LMFDB - Embedded newform 8003.2.a.b.1.7

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:	$1$
Dimension:	$153$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
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)

$f(q)$	$=$	$q-2.55787 q^{2} -0.498344 q^{3} +4.54269 q^{4} +3.86602 q^{5} +1.27470 q^{6} -1.47646 q^{7} -6.50388 q^{8} -2.75165 q^{9} +O(q^{10})$	\(q-2.55787 q^{2} -0.498344 q^{3} +4.54269 q^{4} +3.86602 q^{5} +1.27470 q^{6} -1.47646 q^{7} -6.50388 q^{8} -2.75165 q^{9} -9.88878 q^{10} +3.73534 q^{11} -2.26382 q^{12} +2.20288 q^{13} +3.77659 q^{14} -1.92661 q^{15} +7.55068 q^{16} -5.19471 q^{17} +7.03837 q^{18} +3.91132 q^{19} +17.5622 q^{20} +0.735785 q^{21} -9.55450 q^{22} +1.19239 q^{23} +3.24117 q^{24} +9.94613 q^{25} -5.63468 q^{26} +2.86630 q^{27} -6.70710 q^{28} -0.523105 q^{29} +4.92801 q^{30} -10.1374 q^{31} -6.30589 q^{32} -1.86148 q^{33} +13.2874 q^{34} -5.70803 q^{35} -12.4999 q^{36} +1.39561 q^{37} -10.0047 q^{38} -1.09779 q^{39} -25.1441 q^{40} -5.31569 q^{41} -1.88204 q^{42} -3.78237 q^{43} +16.9685 q^{44} -10.6380 q^{45} -3.04997 q^{46} +2.79800 q^{47} -3.76283 q^{48} -4.82007 q^{49} -25.4409 q^{50} +2.58875 q^{51} +10.0070 q^{52} -1.00000 q^{53} -7.33162 q^{54} +14.4409 q^{55} +9.60271 q^{56} -1.94918 q^{57} +1.33803 q^{58} -6.75570 q^{59} -8.75199 q^{60} -0.471212 q^{61} +25.9301 q^{62} +4.06270 q^{63} +1.02828 q^{64} +8.51639 q^{65} +4.76143 q^{66} -8.90921 q^{67} -23.5980 q^{68} -0.594220 q^{69} +14.6004 q^{70} -3.84201 q^{71} +17.8964 q^{72} -4.56953 q^{73} -3.56980 q^{74} -4.95660 q^{75} +17.7679 q^{76} -5.51507 q^{77} +2.80801 q^{78} +11.4530 q^{79} +29.1911 q^{80} +6.82656 q^{81} +13.5968 q^{82} -0.252093 q^{83} +3.34244 q^{84} -20.0829 q^{85} +9.67480 q^{86} +0.260686 q^{87} -24.2942 q^{88} -6.37869 q^{89} +27.2105 q^{90} -3.25246 q^{91} +5.41666 q^{92} +5.05190 q^{93} -7.15691 q^{94} +15.1213 q^{95} +3.14250 q^{96} +5.29260 q^{97} +12.3291 q^{98} -10.2784 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 153 q - 9 q^{2} - 17 q^{3} + 137 q^{4} - 31 q^{5} - 10 q^{6} - 17 q^{7} - 30 q^{8} + 136 q^{9}+O(q^{10}) $ 153 * q - 9 * q^2 - 17 * q^3 + 137 * q^4 - 31 * q^5 - 10 * q^6 - 17 * q^7 - 30 * q^8 + 136 * q^9	\( 153 q - 9 q^{2} - 17 q^{3} + 137 q^{4} - 31 q^{5} - 10 q^{6} - 17 q^{7} - 30 q^{8} + 136 q^{9} - 34 q^{10} - q^{11} - 60 q^{12} - 101 q^{13} - 16 q^{14} - 14 q^{15} + 97 q^{16} - 12 q^{17} - 45 q^{18} - 45 q^{19} - 52 q^{20} - 76 q^{21} - 46 q^{22} - 28 q^{23} - 30 q^{24} + 84 q^{25} - 22 q^{26} - 68 q^{27} - 64 q^{28} - 14 q^{29} - q^{30} - 70 q^{31} - 54 q^{32} - 85 q^{33} - 59 q^{34} - 16 q^{35} + 87 q^{36} - 167 q^{37} - 48 q^{38} - 28 q^{39} - 68 q^{40} - 38 q^{41} + 2 q^{42} - 71 q^{43} - 10 q^{44} - 151 q^{45} - 37 q^{46} - 37 q^{47} - 166 q^{48} + 74 q^{49} - 3 q^{50} - 11 q^{51} - 183 q^{52} - 153 q^{53} - 40 q^{54} - 88 q^{55} - 69 q^{56} - 26 q^{57} - 43 q^{58} - 34 q^{59} - 12 q^{60} - 90 q^{61} - 37 q^{62} - 36 q^{63} + 58 q^{64} - 19 q^{65} + 52 q^{66} - 86 q^{67} - 22 q^{68} - 81 q^{69} - 144 q^{70} - 50 q^{71} - 190 q^{72} - 171 q^{73} - 14 q^{74} - 69 q^{75} - 88 q^{76} - 72 q^{77} - 61 q^{78} - 13 q^{79} - 84 q^{80} + 117 q^{81} - 124 q^{82} - 72 q^{83} - 106 q^{84} - 193 q^{85} - 44 q^{86} - 65 q^{87} - 89 q^{88} - 10 q^{89} - 152 q^{90} - 67 q^{91} - 29 q^{92} - 129 q^{93} - 43 q^{94} - 29 q^{95} - 106 q^{96} - 177 q^{97} - 69 q^{98} - 11 q^{99}+O(q^{100}) \) 153 * q - 9 * q^2 - 17 * q^3 + 137 * q^4 - 31 * q^5 - 10 * q^6 - 17 * q^7 - 30 * q^8 + 136 * q^9 - 34 * q^10 - q^11 - 60 * q^12 - 101 * q^13 - 16 * q^14 - 14 * q^15 + 97 * q^16 - 12 * q^17 - 45 * q^18 - 45 * q^19 - 52 * q^20 - 76 * q^21 - 46 * q^22 - 28 * q^23 - 30 * q^24 + 84 * q^25 - 22 * q^26 - 68 * q^27 - 64 * q^28 - 14 * q^29 - q^30 - 70 * q^31 - 54 * q^32 - 85 * q^33 - 59 * q^34 - 16 * q^35 + 87 * q^36 - 167 * q^37 - 48 * q^38 - 28 * q^39 - 68 * q^40 - 38 * q^41 + 2 * q^42 - 71 * q^43 - 10 * q^44 - 151 * q^45 - 37 * q^46 - 37 * q^47 - 166 * q^48 + 74 * q^49 - 3 * q^50 - 11 * q^51 - 183 * q^52 - 153 * q^53 - 40 * q^54 - 88 * q^55 - 69 * q^56 - 26 * q^57 - 43 * q^58 - 34 * q^59 - 12 * q^60 - 90 * q^61 - 37 * q^62 - 36 * q^63 + 58 * q^64 - 19 * q^65 + 52 * q^66 - 86 * q^67 - 22 * q^68 - 81 * q^69 - 144 * q^70 - 50 * q^71 - 190 * q^72 - 171 * q^73 - 14 * q^74 - 69 * q^75 - 88 * q^76 - 72 * q^77 - 61 * q^78 - 13 * q^79 - 84 * q^80 + 117 * q^81 - 124 * q^82 - 72 * q^83 - 106 * q^84 - 193 * q^85 - 44 * q^86 - 65 * q^87 - 89 * q^88 - 10 * q^89 - 152 * q^90 - 67 * q^91 - 29 * q^92 - 129 * q^93 - 43 * q^94 - 29 * q^95 - 106 * q^96 - 177 * q^97 - 69 * q^98 - 11 * 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 $

$2$	−2.55787	−1.80869	−0.904343	−	0.426806i	$-0.859639\pi$
$2$	−2.55787	−1.80869	−0.904343	+	0.426806i	$0.859639\pi$
$3$	−0.498344	−0.287719	−0.143859	−	0.989598i	$-0.545951\pi$
$3$	−0.498344	−0.287719	−0.143859	+	0.989598i	$0.545951\pi$
$4$	4.54269	2.27135
$5$	3.86602	1.72894	0.864469	−	0.502686i	$-0.167655\pi$
$5$	3.86602	1.72894	0.864469	+	0.502686i	$0.167655\pi$
$6$	1.27470	0.520393
$7$	−1.47646	−0.558049	−0.279025	−	0.960284i	$-0.590011\pi$
$7$	−1.47646	−0.558049	−0.279025	+	0.960284i	$0.590011\pi$
$8$	−6.50388	−2.29947
$9$	−2.75165	−0.917218
$10$	−9.88878	−3.12711
$11$	3.73534	1.12625	0.563123	−	0.826373i	$-0.309600\pi$
$11$	3.73534	1.12625	0.563123	+	0.826373i	$0.309600\pi$
$12$	−2.26382	−0.653510
$13$	2.20288	0.610969	0.305485	−	0.952197i	$-0.401182\pi$
$13$	2.20288	0.610969	0.305485	+	0.952197i	$0.401182\pi$
$14$	3.77659	1.00934
$15$	−1.92661	−0.497448
$16$	7.55068	1.88767
$17$	−5.19471	−1.25990	−0.629951	−	0.776635i	$-0.716925\pi$
$17$	−5.19471	−1.25990	−0.629951	+	0.776635i	$0.716925\pi$
$18$	7.03837	1.65896
$19$	3.91132	0.897319	0.448660	−	0.893703i	$-0.351902\pi$
$19$	3.91132	0.897319	0.448660	+	0.893703i	$0.351902\pi$
$20$	17.5622	3.92702
$21$	0.735785	0.160561
$22$	−9.55450	−2.03703
$23$	1.19239	0.248630	0.124315	−	0.992243i	$-0.460327\pi$
$23$	1.19239	0.248630	0.124315	+	0.992243i	$0.460327\pi$
$24$	3.24117	0.661600
$25$	9.94613	1.98923
$26$	−5.63468	−1.10505
$27$	2.86630	0.551620
$28$	−6.70710	−1.26752
$29$	−0.523105	−0.0971381	−0.0485690	−	0.998820i	$-0.515466\pi$
