LMFDB - Embedded newform 8021.2.a.d.1.8

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			1.8
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)

$f(q)$	$=$	$q-2.65450 q^{2} +3.02354 q^{3} +5.04638 q^{4} -2.29392 q^{5} -8.02600 q^{6} -0.907848 q^{7} -8.08663 q^{8} +6.14182 q^{9} +O(q^{10})$	\(q-2.65450 q^{2} +3.02354 q^{3} +5.04638 q^{4} -2.29392 q^{5} -8.02600 q^{6} -0.907848 q^{7} -8.08663 q^{8} +6.14182 q^{9} +6.08922 q^{10} -5.06338 q^{11} +15.2580 q^{12} +1.00000 q^{13} +2.40988 q^{14} -6.93577 q^{15} +11.3732 q^{16} -4.41674 q^{17} -16.3035 q^{18} -5.66411 q^{19} -11.5760 q^{20} -2.74492 q^{21} +13.4408 q^{22} -3.57135 q^{23} -24.4503 q^{24} +0.262070 q^{25} -2.65450 q^{26} +9.49942 q^{27} -4.58135 q^{28} +2.11125 q^{29} +18.4110 q^{30} +7.36284 q^{31} -14.0170 q^{32} -15.3094 q^{33} +11.7242 q^{34} +2.08253 q^{35} +30.9940 q^{36} -9.28280 q^{37} +15.0354 q^{38} +3.02354 q^{39} +18.5501 q^{40} -8.65857 q^{41} +7.28639 q^{42} +0.0280117 q^{43} -25.5518 q^{44} -14.0888 q^{45} +9.48016 q^{46} +7.68904 q^{47} +34.3874 q^{48} -6.17581 q^{49} -0.695666 q^{50} -13.3542 q^{51} +5.04638 q^{52} -6.23922 q^{53} -25.2162 q^{54} +11.6150 q^{55} +7.34143 q^{56} -17.1257 q^{57} -5.60432 q^{58} +1.38031 q^{59} -35.0005 q^{60} +3.46261 q^{61} -19.5447 q^{62} -5.57584 q^{63} +14.4616 q^{64} -2.29392 q^{65} +40.6387 q^{66} +7.16812 q^{67} -22.2885 q^{68} -10.7981 q^{69} -5.52808 q^{70} +5.37853 q^{71} -49.6666 q^{72} +14.4477 q^{73} +24.6412 q^{74} +0.792381 q^{75} -28.5833 q^{76} +4.59678 q^{77} -8.02600 q^{78} +11.5290 q^{79} -26.0892 q^{80} +10.2965 q^{81} +22.9842 q^{82} +8.50134 q^{83} -13.8519 q^{84} +10.1316 q^{85} -0.0743571 q^{86} +6.38346 q^{87} +40.9457 q^{88} -0.912168 q^{89} +37.3989 q^{90} -0.907848 q^{91} -18.0224 q^{92} +22.2619 q^{93} -20.4106 q^{94} +12.9930 q^{95} -42.3809 q^{96} +18.3103 q^{97} +16.3937 q^{98} -31.0984 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.65450	−1.87702	−0.938508	−	0.345257i	$-0.887792\pi$
$2$	−2.65450	−1.87702	−0.938508	+	0.345257i	$0.887792\pi$
$3$	3.02354	1.74564	0.872822	−	0.488039i	$-0.162288\pi$
$3$	3.02354	1.74564	0.872822	+	0.488039i	$0.162288\pi$
$4$	5.04638	2.52319
$5$	−2.29392	−1.02587	−0.512936	−	0.858427i	$-0.671442\pi$
$5$	−2.29392	−1.02587	−0.512936	+	0.858427i	$0.671442\pi$
$6$	−8.02600	−3.27660
$7$	−0.907848	−0.343134	−0.171567	−	0.985172i	$-0.554883\pi$
$7$	−0.907848	−0.343134	−0.171567	+	0.985172i	$0.554883\pi$
$8$	−8.08663	−2.85906
$9$	6.14182	2.04727
$10$	6.08922	1.92558
$11$	−5.06338	−1.52667	−0.763333	−	0.646005i	$-0.776439\pi$
$11$	−5.06338	−1.52667	−0.763333	+	0.646005i	$0.776439\pi$
$12$	15.2580	4.40459
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	2.40988	0.644069
$15$	−6.93577	−1.79081
$16$	11.3732	2.84330
$17$	−4.41674	−1.07122	−0.535608	−	0.844467i	$-0.679917\pi$
$17$	−4.41674	−1.07122	−0.535608	+	0.844467i	$0.679917\pi$
$18$	−16.3035	−3.84276
$19$	−5.66411	−1.29944	−0.649718	−	0.760175i	$-0.725113\pi$
$19$	−5.66411	−1.29944	−0.649718	+	0.760175i	$0.725113\pi$
$20$	−11.5760	−2.58847
$21$	−2.74492	−0.598990
$22$	13.4408	2.86558
$23$	−3.57135	−0.744678	−0.372339	−	0.928097i	$-0.621444\pi$
$23$	−3.57135	−0.744678	−0.372339	+	0.928097i	$0.621444\pi$
$24$	−24.4503	−4.99089
$25$	0.262070	0.0524141
$26$	−2.65450	−0.520591
$27$	9.49942	1.82816
$28$	−4.58135	−0.865793
$29$	2.11125	0.392049	0.196025	−	0.980599i	$-0.437197\pi$
$29$	2.11125	0.392049	0.196025	+	0.980599i	$0.437197\pi$
$30$	18.4110	3.36138
$31$	7.36284	1.32240	0.661202	−	0.750208i	$-0.270046\pi$
$31$	7.36284	1.32240	0.661202	+	0.750208i	$0.270046\pi$
$32$	−14.0170	−2.47787
$33$	−15.3094	−2.66502
$34$	11.7242	2.01069
$35$	2.08253	0.352012
$36$	30.9940	5.16566
$37$	−9.28280	−1.52608	−0.763041	−	0.646350i	$-0.776295\pi$
$37$	−9.28280	−1.52608	−0.763041	+	0.646350i	$0.776295\pi$
$38$	15.0354	2.43906
$39$	3.02354	0.484154
$40$	18.5501	2.93303
$41$	−8.65857	−1.35224	−0.676120	−	0.736791i	$-0.736340\pi$
$41$	−8.65857	−1.35224	−0.676120	+	0.736791i	$0.736340\pi$
$42$	7.28639	1.12431
$43$	0.0280117	0.00427174	0.00213587	−	0.999998i	$-0.499320\pi$
$43$	0.0280117	0.00427174	0.00213587	+	0.999998i	$0.499320\pi$
$44$	−25.5518	−3.85207
$45$	−14.0888	−2.10024
$46$	9.48016	1.39777
$47$	7.68904	1.12156	0.560781	−	0.827964i	$-0.310501\pi$
$47$	7.68904	1.12156	0.560781	+	0.827964i	$0.310501\pi$
$48$	34.3874	4.96339
$49$	−6.17581	−0.882259
$50$	−0.695666	−0.0983821
$51$	−13.3542	−1.86996
$52$	5.04638	0.699807
$53$	−6.23922	−0.857023	−0.428511	−	0.903536i	$-0.640962\pi$
$53$	−6.23922	−0.857023	−0.428511	+	0.903536i	$0.640962\pi$
$54$	−25.2162	−3.43150
$55$	11.6150	1.56617
$56$	7.34143	0.981040
$57$	−17.1257	−2.26835
$58$	−5.60432	−0.735883
$59$	1.38031	0.179700	0.0898502	−	0.995955i	$-0.471361\pi$
$59$	1.38031	0.179700	0.0898502	+	0.995955i	$0.471361\pi$
$60$	−35.0005	−4.51855
$61$	3.46261	0.443342	0.221671	−	0.975122i	$-0.428849\pi$
$61$	3.46261	0.443342	0.221671	+	0.975122i	$0.428849\pi$
$62$	−19.5447	−2.48218
$63$	−5.57584	−0.702489
$64$	14.4616	1.80770
$65$	−2.29392	−0.284526
$66$	40.6387	5.00228
$67$	7.16812	0.875725	0.437863	−	0.899042i	$-0.355736\pi$
$67$	7.16812	0.875725	0.437863	+	0.899042i	$0.355736\pi$
$68$	−22.2885	−2.70288
$69$	−10.7981	−1.29994
$70$	−5.52808	−0.660732
$71$	5.37853	0.638314	0.319157	−	0.947702i	$-0.396600\pi$
$71$	5.37853	0.638314	0.319157	+	0.947702i	$0.396600\pi$
$72$	−49.6666	−5.85327
$73$	14.4477	1.69098	0.845490	−	0.533991i	$-0.179309\pi$
$73$	14.4477	1.69098	0.845490	+	0.533991i	$0.179309\pi$
