LMFDB - Embedded newform 4027.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4027,2,Mod(1,4027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4027, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4027 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4027.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:	$32.1557568940$
Analytic rank:	$0$
Dimension:	$174$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	4027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.80755 q^{2} +0.290452 q^{3} +5.88232 q^{4} -1.66261 q^{5} -0.815457 q^{6} +1.40907 q^{7} -10.8998 q^{8} -2.91564 q^{9} +O(q^{10})$	\(q-2.80755 q^{2} +0.290452 q^{3} +5.88232 q^{4} -1.66261 q^{5} -0.815457 q^{6} +1.40907 q^{7} -10.8998 q^{8} -2.91564 q^{9} +4.66785 q^{10} +5.00402 q^{11} +1.70853 q^{12} -2.19562 q^{13} -3.95603 q^{14} -0.482908 q^{15} +18.8371 q^{16} +5.06094 q^{17} +8.18579 q^{18} -5.60124 q^{19} -9.78000 q^{20} +0.409267 q^{21} -14.0490 q^{22} +7.70577 q^{23} -3.16587 q^{24} -2.23573 q^{25} +6.16430 q^{26} -1.71821 q^{27} +8.28860 q^{28} +7.58080 q^{29} +1.35579 q^{30} +0.908551 q^{31} -31.0863 q^{32} +1.45343 q^{33} -14.2088 q^{34} -2.34273 q^{35} -17.1507 q^{36} +5.36885 q^{37} +15.7258 q^{38} -0.637721 q^{39} +18.1221 q^{40} +5.06071 q^{41} -1.14904 q^{42} +0.206506 q^{43} +29.4353 q^{44} +4.84756 q^{45} -21.6343 q^{46} +2.86237 q^{47} +5.47126 q^{48} -5.01452 q^{49} +6.27693 q^{50} +1.46996 q^{51} -12.9153 q^{52} -10.5431 q^{53} +4.82395 q^{54} -8.31973 q^{55} -15.3586 q^{56} -1.62689 q^{57} -21.2834 q^{58} +3.61724 q^{59} -2.84062 q^{60} -10.8258 q^{61} -2.55080 q^{62} -4.10834 q^{63} +49.6022 q^{64} +3.65045 q^{65} -4.08057 q^{66} -2.76545 q^{67} +29.7701 q^{68} +2.23815 q^{69} +6.57733 q^{70} -15.8989 q^{71} +31.7799 q^{72} -2.31996 q^{73} -15.0733 q^{74} -0.649373 q^{75} -32.9483 q^{76} +7.05102 q^{77} +1.79043 q^{78} -8.14656 q^{79} -31.3187 q^{80} +8.24786 q^{81} -14.2082 q^{82} +10.8437 q^{83} +2.40744 q^{84} -8.41437 q^{85} -0.579776 q^{86} +2.20186 q^{87} -54.5429 q^{88} -0.357211 q^{89} -13.6098 q^{90} -3.09378 q^{91} +45.3278 q^{92} +0.263890 q^{93} -8.03625 q^{94} +9.31268 q^{95} -9.02908 q^{96} +13.5102 q^{97} +14.0785 q^{98} -14.5899 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 174 q + 21 q^{2} + 17 q^{3} + 187 q^{4} + 72 q^{5} + 21 q^{6} + 24 q^{7} + 54 q^{8} + 197 q^{9}+O(q^{10}) $ 174 * q + 21 * q^2 + 17 * q^3 + 187 * q^4 + 72 * q^5 + 21 * q^6 + 24 * q^7 + 54 * q^8 + 197 * q^9	\( 174 q + 21 q^{2} + 17 q^{3} + 187 q^{4} + 72 q^{5} + 21 q^{6} + 24 q^{7} + 54 q^{8} + 197 q^{9} + 20 q^{10} + 35 q^{11} + 23 q^{12} + 91 q^{13} + 18 q^{14} + 16 q^{15} + 201 q^{16} + 148 q^{17} + 39 q^{18} + 36 q^{19} + 128 q^{20} + 57 q^{21} + 17 q^{22} + 96 q^{23} + 24 q^{24} + 226 q^{25} + 44 q^{26} + 62 q^{27} + 32 q^{28} + 122 q^{29} + 25 q^{30} + 23 q^{31} + 104 q^{32} + 91 q^{33} + 6 q^{34} + 80 q^{35} + 222 q^{36} + 71 q^{37} + 125 q^{38} + 16 q^{39} + 53 q^{40} + 97 q^{41} + 14 q^{42} + 38 q^{43} + 70 q^{44} + 185 q^{45} - 23 q^{46} + 110 q^{47} + 36 q^{48} + 210 q^{49} + 51 q^{50} + 33 q^{51} + 118 q^{52} + 214 q^{53} + 8 q^{54} + 37 q^{55} + 41 q^{56} + 76 q^{57} + 2 q^{58} + 66 q^{59} - 12 q^{60} + 114 q^{61} + 175 q^{62} + 62 q^{63} + 190 q^{64} + 128 q^{65} + 12 q^{66} - 6 q^{67} + 348 q^{68} + 115 q^{69} - 38 q^{70} + 54 q^{71} + 101 q^{72} + 107 q^{73} + 71 q^{74} - q^{75} + 31 q^{76} + 368 q^{77} - 14 q^{78} - 14 q^{79} + 205 q^{80} + 222 q^{81} + 26 q^{82} + 246 q^{83} + 41 q^{84} + 87 q^{85} + 33 q^{86} + 100 q^{87} - 6 q^{88} + 147 q^{89} + 50 q^{90} - 23 q^{91} + 189 q^{92} + 117 q^{93} + 23 q^{94} + 42 q^{95} + 38 q^{96} + 52 q^{97} + 148 q^{98} + 38 q^{99}+O(q^{100}) \) 174 * q + 21 * q^2 + 17 * q^3 + 187 * q^4 + 72 * q^5 + 21 * q^6 + 24 * q^7 + 54 * q^8 + 197 * q^9 + 20 * q^10 + 35 * q^11 + 23 * q^12 + 91 * q^13 + 18 * q^14 + 16 * q^15 + 201 * q^16 + 148 * q^17 + 39 * q^18 + 36 * q^19 + 128 * q^20 + 57 * q^21 + 17 * q^22 + 96 * q^23 + 24 * q^24 + 226 * q^25 + 44 * q^26 + 62 * q^27 + 32 * q^28 + 122 * q^29 + 25 * q^30 + 23 * q^31 + 104 * q^32 + 91 * q^33 + 6 * q^34 + 80 * q^35 + 222 * q^36 + 71 * q^37 + 125 * q^38 + 16 * q^39 + 53 * q^40 + 97 * q^41 + 14 * q^42 + 38 * q^43 + 70 * q^44 + 185 * q^45 - 23 * q^46 + 110 * q^47 + 36 * q^48 + 210 * q^49 + 51 * q^50 + 33 * q^51 + 118 * q^52 + 214 * q^53 + 8 * q^54 + 37 * q^55 + 41 * q^56 + 76 * q^57 + 2 * q^58 + 66 * q^59 - 12 * q^60 + 114 * q^61 + 175 * q^62 + 62 * q^63 + 190 * q^64 + 128 * q^65 + 12 * q^66 - 6 * q^67 + 348 * q^68 + 115 * q^69 - 38 * q^70 + 54 * q^71 + 101 * q^72 + 107 * q^73 + 71 * q^74 - q^75 + 31 * q^76 + 368 * q^77 - 14 * q^78 - 14 * q^79 + 205 * q^80 + 222 * q^81 + 26 * q^82 + 246 * q^83 + 41 * q^84 + 87 * q^85 + 33 * q^86 + 100 * q^87 - 6 * q^88 + 147 * q^89 + 50 * q^90 - 23 * q^91 + 189 * q^92 + 117 * q^93 + 23 * q^94 + 42 * q^95 + 38 * q^96 + 52 * q^97 + 148 * q^98 + 38 * 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 $

$2$	−2.80755	−1.98524	−0.992618	−	0.121284i	$-0.961299\pi$
$2$	−2.80755	−1.98524	−0.992618	+	0.121284i	$0.961299\pi$
$3$	0.290452	0.167692	0.0838462	−	0.996479i	$-0.473280\pi$
$3$	0.290452	0.167692	0.0838462	+	0.996479i	$0.473280\pi$
$4$	5.88232	2.94116
$5$	−1.66261	−0.743541	−0.371771	−	0.928325i	$-0.621249\pi$
$5$	−1.66261	−0.743541	−0.371771	+	0.928325i	$0.621249\pi$
$6$	−0.815457	−0.332909
$7$	1.40907	0.532578	0.266289	−	0.963893i	$-0.414202\pi$
$7$	1.40907	0.532578	0.266289	+	0.963893i	$0.414202\pi$
$8$	−10.8998	−3.85366
$9$	−2.91564	−0.971879
$10$	4.66785	1.47610
$11$	5.00402	1.50877	0.754385	−	0.656432i	$-0.227935\pi$
$11$	5.00402	1.50877	0.754385	+	0.656432i	$0.227935\pi$
$12$	1.70853	0.493210
$13$	−2.19562	−0.608955	−0.304477	−	0.952520i	$-0.598482\pi$
$13$	−2.19562	−0.608955	−0.304477	+	0.952520i	$0.598482\pi$
$14$	−3.95603	−1.05729
$15$	−0.482908	−0.124686
$16$	18.8371	4.70927
$17$	5.06094	1.22746	0.613729	−	0.789516i	$-0.289669\pi$
$17$	5.06094	1.22746	0.613729	+	0.789516i	$0.289669\pi$
$18$	8.18579	1.92941
$19$	−5.60124	−1.28501	−0.642507	−	0.766280i	$-0.722106\pi$
$19$	−5.60124	−1.28501	−0.642507	+	0.766280i	$0.722106\pi$
$20$	−9.78000	−2.18687
$21$	0.409267	0.0893093
$22$	−14.0490	−2.99526
