LMFDB - Embedded newform 4006.2.a.g.1.37

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:	$1$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.37
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)

$f(q)$	$=$	$q-1.00000 q^{2} +2.62725 q^{3} +1.00000 q^{4} -1.63969 q^{5} -2.62725 q^{6} -1.77173 q^{7} -1.00000 q^{8} +3.90245 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.62725 q^{3} +1.00000 q^{4} -1.63969 q^{5} -2.62725 q^{6} -1.77173 q^{7} -1.00000 q^{8} +3.90245 q^{9} +1.63969 q^{10} +5.40865 q^{11} +2.62725 q^{12} -3.70971 q^{13} +1.77173 q^{14} -4.30788 q^{15} +1.00000 q^{16} -4.07338 q^{17} -3.90245 q^{18} -5.43412 q^{19} -1.63969 q^{20} -4.65477 q^{21} -5.40865 q^{22} +9.15783 q^{23} -2.62725 q^{24} -2.31141 q^{25} +3.70971 q^{26} +2.37097 q^{27} -1.77173 q^{28} +3.45740 q^{29} +4.30788 q^{30} -7.38187 q^{31} -1.00000 q^{32} +14.2099 q^{33} +4.07338 q^{34} +2.90508 q^{35} +3.90245 q^{36} -8.08104 q^{37} +5.43412 q^{38} -9.74634 q^{39} +1.63969 q^{40} -5.01500 q^{41} +4.65477 q^{42} +12.0844 q^{43} +5.40865 q^{44} -6.39882 q^{45} -9.15783 q^{46} -11.9360 q^{47} +2.62725 q^{48} -3.86099 q^{49} +2.31141 q^{50} -10.7018 q^{51} -3.70971 q^{52} +3.96031 q^{53} -2.37097 q^{54} -8.86852 q^{55} +1.77173 q^{56} -14.2768 q^{57} -3.45740 q^{58} -8.71852 q^{59} -4.30788 q^{60} +2.12480 q^{61} +7.38187 q^{62} -6.91407 q^{63} +1.00000 q^{64} +6.08278 q^{65} -14.2099 q^{66} +10.3544 q^{67} -4.07338 q^{68} +24.0599 q^{69} -2.90508 q^{70} -12.6780 q^{71} -3.90245 q^{72} -1.83429 q^{73} +8.08104 q^{74} -6.07266 q^{75} -5.43412 q^{76} -9.58264 q^{77} +9.74634 q^{78} +5.88523 q^{79} -1.63969 q^{80} -5.47823 q^{81} +5.01500 q^{82} +0.686506 q^{83} -4.65477 q^{84} +6.67908 q^{85} -12.0844 q^{86} +9.08346 q^{87} -5.40865 q^{88} -5.41742 q^{89} +6.39882 q^{90} +6.57258 q^{91} +9.15783 q^{92} -19.3940 q^{93} +11.9360 q^{94} +8.91028 q^{95} -2.62725 q^{96} -4.78450 q^{97} +3.86099 q^{98} +21.1070 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9}+O(q^{10}) $ 40 * q - 40 * q^2 - q^3 + 40 * q^4 - 23 * q^5 + q^6 + 12 * q^7 - 40 * q^8 + 29 * q^9	\( 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9} + 23 q^{10} - 28 q^{11} - q^{12} - 12 q^{13} - 12 q^{14} - 14 q^{15} + 40 q^{16} - 10 q^{17} - 29 q^{18} + 3 q^{19} - 23 q^{20} - 40 q^{21} + 28 q^{22} - 10 q^{23} + q^{24} + 43 q^{25} + 12 q^{26} - 7 q^{27} + 12 q^{28} - 37 q^{29} + 14 q^{30} - 16 q^{31} - 40 q^{32} - 11 q^{33} + 10 q^{34} - 24 q^{35} + 29 q^{36} - 17 q^{37} - 3 q^{38} - 10 q^{39} + 23 q^{40} - 58 q^{41} + 40 q^{42} + 37 q^{43} - 28 q^{44} - 66 q^{45} + 10 q^{46} - 34 q^{47} - q^{48} + 28 q^{49} - 43 q^{50} - 7 q^{51} - 12 q^{52} - 43 q^{53} + 7 q^{54} + 28 q^{55} - 12 q^{56} - 25 q^{57} + 37 q^{58} - 92 q^{59} - 14 q^{60} - 37 q^{61} + 16 q^{62} + 14 q^{63} + 40 q^{64} - 54 q^{65} + 11 q^{66} - 10 q^{67} - 10 q^{68} - 49 q^{69} + 24 q^{70} - 87 q^{71} - 29 q^{72} + 12 q^{73} + 17 q^{74} - 31 q^{75} + 3 q^{76} - 53 q^{77} + 10 q^{78} + 14 q^{79} - 23 q^{80} - 4 q^{81} + 58 q^{82} - 42 q^{83} - 40 q^{84} - 24 q^{85} - 37 q^{86} + 24 q^{87} + 28 q^{88} - 118 q^{89} + 66 q^{90} - 35 q^{91} - 10 q^{92} - 22 q^{93} + 34 q^{94} - 18 q^{95} + q^{96} + 2 q^{97} - 28 q^{98} - 48 q^{99}+O(q^{100}) \) 40 * q - 40 * q^2 - q^3 + 40 * q^4 - 23 * q^5 + q^6 + 12 * q^7 - 40 * q^8 + 29 * q^9 + 23 * q^10 - 28 * q^11 - q^12 - 12 * q^13 - 12 * q^14 - 14 * q^15 + 40 * q^16 - 10 * q^17 - 29 * q^18 + 3 * q^19 - 23 * q^20 - 40 * q^21 + 28 * q^22 - 10 * q^23 + q^24 + 43 * q^25 + 12 * q^26 - 7 * q^27 + 12 * q^28 - 37 * q^29 + 14 * q^30 - 16 * q^31 - 40 * q^32 - 11 * q^33 + 10 * q^34 - 24 * q^35 + 29 * q^36 - 17 * q^37 - 3 * q^38 - 10 * q^39 + 23 * q^40 - 58 * q^41 + 40 * q^42 + 37 * q^43 - 28 * q^44 - 66 * q^45 + 10 * q^46 - 34 * q^47 - q^48 + 28 * q^49 - 43 * q^50 - 7 * q^51 - 12 * q^52 - 43 * q^53 + 7 * q^54 + 28 * q^55 - 12 * q^56 - 25 * q^57 + 37 * q^58 - 92 * q^59 - 14 * q^60 - 37 * q^61 + 16 * q^62 + 14 * q^63 + 40 * q^64 - 54 * q^65 + 11 * q^66 - 10 * q^67 - 10 * q^68 - 49 * q^69 + 24 * q^70 - 87 * q^71 - 29 * q^72 + 12 * q^73 + 17 * q^74 - 31 * q^75 + 3 * q^76 - 53 * q^77 + 10 * q^78 + 14 * q^79 - 23 * q^80 - 4 * q^81 + 58 * q^82 - 42 * q^83 - 40 * q^84 - 24 * q^85 - 37 * q^86 + 24 * q^87 + 28 * q^88 - 118 * q^89 + 66 * q^90 - 35 * q^91 - 10 * q^92 - 22 * q^93 + 34 * q^94 - 18 * q^95 + q^96 + 2 * q^97 - 28 * q^98 - 48 * 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
$3$	2.62725	1.51684	0.758422	−	0.651764i	$-0.225971\pi$
$3$	2.62725	1.51684	0.758422	+	0.651764i	$0.225971\pi$
$4$	1.00000	0.500000
$5$	−1.63969	−0.733292	−0.366646	−	0.930360i	$-0.619494\pi$
$5$	−1.63969	−0.733292	−0.366646	+	0.930360i	$0.619494\pi$
$6$	−2.62725	−1.07257
$7$	−1.77173	−0.669649	−0.334825	−	0.942280i	$-0.608677\pi$
$7$	−1.77173	−0.669649	−0.334825	+	0.942280i	$0.608677\pi$
$8$	−1.00000	−0.353553
$9$	3.90245	1.30082
$10$	1.63969	0.518516
$11$	5.40865	1.63077	0.815384	−	0.578920i	$-0.196526\pi$
$11$	5.40865	1.63077	0.815384	+	0.578920i	$0.196526\pi$
$12$	2.62725	0.758422
$13$	−3.70971	−1.02889	−0.514444	−	0.857524i	$-0.672002\pi$
$13$	−3.70971	−1.02889	−0.514444	+	0.857524i	$0.672002\pi$
$14$	1.77173	0.473514
$15$	−4.30788	−1.11229
$16$	1.00000	0.250000
$17$	−4.07338	−0.987939	−0.493970	−	0.869479i	$-0.664455\pi$
$17$	−4.07338	−0.987939	−0.493970	+	0.869479i	$0.664455\pi$
$18$	−3.90245	−0.919817
$19$	−5.43412	−1.24667	−0.623336	−	0.781954i	$-0.714223\pi$
$19$	−5.43412	−1.24667	−0.623336	+	0.781954i	$0.714223\pi$
$20$	−1.63969	−0.366646
$21$	−4.65477	−1.01575
$22$	−5.40865	−1.15313
$23$	9.15783	1.90954	0.954770	−	0.297345i	$-0.0961010\pi$
$23$	9.15783	1.90954	0.954770	+	0.297345i	$0.0961010\pi$
$24$	−2.62725	−0.536286
$25$	−2.31141	−0.462282
$26$	3.70971	0.727534
$27$	2.37097	0.456293
$28$	−1.77173	−0.334825
$29$	3.45740	0.642023	0.321011	−	0.947075i	$-0.395977\pi$
$29$	3.45740	0.642023	0.321011	+	0.947075i	$0.395977\pi$
$30$	4.30788	0.786508
$31$	−7.38187	−1.32582	−0.662911	−	0.748698i	$-0.730679\pi$
$31$	−7.38187	−1.32582	−0.662911	+	0.748698i	$0.730679\pi$
$32$	−1.00000	−0.176777
$33$	14.2099	2.47362
