LMFDB - Embedded newform 8021.2.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8021,2,Mod(1,8021)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8021, 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("8021.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8021 = 13 \cdot 617 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8021.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:	$64.0480074613$
Analytic rank:	$0$
Dimension:	$174$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	8021.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.77267 q^{2} +1.50862 q^{3} +5.68769 q^{4} +1.04517 q^{5} -4.18289 q^{6} -5.21770 q^{7} -10.2247 q^{8} -0.724079 q^{9} +O(q^{10})$	\(q-2.77267 q^{2} +1.50862 q^{3} +5.68769 q^{4} +1.04517 q^{5} -4.18289 q^{6} -5.21770 q^{7} -10.2247 q^{8} -0.724079 q^{9} -2.89792 q^{10} +0.553274 q^{11} +8.58054 q^{12} +1.00000 q^{13} +14.4669 q^{14} +1.57676 q^{15} +16.9744 q^{16} -4.29007 q^{17} +2.00763 q^{18} +3.93403 q^{19} +5.94462 q^{20} -7.87150 q^{21} -1.53404 q^{22} +4.95899 q^{23} -15.4252 q^{24} -3.90761 q^{25} -2.77267 q^{26} -5.61820 q^{27} -29.6767 q^{28} -2.69434 q^{29} -4.37184 q^{30} +5.05754 q^{31} -26.6150 q^{32} +0.834677 q^{33} +11.8949 q^{34} -5.45340 q^{35} -4.11833 q^{36} -3.55070 q^{37} -10.9078 q^{38} +1.50862 q^{39} -10.6866 q^{40} -9.00766 q^{41} +21.8251 q^{42} -5.29575 q^{43} +3.14685 q^{44} -0.756787 q^{45} -13.7496 q^{46} -2.88995 q^{47} +25.6079 q^{48} +20.2244 q^{49} +10.8345 q^{50} -6.47206 q^{51} +5.68769 q^{52} +6.95371 q^{53} +15.5774 q^{54} +0.578266 q^{55} +53.3496 q^{56} +5.93494 q^{57} +7.47051 q^{58} -2.92066 q^{59} +8.96814 q^{60} +13.9305 q^{61} -14.0229 q^{62} +3.77802 q^{63} +39.8457 q^{64} +1.04517 q^{65} -2.31428 q^{66} -13.3403 q^{67} -24.4006 q^{68} +7.48121 q^{69} +15.1205 q^{70} +4.07350 q^{71} +7.40352 q^{72} -5.97365 q^{73} +9.84490 q^{74} -5.89509 q^{75} +22.3756 q^{76} -2.88682 q^{77} -4.18289 q^{78} +9.44860 q^{79} +17.7412 q^{80} -6.30347 q^{81} +24.9753 q^{82} -13.5340 q^{83} -44.7707 q^{84} -4.48386 q^{85} +14.6834 q^{86} -4.06472 q^{87} -5.65708 q^{88} +3.54506 q^{89} +2.09832 q^{90} -5.21770 q^{91} +28.2052 q^{92} +7.62989 q^{93} +8.01287 q^{94} +4.11174 q^{95} -40.1518 q^{96} +2.21895 q^{97} -56.0755 q^{98} -0.400614 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 174 q + 6 q^{2} + 37 q^{3} + 214 q^{4} + 10 q^{5} + 12 q^{6} + 28 q^{7} + 15 q^{8} + 211 q^{9}+O(q^{10}) $ 174 * q + 6 * q^2 + 37 * q^3 + 214 * q^4 + 10 * q^5 + 12 * q^6 + 28 * q^7 + 15 * q^8 + 211 * q^9	\( 174 q + 6 q^{2} + 37 q^{3} + 214 q^{4} + 10 q^{5} + 12 q^{6} + 28 q^{7} + 15 q^{8} + 211 q^{9} + 47 q^{10} + 47 q^{11} + 81 q^{12} + 174 q^{13} + 22 q^{14} + 26 q^{15} + 286 q^{16} + 27 q^{17} + 22 q^{18} + 91 q^{19} + 18 q^{20} + 8 q^{21} + 58 q^{22} + 62 q^{23} + 24 q^{24} + 244 q^{25} + 6 q^{26} + 139 q^{27} + 43 q^{28} + 42 q^{29} + 31 q^{30} + 82 q^{31} + 11 q^{32} + 12 q^{33} + 50 q^{34} + 74 q^{35} + 310 q^{36} + 47 q^{37} + 10 q^{38} + 37 q^{39} + 118 q^{40} + 16 q^{41} + 26 q^{42} + 136 q^{43} + 74 q^{44} + 18 q^{45} + 53 q^{46} + 15 q^{47} + 132 q^{48} + 254 q^{49} - 5 q^{50} + 121 q^{51} + 214 q^{52} + 39 q^{53} + 30 q^{54} + 188 q^{55} + 55 q^{56} + 11 q^{57} + 32 q^{58} + 58 q^{59} + 16 q^{60} + 128 q^{61} + 27 q^{62} + 42 q^{63} + 423 q^{64} + 10 q^{65} + 4 q^{66} + 132 q^{67} + 52 q^{68} + 63 q^{69} - 8 q^{70} + 78 q^{71} + 2 q^{72} + 21 q^{73} - 16 q^{74} + 188 q^{75} + 160 q^{76} + 20 q^{77} + 12 q^{78} + 232 q^{79} + 2 q^{80} + 302 q^{81} + 115 q^{82} + 18 q^{83} - 26 q^{84} + 47 q^{85} + 27 q^{86} + 127 q^{87} + 163 q^{88} + 14 q^{90} + 28 q^{91} + 68 q^{92} + 15 q^{93} + 91 q^{94} + 75 q^{95} - 26 q^{96} + 34 q^{97} - 60 q^{98} + 181 q^{99}+O(q^{100}) \) 174 * q + 6 * q^2 + 37 * q^3 + 214 * q^4 + 10 * q^5 + 12 * q^6 + 28 * q^7 + 15 * q^8 + 211 * q^9 + 47 * q^10 + 47 * q^11 + 81 * q^12 + 174 * q^13 + 22 * q^14 + 26 * q^15 + 286 * q^16 + 27 * q^17 + 22 * q^18 + 91 * q^19 + 18 * q^20 + 8 * q^21 + 58 * q^22 + 62 * q^23 + 24 * q^24 + 244 * q^25 + 6 * q^26 + 139 * q^27 + 43 * q^28 + 42 * q^29 + 31 * q^30 + 82 * q^31 + 11 * q^32 + 12 * q^33 + 50 * q^34 + 74 * q^35 + 310 * q^36 + 47 * q^37 + 10 * q^38 + 37 * q^39 + 118 * q^40 + 16 * q^41 + 26 * q^42 + 136 * q^43 + 74 * q^44 + 18 * q^45 + 53 * q^46 + 15 * q^47 + 132 * q^48 + 254 * q^49 - 5 * q^50 + 121 * q^51 + 214 * q^52 + 39 * q^53 + 30 * q^54 + 188 * q^55 + 55 * q^56 + 11 * q^57 + 32 * q^58 + 58 * q^59 + 16 * q^60 + 128 * q^61 + 27 * q^62 + 42 * q^63 + 423 * q^64 + 10 * q^65 + 4 * q^66 + 132 * q^67 + 52 * q^68 + 63 * q^69 - 8 * q^70 + 78 * q^71 + 2 * q^72 + 21 * q^73 - 16 * q^74 + 188 * q^75 + 160 * q^76 + 20 * q^77 + 12 * q^78 + 232 * q^79 + 2 * q^80 + 302 * q^81 + 115 * q^82 + 18 * q^83 - 26 * q^84 + 47 * q^85 + 27 * q^86 + 127 * q^87 + 163 * q^88 + 14 * q^90 + 28 * q^91 + 68 * q^92 + 15 * q^93 + 91 * q^94 + 75 * q^95 - 26 * q^96 + 34 * q^97 - 60 * q^98 + 181 * 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 $

$2$	−2.77267	−1.96057	−0.980286	−	0.197582i	$-0.936691\pi$
$2$	−2.77267	−1.96057	−0.980286	+	0.197582i	$0.936691\pi$
$3$	1.50862	0.871000	0.435500	−	0.900189i	$-0.356572\pi$
$3$	1.50862	0.871000	0.435500	+	0.900189i	$0.356572\pi$
$4$	5.68769	2.84384
$5$	1.04517	0.467415	0.233708	−	0.972307i	$-0.424914\pi$
$5$	1.04517	0.467415	0.233708	+	0.972307i	$0.424914\pi$
$6$	−4.18289	−1.70766
$7$	−5.21770	−1.97210	−0.986052	−	0.166435i	$-0.946774\pi$
$7$	−5.21770	−1.97210	−0.986052	+	0.166435i	$0.946774\pi$
$8$	−10.2247	−3.61499
$9$	−0.724079	−0.241360
$10$	−2.89792	−0.916402
$11$	0.553274	0.166818	0.0834091	−	0.996515i	$-0.473419\pi$
$11$	0.553274	0.166818	0.0834091	+	0.996515i	$0.473419\pi$
$12$	8.58054	2.47699
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	14.4669	3.86645
$15$	1.57676	0.407119
$16$	16.9744	4.24361
$17$	−4.29007	−1.04049	−0.520247	−	0.854016i	$-0.674160\pi$
$17$	−4.29007	−1.04049	−0.520247	+	0.854016i	$0.674160\pi$
$18$	2.00763	0.473203
$19$	3.93403	0.902529	0.451264	−	0.892390i	$-0.350973\pi$
$19$	3.93403	0.902529	0.451264	+	0.892390i	$0.350973\pi$
$20$	5.94462	1.32926
$21$	−7.87150	−1.71770
$22$	−1.53404	−0.327059
