LMFDB - Embedded newform 8005.2.a.g.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8005,2,Mod(1,8005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8005, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("8005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8005 = 5 \cdot 1601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8005.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:	$63.9202468180$
Analytic rank:	$0$
Dimension:	$137$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	8005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.54897 q^{2} +0.946332 q^{3} +4.49724 q^{4} -1.00000 q^{5} -2.41217 q^{6} +0.0675168 q^{7} -6.36539 q^{8} -2.10446 q^{9} +O(q^{10})$	\(q-2.54897 q^{2} +0.946332 q^{3} +4.49724 q^{4} -1.00000 q^{5} -2.41217 q^{6} +0.0675168 q^{7} -6.36539 q^{8} -2.10446 q^{9} +2.54897 q^{10} +6.06105 q^{11} +4.25588 q^{12} -3.79116 q^{13} -0.172098 q^{14} -0.946332 q^{15} +7.23070 q^{16} +2.49729 q^{17} +5.36419 q^{18} +7.73449 q^{19} -4.49724 q^{20} +0.0638933 q^{21} -15.4494 q^{22} -5.14996 q^{23} -6.02377 q^{24} +1.00000 q^{25} +9.66355 q^{26} -4.83051 q^{27} +0.303639 q^{28} +8.48609 q^{29} +2.41217 q^{30} +7.72073 q^{31} -5.70004 q^{32} +5.73576 q^{33} -6.36552 q^{34} -0.0675168 q^{35} -9.46425 q^{36} -2.53928 q^{37} -19.7150 q^{38} -3.58770 q^{39} +6.36539 q^{40} +6.41253 q^{41} -0.162862 q^{42} +6.82241 q^{43} +27.2580 q^{44} +2.10446 q^{45} +13.1271 q^{46} -8.48363 q^{47} +6.84264 q^{48} -6.99544 q^{49} -2.54897 q^{50} +2.36327 q^{51} -17.0498 q^{52} -5.58549 q^{53} +12.3128 q^{54} -6.06105 q^{55} -0.429771 q^{56} +7.31939 q^{57} -21.6308 q^{58} +12.2880 q^{59} -4.25588 q^{60} -3.46663 q^{61} -19.6799 q^{62} -0.142086 q^{63} +0.0678279 q^{64} +3.79116 q^{65} -14.6203 q^{66} +5.38517 q^{67} +11.2309 q^{68} -4.87357 q^{69} +0.172098 q^{70} +4.44421 q^{71} +13.3957 q^{72} +14.1548 q^{73} +6.47254 q^{74} +0.946332 q^{75} +34.7839 q^{76} +0.409222 q^{77} +9.14493 q^{78} -9.22352 q^{79} -7.23070 q^{80} +1.74210 q^{81} -16.3453 q^{82} +13.6898 q^{83} +0.287344 q^{84} -2.49729 q^{85} -17.3901 q^{86} +8.03065 q^{87} -38.5809 q^{88} -14.9826 q^{89} -5.36419 q^{90} -0.255967 q^{91} -23.1606 q^{92} +7.30637 q^{93} +21.6245 q^{94} -7.73449 q^{95} -5.39413 q^{96} -8.09855 q^{97} +17.8312 q^{98} -12.7552 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 137 q + 4 q^{2} + 20 q^{3} + 152 q^{4} - 137 q^{5} + 14 q^{6} - 30 q^{7} + 24 q^{8} + 163 q^{9}+O(q^{10}) $ 137 * q + 4 * q^2 + 20 * q^3 + 152 * q^4 - 137 * q^5 + 14 * q^6 - 30 * q^7 + 24 * q^8 + 163 * q^9	\( 137 q + 4 q^{2} + 20 q^{3} + 152 q^{4} - 137 q^{5} + 14 q^{6} - 30 q^{7} + 24 q^{8} + 163 q^{9} - 4 q^{10} + 51 q^{11} + 32 q^{12} - 6 q^{13} + 49 q^{14} - 20 q^{15} + 170 q^{16} + 46 q^{17} + 4 q^{18} + 47 q^{19} - 152 q^{20} + 28 q^{21} - 19 q^{22} + 29 q^{23} + 39 q^{24} + 137 q^{25} + 67 q^{26} + 77 q^{27} - 58 q^{28} + 27 q^{29} - 14 q^{30} + 23 q^{31} + 42 q^{32} + 40 q^{33} + 38 q^{34} + 30 q^{35} + 222 q^{36} - 56 q^{37} + 87 q^{38} + 44 q^{39} - 24 q^{40} + 66 q^{41} + 34 q^{42} + 15 q^{43} + 87 q^{44} - 163 q^{45} + 37 q^{46} + 52 q^{47} + 56 q^{48} + 195 q^{49} + 4 q^{50} + 106 q^{51} - 31 q^{52} + 45 q^{53} + 83 q^{54} - 51 q^{55} + 148 q^{56} + 4 q^{57} - 101 q^{58} + 239 q^{59} - 32 q^{60} + 46 q^{61} + 63 q^{62} - 59 q^{63} + 200 q^{64} + 6 q^{65} + 108 q^{66} - 18 q^{67} + 152 q^{68} + 63 q^{69} - 49 q^{70} + 110 q^{71} + 6 q^{72} - 19 q^{73} + 81 q^{74} + 20 q^{75} + 94 q^{76} + 43 q^{77} - 3 q^{78} + 40 q^{79} - 170 q^{80} + 229 q^{81} + 3 q^{82} + 235 q^{83} + 94 q^{84} - 46 q^{85} + 110 q^{86} + 31 q^{87} - 105 q^{88} + 150 q^{89} - 4 q^{90} + 110 q^{91} + 76 q^{92} + 11 q^{93} + 56 q^{94} - 47 q^{95} + 146 q^{96} + 17 q^{97} + 75 q^{98} + 125 q^{99}+O(q^{100}) \) 137 * q + 4 * q^2 + 20 * q^3 + 152 * q^4 - 137 * q^5 + 14 * q^6 - 30 * q^7 + 24 * q^8 + 163 * q^9 - 4 * q^10 + 51 * q^11 + 32 * q^12 - 6 * q^13 + 49 * q^14 - 20 * q^15 + 170 * q^16 + 46 * q^17 + 4 * q^18 + 47 * q^19 - 152 * q^20 + 28 * q^21 - 19 * q^22 + 29 * q^23 + 39 * q^24 + 137 * q^25 + 67 * q^26 + 77 * q^27 - 58 * q^28 + 27 * q^29 - 14 * q^30 + 23 * q^31 + 42 * q^32 + 40 * q^33 + 38 * q^34 + 30 * q^35 + 222 * q^36 - 56 * q^37 + 87 * q^38 + 44 * q^39 - 24 * q^40 + 66 * q^41 + 34 * q^42 + 15 * q^43 + 87 * q^44 - 163 * q^45 + 37 * q^46 + 52 * q^47 + 56 * q^48 + 195 * q^49 + 4 * q^50 + 106 * q^51 - 31 * q^52 + 45 * q^53 + 83 * q^54 - 51 * q^55 + 148 * q^56 + 4 * q^57 - 101 * q^58 + 239 * q^59 - 32 * q^60 + 46 * q^61 + 63 * q^62 - 59 * q^63 + 200 * q^64 + 6 * q^65 + 108 * q^66 - 18 * q^67 + 152 * q^68 + 63 * q^69 - 49 * q^70 + 110 * q^71 + 6 * q^72 - 19 * q^73 + 81 * q^74 + 20 * q^75 + 94 * q^76 + 43 * q^77 - 3 * q^78 + 40 * q^79 - 170 * q^80 + 229 * q^81 + 3 * q^82 + 235 * q^83 + 94 * q^84 - 46 * q^85 + 110 * q^86 + 31 * q^87 - 105 * q^88 + 150 * q^89 - 4 * q^90 + 110 * q^91 + 76 * q^92 + 11 * q^93 + 56 * q^94 - 47 * q^95 + 146 * q^96 + 17 * q^97 + 75 * q^98 + 125 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.54897	−1.80239	−0.901197	−	0.433411i	$-0.857310\pi$
$2$	−2.54897	−1.80239	−0.901197	+	0.433411i	$0.857310\pi$
$3$	0.946332	0.546365	0.273182	−	0.961962i	$-0.411924\pi$
$3$	0.946332	0.546365	0.273182	+	0.961962i	$0.411924\pi$
$4$	4.49724	2.24862
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.41217	−0.984764
$7$	0.0675168	0.0255190	0.0127595	−	0.999919i	$-0.495938\pi$
$7$	0.0675168	0.0255190	0.0127595	+	0.999919i	$0.495938\pi$
$8$	−6.36539	−2.25051
$9$	−2.10446	−0.701485
$10$	2.54897	0.806055
$11$	6.06105	1.82747	0.913737	−	0.406306i	$-0.133183\pi$
$11$	6.06105	1.82747	0.913737	+	0.406306i	$0.133183\pi$
$12$	4.25588	1.22857
$13$	−3.79116	−1.05148	−0.525740	−	0.850646i	$-0.676211\pi$
$13$	−3.79116	−1.05148	−0.525740	+	0.850646i	$0.676211\pi$
$14$	−0.172098	−0.0459952
$15$	−0.946332	−0.244342
$16$	7.23070	1.80767
$17$	2.49729	0.605682	0.302841	−	0.953041i	$-0.402065\pi$
$17$	2.49729	0.605682	0.302841	+	0.953041i	$0.402065\pi$
$18$	5.36419	1.26435
$19$	7.73449	1.77441	0.887206	−	0.461373i	$-0.152643\pi$
$19$	7.73449	1.77441	0.887206	+	0.461373i	$0.152643\pi$
$20$	−4.49724	−1.00561
$21$	0.0638933	0.0139427
$22$	−15.4494	−3.29383
$23$	−5.14996	−1.07384	−0.536921	−	0.843633i	$-0.680413\pi$