$74$	24.6412	2.86448
$75$	0.792381	0.0914963
$76$	−28.5833	−3.27873
$77$	4.59678	0.523852
$78$	−8.02600	−0.908766
$79$	11.5290	1.29712	0.648559	−	0.761165i	$-0.275372\pi$
$79$	11.5290	1.29712	0.648559	+	0.761165i	$0.275372\pi$
$80$	−26.0892	−2.91687
$81$	10.2965	1.14405
$82$	22.9842	2.53818
$83$	8.50134	0.933143	0.466572	−	0.884483i	$-0.345489\pi$
$83$	8.50134	0.933143	0.466572	+	0.884483i	$0.345489\pi$
$84$	−13.8519	−1.51137
$85$	10.1316	1.09893
$86$	−0.0743571	−0.00801814
$87$	6.38346	0.684379
$88$	40.9457	4.36483
$89$	−0.912168	−0.0966896	−0.0483448	−	0.998831i	$-0.515395\pi$
$89$	−0.912168	−0.0966896	−0.0483448	+	0.998831i	$0.515395\pi$
$90$	37.3989	3.94219
$91$	−0.907848	−0.0951683
$92$	−18.0224	−1.87897
$93$	22.2619	2.30845
$94$	−20.4106	−2.10519
$95$	12.9930	1.33306
$96$	−42.3809	−4.32548
$97$	18.3103	1.85913	0.929566	−	0.368656i	$-0.120182\pi$
$97$	18.3103	1.85913	0.929566	+	0.368656i	$0.120182\pi$
$98$	16.3937	1.65601
$99$	−31.0984	−3.12550
$100$	1.32251	0.132251
$101$	1.92087	0.191134	0.0955670	−	0.995423i	$-0.469534\pi$
$101$	1.92087	0.191134	0.0955670	+	0.995423i	$0.469534\pi$
$102$	35.4487	3.50995
$103$	6.07876	0.598958	0.299479	−	0.954103i	$-0.403187\pi$
$103$	6.07876	0.598958	0.299479	+	0.954103i	$0.403187\pi$
$104$	−8.08663	−0.792959
$105$	6.29662	0.614488
$106$	16.5620	1.60865
$107$	−7.93223	−0.766837	−0.383419	−	0.923575i	$-0.625253\pi$
$107$	−7.93223	−0.766837	−0.383419	+	0.923575i	$0.625253\pi$
$108$	47.9377	4.61281
$109$	1.48790	0.142515	0.0712576	−	0.997458i	$-0.477299\pi$
$109$	1.48790	0.142515	0.0712576	+	0.997458i	$0.477299\pi$
$110$	−30.8320	−2.93972
$111$	−28.0669	−2.66400
$112$	−10.3251	−0.975635
$113$	13.5494	1.27462	0.637311	−	0.770607i	$-0.280047\pi$
$113$	13.5494	1.27462	0.637311	+	0.770607i	$0.280047\pi$
$114$	45.4602	4.25774
$115$	8.19239	0.763945
$116$	10.6542	0.989216
$117$	6.14182	0.567811
$118$	−3.66402	−0.337301
$119$	4.00972	0.367571
$120$	56.0870	5.12002
$121$	14.6378	1.33071
$122$	−9.19151	−0.832160
$123$	−26.1796	−2.36053
$124$	37.1557	3.33668
$125$	10.8684	0.972102
$126$	14.8011	1.31858
$127$	−20.4668	−1.81613	−0.908067	−	0.418825i	$-0.862442\pi$
$127$	−20.4668	−1.81613	−0.908067	+	0.418825i	$0.862442\pi$
$128$	−10.3545	−0.915218
$129$	0.0846946	0.00745694
$130$	6.08922	0.534060
$131$	−8.57385	−0.749101	−0.374550	−	0.927207i	$-0.622203\pi$
$131$	−8.57385	−0.749101	−0.374550	+	0.927207i	$0.622203\pi$
$132$	−77.2569	−6.72435
$133$	5.14215	0.445881
$134$	−19.0278	−1.64375
$135$	−21.7909	−1.87546
$136$	35.7165	3.06266
$137$	−2.89443	−0.247288	−0.123644	−	0.992327i	$-0.539458\pi$
$137$	−2.89443	−0.247288	−0.123644	+	0.992327i	$0.539458\pi$
$138$	28.6637	2.44001
$139$	10.3505	0.877921	0.438960	−	0.898506i	$-0.355347\pi$
$139$	10.3505	0.877921	0.438960	+	0.898506i	$0.355347\pi$
$140$	10.5092	0.888194
$141$	23.2482	1.95785
$142$	−14.2773	−1.19813
$143$	−5.06338	−0.423421
$144$	69.8522	5.82102
$145$	−4.84304	−0.402193
$146$	−38.3516	−3.17400
$147$	−18.6728	−1.54011
$148$	−46.8445	−3.85060
$149$	−4.46408	−0.365712	−0.182856	−	0.983140i	$-0.558534\pi$
$149$	−4.46408	−0.365712	−0.182856	+	0.983140i	$0.558534\pi$
$150$	−2.10338	−0.171740
$151$	−0.658724	−0.0536062	−0.0268031	−	0.999641i	$-0.508533\pi$
$151$	−0.658724	−0.0536062	−0.0268031	+	0.999641i	$0.508533\pi$
$152$	45.8036	3.71516
$153$	−27.1268	−2.19307
$154$	−12.2022	−0.983278
$155$	−16.8898	−1.35662
$156$	15.2580	1.22161
$157$	−2.58306	−0.206150	−0.103075	−	0.994674i	$-0.532868\pi$
$157$	−2.58306	−0.206150	−0.103075	+	0.994674i	$0.532868\pi$
$158$	−30.6038	−2.43471
$159$	−18.8646	−1.49606
$160$	32.1538	2.54198
$161$	3.24224	0.255525
$162$	−27.3320	−2.14740
$163$	−3.18786	−0.249692	−0.124846	−	0.992176i	$-0.539844\pi$
$163$	−3.18786	−0.249692	−0.124846	+	0.992176i	$0.539844\pi$
$164$	−43.6944	−3.41196
$165$	35.1184	2.73397
$166$	−22.5668	−1.75152
$167$	−3.06051	−0.236829	−0.118415	−	0.992964i	$-0.537781\pi$
$167$	−3.06051	−0.236829	−0.118415	+	0.992964i	$0.537781\pi$
$168$	22.1971	1.71255
$169$	1.00000	0.0769231
$170$	−26.8945	−2.06271
$171$	−34.7880	−2.66030
$172$	0.141358	0.0107784
$173$	21.0028	1.59682	0.798408	−	0.602116i	$-0.205676\pi$
$173$	21.0028	1.59682	0.798408	+	0.602116i	$0.205676\pi$
$174$	−16.9449	−1.28459
$175$	−0.237920	−0.0179851
$176$	−57.5869	−4.34078
$177$	4.17341	0.313693
$178$	2.42135	0.181488
$179$	20.6068	1.54022	0.770112	−	0.637909i	$-0.220200\pi$
$179$	20.6068	1.54022	0.770112	+	0.637909i	$0.220200\pi$
$180$	−71.0977	−5.29931
$181$	3.16221	0.235045	0.117523	−	0.993070i	$-0.462505\pi$
$181$	3.16221	0.235045	0.117523	+	0.993070i	$0.462505\pi$
$182$	2.40988	0.178633
$183$	10.4694	0.773917
$184$	28.8802	2.12908
$185$	21.2940	1.56557
$186$	−59.0942	−4.33299
$187$	22.3636	1.63539
$188$	38.8018	2.82992
$189$	−8.62403	−0.627306
$190$	−34.4900	−2.50217
$191$	14.1129	1.02117	0.510586	−	0.859827i	$-0.329428\pi$
$191$	14.1129	1.02117	0.510586	+	0.859827i	$0.329428\pi$
$192$	43.7254	3.15561
$193$	−9.98374	−0.718645	−0.359323	−	0.933213i	$-0.616992\pi$
$193$	−9.98374	−0.718645	−0.359323	+	0.933213i	$0.616992\pi$
$194$	−48.6048	−3.48962
$195$	−6.93577	−0.496681
$196$	−31.1655	−2.22611
$197$	−5.68242	−0.404856	−0.202428	−	0.979297i	$-0.564883\pi$
$197$	−5.68242	−0.404856	−0.202428	+	0.979297i	$0.564883\pi$
$198$	82.5507	5.86662
$199$	−13.0159	−0.922672	−0.461336	−	0.887225i	$-0.652630\pi$
$199$	−13.0159	−0.922672	−0.461336	+	0.887225i	$0.652630\pi$
$200$	−2.11927	−0.149855
$201$	21.6731	1.52870
$202$	−5.09896	−0.358762
