LMFDB - Embedded newform 8005.2.a.h.1.10

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			1.10
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)

$f(q)$	$=$	$q-2.41370 q^{2} -2.40190 q^{3} +3.82593 q^{4} +1.00000 q^{5} +5.79746 q^{6} +1.40406 q^{7} -4.40725 q^{8} +2.76911 q^{9} +O(q^{10})$	\(q-2.41370 q^{2} -2.40190 q^{3} +3.82593 q^{4} +1.00000 q^{5} +5.79746 q^{6} +1.40406 q^{7} -4.40725 q^{8} +2.76911 q^{9} -2.41370 q^{10} +1.34681 q^{11} -9.18951 q^{12} +2.31658 q^{13} -3.38898 q^{14} -2.40190 q^{15} +2.98591 q^{16} +7.01916 q^{17} -6.68381 q^{18} -3.78829 q^{19} +3.82593 q^{20} -3.37241 q^{21} -3.25079 q^{22} -4.96342 q^{23} +10.5858 q^{24} +1.00000 q^{25} -5.59153 q^{26} +0.554562 q^{27} +5.37185 q^{28} -2.90494 q^{29} +5.79746 q^{30} +2.69438 q^{31} +1.60743 q^{32} -3.23490 q^{33} -16.9421 q^{34} +1.40406 q^{35} +10.5945 q^{36} +4.17393 q^{37} +9.14379 q^{38} -5.56420 q^{39} -4.40725 q^{40} -2.56702 q^{41} +8.13998 q^{42} -2.91094 q^{43} +5.15280 q^{44} +2.76911 q^{45} +11.9802 q^{46} -0.0759593 q^{47} -7.17184 q^{48} -5.02861 q^{49} -2.41370 q^{50} -16.8593 q^{51} +8.86310 q^{52} -8.51872 q^{53} -1.33855 q^{54} +1.34681 q^{55} -6.18805 q^{56} +9.09909 q^{57} +7.01165 q^{58} -2.94755 q^{59} -9.18951 q^{60} +4.78559 q^{61} -6.50341 q^{62} +3.88801 q^{63} -9.85167 q^{64} +2.31658 q^{65} +7.80806 q^{66} +13.8862 q^{67} +26.8548 q^{68} +11.9216 q^{69} -3.38898 q^{70} +10.1932 q^{71} -12.2042 q^{72} -14.4390 q^{73} -10.0746 q^{74} -2.40190 q^{75} -14.4938 q^{76} +1.89100 q^{77} +13.4303 q^{78} -6.93998 q^{79} +2.98591 q^{80} -9.63935 q^{81} +6.19600 q^{82} +15.1102 q^{83} -12.9026 q^{84} +7.01916 q^{85} +7.02612 q^{86} +6.97737 q^{87} -5.93572 q^{88} +7.64771 q^{89} -6.68381 q^{90} +3.25262 q^{91} -18.9897 q^{92} -6.47162 q^{93} +0.183343 q^{94} -3.78829 q^{95} -3.86089 q^{96} -0.548466 q^{97} +12.1375 q^{98} +3.72947 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 137 q + 17 q^{2} + 46 q^{3} + 147 q^{4} + 137 q^{5} + 11 q^{6} + 53 q^{7} + 42 q^{8} + 165 q^{9}+O(q^{10}) $ 137 * q + 17 * q^2 + 46 * q^3 + 147 * q^4 + 137 * q^5 + 11 * q^6 + 53 * q^7 + 42 * q^8 + 165 * q^9	\( 137 q + 17 q^{2} + 46 q^{3} + 147 q^{4} + 137 q^{5} + 11 q^{6} + 53 q^{7} + 42 q^{8} + 165 q^{9} + 17 q^{10} + 47 q^{11} + 87 q^{12} + 46 q^{13} + 39 q^{14} + 46 q^{15} + 155 q^{16} + 46 q^{17} + 44 q^{18} + 42 q^{19} + 147 q^{20} + 21 q^{21} + 48 q^{22} + 110 q^{23} + 33 q^{24} + 137 q^{25} + 24 q^{26} + 145 q^{27} + 83 q^{28} + 31 q^{29} + 11 q^{30} + 23 q^{31} + 71 q^{32} + 32 q^{33} + 23 q^{34} + 53 q^{35} + 178 q^{36} + 104 q^{37} + 88 q^{38} + 4 q^{39} + 42 q^{40} + 62 q^{41} + 70 q^{42} + 94 q^{43} + 50 q^{44} + 165 q^{45} - 30 q^{46} + 122 q^{47} + 157 q^{48} + 168 q^{49} + 17 q^{50} + 72 q^{51} + 74 q^{52} + 116 q^{53} + 32 q^{54} + 47 q^{55} + 119 q^{56} + 51 q^{57} + 78 q^{58} + 213 q^{59} + 87 q^{60} + 14 q^{61} + 41 q^{62} + 147 q^{63} + 114 q^{64} + 46 q^{65} + 15 q^{66} + 184 q^{67} + 95 q^{68} + 32 q^{69} + 39 q^{70} + 99 q^{71} + 92 q^{72} + 51 q^{73} + 21 q^{74} + 46 q^{75} + 18 q^{76} + 78 q^{77} + 102 q^{78} + 6 q^{79} + 155 q^{80} + 201 q^{81} + 38 q^{82} + 228 q^{83} - 11 q^{84} + 46 q^{85} + 71 q^{86} + 113 q^{87} + 103 q^{88} + 111 q^{89} + 44 q^{90} + 41 q^{91} + 136 q^{92} + 11 q^{93} - 39 q^{94} + 42 q^{95} + 33 q^{96} + 91 q^{97} + 91 q^{98} + 65 q^{99}+O(q^{100}) \) 137 * q + 17 * q^2 + 46 * q^3 + 147 * q^4 + 137 * q^5 + 11 * q^6 + 53 * q^7 + 42 * q^8 + 165 * q^9 + 17 * q^10 + 47 * q^11 + 87 * q^12 + 46 * q^13 + 39 * q^14 + 46 * q^15 + 155 * q^16 + 46 * q^17 + 44 * q^18 + 42 * q^19 + 147 * q^20 + 21 * q^21 + 48 * q^22 + 110 * q^23 + 33 * q^24 + 137 * q^25 + 24 * q^26 + 145 * q^27 + 83 * q^28 + 31 * q^29 + 11 * q^30 + 23 * q^31 + 71 * q^32 + 32 * q^33 + 23 * q^34 + 53 * q^35 + 178 * q^36 + 104 * q^37 + 88 * q^38 + 4 * q^39 + 42 * q^40 + 62 * q^41 + 70 * q^42 + 94 * q^43 + 50 * q^44 + 165 * q^45 - 30 * q^46 + 122 * q^47 + 157 * q^48 + 168 * q^49 + 17 * q^50 + 72 * q^51 + 74 * q^52 + 116 * q^53 + 32 * q^54 + 47 * q^55 + 119 * q^56 + 51 * q^57 + 78 * q^58 + 213 * q^59 + 87 * q^60 + 14 * q^61 + 41 * q^62 + 147 * q^63 + 114 * q^64 + 46 * q^65 + 15 * q^66 + 184 * q^67 + 95 * q^68 + 32 * q^69 + 39 * q^70 + 99 * q^71 + 92 * q^72 + 51 * q^73 + 21 * q^74 + 46 * q^75 + 18 * q^76 + 78 * q^77 + 102 * q^78 + 6 * q^79 + 155 * q^80 + 201 * q^81 + 38 * q^82 + 228 * q^83 - 11 * q^84 + 46 * q^85 + 71 * q^86 + 113 * q^87 + 103 * q^88 + 111 * q^89 + 44 * q^90 + 41 * q^91 + 136 * q^92 + 11 * q^93 - 39 * q^94 + 42 * q^95 + 33 * q^96 + 91 * q^97 + 91 * q^98 + 65 * 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 $

$2$	−2.41370	−1.70674	−0.853371	−	0.521304i	$-0.825446\pi$
$2$	−2.41370	−1.70674	−0.853371	+	0.521304i	$0.825446\pi$
$3$	−2.40190	−1.38674	−0.693368	−	0.720583i	$-0.743874\pi$
$3$	−2.40190	−1.38674	−0.693368	+	0.720583i	$0.743874\pi$
$4$	3.82593	1.91297
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	5.79746	2.36680
$7$	1.40406	0.530685	0.265343	−	0.964154i	$-0.414515\pi$
$7$	1.40406	0.530685	0.265343	+	0.964154i	$0.414515\pi$
$8$	−4.40725	−1.55820
$9$	2.76911	0.923038
$10$	−2.41370	−0.763278
$11$	1.34681	0.406078	0.203039	−	0.979171i	$-0.434918\pi$
$11$	1.34681	0.406078	0.203039	+	0.979171i	$0.434918\pi$
$12$	−9.18951	−2.65278
$13$	2.31658	0.642505	0.321252	−	0.946994i	$-0.395896\pi$
$13$	2.31658	0.642505	0.321252	+	0.946994i	$0.395896\pi$
$14$	−3.38898	−0.905743
$15$	−2.40190	−0.620167
$16$	2.98591	0.746477
$17$	7.01916	1.70240	0.851198	−	0.524845i	$-0.175877\pi$
$17$	7.01916	1.70240	0.851198	+	0.524845i	$0.175877\pi$
$18$	−6.68381	−1.57539
$19$	−3.78829	−0.869094	−0.434547	−	0.900649i	$-0.643091\pi$
$19$	−3.78829	−0.869094	−0.434547	+	0.900649i	$0.643091\pi$
$20$	3.82593	0.855505
$21$	−3.37241	−0.735921
$22$	−3.25079	−0.693070
$23$	−4.96342	−1.03494	−0.517472	−	0.855700i	$-0.673127\pi$
$23$	−4.96342	−1.03494	−0.517472	+	0.855700i	$0.673127\pi$
$24$	10.5858	2.16081
$25$	1.00000	0.200000
$26$	−5.59153	−1.09659
$27$	0.554562	0.106726
$28$	5.37185	1.01518
$29$	−2.90494	−0.539434	−0.269717	−	0.962940i	$-0.586930\pi$
$29$	−2.90494	−0.539434	−0.269717	+	0.962940i	$0.586930\pi$