$23$	−5.14996	−1.07384	−0.536921	+	0.843633i	$0.680413\pi$
$24$	−6.02377	−1.22960
$25$	1.00000	0.200000
$26$	9.66355	1.89518
$27$	−4.83051	−0.929632
$28$	0.303639	0.0573825
$29$	8.48609	1.57583	0.787913	−	0.615786i	$-0.211162\pi$
$29$	8.48609	1.57583	0.787913	+	0.615786i	$0.211162\pi$
$30$	2.41217	0.440400
$31$	7.72073	1.38668	0.693342	−	0.720609i	$-0.256138\pi$
$31$	7.72073	1.38668	0.693342	+	0.720609i	$0.256138\pi$
$32$	−5.70004	−1.00763
$33$	5.73576	0.998468
$34$	−6.36552	−1.09168
$35$	−0.0675168	−0.0114124
$36$	−9.46425	−1.57737
$37$	−2.53928	−0.417455	−0.208727	−	0.977974i	$-0.566932\pi$
$37$	−2.53928	−0.417455	−0.208727	+	0.977974i	$0.566932\pi$
$38$	−19.7150	−3.19819
$39$	−3.58770	−0.574491
$40$	6.36539	1.00646
$41$	6.41253	1.00147	0.500735	−	0.865601i	$-0.333063\pi$
$41$	6.41253	1.00147	0.500735	+	0.865601i	$0.333063\pi$
$42$	−0.162862	−0.0251302
$43$	6.82241	1.04041	0.520204	−	0.854042i	$-0.325856\pi$
$43$	6.82241	1.04041	0.520204	+	0.854042i	$0.325856\pi$
$44$	27.2580	4.10930
$45$	2.10446	0.313714
$46$	13.1271	1.93548
$47$	−8.48363	−1.23746	−0.618732	−	0.785602i	$-0.712353\pi$
$47$	−8.48363	−1.23746	−0.618732	+	0.785602i	$0.712353\pi$
$48$	6.84264	0.987650
$49$	−6.99544	−0.999349
$50$	−2.54897	−0.360479
$51$	2.36327	0.330923
$52$	−17.0498	−2.36438
$53$	−5.58549	−0.767226	−0.383613	−	0.923494i	$-0.625320\pi$
$53$	−5.58549	−0.767226	−0.383613	+	0.923494i	$0.625320\pi$
$54$	12.3128	1.67556
$55$	−6.06105	−0.817271
$56$	−0.429771	−0.0574305
$57$	7.31939	0.969477
$58$	−21.6308	−2.84026
$59$	12.2880	1.59976	0.799879	−	0.600161i	$-0.204897\pi$
$59$	12.2880	1.59976	0.799879	+	0.600161i	$0.204897\pi$
$60$	−4.25588	−0.549432
$61$	−3.46663	−0.443857	−0.221928	−	0.975063i	$-0.571235\pi$
$61$	−3.46663	−0.443857	−0.221928	+	0.975063i	$0.571235\pi$
$62$	−19.6799	−2.49935
$63$	−0.142086	−0.0179012
$64$	0.0678279	0.00847849
$65$	3.79116	0.470236
$66$	−14.6203	−1.79963
$67$	5.38517	0.657903	0.328952	−	0.944347i	$-0.393305\pi$
$67$	5.38517	0.657903	0.328952	+	0.944347i	$0.393305\pi$
$68$	11.2309	1.36195
$69$	−4.87357	−0.586709
$70$	0.172098	0.0205697
$71$	4.44421	0.527431	0.263715	−	0.964601i	$-0.415052\pi$
$71$	4.44421	0.527431	0.263715	+	0.964601i	$0.415052\pi$
$72$	13.3957	1.57870
$73$	14.1548	1.65669	0.828346	−	0.560216i	$-0.189282\pi$
$73$	14.1548	1.65669	0.828346	+	0.560216i	$0.189282\pi$
$74$	6.47254	0.752418
$75$	0.946332	0.109273
$76$	34.7839	3.98998
$77$	0.409222	0.0466352
$78$	9.14493	1.03546
$79$	−9.22352	−1.03773	−0.518863	−	0.854857i	$-0.673645\pi$
$79$	−9.22352	−1.03773	−0.518863	+	0.854857i	$0.673645\pi$
$80$	−7.23070	−0.808416
$81$	1.74210	0.193567
$82$	−16.3453	−1.80504
$83$	13.6898	1.50265	0.751327	−	0.659930i	$-0.229414\pi$
$83$	13.6898	1.50265	0.751327	+	0.659930i	$0.229414\pi$
$84$	0.287344	0.0313518
$85$	−2.49729	−0.270869
$86$	−17.3901	−1.87522
$87$	8.03065	0.860976
$88$	−38.5809	−4.11274
$89$	−14.9826	−1.58816	−0.794078	−	0.607816i	$-0.792046\pi$
$89$	−14.9826	−1.58816	−0.794078	+	0.607816i	$0.792046\pi$
$90$	−5.36419	−0.565436
$91$	−0.255967	−0.0268327
$92$	−23.1606	−2.41466
$93$	7.30637	0.757635
$94$	21.6245	2.23040
$95$	−7.73449	−0.793542
$96$	−5.39413	−0.550536
$97$	−8.09855	−0.822283	−0.411141	−	0.911572i	$-0.634870\pi$
$97$	−8.09855	−0.822283	−0.411141	+	0.911572i	$0.634870\pi$
$98$	17.8312	1.80122
$99$	−12.7552	−1.28195
$100$	4.49724	0.449724
$101$	−6.44064	−0.640867	−0.320434	−	0.947271i	$-0.603829\pi$
$101$	−6.44064	−0.640867	−0.320434	+	0.947271i	$0.603829\pi$
$102$	−6.02389	−0.596454
$103$	−6.92274	−0.682118	−0.341059	−	0.940042i	$-0.610786\pi$
$103$	−6.92274	−0.682118	−0.341059	+	0.940042i	$0.610786\pi$
$104$	24.1322	2.36636
$105$	−0.0638933	−0.00623535
$106$	14.2372	1.38284
$107$	5.86262	0.566761	0.283380	−	0.959008i	$-0.408544\pi$
$107$	5.86262	0.566761	0.283380	+	0.959008i	$0.408544\pi$
$108$	−21.7240	−2.09039
$109$	−12.3346	−1.18144	−0.590720	−	0.806877i	$-0.701156\pi$
$109$	−12.3346	−1.18144	−0.590720	+	0.806877i	$0.701156\pi$
$110$	15.4494	1.47304
$111$	−2.40300	−0.228083
$112$	0.488194	0.0461300
$113$	−11.6738	−1.09818	−0.549089	−	0.835764i	$-0.685025\pi$
$113$	−11.6738	−1.09818	−0.549089	+	0.835764i	$0.685025\pi$
$114$	−18.6569	−1.74738
$115$	5.14996	0.480236
$116$	38.1640	3.54344
$117$	7.97834	0.737597
$118$	−31.3217	−2.88339
$119$	0.168609	0.0154564
$120$	6.02377	0.549892
$121$	25.7363	2.33966
$122$	8.83633	0.800004
$123$	6.06838	0.547168
$124$	34.7220	3.11812
$125$	−1.00000	−0.0894427
$126$	0.362173	0.0322650
$127$	11.4136	1.01280	0.506398	−	0.862300i	$-0.330977\pi$
$127$	11.4136	1.01280	0.506398	+	0.862300i	$0.330977\pi$
$128$	11.2272	0.992352
$129$	6.45626	0.568442
$130$	−9.66355	−0.847550
$131$	−5.34037	−0.466590	−0.233295	−	0.972406i	$-0.574951\pi$
$131$	−5.34037	−0.466590	−0.233295	+	0.972406i	$0.574951\pi$
$132$	25.7951	2.24517
$133$	0.522208	0.0452812
$134$	−13.7266	−1.18580
$135$	4.83051	0.415744
$136$	−15.8962	−1.36309
$137$	17.9942	1.53735	0.768675	−	0.639639i	$-0.220916\pi$
$137$	17.9942	1.53735	0.768675	+	0.639639i	$0.220916\pi$
$138$	12.4226	1.05748
$139$	−19.7477	−1.67498	−0.837488	−	0.546456i	$-0.815977\pi$
$139$	−19.7477	−1.67498	−0.837488	+	0.546456i	$0.815977\pi$
$140$	−0.303639	−0.0256622
$141$	−8.02833	−0.676107
$142$	−11.3282	−0.950637
$143$	−22.9784	−1.92155
$144$	−15.2167	−1.26806
$145$	−8.48609	−0.704731
$146$	−36.0801	−2.98601
$147$	−6.62001	−0.546009
$148$	−11.4198	−0.938698
$149$	12.2999	1.00765	0.503823	−	0.863807i	$-0.331926\pi$
$149$	12.2999	1.00765	0.503823	+	0.863807i	$0.331926\pi$
$150$	−2.41217	−0.196953
$151$	−15.5916	−1.26882	−0.634412	−	0.772995i	$-0.718758\pi$
$151$	−15.5916	−1.26882	−0.634412	+	0.772995i	$0.718758\pi$
$152$	−49.2330	−3.99333
$153$	−5.25544	−0.424877
$154$	−1.04310	−0.0840550
$155$	−7.72073	−0.620144
$156$	−16.1347	−1.29181
$157$	−7.64223	−0.609916	−0.304958	−	0.952366i	$-0.598643\pi$
$157$	−7.64223	−0.609916	−0.304958	+	0.952366i	$0.598643\pi$
$158$	23.5105	1.87039
$159$	−5.28572	−0.419185
$160$	5.70004	0.450628
$161$	−0.347709	−0.0274033
$162$	−4.44057	−0.348884
$163$	−3.70552	−0.290239	−0.145120	−	0.989414i	$-0.546357\pi$
$163$	−3.70552	−0.290239	−0.145120	+	0.989414i	$0.546357\pi$
$164$	28.8387	2.25192
$165$	−5.73576	−0.446528
$166$	−34.8949	−2.70837