$203$	−1.91669	−0.134526
$204$	−67.3904	−4.71827
$205$	19.8621	1.38723
$206$	−16.1361	−1.12425
$207$	−21.9346	−1.52456
$208$	11.3732	0.788590
$209$	28.6796	1.98381
$210$	−16.7144	−1.15340
$211$	0.535478	0.0368638	0.0184319	−	0.999830i	$-0.494133\pi$
$211$	0.535478	0.0368638	0.0184319	+	0.999830i	$0.494133\pi$
$212$	−31.4855	−2.16243
$213$	16.2622	1.11427
$214$	21.0561	1.43937
$215$	−0.0642566	−0.00438226
$216$	−76.8183	−5.22682
$217$	−6.68434	−0.453762
$218$	−3.94964	−0.267503
$219$	43.6834	2.95185
$220$	58.6137	3.95173
$221$	−4.41674	−0.297102
$222$	74.5038	5.00036
$223$	13.3740	0.895587	0.447793	−	0.894137i	$-0.352210\pi$
$223$	13.3740	0.895587	0.447793	+	0.894137i	$0.352210\pi$
$224$	12.7253	0.850243
$225$	1.60959	0.107306
$226$	−35.9670	−2.39249
$227$	−27.2751	−1.81031	−0.905157	−	0.425076i	$-0.860247\pi$
$227$	−27.2751	−1.81031	−0.905157	+	0.425076i	$0.860247\pi$
$228$	−86.4228	−5.72349
$229$	14.7655	0.975732	0.487866	−	0.872919i	$-0.337775\pi$
$229$	14.7655	0.975732	0.487866	+	0.872919i	$0.337775\pi$
$230$	−21.7467	−1.43394
$231$	13.8986	0.914458
$232$	−17.0729	−1.12089
$233$	3.11884	0.204322	0.102161	−	0.994768i	$-0.467424\pi$
$233$	3.11884	0.204322	0.102161	+	0.994768i	$0.467424\pi$
$234$	−16.3035	−1.06579
$235$	−17.6380	−1.15058
$236$	6.96555	0.453419
$237$	34.8585	2.26431
$238$	−10.6438	−0.689936
$239$	27.6863	1.79088	0.895440	−	0.445183i	$-0.146861\pi$
$239$	27.6863	1.79088	0.895440	+	0.445183i	$0.146861\pi$
$240$	−78.8820	−5.09181
$241$	6.45054	0.415516	0.207758	−	0.978180i	$-0.433383\pi$
$241$	6.45054	0.415516	0.207758	+	0.978180i	$0.433383\pi$
$242$	−38.8561	−2.49777
$243$	2.63356	0.168943
$244$	17.4737	1.11864
$245$	14.1668	0.905085
$246$	69.4937	4.43076
$247$	−5.66411	−0.360399
$248$	−59.5405	−3.78083
$249$	25.7042	1.62894
$250$	−28.8503	−1.82465
$251$	−11.4010	−0.719626	−0.359813	−	0.933024i	$-0.617160\pi$
$251$	−11.4010	−0.719626	−0.359813	+	0.933024i	$0.617160\pi$
$252$	−28.1378	−1.77251
$253$	18.0831	1.13688
$254$	54.3291	3.40891
$255$	30.6335	1.91834
$256$	−1.43720	−0.0898250
$257$	−6.19091	−0.386178	−0.193089	−	0.981181i	$-0.561851\pi$
$257$	−6.19091	−0.386178	−0.193089	+	0.981181i	$0.561851\pi$
$258$	−0.224822	−0.0139968
$259$	8.42737	0.523651
$260$	−11.5760	−0.717913
$261$	12.9669	0.802632
$262$	22.7593	1.40607
$263$	−14.7860	−0.911743	−0.455872	−	0.890046i	$-0.650672\pi$
$263$	−14.7860	−0.911743	−0.455872	+	0.890046i	$0.650672\pi$
$264$	123.801	7.61943
$265$	14.3123	0.879196
$266$	−13.6499	−0.836927
$267$	−2.75798	−0.168786
$268$	36.1731	2.20962
$269$	3.23224	0.197073	0.0985366	−	0.995133i	$-0.468584\pi$
$269$	3.23224	0.197073	0.0985366	+	0.995133i	$0.468584\pi$
$270$	57.8440	3.52028
$271$	−15.5555	−0.944927	−0.472464	−	0.881350i	$-0.656635\pi$
$271$	−15.5555	−0.944927	−0.472464	+	0.881350i	$0.656635\pi$
$272$	−50.2325	−3.04579
$273$	−2.74492	−0.166130
$274$	7.68328	0.464164
$275$	−1.32696	−0.0800188
$276$	−54.4915	−3.28000
$277$	3.24445	0.194940	0.0974699	−	0.995238i	$-0.468925\pi$
$277$	3.24445	0.194940	0.0974699	+	0.995238i	$0.468925\pi$
$278$	−27.4755	−1.64787
$279$	45.2212	2.70732
$280$	−16.8407	−1.00642
$281$	16.1221	0.961761	0.480881	−	0.876786i	$-0.340317\pi$
$281$	16.1221	0.961761	0.480881	+	0.876786i	$0.340317\pi$
$282$	−61.7123	−3.67491
$283$	9.49014	0.564130	0.282065	−	0.959395i	$-0.408981\pi$
$283$	9.49014	0.564130	0.282065	+	0.959395i	$0.408981\pi$
$284$	27.1421	1.61059
$285$	39.2850	2.32704
$286$	13.4408	0.794769
$287$	7.86066	0.464000
$288$	−86.0896	−5.07288
$289$	2.50755	0.147503
$290$	12.8559	0.754922
$291$	55.3621	3.24538
$292$	72.9088	4.26667
$293$	12.6370	0.738261	0.369130	−	0.929378i	$-0.379656\pi$
$293$	12.6370	0.738261	0.369130	+	0.929378i	$0.379656\pi$
$294$	49.5671	2.89081
$295$	−3.16631	−0.184350
$296$	75.0665	4.36315
$297$	−48.0992	−2.79100
$298$	11.8499	0.686448
$299$	−3.57135	−0.206537
$300$	3.99866	0.230863
$301$	−0.0254304	−0.00146578
$302$	1.74859	0.100620
$303$	5.80784	0.333652
$304$	−64.4192	−3.69469
$305$	−7.94296	−0.454812
$306$	72.0081	4.11643
$307$	−18.1385	−1.03522	−0.517609	−	0.855617i	$-0.673178\pi$
$307$	−18.1385	−1.03522	−0.517609	+	0.855617i	$0.673178\pi$
$308$	23.1971	1.32178
$309$	18.3794	1.04557
$310$	44.8339	2.54640
$311$	−11.0947	−0.629124	−0.314562	−	0.949237i	$-0.601858\pi$
$311$	−11.0947	−0.629124	−0.314562	+	0.949237i	$0.601858\pi$
$312$	−24.4503	−1.38422
$313$	3.85056	0.217647	0.108823	−	0.994061i	$-0.465292\pi$
$313$	3.85056	0.217647	0.108823	+	0.994061i	$0.465292\pi$
$314$	6.85673	0.386948
$315$	12.7905	0.720664
$316$	58.1799	3.27288
$317$	10.7163	0.601887	0.300943	−	0.953642i	$-0.402698\pi$
$317$	10.7163	0.601887	0.300943	+	0.953642i	$0.402698\pi$
$318$	50.0760	2.80812
$319$	−10.6901	−0.598529
$320$	−33.1738	−1.85447
$321$	−23.9834	−1.33862
$322$	−8.60654	−0.479624
$323$	25.0169	1.39198
$324$	51.9599	2.88666
$325$	0.262070	0.0145371
$326$	8.46218	0.468677
$327$	4.49874	0.248781
$328$	70.0186	3.86613
$329$	−6.98048	−0.384846
$330$	−93.2220	−5.13170
$331$	25.1511	1.38243	0.691216	−	0.722648i	$-0.257075\pi$
$331$	25.1511	1.38243	0.691216	+	0.722648i	$0.257075\pi$
$332$	42.9010	2.35450
$333$	−57.0132	−3.12431
$334$	8.12413	0.444533
$335$	−16.4431	−0.898382
$336$	−31.2185	−1.70311
$337$	−5.24626	−0.285782	−0.142891	−	0.989738i	$-0.545640\pi$
$337$	−5.24626	−0.285782	−0.142891	+	0.989738i	$0.545640\pi$
$338$	−2.65450	−0.144386
$339$	40.9673	2.22504
$340$	51.1281	2.77281
$341$	−37.2809	−2.01887
$342$	92.3447	4.99343
$343$	11.9616	0.645868
