
$619$	−0.483805	−0.0194458	−0.00972288	+	0.999953i	$0.503095\pi$
$620$	16.0543	0.644755
$621$	3.92914	0.157671
$622$	−9.38686	−0.376379
$623$	6.09188	0.244066
$624$	−8.63749	−0.345776
$625$	−24.0061	−0.960244
$626$	−9.34145	−0.373360
$627$	−10.5624	−0.421821
$628$	−0.926391	−0.0369670
$629$	−2.01267	−0.0802504
$630$	1.19433	0.0475834
$631$	−26.2623	−1.04548	−0.522742	−	0.852491i	$-0.675091\pi$
$631$	−26.2623	−1.04548	−0.522742	+	0.852491i	$0.675091\pi$
$632$	−8.41576	−0.334761
$633$	11.7092	0.465400
$634$	4.18423	0.166177
$635$	−13.5214	−0.536579
$636$	3.19094	0.126529
$637$	45.0544	1.78512
$638$	0.924359	0.0365957
$639$	−1.84283	−0.0729013
$640$	−3.74854	−0.148174
$641$	−41.4193	−1.63596	−0.817982	−	0.575244i	$-0.804907\pi$
$641$	−41.4193	−1.63596	−0.817982	+	0.575244i	$0.804907\pi$
$642$	−1.67565	−0.0661328
$643$	19.4139	0.765611	0.382805	−	0.923829i	$-0.374958\pi$
$643$	19.4139	0.765611	0.382805	+	0.923829i	$0.374958\pi$
$644$	1.91332	0.0753954
$645$	24.9156	0.981051
$646$	−3.36707	−0.132475
$647$	−11.1143	−0.436946	−0.218473	−	0.975843i	$-0.570108\pi$
$647$	−11.1143	−0.436946	−0.218473	+	0.975843i	$0.570108\pi$
$648$	3.03218	0.119115
$649$	−13.4234	−0.526914
$650$	−1.32924	−0.0521372
$651$	−4.15418	−0.162815
$652$	10.3607	0.405755
$653$	−10.4415	−0.408608	−0.204304	−	0.978908i	$-0.565493\pi$
$653$	−10.4415	−0.408608	−0.204304	+	0.978908i	$0.565493\pi$
$654$	6.45378	0.252363
$655$	28.2055	1.10208
$656$	7.46707	0.291540
$657$	−5.57621	−0.217549
$658$	0.897304	0.0349805
$659$	22.9462	0.893857	0.446929	−	0.894570i	$-0.352518\pi$
$659$	22.9462	0.893857	0.446929	+	0.894570i	$0.352518\pi$
$660$	−6.60291	−0.257018
$661$	17.4434	0.678471	0.339235	−	0.940702i	$-0.389832\pi$
$661$	17.4434	0.678471	0.339235	+	0.940702i	$0.389832\pi$
$662$	31.2602	1.21496
$663$	6.70084	0.260239
$664$	−17.5050	−0.679326
$665$	−3.74569	−0.145252
$666$	2.08543	0.0808087
$667$	1.07840	0.0417560
$668$	−5.99473	−0.231943
$669$	11.8870	0.459577
$670$	−22.4264	−0.866408
$671$	12.0417	0.464867
$672$	2.48566	0.0958865
$673$	−33.3145	−1.28418	−0.642090	−	0.766629i	$-0.721932\pi$
$673$	−33.3145	−1.28418	−0.642090	+	0.766629i	$0.721932\pi$
$674$	23.9436	0.922274
$675$	0.191449	0.00736886
$676$	−29.5530	−1.13666
$677$	14.1688	0.544552	0.272276	−	0.962219i	$-0.412224\pi$
$677$	14.1688	0.544552	0.272276	+	0.962219i	$0.412224\pi$
$678$	2.65422	0.101935
$679$	7.13202	0.273702
$680$	−6.64909	−0.254981
$681$	−8.46311	−0.324307
$682$	−26.6162	−1.01919
$683$	−20.2258	−0.773921	−0.386960	−	0.922096i	$-0.626475\pi$
$683$	−20.2258	−0.773921	−0.386960	+	0.922096i	$0.626475\pi$
$684$	−3.01039	−0.115105
$685$	17.7819	0.679411
$686$	7.47463	0.285383
$687$	5.95032	0.227019
