LMFDB - Embedded newform 8035.2.a.b.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8035,2,Mod(1,8035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8035, 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("8035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8035 = 5 \cdot 1607 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8035.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:	$64.1597980241$
Analytic rank:	$1$
Dimension:	$114$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	8035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.11941 q^{2} -2.29188 q^{3} +2.49192 q^{4} +1.00000 q^{5} +4.85744 q^{6} +5.02774 q^{7} -1.04258 q^{8} +2.25270 q^{9} +O(q^{10})$	\(q-2.11941 q^{2} -2.29188 q^{3} +2.49192 q^{4} +1.00000 q^{5} +4.85744 q^{6} +5.02774 q^{7} -1.04258 q^{8} +2.25270 q^{9} -2.11941 q^{10} -0.231186 q^{11} -5.71117 q^{12} -1.65306 q^{13} -10.6559 q^{14} -2.29188 q^{15} -2.77418 q^{16} -5.25660 q^{17} -4.77440 q^{18} +3.36492 q^{19} +2.49192 q^{20} -11.5230 q^{21} +0.489979 q^{22} -0.645532 q^{23} +2.38946 q^{24} +1.00000 q^{25} +3.50351 q^{26} +1.71273 q^{27} +12.5287 q^{28} +2.02064 q^{29} +4.85744 q^{30} -5.15678 q^{31} +7.96479 q^{32} +0.529849 q^{33} +11.1409 q^{34} +5.02774 q^{35} +5.61354 q^{36} -0.431387 q^{37} -7.13165 q^{38} +3.78860 q^{39} -1.04258 q^{40} -2.51954 q^{41} +24.4219 q^{42} +6.03045 q^{43} -0.576096 q^{44} +2.25270 q^{45} +1.36815 q^{46} -6.52447 q^{47} +6.35808 q^{48} +18.2781 q^{49} -2.11941 q^{50} +12.0475 q^{51} -4.11928 q^{52} +6.52146 q^{53} -3.62998 q^{54} -0.231186 q^{55} -5.24181 q^{56} -7.71197 q^{57} -4.28257 q^{58} -5.01023 q^{59} -5.71117 q^{60} +2.15347 q^{61} +10.9293 q^{62} +11.3260 q^{63} -11.3323 q^{64} -1.65306 q^{65} -1.12297 q^{66} -4.57050 q^{67} -13.0990 q^{68} +1.47948 q^{69} -10.6559 q^{70} -6.47991 q^{71} -2.34861 q^{72} +4.05265 q^{73} +0.914288 q^{74} -2.29188 q^{75} +8.38510 q^{76} -1.16234 q^{77} -8.02962 q^{78} -3.10894 q^{79} -2.77418 q^{80} -10.6834 q^{81} +5.33996 q^{82} -8.46465 q^{83} -28.7143 q^{84} -5.25660 q^{85} -12.7810 q^{86} -4.63105 q^{87} +0.241029 q^{88} -9.48844 q^{89} -4.77440 q^{90} -8.31114 q^{91} -1.60861 q^{92} +11.8187 q^{93} +13.8281 q^{94} +3.36492 q^{95} -18.2543 q^{96} -2.67900 q^{97} -38.7390 q^{98} -0.520791 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 114 q - 17 q^{2} - 10 q^{3} + 93 q^{4} + 114 q^{5} - 24 q^{6} - 11 q^{7} - 48 q^{8} + 66 q^{9}+O(q^{10}) $ 114 * q - 17 * q^2 - 10 * q^3 + 93 * q^4 + 114 * q^5 - 24 * q^6 - 11 * q^7 - 48 * q^8 + 66 * q^9	\( 114 q - 17 q^{2} - 10 q^{3} + 93 q^{4} + 114 q^{5} - 24 q^{6} - 11 q^{7} - 48 q^{8} + 66 q^{9} - 17 q^{10} - 44 q^{11} - 25 q^{12} - 26 q^{13} - 43 q^{14} - 10 q^{15} + 59 q^{16} - 57 q^{17} - 33 q^{18} - 69 q^{19} + 93 q^{20} - 107 q^{21} - 19 q^{22} - 45 q^{23} - 45 q^{24} + 114 q^{25} - 54 q^{26} - 34 q^{27} - 6 q^{28} - 166 q^{29} - 24 q^{30} - 67 q^{31} - 98 q^{32} - 38 q^{33} - 41 q^{34} - 11 q^{35} - 3 q^{36} - 44 q^{37} - 19 q^{38} - 66 q^{39} - 48 q^{40} - 141 q^{41} + q^{42} - 30 q^{43} - 125 q^{44} + 66 q^{45} - 59 q^{46} - 17 q^{47} - 35 q^{48} - 15 q^{49} - 17 q^{50} - 67 q^{51} - 26 q^{52} - 154 q^{53} - 45 q^{54} - 44 q^{55} - 118 q^{56} - 70 q^{57} + 11 q^{58} - 75 q^{59} - 25 q^{60} - 144 q^{61} - 35 q^{62} - 25 q^{63} + 16 q^{64} - 26 q^{65} - 68 q^{66} - 2 q^{67} - 99 q^{68} - 118 q^{69} - 43 q^{70} - 104 q^{71} - 73 q^{72} - 22 q^{73} - 107 q^{74} - 10 q^{75} - 172 q^{76} - 100 q^{77} - 2 q^{78} - 91 q^{79} + 59 q^{80} - 54 q^{81} + 20 q^{82} - 44 q^{83} - 156 q^{84} - 57 q^{85} - 50 q^{86} + 5 q^{87} - 13 q^{88} - 150 q^{89} - 33 q^{90} - 54 q^{91} - 77 q^{92} - 50 q^{93} - 105 q^{94} - 69 q^{95} - 78 q^{96} - 31 q^{97} - 64 q^{98} - 101 q^{99}+O(q^{100}) \) 114 * q - 17 * q^2 - 10 * q^3 + 93 * q^4 + 114 * q^5 - 24 * q^6 - 11 * q^7 - 48 * q^8 + 66 * q^9 - 17 * q^10 - 44 * q^11 - 25 * q^12 - 26 * q^13 - 43 * q^14 - 10 * q^15 + 59 * q^16 - 57 * q^17 - 33 * q^18 - 69 * q^19 + 93 * q^20 - 107 * q^21 - 19 * q^22 - 45 * q^23 - 45 * q^24 + 114 * q^25 - 54 * q^26 - 34 * q^27 - 6 * q^28 - 166 * q^29 - 24 * q^30 - 67 * q^31 - 98 * q^32 - 38 * q^33 - 41 * q^34 - 11 * q^35 - 3 * q^36 - 44 * q^37 - 19 * q^38 - 66 * q^39 - 48 * q^40 - 141 * q^41 + q^42 - 30 * q^43 - 125 * q^44 + 66 * q^45 - 59 * q^46 - 17 * q^47 - 35 * q^48 - 15 * q^49 - 17 * q^50 - 67 * q^51 - 26 * q^52 - 154 * q^53 - 45 * q^54 - 44 * q^55 - 118 * q^56 - 70 * q^57 + 11 * q^58 - 75 * q^59 - 25 * q^60 - 144 * q^61 - 35 * q^62 - 25 * q^63 + 16 * q^64 - 26 * q^65 - 68 * q^66 - 2 * q^67 - 99 * q^68 - 118 * q^69 - 43 * q^70 - 104 * q^71 - 73 * q^72 - 22 * q^73 - 107 * q^74 - 10 * q^75 - 172 * q^76 - 100 * q^77 - 2 * q^78 - 91 * q^79 + 59 * q^80 - 54 * q^81 + 20 * q^82 - 44 * q^83 - 156 * q^84 - 57 * q^85 - 50 * q^86 + 5 * q^87 - 13 * q^88 - 150 * q^89 - 33 * q^90 - 54 * q^91 - 77 * q^92 - 50 * q^93 - 105 * q^94 - 69 * q^95 - 78 * q^96 - 31 * q^97 - 64 * q^98 - 101 * 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 $

$2$	−2.11941	−1.49865	−0.749326	−	0.662201i	$-0.769622\pi$
$2$	−2.11941	−1.49865	−0.749326	+	0.662201i	$0.769622\pi$
$3$	−2.29188	−1.32322	−0.661608	−	0.749850i	$-0.730126\pi$
$3$	−2.29188	−1.32322	−0.661608	+	0.749850i	$0.730126\pi$
$4$	2.49192	1.24596
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	4.85744	1.98304
$7$	5.02774	1.90031	0.950153	−	0.311784i	$-0.100927\pi$
$7$	5.02774	1.90031	0.950153	+	0.311784i	$0.100927\pi$
$8$	−1.04258	−0.368607
$9$	2.25270	0.750899
$10$	−2.11941	−0.670218
$11$	−0.231186	−0.0697051	−0.0348526	−	0.999392i	$-0.511096\pi$
$11$	−0.231186	−0.0697051	−0.0348526	+	0.999392i	$0.511096\pi$
$12$	−5.71117	−1.64867
$13$	−1.65306	−0.458476	−0.229238	−	0.973370i	$-0.573623\pi$
$13$	−1.65306	−0.458476	−0.229238	+	0.973370i	$0.573623\pi$
$14$	−10.6559	−2.84790
$15$	−2.29188	−0.591760
$16$	−2.77418	−0.693545
$17$	−5.25660	−1.27491	−0.637456	−	0.770487i	$-0.720013\pi$
$17$	−5.25660	−1.27491	−0.637456	+	0.770487i	$0.720013\pi$
$18$	−4.77440	−1.12534
$19$	3.36492	0.771965	0.385982	−	0.922506i	$-0.373863\pi$
$19$	3.36492	0.771965	0.385982	+	0.922506i	$0.373863\pi$
$20$	2.49192	0.557210
$21$	−11.5230	−2.51451
$22$	0.489979	0.104464
$23$	−0.645532	−0.134603	−0.0673013	−	0.997733i	$-0.521439\pi$
