LMFDB - Embedded newform 6038.2.a.e.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6038,2,Mod(1,6038)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6038, 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("6038.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6038 = 2 \cdot 3019 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6038.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:	$48.2136727404$
Analytic rank:	$0$
Dimension:	$70$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	6038.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.94455 q^{3} +1.00000 q^{4} +3.92217 q^{5} -2.94455 q^{6} +4.11176 q^{7} +1.00000 q^{8} +5.67038 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.94455 q^{3} +1.00000 q^{4} +3.92217 q^{5} -2.94455 q^{6} +4.11176 q^{7} +1.00000 q^{8} +5.67038 q^{9} +3.92217 q^{10} +1.02998 q^{11} -2.94455 q^{12} -4.94074 q^{13} +4.11176 q^{14} -11.5490 q^{15} +1.00000 q^{16} +2.10580 q^{17} +5.67038 q^{18} +6.25520 q^{19} +3.92217 q^{20} -12.1073 q^{21} +1.02998 q^{22} -2.20919 q^{23} -2.94455 q^{24} +10.3834 q^{25} -4.94074 q^{26} -7.86307 q^{27} +4.11176 q^{28} -4.46014 q^{29} -11.5490 q^{30} -4.60356 q^{31} +1.00000 q^{32} -3.03283 q^{33} +2.10580 q^{34} +16.1270 q^{35} +5.67038 q^{36} -1.93250 q^{37} +6.25520 q^{38} +14.5483 q^{39} +3.92217 q^{40} +5.65780 q^{41} -12.1073 q^{42} +7.44604 q^{43} +1.02998 q^{44} +22.2402 q^{45} -2.20919 q^{46} -2.50260 q^{47} -2.94455 q^{48} +9.90656 q^{49} +10.3834 q^{50} -6.20064 q^{51} -4.94074 q^{52} +8.47104 q^{53} -7.86307 q^{54} +4.03976 q^{55} +4.11176 q^{56} -18.4188 q^{57} -4.46014 q^{58} +9.52112 q^{59} -11.5490 q^{60} -1.39929 q^{61} -4.60356 q^{62} +23.3152 q^{63} +1.00000 q^{64} -19.3784 q^{65} -3.03283 q^{66} -3.09067 q^{67} +2.10580 q^{68} +6.50507 q^{69} +16.1270 q^{70} +8.51965 q^{71} +5.67038 q^{72} -3.99445 q^{73} -1.93250 q^{74} -30.5745 q^{75} +6.25520 q^{76} +4.23503 q^{77} +14.5483 q^{78} -7.22479 q^{79} +3.92217 q^{80} +6.14208 q^{81} +5.65780 q^{82} +4.94312 q^{83} -12.1073 q^{84} +8.25931 q^{85} +7.44604 q^{86} +13.1331 q^{87} +1.02998 q^{88} -9.56229 q^{89} +22.2402 q^{90} -20.3151 q^{91} -2.20919 q^{92} +13.5554 q^{93} -2.50260 q^{94} +24.5340 q^{95} -2.94455 q^{96} +1.33617 q^{97} +9.90656 q^{98} +5.84039 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 70 q + 70 q^{2} + 25 q^{3} + 70 q^{4} + 18 q^{5} + 25 q^{6} + 50 q^{7} + 70 q^{8} + 89 q^{9}+O(q^{10}) $ 70 * q + 70 * q^2 + 25 * q^3 + 70 * q^4 + 18 * q^5 + 25 * q^6 + 50 * q^7 + 70 * q^8 + 89 * q^9	\( 70 q + 70 q^{2} + 25 q^{3} + 70 q^{4} + 18 q^{5} + 25 q^{6} + 50 q^{7} + 70 q^{8} + 89 q^{9} + 18 q^{10} + 41 q^{11} + 25 q^{12} + 41 q^{13} + 50 q^{14} + 13 q^{15} + 70 q^{16} + 40 q^{17} + 89 q^{18} + 55 q^{19} + 18 q^{20} + 2 q^{21} + 41 q^{22} + 41 q^{23} + 25 q^{24} + 104 q^{25} + 41 q^{26} + 82 q^{27} + 50 q^{28} + 11 q^{29} + 13 q^{30} + 78 q^{31} + 70 q^{32} + 45 q^{33} + 40 q^{34} + 25 q^{35} + 89 q^{36} + 46 q^{37} + 55 q^{38} + 19 q^{39} + 18 q^{40} + 51 q^{41} + 2 q^{42} + 68 q^{43} + 41 q^{44} + 37 q^{45} + 41 q^{46} + 69 q^{47} + 25 q^{48} + 126 q^{49} + 104 q^{50} + 36 q^{51} + 41 q^{52} + 23 q^{53} + 82 q^{54} + 42 q^{55} + 50 q^{56} + 14 q^{57} + 11 q^{58} + 89 q^{59} + 13 q^{60} + 32 q^{61} + 78 q^{62} + 106 q^{63} + 70 q^{64} + 18 q^{65} + 45 q^{66} + 90 q^{67} + 40 q^{68} - 12 q^{69} + 25 q^{70} + 54 q^{71} + 89 q^{72} + 94 q^{73} + 46 q^{74} + 72 q^{75} + 55 q^{76} - 16 q^{77} + 19 q^{78} + 54 q^{79} + 18 q^{80} + 102 q^{81} + 51 q^{82} + 60 q^{83} + 2 q^{84} - 5 q^{85} + 68 q^{86} + 9 q^{87} + 41 q^{88} + 77 q^{89} + 37 q^{90} + 54 q^{91} + 41 q^{92} - 2 q^{93} + 69 q^{94} + 39 q^{95} + 25 q^{96} + 139 q^{97} + 126 q^{98} + 60 q^{99}+O(q^{100}) \) 70 * q + 70 * q^2 + 25 * q^3 + 70 * q^4 + 18 * q^5 + 25 * q^6 + 50 * q^7 + 70 * q^8 + 89 * q^9 + 18 * q^10 + 41 * q^11 + 25 * q^12 + 41 * q^13 + 50 * q^14 + 13 * q^15 + 70 * q^16 + 40 * q^17 + 89 * q^18 + 55 * q^19 + 18 * q^20 + 2 * q^21 + 41 * q^22 + 41 * q^23 + 25 * q^24 + 104 * q^25 + 41 * q^26 + 82 * q^27 + 50 * q^28 + 11 * q^29 + 13 * q^30 + 78 * q^31 + 70 * q^32 + 45 * q^33 + 40 * q^34 + 25 * q^35 + 89 * q^36 + 46 * q^37 + 55 * q^38 + 19 * q^39 + 18 * q^40 + 51 * q^41 + 2 * q^42 + 68 * q^43 + 41 * q^44 + 37 * q^45 + 41 * q^46 + 69 * q^47 + 25 * q^48 + 126 * q^49 + 104 * q^50 + 36 * q^51 + 41 * q^52 + 23 * q^53 + 82 * q^54 + 42 * q^55 + 50 * q^56 + 14 * q^57 + 11 * q^58 + 89 * q^59 + 13 * q^60 + 32 * q^61 + 78 * q^62 + 106 * q^63 + 70 * q^64 + 18 * q^65 + 45 * q^66 + 90 * q^67 + 40 * q^68 - 12 * q^69 + 25 * q^70 + 54 * q^71 + 89 * q^72 + 94 * q^73 + 46 * q^74 + 72 * q^75 + 55 * q^76 - 16 * q^77 + 19 * q^78 + 54 * q^79 + 18 * q^80 + 102 * q^81 + 51 * q^82 + 60 * q^83 + 2 * q^84 - 5 * q^85 + 68 * q^86 + 9 * q^87 + 41 * q^88 + 77 * q^89 + 37 * q^90 + 54 * q^91 + 41 * q^92 - 2 * q^93 + 69 * q^94 + 39 * q^95 + 25 * q^96 + 139 * q^97 + 126 * q^98 + 60 * 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
$3$	−2.94455	−1.70004	−0.850019	−	0.526753i	$-0.823409\pi$
$3$	−2.94455	−1.70004	−0.850019	+	0.526753i	$0.823409\pi$
$4$	1.00000	0.500000
$5$	3.92217	1.75405	0.877024	−	0.480446i	$-0.159525\pi$
$5$	3.92217	1.75405	0.877024	+	0.480446i	$0.159525\pi$
$6$	−2.94455	−1.20211
$7$	4.11176	1.55410	0.777049	−	0.629440i	$-0.216716\pi$
$7$	4.11176	1.55410	0.777049	+	0.629440i	$0.216716\pi$
$8$	1.00000	0.353553
$9$	5.67038	1.89013
$10$	3.92217	1.24030
$11$	1.02998	0.310551	0.155275	−	0.987871i	$-0.450373\pi$
$11$	1.02998	0.310551	0.155275	+	0.987871i	$0.450373\pi$
$12$	−2.94455	−0.850019
$13$	−4.94074	−1.37031	−0.685157	−	0.728395i	$-0.740267\pi$
$13$	−4.94074	−1.37031	−0.685157	+	0.728395i	$0.740267\pi$
$14$	4.11176	1.09891
$15$	−11.5490	−2.98195
$16$	1.00000	0.250000
$17$	2.10580	0.510732	0.255366	−	0.966844i	$-0.417804\pi$
$17$	2.10580	0.510732	0.255366	+	0.966844i	$0.417804\pi$
$18$	5.67038	1.33652
$19$	6.25520	1.43504	0.717521	−	0.696537i	$-0.245277\pi$
$19$	6.25520	1.43504	0.717521	+	0.696537i	$0.245277\pi$
$20$	3.92217	0.877024
$21$	−12.1073	−2.64203
$22$	1.02998	0.219593
$23$	−2.20919	−0.460647	−0.230324	−	0.973114i	$-0.573979\pi$
$23$	−2.20919	−0.460647	−0.230324	+	0.973114i	$0.573979\pi$
