LMFDB - Embedded newform 8003.2.a.d.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8003,2,Mod(1,8003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8003, 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("8003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8003 = 53 \cdot 151 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8003.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:	$63.9042767376$
Analytic rank:	$0$
Dimension:	$179$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	8003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.69327 q^{2} -0.453777 q^{3} +5.25372 q^{4} -2.96502 q^{5} +1.22215 q^{6} +4.09118 q^{7} -8.76316 q^{8} -2.79409 q^{9} +O(q^{10})$	\(q-2.69327 q^{2} -0.453777 q^{3} +5.25372 q^{4} -2.96502 q^{5} +1.22215 q^{6} +4.09118 q^{7} -8.76316 q^{8} -2.79409 q^{9} +7.98562 q^{10} +0.289531 q^{11} -2.38402 q^{12} +2.73005 q^{13} -11.0187 q^{14} +1.34546 q^{15} +13.0941 q^{16} +2.93553 q^{17} +7.52524 q^{18} +2.82028 q^{19} -15.5774 q^{20} -1.85649 q^{21} -0.779785 q^{22} +3.40898 q^{23} +3.97652 q^{24} +3.79136 q^{25} -7.35276 q^{26} +2.62922 q^{27} +21.4939 q^{28} +5.80512 q^{29} -3.62369 q^{30} +9.86426 q^{31} -17.7398 q^{32} -0.131382 q^{33} -7.90619 q^{34} -12.1305 q^{35} -14.6793 q^{36} +2.45824 q^{37} -7.59577 q^{38} -1.23883 q^{39} +25.9830 q^{40} +5.32835 q^{41} +5.00002 q^{42} +4.18853 q^{43} +1.52111 q^{44} +8.28453 q^{45} -9.18131 q^{46} +4.64358 q^{47} -5.94182 q^{48} +9.73777 q^{49} -10.2112 q^{50} -1.33208 q^{51} +14.3429 q^{52} +1.00000 q^{53} -7.08122 q^{54} -0.858466 q^{55} -35.8517 q^{56} -1.27978 q^{57} -15.6348 q^{58} +1.86143 q^{59} +7.06867 q^{60} +9.42087 q^{61} -26.5671 q^{62} -11.4311 q^{63} +21.5898 q^{64} -8.09465 q^{65} +0.353849 q^{66} +1.86364 q^{67} +15.4225 q^{68} -1.54692 q^{69} +32.6706 q^{70} -8.36678 q^{71} +24.4850 q^{72} -14.8423 q^{73} -6.62072 q^{74} -1.72044 q^{75} +14.8169 q^{76} +1.18452 q^{77} +3.33651 q^{78} +16.4452 q^{79} -38.8244 q^{80} +7.18918 q^{81} -14.3507 q^{82} +12.6514 q^{83} -9.75346 q^{84} -8.70392 q^{85} -11.2809 q^{86} -2.63423 q^{87} -2.53720 q^{88} -2.03389 q^{89} -22.3125 q^{90} +11.1691 q^{91} +17.9098 q^{92} -4.47618 q^{93} -12.5064 q^{94} -8.36219 q^{95} +8.04990 q^{96} +17.6433 q^{97} -26.2265 q^{98} -0.808974 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 179 q + 8 q^{2} + 15 q^{3} + 202 q^{4} + 27 q^{5} + 18 q^{6} + 23 q^{7} + 21 q^{8} + 214 q^{9}+O(q^{10}) $ 179 * q + 8 * q^2 + 15 * q^3 + 202 * q^4 + 27 * q^5 + 18 * q^6 + 23 * q^7 + 21 * q^8 + 214 * q^9	\( 179 q + 8 q^{2} + 15 q^{3} + 202 q^{4} + 27 q^{5} + 18 q^{6} + 23 q^{7} + 21 q^{8} + 214 q^{9} + 28 q^{10} + 21 q^{11} + 46 q^{12} + 113 q^{13} - 2 q^{14} + 30 q^{15} + 240 q^{16} + 48 q^{17} + 40 q^{18} + 35 q^{19} + 24 q^{20} + 56 q^{21} + 22 q^{22} + 16 q^{23} + 54 q^{24} + 266 q^{25} + 60 q^{27} + 64 q^{28} + 34 q^{29} - 19 q^{30} + 60 q^{31} + 15 q^{32} + 65 q^{33} + 31 q^{34} - 20 q^{35} + 282 q^{36} + 169 q^{37} + 52 q^{38} + 20 q^{39} + 74 q^{40} + 20 q^{41} + 34 q^{42} + 43 q^{43} + 56 q^{44} + 139 q^{45} + 13 q^{46} + 73 q^{47} + 88 q^{48} + 292 q^{49} + 12 q^{50} + 8 q^{51} + 225 q^{52} + 179 q^{53} - 16 q^{54} + 72 q^{55} - 17 q^{56} + 62 q^{57} + 125 q^{58} + 68 q^{59} + 116 q^{60} + 96 q^{61} + 71 q^{62} + 52 q^{63} + 309 q^{64} - 5 q^{65} + 90 q^{67} + 122 q^{68} + 111 q^{69} + 72 q^{70} + 26 q^{71} + 65 q^{72} + 139 q^{73} - 82 q^{74} + 55 q^{75} + 146 q^{76} + 76 q^{77} - 9 q^{78} + 29 q^{79} + 68 q^{80} + 231 q^{81} + 84 q^{82} + 8 q^{83} - 24 q^{84} + 115 q^{85} - 20 q^{86} + 47 q^{87} + 143 q^{88} + 150 q^{89} + 34 q^{90} + 113 q^{91} - 31 q^{92} + 195 q^{93} + 131 q^{94} + 55 q^{95} + 90 q^{96} + 235 q^{97} + 84 q^{98} + 7 q^{99}+O(q^{100}) \) 179 * q + 8 * q^2 + 15 * q^3 + 202 * q^4 + 27 * q^5 + 18 * q^6 + 23 * q^7 + 21 * q^8 + 214 * q^9 + 28 * q^10 + 21 * q^11 + 46 * q^12 + 113 * q^13 - 2 * q^14 + 30 * q^15 + 240 * q^16 + 48 * q^17 + 40 * q^18 + 35 * q^19 + 24 * q^20 + 56 * q^21 + 22 * q^22 + 16 * q^23 + 54 * q^24 + 266 * q^25 + 60 * q^27 + 64 * q^28 + 34 * q^29 - 19 * q^30 + 60 * q^31 + 15 * q^32 + 65 * q^33 + 31 * q^34 - 20 * q^35 + 282 * q^36 + 169 * q^37 + 52 * q^38 + 20 * q^39 + 74 * q^40 + 20 * q^41 + 34 * q^42 + 43 * q^43 + 56 * q^44 + 139 * q^45 + 13 * q^46 + 73 * q^47 + 88 * q^48 + 292 * q^49 + 12 * q^50 + 8 * q^51 + 225 * q^52 + 179 * q^53 - 16 * q^54 + 72 * q^55 - 17 * q^56 + 62 * q^57 + 125 * q^58 + 68 * q^59 + 116 * q^60 + 96 * q^61 + 71 * q^62 + 52 * q^63 + 309 * q^64 - 5 * q^65 + 90 * q^67 + 122 * q^68 + 111 * q^69 + 72 * q^70 + 26 * q^71 + 65 * q^72 + 139 * q^73 - 82 * q^74 + 55 * q^75 + 146 * q^76 + 76 * q^77 - 9 * q^78 + 29 * q^79 + 68 * q^80 + 231 * q^81 + 84 * q^82 + 8 * q^83 - 24 * q^84 + 115 * q^85 - 20 * q^86 + 47 * q^87 + 143 * q^88 + 150 * q^89 + 34 * q^90 + 113 * q^91 - 31 * q^92 + 195 * q^93 + 131 * q^94 + 55 * q^95 + 90 * q^96 + 235 * q^97 + 84 * q^98 + 7 * 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 $

$2$	−2.69327	−1.90443	−0.952216	−	0.305426i	$-0.901201\pi$
$2$	−2.69327	−1.90443	−0.952216	+	0.305426i	$0.901201\pi$
$3$	−0.453777	−0.261988	−0.130994	−	0.991383i	$-0.541817\pi$
$3$	−0.453777	−0.261988	−0.130994	+	0.991383i	$0.541817\pi$
$4$	5.25372	2.62686
$5$	−2.96502	−1.32600	−0.662999	−	0.748620i	$-0.730717\pi$
$5$	−2.96502	−1.32600	−0.662999	+	0.748620i	$0.730717\pi$
$6$	1.22215	0.498939
$7$	4.09118	1.54632	0.773161	−	0.634210i	$-0.218675\pi$
$7$	4.09118	1.54632	0.773161	+	0.634210i	$0.218675\pi$
$8$	−8.76316	−3.09824
$9$	−2.79409	−0.931362
$10$	7.98562	2.52527
$11$	0.289531	0.0872968	0.0436484	−	0.999047i	$-0.486102\pi$
$11$	0.289531	0.0872968	0.0436484	+	0.999047i	$0.486102\pi$
$12$	−2.38402	−0.688207
$13$	2.73005	0.757178	0.378589	−	0.925565i	$-0.376409\pi$
$13$	2.73005	0.757178	0.378589	+	0.925565i	$0.376409\pi$
$14$	−11.0187	−2.94486
$15$	1.34546	0.347396
$16$	13.0941	3.27353
$17$	2.93553	0.711971	0.355985	−	0.934492i	$-0.384145\pi$
$17$	2.93553	0.711971	0.355985	+	0.934492i	$0.384145\pi$
$18$	7.52524	1.77372
$19$	2.82028	0.647016	0.323508	−	0.946225i	$-0.395138\pi$
$19$	2.82028	0.647016	0.323508	+	0.946225i	$0.395138\pi$
$20$	−15.5774	−3.48321
$21$	−1.85649	−0.405118
