LMFDB - Embedded newform 6010.2.a.g.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6010,2,Mod(1,6010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6010, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6010 = 2 \cdot 5 \cdot 601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6010.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:	$47.9900916148$
Analytic rank:	$0$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	6010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.89176 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.89176 q^{6} +4.20794 q^{7} -1.00000 q^{8} +5.36230 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.89176 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.89176 q^{6} +4.20794 q^{7} -1.00000 q^{8} +5.36230 q^{9} -1.00000 q^{10} +4.26435 q^{11} -2.89176 q^{12} +0.906061 q^{13} -4.20794 q^{14} -2.89176 q^{15} +1.00000 q^{16} -2.67426 q^{17} -5.36230 q^{18} -2.08258 q^{19} +1.00000 q^{20} -12.1684 q^{21} -4.26435 q^{22} +1.19198 q^{23} +2.89176 q^{24} +1.00000 q^{25} -0.906061 q^{26} -6.83120 q^{27} +4.20794 q^{28} +3.06853 q^{29} +2.89176 q^{30} +4.44390 q^{31} -1.00000 q^{32} -12.3315 q^{33} +2.67426 q^{34} +4.20794 q^{35} +5.36230 q^{36} +2.35940 q^{37} +2.08258 q^{38} -2.62011 q^{39} -1.00000 q^{40} +6.95492 q^{41} +12.1684 q^{42} -6.55715 q^{43} +4.26435 q^{44} +5.36230 q^{45} -1.19198 q^{46} -1.32848 q^{47} -2.89176 q^{48} +10.7068 q^{49} -1.00000 q^{50} +7.73334 q^{51} +0.906061 q^{52} +7.66603 q^{53} +6.83120 q^{54} +4.26435 q^{55} -4.20794 q^{56} +6.02233 q^{57} -3.06853 q^{58} -2.85015 q^{59} -2.89176 q^{60} +5.70248 q^{61} -4.44390 q^{62} +22.5642 q^{63} +1.00000 q^{64} +0.906061 q^{65} +12.3315 q^{66} +12.5135 q^{67} -2.67426 q^{68} -3.44693 q^{69} -4.20794 q^{70} +5.58220 q^{71} -5.36230 q^{72} -4.79481 q^{73} -2.35940 q^{74} -2.89176 q^{75} -2.08258 q^{76} +17.9441 q^{77} +2.62011 q^{78} -7.08454 q^{79} +1.00000 q^{80} +3.66732 q^{81} -6.95492 q^{82} +6.81267 q^{83} -12.1684 q^{84} -2.67426 q^{85} +6.55715 q^{86} -8.87347 q^{87} -4.26435 q^{88} +17.1021 q^{89} -5.36230 q^{90} +3.81266 q^{91} +1.19198 q^{92} -12.8507 q^{93} +1.32848 q^{94} -2.08258 q^{95} +2.89176 q^{96} -13.3317 q^{97} -10.7068 q^{98} +22.8667 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q - 27 q^{2} + 6 q^{3} + 27 q^{4} + 27 q^{5} - 6 q^{6} - 27 q^{8} + 37 q^{9}+O(q^{10}) $ 27 * q - 27 * q^2 + 6 * q^3 + 27 * q^4 + 27 * q^5 - 6 * q^6 - 27 * q^8 + 37 * q^9	\( 27 q - 27 q^{2} + 6 q^{3} + 27 q^{4} + 27 q^{5} - 6 q^{6} - 27 q^{8} + 37 q^{9} - 27 q^{10} + 18 q^{11} + 6 q^{12} - 6 q^{13} + 6 q^{15} + 27 q^{16} + 3 q^{17} - 37 q^{18} + 27 q^{19} + 27 q^{20} + 16 q^{21} - 18 q^{22} + 15 q^{23} - 6 q^{24} + 27 q^{25} + 6 q^{26} + 27 q^{27} + 25 q^{29} - 6 q^{30} + 9 q^{31} - 27 q^{32} + 11 q^{33} - 3 q^{34} + 37 q^{36} - 16 q^{37} - 27 q^{38} + 20 q^{39} - 27 q^{40} + 39 q^{41} - 16 q^{42} + 9 q^{43} + 18 q^{44} + 37 q^{45} - 15 q^{46} + 31 q^{47} + 6 q^{48} + 27 q^{49} - 27 q^{50} + 39 q^{51} - 6 q^{52} - 5 q^{53} - 27 q^{54} + 18 q^{55} - 10 q^{57} - 25 q^{58} + 46 q^{59} + 6 q^{60} + 18 q^{61} - 9 q^{62} + 23 q^{63} + 27 q^{64} - 6 q^{65} - 11 q^{66} + 11 q^{67} + 3 q^{68} + 17 q^{69} + 50 q^{71} - 37 q^{72} - 29 q^{73} + 16 q^{74} + 6 q^{75} + 27 q^{76} - 6 q^{77} - 20 q^{78} + 56 q^{79} + 27 q^{80} + 51 q^{81} - 39 q^{82} + 44 q^{83} + 16 q^{84} + 3 q^{85} - 9 q^{86} + 42 q^{87} - 18 q^{88} + 34 q^{89} - 37 q^{90} + 43 q^{91} + 15 q^{92} - 20 q^{93} - 31 q^{94} + 27 q^{95} - 6 q^{96} - 37 q^{97} - 27 q^{98} + 67 q^{99}+O(q^{100}) \) 27 * q - 27 * q^2 + 6 * q^3 + 27 * q^4 + 27 * q^5 - 6 * q^6 - 27 * q^8 + 37 * q^9 - 27 * q^10 + 18 * q^11 + 6 * q^12 - 6 * q^13 + 6 * q^15 + 27 * q^16 + 3 * q^17 - 37 * q^18 + 27 * q^19 + 27 * q^20 + 16 * q^21 - 18 * q^22 + 15 * q^23 - 6 * q^24 + 27 * q^25 + 6 * q^26 + 27 * q^27 + 25 * q^29 - 6 * q^30 + 9 * q^31 - 27 * q^32 + 11 * q^33 - 3 * q^34 + 37 * q^36 - 16 * q^37 - 27 * q^38 + 20 * q^39 - 27 * q^40 + 39 * q^41 - 16 * q^42 + 9 * q^43 + 18 * q^44 + 37 * q^45 - 15 * q^46 + 31 * q^47 + 6 * q^48 + 27 * q^49 - 27 * q^50 + 39 * q^51 - 6 * q^52 - 5 * q^53 - 27 * q^54 + 18 * q^55 - 10 * q^57 - 25 * q^58 + 46 * q^59 + 6 * q^60 + 18 * q^61 - 9 * q^62 + 23 * q^63 + 27 * q^64 - 6 * q^65 - 11 * q^66 + 11 * q^67 + 3 * q^68 + 17 * q^69 + 50 * q^71 - 37 * q^72 - 29 * q^73 + 16 * q^74 + 6 * q^75 + 27 * q^76 - 6 * q^77 - 20 * q^78 + 56 * q^79 + 27 * q^80 + 51 * q^81 - 39 * q^82 + 44 * q^83 + 16 * q^84 + 3 * q^85 - 9 * q^86 + 42 * q^87 - 18 * q^88 + 34 * q^89 - 37 * q^90 + 43 * q^91 + 15 * q^92 - 20 * q^93 - 31 * q^94 + 27 * q^95 - 6 * q^96 - 37 * q^97 - 27 * q^98 + 67 * 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
$3$	−2.89176	−1.66956	−0.834780	−	0.550583i	$-0.814405\pi$
$3$	−2.89176	−1.66956	−0.834780	+	0.550583i	$0.814405\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.89176	1.18056
$7$	4.20794	1.59045	0.795227	−	0.606312i	$-0.207352\pi$
$7$	4.20794	1.59045	0.795227	+	0.606312i	$0.207352\pi$
$8$	−1.00000	−0.353553
$9$	5.36230	1.78743
$10$	−1.00000	−0.316228
$11$	4.26435	1.28575	0.642875	−	0.765971i	$-0.277741\pi$
$11$	4.26435	1.28575	0.642875	+	0.765971i	$0.277741\pi$
$12$	−2.89176	−0.834780
$13$	0.906061	0.251296	0.125648	−	0.992075i	$-0.459899\pi$
$13$	0.906061	0.251296	0.125648	+	0.992075i	$0.459899\pi$
$14$	−4.20794	−1.12462
$15$	−2.89176	−0.746650
$16$	1.00000	0.250000
$17$	−2.67426	−0.648605	−0.324302	−	0.945954i	$-0.605129\pi$
$17$	−2.67426	−0.648605	−0.324302	+	0.945954i	$0.605129\pi$
$18$	−5.36230	−1.26391
$19$	−2.08258	−0.477777	−0.238888	−	0.971047i	$-0.576783\pi$
$19$	−2.08258	−0.477777	−0.238888	+	0.971047i	$0.576783\pi$
$20$	1.00000	0.223607
$21$	−12.1684	−2.65536
$22$	−4.26435	−0.909163
$23$	1.19198	0.248545	0.124273	−	0.992248i	$-0.460340\pi$
$23$	1.19198	0.248545	0.124273	+	0.992248i	$0.460340\pi$
$24$	2.89176	0.590279
$25$	1.00000	0.200000
$26$	−0.906061	−0.177693
$27$	−6.83120	−1.31466
$28$	4.20794	0.795227
$29$	3.06853	0.569812	0.284906	−	0.958555i	$-0.408038\pi$
$29$	3.06853	0.569812	0.284906	+	0.958555i	$0.408038\pi$
$30$	2.89176	0.527961
$31$	4.44390	0.798148	0.399074	−	0.916919i	$-0.369332\pi$