$23$	4.95899	1.03402	0.517010	−	0.855979i	$-0.327045\pi$
$23$	4.95899	1.03402	0.517010	+	0.855979i	$0.327045\pi$
$24$	−15.4252	−3.14866
$25$	−3.90761	−0.781523
$26$	−2.77267	−0.543765
$27$	−5.61820	−1.08122
$28$	−29.6767	−5.60836
$29$	−2.69434	−0.500326	−0.250163	−	0.968204i	$-0.580484\pi$
$29$	−2.69434	−0.500326	−0.250163	+	0.968204i	$0.580484\pi$
$30$	−4.37184	−0.798186
$31$	5.05754	0.908361	0.454181	−	0.890910i	$-0.349932\pi$
$31$	5.05754	0.908361	0.454181	+	0.890910i	$0.349932\pi$
$32$	−26.6150	−4.70491
$33$	0.834677	0.145299
$34$	11.8949	2.03996
$35$	−5.45340	−0.921792
$36$	−4.11833	−0.686389
$37$	−3.55070	−0.583731	−0.291865	−	0.956459i	$-0.594276\pi$
$37$	−3.55070	−0.583731	−0.291865	+	0.956459i	$0.594276\pi$
$38$	−10.9078	−1.76947
$39$	1.50862	0.241572
$40$	−10.6866	−1.68970
$41$	−9.00766	−1.40676	−0.703380	−	0.710814i	$-0.748327\pi$
$41$	−9.00766	−1.40676	−0.703380	+	0.710814i	$0.748327\pi$
$42$	21.8251	3.36768
$43$	−5.29575	−0.807595	−0.403797	−	0.914848i	$-0.632310\pi$
$43$	−5.29575	−0.807595	−0.403797	+	0.914848i	$0.632310\pi$
$44$	3.14685	0.474405
$45$	−0.756787	−0.112815
$46$	−13.7496	−2.02727
$47$	−2.88995	−0.421543	−0.210771	−	0.977535i	$-0.567598\pi$
$47$	−2.88995	−0.421543	−0.210771	+	0.977535i	$0.567598\pi$
$48$	25.6079	3.69618
$49$	20.2244	2.88920
$50$	10.8345	1.53223
$51$	−6.47206	−0.906270
$52$	5.68769	0.788741
$53$	6.95371	0.955165	0.477583	−	0.878587i	$-0.341513\pi$
$53$	6.95371	0.955165	0.477583	+	0.878587i	$0.341513\pi$
$54$	15.5774	2.11982
$55$	0.578266	0.0779734
$56$	53.3496	7.12914
$57$	5.93494	0.786102
$58$	7.47051	0.980925
$59$	−2.92066	−0.380237	−0.190119	−	0.981761i	$-0.560887\pi$
$59$	−2.92066	−0.380237	−0.190119	+	0.981761i	$0.560887\pi$
$60$	8.96814	1.15778
$61$	13.9305	1.78362	0.891809	−	0.452412i	$-0.149436\pi$
$61$	13.9305	1.78362	0.891809	+	0.452412i	$0.149436\pi$
$62$	−14.0229	−1.78091
$63$	3.77802	0.475986
$64$	39.8457	4.98071
$65$	1.04517	0.129638
$66$	−2.31428	−0.284869
$67$	−13.3403	−1.62978	−0.814888	−	0.579618i	$-0.803202\pi$
$67$	−13.3403	−1.62978	−0.814888	+	0.579618i	$0.803202\pi$
$68$	−24.4006	−2.95900
$69$	7.48121	0.900631
$70$	15.1205	1.80724
$71$	4.07350	0.483435	0.241718	−	0.970347i	$-0.422289\pi$
$71$	4.07350	0.483435	0.241718	+	0.970347i	$0.422289\pi$
$72$	7.40352	0.872513
$73$	−5.97365	−0.699163	−0.349582	−	0.936906i	$-0.613676\pi$
$73$	−5.97365	−0.699163	−0.349582	+	0.936906i	$0.613676\pi$
$74$	9.84490	1.14445
$75$	−5.89509	−0.680706
$76$	22.3756	2.56665
$77$	−2.88682	−0.328983
$78$	−4.18289	−0.473619
$79$	9.44860	1.06305	0.531525	−	0.847043i	$-0.321619\pi$
$79$	9.44860	1.06305	0.531525	+	0.847043i	$0.321619\pi$
$80$	17.7412	1.98353
$81$	−6.30347	−0.700386
$82$	24.9753	2.75806
$83$	−13.5340	−1.48555	−0.742773	−	0.669543i	$-0.766490\pi$
$83$	−13.5340	−1.48555	−0.742773	+	0.669543i	$0.766490\pi$
$84$	−44.7707	−4.88488
$85$	−4.48386	−0.486343
$86$	14.6834	1.58335
$87$	−4.06472	−0.435784
$88$	−5.65708	−0.603047
$89$	3.54506	0.375775	0.187888	−	0.982191i	$-0.439836\pi$
$89$	3.54506	0.375775	0.187888	+	0.982191i	$0.439836\pi$
$90$	2.09832	0.221182
$91$	−5.21770	−0.546963
$92$	28.2052	2.94059
$93$	7.62989	0.791182
$94$	8.01287	0.826465
$95$	4.11174	0.421856
$96$	−40.1518	−4.09798
$97$	2.21895	0.225300	0.112650	−	0.993635i	$-0.464066\pi$
$97$	2.21895	0.225300	0.112650	+	0.993635i	$0.464066\pi$
$98$	−56.0755	−5.66448
$99$	−0.400614	−0.0402632
$100$	−22.2253	−2.22253
$101$	4.08627	0.406599	0.203299	−	0.979117i	$-0.434834\pi$
$101$	4.08627	0.406599	0.203299	+	0.979117i	$0.434834\pi$
$102$	17.9449	1.77681
$103$	−2.50898	−0.247217	−0.123609	−	0.992331i	$-0.539447\pi$
$103$	−2.50898	−0.247217	−0.123609	+	0.992331i	$0.539447\pi$
$104$	−10.2247	−1.00262
$105$	−8.22708	−0.802881
$106$	−19.2803	−1.87267
$107$	15.3666	1.48555	0.742775	−	0.669541i	$-0.233509\pi$
$107$	15.3666	1.48555	0.742775	+	0.669541i	$0.233509\pi$
$108$	−31.9546	−3.07483
$109$	−15.4469	−1.47955	−0.739774	−	0.672856i	$-0.765068\pi$
$109$	−15.4469	−1.47955	−0.739774	+	0.672856i	$0.765068\pi$
$110$	−1.60334	−0.152873
$111$	−5.35664	−0.508429
$112$	−88.5675	−8.36884
$113$	5.31493	0.499987	0.249993	−	0.968248i	$-0.419572\pi$
$113$	5.31493	0.499987	0.249993	+	0.968248i	$0.419572\pi$
$114$	−16.4556	−1.54121
$115$	5.18300	0.483317
$116$	−15.3246	−1.42285
$117$	−0.724079	−0.0669411
$118$	8.09802	0.745483
$119$	22.3843	2.05196
$120$	−16.1220	−1.47173
$121$	−10.6939	−0.972172
$122$	−38.6247	−3.49691
$123$	−13.5891	−1.22529
$124$	28.7657	2.58324
$125$	−9.30999	−0.832711
$126$	−10.4752	−0.933206
$127$	−17.2248	−1.52845	−0.764227	−	0.644947i	$-0.776879\pi$
$127$	−17.2248	−1.52845	−0.764227	+	0.644947i	$0.776879\pi$
$128$	−57.2489	−5.06014
$129$	−7.98925	−0.703415
$130$	−2.89792	−0.254164
$131$	−9.15721	−0.800069	−0.400034	−	0.916500i	$-0.631002\pi$
$131$	−9.15721	−0.800069	−0.400034	+	0.916500i	$0.631002\pi$
$132$	4.74739	0.413207
$133$	−20.5266	−1.77988
$134$	36.9882	3.19530
$135$	−5.87199	−0.505381
$136$	43.8648	3.76138
$137$	8.62089	0.736533	0.368266	−	0.929720i	$-0.379951\pi$
$137$	8.62089	0.736533	0.368266	+	0.929720i	$0.379951\pi$
$138$	−20.7429	−1.76575
$139$	13.2796	1.12636	0.563181	−	0.826333i	$-0.309577\pi$
$139$	13.2796	1.12636	0.563181	+	0.826333i	$0.309577\pi$
$140$	−31.0172	−2.62143
$141$	−4.35982	−0.367163
$142$	−11.2945	−0.947810
$143$	0.553274	0.0462671
$144$	−12.2908	−1.02424
$145$	−2.81605	−0.233860
$146$	16.5630	1.37076
$147$	30.5108	2.51649
$148$	−20.1953	−1.66004
$149$	10.5386	0.863352	0.431676	−	0.902029i	$-0.357922\pi$
$149$	10.5386	0.863352	0.431676	+	0.902029i	$0.357922\pi$
$150$	16.3451	1.33457
$151$	7.51533	0.611589	0.305794	−	0.952098i	$-0.401078\pi$
$151$	7.51533	0.611589	0.305794	+	0.952098i	$0.401078\pi$
$152$	−40.2245	−3.26263
$153$	3.10634	0.251133
$154$	8.00418	0.644995
$155$	5.28600	0.424582
$156$	8.58054	0.686993
$157$	13.1468	1.04923	0.524614	−	0.851340i	$-0.324210\pi$
$157$	13.1468	1.04923	0.524614	+	0.851340i	$0.324210\pi$
$158$	−26.1978	−2.08419
$159$	10.4905	0.831948
$160$	−27.8173	−2.19915
$161$	−25.8745	−2.03920
$162$	17.4774	1.37316
$163$	22.7772	1.78404	0.892022	−	0.451991i	$-0.149286\pi$
$163$	22.7772	1.78404	0.892022	+	0.451991i	$0.149286\pi$
$164$	−51.2328	−4.00061
$165$	0.872382	0.0679148
