LMFDB - Embedded newform 8021.2.a.d.1.20

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			1.20
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)

$f(q)$	$=$	$q-2.31194 q^{2} -2.08272 q^{3} +3.34506 q^{4} -3.48244 q^{5} +4.81513 q^{6} +3.73510 q^{7} -3.10970 q^{8} +1.33774 q^{9} +O(q^{10})$	\(q-2.31194 q^{2} -2.08272 q^{3} +3.34506 q^{4} -3.48244 q^{5} +4.81513 q^{6} +3.73510 q^{7} -3.10970 q^{8} +1.33774 q^{9} +8.05119 q^{10} -3.22185 q^{11} -6.96685 q^{12} +1.00000 q^{13} -8.63533 q^{14} +7.25296 q^{15} +0.499321 q^{16} -6.29151 q^{17} -3.09278 q^{18} +8.26055 q^{19} -11.6490 q^{20} -7.77919 q^{21} +7.44872 q^{22} -1.40063 q^{23} +6.47666 q^{24} +7.12738 q^{25} -2.31194 q^{26} +3.46202 q^{27} +12.4942 q^{28} +0.104282 q^{29} -16.7684 q^{30} -3.75644 q^{31} +5.06501 q^{32} +6.71022 q^{33} +14.5456 q^{34} -13.0073 q^{35} +4.47483 q^{36} +1.86304 q^{37} -19.0979 q^{38} -2.08272 q^{39} +10.8294 q^{40} +2.78685 q^{41} +17.9850 q^{42} -12.2119 q^{43} -10.7773 q^{44} -4.65861 q^{45} +3.23818 q^{46} +5.50461 q^{47} -1.03995 q^{48} +6.95100 q^{49} -16.4781 q^{50} +13.1035 q^{51} +3.34506 q^{52} -9.25113 q^{53} -8.00399 q^{54} +11.2199 q^{55} -11.6151 q^{56} -17.2045 q^{57} -0.241093 q^{58} +5.78862 q^{59} +24.2616 q^{60} -1.30231 q^{61} +8.68467 q^{62} +4.99661 q^{63} -12.7086 q^{64} -3.48244 q^{65} -15.5136 q^{66} +7.35654 q^{67} -21.0455 q^{68} +2.91713 q^{69} +30.0720 q^{70} -3.19441 q^{71} -4.15998 q^{72} +5.48180 q^{73} -4.30723 q^{74} -14.8444 q^{75} +27.6321 q^{76} -12.0339 q^{77} +4.81513 q^{78} -9.94242 q^{79} -1.73886 q^{80} -11.2237 q^{81} -6.44302 q^{82} -0.621818 q^{83} -26.0219 q^{84} +21.9098 q^{85} +28.2333 q^{86} -0.217190 q^{87} +10.0190 q^{88} +15.4831 q^{89} +10.7704 q^{90} +3.73510 q^{91} -4.68520 q^{92} +7.82364 q^{93} -12.7263 q^{94} -28.7669 q^{95} -10.5490 q^{96} -0.770175 q^{97} -16.0703 q^{98} -4.31000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.31194	−1.63479	−0.817394	−	0.576079i	$-0.804582\pi$
$2$	−2.31194	−1.63479	−0.817394	+	0.576079i	$0.804582\pi$
$3$	−2.08272	−1.20246	−0.601231	−	0.799075i	$-0.705323\pi$
$3$	−2.08272	−1.20246	−0.601231	+	0.799075i	$0.705323\pi$
$4$	3.34506	1.67253
$5$	−3.48244	−1.55739	−0.778697	−	0.627400i	$-0.784119\pi$
$5$	−3.48244	−1.55739	−0.778697	+	0.627400i	$0.784119\pi$
$6$	4.81513	1.96577
$7$	3.73510	1.41174	0.705868	−	0.708343i	$-0.250557\pi$
$7$	3.73510	1.41174	0.705868	+	0.708343i	$0.250557\pi$
$8$	−3.10970	−1.09945
$9$	1.33774	0.445914
$10$	8.05119	2.54601
$11$	−3.22185	−0.971424	−0.485712	−	0.874119i	$-0.661440\pi$
$11$	−3.22185	−0.971424	−0.485712	+	0.874119i	$0.661440\pi$
$12$	−6.96685	−2.01116
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−8.63533	−2.30789
$15$	7.25296	1.87271
$16$	0.499321	0.124830
$17$	−6.29151	−1.52592	−0.762958	−	0.646449i	$-0.776254\pi$
$17$	−6.29151	−1.52592	−0.762958	+	0.646449i	$0.776254\pi$
$18$	−3.09278	−0.728975
$19$	8.26055	1.89510	0.947550	−	0.319608i	$-0.103551\pi$
$19$	8.26055	1.89510	0.947550	+	0.319608i	$0.103551\pi$
$20$	−11.6490	−2.60479
$21$	−7.77919	−1.69756
$22$	7.44872	1.58807
$23$	−1.40063	−0.292052	−0.146026	−	0.989281i	$-0.546648\pi$
$23$	−1.40063	−0.292052	−0.146026	+	0.989281i	$0.546648\pi$
$24$	6.47666	1.32204
$25$	7.12738	1.42548
$26$	−2.31194	−0.453409
$27$	3.46202	0.666267
$28$	12.4942	2.36117
$29$	0.104282	0.0193646	0.00968232	−	0.999953i	$-0.496918\pi$
$29$	0.104282	0.0193646	0.00968232	+	0.999953i	$0.496918\pi$
$30$	−16.7684	−3.06148
$31$	−3.75644	−0.674677	−0.337338	−	0.941383i	$-0.609527\pi$
$31$	−3.75644	−0.674677	−0.337338	+	0.941383i	$0.609527\pi$
$32$	5.06501	0.895375
$33$	6.71022	1.16810
$34$	14.5456	2.49455
$35$	−13.0073	−2.19863
$36$	4.47483	0.745806
$37$	1.86304	0.306282	0.153141	−	0.988204i	$-0.451061\pi$
$37$	1.86304	0.306282	0.153141	+	0.988204i	$0.451061\pi$
$38$	−19.0979	−3.09809
$39$	−2.08272	−0.333503
$40$	10.8294	1.71227
$41$	2.78685	0.435232	0.217616	−	0.976034i	$-0.430172\pi$
$41$	2.78685	0.435232	0.217616	+	0.976034i	$0.430172\pi$
$42$	17.9850	2.77515
$43$	−12.2119	−1.86230	−0.931152	−	0.364631i	$-0.881195\pi$
$43$	−12.2119	−1.86230	−0.931152	+	0.364631i	$0.881195\pi$
$44$	−10.7773	−1.62474
$45$	−4.65861	−0.694464
$46$	3.23818	0.477443
$47$	5.50461	0.802929	0.401465	−	0.915875i	$-0.368501\pi$
$47$	5.50461	0.802929	0.401465	+	0.915875i	$0.368501\pi$
$48$	−1.03995	−0.150104
$49$	6.95100	0.993000
$50$	−16.4781	−2.33035
$51$	13.1035	1.83485
$52$	3.34506	0.463877
$53$	−9.25113	−1.27074	−0.635370	−	0.772208i	$-0.719152\pi$
$53$	−9.25113	−1.27074	−0.635370	+	0.772208i	$0.719152\pi$
$54$	−8.00399	−1.08921
$55$	11.2199	1.51289
$56$	−11.6151	−1.55213
$57$	−17.2045	−2.27879
$58$	−0.241093	−0.0316571
$59$	5.78862	0.753614	0.376807	−	0.926292i	$-0.377022\pi$
$59$	5.78862	0.753614	0.376807	+	0.926292i	$0.377022\pi$
$60$	24.2616	3.13216
$61$	−1.30231	−0.166744	−0.0833719	−	0.996519i	$-0.526569\pi$
$61$	−1.30231	−0.166744	−0.0833719	+	0.996519i	$0.526569\pi$
$62$	8.68467	1.10295
$63$	4.99661	0.629513
$64$	−12.7086	−1.58858
$65$	−3.48244	−0.431943
$66$	−15.5136	−1.90960
$67$	7.35654	0.898745	0.449372	−	0.893345i	$-0.351648\pi$
$67$	7.35654	0.898745	0.449372	+	0.893345i	$0.351648\pi$
$68$	−21.0455	−2.55214
$69$	2.91713	0.351181
$70$	30.0720	3.59429
$71$	−3.19441	−0.379107	−0.189554	−	0.981870i	$-0.560704\pi$
$71$	−3.19441	−0.379107	−0.189554	+	0.981870i	$0.560704\pi$
$72$	−4.15998	−0.490259
$73$	5.48180	0.641597	0.320798	−	0.947148i	$-0.396049\pi$
$73$	5.48180	0.641597	0.320798	+	0.947148i	$0.396049\pi$
