LMFDB - Embedded newform 6014.2.a.k.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6014,2,Mod(1,6014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6014, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6014 = 2 \cdot 31 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6014.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.0220317756$
Analytic rank:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	6014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.452250 q^{3} +1.00000 q^{4} -3.58205 q^{5} +0.452250 q^{6} -1.19090 q^{7} +1.00000 q^{8} -2.79547 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.452250 q^{3} +1.00000 q^{4} -3.58205 q^{5} +0.452250 q^{6} -1.19090 q^{7} +1.00000 q^{8} -2.79547 q^{9} -3.58205 q^{10} -5.76974 q^{11} +0.452250 q^{12} -3.35699 q^{13} -1.19090 q^{14} -1.61999 q^{15} +1.00000 q^{16} +5.21054 q^{17} -2.79547 q^{18} +0.755101 q^{19} -3.58205 q^{20} -0.538583 q^{21} -5.76974 q^{22} -5.86733 q^{23} +0.452250 q^{24} +7.83111 q^{25} -3.35699 q^{26} -2.62100 q^{27} -1.19090 q^{28} +1.17674 q^{29} -1.61999 q^{30} +1.00000 q^{31} +1.00000 q^{32} -2.60936 q^{33} +5.21054 q^{34} +4.26585 q^{35} -2.79547 q^{36} +2.71167 q^{37} +0.755101 q^{38} -1.51820 q^{39} -3.58205 q^{40} -5.57683 q^{41} -0.538583 q^{42} +6.91476 q^{43} -5.76974 q^{44} +10.0135 q^{45} -5.86733 q^{46} -2.93655 q^{47} +0.452250 q^{48} -5.58177 q^{49} +7.83111 q^{50} +2.35647 q^{51} -3.35699 q^{52} -2.05863 q^{53} -2.62100 q^{54} +20.6675 q^{55} -1.19090 q^{56} +0.341495 q^{57} +1.17674 q^{58} -9.58199 q^{59} -1.61999 q^{60} +11.8770 q^{61} +1.00000 q^{62} +3.32911 q^{63} +1.00000 q^{64} +12.0249 q^{65} -2.60936 q^{66} +15.3278 q^{67} +5.21054 q^{68} -2.65350 q^{69} +4.26585 q^{70} -1.09647 q^{71} -2.79547 q^{72} -6.36693 q^{73} +2.71167 q^{74} +3.54162 q^{75} +0.755101 q^{76} +6.87115 q^{77} -1.51820 q^{78} -7.74805 q^{79} -3.58205 q^{80} +7.20106 q^{81} -5.57683 q^{82} +17.6387 q^{83} -0.538583 q^{84} -18.6645 q^{85} +6.91476 q^{86} +0.532181 q^{87} -5.76974 q^{88} -3.03239 q^{89} +10.0135 q^{90} +3.99783 q^{91} -5.86733 q^{92} +0.452250 q^{93} -2.93655 q^{94} -2.70481 q^{95} +0.452250 q^{96} +1.00000 q^{97} -5.58177 q^{98} +16.1291 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 37 q^{2} + 9 q^{3} + 37 q^{4} + 9 q^{5} + 9 q^{6} + 19 q^{7} + 37 q^{8} + 52 q^{9}+O(q^{10}) $ 37 * q + 37 * q^2 + 9 * q^3 + 37 * q^4 + 9 * q^5 + 9 * q^6 + 19 * q^7 + 37 * q^8 + 52 * q^9	\( 37 q + 37 q^{2} + 9 q^{3} + 37 q^{4} + 9 q^{5} + 9 q^{6} + 19 q^{7} + 37 q^{8} + 52 q^{9} + 9 q^{10} + 5 q^{11} + 9 q^{12} + 16 q^{13} + 19 q^{14} + 22 q^{15} + 37 q^{16} + 3 q^{17} + 52 q^{18} + 36 q^{19} + 9 q^{20} + 6 q^{21} + 5 q^{22} + 11 q^{23} + 9 q^{24} + 58 q^{25} + 16 q^{26} + 24 q^{27} + 19 q^{28} + 5 q^{29} + 22 q^{30} + 37 q^{31} + 37 q^{32} + q^{33} + 3 q^{34} + 28 q^{35} + 52 q^{36} + 21 q^{37} + 36 q^{38} + 38 q^{39} + 9 q^{40} + 21 q^{41} + 6 q^{42} + 14 q^{43} + 5 q^{44} + 55 q^{45} + 11 q^{46} + 59 q^{47} + 9 q^{48} + 82 q^{49} + 58 q^{50} + 46 q^{51} + 16 q^{52} + 8 q^{53} + 24 q^{54} + 25 q^{55} + 19 q^{56} + 5 q^{58} + 41 q^{59} + 22 q^{60} + 16 q^{61} + 37 q^{62} + 23 q^{63} + 37 q^{64} - 46 q^{65} + q^{66} + 45 q^{67} + 3 q^{68} + 68 q^{69} + 28 q^{70} + 55 q^{71} + 52 q^{72} + 29 q^{73} + 21 q^{74} - 12 q^{75} + 36 q^{76} + 30 q^{77} + 38 q^{78} + 25 q^{79} + 9 q^{80} + 73 q^{81} + 21 q^{82} + 70 q^{83} + 6 q^{84} - 21 q^{85} + 14 q^{86} + 37 q^{87} + 5 q^{88} + 55 q^{90} + 18 q^{91} + 11 q^{92} + 9 q^{93} + 59 q^{94} - 9 q^{95} + 9 q^{96} + 37 q^{97} + 82 q^{98} + 33 q^{99}+O(q^{100}) \) 37 * q + 37 * q^2 + 9 * q^3 + 37 * q^4 + 9 * q^5 + 9 * q^6 + 19 * q^7 + 37 * q^8 + 52 * q^9 + 9 * q^10 + 5 * q^11 + 9 * q^12 + 16 * q^13 + 19 * q^14 + 22 * q^15 + 37 * q^16 + 3 * q^17 + 52 * q^18 + 36 * q^19 + 9 * q^20 + 6 * q^21 + 5 * q^22 + 11 * q^23 + 9 * q^24 + 58 * q^25 + 16 * q^26 + 24 * q^27 + 19 * q^28 + 5 * q^29 + 22 * q^30 + 37 * q^31 + 37 * q^32 + q^33 + 3 * q^34 + 28 * q^35 + 52 * q^36 + 21 * q^37 + 36 * q^38 + 38 * q^39 + 9 * q^40 + 21 * q^41 + 6 * q^42 + 14 * q^43 + 5 * q^44 + 55 * q^45 + 11 * q^46 + 59 * q^47 + 9 * q^48 + 82 * q^49 + 58 * q^50 + 46 * q^51 + 16 * q^52 + 8 * q^53 + 24 * q^54 + 25 * q^55 + 19 * q^56 + 5 * q^58 + 41 * q^59 + 22 * q^60 + 16 * q^61 + 37 * q^62 + 23 * q^63 + 37 * q^64 - 46 * q^65 + q^66 + 45 * q^67 + 3 * q^68 + 68 * q^69 + 28 * q^70 + 55 * q^71 + 52 * q^72 + 29 * q^73 + 21 * q^74 - 12 * q^75 + 36 * q^76 + 30 * q^77 + 38 * q^78 + 25 * q^79 + 9 * q^80 + 73 * q^81 + 21 * q^82 + 70 * q^83 + 6 * q^84 - 21 * q^85 + 14 * q^86 + 37 * q^87 + 5 * q^88 + 55 * q^90 + 18 * q^91 + 11 * q^92 + 9 * q^93 + 59 * q^94 - 9 * q^95 + 9 * q^96 + 37 * q^97 + 82 * q^98 + 33 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0.452250	0.261107	0.130553	−	0.991441i	$-0.458325\pi$
$3$	0.452250	0.261107	0.130553	+	0.991441i	$0.458325\pi$
$4$	1.00000	0.500000
$5$	−3.58205	−1.60194	−0.800972	−	0.598702i	$-0.795683\pi$
$5$	−3.58205	−1.60194	−0.800972	+	0.598702i	$0.795683\pi$
$6$	0.452250	0.184630
$7$	−1.19090	−0.450116	−0.225058	−	0.974345i	$-0.572257\pi$
$7$	−1.19090	−0.450116	−0.225058	+	0.974345i	$0.572257\pi$
$8$	1.00000	0.353553
$9$	−2.79547	−0.931823
$10$	−3.58205	−1.13274
$11$	−5.76974	−1.73964	−0.869820	−	0.493369i	$-0.835765\pi$
$11$	−5.76974	−1.73964	−0.869820	+	0.493369i	$0.835765\pi$
$12$	0.452250	0.130553
$13$	−3.35699	−0.931062	−0.465531	−	0.885032i	$-0.654137\pi$
$13$	−3.35699	−0.931062	−0.465531	+	0.885032i	$0.654137\pi$
$14$	−1.19090	−0.318280
$15$	−1.61999	−0.418278
$16$	1.00000	0.250000
$17$	5.21054	1.26374	0.631871	−	0.775073i	$-0.282287\pi$