$688$	−14.6461	−0.558378
$689$	−23.0810	−0.879314
$690$	8.92746	0.339862
$691$	38.7211	1.47302	0.736510	−	0.676427i	$-0.236472\pi$
$691$	38.7211	1.47302	0.736510	+	0.676427i	$0.236472\pi$
$692$	−19.9111	−0.756906
$693$	1.70856	0.0649027
$694$	15.1259	0.574171
$695$	−5.73362	−0.217489
$696$	0.832223	0.0315453
$697$	−5.79285	−0.219420
$698$	−6.84125	−0.258945
$699$	9.09805	0.344120
$700$	0.0932272	0.00352366
$701$	7.63677	0.288437	0.144218	−	0.989546i	$-0.453933\pi$
$701$	7.63677	0.288437	0.144218	+	0.989546i	$0.453933\pi$
$702$	−6.94308	−0.262050
$703$	−6.54035	−0.246674
$704$	24.3054	0.916046
$705$	−3.61267	−0.136061
$706$	5.95744	0.224211
$707$	4.82916	0.181619
$708$	−3.82580	−0.143783
$709$	−43.6622	−1.63977	−0.819884	−	0.572530i	$-0.805962\pi$
$709$	−43.6622	−1.63977	−0.819884	+	0.572530i	$0.805962\pi$
$710$	−4.18713	−0.157140
$711$	−2.77548	−0.104089
$712$	35.1407	1.31695
$713$	−31.0518	−1.16290
$714$	0.544652	0.0203831
$715$	47.7606	1.78615
$716$	−15.7244	−0.587649
$717$	−13.6718	−0.510584
$718$	3.17064	0.118327
$719$	30.5048	1.13764	0.568819	−	0.822463i	$-0.307400\pi$
$719$	30.5048	1.13764	0.568819	+	0.822463i	$0.307400\pi$
$720$	2.82661	0.105341
$721$	0.730660	0.0272112
$722$	8.74528	0.325466
$723$	16.8681	0.627330
$724$	11.8564	0.440640
$725$	0.0525456	0.00195150
$726$	−0.450783	−0.0167301
$727$	0.392483	0.0145564	0.00727820	−	0.999974i	$-0.497683\pi$
$727$	0.392483	0.0145564	0.00727820	+	0.999974i	$0.497683\pi$
$728$	−10.6802	−0.395835
$729$	1.00000	0.0370370
$730$	−12.6698	−0.468930
$731$	11.3622	0.420248
$732$	3.43203	0.126851
$733$	1.62156	0.0598938	0.0299469	−	0.999551i	$-0.490466\pi$
$733$	1.62156	0.0598938	0.0299469	+	0.999551i	$0.490466\pi$
$734$	−9.85411	−0.363722
$735$	−14.7440	−0.543840
$736$	18.5799	0.684865
$737$	−32.0821	−1.18176
$738$	6.00226	0.220946
$739$	−2.62535	−0.0965751	−0.0482876	−	0.998833i	$-0.515376\pi$
$739$	−2.62535	−0.0965751	−0.0482876	+	0.998833i	$0.515376\pi$
$740$	−4.08859	−0.150300
$741$	21.7750	0.799924
$742$	−1.87605	−0.0688718
$743$	6.75851	0.247946	0.123973	−	0.992286i	$-0.460436\pi$
$743$	6.75851	0.247946	0.123973	+	0.992286i	$0.460436\pi$
$744$	−23.9632	−0.878533
$745$	−42.8301	−1.56917
$746$	37.0827	1.35769
$747$	−5.77307	−0.211226
$748$	−3.01112	−0.110097
$749$	−0.850075	−0.0310611
$750$	11.7956	0.430713
$751$	3.14624	0.114808	0.0574040	−	0.998351i	$-0.481718\pi$
$751$	3.14624	0.114808	0.0574040	+	0.998351i	$0.481718\pi$
$752$	2.12363	0.0774409
$753$	−15.7722	−0.574772
$754$	−1.90562	−0.0693986
$755$	−11.3188	−0.411934
$756$	0.486957	0.0177104
$757$	44.3667	1.61253	0.806267	−	0.591551i	$-0.201484\pi$
$757$	44.3667	1.61253	0.806267	+	0.591551i	$0.201484\pi$
$758$	13.1183	0.476477