$74$	−4.30723	−0.500706
$75$	−14.8444	−1.71408
$76$	27.6321	3.16961
$77$	−12.0339	−1.37139
$78$	4.81513	0.545206
$79$	−9.94242	−1.11861	−0.559305	−	0.828962i	$-0.688932\pi$
$79$	−9.94242	−1.11861	−0.559305	+	0.828962i	$0.688932\pi$
$80$	−1.73886	−0.194410
$81$	−11.2237	−1.24707
$82$	−6.44302	−0.711512
$83$	−0.621818	−0.0682534	−0.0341267	−	0.999418i	$-0.510865\pi$
$83$	−0.621818	−0.0682534	−0.0341267	+	0.999418i	$0.510865\pi$
$84$	−26.0219	−2.83922
$85$	21.9098	2.37645
$86$	28.2333	3.04447
$87$	−0.217190	−0.0232852
$88$	10.0190	1.06803
$89$	15.4831	1.64120	0.820602	−	0.571500i	$-0.193638\pi$
$89$	15.4831	1.64120	0.820602	+	0.571500i	$0.193638\pi$
$90$	10.7704	1.13530
$91$	3.73510	0.391545
$92$	−4.68520	−0.488466
$93$	7.82364	0.811273
$94$	−12.7263	−1.31262
$95$	−28.7669	−2.95142
$96$	−10.5490	−1.07665
$97$	−0.770175	−0.0781994	−0.0390997	−	0.999235i	$-0.512449\pi$
$97$	−0.770175	−0.0781994	−0.0390997	+	0.999235i	$0.512449\pi$
$98$	−16.0703	−1.62334
$99$	−4.31000	−0.433172
$100$	23.8415	2.38415
$101$	1.34800	0.134131	0.0670655	−	0.997749i	$-0.478636\pi$
$101$	1.34800	0.134131	0.0670655	+	0.997749i	$0.478636\pi$
$102$	−30.2945	−2.99960
$103$	2.83607	0.279446	0.139723	−	0.990191i	$-0.455379\pi$
$103$	2.83607	0.279446	0.139723	+	0.990191i	$0.455379\pi$
$104$	−3.10970	−0.304932
$105$	27.0906	2.64377
$106$	21.3880	2.07739
$107$	11.3650	1.09869	0.549346	−	0.835595i	$-0.314877\pi$
$107$	11.3650	1.09869	0.549346	+	0.835595i	$0.314877\pi$
$108$	11.5807	1.11435
$109$	4.13841	0.396387	0.198194	−	0.980163i	$-0.436492\pi$
$109$	4.13841	0.396387	0.198194	+	0.980163i	$0.436492\pi$
$110$	−25.9397	−2.47325
$111$	−3.88020	−0.368292
$112$	1.86502	0.176227
$113$	7.66681	0.721233	0.360616	−	0.932714i	$-0.382566\pi$
$113$	7.66681	0.721233	0.360616	+	0.932714i	$0.382566\pi$
$114$	39.7756	3.72533
$115$	4.87762	0.454840
$116$	0.348829	0.0323880
$117$	1.33774	0.123674
$118$	−13.3829	−1.23200
$119$	−23.4994	−2.15419
$120$	−22.5546	−2.05894
$121$	−0.619692	−0.0563357
$122$	3.01086	0.272591
$123$	−5.80423	−0.523350
$124$	−12.5655	−1.12842
$125$	−7.40849	−0.662635
$126$	−11.5519	−1.02912
$127$	13.6763	1.21358	0.606788	−	0.794864i	$-0.292458\pi$
$127$	13.6763	1.21358	0.606788	+	0.794864i	$0.292458\pi$
$128$	19.2516	1.70161
$129$	25.4341	2.23935
$130$	8.05119	0.706136
$131$	13.7127	1.19809	0.599043	−	0.800717i	$-0.295548\pi$
$131$	13.7127	1.19809	0.599043	+	0.800717i	$0.295548\pi$
$132$	22.4461	1.95368
$133$	30.8540	2.67538
$134$	−17.0079	−1.46926
$135$	−12.0563	−1.03764
$136$	19.5647	1.67766
$137$	−12.9073	−1.10275	−0.551374	−	0.834258i	$-0.685896\pi$
$137$	−12.9073	−1.10275	−0.551374	+	0.834258i	$0.685896\pi$
$138$	−6.74423	−0.574107
$139$	3.92133	0.332603	0.166302	−	0.986075i	$-0.446817\pi$
$139$	3.92133	0.332603	0.166302	+	0.986075i	$0.446817\pi$
$140$	−43.5101	−3.67728
$141$	−11.4646	−0.965492
$142$	7.38529	0.619760
$143$	−3.22185	−0.269425
$144$	0.667963	0.0556636
$145$	−0.363155	−0.0301584
$146$	−12.6736	−1.04887
$147$	−14.4770	−1.19404
$148$	6.23198	0.512266
$149$	−0.270485	−0.0221590	−0.0110795	−	0.999939i	$-0.503527\pi$
$149$	−0.270485	−0.0221590	−0.0110795	+	0.999939i	$0.503527\pi$
$150$	34.3193	2.80216
$151$	−13.7367	−1.11787	−0.558937	−	0.829210i	$-0.688791\pi$
$151$	−13.7367	−1.11787	−0.558937	+	0.829210i	$0.688791\pi$
$152$	−25.6879	−2.08356
$153$	−8.41642	−0.680427
$154$	27.8217	2.24194
$155$	13.0816	1.05074
$156$	−6.96685	−0.557794
$157$	−6.40514	−0.511186	−0.255593	−	0.966784i	$-0.582271\pi$
$157$	−6.40514	−0.511186	−0.255593	+	0.966784i	$0.582271\pi$
$158$	22.9863	1.82869
$159$	19.2676	1.52802
$160$	−17.6386	−1.39445
$161$	−5.23151	−0.412301
$162$	25.9484	2.03870
$163$	−11.8260	−0.926282	−0.463141	−	0.886284i	$-0.653278\pi$
$163$	−11.8260	−0.926282	−0.463141	+	0.886284i	$0.653278\pi$
$164$	9.32218	0.727940
$165$	−23.3679	−1.81919
$166$	1.43761	0.111580
$167$	−15.4331	−1.19425	−0.597126	−	0.802147i	$-0.703691\pi$
$167$	−15.4331	−1.19425	−0.597126	+	0.802147i	$0.703691\pi$
$168$	24.1910	1.86638
$169$	1.00000	0.0769231
$170$	−50.6541	−3.88499
$171$	11.0505	0.845052
$172$	−40.8497	−3.11476
$173$	20.1029	1.52840	0.764199	−	0.644980i	$-0.223134\pi$
$173$	20.1029	1.52840	0.764199	+	0.644980i	$0.223134\pi$
$174$	0.502131	0.0380664
$175$	26.6215	2.01240
$176$	−1.60874	−0.121263
$177$	−12.0561	−0.906192
$178$	−35.7960	−2.68302
$179$	21.2247	1.58641	0.793206	−	0.608953i	$-0.208410\pi$
$179$	21.2247	1.58641	0.793206	+	0.608953i	$0.208410\pi$
$180$	−15.5833	−1.16151
$181$	−16.5257	−1.22834	−0.614171	−	0.789173i	$-0.710510\pi$
$181$	−16.5257	−1.22834	−0.614171	+	0.789173i	$0.710510\pi$
$182$	−8.63533	−0.640093
$183$	2.71235	0.200503
$184$	4.35555	0.321096
$185$	−6.48792	−0.477001
$186$	−18.0878	−1.32626
$187$	20.2703	1.48231
$188$	18.4133	1.34292
$189$	12.9310	0.940593
$190$	66.5072	4.82494
$191$	−25.3069	−1.83115	−0.915573	−	0.402153i	$-0.868262\pi$
$191$	−25.3069	−1.83115	−0.915573	+	0.402153i	$0.868262\pi$
$192$	26.4686	1.91021
$193$	−15.5677	−1.12059	−0.560296	−	0.828293i	$-0.689312\pi$
$193$	−15.5677	−1.12059	−0.560296	+	0.828293i	$0.689312\pi$
$194$	1.78060	0.127839
$195$	7.25296	0.519395
$196$	23.2515	1.66082
$197$	−22.5722	−1.60820	−0.804102	−	0.594491i	$-0.797354\pi$
$197$	−22.5722	−1.60820	−0.804102	+	0.594491i	$0.797354\pi$
$198$	9.96447	0.708144
$199$	−1.22742	−0.0870092	−0.0435046	−	0.999053i	$-0.513852\pi$
$199$	−1.22742	−0.0870092	−0.0435046	+	0.999053i	$0.513852\pi$
$200$	−22.1641	−1.56724
$201$	−15.3217	−1.08071
$202$	−3.11649	−0.219276
