LMFDB - Embedded newform 8015.2.a.h.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$1$
Dimension:	$38$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.83849 q^{2} +1.40018 q^{3} +1.38005 q^{4} +1.00000 q^{5} -2.57423 q^{6} +1.00000 q^{7} +1.13977 q^{8} -1.03949 q^{9} +O(q^{10})$	\(q-1.83849 q^{2} +1.40018 q^{3} +1.38005 q^{4} +1.00000 q^{5} -2.57423 q^{6} +1.00000 q^{7} +1.13977 q^{8} -1.03949 q^{9} -1.83849 q^{10} -2.97206 q^{11} +1.93232 q^{12} +3.06950 q^{13} -1.83849 q^{14} +1.40018 q^{15} -4.85556 q^{16} +1.75594 q^{17} +1.91108 q^{18} +4.20856 q^{19} +1.38005 q^{20} +1.40018 q^{21} +5.46411 q^{22} -2.41003 q^{23} +1.59589 q^{24} +1.00000 q^{25} -5.64325 q^{26} -5.65602 q^{27} +1.38005 q^{28} -6.62044 q^{29} -2.57423 q^{30} -0.754362 q^{31} +6.64736 q^{32} -4.16144 q^{33} -3.22827 q^{34} +1.00000 q^{35} -1.43454 q^{36} -1.80758 q^{37} -7.73741 q^{38} +4.29786 q^{39} +1.13977 q^{40} +8.96384 q^{41} -2.57423 q^{42} -10.3682 q^{43} -4.10159 q^{44} -1.03949 q^{45} +4.43081 q^{46} +2.64901 q^{47} -6.79868 q^{48} +1.00000 q^{49} -1.83849 q^{50} +2.45863 q^{51} +4.23606 q^{52} -4.13081 q^{53} +10.3985 q^{54} -2.97206 q^{55} +1.13977 q^{56} +5.89276 q^{57} +12.1716 q^{58} -9.55203 q^{59} +1.93232 q^{60} -4.65463 q^{61} +1.38689 q^{62} -1.03949 q^{63} -2.50999 q^{64} +3.06950 q^{65} +7.65076 q^{66} -11.6411 q^{67} +2.42328 q^{68} -3.37448 q^{69} -1.83849 q^{70} +9.25014 q^{71} -1.18478 q^{72} -8.65687 q^{73} +3.32323 q^{74} +1.40018 q^{75} +5.80803 q^{76} -2.97206 q^{77} -7.90158 q^{78} -9.11079 q^{79} -4.85556 q^{80} -4.80101 q^{81} -16.4799 q^{82} +1.29723 q^{83} +1.93232 q^{84} +1.75594 q^{85} +19.0618 q^{86} -9.26983 q^{87} -3.38748 q^{88} +0.189173 q^{89} +1.91108 q^{90} +3.06950 q^{91} -3.32596 q^{92} -1.05625 q^{93} -4.87017 q^{94} +4.20856 q^{95} +9.30753 q^{96} +1.37751 q^{97} -1.83849 q^{98} +3.08942 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 6 q^{2} - 9 q^{3} + 24 q^{4} + 38 q^{5} - 10 q^{6} + 38 q^{7} - 21 q^{8} + 13 q^{9}+O(q^{10}) $ 38 * q - 6 * q^2 - 9 * q^3 + 24 * q^4 + 38 * q^5 - 10 * q^6 + 38 * q^7 - 21 * q^8 + 13 * q^9	\( 38 q - 6 q^{2} - 9 q^{3} + 24 q^{4} + 38 q^{5} - 10 q^{6} + 38 q^{7} - 21 q^{8} + 13 q^{9} - 6 q^{10} - 18 q^{11} - 20 q^{12} - 25 q^{13} - 6 q^{14} - 9 q^{15} - 21 q^{17} - 7 q^{18} - 14 q^{19} + 24 q^{20} - 9 q^{21} - 11 q^{22} - 16 q^{23} - 10 q^{24} + 38 q^{25} - 21 q^{26} - 15 q^{27} + 24 q^{28} - 52 q^{29} - 10 q^{30} - 30 q^{31} - 8 q^{32} - 13 q^{33} - 9 q^{34} + 38 q^{35} - 16 q^{36} - 47 q^{37} - 10 q^{38} - 50 q^{39} - 21 q^{40} - 35 q^{41} - 10 q^{42} - 18 q^{43} - 22 q^{44} + 13 q^{45} - 17 q^{46} - 23 q^{47} - 13 q^{48} + 38 q^{49} - 6 q^{50} - 5 q^{51} - 41 q^{52} - 12 q^{53} + 35 q^{54} - 18 q^{55} - 21 q^{56} - 3 q^{57} - 16 q^{58} - 16 q^{59} - 20 q^{60} - 47 q^{61} + 14 q^{62} + 13 q^{63} - 55 q^{64} - 25 q^{65} - 6 q^{66} - 54 q^{67} + 31 q^{68} - 95 q^{69} - 6 q^{70} - 41 q^{71} - 59 q^{73} - q^{74} - 9 q^{75} - 23 q^{76} - 18 q^{77} + 19 q^{78} - 117 q^{79} - 38 q^{81} + 19 q^{82} - 21 q^{83} - 20 q^{84} - 21 q^{85} - 12 q^{86} - 14 q^{87} - 40 q^{88} - 96 q^{89} - 7 q^{90} - 25 q^{91} + 53 q^{92} - 53 q^{93} - 28 q^{94} - 14 q^{95} + 40 q^{96} - 70 q^{97} - 6 q^{98} - 52 q^{99}+O(q^{100}) \) 38 * q - 6 * q^2 - 9 * q^3 + 24 * q^4 + 38 * q^5 - 10 * q^6 + 38 * q^7 - 21 * q^8 + 13 * q^9 - 6 * q^10 - 18 * q^11 - 20 * q^12 - 25 * q^13 - 6 * q^14 - 9 * q^15 - 21 * q^17 - 7 * q^18 - 14 * q^19 + 24 * q^20 - 9 * q^21 - 11 * q^22 - 16 * q^23 - 10 * q^24 + 38 * q^25 - 21 * q^26 - 15 * q^27 + 24 * q^28 - 52 * q^29 - 10 * q^30 - 30 * q^31 - 8 * q^32 - 13 * q^33 - 9 * q^34 + 38 * q^35 - 16 * q^36 - 47 * q^37 - 10 * q^38 - 50 * q^39 - 21 * q^40 - 35 * q^41 - 10 * q^42 - 18 * q^43 - 22 * q^44 + 13 * q^45 - 17 * q^46 - 23 * q^47 - 13 * q^48 + 38 * q^49 - 6 * q^50 - 5 * q^51 - 41 * q^52 - 12 * q^53 + 35 * q^54 - 18 * q^55 - 21 * q^56 - 3 * q^57 - 16 * q^58 - 16 * q^59 - 20 * q^60 - 47 * q^61 + 14 * q^62 + 13 * q^63 - 55 * q^64 - 25 * q^65 - 6 * q^66 - 54 * q^67 + 31 * q^68 - 95 * q^69 - 6 * q^70 - 41 * q^71 - 59 * q^73 - q^74 - 9 * q^75 - 23 * q^76 - 18 * q^77 + 19 * q^78 - 117 * q^79 - 38 * q^81 + 19 * q^82 - 21 * q^83 - 20 * q^84 - 21 * q^85 - 12 * q^86 - 14 * q^87 - 40 * q^88 - 96 * q^89 - 7 * q^90 - 25 * q^91 + 53 * q^92 - 53 * q^93 - 28 * q^94 - 14 * q^95 + 40 * q^96 - 70 * q^97 - 6 * q^98 - 52 * 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 $

$2$	−1.83849	−1.30001	−0.650005	−	0.759930i	$-0.725233\pi$
$2$	−1.83849	−1.30001	−0.650005	+	0.759930i	$0.725233\pi$
$3$	1.40018	0.808396	0.404198	−	0.914671i	$-0.367551\pi$
$3$	1.40018	0.808396	0.404198	+	0.914671i	$0.367551\pi$
$4$	1.38005	0.690025
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.57423	−1.05092
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.13977	0.402971
$9$	−1.03949	−0.346495
$10$	−1.83849	−0.581382
$11$	−2.97206	−0.896111	−0.448055	−	0.894006i	$-0.647883\pi$
$11$	−2.97206	−0.896111	−0.448055	+	0.894006i	$0.647883\pi$
$12$	1.93232	0.557813
$13$	3.06950	0.851326	0.425663	−	0.904882i	$-0.360041\pi$
$13$	3.06950	0.851326	0.425663	+	0.904882i	$0.360041\pi$
$14$	−1.83849	−0.491357
$15$	1.40018	0.361526
$16$	−4.85556	−1.21389
$17$	1.75594	0.425877	0.212938	−	0.977066i	$-0.431697\pi$
$17$	1.75594	0.425877	0.212938	+	0.977066i	$0.431697\pi$
$18$	1.91108	0.450447
$19$	4.20856	0.965511	0.482755	−	0.875755i	$-0.339636\pi$
$19$	4.20856	0.965511	0.482755	+	0.875755i	$0.339636\pi$
$20$	1.38005	0.308588
$21$	1.40018	0.305545
$22$	5.46411	1.16495
$23$	−2.41003	−0.502525	−0.251263	−	0.967919i	$-0.580846\pi$
$23$	−2.41003	−0.502525	−0.251263	+	0.967919i	$0.580846\pi$
$24$	1.59589	0.325760
$25$	1.00000	0.200000
$26$	−5.64325	−1.10673
$27$	−5.65602	−1.08850
$28$	1.38005	0.260805
$29$	−6.62044	−1.22938	−0.614692	−	0.788767i	$-0.710720\pi$
$29$	−6.62044	−1.22938	−0.614692	+	0.788767i	$0.710720\pi$
$30$	−2.57423	−0.469987
$31$	−0.754362	−0.135487	−0.0677437	−	0.997703i	$-0.521580\pi$
$31$	−0.754362	−0.135487	−0.0677437	+	0.997703i	$0.521580\pi$
$32$	6.64736	1.17510
$33$	−4.16144	−0.724413
$34$	−3.22827	−0.553644
$35$	1.00000	0.169031
