LMFDB - Embedded newform 4003.2.a.c.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4003,2,Mod(1,4003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4003, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4003.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:	$31.9641159291$
Analytic rank:	$0$
Dimension:	$179$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	4003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.60379 q^{2} +0.316007 q^{3} +4.77975 q^{4} +1.57805 q^{5} -0.822817 q^{6} +2.80041 q^{7} -7.23789 q^{8} -2.90014 q^{9} +O(q^{10})$	\(q-2.60379 q^{2} +0.316007 q^{3} +4.77975 q^{4} +1.57805 q^{5} -0.822817 q^{6} +2.80041 q^{7} -7.23789 q^{8} -2.90014 q^{9} -4.10892 q^{10} +1.05246 q^{11} +1.51043 q^{12} +1.29122 q^{13} -7.29169 q^{14} +0.498675 q^{15} +9.28647 q^{16} +2.11989 q^{17} +7.55137 q^{18} +4.99475 q^{19} +7.54268 q^{20} +0.884949 q^{21} -2.74039 q^{22} +7.80822 q^{23} -2.28722 q^{24} -2.50975 q^{25} -3.36208 q^{26} -1.86448 q^{27} +13.3852 q^{28} +6.12200 q^{29} -1.29845 q^{30} -6.15798 q^{31} -9.70430 q^{32} +0.332584 q^{33} -5.51976 q^{34} +4.41919 q^{35} -13.8619 q^{36} +7.71921 q^{37} -13.0053 q^{38} +0.408036 q^{39} -11.4218 q^{40} +2.40798 q^{41} -2.30423 q^{42} -10.2280 q^{43} +5.03049 q^{44} -4.57657 q^{45} -20.3310 q^{46} +3.26833 q^{47} +2.93459 q^{48} +0.842299 q^{49} +6.53488 q^{50} +0.669901 q^{51} +6.17172 q^{52} -7.78005 q^{53} +4.85474 q^{54} +1.66083 q^{55} -20.2690 q^{56} +1.57838 q^{57} -15.9404 q^{58} +9.71469 q^{59} +2.38354 q^{60} +4.92650 q^{61} +16.0341 q^{62} -8.12158 q^{63} +6.69505 q^{64} +2.03762 q^{65} -0.865981 q^{66} -12.3095 q^{67} +10.1325 q^{68} +2.46745 q^{69} -11.5067 q^{70} +9.20342 q^{71} +20.9909 q^{72} -1.59934 q^{73} -20.0992 q^{74} -0.793099 q^{75} +23.8736 q^{76} +2.94732 q^{77} -1.06244 q^{78} -5.44023 q^{79} +14.6545 q^{80} +8.11123 q^{81} -6.26989 q^{82} +11.0791 q^{83} +4.22983 q^{84} +3.34530 q^{85} +26.6317 q^{86} +1.93460 q^{87} -7.61758 q^{88} +15.9788 q^{89} +11.9164 q^{90} +3.61596 q^{91} +37.3213 q^{92} -1.94596 q^{93} -8.51006 q^{94} +7.88198 q^{95} -3.06663 q^{96} -4.95819 q^{97} -2.19317 q^{98} -3.05228 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 179 q + 22 q^{2} + 16 q^{3} + 196 q^{4} + 61 q^{5} + 7 q^{6} + 21 q^{7} + 60 q^{8} + 221 q^{9}+O(q^{10}) $ 179 * q + 22 * q^2 + 16 * q^3 + 196 * q^4 + 61 * q^5 + 7 * q^6 + 21 * q^7 + 60 * q^8 + 221 * q^9	\( 179 q + 22 q^{2} + 16 q^{3} + 196 q^{4} + 61 q^{5} + 7 q^{6} + 21 q^{7} + 60 q^{8} + 221 q^{9} + 9 q^{10} + 46 q^{11} + 33 q^{12} + 47 q^{13} + 22 q^{14} + 36 q^{15} + 222 q^{16} + 103 q^{17} + 43 q^{18} + 12 q^{19} + 102 q^{20} + 50 q^{21} + 39 q^{22} + 121 q^{23} - 3 q^{24} + 246 q^{25} + 52 q^{26} + 49 q^{27} + 41 q^{28} + 138 q^{29} + 28 q^{30} + 5 q^{31} + 137 q^{32} + 63 q^{33} + 2 q^{34} + 72 q^{35} + 279 q^{36} + 118 q^{37} + 123 q^{38} + q^{39} + 9 q^{40} + 50 q^{41} + 48 q^{42} + 48 q^{43} + 108 q^{44} + 158 q^{45} + 13 q^{46} + 85 q^{47} + 50 q^{48} + 230 q^{49} + 78 q^{50} + 15 q^{51} + 41 q^{52} + 399 q^{53} - 5 q^{54} + 24 q^{55} + 53 q^{56} + 45 q^{57} + 27 q^{58} + 48 q^{59} + 66 q^{60} + 46 q^{61} + 81 q^{62} + 78 q^{63} + 252 q^{64} + 153 q^{65} + 6 q^{66} + 70 q^{67} + 240 q^{68} + 120 q^{69} - 31 q^{70} + 86 q^{71} + 89 q^{72} + 45 q^{73} + 68 q^{74} + 17 q^{75} - 13 q^{76} + 362 q^{77} + 69 q^{78} + 31 q^{79} + 169 q^{80} + 303 q^{81} + 25 q^{82} + 106 q^{83} + 13 q^{84} + 115 q^{85} + 95 q^{86} + 32 q^{87} + 83 q^{88} + 105 q^{89} - 38 q^{90} + 3 q^{91} + 310 q^{92} + 298 q^{93} - 17 q^{94} + 102 q^{95} - 82 q^{96} + 34 q^{97} + 81 q^{98} + 58 q^{99}+O(q^{100}) \) 179 * q + 22 * q^2 + 16 * q^3 + 196 * q^4 + 61 * q^5 + 7 * q^6 + 21 * q^7 + 60 * q^8 + 221 * q^9 + 9 * q^10 + 46 * q^11 + 33 * q^12 + 47 * q^13 + 22 * q^14 + 36 * q^15 + 222 * q^16 + 103 * q^17 + 43 * q^18 + 12 * q^19 + 102 * q^20 + 50 * q^21 + 39 * q^22 + 121 * q^23 - 3 * q^24 + 246 * q^25 + 52 * q^26 + 49 * q^27 + 41 * q^28 + 138 * q^29 + 28 * q^30 + 5 * q^31 + 137 * q^32 + 63 * q^33 + 2 * q^34 + 72 * q^35 + 279 * q^36 + 118 * q^37 + 123 * q^38 + q^39 + 9 * q^40 + 50 * q^41 + 48 * q^42 + 48 * q^43 + 108 * q^44 + 158 * q^45 + 13 * q^46 + 85 * q^47 + 50 * q^48 + 230 * q^49 + 78 * q^50 + 15 * q^51 + 41 * q^52 + 399 * q^53 - 5 * q^54 + 24 * q^55 + 53 * q^56 + 45 * q^57 + 27 * q^58 + 48 * q^59 + 66 * q^60 + 46 * q^61 + 81 * q^62 + 78 * q^63 + 252 * q^64 + 153 * q^65 + 6 * q^66 + 70 * q^67 + 240 * q^68 + 120 * q^69 - 31 * q^70 + 86 * q^71 + 89 * q^72 + 45 * q^73 + 68 * q^74 + 17 * q^75 - 13 * q^76 + 362 * q^77 + 69 * q^78 + 31 * q^79 + 169 * q^80 + 303 * q^81 + 25 * q^82 + 106 * q^83 + 13 * q^84 + 115 * q^85 + 95 * q^86 + 32 * q^87 + 83 * q^88 + 105 * q^89 - 38 * q^90 + 3 * q^91 + 310 * q^92 + 298 * q^93 - 17 * q^94 + 102 * q^95 - 82 * q^96 + 34 * q^97 + 81 * q^98 + 58 * 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 $

$2$	−2.60379	−1.84116	−0.920580	−	0.390553i	$-0.872284\pi$
$2$	−2.60379	−1.84116	−0.920580	+	0.390553i	$0.872284\pi$
$3$	0.316007	0.182447	0.0912233	−	0.995830i	$-0.470922\pi$
$3$	0.316007	0.182447	0.0912233	+	0.995830i	$0.470922\pi$
$4$	4.77975	2.38987
$5$	1.57805	0.705726	0.352863	−	0.935675i	$-0.385208\pi$
$5$	1.57805	0.705726	0.352863	+	0.935675i	$0.385208\pi$
$6$	−0.822817	−0.335914
$7$	2.80041	1.05846	0.529228	−	0.848480i	$-0.322482\pi$
$7$	2.80041	1.05846	0.529228	+	0.848480i	$0.322482\pi$
$8$	−7.23789	−2.55898
$9$	−2.90014	−0.966713
$10$	−4.10892	−1.29936
$11$	1.05246	0.317328	0.158664	−	0.987333i	$-0.449281\pi$
$11$	1.05246	0.317328	0.158664	+	0.987333i	$0.449281\pi$
$12$	1.51043	0.436024
$13$	1.29122	0.358121	0.179061	−	0.983838i	$-0.442694\pi$
$13$	1.29122	0.358121	0.179061	+	0.983838i	$0.442694\pi$
$14$	−7.29169	−1.94879
$15$	0.498675	0.128757
$16$	9.28647	2.32162
$17$	2.11989	0.514149	0.257075	−	0.966392i	$-0.417241\pi$
$17$	2.11989	0.514149	0.257075	+	0.966392i	$0.417241\pi$
$18$	7.55137	1.77987
$19$	4.99475	1.14587	0.572937	−	0.819599i	$-0.305804\pi$
$19$	4.99475	1.14587	0.572937	+	0.819599i	$0.305804\pi$
$20$	7.54268	1.68660
$21$	0.884949	0.193112
$22$	−2.74039	−0.584252
$23$	7.80822	1.62813	0.814063	−	0.580776i	$-0.197251\pi$
$23$	7.80822	1.62813	0.814063	+	0.580776i	$0.197251\pi$