$166$	37.5252	2.91252
$167$	15.5654	1.20448	0.602242	−	0.798314i	$-0.294274\pi$
$167$	15.5654	1.20448	0.602242	+	0.798314i	$0.294274\pi$
$168$	80.4841	6.20948
$169$	1.00000	0.0769231
$170$	12.4323	0.953510
$171$	−2.84855	−0.217834
$172$	−30.1206	−2.29667
$173$	21.7288	1.65201	0.826005	−	0.563662i	$-0.190608\pi$
$173$	21.7288	1.65201	0.826005	+	0.563662i	$0.190608\pi$
$174$	11.2701	0.854386
$175$	20.3888	1.54125
$176$	9.39151	0.707912
$177$	−4.40615	−0.331187
$178$	−9.82927	−0.736735
$179$	−21.5752	−1.61260	−0.806302	−	0.591504i	$-0.798534\pi$
$179$	−21.5752	−1.61260	−0.806302	+	0.591504i	$0.798534\pi$
$180$	−4.30437	−0.320829
$181$	14.0952	1.04769	0.523843	−	0.851815i	$-0.324498\pi$
$181$	14.0952	1.04769	0.523843	+	0.851815i	$0.324498\pi$
$182$	14.4669	1.07236
$183$	21.0158	1.55353
$184$	−50.7044	−3.73797
$185$	−3.71109	−0.272845
$186$	−21.1551	−1.55117
$187$	−2.37358	−0.173573
$188$	−16.4371	−1.19880
$189$	29.3141	2.13229
$190$	−11.4005	−0.827079
$191$	−23.0198	−1.66565	−0.832827	−	0.553533i	$-0.813279\pi$
$191$	−23.0198	−1.66565	−0.832827	+	0.553533i	$0.813279\pi$
$192$	60.1118	4.33820
$193$	−10.1247	−0.728793	−0.364397	−	0.931244i	$-0.618725\pi$
$193$	−10.1247	−0.728793	−0.364397	+	0.931244i	$0.618725\pi$
$194$	−6.15242	−0.441718
$195$	1.57676	0.112914
$196$	115.030	8.21643
$197$	−23.5681	−1.67916	−0.839578	−	0.543239i	$-0.817198\pi$
$197$	−23.5681	−1.67916	−0.839578	+	0.543239i	$0.817198\pi$
$198$	1.11077	0.0789389
$199$	16.0963	1.14103	0.570517	−	0.821286i	$-0.306743\pi$
$199$	16.0963	1.14103	0.570517	+	0.821286i	$0.306743\pi$
$200$	39.9543	2.82520
$201$	−20.1254	−1.41954
$202$	−11.3299	−0.797166
$203$	14.0582	0.986695
$204$	−36.8111	−2.57729
$205$	−9.41456	−0.657542
$206$	6.95657	0.484687
$207$	−3.59070	−0.249571
$208$	16.9744	1.17697
$209$	2.17660	0.150558
$210$	22.8110	1.57411
$211$	−16.3947	−1.12866	−0.564330	−	0.825549i	$-0.690866\pi$
$211$	−16.3947	−1.12866	−0.564330	+	0.825549i	$0.690866\pi$
$212$	39.5505	2.71634
$213$	6.14534	0.421072
$214$	−42.6066	−2.91253
$215$	−5.53497	−0.377482
$216$	57.4447	3.90862
$217$	−26.3887	−1.79138
$218$	42.8292	2.90076
$219$	−9.01195	−0.608971
$220$	3.28900	0.221744
$221$	−4.29007	−0.288581
$222$	14.8522	0.996813
$223$	−6.87255	−0.460220	−0.230110	−	0.973165i	$-0.573909\pi$
$223$	−6.87255	−0.460220	−0.230110	+	0.973165i	$0.573909\pi$
$224$	138.869	9.27858
$225$	2.82942	0.188628
$226$	−14.7365	−0.980260
$227$	2.73147	0.181294	0.0906470	−	0.995883i	$-0.471107\pi$
$227$	2.73147	0.181294	0.0906470	+	0.995883i	$0.471107\pi$
$228$	33.7561	2.23555
$229$	4.46279	0.294909	0.147455	−	0.989069i	$-0.452892\pi$
$229$	4.46279	0.294909	0.147455	+	0.989069i	$0.452892\pi$
$230$	−14.3707	−0.947578
$231$	−4.35510	−0.286544
$232$	27.5489	1.80867
$233$	−20.5058	−1.34338	−0.671688	−	0.740834i	$-0.734431\pi$
$233$	−20.5058	−1.34338	−0.671688	+	0.740834i	$0.734431\pi$
$234$	2.00763	0.131243
$235$	−3.02050	−0.197035
$236$	−16.6118	−1.08134
$237$	14.2543	0.925916
$238$	−62.0642	−4.02302
$239$	−14.3818	−0.930278	−0.465139	−	0.885238i	$-0.653996\pi$
$239$	−14.3818	−0.930278	−0.465139	+	0.885238i	$0.653996\pi$
$240$	26.7647	1.72765
$241$	17.7043	1.14043	0.570216	−	0.821495i	$-0.306859\pi$
$241$	17.7043	1.14043	0.570216	+	0.821495i	$0.306859\pi$
$242$	29.6506	1.90601
$243$	7.34509	0.471188
$244$	79.2324	5.07233
$245$	21.1380	1.35046
$246$	37.6781	2.40227
$247$	3.93403	0.250316
$248$	−51.7120	−3.28372
$249$	−20.4176	−1.29391
$250$	25.8135	1.63259
$251$	24.3548	1.53726	0.768630	−	0.639694i	$-0.220939\pi$
$251$	24.3548	1.53726	0.768630	+	0.639694i	$0.220939\pi$
$252$	21.4882	1.35363
$253$	2.74368	0.172494
$254$	47.7587	2.99665
$255$	−6.76442	−0.423604
$256$	79.0408	4.94005
$257$	9.82799	0.613053	0.306527	−	0.951862i	$-0.400833\pi$
$257$	9.82799	0.613053	0.306527	+	0.951862i	$0.400833\pi$
$258$	22.1516	1.37910
$259$	18.5265	1.15118
$260$	5.94462	0.368670
$261$	1.95091	0.120758
$262$	25.3899	1.56859
$263$	−8.42824	−0.519708	−0.259854	−	0.965648i	$-0.583674\pi$
$263$	−8.42824	−0.519708	−0.259854	+	0.965648i	$0.583674\pi$
$264$	−8.53436	−0.525254
$265$	7.26782	0.446459
$266$	56.9134	3.48959
$267$	5.34813	0.327300
$268$	−75.8755	−4.63483
$269$	−9.27450	−0.565476	−0.282738	−	0.959197i	$-0.591243\pi$
$269$	−9.27450	−0.565476	−0.282738	+	0.959197i	$0.591243\pi$
$270$	16.2811	0.990835
$271$	28.6728	1.74175	0.870875	−	0.491505i	$-0.163553\pi$
$271$	28.6728	1.74175	0.870875	+	0.491505i	$0.163553\pi$
$272$	−72.8214	−4.41545
$273$	−7.87150	−0.476405
$274$	−23.9029	−1.44403
$275$	−2.16198	−0.130372
$276$	42.5508	2.56126
$277$	5.52276	0.331831	0.165915	−	0.986140i	$-0.446942\pi$
$277$	5.52276	0.331831	0.165915	+	0.986140i	$0.446942\pi$
$278$	−36.8200	−2.20832
$279$	−3.66206	−0.219242
$280$	55.7596	3.33227
$281$	26.9768	1.60930	0.804650	−	0.593749i	$-0.202353\pi$
$281$	26.9768	1.60930	0.804650	+	0.593749i	$0.202353\pi$
$282$	12.0883	0.719850
$283$	−3.90860	−0.232342	−0.116171	−	0.993229i	$-0.537062\pi$
$283$	−3.90860	−0.232342	−0.116171	+	0.993229i	$0.537062\pi$
$284$	23.1688	1.37482
$285$	6.20304	0.367436
$286$	−1.53404	−0.0907100
$287$	46.9993	2.77428
$288$	19.2714	1.13558
$289$	1.40466	0.0826271
$290$	7.80797	0.458500
$291$	3.34755	0.196237
$292$	−33.9763	−1.98831
$293$	19.5675	1.14315	0.571573	−	0.820551i	$-0.306333\pi$
$293$	19.5675	1.14315	0.571573	+	0.820551i	$0.306333\pi$
$294$	−84.5964	−4.93376
$295$	−3.05259	−0.177729
$296$	36.3049	2.11018
$297$	−3.10840	−0.180368
$298$	−29.2199	−1.69266
$299$	4.95899	0.286786
$300$	−33.5294	−1.93582
$301$	27.6316	1.59266
$302$	−20.8375	−1.19906
$303$	6.16461	0.354147
$304$	66.7780	3.82998
$305$	14.5598	0.833690
$306$	−8.61286	−0.492365
$307$	23.5333	1.34312	0.671559	−	0.740951i	$-0.265625\pi$
$307$	23.5333	1.34312	0.671559	+	0.740951i	$0.265625\pi$
$308$	−16.4193	−0.935577
$309$	−3.78509	−0.215326
$310$	−14.6563	−0.832424
$311$	−22.8344	−1.29482	−0.647409	−	0.762143i	$-0.724147\pi$
$311$	−22.8344	−1.29482	−0.647409	+	0.762143i	$0.724147\pi$
$312$	−15.4252	−0.873280
$313$	30.9308	1.74831	0.874157	−	0.485644i	$-0.161415\pi$
$313$	30.9308	1.74831	0.874157	+	0.485644i	$0.161415\pi$
$314$	−36.4517	−2.05709
$315$	3.94869	0.222483
$316$	53.7407	3.02315