$167$	3.15093	0.243826	0.121913	−	0.992541i	$-0.461097\pi$
$167$	3.15093	0.243826	0.121913	+	0.992541i	$0.461097\pi$
$168$	−0.406706	−0.0313780
$169$	1.37291	0.105609
$170$	6.36552	0.488213
$171$	−16.2769	−1.24472
$172$	30.6820	2.33948
$173$	−0.645815	−0.0491004	−0.0245502	−	0.999699i	$-0.507815\pi$
$173$	−0.645815	−0.0491004	−0.0245502	+	0.999699i	$0.507815\pi$
$174$	−20.4699	−1.55182
$175$	0.0675168	0.00510379
$176$	43.8256	3.30348
$177$	11.6285	0.874052
$178$	38.1902	2.86248
$179$	10.0338	0.749960	0.374980	−	0.927033i	$-0.377650\pi$
$179$	10.0338	0.749960	0.374980	+	0.927033i	$0.377650\pi$
$180$	9.46425	0.705423
$181$	−17.1632	−1.27573	−0.637865	−	0.770148i	$-0.720182\pi$
$181$	−17.1632	−1.27573	−0.637865	+	0.770148i	$0.720182\pi$
$182$	0.652452	0.0483630
$183$	−3.28058	−0.242508
$184$	32.7815	2.41668
$185$	2.53928	0.186692
$186$	−18.6237	−1.36556
$187$	15.1362	1.10687
$188$	−38.1529	−2.78259
$189$	−0.326141	−0.0237232
$190$	19.7150	1.43027
$191$	−15.1930	−1.09933	−0.549663	−	0.835387i	$-0.685244\pi$
$191$	−15.1930	−1.09933	−0.549663	+	0.835387i	$0.685244\pi$
$192$	0.0641877	0.00463235
$193$	11.3198	0.814819	0.407410	−	0.913246i	$-0.366432\pi$
$193$	11.3198	0.814819	0.407410	+	0.913246i	$0.366432\pi$
$194$	20.6429	1.48208
$195$	3.58770	0.256920
$196$	−31.4602	−2.24716
$197$	21.6710	1.54400	0.771999	−	0.635624i	$-0.219257\pi$
$197$	21.6710	1.54400	0.771999	+	0.635624i	$0.219257\pi$
$198$	32.5126	2.31057
$199$	21.5141	1.52509	0.762546	−	0.646934i	$-0.223949\pi$
$199$	21.5141	1.52509	0.762546	+	0.646934i	$0.223949\pi$
$200$	−6.36539	−0.450101
$201$	5.09616	0.359455
$202$	16.4170	1.15510
$203$	0.572953	0.0402134
$204$	10.6282	0.744121
$205$	−6.41253	−0.447871
$206$	17.6458	1.22944
$207$	10.8379	0.753284
$208$	−27.4127	−1.90073
$209$	46.8791	3.24269
$210$	0.162862	0.0112385
$211$	−4.83297	−0.332715	−0.166358	−	0.986065i	$-0.553201\pi$
$211$	−4.83297	−0.332715	−0.166358	+	0.986065i	$0.553201\pi$
$212$	−25.1193	−1.72520
$213$	4.20570	0.288170
$214$	−14.9436	−1.02153
$215$	−6.82241	−0.465284
$216$	30.7481	2.09214
$217$	0.521279	0.0353867
$218$	31.4405	2.12942
$219$	13.3951	0.905159
$220$	−27.2580	−1.83773
$221$	−9.46764	−0.636862
$222$	6.12517	0.411095
$223$	−12.5660	−0.841483	−0.420742	−	0.907181i	$-0.638230\pi$
$223$	−12.5660	−0.841483	−0.420742	+	0.907181i	$0.638230\pi$
$224$	−0.384848	−0.0257138
$225$	−2.10446	−0.140297
$226$	29.7562	1.97935
$227$	−6.92506	−0.459633	−0.229816	−	0.973234i	$-0.573813\pi$
$227$	−6.92506	−0.459633	−0.229816	+	0.973234i	$0.573813\pi$
$228$	32.9171	2.17999
$229$	−7.78095	−0.514180	−0.257090	−	0.966387i	$-0.582764\pi$
$229$	−7.78095	−0.514180	−0.257090	+	0.966387i	$0.582764\pi$
$230$	−13.1271	−0.865575
$231$	0.387260	0.0254799
$232$	−54.0172	−3.54641
$233$	7.35356	0.481748	0.240874	−	0.970556i	$-0.422566\pi$
$233$	7.35356	0.481748	0.240874	+	0.970556i	$0.422566\pi$
$234$	−20.3365	−1.32944
$235$	8.48363	0.553411
$236$	55.2620	3.59725
$237$	−8.72851	−0.566977
$238$	−0.429779	−0.0278585
$239$	1.38857	0.0898189	0.0449095	−	0.998991i	$-0.485700\pi$
$239$	1.38857	0.0898189	0.0449095	+	0.998991i	$0.485700\pi$
$240$	−6.84264	−0.441690
$241$	23.9250	1.54114	0.770571	−	0.637354i	$-0.219971\pi$
$241$	23.9250	1.54114	0.770571	+	0.637354i	$0.219971\pi$
$242$	−65.6010	−4.21699
$243$	16.1401	1.03539
$244$	−15.5903	−0.998065
$245$	6.99544	0.446922
$246$	−15.4681	−0.986211
$247$	−29.3227	−1.86576
$248$	−49.1454	−3.12074
$249$	12.9551	0.820997
$250$	2.54897	0.161211
$251$	23.8908	1.50798	0.753988	−	0.656888i	$-0.228128\pi$
$251$	23.8908	1.50798	0.753988	+	0.656888i	$0.228128\pi$
$252$	−0.638996	−0.0402530
$253$	−31.2141	−1.96242
$254$	−29.0930	−1.82546
$255$	−2.36327	−0.147993
$256$	−28.7534	−1.79709
$257$	16.1413	1.00687	0.503434	−	0.864034i	$-0.332070\pi$
$257$	16.1413	1.00687	0.503434	+	0.864034i	$0.332070\pi$
$258$	−16.4568	−1.02456
$259$	−0.171444	−0.0106530
$260$	17.0498	1.05738
$261$	−17.8586	−1.10542
$262$	13.6124	0.840979
$263$	−8.33473	−0.513942	−0.256971	−	0.966419i	$-0.582724\pi$
$263$	−8.33473	−0.513942	−0.256971	+	0.966419i	$0.582724\pi$
$264$	−36.5103	−2.24706
$265$	5.58549	0.343114
$266$	−1.33109	−0.0816145
$267$	−14.1785	−0.867712
$268$	24.2184	1.47937
$269$	25.0743	1.52880	0.764402	−	0.644739i	$-0.223034\pi$
$269$	25.0743	1.52880	0.764402	+	0.644739i	$0.223034\pi$
$270$	−12.3128	−0.749334
$271$	27.8765	1.69338	0.846688	−	0.532090i	$-0.178593\pi$
$271$	27.8765	1.69338	0.846688	+	0.532090i	$0.178593\pi$
$272$	18.0572	1.09488
$273$	−0.242230	−0.0146604
$274$	−45.8667	−2.77091
$275$	6.06105	0.365495
$276$	−21.9176	−1.31929
$277$	4.85625	0.291784	0.145892	−	0.989301i	$-0.453395\pi$
$277$	4.85625	0.291784	0.145892	+	0.989301i	$0.453395\pi$
$278$	50.3362	3.01897
$279$	−16.2479	−0.972738
$280$	0.429771	0.0256837
$281$	23.7895	1.41916	0.709581	−	0.704624i	$-0.248884\pi$
$281$	23.7895	1.41916	0.709581	+	0.704624i	$0.248884\pi$
$282$	20.4640	1.21861
$283$	11.8373	0.703657	0.351828	−	0.936065i	$-0.385560\pi$
$283$	11.8373	0.703657	0.351828	+	0.936065i	$0.385560\pi$
$284$	19.9867	1.18599
$285$	−7.31939	−0.433563
$286$	58.5712	3.46339
$287$	0.432954	0.0255564
$288$	11.9955	0.706841
$289$	−10.7635	−0.633149
$290$	21.6308	1.27020
$291$	−7.66391	−0.449267
$292$	63.6575	3.72527
$293$	−20.1044	−1.17451	−0.587255	−	0.809402i	$-0.699791\pi$
$293$	−20.1044	−1.17451	−0.587255	+	0.809402i	$0.699791\pi$
$294$	16.8742	0.984123
$295$	−12.2880	−0.715434
$296$	16.1635	0.939484
$297$	−29.2779	−1.69888
$298$	−31.3520	−1.81617
$299$	19.5243	1.12912
$300$	4.25588	0.245713
$301$	0.460627	0.0265501
$302$	39.7425	2.28692
$303$	−6.09498	−0.350147
$304$	55.9257	3.20756
$305$	3.46663	0.198499
$306$	13.3960	0.765796
$307$	28.2799	1.61402	0.807011	−	0.590537i	$-0.201084\pi$
$307$	28.2799	1.61402	0.807011	+	0.590537i	$0.201084\pi$
$308$	1.84037	0.104865
$309$	−6.55121	−0.372685
$310$	19.6799	1.11774
$311$	−24.4558	−1.38676	−0.693382	−	0.720571i	$-0.743880\pi$
$311$	−24.4558	−1.38676	−0.693382	+	0.720571i	$0.743880\pi$
$312$	22.8371	1.29290
$313$	−20.0092	−1.13099	−0.565494	−	0.824753i	$-0.691314\pi$
$313$	−20.0092	−1.13099	−0.565494	+	0.824753i	$0.691314\pi$
$314$	19.4798	1.09931
$315$	0.142086	0.00800565
$316$	−41.4804	−2.33345
$317$	12.9152	0.725391	0.362695	−	0.931908i	$-0.381857\pi$