$344$	−0.226520	−0.0122132
$345$	24.7701	1.33358
$346$	−55.7521	−2.99725
$347$	−22.1653	−1.18990	−0.594949	−	0.803763i	$-0.702828\pi$
$347$	−22.1653	−1.18990	−0.594949	+	0.803763i	$0.702828\pi$
$348$	32.2134	1.72682
$349$	0.803415	0.0430058	0.0215029	−	0.999769i	$-0.493155\pi$
$349$	0.803415	0.0430058	0.0215029	+	0.999769i	$0.493155\pi$
$350$	0.631559	0.0337583
$351$	9.49942	0.507042
$352$	70.9732	3.78288
$353$	−32.8155	−1.74660	−0.873298	−	0.487187i	$-0.838023\pi$
$353$	−32.8155	−1.74660	−0.873298	+	0.487187i	$0.838023\pi$
$354$	−11.0783	−0.588807
$355$	−12.3379	−0.654829
$356$	−4.60315	−0.243966
$357$	12.1236	0.641648
$358$	−54.7008	−2.89103
$359$	−14.8598	−0.784270	−0.392135	−	0.919908i	$-0.628263\pi$
$359$	−14.8598	−0.784270	−0.392135	+	0.919908i	$0.628263\pi$
$360$	113.931	6.00470
$361$	13.0822	0.688536
$362$	−8.39409	−0.441183
$363$	44.2581	2.32295
$364$	−4.58135	−0.240128
$365$	−33.1420	−1.73473
$366$	−27.7909	−1.45266
$367$	30.5587	1.59515	0.797575	−	0.603219i	$-0.206116\pi$
$367$	30.5587	1.59515	0.797575	+	0.603219i	$0.206116\pi$
$368$	−40.6177	−2.11735
$369$	−53.1793	−2.76841
$370$	−56.5250	−2.93859
$371$	5.66426	0.294074
$372$	112.342	5.82465
$373$	19.9988	1.03550	0.517749	−	0.855532i	$-0.326770\pi$
$373$	19.9988	1.03550	0.517749	+	0.855532i	$0.326770\pi$
$374$	−59.3643	−3.06965
$375$	32.8612	1.69694
$376$	−62.1784	−3.20661
$377$	2.11125	0.108735
$378$	22.8925	1.17746
$379$	14.3645	0.737854	0.368927	−	0.929458i	$-0.379725\pi$
$379$	14.3645	0.737854	0.368927	+	0.929458i	$0.379725\pi$
$380$	65.5678	3.36356
$381$	−61.8822	−3.17032
$382$	−37.4627	−1.91676
$383$	−22.6805	−1.15892	−0.579459	−	0.815001i	$-0.696736\pi$
$383$	−22.6805	−1.15892	−0.579459	+	0.815001i	$0.696736\pi$
$384$	−31.3073	−1.59764
$385$	−10.5446	−0.537405
$386$	26.5019	1.34891
$387$	0.172043	0.00874542
$388$	92.4009	4.69095
$389$	17.1622	0.870160	0.435080	−	0.900392i	$-0.356720\pi$
$389$	17.1622	0.870160	0.435080	+	0.900392i	$0.356720\pi$
$390$	18.4110	0.932278
$391$	15.7737	0.797711
$392$	49.9415	2.52243
$393$	−25.9234	−1.30766
$394$	15.0840	0.759921
$395$	−26.4467	−1.33068
$396$	−156.934	−7.88624
$397$	−32.8020	−1.64628	−0.823142	−	0.567835i	$-0.807781\pi$
$397$	−32.8020	−1.64628	−0.823142	+	0.567835i	$0.807781\pi$
$398$	34.5507	1.73187
$399$	15.5475	0.778350
$400$	2.98058	0.149029
$401$	2.79631	0.139641	0.0698206	−	0.997560i	$-0.477757\pi$
$401$	2.79631	0.139641	0.0698206	+	0.997560i	$0.477757\pi$
$402$	−57.5314	−2.86940
$403$	7.36284	0.366769
$404$	9.69346	0.482268
$405$	−23.6193	−1.17365
$406$	5.08787	0.252507
$407$	47.0023	2.32982
$408$	107.990	5.34632
$409$	38.4388	1.90068	0.950338	−	0.311220i	$-0.100737\pi$
$409$	38.4388	1.90068	0.950338	+	0.311220i	$0.100737\pi$
$410$	−52.7239	−2.60385
$411$	−8.75145	−0.431677
$412$	30.6758	1.51129
$413$	−1.25311	−0.0616614
$414$	58.2254	2.86162
$415$	−19.5014	−0.957286
$416$	−14.0170	−0.687238
$417$	31.2953	1.53254
$418$	−76.1300	−3.72364
$419$	38.7646	1.89378	0.946888	−	0.321562i	$-0.104208\pi$
$419$	38.7646	1.89378	0.946888	+	0.321562i	$0.104208\pi$
$420$	31.7752	1.55047
$421$	2.90414	0.141539	0.0707695	−	0.997493i	$-0.477455\pi$
$421$	2.90414	0.141539	0.0707695	+	0.997493i	$0.477455\pi$
$422$	−1.42143	−0.0691940
$423$	47.2247	2.29614
$424$	50.4543	2.45028
$425$	−1.15750	−0.0561468
$426$	−43.1681	−2.09150
$427$	−3.14352	−0.152126
$428$	−40.0290	−1.93488
$429$	−15.3094	−0.739143
$430$	0.170569	0.00822558
$431$	−25.9864	−1.25172	−0.625860	−	0.779936i	$-0.715252\pi$
$431$	−25.9864	−1.25172	−0.625860	+	0.779936i	$0.715252\pi$
$432$	108.039	5.19803
$433$	20.3091	0.975994	0.487997	−	0.872845i	$-0.337728\pi$
$433$	20.3091	0.975994	0.487997	+	0.872845i	$0.337728\pi$
$434$	17.7436	0.851719
$435$	−14.6431	−0.702085
$436$	7.50852	0.359593
$437$	20.2285	0.967662
$438$	−115.958	−5.54067
$439$	−34.6144	−1.65206	−0.826029	−	0.563628i	$-0.809405\pi$
$439$	−34.6144	−1.65206	−0.826029	+	0.563628i	$0.809405\pi$
$440$	−93.9261	−4.47775
$441$	−37.9307	−1.80622
$442$	11.7242	0.557665
$443$	−5.28148	−0.250931	−0.125465	−	0.992098i	$-0.540042\pi$
$443$	−5.28148	−0.250931	−0.125465	+	0.992098i	$0.540042\pi$
$444$	−141.637	−6.72177
$445$	2.09244	0.0991912
$446$	−35.5012	−1.68103
$447$	−13.4974	−0.638403
$448$	−13.1290	−0.620285
$449$	−19.3324	−0.912354	−0.456177	−	0.889889i	$-0.650782\pi$
$449$	−19.3324	−0.912354	−0.456177	+	0.889889i	$0.650782\pi$
$450$	−4.27266	−0.201415
$451$	43.8416	2.06442
$452$	68.3756	3.21612
$453$	−1.99168	−0.0935774
$454$	72.4019	3.39799
$455$	2.08253	0.0976306
$456$	138.489	6.48535
$457$	−15.1893	−0.710527	−0.355263	−	0.934766i	$-0.615609\pi$
$457$	−15.1893	−0.710527	−0.355263	+	0.934766i	$0.615609\pi$
$458$	−39.1951	−1.83147
$459$	−41.9564	−1.95836
$460$	41.3419	1.92758
$461$	23.3814	1.08898	0.544491	−	0.838767i	$-0.316723\pi$
$461$	23.3814	1.08898	0.544491	+	0.838767i	$0.316723\pi$
$462$	−36.8938	−1.71645
$463$	10.8510	0.504291	0.252145	−	0.967689i	$-0.418864\pi$
$463$	10.8510	0.504291	0.252145	+	0.967689i	$0.418864\pi$
$464$	24.0117	1.11472
$465$	−51.0669	−2.36817
$466$	−8.27898	−0.383516
$467$	−5.31025	−0.245729	−0.122864	−	0.992423i	$-0.539208\pi$
$467$	−5.31025	−0.245729	−0.122864	+	0.992423i	$0.539208\pi$
$468$	30.9940	1.43270
$469$	−6.50756	−0.300491
$470$	46.8202	2.15966
$471$	−7.80999	−0.359865
$472$	−11.1620	−0.513774
$473$	−0.141834	−0.00652153
$474$	−92.5321	−4.25014
$475$	−1.48440	−0.0681088
$476$	20.2346	0.927451
$477$	−38.3201	−1.75456
$478$	−73.4934	−3.36151
$479$	−17.5724	−0.802905	−0.401452	−	0.915880i	$-0.631494\pi$