$30$	5.79746	1.05847
$31$	2.69438	0.483925	0.241962	−	0.970286i	$-0.422209\pi$
$31$	2.69438	0.483925	0.241962	+	0.970286i	$0.422209\pi$
$32$	1.60743	0.284157
$33$	−3.23490	−0.563123
$34$	−16.9421	−2.90555
$35$	1.40406	0.237330
$36$	10.5945	1.76574
$37$	4.17393	0.686190	0.343095	−	0.939301i	$-0.388525\pi$
$37$	4.17393	0.686190	0.343095	+	0.939301i	$0.388525\pi$
$38$	9.14379	1.48332
$39$	−5.56420	−0.890985
$40$	−4.40725	−0.696848
$41$	−2.56702	−0.400900	−0.200450	−	0.979704i	$-0.564240\pi$
$41$	−2.56702	−0.400900	−0.200450	+	0.979704i	$0.564240\pi$
$42$	8.13998	1.25603
$43$	−2.91094	−0.443914	−0.221957	−	0.975056i	$-0.571244\pi$
$43$	−2.91094	−0.443914	−0.221957	+	0.975056i	$0.571244\pi$
$44$	5.15280	0.776814
$45$	2.76911	0.412795
$46$	11.9802	1.76638
$47$	−0.0759593	−0.0110798	−0.00553990	−	0.999985i	$-0.501763\pi$
$47$	−0.0759593	−0.0110798	−0.00553990	+	0.999985i	$0.501763\pi$
$48$	−7.17184	−1.03517
$49$	−5.02861	−0.718373
$50$	−2.41370	−0.341348
$51$	−16.8593	−2.36077
$52$	8.86310	1.22909
$53$	−8.51872	−1.17014	−0.585068	−	0.810984i	$-0.698932\pi$
$53$	−8.51872	−1.17014	−0.585068	+	0.810984i	$0.698932\pi$
$54$	−1.33855	−0.182153
$55$	1.34681	0.181604
$56$	−6.18805	−0.826913
$57$	9.09909	1.20520
$58$	7.01165	0.920674
$59$	−2.94755	−0.383738	−0.191869	−	0.981421i	$-0.561455\pi$
$59$	−2.94755	−0.383738	−0.191869	+	0.981421i	$0.561455\pi$
$60$	−9.18951	−1.18636
$61$	4.78559	0.612731	0.306366	−	0.951914i	$-0.400887\pi$
$61$	4.78559	0.612731	0.306366	+	0.951914i	$0.400887\pi$
$62$	−6.50341	−0.825934
$63$	3.88801	0.489843
$64$	−9.85167	−1.23146
$65$	2.31658	0.287337
$66$	7.80806	0.961105
$67$	13.8862	1.69647	0.848235	−	0.529619i	$-0.177665\pi$
$67$	13.8862	1.69647	0.848235	+	0.529619i	$0.177665\pi$
$68$	26.8548	3.25663
$69$	11.9216	1.43519
$70$	−3.38898	−0.405060
$71$	10.1932	1.20971	0.604857	−	0.796334i	$-0.293230\pi$
$71$	10.1932	1.20971	0.604857	+	0.796334i	$0.293230\pi$
$72$	−12.2042	−1.43828
$73$	−14.4390	−1.68995	−0.844977	−	0.534803i	$-0.820386\pi$
$73$	−14.4390	−1.68995	−0.844977	+	0.534803i	$0.820386\pi$
$74$	−10.0746	−1.17115
$75$	−2.40190	−0.277347
$76$	−14.4938	−1.66255
$77$	1.89100	0.215500
$78$	13.4303	1.52068
$79$	−6.93998	−0.780809	−0.390405	−	0.920643i	$-0.627665\pi$
$79$	−6.93998	−0.780809	−0.390405	+	0.920643i	$0.627665\pi$
$80$	2.98591	0.333834
$81$	−9.63935	−1.07104
$82$	6.19600	0.684233
$83$	15.1102	1.65856	0.829282	−	0.558830i	$-0.188750\pi$
$83$	15.1102	1.65856	0.829282	+	0.558830i	$0.188750\pi$
$84$	−12.9026	−1.40779
$85$	7.01916	0.761334
$86$	7.02612	0.757646
$87$	6.97737	0.748053
$88$	−5.93572	−0.632750
$89$	7.64771	0.810655	0.405328	−	0.914171i	$-0.367157\pi$
$89$	7.64771	0.810655	0.405328	+	0.914171i	$0.367157\pi$
$90$	−6.68381	−0.704535
$91$	3.25262	0.340968
$92$	−18.9897	−1.97981
$93$	−6.47162	−0.671076
$94$	0.183343	0.0189104
$95$	−3.78829	−0.388670
$96$	−3.86089	−0.394050
$97$	−0.548466	−0.0556883	−0.0278441	−	0.999612i	$-0.508864\pi$
$97$	−0.548466	−0.0556883	−0.0278441	+	0.999612i	$0.508864\pi$
$98$	12.1375	1.22608
$99$	3.72947	0.374825
$100$	3.82593	0.382593
$101$	1.85522	0.184601	0.0923005	−	0.995731i	$-0.470578\pi$
$101$	1.85522	0.184601	0.0923005	+	0.995731i	$0.470578\pi$
$102$	40.6932	4.02923
$103$	10.2591	1.01086	0.505432	−	0.862866i	$-0.331333\pi$
$103$	10.2591	1.01086	0.505432	+	0.862866i	$0.331333\pi$
$104$	−10.2098	−1.00115
$105$	−3.37241	−0.329114
$106$	20.5616	1.99712
$107$	11.3811	1.10026	0.550129	−	0.835080i	$-0.314579\pi$
$107$	11.3811	1.10026	0.550129	+	0.835080i	$0.314579\pi$
$108$	2.12172	0.204163
$109$	−11.8649	−1.13645	−0.568224	−	0.822874i	$-0.692369\pi$
$109$	−11.8649	−1.13645	−0.568224	+	0.822874i	$0.692369\pi$
$110$	−3.25079	−0.309950
$111$	−10.0254	−0.951564
$112$	4.19240	0.396144
$113$	8.49649	0.799282	0.399641	−	0.916672i	$-0.369135\pi$
$113$	8.49649	0.799282	0.399641	+	0.916672i	$0.369135\pi$
$114$	−21.9624	−2.05697
$115$	−4.96342	−0.462841
$116$	−11.1141	−1.03192
$117$	6.41488	0.593056
$118$	7.11449	0.654942
$119$	9.85533	0.903436
$120$	10.5858	0.966345
$121$	−9.18611	−0.835101
$122$	−11.5510	−1.04577
$123$	6.16571	0.555943
$124$	10.3085	0.925732
$125$	1.00000	0.0894427
$126$	−9.38447	−0.836035
$127$	7.57221	0.671925	0.335962	−	0.941875i	$-0.390938\pi$
$127$	7.57221	0.671925	0.335962	+	0.941875i	$0.390938\pi$
$128$	20.5641	1.81763
$129$	6.99177	0.615591
$130$	−5.59153	−0.490410
$131$	−2.38150	−0.208073	−0.104036	−	0.994573i	$-0.533176\pi$
$131$	−2.38150	−0.208073	−0.104036	+	0.994573i	$0.533176\pi$
$132$	−12.3765	−1.07724
$133$	−5.31899	−0.461215
$134$	−33.5171	−2.89544
$135$	0.554562	0.0477291
$136$	−30.9352	−2.65267
$137$	18.5906	1.58831	0.794153	−	0.607718i	$-0.207915\pi$
$137$	18.5906	1.58831	0.794153	+	0.607718i	$0.207915\pi$
$138$	−28.7752	−2.44951
$139$	14.9649	1.26931	0.634654	−	0.772797i	$-0.281143\pi$
$139$	14.9649	1.26931	0.634654	+	0.772797i	$0.281143\pi$
$140$	5.37185	0.454004
$141$	0.182446	0.0153648
$142$	−24.6034	−2.06467
$143$	3.11999	0.260907
$144$	8.26832	0.689027
$145$	−2.90494	−0.241242
$146$	34.8513	2.88431
$147$	12.0782	0.996194
$148$	15.9692	1.31266
$149$	4.47845	0.366889	0.183445	−	0.983030i	$-0.441275\pi$
$149$	4.47845	0.366889	0.183445	+	0.983030i	$0.441275\pi$
$150$	5.79746	0.473360
$151$	15.0778	1.22701	0.613507	−	0.789689i	$-0.289758\pi$
$151$	15.0778	1.22701	0.613507	+	0.789689i	$0.289758\pi$
$152$	16.6960	1.35422
$153$	19.4369	1.57138
$154$	−4.56430	−0.367802
$155$	2.69438	0.216418
$156$	−21.2883	−1.70442
$157$	−12.8889	−1.02865	−0.514323	−	0.857596i	$-0.671957\pi$
$157$	−12.8889	−1.02865	−0.514323	+	0.857596i	$0.671957\pi$
$158$	16.7510	1.33264
$159$	20.4611	1.62267
$160$	1.60743	0.127079
$161$	−6.96894	−0.549230
$162$	23.2665	1.82799
$163$	20.1318	1.57684	0.788421	−	0.615136i	$-0.210899\pi$
$163$	20.1318	1.57684	0.788421	+	0.615136i	$0.210899\pi$
$164$	−9.82123	−0.766909
$165$	−3.23490	−0.251836
$166$	−36.4715	−2.83074
$167$	8.58336	0.664201	0.332100	−	0.943244i	$-0.392243\pi$
$167$	8.58336	0.664201	0.332100	+	0.943244i	$0.392243\pi$
$168$	14.8631	1.14671
$169$	−7.63344	−0.587188
$170$	−16.9421	−1.29940
$171$	−10.4902	−0.802207
$172$	−11.1371	−0.849192
$173$	−16.4118	−1.24777	−0.623883	−	0.781517i	$-0.714446\pi$
