LMFDB - Embedded newform 4003.2.a.b.1.11

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:	$1$
Dimension:	$152$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
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)

$f(q)$	$=$	$q-2.57418 q^{2} +1.68195 q^{3} +4.62641 q^{4} -3.90988 q^{5} -4.32965 q^{6} +1.64141 q^{7} -6.76085 q^{8} -0.171031 q^{9} +O(q^{10})$	\(q-2.57418 q^{2} +1.68195 q^{3} +4.62641 q^{4} -3.90988 q^{5} -4.32965 q^{6} +1.64141 q^{7} -6.76085 q^{8} -0.171031 q^{9} +10.0647 q^{10} -2.81413 q^{11} +7.78141 q^{12} -1.31278 q^{13} -4.22528 q^{14} -6.57624 q^{15} +8.15084 q^{16} +6.25005 q^{17} +0.440264 q^{18} +2.24150 q^{19} -18.0887 q^{20} +2.76077 q^{21} +7.24408 q^{22} -6.83949 q^{23} -11.3714 q^{24} +10.2872 q^{25} +3.37934 q^{26} -5.33353 q^{27} +7.59382 q^{28} +2.21320 q^{29} +16.9284 q^{30} +2.29852 q^{31} -7.46004 q^{32} -4.73324 q^{33} -16.0888 q^{34} -6.41770 q^{35} -0.791257 q^{36} +10.0689 q^{37} -5.77003 q^{38} -2.20804 q^{39} +26.4341 q^{40} +5.39843 q^{41} -7.10672 q^{42} -6.85484 q^{43} -13.0193 q^{44} +0.668709 q^{45} +17.6061 q^{46} +2.35069 q^{47} +13.7093 q^{48} -4.30579 q^{49} -26.4810 q^{50} +10.5123 q^{51} -6.07346 q^{52} -0.921929 q^{53} +13.7295 q^{54} +11.0029 q^{55} -11.0973 q^{56} +3.77010 q^{57} -5.69717 q^{58} -5.04597 q^{59} -30.4244 q^{60} -5.37742 q^{61} -5.91680 q^{62} -0.280731 q^{63} +2.90180 q^{64} +5.13282 q^{65} +12.1842 q^{66} +12.8008 q^{67} +28.9153 q^{68} -11.5037 q^{69} +16.5203 q^{70} +3.30042 q^{71} +1.15631 q^{72} -3.61155 q^{73} -25.9192 q^{74} +17.3025 q^{75} +10.3701 q^{76} -4.61913 q^{77} +5.68389 q^{78} +12.8611 q^{79} -31.8688 q^{80} -8.45766 q^{81} -13.8965 q^{82} -0.794973 q^{83} +12.7724 q^{84} -24.4370 q^{85} +17.6456 q^{86} +3.72249 q^{87} +19.0259 q^{88} +4.96940 q^{89} -1.72138 q^{90} -2.15481 q^{91} -31.6423 q^{92} +3.86600 q^{93} -6.05111 q^{94} -8.76400 q^{95} -12.5474 q^{96} +5.63651 q^{97} +11.0839 q^{98} +0.481302 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q - 22 q^{2} - 18 q^{3} + 138 q^{4} - 59 q^{5} - 17 q^{6} - 19 q^{7} - 66 q^{8} + 106 q^{9}+O(q^{10}) $ 152 * q - 22 * q^2 - 18 * q^3 + 138 * q^4 - 59 * q^5 - 17 * q^6 - 19 * q^7 - 66 * q^8 + 106 * q^9	\( 152 q - 22 q^{2} - 18 q^{3} + 138 q^{4} - 59 q^{5} - 17 q^{6} - 19 q^{7} - 66 q^{8} + 106 q^{9} - 15 q^{10} - 40 q^{11} - 53 q^{12} - 59 q^{13} - 36 q^{14} - 40 q^{15} + 118 q^{16} - 93 q^{17} - 59 q^{18} - 16 q^{19} - 108 q^{20} - 62 q^{21} - 37 q^{22} - 107 q^{23} - 31 q^{24} + 101 q^{25} - 64 q^{26} - 63 q^{27} - 53 q^{28} - 124 q^{29} - 68 q^{30} - 15 q^{31} - 129 q^{32} - 49 q^{33} - 76 q^{35} + 45 q^{36} - 98 q^{37} - 125 q^{38} - 47 q^{39} - 7 q^{40} - 56 q^{41} - 84 q^{42} - 62 q^{43} - 114 q^{44} - 142 q^{45} - 3 q^{46} - 111 q^{47} - 92 q^{48} + 117 q^{49} - 64 q^{50} - 21 q^{51} - 85 q^{52} - 347 q^{53} + 3 q^{54} - 16 q^{55} - 73 q^{56} - 115 q^{57} - 29 q^{58} - 50 q^{59} - 54 q^{60} - 62 q^{61} - 55 q^{62} - 70 q^{63} + 64 q^{64} - 147 q^{65} + 34 q^{66} - 86 q^{67} - 174 q^{68} - 104 q^{69} - 7 q^{70} - 86 q^{71} - 139 q^{72} - 27 q^{73} - 52 q^{74} - 49 q^{75} - 11 q^{76} - 346 q^{77} - 59 q^{78} - 17 q^{79} - 149 q^{80} - 8 q^{81} - 31 q^{82} - 106 q^{83} - 51 q^{84} - 69 q^{85} - 85 q^{86} - 32 q^{87} - 113 q^{88} - 59 q^{89} + 10 q^{90} - 9 q^{91} - 314 q^{92} - 230 q^{93} + 7 q^{94} - 74 q^{95} - 54 q^{96} - 60 q^{97} - 77 q^{98} - 96 q^{99}+O(q^{100}) \) 152 * q - 22 * q^2 - 18 * q^3 + 138 * q^4 - 59 * q^5 - 17 * q^6 - 19 * q^7 - 66 * q^8 + 106 * q^9 - 15 * q^10 - 40 * q^11 - 53 * q^12 - 59 * q^13 - 36 * q^14 - 40 * q^15 + 118 * q^16 - 93 * q^17 - 59 * q^18 - 16 * q^19 - 108 * q^20 - 62 * q^21 - 37 * q^22 - 107 * q^23 - 31 * q^24 + 101 * q^25 - 64 * q^26 - 63 * q^27 - 53 * q^28 - 124 * q^29 - 68 * q^30 - 15 * q^31 - 129 * q^32 - 49 * q^33 - 76 * q^35 + 45 * q^36 - 98 * q^37 - 125 * q^38 - 47 * q^39 - 7 * q^40 - 56 * q^41 - 84 * q^42 - 62 * q^43 - 114 * q^44 - 142 * q^45 - 3 * q^46 - 111 * q^47 - 92 * q^48 + 117 * q^49 - 64 * q^50 - 21 * q^51 - 85 * q^52 - 347 * q^53 + 3 * q^54 - 16 * q^55 - 73 * q^56 - 115 * q^57 - 29 * q^58 - 50 * q^59 - 54 * q^60 - 62 * q^61 - 55 * q^62 - 70 * q^63 + 64 * q^64 - 147 * q^65 + 34 * q^66 - 86 * q^67 - 174 * q^68 - 104 * q^69 - 7 * q^70 - 86 * q^71 - 139 * q^72 - 27 * q^73 - 52 * q^74 - 49 * q^75 - 11 * q^76 - 346 * q^77 - 59 * q^78 - 17 * q^79 - 149 * q^80 - 8 * q^81 - 31 * q^82 - 106 * q^83 - 51 * q^84 - 69 * q^85 - 85 * q^86 - 32 * q^87 - 113 * q^88 - 59 * q^89 + 10 * q^90 - 9 * q^91 - 314 * q^92 - 230 * q^93 + 7 * q^94 - 74 * q^95 - 54 * q^96 - 60 * q^97 - 77 * q^98 - 96 * 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 $

$2$	−2.57418	−1.82022	−0.910110	−	0.414366i	$-0.864003\pi$
$2$	−2.57418	−1.82022	−0.910110	+	0.414366i	$0.864003\pi$
$3$	1.68195	0.971077	0.485538	−	0.874215i	$-0.338624\pi$
$3$	1.68195	0.971077	0.485538	+	0.874215i	$0.338624\pi$
$4$	4.62641	2.31320
$5$	−3.90988	−1.74855	−0.874275	−	0.485430i	$-0.838663\pi$
$5$	−3.90988	−1.74855	−0.874275	+	0.485430i	$0.838663\pi$
$6$	−4.32965	−1.76757
$7$	1.64141	0.620393	0.310197	−	0.950672i	$-0.399605\pi$
$7$	1.64141	0.620393	0.310197	+	0.950672i	$0.399605\pi$
$8$	−6.76085	−2.39032
$9$	−0.171031	−0.0570102
$10$	10.0647	3.18275
$11$	−2.81413	−0.848492	−0.424246	−	0.905547i	$-0.639461\pi$
$11$	−2.81413	−0.848492	−0.424246	+	0.905547i	$0.639461\pi$
$12$	7.78141	2.24630
$13$	−1.31278	−0.364100	−0.182050	−	0.983289i	$-0.558273\pi$
$13$	−1.31278	−0.364100	−0.182050	+	0.983289i	$0.558273\pi$
$14$	−4.22528	−1.12925
$15$	−6.57624	−1.69798
$16$	8.15084	2.03771
$17$	6.25005	1.51586	0.757930	−	0.652335i	$-0.226211\pi$
$17$	6.25005	1.51586	0.757930	+	0.652335i	$0.226211\pi$
$18$	0.440264	0.103771
$19$	2.24150	0.514236	0.257118	−	0.966380i	$-0.417227\pi$
$19$	2.24150	0.514236	0.257118	+	0.966380i	$0.417227\pi$
$20$	−18.0887	−4.04476
$21$	2.76077	0.602449
$22$	7.24408	1.54444
$23$	−6.83949	−1.42613	−0.713066	−	0.701097i	$-0.752694\pi$
$23$	−6.83949	−1.42613	−0.713066	+	0.701097i	$0.752694\pi$
$24$	−11.3714	−2.32119
$25$	10.2872	2.05743
$26$	3.37934	0.662743
$27$	−5.33353	−1.02644
$28$	7.59382	1.43510
$29$	2.21320	0.410980	0.205490	−	0.978659i	$-0.434121\pi$