$24$	−2.28722	−0.466877
$25$	−2.50975	−0.501951
$26$	−3.36208	−0.659359
$27$	−1.86448	−0.358820
$28$	13.3852	2.52957
$29$	6.12200	1.13683	0.568414	−	0.822743i	$-0.307557\pi$
$29$	6.12200	1.13683	0.568414	+	0.822743i	$0.307557\pi$
$30$	−1.29845	−0.237063
$31$	−6.15798	−1.10601	−0.553003	−	0.833179i	$-0.686518\pi$
$31$	−6.15798	−1.10601	−0.553003	+	0.833179i	$0.686518\pi$
$32$	−9.70430	−1.71549
$33$	0.332584	0.0578955
$34$	−5.51976	−0.946632
$35$	4.41919	0.746980
$36$	−13.8619	−2.31032
$37$	7.71921	1.26903	0.634515	−	0.772911i	$-0.281200\pi$
$37$	7.71921	1.26903	0.634515	+	0.772911i	$0.281200\pi$
$38$	−13.0053	−2.10974
$39$	0.408036	0.0653380
$40$	−11.4218	−1.80594
$41$	2.40798	0.376064	0.188032	−	0.982163i	$-0.439789\pi$
$41$	2.40798	0.376064	0.188032	+	0.982163i	$0.439789\pi$
$42$	−2.30423	−0.355550
$43$	−10.2280	−1.55976	−0.779880	−	0.625929i	$-0.784720\pi$
$43$	−10.2280	−1.55976	−0.779880	+	0.625929i	$0.784720\pi$
$44$	5.03049	0.758374
$45$	−4.57657	−0.682235
$46$	−20.3310	−2.99764
$47$	3.26833	0.476735	0.238367	−	0.971175i	$-0.423388\pi$
$47$	3.26833	0.476735	0.238367	+	0.971175i	$0.423388\pi$
$48$	2.93459	0.423572
$49$	0.842299	0.120328
$50$	6.53488	0.924172
$51$	0.669901	0.0938048
$52$	6.17172	0.855864
$53$	−7.78005	−1.06867	−0.534336	−	0.845272i	$-0.679438\pi$
$53$	−7.78005	−1.06867	−0.534336	+	0.845272i	$0.679438\pi$
$54$	4.85474	0.660646
$55$	1.66083	0.223947
$56$	−20.2690	−2.70857
$57$	1.57838	0.209061
$58$	−15.9404	−2.09308
$59$	9.71469	1.26475	0.632373	−	0.774664i	$-0.282081\pi$
$59$	9.71469	1.26475	0.632373	+	0.774664i	$0.282081\pi$
$60$	2.38354	0.307714
$61$	4.92650	0.630774	0.315387	−	0.948963i	$-0.397866\pi$
$61$	4.92650	0.630774	0.315387	+	0.948963i	$0.397866\pi$
$62$	16.0341	2.03633
$63$	−8.12158	−1.02322
$64$	6.69505	0.836881
$65$	2.03762	0.252735
$66$	−0.865981	−0.106595
$67$	−12.3095	−1.50384	−0.751919	−	0.659255i	$-0.770872\pi$
$67$	−12.3095	−1.50384	−0.751919	+	0.659255i	$0.770872\pi$
$68$	10.1325	1.22875
$69$	2.46745	0.297046
$70$	−11.5067	−1.37531
$71$	9.20342	1.09225	0.546123	−	0.837705i	$-0.316103\pi$
$71$	9.20342	1.09225	0.546123	+	0.837705i	$0.316103\pi$
$72$	20.9909	2.47380
$73$	−1.59934	−0.187188	−0.0935940	−	0.995610i	$-0.529836\pi$
$73$	−1.59934	−0.187188	−0.0935940	+	0.995610i	$0.529836\pi$
$74$	−20.0992	−2.33649
$75$	−0.793099	−0.0915792
$76$	23.8736	2.73850
$77$	2.94732	0.335878
$78$	−1.06244	−0.120298
$79$	−5.44023	−0.612074	−0.306037	−	0.952020i	$-0.599003\pi$
$79$	−5.44023	−0.612074	−0.306037	+	0.952020i	$0.599003\pi$
$80$	14.6545	1.63843
$81$	8.11123	0.901248
$82$	−6.26989	−0.692394
$83$	11.0791	1.21609	0.608043	−	0.793904i	$-0.291955\pi$
$83$	11.0791	1.21609	0.608043	+	0.793904i	$0.291955\pi$
$84$	4.22983	0.461512
$85$	3.34530	0.362849
$86$	26.6317	2.87177
$87$	1.93460	0.207410
$88$	−7.61758	−0.812036
$89$	15.9788	1.69375	0.846873	−	0.531795i	$-0.178482\pi$
$89$	15.9788	1.69375	0.846873	+	0.531795i	$0.178482\pi$
$90$	11.9164	1.25610
$91$	3.61596	0.379055
$92$	37.3213	3.89101
$93$	−1.94596	−0.201787
$94$	−8.51006	−0.877745
$95$	7.88198	0.808674
$96$	−3.06663	−0.312986
$97$	−4.95819	−0.503428	−0.251714	−	0.967802i	$-0.580994\pi$
$97$	−4.95819	−0.503428	−0.251714	+	0.967802i	$0.580994\pi$
$98$	−2.19317	−0.221544
$99$	−3.05228	−0.306765
$100$	−11.9960	−1.19960
$101$	−1.88212	−0.187277	−0.0936387	−	0.995606i	$-0.529850\pi$
$101$	−1.88212	−0.187277	−0.0936387	+	0.995606i	$0.529850\pi$
$102$	−1.74428	−0.172710
$103$	1.29776	0.127872	0.0639360	−	0.997954i	$-0.479635\pi$
$103$	1.29776	0.127872	0.0639360	+	0.997954i	$0.479635\pi$
$104$	−9.34573	−0.916425
$105$	1.39650	0.136284
$106$	20.2576	1.96760
$107$	−15.1283	−1.46251	−0.731253	−	0.682106i	$-0.761064\pi$
$107$	−15.1283	−1.46251	−0.731253	+	0.682106i	$0.761064\pi$
$108$	−8.91176	−0.857535
$109$	1.82182	0.174499	0.0872493	−	0.996187i	$-0.472192\pi$
$109$	1.82182	0.174499	0.0872493	+	0.996187i	$0.472192\pi$
$110$	−4.32447	−0.412322
$111$	2.43932	0.231530
$112$	26.0059	2.45733
$113$	−1.07750	−0.101363	−0.0506815	−	0.998715i	$-0.516139\pi$
$113$	−1.07750	−0.101363	−0.0506815	+	0.998715i	$0.516139\pi$
$114$	−4.10977	−0.384915
$115$	12.3218	1.14901
$116$	29.2616	2.71687
$117$	−3.74473	−0.346200
$118$	−25.2951	−2.32860
$119$	5.93657	0.544204
$120$	−3.60935	−0.329487
$121$	−9.89233	−0.899303
$122$	−12.8276	−1.16136
$123$	0.760939	0.0686116
$124$	−29.4336	−2.64321
$125$	−11.8508	−1.05997
$126$	21.1469	1.88392
$127$	20.2307	1.79518	0.897592	−	0.440827i	$-0.145315\pi$
$127$	20.2307	1.79518	0.897592	+	0.440827i	$0.145315\pi$
$128$	1.97606	0.174661
$129$	−3.23213	−0.284573
$130$	−5.30554	−0.465327
$131$	9.87709	0.862965	0.431483	−	0.902121i	$-0.357991\pi$
$131$	9.87709	0.862965	0.431483	+	0.902121i	$0.357991\pi$
$132$	1.58967	0.138363
$133$	13.9874	1.21286
$134$	32.0513	2.76881
$135$	−2.94225	−0.253229
$136$	−15.3435	−1.31570
$137$	−8.27990	−0.707399	−0.353700	−	0.935359i	$-0.615077\pi$
$137$	−8.27990	−0.707399	−0.353700	+	0.935359i	$0.615077\pi$
$138$	−6.42474	−0.546910
$139$	8.12202	0.688901	0.344450	−	0.938805i	$-0.388065\pi$
$139$	8.12202	0.688901	0.344450	+	0.938805i	$0.388065\pi$
$140$	21.1226	1.78519
$141$	1.03281	0.0869787
$142$	−23.9638	−2.01100
$143$	1.35896	0.113642
$144$	−26.9321	−2.24434
$145$	9.66084	0.802289
$146$	4.16434	0.344643
$147$	0.266172	0.0219535
$148$	36.8958	3.03282
$149$	−14.6495	−1.20013	−0.600067	−	0.799950i	$-0.704859\pi$
$149$	−14.6495	−1.20013	−0.600067	+	0.799950i	$0.704859\pi$
$150$	2.06507	0.168612
$151$	−7.03608	−0.572588	−0.286294	−	0.958142i	$-0.592423\pi$
$151$	−7.03608	−0.572588	−0.286294	+	0.958142i	$0.592423\pi$
$152$	−36.1514	−2.93227
$153$	−6.14798	−0.497035
$154$	−7.67421	−0.618405
$155$	−9.71761	−0.780537
$156$	1.95031	0.156150
$157$	14.1493	1.12924	0.564619	−	0.825352i	$-0.309023\pi$
$157$	14.1493	1.12924	0.564619	+	0.825352i	$0.309023\pi$
$158$	14.1652	1.12693
$159$	−2.45855	−0.194976
$160$	−15.3139	−1.21067
$161$	21.8662	1.72330
$162$	−21.1200	−1.65934
$163$	20.7437	1.62477	0.812384	−	0.583122i	$-0.198169\pi$
$163$	20.7437	1.62477	0.812384	+	0.583122i	$0.198169\pi$
$164$	11.5095	0.898744
$165$	0.524835	0.0408584
$166$	−28.8476	−2.23901
$167$	2.95856	0.228940	0.114470	−	0.993427i	$-0.463483\pi$