$34$	4.07338	0.698579
$35$	2.90508	0.491049
$36$	3.90245	0.650409
$37$	−8.08104	−1.32852	−0.664258	−	0.747504i	$-0.731252\pi$
$37$	−8.08104	−1.32852	−0.664258	+	0.747504i	$0.731252\pi$
$38$	5.43412	0.881531
$39$	−9.74634	−1.56066
$40$	1.63969	0.259258
$41$	−5.01500	−0.783211	−0.391605	−	0.920133i	$-0.628080\pi$
$41$	−5.01500	−0.783211	−0.391605	+	0.920133i	$0.628080\pi$
$42$	4.65477	0.718246
$43$	12.0844	1.84285	0.921424	−	0.388558i	$-0.127027\pi$
$43$	12.0844	1.84285	0.921424	+	0.388558i	$0.127027\pi$
$44$	5.40865	0.815384
$45$	−6.39882	−0.953879
$46$	−9.15783	−1.35025
$47$	−11.9360	−1.74105	−0.870526	−	0.492123i	$-0.836221\pi$
$47$	−11.9360	−1.74105	−0.870526	+	0.492123i	$0.836221\pi$
$48$	2.62725	0.379211
$49$	−3.86099	−0.551570
$50$	2.31141	0.326883
$51$	−10.7018	−1.49855
$52$	−3.70971	−0.514444
$53$	3.96031	0.543990	0.271995	−	0.962299i	$-0.412317\pi$
$53$	3.96031	0.543990	0.271995	+	0.962299i	$0.412317\pi$
$54$	−2.37097	−0.322648
$55$	−8.86852	−1.19583
$56$	1.77173	0.236757
$57$	−14.2768	−1.89101
$58$	−3.45740	−0.453979
$59$	−8.71852	−1.13505	−0.567527	−	0.823355i	$-0.692100\pi$
$59$	−8.71852	−1.13505	−0.567527	+	0.823355i	$0.692100\pi$
$60$	−4.30788	−0.556145
$61$	2.12480	0.272052	0.136026	−	0.990705i	$-0.456567\pi$
$61$	2.12480	0.272052	0.136026	+	0.990705i	$0.456567\pi$
$62$	7.38187	0.937498
$63$	−6.91407	−0.871091
$64$	1.00000	0.125000
$65$	6.08278	0.754476
$66$	−14.2099	−1.74912
$67$	10.3544	1.26500	0.632498	−	0.774562i	$-0.282030\pi$
$67$	10.3544	1.26500	0.632498	+	0.774562i	$0.282030\pi$
$68$	−4.07338	−0.493970
$69$	24.0599	2.89648
$70$	−2.90508	−0.347224
$71$	−12.6780	−1.50460	−0.752302	−	0.658819i	$-0.771056\pi$
$71$	−12.6780	−1.50460	−0.752302	+	0.658819i	$0.771056\pi$
$72$	−3.90245	−0.459908
$73$	−1.83429	−0.214687	−0.107344	−	0.994222i	$-0.534234\pi$
$73$	−1.83429	−0.214687	−0.107344	+	0.994222i	$0.534234\pi$
$74$	8.08104	0.939402
$75$	−6.07266	−0.701210
$76$	−5.43412	−0.623336
$77$	−9.58264	−1.09204
$78$	9.74634	1.10356
$79$	5.88523	0.662140	0.331070	−	0.943606i	$-0.392590\pi$
$79$	5.88523	0.662140	0.331070	+	0.943606i	$0.392590\pi$
$80$	−1.63969	−0.183323
$81$	−5.47823	−0.608692
$82$	5.01500	0.553814
$83$	0.686506	0.0753538	0.0376769	−	0.999290i	$-0.488004\pi$
$83$	0.686506	0.0753538	0.0376769	+	0.999290i	$0.488004\pi$
$84$	−4.65477	−0.507877
$85$	6.67908	0.724448
$86$	−12.0844	−1.30309
$87$	9.08346	0.973849
$88$	−5.40865	−0.576564
$89$	−5.41742	−0.574246	−0.287123	−	0.957894i	$-0.592699\pi$
$89$	−5.41742	−0.574246	−0.287123	+	0.957894i	$0.592699\pi$
$90$	6.39882	0.674495
$91$	6.57258	0.688994
$92$	9.15783	0.954770
$93$	−19.3940	−2.01107
$94$	11.9360	1.23111
$95$	8.91028	0.914176
$96$	−2.62725	−0.268143
$97$	−4.78450	−0.485792	−0.242896	−	0.970052i	$-0.578097\pi$
$97$	−4.78450	−0.485792	−0.242896	+	0.970052i	$0.578097\pi$
$98$	3.86099	0.390019
$99$	21.1070	2.12133
$100$	−2.31141	−0.231141
$101$	15.9935	1.59141	0.795706	−	0.605683i	$-0.207100\pi$
$101$	15.9935	1.59141	0.795706	+	0.605683i	$0.207100\pi$
$102$	10.7018	1.05964
$103$	−19.2263	−1.89442	−0.947211	−	0.320610i	$-0.896112\pi$
$103$	−19.2263	−1.89442	−0.947211	+	0.320610i	$0.896112\pi$
$104$	3.70971	0.363767
$105$	7.63239	0.744845
$106$	−3.96031	−0.384659
$107$	1.33460	0.129021	0.0645105	−	0.997917i	$-0.479451\pi$
$107$	1.33460	0.129021	0.0645105	+	0.997917i	$0.479451\pi$
$108$	2.37097	0.228146
$109$	−0.563515	−0.0539749	−0.0269875	−	0.999636i	$-0.508591\pi$
$109$	−0.563515	−0.0539749	−0.0269875	+	0.999636i	$0.508591\pi$
$110$	8.86852	0.845580
$111$	−21.2309	−2.01515
$112$	−1.77173	−0.167412
$113$	10.8816	1.02365	0.511826	−	0.859089i	$-0.328969\pi$
$113$	10.8816	1.02365	0.511826	+	0.859089i	$0.328969\pi$
$114$	14.2768	1.33715
$115$	−15.0160	−1.40025
$116$	3.45740	0.321011
$117$	−14.4770	−1.33839
$118$	8.71852	0.802605
$119$	7.21691	0.661573
$120$	4.30788	0.393254
$121$	18.2535	1.65941
$122$	−2.12480	−0.192370
$123$	−13.1757	−1.18801
$124$	−7.38187	−0.662911
$125$	11.9885	1.07228
$126$	6.91407	0.615955
$127$	−17.4001	−1.54401	−0.772004	−	0.635617i	$-0.780746\pi$
$127$	−17.4001	−1.54401	−0.772004	+	0.635617i	$0.780746\pi$
$128$	−1.00000	−0.0883883
$129$	31.7487	2.79532
$130$	−6.08278	−0.533495
$131$	1.37098	0.119783	0.0598913	−	0.998205i	$-0.480925\pi$
$131$	1.37098	0.119783	0.0598913	+	0.998205i	$0.480925\pi$
$132$	14.2099	1.23681
$133$	9.62777	0.834834
$134$	−10.3544	−0.894487
$135$	−3.88766	−0.334596
$136$	4.07338	0.349289
$137$	2.72186	0.232544	0.116272	−	0.993217i	$-0.462906\pi$
$137$	2.72186	0.232544	0.116272	+	0.993217i	$0.462906\pi$
$138$	−24.0599	−2.04812
$139$	16.2013	1.37417	0.687087	−	0.726575i	$-0.258889\pi$
$139$	16.2013	1.37417	0.687087	+	0.726575i	$0.258889\pi$
$140$	2.90508	0.245524
$141$	−31.3590	−2.64090
$142$	12.6780	1.06392
$143$	−20.0645	−1.67788
$144$	3.90245	0.325204
$145$	−5.66907	−0.470791
$146$	1.83429	0.151807
$147$	−10.1438	−0.836646
$148$	−8.08104	−0.664258
$149$	−14.8369	−1.21548	−0.607741	−	0.794135i	$-0.707924\pi$
$149$	−14.8369	−1.21548	−0.607741	+	0.794135i	$0.707924\pi$
$150$	6.07266	0.495831
$151$	−15.3129	−1.24614	−0.623071	−	0.782165i	$-0.714115\pi$
$151$	−15.3129	−1.24614	−0.623071	+	0.782165i	$0.714115\pi$
$152$	5.43412	0.440765
$153$	−15.8962	−1.28513
$154$	9.58264	0.772191
$155$	12.1040	0.972216
$156$	−9.74634	−0.780331
$157$	−5.72582	−0.456970	−0.228485	−	0.973547i	$-0.573377\pi$
$157$	−5.72582	−0.456970	−0.228485	+	0.973547i	$0.573377\pi$
$158$	−5.88523	−0.468204
$159$	10.4047	0.825149
$160$	1.63969	0.129629
$161$	−16.2252	−1.27872
$162$	5.47823	0.430410
$163$	9.77214	0.765413	0.382707	−	0.923870i	$-0.374992\pi$
$163$	9.77214	0.765413	0.382707	+	0.923870i	$0.374992\pi$
$164$	−5.01500	−0.391605
$165$	−23.2998	−1.81389
$166$	−0.686506	−0.0532832
$167$	−20.6808	−1.60033	−0.800165	−	0.599779i	$-0.795255\pi$
$167$	−20.6808	−1.60033	−0.800165	+	0.599779i	$0.795255\pi$
$168$	4.65477	0.359123
$169$	0.761931	0.0586101
$170$	−6.67908	−0.512262
$171$	−21.2064	−1.62169
$172$	12.0844	0.921424
$173$	−4.97391	−0.378160	−0.189080	−	0.981962i	$-0.560551\pi$
$173$	−4.97391	−0.378160	−0.189080	+	0.981962i	$0.560551\pi$