$23$	7.70577	1.60676	0.803382	−	0.595464i	$-0.203032\pi$
$23$	7.70577	1.60676	0.803382	+	0.595464i	$0.203032\pi$
$24$	−3.16587	−0.646230
$25$	−2.23573	−0.447147
$26$	6.16430	1.20892
$27$	−1.71821	−0.330669
$28$	8.28860	1.56640
$29$	7.58080	1.40772	0.703859	−	0.710339i	$-0.251458\pi$
$29$	7.58080	1.40772	0.703859	+	0.710339i	$0.251458\pi$
$30$	1.35579	0.247531
$31$	0.908551	0.163181	0.0815903	−	0.996666i	$-0.474000\pi$
$31$	0.908551	0.163181	0.0815903	+	0.996666i	$0.474000\pi$
$32$	−31.0863	−5.49534
$33$	1.45343	0.253009
$34$	−14.2088	−2.43679
$35$	−2.34273	−0.395994
$36$	−17.1507	−2.85845
$37$	5.36885	0.882633	0.441317	−	0.897351i	$-0.354512\pi$
$37$	5.36885	0.882633	0.441317	+	0.897351i	$0.354512\pi$
$38$	15.7258	2.55105
$39$	−0.637721	−0.102117
$40$	18.1221	2.86536
$41$	5.06071	0.790350	0.395175	−	0.918606i	$-0.370684\pi$
$41$	5.06071	0.790350	0.395175	+	0.918606i	$0.370684\pi$
$42$	−1.14904	−0.177300
$43$	0.206506	0.0314919	0.0157459	−	0.999876i	$-0.494988\pi$
$43$	0.206506	0.0314919	0.0157459	+	0.999876i	$0.494988\pi$
$44$	29.4353	4.43754
$45$	4.84756	0.722632
$46$	−21.6343	−3.18981
$47$	2.86237	0.417520	0.208760	−	0.977967i	$-0.433057\pi$
$47$	2.86237	0.417520	0.208760	+	0.977967i	$0.433057\pi$
$48$	5.47126	0.789708
$49$	−5.01452	−0.716360
$50$	6.27693	0.887691
$51$	1.46996	0.205835
$52$	−12.9153	−1.79103
$53$	−10.5431	−1.44821	−0.724105	−	0.689689i	$-0.757747\pi$
$53$	−10.5431	−1.44821	−0.724105	+	0.689689i	$0.757747\pi$
$54$	4.82395	0.656456
$55$	−8.31973	−1.12183
$56$	−15.3586	−2.05238
$57$	−1.62689	−0.215487
$58$	−21.2834	−2.79465
$59$	3.61724	0.470925	0.235462	−	0.971883i	$-0.424340\pi$
$59$	3.61724	0.470925	0.235462	+	0.971883i	$0.424340\pi$
$60$	−2.84062	−0.366722
$61$	−10.8258	−1.38610	−0.693048	−	0.720891i	$-0.743733\pi$
$61$	−10.8258	−1.38610	−0.693048	+	0.720891i	$0.743733\pi$
$62$	−2.55080	−0.323952
$63$	−4.10834	−0.517602
$64$	49.6022	6.20028
$65$	3.65045	0.452783
$66$	−4.08057	−0.502283
$67$	−2.76545	−0.337853	−0.168927	−	0.985629i	$-0.554030\pi$
$67$	−2.76545	−0.337853	−0.168927	+	0.985629i	$0.554030\pi$
$68$	29.7701	3.61015
$69$	2.23815	0.269442
$70$	6.57733	0.786141
$71$	−15.8989	−1.88685	−0.943426	−	0.331584i	$-0.892417\pi$
$71$	−15.8989	−1.88685	−0.943426	+	0.331584i	$0.892417\pi$
$72$	31.7799	3.74529
$73$	−2.31996	−0.271531	−0.135765	−	0.990741i	$-0.543349\pi$
$73$	−2.31996	−0.271531	−0.135765	+	0.990741i	$0.543349\pi$
$74$	−15.0733	−1.75224
$75$	−0.649373	−0.0749831
$76$	−32.9483	−3.77943
$77$	7.05102	0.803538
$78$	1.79043	0.202726
$79$	−8.14656	−0.916559	−0.458280	−	0.888808i	$-0.651534\pi$
$79$	−8.14656	−0.916559	−0.458280	+	0.888808i	$0.651534\pi$
$80$	−31.3187	−3.50153
$81$	8.24786	0.916429
$82$	−14.2082	−1.56903
$83$	10.8437	1.19025	0.595126	−	0.803632i	$-0.297102\pi$
$83$	10.8437	1.19025	0.595126	+	0.803632i	$0.297102\pi$
$84$	2.40744	0.262673
$85$	−8.41437	−0.912666
$86$	−0.579776	−0.0625188
$87$	2.20186	0.236064
$88$	−54.5429	−5.81429
$89$	−0.357211	−0.0378643	−0.0189321	−	0.999821i	$-0.506027\pi$
$89$	−0.357211	−0.0378643	−0.0189321	+	0.999821i	$0.506027\pi$
$90$	−13.6098	−1.43460
$91$	−3.09378	−0.324316
$92$	45.3278	4.72575
$93$	0.263890	0.0273641
$94$	−8.03625	−0.828876
$95$	9.31268	0.955460
$96$	−9.02908	−0.921527
$97$	13.5102	1.37175	0.685877	−	0.727717i	$-0.259419\pi$
$97$	13.5102	1.37175	0.685877	+	0.727717i	$0.259419\pi$
$98$	14.0785	1.42214
$99$	−14.5899	−1.46634
$100$	−13.1513	−1.31513
$101$	5.13891	0.511340	0.255670	−	0.966764i	$-0.417704\pi$
$101$	5.13891	0.511340	0.255670	+	0.966764i	$0.417704\pi$
$102$	−4.12698	−0.408632
$103$	19.6082	1.93205	0.966027	−	0.258440i	$-0.0832083\pi$
$103$	19.6082	1.93205	0.966027	+	0.258440i	$0.0832083\pi$
$104$	23.9318	2.34670
$105$	−0.680450	−0.0664051
$106$	29.6003	2.87504
$107$	18.5474	1.79304	0.896522	−	0.442998i	$-0.146085\pi$
$107$	18.5474	1.79304	0.896522	+	0.442998i	$0.146085\pi$
$108$	−10.1070	−0.972551
$109$	−2.74994	−0.263397	−0.131698	−	0.991290i	$-0.542043\pi$
$109$	−2.74994	−0.263397	−0.131698	+	0.991290i	$0.542043\pi$
$110$	23.3580	2.22710
$111$	1.55939	0.148011
$112$	26.5427	2.50805
$113$	−8.43829	−0.793807	−0.396904	−	0.917860i	$-0.629915\pi$
$113$	−8.43829	−0.793807	−0.396904	+	0.917860i	$0.629915\pi$
$114$	4.56757	0.427792
$115$	−12.8117	−1.19470
$116$	44.5927	4.14033
$117$	6.40162	0.591830
$118$	−10.1556	−0.934896
$119$	7.13122	0.653718
$120$	5.26360	0.480498
$121$	14.0403	1.27639
$122$	30.3938	2.75173
$123$	1.46989	0.132536
$124$	5.34439	0.479940
$125$	12.0302	1.07601
$126$	11.5343	1.02756
$127$	18.0162	1.59868	0.799338	−	0.600881i	$-0.205184\pi$
$127$	18.0162	1.59868	0.799338	+	0.600881i	$0.205184\pi$
$128$	−77.0880	−6.81368
$129$	0.0599800	0.00528095
$130$	−10.2488	−0.898881
$131$	−15.7423	−1.37541	−0.687707	−	0.725989i	$-0.741383\pi$
$131$	−15.7423	−1.37541	−0.687707	+	0.725989i	$0.741383\pi$
$132$	8.54953	0.744141
$133$	−7.89254	−0.684370
$134$	7.76412	0.670718
$135$	2.85671	0.245866
$136$	−55.1633	−4.73021
$137$	−15.3060	−1.30768	−0.653838	−	0.756634i	$-0.726842\pi$
$137$	−15.3060	−1.30768	−0.653838	+	0.756634i	$0.726842\pi$
$138$	−6.28373	−0.534906
$139$	0.292016	0.0247685	0.0123842	−	0.999923i	$-0.496058\pi$
$139$	0.292016	0.0247685	0.0123842	+	0.999923i	$0.496058\pi$
$140$	−13.7807	−1.16468
$141$	0.831382	0.0700150
$142$	44.6369	3.74585
$143$	−10.9869	−0.918773
$144$	−54.9221	−4.57684
$145$	−12.6039	−1.04670
$146$	6.51340	0.539053
$147$	−1.45648	−0.120128
$148$	31.5813	2.59597
$149$	4.78511	0.392011	0.196006	−	0.980603i	$-0.437203\pi$
$149$	4.78511	0.392011	0.196006	+	0.980603i	$0.437203\pi$
$150$	1.82314	0.148859
$151$	−12.0578	−0.981253	−0.490626	−	0.871370i	$-0.663232\pi$
$151$	−12.0578	−0.981253	−0.490626	+	0.871370i	$0.663232\pi$
$152$	61.0524	4.95201
$153$	−14.7559	−1.19294
$154$	−19.7961	−1.59521
$155$	−1.51056	−0.121331
$156$	−3.75128	−0.300343
$157$	3.43334	0.274010	0.137005	−	0.990570i	$-0.456252\pi$
$157$	3.43334	0.274010	0.137005	+	0.990570i	$0.456252\pi$
$158$	22.8718	1.81959
$159$	−3.06227	−0.242854
$160$	51.6844	4.08601
$161$	10.8580	0.855728
$162$	−23.1562	−1.81933
$163$	6.02508	0.471921	0.235960	−	0.971763i	$-0.424176\pi$
$163$	6.02508	0.471921	0.235960	+	0.971763i	$0.424176\pi$
$164$	29.7687	2.32455
$165$	−2.41648	−0.188123
$166$	−30.4443	−2.36293
