LMFDB - Embedded newform 4006.2.a.i.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4006,2,Mod(1,4006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4006, 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("4006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4006 = 2 \cdot 2003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4006.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:	$31.9880710497$
Analytic rank:	$0$
Dimension:	$46$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	4006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.151617 q^{3} +1.00000 q^{4} -4.25887 q^{5} -0.151617 q^{6} +0.316610 q^{7} +1.00000 q^{8} -2.97701 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.151617 q^{3} +1.00000 q^{4} -4.25887 q^{5} -0.151617 q^{6} +0.316610 q^{7} +1.00000 q^{8} -2.97701 q^{9} -4.25887 q^{10} -2.81572 q^{11} -0.151617 q^{12} -2.07760 q^{13} +0.316610 q^{14} +0.645716 q^{15} +1.00000 q^{16} +3.87133 q^{17} -2.97701 q^{18} -4.54656 q^{19} -4.25887 q^{20} -0.0480033 q^{21} -2.81572 q^{22} +0.526304 q^{23} -0.151617 q^{24} +13.1380 q^{25} -2.07760 q^{26} +0.906215 q^{27} +0.316610 q^{28} +1.76100 q^{29} +0.645716 q^{30} +3.71735 q^{31} +1.00000 q^{32} +0.426911 q^{33} +3.87133 q^{34} -1.34840 q^{35} -2.97701 q^{36} -10.5622 q^{37} -4.54656 q^{38} +0.314999 q^{39} -4.25887 q^{40} -5.27198 q^{41} -0.0480033 q^{42} +1.38884 q^{43} -2.81572 q^{44} +12.6787 q^{45} +0.526304 q^{46} +0.842112 q^{47} -0.151617 q^{48} -6.89976 q^{49} +13.1380 q^{50} -0.586959 q^{51} -2.07760 q^{52} -0.125712 q^{53} +0.906215 q^{54} +11.9918 q^{55} +0.316610 q^{56} +0.689334 q^{57} +1.76100 q^{58} +3.81995 q^{59} +0.645716 q^{60} -0.390718 q^{61} +3.71735 q^{62} -0.942551 q^{63} +1.00000 q^{64} +8.84823 q^{65} +0.426911 q^{66} +5.01583 q^{67} +3.87133 q^{68} -0.0797965 q^{69} -1.34840 q^{70} +11.7422 q^{71} -2.97701 q^{72} +15.5356 q^{73} -10.5622 q^{74} -1.99194 q^{75} -4.54656 q^{76} -0.891486 q^{77} +0.314999 q^{78} -10.0248 q^{79} -4.25887 q^{80} +8.79364 q^{81} -5.27198 q^{82} +8.80515 q^{83} -0.0480033 q^{84} -16.4875 q^{85} +1.38884 q^{86} -0.266998 q^{87} -2.81572 q^{88} +12.4474 q^{89} +12.6787 q^{90} -0.657788 q^{91} +0.526304 q^{92} -0.563612 q^{93} +0.842112 q^{94} +19.3632 q^{95} -0.151617 q^{96} +8.62580 q^{97} -6.89976 q^{98} +8.38244 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q + 46 q^{2} + 21 q^{3} + 46 q^{4} + 23 q^{5} + 21 q^{6} + 26 q^{7} + 46 q^{8} + 59 q^{9}+O(q^{10}) $ 46 * q + 46 * q^2 + 21 * q^3 + 46 * q^4 + 23 * q^5 + 21 * q^6 + 26 * q^7 + 46 * q^8 + 59 * q^9	\( 46 q + 46 q^{2} + 21 q^{3} + 46 q^{4} + 23 q^{5} + 21 q^{6} + 26 q^{7} + 46 q^{8} + 59 q^{9} + 23 q^{10} + 39 q^{11} + 21 q^{12} + 8 q^{13} + 26 q^{14} + 14 q^{15} + 46 q^{16} + 36 q^{17} + 59 q^{18} + 37 q^{19} + 23 q^{20} + 20 q^{21} + 39 q^{22} + 38 q^{23} + 21 q^{24} + 57 q^{25} + 8 q^{26} + 63 q^{27} + 26 q^{28} + 23 q^{29} + 14 q^{30} + 44 q^{31} + 46 q^{32} + 25 q^{33} + 36 q^{34} + 26 q^{35} + 59 q^{36} + 9 q^{37} + 37 q^{38} - 2 q^{39} + 23 q^{40} + 50 q^{41} + 20 q^{42} + 46 q^{43} + 39 q^{44} + 30 q^{45} + 38 q^{46} + 57 q^{47} + 21 q^{48} + 62 q^{49} + 57 q^{50} + 5 q^{51} + 8 q^{52} + 21 q^{53} + 63 q^{54} + 40 q^{55} + 26 q^{56} + 3 q^{57} + 23 q^{58} + 68 q^{59} + 14 q^{60} - q^{61} + 44 q^{62} + 40 q^{63} + 46 q^{64} + 18 q^{65} + 25 q^{66} + 42 q^{67} + 36 q^{68} - 7 q^{69} + 26 q^{70} + 67 q^{71} + 59 q^{72} + 48 q^{73} + 9 q^{74} + 71 q^{75} + 37 q^{76} - 5 q^{77} - 2 q^{78} + 40 q^{79} + 23 q^{80} + 82 q^{81} + 50 q^{82} + 48 q^{83} + 20 q^{84} - 68 q^{85} + 46 q^{86} + 18 q^{87} + 39 q^{88} + 90 q^{89} + 30 q^{90} + 9 q^{91} + 38 q^{92} - 42 q^{93} + 57 q^{94} + 6 q^{95} + 21 q^{96} + 46 q^{97} + 62 q^{98} + 61 q^{99}+O(q^{100}) \) 46 * q + 46 * q^2 + 21 * q^3 + 46 * q^4 + 23 * q^5 + 21 * q^6 + 26 * q^7 + 46 * q^8 + 59 * q^9 + 23 * q^10 + 39 * q^11 + 21 * q^12 + 8 * q^13 + 26 * q^14 + 14 * q^15 + 46 * q^16 + 36 * q^17 + 59 * q^18 + 37 * q^19 + 23 * q^20 + 20 * q^21 + 39 * q^22 + 38 * q^23 + 21 * q^24 + 57 * q^25 + 8 * q^26 + 63 * q^27 + 26 * q^28 + 23 * q^29 + 14 * q^30 + 44 * q^31 + 46 * q^32 + 25 * q^33 + 36 * q^34 + 26 * q^35 + 59 * q^36 + 9 * q^37 + 37 * q^38 - 2 * q^39 + 23 * q^40 + 50 * q^41 + 20 * q^42 + 46 * q^43 + 39 * q^44 + 30 * q^45 + 38 * q^46 + 57 * q^47 + 21 * q^48 + 62 * q^49 + 57 * q^50 + 5 * q^51 + 8 * q^52 + 21 * q^53 + 63 * q^54 + 40 * q^55 + 26 * q^56 + 3 * q^57 + 23 * q^58 + 68 * q^59 + 14 * q^60 - q^61 + 44 * q^62 + 40 * q^63 + 46 * q^64 + 18 * q^65 + 25 * q^66 + 42 * q^67 + 36 * q^68 - 7 * q^69 + 26 * q^70 + 67 * q^71 + 59 * q^72 + 48 * q^73 + 9 * q^74 + 71 * q^75 + 37 * q^76 - 5 * q^77 - 2 * q^78 + 40 * q^79 + 23 * q^80 + 82 * q^81 + 50 * q^82 + 48 * q^83 + 20 * q^84 - 68 * q^85 + 46 * q^86 + 18 * q^87 + 39 * q^88 + 90 * q^89 + 30 * q^90 + 9 * q^91 + 38 * q^92 - 42 * q^93 + 57 * q^94 + 6 * q^95 + 21 * q^96 + 46 * q^97 + 62 * q^98 + 61 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−0.151617	−0.0875360	−0.0437680	−	0.999042i	$-0.513936\pi$
$3$	−0.151617	−0.0875360	−0.0437680	+	0.999042i	$0.513936\pi$
$4$	1.00000	0.500000
$5$	−4.25887	−1.90463	−0.952313	−	0.305123i	$-0.901302\pi$
$5$	−4.25887	−1.90463	−0.952313	+	0.305123i	$0.901302\pi$
$6$	−0.151617	−0.0618973
$7$	0.316610	0.119667	0.0598336	−	0.998208i	$-0.480943\pi$
$7$	0.316610	0.119667	0.0598336	+	0.998208i	$0.480943\pi$
$8$	1.00000	0.353553
$9$	−2.97701	−0.992337
$10$	−4.25887	−1.34677
$11$	−2.81572	−0.848973	−0.424486	−	0.905434i	$-0.639545\pi$
$11$	−2.81572	−0.848973	−0.424486	+	0.905434i	$0.639545\pi$
$12$	−0.151617	−0.0437680
$13$	−2.07760	−0.576223	−0.288111	−	0.957597i	$-0.593027\pi$
$13$	−2.07760	−0.576223	−0.288111	+	0.957597i	$0.593027\pi$
$14$	0.316610	0.0846175
$15$	0.645716	0.166723
$16$	1.00000	0.250000
$17$	3.87133	0.938936	0.469468	−	0.882950i	$-0.344446\pi$
$17$	3.87133	0.938936	0.469468	+	0.882950i	$0.344446\pi$
$18$	−2.97701	−0.701689
$19$	−4.54656	−1.04305	−0.521526	−	0.853236i	$-0.674637\pi$
$19$	−4.54656	−1.04305	−0.521526	+	0.853236i	$0.674637\pi$
$20$	−4.25887	−0.952313
$21$	−0.0480033	−0.0104752
$22$	−2.81572	−0.600314
$23$	0.526304	0.109742	0.0548710	−	0.998493i	$-0.482525\pi$
$23$	0.526304	0.109742	0.0548710	+	0.998493i	$0.482525\pi$
$24$	−0.151617	−0.0309486
$25$	13.1380	2.62760