$24$	−2.94455	−0.601054
$25$	10.3834	2.07669
$26$	−4.94074	−0.968959
$27$	−7.86307	−1.51325
$28$	4.11176	0.777049
$29$	−4.46014	−0.828227	−0.414113	−	0.910225i	$-0.635908\pi$
$29$	−4.46014	−0.828227	−0.414113	+	0.910225i	$0.635908\pi$
$30$	−11.5490	−2.10856
$31$	−4.60356	−0.826823	−0.413412	−	0.910544i	$-0.635663\pi$
$31$	−4.60356	−0.826823	−0.413412	+	0.910544i	$0.635663\pi$
$32$	1.00000	0.176777
$33$	−3.03283	−0.527948
$34$	2.10580	0.361142
$35$	16.1270	2.72596
$36$	5.67038	0.945064
$37$	−1.93250	−0.317702	−0.158851	−	0.987303i	$-0.550779\pi$
$37$	−1.93250	−0.317702	−0.158851	+	0.987303i	$0.550779\pi$
$38$	6.25520	1.01473
$39$	14.5483	2.32959
$40$	3.92217	0.620150
$41$	5.65780	0.883600	0.441800	−	0.897114i	$-0.354340\pi$
$41$	5.65780	0.883600	0.441800	+	0.897114i	$0.354340\pi$
$42$	−12.1073	−1.86819
$43$	7.44604	1.13551	0.567755	−	0.823197i	$-0.307812\pi$
$43$	7.44604	1.13551	0.567755	+	0.823197i	$0.307812\pi$
$44$	1.02998	0.155275
$45$	22.2402	3.31537
$46$	−2.20919	−0.325727
$47$	−2.50260	−0.365041	−0.182521	−	0.983202i	$-0.558426\pi$
$47$	−2.50260	−0.365041	−0.182521	+	0.983202i	$0.558426\pi$
$48$	−2.94455	−0.425009
$49$	9.90656	1.41522
$50$	10.3834	1.46844
$51$	−6.20064	−0.868263
$52$	−4.94074	−0.685157
$53$	8.47104	1.16359	0.581794	−	0.813336i	$-0.302351\pi$
$53$	8.47104	1.16359	0.581794	+	0.813336i	$0.302351\pi$
$54$	−7.86307	−1.07003
$55$	4.03976	0.544721
$56$	4.11176	0.549457
$57$	−18.4188	−2.43962
$58$	−4.46014	−0.585645
$59$	9.52112	1.23954	0.619772	−	0.784782i	$-0.287225\pi$
$59$	9.52112	1.23954	0.619772	+	0.784782i	$0.287225\pi$
$60$	−11.5490	−1.49097
$61$	−1.39929	−0.179160	−0.0895801	−	0.995980i	$-0.528552\pi$
$61$	−1.39929	−0.179160	−0.0895801	+	0.995980i	$0.528552\pi$
$62$	−4.60356	−0.584652
$63$	23.3152	2.93744
$64$	1.00000	0.125000
$65$	−19.3784	−2.40360
$66$	−3.03283	−0.373316
$67$	−3.09067	−0.377585	−0.188793	−	0.982017i	$-0.560457\pi$
$67$	−3.09067	−0.377585	−0.188793	+	0.982017i	$0.560457\pi$
$68$	2.10580	0.255366
$69$	6.50507	0.783118
$70$	16.1270	1.92755
$71$	8.51965	1.01110	0.505548	−	0.862798i	$-0.331290\pi$
$71$	8.51965	1.01110	0.505548	+	0.862798i	$0.331290\pi$
$72$	5.67038	0.668261
$73$	−3.99445	−0.467515	−0.233757	−	0.972295i	$-0.575102\pi$
$73$	−3.99445	−0.467515	−0.233757	+	0.972295i	$0.575102\pi$
$74$	−1.93250	−0.224649
$75$	−30.5745	−3.53044
$76$	6.25520	0.717521
$77$	4.23503	0.482627
$78$	14.5483	1.64727
$79$	−7.22479	−0.812852	−0.406426	−	0.913684i	$-0.633225\pi$
$79$	−7.22479	−0.812852	−0.406426	+	0.913684i	$0.633225\pi$
$80$	3.92217	0.438512
$81$	6.14208	0.682453
$82$	5.65780	0.624799
$83$	4.94312	0.542578	0.271289	−	0.962498i	$-0.412550\pi$
$83$	4.94312	0.542578	0.271289	+	0.962498i	$0.412550\pi$
$84$	−12.1073	−1.32101
$85$	8.25931	0.895848
$86$	7.44604	0.802927
$87$	13.1331	1.40802
$88$	1.02998	0.109796
$89$	−9.56229	−1.01360	−0.506800	−	0.862063i	$-0.669172\pi$
$89$	−9.56229	−1.01360	−0.506800	+	0.862063i	$0.669172\pi$
$90$	22.2402	2.34432
$91$	−20.3151	−2.12960
$92$	−2.20919	−0.230324
$93$	13.5554	1.40563
$94$	−2.50260	−0.258123
$95$	24.5340	2.51713
$96$	−2.94455	−0.300527
$97$	1.33617	0.135667	0.0678336	−	0.997697i	$-0.478391\pi$
$97$	1.33617	0.135667	0.0678336	+	0.997697i	$0.478391\pi$
$98$	9.90656	1.00071
$99$	5.84039	0.586981
$100$	10.3834	1.03834
$101$	3.55459	0.353695	0.176847	−	0.984238i	$-0.443410\pi$
$101$	3.55459	0.353695	0.176847	+	0.984238i	$0.443410\pi$
$102$	−6.20064	−0.613955
$103$	14.1508	1.39432	0.697159	−	0.716917i	$-0.254447\pi$
$103$	14.1508	1.39432	0.697159	+	0.716917i	$0.254447\pi$
$104$	−4.94074	−0.484479
$105$	−47.4868	−4.63424
$106$	8.47104	0.822781
$107$	−12.1633	−1.17587	−0.587935	−	0.808908i	$-0.700059\pi$
$107$	−12.1633	−1.17587	−0.587935	+	0.808908i	$0.700059\pi$
$108$	−7.86307	−0.756625
$109$	−7.72821	−0.740228	−0.370114	−	0.928986i	$-0.620681\pi$
$109$	−7.72821	−0.740228	−0.370114	+	0.928986i	$0.620681\pi$
$110$	4.03976	0.385176
$111$	5.69036	0.540105
$112$	4.11176	0.388525
$113$	15.9759	1.50289	0.751444	−	0.659797i	$-0.229358\pi$
$113$	15.9759	1.50289	0.751444	+	0.659797i	$0.229358\pi$
$114$	−18.4188	−1.72507
$115$	−8.66481	−0.807998
$116$	−4.46014	−0.414113
$117$	−28.0159	−2.59007
$118$	9.52112	0.876491
$119$	8.65854	0.793727
$120$	−11.5490	−1.05428
$121$	−9.93914	−0.903558
$122$	−1.39929	−0.126685
$123$	−16.6597	−1.50215
$124$	−4.60356	−0.413412
$125$	21.1147	1.88856
$126$	23.3152	2.07709
$127$	13.3013	1.18030	0.590148	−	0.807295i	$-0.299069\pi$
$127$	13.3013	1.18030	0.590148	+	0.807295i	$0.299069\pi$
$128$	1.00000	0.0883883
$129$	−21.9253	−1.93041
$130$	−19.3784	−1.69960
$131$	−21.7679	−1.90187	−0.950936	−	0.309388i	$-0.899876\pi$
$131$	−21.7679	−1.90187	−0.950936	+	0.309388i	$0.899876\pi$
$132$	−3.03283	−0.263974
$133$	25.7199	2.23020
$134$	−3.09067	−0.266993
$135$	−30.8403	−2.65431
$136$	2.10580	0.180571
$137$	−19.0427	−1.62693	−0.813463	−	0.581617i	$-0.802420\pi$
$137$	−19.0427	−1.62693	−0.813463	+	0.581617i	$0.802420\pi$
$138$	6.50507	0.553748
$139$	5.97052	0.506413	0.253207	−	0.967412i	$-0.418515\pi$
$139$	5.97052	0.506413	0.253207	+	0.967412i	$0.418515\pi$
$140$	16.1270	1.36298
$141$	7.36902	0.620583
$142$	8.51965	0.714953
$143$	−5.08887	−0.425553
$144$	5.67038	0.472532
$145$	−17.4934	−1.45275
$146$	−3.99445	−0.330583
$147$	−29.1704	−2.40593
$148$	−1.93250	−0.158851
$149$	−20.9939	−1.71989	−0.859945	−	0.510387i	$-0.829502\pi$
$149$	−20.9939	−1.71989	−0.859945	+	0.510387i	$0.829502\pi$
$150$	−30.5745	−2.49640
$151$	−18.4700	−1.50307	−0.751533	−	0.659695i	$-0.770685\pi$
$151$	−18.4700	−1.50307	−0.751533	+	0.659695i	$0.770685\pi$
$152$	6.25520	0.507364
$153$	11.9407	0.965348
$154$	4.23503	0.341269
$155$	−18.0559	−1.45029
$156$	14.5483	1.16479
$157$	−0.274717	−0.0219248	−0.0109624	−	0.999940i	$-0.503490\pi$
$157$	−0.274717	−0.0219248	−0.0109624	+	0.999940i	$0.503490\pi$
$158$	−7.22479	−0.574773
$159$	−24.9434	−1.97814
$160$	3.92217	0.310075
$161$	−9.08365	−0.715892
$162$	6.14208	0.482567
$163$	10.8580	0.850468	0.425234	−	0.905084i	$-0.360192\pi$
$163$	10.8580	0.850468	0.425234	+	0.905084i	$0.360192\pi$
$164$	5.65780	0.441800
$165$	−11.8953	−0.926047
$166$	4.94312	0.383660
$167$	−8.00685	−0.619589	−0.309795	−	0.950804i	$-0.600260\pi$