$167$	−2.20960	−0.170984	−0.0854921	−	0.996339i	$-0.527246\pi$
$167$	−2.20960	−0.170984	−0.0854921	+	0.996339i	$0.527246\pi$
$168$	−4.46092	−0.344168
$169$	−8.17927	−0.629174
$170$	23.6237	1.81186
$171$	16.3312	1.24888
$172$	1.21474	0.0926227
$173$	−0.679197	−0.0516384	−0.0258192	−	0.999667i	$-0.508219\pi$
$173$	−0.679197	−0.0516384	−0.0258192	+	0.999667i	$0.508219\pi$
$174$	−6.18181	−0.468642
$175$	−3.15030	−0.238141
$176$	94.2611	7.10520
$177$	1.05063	0.0789705
$178$	1.00289	0.0751695
$179$	−8.70775	−0.650848	−0.325424	−	0.945568i	$-0.605507\pi$
$179$	−8.70775	−0.650848	−0.325424	+	0.945568i	$0.605507\pi$
$180$	28.5149	2.12538
$181$	−11.0795	−0.823530	−0.411765	−	0.911290i	$-0.635088\pi$
$181$	−11.0795	−0.823530	−0.411765	+	0.911290i	$0.635088\pi$
$182$	8.68592	0.643844
$183$	−3.14436	−0.232438
$184$	−83.9914	−6.19193
$185$	−8.92630	−0.656274
$186$	−0.740884	−0.0543242
$187$	25.3251	1.85195
$188$	16.8374	1.22799
$189$	−2.42107	−0.176107
$190$	−26.1458	−1.89681
$191$	13.1574	0.952038	0.476019	−	0.879435i	$-0.342079\pi$
$191$	13.1574	0.952038	0.476019	+	0.879435i	$0.342079\pi$
$192$	14.4071	1.03974
$193$	−6.31372	−0.454472	−0.227236	−	0.973840i	$-0.572969\pi$
$193$	−6.31372	−0.454472	−0.227236	+	0.973840i	$0.572969\pi$
$194$	−37.9306	−2.72326
$195$	1.06028	0.0759282
$196$	−29.4970	−2.10693
$197$	1.77553	0.126501	0.0632507	−	0.997998i	$-0.479853\pi$
$197$	1.77553	0.126501	0.0632507	+	0.997998i	$0.479853\pi$
$198$	40.9619	2.91104
$199$	24.7746	1.75623	0.878113	−	0.478453i	$-0.158802\pi$
$199$	24.7746	1.75623	0.878113	+	0.478453i	$0.158802\pi$
$200$	24.3690	1.72315
$201$	−0.803229	−0.0566554
$202$	−14.4277	−1.01513
$203$	10.6819	0.749720
$204$	8.64677	0.605395
$205$	−8.41398	−0.587658
$206$	−55.0510	−3.83558
$207$	−22.4672	−1.56158
$208$	−41.3590	−2.86773
$209$	−28.0288	−1.93879
$210$	1.91040	0.131830
$211$	25.4241	1.75027	0.875134	−	0.483881i	$-0.160773\pi$
$211$	25.4241	1.75027	0.875134	+	0.483881i	$0.160773\pi$
$212$	−62.0181	−4.25942
$213$	−4.61786	−0.316411
$214$	−52.0727	−3.55962
$215$	−0.343339	−0.0234155
$216$	18.7281	1.27429
$217$	1.28021	0.0869064
$218$	7.72059	0.522905
$219$	−0.673837	−0.0455337
$220$	−48.9393	−3.29949
$221$	−11.1119	−0.747467
$222$	−4.37807	−0.293837
$223$	−24.4876	−1.63981	−0.819904	−	0.572501i	$-0.805973\pi$
$223$	−24.4876	−1.63981	−0.819904	+	0.572501i	$0.805973\pi$
$224$	−43.8028	−2.92670
$225$	6.51859	0.434573
$226$	23.6909	1.57589
$227$	11.5881	0.769129	0.384565	−	0.923098i	$-0.374352\pi$
$227$	11.5881	0.769129	0.384565	+	0.923098i	$0.374352\pi$
$228$	−9.56990	−0.633782
$229$	−5.28279	−0.349097	−0.174548	−	0.984649i	$-0.555847\pi$
$229$	−5.28279	−0.349097	−0.174548	+	0.984649i	$0.555847\pi$
$230$	35.9694	2.37175
$231$	2.04798	0.134747
$232$	−82.6292	−5.42487
$233$	3.55731	0.233047	0.116524	−	0.993188i	$-0.462825\pi$
$233$	3.55731	0.233047	0.116524	+	0.993188i	$0.462825\pi$
$234$	−17.9729	−1.17492
$235$	−4.75901	−0.310443
$236$	21.2778	1.38506
$237$	−2.36618	−0.153700
$238$	−20.0212	−1.29778
$239$	18.4006	1.19024	0.595119	−	0.803637i	$-0.297105\pi$
$239$	18.4006	1.19024	0.595119	+	0.803637i	$0.297105\pi$
$240$	−9.09656	−0.587180
$241$	−4.82317	−0.310688	−0.155344	−	0.987860i	$-0.549649\pi$
$241$	−4.82317	−0.310688	−0.155344	+	0.987860i	$0.549649\pi$
$242$	−39.4187	−2.53393
$243$	7.55023	0.484347
$244$	−63.6806	−4.07673
$245$	8.33719	0.532643
$246$	−4.12679	−0.263115
$247$	12.2982	0.782515
$248$	−9.90302	−0.628842
$249$	3.14958	0.199596
$250$	−33.7753	−2.13614
$251$	31.6058	1.99494	0.997471	−	0.0710690i	$-0.0226410\pi$
$251$	31.6058	1.99494	0.997471	+	0.0710690i	$0.0226410\pi$
$252$	−24.1666	−1.52235
$253$	38.5599	2.42424
$254$	−50.5813	−3.17375
$255$	−2.44397	−0.153047
$256$	117.224	7.32648
$257$	7.42330	0.463053	0.231526	−	0.972829i	$-0.425628\pi$
$257$	7.42330	0.463053	0.231526	+	0.972829i	$0.425628\pi$
$258$	−0.168397	−0.0104839
$259$	7.56508	0.470071
$260$	21.4731	1.33171
$261$	−22.1029	−1.36813
$262$	44.1973	2.73052
$263$	−4.85061	−0.299101	−0.149551	−	0.988754i	$-0.547783\pi$
$263$	−4.85061	−0.299101	−0.149551	+	0.988754i	$0.547783\pi$
$264$	−15.8421	−0.975012
$265$	17.5291	1.07680
$266$	22.1587	1.35864
$267$	−0.103752	−0.00634955
$268$	−16.2672	−0.993680
$269$	−1.95709	−0.119326	−0.0596630	−	0.998219i	$-0.519003\pi$
$269$	−1.95709	−0.119326	−0.0596630	+	0.998219i	$0.519003\pi$
$270$	−8.02034	−0.488102
$271$	0.367832	0.0223442	0.0111721	−	0.999938i	$-0.496444\pi$
$271$	0.367832	0.0223442	0.0111721	+	0.999938i	$0.496444\pi$
$272$	95.3333	5.78043
$273$	−0.898593	−0.0543853
$274$	42.9722	2.59605
$275$	−11.1877	−0.674641
$276$	13.1655	0.792473
$277$	−1.54673	−0.0929337	−0.0464668	−	0.998920i	$-0.514796\pi$
$277$	−1.54673	−0.0929337	−0.0464668	+	0.998920i	$0.514796\pi$
$278$	−0.819849	−0.0491713
$279$	−2.64900	−0.158592
$280$	25.5353	1.52603
$281$	−7.57221	−0.451720	−0.225860	−	0.974160i	$-0.572519\pi$
$281$	−7.57221	−0.451720	−0.225860	+	0.974160i	$0.572519\pi$
$282$	−2.33414	−0.138996
$283$	−15.2704	−0.907732	−0.453866	−	0.891070i	$-0.649955\pi$
$283$	−15.2704	−0.907732	−0.453866	+	0.891070i	$0.649955\pi$
$284$	−93.5224	−5.54953
$285$	2.70488	0.160223
$286$	30.8463	1.82398
$287$	7.13089	0.420923
$288$	90.6365	5.34081
$289$	8.61314	0.506655
$290$	35.3860	2.07794
$291$	3.92407	0.230033
$292$	−13.6468	−0.798616
$293$	9.61255	0.561571	0.280786	−	0.959770i	$-0.409405\pi$
$293$	9.61255	0.561571	0.280786	+	0.959770i	$0.409405\pi$
$294$	4.08913	0.238483
$295$	−6.01405	−0.350152
$296$	−58.5194	−3.40137
$297$	−8.59795	−0.498904
$298$	−13.4344	−0.778235
$299$	−16.9189	−0.978447
$300$	−3.81982	−0.220537
$301$	0.290981	0.0167719
$302$	33.8529	1.94802
$303$	1.49260	0.0857479
$304$	−105.511	−6.05147
$305$	17.9990	1.03062
$306$	41.4278	2.36827
$307$	15.6057	0.890665	0.445332	−	0.895365i	$-0.353086\pi$
$307$	15.6057	0.890665	0.445332	+	0.895365i	$0.353086\pi$
$308$	41.4764	2.36333
$309$	5.69524	0.323991
$310$	4.24098	0.240871
$311$	−21.0678	−1.19465	−0.597323	−	0.802001i	$-0.703769\pi$
$311$	−21.0678	−1.19465	−0.597323	+	0.802001i	$0.703769\pi$
$312$	6.95103	0.393525
$313$	6.10679	0.345176	0.172588	−	0.984994i	$-0.444787\pi$
$313$	6.10679	0.345176	0.172588	+	0.984994i	$0.444787\pi$
$314$	−9.63926	−0.543975
$315$	6.83055	0.384858