$26$	−2.07760	−0.407451
$27$	0.906215	0.174401
$28$	0.316610	0.0598336
$29$	1.76100	0.327010	0.163505	−	0.986542i	$-0.447720\pi$
$29$	1.76100	0.327010	0.163505	+	0.986542i	$0.447720\pi$
$30$	0.645716	0.117891
$31$	3.71735	0.667656	0.333828	−	0.942634i	$-0.391660\pi$
$31$	3.71735	0.667656	0.333828	+	0.942634i	$0.391660\pi$
$32$	1.00000	0.176777
$33$	0.426911	0.0743156
$34$	3.87133	0.663928
$35$	−1.34840	−0.227921
$36$	−2.97701	−0.496169
$37$	−10.5622	−1.73642	−0.868211	−	0.496196i	$-0.834730\pi$
$37$	−10.5622	−1.73642	−0.868211	+	0.496196i	$0.834730\pi$
$38$	−4.54656	−0.737549
$39$	0.314999	0.0504402
$40$	−4.25887	−0.673387
$41$	−5.27198	−0.823345	−0.411673	−	0.911332i	$-0.635055\pi$
$41$	−5.27198	−0.823345	−0.411673	+	0.911332i	$0.635055\pi$
$42$	−0.0480033	−0.00740708
$43$	1.38884	0.211796	0.105898	−	0.994377i	$-0.466228\pi$
$43$	1.38884	0.211796	0.105898	+	0.994377i	$0.466228\pi$
$44$	−2.81572	−0.424486
$45$	12.6787	1.89003
$46$	0.526304	0.0775993
$47$	0.842112	0.122835	0.0614173	−	0.998112i	$-0.480438\pi$
$47$	0.842112	0.122835	0.0614173	+	0.998112i	$0.480438\pi$
$48$	−0.151617	−0.0218840
$49$	−6.89976	−0.985680
$50$	13.1380	1.85799
$51$	−0.586959	−0.0821907
$52$	−2.07760	−0.288111
$53$	−0.125712	−0.0172678	−0.00863390	−	0.999963i	$-0.502748\pi$
$53$	−0.125712	−0.0172678	−0.00863390	+	0.999963i	$0.502748\pi$
$54$	0.906215	0.123320
$55$	11.9918	1.61698
$56$	0.316610	0.0423088
$57$	0.689334	0.0913045
$58$	1.76100	0.231231
$59$	3.81995	0.497315	0.248658	−	0.968591i	$-0.420011\pi$
$59$	3.81995	0.497315	0.248658	+	0.968591i	$0.420011\pi$
$60$	0.645716	0.0833616
$61$	−0.390718	−0.0500263	−0.0250132	−	0.999687i	$-0.507963\pi$
$61$	−0.390718	−0.0500263	−0.0250132	+	0.999687i	$0.507963\pi$
$62$	3.71735	0.472104
$63$	−0.942551	−0.118750
$64$	1.00000	0.125000
$65$	8.84823	1.09749
$66$	0.426911	0.0525491
$67$	5.01583	0.612781	0.306391	−	0.951906i	$-0.400879\pi$
$67$	5.01583	0.612781	0.306391	+	0.951906i	$0.400879\pi$
$68$	3.87133	0.469468
$69$	−0.0797965	−0.00960637
$70$	−1.34840	−0.161165
$71$	11.7422	1.39354	0.696770	−	0.717295i	$-0.254620\pi$
$71$	11.7422	1.39354	0.696770	+	0.717295i	$0.254620\pi$
$72$	−2.97701	−0.350844
$73$	15.5356	1.81830	0.909150	−	0.416469i	$-0.136733\pi$
$73$	15.5356	1.81830	0.909150	+	0.416469i	$0.136733\pi$
$74$	−10.5622	−1.22784
$75$	−1.99194	−0.230009
$76$	−4.54656	−0.521526
$77$	−0.891486	−0.101594
$78$	0.314999	0.0356666
$79$	−10.0248	−1.12788	−0.563939	−	0.825817i	$-0.690715\pi$
$79$	−10.0248	−1.12788	−0.563939	+	0.825817i	$0.690715\pi$
$80$	−4.25887	−0.476156
$81$	8.79364	0.977071
$82$	−5.27198	−0.582193
$83$	8.80515	0.966490	0.483245	−	0.875485i	$-0.339458\pi$
$83$	8.80515	0.966490	0.483245	+	0.875485i	$0.339458\pi$
$84$	−0.0480033	−0.00523759
$85$	−16.4875	−1.78832
$86$	1.38884	0.149763
$87$	−0.266998	−0.0286252
$88$	−2.81572	−0.300157
$89$	12.4474	1.31942	0.659710	−	0.751521i	$-0.270679\pi$
$89$	12.4474	1.31942	0.659710	+	0.751521i	$0.270679\pi$
$90$	12.6787	1.33645
$91$	−0.657788	−0.0689550
$92$	0.526304	0.0548710
$93$	−0.563612	−0.0584439
$94$	0.842112	0.0868572
$95$	19.3632	1.98662
$96$	−0.151617	−0.0154743
$97$	8.62580	0.875817	0.437909	−	0.899019i	$-0.355719\pi$
$97$	8.62580	0.875817	0.437909	+	0.899019i	$0.355719\pi$
$98$	−6.89976	−0.696981
$99$	8.38244	0.842467
$100$	13.1380	1.31380
$101$	3.82981	0.381080	0.190540	−	0.981679i	$-0.438976\pi$
$101$	3.82981	0.381080	0.190540	+	0.981679i	$0.438976\pi$
$102$	−0.586959	−0.0581176
$103$	15.3123	1.50877	0.754384	−	0.656434i	$-0.227936\pi$
$103$	15.3123	1.50877	0.754384	+	0.656434i	$0.227936\pi$
$104$	−2.07760	−0.203725
$105$	0.204440	0.0199513
$106$	−0.125712	−0.0122102
$107$	4.18750	0.404821	0.202410	−	0.979301i	$-0.435123\pi$
$107$	4.18750	0.404821	0.202410	+	0.979301i	$0.435123\pi$
$108$	0.906215	0.0872006
$109$	14.5828	1.39678	0.698391	−	0.715716i	$-0.253900\pi$
$109$	14.5828	1.39678	0.698391	+	0.715716i	$0.253900\pi$
$110$	11.9918	1.14337
$111$	1.60141	0.151999
$112$	0.316610	0.0299168
$113$	15.7910	1.48550	0.742748	−	0.669571i	$-0.233522\pi$
$113$	15.7910	1.48550	0.742748	+	0.669571i	$0.233522\pi$
$114$	0.689334	0.0645620
$115$	−2.24146	−0.209017
$116$	1.76100	0.163505
$117$	6.18504	0.571807
$118$	3.81995	0.351655
$119$	1.22570	0.112360
$120$	0.645716	0.0589456
$121$	−3.07170	−0.279245
$122$	−0.390718	−0.0353739
$123$	0.799321	0.0720723
$124$	3.71735	0.333828
$125$	−34.6587	−3.09997
$126$	−0.942551	−0.0839691
$127$	−17.7853	−1.57819	−0.789093	−	0.614274i	$-0.789449\pi$
$127$	−17.7853	−1.57819	−0.789093	+	0.614274i	$0.789449\pi$
$128$	1.00000	0.0883883
$129$	−0.210572	−0.0185398
$130$	8.84823	0.776041
$131$	−16.3822	−1.43132	−0.715658	−	0.698451i	$-0.753873\pi$
$131$	−16.3822	−1.43132	−0.715658	+	0.698451i	$0.753873\pi$
$132$	0.426911	0.0371578
$133$	−1.43948	−0.124819
$134$	5.01583	0.433302
$135$	−3.85946	−0.332169
$136$	3.87133	0.331964
$137$	11.3491	0.969621	0.484810	−	0.874619i	$-0.338889\pi$
$137$	11.3491	0.969621	0.484810	+	0.874619i	$0.338889\pi$
$138$	−0.0797965	−0.00679273
$139$	−3.72521	−0.315968	−0.157984	−	0.987442i	$-0.550499\pi$
$139$	−3.72521	−0.315968	−0.157984	+	0.987442i	$0.550499\pi$
$140$	−1.34840	−0.113961
$141$	−0.127678	−0.0107524
$142$	11.7422	0.985382
$143$	5.84995	0.489197
$144$	−2.97701	−0.248084
$145$	−7.49989	−0.622832
$146$	15.5356	1.28573
$147$	1.04612	0.0862824
$148$	−10.5622	−0.868211
$149$	3.53933	0.289953	0.144977	−	0.989435i	$-0.453689\pi$
$149$	3.53933	0.289953	0.144977	+	0.989435i	$0.453689\pi$
$150$	−1.99194	−0.162641
$151$	−21.2643	−1.73046	−0.865231	−	0.501374i	$-0.832828\pi$
$151$	−21.2643	−1.73046	−0.865231	+	0.501374i	$0.832828\pi$
$152$	−4.54656	−0.368774
$153$	−11.5250	−0.931741
$154$	−0.891486	−0.0718380
$155$	−15.8317	−1.27163
$156$	0.314999	0.0252201
$157$	−1.24556	−0.0994065	−0.0497033	−	0.998764i	$-0.515828\pi$
$157$	−1.24556	−0.0994065	−0.0497033	+	0.998764i	$0.515828\pi$
$158$	−10.0248	−0.797530
$159$	0.0190600	0.00151155
$160$	−4.25887	−0.336693
$161$	0.166633	0.0131325
$162$	8.79364	0.690894
$163$	1.19185	0.0933529	0.0466764	−	0.998910i	$-0.485137\pi$
$163$	1.19185	0.0933529	0.0466764	+	0.998910i	$0.485137\pi$
$164$	−5.27198	−0.411673
$165$	−1.81816	−0.141543
$166$	8.80515	0.683412
$167$	24.8556	1.92339	0.961693	−	0.274129i	$-0.0883897\pi$
$167$	24.8556	1.92339	0.961693	+	0.274129i	$0.0883897\pi$