$174$	−9.08346	−0.688615
$175$	4.09519	0.309567
$176$	5.40865	0.407692
$177$	−22.9057	−1.72170
$178$	5.41742	0.406053
$179$	−11.1153	−0.830795	−0.415397	−	0.909640i	$-0.636357\pi$
$179$	−11.1153	−0.830795	−0.415397	+	0.909640i	$0.636357\pi$
$180$	−6.39882	−0.476940
$181$	−8.70612	−0.647121	−0.323560	−	0.946208i	$-0.604880\pi$
$181$	−8.70612	−0.647121	−0.323560	+	0.946208i	$0.604880\pi$
$182$	−6.57258	−0.487192
$183$	5.58238	0.412661
$184$	−9.15783	−0.675124
$185$	13.2504	0.974190
$186$	19.3940	1.42204
$187$	−22.0315	−1.61110
$188$	−11.9360	−0.870526
$189$	−4.20070	−0.305556
$190$	−8.91028	−0.646420
$191$	−14.6291	−1.05853	−0.529264	−	0.848457i	$-0.677532\pi$
$191$	−14.6291	−1.05853	−0.529264	+	0.848457i	$0.677532\pi$
$192$	2.62725	0.189606
$193$	−15.5270	−1.11766	−0.558829	−	0.829283i	$-0.688749\pi$
$193$	−15.5270	−1.11766	−0.558829	+	0.829283i	$0.688749\pi$
$194$	4.78450	0.343507
$195$	15.9810	1.14442
$196$	−3.86099	−0.275785
$197$	−3.79986	−0.270729	−0.135364	−	0.990796i	$-0.543220\pi$
$197$	−3.79986	−0.270729	−0.135364	+	0.990796i	$0.543220\pi$
$198$	−21.1070	−1.50001
$199$	−10.3294	−0.732232	−0.366116	−	0.930569i	$-0.619313\pi$
$199$	−10.3294	−0.732232	−0.366116	+	0.930569i	$0.619313\pi$
$200$	2.31141	0.163441
$201$	27.2037	1.91880
$202$	−15.9935	−1.12530
$203$	−6.12556	−0.429930
$204$	−10.7018	−0.749275
$205$	8.22305	0.574322
$206$	19.2263	1.33956
$207$	35.7380	2.48396
$208$	−3.70971	−0.257222
$209$	−29.3912	−2.03303
$210$	−7.63239	−0.526685
$211$	12.7364	0.876808	0.438404	−	0.898778i	$-0.355544\pi$
$211$	12.7364	0.876808	0.438404	+	0.898778i	$0.355544\pi$
$212$	3.96031	0.271995
$213$	−33.3083	−2.28225
$214$	−1.33460	−0.0912317
$215$	−19.8146	−1.35135
$216$	−2.37097	−0.161324
$217$	13.0786	0.887836
$218$	0.563515	0.0381660
$219$	−4.81914	−0.325647
$220$	−8.86852	−0.597915
$221$	15.1110	1.01648
$222$	21.2309	1.42493
$223$	5.81517	0.389413	0.194706	−	0.980862i	$-0.437625\pi$
$223$	5.81517	0.389413	0.194706	+	0.980862i	$0.437625\pi$
$224$	1.77173	0.118378
$225$	−9.02017	−0.601345
$226$	−10.8816	−0.723832
$227$	10.5432	0.699778	0.349889	−	0.936791i	$-0.386219\pi$
$227$	10.5432	0.699778	0.349889	+	0.936791i	$0.386219\pi$
$228$	−14.2768	−0.945504
$229$	18.5440	1.22543	0.612713	−	0.790306i	$-0.290078\pi$
$229$	18.5440	1.22543	0.612713	+	0.790306i	$0.290078\pi$
$230$	15.0160	0.990127
$231$	−25.1760	−1.65646
$232$	−3.45740	−0.226989
$233$	−29.7044	−1.94600	−0.972999	−	0.230808i	$-0.925863\pi$
$233$	−29.7044	−1.94600	−0.972999	+	0.230808i	$0.925863\pi$
$234$	14.4770	0.946388
$235$	19.5714	1.27670
$236$	−8.71852	−0.567527
$237$	15.4620	1.00436
$238$	−7.21691	−0.467803
$239$	−2.14098	−0.138488	−0.0692441	−	0.997600i	$-0.522059\pi$
$239$	−2.14098	−0.138488	−0.0692441	+	0.997600i	$0.522059\pi$
$240$	−4.30788	−0.278073
$241$	19.5058	1.25648	0.628240	−	0.778020i	$-0.283776\pi$
$241$	19.5058	1.25648	0.628240	+	0.778020i	$0.283776\pi$
$242$	−18.2535	−1.17338
$243$	−21.5056	−1.37958
$244$	2.12480	0.136026
$245$	6.33083	0.404462
$246$	13.1757	0.840049
$247$	20.1590	1.28269
$248$	7.38187	0.468749
$249$	1.80362	0.114300
$250$	−11.9885	−0.758217
$251$	−18.7180	−1.18147	−0.590734	−	0.806866i	$-0.701162\pi$
$251$	−18.7180	−1.18147	−0.590734	+	0.806866i	$0.701162\pi$
$252$	−6.91407	−0.435546
$253$	49.5315	3.11402
$254$	17.4001	1.09178
$255$	17.5476	1.09888
$256$	1.00000	0.0625000
$257$	18.9728	1.18349	0.591745	−	0.806125i	$-0.298439\pi$
$257$	18.9728	1.18349	0.591745	+	0.806125i	$0.298439\pi$
$258$	−31.7487	−1.97659
$259$	14.3174	0.889639
$260$	6.08278	0.377238
$261$	13.4923	0.835154
$262$	−1.37098	−0.0846991
$263$	10.4319	0.643256	0.321628	−	0.946866i	$-0.395770\pi$
$263$	10.4319	0.643256	0.321628	+	0.946866i	$0.395770\pi$
$264$	−14.2099	−0.874558
$265$	−6.49369	−0.398904
$266$	−9.62777	−0.590316
$267$	−14.2329	−0.871042
$268$	10.3544	0.632498
$269$	−8.29987	−0.506052	−0.253026	−	0.967459i	$-0.581426\pi$
$269$	−8.29987	−0.506052	−0.253026	+	0.967459i	$0.581426\pi$
$270$	3.88766	0.236595
$271$	−17.3265	−1.05251	−0.526256	−	0.850326i	$-0.676405\pi$
$271$	−17.3265	−1.05251	−0.526256	+	0.850326i	$0.676405\pi$
$272$	−4.07338	−0.246985
$273$	17.2678	1.04510
$274$	−2.72186	−0.164434
$275$	−12.5016	−0.753875
$276$	24.0599	1.44824
$277$	17.7833	1.06849	0.534247	−	0.845328i	$-0.320595\pi$
$277$	17.7833	1.06849	0.534247	+	0.845328i	$0.320595\pi$
$278$	−16.2013	−0.971688
$279$	−28.8074	−1.72465
$280$	−2.90508	−0.173612
$281$	1.54519	0.0921786	0.0460893	−	0.998937i	$-0.485324\pi$
$281$	1.54519	0.0921786	0.0460893	+	0.998937i	$0.485324\pi$
$282$	31.3590	1.86740
$283$	19.3103	1.14788	0.573940	−	0.818898i	$-0.305414\pi$
$283$	19.3103	1.14788	0.573940	+	0.818898i	$0.305414\pi$
$284$	−12.6780	−0.752302
$285$	23.4096	1.38666
$286$	20.0645	1.18644
$287$	8.88520	0.524477
$288$	−3.90245	−0.229954
$289$	−0.407591	−0.0239760
$290$	5.66907	0.332899
$291$	−12.5701	−0.736871
$292$	−1.83429	−0.107344
$293$	−3.59449	−0.209993	−0.104996	−	0.994473i	$-0.533483\pi$
$293$	−3.59449	−0.209993	−0.104996	+	0.994473i	$0.533483\pi$
$294$	10.1438	0.591598
$295$	14.2957	0.832327
$296$	8.08104	0.469701
$297$	12.8237	0.744108
$298$	14.8369	0.859476
$299$	−33.9729	−1.96470
$300$	−6.07266	−0.350605
$301$	−21.4102	−1.23406
$302$	15.3129	0.881156
$303$	42.0189	2.41393
$304$	−5.43412	−0.311668
$305$	−3.48401	−0.199494
$306$	15.8962	0.908723
$307$	0.894621	0.0510587	0.0255293	−	0.999674i	$-0.491873\pi$
$307$	0.894621	0.0510587	0.0255293	+	0.999674i	$0.491873\pi$
$308$	−9.58264	−0.546022
$309$	−50.5123	−2.87354
$310$	−12.1040	−0.687460
$311$	−19.1128	−1.08379	−0.541893	−	0.840447i	$-0.682292\pi$
$311$	−19.1128	−1.08379	−0.541893	+	0.840447i	$0.682292\pi$
$312$	9.74634	0.551778
$313$	24.1609	1.36565	0.682827	−	0.730580i	$-0.260750\pi$
$313$	24.1609	1.36565	0.682827	+	0.730580i	$0.260750\pi$
$314$	5.72582	0.323127
$315$	11.3369	0.638765
$316$	5.88523	0.331070
$317$	9.02092	0.506666	0.253333	−	0.967379i	$-0.418473\pi$
$317$	9.02092	0.506666	0.253333	+	0.967379i	$0.418473\pi$
$318$	−10.4047	−0.583468
$319$	18.6999	1.04699
$320$	−1.63969	−0.0916615
$321$	3.50634	0.195705
$322$	16.2252	0.904193
$323$	22.1352	1.23164