$29$	−0.523105	−0.0971381	−0.0485690	+	0.998820i	$0.515466\pi$
$30$	4.92801	0.899728
$31$	−10.1374	−1.82073	−0.910364	−	0.413809i	$-0.864198\pi$
$31$	−10.1374	−1.82073	−0.910364	+	0.413809i	$0.864198\pi$
$32$	−6.30589	−1.11473
$33$	−1.86148	−0.324042
$34$	13.2874	2.27877
$35$	−5.70803	−0.964832
$36$	−12.4999	−2.08332
$37$	1.39561	0.229437	0.114719	−	0.993398i	$-0.463403\pi$
$37$	1.39561	0.229437	0.114719	+	0.993398i	$0.463403\pi$
$38$	−10.0047	−1.62297
$39$	−1.09779	−0.175787
$40$	−25.1441	−3.97564
$41$	−5.31569	−0.830172	−0.415086	−	0.909782i	$-0.636248\pi$
$41$	−5.31569	−0.830172	−0.415086	+	0.909782i	$0.636248\pi$
$42$	−1.88204	−0.290405
$43$	−3.78237	−0.576805	−0.288403	−	0.957509i	$-0.593124\pi$
$43$	−3.78237	−0.576805	−0.288403	+	0.957509i	$0.593124\pi$
$44$	16.9685	2.55810
$45$	−10.6380	−1.58581
$46$	−3.04997	−0.449694
$47$	2.79800	0.408130	0.204065	−	0.978957i	$-0.434585\pi$
$47$	2.79800	0.408130	0.204065	+	0.978957i	$0.434585\pi$
$48$	−3.76283	−0.543118
$49$	−4.82007	−0.688581
$50$	−25.4409	−3.59789
$51$	2.58875	0.362498
$52$	10.0070	1.38772
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	−7.33162	−0.997708
$55$	14.4409	1.94721
$56$	9.60271	1.28322
$57$	−1.94918	−0.258176
$58$	1.33803	0.175692
$59$	−6.75570	−0.879517	−0.439759	−	0.898116i	$-0.644936\pi$
$59$	−6.75570	−0.879517	−0.439759	+	0.898116i	$0.644936\pi$
$60$	−8.75199	−1.12988
$61$	−0.471212	−0.0603325	−0.0301662	−	0.999545i	$-0.509604\pi$
$61$	−0.471212	−0.0603325	−0.0301662	+	0.999545i	$0.509604\pi$
$62$	25.9301	3.29312
$63$	4.06270	0.511853
$64$	1.02828	0.128535
$65$	8.51639	1.05633
$66$	4.76143	0.586091
$67$	−8.90921	−1.08843	−0.544216	−	0.838945i	$-0.683173\pi$
$67$	−8.90921	−1.08843	−0.544216	+	0.838945i	$0.683173\pi$
$68$	−23.5980	−2.86167
$69$	−0.594220	−0.0715357
$70$	14.6004	1.74508
$71$	−3.84201	−0.455962	−0.227981	−	0.973666i	$-0.573212\pi$
$71$	−3.84201	−0.455962	−0.227981	+	0.973666i	$0.573212\pi$
$72$	17.8964	2.10911
$73$	−4.56953	−0.534823	−0.267411	−	0.963582i	$-0.586168\pi$
$73$	−4.56953	−0.534823	−0.267411	+	0.963582i	$0.586168\pi$
$74$	−3.56980	−0.414980
$75$	−4.95660	−0.572338
$76$	17.7679	2.03812
$77$	−5.51507	−0.628501
$78$	2.80801	0.317944
$79$	11.4530	1.28856	0.644279	−	0.764790i	$-0.277157\pi$
$79$	11.4530	1.28856	0.644279	+	0.764790i	$0.277157\pi$
$80$	29.1911	3.26366
$81$	6.82656	0.758506
$82$	13.5968	1.50152
$83$	−0.252093	−0.0276709	−0.0138354	−	0.999904i	$-0.504404\pi$
$83$	−0.252093	−0.0276709	−0.0138354	+	0.999904i	$0.504404\pi$
$84$	3.34244	0.364690
$85$	−20.0829	−2.17829
$86$	9.67480	1.04326
$87$	0.260686	0.0279485
$88$	−24.2942	−2.58977
$89$	−6.37869	−0.676139	−0.338070	−	0.941121i	$-0.609774\pi$
$89$	−6.37869	−0.676139	−0.338070	+	0.941121i	$0.609774\pi$
$90$	27.2105	2.86824
$91$	−3.25246	−0.340951
$92$	5.41666	0.564726
$93$	5.05190	0.523858
$94$	−7.15691	−0.738179
$95$	15.1213	1.55141
$96$	3.14250	0.320730
$97$	5.29260	0.537382	0.268691	−	0.963226i	$-0.413409\pi$
$97$	5.29260	0.537382	0.268691	+	0.963226i	$0.413409\pi$
$98$	12.3291	1.24543
$99$	−10.2784	−1.03301
$100$	45.1822	4.51822
$101$	14.6039	1.45314	0.726572	−	0.687091i	$-0.241113\pi$
$101$	14.6039	1.45314	0.726572	+	0.687091i	$0.241113\pi$
$102$	−6.62168	−0.655644
$103$	−0.942775	−0.0928944	−0.0464472	−	0.998921i	$-0.514790\pi$
$103$	−0.942775	−0.0928944	−0.0464472	+	0.998921i	$0.514790\pi$
$104$	−14.3273	−1.40490
$105$	2.84456	0.277601
$106$	2.55787	0.248442
$107$	−11.9403	−1.15431	−0.577155	−	0.816634i	$-0.695837\pi$
$107$	−11.9403	−1.15431	−0.577155	+	0.816634i	$0.695837\pi$
$108$	13.0207	1.25292
$109$	−1.38902	−0.133044	−0.0665220	−	0.997785i	$-0.521190\pi$
$109$	−1.38902	−0.133044	−0.0665220	+	0.997785i	$0.521190\pi$
$110$	−36.9379	−3.52189
$111$	−0.695496	−0.0660135
$112$	−11.1483	−1.05341
$113$	2.74152	0.257900	0.128950	−	0.991651i	$-0.458839\pi$
$113$	2.74152	0.257900	0.128950	+	0.991651i	$0.458839\pi$
$114$	4.98576	0.466959
$115$	4.60980	0.429866
$116$	−2.37630	−0.220634
$117$	−6.06156	−0.560392
$118$	17.2802	1.59077
$119$	7.66977	0.703087
$120$	12.5304	1.14387
$121$	2.95274	0.268431
$122$	1.20530	0.109123
$123$	2.64904	0.238856
$124$	−46.0510	−4.13550
$125$	19.1219	1.71031
$126$	−10.3919	−0.925781
$127$	−2.21926	−0.196927	−0.0984636	−	0.995141i	$-0.531393\pi$
$127$	−2.21926	−0.196927	−0.0984636	+	0.995141i	$0.531393\pi$
$128$	9.98157	0.882254
$129$	1.88492	0.165958
$130$	−21.7838	−1.91057
$131$	−18.2513	−1.59463	−0.797313	−	0.603566i	$-0.793746\pi$
$131$	−18.2513	−1.59463	−0.797313	+	0.603566i	$0.793746\pi$
$132$	−8.45614	−0.736013
$133$	−5.77491	−0.500748
$134$	22.7886	1.96863
$135$	11.0812	0.953717
$136$	33.7857	2.89710
$137$	−9.32578	−0.796755	−0.398378	−	0.917221i	$-0.630427\pi$
$137$	−9.32578	−0.796755	−0.398378	+	0.917221i	$0.630427\pi$
$138$	1.51994	0.129386
$139$	17.3178	1.46888	0.734439	−	0.678675i	$-0.237445\pi$
$139$	17.3178	1.46888	0.734439	+	0.678675i	$0.237445\pi$
$140$	−25.9298	−2.19147
$141$	−1.39437	−0.117427
$142$	9.82735	0.824693
$143$	8.22850	0.688102
$144$	−20.7768	−1.73140
$145$	−2.02233	−0.167946
$146$	11.6883	0.967327
$147$	2.40205	0.198118
$148$	6.33985	0.521132
$149$	1.73880	0.142448	0.0712241	−	0.997460i	$-0.477309\pi$
$149$	1.73880	0.142448	0.0712241	+	0.997460i	$0.477309\pi$
$150$	12.6783	1.03518
$151$	−1.00000	−0.0813788
$151$	−1.00000	−0.0813788
$152$	−25.4388	−2.06336
$153$	14.2940	1.15560
$154$	14.1068	1.13676
$155$	−39.1913	−3.14792
$156$	−4.98693	−0.399274
$157$	−17.6203	−1.40625	−0.703125	−	0.711066i	$-0.748213\pi$
$157$	−17.6203	−1.40625	−0.703125	+	0.711066i	$0.748213\pi$
$158$	−29.2952	−2.33060
$159$	0.498344	0.0395212
$160$	−24.3787	−1.92731
$161$	−1.76051	−0.138748
$162$	−17.4614	−1.37190
$163$	−22.0972	−1.73079	−0.865394	−	0.501092i	$-0.832932\pi$
$163$	−22.0972	−1.73079	−0.865394	+	0.501092i	$0.832932\pi$
$164$	−24.1476	−1.88561
$165$	−7.19653	−0.560249
$166$	0.644822	0.0500479
$167$	−24.1689	−1.87024	−0.935121	−	0.354329i	$-0.884709\pi$
$167$	−24.1689	−1.87024	−0.935121	+	0.354329i	$0.884709\pi$
$168$	−4.78545	−0.369206
$169$	−8.14732	−0.626717
$170$	51.3693	3.93985
$171$	−10.7626	−0.823037
$172$	−17.1821	−1.31013
$173$	−14.3251	−1.08912	−0.544560	−	0.838722i	$-0.683304\pi$