$168$	−0.0480033	−0.00370354
$169$	−8.68358	−0.667968
$170$	−16.4875	−1.26453
$171$	13.5352	1.03506
$172$	1.38884	0.105898
$173$	−11.0963	−0.843639	−0.421819	−	0.906680i	$-0.638608\pi$
$173$	−11.0963	−0.843639	−0.421819	+	0.906680i	$0.638608\pi$
$174$	−0.266998	−0.0202410
$175$	4.15962	0.314438
$176$	−2.81572	−0.212243
$177$	−0.579168	−0.0435330
$178$	12.4474	0.932970
$179$	6.47981	0.484324	0.242162	−	0.970236i	$-0.422144\pi$
$179$	6.47981	0.484324	0.242162	+	0.970236i	$0.422144\pi$
$180$	12.6787	0.945016
$181$	−12.2127	−0.907765	−0.453883	−	0.891062i	$-0.649961\pi$
$181$	−12.2127	−0.907765	−0.453883	+	0.891062i	$0.649961\pi$
$182$	−0.657788	−0.0487585
$183$	0.0592394	0.00437910
$184$	0.526304	0.0387996
$185$	44.9832	3.30723
$186$	−0.563612	−0.0413261
$187$	−10.9006	−0.797131
$188$	0.842112	0.0614173
$189$	0.286917	0.0208701
$190$	19.3632	1.40475
$191$	−4.94244	−0.357623	−0.178811	−	0.983883i	$-0.557225\pi$
$191$	−4.94244	−0.357623	−0.178811	+	0.983883i	$0.557225\pi$
$192$	−0.151617	−0.0109420
$193$	−6.44563	−0.463967	−0.231983	−	0.972720i	$-0.574522\pi$
$193$	−6.44563	−0.463967	−0.231983	+	0.972720i	$0.574522\pi$
$194$	8.62580	0.619296
$195$	−1.34154	−0.0960697
$196$	−6.89976	−0.492840
$197$	−9.84765	−0.701616	−0.350808	−	0.936447i	$-0.614093\pi$
$197$	−9.84765	−0.701616	−0.350808	+	0.936447i	$0.614093\pi$
$198$	8.38244	0.595714
$199$	9.26425	0.656725	0.328363	−	0.944552i	$-0.393503\pi$
$199$	9.26425	0.656725	0.328363	+	0.944552i	$0.393503\pi$
$200$	13.1380	0.928997
$201$	−0.760484	−0.0536404
$202$	3.82981	0.269464
$203$	0.557551	0.0391324
$204$	−0.586959	−0.0410953
$205$	22.4527	1.56816
$206$	15.3123	1.06686
$207$	−1.56681	−0.108901
$208$	−2.07760	−0.144056
$209$	12.8018	0.885522
$210$	0.204440	0.0141077
$211$	10.6996	0.736588	0.368294	−	0.929709i	$-0.379942\pi$
$211$	10.6996	0.736588	0.368294	+	0.929709i	$0.379942\pi$
$212$	−0.125712	−0.00863390
$213$	−1.78031	−0.121985
$214$	4.18750	0.286251
$215$	−5.91490	−0.403393
$216$	0.906215	0.0616601
$217$	1.17695	0.0798965
$218$	14.5828	0.987675
$219$	−2.35545	−0.159167
$220$	11.9918	0.808488
$221$	−8.04308	−0.541036
$222$	1.60141	0.107480
$223$	−13.1371	−0.879723	−0.439861	−	0.898066i	$-0.644972\pi$
$223$	−13.1371	−0.879723	−0.439861	+	0.898066i	$0.644972\pi$
$224$	0.316610	0.0211544
$225$	−39.1120	−2.60746
$226$	15.7910	1.05040
$227$	−22.7688	−1.51122	−0.755608	−	0.655024i	$-0.772658\pi$
$227$	−22.7688	−1.51122	−0.755608	+	0.655024i	$0.772658\pi$
$228$	0.689334	0.0456523
$229$	19.1466	1.26525	0.632623	−	0.774460i	$-0.281978\pi$
$229$	19.1466	1.26525	0.632623	+	0.774460i	$0.281978\pi$
$230$	−2.24146	−0.147798
$231$	0.135164	0.00889315
$232$	1.76100	0.115616
$233$	5.93983	0.389131	0.194566	−	0.980890i	$-0.437670\pi$
$233$	5.93983	0.389131	0.194566	+	0.980890i	$0.437670\pi$
$234$	6.18504	0.404329
$235$	−3.58645	−0.233954
$236$	3.81995	0.248658
$237$	1.51993	0.0987298
$238$	1.22570	0.0794504
$239$	−8.68948	−0.562075	−0.281038	−	0.959697i	$-0.590679\pi$
$239$	−8.68948	−0.562075	−0.281038	+	0.959697i	$0.590679\pi$
$240$	0.645716	0.0416808
$241$	−13.2070	−0.850736	−0.425368	−	0.905020i	$-0.639855\pi$
$241$	−13.2070	−0.850736	−0.425368	+	0.905020i	$0.639855\pi$
$242$	−3.07170	−0.197456
$243$	−4.05191	−0.259930
$244$	−0.390718	−0.0250132
$245$	29.3852	1.87735
$246$	0.799321	0.0509628
$247$	9.44592	0.601030
$248$	3.71735	0.236052
$249$	−1.33501	−0.0846027
$250$	−34.6587	−2.19201
$251$	−22.3008	−1.40761	−0.703806	−	0.710392i	$-0.748518\pi$
$251$	−22.3008	−1.40761	−0.703806	+	0.710392i	$0.748518\pi$
$252$	−0.942551	−0.0593751
$253$	−1.48193	−0.0931679
$254$	−17.7853	−1.11595
$255$	2.49978	0.156542
$256$	1.00000	0.0625000
$257$	−0.337709	−0.0210657	−0.0105329	−	0.999945i	$-0.503353\pi$
$257$	−0.337709	−0.0210657	−0.0105329	+	0.999945i	$0.503353\pi$
$258$	−0.210572	−0.0131096
$259$	−3.34411	−0.207793
$260$	8.84823	0.548744
$261$	−5.24253	−0.324504
$262$	−16.3822	−1.01209
$263$	−5.17844	−0.319316	−0.159658	−	0.987172i	$-0.551039\pi$
$263$	−5.17844	−0.319316	−0.159658	+	0.987172i	$0.551039\pi$
$264$	0.426911	0.0262745
$265$	0.535389	0.0328887
$266$	−1.43948	−0.0882604
$267$	−1.88723	−0.115497
$268$	5.01583	0.306391
$269$	23.0227	1.40372	0.701858	−	0.712317i	$-0.252354\pi$
$269$	23.0227	1.40372	0.701858	+	0.712317i	$0.252354\pi$
$270$	−3.85946	−0.234879
$271$	16.0943	0.977661	0.488831	−	0.872379i	$-0.337424\pi$
$271$	16.0943	0.977661	0.488831	+	0.872379i	$0.337424\pi$
$272$	3.87133	0.234734
$273$	0.0997317	0.00603604
$274$	11.3491	0.685625
$275$	−36.9930	−2.23076
$276$	−0.0797965	−0.00480318
$277$	29.4564	1.76986	0.884931	−	0.465722i	$-0.154205\pi$
$277$	29.4564	1.76986	0.884931	+	0.465722i	$0.154205\pi$
$278$	−3.72521	−0.223423
$279$	−11.0666	−0.662540
$280$	−1.34840	−0.0805824
$281$	3.04802	0.181830	0.0909149	−	0.995859i	$-0.471021\pi$
$281$	3.04802	0.181830	0.0909149	+	0.995859i	$0.471021\pi$
$282$	−0.127678	−0.00760313
$283$	0.466989	0.0277596	0.0138798	−	0.999904i	$-0.495582\pi$
$283$	0.466989	0.0277596	0.0138798	+	0.999904i	$0.495582\pi$
$284$	11.7422	0.696770
$285$	−2.93579	−0.173901
$286$	5.84995	0.345915
$287$	−1.66916	−0.0985274
$288$	−2.97701	−0.175422
$289$	−2.01279	−0.118400
$290$	−7.49989	−0.440409
$291$	−1.30782	−0.0766655
$292$	15.5356	0.909150
$293$	2.83475	0.165608	0.0828038	−	0.996566i	$-0.473613\pi$
$293$	2.83475	0.165608	0.0828038	+	0.996566i	$0.473613\pi$
$294$	1.04612	0.0610109
$295$	−16.2687	−0.947199
$296$	−10.5622	−0.613918
$297$	−2.55165	−0.148062
$298$	3.53933	0.205028
$299$	−1.09345	−0.0632358
$300$	−1.99194	−0.115005
$301$	0.439721	0.0253451
$302$	−21.2643	−1.22362
$303$	−0.580663	−0.0333582
$304$	−4.54656	−0.260763
$305$	1.66402	0.0952814
$306$	−11.5250	−0.658840
$307$	22.3714	1.27680	0.638401	−	0.769704i	$-0.279596\pi$
$307$	22.3714	1.27680	0.638401	+	0.769704i	$0.279596\pi$
$308$	−0.891486	−0.0507971
$309$	−2.32160	−0.132071
$310$	−15.8317	−0.899181
$311$	22.6455	1.28411	0.642056	−	0.766658i	$-0.278082\pi$
$311$	22.6455	1.28411	0.642056	+	0.766658i	$0.278082\pi$
$312$	0.314999	0.0178333
$313$	−5.42830	−0.306826	−0.153413	−	0.988162i	$-0.549026\pi$
$313$	−5.42830	−0.306826	−0.153413	+	0.988162i	$0.549026\pi$
$314$	−1.24556	−0.0702910
$315$	4.01421	0.226175
$316$	−10.0248	−0.563939
$317$	17.5085	0.983375	0.491687	−	0.870772i	$-0.336380\pi$