$36$	−1.43454	−0.239090
$37$	−1.80758	−0.297165	−0.148583	−	0.988900i	$-0.547471\pi$
$37$	−1.80758	−0.297165	−0.148583	+	0.988900i	$0.547471\pi$
$38$	−7.73741	−1.25517
$39$	4.29786	0.688209
$40$	1.13977	0.180214
$41$	8.96384	1.39992	0.699959	−	0.714183i	$-0.253202\pi$
$41$	8.96384	1.39992	0.699959	+	0.714183i	$0.253202\pi$
$42$	−2.57423	−0.397212
$43$	−10.3682	−1.58113	−0.790565	−	0.612378i	$-0.790213\pi$
$43$	−10.3682	−1.58113	−0.790565	+	0.612378i	$0.790213\pi$
$44$	−4.10159	−0.618339
$45$	−1.03949	−0.154957
$46$	4.43081	0.653288
$47$	2.64901	0.386397	0.193199	−	0.981160i	$-0.438114\pi$
$47$	2.64901	0.386397	0.193199	+	0.981160i	$0.438114\pi$
$48$	−6.79868	−0.981305
$49$	1.00000	0.142857
$50$	−1.83849	−0.260002
$51$	2.45863	0.344277
$52$	4.23606	0.587436
$53$	−4.13081	−0.567410	−0.283705	−	0.958912i	$-0.591564\pi$
$53$	−4.13081	−0.567410	−0.283705	+	0.958912i	$0.591564\pi$
$54$	10.3985	1.41506
$55$	−2.97206	−0.400753
$56$	1.13977	0.152309
$57$	5.89276	0.780516
$58$	12.1716	1.59821
$59$	−9.55203	−1.24357	−0.621784	−	0.783189i	$-0.713592\pi$
$59$	−9.55203	−1.24357	−0.621784	+	0.783189i	$0.713592\pi$
$60$	1.93232	0.249462
$61$	−4.65463	−0.595965	−0.297982	−	0.954571i	$-0.596314\pi$
$61$	−4.65463	−0.595965	−0.297982	+	0.954571i	$0.596314\pi$
$62$	1.38689	0.176135
$63$	−1.03949	−0.130963
$64$	−2.50999	−0.313748
$65$	3.06950	0.380725
$66$	7.65076	0.941744
$67$	−11.6411	−1.42218	−0.711091	−	0.703100i	$-0.751799\pi$
$67$	−11.6411	−1.42218	−0.711091	+	0.703100i	$0.751799\pi$
$68$	2.42328	0.293866
$69$	−3.37448	−0.406240
$70$	−1.83849	−0.219742
$71$	9.25014	1.09779	0.548895	−	0.835891i	$-0.315049\pi$
$71$	9.25014	1.09779	0.548895	+	0.835891i	$0.315049\pi$
$72$	−1.18478	−0.139627
$73$	−8.65687	−1.01321	−0.506605	−	0.862178i	$-0.669100\pi$
$73$	−8.65687	−1.01321	−0.506605	+	0.862178i	$0.669100\pi$
$74$	3.32323	0.386317
$75$	1.40018	0.161679
$76$	5.80803	0.666226
$77$	−2.97206	−0.338698
$78$	−7.90158	−0.894678
$79$	−9.11079	−1.02504	−0.512522	−	0.858674i	$-0.671289\pi$
$79$	−9.11079	−1.02504	−0.512522	+	0.858674i	$0.671289\pi$
$80$	−4.85556	−0.542868
$81$	−4.80101	−0.533446
$82$	−16.4799	−1.81991
$83$	1.29723	0.142390	0.0711949	−	0.997462i	$-0.477319\pi$
$83$	1.29723	0.142390	0.0711949	+	0.997462i	$0.477319\pi$
$84$	1.93232	0.210834
$85$	1.75594	0.190458
$86$	19.0618	2.05548
$87$	−9.26983	−0.993830
$88$	−3.38748	−0.361107
$89$	0.189173	0.0200523	0.0100261	−	0.999950i	$-0.496809\pi$
$89$	0.189173	0.0200523	0.0100261	+	0.999950i	$0.496809\pi$
$90$	1.91108	0.201446
$91$	3.06950	0.321771
$92$	−3.32596	−0.346755
$93$	−1.05625	−0.109528
$94$	−4.87017	−0.502320
$95$	4.20856	0.431790
$96$	9.30753	0.949945
$97$	1.37751	0.139865	0.0699325	−	0.997552i	$-0.477722\pi$
$97$	1.37751	0.139865	0.0699325	+	0.997552i	$0.477722\pi$
$98$	−1.83849	−0.185716
$99$	3.08942	0.310498
$100$	1.38005	0.138005
$101$	3.88401	0.386473	0.193237	−	0.981152i	$-0.438101\pi$
$101$	3.88401	0.386473	0.193237	+	0.981152i	$0.438101\pi$
$102$	−4.52017	−0.447564
$103$	9.86949	0.972470	0.486235	−	0.873828i	$-0.338370\pi$
$103$	9.86949	0.972470	0.486235	+	0.873828i	$0.338370\pi$
$104$	3.49854	0.343060
$105$	1.40018	0.136644
$106$	7.59445	0.737638
$107$	−0.618981	−0.0598391	−0.0299196	−	0.999552i	$-0.509525\pi$
$107$	−0.618981	−0.0598391	−0.0299196	+	0.999552i	$0.509525\pi$
$108$	−7.80559	−0.751093
$109$	4.50727	0.431718	0.215859	−	0.976425i	$-0.430745\pi$
$109$	4.50727	0.431718	0.215859	+	0.976425i	$0.430745\pi$
$110$	5.46411	0.520983
$111$	−2.53095	−0.240227
$112$	−4.85556	−0.458808
$113$	−0.324460	−0.0305226	−0.0152613	−	0.999884i	$-0.504858\pi$
$113$	−0.324460	−0.0305226	−0.0152613	+	0.999884i	$0.504858\pi$
$114$	−10.8338	−1.01468
$115$	−2.41003	−0.224736
$116$	−9.13653	−0.848306
$117$	−3.19070	−0.294980
$118$	17.5613	1.61665
$119$	1.75594	0.160966
$120$	1.59589	0.145684
$121$	−2.16684	−0.196985
$122$	8.55750	0.774760
$123$	12.5510	1.13169
$124$	−1.04106	−0.0934896
$125$	1.00000	0.0894427
$126$	1.91108	0.170253
$127$	−5.79603	−0.514315	−0.257157	−	0.966370i	$-0.582786\pi$
$127$	−5.79603	−0.514315	−0.257157	+	0.966370i	$0.582786\pi$
$128$	−8.68013	−0.767223
$129$	−14.5173	−1.27818
$130$	−5.64325	−0.494945
$131$	18.1837	1.58872	0.794359	−	0.607448i	$-0.207807\pi$
$131$	18.1837	1.58872	0.794359	+	0.607448i	$0.207807\pi$
$132$	−5.74299	−0.499863
$133$	4.20856	0.364929
$134$	21.4020	1.84885
$135$	−5.65602	−0.486793
$136$	2.00137	0.171616
$137$	−10.0367	−0.857491	−0.428746	−	0.903425i	$-0.641044\pi$
$137$	−10.0367	−0.857491	−0.428746	+	0.903425i	$0.641044\pi$
$138$	6.20395	0.528115
$139$	−3.21366	−0.272579	−0.136290	−	0.990669i	$-0.543518\pi$
$139$	−3.21366	−0.272579	−0.136290	+	0.990669i	$0.543518\pi$
$140$	1.38005	0.116635
$141$	3.70909	0.312362
$142$	−17.0063	−1.42714
$143$	−9.12275	−0.762882
$144$	5.04729	0.420607
$145$	−6.62044	−0.549798
$146$	15.9156	1.31718
$147$	1.40018	0.115485
$148$	−2.49456	−0.205051
$149$	−7.09649	−0.581367	−0.290684	−	0.956819i	$-0.593883\pi$
$149$	−7.09649	−0.581367	−0.290684	+	0.956819i	$0.593883\pi$
$150$	−2.57423	−0.210185
$151$	−10.5242	−0.856445	−0.428223	−	0.903673i	$-0.640860\pi$
$151$	−10.5242	−0.856445	−0.428223	+	0.903673i	$0.640860\pi$
$152$	4.79681	0.389073
$153$	−1.82527	−0.147564
$154$	5.46411	0.440311
$155$	−0.754362	−0.0605918
$156$	5.93126	0.474881
$157$	−19.2160	−1.53361	−0.766803	−	0.641883i	$-0.778154\pi$
$157$	−19.2160	−1.53361	−0.766803	+	0.641883i	$0.778154\pi$
$158$	16.7501	1.33257
$159$	−5.78389	−0.458692
$160$	6.64736	0.525520
$161$	−2.41003	−0.189937
$162$	8.82662	0.693485
$163$	6.14382	0.481221	0.240611	−	0.970622i	$-0.422652\pi$
$163$	6.14382	0.481221	0.240611	+	0.970622i	$0.422652\pi$
$164$	12.3705	0.965977
$165$	−4.16144	−0.323967
$166$	−2.38495	−0.185108
$167$	13.3499	1.03305	0.516523	−	0.856273i	$-0.327226\pi$
$167$	13.3499	1.03305	0.516523	+	0.856273i	$0.327226\pi$
$168$	1.59589	0.123126
$169$	−3.57817	−0.275244
$170$	−3.22827	−0.247597
$171$	−4.37474	−0.334545
$172$	−14.3086	−1.09102
$173$	−18.2240	−1.38554	−0.692772	−	0.721156i	$-0.743611\pi$
$173$	−18.2240	−1.38554	−0.692772	+	0.721156i	$0.743611\pi$
$174$	17.0425	1.29199
$175$	1.00000	0.0755929
$176$	14.4310	1.08778