$173$	−14.3251	−1.08912	−0.544560	+	0.838722i	$0.683304\pi$
$174$	−0.666801	−0.0505500
$175$	−14.6851	−1.11009
$176$	28.2043	2.12598
$177$	3.36666	0.253054
$178$	16.3158	1.22292
$179$	13.9938	1.04594	0.522972	−	0.852350i	$-0.324823\pi$
$179$	13.9938	1.04594	0.522972	+	0.852350i	$0.324823\pi$
$180$	−48.3250	−3.60193
$181$	−5.43395	−0.403902	−0.201951	−	0.979396i	$-0.564728\pi$
$181$	−5.43395	−0.403902	−0.201951	+	0.979396i	$0.564728\pi$
$182$	8.31938	0.616673
$183$	0.234826	0.0173588
$184$	−7.75515	−0.571717
$185$	5.39547	0.396683
$186$	−12.9221	−0.947495
$187$	−19.4040	−1.41896
$188$	12.7105	0.927005
$189$	−4.23198	−0.307831
$190$	−38.6782	−2.80601
$191$	7.15902	0.518008	0.259004	−	0.965876i	$-0.416606\pi$
$191$	7.15902	0.518008	0.259004	+	0.965876i	$0.416606\pi$
$192$	−0.512438	−0.0369820
$193$	−1.55393	−0.111854	−0.0559272	−	0.998435i	$-0.517811\pi$
$193$	−1.55393	−0.111854	−0.0559272	+	0.998435i	$0.517811\pi$
$194$	−13.5378	−0.971956
$195$	−4.24409	−0.303926
$196$	−21.8961	−1.56401
$197$	0.380963	0.0271425	0.0135712	−	0.999908i	$-0.495680\pi$
$197$	0.380963	0.0271425	0.0135712	+	0.999908i	$0.495680\pi$
$198$	26.2907	1.86840
$199$	4.01035	0.284286	0.142143	−	0.989846i	$-0.454601\pi$
$199$	4.01035	0.284286	0.142143	+	0.989846i	$0.454601\pi$
$200$	−64.6884	−4.57416
$201$	4.43985	0.313163
$202$	−37.3549	−2.62828
$203$	0.772343	0.0542078
$204$	11.7599	0.823358
$205$	−20.5506	−1.43532
$206$	2.41150	0.168017
$207$	−3.28104	−0.228048
$208$	16.6332	1.15331
$209$	14.6101	1.01060
$210$	−7.27601	−0.502092
$211$	12.8248	0.882895	0.441448	−	0.897287i	$-0.354465\pi$
$211$	12.8248	0.882895	0.441448	+	0.897287i	$0.354465\pi$
$212$	−4.54269	−0.311993
$213$	1.91464	0.131189
$214$	30.5417	2.08779
$215$	−14.6227	−0.997261
$216$	−18.6421	−1.26843
$217$	14.9674	1.01606
$218$	3.55293	0.240635
$219$	2.27720	0.153879
$220$	65.6006	4.42279
$221$	−11.4433	−0.769761
$222$	1.77899	0.119398
$223$	11.8414	0.792956	0.396478	−	0.918044i	$-0.370232\pi$
$223$	11.8414	0.792956	0.396478	+	0.918044i	$0.370232\pi$
$224$	9.31039	0.622076
$225$	−27.3683	−1.82455
$226$	−7.01244	−0.466460
$227$	−15.1989	−1.00879	−0.504395	−	0.863473i	$-0.668284\pi$
$227$	−15.1989	−1.00879	−0.504395	+	0.863473i	$0.668284\pi$
$228$	−8.85454	−0.586407
$229$	−4.11371	−0.271842	−0.135921	−	0.990720i	$-0.543399\pi$
$229$	−4.11371	−0.271842	−0.135921	+	0.990720i	$0.543399\pi$
$230$	−11.7913	−0.777493
$231$	2.74840	0.180832
$232$	3.40221	0.223366
$233$	−11.2145	−0.734684	−0.367342	−	0.930086i	$-0.619732\pi$
$233$	−11.2145	−0.734684	−0.367342	+	0.930086i	$0.619732\pi$
$234$	15.5047	1.01357
$235$	10.8171	0.705632
$236$	−30.6891	−1.99769
$237$	−5.70751	−0.370743
$238$	−19.6183	−1.27166
$239$	15.6200	1.01037	0.505186	−	0.863011i	$-0.331424\pi$
$239$	15.6200	1.01037	0.505186	+	0.863011i	$0.331424\pi$
$240$	−14.5472	−0.939018
$241$	−1.54545	−0.0995514	−0.0497757	−	0.998760i	$-0.515851\pi$
$241$	−1.54545	−0.0995514	−0.0497757	+	0.998760i	$0.515851\pi$
$242$	−7.55272	−0.485507
$243$	−12.0009	−0.769857
$244$	−2.14057	−0.137036
$245$	−18.6345	−1.19051
$246$	−6.77590	−0.432016
$247$	8.61618	0.548234
$248$	65.9323	4.18670
$249$	0.125629	0.00796143
$250$	−48.9112	−3.09342
$251$	−7.18530	−0.453532	−0.226766	−	0.973949i	$-0.572815\pi$
$251$	−7.18530	−0.453532	−0.226766	+	0.973949i	$0.572815\pi$
$252$	18.4556	1.16259
$253$	4.45397	0.280019
$254$	5.67657	0.356179
$255$	10.0082	0.626736
$256$	−27.5881	−1.72426
$257$	−0.575534	−0.0359008	−0.0179504	−	0.999839i	$-0.505714\pi$
$257$	−0.575534	−0.0359008	−0.0179504	+	0.999839i	$0.505714\pi$
$258$	−4.82138	−0.300166
$259$	−2.06057	−0.128037
$260$	38.6873	2.39929
$261$	1.43940	0.0890968
$262$	46.6845	2.88418
$263$	−12.6617	−0.780754	−0.390377	−	0.920655i	$-0.627655\pi$
$263$	−12.6617	−0.780754	−0.390377	+	0.920655i	$0.627655\pi$
$264$	12.1069	0.745125
$265$	−3.86602	−0.237488
$266$	14.7715	0.905696
$267$	3.17878	0.194538
$268$	−40.4718	−2.47221
$269$	17.2352	1.05085	0.525424	−	0.850840i	$-0.323907\pi$
$269$	17.2352	1.05085	0.525424	+	0.850840i	$0.323907\pi$
$270$	−28.3442	−1.72497
$271$	18.9175	1.14916	0.574579	−	0.818449i	$-0.305166\pi$
$271$	18.9175	1.14916	0.574579	+	0.818449i	$0.305166\pi$
$272$	−39.2235	−2.37828
$273$	1.62085	0.0980980
$274$	23.8541	1.44108
$275$	37.1522	2.24036
$276$	−2.69936	−0.162482
$277$	6.10063	0.366551	0.183276	−	0.983062i	$-0.441330\pi$
$277$	6.10063	0.366551	0.183276	+	0.983062i	$0.441330\pi$
$278$	−44.2967	−2.65674
$279$	27.8946	1.67000
$280$	37.1243	2.21860
$281$	6.83223	0.407577	0.203788	−	0.979015i	$-0.434675\pi$
$281$	6.83223	0.407577	0.203788	+	0.979015i	$0.434675\pi$
$282$	3.56660	0.212388
$283$	−25.0753	−1.49057	−0.745286	−	0.666745i	$-0.767687\pi$
$283$	−25.0753	−1.49057	−0.745286	+	0.666745i	$0.767687\pi$
$284$	−17.4531	−1.03565
$285$	−7.53559	−0.446370
$286$	−21.0474	−1.24456
$287$	7.84840	0.463277
$288$	17.3516	1.02245
$289$	9.98497	0.587351
$290$	5.17287	0.303761
$291$	−2.63754	−0.154615
$292$	−20.7580	−1.21477
$293$	0.848859	0.0495909	0.0247954	−	0.999693i	$-0.492107\pi$
$293$	0.848859	0.0495909	0.0247954	+	0.999693i	$0.492107\pi$
$294$	−6.14413	−0.358333
$295$	−26.1177	−1.52063
$296$	−9.07690	−0.527584
$297$	10.7066	0.621260
$298$	−4.44763	−0.257644
$299$	2.62669	0.151905
$300$	−22.5163	−1.29998
$301$	5.58451	0.321886
$302$	2.55787	0.147189
$303$	−7.27777	−0.418097
$304$	29.5331	1.69384
$305$	−1.82172	−0.104311
$306$	−36.5623	−2.09013
$307$	−15.5248	−0.886048	−0.443024	−	0.896510i	$-0.646094\pi$
$307$	−15.5248	−0.886048	−0.443024	+	0.896510i	$0.646094\pi$
$308$	−25.0533	−1.42754
$309$	0.469826	0.0267275
$310$	100.246	5.69361
$311$	10.9980	0.623641	0.311821	−	0.950141i	$-0.399061\pi$
$311$	10.9980	0.623641	0.311821	+	0.950141i	$0.399061\pi$
$312$	7.13990	0.404217
$313$	4.16627	0.235492	0.117746	−	0.993044i	$-0.462433\pi$
$313$	4.16627	0.235492	0.117746	+	0.993044i	$0.462433\pi$
$314$	45.0703	2.54347
$315$	15.7065	0.884962
$316$	52.0273	2.92676
$317$	−7.57168	−0.425268	−0.212634	−	0.977132i	$-0.568204\pi$
$317$	−7.57168	−0.425268	−0.212634	+	0.977132i	$0.568204\pi$
$318$	−1.27470	−0.0714815
$319$	−1.95397	−0.109401
$320$	3.97536	0.222229
$321$	5.95037	0.332117
