LMFDB - Embedded newform 8031.2.a.c.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8031,2,Mod(1,8031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8031, 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("8031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8031 = 3 \cdot 2677 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8031.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:	$64.1278578633$
Analytic rank:	$0$
Dimension:	$121$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	8031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.35691 q^{2} -1.00000 q^{3} +3.55501 q^{4} +3.33677 q^{5} +2.35691 q^{6} -1.10286 q^{7} -3.66500 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.35691 q^{2} -1.00000 q^{3} +3.55501 q^{4} +3.33677 q^{5} +2.35691 q^{6} -1.10286 q^{7} -3.66500 q^{8} +1.00000 q^{9} -7.86445 q^{10} -2.40074 q^{11} -3.55501 q^{12} -6.52199 q^{13} +2.59934 q^{14} -3.33677 q^{15} +1.52806 q^{16} -4.62654 q^{17} -2.35691 q^{18} +3.80651 q^{19} +11.8622 q^{20} +1.10286 q^{21} +5.65832 q^{22} -1.55845 q^{23} +3.66500 q^{24} +6.13402 q^{25} +15.3717 q^{26} -1.00000 q^{27} -3.92068 q^{28} +3.95891 q^{29} +7.86445 q^{30} +6.74886 q^{31} +3.72852 q^{32} +2.40074 q^{33} +10.9043 q^{34} -3.67999 q^{35} +3.55501 q^{36} +3.32159 q^{37} -8.97159 q^{38} +6.52199 q^{39} -12.2293 q^{40} +4.04057 q^{41} -2.59934 q^{42} -2.18273 q^{43} -8.53465 q^{44} +3.33677 q^{45} +3.67312 q^{46} -10.6897 q^{47} -1.52806 q^{48} -5.78369 q^{49} -14.4573 q^{50} +4.62654 q^{51} -23.1857 q^{52} -5.55005 q^{53} +2.35691 q^{54} -8.01072 q^{55} +4.04199 q^{56} -3.80651 q^{57} -9.33078 q^{58} -0.345854 q^{59} -11.8622 q^{60} +9.27486 q^{61} -15.9064 q^{62} -1.10286 q^{63} -11.8439 q^{64} -21.7624 q^{65} -5.65832 q^{66} -5.62934 q^{67} -16.4474 q^{68} +1.55845 q^{69} +8.67340 q^{70} +1.62011 q^{71} -3.66500 q^{72} -7.36921 q^{73} -7.82867 q^{74} -6.13402 q^{75} +13.5322 q^{76} +2.64769 q^{77} -15.3717 q^{78} -11.5392 q^{79} +5.09877 q^{80} +1.00000 q^{81} -9.52323 q^{82} +9.00974 q^{83} +3.92068 q^{84} -15.4377 q^{85} +5.14450 q^{86} -3.95891 q^{87} +8.79873 q^{88} +10.5378 q^{89} -7.86445 q^{90} +7.19286 q^{91} -5.54029 q^{92} -6.74886 q^{93} +25.1946 q^{94} +12.7014 q^{95} -3.72852 q^{96} +3.01660 q^{97} +13.6316 q^{98} -2.40074 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 121 q + 7 q^{2} - 121 q^{3} + 123 q^{4} + 24 q^{5} - 7 q^{6} - 14 q^{7} + 18 q^{8} + 121 q^{9}+O(q^{10}) $ 121 * q + 7 * q^2 - 121 * q^3 + 123 * q^4 + 24 * q^5 - 7 * q^6 - 14 * q^7 + 18 * q^8 + 121 * q^9	\( 121 q + 7 q^{2} - 121 q^{3} + 123 q^{4} + 24 q^{5} - 7 q^{6} - 14 q^{7} + 18 q^{8} + 121 q^{9} + 18 q^{10} + 32 q^{11} - 123 q^{12} + 2 q^{13} + 37 q^{14} - 24 q^{15} + 131 q^{16} + 87 q^{17} + 7 q^{18} - 10 q^{19} + 60 q^{20} + 14 q^{21} - 22 q^{22} + 31 q^{23} - 18 q^{24} + 147 q^{25} + 37 q^{26} - 121 q^{27} - 29 q^{28} + 68 q^{29} - 18 q^{30} + 25 q^{31} + 43 q^{32} - 32 q^{33} + 27 q^{34} + 51 q^{35} + 123 q^{36} - 4 q^{37} + 36 q^{38} - 2 q^{39} + 61 q^{40} + 132 q^{41} - 37 q^{42} - 91 q^{43} + 94 q^{44} + 24 q^{45} + 39 q^{47} - 131 q^{48} + 217 q^{49} + 54 q^{50} - 87 q^{51} - 12 q^{52} + 55 q^{53} - 7 q^{54} + 7 q^{55} + 104 q^{56} + 10 q^{57} - 3 q^{58} + 58 q^{59} - 60 q^{60} + 126 q^{61} + 74 q^{62} - 14 q^{63} + 122 q^{64} + 128 q^{65} + 22 q^{66} - 139 q^{67} + 190 q^{68} - 31 q^{69} - 18 q^{70} + 37 q^{71} + 18 q^{72} + 84 q^{73} + 79 q^{74} - 147 q^{75} + 23 q^{76} + 95 q^{77} - 37 q^{78} - 14 q^{79} + 145 q^{80} + 121 q^{81} + 9 q^{82} + 58 q^{83} + 29 q^{84} + 32 q^{85} + 28 q^{86} - 68 q^{87} - 84 q^{88} + 198 q^{89} + 18 q^{90} + 5 q^{91} + 98 q^{92} - 25 q^{93} + 9 q^{94} + 42 q^{95} - 43 q^{96} + 73 q^{97} + 69 q^{98} + 32 q^{99}+O(q^{100}) \) 121 * q + 7 * q^2 - 121 * q^3 + 123 * q^4 + 24 * q^5 - 7 * q^6 - 14 * q^7 + 18 * q^8 + 121 * q^9 + 18 * q^10 + 32 * q^11 - 123 * q^12 + 2 * q^13 + 37 * q^14 - 24 * q^15 + 131 * q^16 + 87 * q^17 + 7 * q^18 - 10 * q^19 + 60 * q^20 + 14 * q^21 - 22 * q^22 + 31 * q^23 - 18 * q^24 + 147 * q^25 + 37 * q^26 - 121 * q^27 - 29 * q^28 + 68 * q^29 - 18 * q^30 + 25 * q^31 + 43 * q^32 - 32 * q^33 + 27 * q^34 + 51 * q^35 + 123 * q^36 - 4 * q^37 + 36 * q^38 - 2 * q^39 + 61 * q^40 + 132 * q^41 - 37 * q^42 - 91 * q^43 + 94 * q^44 + 24 * q^45 + 39 * q^47 - 131 * q^48 + 217 * q^49 + 54 * q^50 - 87 * q^51 - 12 * q^52 + 55 * q^53 - 7 * q^54 + 7 * q^55 + 104 * q^56 + 10 * q^57 - 3 * q^58 + 58 * q^59 - 60 * q^60 + 126 * q^61 + 74 * q^62 - 14 * q^63 + 122 * q^64 + 128 * q^65 + 22 * q^66 - 139 * q^67 + 190 * q^68 - 31 * q^69 - 18 * q^70 + 37 * q^71 + 18 * q^72 + 84 * q^73 + 79 * q^74 - 147 * q^75 + 23 * q^76 + 95 * q^77 - 37 * q^78 - 14 * q^79 + 145 * q^80 + 121 * q^81 + 9 * q^82 + 58 * q^83 + 29 * q^84 + 32 * q^85 + 28 * q^86 - 68 * q^87 - 84 * q^88 + 198 * q^89 + 18 * q^90 + 5 * q^91 + 98 * q^92 - 25 * q^93 + 9 * q^94 + 42 * q^95 - 43 * q^96 + 73 * q^97 + 69 * q^98 + 32 * 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 $

$2$	−2.35691	−1.66658	−0.833292	−	0.552833i	$-0.813547\pi$
$2$	−2.35691	−1.66658	−0.833292	+	0.552833i	$0.813547\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.55501	1.77750
$5$	3.33677	1.49225	0.746124	−	0.665807i	$-0.231913\pi$
$5$	3.33677	1.49225	0.746124	+	0.665807i	$0.231913\pi$
$6$	2.35691	0.962203
$7$	−1.10286	−0.416843	−0.208421	−	0.978039i	$-0.566833\pi$
$7$	−1.10286	−0.416843	−0.208421	+	0.978039i	$0.566833\pi$
$8$	−3.66500	−1.29577
$9$	1.00000	0.333333
$10$	−7.86445	−2.48696
$11$	−2.40074	−0.723851	−0.361926	−	0.932207i	$-0.617881\pi$
$11$	−2.40074	−0.723851	−0.361926	+	0.932207i	$0.617881\pi$
$12$	−3.55501	−1.02624
$13$	−6.52199	−1.80888	−0.904438	−	0.426606i	$-0.859709\pi$
$13$	−6.52199	−1.80888	−0.904438	+	0.426606i	$0.859709\pi$
$14$	2.59934	0.694704
$15$	−3.33677	−0.861550
$16$	1.52806	0.382014
$17$	−4.62654	−1.12210	−0.561051	−	0.827781i	$-0.689603\pi$
$17$	−4.62654	−1.12210	−0.561051	+	0.827781i	$0.689603\pi$
$18$	−2.35691	−0.555528
$19$	3.80651	0.873274	0.436637	−	0.899638i	$-0.356169\pi$
$19$	3.80651	0.873274	0.436637	+	0.899638i	$0.356169\pi$
$20$	11.8622	2.65247
$21$	1.10286	0.240664
$22$	5.65832	1.20636
$23$	−1.55845	−0.324959	−0.162480	−	0.986712i	$-0.551949\pi$