$22$	−0.779785	−0.166251
$23$	3.40898	0.710821	0.355410	−	0.934710i	$-0.384341\pi$
$23$	3.40898	0.710821	0.355410	+	0.934710i	$0.384341\pi$
$24$	3.97652	0.811704
$25$	3.79136	0.758273
$26$	−7.35276	−1.44199
$27$	2.62922	0.505995
$28$	21.4939	4.06197
$29$	5.80512	1.07798	0.538991	−	0.842311i	$-0.318806\pi$
$29$	5.80512	1.07798	0.538991	+	0.842311i	$0.318806\pi$
$30$	−3.62369	−0.661593
$31$	9.86426	1.77167	0.885836	−	0.463998i	$-0.153585\pi$
$31$	9.86426	1.77167	0.885836	+	0.463998i	$0.153585\pi$
$32$	−17.7398	−3.13598
$33$	−0.131382	−0.0228708
$34$	−7.90619	−1.35590
$35$	−12.1305	−2.05042
$36$	−14.6793	−2.44656
$37$	2.45824	0.404133	0.202066	−	0.979372i	$-0.435234\pi$
$37$	2.45824	0.404133	0.202066	+	0.979372i	$0.435234\pi$
$38$	−7.59577	−1.23220
$39$	−1.23883	−0.198372
$40$	25.9830	4.10827
$41$	5.32835	0.832149	0.416074	−	0.909331i	$-0.363406\pi$
$41$	5.32835	0.832149	0.416074	+	0.909331i	$0.363406\pi$
$42$	5.00002	0.771520
$43$	4.18853	0.638745	0.319373	−	0.947629i	$-0.396528\pi$
$43$	4.18853	0.638745	0.319373	+	0.947629i	$0.396528\pi$
$44$	1.52111	0.229317
$45$	8.28453	1.23499
$46$	−9.18131	−1.35371
$47$	4.64358	0.677336	0.338668	−	0.940906i	$-0.390024\pi$
$47$	4.64358	0.677336	0.338668	+	0.940906i	$0.390024\pi$
$48$	−5.94182	−0.857628
$49$	9.73777	1.39111
$50$	−10.2112	−1.44408
$51$	−1.33208	−0.186528
$52$	14.3429	1.98900
$53$	1.00000	0.137361
$53$	1.00000	0.137361
$54$	−7.08122	−0.963632
$55$	−0.858466	−0.115755
$56$	−35.8517	−4.79088
$57$	−1.27978	−0.169511
$58$	−15.6348	−2.05294
$59$	1.86143	0.242337	0.121169	−	0.992632i	$-0.461336\pi$
$59$	1.86143	0.242337	0.121169	+	0.992632i	$0.461336\pi$
$60$	7.06867	0.912562
$61$	9.42087	1.20622	0.603109	−	0.797659i	$-0.293928\pi$
$61$	9.42087	1.20622	0.603109	+	0.797659i	$0.293928\pi$
$62$	−26.5671	−3.37403
$63$	−11.4311	−1.44019
$64$	21.5898	2.69872
$65$	−8.09465	−1.00402
$66$	0.353849	0.0435558
$67$	1.86364	0.227680	0.113840	−	0.993499i	$-0.463685\pi$
$67$	1.86364	0.227680	0.113840	+	0.993499i	$0.463685\pi$
$68$	15.4225	1.87025
$69$	−1.54692	−0.186227
$70$	32.6706	3.90489
$71$	−8.36678	−0.992954	−0.496477	−	0.868050i	$-0.665373\pi$
$71$	−8.36678	−0.992954	−0.496477	+	0.868050i	$0.665373\pi$
$72$	24.4850	2.88559
$73$	−14.8423	−1.73715	−0.868577	−	0.495554i	$-0.834965\pi$
$73$	−14.8423	−1.73715	−0.868577	+	0.495554i	$0.834965\pi$
$74$	−6.62072	−0.769643
$75$	−1.72044	−0.198659
$76$	14.8169	1.69962
$77$	1.18452	0.134989
$78$	3.33651	0.377786
$79$	16.4452	1.85023	0.925114	−	0.379688i	$-0.123969\pi$
$79$	16.4452	1.85023	0.925114	+	0.379688i	$0.123969\pi$
$80$	−38.8244	−4.34070
$81$	7.18918	0.798797
$82$	−14.3507	−1.58477
$83$	12.6514	1.38867	0.694337	−	0.719650i	$-0.255698\pi$
$83$	12.6514	1.38867	0.694337	+	0.719650i	$0.255698\pi$
$84$	−9.75346	−1.06419
$85$	−8.70392	−0.944073
$86$	−11.2809	−1.21645
$87$	−2.63423	−0.282419
$88$	−2.53720	−0.270467
$89$	−2.03389	−0.215592	−0.107796	−	0.994173i	$-0.534379\pi$
$89$	−2.03389	−0.215592	−0.107796	+	0.994173i	$0.534379\pi$
$90$	−22.3125	−2.35194
$91$	11.1691	1.17084
$92$	17.9098	1.86723
$93$	−4.47618	−0.464158
$94$	−12.5064	−1.28994
$95$	−8.36219	−0.857942
$96$	8.04990	0.821590
$97$	17.6433	1.79141	0.895703	−	0.444654i	$-0.146673\pi$
$97$	17.6433	1.79141	0.895703	+	0.444654i	$0.146673\pi$
$98$	−26.2265	−2.64927
$99$	−0.808974	−0.0813049
$100$	19.9188	1.99188
$101$	−14.0999	−1.40300	−0.701498	−	0.712672i	$-0.747485\pi$
$101$	−14.0999	−1.40300	−0.701498	+	0.712672i	$0.747485\pi$
$102$	3.58765	0.355230
$103$	−12.2159	−1.20367	−0.601836	−	0.798620i	$-0.705564\pi$
$103$	−12.2159	−1.20367	−0.601836	+	0.798620i	$0.705564\pi$
$104$	−23.9238	−2.34592
$105$	5.50452	0.537186
$106$	−2.69327	−0.261594
$107$	−13.1052	−1.26693	−0.633463	−	0.773773i	$-0.718367\pi$
$107$	−13.1052	−1.26693	−0.633463	+	0.773773i	$0.718367\pi$
$108$	13.8132	1.32918
$109$	−11.3388	−1.08606	−0.543030	−	0.839713i	$-0.682723\pi$
$109$	−11.3388	−1.08606	−0.543030	+	0.839713i	$0.682723\pi$
$110$	2.31208	0.220448
$111$	−1.11550	−0.105878
$112$	53.5705	5.06194
$113$	15.6175	1.46917	0.734584	−	0.678518i	$-0.237377\pi$
$113$	15.6175	1.46917	0.734584	+	0.678518i	$0.237377\pi$
$114$	3.44679	0.322821
$115$	−10.1077	−0.942548
$116$	30.4985	2.83171
$117$	−7.62798	−0.705207
$118$	−5.01333	−0.461515
$119$	12.0098	1.10094
$120$	−11.7905	−1.07632
$121$	−10.9162	−0.992379
$122$	−25.3730	−2.29716
$123$	−2.41789	−0.218013
$124$	51.8240	4.65394
$125$	3.58363	0.320530
$126$	30.7871	2.74273
$127$	4.21208	0.373762	0.186881	−	0.982383i	$-0.440162\pi$
$127$	4.21208	0.373762	0.186881	+	0.982383i	$0.440162\pi$
$128$	−22.6676	−2.00355
$129$	−1.90066	−0.167344
$130$	21.8011	1.91208
$131$	12.8498	1.12269	0.561344	−	0.827583i	$-0.310284\pi$
$131$	12.8498	1.12269	0.561344	+	0.827583i	$0.310284\pi$
$132$	−0.690247	−0.0600783
$133$	11.5383	1.00049
$134$	−5.01930	−0.433601
$135$	−7.79571	−0.670948
$136$	−25.7245	−2.20586
$137$	−9.18437	−0.784674	−0.392337	−	0.919822i	$-0.628333\pi$
$137$	−9.18437	−0.784674	−0.392337	+	0.919822i	$0.628333\pi$
$138$	4.16627	0.354656
$139$	−3.84393	−0.326038	−0.163019	−	0.986623i	$-0.552123\pi$
$139$	−3.84393	−0.326038	−0.163019	+	0.986623i	$0.552123\pi$
$140$	−63.7300	−5.38617
$141$	−2.10715	−0.177454
$142$	22.5340	1.89101
$143$	0.790432	0.0660993
$144$	−36.5861	−3.04885
$145$	−17.2123	−1.42940
$146$	39.9742	3.30829
$147$	−4.41878	−0.364455
$148$	12.9149	1.06160
$149$	18.5347	1.51842	0.759210	−	0.650846i	$-0.225586\pi$
$149$	18.5347	1.51842	0.759210	+	0.650846i	$0.225586\pi$
$150$	4.63360	0.378332
$151$	−1.00000	−0.0813788
$151$	−1.00000	−0.0813788
$152$	−24.7145	−2.00461
$153$	−8.20213	−0.663103
$154$	−3.19024	−0.257077
$155$	−29.2478	−2.34924
$156$	−6.50848	−0.521095
$157$	−5.53742	−0.441935	−0.220967	−	0.975281i	$-0.570921\pi$
$157$	−5.53742	−0.441935	−0.220967	+	0.975281i	$0.570921\pi$
$158$	−44.2914	−3.52363
$159$	−0.453777	−0.0359869
$160$	52.5988	4.15830
$161$	13.9467	1.09916
$162$	−19.3624	−1.52125
$163$	6.92732	0.542590	0.271295	−	0.962496i	$-0.412548\pi$
$163$	6.92732	0.542590	0.271295	+	0.962496i	$0.412548\pi$
$164$	27.9937	2.18594
$165$	0.389552	0.0303266
$166$	−34.0737	−2.64464
$167$	−10.6096	−0.820998	−0.410499	−	0.911861i	$-0.634645\pi$