$316$	−47.9207	−2.69575
$317$	16.4428	0.923519	0.461759	−	0.887005i	$-0.347218\pi$
$317$	16.4428	0.923519	0.461759	+	0.887005i	$0.347218\pi$
$318$	8.59747	0.482122
$319$	37.9345	2.12392
$320$	−82.4691	−4.61016
$321$	5.38712	0.300680
$322$	−30.4843	−1.69882
$323$	−28.3476	−1.57730
$324$	48.5165	2.69536
$325$	4.90881	0.272292
$326$	−16.9157	−0.936874
$327$	−0.798726	−0.0441696
$328$	−55.1607	−3.04574
$329$	4.03328	0.222362
$330$	6.78438	0.373468
$331$	6.63027	0.364433	0.182216	−	0.983258i	$-0.441673\pi$
$331$	6.63027	0.364433	0.182216	+	0.983258i	$0.441673\pi$
$332$	63.7862	3.50072
$333$	−15.6536	−0.857813
$334$	6.20356	0.339444
$335$	4.59785	0.251208
$336$	7.70938	0.420581
$337$	21.5382	1.17326	0.586629	−	0.809856i	$-0.300455\pi$
$337$	21.5382	1.17326	0.586629	+	0.809856i	$0.300455\pi$
$338$	22.9637	1.24906
$339$	−2.45092	−0.133115
$340$	−49.4960	−2.68430
$341$	4.54641	0.246202
$342$	−45.8506	−2.47932
$343$	−16.9293	−0.914096
$344$	−2.25088	−0.121359
$345$	−3.72118	−0.200341
$346$	1.90688	0.102514
$347$	8.11244	0.435499	0.217749	−	0.976005i	$-0.430128\pi$
$347$	8.11244	0.435499	0.217749	+	0.976005i	$0.430128\pi$
$348$	12.9520	0.694301
$349$	15.5147	0.830483	0.415241	−	0.909711i	$-0.363697\pi$
$349$	15.5147	0.830483	0.415241	+	0.909711i	$0.363697\pi$
$350$	8.84462	0.472765
$351$	3.77253	0.201362
$352$	−155.557	−8.29121
$353$	−11.6399	−0.619529	−0.309765	−	0.950813i	$-0.600250\pi$
$353$	−11.6399	−0.619529	−0.309765	+	0.950813i	$0.600250\pi$
$354$	−2.94970	−0.156775
$355$	26.4336	1.40295
$356$	−2.10123	−0.111365
$357$	2.07127	0.109623
$358$	24.4474	1.29209
$359$	3.13624	0.165524	0.0827622	−	0.996569i	$-0.473626\pi$
$359$	3.13624	0.165524	0.0827622	+	0.996569i	$0.473626\pi$
$360$	−52.8375	−2.78478
$361$	12.3739	0.651260
$362$	31.1061	1.63490
$363$	4.07802	0.214040
$364$	−18.1986	−0.953865
$365$	3.85719	0.201894
$366$	8.82794	0.461444
$367$	−36.1143	−1.88515	−0.942575	−	0.333996i	$-0.891603\pi$
$367$	−36.1143	−1.88515	−0.942575	+	0.333996i	$0.891603\pi$
$368$	145.154	7.56668
$369$	−14.7552	−0.768125
$370$	25.0610	1.30286
$371$	−14.8560	−0.771285
$372$	1.55229	0.0804823
$373$	6.46461	0.334725	0.167362	−	0.985895i	$-0.446475\pi$
$373$	6.46461	0.334725	0.167362	+	0.985895i	$0.446475\pi$
$374$	−71.1014	−3.67656
$375$	3.49419	0.180439
$376$	−31.1993	−1.60898
$377$	−16.6445	−0.857237
$378$	6.79728	0.349614
$379$	−12.4570	−0.639874	−0.319937	−	0.947439i	$-0.603662\pi$
$379$	−12.4570	−0.639874	−0.319937	+	0.947439i	$0.603662\pi$
$380$	54.7802	2.81016
$381$	5.23283	0.268086
$382$	−36.9401	−1.89002
$383$	13.5091	0.690284	0.345142	−	0.938550i	$-0.387831\pi$
$383$	13.5091	0.690284	0.345142	+	0.938550i	$0.387831\pi$
$384$	−22.3903	−1.14260
$385$	−11.7231	−0.597464
$386$	17.7261	0.902233
$387$	−0.602097	−0.0306063
$388$	79.4714	4.03455
$389$	−2.52078	−0.127809	−0.0639044	−	0.997956i	$-0.520355\pi$
$389$	−2.52078	−0.127809	−0.0639044	+	0.997956i	$0.520355\pi$
$390$	−2.97679	−0.150735
$391$	38.9985	1.97224
$392$	54.6573	2.76061
$393$	−4.57239	−0.230646
$394$	−4.98489	−0.251135
$395$	13.5445	0.681499
$396$	−85.8226	−4.31275
$397$	−0.514060	−0.0257999	−0.0129000	−	0.999917i	$-0.504106\pi$
$397$	−0.514060	−0.0257999	−0.0129000	+	0.999917i	$0.504106\pi$
$398$	−69.5559	−3.48652
$399$	−2.29240	−0.114764
$400$	−42.1146	−2.10573
$401$	−6.37958	−0.318581	−0.159291	−	0.987232i	$-0.550921\pi$
$401$	−6.37958	−0.318581	−0.159291	+	0.987232i	$0.550921\pi$
$402$	2.25510	0.112474
$403$	−1.99483	−0.0993695
$404$	30.2287	1.50393
$405$	−13.7130	−0.681402
$406$	−29.9899	−1.48837
$407$	26.8659	1.33169
$408$	−16.0223	−0.793220
$409$	−9.71668	−0.480459	−0.240229	−	0.970716i	$-0.577223\pi$
$409$	−9.71668	−0.480459	−0.240229	+	0.970716i	$0.577223\pi$
$410$	23.6226	1.16664
$411$	−4.44564	−0.219287
$412$	115.342	5.68248
$413$	5.09694	0.250804
$414$	63.0778	3.10011
$415$	−18.0289	−0.885002
$416$	68.2537	3.34641
$417$	0.0848165	0.00415348
$418$	78.6921	3.84896
$419$	35.0639	1.71298	0.856492	−	0.516161i	$-0.172639\pi$
$419$	35.0639	1.71298	0.856492	+	0.516161i	$0.172639\pi$
$420$	−4.00263	−0.195308
$421$	−24.0135	−1.17035	−0.585173	−	0.810909i	$-0.698973\pi$
$421$	−24.0135	−1.17035	−0.585173	+	0.810909i	$0.698973\pi$
$422$	−71.3794	−3.47469
$423$	−8.34565	−0.405779
$424$	114.918	5.58091
$425$	−11.3149	−0.548854
$426$	12.9649	0.628150
$427$	−15.2542	−0.738205
$428$	109.102	5.27363
$429$	−3.19117	−0.154071
$430$	0.963940	0.0464853
$431$	24.5461	1.18235	0.591173	−	0.806545i	$-0.298665\pi$
$431$	24.5461	1.18235	0.591173	+	0.806545i	$0.298665\pi$
$432$	−32.3660	−1.55721
$433$	26.0384	1.25133	0.625663	−	0.780093i	$-0.284828\pi$
$433$	26.0384	1.25133	0.625663	+	0.780093i	$0.284828\pi$
$434$	−3.59425	−0.172530
$435$	−3.66082	−0.175523
$436$	−16.1760	−0.774692
$437$	−43.1619	−2.06471
$438$	1.89183	0.0903950
$439$	28.6554	1.36765	0.683824	−	0.729647i	$-0.260316\pi$
$439$	28.6554	1.36765	0.683824	+	0.729647i	$0.260316\pi$
$440$	90.6834	4.32316
$441$	14.6205	0.696216
$442$	31.1972	1.48390
$443$	32.5266	1.54538	0.772692	−	0.634781i	$-0.218910\pi$
$443$	32.5266	1.54538	0.772692	+	0.634781i	$0.218910\pi$
$444$	9.17284	0.435324
$445$	0.593902	0.0281536
$446$	68.7500	3.25541
$447$	1.38984	0.0657373
$448$	69.8930	3.30213
$449$	4.01359	0.189413	0.0947065	−	0.995505i	$-0.469809\pi$
$449$	4.01359	0.189413	0.0947065	+	0.995505i	$0.469809\pi$
$450$	−18.3012	−0.862729
$451$	25.3239	1.19246
$452$	−49.6367	−2.33471
$453$	−3.50222	−0.164549
$454$	−32.5341	−1.52690
$455$	5.14374	0.241142
$456$	17.7328	0.830414
$457$	−11.8745	−0.555465	−0.277732	−	0.960659i	$-0.589583\pi$
$457$	−11.8745	−0.555465	−0.277732	+	0.960659i	$0.589583\pi$
$458$	14.8317	0.693039
$459$	−8.69575	−0.405883
$460$	−75.3624	−3.51379
$461$	40.0771	1.86657	0.933287	−	0.359131i	$-0.116927\pi$
$461$	40.0771	1.86657	0.933287	+	0.359131i	$0.116927\pi$
$462$	−5.74980	−0.267505
$463$	42.3281	1.96715	0.983577	−	0.180490i	$-0.0577684\pi$
$463$	42.3281	1.96715	0.983577	+	0.180490i	$0.0577684\pi$
$464$	142.800	6.62932
$465$	−0.438746	−0.0203464
$466$	−9.98732	−0.462654
$467$	25.3699	1.17398	0.586989	−	0.809595i	$-0.300313\pi$
$467$	25.3699	1.17398	0.586989	+	0.809595i	$0.300313\pi$
$468$	37.6564	1.74067
$469$	−3.89671	−0.179933
$470$	13.3611	0.616303
$471$	0.997220	0.0459495
