LMFDB - Embedded newform 8003.2.a.d.1.14

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			1.14
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)

$f(q)$	$=$	$q-2.56401 q^{2} +2.69258 q^{3} +4.57412 q^{4} -0.262266 q^{5} -6.90379 q^{6} +3.89440 q^{7} -6.60007 q^{8} +4.24998 q^{9} +O(q^{10})$	\(q-2.56401 q^{2} +2.69258 q^{3} +4.57412 q^{4} -0.262266 q^{5} -6.90379 q^{6} +3.89440 q^{7} -6.60007 q^{8} +4.24998 q^{9} +0.672451 q^{10} -3.45486 q^{11} +12.3162 q^{12} -0.166459 q^{13} -9.98527 q^{14} -0.706172 q^{15} +7.77437 q^{16} +7.26793 q^{17} -10.8970 q^{18} +5.24415 q^{19} -1.19964 q^{20} +10.4860 q^{21} +8.85828 q^{22} +1.20163 q^{23} -17.7712 q^{24} -4.93122 q^{25} +0.426803 q^{26} +3.36567 q^{27} +17.8135 q^{28} -5.93463 q^{29} +1.81063 q^{30} +5.38891 q^{31} -6.73338 q^{32} -9.30249 q^{33} -18.6350 q^{34} -1.02137 q^{35} +19.4399 q^{36} +0.466311 q^{37} -13.4460 q^{38} -0.448205 q^{39} +1.73097 q^{40} +6.20636 q^{41} -26.8861 q^{42} +7.07993 q^{43} -15.8030 q^{44} -1.11462 q^{45} -3.08099 q^{46} -2.67592 q^{47} +20.9331 q^{48} +8.16638 q^{49} +12.6437 q^{50} +19.5695 q^{51} -0.761406 q^{52} +1.00000 q^{53} -8.62960 q^{54} +0.906092 q^{55} -25.7033 q^{56} +14.1203 q^{57} +15.2164 q^{58} +3.96354 q^{59} -3.23012 q^{60} +8.75264 q^{61} -13.8172 q^{62} +16.5511 q^{63} +1.71569 q^{64} +0.0436566 q^{65} +23.8516 q^{66} -4.62963 q^{67} +33.2444 q^{68} +3.23548 q^{69} +2.61880 q^{70} -8.92464 q^{71} -28.0502 q^{72} +9.78235 q^{73} -1.19562 q^{74} -13.2777 q^{75} +23.9874 q^{76} -13.4546 q^{77} +1.14920 q^{78} +3.92846 q^{79} -2.03895 q^{80} -3.68760 q^{81} -15.9131 q^{82} -0.938479 q^{83} +47.9642 q^{84} -1.90613 q^{85} -18.1530 q^{86} -15.9795 q^{87} +22.8023 q^{88} -6.92079 q^{89} +2.85790 q^{90} -0.648260 q^{91} +5.49641 q^{92} +14.5101 q^{93} +6.86107 q^{94} -1.37536 q^{95} -18.1302 q^{96} -16.9009 q^{97} -20.9386 q^{98} -14.6831 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.56401	−1.81303	−0.906513	−	0.422178i	$-0.861266\pi$
$2$	−2.56401	−1.81303	−0.906513	+	0.422178i	$0.861266\pi$
$3$	2.69258	1.55456	0.777281	−	0.629154i	$-0.216599\pi$
$3$	2.69258	1.55456	0.777281	+	0.629154i	$0.216599\pi$
$4$	4.57412	2.28706
$5$	−0.262266	−0.117289	−0.0586444	−	0.998279i	$-0.518678\pi$
$5$	−0.262266	−0.117289	−0.0586444	+	0.998279i	$0.518678\pi$
$6$	−6.90379	−2.81846
$7$	3.89440	1.47195	0.735973	−	0.677011i	$-0.236725\pi$
$7$	3.89440	1.47195	0.735973	+	0.677011i	$0.236725\pi$
$8$	−6.60007	−2.33348
$9$	4.24998	1.41666
$10$	0.672451	0.212648
$11$	−3.45486	−1.04168	−0.520840	−	0.853654i	$-0.674381\pi$
$11$	−3.45486	−1.04168	−0.520840	+	0.853654i	$0.674381\pi$
$12$	12.3162	3.55538
$13$	−0.166459	−0.0461675	−0.0230838	−	0.999734i	$-0.507348\pi$
$13$	−0.166459	−0.0461675	−0.0230838	+	0.999734i	$0.507348\pi$
$14$	−9.98527	−2.66868
$15$	−0.706172	−0.182333
$16$	7.77437	1.94359
$17$	7.26793	1.76273	0.881366	−	0.472434i	$-0.156625\pi$
$17$	7.26793	1.76273	0.881366	+	0.472434i	$0.156625\pi$
$18$	−10.8970	−2.56844
$19$	5.24415	1.20309	0.601545	−	0.798839i	$-0.294552\pi$
$19$	5.24415	1.20309	0.601545	+	0.798839i	$0.294552\pi$
$20$	−1.19964	−0.268247
$21$	10.4860	2.28823
$22$	8.85828	1.88859
$23$	1.20163	0.250557	0.125279	−	0.992122i	$-0.460018\pi$
$23$	1.20163	0.250557	0.125279	+	0.992122i	$0.460018\pi$
$24$	−17.7712	−3.62753
$25$	−4.93122	−0.986243
$26$	0.426803	0.0837029
$27$	3.36567	0.647724
$28$	17.8135	3.36643
$29$	−5.93463	−1.10203	−0.551017	−	0.834494i	$-0.685760\pi$
$29$	−5.93463	−1.10203	−0.551017	+	0.834494i	$0.685760\pi$
$30$	1.81063	0.330574
$31$	5.38891	0.967877	0.483939	−	0.875102i	$-0.339206\pi$
$31$	5.38891	0.967877	0.483939	+	0.875102i	$0.339206\pi$
$32$	−6.73338	−1.19030
$33$	−9.30249	−1.61936
$34$	−18.6350	−3.19588
$35$	−1.02137	−0.172643
$36$	19.4399	3.23999
$37$	0.466311	0.0766610	0.0383305	−	0.999265i	$-0.487796\pi$
$37$	0.466311	0.0766610	0.0383305	+	0.999265i	$0.487796\pi$
$38$	−13.4460	−2.18123
$39$	−0.448205	−0.0717702
$40$	1.73097	0.273691
$41$	6.20636	0.969270	0.484635	−	0.874716i	$-0.338952\pi$
$41$	6.20636	0.969270	0.484635	+	0.874716i	$0.338952\pi$
$42$	−26.8861	−4.14862
$43$	7.07993	1.07968	0.539839	−	0.841768i	$-0.318485\pi$
$43$	7.07993	1.07968	0.539839	+	0.841768i	$0.318485\pi$
$44$	−15.8030	−2.38239
$45$	−1.11462	−0.166158
$46$	−3.08099	−0.454267
$47$	−2.67592	−0.390323	−0.195161	−	0.980771i	$-0.562523\pi$
$47$	−2.67592	−0.390323	−0.195161	+	0.980771i	$0.562523\pi$
$48$	20.9331	3.02143
$49$	8.16638	1.16663
$50$	12.6437	1.78808
$51$	19.5695	2.74027
$52$	−0.761406	−0.105588
$53$	1.00000	0.137361
$53$	1.00000	0.137361
$54$	−8.62960	−1.17434
$55$	0.906092	0.122177
$56$	−25.7033	−3.43475
$57$	14.1203	1.87028
$58$	15.2164	1.99801
$59$	3.96354	0.516008	0.258004	−	0.966144i	$-0.416935\pi$
$59$	3.96354	0.516008	0.258004	+	0.966144i	$0.416935\pi$
$60$	−3.23012	−0.417006
$61$	8.75264	1.12066	0.560330	−	0.828269i	$-0.310674\pi$
$61$	8.75264	1.12066	0.560330	+	0.828269i	$0.310674\pi$
$62$	−13.8172	−1.75479
$63$	16.5511	2.08525
$64$	1.71569	0.214461
$65$	0.0436566	0.00541493
$66$	23.8516	2.93593
$67$	−4.62963	−0.565599	−0.282800	−	0.959179i	$-0.591263\pi$
$67$	−4.62963	−0.565599	−0.282800	+	0.959179i	$0.591263\pi$
$68$	33.2444	4.03148
$69$	3.23548	0.389507
$70$	2.61880	0.313006
$71$	−8.92464	−1.05916	−0.529580	−	0.848260i	$-0.677650\pi$
$71$	−8.92464	−1.05916	−0.529580	+	0.848260i	$0.677650\pi$
$72$	−28.0502	−3.30574
$73$	9.78235	1.14494	0.572469	−	0.819927i	$-0.305986\pi$
$73$	9.78235	1.14494	0.572469	+	0.819927i	$0.305986\pi$