$167$	−10.6096	−0.820998	−0.410499	+	0.911861i	$0.634645\pi$
$168$	16.2687	1.25516
$169$	−5.54685	−0.426681
$170$	23.4420	1.79792
$171$	−7.88010	−0.602606
$172$	22.0054	1.67789
$173$	6.63941	0.504785	0.252393	−	0.967625i	$-0.418783\pi$
$173$	6.63941	0.504785	0.252393	+	0.967625i	$0.418783\pi$
$174$	7.09470	0.537848
$175$	15.5112	1.17253
$176$	3.79116	0.285769
$177$	−0.844673	−0.0634895
$178$	5.47782	0.410580
$179$	2.36820	0.177008	0.0885039	−	0.996076i	$-0.471791\pi$
$179$	2.36820	0.177008	0.0885039	+	0.996076i	$0.471791\pi$
$180$	43.5246	3.24413
$181$	−22.4762	−1.67064	−0.835320	−	0.549763i	$-0.814718\pi$
$181$	−22.4762	−1.67064	−0.835320	+	0.549763i	$0.814718\pi$
$182$	−30.0815	−2.22979
$183$	−4.27498	−0.316015
$184$	−29.8734	−2.20230
$185$	−7.28875	−0.535880
$186$	12.0556	0.883957
$187$	0.849927	0.0621528
$188$	24.3961	1.77927
$189$	10.7566	0.782430
$190$	22.5217	1.63389
$191$	10.9237	0.790409	0.395204	−	0.918593i	$-0.370674\pi$
$191$	10.9237	0.790409	0.395204	+	0.918593i	$0.370674\pi$
$192$	−9.79695	−0.707034
$193$	−23.0827	−1.66153	−0.830766	−	0.556622i	$-0.812097\pi$
$193$	−23.0827	−1.66153	−0.830766	+	0.556622i	$0.812097\pi$
$194$	−47.5182	−3.41161
$195$	3.67317	0.263041
$196$	51.1595	3.65425
$197$	19.4808	1.38795	0.693974	−	0.720000i	$-0.255858\pi$
$197$	19.4808	1.38795	0.693974	+	0.720000i	$0.255858\pi$
$198$	2.17879	0.154840
$199$	−4.50560	−0.319393	−0.159697	−	0.987166i	$-0.551052\pi$
$199$	−4.50560	−0.319393	−0.159697	+	0.987166i	$0.551052\pi$
$200$	−33.2243	−2.34931
$201$	−0.845678	−0.0596495
$202$	37.9750	2.67191
$203$	23.7498	1.66691
$204$	−6.99836	−0.489983
$205$	−15.7987	−1.10343
$206$	32.9008	2.29231
$207$	−9.52498	−0.662032
$208$	35.7476	2.47865
$209$	0.816557	0.0564824
$210$	−14.8252	−1.02303
$211$	14.8049	1.01921	0.509607	−	0.860407i	$-0.329791\pi$
$211$	14.8049	1.01921	0.509607	+	0.860407i	$0.329791\pi$
$212$	5.25372	0.360827
$213$	3.79666	0.260143
$214$	35.2958	2.41277
$215$	−12.4191	−0.846976
$216$	−23.0403	−1.56769
$217$	40.3565	2.73958
$218$	30.5385	2.06833
$219$	6.73508	0.455114
$220$	−4.51014	−0.304073
$221$	8.01413	0.539089
$222$	3.00433	0.201638
$223$	15.5282	1.03984	0.519921	−	0.854214i	$-0.325961\pi$
$223$	15.5282	1.03984	0.519921	+	0.854214i	$0.325961\pi$
$224$	−72.5766	−4.84923
$225$	−10.5934	−0.706227
$226$	−42.0621	−2.79793
$227$	−4.28971	−0.284718	−0.142359	−	0.989815i	$-0.545469\pi$
$227$	−4.28971	−0.284718	−0.142359	+	0.989815i	$0.545469\pi$
$228$	−6.72359	−0.445281
$229$	3.66826	0.242405	0.121203	−	0.992628i	$-0.461325\pi$
$229$	3.66826	0.242405	0.121203	+	0.992628i	$0.461325\pi$
$230$	27.2228	1.79502
$231$	−0.537510	−0.0353655
$232$	−50.8711	−3.33985
$233$	25.2275	1.65271	0.826354	−	0.563151i	$-0.190411\pi$
$233$	25.2275	1.65271	0.826354	+	0.563151i	$0.190411\pi$
$234$	20.5442	1.34302
$235$	−13.7683	−0.898147
$236$	9.77942	0.636586
$237$	−7.46246	−0.484739
$238$	−32.3457	−2.09666
$239$	−18.8412	−1.21873	−0.609367	−	0.792889i	$-0.708576\pi$
$239$	−18.8412	−1.21873	−0.609367	+	0.792889i	$0.708576\pi$
$240$	17.6176	1.13721
$241$	9.11032	0.586847	0.293424	−	0.955982i	$-0.405205\pi$
$241$	9.11032	0.586847	0.293424	+	0.955982i	$0.405205\pi$
$242$	29.4002	1.88992
$243$	−11.1500	−0.715270
$244$	49.4946	3.16857
$245$	−28.8727	−1.84461
$246$	6.51202	0.415192
$247$	7.69948	0.489906
$248$	−86.4420	−5.48907
$249$	−5.74093	−0.363817
$250$	−9.65170	−0.610427
$251$	10.0724	0.635762	0.317881	−	0.948131i	$-0.397029\pi$
$251$	10.0724	0.635762	0.317881	+	0.948131i	$0.397029\pi$
$252$	−60.0559	−3.78317
$253$	0.987004	0.0620524
$254$	−11.3443	−0.711804
$255$	3.94964	0.247336
$256$	17.8705	1.11691
$257$	−27.0196	−1.68543	−0.842717	−	0.538357i	$-0.819045\pi$
$257$	−27.0196	−1.68543	−0.842717	+	0.538357i	$0.819045\pi$
$258$	5.11900	0.318695
$259$	10.0571	0.624919
$260$	−42.5270	−2.63741
$261$	−16.2200	−1.00399
$262$	−34.6079	−2.13808
$263$	17.4395	1.07536	0.537682	−	0.843148i	$-0.319300\pi$
$263$	17.4395	1.07536	0.537682	+	0.843148i	$0.319300\pi$
$264$	1.15133	0.0708592
$265$	−2.96502	−0.182140
$266$	−31.0757	−1.90537
$267$	0.922934	0.0564826
$268$	9.79105	0.598084
$269$	−8.30182	−0.506171	−0.253086	−	0.967444i	$-0.581445\pi$
$269$	−8.30182	−0.506171	−0.253086	+	0.967444i	$0.581445\pi$
$270$	20.9960	1.27777
$271$	−7.92967	−0.481693	−0.240846	−	0.970563i	$-0.577425\pi$
$271$	−7.92967	−0.481693	−0.240846	+	0.970563i	$0.577425\pi$
$272$	38.4382	2.33066
$273$	−5.06829	−0.306747
$274$	24.7360	1.49436
$275$	1.09772	0.0661948
$276$	−8.12707	−0.489192
$277$	11.9318	0.716912	0.358456	−	0.933547i	$-0.383303\pi$
$277$	11.9318	0.716912	0.358456	+	0.933547i	$0.383303\pi$
$278$	10.3528	0.620917
$279$	−27.5616	−1.65007
$280$	106.301	6.35270
$281$	14.3935	0.858641	0.429321	−	0.903152i	$-0.358753\pi$
$281$	14.3935	0.858641	0.429321	+	0.903152i	$0.358753\pi$
$282$	5.67514	0.337949
$283$	6.97207	0.414447	0.207223	−	0.978294i	$-0.433557\pi$
$283$	6.97207	0.414447	0.207223	+	0.978294i	$0.433557\pi$
$284$	−43.9567	−2.60835
$285$	3.79457	0.224771
$286$	−2.12885	−0.125882
$287$	21.7993	1.28677
$288$	49.5664	2.92073
$289$	−8.38266	−0.493098
$290$	46.3574	2.72220
$291$	−8.00613	−0.469327
$292$	−77.9770	−4.56326
$293$	−6.65526	−0.388804	−0.194402	−	0.980922i	$-0.562277\pi$
$293$	−6.65526	−0.388804	−0.194402	+	0.980922i	$0.562277\pi$
$294$	11.9010	0.694079
$295$	−5.51917	−0.321339
$296$	−21.5420	−1.25210
$297$	0.761241	0.0441717
$298$	−49.9189	−2.89173
$299$	9.30666	0.538218
$300$	−9.03869	−0.521849
$301$	17.1361	0.987706
$302$	2.69327	0.154980
$303$	6.39823	0.367569
$304$	36.9291	2.11803
$305$	−27.9331	−1.59944
$306$	22.0906	1.26283
$307$	−23.6948	−1.35234	−0.676168	−	0.736748i	$-0.736361\pi$
$307$	−23.6948	−1.35234	−0.676168	+	0.736748i	$0.736361\pi$
$308$	6.22315	0.354597
$309$	5.54331	0.315348
$310$	78.7722	4.47396
$311$	−29.6880	−1.68345	−0.841727	−	0.539903i	$-0.818461\pi$
$311$	−29.6880	−1.68345	−0.841727	+	0.539903i	$0.818461\pi$
$312$	10.8561	0.614605
$313$	−30.6485	−1.73236	−0.866178	−	0.499735i	$-0.833431\pi$
$313$	−30.6485	−1.73236	−0.866178	+	0.499735i	$0.833431\pi$
$314$	14.9138	0.841634
$315$	33.8935	1.90968
$316$	86.3985	4.86029
$317$	−10.0206	−0.562816	−0.281408	−	0.959588i	$-0.590801\pi$
$317$	−10.0206	−0.562816	−0.281408	+	0.959588i	$0.590801\pi$