$167$	2.95856	0.228940	0.114470	+	0.993427i	$0.463483\pi$
$168$	−6.40516	−0.494169
$169$	−11.3327	−0.871749
$170$	−8.71047	−0.668063
$171$	−14.4855	−1.10773
$172$	−48.8874	−3.72763
$173$	−4.09080	−0.311018	−0.155509	−	0.987834i	$-0.549702\pi$
$173$	−4.09080	−0.311018	−0.155509	+	0.987834i	$0.549702\pi$
$174$	−5.03729	−0.381876
$175$	−7.02834	−0.531292
$176$	9.77363	0.736715
$177$	3.06991	0.230749
$178$	−41.6054	−3.11846
$179$	−0.743413	−0.0555653	−0.0277826	−	0.999614i	$-0.508845\pi$
$179$	−0.743413	−0.0555653	−0.0277826	+	0.999614i	$0.508845\pi$
$180$	−21.8748	−1.63045
$181$	−20.8643	−1.55083	−0.775416	−	0.631450i	$-0.782460\pi$
$181$	−20.8643	−1.55083	−0.775416	+	0.631450i	$0.782460\pi$
$182$	−9.41521	−0.697902
$183$	1.55681	0.115083
$184$	−56.5150	−4.16634
$185$	12.1813	0.895587
$186$	5.06689	0.371522
$187$	2.23110	0.163154
$188$	15.6218	1.13934
$189$	−5.22132	−0.379795
$190$	−20.5231	−1.48890
$191$	−5.63703	−0.407881	−0.203941	−	0.978983i	$-0.565375\pi$
$191$	−5.63703	−0.407881	−0.203941	+	0.978983i	$0.565375\pi$
$192$	2.11568	0.152686
$193$	6.48044	0.466472	0.233236	−	0.972420i	$-0.425069\pi$
$193$	6.48044	0.466472	0.233236	+	0.972420i	$0.425069\pi$
$194$	12.9101	0.926891
$195$	0.643902	0.0461107
$196$	4.02598	0.287570
$197$	20.7252	1.47661	0.738305	−	0.674467i	$-0.235626\pi$
$197$	20.7252	1.47661	0.738305	+	0.674467i	$0.235626\pi$
$198$	7.94750	0.564804
$199$	−13.3778	−0.948325	−0.474163	−	0.880437i	$-0.657249\pi$
$199$	−13.3778	−0.948325	−0.474163	+	0.880437i	$0.657249\pi$
$200$	18.1653	1.28448
$201$	−3.88987	−0.274370
$202$	4.90064	0.344808
$203$	17.1441	1.20328
$204$	3.20195	0.224182
$205$	3.79992	0.265398
$206$	−3.37910	−0.235433
$207$	−22.6449	−1.57393
$208$	11.9909	0.831421
$209$	5.25677	0.363619
$210$	−3.63619	−0.250921
$211$	−0.846497	−0.0582753	−0.0291376	−	0.999575i	$-0.509276\pi$
$211$	−0.846497	−0.0582753	−0.0291376	+	0.999575i	$0.509276\pi$
$212$	−37.1866	−2.55399
$213$	2.90835	0.199277
$214$	39.3909	2.69271
$215$	−16.1404	−1.10076
$216$	13.4949	0.918214
$217$	−17.2449	−1.17066
$218$	−4.74364	−0.321280
$219$	−0.505401	−0.0341518
$220$	7.93837	0.535204
$221$	2.73726	0.184128
$222$	−6.35149	−0.426284
$223$	−16.3250	−1.09321	−0.546603	−	0.837392i	$-0.684079\pi$
$223$	−16.3250	−1.09321	−0.546603	+	0.837392i	$0.684079\pi$
$224$	−27.1760	−1.81577
$225$	7.27863	0.485242
$226$	2.80560	0.186626
$227$	7.25930	0.481817	0.240908	−	0.970548i	$-0.422555\pi$
$227$	7.25930	0.481817	0.240908	+	0.970548i	$0.422555\pi$
$228$	7.54424	0.499629
$229$	−17.4767	−1.15489	−0.577446	−	0.816429i	$-0.695951\pi$
$229$	−17.4767	−1.15489	−0.577446	+	0.816429i	$0.695951\pi$
$230$	−32.0834	−2.11551
$231$	0.931373	0.0612798
$232$	−44.3104	−2.90912
$233$	−25.1407	−1.64702	−0.823510	−	0.567301i	$-0.807987\pi$
$233$	−25.1407	−1.64702	−0.823510	+	0.567301i	$0.807987\pi$
$234$	9.75051	0.637411
$235$	5.15759	0.336444
$236$	46.4338	3.02258
$237$	−1.71915	−0.111671
$238$	−15.4576	−1.00197
$239$	8.78267	0.568104	0.284052	−	0.958809i	$-0.408321\pi$
$239$	8.78267	0.568104	0.284052	+	0.958809i	$0.408321\pi$
$240$	4.63093	0.298926
$241$	2.92332	0.188308	0.0941538	−	0.995558i	$-0.469985\pi$
$241$	2.92332	0.188308	0.0941538	+	0.995558i	$0.469985\pi$
$242$	25.7576	1.65576
$243$	8.15666	0.523250
$244$	23.5474	1.50747
$245$	1.32919	0.0849189
$246$	−1.98133	−0.126325
$247$	6.44935	0.410362
$248$	44.5707	2.83024
$249$	3.50106	0.221871
$250$	30.8570	1.95157
$251$	−17.5870	−1.11008	−0.555040	−	0.831824i	$-0.687297\pi$
$251$	−17.5870	−1.11008	−0.555040	+	0.831824i	$0.687297\pi$
$252$	−38.8191	−2.44537
$253$	8.21783	0.516651
$254$	−52.6766	−3.30522
$255$	1.05714	0.0662005
$256$	−18.5354	−1.15846
$257$	17.8611	1.11414	0.557072	−	0.830464i	$-0.311925\pi$
$257$	17.8611	1.11414	0.557072	+	0.830464i	$0.311925\pi$
$258$	8.41580	0.523945
$259$	21.6169	1.34321
$260$	9.73930	0.604006
$261$	−17.7547	−1.09899
$262$	−25.7179	−1.58886
$263$	2.72274	0.167891	0.0839457	−	0.996470i	$-0.473248\pi$
$263$	2.72274	0.167891	0.0839457	+	0.996470i	$0.473248\pi$
$264$	−2.40721	−0.148153
$265$	−12.2773	−0.754189
$266$	−36.4202	−2.23307
$267$	5.04940	0.309018
$268$	−58.8360	−3.59398
$269$	3.74321	0.228228	0.114114	−	0.993468i	$-0.463597\pi$
$269$	3.74321	0.228228	0.114114	+	0.993468i	$0.463597\pi$
$270$	7.66102	0.466235
$271$	26.4914	1.60924	0.804619	−	0.593791i	$-0.202369\pi$
$271$	26.4914	1.60924	0.804619	+	0.593791i	$0.202369\pi$
$272$	19.6863	1.19366
$273$	1.14267	0.0691574
$274$	21.5591	1.30244
$275$	−2.64141	−0.159283
$276$	11.7938	0.709903
$277$	13.6183	0.818246	0.409123	−	0.912479i	$-0.365835\pi$
$277$	13.6183	0.818246	0.409123	+	0.912479i	$0.365835\pi$
$278$	−21.1481	−1.26838
$279$	17.8590	1.06919
$280$	−31.9856	−1.91151
$281$	−14.4616	−0.862709	−0.431355	−	0.902182i	$-0.641964\pi$
$281$	−14.4616	−0.862709	−0.431355	+	0.902182i	$0.641964\pi$
$282$	−2.68924	−0.160142
$283$	26.0583	1.54901	0.774503	−	0.632570i	$-0.218000\pi$
$283$	26.0583	1.54901	0.774503	+	0.632570i	$0.218000\pi$
$284$	43.9900	2.61033
$285$	2.49076	0.147540
$286$	−3.53845	−0.209233
$287$	6.74334	0.398047
$288$	28.1438	1.65839
$289$	−12.5061	−0.735650
$290$	−25.1548	−1.47714
$291$	−1.56682	−0.0918487
$292$	−7.64442	−0.447356
$293$	−13.1572	−0.768651	−0.384326	−	0.923198i	$-0.625566\pi$
$293$	−13.1572	−0.768651	−0.384326	+	0.923198i	$0.625566\pi$
$294$	−0.693058	−0.0404200
$295$	15.3303	0.892564
$296$	−55.8707	−3.24742
$297$	−1.96229	−0.113864
$298$	38.1443	2.20964
$299$	10.0822	0.583067
$300$	−3.79081	−0.218863
$301$	−28.6427	−1.65094
$302$	18.3205	1.05423
$303$	−0.594761	−0.0341682
$304$	46.3836	2.66028
$305$	7.77428	0.445154
$306$	16.0081	0.915121
$307$	28.1992	1.60941	0.804707	−	0.593672i	$-0.202322\pi$
$307$	28.1992	1.60941	0.804707	+	0.593672i	$0.202322\pi$
$308$	14.0874	0.802705
$309$	0.410101	0.0233298
$310$	25.3027	1.43709
$311$	0.309272	0.0175372	0.00876859	−	0.999962i	$-0.497209\pi$
$311$	0.309272	0.0175372	0.00876859	+	0.999962i	$0.497209\pi$
$312$	−2.95332	−0.167199
$313$	28.9161	1.63444	0.817218	−	0.576328i	$-0.195515\pi$
$313$	28.9161	1.63444	0.817218	+	0.576328i	$0.195515\pi$
$314$	−36.8419	−2.07911
$315$	−12.8163	−0.722115
$316$	−26.0029	−1.46278
$317$	−22.0027	−1.23580	−0.617899	−	0.786258i	$-0.712016\pi$