$324$	−5.47823	−0.304346
$325$	8.57466	0.475637
$326$	−9.77214	−0.541229
$327$	−1.48050	−0.0818716
$328$	5.01500	0.276907
$329$	21.1474	1.16589
$330$	23.2998	1.28261
$331$	18.0606	0.992700	0.496350	−	0.868123i	$-0.334673\pi$
$331$	18.0606	0.992700	0.496350	+	0.868123i	$0.334673\pi$
$332$	0.686506	0.0376769
$333$	−31.5359	−1.72816
$334$	20.6808	1.13160
$335$	−16.9781	−0.927611
$336$	−4.65477	−0.253938
$337$	−10.6885	−0.582239	−0.291119	−	0.956687i	$-0.594028\pi$
$337$	−10.6885	−0.582239	−0.291119	+	0.956687i	$0.594028\pi$
$338$	−0.761931	−0.0414436
$339$	28.5886	1.55272
$340$	6.67908	0.362224
$341$	−39.9259	−2.16211
$342$	21.2064	1.14671
$343$	19.2427	1.03901
$344$	−12.0844	−0.651545
$345$	−39.4509	−2.12396
$346$	4.97391	0.267399
$347$	1.75548	0.0942390	0.0471195	−	0.998889i	$-0.484996\pi$
$347$	1.75548	0.0942390	0.0471195	+	0.998889i	$0.484996\pi$
$348$	9.08346	0.486924
$349$	11.0038	0.589020	0.294510	−	0.955648i	$-0.404844\pi$
$349$	11.0038	0.589020	0.294510	+	0.955648i	$0.404844\pi$
$350$	−4.09519	−0.218897
$351$	−8.79560	−0.469474
$352$	−5.40865	−0.288282
$353$	9.15399	0.487217	0.243609	−	0.969874i	$-0.421669\pi$
$353$	9.15399	0.487217	0.243609	+	0.969874i	$0.421669\pi$
$354$	22.9057	1.21743
$355$	20.7880	1.10331
$356$	−5.41742	−0.287123
$357$	18.9606	1.00350
$358$	11.1153	0.587460
$359$	17.5152	0.924415	0.462207	−	0.886772i	$-0.347058\pi$
$359$	17.5152	0.924415	0.462207	+	0.886772i	$0.347058\pi$
$360$	6.39882	0.337247
$361$	10.5297	0.554193
$362$	8.70612	0.457584
$363$	47.9565	2.51706
$364$	6.57258	0.344497
$365$	3.00767	0.157429
$366$	−5.58238	−0.291796
$367$	30.0660	1.56943	0.784715	−	0.619856i	$-0.212809\pi$
$367$	30.0660	1.56943	0.784715	+	0.619856i	$0.212809\pi$
$368$	9.15783	0.477385
$369$	−19.5708	−1.01881
$370$	−13.2504	−0.688856
$371$	−7.01658	−0.364283
$372$	−19.3940	−1.00553
$373$	−4.36956	−0.226247	−0.113124	−	0.993581i	$-0.536086\pi$
$373$	−4.36956	−0.226247	−0.113124	+	0.993581i	$0.536086\pi$
$374$	22.0315	1.13922
$375$	31.4967	1.62648
$376$	11.9360	0.615555
$377$	−12.8259	−0.660570
$378$	4.20070	0.216061
$379$	−26.0000	−1.33553	−0.667765	−	0.744372i	$-0.732749\pi$
$379$	−26.0000	−1.33553	−0.667765	+	0.744372i	$0.732749\pi$
$380$	8.91028	0.457088
$381$	−45.7144	−2.34202
$382$	14.6291	0.748492
$383$	4.38715	0.224173	0.112087	−	0.993698i	$-0.464247\pi$
$383$	4.38715	0.224173	0.112087	+	0.993698i	$0.464247\pi$
$384$	−2.62725	−0.134071
$385$	15.7126	0.800787
$386$	15.5270	0.790304
$387$	47.1587	2.39721
$388$	−4.78450	−0.242896
$389$	−22.8631	−1.15920	−0.579602	−	0.814900i	$-0.696792\pi$
$389$	−22.8631	−1.15920	−0.579602	+	0.814900i	$0.696792\pi$
$390$	−15.9810	−0.809229
$391$	−37.3033	−1.88651
$392$	3.86099	0.195009
$393$	3.60190	0.181692
$394$	3.79986	0.191434
$395$	−9.64996	−0.485542
$396$	21.1070	1.06067
$397$	−7.51082	−0.376957	−0.188479	−	0.982077i	$-0.560356\pi$
$397$	−7.51082	−0.376957	−0.188479	+	0.982077i	$0.560356\pi$
$398$	10.3294	0.517766
$399$	25.2946	1.26631
$400$	−2.31141	−0.115571
$401$	−4.47261	−0.223352	−0.111676	−	0.993745i	$-0.535622\pi$
$401$	−4.47261	−0.223352	−0.111676	+	0.993745i	$0.535622\pi$
$402$	−27.2037	−1.35680
$403$	27.3846	1.36412
$404$	15.9935	0.795706
$405$	8.98260	0.446349
$406$	6.12556	0.304007
$407$	−43.7075	−2.16650
$408$	10.7018	0.529818
$409$	26.2461	1.29779	0.648894	−	0.760879i	$-0.275232\pi$
$409$	26.2461	1.29779	0.648894	+	0.760879i	$0.275232\pi$
$410$	−8.22305	−0.406107
$411$	7.15101	0.352733
$412$	−19.2263	−0.947211
$413$	15.4468	0.760088
$414$	−35.7380	−1.75643
$415$	−1.12566	−0.0552564
$416$	3.70971	0.181883
$417$	42.5648	2.08441
$418$	29.3912	1.43757
$419$	−14.8673	−0.726317	−0.363158	−	0.931727i	$-0.618302\pi$
$419$	−14.8673	−0.726317	−0.363158	+	0.931727i	$0.618302\pi$
$420$	7.63239	0.372422
$421$	−19.9651	−0.973039	−0.486520	−	0.873670i	$-0.661734\pi$
$421$	−19.9651	−0.973039	−0.486520	+	0.873670i	$0.661734\pi$
$422$	−12.7364	−0.619997
$423$	−46.5799	−2.26479
$424$	−3.96031	−0.192330
$425$	9.41525	0.456707
$426$	33.3083	1.61379
$427$	−3.76456	−0.182180
$428$	1.33460	0.0645105
$429$	−52.7145	−2.54508
$430$	19.8146	0.955547
$431$	10.6763	0.514257	0.257129	−	0.966377i	$-0.417224\pi$
$431$	10.6763	0.514257	0.257129	+	0.966377i	$0.417224\pi$
$432$	2.37097	0.114073
$433$	−8.81503	−0.423623	−0.211812	−	0.977311i	$-0.567936\pi$
$433$	−8.81503	−0.423623	−0.211812	+	0.977311i	$0.567936\pi$
$434$	−13.0786	−0.627795
$435$	−14.8941	−0.714116
$436$	−0.563515	−0.0269875
$437$	−49.7648	−2.38057
$438$	4.81914	0.230267
$439$	−25.9293	−1.23754	−0.618769	−	0.785573i	$-0.712368\pi$
$439$	−25.9293	−1.23754	−0.618769	+	0.785573i	$0.712368\pi$
$440$	8.86852	0.422790
$441$	−15.0673	−0.717491
$442$	−15.1110	−0.718759
$443$	−13.8129	−0.656269	−0.328134	−	0.944631i	$-0.606420\pi$
$443$	−13.8129	−0.656269	−0.328134	+	0.944631i	$0.606420\pi$
$444$	−21.2309	−1.00758
$445$	8.88291	0.421090
$446$	−5.81517	−0.275356
$447$	−38.9802	−1.84370
$448$	−1.77173	−0.0837062
$449$	−13.9359	−0.657675	−0.328837	−	0.944387i	$-0.606657\pi$
$449$	−13.9359	−0.657675	−0.328837	+	0.944387i	$0.606657\pi$
$450$	9.02017	0.425215
$451$	−27.1243	−1.27724
$452$	10.8816	0.511826
$453$	−40.2307	−1.89020
$454$	−10.5432	−0.494818
$455$	−10.7770	−0.505234
$456$	14.2768	0.668573
$457$	0.865730	0.0404971	0.0202486	−	0.999795i	$-0.493554\pi$
$457$	0.865730	0.0404971	0.0202486	+	0.999795i	$0.493554\pi$
$458$	−18.5440	−0.866506
$459$	−9.65785	−0.450790
$460$	−15.0160	−0.700126
$461$	32.0796	1.49410	0.747049	−	0.664769i	$-0.231470\pi$
$461$	32.0796	1.49410	0.747049	+	0.664769i	$0.231470\pi$
$462$	25.1760	1.17129
$463$	10.9448	0.508647	0.254324	−	0.967119i	$-0.418147\pi$
$463$	10.9448	0.508647	0.254324	+	0.967119i	$0.418147\pi$
$464$	3.45740	0.160506
$465$	31.8002	1.47470
$466$	29.7044	1.37603
$467$	−2.39461	−0.110809	−0.0554046	−	0.998464i	$-0.517645\pi$
$467$	−2.39461	−0.110809	−0.0554046	+	0.998464i	$0.517645\pi$
$468$	−14.4770	−0.669197
$469$	−18.3452	−0.847103
$470$	−19.5714	−0.902763
$471$	−15.0432	−0.693153
$472$	8.71852	0.401302
$473$	65.3601	3.00526
$474$	−15.4620	−0.710192
$475$	12.5605	0.576315
$476$	7.21691	0.330786