$31$	4.44390	0.798148	0.399074	+	0.916919i	$0.369332\pi$
$32$	−1.00000	−0.176777
$33$	−12.3315	−2.14664
$34$	2.67426	0.458633
$35$	4.20794	0.711272
$36$	5.36230	0.893716
$37$	2.35940	0.387884	0.193942	−	0.981013i	$-0.437873\pi$
$37$	2.35940	0.387884	0.193942	+	0.981013i	$0.437873\pi$
$38$	2.08258	0.337839
$39$	−2.62011	−0.419554
$40$	−1.00000	−0.158114
$41$	6.95492	1.08618	0.543088	−	0.839676i	$-0.317255\pi$
$41$	6.95492	1.08618	0.543088	+	0.839676i	$0.317255\pi$
$42$	12.1684	1.87762
$43$	−6.55715	−0.999955	−0.499978	−	0.866038i	$-0.666658\pi$
$43$	−6.55715	−0.999955	−0.499978	+	0.866038i	$0.666658\pi$
$44$	4.26435	0.642875
$45$	5.36230	0.799364
$46$	−1.19198	−0.175748
$47$	−1.32848	−0.193779	−0.0968896	−	0.995295i	$-0.530889\pi$
$47$	−1.32848	−0.193779	−0.0968896	+	0.995295i	$0.530889\pi$
$48$	−2.89176	−0.417390
$49$	10.7068	1.52954
$50$	−1.00000	−0.141421
$51$	7.73334	1.08288
$52$	0.906061	0.125648
$53$	7.66603	1.05301	0.526505	−	0.850172i	$-0.323502\pi$
$53$	7.66603	1.05301	0.526505	+	0.850172i	$0.323502\pi$
$54$	6.83120	0.929608
$55$	4.26435	0.575005
$56$	−4.20794	−0.562310
$57$	6.02233	0.797677
$58$	−3.06853	−0.402918
$59$	−2.85015	−0.371058	−0.185529	−	0.982639i	$-0.559400\pi$
$59$	−2.85015	−0.371058	−0.185529	+	0.982639i	$0.559400\pi$
$60$	−2.89176	−0.373325
$61$	5.70248	0.730128	0.365064	−	0.930983i	$-0.381047\pi$
$61$	5.70248	0.730128	0.365064	+	0.930983i	$0.381047\pi$
$62$	−4.44390	−0.564376
$63$	22.5642	2.84283
$64$	1.00000	0.125000
$65$	0.906061	0.112383
$66$	12.3315	1.51790
$67$	12.5135	1.52876	0.764381	−	0.644764i	$-0.223044\pi$
$67$	12.5135	1.52876	0.764381	+	0.644764i	$0.223044\pi$
$68$	−2.67426	−0.324302
$69$	−3.44693	−0.414961
$70$	−4.20794	−0.502945
$71$	5.58220	0.662485	0.331242	−	0.943546i	$-0.392532\pi$
$71$	5.58220	0.662485	0.331242	+	0.943546i	$0.392532\pi$
$72$	−5.36230	−0.631953
$73$	−4.79481	−0.561190	−0.280595	−	0.959826i	$-0.590532\pi$
$73$	−4.79481	−0.561190	−0.280595	+	0.959826i	$0.590532\pi$
$74$	−2.35940	−0.274275
$75$	−2.89176	−0.333912
$76$	−2.08258	−0.238888
$77$	17.9441	2.04493
$78$	2.62011	0.296670
$79$	−7.08454	−0.797073	−0.398536	−	0.917152i	$-0.630482\pi$
$79$	−7.08454	−0.797073	−0.398536	+	0.917152i	$0.630482\pi$
$80$	1.00000	0.111803
$81$	3.66732	0.407480
$82$	−6.95492	−0.768042
$83$	6.81267	0.747788	0.373894	−	0.927471i	$-0.378022\pi$
$83$	6.81267	0.747788	0.373894	+	0.927471i	$0.378022\pi$
$84$	−12.1684	−1.32768
$85$	−2.67426	−0.290065
$86$	6.55715	0.707075
$87$	−8.87347	−0.951336
$88$	−4.26435	−0.454581
$89$	17.1021	1.81282	0.906409	−	0.422400i	$-0.138812\pi$
$89$	17.1021	1.81282	0.906409	+	0.422400i	$0.138812\pi$
$90$	−5.36230	−0.565236
$91$	3.81266	0.399675
$92$	1.19198	0.124273
$93$	−12.8507	−1.33256
$94$	1.32848	0.137023
$95$	−2.08258	−0.213668
$96$	2.89176	0.295139
$97$	−13.3317	−1.35363	−0.676813	−	0.736155i	$-0.736639\pi$
$97$	−13.3317	−1.35363	−0.676813	+	0.736155i	$0.736639\pi$
$98$	−10.7068	−1.08155
$99$	22.8667	2.29819
$100$	1.00000	0.100000
$101$	−2.71216	−0.269870	−0.134935	−	0.990854i	$-0.543083\pi$
$101$	−2.71216	−0.269870	−0.134935	+	0.990854i	$0.543083\pi$
$102$	−7.73334	−0.765715
$103$	4.62090	0.455311	0.227656	−	0.973742i	$-0.426894\pi$
$103$	4.62090	0.455311	0.227656	+	0.973742i	$0.426894\pi$
$104$	−0.906061	−0.0888466
$105$	−12.1684	−1.18751
$106$	−7.66603	−0.744591
$107$	2.81061	0.271712	0.135856	−	0.990729i	$-0.456622\pi$
$107$	2.81061	0.271712	0.135856	+	0.990729i	$0.456622\pi$
$108$	−6.83120	−0.657332
$109$	1.87152	0.179259	0.0896295	−	0.995975i	$-0.471432\pi$
$109$	1.87152	0.179259	0.0896295	+	0.995975i	$0.471432\pi$
$110$	−4.26435	−0.406590
$111$	−6.82284	−0.647595
$112$	4.20794	0.397613
$113$	−7.98332	−0.751008	−0.375504	−	0.926821i	$-0.622530\pi$
$113$	−7.98332	−0.751008	−0.375504	+	0.926821i	$0.622530\pi$
$114$	−6.02233	−0.564043
$115$	1.19198	0.111153
$116$	3.06853	0.284906
$117$	4.85857	0.449175
$118$	2.85015	0.262378
$119$	−11.2532	−1.03158
$120$	2.89176	0.263981
$121$	7.18468	0.653153
$122$	−5.70248	−0.516278
$123$	−20.1120	−1.81344
$124$	4.44390	0.399074
$125$	1.00000	0.0894427
$126$	−22.5642	−2.01018
$127$	−6.62321	−0.587715	−0.293857	−	0.955849i	$-0.594939\pi$
$127$	−6.62321	−0.587715	−0.293857	+	0.955849i	$0.594939\pi$
$128$	−1.00000	−0.0883883
$129$	18.9617	1.66949
$130$	−0.906061	−0.0794668
$131$	6.41887	0.560819	0.280410	−	0.959880i	$-0.409530\pi$
$131$	6.41887	0.560819	0.280410	+	0.959880i	$0.409530\pi$
$132$	−12.3315	−1.07332
$133$	−8.76338	−0.759882
$134$	−12.5135	−1.08100
$135$	−6.83120	−0.587936
$136$	2.67426	0.229316
$137$	−13.1507	−1.12354	−0.561770	−	0.827293i	$-0.689879\pi$
$137$	−13.1507	−1.12354	−0.561770	+	0.827293i	$0.689879\pi$
$138$	3.44693	0.293422
$139$	16.1365	1.36868	0.684341	−	0.729162i	$-0.260090\pi$
$139$	16.1365	1.36868	0.684341	+	0.729162i	$0.260090\pi$
$140$	4.20794	0.355636
$141$	3.84166	0.323526
$142$	−5.58220	−0.468448
$143$	3.86376	0.323104
$144$	5.36230	0.446858
$145$	3.06853	0.254828
$146$	4.79481	0.396821
$147$	−30.9615	−2.55366
$148$	2.35940	0.193942
$149$	−9.89410	−0.810556	−0.405278	−	0.914193i	$-0.632825\pi$
$149$	−9.89410	−0.810556	−0.405278	+	0.914193i	$0.632825\pi$
$150$	2.89176	0.236111
$151$	−8.21131	−0.668227	−0.334114	−	0.942533i	$-0.608437\pi$
$151$	−8.21131	−0.668227	−0.334114	+	0.942533i	$0.608437\pi$
$152$	2.08258	0.168920
$153$	−14.3402	−1.15934
$154$	−17.9441	−1.44598
$155$	4.44390	0.356943
$156$	−2.62011	−0.209777
$157$	−7.53399	−0.601278	−0.300639	−	0.953738i	$-0.597200\pi$
$157$	−7.53399	−0.601278	−0.300639	+	0.953738i	$0.597200\pi$
$158$	7.08454	0.563616
$159$	−22.1683	−1.75806
$160$	−1.00000	−0.0790569
$161$	5.01579	0.395300
$162$	−3.66732	−0.288132
$163$	−7.97281	−0.624478	−0.312239	−	0.950004i	$-0.601079\pi$
$163$	−7.97281	−0.624478	−0.312239	+	0.950004i	$0.601079\pi$
$164$	6.95492	0.543088
$165$	−12.3315	−0.960005
$166$	−6.81267	−0.528766
$167$	19.1593	1.48259	0.741297	−	0.671177i	$-0.234211\pi$
$167$	19.1593	1.48259	0.741297	+	0.671177i	$0.234211\pi$
$168$	12.1684	0.938811
$169$	−12.1791	−0.936850
$170$	2.67426	0.205107
$171$	−11.1674	−0.853993
$172$	−6.55715	−0.499978
$173$	−14.7998	−1.12521	−0.562605	−	0.826726i	$-0.690201\pi$
