LMFDB - Embedded newform 8023.2.a.d.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8023,2,Mod(1,8023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8023, 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("8023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8023 = 71 \cdot 113 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8023.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:	$64.0639775417$
Analytic rank:	$0$
Dimension:	$165$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	8023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.57888 q^{2} -1.57055 q^{3} +4.65062 q^{4} -2.72522 q^{5} +4.05026 q^{6} -1.77487 q^{7} -6.83564 q^{8} -0.533376 q^{9} +O(q^{10})$	\(q-2.57888 q^{2} -1.57055 q^{3} +4.65062 q^{4} -2.72522 q^{5} +4.05026 q^{6} -1.77487 q^{7} -6.83564 q^{8} -0.533376 q^{9} +7.02803 q^{10} +2.89561 q^{11} -7.30403 q^{12} +2.08606 q^{13} +4.57717 q^{14} +4.28010 q^{15} +8.32705 q^{16} +1.99289 q^{17} +1.37551 q^{18} -3.74706 q^{19} -12.6740 q^{20} +2.78752 q^{21} -7.46743 q^{22} -3.35334 q^{23} +10.7357 q^{24} +2.42685 q^{25} -5.37970 q^{26} +5.54934 q^{27} -8.25424 q^{28} -3.16583 q^{29} -11.0379 q^{30} -8.66505 q^{31} -7.80318 q^{32} -4.54769 q^{33} -5.13941 q^{34} +4.83691 q^{35} -2.48053 q^{36} -2.96945 q^{37} +9.66321 q^{38} -3.27626 q^{39} +18.6287 q^{40} -0.699149 q^{41} -7.18867 q^{42} +1.66017 q^{43} +13.4664 q^{44} +1.45357 q^{45} +8.64785 q^{46} -5.47914 q^{47} -13.0780 q^{48} -3.84985 q^{49} -6.25856 q^{50} -3.12992 q^{51} +9.70149 q^{52} +11.6587 q^{53} -14.3111 q^{54} -7.89118 q^{55} +12.1323 q^{56} +5.88493 q^{57} +8.16429 q^{58} +7.78930 q^{59} +19.9051 q^{60} +13.8873 q^{61} +22.3461 q^{62} +0.946671 q^{63} +3.46936 q^{64} -5.68499 q^{65} +11.7280 q^{66} +8.91232 q^{67} +9.26816 q^{68} +5.26658 q^{69} -12.4738 q^{70} +1.00000 q^{71} +3.64596 q^{72} -1.01223 q^{73} +7.65784 q^{74} -3.81149 q^{75} -17.4261 q^{76} -5.13932 q^{77} +8.44909 q^{78} -9.52480 q^{79} -22.6931 q^{80} -7.11538 q^{81} +1.80302 q^{82} +8.94937 q^{83} +12.9637 q^{84} -5.43106 q^{85} -4.28138 q^{86} +4.97209 q^{87} -19.7933 q^{88} +0.131878 q^{89} -3.74858 q^{90} -3.70248 q^{91} -15.5951 q^{92} +13.6089 q^{93} +14.1301 q^{94} +10.2116 q^{95} +12.2553 q^{96} -18.9254 q^{97} +9.92830 q^{98} -1.54445 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9}+O(q^{10}) $ 165 * q + 22 * q^2 + 18 * q^3 + 166 * q^4 + 28 * q^5 + 16 * q^6 + 24 * q^7 + 66 * q^8 + 177 * q^9	\( 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9} + 14 q^{10} + 18 q^{11} + 54 q^{12} + 44 q^{13} + 26 q^{14} + 24 q^{15} + 168 q^{16} + 143 q^{17} + 57 q^{18} + 20 q^{19} + 49 q^{20} + 39 q^{21} + 25 q^{22} + 52 q^{23} + 27 q^{24} + 175 q^{25} + 48 q^{26} + 69 q^{27} + 28 q^{28} + 58 q^{29} - 11 q^{30} + 28 q^{31} + 114 q^{32} + 110 q^{33} + 55 q^{34} + 67 q^{35} + 202 q^{36} + 44 q^{37} + 35 q^{38} + 27 q^{39} + 53 q^{40} + 141 q^{41} + 40 q^{42} + 29 q^{43} + 52 q^{44} + 54 q^{45} + 29 q^{46} + 87 q^{47} + 53 q^{48} + 143 q^{49} + 16 q^{50} + 37 q^{51} + 105 q^{52} + 101 q^{53} - 36 q^{54} + 72 q^{55} + 57 q^{56} + 82 q^{57} + 4 q^{58} + 103 q^{59} + 53 q^{60} + 16 q^{61} + 54 q^{62} + 126 q^{63} + 136 q^{64} + 159 q^{65} + 53 q^{66} + 60 q^{67} + 220 q^{68} + 81 q^{69} + 16 q^{70} + 165 q^{71} + 176 q^{72} + 124 q^{73} + 29 q^{74} + 44 q^{75} + 18 q^{76} + 127 q^{77} - 91 q^{78} + 14 q^{79} + 158 q^{80} + 213 q^{81} + 20 q^{82} + 116 q^{83} + 67 q^{84} + 59 q^{85} + 30 q^{86} + 28 q^{87} + 79 q^{88} + 195 q^{89} + 16 q^{90} - 26 q^{91} + 173 q^{92} + 116 q^{93} + 53 q^{94} + 26 q^{95} - 36 q^{96} + 88 q^{97} + 150 q^{98} + 12 q^{99}+O(q^{100}) \) 165 * q + 22 * q^2 + 18 * q^3 + 166 * q^4 + 28 * q^5 + 16 * q^6 + 24 * q^7 + 66 * q^8 + 177 * q^9 + 14 * q^10 + 18 * q^11 + 54 * q^12 + 44 * q^13 + 26 * q^14 + 24 * q^15 + 168 * q^16 + 143 * q^17 + 57 * q^18 + 20 * q^19 + 49 * q^20 + 39 * q^21 + 25 * q^22 + 52 * q^23 + 27 * q^24 + 175 * q^25 + 48 * q^26 + 69 * q^27 + 28 * q^28 + 58 * q^29 - 11 * q^30 + 28 * q^31 + 114 * q^32 + 110 * q^33 + 55 * q^34 + 67 * q^35 + 202 * q^36 + 44 * q^37 + 35 * q^38 + 27 * q^39 + 53 * q^40 + 141 * q^41 + 40 * q^42 + 29 * q^43 + 52 * q^44 + 54 * q^45 + 29 * q^46 + 87 * q^47 + 53 * q^48 + 143 * q^49 + 16 * q^50 + 37 * q^51 + 105 * q^52 + 101 * q^53 - 36 * q^54 + 72 * q^55 + 57 * q^56 + 82 * q^57 + 4 * q^58 + 103 * q^59 + 53 * q^60 + 16 * q^61 + 54 * q^62 + 126 * q^63 + 136 * q^64 + 159 * q^65 + 53 * q^66 + 60 * q^67 + 220 * q^68 + 81 * q^69 + 16 * q^70 + 165 * q^71 + 176 * q^72 + 124 * q^73 + 29 * q^74 + 44 * q^75 + 18 * q^76 + 127 * q^77 - 91 * q^78 + 14 * q^79 + 158 * q^80 + 213 * q^81 + 20 * q^82 + 116 * q^83 + 67 * q^84 + 59 * q^85 + 30 * q^86 + 28 * q^87 + 79 * q^88 + 195 * q^89 + 16 * q^90 - 26 * q^91 + 173 * q^92 + 116 * q^93 + 53 * q^94 + 26 * q^95 - 36 * q^96 + 88 * q^97 + 150 * q^98 + 12 * 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 $

$2$	−2.57888	−1.82354	−0.911772	−	0.410697i	$-0.865285\pi$
$2$	−2.57888	−1.82354	−0.911772	+	0.410697i	$0.865285\pi$
$3$	−1.57055	−0.906757	−0.453378	−	0.891318i	$-0.649781\pi$
$3$	−1.57055	−0.906757	−0.453378	+	0.891318i	$0.649781\pi$
$4$	4.65062	2.32531
$5$	−2.72522	−1.21876	−0.609379	−	0.792879i	$-0.708581\pi$
$5$	−2.72522	−1.21876	−0.609379	+	0.792879i	$0.708581\pi$
$6$	4.05026	1.65351
$7$	−1.77487	−0.670837	−0.335418	−	0.942069i	$-0.608878\pi$
$7$	−1.77487	−0.670837	−0.335418	+	0.942069i	$0.608878\pi$
$8$	−6.83564	−2.41676
$9$	−0.533376	−0.177792
$10$	7.02803	2.22246
$11$	2.89561	0.873059	0.436529	−	0.899690i	$-0.356208\pi$
$11$	2.89561	0.873059	0.436529	+	0.899690i	$0.356208\pi$
$12$	−7.30403	−2.10849
$13$	2.08606	0.578569	0.289285	−	0.957243i	$-0.406583\pi$
$13$	2.08606	0.578569	0.289285	+	0.957243i	$0.406583\pi$
$14$	4.57717	1.22330
$15$	4.28010	1.10512
$16$	8.32705	2.08176
$17$	1.99289	0.483346	0.241673	−	0.970358i	$-0.422304\pi$
$17$	1.99289	0.483346	0.241673	+	0.970358i	$0.422304\pi$
$18$	1.37551	0.324211
$19$	−3.74706	−0.859633	−0.429817	−	0.902916i	$-0.641422\pi$
$19$	−3.74706	−0.859633	−0.429817	+	0.902916i	$0.641422\pi$
$20$	−12.6740	−2.83399
$21$	2.78752	0.608286
$22$	−7.46743	−1.59206