$17$	5.21054	1.26374	0.631871	+	0.775073i	$0.282287\pi$
$18$	−2.79547	−0.658899
$19$	0.755101	0.173232	0.0866161	−	0.996242i	$-0.472395\pi$
$19$	0.755101	0.173232	0.0866161	+	0.996242i	$0.472395\pi$
$20$	−3.58205	−0.800972
$21$	−0.538583	−0.117528
$22$	−5.76974	−1.23011
$23$	−5.86733	−1.22342	−0.611711	−	0.791081i	$-0.709519\pi$
$23$	−5.86733	−1.22342	−0.611711	+	0.791081i	$0.709519\pi$
$24$	0.452250	0.0923152
$25$	7.83111	1.56622
$26$	−3.35699	−0.658360
$27$	−2.62100	−0.504412
$28$	−1.19090	−0.225058
$29$	1.17674	0.218515	0.109258	−	0.994013i	$-0.465153\pi$
$29$	1.17674	0.218515	0.109258	+	0.994013i	$0.465153\pi$
$30$	−1.61999	−0.295767
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	1.00000	0.176777
$33$	−2.60936	−0.454232
$34$	5.21054	0.893601
$35$	4.26585	0.721060
$36$	−2.79547	−0.465912
$37$	2.71167	0.445796	0.222898	−	0.974842i	$-0.428448\pi$
$37$	2.71167	0.445796	0.222898	+	0.974842i	$0.428448\pi$
$38$	0.755101	0.122494
$39$	−1.51820	−0.243107
$40$	−3.58205	−0.566372
$41$	−5.57683	−0.870954	−0.435477	−	0.900200i	$-0.643420\pi$
$41$	−5.57683	−0.870954	−0.435477	+	0.900200i	$0.643420\pi$
$42$	−0.538583	−0.0831051
$43$	6.91476	1.05449	0.527246	−	0.849713i	$-0.323225\pi$
$43$	6.91476	1.05449	0.527246	+	0.849713i	$0.323225\pi$
$44$	−5.76974	−0.869820
$45$	10.0135	1.49273
$46$	−5.86733	−0.865091
$47$	−2.93655	−0.428340	−0.214170	−	0.976796i	$-0.568705\pi$
$47$	−2.93655	−0.428340	−0.214170	+	0.976796i	$0.568705\pi$
$48$	0.452250	0.0652767
$49$	−5.58177	−0.797396
$50$	7.83111	1.10749
$51$	2.35647	0.329972
$52$	−3.35699	−0.465531
$53$	−2.05863	−0.282774	−0.141387	−	0.989954i	$-0.545156\pi$
$53$	−2.05863	−0.282774	−0.141387	+	0.989954i	$0.545156\pi$
$54$	−2.62100	−0.356673
$55$	20.6675	2.78681
$56$	−1.19090	−0.159140
$57$	0.341495	0.0452321
$58$	1.17674	0.154514
$59$	−9.58199	−1.24747	−0.623734	−	0.781637i	$-0.714385\pi$
$59$	−9.58199	−1.24747	−0.623734	+	0.781637i	$0.714385\pi$
$60$	−1.61999	−0.209139
$61$	11.8770	1.52069	0.760345	−	0.649520i	$-0.225030\pi$
$61$	11.8770	1.52069	0.760345	+	0.649520i	$0.225030\pi$
$62$	1.00000	0.127000
$63$	3.32911	0.419429
$64$	1.00000	0.125000
$65$	12.0249	1.49151
$66$	−2.60936	−0.321191
$67$	15.3278	1.87259	0.936297	−	0.351209i	$-0.114229\pi$
$67$	15.3278	1.87259	0.936297	+	0.351209i	$0.114229\pi$
$68$	5.21054	0.631871
$69$	−2.65350	−0.319444
$70$	4.26585	0.509867
$71$	−1.09647	−0.130127	−0.0650634	−	0.997881i	$-0.520725\pi$
$71$	−1.09647	−0.130127	−0.0650634	+	0.997881i	$0.520725\pi$
$72$	−2.79547	−0.329449
$73$	−6.36693	−0.745193	−0.372596	−	0.927994i	$-0.621532\pi$
$73$	−6.36693	−0.745193	−0.372596	+	0.927994i	$0.621532\pi$
$74$	2.71167	0.315226
$75$	3.54162	0.408951
$76$	0.755101	0.0866161
$77$	6.87115	0.783040
$78$	−1.51820	−0.171902
$79$	−7.74805	−0.871724	−0.435862	−	0.900014i	$-0.643556\pi$
$79$	−7.74805	−0.871724	−0.435862	+	0.900014i	$0.643556\pi$
$80$	−3.58205	−0.400486
$81$	7.20106	0.800118
$82$	−5.57683	−0.615857
$83$	17.6387	1.93609	0.968047	−	0.250770i	$-0.0806837\pi$
$83$	17.6387	1.93609	0.968047	+	0.250770i	$0.0806837\pi$
$84$	−0.538583	−0.0587642
$85$	−18.6645	−2.02444
$86$	6.91476	0.745638
$87$	0.532181	0.0570558
$88$	−5.76974	−0.615056
$89$	−3.03239	−0.321433	−0.160717	−	0.987001i	$-0.551381\pi$
$89$	−3.03239	−0.321433	−0.160717	+	0.987001i	$0.551381\pi$
$90$	10.0135	1.05552
$91$	3.99783	0.419086
$92$	−5.86733	−0.611711
$93$	0.452250	0.0468962
$94$	−2.93655	−0.302882
$95$	−2.70481	−0.277508
$96$	0.452250	0.0461576
$97$	1.00000	0.101535
$97$	1.00000	0.101535
$98$	−5.58177	−0.563844
$99$	16.1291	1.62104
$100$	7.83111	0.783111
$101$	−3.75060	−0.373199	−0.186600	−	0.982436i	$-0.559747\pi$
$101$	−3.75060	−0.373199	−0.186600	+	0.982436i	$0.559747\pi$
$102$	2.35647	0.233325
$103$	16.2480	1.60096	0.800481	−	0.599358i	$-0.204577\pi$
$103$	16.2480	1.60096	0.800481	+	0.599358i	$0.204577\pi$
$104$	−3.35699	−0.329180
$105$	1.92923	0.188274
$106$	−2.05863	−0.199951
$107$	−5.55731	−0.537245	−0.268623	−	0.963246i	$-0.586568\pi$
$107$	−5.55731	−0.537245	−0.268623	+	0.963246i	$0.586568\pi$
$108$	−2.62100	−0.252206
$109$	−4.87043	−0.466502	−0.233251	−	0.972417i	$-0.574936\pi$
$109$	−4.87043	−0.466502	−0.233251	+	0.972417i	$0.574936\pi$
$110$	20.6675	1.97057
$111$	1.22636	0.116400
$112$	−1.19090	−0.112529
$113$	−5.51071	−0.518404	−0.259202	−	0.965823i	$-0.583460\pi$
$113$	−5.51071	−0.518404	−0.259202	+	0.965823i	$0.583460\pi$
$114$	0.341495	0.0319839
$115$	21.0171	1.95985
$116$	1.17674	0.109258
$117$	9.38437	0.867585
$118$	−9.58199	−0.882093
$119$	−6.20521	−0.568831
$120$	−1.61999	−0.147884
$121$	22.2898	2.02635
$122$	11.8770	1.07529
$123$	−2.52212	−0.227412
$124$	1.00000	0.0898027
$125$	−10.1412	−0.907055
$126$	3.32911	0.296581
$127$	3.90606	0.346607	0.173304	−	0.984868i	$-0.444556\pi$
$127$	3.90606	0.346607	0.173304	+	0.984868i	$0.444556\pi$
$128$	1.00000	0.0883883
$129$	3.12720	0.275335
$130$	12.0249	1.05466
$131$	−16.2100	−1.41628	−0.708139	−	0.706073i	$-0.750465\pi$
$131$	−16.2100	−1.41628	−0.708139	+	0.706073i	$0.750465\pi$
$132$	−2.60936	−0.227116
$133$	−0.899246	−0.0779746
$134$	15.3278	1.32412
$135$	9.38857	0.808040
$136$	5.21054	0.446801
$137$	−4.41729	−0.377395	−0.188697	−	0.982035i	$-0.560427\pi$
$137$	−4.41729	−0.377395	−0.188697	+	0.982035i	$0.560427\pi$
$138$	−2.65350	−0.225881
$139$	−1.01851	−0.0863887	−0.0431943	−	0.999067i	$-0.513753\pi$
$139$	−1.01851	−0.0863887	−0.0431943	+	0.999067i	$0.513753\pi$
$140$	4.26585	0.360530
$141$	−1.32806	−0.111842
$142$	−1.09647	−0.0920135
$143$	19.3690	1.61971
$144$	−2.79547	−0.232956
$145$	−4.21515	−0.350049
$146$	−6.36693	−0.526931
