LMFDB - Embedded newform 8041.2.a.j.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$0$
Dimension:	$82$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.57949 q^{2} +2.85867 q^{3} +4.65376 q^{4} +3.17304 q^{5} -7.37390 q^{6} -3.48304 q^{7} -6.84534 q^{8} +5.17198 q^{9} +O(q^{10})$	\(q-2.57949 q^{2} +2.85867 q^{3} +4.65376 q^{4} +3.17304 q^{5} -7.37390 q^{6} -3.48304 q^{7} -6.84534 q^{8} +5.17198 q^{9} -8.18483 q^{10} +1.00000 q^{11} +13.3035 q^{12} +1.45531 q^{13} +8.98446 q^{14} +9.07068 q^{15} +8.34995 q^{16} +1.00000 q^{17} -13.3411 q^{18} +7.42589 q^{19} +14.7666 q^{20} -9.95685 q^{21} -2.57949 q^{22} +6.93883 q^{23} -19.5685 q^{24} +5.06821 q^{25} -3.75394 q^{26} +6.20897 q^{27} -16.2092 q^{28} -6.94836 q^{29} -23.3977 q^{30} +3.05829 q^{31} -7.84792 q^{32} +2.85867 q^{33} -2.57949 q^{34} -11.0518 q^{35} +24.0692 q^{36} +0.00693868 q^{37} -19.1550 q^{38} +4.16023 q^{39} -21.7206 q^{40} +9.65861 q^{41} +25.6836 q^{42} +1.00000 q^{43} +4.65376 q^{44} +16.4109 q^{45} -17.8986 q^{46} -7.07691 q^{47} +23.8697 q^{48} +5.13155 q^{49} -13.0734 q^{50} +2.85867 q^{51} +6.77264 q^{52} +7.85931 q^{53} -16.0160 q^{54} +3.17304 q^{55} +23.8426 q^{56} +21.2282 q^{57} +17.9232 q^{58} -6.07479 q^{59} +42.2127 q^{60} -5.18905 q^{61} -7.88882 q^{62} -18.0142 q^{63} +3.54372 q^{64} +4.61775 q^{65} -7.37390 q^{66} +0.816633 q^{67} +4.65376 q^{68} +19.8358 q^{69} +28.5081 q^{70} +9.08175 q^{71} -35.4040 q^{72} +1.53699 q^{73} -0.0178982 q^{74} +14.4883 q^{75} +34.5583 q^{76} -3.48304 q^{77} -10.7313 q^{78} +10.7383 q^{79} +26.4948 q^{80} +2.23345 q^{81} -24.9143 q^{82} -5.34804 q^{83} -46.3368 q^{84} +3.17304 q^{85} -2.57949 q^{86} -19.8630 q^{87} -6.84534 q^{88} +7.34523 q^{89} -42.3318 q^{90} -5.06888 q^{91} +32.2916 q^{92} +8.74263 q^{93} +18.2548 q^{94} +23.5627 q^{95} -22.4346 q^{96} -11.4670 q^{97} -13.2368 q^{98} +5.17198 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9}+O(q^{10}) $ 82 * q + 8 * q^2 + 6 * q^3 + 98 * q^4 + 11 * q^5 + 10 * q^6 + 8 * q^7 + 30 * q^8 + 108 * q^9	\( 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9} + q^{10} + 82 q^{11} + 3 q^{12} + 26 q^{13} + 17 q^{14} + 66 q^{15} + 122 q^{16} + 82 q^{17} + 18 q^{18} + 12 q^{19} + 9 q^{20} + 22 q^{21} + 8 q^{22} + 50 q^{23} + 15 q^{24} + 117 q^{25} + 36 q^{26} + 30 q^{27} + 11 q^{28} + 33 q^{29} - 26 q^{30} + 40 q^{31} + 58 q^{32} + 6 q^{33} + 8 q^{34} + 16 q^{35} + 160 q^{36} + 31 q^{37} + 18 q^{38} + 41 q^{39} - 29 q^{40} + 42 q^{41} - 51 q^{42} + 82 q^{43} + 98 q^{44} - 2 q^{45} - 19 q^{46} + 84 q^{47} - 46 q^{48} + 136 q^{49} + 59 q^{50} + 6 q^{51} + 45 q^{52} + 83 q^{53} + 24 q^{54} + 11 q^{55} + 21 q^{56} + 23 q^{57} + 14 q^{58} + 96 q^{59} + 184 q^{60} - 6 q^{61} - 23 q^{62} + 8 q^{63} + 148 q^{64} + 5 q^{65} + 10 q^{66} + 78 q^{67} + 98 q^{68} + 61 q^{69} - 3 q^{70} + 155 q^{71} + 50 q^{72} - 23 q^{73} + 10 q^{74} - 19 q^{75} + 44 q^{76} + 8 q^{77} - 27 q^{78} + 31 q^{79} + 19 q^{80} + 150 q^{81} - 12 q^{82} + 54 q^{83} + 8 q^{84} + 11 q^{85} + 8 q^{86} + 20 q^{87} + 30 q^{88} + 25 q^{89} - 81 q^{90} - 14 q^{91} + 60 q^{92} + 36 q^{93} + 19 q^{94} + 111 q^{95} - 6 q^{96} + 2 q^{97} - 5 q^{98} + 108 q^{99}+O(q^{100}) \) 82 * q + 8 * q^2 + 6 * q^3 + 98 * q^4 + 11 * q^5 + 10 * q^6 + 8 * q^7 + 30 * q^8 + 108 * q^9 + q^10 + 82 * q^11 + 3 * q^12 + 26 * q^13 + 17 * q^14 + 66 * q^15 + 122 * q^16 + 82 * q^17 + 18 * q^18 + 12 * q^19 + 9 * q^20 + 22 * q^21 + 8 * q^22 + 50 * q^23 + 15 * q^24 + 117 * q^25 + 36 * q^26 + 30 * q^27 + 11 * q^28 + 33 * q^29 - 26 * q^30 + 40 * q^31 + 58 * q^32 + 6 * q^33 + 8 * q^34 + 16 * q^35 + 160 * q^36 + 31 * q^37 + 18 * q^38 + 41 * q^39 - 29 * q^40 + 42 * q^41 - 51 * q^42 + 82 * q^43 + 98 * q^44 - 2 * q^45 - 19 * q^46 + 84 * q^47 - 46 * q^48 + 136 * q^49 + 59 * q^50 + 6 * q^51 + 45 * q^52 + 83 * q^53 + 24 * q^54 + 11 * q^55 + 21 * q^56 + 23 * q^57 + 14 * q^58 + 96 * q^59 + 184 * q^60 - 6 * q^61 - 23 * q^62 + 8 * q^63 + 148 * q^64 + 5 * q^65 + 10 * q^66 + 78 * q^67 + 98 * q^68 + 61 * q^69 - 3 * q^70 + 155 * q^71 + 50 * q^72 - 23 * q^73 + 10 * q^74 - 19 * q^75 + 44 * q^76 + 8 * q^77 - 27 * q^78 + 31 * q^79 + 19 * q^80 + 150 * q^81 - 12 * q^82 + 54 * q^83 + 8 * q^84 + 11 * q^85 + 8 * q^86 + 20 * q^87 + 30 * q^88 + 25 * q^89 - 81 * q^90 - 14 * q^91 + 60 * q^92 + 36 * q^93 + 19 * q^94 + 111 * q^95 - 6 * q^96 + 2 * q^97 - 5 * q^98 + 108 * 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 $

$2$	−2.57949	−1.82397	−0.911987	−	0.410220i	$-0.865452\pi$
$2$	−2.57949	−1.82397	−0.911987	+	0.410220i	$0.865452\pi$
$3$	2.85867	1.65045	0.825226	−	0.564802i	$-0.191048\pi$
$3$	2.85867	1.65045	0.825226	+	0.564802i	$0.191048\pi$
$4$	4.65376	2.32688
$5$	3.17304	1.41903	0.709514	−	0.704691i	$-0.248914\pi$
$5$	3.17304	1.41903	0.709514	+	0.704691i	$0.248914\pi$
$6$	−7.37390	−3.01038
$7$	−3.48304	−1.31646	−0.658232	−	0.752815i	$-0.728696\pi$
$7$	−3.48304	−1.31646	−0.658232	+	0.752815i	$0.728696\pi$
$8$	−6.84534	−2.42019
$9$	5.17198	1.72399
$10$	−8.18483	−2.58827
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	13.3035	3.84040
$13$	1.45531	0.403629	0.201815	−	0.979424i	$-0.435316\pi$
$13$	1.45531	0.403629	0.201815	+	0.979424i	$0.435316\pi$
$14$	8.98446	2.40120
$15$	9.07068	2.34204
$16$	8.34995	2.08749
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−13.3411	−3.14452
$19$	7.42589	1.70362	0.851808	−	0.523854i	$-0.175506\pi$
$19$	7.42589	1.70362	0.851808	+	0.523854i	$0.175506\pi$
$20$	14.7666	3.30191
$21$	−9.95685	−2.17276
$22$	−2.57949	−0.549949
$23$	6.93883	1.44685	0.723423	−	0.690405i	$-0.242568\pi$
$23$	6.93883	1.44685	0.723423	+	0.690405i	$0.242568\pi$
$24$	−19.5685	−3.99441
$25$	5.06821	1.01364
$26$	−3.75394	−0.736209
$27$	6.20897	1.19492
$28$	−16.2092	−3.06325
$29$	−6.94836	−1.29028	−0.645139	−	0.764065i	$-0.723200\pi$
$29$	−6.94836	−1.29028	−0.645139	+	0.764065i	$0.723200\pi$
$30$	−23.3977	−4.27182
$31$	3.05829	0.549285	0.274642	−	0.961546i	$-0.411441\pi$
$31$	3.05829	0.549285	0.274642	+	0.961546i	$0.411441\pi$
$32$	−7.84792	−1.38733
$33$	2.85867	0.497630
$34$	−2.57949	−0.442379
$35$	−11.0518	−1.86810