$317$	8.97058	0.503838	0.251919	−	0.967748i	$-0.418938\pi$
$317$	8.97058	0.503838	0.251919	+	0.967748i	$0.418938\pi$
$318$	−29.0866	−1.63110
$319$	−1.49071	−0.0834635
$320$	41.6456	2.32806
$321$	23.1824	1.29391
$322$	71.7414	3.99799
$323$	−16.8773	−0.939076
$324$	−35.8522	−1.99179
$325$	−3.90761	−0.216755
$326$	−63.1535	−3.49775
$327$	−23.3035	−1.28869
$328$	92.1010	5.08543
$329$	15.0789	0.831326
$330$	−2.41883	−0.133152
$331$	−5.22320	−0.287093	−0.143546	−	0.989644i	$-0.545851\pi$
$331$	−5.22320	−0.287093	−0.143546	+	0.989644i	$0.545851\pi$
$332$	−76.9771	−4.22466
$333$	2.57098	0.140889
$334$	−43.1576	−2.36148
$335$	−13.9429	−0.761783
$336$	−133.614	−7.28926
$337$	31.0367	1.69068	0.845338	−	0.534232i	$-0.179399\pi$
$337$	31.0367	1.69068	0.845338	+	0.534232i	$0.179399\pi$
$338$	−2.77267	−0.150813
$339$	8.01819	0.435488
$340$	−25.5028	−1.38308
$341$	2.79820	0.151531
$342$	7.89808	0.427079
$343$	−69.0009	−3.72570
$344$	54.1477	2.91945
$345$	7.81915	0.420969
$346$	−60.2468	−3.23889
$347$	−16.5699	−0.889520	−0.444760	−	0.895650i	$-0.646711\pi$
$347$	−16.5699	−0.889520	−0.444760	+	0.895650i	$0.646711\pi$
$348$	−23.1189	−1.23930
$349$	12.7292	0.681376	0.340688	−	0.940176i	$-0.389340\pi$
$349$	12.7292	0.681376	0.340688	+	0.940176i	$0.389340\pi$
$350$	−56.5313	−3.02172
$351$	−5.61820	−0.299878
$352$	−14.7254	−0.784865
$353$	4.14728	0.220738	0.110369	−	0.993891i	$-0.464797\pi$
$353$	4.14728	0.220738	0.110369	+	0.993891i	$0.464797\pi$
$354$	12.2168	0.649316
$355$	4.25751	0.225965
$356$	20.1632	1.06865
$357$	33.7693	1.78726
$358$	59.8208	3.16163
$359$	−14.7990	−0.781062	−0.390531	−	0.920590i	$-0.627709\pi$
$359$	−14.7990	−0.781062	−0.390531	+	0.920590i	$0.627709\pi$
$360$	7.73795	0.407826
$361$	−3.52339	−0.185441
$362$	−39.0813	−2.05407
$363$	−16.1330	−0.846761
$364$	−29.6767	−1.55548
$365$	−6.24350	−0.326800
$366$	−58.2698	−3.04581
$367$	12.9505	0.676012	0.338006	−	0.941144i	$-0.390248\pi$
$367$	12.9505	0.676012	0.338006	+	0.941144i	$0.390248\pi$
$368$	84.1760	4.38798
$369$	6.52226	0.339535
$370$	10.2896	0.534932
$371$	−36.2824	−1.88369
$372$	43.3964	2.25000
$373$	17.9888	0.931424	0.465712	−	0.884936i	$-0.345798\pi$
$373$	17.9888	0.931424	0.465712	+	0.884936i	$0.345798\pi$
$374$	6.58115	0.340303
$375$	−14.0452	−0.725291
$376$	29.5490	1.52387
$377$	−2.69434	−0.138765
$378$	−81.2783	−4.18050
$379$	9.75102	0.500876	0.250438	−	0.968133i	$-0.419425\pi$
$379$	9.75102	0.500876	0.250438	+	0.968133i	$0.419425\pi$
$380$	23.3863	1.19969
$381$	−25.9856	−1.33128
$382$	63.8263	3.26564
$383$	14.4390	0.737801	0.368900	−	0.929469i	$-0.379734\pi$
$383$	14.4390	0.737801	0.368900	+	0.929469i	$0.379734\pi$
$384$	−86.3666	−4.40738
$385$	−3.01722	−0.153772
$386$	28.0725	1.42885
$387$	3.83454	0.194921
$388$	12.6207	0.640719
$389$	35.5593	1.80293	0.901465	−	0.432852i	$-0.142493\pi$
$389$	35.5593	1.80293	0.901465	+	0.432852i	$0.142493\pi$
$390$	−4.37184	−0.221377
$391$	−21.2744	−1.07589
$392$	−206.789	−10.4444
$393$	−13.8147	−0.696860
$394$	65.3465	3.29211
$395$	9.87541	0.496886
$396$	−2.27857	−0.114502
$397$	28.9842	1.45468	0.727339	−	0.686279i	$-0.240757\pi$
$397$	28.9842	1.45468	0.727339	+	0.686279i	$0.240757\pi$
$398$	−44.6296	−2.23708
$399$	−30.9667	−1.55028
$400$	−66.3295	−3.31648
$401$	−27.6850	−1.38252	−0.691262	−	0.722604i	$-0.742945\pi$
$401$	−27.6850	−1.38252	−0.691262	+	0.722604i	$0.742945\pi$
$402$	55.8010	2.78310
$403$	5.05754	0.251934
$404$	23.2414	1.15630
$405$	−6.58822	−0.327371
$406$	−38.9789	−1.93449
$407$	−1.96451	−0.0973770
$408$	66.1751	3.27616
$409$	−15.9641	−0.789374	−0.394687	−	0.918816i	$-0.629147\pi$
$409$	−15.9641	−0.789374	−0.394687	+	0.918816i	$0.629147\pi$
$410$	26.1035	1.28916
$411$	13.0056	0.641520
$412$	−14.2703	−0.703047
$413$	15.2391	0.749868
$414$	9.95581	0.489301
$415$	−14.1453	−0.694367
$416$	−26.6150	−1.30491
$417$	20.0338	0.981061
$418$	−6.03498	−0.295181
$419$	−7.42436	−0.362704	−0.181352	−	0.983418i	$-0.558047\pi$
$419$	−7.42436	−0.362704	−0.181352	+	0.983418i	$0.558047\pi$
$420$	−46.7931	−2.28327
$421$	−31.8692	−1.55321	−0.776604	−	0.629988i	$-0.783060\pi$
$421$	−31.8692	−1.55321	−0.776604	+	0.629988i	$0.783060\pi$
$422$	45.4572	2.21282
$423$	2.09255	0.101743
$424$	−71.0998	−3.45291
$425$	16.7639	0.813170
$426$	−17.0390	−0.825542
$427$	−72.6852	−3.51748
$428$	87.4007	4.22467
$429$	0.834677	0.0402986
$430$	15.3466	0.740081
$431$	−20.8588	−1.00473	−0.502367	−	0.864654i	$-0.667537\pi$
$431$	−20.8588	−1.00473	−0.502367	+	0.864654i	$0.667537\pi$
$432$	−95.3658	−4.58829
$433$	4.65056	0.223492	0.111746	−	0.993737i	$-0.464356\pi$
$433$	4.65056	0.223492	0.111746	+	0.993737i	$0.464356\pi$
$434$	73.1672	3.51214
$435$	−4.24833	−0.203692
$436$	−87.8574	−4.20760
$437$	19.5088	0.933233
$438$	24.9871	1.19393
$439$	22.0461	1.05220	0.526102	−	0.850421i	$-0.323653\pi$
$439$	22.0461	1.05220	0.526102	+	0.850421i	$0.323653\pi$
$440$	−5.91262	−0.281873
$441$	−14.6440	−0.697335
$442$	11.8949	0.565784
$443$	26.3216	1.25058	0.625288	−	0.780394i	$-0.284981\pi$
$443$	26.3216	1.25058	0.625288	+	0.780394i	$0.284981\pi$
$444$	−30.4669	−1.44589
$445$	3.70520	0.175643
$446$	19.0553	0.902294
$447$	15.8986	0.751979
$448$	−207.903	−9.82249
$449$	−2.09729	−0.0989774	−0.0494887	−	0.998775i	$-0.515759\pi$
$449$	−2.09729	−0.0989774	−0.0494887	+	0.998775i	$0.515759\pi$
$450$	−7.84504	−0.369819
$451$	−4.98370	−0.234673
$452$	30.2297	1.42188
$453$	11.3377	0.532694
$454$	−7.57346	−0.355440
$455$	−5.45340	−0.255659
$456$	−60.6833	−2.84175
$457$	37.6209	1.75983	0.879916	−	0.475129i	$-0.157599\pi$
$457$	37.6209	1.75983	0.879916	+	0.475129i	$0.157599\pi$
$458$	−12.3738	−0.578191
$459$	24.1025	1.12501
$460$	29.4793	1.37448
$461$	−21.5169	−1.00214	−0.501071	−	0.865406i	$-0.667060\pi$
$461$	−21.5169	−1.00214	−0.501071	+	0.865406i	$0.667060\pi$
$462$	12.0752	0.561791
$463$	12.1042	0.562528	0.281264	−	0.959630i	$-0.409246\pi$
$463$	12.1042	0.562528	0.281264	+	0.959630i	$0.409246\pi$
$464$	−45.7349	−2.12319
$465$	7.97455	0.369811
$466$	56.8557	2.63379
$467$	5.92069	0.273977	0.136988	−	0.990573i	$-0.456258\pi$
$467$	5.92069	0.273977	0.136988	+	0.990573i	$0.456258\pi$
$468$	−4.11833	−0.190370
$469$	69.6057	3.21409
$470$	8.37483	0.386302
$471$	19.8335	0.913878