$23$	−3.35334	−0.699219	−0.349609	−	0.936896i	$-0.613686\pi$
$23$	−3.35334	−0.699219	−0.349609	+	0.936896i	$0.613686\pi$
$24$	10.7357	2.19142
$25$	2.42685	0.485370
$26$	−5.37970	−1.05505
$27$	5.54934	1.06797
$28$	−8.25424	−1.55990
$29$	−3.16583	−0.587879	−0.293940	−	0.955824i	$-0.594966\pi$
$29$	−3.16583	−0.587879	−0.293940	+	0.955824i	$0.594966\pi$
$30$	−11.0379	−2.01523
$31$	−8.66505	−1.55629	−0.778144	−	0.628085i	$-0.783839\pi$
$31$	−8.66505	−1.55629	−0.778144	+	0.628085i	$0.783839\pi$
$32$	−7.80318	−1.37942
$33$	−4.54769	−0.791652
$34$	−5.13941	−0.881402
$35$	4.83691	0.817587
$36$	−2.48053	−0.413422
$37$	−2.96945	−0.488174	−0.244087	−	0.969753i	$-0.578488\pi$
$37$	−2.96945	−0.488174	−0.244087	+	0.969753i	$0.578488\pi$
$38$	9.66321	1.56758
$39$	−3.27626	−0.524622
$40$	18.6287	2.94545
$41$	−0.699149	−0.109189	−0.0545943	−	0.998509i	$-0.517387\pi$
$41$	−0.699149	−0.109189	−0.0545943	+	0.998509i	$0.517387\pi$
$42$	−7.18867	−1.10924
$43$	1.66017	0.253174	0.126587	−	0.991956i	$-0.459598\pi$
$43$	1.66017	0.253174	0.126587	+	0.991956i	$0.459598\pi$
$44$	13.4664	2.03013
$45$	1.45357	0.216685
$46$	8.64785	1.27506
$47$	−5.47914	−0.799215	−0.399608	−	0.916686i	$-0.630854\pi$
$47$	−5.47914	−0.799215	−0.399608	+	0.916686i	$0.630854\pi$
$48$	−13.0780	−1.88765
$49$	−3.84985	−0.549978
$50$	−6.25856	−0.885094
$51$	−3.12992	−0.438277
$52$	9.70149	1.34535
$53$	11.6587	1.60145	0.800723	−	0.599035i	$-0.204449\pi$
$53$	11.6587	1.60145	0.800723	+	0.599035i	$0.204449\pi$
$54$	−14.3111	−1.94749
$55$	−7.89118	−1.06405
$56$	12.1323	1.62125
$57$	5.88493	0.779479
$58$	8.16429	1.07202
$59$	7.78930	1.01408	0.507040	−	0.861922i	$-0.330740\pi$
$59$	7.78930	1.01408	0.507040	+	0.861922i	$0.330740\pi$
$60$	19.9051	2.56974
$61$	13.8873	1.77809	0.889046	−	0.457818i	$-0.151369\pi$
$61$	13.8873	1.77809	0.889046	+	0.457818i	$0.151369\pi$
$62$	22.3461	2.83796
$63$	0.946671	0.119269
$64$	3.46936	0.433670
$65$	−5.68499	−0.705136
$66$	11.7280	1.44361
$67$	8.91232	1.08881	0.544406	−	0.838822i	$-0.316755\pi$
$67$	8.91232	1.08881	0.544406	+	0.838822i	$0.316755\pi$
$68$	9.26816	1.12393
$69$	5.26658	0.634022
$70$	−12.4738	−1.49091
$71$	1.00000	0.118678
$71$	1.00000	0.118678
$72$	3.64596	0.429681
$73$	−1.01223	−0.118473	−0.0592366	−	0.998244i	$-0.518867\pi$
$73$	−1.01223	−0.118473	−0.0592366	+	0.998244i	$0.518867\pi$
$74$	7.65784	0.890206
$75$	−3.81149	−0.440113
$76$	−17.4261	−1.99892
$77$	−5.13932	−0.585680
$78$	8.44909	0.956671
$79$	−9.52480	−1.07162	−0.535812	−	0.844337i	$-0.679994\pi$
$79$	−9.52480	−1.07162	−0.535812	+	0.844337i	$0.679994\pi$
$80$	−22.6931	−2.53716
$81$	−7.11538	−0.790598
$82$	1.80302	0.199110
$83$	8.94937	0.982321	0.491160	−	0.871069i	$-0.336573\pi$
$83$	8.94937	0.982321	0.491160	+	0.871069i	$0.336573\pi$
$84$	12.9637	1.41445
$85$	−5.43106	−0.589081
$86$	−4.28138	−0.461673
$87$	4.97209	0.533064
$88$	−19.7933	−2.10998
$89$	0.131878	0.0139791	0.00698954	−	0.999976i	$-0.497775\pi$
$89$	0.131878	0.0139791	0.00698954	+	0.999976i	$0.497775\pi$
$90$	−3.74858	−0.395135
$91$	−3.70248	−0.388126
$92$	−15.5951	−1.62590
$93$	13.6089	1.41118
$94$	14.1301	1.45740
$95$	10.2116	1.04768
$96$	12.2553	1.25080
$97$	−18.9254	−1.92158	−0.960792	−	0.277269i	$-0.910571\pi$
$97$	−18.9254	−1.92158	−0.960792	+	0.277269i	$0.910571\pi$
$98$	9.92830	1.00291
$99$	−1.54445	−0.155223
$100$	11.2864	1.12864
$101$	2.63355	0.262048	0.131024	−	0.991379i	$-0.458174\pi$
$101$	2.63355	0.262048	0.131024	+	0.991379i	$0.458174\pi$
$102$	8.07170	0.799217
$103$	−12.7801	−1.25926	−0.629629	−	0.776896i	$-0.716793\pi$
$103$	−12.7801	−1.25926	−0.629629	+	0.776896i	$0.716793\pi$
$104$	−14.2596	−1.39827
$105$	−7.59661	−0.741353
$106$	−30.0664	−2.92030
$107$	1.97512	0.190942	0.0954709	−	0.995432i	$-0.469564\pi$
$107$	1.97512	0.190942	0.0954709	+	0.995432i	$0.469564\pi$
$108$	25.8079	2.48336
$109$	−7.54796	−0.722963	−0.361482	−	0.932379i	$-0.617729\pi$
$109$	−7.54796	−0.722963	−0.361482	+	0.932379i	$0.617729\pi$
$110$	20.3504	1.94034
$111$	4.66366	0.442655
$112$	−14.7794	−1.39652
$113$	−1.00000	−0.0940721
$113$	−1.00000	−0.0940721
$114$	−15.1765	−1.42141
$115$	9.13859	0.852178
$116$	−14.7231	−1.36700
$117$	−1.11266	−0.102865
$118$	−20.0877	−1.84922
$119$	−3.53711	−0.324246
$120$	−29.2572	−2.67081
$121$	−2.61545	−0.237768
$122$	−35.8138	−3.24243
$123$	1.09805	0.0990076
$124$	−40.2979	−3.61886
$125$	7.01241	0.627209
$126$	−2.44135	−0.217493
$127$	−11.3502	−1.00717	−0.503584	−	0.863946i	$-0.667986\pi$
$127$	−11.3502	−1.00717	−0.503584	+	0.863946i	$0.667986\pi$
$128$	6.65928	0.588603
$129$	−2.60738	−0.229567
$130$	14.6609	1.28585
$131$	−19.2771	−1.68424	−0.842122	−	0.539287i	$-0.818694\pi$
$131$	−19.2771	−1.68424	−0.842122	+	0.539287i	$0.818694\pi$
$132$	−21.1496	−1.84084
$133$	6.65052	0.576674
$134$	−22.9838	−1.98550
$135$	−15.1232	−1.30160
$136$	−13.6226	−1.16813
$137$	17.6736	1.50995	0.754977	−	0.655751i	$-0.227648\pi$
$137$	17.6736	1.50995	0.754977	+	0.655751i	$0.227648\pi$
$138$	−13.5819	−1.15617
$139$	13.7259	1.16422	0.582110	−	0.813110i	$-0.302227\pi$
$139$	13.7259	1.16422	0.582110	+	0.813110i	$0.302227\pi$
$140$	22.4946	1.90114
$141$	8.60527	0.724694
$142$	−2.57888	−0.216415
$143$	6.04042	0.505125
$144$	−4.44145	−0.370120
$145$	8.62759	0.716482
$146$	2.61043	0.216041
$147$	6.04637	0.498697
$148$	−13.8098	−1.13516
$149$	−12.9098	−1.05761	−0.528804	−	0.848744i	$-0.677359\pi$
$149$	−12.9098	−1.05761	−0.528804	+	0.848744i	$0.677359\pi$
$150$	9.82937	0.802565
$151$	−12.4053	−1.00953	−0.504764	−	0.863257i	$-0.668421\pi$
$151$	−12.4053	−1.00953	−0.504764	+	0.863257i	$0.668421\pi$
$152$	25.6135	2.07753
$153$	−1.06296	−0.0859350
$154$	13.2537	1.06801
$155$	23.6142	1.89674
$156$	−15.2367	−1.21991
$157$	−4.44372	−0.354647	−0.177324	−	0.984153i	$-0.556744\pi$
$157$	−4.44372	−0.354647	−0.177324	+	0.984153i	$0.556744\pi$
$158$	24.5633	1.95415
$159$	−18.3106	−1.45212
$160$	21.2654	1.68118
$161$	5.95172	0.469062
$162$	18.3497	1.44169
$163$	10.5719	0.828053	0.414026	−	0.910265i	$-0.364122\pi$
$163$	10.5719	0.828053	0.414026	+	0.910265i	$0.364122\pi$
$164$	−3.25148	−0.253898
$165$	12.3935	0.964832
$166$	−23.0793	−1.79130
$167$	−16.0884	−1.24496	−0.622479	−	0.782637i	$-0.713874\pi$