$36$	24.0692	4.01153
$37$	0.00693868	0.00114071	0.000570356	−	1.00000i	$-0.499818\pi$
$37$	0.00693868	0.00114071	0.000570356		1.00000i	$0.499818\pi$
$38$	−19.1550	−3.10735
$39$	4.16023	0.666171
$40$	−21.7206	−3.43432
$41$	9.65861	1.50842	0.754211	−	0.656633i	$-0.228020\pi$
$41$	9.65861	1.50842	0.754211	+	0.656633i	$0.228020\pi$
$42$	25.6836	3.96306
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	4.65376	0.701580
$45$	16.4109	2.44640
$46$	−17.8986	−2.63901
$47$	−7.07691	−1.03227	−0.516137	−	0.856506i	$-0.672630\pi$
$47$	−7.07691	−1.03227	−0.516137	+	0.856506i	$0.672630\pi$
$48$	23.8697	3.44530
$49$	5.13155	0.733079
$50$	−13.0734	−1.84885
$51$	2.85867	0.400294
$52$	6.77264	0.939196
$53$	7.85931	1.07956	0.539780	−	0.841806i	$-0.318507\pi$
$53$	7.85931	1.07956	0.539780	+	0.841806i	$0.318507\pi$
$54$	−16.0160	−2.17950
$55$	3.17304	0.427853
$56$	23.8426	3.18610
$57$	21.2282	2.81174
$58$	17.9232	2.35343
$59$	−6.07479	−0.790870	−0.395435	−	0.918494i	$-0.629406\pi$
$59$	−6.07479	−0.790870	−0.395435	+	0.918494i	$0.629406\pi$
$60$	42.2127	5.44964
$61$	−5.18905	−0.664390	−0.332195	−	0.943211i	$-0.607789\pi$
$61$	−5.18905	−0.664390	−0.332195	+	0.943211i	$0.607789\pi$
$62$	−7.88882	−1.00188
$63$	−18.0142	−2.26958
$64$	3.54372	0.442964
$65$	4.61775	0.572761
$66$	−7.37390	−0.907664
$67$	0.816633	0.0997676	0.0498838	−	0.998755i	$-0.484115\pi$
$67$	0.816633	0.0997676	0.0498838	+	0.998755i	$0.484115\pi$
$68$	4.65376	0.564351
$69$	19.8358	2.38795
$70$	28.5081	3.40737
$71$	9.08175	1.07781	0.538903	−	0.842368i	$-0.318839\pi$
$71$	9.08175	1.07781	0.538903	+	0.842368i	$0.318839\pi$
$72$	−35.4040	−4.17240
$73$	1.53699	0.179891	0.0899456	−	0.995947i	$-0.471331\pi$
$73$	1.53699	0.179891	0.0899456	+	0.995947i	$0.471331\pi$
$74$	−0.0178982	−0.00208063
$75$	14.4883	1.67297
$76$	34.5583	3.96411
$77$	−3.48304	−0.396929
$78$	−10.7313	−1.21508
$79$	10.7383	1.20816	0.604079	−	0.796924i	$-0.293541\pi$
$79$	10.7383	1.20816	0.604079	+	0.796924i	$0.293541\pi$
$80$	26.4948	2.96220
$81$	2.23345	0.248161
$82$	−24.9143	−2.75132
$83$	−5.34804	−0.587023	−0.293512	−	0.955955i	$-0.594824\pi$
$83$	−5.34804	−0.587023	−0.293512	+	0.955955i	$0.594824\pi$
$84$	−46.3368	−5.05576
$85$	3.17304	0.344165
$86$	−2.57949	−0.278153
$87$	−19.8630	−2.12954
$88$	−6.84534	−0.729715
$89$	7.34523	0.778593	0.389296	−	0.921113i	$-0.372718\pi$
$89$	7.34523	0.778593	0.389296	+	0.921113i	$0.372718\pi$
$90$	−42.3318	−4.46216
$91$	−5.06888	−0.531363
$92$	32.2916	3.36663
$93$	8.74263	0.906569
$94$	18.2548	1.88284
$95$	23.5627	2.41748
$96$	−22.4346	−2.28972
$97$	−11.4670	−1.16430	−0.582148	−	0.813083i	$-0.697788\pi$
$97$	−11.4670	−1.16430	−0.582148	+	0.813083i	$0.697788\pi$
$98$	−13.2368	−1.33712
$99$	5.17198	0.519804
$100$	23.5862	2.35862
$101$	7.09074	0.705555	0.352777	−	0.935707i	$-0.385237\pi$
$101$	7.09074	0.705555	0.352777	+	0.935707i	$0.385237\pi$
$102$	−7.37390	−0.730125
$103$	−9.86660	−0.972185	−0.486093	−	0.873907i	$-0.661578\pi$
$103$	−9.86660	−0.972185	−0.486093	+	0.873907i	$0.661578\pi$
$104$	−9.96205	−0.976860
$105$	−31.5935	−3.08321
$106$	−20.2730	−1.96909
$107$	−18.3376	−1.77276	−0.886381	−	0.462956i	$-0.846789\pi$
$107$	−18.3376	−1.77276	−0.886381	+	0.462956i	$0.846789\pi$
$108$	28.8951	2.78043
$109$	6.28953	0.602428	0.301214	−	0.953557i	$-0.402608\pi$
$109$	6.28953	0.602428	0.301214	+	0.953557i	$0.402608\pi$
$110$	−8.18483	−0.780393
$111$	0.0198354	0.00188269
$112$	−29.0832	−2.74810
$113$	−3.49567	−0.328845	−0.164423	−	0.986390i	$-0.552576\pi$
$113$	−3.49567	−0.328845	−0.164423	+	0.986390i	$0.552576\pi$
$114$	−54.7578	−5.12854
$115$	22.0172	2.05311
$116$	−32.3360	−3.00232
$117$	7.52681	0.695854
$118$	15.6698	1.44253
$119$	−3.48304	−0.319290
$120$	−62.0919	−5.66818
$121$	1.00000	0.0909091
$122$	13.3851	1.21183
$123$	27.6108	2.48958
$124$	14.2325	1.27812
$125$	0.216419	0.0193571
$126$	46.4674	4.13965
$127$	−4.44126	−0.394098	−0.197049	−	0.980394i	$-0.563136\pi$
$127$	−4.44126	−0.394098	−0.197049	+	0.980394i	$0.563136\pi$
$128$	6.55487	0.579374
$129$	2.85867	0.251692
$130$	−11.9114	−1.04470
$131$	−6.39916	−0.559097	−0.279548	−	0.960132i	$-0.590185\pi$
$131$	−6.39916	−0.559097	−0.279548	+	0.960132i	$0.590185\pi$
$132$	13.3035	1.15793
$133$	−25.8647	−2.24275
$134$	−2.10650	−0.181973
$135$	19.7013	1.69562
$136$	−6.84534	−0.586983
$137$	−18.3699	−1.56945	−0.784724	−	0.619845i	$-0.787195\pi$
$137$	−18.3699	−1.56945	−0.784724	+	0.619845i	$0.787195\pi$
$138$	−51.1662	−4.35556
$139$	16.9330	1.43624	0.718119	−	0.695920i	$-0.245003\pi$
$139$	16.9330	1.43624	0.718119	+	0.695920i	$0.245003\pi$
$140$	−51.4326	−4.34684
$141$	−20.2305	−1.70372
$142$	−23.4263	−1.96589
$143$	1.45531	0.121699
$144$	43.1858	3.59882
$145$	−22.0474	−1.83094
$146$	−3.96465	−0.328117
$147$	14.6694	1.20991
$148$	0.0322909	0.00265430
$149$	−21.1371	−1.73162	−0.865808	−	0.500376i	$-0.833195\pi$
$149$	−21.1371	−1.73162	−0.865808	+	0.500376i	$0.833195\pi$
$150$	−37.3724	−3.05145
$151$	−10.9796	−0.893511	−0.446755	−	0.894656i	$-0.647421\pi$
$151$	−10.9796	−0.893511	−0.446755	+	0.894656i	$0.647421\pi$
$152$	−50.8327	−4.12308
$153$	5.17198	0.418130
$154$	8.98446	0.723988
$155$	9.70408	0.779451
$156$	19.3607	1.55010
$157$	11.8786	0.948017	0.474008	−	0.880520i	$-0.342807\pi$
$157$	11.8786	0.948017	0.474008	+	0.880520i	$0.342807\pi$
$158$	−27.6994	−2.20365
$159$	22.4672	1.78176
$160$	−24.9018	−1.96866
$161$	−24.1682	−1.90472
$162$	−5.76116	−0.452639
$163$	11.0766	0.867584	0.433792	−	0.901013i	$-0.357175\pi$
$163$	11.0766	0.867584	0.433792	+	0.901013i	$0.357175\pi$
$164$	44.9488	3.50991
$165$	9.07068	0.706151
$166$	13.7952	1.07072
$167$	3.05742	0.236590	0.118295	−	0.992979i	$-0.462257\pi$
$167$	3.05742	0.236590	0.118295	+	0.992979i	$0.462257\pi$
$168$	68.1580	5.25850
$169$	−10.8821	−0.837084
$170$	−8.18483	−0.627748
$171$	38.4066	2.93702
$172$	4.65376	0.354846
$173$	21.1352	1.60688	0.803439	−	0.595387i	$-0.203001\pi$
$173$	21.1352	1.60688	0.803439	+	0.595387i	$0.203001\pi$
$174$	51.2365	3.88423
$175$	−17.6528	−1.33442
$176$	8.34995	0.629401
$177$	−17.3658	−1.30529
$178$	−18.9469	−1.42013