$29$	2.21320	0.410980	0.205490	+	0.978659i	$0.434121\pi$
$30$	16.9284	3.09069
$31$	2.29852	0.412826	0.206413	−	0.978465i	$-0.433821\pi$
$31$	2.29852	0.412826	0.206413	+	0.978465i	$0.433821\pi$
$32$	−7.46004	−1.31876
$33$	−4.73324	−0.823951
$34$	−16.0888	−2.75920
$35$	−6.41770	−1.08479
$36$	−0.791257	−0.131876
$37$	10.0689	1.65532	0.827659	−	0.561231i	$-0.189672\pi$
$37$	10.0689	1.65532	0.827659	+	0.561231i	$0.189672\pi$
$38$	−5.77003	−0.936023
$39$	−2.20804	−0.353569
$40$	26.4341	4.17960
$41$	5.39843	0.843093	0.421547	−	0.906807i	$-0.361487\pi$
$41$	5.39843	0.843093	0.421547	+	0.906807i	$0.361487\pi$
$42$	−7.10672	−1.09659
$43$	−6.85484	−1.04535	−0.522677	−	0.852531i	$-0.675067\pi$
$43$	−6.85484	−1.04535	−0.522677	+	0.852531i	$0.675067\pi$
$44$	−13.0193	−1.96274
$45$	0.668709	0.0996852
$46$	17.6061	2.59588
$47$	2.35069	0.342884	0.171442	−	0.985194i	$-0.445157\pi$
$47$	2.35069	0.342884	0.171442	+	0.985194i	$0.445157\pi$
$48$	13.7093	1.97877
$49$	−4.30579	−0.615112
$50$	−26.4810	−3.74498
$51$	10.5123	1.47202
$52$	−6.07346	−0.842238
$53$	−0.921929	−0.126637	−0.0633184	−	0.997993i	$-0.520168\pi$
$53$	−0.921929	−0.126637	−0.0633184	+	0.997993i	$0.520168\pi$
$54$	13.7295	1.86834
$55$	11.0029	1.48363
$56$	−11.0973	−1.48294
$57$	3.77010	0.499362
$58$	−5.69717	−0.748075
$59$	−5.04597	−0.656929	−0.328465	−	0.944516i	$-0.606531\pi$
$59$	−5.04597	−0.656929	−0.328465	+	0.944516i	$0.606531\pi$
$60$	−30.4244	−3.92777
$61$	−5.37742	−0.688508	−0.344254	−	0.938877i	$-0.611868\pi$
$61$	−5.37742	−0.688508	−0.344254	+	0.938877i	$0.611868\pi$
$62$	−5.91680	−0.751435
$63$	−0.280731	−0.0353687
$64$	2.90180	0.362725
$65$	5.13282	0.636648
$66$	12.1842	1.49977
$67$	12.8008	1.56387	0.781936	−	0.623359i	$-0.214232\pi$
$67$	12.8008	1.56387	0.781936	+	0.623359i	$0.214232\pi$
$68$	28.9153	3.50650
$69$	−11.5037	−1.38488
$70$	16.5203	1.97456
$71$	3.30042	0.391688	0.195844	−	0.980635i	$-0.437255\pi$
$71$	3.30042	0.391688	0.195844	+	0.980635i	$0.437255\pi$
$72$	1.15631	0.136273
$73$	−3.61155	−0.422700	−0.211350	−	0.977410i	$-0.567786\pi$
$73$	−3.61155	−0.422700	−0.211350	+	0.977410i	$0.567786\pi$
$74$	−25.9192	−3.01304
$75$	17.3025	1.99792
$76$	10.3701	1.18953
$77$	−4.61913	−0.526399
$78$	5.68389	0.643574
$79$	12.8611	1.44699	0.723495	−	0.690330i	$-0.242535\pi$
$79$	12.8611	1.44699	0.723495	+	0.690330i	$0.242535\pi$
$80$	−31.8688	−3.56304
$81$	−8.45766	−0.939740
$82$	−13.8965	−1.53462
$83$	−0.794973	−0.0872596	−0.0436298	−	0.999048i	$-0.513892\pi$
$83$	−0.794973	−0.0872596	−0.0436298	+	0.999048i	$0.513892\pi$
$84$	12.7724	1.39359
$85$	−24.4370	−2.65056
$86$	17.6456	1.90277
$87$	3.72249	0.399093
$88$	19.0259	2.02817
$89$	4.96940	0.526755	0.263378	−	0.964693i	$-0.415163\pi$
$89$	4.96940	0.526755	0.263378	+	0.964693i	$0.415163\pi$
$90$	−1.72138	−0.181449
$91$	−2.15481	−0.225885
$92$	−31.6423	−3.29894
$93$	3.86600	0.400886
$94$	−6.05111	−0.624124
$95$	−8.76400	−0.899168
$96$	−12.5474	−1.28062
$97$	5.63651	0.572301	0.286150	−	0.958185i	$-0.407624\pi$
$97$	5.63651	0.572301	0.286150	+	0.958185i	$0.407624\pi$
$98$	11.0839	1.11964
$99$	0.481302	0.0483727
$100$	47.5926	4.75926
$101$	−7.93993	−0.790052	−0.395026	−	0.918670i	$-0.629264\pi$
$101$	−7.93993	−0.790052	−0.395026	+	0.918670i	$0.629264\pi$
$102$	−27.0606	−2.67940
$103$	4.72876	0.465938	0.232969	−	0.972484i	$-0.425156\pi$
$103$	4.72876	0.465938	0.232969	+	0.972484i	$0.425156\pi$
$104$	8.87552	0.870317
$105$	−10.7943	−1.05341
$106$	2.37321	0.230507
$107$	−16.5157	−1.59663	−0.798317	−	0.602237i	$-0.794276\pi$
$107$	−16.5157	−1.59663	−0.798317	+	0.602237i	$0.794276\pi$
$108$	−24.6751	−2.37436
$109$	−18.9129	−1.81153	−0.905764	−	0.423782i	$-0.860702\pi$
$109$	−18.9129	−1.81153	−0.905764	+	0.423782i	$0.860702\pi$
$110$	−28.3235	−2.70054
$111$	16.9354	1.60744
$112$	13.3788	1.26418
$113$	−7.47603	−0.703286	−0.351643	−	0.936134i	$-0.614377\pi$
$113$	−7.47603	−0.703286	−0.351643	+	0.936134i	$0.614377\pi$
$114$	−9.70493	−0.908950
$115$	26.7416	2.49367
$116$	10.2392	0.950681
$117$	0.224526	0.0207574
$118$	12.9892	1.19576
$119$	10.2589	0.940430
$120$	44.4610	4.05871
$121$	−3.08067	−0.280061
$122$	13.8424	1.25324
$123$	9.07991	0.818708
$124$	10.6339	0.954951
$125$	−20.6721	−1.84897
$126$	0.722652	0.0643789
$127$	−5.22643	−0.463770	−0.231885	−	0.972743i	$-0.574489\pi$
$127$	−5.22643	−0.463770	−0.231885	+	0.972743i	$0.574489\pi$
$128$	7.45031	0.658520
$129$	−11.5295	−1.01512
$130$	−13.2128	−1.15884
$131$	13.2445	1.15718	0.578590	−	0.815619i	$-0.303603\pi$
$131$	13.2445	1.15718	0.578590	+	0.815619i	$0.303603\pi$
$132$	−21.8979	−1.90597
$133$	3.67922	0.319028
$134$	−32.9517	−2.84659
$135$	20.8534	1.79478
$136$	−42.2557	−3.62340
$137$	18.4405	1.57548	0.787741	−	0.616007i	$-0.211251\pi$
$137$	18.4405	1.57548	0.787741	+	0.616007i	$0.211251\pi$
$138$	29.6126	2.52079
$139$	−15.7244	−1.33372	−0.666861	−	0.745182i	$-0.732363\pi$
$139$	−15.7244	−1.33372	−0.666861	+	0.745182i	$0.732363\pi$
$140$	−29.6909	−2.50934
$141$	3.95376	0.332966
$142$	−8.49587	−0.712958
$143$	3.69434	0.308936
$144$	−1.39404	−0.116170
$145$	−8.65333	−0.718620
$146$	9.29679	0.769408
$147$	−7.24213	−0.597321
$148$	46.5829	3.82909
$149$	−13.7306	−1.12485	−0.562426	−	0.826848i	$-0.690132\pi$
$149$	−13.7306	−1.12485	−0.562426	+	0.826848i	$0.690132\pi$
$150$	−44.5398	−3.63666
$151$	0.503504	0.0409746	0.0204873	−	0.999790i	$-0.493478\pi$
$151$	0.503504	0.0409746	0.0204873	+	0.999790i	$0.493478\pi$
$152$	−15.1545	−1.22919
$153$	−1.06895	−0.0864195
$154$	11.8905	0.958162
$155$	−8.98693	−0.721848
$156$	−10.2153	−0.817878
$157$	−11.4268	−0.911961	−0.455981	−	0.889990i	$-0.650711\pi$
$157$	−11.4268	−0.911961	−0.455981	+	0.889990i	$0.650711\pi$
$158$	−33.1069	−2.63384
$159$	−1.55064	−0.122974
$160$	29.1678	2.30592
$161$	−11.2264	−0.884763
$162$	21.7715	1.71053
$163$	−12.5192	−0.980578	−0.490289	−	0.871560i	$-0.663109\pi$
$163$	−12.5192	−0.980578	−0.490289	+	0.871560i	$0.663109\pi$
$164$	24.9753	1.95025
$165$	18.5064	1.44072
$166$	2.04640	0.158832
$167$	−24.2451	−1.87614	−0.938070	−	0.346446i	$-0.887388\pi$
$167$	−24.2451	−1.87614	−0.938070	+	0.346446i	$0.887388\pi$
$168$	−18.6652	−1.44005
$169$	−11.2766	−0.867431