$167$	−8.00685	−0.619589	−0.309795	+	0.950804i	$0.600260\pi$
$168$	−12.1073	−0.934097
$169$	11.4109	0.877763
$170$	8.25931	0.633460
$171$	35.4694	2.71241
$172$	7.44604	0.567755
$173$	−9.23675	−0.702257	−0.351129	−	0.936327i	$-0.614202\pi$
$173$	−9.23675	−0.702257	−0.351129	+	0.936327i	$0.614202\pi$
$174$	13.1331	0.995618
$175$	42.6941	3.22737
$176$	1.02998	0.0776377
$177$	−28.0354	−2.10727
$178$	−9.56229	−0.716724
$179$	13.4442	1.00487	0.502434	−	0.864615i	$-0.332438\pi$
$179$	13.4442	1.00487	0.502434	+	0.864615i	$0.332438\pi$
$180$	22.2402	1.65769
$181$	−15.9593	−1.18625	−0.593124	−	0.805111i	$-0.702106\pi$
$181$	−15.9593	−1.18625	−0.593124	+	0.805111i	$0.702106\pi$
$182$	−20.3151	−1.50586
$183$	4.12027	0.304579
$184$	−2.20919	−0.162863
$185$	−7.57961	−0.557264
$186$	13.5554	0.993931
$187$	2.16894	0.158608
$188$	−2.50260	−0.182521
$189$	−32.3311	−2.35174
$190$	24.5340	1.77988
$191$	4.13522	0.299214	0.149607	−	0.988746i	$-0.452199\pi$
$191$	4.13522	0.299214	0.149607	+	0.988746i	$0.452199\pi$
$192$	−2.94455	−0.212505
$193$	−11.5817	−0.833665	−0.416833	−	0.908983i	$-0.636860\pi$
$193$	−11.5817	−0.833665	−0.416833	+	0.908983i	$0.636860\pi$
$194$	1.33617	0.0959313
$195$	57.0608	4.08621
$196$	9.90656	0.707611
$197$	−3.99173	−0.284399	−0.142200	−	0.989838i	$-0.545418\pi$
$197$	−3.99173	−0.284399	−0.142200	+	0.989838i	$0.545418\pi$
$198$	5.84039	0.415058
$199$	7.14816	0.506720	0.253360	−	0.967372i	$-0.418464\pi$
$199$	7.14816	0.506720	0.253360	+	0.967372i	$0.418464\pi$
$200$	10.3834	0.734219
$201$	9.10063	0.641909
$202$	3.55459	0.250100
$203$	−18.3390	−1.28715
$204$	−6.20064	−0.434132
$205$	22.1909	1.54988
$206$	14.1508	0.985931
$207$	−12.5269	−0.870682
$208$	−4.94074	−0.342579
$209$	6.44274	0.445654
$210$	−47.4868	−3.27690
$211$	22.5598	1.55308	0.776540	−	0.630068i	$-0.216973\pi$
$211$	22.5598	1.55308	0.776540	+	0.630068i	$0.216973\pi$
$212$	8.47104	0.581794
$213$	−25.0865	−1.71890
$214$	−12.1633	−0.831466
$215$	29.2047	1.99174
$216$	−7.86307	−0.535014
$217$	−18.9287	−1.28496
$218$	−7.72821	−0.523420
$219$	11.7619	0.794792
$220$	4.03976	0.272361
$221$	−10.4042	−0.699863
$222$	5.69036	0.381912
$223$	−6.31823	−0.423100	−0.211550	−	0.977367i	$-0.567851\pi$
$223$	−6.31823	−0.423100	−0.211550	+	0.977367i	$0.567851\pi$
$224$	4.11176	0.274728
$225$	58.8780	3.92520
$226$	15.9759	1.06270
$227$	24.5142	1.62706	0.813532	−	0.581520i	$-0.197542\pi$
$227$	24.5142	1.62706	0.813532	+	0.581520i	$0.197542\pi$
$228$	−18.4188	−1.21981
$229$	24.6835	1.63113	0.815565	−	0.578665i	$-0.196426\pi$
$229$	24.6835	1.63113	0.815565	+	0.578665i	$0.196426\pi$
$230$	−8.66481	−0.571341
$231$	−12.4703	−0.820484
$232$	−4.46014	−0.292822
$233$	20.6435	1.35240	0.676201	−	0.736717i	$-0.263625\pi$
$233$	20.6435	1.35240	0.676201	+	0.736717i	$0.263625\pi$
$234$	−28.0159	−1.83146
$235$	−9.81561	−0.640300
$236$	9.52112	0.619772
$237$	21.2738	1.38188
$238$	8.65854	0.561250
$239$	19.0423	1.23175	0.615873	−	0.787846i	$-0.288804\pi$
$239$	19.0423	1.23175	0.615873	+	0.787846i	$0.288804\pi$
$240$	−11.5490	−0.745487
$241$	18.0799	1.16463	0.582313	−	0.812964i	$-0.302148\pi$
$241$	18.0799	1.16463	0.582313	+	0.812964i	$0.302148\pi$
$242$	−9.93914	−0.638912
$243$	5.50355	0.353053
$244$	−1.39929	−0.0895801
$245$	38.8552	2.48237
$246$	−16.6597	−1.06218
$247$	−30.9053	−1.96646
$248$	−4.60356	−0.292326
$249$	−14.5553	−0.922402
$250$	21.1147	1.33541
$251$	−16.0910	−1.01566	−0.507828	−	0.861459i	$-0.669551\pi$
$251$	−16.0910	−1.01566	−0.507828	+	0.861459i	$0.669551\pi$
$252$	23.3152	1.46872
$253$	−2.27542	−0.143055
$254$	13.3013	0.834596
$255$	−24.3200	−1.52298
$256$	1.00000	0.0625000
$257$	15.0980	0.941787	0.470893	−	0.882190i	$-0.343932\pi$
$257$	15.0980	0.941787	0.470893	+	0.882190i	$0.343932\pi$
$258$	−21.9253	−1.36501
$259$	−7.94599	−0.493740
$260$	−19.3784	−1.20180
$261$	−25.2907	−1.56545
$262$	−21.7679	−1.34483
$263$	29.1849	1.79962	0.899809	−	0.436284i	$-0.143706\pi$
$263$	29.1849	1.79962	0.899809	+	0.436284i	$0.143706\pi$
$264$	−3.03283	−0.186658
$265$	33.2249	2.04099
$266$	25.7199	1.57699
$267$	28.1567	1.72316
$268$	−3.09067	−0.188793
$269$	−28.0648	−1.71114	−0.855570	−	0.517688i	$-0.826793\pi$
$269$	−28.0648	−1.71114	−0.855570	+	0.517688i	$0.826793\pi$
$270$	−30.8403	−1.87688
$271$	−9.08897	−0.552115	−0.276058	−	0.961141i	$-0.589028\pi$
$271$	−9.08897	−0.552115	−0.276058	+	0.961141i	$0.589028\pi$
$272$	2.10580	0.127683
$273$	59.8189	3.62041
$274$	−19.0427	−1.15041
$275$	10.6947	0.644917
$276$	6.50507	0.391559
$277$	−2.82397	−0.169676	−0.0848381	−	0.996395i	$-0.527037\pi$
$277$	−2.82397	−0.169676	−0.0848381	+	0.996395i	$0.527037\pi$
$278$	5.97052	0.358088
$279$	−26.1039	−1.56280
$280$	16.1270	0.963774
$281$	−29.6622	−1.76950	−0.884748	−	0.466069i	$-0.845670\pi$
$281$	−29.6622	−1.76950	−0.884748	+	0.466069i	$0.845670\pi$
$282$	7.36902	0.438819
$283$	1.97216	0.117232	0.0586162	−	0.998281i	$-0.481331\pi$
$283$	1.97216	0.117232	0.0586162	+	0.998281i	$0.481331\pi$
$284$	8.51965	0.505548
$285$	−72.2415	−4.27922
$286$	−5.08887	−0.300911
$287$	23.2635	1.37320
$288$	5.67038	0.334130
$289$	−12.5656	−0.739153
$290$	−17.4934	−1.02725
$291$	−3.93441	−0.230639
$292$	−3.99445	−0.233757
$293$	−25.9350	−1.51514	−0.757569	−	0.652756i	$-0.773613\pi$
$293$	−25.9350	−1.51514	−0.757569	+	0.652756i	$0.773613\pi$
$294$	−29.1704	−1.70125
$295$	37.3435	2.17422
$296$	−1.93250	−0.112325
$297$	−8.09882	−0.469941
$298$	−20.9939	−1.21615
$299$	10.9150	0.631232
$300$	−30.5745	−1.76522
$301$	30.6163	1.76470
$302$	−18.4700	−1.06283
$303$	−10.4667	−0.601295
$304$	6.25520	0.358760
$305$	−5.48824	−0.314256
$306$	11.9407	0.682604
$307$	−20.8008	−1.18717	−0.593583	−	0.804773i	$-0.702287\pi$
$307$	−20.8008	−1.18717	−0.593583	+	0.804773i	$0.702287\pi$
$308$	4.23503	0.241313
$309$	−41.6677	−2.37039
$310$	−18.0559	−1.02551
$311$	29.3554	1.66459	0.832297	−	0.554330i	$-0.187026\pi$
$311$	29.3554	1.66459	0.832297	+	0.554330i	$0.187026\pi$
$312$	14.5483	0.823633
$313$	8.50388	0.480668	0.240334	−	0.970690i	$-0.422743\pi$
$313$	8.50388	0.480668	0.240334	+	0.970690i	$0.422743\pi$
$314$	−0.274717	−0.0155032
$315$	91.4464	5.15242
$316$	−7.22479	−0.406426
$317$	5.38318	0.302349	0.151175	−	0.988507i	$-0.451694\pi$