$472$	29.8630	1.37456
$473$	−2.93000	−0.134722
$474$	−39.5224	−1.81533
$475$	−15.3727	−0.705347
$476$	127.315	5.83546
$477$	−5.03503	−0.230538
$478$	39.8758	1.82388
$479$	36.1000	1.64945	0.824726	−	0.565532i	$-0.191329\pi$
$479$	36.1000	1.64945	0.824726	+	0.565532i	$0.191329\pi$
$480$	−41.9656	−1.91546
$481$	−3.55070	−0.161898
$482$	−49.0881	−2.23590
$483$	−39.0347	−1.77614
$484$	−60.8235	−2.76471
$485$	2.31919	0.105309
$486$	−20.3655	−0.923798
$487$	7.13614	0.323370	0.161685	−	0.986842i	$-0.448307\pi$
$487$	7.13614	0.323370	0.161685	+	0.986842i	$0.448307\pi$
$488$	−142.436	−6.44776
$489$	34.3620	1.55390
$490$	−58.6086	−2.64767
$491$	9.35272	0.422083	0.211041	−	0.977477i	$-0.432315\pi$
$491$	9.35272	0.422083	0.211041	+	0.977477i	$0.432315\pi$
$492$	−77.2906	−3.48453
$493$	11.5589	0.520586
$494$	−10.9078	−0.490764
$495$	−0.418710	−0.0188196
$496$	85.8489	3.85473
$497$	−21.2543	−0.953385
$498$	56.6111	2.53681
$499$	2.98399	0.133582	0.0667908	−	0.997767i	$-0.478724\pi$
$499$	2.98399	0.133582	0.0667908	+	0.997767i	$0.478724\pi$
$500$	−52.9524	−2.36810
$501$	23.4821	1.04910
$502$	−67.5277	−3.01391
$503$	−12.8578	−0.573300	−0.286650	−	0.958035i	$-0.592542\pi$
$503$	−12.8578	−0.573300	−0.286650	+	0.958035i	$0.592542\pi$
$504$	−38.6293	−1.72069
$505$	4.27085	0.190051
$506$	−7.60731	−0.338186
$507$	1.50862	0.0670000
$508$	−97.9694	−4.34669
$509$	−10.9431	−0.485045	−0.242522	−	0.970146i	$-0.577975\pi$
$509$	−10.9431	−0.485045	−0.242522	+	0.970146i	$0.577975\pi$
$510$	18.7555	0.830507
$511$	31.1687	1.37882
$512$	−104.656	−4.62519
$513$	−22.1022	−0.975836
$514$	−27.2498	−1.20194
$515$	−2.62232	−0.115553
$516$	−45.4404	−2.00040
$517$	−1.59893	−0.0703210
$518$	−51.3677	−2.25697
$519$	32.7804	1.43890
$520$	−10.6866	−0.468639
$521$	−23.2588	−1.01899	−0.509494	−	0.860474i	$-0.670167\pi$
$521$	−23.2588	−1.01899	−0.509494	+	0.860474i	$0.670167\pi$
$522$	−5.40923	−0.236756
$523$	21.2881	0.930862	0.465431	−	0.885084i	$-0.345899\pi$
$523$	21.2881	0.930862	0.465431	+	0.885084i	$0.345899\pi$
$524$	−52.0834	−2.27527
$525$	30.7588	1.34242
$526$	23.3687	1.01892
$527$	−21.6972	−0.945144
$528$	14.1682	0.616591
$529$	1.59155	0.0691980
$530$	−20.1513	−0.875315
$531$	2.11479	0.0917739
$532$	−116.749	−5.06171
$533$	−9.00766	−0.390165
$534$	−14.8286	−0.641696
$535$	16.0608	0.694369
$536$	136.401	5.89163
$537$	−32.5486	−1.40458
$538$	25.7151	1.10866
$539$	11.1896	0.481971
$540$	−33.3981	−1.43722
$541$	−6.49856	−0.279395	−0.139697	−	0.990194i	$-0.544613\pi$
$541$	−6.49856	−0.279395	−0.139697	+	0.990194i	$0.544613\pi$
$542$	−79.5002	−3.41483
$543$	21.2642	0.912534
$544$	114.180	4.89543
$545$	−16.1447	−0.691563
$546$	21.8251	0.934027
$547$	42.2008	1.80438	0.902188	−	0.431344i	$-0.141960\pi$
$547$	42.2008	1.80438	0.902188	+	0.431344i	$0.141960\pi$
$548$	49.0330	2.09458
$549$	−10.0868	−0.430493
$550$	5.99445	0.255604
$551$	−10.5996	−0.451559
$552$	−76.4934	−3.25577
$553$	−49.2999	−2.09645
$554$	−15.3128	−0.650578
$555$	−5.59861	−0.237648
$556$	75.5303	3.20320
$557$	−26.8226	−1.13651	−0.568255	−	0.822853i	$-0.692381\pi$
$557$	−26.8226	−1.13651	−0.568255	+	0.822853i	$0.692381\pi$
$558$	10.1537	0.429839
$559$	−5.29575	−0.223986
$560$	−92.5683	−3.91173
$561$	−3.58082	−0.151182
$562$	−74.7977	−3.15515
$563$	−20.6372	−0.869752	−0.434876	−	0.900490i	$-0.643208\pi$
$563$	−20.6372	−0.869752	−0.434876	+	0.900490i	$0.643208\pi$
$564$	−24.7973	−1.04416
$565$	5.55502	0.233701
$566$	10.8373	0.455524
$567$	32.8896	1.38123
$568$	−41.6505	−1.74761
$569$	−18.8174	−0.788868	−0.394434	−	0.918924i	$-0.629059\pi$
$569$	−18.8174	−0.788868	−0.394434	+	0.918924i	$0.629059\pi$
$570$	−17.1990	−0.720386
$571$	4.17158	0.174575	0.0872876	−	0.996183i	$-0.472180\pi$
$571$	4.17158	0.174575	0.0872876	+	0.996183i	$0.472180\pi$
$572$	3.14685	0.131576
$573$	−34.7280	−1.45078
$574$	−130.313	−5.43918
$575$	−19.3778	−0.808111
$576$	−28.8514	−1.20214
$577$	6.72289	0.279877	0.139939	−	0.990160i	$-0.455309\pi$
$577$	6.72289	0.279877	0.139939	+	0.990160i	$0.455309\pi$
$578$	−3.89466	−0.161996
$579$	−15.2743	−0.634779
$580$	−16.0168	−0.665062
$581$	70.6162	2.92965
$582$	−9.28163	−0.384736
$583$	3.84730	0.159339
$584$	61.0791	2.52747
$585$	−0.756787	−0.0312893
$586$	−54.2542	−2.24122
$587$	9.68705	0.399827	0.199914	−	0.979814i	$-0.435934\pi$
$587$	9.68705	0.399827	0.199914	+	0.979814i	$0.435934\pi$
$588$	173.536	7.15651
$589$	19.8965	0.819822
$590$	8.46383	0.348450
$591$	−35.5552	−1.46254
$592$	−60.2711	−2.47713
$593$	7.15692	0.293899	0.146950	−	0.989144i	$-0.453054\pi$
$593$	7.15692	0.293899	0.146950	+	0.989144i	$0.453054\pi$
$594$	8.61857	0.353624
$595$	23.3954	0.959119
$596$	59.9400	2.45524
$597$	24.2831	0.993840
$598$	−13.7496	−0.562264
$599$	19.4625	0.795218	0.397609	−	0.917555i	$-0.369840\pi$
$599$	19.4625	0.795218	0.397609	+	0.917555i	$0.369840\pi$
$600$	60.2757	2.46075
$601$	11.5497	0.471121	0.235560	−	0.971860i	$-0.424307\pi$
$601$	11.5497	0.471121	0.235560	+	0.971860i	$0.424307\pi$
$602$	−76.6134	−3.12253
$603$	9.65943	0.393362
$604$	42.7449	1.73926
$605$	−11.1770	−0.454408
$606$	−17.0924	−0.694332
$607$	6.24626	0.253528	0.126764	−	0.991933i	$-0.459541\pi$
$607$	6.24626	0.253528	0.126764	+	0.991933i	$0.459541\pi$
$608$	−104.704	−4.24632
$609$	21.2085	0.859411
$610$	−40.3694	−1.63451
$611$	−2.88995	−0.116915
$612$	17.6679	0.714184
$613$	38.9404	1.57279	0.786393	−	0.617726i	$-0.211946\pi$
$613$	38.9404	1.57279	0.786393	+	0.617726i	$0.211946\pi$
$614$	−65.2501	−2.63328
$615$	−14.2030	−0.572719
$616$	29.5169	1.18927
$617$	−1.00000	−0.0402585
$617$	−1.00000	−0.0402585
$618$	10.4948	0.422162
$619$	24.9618	1.00330	0.501650	−	0.865071i	$-0.332727\pi$
$619$	24.9618	1.00330	0.501650	+	0.865071i	$0.332727\pi$
$620$	30.0651	1.20745
$621$	−27.8606	−1.11801
$622$	63.3121	2.53858
$623$	−18.4970	−0.741068
$624$	25.6079	1.02514
$625$	9.80752	0.392301
$626$	−85.7609	−3.42770
$627$	3.28365	0.131136
$628$	74.7749	2.98384
$629$	15.2327	0.607368
$630$	−10.9484	−0.436195
$631$	19.7957	0.788055	0.394027	−	0.919099i	$-0.371082\pi$
$631$	19.7957	0.788055	0.394027	+	0.919099i	$0.371082\pi$
$632$	−96.6094	−3.84292
$633$	−24.7334	−0.983063
$634$	−24.8724	−0.987811
$635$	−18.0029	−0.714423
$636$	59.6665	2.36593