$759$	12.7712	0.463565
$760$	−21.6068	−0.783762
$761$	−3.97816	−0.144208	−0.0721042	−	0.997397i	$-0.522971\pi$
$761$	−3.97816	−0.144208	−0.0721042	+	0.997397i	$0.522971\pi$
$762$	6.38905	0.231451
$763$	3.27406	0.118529
$764$	10.9032	0.394463
$765$	−2.19284	−0.0792823
$766$	7.28787	0.263322
$767$	27.6731	0.999217
$768$	16.7267	0.603573
$769$	−15.8807	−0.572673	−0.286336	−	0.958129i	$-0.592437\pi$
$769$	−15.8807	−0.572673	−0.286336	+	0.958129i	$0.592437\pi$
$770$	3.88204	0.139899
$771$	−8.25281	−0.297218
$772$	−5.98584	−0.215435
$773$	−2.79573	−0.100555	−0.0502777	−	0.998735i	$-0.516011\pi$
$773$	−2.79573	−0.100555	−0.0502777	+	0.998735i	$0.516011\pi$
$774$	−11.7730	−0.423172
$775$	−1.51301	−0.0543489
$776$	41.1408	1.47687
$777$	1.05796	0.0379540
$778$	14.6676	0.525858
$779$	−18.8244	−0.674453
$780$	13.6123	0.487398
$781$	−5.98990	−0.214335
$782$	4.07118	0.145585
$783$	0.274463	0.00980852
$784$	8.66695	0.309534
$785$	−2.19284	−0.0782658
$786$	−13.3275	−0.475377
$787$	31.6708	1.12894	0.564470	−	0.825453i	$-0.309080\pi$
$787$	31.6708	1.12894	0.564470	+	0.825453i	$0.309080\pi$
$788$	−13.7354	−0.489304
$789$	9.74789	0.347034
$790$	−6.30621	−0.224365
$791$	1.34651	0.0478764
$792$	9.85574	0.350208
$793$	−24.8248	−0.881553
$794$	14.6129	0.518592
$795$	7.55321	0.267885
$796$	−6.84344	−0.242559
$797$	50.0748	1.77374	0.886870	−	0.462019i	$-0.152875\pi$
$797$	50.0748	1.77374	0.886870	+	0.462019i	$0.152875\pi$
$798$	1.76989	0.0626536
$799$	−1.64748	−0.0582837
$800$	0.905313	0.0320077
$801$	11.5892	0.409486
$802$	−13.9613	−0.492992
$803$	−18.1248	−0.639610
$804$	−9.14375	−0.322475
$805$	4.52898	0.159626
$806$	54.8708	1.93274
$807$	−29.6145	−1.04248
$808$	27.8568	0.980000
$809$	12.4234	0.436782	0.218391	−	0.975861i	$-0.429919\pi$
$809$	12.4234	0.436782	0.218391	+	0.975861i	$0.429919\pi$
$810$	2.27211	0.0798339
$811$	−46.4269	−1.63027	−0.815135	−	0.579272i	$-0.803337\pi$
$811$	−46.4269	−1.63027	−0.815135	+	0.579272i	$0.803337\pi$
$812$	0.133652	0.00469026
$813$	−22.5063	−0.789329
$814$	6.77843	0.237584
$815$	24.5245	0.859056
$816$	1.28902	0.0451246
$817$	36.9226	1.29176
$818$	10.5311	0.368210
$819$	−3.52229	−0.123079
$820$	−11.7678	−0.410948
$821$	−2.69251	−0.0939693	−0.0469846	−	0.998896i	$-0.514961\pi$
$821$	−2.69251	−0.0939693	−0.0469846	+	0.998896i	$0.514961\pi$
$822$	−8.40222	−0.293061
$823$	1.68351	0.0586833	0.0293417	−	0.999569i	$-0.490659\pi$
$823$	1.68351	0.0586833	0.0293417	+	0.999569i	$0.490659\pi$
$824$	4.21478	0.146829
$825$	0.622280	0.0216650
$826$	2.24930	0.0782631
$827$	27.7082	0.963510	0.481755	−	0.876306i	$-0.339999\pi$
$827$	27.7082	0.963510	0.481755	+	0.876306i	$0.339999\pi$
$828$	3.63992	0.126496