$147$	−2.52436	−0.208205
$148$	2.71167	0.222898
$149$	19.7716	1.61975	0.809876	−	0.586601i	$-0.199534\pi$
$149$	19.7716	1.61975	0.809876	+	0.586601i	$0.199534\pi$
$150$	3.54162	0.289172
$151$	20.3732	1.65795	0.828973	−	0.559288i	$-0.188926\pi$
$151$	20.3732	1.65795	0.828973	+	0.559288i	$0.188926\pi$
$152$	0.755101	0.0612468
$153$	−14.5659	−1.17758
$154$	6.87115	0.553693
$155$	−3.58205	−0.287717
$156$	−1.51820	−0.121553
$157$	7.81245	0.623501	0.311751	−	0.950164i	$-0.399085\pi$
$157$	7.81245	0.623501	0.311751	+	0.950164i	$0.399085\pi$
$158$	−7.74805	−0.616402
$159$	−0.931014	−0.0738342
$160$	−3.58205	−0.283186
$161$	6.98737	0.550682
$162$	7.20106	0.565769
$163$	4.70302	0.368369	0.184184	−	0.982892i	$-0.441036\pi$
$163$	4.70302	0.368369	0.184184	+	0.982892i	$0.441036\pi$
$164$	−5.57683	−0.435477
$165$	9.34688	0.727654
$166$	17.6387	1.36902
$167$	21.0241	1.62689	0.813447	−	0.581639i	$-0.197588\pi$
$167$	21.0241	1.62689	0.813447	+	0.581639i	$0.197588\pi$
$168$	−0.538583	−0.0415526
$169$	−1.73060	−0.133123
$170$	−18.6645	−1.43150
$171$	−2.11086	−0.161422
$172$	6.91476	0.527246
$173$	11.7878	0.896207	0.448104	−	0.893982i	$-0.352100\pi$
$173$	11.7878	0.896207	0.448104	+	0.893982i	$0.352100\pi$
$174$	0.532181	0.0403446
$175$	−9.32603	−0.704982
$176$	−5.76974	−0.434910
$177$	−4.33346	−0.325723
$178$	−3.03239	−0.227288
$179$	1.19508	0.0893242	0.0446621	−	0.999002i	$-0.485779\pi$
$179$	1.19508	0.0893242	0.0446621	+	0.999002i	$0.485779\pi$
$180$	10.0135	0.746364
$181$	5.71941	0.425120	0.212560	−	0.977148i	$-0.431820\pi$
$181$	5.71941	0.425120	0.212560	+	0.977148i	$0.431820\pi$
$182$	3.99783	0.296339
$183$	5.37136	0.397062
$184$	−5.86733	−0.432545
$185$	−9.71336	−0.714140
$186$	0.452250	0.0331606
$187$	−30.0635	−2.19846
$188$	−2.93655	−0.214170
$189$	3.12134	0.227044
$190$	−2.70481	−0.196228
$191$	16.1390	1.16778	0.583889	−	0.811834i	$-0.301530\pi$
$191$	16.1390	1.16778	0.583889	+	0.811834i	$0.301530\pi$
$192$	0.452250	0.0326384
$193$	−6.15460	−0.443018	−0.221509	−	0.975158i	$-0.571098\pi$
$193$	−6.15460	−0.443018	−0.221509	+	0.975158i	$0.571098\pi$
$194$	1.00000	0.0717958
$195$	5.43828	0.389443
$196$	−5.58177	−0.398698
$197$	−8.60053	−0.612762	−0.306381	−	0.951909i	$-0.599118\pi$
$197$	−8.60053	−0.612762	−0.306381	+	0.951909i	$0.599118\pi$
$198$	16.1291	1.14625
$199$	−10.2350	−0.725543	−0.362772	−	0.931878i	$-0.618170\pi$
$199$	−10.2350	−0.725543	−0.362772	+	0.931878i	$0.618170\pi$
$200$	7.83111	0.553743
$201$	6.93202	0.488947
$202$	−3.75060	−0.263892
$203$	−1.40137	−0.0983572
$204$	2.35647	0.164986
$205$	19.9765	1.39522
$206$	16.2480	1.13205
$207$	16.4019	1.14001
$208$	−3.35699	−0.232766
$209$	−4.35673	−0.301362
$210$	1.92923	0.133130
$211$	−21.7752	−1.49906	−0.749532	−	0.661968i	$-0.769722\pi$
$211$	−21.7752	−1.49906	−0.749532	+	0.661968i	$0.769722\pi$
$212$	−2.05863	−0.141387
$213$	−0.495878	−0.0339770
$214$	−5.55731	−0.379890
$215$	−24.7690	−1.68923
$216$	−2.62100	−0.178337
$217$	−1.19090	−0.0808432
$218$	−4.87043	−0.329867
$219$	−2.87945	−0.194575
$220$	20.6675	1.39340
$221$	−17.4918	−1.17662
$222$	1.22636	0.0823076
$223$	28.2447	1.89141	0.945703	−	0.325033i	$-0.105375\pi$
$223$	28.2447	1.89141	0.945703	+	0.325033i	$0.105375\pi$
$224$	−1.19090	−0.0795700
$225$	−21.8916	−1.45944
$226$	−5.51071	−0.366567
$227$	−19.4163	−1.28870	−0.644352	−	0.764729i	$-0.722873\pi$
$227$	−19.4163	−1.28870	−0.644352	+	0.764729i	$0.722873\pi$
$228$	0.341495	0.0226160
$229$	−20.4498	−1.35136	−0.675681	−	0.737195i	$-0.736150\pi$
$229$	−20.4498	−1.35136	−0.675681	+	0.737195i	$0.736150\pi$
$230$	21.0171	1.38583
$231$	3.10748	0.204457
$232$	1.17674	0.0772568
$233$	8.01544	0.525109	0.262554	−	0.964917i	$-0.415435\pi$
$233$	8.01544	0.525109	0.262554	+	0.964917i	$0.415435\pi$
$234$	9.38437	0.613475
$235$	10.5189	0.686176
$236$	−9.58199	−0.623734
$237$	−3.50406	−0.227613
$238$	−6.20521	−0.402224
$239$	−6.70660	−0.433814	−0.216907	−	0.976192i	$-0.569597\pi$
$239$	−6.70660	−0.433814	−0.216907	+	0.976192i	$0.569597\pi$
$240$	−1.61999	−0.104570
$241$	−6.51301	−0.419540	−0.209770	−	0.977751i	$-0.567272\pi$
$241$	−6.51301	−0.419540	−0.209770	+	0.977751i	$0.567272\pi$
$242$	22.2898	1.43285
$243$	11.1197	0.713329
$244$	11.8770	0.760345
$245$	19.9942	1.27738
$246$	−2.52212	−0.160805
$247$	−2.53487	−0.161290
$248$	1.00000	0.0635001
$249$	7.97709	0.505527
$250$	−10.1412	−0.641385
$251$	−6.37065	−0.402112	−0.201056	−	0.979580i	$-0.564437\pi$
$251$	−6.37065	−0.402112	−0.201056	+	0.979580i	$0.564437\pi$
$252$	3.32911	0.209714
$253$	33.8529	2.12832
$254$	3.90606	0.245088
$255$	−8.44100	−0.528596
$256$	1.00000	0.0625000
$257$	−2.57670	−0.160730	−0.0803652	−	0.996765i	$-0.525609\pi$
$257$	−2.57670	−0.160730	−0.0803652	+	0.996765i	$0.525609\pi$
$258$	3.12720	0.194691
$259$	−3.22932	−0.200660
$260$	12.0249	0.745754
$261$	−3.28954	−0.203618
$262$	−16.2100	−1.00146
$263$	8.08633	0.498625	0.249312	−	0.968423i	$-0.419795\pi$
$263$	8.08633	0.498625	0.249312	+	0.968423i	$0.419795\pi$
$264$	−2.60936	−0.160595
$265$	7.37411	0.452988
$266$	−0.899246	−0.0551363
$267$	−1.37140	−0.0839284
$268$	15.3278	0.936297
$269$	9.41413	0.573989	0.286995	−	0.957932i	$-0.407344\pi$
$269$	9.41413	0.573989	0.286995	+	0.957932i	$0.407344\pi$
$270$	9.38857	0.571370
$271$	−7.98077	−0.484797	−0.242399	−	0.970177i	$-0.577934\pi$
$271$	−7.98077	−0.484797	−0.242399	+	0.970177i	$0.577934\pi$
$272$	5.21054	0.315936
$273$	1.80802	0.109426
$274$	−4.41729	−0.266859
$275$	−45.1834	−2.72466
$276$	−2.65350	−0.159722
$277$	−17.6353	−1.05960	−0.529802	−	0.848121i	$-0.677734\pi$
$277$	−17.6353	−1.05960	−0.529802	+	0.848121i	$0.677734\pi$
$278$	−1.01851	−0.0610860