$167$	−16.0884	−1.24496	−0.622479	+	0.782637i	$0.713874\pi$
$168$	−19.0544	−1.47008
$169$	−8.64835	−0.665257
$170$	14.0061	1.07422
$171$	1.99859	0.152836
$172$	7.72082	0.588707
$173$	4.71930	0.358802	0.179401	−	0.983776i	$-0.442584\pi$
$173$	4.71930	0.358802	0.179401	+	0.983776i	$0.442584\pi$
$174$	−12.8224	−0.972065
$175$	−4.30734	−0.325604
$176$	24.1119	1.81750
$177$	−12.2335	−0.919525
$178$	−0.340098	−0.0254915
$179$	20.4645	1.52959	0.764796	−	0.644273i	$-0.222840\pi$
$179$	20.4645	1.52959	0.764796	+	0.644273i	$0.222840\pi$
$180$	6.76000	0.503861
$181$	−19.1155	−1.42084	−0.710422	−	0.703776i	$-0.751496\pi$
$181$	−19.1155	−1.42084	−0.710422	+	0.703776i	$0.751496\pi$
$182$	9.54826	0.707764
$183$	−21.8107	−1.61230
$184$	22.9222	1.68985
$185$	8.09241	0.594966
$186$	−35.0957	−2.57334
$187$	5.77062	0.421989
$188$	−25.4814	−1.85842
$189$	−9.84934	−0.716434
$190$	−26.3344	−1.91050
$191$	−23.2767	−1.68424	−0.842121	−	0.539289i	$-0.818693\pi$
$191$	−23.2767	−1.68424	−0.842121	+	0.539289i	$0.818693\pi$
$192$	−5.44881	−0.393234
$193$	6.10364	0.439349	0.219675	−	0.975573i	$-0.429500\pi$
$193$	6.10364	0.439349	0.219675	+	0.975573i	$0.429500\pi$
$194$	48.8064	3.50409
$195$	8.92855	0.639387
$196$	−17.9042	−1.27887
$197$	−8.76024	−0.624142	−0.312071	−	0.950059i	$-0.601023\pi$
$197$	−8.76024	−0.624142	−0.312071	+	0.950059i	$0.601023\pi$
$198$	3.98295	0.283056
$199$	−22.9980	−1.63028	−0.815141	−	0.579263i	$-0.803341\pi$
$199$	−22.9980	−1.63028	−0.815141	+	0.579263i	$0.803341\pi$
$200$	−16.5891	−1.17302
$201$	−13.9972	−0.987288
$202$	−6.79160	−0.477856
$203$	5.61892	0.394371
$204$	−14.5561	−1.01913
$205$	1.90534	0.133075
$206$	32.9583	2.29631
$207$	1.78859	0.124316
$208$	17.3707	1.20444
$209$	−10.8500	−0.750510
$210$	19.5907	1.35189
$211$	−6.32343	−0.435323	−0.217661	−	0.976024i	$-0.569843\pi$
$211$	−6.32343	−0.435323	−0.217661	+	0.976024i	$0.569843\pi$
$212$	54.2202	3.72386
$213$	−1.57055	−0.107612
$214$	−5.09359	−0.348191
$215$	−4.52434	−0.308557
$216$	−37.9333	−2.58103
$217$	15.3793	1.04402
$218$	19.4653	1.31836
$219$	1.58976	0.107426
$220$	−36.6989	−2.47424
$221$	4.15728	0.279649
$222$	−12.0270	−0.807201
$223$	3.46349	0.231932	0.115966	−	0.993253i	$-0.463004\pi$
$223$	3.46349	0.231932	0.115966	+	0.993253i	$0.463004\pi$
$224$	13.8496	0.925365
$225$	−1.29442	−0.0862949
$226$	2.57888	0.171545
$227$	−12.7062	−0.843339	−0.421670	−	0.906750i	$-0.638556\pi$
$227$	−12.7062	−0.843339	−0.421670	+	0.906750i	$0.638556\pi$
$228$	27.3686	1.81253
$229$	19.4504	1.28532	0.642660	−	0.766151i	$-0.277831\pi$
$229$	19.4504	1.28532	0.642660	+	0.766151i	$0.277831\pi$
$230$	−23.5673	−1.55398
$231$	8.07155	0.531069
$232$	21.6404	1.42077
$233$	−7.85862	−0.514836	−0.257418	−	0.966300i	$-0.582872\pi$
$233$	−7.85862	−0.514836	−0.257418	+	0.966300i	$0.582872\pi$
$234$	2.86940	0.187579
$235$	14.9319	0.974050
$236$	36.2251	2.35805
$237$	14.9592	0.971702
$238$	9.12177	0.591277
$239$	−20.4216	−1.32096	−0.660482	−	0.750842i	$-0.729648\pi$
$239$	−20.4216	−1.32096	−0.660482	+	0.750842i	$0.729648\pi$
$240$	35.6406	2.30059
$241$	9.52294	0.613426	0.306713	−	0.951802i	$-0.400771\pi$
$241$	9.52294	0.613426	0.306713	+	0.951802i	$0.400771\pi$
$242$	6.74494	0.433581
$243$	−5.47296	−0.351091
$244$	64.5848	4.13462
$245$	10.4917	0.670290
$246$	−2.83173	−0.180545
$247$	−7.81659	−0.497358
$248$	59.2311	3.76118
$249$	−14.0554	−0.890726
$250$	−18.0842	−1.14374
$251$	−8.86219	−0.559376	−0.279688	−	0.960091i	$-0.590231\pi$
$251$	−8.86219	−0.559376	−0.279688	+	0.960091i	$0.590231\pi$
$252$	4.40261	0.277338
$253$	−9.70995	−0.610459
$254$	29.2708	1.83662
$255$	8.52975	0.534153
$256$	−24.1122	−1.50701
$257$	12.3437	0.769977	0.384989	−	0.922921i	$-0.374205\pi$
$257$	12.3437	0.769977	0.384989	+	0.922921i	$0.374205\pi$
$258$	6.72412	0.418625
$259$	5.27037	0.327485
$260$	−26.4387	−1.63966
$261$	1.68858	0.104520
$262$	49.7132	3.07129
$263$	−16.2657	−1.00298	−0.501492	−	0.865162i	$-0.667215\pi$
$263$	−16.2657	−1.00298	−0.501492	+	0.865162i	$0.667215\pi$
$264$	31.0864	1.91324
$265$	−31.7726	−1.95177
$266$	−17.1509	−1.05159
$267$	−0.207121	−0.0126756
$268$	41.4478	2.53183
$269$	−27.9639	−1.70499	−0.852496	−	0.522734i	$-0.824912\pi$
$269$	−27.9639	−1.70499	−0.852496	+	0.522734i	$0.824912\pi$
$270$	39.0009	2.37352
$271$	22.8012	1.38507	0.692537	−	0.721382i	$-0.256493\pi$
$271$	22.8012	1.38507	0.692537	+	0.721382i	$0.256493\pi$
$272$	16.5948	1.00621
$273$	5.81493	0.351935
$274$	−45.5780	−2.75347
$275$	7.02721	0.423757
$276$	24.4929	1.47430
$277$	−29.1633	−1.75225	−0.876125	−	0.482083i	$-0.839880\pi$
$277$	−29.1633	−1.75225	−0.876125	+	0.482083i	$0.839880\pi$
$278$	−35.3976	−2.12300
$279$	4.62173	0.276696
$280$	−33.0634	−1.97591
$281$	15.3048	0.913011	0.456505	−	0.889721i	$-0.349101\pi$
$281$	15.3048	0.913011	0.456505	+	0.889721i	$0.349101\pi$
$282$	−22.1919	−1.32151
$283$	−28.2265	−1.67789	−0.838945	−	0.544216i	$-0.816827\pi$
$283$	−28.2265	−1.67789	−0.838945	+	0.544216i	$0.816827\pi$
$284$	4.65062	0.275964
$285$	−16.0378	−0.949995
$286$	−15.5775	−0.921118
$287$	1.24090	0.0732478
$288$	4.16203	0.245250
$289$	−13.0284	−0.766377
$290$	−22.2495	−1.30654
$291$	29.7233	1.74241
$292$	−4.70752	−0.275487
$293$	12.6716	0.740285	0.370142	−	0.928975i	$-0.379309\pi$
$293$	12.6716	0.740285	0.370142	+	0.928975i	$0.379309\pi$
$294$	−15.5929	−0.909395
$295$	−21.2276	−1.23592
$296$	20.2981	1.17980
$297$	16.0687	0.932401
$298$	33.2927	1.92859
$299$	−6.99527	−0.404547
$300$	−17.7258	−1.02340
$301$	−2.94658	−0.169838
$302$	31.9918	1.84092
$303$	−4.13612	−0.237614
$304$	−31.2019	−1.78955
$305$	−37.8461	−2.16706
$306$	2.74124	0.156706
$307$	22.6632	1.29346	0.646729	−	0.762720i	$-0.276136\pi$
$307$	22.6632	1.29346	0.646729	+	0.762720i	$0.276136\pi$
$308$	−23.9010	−1.36189
$309$	20.0717	1.14184
$310$	−60.8982	−3.45879
$311$	−5.44478	−0.308745	−0.154373	−	0.988013i	$-0.549336\pi$
$311$	−5.44478	−0.308745	−0.154373	+	0.988013i	$0.549336\pi$
$312$	22.3953	1.26789
$313$	9.14422	0.516862	0.258431	−	0.966030i	$-0.416795\pi$
$313$	9.14422	0.516862	0.258431	+	0.966030i	$0.416795\pi$
$314$	11.4598	0.646715
$315$	−2.57989	−0.145360
$316$	−44.2962	−2.49186
$317$	−8.42831	−0.473381	−0.236690	−	0.971585i	$-0.576063\pi$