$317$	−22.0027	−1.23580	−0.617899	+	0.786258i	$0.712016\pi$
$318$	6.40155	0.358981
$319$	6.44316	0.360748
$320$	10.5651	0.590609
$321$	−4.78064	−0.266829
$322$	−56.9351	−3.17287
$323$	10.5883	0.589151
$324$	38.7696	2.15387
$325$	−3.24065	−0.179759
$326$	−54.0122	−2.99146
$327$	0.575708	0.0318367
$328$	−17.4287	−0.962339
$329$	9.15266	0.504603
$330$	−1.36656	−0.0752268
$331$	20.2690	1.11409	0.557043	−	0.830483i	$-0.311936\pi$
$331$	20.2690	1.11409	0.557043	+	0.830483i	$0.311936\pi$
$332$	52.9551	2.90629
$333$	−22.3868	−1.22679
$334$	−7.70349	−0.421516
$335$	−19.4249	−1.06130
$336$	8.21806	0.448332
$337$	−24.8441	−1.35334	−0.676671	−	0.736285i	$-0.736578\pi$
$337$	−24.8441	−1.35334	−0.676671	+	0.736285i	$0.736578\pi$
$338$	29.5081	1.60503
$339$	−0.340498	−0.0184933
$340$	15.9897	0.867162
$341$	−6.48102	−0.350967
$342$	37.7172	2.03951
$343$	−17.2441	−0.931093
$344$	74.0293	3.99139
$345$	3.89377	0.209633
$346$	10.6516	0.572634
$347$	−27.5664	−1.47984	−0.739920	−	0.672695i	$-0.765137\pi$
$347$	−27.5664	−1.47984	−0.739920	+	0.672695i	$0.765137\pi$
$348$	9.24687	0.495684
$349$	34.9196	1.86920	0.934602	−	0.355694i	$-0.115756\pi$
$349$	34.9196	1.86920	0.934602	+	0.355694i	$0.115756\pi$
$350$	18.3003	0.978195
$351$	−2.40747	−0.128501
$352$	−10.2134	−0.544375
$353$	19.6082	1.04364	0.521821	−	0.853055i	$-0.325253\pi$
$353$	19.6082	1.04364	0.521821	+	0.853055i	$0.325253\pi$
$354$	−7.99341	−0.424845
$355$	14.5235	0.770826
$356$	76.3745	4.04784
$357$	1.87600	0.0992883
$358$	1.93569	0.102305
$359$	−2.13875	−0.112879	−0.0564393	−	0.998406i	$-0.517975\pi$
$359$	−2.13875	−0.112879	−0.0564393	+	0.998406i	$0.517975\pi$
$360$	33.1247	1.74582
$361$	5.94756	0.313029
$362$	54.3264	2.85533
$363$	−3.12604	−0.164075
$364$	17.2834	0.905894
$365$	−2.52383	−0.132103
$366$	−4.05361	−0.211886
$367$	21.8872	1.14250	0.571252	−	0.820775i	$-0.306458\pi$
$367$	21.8872	1.14250	0.571252	+	0.820775i	$0.306458\pi$
$368$	72.5108	3.77989
$369$	−6.98348	−0.363546
$370$	−31.7176	−1.64892
$371$	−21.7873	−1.13114
$372$	−9.30121	−0.482245
$373$	−14.4774	−0.749613	−0.374807	−	0.927103i	$-0.622291\pi$
$373$	−14.4774	−0.749613	−0.374807	+	0.927103i	$0.622291\pi$
$374$	−5.80932	−0.300393
$375$	−3.74493	−0.193387
$376$	−23.6558	−1.21995
$377$	7.90488	0.407122
$378$	13.5953	0.699264
$379$	−14.3066	−0.734881	−0.367440	−	0.930047i	$-0.619766\pi$
$379$	−14.3066	−0.734881	−0.367440	+	0.930047i	$0.619766\pi$
$380$	37.6738	1.93263
$381$	6.39304	0.327525
$382$	14.6777	0.750975
$383$	−0.423718	−0.0216510	−0.0108255	−	0.999941i	$-0.503446\pi$
$383$	−0.423718	−0.0216510	−0.0108255	+	0.999941i	$0.503446\pi$
$384$	0.624449	0.0318663
$385$	4.65102	0.237038
$386$	−16.8737	−0.858850
$387$	29.6627	1.50784
$388$	−23.6989	−1.20313
$389$	3.44354	0.174595	0.0872973	−	0.996182i	$-0.472177\pi$
$389$	3.44354	0.174595	0.0872973	+	0.996182i	$0.472177\pi$
$390$	−1.67659	−0.0848973
$391$	16.5526	0.837100
$392$	−6.09646	−0.307918
$393$	3.12123	0.157445
$394$	−53.9642	−2.71868
$395$	−8.58496	−0.431956
$396$	−14.5891	−0.733130
$397$	1.88424	0.0945674	0.0472837	−	0.998881i	$-0.484944\pi$
$397$	1.88424	0.0945674	0.0472837	+	0.998881i	$0.484944\pi$
$398$	34.8330	1.74602
$399$	4.42010	0.221282
$400$	−23.3068	−1.16534
$401$	25.2574	1.26129	0.630646	−	0.776070i	$-0.282790\pi$
$401$	25.2574	1.26129	0.630646	+	0.776070i	$0.282790\pi$
$402$	10.1284	0.505160
$403$	−7.95133	−0.396084
$404$	−8.99603	−0.447569
$405$	12.7999	0.636034
$406$	−44.6398	−2.21543
$407$	8.12415	0.402699
$408$	−4.84866	−0.240045
$409$	−28.1709	−1.39296	−0.696480	−	0.717576i	$-0.745252\pi$
$409$	−28.1709	−1.39296	−0.696480	+	0.717576i	$0.745252\pi$
$410$	−9.89421	−0.488640
$411$	−2.61650	−0.129063
$412$	6.20296	0.305598
$413$	27.2051	1.33868
$414$	58.9627	2.89786
$415$	17.4833	0.858223
$416$	−12.5304	−0.614355
$417$	2.56661	0.125688
$418$	−13.6876	−0.669480
$419$	−0.273174	−0.0133454	−0.00667270	−	0.999978i	$-0.502124\pi$
$419$	−0.273174	−0.0133454	−0.00667270	+	0.999978i	$0.502124\pi$
$420$	6.67489	0.325701
$421$	−25.5604	−1.24574	−0.622870	−	0.782325i	$-0.714033\pi$
$421$	−25.5604	−1.24574	−0.622870	+	0.782325i	$0.714033\pi$
$422$	2.20411	0.107294
$423$	−9.47861	−0.460866
$424$	56.3111	2.73471
$425$	−5.32041	−0.258078
$426$	−7.57273	−0.366900
$427$	13.7962	0.667647
$428$	−72.3093	−3.49520
$429$	0.429441	0.0207336
$430$	42.0262	2.02668
$431$	−16.5368	−0.796549	−0.398274	−	0.917266i	$-0.630391\pi$
$431$	−16.5368	−0.796549	−0.398274	+	0.917266i	$0.630391\pi$
$432$	−17.3145	−0.833044
$433$	−10.5317	−0.506121	−0.253060	−	0.967450i	$-0.581437\pi$
$433$	−10.5317	−0.506121	−0.253060	+	0.967450i	$0.581437\pi$
$434$	44.9021	2.15537
$435$	3.05289	0.146375
$436$	8.70783	0.417030
$437$	39.0001	1.86563
$438$	1.31596	0.0628790
$439$	9.90432	0.472708	0.236354	−	0.971667i	$-0.424048\pi$
$439$	9.90432	0.472708	0.236354	+	0.971667i	$0.424048\pi$
$440$	−12.0209	−0.573075
$441$	−2.44279	−0.116323
$442$	−7.12725	−0.339009
$443$	32.6369	1.55062	0.775312	−	0.631578i	$-0.217593\pi$
$443$	32.6369	1.55062	0.775312	+	0.631578i	$0.217593\pi$
$444$	11.6593	0.553328
$445$	25.2153	1.19532
$446$	42.5071	2.01277
$447$	−4.62934	−0.218960
$448$	18.7489	0.885802
$449$	37.4935	1.76943	0.884713	−	0.466136i	$-0.154354\pi$
$449$	37.4935	1.76943	0.884713	+	0.466136i	$0.154354\pi$
$450$	−18.9521	−0.893409
$451$	2.53430	0.119336
$452$	−5.15019	−0.242245
$453$	−2.22345	−0.104467
$454$	−18.9017	−0.887102
$455$	5.70617	0.267509
$456$	−11.4241	−0.534983
$457$	26.4903	1.23916	0.619581	−	0.784932i	$-0.287302\pi$
$457$	26.4903	1.23916	0.619581	+	0.784932i	$0.287302\pi$
$458$	45.5057	2.12634
$459$	−3.95251	−0.184487
$460$	58.8949	2.74599
$461$	4.02442	0.187436	0.0937179	−	0.995599i	$-0.470125\pi$
$461$	4.02442	0.187436	0.0937179	+	0.995599i	$0.470125\pi$
$462$	−2.42510	−0.112826
$463$	5.17675	0.240584	0.120292	−	0.992739i	$-0.461617\pi$
$463$	5.17675	0.240584	0.120292	+	0.992739i	$0.461617\pi$
$464$	56.8518	2.63928
$465$	−3.07083	−0.142406
$466$	65.4612	3.03243
$467$	−3.19518	−0.147855	−0.0739276	−	0.997264i	$-0.523553\pi$
$467$	−3.19518	−0.147855	−0.0739276	+	0.997264i	$0.523553\pi$
$468$	−17.8989	−0.827375
$469$	−34.4715	−1.59175
$470$	−13.4293	−0.619448
$471$	4.47128	0.206026
$472$	−70.3138	−3.23646
$473$	−10.7646	−0.494956