$179$	−8.58174	−0.641429	−0.320715	−	0.947176i	$-0.603923\pi$
$179$	−8.58174	−0.641429	−0.320715	+	0.947176i	$0.603923\pi$
$180$	76.3725	5.69247
$181$	−19.8941	−1.47872	−0.739359	−	0.673311i	$-0.764871\pi$
$181$	−19.8941	−1.47872	−0.739359	+	0.673311i	$0.764871\pi$
$182$	13.0751	0.969193
$183$	−14.8338	−1.09654
$184$	−47.4986	−3.50164
$185$	0.0220167	0.00161870
$186$	−22.5515	−1.65356
$187$	1.00000	0.0731272
$188$	−32.9342	−2.40197
$189$	−21.6261	−1.57307
$190$	−60.7797	−4.40942
$191$	15.0403	1.08828	0.544140	−	0.838994i	$-0.316856\pi$
$191$	15.0403	1.08828	0.544140	+	0.838994i	$0.316856\pi$
$192$	10.1303	0.731092
$193$	−3.21273	−0.231257	−0.115629	−	0.993293i	$-0.536888\pi$
$193$	−3.21273	−0.231257	−0.115629	+	0.993293i	$0.536888\pi$
$194$	29.5790	2.12365
$195$	13.2006	0.945315
$196$	23.8810	1.70579
$197$	8.96272	0.638568	0.319284	−	0.947659i	$-0.396558\pi$
$197$	8.96272	0.638568	0.319284	+	0.947659i	$0.396558\pi$
$198$	−13.3411	−0.948108
$199$	−6.56383	−0.465298	−0.232649	−	0.972561i	$-0.574739\pi$
$199$	−6.56383	−0.465298	−0.232649	+	0.972561i	$0.574739\pi$
$200$	−34.6936	−2.45321
$201$	2.33448	0.164662
$202$	−18.2905	−1.28691
$203$	24.2014	1.69860
$204$	13.3035	0.931435
$205$	30.6472	2.14049
$206$	25.4508	1.77324
$207$	35.8875	2.49435
$208$	12.1517	0.842570
$209$	7.42589	0.513660
$210$	81.4951	5.62370
$211$	−1.86867	−0.128644	−0.0643222	−	0.997929i	$-0.520489\pi$
$211$	−1.86867	−0.128644	−0.0643222	+	0.997929i	$0.520489\pi$
$212$	36.5754	2.51201
$213$	25.9617	1.77887
$214$	47.3016	3.23347
$215$	3.17304	0.216400
$216$	−42.5025	−2.89193
$217$	−10.6521	−0.723114
$218$	−16.2238	−1.09881
$219$	4.39375	0.296902
$220$	14.7666	0.995562
$221$	1.45531	0.0978944
$222$	−0.0511651	−0.00343398
$223$	7.41821	0.496760	0.248380	−	0.968663i	$-0.420102\pi$
$223$	7.41821	0.496760	0.248380	+	0.968663i	$0.420102\pi$
$224$	27.3346	1.82637
$225$	26.2127	1.74751
$226$	9.01705	0.599805
$227$	12.5393	0.832263	0.416132	−	0.909304i	$-0.363386\pi$
$227$	12.5393	0.832263	0.416132	+	0.909304i	$0.363386\pi$
$228$	98.7907	6.54258
$229$	27.1169	1.79193	0.895966	−	0.444123i	$-0.146485\pi$
$229$	27.1169	1.79193	0.895966	+	0.444123i	$0.146485\pi$
$230$	−56.7931	−3.74483
$231$	−9.95685	−0.655113
$232$	47.5638	3.12272
$233$	1.97622	0.129466	0.0647331	−	0.997903i	$-0.479380\pi$
$233$	1.97622	0.129466	0.0647331	+	0.997903i	$0.479380\pi$
$234$	−19.4153	−1.26922
$235$	−22.4553	−1.46482
$236$	−28.2706	−1.84026
$237$	30.6974	1.99401
$238$	8.98446	0.582376
$239$	3.06804	0.198455	0.0992273	−	0.995065i	$-0.468363\pi$
$239$	3.06804	0.198455	0.0992273	+	0.995065i	$0.468363\pi$
$240$	75.7397	4.88898
$241$	26.1365	1.68360	0.841799	−	0.539791i	$-0.181497\pi$
$241$	26.1365	1.68360	0.841799	+	0.539791i	$0.181497\pi$
$242$	−2.57949	−0.165816
$243$	−12.2422	−0.785339
$244$	−24.1486	−1.54596
$245$	16.2826	1.04026
$246$	−71.2216	−4.54092
$247$	10.8069	0.687629
$248$	−20.9350	−1.32937
$249$	−15.2883	−0.968854
$250$	−0.558251	−0.0353069
$251$	−24.3383	−1.53622	−0.768111	−	0.640317i	$-0.778803\pi$
$251$	−24.3383	−1.53622	−0.768111	+	0.640317i	$0.778803\pi$
$252$	−83.8338	−5.28103
$253$	6.93883	0.436240
$254$	11.4562	0.718824
$255$	9.07068	0.568028
$256$	−23.9956	−1.49973
$257$	−4.65408	−0.290313	−0.145157	−	0.989409i	$-0.546369\pi$
$257$	−4.65408	−0.290313	−0.145157	+	0.989409i	$0.546369\pi$
$258$	−7.37390	−0.459079
$259$	−0.0241677	−0.00150171
$260$	21.4899	1.33275
$261$	−35.9368	−2.22443
$262$	16.5066	1.01978
$263$	−10.9858	−0.677416	−0.338708	−	0.940892i	$-0.609990\pi$
$263$	−10.9858	−0.677416	−0.338708	+	0.940892i	$0.609990\pi$
$264$	−19.5685	−1.20436
$265$	24.9379	1.53193
$266$	66.7176	4.09072
$267$	20.9976	1.28503
$268$	3.80041	0.232147
$269$	29.4175	1.79362	0.896809	−	0.442418i	$-0.145879\pi$
$269$	29.4175	1.79362	0.896809	+	0.442418i	$0.145879\pi$
$270$	−50.8194	−3.09277
$271$	3.62963	0.220484	0.110242	−	0.993905i	$-0.464837\pi$
$271$	3.62963	0.220484	0.110242	+	0.993905i	$0.464837\pi$
$272$	8.34995	0.506290
$273$	−14.4903	−0.876990
$274$	47.3850	2.86263
$275$	5.06821	0.305624
$276$	92.3110	5.55647
$277$	−14.9625	−0.899012	−0.449506	−	0.893277i	$-0.648400\pi$
$277$	−14.9625	−0.899012	−0.449506	+	0.893277i	$0.648400\pi$
$278$	−43.6785	−2.61966
$279$	15.8174	0.946964
$280$	75.6535	4.52116
$281$	−15.9304	−0.950328	−0.475164	−	0.879897i	$-0.657611\pi$
$281$	−15.9304	−0.950328	−0.475164	+	0.879897i	$0.657611\pi$
$282$	52.1844	3.10754
$283$	8.00925	0.476100	0.238050	−	0.971253i	$-0.423492\pi$
$283$	8.00925	0.476100	0.238050	+	0.971253i	$0.423492\pi$
$284$	42.2643	2.50792
$285$	67.3579	3.98994
$286$	−3.75394	−0.221975
$287$	−33.6413	−1.98578
$288$	−40.5893	−2.39175
$289$	1.00000	0.0588235
$290$	56.8711	3.33959
$291$	−32.7803	−1.92162
$292$	7.15279	0.418585
$293$	7.43616	0.434425	0.217212	−	0.976124i	$-0.430304\pi$
$293$	7.43616	0.434425	0.217212	+	0.976124i	$0.430304\pi$
$294$	−37.8396	−2.20685
$295$	−19.2756	−1.12227
$296$	−0.0474976	−0.00276074
$297$	6.20897	0.360281
$298$	54.5228	3.15842
$299$	10.0981	0.583989
$300$	67.4251	3.89279
$301$	−3.48304	−0.200759
$302$	28.3219	1.62974
$303$	20.2701	1.16448
$304$	62.0058	3.55628
$305$	−16.4651	−0.942788
$306$	−13.3411	−0.762658
$307$	8.80069	0.502282	0.251141	−	0.967951i	$-0.419194\pi$
$307$	8.80069	0.502282	0.251141	+	0.967951i	$0.419194\pi$
$308$	−16.2092	−0.923606
$309$	−28.2053	−1.60455
$310$	−25.0316	−1.42170
$311$	19.6857	1.11628	0.558138	−	0.829748i	$-0.311516\pi$
$311$	19.6857	1.11628	0.558138	+	0.829748i	$0.311516\pi$
$312$	−28.4782	−1.61226
$313$	21.9272	1.23940	0.619700	−	0.784839i	$-0.287254\pi$
$313$	21.9272	1.23940	0.619700	+	0.784839i	$0.287254\pi$
$314$	−30.6407	−1.72916
$315$	−57.1599	−3.22059
$316$	49.9737	2.81124
$317$	−6.91146	−0.388186	−0.194093	−	0.980983i	$-0.562176\pi$
$317$	−6.91146	−0.388186	−0.194093	+	0.980983i	$0.562176\pi$
$318$	−57.9538	−3.24989
$319$	−6.94836	−0.389033
$320$	11.2444	0.628579
$321$	−52.4211	−2.92586
$322$	62.3416	3.47416
$323$	7.42589	0.413188
$324$	10.3939	0.577441
$325$	7.37579	0.409135
$326$	−28.5719	−1.58245
$327$	17.9797	0.994279
$328$	−66.1164	−3.65067
$329$	24.6491	1.35895