$203$	0.389503	0.0273378
$204$	43.8320	3.06885
$205$	−9.70502	−0.677828
$206$	−6.55682	−0.456835
$207$	−1.87369	−0.130230
$208$	0.499321	0.0346217
$209$	−26.6142	−1.84095
$210$	−62.6317	−4.32200
$211$	−3.06953	−0.211315	−0.105658	−	0.994403i	$-0.533695\pi$
$211$	−3.06953	−0.211315	−0.105658	+	0.994403i	$0.533695\pi$
$212$	−30.9456	−2.12535
$213$	6.65308	0.455862
$214$	−26.2751	−1.79613
$215$	42.5274	2.90034
$216$	−10.7659	−0.732525
$217$	−14.0307	−0.952466
$218$	−9.56774	−0.648009
$219$	−11.4171	−0.771495
$220$	37.5312	2.53036
$221$	−6.29151	−0.423213
$222$	8.97078	0.602079
$223$	−18.6339	−1.24782	−0.623908	−	0.781498i	$-0.714456\pi$
$223$	−18.6339	−1.24782	−0.623908	+	0.781498i	$0.714456\pi$
$224$	18.9183	1.26403
$225$	9.53460	0.635640
$226$	−17.7252	−1.17906
$227$	−1.37119	−0.0910092	−0.0455046	−	0.998964i	$-0.514490\pi$
$227$	−1.37119	−0.0910092	−0.0455046	+	0.998964i	$0.514490\pi$
$228$	−57.5500	−3.81134
$229$	0.0891121	0.00588869	0.00294435	−	0.999996i	$-0.499063\pi$
$229$	0.0891121	0.00588869	0.00294435	+	0.999996i	$0.499063\pi$
$230$	−11.2768	−0.743567
$231$	25.0634	1.64905
$232$	−0.324286	−0.0212904
$233$	−3.22047	−0.210980	−0.105490	−	0.994420i	$-0.533641\pi$
$233$	−3.22047	−0.210980	−0.105490	+	0.994420i	$0.533641\pi$
$234$	−3.09278	−0.202181
$235$	−19.1695	−1.25048
$236$	19.3633	1.26044
$237$	20.7073	1.34508
$238$	54.3293	3.52164
$239$	−20.6504	−1.33576	−0.667880	−	0.744269i	$-0.732798\pi$
$239$	−20.6504	−1.33576	−0.667880	+	0.744269i	$0.732798\pi$
$240$	3.62156	0.233771
$241$	−7.03951	−0.453455	−0.226727	−	0.973958i	$-0.572803\pi$
$241$	−7.03951	−0.453455	−0.226727	+	0.973958i	$0.572803\pi$
$242$	1.43269	0.0920969
$243$	12.9897	0.833293
$244$	−4.35631	−0.278884
$245$	−24.2064	−1.54649
$246$	13.4190	0.855567
$247$	8.26055	0.525606
$248$	11.6814	0.741771
$249$	1.29508	0.0820722
$250$	17.1280	1.08327
$251$	−18.3210	−1.15641	−0.578207	−	0.815890i	$-0.696247\pi$
$251$	−18.3210	−1.15641	−0.578207	+	0.815890i	$0.696247\pi$
$252$	16.7140	1.05288
$253$	4.51263	0.283706
$254$	−31.6188	−1.98394
$255$	−45.6321	−2.85759
$256$	−19.0912	−1.19320
$257$	14.8894	0.928777	0.464389	−	0.885632i	$-0.346274\pi$
$257$	14.8894	0.928777	0.464389	+	0.885632i	$0.346274\pi$
$258$	−58.8022	−3.66086
$259$	6.95864	0.432389
$260$	−11.6490	−0.722439
$261$	0.139502	0.00863497
$262$	−31.7030	−1.95861
$263$	−27.6156	−1.70285	−0.851426	−	0.524474i	$-0.824262\pi$
$263$	−27.6156	−1.70285	−0.851426	+	0.524474i	$0.824262\pi$
$264$	−20.8668	−1.28426
$265$	32.2165	1.97904
$266$	−71.3326	−4.37368
$267$	−32.2470	−1.97349
$268$	24.6081	1.50318
$269$	14.5837	0.889184	0.444592	−	0.895733i	$-0.353349\pi$
$269$	14.5837	0.889184	0.444592	+	0.895733i	$0.353349\pi$
$270$	27.8734	1.69632
$271$	−21.9051	−1.33064	−0.665320	−	0.746558i	$-0.731705\pi$
$271$	−21.9051	−1.33064	−0.665320	+	0.746558i	$0.731705\pi$
$272$	−3.14148	−0.190480
$273$	−7.77919	−0.470818
$274$	29.8409	1.80276
$275$	−22.9634	−1.38474
$276$	9.75799	0.587362
$277$	−2.77705	−0.166856	−0.0834282	−	0.996514i	$-0.526587\pi$
$277$	−2.77705	−0.166856	−0.0834282	+	0.996514i	$0.526587\pi$
$278$	−9.06589	−0.543736
$279$	−5.02515	−0.300848
$280$	40.4488	2.41728
$281$	2.59004	0.154509	0.0772543	−	0.997011i	$-0.475385\pi$
$281$	2.59004	0.154509	0.0772543	+	0.997011i	$0.475385\pi$
$282$	26.5054	1.57837
$283$	−25.1856	−1.49713	−0.748565	−	0.663062i	$-0.769257\pi$
$283$	−25.1856	−1.49713	−0.748565	+	0.663062i	$0.769257\pi$
$284$	−10.6855	−0.634069
$285$	59.9135	3.54897
$286$	7.44872	0.440452
$287$	10.4092	0.614433
$288$	6.77568	0.399261
$289$	22.5831	1.32842
$290$	0.839593	0.0493026
$291$	1.60406	0.0940318
$292$	18.3370	1.07309
$293$	−27.9599	−1.63343	−0.816717	−	0.577038i	$-0.804208\pi$
$293$	−27.9599	−1.63343	−0.816717	+	0.577038i	$0.804208\pi$
$294$	33.4700	1.95201
$295$	−20.1585	−1.17367
$296$	−5.79350	−0.336740
$297$	−11.1541	−0.647228
$298$	0.625345	0.0362253
$299$	−1.40063	−0.0810007
$300$	−49.6554	−2.86686
$301$	−45.6129	−2.62908
$302$	31.7583	1.82749
$303$	−2.80751	−0.161287
$304$	4.12467	0.236566
$305$	4.53522	0.259686
$306$	19.4583	1.11235
$307$	−9.70263	−0.553758	−0.276879	−	0.960905i	$-0.589300\pi$
$307$	−9.70263	−0.553758	−0.276879	+	0.960905i	$0.589300\pi$
$308$	−40.2543	−2.29370
$309$	−5.90675	−0.336023
$310$	−30.2438	−1.71773
$311$	18.6039	1.05493	0.527466	−	0.849576i	$-0.323142\pi$
$311$	18.6039	1.05493	0.527466	+	0.849576i	$0.323142\pi$
$312$	6.47666	0.366669
$313$	6.48153	0.366358	0.183179	−	0.983080i	$-0.441361\pi$
$313$	6.48153	0.366358	0.183179	+	0.983080i	$0.441361\pi$
$314$	14.8083	0.835681
$315$	−17.4004	−0.980400
$316$	−33.2580	−1.87091
$317$	25.2738	1.41952	0.709759	−	0.704445i	$-0.248804\pi$
$317$	25.2738	1.41952	0.709759	+	0.704445i	$0.248804\pi$
$318$	−44.5454	−2.49798
$319$	−0.335980	−0.0188113
$320$	44.2570	2.47404
$321$	−23.6701	−1.32114
$322$	12.0949	0.674024
$323$	−51.9713	−2.89176
$324$	−37.5439	−2.08577
$325$	7.12738	0.395356
$326$	27.3410	1.51428
$327$	−8.61916	−0.476641
$328$	−8.66627	−0.478515
$329$	20.5603	1.13352
$330$	54.0253	2.97399
$331$	1.92783	0.105963	0.0529816	−	0.998595i	$-0.483128\pi$
$331$	1.92783	0.105963	0.0529816	+	0.998595i	$0.483128\pi$
$332$	−2.08002	−0.114156
$333$	2.49227	0.136575
$334$	35.6805	1.95235
$335$	−25.6187	−1.39970
$336$	−3.88431	−0.211907
$337$	19.4572	1.05990	0.529952	−	0.848028i	$-0.322210\pi$
$337$	19.4572	1.05990	0.529952	+	0.848028i	$0.322210\pi$
$338$	−2.31194	−0.125753
$339$	−15.9678	−0.867255
$340$	73.2897	3.97469
$341$	12.1027	0.655397
$342$	−25.5481	−1.38148