$279$	−2.79547	−0.167360
$280$	4.26585	0.254933
$281$	16.2457	0.969139	0.484569	−	0.874753i	$-0.338976\pi$
$281$	16.2457	0.969139	0.484569	+	0.874753i	$0.338976\pi$
$282$	−1.32806	−0.0790846
$283$	1.74815	0.103917	0.0519585	−	0.998649i	$-0.483454\pi$
$283$	1.74815	0.103917	0.0519585	+	0.998649i	$0.483454\pi$
$284$	−1.09647	−0.0650634
$285$	−1.22325	−0.0724592
$286$	19.3690	1.14531
$287$	6.64142	0.392030
$288$	−2.79547	−0.164725
$289$	10.1498	0.597046
$290$	−4.21515	−0.247522
$291$	0.452250	0.0265114
$292$	−6.36693	−0.372596
$293$	1.28515	0.0750794	0.0375397	−	0.999295i	$-0.488048\pi$
$293$	1.28515	0.0750794	0.0375397	+	0.999295i	$0.488048\pi$
$294$	−2.52436	−0.147223
$295$	34.3232	1.99837
$296$	2.71167	0.157613
$297$	15.1225	0.877496
$298$	19.7716	1.14534
$299$	19.6966	1.13908
$300$	3.54162	0.204476
$301$	−8.23476	−0.474643
$302$	20.3732	1.17235
$303$	−1.69621	−0.0974448
$304$	0.755101	0.0433080
$305$	−42.5439	−2.43606
$306$	−14.5659	−0.832678
$307$	−12.5910	−0.718606	−0.359303	−	0.933221i	$-0.616986\pi$
$307$	−12.5910	−0.718606	−0.359303	+	0.933221i	$0.616986\pi$
$308$	6.87115	0.391520
$309$	7.34816	0.418022
$310$	−3.58205	−0.203447
$311$	−32.2169	−1.82685	−0.913427	−	0.407004i	$-0.866574\pi$
$311$	−32.2169	−1.82685	−0.913427	+	0.407004i	$0.866574\pi$
$312$	−1.51820	−0.0859512
$313$	−4.72324	−0.266973	−0.133487	−	0.991051i	$-0.542617\pi$
$313$	−4.72324	−0.266973	−0.133487	+	0.991051i	$0.542617\pi$
$314$	7.81245	0.440882
$315$	−11.9251	−0.671901
$316$	−7.74805	−0.435862
$317$	25.1622	1.41325	0.706626	−	0.707587i	$-0.250216\pi$
$317$	25.1622	1.41325	0.706626	+	0.707587i	$0.250216\pi$
$318$	−0.931014	−0.0522087
$319$	−6.78948	−0.380138
$320$	−3.58205	−0.200243
$321$	−2.51329	−0.140278
$322$	6.98737	0.389391
$323$	3.93449	0.218921
$324$	7.20106	0.400059
$325$	−26.2890	−1.45825
$326$	4.70302	0.260476
$327$	−2.20265	−0.121807
$328$	−5.57683	−0.307929
$329$	3.49712	0.192803
$330$	9.34688	0.514529
$331$	−15.0336	−0.826320	−0.413160	−	0.910658i	$-0.635575\pi$
$331$	−15.0336	−0.826320	−0.413160	+	0.910658i	$0.635575\pi$
$332$	17.6387	0.968047
$333$	−7.58040	−0.415403
$334$	21.0241	1.15039
$335$	−54.9052	−2.99979
$336$	−0.538583	−0.0293821
$337$	−24.5753	−1.33870	−0.669351	−	0.742946i	$-0.733428\pi$
$337$	−24.5753	−1.33870	−0.669351	+	0.742946i	$0.733428\pi$
$338$	−1.73060	−0.0941324
$339$	−2.49222	−0.135359
$340$	−18.6645	−1.01222
$341$	−5.76974	−0.312449
$342$	−2.11086	−0.114142
$343$	14.9836	0.809037
$344$	6.91476	0.372819
$345$	9.50499	0.511731
$346$	11.7878	0.633714
$347$	−1.78996	−0.0960901	−0.0480451	−	0.998845i	$-0.515299\pi$
$347$	−1.78996	−0.0960901	−0.0480451	+	0.998845i	$0.515299\pi$
$348$	0.532181	0.0285279
$349$	−12.4063	−0.664096	−0.332048	−	0.943262i	$-0.607740\pi$
$349$	−12.4063	−0.664096	−0.332048	+	0.943262i	$0.607740\pi$
$350$	−9.32603	−0.498497
$351$	8.79869	0.469639
$352$	−5.76974	−0.307528
$353$	3.15755	0.168059	0.0840297	−	0.996463i	$-0.473221\pi$
$353$	3.15755	0.168059	0.0840297	+	0.996463i	$0.473221\pi$
$354$	−4.33346	−0.230321
$355$	3.92761	0.208456
$356$	−3.03239	−0.160717
$357$	−2.80631	−0.148526
$358$	1.19508	0.0631618
$359$	−6.93463	−0.365996	−0.182998	−	0.983113i	$-0.558580\pi$
$359$	−6.93463	−0.365996	−0.182998	+	0.983113i	$0.558580\pi$
$360$	10.0135	0.527759
$361$	−18.4298	−0.969991
$362$	5.71941	0.300605
$363$	10.0806	0.529094
$364$	3.99783	0.209543
$365$	22.8067	1.19376
$366$	5.37136	0.280766
$367$	−35.3439	−1.84494	−0.922468	−	0.386075i	$-0.873831\pi$
$367$	−35.3439	−1.84494	−0.922468	+	0.386075i	$0.873831\pi$
$368$	−5.86733	−0.305856
$369$	15.5898	0.811575
$370$	−9.71336	−0.504973
$371$	2.45161	0.127281
$372$	0.452250	0.0234481
$373$	−10.4583	−0.541510	−0.270755	−	0.962648i	$-0.587273\pi$
$373$	−10.4583	−0.541510	−0.270755	+	0.962648i	$0.587273\pi$
$374$	−30.0635	−1.55454
$375$	−4.58635	−0.236838
$376$	−2.93655	−0.151441
$377$	−3.95031	−0.203451
$378$	3.12134	0.160544
$379$	13.6031	0.698743	0.349372	−	0.936984i	$-0.386395\pi$
$379$	13.6031	0.698743	0.349372	+	0.936984i	$0.386395\pi$
$380$	−2.70481	−0.138754
$381$	1.76652	0.0905015
$382$	16.1390	0.825744
$383$	9.53323	0.487125	0.243563	−	0.969885i	$-0.421684\pi$
$383$	9.53323	0.487125	0.243563	+	0.969885i	$0.421684\pi$
$384$	0.452250	0.0230788
$385$	−24.6128	−1.25439
$386$	−6.15460	−0.313261
$387$	−19.3300	−0.982599
$388$	1.00000	0.0507673
$389$	−25.0013	−1.26762	−0.633809	−	0.773489i	$-0.718510\pi$
$389$	−25.0013	−1.26762	−0.633809	+	0.773489i	$0.718510\pi$
$390$	5.43828	0.275378
$391$	−30.5720	−1.54609
$392$	−5.58177	−0.281922
$393$	−7.33100	−0.369800
$394$	−8.60053	−0.433288
$395$	27.7539	1.39645
$396$	16.1291	0.810519
$397$	23.8693	1.19796	0.598982	−	0.800762i	$-0.295572\pi$
$397$	23.8693	1.19796	0.598982	+	0.800762i	$0.295572\pi$
$398$	−10.2350	−0.513037
$399$	−0.406684	−0.0203597
$400$	7.83111	0.391555
$401$	21.4973	1.07352	0.536762	−	0.843734i	$-0.319647\pi$
$401$	21.4973	1.07352	0.536762	+	0.843734i	$0.319647\pi$
$402$	6.93202	0.345738
$403$	−3.35699	−0.167224
$404$	−3.75060	−0.186600
$405$	−25.7946	−1.28174
$406$	−1.40137	−0.0695491
$407$	−15.6456	−0.775525
$408$	2.35647	0.116663
$409$	29.0846	1.43814	0.719070	−	0.694938i	$-0.244568\pi$
$409$	29.0846	1.43814	0.719070	+	0.694938i	$0.244568\pi$
$410$	19.9765	0.986569
$411$	−1.99772	−0.0985404
$412$	16.2480	0.800481
$413$	11.4111	0.561506
$414$	16.4019	0.806111
$415$	−63.1826	−3.10151
$416$	−3.35699	−0.164590
$417$	−0.460620	−0.0225567
$418$	−4.35673	−0.213095
$419$	−20.3085	−0.992137	−0.496069	−	0.868283i	$-0.665224\pi$
$419$	−20.3085	−0.992137	−0.496069	+	0.868283i	$0.665224\pi$
$420$	1.92923	0.0941369