$829$	25.3435	0.880215	0.440108	−	0.897945i	$-0.354940\pi$
$829$	25.3435	0.880215	0.440108	+	0.897945i	$0.354940\pi$
$830$	−13.1171	−0.455300
$831$	23.6687	0.821059
$832$	−50.1071	−1.73715
$833$	−6.72369	−0.232962
$834$	2.70922	0.0938127
$835$	−14.1900	−0.491065
$836$	−9.78491	−0.338418
$837$	−7.90295	−0.273166
$838$	−26.2923	−0.908252
$839$	−3.20308	−0.110583	−0.0552913	−	0.998470i	$-0.517609\pi$
$839$	−3.20308	−0.110583	−0.0552913	+	0.998470i	$0.517609\pi$
$840$	3.49509	0.120592
$841$	−28.9247	−0.997402
$842$	25.5064	0.879009
$843$	−24.2468	−0.835105
$844$	10.8473	0.373380
$845$	−69.9544	−2.40650
$846$	1.70704	0.0586893
$847$	−0.228686	−0.00785775
$848$	−4.44000	−0.152470
$849$	27.2743	0.936051
$850$	0.198370	0.00680403
$851$	7.90806	0.271085
$852$	−1.70718	−0.0584872
$853$	−27.5184	−0.942213	−0.471106	−	0.882076i	$-0.656145\pi$
$853$	−27.5184	−0.942213	−0.471106	+	0.882076i	$0.656145\pi$
$854$	−2.01778	−0.0690471
$855$	−7.12583	−0.243698
$856$	−4.90362	−0.167602
$857$	52.6148	1.79729	0.898644	−	0.438678i	$-0.144553\pi$
$857$	52.6148	1.79729	0.898644	+	0.438678i	$0.144553\pi$
$858$	−22.5676	−0.770446
$859$	−28.0071	−0.955590	−0.477795	−	0.878471i	$-0.658564\pi$
$859$	−28.0071	−0.955590	−0.477795	+	0.878471i	$0.658564\pi$
$860$	23.0816	0.787076
$861$	3.04500	0.103773
$862$	37.8921	1.29061
$863$	−2.51205	−0.0855113	−0.0427557	−	0.999086i	$-0.513614\pi$
$863$	−2.51205	−0.0855113	−0.0427557	+	0.999086i	$0.513614\pi$
$864$	4.72875	0.160875
$865$	−47.1311	−1.60251
$866$	−8.51949	−0.289504
$867$	−1.00000	−0.0339618
$868$	−3.84839	−0.130623
$869$	−9.02136	−0.306029
$870$	0.623612	0.0211424
$871$	66.1392	2.24104
$872$	18.8863	0.639570
$873$	13.5680	0.459208
$874$	13.2297	0.447500
$875$	5.98400	0.202296
$876$	−5.16575	−0.174535
$877$	−22.2006	−0.749661	−0.374831	−	0.927093i	$-0.622299\pi$
$877$	−22.2006	−0.749661	−0.374831	+	0.927093i	$0.622299\pi$
$878$	−27.7921	−0.937938
$879$	−10.2125	−0.344458
$880$	9.18754	0.309712
$881$	−17.2029	−0.579581	−0.289791	−	0.957090i	$-0.593586\pi$
$881$	−17.2029	−0.579581	−0.289791	+	0.957090i	$0.593586\pi$
$882$	6.96676	0.234583
$883$	32.8087	1.10410	0.552051	−	0.833811i	$-0.313845\pi$
$883$	32.8087	1.10410	0.552051	+	0.833811i	$0.313845\pi$
$884$	6.20760	0.208784
$885$	−9.05598	−0.304413
$886$	25.0289	0.840861
$887$	−34.8353	−1.16965	−0.584827	−	0.811158i	$-0.698838\pi$
$887$	−34.8353	−1.16965	−0.584827	+	0.811158i	$0.698838\pi$
$888$	6.10278	0.204796
$889$	3.24122	0.108707
$890$	26.3321	0.882654
$891$	3.25038	0.108892
$892$	11.0120	0.368709
$893$	−5.35364	−0.179153
$894$	20.2379	0.676855
$895$	−37.2209	−1.24416
$896$	0.898567	0.0300190
$897$	−26.3285	−0.879084
$898$	4.94083	0.164878
$899$	−2.16907	−0.0723425