$343$	−0.183032	−0.00988283
$344$	37.9755	2.04750
$345$	−10.1587	−0.546928
$346$	−46.4768	−2.49861
$347$	−8.11935	−0.435870	−0.217935	−	0.975963i	$-0.569932\pi$
$347$	−8.11935	−0.435870	−0.217935	+	0.975963i	$0.569932\pi$
$348$	−0.726515	−0.0389453
$349$	−2.90878	−0.155703	−0.0778516	−	0.996965i	$-0.524806\pi$
$349$	−2.90878	−0.155703	−0.0778516	+	0.996965i	$0.524806\pi$
$350$	−61.5473	−3.28984
$351$	3.46202	0.184789
$352$	−16.3187	−0.869789
$353$	19.4860	1.03713	0.518567	−	0.855037i	$-0.326466\pi$
$353$	19.4860	1.03713	0.518567	+	0.855037i	$0.326466\pi$
$354$	27.8730	1.48143
$355$	11.1244	0.590419
$356$	51.7919	2.74497
$357$	48.9429	2.59033
$358$	−49.0703	−2.59345
$359$	−8.12787	−0.428973	−0.214486	−	0.976727i	$-0.568808\pi$
$359$	−8.12787	−0.428973	−0.214486	+	0.976727i	$0.568808\pi$
$360$	14.4869	0.763526
$361$	49.2367	2.59140
$362$	38.2063	2.00808
$363$	1.29065	0.0677415
$364$	12.4942	0.654872
$365$	−19.0901	−0.999219
$366$	−6.27080	−0.327780
$367$	2.05523	0.107282	0.0536412	−	0.998560i	$-0.482917\pi$
$367$	2.05523	0.107282	0.0536412	+	0.998560i	$0.482917\pi$
$368$	−0.699365	−0.0364569
$369$	3.72808	0.194076
$370$	14.9997	0.779796
$371$	−34.5539	−1.79395
$372$	26.1706	1.35688
$373$	−19.8897	−1.02985	−0.514924	−	0.857236i	$-0.672180\pi$
$373$	−19.8897	−1.02985	−0.514924	+	0.857236i	$0.672180\pi$
$374$	−46.8637	−2.42326
$375$	15.4298	0.796793
$376$	−17.1177	−0.882778
$377$	0.104282	0.00537079
$378$	−29.8957	−1.53767
$379$	26.5419	1.36336	0.681682	−	0.731649i	$-0.261249\pi$
$379$	26.5419	1.36336	0.681682	+	0.731649i	$0.261249\pi$
$380$	−96.2270	−4.93634
$381$	−28.4840	−1.45928
$382$	58.5081	2.99353
$383$	−24.8137	−1.26792	−0.633962	−	0.773365i	$-0.718572\pi$
$383$	−24.8137	−1.26792	−0.633962	+	0.773365i	$0.718572\pi$
$384$	−40.0957	−2.04613
$385$	41.9075	2.13580
$386$	35.9917	1.83193
$387$	−16.3364	−0.830428
$388$	−2.57628	−0.130791
$389$	10.8954	0.552416	0.276208	−	0.961098i	$-0.410922\pi$
$389$	10.8954	0.552416	0.276208	+	0.961098i	$0.410922\pi$
$390$	−16.7684	−0.849101
$391$	8.81209	0.445647
$392$	−21.6155	−1.09175
$393$	−28.5598	−1.44065
$394$	52.1856	2.62907
$395$	34.6239	1.74212
$396$	−14.4172	−0.724493
$397$	−10.2710	−0.515485	−0.257742	−	0.966214i	$-0.582979\pi$
$397$	−10.2710	−0.515485	−0.257742	+	0.966214i	$0.582979\pi$
$398$	2.83771	0.142242
$399$	−64.2604	−3.21704
$400$	3.55885	0.177943
$401$	−10.7811	−0.538384	−0.269192	−	0.963086i	$-0.586757\pi$
$401$	−10.7811	−0.538384	−0.269192	+	0.963086i	$0.586757\pi$
$402$	35.4227	1.76673
$403$	−3.75644	−0.187122
$404$	4.50915	0.224338
$405$	39.0858	1.94219
$406$	−0.900508	−0.0446915
$407$	−6.00243	−0.297529
$408$	−40.7480	−2.01732
$409$	12.2269	0.604583	0.302292	−	0.953216i	$-0.402248\pi$
$409$	12.2269	0.604583	0.302292	+	0.953216i	$0.402248\pi$
$410$	22.4374	1.10811
$411$	26.8824	1.32601
$412$	9.48683	0.467383
$413$	21.6211	1.06390
$414$	4.33185	0.212899
$415$	2.16545	0.106298
$416$	5.06501	0.248332
$417$	−8.16706	−0.399943
$418$	61.5305	3.00956
$419$	22.3888	1.09376	0.546882	−	0.837209i	$-0.315815\pi$
$419$	22.3888	1.09376	0.546882	+	0.837209i	$0.315815\pi$
$420$	90.6197	4.42179
$421$	27.4609	1.33836	0.669181	−	0.743099i	$-0.266645\pi$
$421$	27.4609	1.33836	0.669181	+	0.743099i	$0.266645\pi$
$422$	7.09658	0.345456
$423$	7.36375	0.358038
$424$	28.7683	1.39711
$425$	−44.8420	−2.17516
$426$	−15.3815	−0.745237
$427$	−4.86426	−0.235398
$428$	38.0165	1.83760
$429$	6.71022	0.323973
$430$	−98.3207	−4.74144
$431$	18.9573	0.913139	0.456570	−	0.889688i	$-0.349078\pi$
$431$	18.9573	0.913139	0.456570	+	0.889688i	$0.349078\pi$
$432$	1.72866	0.0831703
$433$	−25.9495	−1.24705	−0.623526	−	0.781803i	$-0.714300\pi$
$433$	−25.9495	−1.24705	−0.623526	+	0.781803i	$0.714300\pi$
$434$	32.4381	1.55708
$435$	0.756352	0.0362643
$436$	13.8432	0.662970
$437$	−11.5700	−0.553468
$438$	26.3956	1.26123
$439$	21.9613	1.04816	0.524078	−	0.851670i	$-0.324410\pi$
$439$	21.9613	1.04816	0.524078	+	0.851670i	$0.324410\pi$
$440$	−34.8905	−1.66334
$441$	9.29864	0.442793
$442$	14.5456	0.691863
$443$	30.0848	1.42937	0.714685	−	0.699446i	$-0.246570\pi$
$443$	30.0848	1.42937	0.714685	+	0.699446i	$0.246570\pi$
$444$	−12.9795	−0.615980
$445$	−53.9189	−2.55600
$446$	43.0804	2.03991
$447$	0.563346	0.0266454
$448$	−47.4681	−2.24266
$449$	36.2070	1.70872	0.854358	−	0.519685i	$-0.173951\pi$
$449$	36.2070	1.70872	0.854358	+	0.519685i	$0.173951\pi$
$450$	−22.0434	−1.03914
$451$	−8.97880	−0.422795
$452$	25.6460	1.20628
$453$	28.6097	1.34420
$454$	3.17011	0.148781
$455$	−13.0073	−0.609790
$456$	53.5008	2.50540
$457$	5.38898	0.252086	0.126043	−	0.992025i	$-0.459772\pi$
$457$	5.38898	0.252086	0.126043	+	0.992025i	$0.459772\pi$
$458$	−0.206022	−0.00962676
$459$	−21.7814	−1.01667
$460$	16.3159	0.760735
$461$	−31.6686	−1.47495	−0.737476	−	0.675373i	$-0.763983\pi$
$461$	−31.6686	−1.47495	−0.737476	+	0.675373i	$0.763983\pi$
$462$	−57.9450	−2.69585
$463$	2.28569	0.106225	0.0531126	−	0.998589i	$-0.483086\pi$
$463$	2.28569	0.106225	0.0531126	+	0.998589i	$0.483086\pi$
$464$	0.0520701	0.00241729
$465$	−27.2453	−1.26347
$466$	7.44552	0.344907
$467$	0.216472	0.0100171	0.00500857	−	0.999987i	$-0.498406\pi$
$467$	0.216472	0.0100171	0.00500857	+	0.999987i	$0.498406\pi$
$468$	4.47483	0.206849
$469$	27.4774	1.26879
$470$	44.3186	2.04427
$471$	13.3401	0.614681
$472$	−18.0009	−0.828558
$473$	39.3450	1.80909
$474$	−47.8741	−2.19893
$475$	58.8761	2.70142
$476$	−78.6071	−3.60295
$477$	−12.3756	−0.566641
$478$	47.7424	2.18368
$479$	−28.4731	−1.30097	−0.650485	−	0.759519i	$-0.725434\pi$