$318$	1.22215	0.0685346
$319$	1.68076	0.0941045
$320$	−64.0142	−3.57850
$321$	5.94683	0.331920
$322$	−37.5624	−2.09327
$323$	8.27901	0.460656
$324$	37.7699	2.09833
$325$	10.3506	0.574148
$326$	−18.6572	−1.03333
$327$	5.14529	0.284535
$328$	−46.6932	−2.57820
$329$	18.9977	1.04738
$330$	−1.04917	−0.0577549
$331$	−1.58712	−0.0872358	−0.0436179	−	0.999048i	$-0.513888\pi$
$331$	−1.58712	−0.0872358	−0.0436179	+	0.999048i	$0.513888\pi$
$332$	66.4671	3.64785
$333$	−6.86854	−0.376394
$334$	28.5746	1.56353
$335$	−5.52574	−0.301903
$336$	−24.3091	−1.32617
$337$	−15.4348	−0.840786	−0.420393	−	0.907342i	$-0.638108\pi$
$337$	−15.4348	−0.840786	−0.420393	+	0.907342i	$0.638108\pi$
$338$	14.9392	0.812585
$339$	−7.08685	−0.384905
$340$	−45.7280	−2.47995
$341$	2.85601	0.154661
$342$	21.2232	1.14762
$343$	11.2007	0.604782
$344$	−36.7048	−1.97899
$345$	4.58664	0.246937
$346$	−17.8818	−0.961329
$347$	−35.4051	−1.90064	−0.950322	−	0.311270i	$-0.899246\pi$
$347$	−35.4051	−1.90064	−0.950322	+	0.311270i	$0.899246\pi$
$348$	−13.8395	−0.741875
$349$	12.9036	0.690716	0.345358	−	0.938471i	$-0.387757\pi$
$349$	12.9036	0.690716	0.345358	+	0.938471i	$0.387757\pi$
$350$	−41.7758	−2.23301
$351$	7.17790	0.383128
$352$	−5.13621	−0.273761
$353$	12.4858	0.664554	0.332277	−	0.943182i	$-0.392183\pi$
$353$	12.4858	0.664554	0.332277	+	0.943182i	$0.392183\pi$
$354$	2.27494	0.120911
$355$	24.8077	1.31666
$356$	−10.6855	−0.566330
$357$	−5.44977	−0.288432
$358$	−6.37822	−0.337099
$359$	−24.8476	−1.31141	−0.655704	−	0.755018i	$-0.727628\pi$
$359$	−24.8476	−1.31141	−0.655704	+	0.755018i	$0.727628\pi$
$360$	−72.5986	−3.82628
$361$	−11.0460	−0.581371
$362$	60.5345	3.18162
$363$	4.95351	0.259992
$364$	58.6794	3.07564
$365$	44.0076	2.30346
$366$	11.5137	0.601830
$367$	37.9061	1.97868	0.989341	−	0.145616i	$-0.0465165\pi$
$367$	37.9061	1.97868	0.989341	+	0.145616i	$0.0465165\pi$
$368$	44.6376	2.32690
$369$	−14.8879	−0.775032
$370$	19.6306	1.02055
$371$	4.09118	0.212404
$372$	−23.5166	−1.21928
$373$	−13.8964	−0.719531	−0.359765	−	0.933043i	$-0.617143\pi$
$373$	−13.8964	−0.719531	−0.359765	+	0.933043i	$0.617143\pi$
$374$	−2.28908	−0.118366
$375$	−1.62617	−0.0839751
$376$	−40.6924	−2.09855
$377$	15.8482	0.816225
$378$	−28.9706	−1.49008
$379$	25.7333	1.32183	0.660915	−	0.750461i	$-0.270169\pi$
$379$	25.7333	1.32183	0.660915	+	0.750461i	$0.270169\pi$
$380$	−43.9326	−2.25369
$381$	−1.91135	−0.0979213
$382$	−29.4204	−1.50528
$383$	3.09100	0.157943	0.0789715	−	0.996877i	$-0.474836\pi$
$383$	3.09100	0.157943	0.0789715	+	0.996877i	$0.474836\pi$
$384$	10.2860	0.524908
$385$	−3.51214	−0.178995
$386$	62.1681	3.16427
$387$	−11.7031	−0.594903
$388$	92.6929	4.70577
$389$	−15.6563	−0.793804	−0.396902	−	0.917861i	$-0.629915\pi$
$389$	−15.6563	−0.793804	−0.396902	+	0.917861i	$0.629915\pi$
$390$	−9.89284	−0.500944
$391$	10.0072	0.506084
$392$	−85.3336	−4.31000
$393$	−5.83093	−0.294131
$394$	−52.4671	−2.64325
$395$	−48.7604	−2.45340
$396$	−4.25012	−0.213577
$397$	−0.271106	−0.0136064	−0.00680321	−	0.999977i	$-0.502166\pi$
$397$	−0.271106	−0.0136064	−0.00680321	+	0.999977i	$0.502166\pi$
$398$	12.1348	0.608263
$399$	−5.23580	−0.262118
$400$	49.6446	2.48223
$401$	−24.5164	−1.22429	−0.612144	−	0.790746i	$-0.709693\pi$
$401$	−24.5164	−1.22429	−0.612144	+	0.790746i	$0.709693\pi$
$402$	2.27764	0.113598
$403$	26.9299	1.34147
$404$	−74.0771	−3.68547
$405$	−21.3161	−1.05920
$406$	−63.9647	−3.17451
$407$	0.711737	0.0352795
$408$	11.6732	0.577910
$409$	7.08285	0.350224	0.175112	−	0.984548i	$-0.443971\pi$
$409$	7.08285	0.350224	0.175112	+	0.984548i	$0.443971\pi$
$410$	42.5502	2.10140
$411$	4.16766	0.205575
$412$	−64.1791	−3.16188
$413$	7.61544	0.374731
$414$	25.6534	1.26079
$415$	−37.5118	−1.84138
$416$	−48.4304	−2.37449
$417$	1.74429	0.0854182
$418$	−2.19921	−0.107567
$419$	9.08054	0.443614	0.221807	−	0.975091i	$-0.428805\pi$
$419$	9.08054	0.443614	0.221807	+	0.975091i	$0.428805\pi$
$420$	28.9192	1.41111
$421$	4.99341	0.243364	0.121682	−	0.992569i	$-0.461171\pi$
$421$	4.99341	0.243364	0.121682	+	0.992569i	$0.461171\pi$
$422$	−39.8738	−1.94102
$423$	−12.9746	−0.630845
$424$	−8.76316	−0.425577
$425$	11.1297	0.539868
$426$	−10.2254	−0.495424
$427$	38.5425	1.86520
$428$	−68.8510	−3.32804
$429$	−0.358680	−0.0173172
$430$	33.4480	1.61301
$431$	0.0170197	0.000819808 0	0.000409904	−	1.00000i	$-0.499870\pi$
$431$	0.0170197	0.000819808 0	0.000409904		1.00000i	$0.499870\pi$
$432$	34.4274	1.65639
$433$	−24.6985	−1.18693	−0.593466	−	0.804859i	$-0.702241\pi$
$433$	−24.6985	−1.18693	−0.593466	+	0.804859i	$0.702241\pi$
$434$	−108.691	−5.21734
$435$	7.81055	0.374487
$436$	−59.5709	−2.85293
$437$	9.61426	0.459912
$438$	−18.1394	−0.866734
$439$	−11.1712	−0.533173	−0.266587	−	0.963811i	$-0.585896\pi$
$439$	−11.1712	−0.533173	−0.266587	+	0.963811i	$0.585896\pi$
$440$	7.52287	0.358639
$441$	−27.2082	−1.29563
$442$	−21.5842	−1.02666
$443$	6.25001	0.296947	0.148473	−	0.988916i	$-0.452564\pi$
$443$	6.25001	0.296947	0.148473	+	0.988916i	$0.452564\pi$
$444$	−5.86050	−0.278127
$445$	6.03054	0.285875
$446$	−41.8216	−1.98031
$447$	−8.41061	−0.397808
$448$	88.3277	4.17309
$449$	−3.10116	−0.146353	−0.0731763	−	0.997319i	$-0.523314\pi$
$449$	−3.10116	−0.146353	−0.0731763	+	0.997319i	$0.523314\pi$
$450$	28.5309	1.34496
$451$	1.54272	0.0726439
$452$	82.0498	3.85930
$453$	0.453777	0.0213203
$454$	11.5534	0.542227
$455$	−33.1167	−1.55253
$456$	11.2149	0.525185
$457$	18.1698	0.849948	0.424974	−	0.905206i	$-0.360283\pi$
$457$	18.1698	0.849948	0.424974	+	0.905206i	$0.360283\pi$
$458$	−9.87962	−0.461644
$459$	7.71817	0.360253
$460$	−53.1030	−2.47594
$461$	−30.5544	−1.42306	−0.711530	−	0.702656i	$-0.751997\pi$
$461$	−30.5544	−1.42306	−0.711530	+	0.702656i	$0.751997\pi$
$462$	1.44766	0.0673513
$463$	6.33363	0.294349	0.147174	−	0.989111i	$-0.452982\pi$
$463$	6.33363	0.294349	0.147174	+	0.989111i	$0.452982\pi$
$464$	76.0130	3.52881
$465$	13.2720	0.615473
$466$	−67.9445	−3.14747
$467$	21.8018	1.00887	0.504434	−	0.863450i	$-0.331701\pi$
$467$	21.8018	1.00887	0.504434	+	0.863450i	$0.331701\pi$
$468$	−40.0753	−1.85248
$469$	7.62450	0.352067
$470$	37.0819	1.71046
$471$	2.51276	0.115782
$472$	−16.3120	−0.750820
$473$	1.21271	0.0557604