$74$	−1.19562	−0.138988
$75$	−13.2777	−1.53318
$76$	23.9874	2.75154
$77$	−13.4546	−1.53330
$78$	1.14920	0.130121
$79$	3.92846	0.441986	0.220993	−	0.975275i	$-0.429070\pi$
$79$	3.92846	0.441986	0.220993	+	0.975275i	$0.429070\pi$
$80$	−2.03895	−0.227962
$81$	−3.68760	−0.409734
$82$	−15.9131	−1.75731
$83$	−0.938479	−0.103011	−0.0515057	−	0.998673i	$-0.516402\pi$
$83$	−0.938479	−0.103011	−0.0515057	+	0.998673i	$0.516402\pi$
$84$	47.9642	5.23332
$85$	−1.90613	−0.206749
$86$	−18.1530	−1.95749
$87$	−15.9795	−1.71318
$88$	22.8023	2.43074
$89$	−6.92079	−0.733602	−0.366801	−	0.930299i	$-0.619547\pi$
$89$	−6.92079	−0.733602	−0.366801	+	0.930299i	$0.619547\pi$
$90$	2.85790	0.301250
$91$	−0.648260	−0.0679561
$92$	5.49641	0.573040
$93$	14.5101	1.50462
$94$	6.86107	0.707665
$95$	−1.37536	−0.141109
$96$	−18.1302	−1.85040
$97$	−16.9009	−1.71602	−0.858012	−	0.513629i	$-0.828301\pi$
$97$	−16.9009	−1.71602	−0.858012	+	0.513629i	$0.828301\pi$
$98$	−20.9386	−2.11512
$99$	−14.6831	−1.47571
$100$	−22.5560	−2.25560
$101$	0.135969	0.0135294	0.00676470	−	0.999977i	$-0.497847\pi$
$101$	0.135969	0.0135294	0.00676470	+	0.999977i	$0.497847\pi$
$102$	−50.1762	−4.96819
$103$	5.88856	0.580217	0.290108	−	0.956994i	$-0.406309\pi$
$103$	5.88856	0.580217	0.290108	+	0.956994i	$0.406309\pi$
$104$	1.09864	0.107731
$105$	−2.75012	−0.268384
$106$	−2.56401	−0.249038
$107$	12.3962	1.19839	0.599193	−	0.800604i	$-0.295488\pi$
$107$	12.3962	1.19839	0.599193	+	0.800604i	$0.295488\pi$
$108$	15.3950	1.48139
$109$	11.1232	1.06541	0.532706	−	0.846301i	$-0.321175\pi$
$109$	11.1232	1.06541	0.532706	+	0.846301i	$0.321175\pi$
$110$	−2.32323	−0.221511
$111$	1.25558	0.119174
$112$	30.2765	2.86086
$113$	−16.6346	−1.56485	−0.782426	−	0.622744i	$-0.786018\pi$
$113$	−16.6346	−1.56485	−0.782426	+	0.622744i	$0.786018\pi$
$114$	−36.2045	−3.39086
$115$	−0.315147	−0.0293876
$116$	−27.1457	−2.52042
$117$	−0.707449	−0.0654037
$118$	−10.1625	−0.935537
$119$	28.3042	2.59465
$120$	4.66078	0.425469
$121$	0.936069	0.0850971
$122$	−22.4418	−2.03179
$123$	16.7111	1.50679
$124$	24.6496	2.21360
$125$	2.60462	0.232964
$126$	−42.4372	−3.78061
$127$	−7.02740	−0.623581	−0.311790	−	0.950151i	$-0.600929\pi$
$127$	−7.02740	−0.623581	−0.311790	+	0.950151i	$0.600929\pi$
$128$	9.06772	0.801481
$129$	19.0633	1.67843
$130$	−0.111936	−0.00981741
$131$	12.1077	1.05786	0.528928	−	0.848666i	$-0.322594\pi$
$131$	12.1077	1.05786	0.528928	+	0.848666i	$0.322594\pi$
$132$	−42.5507	−3.70357
$133$	20.4228	1.77088
$134$	11.8704	1.02545
$135$	−0.882701	−0.0759708
$136$	−47.9688	−4.11329
$137$	7.41889	0.633839	0.316919	−	0.948452i	$-0.397352\pi$
$137$	7.41889	0.633839	0.316919	+	0.948452i	$0.397352\pi$
$138$	−8.29580	−0.706185
$139$	−10.6239	−0.901103	−0.450552	−	0.892750i	$-0.648773\pi$
$139$	−10.6239	−0.901103	−0.450552	+	0.892750i	$0.648773\pi$
$140$	−4.67187	−0.394845
$141$	−7.20512	−0.606780
$142$	22.8828	1.92028
$143$	0.575094	0.0480918
$144$	33.0409	2.75341
$145$	1.55645	0.129256
$146$	−25.0820	−2.07580
$147$	21.9886	1.81359
$148$	2.13296	0.175329
$149$	−20.4347	−1.67408	−0.837039	−	0.547144i	$-0.815715\pi$
$149$	−20.4347	−1.67408	−0.837039	+	0.547144i	$0.815715\pi$
$150$	34.0441	2.77969
$151$	−1.00000	−0.0813788
$151$	−1.00000	−0.0813788
$152$	−34.6117	−2.80738
$153$	30.8886	2.49719
$154$	34.4977	2.77991
$155$	−1.41333	−0.113521
$156$	−2.05014	−0.164143
$157$	7.32587	0.584668	0.292334	−	0.956316i	$-0.405568\pi$
$157$	7.32587	0.584668	0.292334	+	0.956316i	$0.405568\pi$
$158$	−10.0726	−0.801333
$159$	2.69258	0.213535
$160$	1.76594	0.139609
$161$	4.67963	0.368807
$162$	9.45504	0.742858
$163$	14.2762	1.11820	0.559099	−	0.829101i	$-0.311147\pi$
$163$	14.2762	1.11820	0.559099	+	0.829101i	$0.311147\pi$
$164$	28.3886	2.21678
$165$	2.43972	0.189932
$166$	2.40626	0.186762
$167$	−0.900515	−0.0696839	−0.0348420	−	0.999393i	$-0.511093\pi$
$167$	−0.900515	−0.0696839	−0.0348420	+	0.999393i	$0.511093\pi$
$168$	−69.2082	−5.33953
$169$	−12.9723	−0.997869
$170$	4.88733	0.374841
$171$	22.2875	1.70437
$172$	32.3845	2.46929
$173$	−15.2466	−1.15917	−0.579587	−	0.814910i	$-0.696786\pi$
$173$	−15.2466	−1.15917	−0.579587	+	0.814910i	$0.696786\pi$
$174$	40.9714	3.10604
$175$	−19.2041	−1.45170
$176$	−26.8594	−2.02460
$177$	10.6721	0.802167
$178$	17.7449	1.33004
$179$	12.6673	0.946795	0.473398	−	0.880849i	$-0.343027\pi$
$179$	12.6673	0.946795	0.473398	+	0.880849i	$0.343027\pi$
$180$	−5.09843	−0.380015
$181$	8.15223	0.605951	0.302975	−	0.952998i	$-0.402020\pi$
$181$	8.15223	0.605951	0.302975	+	0.952998i	$0.402020\pi$
$182$	1.66214	0.123206
$183$	23.5672	1.74213
$184$	−7.93084	−0.584670
$185$	−0.122297	−0.00899148
$186$	−37.2039	−2.72792
$187$	−25.1097	−1.83620
$188$	−12.2400	−0.892692
$189$	13.1073	0.953415
$190$	3.52643	0.255834
$191$	−12.5527	−0.908282	−0.454141	−	0.890930i	$-0.650054\pi$
$191$	−12.5527	−0.908282	−0.454141	+	0.890930i	$0.650054\pi$
$192$	4.61962	0.333393
$193$	2.81662	0.202745	0.101372	−	0.994849i	$-0.467677\pi$
$193$	2.81662	0.202745	0.101372	+	0.994849i	$0.467677\pi$
$194$	43.3340	3.11120
$195$	0.117549	0.00841785
$196$	37.3540	2.66814
$197$	12.7196	0.906231	0.453115	−	0.891452i	$-0.350313\pi$
$197$	12.7196	0.906231	0.453115	+	0.891452i	$0.350313\pi$
$198$	37.6475	2.67549
$199$	14.5711	1.03291	0.516457	−	0.856313i	$-0.327250\pi$
$199$	14.5711	1.03291	0.516457	+	0.856313i	$0.327250\pi$
$200$	32.5464	2.30138
$201$	−12.4656	−0.879259
$202$	−0.348625	−0.0245291
$203$	−23.1118	−1.62213
$204$	89.5132	6.26718
$205$	−1.62772	−0.113685
$206$	−15.0983	−1.05195