$330$	−23.3977	−1.28800
$331$	−16.1677	−0.888657	−0.444328	−	0.895864i	$-0.646558\pi$
$331$	−16.1677	−0.888657	−0.444328	+	0.895864i	$0.646558\pi$
$332$	−24.8885	−1.36593
$333$	0.0358867	0.00196658
$334$	−7.88657	−0.431534
$335$	2.59121	0.141573
$336$	−83.1392	−4.53561
$337$	6.93240	0.377632	0.188816	−	0.982013i	$-0.439535\pi$
$337$	6.93240	0.377632	0.188816	+	0.982013i	$0.439535\pi$
$338$	28.0702	1.52682
$339$	−9.99297	−0.542744
$340$	14.7666	0.800830
$341$	3.05829	0.165616
$342$	−99.0693	−5.35706
$343$	6.50787	0.351392
$344$	−6.84534	−0.369076
$345$	62.9399	3.38857
$346$	−54.5180	−2.93090
$347$	11.7894	0.632890	0.316445	−	0.948611i	$-0.397511\pi$
$347$	11.7894	0.632890	0.316445	+	0.948611i	$0.397511\pi$
$348$	−92.4378	−4.95519
$349$	−18.0749	−0.967529	−0.483764	−	0.875198i	$-0.660731\pi$
$349$	−18.0749	−0.967529	−0.483764	+	0.875198i	$0.660731\pi$
$350$	45.5351	2.43395
$351$	9.03595	0.482303
$352$	−7.84792	−0.418296
$353$	−19.7171	−1.04944	−0.524718	−	0.851276i	$-0.675829\pi$
$353$	−19.7171	−1.04944	−0.524718	+	0.851276i	$0.675829\pi$
$354$	44.7949	2.38082
$355$	28.8168	1.52944
$356$	34.1829	1.81169
$357$	−9.95685	−0.526972
$358$	22.1365	1.16995
$359$	31.3533	1.65477	0.827383	−	0.561639i	$-0.189829\pi$
$359$	31.3533	1.65477	0.827383	+	0.561639i	$0.189829\pi$
$360$	−112.338	−5.92075
$361$	36.1439	1.90231
$362$	51.3166	2.69714
$363$	2.85867	0.150041
$364$	−23.5894	−1.23642
$365$	4.87694	0.255271
$366$	38.2635	2.00007
$367$	−4.68191	−0.244394	−0.122197	−	0.992506i	$-0.538994\pi$
$367$	−4.68191	−0.244394	−0.122197	+	0.992506i	$0.538994\pi$
$368$	57.9389	3.02027
$369$	49.9541	2.60051
$370$	−0.0567919	−0.00295247
$371$	−27.3743	−1.42120
$372$	40.6861	2.10948
$373$	−24.5168	−1.26943	−0.634715	−	0.772746i	$-0.718883\pi$
$373$	−24.5168	−1.26943	−0.634715	+	0.772746i	$0.718883\pi$
$374$	−2.57949	−0.133382
$375$	0.618671	0.0319480
$376$	48.4438	2.49830
$377$	−10.1120	−0.520793
$378$	55.7843	2.86923
$379$	−26.7238	−1.37271	−0.686356	−	0.727266i	$-0.740791\pi$
$379$	−26.7238	−1.37271	−0.686356	+	0.727266i	$0.740791\pi$
$380$	109.655	5.62518
$381$	−12.6961	−0.650440
$382$	−38.7964	−1.98499
$383$	19.4974	0.996268	0.498134	−	0.867100i	$-0.334019\pi$
$383$	19.4974	0.996268	0.498134	+	0.867100i	$0.334019\pi$
$384$	18.7382	0.956229
$385$	−11.0518	−0.563254
$386$	8.28719	0.421807
$387$	5.17198	0.262907
$388$	−53.3646	−2.70918
$389$	26.8144	1.35954	0.679771	−	0.733424i	$-0.262079\pi$
$389$	26.8144	1.35954	0.679771	+	0.733424i	$0.262079\pi$
$390$	−34.0508	−1.72423
$391$	6.93883	0.350912
$392$	−35.1272	−1.77419
$393$	−18.2931	−0.922763
$394$	−23.1192	−1.16473
$395$	34.0732	1.71441
$396$	24.0692	1.20952
$397$	−5.23791	−0.262883	−0.131442	−	0.991324i	$-0.541961\pi$
$397$	−5.23791	−0.262883	−0.131442	+	0.991324i	$0.541961\pi$
$398$	16.9313	0.848691
$399$	−73.9385	−3.70155
$400$	42.3193	2.11596
$401$	34.8427	1.73996	0.869981	−	0.493085i	$-0.164131\pi$
$401$	34.8427	1.73996	0.869981	+	0.493085i	$0.164131\pi$
$402$	−6.02177	−0.300339
$403$	4.45074	0.221707
$404$	32.9986	1.64174
$405$	7.08684	0.352148
$406$	−62.4272	−3.09821
$407$	0.00693868	0.000343938 0
$408$	−19.5685	−0.968787
$409$	3.69784	0.182846	0.0914232	−	0.995812i	$-0.470858\pi$
$409$	3.69784	0.182846	0.0914232	+	0.995812i	$0.470858\pi$
$410$	−79.0540	−3.90420
$411$	−52.5135	−2.59030
$412$	−45.9168	−2.26216
$413$	21.1587	1.04115
$414$	−92.5713	−4.54963
$415$	−16.9696	−0.833003
$416$	−11.4211	−0.559966
$417$	48.4058	2.37044
$418$	−19.1550	−0.936902
$419$	15.9091	0.777213	0.388606	−	0.921404i	$-0.372957\pi$
$419$	15.9091	0.777213	0.388606	+	0.921404i	$0.372957\pi$
$420$	−147.029	−7.17426
$421$	−35.7580	−1.74274	−0.871368	−	0.490630i	$-0.836767\pi$
$421$	−35.7580	−1.74274	−0.871368	+	0.490630i	$0.836767\pi$
$422$	4.82021	0.234644
$423$	−36.6016	−1.77963
$424$	−53.7997	−2.61274
$425$	5.06821	0.245844
$426$	−66.9679	−3.24461
$427$	18.0737	0.874646
$428$	−85.3388	−4.12501
$429$	4.16023	0.200858
$430$	−8.18483	−0.394707
$431$	−0.873990	−0.0420986	−0.0210493	−	0.999778i	$-0.506701\pi$
$431$	−0.873990	−0.0420986	−0.0210493	+	0.999778i	$0.506701\pi$
$432$	51.8446	2.49438
$433$	−29.4113	−1.41342	−0.706708	−	0.707506i	$-0.749820\pi$
$433$	−29.4113	−1.41342	−0.706708	+	0.707506i	$0.749820\pi$
$434$	27.4771	1.31894
$435$	−63.0263	−3.02188
$436$	29.2700	1.40178
$437$	51.5270	2.46487
$438$	−11.3336	−0.541541
$439$	10.1115	0.482595	0.241298	−	0.970451i	$-0.422427\pi$
$439$	10.1115	0.482595	0.241298	+	0.970451i	$0.422427\pi$
$440$	−21.7206	−1.03549
$441$	26.5403	1.26382
$442$	−3.75394	−0.178557
$443$	−15.5779	−0.740129	−0.370065	−	0.929006i	$-0.620664\pi$
$443$	−15.5779	−0.740129	−0.370065	+	0.929006i	$0.620664\pi$
$444$	0.0923091	0.00438079
$445$	23.3067	1.10485
$446$	−19.1352	−0.906078
$447$	−60.4239	−2.85795
$448$	−12.3429	−0.583147
$449$	34.1424	1.61128	0.805639	−	0.592406i	$-0.201822\pi$
$449$	34.1424	1.61128	0.805639	+	0.592406i	$0.201822\pi$
$450$	−67.6153	−3.18741
$451$	9.65861	0.454806
$452$	−16.2680	−0.765183
$453$	−31.3871	−1.47470
$454$	−32.3450	−1.51803
$455$	−16.0838	−0.754020
$456$	−145.314	−6.80495
$457$	−23.1660	−1.08366	−0.541831	−	0.840488i	$-0.682269\pi$
$457$	−23.1660	−1.08366	−0.541831	+	0.840488i	$0.682269\pi$
$458$	−69.9476	−3.26844
$459$	6.20897	0.289810
$460$	102.463	4.77735
$461$	−0.00762920	−0.000355327 0	−0.000177664	−	1.00000i	$-0.500057\pi$
$461$	−0.00762920	−0.000355327 0	−0.000177664		1.00000i	$0.500057\pi$
$462$	25.6836	1.19491
$463$	22.0841	1.02634	0.513168	−	0.858288i	$-0.328472\pi$
$463$	22.0841	1.02634	0.513168	+	0.858288i	$0.328472\pi$
$464$	−58.0184	−2.69344
$465$	27.7407	1.28645
$466$	−5.09763	−0.236143
$467$	−1.31579	−0.0608874	−0.0304437	−	0.999536i	$-0.509692\pi$
$467$	−1.31579	−0.0608874	−0.0304437	+	0.999536i	$0.509692\pi$
$468$	35.0280	1.61917
$469$	−2.84436	−0.131341
$470$	57.9233	2.67180
$471$	33.9570	1.56466
$472$	41.5840	1.91406
$473$	1.00000	0.0459800
$474$	−79.1835	−3.63702
$475$	37.6360	1.72686
$476$	−16.2092	−0.742948
$477$	40.6482	1.86115
$478$	−7.91396	−0.361976
$479$	16.6264	0.759680	0.379840	−	0.925052i	$-0.375979\pi$