$173$	−14.7998	−1.12521	−0.562605	+	0.826726i	$0.690201\pi$
$174$	8.87347	0.672696
$175$	4.20794	0.318091
$176$	4.26435	0.321438
$177$	8.24196	0.619504
$178$	−17.1021	−1.28186
$179$	6.48055	0.484379	0.242189	−	0.970229i	$-0.422134\pi$
$179$	6.48055	0.484379	0.242189	+	0.970229i	$0.422134\pi$
$180$	5.36230	0.399682
$181$	10.7816	0.801386	0.400693	−	0.916212i	$-0.368769\pi$
$181$	10.7816	0.801386	0.400693	+	0.916212i	$0.368769\pi$
$182$	−3.81266	−0.282613
$183$	−16.4902	−1.21899
$184$	−1.19198	−0.0878740
$185$	2.35940	0.173467
$186$	12.8507	0.942260
$187$	−11.4040	−0.833943
$188$	−1.32848	−0.0968896
$189$	−28.7453	−2.09091
$190$	2.08258	0.151086
$191$	1.34269	0.0971534	0.0485767	−	0.998819i	$-0.484531\pi$
$191$	1.34269	0.0971534	0.0485767	+	0.998819i	$0.484531\pi$
$192$	−2.89176	−0.208695
$193$	−23.9676	−1.72523	−0.862613	−	0.505865i	$-0.831173\pi$
$193$	−23.9676	−1.72523	−0.862613	+	0.505865i	$0.831173\pi$
$194$	13.3317	0.957157
$195$	−2.62011	−0.187630
$196$	10.7068	0.764771
$197$	5.07712	0.361730	0.180865	−	0.983508i	$-0.442110\pi$
$197$	5.07712	0.361730	0.180865	+	0.983508i	$0.442110\pi$
$198$	−22.8667	−1.62507
$199$	3.36771	0.238731	0.119365	−	0.992850i	$-0.461914\pi$
$199$	3.36771	0.238731	0.119365	+	0.992850i	$0.461914\pi$
$200$	−1.00000	−0.0707107
$201$	−36.1860	−2.55236
$202$	2.71216	0.190827
$203$	12.9122	0.906259
$204$	7.73334	0.541442
$205$	6.95492	0.485753
$206$	−4.62090	−0.321954
$207$	6.39176	0.444258
$208$	0.906061	0.0628241
$209$	−8.88085	−0.614302
$210$	12.1684	0.839698
$211$	−25.1920	−1.73429	−0.867144	−	0.498058i	$-0.834047\pi$
$211$	−25.1920	−1.73429	−0.867144	+	0.498058i	$0.834047\pi$
$212$	7.66603	0.526505
$213$	−16.1424	−1.10606
$214$	−2.81061	−0.192129
$215$	−6.55715	−0.447194
$216$	6.83120	0.464804
$217$	18.6997	1.26942
$218$	−1.87152	−0.126755
$219$	13.8655	0.936941
$220$	4.26435	0.287502
$221$	−2.42305	−0.162992
$222$	6.82284	0.457919
$223$	0.363659	0.0243524	0.0121762	−	0.999926i	$-0.496124\pi$
$223$	0.363659	0.0243524	0.0121762	+	0.999926i	$0.496124\pi$
$224$	−4.20794	−0.281155
$225$	5.36230	0.357486
$226$	7.98332	0.531043
$227$	19.5276	1.29609	0.648046	−	0.761601i	$-0.275586\pi$
$227$	19.5276	1.29609	0.648046	+	0.761601i	$0.275586\pi$
$228$	6.02233	0.398839
$229$	6.56832	0.434047	0.217023	−	0.976166i	$-0.430365\pi$
$229$	6.56832	0.434047	0.217023	+	0.976166i	$0.430365\pi$
$230$	−1.19198	−0.0785969
$231$	−51.8902	−3.41413
$232$	−3.06853	−0.201459
$233$	−16.1199	−1.05605	−0.528026	−	0.849228i	$-0.677068\pi$
$233$	−16.1199	−1.05605	−0.528026	+	0.849228i	$0.677068\pi$
$234$	−4.85857	−0.317615
$235$	−1.32848	−0.0866607
$236$	−2.85015	−0.185529
$237$	20.4868	1.33076
$238$	11.2532	0.729434
$239$	−9.08343	−0.587558	−0.293779	−	0.955873i	$-0.594913\pi$
$239$	−9.08343	−0.587558	−0.293779	+	0.955873i	$0.594913\pi$
$240$	−2.89176	−0.186663
$241$	10.5563	0.679990	0.339995	−	0.940427i	$-0.389575\pi$
$241$	10.5563	0.679990	0.339995	+	0.940427i	$0.389575\pi$
$242$	−7.18468	−0.461849
$243$	9.88856	0.634352
$244$	5.70248	0.365064
$245$	10.7068	0.684032
$246$	20.1120	1.28229
$247$	−1.88695	−0.120063
$248$	−4.44390	−0.282188
$249$	−19.7006	−1.24848
$250$	−1.00000	−0.0632456
$251$	−18.7151	−1.18129	−0.590645	−	0.806932i	$-0.701127\pi$
$251$	−18.7151	−1.18129	−0.590645	+	0.806932i	$0.701127\pi$
$252$	22.5642	1.42141
$253$	5.08303	0.319567
$254$	6.62321	0.415577
$255$	7.73334	0.484281
$256$	1.00000	0.0625000
$257$	8.76222	0.546572	0.273286	−	0.961933i	$-0.411889\pi$
$257$	8.76222	0.546572	0.273286	+	0.961933i	$0.411889\pi$
$258$	−18.9617	−1.18050
$259$	9.92824	0.616911
$260$	0.906061	0.0561915
$261$	16.4544	1.01850
$262$	−6.41887	−0.396559
$263$	−9.52907	−0.587588	−0.293794	−	0.955869i	$-0.594918\pi$
$263$	−9.52907	−0.587588	−0.293794	+	0.955869i	$0.594918\pi$
$264$	12.3315	0.758951
$265$	7.66603	0.470920
$266$	8.76338	0.537317
$267$	−49.4552	−3.02661
$268$	12.5135	0.764381
$269$	25.1340	1.53244	0.766222	−	0.642576i	$-0.222134\pi$
$269$	25.1340	1.53244	0.766222	+	0.642576i	$0.222134\pi$
$270$	6.83120	0.415733
$271$	12.7312	0.773366	0.386683	−	0.922213i	$-0.373621\pi$
$271$	12.7312	0.773366	0.386683	+	0.922213i	$0.373621\pi$
$272$	−2.67426	−0.162151
$273$	−11.0253	−0.667281
$274$	13.1507	0.794463
$275$	4.26435	0.257150
$276$	−3.44693	−0.207481
$277$	16.9759	1.01998	0.509991	−	0.860179i	$-0.329649\pi$
$277$	16.9759	1.01998	0.509991	+	0.860179i	$0.329649\pi$
$278$	−16.1365	−0.967804
$279$	23.8295	1.42664
$280$	−4.20794	−0.251473
$281$	19.7231	1.17658	0.588291	−	0.808649i	$-0.299801\pi$
$281$	19.7231	1.17658	0.588291	+	0.808649i	$0.299801\pi$
$282$	−3.84166	−0.228767
$283$	−0.0764318	−0.00454340	−0.00227170	−	0.999997i	$-0.500723\pi$
$283$	−0.0764318	−0.00454340	−0.00227170	+	0.999997i	$0.500723\pi$
$284$	5.58220	0.331242
$285$	6.02233	0.356732
$286$	−3.86376	−0.228469
$287$	29.2659	1.72751
$288$	−5.36230	−0.315976
$289$	−9.84831	−0.579312
$290$	−3.06853	−0.180190
$291$	38.5520	2.25996
$292$	−4.79481	−0.280595
$293$	−23.4959	−1.37265	−0.686323	−	0.727297i	$-0.740776\pi$
$293$	−23.4959	−1.37265	−0.686323	+	0.727297i	$0.740776\pi$
$294$	30.9615	1.80571
$295$	−2.85015	−0.165942
$296$	−2.35940	−0.137138
$297$	−29.1306	−1.69033
$298$	9.89410	0.573150
$299$	1.08001	0.0624585
$300$	−2.89176	−0.166956
$301$	−27.5921	−1.59038
$302$	8.21131	0.472508
$303$	7.84294	0.450565
$304$	−2.08258	−0.119444
$305$	5.70248	0.326523
$306$	14.3402	0.819775
$307$	11.9714	0.683245	0.341623	−	0.939837i	$-0.389024\pi$
$307$	11.9714	0.683245	0.341623	+	0.939837i	$0.389024\pi$
$308$	17.9441	1.02246
$309$	−13.3626	−0.760169
$310$	−4.44390	−0.252397
$311$	22.6672	1.28534	0.642670	−	0.766143i	$-0.277827\pi$
$311$	22.6672	1.28534	0.642670	+	0.766143i	$0.277827\pi$
$312$	2.62011	0.148335
$313$	−32.9902	−1.86472	−0.932359	−	0.361533i	$-0.882253\pi$
$313$	−32.9902	−1.86472	−0.932359	+	0.361533i	$0.882253\pi$
$314$	7.53399	0.425168
$315$	22.5642	1.27135
$316$	−7.08454	−0.398536
$317$	31.8581	1.78933	0.894665	−	0.446738i	$-0.147414\pi$
$317$	31.8581	1.78933	0.894665	+	0.446738i	$0.147414\pi$
$318$	22.1683	1.24314
$319$	13.0853	0.732636
$320$	1.00000	0.0559017
$321$	−8.12762	−0.453639