$23$	−1.55845	−0.324959	−0.162480	+	0.986712i	$0.551949\pi$
$24$	3.66500	0.748116
$25$	6.13402	1.22680
$26$	15.3717	3.01464
$27$	−1.00000	−0.192450
$28$	−3.92068	−0.740939
$29$	3.95891	0.735151	0.367575	−	0.929994i	$-0.380188\pi$
$29$	3.95891	0.735151	0.367575	+	0.929994i	$0.380188\pi$
$30$	7.86445	1.43585
$31$	6.74886	1.21213	0.606065	−	0.795415i	$-0.292747\pi$
$31$	6.74886	1.21213	0.606065	+	0.795415i	$0.292747\pi$
$32$	3.72852	0.659116
$33$	2.40074	0.417916
$34$	10.9043	1.87008
$35$	−3.67999	−0.622033
$36$	3.55501	0.592501
$37$	3.32159	0.546066	0.273033	−	0.962005i	$-0.411973\pi$
$37$	3.32159	0.546066	0.273033	+	0.962005i	$0.411973\pi$
$38$	−8.97159	−1.45538
$39$	6.52199	1.04435
$40$	−12.2293	−1.93362
$41$	4.04057	0.631030	0.315515	−	0.948921i	$-0.397823\pi$
$41$	4.04057	0.631030	0.315515	+	0.948921i	$0.397823\pi$
$42$	−2.59934	−0.401087
$43$	−2.18273	−0.332864	−0.166432	−	0.986053i	$-0.553225\pi$
$43$	−2.18273	−0.332864	−0.166432	+	0.986053i	$0.553225\pi$
$44$	−8.53465	−1.28665
$45$	3.33677	0.497416
$46$	3.67312	0.541572
$47$	−10.6897	−1.55925	−0.779625	−	0.626247i	$-0.784590\pi$
$47$	−10.6897	−1.55925	−0.779625	+	0.626247i	$0.784590\pi$
$48$	−1.52806	−0.220556
$49$	−5.78369	−0.826242
$50$	−14.4573	−2.04457
$51$	4.62654	0.647846
$52$	−23.1857	−3.21528
$53$	−5.55005	−0.762358	−0.381179	−	0.924501i	$-0.624482\pi$
$53$	−5.55005	−0.762358	−0.381179	+	0.924501i	$0.624482\pi$
$54$	2.35691	0.320734
$55$	−8.01072	−1.08017
$56$	4.04199	0.540134
$57$	−3.80651	−0.504185
$58$	−9.33078	−1.22519
$59$	−0.345854	−0.0450263	−0.0225132	−	0.999747i	$-0.507167\pi$
$59$	−0.345854	−0.0450263	−0.0225132	+	0.999747i	$0.507167\pi$
$60$	−11.8622	−1.53141
$61$	9.27486	1.18752	0.593762	−	0.804640i	$-0.297642\pi$
$61$	9.27486	1.18752	0.593762	+	0.804640i	$0.297642\pi$
$62$	−15.9064	−2.02012
$63$	−1.10286	−0.138948
$64$	−11.8439	−1.48049
$65$	−21.7624	−2.69929
$66$	−5.65832	−0.696492
$67$	−5.62934	−0.687733	−0.343867	−	0.939018i	$-0.611737\pi$
$67$	−5.62934	−0.687733	−0.343867	+	0.939018i	$0.611737\pi$
$68$	−16.4474	−1.99454
$69$	1.55845	0.187615
$70$	8.67340	1.03667
$71$	1.62011	0.192272	0.0961361	−	0.995368i	$-0.469352\pi$
$71$	1.62011	0.192272	0.0961361	+	0.995368i	$0.469352\pi$
$72$	−3.66500	−0.431925
$73$	−7.36921	−0.862501	−0.431251	−	0.902232i	$-0.641927\pi$
$73$	−7.36921	−0.862501	−0.431251	+	0.902232i	$0.641927\pi$
$74$	−7.82867	−0.910065
$75$	−6.13402	−0.708295
$76$	13.5322	1.55225
$77$	2.64769	0.301732
$78$	−15.3717	−1.74050
$79$	−11.5392	−1.29826	−0.649128	−	0.760679i	$-0.724866\pi$
$79$	−11.5392	−1.29826	−0.649128	+	0.760679i	$0.724866\pi$
$80$	5.09877	0.570060
$81$	1.00000	0.111111
$82$	−9.52323	−1.05167
$83$	9.00974	0.988947	0.494474	−	0.869193i	$-0.335361\pi$
$83$	9.00974	0.988947	0.494474	+	0.869193i	$0.335361\pi$
$84$	3.92068	0.427781
$85$	−15.4377	−1.67445
$86$	5.14450	0.554745
$87$	−3.95891	−0.424440
$88$	8.79873	0.937948
$89$	10.5378	1.11700	0.558502	−	0.829503i	$-0.311376\pi$
$89$	10.5378	1.11700	0.558502	+	0.829503i	$0.311376\pi$
$90$	−7.86445	−0.828986
$91$	7.19286	0.754017
$92$	−5.54029	−0.577616
$93$	−6.74886	−0.699824
$94$	25.1946	2.59862
$95$	12.7014	1.30314
$96$	−3.72852	−0.380541
$97$	3.01660	0.306289	0.153145	−	0.988204i	$-0.451060\pi$
$97$	3.01660	0.306289	0.153145	+	0.988204i	$0.451060\pi$
$98$	13.6316	1.37700
$99$	−2.40074	−0.241284
$100$	21.8065	2.18065
$101$	9.63789	0.959006	0.479503	−	0.877540i	$-0.340817\pi$
$101$	9.63789	0.959006	0.479503	+	0.877540i	$0.340817\pi$
$102$	−10.9043	−1.07969
$103$	12.0143	1.18380	0.591900	−	0.806012i	$-0.298378\pi$
$103$	12.0143	1.18380	0.591900	+	0.806012i	$0.298378\pi$
$104$	23.9031	2.34389
$105$	3.67999	0.359131
$106$	13.0809	1.27053
$107$	7.56816	0.731642	0.365821	−	0.930685i	$-0.380788\pi$
$107$	7.56816	0.731642	0.365821	+	0.930685i	$0.380788\pi$
$108$	−3.55501	−0.342081
$109$	−2.62194	−0.251136	−0.125568	−	0.992085i	$-0.540075\pi$
$109$	−2.62194	−0.251136	−0.125568	+	0.992085i	$0.540075\pi$
$110$	18.8805	1.80019
$111$	−3.32159	−0.315271
$112$	−1.68524	−0.159240
$113$	−13.3349	−1.25444	−0.627221	−	0.778841i	$-0.715808\pi$
$113$	−13.3349	−1.25444	−0.627221	+	0.778841i	$0.715808\pi$
$114$	8.97159	0.840267
$115$	−5.20018	−0.484919
$116$	14.0739	1.30673
$117$	−6.52199	−0.602958
$118$	0.815145	0.0750402
$119$	5.10244	0.467740
$120$	12.2293	1.11637
$121$	−5.23644	−0.476040
$122$	−21.8600	−1.97911
$123$	−4.04057	−0.364326
$124$	23.9922	2.15457
$125$	3.78395	0.338447
$126$	2.59934	0.231568
$127$	−5.65816	−0.502080	−0.251040	−	0.967977i	$-0.580773\pi$
$127$	−5.65816	−0.502080	−0.251040	+	0.967977i	$0.580773\pi$
$128$	20.4579	1.80824
$129$	2.18273	0.192179
$130$	51.2919	4.49859
$131$	9.46184	0.826685	0.413342	−	0.910576i	$-0.364361\pi$
$131$	9.46184	0.826685	0.413342	+	0.910576i	$0.364361\pi$
$132$	8.53465	0.742846
$133$	−4.19806	−0.364018
$134$	13.2678	1.14617
$135$	−3.33677	−0.287183
$136$	16.9563	1.45399
$137$	−17.2078	−1.47016	−0.735081	−	0.677979i	$-0.762856\pi$
$137$	−17.2078	−1.47016	−0.735081	+	0.677979i	$0.762856\pi$
$138$	−3.67312	−0.312677
$139$	8.76989	0.743853	0.371926	−	0.928262i	$-0.378697\pi$
$139$	8.76989	0.743853	0.371926	+	0.928262i	$0.378697\pi$
$140$	−13.0824	−1.10566
$141$	10.6897	0.900233
$142$	−3.81846	−0.320438
$143$	15.6576	1.30936
$144$	1.52806	0.127338
$145$	13.2100	1.09703
$146$	17.3685	1.43743
$147$	5.78369	0.477031
$148$	11.8083	0.970634
$149$	−0.693754	−0.0568345	−0.0284173	−	0.999596i	$-0.509047\pi$
$149$	−0.693754	−0.0568345	−0.0284173	+	0.999596i	$0.509047\pi$
$150$	14.4573	1.18043
$151$	0.357382	0.0290833	0.0145417	−	0.999894i	$-0.495371\pi$
$151$	0.357382	0.0290833	0.0145417	+	0.999894i	$0.495371\pi$
$152$	−13.9509	−1.13157
$153$	−4.62654	−0.374034
$154$	−6.24035	−0.502862
$155$	22.5194	1.80880
$156$	23.1857	1.85634
$157$	−8.44125	−0.673685	−0.336843	−	0.941561i	$-0.609359\pi$
$157$	−8.44125	−0.673685	−0.336843	+	0.941561i	$0.609359\pi$
$158$	27.1967	2.16365
$159$	5.55005	0.440148
$160$	12.4412	0.983564
$161$	1.71875	0.135457
$162$	−2.35691	−0.185176
$163$	−3.58681	−0.280940	−0.140470	−	0.990085i	$-0.544861\pi$
$163$	−3.58681	−0.280940	−0.140470	+	0.990085i	$0.544861\pi$
$164$	14.3642	1.12166
$165$	8.01072	0.623634
$166$	−21.2351	−1.64816