$479$	16.6264	0.759680	0.379840	+	0.925052i	$0.375979\pi$
$480$	−71.1860	−3.24918
$481$	0.0100979	0.000460424 0
$482$	−67.4187	−3.07084
$483$	−69.0889	−3.14365
$484$	4.65376	0.211534
$485$	−36.3853	−1.65217
$486$	31.5787	1.43244
$487$	24.5535	1.11262	0.556312	−	0.830973i	$-0.312216\pi$
$487$	24.5535	1.11262	0.556312	+	0.830973i	$0.312216\pi$
$488$	35.5208	1.60795
$489$	31.6643	1.43191
$490$	−42.0009	−1.89741
$491$	−14.2777	−0.644346	−0.322173	−	0.946681i	$-0.604413\pi$
$491$	−14.2777	−0.644346	−0.322173	+	0.946681i	$0.604413\pi$
$492$	128.494	5.79295
$493$	−6.94836	−0.312938
$494$	−27.8764	−1.25422
$495$	16.4109	0.737616
$496$	25.5366	1.14663
$497$	−31.6321	−1.41889
$498$	39.4359	1.76716
$499$	−32.9454	−1.47484	−0.737420	−	0.675434i	$-0.763956\pi$
$499$	−32.9454	−1.47484	−0.737420	+	0.675434i	$0.763956\pi$
$500$	1.00716	0.0450417
$501$	8.74014	0.390480
$502$	62.7804	2.80203
$503$	−21.7659	−0.970493	−0.485246	−	0.874377i	$-0.661270\pi$
$503$	−21.7659	−0.970493	−0.485246	+	0.874377i	$0.661270\pi$
$504$	123.313	5.49281
$505$	22.4992	1.00120
$506$	−17.8986	−0.795691
$507$	−31.1083	−1.38157
$508$	−20.6685	−0.917018
$509$	16.2226	0.719054	0.359527	−	0.933135i	$-0.382938\pi$
$509$	16.2226	0.719054	0.359527	+	0.933135i	$0.382938\pi$
$510$	−23.3977	−1.03607
$511$	−5.35340	−0.236820
$512$	48.7867	2.15609
$513$	46.1072	2.03568
$514$	12.0051	0.529524
$515$	−31.3072	−1.37956
$516$	13.3035	0.585656
$517$	−7.07691	−0.311242
$518$	0.0623403	0.00273907
$519$	60.4185	2.65208
$520$	−31.6100	−1.38619
$521$	24.9552	1.09331	0.546654	−	0.837359i	$-0.315901\pi$
$521$	24.9552	1.09331	0.546654	+	0.837359i	$0.315901\pi$
$522$	92.6985	4.05730
$523$	−28.4717	−1.24498	−0.622490	−	0.782628i	$-0.713879\pi$
$523$	−28.4717	−1.24498	−0.622490	+	0.782628i	$0.713879\pi$
$524$	−29.7801	−1.30095
$525$	−50.4634	−2.20240
$526$	28.3378	1.23559
$527$	3.05829	0.133221
$528$	23.8697	1.03880
$529$	25.1473	1.09336
$530$	−64.3271	−2.79419
$531$	−31.4187	−1.36346
$532$	−120.368	−5.21861
$533$	14.0562	0.608843
$534$	−54.1630	−2.34386
$535$	−58.1860	−2.51560
$536$	−5.59013	−0.241457
$537$	−24.5323	−1.05865
$538$	−75.8822	−3.27151
$539$	5.13155	0.221032
$540$	91.6853	3.94551
$541$	27.7773	1.19424	0.597120	−	0.802152i	$-0.296311\pi$
$541$	27.7773	1.19424	0.597120	+	0.802152i	$0.296311\pi$
$542$	−9.36258	−0.402157
$543$	−56.8707	−2.44055
$544$	−7.84792	−0.336477
$545$	19.9570	0.854862
$546$	37.3774	1.59961
$547$	−38.0504	−1.62692	−0.813458	−	0.581624i	$-0.802418\pi$
$547$	−38.0504	−1.62692	−0.813458	+	0.581624i	$0.802418\pi$
$548$	−85.4892	−3.65192
$549$	−26.8377	−1.14540
$550$	−13.0734	−0.557451
$551$	−51.5978	−2.19814
$552$	−135.783	−5.77930
$553$	−37.4021	−1.59050
$554$	38.5957	1.63977
$555$	0.0629385	0.00267159
$556$	78.8021	3.34195
$557$	36.3403	1.53979	0.769893	−	0.638173i	$-0.220309\pi$
$557$	36.3403	1.53979	0.769893	+	0.638173i	$0.220309\pi$
$558$	−40.8008	−1.72724
$559$	1.45531	0.0615528
$560$	−92.2822	−3.89964
$561$	2.85867	0.120693
$562$	41.0923	1.73337
$563$	14.2735	0.601556	0.300778	−	0.953694i	$-0.402754\pi$
$563$	14.2735	0.601556	0.300778	+	0.953694i	$0.402754\pi$
$564$	−94.1480	−3.96435
$565$	−11.0919	−0.466641
$566$	−20.6598	−0.868394
$567$	−7.77919	−0.326695
$568$	−62.1676	−2.60850
$569$	13.8749	0.581666	0.290833	−	0.956774i	$-0.406068\pi$
$569$	13.8749	0.581666	0.290833	+	0.956774i	$0.406068\pi$
$570$	−173.749	−7.27754
$571$	−9.32921	−0.390415	−0.195208	−	0.980762i	$-0.562538\pi$
$571$	−9.32921	−0.390415	−0.195208	+	0.980762i	$0.562538\pi$
$572$	6.77264	0.283178
$573$	42.9953	1.79615
$574$	86.7773	3.62202
$575$	35.1674	1.46658
$576$	18.3280	0.763668
$577$	−44.0516	−1.83389	−0.916946	−	0.399012i	$-0.869353\pi$
$577$	−44.0516	−1.83389	−0.916946	+	0.399012i	$0.869353\pi$
$578$	−2.57949	−0.107293
$579$	−9.18412	−0.381679
$580$	−102.603	−4.26038
$581$	18.6274	0.772796
$582$	84.5564	3.50498
$583$	7.85931	0.325500
$584$	−10.5212	−0.435371
$585$	23.8829	0.987436
$586$	−19.1815	−0.792379
$587$	25.4858	1.05191	0.525955	−	0.850512i	$-0.323708\pi$
$587$	25.4858	1.05191	0.525955	+	0.850512i	$0.323708\pi$
$588$	68.2679	2.81532
$589$	22.7105	0.935771
$590$	49.7211	2.04699
$591$	25.6215	1.05393
$592$	0.0579376	0.00238122
$593$	16.1458	0.663027	0.331514	−	0.943450i	$-0.392441\pi$
$593$	16.1458	0.663027	0.331514	+	0.943450i	$0.392441\pi$
$594$	−16.0160	−0.657143
$595$	−11.0518	−0.453081
$596$	−98.3668	−4.02926
$597$	−18.7638	−0.767952
$598$	−26.0480	−1.06518
$599$	−16.2707	−0.664802	−0.332401	−	0.943138i	$-0.607859\pi$
$599$	−16.2707	−0.664802	−0.332401	+	0.943138i	$0.607859\pi$
$600$	−99.1774	−4.04890
$601$	−16.7779	−0.684385	−0.342193	−	0.939630i	$-0.611170\pi$
$601$	−16.7779	−0.684385	−0.342193	+	0.939630i	$0.611170\pi$
$602$	8.98446	0.366179
$603$	4.22361	0.171999
$604$	−51.0966	−2.07909
$605$	3.17304	0.129003
$606$	−52.2864	−2.12399
$607$	−4.21312	−0.171005	−0.0855027	−	0.996338i	$-0.527250\pi$
$607$	−4.21312	−0.171005	−0.0855027	+	0.996338i	$0.527250\pi$
$608$	−58.2778	−2.36348
$609$	69.1837	2.80347
$610$	42.4715	1.71962
$611$	−10.2991	−0.416655
$612$	24.0692	0.972938
$613$	27.4560	1.10894	0.554469	−	0.832205i	$-0.312922\pi$
$613$	27.4560	1.10894	0.554469	+	0.832205i	$0.312922\pi$
$614$	−22.7013	−0.916149
$615$	87.6101	3.53278
$616$	23.8426	0.960645
$617$	−2.72131	−0.109556	−0.0547779	−	0.998499i	$-0.517445\pi$
$617$	−2.72131	−0.109556	−0.0547779	+	0.998499i	$0.517445\pi$
$618$	72.7553	2.92665
$619$	−21.2527	−0.854220	−0.427110	−	0.904200i	$-0.640468\pi$
$619$	−21.2527	−0.854220	−0.427110	+	0.904200i	$0.640468\pi$
$620$	45.1605	1.81369
$621$	43.0830	1.72886
$622$	−50.7791	−2.03606
$623$	−25.5837	−1.02499
$624$	34.7377	1.39062
$625$	−24.6543	−0.986173
$626$	−56.5610	−2.26063
$627$	21.2282	0.847771
$628$	55.2802	2.20592
$629$	0.00693868	0.000276663 0
$630$	147.443	5.87428
$631$	3.66855	0.146043	0.0730214	−	0.997330i	$-0.476736\pi$
$631$	3.66855	0.146043	0.0730214	+	0.997330i	$0.476736\pi$
$632$	−73.5076	−2.92398
$633$	−5.34190	−0.212322
$634$	17.8280	0.708042
$635$	−14.0923	−0.559236
$636$	104.557	4.14595
$637$	7.46798	0.295892