$322$	−5.01579	−0.279519
$323$	5.56937	0.309888
$324$	3.66732	0.203740
$325$	0.906061	0.0502592
$326$	7.97281	0.441573
$327$	−5.41199	−0.299284
$328$	−6.95492	−0.384021
$329$	−5.59018	−0.308197
$330$	12.3315	0.678826
$331$	−4.54803	−0.249983	−0.124991	−	0.992158i	$-0.539890\pi$
$331$	−4.54803	−0.249983	−0.124991	+	0.992158i	$0.539890\pi$
$332$	6.81267	0.373894
$333$	12.6518	0.693316
$334$	−19.1593	−1.04835
$335$	12.5135	0.683684
$336$	−12.1684	−0.663839
$337$	14.3284	0.780516	0.390258	−	0.920706i	$-0.372386\pi$
$337$	14.3284	0.780516	0.390258	+	0.920706i	$0.372386\pi$
$338$	12.1791	0.662453
$339$	23.0859	1.25385
$340$	−2.67426	−0.145032
$341$	18.9504	1.02622
$342$	11.1674	0.603864
$343$	15.5980	0.842211
$344$	6.55715	0.353538
$345$	−3.44693	−0.185576
$346$	14.7998	0.795644
$347$	−13.4444	−0.721735	−0.360868	−	0.932617i	$-0.617519\pi$
$347$	−13.4444	−0.721735	−0.360868	+	0.932617i	$0.617519\pi$
$348$	−8.87347	−0.475668
$349$	5.75880	0.308261	0.154131	−	0.988050i	$-0.450742\pi$
$349$	5.75880	0.308261	0.154131	+	0.988050i	$0.450742\pi$
$350$	−4.20794	−0.224924
$351$	−6.18948	−0.330370
$352$	−4.26435	−0.227291
$353$	−15.7809	−0.839932	−0.419966	−	0.907540i	$-0.637958\pi$
$353$	−15.7809	−0.839932	−0.419966	+	0.907540i	$0.637958\pi$
$354$	−8.24196	−0.438055
$355$	5.58220	0.296272
$356$	17.1021	0.906409
$357$	32.5415	1.72228
$358$	−6.48055	−0.342508
$359$	17.9232	0.945952	0.472976	−	0.881075i	$-0.343180\pi$
$359$	17.9232	0.945952	0.472976	+	0.881075i	$0.343180\pi$
$360$	−5.36230	−0.282618
$361$	−14.6629	−0.771729
$362$	−10.7816	−0.566666
$363$	−20.7764	−1.09048
$364$	3.81266	0.199837
$365$	−4.79481	−0.250972
$366$	16.4902	0.861957
$367$	2.59370	0.135390	0.0676949	−	0.997706i	$-0.478436\pi$
$367$	2.59370	0.135390	0.0676949	+	0.997706i	$0.478436\pi$
$368$	1.19198	0.0621363
$369$	37.2943	1.94146
$370$	−2.35940	−0.122660
$371$	32.2582	1.67476
$372$	−12.8507	−0.666278
$373$	−19.7670	−1.02350	−0.511749	−	0.859135i	$-0.671002\pi$
$373$	−19.7670	−1.02350	−0.511749	+	0.859135i	$0.671002\pi$
$374$	11.4040	0.589687
$375$	−2.89176	−0.149330
$376$	1.32848	0.0685113
$377$	2.78028	0.143192
$378$	28.7453	1.47850
$379$	−3.20343	−0.164549	−0.0822745	−	0.996610i	$-0.526218\pi$
$379$	−3.20343	−0.164549	−0.0822745	+	0.996610i	$0.526218\pi$
$380$	−2.08258	−0.106834
$381$	19.1528	0.981225
$382$	−1.34269	−0.0686979
$383$	−15.3453	−0.784109	−0.392055	−	0.919942i	$-0.628236\pi$
$383$	−15.3453	−0.784109	−0.392055	+	0.919942i	$0.628236\pi$
$384$	2.89176	0.147570
$385$	17.9441	0.914518
$386$	23.9676	1.21992
$387$	−35.1613	−1.78735
$388$	−13.3317	−0.676813
$389$	−25.4208	−1.28888	−0.644442	−	0.764653i	$-0.722910\pi$
$389$	−25.4208	−1.28888	−0.644442	+	0.764653i	$0.722910\pi$
$390$	2.62011	0.132675
$391$	−3.18767	−0.161208
$392$	−10.7068	−0.540775
$393$	−18.5618	−0.936321
$394$	−5.07712	−0.255782
$395$	−7.08454	−0.356462
$396$	22.8667	1.14910
$397$	28.4231	1.42652	0.713258	−	0.700901i	$-0.247219\pi$
$397$	28.4231	1.42652	0.713258	+	0.700901i	$0.247219\pi$
$398$	−3.36771	−0.168808
$399$	25.3416	1.26867
$400$	1.00000	0.0500000
$401$	27.1159	1.35411	0.677053	−	0.735934i	$-0.263257\pi$
$401$	27.1159	1.35411	0.677053	+	0.735934i	$0.263257\pi$
$402$	36.1860	1.80479
$403$	4.02645	0.200572
$404$	−2.71216	−0.134935
$405$	3.66732	0.182231
$406$	−12.9122	−0.640822
$407$	10.0613	0.498722
$408$	−7.73334	−0.382857
$409$	4.62370	0.228627	0.114314	−	0.993445i	$-0.463533\pi$
$409$	4.62370	0.228627	0.114314	+	0.993445i	$0.463533\pi$
$410$	−6.95492	−0.343479
$411$	38.0287	1.87582
$412$	4.62090	0.227656
$413$	−11.9933	−0.590151
$414$	−6.39176	−0.314138
$415$	6.81267	0.334421
$416$	−0.906061	−0.0444233
$417$	−46.6630	−2.28510
$418$	8.88085	0.434377
$419$	1.48538	0.0725656	0.0362828	−	0.999342i	$-0.488448\pi$
$419$	1.48538	0.0725656	0.0362828	+	0.999342i	$0.488448\pi$
$420$	−12.1684	−0.593756
$421$	0.471708	0.0229896	0.0114948	−	0.999934i	$-0.496341\pi$
$421$	0.471708	0.0229896	0.0114948	+	0.999934i	$0.496341\pi$
$422$	25.1920	1.22633
$423$	−7.12372	−0.346367
$424$	−7.66603	−0.372295
$425$	−2.67426	−0.129721
$426$	16.1424	0.782102
$427$	23.9957	1.16123
$428$	2.81061	0.135856
$429$	−11.1731	−0.539442
$430$	6.55715	0.316214
$431$	−12.2568	−0.590391	−0.295195	−	0.955437i	$-0.595385\pi$
$431$	−12.2568	−0.590391	−0.295195	+	0.955437i	$0.595385\pi$
$432$	−6.83120	−0.328666
$433$	5.68217	0.273068	0.136534	−	0.990635i	$-0.456404\pi$
$433$	5.68217	0.273068	0.136534	+	0.990635i	$0.456404\pi$
$434$	−18.6997	−0.897614
$435$	−8.87347	−0.425450
$436$	1.87152	0.0896295
$437$	−2.48240	−0.118749
$438$	−13.8655	−0.662517
$439$	−12.6602	−0.604239	−0.302119	−	0.953270i	$-0.597694\pi$
$439$	−12.6602	−0.604239	−0.302119	+	0.953270i	$0.597694\pi$
$440$	−4.26435	−0.203295
$441$	57.4130	2.73395
$442$	2.42305	0.115253
$443$	0.458949	0.0218053	0.0109027	−	0.999941i	$-0.496530\pi$
$443$	0.458949	0.0218053	0.0109027	+	0.999941i	$0.496530\pi$
$444$	−6.82284	−0.323798
$445$	17.1021	0.810717
$446$	−0.363659	−0.0172198
$447$	28.6114	1.35327
$448$	4.20794	0.198807
$449$	−19.8371	−0.936171	−0.468085	−	0.883683i	$-0.655056\pi$
$449$	−19.8371	−0.936171	−0.468085	+	0.883683i	$0.655056\pi$
$450$	−5.36230	−0.252781
$451$	29.6582	1.39655
$452$	−7.98332	−0.375504
$453$	23.7452	1.11565
$454$	−19.5276	−0.916475
$455$	3.81266	0.178740
$456$	−6.02233	−0.282021
$457$	−35.1418	−1.64387	−0.821933	−	0.569584i	$-0.807104\pi$
$457$	−35.1418	−1.64387	−0.821933	+	0.569584i	$0.807104\pi$
$458$	−6.56832	−0.306917
$459$	18.2684	0.852697
$460$	1.19198	0.0555764
$461$	−15.4652	−0.720285	−0.360142	−	0.932897i	$-0.617272\pi$
$461$	−15.4652	−0.720285	−0.360142	+	0.932897i	$0.617272\pi$
$462$	51.8902	2.41415
$463$	−2.33503	−0.108518	−0.0542589	−	0.998527i	$-0.517280\pi$
$463$	−2.33503	−0.108518	−0.0542589	+	0.998527i	$0.517280\pi$
$464$	3.06853	0.142453
$465$	−12.8507	−0.595937
$466$	16.1199	0.746741
$467$	−20.1646	−0.933108	−0.466554	−	0.884493i	$-0.654505\pi$
$467$	−20.1646	−0.933108	−0.466554	+	0.884493i	$0.654505\pi$
$468$	4.85857	0.224587
$469$	52.6559	2.43143
$470$	1.32848	0.0612784
$471$	21.7865	1.00387
$472$	2.85015	0.131189
$473$	−27.9620	−1.28569
$474$	−20.4868	−0.940990
$475$	−2.08258	−0.0955554