$317$	5.38318	0.302349	0.151175	+	0.988507i	$0.451694\pi$
$318$	−24.9434	−1.39876
$319$	−4.59386	−0.257207
$320$	3.92217	0.219256
$321$	35.8155	1.99902
$322$	−9.08365	−0.506212
$323$	13.1722	0.732921
$324$	6.14208	0.341227
$325$	−51.3018	−2.84571
$326$	10.8580	0.601371
$327$	22.7561	1.25842
$328$	5.65780	0.312400
$329$	−10.2901	−0.567310
$330$	−11.8953	−0.654814
$331$	−3.40324	−0.187059	−0.0935294	−	0.995617i	$-0.529815\pi$
$331$	−3.40324	−0.187059	−0.0935294	+	0.995617i	$0.529815\pi$
$332$	4.94312	0.271289
$333$	−10.9580	−0.600497
$334$	−8.00685	−0.438116
$335$	−12.1221	−0.662302
$336$	−12.1073	−0.660506
$337$	9.82078	0.534972	0.267486	−	0.963562i	$-0.413807\pi$
$337$	9.82078	0.534972	0.267486	+	0.963562i	$0.413807\pi$
$338$	11.4109	0.620672
$339$	−47.0419	−2.55497
$340$	8.25931	0.447924
$341$	−4.74158	−0.256771
$342$	35.4694	1.91796
$343$	11.9511	0.645297
$344$	7.44604	0.401464
$345$	25.5140	1.37363
$346$	−9.23675	−0.496571
$347$	12.6673	0.680014	0.340007	−	0.940423i	$-0.389571\pi$
$347$	12.6673	0.680014	0.340007	+	0.940423i	$0.389571\pi$
$348$	13.1331	0.704008
$349$	16.9810	0.908974	0.454487	−	0.890753i	$-0.349823\pi$
$349$	16.9810	0.908974	0.454487	+	0.890753i	$0.349823\pi$
$350$	42.6941	2.28210
$351$	38.8494	2.07363
$352$	1.02998	0.0548982
$353$	11.8527	0.630854	0.315427	−	0.948950i	$-0.397852\pi$
$353$	11.8527	0.630854	0.315427	+	0.948950i	$0.397852\pi$
$354$	−28.0354	−1.49007
$355$	33.4155	1.77351
$356$	−9.56229	−0.506800
$357$	−25.4955	−1.34937
$358$	13.4442	0.710549
$359$	−30.9608	−1.63405	−0.817024	−	0.576604i	$-0.804378\pi$
$359$	−30.9608	−1.63405	−0.817024	+	0.576604i	$0.804378\pi$
$360$	22.2402	1.17216
$361$	20.1275	1.05934
$362$	−15.9593	−0.838805
$363$	29.2663	1.53608
$364$	−20.3151	−1.06480
$365$	−15.6669	−0.820043
$366$	4.12027	0.215370
$367$	24.7004	1.28935	0.644675	−	0.764457i	$-0.276993\pi$
$367$	24.7004	1.28935	0.644675	+	0.764457i	$0.276993\pi$
$368$	−2.20919	−0.115162
$369$	32.0819	1.67012
$370$	−7.57961	−0.394045
$371$	34.8309	1.80833
$372$	13.5554	0.702815
$373$	−28.5385	−1.47767	−0.738835	−	0.673886i	$-0.764624\pi$
$373$	−28.5385	−1.47767	−0.738835	+	0.673886i	$0.764624\pi$
$374$	2.16894	0.112153
$375$	−62.1734	−3.21062
$376$	−2.50260	−0.129062
$377$	22.0364	1.13493
$378$	−32.3311	−1.66293
$379$	−28.8227	−1.48052	−0.740261	−	0.672320i	$-0.765298\pi$
$379$	−28.8227	−1.48052	−0.740261	+	0.672320i	$0.765298\pi$
$380$	24.5340	1.25857
$381$	−39.1663	−2.00655
$382$	4.13522	0.211576
$383$	−16.0747	−0.821376	−0.410688	−	0.911776i	$-0.634712\pi$
$383$	−16.0747	−0.821376	−0.410688	+	0.911776i	$0.634712\pi$
$384$	−2.94455	−0.150263
$385$	16.6105	0.846551
$386$	−11.5817	−0.589491
$387$	42.2219	2.14626
$388$	1.33617	0.0678336
$389$	−15.4651	−0.784114	−0.392057	−	0.919941i	$-0.628236\pi$
$389$	−15.4651	−0.784114	−0.392057	+	0.919941i	$0.628236\pi$
$390$	57.0608	2.88938
$391$	−4.65211	−0.235267
$392$	9.90656	0.500357
$393$	64.0967	3.23325
$394$	−3.99173	−0.201101
$395$	−28.3368	−1.42578
$396$	5.84039	0.293490
$397$	20.9132	1.04960	0.524801	−	0.851225i	$-0.324140\pi$
$397$	20.9132	1.04960	0.524801	+	0.851225i	$0.324140\pi$
$398$	7.14816	0.358305
$399$	−75.7335	−3.79142
$400$	10.3834	0.519171
$401$	34.6561	1.73064	0.865321	−	0.501218i	$-0.167114\pi$
$401$	34.6561	1.73064	0.865321	+	0.501218i	$0.167114\pi$
$402$	9.10063	0.453898
$403$	22.7450	1.13301
$404$	3.55459	0.176847
$405$	24.0903	1.19706
$406$	−18.3390	−0.910150
$407$	−1.99044	−0.0986626
$408$	−6.20064	−0.306977
$409$	−4.45201	−0.220138	−0.110069	−	0.993924i	$-0.535107\pi$
$409$	−4.45201	−0.220138	−0.110069	+	0.993924i	$0.535107\pi$
$410$	22.1909	1.09593
$411$	56.0721	2.76583
$412$	14.1508	0.697159
$413$	39.1486	1.92638
$414$	−12.5269	−0.615665
$415$	19.3878	0.951707
$416$	−4.94074	−0.242240
$417$	−17.5805	−0.860921
$418$	6.44274	0.315125
$419$	−16.7086	−0.816267	−0.408133	−	0.912922i	$-0.633820\pi$
$419$	−16.7086	−0.816267	−0.408133	+	0.912922i	$0.633820\pi$
$420$	−47.4868	−2.31712
$421$	−16.6892	−0.813382	−0.406691	−	0.913566i	$-0.633317\pi$
$421$	−16.6892	−0.813382	−0.406691	+	0.913566i	$0.633317\pi$
$422$	22.5598	1.09819
$423$	−14.1907	−0.689974
$424$	8.47104	0.411390
$425$	21.8654	1.06063
$426$	−25.0865	−1.21545
$427$	−5.75352	−0.278433
$428$	−12.1633	−0.587935
$429$	14.9844	0.723455
$430$	29.2047	1.40837
$431$	13.2993	0.640606	0.320303	−	0.947315i	$-0.396215\pi$
$431$	13.2993	0.640606	0.320303	+	0.947315i	$0.396215\pi$
$432$	−7.86307	−0.378312
$433$	−18.6592	−0.896703	−0.448351	−	0.893857i	$-0.647989\pi$
$433$	−18.6592	−0.896703	−0.448351	+	0.893857i	$0.647989\pi$
$434$	−18.9287	−0.908607
$435$	51.5103	2.46973
$436$	−7.72821	−0.370114
$437$	−13.8189	−0.661048
$438$	11.7619	0.562003
$439$	9.57964	0.457211	0.228606	−	0.973519i	$-0.426583\pi$
$439$	9.57964	0.457211	0.228606	+	0.973519i	$0.426583\pi$
$440$	4.03976	0.192588
$441$	56.1740	2.67495
$442$	−10.4042	−0.494878
$443$	−7.91109	−0.375867	−0.187934	−	0.982182i	$-0.560179\pi$
$443$	−7.91109	−0.375867	−0.187934	+	0.982182i	$0.560179\pi$
$444$	5.69036	0.270052
$445$	−37.5049	−1.77790
$446$	−6.31823	−0.299177
$447$	61.8177	2.92388
$448$	4.11176	0.194262
$449$	6.14953	0.290214	0.145107	−	0.989416i	$-0.453647\pi$
$449$	6.14953	0.290214	0.145107	+	0.989416i	$0.453647\pi$
$450$	58.8780	2.77553
$451$	5.82743	0.274403
$452$	15.9759	0.751444
$453$	54.3858	2.55527
$454$	24.5142	1.15051
$455$	−79.6794	−3.73543
$456$	−18.4188	−0.862537
$457$	−16.2463	−0.759968	−0.379984	−	0.924993i	$-0.624070\pi$
$457$	−16.2463	−0.759968	−0.379984	+	0.924993i	$0.624070\pi$
$458$	24.6835	1.15338
$459$	−16.5581	−0.772864
$460$	−8.66481	−0.403999
$461$	−19.1425	−0.891554	−0.445777	−	0.895144i	$-0.647073\pi$
$461$	−19.1425	−0.891554	−0.445777	+	0.895144i	$0.647073\pi$
$462$	−12.4703	−0.580170
$463$	12.0943	0.562069	0.281034	−	0.959698i	$-0.409323\pi$
$463$	12.0943	0.562069	0.281034	+	0.959698i	$0.409323\pi$
$464$	−4.46014	−0.207057
$465$	53.1666	2.46554
$466$	20.6435	0.956293
$467$	27.9099	1.29152	0.645758	−	0.763542i	$-0.276541\pi$
$467$	27.9099	1.29152	0.645758	+	0.763542i	$0.276541\pi$
$468$	−28.0159	−1.29503
$469$	−12.7081	−0.586804
$470$	−9.81561	−0.452760
$471$	0.808919	0.0372730
$472$	9.52112	0.438245
$473$	7.66928	0.352634
$474$	21.2738	0.977136