$474$	4.47631	0.205604
$475$	−12.5356	−0.575173
$476$	28.3753	1.30058
$477$	22.5632	1.03310
$478$	−22.8683	−1.04597
$479$	−22.4429	−1.02544	−0.512722	−	0.858555i	$-0.671363\pi$
$479$	−22.4429	−1.02544	−0.512722	+	0.858555i	$0.671363\pi$
$480$	−4.83929	−0.220883
$481$	9.96723	0.454466
$482$	−7.61173	−0.346705
$483$	6.90988	0.314410
$484$	−47.2828	−2.14922
$485$	−7.82428	−0.355282
$486$	−21.2383	−0.963387
$487$	17.1500	0.777140	0.388570	−	0.921419i	$-0.372969\pi$
$487$	17.1500	0.777140	0.388570	+	0.921419i	$0.372969\pi$
$488$	−35.6575	−1.61414
$489$	6.55514	0.296434
$490$	−3.46094	−0.156349
$491$	−35.6549	−1.60908	−0.804541	−	0.593897i	$-0.797588\pi$
$491$	−35.6549	−1.60908	−0.804541	+	0.593897i	$0.797588\pi$
$492$	3.63709	0.163973
$493$	12.9780	0.584499
$494$	−16.7928	−0.755543
$495$	−4.81665	−0.216492
$496$	−57.1859	−2.56772
$497$	25.7734	1.15609
$498$	−9.11604	−0.408500
$499$	−37.9495	−1.69886	−0.849428	−	0.527705i	$-0.823053\pi$
$499$	−37.9495	−1.69886	−0.849428	+	0.527705i	$0.823053\pi$
$500$	−56.6437	−2.53318
$501$	0.934926	0.0417694
$502$	45.7928	2.04383
$503$	8.56576	0.381929	0.190964	−	0.981597i	$-0.438839\pi$
$503$	8.56576	0.381929	0.190964	+	0.981597i	$0.438839\pi$
$504$	58.7831	2.61841
$505$	−2.97008	−0.132167
$506$	−21.3975	−0.951237
$507$	−3.58122	−0.159048
$508$	96.6976	4.29026
$509$	−9.18837	−0.407267	−0.203634	−	0.979047i	$-0.565275\pi$
$509$	−9.18837	−0.407267	−0.203634	+	0.979047i	$0.565275\pi$
$510$	−2.75257	−0.121886
$511$	−4.47880	−0.198130
$512$	44.3101	1.95825
$513$	−9.31264	−0.411163
$514$	−46.5066	−2.05132
$515$	2.04793	0.0902426
$516$	−15.4487	−0.680093
$517$	3.43978	0.151281
$518$	−56.2861	−2.47307
$519$	−1.29272	−0.0567442
$520$	−14.7480	−0.646745
$521$	29.8781	1.30898	0.654492	−	0.756069i	$-0.272883\pi$
$521$	29.8781	1.30898	0.654492	+	0.756069i	$0.272883\pi$
$522$	46.2295	2.02341
$523$	30.1708	1.31928	0.659639	−	0.751582i	$-0.270709\pi$
$523$	30.1708	1.31928	0.659639	+	0.751582i	$0.270709\pi$
$524$	47.2100	2.06238
$525$	−2.22100	−0.0969325
$526$	−7.08946	−0.309115
$527$	−13.0543	−0.568652
$528$	3.08854	0.134411
$529$	37.9683	1.65080
$530$	31.9676	1.38858
$531$	−28.1740	−1.22265
$532$	66.8560	2.89858
$533$	3.10925	0.134676
$534$	−13.1476	−0.568953
$535$	−23.8732	−1.03213
$536$	89.0944	3.84829
$537$	−0.234924	−0.0101377
$538$	−9.74655	−0.420204
$539$	0.886485	0.0381836
$540$	−14.0632	−0.605185
$541$	−32.6813	−1.40508	−0.702540	−	0.711644i	$-0.747951\pi$
$541$	−32.6813	−1.40508	−0.702540	+	0.711644i	$0.747951\pi$
$542$	−68.9782	−2.96287
$543$	−6.59327	−0.282944
$544$	−20.5721	−0.882020
$545$	2.87493	0.123148
$546$	−2.97527	−0.127330
$547$	−2.91069	−0.124452	−0.0622261	−	0.998062i	$-0.519820\pi$
$547$	−2.91069	−0.124452	−0.0622261	+	0.998062i	$0.519820\pi$
$548$	−39.5758	−1.69059
$549$	−14.2876	−0.609778
$550$	6.87769	0.293266
$551$	30.5779	1.30266
$552$	−17.8591	−0.760135
$553$	−15.2349	−0.647853
$554$	−35.4593	−1.50652
$555$	3.84938	0.163397
$556$	38.8212	1.64639
$557$	39.1827	1.66022	0.830112	−	0.557597i	$-0.188276\pi$
$557$	39.1827	1.66022	0.830112	+	0.557597i	$0.188276\pi$
$558$	−46.5012	−1.96855
$559$	−13.2067	−0.558583
$560$	41.0387	1.73420
$561$	0.705043	0.0297669
$562$	37.6551	1.58839
$563$	−11.1208	−0.468687	−0.234344	−	0.972154i	$-0.575294\pi$
$563$	−11.1208	−0.468687	−0.234344	+	0.972154i	$0.575294\pi$
$564$	4.93659	0.207868
$565$	−1.70036	−0.0715345
$566$	−67.8505	−2.85197
$567$	22.7148	0.953931
$568$	−66.6133	−2.79503
$569$	6.35464	0.266400	0.133200	−	0.991089i	$-0.457475\pi$
$569$	6.35464	0.266400	0.133200	+	0.991089i	$0.457475\pi$
$570$	−6.48543	−0.271645
$571$	−19.9842	−0.836314	−0.418157	−	0.908375i	$-0.637324\pi$
$571$	−19.9842	−0.836314	−0.418157	+	0.908375i	$0.637324\pi$
$572$	6.49548	0.271590
$573$	−1.78134	−0.0744166
$574$	−17.5583	−0.732868
$575$	−19.5967	−0.817239
$576$	−19.4166	−0.809024
$577$	17.2186	0.716820	0.358410	−	0.933564i	$-0.383319\pi$
$577$	17.2186	0.716820	0.358410	+	0.933564i	$0.383319\pi$
$578$	32.5632	1.35445
$579$	2.04786	0.0851063
$580$	46.1763	1.91737
$581$	31.0259	1.28717
$582$	4.07968	0.169108
$583$	−8.18818	−0.339120
$584$	11.5758	0.479010
$585$	−5.90938	−0.244323
$586$	34.2586	1.41521
$587$	0.550926	0.0227391	0.0113696	−	0.999935i	$-0.496381\pi$
$587$	0.550926	0.0227391	0.0113696	+	0.999935i	$0.496381\pi$
$588$	1.27224	0.0524661
$589$	−30.7576	−1.26734
$590$	−39.9169	−1.64335
$591$	6.54931	0.269403
$592$	71.6842	2.94620
$593$	44.4417	1.82500	0.912501	−	0.409075i	$-0.134148\pi$
$593$	44.4417	1.82500	0.912501	+	0.409075i	$0.134148\pi$
$594$	5.10941	0.209642
$595$	9.36821	0.384059
$596$	−70.0209	−2.86817
$597$	−4.22747	−0.173019
$598$	−26.2519	−1.07352
$599$	32.7136	1.33664	0.668320	−	0.743874i	$-0.267014\pi$
$599$	32.7136	1.33664	0.668320	+	0.743874i	$0.267014\pi$
$600$	5.74036	0.234349
$601$	−24.3815	−0.994543	−0.497271	−	0.867595i	$-0.665665\pi$
$601$	−24.3815	−0.994543	−0.497271	+	0.867595i	$0.665665\pi$
$602$	74.5797	3.03964
$603$	35.6991	1.45378
$604$	−33.6307	−1.36841
$605$	−15.6106	−0.634661
$606$	1.54864	0.0629091
$607$	−18.5698	−0.753725	−0.376863	−	0.926269i	$-0.622997\pi$
$607$	−18.5698	−0.753725	−0.376863	+	0.926269i	$0.622997\pi$
$608$	−48.4706	−1.96574
$609$	5.41766	0.219535
$610$	−20.2426	−0.819600
$611$	4.22015	0.170729
$612$	−29.3858	−1.18785
$613$	20.3171	0.820601	0.410300	−	0.911950i	$-0.365424\pi$
$613$	20.3171	0.820601	0.410300	+	0.911950i	$0.365424\pi$
$614$	−73.4250	−2.96319
$615$	1.20080	0.0484210
$616$	−21.3323	−0.859505
$617$	39.9142	1.60689	0.803443	−	0.595381i	$-0.202999\pi$
$617$	39.9142	1.60689	0.803443	+	0.595381i	$0.202999\pi$
$618$	−1.06782	−0.0429540
$619$	4.22030	0.169628	0.0848141	−	0.996397i	$-0.472970\pi$
$619$	4.22030	0.169628	0.0848141	+	0.996397i	$0.472970\pi$
$620$	−46.4477	−1.86538
$621$	−14.5583	−0.584205
$622$	−0.805280	−0.0322888
$623$	44.7471	1.79276
$624$	3.78921	0.151690
$625$	−6.15237	−0.246095
$626$	−75.2917	−3.00926
$627$	1.66118	0.0663410
$628$	67.6301	2.69873
$629$	16.3639	0.652471
$630$	33.3709	1.32953
$631$	−18.7980	−0.748336	−0.374168	−	0.927361i	$-0.622072\pi$
$631$	−18.7980	−0.748336	−0.374168	+	0.927361i	$0.622072\pi$
$632$	39.3758	1.56628
$633$	−0.267499	−0.0106321
$634$	57.2906	2.27530