$173$	−16.4118	−1.24777	−0.623883	+	0.781517i	$0.714446\pi$
$174$	−16.8413	−1.27673
$175$	1.40406	0.106137
$176$	4.02144	0.303128
$177$	7.07971	0.532144
$178$	−18.4592	−1.38358
$179$	−20.9673	−1.56717	−0.783585	−	0.621284i	$-0.786611\pi$
$179$	−20.9673	−1.56717	−0.783585	+	0.621284i	$0.786611\pi$
$180$	10.5945	0.789664
$181$	−10.1115	−0.751584	−0.375792	−	0.926704i	$-0.622629\pi$
$181$	−10.1115	−0.751584	−0.375792	+	0.926704i	$0.622629\pi$
$182$	−7.85085	−0.581944
$183$	−11.4945	−0.849697
$184$	21.8750	1.61265
$185$	4.17393	0.306873
$186$	15.6205	1.14535
$187$	9.45346	0.691305
$188$	−0.290615	−0.0211953
$189$	0.778640	0.0566377
$190$	9.14379	0.663360
$191$	26.9392	1.94925	0.974626	−	0.223841i	$-0.0718596\pi$
$191$	26.9392	1.94925	0.974626	+	0.223841i	$0.0718596\pi$
$192$	23.6627	1.70771
$193$	−10.1676	−0.731877	−0.365938	−	0.930639i	$-0.619252\pi$
$193$	−10.1676	−0.731877	−0.365938	+	0.930639i	$0.619252\pi$
$194$	1.32383	0.0950455
$195$	−5.56420	−0.398460
$196$	−19.2391	−1.37422
$197$	−7.17979	−0.511539	−0.255769	−	0.966738i	$-0.582329\pi$
$197$	−7.17979	−0.511539	−0.255769	+	0.966738i	$0.582329\pi$
$198$	−9.00180	−0.639730
$199$	10.0608	0.713193	0.356596	−	0.934259i	$-0.383937\pi$
$199$	10.0608	0.713193	0.356596	+	0.934259i	$0.383937\pi$
$200$	−4.40725	−0.311640
$201$	−33.3533	−2.35256
$202$	−4.47793	−0.315066
$203$	−4.07871	−0.286270
$204$	−64.5026	−4.51608
$205$	−2.56702	−0.179288
$206$	−24.7625	−1.72528
$207$	−13.7443	−0.955293
$208$	6.91710	0.479615
$209$	−5.10210	−0.352920
$210$	8.13998	0.561712
$211$	9.45875	0.651167	0.325584	−	0.945513i	$-0.394439\pi$
$211$	9.45875	0.651167	0.325584	+	0.945513i	$0.394439\pi$
$212$	−32.5921	−2.23843
$213$	−24.4831	−1.67755
$214$	−27.4707	−1.87785
$215$	−2.91094	−0.198524
$216$	−2.44410	−0.166300
$217$	3.78307	0.256812
$218$	28.6382	1.93962
$219$	34.6809	2.34352
$220$	5.15280	0.347402
$221$	16.2605	1.09380
$222$	24.1982	1.62407
$223$	9.90171	0.663067	0.331534	−	0.943443i	$-0.392434\pi$
$223$	9.90171	0.663067	0.331534	+	0.943443i	$0.392434\pi$
$224$	2.25693	0.150798
$225$	2.76911	0.184608
$226$	−20.5080	−1.36417
$227$	0.979376	0.0650035	0.0325017	−	0.999472i	$-0.489653\pi$
$227$	0.979376	0.0650035	0.0325017	+	0.999472i	$0.489653\pi$
$228$	34.8125	2.30552
$229$	11.7003	0.773180	0.386590	−	0.922252i	$-0.373653\pi$
$229$	11.7003	0.773180	0.386590	+	0.922252i	$0.373653\pi$
$230$	11.9802	0.789950
$231$	−4.54199	−0.298841
$232$	12.8028	0.840545
$233$	8.59031	0.562770	0.281385	−	0.959595i	$-0.409206\pi$
$233$	8.59031	0.562770	0.281385	+	0.959595i	$0.409206\pi$
$234$	−15.4836	−1.01219
$235$	−0.0759593	−0.00495504
$236$	−11.2771	−0.734079
$237$	16.6691	1.08278
$238$	−23.7878	−1.54193
$239$	−15.7697	−1.02005	−0.510027	−	0.860158i	$-0.670365\pi$
$239$	−15.7697	−1.02005	−0.510027	+	0.860158i	$0.670365\pi$
$240$	−7.17184	−0.462941
$241$	−30.4870	−1.96384	−0.981922	−	0.189288i	$-0.939382\pi$
$241$	−30.4870	−1.96384	−0.981922	+	0.189288i	$0.939382\pi$
$242$	22.1725	1.42530
$243$	21.4890	1.37852
$244$	18.3093	1.17214
$245$	−5.02861	−0.321266
$246$	−14.8822	−0.948852
$247$	−8.77589	−0.558397
$248$	−11.8748	−0.754051
$249$	−36.2933	−2.29999
$250$	−2.41370	−0.152656
$251$	11.2015	0.707031	0.353515	−	0.935429i	$-0.384986\pi$
$251$	11.2015	0.707031	0.353515	+	0.935429i	$0.384986\pi$
$252$	14.8753	0.937053
$253$	−6.68477	−0.420268
$254$	−18.2770	−1.14680
$255$	−16.8593	−1.05577
$256$	−29.9321	−1.87076
$257$	−5.00657	−0.312301	−0.156151	−	0.987733i	$-0.549909\pi$
$257$	−5.00657	−0.312301	−0.156151	+	0.987733i	$0.549909\pi$
$258$	−16.8760	−1.05066
$259$	5.86045	0.364151
$260$	8.86310	0.549666
$261$	−8.04411	−0.497918
$262$	5.74822	0.355126
$263$	−12.5781	−0.775599	−0.387799	−	0.921744i	$-0.626765\pi$
$263$	−12.5781	−0.775599	−0.387799	+	0.921744i	$0.626765\pi$
$264$	14.2570	0.877458
$265$	−8.51872	−0.523301
$266$	12.8384	0.787175
$267$	−18.3690	−1.12417
$268$	53.1277	3.24529
$269$	−22.8203	−1.39138	−0.695690	−	0.718342i	$-0.744901\pi$
$269$	−22.8203	−1.39138	−0.695690	+	0.718342i	$0.744901\pi$
$270$	−1.33855	−0.0814613
$271$	0.336467	0.0204389	0.0102195	−	0.999948i	$-0.496747\pi$
$271$	0.336467	0.0204389	0.0102195	+	0.999948i	$0.496747\pi$
$272$	20.9585	1.27080
$273$	−7.81247	−0.472832
$274$	−44.8722	−2.71083
$275$	1.34681	0.0812156
$276$	45.6114	2.74548
$277$	−11.1591	−0.670487	−0.335244	−	0.942132i	$-0.608819\pi$
$277$	−11.1591	−0.670487	−0.335244	+	0.942132i	$0.608819\pi$
$278$	−36.1208	−2.16638
$279$	7.46104	0.446681
$280$	−6.18805	−0.369807
$281$	19.1670	1.14340	0.571702	−	0.820461i	$-0.306283\pi$
$281$	19.1670	1.14340	0.571702	+	0.820461i	$0.306283\pi$
$282$	−0.440370	−0.0262237
$283$	13.2674	0.788662	0.394331	−	0.918968i	$-0.370976\pi$
$283$	13.2674	0.788662	0.394331	+	0.918968i	$0.370976\pi$
$284$	38.9986	2.31414
$285$	9.09909	0.538984
$286$	−7.53072	−0.445301
$287$	−3.60425	−0.212752
$288$	4.45117	0.262287
$289$	32.2686	1.89815
$290$	7.01165	0.411738
$291$	1.31736	0.0772249
$292$	−55.2426	−3.23283
$293$	2.12468	0.124125	0.0620625	−	0.998072i	$-0.480232\pi$
$293$	2.12468	0.124125	0.0620625	+	0.998072i	$0.480232\pi$
$294$	−29.1532	−1.70025
$295$	−2.94755	−0.171613
$296$	−18.3956	−1.06922
$297$	0.746889	0.0433389
$298$	−10.8096	−0.626185
$299$	−11.4982	−0.664956
$300$	−9.18951	−0.530556
$301$	−4.08713	−0.235578
$302$	−36.3932	−2.09420
$303$	−4.45604	−0.255993
$304$	−11.3115	−0.648758
$305$	4.78559	0.274022
$306$	−46.9147	−2.68193
$307$	21.2778	1.21439	0.607194	−	0.794554i	$-0.292295\pi$
$307$	21.2778	1.21439	0.607194	+	0.794554i	$0.292295\pi$
$308$	7.23484	0.412244
$309$	−24.6414	−1.40180
$310$	−6.50341	−0.369369
$311$	−16.1454	−0.915520	−0.457760	−	0.889076i	$-0.651348\pi$
$311$	−16.1454	−0.915520	−0.457760	+	0.889076i	$0.651348\pi$
$312$	24.5228	1.38833
$313$	−17.2386	−0.974382	−0.487191	−	0.873296i	$-0.661978\pi$
$313$	−17.2386	−0.974382	−0.487191	+	0.873296i	$0.661978\pi$
$314$	31.1099	1.75563
$315$	3.88801	0.219064
$316$	−26.5519	−1.49366
$317$	29.1411	1.63673	0.818364	−	0.574700i	$-0.194881\pi$
$317$	29.1411	1.63673	0.818364	+	0.574700i	$0.194881\pi$
$318$	−49.3869	−2.76948
$319$	−3.91240	−0.219052
$320$	−9.85167	−0.550725