$167$	−8.59941	−0.665442	−0.332721	−	0.943025i	$-0.607967\pi$
$167$	−8.59941	−0.665442	−0.332721	+	0.943025i	$0.607967\pi$
$168$	−4.04199	−0.311847
$169$	29.5364	2.27203
$170$	36.3852	2.79062
$171$	3.80651	0.291091
$172$	−7.75963	−0.591666
$173$	0.261439	0.0198769	0.00993843	−	0.999951i	$-0.496836\pi$
$173$	0.261439	0.0198769	0.00993843	+	0.999951i	$0.496836\pi$
$174$	9.33078	0.707364
$175$	−6.76497	−0.511384
$176$	−3.66847	−0.276521
$177$	0.345854	0.0259960
$178$	−24.8366	−1.86158
$179$	0.614536	0.0459326	0.0229663	−	0.999736i	$-0.492689\pi$
$179$	0.614536	0.0459326	0.0229663	+	0.999736i	$0.492689\pi$
$180$	11.8622	0.884158
$181$	−10.2445	−0.761464	−0.380732	−	0.924685i	$-0.624328\pi$
$181$	−10.2445	−0.761464	−0.380732	+	0.924685i	$0.624328\pi$
$182$	−16.9529	−1.25663
$183$	−9.27486	−0.685618
$184$	5.71172	0.421074
$185$	11.0834	0.814865
$186$	15.9064	1.16632
$187$	11.1071	0.812234
$188$	−38.0019	−2.77157
$189$	1.10286	0.0802214
$190$	−29.9361	−2.17179
$191$	−25.3577	−1.83482	−0.917409	−	0.397945i	$-0.869724\pi$
$191$	−25.3577	−1.83482	−0.917409	+	0.397945i	$0.869724\pi$
$192$	11.8439	0.854759
$193$	14.8688	1.07028	0.535139	−	0.844764i	$-0.320259\pi$
$193$	14.8688	1.07028	0.535139	+	0.844764i	$0.320259\pi$
$194$	−7.10984	−0.510456
$195$	21.7624	1.55844
$196$	−20.5611	−1.46865
$197$	26.2793	1.87232	0.936162	−	0.351569i	$-0.114352\pi$
$197$	26.2793	1.87232	0.936162	+	0.351569i	$0.114352\pi$
$198$	5.65832	0.402120
$199$	−21.9366	−1.55504	−0.777521	−	0.628857i	$-0.783523\pi$
$199$	−21.9366	−1.55504	−0.777521	+	0.628857i	$0.783523\pi$
$200$	−22.4812	−1.58966
$201$	5.62934	0.397063
$202$	−22.7156	−1.59826
$203$	−4.36613	−0.306442
$204$	16.4474	1.15155
$205$	13.4824	0.941654
$206$	−28.3165	−1.97290
$207$	−1.55845	−0.108320
$208$	−9.96597	−0.691016
$209$	−9.13846	−0.632120
$210$	−8.67340	−0.598522
$211$	−17.8328	−1.22766	−0.613832	−	0.789437i	$-0.710373\pi$
$211$	−17.8328	−1.22766	−0.613832	+	0.789437i	$0.710373\pi$
$212$	−19.7305	−1.35509
$213$	−1.62011	−0.111008
$214$	−17.8374	−1.21934
$215$	−7.28327	−0.496715
$216$	3.66500	0.249372
$217$	−7.44306	−0.505268
$218$	6.17967	0.418540
$219$	7.36921	0.497965
$220$	−28.4782	−1.92000
$221$	30.1743	2.02974
$222$	7.82867	0.525426
$223$	8.32237	0.557307	0.278654	−	0.960392i	$-0.410112\pi$
$223$	8.32237	0.557307	0.278654	+	0.960392i	$0.410112\pi$
$224$	−4.11204	−0.274748
$225$	6.13402	0.408934
$226$	31.4291	2.09063
$227$	10.1227	0.671865	0.335933	−	0.941886i	$-0.390949\pi$
$227$	10.1227	0.671865	0.335933	+	0.941886i	$0.390949\pi$
$228$	−13.5322	−0.896190
$229$	15.8104	1.04478	0.522390	−	0.852707i	$-0.325040\pi$
$229$	15.8104	1.04478	0.522390	+	0.852707i	$0.325040\pi$
$230$	12.2563	0.808159
$231$	−2.64769	−0.174205
$232$	−14.5094	−0.952590
$233$	28.8424	1.88953	0.944764	−	0.327751i	$-0.106291\pi$
$233$	28.8424	1.88953	0.944764	+	0.327751i	$0.106291\pi$
$234$	15.3717	1.00488
$235$	−35.6690	−2.32679
$236$	−1.22951	−0.0800344
$237$	11.5392	0.749548
$238$	−12.0260	−0.779528
$239$	12.2060	0.789543	0.394772	−	0.918779i	$-0.370824\pi$
$239$	12.2060	0.789543	0.394772	+	0.918779i	$0.370824\pi$
$240$	−5.09877	−0.329124
$241$	−10.1272	−0.652350	−0.326175	−	0.945309i	$-0.605760\pi$
$241$	−10.1272	−0.652350	−0.326175	+	0.945309i	$0.605760\pi$
$242$	12.3418	0.793360
$243$	−1.00000	−0.0641500
$244$	32.9722	2.11083
$245$	−19.2988	−1.23296
$246$	9.52323	0.607179
$247$	−24.8260	−1.57964
$248$	−24.7346	−1.57065
$249$	−9.00974	−0.570969
$250$	−8.91841	−0.564050
$251$	0.783979	0.0494843	0.0247422	−	0.999694i	$-0.492124\pi$
$251$	0.783979	0.0494843	0.0247422	+	0.999694i	$0.492124\pi$
$252$	−3.92068	−0.246980
$253$	3.74143	0.235222
$254$	13.3357	0.836759
$255$	15.4377	0.966746
$256$	−24.5295	−1.53310
$257$	17.0565	1.06396	0.531978	−	0.846758i	$-0.321449\pi$
$257$	17.0565	1.06396	0.531978	+	0.846758i	$0.321449\pi$
$258$	−5.14450	−0.320282
$259$	−3.66325	−0.227624
$260$	−77.3654	−4.79800
$261$	3.95891	0.245050
$262$	−22.3007	−1.37774
$263$	28.6443	1.76628	0.883142	−	0.469105i	$-0.155423\pi$
$263$	28.6443	1.76628	0.883142	+	0.469105i	$0.155423\pi$
$264$	−8.79873	−0.541524
$265$	−18.5192	−1.13763
$266$	9.89443	0.606667
$267$	−10.5378	−0.644902
$268$	−20.0123	−1.22245
$269$	21.2890	1.29801	0.649007	−	0.760782i	$-0.275184\pi$
$269$	21.2890	1.29801	0.649007	+	0.760782i	$0.275184\pi$
$270$	7.86445	0.478615
$271$	−3.54658	−0.215439	−0.107720	−	0.994181i	$-0.534355\pi$
$271$	−3.54658	−0.215439	−0.107720	+	0.994181i	$0.534355\pi$
$272$	−7.06962	−0.428659
$273$	−7.19286	−0.435332
$274$	40.5572	2.45015
$275$	−14.7262	−0.888023
$276$	5.54029	0.333487
$277$	23.4823	1.41091	0.705457	−	0.708753i	$-0.250742\pi$
$277$	23.4823	1.41091	0.705457	+	0.708753i	$0.250742\pi$
$278$	−20.6698	−1.23969
$279$	6.74886	0.404044
$280$	13.4872	0.806014
$281$	17.3395	1.03439	0.517195	−	0.855867i	$-0.326976\pi$
$281$	17.3395	1.03439	0.517195	+	0.855867i	$0.326976\pi$
$282$	−25.1946	−1.50031
$283$	−12.7926	−0.760440	−0.380220	−	0.924896i	$-0.624152\pi$
$283$	−12.7926	−0.760440	−0.380220	+	0.924896i	$0.624152\pi$
$284$	5.75952	0.341765
$285$	−12.7014	−0.752369
$286$	−36.9035	−2.18215
$287$	−4.45619	−0.263040
$288$	3.72852	0.219705
$289$	4.40490	0.259112
$290$	−31.1346	−1.82829
$291$	−3.01660	−0.176836
$292$	−26.1976	−1.53310
$293$	23.6288	1.38041	0.690205	−	0.723614i	$-0.257520\pi$
$293$	23.6288	1.38041	0.690205	+	0.723614i	$0.257520\pi$
$294$	−13.6316	−0.795013
$295$	−1.15403	−0.0671904
$296$	−12.1736	−0.707578
$297$	2.40074	0.139305
$298$	1.63511	0.0947195
$299$	10.1642	0.587810
$300$	−21.8065	−1.25900
$301$	2.40725	0.138752
$302$	−0.842315	−0.0484698
$303$	−9.63789	−0.553682
$304$	5.81657	0.333603
$305$	30.9481	1.77208
$306$	10.9043	0.623359
$307$	−30.3611	−1.73280	−0.866400	−	0.499350i	$-0.833572\pi$
$307$	−30.3611	−1.73280	−0.866400	+	0.499350i	$0.833572\pi$
$308$	9.41255	0.536330
$309$	−12.0143	−0.683467
$310$	−53.0760	−3.01452
$311$	−23.6181	−1.33926	−0.669630	−	0.742695i	$-0.733547\pi$
$311$	−23.6181	−1.33926	−0.669630	+	0.742695i	$0.733547\pi$
$312$	−23.9031	−1.35325
$313$	−4.98130	−0.281560	−0.140780	−	0.990041i	$-0.544961\pi$
$313$	−4.98130	−0.281560	−0.140780	+	0.990041i	$0.544961\pi$
$314$	19.8952	1.12275
$315$	−3.67999	−0.207344
$316$	−41.0218	−2.30765