$635$	31.9251	1.26691
$636$	−11.7512	−0.465967
$637$	1.08760	0.0430922
$638$	−16.7767	−0.664194
$639$	−26.6912	−1.05589
$640$	3.11833	0.123263
$641$	−28.1705	−1.11267	−0.556335	−	0.830958i	$-0.687793\pi$
$641$	−28.1705	−1.11267	−0.556335	+	0.830958i	$0.687793\pi$
$642$	12.4478	0.491276
$643$	26.9209	1.06166	0.530829	−	0.847479i	$-0.321881\pi$
$643$	26.9209	1.06166	0.530829	+	0.847479i	$0.321881\pi$
$644$	104.515	4.11847
$645$	−5.10046	−0.200831
$646$	−27.5699	−1.08472
$647$	30.6505	1.20499	0.602497	−	0.798121i	$-0.294173\pi$
$647$	30.6505	1.20499	0.602497	+	0.798121i	$0.294173\pi$
$648$	−58.7081	−2.30627
$649$	10.2243	0.401339
$650$	8.43800	0.330965
$651$	−5.44950	−0.213583
$652$	99.1494	3.88299
$653$	9.10101	0.356150	0.178075	−	0.984017i	$-0.443013\pi$
$653$	9.10101	0.356150	0.178075	+	0.984017i	$0.443013\pi$
$654$	−1.49902	−0.0586165
$655$	15.5866	0.609017
$656$	22.3617	0.873076
$657$	4.63830	0.180957
$658$	−23.8317	−0.929055
$659$	−13.7459	−0.535464	−0.267732	−	0.963493i	$-0.586274\pi$
$659$	−13.7459	−0.535464	−0.267732	+	0.963493i	$0.586274\pi$
$660$	2.50858	0.0976463
$661$	22.9405	0.892281	0.446140	−	0.894963i	$-0.352798\pi$
$661$	22.9405	0.892281	0.446140	+	0.894963i	$0.352798\pi$
$662$	−52.7764	−2.05121
$663$	0.864992	0.0335935
$664$	−80.1890	−3.11194
$665$	22.0728	0.855945
$666$	58.2906	2.25871
$667$	47.8020	1.85090
$668$	14.1412	0.547139
$669$	−5.15883	−0.199452
$670$	50.5786	1.95402
$671$	5.18494	0.200163
$672$	−8.58781	−0.331282
$673$	28.5212	1.09941	0.549705	−	0.835359i	$-0.314740\pi$
$673$	28.5212	1.09941	0.549705	+	0.835359i	$0.314740\pi$
$674$	64.6888	2.49172
$675$	4.67940	0.180110
$676$	−54.1676	−2.08337
$677$	−41.0183	−1.57646	−0.788230	−	0.615381i	$-0.789002\pi$
$677$	−41.0183	−1.57646	−0.788230	+	0.615381i	$0.789002\pi$
$678$	0.886588	0.0340492
$679$	−13.8850	−0.532856
$680$	−24.2129	−0.928522
$681$	2.29399	0.0879058
$682$	16.8752	0.646186
$683$	5.38299	0.205974	0.102987	−	0.994683i	$-0.467160\pi$
$683$	5.38299	0.205974	0.102987	+	0.994683i	$0.467160\pi$
$684$	−69.2369	−2.64734
$685$	−13.0661	−0.499230
$686$	44.9001	1.71429
$687$	−5.52276	−0.210706
$688$	−94.9823	−3.62117
$689$	−10.0458	−0.382714
$690$	−10.1386	−0.385969
$691$	−17.1577	−0.652708	−0.326354	−	0.945248i	$-0.605820\pi$
$691$	−17.1577	−0.652708	−0.326354	+	0.945248i	$0.605820\pi$
$692$	−19.5530	−0.743293
$693$	−8.54763	−0.324698
$694$	71.7771	2.72462
$695$	12.8170	0.486175
$696$	−14.0024	−0.530759
$697$	5.10466	0.193353
$698$	−90.9235	−3.44151
$699$	−7.94463	−0.300493
$700$	−33.5937	−1.26972
$701$	4.88828	0.184628	0.0923139	−	0.995730i	$-0.470574\pi$
$701$	4.88828	0.184628	0.0923139	+	0.995730i	$0.470574\pi$
$702$	6.26855	0.236591
$703$	38.5555	1.45415
$704$	7.04627	0.265566
$705$	1.62983	0.0613831
$706$	−51.0558	−1.92151
$707$	−5.27070	−0.198225
$708$	14.6734	0.551460
$709$	46.9593	1.76359	0.881796	−	0.471631i	$-0.156335\pi$
$709$	46.9593	1.76359	0.881796	+	0.471631i	$0.156335\pi$
$710$	−37.8161	−1.41921
$711$	15.7774	0.591700
$712$	−115.653	−4.33426
$713$	−48.0829	−1.80072
$714$	−4.88471	−0.182806
$715$	2.14451	0.0802001
$716$	−3.55332	−0.132794
$717$	2.77538	0.103649
$718$	5.56885	0.207828
$719$	19.9077	0.742431	0.371215	−	0.928547i	$-0.378941\pi$
$719$	19.9077	0.742431	0.371215	+	0.928547i	$0.378941\pi$
$720$	−42.5002	−1.58389
$721$	3.63426	0.135347
$722$	−15.4862	−0.576337
$723$	0.923790	0.0343561
$724$	−99.7262	−3.70629
$725$	−15.3647	−0.570631
$726$	8.13958	0.302088
$727$	33.7961	1.25343	0.626714	−	0.779249i	$-0.284399\pi$
$727$	33.7961	1.25343	0.626714	+	0.779249i	$0.284399\pi$
$728$	−26.1719	−0.969995
$729$	−21.7561	−0.805782
$730$	6.57154	0.243224
$731$	−21.6823	−0.801950
$732$	7.44115	0.275033
$733$	47.7228	1.76268	0.881341	−	0.472480i	$-0.156641\pi$
$733$	47.7228	1.76268	0.881341	+	0.472480i	$0.156641\pi$
$734$	−56.9899	−2.10353
$735$	0.420034	0.0154932
$736$	−75.7733	−2.79304
$737$	−12.9552	−0.477211
$738$	18.1836	0.669346
$739$	−49.6785	−1.82745	−0.913727	−	0.406328i	$-0.866809\pi$
$739$	−49.6785	−1.82745	−0.913727	+	0.406328i	$0.866809\pi$
$740$	58.2235	2.14034
$741$	2.03804	0.0748692
$742$	56.7297	2.08261
$743$	−38.4405	−1.41025	−0.705123	−	0.709085i	$-0.749108\pi$
$743$	−38.4405	−1.41025	−0.705123	+	0.709085i	$0.749108\pi$
$744$	14.0847	0.516369
$745$	−23.1177	−0.846966
$746$	37.6963	1.38016
$747$	−32.1308	−1.17561
$748$	10.6641	0.389918
$749$	−42.3654	−1.54800
$750$	9.75102	0.356057
$751$	6.82033	0.248878	0.124439	−	0.992227i	$-0.460287\pi$
$751$	6.82033	0.248878	0.124439	+	0.992227i	$0.460287\pi$
$752$	30.3513	1.10680
$753$	−5.55760	−0.202530
$754$	−20.5827	−0.749577
$755$	−11.1033	−0.404090
$756$	−24.9566	−0.907663
$757$	8.52901	0.309992	0.154996	−	0.987915i	$-0.450464\pi$
$757$	8.52901	0.309992	0.154996	+	0.987915i	$0.450464\pi$
$758$	37.2514	1.35303
$759$	2.59689	0.0942612
$760$	−57.0489	−2.06938
$761$	8.47951	0.307382	0.153691	−	0.988119i	$-0.450884\pi$
$761$	8.47951	0.307382	0.153691	+	0.988119i	$0.450884\pi$
$762$	−16.6462	−0.603027
$763$	5.10184	0.184699
$764$	−26.9436	−0.974784
$765$	−9.70184	−0.350771
$766$	1.10328	0.0398630
$767$	12.5438	0.452932
$768$	−5.85730	−0.211357
$769$	7.67339	0.276709	0.138355	−	0.990383i	$-0.455819\pi$
$769$	7.67339	0.276709	0.138355	+	0.990383i	$0.455819\pi$
$770$	−12.1103	−0.436425
$771$	5.64423	0.203272
$772$	30.9748	1.11481
$773$	−41.6953	−1.49967	−0.749837	−	0.661622i	$-0.769868\pi$
$773$	−41.6953	−1.49967	−0.749837	+	0.661622i	$0.769868\pi$
$774$	−77.2356	−2.77618
$775$	15.4550	0.555160
$776$	35.8868	1.28826
$777$	6.83110	0.245065
$778$	−8.96628	−0.321457
$779$	12.0273	0.430922
$780$	3.07769	0.110199
$781$	9.68622	0.346600
$782$	−43.0995	−1.54124
$783$	−11.4144	−0.407917
$784$	7.82199	0.279357
$785$	22.3283	0.796932
$786$	−8.12704	−0.289882
$787$	−19.7776	−0.704994	−0.352497	−	0.935813i	$-0.614667\pi$
$787$	−19.7776	−0.704994	−0.352497	+	0.935813i	$0.614667\pi$
$788$	99.0613	3.52891
$789$	0.860405	0.0306312
$790$	22.3535	0.795301
$791$	−3.01745	−0.107288
$792$	22.0920	0.785006
$793$	6.36122	0.225894
$794$	−4.90618	−0.174114
$795$	−3.87972	−0.137599
$796$	−63.9423	−2.26638
$797$	−46.4327	−1.64473	−0.822366	−	0.568959i	$-0.807346\pi$
$797$	−46.4327	−1.64473	−0.822366	+	0.568959i	$0.807346\pi$