$476$	−11.2532	−0.515788
$477$	41.1075	1.88218
$478$	9.08343	0.415466
$479$	31.6162	1.44458	0.722290	−	0.691591i	$-0.243090\pi$
$479$	31.6162	1.44458	0.722290	+	0.691591i	$0.243090\pi$
$480$	2.89176	0.131990
$481$	2.13777	0.0974737
$482$	−10.5563	−0.480825
$483$	−14.5045	−0.659977
$484$	7.18468	0.326577
$485$	−13.3317	−0.605360
$486$	−9.88856	−0.448554
$487$	−20.0478	−0.908451	−0.454225	−	0.890887i	$-0.650084\pi$
$487$	−20.0478	−0.908451	−0.454225	+	0.890887i	$0.650084\pi$
$488$	−5.70248	−0.258139
$489$	23.0555	1.04260
$490$	−10.7068	−0.483683
$491$	39.9798	1.80426	0.902131	−	0.431461i	$-0.142002\pi$
$491$	39.9798	1.80426	0.902131	+	0.431461i	$0.142002\pi$
$492$	−20.1120	−0.906718
$493$	−8.20607	−0.369583
$494$	1.88695	0.0848977
$495$	22.8667	1.02778
$496$	4.44390	0.199537
$497$	23.4896	1.05365
$498$	19.7006	0.882806
$499$	23.9476	1.07204	0.536020	−	0.844205i	$-0.319927\pi$
$499$	23.9476	1.07204	0.536020	+	0.844205i	$0.319927\pi$
$500$	1.00000	0.0447214
$501$	−55.4043	−2.47528
$502$	18.7151	0.835298
$503$	3.45759	0.154167	0.0770833	−	0.997025i	$-0.475439\pi$
$503$	3.45759	0.154167	0.0770833	+	0.997025i	$0.475439\pi$
$504$	−22.5642	−1.00509
$505$	−2.71216	−0.120690
$506$	−5.08303	−0.225968
$507$	35.2189	1.56413
$508$	−6.62321	−0.293857
$509$	−6.44424	−0.285636	−0.142818	−	0.989749i	$-0.545616\pi$
$509$	−6.44424	−0.285636	−0.142818	+	0.989749i	$0.545616\pi$
$510$	−7.73334	−0.342438
$511$	−20.1763	−0.892547
$512$	−1.00000	−0.0441942
$513$	14.2265	0.628116
$514$	−8.76222	−0.386485
$515$	4.62090	0.203621
$516$	18.9617	0.834743
$517$	−5.66512	−0.249152
$518$	−9.92824	−0.436222
$519$	42.7976	1.87861
$520$	−0.906061	−0.0397334
$521$	−2.72615	−0.119435	−0.0597173	−	0.998215i	$-0.519020\pi$
$521$	−2.72615	−0.119435	−0.0597173	+	0.998215i	$0.519020\pi$
$522$	−16.4544	−0.720188
$523$	29.8519	1.30533	0.652667	−	0.757645i	$-0.273650\pi$
$523$	29.8519	1.30533	0.652667	+	0.757645i	$0.273650\pi$
$524$	6.41887	0.280410
$525$	−12.1684	−0.531072
$526$	9.52907	0.415487
$527$	−11.8842	−0.517683
$528$	−12.3315	−0.536659
$529$	−21.5792	−0.938225
$530$	−7.66603	−0.332991
$531$	−15.2834	−0.663241
$532$	−8.76338	−0.379941
$533$	6.30158	0.272952
$534$	49.4552	2.14014
$535$	2.81061	0.121513
$536$	−12.5135	−0.540499
$537$	−18.7402	−0.808700
$538$	−25.1340	−1.08360
$539$	45.6575	1.96661
$540$	−6.83120	−0.293968
$541$	−36.1290	−1.55331	−0.776654	−	0.629928i	$-0.783085\pi$
$541$	−36.1290	−1.55331	−0.776654	+	0.629928i	$0.783085\pi$
$542$	−12.7312	−0.546853
$543$	−31.1777	−1.33796
$544$	2.67426	0.114658
$545$	1.87152	0.0801670
$546$	11.0253	0.471839
$547$	4.30158	0.183922	0.0919611	−	0.995763i	$-0.470686\pi$
$547$	4.30158	0.183922	0.0919611	+	0.995763i	$0.470686\pi$
$548$	−13.1507	−0.561770
$549$	30.5784	1.30505
$550$	−4.26435	−0.181833
$551$	−6.39047	−0.272243
$552$	3.44693	0.146711
$553$	−29.8113	−1.26771
$554$	−16.9759	−0.721237
$555$	−6.82284	−0.289613
$556$	16.1365	0.684341
$557$	−19.3597	−0.820296	−0.410148	−	0.912019i	$-0.634523\pi$
$557$	−19.3597	−0.820296	−0.410148	+	0.912019i	$0.634523\pi$
$558$	−23.8295	−1.00878
$559$	−5.94118	−0.251285
$560$	4.20794	0.177818
$561$	32.9777	1.39232
$562$	−19.7231	−0.831969
$563$	47.1103	1.98546	0.992732	−	0.120345i	$-0.0384002\pi$
$563$	47.1103	1.98546	0.992732	+	0.120345i	$0.0384002\pi$
$564$	3.84166	0.161763
$565$	−7.98332	−0.335861
$566$	0.0764318	0.00321267
$567$	15.4319	0.648078
$568$	−5.58220	−0.234224
$569$	26.7585	1.12177	0.560887	−	0.827892i	$-0.310460\pi$
$569$	26.7585	1.12177	0.560887	+	0.827892i	$0.310460\pi$
$570$	−6.02233	−0.252248
$571$	−18.3360	−0.767337	−0.383669	−	0.923471i	$-0.625340\pi$
$571$	−18.3360	−0.767337	−0.383669	+	0.923471i	$0.625340\pi$
$572$	3.86376	0.161552
$573$	−3.88273	−0.162204
$574$	−29.2659	−1.22154
$575$	1.19198	0.0497091
$576$	5.36230	0.223429
$577$	−31.3314	−1.30434	−0.652171	−	0.758072i	$-0.726142\pi$
$577$	−31.3314	−1.30434	−0.652171	+	0.758072i	$0.726142\pi$
$578$	9.84831	0.409636
$579$	69.3086	2.88037
$580$	3.06853	0.127414
$581$	28.6673	1.18932
$582$	−38.5520	−1.59803
$583$	32.6906	1.35391
$584$	4.79481	0.198411
$585$	4.85857	0.200877
$586$	23.4959	0.970607
$587$	13.8323	0.570922	0.285461	−	0.958390i	$-0.407853\pi$
$587$	13.8323	0.570922	0.285461	+	0.958390i	$0.407853\pi$
$588$	−30.9615	−1.27683
$589$	−9.25478	−0.381337
$590$	2.85015	0.117339
$591$	−14.6818	−0.603930
$592$	2.35940	0.0969709
$593$	5.06440	0.207970	0.103985	−	0.994579i	$-0.466841\pi$
$593$	5.06440	0.207970	0.103985	+	0.994579i	$0.466841\pi$
$594$	29.1306	1.19524
$595$	−11.2532	−0.461334
$596$	−9.89410	−0.405278
$597$	−9.73863	−0.398576
$598$	−1.08001	−0.0441648
$599$	−15.8614	−0.648079	−0.324040	−	0.946044i	$-0.605041\pi$
$599$	−15.8614	−0.648079	−0.324040	+	0.946044i	$0.605041\pi$
$600$	2.89176	0.118056
$601$	−1.00000	−0.0407909
$601$	−1.00000	−0.0407909
$602$	27.5921	1.12457
$603$	67.1009	2.73256
$604$	−8.21131	−0.334114
$605$	7.18468	0.292099
$606$	−7.84294	−0.318597
$607$	18.9503	0.769169	0.384584	−	0.923090i	$-0.374345\pi$
$607$	18.9503	0.769169	0.384584	+	0.923090i	$0.374345\pi$
$608$	2.08258	0.0844598
$609$	−37.3391	−1.51305
$610$	−5.70248	−0.230887
$611$	−1.20369	−0.0486960
$612$	−14.3402	−0.579668
$613$	−11.9406	−0.482276	−0.241138	−	0.970491i	$-0.577521\pi$
$613$	−11.9406	−0.482276	−0.241138	+	0.970491i	$0.577521\pi$
$614$	−11.9714	−0.483127
$615$	−20.1120	−0.810993
$616$	−17.9441	−0.722990
$617$	−5.65492	−0.227659	−0.113829	−	0.993500i	$-0.536312\pi$
$617$	−5.65492	−0.227659	−0.113829	+	0.993500i	$0.536312\pi$
$618$	13.3626	0.537521
$619$	15.7570	0.633328	0.316664	−	0.948538i	$-0.397437\pi$
$619$	15.7570	0.633328	0.316664	+	0.948538i	$0.397437\pi$
$620$	4.44390	0.178471
$621$	−8.14266	−0.326754
$622$	−22.6672	−0.908872
$623$	71.9647	2.88320
$624$	−2.62011	−0.104889
$625$	1.00000	0.0400000
$626$	32.9902	1.31855
$627$	25.6813	1.02561
$628$	−7.53399	−0.300639
$629$	−6.30967	−0.251583
$630$	−22.5642	−0.898981
$631$	6.41985	0.255570	0.127785	−	0.991802i	$-0.459213\pi$
$631$	6.41985	0.255570	0.127785	+	0.991802i	$0.459213\pi$
$632$	7.08454	0.281808
$633$	72.8493	2.89550
$634$	−31.8581	−1.26525
$635$	−6.62321	−0.262834
$636$	−22.1683	−0.879032