$317$	28.9978	1.62868	0.814338	−	0.580391i	$-0.197100\pi$
$317$	28.9978	1.62868	0.814338	+	0.580391i	$0.197100\pi$
$318$	−13.0809	−0.733543
$319$	−9.50432	−0.532140
$320$	−39.5203	−2.20925
$321$	−7.56816	−0.422413
$322$	−4.05094	−0.225750
$323$	−17.6110	−0.979902
$324$	3.55501	0.197500
$325$	−40.0060	−2.21913
$326$	8.45377	0.468211
$327$	2.62194	0.144994
$328$	−14.8087	−0.817673
$329$	11.7892	0.649962
$330$	−18.8805	−1.03934
$331$	14.4044	0.791738	0.395869	−	0.918307i	$-0.370443\pi$
$331$	14.4044	0.791738	0.395869	+	0.918307i	$0.370443\pi$
$332$	32.0297	1.75786
$333$	3.32159	0.182022
$334$	20.2680	1.10902
$335$	−18.7838	−1.02627
$336$	1.68524	0.0919372
$337$	1.09219	0.0594954	0.0297477	−	0.999557i	$-0.490530\pi$
$337$	1.09219	0.0594954	0.0297477	+	0.999557i	$0.490530\pi$
$338$	−69.6145	−3.78653
$339$	13.3349	0.724252
$340$	−54.8811	−2.97635
$341$	−16.2023	−0.877402
$342$	−8.97159	−0.485128
$343$	14.0987	0.761256
$344$	7.99972	0.431316
$345$	5.20018	0.279968
$346$	−0.616188	−0.0331265
$347$	36.8017	1.97562	0.987809	−	0.155668i	$-0.0497529\pi$
$347$	36.8017	1.97562	0.987809	+	0.155668i	$0.0497529\pi$
$348$	−14.0739	−0.754443
$349$	−1.19105	−0.0637557	−0.0318778	−	0.999492i	$-0.510149\pi$
$349$	−1.19105	−0.0637557	−0.0318778	+	0.999492i	$0.510149\pi$
$350$	15.9444	0.852265
$351$	6.52199	0.348118
$352$	−8.95122	−0.477102
$353$	2.08841	0.111155	0.0555773	−	0.998454i	$-0.482300\pi$
$353$	2.08841	0.111155	0.0555773	+	0.998454i	$0.482300\pi$
$354$	−0.815145	−0.0433245
$355$	5.40595	0.286918
$356$	37.4619	1.98548
$357$	−5.10244	−0.270050
$358$	−1.44840	−0.0765505
$359$	−30.0611	−1.58657	−0.793283	−	0.608854i	$-0.791630\pi$
$359$	−30.0611	−1.58657	−0.793283	+	0.608854i	$0.791630\pi$
$360$	−12.2293	−0.644539
$361$	−4.51046	−0.237393
$362$	24.1452	1.26904
$363$	5.23644	0.274842
$364$	25.5707	1.34027
$365$	−24.5893	−1.28707
$366$	21.8600	1.14264
$367$	10.8863	0.568262	0.284131	−	0.958785i	$-0.408295\pi$
$367$	10.8863	0.568262	0.284131	+	0.958785i	$0.408295\pi$
$368$	−2.38140	−0.124139
$369$	4.04057	0.210343
$370$	−26.1225	−1.35804
$371$	6.12094	0.317783
$372$	−23.9922	−1.24394
$373$	3.73160	0.193215	0.0966076	−	0.995323i	$-0.469201\pi$
$373$	3.73160	0.193215	0.0966076	+	0.995323i	$0.469201\pi$
$374$	−26.1785	−1.35366
$375$	−3.78395	−0.195402
$376$	39.1777	2.02044
$377$	−25.8200	−1.32980
$378$	−2.59934	−0.133696
$379$	−10.4218	−0.535334	−0.267667	−	0.963511i	$-0.586253\pi$
$379$	−10.4218	−0.535334	−0.267667	+	0.963511i	$0.586253\pi$
$380$	45.1537	2.31634
$381$	5.65816	0.289876
$382$	59.7657	3.05788
$383$	−9.72823	−0.497089	−0.248545	−	0.968620i	$-0.579952\pi$
$383$	−9.72823	−0.497089	−0.248545	+	0.968620i	$0.579952\pi$
$384$	−20.4579	−1.04399
$385$	8.83472	0.450259
$386$	−35.0443	−1.78371
$387$	−2.18273	−0.110955
$388$	10.7240	0.544430
$389$	20.2283	1.02561	0.512807	−	0.858504i	$-0.328605\pi$
$389$	20.2283	1.02561	0.512807	+	0.858504i	$0.328605\pi$
$390$	−51.2919	−2.59726
$391$	7.21023	0.364637
$392$	21.1973	1.07062
$393$	−9.46184	−0.477287
$394$	−61.9379	−3.12039
$395$	−38.5035	−1.93732
$396$	−8.53465	−0.428882
$397$	−2.50527	−0.125736	−0.0628679	−	0.998022i	$-0.520025\pi$
$397$	−2.50527	−0.125736	−0.0628679	+	0.998022i	$0.520025\pi$
$398$	51.7024	2.59161
$399$	4.19806	0.210166
$400$	9.37312	0.468656
$401$	24.1917	1.20808	0.604038	−	0.796956i	$-0.293558\pi$
$401$	24.1917	1.20808	0.604038	+	0.796956i	$0.293558\pi$
$402$	−13.2678	−0.661739
$403$	−44.0160	−2.19259
$404$	34.2628	1.70464
$405$	3.33677	0.165805
$406$	10.2906	0.510712
$407$	−7.97428	−0.395270
$408$	−16.9563	−0.839462
$409$	−2.23803	−0.110663	−0.0553316	−	0.998468i	$-0.517622\pi$
$409$	−2.23803	−0.110663	−0.0553316	+	0.998468i	$0.517622\pi$
$410$	−31.7768	−1.56934
$411$	17.2078	0.848799
$412$	42.7107	2.10421
$413$	0.381429	0.0187689
$414$	3.67312	0.180524
$415$	30.0634	1.47575
$416$	−24.3174	−1.19226
$417$	−8.76989	−0.429464
$418$	21.5385	1.05348
$419$	−23.3152	−1.13902	−0.569512	−	0.821983i	$-0.692868\pi$
$419$	−23.3152	−1.13902	−0.569512	+	0.821983i	$0.692868\pi$
$420$	13.0824	0.638356
$421$	−11.2000	−0.545856	−0.272928	−	0.962035i	$-0.587992\pi$
$421$	−11.2000	−0.545856	−0.272928	+	0.962035i	$0.587992\pi$
$422$	42.0303	2.04600
$423$	−10.6897	−0.519750
$424$	20.3410	0.987844
$425$	−28.3793	−1.37660
$426$	3.81846	0.185005
$427$	−10.2289	−0.495011
$428$	26.9049	1.30050
$429$	−15.6576	−0.755957
$430$	17.1660	0.827817
$431$	12.8356	0.618270	0.309135	−	0.951018i	$-0.399960\pi$
$431$	12.8356	0.618270	0.309135	+	0.951018i	$0.399960\pi$
$432$	−1.52806	−0.0735187
$433$	−15.0415	−0.722851	−0.361425	−	0.932401i	$-0.617710\pi$
$433$	−15.0415	−0.722851	−0.361425	+	0.932401i	$0.617710\pi$
$434$	17.5426	0.842071
$435$	−13.2100	−0.633369
$436$	−9.32102	−0.446396
$437$	−5.93226	−0.283778
$438$	−17.3685	−0.829901
$439$	−1.66338	−0.0793887	−0.0396944	−	0.999212i	$-0.512638\pi$
$439$	−1.66338	−0.0793887	−0.0396944	+	0.999212i	$0.512638\pi$
$440$	29.3593	1.39965
$441$	−5.78369	−0.275414
$442$	−71.1179	−3.38274
$443$	39.4869	1.87608	0.938040	−	0.346526i	$-0.112639\pi$
$443$	39.4869	1.87608	0.938040	+	0.346526i	$0.112639\pi$
$444$	−11.8083	−0.560396
$445$	35.1621	1.66685
$446$	−19.6151	−0.928800
$447$	0.693754	0.0328134
$448$	13.0622	0.617130
$449$	16.0583	0.757837	0.378918	−	0.925430i	$-0.376296\pi$
$449$	16.0583	0.757837	0.378918	+	0.925430i	$0.376296\pi$
$450$	−14.4573	−0.681524
$451$	−9.70036	−0.456772
$452$	−47.4056	−2.22977
$453$	−0.357382	−0.0167913
$454$	−23.8582	−1.11972
$455$	24.0009	1.12518
$456$	13.9509	0.653310
$457$	8.07791	0.377869	0.188934	−	0.981990i	$-0.439497\pi$
$457$	8.07791	0.377869	0.188934	+	0.981990i	$0.439497\pi$
$458$	−37.2636	−1.74121
$459$	4.62654	0.215949
$460$	−18.4867	−0.861946
$461$	21.9013	1.02004	0.510022	−	0.860161i	$-0.329637\pi$
$461$	21.9013	1.02004	0.510022	+	0.860161i	$0.329637\pi$
$462$	6.24035	0.290327
$463$	13.0961	0.608629	0.304315	−	0.952572i	$-0.401573\pi$
$463$	13.0961	0.608629	0.304315	+	0.952572i	$0.401573\pi$
$464$	6.04944	0.280838
$465$	−22.5194	−1.04431
$466$	−67.9788	−3.14906
$467$	3.20079	0.148115	0.0740574	−	0.997254i	$-0.476405\pi$
$467$	3.20079	0.148115	0.0740574	+	0.997254i	$0.476405\pi$
$468$	−23.1857	−1.07176
$469$	6.20839	0.286677
$470$	84.0684	3.87779