$317$	12.9152	0.725391	0.362695	+	0.931908i	$0.381857\pi$
$318$	13.4731	0.755536
$319$	51.4345	2.87978
$320$	−0.0678279	−0.00379170
$321$	5.54798	0.309658
$322$	0.886299	0.0493915
$323$	19.3153	1.07473
$324$	7.83466	0.435259
$325$	−3.79116	−0.210296
$326$	9.44527	0.523125
$327$	−11.6726	−0.645497
$328$	−40.8183	−2.25381
$329$	−0.572788	−0.0315788
$330$	14.6203	0.804820
$331$	−10.3700	−0.569986	−0.284993	−	0.958530i	$-0.591991\pi$
$331$	−10.3700	−0.569986	−0.284993	+	0.958530i	$0.591991\pi$
$332$	61.5665	3.37890
$333$	5.34380	0.292839
$334$	−8.03162	−0.439471
$335$	−5.38517	−0.294223
$336$	0.461993	0.0252038
$337$	−22.6814	−1.23553	−0.617767	−	0.786361i	$-0.711963\pi$
$337$	−22.6814	−1.23553	−0.617767	+	0.786361i	$0.711963\pi$
$338$	−3.49951	−0.190348
$339$	−11.0473	−0.600006
$340$	−11.2309	−0.609082
$341$	46.7957	2.53413
$342$	41.4893	2.24348
$343$	−0.944928	−0.0510213
$344$	−43.4273	−2.34144
$345$	4.87357	0.262384
$346$	1.64616	0.0884982
$347$	4.75313	0.255162	0.127581	−	0.991828i	$-0.459279\pi$
$347$	4.75313	0.255162	0.127581	+	0.991828i	$0.459279\pi$
$348$	36.1158	1.93601
$349$	−11.2482	−0.602100	−0.301050	−	0.953608i	$-0.597337\pi$
$349$	−11.2482	−0.602100	−0.301050	+	0.953608i	$0.597337\pi$
$350$	−0.172098	−0.00919904
$351$	18.3132	0.977489
$352$	−34.5482	−1.84143
$353$	27.9776	1.48910	0.744549	−	0.667568i	$-0.232665\pi$
$353$	27.9776	1.48910	0.744549	+	0.667568i	$0.232665\pi$
$354$	−29.6407	−1.57539
$355$	−4.44421	−0.235874
$356$	−67.3805	−3.57116
$357$	0.159560	0.00844482
$358$	−25.5758	−1.35172
$359$	3.52677	0.186136	0.0930679	−	0.995660i	$-0.470333\pi$
$359$	3.52677	0.186136	0.0930679	+	0.995660i	$0.470333\pi$
$360$	−13.3957	−0.706015
$361$	40.8223	2.14854
$362$	43.7484	2.29937
$363$	24.3551	1.27831
$364$	−1.15115	−0.0603365
$365$	−14.1548	−0.740896
$366$	8.36210	0.437094
$367$	8.99905	0.469746	0.234873	−	0.972026i	$-0.424532\pi$
$367$	8.99905	0.469746	0.234873	+	0.972026i	$0.424532\pi$
$368$	−37.2378	−1.94115
$369$	−13.4949	−0.702516
$370$	−6.47254	−0.336492
$371$	−0.377114	−0.0195788
$372$	32.8585	1.70363
$373$	−10.0275	−0.519206	−0.259603	−	0.965715i	$-0.583592\pi$
$373$	−10.0275	−0.519206	−0.259603	+	0.965715i	$0.583592\pi$
$374$	−38.5817	−1.99501
$375$	−0.946332	−0.0488684
$376$	54.0016	2.78492
$377$	−32.1721	−1.65695
$378$	0.831322	0.0427586
$379$	5.23246	0.268773	0.134387	−	0.990929i	$-0.457094\pi$
$379$	5.23246	0.268773	0.134387	+	0.990929i	$0.457094\pi$
$380$	−34.7839	−1.78437
$381$	10.8011	0.553356
$382$	38.7264	1.98142
$383$	22.5442	1.15196	0.575978	−	0.817465i	$-0.304622\pi$
$383$	22.5442	1.15196	0.575978	+	0.817465i	$0.304622\pi$
$384$	10.6246	0.542187
$385$	−0.409222	−0.0208559
$386$	−28.8539	−1.46862
$387$	−14.3575	−0.729830
$388$	−36.4211	−1.84900
$389$	9.94723	0.504345	0.252172	−	0.967682i	$-0.418855\pi$
$389$	9.94723	0.504345	0.252172	+	0.967682i	$0.418855\pi$
$390$	−9.14493	−0.463071
$391$	−12.8610	−0.650406
$392$	44.5287	2.24904
$393$	−5.05376	−0.254929
$394$	−55.2388	−2.78289
$395$	9.22352	0.464085
$396$	−57.3632	−2.88261
$397$	15.5752	0.781699	0.390850	−	0.920455i	$-0.372181\pi$
$397$	15.5752	0.781699	0.390850	+	0.920455i	$0.372181\pi$
$398$	−54.8387	−2.74881
$399$	0.494182	0.0247400
$400$	7.23070	0.361535
$401$	0.253899	0.0126791	0.00633956	−	0.999980i	$-0.497982\pi$
$401$	0.253899	0.0126791	0.00633956	+	0.999980i	$0.497982\pi$
$402$	−12.9899	−0.647880
$403$	−29.2705	−1.45807
$404$	−28.9651	−1.44107
$405$	−1.74210	−0.0865659
$406$	−1.46044	−0.0724804
$407$	−15.3907	−0.762888
$408$	−15.0431	−0.744745
$409$	−26.0734	−1.28925	−0.644623	−	0.764500i	$-0.722986\pi$
$409$	−26.0734	−1.28925	−0.644623	+	0.764500i	$0.722986\pi$
$410$	16.3453	0.807239
$411$	17.0285	0.839954
$412$	−31.1332	−1.53382
$413$	0.829645	0.0408242
$414$	−27.6254	−1.35771
$415$	−13.6898	−0.672007
$416$	21.6098	1.05951
$417$	−18.6879	−0.915148
$418$	−119.493	−5.84461
$419$	−29.1293	−1.42306	−0.711529	−	0.702657i	$-0.751997\pi$
$419$	−29.1293	−1.42306	−0.711529	+	0.702657i	$0.751997\pi$
$420$	−0.287344	−0.0140209
$421$	0.550347	0.0268223	0.0134111	−	0.999910i	$-0.495731\pi$
$421$	0.550347	0.0268223	0.0134111	+	0.999910i	$0.495731\pi$
$422$	12.3191	0.599684
$423$	17.8534	0.868064
$424$	35.5538	1.72665
$425$	2.49729	0.121136
$426$	−10.7202	−0.519395
$427$	−0.234056	−0.0113268
$428$	26.3656	1.27443
$429$	−21.7452	−1.04987
$430$	17.3901	0.838625
$431$	13.1993	0.635787	0.317894	−	0.948126i	$-0.397024\pi$
$431$	13.1993	0.635787	0.317894	+	0.948126i	$0.397024\pi$
$432$	−34.9279	−1.68047
$433$	−9.42358	−0.452868	−0.226434	−	0.974026i	$-0.572707\pi$
$433$	−9.42358	−0.452868	−0.226434	+	0.974026i	$0.572707\pi$
$434$	−1.32872	−0.0637808
$435$	−8.03065	−0.385040
$436$	−55.4716	−2.65661
$437$	−39.8323	−1.90544
$438$	−34.1438	−1.63145
$439$	−13.8974	−0.663286	−0.331643	−	0.943405i	$-0.607603\pi$
$439$	−13.8974	−0.663286	−0.331643	+	0.943405i	$0.607603\pi$
$440$	38.5809	1.83927
$441$	14.7216	0.701029
$442$	24.1327	1.14788
$443$	−38.8628	−1.84643	−0.923214	−	0.384287i	$-0.874447\pi$
$443$	−38.8628	−1.84643	−0.923214	+	0.384287i	$0.874447\pi$
$444$	−10.8069	−0.512872
$445$	14.9826	0.710245
$446$	32.0304	1.51668
$447$	11.6398	0.550542
$448$	0.00457952	0.000216362 0
$449$	23.1723	1.09357	0.546785	−	0.837273i	$-0.315852\pi$
$449$	23.1723	1.09357	0.546785	+	0.837273i	$0.315852\pi$
$450$	5.36419	0.252870
$451$	38.8666	1.83016
$452$	−52.4999	−2.46939
$453$	−14.7548	−0.693241
$454$	17.6518	0.828439
$455$	0.255967	0.0119999
$456$	−46.5908	−2.18181
$457$	13.7193	0.641763	0.320882	−	0.947119i	$-0.396021\pi$
$457$	13.7193	0.641763	0.320882	+	0.947119i	$0.396021\pi$
$458$	19.8334	0.926754
$459$	−12.0632	−0.563061
$460$	23.1606	1.07987
$461$	14.0534	0.654531	0.327265	−	0.944932i	$-0.393873\pi$
$461$	14.0534	0.654531	0.327265	+	0.944932i	$0.393873\pi$
$462$	−0.987114	−0.0459247
$463$	−22.5940	−1.05003	−0.525016	−	0.851092i	$-0.675941\pi$
$463$	−22.5940	−1.05003	−0.525016	+	0.851092i	$0.675941\pi$
$464$	61.3603	2.84858
$465$	−7.30637	−0.338825
$466$	−18.7440	−0.868299
$467$	−28.8706	−1.33597	−0.667986	−	0.744174i	$-0.732844\pi$
$467$	−28.8706	−1.33597	−0.667986	+	0.744174i	$0.732844\pi$
$468$	35.8805	1.65858
$469$	0.363590	0.0167890
$470$	−21.6245	−0.997464
$471$	−7.23209	−0.333237