$479$	−17.5724	−0.802905	−0.401452	+	0.915880i	$0.631494\pi$
$480$	97.2184	4.43739
$481$	−9.28280	−0.423259
$482$	−17.1230	−0.779930
$483$	9.80306	0.446055
$484$	73.8681	3.35764
$485$	−42.0024	−1.90723
$486$	−6.99078	−0.317108
$487$	−24.7856	−1.12314	−0.561572	−	0.827428i	$-0.689803\pi$
$487$	−24.7856	−1.12314	−0.561572	+	0.827428i	$0.689803\pi$
$488$	−28.0009	−1.26754
$489$	−9.63863	−0.435874
$490$	−37.6059	−1.69886
$491$	16.7342	0.755205	0.377602	−	0.925968i	$-0.376749\pi$
$491$	16.7342	0.755205	0.377602	+	0.925968i	$0.376749\pi$
$492$	−132.112	−5.95607
$493$	−9.32484	−0.419970
$494$	15.0354	0.676475
$495$	71.3372	3.20637
$496$	83.7391	3.76000
$497$	−4.88289	−0.219027
$498$	−68.2318	−3.05754
$499$	17.3629	0.777271	0.388635	−	0.921392i	$-0.372947\pi$
$499$	17.3629	0.777271	0.388635	+	0.921392i	$0.372947\pi$
$500$	54.8463	2.45280
$501$	−9.25358	−0.413420
$502$	30.2641	1.35075
$503$	−38.1700	−1.70192	−0.850958	−	0.525233i	$-0.823978\pi$
$503$	−38.1700	−1.70192	−0.850958	+	0.525233i	$0.823978\pi$
$504$	45.0897	2.00846
$505$	−4.40633	−0.196079
$506$	−48.0016	−2.13393
$507$	3.02354	0.134280
$508$	−103.283	−4.58245
$509$	21.8081	0.966626	0.483313	−	0.875448i	$-0.339433\pi$
$509$	21.8081	0.966626	0.483313	+	0.875448i	$0.339433\pi$
$510$	−81.3166	−3.60076
$511$	−13.1163	−0.580233
$512$	24.5241	1.08382
$513$	−53.8058	−2.37558
$514$	16.4338	0.724863
$515$	−13.9442	−0.614455
$516$	0.427401	0.0188153
$517$	−38.9326	−1.71225
$518$	−22.3705	−0.982902
$519$	63.5030	2.78747
$520$	18.5501	0.813475
$521$	29.4308	1.28938	0.644692	−	0.764442i	$-0.276985\pi$
$521$	29.4308	1.28938	0.644692	+	0.764442i	$0.276985\pi$
$522$	−34.4207	−1.50655
$523$	−0.392292	−0.0171537	−0.00857687	−	0.999963i	$-0.502730\pi$
$523$	−0.392292	−0.0171537	−0.00857687	+	0.999963i	$0.502730\pi$
$524$	−43.2669	−1.89012
$525$	−0.719362	−0.0313955
$526$	39.2494	1.71136
$527$	−32.5197	−1.41658
$528$	−174.117	−7.57745
$529$	−10.2455	−0.445455
$530$	−37.9920	−1.65027
$531$	8.47758	0.367896
$532$	25.9493	1.12504
$533$	−8.65857	−0.375044
$534$	7.32107	0.316813
$535$	18.1959	0.786677
$536$	−57.9659	−2.50375
$537$	62.3055	2.68868
$538$	−8.57999	−0.369910
$539$	31.2705	1.34692
$540$	−109.965	−4.73215
$541$	9.79950	0.421314	0.210657	−	0.977560i	$-0.432440\pi$
$541$	9.79950	0.421314	0.210657	+	0.977560i	$0.432440\pi$
$542$	41.2920	1.77364
$543$	9.56107	0.410305
$544$	61.9092	2.65434
$545$	−3.41313	−0.146202
$546$	7.28639	0.311829
$547$	33.4061	1.42834	0.714170	−	0.699972i	$-0.246804\pi$
$547$	33.4061	1.42834	0.714170	+	0.699972i	$0.246804\pi$
$548$	−14.6064	−0.623955
$549$	21.2667	0.907642
$550$	3.52242	0.150197
$551$	−11.9584	−0.509444
$552$	87.3205	3.71661
$553$	−10.4666	−0.445085
$554$	−8.61239	−0.365905
$555$	64.3833	2.73292
$556$	52.2328	2.21516
$557$	−2.78742	−0.118107	−0.0590533	−	0.998255i	$-0.518808\pi$
$557$	−2.78742	−0.118107	−0.0590533	+	0.998255i	$0.518808\pi$
$558$	−120.040	−5.08169
$559$	0.0280117	0.00118477
$560$	23.6851	1.00088
$561$	67.6174	2.85481
$562$	−42.7960	−1.80524
$563$	27.5610	1.16156	0.580778	−	0.814062i	$-0.302748\pi$
$563$	27.5610	1.16156	0.580778	+	0.814062i	$0.302748\pi$
$564$	117.319	4.94002
$565$	−31.0813	−1.30760
$566$	−25.1916	−1.05888
$567$	−9.34763	−0.392563
$568$	−43.4942	−1.82498
$569$	−40.6050	−1.70225	−0.851125	−	0.524963i	$-0.824079\pi$
$569$	−40.6050	−1.70225	−0.851125	+	0.524963i	$0.824079\pi$
$570$	−104.282	−4.36790
$571$	−31.0115	−1.29779	−0.648896	−	0.760877i	$-0.724769\pi$
$571$	−31.0115	−1.29779	−0.648896	+	0.760877i	$0.724769\pi$
$572$	−25.5518	−1.06837
$573$	42.6709	1.78260
$574$	−20.8661	−0.870936
$575$	−0.935945	−0.0390316
$576$	88.8207	3.70086
$577$	33.6111	1.39925	0.699625	−	0.714510i	$-0.253350\pi$
$577$	33.6111	1.39925	0.699625	+	0.714510i	$0.253350\pi$
$578$	−6.65630	−0.276865
$579$	−30.1863	−1.25450
$580$	−24.4398	−1.01481
$581$	−7.71792	−0.320193
$582$	−146.959	−6.09164
$583$	31.5915	1.30839
$584$	−116.834	−4.83461
$585$	−14.0888	−0.582502
$586$	−33.5449	−1.38573
$587$	24.5368	1.01274	0.506372	−	0.862315i	$-0.330986\pi$
$587$	24.5368	1.01274	0.506372	+	0.862315i	$0.330986\pi$
$588$	−94.2303	−3.88599
$589$	−41.7039	−1.71838
$590$	8.40498	0.346028
$591$	−17.1810	−0.706734
$592$	−105.575	−4.33911
$593$	27.6092	1.13377	0.566887	−	0.823796i	$-0.308148\pi$
$593$	27.6092	1.13377	0.566887	+	0.823796i	$0.308148\pi$
$594$	127.679	5.23875
$595$	−9.19799	−0.377081
$596$	−22.5275	−0.922762
$597$	−39.3541	−1.61066
$598$	9.48016	0.387672
$599$	11.7142	0.478629	0.239314	−	0.970942i	$-0.423077\pi$
$599$	11.7142	0.478629	0.239314	+	0.970942i	$0.423077\pi$
$600$	−6.40769	−0.261593
$601$	−28.3765	−1.15750	−0.578751	−	0.815505i	$-0.696460\pi$
$601$	−28.3765	−1.15750	−0.578751	+	0.815505i	$0.696460\pi$
$602$	0.0675050	0.00275130
$603$	44.0253	1.79285
$604$	−3.32418	−0.135259
$605$	−33.5780	−1.36514
$606$	−15.4169	−0.626270
$607$	−40.0732	−1.62652	−0.813261	−	0.581898i	$-0.802310\pi$
$607$	−40.0732	−1.62652	−0.813261	+	0.581898i	$0.802310\pi$
$608$	79.3937	3.21984
$609$	−5.79521	−0.234834
$610$	21.0846	0.853690
$611$	7.68904	0.311065
$612$	−136.892	−5.53354
$613$	1.46620	0.0592192	0.0296096	−	0.999562i	$-0.490574\pi$
$613$	1.46620	0.0592192	0.0296096	+	0.999562i	$0.490574\pi$
$614$	48.1487	1.94312
$615$	60.0538	2.42160
$616$	−37.1725	−1.49772
$617$	−1.00000	−0.0402585
$617$	−1.00000	−0.0402585
$618$	−48.7882	−1.96255
$619$	−33.4063	−1.34271	−0.671356	−	0.741135i	$-0.734288\pi$
$619$	−33.4063	−1.34271	−0.671356	+	0.741135i	$0.734288\pi$