$23$	−0.645532	−0.134603	−0.0673013	+	0.997733i	$0.521439\pi$
$24$	2.38946	0.487747
$25$	1.00000	0.200000
$26$	3.50351	0.687096
$27$	1.71273	0.329615
$28$	12.5287	2.36770
$29$	2.02064	0.375223	0.187612	−	0.982243i	$-0.439925\pi$
$29$	2.02064	0.375223	0.187612	+	0.982243i	$0.439925\pi$
$30$	4.85744	0.886842
$31$	−5.15678	−0.926184	−0.463092	−	0.886310i	$-0.653260\pi$
$31$	−5.15678	−0.926184	−0.463092	+	0.886310i	$0.653260\pi$
$32$	7.96479	1.40799
$33$	0.529849	0.0922349
$34$	11.1409	1.91065
$35$	5.02774	0.849843
$36$	5.61354	0.935589
$37$	−0.431387	−0.0709196	−0.0354598	−	0.999371i	$-0.511290\pi$
$37$	−0.431387	−0.0709196	−0.0354598	+	0.999371i	$0.511290\pi$
$38$	−7.13165	−1.15691
$39$	3.78860	0.606662
$40$	−1.04258	−0.164846
$41$	−2.51954	−0.393487	−0.196743	−	0.980455i	$-0.563037\pi$
$41$	−2.51954	−0.393487	−0.196743	+	0.980455i	$0.563037\pi$
$42$	24.4219	3.76838
$43$	6.03045	0.919635	0.459817	−	0.888014i	$-0.347915\pi$
$43$	6.03045	0.919635	0.459817	+	0.888014i	$0.347915\pi$
$44$	−0.576096	−0.0868498
$45$	2.25270	0.335812
$46$	1.36815	0.201723
$47$	−6.52447	−0.951692	−0.475846	−	0.879529i	$-0.657858\pi$
$47$	−6.52447	−0.951692	−0.475846	+	0.879529i	$0.657858\pi$
$48$	6.35808	0.917709
$49$	18.2781	2.61116
$50$	−2.11941	−0.299730
$51$	12.0475	1.68698
$52$	−4.11928	−0.571242
$53$	6.52146	0.895792	0.447896	−	0.894086i	$-0.352173\pi$
$53$	6.52146	0.895792	0.447896	+	0.894086i	$0.352173\pi$
$54$	−3.62998	−0.493978
$55$	−0.231186	−0.0311731
$56$	−5.24181	−0.700467
$57$	−7.71197	−1.02148
$58$	−4.28257	−0.562329
$59$	−5.01023	−0.652277	−0.326138	−	0.945322i	$-0.605748\pi$
$59$	−5.01023	−0.652277	−0.326138	+	0.945322i	$0.605748\pi$
$60$	−5.71117	−0.737309
$61$	2.15347	0.275724	0.137862	−	0.990451i	$-0.455977\pi$
$61$	2.15347	0.275724	0.137862	+	0.990451i	$0.455977\pi$
$62$	10.9293	1.38803
$63$	11.3260	1.42694
$64$	−11.3323	−1.41654
$65$	−1.65306	−0.205037
$66$	−1.12297	−0.138228
$67$	−4.57050	−0.558376	−0.279188	−	0.960236i	$-0.590065\pi$
$67$	−4.57050	−0.558376	−0.279188	+	0.960236i	$0.590065\pi$
$68$	−13.0990	−1.58849
$69$	1.47948	0.178108
$70$	−10.6559	−1.27362
$71$	−6.47991	−0.769024	−0.384512	−	0.923120i	$-0.625630\pi$
$71$	−6.47991	−0.769024	−0.384512	+	0.923120i	$0.625630\pi$
$72$	−2.34861	−0.276787
$73$	4.05265	0.474327	0.237164	−	0.971470i	$-0.423782\pi$
$73$	4.05265	0.474327	0.237164	+	0.971470i	$0.423782\pi$
$74$	0.914288	0.106284
$75$	−2.29188	−0.264643
$76$	8.38510	0.961837
$77$	−1.16234	−0.132461
$78$	−8.02962	−0.909175
$79$	−3.10894	−0.349783	−0.174892	−	0.984588i	$-0.555957\pi$
$79$	−3.10894	−0.349783	−0.174892	+	0.984588i	$0.555957\pi$
$80$	−2.77418	−0.310163
$81$	−10.6834	−1.18705
$82$	5.33996	0.589700
$83$	−8.46465	−0.929116	−0.464558	−	0.885543i	$-0.653787\pi$
$83$	−8.46465	−0.929116	−0.464558	+	0.885543i	$0.653787\pi$
$84$	−28.7143	−3.13298
$85$	−5.25660	−0.570158
$86$	−12.7810	−1.37821
$87$	−4.63105	−0.496501
$88$	0.241029	0.0256938
$89$	−9.48844	−1.00577	−0.502886	−	0.864353i	$-0.667729\pi$
$89$	−9.48844	−1.00577	−0.502886	+	0.864353i	$0.667729\pi$
$90$	−4.77440	−0.503266
$91$	−8.31114	−0.871244
$92$	−1.60861	−0.167709
$93$	11.8187	1.22554
$94$	13.8281	1.42626
$95$	3.36492	0.345233
$96$	−18.2543	−1.86307
$97$	−2.67900	−0.272012	−0.136006	−	0.990708i	$-0.543427\pi$
$97$	−2.67900	−0.272012	−0.136006	+	0.990708i	$0.543427\pi$
$98$	−38.7390	−3.91323
$99$	−0.520791	−0.0523415
$100$	2.49192	0.249192
$101$	−11.5059	−1.14488	−0.572438	−	0.819948i	$-0.694002\pi$
$101$	−11.5059	−1.14488	−0.572438	+	0.819948i	$0.694002\pi$
$102$	−25.5336	−2.52820
$103$	5.08986	0.501519	0.250759	−	0.968049i	$-0.419320\pi$
$103$	5.08986	0.501519	0.250759	+	0.968049i	$0.419320\pi$
$104$	1.72344	0.168997
$105$	−11.5230	−1.12452
$106$	−13.8217	−1.34248
$107$	7.76984	0.751138	0.375569	−	0.926794i	$-0.377447\pi$
$107$	7.76984	0.751138	0.375569	+	0.926794i	$0.377447\pi$
$108$	4.26798	0.410686
$109$	7.07226	0.677399	0.338700	−	0.940895i	$-0.390013\pi$
$109$	7.07226	0.677399	0.338700	+	0.940895i	$0.390013\pi$
$110$	0.489979	0.0467176
$111$	0.988686	0.0938419
$112$	−13.9478	−1.31795
$113$	10.0980	0.949941	0.474970	−	0.880002i	$-0.342459\pi$
$113$	10.0980	0.949941	0.474970	+	0.880002i	$0.342459\pi$
$114$	16.3449	1.53084
$115$	−0.645532	−0.0601961
$116$	5.03527	0.467513
$117$	−3.72384	−0.344269
$118$	10.6188	0.977536
$119$	−26.4288	−2.42272
$120$	2.38946	0.218127
$121$	−10.9466	−0.995141
$122$	−4.56410	−0.413214
$123$	5.77448	0.520668
$124$	−12.8503	−1.15399
$125$	1.00000	0.0894427
$126$	−24.0044	−2.13848
$127$	−21.9348	−1.94640	−0.973198	−	0.229971i	$-0.926137\pi$
$127$	−21.9348	−1.94640	−0.973198	+	0.229971i	$0.926137\pi$
$128$	8.08835	0.714915
$129$	−13.8210	−1.21687
$130$	3.50351	0.307279
$131$	5.33356	0.465995	0.232998	−	0.972477i	$-0.425147\pi$
$131$	5.33356	0.465995	0.232998	+	0.972477i	$0.425147\pi$
$132$	1.32034	0.114921
$133$	16.9179	1.46697
$134$	9.68679	0.836812
$135$	1.71273	0.147408
$136$	5.48042	0.469942
$137$	9.30539	0.795013	0.397507	−	0.917599i	$-0.369876\pi$
$137$	9.30539	0.795013	0.397507	+	0.917599i	$0.369876\pi$
$138$	−3.13563	−0.266922
$139$	−9.19402	−0.779827	−0.389913	−	0.920852i	$-0.627495\pi$
$139$	−9.19402	−0.779827	−0.389913	+	0.920852i	$0.627495\pi$
$140$	12.5287	1.05887
$141$	14.9533	1.25929
$142$	13.7336	1.15250
$143$	0.382163	0.0319581
$144$	−6.24938	−0.520782
$145$	2.02064	0.167805
$146$	−8.58925	−0.710852
$147$	−41.8912	−3.45513
$148$	−1.07498	−0.0883629
$149$	−13.9041	−1.13907	−0.569536	−	0.821967i	$-0.692877\pi$
$149$	−13.9041	−1.13907	−0.569536	+	0.821967i	$0.692877\pi$
$150$	4.85744	0.396608
$151$	18.9790	1.54449	0.772244	−	0.635326i	$-0.219134\pi$
$151$	18.9790	1.54449	0.772244	+	0.635326i	$0.219134\pi$
$152$	−3.50819	−0.284552
$153$	−11.8415	−0.957330
$154$	2.46348	0.198513
$155$	−5.15678	−0.414202
$156$	9.44089	0.755876
$157$	15.5029	1.23727	0.618634	−	0.785680i	$-0.287687\pi$
$157$	15.5029	1.23727	0.618634	+	0.785680i	$0.287687\pi$
$158$	6.58913	0.524203
$159$	−14.9464	−1.18533
$160$	7.96479	0.629672
$161$	−3.24556	−0.255786
$162$	22.6427	1.77898
$163$	−10.1489	−0.794922	−0.397461	−	0.917619i	$-0.630109\pi$
$163$	−10.1489	−0.794922	−0.397461	+	0.917619i	$0.630109\pi$
$164$	−6.27850	−0.490268
$165$	0.529849	0.0412487
$166$	17.9401	1.39242