$317$	17.5085	0.983375	0.491687	+	0.870772i	$0.336380\pi$
$318$	0.0190600	0.00106883
$319$	−4.95850	−0.277623
$320$	−4.25887	−0.238078
$321$	−0.634895	−0.0354364
$322$	0.166633	0.00928609
$323$	−17.6012	−0.979358
$324$	8.79364	0.488536
$325$	−27.2955	−1.51408
$326$	1.19185	0.0660104
$327$	−2.21100	−0.122269
$328$	−5.27198	−0.291096
$329$	0.266621	0.0146993
$330$	−1.81816	−0.100086
$331$	−30.3062	−1.66578	−0.832890	−	0.553439i	$-0.813315\pi$
$331$	−30.3062	−1.66578	−0.832890	+	0.553439i	$0.813315\pi$
$332$	8.80515	0.483245
$333$	31.4439	1.72312
$334$	24.8556	1.36004
$335$	−21.3618	−1.16712
$336$	−0.0480033	−0.00261880
$337$	−7.24125	−0.394456	−0.197228	−	0.980358i	$-0.563194\pi$
$337$	−7.24125	−0.394456	−0.197228	+	0.980358i	$0.563194\pi$
$338$	−8.68358	−0.472324
$339$	−2.39419	−0.130034
$340$	−16.4875	−0.894161
$341$	−10.4670	−0.566821
$342$	13.5352	0.731897
$343$	−4.40080	−0.237621
$344$	1.38884	0.0748813
$345$	0.339843	0.0182965
$346$	−11.0963	−0.596543
$347$	9.49912	0.509939	0.254970	−	0.966949i	$-0.417934\pi$
$347$	9.49912	0.509939	0.254970	+	0.966949i	$0.417934\pi$
$348$	−0.266998	−0.0143126
$349$	−9.56704	−0.512112	−0.256056	−	0.966662i	$-0.582423\pi$
$349$	−9.56704	−0.512112	−0.256056	+	0.966662i	$0.582423\pi$
$350$	4.15962	0.222341
$351$	−1.88275	−0.100494
$352$	−2.81572	−0.150079
$353$	8.92954	0.475272	0.237636	−	0.971354i	$-0.423628\pi$
$353$	8.92954	0.475272	0.237636	+	0.971354i	$0.423628\pi$
$354$	−0.579168	−0.0307825
$355$	−50.0084	−2.65417
$356$	12.4474	0.659710
$357$	−0.185837	−0.00983553
$358$	6.47981	0.342469
$359$	9.44027	0.498238	0.249119	−	0.968473i	$-0.419859\pi$
$359$	9.44027	0.498238	0.249119	+	0.968473i	$0.419859\pi$
$360$	12.6787	0.668227
$361$	1.67116	0.0879560
$362$	−12.2127	−0.641887
$363$	0.465721	0.0244440
$364$	−0.657788	−0.0344775
$365$	−66.1640	−3.46318
$366$	0.0592394	0.00309649
$367$	9.00053	0.469824	0.234912	−	0.972017i	$-0.424520\pi$
$367$	9.00053	0.469824	0.234912	+	0.972017i	$0.424520\pi$
$368$	0.526304	0.0274355
$369$	15.6948	0.817036
$370$	44.9832	2.33857
$371$	−0.0398015	−0.00206639
$372$	−0.563612	−0.0292219
$373$	−26.5672	−1.37560	−0.687799	−	0.725901i	$-0.741423\pi$
$373$	−26.5672	−1.37560	−0.687799	+	0.725901i	$0.741423\pi$
$374$	−10.9006	−0.563657
$375$	5.25484	0.271359
$376$	0.842112	0.0434286
$377$	−3.65866	−0.188431
$378$	0.286917	0.0147574
$379$	35.2014	1.80818	0.904088	−	0.427347i	$-0.140552\pi$
$379$	35.2014	1.80818	0.904088	+	0.427347i	$0.140552\pi$
$380$	19.3632	0.993311
$381$	2.69654	0.138148
$382$	−4.94244	−0.252877
$383$	−7.29506	−0.372760	−0.186380	−	0.982478i	$-0.559676\pi$
$383$	−7.29506	−0.372760	−0.186380	+	0.982478i	$0.559676\pi$
$384$	−0.151617	−0.00773716
$385$	3.79672	0.193499
$386$	−6.44563	−0.328074
$387$	−4.13460	−0.210173
$388$	8.62580	0.437909
$389$	29.9824	1.52017	0.760084	−	0.649825i	$-0.225158\pi$
$389$	29.9824	1.52017	0.760084	+	0.649825i	$0.225158\pi$
$390$	−1.34154	−0.0679315
$391$	2.03750	0.103041
$392$	−6.89976	−0.348490
$393$	2.48381	0.125292
$394$	−9.84765	−0.496117
$395$	42.6943	2.14818
$396$	8.38244	0.421234
$397$	33.9815	1.70548	0.852740	−	0.522335i	$-0.174939\pi$
$397$	33.9815	1.70548	0.852740	+	0.522335i	$0.174939\pi$
$398$	9.26425	0.464375
$399$	0.218250	0.0109262
$400$	13.1380	0.656900
$401$	10.9872	0.548672	0.274336	−	0.961634i	$-0.411542\pi$
$401$	10.9872	0.548672	0.274336	+	0.961634i	$0.411542\pi$
$402$	−0.760484	−0.0379295
$403$	−7.72316	−0.384718
$404$	3.82981	0.190540
$405$	−37.4510	−1.86095
$406$	0.557551	0.0276708
$407$	29.7403	1.47417
$408$	−0.586959	−0.0290588
$409$	−4.65801	−0.230324	−0.115162	−	0.993347i	$-0.536739\pi$
$409$	−4.65801	−0.230324	−0.115162	+	0.993347i	$0.536739\pi$
$410$	22.4527	1.10886
$411$	−1.72072	−0.0848767
$412$	15.3123	0.754384
$413$	1.20943	0.0595123
$414$	−1.56681	−0.0770047
$415$	−37.5000	−1.84080
$416$	−2.07760	−0.101863
$417$	0.564804	0.0276586
$418$	12.8018	0.626159
$419$	−21.7253	−1.06135	−0.530676	−	0.847575i	$-0.678062\pi$
$419$	−21.7253	−1.06135	−0.530676	+	0.847575i	$0.678062\pi$
$420$	0.204440	0.00997566
$421$	1.67774	0.0817683	0.0408841	−	0.999164i	$-0.486983\pi$
$421$	1.67774	0.0817683	0.0408841	+	0.999164i	$0.486983\pi$
$422$	10.6996	0.520847
$423$	−2.50698	−0.121893
$424$	−0.125712	−0.00610509
$425$	50.8615	2.46715
$426$	−1.78031	−0.0862563
$427$	−0.123705	−0.00598651
$428$	4.18750	0.202410
$429$	−0.886950	−0.0428223
$430$	−5.91490	−0.285242
$431$	−19.4684	−0.937758	−0.468879	−	0.883262i	$-0.655342\pi$
$431$	−19.4684	−0.937758	−0.468879	+	0.883262i	$0.655342\pi$
$432$	0.906215	0.0436003
$433$	20.4265	0.981635	0.490818	−	0.871262i	$-0.336698\pi$
$433$	20.4265	0.981635	0.490818	+	0.871262i	$0.336698\pi$
$434$	1.17695	0.0564954
$435$	1.13711	0.0545202
$436$	14.5828	0.698391
$437$	−2.39287	−0.114466
$438$	−2.35545	−0.112548
$439$	−29.5525	−1.41046	−0.705231	−	0.708977i	$-0.749157\pi$
$439$	−29.5525	−1.41046	−0.705231	+	0.708977i	$0.749157\pi$
$440$	11.9918	0.571687
$441$	20.5407	0.978127
$442$	−8.04308	−0.382570
$443$	0.0235283	0.00111786	0.000558932	−	1.00000i	$-0.499822\pi$
$443$	0.0235283	0.00111786	0.000558932		1.00000i	$0.499822\pi$
$444$	1.60141	0.0759997
$445$	−53.0118	−2.51300
$446$	−13.1371	−0.622058
$447$	−0.536622	−0.0253813
$448$	0.316610	0.0149584
$449$	33.4772	1.57989	0.789943	−	0.613181i	$-0.210110\pi$
$449$	33.4772	1.57989	0.789943	+	0.613181i	$0.210110\pi$
$450$	−39.1120	−1.84376
$451$	14.8444	0.698998
$452$	15.7910	0.742748
$453$	3.22402	0.151478
$454$	−22.7688	−1.06859
$455$	2.80144	0.131333
$456$	0.689334	0.0322810
$457$	−12.7206	−0.595045	−0.297523	−	0.954715i	$-0.596160\pi$
$457$	−12.7206	−0.595045	−0.297523	+	0.954715i	$0.596160\pi$
$458$	19.1466	0.894664
$459$	3.50826	0.163752
$460$	−2.24146	−0.104509
$461$	−37.0880	−1.72736	−0.863680	−	0.504040i	$-0.831846\pi$
$461$	−37.0880	−1.72736	−0.863680	+	0.504040i	$0.831846\pi$
$462$	0.135164	0.00628841
$463$	−8.33611	−0.387412	−0.193706	−	0.981060i	$-0.562051\pi$
$463$	−8.33611	−0.387412	−0.193706	+	0.981060i	$0.562051\pi$
$464$	1.76100	0.0817526
$465$	2.40035	0.111314
$466$	5.93983	0.275157
$467$	36.9787	1.71117	0.855585	−	0.517663i	$-0.173198\pi$
$467$	36.9787	1.71117	0.855585	+	0.517663i	$0.173198\pi$
$468$	6.18504	0.285904
$469$	1.58806	0.0733299
$470$	−3.58645	−0.165430
$471$	0.188848	0.00870165
$472$	3.81995	0.175827