$207$	5.10691	0.354955
$208$	−1.29412	−0.0897308
$209$	−18.1178	−1.25323
$210$	7.05131	0.486587
$211$	−22.9249	−1.57822	−0.789109	−	0.614254i	$-0.789457\pi$
$211$	−22.9249	−1.57822	−0.789109	+	0.614254i	$0.789457\pi$
$212$	4.57412	0.314152
$213$	−24.0303	−1.64653
$214$	−31.7839	−2.17271
$215$	−1.85682	−0.126634
$216$	−22.2137	−1.51145
$217$	20.9866	1.42466
$218$	−28.5200	−1.93162
$219$	26.3397	1.77988
$220$	4.14458	0.279427
$221$	−1.20981	−0.0813809
$222$	−3.21931	−0.216066
$223$	14.7938	0.990663	0.495332	−	0.868704i	$-0.335047\pi$
$223$	14.7938	0.990663	0.495332	+	0.868704i	$0.335047\pi$
$224$	−26.2225	−1.75206
$225$	−20.9576	−1.39717
$226$	42.6512	2.83712
$227$	6.12605	0.406600	0.203300	−	0.979116i	$-0.434833\pi$
$227$	6.12605	0.406600	0.203300	+	0.979116i	$0.434833\pi$
$228$	64.5879	4.27744
$229$	7.62416	0.503819	0.251909	−	0.967751i	$-0.418942\pi$
$229$	7.62416	0.503819	0.251909	+	0.967751i	$0.418942\pi$
$230$	0.808038	0.0532804
$231$	−36.2276	−2.38360
$232$	39.1690	2.57157
$233$	−10.7039	−0.701238	−0.350619	−	0.936518i	$-0.614029\pi$
$233$	−10.7039	−0.701238	−0.350619	+	0.936518i	$0.614029\pi$
$234$	1.81390	0.118579
$235$	0.701802	0.0457805
$236$	18.1297	1.18014
$237$	10.5777	0.687095
$238$	−72.5723	−4.70416
$239$	3.98187	0.257566	0.128783	−	0.991673i	$-0.458893\pi$
$239$	3.98187	0.257566	0.128783	+	0.991673i	$0.458893\pi$
$240$	−5.49004	−0.354380
$241$	13.1778	0.848855	0.424428	−	0.905462i	$-0.360475\pi$
$241$	13.1778	0.848855	0.424428	+	0.905462i	$0.360475\pi$
$242$	−2.40009	−0.154283
$243$	−20.0262	−1.28468
$244$	40.0357	2.56302
$245$	−2.14176	−0.136832
$246$	−42.8474	−2.73185
$247$	−0.872937	−0.0555437
$248$	−35.5672	−2.25852
$249$	−2.52693	−0.160138
$250$	−6.67826	−0.422370
$251$	−5.79688	−0.365896	−0.182948	−	0.983123i	$-0.558564\pi$
$251$	−5.79688	−0.365896	−0.182948	+	0.983123i	$0.558564\pi$
$252$	75.7070	4.76909
$253$	−4.15147	−0.261000
$254$	18.0183	1.13057
$255$	−5.13241	−0.321404
$256$	−26.6811	−1.66757
$257$	4.11855	0.256908	0.128454	−	0.991715i	$-0.458999\pi$
$257$	4.11855	0.256908	0.128454	+	0.991715i	$0.458999\pi$
$258$	−48.8783	−3.04303
$259$	1.81600	0.112841
$260$	0.199691	0.0123843
$261$	−25.2221	−1.56121
$262$	−31.0443	−1.91792
$263$	−10.2111	−0.629640	−0.314820	−	0.949151i	$-0.601944\pi$
$263$	−10.2111	−0.629640	−0.314820	+	0.949151i	$0.601944\pi$
$264$	61.3971	3.77873
$265$	−0.262266	−0.0161109
$266$	−52.3642	−3.21066
$267$	−18.6348	−1.14043
$268$	−21.1765	−1.29356
$269$	30.0784	1.83391	0.916956	−	0.398989i	$-0.130639\pi$
$269$	30.0784	1.83391	0.916956	+	0.398989i	$0.130639\pi$
$270$	2.26325	0.137737
$271$	19.0067	1.15457	0.577287	−	0.816541i	$-0.304111\pi$
$271$	19.0067	1.15457	0.577287	+	0.816541i	$0.304111\pi$
$272$	56.5035	3.42603
$273$	−1.74549	−0.105642
$274$	−19.0221	−1.14917
$275$	17.0367	1.02735
$276$	14.7995	0.890826
$277$	7.46570	0.448570	0.224285	−	0.974524i	$-0.427995\pi$
$277$	7.46570	0.448570	0.224285	+	0.974524i	$0.427995\pi$
$278$	27.2396	1.63372
$279$	22.9028	1.37115
$280$	6.74111	0.402858
$281$	6.75243	0.402816	0.201408	−	0.979507i	$-0.435448\pi$
$281$	6.75243	0.402816	0.201408	+	0.979507i	$0.435448\pi$
$282$	18.4740	1.10011
$283$	20.9320	1.24428	0.622141	−	0.782906i	$-0.286263\pi$
$283$	20.9320	1.24428	0.622141	+	0.782906i	$0.286263\pi$
$284$	−40.8224	−2.42236
$285$	−3.70327	−0.219363
$286$	−1.47454	−0.0871916
$287$	24.1701	1.42671
$288$	−28.6167	−1.68626
$289$	35.8228	2.10722
$290$	−3.99075	−0.234345
$291$	−45.5070	−2.66767
$292$	44.7457	2.61854
$293$	−19.0165	−1.11096	−0.555479	−	0.831531i	$-0.687465\pi$
$293$	−19.0165	−1.11096	−0.555479	+	0.831531i	$0.687465\pi$
$294$	−56.3789	−3.28809
$295$	−1.03950	−0.0605220
$296$	−3.07768	−0.178887
$297$	−11.6279	−0.674721
$298$	52.3947	3.03515
$299$	−0.200023	−0.0115676
$300$	−60.7338	−3.50647
$301$	27.5721	1.58923
$302$	2.56401	0.147542
$303$	0.366107	0.0210323
$304$	40.7699	2.33832
$305$	−2.29552	−0.131441
$306$	−79.1985	−4.52747
$307$	−16.8246	−0.960229	−0.480114	−	0.877206i	$-0.659405\pi$
$307$	−16.8246	−0.960229	−0.480114	+	0.877206i	$0.659405\pi$
$308$	−61.5431	−3.50675
$309$	15.8554	0.901982
$310$	3.62378	0.205817
$311$	21.8305	1.23789	0.618946	−	0.785433i	$-0.287560\pi$
$311$	21.8305	1.23789	0.618946	+	0.785433i	$0.287560\pi$
$312$	2.95818	0.167474
$313$	−10.8267	−0.611964	−0.305982	−	0.952037i	$-0.598985\pi$
$313$	−10.8267	−0.611964	−0.305982	+	0.952037i	$0.598985\pi$
$314$	−18.7836	−1.06002
$315$	−4.34080	−0.244576
$316$	17.9693	1.01085
$317$	29.0212	1.62999	0.814997	−	0.579465i	$-0.196738\pi$
$317$	29.0212	1.62999	0.814997	+	0.579465i	$0.196738\pi$
$318$	−6.90379	−0.387145
$319$	20.5033	1.14797
$320$	−0.449966	−0.0251539
$321$	33.3778	1.86296
$322$	−11.9986	−0.668656
$323$	38.1141	2.12072
$324$	−16.8676	−0.937087
$325$	0.820847	0.0455324
$326$	−36.6042	−2.02732
$327$	29.9501	1.65625
$328$	−40.9624	−2.26177
$329$	−10.4211	−0.574534
$330$	−6.25547	−0.344352
$331$	24.1845	1.32930	0.664650	−	0.747155i	$-0.268581\pi$
$331$	24.1845	1.32930	0.664650	+	0.747155i	$0.268581\pi$
$332$	−4.29272	−0.235594
$333$	1.98181	0.108603
$334$	2.30892	0.126339
$335$	1.21419	0.0663385
$336$	81.5219	4.44738
$337$	−22.6476	−1.23369	−0.616847	−	0.787083i	$-0.711590\pi$
$337$	−22.6476	−1.23369	−0.616847	+	0.787083i	$0.711590\pi$
$338$	33.2610	1.80916
$339$	−44.7900	−2.43266
$340$	−8.71888	−0.472847
$341$	−18.6179	−1.00822
$342$	−57.1453	−3.09007
$343$	4.54234	0.245263
$344$	−46.7280	−2.51941
$345$	−0.848557	−0.0456848
$346$	39.0923	2.10161
$347$	−31.4486	−1.68825	−0.844126	−	0.536145i	$-0.819880\pi$