$322$	4.50316	0.250951
$323$	−20.3182	−1.13053
$324$	31.0110	1.72283
$325$	21.9101	1.21536
$326$	56.5218	3.13045
$327$	0.692210	0.0382793
$328$	34.5726	1.90895
$329$	−4.13113	−0.227757
$330$	18.4078	1.01332
$331$	−19.1549	−1.05285	−0.526424	−	0.850222i	$-0.676468\pi$
$331$	−19.1549	−1.05285	−0.526424	+	0.850222i	$0.676468\pi$
$332$	−1.14518	−0.0628501
$333$	−3.84025	−0.210444
$334$	61.8208	3.38268
$335$	−34.4432	−1.88183
$336$	5.55567	0.303087
$337$	18.6914	1.01818	0.509092	−	0.860712i	$-0.329981\pi$
$337$	18.6914	1.01818	0.509092	+	0.860712i	$0.329981\pi$
$338$	20.8398	1.13353
$339$	−1.36622	−0.0742027
$340$	−91.2302	−4.94765
$341$	−37.8665	−2.05059
$342$	27.5293	1.48862
$343$	17.4518	0.942311
$344$	24.6000	1.32635
$345$	−2.29727	−0.123681
$346$	36.6419	1.96988
$347$	24.4392	1.31196	0.655982	−	0.754777i	$-0.272255\pi$
$347$	24.4392	1.31196	0.655982	+	0.754777i	$0.272255\pi$
$348$	1.18422	0.0634807
$349$	11.5737	0.619524	0.309762	−	0.950814i	$-0.399751\pi$
$349$	11.5737	0.619524	0.309762	+	0.950814i	$0.399751\pi$
$350$	37.5625	2.00780
$351$	6.31412	0.337023
$352$	−23.5546	−1.25547
$353$	−5.28568	−0.281328	−0.140664	−	0.990057i	$-0.544924\pi$
$353$	−5.28568	−0.281328	−0.140664	+	0.990057i	$0.544924\pi$
$354$	−8.61148	−0.457695
$355$	−14.8533	−0.788330
$356$	−28.9764	−1.53575
$357$	−3.82218	−0.202291
$358$	−35.7942	−1.89178
$359$	12.9836	0.685248	0.342624	−	0.939473i	$-0.388684\pi$
$359$	12.9836	0.685248	0.342624	+	0.939473i	$0.388684\pi$
$360$	69.1879	3.64652
$361$	−3.70155	−0.194819
$362$	13.8993	0.730532
$363$	−1.47148	−0.0772327
$364$	−14.7749	−0.774418
$365$	−17.6659	−0.924676
$366$	−0.600653	−0.0313966
$367$	−23.4425	−1.22369	−0.611843	−	0.790979i	$-0.709572\pi$
$367$	−23.4425	−1.22369	−0.611843	+	0.790979i	$0.709572\pi$
$368$	9.00334	0.469332
$369$	14.6269	0.761448
$370$	−13.8009	−0.717476
$371$	1.47646	0.0766540
$372$	22.9492	1.18986
$373$	−22.4783	−1.16388	−0.581942	−	0.813230i	$-0.697707\pi$
$373$	−22.4783	−1.16388	−0.581942	+	0.813230i	$0.697707\pi$
$374$	49.6328	2.56645
$375$	−9.52927	−0.492089
$376$	−18.1978	−0.938482
$377$	−1.15234	−0.0593484
$378$	10.8248	0.556770
$379$	5.91795	0.303985	0.151992	−	0.988382i	$-0.451431\pi$
$379$	5.91795	0.303985	0.151992	+	0.988382i	$0.451431\pi$
$380$	68.6913	3.52379
$381$	1.10595	0.0566597
$382$	−18.3118	−0.936914
$383$	22.4080	1.14499	0.572497	−	0.819907i	$-0.305975\pi$
$383$	22.4080	1.14499	0.572497	+	0.819907i	$0.305975\pi$
$384$	−4.97425	−0.253841
$385$	−21.3214	−1.08664
$386$	3.97475	0.202310
$387$	10.4078	0.529056
$388$	24.0427	1.22058
$389$	17.7006	0.897454	0.448727	−	0.893669i	$-0.351877\pi$
$389$	17.7006	0.897454	0.448727	+	0.893669i	$0.351877\pi$
$390$	10.8558	0.549706
$391$	−6.19411	−0.313250
$392$	31.3491	1.58337
$393$	9.09544	0.458804
$394$	−0.974453	−0.0490922
$395$	44.2774	2.22784
$396$	−46.6914	−2.34633
$397$	−4.35991	−0.218818	−0.109409	−	0.993997i	$-0.534896\pi$
$397$	−4.35991	−0.218818	−0.109409	+	0.993997i	$0.534896\pi$
$398$	−10.2579	−0.514184
$399$	2.87789	0.144075
$400$	75.1000	3.75500
$401$	−35.7386	−1.78470	−0.892351	−	0.451343i	$-0.850945\pi$
$401$	−35.7386	−1.78470	−0.892351	+	0.451343i	$0.850945\pi$
$402$	−11.3566	−0.566413
$403$	−22.3314	−1.11241
$404$	66.3411	3.30059
$405$	26.3916	1.31141
$406$	−1.97555	−0.0980450
$407$	5.21309	0.258403
$408$	−16.8369	−0.833551
$409$	−7.67047	−0.379281	−0.189640	−	0.981854i	$-0.560732\pi$
$409$	−7.67047	−0.379281	−0.189640	+	0.981854i	$0.560732\pi$
$410$	52.5657	2.59604
$411$	4.64745	0.229242
$412$	−4.28274	−0.210995
$413$	9.97452	0.490814
$414$	8.39247	0.412468
$415$	−0.974599	−0.0478412
$416$	−13.8911	−0.681068
$417$	−8.63023	−0.422624
$418$	−37.3707	−1.82786
$419$	37.8057	1.84693	0.923464	−	0.383686i	$-0.125345\pi$
$419$	37.8057	1.84693	0.923464	+	0.383686i	$0.125345\pi$
$420$	12.9220	0.630527
$421$	18.9542	0.923770	0.461885	−	0.886940i	$-0.347173\pi$
$421$	18.9542	0.923770	0.461885	+	0.886940i	$0.347173\pi$
$422$	−32.8041	−1.59688
$423$	−7.69912	−0.374344
$424$	6.50388	0.315856
$425$	−51.6672	−2.50623
$426$	−4.89740	−0.237280
$427$	0.695725	0.0336685
$428$	−54.2410	−2.62184
$429$	−4.10062	−0.197980
$430$	37.4030	1.80373
$431$	37.0324	1.78379	0.891894	−	0.452244i	$-0.149376\pi$
$431$	37.0324	1.78379	0.891894	+	0.452244i	$0.149376\pi$
$432$	21.6425	1.04128
$433$	−30.2702	−1.45469	−0.727347	−	0.686270i	$-0.759247\pi$
$433$	−30.2702	−1.45469	−0.727347	+	0.686270i	$0.759247\pi$
$434$	−38.2847	−1.83773
$435$	1.00782	0.0483212
$436$	−6.30990	−0.302189
$437$	4.66382	0.223101
$438$	−5.82477	−0.278318
$439$	10.8536	0.518014	0.259007	−	0.965875i	$-0.416605\pi$
$439$	10.8536	0.518014	0.259007	+	0.965875i	$0.416605\pi$
$440$	−93.9218	−4.47755
$441$	13.2632	0.631579
$442$	29.2705	1.39226
$443$	−4.71355	−0.223947	−0.111974	−	0.993711i	$-0.535717\pi$
$443$	−4.71355	−0.223947	−0.111974	+	0.993711i	$0.535717\pi$
$444$	−3.15942	−0.149940
$445$	−24.6602	−1.16900
$446$	−30.2886	−1.43421
$447$	−0.866521	−0.0409850
$448$	−1.51822	−0.0717290
$449$	−36.2134	−1.70902	−0.854508	−	0.519439i	$-0.826141\pi$
$449$	−36.2134	−1.70902	−0.854508	+	0.519439i	$0.826141\pi$
$450$	70.0046	3.30005
$451$	−19.8559	−0.934978
$452$	12.4539	0.585780
$453$	0.498344	0.0234142
$454$	38.8769	1.82458
$455$	−12.5741	−0.589483
$456$	12.6773	0.593667
$457$	−35.8642	−1.67766	−0.838829	−	0.544396i	$-0.816759\pi$
$457$	−35.8642	−1.67766	−0.838829	+	0.544396i	$0.816759\pi$
$458$	10.5223	0.491676
$459$	−14.8896	−0.694987
$460$	20.9409	0.976376
$461$	5.46205	0.254393	0.127196	−	0.991878i	$-0.459402\pi$
$461$	5.46205	0.254393	0.127196	+	0.991878i	$0.459402\pi$
$462$	−7.03005	−0.327068
$463$	−19.4865	−0.905615	−0.452807	−	0.891608i	$-0.649578\pi$
$463$	−19.4865	−0.905615	−0.452807	+	0.891608i	$0.649578\pi$
$464$	−3.94979	−0.183365
$465$	19.5308	0.905718
$466$	28.6851	1.32881
$467$	23.4282	1.08413	0.542063	−	0.840338i	$-0.317643\pi$
$467$	23.4282	1.08413	0.542063	+	0.840338i	$0.317643\pi$
$468$	−27.5358	−1.27284
$469$	13.1541	0.607399
$470$	−27.6688	−1.27627
$471$	8.78095	0.404605
$472$	43.9382	2.02242
$473$	−14.1284	−0.649625
$474$	14.5991	0.670557
$475$	38.9025	1.78497
$476$	34.8414	1.59695
$477$	2.75165	0.125990
$478$	−39.9538	−1.82745