$474$	20.0984	0.923152
$475$	10.6927	0.490615
$476$	63.0961	2.89200
$477$	−2.79409	−0.127932
$478$	50.7444	2.32099
$479$	8.88783	0.406095	0.203048	−	0.979169i	$-0.434915\pi$
$479$	8.88783	0.406095	0.203048	+	0.979169i	$0.434915\pi$
$480$	−23.8682	−1.08943
$481$	6.71112	0.306001
$482$	−24.5366	−1.11761
$483$	−6.32872	−0.287967
$484$	−57.3505	−2.60684
$485$	−52.3128	−2.37540
$486$	30.0299	1.36218
$487$	−17.1265	−0.776076	−0.388038	−	0.921643i	$-0.626847\pi$
$487$	−17.1265	−0.776076	−0.388038	+	0.921643i	$0.626847\pi$
$488$	−82.5565	−3.73716
$489$	−3.14346	−0.142152
$490$	77.7621	3.51294
$491$	−1.93771	−0.0874475	−0.0437238	−	0.999044i	$-0.513922\pi$
$491$	−1.93771	−0.0874475	−0.0437238	+	0.999044i	$0.513922\pi$
$492$	−12.7029	−0.572691
$493$	17.0411	0.767492
$494$	−20.7368	−0.932993
$495$	2.39863	0.107810
$496$	129.164	5.79963
$497$	−34.2300	−1.53543
$498$	15.4619	0.692864
$499$	26.0866	1.16780	0.583898	−	0.811827i	$-0.301527\pi$
$499$	26.0866	1.16780	0.583898	+	0.811827i	$0.301527\pi$
$500$	18.8274	0.841987
$501$	4.81441	0.215092
$502$	−27.1276	−1.21077
$503$	24.7992	1.10574	0.552871	−	0.833267i	$-0.313532\pi$
$503$	24.7992	1.10574	0.552871	+	0.833267i	$0.313532\pi$
$504$	100.173	4.46205
$505$	41.8066	1.86037
$506$	−2.65827	−0.118175
$507$	2.51704	0.111785
$508$	22.1291	0.981821
$509$	24.4694	1.08459	0.542293	−	0.840189i	$-0.317556\pi$
$509$	24.4694	1.08459	0.542293	+	0.840189i	$0.317556\pi$
$510$	−10.6375	−0.471035
$511$	−60.7224	−2.68620
$512$	−2.79499	−0.123522
$513$	7.41514	0.327386
$514$	72.7711	3.20979
$515$	36.2205	1.59607
$516$	−9.98554	−0.439589
$517$	1.34446	0.0591293
$518$	−27.0866	−1.19012
$519$	−3.01282	−0.132248
$520$	70.9347	3.11069
$521$	−17.2504	−0.755755	−0.377878	−	0.925856i	$-0.623346\pi$
$521$	−17.2504	−0.755755	−0.377878	+	0.925856i	$0.623346\pi$
$522$	43.6849	1.91203
$523$	−9.13924	−0.399631	−0.199816	−	0.979834i	$-0.564034\pi$
$523$	−9.13924	−0.399631	−0.199816	+	0.979834i	$0.564034\pi$
$524$	67.5090	2.94914
$525$	−7.03861	−0.307190
$526$	−46.9692	−2.04796
$527$	28.9568	1.26138
$528$	−1.72034	−0.0748682
$529$	−11.3789	−0.494734
$530$	7.98562	0.346873
$531$	−5.20099	−0.225704
$532$	60.6188	2.62816
$533$	14.5466	0.630085
$534$	−2.48571	−0.107567
$535$	38.8572	1.67994
$536$	−16.3314	−0.705408
$537$	−1.07464	−0.0463740
$538$	22.3591	0.963968
$539$	2.81938	0.121440
$540$	−40.9565	−1.76249
$541$	−29.1258	−1.25222	−0.626109	−	0.779736i	$-0.715353\pi$
$541$	−29.1258	−1.25222	−0.626109	+	0.779736i	$0.715353\pi$
$542$	21.3568	0.917351
$543$	10.1992	0.437689
$544$	−52.0756	−2.23272
$545$	33.6198	1.44012
$546$	13.6503	0.584178
$547$	26.2326	1.12162	0.560812	−	0.827943i	$-0.310489\pi$
$547$	26.2326	1.12162	0.560812	+	0.827943i	$0.310489\pi$
$548$	−48.2521	−2.06123
$549$	−26.3227	−1.12343
$550$	−2.95645	−0.126064
$551$	16.3720	0.697472
$552$	13.5559	0.576976
$553$	67.2803	2.86105
$554$	−32.1356	−1.36531
$555$	3.30747	0.140394
$556$	−20.1949	−0.856456
$557$	−10.6817	−0.452600	−0.226300	−	0.974058i	$-0.572663\pi$
$557$	−10.6817	−0.452600	−0.226300	+	0.974058i	$0.572663\pi$
$558$	74.2309	3.14244
$559$	11.4349	0.483644
$560$	−158.838	−6.71212
$561$	−0.385677	−0.0162833
$562$	−38.7655	−1.63522
$563$	31.3510	1.32129	0.660643	−	0.750701i	$-0.270284\pi$
$563$	31.3510	1.32129	0.660643	+	0.750701i	$0.270284\pi$
$564$	−11.0704	−0.466147
$565$	−46.3062	−1.94811
$566$	−18.7777	−0.789285
$567$	29.4122	1.23520
$568$	73.3194	3.07641
$569$	−17.4286	−0.730646	−0.365323	−	0.930881i	$-0.619041\pi$
$569$	−17.4286	−0.730646	−0.365323	+	0.930881i	$0.619041\pi$
$570$	−10.2198	−0.428061
$571$	−40.5091	−1.69525	−0.847627	−	0.530593i	$-0.821969\pi$
$571$	−40.5091	−1.69525	−0.847627	+	0.530593i	$0.821969\pi$
$572$	4.15271	0.173634
$573$	−4.95691	−0.207078
$574$	−58.7114	−2.45056
$575$	12.9247	0.538996
$576$	−60.3237	−2.51349
$577$	−40.4024	−1.68197	−0.840987	−	0.541056i	$-0.818025\pi$
$577$	−40.4024	−1.68197	−0.840987	+	0.541056i	$0.818025\pi$
$578$	22.5768	0.939071
$579$	10.4744	0.435302
$580$	−90.4286	−3.75484
$581$	51.7593	2.14734
$582$	21.5627	0.893802
$583$	0.289531	0.0119911
$584$	130.065	5.38213
$585$	22.6171	0.935104
$586$	17.9244	0.740451
$587$	−5.50421	−0.227183	−0.113592	−	0.993528i	$-0.536236\pi$
$587$	−5.50421	−0.227183	−0.113592	+	0.993528i	$0.536236\pi$
$588$	−23.2150	−0.957372
$589$	27.8199	1.14630
$590$	14.8646	0.611968
$591$	−8.83994	−0.363627
$592$	32.1886	1.32294
$593$	11.5430	0.474016	0.237008	−	0.971508i	$-0.423833\pi$
$593$	11.5430	0.474016	0.237008	+	0.971508i	$0.423833\pi$
$594$	−2.05023	−0.0841220
$595$	−35.6093	−1.45984
$596$	97.3760	3.98868
$597$	2.04454	0.0836774
$598$	−25.0654	−1.02500
$599$	−0.709927	−0.0290068	−0.0145034	−	0.999895i	$-0.504617\pi$
$599$	−0.709927	−0.0290068	−0.0145034	+	0.999895i	$0.504617\pi$
$600$	15.0764	0.615493
$601$	−5.40074	−0.220301	−0.110150	−	0.993915i	$-0.535133\pi$
$601$	−5.40074	−0.220301	−0.110150	+	0.993915i	$0.535133\pi$
$602$	−46.1521	−1.88102
$603$	−5.20718	−0.212053
$604$	−5.25372	−0.213771
$605$	32.3667	1.31589
$606$	−17.2322	−0.700009
$607$	36.4140	1.47800	0.738999	−	0.673707i	$-0.235299\pi$
$607$	36.4140	1.47800	0.738999	+	0.673707i	$0.235299\pi$
$608$	−50.0310	−2.02903
$609$	−10.7771	−0.436711
$610$	75.2315	3.04603
$611$	12.6772	0.512864
$612$	−43.0917	−1.74188
$613$	5.89879	0.238250	0.119125	−	0.992879i	$-0.461991\pi$
$613$	5.89879	0.238250	0.119125	+	0.992879i	$0.461991\pi$
$614$	63.8167	2.57543
$615$	7.16909	0.289085
$616$	−10.3802	−0.418229
$617$	−23.1266	−0.931044	−0.465522	−	0.885036i	$-0.654133\pi$
$617$	−23.1266	−0.931044	−0.465522	+	0.885036i	$0.654133\pi$
$618$	−14.9297	−0.600559
$619$	26.8935	1.08094	0.540471	−	0.841363i	$-0.318246\pi$
$619$	26.8935	1.08094	0.540471	+	0.841363i	$0.318246\pi$
$620$	−153.660	−6.17112
$621$	8.96297	0.359672
$622$	79.9580	3.20602
$623$	−8.32102	−0.333375
$624$	−16.2214	−0.649377
$625$	−29.5824	−1.18330
$626$	82.5448	3.29915
$627$	−0.370535	−0.0147977
$628$	−29.0921	−1.16090
$629$	7.21625	0.287731
$630$	−91.2845	−3.63686
$631$	−9.78969	−0.389721	−0.194861	−	0.980831i	$-0.562425\pi$
$631$	−9.78969	−0.389721	−0.194861	+	0.980831i	$0.562425\pi$
$632$	−144.112	−5.73246
$633$	−6.71815	−0.267022
$634$	26.9883	1.07184