$347$	−31.4486	−1.68825	−0.844126	+	0.536145i	$0.819880\pi$
$348$	−73.0920	−3.91814
$349$	5.91136	0.316428	0.158214	−	0.987405i	$-0.449426\pi$
$349$	5.91136	0.316428	0.158214	+	0.987405i	$0.449426\pi$
$350$	49.2395	2.63196
$351$	−0.560247	−0.0299038
$352$	23.2629	1.23992
$353$	−16.0938	−0.856584	−0.428292	−	0.903640i	$-0.640885\pi$
$353$	−16.0938	−0.856584	−0.428292	+	0.903640i	$0.640885\pi$
$354$	−27.3634	−1.45435
$355$	2.34063	0.124228
$356$	−31.6565	−1.67779
$357$	76.2114	4.03354
$358$	−32.4789	−1.71656
$359$	15.8079	0.834308	0.417154	−	0.908836i	$-0.363028\pi$
$359$	15.8079	0.834308	0.417154	+	0.908836i	$0.363028\pi$
$360$	7.35660	0.387727
$361$	8.50108	0.447425
$362$	−20.9024	−1.09860
$363$	2.52044	0.132289
$364$	−2.96522	−0.155420
$365$	−2.56558	−0.134288
$366$	−60.4263	−3.15854
$367$	−11.1693	−0.583032	−0.291516	−	0.956566i	$-0.594160\pi$
$367$	−11.1693	−0.583032	−0.291516	+	0.956566i	$0.594160\pi$
$368$	9.34191	0.486981
$369$	26.3769	1.37313
$370$	0.313571	0.0163018
$371$	3.89440	0.202187
$372$	66.3709	3.44117
$373$	−25.1595	−1.30271	−0.651355	−	0.758773i	$-0.725799\pi$
$373$	−25.1595	−1.30271	−0.651355	+	0.758773i	$0.725799\pi$
$374$	64.3814	3.32908
$375$	7.01314	0.362157
$376$	17.6612	0.910809
$377$	0.987874	0.0508781
$378$	−33.6072	−1.72857
$379$	10.1377	0.520736	0.260368	−	0.965509i	$-0.416156\pi$
$379$	10.1377	0.520736	0.260368	+	0.965509i	$0.416156\pi$
$380$	−6.29107	−0.322725
$381$	−18.9218	−0.969395
$382$	32.1852	1.64674
$383$	15.4285	0.788359	0.394180	−	0.919033i	$-0.371029\pi$
$383$	15.4285	0.788359	0.394180	+	0.919033i	$0.371029\pi$
$384$	24.4156	1.24595
$385$	3.52869	0.179839
$386$	−7.22183	−0.367581
$387$	30.0896	1.52954
$388$	−77.3067	−3.92466
$389$	−35.2661	−1.78806	−0.894031	−	0.448006i	$-0.852134\pi$
$389$	−35.2661	−1.78806	−0.894031	+	0.448006i	$0.852134\pi$
$390$	−0.301396	−0.0152618
$391$	8.73336	0.441665
$392$	−53.8987	−2.72229
$393$	32.6010	1.64450
$394$	−32.6130	−1.64302
$395$	−1.03030	−0.0518401
$396$	−67.1623	−3.37503
$397$	11.9242	0.598460	0.299230	−	0.954181i	$-0.403270\pi$
$397$	11.9242	0.598460	0.299230	+	0.954181i	$0.403270\pi$
$398$	−37.3603	−1.87270
$399$	54.9901	2.75295
$400$	−38.3371	−1.91685
$401$	38.8623	1.94069	0.970344	−	0.241726i	$-0.0777136\pi$
$401$	38.8623	1.94069	0.970344	+	0.241726i	$0.0777136\pi$
$402$	31.9620	1.59412
$403$	−0.897035	−0.0446845
$404$	0.621938	0.0309426
$405$	0.967133	0.0480572
$406$	59.2589	2.94097
$407$	−1.61104	−0.0798563
$408$	−129.160	−6.39437
$409$	−11.5024	−0.568756	−0.284378	−	0.958712i	$-0.591787\pi$
$409$	−11.5024	−0.568756	−0.284378	+	0.958712i	$0.591787\pi$
$410$	4.17347	0.206113
$411$	19.9760	0.985341
$412$	26.9350	1.32699
$413$	15.4356	0.759537
$414$	−13.0941	−0.643542
$415$	0.246131	0.0120821
$416$	1.12083	0.0549534
$417$	−28.6056	−1.40082
$418$	46.4541	2.27215
$419$	7.47882	0.365364	0.182682	−	0.983172i	$-0.441522\pi$
$419$	7.47882	0.365364	0.182682	+	0.983172i	$0.441522\pi$
$420$	−12.5794	−0.613811
$421$	21.4258	1.04423	0.522115	−	0.852875i	$-0.325143\pi$
$421$	21.4258	1.04423	0.522115	+	0.852875i	$0.325143\pi$
$422$	58.7796	2.86135
$423$	−11.3726	−0.552955
$424$	−6.60007	−0.320528
$425$	−35.8397	−1.73848
$426$	61.6138	2.98520
$427$	34.0863	1.64955
$428$	56.7018	2.74078
$429$	1.54849	0.0747616
$430$	4.76091	0.229591
$431$	−4.41599	−0.212711	−0.106355	−	0.994328i	$-0.533918\pi$
$431$	−4.41599	−0.212711	−0.106355	+	0.994328i	$0.533918\pi$
$432$	26.1660	1.25891
$433$	24.9243	1.19778	0.598892	−	0.800830i	$-0.295608\pi$
$433$	24.9243	1.19778	0.598892	+	0.800830i	$0.295608\pi$
$434$	−53.8098	−2.58295
$435$	4.19087	0.200937
$436$	50.8790	2.43666
$437$	6.30153	0.301443
$438$	−67.5353	−3.22696
$439$	13.4580	0.642314	0.321157	−	0.947026i	$-0.395928\pi$
$439$	13.4580	0.642314	0.321157	+	0.947026i	$0.395928\pi$
$440$	−5.98027	−0.285098
$441$	34.7069	1.65271
$442$	3.10197	0.147546
$443$	−5.12990	−0.243729	−0.121864	−	0.992547i	$-0.538887\pi$
$443$	−5.12990	−0.243729	−0.121864	+	0.992547i	$0.538887\pi$
$444$	5.74317	0.272559
$445$	1.81509	0.0860433
$446$	−37.9313	−1.79610
$447$	−55.0221	−2.60246
$448$	6.68158	0.315675
$449$	13.5664	0.640236	0.320118	−	0.947378i	$-0.396277\pi$
$449$	13.5664	0.640236	0.320118	+	0.947378i	$0.396277\pi$
$450$	53.7353	2.53311
$451$	−21.4421	−1.00967
$452$	−76.0887	−3.57891
$453$	−2.69258	−0.126508
$454$	−15.7072	−0.737177
$455$	0.170016	0.00797049
$456$	−93.1948	−4.36425
$457$	−38.8741	−1.81846	−0.909228	−	0.416299i	$-0.863327\pi$
$457$	−38.8741	−1.81846	−0.909228	+	0.416299i	$0.863327\pi$
$458$	−19.5484	−0.913436
$459$	24.4615	1.14176
$460$	−1.44152	−0.0672112
$461$	−7.16442	−0.333680	−0.166840	−	0.985984i	$-0.553356\pi$
$461$	−7.16442	−0.333680	−0.166840	+	0.985984i	$0.553356\pi$
$462$	92.8879	4.32153
$463$	−24.3407	−1.13121	−0.565603	−	0.824677i	$-0.691357\pi$
$463$	−24.3407	−1.13121	−0.565603	+	0.824677i	$0.691357\pi$
$464$	−46.1380	−2.14190
$465$	−3.80550	−0.176476
$466$	27.4449	1.27136
$467$	−17.2346	−0.797520	−0.398760	−	0.917055i	$-0.630559\pi$
$467$	−17.2346	−0.797520	−0.398760	+	0.917055i	$0.630559\pi$
$468$	−3.23596	−0.149582
$469$	−18.0296	−0.832532
$470$	−1.79942	−0.0830012
$471$	19.7255	0.908903
$472$	−26.1596	−1.20409
$473$	−24.4602	−1.12468
$474$	−27.1213	−1.24572
$475$	−25.8600	−1.18654
$476$	129.467	5.93412
$477$	4.24998	0.194593
$478$	−10.2095	−0.466973
$479$	17.2221	0.786898	0.393449	−	0.919347i	$-0.371282\pi$
$479$	17.2221	0.786898	0.393449	+	0.919347i	$0.371282\pi$
$480$	4.75492	0.217031
$481$	−0.0776218	−0.00353925