$620$	−85.2322	−3.42301
$621$	−33.9258	−1.36139
$622$	29.4510	1.18088
$623$	0.828110	0.0331775
$624$	34.3874	1.37660
$625$	−26.2417	−1.04967
$626$	−10.2213	−0.408526
$627$	86.7139	3.46302
$628$	−13.0351	−0.520157
$629$	40.9996	1.63476
$630$	−33.9525	−1.35270
$631$	−47.0736	−1.87397	−0.936986	−	0.349367i	$-0.886397\pi$
$631$	−47.0736	−1.87397	−0.936986	+	0.349367i	$0.886397\pi$
$632$	−93.2310	−3.70853
$633$	1.61904	0.0643511
$634$	−28.4464	−1.12975
$635$	46.9492	1.86312
$636$	−95.1978	−3.77484
$637$	−6.17581	−0.244695
$638$	28.3768	1.12345
$639$	33.0340	1.30680
$640$	23.7524	0.938896
$641$	−4.00225	−0.158079	−0.0790397	−	0.996871i	$-0.525185\pi$
$641$	−4.00225	−0.158079	−0.0790397	+	0.996871i	$0.525185\pi$
$642$	63.6641	2.51262
$643$	31.1335	1.22779	0.613893	−	0.789389i	$-0.289602\pi$
$643$	31.1335	1.22779	0.613893	+	0.789389i	$0.289602\pi$
$644$	16.3616	0.644737
$645$	−0.194283	−0.00764987
$646$	−66.4074	−2.61276
$647$	29.3837	1.15519	0.577595	−	0.816323i	$-0.303991\pi$
$647$	29.3837	1.15519	0.577595	+	0.816323i	$0.303991\pi$
$648$	−83.2637	−3.27091
$649$	−6.98901	−0.274343
$650$	−0.695666	−0.0272863
$651$	−20.2104	−0.792107
$652$	−16.0872	−0.630022
$653$	43.2889	1.69403	0.847013	−	0.531572i	$-0.178398\pi$
$653$	43.2889	1.69403	0.847013	+	0.531572i	$0.178398\pi$
$654$	−11.9419	−0.466966
$655$	19.6677	0.768482
$656$	−98.4757	−3.84483
$657$	88.7354	3.46190
$658$	18.5297	0.722363
$659$	−4.47855	−0.174460	−0.0872298	−	0.996188i	$-0.527801\pi$
$659$	−4.47855	−0.174460	−0.0872298	+	0.996188i	$0.527801\pi$
$660$	177.221	6.89832
$661$	−10.0258	−0.389958	−0.194979	−	0.980807i	$-0.562464\pi$
$661$	−10.0258	−0.389958	−0.194979	+	0.980807i	$0.562464\pi$
$662$	−66.7638	−2.59485
$663$	−13.3542	−0.518634
$664$	−68.7472	−2.66791
$665$	−11.7957	−0.457417
$666$	151.342	5.86437
$667$	−7.54002	−0.291951
$668$	−15.4445	−0.597566
$669$	40.4368	1.56338
$670$	43.6482	1.68628
$671$	−17.5325	−0.676836
$672$	38.4754	1.48422
$673$	−31.4415	−1.21198	−0.605991	−	0.795472i	$-0.707223\pi$
$673$	−31.4415	−1.21198	−0.605991	+	0.795472i	$0.707223\pi$
$674$	13.9262	0.536417
$675$	2.48952	0.0958216
$676$	5.04638	0.194092
$677$	2.12632	0.0817212	0.0408606	−	0.999165i	$-0.486990\pi$
$677$	2.12632	0.0817212	0.0408606	+	0.999165i	$0.486990\pi$
$678$	−108.748	−4.17643
$679$	−16.6230	−0.637932
$680$	−81.9308	−3.14190
$681$	−82.4676	−3.16017
$682$	98.9621	3.78945
$683$	11.6988	0.447641	0.223820	−	0.974630i	$-0.428147\pi$
$683$	11.6988	0.447641	0.223820	+	0.974630i	$0.428147\pi$
$684$	−175.553	−6.71245
$685$	6.63960	0.253686
$686$	−31.7522	−1.21230
$687$	44.6442	1.70328
$688$	0.318583	0.0121459
$689$	−6.23922	−0.237695
$690$	−65.7522	−2.50314
$691$	10.3531	0.393852	0.196926	−	0.980418i	$-0.436904\pi$
$691$	10.3531	0.393852	0.196926	+	0.980418i	$0.436904\pi$
$692$	105.988	4.02907
$693$	28.2326	1.07247
$694$	58.8380	2.23346
$695$	−23.7433	−0.900635
$696$	−51.6207	−1.95668
$697$	38.2426	1.44854
$698$	−2.13267	−0.0807226
$699$	9.42996	0.356674
$700$	−1.20064	−0.0453798
$701$	−49.4878	−1.86913	−0.934565	−	0.355793i	$-0.884211\pi$
$701$	−49.4878	−1.86913	−0.934565	+	0.355793i	$0.884211\pi$
$702$	−25.2162	−0.951726
$703$	52.5788	1.98305
$704$	−73.2247	−2.75976
$705$	−53.3294	−2.00850
$706$	87.1089	3.27839
$707$	−1.74386	−0.0655846
$708$	21.0606	0.791507
$709$	−39.5432	−1.48508	−0.742538	−	0.669804i	$-0.766378\pi$
$709$	−39.5432	−1.48508	−0.742538	+	0.669804i	$0.766378\pi$
$710$	32.7510	1.22912
$711$	70.8092	2.65555
$712$	7.37637	0.276441
$713$	−26.2953	−0.984766
$714$	−32.1821	−1.20438
$715$	11.6150	0.434376
$716$	103.990	3.88628
$717$	83.7108	3.12624
$718$	39.4453	1.47209
$719$	28.8068	1.07431	0.537157	−	0.843482i	$-0.319498\pi$
$719$	28.8068	1.07431	0.537157	+	0.843482i	$0.319498\pi$
$720$	−160.235	−5.97162
$721$	−5.51859	−0.205523
$722$	−34.7267	−1.29239
$723$	19.5035	0.725342
$724$	15.9577	0.593064
$725$	0.553296	0.0205489
$726$	−117.483	−4.36021
$727$	−49.2090	−1.82506	−0.912530	−	0.409010i	$-0.865874\pi$
$727$	−49.2090	−1.82506	−0.912530	+	0.409010i	$0.865874\pi$
$728$	7.34143	0.272092
$729$	−22.9267	−0.849138
$730$	87.9754	3.25612
$731$	−0.123720	−0.00457596
$732$	52.8324	1.95274
$733$	−35.0893	−1.29605	−0.648027	−	0.761618i	$-0.724405\pi$
$733$	−35.0893	−1.29605	−0.648027	+	0.761618i	$0.724405\pi$
$734$	−81.1181	−2.99412
$735$	42.8340	1.57996
$736$	50.0595	1.84522
$737$	−36.2949	−1.33694
$738$	141.165	5.19634
$739$	45.2440	1.66433	0.832164	−	0.554529i	$-0.187102\pi$
$739$	45.2440	1.66433	0.832164	+	0.554529i	$0.187102\pi$
$740$	107.458	3.95022
$741$	−17.1257	−0.629128
$742$	−15.0358	−0.551982
$743$	−41.8554	−1.53552	−0.767762	−	0.640735i	$-0.778630\pi$
$743$	−41.8554	−1.53552	−0.767762	+	0.640735i	$0.778630\pi$
$744$	−180.023	−6.59998
$745$	10.2403	0.375174
$746$	−53.0868	−1.94365
$747$	52.2137	1.91040
$748$	112.855	4.12640
$749$	7.20125	0.263128
$750$	−87.2301	−3.18519
$751$	−51.4060	−1.87583	−0.937916	−	0.346863i	$-0.887247\pi$
$751$	−51.4060	−1.87583	−0.937916	+	0.346863i	$0.887247\pi$
$752$	87.4491	3.18894
$753$	−34.4715	−1.25621
$754$	−5.60432	−0.204097
$755$	1.51106	0.0549932
$756$	−43.5202	−1.58281
$757$	32.3777	1.17679	0.588393	−	0.808575i	$-0.299761\pi$
$757$	32.3777	1.17679	0.588393	+	0.808575i	$0.299761\pi$
$758$	−38.1306	−1.38496
$759$	54.6751	1.98458
$760$	−105.070	−3.81128
$761$	−32.9674	−1.19507	−0.597534	−	0.801843i	$-0.703853\pi$
$761$	−32.9674	−1.19507	−0.597534	+	0.801843i	$0.703853\pi$
$762$	164.267	5.95075
$763$	−1.35079	−0.0489018
$764$	71.2190	2.57661
