LMFDB - Embedded newform 6002.2.a.d.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6002,2,Mod(1,6002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6002, 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("6002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6002 = 2 \cdot 3001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6002.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:	$47.9262112932$
Analytic rank:	$0$
Dimension:	$79$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	6002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.46614 q^{3} +1.00000 q^{4} +2.56513 q^{5} -2.46614 q^{6} +4.43338 q^{7} +1.00000 q^{8} +3.08187 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.46614 q^{3} +1.00000 q^{4} +2.56513 q^{5} -2.46614 q^{6} +4.43338 q^{7} +1.00000 q^{8} +3.08187 q^{9} +2.56513 q^{10} +3.67527 q^{11} -2.46614 q^{12} +1.13195 q^{13} +4.43338 q^{14} -6.32599 q^{15} +1.00000 q^{16} +3.53560 q^{17} +3.08187 q^{18} +2.46851 q^{19} +2.56513 q^{20} -10.9334 q^{21} +3.67527 q^{22} -7.15371 q^{23} -2.46614 q^{24} +1.57990 q^{25} +1.13195 q^{26} -0.201899 q^{27} +4.43338 q^{28} -2.55841 q^{29} -6.32599 q^{30} +6.93330 q^{31} +1.00000 q^{32} -9.06376 q^{33} +3.53560 q^{34} +11.3722 q^{35} +3.08187 q^{36} +7.51805 q^{37} +2.46851 q^{38} -2.79154 q^{39} +2.56513 q^{40} +7.90098 q^{41} -10.9334 q^{42} -1.83550 q^{43} +3.67527 q^{44} +7.90540 q^{45} -7.15371 q^{46} +7.77943 q^{47} -2.46614 q^{48} +12.6549 q^{49} +1.57990 q^{50} -8.71931 q^{51} +1.13195 q^{52} +1.20720 q^{53} -0.201899 q^{54} +9.42757 q^{55} +4.43338 q^{56} -6.08769 q^{57} -2.55841 q^{58} +0.937152 q^{59} -6.32599 q^{60} -5.37018 q^{61} +6.93330 q^{62} +13.6631 q^{63} +1.00000 q^{64} +2.90359 q^{65} -9.06376 q^{66} -10.9095 q^{67} +3.53560 q^{68} +17.6421 q^{69} +11.3722 q^{70} -10.0353 q^{71} +3.08187 q^{72} -5.36832 q^{73} +7.51805 q^{74} -3.89627 q^{75} +2.46851 q^{76} +16.2939 q^{77} -2.79154 q^{78} -15.8799 q^{79} +2.56513 q^{80} -8.74769 q^{81} +7.90098 q^{82} -5.33653 q^{83} -10.9334 q^{84} +9.06929 q^{85} -1.83550 q^{86} +6.30941 q^{87} +3.67527 q^{88} -1.91352 q^{89} +7.90540 q^{90} +5.01835 q^{91} -7.15371 q^{92} -17.0985 q^{93} +7.77943 q^{94} +6.33205 q^{95} -2.46614 q^{96} -19.4755 q^{97} +12.6549 q^{98} +11.3267 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 79 q + 79 q^{2} + 17 q^{3} + 79 q^{4} + 18 q^{5} + 17 q^{6} + 19 q^{7} + 79 q^{8} + 118 q^{9}+O(q^{10}) $ 79 * q + 79 * q^2 + 17 * q^3 + 79 * q^4 + 18 * q^5 + 17 * q^6 + 19 * q^7 + 79 * q^8 + 118 * q^9	\( 79 q + 79 q^{2} + 17 q^{3} + 79 q^{4} + 18 q^{5} + 17 q^{6} + 19 q^{7} + 79 q^{8} + 118 q^{9} + 18 q^{10} + 28 q^{11} + 17 q^{12} + 47 q^{13} + 19 q^{14} + 14 q^{15} + 79 q^{16} + 36 q^{17} + 118 q^{18} + 29 q^{19} + 18 q^{20} + 45 q^{21} + 28 q^{22} + 23 q^{23} + 17 q^{24} + 161 q^{25} + 47 q^{26} + 50 q^{27} + 19 q^{28} + 53 q^{29} + 14 q^{30} + 29 q^{31} + 79 q^{32} + 34 q^{33} + 36 q^{34} + 33 q^{35} + 118 q^{36} + 89 q^{37} + 29 q^{38} - 7 q^{39} + 18 q^{40} + 58 q^{41} + 45 q^{42} + 88 q^{43} + 28 q^{44} + 45 q^{45} + 23 q^{46} + 3 q^{47} + 17 q^{48} + 162 q^{49} + 161 q^{50} + 29 q^{51} + 47 q^{52} + 88 q^{53} + 50 q^{54} + 37 q^{55} + 19 q^{56} + 54 q^{57} + 53 q^{58} + 37 q^{59} + 14 q^{60} + 55 q^{61} + 29 q^{62} + 21 q^{63} + 79 q^{64} + 55 q^{65} + 34 q^{66} + 107 q^{67} + 36 q^{68} + 39 q^{69} + 33 q^{70} - 5 q^{71} + 118 q^{72} + 71 q^{73} + 89 q^{74} + 37 q^{75} + 29 q^{76} + 61 q^{77} - 7 q^{78} + 29 q^{79} + 18 q^{80} + 215 q^{81} + 58 q^{82} + 42 q^{83} + 45 q^{84} + 84 q^{85} + 88 q^{86} + 15 q^{87} + 28 q^{88} + 72 q^{89} + 45 q^{90} + 70 q^{91} + 23 q^{92} + 97 q^{93} + 3 q^{94} - 18 q^{95} + 17 q^{96} + 93 q^{97} + 162 q^{98} + 49 q^{99}+O(q^{100}) \) 79 * q + 79 * q^2 + 17 * q^3 + 79 * q^4 + 18 * q^5 + 17 * q^6 + 19 * q^7 + 79 * q^8 + 118 * q^9 + 18 * q^10 + 28 * q^11 + 17 * q^12 + 47 * q^13 + 19 * q^14 + 14 * q^15 + 79 * q^16 + 36 * q^17 + 118 * q^18 + 29 * q^19 + 18 * q^20 + 45 * q^21 + 28 * q^22 + 23 * q^23 + 17 * q^24 + 161 * q^25 + 47 * q^26 + 50 * q^27 + 19 * q^28 + 53 * q^29 + 14 * q^30 + 29 * q^31 + 79 * q^32 + 34 * q^33 + 36 * q^34 + 33 * q^35 + 118 * q^36 + 89 * q^37 + 29 * q^38 - 7 * q^39 + 18 * q^40 + 58 * q^41 + 45 * q^42 + 88 * q^43 + 28 * q^44 + 45 * q^45 + 23 * q^46 + 3 * q^47 + 17 * q^48 + 162 * q^49 + 161 * q^50 + 29 * q^51 + 47 * q^52 + 88 * q^53 + 50 * q^54 + 37 * q^55 + 19 * q^56 + 54 * q^57 + 53 * q^58 + 37 * q^59 + 14 * q^60 + 55 * q^61 + 29 * q^62 + 21 * q^63 + 79 * q^64 + 55 * q^65 + 34 * q^66 + 107 * q^67 + 36 * q^68 + 39 * q^69 + 33 * q^70 - 5 * q^71 + 118 * q^72 + 71 * q^73 + 89 * q^74 + 37 * q^75 + 29 * q^76 + 61 * q^77 - 7 * q^78 + 29 * q^79 + 18 * q^80 + 215 * q^81 + 58 * q^82 + 42 * q^83 + 45 * q^84 + 84 * q^85 + 88 * q^86 + 15 * q^87 + 28 * q^88 + 72 * q^89 + 45 * q^90 + 70 * q^91 + 23 * q^92 + 97 * q^93 + 3 * q^94 - 18 * q^95 + 17 * q^96 + 93 * q^97 + 162 * q^98 + 49 * 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
$3$	−2.46614	−1.42383	−0.711915	−	0.702266i	$-0.752172\pi$
$3$	−2.46614	−1.42383	−0.711915	+	0.702266i	$0.752172\pi$
$4$	1.00000	0.500000
$5$	2.56513	1.14716	0.573581	−	0.819149i	$-0.305554\pi$
$5$	2.56513	1.14716	0.573581	+	0.819149i	$0.305554\pi$
$6$	−2.46614	−1.00680
$7$	4.43338	1.67566	0.837831	−	0.545930i	$-0.183824\pi$
$7$	4.43338	1.67566	0.837831	+	0.545930i	$0.183824\pi$
$8$	1.00000	0.353553
$9$	3.08187	1.02729
$10$	2.56513	0.811166
$11$	3.67527	1.10814	0.554069	−	0.832471i	$-0.313075\pi$
$11$	3.67527	1.10814	0.554069	+	0.832471i	$0.313075\pi$
$12$	−2.46614	−0.711915
$13$	1.13195	0.313945	0.156973	−	0.987603i	$-0.449827\pi$
$13$	1.13195	0.313945	0.156973	+	0.987603i	$0.449827\pi$
$14$	4.43338	1.18487
$15$	−6.32599	−1.63336
$16$	1.00000	0.250000
$17$	3.53560	0.857510	0.428755	−	0.903421i	$-0.358952\pi$
$17$	3.53560	0.857510	0.428755	+	0.903421i	$0.358952\pi$
$18$	3.08187	0.726403
$19$	2.46851	0.566314	0.283157	−	0.959074i	$-0.408618\pi$
$19$	2.46851	0.566314	0.283157	+	0.959074i	$0.408618\pi$
$20$	2.56513	0.573581
$21$	−10.9334	−2.38586
$22$	3.67527	0.783571
$23$	−7.15371	−1.49165	−0.745826	−	0.666141i	$-0.767945\pi$
$23$	−7.15371	−1.49165	−0.745826	+	0.666141i	$0.767945\pi$
$24$	−2.46614	−0.503400