$900$	0.177356	0.00591188
$901$	3.44449	0.114753
$902$	19.5096	0.649599
$903$	−5.97255	−0.198754
$904$	7.76729	0.258336
$905$	28.0651	0.932914
$906$	5.34831	0.177686
$907$	−7.16022	−0.237751	−0.118876	−	0.992909i	$-0.537929\pi$
$907$	−7.16022	−0.237751	−0.118876	+	0.992909i	$0.537929\pi$
$908$	−7.84015	−0.260185
$909$	9.18705	0.304715
$910$	−8.00304	−0.265298
$911$	−22.0395	−0.730201	−0.365100	−	0.930968i	$-0.618965\pi$
$911$	−22.0395	−0.730201	−0.365100	+	0.930968i	$0.618965\pi$
$912$	4.18877	0.138704
$913$	−18.7646	−0.621019
$914$	5.37972	0.177945
$915$	8.12387	0.268567
$916$	5.51232	0.182132
$917$	−6.76117	−0.223273
$918$	1.03615	0.0341981
$919$	−31.6408	−1.04373	−0.521866	−	0.853027i	$-0.674764\pi$
$919$	−31.6408	−1.04373	−0.521866	+	0.853027i	$0.674764\pi$
$920$	26.1252	0.861323
$921$	25.0091	0.824077
$922$	18.3396	0.603982
$923$	12.3485	0.406457
$924$	1.58279	0.0520700
$925$	0.385323	0.0126693
$926$	−5.43036	−0.178453
$927$	1.39001	0.0456541
$928$	1.29787	0.0426046
$929$	14.7815	0.484965	0.242482	−	0.970156i	$-0.422038\pi$
$929$	14.7815	0.484965	0.242482	+	0.970156i	$0.422038\pi$
$930$	−17.9564	−0.588813
$931$	−21.8492	−0.716080
$932$	8.42835	0.276080
$933$	−9.05936	−0.296590
$934$	25.3866	0.830675
$935$	−7.12756	−0.233096
$936$	−20.3182	−0.664120
$937$	−23.0330	−0.752456	−0.376228	−	0.926527i	$-0.622779\pi$
$937$	−23.0330	−0.752456	−0.376228	+	0.926527i	$0.622779\pi$
$938$	5.37587	0.175528
$939$	−9.01553	−0.294211
$940$	−3.34674	−0.109159
$941$	5.53832	0.180544	0.0902720	−	0.995917i	$-0.471226\pi$
$941$	5.53832	0.180544	0.0902720	+	0.995917i	$0.471226\pi$
$942$	1.03615	0.0337596
$943$	22.7609	0.741197
$944$	5.32337	0.173261
$945$	1.15266	0.0374962
$946$	−38.2667	−1.24416
$947$	58.5669	1.90317	0.951584	−	0.307388i	$-0.0994551\pi$
$947$	58.5669	1.90317	0.951584	+	0.307388i	$0.0994551\pi$
$948$	−2.57118	−0.0835081
$949$	37.3653	1.21293
$950$	0.644620	0.0209142
$951$	4.03825	0.130949
$952$	1.59386	0.0516574
$953$	−2.91530	−0.0944357	−0.0472179	−	0.998885i	$-0.515036\pi$
$953$	−2.91530	−0.0944357	−0.0472179	+	0.998885i	$0.515036\pi$
$954$	−3.56901	−0.115551
$955$	25.8087	0.835150
$956$	−12.6655	−0.409631
$957$	0.892109	0.0288378
$958$	14.7419	0.476289
$959$	−4.26252	−0.137644
$960$	16.3975	0.529226
$961$	31.4566	1.01473
$962$	−13.9741	−0.450544
$963$	−1.61719	−0.0521133
$964$	15.6264	0.503294
$965$	−14.1690	−0.456115
$966$	−2.14001	−0.0688538
$967$	4.44661	0.142993	0.0714967	−	0.997441i	$-0.477222\pi$
$967$	4.44661	0.142993	0.0714967	+	0.997441i	$0.477222\pi$
$968$	−1.31917	−0.0423996
$969$	−3.24959	−0.104392
$970$	30.8281	0.989831
$971$	−30.6115	−0.982369	−0.491185	−	0.871055i	$-0.663436\pi$