$477$	15.4549	0.707632
$478$	2.14098	0.0979260
$479$	25.4168	1.16133	0.580663	−	0.814144i	$-0.302794\pi$
$479$	25.4168	1.16133	0.580663	+	0.814144i	$0.302794\pi$
$480$	4.30788	0.196627
$481$	29.9783	1.36689
$482$	−19.5058	−0.888465
$483$	−42.6276	−1.93962
$484$	18.2535	0.829703
$485$	7.84510	0.356228
$486$	21.5056	0.975513
$487$	−16.0677	−0.728099	−0.364049	−	0.931380i	$-0.618606\pi$
$487$	−16.0677	−0.728099	−0.364049	+	0.931380i	$0.618606\pi$
$488$	−2.12480	−0.0961851
$489$	25.6739	1.16101
$490$	−6.33083	−0.285998
$491$	3.14732	0.142036	0.0710182	−	0.997475i	$-0.477375\pi$
$491$	3.14732	0.142036	0.0710182	+	0.997475i	$0.477375\pi$
$492$	−13.1757	−0.594004
$493$	−14.0833	−0.634280
$494$	−20.1590	−0.906996
$495$	−34.6090	−1.55556
$496$	−7.38187	−0.331456
$497$	22.4620	1.00756
$498$	−1.80362	−0.0808223
$499$	−30.7225	−1.37533	−0.687663	−	0.726030i	$-0.741363\pi$
$499$	−30.7225	−1.37533	−0.687663	+	0.726030i	$0.741363\pi$
$500$	11.9885	0.536140
$501$	−54.3338	−2.42745
$502$	18.7180	0.835425
$503$	20.9859	0.935714	0.467857	−	0.883804i	$-0.345026\pi$
$503$	20.9859	0.935714	0.467857	+	0.883804i	$0.345026\pi$
$504$	6.91407	0.307977
$505$	−26.2244	−1.16697
$506$	−49.5315	−2.20194
$507$	2.00178	0.0889023
$508$	−17.4001	−0.772004
$509$	29.9015	1.32536	0.662680	−	0.748903i	$-0.269419\pi$
$509$	29.9015	1.32536	0.662680	+	0.748903i	$0.269419\pi$
$510$	−17.5476	−0.777022
$511$	3.24986	0.143765
$512$	−1.00000	−0.0441942
$513$	−12.8841	−0.568848
$514$	−18.9728	−0.836854
$515$	31.5252	1.38917
$516$	31.7487	1.39766
$517$	−64.5579	−2.83925
$518$	−14.3174	−0.629070
$519$	−13.0677	−0.573609
$520$	−6.08278	−0.266747
$521$	−19.4189	−0.850757	−0.425378	−	0.905016i	$-0.639859\pi$
$521$	−19.4189	−0.850757	−0.425378	+	0.905016i	$0.639859\pi$
$522$	−13.4923	−0.590543
$523$	41.2406	1.80333	0.901663	−	0.432440i	$-0.142347\pi$
$523$	41.2406	1.80333	0.901663	+	0.432440i	$0.142347\pi$
$524$	1.37098	0.0598913
$525$	10.7591	0.469565
$526$	−10.4319	−0.454850
$527$	30.0691	1.30983
$528$	14.2099	0.618406
$529$	60.8659	2.64634
$530$	6.49369	0.282068
$531$	−34.0236	−1.47650
$532$	9.62777	0.417417
$533$	18.6042	0.805836
$534$	14.2329	0.615919
$535$	−2.18834	−0.0946102
$536$	−10.3544	−0.447243
$537$	−29.2026	−1.26019
$538$	8.29987	0.357833
$539$	−20.8827	−0.899483
$540$	−3.88766	−0.167298
$541$	8.66124	0.372376	0.186188	−	0.982514i	$-0.440387\pi$
$541$	8.66124	0.372376	0.186188	+	0.982514i	$0.440387\pi$
$542$	17.3265	0.744238
$543$	−22.8732	−0.981582
$544$	4.07338	0.174645
$545$	0.923991	0.0395794
$546$	−17.2678	−0.738995
$547$	−20.1614	−0.862038	−0.431019	−	0.902343i	$-0.641846\pi$
$547$	−20.1614	−0.862038	−0.431019	+	0.902343i	$0.641846\pi$
$548$	2.72186	0.116272
$549$	8.29192	0.353891
$550$	12.5016	0.533070
$551$	−18.7879	−0.800392
$552$	−24.0599	−1.02406
$553$	−10.4270	−0.443402
$554$	−17.7833	−0.755539
$555$	34.8122	1.47769
$556$	16.2013	0.687087
$557$	1.69769	0.0719334	0.0359667	−	0.999353i	$-0.488549\pi$
$557$	1.69769	0.0719334	0.0359667	+	0.999353i	$0.488549\pi$
$558$	28.8074	1.21951
$559$	−44.8295	−1.89608
$560$	2.90508	0.122762
$561$	−57.8822	−2.44379
$562$	−1.54519	−0.0651801
$563$	−22.3222	−0.940769	−0.470384	−	0.882462i	$-0.655885\pi$
$563$	−22.3222	−0.940769	−0.470384	+	0.882462i	$0.655885\pi$
$564$	−31.3590	−1.32045
$565$	−17.8424	−0.750637
$566$	−19.3103	−0.811673
$567$	9.70591	0.407610
$568$	12.6780	0.531958
$569$	−4.63088	−0.194137	−0.0970683	−	0.995278i	$-0.530947\pi$
$569$	−4.63088	−0.194137	−0.0970683	+	0.995278i	$0.530947\pi$
$570$	−23.4096	−0.980518
$571$	15.8742	0.664316	0.332158	−	0.943224i	$-0.392223\pi$
$571$	15.8742	0.664316	0.332158	+	0.943224i	$0.392223\pi$
$572$	−20.0645	−0.838939
$573$	−38.4344	−1.60562
$574$	−8.88520	−0.370861
$575$	−21.1675	−0.882747
$576$	3.90245	0.162602
$577$	22.5132	0.937235	0.468618	−	0.883401i	$-0.344752\pi$
$577$	22.5132	0.937235	0.468618	+	0.883401i	$0.344752\pi$
$578$	0.407591	0.0169536
$579$	−40.7934	−1.69531
$580$	−5.66907	−0.235395
$581$	−1.21630	−0.0504606
$582$	12.5701	0.521046
$583$	21.4199	0.887122
$584$	1.83429	0.0759034
$585$	23.7377	0.981435
$586$	3.59449	0.148487
$587$	2.96026	0.122183	0.0610914	−	0.998132i	$-0.480542\pi$
$587$	2.96026	0.122183	0.0610914	+	0.998132i	$0.480542\pi$
$588$	−10.1438	−0.418323
$589$	40.1140	1.65287
$590$	−14.2957	−0.588544
$591$	−9.98318	−0.410653
$592$	−8.08104	−0.332129
$593$	30.4925	1.25218	0.626089	−	0.779752i	$-0.284655\pi$
$593$	30.4925	1.25218	0.626089	+	0.779752i	$0.284655\pi$
$594$	−12.8237	−0.526164
$595$	−11.8335	−0.485126
$596$	−14.8369	−0.607741
$597$	−27.1379	−1.11068
$598$	33.9729	1.38925
$599$	−34.2121	−1.39787	−0.698934	−	0.715186i	$-0.746342\pi$
$599$	−34.2121	−1.39787	−0.698934	+	0.715186i	$0.746342\pi$
$600$	6.07266	0.247915
$601$	19.4760	0.794443	0.397222	−	0.917723i	$-0.369974\pi$
$601$	19.4760	0.794443	0.397222	+	0.917723i	$0.369974\pi$
$602$	21.4102	0.872614
$603$	40.4077	1.64553
$604$	−15.3129	−0.623071
$605$	−29.9301	−1.21683
$606$	−42.0189	−1.70690
$607$	−9.48861	−0.385131	−0.192565	−	0.981284i	$-0.561681\pi$
$607$	−9.48861	−0.385131	−0.192565	+	0.981284i	$0.561681\pi$
$608$	5.43412	0.220383
$609$	−16.0934	−0.652137
$610$	3.48401	0.141064
$611$	44.2792	1.79135
$612$	−15.8962	−0.642564
$613$	−2.22364	−0.0898121	−0.0449061	−	0.998991i	$-0.514299\pi$
$613$	−2.22364	−0.0898121	−0.0449061	+	0.998991i	$0.514299\pi$
$614$	−0.894621	−0.0361039
$615$	21.6040	0.871158
$616$	9.58264	0.386096
$617$	20.5208	0.826137	0.413068	−	0.910700i	$-0.364457\pi$
$617$	20.5208	0.826137	0.413068	+	0.910700i	$0.364457\pi$
$618$	50.5123	2.03190
$619$	−34.0160	−1.36722	−0.683610	−	0.729848i	$-0.739591\pi$
$619$	−34.0160	−1.36722	−0.683610	+	0.729848i	$0.739591\pi$
$620$	12.1040	0.486108
$621$	21.7129	0.871310
$622$	19.1128	0.766353
$623$	9.59819	0.384543
$624$	−9.74634	−0.390166
$625$	−8.10032	−0.324013
$626$	−24.1609	−0.965664
$627$	−77.2182	−3.08380
$628$	−5.72582	−0.228485
$629$	32.9171	1.31249
$630$	−11.3369	−0.451675
$631$	−20.5266	−0.817150	−0.408575	−	0.912725i	$-0.633974\pi$
$631$	−20.5266	−0.817150	−0.408575	+	0.912725i	$0.633974\pi$
$632$	−5.88523	−0.234102
$633$	33.4617	1.32998