$638$	17.9232	0.709586
$639$	46.9706	1.85813
$640$	20.7989	0.822148
$641$	−28.3812	−1.12099	−0.560494	−	0.828158i	$-0.689389\pi$
$641$	−28.3812	−1.12099	−0.560494	+	0.828158i	$0.689389\pi$
$642$	135.220	5.33669
$643$	1.72159	0.0678931	0.0339465	−	0.999424i	$-0.489192\pi$
$643$	1.72159	0.0678931	0.0339465	+	0.999424i	$0.489192\pi$
$644$	−112.473	−4.43206
$645$	9.07068	0.357158
$646$	−19.1550	−0.753643
$647$	42.4169	1.66758	0.833790	−	0.552082i	$-0.186167\pi$
$647$	42.4169	1.66758	0.833790	+	0.552082i	$0.186167\pi$
$648$	−15.2887	−0.600598
$649$	−6.07479	−0.238456
$650$	−19.0257	−0.746251
$651$	−30.4509	−1.19347
$652$	51.5477	2.01876
$653$	3.21274	0.125724	0.0628621	−	0.998022i	$-0.479977\pi$
$653$	3.21274	0.125724	0.0628621	+	0.998022i	$0.479977\pi$
$654$	−46.3784	−1.81354
$655$	−20.3048	−0.793374
$656$	80.6489	3.14881
$657$	7.94929	0.310131
$658$	−63.5822	−2.47869
$659$	−24.7268	−0.963219	−0.481610	−	0.876386i	$-0.659948\pi$
$659$	−24.7268	−0.963219	−0.481610	+	0.876386i	$0.659948\pi$
$660$	42.2127	1.64313
$661$	−41.4402	−1.61184	−0.805919	−	0.592026i	$-0.798328\pi$
$661$	−41.4402	−1.61184	−0.805919	+	0.592026i	$0.798328\pi$
$662$	41.7044	1.62089
$663$	4.16023	0.161570
$664$	36.6091	1.42071
$665$	−82.0697	−3.18253
$666$	−0.0925694	−0.00358699
$667$	−48.2134	−1.86683
$668$	14.2285	0.550516
$669$	21.2062	0.819879
$670$	−6.68400	−0.258225
$671$	−5.18905	−0.200321
$672$	78.1406	3.01434
$673$	24.3170	0.937351	0.468675	−	0.883370i	$-0.344731\pi$
$673$	24.3170	0.937351	0.468675	+	0.883370i	$0.344731\pi$
$674$	−17.8820	−0.688790
$675$	31.4684	1.21122
$676$	−50.6426	−1.94779
$677$	−5.12549	−0.196989	−0.0984944	−	0.995138i	$-0.531403\pi$
$677$	−5.12549	−0.196989	−0.0984944	+	0.995138i	$0.531403\pi$
$678$	25.7767	0.989950
$679$	39.9400	1.53275
$680$	−21.7206	−0.832945
$681$	35.8457	1.37361
$682$	−7.88882	−0.302078
$683$	−24.9339	−0.954070	−0.477035	−	0.878884i	$-0.658289\pi$
$683$	−24.9339	−0.954070	−0.477035	+	0.878884i	$0.658289\pi$
$684$	178.735	6.83410
$685$	−58.2886	−2.22709
$686$	−16.7870	−0.640929
$687$	77.5181	2.95750
$688$	8.34995	0.318339
$689$	11.4377	0.435742
$690$	−162.353	−6.18066
$691$	48.0767	1.82892	0.914462	−	0.404672i	$-0.132614\pi$
$691$	48.0767	1.82892	0.914462	+	0.404672i	$0.132614\pi$
$692$	98.3580	3.73901
$693$	−18.0142	−0.684303
$694$	−30.4107	−1.15437
$695$	53.7291	2.03806
$696$	135.969	5.15390
$697$	9.65861	0.365846
$698$	46.6241	1.76475
$699$	5.64935	0.213678
$700$	−82.1516	−3.10504
$701$	−21.5113	−0.812469	−0.406235	−	0.913769i	$-0.633158\pi$
$701$	−21.5113	−0.812469	−0.406235	+	0.913769i	$0.633158\pi$
$702$	−23.3081	−0.879709
$703$	0.0515259	0.00194334
$704$	3.54372	0.133559
$705$	−64.1923	−2.41762
$706$	50.8600	1.91414
$707$	−24.6973	−0.928838
$708$	−80.8162	−3.03726
$709$	26.3183	0.988405	0.494202	−	0.869347i	$-0.335460\pi$
$709$	26.3183	0.988405	0.494202	+	0.869347i	$0.335460\pi$
$710$	−74.3326	−2.78965
$711$	55.5385	2.08286
$712$	−50.2806	−1.88434
$713$	21.2209	0.794730
$714$	25.6836	0.961184
$715$	4.61775	0.172694
$716$	−39.9374	−1.49253
$717$	8.77049	0.327540
$718$	−80.8755	−3.01825
$719$	47.8250	1.78357	0.891787	−	0.452456i	$-0.149452\pi$
$719$	47.8250	1.78357	0.891787	+	0.452456i	$0.149452\pi$
$720$	137.030	5.10682
$721$	34.3658	1.27985
$722$	−93.2327	−3.46976
$723$	74.7155	2.77870
$724$	−92.5824	−3.44080
$725$	−35.2157	−1.30788
$726$	−7.37390	−0.273671
$727$	−7.77841	−0.288485	−0.144243	−	0.989542i	$-0.546075\pi$
$727$	−7.77841	−0.288485	−0.144243	+	0.989542i	$0.546075\pi$
$728$	34.6982	1.28600
$729$	−41.6968	−1.54433
$730$	−12.5800	−0.465607
$731$	1.00000	0.0369863
$732$	−69.0328	−2.55153
$733$	−33.3170	−1.23059	−0.615295	−	0.788297i	$-0.710963\pi$
$733$	−33.3170	−1.23059	−0.615295	+	0.788297i	$0.710963\pi$
$734$	12.0769	0.445767
$735$	46.5467	1.71690
$736$	−54.4554	−2.00725
$737$	0.816633	0.0300811
$738$	−128.856	−4.74326
$739$	−10.0595	−0.370045	−0.185022	−	0.982734i	$-0.559236\pi$
$739$	−10.0595	−0.370045	−0.185022	+	0.982734i	$0.559236\pi$
$740$	0.102461	0.00376653
$741$	30.8935	1.13490
$742$	70.6117	2.59224
$743$	−21.3763	−0.784220	−0.392110	−	0.919918i	$-0.628255\pi$
$743$	−21.3763	−0.784220	−0.392110	+	0.919918i	$0.628255\pi$
$744$	−59.8463	−2.19407
$745$	−67.0689	−2.45721
$746$	63.2407	2.31541
$747$	−27.6600	−1.01202
$748$	4.65376	0.170158
$749$	63.8706	2.33378
$750$	−1.59585	−0.0582724
$751$	15.6299	0.570344	0.285172	−	0.958476i	$-0.407949\pi$
$751$	15.6299	0.570344	0.285172	+	0.958476i	$0.407949\pi$
$752$	−59.0918	−2.15486
$753$	−69.5752	−2.53546
$754$	26.0837	0.949913
$755$	−34.8389	−1.26792
$756$	−100.643	−3.66034
$757$	−21.5597	−0.783601	−0.391800	−	0.920050i	$-0.628148\pi$
$757$	−21.5597	−0.783601	−0.391800	+	0.920050i	$0.628148\pi$
$758$	68.9338	2.50379
$759$	19.8358	0.719994
$760$	−161.295	−5.85077
$761$	40.7739	1.47805	0.739027	−	0.673676i	$-0.235286\pi$
$761$	40.7739	1.47805	0.739027	+	0.673676i	$0.235286\pi$
$762$	32.7494	1.18638
$763$	−21.9067	−0.793075
$764$	69.9941	2.53230
$765$	16.4109	0.593338
$766$	−50.2932	−1.81717
$767$	−8.84067	−0.319218
$768$	−68.5956	−2.47523
$769$	−12.8762	−0.464327	−0.232164	−	0.972677i	$-0.574580\pi$
$769$	−12.8762	−0.464327	−0.232164	+	0.972677i	$0.574580\pi$
$770$	28.5081	1.02736
$771$	−13.3045	−0.479149
$772$	−14.9513	−0.538108
$773$	−36.4363	−1.31052	−0.655262	−	0.755402i	$-0.727442\pi$
$773$	−36.4363	−1.31052	−0.655262	+	0.755402i	$0.727442\pi$
$774$	−13.3411	−0.479535
$775$	15.5000	0.556778
$776$	78.4954	2.81782
$777$	−0.0690874	−0.00247850
$778$	−69.1673	−2.47977
$779$	71.7238	2.56977
$780$	61.4324	2.19963
$781$	9.08175	0.324971
$782$	−17.8986	−0.640053
$783$	−43.1422	−1.54178
$784$	42.8482	1.53029
$785$	37.6914	1.34526
$786$	47.1867	1.68310
$787$	22.6060	0.805817	0.402909	−	0.915240i	$-0.367999\pi$
$787$	22.6060	0.805817	0.402909	+	0.915240i	$0.367999\pi$
$788$	41.7104	1.48587
$789$	−31.4049	−1.11804
$790$	−87.8915	−3.12704
$791$	12.1756	0.432913
$792$	−35.4040	−1.25803
$793$	−7.55165	−0.268167
$794$	13.5111	0.479492
$795$	71.2893	2.52837
$796$	−30.5465	−1.08269
$797$	−42.2821	−1.49771	−0.748854	−	0.662735i	$-0.769396\pi$