$635$	−12.4889	−0.495608
$636$	−2.38402	−0.0945325
$637$	26.5846	1.05332
$638$	−4.52674	−0.179216
$639$	23.3775	0.924800
$640$	67.2100	2.65671
$641$	−22.1728	−0.875774	−0.437887	−	0.899030i	$-0.644273\pi$
$641$	−22.1728	−0.875774	−0.437887	+	0.899030i	$0.644273\pi$
$642$	−16.0164	−0.632119
$643$	−10.3845	−0.409526	−0.204763	−	0.978812i	$-0.565642\pi$
$643$	−10.3845	−0.409526	−0.204763	+	0.978812i	$0.565642\pi$
$644$	73.2723	2.88733
$645$	5.63551	0.221898
$646$	−22.2976	−0.877289
$647$	−22.7354	−0.893819	−0.446909	−	0.894579i	$-0.647475\pi$
$647$	−22.7354	−0.893819	−0.446909	+	0.894579i	$0.647475\pi$
$648$	−62.9999	−2.47487
$649$	0.538940	0.0211553
$650$	−27.8770	−1.09343
$651$	−18.3129	−0.717737
$652$	36.3942	1.42531
$653$	−24.0965	−0.942968	−0.471484	−	0.881875i	$-0.656281\pi$
$653$	−24.0965	−0.942968	−0.471484	+	0.881875i	$0.656281\pi$
$654$	−13.8577	−0.541878
$655$	−38.0998	−1.48868
$656$	69.7702	2.72407
$657$	41.4705	1.61792
$658$	−51.1661	−1.99466
$659$	4.41495	0.171982	0.0859911	−	0.996296i	$-0.472594\pi$
$659$	4.41495	0.171982	0.0859911	+	0.996296i	$0.472594\pi$
$660$	2.04660	0.0796637
$661$	−49.7370	−1.93454	−0.967272	−	0.253740i	$-0.918339\pi$
$661$	−49.7370	−1.93454	−0.967272	+	0.253740i	$0.918339\pi$
$662$	4.27454	0.166135
$663$	−3.63663	−0.141235
$664$	−110.866	−4.30245
$665$	−34.2112	−1.32665
$666$	18.4989	0.716816
$667$	19.7895	0.766253
$668$	−55.7400	−2.15665
$669$	−7.04633	−0.272427
$670$	14.8823	0.574955
$671$	2.72763	0.105299
$672$	32.9336	1.27044
$673$	−4.42229	−0.170467	−0.0852334	−	0.996361i	$-0.527164\pi$
$673$	−4.42229	−0.170467	−0.0852334	+	0.996361i	$0.527164\pi$
$674$	41.5701	1.60122
$675$	9.96835	0.383682
$676$	−29.1416	−1.12083
$677$	−44.4463	−1.70821	−0.854105	−	0.520101i	$-0.825894\pi$
$677$	−44.4463	−1.70821	−0.854105	+	0.520101i	$0.825894\pi$
$678$	19.0868	0.733025
$679$	72.1819	2.77009
$680$	76.2738	2.92497
$681$	1.94658	0.0745929
$682$	−7.69200	−0.294542
$683$	36.0209	1.37830	0.689150	−	0.724619i	$-0.257984\pi$
$683$	36.0209	1.37830	0.689150	+	0.724619i	$0.257984\pi$
$684$	−41.3998	−1.58296
$685$	27.2319	1.04048
$686$	−30.1666	−1.15177
$687$	−1.66457	−0.0635074
$688$	54.8452	2.09095
$689$	2.73005	0.104006
$690$	−12.3531	−0.470274
$691$	−21.3575	−0.812476	−0.406238	−	0.913767i	$-0.633160\pi$
$691$	−21.3575	−0.812476	−0.406238	+	0.913767i	$0.633160\pi$
$692$	34.8816	1.32600
$693$	−3.30966	−0.125724
$694$	95.3555	3.61964
$695$	11.3973	0.432326
$696$	23.0842	0.875003
$697$	15.6415	0.592466
$698$	−34.7530	−1.31542
$699$	−11.4477	−0.432990
$700$	81.4913	3.08008
$701$	12.9315	0.488415	0.244208	−	0.969723i	$-0.421472\pi$
$701$	12.9315	0.488415	0.244208	+	0.969723i	$0.421472\pi$
$702$	−19.3321	−0.729641
$703$	6.93293	0.261480
$704$	6.25090	0.235590
$705$	6.24776	0.235304
$706$	−33.6277	−1.26560
$707$	−57.6854	−2.16948
$708$	−4.43768	−0.166778
$709$	−13.4308	−0.504403	−0.252202	−	0.967675i	$-0.581155\pi$
$709$	−13.4308	−0.504403	−0.252202	+	0.967675i	$0.581155\pi$
$710$	−66.8139	−2.50748
$711$	−45.9493	−1.72323
$712$	17.8233	0.667957
$713$	33.6270	1.25934
$714$	14.6777	0.549300
$715$	−2.34365	−0.0876475
$716$	12.4419	0.464975
$717$	8.54969	0.319294
$718$	66.9215	2.49749
$719$	−8.02276	−0.299199	−0.149599	−	0.988747i	$-0.547798\pi$
$719$	−8.02276	−0.299199	−0.149599	+	0.988747i	$0.547798\pi$
$720$	108.479	4.04277
$721$	−49.9776	−1.86126
$722$	29.7500	1.10718
$723$	−4.13406	−0.153747
$724$	−118.084	−4.38854
$725$	22.0093	0.817405
$726$	−13.3412	−0.495137
$727$	8.96321	0.332427	0.166214	−	0.986090i	$-0.446846\pi$
$727$	8.96321	0.332427	0.166214	+	0.986090i	$0.446846\pi$
$728$	−97.8767	−3.62755
$729$	−16.5079	−0.611405
$730$	−118.525	−4.38679
$731$	12.2956	0.454768
$732$	−22.4595	−0.830128
$733$	−13.3742	−0.493988	−0.246994	−	0.969017i	$-0.579443\pi$
$733$	−13.3742	−0.493988	−0.246994	+	0.969017i	$0.579443\pi$
$734$	−102.091	−3.76827
$735$	13.1018	0.483267
$736$	−60.4745	−2.22912
$737$	0.539582	0.0198757
$738$	40.0971	1.47600
$739$	44.6346	1.64191	0.820956	−	0.570992i	$-0.193441\pi$
$739$	44.6346	1.64191	0.820956	+	0.570992i	$0.193441\pi$
$740$	−38.2931	−1.40768
$741$	−3.49385	−0.128350
$742$	−11.0187	−0.404508
$743$	0.00225327	8.26645e−5 0	4.13323e−5	−	1.00000i	$-0.499987\pi$
$743$	0.00225327	8.26645e−5 0	4.13323e−5		1.00000i	$0.499987\pi$
$744$	39.2254	1.43807
$745$	−54.9557	−2.01342
$746$	37.4269	1.37030
$747$	−35.3492	−1.29336
$748$	4.46528	0.163267
$749$	−53.6157	−1.95907
$750$	4.37972	0.159925
$751$	27.9448	1.01972	0.509860	−	0.860257i	$-0.329697\pi$
$751$	27.9448	1.01972	0.509860	+	0.860257i	$0.329697\pi$
$752$	60.8037	2.21728
$753$	−4.57061	−0.166562
$754$	−42.6836	−1.55445
$755$	2.96502	0.107908
$756$	56.5124	2.05533
$757$	2.71069	0.0985216	0.0492608	−	0.998786i	$-0.484313\pi$
$757$	2.71069	0.0985216	0.0492608	+	0.998786i	$0.484313\pi$
$758$	−69.3067	−2.51733
$759$	−0.447880	−0.0162570
$760$	73.2792	2.65811
$761$	−30.1432	−1.09269	−0.546345	−	0.837560i	$-0.683981\pi$
$761$	−30.1432	−1.09269	−0.546345	+	0.837560i	$0.683981\pi$
$762$	5.14778	0.186484
$763$	−46.3891	−1.67940
$764$	57.3899	2.07629
$765$	24.3195	0.879273
$766$	−8.32492	−0.300791
$767$	5.08178	0.183492
$768$	−8.10924	−0.292617
$769$	34.6513	1.24956	0.624780	−	0.780801i	$-0.285189\pi$
$769$	34.6513	1.24956	0.624780	+	0.780801i	$0.285189\pi$
$770$	9.45915	0.340884
$771$	12.2609	0.441564
$772$	−121.270	−4.36461
$773$	−28.4177	−1.02212	−0.511058	−	0.859547i	$-0.670746\pi$
$773$	−28.4177	−1.02212	−0.511058	+	0.859547i	$0.670746\pi$
$774$	31.5197	1.13295
$775$	37.3990	1.34341
$776$	−154.611	−5.55021
$777$	−4.56369	−0.163722
$778$	42.1666	1.51175
$779$	15.0274	0.538413
$780$	19.2978	0.690972
$781$	−2.42244	−0.0866817
$782$	−26.9520	−0.963802
$783$	15.2630	0.545453
$784$	127.508	4.55385
$785$	16.4186	0.586005
$786$	15.7043	0.560153
$787$	45.6712	1.62800	0.814002	−	0.580862i	$-0.197285\pi$
$787$	45.6712	1.62800	0.814002	+	0.580862i	$0.197285\pi$
$788$	102.347	3.64595
$789$	−7.91363	−0.281733
$790$	131.325	4.67234
$791$	63.8939	2.27181
$792$	7.08917	0.251903
$793$	25.7194	0.913323
$794$	0.730162	0.0259125
$795$	1.34546	0.0477186
$796$	−23.6711	−0.839002
$797$	10.3565	0.366846	0.183423	−	0.983034i	$-0.441282\pi$
$797$	10.3565	0.366846	0.183423	+	0.983034i	$0.441282\pi$