$971$	−30.6115	−0.982369	−0.491185	+	0.871055i	$0.663436\pi$
$972$	0.926391	0.0297140
$973$	1.37441	0.0440617
$974$	−3.36378	−0.107782
$975$	−1.28287	−0.0410846
$976$	−4.77545	−0.152858
$977$	−17.2116	−0.550649	−0.275324	−	0.961351i	$-0.588785\pi$
$977$	−17.2116	−0.550649	−0.275324	+	0.961351i	$0.588785\pi$
$978$	−11.5882	−0.370550
$979$	37.6694	1.20392
$980$	−13.6587	−0.436311
$981$	6.22861	0.198864
$982$	7.62486	0.243319
$983$	37.5024	1.19614	0.598071	−	0.801443i	$-0.295934\pi$
$983$	37.5024	1.19614	0.598071	+	0.801443i	$0.295934\pi$
$984$	17.5650	0.559951
$985$	−32.5128	−1.03594
$986$	0.284385	0.00905667
$987$	0.865997	0.0275650
$988$	20.1722	0.641762
$989$	−44.6439	−1.41959
$990$	7.38522	0.234718
$991$	15.6344	0.496642	0.248321	−	0.968678i	$-0.420121\pi$
$991$	15.6344	0.496642	0.248321	+	0.968678i	$0.420121\pi$
$992$	−37.3711	−1.18653
$993$	30.1696	0.957403
$994$	1.00370	0.0318355
$995$	−16.1990	−0.513541
$996$	−5.34812	−0.169462
$997$	−33.0234	−1.04586	−0.522930	−	0.852375i	$-0.675161\pi$
$997$	−33.0234	−1.04586	−0.522930	+	0.852375i	$0.675161\pi$
$998$	−18.6342	−0.589856
$999$	2.01267	0.0636780

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.c.1.14	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.c.1.14	✓	39	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.03615 q^{2} -1.00000 q^{3} -0.926391 q^{4} -2.19284 q^{5} +1.03615 q^{6} +0.525649 q^{7} +3.03218 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.03615 q^{2} -1.00000 q^{3} -0.926391 q^{4} -2.19284 q^{5} +1.03615 q^{6} +0.525649 q^{7} +3.03218 q^{8} +1.00000 q^{9} +2.27211 q^{10} +3.25038 q^{11} +0.926391 q^{12} -6.70084 q^{13} -0.544652 q^{14} +2.19284 q^{15} -1.28902 q^{16} +1.00000 q^{17} -1.03615 q^{18} +3.24959 q^{19} +2.03143 q^{20} -0.525649 q^{21} -3.36788 q^{22} -3.92914 q^{23} -3.03218 q^{24} -0.191449 q^{25} +6.94308 q^{26} -1.00000 q^{27} -0.486957 q^{28} -0.274463 q^{29} -2.27211 q^{30} +7.90295 q^{31} -4.72875 q^{32} -3.25038 q^{33} -1.03615 q^{34} -1.15266 q^{35} -0.926391 q^{36} -2.01267 q^{37} -3.36707 q^{38} +6.70084 q^{39} -6.64909 q^{40} -5.79285 q^{41} +0.544652 q^{42} +11.3622 q^{43} -3.01112 q^{44} -2.19284 q^{45} +4.07118 q^{46} -1.64748 q^{47} +1.28902 q^{48} -6.72369 q^{49} +0.198370 q^{50} -1.00000 q^{51} +6.20760 q^{52} +3.44449 q^{53} +1.03615 q^{54} -7.12756 q^{55} +1.59386 q^{56} -3.24959 q^{57} +0.284385 q^{58} -4.12979 q^{59} -2.03143 q^{60} +3.70472 q^{61} -8.18865 q^{62} +0.525649 q^{63} +7.47773 q^{64} +14.6939 q^{65} +3.36788 q^{66} -9.87028 q^{67} -0.926391 q^{68} +3.92914 q^{69} +1.19433 q^{70} -1.84283 q^{71} +3.03218 q^{72} -5.57621 q^{73} +2.08543 q^{74} +0.191449 q^{75} -3.01039 q^{76} +1.70856 q^{77} -6.94308 q^{78} -2.77548 