$479$	−28.4731	−1.30097	−0.650485	+	0.759519i	$0.725434\pi$
$480$	36.7363	1.67678
$481$	1.86304	0.0849472
$482$	16.2749	0.741302
$483$	10.8958	0.495776
$484$	−2.07291	−0.0942232
$485$	2.68209	0.121787
$486$	−30.0315	−1.36226
$487$	−7.08285	−0.320955	−0.160477	−	0.987040i	$-0.551303\pi$
$487$	−7.08285	−0.320955	−0.160477	+	0.987040i	$0.551303\pi$
$488$	4.04980	0.183326
$489$	24.6303	1.11382
$490$	55.9638	2.52819
$491$	−16.7445	−0.755668	−0.377834	−	0.925873i	$-0.623331\pi$
$491$	−16.7445	−0.755668	−0.377834	+	0.925873i	$0.623331\pi$
$492$	−19.4155	−0.875320
$493$	−0.656090	−0.0295488
$494$	−19.0979	−0.859255
$495$	15.0093	0.674619
$496$	−1.87567	−0.0842201
$497$	−11.9315	−0.535199
$498$	−2.99414	−0.134171
$499$	14.1871	0.635102	0.317551	−	0.948241i	$-0.397140\pi$
$499$	14.1871	0.635102	0.317551	+	0.948241i	$0.397140\pi$
$500$	−24.7819	−1.10828
$501$	32.1430	1.43604
$502$	42.3571	1.89049
$503$	−37.2961	−1.66295	−0.831477	−	0.555560i	$-0.812504\pi$
$503$	−37.2961	−1.66295	−0.831477	+	0.555560i	$0.812504\pi$
$504$	−15.5380	−0.692116
$505$	−4.69433	−0.208895
$506$	−10.4329	−0.463800
$507$	−2.08272	−0.0924971
$508$	45.7481	2.02974
$509$	44.1877	1.95858	0.979292	−	0.202452i	$-0.0648911\pi$
$509$	44.1877	1.95858	0.979292	+	0.202452i	$0.0648911\pi$
$510$	105.499	4.67156
$511$	20.4751	0.905765
$512$	5.63455	0.249014
$513$	28.5982	1.26264
$514$	−34.4235	−1.51835
$515$	−9.87644	−0.435208
$516$	85.0788	3.74538
$517$	−17.7350	−0.779985
$518$	−16.0880	−0.706864
$519$	−41.8689	−1.83784
$520$	10.8294	0.474899
$521$	28.8649	1.26459	0.632297	−	0.774726i	$-0.282112\pi$
$521$	28.8649	1.26459	0.632297	+	0.774726i	$0.282112\pi$
$522$	−0.322521	−0.0141163
$523$	−5.96555	−0.260855	−0.130428	−	0.991458i	$-0.541635\pi$
$523$	−5.96555	−0.260855	−0.130428	+	0.991458i	$0.541635\pi$
$524$	45.8699	2.00384
$525$	−55.4453	−2.41983
$526$	63.8457	2.78380
$527$	23.6337	1.02950
$528$	3.35056	0.145814
$529$	−21.0382	−0.914706
$530$	−74.4826	−3.23532
$531$	7.74368	0.336047
$532$	103.209	4.47466
$533$	2.78685	0.120712
$534$	74.5532	3.22623
$535$	−39.5778	−1.71110
$536$	−22.8767	−0.988122
$537$	−44.2053	−1.90760
$538$	−33.7166	−1.45363
$539$	−22.3951	−0.964623
$540$	−40.3291	−1.73549
$541$	−24.9679	−1.07345	−0.536727	−	0.843756i	$-0.680340\pi$
$541$	−24.9679	−1.07345	−0.536727	+	0.843756i	$0.680340\pi$
$542$	50.6433	2.17531
$543$	34.4184	1.47703
$544$	−31.8665	−1.36627
$545$	−14.4117	−0.617331
$546$	17.9850	0.769688
$547$	−2.05129	−0.0877067	−0.0438533	−	0.999038i	$-0.513963\pi$
$547$	−2.05129	−0.0877067	−0.0438533	+	0.999038i	$0.513963\pi$
$548$	−43.1758	−1.84438
$549$	−1.74216	−0.0743534
$550$	53.0899	2.26376
$551$	0.861425	0.0366979
$552$	−9.07142	−0.386105
$553$	−37.1360	−1.57918
$554$	6.42036	0.272775
$555$	13.5125	0.573576
$556$	13.1171	0.556289
$557$	44.7740	1.89714	0.948569	−	0.316571i	$-0.102532\pi$
$557$	44.7740	1.89714	0.948569	+	0.316571i	$0.102532\pi$
$558$	11.6178	0.491823
$559$	−12.2119	−0.516510
$560$	−6.49480	−0.274456
$561$	−42.2174	−1.78242
$562$	−5.98801	−0.252589
$563$	10.5569	0.444920	0.222460	−	0.974942i	$-0.428591\pi$
$563$	10.5569	0.444920	0.222460	+	0.974942i	$0.428591\pi$
$564$	−38.3497	−1.61482
$565$	−26.6992	−1.12324
$566$	58.2276	2.44749
$567$	−41.9216	−1.76054
$568$	9.93368	0.416808
$569$	2.79144	0.117023	0.0585117	−	0.998287i	$-0.481365\pi$
$569$	2.79144	0.117023	0.0585117	+	0.998287i	$0.481365\pi$
$570$	−138.516	−5.80181
$571$	−3.92528	−0.164268	−0.0821339	−	0.996621i	$-0.526174\pi$
$571$	−3.92528	−0.164268	−0.0821339	+	0.996621i	$0.526174\pi$
$572$	−10.7773	−0.450621
$573$	52.7074	2.20188
$574$	−24.0653	−1.00447
$575$	−9.98285	−0.416314
$576$	−17.0009	−0.708370
$577$	18.9962	0.790823	0.395411	−	0.918504i	$-0.370602\pi$
$577$	18.9962	0.790823	0.395411	+	0.918504i	$0.370602\pi$
$578$	−52.2107	−2.17168
$579$	32.4233	1.34747
$580$	−1.21478	−0.0504409
$581$	−2.32256	−0.0963559
$582$	−3.70850	−0.153722
$583$	29.8057	1.23443
$584$	−17.0468	−0.705401
$585$	−4.65861	−0.192610
$586$	64.6416	2.67032
$587$	22.9354	0.946643	0.473322	−	0.880890i	$-0.343055\pi$
$587$	22.9354	0.946643	0.473322	+	0.880890i	$0.343055\pi$
$588$	−48.4265	−1.99708
$589$	−31.0303	−1.27858
$590$	46.6052	1.91871
$591$	47.0117	1.93380
$592$	0.930254	0.0382332
$593$	1.49539	0.0614082	0.0307041	−	0.999529i	$-0.490225\pi$
$593$	1.49539	0.0614082	0.0307041	+	0.999529i	$0.490225\pi$
$594$	25.7876	1.05808
$595$	81.8354	3.35492
$596$	−0.904790	−0.0370616
$597$	2.55637	0.104625
$598$	3.23818	0.132419
$599$	35.8287	1.46392	0.731960	−	0.681347i	$-0.238606\pi$
$599$	35.8287	1.46392	0.731960	+	0.681347i	$0.238606\pi$
$600$	46.1616	1.88454
$601$	−38.6940	−1.57836	−0.789181	−	0.614161i	$-0.789495\pi$
$601$	−38.6940	−1.57836	−0.789181	+	0.614161i	$0.789495\pi$
$602$	105.454	4.29799
$603$	9.84116	0.400763
$604$	−45.9500	−1.86968
$605$	2.15804	0.0877368
$606$	6.49080	0.263671
$607$	−3.84723	−0.156154	−0.0780771	−	0.996947i	$-0.524878\pi$
$607$	−3.84723	−0.156154	−0.0780771	+	0.996947i	$0.524878\pi$
$608$	41.8398	1.69683
$609$	−0.811228	−0.0328726
$610$	−10.4851	−0.424531
$611$	5.50461	0.222693
$612$	−28.1535	−1.13804
$613$	−18.5960	−0.751083	−0.375542	−	0.926805i	$-0.622543\pi$
$613$	−18.5960	−0.751083	−0.375542	+	0.926805i	$0.622543\pi$
$614$	22.4319	0.905278
$615$	20.2129	0.815063
$616$	37.4220	1.50777
$617$	−1.00000	−0.0402585
$617$	−1.00000	−0.0402585
$618$	13.6561	0.549327
$619$	18.6454	0.749422	0.374711	−	0.927142i	$-0.377742\pi$
$619$	18.6454	0.749422	0.374711	+	0.927142i	$0.377742\pi$