$472$	−78.2178	−3.60026
$473$	41.3509	1.90132
$474$	22.2487	1.02192
$475$	7.73449	0.354883
$476$	0.758276	0.0347555
$477$	11.7544	0.538198
$478$	−3.53941	−0.161889
$479$	−9.99710	−0.456779	−0.228390	−	0.973570i	$-0.573346\pi$
$479$	−9.99710	−0.456779	−0.228390	+	0.973570i	$0.573346\pi$
$480$	5.39413	0.246207
$481$	9.62682	0.438945
$482$	−60.9840	−2.77774
$483$	−0.329048	−0.0149722
$484$	115.742	5.26101
$485$	8.09855	0.367736
$486$	−41.1407	−1.86618
$487$	15.8220	0.716964	0.358482	−	0.933537i	$-0.383294\pi$
$487$	15.8220	0.716964	0.358482	+	0.933537i	$0.383294\pi$
$488$	22.0665	0.998902
$489$	−3.50666	−0.158576
$490$	−17.8312	−0.805530
$491$	−1.09278	−0.0493163	−0.0246582	−	0.999696i	$-0.507850\pi$
$491$	−1.09278	−0.0493163	−0.0246582	+	0.999696i	$0.507850\pi$
$492$	27.2910	1.23037
$493$	21.1922	0.954450
$494$	74.7426	3.36283
$495$	12.7552	0.573304
$496$	55.8262	2.50667
$497$	0.300059	0.0134595
$498$	−33.0222	−1.47976
$499$	−13.1216	−0.587404	−0.293702	−	0.955897i	$-0.594887\pi$
$499$	−13.1216	−0.587404	−0.293702	+	0.955897i	$0.594887\pi$
$500$	−4.49724	−0.201123
$501$	2.98183	0.133218
$502$	−60.8970	−2.71797
$503$	4.55584	0.203135	0.101567	−	0.994829i	$-0.467614\pi$
$503$	4.55584	0.203135	0.101567	+	0.994829i	$0.467614\pi$
$504$	0.904434	0.0402867
$505$	6.44064	0.286605
$506$	79.5639	3.53705
$507$	1.29923	0.0577008
$508$	51.3298	2.27739
$509$	7.13663	0.316325	0.158163	−	0.987413i	$-0.449443\pi$
$509$	7.13663	0.316325	0.158163	+	0.987413i	$0.449443\pi$
$510$	6.02389	0.266742
$511$	0.955686	0.0422771
$512$	50.8371	2.24671
$513$	−37.3615	−1.64955
$514$	−41.1437	−1.81477
$515$	6.92274	0.305052
$516$	29.0354	1.27821
$517$	−51.4197	−2.26143
$518$	0.437005	0.0192009
$519$	−0.611155	−0.0268267
$520$	−24.1322	−1.05827
$521$	−3.64052	−0.159494	−0.0797471	−	0.996815i	$-0.525411\pi$
$521$	−3.64052	−0.159494	−0.0797471	+	0.996815i	$0.525411\pi$
$522$	45.5210	1.99240
$523$	14.5037	0.634203	0.317102	−	0.948392i	$-0.397290\pi$
$523$	14.5037	0.634203	0.317102	+	0.948392i	$0.397290\pi$
$524$	−24.0169	−1.04918
$525$	0.0638933	0.00278853
$526$	21.2450	0.926325
$527$	19.2809	0.839889
$528$	41.4735	1.80490
$529$	3.52210	0.153135
$530$	−14.2372	−0.618426
$531$	−25.8595	−1.12221
$532$	2.34849	0.101820
$533$	−24.3109	−1.05302
$534$	36.1406	1.56396
$535$	−5.86262	−0.253463
$536$	−34.2787	−1.48061
$537$	9.49528	0.409752
$538$	−63.9135	−2.75551
$539$	−42.3997	−1.82628
$540$	21.7240	0.934851
$541$	−35.5389	−1.52794	−0.763969	−	0.645253i	$-0.776752\pi$
$541$	−35.5389	−1.52794	−0.763969	+	0.645253i	$0.776752\pi$
$542$	−71.0563	−3.05213
$543$	−16.2421	−0.697014
$544$	−14.2347	−0.610306
$545$	12.3346	0.528356
$546$	0.617436	0.0264238
$547$	−16.4586	−0.703718	−0.351859	−	0.936053i	$-0.614450\pi$
$547$	−16.4586	−0.703718	−0.351859	+	0.936053i	$0.614450\pi$
$548$	80.9244	3.45692
$549$	7.29537	0.311359
$550$	−15.4494	−0.658765
$551$	65.6355	2.79617
$552$	31.0222	1.32039
$553$	−0.622742	−0.0264817
$554$	−12.3784	−0.525910
$555$	2.40300	0.102002
$556$	−88.8101	−3.76639
$557$	−11.6781	−0.494816	−0.247408	−	0.968911i	$-0.579579\pi$
$557$	−11.6781	−0.494816	−0.247408	+	0.968911i	$0.579579\pi$
$558$	41.4155	1.75326
$559$	−25.8648	−1.09397
$560$	−0.488194	−0.0206299
$561$	14.3239	0.604754
$562$	−60.6387	−2.55789
$563$	−13.7754	−0.580564	−0.290282	−	0.956941i	$-0.593749\pi$
$563$	−13.7754	−0.580564	−0.290282	+	0.956941i	$0.593749\pi$
$564$	−36.1053	−1.52031
$565$	11.6738	0.491121
$566$	−30.1730	−1.26827
$567$	0.117621	0.00493963
$568$	−28.2891	−1.18699
$569$	32.9404	1.38094	0.690468	−	0.723363i	$-0.257405\pi$
$569$	32.9404	1.38094	0.690468	+	0.723363i	$0.257405\pi$
$570$	18.6569	0.781451
$571$	19.5305	0.817327	0.408663	−	0.912685i	$-0.365995\pi$
$571$	19.5305	0.817327	0.408663	+	0.912685i	$0.365995\pi$
$572$	−103.339	−4.32084
$573$	−14.3776	−0.600633
$574$	−1.10359	−0.0460628
$575$	−5.14996	−0.214768
$576$	−0.142741	−0.00594754
$577$	3.44500	0.143417	0.0717087	−	0.997426i	$-0.477155\pi$
$577$	3.44500	0.143417	0.0717087	+	0.997426i	$0.477155\pi$
$578$	27.4359	1.14118
$579$	10.7123	0.445189
$580$	−38.1640	−1.58467
$581$	0.924294	0.0383462
$582$	19.5351	0.809755
$583$	−33.8539	−1.40208
$584$	−90.1007	−3.72840
$585$	−7.97834	−0.329864
$586$	51.2454	2.11693
$587$	6.65496	0.274679	0.137340	−	0.990524i	$-0.456145\pi$
$587$	6.65496	0.274679	0.137340	+	0.990524i	$0.456145\pi$
$588$	−29.7718	−1.22777
$589$	59.7159	2.46055
$590$	31.3217	1.28949
$591$	20.5080	0.843586
$592$	−18.3608	−0.754622
$593$	2.03240	0.0834608	0.0417304	−	0.999129i	$-0.486713\pi$
$593$	2.03240	0.0834608	0.0417304	+	0.999129i	$0.486713\pi$
$594$	74.6285	3.06205
$595$	−0.168609	−0.00691230
$596$	55.3155	2.26581
$597$	20.3594	0.833256
$598$	−49.7669	−2.03512
$599$	−1.51349	−0.0618395	−0.0309197	−	0.999522i	$-0.509844\pi$
$599$	−1.51349	−0.0618395	−0.0309197	+	0.999522i	$0.509844\pi$
$600$	−6.02377	−0.245919
$601$	29.1793	1.19025	0.595124	−	0.803634i	$-0.297103\pi$
$601$	29.1793	1.19025	0.595124	+	0.803634i	$0.297103\pi$
$602$	−1.17412	−0.0478537
$603$	−11.3329	−0.461510
$604$	−70.1191	−2.85311
$605$	−25.7363	−1.04633
$606$	15.5359	0.631103
$607$	38.7430	1.57253	0.786264	−	0.617890i	$-0.212012\pi$
$607$	38.7430	1.57253	0.786264	+	0.617890i	$0.212012\pi$
$608$	−44.0869	−1.78796
$609$	0.542204	0.0219712
$610$	−8.83633	−0.357773
$611$	32.1628	1.30117
$612$	−23.6350	−0.955388
$613$	−1.59007	−0.0642222	−0.0321111	−	0.999484i	$-0.510223\pi$
$613$	−1.59007	−0.0642222	−0.0321111	+	0.999484i	$0.510223\pi$
$614$	−72.0847	−2.90910
$615$	−6.06838	−0.244701
$616$	−2.60486	−0.104953
$617$	5.58671	0.224913	0.112456	−	0.993657i	$-0.464128\pi$
$617$	5.58671	0.224913	0.112456	+	0.993657i	$0.464128\pi$
$618$	16.6988	0.671725
$619$	−28.2443	−1.13523	−0.567616	−	0.823293i	$-0.692134\pi$
$619$	−28.2443	−1.13523	−0.567616	+	0.823293i	$0.692134\pi$
$620$	−34.7220	−1.39447
$621$	24.8769	0.998277
$622$	62.3372	2.49949
$623$	−1.01158	−0.0405281
$624$	−25.9415	−1.03849
$625$	1.00000	0.0400000
$626$	51.0028	2.03848
$627$	44.3632	1.77169
$628$	−34.3690	−1.37147
$629$	−6.34132	−0.252845
$630$	−0.362173	−0.0144293
$631$	−20.0163	−0.796836	−0.398418	−	0.917204i	$-0.630441\pi$
$631$	−20.0163	−0.796836	−0.398418	+	0.917204i	$0.630441\pi$
$632$	58.7113	2.33541
$633$	−4.57359	−0.181784