$317$	−8.42831	−0.473381	−0.236690	+	0.971585i	$0.576063\pi$
$318$	47.2207	2.64801
$319$	−9.16700	−0.513253
$320$	−9.45480	−0.528539
$321$	−3.10202	−0.173138
$322$	−15.3488	−0.855354
$323$	−7.46745	−0.415500
$324$	−33.0910	−1.83839
$325$	5.06256	0.280820
$326$	−27.2636	−1.50999
$327$	11.8544	0.655552
$328$	4.77913	0.263883
$329$	9.72475	0.536143
$330$	−31.9613	−1.75941
$331$	15.5822	0.856476	0.428238	−	0.903666i	$-0.359134\pi$
$331$	15.5822	0.856476	0.428238	+	0.903666i	$0.359134\pi$
$332$	41.6201	2.28420
$333$	1.58383	0.0867934
$334$	41.4900	2.27023
$335$	−24.2881	−1.32700
$336$	23.2118	1.26631
$337$	−7.86298	−0.428324	−0.214162	−	0.976798i	$-0.568702\pi$
$337$	−7.86298	−0.428324	−0.214162	+	0.976798i	$0.568702\pi$
$338$	22.3030	1.21313
$339$	1.57055	0.0853005
$340$	−25.2578	−1.36980
$341$	−25.0906	−1.35873
$342$	−5.15412	−0.278703
$343$	19.2570	1.03978
$344$	−11.3483	−0.611861
$345$	−14.3526	−0.772719
$346$	−12.1705	−0.654291
$347$	23.6692	1.27063	0.635315	−	0.772253i	$-0.280870\pi$
$347$	23.6692	1.27063	0.635315	+	0.772253i	$0.280870\pi$
$348$	23.1233	1.23954
$349$	−2.96462	−0.158693	−0.0793463	−	0.996847i	$-0.525283\pi$
$349$	−2.96462	−0.158693	−0.0793463	+	0.996847i	$0.525283\pi$
$350$	11.1081	0.593753
$351$	11.5763	0.617895
$352$	−22.5949	−1.20431
$353$	17.2525	0.918258	0.459129	−	0.888370i	$-0.348162\pi$
$353$	17.2525	0.918258	0.459129	+	0.888370i	$0.348162\pi$
$354$	31.5487	1.67679
$355$	−2.72522	−0.144640
$356$	0.613316	0.0325057
$357$	5.55520	0.294012
$358$	−52.7756	−2.78928
$359$	−22.7866	−1.20263	−0.601316	−	0.799011i	$-0.705357\pi$
$359$	−22.7866	−1.20263	−0.601316	+	0.799011i	$0.705357\pi$
$360$	−9.93607	−0.523677
$361$	−4.95958	−0.261030
$362$	49.2966	2.59097
$363$	4.10770	0.215598
$364$	−17.2188	−0.902513
$365$	2.75857	0.144390
$366$	56.2473	2.94009
$367$	9.29939	0.485424	0.242712	−	0.970098i	$-0.421963\pi$
$367$	9.29939	0.485424	0.242712	+	0.970098i	$0.421963\pi$
$368$	−27.9234	−1.45561
$369$	0.372909	0.0194129
$370$	−20.8693	−1.08495
$371$	−20.6926	−1.07431
$372$	63.2898	3.28142
$373$	25.2912	1.30953	0.654763	−	0.755834i	$-0.272768\pi$
$373$	25.2912	1.30953	0.654763	+	0.755834i	$0.272768\pi$
$374$	−14.8817	−0.769516
$375$	−11.0133	−0.568726
$376$	37.4534	1.93151
$377$	−6.60411	−0.340129
$378$	25.4003	1.30645
$379$	−6.20325	−0.318640	−0.159320	−	0.987227i	$-0.550930\pi$
$379$	−6.20325	−0.318640	−0.159320	+	0.987227i	$0.550930\pi$
$380$	47.4902	2.43619
$381$	17.8261	0.913257
$382$	60.0278	3.07129
$383$	21.4769	1.09742	0.548708	−	0.836014i	$-0.315120\pi$
$383$	21.4769	1.09742	0.548708	+	0.836014i	$0.315120\pi$
$384$	−10.4587	−0.533719
$385$	14.0058	0.713802
$386$	−15.7405	−0.801173
$387$	−0.885495	−0.0450122
$388$	−88.0150	−4.46828
$389$	22.9119	1.16168	0.580840	−	0.814018i	$-0.302724\pi$
$389$	22.9119	1.16168	0.580840	+	0.814018i	$0.302724\pi$
$390$	−23.0257	−1.16595
$391$	−6.68281	−0.337964
$392$	26.3162	1.32917
$393$	30.2756	1.52720
$394$	22.5916	1.13815
$395$	25.9572	1.30605
$396$	−7.18264	−0.360941
$397$	−25.2394	−1.26673	−0.633366	−	0.773853i	$-0.718327\pi$
$397$	−25.2394	−1.26673	−0.633366	+	0.773853i	$0.718327\pi$
$398$	59.3090	2.97289
$399$	−10.4450	−0.522903
$400$	20.2085	1.01042
$401$	−18.4144	−0.919569	−0.459785	−	0.888030i	$-0.652073\pi$
$401$	−18.4144	−0.919569	−0.459785	+	0.888030i	$0.652073\pi$
$402$	36.0972	1.80036
$403$	−18.0758	−0.900421
$404$	12.2476	0.609343
$405$	19.3910	0.963547
$406$	−14.4905	−0.719153
$407$	−8.59835	−0.426204
$408$	21.3950	1.05921
$409$	−2.62181	−0.129640	−0.0648201	−	0.997897i	$-0.520647\pi$
$409$	−2.62181	−0.129640	−0.0648201	+	0.997897i	$0.520647\pi$
$410$	−4.91364	−0.242667
$411$	−27.7572	−1.36916
$412$	−59.4353	−2.92816
$413$	−13.8250	−0.680282
$414$	−4.61256	−0.226695
$415$	−24.3890	−1.19721
$416$	−16.2779	−0.798090
$417$	−21.5573	−1.05566
$418$	27.9809	1.36859
$419$	13.8412	0.676186	0.338093	−	0.941113i	$-0.390218\pi$
$419$	13.8412	0.676186	0.338093	+	0.941113i	$0.390218\pi$
$420$	−35.3289	−1.72388
$421$	13.1685	0.641791	0.320896	−	0.947115i	$-0.396016\pi$
$421$	13.1685	0.641791	0.320896	+	0.947115i	$0.396016\pi$
$422$	16.3074	0.793830
$423$	2.92244	0.142094
$424$	−79.6946	−3.87031
$425$	4.83644	0.234602
$426$	4.05026	0.196236
$427$	−24.6482	−1.19281
$428$	9.18553	0.443999
$429$	−9.48677	−0.458026
$430$	11.6677	0.562668
$431$	5.56814	0.268208	0.134104	−	0.990967i	$-0.457184\pi$
$431$	5.56814	0.268208	0.134104	+	0.990967i	$0.457184\pi$
$432$	46.2096	2.22326
$433$	4.32065	0.207637	0.103819	−	0.994596i	$-0.466894\pi$
$433$	4.32065	0.207637	0.103819	+	0.994596i	$0.466894\pi$
$434$	−39.6614	−1.90381
$435$	−13.5501	−0.649675
$436$	−35.1027	−1.68111
$437$	12.5651	0.601072
$438$	−4.09981	−0.195897
$439$	−37.1098	−1.77115	−0.885576	−	0.464494i	$-0.846236\pi$
$439$	−37.1098	−1.77115	−0.885576	+	0.464494i	$0.846236\pi$
$440$	53.9413	2.57155
$441$	2.05342	0.0977817
$442$	−10.7211	−0.509952
$443$	−34.4299	−1.63582	−0.817908	−	0.575350i	$-0.804866\pi$
$443$	−34.4299	−1.63582	−0.817908	+	0.575350i	$0.804866\pi$
$444$	21.6889	1.02931
$445$	−0.359398	−0.0170371
$446$	−8.93192	−0.422938
$447$	20.2754	0.958993
$448$	−6.15766	−0.290922
$449$	29.3707	1.38609	0.693045	−	0.720895i	$-0.256269\pi$
$449$	29.3707	1.38609	0.693045	+	0.720895i	$0.256269\pi$
$450$	3.33816	0.157363
$451$	−2.02446	−0.0953281
$452$	−4.65062	−0.218747
$453$	19.4831	0.915397
$454$	32.7677	1.53787
$455$	10.0901	0.473031
$456$	−40.2273	−1.88381
$457$	−4.47634	−0.209394	−0.104697	−	0.994504i	$-0.533387\pi$
$457$	−4.47634	−0.209394	−0.104697	+	0.994504i	$0.533387\pi$
$458$	−50.1603	−2.34384
$459$	11.0592	0.516199
$460$	42.5002	1.98158
$461$	−17.4007	−0.810430	−0.405215	−	0.914221i	$-0.632803\pi$
$461$	−17.4007	−0.810430	−0.405215	+	0.914221i	$0.632803\pi$
$462$	−20.8156	−0.968428
$463$	−3.66424	−0.170292	−0.0851459	−	0.996368i	$-0.527136\pi$
$463$	−3.66424	−0.170292	−0.0851459	+	0.996368i	$0.527136\pi$
$464$	−26.3620	−1.22382
$465$	−37.0873	−1.71988
$466$	20.2665	0.938825
$467$	−15.3110	−0.708507	−0.354254	−	0.935149i	$-0.615265\pi$
$467$	−15.3110	−0.708507	−0.354254	+	0.935149i	$0.615265\pi$
$468$	−5.17454	−0.239193
$469$	−15.8182	−0.730415
$470$	−38.5076	−1.77622
$471$	6.97908	0.321579