$620$	43.7587	1.75739
$621$	−4.84903	−0.194585
$622$	−43.0112	−1.72459
$623$	57.8310	2.31695
$624$	−1.03995	−0.0416313
$625$	−9.83732	−0.393493
$626$	−14.9849	−0.598917
$627$	55.4301	2.21367
$628$	−21.4256	−0.854975
$629$	−11.7213	−0.467360
$630$	40.2286	1.60275
$631$	−15.5433	−0.618769	−0.309384	−	0.950937i	$-0.600123\pi$
$631$	−15.5433	−0.618769	−0.309384	+	0.950937i	$0.600123\pi$
$632$	30.9180	1.22985
$633$	6.39299	0.254099
$634$	−58.4315	−2.32061
$635$	−47.6269	−1.89002
$636$	64.4512	2.55566
$637$	6.95100	0.275409
$638$	0.776766	0.0307525
$639$	−4.27330	−0.169049
$640$	−67.0424	−2.65008
$641$	18.7434	0.740319	0.370159	−	0.928968i	$-0.379303\pi$
$641$	18.7434	0.740319	0.370159	+	0.928968i	$0.379303\pi$
$642$	54.7238	2.15978
$643$	−48.8770	−1.92752	−0.963761	−	0.266768i	$-0.914044\pi$
$643$	−48.8770	−1.92752	−0.963761	+	0.266768i	$0.914044\pi$
$644$	−17.4997	−0.689586
$645$	−88.5728	−3.48755
$646$	120.155	4.72742
$647$	13.9859	0.549843	0.274922	−	0.961467i	$-0.411348\pi$
$647$	13.9859	0.549843	0.274922	+	0.961467i	$0.411348\pi$
$648$	34.9023	1.37109
$649$	−18.6500	−0.732078
$650$	−16.4781	−0.646323
$651$	29.2221	1.14530
$652$	−39.5587	−1.54924
$653$	−30.0490	−1.17591	−0.587953	−	0.808895i	$-0.700066\pi$
$653$	−30.0490	−1.17591	−0.587953	+	0.808895i	$0.700066\pi$
$654$	19.9270	0.779206
$655$	−47.7537	−1.86589
$656$	1.39153	0.0543302
$657$	7.33324	0.286097
$658$	−47.5341	−1.85307
$659$	24.7147	0.962748	0.481374	−	0.876515i	$-0.340138\pi$
$659$	24.7147	0.962748	0.481374	+	0.876515i	$0.340138\pi$
$660$	−78.1673	−3.04266
$661$	38.2507	1.48778	0.743890	−	0.668303i	$-0.232979\pi$
$661$	38.2507	1.48778	0.743890	+	0.668303i	$0.232979\pi$
$662$	−4.45703	−0.173227
$663$	13.1035	0.508897
$664$	1.93367	0.0750410
$665$	−107.447	−4.16662
$666$	−5.76197	−0.223272
$667$	−0.146061	−0.00565549
$668$	−51.6248	−1.99742
$669$	38.8092	1.50045
$670$	59.2289	2.28821
$671$	4.19585	0.161979
$672$	−39.4017	−1.51995
$673$	−41.0999	−1.58429	−0.792143	−	0.610336i	$-0.791034\pi$
$673$	−41.0999	−1.58429	−0.792143	+	0.610336i	$0.791034\pi$
$674$	−44.9840	−1.73272
$675$	24.6752	0.949748
$676$	3.34506	0.128656
$677$	−20.1152	−0.773092	−0.386546	−	0.922270i	$-0.626332\pi$
$677$	−20.1152	−0.773092	−0.386546	+	0.922270i	$0.626332\pi$
$678$	36.9167	1.41778
$679$	−2.87668	−0.110397
$680$	−68.1330	−2.61278
$681$	2.85582	0.109435
$682$	−27.9807	−1.07144
$683$	−29.1170	−1.11413	−0.557065	−	0.830469i	$-0.688073\pi$
$683$	−29.1170	−1.11413	−0.557065	+	0.830469i	$0.688073\pi$
$684$	36.9646	1.41338
$685$	44.9490	1.71741
$686$	0.423160	0.0161563
$687$	−0.185596	−0.00708093
$688$	−6.09768	−0.232472
$689$	−9.25113	−0.352440
$690$	23.4864	0.894111
$691$	18.4971	0.703662	0.351831	−	0.936064i	$-0.385559\pi$
$691$	18.4971	0.703662	0.351831	+	0.936064i	$0.385559\pi$
$692$	67.2456	2.55630
$693$	−16.0983	−0.611524
$694$	18.7715	0.712555
$695$	−13.6558	−0.517994
$696$	0.675398	0.0256009
$697$	−17.5335	−0.664128
$698$	6.72491	0.254542
$699$	6.70734	0.253695
$700$	89.0507	3.36580
$701$	0.513776	0.0194050	0.00970252	−	0.999953i	$-0.496912\pi$
$701$	0.513776	0.0194050	0.00970252	+	0.999953i	$0.496912\pi$
$702$	−8.00399	−0.302091
$703$	15.3897	0.580434
$704$	40.9453	1.54318
$705$	39.9247	1.50365
$706$	−45.0504	−1.69549
$707$	5.03492	0.189358
$708$	−40.3284	−1.51563
$709$	40.1805	1.50901	0.754506	−	0.656293i	$-0.227877\pi$
$709$	40.1805	1.50901	0.754506	+	0.656293i	$0.227877\pi$
$710$	−25.7188	−0.965210
$711$	−13.3004	−0.498804
$712$	−48.1478	−1.80442
$713$	5.26140	0.197041
$714$	−113.153	−4.23464
$715$	11.2199	0.419600
$716$	70.9981	2.65332
$717$	43.0090	1.60620
$718$	18.7912	0.701280
$719$	−44.4427	−1.65743	−0.828716	−	0.559670i	$-0.810928\pi$
$719$	−44.4427	−1.65743	−0.828716	+	0.559670i	$0.810928\pi$
$720$	−2.32614	−0.0866901
$721$	10.5930	0.394504
$722$	−113.832	−4.23640
$723$	14.6614	0.545262
$724$	−55.2793	−2.05444
$725$	0.743257	0.0276039
$726$	−2.98390	−0.110743
$727$	−49.7844	−1.84640	−0.923201	−	0.384317i	$-0.874437\pi$
$727$	−49.7844	−1.84640	−0.923201	+	0.384317i	$0.874437\pi$
$728$	−11.6151	−0.430483
$729$	6.61695	0.245072
$730$	44.1350	1.63351
$731$	76.8316	2.84172
$732$	9.07299	0.335348
$733$	29.4552	1.08795	0.543977	−	0.839100i	$-0.316918\pi$
$733$	29.4552	1.08795	0.543977	+	0.839100i	$0.316918\pi$
$734$	−4.75158	−0.175384
$735$	50.4153	1.85960
$736$	−7.09422	−0.261496
$737$	−23.7017	−0.873062
$738$	−8.61910	−0.317273
$739$	11.2284	0.413043	0.206522	−	0.978442i	$-0.433786\pi$
$739$	11.2284	0.413043	0.206522	+	0.978442i	$0.433786\pi$
$740$	−21.7025	−0.797800
$741$	−17.2045	−0.632021
$742$	79.8866	2.93273
$743$	44.8888	1.64681	0.823405	−	0.567454i	$-0.192071\pi$
$743$	44.8888	1.64681	0.823405	+	0.567454i	$0.192071\pi$
$744$	−24.3292	−0.891951
$745$	0.941948	0.0345103
$746$	45.9837	1.68358
$747$	−0.831833	−0.0304352
$748$	67.8054	2.47921
$749$	42.4493	1.55106
$750$	−35.6728	−1.30259
$751$	−16.1942	−0.590933	−0.295467	−	0.955353i	$-0.595475\pi$
$751$	−16.1942	−0.590933	−0.295467	+	0.955353i	$0.595475\pi$
$752$	2.74857	0.100230
$753$	38.1577	1.39054
$754$	−0.241093	−0.00878010
$755$	47.8371	1.74097
$756$	43.2551	1.57317
$757$	37.0587	1.34692	0.673461	−	0.739223i	$-0.264807\pi$
$757$	37.0587	1.34692	0.673461	+	0.739223i	$0.264807\pi$
$758$	−61.3632	−2.22881
$759$	−9.39856	−0.341146
$760$	89.4564	3.24493
$761$	5.19481	0.188312	0.0941559	−	0.995557i	$-0.469985\pi$
$761$	5.19481	0.188312	0.0941559	+	0.995557i	$0.469985\pi$
$762$	65.8532	2.38561
$763$	15.4574	0.559595
$764$	−84.6533	−3.06265