$167$	−2.61088	−0.202036	−0.101018	−	0.994885i	$-0.532210\pi$
$167$	−2.61088	−0.202036	−0.101018	+	0.994885i	$0.532210\pi$
$168$	12.0136	0.926868
$169$	−10.2674	−0.789800
$170$	11.1409	0.854469
$171$	7.58014	0.579667
$172$	15.0274	1.14583
$173$	−22.8708	−1.73883	−0.869417	−	0.494079i	$-0.835505\pi$
$173$	−22.8708	−1.73883	−0.869417	+	0.494079i	$0.835505\pi$
$174$	9.81512	0.744083
$175$	5.02774	0.380061
$176$	0.641351	0.0483436
$177$	11.4828	0.863102
$178$	20.1099	1.50730
$179$	−18.7062	−1.39817	−0.699083	−	0.715041i	$-0.746408\pi$
$179$	−18.7062	−1.39817	−0.699083	+	0.715041i	$0.746408\pi$
$180$	5.61354	0.418408
$181$	−5.69500	−0.423306	−0.211653	−	0.977345i	$-0.567885\pi$
$181$	−5.69500	−0.423306	−0.211653	+	0.977345i	$0.567885\pi$
$182$	17.6147	1.30569
$183$	−4.93549	−0.364842
$184$	0.673018	0.0496155
$185$	−0.431387	−0.0317162
$186$	−25.0487	−1.83666
$187$	1.21525	0.0888679
$188$	−16.2585	−1.18577
$189$	8.61114	0.626368
$190$	−7.13165	−0.517385
$191$	12.7152	0.920038	0.460019	−	0.887909i	$-0.347843\pi$
$191$	12.7152	0.920038	0.460019	+	0.887909i	$0.347843\pi$
$192$	25.9723	1.87439
$193$	9.19791	0.662080	0.331040	−	0.943617i	$-0.392600\pi$
$193$	9.19791	0.662080	0.331040	+	0.943617i	$0.392600\pi$
$194$	5.67792	0.407651
$195$	3.78860	0.271307
$196$	45.5476	3.25340
$197$	4.36748	0.311170	0.155585	−	0.987823i	$-0.450274\pi$
$197$	4.36748	0.311170	0.155585	+	0.987823i	$0.450274\pi$
$198$	1.10377	0.0784417
$199$	−10.6592	−0.755611	−0.377806	−	0.925885i	$-0.623321\pi$
$199$	−10.6592	−0.755611	−0.377806	+	0.925885i	$0.623321\pi$
$200$	−1.04258	−0.0737215
$201$	10.4750	0.738852
$202$	24.3857	1.71577
$203$	10.1592	0.713039
$204$	30.0213	2.10191
$205$	−2.51954	−0.175973
$206$	−10.7875	−0.751603
$207$	−1.45419	−0.101073
$208$	4.58588	0.317973
$209$	−0.777921	−0.0538099
$210$	24.4219	1.68527
$211$	−24.4316	−1.68194	−0.840972	−	0.541079i	$-0.818016\pi$
$211$	−24.4316	−1.68194	−0.840972	+	0.541079i	$0.818016\pi$
$212$	16.2510	1.11612
$213$	14.8512	1.01758
$214$	−16.4675	−1.12570
$215$	6.03045	0.411273
$216$	−1.78565	−0.121498
$217$	−25.9269	−1.76003
$218$	−14.9890	−1.01519
$219$	−9.28818	−0.627637
$220$	−0.576096	−0.0388404
$221$	8.68946	0.584516
$222$	−2.09543	−0.140636
$223$	−1.89638	−0.126991	−0.0634954	−	0.997982i	$-0.520225\pi$
$223$	−1.89638	−0.126991	−0.0634954	+	0.997982i	$0.520225\pi$
$224$	40.0449	2.67561
$225$	2.25270	0.150180
$226$	−21.4019	−1.42363
$227$	14.1193	0.937134	0.468567	−	0.883428i	$-0.344770\pi$
$227$	14.1193	0.937134	0.468567	+	0.883428i	$0.344770\pi$
$228$	−19.2176	−1.27272
$229$	−20.6926	−1.36741	−0.683703	−	0.729761i	$-0.739631\pi$
$229$	−20.6926	−1.36741	−0.683703	+	0.729761i	$0.739631\pi$
$230$	1.36815	0.0902131
$231$	2.66394	0.175275
$232$	−2.10668	−0.138310
$233$	8.02440	0.525696	0.262848	−	0.964837i	$-0.415338\pi$
$233$	8.02440	0.525696	0.262848	+	0.964837i	$0.415338\pi$
$234$	7.89235	0.515939
$235$	−6.52447	−0.425610
$236$	−12.4851	−0.812710
$237$	7.12530	0.462838
$238$	56.0136	3.63082
$239$	−25.2468	−1.63308	−0.816539	−	0.577290i	$-0.804110\pi$
$239$	−25.2468	−1.63308	−0.816539	+	0.577290i	$0.804110\pi$
$240$	6.35808	0.410412
$241$	25.1961	1.62302	0.811512	−	0.584335i	$-0.198645\pi$
$241$	25.1961	1.62302	0.811512	+	0.584335i	$0.198645\pi$
$242$	23.2003	1.49137
$243$	19.3470	1.24111
$244$	5.36628	0.343541
$245$	18.2781	1.16775
$246$	−12.2385	−0.780300
$247$	−5.56240	−0.353927
$248$	5.37635	0.341398
$249$	19.3999	1.22942
$250$	−2.11941	−0.134044
$251$	25.9699	1.63921	0.819603	−	0.572931i	$-0.194194\pi$
$251$	25.9699	1.63921	0.819603	+	0.572931i	$0.194194\pi$
$252$	28.2234	1.77791
$253$	0.149238	0.00938250
$254$	46.4888	2.91697
$255$	12.0475	0.754442
$256$	5.52213	0.345133
$257$	−7.73424	−0.482449	−0.241224	−	0.970469i	$-0.577549\pi$
$257$	−7.73424	−0.482449	−0.241224	+	0.970469i	$0.577549\pi$
$258$	29.2925	1.82367
$259$	−2.16890	−0.134769
$260$	−4.11928	−0.255467
$261$	4.55189	0.281755
$262$	−11.3040	−0.698365
$263$	−10.3640	−0.639074	−0.319537	−	0.947574i	$-0.603527\pi$
$263$	−10.3640	−0.639074	−0.319537	+	0.947574i	$0.603527\pi$
$264$	−0.552410	−0.0339985
$265$	6.52146	0.400610
$266$	−35.8561	−2.19848
$267$	21.7463	1.33085
$268$	−11.3893	−0.695714
$269$	9.91829	0.604729	0.302364	−	0.953192i	$-0.402224\pi$
$269$	9.91829	0.604729	0.302364	+	0.953192i	$0.402224\pi$
$270$	−3.62998	−0.220914
$271$	9.00391	0.546948	0.273474	−	0.961879i	$-0.411827\pi$
$271$	9.00391	0.546948	0.273474	+	0.961879i	$0.411827\pi$
$272$	14.5827	0.884209
$273$	19.0481	1.15284
$274$	−19.7220	−1.19145
$275$	−0.231186	−0.0139410
$276$	3.68674	0.221916
$277$	26.2561	1.57757	0.788787	−	0.614667i	$-0.210709\pi$
$277$	26.2561	1.57757	0.788787	+	0.614667i	$0.210709\pi$
$278$	19.4859	1.16869
$279$	−11.6167	−0.695471
$280$	−5.24181	−0.313258
$281$	−16.2231	−0.967788	−0.483894	−	0.875127i	$-0.660778\pi$
$281$	−16.2231	−0.967788	−0.483894	+	0.875127i	$0.660778\pi$
$282$	−31.6922	−1.88724
$283$	28.1886	1.67564	0.837818	−	0.545949i	$-0.183831\pi$
$283$	28.1886	1.67564	0.837818	+	0.545949i	$0.183831\pi$
$284$	−16.1474	−0.958173
$285$	−7.71197	−0.456818
$286$	−0.809963	−0.0478941
$287$	−12.6676	−0.747745
$288$	17.9423	1.05726
$289$	10.6318	0.625401
$290$	−4.28257	−0.251481
$291$	6.13995	0.359930
$292$	10.0989	0.590992
$293$	−11.7627	−0.687184	−0.343592	−	0.939119i	$-0.611644\pi$
$293$	−11.7627	−0.687184	−0.343592	+	0.939119i	$0.611644\pi$
$294$	88.7849	5.17804
$295$	−5.01023	−0.291707
$296$	0.449755	0.0261415
$297$	−0.395958	−0.0229758
$298$	29.4686	1.70707
$299$	1.06710	0.0617120
$300$	−5.71117	−0.329734
$301$	30.3195	1.74759
$302$	−40.2244	−2.31465
$303$	26.3700	1.51492
$304$	−9.33488	−0.535392
$305$	2.15347	0.123308
$306$	25.0971	1.43470
$307$	29.9550	1.70962	0.854811	−	0.518939i	$-0.173673\pi$
$307$	29.9550	1.70962	0.854811	+	0.518939i	$0.173673\pi$
$308$	−2.89646	−0.165041
$309$	−11.6653	−0.663617
$310$	10.9293	0.620745
$311$	−5.16659	−0.292970	−0.146485	−	0.989213i	$-0.546796\pi$
$311$	−5.16659	−0.292970	−0.146485	+	0.989213i	$0.546796\pi$
$312$	−3.94992	−0.223620
$313$	8.76738	0.495562	0.247781	−	0.968816i	$-0.420299\pi$
$313$	8.76738	0.495562	0.247781	+	0.968816i	$0.420299\pi$
$314$	−32.8571	−1.85423
$315$	11.3260	0.638146
$316$	−7.74722	−0.435815
$317$	−26.1157	−1.46680	−0.733401	−	0.679796i	$-0.762068\pi$