$475$	64.9504	2.98013
$476$	8.65854	0.396864
$477$	48.0341	2.19933
$478$	19.0423	0.870975
$479$	−2.41633	−0.110405	−0.0552024	−	0.998475i	$-0.517580\pi$
$479$	−2.41633	−0.110405	−0.0552024	+	0.998475i	$0.517580\pi$
$480$	−11.5490	−0.527139
$481$	9.54800	0.435351
$482$	18.0799	0.823515
$483$	26.7473	1.21704
$484$	−9.93914	−0.451779
$485$	5.24068	0.237967
$486$	5.50355	0.249646
$487$	11.8739	0.538058	0.269029	−	0.963132i	$-0.413297\pi$
$487$	11.8739	0.538058	0.269029	+	0.963132i	$0.413297\pi$
$488$	−1.39929	−0.0633427
$489$	−31.9721	−1.44583
$490$	38.8552	1.75530
$491$	−25.7841	−1.16362	−0.581811	−	0.813324i	$-0.697656\pi$
$491$	−25.7841	−1.16362	−0.581811	+	0.813324i	$0.697656\pi$
$492$	−16.6597	−0.751076
$493$	−9.39216	−0.423002
$494$	−30.9053	−1.39050
$495$	22.9070	1.02959
$496$	−4.60356	−0.206706
$497$	35.0307	1.57134
$498$	−14.5553	−0.652237
$499$	22.1017	0.989406	0.494703	−	0.869062i	$-0.335277\pi$
$499$	22.1017	0.989406	0.494703	+	0.869062i	$0.335277\pi$
$500$	21.1147	0.944279
$501$	23.5766	1.05332
$502$	−16.0910	−0.718177
$503$	26.6878	1.18995	0.594974	−	0.803745i	$-0.297162\pi$
$503$	26.6878	1.18995	0.594974	+	0.803745i	$0.297162\pi$
$504$	23.3152	1.03854
$505$	13.9417	0.620398
$506$	−2.27542	−0.101155
$507$	−33.6000	−1.49223
$508$	13.3013	0.590148
$509$	9.33750	0.413878	0.206939	−	0.978354i	$-0.433650\pi$
$509$	9.33750	0.413878	0.206939	+	0.978354i	$0.433650\pi$
$510$	−24.3200	−1.07691
$511$	−16.4242	−0.726564
$512$	1.00000	0.0441942
$513$	−49.1851	−2.17158
$514$	15.0980	0.665944
$515$	55.5018	2.44570
$516$	−21.9253	−0.965206
$517$	−2.57763	−0.113364
$518$	−7.94599	−0.349127
$519$	27.1981	1.19386
$520$	−19.3784	−0.849800
$521$	9.67529	0.423882	0.211941	−	0.977282i	$-0.432021\pi$
$521$	9.67529	0.423882	0.211941	+	0.977282i	$0.432021\pi$
$522$	−25.2907	−1.10694
$523$	−4.15314	−0.181604	−0.0908020	−	0.995869i	$-0.528943\pi$
$523$	−4.15314	−0.181604	−0.0908020	+	0.995869i	$0.528943\pi$
$524$	−21.7679	−0.950936
$525$	−125.715	−5.48666
$526$	29.1849	1.27252
$527$	−9.69417	−0.422285
$528$	−3.03283	−0.131987
$529$	−18.1195	−0.787804
$530$	33.2249	1.44320
$531$	53.9884	2.34290
$532$	25.7199	1.11510
$533$	−27.9537	−1.21081
$534$	28.1567	1.21846
$535$	−47.7066	−2.06253
$536$	−3.09067	−0.133496
$537$	−39.5872	−1.70831
$538$	−28.0648	−1.20996
$539$	10.2036	0.439499
$540$	−30.8403	−1.32716
$541$	−28.9984	−1.24674	−0.623370	−	0.781927i	$-0.714237\pi$
$541$	−28.9984	−1.24674	−0.623370	+	0.781927i	$0.714237\pi$
$542$	−9.08897	−0.390405
$543$	46.9931	2.01667
$544$	2.10580	0.0902855
$545$	−30.3113	−1.29840
$546$	59.8189	2.56001
$547$	−35.1756	−1.50400	−0.751999	−	0.659164i	$-0.770910\pi$
$547$	−35.1756	−1.50400	−0.751999	+	0.659164i	$0.770910\pi$
$548$	−19.0427	−0.813463
$549$	−7.93448	−0.338635
$550$	10.6947	0.456025
$551$	−27.8991	−1.18854
$552$	6.50507	0.276874
$553$	−29.7066	−1.26325
$554$	−2.82397	−0.119979
$555$	22.3186	0.947370
$556$	5.97052	0.253207
$557$	−29.8949	−1.26669	−0.633344	−	0.773871i	$-0.718318\pi$
$557$	−29.8949	−1.26669	−0.633344	+	0.773871i	$0.718318\pi$
$558$	−26.1039	−1.10507
$559$	−36.7890	−1.55601
$560$	16.1270	0.681491
$561$	−6.38654	−0.269640
$562$	−29.6622	−1.25122
$563$	−29.1092	−1.22681	−0.613404	−	0.789769i	$-0.710200\pi$
$563$	−29.1092	−1.22681	−0.613404	+	0.789769i	$0.710200\pi$
$564$	7.36902	0.310292
$565$	62.6603	2.63614
$566$	1.97216	0.0828959
$567$	25.2548	1.06060
$568$	8.51965	0.357476
$569$	14.3514	0.601642	0.300821	−	0.953681i	$-0.402739\pi$
$569$	14.3514	0.601642	0.300821	+	0.953681i	$0.402739\pi$
$570$	−72.2415	−3.02586
$571$	13.4411	0.562493	0.281247	−	0.959635i	$-0.409252\pi$
$571$	13.4411	0.562493	0.281247	+	0.959635i	$0.409252\pi$
$572$	−5.08887	−0.212776
$573$	−12.1764	−0.508675
$574$	23.2635	0.971000
$575$	−22.9389	−0.956620
$576$	5.67038	0.236266
$577$	10.6132	0.441832	0.220916	−	0.975293i	$-0.429095\pi$
$577$	10.6132	0.441832	0.220916	+	0.975293i	$0.429095\pi$
$578$	−12.5656	−0.522660
$579$	34.1028	1.41726
$580$	−17.4934	−0.726375
$581$	20.3249	0.843219
$582$	−3.93441	−0.163087
$583$	8.72502	0.361353
$584$	−3.99445	−0.165291
$585$	−109.883	−4.54311
$586$	−25.9350	−1.07136
$587$	22.5510	0.930780	0.465390	−	0.885106i	$-0.345914\pi$
$587$	22.5510	0.930780	0.465390	+	0.885106i	$0.345914\pi$
$588$	−29.1704	−1.20297
$589$	−28.7962	−1.18653
$590$	37.3435	1.53741
$591$	11.7539	0.483489
$592$	−1.93250	−0.0794254
$593$	17.0871	0.701685	0.350842	−	0.936435i	$-0.385895\pi$
$593$	17.0871	0.701685	0.350842	+	0.936435i	$0.385895\pi$
$594$	−8.09882	−0.332299
$595$	33.9603	1.39224
$596$	−20.9939	−0.859945
$597$	−21.0481	−0.861443
$598$	10.9150	0.446349
$599$	−5.81903	−0.237759	−0.118880	−	0.992909i	$-0.537930\pi$
$599$	−5.81903	−0.237759	−0.118880	+	0.992909i	$0.537930\pi$
$600$	−30.5745	−1.24820
$601$	−12.3378	−0.503270	−0.251635	−	0.967822i	$-0.580968\pi$
$601$	−12.3378	−0.503270	−0.251635	+	0.967822i	$0.580968\pi$
$602$	30.6163	1.24783
$603$	−17.5253	−0.713684
$604$	−18.4700	−0.751533
$605$	−38.9830	−1.58488
$606$	−10.4667	−0.425179
$607$	14.4126	0.584989	0.292495	−	0.956267i	$-0.405515\pi$
$607$	14.4126	0.584989	0.292495	+	0.956267i	$0.405515\pi$
$608$	6.25520	0.253682
$609$	54.0002	2.18820
$610$	−5.48824	−0.222212
$611$	12.3647	0.500221
$612$	11.9407	0.482674
$613$	−10.0908	−0.407565	−0.203783	−	0.979016i	$-0.565324\pi$
$613$	−10.0908	−0.407565	−0.203783	+	0.979016i	$0.565324\pi$
$614$	−20.8008	−0.839453
$615$	−65.3421	−2.63485
$616$	4.23503	0.170634
$617$	−35.0823	−1.41236	−0.706180	−	0.708032i	$-0.749583\pi$
$617$	−35.0823	−1.41236	−0.706180	+	0.708032i	$0.749583\pi$
$618$	−41.6677	−1.67612
$619$	−10.2759	−0.413025	−0.206512	−	0.978444i	$-0.566211\pi$
$619$	−10.2759	−0.413025	−0.206512	+	0.978444i	$0.566211\pi$
$620$	−18.0559	−0.725144
$621$	17.3710	0.697075
$622$	29.3554	1.17705
$623$	−39.3178	−1.57524
$624$	14.5483	0.582397
$625$	30.8984	1.23594
$626$	8.50388	0.339883
$627$	−18.9710	−0.757628
$628$	−0.274717	−0.0109624
$629$	−4.06947	−0.162260
$630$	91.4464	3.64331
$631$	−2.77505	−0.110473	−0.0552364	−	0.998473i	$-0.517591\pi$
$631$	−2.77505	−0.110473	−0.0552364	+	0.998473i	$0.517591\pi$
$632$	−7.22479	−0.287387
$633$	−66.4285	−2.64029
$634$	5.38318	0.213793
$635$	52.1699	2.07030
$636$	−24.9434	−0.989071