$421$	18.0720	0.880776	0.440388	−	0.897808i	$-0.354841\pi$
$421$	18.0720	0.880776	0.440388	+	0.897808i	$0.354841\pi$
$422$	−21.7752	−1.06000
$423$	8.20904	0.399137
$424$	−2.05863	−0.0999757
$425$	40.8043	1.97930
$426$	−0.495878	−0.0240254
$427$	−14.1442	−0.684487
$428$	−5.55731	−0.268623
$429$	8.75962	0.422918
$430$	−24.7690	−1.19447
$431$	33.1822	1.59833	0.799166	−	0.601110i	$-0.205275\pi$
$431$	33.1822	1.59833	0.799166	+	0.601110i	$0.205275\pi$
$432$	−2.62100	−0.126103
$433$	−24.7240	−1.18816	−0.594080	−	0.804406i	$-0.702484\pi$
$433$	−24.7240	−1.18816	−0.594080	+	0.804406i	$0.702484\pi$
$434$	−1.19090	−0.0571648
$435$	−1.90630	−0.0914002
$436$	−4.87043	−0.233251
$437$	−4.43043	−0.211936
$438$	−2.87945	−0.137585
$439$	28.4237	1.35659	0.678294	−	0.734790i	$-0.262719\pi$
$439$	28.4237	1.35659	0.678294	+	0.734790i	$0.262719\pi$
$440$	20.6675	0.985284
$441$	15.6037	0.743032
$442$	−17.4918	−0.831998
$443$	3.92099	0.186292	0.0931459	−	0.995652i	$-0.470308\pi$
$443$	3.92099	0.186292	0.0931459	+	0.995652i	$0.470308\pi$
$444$	1.22636	0.0582002
$445$	10.8622	0.514918
$446$	28.2447	1.33743
$447$	8.94171	0.422929
$448$	−1.19090	−0.0562645
$449$	−19.6099	−0.925451	−0.462725	−	0.886502i	$-0.653128\pi$
$449$	−19.6099	−0.925451	−0.462725	+	0.886502i	$0.653128\pi$
$450$	−21.8916	−1.03198
$451$	32.1768	1.51515
$452$	−5.51071	−0.259202
$453$	9.21378	0.432901
$454$	−19.4163	−0.911251
$455$	−14.3204	−0.671352
$456$	0.341495	0.0159920
$457$	−7.17138	−0.335463	−0.167731	−	0.985833i	$-0.553644\pi$
$457$	−7.17138	−0.335463	−0.167731	+	0.985833i	$0.553644\pi$
$458$	−20.4498	−0.955557
$459$	−13.6569	−0.637447
$460$	21.0171	0.979927
$461$	30.8813	1.43828	0.719142	−	0.694863i	$-0.244535\pi$
$461$	30.8813	1.43828	0.719142	+	0.694863i	$0.244535\pi$
$462$	3.10748	0.144573
$463$	18.1112	0.841697	0.420848	−	0.907131i	$-0.361732\pi$
$463$	18.1112	0.841697	0.420848	+	0.907131i	$0.361732\pi$
$464$	1.17674	0.0546288
$465$	−1.61999	−0.0751250
$466$	8.01544	0.371308
$467$	33.2115	1.53684	0.768422	−	0.639943i	$-0.221042\pi$
$467$	33.2115	1.53684	0.768422	+	0.639943i	$0.221042\pi$
$468$	9.38437	0.433793
$469$	−18.2539	−0.842885
$470$	10.5189	0.485200
$471$	3.53318	0.162800
$472$	−9.58199	−0.441047
$473$	−39.8963	−1.83444
$474$	−3.50406	−0.160947
$475$	5.91328	0.271320
$476$	−6.20521	−0.284415
$477$	5.75483	0.263495
$478$	−6.70660	−0.306753
$479$	−9.29086	−0.424510	−0.212255	−	0.977214i	$-0.568081\pi$
$479$	−9.29086	−0.424510	−0.212255	+	0.977214i	$0.568081\pi$
$480$	−1.61999	−0.0739419
$481$	−9.10307	−0.415064
$482$	−6.51301	−0.296660
$483$	3.16004	0.143787
$484$	22.2898	1.01317
$485$	−3.58205	−0.162653
$486$	11.1197	0.504399
$487$	−12.3409	−0.559218	−0.279609	−	0.960114i	$-0.590205\pi$
$487$	−12.3409	−0.559218	−0.279609	+	0.960114i	$0.590205\pi$
$488$	11.8770	0.537645
$489$	2.12694	0.0961836
$490$	19.9942	0.903246
$491$	−34.4050	−1.55267	−0.776337	−	0.630318i	$-0.782924\pi$
$491$	−34.4050	−1.55267	−0.776337	+	0.630318i	$0.782924\pi$
$492$	−2.52212	−0.113706
$493$	6.13146	0.276147
$494$	−2.53487	−0.114049
$495$	−57.7754	−2.59681
$496$	1.00000	0.0449013
$497$	1.30578	0.0585721
$498$	7.97709	0.357462
$499$	28.3720	1.27010	0.635052	−	0.772469i	$-0.280979\pi$
$499$	28.3720	1.27010	0.635052	+	0.772469i	$0.280979\pi$
$500$	−10.1412	−0.453528
$501$	9.50816	0.424793
$502$	−6.37065	−0.284336
$503$	−0.673643	−0.0300363	−0.0150181	−	0.999887i	$-0.504781\pi$
$503$	−0.673643	−0.0300363	−0.0150181	+	0.999887i	$0.504781\pi$
$504$	3.32911	0.148290
$505$	13.4349	0.597844
$506$	33.8529	1.50495
$507$	−0.782666	−0.0347594
$508$	3.90606	0.173304
$509$	2.68906	0.119190	0.0595951	−	0.998223i	$-0.481019\pi$
$509$	2.68906	0.119190	0.0595951	+	0.998223i	$0.481019\pi$
$510$	−8.44100	−0.373774
$511$	7.58235	0.335423
$512$	1.00000	0.0441942
$513$	−1.97912	−0.0873804
$514$	−2.57670	−0.113654
$515$	−58.2012	−2.56465
$516$	3.12720	0.137667
$517$	16.9431	0.745157
$518$	−3.22932	−0.141888
$519$	5.33102	0.234006
$520$	12.0249	0.527328
$521$	−17.7079	−0.775799	−0.387899	−	0.921702i	$-0.626799\pi$
$521$	−17.7079	−0.775799	−0.387899	+	0.921702i	$0.626799\pi$
$522$	−3.28954	−0.143979
$523$	36.2977	1.58719	0.793593	−	0.608449i	$-0.208208\pi$
$523$	36.2977	1.58719	0.793593	+	0.608449i	$0.208208\pi$
$524$	−16.2100	−0.708139
$525$	−4.21770	−0.184076
$526$	8.08633	0.352581
$527$	5.21054	0.226975
$528$	−2.60936	−0.113558
$529$	11.4256	0.496763
$530$	7.37411	0.320311
$531$	26.7862	1.16242
$532$	−0.899246	−0.0389873
$533$	18.7214	0.810912
$534$	−1.37140	−0.0593463
$535$	19.9066	0.860636
$536$	15.3278	0.662062
$537$	0.540474	0.0233232
$538$	9.41413	0.405872
$539$	32.2053	1.38718
$540$	9.38857	0.404020
$541$	44.3112	1.90509	0.952543	−	0.304405i	$-0.0984576\pi$
$541$	44.3112	1.90509	0.952543	+	0.304405i	$0.0984576\pi$
$542$	−7.98077	−0.342803
$543$	2.58660	0.111002
$544$	5.21054	0.223400
$545$	17.4461	0.747310
$546$	1.80802	0.0773760
$547$	−14.2361	−0.608694	−0.304347	−	0.952561i	$-0.598438\pi$
$547$	−14.2361	−0.608694	−0.304347	+	0.952561i	$0.598438\pi$
$548$	−4.41729	−0.188697
$549$	−33.2017	−1.41701
$550$	−45.1834	−1.92663
$551$	0.888558	0.0378539
$552$	−2.65350	−0.112941
$553$	9.22711	0.392377
$554$	−17.6353	−0.749254
$555$	−4.39287	−0.186467
$556$	−1.01851	−0.0431943
$557$	7.23145	0.306407	0.153203	−	0.988195i	$-0.451041\pi$
$557$	7.23145	0.306407	0.153203	+	0.988195i	$0.451041\pi$
$558$	−2.79547	−0.118342
$559$	−23.2128	−0.981797
$560$	4.26585	0.180265
$561$	−13.5962	−0.574032
$562$	16.2457	0.685285
$563$	−35.3704	−1.49068	−0.745342	−	0.666682i	$-0.767714\pi$
$563$	−35.3704	−1.49068	−0.745342	+	0.666682i	$0.767714\pi$
$564$	−1.32806	−0.0559212