$472$	−53.2448	−2.45079
$473$	4.80720	0.221035
$474$	−38.5779	−1.77194
$475$	−9.09354	−0.417240
$476$	−16.4497	−0.753973
$477$	−6.21847	−0.284724
$478$	52.6649	2.40884
$479$	5.24853	0.239811	0.119906	−	0.992785i	$-0.461741\pi$
$479$	5.24853	0.239811	0.119906	+	0.992785i	$0.461741\pi$
$480$	−33.3984	−1.52442
$481$	−6.19445	−0.282442
$482$	−24.5585	−1.11861
$483$	−9.34748	−0.425325
$484$	−12.1635	−0.552886
$485$	51.5760	2.34195
$486$	14.1141	0.640229
$487$	10.6175	0.481123	0.240561	−	0.970634i	$-0.422668\pi$
$487$	10.6175	0.481123	0.240561	+	0.970634i	$0.422668\pi$
$488$	−94.9288	−4.29723
$489$	−16.6036	−0.750843
$490$	−27.0568	−1.22230
$491$	−39.4942	−1.78235	−0.891173	−	0.453663i	$-0.850117\pi$
$491$	−39.4942	−1.78235	−0.891173	+	0.453663i	$0.850117\pi$
$492$	5.10660	0.230223
$493$	−6.30913	−0.284149
$494$	20.1580	0.906953
$495$	4.20897	0.189179
$496$	−72.1543	−3.23982
$497$	−1.77487	−0.0796137
$498$	36.2472	1.62428
$499$	−29.3989	−1.31607	−0.658037	−	0.752985i	$-0.728613\pi$
$499$	−29.3989	−1.31607	−0.658037	+	0.752985i	$0.728613\pi$
$500$	32.6121	1.45846
$501$	25.2676	1.12887
$502$	22.8545	1.02005
$503$	25.4323	1.13397	0.566986	−	0.823728i	$-0.308109\pi$
$503$	25.4323	1.13397	0.566986	+	0.823728i	$0.308109\pi$
$504$	−6.47110	−0.288246
$505$	−7.17701	−0.319373
$506$	25.0408	1.11320
$507$	13.5827	0.603227
$508$	−52.7856	−2.34198
$509$	6.19617	0.274641	0.137320	−	0.990527i	$-0.456151\pi$
$509$	6.19617	0.274641	0.137320	+	0.990527i	$0.456151\pi$
$510$	−21.9972	−0.974052
$511$	1.79658	0.0794761
$512$	48.8639	2.15950
$513$	−20.7937	−0.918064
$514$	−31.8329	−1.40409
$515$	34.8285	1.53473
$516$	−12.1259	−0.533814
$517$	−15.8655	−0.697762
$518$	−13.5917	−0.597183
$519$	−7.41190	−0.325346
$520$	38.8605	1.70415
$521$	−40.3806	−1.76910	−0.884552	−	0.466441i	$-0.845536\pi$
$521$	−40.3806	−1.76910	−0.884552	+	0.466441i	$0.845536\pi$
$522$	−4.35464	−0.190597
$523$	−3.63957	−0.159147	−0.0795737	−	0.996829i	$-0.525356\pi$
$523$	−3.63957	−0.159147	−0.0795737	+	0.996829i	$0.525356\pi$
$524$	−89.6503	−3.91639
$525$	6.76488	0.295244
$526$	41.9472	1.82899
$527$	−17.2685	−0.752226
$528$	−37.8689	−1.64803
$529$	−11.7551	−0.511093
$530$	81.9376	3.55914
$531$	−4.15463	−0.180295
$532$	30.9291	1.34095
$533$	−1.45847	−0.0631732
$534$	0.534141	0.0231146
$535$	−5.38264	−0.232712
$536$	−60.9214	−2.63140
$537$	−32.1406	−1.38697
$538$	72.1157	3.10913
$539$	−11.1477	−0.480163
$540$	−70.3323	−3.02662
$541$	−7.30402	−0.314024	−0.157012	−	0.987597i	$-0.550186\pi$
$541$	−7.30402	−0.314024	−0.157012	+	0.987597i	$0.550186\pi$
$542$	−58.8016	−2.52574
$543$	30.0218	1.28836
$544$	−15.5508	−0.666737
$545$	20.5699	0.881117
$546$	−14.9960	−0.641770
$547$	−3.97025	−0.169756	−0.0848779	−	0.996391i	$-0.527050\pi$
$547$	−3.97025	−0.169756	−0.0848779	+	0.996391i	$0.527050\pi$
$548$	82.1931	3.51111
$549$	−7.40717	−0.316130
$550$	−18.1223	−0.772739
$551$	11.8625	0.505361
$552$	−36.0004	−1.53228
$553$	16.9052	0.718884
$554$	75.2086	3.19531
$555$	−12.7095	−0.539489
$556$	63.8342	2.70717
$557$	12.2737	0.520052	0.260026	−	0.965602i	$-0.416269\pi$
$557$	12.2737	0.520052	0.260026	+	0.965602i	$0.416269\pi$
$558$	−11.9189	−0.504567
$559$	3.46322	0.146478
$560$	40.2772	1.70202
$561$	−9.06303	−0.382642
$562$	−39.4694	−1.66491
$563$	12.8156	0.540111	0.270056	−	0.962845i	$-0.412958\pi$
$563$	12.8156	0.540111	0.270056	+	0.962845i	$0.412958\pi$
$564$	40.0198	1.68514
$565$	2.72522	0.114651
$566$	72.7927	3.05971
$567$	12.6289	0.530362
$568$	−6.83564	−0.286817
$569$	11.1660	0.468103	0.234052	−	0.972224i	$-0.424802\pi$
$569$	11.1660	0.468103	0.234052	+	0.972224i	$0.424802\pi$
$570$	41.3595	1.73236
$571$	16.5904	0.694286	0.347143	−	0.937812i	$-0.387152\pi$
$571$	16.5904	0.694286	0.347143	+	0.937812i	$0.387152\pi$
$572$	28.0917	1.17457
$573$	36.5572	1.52720
$574$	−3.20012	−0.133570
$575$	−8.13805	−0.339380
$576$	−1.85047	−0.0771031
$577$	23.8612	0.993355	0.496678	−	0.867935i	$-0.334553\pi$
$577$	23.8612	0.993355	0.496678	+	0.867935i	$0.334553\pi$
$578$	33.5987	1.39752
$579$	−9.58606	−0.398383
$580$	40.1237	1.66604
$581$	−15.8839	−0.658977
$582$	−76.6528	−3.17736
$583$	33.7590	1.39816
$584$	6.91927	0.286321
$585$	3.03224	0.125368
$586$	−32.6786	−1.34994
$587$	8.15335	0.336525	0.168262	−	0.985742i	$-0.446184\pi$
$587$	8.15335	0.336525	0.168262	+	0.985742i	$0.446184\pi$
$588$	28.1194	1.15962
$589$	32.4684	1.33784
$590$	54.7434	2.25375
$591$	13.7584	0.565945
$592$	−24.7267	−1.01626
$593$	12.9235	0.530704	0.265352	−	0.964152i	$-0.414512\pi$
$593$	12.9235	0.530704	0.265352	+	0.964152i	$0.414512\pi$
$594$	−41.4393	−1.70027
$595$	9.63941	0.395177
$596$	−60.0384	−2.45927
$597$	36.1194	1.47827
$598$	18.0400	0.737708
$599$	27.8357	1.13734	0.568668	−	0.822567i	$-0.307459\pi$
$599$	27.8357	1.13734	0.568668	+	0.822567i	$0.307459\pi$
$600$	26.0540	1.06365
$601$	−31.7759	−1.29617	−0.648083	−	0.761570i	$-0.724429\pi$
$601$	−31.7759	−1.29617	−0.648083	+	0.761570i	$0.724429\pi$
$602$	7.59888	0.309707
$603$	−4.75361	−0.193582
$604$	−57.6924	−2.34747
$605$	7.12770	0.289782
$606$	10.6665	0.433299
$607$	40.1633	1.63018	0.815090	−	0.579335i	$-0.196688\pi$
$607$	40.1633	1.63018	0.815090	+	0.579335i	$0.196688\pi$
$608$	29.2389	1.18580
$609$	−8.82479	−0.357599
$610$	97.6006	3.95173
$611$	−11.4298	−0.462402
$612$	−4.94341	−0.199826
$613$	−0.879916	−0.0355395	−0.0177697	−	0.999842i	$-0.505657\pi$
$613$	−0.879916	−0.0355395	−0.0177697	+	0.999842i	$0.505657\pi$
$614$	−58.4458	−2.35868
$615$	−2.99243	−0.120666
$616$	35.1305	1.41545
$617$	−6.62031	−0.266524	−0.133262	−	0.991081i	$-0.542545\pi$
$617$	−6.62031	−0.266524	−0.133262	+	0.991081i	$0.542545\pi$
$618$	−51.7625	−2.08220
$619$	−25.4522	−1.02301	−0.511506	−	0.859280i	$-0.670912\pi$
$619$	−25.4522	−1.02301	−0.511506	+	0.859280i	$0.670912\pi$
$620$	109.821	4.41051
$621$	−18.6088	−0.746745
$622$	14.0414	0.563011
$623$	−0.234067	−0.00937768
$624$	−27.2816	−1.09214
$625$	−31.2446	−1.24979
$626$	−23.5819	−0.942520
$627$	17.0405	0.680531
$628$	−20.6661	−0.824665
$629$	−5.91777	−0.235957
$630$	6.65323	0.265071
$631$	47.4670	1.88963	0.944816	−	0.327601i	$-0.106240\pi$
$631$	47.4670	1.88963	0.944816	+	0.327601i	$0.106240\pi$
$632$	65.1081	2.58986