$637$	−48.9457	−1.93930
$638$	−4.59386	−0.181873
$639$	48.3096	1.91110
$640$	3.92217	0.155037
$641$	43.7493	1.72799	0.863996	−	0.503498i	$-0.167954\pi$
$641$	43.7493	1.72799	0.863996	+	0.503498i	$0.167954\pi$
$642$	35.8155	1.41352
$643$	−22.4088	−0.883719	−0.441859	−	0.897084i	$-0.645681\pi$
$643$	−22.4088	−0.883719	−0.441859	+	0.897084i	$0.645681\pi$
$644$	−9.08365	−0.357946
$645$	−85.9946	−3.38603
$646$	13.1722	0.518254
$647$	44.4140	1.74609	0.873047	−	0.487636i	$-0.162141\pi$
$647$	44.4140	1.74609	0.873047	+	0.487636i	$0.162141\pi$
$648$	6.14208	0.241284
$649$	9.80658	0.384942
$650$	−51.3018	−2.01222
$651$	55.7366	2.18449
$652$	10.8580	0.425234
$653$	−5.30863	−0.207743	−0.103871	−	0.994591i	$-0.533123\pi$
$653$	−5.30863	−0.207743	−0.103871	+	0.994591i	$0.533123\pi$
$654$	22.7561	0.889834
$655$	−85.3775	−3.33597
$656$	5.65780	0.220900
$657$	−22.6500	−0.883662
$658$	−10.2901	−0.401149
$659$	21.1458	0.823723	0.411862	−	0.911246i	$-0.364879\pi$
$659$	21.1458	0.823723	0.411862	+	0.911246i	$0.364879\pi$
$660$	−11.8953	−0.463023
$661$	−40.3332	−1.56878	−0.784389	−	0.620269i	$-0.787023\pi$
$661$	−40.3332	−1.56878	−0.784389	+	0.620269i	$0.787023\pi$
$662$	−3.40324	−0.132271
$663$	30.6357	1.18979
$664$	4.94312	0.191830
$665$	100.878	3.91187
$666$	−10.9580	−0.424615
$667$	9.85328	0.381521
$668$	−8.00685	−0.309795
$669$	18.6044	0.719286
$670$	−12.1221	−0.468319
$671$	−1.44124	−0.0556384
$672$	−12.1073	−0.467049
$673$	−0.291878	−0.0112511	−0.00562553	−	0.999984i	$-0.501791\pi$
$673$	−0.291878	−0.0112511	−0.00562553	+	0.999984i	$0.501791\pi$
$674$	9.82078	0.378282
$675$	−81.6456	−3.14254
$676$	11.4109	0.438881
$677$	23.6103	0.907419	0.453710	−	0.891150i	$-0.350100\pi$
$677$	23.6103	0.907419	0.453710	+	0.891150i	$0.350100\pi$
$678$	−47.0419	−1.80663
$679$	5.49400	0.210840
$680$	8.25931	0.316730
$681$	−72.1833	−2.76607
$682$	−4.74158	−0.181564
$683$	15.7291	0.601859	0.300929	−	0.953646i	$-0.402703\pi$
$683$	15.7291	0.601859	0.300929	+	0.953646i	$0.402703\pi$
$684$	35.4694	1.35621
$685$	−74.6886	−2.85371
$686$	11.9511	0.456294
$687$	−72.6818	−2.77298
$688$	7.44604	0.283878
$689$	−41.8532	−1.59448
$690$	25.5140	0.971301
$691$	−37.8642	−1.44042	−0.720211	−	0.693755i	$-0.755955\pi$
$691$	−37.8642	−1.44042	−0.720211	+	0.693755i	$0.755955\pi$
$692$	−9.23675	−0.351129
$693$	24.0143	0.912226
$694$	12.6673	0.480843
$695$	23.4174	0.888273
$696$	13.1331	0.497809
$697$	11.9142	0.451282
$698$	16.9810	0.642742
$699$	−60.7859	−2.29913
$700$	42.6941	1.61369
$701$	−9.11094	−0.344115	−0.172058	−	0.985087i	$-0.555042\pi$
$701$	−9.11094	−0.344115	−0.172058	+	0.985087i	$0.555042\pi$
$702$	38.8494	1.46628
$703$	−12.0882	−0.455915
$704$	1.02998	0.0388189
$705$	28.9026	1.08853
$706$	11.8527	0.446081
$707$	14.6156	0.549677
$708$	−28.0354	−1.05364
$709$	24.5138	0.920635	0.460318	−	0.887754i	$-0.347736\pi$
$709$	24.5138	0.920635	0.460318	+	0.887754i	$0.347736\pi$
$710$	33.4155	1.25406
$711$	−40.9673	−1.53639
$712$	−9.56229	−0.358362
$713$	10.1701	0.380874
$714$	−25.4955	−0.954146
$715$	−19.9594	−0.746440
$716$	13.4442	0.502434
$717$	−56.0711	−2.09401
$718$	−30.9608	−1.15545
$719$	3.17470	0.118396	0.0591981	−	0.998246i	$-0.481146\pi$
$719$	3.17470	0.118396	0.0591981	+	0.998246i	$0.481146\pi$
$720$	22.2402	0.828844
$721$	58.1846	2.16691
$722$	20.1275	0.749069
$723$	−53.2371	−1.97991
$724$	−15.9593	−0.593124
$725$	−46.3115	−1.71997
$726$	29.2663	1.08617
$727$	44.7925	1.66126	0.830631	−	0.556823i	$-0.187980\pi$
$727$	44.7925	1.66126	0.830631	+	0.556823i	$0.187980\pi$
$728$	−20.3151	−0.752929
$729$	−34.6317	−1.28266
$730$	−15.6669	−0.579858
$731$	15.6799	0.579941
$732$	4.12027	0.152289
$733$	48.4544	1.78970	0.894852	−	0.446363i	$-0.147281\pi$
$733$	48.4544	1.78970	0.894852	+	0.446363i	$0.147281\pi$
$734$	24.7004	0.911709
$735$	−114.411	−4.22012
$736$	−2.20919	−0.0814317
$737$	−3.18333	−0.117259
$738$	32.0819	1.18095
$739$	−13.4063	−0.493160	−0.246580	−	0.969122i	$-0.579307\pi$
$739$	−13.4063	−0.493160	−0.246580	+	0.969122i	$0.579307\pi$
$740$	−7.57961	−0.278632
$741$	91.0023	3.34305
$742$	34.8309	1.27868
$743$	−38.5771	−1.41526	−0.707628	−	0.706585i	$-0.750235\pi$
$743$	−38.5771	−1.41526	−0.707628	+	0.706585i	$0.750235\pi$
$744$	13.5554	0.496965
$745$	−82.3418	−3.01677
$746$	−28.5385	−1.04487
$747$	28.0294	1.02554
$748$	2.16894	0.0793041
$749$	−50.0126	−1.82742
$750$	−62.1734	−2.27025
$751$	−0.140674	−0.00513326	−0.00256663	−	0.999997i	$-0.500817\pi$
$751$	−0.140674	−0.00513326	−0.00256663	+	0.999997i	$0.500817\pi$
$752$	−2.50260	−0.0912603
$753$	47.3808	1.72665
$754$	22.0364	0.802518
$755$	−72.4425	−2.63645
$756$	−32.3311	−1.17587
$757$	42.9410	1.56072	0.780359	−	0.625331i	$-0.215036\pi$
$757$	42.9410	1.56072	0.780359	+	0.625331i	$0.215036\pi$
$758$	−28.8227	−1.04689
$759$	6.70010	0.243198
$760$	24.5340	0.889940
$761$	26.5142	0.961139	0.480569	−	0.876957i	$-0.340430\pi$
$761$	26.5142	0.961139	0.480569	+	0.876957i	$0.340430\pi$
$762$	−39.1663	−1.41884
$763$	−31.7765	−1.15039
$764$	4.13522	0.149607
$765$	46.8334	1.69327
$766$	−16.0747	−0.580801
$767$	−47.0414	−1.69857
$768$	−2.94455	−0.106252
$769$	13.5614	0.489037	0.244519	−	0.969645i	$-0.421370\pi$
$769$	13.5614	0.489037	0.244519	+	0.969645i	$0.421370\pi$
$770$	16.6105	0.598602
$771$	−44.4568	−1.60107
$772$	−11.5817	−0.416833
$773$	23.1602	0.833014	0.416507	−	0.909133i	$-0.363254\pi$
$773$	23.1602	0.833014	0.416507	+	0.909133i	$0.363254\pi$
$774$	42.2219	1.51764
$775$	−47.8007	−1.71705
$776$	1.33617	0.0479656
$777$	23.3974	0.839376
$778$	−15.4651	−0.554452
$779$	35.3907	1.26800
$780$	57.0608	2.04310
$781$	8.77507	0.313997
$782$	−4.65211	−0.166359
$783$	35.0704	1.25331
$784$	9.90656	0.353806
$785$	−1.07749	−0.0384572
$786$	64.0967	2.28626
$787$	−18.8258	−0.671066	−0.335533	−	0.942028i	$-0.608916\pi$
$787$	−18.8258	−0.671066	−0.335533	+	0.942028i	$0.608916\pi$
$788$	−3.99173	−0.142200
$789$	−85.9364	−3.05942
$790$	−28.3368	−1.00818
$791$	65.6891	2.33564
$792$	5.84039	0.207529
$793$	6.91351	0.245506
$794$	20.9132	0.742181
$795$	−97.8324	−3.46976
$796$	7.14816	0.253360
$797$	12.7323	0.451000	0.225500	−	0.974243i	$-0.427599\pi$
$797$	12.7323	0.451000	0.225500	+	0.974243i	$0.427599\pi$
$798$	−75.7335	−2.68094