$472$	−39.4272	−1.81478
$473$	1.03336	0.0475140
$474$	6.64317	0.305131
$475$	12.5229	0.574589
$476$	41.9481	1.92269
$477$	30.7400	1.40749
$478$	−51.6607	−2.36290
$479$	7.21392	0.329612	0.164806	−	0.986326i	$-0.447300\pi$
$479$	7.21392	0.329612	0.164806	+	0.986326i	$0.447300\pi$
$480$	15.0118	0.685193
$481$	−11.7879	−0.537484
$482$	13.5413	0.616788
$483$	3.15372	0.143499
$484$	82.5893	3.75406
$485$	−22.4622	−1.01996
$486$	−21.1976	−0.961543
$487$	28.8318	1.30649	0.653247	−	0.757145i	$-0.273406\pi$
$487$	28.8318	1.30649	0.653247	+	0.757145i	$0.273406\pi$
$488$	117.999	5.34155
$489$	1.75000	0.0791375
$490$	−23.4071	−1.05742
$491$	30.3436	1.36939	0.684694	−	0.728831i	$-0.259936\pi$
$491$	30.3436	1.36939	0.684694	+	0.728831i	$0.259936\pi$
$492$	8.64638	0.389809
$493$	38.3660	1.72792
$494$	−34.5277	−1.55348
$495$	24.2573	1.09029
$496$	17.1144	0.768460
$497$	−22.4026	−1.00490
$498$	−8.84259	−0.396246
$499$	7.16663	0.320822	0.160411	−	0.987050i	$-0.448718\pi$
$499$	7.16663	0.320822	0.160411	+	0.987050i	$0.448718\pi$
$500$	70.7655	3.16473
$501$	−0.641783	−0.0286727
$502$	−88.7349	−3.96043
$503$	−10.6338	−0.474139	−0.237069	−	0.971493i	$-0.576187\pi$
$503$	−10.6338	−0.474139	−0.237069	+	0.971493i	$0.576187\pi$
$504$	44.7800	1.99466
$505$	−8.54399	−0.380203
$506$	−108.259	−4.81268
$507$	−2.37568	−0.105508
$508$	105.977	4.70197
$509$	−32.8438	−1.45578	−0.727888	−	0.685696i	$-0.759498\pi$
$509$	−32.8438	−1.45578	−0.727888	+	0.685696i	$0.759498\pi$
$510$	6.86155	0.303835
$511$	−3.26899	−0.144611
$512$	−174.935	−7.73110
$513$	9.62410	0.424914
$514$	−20.8413	−0.919268
$515$	−32.6008	−1.43656
$516$	0.352822	0.0155321
$517$	14.3234	0.629942
$518$	−21.2393	−0.933202
$519$	−0.197274	−0.00865937
$520$	−39.7892	−1.74487
$521$	−44.2710	−1.93955	−0.969775	−	0.244003i	$-0.921539\pi$
$521$	−44.2710	−1.93955	−0.969775	+	0.244003i	$0.921539\pi$
$522$	62.0548	2.71607
$523$	2.26456	0.0990222	0.0495111	−	0.998774i	$-0.484234\pi$
$523$	2.26456	0.0990222	0.0495111	+	0.998774i	$0.484234\pi$
$524$	−92.6014	−4.04531
$525$	−0.915011	−0.0399344
$526$	13.6183	0.593787
$527$	4.59812	0.200297
$528$	27.3783	1.19149
$529$	36.3789	1.58169
$530$	−49.2138	−2.13771
$531$	−10.5466	−0.457682
$532$	−46.4265	−2.01284
$533$	−11.1114	−0.481287
$534$	0.291290	0.0126053
$535$	−30.8371	−1.33320
$536$	30.1428	1.30197
$537$	−2.52918	−0.109142
$538$	5.49462	0.236890
$539$	−25.0928	−1.08082
$540$	16.8041	0.723132
$541$	−10.1558	−0.436630	−0.218315	−	0.975878i	$-0.570056\pi$
$541$	−10.1558	−0.436630	−0.218315	+	0.975878i	$0.570056\pi$
$542$	−1.03270	−0.0443585
$543$	−3.21805	−0.138100
$544$	−157.326	−6.74530
$545$	4.57208	0.195846
$546$	2.52284	0.107968
$547$	19.4594	0.832026	0.416013	−	0.909359i	$-0.363427\pi$
$547$	19.4594	0.832026	0.416013	+	0.909359i	$0.363427\pi$
$548$	−90.0346	−3.84609
$549$	31.5640	1.34712
$550$	31.4099	1.33932
$551$	−42.4619	−1.80894
$552$	−24.3954	−1.03834
$553$	−11.4791	−0.488139
$554$	4.34250	0.184495
$555$	−2.59266	−0.110052
$556$	1.71773	0.0728481
$557$	16.9120	0.716582	0.358291	−	0.933610i	$-0.383359\pi$
$557$	16.9120	0.716582	0.358291	+	0.933610i	$0.383359\pi$
$558$	7.43721	0.314842
$559$	−0.453408	−0.0191771
$560$	−44.1302	−1.86484
$561$	7.35571	0.310558
$562$	21.2593	0.896771
$563$	19.8360	0.835988	0.417994	−	0.908450i	$-0.362733\pi$
$563$	19.8360	0.835988	0.417994	+	0.908450i	$0.362733\pi$
$564$	4.89045	0.205925
$565$	14.0296	0.590228
$566$	42.8724	1.80206
$567$	11.6218	0.488070
$568$	173.295	7.27129
$569$	8.35503	0.350261	0.175130	−	0.984545i	$-0.443965\pi$
$569$	8.35503	0.350261	0.175130	+	0.984545i	$0.443965\pi$
$570$	−7.59409	−0.318081
$571$	44.4734	1.86116	0.930578	−	0.366094i	$-0.119305\pi$
$571$	44.4734	1.86116	0.930578	+	0.366094i	$0.119305\pi$
$572$	−64.6286	−2.70226
$573$	3.82160	0.159649
$574$	−20.0203	−0.835632
$575$	−17.2280	−0.718459
$576$	−144.622	−6.02592
$577$	8.60731	0.358327	0.179163	−	0.983819i	$-0.442661\pi$
$577$	8.60731	0.358327	0.179163	+	0.983819i	$0.442661\pi$
$578$	−24.1818	−1.00583
$579$	−1.83383	−0.0762114
$580$	−74.1402	−3.07850
$581$	15.2796	0.633903
$582$	−11.0170	−0.456669
$583$	−52.7581	−2.18502
$584$	25.2871	1.04639
$585$	−10.6434	−0.440050
$586$	−26.9877	−1.11485
$587$	−19.5518	−0.806990	−0.403495	−	0.914982i	$-0.632205\pi$
$587$	−19.5518	−0.806990	−0.403495	+	0.914982i	$0.632205\pi$
$588$	−8.56747	−0.353316
$589$	−5.08901	−0.209689
$590$	16.8847	0.695134
$591$	0.515706	0.0212133
$592$	101.133	4.15656
$593$	33.0068	1.35542	0.677712	−	0.735327i	$-0.262971\pi$
$593$	33.0068	1.35542	0.677712	+	0.735327i	$0.262971\pi$
$594$	24.1392	0.990442
$595$	−11.8564	−0.486066
$596$	28.1475	1.15297
$597$	7.19583	0.294506
$598$	47.5007	1.94245
$599$	18.4843	0.755246	0.377623	−	0.925959i	$-0.376741\pi$
$599$	18.4843	0.755246	0.377623	+	0.925959i	$0.376741\pi$
$600$	7.07803	0.288959
$601$	−15.4958	−0.632087	−0.316044	−	0.948745i	$-0.602355\pi$
$601$	−15.4958	−0.632087	−0.316044	+	0.948745i	$0.602355\pi$
$602$	−0.816944	−0.0332962
$603$	8.06304	0.328352
$604$	−70.9281	−2.88602
$605$	−23.3435	−0.949047
$606$	−4.19056	−0.170230
$607$	−7.09367	−0.287923	−0.143962	−	0.989583i	$-0.545984\pi$
$607$	−7.09367	−0.287923	−0.143962	+	0.989583i	$0.545984\pi$
$608$	174.122	7.06159
$609$	3.10257	0.125722
$610$	−50.5331	−2.04602
$611$	−6.28468	−0.254251
$612$	−86.7988	−3.50863
$613$	21.0160	0.848829	0.424415	−	0.905468i	$-0.360480\pi$
$613$	21.0160	0.848829	0.424415	+	0.905468i	$0.360480\pi$
$614$	−43.8138	−1.76818
$615$	−2.44385	−0.0985457
$616$	−76.8547	−3.09656
$617$	−6.54321	−0.263420	−0.131710	−	0.991288i	$-0.542047\pi$
$617$	−6.54321	−0.263420	−0.131710	+	0.991288i	$0.542047\pi$
$618$	−15.9897	−0.643198
$619$	13.3357	0.536007	0.268004	−	0.963418i	$-0.413636\pi$
$619$	13.3357	0.536007	0.268004	+	0.963418i	$0.413636\pi$
$620$	−8.88562	−0.356855
$621$	−13.2401	−0.531307
$622$	59.1489	2.37165
$623$	−0.503335	−0.0201657
$624$	−12.0128	−0.480896
$625$	−8.82283	−0.352913
$626$	−17.1451	−0.685256
$627$	−8.14100	−0.325120
$628$	20.1960	0.805908
$629$	27.1714	1.08340
$630$	−19.1771	−0.764034
$631$	6.95539	0.276890	0.138445	−	0.990370i	$-0.455790\pi$
$631$	6.95539	0.276890	0.138445	+	0.990370i	$0.455790\pi$
$632$	88.7958	3.53211
$633$	7.38448	0.293507
$634$	−46.1639	−1.83340