$637$	20.2244	0.801319
$638$	4.13323	0.163636
$639$	−2.94953	−0.116682
$640$	−59.8350	−2.36518
$641$	−17.1550	−0.677583	−0.338792	−	0.940861i	$-0.610018\pi$
$641$	−17.1550	−0.677583	−0.338792	+	0.940861i	$0.610018\pi$
$642$	−64.2770	−2.53681
$643$	−8.41961	−0.332037	−0.166019	−	0.986123i	$-0.553091\pi$
$643$	−8.41961	−0.332037	−0.166019	+	0.986123i	$0.553091\pi$
$644$	−147.166	−5.79916
$645$	−8.35015	−0.328787
$646$	46.7950	1.84113
$647$	−17.3306	−0.681334	−0.340667	−	0.940184i	$-0.610653\pi$
$647$	−17.3306	−0.681334	−0.340667	+	0.940184i	$0.610653\pi$
$648$	64.4514	2.53189
$649$	−1.61592	−0.0634306
$650$	10.8345	0.424965
$651$	−39.8104	−1.56029
$652$	129.549	5.07355
$653$	−36.5380	−1.42984	−0.714922	−	0.699205i	$-0.753538\pi$
$653$	−36.5380	−1.42984	−0.714922	+	0.699205i	$0.753538\pi$
$654$	64.6128	2.52656
$655$	−9.57086	−0.373964
$656$	−152.900	−5.96974
$657$	4.32540	0.168750
$658$	−41.8088	−1.62988
$659$	24.8115	0.966519	0.483259	−	0.875477i	$-0.339453\pi$
$659$	24.8115	0.966519	0.483259	+	0.875477i	$0.339453\pi$
$660$	4.96184	0.193139
$661$	28.0148	1.08965	0.544825	−	0.838550i	$-0.316596\pi$
$661$	28.0148	1.08965	0.544825	+	0.838550i	$0.316596\pi$
$662$	14.4822	0.562866
$663$	−6.47206	−0.251354
$664$	138.381	5.37024
$665$	−21.4538	−0.831944
$666$	−7.12848	−0.276223
$667$	−13.3612	−0.517347
$668$	88.5309	3.42536
$669$	−10.3680	−0.400851
$670$	38.6591	1.49353
$671$	7.70738	0.297540
$672$	209.500	8.08164
$673$	−27.5077	−1.06035	−0.530173	−	0.847890i	$-0.677873\pi$
$673$	−27.5077	−1.06035	−0.530173	+	0.847890i	$0.677873\pi$
$674$	−86.0545	−3.31469
$675$	21.9538	0.845001
$676$	5.68769	0.218757
$677$	−1.98552	−0.0763097	−0.0381549	−	0.999272i	$-0.512148\pi$
$677$	−1.98552	−0.0763097	−0.0381549	+	0.999272i	$0.512148\pi$
$678$	−22.2318	−0.853806
$679$	−11.5778	−0.444316
$680$	45.8463	1.75813
$681$	4.12074	0.157907
$682$	−7.75849	−0.297088
$683$	−8.55275	−0.327262	−0.163631	−	0.986522i	$-0.552321\pi$
$683$	−8.55275	−0.327262	−0.163631	+	0.986522i	$0.552321\pi$
$684$	−16.2017	−0.619486
$685$	9.01032	0.344267
$686$	191.317	7.30450
$687$	6.73263	0.256866
$688$	−89.8924	−3.42712
$689$	6.95371	0.264915
$690$	−21.6799	−0.825340
$691$	29.8007	1.13367	0.566836	−	0.823831i	$-0.308167\pi$
$691$	29.8007	1.13367	0.566836	+	0.823831i	$0.308167\pi$
$692$	123.587	4.69806
$693$	2.09028	0.0794032
$694$	45.9429	1.74397
$695$	13.8795	0.526479
$696$	41.5607	1.57535
$697$	38.6435	1.46373
$698$	−35.2937	−1.33589
$699$	−30.9353	−1.17008
$700$	115.965	4.38306
$701$	48.3142	1.82480	0.912402	−	0.409296i	$-0.134226\pi$
$701$	48.3142	1.82480	0.912402	+	0.409296i	$0.134226\pi$
$702$	15.5774	0.587932
$703$	−13.9686	−0.526834
$704$	22.0456	0.830874
$705$	−4.55677	−0.171618
$706$	−11.4990	−0.432772
$707$	−21.3209	−0.801855
$708$	−25.0608	−0.941844
$709$	24.5040	0.920266	0.460133	−	0.887850i	$-0.347802\pi$
$709$	24.5040	0.920266	0.460133	+	0.887850i	$0.347802\pi$
$710$	−11.8047	−0.443021
$711$	−6.84153	−0.256577
$712$	−36.2473	−1.35842
$713$	25.0803	0.939264
$714$	−93.6310	−3.50405
$715$	0.578266	0.0216259
$716$	−122.713	−4.58600
$717$	−21.6965	−0.810272
$718$	41.0327	1.53133
$719$	−3.71555	−0.138566	−0.0692832	−	0.997597i	$-0.522071\pi$
$719$	−3.71555	−0.138566	−0.0692832	+	0.997597i	$0.522071\pi$
$720$	−12.8460	−0.478743
$721$	13.0911	0.487538
$722$	9.76919	0.363571
$723$	26.7089	0.993316
$724$	80.1690	2.97946
$725$	10.5284	0.391016
$726$	44.7314	1.66014
$727$	−4.26888	−0.158324	−0.0791619	−	0.996862i	$-0.525224\pi$
$727$	−4.26888	−0.158324	−0.0791619	+	0.996862i	$0.525224\pi$
$728$	53.3496	1.97727
$729$	29.9913	1.11079
$730$	17.3112	0.640715
$731$	22.7191	0.840297
$732$	119.531	4.41800
$733$	−24.4633	−0.903573	−0.451786	−	0.892126i	$-0.649213\pi$
$733$	−24.4633	−0.903573	−0.451786	+	0.892126i	$0.649213\pi$
$734$	−35.9075	−1.32537
$735$	31.8891	1.17625
$736$	−131.983	−4.86497
$737$	−7.38084	−0.271877
$738$	−18.0841	−0.665683
$739$	29.2596	1.07633	0.538167	−	0.842838i	$-0.319117\pi$
$739$	29.2596	1.07633	0.538167	+	0.842838i	$0.319117\pi$
$740$	−21.1075	−0.775928
$741$	5.93494	0.218026
$742$	100.599	3.69310
$743$	21.7369	0.797448	0.398724	−	0.917071i	$-0.369453\pi$
$743$	21.7369	0.797448	0.398724	+	0.917071i	$0.369453\pi$
$744$	−78.0136	−2.86012
$745$	11.0146	0.403544
$746$	−49.8770	−1.82613
$747$	9.79966	0.358551
$748$	−13.5002	−0.493616
$749$	−80.1785	−2.92966
$750$	38.9427	1.42199
$751$	−13.6621	−0.498537	−0.249269	−	0.968434i	$-0.580190\pi$
$751$	−13.6621	−0.498537	−0.249269	+	0.968434i	$0.580190\pi$
$752$	−49.0553	−1.78886
$753$	36.7420	1.33895
$754$	7.47051	0.272060
$755$	7.85482	0.285866
$756$	166.729	6.06389
$757$	2.46350	0.0895376	0.0447688	−	0.998997i	$-0.485745\pi$
$757$	2.46350	0.0895376	0.0447688	+	0.998997i	$0.485745\pi$
$758$	−27.0363	−0.982004
$759$	4.13915	0.150242
$760$	−42.0415	−1.52501
$761$	15.1109	0.547771	0.273886	−	0.961762i	$-0.411691\pi$
$761$	15.1109	0.547771	0.273886	+	0.961762i	$0.411691\pi$
$762$	72.0495	2.61008
$763$	80.5974	2.91782
$764$	−130.930	−4.73686
$765$	3.24667	0.117383
$766$	−40.0347	−1.44651
$767$	−2.92066	−0.105459
$768$	119.242	4.30278
$769$	−10.3266	−0.372388	−0.186194	−	0.982513i	$-0.559615\pi$
$769$	−10.3266	−0.372388	−0.186194	+	0.982513i	$0.559615\pi$
$770$	8.36575	0.301481
$771$	14.8267	0.533969
$772$	−57.5863	−2.07257
$773$	−13.5048	−0.485733	−0.242866	−	0.970060i	$-0.578088\pi$
$773$	−13.5048	−0.485733	−0.242866	+	0.970060i	$0.578088\pi$
$774$	−10.6319	−0.382156
$775$	−19.7629	−0.709905
$776$	−22.6882	−0.814459
$777$	27.9493	1.00268
$778$	−98.5942	−3.53478
$779$	−35.4364	−1.26964
$780$	8.96814	0.321111
$781$	2.25376	0.0806459
$782$	58.9868	2.10936
$783$	15.1373	0.540964
$784$	343.298	12.2606
$785$	13.7407	0.490426
$786$	38.3036	1.36624
$787$	−21.6645	−0.772257	−0.386128	−	0.922445i	$-0.626188\pi$
$787$	−21.6645	−0.772257	−0.386128	+	0.922445i	$0.626188\pi$
$788$	−134.048	−4.77526
$789$	−12.7150	−0.452665
$790$	−27.3812	−0.974181
$791$	−27.7317	−0.986026
$792$	4.09617	0.145551
$793$	13.9305	0.494687
$794$	−80.3637	−2.85200
$795$	10.9644	0.388866
$796$	91.5505	3.24492
$797$	36.3411	1.28727	0.643634	−	0.765333i	$-0.277426\pi$
$797$	36.3411	1.28727	0.643634	+	0.765333i	$0.277426\pi$
$798$	85.8605	3.03943