$798$	14.1014	0.499186
$799$	13.6314	0.482244
$800$	−67.2579	−2.37793
$801$	5.68287	0.200794
$802$	66.0293	2.33157
$803$	−4.29729	−0.151648
$804$	−4.44296	−0.156691
$805$	−41.3524	−1.45748
$806$	−72.5295	−2.55474
$807$	3.76718	0.132611
$808$	123.560	4.34682
$809$	28.8651	1.01484	0.507422	−	0.861698i	$-0.330599\pi$
$809$	28.8651	1.01484	0.507422	+	0.861698i	$0.330599\pi$
$810$	57.4100	2.01718
$811$	−3.39423	−0.119187	−0.0595937	−	0.998223i	$-0.518981\pi$
$811$	−3.39423	−0.119187	−0.0595937	+	0.998223i	$0.518981\pi$
$812$	124.775	4.37873
$813$	3.59830	0.126198
$814$	−1.91690	−0.0671874
$815$	−20.5397	−0.719473
$816$	−17.4424	−0.610606
$817$	11.8128	0.413278
$818$	−19.0760	−0.666978
$819$	−31.2075	−1.09048
$820$	−83.0019	−2.89855
$821$	9.17767	0.320303	0.160151	−	0.987092i	$-0.448802\pi$
$821$	9.17767	0.320303	0.160151	+	0.987092i	$0.448802\pi$
$822$	−11.2246	−0.391504
$823$	48.3640	1.68586	0.842931	−	0.538021i	$-0.180828\pi$
$823$	48.3640	1.68586	0.842931	+	0.538021i	$0.180828\pi$
$824$	107.050	3.72927
$825$	−0.498119	−0.0173423
$826$	−20.5105	−0.713650
$827$	38.6146	1.34276	0.671381	−	0.741112i	$-0.265701\pi$
$827$	38.6146	1.34276	0.671381	+	0.741112i	$0.265701\pi$
$828$	−50.0416	−1.73906
$829$	−39.9051	−1.38596	−0.692982	−	0.720955i	$-0.743703\pi$
$829$	−39.9051	−1.38596	−0.692982	+	0.720955i	$0.743703\pi$
$830$	101.029	3.50678
$831$	−5.41438	−0.187823
$832$	58.9411	2.04341
$833$	28.5855	0.990430
$834$	−4.69785	−0.162673
$835$	31.4578	1.08864
$836$	4.28996	0.148371
$837$	25.9354	0.896457
$838$	−24.4564	−0.844832
$839$	−0.569828	−0.0196727	−0.00983633	−	0.999952i	$-0.503131\pi$
$839$	−0.569828	−0.0196727	−0.00983633	+	0.999952i	$0.503131\pi$
$840$	−48.2370	−1.66433
$841$	4.69937	0.162047
$842$	−13.4486	−0.463470
$843$	−6.53142	−0.224954
$844$	77.7811	2.67733
$845$	16.4465	0.565778
$846$	34.9441	1.20140
$847$	−44.6600	−1.53454
$848$	13.0941	0.449654
$849$	−3.16377	−0.108580
$850$	−29.9752	−1.02814
$851$	8.38010	0.287266
$852$	19.9466	0.683358
$853$	−10.0335	−0.343540	−0.171770	−	0.985137i	$-0.554949\pi$
$853$	−10.0335	−0.343540	−0.171770	+	0.985137i	$0.554949\pi$
$854$	−103.805	−3.55215
$855$	23.3647	0.799055
$856$	114.843	3.92524
$857$	18.9862	0.648556	0.324278	−	0.945962i	$-0.394879\pi$
$857$	18.9862	0.648556	0.324278	+	0.945962i	$0.394879\pi$
$858$	0.966024	0.0329795
$859$	41.4489	1.41422	0.707109	−	0.707104i	$-0.249999\pi$
$859$	41.4489	1.41422	0.707109	+	0.707104i	$0.249999\pi$
$860$	−65.2465	−2.22489
$861$	−9.89201	−0.337119
$862$	−0.0458386	−0.00156127
$863$	42.8541	1.45877	0.729385	−	0.684104i	$-0.239806\pi$
$863$	42.8541	1.45877	0.729385	+	0.684104i	$0.239806\pi$
$864$	−46.6418	−1.58679
$865$	−19.6860	−0.669345
$866$	66.5197	2.26043
$867$	3.80386	0.129186
$868$	212.022	7.19648
$869$	4.76139	0.161519
$870$	−21.0360	−0.713186
$871$	5.08783	0.172394
$872$	99.3637	3.36488
$873$	−49.2969	−1.66845
$874$	−25.8938	−0.875872
$875$	14.6613	0.495642
$876$	35.3842	1.19552
$877$	−23.4960	−0.793405	−0.396703	−	0.917947i	$-0.629846\pi$
$877$	−23.4960	−0.793405	−0.396703	+	0.917947i	$0.629846\pi$
$878$	30.0872	1.01539
$879$	3.02001	0.101862
$880$	−11.2409	−0.378929
$881$	−9.94408	−0.335025	−0.167512	−	0.985870i	$-0.553573\pi$
$881$	−9.94408	−0.335025	−0.167512	+	0.985870i	$0.553573\pi$
$882$	73.2790	2.46743
$883$	43.9829	1.48014	0.740071	−	0.672528i	$-0.234792\pi$
$883$	43.9829	1.48014	0.740071	+	0.672528i	$0.234792\pi$
$884$	42.1040	1.41611
$885$	2.50448	0.0841870
$886$	−16.8330	−0.565515
$887$	34.6272	1.16267	0.581333	−	0.813666i	$-0.302531\pi$
$887$	34.6272	1.16267	0.581333	+	0.813666i	$0.302531\pi$
$888$	9.77526	0.328036
$889$	17.2324	0.577956
$890$	−16.2419	−0.544429
$891$	2.08149	0.0697325
$892$	81.5806	2.73152
$893$	13.0962	0.438247
$894$	22.6521	0.757599
$895$	−7.02178	−0.234712
$896$	−92.7373	−3.09814
$897$	−4.22315	−0.141007
$898$	8.35226	0.278718
$899$	57.2632	1.90983
$900$	−55.6548	−1.85516
$901$	2.93553	0.0977967
$902$	−4.15497	−0.138345
$903$	−7.77595	−0.258768
$904$	−136.858	−4.55184
$905$	66.6424	2.21527
$906$	−1.22215	−0.0406031
$907$	27.4301	0.910802	0.455401	−	0.890286i	$-0.349496\pi$
$907$	27.4301	0.910802	0.455401	+	0.890286i	$0.349496\pi$
$908$	−22.5370	−0.747915
$909$	39.3964	1.30670
$910$	89.1923	2.95670
$911$	−24.9970	−0.828188	−0.414094	−	0.910234i	$-0.635902\pi$
$911$	−24.9970	−0.828188	−0.414094	+	0.910234i	$0.635902\pi$
$912$	−16.7576	−0.554899
$913$	3.66298	0.121227
$914$	−48.9363	−1.61867
$915$	12.6754	0.419036
$916$	19.2720	0.636765
$917$	52.5707	1.73604
$918$	−20.7871	−0.686078
$919$	−21.0756	−0.695220	−0.347610	−	0.937639i	$-0.613007\pi$
$919$	−21.0756	−0.695220	−0.347610	+	0.937639i	$0.613007\pi$
$920$	88.5753	2.92024
$921$	10.7522	0.354296
$922$	82.2913	2.71012
$923$	−22.8417	−0.751843
$924$	−2.82393	−0.0929003
$925$	9.32010	0.306443
$926$	−17.0582	−0.560567
$927$	34.1324	1.12105
$928$	−102.981	−3.38053
$929$	−10.8521	−0.356046	−0.178023	−	0.984026i	$-0.556970\pi$
$929$	−10.8521	−0.356046	−0.178023	+	0.984026i	$0.556970\pi$
$930$	−35.7450	−1.17213
$931$	27.4632	0.900070
$932$	132.538	4.34143
$933$	13.4718	0.441046
$934$	−58.7183	−1.92132
$935$	−2.52005	−0.0824145
$936$	66.8452	2.18490
$937$	45.7616	1.49497	0.747483	−	0.664281i	$-0.231262\pi$
$937$	45.7616	1.49497	0.747483	+	0.664281i	$0.231262\pi$
$938$	−20.5349	−0.670487
$939$	13.9076	0.453857
$940$	−72.3350	−2.35931
$941$	33.6169	1.09588	0.547939	−	0.836518i	$-0.315413\pi$
$941$	33.6169	1.09588	0.547939	+	0.836518i	$0.315413\pi$
$942$	−6.76754	−0.220498
$943$	18.1642	0.591509
$944$	24.3738	0.793299
$945$	−31.8937	−1.03750
$946$	−3.26616	−0.106192
$947$	14.9165	0.484720	0.242360	−	0.970186i	$-0.422079\pi$
$947$	14.9165	0.484720	0.242360	+	0.970186i	$0.422079\pi$
$948$	−39.2057	−1.27334
$949$	−40.5200	−1.31534
$950$	−28.7984	−0.934342
$951$	4.54714	0.147451
$952$	−105.244	−3.41097
$953$	29.5126	0.956006	0.478003	−	0.878358i	$-0.341361\pi$
$953$	29.5126	0.956006	0.478003	+	0.878358i	$0.341361\pi$
$954$	7.52524	0.243639
$955$	−32.3889	−1.04808
$956$	−98.9862	−3.20144
$957$	−0.762691	−0.0246543
$958$	−23.9374	−0.773381
$959$	−37.5749	−1.21336
$960$	29.0482	0.937526
$961$	66.3036	2.13883
$962$	−18.0749	−0.582757