$634$	−9.02092	−0.358267
$635$	28.5308	1.13221
$636$	10.4047	0.412574
$637$	14.3231	0.567503
$638$	−18.6999	−0.740334
$639$	−49.4753	−1.95721
$640$	1.63969	0.0648145
$641$	7.85199	0.310135	0.155068	−	0.987904i	$-0.450440\pi$
$641$	7.85199	0.310135	0.155068	+	0.987904i	$0.450440\pi$
$642$	−3.50634	−0.138384
$643$	25.4270	1.00274	0.501372	−	0.865232i	$-0.332829\pi$
$643$	25.4270	1.00274	0.501372	+	0.865232i	$0.332829\pi$
$644$	−16.2252	−0.639361
$645$	−52.0580	−2.04978
$646$	−22.1352	−0.870899
$647$	−31.7253	−1.24725	−0.623626	−	0.781723i	$-0.714341\pi$
$647$	−31.7253	−1.24725	−0.623626	+	0.781723i	$0.714341\pi$
$648$	5.47823	0.215205
$649$	−47.1554	−1.85101
$650$	−8.57466	−0.336326
$651$	34.3609	1.34671
$652$	9.77214	0.382707
$653$	13.1803	0.515787	0.257893	−	0.966173i	$-0.416972\pi$
$653$	13.1803	0.515787	0.257893	+	0.966173i	$0.416972\pi$
$654$	1.48050	0.0578920
$655$	−2.24798	−0.0878357
$656$	−5.01500	−0.195803
$657$	−7.15822	−0.279269
$658$	−21.1474	−0.824412
$659$	−18.5180	−0.721360	−0.360680	−	0.932690i	$-0.617455\pi$
$659$	−18.5180	−0.721360	−0.360680	+	0.932690i	$0.617455\pi$
$660$	−23.2998	−0.906944
$661$	48.4351	1.88391	0.941954	−	0.335742i	$-0.108987\pi$
$661$	48.4351	1.88391	0.941954	+	0.335742i	$0.108987\pi$
$662$	−18.0606	−0.701945
$663$	39.7005	1.54184
$664$	−0.686506	−0.0266416
$665$	−15.7866	−0.612177
$666$	31.5359	1.22199
$667$	31.6623	1.22597
$668$	−20.6808	−0.800165
$669$	15.2779	0.590678
$670$	16.9781	0.655920
$671$	11.4923	0.443655
$672$	4.65477	0.179562
$673$	−33.3637	−1.28607	−0.643037	−	0.765835i	$-0.722326\pi$
$673$	−33.3637	−1.28607	−0.643037	+	0.765835i	$0.722326\pi$
$674$	10.6885	0.411705
$675$	−5.48028	−0.210936
$676$	0.761931	0.0293050
$677$	−15.0186	−0.577210	−0.288605	−	0.957448i	$-0.593191\pi$
$677$	−15.0186	−0.577210	−0.288605	+	0.957448i	$0.593191\pi$
$678$	−28.5886	−1.09794
$679$	8.47681	0.325310
$680$	−6.67908	−0.256131
$681$	27.6997	1.06145
$682$	39.9259	1.52884
$683$	22.2049	0.849645	0.424823	−	0.905277i	$-0.360336\pi$
$683$	22.2049	0.849645	0.424823	+	0.905277i	$0.360336\pi$
$684$	−21.2064	−0.810847
$685$	−4.46301	−0.170523
$686$	−19.2427	−0.734689
$687$	48.7199	1.85878
$688$	12.0844	0.460712
$689$	−14.6916	−0.559705
$690$	39.4509	1.50187
$691$	28.3355	1.07793	0.538966	−	0.842327i	$-0.318815\pi$
$691$	28.3355	1.07793	0.538966	+	0.842327i	$0.318815\pi$
$692$	−4.97391	−0.189080
$693$	−37.3958	−1.42055
$694$	−1.75548	−0.0666370
$695$	−26.5651	−1.00767
$696$	−9.08346	−0.344308
$697$	20.4280	0.773765
$698$	−11.0038	−0.416500
$699$	−78.0409	−2.95178
$700$	4.09519	0.154783
$701$	19.0907	0.721044	0.360522	−	0.932751i	$-0.382599\pi$
$701$	19.0907	0.721044	0.360522	+	0.932751i	$0.382599\pi$
$702$	8.79560	0.331968
$703$	43.9134	1.65622
$704$	5.40865	0.203846
$705$	51.4191	1.93656
$706$	−9.15399	−0.344515
$707$	−28.3361	−1.06569
$708$	−22.9057	−0.860851
$709$	35.9041	1.34841	0.674204	−	0.738545i	$-0.264487\pi$
$709$	35.9041	1.34841	0.674204	+	0.738545i	$0.264487\pi$
$710$	−20.7880	−0.780161
$711$	22.9668	0.861323
$712$	5.41742	0.203027
$713$	−67.6019	−2.53171
$714$	−18.9606	−0.709584
$715$	32.8996	1.23038
$716$	−11.1153	−0.415397
$717$	−5.62488	−0.210065
$718$	−17.5152	−0.653660
$719$	−14.0349	−0.523414	−0.261707	−	0.965147i	$-0.584285\pi$
$719$	−14.0349	−0.523414	−0.261707	+	0.965147i	$0.584285\pi$
$720$	−6.39882	−0.238470
$721$	34.0637	1.26860
$722$	−10.5297	−0.391874
$723$	51.2467	1.90588
$724$	−8.70612	−0.323560
$725$	−7.99147	−0.296796
$726$	−47.9565	−1.77983
$727$	−16.4993	−0.611926	−0.305963	−	0.952043i	$-0.598978\pi$
$727$	−16.4993	−0.611926	−0.305963	+	0.952043i	$0.598978\pi$
$728$	−6.57258	−0.243596
$729$	−40.0659	−1.48392
$730$	−3.00767	−0.111319
$731$	−49.2242	−1.82062
$732$	5.58238	0.206331
$733$	7.51094	0.277423	0.138711	−	0.990333i	$-0.455704\pi$
$733$	7.51094	0.277423	0.138711	+	0.990333i	$0.455704\pi$
$734$	−30.0660	−1.10976
$735$	16.6327	0.613506
$736$	−9.15783	−0.337562
$737$	56.0035	2.06291
$738$	19.5708	0.720410
$739$	32.6985	1.20284	0.601418	−	0.798935i	$-0.294603\pi$
$739$	32.6985	1.20284	0.601418	+	0.798935i	$0.294603\pi$
$740$	13.2504	0.487095
$741$	52.9628	1.94564
$742$	7.01658	0.257587
$743$	−24.3409	−0.892981	−0.446490	−	0.894788i	$-0.647326\pi$
$743$	−24.3409	−0.892981	−0.446490	+	0.894788i	$0.647326\pi$
$744$	19.3940	0.711019
$745$	24.3279	0.891304
$746$	4.36956	0.159981
$747$	2.67906	0.0980215
$748$	−22.0315	−0.805550
$749$	−2.36455	−0.0863989
$750$	−31.4967	−1.15010
$751$	−7.50568	−0.273886	−0.136943	−	0.990579i	$-0.543728\pi$
$751$	−7.50568	−0.273886	−0.136943	+	0.990579i	$0.543728\pi$
$752$	−11.9360	−0.435263
$753$	−49.1769	−1.79210
$754$	12.8259	0.467093
$755$	25.1084	0.913787
$756$	−4.20070	−0.152778
$757$	−38.7412	−1.40807	−0.704036	−	0.710165i	$-0.748620\pi$
$757$	−38.7412	−1.40807	−0.704036	+	0.710165i	$0.748620\pi$
$758$	26.0000	0.944362
$759$	130.132	4.72348
$760$	−8.91028	−0.323210
$761$	−10.0790	−0.365363	−0.182681	−	0.983172i	$-0.558478\pi$
$761$	−10.0790	−0.365363	−0.182681	+	0.983172i	$0.558478\pi$
$762$	45.7144	1.65606
$763$	0.998394	0.0361443
$764$	−14.6291	−0.529264
$765$	26.0648	0.942375
$766$	−4.38715	−0.158514
$767$	32.3432	1.16784
$768$	2.62725	0.0948028
$769$	−35.3064	−1.27318	−0.636592	−	0.771201i	$-0.719656\pi$
$769$	−35.3064	−1.27318	−0.636592	+	0.771201i	$0.719656\pi$
$770$	−15.7126	−0.566242
$771$	49.8463	1.79517
$772$	−15.5270	−0.558829
$773$	49.8306	1.79228	0.896140	−	0.443771i	$-0.146360\pi$
$773$	49.8306	1.79228	0.896140	+	0.443771i	$0.146360\pi$
$774$	−47.1587	−1.69508
$775$	17.0625	0.612904
$776$	4.78450	0.171753
$777$	37.6154	1.34944
$778$	22.8631	0.819681
$779$	27.2521	0.976407
$780$	15.9810	0.572211
$781$	−68.5709	−2.45366
$782$	37.3033	1.33396
$783$	8.19738	0.292951
$784$	−3.86099	−0.137892
$785$	9.38858	0.335093
$786$	−3.60190	−0.128475
$787$	22.0927	0.787520	0.393760	−	0.919213i	$-0.371174\pi$
$787$	22.0927	0.787520	0.393760	+	0.919213i	$0.371174\pi$
$788$	−3.79986	−0.135364
$789$	27.4071	0.975719
$790$	9.64996	0.343330
$791$	−19.2792	−0.685488
$792$	−21.1070	−0.750004
$793$	−7.88238	−0.279911
$794$	7.51082	0.266549
$795$	−17.0605	−0.605075