$321$	−27.3364	−1.52577
$322$	16.8209	0.937393
$323$	−26.5906	−1.47954
$324$	−36.8795	−2.04886
$325$	2.31658	0.128501
$326$	−48.5920	−2.69126
$327$	28.4982	1.57595
$328$	11.3135	0.624683
$329$	−0.106651	−0.00587988
$330$	7.80806	0.429819
$331$	−4.75231	−0.261210	−0.130605	−	0.991434i	$-0.541692\pi$
$331$	−4.75231	−0.261210	−0.130605	+	0.991434i	$0.541692\pi$
$332$	57.8108	3.17278
$333$	11.5581	0.633379
$334$	−20.7176	−1.13362
$335$	13.8862	0.758685
$336$	−10.0697	−0.549348
$337$	−4.33774	−0.236292	−0.118146	−	0.992996i	$-0.537695\pi$
$337$	−4.33774	−0.236292	−0.118146	+	0.992996i	$0.537695\pi$
$338$	18.4248	1.00218
$339$	−20.4077	−1.10839
$340$	26.8548	1.45641
$341$	3.62881	0.196511
$342$	25.3202	1.36916
$343$	−16.8889	−0.911915
$344$	12.8292	0.691706
$345$	11.9216	0.641839
$346$	39.6131	2.12962
$347$	−20.2349	−1.08627	−0.543134	−	0.839646i	$-0.682762\pi$
$347$	−20.2349	−1.08627	−0.543134	+	0.839646i	$0.682762\pi$
$348$	26.6950	1.43100
$349$	17.3333	0.927832	0.463916	−	0.885879i	$-0.346444\pi$
$349$	17.3333	0.927832	0.463916	+	0.885879i	$0.346444\pi$
$350$	−3.38898	−0.181149
$351$	1.28469	0.0685717
$352$	2.16490	0.115390
$353$	18.5967	0.989801	0.494901	−	0.868950i	$-0.335204\pi$
$353$	18.5967	0.989801	0.494901	+	0.868950i	$0.335204\pi$
$354$	−17.0883	−0.908232
$355$	10.1932	0.541000
$356$	29.2596	1.55076
$357$	−23.6715	−1.25283
$358$	50.6088	2.67476
$359$	13.3428	0.704207	0.352104	−	0.935961i	$-0.385466\pi$
$359$	13.3428	0.704207	0.352104	+	0.935961i	$0.385466\pi$
$360$	−12.2042	−0.643217
$361$	−4.64885	−0.244676
$362$	24.4062	1.28276
$363$	22.0641	1.15806
$364$	12.4443	0.652260
$365$	−14.4390	−0.755770
$366$	27.7442	1.45021
$367$	−33.6548	−1.75677	−0.878383	−	0.477958i	$-0.841377\pi$
$367$	−33.6548	−1.75677	−0.878383	+	0.477958i	$0.841377\pi$
$368$	−14.8203	−0.772562
$369$	−7.10836	−0.370046
$370$	−10.0746	−0.523754
$371$	−11.9608	−0.620974
$372$	−24.7600	−1.28375
$373$	14.8456	0.768675	0.384337	−	0.923193i	$-0.374430\pi$
$373$	14.8456	0.768675	0.384337	+	0.923193i	$0.374430\pi$
$374$	−22.8178	−1.17988
$375$	−2.40190	−0.124033
$376$	0.334772	0.0172645
$377$	−6.72953	−0.346589
$378$	−1.87940	−0.0966659
$379$	−25.0233	−1.28536	−0.642680	−	0.766135i	$-0.722178\pi$
$379$	−25.0233	−1.28536	−0.642680	+	0.766135i	$0.722178\pi$
$380$	−14.4938	−0.743514
$381$	−18.1877	−0.931783
$382$	−65.0230	−3.32687
$383$	32.7703	1.67448	0.837242	−	0.546832i	$-0.184166\pi$
$383$	32.7703	1.67448	0.837242	+	0.546832i	$0.184166\pi$
$384$	−49.3928	−2.52057
$385$	1.89100	0.0963743
$386$	24.5414	1.24912
$387$	−8.06072	−0.409749
$388$	−2.09839	−0.106530
$389$	−3.55272	−0.180130	−0.0900650	−	0.995936i	$-0.528707\pi$
$389$	−3.55272	−0.180130	−0.0900650	+	0.995936i	$0.528707\pi$
$390$	13.4303	0.680069
$391$	−34.8390	−1.76188
$392$	22.1624	1.11937
$393$	5.72012	0.288542
$394$	17.3298	0.873064
$395$	−6.93998	−0.349189
$396$	14.2687	0.717029
$397$	−5.89121	−0.295671	−0.147836	−	0.989012i	$-0.547231\pi$
$397$	−5.89121	−0.295671	−0.147836	+	0.989012i	$0.547231\pi$
$398$	−24.2838	−1.21724
$399$	12.7757	0.639584
$400$	2.98591	0.149295
$401$	−8.70204	−0.434559	−0.217280	−	0.976109i	$-0.569718\pi$
$401$	−8.70204	−0.434559	−0.217280	+	0.976109i	$0.569718\pi$
$402$	80.5047	4.01521
$403$	6.24175	0.310924
$404$	7.09794	0.353136
$405$	−9.63935	−0.478983
$406$	9.84478	0.488588
$407$	5.62148	0.278646
$408$	74.3032	3.67856
$409$	−10.1538	−0.502075	−0.251038	−	0.967977i	$-0.580772\pi$
$409$	−10.1538	−0.502075	−0.251038	+	0.967977i	$0.580772\pi$
$410$	6.19600	0.305998
$411$	−44.6528	−2.20256
$412$	39.2508	1.93375
$413$	−4.13854	−0.203644
$414$	33.1745	1.63044
$415$	15.1102	0.741733
$416$	3.72375	0.182572
$417$	−35.9442	−1.76020
$418$	12.3149	0.602343
$419$	12.3635	0.603997	0.301998	−	0.953308i	$-0.402346\pi$
$419$	12.3635	0.603997	0.301998	+	0.953308i	$0.402346\pi$
$420$	−12.9026	−0.629584
$421$	−4.97291	−0.242365	−0.121182	−	0.992630i	$-0.538669\pi$
$421$	−4.97291	−0.242365	−0.121182	+	0.992630i	$0.538669\pi$
$422$	−22.8306	−1.11137
$423$	−0.210340	−0.0102271
$424$	37.5442	1.82331
$425$	7.01916	0.340479
$426$	59.0948	2.86315
$427$	6.71925	0.325168
$428$	43.5435	2.10476
$429$	−7.49390	−0.361809
$430$	7.02612	0.338830
$431$	23.3955	1.12692	0.563462	−	0.826142i	$-0.309469\pi$
$431$	23.3955	1.12692	0.563462	+	0.826142i	$0.309469\pi$
$432$	1.65587	0.0796681
$433$	−32.6466	−1.56890	−0.784449	−	0.620193i	$-0.787054\pi$
$433$	−32.6466	−1.56890	−0.784449	+	0.620193i	$0.787054\pi$
$434$	−9.13119	−0.438311
$435$	6.97737	0.334539
$436$	−45.3942	−2.17399
$437$	18.8029	0.899463
$438$	−83.7093	−3.99978
$439$	−29.8033	−1.42244	−0.711218	−	0.702972i	$-0.751856\pi$
$439$	−29.8033	−1.42244	−0.711218	+	0.702972i	$0.751856\pi$
$440$	−5.93572	−0.282975
$441$	−13.9248	−0.663086
$442$	−39.2478	−1.86683
$443$	−31.8442	−1.51297	−0.756483	−	0.654014i	$-0.773084\pi$
$443$	−31.8442	−1.51297	−0.756483	+	0.654014i	$0.773084\pi$
$444$	−38.3563	−1.82031
$445$	7.64771	0.362536
$446$	−23.8997	−1.13168
$447$	−10.7568	−0.508778
$448$	−13.8323	−0.653517
$449$	−1.57389	−0.0742764	−0.0371382	−	0.999310i	$-0.511824\pi$
$449$	−1.57389	−0.0742764	−0.0371382	+	0.999310i	$0.511824\pi$
$450$	−6.68381	−0.315078
$451$	−3.45728	−0.162797
$452$	32.5070	1.52900
$453$	−36.2153	−1.70154
$454$	−2.36392	−0.110944
$455$	3.25262	0.152485
$456$	−40.1020	−1.87795
$457$	−31.1578	−1.45750	−0.728751	−	0.684779i	$-0.759899\pi$
$457$	−31.1578	−1.45750	−0.728751	+	0.684779i	$0.759899\pi$
$458$	−28.2411	−1.31962
$459$	3.89256	0.181689
$460$	−18.9897	−0.885400
$461$	19.1206	0.890533	0.445267	−	0.895398i	$-0.353109\pi$
$461$	19.1206	0.890533	0.445267	+	0.895398i	$0.353109\pi$
$462$	10.9630	0.510045
$463$	3.06584	0.142481	0.0712407	−	0.997459i	$-0.477304\pi$
$463$	3.06584	0.142481	0.0712407	+	0.997459i	$0.477304\pi$
$464$	−8.67388	−0.402675
$465$	−6.47162	−0.300114
$466$	−20.7344	−0.960503
$467$	−18.9796	−0.878271	−0.439136	−	0.898421i	$-0.644715\pi$
$467$	−18.9796	−0.878271	−0.439136	+	0.898421i	$0.644715\pi$
$468$	24.5429	1.13450
$469$	19.4971	0.900292
$470$	0.183343	0.00845697
$471$	30.9578	1.42646
$472$	12.9906	0.597941
$473$	−3.92047	−0.180264
$474$	−40.2342	−1.84802
$475$	−3.78829	−0.173819
$476$	37.7058	1.72824