$765$	29.3097	1.05969
$766$	57.3679	2.07279
$767$	5.78862	0.209015
$768$	39.7617	1.43478
$769$	−10.7394	−0.387273	−0.193636	−	0.981073i	$-0.562028\pi$
$769$	−10.7394	−0.387273	−0.193636	+	0.981073i	$0.562028\pi$
$770$	−96.8875	−3.49158
$771$	−31.0106	−1.11682
$772$	−52.0751	−1.87422
$773$	−46.0886	−1.65769	−0.828846	−	0.559477i	$-0.811002\pi$
$773$	−46.0886	−1.65769	−0.828846	+	0.559477i	$0.811002\pi$
$774$	37.7689	1.35757
$775$	−26.7736	−0.961736
$776$	2.39502	0.0859761
$777$	−14.4929	−0.519931
$778$	−25.1894	−0.903083
$779$	23.0209	0.824809
$780$	24.2616	0.868705
$781$	10.2919	0.368274
$782$	−20.3730	−0.728538
$783$	0.361026	0.0129020
$784$	3.47078	0.123956
$785$	22.3055	0.796118
$786$	66.0285	2.35516
$787$	45.8169	1.63320	0.816598	−	0.577207i	$-0.195857\pi$
$787$	45.8169	1.63320	0.816598	+	0.577207i	$0.195857\pi$
$788$	−75.5055	−2.68977
$789$	57.5158	2.04762
$790$	−80.0483	−2.84799
$791$	28.6363	1.01819
$792$	13.4028	0.476249
$793$	−1.30231	−0.0462464
$794$	23.7458	0.842708
$795$	−67.0981	−2.37972
$796$	−4.10578	−0.145526
$797$	23.3620	0.827523	0.413761	−	0.910385i	$-0.364215\pi$
$797$	23.3620	0.827523	0.413761	+	0.910385i	$0.364215\pi$
$798$	148.566	5.25918
$799$	−34.6323	−1.22520
$800$	36.1003	1.27634
$801$	20.7124	0.731836
$802$	24.9253	0.880144
$803$	−17.6615	−0.623262
$804$	−51.2519	−1.80752
$805$	18.2184	0.642115
$806$	8.68467	0.305904
$807$	−30.3739	−1.06921
$808$	−4.19188	−0.147470
$809$	−43.6936	−1.53618	−0.768092	−	0.640339i	$-0.778794\pi$
$809$	−43.6936	−1.53618	−0.768092	+	0.640339i	$0.778794\pi$
$810$	−90.3639	−3.17506
$811$	−15.6767	−0.550482	−0.275241	−	0.961375i	$-0.588758\pi$
$811$	−15.6767	−0.550482	−0.275241	+	0.961375i	$0.588758\pi$
$812$	1.30291	0.0457233
$813$	45.6223	1.60004
$814$	13.8772	0.486397
$815$	41.1833	1.44259
$816$	6.54285	0.229045
$817$	−100.877	−3.52925
$818$	−28.2679	−0.988365
$819$	4.99661	0.174596
$820$	−32.4639	−1.13369
$821$	−33.8341	−1.18082	−0.590409	−	0.807104i	$-0.701034\pi$
$821$	−33.8341	−1.18082	−0.590409	+	0.807104i	$0.701034\pi$
$822$	−62.1505	−2.16775
$823$	48.3343	1.68483	0.842414	−	0.538831i	$-0.181134\pi$
$823$	48.3343	1.68483	0.842414	+	0.538831i	$0.181134\pi$
$824$	−8.81934	−0.307236
$825$	47.8263	1.66510
$826$	−49.9866	−1.73926
$827$	−46.6181	−1.62107	−0.810534	−	0.585691i	$-0.800823\pi$
$827$	−46.6181	−1.62107	−0.810534	+	0.585691i	$0.800823\pi$
$828$	−6.26760	−0.217814
$829$	−36.4561	−1.26617	−0.633086	−	0.774082i	$-0.718212\pi$
$829$	−36.4561	−1.26617	−0.633086	+	0.774082i	$0.718212\pi$
$830$	−5.00638	−0.173774
$831$	5.78382	0.200639
$832$	−12.7086	−0.440593
$833$	−43.7323	−1.51523
$834$	18.8817	0.653821
$835$	53.7450	1.85992
$836$	−89.0263	−3.07904
$837$	−13.0049	−0.449515
$838$	−51.7616	−1.78807
$839$	36.0135	1.24333	0.621663	−	0.783285i	$-0.286457\pi$
$839$	36.0135	1.24333	0.621663	+	0.783285i	$0.286457\pi$
$840$	−84.2436	−2.90668
$841$	−28.9891	−0.999625
$842$	−63.4879	−2.18794
$843$	−5.39433	−0.185791
$844$	−10.2678	−0.353432
$845$	−3.48244	−0.119800
$846$	−17.0245	−0.585316
$847$	−2.31461	−0.0795311
$848$	−4.61928	−0.158627
$849$	52.4547	1.80024
$850$	103.672	3.55592
$851$	−2.60943	−0.0894502
$852$	22.2550	0.762443
$853$	21.8274	0.747357	0.373679	−	0.927558i	$-0.378096\pi$
$853$	21.8274	0.747357	0.373679	+	0.927558i	$0.378096\pi$
$854$	11.2459	0.384826
$855$	−38.4827	−1.31608
$856$	−35.3417	−1.20795
$857$	17.7530	0.606432	0.303216	−	0.952922i	$-0.401940\pi$
$857$	17.7530	0.606432	0.303216	+	0.952922i	$0.401940\pi$
$858$	−15.5136	−0.529627
$859$	51.0100	1.74044	0.870220	−	0.492664i	$-0.163977\pi$
$859$	51.0100	1.74044	0.870220	+	0.492664i	$0.163977\pi$
$860$	142.257	4.85091
$861$	−21.6794	−0.738832
$862$	−43.8281	−1.49279
$863$	−25.5122	−0.868444	−0.434222	−	0.900806i	$-0.642977\pi$
$863$	−25.5122	−0.868444	−0.434222	+	0.900806i	$0.642977\pi$
$864$	17.5352	0.596559
$865$	−70.0073	−2.38032
$866$	59.9936	2.03866
$867$	−47.0344	−1.59737
$868$	−46.9336	−1.59303
$869$	32.0330	1.08664
$870$	−1.74864	−0.0592845
$871$	7.35654	0.249267
$872$	−12.8692	−0.435807
$873$	−1.03030	−0.0348702
$874$	26.7491	0.904803
$875$	−27.6715	−0.935466
$876$	−38.1909	−1.29035
$877$	47.1418	1.59187	0.795934	−	0.605384i	$-0.206980\pi$
$877$	47.1418	1.59187	0.795934	+	0.605384i	$0.206980\pi$
$878$	−50.7732	−1.71351
$879$	58.2328	1.96414
$880$	5.60233	0.188854
$881$	43.8357	1.47686	0.738431	−	0.674329i	$-0.235567\pi$
$881$	43.8357	1.47686	0.738431	+	0.674329i	$0.235567\pi$
$882$	−21.4979	−0.723872
$883$	21.2111	0.713812	0.356906	−	0.934140i	$-0.383832\pi$
$883$	21.2111	0.713812	0.356906	+	0.934140i	$0.383832\pi$
$884$	−21.0455	−0.707837
$885$	41.9846	1.41130
$886$	−69.5542	−2.33672
$887$	8.35758	0.280620	0.140310	−	0.990108i	$-0.455190\pi$
$887$	8.35758	0.280620	0.140310	+	0.990108i	$0.455190\pi$
$888$	12.0663	0.404917
$889$	51.0824	1.71325
$890$	124.657	4.17852
$891$	36.1610	1.21144
$892$	−62.3315	−2.08701
$893$	45.4711	1.52163
$894$	−1.30242	−0.0435595
$895$	−73.9139	−2.47067
$896$	71.9066	2.40223
$897$	2.91713	0.0974002
$898$	−83.7085	−2.79339
$899$	−0.391729	−0.0130649
$900$	31.8939	1.06313
$901$	58.2036	1.93904
$902$	20.7584	0.691180
$903$	94.9991	3.16137
$904$	−23.8415	−0.792957
$905$	57.5496	1.91301
$906$	−66.1438	−2.19748
$907$	28.9287	0.960563	0.480282	−	0.877114i	$-0.340534\pi$
$907$	28.9287	0.960563	0.480282	+	0.877114i	$0.340534\pi$
$908$	−4.58672	−0.152216
$909$	1.80328	0.0598109
$910$	30.0720	0.996878
$911$	17.7547	0.588241	0.294121	−	0.955768i	$-0.404973\pi$