$479$	−12.6939	−0.580000	−0.290000	−	0.957027i	$-0.593655\pi$
$479$	−12.6939	−0.580000	−0.290000	+	0.957027i	$0.593655\pi$
$480$	12.1490	0.554523
$481$	3.07437	0.140179
$482$	3.95307	0.180057
$483$	0.877341	0.0399204
$484$	13.4134	0.609700
$485$	20.4613	0.929101
$486$	30.6967	1.39243
$487$	7.80000	0.353452	0.176726	−	0.984260i	$-0.443449\pi$
$487$	7.80000	0.353452	0.176726	+	0.984260i	$0.443449\pi$
$488$	3.06470	0.138733
$489$	11.0120	0.497980
$490$	47.6646	2.15327
$491$	20.8642	0.941587	0.470793	−	0.882243i	$-0.343968\pi$
$491$	20.8642	0.941587	0.470793	+	0.882243i	$0.343968\pi$
$492$	12.0338	0.542525
$493$	2.71737	0.122384
$494$	−22.0391	−0.991584
$495$	−39.7363	−1.78602
$496$	−76.5441	−3.43693
$497$	5.67257	0.254449
$498$	−0.321343	−0.0143997
$499$	9.37157	0.419529	0.209765	−	0.977752i	$-0.432730\pi$
$499$	9.37157	0.419529	0.209765	+	0.977752i	$0.432730\pi$
$500$	86.8648	3.88471
$501$	12.0444	0.538104
$502$	18.3791	0.820298
$503$	20.0239	0.892823	0.446411	−	0.894828i	$-0.352702\pi$
$503$	20.0239	0.892823	0.446411	+	0.894828i	$0.352702\pi$
$504$	−26.4233	−1.17699
$505$	56.4590	2.51239
$506$	−11.3927	−0.506466
$507$	4.06017	0.180318
$508$	−10.0814	−0.447290
$509$	31.6688	1.40369	0.701847	−	0.712328i	$-0.252359\pi$
$509$	31.6688	1.40369	0.701847	+	0.712328i	$0.252359\pi$
$510$	−25.5996	−1.13357
$511$	6.74672	0.298457
$512$	50.6036	2.23638
$513$	11.2110	0.494979
$514$	1.47214	0.0649333
$515$	−3.64479	−0.160609
$516$	8.56261	0.376948
$517$	10.4515	0.459655
$518$	5.27066	0.231580
$519$	7.13885	0.313361
$520$	−55.3895	−2.42899
$521$	6.52949	0.286062	0.143031	−	0.989718i	$-0.454315\pi$
$521$	6.52949	0.286062	0.143031	+	0.989718i	$0.454315\pi$
$522$	−3.68180	−0.161148
$523$	−13.5258	−0.591442	−0.295721	−	0.955274i	$-0.595560\pi$
$523$	−13.5258	−0.591442	−0.295721	+	0.955274i	$0.595560\pi$
$524$	−82.9102	−3.62195
$525$	7.31821	0.319393
$526$	32.3870	1.41214
$527$	52.6607	2.29394
$528$	−14.0555	−0.611685
$529$	−21.5782	−0.938183
$530$	9.88878	0.429541
$531$	18.5893	0.806709
$532$	−26.2336	−1.13737
$533$	−11.7098	−0.507209
$534$	−8.13090	−0.351859
$535$	−46.1614	−1.99573
$536$	57.9444	2.50282
$537$	−6.97371	−0.300938
$538$	−44.0854	−1.90066
$539$	−18.0046	−0.775512
$540$	50.3384	2.16622
$541$	3.39391	0.145916	0.0729579	−	0.997335i	$-0.476756\pi$
$541$	3.39391	0.145916	0.0729579	+	0.997335i	$0.476756\pi$
$542$	−48.3885	−2.07847
$543$	2.70797	0.116210
$544$	32.7572	1.40445
$545$	−5.36999	−0.230025
$546$	−4.14591	−0.177429
$547$	37.1288	1.58751	0.793757	−	0.608235i	$-0.208122\pi$
$547$	37.1288	1.58751	0.793757	+	0.608235i	$0.208122\pi$
$548$	−42.3642	−1.80971
$549$	1.29661	0.0553380
$550$	−95.0304	−4.05211
$551$	−2.04603	−0.0871638
$552$	3.86473	0.164494
$553$	−16.9098	−0.719079
$554$	−15.6046	−0.662976
$555$	−2.68880	−0.114133
$556$	78.6695	3.33633
$557$	30.4257	1.28918	0.644589	−	0.764530i	$-0.277029\pi$
$557$	30.4257	1.28918	0.644589	+	0.764530i	$0.277029\pi$
$558$	−71.3506	−3.02051
$559$	−8.33210	−0.352410
$560$	−43.0995	−1.82128
$561$	9.66985	0.408262
$562$	−17.4760	−0.737179
$563$	−12.8657	−0.542223	−0.271112	−	0.962548i	$-0.587391\pi$
$563$	−12.8657	−0.542223	−0.271112	+	0.962548i	$0.587391\pi$
$564$	−6.33418	−0.266717
$565$	10.5988	0.445893
$566$	64.1393	2.69598
$567$	−10.0791	−0.423284
$568$	24.9879	1.04847
$569$	−13.2534	−0.555613	−0.277807	−	0.960637i	$-0.589607\pi$
$569$	−13.2534	−0.555613	−0.277807	+	0.960637i	$0.589607\pi$
$570$	19.2751	0.807343
$571$	2.86523	0.119906	0.0599530	−	0.998201i	$-0.480905\pi$
$571$	2.86523	0.119906	0.0599530	+	0.998201i	$0.480905\pi$
$572$	37.3796	1.56292
$573$	−3.56765	−0.149041
$574$	−20.0752	−0.837922
$575$	11.8597	0.494582
$576$	−2.82947	−0.117895
$577$	−44.6372	−1.85827	−0.929136	−	0.369738i	$-0.879447\pi$
$577$	−44.6372	−1.85827	−0.929136	+	0.369738i	$0.879447\pi$
$578$	−25.5402	−1.06233
$579$	0.774392	0.0321826
$580$	−9.18684	−0.381463
$581$	0.372206	0.0154417
$582$	6.74647	0.279650
$583$	−3.73534	−0.154702
$584$	29.7196	1.22981
$585$	−23.4341	−0.968883
$586$	−2.17127	−0.0896944
$587$	−32.7787	−1.35292	−0.676460	−	0.736479i	$-0.736487\pi$
$587$	−32.7787	−1.35292	−0.676460	+	0.736479i	$0.736487\pi$
$588$	10.9118	0.449994
$589$	−39.6506	−1.63377
$590$	66.8056	2.75034
$591$	−0.189851	−0.00780941
$592$	10.5378	0.433102
$593$	33.8525	1.39016	0.695079	−	0.718934i	$-0.255369\pi$
$593$	33.8525	1.39016	0.695079	+	0.718934i	$0.255369\pi$
$594$	−27.3861	−1.12366
$595$	29.6515	1.21559
$596$	7.89884	0.323549
$597$	−1.99853	−0.0817945
$598$	−6.71873	−0.274749
$599$	−7.30303	−0.298394	−0.149197	−	0.988807i	$-0.547669\pi$
$599$	−7.30303	−0.298394	−0.149197	+	0.988807i	$0.547669\pi$
$600$	32.2371	1.31607
$601$	−17.2323	−0.702918	−0.351459	−	0.936203i	$-0.614314\pi$
$601$	−17.2323	−0.702918	−0.351459	+	0.936203i	$0.614314\pi$
$602$	−14.2844	−0.582190
$603$	24.5151	0.998330
$604$	−4.54269	−0.184840
$605$	11.4154	0.464100
$606$	18.6156	0.756206
$607$	−33.3527	−1.35375	−0.676873	−	0.736100i	$-0.736665\pi$
$607$	−33.3527	−1.35375	−0.676873	+	0.736100i	$0.736665\pi$
$608$	−24.6644	−1.00027
$609$	−0.384892	−0.0155966
$610$	4.65971	0.188666
$611$	6.16366	0.249355
$612$	64.9334	2.62478
$613$	7.05887	0.285105	0.142553	−	0.989787i	$-0.454469\pi$
$613$	7.05887	0.285105	0.142553	+	0.989787i	$0.454469\pi$
$614$	39.7104	1.60258
$615$	10.2413	0.412967
$616$	35.8694	1.44522
$617$	−28.4749	−1.14636	−0.573179	−	0.819430i	$-0.694290\pi$
$617$	−28.4749	−1.14636	−0.573179	+	0.819430i	$0.694290\pi$
$618$	−1.20175	−0.0483416
$619$	2.07817	0.0835289	0.0417644	−	0.999127i	$-0.486702\pi$
$619$	2.07817	0.0835289	0.0417644	+	0.999127i	$0.486702\pi$
$620$	−178.034	−7.15003
$621$	3.41775	0.137149
$622$	−28.1315	−1.12797
$623$	9.41787	0.377319
$624$	−8.28907	−0.331828
$625$	24.1949	0.967796
$626$	−10.6568	−0.425931
$627$	−7.28086	−0.290769
$628$	−80.0435	−3.19408
$629$	−7.24980	−0.289069
$630$	−40.1752	−1.60062
$631$	7.69549	0.306353	0.153176	−	0.988199i	$-0.451050\pi$
$631$	7.69549	0.306353	0.153176	+	0.988199i	$0.451050\pi$
$632$	−74.4886	−2.96300
$633$	−6.39116	−0.254026
$634$	19.3674	0.769176
$635$	−8.57970	−0.340475
$636$	2.26382	0.0897664
$637$	−10.6180	−0.420702
$638$	4.99800	0.197873