$170$	62.9051	4.82460
$171$	−0.383365	−0.0293167
$172$	−31.7133	−2.41812
$173$	2.60144	0.197784	0.0988920	−	0.995098i	$-0.468470\pi$
$173$	2.60144	0.197784	0.0988920	+	0.995098i	$0.468470\pi$
$174$	−9.58238	−0.726438
$175$	16.8854	1.27642
$176$	−22.9375	−1.72898
$177$	−8.48709	−0.637929
$178$	−12.7921	−0.958811
$179$	−16.3474	−1.22187	−0.610933	−	0.791682i	$-0.709205\pi$
$179$	−16.3474	−1.22187	−0.610933	+	0.791682i	$0.709205\pi$
$180$	3.09372	0.230592
$181$	−11.2401	−0.835467	−0.417734	−	0.908570i	$-0.637175\pi$
$181$	−11.2401	−0.835467	−0.417734	+	0.908570i	$0.637175\pi$
$182$	5.54687	0.411161
$183$	−9.04457	−0.668594
$184$	46.2408	3.40892
$185$	−39.3682	−2.89441
$186$	−9.95179	−0.729701
$187$	−17.5885	−1.28620
$188$	10.8753	0.793160
$189$	−8.75448	−0.636795
$190$	22.5601	1.63668
$191$	7.65034	0.553559	0.276780	−	0.960933i	$-0.410733\pi$
$191$	7.65034	0.553559	0.276780	+	0.960933i	$0.410733\pi$
$192$	4.88070	0.352234
$193$	−18.8090	−1.35390	−0.676952	−	0.736027i	$-0.736700\pi$
$193$	−18.8090	−1.35390	−0.676952	+	0.736027i	$0.736700\pi$
$194$	−14.5094	−1.04171
$195$	8.63316	0.618234
$196$	−19.9203	−1.42288
$197$	−1.69956	−0.121089	−0.0605444	−	0.998166i	$-0.519284\pi$
$197$	−1.69956	−0.121089	−0.0605444	+	0.998166i	$0.519284\pi$
$198$	−1.23896	−0.0880490
$199$	9.35245	0.662978	0.331489	−	0.943459i	$-0.392449\pi$
$199$	9.35245	0.662978	0.331489	+	0.943459i	$0.392449\pi$
$200$	−69.5499	−4.91792
$201$	21.5304	1.51864
$202$	20.4388	1.43807
$203$	3.63275	0.254969
$204$	48.6342	3.40508
$205$	−21.1072	−1.47419
$206$	−12.1727	−0.848110
$207$	1.16976	0.0813041
$208$	−10.7003	−0.741930
$209$	−6.30788	−0.436325
$210$	27.7864	1.91745
$211$	16.3239	1.12378	0.561890	−	0.827212i	$-0.310074\pi$
$211$	16.3239	1.12378	0.561890	+	0.827212i	$0.310074\pi$
$212$	−4.26522	−0.292937
$213$	5.55115	0.380359
$214$	42.5145	2.90623
$215$	26.8016	1.82785
$216$	36.0592	2.45352
$217$	3.77280	0.256115
$218$	48.6853	3.29738
$219$	−6.07447	−0.410474
$220$	50.9039	3.43194
$221$	−8.20496	−0.551925
$222$	−43.5949	−2.92590
$223$	−11.9494	−0.800192	−0.400096	−	0.916473i	$-0.631023\pi$
$223$	−11.9494	−0.800192	−0.400096	+	0.916473i	$0.631023\pi$
$224$	−12.2449	−0.818150
$225$	−1.75942	−0.117295
$226$	19.2447	1.28014
$227$	8.50040	0.564192	0.282096	−	0.959386i	$-0.408970\pi$
$227$	8.50040	0.564192	0.282096	+	0.959386i	$0.408970\pi$
$228$	17.4420	1.15513
$229$	3.78194	0.249918	0.124959	−	0.992162i	$-0.460120\pi$
$229$	3.78194	0.249918	0.124959	+	0.992162i	$0.460120\pi$
$230$	−68.8377	−4.53902
$231$	−7.76916	−0.511173
$232$	−14.9631	−0.982375
$233$	12.7680	0.836457	0.418228	−	0.908342i	$-0.362651\pi$
$233$	12.7680	0.836457	0.418228	+	0.908342i	$0.362651\pi$
$234$	−0.577970	−0.0377831
$235$	−9.19093	−0.599550
$236$	−23.3447	−1.51961
$237$	21.6318	1.40514
$238$	−26.4082	−1.71179
$239$	8.46041	0.547258	0.273629	−	0.961835i	$-0.411776\pi$
$239$	8.46041	0.547258	0.273629	+	0.961835i	$0.411776\pi$
$240$	−53.6019	−3.45998
$241$	25.3492	1.63288	0.816442	−	0.577427i	$-0.195943\pi$
$241$	25.3492	1.63288	0.816442	+	0.577427i	$0.195943\pi$
$242$	7.93021	0.509773
$243$	1.77519	0.113879
$244$	−24.8781	−1.59266
$245$	16.8351	1.07556
$246$	−23.3733	−1.49023
$247$	−2.94260	−0.187233
$248$	−15.5399	−0.986788
$249$	−1.33711	−0.0847357
$250$	53.2138	3.36554
$251$	−16.1833	−1.02148	−0.510740	−	0.859735i	$-0.670629\pi$
$251$	−16.1833	−1.02148	−0.510740	+	0.859735i	$0.670629\pi$
$252$	−1.29877	−0.0818151
$253$	19.2472	1.21006
$254$	13.4538	0.844165
$255$	−41.1018	−2.57390
$256$	−24.9820	−1.56138
$257$	−7.52711	−0.469528	−0.234764	−	0.972052i	$-0.575432\pi$
$257$	−7.52711	−0.469528	−0.234764	+	0.972052i	$0.575432\pi$
$258$	29.6791	1.84774
$259$	16.5272	1.02695
$260$	23.7465	1.47270
$261$	−0.378524	−0.0234301
$262$	−34.0938	−2.10632
$263$	1.37815	0.0849805	0.0424902	−	0.999097i	$-0.486471\pi$
$263$	1.37815	0.0849805	0.0424902	+	0.999097i	$0.486471\pi$
$264$	32.0007	1.96951
$265$	3.60463	0.221431
$266$	−9.47097	−0.580702
$267$	8.35830	0.511520
$268$	59.2219	3.61755
$269$	−22.4390	−1.36813	−0.684064	−	0.729422i	$-0.739789\pi$
$269$	−22.4390	−1.36813	−0.684064	+	0.729422i	$0.739789\pi$
$270$	−53.6806	−3.26689
$271$	−1.74848	−0.106213	−0.0531063	−	0.998589i	$-0.516912\pi$
$271$	−1.74848	−0.106213	−0.0531063	+	0.998589i	$0.516912\pi$
$272$	50.9432	3.08888
$273$	−3.62429	−0.219352
$274$	−47.4693	−2.86772
$275$	−28.9494	−1.74571
$276$	−53.2209	−3.20352
$277$	−1.62754	−0.0977894	−0.0488947	−	0.998804i	$-0.515570\pi$
$277$	−1.62754	−0.0977894	−0.0488947	+	0.998804i	$0.515570\pi$
$278$	40.4773	2.42767
$279$	−0.393117	−0.0235353
$280$	43.3891	2.59300
$281$	10.5531	0.629546	0.314773	−	0.949167i	$-0.398072\pi$
$281$	10.5531	0.629546	0.314773	+	0.949167i	$0.398072\pi$
$282$	−10.1777	−0.606073
$283$	−11.1400	−0.662203	−0.331101	−	0.943595i	$-0.607420\pi$
$283$	−11.1400	−0.662203	−0.331101	+	0.943595i	$0.607420\pi$
$284$	15.2691	0.906053
$285$	−14.7407	−0.873161
$286$	−9.50990	−0.562332
$287$	8.86101	0.523049
$288$	1.27589	0.0751828
$289$	22.0632	1.29783
$290$	22.2752	1.30805
$291$	9.48035	0.555748
$292$	−16.7085	−0.977792
$293$	2.72502	0.159197	0.0795986	−	0.996827i	$-0.474636\pi$
$293$	2.72502	0.159197	0.0795986	+	0.996827i	$0.474636\pi$
$294$	18.6426	1.08726
$295$	19.7291	1.14867
$296$	−68.0744	−3.95674
$297$	15.0092	0.870924
$298$	35.3450	2.04748
$299$	8.97876	0.519255
$300$	80.0485	4.62160
$301$	−11.2516	−0.648530
$302$	−1.29611	−0.0745828
$303$	−13.3546	−0.767201
$304$	18.2701	1.04786
$305$	21.0251	1.20389
$306$	2.75167	0.157303
$307$	−3.92758	−0.224159	−0.112080	−	0.993699i	$-0.535751\pi$
$307$	−3.92758	−0.224159	−0.112080	+	0.993699i	$0.535751\pi$
$308$	−21.3700	−1.21767
$309$	7.95355	0.452462
$310$	23.1340	1.31392
$311$	11.5196	0.653217	0.326609	−	0.945160i	$-0.394094\pi$
$311$	11.5196	0.653217	0.326609	+	0.945160i	$0.394094\pi$
$312$	14.9282	0.845144
$313$	26.4712	1.49624	0.748121	−	0.663562i	$-0.230956\pi$
$313$	26.4712	1.49624	0.748121	+	0.663562i	$0.230956\pi$
$314$	29.4148	1.65997
$315$	1.09762	0.0618440
$316$	59.5008	3.34718
$317$	−33.7517	−1.89569	−0.947844	−	0.318736i	$-0.896742\pi$
$317$	−33.7517	−1.89569	−0.947844	+	0.318736i	$0.896742\pi$