$317$	−26.1157	−1.46680	−0.733401	+	0.679796i	$0.762068\pi$
$318$	31.6776	1.77639
$319$	−0.467143	−0.0261550
$320$	−11.3323	−0.633497
$321$	−17.8075	−0.993918
$322$	6.87869	0.383335
$323$	−17.6880	−0.984187
$324$	−26.6223	−1.47902
$325$	−1.65306	−0.0916951
$326$	21.5097	1.19131
$327$	−16.2087	−0.896345
$328$	2.62682	0.145042
$329$	−32.8033	−1.80851
$330$	−1.12297	−0.0618175
$331$	−27.5326	−1.51333	−0.756663	−	0.653805i	$-0.773172\pi$
$331$	−27.5326	−1.51333	−0.756663	+	0.653805i	$0.773172\pi$
$332$	−21.0932	−1.15764
$333$	−0.971784	−0.0532534
$334$	5.53355	0.302782
$335$	−4.57050	−0.249713
$336$	31.9667	1.74393
$337$	−20.6364	−1.12414	−0.562068	−	0.827091i	$-0.689994\pi$
$337$	−20.6364	−1.12414	−0.562068	+	0.827091i	$0.689994\pi$
$338$	21.7609	1.18364
$339$	−23.1434	−1.25698
$340$	−13.0990	−0.710394
$341$	1.19217	0.0645598
$342$	−16.0655	−0.868720
$343$	56.7035	3.06170
$344$	−6.28722	−0.338984
$345$	1.47948	0.0796524
$346$	48.4727	2.60591
$347$	−12.2013	−0.655000	−0.327500	−	0.944851i	$-0.606206\pi$
$347$	−12.2013	−0.655000	−0.327500	+	0.944851i	$0.606206\pi$
$348$	−11.5402	−0.618620
$349$	4.74458	0.253971	0.126986	−	0.991905i	$-0.459470\pi$
$349$	4.74458	0.253971	0.126986	+	0.991905i	$0.459470\pi$
$350$	−10.6559	−0.569580
$351$	−2.83124	−0.151120
$352$	−1.84135	−0.0981441
$353$	20.0171	1.06540	0.532701	−	0.846304i	$-0.321177\pi$
$353$	20.0171	1.06540	0.532701	+	0.846304i	$0.321177\pi$
$354$	−24.3369	−1.29349
$355$	−6.47991	−0.343918
$356$	−23.6444	−1.25315
$357$	60.5715	3.20578
$358$	39.6461	2.09536
$359$	3.49378	0.184395	0.0921974	−	0.995741i	$-0.470611\pi$
$359$	3.49378	0.184395	0.0921974	+	0.995741i	$0.470611\pi$
$360$	−2.34861	−0.123783
$361$	−7.67734	−0.404070
$362$	12.0701	0.634388
$363$	25.0881	1.31679
$364$	−20.7107	−1.08553
$365$	4.05265	0.212126
$366$	10.4604	0.546772
$367$	4.43798	0.231661	0.115830	−	0.993269i	$-0.463047\pi$
$367$	4.43798	0.231661	0.115830	+	0.993269i	$0.463047\pi$
$368$	1.79082	0.0933530
$369$	−5.67577	−0.295469
$370$	0.914288	0.0475316
$371$	32.7882	1.70228
$372$	29.4512	1.52697
$373$	−1.42465	−0.0737657	−0.0368829	−	0.999320i	$-0.511743\pi$
$373$	−1.42465	−0.0737657	−0.0368829	+	0.999320i	$0.511743\pi$
$374$	−2.57562	−0.133182
$375$	−2.29188	−0.118352
$376$	6.80228	0.350801
$377$	−3.34023	−0.172031
$378$	−18.2506	−0.938709
$379$	−16.5715	−0.851220	−0.425610	−	0.904907i	$-0.639940\pi$
$379$	−16.5715	−0.851220	−0.425610	+	0.904907i	$0.639940\pi$
$380$	8.38510	0.430146
$381$	50.2718	2.57550
$382$	−26.9487	−1.37882
$383$	−2.21075	−0.112964	−0.0564821	−	0.998404i	$-0.517988\pi$
$383$	−2.21075	−0.112964	−0.0564821	+	0.998404i	$0.517988\pi$
$384$	−18.5375	−0.945987
$385$	−1.16234	−0.0592384
$386$	−19.4942	−0.992228
$387$	13.5848	0.690553
$388$	−6.67586	−0.338915
$389$	−25.3620	−1.28590	−0.642952	−	0.765907i	$-0.722290\pi$
$389$	−25.3620	−1.28590	−0.642952	+	0.765907i	$0.722290\pi$
$390$	−8.02962	−0.406596
$391$	3.39330	0.171607
$392$	−19.0564	−0.962494
$393$	−12.2239	−0.616612
$394$	−9.25650	−0.466336
$395$	−3.10894	−0.156428
$396$	−1.29777	−0.0652154
$397$	13.3667	0.670858	0.335429	−	0.942066i	$-0.391119\pi$
$397$	13.3667	0.670858	0.335429	+	0.942066i	$0.391119\pi$
$398$	22.5913	1.13240
$399$	−38.7738	−1.94112
$400$	−2.77418	−0.138709
$401$	−14.4772	−0.722957	−0.361479	−	0.932380i	$-0.617728\pi$
$401$	−14.4772	−0.722957	−0.361479	+	0.932380i	$0.617728\pi$
$402$	−22.2009	−1.10728
$403$	8.52445	0.424633
$404$	−28.6717	−1.42647
$405$	−10.6834	−0.530865
$406$	−21.5316	−1.06860
$407$	0.0997306	0.00494346
$408$	−12.5604	−0.621834
$409$	32.0130	1.58294	0.791470	−	0.611209i	$-0.209316\pi$
$409$	32.0130	1.58294	0.791470	+	0.611209i	$0.209316\pi$
$410$	5.33996	0.263722
$411$	−21.3268	−1.05197
$412$	12.6835	0.624872
$413$	−25.1901	−1.23953
$414$	3.08202	0.151473
$415$	−8.46465	−0.415513
$416$	−13.1663	−0.645529
$417$	21.0716	1.03188
$418$	1.64874	0.0806424
$419$	−1.34917	−0.0659111	−0.0329555	−	0.999457i	$-0.510492\pi$
$419$	−1.34917	−0.0659111	−0.0329555	+	0.999457i	$0.510492\pi$
$420$	−28.7143	−1.40111
$421$	−19.0637	−0.929109	−0.464555	−	0.885544i	$-0.653786\pi$
$421$	−19.0637	−0.929109	−0.464555	+	0.885544i	$0.653786\pi$
$422$	51.7808	2.52065
$423$	−14.6977	−0.714625
$424$	−6.79914	−0.330196
$425$	−5.25660	−0.254982
$426$	−31.4758	−1.52501
$427$	10.8271	0.523960
$428$	19.3618	0.935888
$429$	−0.875871	−0.0422875
$430$	−12.7810	−0.616356
$431$	−13.0164	−0.626979	−0.313490	−	0.949592i	$-0.601498\pi$
$431$	−13.0164	−0.626979	−0.313490	+	0.949592i	$0.601498\pi$
$432$	−4.75141	−0.228602
$433$	3.86183	0.185588	0.0927938	−	0.995685i	$-0.470420\pi$
$433$	3.86183	0.185588	0.0927938	+	0.995685i	$0.470420\pi$
$434$	54.9499	2.63768
$435$	−4.63105	−0.222042
$436$	17.6235	0.844012
$437$	−2.17216	−0.103909
$438$	19.6855	0.940610
$439$	−10.0592	−0.480100	−0.240050	−	0.970761i	$-0.577164\pi$
$439$	−10.0592	−0.480100	−0.240050	+	0.970761i	$0.577164\pi$
$440$	0.241029	0.0114906
$441$	41.1751	1.96072
$442$	−18.4166	−0.875986
$443$	−35.1430	−1.66970	−0.834848	−	0.550481i	$-0.814444\pi$
$443$	−35.1430	−1.66970	−0.834848	+	0.550481i	$0.814444\pi$
$444$	2.46372	0.116923
$445$	−9.48844	−0.449795
$446$	4.01921	0.190315
$447$	31.8666	1.50724
$448$	−56.9760	−2.69186
$449$	5.00191	0.236055	0.118027	−	0.993010i	$-0.462343\pi$
$449$	5.00191	0.236055	0.118027	+	0.993010i	$0.462343\pi$
$450$	−4.77440	−0.225067
$451$	0.582483	0.0274280
$452$	25.1634	1.18359
$453$	−43.4975	−2.04369
$454$	−29.9248	−1.40444
$455$	−8.31114	−0.389632
$456$	8.04034	0.376523
$457$	−2.40650	−0.112571	−0.0562856	−	0.998415i	$-0.517926\pi$
$457$	−2.40650	−0.112571	−0.0562856	+	0.998415i	$0.517926\pi$
$458$	43.8562	2.04927
$459$	−9.00312	−0.420230
$460$	−1.60861	−0.0750019
$461$	−34.5833	−1.61070	−0.805352	−	0.592797i	$-0.798024\pi$
$461$	−34.5833	−1.61070	−0.805352	+	0.592797i	$0.798024\pi$
$462$	−5.64600	−0.262676
$463$	12.2922	0.571269	0.285635	−	0.958339i	$-0.407796\pi$
$463$	12.2922	0.571269	0.285635	+	0.958339i	$0.407796\pi$
$464$	−5.60562	−0.260234
$465$	11.8187	0.548079
$466$	−17.0070	−0.787836
$467$	−12.2822	−0.568354	−0.284177	−	0.958772i	$-0.591720\pi$
$467$	−12.2822	−0.568354	−0.284177	+	0.958772i	$0.591720\pi$
$468$	−9.27950	−0.428945
$469$	−22.9793	−1.06109
$470$	13.8281	0.637841