$477$	−23.5893	−1.08008
$478$	38.0632	1.74097
$479$	−42.6603	−1.94920	−0.974599	−	0.223955i	$-0.928103\pi$
$479$	−42.6603	−1.94920	−0.974599	+	0.223955i	$0.928103\pi$
$480$	−3.86089	−0.176225
$481$	9.66925	0.440880
$482$	73.5865	3.35177
$483$	16.7387	0.761637
$484$	−35.1455	−1.59752
$485$	−0.548466	−0.0249045
$486$	−51.8680	−2.35278
$487$	11.7319	0.531624	0.265812	−	0.964025i	$-0.414360\pi$
$487$	11.7319	0.531624	0.265812	+	0.964025i	$0.414360\pi$
$488$	−21.0913	−0.954758
$489$	−48.3545	−2.18667
$490$	12.1375	0.548318
$491$	12.4886	0.563601	0.281800	−	0.959473i	$-0.409068\pi$
$491$	12.4886	0.563601	0.281800	+	0.959473i	$0.409068\pi$
$492$	23.5896	1.06350
$493$	−20.3902	−0.918330
$494$	21.1823	0.953039
$495$	3.72947	0.167627
$496$	8.04516	0.361238
$497$	14.3119	0.641977
$498$	87.6010	3.92549
$499$	−27.7358	−1.24163	−0.620814	−	0.783958i	$-0.713198\pi$
$499$	−27.7358	−1.24163	−0.620814	+	0.783958i	$0.713198\pi$
$500$	3.82593	0.171101
$501$	−20.6164	−0.921071
$502$	−27.0370	−1.20672
$503$	−30.8615	−1.37605	−0.688023	−	0.725689i	$-0.741521\pi$
$503$	−30.8615	−1.37605	−0.688023	+	0.725689i	$0.741521\pi$
$504$	−17.1354	−0.763273
$505$	1.85522	0.0825560
$506$	16.1350	0.717289
$507$	18.3348	0.814275
$508$	28.9708	1.28537
$509$	34.8535	1.54485	0.772427	−	0.635103i	$-0.219042\pi$
$509$	34.8535	1.54485	0.772427	+	0.635103i	$0.219042\pi$
$510$	40.6932	1.80193
$511$	−20.2732	−0.896834
$512$	31.1189	1.37528
$513$	−2.10084	−0.0927545
$514$	12.0844	0.533018
$515$	10.2591	0.452072
$516$	26.7501	1.17761
$517$	−0.102303	−0.00449926
$518$	−14.1454	−0.621511
$519$	39.4195	1.73032
$520$	−10.2098	−0.447728
$521$	6.73237	0.294951	0.147475	−	0.989066i	$-0.452885\pi$
$521$	6.73237	0.294951	0.147475	+	0.989066i	$0.452885\pi$
$522$	19.4161	0.849817
$523$	8.90804	0.389522	0.194761	−	0.980851i	$-0.437607\pi$
$523$	8.90804	0.389522	0.194761	+	0.980851i	$0.437607\pi$
$524$	−9.11147	−0.398036
$525$	−3.37241	−0.147184
$526$	30.3597	1.32375
$527$	18.9123	0.823831
$528$	−9.65909	−0.420358
$529$	1.63551	0.0711093
$530$	20.5616	0.893140
$531$	−8.16210	−0.354205
$532$	−20.3501	−0.882290
$533$	−5.94670	−0.257580
$534$	44.3372	1.91866
$535$	11.3811	0.492050
$536$	−61.2001	−2.64344
$537$	50.3614	2.17325
$538$	55.0814	2.37473
$539$	−6.77257	−0.291715
$540$	2.12172	0.0913043
$541$	27.0600	1.16340	0.581701	−	0.813403i	$-0.302387\pi$
$541$	27.0600	1.16340	0.581701	+	0.813403i	$0.302387\pi$
$542$	−0.812130	−0.0348840
$543$	24.2869	1.04225
$544$	11.2828	0.483747
$545$	−11.8649	−0.508235
$546$	18.8569	0.807003
$547$	18.3798	0.785866	0.392933	−	0.919567i	$-0.371461\pi$
$547$	18.3798	0.785866	0.392933	+	0.919567i	$0.371461\pi$
$548$	71.1266	3.03838
$549$	13.2518	0.565575
$550$	−3.25079	−0.138614
$551$	11.0048	0.468818
$552$	−52.5416	−2.23632
$553$	−9.74416	−0.414364
$554$	26.9348	1.14435
$555$	−10.0254	−0.425553
$556$	57.2548	2.42814
$557$	−2.20607	−0.0934744	−0.0467372	−	0.998907i	$-0.514882\pi$
$557$	−2.20607	−0.0934744	−0.0467372	+	0.998907i	$0.514882\pi$
$558$	−18.0087	−0.762369
$559$	−6.74343	−0.285217
$560$	4.19240	0.177161
$561$	−22.7062	−0.958658
$562$	−46.2632	−1.95150
$563$	26.2511	1.10635	0.553177	−	0.833064i	$-0.313415\pi$
$563$	26.2511	1.10635	0.553177	+	0.833064i	$0.313415\pi$
$564$	0.698028	0.0293923
$565$	8.49649	0.357450
$566$	−32.0234	−1.34604
$567$	−13.5342	−0.568384
$568$	−44.9241	−1.88498
$569$	37.4016	1.56796	0.783979	−	0.620787i	$-0.213187\pi$
$569$	37.4016	1.56796	0.783979	+	0.620787i	$0.213187\pi$
$570$	−21.9624	−0.919906
$571$	13.7445	0.575188	0.287594	−	0.957752i	$-0.407145\pi$
$571$	13.7445	0.575188	0.287594	+	0.957752i	$0.407145\pi$
$572$	11.9369	0.499106
$573$	−64.7052	−2.70310
$574$	8.69956	0.363113
$575$	−4.96342	−0.206989
$576$	−27.2804	−1.13668
$577$	−35.8908	−1.49415	−0.747077	−	0.664737i	$-0.768543\pi$
$577$	−35.8908	−1.49415	−0.747077	+	0.664737i	$0.768543\pi$
$578$	−77.8865	−3.23965
$579$	24.4214	1.01492
$580$	−11.1141	−0.461488
$581$	21.2157	0.880176
$582$	−3.17971	−0.131803
$583$	−11.4731	−0.475167
$584$	63.6362	2.63329
$585$	6.41488	0.265223
$586$	−5.12833	−0.211849
$587$	35.1146	1.44934	0.724668	−	0.689098i	$-0.241993\pi$
$587$	35.1146	1.44934	0.724668	+	0.689098i	$0.241993\pi$
$588$	46.2105	1.90569
$589$	−10.2071	−0.420576
$590$	7.11449	0.292899
$591$	17.2451	0.709369
$592$	12.4630	0.512225
$593$	47.6283	1.95586	0.977929	−	0.208936i	$-0.0669999\pi$
$593$	47.6283	1.95586	0.977929	+	0.208936i	$0.0669999\pi$
$594$	−1.80276	−0.0739683
$595$	9.85533	0.404029
$596$	17.1343	0.701847
$597$	−24.1651	−0.989010
$598$	27.7531	1.13491
$599$	−12.7183	−0.519658	−0.259829	−	0.965655i	$-0.583666\pi$
$599$	−12.7183	−0.519658	−0.259829	+	0.965655i	$0.583666\pi$
$600$	10.5858	0.432162
$601$	30.3922	1.23972	0.619862	−	0.784711i	$-0.287188\pi$
$601$	30.3922	1.23972	0.619862	+	0.784711i	$0.287188\pi$
$602$	9.86510	0.402072
$603$	38.4525	1.56591
$604$	57.6867	2.34724
$605$	−9.18611	−0.373468
$606$	10.7555	0.436914
$607$	−22.7485	−0.923333	−0.461667	−	0.887054i	$-0.652748\pi$
$607$	−22.7485	−0.923333	−0.461667	+	0.887054i	$0.652748\pi$
$608$	−6.08942	−0.246959
$609$	9.79665	0.396980
$610$	−11.5510	−0.467684
$611$	−0.175966	−0.00711882
$612$	74.3641	3.00599
$613$	−13.1111	−0.529552	−0.264776	−	0.964310i	$-0.585298\pi$
$613$	−13.1111	−0.529552	−0.264776	+	0.964310i	$0.585298\pi$
$614$	−51.3582	−2.07265
$615$	6.16571	0.248625
$616$	−8.33412	−0.335791
$617$	34.9189	1.40578	0.702891	−	0.711298i	$-0.251892\pi$
$617$	34.9189	1.40578	0.702891	+	0.711298i	$0.251892\pi$
$618$	59.4770	2.39251
$619$	−15.2192	−0.611712	−0.305856	−	0.952078i	$-0.598943\pi$
$619$	−15.2192	−0.611712	−0.305856	+	0.952078i	$0.598943\pi$
$620$	10.3085	0.414000
$621$	−2.75252	−0.110455
$622$	38.9700	1.56256
$623$	10.7378	0.430203
$624$	−16.6142	−0.665099
$625$	1.00000	0.0400000
$626$	41.6087	1.66302
$627$	12.2547	0.489407
$628$	−49.3121	−1.96777
$629$	29.2975	1.16817
$630$	−9.38447	−0.373886
$631$	23.0461	0.917450	0.458725	−	0.888578i	$-0.348306\pi$
$631$	23.0461	0.917450	0.458725	+	0.888578i	$0.348306\pi$
$632$	30.5863	1.21666
$633$	−22.7190	−0.902998
$634$	−70.3378	−2.79347
$635$	7.57221	0.300494
$636$	78.2828	3.10412
$637$	−11.6492	−0.461558