$639$	10.5719	0.418217
$640$	38.5890	1.52536
$641$	−0.932262	−0.0368221	−0.0184111	−	0.999831i	$-0.505861\pi$
$641$	−0.932262	−0.0368221	−0.0184111	+	0.999831i	$0.505861\pi$
$642$	−15.2203	−0.600696
$643$	40.5834	1.60046	0.800228	−	0.599697i	$-0.204712\pi$
$643$	40.5834	1.60046	0.800228	+	0.599697i	$0.204712\pi$
$644$	−7.99747	−0.315145
$645$	7.28714	0.286931
$646$	51.9712	2.04478
$647$	25.0302	0.984040	0.492020	−	0.870584i	$-0.336259\pi$
$647$	25.0302	0.984040	0.492020	+	0.870584i	$0.336259\pi$
$648$	−44.3991	−1.74416
$649$	−25.2348	−0.990553
$650$	−56.0433	−2.19820
$651$	−7.45893	−0.292338
$652$	−100.381	−3.93122
$653$	43.0165	1.68336	0.841682	−	0.539973i	$-0.181566\pi$
$653$	43.0165	1.68336	0.841682	+	0.539973i	$0.181566\pi$
$654$	−1.77058	−0.0692353
$655$	−70.5600	−2.75701
$656$	−40.1371	−1.56709
$657$	12.5738	0.490549
$658$	10.5669	0.411940
$659$	7.51317	0.292671	0.146336	−	0.989235i	$-0.453252\pi$
$659$	7.51317	0.292671	0.146336	+	0.989235i	$0.453252\pi$
$660$	−32.6916	−1.27252
$661$	−33.8268	−1.31571	−0.657854	−	0.753145i	$-0.728536\pi$
$661$	−33.8268	−1.31571	−0.657854	+	0.753145i	$0.728536\pi$
$662$	48.9957	1.90427
$663$	5.70271	0.221475
$664$	1.63958	0.0636282
$665$	−22.3259	−0.865763
$666$	9.82284	0.380627
$667$	−0.623744	−0.0241515
$668$	−109.792	−4.24797
$669$	−5.90107	−0.228148
$670$	88.1012	3.40365
$671$	−1.76014	−0.0679493
$672$	−4.63977	−0.178983
$673$	−19.3024	−0.744052	−0.372026	−	0.928222i	$-0.621337\pi$
$673$	−19.3024	−0.744052	−0.372026	+	0.928222i	$0.621337\pi$
$674$	−47.8100	−1.84157
$675$	28.5086	1.09730
$676$	−37.0108	−1.42349
$677$	0.844994	0.0324758	0.0162379	−	0.999868i	$-0.494831\pi$
$677$	0.844994	0.0324758	0.0162379	+	0.999868i	$0.494831\pi$
$678$	3.49460	0.134209
$679$	−7.81431	−0.299886
$680$	130.616	5.00891
$681$	7.57430	0.290248
$682$	96.8576	3.70887
$683$	−36.6169	−1.40111	−0.700553	−	0.713600i	$-0.747063\pi$
$683$	−36.6169	−1.40111	−0.700553	+	0.713600i	$0.747063\pi$
$684$	−48.8912	−1.86940
$685$	−36.0537	−1.37754
$686$	−44.6395	−1.70435
$687$	2.05004	0.0782140
$688$	−28.5594	−1.08882
$689$	−2.20288	−0.0839231
$690$	5.87611	0.223700
$691$	−1.03405	−0.0393371	−0.0196686	−	0.999807i	$-0.506261\pi$
$691$	−1.03405	−0.0393371	−0.0196686	+	0.999807i	$0.506261\pi$
$692$	−65.0748	−2.47377
$693$	15.1756	0.576472
$694$	−62.5122	−2.37293
$695$	66.9511	2.53960
$696$	−1.69547	−0.0642666
$697$	27.6135	1.04593
$698$	−29.6039	−1.12053
$699$	5.58866	0.211383
$700$	−66.7097	−2.52139
$701$	−26.3603	−0.995615	−0.497807	−	0.867288i	$-0.665861\pi$
$701$	−26.3603	−0.995615	−0.497807	+	0.867288i	$0.665861\pi$
$702$	−16.1507	−0.609569
$703$	5.45870	0.205879
$704$	3.84098	0.144762
$705$	−5.39065	−0.203024
$706$	13.5201	0.508835
$707$	−21.5621	−0.810925
$708$	15.2937	0.574773
$709$	−42.7996	−1.60737	−0.803686	−	0.595054i	$-0.797131\pi$
$709$	−42.7996	−1.60737	−0.803686	+	0.595054i	$0.797131\pi$
$710$	37.9927	1.42584
$711$	−31.5146	−1.18189
$712$	41.4862	1.55476
$713$	−12.0877	−0.452688
$714$	9.77665	0.365882
$715$	31.8116	1.18969
$716$	63.5694	2.37570
$717$	−7.78412	−0.290703
$718$	−33.2103	−1.23940
$719$	1.29433	0.0482705	0.0241353	−	0.999709i	$-0.492317\pi$
$719$	1.29433	0.0482705	0.0241353	+	0.999709i	$0.492317\pi$
$720$	−80.3238	−2.99349
$721$	1.39197	0.0518397
$722$	9.46809	0.352366
$723$	0.770167	0.0286428
$724$	−24.6847	−0.917401
$725$	−5.20287	−0.193230
$726$	3.76385	0.139690
$727$	−21.5499	−0.799242	−0.399621	−	0.916681i	$-0.630858\pi$
$727$	−21.5499	−0.799242	−0.399621	+	0.916681i	$0.630858\pi$
$728$	21.1536	0.784005
$729$	−14.4991	−0.537004
$730$	45.1871	1.67245
$731$	19.6483	0.726718
$732$	1.06674	0.0394279
$733$	7.96269	0.294109	0.147054	−	0.989128i	$-0.453021\pi$
$733$	7.96269	0.294109	0.147054	+	0.989128i	$0.453021\pi$
$734$	59.9627	2.21326
$735$	9.28639	0.342534
$736$	−7.51907	−0.277157
$737$	−33.2789	−1.22584
$738$	−37.4138	−1.37722
$739$	52.1757	1.91931	0.959657	−	0.281172i	$-0.0907232\pi$
$739$	52.1757	1.91931	0.959657	+	0.281172i	$0.0907232\pi$
$740$	24.5100	0.901005
$741$	−4.29382	−0.157737
$742$	−3.77659	−0.138643
$743$	4.07451	0.149479	0.0747396	−	0.997203i	$-0.476187\pi$
$743$	4.07451	0.149479	0.0747396	+	0.997203i	$0.476187\pi$
$744$	−32.8569	−1.20459
$745$	6.72224	0.246284
$746$	57.4967	2.10510
$747$	0.693674	0.0253802
$748$	−88.1463	−3.22295
$749$	17.6293	0.644162
$750$	24.3746	0.890035
$751$	−10.9751	−0.400487	−0.200243	−	0.979746i	$-0.564173\pi$
$751$	−10.9751	−0.400487	−0.200243	+	0.979746i	$0.564173\pi$
$752$	21.1268	0.770415
$753$	3.58075	0.130490
$754$	2.94753	0.107343
$755$	−3.86602	−0.140699
$756$	−19.2246	−0.699191
$757$	−12.2752	−0.446151	−0.223075	−	0.974801i	$-0.571610\pi$
$757$	−12.2752	−0.446151	−0.223075	+	0.974801i	$0.571610\pi$
$758$	−15.1373	−0.549813
$759$	−2.21961	−0.0805668
$760$	−98.3468	−3.56741
$761$	17.2888	0.626717	0.313358	−	0.949635i	$-0.398546\pi$
$761$	17.2888	0.626717	0.313358	+	0.949635i	$0.398546\pi$
$762$	−2.82888	−0.102480
$763$	2.05083	0.0742451
$764$	32.5212	1.17658
$765$	55.2611	1.99797
$766$	−57.3166	−2.07093
$767$	−14.8820	−0.537358
$768$	13.7484	0.496101
$769$	4.07055	0.146788	0.0733939	−	0.997303i	$-0.476617\pi$
$769$	4.07055	0.146788	0.0733939	+	0.997303i	$0.476617\pi$
$770$	54.5373	1.96539
$771$	0.286814	0.0103293
$772$	−7.05903	−0.254060
$773$	−26.0782	−0.937968	−0.468984	−	0.883207i	$-0.655380\pi$
$773$	−26.0782	−0.937968	−0.468984	+	0.883207i	$0.655380\pi$
$774$	−26.6217	−0.956897
$775$	−100.828	−3.62184
$776$	−34.4224	−1.23569
$777$	1.02687	0.0368388
$778$	−45.2757	−1.62321
$779$	−20.7914	−0.744929
$780$	−19.2796	−0.690320
$781$	−14.3512	−0.513526
$782$	15.8437	0.566570
$783$	−1.49938	−0.0535833
$784$	−36.3948	−1.29981
$785$	−68.1203	−2.43132
$786$	−23.2649	−0.829833
$787$	−46.0299	−1.64079	−0.820393	−	0.571799i	$-0.806246\pi$
$787$	−46.0299	−1.64079	−0.820393	+	0.571799i	$0.806246\pi$
$788$	1.73060	0.0616500
$789$	6.30988	0.224638
$790$	−113.256	−4.02946
$791$	−4.04774	−0.143921
$792$	66.8491	2.37538
$793$	−1.03802	−0.0368613
$794$	11.1521	0.395772
$795$	1.92661	0.0683298
$796$	18.2178	0.645712
$797$	−4.65884	−0.165025	−0.0825123	−	0.996590i	$-0.526294\pi$
$797$	−4.65884	−0.165025	−0.0825123	+	0.996590i	$0.526294\pi$