$635$	−29.9538	−1.18868
$636$	−18.0133	−0.714272
$637$	11.0100	0.436231
$638$	−106.503	−4.21649
$639$	46.3554	1.83379
$640$	128.167	5.06625
$641$	27.2974	1.07818	0.539091	−	0.842247i	$-0.318768\pi$
$641$	27.2974	1.07818	0.539091	+	0.842247i	$0.318768\pi$
$642$	−15.1246	−0.596921
$643$	17.3998	0.686182	0.343091	−	0.939302i	$-0.388526\pi$
$643$	17.3998	0.686182	0.343091	+	0.939302i	$0.388526\pi$
$644$	63.8701	2.51683
$645$	−0.0997233	−0.00392660
$646$	79.5871	3.13131
$647$	44.8747	1.76421	0.882104	−	0.471055i	$-0.156127\pi$
$647$	44.8747	1.76421	0.882104	+	0.471055i	$0.156127\pi$
$648$	−89.9000	−3.53161
$649$	18.1008	0.710517
$650$	−13.7817	−0.540564
$651$	0.371839	0.0145735
$652$	35.4415	1.38799
$653$	−24.4236	−0.955770	−0.477885	−	0.878422i	$-0.658596\pi$
$653$	−24.4236	−0.955770	−0.477885	+	0.878422i	$0.658596\pi$
$654$	2.24246	0.0876871
$655$	26.1733	1.02268
$656$	95.3289	3.72197
$657$	6.76416	0.263895
$658$	−11.3236	−0.441441
$659$	−48.5875	−1.89270	−0.946351	−	0.323142i	$-0.895261\pi$
$659$	−48.5875	−1.89270	−0.946351	+	0.323142i	$0.895261\pi$
$660$	−14.2145	−0.553299
$661$	−40.9706	−1.59357	−0.796785	−	0.604263i	$-0.793468\pi$
$661$	−40.9706	−1.59357	−0.796785	+	0.604263i	$0.793468\pi$
$662$	−18.6148	−0.723485
$663$	−3.22747	−0.125344
$664$	−118.194	−4.58683
$665$	13.1222	0.508857
$666$	43.9483	1.70296
$667$	58.4159	2.26187
$668$	−12.9976	−0.502892
$669$	−7.11245	−0.274983
$670$	−12.9087	−0.498706
$671$	−54.1724	−2.09130
$672$	−12.7226	−0.490785
$673$	−22.9087	−0.883066	−0.441533	−	0.897245i	$-0.645565\pi$
$673$	−22.9087	−0.883066	−0.441533	+	0.897245i	$0.645565\pi$
$674$	−60.4694	−2.32919
$675$	3.84145	0.147858
$676$	−48.1131	−1.85050
$677$	8.96214	0.344443	0.172222	−	0.985058i	$-0.444906\pi$
$677$	8.96214	0.344443	0.172222	+	0.985058i	$0.444906\pi$
$678$	6.88106	0.264266
$679$	19.0368	0.730567
$680$	91.7149	3.51711
$681$	3.36578	0.128977
$682$	−12.7643	−0.488769
$683$	−30.5765	−1.16998	−0.584989	−	0.811042i	$-0.698901\pi$
$683$	−30.5765	−1.16998	−0.584989	+	0.811042i	$0.698901\pi$
$684$	96.0654	3.67315
$685$	25.4478	0.972311
$686$	47.5298	1.81470
$687$	−1.53440	−0.0585408
$688$	3.88997	0.148304
$689$	23.1487	0.881894
$690$	10.4474	0.397725
$691$	−9.81338	−0.373319	−0.186659	−	0.982425i	$-0.559766\pi$
$691$	−9.81338	−0.373319	−0.186659	+	0.982425i	$0.559766\pi$
$692$	−3.99526	−0.151877
$693$	−20.5582	−0.780942
$694$	−22.7761	−0.864568
$695$	−0.485508	−0.0184164
$696$	−23.9998	−0.909710
$697$	25.6120	0.970122
$698$	−43.5583	−1.64870
$699$	1.03323	0.0390803
$700$	−18.5311	−0.700410
$701$	−16.0568	−0.606457	−0.303229	−	0.952918i	$-0.598065\pi$
$701$	−16.0568	−0.606457	−0.303229	+	0.952918i	$0.598065\pi$
$702$	−10.5915	−0.399752
$703$	−30.0722	−1.13420
$704$	248.211	9.35480
$705$	−1.38226	−0.0520590
$706$	32.6796	1.22991
$707$	7.24108	0.272329
$708$	6.18017	0.232265
$709$	−41.9871	−1.57686	−0.788430	−	0.615125i	$-0.789106\pi$
$709$	−41.9871	−1.57686	−0.788430	+	0.615125i	$0.789106\pi$
$710$	−74.2137	−2.78519
$711$	23.7524	0.890785
$712$	3.89353	0.145916
$713$	7.00108	0.262193
$714$	−5.81520	−0.217628
$715$	18.2669	0.683145
$716$	−51.2218	−1.91425
$717$	5.34450	0.199594
$718$	−8.80514	−0.328605
$719$	29.0418	1.08308	0.541539	−	0.840676i	$-0.317842\pi$
$719$	29.0418	1.08308	0.541539	+	0.840676i	$0.317842\pi$
$720$	91.3139	3.40307
$721$	27.6293	1.02897
$722$	−34.7404	−1.29290
$723$	−1.40090	−0.0520999
$724$	−65.1730	−2.42213
$725$	−16.9486	−0.629457
$726$	−11.4492	−0.424921
$727$	52.6711	1.95346	0.976732	−	0.214463i	$-0.0688000\pi$
$727$	52.6711	1.95346	0.976732	+	0.214463i	$0.0688000\pi$
$728$	33.7216	1.24980
$729$	−22.5506	−0.835207
$730$	−10.8292	−0.400808
$731$	1.04512	0.0386550
$732$	−18.4961	−0.683637
$733$	27.4870	1.01526	0.507628	−	0.861576i	$-0.330522\pi$
$733$	27.4870	1.01526	0.507628	+	0.861576i	$0.330522\pi$
$734$	101.393	3.74247
$735$	2.42155	0.0893203
$736$	−239.544	−8.82972
$737$	−13.8384	−0.509743
$738$	41.4259	1.52491
$739$	−20.8534	−0.767103	−0.383552	−	0.923519i	$-0.625299\pi$
$739$	−20.8534	−0.767103	−0.383552	+	0.923519i	$0.625299\pi$
$740$	−52.5073	−1.93021
$741$	3.57203	0.131222
$742$	41.7089	1.53118
$743$	−27.7996	−1.01987	−0.509935	−	0.860213i	$-0.670330\pi$
$743$	−27.7996	−1.01987	−0.509935	+	0.860213i	$0.670330\pi$
$744$	−2.87635	−0.105452
$745$	−7.95576	−0.291476
$746$	−18.1497	−0.664508
$747$	−31.6164	−1.15678
$748$	148.970	5.44689
$749$	26.1346	0.954937
$750$	−9.81010	−0.358214
$751$	29.4418	1.07435	0.537174	−	0.843472i	$-0.319492\pi$
$751$	29.4418	1.07435	0.537174	+	0.843472i	$0.319492\pi$
$752$	53.9187	1.96621
$753$	9.17997	0.334537
$754$	46.7303	1.70182
$755$	20.0475	0.729602
$756$	−14.2415	−0.517959
$757$	−3.97422	−0.144446	−0.0722228	−	0.997389i	$-0.523009\pi$
$757$	−3.97422	−0.144446	−0.0722228	+	0.997389i	$0.523009\pi$
$758$	34.9737	1.27030
$759$	11.1998	0.406526
$760$	−101.506	−3.68202
$761$	−13.9392	−0.505296	−0.252648	−	0.967558i	$-0.581301\pi$
$761$	−13.9392	−0.505296	−0.252648	+	0.967558i	$0.581301\pi$
$762$	−14.6914	−0.532214
$763$	−3.87486	−0.140279
$764$	77.3962	2.80010
$765$	24.5332	0.887001
$766$	−37.9275	−1.37038
$767$	−7.94207	−0.286772
$768$	34.0478	1.22859
$769$	−30.6344	−1.10471	−0.552353	−	0.833610i	$-0.686270\pi$
$769$	−30.6344	−1.10471	−0.552353	+	0.833610i	$0.686270\pi$
$770$	32.9131	1.18611
$771$	2.15611	0.0776504
$772$	−37.1393	−1.33667
$773$	−2.23805	−0.0804972	−0.0402486	−	0.999190i	$-0.512815\pi$
$773$	−2.23805	−0.0804972	−0.0402486	+	0.999190i	$0.512815\pi$
$774$	1.69042	0.0607607
$775$	−2.03128	−0.0729656
$776$	−147.259	−5.28628
$777$	2.19729	0.0788274
$778$	7.07721	0.253730
$779$	−28.3463	−1.01561
$780$	6.23691	0.223317
$781$	−79.5585	−2.84683
$782$	−109.490	−3.91536
$783$	−13.0254	−0.465489
$784$	−94.4589	−3.37353
$785$	−5.70830	−0.203738
$786$	12.8372	0.457887
$787$	−20.2256	−0.720966	−0.360483	−	0.932766i	$-0.617388\pi$
$787$	−20.2256	−0.720966	−0.360483	+	0.932766i	$0.617388\pi$
$788$	10.4442	0.372061
$789$	−1.40887	−0.0501570
$790$	−38.0269	−1.35294
$791$	−11.8901	−0.422764
$792$	159.027	5.65079
$793$	23.7692	0.844070
$794$	1.44325	0.0512189
$795$	5.09136	0.180572
$796$	145.732	5.16535
$797$	53.7971	1.90559	0.952796	−	0.303610i	$-0.0981921\pi$
$797$	53.7971	1.90559	0.952796	+	0.303610i	$0.0981921\pi$