$471$	−35.5308	−1.63717
$472$	5.22356	0.240434
$473$	−1.39415	−0.0641033
$474$	−15.1015	−0.693634
$475$	3.36492	0.154393
$476$	−65.8584	−3.01861
$477$	14.6909	0.672649
$478$	53.5084	2.44742
$479$	11.2447	0.513783	0.256892	−	0.966440i	$-0.417302\pi$
$479$	11.2447	0.513783	0.256892	+	0.966440i	$0.417302\pi$
$480$	−18.2543	−0.833192
$481$	0.713108	0.0325149
$482$	−53.4010	−2.43235
$483$	7.43843	0.338460
$484$	−27.2779	−1.23991
$485$	−2.67900	−0.121647
$486$	−41.0042	−1.85999
$487$	−8.57149	−0.388411	−0.194206	−	0.980961i	$-0.562213\pi$
$487$	−8.57149	−0.388411	−0.194206	+	0.980961i	$0.562213\pi$
$488$	−2.24517	−0.101634
$489$	23.2600	1.05185
$490$	−38.7390	−1.75005
$491$	4.83028	0.217987	0.108994	−	0.994042i	$-0.465237\pi$
$491$	4.83028	0.217987	0.108994	+	0.994042i	$0.465237\pi$
$492$	14.3895	0.648731
$493$	−10.6217	−0.478377
$494$	11.7890	0.530414
$495$	−0.520791	−0.0234078
$496$	14.3058	0.642350
$497$	−32.5793	−1.46138
$498$	−41.1165	−1.84247
$499$	−31.6396	−1.41638	−0.708192	−	0.706020i	$-0.750489\pi$
$499$	−31.6396	−1.41638	−0.708192	+	0.706020i	$0.750489\pi$
$500$	2.49192	0.111442
$501$	5.98382	0.267337
$502$	−55.0410	−2.45660
$503$	30.3895	1.35500	0.677500	−	0.735523i	$-0.263063\pi$
$503$	30.3895	1.35500	0.677500	+	0.735523i	$0.263063\pi$
$504$	−11.8082	−0.525980
$505$	−11.5059	−0.512004
$506$	−0.316297	−0.0140611
$507$	23.5316	1.04508
$508$	−54.6596	−2.42513
$509$	16.4492	0.729098	0.364549	−	0.931184i	$-0.381223\pi$
$509$	16.4492	0.729098	0.364549	+	0.931184i	$0.381223\pi$
$510$	−25.5336	−1.13065
$511$	20.3757	0.901367
$512$	−27.8804	−1.23215
$513$	5.76319	0.254451
$514$	16.3921	0.723023
$515$	5.08986	0.224286
$516$	−34.4409	−1.51618
$517$	1.50837	0.0663378
$518$	4.59680	0.201972
$519$	52.4170	2.30085
$520$	1.72344	0.0755780
$521$	−2.59459	−0.113671	−0.0568355	−	0.998384i	$-0.518101\pi$
$521$	−2.59459	−0.113671	−0.0568355	+	0.998384i	$0.518101\pi$
$522$	−9.64733	−0.422252
$523$	20.6817	0.904347	0.452174	−	0.891930i	$-0.350649\pi$
$523$	20.6817	0.904347	0.452174	+	0.891930i	$0.350649\pi$
$524$	13.2908	0.580611
$525$	−11.5230	−0.502903
$526$	21.9657	0.957749
$527$	27.1071	1.18080
$528$	−1.46990	−0.0639690
$529$	−22.5833	−0.981882
$530$	−13.8217	−0.600376
$531$	−11.2865	−0.489794
$532$	42.1581	1.82778
$533$	4.16495	0.180404
$534$	−46.0895	−1.99449
$535$	7.76984	0.335919
$536$	4.76511	0.205822
$537$	42.8722	1.85007
$538$	−21.0210	−0.906278
$539$	−4.22565	−0.182011
$540$	4.26798	0.183664
$541$	−22.1520	−0.952390	−0.476195	−	0.879340i	$-0.657984\pi$
$541$	−22.1520	−0.952390	−0.476195	+	0.879340i	$0.657984\pi$
$542$	−19.0830	−0.819686
$543$	13.0522	0.560125
$544$	−41.8677	−1.79506
$545$	7.07226	0.302942
$546$	−40.3708	−1.72771
$547$	−15.8819	−0.679063	−0.339531	−	0.940595i	$-0.610268\pi$
$547$	−15.8819	−0.679063	−0.339531	+	0.940595i	$0.610268\pi$
$548$	23.1883	0.990554
$549$	4.85112	0.207041
$550$	0.489979	0.0208928
$551$	6.79928	0.289659
$552$	−1.54247	−0.0656520
$553$	−15.6309	−0.664695
$554$	−55.6475	−2.36424
$555$	0.988686	0.0419674
$556$	−22.9108	−0.971632
$557$	−21.6932	−0.919169	−0.459585	−	0.888134i	$-0.652002\pi$
$557$	−21.6932	−0.919169	−0.459585	+	0.888134i	$0.652002\pi$
$558$	24.6205	1.04227
$559$	−9.96868	−0.421630
$560$	−13.9478	−0.589404
$561$	−2.78520	−0.117591
$562$	34.3835	1.45038
$563$	−43.9868	−1.85382	−0.926911	−	0.375282i	$-0.877546\pi$
$563$	−43.9868	−1.85382	−0.926911	+	0.375282i	$0.877546\pi$
$564$	37.2624	1.56903
$565$	10.0980	0.424826
$566$	−59.7433	−2.51120
$567$	−53.7136	−2.25576
$568$	6.75582	0.283468
$569$	−3.49017	−0.146316	−0.0731578	−	0.997320i	$-0.523308\pi$
$569$	−3.49017	−0.146316	−0.0731578	+	0.997320i	$0.523308\pi$
$570$	16.3449	0.684611
$571$	40.3344	1.68794	0.843972	−	0.536388i	$-0.180212\pi$
$571$	40.3344	1.68794	0.843972	+	0.536388i	$0.180212\pi$
$572$	0.952320	0.0398185
$573$	−29.1416	−1.21741
$574$	26.8479	1.12061
$575$	−0.645532	−0.0269205
$576$	−25.5283	−1.06368
$577$	40.7402	1.69604	0.848018	−	0.529968i	$-0.177796\pi$
$577$	40.7402	1.69604	0.848018	+	0.529968i	$0.177796\pi$
$578$	−22.5332	−0.937258
$579$	−21.0805	−0.876075
$580$	5.03527	0.209078
$581$	−42.5580	−1.76560
$582$	−13.0131	−0.539410
$583$	−1.50767	−0.0624413
$584$	−4.22521	−0.174841
$585$	−3.72384	−0.153962
$586$	24.9300	1.02985
$587$	36.1181	1.49075	0.745377	−	0.666643i	$-0.232269\pi$
$587$	36.1181	1.49075	0.745377	+	0.666643i	$0.232269\pi$
$588$	−104.390	−4.30495
$589$	−17.3521	−0.714982
$590$	10.6188	0.437167
$591$	−10.0097	−0.411745
$592$	1.19675	0.0491859
$593$	−4.53601	−0.186272	−0.0931358	−	0.995653i	$-0.529689\pi$
$593$	−4.53601	−0.186272	−0.0931358	+	0.995653i	$0.529689\pi$
$594$	0.839200	0.0344328
$595$	−26.4288	−1.08347
$596$	−34.6480	−1.41924
$597$	24.4296	0.999837
$598$	−2.26163	−0.0924849
$599$	15.1251	0.617996	0.308998	−	0.951063i	$-0.400006\pi$
$599$	15.1251	0.617996	0.308998	+	0.951063i	$0.400006\pi$
$600$	2.38946	0.0975494
$601$	16.6366	0.678620	0.339310	−	0.940675i	$-0.389807\pi$
$601$	16.6366	0.678620	0.339310	+	0.940675i	$0.389807\pi$
$602$	−64.2596	−2.61903
$603$	−10.2960	−0.419284
$604$	47.2941	1.92437
$605$	−10.9466	−0.445041
$606$	−55.8890	−2.27034
$607$	−19.6411	−0.797209	−0.398604	−	0.917123i	$-0.630505\pi$
$607$	−19.6411	−0.797209	−0.398604	+	0.917123i	$0.630505\pi$
$608$	26.8009	1.08692
$609$	−23.2837	−0.943504
$610$	−4.56410	−0.184795
$611$	10.7853	0.436328
$612$	−29.5081	−1.19279
$613$	−8.68534	−0.350798	−0.175399	−	0.984497i	$-0.556121\pi$
$613$	−8.68534	−0.350798	−0.175399	+	0.984497i	$0.556121\pi$
$614$	−63.4871	−2.56213
$615$	5.77448	0.232850
$616$	1.21183	0.0488261
$617$	32.5715	1.31128	0.655640	−	0.755074i	$-0.272399\pi$
$617$	32.5715	1.31128	0.655640	+	0.755074i	$0.272399\pi$
$618$	24.7237	0.994532
$619$	29.3154	1.17829	0.589143	−	0.808029i	$-0.299466\pi$
$619$	29.3154	1.17829	0.589143	+	0.808029i	$0.299466\pi$
$620$	−12.8503	−0.516079
$621$	−1.10562	−0.0443670
$622$	10.9501	0.439061
$623$	−47.7054	−1.91128
$624$	−10.5103	−0.420747
$625$	1.00000	0.0400000
$626$	−18.5817	−0.742675
$627$	1.78290	0.0712021
$628$	38.6320	1.54158
$629$	2.26763	0.0904162
$630$	−24.0044	−0.956359
$631$	−18.4773	−0.735569	−0.367785	−	0.929911i	$-0.619884\pi$
$631$	−18.4773	−0.735569	−0.367785	+	0.929911i	$0.619884\pi$
$632$	3.24132	0.128933