$25$	1.57990	0.315981
$26$	1.13195	0.221993
$27$	−0.201899	−0.0388555
$28$	4.43338	0.837831
$29$	−2.55841	−0.475085	−0.237543	−	0.971377i	$-0.576342\pi$
$29$	−2.55841	−0.475085	−0.237543	+	0.971377i	$0.576342\pi$
$30$	−6.32599	−1.15496
$31$	6.93330	1.24526	0.622628	−	0.782518i	$-0.286065\pi$
$31$	6.93330	1.24526	0.622628	+	0.782518i	$0.286065\pi$
$32$	1.00000	0.176777
$33$	−9.06376	−1.57780
$34$	3.53560	0.606351
$35$	11.3722	1.92225
$36$	3.08187	0.513645
$37$	7.51805	1.23596	0.617980	−	0.786194i	$-0.287951\pi$
$37$	7.51805	1.23596	0.617980	+	0.786194i	$0.287951\pi$
$38$	2.46851	0.400445
$39$	−2.79154	−0.447005
$40$	2.56513	0.405583
$41$	7.90098	1.23393	0.616963	−	0.786992i	$-0.288363\pi$
$41$	7.90098	1.23393	0.616963	+	0.786992i	$0.288363\pi$
$42$	−10.9334	−1.68705
$43$	−1.83550	−0.279911	−0.139956	−	0.990158i	$-0.544696\pi$
$43$	−1.83550	−0.279911	−0.139956	+	0.990158i	$0.544696\pi$
$44$	3.67527	0.554069
$45$	7.90540	1.17847
$46$	−7.15371	−1.05476
$47$	7.77943	1.13475	0.567373	−	0.823461i	$-0.307960\pi$
$47$	7.77943	1.13475	0.567373	+	0.823461i	$0.307960\pi$
$48$	−2.46614	−0.355957
$49$	12.6549	1.80784
$50$	1.57990	0.223432
$51$	−8.71931	−1.22095
$52$	1.13195	0.156973
$53$	1.20720	0.165821	0.0829106	−	0.996557i	$-0.473578\pi$
$53$	1.20720	0.165821	0.0829106	+	0.996557i	$0.473578\pi$
$54$	−0.201899	−0.0274750
$55$	9.42757	1.27121
$56$	4.43338	0.592436
$57$	−6.08769	−0.806335
$58$	−2.55841	−0.335936
$59$	0.937152	0.122007	0.0610034	−	0.998138i	$-0.480570\pi$
$59$	0.937152	0.122007	0.0610034	+	0.998138i	$0.480570\pi$
$60$	−6.32599	−0.816681
$61$	−5.37018	−0.687581	−0.343791	−	0.939046i	$-0.611711\pi$
$61$	−5.37018	−0.687581	−0.343791	+	0.939046i	$0.611711\pi$
$62$	6.93330	0.880529
$63$	13.6631	1.72139
$64$	1.00000	0.125000
$65$	2.90359	0.360146
$66$	−9.06376	−1.11567
$67$	−10.9095	−1.33281	−0.666403	−	0.745592i	$-0.732167\pi$
$67$	−10.9095	−1.33281	−0.666403	+	0.745592i	$0.732167\pi$
$68$	3.53560	0.428755
$69$	17.6421	2.12386
$70$	11.3722	1.35924
$71$	−10.0353	−1.19098	−0.595488	−	0.803364i	$-0.703041\pi$
$71$	−10.0353	−1.19098	−0.595488	+	0.803364i	$0.703041\pi$
$72$	3.08187	0.363202
$73$	−5.36832	−0.628315	−0.314157	−	0.949371i	$-0.601722\pi$
$73$	−5.36832	−0.628315	−0.314157	+	0.949371i	$0.601722\pi$
$74$	7.51805	0.873955
$75$	−3.89627	−0.449902
$76$	2.46851	0.283157
$77$	16.2939	1.85686
$78$	−2.79154	−0.316080
$79$	−15.8799	−1.78663	−0.893315	−	0.449432i	$-0.851626\pi$
$79$	−15.8799	−1.78663	−0.893315	+	0.449432i	$0.851626\pi$
$80$	2.56513	0.286790
$81$	−8.74769	−0.971966
$82$	7.90098	0.872517
$83$	−5.33653	−0.585760	−0.292880	−	0.956149i	$-0.594614\pi$
$83$	−5.33653	−0.585760	−0.292880	+	0.956149i	$0.594614\pi$
$84$	−10.9334	−1.19293
$85$	9.06929	0.983703
$86$	−1.83550	−0.197927
$87$	6.30941	0.676440
$88$	3.67527	0.391786
$89$	−1.91352	−0.202833	−0.101416	−	0.994844i	$-0.532337\pi$
$89$	−1.91352	−0.202833	−0.101416	+	0.994844i	$0.532337\pi$
$90$	7.90540	0.833302
$91$	5.01835	0.526066
$92$	−7.15371	−0.745826
$93$	−17.0985	−1.77303
$94$	7.77943	0.802387
$95$	6.33205	0.649654
$96$	−2.46614	−0.251700
$97$	−19.4755	−1.97744	−0.988719	−	0.149781i	$-0.952143\pi$
$97$	−19.4755	−1.97744	−0.988719	+	0.149781i	$0.952143\pi$
$98$	12.6549	1.27834
$99$	11.3267	1.13838
$100$	1.57990	0.157990
$101$	−8.42739	−0.838556	−0.419278	−	0.907858i	$-0.637717\pi$
$101$	−8.42739	−0.838556	−0.419278	+	0.907858i	$0.637717\pi$
$102$	−8.71931	−0.863340
$103$	4.74876	0.467910	0.233955	−	0.972247i	$-0.424833\pi$
$103$	4.74876	0.467910	0.233955	+	0.972247i	$0.424833\pi$
$104$	1.13195	0.110996
$105$	−28.0455	−2.73696
$106$	1.20720	0.117253
$107$	−13.4195	−1.29731	−0.648657	−	0.761081i	$-0.724669\pi$
$107$	−13.4195	−1.29731	−0.648657	+	0.761081i	$0.724669\pi$
$108$	−0.201899	−0.0194278
$109$	18.1594	1.73935	0.869676	−	0.493622i	$-0.164327\pi$
$109$	18.1594	1.73935	0.869676	+	0.493622i	$0.164327\pi$
$110$	9.42757	0.898883
$111$	−18.5406	−1.75979
$112$	4.43338	0.418915
$113$	−7.64765	−0.719430	−0.359715	−	0.933062i	$-0.617126\pi$
$113$	−7.64765	−0.719430	−0.359715	+	0.933062i	$0.617126\pi$
$114$	−6.08769	−0.570165
$115$	−18.3502	−1.71117
$116$	−2.55841	−0.237543
$117$	3.48851	0.322513
$118$	0.937152	0.0862718
$119$	15.6747	1.43690
$120$	−6.32599	−0.577481
$121$	2.50764	0.227968
$122$	−5.37018	−0.486193
$123$	−19.4850	−1.75690
$124$	6.93330	0.622628
$125$	−8.77300	−0.784681
$126$	13.6631	1.21721
$127$	17.7809	1.57780	0.788902	−	0.614520i	$-0.210650\pi$
$127$	17.7809	1.57780	0.788902	+	0.614520i	$0.210650\pi$
$128$	1.00000	0.0883883
$129$	4.52661	0.398546
$130$	2.90359	0.254662
$131$	−5.42168	−0.473694	−0.236847	−	0.971547i	$-0.576114\pi$
$131$	−5.42168	−0.473694	−0.236847	+	0.971547i	$0.576114\pi$
$132$	−9.06376	−0.788899
$133$	10.9438	0.948951
$134$	−10.9095	−0.942436
$135$	−0.517898	−0.0445736
$136$	3.53560	0.303176
$137$	22.3737	1.91151	0.955757	−	0.294156i	$-0.0950387\pi$
$137$	22.3737	1.91151	0.955757	+	0.294156i	$0.0950387\pi$
$138$	17.6421	1.50179
$139$	−11.1363	−0.944567	−0.472283	−	0.881447i	$-0.656570\pi$
$139$	−11.1363	−0.944567	−0.472283	+	0.881447i	$0.656570\pi$
$140$	11.3722	0.961127
$141$	−19.1852	−1.61568
$142$	−10.0353	−0.842147
$143$	4.16021	0.347894
$144$	3.08187	0.256822
$145$	−6.56266	−0.545000
$146$	−5.36832	−0.444286
$147$	−31.2088	−2.57406
$148$	7.51805	0.617980
$149$	−3.79406	−0.310821	−0.155411	−	0.987850i	$-0.549670\pi$
$149$	−3.79406	−0.310821	−0.155411	+	0.987850i	$0.549670\pi$
$150$	−3.89627	−0.318129
$151$	−7.37624	−0.600270	−0.300135	−	0.953897i	$-0.597032\pi$
$151$	−7.37624	−0.600270	−0.300135	+	0.953897i	$0.597032\pi$
$152$	2.46851	0.200222
$153$	10.8963	0.880911
$154$	16.2939	1.31300
$155$	17.7848	1.42851
$156$	−2.79154	−0.223502
$157$	0.500929	0.0399785	0.0199893	−	0.999800i	$-0.493637\pi$
$157$	0.500929	0.0399785	0.0199893	+	0.999800i	$0.493637\pi$
$158$	−15.8799	−1.26334
$159$	−2.97712	−0.236101
$160$	2.56513	0.202792
$161$	−31.7151	−2.49950
$162$	−8.74769	−0.687284
$163$	9.81805	0.769009	0.384505	−	0.923123i	$-0.374372\pi$
$163$	9.81805	0.769009	0.384505	+	0.923123i	$0.374372\pi$
$164$	7.90098	0.616963
$165$	−23.2497	−1.80999
$166$	−5.33653	−0.414195
$167$	−9.38529	−0.726256	−0.363128	−	0.931739i	$-0.618291\pi$