$798$	6.43603	0.227833
$799$	14.4863	0.512489
$800$	69.5008	2.45722
$801$	1.04150	0.0367995
$802$	17.9110	0.632459
$803$	−11.6091	−0.409678
$804$	−4.72485	−0.166633
$805$	−18.0526	−0.636269
$806$	5.60058	0.197272
$807$	−0.568440	−0.0200100
$808$	−56.0131	−1.97053
$809$	2.17674	0.0765300	0.0382650	−	0.999268i	$-0.487817\pi$
$809$	2.17674	0.0765300	0.0382650	+	0.999268i	$0.487817\pi$
$810$	38.4998	1.35274
$811$	−15.4304	−0.541834	−0.270917	−	0.962603i	$-0.587327\pi$
$811$	−15.4304	−0.541834	−0.270917	+	0.962603i	$0.587327\pi$
$812$	62.8342	2.20505
$813$	0.106837	0.00374695
$814$	−75.4272	−2.64372
$815$	−10.0174	−0.350893
$816$	27.6897	0.969334
$817$	−1.15669	−0.0404675
$818$	27.2800	0.953824
$819$	9.02033	0.315196
$820$	−49.4937	−1.72840
$821$	22.8193	0.796400	0.398200	−	0.917299i	$-0.369635\pi$
$821$	22.8193	0.796400	0.398200	+	0.917299i	$0.369635\pi$
$822$	12.4814	0.435337
$823$	−15.3082	−0.533612	−0.266806	−	0.963750i	$-0.585968\pi$
$823$	−15.3082	−0.533612	−0.266806	+	0.963750i	$0.585968\pi$
$824$	−213.726	−7.44549
$825$	−3.24948	−0.113132
$826$	−14.3099	−0.497905
$827$	−1.94467	−0.0676229	−0.0338115	−	0.999428i	$-0.510765\pi$
$827$	−1.94467	−0.0676229	−0.0338115	+	0.999428i	$0.510765\pi$
$828$	−132.160	−4.59286
$829$	−36.5917	−1.27088	−0.635442	−	0.772149i	$-0.719182\pi$
$829$	−36.5917	−1.27088	−0.635442	+	0.772149i	$0.719182\pi$
$830$	50.6169	1.75694
$831$	−0.449249	−0.0155843
$832$	−108.908	−3.77569
$833$	−25.3782	−0.879303
$834$	−0.238126	−0.00824564
$835$	3.67370	0.127134
$836$	−164.874	−5.70229
$837$	−1.56108	−0.0539588
$838$	−98.4435	−3.40068
$839$	−50.6297	−1.74793	−0.873966	−	0.485987i	$-0.838460\pi$
$839$	−50.6297	−1.74793	−0.873966	+	0.485987i	$0.838460\pi$
$840$	7.41677	0.255903
$841$	28.4685	0.981672
$842$	67.4190	2.32341
$843$	−2.19936	−0.0757500
$844$	149.553	5.14782
$845$	13.5989	0.467817
$846$	23.4308	0.805567
$847$	19.7837	0.679776
$848$	−198.602	−6.82001
$849$	−4.43532	−0.152220
$850$	31.7672	1.08960
$851$	41.3711	1.41818
$852$	−27.1637	−0.930615
$853$	52.5281	1.79853	0.899264	−	0.437406i	$-0.144103\pi$
$853$	52.5281	1.79853	0.899264	+	0.437406i	$0.144103\pi$
$854$	42.8270	1.46551
$855$	−27.1524	−0.928592
$856$	−202.163	−6.90979
$857$	2.57822	0.0880704	0.0440352	−	0.999030i	$-0.485979\pi$
$857$	2.57822	0.0880704	0.0440352	+	0.999030i	$0.485979\pi$
$858$	8.95936	0.305868
$859$	57.8361	1.97334	0.986671	−	0.162731i	$-0.0520301\pi$
$859$	57.8361	1.97334	0.986671	+	0.162731i	$0.0520301\pi$
$860$	−2.01963	−0.0688688
$861$	2.07118	0.0705856
$862$	−68.9144	−2.34723
$863$	−49.9739	−1.70113	−0.850565	−	0.525870i	$-0.823740\pi$
$863$	−49.9739	−1.70113	−0.850565	+	0.525870i	$0.823740\pi$
$864$	53.4128	1.81714
$865$	1.12924	0.0383953
$866$	−73.1041	−2.48418
$867$	2.50170	0.0849622
$868$	7.53061	0.255606
$869$	−40.7656	−1.38288
$870$	10.2779	0.348455
$871$	6.07186	0.205737
$872$	29.9738	1.01504
$873$	−39.3909	−1.33318
$874$	121.179	4.09894
$875$	16.9514	0.573061
$876$	−3.96372	−0.133922
$877$	30.9147	1.04391	0.521957	−	0.852972i	$-0.325202\pi$
$877$	30.9147	1.04391	0.521957	+	0.852972i	$0.325202\pi$
$878$	−80.4514	−2.71510
$879$	2.79198	0.0941713
$880$	−156.719	−5.28301
$881$	32.9767	1.11101	0.555506	−	0.831512i	$-0.312524\pi$
$881$	32.9767	1.11101	0.555506	+	0.831512i	$0.312524\pi$
$882$	−41.0478	−1.38215
$883$	−34.2919	−1.15401	−0.577007	−	0.816739i	$-0.695780\pi$
$883$	−34.2919	−1.15401	−0.577007	+	0.816739i	$0.695780\pi$
$884$	−65.3637	−2.19842
$885$	−1.74679	−0.0587178
$886$	−91.3199	−3.06795
$887$	−13.1511	−0.441571	−0.220786	−	0.975322i	$-0.570862\pi$
$887$	−13.1511	−0.441571	−0.220786	+	0.975322i	$0.570862\pi$
$888$	−16.9971	−0.570384
$889$	25.3860	0.851420
$890$	−1.66741	−0.0558916
$891$	41.2725	1.38268
$892$	−144.044	−4.82294
$893$	−16.0329	−0.536519
$894$	−3.90205	−0.130504
$895$	14.4776	0.483932
$896$	−108.622	−3.62882
$897$	−4.91413	−0.164078
$898$	−11.2683	−0.376030
$899$	6.88754	0.229712
$900$	38.3444	1.27815
$901$	−53.3582	−1.77762
$902$	−71.0981	−2.36731
$903$	0.0845161	0.00281252
$904$	91.9756	3.05906
$905$	18.4208	0.612329
$906$	9.83265	0.326668
$907$	−0.576523	−0.0191431	−0.00957156	−	0.999954i	$-0.503047\pi$
$907$	−0.576523	−0.0191431	−0.00957156	+	0.999954i	$0.503047\pi$
$908$	68.1650	2.26213
$909$	−14.9832	−0.496961
$910$	−14.4413	−0.478724
$911$	45.3247	1.50167	0.750837	−	0.660487i	$-0.229650\pi$
$911$	45.3247	1.50167	0.750837	+	0.660487i	$0.229650\pi$
$912$	−30.6458	−1.01479
$913$	54.2622	1.79582
$914$	33.3382	1.10273
$915$	5.22784	0.172827
$916$	−31.0751	−1.02675
$917$	−22.1820	−0.732515
$918$	24.4137	0.805773
$919$	4.30281	0.141937	0.0709683	−	0.997479i	$-0.477391\pi$
$919$	4.30281	0.141937	0.0709683	+	0.997479i	$0.477391\pi$
$920$	139.645	4.60395
$921$	4.53271	0.149358
$922$	−112.518	−3.70559
$923$	34.9079	1.14901
$924$	12.0469	0.396313
$925$	−12.0033	−0.394667
$926$	−118.838	−3.90526
$927$	−57.1705	−1.87772
$928$	−235.659	−7.73589
$929$	47.2490	1.55019	0.775095	−	0.631844i	$-0.217702\pi$
$929$	47.2490	1.55019	0.775095	+	0.631844i	$0.217702\pi$
$930$	1.23180	0.0403923
$931$	28.0876	0.920533
$932$	20.9253	0.685430
$933$	−6.11918	−0.200333
$934$	−71.2271	−2.33062
$935$	−42.1057	−1.37700
$936$	−69.7764	−2.28071
$937$	4.10334	0.134050	0.0670251	−	0.997751i	$-0.478649\pi$
$937$	4.10334	0.134050	0.0670251	+	0.997751i	$0.478649\pi$
$938$	10.9402	0.357210
$939$	1.77373	0.0578835
$940$	−27.9940	−0.913064
$941$	37.1625	1.21146	0.605732	−	0.795669i	$-0.292880\pi$
$941$	37.1625	1.21146	0.605732	+	0.795669i	$0.292880\pi$
$942$	−2.79974	−0.0912205
$943$	38.9967	1.26991
$944$	68.1382	2.21771
$945$	4.02530	0.130943
$946$	−2.90121	−0.0943265
$947$	9.05037	0.294098	0.147049	−	0.989129i	$-0.453023\pi$
$947$	9.05037	0.294098	0.147049	+	0.989129i	$0.453023\pi$
$948$	−13.9186	−0.452056
$949$	5.09375	0.165350
$950$	−35.1586	−1.14070
$951$	4.77583	0.154867
$952$	−77.7289	−2.51921
$953$	−10.6271	−0.344247	−0.172123	−	0.985075i	$-0.555063\pi$
$953$	−10.6271	−0.344247	−0.172123	+	0.985075i	$0.555063\pi$
$954$	−86.3039	−2.79419
$955$	−21.8756	−0.707879
$956$	108.239	3.50068
$957$	11.0181	0.356166
$958$	−20.2534	−0.654358
$959$	−21.5672	−0.696440
$960$	−23.9533	−0.773089
$961$	−30.1745	−0.973372
$962$	33.0952	1.06703
$963$	−54.0775	−1.74262