$471$	8.44125	0.388952
$472$	1.26756	0.0583440
$473$	5.24018	0.240944
$474$	−27.1967	−1.24919
$475$	23.3492	1.07134
$476$	18.1392	0.831409
$477$	−5.55005	−0.254119
$478$	−28.7685	−1.31584
$479$	17.6242	0.805271	0.402635	−	0.915360i	$-0.368094\pi$
$479$	17.6242	0.805271	0.402635	+	0.915360i	$0.368094\pi$
$480$	−12.4412	−0.567861
$481$	−21.6634	−0.987765
$482$	23.8688	1.08720
$483$	−1.71875	−0.0782060
$484$	−18.6156	−0.846162
$485$	10.0657	0.457059
$486$	2.35691	0.106911
$487$	17.3026	0.784058	0.392029	−	0.919953i	$-0.371773\pi$
$487$	17.3026	0.784058	0.392029	+	0.919953i	$0.371773\pi$
$488$	−33.9924	−1.53876
$489$	3.58681	0.162201
$490$	45.4856	2.05483
$491$	19.3602	0.873715	0.436858	−	0.899531i	$-0.356091\pi$
$491$	19.3602	0.873715	0.436858	+	0.899531i	$0.356091\pi$
$492$	−14.3642	−0.647590
$493$	−18.3161	−0.824914
$494$	58.5127	2.63261
$495$	−8.01072	−0.360055
$496$	10.3126	0.463051
$497$	−1.78676	−0.0801473
$498$	21.2351	0.951568
$499$	37.9895	1.70065	0.850323	−	0.526261i	$-0.176407\pi$
$499$	37.9895	1.70065	0.850323	+	0.526261i	$0.176407\pi$
$500$	13.4520	0.601590
$501$	8.59941	0.384193
$502$	−1.84777	−0.0824698
$503$	−40.0558	−1.78600	−0.892999	−	0.450058i	$-0.851403\pi$
$503$	−40.0558	−1.78600	−0.892999	+	0.450058i	$0.851403\pi$
$504$	4.04199	0.180045
$505$	32.1594	1.43107
$506$	−8.81821	−0.392017
$507$	−29.5364	−1.31176
$508$	−20.1148	−0.892449
$509$	11.9760	0.530825	0.265413	−	0.964135i	$-0.414492\pi$
$509$	11.9760	0.530825	0.265413	+	0.964135i	$0.414492\pi$
$510$	−36.3852	−1.61116
$511$	8.12723	0.359527
$512$	16.8981	0.746796
$513$	−3.80651	−0.168062
$514$	−40.2006	−1.77317
$515$	40.0888	1.76652
$516$	7.75963	0.341599
$517$	25.6632	1.12866
$518$	8.63395	0.379354
$519$	−0.261439	−0.0114759
$520$	79.7592	3.49767
$521$	−32.3901	−1.41904	−0.709519	−	0.704686i	$-0.751088\pi$
$521$	−32.3901	−1.41904	−0.709519	+	0.704686i	$0.751088\pi$
$522$	−9.33078	−0.408397
$523$	26.6036	1.16329	0.581646	−	0.813442i	$-0.302409\pi$
$523$	26.6036	1.16329	0.581646	+	0.813442i	$0.302409\pi$
$524$	33.6369	1.46943
$525$	6.76497	0.295248
$526$	−67.5120	−2.94366
$527$	−31.2239	−1.36013
$528$	3.66847	0.159650
$529$	−20.5712	−0.894402
$530$	43.6481	1.89595
$531$	−0.345854	−0.0150088
$532$	−14.9241	−0.647043
$533$	−26.3525	−1.14146
$534$	24.8366	1.07478
$535$	25.2532	1.09179
$536$	20.6316	0.891147
$537$	−0.614536	−0.0265192
$538$	−50.1762	−2.16325
$539$	13.8852	0.598076
$540$	−11.8622	−0.510469
$541$	−17.6317	−0.758046	−0.379023	−	0.925387i	$-0.623740\pi$
$541$	−17.6317	−0.758046	−0.379023	+	0.925387i	$0.623740\pi$
$542$	8.35896	0.359048
$543$	10.2445	0.439632
$544$	−17.2502	−0.739595
$545$	−8.74881	−0.374758
$546$	16.9529	0.725517
$547$	0.861170	0.0368210	0.0184105	−	0.999831i	$-0.494139\pi$
$547$	0.861170	0.0368210	0.0184105	+	0.999831i	$0.494139\pi$
$548$	−61.1739	−2.61322
$549$	9.27486	0.395842
$550$	34.7083	1.47996
$551$	15.0696	0.641988
$552$	−5.71172	−0.243107
$553$	12.7261	0.541169
$554$	−55.3455	−2.35141
$555$	−11.0834	−0.470463
$556$	31.1770	1.32220
$557$	6.77340	0.286998	0.143499	−	0.989650i	$-0.454165\pi$
$557$	6.77340	0.286998	0.143499	+	0.989650i	$0.454165\pi$
$558$	−15.9064	−0.673373
$559$	14.2358	0.602109
$560$	−5.62324	−0.237625
$561$	−11.1071	−0.468944
$562$	−40.8677	−1.72390
$563$	−42.7958	−1.80363	−0.901814	−	0.432124i	$-0.857764\pi$
$563$	−42.7958	−1.80363	−0.901814	+	0.432124i	$0.857764\pi$
$564$	38.0019	1.60017
$565$	−44.4955	−1.87194
$566$	30.1509	1.26734
$567$	−1.10286	−0.0463159
$568$	−5.93773	−0.249141
$569$	5.93731	0.248905	0.124453	−	0.992226i	$-0.460283\pi$
$569$	5.93731	0.248905	0.124453	+	0.992226i	$0.460283\pi$
$570$	29.9361	1.25389
$571$	26.4543	1.10708	0.553539	−	0.832823i	$-0.313277\pi$
$571$	26.4543	1.10708	0.553539	+	0.832823i	$0.313277\pi$
$572$	55.6629	2.32738
$573$	25.3577	1.05933
$574$	10.5028	0.438379
$575$	−9.55955	−0.398661
$576$	−11.8439	−0.493495
$577$	−7.65073	−0.318504	−0.159252	−	0.987238i	$-0.550908\pi$
$577$	−7.65073	−0.318504	−0.159252	+	0.987238i	$0.550908\pi$
$578$	−10.3819	−0.431832
$579$	−14.8688	−0.617925
$580$	46.9615	1.94997
$581$	−9.93650	−0.412236
$582$	7.10984	0.294712
$583$	13.3242	0.551834
$584$	27.0082	1.11761
$585$	−21.7624	−0.899763
$586$	−55.6909	−2.30057
$587$	−0.765980	−0.0316154	−0.0158077	−	0.999875i	$-0.505032\pi$
$587$	−0.765980	−0.0316154	−0.0158077	+	0.999875i	$0.505032\pi$
$588$	20.5611	0.847924
$589$	25.6896	1.05852
$590$	2.71995	0.111978
$591$	−26.2793	−1.08099
$592$	5.07557	0.208605
$593$	48.3448	1.98528	0.992642	−	0.121085i	$-0.0386374\pi$
$593$	48.3448	1.98528	0.992642	+	0.121085i	$0.0386374\pi$
$594$	−5.65832	−0.232164
$595$	17.0257	0.697984
$596$	−2.46630	−0.101024
$597$	21.9366	0.897804
$598$	−23.9560	−0.979635
$599$	9.64407	0.394046	0.197023	−	0.980399i	$-0.436873\pi$
$599$	9.64407	0.394046	0.197023	+	0.980399i	$0.436873\pi$
$600$	22.4812	0.917791
$601$	15.4084	0.628520	0.314260	−	0.949337i	$-0.398244\pi$
$601$	15.4084	0.628520	0.314260	+	0.949337i	$0.398244\pi$
$602$	−5.67367	−0.231242
$603$	−5.62934	−0.229244
$604$	1.27049	0.0516957
$605$	−17.4728	−0.710369
$606$	22.7156	0.922759
$607$	7.39001	0.299951	0.149976	−	0.988690i	$-0.452080\pi$
$607$	7.39001	0.299951	0.149976	+	0.988690i	$0.452080\pi$
$608$	14.1927	0.575589
$609$	4.36613	0.176925
$610$	−72.9417	−2.95332
$611$	69.7180	2.82049
$612$	−16.4474	−0.664846
$613$	−17.7515	−0.716976	−0.358488	−	0.933534i	$-0.616708\pi$
$613$	−17.7515	−0.716976	−0.358488	+	0.933534i	$0.616708\pi$
$614$	71.5583	2.88786
$615$	−13.4824	−0.543664
$616$	−9.70379	−0.390977
$617$	40.9806	1.64982	0.824908	−	0.565267i	$-0.191227\pi$
$617$	40.9806	1.64982	0.824908	+	0.565267i	$0.191227\pi$
$618$	28.3165	1.13906
$619$	19.9670	0.802542	0.401271	−	0.915959i	$-0.368569\pi$
$619$	19.9670	0.802542	0.401271	+	0.915959i	$0.368569\pi$
$620$	80.0565	3.21515
$621$	1.55845	0.0625384
$622$	55.6657	2.23199
$623$	−11.6217	−0.465615
$624$	9.96597	0.398958
$625$	−18.0439	−0.721757
$626$	11.7405	0.469243
$627$	9.13846	0.364955
$628$	−30.0087	−1.19748
$629$	−15.3675	−0.612741
$630$	8.67340	0.345557
$631$	−13.0999	−0.521500	−0.260750	−	0.965406i	$-0.583970\pi$
$631$	−13.0999	−0.521500	−0.260750	+	0.965406i	$0.583970\pi$
$632$	42.2910	1.68225
$633$	17.8328	0.708792