$167$	−9.38529	−0.726256	−0.363128	+	0.931739i	$0.618291\pi$
$168$	−10.9334	−0.843527
$169$	−11.7187	−0.901438
$170$	9.06929	0.695583
$171$	7.60761	0.581769
$172$	−1.83550	−0.139956
$173$	−14.4244	−1.09667	−0.548334	−	0.836259i	$-0.684738\pi$
$173$	−14.4244	−1.09667	−0.548334	+	0.836259i	$0.684738\pi$
$174$	6.30941	0.478315
$175$	7.00431	0.529476
$176$	3.67527	0.277034
$177$	−2.31115	−0.173717
$178$	−1.91352	−0.143424
$179$	−18.0501	−1.34912	−0.674562	−	0.738218i	$-0.735668\pi$
$179$	−18.0501	−1.34912	−0.674562	+	0.738218i	$0.735668\pi$
$180$	7.90540	0.589234
$181$	12.8756	0.957034	0.478517	−	0.878078i	$-0.341174\pi$
$181$	12.8756	0.957034	0.478517	+	0.878078i	$0.341174\pi$
$182$	5.01835	0.371985
$183$	13.2436	0.978998
$184$	−7.15371	−0.527378
$185$	19.2848	1.41785
$186$	−17.0985	−1.25372
$187$	12.9943	0.950239
$188$	7.77943	0.567373
$189$	−0.895096	−0.0651087
$190$	6.33205	0.459375
$191$	−4.92928	−0.356670	−0.178335	−	0.983970i	$-0.557071\pi$
$191$	−4.92928	−0.356670	−0.178335	+	0.983970i	$0.557071\pi$
$192$	−2.46614	−0.177979
$193$	−2.42348	−0.174446	−0.0872231	−	0.996189i	$-0.527799\pi$
$193$	−2.42348	−0.174446	−0.0872231	+	0.996189i	$0.527799\pi$
$194$	−19.4755	−1.39826
$195$	−7.16068	−0.512787
$196$	12.6549	0.903920
$197$	3.69996	0.263611	0.131806	−	0.991276i	$-0.457923\pi$
$197$	3.69996	0.263611	0.131806	+	0.991276i	$0.457923\pi$
$198$	11.3267	0.804954
$199$	−1.19445	−0.0846721	−0.0423360	−	0.999103i	$-0.513480\pi$
$199$	−1.19445	−0.0846721	−0.0423360	+	0.999103i	$0.513480\pi$
$200$	1.57990	0.111716
$201$	26.9044	1.89769
$202$	−8.42739	−0.592949
$203$	−11.3424	−0.796082
$204$	−8.71931	−0.610474
$205$	20.2671	1.41551
$206$	4.74876	0.330862
$207$	−22.0468	−1.53236
$208$	1.13195	0.0784863
$209$	9.07244	0.627554
$210$	−28.0455	−1.93532
$211$	16.1453	1.11149	0.555744	−	0.831353i	$-0.312433\pi$
$211$	16.1453	1.11149	0.555744	+	0.831353i	$0.312433\pi$
$212$	1.20720	0.0829106
$213$	24.7486	1.69575
$214$	−13.4195	−0.917339
$215$	−4.70830	−0.321104
$216$	−0.201899	−0.0137375
$217$	30.7380	2.08663
$218$	18.1594	1.22991
$219$	13.2391	0.894613
$220$	9.42757	0.635606
$221$	4.00211	0.269211
$222$	−18.5406	−1.24436
$223$	27.7915	1.86106	0.930529	−	0.366219i	$-0.119348\pi$
$223$	27.7915	1.86106	0.930529	+	0.366219i	$0.119348\pi$
$224$	4.43338	0.296218
$225$	4.86905	0.324604
$226$	−7.64765	−0.508714
$227$	18.2547	1.21160	0.605802	−	0.795615i	$-0.292852\pi$
$227$	18.2547	1.21160	0.605802	+	0.795615i	$0.292852\pi$
$228$	−6.08769	−0.403167
$229$	3.21289	0.212314	0.106157	−	0.994349i	$-0.466145\pi$
$229$	3.21289	0.212314	0.106157	+	0.994349i	$0.466145\pi$
$230$	−18.3502	−1.20998
$231$	−40.1831	−2.64385
$232$	−2.55841	−0.167968
$233$	−22.7669	−1.49151	−0.745756	−	0.666220i	$-0.767911\pi$
$233$	−22.7669	−1.49151	−0.745756	+	0.666220i	$0.767911\pi$
$234$	3.48851	0.228051
$235$	19.9553	1.30174
$236$	0.937152	0.0610034
$237$	39.1621	2.54385
$238$	15.6747	1.01604
$239$	−2.12156	−0.137232	−0.0686160	−	0.997643i	$-0.521858\pi$
$239$	−2.12156	−0.137232	−0.0686160	+	0.997643i	$0.521858\pi$
$240$	−6.32599	−0.408341
$241$	2.09872	0.135190	0.0675952	−	0.997713i	$-0.478467\pi$
$241$	2.09872	0.135190	0.0675952	+	0.997713i	$0.478467\pi$
$242$	2.50764	0.161197
$243$	22.1788	1.42277
$244$	−5.37018	−0.343791
$245$	32.4614	2.07389
$246$	−19.4850	−1.24232
$247$	2.79422	0.177792
$248$	6.93330	0.440265
$249$	13.1606	0.834022
$250$	−8.77300	−0.554853
$251$	23.9086	1.50910	0.754548	−	0.656245i	$-0.227856\pi$
$251$	23.9086	1.50910	0.754548	+	0.656245i	$0.227856\pi$
$252$	13.6631	0.860694
$253$	−26.2918	−1.65295
$254$	17.7809	1.11568
$255$	−22.3662	−1.40062
$256$	1.00000	0.0625000
$257$	0.0272161	0.00169770	0.000848848	−	1.00000i	$-0.499730\pi$
$257$	0.0272161	0.00169770	0.000848848		1.00000i	$0.499730\pi$
$258$	4.52661	0.281814
$259$	33.3304	2.07105
$260$	2.90359	0.180073
$261$	−7.88469	−0.488050
$262$	−5.42168	−0.334953
$263$	−2.21749	−0.136736	−0.0683682	−	0.997660i	$-0.521779\pi$
$263$	−2.21749	−0.136736	−0.0683682	+	0.997660i	$0.521779\pi$
$264$	−9.06376	−0.557836
$265$	3.09662	0.190224
$266$	10.9438	0.671010
$267$	4.71901	0.288799
$268$	−10.9095	−0.666403
$269$	8.10970	0.494457	0.247229	−	0.968957i	$-0.420480\pi$
$269$	8.10970	0.494457	0.247229	+	0.968957i	$0.420480\pi$
$270$	−0.517898	−0.0315183
$271$	−30.1816	−1.83340	−0.916702	−	0.399572i	$-0.869159\pi$
$271$	−30.1816	−1.83340	−0.916702	+	0.399572i	$0.869159\pi$
$272$	3.53560	0.214378
$273$	−12.3760	−0.749028
$274$	22.3737	1.35164
$275$	5.80658	0.350150
$276$	17.6421	1.06193
$277$	−24.2097	−1.45462	−0.727311	−	0.686308i	$-0.759230\pi$
$277$	−24.2097	−1.45462	−0.727311	+	0.686308i	$0.759230\pi$
$278$	−11.1363	−0.667910
$279$	21.3675	1.27924
$280$	11.3722	0.679620
$281$	−22.7688	−1.35827	−0.679135	−	0.734013i	$-0.737645\pi$
$281$	−22.7688	−1.35827	−0.679135	+	0.734013i	$0.737645\pi$
$282$	−19.1852	−1.14246
$283$	−22.9321	−1.36317	−0.681585	−	0.731739i	$-0.738709\pi$
$283$	−22.9321	−1.36317	−0.681585	+	0.731739i	$0.738709\pi$
$284$	−10.0353	−0.595488
$285$	−15.6157	−0.924997
$286$	4.16021	0.245999
$287$	35.0281	2.06764
$288$	3.08187	0.181601
$289$	−4.49950	−0.264676
$290$	−6.56266	−0.385373
$291$	48.0294	2.81553
$292$	−5.36832	−0.314157
$293$	14.6819	0.857728	0.428864	−	0.903369i	$-0.358914\pi$
$293$	14.6819	0.857728	0.428864	+	0.903369i	$0.358914\pi$
$294$	−31.2088	−1.82013
$295$	2.40392	0.139962
$296$	7.51805	0.436978
$297$	−0.742035	−0.0430572
$298$	−3.79406	−0.219784
$299$	−8.09761	−0.468297
$300$	−3.89627	−0.224951
$301$	−8.13748	−0.469036
$302$	−7.37624	−0.424455
$303$	20.7832	1.19396
$304$	2.46851	0.141579
$305$	−13.7752	−0.788767
$306$	10.8963	0.622898
$307$	−20.8393	−1.18936	−0.594680	−	0.803962i	$-0.702721\pi$
$307$	−20.8393	−1.18936	−0.594680	+	0.803962i	$0.702721\pi$
$308$	16.2939	0.928431
$309$	−11.7111	−0.666223
$310$	17.7848	1.01011
$311$	−3.68554	−0.208988	−0.104494	−	0.994526i	$-0.533322\pi$
$311$	−3.68554	−0.208988	−0.104494	+	0.994526i	$0.533322\pi$
$312$	−2.79154	−0.158040
$313$	33.0703	1.86924	0.934621	−	0.355645i	$-0.115739\pi$
$313$	33.0703	1.86924	0.934621	+	0.355645i	$0.115739\pi$
$314$	0.500929	0.0282691
$315$	35.0477	1.97471
$316$	−15.8799	−0.893315
$317$	29.2177	1.64103	0.820513	−	0.571627i	$-0.193688\pi$