$799$	−5.26997	−0.186438
$800$	10.3834	0.367110
$801$	−54.2218	−1.91583
$802$	34.6561	1.22375
$803$	−4.11420	−0.145187
$804$	9.10063	0.320954
$805$	−35.6276	−1.25571
$806$	22.7450	0.801158
$807$	82.6381	2.90900
$808$	3.55459	0.125050
$809$	8.06799	0.283655	0.141828	−	0.989891i	$-0.454702\pi$
$809$	8.06799	0.283655	0.141828	+	0.989891i	$0.454702\pi$
$810$	24.0903	0.846447
$811$	−25.6990	−0.902414	−0.451207	−	0.892419i	$-0.649006\pi$
$811$	−25.6990	−0.902414	−0.451207	+	0.892419i	$0.649006\pi$
$812$	−18.3390	−0.643573
$813$	26.7629	0.938617
$814$	−1.99044	−0.0697650
$815$	42.5871	1.49176
$816$	−6.20064	−0.217066
$817$	46.5765	1.62951
$818$	−4.45201	−0.155661
$819$	−115.195	−4.02522
$820$	22.1909	0.774938
$821$	−25.7792	−0.899699	−0.449850	−	0.893104i	$-0.648522\pi$
$821$	−25.7792	−0.899699	−0.449850	+	0.893104i	$0.648522\pi$
$822$	56.0721	1.95574
$823$	20.8899	0.728175	0.364087	−	0.931365i	$-0.381381\pi$
$823$	20.8899	0.728175	0.364087	+	0.931365i	$0.381381\pi$
$824$	14.1508	0.492966
$825$	−31.4912	−1.09638
$826$	39.1486	1.36215
$827$	−32.6405	−1.13502	−0.567511	−	0.823366i	$-0.692093\pi$
$827$	−32.6405	−1.13502	−0.567511	+	0.823366i	$0.692093\pi$
$828$	−12.5269	−0.435341
$829$	16.9038	0.587094	0.293547	−	0.955945i	$-0.405164\pi$
$829$	16.9038	0.587094	0.293547	+	0.955945i	$0.405164\pi$
$830$	19.3878	0.672959
$831$	8.31534	0.288456
$832$	−4.94074	−0.171289
$833$	20.8612	0.722799
$834$	−17.5805	−0.608763
$835$	−31.4043	−1.08679
$836$	6.44274	0.222827
$837$	36.1981	1.25119
$838$	−16.7086	−0.577188
$839$	−52.6935	−1.81918	−0.909591	−	0.415504i	$-0.863605\pi$
$839$	−52.6935	−1.81918	−0.909591	+	0.415504i	$0.863605\pi$
$840$	−47.4868	−1.63845
$841$	−9.10717	−0.314040
$842$	−16.6892	−0.575148
$843$	87.3418	3.00821
$844$	22.5598	0.776540
$845$	44.7556	1.53964
$846$	−14.1907	−0.487885
$847$	−40.8673	−1.40422
$848$	8.47104	0.290897
$849$	−5.80711	−0.199300
$850$	21.8654	0.749978
$851$	4.26926	0.146349
$852$	−25.0865	−0.859451
$853$	15.1776	0.519672	0.259836	−	0.965653i	$-0.416332\pi$
$853$	15.1776	0.519672	0.259836	+	0.965653i	$0.416332\pi$
$854$	−5.75352	−0.196882
$855$	139.117	4.75770
$856$	−12.1633	−0.415733
$857$	−40.2756	−1.37579	−0.687895	−	0.725810i	$-0.741465\pi$
$857$	−40.2756	−1.37579	−0.687895	+	0.725810i	$0.741465\pi$
$858$	14.9844	0.511560
$859$	−25.5355	−0.871260	−0.435630	−	0.900126i	$-0.643474\pi$
$859$	−25.5355	−0.871260	−0.435630	+	0.900126i	$0.643474\pi$
$860$	29.2047	0.995870
$861$	−68.5006	−2.33449
$862$	13.2993	0.452977
$863$	−44.6394	−1.51954	−0.759771	−	0.650191i	$-0.774689\pi$
$863$	−44.6394	−1.51954	−0.759771	+	0.650191i	$0.774689\pi$
$864$	−7.86307	−0.267507
$865$	−36.2281	−1.23179
$866$	−18.6592	−0.634065
$867$	37.0001	1.25659
$868$	−18.9287	−0.642482
$869$	−7.44139	−0.252432
$870$	51.5103	1.74636
$871$	15.2702	0.517410
$872$	−7.72821	−0.261710
$873$	7.57658	0.256428
$874$	−13.8189	−0.467432
$875$	86.8186	2.93500
$876$	11.7619	0.397396
$877$	−5.34365	−0.180442	−0.0902210	−	0.995922i	$-0.528757\pi$
$877$	−5.34365	−0.180442	−0.0902210	+	0.995922i	$0.528757\pi$
$878$	9.57964	0.323297
$879$	76.3669	2.57579
$880$	4.03976	0.136180
$881$	41.2291	1.38904	0.694521	−	0.719472i	$-0.255616\pi$
$881$	41.2291	1.38904	0.694521	+	0.719472i	$0.255616\pi$
$882$	56.1740	1.89148
$883$	37.2525	1.25365	0.626823	−	0.779162i	$-0.284355\pi$
$883$	37.2525	1.25365	0.626823	+	0.779162i	$0.284355\pi$
$884$	−10.4042	−0.349932
$885$	−109.960	−3.69626
$886$	−7.91109	−0.265778
$887$	−20.5275	−0.689246	−0.344623	−	0.938741i	$-0.611993\pi$
$887$	−20.5275	−0.689246	−0.344623	+	0.938741i	$0.611993\pi$
$888$	5.69036	0.190956
$889$	54.6916	1.83430
$890$	−37.5049	−1.25717
$891$	6.32623	0.211937
$892$	−6.31823	−0.211550
$893$	−15.6542	−0.523849
$894$	61.8177	2.06749
$895$	52.7305	1.76259
$896$	4.11176	0.137364
$897$	−32.1398	−1.07312
$898$	6.14953	0.205213
$899$	20.5325	0.684797
$900$	58.8780	1.96260
$901$	17.8383	0.594281
$902$	5.82743	0.194032
$903$	−90.1514	−3.00005
$904$	15.9759	0.531351
$905$	−62.5953	−2.08074
$906$	54.3858	1.80685
$907$	−35.9072	−1.19228	−0.596139	−	0.802881i	$-0.703299\pi$
$907$	−35.9072	−1.19228	−0.596139	+	0.802881i	$0.703299\pi$
$908$	24.5142	0.813532
$909$	20.1559	0.668528
$910$	−79.6794	−2.64135
$911$	−31.6003	−1.04696	−0.523482	−	0.852037i	$-0.675367\pi$
$911$	−31.6003	−1.04696	−0.523482	+	0.852037i	$0.675367\pi$
$912$	−18.4188	−0.609906
$913$	5.09132	0.168498
$914$	−16.2463	−0.537378
$915$	16.1604	0.534246
$916$	24.6835	0.815565
$917$	−89.5044	−2.95570
$918$	−16.5581	−0.546498
$919$	21.8877	0.722009	0.361004	−	0.932564i	$-0.382434\pi$
$919$	21.8877	0.722009	0.361004	+	0.932564i	$0.382434\pi$
$920$	−8.66481	−0.285670
$921$	61.2491	2.01823
$922$	−19.1425	−0.630424
$923$	−42.0934	−1.38552
$924$	−12.4703	−0.410242
$925$	−20.0660	−0.659766
$926$	12.0943	0.397443
$927$	80.2403	2.63544
$928$	−4.46014	−0.146411
$929$	−39.4904	−1.29564	−0.647819	−	0.761794i	$-0.724319\pi$
$929$	−39.4904	−1.29564	−0.647819	+	0.761794i	$0.724319\pi$
$930$	53.1666	1.74340
$931$	61.9675	2.03090
$932$	20.6435	0.676201
$933$	−86.4386	−2.82987
$934$	27.9099	0.913240
$935$	8.50693	0.278206
$936$	−28.0159	−0.915728
$937$	−37.9399	−1.23944	−0.619721	−	0.784822i	$-0.712754\pi$
$937$	−37.9399	−1.23944	−0.619721	+	0.784822i	$0.712754\pi$
$938$	−12.7081	−0.414933
$939$	−25.0401	−0.817153
$940$	−9.81561	−0.320150
$941$	−22.6091	−0.737036	−0.368518	−	0.929621i	$-0.620135\pi$
$941$	−22.6091	−0.737036	−0.368518	+	0.929621i	$0.620135\pi$
$942$	0.808919	0.0263560
$943$	−12.4991	−0.407028
$944$	9.52112	0.309886
$945$	−126.808	−4.12506
$946$	7.66928	0.249350
$947$	−14.9394	−0.485466	−0.242733	−	0.970093i	$-0.578044\pi$
$947$	−14.9394	−0.485466	−0.242733	+	0.970093i	$0.578044\pi$
$948$	21.2738	0.690939
$949$	19.7355	0.640642
$950$	64.9504	2.10727
$951$	−15.8510	−0.514005
$952$	8.65854	0.280625
$953$	17.7735	0.575740	0.287870	−	0.957669i	$-0.407053\pi$
$953$	17.7735	0.575740	0.287870	+	0.957669i	$0.407053\pi$
$954$	48.0341	1.55516
$955$	16.2190	0.524836
$956$	19.0423	0.615873
$957$	13.5268	0.437261
$958$	−2.41633	−0.0780680
$959$	−78.2989	−2.52840
$960$	−11.5490	−0.372743
$961$	−9.80727	−0.316363
$962$	9.54800	0.307840
$963$	−68.9706	−2.22255
$964$	18.0799	0.582313