$318$	3.99164	0.223840
$319$	−6.22822	−0.348713
$320$	−11.3457	−0.634244
$321$	−27.7787	−1.55045
$322$	28.8987	1.61046
$323$	14.0095	0.779510
$324$	−39.1286	−2.17381
$325$	−13.5048	−0.749111
$326$	32.2266	1.78487
$327$	−31.8106	−1.75913
$328$	−36.4980	−2.01526
$329$	3.85844	0.212723
$330$	−47.6388	−2.62243
$331$	35.5910	1.95626	0.978128	−	0.208005i	$-0.0666970\pi$
$331$	35.5910	1.95626	0.978128	+	0.208005i	$0.0666970\pi$
$332$	−3.67787	−0.201849
$333$	−1.72209	−0.0943700
$334$	62.4112	3.41499
$335$	−50.0497	−2.73451
$336$	22.5026	1.22762
$337$	−7.41648	−0.404002	−0.202001	−	0.979385i	$-0.564744\pi$
$337$	−7.41648	−0.404002	−0.202001	+	0.979385i	$0.564744\pi$
$338$	29.0280	1.57892
$339$	−12.5743	−0.682945
$340$	−113.055	−6.13129
$341$	−6.46833	−0.350280
$342$	0.986852	0.0533629
$343$	−18.5574	−1.00200
$344$	46.3446	2.49873
$345$	44.9781	2.42154
$346$	−6.69658	−0.360011
$347$	6.04385	0.324451	0.162225	−	0.986754i	$-0.448133\pi$
$347$	6.04385	0.324451	0.162225	+	0.986754i	$0.448133\pi$
$348$	17.2218	0.923184
$349$	−20.4992	−1.09730	−0.548649	−	0.836053i	$-0.684858\pi$
$349$	−20.4992	−1.09730	−0.548649	+	0.836053i	$0.684858\pi$
$350$	−43.4661	−2.32336
$351$	7.00176	0.373726
$352$	20.9935	1.11896
$353$	32.7765	1.74452	0.872259	−	0.489044i	$-0.162654\pi$
$353$	32.7765	1.74452	0.872259	+	0.489044i	$0.162654\pi$
$354$	21.8473	1.16117
$355$	−12.9042	−0.684886
$356$	22.9905	1.21849
$357$	17.2550	0.913229
$358$	42.0813	2.22407
$359$	−19.5331	−1.03092	−0.515458	−	0.856915i	$-0.672378\pi$
$359$	−19.5331	−1.03092	−0.515458	+	0.856915i	$0.672378\pi$
$360$	−4.52104	−0.238280
$361$	−13.9757	−0.735561
$362$	28.9340	1.52073
$363$	−5.18155	−0.271961
$364$	−9.96902	−0.522519
$365$	14.1207	0.739113
$366$	23.2824	1.21699
$367$	−15.1994	−0.793401	−0.396701	−	0.917948i	$-0.629845\pi$
$367$	−15.1994	−0.793401	−0.396701	+	0.917948i	$0.629845\pi$
$368$	−55.7476	−2.90604
$369$	−0.923297	−0.0480649
$370$	101.341	5.26846
$371$	−1.51326	−0.0785646
$372$	17.8857	0.927331
$373$	−15.9565	−0.826195	−0.413097	−	0.910687i	$-0.635553\pi$
$373$	−15.9565	−0.826195	−0.413097	+	0.910687i	$0.635553\pi$
$374$	45.2759	2.34116
$375$	−34.7696	−1.79549
$376$	−15.8927	−0.819603
$377$	−2.90544	−0.149638
$378$	22.5356	1.15911
$379$	3.62806	0.186361	0.0931805	−	0.995649i	$-0.470297\pi$
$379$	3.62806	0.186361	0.0931805	+	0.995649i	$0.470297\pi$
$380$	−40.5459	−2.07996
$381$	−8.79061	−0.450357
$382$	−19.6934	−1.00760
$383$	−33.0296	−1.68773	−0.843866	−	0.536554i	$-0.819726\pi$
$383$	−33.0296	−1.68773	−0.843866	+	0.536554i	$0.819726\pi$
$384$	12.5311	0.639474
$385$	18.0602	0.920435
$386$	48.4179	2.46440
$387$	1.17239	0.0595958
$388$	26.0768	1.32385
$389$	33.2699	1.68685	0.843425	−	0.537248i	$-0.180536\pi$
$389$	33.2699	1.68685	0.843425	+	0.537248i	$0.180536\pi$
$390$	−22.2233	−1.12532
$391$	−42.7472	−2.16182
$392$	29.1108	1.47032
$393$	22.2767	1.12371
$394$	4.37498	0.220408
$395$	−50.2854	−2.53013
$396$	2.22670	0.111896
$397$	6.25079	0.313718	0.156859	−	0.987621i	$-0.449863\pi$
$397$	6.25079	0.313718	0.156859	+	0.987621i	$0.449863\pi$
$398$	−24.0749	−1.20677
$399$	6.18827	0.309801
$400$	83.8489	4.19245
$401$	9.72971	0.485878	0.242939	−	0.970042i	$-0.421888\pi$
$401$	9.72971	0.485878	0.242939	+	0.970042i	$0.421888\pi$
$402$	−55.4232	−2.76426
$403$	−3.01745	−0.150310
$404$	−36.7333	−1.82755
$405$	33.0684	1.64318
$406$	−9.35137	−0.464101
$407$	−28.3352	−1.40452
$408$	−71.0721	−3.51859
$409$	−38.9591	−1.92640	−0.963202	−	0.268777i	$-0.913381\pi$
$409$	−38.9591	−1.92640	−0.963202	+	0.268777i	$0.913381\pi$
$410$	54.3338	2.68335
$411$	31.0161	1.52991
$412$	21.8772	1.07781
$413$	−8.28249	−0.407555
$414$	−3.01118	−0.147991
$415$	3.10825	0.152578
$416$	9.79340	0.480161
$417$	−26.4476	−1.29515
$418$	16.2376	0.794208
$419$	8.35650	0.408242	0.204121	−	0.978946i	$-0.434566\pi$
$419$	8.35650	0.408242	0.204121	+	0.978946i	$0.434566\pi$
$420$	−49.9387	−2.43676
$421$	−25.5645	−1.24594	−0.622968	−	0.782248i	$-0.714073\pi$
$421$	−25.5645	−1.24594	−0.622968	+	0.782248i	$0.714073\pi$
$422$	−42.0206	−2.04553
$423$	−0.402040	−0.0195479
$424$	6.23303	0.302703
$425$	64.2953	3.11878
$426$	−14.2897	−0.692337
$427$	−8.82653	−0.427146
$428$	−76.4085	−3.69334
$429$	6.21371	0.300001
$430$	−68.9922	−3.32710
$431$	−14.5800	−0.702295	−0.351147	−	0.936320i	$-0.614208\pi$
$431$	−14.5800	−0.702295	−0.351147	+	0.936320i	$0.614208\pi$
$432$	−43.4727	−2.09158
$433$	−21.9601	−1.05533	−0.527667	−	0.849451i	$-0.676933\pi$
$433$	−21.9601	−1.05533	−0.527667	+	0.849451i	$0.676933\pi$
$434$	−9.71188	−0.466185
$435$	−14.5545	−0.697835
$436$	−87.4989	−4.19044
$437$	−15.3307	−0.733369
$438$	15.6368	0.747154
$439$	−34.2330	−1.63385	−0.816927	−	0.576741i	$-0.804324\pi$
$439$	−34.2330	−1.63385	−0.816927	+	0.576741i	$0.804324\pi$
$440$	−74.3890	−3.54636
$441$	0.736421	0.0350677
$442$	21.1210	1.00463
$443$	−24.1910	−1.14935	−0.574675	−	0.818381i	$-0.694872\pi$
$443$	−24.1910	−1.14935	−0.574675	+	0.818381i	$0.694872\pi$
$444$	78.3503	3.71834
$445$	−19.4298	−0.921059
$446$	30.7600	1.45653
$447$	−23.0942	−1.09232
$448$	4.76304	0.225032
$449$	−32.6112	−1.53902	−0.769509	−	0.638636i	$-0.779499\pi$
$449$	−32.6112	−1.53902	−0.769509	+	0.638636i	$0.779499\pi$
$450$	4.52906	0.213502
$451$	−15.1919	−0.715358
$452$	−34.5872	−1.62684
$453$	0.846871	0.0397895
$454$	−21.8816	−1.02695
$455$	8.42504	0.394972
$456$	−25.4891	−1.19364
$457$	23.0892	1.08007	0.540034	−	0.841643i	$-0.318411\pi$
$457$	23.0892	1.08007	0.540034	+	0.841643i	$0.318411\pi$
$458$	−9.73540	−0.454905
$459$	−33.3348	−1.55594
$460$	123.717	5.76836
$461$	12.9303	0.602223	0.301112	−	0.953589i	$-0.402642\pi$
$461$	12.9303	0.602223	0.301112	+	0.953589i	$0.402642\pi$
$462$	19.9992	0.930449
$463$	3.75957	0.174722	0.0873610	−	0.996177i	$-0.472157\pi$
$463$	3.75957	0.174722	0.0873610	+	0.996177i	$0.472157\pi$
$464$	18.0394	0.837459
$465$	−15.1156	−0.700969
$466$	−32.8670	−1.52254
$467$	−9.98448	−0.462026	−0.231013	−	0.972951i	$-0.574204\pi$
$467$	−9.98448	−0.462026	−0.231013	+	0.972951i	$0.574204\pi$
$468$	1.03875	0.0480162
$469$	21.0114	0.970215
$470$	23.6591	1.09131
$471$	−19.2194	−0.885584
$472$	34.1151	1.57027
$473$	19.2904	0.886974
$474$	−55.6842	−2.55766