$177$	−13.3746	−1.00530
$178$	−0.347792	−0.0260681
$179$	23.8179	1.78024	0.890118	−	0.455730i	$-0.150622\pi$
$179$	23.8179	1.78024	0.890118	+	0.455730i	$0.150622\pi$
$180$	−1.43454	−0.106924
$181$	−14.6218	−1.08683	−0.543414	−	0.839465i	$-0.682869\pi$
$181$	−14.6218	−1.08683	−0.543414	+	0.839465i	$0.682869\pi$
$182$	−5.64325	−0.418305
$183$	−6.51734	−0.481776
$184$	−2.74689	−0.202503
$185$	−1.80758	−0.132896
$186$	1.94190	0.142387
$187$	−5.21875	−0.381633
$188$	3.65576	0.266624
$189$	−5.65602	−0.411415
$190$	−7.73741	−0.561330
$191$	8.68314	0.628290	0.314145	−	0.949375i	$-0.398282\pi$
$191$	8.68314	0.628290	0.314145	+	0.949375i	$0.398282\pi$
$192$	−3.51444	−0.253633
$193$	19.7408	1.42097	0.710486	−	0.703711i	$-0.248475\pi$
$193$	19.7408	1.42097	0.710486	+	0.703711i	$0.248475\pi$
$194$	−2.53254	−0.181826
$195$	4.29786	0.307776
$196$	1.38005	0.0985749
$197$	−6.72227	−0.478942	−0.239471	−	0.970904i	$-0.576974\pi$
$197$	−6.72227	−0.478942	−0.239471	+	0.970904i	$0.576974\pi$
$198$	−5.67987	−0.403650
$199$	−19.8315	−1.40582	−0.702909	−	0.711280i	$-0.748116\pi$
$199$	−19.8315	−1.40582	−0.702909	+	0.711280i	$0.748116\pi$
$200$	1.13977	0.0805942
$201$	−16.2996	−1.14969
$202$	−7.14072	−0.502419
$203$	−6.62044	−0.464664
$204$	3.39303	0.237560
$205$	8.96384	0.626062
$206$	−18.1450	−1.26422
$207$	2.50519	0.174123
$208$	−14.9041	−1.03342
$209$	−12.5081	−0.865205
$210$	−2.57423	−0.177638
$211$	−4.86225	−0.334731	−0.167365	−	0.985895i	$-0.553526\pi$
$211$	−4.86225	−0.334731	−0.167365	+	0.985895i	$0.553526\pi$
$212$	−5.70072	−0.391527
$213$	12.9519	0.887449
$214$	1.13799	0.0777915
$215$	−10.3682	−0.707103
$216$	−6.44659	−0.438635
$217$	−0.754362	−0.0512094
$218$	−8.28658	−0.561238
$219$	−12.1212	−0.819075
$220$	−4.10159	−0.276529
$221$	5.38984	0.362560
$222$	4.65313	0.312298
$223$	18.8690	1.26356	0.631779	−	0.775148i	$-0.282325\pi$
$223$	18.8690	1.26356	0.631779	+	0.775148i	$0.282325\pi$
$224$	6.64736	0.444145
$225$	−1.03949	−0.0692990
$226$	0.596516	0.0396797
$227$	−26.7843	−1.77773	−0.888867	−	0.458166i	$-0.848507\pi$
$227$	−26.7843	−1.77773	−0.888867	+	0.458166i	$0.848507\pi$
$228$	8.13230	0.538575
$229$	−1.00000	−0.0660819
$229$	−1.00000	−0.0660819
$230$	4.43081	0.292159
$231$	−4.16144	−0.273802
$232$	−7.54581	−0.495406
$233$	−5.74840	−0.376590	−0.188295	−	0.982112i	$-0.560296\pi$
$233$	−5.74840	−0.376590	−0.188295	+	0.982112i	$0.560296\pi$
$234$	5.86607	0.383477
$235$	2.64901	0.172802
$236$	−13.1823	−0.858093
$237$	−12.7568	−0.828641
$238$	−3.22827	−0.209258
$239$	−13.7941	−0.892267	−0.446134	−	0.894966i	$-0.647199\pi$
$239$	−13.7941	−0.892267	−0.446134	+	0.894966i	$0.647199\pi$
$240$	−6.79868	−0.438853
$241$	−14.9793	−0.964901	−0.482451	−	0.875923i	$-0.660253\pi$
$241$	−14.9793	−0.964901	−0.482451	+	0.875923i	$0.660253\pi$
$242$	3.98371	0.256083
$243$	10.2458	0.657266
$244$	−6.42362	−0.411230
$245$	1.00000	0.0638877
$246$	−23.0750	−1.47121
$247$	12.9182	0.821964
$248$	−0.859802	−0.0545975
$249$	1.81636	0.115107
$250$	−1.83849	−0.116276
$251$	−2.62229	−0.165517	−0.0827586	−	0.996570i	$-0.526373\pi$
$251$	−2.62229	−0.165517	−0.0827586	+	0.996570i	$0.526373\pi$
$252$	−1.43454	−0.0903676
$253$	7.16275	0.450318
$254$	10.6560	0.668614
$255$	2.45863	0.153966
$256$	20.9783	1.31114
$257$	−20.3499	−1.26939	−0.634695	−	0.772763i	$-0.718874\pi$
$257$	−20.3499	−1.26939	−0.634695	+	0.772763i	$0.718874\pi$
$258$	26.6900	1.66165
$259$	−1.80758	−0.112318
$260$	4.23606	0.262709
$261$	6.88185	0.425976
$262$	−33.4306	−2.06535
$263$	0.396438	0.0244454	0.0122227	−	0.999925i	$-0.496109\pi$
$263$	0.396438	0.0244454	0.0122227	+	0.999925i	$0.496109\pi$
$264$	−4.74310	−0.291917
$265$	−4.13081	−0.253753
$266$	−7.73741	−0.474411
$267$	0.264877	0.0162102
$268$	−16.0652	−0.981340
$269$	22.7538	1.38733	0.693663	−	0.720300i	$-0.255996\pi$
$269$	22.7538	1.38733	0.693663	+	0.720300i	$0.255996\pi$
$270$	10.3985	0.632835
$271$	2.98662	0.181424	0.0907121	−	0.995877i	$-0.471086\pi$
$271$	2.98662	0.181424	0.0907121	+	0.995877i	$0.471086\pi$
$272$	−8.52606	−0.516968
$273$	4.29786	0.260119
$274$	18.4523	1.11475
$275$	−2.97206	−0.179222
$276$	−4.65695	−0.280315
$277$	−4.73396	−0.284436	−0.142218	−	0.989835i	$-0.545423\pi$
$277$	−4.73396	−0.284436	−0.142218	+	0.989835i	$0.545423\pi$
$278$	5.90829	0.354356
$279$	0.784148	0.0469457
$280$	1.13977	0.0681145
$281$	4.87195	0.290636	0.145318	−	0.989385i	$-0.453579\pi$
$281$	4.87195	0.290636	0.145318	+	0.989385i	$0.453579\pi$
$282$	−6.81914	−0.406074
$283$	1.18018	0.0701546	0.0350773	−	0.999385i	$-0.488832\pi$
$283$	1.18018	0.0701546	0.0350773	+	0.999385i	$0.488832\pi$
$284$	12.7656	0.757502
$285$	5.89276	0.349057
$286$	16.7721	0.991754
$287$	8.96384	0.529119
$288$	−6.90983	−0.407166
$289$	−13.9167	−0.818629
$290$	12.1716	0.714742
$291$	1.92877	0.113066
$292$	−11.9469	−0.699139
$293$	−6.65273	−0.388657	−0.194328	−	0.980937i	$-0.562253\pi$
$293$	−6.65273	−0.388657	−0.194328	+	0.980937i	$0.562253\pi$
$294$	−2.57423	−0.150132
$295$	−9.55203	−0.556141
$296$	−2.06024	−0.119749
$297$	16.8101	0.975418
$298$	13.0468	0.755783
$299$	−7.39758	−0.427813
$300$	1.93232	0.111563
$301$	−10.3682	−0.597611
$302$	19.3486	1.11339
$303$	5.43833	0.312424
$304$	−20.4349	−1.17202
$305$	−4.65463	−0.266524
$306$	3.35574	0.191835
$307$	5.83221	0.332862	0.166431	−	0.986053i	$-0.446776\pi$
$307$	5.83221	0.332862	0.166431	+	0.986053i	$0.446776\pi$
$308$	−4.10159	−0.233710
$309$	13.8191	0.786141
$310$	1.38689	0.0787699
$311$	−15.2493	−0.864707	−0.432353	−	0.901704i	$-0.642317\pi$
$311$	−15.2493	−0.864707	−0.432353	+	0.901704i	$0.642317\pi$
$312$	4.89859	0.277328
$313$	9.52050	0.538131	0.269065	−	0.963122i	$-0.413285\pi$
$313$	9.52050	0.538131	0.269065	+	0.963122i	$0.413285\pi$
$314$	35.3285	1.99370
$315$	−1.03949	−0.0585684
$316$	−12.5733	−0.707305
$317$	29.9578	1.68260	0.841299	−	0.540570i	$-0.181792\pi$
$317$	29.9578	1.68260	0.841299	+	0.540570i	$0.181792\pi$
$318$	10.6336	0.596304
$319$	19.6764	1.10167
$320$	−2.50999	−0.140313
$321$	−0.866687	−0.0483738
$322$	4.43081	0.246920
$323$	7.38997	0.411189
$324$	−6.62564	−0.368091
$325$	3.06950	0.170265
$326$	−11.2954	−0.625592
$327$	6.31101	0.348999