$634$	−68.3450	−2.71433
$635$	−18.8799	−0.749228
$636$	19.7305	0.782364
$637$	37.7212	1.49457
$638$	22.4008	0.886856
$639$	1.62011	0.0640908
$640$	68.2632	2.69834
$641$	11.4540	0.452407	0.226203	−	0.974080i	$-0.427369\pi$
$641$	11.4540	0.452407	0.226203	+	0.974080i	$0.427369\pi$
$642$	17.8374	0.703988
$643$	−37.2576	−1.46929	−0.734647	−	0.678449i	$-0.762652\pi$
$643$	−37.2576	−1.46929	−0.734647	+	0.678449i	$0.762652\pi$
$644$	6.11018	0.240775
$645$	7.28327	0.286778
$646$	41.5075	1.63309
$647$	9.77332	0.384229	0.192114	−	0.981373i	$-0.438466\pi$
$647$	9.77332	0.384229	0.192114	+	0.981373i	$0.438466\pi$
$648$	−3.66500	−0.143975
$649$	0.830306	0.0325923
$650$	94.2904	3.69837
$651$	7.44306	0.291717
$652$	−12.7511	−0.499372
$653$	−26.7857	−1.04821	−0.524104	−	0.851655i	$-0.675600\pi$
$653$	−26.7857	−1.04821	−0.524104	+	0.851655i	$0.675600\pi$
$654$	−6.17967	−0.241644
$655$	31.5720	1.23362
$656$	6.17421	0.241063
$657$	−7.36921	−0.287500
$658$	−27.7861	−1.08322
$659$	−44.3678	−1.72832	−0.864162	−	0.503214i	$-0.832151\pi$
$659$	−44.3678	−1.72832	−0.864162	+	0.503214i	$0.832151\pi$
$660$	28.4782	1.10851
$661$	43.2590	1.68258	0.841291	−	0.540583i	$-0.181796\pi$
$661$	43.2590	1.68258	0.841291	+	0.540583i	$0.181796\pi$
$662$	−33.9499	−1.31950
$663$	−30.1743	−1.17187
$664$	−33.0207	−1.28145
$665$	−14.0079	−0.543205
$666$	−7.82867	−0.303355
$667$	−6.16976	−0.238894
$668$	−30.5709	−1.18283
$669$	−8.32237	−0.321762
$670$	44.2716	1.71036
$671$	−22.2666	−0.859591
$672$	4.11204	0.158626
$673$	34.2536	1.32038	0.660189	−	0.751099i	$-0.270476\pi$
$673$	34.2536	1.32038	0.660189	+	0.751099i	$0.270476\pi$
$674$	−2.57419	−0.0991541
$675$	−6.13402	−0.236098
$676$	105.002	4.03854
$677$	−14.8948	−0.572453	−0.286226	−	0.958162i	$-0.592401\pi$
$677$	−14.8948	−0.572453	−0.286226	+	0.958162i	$0.592401\pi$
$678$	−31.4291	−1.20703
$679$	−3.32689	−0.127674
$680$	56.5792	2.16971
$681$	−10.1227	−0.387902
$682$	38.1872	1.46226
$683$	−38.6005	−1.47701	−0.738504	−	0.674250i	$-0.764467\pi$
$683$	−38.6005	−1.47701	−0.738504	+	0.674250i	$0.764467\pi$
$684$	13.5322	0.517416
$685$	−57.4185	−2.19385
$686$	−33.2292	−1.26870
$687$	−15.8104	−0.603204
$688$	−3.33534	−0.127159
$689$	36.1974	1.37901
$690$	−12.2563	−0.466591
$691$	−3.73230	−0.141983	−0.0709917	−	0.997477i	$-0.522616\pi$
$691$	−3.73230	−0.141983	−0.0709917	+	0.997477i	$0.522616\pi$
$692$	0.929418	0.0353312
$693$	2.64769	0.100577
$694$	−86.7382	−3.29254
$695$	29.2631	1.11001
$696$	14.5094	0.549978
$697$	−18.6938	−0.708080
$698$	2.80720	0.106254
$699$	−28.8424	−1.09092
$700$	−24.0495	−0.908987
$701$	11.4213	0.431375	0.215688	−	0.976462i	$-0.430801\pi$
$701$	11.4213	0.431375	0.215688	+	0.976462i	$0.430801\pi$
$702$	−15.3717	−0.580168
$703$	12.6437	0.476865
$704$	28.4341	1.07165
$705$	35.6690	1.34337
$706$	−4.92218	−0.185249
$707$	−10.6293	−0.399755
$708$	1.22951	0.0462079
$709$	28.9387	1.08681	0.543407	−	0.839469i	$-0.317134\pi$
$709$	28.9387	1.08681	0.543407	+	0.839469i	$0.317134\pi$
$710$	−12.7413	−0.478173
$711$	−11.5392	−0.432752
$712$	−38.6210	−1.44738
$713$	−10.5177	−0.393893
$714$	12.0260	0.450061
$715$	52.2458	1.95388
$716$	2.18468	0.0816453
$717$	−12.2060	−0.455843
$718$	70.8512	2.64414
$719$	−26.9025	−1.00329	−0.501647	−	0.865072i	$-0.667273\pi$
$719$	−26.9025	−1.00329	−0.501647	+	0.865072i	$0.667273\pi$
$720$	5.09877	0.190020
$721$	−13.2501	−0.493458
$722$	10.6307	0.395635
$723$	10.1272	0.376634
$724$	−36.4191	−1.35351
$725$	24.2840	0.901886
$726$	−12.3418	−0.458047
$727$	51.2850	1.90206	0.951028	−	0.309104i	$-0.100029\pi$
$727$	51.2850	1.90206	0.951028	+	0.309104i	$0.100029\pi$
$728$	−26.3619	−0.977035
$729$	1.00000	0.0370370
$730$	57.9548	2.14500
$731$	10.0985	0.373507
$732$	−32.9722	−1.21869
$733$	7.88677	0.291305	0.145652	−	0.989336i	$-0.453472\pi$
$733$	7.88677	0.291305	0.145652	+	0.989336i	$0.453472\pi$
$734$	−25.6581	−0.947056
$735$	19.2988	0.711849
$736$	−5.81071	−0.214186
$737$	13.5146	0.497816
$738$	−9.52323	−0.350555
$739$	−4.10262	−0.150917	−0.0754587	−	0.997149i	$-0.524042\pi$
$739$	−4.10262	−0.150917	−0.0754587	+	0.997149i	$0.524042\pi$
$740$	39.4014	1.44843
$741$	24.8260	0.912008
$742$	−14.4265	−0.529613
$743$	49.3862	1.81181	0.905903	−	0.423486i	$-0.139194\pi$
$743$	49.3862	1.81181	0.905903	+	0.423486i	$0.139194\pi$
$744$	24.7346	0.906814
$745$	−2.31490	−0.0848112
$746$	−8.79504	−0.322009
$747$	9.00974	0.329649
$748$	39.4859	1.44375
$749$	−8.34664	−0.304979
$750$	8.91841	0.325654
$751$	18.9043	0.689829	0.344915	−	0.938634i	$-0.387908\pi$
$751$	18.9043	0.689829	0.344915	+	0.938634i	$0.387908\pi$
$752$	−16.3344	−0.595655
$753$	−0.783979	−0.0285698
$754$	60.8553	2.21622
$755$	1.19250	0.0433995
$756$	3.92068	0.142594
$757$	3.15362	0.114620	0.0573102	−	0.998356i	$-0.481748\pi$
$757$	3.15362	0.114620	0.0573102	+	0.998356i	$0.481748\pi$
$758$	24.5633	0.892180
$759$	−3.74143	−0.135805
$760$	−46.5509	−1.68858
$761$	−23.5186	−0.852548	−0.426274	−	0.904594i	$-0.640174\pi$
$761$	−23.5186	−0.852548	−0.426274	+	0.904594i	$0.640174\pi$
$762$	−13.3357	−0.483103
$763$	2.89164	0.104684
$764$	−90.1468	−3.26140
$765$	−15.4377	−0.558151
$766$	22.9285	0.828441
$767$	2.25566	0.0814470
$768$	24.5295	0.885134
$769$	33.5440	1.20963	0.604814	−	0.796367i	$-0.293248\pi$
$769$	33.5440	1.20963	0.604814	+	0.796367i	$0.293248\pi$
$770$	−20.8226	−0.750394
$771$	−17.0565	−0.614275
$772$	52.8586	1.90242
$773$	18.7941	0.675977	0.337989	−	0.941150i	$-0.390253\pi$
$773$	18.7941	0.675977	0.337989	+	0.941150i	$0.390253\pi$
$774$	5.14450	0.184915
$775$	41.3976	1.48705
$776$	−11.0558	−0.396881
$777$	3.66325	0.131419
$778$	−47.6762	−1.70927
$779$	15.3805	0.551062
$780$	77.3654	2.77012
$781$	−3.88948	−0.139176
$782$	−16.9938	−0.607698
$783$	−3.95891	−0.141480
$784$	−8.83781	−0.315636
$785$	−28.1665	−1.00531
$786$	22.3007	0.795438
$787$	−29.0618	−1.03594	−0.517970	−	0.855399i	$-0.673312\pi$
$787$	−29.0618	−1.03594	−0.517970	+	0.855399i	$0.673312\pi$
$788$	93.4231	3.32806
$789$	−28.6443	−1.01976
$790$	90.7491	3.22871
$791$	14.7066	0.522905
$792$	8.79873	0.312649
$793$	−60.4906	−2.14808
$794$	5.90469	0.209549
$795$	18.5192	0.656809
$796$	−77.9846	−2.76409
$797$	−18.6241	−0.659698	−0.329849	−	0.944034i	$-0.606998\pi$