$475$	23.0587	1.05800
$476$	47.4618	2.17541
$477$	0.157678	0.00721959
$478$	−21.7786	−0.996131
$479$	−17.3875	−0.794455	−0.397228	−	0.917720i	$-0.630028\pi$
$479$	−17.3875	−0.794455	−0.397228	+	0.917720i	$0.630028\pi$
$480$	49.0590	2.23922
$481$	−13.2183	−0.602702
$482$	−65.2534	−2.97221
$483$	−18.8823	−0.859172
$484$	−14.2525	−0.647839
$485$	−22.0381	−1.00070
$486$	−4.56967	−0.207284
$487$	24.3573	1.10374	0.551868	−	0.833931i	$-0.313915\pi$
$487$	24.3573	1.10374	0.551868	+	0.833931i	$0.313915\pi$
$488$	36.3559	1.64576
$489$	−21.0567	−0.952216
$490$	−43.3366	−1.95775
$491$	21.9248	0.989451	0.494725	−	0.869049i	$-0.335269\pi$
$491$	21.9248	0.989451	0.494725	+	0.869049i	$0.335269\pi$
$492$	42.0074	1.89384
$493$	13.8326	0.622989
$494$	7.57479	0.340806
$495$	−1.88183	−0.0845821
$496$	18.7349	0.841220
$497$	5.41733	0.243000
$498$	3.44196	0.154238
$499$	1.44106	0.0645107	0.0322554	−	0.999480i	$-0.489731\pi$
$499$	1.44106	0.0645107	0.0322554	+	0.999480i	$0.489731\pi$
$500$	−95.6377	−4.27705
$501$	−40.7791	−1.82188
$502$	41.6587	1.85932
$503$	−24.1921	−1.07867	−0.539337	−	0.842090i	$-0.681325\pi$
$503$	−24.1921	−1.07867	−0.539337	+	0.842090i	$0.681325\pi$
$504$	1.89798	0.0845427
$505$	31.0441	1.38145
$506$	−49.5458	−2.20258
$507$	−18.9667	−0.842342
$508$	−24.1796	−1.07280
$509$	−18.4215	−0.816518	−0.408259	−	0.912866i	$-0.633864\pi$
$509$	−18.4215	−0.816518	−0.408259	+	0.912866i	$0.633864\pi$
$510$	105.804	4.68506
$511$	−5.92803	−0.262240
$512$	49.4077	2.18353
$513$	−11.9551	−0.527831
$514$	19.3762	0.854646
$515$	−18.4889	−0.814717
$516$	−53.3403	−2.34818
$517$	−6.61516	−0.290934
$518$	−42.5439	−1.86927
$519$	4.37551	0.192063
$520$	−34.7022	−1.52179
$521$	8.66130	0.379459	0.189729	−	0.981836i	$-0.439239\pi$
$521$	8.66130	0.379459	0.189729	+	0.981836i	$0.439239\pi$
$522$	0.974390	0.0426479
$523$	−24.7933	−1.08414	−0.542068	−	0.840335i	$-0.682358\pi$
$523$	−24.7933	−1.08414	−0.542068	+	0.840335i	$0.682358\pi$
$524$	61.2746	2.67679
$525$	28.4005	1.23950
$526$	−3.54761	−0.154683
$527$	14.3659	0.625787
$528$	−38.5799	−1.67897
$529$	23.7786	1.03385
$530$	−9.27898	−0.403053
$531$	0.863015	0.0374517
$532$	17.0216	0.737978
$533$	−7.08696	−0.306970
$534$	−21.5158	−0.931079
$535$	64.5745	2.79180
$536$	−86.5446	−3.73816
$537$	−27.4957	−1.18653
$538$	57.7619	2.49029
$539$	12.1170	0.521918
$540$	96.4766	4.15169
$541$	−18.0975	−0.778074	−0.389037	−	0.921222i	$-0.627192\pi$
$541$	−18.0975	−0.778074	−0.389037	+	0.921222i	$0.627192\pi$
$542$	4.50091	0.193330
$543$	−18.9053	−0.811303
$544$	−46.6256	−1.99906
$545$	73.9472	3.16755
$546$	9.32957	0.399269
$547$	12.7052	0.543235	0.271618	−	0.962405i	$-0.412441\pi$
$547$	12.7052	0.543235	0.271618	+	0.962405i	$0.412441\pi$
$548$	85.3135	3.64441
$549$	0.919703	0.0392520
$550$	74.5210	3.17758
$551$	4.96089	0.211341
$552$	77.7749	3.31032
$553$	21.1103	0.897702
$554$	4.18958	0.177998
$555$	−66.2155	−2.81069
$556$	−72.7473	−3.08517
$557$	7.53352	0.319205	0.159603	−	0.987181i	$-0.448979\pi$
$557$	7.53352	0.319205	0.159603	+	0.987181i	$0.448979\pi$
$558$	1.01195	0.0428395
$559$	8.99891	0.380613
$560$	−52.3096	−2.21049
$561$	−29.5830	−1.24899
$562$	−27.1656	−1.14591
$563$	−14.0284	−0.591226	−0.295613	−	0.955308i	$-0.595524\pi$
$563$	−14.0284	−0.591226	−0.295613	+	0.955308i	$0.595524\pi$
$564$	18.2917	0.770219
$565$	29.2304	1.22973
$566$	28.6763	1.20536
$567$	−13.8824	−0.583008
$568$	−22.3136	−0.936259
$569$	−33.5442	−1.40624	−0.703122	−	0.711069i	$-0.748211\pi$
$569$	−33.5442	−1.40624	−0.703122	+	0.711069i	$0.748211\pi$
$570$	37.9451	1.58935
$571$	8.51441	0.356317	0.178158	−	0.984002i	$-0.442986\pi$
$571$	8.51441	0.356317	0.178158	+	0.984002i	$0.442986\pi$
$572$	17.0915	0.714632
$573$	12.8675	0.537549
$574$	−22.8099	−0.952065
$575$	−70.3589	−2.93417
$576$	−0.496297	−0.0206790
$577$	−33.8241	−1.40812	−0.704058	−	0.710142i	$-0.748631\pi$
$577$	−33.8241	−1.40812	−0.704058	+	0.710142i	$0.748631\pi$
$578$	−56.7946	−2.36234
$579$	−31.6359	−1.31474
$580$	−40.0338	−1.66231
$581$	−1.30487	−0.0541353
$582$	−24.4041	−1.01158
$583$	2.59443	0.107450
$584$	24.4172	1.01039
$585$	−0.877869	−0.0362954
$586$	−7.01469	−0.289774
$587$	27.3114	1.12726	0.563631	−	0.826027i	$-0.309404\pi$
$587$	27.3114	1.12726	0.563631	+	0.826027i	$0.309404\pi$
$588$	−33.5051	−1.38173
$589$	5.15214	0.212290
$590$	−50.7864	−2.09084
$591$	−2.85858	−0.117586
$592$	82.0701	3.37306
$593$	5.31376	0.218210	0.109105	−	0.994030i	$-0.465202\pi$
$593$	5.31376	0.218210	0.109105	+	0.994030i	$0.465202\pi$
$594$	−38.6365	−1.58527
$595$	−40.1110	−1.64439
$596$	−63.5232	−2.60201
$597$	15.7304	0.643802
$598$	−23.1129	−0.945159
$599$	−30.7507	−1.25644	−0.628220	−	0.778036i	$-0.716216\pi$
$599$	−30.7507	−1.25644	−0.628220	+	0.778036i	$0.716216\pi$
$600$	−116.980	−4.77568
$601$	−32.0551	−1.30756	−0.653778	−	0.756686i	$-0.726817\pi$
$601$	−32.0551	−1.30756	−0.653778	+	0.756686i	$0.726817\pi$
$602$	28.9636	1.18047
$603$	−2.18934	−0.0891566
$604$	2.32942	0.0947826
$605$	12.0451	0.489701
$606$	34.3771	1.39648
$607$	3.40148	0.138062	0.0690308	−	0.997615i	$-0.478009\pi$
$607$	3.40148	0.138062	0.0690308	+	0.997615i	$0.478009\pi$
$608$	−16.7217	−0.678154
$609$	6.11013	0.247595
$610$	−54.1223	−2.19135
$611$	−3.08595	−0.124844
$612$	−4.94540	−0.199906
$613$	−3.89362	−0.157262	−0.0786309	−	0.996904i	$-0.525055\pi$
$613$	−3.89362	−0.157262	−0.0786309	+	0.996904i	$0.525055\pi$
$614$	10.1103	0.408019
$615$	−35.5013	−1.43155
$616$	31.2293	1.25826
$617$	−12.4463	−0.501068	−0.250534	−	0.968108i	$-0.580606\pi$
$617$	−12.4463	−0.501068	−0.250534	+	0.968108i	$0.580606\pi$
$618$	−20.4739	−0.823580
$619$	−3.98933	−0.160345	−0.0801724	−	0.996781i	$-0.525547\pi$
$619$	−3.98933	−0.160345	−0.0801724	+	0.996781i	$0.525547\pi$
$620$	−41.5772	−1.66978
$621$	36.4786	1.46384
$622$	−29.6536	−1.18900
$623$	8.15680	0.326795
$624$	−17.9974	−0.720471
$625$	29.3897	1.17559
$626$	−68.1418	−2.72349
$627$	−10.6096	−0.423705
$628$	−52.8652	−2.10955
$629$	62.9312	2.50923
$630$	−2.82548	−0.112570
$631$	39.4303	1.56970	0.784849	−	0.619687i	$-0.212741\pi$
$631$	39.4303	1.56970	0.784849	+	0.619687i	$0.212741\pi$
$632$	−86.9522	−3.45877
$633$	27.4560	1.09128
$634$	86.8831	3.45057