$633$	9.93125	0.394732
$634$	21.7356	0.863231
$635$	30.9319	1.22749
$636$	−85.1555	−3.37663
$637$	−8.03102	−0.318201
$638$	23.6406	0.935940
$639$	−0.533376	−0.0211000
$640$	−18.1480	−0.717364
$641$	−12.5418	−0.495372	−0.247686	−	0.968840i	$-0.579670\pi$
$641$	−12.5418	−0.495372	−0.247686	+	0.968840i	$0.579670\pi$
$642$	7.99974	0.315724
$643$	−6.83127	−0.269399	−0.134699	−	0.990886i	$-0.543007\pi$
$643$	−6.83127	−0.269399	−0.134699	+	0.990886i	$0.543007\pi$
$644$	27.6792	1.09071
$645$	7.10569	0.279786
$646$	19.2577	0.757683
$647$	1.86779	0.0734306	0.0367153	−	0.999326i	$-0.488311\pi$
$647$	1.86779	0.0734306	0.0367153	+	0.999326i	$0.488311\pi$
$648$	48.6382	1.91069
$649$	22.5548	0.885352
$650$	−13.0557	−0.512088
$651$	−24.1540	−0.946668
$652$	49.1658	1.92548
$653$	−0.147276	−0.00576337	−0.00288169	−	0.999996i	$-0.500917\pi$
$653$	−0.147276	−0.00576337	−0.00288169	+	0.999996i	$0.500917\pi$
$654$	−30.5712	−1.19543
$655$	52.5343	2.05269
$656$	−5.82184	−0.227305
$657$	0.539902	0.0210636
$658$	−25.0790	−0.977680
$659$	0.343073	0.0133642	0.00668212	−	0.999978i	$-0.497873\pi$
$659$	0.343073	0.0133642	0.00668212	+	0.999978i	$0.497873\pi$
$660$	57.6374	2.24353
$661$	−27.8667	−1.08389	−0.541944	−	0.840415i	$-0.682311\pi$
$661$	−27.8667	−1.08389	−0.541944	+	0.840415i	$0.682311\pi$
$662$	−40.1847	−1.56182
$663$	−6.52921	−0.253574
$664$	−61.1746	−2.37404
$665$	−18.1242	−0.702825
$666$	−4.08451	−0.158272
$667$	10.6161	0.411056
$668$	−74.8210	−2.89491
$669$	−5.43957	−0.210306
$670$	62.6360	2.41984
$671$	40.2123	1.55238
$672$	−21.7515	−0.839081
$673$	−47.7617	−1.84108	−0.920539	−	0.390651i	$-0.872250\pi$
$673$	−47.7617	−1.84108	−0.920539	+	0.390651i	$0.872250\pi$
$674$	20.2777	0.781067
$675$	13.4674	0.518361
$676$	−40.2202	−1.54693
$677$	5.60139	0.215279	0.107639	−	0.994190i	$-0.465671\pi$
$677$	5.60139	0.215279	0.107639	+	0.994190i	$0.465671\pi$
$678$	−4.05026	−0.155549
$679$	33.5901	1.28907
$680$	37.1248	1.42367
$681$	19.9557	0.764704
$682$	64.7056	2.47771
$683$	43.3178	1.65751	0.828755	−	0.559611i	$-0.189049\pi$
$683$	43.3178	1.65751	0.828755	+	0.559611i	$0.189049\pi$
$684$	9.29468	0.355391
$685$	−48.1644	−1.84027
$686$	−49.6616	−1.89609
$687$	−30.5479	−1.16547
$688$	13.8243	0.527047
$689$	24.3208	0.926547
$690$	37.0137	1.40909
$691$	37.3362	1.42034	0.710168	−	0.704032i	$-0.248619\pi$
$691$	37.3362	1.42034	0.710168	+	0.704032i	$0.248619\pi$
$692$	21.9477	0.834326
$693$	2.74119	0.104129
$694$	−61.0401	−2.31705
$695$	−37.4063	−1.41890
$696$	−33.9874	−1.28829
$697$	−1.39332	−0.0527759
$698$	7.64541	0.289383
$699$	12.3424	0.466831
$700$	−20.0318	−0.757131
$701$	4.28586	0.161875	0.0809374	−	0.996719i	$-0.474209\pi$
$701$	4.28586	0.161875	0.0809374	+	0.996719i	$0.474209\pi$
$702$	−29.8538	−1.12676
$703$	11.1267	0.419651
$704$	10.0459	0.378620
$705$	−23.4513	−0.883226
$706$	−44.4921	−1.67448
$707$	−4.67420	−0.175791
$708$	−56.8933	−2.13818
$709$	20.9812	0.787964	0.393982	−	0.919118i	$-0.371097\pi$
$709$	20.9812	0.787964	0.393982	+	0.919118i	$0.371097\pi$
$710$	7.02803	0.263757
$711$	5.08030	0.190526
$712$	−0.901473	−0.0337841
$713$	29.0568	1.08819
$714$	−14.3262	−0.536144
$715$	−16.4615	−0.615625
$716$	95.1728	3.55678
$717$	32.0732	1.19779
$718$	58.7640	2.19305
$719$	45.7127	1.70479	0.852397	−	0.522894i	$-0.175148\pi$
$719$	45.7127	1.70479	0.852397	+	0.522894i	$0.175148\pi$
$720$	12.1039	0.451087
$721$	22.6829	0.844756
$722$	12.7902	0.476000
$723$	−14.9562	−0.556229
$724$	−88.8990	−3.30391
$725$	−7.68299	−0.285339
$726$	−10.5933	−0.393153
$727$	23.1162	0.857331	0.428665	−	0.903463i	$-0.358984\pi$
$727$	23.1162	0.857331	0.428665	+	0.903463i	$0.358984\pi$
$728$	25.3088	0.938007
$729$	29.9417	1.10895
$730$	−7.11402	−0.263302
$731$	3.30853	0.122370
$732$	−101.434	−3.74909
$733$	−33.1291	−1.22365	−0.611826	−	0.790992i	$-0.709565\pi$
$733$	−33.1291	−1.22365	−0.611826	+	0.790992i	$0.709565\pi$
$734$	−23.9820	−0.885192
$735$	−16.4777	−0.607790
$736$	26.1667	0.964516
$737$	25.8066	0.950597
$738$	−0.961688	−0.0354002
$739$	24.1934	0.889970	0.444985	−	0.895538i	$-0.353209\pi$
$739$	24.1934	0.889970	0.444985	+	0.895538i	$0.353209\pi$
$740$	37.6347	1.38348
$741$	12.2763	0.450982
$742$	53.3638	1.95905
$743$	−23.6557	−0.867842	−0.433921	−	0.900951i	$-0.642870\pi$
$743$	−23.6557	−0.867842	−0.433921	+	0.900951i	$0.642870\pi$
$744$	−93.0254	−3.41048
$745$	35.1820	1.28897
$746$	−65.2228	−2.38798
$747$	−4.77338	−0.174649
$748$	26.8370	0.981256
$749$	−3.50557	−0.128091
$750$	28.4021	1.03710
$751$	−43.7971	−1.59818	−0.799089	−	0.601212i	$-0.794685\pi$
$751$	−43.7971	−1.59818	−0.799089	+	0.601212i	$0.794685\pi$
$752$	−45.6251	−1.66378
$753$	13.9185	0.507218
$754$	17.0312	0.620240
$755$	33.8072	1.23037
$756$	−45.8056	−1.66593
$757$	−4.81085	−0.174853	−0.0874266	−	0.996171i	$-0.527864\pi$
$757$	−4.81085	−0.174853	−0.0874266	+	0.996171i	$0.527864\pi$
$758$	15.9974	0.581053
$759$	15.2499	0.553538
$760$	−69.8026	−2.53201
$761$	26.9913	0.978434	0.489217	−	0.872162i	$-0.337283\pi$
$761$	26.9913	0.978434	0.489217	+	0.872162i	$0.337283\pi$
$762$	−45.9713	−1.66536
$763$	13.3966	0.484990
$764$	−108.251	−3.91639
$765$	2.89680	0.104734
$766$	−55.3862	−2.00119
$767$	16.2490	0.586716
$768$	37.8694	1.36649
$769$	48.7723	1.75877	0.879387	−	0.476107i	$-0.157953\pi$
$769$	48.7723	1.75877	0.879387	+	0.476107i	$0.157953\pi$
$770$	−36.1193	−1.30165
$771$	−19.3864	−0.698182
$772$	28.3857	1.02162
$773$	37.8039	1.35971	0.679855	−	0.733346i	$-0.262042\pi$
$773$	37.8039	1.35971	0.679855	+	0.733346i	$0.262042\pi$
$774$	2.28358	0.0820818
$775$	−21.0288	−0.755376
$776$	129.367	4.64401
$777$	−8.27737	−0.296949
$778$	−59.0871	−2.11837
$779$	2.61975	0.0938622
$780$	41.5233	1.48677
$781$	2.89561	0.103613
$782$	17.2342	0.616293
$783$	−17.5683	−0.627838
$784$	−32.0579	−1.14492
$785$	12.1101	0.432229
$786$	−78.0770	−2.78492
$787$	3.78266	0.134837	0.0674186	−	0.997725i	$-0.478524\pi$
$787$	3.78266	0.134837	0.0674186	+	0.997725i	$0.478524\pi$
$788$	−40.7406	−1.45132
$789$	25.5460	0.909463
$790$	−66.9405	−2.38164
$791$	1.77487	0.0631070
$792$	10.5573	0.375137
$793$	28.9698	1.02875
$794$	65.0895	2.30994
$795$	49.9004	1.76978
$796$	−106.955	−3.79091
$797$	42.6499	1.51074	0.755368	−	0.655301i	$-0.227458\pi$