$798$	−11.5090	−0.407415
$799$	6.92851	0.245113
$800$	24.3554	0.861093
$801$	−46.3407	−1.63737
$802$	−65.7650	−2.32224
$803$	−1.68323	−0.0594001
$804$	−18.5926	−0.655710
$805$	34.5060	1.21618
$806$	20.7036	0.729254
$807$	1.18288	0.0416394
$808$	13.6225	0.479239
$809$	27.6798	0.973171	0.486585	−	0.873633i	$-0.338242\pi$
$809$	27.6798	0.973171	0.486585	+	0.873633i	$0.338242\pi$
$810$	−33.3284	−1.17104
$811$	−10.3944	−0.364996	−0.182498	−	0.983206i	$-0.558418\pi$
$811$	−10.3944	−0.364996	−0.182498	+	0.983206i	$0.558418\pi$
$812$	81.9445	2.87569
$813$	8.37147	0.293600
$814$	−21.1536	−0.741434
$815$	32.7346	1.14664
$816$	6.22101	0.217779
$817$	−51.0865	−1.78729
$818$	73.3512	2.56466
$819$	−10.4868	−0.366438
$820$	18.1627	0.634267
$821$	6.60043	0.230357	0.115178	−	0.993345i	$-0.463256\pi$
$821$	6.60043	0.230357	0.115178	+	0.993345i	$0.463256\pi$
$822$	6.81284	0.237625
$823$	−16.2879	−0.567760	−0.283880	−	0.958860i	$-0.591622\pi$
$823$	−16.2879	−0.567760	−0.283880	+	0.958860i	$0.591622\pi$
$824$	−9.39303	−0.327222
$825$	−0.834704	−0.0290607
$826$	−70.8366	−2.46472
$827$	−21.8128	−0.758504	−0.379252	−	0.925293i	$-0.623819\pi$
$827$	−21.8128	−0.758504	−0.379252	+	0.925293i	$0.623819\pi$
$828$	−108.237	−3.76150
$829$	−51.6223	−1.79292	−0.896458	−	0.443129i	$-0.853868\pi$
$829$	−51.6223	−1.79292	−0.896458	+	0.443129i	$0.853868\pi$
$830$	−45.5230	−1.58013
$831$	4.30349	0.149286
$832$	8.64481	0.299705
$833$	1.78558	0.0618668
$834$	−6.68294	−0.231411
$835$	4.66877	0.161569
$836$	25.1260	0.869002
$837$	11.4815	0.396857
$838$	0.711288	0.0245710
$839$	−29.8961	−1.03213	−0.516064	−	0.856550i	$-0.672603\pi$
$839$	−29.8961	−1.03213	−0.516064	+	0.856550i	$0.672603\pi$
$840$	−10.1077	−0.348748
$841$	8.47893	0.292377
$842$	66.5542	2.29361
$843$	−4.56998	−0.157398
$844$	−4.04604	−0.139270
$845$	−17.8836	−0.615216
$846$	24.6804	0.848528
$847$	−27.7026	−0.951872
$848$	−72.2492	−2.48105
$849$	8.23461	0.282611
$850$	13.8532	0.475162
$851$	60.2733	2.06614
$852$	13.9011	0.476246
$853$	−11.5788	−0.396451	−0.198225	−	0.980156i	$-0.563518\pi$
$853$	−11.5788	−0.396451	−0.198225	+	0.980156i	$0.563518\pi$
$854$	−35.9226	−1.22924
$855$	−22.8588	−0.781756
$856$	109.497	3.74252
$857$	27.6406	0.944184	0.472092	−	0.881549i	$-0.343499\pi$
$857$	27.6406	0.944184	0.472092	+	0.881549i	$0.343499\pi$
$858$	−1.11818	−0.0381739
$859$	−38.4781	−1.31286	−0.656428	−	0.754388i	$-0.727934\pi$
$859$	−38.4781	−1.31286	−0.656428	+	0.754388i	$0.727934\pi$
$860$	−77.1468	−2.63068
$861$	2.13094	0.0726223
$862$	43.0584	1.46657
$863$	−22.9487	−0.781181	−0.390591	−	0.920564i	$-0.627729\pi$
$863$	−22.9487	−0.781181	−0.390591	+	0.920564i	$0.627729\pi$
$864$	18.0935	0.615554
$865$	−6.45550	−0.219493
$866$	27.4224	0.931850
$867$	−3.95200	−0.134217
$868$	−82.4261	−2.79772
$869$	−5.72562	−0.194228
$870$	−7.94910	−0.269500
$871$	−15.8943	−0.538557
$872$	−13.1861	−0.446538
$873$	14.3794	0.486670
$874$	−101.548	−3.43492
$875$	−33.1870	−1.12193
$876$	−2.41569	−0.0816185
$877$	14.9014	0.503184	0.251592	−	0.967833i	$-0.419046\pi$
$877$	14.9014	0.503184	0.251592	+	0.967833i	$0.419046\pi$
$878$	−25.7888	−0.870331
$879$	−4.15776	−0.140238
$880$	15.4233	0.519919
$881$	54.6260	1.84040	0.920198	−	0.391454i	$-0.128028\pi$
$881$	54.6260	1.84040	0.920198	+	0.391454i	$0.128028\pi$
$882$	6.36051	0.214170
$883$	−5.20588	−0.175192	−0.0875960	−	0.996156i	$-0.527918\pi$
$883$	−5.20588	−0.175192	−0.0875960	+	0.996156i	$0.527918\pi$
$884$	13.0834	0.440042
$885$	4.84448	0.162845
$886$	−84.9797	−2.85495
$887$	−58.5267	−1.96514	−0.982568	−	0.185905i	$-0.940478\pi$
$887$	−58.5267	−1.96514	−0.982568	+	0.185905i	$0.940478\pi$
$888$	−17.6555	−0.592481
$889$	56.6543	1.90012
$890$	−65.6555	−2.20078
$891$	8.53673	0.285991
$892$	−78.0296	−2.61262
$893$	16.3245	0.546279
$894$	12.0539	0.403141
$895$	−1.17314	−0.0392139
$896$	5.53378	0.184871
$897$	3.18603	0.106379
$898$	−97.6253	−3.25780
$899$	−37.6992	−1.25734
$900$	34.7900	1.15967
$901$	−16.4929	−0.549457
$902$	−6.59880	−0.219716
$903$	−9.05129	−0.301208
$904$	7.79884	0.259386
$905$	−32.9250	−1.09446
$906$	5.78941	0.192340
$907$	−3.69292	−0.122621	−0.0613107	−	0.998119i	$-0.519528\pi$
$907$	−3.69292	−0.122621	−0.0613107	+	0.998119i	$0.519528\pi$
$908$	34.6976	1.15148
$909$	5.45840	0.181044
$910$	−14.8577	−0.492528
$911$	7.84245	0.259832	0.129916	−	0.991525i	$-0.458529\pi$
$911$	7.84245	0.259832	0.129916	+	0.991525i	$0.458529\pi$
$912$	14.6576	0.485360
$913$	11.6603	0.385898
$914$	−68.9752	−2.28150
$915$	2.45673	0.0812169
$916$	−83.5341	−2.76005
$917$	27.6599	0.913410
$918$	10.2915	0.339671
$919$	−7.00565	−0.231095	−0.115548	−	0.993302i	$-0.536862\pi$
$919$	−7.00565	−0.231095	−0.115548	+	0.993302i	$0.536862\pi$
$920$	−89.1836	−2.94030
$921$	8.91115	0.293632
$922$	−10.4788	−0.345099
$923$	11.8837	0.391156
$924$	4.45172	0.146451
$925$	−19.3733	−0.636990
$926$	−13.4792	−0.442954
$927$	−3.76368	−0.123616
$928$	−59.4098	−1.95022
$929$	33.0564	1.08455	0.542273	−	0.840202i	$-0.317564\pi$
$929$	33.0564	1.08455	0.542273	+	0.840202i	$0.317564\pi$
$930$	7.99581	0.262193
$931$	4.20708	0.137881
$932$	−120.166	−3.93617
$933$	0.0977320	0.00319960
$934$	8.31959	0.272225
$935$	3.52079	0.115142
$936$	27.1039	0.885920
$937$	−32.8800	−1.07414	−0.537071	−	0.843537i	$-0.680469\pi$
$937$	−32.8800	−1.07414	−0.537071	+	0.843537i	$0.680469\pi$
$938$	89.7567	2.93066
$939$	9.13770	0.298198
$940$	24.6520	0.804059
$941$	6.45007	0.210266	0.105133	−	0.994458i	$-0.466473\pi$
$941$	6.45007	0.210266	0.105133	+	0.994458i	$0.466473\pi$
$942$	−11.6423	−0.379326
$943$	18.8021	0.612279
$944$	90.2152	2.93626
$945$	−8.23952	−0.268032
$946$	28.0288	0.911293
$947$	−35.1309	−1.14160	−0.570801	−	0.821088i	$-0.693367\pi$
$947$	−35.1309	−1.14160	−0.570801	+	0.821088i	$0.693367\pi$
$948$	−8.21710	−0.266879
$949$	−2.06510	−0.0670360
$950$	32.6401	1.05899
$951$	−6.95302	−0.225467
$952$	−42.9682	−1.39261
$953$	−35.5361	−1.15113	−0.575563	−	0.817758i	$-0.695217\pi$
$953$	−35.5361	−1.15113	−0.575563	+	0.817758i	$0.695217\pi$
$954$	−58.7500	−1.90210
$955$	−8.89552	−0.287852
$956$	41.9789	1.35770
$957$	2.03608	0.0658172
$958$	58.4368	1.88801
$959$	−23.1871	−0.748751
$960$	3.33866	0.107755
$961$	6.92070	0.223248
$962$	−25.9526	−0.836746
$963$	43.8741	1.41382