$328$	10.2168	0.564126
$329$	2.64901	0.146044
$330$	7.65076	0.421161
$331$	13.0131	0.715265	0.357633	−	0.933862i	$-0.383584\pi$
$331$	13.0131	0.715265	0.357633	+	0.933862i	$0.383584\pi$
$332$	1.79024	0.0982524
$333$	1.87896	0.102966
$334$	−24.5437	−1.34297
$335$	−11.6411	−0.636019
$336$	−6.79868	−0.370898
$337$	3.49677	0.190481	0.0952405	−	0.995454i	$-0.469638\pi$
$337$	3.49677	0.190481	0.0952405	+	0.995454i	$0.469638\pi$
$338$	6.57844	0.357820
$339$	−0.454303	−0.0246744
$340$	2.42328	0.131421
$341$	2.24201	0.121412
$342$	8.04292	0.434911
$343$	1.00000	0.0539949
$344$	−11.8174	−0.637149
$345$	−3.37448	−0.181676
$346$	33.5046	1.80122
$347$	−8.69376	−0.466706	−0.233353	−	0.972392i	$-0.574970\pi$
$347$	−8.69376	−0.466706	−0.233353	+	0.972392i	$0.574970\pi$
$348$	−12.7928	−0.685767
$349$	1.32425	0.0708857	0.0354428	−	0.999372i	$-0.488716\pi$
$349$	1.32425	0.0708857	0.0354428	+	0.999372i	$0.488716\pi$
$350$	−1.83849	−0.0982715
$351$	−17.3612	−0.926670
$352$	−19.7564	−1.05302
$353$	6.53102	0.347611	0.173806	−	0.984780i	$-0.444394\pi$
$353$	6.53102	0.347611	0.173806	+	0.984780i	$0.444394\pi$
$354$	24.5891	1.30689
$355$	9.25014	0.490946
$356$	0.261068	0.0138366
$357$	2.45863	0.130125
$358$	−43.7891	−2.31432
$359$	−23.1911	−1.22398	−0.611990	−	0.790865i	$-0.709631\pi$
$359$	−23.1911	−1.22398	−0.611990	+	0.790865i	$0.709631\pi$
$360$	−1.18478	−0.0624433
$361$	−1.28799	−0.0677890
$362$	26.8820	1.41289
$363$	−3.03397	−0.159242
$364$	4.23606	0.222030
$365$	−8.65687	−0.453121
$366$	11.9821	0.626313
$367$	6.44042	0.336187	0.168093	−	0.985771i	$-0.446239\pi$
$367$	6.44042	0.336187	0.168093	+	0.985771i	$0.446239\pi$
$368$	11.7020	0.610011
$369$	−9.31778	−0.485064
$370$	3.32323	0.172766
$371$	−4.13081	−0.214461
$372$	−1.45767	−0.0755767
$373$	−18.7115	−0.968844	−0.484422	−	0.874834i	$-0.660970\pi$
$373$	−18.7115	−0.968844	−0.484422	+	0.874834i	$0.660970\pi$
$374$	9.59463	0.496127
$375$	1.40018	0.0723052
$376$	3.01927	0.155707
$377$	−20.3214	−1.04661
$378$	10.3985	0.534843
$379$	13.7910	0.708395	0.354198	−	0.935171i	$-0.384754\pi$
$379$	13.7910	0.708395	0.354198	+	0.935171i	$0.384754\pi$
$380$	5.80803	0.297945
$381$	−8.11551	−0.415770
$382$	−15.9639	−0.816783
$383$	29.6775	1.51645	0.758226	−	0.651992i	$-0.226066\pi$
$383$	29.6775	1.51645	0.758226	+	0.651992i	$0.226066\pi$
$384$	−12.1538	−0.620220
$385$	−2.97206	−0.151470
$386$	−36.2933	−1.84728
$387$	10.7776	0.547854
$388$	1.90103	0.0965103
$389$	−21.8428	−1.10747	−0.553736	−	0.832692i	$-0.686798\pi$
$389$	−21.8428	−1.10747	−0.553736	+	0.832692i	$0.686798\pi$
$390$	−7.90158	−0.400112
$391$	−4.23185	−0.214014
$392$	1.13977	0.0575673
$393$	25.4605	1.28431
$394$	12.3588	0.622629
$395$	−9.11079	−0.458413
$396$	4.26355	0.214251
$397$	12.1479	0.609685	0.304843	−	0.952403i	$-0.401396\pi$
$397$	12.1479	0.609685	0.304843	+	0.952403i	$0.401396\pi$
$398$	36.4601	1.82758
$399$	5.89276	0.295007
$400$	−4.85556	−0.242778
$401$	31.4443	1.57025	0.785126	−	0.619336i	$-0.212598\pi$
$401$	31.4443	1.57025	0.785126	+	0.619336i	$0.212598\pi$
$402$	29.9667	1.49460
$403$	−2.31551	−0.115344
$404$	5.36012	0.266676
$405$	−4.80101	−0.238564
$406$	12.1716	0.604067
$407$	5.37226	0.266293
$408$	2.80229	0.138734
$409$	−4.19537	−0.207448	−0.103724	−	0.994606i	$-0.533076\pi$
$409$	−4.19537	−0.207448	−0.103724	+	0.994606i	$0.533076\pi$
$410$	−16.4799	−0.813886
$411$	−14.0532	−0.693193
$412$	13.6204	0.671028
$413$	−9.55203	−0.470025
$414$	−4.60577	−0.226361
$415$	1.29723	0.0636786
$416$	20.4041	1.00039
$417$	−4.49972	−0.220352
$418$	22.9961	1.12477
$419$	−15.4039	−0.752532	−0.376266	−	0.926512i	$-0.622792\pi$
$419$	−15.4039	−0.752532	−0.376266	+	0.926512i	$0.622792\pi$
$420$	1.93232	0.0942877
$421$	15.4831	0.754602	0.377301	−	0.926091i	$-0.376852\pi$
$421$	15.4831	0.754602	0.377301	+	0.926091i	$0.376852\pi$
$422$	8.93920	0.435153
$423$	−2.75360	−0.133885
$424$	−4.70818	−0.228650
$425$	1.75594	0.0851754
$426$	−23.8119	−1.15369
$427$	−4.65463	−0.225253
$428$	−0.854224	−0.0412905
$429$	−12.7735	−0.616711
$430$	19.0618	0.919240
$431$	−22.3280	−1.07550	−0.537752	−	0.843103i	$-0.680726\pi$
$431$	−22.3280	−1.07550	−0.537752	+	0.843103i	$0.680726\pi$
$432$	27.4632	1.32132
$433$	−36.1962	−1.73948	−0.869739	−	0.493511i	$-0.835713\pi$
$433$	−36.1962	−1.73948	−0.869739	+	0.493511i	$0.835713\pi$
$434$	1.38689	0.0665727
$435$	−9.26983	−0.444454
$436$	6.22025	0.297896
$437$	−10.1428	−0.485194
$438$	22.2847	1.06481
$439$	−30.9651	−1.47788	−0.738941	−	0.673770i	$-0.764674\pi$
$439$	−30.9651	−1.47788	−0.738941	+	0.673770i	$0.764674\pi$
$440$	−3.38748	−0.161492
$441$	−1.03949	−0.0494993
$442$	−9.90918	−0.471332
$443$	20.5268	0.975258	0.487629	−	0.873051i	$-0.337862\pi$
$443$	20.5268	0.975258	0.487629	+	0.873051i	$0.337862\pi$
$444$	−3.49284	−0.165763
$445$	0.189173	0.00896765
$446$	−34.6904	−1.64264
$447$	−9.93640	−0.469975
$448$	−2.50999	−0.118586
$449$	4.47215	0.211054	0.105527	−	0.994416i	$-0.466347\pi$
$449$	4.47215	0.211054	0.105527	+	0.994416i	$0.466347\pi$
$450$	1.91108	0.0900894
$451$	−26.6411	−1.25448
$452$	−0.447770	−0.0210613
$453$	−14.7358	−0.692347
$454$	49.2426	2.31107
$455$	3.06950	0.143900
$456$	6.71642	0.314525
$457$	−30.2590	−1.41545	−0.707727	−	0.706486i	$-0.750279\pi$
$457$	−30.2590	−1.41545	−0.707727	+	0.706486i	$0.750279\pi$
$458$	1.83849	0.0859070
$459$	−9.93161	−0.463568
$460$	−3.32596	−0.155073
$461$	34.4684	1.60536	0.802678	−	0.596413i	$-0.203408\pi$
$461$	34.4684	1.60536	0.802678	+	0.596413i	$0.203408\pi$
$462$	7.65076	0.355946
$463$	−4.33867	−0.201635	−0.100818	−	0.994905i	$-0.532146\pi$
$463$	−4.33867	−0.201635	−0.100818	+	0.994905i	$0.532146\pi$
$464$	32.1460	1.49234
$465$	−1.05625	−0.0489822
$466$	10.5684	0.489571
$467$	−20.4557	−0.946575	−0.473287	−	0.880908i	$-0.656933\pi$
$467$	−20.4557	−0.946575	−0.473287	+	0.880908i	$0.656933\pi$
$468$	−4.40332	−0.203544
$469$	−11.6411	−0.537534
$470$	−4.87017	−0.224644
$471$	−26.9060	−1.23976
$472$	−10.8872	−0.501122
$473$	30.8148	1.41687
$474$	23.4532	1.07724
$475$	4.20856	0.193102
$476$	2.42328	0.111071
$477$	4.29391	0.196605
$478$	25.3604	1.15996
$479$	−15.0741	−0.688755	−0.344378	−	0.938831i	$-0.611910\pi$