$637$	9.70101	0.384368
$638$	−13.0853	−0.518052
$639$	29.9334	1.18415
$640$	−1.00000	−0.0395285
$641$	−9.57279	−0.378102	−0.189051	−	0.981967i	$-0.560541\pi$
$641$	−9.57279	−0.378102	−0.189051	+	0.981967i	$0.560541\pi$
$642$	8.12762	0.320771
$643$	3.81510	0.150453	0.0752264	−	0.997166i	$-0.476032\pi$
$643$	3.81510	0.150453	0.0752264	+	0.997166i	$0.476032\pi$
$644$	5.01579	0.197650
$645$	18.9617	0.746617
$646$	−5.56937	−0.219124
$647$	44.0570	1.73206	0.866029	−	0.499994i	$-0.166664\pi$
$647$	44.0570	1.73206	0.866029	+	0.499994i	$0.166664\pi$
$648$	−3.66732	−0.144066
$649$	−12.1540	−0.477088
$650$	−0.906061	−0.0355386
$651$	−54.0751	−2.11937
$652$	−7.97281	−0.312239
$653$	−15.2044	−0.594993	−0.297497	−	0.954723i	$-0.596152\pi$
$653$	−15.2044	−0.594993	−0.297497	+	0.954723i	$0.596152\pi$
$654$	5.41199	0.211625
$655$	6.41887	0.250806
$656$	6.95492	0.271544
$657$	−25.7112	−1.00309
$658$	5.59018	0.217928
$659$	21.3091	0.830083	0.415042	−	0.909802i	$-0.363767\pi$
$659$	21.3091	0.830083	0.415042	+	0.909802i	$0.363767\pi$
$660$	−12.3315	−0.480003
$661$	−20.9676	−0.815546	−0.407773	−	0.913083i	$-0.633695\pi$
$661$	−20.9676	−0.815546	−0.407773	+	0.913083i	$0.633695\pi$
$662$	4.54803	0.176764
$663$	7.00688	0.272125
$664$	−6.81267	−0.264383
$665$	−8.76338	−0.339829
$666$	−12.6518	−0.490248
$667$	3.65763	0.141624
$668$	19.1593	0.741297
$669$	−1.05162	−0.0406578
$670$	−12.5135	−0.483437
$671$	24.3174	0.938761
$672$	12.1684	0.469405
$673$	42.8034	1.64995	0.824976	−	0.565168i	$-0.191189\pi$
$673$	42.8034	1.64995	0.824976	+	0.565168i	$0.191189\pi$
$674$	−14.3284	−0.551908
$675$	−6.83120	−0.262933
$676$	−12.1791	−0.468425
$677$	14.8562	0.570969	0.285485	−	0.958383i	$-0.407845\pi$
$677$	14.8562	0.570969	0.285485	+	0.958383i	$0.407845\pi$
$678$	−23.0859	−0.886608
$679$	−56.0989	−2.15288
$680$	2.67426	0.102553
$681$	−56.4692	−2.16390
$682$	−18.9504	−0.725647
$683$	22.5296	0.862071	0.431036	−	0.902335i	$-0.358148\pi$
$683$	22.5296	0.862071	0.431036	+	0.902335i	$0.358148\pi$
$684$	−11.1674	−0.426997
$685$	−13.1507	−0.502463
$686$	−15.5980	−0.595533
$687$	−18.9940	−0.724667
$688$	−6.55715	−0.249989
$689$	6.94589	0.264617
$690$	3.44693	0.131222
$691$	15.0548	0.572713	0.286356	−	0.958123i	$-0.407556\pi$
$691$	15.0548	0.572713	0.286356	+	0.958123i	$0.407556\pi$
$692$	−14.7998	−0.562605
$693$	96.2218	3.65516
$694$	13.4444	0.510344
$695$	16.1365	0.612093
$696$	8.87347	0.336348
$697$	−18.5993	−0.704498
$698$	−5.75880	−0.217974
$699$	46.6150	1.76314
$700$	4.20794	0.159045
$701$	17.8011	0.672339	0.336169	−	0.941802i	$-0.390869\pi$
$701$	17.8011	0.672339	0.336169	+	0.941802i	$0.390869\pi$
$702$	6.18948	0.233607
$703$	−4.91365	−0.185322
$704$	4.26435	0.160719
$705$	3.84166	0.144685
$706$	15.7809	0.593922
$707$	−11.4126	−0.429216
$708$	8.24196	0.309752
$709$	−8.79560	−0.330326	−0.165163	−	0.986266i	$-0.552815\pi$
$709$	−8.79560	−0.330326	−0.165163	+	0.986266i	$0.552815\pi$
$710$	−5.58220	−0.209496
$711$	−37.9894	−1.42471
$712$	−17.1021	−0.640928
$713$	5.29705	0.198376
$714$	−32.5415	−1.21783
$715$	3.86376	0.144497
$716$	6.48055	0.242189
$717$	26.2671	0.980963
$718$	−17.9232	−0.668889
$719$	7.67146	0.286097	0.143049	−	0.989716i	$-0.454309\pi$
$719$	7.67146	0.286097	0.143049	+	0.989716i	$0.454309\pi$
$720$	5.36230	0.199841
$721$	19.4445	0.724151
$722$	14.6629	0.545695
$723$	−30.5263	−1.13528
$724$	10.7816	0.400693
$725$	3.06853	0.113962
$726$	20.7764	0.771085
$727$	−1.17005	−0.0433946	−0.0216973	−	0.999765i	$-0.506907\pi$
$727$	−1.17005	−0.0433946	−0.0216973	+	0.999765i	$0.506907\pi$
$728$	−3.81266	−0.141306
$729$	−39.5974	−1.46657
$730$	4.79481	0.177464
$731$	17.5355	0.648576
$732$	−16.4902	−0.609496
$733$	−29.2608	−1.08077	−0.540387	−	0.841417i	$-0.681722\pi$
$733$	−29.2608	−1.08077	−0.540387	+	0.841417i	$0.681722\pi$
$734$	−2.59370	−0.0957351
$735$	−30.9615	−1.14203
$736$	−1.19198	−0.0439370
$737$	53.3618	1.96561
$738$	−37.2943	−1.37282
$739$	16.5207	0.607723	0.303862	−	0.952716i	$-0.401724\pi$
$739$	16.5207	0.607723	0.303862	+	0.952716i	$0.401724\pi$
$740$	2.35940	0.0867334
$741$	5.45660	0.200453
$742$	−32.2582	−1.18424
$743$	−11.0108	−0.403948	−0.201974	−	0.979391i	$-0.564736\pi$
$743$	−11.0108	−0.403948	−0.201974	+	0.979391i	$0.564736\pi$
$744$	12.8507	0.471130
$745$	−9.89410	−0.362492
$746$	19.7670	0.723722
$747$	36.5315	1.33662
$748$	−11.4040	−0.416972
$749$	11.8269	0.432145
$750$	2.89176	0.105592
$751$	−18.7177	−0.683017	−0.341509	−	0.939879i	$-0.610938\pi$
$751$	−18.7177	−0.683017	−0.341509	+	0.939879i	$0.610938\pi$
$752$	−1.32848	−0.0484448
$753$	54.1198	1.97223
$754$	−2.78028	−0.101252
$755$	−8.21131	−0.298840
$756$	−28.7453	−1.04546
$757$	25.0011	0.908680	0.454340	−	0.890828i	$-0.349875\pi$
$757$	25.0011	0.908680	0.454340	+	0.890828i	$0.349875\pi$
$758$	3.20343	0.116354
$759$	−14.6989	−0.533537
$760$	2.08258	0.0755431
$761$	−18.4922	−0.670342	−0.335171	−	0.942157i	$-0.608794\pi$
$761$	−18.4922	−0.670342	−0.335171	+	0.942157i	$0.608794\pi$
$762$	−19.1528	−0.693831
$763$	7.87524	0.285103
$764$	1.34269	0.0485767
$765$	−14.3402	−0.518471
$766$	15.3453	0.554449
$767$	−2.58241	−0.0932455
$768$	−2.89176	−0.104348
$769$	10.7257	0.386780	0.193390	−	0.981122i	$-0.438052\pi$
$769$	10.7257	0.386780	0.193390	+	0.981122i	$0.438052\pi$
$770$	−17.9441	−0.646662
$771$	−25.3383	−0.912536
$772$	−23.9676	−0.862613
$773$	15.2134	0.547189	0.273594	−	0.961845i	$-0.411787\pi$
$773$	15.2134	0.547189	0.273594	+	0.961845i	$0.411787\pi$
$774$	35.1613	1.26385
$775$	4.44390	0.159630
$776$	13.3317	0.478579
$777$	−28.7101	−1.02997
$778$	25.4208	0.911378
$779$	−14.4842	−0.518950
$780$	−2.62011	−0.0938152
$781$	23.8044	0.851790
$782$	3.18767	0.113991
$783$	−20.9617	−0.749112
$784$	10.7068	0.382385
$785$	−7.53399	−0.268900
$786$	18.5618	0.662079
$787$	38.7094	1.37984	0.689921	−	0.723885i	$-0.257645\pi$
$787$	38.7094	1.37984	0.689921	+	0.723885i	$0.257645\pi$
$788$	5.07712	0.180865
$789$	27.5558	0.981013
$790$	7.08454	0.252057
$791$	−33.5934	−1.19444
$792$	−22.8667	−0.812533
$793$	5.16680	0.183478
$794$	−28.4231	−1.00870
$795$	−22.1683	−0.786230
$796$	3.36771	0.119365
$797$	−29.3155	−1.03841	−0.519204	−	0.854650i	$-0.673772\pi$