$473$	−3.91059	−0.179809
$474$	1.51993	0.0698125
$475$	−59.7326	−2.74072
$476$	1.22570	0.0561799
$477$	0.374245	0.0171355
$478$	−8.68948	−0.397447
$479$	22.5686	1.03119	0.515593	−	0.856834i	$-0.327572\pi$
$479$	22.5686	1.03119	0.515593	+	0.856834i	$0.327572\pi$
$480$	0.645716	0.0294728
$481$	21.9441	1.00056
$482$	−13.2070	−0.601561
$483$	−0.0252643	−0.00114957
$484$	−3.07170	−0.139623
$485$	−36.7362	−1.66810
$486$	−4.05191	−0.183798
$487$	−15.5946	−0.706658	−0.353329	−	0.935499i	$-0.614950\pi$
$487$	−15.5946	−0.706658	−0.353329	+	0.935499i	$0.614950\pi$
$488$	−0.390718	−0.0176870
$489$	−0.180704	−0.00817173
$490$	29.3852	1.32749
$491$	−11.5749	−0.522367	−0.261183	−	0.965289i	$-0.584113\pi$
$491$	−11.5749	−0.522367	−0.261183	+	0.965289i	$0.584113\pi$
$492$	0.799321	0.0360362
$493$	6.81743	0.307042
$494$	9.44592	0.424992
$495$	−35.6998	−1.60459
$496$	3.71735	0.166914
$497$	3.71769	0.166761
$498$	−1.33501	−0.0598231
$499$	−4.01918	−0.179923	−0.0899616	−	0.995945i	$-0.528674\pi$
$499$	−4.01918	−0.179923	−0.0899616	+	0.995945i	$0.528674\pi$
$500$	−34.6587	−1.54998
$501$	−3.76853	−0.168365
$502$	−22.3008	−0.995332
$503$	32.6417	1.45542	0.727711	−	0.685884i	$-0.240584\pi$
$503$	32.6417	1.45542	0.727711	+	0.685884i	$0.240584\pi$
$504$	−0.942551	−0.0419846
$505$	−16.3107	−0.725815
$506$	−1.48193	−0.0658797
$507$	1.31658	0.0584712
$508$	−17.7853	−0.789093
$509$	11.8935	0.527171	0.263585	−	0.964636i	$-0.415095\pi$
$509$	11.8935	0.527171	0.263585	+	0.964636i	$0.415095\pi$
$510$	2.49978	0.110692
$511$	4.91871	0.217591
$512$	1.00000	0.0441942
$513$	−4.12016	−0.181909
$514$	−0.337709	−0.0148957
$515$	−65.2132	−2.87364
$516$	−0.210572	−0.00926989
$517$	−2.37115	−0.104283
$518$	−3.34411	−0.146932
$519$	1.68239	0.0738487
$520$	8.84823	0.388021
$521$	−11.8208	−0.517880	−0.258940	−	0.965893i	$-0.583373\pi$
$521$	−11.8208	−0.517880	−0.258940	+	0.965893i	$0.583373\pi$
$522$	−5.24253	−0.229459
$523$	23.5362	1.02917	0.514583	−	0.857440i	$-0.327947\pi$
$523$	23.5362	1.02917	0.514583	+	0.857440i	$0.327947\pi$
$524$	−16.3822	−0.715658
$525$	−0.630668	−0.0275246
$526$	−5.17844	−0.225791
$527$	14.3911	0.626886
$528$	0.426911	0.0185789
$529$	−22.7230	−0.987957
$530$	0.535389	0.0232558
$531$	−11.3720	−0.493504
$532$	−1.43948	−0.0624095
$533$	10.9531	0.474430
$534$	−1.88723	−0.0816684
$535$	−17.8340	−0.771032
$536$	5.01583	0.216651
$537$	−0.982448	−0.0423957
$538$	23.0227	0.992577
$539$	19.4278	0.836815
$540$	−3.85946	−0.166084
$541$	−24.2973	−1.04462	−0.522311	−	0.852755i	$-0.674930\pi$
$541$	−24.2973	−1.04462	−0.522311	+	0.852755i	$0.674930\pi$
$542$	16.0943	0.691311
$543$	1.85165	0.0794621
$544$	3.87133	0.165982
$545$	−62.1065	−2.66035
$546$	0.0997317	0.00426812
$547$	−37.7868	−1.61564	−0.807822	−	0.589426i	$-0.799354\pi$
$547$	−37.7868	−1.61564	−0.807822	+	0.589426i	$0.799354\pi$
$548$	11.3491	0.484810
$549$	1.16317	0.0496430
$550$	−36.9930	−1.57739
$551$	−8.00650	−0.341088
$552$	−0.0797965	−0.00339636
$553$	−3.17395	−0.134970
$554$	29.4564	1.25148
$555$	−6.82021	−0.289502
$556$	−3.72521	−0.157984
$557$	−28.1337	−1.19206	−0.596031	−	0.802961i	$-0.703257\pi$
$557$	−28.1337	−1.19206	−0.596031	+	0.802961i	$0.703257\pi$
$558$	−11.0666	−0.468486
$559$	−2.88546	−0.122042
$560$	−1.34840	−0.0569803
$561$	1.65271	0.0697776
$562$	3.04802	0.128573
$563$	−33.3195	−1.40425	−0.702124	−	0.712055i	$-0.747765\pi$
$563$	−33.3195	−1.40425	−0.702124	+	0.712055i	$0.747765\pi$
$564$	−0.127678	−0.00537622
$565$	−67.2521	−2.82932
$566$	0.466989	0.0196290
$567$	2.78415	0.116923
$568$	11.7422	0.492691
$569$	−26.7422	−1.12109	−0.560546	−	0.828124i	$-0.689409\pi$
$569$	−26.7422	−1.12109	−0.560546	+	0.828124i	$0.689409\pi$
$570$	−2.93579	−0.122967
$571$	5.99335	0.250814	0.125407	−	0.992105i	$-0.459976\pi$
$571$	5.99335	0.250814	0.125407	+	0.992105i	$0.459976\pi$
$572$	5.84995	0.244599
$573$	0.749357	0.0313049
$574$	−1.66916	−0.0696694
$575$	6.91458	0.288358
$576$	−2.97701	−0.124042
$577$	11.8348	0.492689	0.246345	−	0.969182i	$-0.420771\pi$
$577$	11.8348	0.492689	0.246345	+	0.969182i	$0.420771\pi$
$578$	−2.01279	−0.0837212
$579$	0.977266	0.0406138
$580$	−7.49989	−0.311416
$581$	2.78780	0.115657
$582$	−1.30782	−0.0542107
$583$	0.353969	0.0146599
$584$	15.5356	0.642866
$585$	−26.3413	−1.08908
$586$	2.83475	0.117102
$587$	38.1811	1.57590	0.787952	−	0.615736i	$-0.211141\pi$
$587$	38.1811	1.57590	0.787952	+	0.615736i	$0.211141\pi$
$588$	1.04612	0.0431412
$589$	−16.9011	−0.696399
$590$	−16.2687	−0.669771
$591$	1.49307	0.0614166
$592$	−10.5622	−0.434105
$593$	−8.98425	−0.368939	−0.184469	−	0.982838i	$-0.559057\pi$
$593$	−8.98425	−0.368939	−0.184469	+	0.982838i	$0.559057\pi$
$594$	−2.55165	−0.104696
$595$	−5.22011	−0.214003
$596$	3.53933	0.144977
$597$	−1.40462	−0.0574871
$598$	−1.09345	−0.0447144
$599$	−6.77431	−0.276791	−0.138395	−	0.990377i	$-0.544194\pi$
$599$	−6.77431	−0.276791	−0.138395	+	0.990377i	$0.544194\pi$
$600$	−1.99194	−0.0813206
$601$	23.4772	0.957654	0.478827	−	0.877909i	$-0.341062\pi$
$601$	23.4772	0.957654	0.478827	+	0.877909i	$0.341062\pi$
$602$	0.439721	0.0179217
$603$	−14.9322	−0.608086
$604$	−21.2643	−0.865231
$605$	13.0820	0.531858
$606$	−0.580663	−0.0235878
$607$	−22.0982	−0.896940	−0.448470	−	0.893798i	$-0.648031\pi$
$607$	−22.0982	−0.896940	−0.448470	+	0.893798i	$0.648031\pi$
$608$	−4.54656	−0.184387
$609$	−0.0845341	−0.00342549
$610$	1.66402	0.0673741
$611$	−1.74957	−0.0707801
$612$	−11.5250	−0.465871
$613$	−22.8656	−0.923531	−0.461766	−	0.887002i	$-0.652784\pi$
$613$	−22.8656	−0.923531	−0.461766	+	0.887002i	$0.652784\pi$
$614$	22.3714	0.902836
$615$	−3.40421	−0.137271
$616$	−0.891486	−0.0359190
$617$	42.4922	1.71067	0.855336	−	0.518073i	$-0.173350\pi$
$617$	42.4922	1.71067	0.855336	+	0.518073i	$0.173350\pi$
$618$	−2.32160	−0.0933886
$619$	−8.50544	−0.341863	−0.170931	−	0.985283i	$-0.554678\pi$
$619$	−8.50544	−0.341863	−0.170931	+	0.985283i	$0.554678\pi$
$620$	−15.8317	−0.635817
$621$	0.476944	0.0191391
$622$	22.6455	0.908004
$623$	3.94096	0.157891
$624$	0.314999	0.0126100
$625$	81.9169	3.27668
$626$	−5.42830	−0.216958
$627$	−1.94097	−0.0775150
$628$	−1.24556	−0.0497033
$629$	−40.8899	−1.63039
$630$	4.01421	0.159930
$631$	6.25992	0.249204	0.124602	−	0.992207i	$-0.460235\pi$
$631$	6.25992	0.249204	0.124602	+	0.992207i	$0.460235\pi$
$632$	−10.0248	−0.398765