$635$	20.4347	0.810926
$636$	−7.17391	−0.284464
$637$	5.65256	0.223962
$638$	16.0326	0.634736
$639$	−0.564472	−0.0223302
$640$	−29.1298	−1.15146
$641$	−19.0244	−0.751417	−0.375709	−	0.926738i	$-0.622601\pi$
$641$	−19.0244	−0.751417	−0.375709	+	0.926738i	$0.622601\pi$
$642$	71.5074	2.82217
$643$	−21.0604	−0.830541	−0.415270	−	0.909698i	$-0.636313\pi$
$643$	−21.0604	−0.830541	−0.415270	+	0.909698i	$0.636313\pi$
$644$	−51.9378	−2.04664
$645$	45.0791	1.77499
$646$	−36.0630	−1.41888
$647$	15.9164	0.625739	0.312870	−	0.949796i	$-0.398710\pi$
$647$	15.9164	0.625739	0.312870	+	0.949796i	$0.398710\pi$
$648$	57.1810	2.24628
$649$	14.2000	0.557399
$650$	34.7638	1.36355
$651$	6.34568	0.248707
$652$	−57.9189	−2.26828
$653$	−33.5859	−1.31432	−0.657159	−	0.753752i	$-0.728242\pi$
$653$	−33.5859	−1.31432	−0.657159	+	0.753752i	$0.728242\pi$
$654$	81.8864	3.20201
$655$	−51.7845	−2.02339
$656$	44.0017	1.71798
$657$	0.617686	0.0240982
$658$	−9.93233	−0.387202
$659$	34.1333	1.32965	0.664823	−	0.747001i	$-0.268507\pi$
$659$	34.1333	1.32965	0.664823	+	0.747001i	$0.268507\pi$
$660$	85.6181	3.33268
$661$	23.2609	0.904742	0.452371	−	0.891830i	$-0.350578\pi$
$661$	23.2609	0.904742	0.452371	+	0.891830i	$0.350578\pi$
$662$	−91.6176	−3.56082
$663$	−13.8004	−0.535962
$664$	5.37469	0.208579
$665$	−14.3853	−0.557838
$666$	4.43297	0.171774
$667$	−15.1371	−0.586112
$668$	−112.168	−4.33990
$669$	−20.0984	−0.777048
$670$	128.837	4.97741
$671$	15.1328	0.584193
$672$	−20.5954	−0.794486
$673$	−31.3343	−1.20785	−0.603925	−	0.797041i	$-0.706397\pi$
$673$	−31.3343	−1.20785	−0.603925	+	0.797041i	$0.706397\pi$
$674$	19.0914	0.735372
$675$	−54.8668	−2.11182
$676$	−52.1702	−2.00655
$677$	10.7206	0.412027	0.206013	−	0.978549i	$-0.433951\pi$
$677$	10.7206	0.412027	0.206013	+	0.978549i	$0.433951\pi$
$678$	32.3686	1.24311
$679$	9.25180	0.355052
$680$	165.215	6.33569
$681$	14.2973	0.547873
$682$	16.6507	0.637587
$683$	−29.1085	−1.11380	−0.556902	−	0.830578i	$-0.688010\pi$
$683$	−29.1085	−1.11380	−0.556902	+	0.830578i	$0.688010\pi$
$684$	−1.77361	−0.0678155
$685$	−72.1003	−2.75481
$686$	47.7701	1.82387
$687$	6.36105	0.242689
$688$	−55.8727	−2.13013
$689$	1.21029	0.0461085
$690$	−115.782	−4.40774
$691$	16.2246	0.617214	0.308607	−	0.951190i	$-0.400137\pi$
$691$	16.2246	0.617214	0.308607	+	0.951190i	$0.400137\pi$
$692$	12.0353	0.457515
$693$	0.790012	0.0300101
$694$	−15.5580	−0.590572
$695$	61.4803	2.33208
$696$	−25.1672	−0.953962
$697$	33.7405	1.27801
$698$	52.7687	1.99732
$699$	21.4751	0.812263
$700$	78.1187	2.95261
$701$	36.6427	1.38398	0.691988	−	0.721909i	$-0.256735\pi$
$701$	36.6427	1.38398	0.691988	+	0.721909i	$0.256735\pi$
$702$	−18.0238	−0.680264
$703$	22.5695	0.851224
$704$	−8.16605	−0.307770
$705$	−15.4587	−0.582209
$706$	−84.3727	−3.17541
$707$	−13.0326	−0.490143
$708$	−39.2647	−1.47566
$709$	−18.0859	−0.679230	−0.339615	−	0.940564i	$-0.610297\pi$
$709$	−18.0859	−0.679230	−0.339615	+	0.940564i	$0.610297\pi$
$710$	33.2178	1.24664
$711$	−2.19965	−0.0824932
$712$	−33.5974	−1.25911
$713$	−15.7207	−0.588745
$714$	−44.4174	−1.66228
$715$	−14.4444	−0.540190
$716$	−75.6300	−2.82642
$717$	14.2300	0.531430
$718$	50.2817	1.87650
$719$	38.4342	1.43335	0.716676	−	0.697406i	$-0.245662\pi$
$719$	38.4342	1.43335	0.716676	+	0.697406i	$0.245662\pi$
$720$	5.45054	0.203130
$721$	7.76181	0.289065
$722$	35.9759	1.33888
$723$	42.6362	1.58566
$724$	−52.0011	−1.93261
$725$	22.7675	0.845563
$726$	13.3383	0.495029
$727$	−35.6788	−1.32326	−0.661628	−	0.749833i	$-0.730134\pi$
$727$	−35.6788	−1.32326	−0.661628	+	0.749833i	$0.730134\pi$
$728$	14.5683	0.539938
$729$	28.3588	1.05032
$730$	−36.3493	−1.34535
$731$	−42.8431	−1.58461
$732$	−41.8439	−1.54659
$733$	−40.9054	−1.51088	−0.755438	−	0.655220i	$-0.772576\pi$
$733$	−40.9054	−1.51088	−0.755438	+	0.655220i	$0.772576\pi$
$734$	39.1260	1.44417
$735$	28.3159	1.04445
$736$	51.0228	1.88073
$737$	−36.0232	−1.32693
$738$	2.37673	0.0874887
$739$	18.0475	0.663887	0.331943	−	0.943299i	$-0.392296\pi$
$739$	18.0475	0.663887	0.331943	+	0.943299i	$0.392296\pi$
$740$	−182.133	−6.69536
$741$	−4.94932	−0.181818
$742$	3.89541	0.143005
$743$	−27.9337	−1.02479	−0.512394	−	0.858750i	$-0.671241\pi$
$743$	−27.9337	−1.02479	−0.512394	+	0.858750i	$0.671241\pi$
$744$	−26.1375	−0.958246
$745$	53.6849	1.96686
$746$	41.0749	1.50386
$747$	0.135965	0.00497469
$748$	−81.3714	−2.97523
$749$	−27.1090	−0.990541
$750$	89.5032	3.26819
$751$	−1.70135	−0.0620830	−0.0310415	−	0.999518i	$-0.509882\pi$
$751$	−1.70135	−0.0620830	−0.0310415	+	0.999518i	$0.509882\pi$
$752$	19.1601	0.698698
$753$	−27.2196	−0.991936
$754$	7.47914	0.272374
$755$	−1.96864	−0.0716461
$756$	−40.5018	−1.47304
$757$	−22.2521	−0.808766	−0.404383	−	0.914590i	$-0.632514\pi$
$757$	−22.2521	−0.808766	−0.404383	+	0.914590i	$0.632514\pi$
$758$	−9.33929	−0.339218
$759$	32.3729	1.17506
$760$	59.2521	2.14930
$761$	20.3333	0.737080	0.368540	−	0.929612i	$-0.379858\pi$
$761$	20.3333	0.737080	0.368540	+	0.929612i	$0.379858\pi$
$762$	22.6286	0.819749
$763$	−31.0438	−1.12386
$764$	35.3936	1.28050
$765$	4.17947	0.151109
$766$	85.0241	3.07205
$767$	6.62426	0.239188
$768$	−42.0186	−1.51622
$769$	14.6082	0.526784	0.263392	−	0.964689i	$-0.415159\pi$
$769$	14.6082	0.526784	0.263392	+	0.964689i	$0.415159\pi$
$770$	−46.4903	−1.67539
$771$	−12.6603	−0.455948
$772$	−87.0183	−3.13186
$773$	−4.03237	−0.145034	−0.0725171	−	0.997367i	$-0.523103\pi$
$773$	−4.03237	−0.145034	−0.0725171	+	0.997367i	$0.523103\pi$
$774$	−3.01794	−0.108478
$775$	23.6452	0.849361
$776$	−38.1076	−1.36798
$777$	27.7979	0.997245
$778$	−85.6427	−3.07044
$779$	12.1006	0.433549
$780$	39.9405	1.43010
$781$	−9.28780	−0.332344
$782$	110.039	3.93499
$783$	−11.8041	−0.421846
$784$	−35.0958	−1.25342
$785$	44.6776	1.59461
$786$	−57.3442	−2.04540
$787$	−4.46744	−0.159247	−0.0796235	−	0.996825i	$-0.525372\pi$
$787$	−4.46744	−0.159247	−0.0796235	+	0.996825i	$0.525372\pi$
$788$	−7.86287	−0.280103
$789$	2.31799	0.0825226
$790$	129.444	4.60540
$791$	−12.2712	−0.436314
$792$	−3.25401	−0.115626
$793$	7.05938	0.250686
$794$	−16.0907	−0.571037
$795$	6.06283	0.215026
$796$	43.2683	1.53360
$797$	28.1389	0.996732	0.498366	−	0.866967i	$-0.333934\pi$