$317$	29.2177	1.64103	0.820513	+	0.571627i	$0.193688\pi$
$318$	−2.97712	−0.166949
$319$	−9.40287	−0.526459
$320$	2.56513	0.143395
$321$	33.0945	1.84715
$322$	−31.7151	−1.76742
$323$	8.72766	0.485620
$324$	−8.74769	−0.485983
$325$	1.78837	0.0992006
$326$	9.81805	0.543772
$327$	−44.7836	−2.47654
$328$	7.90098	0.436259
$329$	34.4892	1.90145
$330$	−23.2497	−1.27986
$331$	5.20702	0.286203	0.143102	−	0.989708i	$-0.454292\pi$
$331$	5.20702	0.286203	0.143102	+	0.989708i	$0.454292\pi$
$332$	−5.33653	−0.292880
$333$	23.1696	1.26969
$334$	−9.38529	−0.513540
$335$	−27.9843	−1.52894
$336$	−10.9334	−0.596464
$337$	34.3520	1.87127	0.935637	−	0.352963i	$-0.114826\pi$
$337$	34.3520	1.87127	0.935637	+	0.352963i	$0.114826\pi$
$338$	−11.7187	−0.637413
$339$	18.8602	1.02435
$340$	9.06929	0.491851
$341$	25.4818	1.37991
$342$	7.60761	0.411373
$343$	25.0702	1.35367
$344$	−1.83550	−0.0989636
$345$	45.2543	2.43641
$346$	−14.4244	−0.775462
$347$	−36.0981	−1.93785	−0.968923	−	0.247361i	$-0.920437\pi$
$347$	−36.0981	−1.93785	−0.968923	+	0.247361i	$0.920437\pi$
$348$	6.30941	0.338220
$349$	15.1530	0.811120	0.405560	−	0.914069i	$-0.367077\pi$
$349$	15.1530	0.811120	0.405560	+	0.914069i	$0.367077\pi$
$350$	7.00431	0.374396
$351$	−0.228539	−0.0121985
$352$	3.67527	0.195893
$353$	4.82243	0.256672	0.128336	−	0.991731i	$-0.459036\pi$
$353$	4.82243	0.256672	0.128336	+	0.991731i	$0.459036\pi$
$354$	−2.31115	−0.122836
$355$	−25.7420	−1.36624
$356$	−1.91352	−0.101416
$357$	−38.6560	−2.04589
$358$	−18.0501	−0.953975
$359$	−23.4350	−1.23685	−0.618426	−	0.785843i	$-0.712229\pi$
$359$	−23.4350	−1.23685	−0.618426	+	0.785843i	$0.712229\pi$
$360$	7.90540	0.416651
$361$	−12.9065	−0.679288
$362$	12.8756	0.676726
$363$	−6.18421	−0.324587
$364$	5.01835	0.263033
$365$	−13.7705	−0.720779
$366$	13.2436	0.692256
$367$	−0.821555	−0.0428848	−0.0214424	−	0.999770i	$-0.506826\pi$
$367$	−0.821555	−0.0428848	−0.0214424	+	0.999770i	$0.506826\pi$
$368$	−7.15371	−0.372913
$369$	24.3498	1.26760
$370$	19.2848	1.00257
$371$	5.35196	0.277860
$372$	−17.0985	−0.886516
$373$	14.9917	0.776243	0.388122	−	0.921608i	$-0.373124\pi$
$373$	14.9917	0.776243	0.388122	+	0.921608i	$0.373124\pi$
$374$	12.9943	0.671920
$375$	21.6355	1.11725
$376$	7.77943	0.401193
$377$	−2.89598	−0.149151
$378$	−0.895096	−0.0460388
$379$	12.0765	0.620328	0.310164	−	0.950683i	$-0.399616\pi$
$379$	12.0765	0.620328	0.310164	+	0.950683i	$0.399616\pi$
$380$	6.33205	0.324827
$381$	−43.8504	−2.24652
$382$	−4.92928	−0.252204
$383$	−37.8443	−1.93375	−0.966876	−	0.255246i	$-0.917844\pi$
$383$	−37.8443	−1.93375	−0.966876	+	0.255246i	$0.917844\pi$
$384$	−2.46614	−0.125850
$385$	41.7960	2.13012
$386$	−2.42348	−0.123352
$387$	−5.65677	−0.287550
$388$	−19.4755	−0.988719
$389$	35.3190	1.79075	0.895373	−	0.445317i	$-0.146909\pi$
$389$	35.3190	1.79075	0.895373	+	0.445317i	$0.146909\pi$
$390$	−7.16068	−0.362595
$391$	−25.2927	−1.27911
$392$	12.6549	0.639168
$393$	13.3706	0.674460
$394$	3.69996	0.186401
$395$	−40.7341	−2.04955
$396$	11.3267	0.569189
$397$	−2.14288	−0.107548	−0.0537742	−	0.998553i	$-0.517125\pi$
$397$	−2.14288	−0.107548	−0.0537742	+	0.998553i	$0.517125\pi$
$398$	−1.19445	−0.0598722
$399$	−26.9891	−1.35114
$400$	1.57990	0.0789952
$401$	33.5013	1.67298	0.836488	−	0.547985i	$-0.184605\pi$
$401$	33.5013	1.67298	0.836488	+	0.547985i	$0.184605\pi$
$402$	26.9044	1.34187
$403$	7.84812	0.390943
$404$	−8.42739	−0.419278
$405$	−22.4390	−1.11500
$406$	−11.3424	−0.562915
$407$	27.6309	1.36961
$408$	−8.71931	−0.431670
$409$	8.50282	0.420438	0.210219	−	0.977654i	$-0.432582\pi$
$409$	8.50282	0.420438	0.210219	+	0.977654i	$0.432582\pi$
$410$	20.2671	1.00092
$411$	−55.1768	−2.72167
$412$	4.74876	0.233955
$413$	4.15475	0.204442
$414$	−22.0468	−1.08354
$415$	−13.6889	−0.671961
$416$	1.13195	0.0554982
$417$	27.4637	1.34490
$418$	9.07244	0.443748
$419$	−26.2829	−1.28400	−0.642002	−	0.766703i	$-0.721896\pi$
$419$	−26.2829	−1.28400	−0.642002	+	0.766703i	$0.721896\pi$
$420$	−28.0455	−1.36848
$421$	−33.3649	−1.62610	−0.813052	−	0.582191i	$-0.802196\pi$
$421$	−33.3649	−1.62610	−0.813052	+	0.582191i	$0.802196\pi$
$422$	16.1453	0.785941
$423$	23.9752	1.16571
$424$	1.20720	0.0586266
$425$	5.58591	0.270957
$426$	24.7486	1.19907
$427$	−23.8081	−1.15215
$428$	−13.4195	−0.648657
$429$	−10.2597	−0.495342
$430$	−4.70830	−0.227054
$431$	10.7372	0.517195	0.258597	−	0.965985i	$-0.416740\pi$
$431$	10.7372	0.517195	0.258597	+	0.965985i	$0.416740\pi$
$432$	−0.201899	−0.00971388
$433$	20.3370	0.977335	0.488667	−	0.872470i	$-0.337483\pi$
$433$	20.3370	0.977335	0.488667	+	0.872470i	$0.337483\pi$
$434$	30.7380	1.47547
$435$	16.1845	0.775986
$436$	18.1594	0.869676
$437$	−17.6590	−0.844743
$438$	13.2391	0.632587
$439$	17.7148	0.845481	0.422740	−	0.906251i	$-0.361068\pi$
$439$	17.7148	0.845481	0.422740	+	0.906251i	$0.361068\pi$
$440$	9.42757	0.449442
$441$	39.0007	1.85718
$442$	4.00211	0.190361
$443$	2.62560	0.124746	0.0623730	−	0.998053i	$-0.480133\pi$
$443$	2.62560	0.124746	0.0623730	+	0.998053i	$0.480133\pi$
$444$	−18.5406	−0.879897
$445$	−4.90843	−0.232682
$446$	27.7915	1.31597
$447$	9.35670	0.442557
$448$	4.43338	0.209458
$449$	12.8518	0.606512	0.303256	−	0.952909i	$-0.401926\pi$
$449$	12.8518	0.606512	0.303256	+	0.952909i	$0.401926\pi$
$450$	4.86905	0.229529
$451$	29.0383	1.36736
$452$	−7.64765	−0.359715
$453$	18.1909	0.854681
$454$	18.2547	0.856734
$455$	12.8727	0.603483
$456$	−6.08769	−0.285082
$457$	25.7884	1.20633	0.603166	−	0.797616i	$-0.293906\pi$
$457$	25.7884	1.20633	0.603166	+	0.797616i	$0.293906\pi$
$458$	3.21289	0.150129
$459$	−0.713836	−0.0333190
$460$	−18.3502	−0.855583
$461$	14.8728	0.692693	0.346347	−	0.938107i	$-0.387422\pi$
$461$	14.8728	0.692693	0.346347	+	0.938107i	$0.387422\pi$
$462$	−40.1831	−1.86949
$463$	13.7573	0.639357	0.319678	−	0.947526i	$-0.396425\pi$
$463$	13.7573	0.639357	0.319678	+	0.947526i	$0.396425\pi$
$464$	−2.55841	−0.118771
$465$	−43.8599	−2.03396
$466$	−22.7669	−1.05466
$467$	4.34714	0.201161	0.100581	−	0.994929i	$-0.467930\pi$
$467$	4.34714	0.201161	0.100581	+	0.994929i	$0.467930\pi$
$468$	3.48851	0.161256
$469$	−48.3659	−2.23333
$470$	19.9553	0.920467
$471$	−1.23536	−0.0569226
$472$	0.937152	0.0431359
$473$	−6.74597	−0.310180
$474$	39.1621	1.79878