$965$	−45.4252	−1.46229
$966$	26.7473	0.860579
$967$	21.7645	0.699898	0.349949	−	0.936769i	$-0.386199\pi$
$967$	21.7645	0.699898	0.349949	+	0.936769i	$0.386199\pi$
$968$	−9.93914	−0.319456
$969$	−38.7862	−1.24599
$970$	5.24068	0.168268
$971$	−12.6315	−0.405363	−0.202681	−	0.979245i	$-0.564966\pi$
$971$	−12.6315	−0.405363	−0.202681	+	0.979245i	$0.564966\pi$
$972$	5.50355	0.176527
$973$	24.5494	0.787016
$974$	11.8739	0.380464
$975$	151.061	4.83782
$976$	−1.39929	−0.0447900
$977$	−5.67961	−0.181707	−0.0908534	−	0.995864i	$-0.528959\pi$
$977$	−5.67961	−0.181707	−0.0908534	+	0.995864i	$0.528959\pi$
$978$	−31.9721	−1.02235
$979$	−9.84898	−0.314775
$980$	38.8552	1.24118
$981$	−43.8219	−1.39912
$982$	−25.7841	−0.822805
$983$	−1.13121	−0.0360798	−0.0180399	−	0.999837i	$-0.505743\pi$
$983$	−1.13121	−0.0360798	−0.0180399	+	0.999837i	$0.505743\pi$
$984$	−16.6597	−0.531091
$985$	−15.6563	−0.498850
$986$	−9.39216	−0.299107
$987$	30.2996	0.964448
$988$	−30.9053	−0.983229
$989$	−16.4497	−0.523070
$990$	22.9070	0.728032
$991$	31.7524	1.00865	0.504325	−	0.863514i	$-0.331741\pi$
$991$	31.7524	1.00865	0.504325	+	0.863514i	$0.331741\pi$
$992$	−4.60356	−0.146163
$993$	10.0210	0.318007
$994$	35.0307	1.11111
$995$	28.0363	0.888811
$996$	−14.5553	−0.461201
$997$	−40.6598	−1.28771	−0.643855	−	0.765148i	$-0.722666\pi$
$997$	−40.6598	−1.28771	−0.643855	+	0.765148i	$0.722666\pi$
$998$	22.1017	0.699616
$999$	15.1954	0.480762

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6038.2.a.e.1.3	✓	70

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6038.2.a.e.1.3	✓	70	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:	\( N \)	\(=\)	\( 6038 = 2 \cdot 3019 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6038.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.94455 q^{3} +1.00000 q^{4} +3.92217 q^{5} -2.94455 q^{6} +4.11176 q^{7} +1.00000 q^{8} +5.67038 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.94455 q^{3} +1.00000 q^{4} +3.92217 q^{5} -2.94455 q^{6} +4.11176 q^{7} +1.00000 q^{8} +5.67038 q^{9} +3.92217 q^{10} +1.02998 q^{11} -2.94455 q^{12} -4.94074 q^{13} +4.11176 q^{14} -11.5490 q^{15} +1.00000 q^{16} +2.10580 q^{17} +5.67038 q^{18} +6.25520 q^{19} +3.92217 q^{20} -12.1073 q^{21} +1.02998 q^{22} -2.20919 q^{23} -2.94455 q^{24} +10.3834 q^{25} -4.94074 q^{26} -7.86307 q^{27} +4.11176 q^{28} -4.46014 q^{29} -11.5490 q^{30} -4.60356 q^{31} +1.00000 q^{32} -3.03283 q^{33} +2.10580 q^{34} +16.1270 q^{35} +5.67038 q^{36} -1.93250 q^{37} +6.25520 q^{38} +14.5483 q^{39} +3.92217 q^{40} +5.65780 q^{41} -12.1073 q^{42} +7.44604 q^{43} +1.02998 q^{44} +22.2402 q^{45} -2.20919 q^{46} -2.50260 q^{47} -2.94455 q^{48} +9.90656 q^{49} +10.3834 q^{50} -6.20064 q^{51} -4.94074 q^{52} +8.47104 q^{53} -7.86307 q^{54} +4.03976 q^{55} +4.11176 q^{56} -18.4188 q^{57} -4.46014 q^{58} +9.52112 q^{59} -11.5490 q^{60} -1.39929 q^{61} -4.60356 q^{62} +23.3152 q^{63} +1.00000 q^{64} -19.3784 q^{65} -3.03283 q^{66} -3.09067 q^{67} +2.10580 q^{68} +6.50507 q^{69} +16.1270 q^{70} +8.51965 q^{71} +5.67038 q^{72} -3.99445 q^{73} -1.93250 q^{74} -30.5745 q^{75} +6.25520 q^{76} +4.23503 q^{77} +14.5483 q^{78} -7.22479 q^{79} +3.92217 q^{80} +6.14208 q^{81} +5.65780 q^{82} +4.94312 q^{83} -12.1073 q^{84} +8.25931 q^{85} +7.44604 q^{86} +13.1331 q^{87} +1.02998 q^{88} -9.56229 q^{89} +22.2402 q^{90} -20.3151 q^{91} -2.20919 q^{92} +13.5554 q^{93} -2.50260 q^{94} +24.5340 q^{95} -2.94455 q^{96} +1.33617 q^{97} +9.90656 q^{98} +5.84039 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 70 q + 70 q^{2} + 25 q^{3} + 70 q^{4} + 18 q^{5} + 25 q^{6} + 50 q^{7} + 70 q^{8} + 89 q^{9}+O(q^{10}) \) 70 * q + 70 * q^2 + 25 * q^3 + 70 * q^4 + 18 * q^5 + 25 * q^6 + 50 * q^7 + 70 * q^8 + 89 * q^9	\( 70 q + 70 q^{2} + 25 q^{3} + 70 q^{4} + 18 q^{5} + 25 q^{6} + 50 q^{7} + 70 q^{8} + 89 q^{9} + 18 q^{10} + 41 q^{11} + 25 q^{12} + 41 q^{13} + 50 q^{14} + 13 q^{15} + 70 q^{16} + 40 q^{17} + 89 q^{18} + 55 q^{19} + 18 q^{20} + 2 q^{21} + 41 q^{22} + 41 q^{23} + 25 q^{24} + 104 q^{25} + 41 q^{26} + 82 q^{27} + 50 q^{28} + 11 q^{29} + 13 q^{30} + 78 q^{31} + 70 q^{32} + 45 q^{33} + 40 q^{34} + 25 q^{35} + 89 q^{36} + 46 q^{37} + 55 q^{38} + 19 q^{39} + 18 q^{40} + 51 q^{41} + 2 q^{42} + 68 q^{43} + 41 q^{44} + 37 q^{45} + 41 q^{46} + 69 q^{47} + 25 q^{48} + 126 q^{49} + 104 q^{50} + 36 q^{51} + 41 q^{52} + 23 q^{53} + 82 q^{54} + 42 q^{55} + 50 q^{56} + 14 q^{57} + 11 q^{58} + 89 q^{59} + 13 q^{60} + 32 q^{61} + 78 q^{62} + 106 q^{63} + 70 q^{64} + 18 q^{65} + 45 q^{66} + 90 q^{67} + 40 q^{68} - 12 q^{69} + 25 q^{70} + 54 q^{71} + 89 q^{72} + 94 q^{73} + 46 q^{74} + 72 q^{75} + 55 q^{76} - 16 q^{77} + 19 q^{78} + 54 q^{79} + 18 q^{80} + 102 q^{81} + 51 q^{82} + 60 q^{83} + 2 q^{84} - 5 q^{85} + 68 q^{86} + 9 q^{87} + 41 q^{88} + 77 q^{89} + 37 q^{90} + 54 q^{91} + 41 q^{92} - 2 q^{93} + 69 q^{94} + 39 q^{95} + 25 q^{96} + 139 q^{97} + 126 q^{98} + 60 q^{99}+O(q^{100}) \) 70 * q + 70 * q^2 + 25 * q^3 + 70 * q^4 + 18 * q^5 + 25 * q^6 + 50 * q^7 + 70 * q^8 + 89 * q^9 + 18 * q^10 + 41 * q^11 + 25 * q^12 + 41 * q^13 + 50 * q^14 + 13 * q^15 + 70 * q^16 + 40 * q^17 + 89 * q^18 + 55 * q^19 + 18 * q^20 + 2 * q^21 + 41 * q^22 + 41 * q^23 + 25 * q^24 + 104 * q^25 + 41 * q^26 + 82 * q^27 + 50 * q^28 + 11 * q^29 + 13 * q^30 + 78 * q^31 + 70 * q^32 + 45 * q^33 + 40 * q^34 + 25 * q^35 + 89 * q^36 + 46 * q^37 + 55 * q^38 + 19 * q^39 + 18 * q^40 + 51 * q^41 + 2 * q^42 + 68 * q^43 + 41 * q^44 + 37 * q^45 + 41 * q^46 + 69 * q^47 + 25 * q^48 + 126 * q^49 + 104 * q^50 + 36 * q^51 + 41 * q^52 + 23 * q^53 + 82 * q^54 + 42 * q^55 + 50 * q^56 + 14 * q^57 + 11 * q^58 + 89 * q^59 + 13 * q^60 + 32 * q^61 + 78 * q^62 + 106 * q^63 + 70 * q^64 + 18 * q^65 + 45 * q^66 + 90 * q^67 + 40 * q^68 - 12 * q^69 + 25 * q^70 + 54 * q^71 + 89 * q^72 + 94 * q^73 + 46 * q^74 + 72 * q^75 + 55 * q^76 - 16 * q^77 + 19 * q^78 + 54 * q^79 + 18 * q^80 + 102 * q^81 + 51 * q^82 + 60 * q^83 + 2 * q^84 - 5 * q^85 + 68 * q^86 + 9 * q^87 + 41 * q^88 + 77 * q^89 + 37 * q^90 + 54 * q^91 + 41 * q^92 - 2 * q^93 + 69 * q^94 + 39 * q^95 + 25 * q^96 + 139 * q^97 + 126 * q^98 + 60 * q^99

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