$797$	−42.2821	−1.49771	−0.748854	+	0.662735i	$0.769396\pi$
$798$	190.723	6.75154
$799$	−7.07691	−0.250363
$800$	−39.7749	−1.40625
$801$	37.9894	1.34229
$802$	−89.8764	−3.17364
$803$	1.53699	0.0542393
$804$	10.8641	0.383148
$805$	−76.6867	−2.70285
$806$	−11.4806	−0.404388
$807$	84.0949	2.96028
$808$	−48.5385	−1.70758
$809$	−42.0314	−1.47775	−0.738873	−	0.673845i	$-0.764642\pi$
$809$	−42.0314	−1.47775	−0.738873	+	0.673845i	$0.764642\pi$
$810$	−18.2804	−0.642308
$811$	−15.4375	−0.542085	−0.271043	−	0.962567i	$-0.587368\pi$
$811$	−15.4375	−0.542085	−0.271043	+	0.962567i	$0.587368\pi$
$812$	112.627	3.95245
$813$	10.3759	0.363899
$814$	−0.0178982	−0.000627333 0
$815$	35.1465	1.23113
$816$	23.8697	0.835608
$817$	7.42589	0.259799
$818$	−9.53853	−0.333507
$819$	−26.2162	−0.916067
$820$	142.625	4.98067
$821$	13.8982	0.485051	0.242525	−	0.970145i	$-0.422024\pi$
$821$	13.8982	0.485051	0.242525	+	0.970145i	$0.422024\pi$
$822$	135.458	4.72464
$823$	−4.78934	−0.166946	−0.0834729	−	0.996510i	$-0.526601\pi$
$823$	−4.78934	−0.166946	−0.0834729	+	0.996510i	$0.526601\pi$
$824$	67.5402	2.35288
$825$	14.4883	0.504418
$826$	−54.5787	−1.89903
$827$	40.4287	1.40584	0.702922	−	0.711267i	$-0.251878\pi$
$827$	40.4287	1.40584	0.702922	+	0.711267i	$0.251878\pi$
$828$	167.012	5.80406
$829$	−45.4337	−1.57798	−0.788989	−	0.614408i	$-0.789395\pi$
$829$	−45.4337	−1.57798	−0.788989	+	0.614408i	$0.789395\pi$
$830$	43.7728	1.51938
$831$	−42.7730	−1.48378
$832$	5.15719	0.178793
$833$	5.13155	0.177798
$834$	−124.862	−4.32363
$835$	9.70131	0.335728
$836$	34.5583	1.19522
$837$	18.9888	0.656350
$838$	−41.0375	−1.41762
$839$	−5.28211	−0.182359	−0.0911794	−	0.995834i	$-0.529064\pi$
$839$	−5.28211	−0.182359	−0.0911794	+	0.995834i	$0.529064\pi$
$840$	216.268	7.46196
$841$	19.2797	0.664816
$842$	92.2372	3.17870
$843$	−45.5397	−1.56847
$844$	−8.69633	−0.299340
$845$	−34.5293	−1.18785
$846$	94.4135	3.24600
$847$	−3.48304	−0.119679
$848$	65.6249	2.25357
$849$	22.8958	0.785781
$850$	−13.0734	−0.448413
$851$	0.0481463	0.00165043
$852$	120.819	4.13921
$853$	25.8875	0.886370	0.443185	−	0.896430i	$-0.353848\pi$
$853$	25.8875	0.886370	0.443185	+	0.896430i	$0.353848\pi$
$854$	−46.6208	−1.59533
$855$	121.866	4.16772
$856$	125.527	4.29043
$857$	−19.4618	−0.664804	−0.332402	−	0.943138i	$-0.607859\pi$
$857$	−19.4618	−0.664804	−0.332402	+	0.943138i	$0.607859\pi$
$858$	−10.7313	−0.366360
$859$	18.9855	0.647777	0.323889	−	0.946095i	$-0.395010\pi$
$859$	18.9855	0.647777	0.323889	+	0.946095i	$0.395010\pi$
$860$	14.7666	0.503536
$861$	−96.1693	−3.27744
$862$	2.25445	0.0767867
$863$	20.6580	0.703205	0.351603	−	0.936149i	$-0.385637\pi$
$863$	20.6580	0.703205	0.351603	+	0.936149i	$0.385637\pi$
$864$	−48.7275	−1.65774
$865$	67.0629	2.28021
$866$	75.8660	2.57803
$867$	2.85867	0.0970854
$868$	−49.5725	−1.68260
$869$	10.7383	0.364274
$870$	162.576	5.51183
$871$	1.18845	0.0402691
$872$	−43.0540	−1.45799
$873$	−59.3071	−2.00724
$874$	−132.913	−4.49586
$875$	−0.753797	−0.0254830
$876$	20.4474	0.690855
$877$	−54.9034	−1.85396	−0.926978	−	0.375117i	$-0.877603\pi$
$877$	−54.9034	−1.85396	−0.926978	+	0.375117i	$0.877603\pi$
$878$	−26.0825	−0.880241
$879$	21.2575	0.716998
$880$	26.4948	0.893138
$881$	−18.1700	−0.612162	−0.306081	−	0.952005i	$-0.599018\pi$
$881$	−18.1700	−0.612162	−0.306081	+	0.952005i	$0.599018\pi$
$882$	−68.4604	−2.30518
$883$	−43.5776	−1.46650	−0.733251	−	0.679958i	$-0.761998\pi$
$883$	−43.5776	−1.46650	−0.733251	+	0.679958i	$0.761998\pi$
$884$	6.77264	0.227788
$885$	−55.1024	−1.85225
$886$	40.1831	1.34998
$887$	−28.5835	−0.959741	−0.479870	−	0.877339i	$-0.659316\pi$
$887$	−28.5835	−0.959741	−0.479870	+	0.877339i	$0.659316\pi$
$888$	−0.135780	−0.00455647
$889$	15.4691	0.518816
$890$	−60.1194	−2.01521
$891$	2.23345	0.0748234
$892$	34.5226	1.15590
$893$	−52.5524	−1.75860
$894$	155.863	5.21283
$895$	−27.2302	−0.910207
$896$	−22.8309	−0.762725
$897$	28.8671	0.963846
$898$	−88.0699	−2.93893
$899$	−21.2501	−0.708730
$900$	121.987	4.06625
$901$	7.85931	0.261832
$902$	−24.9143	−0.829554
$903$	−9.95685	−0.331343
$904$	23.9291	0.795869
$905$	−63.1249	−2.09834
$906$	80.9628	2.68981
$907$	16.8456	0.559350	0.279675	−	0.960095i	$-0.409773\pi$
$907$	16.8456	0.559350	0.279675	+	0.960095i	$0.409773\pi$
$908$	58.3549	1.93658
$909$	36.6732	1.21637
$910$	41.4879	1.37531
$911$	56.7182	1.87916	0.939579	−	0.342332i	$-0.111217\pi$
$911$	56.7182	1.87916	0.939579	+	0.342332i	$0.111217\pi$
$912$	177.254	5.86947
$913$	−5.34804	−0.176994
$914$	59.7565	1.97657
$915$	−47.0682	−1.55603
$916$	126.195	4.16961
$917$	22.2885	0.736031
$918$	−16.0160	−0.528606
$919$	−6.06103	−0.199935	−0.0999675	−	0.994991i	$-0.531874\pi$
$919$	−6.06103	−0.199935	−0.0999675	+	0.994991i	$0.531874\pi$
$920$	−150.715	−4.96893
$921$	25.1582	0.828992
$922$	0.0196794	0.000648108 0
$923$	13.2167	0.435033
$924$	−46.3368	−1.52437
$925$	0.0351667	0.00115627
$926$	−56.9657	−1.87201
$927$	−51.0299	−1.67604
$928$	54.5301	1.79004
$929$	45.9885	1.50884	0.754418	−	0.656395i	$-0.227919\pi$
$929$	45.9885	1.50884	0.754418	+	0.656395i	$0.227919\pi$
$930$	−71.5569	−2.34644
$931$	38.1064	1.24889
$932$	9.19683	0.301252
$933$	56.2750	1.84236
$934$	3.39406	0.111057
$935$	3.17304	0.103770
$936$	−51.5236	−1.68410
$937$	−16.8144	−0.549304	−0.274652	−	0.961544i	$-0.588563\pi$
$937$	−16.8144	−0.549304	−0.274652	+	0.961544i	$0.588563\pi$
$938$	7.33700	0.239562
$939$	62.6827	2.04557
$940$	−104.502	−3.40847
$941$	3.83010	0.124858	0.0624289	−	0.998049i	$-0.480115\pi$
$941$	3.83010	0.124858	0.0624289	+	0.998049i	$0.480115\pi$
$942$	−87.5917	−2.85389
$943$	67.0194	2.18245
$944$	−50.7242	−1.65093
$945$	−68.6205	−2.23223
$946$	−2.57949	−0.0838664
$947$	−55.8572	−1.81511	−0.907557	−	0.419929i	$-0.862055\pi$
$947$	−55.8572	−1.81511	−0.907557	+	0.419929i	$0.862055\pi$
$948$	142.858	4.63982
$949$	2.23679	0.0726093
$950$	−97.0815	−3.14974
$951$	−19.7576	−0.640683
$952$	23.8426	0.772742
$953$	−17.6334	−0.571202	−0.285601	−	0.958349i	$-0.592193\pi$
$953$	−17.6334	−0.571202	−0.285601	+	0.958349i	$0.592193\pi$
$954$	−104.852	−3.39470
$955$	47.7236	1.54430