$475$	3.90000	0.178944
$476$	15.6747	0.718448
$477$	3.72042	0.170346
$478$	−2.12156	−0.0970377
$479$	−39.5237	−1.80588	−0.902941	−	0.429764i	$-0.858597\pi$
$479$	−39.5237	−1.80588	−0.902941	+	0.429764i	$0.858597\pi$
$480$	−6.32599	−0.288740
$481$	8.51002	0.388024
$482$	2.09872	0.0955940
$483$	78.2141	3.55886
$484$	2.50764	0.113984
$485$	−49.9573	−2.26844
$486$	22.1788	1.00605
$487$	−29.4068	−1.33255	−0.666275	−	0.745706i	$-0.732112\pi$
$487$	−29.4068	−1.33255	−0.666275	+	0.745706i	$0.732112\pi$
$488$	−5.37018	−0.243097
$489$	−24.2127	−1.09494
$490$	32.4614	1.46646
$491$	8.85535	0.399636	0.199818	−	0.979833i	$-0.435965\pi$
$491$	8.85535	0.399636	0.199818	+	0.979833i	$0.435965\pi$
$492$	−19.4850	−0.878450
$493$	−9.04553	−0.407390
$494$	2.79422	0.125718
$495$	29.0545	1.30590
$496$	6.93330	0.311314
$497$	−44.4905	−1.99567
$498$	13.1606	0.589743
$499$	−34.9751	−1.56570	−0.782850	−	0.622210i	$-0.786235\pi$
$499$	−34.9751	−1.56570	−0.782850	+	0.622210i	$0.786235\pi$
$500$	−8.77300	−0.392341
$501$	23.1455	1.03406
$502$	23.9086	1.06709
$503$	−16.1372	−0.719522	−0.359761	−	0.933045i	$-0.617142\pi$
$503$	−16.1372	−0.719522	−0.359761	+	0.933045i	$0.617142\pi$
$504$	13.6631	0.608603
$505$	−21.6174	−0.961960
$506$	−26.2918	−1.16882
$507$	28.9000	1.28349
$508$	17.7809	0.788902
$509$	34.9569	1.54944	0.774719	−	0.632306i	$-0.217891\pi$
$509$	34.9569	1.54944	0.774719	+	0.632306i	$0.217891\pi$
$510$	−22.3662	−0.990391
$511$	−23.7998	−1.05284
$512$	1.00000	0.0441942
$513$	−0.498389	−0.0220044
$514$	0.0272161	0.00120045
$515$	12.1812	0.536768
$516$	4.52661	0.199273
$517$	28.5915	1.25745
$518$	33.3304	1.46445
$519$	35.5727	1.56147
$520$	2.90359	0.127331
$521$	9.04961	0.396471	0.198235	−	0.980154i	$-0.436479\pi$
$521$	9.04961	0.396471	0.198235	+	0.980154i	$0.436479\pi$
$522$	−7.88469	−0.345103
$523$	−32.4427	−1.41862	−0.709310	−	0.704897i	$-0.750993\pi$
$523$	−32.4427	−1.41862	−0.709310	+	0.704897i	$0.750993\pi$
$524$	−5.42168	−0.236847
$525$	−17.2737	−0.753884
$526$	−2.21749	−0.0966872
$527$	24.5134	1.06782
$528$	−9.06376	−0.394449
$529$	28.1756	1.22502
$530$	3.09662	0.134509
$531$	2.88818	0.125336
$532$	10.9438	0.474475
$533$	8.94348	0.387385
$534$	4.71901	0.204212
$535$	−34.4228	−1.48823
$536$	−10.9095	−0.471218
$537$	44.5141	1.92092
$538$	8.10970	0.349634
$539$	46.5102	2.00333
$540$	−0.517898	−0.0222868
$541$	−7.09284	−0.304945	−0.152473	−	0.988308i	$-0.548724\pi$
$541$	−7.09284	−0.304945	−0.152473	+	0.988308i	$0.548724\pi$
$542$	−30.1816	−1.29641
$543$	−31.7530	−1.36265
$544$	3.53560	0.151588
$545$	46.5812	1.99532
$546$	−12.3760	−0.529643
$547$	−22.3910	−0.957370	−0.478685	−	0.877987i	$-0.658886\pi$
$547$	−22.3910	−0.957370	−0.478685	+	0.877987i	$0.658886\pi$
$548$	22.3737	0.955757
$549$	−16.5502	−0.706345
$550$	5.80658	0.247593
$551$	−6.31546	−0.269047
$552$	17.6421	0.750897
$553$	−70.4017	−2.99378
$554$	−24.2097	−1.02857
$555$	−47.5591	−2.01877
$556$	−11.1363	−0.472283
$557$	1.09257	0.0462939	0.0231469	−	0.999732i	$-0.492631\pi$
$557$	1.09257	0.0462939	0.0231469	+	0.999732i	$0.492631\pi$
$558$	21.3675	0.904559
$559$	−2.07769	−0.0878768
$560$	11.3722	0.480564
$561$	−32.0459	−1.35298
$562$	−22.7688	−0.960442
$563$	−9.34877	−0.394004	−0.197002	−	0.980403i	$-0.563120\pi$
$563$	−9.34877	−0.394004	−0.197002	+	0.980403i	$0.563120\pi$
$564$	−19.1852	−0.807842
$565$	−19.6172	−0.825303
$566$	−22.9321	−0.963907
$567$	−38.7819	−1.62869
$568$	−10.0353	−0.421073
$569$	27.8355	1.16692	0.583461	−	0.812141i	$-0.301698\pi$
$569$	27.8355	1.16692	0.583461	+	0.812141i	$0.301698\pi$
$570$	−15.6157	−0.654071
$571$	38.6121	1.61587	0.807933	−	0.589275i	$-0.200586\pi$
$571$	38.6121	1.61587	0.807933	+	0.589275i	$0.200586\pi$
$572$	4.16021	0.173947
$573$	12.1563	0.507837
$574$	35.0281	1.46204
$575$	−11.3022	−0.471333
$576$	3.08187	0.128411
$577$	0.0757334	0.00315282	0.00157641	−	0.999999i	$-0.499498\pi$
$577$	0.0757334	0.00315282	0.00157641	+	0.999999i	$0.499498\pi$
$578$	−4.49950	−0.187155
$579$	5.97666	0.248382
$580$	−6.56266	−0.272500
$581$	−23.6589	−0.981535
$582$	48.0294	1.99088
$583$	4.43678	0.183753
$584$	−5.36832	−0.222143
$585$	8.94849	0.369974
$586$	14.6819	0.606505
$587$	32.6928	1.34938	0.674688	−	0.738103i	$-0.264278\pi$
$587$	32.6928	1.34938	0.674688	+	0.738103i	$0.264278\pi$
$588$	−31.2088	−1.28703
$589$	17.1149	0.705207
$590$	2.40392	0.0989678
$591$	−9.12463	−0.375337
$592$	7.51805	0.308990
$593$	−46.6777	−1.91682	−0.958412	−	0.285387i	$-0.907878\pi$
$593$	−46.6777	−1.91682	−0.958412	+	0.285387i	$0.907878\pi$
$594$	−0.742035	−0.0304461
$595$	40.2076	1.64835
$596$	−3.79406	−0.155411
$597$	2.94568	0.120559
$598$	−8.09761	−0.331136
$599$	36.3401	1.48482	0.742409	−	0.669947i	$-0.233683\pi$
$599$	36.3401	1.48482	0.742409	+	0.669947i	$0.233683\pi$
$600$	−3.89627	−0.159065
$601$	36.6798	1.49620	0.748100	−	0.663586i	$-0.230966\pi$
$601$	36.6798	1.49620	0.748100	+	0.663586i	$0.230966\pi$
$602$	−8.13748	−0.331659
$603$	−33.6216	−1.36918
$604$	−7.37624	−0.300135
$605$	6.43244	0.261516
$606$	20.7832	0.844258
$607$	−27.7909	−1.12800	−0.563999	−	0.825776i	$-0.690738\pi$
$607$	−27.7909	−1.12800	−0.563999	+	0.825776i	$0.690738\pi$
$608$	2.46851	0.100111
$609$	27.9720	1.13348
$610$	−13.7752	−0.557743
$611$	8.80589	0.356248
$612$	10.8963	0.440456
$613$	28.2178	1.13971	0.569853	−	0.821747i	$-0.307000\pi$
$613$	28.2178	1.13971	0.569853	+	0.821747i	$0.307000\pi$
$614$	−20.8393	−0.841005
$615$	−49.9815	−2.01545
$616$	16.2939	0.656500
$617$	20.6059	0.829561	0.414780	−	0.909922i	$-0.363858\pi$
$617$	20.6059	0.829561	0.414780	+	0.909922i	$0.363858\pi$
$618$	−11.7111	−0.471091
$619$	−29.7195	−1.19453	−0.597263	−	0.802045i	$-0.703745\pi$
$619$	−29.7195	−1.19453	−0.597263	+	0.802045i	$0.703745\pi$
$620$	17.7848	0.714256
$621$	1.44433	0.0579589
$622$	−3.68554	−0.147776
$623$	−8.48336	−0.339879
$624$	−2.79154	−0.111751
$625$	−30.4034	−1.21614
$626$	33.0703	1.32175
$627$	−22.3739	−0.893529
$628$	0.500929	0.0199893
$629$	26.5808	1.05985
$630$	35.0477	1.39633
$631$	−23.7540	−0.945632	−0.472816	−	0.881161i	$-0.656762\pi$
$631$	−23.7540	−0.945632	−0.472816	+	0.881161i	$0.656762\pi$
$632$	−15.8799	−0.631669
$633$	−39.8167	−1.58257
$634$	29.2177	1.16038
$635$	45.6105	1.81000
$636$	−2.97712	−0.118051