$633$	−1.62223	−0.0644780
$634$	17.5085	0.695351
$635$	75.7451	3.00585
$636$	0.0190600	0.000755777 0
$637$	14.3349	0.567971
$638$	−4.95850	−0.196309
$639$	−34.9566	−1.38286
$640$	−4.25887	−0.168347
$641$	22.6069	0.892919	0.446460	−	0.894804i	$-0.352685\pi$
$641$	22.6069	0.892919	0.446460	+	0.894804i	$0.352685\pi$
$642$	−0.634895	−0.0250573
$643$	44.9565	1.77291	0.886455	−	0.462815i	$-0.153160\pi$
$643$	44.9565	1.77291	0.886455	+	0.462815i	$0.153160\pi$
$644$	0.166633	0.00656626
$645$	0.896797	0.0353114
$646$	−17.6012	−0.692511
$647$	14.6398	0.575548	0.287774	−	0.957698i	$-0.407085\pi$
$647$	14.6398	0.575548	0.287774	+	0.957698i	$0.407085\pi$
$648$	8.79364	0.345447
$649$	−10.7559	−0.422207
$650$	−27.2955	−1.07062
$651$	−0.178445	−0.00699382
$652$	1.19185	0.0466764
$653$	13.0275	0.509806	0.254903	−	0.966967i	$-0.417957\pi$
$653$	13.0275	0.509806	0.254903	+	0.966967i	$0.417957\pi$
$654$	−2.21100	−0.0864571
$655$	69.7695	2.72612
$656$	−5.27198	−0.205836
$657$	−46.2495	−1.80437
$658$	0.266621	0.0103940
$659$	20.8390	0.811773	0.405886	−	0.913924i	$-0.366963\pi$
$659$	20.8390	0.811773	0.405886	+	0.913924i	$0.366963\pi$
$660$	−1.81816	−0.0707717
$661$	25.2011	0.980210	0.490105	−	0.871663i	$-0.336958\pi$
$661$	25.2011	0.980210	0.490105	+	0.871663i	$0.336958\pi$
$662$	−30.3062	−1.17788
$663$	1.21947	0.0473601
$664$	8.80515	0.341706
$665$	6.13058	0.237734
$666$	31.4439	1.21843
$667$	0.926823	0.0358867
$668$	24.8556	0.961693
$669$	1.99180	0.0770074
$670$	−21.3618	−0.825278
$671$	1.10015	0.0424710
$672$	−0.0480033	−0.00185177
$673$	−40.0044	−1.54206	−0.771028	−	0.636801i	$-0.780257\pi$
$673$	−40.0044	−1.54206	−0.771028	+	0.636801i	$0.780257\pi$
$674$	−7.24125	−0.278923
$675$	11.9059	0.458256
$676$	−8.68358	−0.333984
$677$	−21.2831	−0.817975	−0.408988	−	0.912540i	$-0.634118\pi$
$677$	−21.2831	−0.817975	−0.408988	+	0.912540i	$0.634118\pi$
$678$	−2.39419	−0.0919482
$679$	2.73101	0.104807
$680$	−16.4875	−0.632267
$681$	3.45213	0.132286
$682$	−10.4670	−0.400803
$683$	8.77417	0.335734	0.167867	−	0.985810i	$-0.446312\pi$
$683$	8.77417	0.335734	0.167867	+	0.985810i	$0.446312\pi$
$684$	13.5352	0.517529
$685$	−48.3345	−1.84676
$686$	−4.40080	−0.168023
$687$	−2.90295	−0.110754
$688$	1.38884	0.0529491
$689$	0.261178	0.00995010
$690$	0.339843	0.0129376
$691$	−44.7958	−1.70411	−0.852056	−	0.523451i	$-0.824644\pi$
$691$	−44.7958	−1.70411	−0.852056	+	0.523451i	$0.824644\pi$
$692$	−11.0963	−0.421819
$693$	2.65396	0.100816
$694$	9.49912	0.360582
$695$	15.8652	0.601801
$696$	−0.266998	−0.0101205
$697$	−20.4096	−0.773068
$698$	−9.56704	−0.362118
$699$	−0.900578	−0.0340630
$700$	4.15962	0.157219
$701$	−11.8006	−0.445703	−0.222852	−	0.974852i	$-0.571537\pi$
$701$	−11.8006	−0.445703	−0.222852	+	0.974852i	$0.571537\pi$
$702$	−1.88275	−0.0710599
$703$	48.0218	1.81118
$704$	−2.81572	−0.106122
$705$	0.543765	0.0204794
$706$	8.92954	0.336068
$707$	1.21255	0.0456028
$708$	−0.579168	−0.0217665
$709$	−41.0315	−1.54097	−0.770484	−	0.637459i	$-0.779986\pi$
$709$	−41.0315	−1.54097	−0.770484	+	0.637459i	$0.779986\pi$
$710$	−50.0084	−1.87678
$711$	29.8439	1.11923
$712$	12.4474	0.466485
$713$	1.95645	0.0732698
$714$	−0.185837	−0.00695477
$715$	−24.9142	−0.931737
$716$	6.47981	0.242162
$717$	1.31747	0.0492018
$718$	9.44027	0.352308
$719$	38.7514	1.44518	0.722592	−	0.691275i	$-0.242951\pi$
$719$	38.7514	1.44518	0.722592	+	0.691275i	$0.242951\pi$
$720$	12.6787	0.472508
$721$	4.84803	0.180550
$722$	1.67116	0.0621943
$723$	2.00240	0.0744700
$724$	−12.2127	−0.453883
$725$	23.1361	0.859252
$726$	0.465721	0.0172845
$727$	−11.2418	−0.416934	−0.208467	−	0.978029i	$-0.566847\pi$
$727$	−11.2418	−0.416934	−0.208467	+	0.978029i	$0.566847\pi$
$728$	−0.657788	−0.0243793
$729$	−25.7666	−0.954318
$730$	−66.1640	−2.44884
$731$	5.37666	0.198863
$732$	0.0592394	0.00218955
$733$	38.0874	1.40679	0.703395	−	0.710799i	$-0.251666\pi$
$733$	38.0874	1.40679	0.703395	+	0.710799i	$0.251666\pi$
$734$	9.00053	0.332215
$735$	−4.45529	−0.164336
$736$	0.526304	0.0193998
$737$	−14.1232	−0.520235
$738$	15.6948	0.577732
$739$	11.4479	0.421120	0.210560	−	0.977581i	$-0.432471\pi$
$739$	11.4479	0.421120	0.210560	+	0.977581i	$0.432471\pi$
$740$	44.9832	1.65362
$741$	−1.43216	−0.0526117
$742$	−0.0398015	−0.00146116
$743$	19.5250	0.716305	0.358152	−	0.933663i	$-0.383407\pi$
$743$	19.5250	0.716305	0.358152	+	0.933663i	$0.383407\pi$
$744$	−0.563612	−0.0206630
$745$	−15.0736	−0.552253
$746$	−26.5672	−0.972694
$747$	−26.2130	−0.959085
$748$	−10.9006	−0.398565
$749$	1.32580	0.0484438
$750$	5.25484	0.191880
$751$	5.94552	0.216955	0.108477	−	0.994099i	$-0.465402\pi$
$751$	5.94552	0.216955	0.108477	+	0.994099i	$0.465402\pi$
$752$	0.842112	0.0307087
$753$	3.38117	0.123217
$754$	−3.65866	−0.133241
$755$	90.5618	3.29588
$756$	0.286917	0.0104351
$757$	−41.3453	−1.50272	−0.751361	−	0.659892i	$-0.770602\pi$
$757$	−41.3453	−1.50272	−0.751361	+	0.659892i	$0.770602\pi$
$758$	35.2014	1.27857
$759$	0.224685	0.00815554
$760$	19.3632	0.702377
$761$	15.2791	0.553865	0.276933	−	0.960889i	$-0.410682\pi$
$761$	15.2791	0.553865	0.276933	+	0.960889i	$0.410682\pi$
$762$	2.69654	0.0976854
$763$	4.61707	0.167149
$764$	−4.94244	−0.178811
$765$	49.0835	1.77462
$766$	−7.29506	−0.263581
$767$	−7.93633	−0.286564
$768$	−0.151617	−0.00547100
$769$	34.0301	1.22716	0.613579	−	0.789633i	$-0.289729\pi$
$769$	34.0301	1.22716	0.613579	+	0.789633i	$0.289729\pi$
$770$	3.79672	0.136824
$771$	0.0512024	0.00184401
$772$	−6.44563	−0.231983
$773$	−13.1289	−0.472213	−0.236107	−	0.971727i	$-0.575871\pi$
$773$	−13.1289	−0.472213	−0.236107	+	0.971727i	$0.575871\pi$
$774$	−4.13460	−0.148615
$775$	48.8385	1.75433
$776$	8.62580	0.309648
$777$	0.507023	0.0181893
$778$	29.9824	1.07492
$779$	23.9694	0.858791
$780$	−1.34154	−0.0480348
$781$	−33.0627	−1.18308
$782$	2.03750	0.0728607
$783$	1.59585	0.0570310
$784$	−6.89976	−0.246420
$785$	5.30468	0.189332
$786$	2.48381	0.0885945
$787$	49.7556	1.77360	0.886798	−	0.462157i	$-0.152924\pi$
$787$	49.7556	1.77360	0.886798	+	0.462157i	$0.152924\pi$
$788$	−9.84765	−0.350808
$789$	0.785138	0.0279517
$790$	42.6943	1.51900
$791$	4.99960	0.177765
$792$	8.38244	0.297857
$793$	0.811755	0.0288263
$794$	33.9815	1.20596
$795$	−0.0811740	−0.00287894
$796$	9.26425	0.328363
$797$	36.0760	1.27788	0.638939	−	0.769258i	$-0.279374\pi$