$798$	−7.36127	−0.260586
$799$	−14.5348	−0.514204
$800$	−62.7192	−2.21746
$801$	17.5519	0.620167
$802$	91.4147	3.22796
$803$	−17.0687	−0.602342
$804$	20.1689	0.711301
$805$	−6.80619	−0.239887
$806$	57.1209	2.01200
$807$	−8.58906	−0.302349
$808$	−94.9820	−3.34146
$809$	−45.4005	−1.59620	−0.798098	−	0.602527i	$-0.794160\pi$
$809$	−45.4005	−1.59620	−0.798098	+	0.602527i	$0.794160\pi$
$810$	−67.5063	−2.37193
$811$	−46.3228	−1.62661	−0.813306	−	0.581836i	$-0.802335\pi$
$811$	−46.3228	−1.62661	−0.813306	+	0.581836i	$0.802335\pi$
$812$	3.50852	0.123125
$813$	−9.42743	−0.330634
$814$	−13.3344	−0.467370
$815$	−85.4283	−2.99242
$816$	19.5468	0.684275
$817$	−14.7941	−0.517578
$818$	19.6201	0.686000
$819$	8.94965	0.312726
$820$	−93.3550	−3.26010
$821$	−18.4985	−0.645604	−0.322802	−	0.946467i	$-0.604625\pi$
$821$	−18.4985	−0.645604	−0.322802	+	0.946467i	$0.604625\pi$
$822$	−11.8876	−0.414626
$823$	−42.2939	−1.47427	−0.737136	−	0.675744i	$-0.763822\pi$
$823$	−42.2939	−1.47427	−0.737136	+	0.675744i	$0.763822\pi$
$824$	6.13169	0.213608
$825$	−18.5146	−0.644594
$826$	−25.5135	−0.887728
$827$	43.3852	1.50865	0.754325	−	0.656501i	$-0.227964\pi$
$827$	43.3852	1.50865	0.754325	+	0.656501i	$0.227964\pi$
$828$	−14.9048	−0.517976
$829$	30.8204	1.07044	0.535218	−	0.844714i	$-0.320230\pi$
$829$	30.8204	1.07044	0.535218	+	0.844714i	$0.320230\pi$
$830$	2.49290	0.0865297
$831$	−3.04021	−0.105464
$832$	2.26518	0.0785311
$833$	25.0388	0.867544
$834$	22.0750	0.764395
$835$	−93.4373	−3.23353
$836$	66.3692	2.29543
$837$	−29.0568	−1.00435
$838$	−96.7019	−3.34051
$839$	45.2318	1.56157	0.780787	−	0.624797i	$-0.214818\pi$
$839$	45.2318	1.56157	0.780787	+	0.624797i	$0.214818\pi$
$840$	−18.5007	−0.638334
$841$	−28.7264	−0.990564
$842$	−48.4823	−1.67081
$843$	−3.40480	−0.117268
$844$	58.2591	2.00536
$845$	−31.4977	−1.08355
$846$	19.6933	0.677071
$847$	−4.35960	−0.149798
$848$	−7.55068	−0.259291
$849$	12.4961	0.428866
$850$	132.158	4.53298
$851$	1.66411	0.0570451
$852$	8.69762	0.297976
$853$	−17.4016	−0.595818	−0.297909	−	0.954594i	$-0.596289\pi$
$853$	−17.4016	−0.595818	−0.297909	+	0.954594i	$0.596289\pi$
$854$	−1.77957	−0.0608958
$855$	−41.6085	−1.42298
$856$	77.6581	2.65430
$857$	−6.42925	−0.219619	−0.109810	−	0.993953i	$-0.535024\pi$
$857$	−6.42925	−0.219619	−0.109810	+	0.993953i	$0.535024\pi$
$858$	10.4889	0.358084
$859$	−21.0255	−0.717380	−0.358690	−	0.933457i	$-0.616776\pi$
$859$	−21.0255	−0.717380	−0.358690	+	0.933457i	$0.616776\pi$
$860$	−66.4265	−2.26513
$861$	−3.91120	−0.133293
$862$	−94.7241	−3.22631
$863$	−23.8923	−0.813302	−0.406651	−	0.913584i	$-0.633304\pi$
$863$	−23.8923	−0.813302	−0.406651	+	0.913584i	$0.633304\pi$
$864$	−18.0746	−0.614910
$865$	−55.3814	−1.88302
$866$	77.4273	2.63109
$867$	−4.97595	−0.168992
$868$	67.9924	2.30781
$869$	42.7807	1.45123
$870$	−2.57787	−0.0873979
$871$	−19.6259	−0.664999
$872$	9.03402	0.305931
$873$	−14.5634	−0.492897
$874$	−11.9294	−0.403519
$875$	−28.2327	−0.954438
$876$	10.3446	0.349512
$877$	4.61639	0.155885	0.0779423	−	0.996958i	$-0.475165\pi$
$877$	4.61639	0.155885	0.0779423	+	0.996958i	$0.475165\pi$
$878$	−27.7621	−0.936924
$879$	−0.423024	−0.0142682
$880$	109.039	3.67569
$881$	43.9708	1.48141	0.740707	−	0.671828i	$-0.234491\pi$
$881$	43.9708	1.48141	0.740707	+	0.671828i	$0.234491\pi$
$882$	−33.9254	−1.14233
$883$	12.4428	0.418734	0.209367	−	0.977837i	$-0.432860\pi$
$883$	12.4428	0.418734	0.209367	+	0.977837i	$0.432860\pi$
$884$	−51.9835	−1.74839
$885$	13.0156	0.437514
$886$	12.0566	0.405051
$887$	22.9618	0.770983	0.385491	−	0.922711i	$-0.374032\pi$
$887$	22.9618	0.770983	0.385491	+	0.922711i	$0.374032\pi$
$888$	4.52342	0.151796
$889$	3.27664	0.109895
$890$	63.0774	2.11436
$891$	25.4995	0.854265
$892$	53.7917	1.80108
$893$	10.9439	0.366223
$894$	2.21645	0.0741291
$895$	54.1003	1.80837
$896$	−14.7374	−0.492341
$897$	−1.30900	−0.0437061
$898$	92.6291	3.09107
$899$	5.30291	0.176862
$900$	−124.326	−4.14420
$901$	5.19471	0.173061
$902$	50.7888	1.69108
$903$	−2.78301	−0.0926127
$904$	−17.8305	−0.593033
$905$	−21.0078	−0.698322
$906$	−1.27470	−0.0423490
$907$	−25.1422	−0.834832	−0.417416	−	0.908715i	$-0.637064\pi$
$907$	−25.1422	−0.834832	−0.417416	+	0.908715i	$0.637064\pi$
$908$	−69.0442	−2.29131
$909$	−40.1849	−1.33285
$910$	32.1629	1.06619
$911$	30.1805	0.999925	0.499963	−	0.866047i	$-0.333347\pi$
$911$	30.1805	0.999925	0.499963	+	0.866047i	$0.333347\pi$
$912$	−14.7177	−0.487350
$913$	−0.941654	−0.0311642
$914$	91.7360	3.03436
$915$	0.907841	0.0300123
$916$	−18.6873	−0.617446
$917$	26.9473	0.889880
$918$	38.0856	1.25701
$919$	−22.9841	−0.758175	−0.379088	−	0.925361i	$-0.623762\pi$
$919$	−22.9841	−0.758175	−0.379088	+	0.925361i	$0.623762\pi$
$920$	−29.9816	−0.988464
$921$	7.73669	0.254933
$922$	−13.9712	−0.460117
$923$	−8.46348	−0.278579
$924$	12.4852	0.410731
$925$	13.8810	0.456403
$926$	49.8439	1.63797
$927$	2.59419	0.0852044
$928$	3.29864	0.108283
$929$	20.0132	0.656613	0.328306	−	0.944571i	$-0.393522\pi$
$929$	20.0132	0.656613	0.328306	+	0.944571i	$0.393522\pi$
$930$	−49.9571	−1.63816
$931$	−18.8528	−0.617877
$932$	−50.9439	−1.66872
$933$	−5.48080	−0.179433
$934$	−59.9262	−1.96084
$935$	−75.0162	−2.45329
$936$	39.4237	1.28860
$937$	8.28447	0.270642	0.135321	−	0.990802i	$-0.456793\pi$
$937$	8.28447	0.270642	0.135321	+	0.990802i	$0.456793\pi$
$938$	−33.6464	−1.09859
$939$	−2.07624	−0.0677554
$940$	49.1389	1.60273
$941$	11.6577	0.380031	0.190015	−	0.981781i	$-0.439146\pi$
$941$	11.6577	0.380031	0.190015	+	0.981781i	$0.439146\pi$
$942$	−22.4605	−0.731803
$943$	−6.33837	−0.206406
$944$	−51.0101	−1.66024
$945$	−16.3609	−0.532221
$946$	36.1386	1.17497
$947$	51.4962	1.67340	0.836700	−	0.547661i	$-0.184482\pi$
$947$	51.4962	1.67340	0.836700	+	0.547661i	$0.184482\pi$
$948$	−25.9275	−0.842085
$949$	−10.0661	−0.326760
$950$	−99.5076	−3.22845
$951$	3.77330	0.122358
$952$	−49.8833	−1.61673
$953$	18.2894	0.592453	0.296226	−	0.955118i	$-0.404272\pi$
$953$	18.2894	0.592453	0.296226	+	0.955118i	$0.404272\pi$
$954$	−7.03837	−0.227876
$955$	27.6769	0.895604
$956$	70.9567	2.29490
$957$	0.973750	0.0314769
$958$	32.4694	1.04904
$959$	13.7691	0.444629
$960$	−1.98110	−0.0639396
$961$	71.7665	2.31505