$479$	−15.0741	−0.688755	−0.344378	+	0.938831i	$0.611910\pi$
$480$	9.30753	0.424829
$481$	−5.54838	−0.252984
$482$	27.5393	1.25438
$483$	−3.37448	−0.153544
$484$	−2.99034	−0.135925
$485$	1.37751	0.0625495
$486$	−18.8367	−0.854452
$487$	17.6038	0.797705	0.398853	−	0.917015i	$-0.369408\pi$
$487$	17.6038	0.797705	0.398853	+	0.917015i	$0.369408\pi$
$488$	−5.30523	−0.240156
$489$	8.60248	0.389017
$490$	−1.83849	−0.0830546
$491$	14.1186	0.637165	0.318583	−	0.947895i	$-0.396793\pi$
$491$	14.1186	0.637165	0.318583	+	0.947895i	$0.396793\pi$
$492$	17.3210	0.780893
$493$	−11.6251	−0.523567
$494$	−23.7500	−1.06856
$495$	3.08942	0.138859
$496$	3.66285	0.164467
$497$	9.25014	0.414925
$498$	−3.33937	−0.149641
$499$	14.0299	0.628065	0.314033	−	0.949412i	$-0.398320\pi$
$499$	14.0299	0.628065	0.314033	+	0.949412i	$0.398320\pi$
$500$	1.38005	0.0617177
$501$	18.6923	0.835110
$502$	4.82105	0.215174
$503$	22.7381	1.01384	0.506921	−	0.861993i	$-0.330784\pi$
$503$	22.7381	1.01384	0.506921	+	0.861993i	$0.330784\pi$
$504$	−1.18478	−0.0527742
$505$	3.88401	0.172836
$506$	−13.1687	−0.585418
$507$	−5.01010	−0.222506
$508$	−7.99881	−0.354890
$509$	14.5981	0.647051	0.323526	−	0.946219i	$-0.395132\pi$
$509$	14.5981	0.647051	0.323526	+	0.946219i	$0.395132\pi$
$510$	−4.52017	−0.200157
$511$	−8.65687	−0.382957
$512$	−21.2082	−0.937278
$513$	−23.8037	−1.05096
$514$	37.4131	1.65022
$515$	9.86949	0.434902
$516$	−20.0346	−0.881975
$517$	−7.87301	−0.346255
$518$	3.32323	0.146014
$519$	−25.5169	−1.12007
$520$	3.49854	0.153421
$521$	−28.4333	−1.24568	−0.622842	−	0.782348i	$-0.714022\pi$
$521$	−28.4333	−1.24568	−0.622842	+	0.782348i	$0.714022\pi$
$522$	−12.6522	−0.553773
$523$	−0.773708	−0.0338319	−0.0169159	−	0.999857i	$-0.505385\pi$
$523$	−0.773708	−0.0338319	−0.0169159	+	0.999857i	$0.505385\pi$
$524$	25.0944	1.09625
$525$	1.40018	0.0611090
$526$	−0.728849	−0.0317793
$527$	−1.32461	−0.0577010
$528$	20.2061	0.879358
$529$	−17.1918	−0.747468
$530$	7.59445	0.329882
$531$	9.92919	0.430890
$532$	5.80803	0.251810
$533$	27.5145	1.19179
$534$	−0.486973	−0.0210734
$535$	−0.618981	−0.0267609
$536$	−13.2682	−0.573098
$537$	33.3495	1.43914
$538$	−41.8327	−1.80354
$539$	−2.97206	−0.128016
$540$	−7.80559	−0.335899
$541$	4.93959	0.212370	0.106185	−	0.994346i	$-0.466136\pi$
$541$	4.93959	0.212370	0.106185	+	0.994346i	$0.466136\pi$
$542$	−5.49087	−0.235853
$543$	−20.4732	−0.878588
$544$	11.6723	0.500447
$545$	4.50727	0.193070
$546$	−7.90158	−0.338157
$547$	−12.1315	−0.518704	−0.259352	−	0.965783i	$-0.583509\pi$
$547$	−12.1315	−0.518704	−0.259352	+	0.965783i	$0.583509\pi$
$548$	−13.8511	−0.591690
$549$	4.83842	0.206499
$550$	5.46411	0.232991
$551$	−27.8625	−1.18698
$552$	−3.84614	−0.163703
$553$	−9.11079	−0.387430
$554$	8.70335	0.369770
$555$	−2.53095	−0.107433
$556$	−4.43502	−0.188087
$557$	38.3130	1.62338	0.811688	−	0.584092i	$-0.198549\pi$
$557$	38.3130	1.62338	0.811688	+	0.584092i	$0.198549\pi$
$558$	−1.44165	−0.0610299
$559$	−31.8251	−1.34606
$560$	−4.85556	−0.205185
$561$	−7.30721	−0.308511
$562$	−8.95703	−0.377830
$563$	0.678110	0.0285789	0.0142895	−	0.999898i	$-0.495451\pi$
$563$	0.678110	0.0285789	0.0142895	+	0.999898i	$0.495451\pi$
$564$	5.11873	0.215538
$565$	−0.324460	−0.0136501
$566$	−2.16975	−0.0912016
$567$	−4.80101	−0.201624
$568$	10.5431	0.442377
$569$	−12.7635	−0.535073	−0.267537	−	0.963548i	$-0.586210\pi$
$569$	−12.7635	−0.535073	−0.267537	+	0.963548i	$0.586210\pi$
$570$	−10.8338	−0.453778
$571$	19.7174	0.825147	0.412574	−	0.910924i	$-0.364630\pi$
$571$	19.7174	0.825147	0.412574	+	0.910924i	$0.364630\pi$
$572$	−12.5898	−0.526408
$573$	12.1580	0.507908
$574$	−16.4799	−0.687860
$575$	−2.41003	−0.100505
$576$	2.60910	0.108712
$577$	−1.76926	−0.0736551	−0.0368276	−	0.999322i	$-0.511725\pi$
$577$	−1.76926	−0.0736551	−0.0368276	+	0.999322i	$0.511725\pi$
$578$	25.5857	1.06423
$579$	27.6407	1.14871
$580$	−9.13653	−0.379374
$581$	1.29723	0.0538183
$582$	−3.54602	−0.146987
$583$	12.2770	0.508462
$584$	−9.86687	−0.408294
$585$	−3.19070	−0.131919
$586$	12.2310	0.505258
$587$	−11.7144	−0.483505	−0.241753	−	0.970338i	$-0.577722\pi$
$587$	−11.7144	−0.483505	−0.241753	+	0.970338i	$0.577722\pi$
$588$	1.93232	0.0796876
$589$	−3.17478	−0.130815
$590$	17.5613	0.722988
$591$	−9.41241	−0.387175
$592$	8.77684	0.360726
$593$	−33.5094	−1.37607	−0.688033	−	0.725679i	$-0.741526\pi$
$593$	−33.5094	−1.37607	−0.688033	+	0.725679i	$0.741526\pi$
$594$	−30.9051	−1.26805
$595$	1.75594	0.0719863
$596$	−9.79351	−0.401158
$597$	−27.7678	−1.13646
$598$	13.6004	0.556161
$599$	−8.86781	−0.362329	−0.181164	−	0.983453i	$-0.557987\pi$
$599$	−8.86781	−0.362329	−0.181164	+	0.983453i	$0.557987\pi$
$600$	1.59589	0.0651521
$601$	−23.7720	−0.969682	−0.484841	−	0.874602i	$-0.661122\pi$
$601$	−23.7720	−0.969682	−0.484841	+	0.874602i	$0.661122\pi$
$602$	19.0618	0.776900
$603$	12.1007	0.492779
$604$	−14.5239	−0.590968
$605$	−2.16684	−0.0880945
$606$	−9.99832	−0.406154
$607$	6.90729	0.280358	0.140179	−	0.990126i	$-0.455232\pi$
$607$	6.90729	0.280358	0.140179	+	0.990126i	$0.455232\pi$
$608$	27.9758	1.13457
$609$	−9.26983	−0.375633
$610$	8.55750	0.346483
$611$	8.13112	0.328950
$612$	−2.51896	−0.101823
$613$	13.1520	0.531206	0.265603	−	0.964082i	$-0.414429\pi$
$613$	13.1520	0.531206	0.265603	+	0.964082i	$0.414429\pi$
$614$	−10.7225	−0.432724
$615$	12.5510	0.506106
$616$	−3.38748	−0.136485
$617$	44.1655	1.77804	0.889018	−	0.457872i	$-0.151388\pi$
$617$	44.1655	1.77804	0.889018	+	0.457872i	$0.151388\pi$
$618$	−25.4063	−1.02199
$619$	2.82729	0.113638	0.0568192	−	0.998384i	$-0.481904\pi$
$619$	2.82729	0.113638	0.0568192	+	0.998384i	$0.481904\pi$
$620$	−1.04106	−0.0418098
$621$	13.6312	0.547000
$622$	28.0356	1.12413
$623$	0.189173	0.00757905
$624$	−20.8685	−0.835410
$625$	1.00000	0.0400000
$626$	−17.5034	−0.699575
$627$	−17.5137	−0.699428
$628$	−26.5191	−1.05823
$629$	−3.17400	−0.126556
$630$	1.91108	0.0761394
$631$	20.9938	0.835750	0.417875	−	0.908505i	$-0.362775\pi$
$631$	20.9938	0.835750	0.417875	+	0.908505i	$0.362775\pi$
$632$	−10.3842	−0.413063
$633$	−6.80804	−0.270595
$634$	−55.0771	−2.18739
$635$	−5.79603	−0.230009
$636$	−7.98205	−0.316509
$637$	3.06950	0.121618