$911$	17.7547	0.588241	0.294121	+	0.955768i	$0.404973\pi$
$912$	−8.59055	−0.284461
$913$	2.00340	0.0663030
$914$	−12.4590	−0.412107
$915$	−9.44561	−0.312262
$916$	0.298086	0.00984902
$917$	51.2184	1.69138
$918$	50.3572	1.66203
$919$	6.77847	0.223601	0.111801	−	0.993731i	$-0.464338\pi$
$919$	6.77847	0.223601	0.111801	+	0.993731i	$0.464338\pi$
$920$	−15.1680	−0.500073
$921$	20.2079	0.665873
$922$	73.2158	2.41123
$923$	−3.19441	−0.105145
$924$	83.8386	2.75809
$925$	13.2786	0.436597
$926$	−5.28439	−0.173656
$927$	3.79393	0.124609
$928$	0.528188	0.0173386
$929$	46.1055	1.51267	0.756337	−	0.654182i	$-0.226987\pi$
$929$	46.1055	1.51267	0.756337	+	0.654182i	$0.226987\pi$
$930$	62.9896	2.06551
$931$	57.4191	1.88183
$932$	−10.7727	−0.352870
$933$	−38.7469	−1.26852
$934$	−0.500471	−0.0163759
$935$	−70.5901	−2.30854
$936$	−4.15998	−0.135973
$937$	−5.94091	−0.194081	−0.0970405	−	0.995280i	$-0.530938\pi$
$937$	−5.94091	−0.194081	−0.0970405	+	0.995280i	$0.530938\pi$
$938$	−63.5262	−2.07420
$939$	−13.4992	−0.440531
$940$	−64.1230	−2.09146
$941$	28.5486	0.930657	0.465329	−	0.885138i	$-0.345936\pi$
$941$	28.5486	0.930657	0.465329	+	0.885138i	$0.345936\pi$
$942$	−30.8416	−1.00487
$943$	−3.90335	−0.127111
$944$	2.89038	0.0940738
$945$	−45.0315	−1.46487
$946$	−90.9634	−2.95747
$947$	59.9406	1.94781	0.973904	−	0.226961i	$-0.0728789\pi$
$947$	59.9406	1.94781	0.973904	+	0.226961i	$0.0728789\pi$
$948$	69.2673	2.24970
$949$	5.48180	0.177947
$950$	−136.118	−4.41625
$951$	−52.6384	−1.70692
$952$	73.0763	2.36842
$953$	53.6429	1.73766	0.868832	−	0.495106i	$-0.164871\pi$
$953$	53.6429	1.73766	0.868832	+	0.495106i	$0.164871\pi$
$954$	28.6117	0.926338
$955$	88.1298	2.85181
$956$	−69.0767	−2.23410
$957$	0.699754	0.0226198
$958$	65.8281	2.12681
$959$	−48.2102	−1.55679
$960$	−92.1753	−2.97494
$961$	−16.8891	−0.544811
$962$	−4.30723	−0.138871
$963$	15.2034	0.489922
$964$	−23.5476	−0.758417
$965$	54.2137	1.74520
$966$	−25.1904	−0.810488
$967$	41.7833	1.34366	0.671830	−	0.740706i	$-0.265509\pi$
$967$	41.7833	1.34366	0.671830	+	0.740706i	$0.265509\pi$
$968$	1.92706	0.0619380
$969$	108.242	3.47723
$970$	−6.20082	−0.199096
$971$	−9.82459	−0.315286	−0.157643	−	0.987496i	$-0.550390\pi$
$971$	−9.82459	−0.315286	−0.157643	+	0.987496i	$0.550390\pi$
$972$	43.4515	1.39371
$973$	14.6466	0.469548
$974$	16.3751	0.524693
$975$	−14.8444	−0.475401
$976$	−0.650271	−0.0208147
$977$	−48.6090	−1.55514	−0.777569	−	0.628797i	$-0.783547\pi$
$977$	−48.6090	−1.55514	−0.777569	+	0.628797i	$0.783547\pi$
$978$	−56.9437	−1.82086
$979$	−49.8842	−1.59431
$980$	−80.9720	−2.58656
$981$	5.53612	0.176755
$982$	38.7122	1.23536
$983$	−60.7567	−1.93784	−0.968918	−	0.247381i	$-0.920430\pi$
$983$	−60.7567	−1.93784	−0.968918	+	0.247381i	$0.920430\pi$
$984$	18.0495	0.575395
$985$	78.6064	2.50461
$986$	1.51684	0.0483060
$987$	−42.8214	−1.36302
$988$	27.6321	0.879093
$989$	17.1045	0.543890
$990$	−34.7007	−1.10286
$991$	48.3482	1.53583	0.767915	−	0.640552i	$-0.221294\pi$
$991$	48.3482	1.53583	0.767915	+	0.640552i	$0.221294\pi$
$992$	−19.0264	−0.604089
$993$	−4.01514	−0.127417
$994$	27.5848	0.874937
$995$	4.27440	0.135508
$996$	4.33211	0.137268
$997$	46.7175	1.47956	0.739779	−	0.672849i	$-0.234930\pi$
$997$	46.7175	1.47956	0.739779	+	0.672849i	$0.234930\pi$
$998$	−32.7997	−1.03826
$999$	6.44989	0.204065

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8021.2.a.d.1.20	✓	174

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8021.2.a.d.1.20	✓	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)

\(f(q)\)	\(=\)	\(q-2.31194 q^{2} -2.08272 q^{3} +3.34506 q^{4} -3.48244 q^{5} +4.81513 q^{6} +3.73510 q^{7} -3.10970 q^{8} +1.33774 q^{9} +O(q^{10})\)	\(q-2.31194 q^{2} -2.08272 q^{3} +3.34506 q^{4} -3.48244 q^{5} +4.81513 q^{6} +3.73510 q^{7} -3.10970 q^{8} +1.33774 q^{9} +8.05119 q^{10} -3.22185 q^{11} -6.96685 q^{12} +1.00000 q^{13} -8.63533 q^{14} +7.25296 q^{15} +0.499321 q^{16} -6.29151 q^{17} -3.09278 q^{18} +8.26055 q^{19} -11.6490 q^{20} -7.77919 q^{21} +7.44872 q^{22} -1.40063 q^{23} +6.47666 q^{24} +7.12738 q^{25} -2.31194 q^{26} +3.46202 q^{27} +12.4942 q^{28} +0.104282 q^{29} -16.7684 q^{30} -3.75644 q^{31} +5.06501 q^{32} +6.71022 q^{33} +14.5456 q^{34} -13.0073 q^{35} +4.47483 q^{36} +1.86304 q^{37} -19.0979 q^{38} -2.08272 q^{39} +10.8294 q^{40} +2.78685 q^{41} +17.9850 q^{42} -12.2119 q^{43} -10.7773 q^{44} -4.65861 q^{45} +3.23818 q^{46} +5.50461 q^{47} -1.03995 q^{48} +6.95100 q^{49} -16.4781 q^{50} +13.1035 q^{51} +3.34506 q^{52} -9.25113 q^{53} -8.00399 q^{54} +11.2199 q^{55} -11.6151 q^{56} -17.2045 q^{57} -0.241093 q^{58} +5.78862 q^{59} +24.2616 q^{60} -1.30231 q^{61} +8.68467 q^{62} +4.99661 q^{63} -12.7086 q^{64} -3.48244 q^{65} -15.5136 q^{66} +7.35654 q^{67} -21.0455 q^{68} +2.91713 q^{69} +30.0720 q^{70} -3.19441 q^{71} -4.15998 q^{72} +5.48180 q^{73} -4.30723 q^{74} -14.8444 q^{75} +27.6321 q^{76} -12.0339 q^{77} +4.81513 q^{78} -9.94242 q^{79} -1.73886 q^{80} -11.2237 q^{81} -6.44302 q^{82} -0.621818 q^{83} -26.0219 q^{84} +21.9098 q^{85} +28.2333 q^{86} -0.217190 q^{87} +10.0190 q^{88} +15.4831 q^{89} +10.7704 q^{90} +3.73510 q^{91} -4.68520 q^{92} +7.82364 q^{93} -12.7263 q^{94} -28.7669 q^{95} -10.5490 q^{96} -0.770175 q^{97} -16.0703 q^{98} -4.31000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 174 q + 6 q^{2} + 37 q^{3} + 214 q^{4} + 10 q^{5} + 12 q^{6} + 28 q^{7} + 15 q^{8} + 211 q^{9}+O(q^{10}) \) 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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