$565$	19.7397	0.830454
$566$	1.74815	0.0734804
$567$	−8.57571	−0.360146
$568$	−1.09647	−0.0460067
$569$	32.2877	1.35357	0.676786	−	0.736180i	$-0.263372\pi$
$569$	32.2877	1.35357	0.676786	+	0.736180i	$0.263372\pi$
$570$	−1.22325	−0.0512364
$571$	28.8795	1.20857	0.604284	−	0.796769i	$-0.293459\pi$
$571$	28.8795	1.20857	0.604284	+	0.796769i	$0.293459\pi$
$572$	19.3690	0.809857
$573$	7.29887	0.304915
$574$	6.64142	0.277207
$575$	−45.9477	−1.91615
$576$	−2.79547	−0.116478
$577$	−9.18739	−0.382476	−0.191238	−	0.981544i	$-0.561250\pi$
$577$	−9.18739	−0.382476	−0.191238	+	0.981544i	$0.561250\pi$
$578$	10.1498	0.422175
$579$	−2.78342	−0.115675
$580$	−4.21515	−0.175024
$581$	−21.0058	−0.871467
$582$	0.452250	0.0187464
$583$	11.8777	0.491925
$584$	−6.36693	−0.263465
$585$	−33.6153	−1.38982
$586$	1.28515	0.0530892
$587$	44.1468	1.82213	0.911067	−	0.412258i	$-0.135260\pi$
$587$	44.1468	1.82213	0.911067	+	0.412258i	$0.135260\pi$
$588$	−2.52436	−0.104103
$589$	0.755101	0.0311134
$590$	34.3232	1.41306
$591$	−3.88959	−0.159996
$592$	2.71167	0.111449
$593$	−16.6630	−0.684266	−0.342133	−	0.939652i	$-0.611149\pi$
$593$	−16.6630	−0.684266	−0.342133	+	0.939652i	$0.611149\pi$
$594$	15.1225	0.620483
$595$	22.2274	0.911235
$596$	19.7716	0.809876
$597$	−4.62880	−0.189444
$598$	19.6966	0.805453
$599$	−7.29867	−0.298215	−0.149108	−	0.988821i	$-0.547640\pi$
$599$	−7.29867	−0.298215	−0.149108	+	0.988821i	$0.547640\pi$
$600$	3.54162	0.144586
$601$	5.63534	0.229870	0.114935	−	0.993373i	$-0.463334\pi$
$601$	5.63534	0.229870	0.114935	+	0.993373i	$0.463334\pi$
$602$	−8.23476	−0.335624
$603$	−42.8485	−1.74493
$604$	20.3732	0.828973
$605$	−79.8434	−3.24610
$606$	−1.69621	−0.0689039
$607$	−29.1054	−1.18135	−0.590676	−	0.806909i	$-0.701139\pi$
$607$	−29.1054	−1.18135	−0.590676	+	0.806909i	$0.701139\pi$
$608$	0.755101	0.0306234
$609$	−0.633772	−0.0256817
$610$	−42.5439	−1.72255
$611$	9.85798	0.398811
$612$	−14.5659	−0.588792
$613$	−19.1278	−0.772566	−0.386283	−	0.922380i	$-0.626241\pi$
$613$	−19.1278	−0.772566	−0.386283	+	0.922380i	$0.626241\pi$
$614$	−12.5910	−0.508131
$615$	9.03438	0.364301
$616$	6.87115	0.276847
$617$	0.317699	0.0127901	0.00639503	−	0.999980i	$-0.497964\pi$
$617$	0.317699	0.0127901	0.00639503	+	0.999980i	$0.497964\pi$
$618$	7.34816	0.295586
$619$	12.2321	0.491649	0.245825	−	0.969314i	$-0.420941\pi$
$619$	12.2321	0.491649	0.245825	+	0.969314i	$0.420941\pi$
$620$	−3.58205	−0.143859
$621$	15.3783	0.617109
$622$	−32.2169	−1.29178
$623$	3.61126	0.144682
$624$	−1.51820	−0.0607767
$625$	−2.82928	−0.113171
$626$	−4.72324	−0.188779
$627$	−1.97033	−0.0786876
$628$	7.81245	0.311751
$629$	14.1293	0.563372
$630$	−11.9251	−0.475106
$631$	−31.4092	−1.25038	−0.625190	−	0.780472i	$-0.714979\pi$
$631$	−31.4092	−1.25038	−0.625190	+	0.780472i	$0.714979\pi$
$632$	−7.74805	−0.308201
$633$	−9.84783	−0.391416
$634$	25.1622	0.999320
$635$	−13.9917	−0.555245
$636$	−0.931014	−0.0369171
$637$	18.7380	0.742425
$638$	−6.78948	−0.268798
$639$	3.06514	0.121255
$640$	−3.58205	−0.141593
$641$	18.7455	0.740404	0.370202	−	0.928951i	$-0.379289\pi$
$641$	18.7455	0.740404	0.370202	+	0.928951i	$0.379289\pi$
$642$	−2.51329	−0.0991918
$643$	23.4182	0.923525	0.461763	−	0.887003i	$-0.347217\pi$
$643$	23.4182	0.923525	0.461763	+	0.887003i	$0.347217\pi$
$644$	6.98737	0.275341
$645$	−11.2018	−0.441071
$646$	3.93449	0.154800
$647$	1.22881	0.0483095	0.0241547	−	0.999708i	$-0.492311\pi$
$647$	1.22881	0.0483095	0.0241547	+	0.999708i	$0.492311\pi$
$648$	7.20106	0.282884
$649$	55.2855	2.17015
$650$	−26.2890	−1.03114
$651$	−0.538583	−0.0211087
$652$	4.70302	0.184184
$653$	19.9797	0.781867	0.390934	−	0.920419i	$-0.372152\pi$
$653$	19.9797	0.781867	0.390934	+	0.920419i	$0.372152\pi$
$654$	−2.20265	−0.0861305
$655$	58.0652	2.26880
$656$	−5.57683	−0.217738
$657$	17.7986	0.694388
$658$	3.49712	0.136332
$659$	−15.8038	−0.615627	−0.307814	−	0.951447i	$-0.599597\pi$
$659$	−15.8038	−0.615627	−0.307814	+	0.951447i	$0.599597\pi$
$660$	9.34688	0.363827
$661$	−1.08955	−0.0423785	−0.0211893	−	0.999775i	$-0.506745\pi$
$661$	−1.08955	−0.0423785	−0.0211893	+	0.999775i	$0.506745\pi$
$662$	−15.0336	−0.584297
$663$	−7.91065	−0.307224
$664$	17.6387	0.684512
$665$	3.22115	0.124911
$666$	−7.58040	−0.293735
$667$	−6.90432	−0.267337
$668$	21.0241	0.813447
$669$	12.7737	0.493859
$670$	−54.9052	−2.12117
$671$	−68.5269	−2.64545
$672$	−0.538583	−0.0207763
$673$	44.2313	1.70499	0.852495	−	0.522735i	$-0.175088\pi$
$673$	44.2313	1.70499	0.852495	+	0.522735i	$0.175088\pi$
$674$	−24.5753	−0.946605
$675$	−20.5254	−0.790022
$676$	−1.73060	−0.0665616
$677$	29.5153	1.13436	0.567182	−	0.823593i	$-0.308034\pi$
$677$	29.5153	1.13436	0.567182	+	0.823593i	$0.308034\pi$
$678$	−2.49222	−0.0957132
$679$	−1.19090	−0.0457024
$680$	−18.6645	−0.715749
$681$	−8.78102	−0.336489
$682$	−5.76974	−0.220935
$683$	7.59757	0.290713	0.145356	−	0.989379i	$-0.453567\pi$
$683$	7.59757	0.290713	0.145356	+	0.989379i	$0.453567\pi$
$684$	−2.11086	−0.0807108
$685$	15.8230	0.604565
$686$	14.9836	0.572075
$687$	−9.24843	−0.352850
$688$	6.91476	0.263623
$689$	6.91079	0.263280
$690$	9.50499	0.361849
$691$	23.6450	0.899499	0.449750	−	0.893155i	$-0.351513\pi$
$691$	23.6450	0.899499	0.449750	+	0.893155i	$0.351513\pi$
$692$	11.7878	0.448104
$693$	−19.2081	−0.729655
$694$	−1.78996	−0.0679460
$695$	3.64835	0.138390
$696$	0.532181	0.0201723
$697$	−29.0583	−1.10066
$698$	−12.4063	−0.469587
$699$	3.62498	0.137110
$700$	−9.32603	−0.352491
$701$	−17.2330	−0.650882	−0.325441	−	0.945562i	$-0.605513\pi$
$701$	−17.2330	−0.650882	−0.325441	+	0.945562i	$0.605513\pi$
$702$	8.79869	0.332085
$703$	2.04759	0.0772262