$638$	−36.1748	−1.43218
$639$	−9.61538	−0.380379
$640$	−8.68013	−0.343112
$641$	−31.0954	−1.22820	−0.614098	−	0.789230i	$-0.710480\pi$
$641$	−31.0954	−1.22820	−0.614098	+	0.789230i	$0.710480\pi$
$642$	1.59340	0.0628863
$643$	37.8903	1.49425	0.747124	−	0.664685i	$-0.231434\pi$
$643$	37.8903	1.49425	0.747124	+	0.664685i	$0.231434\pi$
$644$	−3.32596	−0.131061
$645$	−14.5173	−0.571619
$646$	−13.5864	−0.534549
$647$	−41.3366	−1.62511	−0.812556	−	0.582884i	$-0.801924\pi$
$647$	−41.3366	−1.62511	−0.812556	+	0.582884i	$0.801924\pi$
$648$	−5.47207	−0.214963
$649$	28.3892	1.11437
$650$	−5.64325	−0.221346
$651$	−1.05625	−0.0413975
$652$	8.47877	0.332054
$653$	−27.5810	−1.07933	−0.539663	−	0.841881i	$-0.681448\pi$
$653$	−27.5810	−1.07933	−0.539663	+	0.841881i	$0.681448\pi$
$654$	−11.6027	−0.453703
$655$	18.1837	0.710496
$656$	−43.5245	−1.69935
$657$	8.99869	0.351072
$658$	−4.87017	−0.189859
$659$	3.61077	0.140656	0.0703278	−	0.997524i	$-0.477595\pi$
$659$	3.61077	0.140656	0.0703278	+	0.997524i	$0.477595\pi$
$660$	−5.74299	−0.223545
$661$	−47.6906	−1.85495	−0.927475	−	0.373886i	$-0.878025\pi$
$661$	−47.6906	−1.85495	−0.927475	+	0.373886i	$0.878025\pi$
$662$	−23.9245	−0.929852
$663$	7.54677	0.293092
$664$	1.47855	0.0573789
$665$	4.20856	0.163201
$666$	−3.45445	−0.133857
$667$	15.9554	0.617797
$668$	18.4235	0.712827
$669$	26.4200	1.02146
$670$	21.4020	0.826831
$671$	13.8339	0.534050
$672$	9.30753	0.359046
$673$	−32.4333	−1.25021	−0.625106	−	0.780540i	$-0.714944\pi$
$673$	−32.4333	−1.25021	−0.625106	+	0.780540i	$0.714944\pi$
$674$	−6.42878	−0.247627
$675$	−5.65602	−0.217700
$676$	−4.93806	−0.189925
$677$	20.2467	0.778142	0.389071	−	0.921208i	$-0.372796\pi$
$677$	20.2467	0.778142	0.389071	+	0.921208i	$0.372796\pi$
$678$	0.835232	0.0320769
$679$	1.37751	0.0528640
$680$	2.00137	0.0767490
$681$	−37.5029	−1.43711
$682$	−4.12192	−0.157836
$683$	19.3491	0.740374	0.370187	−	0.928957i	$-0.379294\pi$
$683$	19.3491	0.740374	0.370187	+	0.928957i	$0.379294\pi$
$684$	−6.03736	−0.230844
$685$	−10.0367	−0.383482
$686$	−1.83849	−0.0701939
$687$	−1.40018	−0.0534203
$688$	50.3433	1.91932
$689$	−12.6795	−0.483051
$690$	6.20395	0.236180
$691$	−8.78665	−0.334260	−0.167130	−	0.985935i	$-0.553450\pi$
$691$	−8.78665	−0.334260	−0.167130	+	0.985935i	$0.553450\pi$
$692$	−25.1500	−0.956060
$693$	3.08942	0.117357
$694$	15.9834	0.606722
$695$	−3.21366	−0.121901
$696$	−10.5655	−0.400485
$697$	15.7399	0.596192
$698$	−2.43463	−0.0921521
$699$	−8.04882	−0.304434
$700$	1.38005	0.0521610
$701$	−51.4426	−1.94296	−0.971480	−	0.237121i	$-0.923796\pi$
$701$	−51.4426	−1.94296	−0.971480	+	0.237121i	$0.923796\pi$
$702$	31.9183	1.20468
$703$	−7.60734	−0.286916
$704$	7.45984	0.281153
$705$	3.70909	0.139693
$706$	−12.0072	−0.451898
$707$	3.88401	0.146073
$708$	−18.4576	−0.693679
$709$	3.49347	0.131200	0.0656000	−	0.997846i	$-0.479104\pi$
$709$	3.49347	0.131200	0.0656000	+	0.997846i	$0.479104\pi$
$710$	−17.0063	−0.638235
$711$	9.47053	0.355173
$712$	0.215614	0.00808048
$713$	1.81803	0.0680858
$714$	−4.52017	−0.169163
$715$	−9.12275	−0.341171
$716$	32.8699	1.22841
$717$	−19.3143	−0.721306
$718$	42.6367	1.59119
$719$	5.48477	0.204548	0.102274	−	0.994756i	$-0.467388\pi$
$719$	5.48477	0.204548	0.102274	+	0.994756i	$0.467388\pi$
$720$	5.04729	0.188101
$721$	9.86949	0.367559
$722$	2.36796	0.0881263
$723$	−20.9738	−0.780023
$724$	−20.1788	−0.749938
$725$	−6.62044	−0.245877
$726$	5.57793	0.207016
$727$	−21.5851	−0.800546	−0.400273	−	0.916396i	$-0.631085\pi$
$727$	−21.5851	−0.800546	−0.400273	+	0.916396i	$0.631085\pi$
$728$	3.49854	0.129664
$729$	28.7490	1.06478
$730$	15.9156	0.589062
$731$	−18.2058	−0.673367
$732$	−8.99425	−0.332437
$733$	39.3586	1.45374	0.726872	−	0.686773i	$-0.240973\pi$
$733$	39.3586	1.45374	0.726872	+	0.686773i	$0.240973\pi$
$734$	−11.8406	−0.437046
$735$	1.40018	0.0516466
$736$	−16.0203	−0.590517
$737$	34.5980	1.27443
$738$	17.1307	0.630588
$739$	−25.3363	−0.932011	−0.466006	−	0.884782i	$-0.654307\pi$
$739$	−25.3363	−0.932011	−0.466006	+	0.884782i	$0.654307\pi$
$740$	−2.49456	−0.0917017
$741$	18.0878	0.664473
$742$	7.59445	0.278801
$743$	44.2113	1.62196	0.810978	−	0.585077i	$-0.198936\pi$
$743$	44.2113	1.62196	0.810978	+	0.585077i	$0.198936\pi$
$744$	−1.20388	−0.0441364
$745$	−7.09649	−0.259995
$746$	34.4009	1.25951
$747$	−1.34845	−0.0493373
$748$	−7.20214	−0.263336
$749$	−0.618981	−0.0226171
$750$	−2.57423	−0.0939974
$751$	−21.0995	−0.769933	−0.384966	−	0.922931i	$-0.625787\pi$
$751$	−21.0995	−0.769933	−0.384966	+	0.922931i	$0.625787\pi$
$752$	−12.8624	−0.469044
$753$	−3.67168	−0.133804
$754$	37.3608	1.36060
$755$	−10.5242	−0.383014
$756$	−7.80559	−0.283887
$757$	−13.7565	−0.499990	−0.249995	−	0.968247i	$-0.580429\pi$
$757$	−13.7565	−0.499990	−0.249995	+	0.968247i	$0.580429\pi$
$758$	−25.3546	−0.920921
$759$	10.0292	0.364036
$760$	4.79681	0.173999
$761$	14.8894	0.539740	0.269870	−	0.962897i	$-0.413019\pi$
$761$	14.8894	0.539740	0.269870	+	0.962897i	$0.413019\pi$
$762$	14.9203	0.540505
$763$	4.50727	0.163174
$764$	11.9832	0.433536
$765$	−1.82527	−0.0659928
$766$	−54.5619	−1.97140
$767$	−29.3199	−1.05868
$768$	29.3735	1.05992
$769$	−21.5622	−0.777554	−0.388777	−	0.921332i	$-0.627102\pi$
$769$	−21.5622	−0.777554	−0.388777	+	0.921332i	$0.627102\pi$
$770$	5.46411	0.196913
$771$	−28.4936	−1.02617
$772$	27.2433	0.980506
$773$	21.4999	0.773297	0.386649	−	0.922227i	$-0.373633\pi$
$773$	21.4999	0.773297	0.386649	+	0.922227i	$0.373633\pi$
$774$	−19.8144	−0.712215
$775$	−0.754362	−0.0270975
$776$	1.57005	0.0563615
$777$	−2.53095	−0.0907974
$778$	40.1577	1.43972
$779$	37.7249	1.35164
$780$	5.93126	0.212373
$781$	−27.4920	−0.983741
$782$	7.78022	0.278220
$783$	37.4454	1.33819
$784$	−4.85556	−0.173413
$785$	−19.2160	−0.685849
$786$	−46.8090	−1.66962
$787$	3.94725	0.140704	0.0703521	−	0.997522i	$-0.477588\pi$
$787$	3.94725	0.140704	0.0703521	+	0.997522i	$0.477588\pi$
$788$	−9.27706	−0.330482
$789$	0.555087	0.0197616
$790$	16.7501	0.595942
$791$	−0.324460	−0.0115365
$792$	3.52124	0.125122
$793$	−14.2874	−0.507360
$794$	−22.3338	−0.792596
$795$	−5.78389	−0.205133
$796$	−27.3685	−0.970049
$797$	21.5932	0.764869	0.382435	−	0.923983i	$-0.375086\pi$