$638$	9.44334	0.373865
$639$	28.2262	1.11661
$640$	20.5641	0.812867
$641$	23.0157	0.909064	0.454532	−	0.890730i	$-0.349807\pi$
$641$	23.0157	0.909064	0.454532	+	0.890730i	$0.349807\pi$
$642$	65.9817	2.60409
$643$	−5.65904	−0.223171	−0.111585	−	0.993755i	$-0.535593\pi$
$643$	−5.65904	−0.223171	−0.111585	+	0.993755i	$0.535593\pi$
$644$	−26.6627	−1.05066
$645$	6.99177	0.275301
$646$	64.1817	2.52519
$647$	35.8576	1.40971	0.704854	−	0.709352i	$-0.251012\pi$
$647$	35.8576	1.40971	0.704854	+	0.709352i	$0.251012\pi$
$648$	42.4830	1.66889
$649$	−3.96978	−0.155828
$650$	−5.59153	−0.219318
$651$	−9.08655	−0.356130
$652$	77.0229	3.01645
$653$	−11.6807	−0.457101	−0.228551	−	0.973532i	$-0.573399\pi$
$653$	−11.6807	−0.457101	−0.228551	+	0.973532i	$0.573399\pi$
$654$	−68.7860	−2.68975
$655$	−2.38150	−0.0930529
$656$	−7.66487	−0.299263
$657$	−39.9832	−1.55989
$658$	0.257424	0.0100354
$659$	14.2436	0.554853	0.277426	−	0.960747i	$-0.410519\pi$
$659$	14.2436	0.554853	0.277426	+	0.960747i	$0.410519\pi$
$660$	−12.3765	−0.481755
$661$	19.7456	0.768014	0.384007	−	0.923330i	$-0.374544\pi$
$661$	19.7456	0.768014	0.384007	+	0.923330i	$0.374544\pi$
$662$	11.4706	0.445819
$663$	−39.0560	−1.51681
$664$	−66.5947	−2.58437
$665$	−5.31899	−0.206262
$666$	−27.8977	−1.08102
$667$	14.4184	0.558284
$668$	32.8394	1.27059
$669$	−23.7829	−0.919500
$670$	−33.5171	−1.29488
$671$	6.44526	0.248817
$672$	−5.42092	−0.209117
$673$	32.5239	1.25370	0.626852	−	0.779139i	$-0.284343\pi$
$673$	32.5239	1.25370	0.626852	+	0.779139i	$0.284343\pi$
$674$	10.4700	0.403289
$675$	0.554562	0.0213451
$676$	−29.2051	−1.12327
$677$	−6.87132	−0.264086	−0.132043	−	0.991244i	$-0.542154\pi$
$677$	−6.87132	−0.264086	−0.132043	+	0.991244i	$0.542154\pi$
$678$	49.2580	1.89174
$679$	−0.770079	−0.0295529
$680$	−30.9352	−1.18631
$681$	−2.35236	−0.0901427
$682$	−8.75885	−0.335394
$683$	35.3606	1.35304	0.676519	−	0.736425i	$-0.263488\pi$
$683$	35.3606	1.35304	0.676519	+	0.736425i	$0.263488\pi$
$684$	−40.1349	−1.53460
$685$	18.5906	0.710312
$686$	40.7647	1.55640
$687$	−28.1030	−1.07220
$688$	−8.69178	−0.331371
$689$	−19.7343	−0.751818
$690$	−28.7752	−1.09545
$691$	−21.1252	−0.803641	−0.401820	−	0.915719i	$-0.631622\pi$
$691$	−21.1252	−0.803641	−0.401820	+	0.915719i	$0.631622\pi$
$692$	−62.7905	−2.38694
$693$	5.23640	0.198914
$694$	48.8410	1.85398
$695$	14.9649	0.567652
$696$	−30.7510	−1.16562
$697$	−18.0183	−0.682491
$698$	−41.8374	−1.58357
$699$	−20.6330	−0.780413
$700$	5.37185	0.203037
$701$	19.7411	0.745610	0.372805	−	0.927910i	$-0.378396\pi$
$701$	19.7411	0.745610	0.372805	+	0.927910i	$0.378396\pi$
$702$	−3.10085	−0.117034
$703$	−15.8121	−0.596363
$704$	−13.2683	−0.500068
$705$	0.182446	0.00687133
$706$	−44.8868	−1.68934
$707$	2.60484	0.0979650
$708$	27.0865	1.01797
$709$	35.3436	1.32736	0.663678	−	0.748018i	$-0.268994\pi$
$709$	35.3436	1.32736	0.663678	+	0.748018i	$0.268994\pi$
$710$	−24.6034	−0.923348
$711$	−19.2176	−0.720717
$712$	−33.7054	−1.26316
$713$	−13.3733	−0.500835
$714$	57.1358	2.13825
$715$	3.11999	0.116681
$716$	−80.2196	−2.99795
$717$	37.8771	1.41455
$718$	−32.2055	−1.20190
$719$	35.8098	1.33548	0.667740	−	0.744395i	$-0.267262\pi$
$719$	35.8098	1.33548	0.667740	+	0.744395i	$0.267262\pi$
$720$	8.26832	0.308142
$721$	14.4045	0.536451
$722$	11.2209	0.417599
$723$	73.2268	2.72333
$724$	−38.6861	−1.43776
$725$	−2.90494	−0.107887
$726$	−53.2561	−1.97652
$727$	12.3396	0.457649	0.228824	−	0.973468i	$-0.426512\pi$
$727$	12.3396	0.457649	0.228824	+	0.973468i	$0.426512\pi$
$728$	−14.3351	−0.531296
$729$	−22.6965	−0.840609
$730$	34.8513	1.28990
$731$	−20.4323	−0.755717
$732$	−43.9772	−1.62544
$733$	−16.9740	−0.626948	−0.313474	−	0.949597i	$-0.601493\pi$
$733$	−16.9740	−0.626948	−0.313474	+	0.949597i	$0.601493\pi$
$734$	81.2325	2.99835
$735$	12.0782	0.445512
$736$	−7.97836	−0.294086
$737$	18.7021	0.688899
$738$	17.1574	0.631574
$739$	32.4712	1.19447	0.597235	−	0.802066i	$-0.296266\pi$
$739$	32.4712	1.19447	0.597235	+	0.802066i	$0.296266\pi$
$740$	15.9692	0.587039
$741$	21.0788	0.774349
$742$	28.8698	1.05984
$743$	29.8691	1.09579	0.547896	−	0.836546i	$-0.315429\pi$
$743$	29.8691	1.09579	0.547896	+	0.836546i	$0.315429\pi$
$744$	28.5221	1.04567
$745$	4.47845	0.164078
$746$	−35.8327	−1.31193
$747$	41.8420	1.53092
$748$	36.1683	1.32244
$749$	15.9798	0.583890
$750$	5.79746	0.211693
$751$	4.94347	0.180390	0.0901948	−	0.995924i	$-0.471251\pi$
$751$	4.94347	0.180390	0.0901948	+	0.995924i	$0.471251\pi$
$752$	−0.226807	−0.00827081
$753$	−26.9048	−0.980466
$754$	16.2431	0.591537
$755$	15.0778	0.548737
$756$	2.97902	0.108346
$757$	49.0017	1.78100	0.890498	−	0.454988i	$-0.150356\pi$
$757$	49.0017	1.78100	0.890498	+	0.454988i	$0.150356\pi$
$758$	60.3987	2.19378
$759$	16.0561	0.582801
$760$	16.6960	0.605626
$761$	7.98010	0.289278	0.144639	−	0.989484i	$-0.453798\pi$
$761$	7.98010	0.289278	0.144639	+	0.989484i	$0.453798\pi$
$762$	43.8995	1.59031
$763$	−16.6590	−0.603096
$764$	103.068	3.72885
$765$	19.4369	0.702741
$766$	−79.0976	−2.85791
$767$	−6.82824	−0.246554
$768$	71.8939	2.59425
$769$	31.1557	1.12350	0.561752	−	0.827306i	$-0.310127\pi$
$769$	31.1557	1.12350	0.561752	+	0.827306i	$0.310127\pi$
$770$	−4.56430	−0.164486
$771$	12.0253	0.433080
$772$	−38.9004	−1.40006
$773$	45.7251	1.64462	0.822308	−	0.569042i	$-0.192686\pi$
$773$	45.7251	1.64462	0.822308	+	0.569042i	$0.192686\pi$
$774$	19.4561	0.699336
$775$	2.69438	0.0967849
$776$	2.41723	0.0867734
$777$	−14.0762	−0.504981
$778$	8.57519	0.307435
$779$	9.72460	0.348420
$780$	−21.2883	−0.762242
$781$	13.7283	0.491238
$782$	84.0908	3.00708
$783$	−1.61097	−0.0575714
$784$	−15.0150	−0.536249
$785$	−12.8889	−0.460025
$786$	−13.8066	−0.492467
$787$	4.30557	0.153477	0.0767384	−	0.997051i	$-0.475549\pi$
$787$	4.30557	0.153477	0.0767384	+	0.997051i	$0.475549\pi$
$788$	−27.4694	−0.978557
$789$	30.2113	1.07555
$790$	16.7510	0.595975
$791$	11.9296	0.424167
$792$	−16.4367	−0.584053
$793$	11.0862	0.393683
$794$	14.2196	0.504634
$795$	20.4611	0.725681
$796$	38.4920	1.36431
$797$	−28.9588	−1.02577	−0.512887	−	0.858456i	$-0.671424\pi$
$797$	−28.9588	−1.02577	−0.512887	+	0.858456i	$0.671424\pi$
$798$	−30.8366	−1.09160
$799$	−0.533170	−0.0188622