$797$	42.6499	1.51074	0.755368	+	0.655301i	$0.227458\pi$
$798$	26.9363	0.953536
$799$	−10.9193	−0.386297
$800$	−18.9371	−0.669529
$801$	−0.0703407	−0.00248537
$802$	47.4884	1.67687
$803$	−2.93104	−0.103434
$804$	−65.0958	−2.29575
$805$	−16.2198	−0.571672
$806$	46.6154	1.64196
$807$	43.9187	1.54601
$808$	−18.0020	−0.633307
$809$	4.71332	0.165712	0.0828558	−	0.996562i	$-0.473596\pi$
$809$	4.71332	0.165712	0.0828558	+	0.996562i	$0.473596\pi$
$810$	−50.0071	−1.75707
$811$	8.18474	0.287405	0.143703	−	0.989621i	$-0.454099\pi$
$811$	8.18474	0.287405	0.143703	+	0.989621i	$0.454099\pi$
$812$	26.1315	0.917035
$813$	−35.8104	−1.25593
$814$	22.1741	0.777202
$815$	−28.8107	−1.00920
$816$	−26.0630	−0.912388
$817$	−6.22075	−0.217636
$818$	6.76133	0.236404
$819$	1.97481	0.0690056
$820$	8.86101	0.309440
$821$	−31.5707	−1.10182	−0.550912	−	0.834563i	$-0.685720\pi$
$821$	−31.5707	−1.10182	−0.550912	+	0.834563i	$0.685720\pi$
$822$	71.5825	2.49673
$823$	−1.23198	−0.0429443	−0.0214721	−	0.999769i	$-0.506835\pi$
$823$	−1.23198	−0.0429443	−0.0214721	+	0.999769i	$0.506835\pi$
$824$	87.3599	3.04333
$825$	−11.0366	−0.384244
$826$	35.6529	1.24052
$827$	−41.6568	−1.44855	−0.724275	−	0.689512i	$-0.757825\pi$
$827$	−41.6568	−1.44855	−0.724275	+	0.689512i	$0.757825\pi$
$828$	8.31805	0.289072
$829$	40.4241	1.40399	0.701994	−	0.712183i	$-0.252293\pi$
$829$	40.4241	1.40399	0.701994	+	0.712183i	$0.252293\pi$
$830$	62.8964	2.18317
$831$	45.8023	1.58887
$832$	7.23731	0.250908
$833$	−7.67231	−0.265830
$834$	55.5936	1.92505
$835$	43.8445	1.51730
$836$	−50.4593	−1.74517
$837$	−48.0853	−1.66207
$838$	−35.6947	−1.23305
$839$	−23.2547	−0.802843	−0.401422	−	0.915893i	$-0.631484\pi$
$839$	−23.2547	−0.802843	−0.401422	+	0.915893i	$0.631484\pi$
$840$	51.9276	1.79167
$841$	−18.9775	−0.654398
$842$	−33.9599	−1.17033
$843$	−24.0370	−0.827879
$844$	−29.4079	−1.01226
$845$	23.5687	0.810788
$846$	−7.53663	−0.259115
$847$	4.64208	0.159504
$848$	97.0825	3.33383
$849$	44.3311	1.52144
$850$	−12.4726	−0.427806
$851$	9.95755	0.341340
$852$	−7.30403	−0.250232
$853$	23.8281	0.815860	0.407930	−	0.913013i	$-0.366251\pi$
$853$	23.8281	0.815860	0.407930	+	0.913013i	$0.366251\pi$
$854$	63.5647	2.17514
$855$	−5.44660	−0.186270
$856$	−13.5012	−0.461461
$857$	−18.8442	−0.643706	−0.321853	−	0.946790i	$-0.604306\pi$
$857$	−18.8442	−0.643706	−0.321853	+	0.946790i	$0.604306\pi$
$858$	24.4652	0.835230
$859$	−3.62525	−0.123692	−0.0618460	−	0.998086i	$-0.519699\pi$
$859$	−3.62525	−0.123692	−0.0618460	+	0.998086i	$0.519699\pi$
$860$	−21.0410	−0.717492
$861$	−1.94889	−0.0664179
$862$	−14.3596	−0.489089
$863$	−12.4719	−0.424547	−0.212274	−	0.977210i	$-0.568087\pi$
$863$	−12.4719	−0.424547	−0.212274	+	0.977210i	$0.568087\pi$
$864$	−43.3025	−1.47318
$865$	−12.8612	−0.437293
$866$	−11.1424	−0.378635
$867$	20.4618	0.694918
$868$	71.5234	2.42766
$869$	−27.5801	−0.935590
$870$	34.9440	1.18471
$871$	18.5916	0.629954
$872$	51.5951	1.74723
$873$	10.0944	0.341642
$874$	−32.4040	−1.09608
$875$	−12.4461	−0.420755
$876$	7.39340	0.249800
$877$	−41.1420	−1.38927	−0.694634	−	0.719364i	$-0.744433\pi$
$877$	−41.1420	−1.38927	−0.694634	+	0.719364i	$0.744433\pi$
$878$	95.7016	3.22977
$879$	−19.9014	−0.671258
$880$	−65.7102	−2.21509
$881$	20.9478	0.705750	0.352875	−	0.935670i	$-0.385204\pi$
$881$	20.9478	0.705750	0.352875	+	0.935670i	$0.385204\pi$
$882$	−5.29551	−0.178309
$883$	31.9018	1.07358	0.536791	−	0.843715i	$-0.319636\pi$
$883$	31.9018	1.07358	0.536791	+	0.843715i	$0.319636\pi$
$884$	19.3339	0.650271
$885$	33.3390	1.12068
$886$	88.7907	2.98298
$887$	−27.4102	−0.920345	−0.460173	−	0.887829i	$-0.652212\pi$
$887$	−27.4102	−0.920345	−0.460173	+	0.887829i	$0.652212\pi$
$888$	−31.8791	−1.06979
$889$	20.1451	0.675646
$890$	0.926845	0.0310679
$891$	−20.6034	−0.690238
$892$	16.1074	0.539315
$893$	20.5307	0.687032
$894$	−52.2878	−1.74877
$895$	−55.7705	−1.86420
$896$	−11.8193	−0.394856
$897$	10.9864	0.366825
$898$	−75.7435	−2.52759
$899$	27.4321	0.914910
$900$	−6.01988	−0.200663
$901$	23.2344	0.774052
$902$	5.22084	0.173835
$903$	4.62775	0.154002
$904$	6.83564	0.227350
$905$	52.0941	1.73167
$906$	−50.2447	−1.66927
$907$	46.1381	1.53199	0.765995	−	0.642846i	$-0.222247\pi$
$907$	46.1381	1.53199	0.765995	+	0.642846i	$0.222247\pi$
$908$	−59.0917	−1.96103
$909$	−1.40467	−0.0465900
$910$	−26.0211	−0.862593
$911$	43.5579	1.44314	0.721569	−	0.692343i	$-0.243421\pi$
$911$	43.5579	1.44314	0.721569	+	0.692343i	$0.243421\pi$
$912$	49.0041	1.62269
$913$	25.9139	0.857624
$914$	11.5439	0.381840
$915$	59.4392	1.96500
$916$	90.4566	2.98877
$917$	34.2142	1.12985
$918$	−28.5203	−0.941312
$919$	35.3372	1.16567	0.582833	−	0.812592i	$-0.301944\pi$
$919$	35.3372	1.16567	0.582833	+	0.812592i	$0.301944\pi$
$920$	−62.4681	−2.05951
$921$	−35.5937	−1.17285
$922$	44.8743	1.47786
$923$	2.08606	0.0686636
$924$	37.5377	1.23490
$925$	−7.20640	−0.236945
$926$	9.44964	0.310534
$927$	6.81658	0.223886
$928$	24.7035	0.810932
$929$	26.2798	0.862212	0.431106	−	0.902301i	$-0.358123\pi$
$929$	26.2798	0.862212	0.431106	+	0.902301i	$0.358123\pi$
$930$	95.6436	3.13628
$931$	14.4256	0.472780
$932$	−36.5475	−1.19715
$933$	8.55130	0.279957
$934$	39.4852	1.29199
$935$	−15.7262	−0.514303
$936$	7.60571	0.248600
$937$	−5.90715	−0.192978	−0.0964890	−	0.995334i	$-0.530761\pi$
$937$	−5.90715	−0.192978	−0.0964890	+	0.995334i	$0.530761\pi$
$938$	40.7932	1.33194
$939$	−14.3614	−0.468668
$940$	69.4426	2.26497
$941$	−3.37466	−0.110011	−0.0550053	−	0.998486i	$-0.517518\pi$
$941$	−3.37466	−0.110011	−0.0550053	+	0.998486i	$0.517518\pi$
$942$	−17.9982	−0.586413
$943$	2.34448	0.0763468
$944$	64.8619	2.11107
$945$	26.8417	0.873159
$946$	−12.3972	−0.403068
$947$	33.4885	1.08823	0.544116	−	0.839010i	$-0.316865\pi$
$947$	33.4885	1.08823	0.544116	+	0.839010i	$0.316865\pi$
$948$	69.5694	2.25951
$949$	−2.11158	−0.0685449
$950$	23.4512	0.760856
$951$	13.2371	0.429241
$952$	24.1784	0.783626
$953$	−23.5514	−0.762903	−0.381452	−	0.924389i	$-0.624576\pi$
$953$	−23.5514	−0.762903	−0.381452	+	0.924389i	$0.624576\pi$
$954$	16.0367	0.519207
$955$	63.4342	2.05268
$956$	−94.9732	−3.07165
$957$	14.3972	0.465396
$958$	−13.5353	−0.437306
$959$	−31.3682	−1.01293