$633$	55.9943	2.22557
$634$	55.3499	2.19823
$635$	−21.9348	−0.870454
$636$	−37.2452	−1.47687
$637$	−30.2148	−1.19715
$638$	0.990070	0.0391972
$639$	−14.5973	−0.577459
$640$	8.08835	0.319720
$641$	17.4412	0.688886	0.344443	−	0.938807i	$-0.388068\pi$
$641$	17.4412	0.688886	0.344443	+	0.938807i	$0.388068\pi$
$642$	37.7415	1.48954
$643$	6.76002	0.266589	0.133295	−	0.991076i	$-0.457444\pi$
$643$	6.76002	0.266589	0.133295	+	0.991076i	$0.457444\pi$
$644$	−8.08768	−0.318699
$645$	−13.8210	−0.544203
$646$	37.4882	1.47495
$647$	33.7704	1.32765	0.663825	−	0.747888i	$-0.268932\pi$
$647$	33.7704	1.32765	0.663825	+	0.747888i	$0.268932\pi$
$648$	11.1383	0.437555
$649$	1.15829	0.0454670
$650$	3.50351	0.137419
$651$	59.4213	2.32890
$652$	−25.2902	−0.990441
$653$	7.19268	0.281471	0.140736	−	0.990047i	$-0.455053\pi$
$653$	7.19268	0.281471	0.140736	+	0.990047i	$0.455053\pi$
$654$	34.3530	1.34331
$655$	5.33356	0.208399
$656$	6.98967	0.272901
$657$	9.12940	0.356172
$658$	69.5239	2.71032
$659$	3.24048	0.126231	0.0631155	−	0.998006i	$-0.479896\pi$
$659$	3.24048	0.126231	0.0631155	+	0.998006i	$0.479896\pi$
$660$	1.32034	0.0513942
$661$	−14.8570	−0.577869	−0.288935	−	0.957349i	$-0.593301\pi$
$661$	−14.8570	−0.577869	−0.288935	+	0.957349i	$0.593301\pi$
$662$	58.3529	2.26795
$663$	−19.9152	−0.773441
$664$	8.82507	0.342479
$665$	16.9179	0.656049
$666$	2.05961	0.0798084
$667$	−1.30439	−0.0505060
$668$	−6.50611	−0.251729
$669$	4.34626	0.168036
$670$	9.68679	0.374234
$671$	−0.497852	−0.0192194
$672$	−91.7779	−3.54041
$673$	14.5464	0.560724	0.280362	−	0.959894i	$-0.409545\pi$
$673$	14.5464	0.560724	0.280362	+	0.959894i	$0.409545\pi$
$674$	43.7371	1.68469
$675$	1.71273	0.0659229
$676$	−25.5855	−0.984059
$677$	−27.6906	−1.06424	−0.532118	−	0.846670i	$-0.678604\pi$
$677$	−27.6906	−1.06424	−0.532118	+	0.846670i	$0.678604\pi$
$678$	49.0504	1.88377
$679$	−13.4693	−0.516905
$680$	5.48042	0.210164
$681$	−32.3598	−1.24003
$682$	−2.52671	−0.0967527
$683$	2.82161	0.107966	0.0539830	−	0.998542i	$-0.482808\pi$
$683$	2.82161	0.107966	0.0539830	+	0.998542i	$0.482808\pi$
$684$	18.8891	0.722242
$685$	9.30539	0.355541
$686$	−120.178	−4.58843
$687$	47.4249	1.80937
$688$	−16.7295	−0.637808
$689$	−10.7804	−0.410699
$690$	−3.13563	−0.119371
$691$	16.5441	0.629368	0.314684	−	0.949196i	$-0.398101\pi$
$691$	16.5441	0.629368	0.314684	+	0.949196i	$0.398101\pi$
$692$	−56.9921	−2.16652
$693$	−2.61840	−0.0994649
$694$	25.8596	0.981617
$695$	−9.19402	−0.348749
$696$	4.82824	0.183014
$697$	13.2442	0.501661
$698$	−10.0557	−0.380615
$699$	−18.3909	−0.695609
$700$	12.5287	0.473541
$701$	3.55319	0.134202	0.0671011	−	0.997746i	$-0.478625\pi$
$701$	3.55319	0.134202	0.0671011	+	0.997746i	$0.478625\pi$
$702$	6.00056	0.226477
$703$	−1.45158	−0.0547474
$704$	2.61988	0.0987403
$705$	14.9533	0.563173
$706$	−42.4245	−1.59667
$707$	−57.8485	−2.17562
$708$	28.6143	1.07539
$709$	14.4148	0.541360	0.270680	−	0.962669i	$-0.412751\pi$
$709$	14.4148	0.541360	0.270680	+	0.962669i	$0.412751\pi$
$710$	13.7336	0.515414
$711$	−7.00350	−0.262652
$712$	9.89245	0.370735
$713$	3.32886	0.124667
$714$	−128.376	−4.80436
$715$	0.382163	0.0142921
$716$	−46.6143	−1.74206
$717$	57.8625	2.16091
$718$	−7.40478	−0.276344
$719$	−9.27528	−0.345909	−0.172955	−	0.984930i	$-0.555331\pi$
$719$	−9.27528	−0.345909	−0.172955	+	0.984930i	$0.555331\pi$
$720$	−6.24938	−0.232901
$721$	25.5905	0.953039
$722$	16.2715	0.605561
$723$	−57.7464	−2.14761
$724$	−14.1915	−0.527422
$725$	2.02064	0.0750446
$726$	−53.1722	−1.97340
$727$	−26.5985	−0.986484	−0.493242	−	0.869892i	$-0.664188\pi$
$727$	−26.5985	−0.986484	−0.493242	+	0.869892i	$0.664188\pi$
$728$	8.66502	0.321147
$729$	−12.2905	−0.455203
$730$	−8.58925	−0.317903
$731$	−31.6996	−1.17245
$732$	−12.2988	−0.454578
$733$	−41.7158	−1.54081	−0.770404	−	0.637556i	$-0.779946\pi$
$733$	−41.7158	−1.54081	−0.770404	+	0.637556i	$0.779946\pi$
$734$	−9.40592	−0.347179
$735$	−41.8912	−1.54518
$736$	−5.14153	−0.189519
$737$	1.05664	0.0389217
$738$	12.0293	0.442805
$739$	33.2470	1.22301	0.611506	−	0.791240i	$-0.290564\pi$
$739$	33.2470	1.22301	0.611506	+	0.791240i	$0.290564\pi$
$740$	−1.07498	−0.0395171
$741$	12.7483	0.468322
$742$	−69.4918	−2.55112
$743$	13.2038	0.484400	0.242200	−	0.970226i	$-0.422131\pi$
$743$	13.2038	0.484400	0.242200	+	0.970226i	$0.422131\pi$
$744$	−12.3219	−0.451744
$745$	−13.9041	−0.509408
$746$	3.01943	0.110549
$747$	−19.0683	−0.697672
$748$	3.02831	0.110726
$749$	39.0647	1.42739
$750$	4.85744	0.177368
$751$	−3.03014	−0.110571	−0.0552856	−	0.998471i	$-0.517607\pi$
$751$	−3.03014	−0.110571	−0.0552856	+	0.998471i	$0.517607\pi$
$752$	18.1001	0.660041
$753$	−59.5198	−2.16902
$754$	7.07934	0.257814
$755$	18.9790	0.690716
$756$	21.4583	0.780430
$757$	−5.20548	−0.189196	−0.0945982	−	0.995516i	$-0.530157\pi$
$757$	−5.20548	−0.189196	−0.0945982	+	0.995516i	$0.530157\pi$
$758$	35.1218	1.27568
$759$	−0.342034	−0.0124151
$760$	−3.50819	−0.127255
$761$	27.8686	1.01024	0.505118	−	0.863050i	$-0.331449\pi$
$761$	27.8686	1.01024	0.505118	+	0.863050i	$0.331449\pi$
$762$	−106.547	−3.85978
$763$	35.5574	1.28727
$764$	31.6852	1.14633
$765$	−11.8415	−0.428131
$766$	4.68550	0.169294
$767$	8.28220	0.299053
$768$	−12.6560	−0.456685
$769$	−7.23198	−0.260792	−0.130396	−	0.991462i	$-0.541625\pi$
$769$	−7.23198	−0.260792	−0.130396	+	0.991462i	$0.541625\pi$
$770$	2.46348	0.0887778
$771$	17.7259	0.638383
$772$	22.9205	0.824925
$773$	−21.5482	−0.775035	−0.387517	−	0.921862i	$-0.626667\pi$
$773$	−21.5482	−0.775035	−0.387517	+	0.921862i	$0.626667\pi$
$774$	−28.7918	−1.03490
$775$	−5.15678	−0.185237
$776$	2.79307	0.100265
$777$	4.97085	0.178328
$778$	53.7526	1.92712
$779$	−8.47806	−0.303758
$780$	9.44089	0.338038
$781$	1.49806	0.0536049
$782$	−7.19181	−0.257179
$783$	3.46080	0.123679
$784$	−50.7068	−1.81096
$785$	15.5029	0.553323
$786$	25.9074	0.924088
$787$	−19.3100	−0.688326	−0.344163	−	0.938910i	$-0.611837\pi$
$787$	−19.3100	−0.688326	−0.344163	+	0.938910i	$0.611837\pi$
$788$	10.8834	0.387705
$789$	23.7531	0.845632
$790$	6.58913	0.234431
$791$	50.7701	1.80518
$792$	0.542966	0.0192935
$793$	−3.55981	−0.126413
$794$	−28.3297	−1.00538
$795$	−14.9464	−0.530094
$796$	−26.5619	−0.941461
$797$	−33.3654	−1.18186	−0.590931	−	0.806722i	$-0.701239\pi$