$797$	21.5932	0.764869	0.382435	+	0.923983i	$0.375086\pi$
$798$	−10.8338	−0.383512
$799$	4.65148	0.164558
$800$	6.64736	0.235020
$801$	−0.196642	−0.00694801
$802$	−57.8100	−2.04134
$803$	25.7288	0.907948
$804$	−22.4943	−0.793312
$805$	−2.41003	−0.0849423
$806$	4.25705	0.149948
$807$	31.8596	1.12151
$808$	4.42689	0.155738
$809$	−2.96928	−0.104394	−0.0521971	−	0.998637i	$-0.516622\pi$
$809$	−2.96928	−0.104394	−0.0521971	+	0.998637i	$0.516622\pi$
$810$	8.82662	0.310136
$811$	41.3798	1.45304	0.726521	−	0.687144i	$-0.241136\pi$
$811$	41.3798	1.45304	0.726521	+	0.687144i	$0.241136\pi$
$812$	−9.13653	−0.320629
$813$	4.18181	0.146663
$814$	−9.87685	−0.346183
$815$	6.14382	0.215209
$816$	−11.9380	−0.417915
$817$	−43.6351	−1.52660
$818$	7.71315	0.269684
$819$	−3.19070	−0.111492
$820$	12.3705	0.431998
$821$	−34.9237	−1.21885	−0.609423	−	0.792845i	$-0.708599\pi$
$821$	−34.9237	−1.21885	−0.609423	+	0.792845i	$0.708599\pi$
$822$	25.8367	0.901157
$823$	−51.3545	−1.79011	−0.895053	−	0.445960i	$-0.852862\pi$
$823$	−51.3545	−1.79011	−0.895053	+	0.445960i	$0.852862\pi$
$824$	11.2490	0.391877
$825$	−4.16144	−0.144883
$826$	17.5613	0.611036
$827$	53.4526	1.85873	0.929365	−	0.369163i	$-0.120355\pi$
$827$	53.4526	1.85873	0.929365	+	0.369163i	$0.120355\pi$
$828$	3.45728	0.120149
$829$	16.1525	0.560999	0.280500	−	0.959854i	$-0.409500\pi$
$829$	16.1525	0.560999	0.280500	+	0.959854i	$0.409500\pi$
$830$	−2.38495	−0.0827828
$831$	−6.62842	−0.229937
$832$	−7.70440	−0.267102
$833$	1.75594	0.0608396
$834$	8.27270	0.286460
$835$	13.3499	0.461992
$836$	−17.2618	−0.597013
$837$	4.26669	0.147478
$838$	28.3200	0.978298
$839$	−7.39052	−0.255149	−0.127574	−	0.991829i	$-0.540719\pi$
$839$	−7.39052	−0.255149	−0.127574	+	0.991829i	$0.540719\pi$
$840$	1.59589	0.0550635
$841$	14.8302	0.511387
$842$	−28.4656	−0.980989
$843$	6.82162	0.234949
$844$	−6.71014	−0.230973
$845$	−3.57817	−0.123093
$846$	5.06247	0.174051
$847$	−2.16684	−0.0744534
$848$	20.0574	0.688773
$849$	1.65247	0.0567127
$850$	−3.22827	−0.110729
$851$	4.35633	0.149333
$852$	17.8743	0.612362
$853$	−37.7379	−1.29212	−0.646061	−	0.763286i	$-0.723585\pi$
$853$	−37.7379	−1.29212	−0.646061	+	0.763286i	$0.723585\pi$
$854$	8.55750	0.292832
$855$	−4.37474	−0.149613
$856$	−0.705498	−0.0241134
$857$	−50.8607	−1.73737	−0.868683	−	0.495368i	$-0.835033\pi$
$857$	−50.8607	−1.73737	−0.868683	+	0.495368i	$0.835033\pi$
$858$	23.4840	0.801731
$859$	5.97123	0.203736	0.101868	−	0.994798i	$-0.467518\pi$
$859$	5.97123	0.203736	0.101868	+	0.994798i	$0.467518\pi$
$860$	−14.3086	−0.487918
$861$	12.5510	0.427738
$862$	41.0499	1.39817
$863$	−36.9986	−1.25945	−0.629724	−	0.776819i	$-0.716832\pi$
$863$	−36.9986	−1.25945	−0.629724	+	0.776819i	$0.716832\pi$
$864$	−37.5976	−1.27910
$865$	−18.2240	−0.619634
$866$	66.5464	2.26134
$867$	−19.4859	−0.661777
$868$	−1.04106	−0.0353358
$869$	27.0778	0.918553
$870$	17.0425	0.577795
$871$	−35.7322	−1.21074
$872$	5.13727	0.173970
$873$	−1.43190	−0.0484625
$874$	18.6474	0.630756
$875$	1.00000	0.0338062
$876$	−16.7279	−0.565182
$877$	−39.3444	−1.32857	−0.664283	−	0.747481i	$-0.731263\pi$
$877$	−39.3444	−1.32857	−0.664283	+	0.747481i	$0.731263\pi$
$878$	56.9290	1.92126
$879$	−9.31505	−0.314189
$880$	14.4310	0.486470
$881$	−29.5308	−0.994919	−0.497460	−	0.867487i	$-0.665734\pi$
$881$	−29.5308	−0.994919	−0.497460	+	0.867487i	$0.665734\pi$
$882$	1.91108	0.0643496
$883$	16.1436	0.543276	0.271638	−	0.962400i	$-0.412435\pi$
$883$	16.1436	0.543276	0.271638	+	0.962400i	$0.412435\pi$
$884$	7.43825	0.250175
$885$	−13.3746	−0.449582
$886$	−37.7383	−1.26784
$887$	−47.4892	−1.59453	−0.797266	−	0.603628i	$-0.793721\pi$
$887$	−47.4892	−1.59453	−0.797266	+	0.603628i	$0.793721\pi$
$888$	−2.88471	−0.0968046
$889$	−5.79603	−0.194393
$890$	−0.347792	−0.0116580
$891$	14.2689	0.478027
$892$	26.0401	0.871886
$893$	11.1485	0.373071
$894$	18.2680	0.610972
$895$	23.8179	0.796146
$896$	−8.68013	−0.289983
$897$	−10.3580	−0.345842
$898$	−8.22201	−0.274372
$899$	4.99421	0.166566
$900$	−1.43454	−0.0478180
$901$	−7.25343	−0.241647
$902$	48.9794	1.63084
$903$	−14.5173	−0.483107
$904$	−0.369811	−0.0122997
$905$	−14.6218	−0.486044
$906$	27.0916	0.900058
$907$	−50.9264	−1.69098	−0.845492	−	0.533988i	$-0.820693\pi$
$907$	−50.9264	−1.69098	−0.845492	+	0.533988i	$0.820693\pi$
$908$	−36.9636	−1.22668
$909$	−4.03737	−0.133911
$910$	−5.64325	−0.187072
$911$	4.55907	0.151049	0.0755243	−	0.997144i	$-0.475937\pi$
$911$	4.55907	0.151049	0.0755243	+	0.997144i	$0.475937\pi$
$912$	−28.6127	−0.947460
$913$	−3.85546	−0.127597
$914$	55.6308	1.84010
$915$	−6.51734	−0.215457
$916$	−1.38005	−0.0455981
$917$	18.1837	0.600479
$918$	18.2592	0.602643
$919$	−14.3937	−0.474804	−0.237402	−	0.971412i	$-0.576296\pi$
$919$	−14.3937	−0.474804	−0.237402	+	0.971412i	$0.576296\pi$
$920$	−2.74689	−0.0905621
$921$	8.16617	0.269085
$922$	−63.3699	−2.08698
$923$	28.3933	0.934577
$924$	−5.74299	−0.188930
$925$	−1.80758	−0.0594330
$926$	7.97660	0.262127
$927$	−10.2592	−0.336956
$928$	−44.0085	−1.44465
$929$	29.6862	0.973972	0.486986	−	0.873410i	$-0.338096\pi$
$929$	29.6862	0.973972	0.486986	+	0.873410i	$0.338096\pi$
$930$	1.94190	0.0636773
$931$	4.20856	0.137930
$932$	−7.93308	−0.259857
$933$	−21.3518	−0.699026
$934$	37.6075	1.23056
$935$	−5.21875	−0.170671
$936$	−3.63668	−0.118868
$937$	9.15619	0.299120	0.149560	−	0.988753i	$-0.452214\pi$
$937$	9.15619	0.299120	0.149560	+	0.988753i	$0.452214\pi$
$938$	21.4020	0.698800
$939$	13.3305	0.435023
$940$	3.65576	0.119238
$941$	36.4913	1.18958	0.594791	−	0.803881i	$-0.297235\pi$
$941$	36.4913	1.18958	0.594791	+	0.803881i	$0.297235\pi$
$942$	49.4664	1.61170
$943$	−21.6031	−0.703494
$944$	46.3805	1.50956
$945$	−5.65602	−0.183990
$946$	−56.6528	−1.84194
$947$	11.6754	0.379401	0.189700	−	0.981842i	$-0.439248\pi$
$947$	11.6754	0.379401	0.189700	+	0.981842i	$0.439248\pi$
$948$	−17.6050	−0.571783
$949$	−26.5722	−0.862571
$950$	−7.73741	−0.251035
$951$	41.9464	1.36021
$952$	2.00137	0.0648648
$953$	14.9165	0.483192	0.241596	−	0.970377i	$-0.422329\pi$
$953$	14.9165	0.483192	0.241596	+	0.970377i	$0.422329\pi$
$954$	−7.89432	−0.255588
$955$	8.68314	0.280980