$482$	−33.7879	−1.53900
$483$	12.6003	0.573333
$484$	4.28169	0.194622
$485$	4.43252	0.201271
$486$	51.3472	2.32916
$487$	0.103506	0.00469031	0.00234516	−	0.999997i	$-0.499254\pi$
$487$	0.103506	0.00469031	0.00234516	+	0.999997i	$0.499254\pi$
$488$	−57.7680	−2.61504
$489$	38.4398	1.73831
$490$	5.49149	0.248080
$491$	−7.12179	−0.321402	−0.160701	−	0.987003i	$-0.551376\pi$
$491$	−7.12179	−0.321402	−0.160701	+	0.987003i	$0.551376\pi$
$492$	76.4387	3.44612
$493$	−43.1325	−1.94259
$494$	2.23822	0.100702
$495$	3.85088	0.173084
$496$	41.8954	1.88116
$497$	−34.7561	−1.55903
$498$	6.47906	0.290334
$499$	−22.5359	−1.00885	−0.504423	−	0.863457i	$-0.668295\pi$
$499$	−22.5359	−1.00885	−0.504423	+	0.863457i	$0.668295\pi$
$500$	11.9139	0.532804
$501$	−2.42471	−0.108328
$502$	14.8632	0.663378
$503$	−41.7602	−1.86199	−0.930997	−	0.365027i	$-0.881060\pi$
$503$	−41.7602	−1.86199	−0.930997	+	0.365027i	$0.881060\pi$
$504$	−109.239	−4.86588
$505$	−0.0356600	−0.00158685
$506$	10.6444	0.473201
$507$	−34.9289	−1.55125
$508$	−32.1442	−1.42617
$509$	−21.5862	−0.956791	−0.478396	−	0.878144i	$-0.658782\pi$
$509$	−21.5862	−0.956791	−0.478396	+	0.878144i	$0.658782\pi$
$510$	13.1595	0.582713
$511$	38.0964	1.68529
$512$	50.2750	2.22186
$513$	17.6501	0.779270
$514$	−10.5600	−0.465781
$515$	−1.54437	−0.0680530
$516$	87.1977	3.83867
$517$	9.24492	0.406591
$518$	−4.65624	−0.204583
$519$	−41.0526	−1.80201
$520$	−0.288137	−0.0126356
$521$	22.2701	0.975671	0.487835	−	0.872936i	$-0.337787\pi$
$521$	22.2701	0.975671	0.487835	+	0.872936i	$0.337787\pi$
$522$	64.6695	2.83051
$523$	25.0028	1.09329	0.546647	−	0.837363i	$-0.315904\pi$
$523$	25.0028	1.09329	0.546647	+	0.837363i	$0.315904\pi$
$524$	55.3822	2.41938
$525$	−51.7087	−2.25675
$526$	26.1812	1.14155
$527$	39.1662	1.70611
$528$	−72.3209	−3.14736
$529$	−21.5561	−0.937221
$530$	0.672451	0.0292094
$531$	16.8450	0.731009
$532$	93.4165	4.05012
$533$	−1.03311	−0.0447488
$534$	47.7796	2.06763
$535$	−3.25110	−0.140557
$536$	30.5559	1.31981
$537$	34.1076	1.47185
$538$	−77.1212	−3.32493
$539$	−28.2137	−1.21525
$540$	−4.03758	−0.173750
$541$	11.1082	0.477579	0.238789	−	0.971071i	$-0.423249\pi$
$541$	11.1082	0.477579	0.238789	+	0.971071i	$0.423249\pi$
$542$	−48.7332	−2.09327
$543$	21.9505	0.941987
$544$	−48.9377	−2.09819
$545$	−2.91724	−0.124961
$546$	4.47545	0.191531
$547$	−2.39531	−0.102416	−0.0512080	−	0.998688i	$-0.516307\pi$
$547$	−2.39531	−0.102416	−0.0512080	+	0.998688i	$0.516307\pi$
$548$	33.9349	1.44963
$549$	37.1985	1.58760
$550$	−43.6821	−1.86261
$551$	−31.1221	−1.32584
$552$	−21.3544	−0.908905
$553$	15.2990	0.650580
$554$	−19.1421	−0.813270
$555$	−0.329295	−0.0139778
$556$	−48.5948	−2.06088
$557$	0.694547	0.0294289	0.0147144	−	0.999892i	$-0.495316\pi$
$557$	0.694547	0.0294289	0.0147144	+	0.999892i	$0.495316\pi$
$558$	−58.7229	−2.48594
$559$	−1.17852	−0.0498461
$560$	−7.94050	−0.335547
$561$	−67.6098	−2.85449
$562$	−17.3133	−0.730316
$563$	−18.9558	−0.798892	−0.399446	−	0.916757i	$-0.630798\pi$
$563$	−18.9558	−0.798892	−0.399446	+	0.916757i	$0.630798\pi$
$564$	−32.9571	−1.38774
$565$	4.36269	0.183540
$566$	−53.6699	−2.25591
$567$	−14.3610	−0.603106
$568$	58.9032	2.47152
$569$	3.21375	0.134727	0.0673636	−	0.997728i	$-0.478541\pi$
$569$	3.21375	0.134727	0.0673636	+	0.997728i	$0.478541\pi$
$570$	9.49520	0.397710
$571$	−38.7018	−1.61962	−0.809809	−	0.586693i	$-0.800429\pi$
$571$	−38.7018	−1.61962	−0.809809	+	0.586693i	$0.800429\pi$
$572$	2.63055	0.109989
$573$	−33.7992	−1.41198
$574$	−61.9722	−2.58667
$575$	−5.92550	−0.247110
$576$	7.29164	0.303818
$577$	7.62554	0.317455	0.158728	−	0.987322i	$-0.449261\pi$
$577$	7.62554	0.317455	0.158728	+	0.987322i	$0.449261\pi$
$578$	−91.8499	−3.82045
$579$	7.58397	0.315179
$580$	7.11940	0.295617
$581$	−3.65481	−0.151627
$582$	116.680	4.83655
$583$	−3.45486	−0.143086
$584$	−64.5642	−2.67169
$585$	0.185540	0.00767112
$586$	48.7585	2.01420
$587$	−13.8405	−0.571258	−0.285629	−	0.958340i	$-0.592203\pi$
$587$	−13.8405	−0.571258	−0.285629	+	0.958340i	$0.592203\pi$
$588$	100.579	4.14779
$589$	28.2603	1.16444
$590$	2.66528	0.109728
$591$	34.2484	1.40879
$592$	3.62527	0.148998
$593$	−40.1117	−1.64719	−0.823596	−	0.567177i	$-0.808035\pi$
$593$	−40.1117	−1.64719	−0.823596	+	0.567177i	$0.808035\pi$
$594$	29.8141	1.22329
$595$	−7.42324	−0.304323
$596$	−93.4710	−3.82872
$597$	39.2337	1.60573
$598$	0.512859	0.0209724
$599$	2.89382	0.118238	0.0591192	−	0.998251i	$-0.481171\pi$
$599$	2.89382	0.118238	0.0591192	+	0.998251i	$0.481171\pi$
$600$	87.6337	3.57763
$601$	−45.2517	−1.84585	−0.922927	−	0.384974i	$-0.874210\pi$
$601$	−45.2517	−1.84585	−0.922927	+	0.384974i	$0.874210\pi$
$602$	−70.6950	−2.88131
$603$	−19.6758	−0.801262
$604$	−4.57412	−0.186118
$605$	−0.245499	−0.00998095
$606$	−0.938699	−0.0381320
$607$	2.34712	0.0952666	0.0476333	−	0.998865i	$-0.484832\pi$
$607$	2.34712	0.0952666	0.0476333	+	0.998865i	$0.484832\pi$
$608$	−35.3108	−1.43204
$609$	−62.2305	−2.52171
$610$	5.88572	0.238306
$611$	0.445431	0.0180202
$612$	141.288	5.71123
$613$	22.2345	0.898042	0.449021	−	0.893521i	$-0.351773\pi$
$613$	22.2345	0.898042	0.449021	+	0.893521i	$0.351773\pi$
$614$	43.1383	1.74092
$615$	−4.38275	−0.176730
$616$	88.8015	3.57791
$617$	−23.5837	−0.949442	−0.474721	−	0.880136i	$-0.657451\pi$
$617$	−23.5837	−0.949442	−0.474721	+	0.880136i	$0.657451\pi$
$618$	−40.6533	−1.63532
$619$	25.7439	1.03474	0.517368	−	0.855763i	$-0.326912\pi$
$619$	25.7439	1.03474	0.517368	+	0.855763i	$0.326912\pi$
$620$	−6.46474	−0.259630
$621$	4.04429	0.162292