$797$	−33.3654	−1.18186	−0.590931	+	0.806722i	$0.701239\pi$
$798$	82.1777	2.90906
$799$	34.2965	1.21332
$800$	7.96479	0.281598
$801$	−21.3746	−0.755233
$802$	30.6832	1.08346
$803$	−0.936916	−0.0330630
$804$	26.1029	0.920579
$805$	−3.24556	−0.114391
$806$	−18.0668	−0.636377
$807$	−22.7315	−0.800186
$808$	11.9958	0.422010
$809$	−12.2279	−0.429909	−0.214954	−	0.976624i	$-0.568960\pi$
$809$	−12.2279	−0.429909	−0.214954	+	0.976624i	$0.568960\pi$
$810$	22.6427	0.795582
$811$	21.2114	0.744833	0.372416	−	0.928066i	$-0.378529\pi$
$811$	21.2114	0.744833	0.372416	+	0.928066i	$0.378529\pi$
$812$	25.3160	0.888417
$813$	−20.6358	−0.723731
$814$	−0.211370	−0.00740853
$815$	−10.1489	−0.355500
$816$	−33.4218	−1.17000
$817$	20.2920	0.709926
$818$	−67.8487	−2.37228
$819$	−18.7225	−0.654216
$820$	−6.27850	−0.219255
$821$	48.3777	1.68839	0.844197	−	0.536033i	$-0.180078\pi$
$821$	48.3777	1.68839	0.844197	+	0.536033i	$0.180078\pi$
$822$	45.2003	1.57654
$823$	−55.8119	−1.94548	−0.972739	−	0.231901i	$-0.925506\pi$
$823$	−55.8119	−1.94548	−0.972739	+	0.231901i	$0.925506\pi$
$824$	−5.30658	−0.184864
$825$	0.529849	0.0184470
$826$	53.3883	1.85762
$827$	31.0264	1.07889	0.539447	−	0.842019i	$-0.318633\pi$
$827$	31.0264	1.07889	0.539447	+	0.842019i	$0.318633\pi$
$828$	−3.62371	−0.125933
$829$	−4.14652	−0.144015	−0.0720073	−	0.997404i	$-0.522940\pi$
$829$	−4.14652	−0.144015	−0.0720073	+	0.997404i	$0.522940\pi$
$830$	17.9401	0.622710
$831$	−60.1756	−2.08747
$832$	18.7330	0.649450
$833$	−96.0808	−3.32900
$834$	−44.6594	−1.54643
$835$	−2.61088	−0.0903534
$836$	−1.93852	−0.0670450
$837$	−8.83215	−0.305284
$838$	2.85944	0.0987778
$839$	3.25040	0.112216	0.0561081	−	0.998425i	$-0.482131\pi$
$839$	3.25040	0.112216	0.0561081	+	0.998425i	$0.482131\pi$
$840$	12.0136	0.414508
$841$	−24.9170	−0.859208
$842$	40.4040	1.39241
$843$	37.1813	1.28059
$844$	−60.8817	−2.09563
$845$	−10.2674	−0.353209
$846$	31.1504	1.07097
$847$	−55.0364	−1.89107
$848$	−18.0917	−0.621272
$849$	−64.6047	−2.21723
$850$	11.1409	0.382130
$851$	0.278474	0.00954596
$852$	37.0079	1.26787
$853$	−24.7657	−0.847961	−0.423980	−	0.905671i	$-0.639367\pi$
$853$	−24.7657	−0.847961	−0.423980	+	0.905671i	$0.639367\pi$
$854$	−22.9471	−0.785234
$855$	7.58014	0.259235
$856$	−8.10067	−0.276875
$857$	−40.7937	−1.39348	−0.696742	−	0.717321i	$-0.745368\pi$
$857$	−40.7937	−1.39348	−0.696742	+	0.717321i	$0.745368\pi$
$858$	1.85633	0.0633742
$859$	2.13963	0.0730031	0.0365016	−	0.999334i	$-0.488379\pi$
$859$	2.13963	0.0730031	0.0365016	+	0.999334i	$0.488379\pi$
$860$	15.0274	0.512430
$861$	29.0326	0.989428
$862$	27.5872	0.939624
$863$	−2.48437	−0.0845690	−0.0422845	−	0.999106i	$-0.513464\pi$
$863$	−2.48437	−0.0845690	−0.0422845	+	0.999106i	$0.513464\pi$
$864$	13.6415	0.464094
$865$	−22.8708	−0.777630
$866$	−8.18481	−0.278131
$867$	−24.3668	−0.827540
$868$	−64.6078	−2.19293
$869$	0.718743	0.0243817
$870$	9.81512	0.332764
$871$	7.55531	0.256002
$872$	−7.37339	−0.249694
$873$	−6.03498	−0.204253
$874$	4.60371	0.155723
$875$	5.02774	0.169969
$876$	−23.1454	−0.782010
$877$	28.1626	0.950982	0.475491	−	0.879721i	$-0.342270\pi$
$877$	28.1626	0.950982	0.475491	+	0.879721i	$0.342270\pi$
$878$	21.3196	0.719503
$879$	26.9586	0.909292
$880$	0.641351	0.0216199
$881$	26.4001	0.889443	0.444722	−	0.895669i	$-0.353303\pi$
$881$	26.4001	0.889443	0.444722	+	0.895669i	$0.353303\pi$
$882$	−87.2671	−2.93844
$883$	−29.3778	−0.988641	−0.494320	−	0.869280i	$-0.664583\pi$
$883$	−29.3778	−0.988641	−0.494320	+	0.869280i	$0.664583\pi$
$884$	21.6534	0.728283
$885$	11.4828	0.385991
$886$	74.4826	2.50229
$887$	27.6860	0.929606	0.464803	−	0.885414i	$-0.346125\pi$
$887$	27.6860	0.929606	0.464803	+	0.885414i	$0.346125\pi$
$888$	−1.03078	−0.0345908
$889$	−110.282	−3.69875
$890$	20.1099	0.674086
$891$	2.46986	0.0827435
$892$	−4.72561	−0.158225
$893$	−21.9543	−0.734673
$894$	−67.5385	−2.25882
$895$	−18.7062	−0.625279
$896$	40.6661	1.35856
$897$	−2.44566	−0.0816583
$898$	−10.6011	−0.353764
$899$	−10.4200	−0.347526
$900$	5.61354	0.187118
$901$	−34.2807	−1.14206
$902$	−1.23452	−0.0411051
$903$	−69.4886	−2.31243
$904$	−10.5280	−0.350155
$905$	−5.69500	−0.189308
$906$	92.1892	3.06278
$907$	17.0877	0.567388	0.283694	−	0.958915i	$-0.408440\pi$
$907$	17.0877	0.567388	0.283694	+	0.958915i	$0.408440\pi$
$908$	35.1843	1.16763
$909$	−25.9192	−0.859687
$910$	17.6147	0.583923
$911$	−46.6401	−1.54525	−0.772627	−	0.634860i	$-0.781058\pi$
$911$	−46.6401	−1.54525	−0.772627	+	0.634860i	$0.781058\pi$
$912$	21.3944	0.708439
$913$	1.95691	0.0647642
$914$	5.10036	0.168705
$915$	−4.93549	−0.163162
$916$	−51.5643	−1.70373
$917$	26.8157	0.885534
$918$	19.0813	0.629778
$919$	14.5869	0.481179	0.240589	−	0.970627i	$-0.422659\pi$
$919$	14.5869	0.481179	0.240589	+	0.970627i	$0.422659\pi$
$920$	0.673018	0.0221887
$921$	−68.6532	−2.26220
$922$	73.2963	2.41389
$923$	10.7117	0.352579
$924$	6.63833	0.218385
$925$	−0.431387	−0.0141839
$926$	−26.0524	−0.856134
$927$	11.4659	0.376590
$928$	16.0940	0.528311
$929$	−9.02544	−0.296115	−0.148058	−	0.988979i	$-0.547302\pi$
$929$	−9.02544	−0.296115	−0.148058	+	0.988979i	$0.547302\pi$
$930$	−25.0487	−0.821380
$931$	61.5044	2.01573
$932$	19.9962	0.654996
$933$	11.8412	0.387663
$934$	26.0311	0.851765
$935$	1.21525	0.0397429
$936$	3.88239	0.126900
$937$	21.8535	0.713923	0.356962	−	0.934119i	$-0.383813\pi$
$937$	21.8535	0.713923	0.356962	+	0.934119i	$0.383813\pi$
$938$	48.7027	1.59020
$939$	−20.0938	−0.655735
$940$	−16.2585	−0.530292
$941$	−25.8699	−0.843333	−0.421667	−	0.906751i	$-0.638555\pi$
$941$	−25.8699	−0.843333	−0.421667	+	0.906751i	$0.638555\pi$
$942$	75.3044	2.45355
$943$	1.62645	0.0529643
$944$	13.8993	0.452383
$945$	8.61114	0.280120
$946$	2.95479	0.0960685
$947$	31.7413	1.03145	0.515727	−	0.856753i	$-0.327522\pi$
$947$	31.7413	1.03145	0.515727	+	0.856753i	$0.327522\pi$
$948$	17.7557	0.576678
$949$	−6.69927	−0.217467
$950$	−7.13165	−0.231381
$951$	59.8539	1.94090
$952$	27.5541	0.893034
$953$	−5.81864	−0.188484	−0.0942421	−	0.995549i	$-0.530043\pi$
$953$	−5.81864	−0.188484	−0.0942421	+	0.995549i	$0.530043\pi$
$954$	−31.1361	−1.00807
$955$	12.7152	0.411454
$956$	−62.9129	−2.03475
$957$	1.07063	0.0346087
$958$	−23.8322	−0.769983
$959$	46.7851	1.51077
$960$	25.9723	0.838253
$961$	−4.40766	−0.142182
$962$	−1.51137	−0.0487285