$797$	−29.3155	−1.03841	−0.519204	+	0.854650i	$0.673772\pi$
$798$	−25.3416	−0.897084
$799$	3.55272	0.125686
$800$	−1.00000	−0.0353553
$801$	91.7065	3.24029
$802$	−27.1159	−0.957497
$803$	−20.4468	−0.721550
$804$	−36.1860	−1.27618
$805$	5.01579	0.176783
$806$	−4.02645	−0.141826
$807$	−72.6815	−2.55851
$808$	2.71216	0.0954136
$809$	−13.0781	−0.459802	−0.229901	−	0.973214i	$-0.573840\pi$
$809$	−13.0781	−0.459802	−0.229901	+	0.973214i	$0.573840\pi$
$810$	−3.66732	−0.128857
$811$	9.74292	0.342120	0.171060	−	0.985261i	$-0.445281\pi$
$811$	9.74292	0.342120	0.171060	+	0.985261i	$0.445281\pi$
$812$	12.9122	0.453130
$813$	−36.8157	−1.29118
$814$	−10.0613	−0.352649
$815$	−7.97281	−0.279275
$816$	7.73334	0.270721
$817$	13.6558	0.477755
$818$	−4.62370	−0.161664
$819$	20.4446	0.714392
$820$	6.95492	0.242876
$821$	32.0651	1.11908	0.559540	−	0.828803i	$-0.310978\pi$
$821$	32.0651	1.11908	0.559540	+	0.828803i	$0.310978\pi$
$822$	−38.0287	−1.32640
$823$	40.2371	1.40258	0.701288	−	0.712878i	$-0.252609\pi$
$823$	40.2371	1.40258	0.701288	+	0.712878i	$0.252609\pi$
$824$	−4.62090	−0.160977
$825$	−12.3315	−0.429327
$826$	11.9933	0.417299
$827$	−44.0201	−1.53073	−0.765364	−	0.643598i	$-0.777441\pi$
$827$	−44.0201	−1.53073	−0.765364	+	0.643598i	$0.777441\pi$
$828$	6.39176	0.222129
$829$	11.3628	0.394646	0.197323	−	0.980339i	$-0.436775\pi$
$829$	11.3628	0.394646	0.197323	+	0.980339i	$0.436775\pi$
$830$	−6.81267	−0.236471
$831$	−49.0903	−1.70292
$832$	0.906061	0.0314120
$833$	−28.6328	−0.992068
$834$	46.6630	1.61581
$835$	19.1593	0.663036
$836$	−8.88085	−0.307151
$837$	−30.3572	−1.04930
$838$	−1.48538	−0.0513116
$839$	−9.36950	−0.323471	−0.161736	−	0.986834i	$-0.551709\pi$
$839$	−9.36950	−0.323471	−0.161736	+	0.986834i	$0.551709\pi$
$840$	12.1684	0.419849
$841$	−19.5841	−0.675314
$842$	−0.471708	−0.0162561
$843$	−57.0345	−1.96437
$844$	−25.1920	−0.867144
$845$	−12.1791	−0.418972
$846$	7.12372	0.244918
$847$	30.2327	1.03881
$848$	7.66603	0.263253
$849$	0.221023	0.00758548
$850$	2.67426	0.0917265
$851$	2.81237	0.0964067
$852$	−16.1424	−0.553029
$853$	−4.36636	−0.149501	−0.0747506	−	0.997202i	$-0.523816\pi$
$853$	−4.36636	−0.149501	−0.0747506	+	0.997202i	$0.523816\pi$
$854$	−23.9957	−0.821116
$855$	−11.1674	−0.381917
$856$	−2.81061	−0.0960647
$857$	1.59331	0.0544265	0.0272132	−	0.999630i	$-0.491337\pi$
$857$	1.59331	0.0544265	0.0272132	+	0.999630i	$0.491337\pi$
$858$	11.1731	0.381443
$859$	−55.5027	−1.89373	−0.946864	−	0.321635i	$-0.895767\pi$
$859$	−55.5027	−1.89373	−0.946864	+	0.321635i	$0.895767\pi$
$860$	−6.55715	−0.223597
$861$	−84.6301	−2.88418
$862$	12.2568	0.417469
$863$	7.98803	0.271916	0.135958	−	0.990715i	$-0.456589\pi$
$863$	7.98803	0.271916	0.135958	+	0.990715i	$0.456589\pi$
$864$	6.83120	0.232402
$865$	−14.7998	−0.503209
$866$	−5.68217	−0.193088
$867$	28.4790	0.967197
$868$	18.6997	0.634709
$869$	−30.2110	−1.02484
$870$	8.87347	0.300839
$871$	11.3380	0.384172
$872$	−1.87152	−0.0633776
$873$	−71.4883	−2.41951
$874$	2.48240	0.0839683
$875$	4.20794	0.142254
$876$	13.8655	0.468470
$877$	49.7193	1.67890	0.839450	−	0.543437i	$-0.182877\pi$
$877$	49.7193	1.67890	0.839450	+	0.543437i	$0.182877\pi$
$878$	12.6602	0.427261
$879$	67.9446	2.29171
$880$	4.26435	0.143751
$881$	−0.216181	−0.00728331	−0.00364166	−	0.999993i	$-0.501159\pi$
$881$	−0.216181	−0.00728331	−0.00364166	+	0.999993i	$0.501159\pi$
$882$	−57.4130	−1.93320
$883$	−44.1865	−1.48699	−0.743497	−	0.668739i	$-0.766834\pi$
$883$	−44.1865	−1.48699	−0.743497	+	0.668739i	$0.766834\pi$
$884$	−2.42305	−0.0814959
$885$	8.24196	0.277051
$886$	−0.458949	−0.0154187
$887$	−11.9702	−0.401919	−0.200960	−	0.979600i	$-0.564406\pi$
$887$	−11.9702	−0.401919	−0.200960	+	0.979600i	$0.564406\pi$
$888$	6.82284	0.228960
$889$	−27.8701	−0.934733
$890$	−17.1021	−0.573264
$891$	15.6388	0.523918
$892$	0.363659	0.0121762
$893$	2.76667	0.0925832
$894$	−28.6114	−0.956908
$895$	6.48055	0.216621
$896$	−4.20794	−0.140578
$897$	−3.12313	−0.104278
$898$	19.8371	0.661973
$899$	13.6363	0.454795
$900$	5.36230	0.178743
$901$	−20.5010	−0.682987
$902$	−29.6582	−0.987510
$903$	79.7898	2.65524
$904$	7.98332	0.265521
$905$	10.7816	0.358391
$906$	−23.7452	−0.788880
$907$	−34.1194	−1.13292	−0.566459	−	0.824090i	$-0.691687\pi$
$907$	−34.1194	−1.13292	−0.566459	+	0.824090i	$0.691687\pi$
$908$	19.5276	0.648046
$909$	−14.5434	−0.482375
$910$	−3.81266	−0.126388
$911$	12.2468	0.405755	0.202877	−	0.979204i	$-0.434971\pi$
$911$	12.2468	0.405755	0.202877	+	0.979204i	$0.434971\pi$
$912$	6.02233	0.199419
$913$	29.0516	0.961468
$914$	35.1418	1.16239
$915$	−16.4902	−0.545150
$916$	6.56832	0.217023
$917$	27.0102	0.891957
$918$	−18.2684	−0.602948
$919$	31.9590	1.05423	0.527115	−	0.849794i	$-0.323274\pi$
$919$	31.9590	1.05423	0.527115	+	0.849794i	$0.323274\pi$
$920$	−1.19198	−0.0392985
$921$	−34.6185	−1.14072
$922$	15.4652	0.509318
$923$	5.05781	0.166480
$924$	−51.8902	−1.70706
$925$	2.35940	0.0775767
$926$	2.33503	0.0767337
$927$	24.7786	0.813837
$928$	−3.06853	−0.100729
$929$	1.35036	0.0443038	0.0221519	−	0.999755i	$-0.492948\pi$
$929$	1.35036	0.0443038	0.0221519	+	0.999755i	$0.492948\pi$
$930$	12.8507	0.421391
$931$	−22.2978	−0.730779
$932$	−16.1199	−0.528026
$933$	−65.5482	−2.14595
$934$	20.1646	0.659807
$935$	−11.4040	−0.372951
$936$	−4.85857	−0.158807
$937$	−9.73146	−0.317913	−0.158956	−	0.987286i	$-0.550813\pi$
$937$	−9.73146	−0.317913	−0.158956	+	0.987286i	$0.550813\pi$
$938$	−52.6559	−1.71928
$939$	95.4000	3.11326
$940$	−1.32848	−0.0433303
$941$	33.9140	1.10557	0.552783	−	0.833325i	$-0.313566\pi$
$941$	33.9140	1.10557	0.552783	+	0.833325i	$0.313566\pi$
$942$	−21.7865	−0.709843
$943$	8.29013	0.269964
$944$	−2.85015	−0.0927645
$945$	−28.7453	−0.935085
$946$	27.9620	0.909122
$947$	−14.0508	−0.456590	−0.228295	−	0.973592i	$-0.573315\pi$
$947$	−14.0508	−0.456590	−0.228295	+	0.973592i	$0.573315\pi$
$948$	20.4868	0.665381
$949$	−4.34439	−0.141025
$950$	2.08258	0.0675678
$951$	−92.1261	−2.98739
$952$	11.2532	0.364717
$953$	13.5851	0.440063	0.220032	−	0.975493i	$-0.429384\pi$
$953$	13.5851	0.440063	0.220032	+	0.975493i	$0.429384\pi$
$954$	−41.1075	−1.33090
$955$	1.34269	0.0434483
$956$	−9.08343	−0.293779