$622$	−55.9735	−2.24433
$623$	−26.9523	−1.07982
$624$	−3.48451	−0.139492
$625$	23.9730	0.958919
$626$	27.7598	1.10951
$627$	−48.7836	−1.94823
$628$	33.5095	1.33717
$629$	3.38911	0.135133
$630$	11.1298	0.443423
$631$	−37.8587	−1.50713	−0.753566	−	0.657372i	$-0.771668\pi$
$631$	−37.8587	−1.50713	−0.753566	+	0.657372i	$0.771668\pi$
$632$	−25.9281	−1.03136
$633$	−61.7272	−2.45344
$634$	−74.4106	−2.95522
$635$	1.84305	0.0731391
$636$	12.3162	0.488369
$637$	−1.35937	−0.0538602
$638$	−52.5706	−2.08129
$639$	−37.9295	−1.50047
$640$	−2.37815	−0.0940048
$641$	12.8825	0.508827	0.254414	−	0.967095i	$-0.418118\pi$
$641$	12.8825	0.508827	0.254414	+	0.967095i	$0.418118\pi$
$642$	−85.5808	−3.37760
$643$	28.4810	1.12318	0.561591	−	0.827415i	$-0.310189\pi$
$643$	28.4810	1.12318	0.561591	+	0.827415i	$0.310189\pi$
$644$	21.4052	0.843484
$645$	−4.99964	−0.196861
$646$	−97.7247	−3.84493
$647$	−20.8361	−0.819150	−0.409575	−	0.912276i	$-0.634323\pi$
$647$	−20.8361	−0.819150	−0.409575	+	0.912276i	$0.634323\pi$
$648$	24.3384	0.956104
$649$	−13.6935	−0.537516
$650$	−2.10466	−0.0825514
$651$	56.5081	2.21473
$652$	65.3011	2.55739
$653$	−15.4973	−0.606457	−0.303228	−	0.952918i	$-0.598065\pi$
$653$	−15.4973	−0.606457	−0.303228	+	0.952918i	$0.598065\pi$
$654$	−76.7923	−3.00282
$655$	−3.17544	−0.124075
$656$	48.2505	1.88386
$657$	41.5748	1.62199
$658$	26.7198	1.04164
$659$	14.1615	0.551652	0.275826	−	0.961208i	$-0.411049\pi$
$659$	14.1615	0.551652	0.275826	+	0.961208i	$0.411049\pi$
$660$	11.1596	0.434387
$661$	−39.5135	−1.53690	−0.768448	−	0.639912i	$-0.778971\pi$
$661$	−39.5135	−1.53690	−0.768448	+	0.639912i	$0.778971\pi$
$662$	−62.0091	−2.41005
$663$	−3.25752	−0.126512
$664$	6.19403	0.240375
$665$	−5.35621	−0.207705
$666$	−5.08138	−0.196899
$667$	−7.13123	−0.276122
$668$	−4.11907	−0.159371
$669$	39.8334	1.54005
$670$	−3.11320	−0.120273
$671$	−30.2391	−1.16737
$672$	−70.6061	−2.72369
$673$	26.0436	1.00391	0.501954	−	0.864895i	$-0.332615\pi$
$673$	26.0436	1.00391	0.501954	+	0.864895i	$0.332615\pi$
$674$	58.0686	2.23672
$675$	−16.5969	−0.638813
$676$	−59.3369	−2.28219
$677$	47.3212	1.81870	0.909351	−	0.416030i	$-0.136579\pi$
$677$	47.3212	1.81870	0.909351	+	0.416030i	$0.136579\pi$
$678$	114.842	4.41047
$679$	−65.8189	−2.52590
$680$	12.5806	0.482444
$681$	16.4949	0.632085
$682$	47.7365	1.82793
$683$	−11.4830	−0.439384	−0.219692	−	0.975569i	$-0.570505\pi$
$683$	−11.4830	−0.439384	−0.219692	+	0.975569i	$0.570505\pi$
$684$	101.946	3.89800
$685$	−1.94572	−0.0743422
$686$	−11.6466	−0.444669
$687$	20.5287	0.783217
$688$	55.0419	2.09845
$689$	−0.166459	−0.00634159
$690$	2.17571	0.0828277
$691$	−3.92658	−0.149374	−0.0746870	−	0.997207i	$-0.523796\pi$
$691$	−3.92658	−0.149374	−0.0746870	+	0.997207i	$0.523796\pi$
$692$	−69.7397	−2.65110
$693$	−57.1819	−2.17216
$694$	80.6345	3.06084
$695$	2.78627	0.105689
$696$	105.466	3.99766
$697$	45.1074	1.70856
$698$	−15.1568	−0.573692
$699$	−28.8212	−1.09012
$700$	−87.8422	−3.32012
$701$	−2.36593	−0.0893600	−0.0446800	−	0.999001i	$-0.514227\pi$
$701$	−2.36593	−0.0893600	−0.0446800	+	0.999001i	$0.514227\pi$
$702$	1.43648	0.0542164
$703$	2.44540	0.0922301
$704$	−5.92746	−0.223400
$705$	1.88966	0.0711686
$706$	41.2645	1.55301
$707$	0.529517	0.0199145
$708$	48.8157	1.83461
$709$	−28.6051	−1.07429	−0.537143	−	0.843491i	$-0.680496\pi$
$709$	−28.6051	−1.07429	−0.537143	+	0.843491i	$0.680496\pi$
$710$	−6.00138	−0.225228
$711$	16.6959	0.626145
$712$	45.6777	1.71184
$713$	6.47548	0.242509
$714$	−195.407	−7.31291
$715$	−0.150827	−0.00564063
$716$	57.9416	2.16538
$717$	10.7215	0.400402
$718$	−40.5315	−1.51262
$719$	23.3826	0.872024	0.436012	−	0.899941i	$-0.356390\pi$
$719$	23.3826	0.872024	0.436012	+	0.899941i	$0.356390\pi$
$720$	−8.66550	−0.322944
$721$	22.9324	0.854048
$722$	−21.7968	−0.811194
$723$	35.4822	1.31960
$724$	37.2893	1.38585
$725$	29.2649	1.08687
$726$	−6.46242	−0.239843
$727$	22.6585	0.840358	0.420179	−	0.907441i	$-0.361967\pi$
$727$	22.6585	0.840358	0.420179	+	0.907441i	$0.361967\pi$
$728$	4.27856	0.158574
$729$	−42.8593	−1.58738
$730$	6.57815	0.243468
$731$	51.4564	1.90318
$732$	107.799	3.98437
$733$	23.2022	0.856992	0.428496	−	0.903544i	$-0.359044\pi$
$733$	23.2022	0.856992	0.428496	+	0.903544i	$0.359044\pi$
$734$	28.6381	1.05705
$735$	−5.76686	−0.212714
$736$	−8.09103	−0.298239
$737$	15.9947	0.589174
$738$	−67.6305	−2.48951
$739$	0.410417	0.0150974	0.00754872	−	0.999972i	$-0.497597\pi$
$739$	0.410417	0.0150974	0.00754872	+	0.999972i	$0.497597\pi$
$740$	−0.559404	−0.0205641
$741$	−2.35045	−0.0863460
$742$	−9.98527	−0.366571
$743$	0.183244	0.00672259	0.00336129	−	0.999994i	$-0.498930\pi$
$743$	0.183244	0.00672259	0.00336129	+	0.999994i	$0.498930\pi$
$744$	−95.7675	−3.51101
$745$	5.35933	0.196351
$746$	64.5091	2.36185
$747$	−3.98852	−0.145932
$748$	−114.855	−4.19951
$749$	48.2758	1.76396
$750$	−17.9817	−0.656600
$751$	41.6066	1.51825	0.759123	−	0.650947i	$-0.225628\pi$
$751$	41.6066	1.51825	0.759123	+	0.650947i	$0.225628\pi$
$752$	−20.8036	−0.758628
$753$	−15.6085	−0.568807
$754$	−2.53291	−0.0922433
$755$	0.262266	0.00954483
$756$	59.9544	2.18052
$757$	−23.3698	−0.849390	−0.424695	−	0.905337i	$-0.639619\pi$
$757$	−23.3698	−0.849390	−0.424695	+	0.905337i	$0.639619\pi$
$758$	−25.9930	−0.944108
$759$	−11.1782	−0.405741
$760$	9.07748	0.329275
$761$	−22.4625	−0.814265	−0.407133	−	0.913369i	$-0.633471\pi$
$761$	−22.4625	−0.814265	−0.407133	+	0.913369i	$0.633471\pi$
$762$	48.5157	1.75754
$763$	43.3183	1.56823
$764$	−57.4176	−2.07730
$765$	−8.10102	−0.292893