$799$	12.3981	0.438612
$800$	104.001	3.67700
$801$	−2.56690	−0.0906970
$802$	76.7614	2.71054
$803$	−3.30507	−0.116633
$804$	−114.467	−4.03694
$805$	−27.0433	−0.953152
$806$	−14.0229	−0.493935
$807$	−13.9917	−0.492530
$808$	−41.7810	−1.46985
$809$	22.1365	0.778279	0.389139	−	0.921179i	$-0.372772\pi$
$809$	22.1365	0.778279	0.389139	+	0.921179i	$0.372772\pi$
$810$	18.2669	0.641835
$811$	43.2537	1.51884	0.759421	−	0.650599i	$-0.225482\pi$
$811$	43.2537	1.51884	0.759421	+	0.650599i	$0.225482\pi$
$812$	79.9589	2.80601
$813$	43.2563	1.51706
$814$	5.44693	0.190915
$815$	23.8061	0.833890
$816$	−109.860	−3.84585
$817$	−20.8337	−0.728877
$818$	44.2632	1.54762
$819$	3.77802	0.132015
$820$	−53.5471	−1.86995
$821$	−28.0632	−0.979411	−0.489705	−	0.871888i	$-0.662896\pi$
$821$	−28.0632	−0.979411	−0.489705	+	0.871888i	$0.662896\pi$
$822$	−36.0603	−1.25775
$823$	15.0355	0.524106	0.262053	−	0.965053i	$-0.415600\pi$
$823$	15.0355	0.524106	0.262053	+	0.965053i	$0.415600\pi$
$824$	25.6537	0.893688
$825$	−3.26160	−0.113554
$826$	−42.2530	−1.47017
$827$	7.99169	0.277898	0.138949	−	0.990300i	$-0.455628\pi$
$827$	7.99169	0.277898	0.138949	+	0.990300i	$0.455628\pi$
$828$	−20.4228	−0.709740
$829$	9.94090	0.345262	0.172631	−	0.984987i	$-0.444773\pi$
$829$	9.94090	0.345262	0.172631	+	0.984987i	$0.444773\pi$
$830$	39.2203	1.36136
$831$	8.33173	0.289024
$832$	39.8457	1.38140
$833$	−86.7639	−3.00619
$834$	−55.5472	−1.92344
$835$	16.2685	0.562994
$836$	12.3798	0.428165
$837$	−28.4143	−0.982142
$838$	20.5853	0.711107
$839$	−19.2557	−0.664780	−0.332390	−	0.943142i	$-0.607855\pi$
$839$	−19.2557	−0.664780	−0.332390	+	0.943142i	$0.607855\pi$
$840$	84.1197	2.90241
$841$	−21.7405	−0.749674
$842$	88.3627	3.04518
$843$	40.6976	1.40170
$844$	−93.2482	−3.20974
$845$	1.04517	0.0359550
$846$	−5.80195	−0.199475
$847$	55.7975	1.91722
$848$	118.035	4.05335
$849$	−5.89658	−0.202370
$850$	−46.4808	−1.59428
$851$	−17.6079	−0.603590
$852$	34.9528	1.19746
$853$	−19.3306	−0.661867	−0.330933	−	0.943654i	$-0.607364\pi$
$853$	−19.3306	−0.661867	−0.330933	+	0.943654i	$0.607364\pi$
$854$	201.532	6.89628
$855$	−2.97723	−0.101819
$856$	−157.120	−5.37025
$857$	−37.9255	−1.29551	−0.647755	−	0.761848i	$-0.724292\pi$
$857$	−37.9255	−1.29551	−0.647755	+	0.761848i	$0.724292\pi$
$858$	−2.31428	−0.0790083
$859$	21.9901	0.750292	0.375146	−	0.926966i	$-0.377593\pi$
$859$	21.9901	0.750292	0.375146	+	0.926966i	$0.377593\pi$
$860$	−31.4812	−1.07350
$861$	70.9039	2.41640
$862$	57.8346	1.96986
$863$	−20.3452	−0.692558	−0.346279	−	0.938132i	$-0.612555\pi$
$863$	−20.3452	−0.692558	−0.346279	+	0.938132i	$0.612555\pi$
$864$	149.528	5.08706
$865$	22.7104	0.772175
$866$	−12.8945	−0.438172
$867$	2.11909	0.0719682
$868$	−150.091	−5.09442
$869$	5.22766	0.177336
$870$	11.7792	0.399353
$871$	−13.3403	−0.452019
$872$	157.941	5.34855
$873$	−1.60670	−0.0543784
$874$	−54.0915	−1.82967
$875$	48.5767	1.64219
$876$	−51.2572	−1.73182
$877$	−35.9951	−1.21547	−0.607734	−	0.794141i	$-0.707921\pi$
$877$	−35.9951	−1.21547	−0.607734	+	0.794141i	$0.707921\pi$
$878$	−61.1266	−2.06292
$879$	29.5198	0.995680
$880$	9.81575	0.330889
$881$	7.44088	0.250690	0.125345	−	0.992113i	$-0.459996\pi$
$881$	7.44088	0.250690	0.125345	+	0.992113i	$0.459996\pi$
$882$	40.6031	1.36718
$883$	27.5143	0.925930	0.462965	−	0.886377i	$-0.346786\pi$
$883$	27.5143	0.925930	0.462965	+	0.886377i	$0.346786\pi$
$884$	−24.4006	−0.820680
$885$	−4.60519	−0.154802
$886$	−72.9811	−2.45185
$887$	45.7368	1.53569	0.767845	−	0.640635i	$-0.221329\pi$
$887$	45.7368	1.53569	0.767845	+	0.640635i	$0.221329\pi$
$888$	54.7702	1.83797
$889$	89.8739	3.01427
$890$	−10.2733	−0.344361
$891$	−3.48755	−0.116837
$892$	−39.0889	−1.30879
$893$	−11.3692	−0.380454
$894$	−44.0816	−1.47431
$895$	−22.5498	−0.753756
$896$	298.708	9.97912
$897$	7.48121	0.249790
$898$	5.81510	0.194052
$899$	−13.6267	−0.454477
$900$	16.0929	0.536429
$901$	−29.8319	−0.993843
$902$	13.8182	0.460094
$903$	41.6855	1.38721
$904$	−54.3438	−1.80745
$905$	14.7319	0.489705
$906$	−31.4358	−1.04438
$907$	−39.4481	−1.30985	−0.654927	−	0.755692i	$-0.727300\pi$
$907$	−39.4481	−1.30985	−0.654927	+	0.755692i	$0.727300\pi$
$908$	15.5357	0.515572
$909$	−2.95878	−0.0981365
$910$	15.1205	0.501238
$911$	−33.7942	−1.11965	−0.559825	−	0.828611i	$-0.689132\pi$
$911$	−33.7942	−1.11965	−0.559825	+	0.828611i	$0.689132\pi$
$912$	100.742	3.33591
$913$	−7.48799	−0.247816
$914$	−104.310	−3.45028
$915$	21.9651	0.726144
$916$	25.3829	0.838676
$917$	47.7796	1.57782
$918$	−66.8281	−2.20566
$919$	−40.9481	−1.35075	−0.675377	−	0.737473i	$-0.736019\pi$
$919$	−40.9481	−1.35075	−0.675377	+	0.737473i	$0.736019\pi$
$920$	−52.9948	−1.74719
$921$	35.5027	1.16986
$922$	59.6592	1.96477
$923$	4.07350	0.134081
$924$	−24.7704	−0.814887
$925$	13.8748	0.456199
$926$	−33.5608	−1.10288
$927$	1.81670	0.0596682
$928$	71.7098	2.35399
$929$	19.8992	0.652870	0.326435	−	0.945220i	$-0.394153\pi$
$929$	19.8992	0.652870	0.326435	+	0.945220i	$0.394153\pi$
$930$	−22.1108	−0.725041
$931$	79.5634	2.60758
$932$	−116.630	−3.82036
$933$	−34.4483	−1.12779
$934$	−16.4161	−0.537151
$935$	−2.48080	−0.0811309
$936$	7.40352	0.241991
$937$	−22.5658	−0.737192	−0.368596	−	0.929590i	$-0.620161\pi$
$937$	−22.5658	−0.737192	−0.368596	+	0.929590i	$0.620161\pi$
$938$	−192.993	−6.30146
$939$	46.6627	1.52278
$940$	−17.1796	−0.560338
$941$	−44.2464	−1.44239	−0.721196	−	0.692731i	$-0.756407\pi$
$941$	−44.2464	−1.44239	−0.721196	+	0.692731i	$0.756407\pi$
$942$	−54.9916	−1.79172
$943$	−44.6689	−1.45462
$944$	−49.5765	−1.61358
$945$	30.6383	0.996664
$946$	8.12392	0.264131
$947$	33.7246	1.09590	0.547951	−	0.836510i	$-0.315408\pi$
$947$	33.7246	1.09590	0.547951	+	0.836510i	$0.315408\pi$
$948$	81.0740	2.63316
$949$	−5.97365	−0.193913
$950$	42.6233	1.38288
$951$	13.5332	0.438843
$952$	−228.873	−7.41783
$953$	−13.3167	−0.431370	−0.215685	−	0.976463i	$-0.569198\pi$
$953$	−13.3167	−0.431370	−0.215685	+	0.976463i	$0.569198\pi$
$954$	13.9605	0.451987
$955$	−24.0597	−0.778553
$956$	−81.7990	−2.64557
$957$	−2.24890	−0.0726967
$958$	−100.093	−3.23387
$959$	−44.9812	−1.45252
$960$	62.8272	2.02774
$961$	−5.42128	−0.174880
$962$	9.84490	0.317412
$963$	−11.1267	−0.358552
$964$	100.696	3.24321