$962$	−7.86384	−0.253540
$963$	32.8555	1.05875
$964$	−7.02052	−0.226116
$965$	−6.00753	−0.193389
$966$	−2.24412	−0.0722035
$967$	28.4295	0.914231	0.457115	−	0.889407i	$-0.348883\pi$
$967$	28.4295	0.914231	0.457115	+	0.889407i	$0.348883\pi$
$968$	−19.2043	−0.617248
$969$	10.1254	0.325276
$970$	−52.3374	−1.68045
$971$	−6.45816	−0.207252	−0.103626	−	0.994616i	$-0.533045\pi$
$971$	−6.45816	−0.207252	−0.103626	+	0.994616i	$0.533045\pi$
$972$	−54.5163	−1.74861
$973$	−25.5691	−0.819706
$974$	−19.9514	−0.639284
$975$	−10.9188	−0.349681
$976$	−3.55797	−0.113888
$977$	32.9445	1.05399	0.526993	−	0.849869i	$-0.323319\pi$
$977$	32.9445	1.05399	0.526993	+	0.849869i	$0.323319\pi$
$978$	−28.1673	−0.900690
$979$	−23.8265	−0.761500
$980$	−84.6508	−2.70407
$981$	3.82210	0.122030
$982$	−53.3678	−1.70304
$983$	−58.3607	−1.86142	−0.930708	−	0.365763i	$-0.880808\pi$
$983$	−58.3607	−1.86142	−0.930708	+	0.365763i	$0.880808\pi$
$984$	−17.2290	−0.549242
$985$	1.47281	0.0469277
$986$	−6.95069	−0.221355
$987$	2.05872	0.0655299
$988$	39.1407	1.24523
$989$	−4.51005	−0.143411
$990$	101.640	3.23034
$991$	0.429961	0.0136582	0.00682908	−	0.999977i	$-0.497826\pi$
$991$	0.429961	0.0136582	0.00682908	+	0.999977i	$0.497826\pi$
$992$	63.9252	2.02963
$993$	9.54573	0.302925
$994$	−14.5097	−0.460219
$995$	15.5041	0.491513
$996$	0.570695	0.0180832
$997$	55.6201	1.76151	0.880753	−	0.473577i	$-0.157037\pi$
$997$	55.6201	1.76151	0.880753	+	0.473577i	$0.157037\pi$
$998$	−23.9712	−0.758796
$999$	4.00025	0.126562

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8003.2.a.b.1.7	✓	153

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8003.2.a.b.1.7	✓	153	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)

\(f(q)\)	\(=\)	\(q-2.55787 q^{2} -0.498344 q^{3} +4.54269 q^{4} +3.86602 q^{5} +1.27470 q^{6} -1.47646 q^{7} -6.50388 q^{8} -2.75165 q^{9} +O(q^{10})\)	\(q-2.55787 q^{2} -0.498344 q^{3} +4.54269 q^{4} +3.86602 q^{5} +1.27470 q^{6} -1.47646 q^{7} -6.50388 q^{8} -2.75165 q^{9} -9.88878 q^{10} +3.73534 q^{11} -2.26382 q^{12} +2.20288 q^{13} +3.77659 q^{14} -1.92661 q^{15} +7.55068 q^{16} -5.19471 q^{17} +7.03837 q^{18} +3.91132 q^{19} +17.5622 q^{20} +0.735785 q^{21} -9.55450 q^{22} +1.19239 q^{23} +3.24117 q^{24} +9.94613 q^{25} -5.63468 q^{26} +2.86630 q^{27} -6.70710 q^{28} -0.523105 q^{29} +4.92801 q^{30} -10.1374 q^{31} -6.30589 q^{32} -1.86148 q^{33} +13.2874 q^{34} -5.70803 q^{35} -12.4999 q^{36} +1.39561 q^{37} -10.0047 q^{38} -1.09779 q^{39} -25.1441 q^{40} -5.31569 q^{41} -1.88204 q^{42} -3.78237 q^{43} +16.9685 q^{44} -10.6380 q^{45} -3.04997 q^{46} +2.79800 q^{47} -3.76283 q^{48} -4.82007 q^{49} -25.4409 q^{50} +2.58875 q^{51} +10.0070 q^{52} -1.00000 q^{53} -7.33162 q^{54} +14.4409 q^{55} +9.60271 q^{56} -1.94918 q^{57} +1.33803 q^{58} -6.75570 q^{59} -8.75199 q^{60} -0.471212 q^{61} +25.9301 q^{62} +4.06270 q^{63} +1.02828 q^{64} +8.51639 q^{65} +4.76143 q^{66} -8.90921 q^{67} -23.5980 q^{68} -0.594220 q^{69} +14.6004 q^{70} -3.84201 q^{71} +17.8964 q^{72} -4.56953 q^{73} -3.56980 q^{74} -4.95660 q^{75} +17.7679 q^{76} -5.51507 q^{77} +2.80801 q^{78} +11.4530 q^{79} +29.1911 q^{80} +6.82656 q^{81} +13.5968 q^{82} -0.252093 q^{83} +3.34244 q^{84} -20.0829 q^{85} +9.67480 q^{86} +0.260686 q^{87} -24.2942 q^{88} -6.37869 q^{89} +27.2105 q^{90} -3.25246 q^{91} +5.41666 q^{92} +5.05190 q^{93} -7.15691 q^{94} +15.1213 q^{95} +3.14250 q^{96} +5.29260 q^{97} +12.3291 q^{98} -10.2784 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 153 q - 9 q^{2} - 17 q^{3} + 137 q^{4} - 31 q^{5} - 10 q^{6} - 17 q^{7} - 30 q^{8} + 136 q^{9}+O(q^{10}) \) 153 * q - 9 * q^2 - 17 * q^3 + 137 * q^4 - 31 * q^5 - 10 * q^6 - 17 * q^7 - 30 * q^8 + 136 * q^9	\( 153 q - 9 q^{2} - 17 q^{3} + 137 q^{4} - 31 q^{5} - 10 q^{6} - 17 q^{7} - 30 q^{8} + 136 q^{9} - 34 q^{10} - q^{11} - 60 q^{12} - 101 q^{13} - 16 q^{14} - 14 q^{15} + 97 q^{16} - 12 q^{17} - 45 q^{18} - 45 q^{19} - 52 q^{20} - 76 q^{21} - 46 q^{22} - 28 q^{23} - 30 q^{24} + 84 q^{25} - 22 q^{26} - 68 q^{27} - 64 q^{28} - 14 q^{29} - q^{30} - 70 q^{31} - 54 q^{32} - 85 q^{33} - 59 q^{34} - 16 q^{35} + 87 q^{36} - 167 q^{37} - 48 q^{38} - 28 q^{39} - 68 q^{40} - 38 q^{41} + 2 q^{42} - 71 q^{43} - 10 q^{44} - 151 q^{45} - 37 q^{46} - 37 q^{47} - 166 q^{48} + 74 q^{49} - 3 q^{50} - 11 q^{51} - 183 q^{52} - 153 q^{53} - 40 q^{54} - 88 q^{55} - 69 q^{56} - 26 q^{57} - 43 q^{58} - 34 q^{59} - 12 q^{60} - 90 q^{61} - 37 q^{62} - 36 q^{63} + 58 q^{64} - 19 q^{65} + 52 q^{66} - 86 q^{67} - 22 q^{68} - 81 q^{69} - 144 q^{70} - 50 q^{71} - 190 q^{72} - 171 q^{73} - 14 q^{74} - 69 q^{75} - 88 q^{76} - 72 q^{77} - 61 q^{78} - 13 q^{79} - 84 q^{80} + 117 q^{81} - 124 q^{82} - 72 q^{83} - 106 q^{84} - 193 q^{85} - 44 q^{86} - 65 q^{87} - 89 q^{88} - 10 q^{89} - 152 q^{90} - 67 q^{91} - 29 q^{92} - 129 q^{93} - 43 q^{94} - 29 q^{95} - 106 q^{96} - 177 q^{97} - 69 q^{98} - 11 q^{99}+O(q^{100}) \) 153 * q - 9 * q^2 - 17 * q^3 + 137 * q^4 - 31 * q^5 - 10 * q^6 - 17 * q^7 - 30 * q^8 + 136 * q^9 - 34 * q^10 - q^11 - 60 * q^12 - 101 * q^13 - 16 * q^14 - 14 * q^15 + 97 * q^16 - 12 * q^17 - 45 * q^18 - 45 * q^19 - 52 * q^20 - 76 * q^21 - 46 * q^22 - 28 * q^23 - 30 * q^24 + 84 * q^25 - 22 * q^26 - 68 * q^27 - 64 * q^28 - 14 * q^29 - q^30 - 70 * q^31 - 54 * q^32 - 85 * q^33 - 59 * q^34 - 16 * q^35 + 87 * q^36 - 167 * q^37 - 48 * q^38 - 28 * q^39 - 68 * q^40 - 38 * q^41 + 2 * q^42 - 71 * q^43 - 10 * q^44 - 151 * q^45 - 37 * q^46 - 37 * q^47 - 166 * q^48 + 74 * q^49 - 3 * q^50 - 11 * q^51 - 183 * q^52 - 153 * q^53 - 40 * q^54 - 88 * q^55 - 69 * q^56 - 26 * q^57 - 43 * q^58 - 34 * q^59 - 12 * q^60 - 90 * q^61 - 37 * q^62 - 36 * q^63 + 58 * q^64 - 19 * q^65 + 52 * q^66 - 86 * q^67 - 22 * q^68 - 81 * q^69 - 144 * q^70 - 50 * q^71 - 190 * q^72 - 171 * q^73 - 14 * q^74 - 69 * q^75 - 88 * q^76 - 72 * q^77 - 61 * q^78 - 13 * q^79 - 84 * q^80 + 117 * q^81 - 124 * q^82 - 72 * q^83 - 106 * q^84 - 193 * q^85 - 44 * q^86 - 65 * q^87 - 89 * q^88 - 10 * q^89 - 152 * q^90 - 67 * q^91 - 29 * q^92 - 129 * q^93 - 43 * q^94 - 29 * q^95 - 106 * q^96 - 177 * q^97 - 69 * q^98 - 11 * q^99

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