$766$	−39.5588	−1.42932
$767$	−0.659767	−0.0238228
$768$	−71.8409	−2.59233
$769$	45.7865	1.65110	0.825552	−	0.564326i	$-0.190864\pi$
$769$	45.7865	1.65110	0.825552	+	0.564326i	$0.190864\pi$
$770$	−9.04758	−0.326052
$771$	11.0895	0.399379
$772$	12.8836	0.463690
$773$	41.8361	1.50474	0.752371	−	0.658740i	$-0.228910\pi$
$773$	41.8361	1.50474	0.752371	+	0.658740i	$0.228910\pi$
$774$	−77.1498	−2.77309
$775$	−26.5739	−0.954563
$776$	111.547	4.00430
$777$	4.88973	0.175418
$778$	90.4224	3.24180
$779$	32.5470	1.16612
$780$	0.537683	0.0192521
$781$	30.8334	1.10331
$782$	−22.3924	−0.800750
$783$	−19.9740	−0.713813
$784$	63.4884	2.26744
$785$	−1.92133	−0.0685751
$786$	−83.5891	−2.98153
$787$	3.49860	0.124712	0.0623559	−	0.998054i	$-0.480139\pi$
$787$	3.49860	0.124712	0.0623559	+	0.998054i	$0.480139\pi$
$788$	58.1808	2.07261
$789$	−27.4941	−0.978814
$790$	2.64170	0.0939874
$791$	−64.7819	−2.30338
$792$	96.9095	3.44353
$793$	−1.45696	−0.0517381
$794$	−30.5738	−1.08502
$795$	−0.706172	−0.0250453
$796$	66.6498	2.36234
$797$	14.5251	0.514507	0.257254	−	0.966344i	$-0.417182\pi$
$797$	14.5251	0.514507	0.257254	+	0.966344i	$0.417182\pi$
$798$	−140.995	−4.99116
$799$	−19.4484	−0.688034
$800$	33.2037	1.17393
$801$	−29.4132	−1.03926
$802$	−99.6431	−3.51852
$803$	−33.7967	−1.19266
$804$	−57.0194	−2.01092
$805$	−1.22731	−0.0432569
$806$	2.30000	0.0810141
$807$	80.9884	2.85093
$808$	−0.897403	−0.0315705
$809$	27.8088	0.977706	0.488853	−	0.872366i	$-0.337415\pi$
$809$	27.8088	0.977706	0.488853	+	0.872366i	$0.337415\pi$
$810$	−2.47973	−0.0871290
$811$	23.0371	0.808940	0.404470	−	0.914551i	$-0.367456\pi$
$811$	23.0371	0.808940	0.404470	+	0.914551i	$0.367456\pi$
$812$	−105.716	−3.70992
$813$	51.1770	1.79486
$814$	4.13071	0.144781
$815$	−3.74416	−0.131152
$816$	152.140	5.32597
$817$	37.1282	1.29895
$818$	29.4922	1.03117
$819$	−2.75509	−0.0962707
$820$	−7.44537	−0.260004
$821$	−39.3618	−1.37374	−0.686868	−	0.726782i	$-0.741015\pi$
$821$	−39.3618	−1.37374	−0.686868	+	0.726782i	$0.741015\pi$
$822$	−51.2185	−1.78645
$823$	−47.0448	−1.63988	−0.819939	−	0.572451i	$-0.805993\pi$
$823$	−47.0448	−1.63988	−0.819939	+	0.572451i	$0.805993\pi$
$824$	−38.8649	−1.35392
$825$	45.8726	1.59708
$826$	−39.5770	−1.37706
$827$	−20.0574	−0.697463	−0.348732	−	0.937223i	$-0.613388\pi$
$827$	−20.0574	−0.697463	−0.348732	+	0.937223i	$0.613388\pi$
$828$	23.3596	0.811803
$829$	−13.3578	−0.463936	−0.231968	−	0.972723i	$-0.574516\pi$
$829$	−13.3578	−0.463936	−0.231968	+	0.972723i	$0.574516\pi$
$830$	−0.631081	−0.0219051
$831$	20.1020	0.697330
$832$	−0.285592	−0.00990112
$833$	59.3527	2.05645
$834$	73.3448	2.53972
$835$	0.236174	0.00817315
$836$	−82.8731	−2.86623
$837$	18.1373	0.626917
$838$	−19.1757	−0.662415
$839$	−9.90560	−0.341979	−0.170990	−	0.985273i	$-0.554696\pi$
$839$	−9.90560	−0.341979	−0.170990	+	0.985273i	$0.554696\pi$
$840$	18.1510	0.626268
$841$	6.21983	0.214477
$842$	−54.9359	−1.89322
$843$	18.1815	0.626202
$844$	−104.861	−3.60948
$845$	3.40219	0.117039
$846$	29.1594	1.00252
$847$	3.64543	0.125258
$848$	7.77437	0.266973
$849$	56.3612	1.93431
$850$	91.8933	3.15191
$851$	0.560333	0.0192080
$852$	−109.918	−3.76571
$853$	−32.9605	−1.12855	−0.564273	−	0.825588i	$-0.690844\pi$
$853$	−32.9605	−1.12855	−0.564273	+	0.825588i	$0.690844\pi$
$854$	−87.3975	−2.99068
$855$	−5.84526	−0.199904
$856$	−81.8158	−2.79641
$857$	53.0727	1.81293	0.906464	−	0.422282i	$-0.138771\pi$
$857$	53.0727	1.81293	0.906464	+	0.422282i	$0.138771\pi$
$858$	−3.97033	−0.135545
$859$	8.28653	0.282733	0.141366	−	0.989957i	$-0.454850\pi$
$859$	8.28653	0.282733	0.141366	+	0.989957i	$0.454850\pi$
$860$	−8.49334	−0.289621
$861$	65.0798	2.21791
$862$	11.3226	0.385650
$863$	27.7846	0.945799	0.472899	−	0.881117i	$-0.343207\pi$
$863$	27.7846	0.945799	0.472899	+	0.881117i	$0.343207\pi$
$864$	−22.6623	−0.770989
$865$	3.99865	0.135958
$866$	−63.9059	−2.17161
$867$	96.4557	3.27581
$868$	95.9953	3.25829
$869$	−13.5723	−0.460408
$870$	−10.7454	−0.364303
$871$	0.770645	0.0261123
$872$	−73.4140	−2.48611
$873$	−71.8284	−2.43102
$874$	−16.1571	−0.546524
$875$	10.1434	0.342911
$876$	120.481	4.07069
$877$	10.9441	0.369555	0.184777	−	0.982780i	$-0.440844\pi$
$877$	10.9441	0.369555	0.184777	+	0.982780i	$0.440844\pi$
$878$	−34.5063	−1.16453
$879$	−51.2035	−1.72705
$880$	7.04429	0.237463
$881$	24.0035	0.808700	0.404350	−	0.914604i	$-0.367498\pi$
$881$	24.0035	0.808700	0.404350	+	0.914604i	$0.367498\pi$
$882$	−88.9888	−2.99641
$883$	−52.1488	−1.75495	−0.877474	−	0.479624i	$-0.840773\pi$
$883$	−52.1488	−1.75495	−0.877474	+	0.479624i	$0.840773\pi$
$884$	−5.53384	−0.186123
$885$	−2.79894	−0.0940852
$886$	13.1531	0.441887
$887$	40.3475	1.35474	0.677369	−	0.735643i	$-0.263120\pi$
$887$	40.3475	1.35474	0.677369	+	0.735643i	$0.263120\pi$
$888$	−8.28691	−0.278090
$889$	−27.3675	−0.917878
$890$	−4.65389	−0.155999
$891$	12.7402	0.426811
$892$	67.6685	2.26571
$893$	−14.0329	−0.469593
$894$	141.077	4.71832
$895$	−3.32219	−0.111049
$896$	35.3134	1.17974
$897$	−0.538576	−0.0179825
$898$	−34.7842	−1.16076
$899$	−31.9812	−1.06663
$900$	−95.8626	−3.19542
$901$	7.26793	0.242130
$902$	54.9777	1.83056
$903$	74.2400	2.47055
$904$	109.790	3.65155
$905$	−2.13805	−0.0710712
$906$	6.90379	0.229363
$907$	41.6873	1.38420	0.692101	−	0.721800i	$-0.256685\pi$
$907$	41.6873	1.38420	0.692101	+	0.721800i	$0.256685\pi$
$908$	28.0213	0.929921
$909$	0.577865	0.0191666
$910$	−0.435923	−0.0144507
$911$	−50.0417	−1.65796	−0.828978	−	0.559281i	$-0.811077\pi$
$911$	−50.0417	−1.65796	−0.828978	+	0.559281i	$0.811077\pi$