$965$	−10.5821	−0.340649
$966$	108.230	3.48225
$967$	59.2567	1.90557	0.952783	−	0.303651i	$-0.0982056\pi$
$967$	59.2567	1.90557	0.952783	+	0.303651i	$0.0982056\pi$
$968$	109.342	3.51439
$969$	−25.4613	−0.817935
$970$	−6.43034	−0.206466
$971$	42.4319	1.36170	0.680852	−	0.732421i	$-0.261609\pi$
$971$	42.4319	1.36170	0.680852	+	0.732421i	$0.261609\pi$
$972$	41.7766	1.33998
$973$	−69.2890	−2.22130
$974$	−19.7862	−0.633990
$975$	−5.89509	−0.188794
$976$	236.462	7.56898
$977$	−4.03113	−0.128967	−0.0644836	−	0.997919i	$-0.520540\pi$
$977$	−4.03113	−0.128967	−0.0644836	+	0.997919i	$0.520540\pi$
$978$	−95.2744	−3.04654
$979$	1.96139	0.0626862
$980$	120.226	3.84049
$981$	11.1848	0.357103
$982$	−25.9320	−0.827523
$983$	34.2016	1.09086	0.545430	−	0.838156i	$-0.316366\pi$
$983$	34.2016	1.09086	0.545430	+	0.838156i	$0.316366\pi$
$984$	138.945	4.42941
$985$	−24.6327	−0.784863
$986$	−32.0490	−1.02065
$987$	22.7482	0.724085
$988$	22.3756	0.711861
$989$	−26.2616	−0.835069
$990$	1.16095	0.0368973
$991$	48.4900	1.54034	0.770168	−	0.637841i	$-0.220172\pi$
$991$	48.4900	1.54034	0.770168	+	0.637841i	$0.220172\pi$
$992$	−134.606	−4.27376
$993$	−7.87980	−0.250058
$994$	58.9311	1.86918
$995$	16.8234	0.533337
$996$	−116.129	−3.67968
$997$	−33.7453	−1.06872	−0.534362	−	0.845256i	$-0.679448\pi$
$997$	−33.7453	−1.06872	−0.534362	+	0.845256i	$0.679448\pi$
$998$	−8.27360	−0.261896
$999$	19.9485	0.631144

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8021.2.a.d.1.2	✓	174

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8021.2.a.d.1.2	✓	174	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:	\( N \)	\(=\)	\( 8021 = 13 \cdot 617 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8021.a (trivial)

\(f(q)\)	\(=\)	\(q-2.77267 q^{2} +1.50862 q^{3} +5.68769 q^{4} +1.04517 q^{5} -4.18289 q^{6} -5.21770 q^{7} -10.2247 q^{8} -0.724079 q^{9} +O(q^{10})\)	\(q-2.77267 q^{2} +1.50862 q^{3} +5.68769 q^{4} +1.04517 q^{5} -4.18289 q^{6} -5.21770 q^{7} -10.2247 q^{8} -0.724079 q^{9} -2.89792 q^{10} +0.553274 q^{11} +8.58054 q^{12} +1.00000 q^{13} +14.4669 q^{14} +1.57676 q^{15} +16.9744 q^{16} -4.29007 q^{17} +2.00763 q^{18} +3.93403 q^{19} +5.94462 q^{20} -7.87150 q^{21} -1.53404 q^{22} +4.95899 q^{23} -15.4252 q^{24} -3.90761 q^{25} -2.77267 q^{26} -5.61820 q^{27} -29.6767 q^{28} -2.69434 q^{29} -4.37184 q^{30} +5.05754 q^{31} -26.6150 q^{32} +0.834677 q^{33} +11.8949 q^{34} -5.45340 q^{35} -4.11833 q^{36} -3.55070 q^{37} -10.9078 q^{38} +1.50862 q^{39} -10.6866 q^{40} -9.00766 q^{41} +21.8251 q^{42} -5.29575 q^{43} +3.14685 q^{44} -0.756787 q^{45} -13.7496 q^{46} -2.88995 q^{47} +25.6079 q^{48} +20.2244 q^{49} +10.8345 q^{50} -6.47206 q^{51} +5.68769 q^{52} +6.95371 q^{53} +15.5774 q^{54} +0.578266 q^{55} +53.3496 q^{56} +5.93494 q^{57} +7.47051 q^{58} -2.92066 q^{59} +8.96814 q^{60} +13.9305 q^{61} -14.0229 q^{62} +3.77802 q^{63} +39.8457 q^{64} +1.04517 q^{65} -2.31428 q^{66} -13.3403 q^{67} -24.4006 q^{68} +7.48121 q^{69} +15.1205 q^{70} +4.07350 q^{71} +7.40352 q^{72} -5.97365 q^{73} +9.84490 q^{74} -5.89509 q^{75} +22.3756 q^{76} -2.88682 q^{77} -4.18289 q^{78} +9.44860 q^{79} +17.7412 q^{80} -6.30347 q^{81} +24.9753 q^{82} -13.5340 q^{83} -44.7707 q^{84} -4.48386 q^{85} +14.6834 q^{86} -4.06472 q^{87} -5.65708 q^{88} +3.54506 q^{89} +2.09832 q^{90} -5.21770 q^{91} +28.2052 q^{92} +7.62989 q^{93} +8.01287 q^{94} +4.11174 q^{95} -40.1518 q^{96} +2.21895 q^{97} -56.0755 q^{98} -0.400614 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 174 q + 6 q^{2} + 37 q^{3} + 214 q^{4} + 10 q^{5} + 12 q^{6} + 28 q^{7} + 15 q^{8} + 211 q^{9}+O(q^{10}) \) 174 * q + 6 * q^2 + 37 * q^3 + 214 * q^4 + 10 * q^5 + 12 * q^6 + 28 * q^7 + 15 * q^8 + 211 * q^9	\( 174 q + 6 q^{2} + 37 q^{3} + 214 q^{4} + 10 q^{5} + 12 q^{6} + 28 q^{7} + 15 q^{8} + 211 q^{9} + 47 q^{10} + 47 q^{11} + 81 q^{12} + 174 q^{13} + 22 q^{14} + 26 q^{15} + 286 q^{16} + 27 q^{17} + 22 q^{18} + 91 q^{19} + 18 q^{20} + 8 q^{21} + 58 q^{22} + 62 q^{23} + 24 q^{24} + 244 q^{25} + 6 q^{26} + 139 q^{27} + 43 q^{28} + 42 q^{29} + 31 q^{30} + 82 q^{31} + 11 q^{32} + 12 q^{33} + 50 q^{34} + 74 q^{35} + 310 q^{36} + 47 q^{37} + 10 q^{38} + 37 q^{39} + 118 q^{40} + 16 q^{41} + 26 q^{42} + 136 q^{43} + 74 q^{44} + 18 q^{45} + 53 q^{46} + 15 q^{47} + 132 q^{48} + 254 q^{49} - 5 q^{50} + 121 q^{51} + 214 q^{52} + 39 q^{53} + 30 q^{54} + 188 q^{55} + 55 q^{56} + 11 q^{57} + 32 q^{58} + 58 q^{59} + 16 q^{60} + 128 q^{61} + 27 q^{62} + 42 q^{63} + 423 q^{64} + 10 q^{65} + 4 q^{66} + 132 q^{67} + 52 q^{68} + 63 q^{69} - 8 q^{70} + 78 q^{71} + 2 q^{72} + 21 q^{73} - 16 q^{74} + 188 q^{75} + 160 q^{76} + 20 q^{77} + 12 q^{78} + 232 q^{79} + 2 q^{80} + 302 q^{81} + 115 q^{82} + 18 q^{83} - 26 q^{84} + 47 q^{85} + 27 q^{86} + 127 q^{87} + 163 q^{88} + 14 q^{90} + 28 q^{91} + 68 q^{92} + 15 q^{93} + 91 q^{94} + 75 q^{95} - 26 q^{96} + 34 q^{97} - 60 q^{98} + 181 q^{99}+O(q^{100}) \) 174 * q + 6 * q^2 + 37 * q^3 + 214 * q^4 + 10 * q^5 + 12 * q^6 + 28 * q^7 + 15 * q^8 + 211 * q^9 + 47 * q^10 + 47 * q^11 + 81 * q^12 + 174 * q^13 + 22 * q^14 + 26 * q^15 + 286 * q^16 + 27 * q^17 + 22 * q^18 + 91 * q^19 + 18 * q^20 + 8 * q^21 + 58 * q^22 + 62 * q^23 + 24 * q^24 + 244 * q^25 + 6 * q^26 + 139 * q^27 + 43 * q^28 + 42 * q^29 + 31 * q^30 + 82 * q^31 + 11 * q^32 + 12 * q^33 + 50 * q^34 + 74 * q^35 + 310 * q^36 + 47 * q^37 + 10 * q^38 + 37 * q^39 + 118 * q^40 + 16 * q^41 + 26 * q^42 + 136 * q^43 + 74 * q^44 + 18 * q^45 + 53 * q^46 + 15 * q^47 + 132 * q^48 + 254 * q^49 - 5 * q^50 + 121 * q^51 + 214 * q^52 + 39 * q^53 + 30 * q^54 + 188 * q^55 + 55 * q^56 + 11 * q^57 + 32 * q^58 + 58 * q^59 + 16 * q^60 + 128 * q^61 + 27 * q^62 + 42 * q^63 + 423 * q^64 + 10 * q^65 + 4 * q^66 + 132 * q^67 + 52 * q^68 + 63 * q^69 - 8 * q^70 + 78 * q^71 + 2 * q^72 + 21 * q^73 - 16 * q^74 + 188 * q^75 + 160 * q^76 + 20 * q^77 + 12 * q^78 + 232 * q^79 + 2 * q^80 + 302 * q^81 + 115 * q^82 + 18 * q^83 - 26 * q^84 + 47 * q^85 + 27 * q^86 + 127 * q^87 + 163 * q^88 + 14 * q^90 + 28 * q^91 + 68 * q^92 + 15 * q^93 + 91 * q^94 + 75 * q^95 - 26 * q^96 + 34 * q^97 - 60 * q^98 + 181 * q^99

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