$957$	−37.8396	−1.22318
$958$	−31.6162	−1.02147
$959$	−55.3374	−1.78694
$960$	−2.89176	−0.0933313
$961$	−11.2517	−0.362959
$962$	−2.13777	−0.0689243
$963$	15.0713	0.485666
$964$	10.5563	0.339995
$965$	−23.9676	−0.771544
$966$	14.5045	0.466674
$967$	22.3459	0.718594	0.359297	−	0.933223i	$-0.383016\pi$
$967$	22.3459	0.718594	0.359297	+	0.933223i	$0.383016\pi$
$968$	−7.18468	−0.230924
$969$	−16.1053	−0.517377
$970$	13.3317	0.428054
$971$	39.4861	1.26717	0.633584	−	0.773674i	$-0.281583\pi$
$971$	39.4861	1.26717	0.633584	+	0.773674i	$0.281583\pi$
$972$	9.88856	0.317176
$973$	67.9016	2.17682
$974$	20.0478	0.642372
$975$	−2.62011	−0.0839108
$976$	5.70248	0.182532
$977$	34.6961	1.11003	0.555014	−	0.831841i	$-0.312713\pi$
$977$	34.6961	1.11003	0.555014	+	0.831841i	$0.312713\pi$
$978$	−23.0555	−0.737233
$979$	72.9293	2.33083
$980$	10.7068	0.342016
$981$	10.0356	0.320413
$982$	−39.9798	−1.27581
$983$	58.2396	1.85755	0.928777	−	0.370638i	$-0.120861\pi$
$983$	58.2396	1.85755	0.928777	+	0.370638i	$0.120861\pi$
$984$	20.1120	0.641146
$985$	5.07712	0.161770
$986$	8.20607	0.261334
$987$	16.1655	0.514553
$988$	−1.88695	−0.0600317
$989$	−7.81599	−0.248534
$990$	−22.8667	−0.726752
$991$	−49.4042	−1.56938	−0.784688	−	0.619891i	$-0.787177\pi$
$991$	−49.4042	−1.56938	−0.784688	+	0.619891i	$0.787177\pi$
$992$	−4.44390	−0.141094
$993$	13.1518	0.417361
$994$	−23.4896	−0.745044
$995$	3.36771	0.106764
$996$	−19.7006	−0.624238
$997$	33.1900	1.05114	0.525569	−	0.850751i	$-0.323852\pi$
$997$	33.1900	1.05114	0.525569	+	0.850751i	$0.323852\pi$
$998$	−23.9476	−0.758047
$999$	−16.1176	−0.509937

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.g.1.2	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.g.1.2	✓	27	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:	\( N \)	\(=\)	\( 6010 = 2 \cdot 5 \cdot 601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6010.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.89176 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.89176 q^{6} +4.20794 q^{7} -1.00000 q^{8} +5.36230 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.89176 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.89176 q^{6} +4.20794 q^{7} -1.00000 q^{8} +5.36230 q^{9} -1.00000 q^{10} +4.26435 q^{11} -2.89176 q^{12} +0.906061 q^{13} -4.20794 q^{14} -2.89176 q^{15} +1.00000 q^{16} -2.67426 q^{17} -5.36230 q^{18} -2.08258 q^{19} +1.00000 q^{20} -12.1684 q^{21} -4.26435 q^{22} +1.19198 q^{23} +2.89176 q^{24} +1.00000 q^{25} -0.906061 q^{26} -6.83120 q^{27} +4.20794 q^{28} +3.06853 q^{29} +2.89176 q^{30} +4.44390 q^{31} -1.00000 q^{32} -12.3315 q^{33} +2.67426 q^{34} +4.20794 q^{35} +5.36230 q^{36} +2.35940 q^{37} +2.08258 q^{38} -2.62011 q^{39} -1.00000 q^{40} +6.95492 q^{41} +12.1684 q^{42} -6.55715 q^{43} +4.26435 q^{44} +5.36230 q^{45} -1.19198 q^{46} -1.32848 q^{47} -2.89176 q^{48} +10.7068 q^{49} -1.00000 q^{50} +7.73334 q^{51} +0.906061 q^{52} +7.66603 q^{53} +6.83120 q^{54} +4.26435 q^{55} -4.20794 q^{56} +6.02233 q^{57} -3.06853 q^{58} -2.85015 q^{59} -2.89176 q^{60} +5.70248 q^{61} -4.44390 q^{62} +22.5642 q^{63} +1.00000 q^{64} +0.906061 q^{65} +12.3315 q^{66} +12.5135 q^{67} -2.67426 q^{68} -3.44693 q^{69} -4.20794 q^{70} +5.58220 q^{71} -5.36230 q^{72} -4.79481 q^{73} -2.35940 q^{74} -2.89176 q^{75} -2.08258 q^{76} +17.9441 q^{77} +2.62011 q^{78} -7.08454 q^{79} +1.00000 q^{80} +3.66732 q^{81} -6.95492 q^{82} +6.81267 q^{83} -12.1684 q^{84} -2.67426 q^{85} +6.55715 q^{86} -8.87347 q^{87} -4.26435 q^{88} +17.1021 q^{89} -5.36230 q^{90} +3.81266 q^{91} +1.19198 q^{92} -12.8507 q^{93} +1.32848 q^{94} -2.08258 q^{95} +2.89176 q^{96} -13.3317 q^{97} -10.7068 q^{98} +22.8667 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 27 q^{2} + 6 q^{3} + 27 q^{4} + 27 q^{5} - 6 q^{6} - 27 q^{8} + 37 q^{9}+O(q^{10}) \) 27 * q - 27 * q^2 + 6 * q^3 + 27 * q^4 + 27 * q^5 - 6 * q^6 - 27 * q^8 + 37 * q^9	\( 27 q - 27 q^{2} + 6 q^{3} + 27 q^{4} + 27 q^{5} - 6 q^{6} - 27 q^{8} + 37 q^{9} - 27 q^{10} + 18 q^{11} + 6 q^{12} - 6 q^{13} + 6 q^{15} + 27 q^{16} + 3 q^{17} - 37 q^{18} + 27 q^{19} + 27 q^{20} + 16 q^{21} - 18 q^{22} + 15 q^{23} - 6 q^{24} + 27 q^{25} + 6 q^{26} + 27 q^{27} + 25 q^{29} - 6 q^{30} + 9 q^{31} - 27 q^{32} + 11 q^{33} - 3 q^{34} + 37 q^{36} - 16 q^{37} - 27 q^{38} + 20 q^{39} - 27 q^{40} + 39 q^{41} - 16 q^{42} + 9 q^{43} + 18 q^{44} + 37 q^{45} - 15 q^{46} + 31 q^{47} + 6 q^{48} + 27 q^{49} - 27 q^{50} + 39 q^{51} - 6 q^{52} - 5 q^{53} - 27 q^{54} + 18 q^{55} - 10 q^{57} - 25 q^{58} + 46 q^{59} + 6 q^{60} + 18 q^{61} - 9 q^{62} + 23 q^{63} + 27 q^{64} - 6 q^{65} - 11 q^{66} + 11 q^{67} + 3 q^{68} + 17 q^{69} + 50 q^{71} - 37 q^{72} - 29 q^{73} + 16 q^{74} + 6 q^{75} + 27 q^{76} - 6 q^{77} - 20 q^{78} + 56 q^{79} + 27 q^{80} + 51 q^{81} - 39 q^{82} + 44 q^{83} + 16 q^{84} + 3 q^{85} - 9 q^{86} + 42 q^{87} - 18 q^{88} + 34 q^{89} - 37 q^{90} + 43 q^{91} + 15 q^{92} - 20 q^{93} - 31 q^{94} + 27 q^{95} - 6 q^{96} - 37 q^{97} - 27 q^{98} + 67 q^{99}+O(q^{100}) \) 27 * q - 27 * q^2 + 6 * q^3 + 27 * q^4 + 27 * q^5 - 6 * q^6 - 27 * q^8 + 37 * q^9 - 27 * q^10 + 18 * q^11 + 6 * q^12 - 6 * q^13 + 6 * q^15 + 27 * q^16 + 3 * q^17 - 37 * q^18 + 27 * q^19 + 27 * q^20 + 16 * q^21 - 18 * q^22 + 15 * q^23 - 6 * q^24 + 27 * q^25 + 6 * q^26 + 27 * q^27 + 25 * q^29 - 6 * q^30 + 9 * q^31 - 27 * q^32 + 11 * q^33 - 3 * q^34 + 37 * q^36 - 16 * q^37 - 27 * q^38 + 20 * q^39 - 27 * q^40 + 39 * q^41 - 16 * q^42 + 9 * q^43 + 18 * q^44 + 37 * q^45 - 15 * q^46 + 31 * q^47 + 6 * q^48 + 27 * q^49 - 27 * q^50 + 39 * q^51 - 6 * q^52 - 5 * q^53 - 27 * q^54 + 18 * q^55 - 10 * q^57 - 25 * q^58 + 46 * q^59 + 6 * q^60 + 18 * q^61 - 9 * q^62 + 23 * q^63 + 27 * q^64 - 6 * q^65 - 11 * q^66 + 11 * q^67 + 3 * q^68 + 17 * q^69 + 50 * q^71 - 37 * q^72 - 29 * q^73 + 16 * q^74 + 6 * q^75 + 27 * q^76 - 6 * q^77 - 20 * q^78 + 56 * q^79 + 27 * q^80 + 51 * q^81 - 39 * q^82 + 44 * q^83 + 16 * q^84 + 3 * q^85 - 9 * q^86 + 42 * q^87 - 18 * q^88 + 34 * q^89 - 37 * q^90 + 43 * q^91 + 15 * q^92 - 20 * q^93 - 31 * q^94 + 27 * q^95 - 6 * q^96 - 37 * q^97 - 27 * q^98 + 67 * q^99

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