$963$	36.6170	1.17997
$964$	47.8631	1.54157
$965$	68.4409	2.20319
$966$	17.0450	0.548413
$967$	22.3483	0.718674	0.359337	−	0.933208i	$-0.383003\pi$
$967$	22.3483	0.718674	0.359337	+	0.933208i	$0.383003\pi$
$968$	95.6601	3.07463
$969$	−3.75683	−0.120687
$970$	140.893	4.52379
$971$	−10.7340	−0.344469	−0.172235	−	0.985056i	$-0.555099\pi$
$971$	−10.7340	−0.344469	−0.172235	+	0.985056i	$0.555099\pi$
$972$	−58.5788	−1.87891
$973$	−15.7262	−0.504160
$974$	46.1264	1.47798
$975$	−4.69687	−0.150420
$976$	123.358	3.94860
$977$	35.3457	1.13081	0.565404	−	0.824814i	$-0.308720\pi$
$977$	35.3457	1.13081	0.565404	+	0.824814i	$0.308720\pi$
$978$	8.46620	0.270719
$979$	−0.588874	−0.0188205
$980$	−151.689	−4.84553
$981$	31.6816	1.01152
$982$	5.21878	0.166538
$983$	−13.7163	−0.437482	−0.218741	−	0.975783i	$-0.570195\pi$
$983$	−13.7163	−0.437482	−0.218741	+	0.975783i	$0.570195\pi$
$984$	21.1883	0.675459
$985$	−57.7610	−1.84042
$986$	−45.8963	−1.46164
$987$	−8.62074	−0.274401
$988$	40.4509	1.28692
$989$	14.2786	0.454034
$990$	−6.46016	−0.205317
$991$	−52.8934	−1.68022	−0.840108	−	0.542420i	$-0.817508\pi$
$991$	−52.8934	−1.68022	−0.840108	+	0.542420i	$0.817508\pi$
$992$	−174.990	−5.55593
$993$	0.720197	0.0228548
$994$	92.1908	2.92411
$995$	13.3592	0.423515
$996$	−30.1612	−0.955695
$997$	19.5050	0.617730	0.308865	−	0.951106i	$-0.400051\pi$
$997$	19.5050	0.617730	0.308865	+	0.951106i	$0.400051\pi$
$998$	−70.2583	−2.22399
$999$	6.46327	0.204489

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8003.2.a.d.1.6	✓	179

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8003.2.a.d.1.6	✓	179	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:	\( N \)	\(=\)	\( 8003 = 53 \cdot 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8003.a (trivial)

\(f(q)\)	\(=\)	\(q-2.69327 q^{2} -0.453777 q^{3} +5.25372 q^{4} -2.96502 q^{5} +1.22215 q^{6} +4.09118 q^{7} -8.76316 q^{8} -2.79409 q^{9} +O(q^{10})\)	\(q-2.69327 q^{2} -0.453777 q^{3} +5.25372 q^{4} -2.96502 q^{5} +1.22215 q^{6} +4.09118 q^{7} -8.76316 q^{8} -2.79409 q^{9} +7.98562 q^{10} +0.289531 q^{11} -2.38402 q^{12} +2.73005 q^{13} -11.0187 q^{14} +1.34546 q^{15} +13.0941 q^{16} +2.93553 q^{17} +7.52524 q^{18} +2.82028 q^{19} -15.5774 q^{20} -1.85649 q^{21} -0.779785 q^{22} +3.40898 q^{23} +3.97652 q^{24} +3.79136 q^{25} -7.35276 q^{26} +2.62922 q^{27} +21.4939 q^{28} +5.80512 q^{29} -3.62369 q^{30} +9.86426 q^{31} -17.7398 q^{32} -0.131382 q^{33} -7.90619 q^{34} -12.1305 q^{35} -14.6793 q^{36} +2.45824 q^{37} -7.59577 q^{38} -1.23883 q^{39} +25.9830 q^{40} +5.32835 q^{41} +5.00002 q^{42} +4.18853 q^{43} +1.52111 q^{44} +8.28453 q^{45} -9.18131 q^{46} +4.64358 q^{47} -5.94182 q^{48} +9.73777 q^{49} -10.2112 q^{50} -1.33208 q^{51} +14.3429 q^{52} +1.00000 q^{53} -7.08122 q^{54} -0.858466 q^{55} -35.8517 q^{56} -1.27978 q^{57} -15.6348 q^{58} +1.86143 q^{59} +7.06867 q^{60} +9.42087 q^{61} -26.5671 q^{62} -11.4311 q^{63} +21.5898 q^{64} -8.09465 q^{65} +0.353849 q^{66} +1.86364 q^{67} +15.4225 q^{68} -1.54692 q^{69} +32.6706 q^{70} -8.36678 q^{71} +24.4850 q^{72} -14.8423 q^{73} -6.62072 q^{74} -1.72044 q^{75} +14.8169 q^{76} +1.18452 q^{77} +3.33651 q^{78} +16.4452 q^{79} -38.8244 q^{80} +7.18918 q^{81} -14.3507 q^{82} +12.6514 q^{83} -9.75346 q^{84} -8.70392 q^{85} -11.2809 q^{86} -2.63423 q^{87} -2.53720 q^{88} -2.03389 q^{89} -22.3125 q^{90} +11.1691 q^{91} +17.9098 q^{92} -4.47618 q^{93} -12.5064 q^{94} -8.36219 q^{95} +8.04990 q^{96} +17.6433 q^{97} -26.2265 q^{98} -0.808974 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 179 q + 8 q^{2} + 15 q^{3} + 202 q^{4} + 27 q^{5} + 18 q^{6} + 23 q^{7} + 21 q^{8} + 214 q^{9}+O(q^{10}) \) 179 * q + 8 * q^2 + 15 * q^3 + 202 * q^4 + 27 * q^5 + 18 * q^6 + 23 * q^7 + 21 * q^8 + 214 * q^9	\( 179 q + 8 q^{2} + 15 q^{3} + 202 q^{4} + 27 q^{5} + 18 q^{6} + 23 q^{7} + 21 q^{8} + 214 q^{9} + 28 q^{10} + 21 q^{11} + 46 q^{12} + 113 q^{13} - 2 q^{14} + 30 q^{15} + 240 q^{16} + 48 q^{17} + 40 q^{18} + 35 q^{19} + 24 q^{20} + 56 q^{21} + 22 q^{22} + 16 q^{23} + 54 q^{24} + 266 q^{25} + 60 q^{27} + 64 q^{28} + 34 q^{29} - 19 q^{30} + 60 q^{31} + 15 q^{32} + 65 q^{33} + 31 q^{34} - 20 q^{35} + 282 q^{36} + 169 q^{37} + 52 q^{38} + 20 q^{39} + 74 q^{40} + 20 q^{41} + 34 q^{42} + 43 q^{43} + 56 q^{44} + 139 q^{45} + 13 q^{46} + 73 q^{47} + 88 q^{48} + 292 q^{49} + 12 q^{50} + 8 q^{51} + 225 q^{52} + 179 q^{53} - 16 q^{54} + 72 q^{55} - 17 q^{56} + 62 q^{57} + 125 q^{58} + 68 q^{59} + 116 q^{60} + 96 q^{61} + 71 q^{62} + 52 q^{63} + 309 q^{64} - 5 q^{65} + 90 q^{67} + 122 q^{68} + 111 q^{69} + 72 q^{70} + 26 q^{71} + 65 q^{72} + 139 q^{73} - 82 q^{74} + 55 q^{75} + 146 q^{76} + 76 q^{77} - 9 q^{78} + 29 q^{79} + 68 q^{80} + 231 q^{81} + 84 q^{82} + 8 q^{83} - 24 q^{84} + 115 q^{85} - 20 q^{86} + 47 q^{87} + 143 q^{88} + 150 q^{89} + 34 q^{90} + 113 q^{91} - 31 q^{92} + 195 q^{93} + 131 q^{94} + 55 q^{95} + 90 q^{96} + 235 q^{97} + 84 q^{98} + 7 q^{99}+O(q^{100}) \) 179 * q + 8 * q^2 + 15 * q^3 + 202 * q^4 + 27 * q^5 + 18 * q^6 + 23 * q^7 + 21 * q^8 + 214 * q^9 + 28 * q^10 + 21 * q^11 + 46 * q^12 + 113 * q^13 - 2 * q^14 + 30 * q^15 + 240 * q^16 + 48 * q^17 + 40 * q^18 + 35 * q^19 + 24 * q^20 + 56 * q^21 + 22 * q^22 + 16 * q^23 + 54 * q^24 + 266 * q^25 + 60 * q^27 + 64 * q^28 + 34 * q^29 - 19 * q^30 + 60 * q^31 + 15 * q^32 + 65 * q^33 + 31 * q^34 - 20 * q^35 + 282 * q^36 + 169 * q^37 + 52 * q^38 + 20 * q^39 + 74 * q^40 + 20 * q^41 + 34 * q^42 + 43 * q^43 + 56 * q^44 + 139 * q^45 + 13 * q^46 + 73 * q^47 + 88 * q^48 + 292 * q^49 + 12 * q^50 + 8 * q^51 + 225 * q^52 + 179 * q^53 - 16 * q^54 + 72 * q^55 - 17 * q^56 + 62 * q^57 + 125 * q^58 + 68 * q^59 + 116 * q^60 + 96 * q^61 + 71 * q^62 + 52 * q^63 + 309 * q^64 - 5 * q^65 + 90 * q^67 + 122 * q^68 + 111 * q^69 + 72 * q^70 + 26 * q^71 + 65 * q^72 + 139 * q^73 - 82 * q^74 + 55 * q^75 + 146 * q^76 + 76 * q^77 - 9 * q^78 + 29 * q^79 + 68 * q^80 + 231 * q^81 + 84 * q^82 + 8 * q^83 - 24 * q^84 + 115 * q^85 - 20 * q^86 + 47 * q^87 + 143 * q^88 + 150 * q^89 + 34 * q^90 + 113 * q^91 - 31 * q^92 + 195 * q^93 + 131 * q^94 + 55 * q^95 + 90 * q^96 + 235 * q^97 + 84 * q^98 + 7 * q^99

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