$765$	62.2267	2.24981
$766$	60.2054	2.17531
$767$	1.38031	0.0498399
$768$	−4.34544	−0.156802
$769$	11.2067	0.404124	0.202062	−	0.979373i	$-0.435236\pi$
$769$	11.2067	0.404124	0.202062	+	0.979373i	$0.435236\pi$
$770$	27.9908	1.00872
$771$	−18.7185	−0.674130
$772$	−50.3818	−1.81328
$773$	−26.2051	−0.942532	−0.471266	−	0.881991i	$-0.656203\pi$
$773$	−26.2051	−0.942532	−0.471266	+	0.881991i	$0.656203\pi$
$774$	−0.456688	−0.0164153
$775$	1.92958	0.0693126
$776$	−148.069	−5.31536
$777$	25.4805	0.914108
$778$	−45.5572	−1.63331
$779$	49.0431	1.75715
$780$	−35.0005	−1.25322
$781$	−27.2336	−0.974493
$782$	−41.8713	−1.49732
$783$	20.0557	0.716731
$784$	−70.2388	−2.50853
$785$	5.92533	0.211484
$786$	68.8137	2.45451
$787$	−4.34426	−0.154856	−0.0774281	−	0.996998i	$-0.524671\pi$
$787$	−4.34426	−0.154856	−0.0774281	+	0.996998i	$0.524671\pi$
$788$	−28.6757	−1.02153
$789$	−44.7061	−1.59158
$790$	70.2028	2.49770
$791$	−12.3008	−0.437367
$792$	251.481	8.93599
$793$	3.46261	0.122961
$794$	87.0730	3.09010
$795$	43.2738	1.53476
$796$	−65.6832	−2.32808
$797$	−2.48274	−0.0879432	−0.0439716	−	0.999033i	$-0.514001\pi$
$797$	−2.48274	−0.0879432	−0.0439716	+	0.999033i	$0.514001\pi$
$798$	−41.2709	−1.46098
$799$	−33.9605	−1.20143
$800$	−3.67343	−0.129875
$801$	−5.60237	−0.197950
$802$	−7.42282	−0.262109
$803$	−73.1544	−2.58156
$804$	109.371	3.85721
$805$	−7.43745	−0.262136
$806$	−19.5447	−0.688432
$807$	9.77282	0.344020
$808$	−15.5334	−0.546463
$809$	39.8180	1.39993	0.699963	−	0.714180i	$-0.253200\pi$
$809$	39.8180	1.39993	0.699963	+	0.714180i	$0.253200\pi$
$810$	62.6974	2.20296
$811$	−37.9839	−1.33380	−0.666898	−	0.745149i	$-0.732378\pi$
$811$	−37.9839	−1.33380	−0.666898	+	0.745149i	$0.732378\pi$
$812$	−9.67238	−0.339434
$813$	−47.0326	−1.64951
$814$	−124.768	−4.37311
$815$	7.31270	0.256153
$816$	−151.880	−5.31687
$817$	−0.158661	−0.00555086
$818$	−102.036	−3.56760
$819$	−5.57584	−0.194835
$820$	100.232	3.50024
$821$	22.4287	0.782766	0.391383	−	0.920228i	$-0.371997\pi$
$821$	22.4287	0.782766	0.391383	+	0.920228i	$0.371997\pi$
$822$	23.2307	0.810265
$823$	−10.7993	−0.376440	−0.188220	−	0.982127i	$-0.560272\pi$
$823$	−10.7993	−0.376440	−0.188220	+	0.982127i	$0.560272\pi$
$824$	−49.1567	−1.71245
$825$	−4.01213	−0.139684
$826$	3.32638	0.115739
$827$	2.52257	0.0877182	0.0438591	−	0.999038i	$-0.486035\pi$
$827$	2.52257	0.0877182	0.0438591	+	0.999038i	$0.486035\pi$
$828$	−110.690	−3.84675
$829$	18.2207	0.632832	0.316416	−	0.948621i	$-0.397521\pi$
$829$	18.2207	0.632832	0.316416	+	0.948621i	$0.397521\pi$
$830$	51.7665	1.79684
$831$	9.80973	0.340296
$832$	14.4616	0.501367
$833$	27.2769	0.945089
$834$	−83.0734	−2.87660
$835$	7.02056	0.242957
$836$	144.728	5.00552
$837$	69.9427	2.41757
$838$	−102.901	−3.55465
$839$	22.9020	0.790664	0.395332	−	0.918538i	$-0.370630\pi$
$839$	22.9020	0.790664	0.395332	+	0.918538i	$0.370630\pi$
$840$	−50.9185	−1.75685
$841$	−24.5426	−0.846297
$842$	−7.70904	−0.265671
$843$	48.7457	1.67889
$844$	2.70222	0.0930144
$845$	−2.29392	−0.0789133
$846$	−125.358	−4.30990
$847$	−13.2889	−0.456613
$848$	−70.9600	−2.43678
$849$	28.6938	0.984770
$850$	3.07257	0.105388
$851$	33.1521	1.13644
$852$	82.0654	2.81151
$853$	51.7312	1.77124	0.885621	−	0.464408i	$-0.153733\pi$
$853$	51.7312	1.77124	0.885621	+	0.464408i	$0.153733\pi$
$854$	8.34449	0.285543
$855$	79.8008	2.72913
$856$	64.1450	2.19243
$857$	18.5378	0.633240	0.316620	−	0.948552i	$-0.397452\pi$
$857$	18.5378	0.633240	0.316620	+	0.948552i	$0.397452\pi$
$858$	40.6387	1.38738
$859$	17.6486	0.602164	0.301082	−	0.953598i	$-0.402652\pi$
$859$	17.6486	0.602164	0.301082	+	0.953598i	$0.402652\pi$
$860$	−0.324263	−0.0110573
$861$	23.7671	0.809979
$862$	68.9809	2.34950
$863$	13.5377	0.460827	0.230414	−	0.973093i	$-0.425992\pi$
$863$	13.5377	0.460827	0.230414	+	0.973093i	$0.425992\pi$
$864$	−133.153	−4.52996
$865$	−48.1789	−1.63813
$866$	−53.9106	−1.83196
$867$	7.58169	0.257488
$868$	−33.7317	−1.14493
$869$	−58.3759	−1.98027
$870$	38.8703	1.31783
$871$	7.16812	0.242883
$872$	−12.0321	−0.407459
$873$	112.459	3.80615
$874$	−53.6967	−1.81632
$875$	−9.86688	−0.333562
$876$	220.443	7.44808
$877$	−40.4816	−1.36697	−0.683483	−	0.729967i	$-0.739535\pi$
$877$	−40.4816	−1.36697	−0.683483	+	0.729967i	$0.739535\pi$
$878$	91.8841	3.10094
$879$	38.2085	1.28874
$880$	132.100	4.45308
$881$	45.0085	1.51637	0.758187	−	0.652037i	$-0.226085\pi$
$881$	45.0085	1.51637	0.758187	+	0.652037i	$0.226085\pi$
$882$	100.687	3.39031
$883$	0.224509	0.00755533	0.00377766	−	0.999993i	$-0.498798\pi$
$883$	0.224509	0.00755533	0.00377766	+	0.999993i	$0.498798\pi$
$884$	−22.2885	−0.749645
$885$	−9.57348	−0.321809
$886$	14.0197	0.471001
$887$	14.4994	0.486843	0.243422	−	0.969921i	$-0.421730\pi$
$887$	14.4994	0.486843	0.243422	+	0.969921i	$0.421730\pi$
$888$	226.967	7.61651
$889$	18.5807	0.623178
$890$	−5.55439	−0.186184
$891$	−52.1349	−1.74659
$892$	67.4901	2.25974
$893$	−43.5516	−1.45740
$894$	35.8288	1.19829
$895$	−47.2703	−1.58007
$896$	9.40032	0.314042
$897$	−10.7981	−0.360539
$898$	51.3180	1.71250
$899$	15.5448	0.518448
$900$	8.12260	0.270753
$901$	27.5570	0.918056
$902$	−116.378	−3.87495
$903$	−0.0768898	−0.00255873
$904$	−109.569	−3.64422
$905$	−7.25385	−0.241126
$906$	5.28693	0.175646
$907$	−26.5777	−0.882498	−0.441249	−	0.897385i	$-0.645464\pi$
$907$	−26.5777	−0.882498	−0.441249	+	0.897385i	$0.645464\pi$
$908$	−137.641	−4.56777
$909$	11.7976	0.391303
$910$	−5.52808	−0.183254
$911$	−43.5875	−1.44412	−0.722060	−	0.691831i	$-0.756804\pi$