$634$	−32.9205	−1.30744
$635$	−11.4136	−0.452936
$636$	−23.7712	−0.942588
$637$	26.5209	1.05079
$638$	−131.105	−5.19050
$639$	−9.35264	−0.369985
$640$	−11.2272	−0.443794
$641$	27.3966	1.08210	0.541051	−	0.840990i	$-0.318027\pi$
$641$	27.3966	1.08210	0.541051	+	0.840990i	$0.318027\pi$
$642$	−14.1416	−0.558126
$643$	12.4859	0.492395	0.246197	−	0.969220i	$-0.420819\pi$
$643$	12.4859	0.492395	0.246197	+	0.969220i	$0.420819\pi$
$644$	−1.56373	−0.0616196
$645$	−6.45626	−0.254215
$646$	−49.2340	−1.93709
$647$	27.7258	1.09001	0.545007	−	0.838431i	$-0.316527\pi$
$647$	27.7258	1.09001	0.545007	+	0.838431i	$0.316527\pi$
$648$	−11.0892	−0.435624
$649$	74.4780	2.92352
$650$	9.66355	0.379036
$651$	0.493303	0.0193341
$652$	−16.6646	−0.652638
$653$	20.3329	0.795689	0.397844	−	0.917453i	$-0.369758\pi$
$653$	20.3329	0.795689	0.397844	+	0.917453i	$0.369758\pi$
$654$	29.7531	1.16344
$655$	5.34037	0.208665
$656$	46.3671	1.81033
$657$	−29.7881	−1.16215
$658$	1.46002	0.0569174
$659$	−8.46730	−0.329839	−0.164920	−	0.986307i	$-0.552736\pi$
$659$	−8.46730	−0.329839	−0.164920	+	0.986307i	$0.552736\pi$
$660$	−25.7951	−1.00407
$661$	17.3428	0.674555	0.337278	−	0.941405i	$-0.390494\pi$
$661$	17.3428	0.674555	0.337278	+	0.941405i	$0.390494\pi$
$662$	26.4328	1.02734
$663$	−8.95953	−0.347959
$664$	−87.1411	−3.38173
$665$	−0.522208	−0.0202504
$666$	−13.6212	−0.527810
$667$	−43.7030	−1.69219
$668$	14.1705	0.548273
$669$	−11.8916	−0.459757
$670$	13.7266	0.530306
$671$	−21.0114	−0.811137
$672$	−0.364194	−0.0140491
$673$	28.9656	1.11654	0.558270	−	0.829659i	$-0.311465\pi$
$673$	28.9656	1.11654	0.558270	+	0.829659i	$0.311465\pi$
$674$	57.8142	2.22692
$675$	−4.83051	−0.185926
$676$	6.17431	0.237474
$677$	19.8966	0.764689	0.382344	−	0.924020i	$-0.375117\pi$
$677$	19.8966	0.764689	0.382344	+	0.924020i	$0.375117\pi$
$678$	28.1592	1.08145
$679$	−0.546788	−0.0209838
$680$	15.8962	0.609593
$681$	−6.55341	−0.251127
$682$	−119.281	−4.56749
$683$	−33.8985	−1.29709	−0.648545	−	0.761176i	$-0.724622\pi$
$683$	−33.8985	−1.29709	−0.648545	+	0.761176i	$0.724622\pi$
$684$	−73.2011	−2.79891
$685$	−17.9942	−0.687524
$686$	2.40859	0.0919604
$687$	−7.36336	−0.280930
$688$	49.3307	1.88072
$689$	21.1755	0.806722
$690$	−12.4226	−0.472920
$691$	−24.0506	−0.914928	−0.457464	−	0.889228i	$-0.651242\pi$
$691$	−24.0506	−0.914928	−0.457464	+	0.889228i	$0.651242\pi$
$692$	−2.90439	−0.110408
$693$	−0.861191	−0.0327139
$694$	−12.1156	−0.459902
$695$	19.7477	0.749072
$696$	−51.1182	−1.93763
$697$	16.0140	0.606572
$698$	28.6712	1.08522
$699$	6.95891	0.263210
$700$	0.303639	0.0114765
$701$	41.9527	1.58453	0.792266	−	0.610175i	$-0.208901\pi$
$701$	41.9527	1.58453	0.792266	+	0.610175i	$0.208901\pi$
$702$	−46.6799	−1.76182
$703$	−19.6400	−0.740737
$704$	0.411108	0.0154942
$705$	8.02833	0.302364
$706$	−71.3140	−2.68394
$707$	−0.434851	−0.0163543
$708$	52.2962	1.96541
$709$	11.1954	0.420452	0.210226	−	0.977653i	$-0.432580\pi$
$709$	11.1954	0.420452	0.210226	+	0.977653i	$0.432580\pi$
$710$	11.3282	0.425138
$711$	19.4105	0.727950
$712$	95.3703	3.57415
$713$	−39.7614	−1.48908
$714$	−0.406714	−0.0152209
$715$	22.9784	0.859344
$716$	45.1243	1.68637
$717$	1.31404	0.0490739
$718$	−8.98963	−0.335490
$719$	−17.4610	−0.651184	−0.325592	−	0.945510i	$-0.605564\pi$
$719$	−17.4610	−0.651184	−0.325592	+	0.945510i	$0.605564\pi$
$720$	15.2167	0.567092
$721$	−0.467401	−0.0174069
$722$	−104.055	−3.87252
$723$	22.6409	0.842026
$724$	−77.1870	−2.86863
$725$	8.48609	0.315165
$726$	−62.0803	−2.30401
$727$	4.37863	0.162394	0.0811972	−	0.996698i	$-0.474126\pi$
$727$	4.37863	0.162394	0.0811972	+	0.996698i	$0.474126\pi$
$728$	1.62933	0.0603870
$729$	10.0476	0.372134
$730$	36.0801	1.33538
$731$	17.0375	0.630156
$732$	−14.7536	−0.545308
$733$	38.4789	1.42125	0.710625	−	0.703571i	$-0.248412\pi$
$733$	38.4789	1.42125	0.710625	+	0.703571i	$0.248412\pi$
$734$	−22.9383	−0.846668
$735$	6.62001	0.244183
$736$	29.3550	1.08204
$737$	32.6398	1.20230
$738$	34.3981	1.26621
$739$	−32.5853	−1.19867	−0.599334	−	0.800499i	$-0.704568\pi$
$739$	−32.5853	−1.19867	−0.599334	+	0.800499i	$0.704568\pi$
$740$	11.4198	0.419798
$741$	−27.7490	−1.01938
$742$	0.961252	0.0352887
$743$	−23.9714	−0.879425	−0.439713	−	0.898139i	$-0.644920\pi$
$743$	−23.9714	−0.879425	−0.439713	+	0.898139i	$0.644920\pi$
$744$	−46.5079	−1.70506
$745$	−12.2999	−0.450633
$746$	25.5599	0.935814
$747$	−28.8096	−1.05409
$748$	68.0711	2.48893
$749$	0.395825	0.0144631
$750$	2.41217	0.0880800
$751$	49.4755	1.80539	0.902693	−	0.430284i	$-0.141587\pi$
$751$	49.4755	1.80539	0.902693	+	0.430284i	$0.141587\pi$
$752$	−61.3426	−2.23693
$753$	22.6087	0.823905
$754$	82.0057	2.98647
$755$	15.5916	0.567436
$756$	−1.46673	−0.0533446
$757$	21.7348	0.789964	0.394982	−	0.918689i	$-0.370751\pi$
$757$	21.7348	0.789964	0.394982	+	0.918689i	$0.370751\pi$
$758$	−13.3374	−0.484435
$759$	−29.5389	−1.07220
$760$	49.2330	1.78587
$761$	29.7243	1.07751	0.538753	−	0.842464i	$-0.318896\pi$
$761$	29.7243	1.07751	0.538753	+	0.842464i	$0.318896\pi$
$762$	−27.5316	−0.997365
$763$	−0.832792	−0.0301491
$764$	−68.3265	−2.47197
$765$	5.25544	0.190011
$766$	−57.4645	−2.07628
$767$	−46.5857	−1.68211
$768$	−27.2103	−0.981866
$769$	−34.7155	−1.25187	−0.625936	−	0.779875i	$-0.715283\pi$
$769$	−34.7155	−1.25187	−0.625936	+	0.779875i	$0.715283\pi$
$770$	1.04310	0.0375905
$771$	15.2750	0.550117
$772$	50.9080	1.83222
$773$	51.8003	1.86313	0.931565	−	0.363576i	$-0.118444\pi$
$773$	51.8003	1.86313	0.931565	+	0.363576i	$0.118444\pi$
$774$	36.5967	1.31544
$775$	7.72073	0.277337
$776$	51.5504	1.85055
$777$	−0.162243	−0.00582043
$778$	−25.3552	−0.909027
$779$	49.5976	1.77702
$780$	16.1347	0.577716
$781$	26.9366	0.963866
$782$	32.7822	1.17229
$783$	−40.9921	−1.46494
$784$	−50.5819	−1.80650
$785$	7.64223	0.272763
$786$	12.8819	0.459481
$787$	11.4194	0.407058	0.203529	−	0.979069i	$-0.434759\pi$
$787$	11.4194	0.407058	0.203529	+	0.979069i	$0.434759\pi$
$788$	97.4599	3.47187
$789$	−7.88742	−0.280800
$790$	−23.5105	−0.836464
$791$	−0.788178	−0.0280244
$792$	81.1919	2.88503
$793$	13.1426	0.466706
$794$	−39.7008	−1.40893
$795$	5.28572	0.187465
$796$	96.7539	3.42935
$797$	7.72680	0.273697	0.136849	−	0.990592i	$-0.456303\pi$
$797$	7.72680	0.273697	0.136849	+	0.990592i	$0.456303\pi$