q^{79} +2.82661 q^{80} +1.00000 q^{81} +6.00226 q^{82} -5.77307 q^{83} +0.486957 q^{84} -2.19284 q^{85} -11.7730 q^{86} +0.274463 q^{87} +9.85574 q^{88} +11.5892 q^{89} +2.27211 q^{90} -3.52229 q^{91} +3.63992 q^{92} -7.90295 q^{93} +1.70704 q^{94} -7.12583 q^{95} +4.72875 q^{96} +13.5680 q^{97} +6.96676 q^{98} +3.25038 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9}+O(q^{10}) \) 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9	\( 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9} + 4 q^{10} + q^{11} - 30 q^{12} - 26 q^{13} - 4 q^{14} + 3 q^{15} + 8 q^{16} + 39 q^{17} - 4 q^{18} - 14 q^{19} - 14 q^{20} + 5 q^{21} - 17 q^{22} + 2 q^{23} + 3 q^{24} - 6 q^{25} - 17 q^{26} - 39 q^{27} - 14 q^{28} - 7 q^{29} - 4 q^{30} - q^{31} - 30 q^{32} - q^{33} - 4 q^{34} + q^{35} + 30 q^{36} - 24 q^{37} - 20 q^{38} + 26 q^{39} + 12 q^{40} + q^{41} + 4 q^{42} - 41 q^{43} - 2 q^{44} - 3 q^{45} - 6 q^{46} - 9 q^{47} - 8 q^{48} - 10 q^{49} - 9 q^{50} - 39 q^{51} - 37 q^{52} - 47 q^{53} + 4 q^{54} - 39 q^{55} + 8 q^{56} + 14 q^{57} - 27 q^{58} + 41 q^{59} + 14 q^{60} - 41 q^{61} + 36 q^{62} - 5 q^{63} - 47 q^{64} - 39 q^{65} + 17 q^{66} - 36 q^{67} + 30 q^{68} - 2 q^{69} - 52 q^{70} - 2 q^{71} - 3 q^{72} - 63 q^{73} - 6 q^{74} + 6 q^{75} - 34 q^{76} - 64 q^{77} + 17 q^{78} + 20 q^{79} - 28 q^{80} + 39 q^{81} - 37 q^{82} + 45 q^{83} + 14 q^{84} - 3 q^{85} + 32 q^{86} + 7 q^{87} + 6 q^{88} - 32 q^{89} + 4 q^{90} - 11 q^{91} + 28 q^{92} + q^{93} - 44 q^{94} + 22 q^{95} + 30 q^{96} - 20 q^{97} + 63 q^{98} + q^{99}+O(q^{100}) \) 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9 + 4 * q^10 + q^11 - 30 * q^12 - 26 * q^13 - 4 * q^14 + 3 * q^15 + 8 * q^16 + 39 * q^17 - 4 * q^18 - 14 * q^19 - 14 * q^20 + 5 * q^21 - 17 * q^22 + 2 * q^23 + 3 * q^24 - 6 * q^25 - 17 * q^26 - 39 * q^27 - 14 * q^28 - 7 * q^29 - 4 * q^30 - q^31 - 30 * q^32 - q^33 - 4 * q^34 + q^35 + 30 * q^36 - 24 * q^37 - 20 * q^38 + 26 * q^39 + 12 * q^40 + q^41 + 4 * q^42 - 41 * q^43 - 2 * q^44 - 3 * q^45 - 6 * q^46 - 9 * q^47 - 8 * q^48 - 10 * q^49 - 9 * q^50 - 39 * q^51 - 37 * q^52 - 47 * q^53 + 4 * q^54 - 39 * q^55 + 8 * q^56 + 14 * q^57 - 27 * q^58 + 41 * q^59 + 14 * q^60 - 41 * q^61 + 36 * q^62 - 5 * q^63 - 47 * q^64 - 39 * q^65 + 17 * q^66 - 36 * q^67 + 30 * q^68 - 2 * q^69 - 52 * q^70 - 2 * q^71 - 3 * q^72 - 63 * q^73 - 6 * q^74 + 6 * q^75 - 34 * q^76 - 64 * q^77 + 17 * q^78 + 20 * q^79 - 28 * q^80 + 39 * q^81 - 37 * q^82 + 45 * q^83 + 14 * q^84 - 3 * q^85 + 32 * q^86 + 7 * q^87 + 6 * q^88 - 32 * q^89 + 4 * q^90 - 11 * q^91 + 28 * q^92 + q^93 - 44 * q^94 + 22 * q^95 + 30 * q^96 - 20 * q^97 + 63 * q^98 + q^99

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