$637$	14.3246	0.567563
$638$	−9.40287	−0.372263
$639$	−30.9276	−1.22348
$640$	2.56513	0.101396
$641$	−22.0990	−0.872858	−0.436429	−	0.899739i	$-0.643757\pi$
$641$	−22.0990	−0.872858	−0.436429	+	0.899739i	$0.643757\pi$
$642$	33.0945	1.30613
$643$	−8.69644	−0.342954	−0.171477	−	0.985188i	$-0.554854\pi$
$643$	−8.69644	−0.342954	−0.171477	+	0.985188i	$0.554854\pi$
$644$	−31.7151	−1.24975
$645$	11.6114	0.457197
$646$	8.72766	0.343385
$647$	20.8810	0.820915	0.410458	−	0.911880i	$-0.365369\pi$
$647$	20.8810	0.820915	0.410458	+	0.911880i	$0.365369\pi$
$648$	−8.74769	−0.343642
$649$	3.44429	0.135200
$650$	1.78837	0.0701454
$651$	−75.8042	−2.97100
$652$	9.81805	0.384505
$653$	1.47722	0.0578083	0.0289041	−	0.999582i	$-0.490798\pi$
$653$	1.47722	0.0578083	0.0289041	+	0.999582i	$0.490798\pi$
$654$	−44.7836	−1.75118
$655$	−13.9073	−0.543404
$656$	7.90098	0.308481
$657$	−16.5445	−0.645461
$658$	34.4892	1.34453
$659$	18.4341	0.718090	0.359045	−	0.933320i	$-0.383102\pi$
$659$	18.4341	0.718090	0.359045	+	0.933320i	$0.383102\pi$
$660$	−23.2497	−0.904995
$661$	−15.7103	−0.611060	−0.305530	−	0.952183i	$-0.598834\pi$
$661$	−15.7103	−0.611060	−0.305530	+	0.952183i	$0.598834\pi$
$662$	5.20702	0.202376
$663$	−9.86979	−0.383311
$664$	−5.33653	−0.207097
$665$	28.0724	1.08860
$666$	23.1696	0.897805
$667$	18.3021	0.708661
$668$	−9.38529	−0.363128
$669$	−68.5379	−2.64983
$670$	−27.9843	−1.08113
$671$	−19.7369	−0.761934
$672$	−10.9334	−0.421764
$673$	15.6903	0.604815	0.302407	−	0.953179i	$-0.402210\pi$
$673$	15.6903	0.604815	0.302407	+	0.953179i	$0.402210\pi$
$674$	34.3520	1.32319
$675$	−0.318981	−0.0122776
$676$	−11.7187	−0.450719
$677$	5.52983	0.212529	0.106264	−	0.994338i	$-0.466111\pi$
$677$	5.52983	0.212529	0.106264	+	0.994338i	$0.466111\pi$
$678$	18.8602	0.724322
$679$	−86.3424	−3.31352
$680$	9.06929	0.347792
$681$	−45.0186	−1.72512
$682$	25.4818	0.975747
$683$	15.2253	0.582582	0.291291	−	0.956635i	$-0.405915\pi$
$683$	15.2253	0.582582	0.291291	+	0.956635i	$0.405915\pi$
$684$	7.60761	0.290884
$685$	57.3915	2.19282
$686$	25.0702	0.957186
$687$	−7.92345	−0.302299
$688$	−1.83550	−0.0699778
$689$	1.36648	0.0520588
$690$	45.2543	1.72280
$691$	−10.9668	−0.417197	−0.208598	−	0.978001i	$-0.566890\pi$
$691$	−10.9668	−0.417197	−0.208598	+	0.978001i	$0.566890\pi$
$692$	−14.4244	−0.548334
$693$	50.2156	1.90753
$694$	−36.0981	−1.37026
$695$	−28.5660	−1.08357
$696$	6.30941	0.239158
$697$	27.9347	1.05810
$698$	15.1530	0.573548
$699$	56.1465	2.12366
$700$	7.00431	0.264738
$701$	−24.5628	−0.927725	−0.463862	−	0.885907i	$-0.653537\pi$
$701$	−24.5628	−0.927725	−0.463862	+	0.885907i	$0.653537\pi$
$702$	−0.228539	−0.00862565
$703$	18.5583	0.699941
$704$	3.67527	0.138517
$705$	−49.2125	−1.85345
$706$	4.82243	0.181495
$707$	−37.3618	−1.40514
$708$	−2.31115	−0.0868584
$709$	37.4575	1.40675	0.703373	−	0.710821i	$-0.251676\pi$
$709$	37.4575	1.40675	0.703373	+	0.710821i	$0.251676\pi$
$710$	−25.7420	−0.966079
$711$	−48.9398	−1.83539
$712$	−1.91352	−0.0717121
$713$	−49.5988	−1.85749
$714$	−38.6560	−1.44667
$715$	10.6715	0.399091
$716$	−18.0501	−0.674562
$717$	5.23206	0.195395
$718$	−23.4350	−0.874586
$719$	−7.27019	−0.271132	−0.135566	−	0.990768i	$-0.543285\pi$
$719$	−7.27019	−0.271132	−0.135566	+	0.990768i	$0.543285\pi$
$720$	7.90540	0.294617
$721$	21.0531	0.784058
$722$	−12.9065	−0.480329
$723$	−5.17574	−0.192488
$724$	12.8756	0.478517
$725$	−4.04204	−0.150118
$726$	−6.18421	−0.229518
$727$	24.1976	0.897438	0.448719	−	0.893673i	$-0.351880\pi$
$727$	24.1976	0.897438	0.448719	+	0.893673i	$0.351880\pi$
$728$	5.01835	0.185992
$729$	−28.4530	−1.05381
$730$	−13.7705	−0.509668
$731$	−6.48960	−0.240027
$732$	13.2436	0.489499
$733$	22.4750	0.830134	0.415067	−	0.909791i	$-0.363758\pi$
$733$	22.4750	0.830134	0.415067	+	0.909791i	$0.363758\pi$
$734$	−0.821555	−0.0303241
$735$	−80.0546	−2.95286
$736$	−7.15371	−0.263689
$737$	−40.0954	−1.47693
$738$	24.3498	0.896328
$739$	19.1416	0.704135	0.352067	−	0.935975i	$-0.385479\pi$
$739$	19.1416	0.704135	0.352067	+	0.935975i	$0.385479\pi$
$740$	19.2848	0.708923
$741$	−6.89094	−0.253145
$742$	5.35196	0.196477
$743$	−22.6811	−0.832089	−0.416045	−	0.909344i	$-0.636584\pi$
$743$	−22.6811	−0.832089	−0.416045	+	0.909344i	$0.636584\pi$
$744$	−17.0985	−0.626862
$745$	−9.73226	−0.356563
$746$	14.9917	0.548887
$747$	−16.4465	−0.601745
$748$	12.9943	0.475119
$749$	−59.4939	−2.17386
$750$	21.6355	0.790016
$751$	7.81467	0.285161	0.142581	−	0.989783i	$-0.454460\pi$
$751$	7.81467	0.285161	0.142581	+	0.989783i	$0.454460\pi$
$752$	7.77943	0.283686
$753$	−58.9620	−2.14869
$754$	−2.89598	−0.105466
$755$	−18.9210	−0.688606
$756$	−0.895096	−0.0325543
$757$	6.95047	0.252619	0.126309	−	0.991991i	$-0.459687\pi$
$757$	6.95047	0.252619	0.126309	+	0.991991i	$0.459687\pi$
$758$	12.0765	0.438638
$759$	64.8395	2.35352
$760$	6.33205	0.229687
$761$	−27.6455	−1.00215	−0.501075	−	0.865404i	$-0.667062\pi$
$761$	−27.6455	−1.00215	−0.501075	+	0.865404i	$0.667062\pi$
$762$	−43.8504	−1.58853
$763$	80.5075	2.91457
$764$	−4.92928	−0.178335
$765$	27.9504	1.01055
$766$	−37.8443	−1.36737
$767$	1.06081	0.0383035
$768$	−2.46614	−0.0889893
$769$	22.0253	0.794253	0.397126	−	0.917764i	$-0.370007\pi$
$769$	22.0253	0.794253	0.397126	+	0.917764i	$0.370007\pi$
$770$	41.7960	1.50622
$771$	−0.0671189	−0.00241723
$772$	−2.42348	−0.0872231
$773$	26.3755	0.948660	0.474330	−	0.880347i	$-0.342690\pi$
$773$	26.3755	0.948660	0.474330	+	0.880347i	$0.342690\pi$
$774$	−5.65677	−0.203328
$775$	10.9539	0.393477
$776$	−19.4755	−0.699130
$777$	−82.1975	−2.94882
$778$	35.3190	1.26625
$779$	19.5036	0.698790
$780$	−7.16068	−0.256393
$781$	−36.8826	−1.31976
$782$	−25.2927	−0.904465
$783$	0.516541	0.0184597
$784$	12.6549	0.451960
$785$	1.28495	0.0458618
$786$	13.3706	0.476915
$787$	−4.18006	−0.149003	−0.0745015	−	0.997221i	$-0.523737\pi$
$787$	−4.18006	−0.149003	−0.0745015	+	0.997221i	$0.523737\pi$
$788$	3.69996	0.131806
$789$	5.46865	0.194689
$790$	−40.7341	−1.44925
$791$	−33.9049	−1.20552
$792$	11.3267	0.402477
$793$	−6.07876	−0.215863
$794$	−2.14288	−0.0760481
$795$	−7.63671	−0.270846
$796$	−1.19445	−0.0423360
$797$	−3.54296	−0.125498	−0.0627490	−	0.998029i	$-0.519987\pi$
$797$	−3.54296	−0.125498	−0.0627490	+	0.998029i	$0.519987\pi$