$798$	−1.25965	−0.0445913
$799$	−21.1861	−0.749510
$800$	−5.70004	−0.201527
$801$	31.5303	1.11407
$802$	−0.647181	−0.0228528
$803$	85.7928	3.02756
$804$	22.9187	0.808279
$805$	0.347709	0.0122551
$806$	74.6097	2.62801
$807$	23.7286	0.835285
$808$	40.9972	1.44228
$809$	−27.8291	−0.978421	−0.489210	−	0.872166i	$-0.662715\pi$
$809$	−27.8291	−0.978421	−0.489210	+	0.872166i	$0.662715\pi$
$810$	4.44057	0.156026
$811$	−48.8991	−1.71708	−0.858540	−	0.512746i	$-0.828628\pi$
$811$	−48.8991	−1.71708	−0.858540	+	0.512746i	$0.828628\pi$
$812$	2.57671	0.0904248
$813$	26.3804	0.925201
$814$	39.2304	1.37502
$815$	3.70552	0.129799
$816$	17.0881	0.598202
$817$	52.7678	1.84611
$818$	66.4603	2.32373
$819$	0.538672	0.0188227
$820$	−28.8387	−1.00709
$821$	21.7050	0.757508	0.378754	−	0.925497i	$-0.376353\pi$
$821$	21.7050	0.757508	0.378754	+	0.925497i	$0.376353\pi$
$822$	−43.4051	−1.51393
$823$	23.5223	0.819935	0.409967	−	0.912100i	$-0.365540\pi$
$823$	23.5223	0.819935	0.409967	+	0.912100i	$0.365540\pi$
$824$	44.0659	1.53511
$825$	5.73576	0.199694
$826$	−2.11474	−0.0735812
$827$	−1.74407	−0.0606473	−0.0303236	−	0.999540i	$-0.509654\pi$
$827$	−1.74407	−0.0606473	−0.0303236	+	0.999540i	$0.509654\pi$
$828$	48.7405	1.69385
$829$	−37.8916	−1.31603	−0.658014	−	0.753006i	$-0.728603\pi$
$829$	−37.8916	−1.31603	−0.658014	+	0.753006i	$0.728603\pi$
$830$	34.8949	1.21122
$831$	4.59563	0.159421
$832$	−0.257147	−0.00891496
$833$	−17.4697	−0.605288
$834$	47.6348	1.64946
$835$	−3.15093	−0.109042
$836$	210.827	7.29159
$837$	−37.2950	−1.28911
$838$	74.2496	2.56491
$839$	13.7580	0.474978	0.237489	−	0.971390i	$-0.423676\pi$
$839$	13.7580	0.474978	0.237489	+	0.971390i	$0.423676\pi$
$840$	0.406706	0.0140327
$841$	43.0136	1.48323
$842$	−1.40282	−0.0483443
$843$	22.5127	0.775380
$844$	−21.7350	−0.748150
$845$	−1.37291	−0.0472296
$846$	−45.5078	−1.56459
$847$	1.73763	0.0597057
$848$	−40.3870	−1.38689
$849$	11.2021	0.384453
$850$	−6.36552	−0.218335
$851$	13.0772	0.448280
$852$	18.9140	0.647984
$853$	47.1646	1.61489	0.807443	−	0.589945i	$-0.200851\pi$
$853$	47.1646	1.61489	0.807443	+	0.589945i	$0.200851\pi$
$854$	0.596601	0.0204153
$855$	16.2769	0.556658
$856$	−37.3178	−1.27550
$857$	−24.5249	−0.837755	−0.418877	−	0.908043i	$-0.637576\pi$
$857$	−24.5249	−0.837755	−0.418877	+	0.908043i	$0.637576\pi$
$858$	55.4278	1.89227
$859$	26.7089	0.911294	0.455647	−	0.890160i	$-0.349408\pi$
$859$	26.7089	0.911294	0.455647	+	0.890160i	$0.349408\pi$
$860$	−30.6820	−1.04625
$861$	0.409718	0.0139631
$862$	−33.6446	−1.14594
$863$	8.27769	0.281776	0.140888	−	0.990026i	$-0.455004\pi$
$863$	8.27769	0.281776	0.140888	+	0.990026i	$0.455004\pi$
$864$	27.5341	0.936729
$865$	0.645815	0.0219584
$866$	24.0204	0.816247
$867$	−10.1859	−0.345930
$868$	2.34432	0.0795713
$869$	−55.9042	−1.89642
$870$	20.4699	0.693994
$871$	−20.4161	−0.691772
$872$	78.5145	2.65883
$873$	17.0430	0.576819
$874$	101.531	3.43435
$875$	−0.0675168	−0.00228248
$876$	60.2411	2.03536
$877$	−20.6538	−0.697428	−0.348714	−	0.937229i	$-0.613382\pi$
$877$	−20.6538	−0.697428	−0.348714	+	0.937229i	$0.613382\pi$
$878$	35.4240	1.19550
$879$	−19.0254	−0.641711
$880$	−43.8256	−1.47736
$881$	45.8526	1.54481	0.772406	−	0.635129i	$-0.219053\pi$
$881$	45.8526	1.54481	0.772406	+	0.635129i	$0.219053\pi$
$882$	−37.5249	−1.26353
$883$	27.4489	0.923729	0.461865	−	0.886950i	$-0.347181\pi$
$883$	27.4489	0.923729	0.461865	+	0.886950i	$0.347181\pi$
$884$	−42.5782	−1.43206
$885$	−11.6285	−0.390888
$886$	99.0600	3.32799
$887$	54.5081	1.83020	0.915102	−	0.403222i	$-0.132110\pi$
$887$	54.5081	1.83020	0.915102	+	0.403222i	$0.132110\pi$
$888$	15.2960	0.513301
$889$	0.770612	0.0258455
$890$	−38.1902	−1.28014
$891$	10.5590	0.353739
$892$	−56.5124	−1.89218
$893$	−65.6165	−2.19577
$894$	−29.6694	−0.992294
$895$	−10.0338	−0.335392
$896$	0.758024	0.0253238
$897$	18.4765	0.616912
$898$	−59.0655	−1.97104
$899$	65.5187	2.18517
$900$	−9.46425	−0.315475
$901$	−13.9486	−0.464695
$902$	−99.0699	−3.29867
$903$	0.435906	0.0145060
$904$	74.3083	2.47146
$905$	17.1632	0.570524
$906$	37.6095	1.24949
$907$	−19.3930	−0.643934	−0.321967	−	0.946751i	$-0.604344\pi$
$907$	−19.3930	−0.643934	−0.321967	+	0.946751i	$0.604344\pi$
$908$	−31.1437	−1.03354
$909$	13.5540	0.449559
$910$	−0.652452	−0.0216286
$911$	−1.82738	−0.0605438	−0.0302719	−	0.999542i	$-0.509637\pi$
$911$	−1.82738	−0.0605438	−0.0302719	+	0.999542i	$0.509637\pi$
$912$	52.9243	1.75250
$913$	82.9747	2.74606
$914$	−34.9702	−1.15671
$915$	3.28058	0.108453
$916$	−34.9928	−1.15620
$917$	−0.360565	−0.0119069
$918$	30.7487	1.01486
$919$	−27.9046	−0.920488	−0.460244	−	0.887793i	$-0.652238\pi$
$919$	−27.9046	−0.920488	−0.460244	+	0.887793i	$0.652238\pi$
$920$	−32.7815	−1.08077
$921$	26.7622	0.881845
$922$	−35.8216	−1.17972
$923$	−16.8487	−0.554582
$924$	1.74160	0.0572945
$925$	−2.53928	−0.0834910
$926$	57.5914	1.89257
$927$	14.5686	0.478496
$928$	−48.3710	−1.58786
$929$	4.92689	0.161646	0.0808230	−	0.996728i	$-0.474245\pi$
$929$	4.92689	0.161646	0.0808230	+	0.996728i	$0.474245\pi$
$930$	18.6237	0.610695
$931$	−54.1061	−1.77326
$932$	33.0707	1.08327
$933$	−23.1433	−0.757679
$934$	73.5903	2.40795
$935$	−15.1362	−0.495007
$936$	−50.7852	−1.65997
$937$	1.12738	0.0368298	0.0184149	−	0.999830i	$-0.494138\pi$
$937$	1.12738	0.0368298	0.0184149	+	0.999830i	$0.494138\pi$
$938$	−0.926778	−0.0302604
$939$	−18.9353	−0.617932
$940$	38.1529	1.24441
$941$	35.2870	1.15032	0.575162	−	0.818039i	$-0.304939\pi$
$941$	35.2870	1.15032	0.575162	+	0.818039i	$0.304939\pi$
$942$	18.4344	0.600624
$943$	−33.0243	−1.07542
$944$	88.8506	2.89184
$945$	0.326141	0.0106094
$946$	−105.402	−3.42692
$947$	−30.1112	−0.978482	−0.489241	−	0.872149i	$-0.662726\pi$
$947$	−30.1112	−0.978482	−0.489241	+	0.872149i	$0.662726\pi$
$948$	−39.2542	−1.27492
$949$	−53.6631	−1.74198
$950$	−19.7150	−0.639638
$951$	12.2221	0.396328
$952$	−1.07326	−0.0347847
$953$	20.4086	0.661100	0.330550	−	0.943788i	$-0.392766\pi$
$953$	20.4086	0.661100	0.330550	+	0.943788i	$0.392766\pi$
$954$	−29.9616	−0.970044
$955$	15.1930	0.491633
$956$	6.24472	0.201969
$957$	48.6741	1.57341
$958$	25.4823	0.823296
$959$	1.21491	0.0392316
$960$	−0.0641877	−0.00207165
$961$	28.6096	0.922891
$962$	−24.5385	−0.791152
$963$	−12.3376	−0.397574
$964$	107.596	3.46544