$797$	−18.6241	−0.659698	−0.329849	+	0.944034i	$0.606998\pi$
$798$	−9.89443	−0.350259
$799$	49.4562	1.74964
$800$	22.8708	0.808605
$801$	10.5378	0.372334
$802$	−57.0175	−2.01336
$803$	17.6916	0.624322
$804$	20.0123	0.705781
$805$	5.73508	0.202135
$806$	103.742	3.65414
$807$	−21.2890	−0.749409
$808$	−35.3229	−1.24266
$809$	36.0963	1.26908	0.634539	−	0.772891i	$-0.281190\pi$
$809$	36.0963	1.26908	0.634539	+	0.772891i	$0.281190\pi$
$810$	−7.86445	−0.276329
$811$	2.02513	0.0711120	0.0355560	−	0.999368i	$-0.488680\pi$
$811$	2.02513	0.0711120	0.0355560	+	0.999368i	$0.488680\pi$
$812$	−15.5216	−0.544702
$813$	3.54658	0.124384
$814$	18.7946	0.658751
$815$	−11.9683	−0.419233
$816$	7.06962	0.247486
$817$	−8.30860	−0.290681
$818$	5.27482	0.184430
$819$	7.19286	0.251339
$820$	47.9301	1.67379
$821$	54.1714	1.89060	0.945298	−	0.326209i	$-0.105771\pi$
$821$	54.1714	1.89060	0.945298	+	0.326209i	$0.105771\pi$
$822$	−40.5572	−1.41459
$823$	−5.52811	−0.192698	−0.0963489	−	0.995348i	$-0.530716\pi$
$823$	−5.52811	−0.192698	−0.0963489	+	0.995348i	$0.530716\pi$
$824$	−44.0323	−1.53394
$825$	14.7262	0.512700
$826$	−0.898992	−0.0312799
$827$	11.6819	0.406219	0.203109	−	0.979156i	$-0.434895\pi$
$827$	11.6819	0.406219	0.203109	+	0.979156i	$0.434895\pi$
$828$	−5.54029	−0.192539
$829$	−13.0312	−0.452591	−0.226295	−	0.974059i	$-0.572661\pi$
$829$	−13.0312	−0.452591	−0.226295	+	0.974059i	$0.572661\pi$
$830$	−70.8566	−2.45947
$831$	−23.4823	−0.814591
$832$	77.2457	2.67801
$833$	26.7585	0.927128
$834$	20.6698	0.715737
$835$	−28.6942	−0.993005
$836$	−32.4873	−1.12360
$837$	−6.74886	−0.233275
$838$	54.9519	1.89828
$839$	−41.3416	−1.42727	−0.713636	−	0.700517i	$-0.752953\pi$
$839$	−41.3416	−1.42727	−0.713636	+	0.700517i	$0.752953\pi$
$840$	−13.4872	−0.465352
$841$	−13.3270	−0.459553
$842$	26.3974	0.909714
$843$	−17.3395	−0.597206
$844$	−63.3959	−2.18218
$845$	98.5561	3.39043
$846$	25.1946	0.866207
$847$	5.77507	0.198434
$848$	−8.48079	−0.291232
$849$	12.7926	0.439040
$850$	66.8873	2.29422
$851$	−5.17652	−0.177449
$852$	−5.75952	−0.197318
$853$	2.47366	0.0846964	0.0423482	−	0.999103i	$-0.486516\pi$
$853$	2.47366	0.0846964	0.0423482	+	0.999103i	$0.486516\pi$
$854$	24.1085	0.824978
$855$	12.7014	0.434380
$856$	−27.7373	−0.948042
$857$	33.7629	1.15332	0.576659	−	0.816985i	$-0.304356\pi$
$857$	33.7629	1.15332	0.576659	+	0.816985i	$0.304356\pi$
$858$	36.9035	1.25987
$859$	19.9444	0.680494	0.340247	−	0.940336i	$-0.389489\pi$
$859$	19.9444	0.680494	0.340247	+	0.940336i	$0.389489\pi$
$860$	−25.8921	−0.882912
$861$	4.45619	0.151866
$862$	−30.2524	−1.03040
$863$	−37.7981	−1.28666	−0.643330	−	0.765589i	$-0.722448\pi$
$863$	−37.7981	−1.28666	−0.643330	+	0.765589i	$0.722448\pi$
$864$	−3.72852	−0.126847
$865$	0.872362	0.0296612
$866$	35.4515	1.20469
$867$	−4.40490	−0.149598
$868$	−26.4601	−0.898115
$869$	27.7025	0.939744
$870$	31.1346	1.05556
$871$	36.7145	1.24402
$872$	9.60942	0.325416
$873$	3.01660	0.102096
$874$	13.9818	0.472940
$875$	−4.17317	−0.141079
$876$	26.1976	0.885135
$877$	−14.9957	−0.506369	−0.253185	−	0.967418i	$-0.581478\pi$
$877$	−14.9957	−0.506369	−0.253185	+	0.967418i	$0.581478\pi$
$878$	3.92043	0.132308
$879$	−23.6288	−0.796980
$880$	−12.2408	−0.412638
$881$	−28.8440	−0.971778	−0.485889	−	0.874021i	$-0.661504\pi$
$881$	−28.8440	−0.971778	−0.485889	+	0.874021i	$0.661504\pi$
$882$	13.6316	0.459001
$883$	1.90055	0.0639587	0.0319794	−	0.999489i	$-0.489819\pi$
$883$	1.90055	0.0639587	0.0319794	+	0.999489i	$0.489819\pi$
$884$	107.270	3.60787
$885$	1.15403	0.0387924
$886$	−93.0670	−3.12665
$887$	17.1302	0.575175	0.287588	−	0.957754i	$-0.407147\pi$
$887$	17.1302	0.575175	0.287588	+	0.957754i	$0.407147\pi$
$888$	12.1736	0.408520
$889$	6.24017	0.209288
$890$	−82.8739	−2.77794
$891$	−2.40074	−0.0804279
$892$	29.5861	0.990615
$893$	−40.6904	−1.36165
$894$	−1.63511	−0.0546863
$895$	2.05056	0.0685428
$896$	−22.5622	−0.753751
$897$	−10.1642	−0.339372
$898$	−37.8478	−1.26300
$899$	26.7181	0.891099
$900$	21.8065	0.726882
$901$	25.6776	0.855443
$902$	22.8628	0.761249
$903$	−2.40725	−0.0801084
$904$	48.8724	1.62547
$905$	−34.1834	−1.13629
$906$	0.842315	0.0279840
$907$	−40.5782	−1.34738	−0.673689	−	0.739015i	$-0.735291\pi$
$907$	−40.5782	−1.34738	−0.673689	+	0.739015i	$0.735291\pi$
$908$	35.9862	1.19424
$909$	9.63789	0.319669
$910$	−56.5679	−1.87521
$911$	2.23382	0.0740097	0.0370049	−	0.999315i	$-0.488218\pi$
$911$	2.23382	0.0740097	0.0370049	+	0.999315i	$0.488218\pi$
$912$	−5.81657	−0.192606
$913$	−21.6301	−0.715851
$914$	−19.0389	−0.629750
$915$	−30.9481	−1.02311
$916$	56.2060	1.85710
$917$	−10.4351	−0.344598
$918$	−10.9043	−0.359896
$919$	−8.36156	−0.275822	−0.137911	−	0.990445i	$-0.544039\pi$
$919$	−8.36156	−0.275822	−0.137911	+	0.990445i	$0.544039\pi$
$920$	19.0587	0.628346
$921$	30.3611	1.00043
$922$	−51.6193	−1.69999
$923$	−10.5664	−0.347797
$924$	−9.41255	−0.309650
$925$	20.3747	0.669915
$926$	−30.8664	−1.01433
$927$	12.0143	0.394600
$928$	14.7609	0.484549
$929$	38.1004	1.25003	0.625017	−	0.780611i	$-0.285092\pi$
$929$	38.1004	1.25003	0.625017	+	0.780611i	$0.285092\pi$
$930$	53.0760	1.74043
$931$	−22.0157	−0.721536
$932$	102.535	3.35864
$933$	23.6181	0.773222
$934$	−7.54396	−0.246846
$935$	37.0619	1.21205
$936$	23.9031	0.781298
$937$	−7.88824	−0.257698	−0.128849	−	0.991664i	$-0.541128\pi$
$937$	−7.88824	−0.257698	−0.128849	+	0.991664i	$0.541128\pi$
$938$	−14.6326	−0.477771
$939$	4.98130	0.162559
$940$	−126.803	−4.13587
$941$	−5.62262	−0.183292	−0.0916461	−	0.995792i	$-0.529213\pi$
$941$	−5.62262	−0.183292	−0.0916461	+	0.995792i	$0.529213\pi$
$942$	−19.8952	−0.648222
$943$	−6.29701	−0.205059
$944$	−0.528484	−0.0172007
$945$	3.67999	0.119710
$946$	−12.3506	−0.401553
$947$	−38.0116	−1.23521	−0.617606	−	0.786488i	$-0.711897\pi$
$947$	−38.0116	−1.23521	−0.617606	+	0.786488i	$0.711897\pi$
$948$	41.0218	1.33232
$949$	48.0619	1.56016
$950$	−55.0319	−1.78547
$951$	−28.9978	−0.940317
$952$	−18.7005	−0.606085
$953$	−5.78837	−0.187504	−0.0937518	−	0.995596i	$-0.529886\pi$
$953$	−5.78837	−0.187504	−0.0937518	+	0.995596i	$0.529886\pi$
$954$	13.0809	0.423511
$955$	−84.6127	−2.73800
$956$	43.3925	1.40342
$957$	9.50432	0.307231
$958$	−41.5386	−1.34205
$959$	18.9778	0.612826
$960$	39.5203	1.27551
$961$	14.5471	0.469261