$704$	−5.76974	−0.217455
$705$	4.75717	0.179165
$706$	3.15755	0.118836
$707$	4.46658	0.167983
$708$	−4.33346	−0.162861
$709$	−37.0432	−1.39119	−0.695593	−	0.718436i	$-0.744858\pi$
$709$	−37.0432	−1.39119	−0.695593	+	0.718436i	$0.744858\pi$
$710$	3.92761	0.147400
$711$	21.6594	0.812292
$712$	−3.03239	−0.113644
$713$	−5.86733	−0.219733
$714$	−2.80631	−0.105023
$715$	−69.3806	−2.59469
$716$	1.19508	0.0446621
$717$	−3.03306	−0.113272
$718$	−6.93463	−0.258798
$719$	−42.0586	−1.56852	−0.784261	−	0.620432i	$-0.786957\pi$
$719$	−42.0586	−1.56852	−0.784261	+	0.620432i	$0.786957\pi$
$720$	10.0135	0.373182
$721$	−19.3497	−0.720619
$722$	−18.4298	−0.685887
$723$	−2.94551	−0.109545
$724$	5.71941	0.212560
$725$	9.21518	0.342243
$726$	10.0806	0.374126
$727$	9.85627	0.365549	0.182774	−	0.983155i	$-0.441492\pi$
$727$	9.85627	0.365549	0.182774	+	0.983155i	$0.441492\pi$
$728$	3.99783	0.148169
$729$	−16.5743	−0.613863
$730$	22.8067	0.844113
$731$	36.0297	1.33261
$732$	5.37136	0.198531
$733$	33.1551	1.22461	0.612305	−	0.790622i	$-0.290242\pi$
$733$	33.1551	1.22461	0.612305	+	0.790622i	$0.290242\pi$
$734$	−35.3439	−1.30457
$735$	9.04238	0.333533
$736$	−5.86733	−0.216273
$737$	−88.4376	−3.25764
$738$	15.5898	0.573870
$739$	−34.7357	−1.27777	−0.638887	−	0.769301i	$-0.720605\pi$
$739$	−34.7357	−1.27777	−0.638887	+	0.769301i	$0.720605\pi$
$740$	−9.71336	−0.357070
$741$	−1.14640	−0.0421139
$742$	2.45161	0.0900013
$743$	−3.68297	−0.135115	−0.0675576	−	0.997715i	$-0.521521\pi$
$743$	−3.68297	−0.135115	−0.0675576	+	0.997715i	$0.521521\pi$
$744$	0.452250	0.0165803
$745$	−70.8229	−2.59475
$746$	−10.4583	−0.382906
$747$	−49.3083	−1.80410
$748$	−30.0635	−1.09923
$749$	6.61817	0.241823
$750$	−4.58635	−0.167470
$751$	−22.5981	−0.824618	−0.412309	−	0.911044i	$-0.635278\pi$
$751$	−22.5981	−0.824618	−0.412309	+	0.911044i	$0.635278\pi$
$752$	−2.93655	−0.107085
$753$	−2.88113	−0.104994
$754$	−3.95031	−0.143862
$755$	−72.9778	−2.65594
$756$	3.12134	0.113522
$757$	−20.4501	−0.743272	−0.371636	−	0.928379i	$-0.621203\pi$
$757$	−20.4501	−0.743272	−0.371636	+	0.928379i	$0.621203\pi$
$758$	13.6031	0.494086
$759$	15.3100	0.555718
$760$	−2.70481	−0.0981139
$761$	23.1791	0.840241	0.420121	−	0.907468i	$-0.361988\pi$
$761$	23.1791	0.840241	0.420121	+	0.907468i	$0.361988\pi$
$762$	1.76652	0.0639942
$763$	5.80017	0.209980
$764$	16.1390	0.583889
$765$	52.1759	1.88642
$766$	9.53323	0.344450
$767$	32.1667	1.16147
$768$	0.452250	0.0163192
$769$	54.1972	1.95440	0.977200	−	0.212321i	$-0.0681024\pi$
$769$	54.1972	1.95440	0.977200	+	0.212321i	$0.0681024\pi$
$770$	−24.6128	−0.886985
$771$	−1.16532	−0.0419678
$772$	−6.15460	−0.221509
$773$	23.6704	0.851365	0.425682	−	0.904873i	$-0.360034\pi$
$773$	23.6704	0.851365	0.425682	+	0.904873i	$0.360034\pi$
$774$	−19.3300	−0.694803
$775$	7.83111	0.281302
$776$	1.00000	0.0358979
$777$	−1.46046	−0.0523937
$778$	−25.0013	−0.896342
$779$	−4.21107	−0.150877
$780$	5.43828	0.194722
$781$	6.32633	0.226374
$782$	−30.5720	−1.09325
$783$	−3.08424	−0.110222
$784$	−5.58177	−0.199349
$785$	−27.9846	−0.998813
$786$	−7.33100	−0.261488
$787$	48.9092	1.74342	0.871712	−	0.490019i	$-0.163010\pi$
$787$	48.9092	1.74342	0.871712	+	0.490019i	$0.163010\pi$
$788$	−8.60053	−0.306381
$789$	3.65705	0.130194
$790$	27.7539	0.987440
$791$	6.56268	0.233342
$792$	16.1291	0.573123
$793$	−39.8709	−1.41586
$794$	23.8693	0.847089
$795$	3.33494	0.118278
$796$	−10.2350	−0.362772
$797$	2.17424	0.0770154	0.0385077	−	0.999258i	$-0.487740\pi$
$797$	2.17424	0.0770154	0.0385077	+	0.999258i	$0.487740\pi$
$798$	−0.406684	−0.0143965
$799$	−15.3010	−0.541311
$800$	7.83111	0.276872
$801$	8.47697	0.299519
$802$	21.4973	0.759096
$803$	36.7355	1.29637
$804$	6.93202	0.244474
$805$	−25.0291	−0.882162
$806$	−3.35699	−0.118245
$807$	4.25754	0.149873
$808$	−3.75060	−0.131946
$809$	−18.0941	−0.636156	−0.318078	−	0.948065i	$-0.603037\pi$
$809$	−18.0941	−0.636156	−0.318078	+	0.948065i	$0.603037\pi$
$810$	−25.7946	−0.906329
$811$	33.0356	1.16004	0.580018	−	0.814604i	$-0.303045\pi$
$811$	33.0356	1.16004	0.580018	+	0.814604i	$0.303045\pi$
$812$	−1.40137	−0.0491786
$813$	−3.60931	−0.126584
$814$	−15.6456	−0.548379
$815$	−16.8465	−0.590106
$816$	2.35647	0.0824930
$817$	5.22134	0.182672
$818$	29.0846	1.01692
$819$	−11.1758	−0.390514
$820$	19.9765	0.697609
$821$	5.68002	0.198234	0.0991170	−	0.995076i	$-0.468398\pi$
$821$	5.68002	0.198234	0.0991170	+	0.995076i	$0.468398\pi$
$822$	−1.99772	−0.0696786
$823$	27.6747	0.964678	0.482339	−	0.875985i	$-0.339787\pi$
$823$	27.6747	0.964678	0.482339	+	0.875985i	$0.339787\pi$
$824$	16.2480	0.566026
$825$	−20.4342	−0.711428
$826$	11.4111	0.397044
$827$	−37.2064	−1.29379	−0.646896	−	0.762578i	$-0.723933\pi$
$827$	−37.2064	−1.29379	−0.646896	+	0.762578i	$0.723933\pi$
$828$	16.4019	0.570007
$829$	−46.9672	−1.63124	−0.815618	−	0.578590i	$-0.803603\pi$
$829$	−46.9672	−1.63124	−0.815618	+	0.578590i	$0.803603\pi$
$830$	−63.1826	−2.19310
$831$	−7.97559	−0.276670
$832$	−3.35699	−0.116383
$833$	−29.0841	−1.00770
$834$	−0.460620	−0.0159500
$835$	−75.3095	−2.60619
$836$	−4.35673	−0.150681
$837$	−2.62100	−0.0905951
$838$	−20.3085	−0.701547
$839$	−19.6603	−0.678748	−0.339374	−	0.940652i	$-0.610215\pi$
$839$	−19.6603	−0.678748	−0.339374	+	0.940652i	$0.610215\pi$
$840$	1.92923	0.0665648
$841$	−27.6153	−0.952251
$842$	18.0720	0.622803
$843$	7.34714	0.253049
$844$	−21.7752	−0.749532
$845$	6.19911	0.213256
$846$	8.20904	0.282232
$847$	−26.5449	−0.912092
$848$	−2.05863	−0.0706935
$849$	0.790604	0.0271334
$850$	40.8043	1.39958
$851$	−15.9103	−0.545397
$852$	−0.495878	−0.0169885
$853$	5.28388	0.180916	0.0904582	−	0.995900i	$-0.471167\pi$