$796$	−10.3294	−0.366116
$797$	47.0403	1.66625	0.833126	−	0.553083i	$-0.186549\pi$
$797$	47.0403	1.66625	0.833126	+	0.553083i	$0.186549\pi$
$798$	−25.2946	−0.895418
$799$	48.6200	1.72005
$800$	2.31141	0.0817207
$801$	−21.1412	−0.746989
$802$	4.47261	0.157933
$803$	−9.92102	−0.350105
$804$	27.2037	0.959400
$805$	26.6043	0.937677
$806$	−27.3846	−0.964580
$807$	−21.8059	−0.767602
$808$	−15.9935	−0.562649
$809$	44.3100	1.55786	0.778928	−	0.627113i	$-0.215764\pi$
$809$	44.3100	1.55786	0.778928	+	0.627113i	$0.215764\pi$
$810$	−8.98260	−0.315616
$811$	24.1379	0.847596	0.423798	−	0.905757i	$-0.360697\pi$
$811$	24.1379	0.847596	0.423798	+	0.905757i	$0.360697\pi$
$812$	−6.12556	−0.214965
$813$	−45.5212	−1.59650
$814$	43.7075	1.53195
$815$	−16.0233	−0.561272
$816$	−10.7018	−0.374638
$817$	−65.6679	−2.29743
$818$	−26.2461	−0.917674
$819$	25.6492	0.896255
$820$	8.22305	0.287161
$821$	−17.9021	−0.624787	−0.312393	−	0.949953i	$-0.601131\pi$
$821$	−17.9021	−0.624787	−0.312393	+	0.949953i	$0.601131\pi$
$822$	−7.15101	−0.249420
$823$	16.8809	0.588430	0.294215	−	0.955739i	$-0.404942\pi$
$823$	16.8809	0.588430	0.294215	+	0.955739i	$0.404942\pi$
$824$	19.2263	0.669779
$825$	−32.8449	−1.14351
$826$	−15.4468	−0.537464
$827$	13.0020	0.452123	0.226062	−	0.974113i	$-0.427415\pi$
$827$	13.0020	0.452123	0.226062	+	0.974113i	$0.427415\pi$
$828$	35.7380	1.24198
$829$	−53.3184	−1.85182	−0.925912	−	0.377739i	$-0.876702\pi$
$829$	−53.3184	−1.85182	−0.925912	+	0.377739i	$0.876702\pi$
$830$	1.12566	0.0390722
$831$	46.7212	1.62074
$832$	−3.70971	−0.128611
$833$	15.7273	0.544917
$834$	−42.5648	−1.47390
$835$	33.9102	1.17351
$836$	−29.3912	−1.01652
$837$	−17.5022	−0.604964
$838$	14.8673	0.513584
$839$	7.93919	0.274091	0.137046	−	0.990565i	$-0.456239\pi$
$839$	7.93919	0.274091	0.137046	+	0.990565i	$0.456239\pi$
$840$	−7.63239	−0.263342
$841$	−17.0464	−0.587807
$842$	19.9651	0.688043
$843$	4.05961	0.139821
$844$	12.7364	0.438404
$845$	−1.24933	−0.0429783
$846$	46.5799	1.60145
$847$	−32.3401	−1.11122
$848$	3.96031	0.135998
$849$	50.7331	1.74115
$850$	−9.41525	−0.322940
$851$	−74.0048	−2.53685
$852$	−33.3083	−1.14112
$853$	−8.82951	−0.302317	−0.151158	−	0.988510i	$-0.548300\pi$
$853$	−8.82951	−0.302317	−0.151158	+	0.988510i	$0.548300\pi$
$854$	3.76456	0.128821
$855$	34.7719	1.18918
$856$	−1.33460	−0.0456158
$857$	−12.7551	−0.435704	−0.217852	−	0.975982i	$-0.569905\pi$
$857$	−12.7551	−0.435704	−0.217852	+	0.975982i	$0.569905\pi$
$858$	52.7145	1.79964
$859$	−29.1761	−0.995476	−0.497738	−	0.867327i	$-0.665836\pi$
$859$	−29.1761	−0.995476	−0.497738	+	0.867327i	$0.665836\pi$
$860$	−19.8146	−0.675674
$861$	23.3436	0.795549
$862$	−10.6763	−0.363635
$863$	6.27029	0.213443	0.106722	−	0.994289i	$-0.465965\pi$
$863$	6.27029	0.213443	0.106722	+	0.994289i	$0.465965\pi$
$864$	−2.37097	−0.0806620
$865$	8.15569	0.277302
$866$	8.81503	0.299547
$867$	−1.07084	−0.0363678
$868$	13.0786	0.443918
$869$	31.8311	1.07980
$870$	14.8941	0.504956
$871$	−38.4119	−1.30154
$872$	0.563515	0.0190830
$873$	−18.6713	−0.631927
$874$	49.7648	1.68332
$875$	−21.2403	−0.718052
$876$	−4.81914	−0.162824
$877$	5.19941	0.175572	0.0877858	−	0.996139i	$-0.472021\pi$
$877$	5.19941	0.175572	0.0877858	+	0.996139i	$0.472021\pi$
$878$	25.9293	0.875072
$879$	−9.44364	−0.318526
$880$	−8.86852	−0.298958
$881$	−31.5089	−1.06156	−0.530781	−	0.847509i	$-0.678101\pi$
$881$	−31.5089	−1.06156	−0.530781	+	0.847509i	$0.678101\pi$
$882$	15.0673	0.507343
$883$	15.5975	0.524899	0.262449	−	0.964946i	$-0.415470\pi$
$883$	15.5975	0.524899	0.262449	+	0.964946i	$0.415470\pi$
$884$	15.1110	0.508239
$885$	37.5584	1.26251
$886$	13.8129	0.464052
$887$	−12.2907	−0.412681	−0.206340	−	0.978480i	$-0.566155\pi$
$887$	−12.2907	−0.412681	−0.206340	+	0.978480i	$0.566155\pi$
$888$	21.2309	0.712463
$889$	30.8282	1.03394
$890$	−8.88291	−0.297756
$891$	−29.6298	−0.992636
$892$	5.81517	0.194706
$893$	64.8619	2.17052
$894$	38.9802	1.30369
$895$	18.2256	0.609215
$896$	1.77173	0.0591892
$897$	−89.2553	−2.98015
$898$	13.9359	0.465046
$899$	−25.5221	−0.851209
$900$	−9.02017	−0.300672
$901$	−16.1318	−0.537429
$902$	27.1243	0.903142
$903$	−56.2499	−1.87188
$904$	−10.8816	−0.361916
$905$	14.2754	0.474529
$906$	40.2307	1.33658
$907$	38.3176	1.27232	0.636158	−	0.771559i	$-0.280523\pi$
$907$	38.3176	1.27232	0.636158	+	0.771559i	$0.280523\pi$
$908$	10.5432	0.349889
$909$	62.4139	2.07014
$910$	10.7770	0.357254
$911$	57.0839	1.89127	0.945637	−	0.325223i	$-0.105439\pi$
$911$	57.0839	1.89127	0.945637	+	0.325223i	$0.105439\pi$
$912$	−14.2768	−0.472752
$913$	3.71307	0.122885
$914$	−0.865730	−0.0286358
$915$	−9.15338	−0.302601
$916$	18.5440	0.612713
$917$	−2.42899	−0.0802124
$918$	9.65785	0.318756
$919$	25.4132	0.838304	0.419152	−	0.907916i	$-0.362327\pi$
$919$	25.4132	0.838304	0.419152	+	0.907916i	$0.362327\pi$
$920$	15.0160	0.495064
$921$	2.35039	0.0774481
$922$	−32.0796	−1.05649
$923$	47.0317	1.54807
$924$	−25.1760	−0.828230
$925$	18.6786	0.614149
$926$	−10.9448	−0.359668
$927$	−75.0297	−2.46430
$928$	−3.45740	−0.113495
$929$	42.7070	1.40117	0.700586	−	0.713568i	$-0.252922\pi$
$929$	42.7070	1.40117	0.700586	+	0.713568i	$0.252922\pi$
$930$	−31.8002	−1.04277
$931$	20.9811	0.687627
$932$	−29.7044	−0.972999
$933$	−50.2141	−1.64394
$934$	2.39461	0.0783539
$935$	36.1248	1.18141
$936$	14.4770	0.473194
$937$	1.11449	0.0364089	0.0182045	−	0.999834i	$-0.494205\pi$
$937$	1.11449	0.0364089	0.0182045	+	0.999834i	$0.494205\pi$
$938$	18.3452	0.598992
$939$	63.4768	2.07149
$940$	19.5714	0.638350
$941$	−19.2891	−0.628807	−0.314404	−	0.949289i	$-0.601805\pi$
$941$	−19.2891	−0.628807	−0.314404	+	0.949289i	$0.601805\pi$
$942$	15.0432	0.490133
$943$	−45.9265	−1.49557
$944$	−8.71852	−0.283764
$945$	6.88786	0.224062
$946$	−65.3601	−2.12504
$947$	30.1595	0.980052	0.490026	−	0.871708i	$-0.336987\pi$
$947$	30.1595	0.980052	0.490026	+	0.871708i	$0.336987\pi$
$948$	15.4620	0.502182
$949$	6.80467	0.220889
$950$	−12.5605	−0.407516
$951$	23.7002	0.768533
$952$	−7.21691	−0.233901
$953$	−40.2038	−1.30233	−0.651164	−	0.758937i	$-0.725719\pi$
$953$	−40.2038	−1.30233	−0.651164	+	0.758937i	$0.725719\pi$