$800$	1.60743	0.0568313
$801$	21.1774	0.748266
$802$	21.0041	0.741681
$803$	−19.4465	−0.686253
$804$	−127.607	−4.50037
$805$	−6.96894	−0.245623
$806$	−15.0657	−0.530666
$807$	54.8121	1.92948
$808$	−8.17641	−0.287645
$809$	−8.36970	−0.294263	−0.147132	−	0.989117i	$-0.547004\pi$
$809$	−8.36970	−0.294263	−0.147132	+	0.989117i	$0.547004\pi$
$810$	23.2665	0.817500
$811$	−48.3799	−1.69885	−0.849424	−	0.527711i	$-0.823050\pi$
$811$	−48.3799	−1.69885	−0.849424	+	0.527711i	$0.823050\pi$
$812$	−15.6049	−0.547624
$813$	−0.808160	−0.0283434
$814$	−13.5686	−0.475578
$815$	20.1318	0.705185
$816$	−50.3403	−1.76226
$817$	11.0275	0.385803
$818$	24.5083	0.856913
$819$	9.00689	0.314726
$820$	−9.82123	−0.342972
$821$	−17.5754	−0.613387	−0.306694	−	0.951808i	$-0.599223\pi$
$821$	−17.5754	−0.613387	−0.306694	+	0.951808i	$0.599223\pi$
$822$	107.778	3.75920
$823$	−47.7046	−1.66288	−0.831438	−	0.555617i	$-0.812482\pi$
$823$	−47.7046	−1.66288	−0.831438	+	0.555617i	$0.812482\pi$
$824$	−45.2147	−1.57513
$825$	−3.23490	−0.112625
$826$	9.98918	0.347568
$827$	−29.6597	−1.03137	−0.515684	−	0.856779i	$-0.672462\pi$
$827$	−29.6597	−1.03137	−0.515684	+	0.856779i	$0.672462\pi$
$828$	−52.5847	−1.82744
$829$	46.6169	1.61907	0.809537	−	0.587069i	$-0.199718\pi$
$829$	46.6169	1.61907	0.809537	+	0.587069i	$0.199718\pi$
$830$	−36.4715	−1.26595
$831$	26.8031	0.929789
$832$	−22.8222	−0.791218
$833$	−35.2966	−1.22296
$834$	86.7584	3.00420
$835$	8.58336	0.297040
$836$	−19.5203	−0.675124
$837$	1.49420	0.0516471
$838$	−29.8418	−1.03087
$839$	21.4384	0.740135	0.370067	−	0.929005i	$-0.379335\pi$
$839$	21.4384	0.740135	0.370067	+	0.929005i	$0.379335\pi$
$840$	14.8631	0.512825
$841$	−20.5613	−0.709011
$842$	12.0031	0.413654
$843$	−46.0371	−1.58560
$844$	36.1886	1.24566
$845$	−7.63344	−0.262598
$846$	0.507697	0.0174550
$847$	−12.8979	−0.443176
$848$	−25.4361	−0.873480
$849$	−31.8668	−1.09367
$850$	−16.9421	−0.581110
$851$	−20.7170	−0.710168
$852$	−93.6707	−3.20911
$853$	−0.0493458	−0.00168957	−0.000844785	−	1.00000i	$-0.500269\pi$
$853$	−0.0493458	−0.00168957	−0.000844785		1.00000i	$0.500269\pi$
$854$	−16.2182	−0.554977
$855$	−10.4902	−0.358758
$856$	−50.1596	−1.71442
$857$	37.8754	1.29380	0.646899	−	0.762576i	$-0.276065\pi$
$857$	37.8754	1.29380	0.646899	+	0.762576i	$0.276065\pi$
$858$	18.0880	0.617515
$859$	23.6822	0.808027	0.404014	−	0.914753i	$-0.367615\pi$
$859$	23.6822	0.808027	0.404014	+	0.914753i	$0.367615\pi$
$860$	−11.1371	−0.379770
$861$	8.65703	0.295031
$862$	−56.4697	−1.92337
$863$	−8.58667	−0.292294	−0.146147	−	0.989263i	$-0.546687\pi$
$863$	−8.58667	−0.292294	−0.146147	+	0.989263i	$0.546687\pi$
$864$	0.891422	0.0303268
$865$	−16.4118	−0.558018
$866$	78.7991	2.67770
$867$	−77.5058	−2.63223
$868$	14.4738	0.491272
$869$	−9.34683	−0.317069
$870$	−16.8413	−0.570972
$871$	32.1686	1.08999
$872$	52.2915	1.77081
$873$	−1.51876	−0.0514024
$874$	−45.3844	−1.53515
$875$	1.40406	0.0474659
$876$	132.687	4.48308
$877$	15.8419	0.534942	0.267471	−	0.963566i	$-0.413812\pi$
$877$	15.8419	0.534942	0.267471	+	0.963566i	$0.413812\pi$
$878$	71.9362	2.42773
$879$	−5.10326	−0.172129
$880$	4.02144	0.135563
$881$	−1.53600	−0.0517491	−0.0258746	−	0.999665i	$-0.508237\pi$
$881$	−1.53600	−0.0517491	−0.0258746	+	0.999665i	$0.508237\pi$
$882$	33.6103	1.13172
$883$	15.5534	0.523415	0.261707	−	0.965147i	$-0.415715\pi$
$883$	15.5534	0.523415	0.261707	+	0.965147i	$0.415715\pi$
$884$	62.2115	2.09240
$885$	7.07971	0.237982
$886$	76.8624	2.58224
$887$	−33.0438	−1.10950	−0.554751	−	0.832016i	$-0.687187\pi$
$887$	−33.0438	−1.10950	−0.554751	+	0.832016i	$0.687187\pi$
$888$	44.1843	1.48273
$889$	10.6318	0.356581
$890$	−18.4592	−0.618755
$891$	−12.9823	−0.434925
$892$	37.8833	1.26843
$893$	0.287756	0.00962938
$894$	25.9636	0.868353
$895$	−20.9673	−0.700860
$896$	28.8732	0.964587
$897$	27.6174	0.922119
$898$	3.79889	0.126771
$899$	−7.82701	−0.261045
$900$	10.5945	0.353148
$901$	−59.7942	−1.99204
$902$	8.34482	0.277852
$903$	9.81688	0.326685
$904$	−37.4462	−1.24544
$905$	−10.1115	−0.336119
$906$	87.4128	2.90410
$907$	−39.6927	−1.31797	−0.658987	−	0.752154i	$-0.729015\pi$
$907$	−39.6927	−1.31797	−0.658987	+	0.752154i	$0.729015\pi$
$908$	3.74703	0.124350
$909$	5.13731	0.170394
$910$	−7.85085	−0.260253
$911$	44.7037	1.48110	0.740551	−	0.672001i	$-0.234565\pi$
$911$	44.7037	1.48110	0.740551	+	0.672001i	$0.234565\pi$
$912$	27.1690	0.899657
$913$	20.3506	0.673506
$914$	75.2056	2.48758
$915$	−11.4945	−0.379996
$916$	44.7647	1.47907
$917$	−3.34377	−0.110421
$918$	−9.39546	−0.310096
$919$	39.7655	1.31174	0.655871	−	0.754873i	$-0.272301\pi$
$919$	39.7655	1.31174	0.655871	+	0.754873i	$0.272301\pi$
$920$	21.8750	0.721199
$921$	−51.1071	−1.68404
$922$	−46.1512	−1.51991
$923$	23.6135	0.777247
$924$	−17.3774	−0.571673
$925$	4.17393	0.137238
$926$	−7.40000	−0.243179
$927$	28.4088	0.933066
$928$	−4.66949	−0.153284
$929$	−11.6032	−0.380688	−0.190344	−	0.981717i	$-0.560960\pi$
$929$	−11.6032	−0.380688	−0.190344	+	0.981717i	$0.560960\pi$
$930$	15.6205	0.512217
$931$	19.0498	0.624334
$932$	32.8660	1.07656
$933$	38.7795	1.26958
$934$	45.8110	1.49898
$935$	9.45346	0.309161
$936$	−28.2720	−0.924100
$937$	−23.0871	−0.754222	−0.377111	−	0.926168i	$-0.623082\pi$
$937$	−23.0871	−0.754222	−0.377111	+	0.926168i	$0.623082\pi$
$938$	−47.0601	−1.53657
$939$	41.4053	1.35121
$940$	−0.290615	−0.00947882
$941$	24.3347	0.793287	0.396644	−	0.917973i	$-0.370175\pi$
$941$	24.3347	0.793287	0.396644	+	0.917973i	$0.370175\pi$
$942$	−74.7228	−2.43460
$943$	12.7412	0.414910
$944$	−8.80111	−0.286452
$945$	0.778640	0.0253291
$946$	9.46283	0.307663
$947$	−9.17030	−0.297995	−0.148997	−	0.988838i	$-0.547605\pi$
$947$	−9.17030	−0.297995	−0.148997	+	0.988838i	$0.547605\pi$
$948$	63.7750	2.07132
$949$	−33.4491	−1.08580
$950$	9.14379	0.296664
$951$	−69.9940	−2.26971
$952$	−43.4349	−1.40773
$953$	22.8830	0.741253	0.370627	−	0.928782i	$-0.379143\pi$
$953$	22.8830	0.741253	0.370627	+	0.928782i	$0.379143\pi$
$954$	56.9375	1.84342
$955$	26.9392	0.871732
$956$	−60.3337	−1.95133
$957$	9.39718	0.303768
$958$	102.969	3.32678
$959$	26.1024	0.842890
$960$	23.6627	0.763711
$961$	−23.7403	−0.765817
$962$	−23.3387	−0.752468