$964$	−28.3714	−0.913782
$965$	10.4972	0.337918
$966$	−8.85421	−0.284879
$967$	−2.04280	−0.0656921	−0.0328461	−	0.999460i	$-0.510457\pi$
$967$	−2.04280	−0.0656921	−0.0328461	+	0.999460i	$0.510457\pi$
$968$	−153.036	−4.91877
$969$	−8.23360	−0.264501
$970$	63.0637	2.02485
$971$	−15.7845	−0.506550	−0.253275	−	0.967394i	$-0.581508\pi$
$971$	−15.7845	−0.506550	−0.253275	+	0.967394i	$0.581508\pi$
$972$	44.4129	1.42454
$973$	0.411471	0.0131911
$974$	−80.9467	−2.59370
$975$	1.42577	0.0456613
$976$	−203.926	−6.52750
$977$	−43.2492	−1.38367	−0.691833	−	0.722058i	$-0.743196\pi$
$977$	−43.2492	−1.38367	−0.691833	+	0.722058i	$0.743196\pi$
$978$	−4.91319	−0.157107
$979$	−1.78749	−0.0571285
$980$	49.0420	1.56659
$981$	8.01784	0.255990
$982$	−85.1911	−2.71856
$983$	−36.8090	−1.17402	−0.587012	−	0.809578i	$-0.699696\pi$
$983$	−36.8090	−1.17402	−0.587012	+	0.809578i	$0.699696\pi$
$984$	−16.0215	−0.510748
$985$	−2.95201	−0.0940590
$986$	−107.714	−3.43032
$987$	1.17147	0.0372884
$988$	72.3419	2.30150
$989$	1.59129	0.0506000
$990$	−68.1036	−2.16447
$991$	−20.1774	−0.640955	−0.320477	−	0.947256i	$-0.603843\pi$
$991$	−20.1774	−0.640955	−0.320477	+	0.947256i	$0.603843\pi$
$992$	−28.2435	−0.896732
$993$	1.92577	0.0611126
$994$	62.8965	1.99496
$995$	−41.1905	−1.30583
$996$	18.5268	0.587045
$997$	39.1053	1.23848	0.619239	−	0.785203i	$-0.287441\pi$
$997$	39.1053	1.23848	0.619239	+	0.785203i	$0.287441\pi$
$998$	−20.1206	−0.636908
$999$	−9.22480	−0.291860

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4027.2.a.c.1.1	✓	174

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4027.2.a.c.1.1	✓	174	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:	\( N \)	\(=\)	\( 4027 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.80755 q^{2} +0.290452 q^{3} +5.88232 q^{4} -1.66261 q^{5} -0.815457 q^{6} +1.40907 q^{7} -10.8998 q^{8} -2.91564 q^{9} +O(q^{10})\)	\(q-2.80755 q^{2} +0.290452 q^{3} +5.88232 q^{4} -1.66261 q^{5} -0.815457 q^{6} +1.40907 q^{7} -10.8998 q^{8} -2.91564 q^{9} +4.66785 q^{10} +5.00402 q^{11} +1.70853 q^{12} -2.19562 q^{13} -3.95603 q^{14} -0.482908 q^{15} +18.8371 q^{16} +5.06094 q^{17} +8.18579 q^{18} -5.60124 q^{19} -9.78000 q^{20} +0.409267 q^{21} -14.0490 q^{22} +7.70577 q^{23} -3.16587 q^{24} -2.23573 q^{25} +6.16430 q^{26} -1.71821 q^{27} +8.28860 q^{28} +7.58080 q^{29} +1.35579 q^{30} +0.908551 q^{31} -31.0863 q^{32} +1.45343 q^{33} -14.2088 q^{34} -2.34273 q^{35} -17.1507 q^{36} +5.36885 q^{37} +15.7258 q^{38} -0.637721 q^{39} +18.1221 q^{40} +5.06071 q^{41} -1.14904 q^{42} +0.206506 q^{43} +29.4353 q^{44} +4.84756 q^{45} -21.6343 q^{46} +2.86237 q^{47} +5.47126 q^{48} -5.01452 q^{49} +6.27693 q^{50} +1.46996 q^{51} -12.9153 q^{52} -10.5431 q^{53} +4.82395 q^{54} -8.31973 q^{55} -15.3586 q^{56} -1.62689 q^{57} -21.2834 q^{58} +3.61724 q^{59} -2.84062 q^{60} -10.8258 q^{61} -2.55080 q^{62} -4.10834 q^{63} +49.6022 q^{64} +3.65045 q^{65} -4.08057 q^{66} -2.76545 q^{67} +29.7701 q^{68} +2.23815 q^{69} +6.57733 q^{70} -15.8989 q^{71} +31.7799 q^{72} -2.31996 q^{73} -15.0733 q^{74} -0.649373 q^{75} -32.9483 q^{76} +7.05102 q^{77} +1.79043 q^{78} -8.14656 q^{79} -31.3187 q^{80} +8.24786 q^{81} -14.2082 q^{82} +10.8437 q^{83} +2.40744 q^{84} -8.41437 q^{85} -0.579776 q^{86} +2.20186 q^{87} -54.5429 q^{88} -0.357211 q^{89} -13.6098 q^{90} -3.09378 q^{91} +45.3278 q^{92} +0.263890 q^{93} -8.03625 q^{94} +9.31268 q^{95} -9.02908 q^{96} +13.5102 q^{97} +14.0785 q^{98} -14.5899 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 174 q + 21 q^{2} + 17 q^{3} + 187 q^{4} + 72 q^{5} + 21 q^{6} + 24 q^{7} + 54 q^{8} + 197 q^{9}+O(q^{10}) \) 174 * q + 21 * q^2 + 17 * q^3 + 187 * q^4 + 72 * q^5 + 21 * q^6 + 24 * q^7 + 54 * q^8 + 197 * q^9	\( 174 q + 21 q^{2} + 17 q^{3} + 187 q^{4} + 72 q^{5} + 21 q^{6} + 24 q^{7} + 54 q^{8} + 197 q^{9} + 20 q^{10} + 35 q^{11} + 23 q^{12} + 91 q^{13} + 18 q^{14} + 16 q^{15} + 201 q^{16} + 148 q^{17} + 39 q^{18} + 36 q^{19} + 128 q^{20} + 57 q^{21} + 17 q^{22} + 96 q^{23} + 24 q^{24} + 226 q^{25} + 44 q^{26} + 62 q^{27} + 32 q^{28} + 122 q^{29} + 25 q^{30} + 23 q^{31} + 104 q^{32} + 91 q^{33} + 6 q^{34} + 80 q^{35} + 222 q^{36} + 71 q^{37} + 125 q^{38} + 16 q^{39} + 53 q^{40} + 97 q^{41} + 14 q^{42} + 38 q^{43} + 70 q^{44} + 185 q^{45} - 23 q^{46} + 110 q^{47} + 36 q^{48} + 210 q^{49} + 51 q^{50} + 33 q^{51} + 118 q^{52} + 214 q^{53} + 8 q^{54} + 37 q^{55} + 41 q^{56} + 76 q^{57} + 2 q^{58} + 66 q^{59} - 12 q^{60} + 114 q^{61} + 175 q^{62} + 62 q^{63} + 190 q^{64} + 128 q^{65} + 12 q^{66} - 6 q^{67} + 348 q^{68} + 115 q^{69} - 38 q^{70} + 54 q^{71} + 101 q^{72} + 107 q^{73} + 71 q^{74} - q^{75} + 31 q^{76} + 368 q^{77} - 14 q^{78} - 14 q^{79} + 205 q^{80} + 222 q^{81} + 26 q^{82} + 246 q^{83} + 41 q^{84} + 87 q^{85} + 33 q^{86} + 100 q^{87} - 6 q^{88} + 147 q^{89} + 50 q^{90} - 23 q^{91} + 189 q^{92} + 117 q^{93} + 23 q^{94} + 42 q^{95} + 38 q^{96} + 52 q^{97} + 148 q^{98} + 38 q^{99}+O(q^{100}) \) 174 * q + 21 * q^2 + 17 * q^3 + 187 * q^4 + 72 * q^5 + 21 * q^6 + 24 * q^7 + 54 * q^8 + 197 * q^9 + 20 * q^10 + 35 * q^11 + 23 * q^12 + 91 * q^13 + 18 * q^14 + 16 * q^15 + 201 * q^16 + 148 * q^17 + 39 * q^18 + 36 * q^19 + 128 * q^20 + 57 * q^21 + 17 * q^22 + 96 * q^23 + 24 * q^24 + 226 * q^25 + 44 * q^26 + 62 * q^27 + 32 * q^28 + 122 * q^29 + 25 * q^30 + 23 * q^31 + 104 * q^32 + 91 * q^33 + 6 * q^34 + 80 * q^35 + 222 * q^36 + 71 * q^37 + 125 * q^38 + 16 * q^39 + 53 * q^40 + 97 * q^41 + 14 * q^42 + 38 * q^43 + 70 * q^44 + 185 * q^45 - 23 * q^46 + 110 * q^47 + 36 * q^48 + 210 * q^49 + 51 * q^50 + 33 * q^51 + 118 * q^52 + 214 * q^53 + 8 * q^54 + 37 * q^55 + 41 * q^56 + 76 * q^57 + 2 * q^58 + 66 * q^59 - 12 * q^60 + 114 * q^61 + 175 * q^62 + 62 * q^63 + 190 * q^64 + 128 * q^65 + 12 * q^66 - 6 * q^67 + 348 * q^68 + 115 * q^69 - 38 * q^70 + 54 * q^71 + 101 * q^72 + 107 * q^73 + 71 * q^74 - q^75 + 31 * q^76 + 368 * q^77 - 14 * q^78 - 14 * q^79 + 205 * q^80 + 222 * q^81 + 26 * q^82 + 246 * q^83 + 41 * q^84 + 87 * q^85 + 33 * q^86 + 100 * q^87 - 6 * q^88 + 147 * q^89 + 50 * q^90 - 23 * q^91 + 189 * q^92 + 117 * q^93 + 23 * q^94 + 42 * q^95 + 38 * q^96 + 52 * q^97 + 148 * q^98 + 38 * q^99

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