$912$	109.776	3.63505
$913$	3.24231	0.107305
$914$	99.6735	3.29691
$915$	−6.18086	−0.204333
$916$	34.8739	1.15226
$917$	47.1524	1.55711
$918$	−62.7194	−2.07005
$919$	−30.3189	−1.00013	−0.500064	−	0.865988i	$-0.666690\pi$
$919$	−30.3189	−1.00013	−0.500064	+	0.865988i	$0.666690\pi$
$920$	2.07999	0.0685752
$921$	−45.3015	−1.49273
$922$	18.3696	0.604971
$923$	1.48559	0.0488987
$924$	−165.710	−5.45145
$925$	−2.29948	−0.0756064
$926$	62.4096	2.05091
$927$	25.0263	0.821970
$928$	39.9601	1.31175
$929$	21.4228	0.702860	0.351430	−	0.936214i	$-0.385695\pi$
$929$	21.4228	0.702860	0.351430	+	0.936214i	$0.385695\pi$
$930$	9.75732	0.319955
$931$	42.8257	1.40356
$932$	−48.9611	−1.60377
$933$	58.7803	1.92438
$934$	44.1895	1.44592
$935$	6.58542	0.215366
$936$	4.66921	0.152618
$937$	12.9879	0.424297	0.212148	−	0.977237i	$-0.431954\pi$
$937$	12.9879	0.424297	0.212148	+	0.977237i	$0.431954\pi$
$938$	46.2281	1.50940
$939$	−29.1519	−0.951335
$940$	3.21013	0.104703
$941$	−24.8041	−0.808590	−0.404295	−	0.914629i	$-0.632483\pi$
$941$	−24.8041	−0.808590	−0.404295	+	0.914629i	$0.632483\pi$
$942$	−50.5763	−1.64786
$943$	7.45775	0.242858
$944$	30.8140	1.00291
$945$	−3.43759	−0.111825
$946$	62.7160	2.03907
$947$	10.3296	0.335668	0.167834	−	0.985815i	$-0.446323\pi$
$947$	10.3296	0.335668	0.167834	+	0.985815i	$0.446323\pi$
$948$	48.3837	1.57143
$949$	−1.62836	−0.0528589
$950$	66.3053	2.15123
$951$	78.1419	2.53393
$952$	−186.810	−6.05455
$953$	−5.65615	−0.183221	−0.0916104	−	0.995795i	$-0.529201\pi$
$953$	−5.65615	−0.183221	−0.0916104	+	0.995795i	$0.529201\pi$
$954$	−10.8970	−0.352803
$955$	3.29215	0.106531
$956$	18.2136	0.589069
$957$	55.2068	1.78458
$958$	−44.1575	−1.42667
$959$	28.8922	0.932977
$960$	−1.21157	−0.0391032
$961$	−1.95961	−0.0632133
$962$	0.199023	0.00641675
$963$	52.6836	1.69771
$964$	60.2768	1.94139
$965$	−0.738703	−0.0237797
$966$	−32.3072	−1.03947
$967$	−43.9450	−1.41318	−0.706588	−	0.707625i	$-0.749767\pi$
$967$	−43.9450	−1.41318	−0.706588	+	0.707625i	$0.749767\pi$
$968$	−6.17812	−0.198572
$969$	102.625	3.29680
$970$	−11.3650	−0.364909
$971$	3.23001	0.103656	0.0518279	−	0.998656i	$-0.483495\pi$
$971$	3.23001	0.103656	0.0518279	+	0.998656i	$0.483495\pi$
$972$	−91.6023	−2.93814
$973$	−41.3736	−1.32638
$974$	−0.265391	−0.00850366
$975$	2.21019	0.0707829
$976$	68.0462	2.17811
$977$	−49.7017	−1.59010	−0.795049	−	0.606545i	$-0.792555\pi$
$977$	−49.7017	−1.59010	−0.795049	+	0.606545i	$0.792555\pi$
$978$	−98.5598	−3.15159
$979$	23.9104	0.764178
$980$	−9.79669	−0.312944
$981$	47.2735	1.50933
$982$	18.2603	0.582710
$983$	44.8177	1.42946	0.714732	−	0.699398i	$-0.246549\pi$
$983$	44.8177	1.42946	0.714732	+	0.699398i	$0.246549\pi$
$984$	−110.294	−3.51606
$985$	−3.33591	−0.106291
$986$	110.592	3.52196
$987$	−28.0596	−0.893148
$988$	−3.99292	−0.127032
$989$	8.50746	0.270521
$990$	−9.87366	−0.313806
$991$	1.57384	0.0499946	0.0249973	−	0.999688i	$-0.492042\pi$
$991$	1.57384	0.0499946	0.0249973	+	0.999688i	$0.492042\pi$
$992$	−36.2856	−1.15207
$993$	65.1186	2.06648
$994$	89.1149	2.82655
$995$	−3.82149	−0.121149
$996$	−11.5585	−0.366245
$997$	−32.8263	−1.03962	−0.519810	−	0.854282i	$-0.673997\pi$
$997$	−32.8263	−1.03962	−0.519810	+	0.854282i	$0.673997\pi$
$998$	57.7822	1.82906
$999$	1.56945	0.0496552

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8003.2.a.d.1.14	✓	179

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8003.2.a.d.1.14	✓	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)

\(f(q)\)	\(=\)	\(q-2.56401 q^{2} +2.69258 q^{3} +4.57412 q^{4} -0.262266 q^{5} -6.90379 q^{6} +3.89440 q^{7} -6.60007 q^{8} +4.24998 q^{9} +O(q^{10})\)	\(q-2.56401 q^{2} +2.69258 q^{3} +4.57412 q^{4} -0.262266 q^{5} -6.90379 q^{6} +3.89440 q^{7} -6.60007 q^{8} +4.24998 q^{9} +0.672451 q^{10} -3.45486 q^{11} +12.3162 q^{12} -0.166459 q^{13} -9.98527 q^{14} -0.706172 q^{15} +7.77437 q^{16} +7.26793 q^{17} -10.8970 q^{18} +5.24415 q^{19} -1.19964 q^{20} +10.4860 q^{21} +8.85828 q^{22} +1.20163 q^{23} -17.7712 q^{24} -4.93122 q^{25} +0.426803 q^{26} +3.36567 q^{27} +17.8135 q^{28} -5.93463 q^{29} +1.81063 q^{30} +5.38891 q^{31} -6.73338 q^{32} -9.30249 q^{33} -18.6350 q^{34} -1.02137 q^{35} +19.4399 q^{36} +0.466311 q^{37} -13.4460 q^{38} -0.448205 q^{39} +1.73097 q^{40} +6.20636 q^{41} -26.8861 q^{42} +7.07993 q^{43} -15.8030 q^{44} -1.11462 q^{45} -3.08099 q^{46} -2.67592 q^{47} +20.9331 q^{48} +8.16638 q^{49} +12.6437 q^{50} +19.5695 q^{51} -0.761406 q^{52} +1.00000 q^{53} -8.62960 q^{54} +0.906092 q^{55} -25.7033 q^{56} +14.1203 q^{57} +15.2164 q^{58} +3.96354 q^{59} -3.23012 q^{60} +8.75264 q^{61} -13.8172 q^{62} +16.5511 q^{63} +1.71569 q^{64} +0.0436566 q^{65} +23.8516 q^{66} -4.62963 q^{67} +33.2444 q^{68} +3.23548 q^{69} +2.61880 q^{70} -8.92464 q^{71} -28.0502 q^{72} +9.78235 q^{73} -1.19562 q^{74} -13.2777 q^{75} +23.9874 q^{76} -13.4546 q^{77} +1.14920 q^{78} +3.92846 q^{79} -2.03895 q^{80} -3.68760 q^{81} -15.9131 q^{82} -0.938479 q^{83} +47.9642 q^{84} -1.90613 q^{85} -18.1530 q^{86} -15.9795 q^{87} +22.8023 q^{88} -6.92079 q^{89} +2.85790 q^{90} -0.648260 q^{91} +5.49641 q^{92} +14.5101 q^{93} +6.86107 q^{94} -1.37536 q^{95} -18.1302 q^{96} -16.9009 q^{97} -20.9386 q^{98} -14.6831 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 179 q + 8 q^{2} + 15 q^{3} + 202 q^{4} + 27 q^{5} + 18 q^{6} + 23 q^{7} + 21 q^{8} + 214 q^{9}+O(q^{10}) \) 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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