$797$	36.0760	1.27788	0.638939	+	0.769258i	$0.279374\pi$
$798$	0.218250	0.00772596
$799$	3.26009	0.115334
$800$	13.1380	0.464498
$801$	−37.0560	−1.30931
$802$	10.9872	0.387970
$803$	−43.7438	−1.54369
$804$	−0.760484	−0.0268202
$805$	−0.709668	−0.0250125
$806$	−7.72316	−0.272037
$807$	−3.49062	−0.122876
$808$	3.82981	0.134732
$809$	−27.1010	−0.952819	−0.476410	−	0.879224i	$-0.658062\pi$
$809$	−27.1010	−0.952819	−0.476410	+	0.879224i	$0.658062\pi$
$810$	−37.4510	−1.31589
$811$	−5.13865	−0.180442	−0.0902212	−	0.995922i	$-0.528757\pi$
$811$	−5.13865	−0.180442	−0.0902212	+	0.995922i	$0.528757\pi$
$812$	0.557551	0.0195662
$813$	−2.44017	−0.0855805
$814$	29.7403	1.04240
$815$	−5.07594	−0.177802
$816$	−0.586959	−0.0205477
$817$	−6.31444	−0.220914
$818$	−4.65801	−0.162863
$819$	1.95824	0.0684266
$820$	22.4527	0.784082
$821$	−11.2157	−0.391432	−0.195716	−	0.980661i	$-0.562703\pi$
$821$	−11.2157	−0.391432	−0.195716	+	0.980661i	$0.562703\pi$
$822$	−1.72072	−0.0600169
$823$	45.8804	1.59929	0.799646	−	0.600472i	$-0.205021\pi$
$823$	45.8804	1.59929	0.799646	+	0.600472i	$0.205021\pi$
$824$	15.3123	0.533430
$825$	5.60875	0.195272
$826$	1.20943	0.0420816
$827$	47.7110	1.65908	0.829538	−	0.558451i	$-0.188604\pi$
$827$	47.7110	1.65908	0.829538	+	0.558451i	$0.188604\pi$
$828$	−1.56681	−0.0544505
$829$	−35.7095	−1.24024	−0.620120	−	0.784507i	$-0.712916\pi$
$829$	−35.7095	−1.24024	−0.620120	+	0.784507i	$0.712916\pi$
$830$	−37.5000	−1.30164
$831$	−4.46608	−0.154927
$832$	−2.07760	−0.0720278
$833$	−26.7113	−0.925490
$834$	0.564804	0.0195576
$835$	−105.857	−3.66333
$836$	12.8018	0.442761
$837$	3.36872	0.116440
$838$	−21.7253	−0.750489
$839$	47.2226	1.63030	0.815152	−	0.579247i	$-0.196653\pi$
$839$	47.2226	1.63030	0.815152	+	0.579247i	$0.196653\pi$
$840$	0.204440	0.00705385
$841$	−25.8989	−0.893064
$842$	1.67774	0.0578189
$843$	−0.462131	−0.0159166
$844$	10.6996	0.368294
$845$	36.9823	1.27223
$846$	−2.50698	−0.0861917
$847$	−0.972530	−0.0334165
$848$	−0.125712	−0.00431695
$849$	−0.0708033	−0.00242996
$850$	50.8615	1.74454
$851$	−5.55895	−0.190558
$852$	−1.78031	−0.0609924
$853$	−0.199822	−0.00684179	−0.00342089	−	0.999994i	$-0.501089\pi$
$853$	−0.199822	−0.00684179	−0.00342089	+	0.999994i	$0.501089\pi$
$854$	−0.123705	−0.00423310
$855$	−57.6445	−1.97140
$856$	4.18750	0.143126
$857$	−10.1129	−0.345451	−0.172726	−	0.984970i	$-0.555257\pi$
$857$	−10.1129	−0.345451	−0.172726	+	0.984970i	$0.555257\pi$
$858$	−0.886950	−0.0302800
$859$	44.6656	1.52397	0.761985	−	0.647595i	$-0.224225\pi$
$859$	44.6656	1.52397	0.761985	+	0.647595i	$0.224225\pi$
$860$	−5.91490	−0.201696
$861$	0.253073	0.00862470
$862$	−19.4684	−0.663095
$863$	−20.2343	−0.688784	−0.344392	−	0.938826i	$-0.611915\pi$
$863$	−20.2343	−0.688784	−0.344392	+	0.938826i	$0.611915\pi$
$864$	0.906215	0.0308301
$865$	47.2579	1.60682
$866$	20.4265	0.694121
$867$	0.305173	0.0103642
$868$	1.17695	0.0399483
$869$	28.2270	0.957537
$870$	1.13711	0.0385516
$871$	−10.4209	−0.353098
$872$	14.5828	0.493837
$873$	−25.6791	−0.869106
$874$	−2.39287	−0.0809400
$875$	−10.9733	−0.370965
$876$	−2.35545	−0.0795833
$877$	−0.437468	−0.0147723	−0.00738613	−	0.999973i	$-0.502351\pi$
$877$	−0.437468	−0.0147723	−0.00738613	+	0.999973i	$0.502351\pi$
$878$	−29.5525	−0.997347
$879$	−0.429795	−0.0144966
$880$	11.9918	0.404244
$881$	14.9120	0.502398	0.251199	−	0.967936i	$-0.419175\pi$
$881$	14.9120	0.502398	0.251199	+	0.967936i	$0.419175\pi$
$882$	20.5407	0.691640
$883$	54.7676	1.84308	0.921538	−	0.388288i	$-0.126933\pi$
$883$	54.7676	1.84308	0.921538	+	0.388288i	$0.126933\pi$
$884$	−8.04308	−0.270518
$885$	2.46660	0.0829140
$886$	0.0235283	0.000790449 0
$887$	1.04000	0.0349197	0.0174599	−	0.999848i	$-0.494442\pi$
$887$	1.04000	0.0349197	0.0174599	+	0.999848i	$0.494442\pi$
$888$	1.60141	0.0537399
$889$	−5.63099	−0.188857
$890$	−53.0118	−1.77696
$891$	−24.7605	−0.829507
$892$	−13.1371	−0.439861
$893$	−3.82871	−0.128123
$894$	−0.536622	−0.0179473
$895$	−27.5967	−0.922455
$896$	0.316610	0.0105772
$897$	0.165785	0.00553540
$898$	33.4772	1.11715
$899$	6.54627	0.218330
$900$	−39.1120	−1.30373
$901$	−0.486671	−0.0162134
$902$	14.8444	0.494266
$903$	−0.0666690	−0.00221861
$904$	15.7910	0.525202
$905$	52.0125	1.72895
$906$	3.22402	0.107111
$907$	55.3473	1.83778	0.918888	−	0.394518i	$-0.129089\pi$
$907$	55.3473	1.83778	0.918888	+	0.394518i	$0.129089\pi$
$908$	−22.7688	−0.755608
$909$	−11.4014	−0.378160
$910$	2.80144	0.0928667
$911$	17.5551	0.581626	0.290813	−	0.956780i	$-0.406074\pi$
$911$	17.5551	0.581626	0.290813	+	0.956780i	$0.406074\pi$
$912$	0.689334	0.0228261
$913$	−24.7929	−0.820524
$914$	−12.7206	−0.420761
$915$	−0.252293	−0.00834055
$916$	19.1466	0.632623
$917$	−5.18675	−0.171282
$918$	3.50826	0.115790
$919$	−13.3803	−0.441376	−0.220688	−	0.975344i	$-0.570830\pi$
$919$	−13.3803	−0.441376	−0.220688	+	0.975344i	$0.570830\pi$
$920$	−2.24146	−0.0738988
$921$	−3.39188	−0.111766
$922$	−37.0880	−1.22143
$923$	−24.3955	−0.802989
$924$	0.135164	0.00444657
$925$	−138.767	−4.56262
$926$	−8.33611	−0.273942
$927$	−45.5850	−1.49721
$928$	1.76100	0.0578078
$929$	52.4485	1.72078	0.860389	−	0.509638i	$-0.170221\pi$
$929$	52.4485	1.72078	0.860389	+	0.509638i	$0.170221\pi$
$930$	2.40035	0.0787107
$931$	31.3701	1.02811
$932$	5.93983	0.194566
$933$	−3.43344	−0.112406
$934$	36.9787	1.20998
$935$	46.4243	1.51824
$936$	6.18504	0.202164
$937$	37.4761	1.22429	0.612146	−	0.790745i	$-0.290306\pi$
$937$	37.4761	1.22429	0.612146	+	0.790745i	$0.290306\pi$
$938$	1.58806	0.0518520
$939$	0.823021	0.0268583
$940$	−3.58645	−0.116977
$941$	−18.1208	−0.590721	−0.295361	−	0.955386i	$-0.595440\pi$
$941$	−18.1208	−0.590721	−0.295361	+	0.955386i	$0.595440\pi$
$942$	0.188848	0.00615299
$943$	−2.77466	−0.0903555
$944$	3.81995	0.124329
$945$	−1.22194	−0.0397497
$946$	−3.91059	−0.127144
$947$	26.9861	0.876929	0.438465	−	0.898748i	$-0.355522\pi$
$947$	26.9861	0.876929	0.438465	+	0.898748i	$0.355522\pi$
$948$	1.51993	0.0493649
$949$	−32.2767	−1.04775
$950$	−59.7326	−1.93798
$951$	−2.65458	−0.0860807
$952$	1.22570	0.0397252
$953$	39.9218	1.29319	0.646597	−	0.762832i	$-0.276192\pi$
$953$	39.9218	1.29319	0.646597	+	0.762832i	$0.276192\pi$
$954$	0.374245	0.0121166
$955$	21.0492	0.681137
$956$	−8.68948	−0.281038
$957$	0.751792	0.0243020
$958$	22.5686	0.729159
$959$	3.59324	0.116032
$960$	0.645716	0.0208404