$965$	−11.3198	−0.364398
$966$	0.838733	0.0269858
$967$	32.2144	1.03595	0.517973	−	0.855397i	$-0.326687\pi$
$967$	32.2144	1.03595	0.517973	+	0.855397i	$0.326687\pi$
$968$	−163.821	−5.26542
$969$	18.2787	0.587195
$970$	−20.6429	−0.662805
$971$	32.3786	1.03908	0.519540	−	0.854446i	$-0.326103\pi$
$971$	32.3786	1.03908	0.519540	+	0.854446i	$0.326103\pi$
$972$	72.5861	2.32820
$973$	−1.33330	−0.0427436
$974$	−40.3298	−1.29225
$975$	−3.58770	−0.114898
$976$	−25.0662	−0.802348
$977$	2.45316	0.0784835	0.0392417	−	0.999230i	$-0.487506\pi$
$977$	2.45316	0.0784835	0.0392417	+	0.999230i	$0.487506\pi$
$978$	8.93836	0.285817
$979$	−90.8104	−2.90231
$980$	31.4602	1.00496
$981$	25.9576	0.828762
$982$	2.78545	0.0888874
$983$	−41.1897	−1.31375	−0.656874	−	0.754000i	$-0.728122\pi$
$983$	−41.1897	−1.31375	−0.656874	+	0.754000i	$0.728122\pi$
$984$	−38.6276	−1.23140
$985$	−21.6710	−0.690497
$986$	−54.0183	−1.72029
$987$	−0.542047	−0.0172536
$988$	−131.871	−4.19538
$989$	−35.1351	−1.11723
$990$	−32.5126	−1.03332
$991$	−30.2879	−0.962125	−0.481063	−	0.876686i	$-0.659749\pi$
$991$	−30.2879	−0.962125	−0.481063	+	0.876686i	$0.659749\pi$
$992$	−44.0084	−1.39727
$993$	−9.81344	−0.311420
$994$	−0.764841	−0.0242593
$995$	−21.5141	−0.682042
$996$	58.2623	1.84611
$997$	9.09524	0.288049	0.144025	−	0.989574i	$-0.453996\pi$
$997$	9.09524	0.288049	0.144025	+	0.989574i	$0.453996\pi$
$998$	33.4466	1.05873
$999$	12.2660	0.388079

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8005.2.a.g.1.6	✓	137

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8005.2.a.g.1.6	✓	137	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:	\( N \)	\(=\)	\( 8005 = 5 \cdot 1601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8005.a (trivial)

\(f(q)\)	\(=\)	\(q-2.54897 q^{2} +0.946332 q^{3} +4.49724 q^{4} -1.00000 q^{5} -2.41217 q^{6} +0.0675168 q^{7} -6.36539 q^{8} -2.10446 q^{9} +O(q^{10})\)	\(q-2.54897 q^{2} +0.946332 q^{3} +4.49724 q^{4} -1.00000 q^{5} -2.41217 q^{6} +0.0675168 q^{7} -6.36539 q^{8} -2.10446 q^{9} +2.54897 q^{10} +6.06105 q^{11} +4.25588 q^{12} -3.79116 q^{13} -0.172098 q^{14} -0.946332 q^{15} +7.23070 q^{16} +2.49729 q^{17} +5.36419 q^{18} +7.73449 q^{19} -4.49724 q^{20} +0.0638933 q^{21} -15.4494 q^{22} -5.14996 q^{23} -6.02377 q^{24} +1.00000 q^{25} +9.66355 q^{26} -4.83051 q^{27} +0.303639 q^{28} +8.48609 q^{29} +2.41217 q^{30} +7.72073 q^{31} -5.70004 q^{32} +5.73576 q^{33} -6.36552 q^{34} -0.0675168 q^{35} -9.46425 q^{36} -2.53928 q^{37} -19.7150 q^{38} -3.58770 q^{39} +6.36539 q^{40} +6.41253 q^{41} -0.162862 q^{42} +6.82241 q^{43} +27.2580 q^{44} +2.10446 q^{45} +13.1271 q^{46} -8.48363 q^{47} +6.84264 q^{48} -6.99544 q^{49} -2.54897 q^{50} +2.36327 q^{51} -17.0498 q^{52} -5.58549 q^{53} +12.3128 q^{54} -6.06105 q^{55} -0.429771 q^{56} +7.31939 q^{57} -21.6308 q^{58} +12.2880 q^{59} -4.25588 q^{60} -3.46663 q^{61} -19.6799 q^{62} -0.142086 q^{63} +0.0678279 q^{64} +3.79116 q^{65} -14.6203 q^{66} +5.38517 q^{67} +11.2309 q^{68} -4.87357 q^{69} +0.172098 q^{70} +4.44421 q^{71} +13.3957 q^{72} +14.1548 q^{73} +6.47254 q^{74} +0.946332 q^{75} +34.7839 q^{76} +0.409222 q^{77} +9.14493 q^{78} -9.22352 q^{79} -7.23070 q^{80} +1.74210 q^{81} -16.3453 q^{82} +13.6898 q^{83} +0.287344 q^{84} -2.49729 q^{85} -17.3901 q^{86} +8.03065 q^{87} -38.5809 q^{88} -14.9826 q^{89} -5.36419 q^{90} -0.255967 q^{91} -23.1606 q^{92} +7.30637 q^{93} +21.6245 q^{94} -7.73449 q^{95} -5.39413 q^{96} -8.09855 q^{97} +17.8312 q^{98} -12.7552 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 137 q + 4 q^{2} + 20 q^{3} + 152 q^{4} - 137 q^{5} + 14 q^{6} - 30 q^{7} + 24 q^{8} + 163 q^{9}+O(q^{10}) \) 137 * q + 4 * q^2 + 20 * q^3 + 152 * q^4 - 137 * q^5 + 14 * q^6 - 30 * q^7 + 24 * q^8 + 163 * q^9	\( 137 q + 4 q^{2} + 20 q^{3} + 152 q^{4} - 137 q^{5} + 14 q^{6} - 30 q^{7} + 24 q^{8} + 163 q^{9} - 4 q^{10} + 51 q^{11} + 32 q^{12} - 6 q^{13} + 49 q^{14} - 20 q^{15} + 170 q^{16} + 46 q^{17} + 4 q^{18} + 47 q^{19} - 152 q^{20} + 28 q^{21} - 19 q^{22} + 29 q^{23} + 39 q^{24} + 137 q^{25} + 67 q^{26} + 77 q^{27} - 58 q^{28} + 27 q^{29} - 14 q^{30} + 23 q^{31} + 42 q^{32} + 40 q^{33} + 38 q^{34} + 30 q^{35} + 222 q^{36} - 56 q^{37} + 87 q^{38} + 44 q^{39} - 24 q^{40} + 66 q^{41} + 34 q^{42} + 15 q^{43} + 87 q^{44} - 163 q^{45} + 37 q^{46} + 52 q^{47} + 56 q^{48} + 195 q^{49} + 4 q^{50} + 106 q^{51} - 31 q^{52} + 45 q^{53} + 83 q^{54} - 51 q^{55} + 148 q^{56} + 4 q^{57} - 101 q^{58} + 239 q^{59} - 32 q^{60} + 46 q^{61} + 63 q^{62} - 59 q^{63} + 200 q^{64} + 6 q^{65} + 108 q^{66} - 18 q^{67} + 152 q^{68} + 63 q^{69} - 49 q^{70} + 110 q^{71} + 6 q^{72} - 19 q^{73} + 81 q^{74} + 20 q^{75} + 94 q^{76} + 43 q^{77} - 3 q^{78} + 40 q^{79} - 170 q^{80} + 229 q^{81} + 3 q^{82} + 235 q^{83} + 94 q^{84} - 46 q^{85} + 110 q^{86} + 31 q^{87} - 105 q^{88} + 150 q^{89} - 4 q^{90} + 110 q^{91} + 76 q^{92} + 11 q^{93} + 56 q^{94} - 47 q^{95} + 146 q^{96} + 17 q^{97} + 75 q^{98} + 125 q^{99}+O(q^{100}) \) 137 * q + 4 * q^2 + 20 * q^3 + 152 * q^4 - 137 * q^5 + 14 * q^6 - 30 * q^7 + 24 * q^8 + 163 * q^9 - 4 * q^10 + 51 * q^11 + 32 * q^12 - 6 * q^13 + 49 * q^14 - 20 * q^15 + 170 * q^16 + 46 * q^17 + 4 * q^18 + 47 * q^19 - 152 * q^20 + 28 * q^21 - 19 * q^22 + 29 * q^23 + 39 * q^24 + 137 * q^25 + 67 * q^26 + 77 * q^27 - 58 * q^28 + 27 * q^29 - 14 * q^30 + 23 * q^31 + 42 * q^32 + 40 * q^33 + 38 * q^34 + 30 * q^35 + 222 * q^36 - 56 * q^37 + 87 * q^38 + 44 * q^39 - 24 * q^40 + 66 * q^41 + 34 * q^42 + 15 * q^43 + 87 * q^44 - 163 * q^45 + 37 * q^46 + 52 * q^47 + 56 * q^48 + 195 * q^49 + 4 * q^50 + 106 * q^51 - 31 * q^52 + 45 * q^53 + 83 * q^54 - 51 * q^55 + 148 * q^56 + 4 * q^57 - 101 * q^58 + 239 * q^59 - 32 * q^60 + 46 * q^61 + 63 * q^62 - 59 * q^63 + 200 * q^64 + 6 * q^65 + 108 * q^66 - 18 * q^67 + 152 * q^68 + 63 * q^69 - 49 * q^70 + 110 * q^71 + 6 * q^72 - 19 * q^73 + 81 * q^74 + 20 * q^75 + 94 * q^76 + 43 * q^77 - 3 * q^78 + 40 * q^79 - 170 * q^80 + 229 * q^81 + 3 * q^82 + 235 * q^83 + 94 * q^84 - 46 * q^85 + 110 * q^86 + 31 * q^87 - 105 * q^88 + 150 * q^89 - 4 * q^90 + 110 * q^91 + 76 * q^92 + 11 * q^93 + 56 * q^94 - 47 * q^95 + 146 * q^96 + 17 * q^97 + 75 * q^98 + 125 * q^99

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