$797$	28.1389	0.996732	0.498366	+	0.866967i	$0.333934\pi$
$798$	−15.9297	−0.563906
$799$	14.6920	0.519764
$800$	−76.7425	−2.71326
$801$	−0.849919	−0.0300304
$802$	−25.0460	−0.884406
$803$	10.1634	0.358658
$804$	99.6085	3.51292
$805$	43.8938	1.54705
$806$	7.76747	0.273598
$807$	−37.7413	−1.32856
$808$	53.6807	1.88848
$809$	16.2523	0.571400	0.285700	−	0.958319i	$-0.407774\pi$
$809$	16.2523	0.571400	0.285700	+	0.958319i	$0.407774\pi$
$810$	−85.1241	−2.99096
$811$	43.6465	1.53264	0.766318	−	0.642461i	$-0.222087\pi$
$811$	43.6465	1.53264	0.766318	+	0.642461i	$0.222087\pi$
$812$	16.8066	0.589796
$813$	−2.94086	−0.103141
$814$	72.9400	2.55654
$815$	48.9485	1.71459
$816$	85.6841	2.99954
$817$	−15.3651	−0.537558
$818$	100.288	3.50648
$819$	0.368538	0.0128778
$820$	−97.6506	−3.41011
$821$	−0.500515	−0.0174681	−0.00873404	−	0.999962i	$-0.502780\pi$
$821$	−0.500515	−0.0174681	−0.00873404	+	0.999962i	$0.502780\pi$
$822$	−79.8412	−2.78478
$823$	16.6432	0.580146	0.290073	−	0.957004i	$-0.406320\pi$
$823$	16.6432	0.580146	0.290073	+	0.957004i	$0.406320\pi$
$824$	−31.9704	−1.11374
$825$	−48.6915	−1.69522
$826$	21.3206	0.741839
$827$	28.2338	0.981785	0.490892	−	0.871220i	$-0.336671\pi$
$827$	28.2338	0.981785	0.490892	+	0.871220i	$0.336671\pi$
$828$	5.41180	0.188073
$829$	26.1145	0.906994	0.453497	−	0.891258i	$-0.350176\pi$
$829$	26.1145	0.906994	0.453497	+	0.891258i	$0.350176\pi$
$830$	−8.00119	−0.277725
$831$	−2.73745	−0.0949610
$832$	−3.80943	−0.132068
$833$	−26.9114	−0.932425
$834$	68.0810	2.35745
$835$	94.7953	3.28053
$836$	−29.1828	−1.00931
$837$	−12.2592	−0.423740
$838$	−21.5112	−0.743090
$839$	−0.0732583	−0.00252916	−0.00126458	−	0.999999i	$-0.500403\pi$
$839$	−0.0732583	−0.00252916	−0.00126458	+	0.999999i	$0.500403\pi$
$840$	72.9785	2.51800
$841$	−24.1018	−0.831095
$842$	65.8075	2.26788
$843$	17.7498	0.611337
$844$	75.5208	2.59953
$845$	44.0902	1.51675
$846$	1.03492	0.0355815
$847$	−5.05664	−0.173748
$848$	−7.51450	−0.258049
$849$	−18.7369	−0.643050
$850$	−165.508	−5.67687
$851$	−68.8662	−2.36070
$852$	25.6819	0.879847
$853$	32.5591	1.11480	0.557401	−	0.830243i	$-0.311798\pi$
$853$	32.5591	1.11480	0.557401	+	0.830243i	$0.311798\pi$
$854$	22.7211	0.777499
$855$	1.49891	0.0512617
$856$	111.660	3.81647
$857$	−21.6975	−0.741172	−0.370586	−	0.928798i	$-0.620843\pi$
$857$	−21.6975	−0.741172	−0.370586	+	0.928798i	$0.620843\pi$
$858$	−15.9952	−0.546067
$859$	9.29798	0.317243	0.158621	−	0.987339i	$-0.449295\pi$
$859$	9.29798	0.317243	0.158621	+	0.987339i	$0.449295\pi$
$860$	123.995	4.22820
$861$	14.9038	0.507921
$862$	37.5316	1.27833
$863$	−41.6038	−1.41621	−0.708105	−	0.706108i	$-0.750449\pi$
$863$	−41.6038	−1.41621	−0.708105	+	0.706108i	$0.750449\pi$
$864$	39.7883	1.35363
$865$	−10.1713	−0.345835
$866$	56.5292	1.92094
$867$	37.1093	1.26030
$868$	17.4545	0.592445
$869$	−36.1929	−1.22776
$870$	37.4659	1.27021
$871$	−16.8047	−0.569406
$872$	127.867	4.33014
$873$	−0.964016	−0.0326270
$874$	39.4641	1.33489
$875$	−33.9314	−1.14709
$876$	−28.1030	−0.949511
$877$	−42.0490	−1.41989	−0.709947	−	0.704256i	$-0.751281\pi$
$877$	−42.0490	−1.41989	−0.709947	+	0.704256i	$0.751281\pi$
$878$	88.1220	2.97398
$879$	4.58336	0.154593
$880$	89.6829	3.02321
$881$	40.7302	1.37223	0.686117	−	0.727491i	$-0.259314\pi$
$881$	40.7302	1.37223	0.686117	+	0.727491i	$0.259314\pi$
$882$	−1.89568	−0.0638309
$883$	−12.3268	−0.414829	−0.207414	−	0.978253i	$-0.566505\pi$
$883$	−12.3268	−0.414829	−0.207414	+	0.978253i	$0.566505\pi$
$884$	−37.9595	−1.27672
$885$	33.1835	1.11545
$886$	62.2721	2.09207
$887$	26.3564	0.884962	0.442481	−	0.896778i	$-0.354098\pi$
$887$	26.3564	0.884962	0.442481	+	0.896778i	$0.354098\pi$
$888$	−114.498	−3.84230
$889$	−8.57869	−0.287720
$890$	50.0157	1.67653
$891$	23.8009	0.797362
$892$	−55.2829	−1.85101
$893$	5.26908	0.176323
$894$	59.4486	1.98826
$895$	63.9165	2.13649
$896$	12.2290	0.408541
$897$	15.1019	0.504236
$898$	83.9472	2.80135
$899$	5.08707	0.169663
$900$	−8.13979	−0.271326
$901$	−5.76211	−0.191964
$902$	39.1067	1.30211
$903$	−18.9246	−0.629773
$904$	50.5444	1.68108
$905$	43.9473	1.46086
$906$	−2.18000	−0.0724256
$907$	5.15926	0.171310	0.0856552	−	0.996325i	$-0.472702\pi$
$907$	5.15926	0.171310	0.0856552	+	0.996325i	$0.472702\pi$
$908$	39.3263	1.30509
$909$	1.35797	0.0450410
$910$	−21.6876	−0.718936
$911$	−53.0668	−1.75818	−0.879090	−	0.476655i	$-0.841849\pi$
$911$	−53.0668	−1.75818	−0.879090	+	0.476655i	$0.841849\pi$
$912$	30.7295	1.01756
$913$	2.23716	0.0740391
$914$	−59.4358	−1.96596
$915$	35.3632	1.16907
$916$	17.4968	0.578111
$917$	21.7396	0.717906
$918$	85.8099	2.83215
$919$	23.8029	0.785187	0.392593	−	0.919712i	$-0.371578\pi$
$919$	23.8029	0.785187	0.392593	+	0.919712i	$0.371578\pi$
$920$	−180.796	−5.96066
$921$	−6.60602	−0.217676
$922$	−33.2849	−1.09618
$923$	−4.33273	−0.142613
$924$	−35.9433	−1.18245
$925$	103.580	3.40570
$926$	−9.67781	−0.318033
$927$	−0.808762	−0.0265632
$928$	−16.5105	−0.541985
$929$	3.70963	0.121709	0.0608544	−	0.998147i	$-0.480617\pi$
$929$	3.70963	0.121709	0.0608544	+	0.998147i	$0.480617\pi$
$930$	38.9103	1.27592
$931$	−9.65143	−0.316313
$932$	59.0698	1.93489
$933$	19.3755	0.634324
$934$	25.7019	0.840990
$935$	68.7688	2.24898
$936$	−1.51799	−0.0496169
$937$	−2.80367	−0.0915918	−0.0457959	−	0.998951i	$-0.514582\pi$
$937$	−2.80367	−0.0915918	−0.0457959	+	0.998951i	$0.514582\pi$
$938$	−54.0871	−1.76601
$939$	44.5234	1.45297
$940$	−42.5210	−1.38688
$941$	−28.9946	−0.945198	−0.472599	−	0.881278i	$-0.656684\pi$
$941$	−28.9946	−0.945198	−0.472599	+	0.881278i	$0.656684\pi$
$942$	49.4743	1.61196
$943$	−36.9225	−1.20236
$944$	−41.1289	−1.33863
$945$	34.2290	1.11347
$946$	−49.6570	−1.61449
$947$	32.6491	1.06095	0.530477	−	0.847699i	$-0.322013\pi$
$947$	32.6491	1.06095	0.530477	+	0.847699i	$0.322013\pi$
$948$	100.078	3.25037
$949$	4.74118	0.153905
$950$	−59.3572	−1.92580
$951$	−56.7689	−1.84086
$952$	−69.3587	−2.24793
$953$	33.8079	1.09515	0.547573	−	0.836758i	$-0.315552\pi$
$953$	33.8079	1.09515	0.547573	+	0.836758i	$0.315552\pi$
$954$	−0.405892	−0.0131412
$955$	−29.9119	−0.967927
$956$	39.1413	1.26592
$957$	−10.4756	−0.338628
$958$	44.7586	1.44608
$959$	30.2684	0.977418
$960$	−19.0829	−0.615899