$798$	−26.9891	−0.955403
$799$	27.5050	0.973056
$800$	1.57990	0.0558580
$801$	−5.89721	−0.208368
$802$	33.5013	1.18297
$803$	−19.7301	−0.696259
$804$	26.9044	0.948844
$805$	−81.3535	−2.86733
$806$	7.84812	0.276438
$807$	−19.9997	−0.704023
$808$	−8.42739	−0.296474
$809$	−15.2192	−0.535079	−0.267540	−	0.963547i	$-0.586211\pi$
$809$	−15.2192	−0.535079	−0.267540	+	0.963547i	$0.586211\pi$
$810$	−22.4390	−0.788426
$811$	−20.0393	−0.703676	−0.351838	−	0.936061i	$-0.614443\pi$
$811$	−20.0393	−0.703676	−0.351838	+	0.936061i	$0.614443\pi$
$812$	−11.3424	−0.398041
$813$	74.4322	2.61045
$814$	27.6309	0.968462
$815$	25.1846	0.882178
$816$	−8.71931	−0.305237
$817$	−4.53095	−0.158518
$818$	8.50282	0.297294
$819$	15.4659	0.540422
$820$	20.2671	0.707756
$821$	15.6135	0.544915	0.272458	−	0.962168i	$-0.412164\pi$
$821$	15.6135	0.544915	0.272458	+	0.962168i	$0.412164\pi$
$822$	−55.1768	−1.92451
$823$	−0.324498	−0.0113113	−0.00565564	−	0.999984i	$-0.501800\pi$
$823$	−0.324498	−0.0113113	−0.00565564	+	0.999984i	$0.501800\pi$
$824$	4.74876	0.165431
$825$	−14.3199	−0.498553
$826$	4.15475	0.144562
$827$	5.05147	0.175657	0.0878285	−	0.996136i	$-0.472007\pi$
$827$	5.05147	0.175657	0.0878285	+	0.996136i	$0.472007\pi$
$828$	−22.0468	−0.766179
$829$	26.8501	0.932541	0.466270	−	0.884642i	$-0.345597\pi$
$829$	26.8501	0.932541	0.466270	+	0.884642i	$0.345597\pi$
$830$	−13.6889	−0.475149
$831$	59.7047	2.07113
$832$	1.13195	0.0392432
$833$	44.7427	1.55024
$834$	27.4637	0.950989
$835$	−24.0745	−0.833133
$836$	9.07244	0.313777
$837$	−1.39983	−0.0483851
$838$	−26.2829	−0.907928
$839$	1.22732	0.0423716	0.0211858	−	0.999776i	$-0.493256\pi$
$839$	1.22732	0.0423716	0.0211858	+	0.999776i	$0.493256\pi$
$840$	−28.0455	−0.967662
$841$	−22.4545	−0.774294
$842$	−33.3649	−1.14983
$843$	56.1510	1.93394
$844$	16.1453	0.555744
$845$	−30.0600	−1.03410
$846$	23.9752	0.824283
$847$	11.1173	0.381996
$848$	1.20720	0.0414553
$849$	56.5538	1.94092
$850$	5.58591	0.191595
$851$	−53.7819	−1.84362
$852$	24.7486	0.847873
$853$	−28.1574	−0.964092	−0.482046	−	0.876146i	$-0.660106\pi$
$853$	−28.1574	−0.964092	−0.482046	+	0.876146i	$0.660106\pi$
$854$	−23.8081	−0.814695
$855$	19.5145	0.667383
$856$	−13.4195	−0.458670
$857$	−38.0675	−1.30036	−0.650181	−	0.759779i	$-0.725307\pi$
$857$	−38.0675	−1.30036	−0.650181	+	0.759779i	$0.725307\pi$
$858$	−10.2597	−0.350260
$859$	12.6085	0.430195	0.215098	−	0.976593i	$-0.430993\pi$
$859$	12.6085	0.430195	0.215098	+	0.976593i	$0.430993\pi$
$860$	−4.70830	−0.160552
$861$	−86.3843	−2.94397
$862$	10.7372	0.365712
$863$	46.7068	1.58992	0.794959	−	0.606663i	$-0.207492\pi$
$863$	46.7068	1.58992	0.794959	+	0.606663i	$0.207492\pi$
$864$	−0.201899	−0.00686875
$865$	−37.0005	−1.25806
$866$	20.3370	0.691080
$867$	11.0964	0.376854
$868$	30.7380	1.04331
$869$	−58.3630	−1.97983
$870$	16.1845	0.548705
$871$	−12.3490	−0.418428
$872$	18.1594	0.614954
$873$	−60.0210	−2.03140
$874$	−17.6590	−0.597324
$875$	−38.8941	−1.31486
$876$	13.2391	0.447306
$877$	49.0425	1.65605	0.828024	−	0.560693i	$-0.189465\pi$
$877$	49.0425	1.65605	0.828024	+	0.560693i	$0.189465\pi$
$878$	17.7148	0.597845
$879$	−36.2078	−1.22126
$880$	9.42757	0.317803
$881$	−1.83093	−0.0616855	−0.0308428	−	0.999524i	$-0.509819\pi$
$881$	−1.83093	−0.0616855	−0.0308428	+	0.999524i	$0.509819\pi$
$882$	39.0007	1.31322
$883$	2.80754	0.0944811	0.0472406	−	0.998884i	$-0.484957\pi$
$883$	2.80754	0.0944811	0.0472406	+	0.998884i	$0.484957\pi$
$884$	4.00211	0.134606
$885$	−5.92841	−0.199281
$886$	2.62560	0.0882087
$887$	25.3424	0.850914	0.425457	−	0.904979i	$-0.360113\pi$
$887$	25.3424	0.850914	0.425457	+	0.904979i	$0.360113\pi$
$888$	−18.5406	−0.622181
$889$	78.8297	2.64386
$890$	−4.90843	−0.164531
$891$	−32.1502	−1.07707
$892$	27.7915	0.930529
$893$	19.2036	0.642623
$894$	9.35670	0.312935
$895$	−46.3008	−1.54766
$896$	4.43338	0.148109
$897$	19.9699	0.666775
$898$	12.8518	0.428869
$899$	−17.7382	−0.591603
$900$	4.86905	0.162302
$901$	4.26817	0.142193
$902$	29.0383	0.966869
$903$	20.0682	0.667828
$904$	−7.64765	−0.254357
$905$	33.0276	1.09787
$906$	18.1909	0.604351
$907$	31.6335	1.05037	0.525186	−	0.850987i	$-0.323996\pi$
$907$	31.6335	1.05037	0.525186	+	0.850987i	$0.323996\pi$
$908$	18.2547	0.605802
$909$	−25.9721	−0.861440
$910$	12.8727	0.426727
$911$	−22.8365	−0.756608	−0.378304	−	0.925681i	$-0.623493\pi$
$911$	−22.8365	−0.756608	−0.378304	+	0.925681i	$0.623493\pi$
$912$	−6.08769	−0.201584
$913$	−19.6132	−0.649102
$914$	25.7884	0.853005
$915$	33.9717	1.12307
$916$	3.21289	0.106157
$917$	−24.0364	−0.793751
$918$	−0.713836	−0.0235601
$919$	50.1262	1.65351	0.826756	−	0.562561i	$-0.190184\pi$
$919$	50.1262	1.65351	0.826756	+	0.562561i	$0.190184\pi$
$920$	−18.3502	−0.604988
$921$	51.3927	1.69345
$922$	14.8728	0.489808
$923$	−11.3595	−0.373901
$924$	−40.1831	−1.32193
$925$	11.8778	0.390539
$926$	13.7573	0.452093
$927$	14.6351	0.480679
$928$	−2.55841	−0.0839840
$929$	36.0972	1.18431	0.592155	−	0.805824i	$-0.298277\pi$
$929$	36.0972	1.18431	0.592155	+	0.805824i	$0.298277\pi$
$930$	−43.8599	−1.43822
$931$	31.2387	1.02381
$932$	−22.7669	−0.745756
$933$	9.08906	0.297563
$934$	4.34714	0.142243
$935$	33.3321	1.09008
$936$	3.48851	0.114025
$937$	−27.5203	−0.899049	−0.449524	−	0.893268i	$-0.648407\pi$
$937$	−27.5203	−0.899049	−0.449524	+	0.893268i	$0.648407\pi$
$938$	−48.3659	−1.57920
$939$	−81.5560	−2.66148
$940$	19.9553	0.650869
$941$	−35.6776	−1.16306	−0.581528	−	0.813527i	$-0.697545\pi$
$941$	−35.6776	−1.16306	−0.581528	+	0.813527i	$0.697545\pi$
$942$	−1.23536	−0.0402503
$943$	−56.5213	−1.84059
$944$	0.937152	0.0305017
$945$	−2.29604	−0.0746902
$946$	−6.74597	−0.219330
$947$	23.8023	0.773470	0.386735	−	0.922191i	$-0.373603\pi$
$947$	23.8023	0.773470	0.386735	+	0.922191i	$0.373603\pi$
$948$	39.1621	1.27193
$949$	−6.07665	−0.197256
$950$	3.90000	0.126533
$951$	−72.0549	−2.33654
$952$	15.6747	0.508020
$953$	−38.8627	−1.25889	−0.629443	−	0.777047i	$-0.716717\pi$
$953$	−38.8627	−1.25889	−0.629443	+	0.777047i	$0.716717\pi$
$954$	3.72042	0.120453
$955$	−12.6443	−0.409158
$956$	−2.12156	−0.0686160
$957$	23.1888	0.749588
$958$	−39.5237	−1.27695
$959$	99.1912	3.20305
$960$	−6.32599	−0.204170
$961$	17.0706	0.550664
$962$	8.51002	0.274374
$963$	−41.3572	−1.33272