$956$	14.2779	0.461780
$957$	−19.8630	−0.642081
$958$	−42.8876	−1.38564
$959$	63.9831	2.06612
$960$	32.1439	1.03744
$961$	−21.6469	−0.698286
$962$	−0.0260474	−0.000839802 0
$963$	−94.8417	−3.05623
$964$	121.633	3.91753
$965$	−10.1941	−0.328160
$966$	178.214	5.73394
$967$	32.0118	1.02943	0.514716	−	0.857361i	$-0.327898\pi$
$967$	32.0118	1.02943	0.514716	+	0.857361i	$0.327898\pi$
$968$	−6.84534	−0.220017
$969$	21.2282	0.681947
$970$	93.8553	3.01351
$971$	47.9414	1.53851	0.769256	−	0.638940i	$-0.220627\pi$
$971$	47.9414	1.53851	0.769256	+	0.638940i	$0.220627\pi$
$972$	−56.9724	−1.82739
$973$	−58.9783	−1.89076
$974$	−63.3354	−2.02940
$975$	21.0849	0.675258
$976$	−43.3283	−1.38691
$977$	54.1739	1.73318	0.866588	−	0.499025i	$-0.166308\pi$
$977$	54.1739	1.73318	0.866588	+	0.499025i	$0.166308\pi$
$978$	−81.6776	−2.61176
$979$	7.34523	0.234755
$980$	75.7755	2.42056
$981$	32.5293	1.03858
$982$	36.8293	1.17527
$983$	33.1749	1.05811	0.529057	−	0.848586i	$-0.322546\pi$
$983$	33.1749	1.05811	0.529057	+	0.848586i	$0.322546\pi$
$984$	−189.005	−6.02526
$985$	28.4391	0.906146
$986$	17.9232	0.570791
$987$	70.4637	2.24288
$988$	50.2929	1.60003
$989$	6.93883	0.220642
$990$	−42.3318	−1.34539
$991$	−17.6291	−0.560006	−0.280003	−	0.959999i	$-0.590335\pi$
$991$	−17.6291	−0.560006	−0.280003	+	0.959999i	$0.590335\pi$
$992$	−24.0012	−0.762039
$993$	−46.2181	−1.46669
$994$	81.5946	2.58802
$995$	−20.8273	−0.660271
$996$	−71.1479	−2.25441
$997$	−11.3245	−0.358651	−0.179326	−	0.983790i	$-0.557392\pi$
$997$	−11.3245	−0.358651	−0.179326	+	0.983790i	$0.557392\pi$
$998$	84.9824	2.69007
$999$	0.0430821	0.00136306

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.j.1.5	✓	82

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.j.1.5	✓	82	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.57949 q^{2} +2.85867 q^{3} +4.65376 q^{4} +3.17304 q^{5} -7.37390 q^{6} -3.48304 q^{7} -6.84534 q^{8} +5.17198 q^{9} +O(q^{10})\)	\(q-2.57949 q^{2} +2.85867 q^{3} +4.65376 q^{4} +3.17304 q^{5} -7.37390 q^{6} -3.48304 q^{7} -6.84534 q^{8} +5.17198 q^{9} -8.18483 q^{10} +1.00000 q^{11} +13.3035 q^{12} +1.45531 q^{13} +8.98446 q^{14} +9.07068 q^{15} +8.34995 q^{16} +1.00000 q^{17} -13.3411 q^{18} +7.42589 q^{19} +14.7666 q^{20} -9.95685 q^{21} -2.57949 q^{22} +6.93883 q^{23} -19.5685 q^{24} +5.06821 q^{25} -3.75394 q^{26} +6.20897 q^{27} -16.2092 q^{28} -6.94836 q^{29} -23.3977 q^{30} +3.05829 q^{31} -7.84792 q^{32} +2.85867 q^{33} -2.57949 q^{34} -11.0518 q^{35} +24.0692 q^{36} +0.00693868 q^{37} -19.1550 q^{38} +4.16023 q^{39} -21.7206 q^{40} +9.65861 q^{41} +25.6836 q^{42} +1.00000 q^{43} +4.65376 q^{44} +16.4109 q^{45} -17.8986 q^{46} -7.07691 q^{47} +23.8697 q^{48} +5.13155 q^{49} -13.0734 q^{50} +2.85867 q^{51} +6.77264 q^{52} +7.85931 q^{53} -16.0160 q^{54} +3.17304 q^{55} +23.8426 q^{56} +21.2282 q^{57} +17.9232 q^{58} -6.07479 q^{59} +42.2127 q^{60} -5.18905 q^{61} -7.88882 q^{62} -18.0142 q^{63} +3.54372 q^{64} +4.61775 q^{65} -7.37390 q^{66} +0.816633 q^{67} +4.65376 q^{68} +19.8358 q^{69} +28.5081 q^{70} +9.08175 q^{71} -35.4040 q^{72} +1.53699 q^{73} -0.0178982 q^{74} +14.4883 q^{75} +34.5583 q^{76} -3.48304 q^{77} -10.7313 q^{78} +10.7383 q^{79} +26.4948 q^{80} +2.23345 q^{81} -24.9143 q^{82} -5.34804 q^{83} -46.3368 q^{84} +3.17304 q^{85} -2.57949 q^{86} -19.8630 q^{87} -6.84534 q^{88} +7.34523 q^{89} -42.3318 q^{90} -5.06888 q^{91} +32.2916 q^{92} +8.74263 q^{93} +18.2548 q^{94} +23.5627 q^{95} -22.4346 q^{96} -11.4670 q^{97} -13.2368 q^{98} +5.17198 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9}+O(q^{10}) \) 82 * q + 8 * q^2 + 6 * q^3 + 98 * q^4 + 11 * q^5 + 10 * q^6 + 8 * q^7 + 30 * q^8 + 108 * q^9	\( 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9} + q^{10} + 82 q^{11} + 3 q^{12} + 26 q^{13} + 17 q^{14} + 66 q^{15} + 122 q^{16} + 82 q^{17} + 18 q^{18} + 12 q^{19} + 9 q^{20} + 22 q^{21} + 8 q^{22} + 50 q^{23} + 15 q^{24} + 117 q^{25} + 36 q^{26} + 30 q^{27} + 11 q^{28} + 33 q^{29} - 26 q^{30} + 40 q^{31} + 58 q^{32} + 6 q^{33} + 8 q^{34} + 16 q^{35} + 160 q^{36} + 31 q^{37} + 18 q^{38} + 41 q^{39} - 29 q^{40} + 42 q^{41} - 51 q^{42} + 82 q^{43} + 98 q^{44} - 2 q^{45} - 19 q^{46} + 84 q^{47} - 46 q^{48} + 136 q^{49} + 59 q^{50} + 6 q^{51} + 45 q^{52} + 83 q^{53} + 24 q^{54} + 11 q^{55} + 21 q^{56} + 23 q^{57} + 14 q^{58} + 96 q^{59} + 184 q^{60} - 6 q^{61} - 23 q^{62} + 8 q^{63} + 148 q^{64} + 5 q^{65} + 10 q^{66} + 78 q^{67} + 98 q^{68} + 61 q^{69} - 3 q^{70} + 155 q^{71} + 50 q^{72} - 23 q^{73} + 10 q^{74} - 19 q^{75} + 44 q^{76} + 8 q^{77} - 27 q^{78} + 31 q^{79} + 19 q^{80} + 150 q^{81} - 12 q^{82} + 54 q^{83} + 8 q^{84} + 11 q^{85} + 8 q^{86} + 20 q^{87} + 30 q^{88} + 25 q^{89} - 81 q^{90} - 14 q^{91} + 60 q^{92} + 36 q^{93} + 19 q^{94} + 111 q^{95} - 6 q^{96} + 2 q^{97} - 5 q^{98} + 108 q^{99}+O(q^{100}) \) 82 * q + 8 * q^2 + 6 * q^3 + 98 * q^4 + 11 * q^5 + 10 * q^6 + 8 * q^7 + 30 * q^8 + 108 * q^9 + q^10 + 82 * q^11 + 3 * q^12 + 26 * q^13 + 17 * q^14 + 66 * q^15 + 122 * q^16 + 82 * q^17 + 18 * q^18 + 12 * q^19 + 9 * q^20 + 22 * q^21 + 8 * q^22 + 50 * q^23 + 15 * q^24 + 117 * q^25 + 36 * q^26 + 30 * q^27 + 11 * q^28 + 33 * q^29 - 26 * q^30 + 40 * q^31 + 58 * q^32 + 6 * q^33 + 8 * q^34 + 16 * q^35 + 160 * q^36 + 31 * q^37 + 18 * q^38 + 41 * q^39 - 29 * q^40 + 42 * q^41 - 51 * q^42 + 82 * q^43 + 98 * q^44 - 2 * q^45 - 19 * q^46 + 84 * q^47 - 46 * q^48 + 136 * q^49 + 59 * q^50 + 6 * q^51 + 45 * q^52 + 83 * q^53 + 24 * q^54 + 11 * q^55 + 21 * q^56 + 23 * q^57 + 14 * q^58 + 96 * q^59 + 184 * q^60 - 6 * q^61 - 23 * q^62 + 8 * q^63 + 148 * q^64 + 5 * q^65 + 10 * q^66 + 78 * q^67 + 98 * q^68 + 61 * q^69 - 3 * q^70 + 155 * q^71 + 50 * q^72 - 23 * q^73 + 10 * q^74 - 19 * q^75 + 44 * q^76 + 8 * q^77 - 27 * q^78 + 31 * q^79 + 19 * q^80 + 150 * q^81 - 12 * q^82 + 54 * q^83 + 8 * q^84 + 11 * q^85 + 8 * q^86 + 20 * q^87 + 30 * q^88 + 25 * q^89 - 81 * q^90 - 14 * q^91 + 60 * q^92 + 36 * q^93 + 19 * q^94 + 111 * q^95 - 6 * q^96 + 2 * q^97 - 5 * q^98 + 108 * q^99

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