$961$	−25.7168	−0.829575
$962$	34.0262	1.09705
$963$	2.82469	0.0910245
$964$	117.276	3.77720
$965$	73.5410	2.36737
$966$	48.6064	1.56388
$967$	50.2856	1.61708	0.808538	−	0.588445i	$-0.200259\pi$
$967$	50.2856	1.61708	0.808538	+	0.588445i	$0.200259\pi$
$968$	20.8280	0.669437
$969$	23.5634	0.756964
$970$	56.7300	1.82149
$971$	−18.1070	−0.581082	−0.290541	−	0.956863i	$-0.593835\pi$
$971$	−18.1070	−0.581082	−0.290541	+	0.956863i	$0.593835\pi$
$972$	8.21277	0.263425
$973$	−25.8101	−0.827432
$974$	−62.7002	−2.00904
$975$	−22.7144	−0.727444
$976$	−43.8305	−1.40298
$977$	−4.15102	−0.132803	−0.0664015	−	0.997793i	$-0.521152\pi$
$977$	−4.15102	−0.132803	−0.0664015	+	0.997793i	$0.521152\pi$
$978$	54.2037	1.73324
$979$	−13.9845	−0.446948
$980$	77.8861	2.48798
$981$	3.23469	0.103276
$982$	−56.4383	−1.80102
$983$	33.6068	1.07189	0.535945	−	0.844253i	$-0.319955\pi$
$983$	33.6068	1.07189	0.535945	+	0.844253i	$0.319955\pi$
$984$	−61.3879	−1.95698
$985$	6.64508	0.211730
$986$	−35.6076	−1.13398
$987$	6.48972	0.206570
$988$	−13.6137	−0.433109
$989$	46.8836	1.49081
$990$	4.84418	0.153958
$991$	−43.3944	−1.37847	−0.689234	−	0.724538i	$-0.742053\pi$
$991$	−43.3944	−1.37847	−0.689234	+	0.724538i	$0.742053\pi$
$992$	−17.1470	−0.544419
$993$	59.8623	1.89967
$994$	−13.9452	−0.442314
$995$	−36.5669	−1.15925
$996$	−6.18601	−0.196011
$997$	−43.0154	−1.36231	−0.681155	−	0.732139i	$-0.738522\pi$
$997$	−43.0154	−1.36231	−0.681155	+	0.732139i	$0.738522\pi$
$998$	−3.70955	−0.117424
$999$	−53.7028	−1.69908

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4003.2.a.b.1.11	✓	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4003.2.a.b.1.11	✓	152	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)

\(f(q)\)	\(=\)	\(q-2.57418 q^{2} +1.68195 q^{3} +4.62641 q^{4} -3.90988 q^{5} -4.32965 q^{6} +1.64141 q^{7} -6.76085 q^{8} -0.171031 q^{9} +O(q^{10})\)	\(q-2.57418 q^{2} +1.68195 q^{3} +4.62641 q^{4} -3.90988 q^{5} -4.32965 q^{6} +1.64141 q^{7} -6.76085 q^{8} -0.171031 q^{9} +10.0647 q^{10} -2.81413 q^{11} +7.78141 q^{12} -1.31278 q^{13} -4.22528 q^{14} -6.57624 q^{15} +8.15084 q^{16} +6.25005 q^{17} +0.440264 q^{18} +2.24150 q^{19} -18.0887 q^{20} +2.76077 q^{21} +7.24408 q^{22} -6.83949 q^{23} -11.3714 q^{24} +10.2872 q^{25} +3.37934 q^{26} -5.33353 q^{27} +7.59382 q^{28} +2.21320 q^{29} +16.9284 q^{30} +2.29852 q^{31} -7.46004 q^{32} -4.73324 q^{33} -16.0888 q^{34} -6.41770 q^{35} -0.791257 q^{36} +10.0689 q^{37} -5.77003 q^{38} -2.20804 q^{39} +26.4341 q^{40} +5.39843 q^{41} -7.10672 q^{42} -6.85484 q^{43} -13.0193 q^{44} +0.668709 q^{45} +17.6061 q^{46} +2.35069 q^{47} +13.7093 q^{48} -4.30579 q^{49} -26.4810 q^{50} +10.5123 q^{51} -6.07346 q^{52} -0.921929 q^{53} +13.7295 q^{54} +11.0029 q^{55} -11.0973 q^{56} +3.77010 q^{57} -5.69717 q^{58} -5.04597 q^{59} -30.4244 q^{60} -5.37742 q^{61} -5.91680 q^{62} -0.280731 q^{63} +2.90180 q^{64} +5.13282 q^{65} +12.1842 q^{66} +12.8008 q^{67} +28.9153 q^{68} -11.5037 q^{69} +16.5203 q^{70} +3.30042 q^{71} +1.15631 q^{72} -3.61155 q^{73} -25.9192 q^{74} +17.3025 q^{75} +10.3701 q^{76} -4.61913 q^{77} +5.68389 q^{78} +12.8611 q^{79} -31.8688 q^{80} -8.45766 q^{81} -13.8965 q^{82} -0.794973 q^{83} +12.7724 q^{84} -24.4370 q^{85} +17.6456 q^{86} +3.72249 q^{87} +19.0259 q^{88} +4.96940 q^{89} -1.72138 q^{90} -2.15481 q^{91} -31.6423 q^{92} +3.86600 q^{93} -6.05111 q^{94} -8.76400 q^{95} -12.5474 q^{96} +5.63651 q^{97} +11.0839 q^{98} +0.481302 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q - 22 q^{2} - 18 q^{3} + 138 q^{4} - 59 q^{5} - 17 q^{6} - 19 q^{7} - 66 q^{8} + 106 q^{9}+O(q^{10}) \) 152 * q - 22 * q^2 - 18 * q^3 + 138 * q^4 - 59 * q^5 - 17 * q^6 - 19 * q^7 - 66 * q^8 + 106 * q^9	\( 152 q - 22 q^{2} - 18 q^{3} + 138 q^{4} - 59 q^{5} - 17 q^{6} - 19 q^{7} - 66 q^{8} + 106 q^{9} - 15 q^{10} - 40 q^{11} - 53 q^{12} - 59 q^{13} - 36 q^{14} - 40 q^{15} + 118 q^{16} - 93 q^{17} - 59 q^{18} - 16 q^{19} - 108 q^{20} - 62 q^{21} - 37 q^{22} - 107 q^{23} - 31 q^{24} + 101 q^{25} - 64 q^{26} - 63 q^{27} - 53 q^{28} - 124 q^{29} - 68 q^{30} - 15 q^{31} - 129 q^{32} - 49 q^{33} - 76 q^{35} + 45 q^{36} - 98 q^{37} - 125 q^{38} - 47 q^{39} - 7 q^{40} - 56 q^{41} - 84 q^{42} - 62 q^{43} - 114 q^{44} - 142 q^{45} - 3 q^{46} - 111 q^{47} - 92 q^{48} + 117 q^{49} - 64 q^{50} - 21 q^{51} - 85 q^{52} - 347 q^{53} + 3 q^{54} - 16 q^{55} - 73 q^{56} - 115 q^{57} - 29 q^{58} - 50 q^{59} - 54 q^{60} - 62 q^{61} - 55 q^{62} - 70 q^{63} + 64 q^{64} - 147 q^{65} + 34 q^{66} - 86 q^{67} - 174 q^{68} - 104 q^{69} - 7 q^{70} - 86 q^{71} - 139 q^{72} - 27 q^{73} - 52 q^{74} - 49 q^{75} - 11 q^{76} - 346 q^{77} - 59 q^{78} - 17 q^{79} - 149 q^{80} - 8 q^{81} - 31 q^{82} - 106 q^{83} - 51 q^{84} - 69 q^{85} - 85 q^{86} - 32 q^{87} - 113 q^{88} - 59 q^{89} + 10 q^{90} - 9 q^{91} - 314 q^{92} - 230 q^{93} + 7 q^{94} - 74 q^{95} - 54 q^{96} - 60 q^{97} - 77 q^{98} - 96 q^{99}+O(q^{100}) \) 152 * q - 22 * q^2 - 18 * q^3 + 138 * q^4 - 59 * q^5 - 17 * q^6 - 19 * q^7 - 66 * q^8 + 106 * q^9 - 15 * q^10 - 40 * q^11 - 53 * q^12 - 59 * q^13 - 36 * q^14 - 40 * q^15 + 118 * q^16 - 93 * q^17 - 59 * q^18 - 16 * q^19 - 108 * q^20 - 62 * q^21 - 37 * q^22 - 107 * q^23 - 31 * q^24 + 101 * q^25 - 64 * q^26 - 63 * q^27 - 53 * q^28 - 124 * q^29 - 68 * q^30 - 15 * q^31 - 129 * q^32 - 49 * q^33 - 76 * q^35 + 45 * q^36 - 98 * q^37 - 125 * q^38 - 47 * q^39 - 7 * q^40 - 56 * q^41 - 84 * q^42 - 62 * q^43 - 114 * q^44 - 142 * q^45 - 3 * q^46 - 111 * q^47 - 92 * q^48 + 117 * q^49 - 64 * q^50 - 21 * q^51 - 85 * q^52 - 347 * q^53 + 3 * q^54 - 16 * q^55 - 73 * q^56 - 115 * q^57 - 29 * q^58 - 50 * q^59 - 54 * q^60 - 62 * q^61 - 55 * q^62 - 70 * q^63 + 64 * q^64 - 147 * q^65 + 34 * q^66 - 86 * q^67 - 174 * q^68 - 104 * q^69 - 7 * q^70 - 86 * q^71 - 139 * q^72 - 27 * q^73 - 52 * q^74 - 49 * q^75 - 11 * q^76 - 346 * q^77 - 59 * q^78 - 17 * q^79 - 149 * q^80 - 8 * q^81 - 31 * q^82 - 106 * q^83 - 51 * q^84 - 69 * q^85 - 85 * q^86 - 32 * q^87 - 113 * q^88 - 59 * q^89 + 10 * q^90 - 9 * q^91 - 314 * q^92 - 230 * q^93 + 7 * q^94 - 74 * q^95 - 54 * q^96 - 60 * q^97 - 77 * q^98 - 96 * q^99

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