$956$	−19.0366	−0.615686
$957$	27.5505	0.890582
$958$	27.7137	0.895388
$959$	−10.0367	−0.324101
$960$	−3.51444	−0.113428
$961$	−30.4309	−0.981643
$962$	10.2006	0.328882
$963$	0.643422	0.0207340
$964$	−20.6722	−0.665806
$965$	19.7408	0.635478
$966$	6.20395	0.199609
$967$	−15.3807	−0.494611	−0.247306	−	0.968938i	$-0.579545\pi$
$967$	−15.3807	−0.494611	−0.247306	+	0.968938i	$0.579545\pi$
$968$	−2.46970	−0.0793793
$969$	10.3473	0.332404
$970$	−2.53254	−0.0813150
$971$	8.95986	0.287536	0.143768	−	0.989611i	$-0.454078\pi$
$971$	8.95986	0.287536	0.143768	+	0.989611i	$0.454078\pi$
$972$	14.1397	0.453530
$973$	−3.21366	−0.103025
$974$	−32.3645	−1.03702
$975$	4.29786	0.137642
$976$	22.6009	0.723436
$977$	−22.2090	−0.710529	−0.355264	−	0.934766i	$-0.615609\pi$
$977$	−22.2090	−0.710529	−0.355264	+	0.934766i	$0.615609\pi$
$978$	−15.8156	−0.505726
$979$	−0.562233	−0.0179691
$980$	1.38005	0.0440841
$981$	−4.68524	−0.149588
$982$	−25.9570	−0.828321
$983$	−5.94266	−0.189541	−0.0947707	−	0.995499i	$-0.530212\pi$
$983$	−5.94266	−0.189541	−0.0947707	+	0.995499i	$0.530212\pi$
$984$	14.3053	0.456037
$985$	−6.72227	−0.214189
$986$	21.3726	0.680642
$987$	3.70909	0.118062
$988$	17.8277	0.567176
$989$	24.9875	0.794558
$990$	−5.67987	−0.180518
$991$	−5.52963	−0.175654	−0.0878272	−	0.996136i	$-0.527992\pi$
$991$	−5.52963	−0.175654	−0.0878272	+	0.996136i	$0.527992\pi$
$992$	−5.01451	−0.159211
$993$	18.2207	0.578218
$994$	−17.0063	−0.539407
$995$	−19.8315	−0.628701
$996$	2.50667	0.0794269
$997$	−23.4266	−0.741927	−0.370963	−	0.928648i	$-0.620972\pi$
$997$	−23.4266	−0.741927	−0.370963	+	0.928648i	$0.620972\pi$
$998$	−25.7939	−0.816490
$999$	10.2237	0.323465

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.h.1.9	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.h.1.9	✓	38	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-1.83849 q^{2} +1.40018 q^{3} +1.38005 q^{4} +1.00000 q^{5} -2.57423 q^{6} +1.00000 q^{7} +1.13977 q^{8} -1.03949 q^{9} +O(q^{10})\)	\(q-1.83849 q^{2} +1.40018 q^{3} +1.38005 q^{4} +1.00000 q^{5} -2.57423 q^{6} +1.00000 q^{7} +1.13977 q^{8} -1.03949 q^{9} -1.83849 q^{10} -2.97206 q^{11} +1.93232 q^{12} +3.06950 q^{13} -1.83849 q^{14} +1.40018 q^{15} -4.85556 q^{16} +1.75594 q^{17} +1.91108 q^{18} +4.20856 q^{19} +1.38005 q^{20} +1.40018 q^{21} +5.46411 q^{22} -2.41003 q^{23} +1.59589 q^{24} +1.00000 q^{25} -5.64325 q^{26} -5.65602 q^{27} +1.38005 q^{28} -6.62044 q^{29} -2.57423 q^{30} -0.754362 q^{31} +6.64736 q^{32} -4.16144 q^{33} -3.22827 q^{34} +1.00000 q^{35} -1.43454 q^{36} -1.80758 q^{37} -7.73741 q^{38} +4.29786 q^{39} +1.13977 q^{40} +8.96384 q^{41} -2.57423 q^{42} -10.3682 q^{43} -4.10159 q^{44} -1.03949 q^{45} +4.43081 q^{46} +2.64901 q^{47} -6.79868 q^{48} +1.00000 q^{49} -1.83849 q^{50} +2.45863 q^{51} +4.23606 q^{52} -4.13081 q^{53} +10.3985 q^{54} -2.97206 q^{55} +1.13977 q^{56} +5.89276 q^{57} +12.1716 q^{58} -9.55203 q^{59} +1.93232 q^{60} -4.65463 q^{61} +1.38689 q^{62} -1.03949 q^{63} -2.50999 q^{64} +3.06950 q^{65} +7.65076 q^{66} -11.6411 q^{67} +2.42328 q^{68} -3.37448 q^{69} -1.83849 q^{70} +9.25014 q^{71} -1.18478 q^{72} -8.65687 q^{73} +3.32323 q^{74} +1.40018 q^{75} +5.80803 q^{76} -2.97206 q^{77} -7.90158 q^{78} -9.11079 q^{79} -4.85556 q^{80} -4.80101 q^{81} -16.4799 q^{82} +1.29723 q^{83} +1.93232 q^{84} +1.75594 q^{85} +19.0618 q^{86} -9.26983 q^{87} -3.38748 q^{88} +0.189173 q^{89} +1.91108 q^{90} +3.06950 q^{91} -3.32596 q^{92} -1.05625 q^{93} -4.87017 q^{94} +4.20856 q^{95} +9.30753 q^{96} +1.37751 q^{97} -1.83849 q^{98} +3.08942 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 6 q^{2} - 9 q^{3} + 24 q^{4} + 38 q^{5} - 10 q^{6} + 38 q^{7} - 21 q^{8} + 13 q^{9}+O(q^{10}) \) 38 * q - 6 * q^2 - 9 * q^3 + 24 * q^4 + 38 * q^5 - 10 * q^6 + 38 * q^7 - 21 * q^8 + 13 * q^9	\( 38 q - 6 q^{2} - 9 q^{3} + 24 q^{4} + 38 q^{5} - 10 q^{6} + 38 q^{7} - 21 q^{8} + 13 q^{9} - 6 q^{10} - 18 q^{11} - 20 q^{12} - 25 q^{13} - 6 q^{14} - 9 q^{15} - 21 q^{17} - 7 q^{18} - 14 q^{19} + 24 q^{20} - 9 q^{21} - 11 q^{22} - 16 q^{23} - 10 q^{24} + 38 q^{25} - 21 q^{26} - 15 q^{27} + 24 q^{28} - 52 q^{29} - 10 q^{30} - 30 q^{31} - 8 q^{32} - 13 q^{33} - 9 q^{34} + 38 q^{35} - 16 q^{36} - 47 q^{37} - 10 q^{38} - 50 q^{39} - 21 q^{40} - 35 q^{41} - 10 q^{42} - 18 q^{43} - 22 q^{44} + 13 q^{45} - 17 q^{46} - 23 q^{47} - 13 q^{48} + 38 q^{49} - 6 q^{50} - 5 q^{51} - 41 q^{52} - 12 q^{53} + 35 q^{54} - 18 q^{55} - 21 q^{56} - 3 q^{57} - 16 q^{58} - 16 q^{59} - 20 q^{60} - 47 q^{61} + 14 q^{62} + 13 q^{63} - 55 q^{64} - 25 q^{65} - 6 q^{66} - 54 q^{67} + 31 q^{68} - 95 q^{69} - 6 q^{70} - 41 q^{71} - 59 q^{73} - q^{74} - 9 q^{75} - 23 q^{76} - 18 q^{77} + 19 q^{78} - 117 q^{79} - 38 q^{81} + 19 q^{82} - 21 q^{83} - 20 q^{84} - 21 q^{85} - 12 q^{86} - 14 q^{87} - 40 q^{88} - 96 q^{89} - 7 q^{90} - 25 q^{91} + 53 q^{92} - 53 q^{93} - 28 q^{94} - 14 q^{95} + 40 q^{96} - 70 q^{97} - 6 q^{98} - 52 q^{99}+O(q^{100}) \) 38 * q - 6 * q^2 - 9 * q^3 + 24 * q^4 + 38 * q^5 - 10 * q^6 + 38 * q^7 - 21 * q^8 + 13 * q^9 - 6 * q^10 - 18 * q^11 - 20 * q^12 - 25 * q^13 - 6 * q^14 - 9 * q^15 - 21 * q^17 - 7 * q^18 - 14 * q^19 + 24 * q^20 - 9 * q^21 - 11 * q^22 - 16 * q^23 - 10 * q^24 + 38 * q^25 - 21 * q^26 - 15 * q^27 + 24 * q^28 - 52 * q^29 - 10 * q^30 - 30 * q^31 - 8 * q^32 - 13 * q^33 - 9 * q^34 + 38 * q^35 - 16 * q^36 - 47 * q^37 - 10 * q^38 - 50 * q^39 - 21 * q^40 - 35 * q^41 - 10 * q^42 - 18 * q^43 - 22 * q^44 + 13 * q^45 - 17 * q^46 - 23 * q^47 - 13 * q^48 + 38 * q^49 - 6 * q^50 - 5 * q^51 - 41 * q^52 - 12 * q^53 + 35 * q^54 - 18 * q^55 - 21 * q^56 - 3 * q^57 - 16 * q^58 - 16 * q^59 - 20 * q^60 - 47 * q^61 + 14 * q^62 + 13 * q^63 - 55 * q^64 - 25 * q^65 - 6 * q^66 - 54 * q^67 + 31 * q^68 - 95 * q^69 - 6 * q^70 - 41 * q^71 - 59 * q^73 - q^74 - 9 * q^75 - 23 * q^76 - 18 * q^77 + 19 * q^78 - 117 * q^79 - 38 * q^81 + 19 * q^82 - 21 * q^83 - 20 * q^84 - 21 * q^85 - 12 * q^86 - 14 * q^87 - 40 * q^88 - 96 * q^89 - 7 * q^90 - 25 * q^91 + 53 * q^92 - 53 * q^93 - 28 * q^94 - 14 * q^95 + 40 * q^96 - 70 * q^97 - 6 * q^98 - 52 * q^99

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