$964$	2.09872	0.0675952
$965$	−6.21656	−0.200118
$966$	78.2141	2.51650
$967$	−47.0830	−1.51409	−0.757044	−	0.653364i	$-0.773357\pi$
$967$	−47.0830	−1.51409	−0.757044	+	0.653364i	$0.773357\pi$
$968$	2.50764	0.0805987
$969$	−21.5237	−0.691440
$970$	−49.9573	−1.60403
$971$	−8.39814	−0.269509	−0.134755	−	0.990879i	$-0.543025\pi$
$971$	−8.39814	−0.269509	−0.134755	+	0.990879i	$0.543025\pi$
$972$	22.1788	0.711384
$973$	−49.3714	−1.58277
$974$	−29.4068	−0.942256
$975$	−4.41037	−0.141245
$976$	−5.37018	−0.171895
$977$	−5.14375	−0.164563	−0.0822816	−	0.996609i	$-0.526221\pi$
$977$	−5.14375	−0.164563	−0.0822816	+	0.996609i	$0.526221\pi$
$978$	−24.2127	−0.774238
$979$	−7.03271	−0.224766
$980$	32.4614	1.03694
$981$	55.9648	1.78682
$982$	8.85535	0.282586
$983$	10.2900	0.328200	0.164100	−	0.986444i	$-0.447528\pi$
$983$	10.2900	0.328200	0.164100	+	0.986444i	$0.447528\pi$
$984$	−19.4850	−0.621158
$985$	9.49088	0.302405
$986$	−9.04553	−0.288068
$987$	−85.0553	−2.70734
$988$	2.79422	0.0888959
$989$	13.1306	0.417530
$990$	29.0545	0.923413
$991$	1.99620	0.0634114	0.0317057	−	0.999497i	$-0.489906\pi$
$991$	1.99620	0.0634114	0.0317057	+	0.999497i	$0.489906\pi$
$992$	6.93330	0.220132
$993$	−12.8413	−0.407505
$994$	−44.4905	−1.41115
$995$	−3.06391	−0.0971326
$996$	13.1606	0.417011
$997$	33.6241	1.06489	0.532444	−	0.846466i	$-0.321274\pi$
$997$	33.6241	1.06489	0.532444	+	0.846466i	$0.321274\pi$
$998$	−34.9751	−1.10712
$999$	−1.51789	−0.0480238

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6002.2.a.d.1.13	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6002.2.a.d.1.13	✓	79	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:	\( N \)	\(=\)	\( 6002 = 2 \cdot 3001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6002.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.46614 q^{3} +1.00000 q^{4} +2.56513 q^{5} -2.46614 q^{6} +4.43338 q^{7} +1.00000 q^{8} +3.08187 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.46614 q^{3} +1.00000 q^{4} +2.56513 q^{5} -2.46614 q^{6} +4.43338 q^{7} +1.00000 q^{8} +3.08187 q^{9} +2.56513 q^{10} +3.67527 q^{11} -2.46614 q^{12} +1.13195 q^{13} +4.43338 q^{14} -6.32599 q^{15} +1.00000 q^{16} +3.53560 q^{17} +3.08187 q^{18} +2.46851 q^{19} +2.56513 q^{20} -10.9334 q^{21} +3.67527 q^{22} -7.15371 q^{23} -2.46614 q^{24} +1.57990 q^{25} +1.13195 q^{26} -0.201899 q^{27} +4.43338 q^{28} -2.55841 q^{29} -6.32599 q^{30} +6.93330 q^{31} +1.00000 q^{32} -9.06376 q^{33} +3.53560 q^{34} +11.3722 q^{35} +3.08187 q^{36} +7.51805 q^{37} +2.46851 q^{38} -2.79154 q^{39} +2.56513 q^{40} +7.90098 q^{41} -10.9334 q^{42} -1.83550 q^{43} +3.67527 q^{44} +7.90540 q^{45} -7.15371 q^{46} +7.77943 q^{47} -2.46614 q^{48} +12.6549 q^{49} +1.57990 q^{50} -8.71931 q^{51} +1.13195 q^{52} +1.20720 q^{53} -0.201899 q^{54} +9.42757 q^{55} +4.43338 q^{56} -6.08769 q^{57} -2.55841 q^{58} +0.937152 q^{59} -6.32599 q^{60} -5.37018 q^{61} +6.93330 q^{62} +13.6631 q^{63} +1.00000 q^{64} +2.90359 q^{65} -9.06376 q^{66} -10.9095 q^{67} +3.53560 q^{68} +17.6421 q^{69} +11.3722 q^{70} -10.0353 q^{71} +3.08187 q^{72} -5.36832 q^{73} +7.51805 q^{74} -3.89627 q^{75} +2.46851 q^{76} +16.2939 q^{77} -2.79154 q^{78} -15.8799 q^{79} +2.56513 q^{80} -8.74769 q^{81} +7.90098 q^{82} -5.33653 q^{83} -10.9334 q^{84} +9.06929 q^{85} -1.83550 q^{86} +6.30941 q^{87} +3.67527 q^{88} -1.91352 q^{89} +7.90540 q^{90} +5.01835 q^{91} -7.15371 q^{92} -17.0985 q^{93} +7.77943 q^{94} +6.33205 q^{95} -2.46614 q^{96} -19.4755 q^{97} +12.6549 q^{98} +11.3267 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q + 79 q^{2} + 17 q^{3} + 79 q^{4} + 18 q^{5} + 17 q^{6} + 19 q^{7} + 79 q^{8} + 118 q^{9}+O(q^{10}) \) 79 * q + 79 * q^2 + 17 * q^3 + 79 * q^4 + 18 * q^5 + 17 * q^6 + 19 * q^7 + 79 * q^8 + 118 * q^9	\( 79 q + 79 q^{2} + 17 q^{3} + 79 q^{4} + 18 q^{5} + 17 q^{6} + 19 q^{7} + 79 q^{8} + 118 q^{9} + 18 q^{10} + 28 q^{11} + 17 q^{12} + 47 q^{13} + 19 q^{14} + 14 q^{15} + 79 q^{16} + 36 q^{17} + 118 q^{18} + 29 q^{19} + 18 q^{20} + 45 q^{21} + 28 q^{22} + 23 q^{23} + 17 q^{24} + 161 q^{25} + 47 q^{26} + 50 q^{27} + 19 q^{28} + 53 q^{29} + 14 q^{30} + 29 q^{31} + 79 q^{32} + 34 q^{33} + 36 q^{34} + 33 q^{35} + 118 q^{36} + 89 q^{37} + 29 q^{38} - 7 q^{39} + 18 q^{40} + 58 q^{41} + 45 q^{42} + 88 q^{43} + 28 q^{44} + 45 q^{45} + 23 q^{46} + 3 q^{47} + 17 q^{48} + 162 q^{49} + 161 q^{50} + 29 q^{51} + 47 q^{52} + 88 q^{53} + 50 q^{54} + 37 q^{55} + 19 q^{56} + 54 q^{57} + 53 q^{58} + 37 q^{59} + 14 q^{60} + 55 q^{61} + 29 q^{62} + 21 q^{63} + 79 q^{64} + 55 q^{65} + 34 q^{66} + 107 q^{67} + 36 q^{68} + 39 q^{69} + 33 q^{70} - 5 q^{71} + 118 q^{72} + 71 q^{73} + 89 q^{74} + 37 q^{75} + 29 q^{76} + 61 q^{77} - 7 q^{78} + 29 q^{79} + 18 q^{80} + 215 q^{81} + 58 q^{82} + 42 q^{83} + 45 q^{84} + 84 q^{85} + 88 q^{86} + 15 q^{87} + 28 q^{88} + 72 q^{89} + 45 q^{90} + 70 q^{91} + 23 q^{92} + 97 q^{93} + 3 q^{94} - 18 q^{95} + 17 q^{96} + 93 q^{97} + 162 q^{98} + 49 q^{99}+O(q^{100}) \) 79 * q + 79 * q^2 + 17 * q^3 + 79 * q^4 + 18 * q^5 + 17 * q^6 + 19 * q^7 + 79 * q^8 + 118 * q^9 + 18 * q^10 + 28 * q^11 + 17 * q^12 + 47 * q^13 + 19 * q^14 + 14 * q^15 + 79 * q^16 + 36 * q^17 + 118 * q^18 + 29 * q^19 + 18 * q^20 + 45 * q^21 + 28 * q^22 + 23 * q^23 + 17 * q^24 + 161 * q^25 + 47 * q^26 + 50 * q^27 + 19 * q^28 + 53 * q^29 + 14 * q^30 + 29 * q^31 + 79 * q^32 + 34 * q^33 + 36 * q^34 + 33 * q^35 + 118 * q^36 + 89 * q^37 + 29 * q^38 - 7 * q^39 + 18 * q^40 + 58 * q^41 + 45 * q^42 + 88 * q^43 + 28 * q^44 + 45 * q^45 + 23 * q^46 + 3 * q^47 + 17 * q^48 + 162 * q^49 + 161 * q^50 + 29 * q^51 + 47 * q^52 + 88 * q^53 + 50 * q^54 + 37 * q^55 + 19 * q^56 + 54 * q^57 + 53 * q^58 + 37 * q^59 + 14 * q^60 + 55 * q^61 + 29 * q^62 + 21 * q^63 + 79 * q^64 + 55 * q^65 + 34 * q^66 + 107 * q^67 + 36 * q^68 + 39 * q^69 + 33 * q^70 - 5 * q^71 + 118 * q^72 + 71 * q^73 + 89 * q^74 + 37 * q^75 + 29 * q^76 + 61 * q^77 - 7 * q^78 + 29 * q^79 + 18 * q^80 + 215 * q^81 + 58 * q^82 + 42 * q^83 + 45 * q^84 + 84 * q^85 + 88 * q^86 + 15 * q^87 + 28 * q^88 + 72 * q^89 + 45 * q^90 + 70 * q^91 + 23 * q^92 + 97 * q^93 + 3 * q^94 - 18 * q^95 + 17 * q^96 + 93 * q^97 + 162 * q^98 + 49 * q^99

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