$962$	51.0585	1.64619
$963$	7.56816	0.243881
$964$	−36.0022	−1.15955
$965$	49.6137	1.59712
$966$	4.05094	0.130337
$967$	52.3884	1.68470	0.842348	−	0.538934i	$-0.181173\pi$
$967$	52.3884	1.68470	0.842348	+	0.538934i	$0.181173\pi$
$968$	19.1916	0.616840
$969$	17.6110	0.565747
$970$	−23.7239	−0.761728
$971$	46.7727	1.50101	0.750504	−	0.660866i	$-0.229811\pi$
$971$	46.7727	1.50101	0.750504	+	0.660866i	$0.229811\pi$
$972$	−3.55501	−0.114027
$973$	−9.67198	−0.310070
$974$	−40.7807	−1.30670
$975$	40.0060	1.28122
$976$	14.1725	0.453651
$977$	−26.3156	−0.841909	−0.420955	−	0.907082i	$-0.638305\pi$
$977$	−26.3156	−0.841909	−0.420955	+	0.907082i	$0.638305\pi$
$978$	−8.45377	−0.270322
$979$	−25.2985	−0.808544
$980$	−68.6075	−2.19159
$981$	−2.62194	−0.0837121
$982$	−45.6303	−1.45612
$983$	13.5544	0.432317	0.216158	−	0.976358i	$-0.430647\pi$
$983$	13.5544	0.432317	0.216158	+	0.976358i	$0.430647\pi$
$984$	14.8087	0.472084
$985$	87.6880	2.79397
$986$	43.1692	1.37479
$987$	−11.7892	−0.375256
$988$	−88.2568	−2.80782
$989$	3.40168	0.108167
$990$	18.8805	0.600062
$991$	−11.8623	−0.376820	−0.188410	−	0.982090i	$-0.560333\pi$
$991$	−11.8623	−0.376820	−0.188410	+	0.982090i	$0.560333\pi$
$992$	25.1633	0.798934
$993$	−14.4044	−0.457110
$994$	4.21123	0.133572
$995$	−73.1972	−2.32051
$996$	−32.0297	−1.01490
$997$	12.5637	0.397897	0.198948	−	0.980010i	$-0.436247\pi$
$997$	12.5637	0.397897	0.198948	+	0.980010i	$0.436247\pi$
$998$	−89.5378	−2.83427
$999$	−3.32159	−0.105090

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8031.2.a.c.1.14	✓	121

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8031.2.a.c.1.14	✓	121	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:	\( N \)	\(=\)	\( 8031 = 3 \cdot 2677 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.35691 q^{2} -1.00000 q^{3} +3.55501 q^{4} +3.33677 q^{5} +2.35691 q^{6} -1.10286 q^{7} -3.66500 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.35691 q^{2} -1.00000 q^{3} +3.55501 q^{4} +3.33677 q^{5} +2.35691 q^{6} -1.10286 q^{7} -3.66500 q^{8} +1.00000 q^{9} -7.86445 q^{10} -2.40074 q^{11} -3.55501 q^{12} -6.52199 q^{13} +2.59934 q^{14} -3.33677 q^{15} +1.52806 q^{16} -4.62654 q^{17} -2.35691 q^{18} +3.80651 q^{19} +11.8622 q^{20} +1.10286 q^{21} +5.65832 q^{22} -1.55845 q^{23} +3.66500 q^{24} +6.13402 q^{25} +15.3717 q^{26} -1.00000 q^{27} -3.92068 q^{28} +3.95891 q^{29} +7.86445 q^{30} +6.74886 q^{31} +3.72852 q^{32} +2.40074 q^{33} +10.9043 q^{34} -3.67999 q^{35} +3.55501 q^{36} +3.32159 q^{37} -8.97159 q^{38} +6.52199 q^{39} -12.2293 q^{40} +4.04057 q^{41} -2.59934 q^{42} -2.18273 q^{43} -8.53465 q^{44} +3.33677 q^{45} +3.67312 q^{46} -10.6897 q^{47} -1.52806 q^{48} -5.78369 q^{49} -14.4573 q^{50} +4.62654 q^{51} -23.1857 q^{52} -5.55005 q^{53} +2.35691 q^{54} -8.01072 q^{55} +4.04199 q^{56} -3.80651 q^{57} -9.33078 q^{58} -0.345854 q^{59} -11.8622 q^{60} +9.27486 q^{61} -15.9064 q^{62} -1.10286 q^{63} -11.8439 q^{64} -21.7624 q^{65} -5.65832 q^{66} -5.62934 q^{67} -16.4474 q^{68} +1.55845 q^{69} +8.67340 q^{70} +1.62011 q^{71} -3.66500 q^{72} -7.36921 q^{73} -7.82867 q^{74} -6.13402 q^{75} +13.5322 q^{76} +2.64769 q^{77} -15.3717 q^{78} -11.5392 q^{79} +5.09877 q^{80} +1.00000 q^{81} -9.52323 q^{82} +9.00974 q^{83} +3.92068 q^{84} -15.4377 q^{85} +5.14450 q^{86} -3.95891 q^{87} +8.79873 q^{88} +10.5378 q^{89} -7.86445 q^{90} +7.19286 q^{91} -5.54029 q^{92} -6.74886 q^{93} +25.1946 q^{94} +12.7014 q^{95} -3.72852 q^{96} +3.01660 q^{97} +13.6316 q^{98} -2.40074 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 121 q + 7 q^{2} - 121 q^{3} + 123 q^{4} + 24 q^{5} - 7 q^{6} - 14 q^{7} + 18 q^{8} + 121 q^{9}+O(q^{10}) \) 121 * q + 7 * q^2 - 121 * q^3 + 123 * q^4 + 24 * q^5 - 7 * q^6 - 14 * q^7 + 18 * q^8 + 121 * q^9	\( 121 q + 7 q^{2} - 121 q^{3} + 123 q^{4} + 24 q^{5} - 7 q^{6} - 14 q^{7} + 18 q^{8} + 121 q^{9} + 18 q^{10} + 32 q^{11} - 123 q^{12} + 2 q^{13} + 37 q^{14} - 24 q^{15} + 131 q^{16} + 87 q^{17} + 7 q^{18} - 10 q^{19} + 60 q^{20} + 14 q^{21} - 22 q^{22} + 31 q^{23} - 18 q^{24} + 147 q^{25} + 37 q^{26} - 121 q^{27} - 29 q^{28} + 68 q^{29} - 18 q^{30} + 25 q^{31} + 43 q^{32} - 32 q^{33} + 27 q^{34} + 51 q^{35} + 123 q^{36} - 4 q^{37} + 36 q^{38} - 2 q^{39} + 61 q^{40} + 132 q^{41} - 37 q^{42} - 91 q^{43} + 94 q^{44} + 24 q^{45} + 39 q^{47} - 131 q^{48} + 217 q^{49} + 54 q^{50} - 87 q^{51} - 12 q^{52} + 55 q^{53} - 7 q^{54} + 7 q^{55} + 104 q^{56} + 10 q^{57} - 3 q^{58} + 58 q^{59} - 60 q^{60} + 126 q^{61} + 74 q^{62} - 14 q^{63} + 122 q^{64} + 128 q^{65} + 22 q^{66} - 139 q^{67} + 190 q^{68} - 31 q^{69} - 18 q^{70} + 37 q^{71} + 18 q^{72} + 84 q^{73} + 79 q^{74} - 147 q^{75} + 23 q^{76} + 95 q^{77} - 37 q^{78} - 14 q^{79} + 145 q^{80} + 121 q^{81} + 9 q^{82} + 58 q^{83} + 29 q^{84} + 32 q^{85} + 28 q^{86} - 68 q^{87} - 84 q^{88} + 198 q^{89} + 18 q^{90} + 5 q^{91} + 98 q^{92} - 25 q^{93} + 9 q^{94} + 42 q^{95} - 43 q^{96} + 73 q^{97} + 69 q^{98} + 32 q^{99}+O(q^{100}) \) 121 * q + 7 * q^2 - 121 * q^3 + 123 * q^4 + 24 * q^5 - 7 * q^6 - 14 * q^7 + 18 * q^8 + 121 * q^9 + 18 * q^10 + 32 * q^11 - 123 * q^12 + 2 * q^13 + 37 * q^14 - 24 * q^15 + 131 * q^16 + 87 * q^17 + 7 * q^18 - 10 * q^19 + 60 * q^20 + 14 * q^21 - 22 * q^22 + 31 * q^23 - 18 * q^24 + 147 * q^25 + 37 * q^26 - 121 * q^27 - 29 * q^28 + 68 * q^29 - 18 * q^30 + 25 * q^31 + 43 * q^32 - 32 * q^33 + 27 * q^34 + 51 * q^35 + 123 * q^36 - 4 * q^37 + 36 * q^38 - 2 * q^39 + 61 * q^40 + 132 * q^41 - 37 * q^42 - 91 * q^43 + 94 * q^44 + 24 * q^45 + 39 * q^47 - 131 * q^48 + 217 * q^49 + 54 * q^50 - 87 * q^51 - 12 * q^52 + 55 * q^53 - 7 * q^54 + 7 * q^55 + 104 * q^56 + 10 * q^57 - 3 * q^58 + 58 * q^59 - 60 * q^60 + 126 * q^61 + 74 * q^62 - 14 * q^63 + 122 * q^64 + 128 * q^65 + 22 * q^66 - 139 * q^67 + 190 * q^68 - 31 * q^69 - 18 * q^70 + 37 * q^71 + 18 * q^72 + 84 * q^73 + 79 * q^74 - 147 * q^75 + 23 * q^76 + 95 * q^77 - 37 * q^78 - 14 * q^79 + 145 * q^80 + 121 * q^81 + 9 * q^82 + 58 * q^83 + 29 * q^84 + 32 * q^85 + 28 * q^86 - 68 * q^87 - 84 * q^88 + 198 * q^89 + 18 * q^90 + 5 * q^91 + 98 * q^92 - 25 * q^93 + 9 * q^94 + 42 * q^95 - 43 * q^96 + 73 * q^97 + 69 * q^98 + 32 * q^99

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