$963$	31.5157	1.01558
$964$	−116.641	−3.75677
$965$	−10.1676	−0.327305
$966$	−40.4021	−1.29992
$967$	13.6453	0.438802	0.219401	−	0.975635i	$-0.429590\pi$
$967$	13.6453	0.438802	0.219401	+	0.975635i	$0.429590\pi$
$968$	40.4855	1.30125
$969$	63.8679	2.05173
$970$	1.32383	0.0425056
$971$	−5.33034	−0.171059	−0.0855293	−	0.996336i	$-0.527258\pi$
$971$	−5.33034	−0.171059	−0.0855293	+	0.996336i	$0.527258\pi$
$972$	82.2157	2.63707
$973$	21.0117	0.673603
$974$	−28.3173	−0.907344
$975$	−5.56420	−0.178197
$976$	14.2893	0.457390
$977$	14.2629	0.456310	0.228155	−	0.973625i	$-0.426731\pi$
$977$	14.2629	0.456310	0.228155	+	0.973625i	$0.426731\pi$
$978$	116.713	3.73207
$979$	10.3000	0.329189
$980$	−19.2391	−0.614572
$981$	−32.8552	−1.04898
$982$	−30.1436	−0.961921
$983$	17.6047	0.561501	0.280751	−	0.959781i	$-0.409417\pi$
$983$	17.6047	0.561501	0.280751	+	0.959781i	$0.409417\pi$
$984$	−27.1738	−0.866270
$985$	−7.17979	−0.228767
$986$	49.2158	1.56735
$987$	0.256166	0.00815385
$988$	−33.5760	−1.06819
$989$	14.4482	0.459426
$990$	−9.00180	−0.286096
$991$	−26.9714	−0.856775	−0.428387	−	0.903595i	$-0.640918\pi$
$991$	−26.9714	−0.856775	−0.428387	+	0.903595i	$0.640918\pi$
$992$	4.33103	0.137510
$993$	11.4146	0.362230
$994$	−34.5446	−1.09569
$995$	10.0608	0.318949
$996$	−138.856	−4.39981
$997$	−26.7375	−0.846786	−0.423393	−	0.905946i	$-0.639161\pi$
$997$	−26.7375	−0.846786	−0.423393	+	0.905946i	$0.639161\pi$
$998$	66.9459	2.11914
$999$	2.31470	0.0732340

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8005.2.a.h.1.10	✓	137

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8005.2.a.h.1.10	✓	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)

\(f(q)\)	\(=\)	\(q-2.41370 q^{2} -2.40190 q^{3} +3.82593 q^{4} +1.00000 q^{5} +5.79746 q^{6} +1.40406 q^{7} -4.40725 q^{8} +2.76911 q^{9} +O(q^{10})\)	\(q-2.41370 q^{2} -2.40190 q^{3} +3.82593 q^{4} +1.00000 q^{5} +5.79746 q^{6} +1.40406 q^{7} -4.40725 q^{8} +2.76911 q^{9} -2.41370 q^{10} +1.34681 q^{11} -9.18951 q^{12} +2.31658 q^{13} -3.38898 q^{14} -2.40190 q^{15} +2.98591 q^{16} +7.01916 q^{17} -6.68381 q^{18} -3.78829 q^{19} +3.82593 q^{20} -3.37241 q^{21} -3.25079 q^{22} -4.96342 q^{23} +10.5858 q^{24} +1.00000 q^{25} -5.59153 q^{26} +0.554562 q^{27} +5.37185 q^{28} -2.90494 q^{29} +5.79746 q^{30} +2.69438 q^{31} +1.60743 q^{32} -3.23490 q^{33} -16.9421 q^{34} +1.40406 q^{35} +10.5945 q^{36} +4.17393 q^{37} +9.14379 q^{38} -5.56420 q^{39} -4.40725 q^{40} -2.56702 q^{41} +8.13998 q^{42} -2.91094 q^{43} +5.15280 q^{44} +2.76911 q^{45} +11.9802 q^{46} -0.0759593 q^{47} -7.17184 q^{48} -5.02861 q^{49} -2.41370 q^{50} -16.8593 q^{51} +8.86310 q^{52} -8.51872 q^{53} -1.33855 q^{54} +1.34681 q^{55} -6.18805 q^{56} +9.09909 q^{57} +7.01165 q^{58} -2.94755 q^{59} -9.18951 q^{60} +4.78559 q^{61} -6.50341 q^{62} +3.88801 q^{63} -9.85167 q^{64} +2.31658 q^{65} +7.80806 q^{66} +13.8862 q^{67} +26.8548 q^{68} +11.9216 q^{69} -3.38898 q^{70} +10.1932 q^{71} -12.2042 q^{72} -14.4390 q^{73} -10.0746 q^{74} -2.40190 q^{75} -14.4938 q^{76} +1.89100 q^{77} +13.4303 q^{78} -6.93998 q^{79} +2.98591 q^{80} -9.63935 q^{81} +6.19600 q^{82} +15.1102 q^{83} -12.9026 q^{84} +7.01916 q^{85} +7.02612 q^{86} +6.97737 q^{87} -5.93572 q^{88} +7.64771 q^{89} -6.68381 q^{90} +3.25262 q^{91} -18.9897 q^{92} -6.47162 q^{93} +0.183343 q^{94} -3.78829 q^{95} -3.86089 q^{96} -0.548466 q^{97} +12.1375 q^{98} +3.72947 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 137 q + 17 q^{2} + 46 q^{3} + 147 q^{4} + 137 q^{5} + 11 q^{6} + 53 q^{7} + 42 q^{8} + 165 q^{9}+O(q^{10}) \) 137 * q + 17 * q^2 + 46 * q^3 + 147 * q^4 + 137 * q^5 + 11 * q^6 + 53 * q^7 + 42 * q^8 + 165 * q^9	\( 137 q + 17 q^{2} + 46 q^{3} + 147 q^{4} + 137 q^{5} + 11 q^{6} + 53 q^{7} + 42 q^{8} + 165 q^{9} + 17 q^{10} + 47 q^{11} + 87 q^{12} + 46 q^{13} + 39 q^{14} + 46 q^{15} + 155 q^{16} + 46 q^{17} + 44 q^{18} + 42 q^{19} + 147 q^{20} + 21 q^{21} + 48 q^{22} + 110 q^{23} + 33 q^{24} + 137 q^{25} + 24 q^{26} + 145 q^{27} + 83 q^{28} + 31 q^{29} + 11 q^{30} + 23 q^{31} + 71 q^{32} + 32 q^{33} + 23 q^{34} + 53 q^{35} + 178 q^{36} + 104 q^{37} + 88 q^{38} + 4 q^{39} + 42 q^{40} + 62 q^{41} + 70 q^{42} + 94 q^{43} + 50 q^{44} + 165 q^{45} - 30 q^{46} + 122 q^{47} + 157 q^{48} + 168 q^{49} + 17 q^{50} + 72 q^{51} + 74 q^{52} + 116 q^{53} + 32 q^{54} + 47 q^{55} + 119 q^{56} + 51 q^{57} + 78 q^{58} + 213 q^{59} + 87 q^{60} + 14 q^{61} + 41 q^{62} + 147 q^{63} + 114 q^{64} + 46 q^{65} + 15 q^{66} + 184 q^{67} + 95 q^{68} + 32 q^{69} + 39 q^{70} + 99 q^{71} + 92 q^{72} + 51 q^{73} + 21 q^{74} + 46 q^{75} + 18 q^{76} + 78 q^{77} + 102 q^{78} + 6 q^{79} + 155 q^{80} + 201 q^{81} + 38 q^{82} + 228 q^{83} - 11 q^{84} + 46 q^{85} + 71 q^{86} + 113 q^{87} + 103 q^{88} + 111 q^{89} + 44 q^{90} + 41 q^{91} + 136 q^{92} + 11 q^{93} - 39 q^{94} + 42 q^{95} + 33 q^{96} + 91 q^{97} + 91 q^{98} + 65 q^{99}+O(q^{100}) \) 137 * q + 17 * q^2 + 46 * q^3 + 147 * q^4 + 137 * q^5 + 11 * q^6 + 53 * q^7 + 42 * q^8 + 165 * q^9 + 17 * q^10 + 47 * q^11 + 87 * q^12 + 46 * q^13 + 39 * q^14 + 46 * q^15 + 155 * q^16 + 46 * q^17 + 44 * q^18 + 42 * q^19 + 147 * q^20 + 21 * q^21 + 48 * q^22 + 110 * q^23 + 33 * q^24 + 137 * q^25 + 24 * q^26 + 145 * q^27 + 83 * q^28 + 31 * q^29 + 11 * q^30 + 23 * q^31 + 71 * q^32 + 32 * q^33 + 23 * q^34 + 53 * q^35 + 178 * q^36 + 104 * q^37 + 88 * q^38 + 4 * q^39 + 42 * q^40 + 62 * q^41 + 70 * q^42 + 94 * q^43 + 50 * q^44 + 165 * q^45 - 30 * q^46 + 122 * q^47 + 157 * q^48 + 168 * q^49 + 17 * q^50 + 72 * q^51 + 74 * q^52 + 116 * q^53 + 32 * q^54 + 47 * q^55 + 119 * q^56 + 51 * q^57 + 78 * q^58 + 213 * q^59 + 87 * q^60 + 14 * q^61 + 41 * q^62 + 147 * q^63 + 114 * q^64 + 46 * q^65 + 15 * q^66 + 184 * q^67 + 95 * q^68 + 32 * q^69 + 39 * q^70 + 99 * q^71 + 92 * q^72 + 51 * q^73 + 21 * q^74 + 46 * q^75 + 18 * q^76 + 78 * q^77 + 102 * q^78 + 6 * q^79 + 155 * q^80 + 201 * q^81 + 38 * q^82 + 228 * q^83 - 11 * q^84 + 46 * q^85 + 71 * q^86 + 113 * q^87 + 103 * q^88 + 111 * q^89 + 44 * q^90 + 41 * q^91 + 136 * q^92 + 11 * q^93 - 39 * q^94 + 42 * q^95 + 33 * q^96 + 91 * q^97 + 91 * q^98 + 65 * q^99

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