$964$	13.9727	0.450031
$965$	10.2265	0.329202
$966$	−17.9919	−0.578880
$967$	−57.7192	−1.85612	−0.928062	−	0.372425i	$-0.878526\pi$
$967$	−57.7192	−1.85612	−0.928062	+	0.372425i	$0.878526\pi$
$968$	71.5996	2.30130
$969$	3.34599	0.107489
$970$	20.3728	0.654131
$971$	37.2682	1.19599	0.597996	−	0.801499i	$-0.295964\pi$
$971$	37.2682	1.19599	0.597996	+	0.801499i	$0.295964\pi$
$972$	38.9868	1.25050
$973$	22.7450	0.729171
$974$	−44.6550	−1.43084
$975$	−1.02407	−0.0327965
$976$	45.7499	1.46442
$977$	34.3101	1.09768	0.548838	−	0.835929i	$-0.315070\pi$
$977$	34.3101	1.09768	0.548838	+	0.835929i	$0.315070\pi$
$978$	−17.0682	−0.545782
$979$	16.8170	0.537474
$980$	6.35320	0.202945
$981$	−5.28353	−0.168690
$982$	92.8379	2.96258
$983$	−25.9514	−0.827721	−0.413860	−	0.910340i	$-0.635820\pi$
$983$	−25.9514	−0.827721	−0.413860	+	0.910340i	$0.635820\pi$
$984$	−5.50759	−0.175576
$985$	32.7055	1.04208
$986$	−33.7920	−1.07616
$987$	2.89231	0.0920631
$988$	30.8262	0.980713
$989$	−79.8627	−2.53949
$990$	12.5416	0.398597
$991$	−18.3337	−0.582390	−0.291195	−	0.956664i	$-0.594053\pi$
$991$	−18.3337	−0.582390	−0.291195	+	0.956664i	$0.594053\pi$
$992$	59.7589	1.89735
$993$	6.40515	0.203261
$994$	−67.1085	−2.12855
$995$	−21.1108	−0.669258
$996$	16.7342	0.530243
$997$	18.4122	0.583121	0.291560	−	0.956552i	$-0.405826\pi$
$997$	18.4122	0.583121	0.291560	+	0.956552i	$0.405826\pi$
$998$	98.8128	3.12787
$999$	−14.3923	−0.455354

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4003.2.a.c.1.9	✓	179

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4003.2.a.c.1.9	✓	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:	\( N \)	\(=\)	\( 4003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4003.a (trivial)

\(f(q)\)	\(=\)	\(q-2.60379 q^{2} +0.316007 q^{3} +4.77975 q^{4} +1.57805 q^{5} -0.822817 q^{6} +2.80041 q^{7} -7.23789 q^{8} -2.90014 q^{9} +O(q^{10})\)	\(q-2.60379 q^{2} +0.316007 q^{3} +4.77975 q^{4} +1.57805 q^{5} -0.822817 q^{6} +2.80041 q^{7} -7.23789 q^{8} -2.90014 q^{9} -4.10892 q^{10} +1.05246 q^{11} +1.51043 q^{12} +1.29122 q^{13} -7.29169 q^{14} +0.498675 q^{15} +9.28647 q^{16} +2.11989 q^{17} +7.55137 q^{18} +4.99475 q^{19} +7.54268 q^{20} +0.884949 q^{21} -2.74039 q^{22} +7.80822 q^{23} -2.28722 q^{24} -2.50975 q^{25} -3.36208 q^{26} -1.86448 q^{27} +13.3852 q^{28} +6.12200 q^{29} -1.29845 q^{30} -6.15798 q^{31} -9.70430 q^{32} +0.332584 q^{33} -5.51976 q^{34} +4.41919 q^{35} -13.8619 q^{36} +7.71921 q^{37} -13.0053 q^{38} +0.408036 q^{39} -11.4218 q^{40} +2.40798 q^{41} -2.30423 q^{42} -10.2280 q^{43} +5.03049 q^{44} -4.57657 q^{45} -20.3310 q^{46} +3.26833 q^{47} +2.93459 q^{48} +0.842299 q^{49} +6.53488 q^{50} +0.669901 q^{51} +6.17172 q^{52} -7.78005 q^{53} +4.85474 q^{54} +1.66083 q^{55} -20.2690 q^{56} +1.57838 q^{57} -15.9404 q^{58} +9.71469 q^{59} +2.38354 q^{60} +4.92650 q^{61} +16.0341 q^{62} -8.12158 q^{63} +6.69505 q^{64} +2.03762 q^{65} -0.865981 q^{66} -12.3095 q^{67} +10.1325 q^{68} +2.46745 q^{69} -11.5067 q^{70} +9.20342 q^{71} +20.9909 q^{72} -1.59934 q^{73} -20.0992 q^{74} -0.793099 q^{75} +23.8736 q^{76} +2.94732 q^{77} -1.06244 q^{78} -5.44023 q^{79} +14.6545 q^{80} +8.11123 q^{81} -6.26989 q^{82} +11.0791 q^{83} +4.22983 q^{84} +3.34530 q^{85} +26.6317 q^{86} +1.93460 q^{87} -7.61758 q^{88} +15.9788 q^{89} +11.9164 q^{90} +3.61596 q^{91} +37.3213 q^{92} -1.94596 q^{93} -8.51006 q^{94} +7.88198 q^{95} -3.06663 q^{96} -4.95819 q^{97} -2.19317 q^{98} -3.05228 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 179 q + 22 q^{2} + 16 q^{3} + 196 q^{4} + 61 q^{5} + 7 q^{6} + 21 q^{7} + 60 q^{8} + 221 q^{9}+O(q^{10}) \) 179 * q + 22 * q^2 + 16 * q^3 + 196 * q^4 + 61 * q^5 + 7 * q^6 + 21 * q^7 + 60 * q^8 + 221 * q^9	\( 179 q + 22 q^{2} + 16 q^{3} + 196 q^{4} + 61 q^{5} + 7 q^{6} + 21 q^{7} + 60 q^{8} + 221 q^{9} + 9 q^{10} + 46 q^{11} + 33 q^{12} + 47 q^{13} + 22 q^{14} + 36 q^{15} + 222 q^{16} + 103 q^{17} + 43 q^{18} + 12 q^{19} + 102 q^{20} + 50 q^{21} + 39 q^{22} + 121 q^{23} - 3 q^{24} + 246 q^{25} + 52 q^{26} + 49 q^{27} + 41 q^{28} + 138 q^{29} + 28 q^{30} + 5 q^{31} + 137 q^{32} + 63 q^{33} + 2 q^{34} + 72 q^{35} + 279 q^{36} + 118 q^{37} + 123 q^{38} + q^{39} + 9 q^{40} + 50 q^{41} + 48 q^{42} + 48 q^{43} + 108 q^{44} + 158 q^{45} + 13 q^{46} + 85 q^{47} + 50 q^{48} + 230 q^{49} + 78 q^{50} + 15 q^{51} + 41 q^{52} + 399 q^{53} - 5 q^{54} + 24 q^{55} + 53 q^{56} + 45 q^{57} + 27 q^{58} + 48 q^{59} + 66 q^{60} + 46 q^{61} + 81 q^{62} + 78 q^{63} + 252 q^{64} + 153 q^{65} + 6 q^{66} + 70 q^{67} + 240 q^{68} + 120 q^{69} - 31 q^{70} + 86 q^{71} + 89 q^{72} + 45 q^{73} + 68 q^{74} + 17 q^{75} - 13 q^{76} + 362 q^{77} + 69 q^{78} + 31 q^{79} + 169 q^{80} + 303 q^{81} + 25 q^{82} + 106 q^{83} + 13 q^{84} + 115 q^{85} + 95 q^{86} + 32 q^{87} + 83 q^{88} + 105 q^{89} - 38 q^{90} + 3 q^{91} + 310 q^{92} + 298 q^{93} - 17 q^{94} + 102 q^{95} - 82 q^{96} + 34 q^{97} + 81 q^{98} + 58 q^{99}+O(q^{100}) \) 179 * q + 22 * q^2 + 16 * q^3 + 196 * q^4 + 61 * q^5 + 7 * q^6 + 21 * q^7 + 60 * q^8 + 221 * q^9 + 9 * q^10 + 46 * q^11 + 33 * q^12 + 47 * q^13 + 22 * q^14 + 36 * q^15 + 222 * q^16 + 103 * q^17 + 43 * q^18 + 12 * q^19 + 102 * q^20 + 50 * q^21 + 39 * q^22 + 121 * q^23 - 3 * q^24 + 246 * q^25 + 52 * q^26 + 49 * q^27 + 41 * q^28 + 138 * q^29 + 28 * q^30 + 5 * q^31 + 137 * q^32 + 63 * q^33 + 2 * q^34 + 72 * q^35 + 279 * q^36 + 118 * q^37 + 123 * q^38 + q^39 + 9 * q^40 + 50 * q^41 + 48 * q^42 + 48 * q^43 + 108 * q^44 + 158 * q^45 + 13 * q^46 + 85 * q^47 + 50 * q^48 + 230 * q^49 + 78 * q^50 + 15 * q^51 + 41 * q^52 + 399 * q^53 - 5 * q^54 + 24 * q^55 + 53 * q^56 + 45 * q^57 + 27 * q^58 + 48 * q^59 + 66 * q^60 + 46 * q^61 + 81 * q^62 + 78 * q^63 + 252 * q^64 + 153 * q^65 + 6 * q^66 + 70 * q^67 + 240 * q^68 + 120 * q^69 - 31 * q^70 + 86 * q^71 + 89 * q^72 + 45 * q^73 + 68 * q^74 + 17 * q^75 - 13 * q^76 + 362 * q^77 + 69 * q^78 + 31 * q^79 + 169 * q^80 + 303 * q^81 + 25 * q^82 + 106 * q^83 + 13 * q^84 + 115 * q^85 + 95 * q^86 + 32 * q^87 + 83 * q^88 + 105 * q^89 - 38 * q^90 + 3 * q^91 + 310 * q^92 + 298 * q^93 - 17 * q^94 + 102 * q^95 - 82 * q^96 + 34 * q^97 + 81 * q^98 + 58 * q^99

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