$963$	17.5031	0.564029
$964$	62.7867	2.02222
$965$	9.19791	0.296091
$966$	−15.7651	−0.507234
$967$	−46.7413	−1.50310	−0.751550	−	0.659676i	$-0.770693\pi$
$967$	−46.7413	−1.50310	−0.751550	+	0.659676i	$0.770693\pi$
$968$	11.4126	0.366816
$969$	40.5387	1.30229
$970$	5.67792	0.182307
$971$	−35.2526	−1.13131	−0.565655	−	0.824642i	$-0.691377\pi$
$971$	−35.2526	−1.13131	−0.565655	+	0.824642i	$0.691377\pi$
$972$	48.2110	1.54637
$973$	−46.2251	−1.48191
$974$	18.1665	0.582093
$975$	3.78860	0.121332
$976$	−5.97412	−0.191227
$977$	−42.3603	−1.35523	−0.677613	−	0.735419i	$-0.736986\pi$
$977$	−42.3603	−1.35523	−0.677613	+	0.735419i	$0.736986\pi$
$978$	−49.2976	−1.57636
$979$	2.19359	0.0701075
$980$	45.5476	1.45497
$981$	15.9316	0.508658
$982$	−10.2374	−0.326687
$983$	−48.3359	−1.54168	−0.770838	−	0.637031i	$-0.780162\pi$
$983$	−48.3359	−1.54168	−0.770838	+	0.637031i	$0.780162\pi$
$984$	−6.02036	−0.191922
$985$	4.36748	0.139159
$986$	22.5118	0.716920
$987$	75.1812	2.39304
$988$	−13.8610	−0.440979
$989$	−3.89284	−0.123785
$990$	1.10377	0.0350802
$991$	43.9266	1.39538	0.697688	−	0.716402i	$-0.254212\pi$
$991$	43.9266	1.39538	0.697688	+	0.716402i	$0.254212\pi$
$992$	−41.0727	−1.30406
$993$	63.1012	2.00246
$994$	69.0490	2.19010
$995$	−10.6592	−0.337920
$996$	48.3430	1.53181
$997$	7.89612	0.250073	0.125036	−	0.992152i	$-0.460095\pi$
$997$	7.89612	0.250073	0.125036	+	0.992152i	$0.460095\pi$
$998$	67.0575	2.12267
$999$	−0.738848	−0.0233761

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8035.2.a.b.1.20	✓	114

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8035.2.a.b.1.20	✓	114	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:	\( N \)	\(=\)	\( 8035 = 5 \cdot 1607 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8035.a (trivial)

\(f(q)\)	\(=\)	\(q-2.11941 q^{2} -2.29188 q^{3} +2.49192 q^{4} +1.00000 q^{5} +4.85744 q^{6} +5.02774 q^{7} -1.04258 q^{8} +2.25270 q^{9} +O(q^{10})\)	\(q-2.11941 q^{2} -2.29188 q^{3} +2.49192 q^{4} +1.00000 q^{5} +4.85744 q^{6} +5.02774 q^{7} -1.04258 q^{8} +2.25270 q^{9} -2.11941 q^{10} -0.231186 q^{11} -5.71117 q^{12} -1.65306 q^{13} -10.6559 q^{14} -2.29188 q^{15} -2.77418 q^{16} -5.25660 q^{17} -4.77440 q^{18} +3.36492 q^{19} +2.49192 q^{20} -11.5230 q^{21} +0.489979 q^{22} -0.645532 q^{23} +2.38946 q^{24} +1.00000 q^{25} +3.50351 q^{26} +1.71273 q^{27} +12.5287 q^{28} +2.02064 q^{29} +4.85744 q^{30} -5.15678 q^{31} +7.96479 q^{32} +0.529849 q^{33} +11.1409 q^{34} +5.02774 q^{35} +5.61354 q^{36} -0.431387 q^{37} -7.13165 q^{38} +3.78860 q^{39} -1.04258 q^{40} -2.51954 q^{41} +24.4219 q^{42} +6.03045 q^{43} -0.576096 q^{44} +2.25270 q^{45} +1.36815 q^{46} -6.52447 q^{47} +6.35808 q^{48} +18.2781 q^{49} -2.11941 q^{50} +12.0475 q^{51} -4.11928 q^{52} +6.52146 q^{53} -3.62998 q^{54} -0.231186 q^{55} -5.24181 q^{56} -7.71197 q^{57} -4.28257 q^{58} -5.01023 q^{59} -5.71117 q^{60} +2.15347 q^{61} +10.9293 q^{62} +11.3260 q^{63} -11.3323 q^{64} -1.65306 q^{65} -1.12297 q^{66} -4.57050 q^{67} -13.0990 q^{68} +1.47948 q^{69} -10.6559 q^{70} -6.47991 q^{71} -2.34861 q^{72} +4.05265 q^{73} +0.914288 q^{74} -2.29188 q^{75} +8.38510 q^{76} -1.16234 q^{77} -8.02962 q^{78} -3.10894 q^{79} -2.77418 q^{80} -10.6834 q^{81} +5.33996 q^{82} -8.46465 q^{83} -28.7143 q^{84} -5.25660 q^{85} -12.7810 q^{86} -4.63105 q^{87} +0.241029 q^{88} -9.48844 q^{89} -4.77440 q^{90} -8.31114 q^{91} -1.60861 q^{92} +11.8187 q^{93} +13.8281 q^{94} +3.36492 q^{95} -18.2543 q^{96} -2.67900 q^{97} -38.7390 q^{98} -0.520791 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 114 q - 17 q^{2} - 10 q^{3} + 93 q^{4} + 114 q^{5} - 24 q^{6} - 11 q^{7} - 48 q^{8} + 66 q^{9}+O(q^{10}) \) 114 * q - 17 * q^2 - 10 * q^3 + 93 * q^4 + 114 * q^5 - 24 * q^6 - 11 * q^7 - 48 * q^8 + 66 * q^9	\( 114 q - 17 q^{2} - 10 q^{3} + 93 q^{4} + 114 q^{5} - 24 q^{6} - 11 q^{7} - 48 q^{8} + 66 q^{9} - 17 q^{10} - 44 q^{11} - 25 q^{12} - 26 q^{13} - 43 q^{14} - 10 q^{15} + 59 q^{16} - 57 q^{17} - 33 q^{18} - 69 q^{19} + 93 q^{20} - 107 q^{21} - 19 q^{22} - 45 q^{23} - 45 q^{24} + 114 q^{25} - 54 q^{26} - 34 q^{27} - 6 q^{28} - 166 q^{29} - 24 q^{30} - 67 q^{31} - 98 q^{32} - 38 q^{33} - 41 q^{34} - 11 q^{35} - 3 q^{36} - 44 q^{37} - 19 q^{38} - 66 q^{39} - 48 q^{40} - 141 q^{41} + q^{42} - 30 q^{43} - 125 q^{44} + 66 q^{45} - 59 q^{46} - 17 q^{47} - 35 q^{48} - 15 q^{49} - 17 q^{50} - 67 q^{51} - 26 q^{52} - 154 q^{53} - 45 q^{54} - 44 q^{55} - 118 q^{56} - 70 q^{57} + 11 q^{58} - 75 q^{59} - 25 q^{60} - 144 q^{61} - 35 q^{62} - 25 q^{63} + 16 q^{64} - 26 q^{65} - 68 q^{66} - 2 q^{67} - 99 q^{68} - 118 q^{69} - 43 q^{70} - 104 q^{71} - 73 q^{72} - 22 q^{73} - 107 q^{74} - 10 q^{75} - 172 q^{76} - 100 q^{77} - 2 q^{78} - 91 q^{79} + 59 q^{80} - 54 q^{81} + 20 q^{82} - 44 q^{83} - 156 q^{84} - 57 q^{85} - 50 q^{86} + 5 q^{87} - 13 q^{88} - 150 q^{89} - 33 q^{90} - 54 q^{91} - 77 q^{92} - 50 q^{93} - 105 q^{94} - 69 q^{95} - 78 q^{96} - 31 q^{97} - 64 q^{98} - 101 q^{99}+O(q^{100}) \) 114 * q - 17 * q^2 - 10 * q^3 + 93 * q^4 + 114 * q^5 - 24 * q^6 - 11 * q^7 - 48 * q^8 + 66 * q^9 - 17 * q^10 - 44 * q^11 - 25 * q^12 - 26 * q^13 - 43 * q^14 - 10 * q^15 + 59 * q^16 - 57 * q^17 - 33 * q^18 - 69 * q^19 + 93 * q^20 - 107 * q^21 - 19 * q^22 - 45 * q^23 - 45 * q^24 + 114 * q^25 - 54 * q^26 - 34 * q^27 - 6 * q^28 - 166 * q^29 - 24 * q^30 - 67 * q^31 - 98 * q^32 - 38 * q^33 - 41 * q^34 - 11 * q^35 - 3 * q^36 - 44 * q^37 - 19 * q^38 - 66 * q^39 - 48 * q^40 - 141 * q^41 + q^42 - 30 * q^43 - 125 * q^44 + 66 * q^45 - 59 * q^46 - 17 * q^47 - 35 * q^48 - 15 * q^49 - 17 * q^50 - 67 * q^51 - 26 * q^52 - 154 * q^53 - 45 * q^54 - 44 * q^55 - 118 * q^56 - 70 * q^57 + 11 * q^58 - 75 * q^59 - 25 * q^60 - 144 * q^61 - 35 * q^62 - 25 * q^63 + 16 * q^64 - 26 * q^65 - 68 * q^66 - 2 * q^67 - 99 * q^68 - 118 * q^69 - 43 * q^70 - 104 * q^71 - 73 * q^72 - 22 * q^73 - 107 * q^74 - 10 * q^75 - 172 * q^76 - 100 * q^77 - 2 * q^78 - 91 * q^79 + 59 * q^80 - 54 * q^81 + 20 * q^82 - 44 * q^83 - 156 * q^84 - 57 * q^85 - 50 * q^86 + 5 * q^87 - 13 * q^88 - 150 * q^89 - 33 * q^90 - 54 * q^91 - 77 * q^92 - 50 * q^93 - 105 * q^94 - 69 * q^95 - 78 * q^96 - 31 * q^97 - 64 * q^98 - 101 * q^99

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