$954$	−15.4549	−0.500371
$955$	23.9873	0.776210
$956$	−2.14098	−0.0692441
$957$	49.1292	1.58812
$958$	−25.4168	−0.821181
$959$	−4.82239	−0.155723
$960$	−4.30788	−0.139036
$961$	23.4920	0.757806
$962$	−29.9783	−0.966539
$963$	5.20823	0.167833
$964$	19.5058	0.628240
$965$	25.4595	0.819571
$966$	42.6276	1.37152
$967$	−46.2171	−1.48624	−0.743121	−	0.669158i	$-0.766655\pi$
$967$	−46.2171	−1.48624	−0.743121	+	0.669158i	$0.766655\pi$
$968$	−18.2535	−0.586689
$969$	58.1548	1.86820
$970$	−7.84510	−0.251891
$971$	−5.15470	−0.165422	−0.0827111	−	0.996574i	$-0.526358\pi$
$971$	−5.15470	−0.165422	−0.0827111	+	0.996574i	$0.526358\pi$
$972$	−21.5056	−0.689792
$973$	−28.7042	−0.920215
$974$	16.0677	0.514844
$975$	22.5278	0.721467
$976$	2.12480	0.0680131
$977$	4.77754	0.152847	0.0764235	−	0.997075i	$-0.475650\pi$
$977$	4.77754	0.152847	0.0764235	+	0.997075i	$0.475650\pi$
$978$	−25.6739	−0.820960
$979$	−29.3009	−0.936462
$980$	6.33083	0.202231
$981$	−2.19909	−0.0702115
$982$	−3.14732	−0.100435
$983$	0.912544	0.0291056	0.0145528	−	0.999894i	$-0.495368\pi$
$983$	0.912544	0.0291056	0.0145528	+	0.999894i	$0.495368\pi$
$984$	13.1757	0.420025
$985$	6.23059	0.198523
$986$	14.0833	0.448503
$987$	55.5595	1.76848
$988$	20.1590	0.641343
$989$	110.667	3.51899
$990$	34.6090	1.09994
$991$	−3.41996	−0.108639	−0.0543193	−	0.998524i	$-0.517299\pi$
$991$	−3.41996	−0.108639	−0.0543193	+	0.998524i	$0.517299\pi$
$992$	7.38187	0.234375
$993$	47.4497	1.50577
$994$	−22.4620	−0.712450
$995$	16.9370	0.536940
$996$	1.80362	0.0571500
$997$	17.8808	0.566291	0.283146	−	0.959077i	$-0.408622\pi$
$997$	17.8808	0.566291	0.283146	+	0.959077i	$0.408622\pi$
$998$	30.7225	0.972502
$999$	−19.1599	−0.606192

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4006.2.a.g.1.37	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4006.2.a.g.1.37	✓	40	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.62725 q^{3} +1.00000 q^{4} -1.63969 q^{5} -2.62725 q^{6} -1.77173 q^{7} -1.00000 q^{8} +3.90245 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.62725 q^{3} +1.00000 q^{4} -1.63969 q^{5} -2.62725 q^{6} -1.77173 q^{7} -1.00000 q^{8} +3.90245 q^{9} +1.63969 q^{10} +5.40865 q^{11} +2.62725 q^{12} -3.70971 q^{13} +1.77173 q^{14} -4.30788 q^{15} +1.00000 q^{16} -4.07338 q^{17} -3.90245 q^{18} -5.43412 q^{19} -1.63969 q^{20} -4.65477 q^{21} -5.40865 q^{22} +9.15783 q^{23} -2.62725 q^{24} -2.31141 q^{25} +3.70971 q^{26} +2.37097 q^{27} -1.77173 q^{28} +3.45740 q^{29} +4.30788 q^{30} -7.38187 q^{31} -1.00000 q^{32} +14.2099 q^{33} +4.07338 q^{34} +2.90508 q^{35} +3.90245 q^{36} -8.08104 q^{37} +5.43412 q^{38} -9.74634 q^{39} +1.63969 q^{40} -5.01500 q^{41} +4.65477 q^{42} +12.0844 q^{43} +5.40865 q^{44} -6.39882 q^{45} -9.15783 q^{46} -11.9360 q^{47} +2.62725 q^{48} -3.86099 q^{49} +2.31141 q^{50} -10.7018 q^{51} -3.70971 q^{52} +3.96031 q^{53} -2.37097 q^{54} -8.86852 q^{55} +1.77173 q^{56} -14.2768 q^{57} -3.45740 q^{58} -8.71852 q^{59} -4.30788 q^{60} +2.12480 q^{61} +7.38187 q^{62} -6.91407 q^{63} +1.00000 q^{64} +6.08278 q^{65} -14.2099 q^{66} +10.3544 q^{67} -4.07338 q^{68} +24.0599 q^{69} -2.90508 q^{70} -12.6780 q^{71} -3.90245 q^{72} -1.83429 q^{73} +8.08104 q^{74} -6.07266 q^{75} -5.43412 q^{76} -9.58264 q^{77} +9.74634 q^{78} +5.88523 q^{79} -1.63969 q^{80} -5.47823 q^{81} +5.01500 q^{82} +0.686506 q^{83} -4.65477 q^{84} +6.67908 q^{85} -12.0844 q^{86} +9.08346 q^{87} -5.40865 q^{88} -5.41742 q^{89} +6.39882 q^{90} +6.57258 q^{91} +9.15783 q^{92} -19.3940 q^{93} +11.9360 q^{94} +8.91028 q^{95} -2.62725 q^{96} -4.78450 q^{97} +3.86099 q^{98} +21.1070 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9}+O(q^{10}) \) 40 * q - 40 * q^2 - q^3 + 40 * q^4 - 23 * q^5 + q^6 + 12 * q^7 - 40 * q^8 + 29 * q^9	\( 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9} + 23 q^{10} - 28 q^{11} - q^{12} - 12 q^{13} - 12 q^{14} - 14 q^{15} + 40 q^{16} - 10 q^{17} - 29 q^{18} + 3 q^{19} - 23 q^{20} - 40 q^{21} + 28 q^{22} - 10 q^{23} + q^{24} + 43 q^{25} + 12 q^{26} - 7 q^{27} + 12 q^{28} - 37 q^{29} + 14 q^{30} - 16 q^{31} - 40 q^{32} - 11 q^{33} + 10 q^{34} - 24 q^{35} + 29 q^{36} - 17 q^{37} - 3 q^{38} - 10 q^{39} + 23 q^{40} - 58 q^{41} + 40 q^{42} + 37 q^{43} - 28 q^{44} - 66 q^{45} + 10 q^{46} - 34 q^{47} - q^{48} + 28 q^{49} - 43 q^{50} - 7 q^{51} - 12 q^{52} - 43 q^{53} + 7 q^{54} + 28 q^{55} - 12 q^{56} - 25 q^{57} + 37 q^{58} - 92 q^{59} - 14 q^{60} - 37 q^{61} + 16 q^{62} + 14 q^{63} + 40 q^{64} - 54 q^{65} + 11 q^{66} - 10 q^{67} - 10 q^{68} - 49 q^{69} + 24 q^{70} - 87 q^{71} - 29 q^{72} + 12 q^{73} + 17 q^{74} - 31 q^{75} + 3 q^{76} - 53 q^{77} + 10 q^{78} + 14 q^{79} - 23 q^{80} - 4 q^{81} + 58 q^{82} - 42 q^{83} - 40 q^{84} - 24 q^{85} - 37 q^{86} + 24 q^{87} + 28 q^{88} - 118 q^{89} + 66 q^{90} - 35 q^{91} - 10 q^{92} - 22 q^{93} + 34 q^{94} - 18 q^{95} + q^{96} + 2 q^{97} - 28 q^{98} - 48 q^{99}+O(q^{100}) \) 40 * q - 40 * q^2 - q^3 + 40 * q^4 - 23 * q^5 + q^6 + 12 * q^7 - 40 * q^8 + 29 * q^9 + 23 * q^10 - 28 * q^11 - q^12 - 12 * q^13 - 12 * q^14 - 14 * q^15 + 40 * q^16 - 10 * q^17 - 29 * q^18 + 3 * q^19 - 23 * q^20 - 40 * q^21 + 28 * q^22 - 10 * q^23 + q^24 + 43 * q^25 + 12 * q^26 - 7 * q^27 + 12 * q^28 - 37 * q^29 + 14 * q^30 - 16 * q^31 - 40 * q^32 - 11 * q^33 + 10 * q^34 - 24 * q^35 + 29 * q^36 - 17 * q^37 - 3 * q^38 - 10 * q^39 + 23 * q^40 - 58 * q^41 + 40 * q^42 + 37 * q^43 - 28 * q^44 - 66 * q^45 + 10 * q^46 - 34 * q^47 - q^48 + 28 * q^49 - 43 * q^50 - 7 * q^51 - 12 * q^52 - 43 * q^53 + 7 * q^54 + 28 * q^55 - 12 * q^56 - 25 * q^57 + 37 * q^58 - 92 * q^59 - 14 * q^60 - 37 * q^61 + 16 * q^62 + 14 * q^63 + 40 * q^64 - 54 * q^65 + 11 * q^66 - 10 * q^67 - 10 * q^68 - 49 * q^69 + 24 * q^70 - 87 * q^71 - 29 * q^72 + 12 * q^73 + 17 * q^74 - 31 * q^75 + 3 * q^76 - 53 * q^77 + 10 * q^78 + 14 * q^79 - 23 * q^80 - 4 * q^81 + 58 * q^82 - 42 * q^83 - 40 * q^84 - 24 * q^85 - 37 * q^86 + 24 * q^87 + 28 * q^88 - 118 * q^89 + 66 * q^90 - 35 * q^91 - 10 * q^92 - 22 * q^93 + 34 * q^94 - 18 * q^95 + q^96 + 2 * q^97 - 28 * q^98 - 48 * q^99

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