$911$	−43.5875	−1.44412	−0.722060	+	0.691831i	$0.756804\pi$
$912$	−194.774	−6.44962
$913$	−43.0455	−1.42460
$914$	40.3201	1.33367
$915$	−24.0159	−0.793940
$916$	74.5124	2.46196
$917$	7.78375	0.257042
$918$	111.373	3.67587
$919$	15.8749	0.523664	0.261832	−	0.965113i	$-0.415673\pi$
$919$	15.8749	0.523664	0.261832	+	0.965113i	$0.415673\pi$
$920$	−66.2488	−2.18416
$921$	−54.8425	−1.80712
$922$	−62.0661	−2.04404
$923$	5.37853	0.177037
$924$	70.1375	2.30735
$925$	−2.43275	−0.0799882
$926$	−28.8041	−0.946562
$927$	37.3346	1.22623
$928$	−29.5933	−0.971448
$929$	−23.6523	−0.776005	−0.388003	−	0.921658i	$-0.626835\pi$
$929$	−23.6523	−0.776005	−0.388003	+	0.921658i	$0.626835\pi$
$930$	135.557	4.44510
$931$	34.9805	1.14644
$932$	15.7389	0.515544
$933$	−33.5454	−1.09823
$934$	14.0961	0.461237
$935$	−51.3003	−1.67770
$936$	−49.6666	−1.62340
$937$	24.6274	0.804543	0.402271	−	0.915520i	$-0.368221\pi$
$937$	24.6274	0.804543	0.402271	+	0.915520i	$0.368221\pi$
$938$	17.2743	0.564027
$939$	11.6423	0.379934
$940$	−89.0083	−2.90313
$941$	60.4737	1.97139	0.985693	−	0.168548i	$-0.0539079\pi$
$941$	60.4737	1.97139	0.985693	+	0.168548i	$0.0539079\pi$
$942$	20.7316	0.675473
$943$	30.9228	1.00698
$944$	15.6985	0.510943
$945$	19.7828	0.643536
$946$	0.376498	0.0122410
$947$	46.1700	1.50032	0.750162	−	0.661254i	$-0.229976\pi$
$947$	46.1700	1.50032	0.750162	+	0.661254i	$0.229976\pi$
$948$	175.910	5.71328
$949$	14.4477	0.468993
$950$	3.94033	0.127841
$951$	32.4012	1.05068
$952$	−32.4252	−1.05091
$953$	57.6275	1.86674	0.933368	−	0.358920i	$-0.116855\pi$
$953$	57.6275	1.86674	0.933368	+	0.358920i	$0.116855\pi$
$954$	101.721	3.29334
$955$	−32.3738	−1.04759
$956$	139.716	4.51873
$957$	−32.3219	−1.04482
$958$	46.6461	1.50707
$959$	2.62771	0.0848531
$960$	−100.303	−3.23725
$961$	23.2114	0.748754
$962$	24.6412	0.794464
$963$	−48.7183	−1.56992
$964$	32.5519	1.04843
$965$	22.9019	0.737239
$966$	−26.0223	−0.837252
$967$	24.7321	0.795330	0.397665	−	0.917531i	$-0.369821\pi$
$967$	24.7321	0.795330	0.397665	+	0.917531i	$0.369821\pi$
$968$	−118.371	−3.80458
$969$	75.6397	2.42990
$970$	111.496	3.57991
$971$	39.8658	1.27936	0.639678	−	0.768643i	$-0.279068\pi$
$971$	39.8658	1.27936	0.639678	+	0.768643i	$0.279068\pi$
$972$	13.2899	0.426275
$973$	−9.39671	−0.301245
$974$	65.7935	2.10816
$975$	0.792381	0.0253765
$976$	39.3810	1.26056
$977$	18.4021	0.588736	0.294368	−	0.955692i	$-0.404891\pi$
$977$	18.4021	0.588736	0.294368	+	0.955692i	$0.404891\pi$
$978$	25.5858	0.818143
$979$	4.61865	0.147613
$980$	71.4912	2.28370
$981$	9.13842	0.291767
$982$	−44.4210	−1.41753
$983$	−19.2158	−0.612890	−0.306445	−	0.951888i	$-0.599140\pi$
$983$	−19.2158	−0.612890	−0.306445	+	0.951888i	$0.599140\pi$
$984$	211.704	6.74889
$985$	13.0350	0.415330
$986$	24.7528	0.788290
$987$	−21.1058	−0.671805
$988$	−28.5833	−0.909355
$989$	−0.100040	−0.00318107
$990$	−189.365	−6.01840
$991$	55.0929	1.75008	0.875041	−	0.484048i	$-0.160834\pi$
$991$	55.0929	1.75008	0.875041	+	0.484048i	$0.160834\pi$
$992$	−103.205	−3.27675
$993$	76.0456	2.41323
$994$	12.9616	0.411118
$995$	29.8574	0.946544
$996$	129.713	4.11012
$997$	21.2131	0.671826	0.335913	−	0.941893i	$-0.390955\pi$
$997$	21.2131	0.671826	0.335913	+	0.941893i	$0.390955\pi$
$998$	−46.0899	−1.45895
$999$	−88.1812	−2.78993

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8021.2.a.d.1.8	✓	174

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8021.2.a.d.1.8	✓	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)

\(f(q)\)	\(=\)	\(q-2.65450 q^{2} +3.02354 q^{3} +5.04638 q^{4} -2.29392 q^{5} -8.02600 q^{6} -0.907848 q^{7} -8.08663 q^{8} +6.14182 q^{9} +O(q^{10})\)	\(q-2.65450 q^{2} +3.02354 q^{3} +5.04638 q^{4} -2.29392 q^{5} -8.02600 q^{6} -0.907848 q^{7} -8.08663 q^{8} +6.14182 q^{9} +6.08922 q^{10} -5.06338 q^{11} +15.2580 q^{12} +1.00000 q^{13} +2.40988 q^{14} -6.93577 q^{15} +11.3732 q^{16} -4.41674 q^{17} -16.3035 q^{18} -5.66411 q^{19} -11.5760 q^{20} -2.74492 q^{21} +13.4408 q^{22} -3.57135 q^{23} -24.4503 q^{24} +0.262070 q^{25} -2.65450 q^{26} +9.49942 q^{27} -4.58135 q^{28} +2.11125 q^{29} +18.4110 q^{30} +7.36284 q^{31} -14.0170 q^{32} -15.3094 q^{33} +11.7242 q^{34} +2.08253 q^{35} +30.9940 q^{36} -9.28280 q^{37} +15.0354 q^{38} +3.02354 q^{39} +18.5501 q^{40} -8.65857 q^{41} +7.28639 q^{42} +0.0280117 q^{43} -25.5518 q^{44} -14.0888 q^{45} +9.48016 q^{46} +7.68904 q^{47} +34.3874 q^{48} -6.17581 q^{49} -0.695666 q^{50} -13.3542 q^{51} +5.04638 q^{52} -6.23922 q^{53} -25.2162 q^{54} +11.6150 q^{55} +7.34143 q^{56} -17.1257 q^{57} -5.60432 q^{58} +1.38031 q^{59} -35.0005 q^{60} +3.46261 q^{61} -19.5447 q^{62} -5.57584 q^{63} +14.4616 q^{64} -2.29392 q^{65} +40.6387 q^{66} +7.16812 q^{67} -22.2885 q^{68} -10.7981 q^{69} -5.52808 q^{70} +5.37853 q^{71} -49.6666 q^{72} +14.4477 q^{73} +24.6412 q^{74} +0.792381 q^{75} -28.5833 q^{76} +4.59678 q^{77} -8.02600 q^{78} +11.5290 q^{79} -26.0892 q^{80} +10.2965 q^{81} +22.9842 q^{82} +8.50134 q^{83} -13.8519 q^{84} +10.1316 q^{85} -0.0743571 q^{86} +6.38346 q^{87} +40.9457 q^{88} -0.912168 q^{89} +37.3989 q^{90} -0.907848 q^{91} -18.0224 q^{92} +22.2619 q^{93} -20.4106 q^{94} +12.9930 q^{95} -42.3809 q^{96} +18.3103 q^{97} +16.3937 q^{98} -31.0984 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 174 q + 6 q^{2} + 37 q^{3} + 214 q^{4} + 10 q^{5} + 12 q^{6} + 28 q^{7} + 15 q^{8} + 211 q^{9}+O(q^{10}) \) 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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