$961$	−17.1813	−0.554236
$962$	21.9441	0.707506
$963$	−12.4662	−0.401719
$964$	−13.2070	−0.425368
$965$	27.4511	0.883683
$966$	−0.0252643	−0.000812867 0
$967$	3.23269	0.103956	0.0519782	−	0.998648i	$-0.483447\pi$
$967$	3.23269	0.103956	0.0519782	+	0.998648i	$0.483447\pi$
$968$	−3.07170	−0.0987282
$969$	2.66864	0.0857291
$970$	−36.7362	−1.17953
$971$	43.7918	1.40535	0.702673	−	0.711513i	$-0.251990\pi$
$971$	43.7918	1.40535	0.702673	+	0.711513i	$0.251990\pi$
$972$	−4.05191	−0.129965
$973$	−1.17944	−0.0378110
$974$	−15.5946	−0.499682
$975$	4.13845	0.132537
$976$	−0.390718	−0.0125066
$977$	51.3742	1.64361	0.821804	−	0.569771i	$-0.192968\pi$
$977$	51.3742	1.64361	0.821804	+	0.569771i	$0.192968\pi$
$978$	−0.180704	−0.00577829
$979$	−35.0484	−1.12015
$980$	29.3852	0.938675
$981$	−43.4133	−1.38608
$982$	−11.5749	−0.369369
$983$	32.2716	1.02930	0.514652	−	0.857399i	$-0.327921\pi$
$983$	32.2716	1.02930	0.514652	+	0.857399i	$0.327921\pi$
$984$	0.799321	0.0254814
$985$	41.9399	1.33632
$986$	6.81743	0.217111
$987$	−0.0404242	−0.00128672
$988$	9.44592	0.300515
$989$	0.730952	0.0232429
$990$	−35.6998	−1.13461
$991$	−39.3854	−1.25112	−0.625559	−	0.780177i	$-0.715129\pi$
$991$	−39.3854	−1.25112	−0.625559	+	0.780177i	$0.715129\pi$
$992$	3.71735	0.118026
$993$	4.59493	0.145816
$994$	3.71769	0.117918
$995$	−39.4553	−1.25082
$996$	−1.33501	−0.0423013
$997$	−11.2480	−0.356227	−0.178114	−	0.984010i	$-0.556999\pi$
$997$	−11.2480	−0.356227	−0.178114	+	0.984010i	$0.556999\pi$
$998$	−4.01918	−0.127225
$999$	−9.57166	−0.302834

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4006.2.a.i.1.19	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4006.2.a.i.1.19	✓	46	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:	\( N \)	\(=\)	\( 4006 = 2 \cdot 2003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4006.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.151617 q^{3} +1.00000 q^{4} -4.25887 q^{5} -0.151617 q^{6} +0.316610 q^{7} +1.00000 q^{8} -2.97701 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.151617 q^{3} +1.00000 q^{4} -4.25887 q^{5} -0.151617 q^{6} +0.316610 q^{7} +1.00000 q^{8} -2.97701 q^{9} -4.25887 q^{10} -2.81572 q^{11} -0.151617 q^{12} -2.07760 q^{13} +0.316610 q^{14} +0.645716 q^{15} +1.00000 q^{16} +3.87133 q^{17} -2.97701 q^{18} -4.54656 q^{19} -4.25887 q^{20} -0.0480033 q^{21} -2.81572 q^{22} +0.526304 q^{23} -0.151617 q^{24} +13.1380 q^{25} -2.07760 q^{26} +0.906215 q^{27} +0.316610 q^{28} +1.76100 q^{29} +0.645716 q^{30} +3.71735 q^{31} +1.00000 q^{32} +0.426911 q^{33} +3.87133 q^{34} -1.34840 q^{35} -2.97701 q^{36} -10.5622 q^{37} -4.54656 q^{38} +0.314999 q^{39} -4.25887 q^{40} -5.27198 q^{41} -0.0480033 q^{42} +1.38884 q^{43} -2.81572 q^{44} +12.6787 q^{45} +0.526304 q^{46} +0.842112 q^{47} -0.151617 q^{48} -6.89976 q^{49} +13.1380 q^{50} -0.586959 q^{51} -2.07760 q^{52} -0.125712 q^{53} +0.906215 q^{54} +11.9918 q^{55} +0.316610 q^{56} +0.689334 q^{57} +1.76100 q^{58} +3.81995 q^{59} +0.645716 q^{60} -0.390718 q^{61} +3.71735 q^{62} -0.942551 q^{63} +1.00000 q^{64} +8.84823 q^{65} +0.426911 q^{66} +5.01583 q^{67} +3.87133 q^{68} -0.0797965 q^{69} -1.34840 q^{70} +11.7422 q^{71} -2.97701 q^{72} +15.5356 q^{73} -10.5622 q^{74} -1.99194 q^{75} -4.54656 q^{76} -0.891486 q^{77} +0.314999 q^{78} -10.0248 q^{79} -4.25887 q^{80} +8.79364 q^{81} -5.27198 q^{82} +8.80515 q^{83} -0.0480033 q^{84} -16.4875 q^{85} +1.38884 q^{86} -0.266998 q^{87} -2.81572 q^{88} +12.4474 q^{89} +12.6787 q^{90} -0.657788 q^{91} +0.526304 q^{92} -0.563612 q^{93} +0.842112 q^{94} +19.3632 q^{95} -0.151617 q^{96} +8.62580 q^{97} -6.89976 q^{98} +8.38244 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q + 46 q^{2} + 21 q^{3} + 46 q^{4} + 23 q^{5} + 21 q^{6} + 26 q^{7} + 46 q^{8} + 59 q^{9}+O(q^{10}) \) 46 * q + 46 * q^2 + 21 * q^3 + 46 * q^4 + 23 * q^5 + 21 * q^6 + 26 * q^7 + 46 * q^8 + 59 * q^9	\( 46 q + 46 q^{2} + 21 q^{3} + 46 q^{4} + 23 q^{5} + 21 q^{6} + 26 q^{7} + 46 q^{8} + 59 q^{9} + 23 q^{10} + 39 q^{11} + 21 q^{12} + 8 q^{13} + 26 q^{14} + 14 q^{15} + 46 q^{16} + 36 q^{17} + 59 q^{18} + 37 q^{19} + 23 q^{20} + 20 q^{21} + 39 q^{22} + 38 q^{23} + 21 q^{24} + 57 q^{25} + 8 q^{26} + 63 q^{27} + 26 q^{28} + 23 q^{29} + 14 q^{30} + 44 q^{31} + 46 q^{32} + 25 q^{33} + 36 q^{34} + 26 q^{35} + 59 q^{36} + 9 q^{37} + 37 q^{38} - 2 q^{39} + 23 q^{40} + 50 q^{41} + 20 q^{42} + 46 q^{43} + 39 q^{44} + 30 q^{45} + 38 q^{46} + 57 q^{47} + 21 q^{48} + 62 q^{49} + 57 q^{50} + 5 q^{51} + 8 q^{52} + 21 q^{53} + 63 q^{54} + 40 q^{55} + 26 q^{56} + 3 q^{57} + 23 q^{58} + 68 q^{59} + 14 q^{60} - q^{61} + 44 q^{62} + 40 q^{63} + 46 q^{64} + 18 q^{65} + 25 q^{66} + 42 q^{67} + 36 q^{68} - 7 q^{69} + 26 q^{70} + 67 q^{71} + 59 q^{72} + 48 q^{73} + 9 q^{74} + 71 q^{75} + 37 q^{76} - 5 q^{77} - 2 q^{78} + 40 q^{79} + 23 q^{80} + 82 q^{81} + 50 q^{82} + 48 q^{83} + 20 q^{84} - 68 q^{85} + 46 q^{86} + 18 q^{87} + 39 q^{88} + 90 q^{89} + 30 q^{90} + 9 q^{91} + 38 q^{92} - 42 q^{93} + 57 q^{94} + 6 q^{95} + 21 q^{96} + 46 q^{97} + 62 q^{98} + 61 q^{99}+O(q^{100}) \) 46 * q + 46 * q^2 + 21 * q^3 + 46 * q^4 + 23 * q^5 + 21 * q^6 + 26 * q^7 + 46 * q^8 + 59 * q^9 + 23 * q^10 + 39 * q^11 + 21 * q^12 + 8 * q^13 + 26 * q^14 + 14 * q^15 + 46 * q^16 + 36 * q^17 + 59 * q^18 + 37 * q^19 + 23 * q^20 + 20 * q^21 + 39 * q^22 + 38 * q^23 + 21 * q^24 + 57 * q^25 + 8 * q^26 + 63 * q^27 + 26 * q^28 + 23 * q^29 + 14 * q^30 + 44 * q^31 + 46 * q^32 + 25 * q^33 + 36 * q^34 + 26 * q^35 + 59 * q^36 + 9 * q^37 + 37 * q^38 - 2 * q^39 + 23 * q^40 + 50 * q^41 + 20 * q^42 + 46 * q^43 + 39 * q^44 + 30 * q^45 + 38 * q^46 + 57 * q^47 + 21 * q^48 + 62 * q^49 + 57 * q^50 + 5 * q^51 + 8 * q^52 + 21 * q^53 + 63 * q^54 + 40 * q^55 + 26 * q^56 + 3 * q^57 + 23 * q^58 + 68 * q^59 + 14 * q^60 - q^61 + 44 * q^62 + 40 * q^63 + 46 * q^64 + 18 * q^65 + 25 * q^66 + 42 * q^67 + 36 * q^68 - 7 * q^69 + 26 * q^70 + 67 * q^71 + 59 * q^72 + 48 * q^73 + 9 * q^74 + 71 * q^75 + 37 * q^76 - 5 * q^77 - 2 * q^78 + 40 * q^79 + 23 * q^80 + 82 * q^81 + 50 * q^82 + 48 * q^83 + 20 * q^84 - 68 * q^85 + 46 * q^86 + 18 * q^87 + 39 * q^88 + 90 * q^89 + 30 * q^90 + 9 * q^91 + 38 * q^92 - 42 * q^93 + 57 * q^94 + 6 * q^95 + 21 * q^96 + 46 * q^97 + 62 * q^98 + 61 * q^99

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