$960$	14.8492	0.479257
$961$	44.0831	1.42204
$962$	15.9747	0.515046
$963$	−1.05348	−0.0339479
$964$	44.2876	1.42641
$965$	−16.6338	−0.535460
$966$	24.1060	0.775598
$967$	−33.3645	−1.07293	−0.536465	−	0.843923i	$-0.680241\pi$
$967$	−33.3645	−1.07293	−0.536465	+	0.843923i	$0.680241\pi$
$968$	17.8783	0.574630
$969$	11.7280	0.376758
$970$	−133.008	−4.27064
$971$	−43.4276	−1.39366	−0.696829	−	0.717238i	$-0.745406\pi$
$971$	−43.4276	−1.39366	−0.696829	+	0.717238i	$0.745406\pi$
$972$	−25.4527	−0.816395
$973$	−24.3617	−0.781001
$974$	−27.3811	−0.877348
$975$	−7.95100	−0.254636
$976$	115.641	3.70156
$977$	38.3867	1.22810	0.614049	−	0.789268i	$-0.289540\pi$
$977$	38.3867	1.22810	0.614049	+	0.789268i	$0.289540\pi$
$978$	42.8188	1.36919
$979$	0.381868	0.0122046
$980$	48.7929	1.55863
$981$	4.02590	0.128537
$982$	101.851	3.25019
$983$	42.7916	1.36484	0.682421	−	0.730960i	$-0.260927\pi$
$983$	42.7916	1.36484	0.682421	+	0.730960i	$0.260927\pi$
$984$	−7.50585	−0.239278
$985$	23.8736	0.760677
$986$	16.2705	0.518158
$987$	−15.2732	−0.486151
$988$	−36.3520	−1.15651
$989$	−5.56711	−0.177024
$990$	−10.8544	−0.344976
$991$	4.82503	0.153272	0.0766361	−	0.997059i	$-0.475582\pi$
$991$	4.82503	0.153272	0.0766361	+	0.997059i	$0.475582\pi$
$992$	67.6149	2.14678
$993$	−24.4726	−0.776616
$994$	4.57717	0.145179
$995$	62.6746	1.98692
$996$	−65.3664	−2.07122
$997$	10.0240	0.317465	0.158732	−	0.987322i	$-0.449259\pi$
$997$	10.0240	0.317465	0.158732	+	0.987322i	$0.449259\pi$
$998$	75.8162	2.39992
$999$	−16.4785	−0.521356

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8023.2.a.d.1.7	✓	165

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8023.2.a.d.1.7	✓	165	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:	\( N \)	\(=\)	\( 8023 = 71 \cdot 113 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.57888 q^{2} -1.57055 q^{3} +4.65062 q^{4} -2.72522 q^{5} +4.05026 q^{6} -1.77487 q^{7} -6.83564 q^{8} -0.533376 q^{9} +O(q^{10})\)	\(q-2.57888 q^{2} -1.57055 q^{3} +4.65062 q^{4} -2.72522 q^{5} +4.05026 q^{6} -1.77487 q^{7} -6.83564 q^{8} -0.533376 q^{9} +7.02803 q^{10} +2.89561 q^{11} -7.30403 q^{12} +2.08606 q^{13} +4.57717 q^{14} +4.28010 q^{15} +8.32705 q^{16} +1.99289 q^{17} +1.37551 q^{18} -3.74706 q^{19} -12.6740 q^{20} +2.78752 q^{21} -7.46743 q^{22} -3.35334 q^{23} +10.7357 q^{24} +2.42685 q^{25} -5.37970 q^{26} +5.54934 q^{27} -8.25424 q^{28} -3.16583 q^{29} -11.0379 q^{30} -8.66505 q^{31} -7.80318 q^{32} -4.54769 q^{33} -5.13941 q^{34} +4.83691 q^{35} -2.48053 q^{36} -2.96945 q^{37} +9.66321 q^{38} -3.27626 q^{39} +18.6287 q^{40} -0.699149 q^{41} -7.18867 q^{42} +1.66017 q^{43} +13.4664 q^{44} +1.45357 q^{45} +8.64785 q^{46} -5.47914 q^{47} -13.0780 q^{48} -3.84985 q^{49} -6.25856 q^{50} -3.12992 q^{51} +9.70149 q^{52} +11.6587 q^{53} -14.3111 q^{54} -7.89118 q^{55} +12.1323 q^{56} +5.88493 q^{57} +8.16429 q^{58} +7.78930 q^{59} +19.9051 q^{60} +13.8873 q^{61} +22.3461 q^{62} +0.946671 q^{63} +3.46936 q^{64} -5.68499 q^{65} +11.7280 q^{66} +8.91232 q^{67} +9.26816 q^{68} +5.26658 q^{69} -12.4738 q^{70} +1.00000 q^{71} +3.64596 q^{72} -1.01223 q^{73} +7.65784 q^{74} -3.81149 q^{75} -17.4261 q^{76} -5.13932 q^{77} +8.44909 q^{78} -9.52480 q^{79} -22.6931 q^{80} -7.11538 q^{81} +1.80302 q^{82} +8.94937 q^{83} +12.9637 q^{84} -5.43106 q^{85} -4.28138 q^{86} +4.97209 q^{87} -19.7933 q^{88} +0.131878 q^{89} -3.74858 q^{90} -3.70248 q^{91} -15.5951 q^{92} +13.6089 q^{93} +14.1301 q^{94} +10.2116 q^{95} +12.2553 q^{96} -18.9254 q^{97} +9.92830 q^{98} -1.54445 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9}+O(q^{10}) \) 165 * q + 22 * q^2 + 18 * q^3 + 166 * q^4 + 28 * q^5 + 16 * q^6 + 24 * q^7 + 66 * q^8 + 177 * q^9	\( 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9} + 14 q^{10} + 18 q^{11} + 54 q^{12} + 44 q^{13} + 26 q^{14} + 24 q^{15} + 168 q^{16} + 143 q^{17} + 57 q^{18} + 20 q^{19} + 49 q^{20} + 39 q^{21} + 25 q^{22} + 52 q^{23} + 27 q^{24} + 175 q^{25} + 48 q^{26} + 69 q^{27} + 28 q^{28} + 58 q^{29} - 11 q^{30} + 28 q^{31} + 114 q^{32} + 110 q^{33} + 55 q^{34} + 67 q^{35} + 202 q^{36} + 44 q^{37} + 35 q^{38} + 27 q^{39} + 53 q^{40} + 141 q^{41} + 40 q^{42} + 29 q^{43} + 52 q^{44} + 54 q^{45} + 29 q^{46} + 87 q^{47} + 53 q^{48} + 143 q^{49} + 16 q^{50} + 37 q^{51} + 105 q^{52} + 101 q^{53} - 36 q^{54} + 72 q^{55} + 57 q^{56} + 82 q^{57} + 4 q^{58} + 103 q^{59} + 53 q^{60} + 16 q^{61} + 54 q^{62} + 126 q^{63} + 136 q^{64} + 159 q^{65} + 53 q^{66} + 60 q^{67} + 220 q^{68} + 81 q^{69} + 16 q^{70} + 165 q^{71} + 176 q^{72} + 124 q^{73} + 29 q^{74} + 44 q^{75} + 18 q^{76} + 127 q^{77} - 91 q^{78} + 14 q^{79} + 158 q^{80} + 213 q^{81} + 20 q^{82} + 116 q^{83} + 67 q^{84} + 59 q^{85} + 30 q^{86} + 28 q^{87} + 79 q^{88} + 195 q^{89} + 16 q^{90} - 26 q^{91} + 173 q^{92} + 116 q^{93} + 53 q^{94} + 26 q^{95} - 36 q^{96} + 88 q^{97} + 150 q^{98} + 12 q^{99}+O(q^{100}) \) 165 * q + 22 * q^2 + 18 * q^3 + 166 * q^4 + 28 * q^5 + 16 * q^6 + 24 * q^7 + 66 * q^8 + 177 * q^9 + 14 * q^10 + 18 * q^11 + 54 * q^12 + 44 * q^13 + 26 * q^14 + 24 * q^15 + 168 * q^16 + 143 * q^17 + 57 * q^18 + 20 * q^19 + 49 * q^20 + 39 * q^21 + 25 * q^22 + 52 * q^23 + 27 * q^24 + 175 * q^25 + 48 * q^26 + 69 * q^27 + 28 * q^28 + 58 * q^29 - 11 * q^30 + 28 * q^31 + 114 * q^32 + 110 * q^33 + 55 * q^34 + 67 * q^35 + 202 * q^36 + 44 * q^37 + 35 * q^38 + 27 * q^39 + 53 * q^40 + 141 * q^41 + 40 * q^42 + 29 * q^43 + 52 * q^44 + 54 * q^45 + 29 * q^46 + 87 * q^47 + 53 * q^48 + 143 * q^49 + 16 * q^50 + 37 * q^51 + 105 * q^52 + 101 * q^53 - 36 * q^54 + 72 * q^55 + 57 * q^56 + 82 * q^57 + 4 * q^58 + 103 * q^59 + 53 * q^60 + 16 * q^61 + 54 * q^62 + 126 * q^63 + 136 * q^64 + 159 * q^65 + 53 * q^66 + 60 * q^67 + 220 * q^68 + 81 * q^69 + 16 * q^70 + 165 * q^71 + 176 * q^72 + 124 * q^73 + 29 * q^74 + 44 * q^75 + 18 * q^76 + 127 * q^77 - 91 * q^78 + 14 * q^79 + 158 * q^80 + 213 * q^81 + 20 * q^82 + 116 * q^83 + 67 * q^84 + 59 * q^85 + 30 * q^86 + 28 * q^87 + 79 * q^88 + 195 * q^89 + 16 * q^90 - 26 * q^91 + 173 * q^92 + 116 * q^93 + 53 * q^94 + 26 * q^95 - 36 * q^96 + 88 * q^97 + 150 * q^98 + 12 * q^99

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