$853$	5.28388	0.180916	0.0904582	+	0.995900i	$0.471167\pi$
$854$	−14.1442	−0.484005
$855$	7.56122	0.258588
$856$	−5.55731	−0.189945
$857$	18.1862	0.621228	0.310614	−	0.950536i	$-0.399465\pi$
$857$	18.1862	0.621228	0.310614	+	0.950536i	$0.399465\pi$
$858$	8.75962	0.299048
$859$	51.4102	1.75409	0.877047	−	0.480404i	$-0.159510\pi$
$859$	51.4102	1.75409	0.877047	+	0.480404i	$0.159510\pi$
$860$	−24.7690	−0.844617
$861$	3.00358	0.102362
$862$	33.1822	1.13019
$863$	8.43409	0.287100	0.143550	−	0.989643i	$-0.454148\pi$
$863$	8.43409	0.287100	0.143550	+	0.989643i	$0.454148\pi$
$864$	−2.62100	−0.0891683
$865$	−42.2244	−1.43567
$866$	−24.7240	−0.840156
$867$	4.59024	0.155893
$868$	−1.19090	−0.0404216
$869$	44.7042	1.51649
$870$	−1.90630	−0.0646297
$871$	−51.4555	−1.74350
$872$	−4.87043	−0.164933
$873$	−2.79547	−0.0946123
$874$	−4.43043	−0.149861
$875$	12.0771	0.408280
$876$	−2.87945	−0.0972875
$877$	52.7906	1.78261	0.891306	−	0.453402i	$-0.149790\pi$
$877$	52.7906	1.78261	0.891306	+	0.453402i	$0.149790\pi$
$878$	28.4237	0.959253
$879$	0.581211	0.0196037
$880$	20.6675	0.696701
$881$	−41.6338	−1.40268	−0.701340	−	0.712827i	$-0.747414\pi$
$881$	−41.6338	−1.40268	−0.701340	+	0.712827i	$0.747414\pi$
$882$	15.6037	0.525403
$883$	−8.21754	−0.276542	−0.138271	−	0.990394i	$-0.544155\pi$
$883$	−8.21754	−0.276542	−0.138271	+	0.990394i	$0.544155\pi$
$884$	−17.4918	−0.588311
$885$	15.5227	0.521789
$886$	3.92099	0.131728
$887$	−6.19513	−0.208012	−0.104006	−	0.994577i	$-0.533166\pi$
$887$	−6.19513	−0.208012	−0.104006	+	0.994577i	$0.533166\pi$
$888$	1.22636	0.0411538
$889$	−4.65171	−0.156013
$890$	10.8622	0.364102
$891$	−41.5482	−1.39192
$892$	28.2447	0.945703
$893$	−2.21739	−0.0742022
$894$	8.94171	0.299056
$895$	−4.28083	−0.143092
$896$	−1.19090	−0.0397850
$897$	8.90779	0.297422
$898$	−19.6099	−0.654392
$899$	1.17674	0.0392465
$900$	−21.8916	−0.729721
$901$	−10.7266	−0.357354
$902$	32.1768	1.07137
$903$	−3.72417	−0.123933
$904$	−5.51071	−0.183284
$905$	−20.4872	−0.681019
$906$	9.21378	0.306107
$907$	45.5867	1.51368	0.756841	−	0.653599i	$-0.226742\pi$
$907$	45.5867	1.51368	0.756841	+	0.653599i	$0.226742\pi$
$908$	−19.4163	−0.644352
$909$	10.4847	0.347756
$910$	−14.3204	−0.474718
$911$	−14.5860	−0.483257	−0.241629	−	0.970369i	$-0.577682\pi$
$911$	−14.5860	−0.483257	−0.241629	+	0.970369i	$0.577682\pi$
$912$	0.341495	0.0113080
$913$	−101.770	−3.36811
$914$	−7.17138	−0.237208
$915$	−19.2405	−0.636071
$916$	−20.4498	−0.675681
$917$	19.3045	0.637489
$918$	−13.6569	−0.450743
$919$	24.4842	0.807658	0.403829	−	0.914834i	$-0.367679\pi$
$919$	24.4842	0.807658	0.403829	+	0.914834i	$0.367679\pi$
$920$	21.0171	0.692913
$921$	−5.69428	−0.187633
$922$	30.8813	1.01702
$923$	3.68083	0.121156
$924$	3.10748	0.102229
$925$	21.2354	0.698216
$926$	18.1112	0.595170
$927$	−45.4208	−1.49181
$928$	1.17674	0.0386284
$929$	−43.2079	−1.41761	−0.708803	−	0.705406i	$-0.750765\pi$
$929$	−43.2079	−1.41761	−0.708803	+	0.705406i	$0.750765\pi$
$930$	−1.61999	−0.0531214
$931$	−4.21480	−0.138135
$932$	8.01544	0.262554
$933$	−14.5701	−0.477004
$934$	33.2115	1.08671
$935$	107.689	3.52180
$936$	9.38437	0.306738
$937$	−46.2338	−1.51039	−0.755196	−	0.655499i	$-0.772458\pi$
$937$	−46.2338	−1.51039	−0.755196	+	0.655499i	$0.772458\pi$
$938$	−18.2539	−0.596010
$939$	−2.13609	−0.0697085
$940$	10.5189	0.343088
$941$	31.5310	1.02788	0.513940	−	0.857826i	$-0.328185\pi$
$941$	31.5310	1.02788	0.513940	+	0.857826i	$0.328185\pi$
$942$	3.53318	0.115117
$943$	32.7211	1.06554
$944$	−9.58199	−0.311867
$945$	−11.1808	−0.363712
$946$	−39.8963	−1.29714
$947$	46.8463	1.52230	0.761150	−	0.648575i	$-0.224635\pi$
$947$	46.8463	1.52230	0.761150	+	0.648575i	$0.224635\pi$
$948$	−3.50406	−0.113807
$949$	21.3737	0.693821
$950$	5.91328	0.191852
$951$	11.3796	0.369010
$952$	−6.20521	−0.201112
$953$	9.91198	0.321081	0.160540	−	0.987029i	$-0.448676\pi$
$953$	9.91198	0.321081	0.160540	+	0.987029i	$0.448676\pi$
$954$	5.75483	0.186319
$955$	−57.8108	−1.87071
$956$	−6.70660	−0.216907
$957$	−3.07055	−0.0992566
$958$	−9.29086	−0.300174
$959$	5.26053	0.169872
$960$	−1.61999	−0.0522848
$961$	1.00000	0.0322581
$962$	−9.10307	−0.293495
$963$	15.5353	0.500617
$964$	−6.51301	−0.209770
$965$	22.0461	0.709689
$966$	3.16004	0.101673
$967$	42.6219	1.37063	0.685314	−	0.728247i	$-0.259665\pi$
$967$	42.6219	1.37063	0.685314	+	0.728247i	$0.259665\pi$
$968$	22.2898	0.716423
$969$	1.77937	0.0571617
$970$	−3.58205	−0.115013
$971$	23.4758	0.753373	0.376687	−	0.926341i	$-0.377063\pi$
$971$	23.4758	0.753373	0.376687	+	0.926341i	$0.377063\pi$
$972$	11.1197	0.356664
$973$	1.21294	0.0388849
$974$	−12.3409	−0.395427
$975$	−11.8892	−0.380759
$976$	11.8770	0.380172
$977$	10.0995	0.323111	0.161556	−	0.986864i	$-0.448349\pi$
$977$	10.0995	0.323111	0.161556	+	0.986864i	$0.448349\pi$
$978$	2.12694	0.0680121
$979$	17.4961	0.559178
$980$	19.9942	0.638691
$981$	13.6151	0.434698
$982$	−34.4050	−1.09791
$983$	36.0587	1.15010	0.575048	−	0.818120i	$-0.304983\pi$
$983$	36.0587	1.15010	0.575048	+	0.818120i	$0.304983\pi$
$984$	−2.52212	−0.0804023
$985$	30.8076	0.981610
$986$	6.13146	0.195265
$987$	1.58158	0.0503421
$988$	−2.53487	−0.0806449
$989$	−40.5712	−1.29009
$990$	−57.7754	−1.83622
$991$	43.2842	1.37497	0.687483	−	0.726200i	$-0.258715\pi$
$991$	43.2842	1.37497	0.687483	+	0.726200i	$0.258715\pi$
$992$	1.00000	0.0317500
$993$	−6.79894	−0.215758
$994$	1.30578	0.0414168
$995$	36.6625	1.16228
$996$	7.97709	0.252764
$997$	−23.2831	−0.737382	−0.368691	−	0.929552i	$-0.620194\pi$
$997$	−23.2831	−0.737382	−0.368691	+	0.929552i	$0.620194\pi$
$998$	28.3720	0.898100
$999$	−7.10730	−0.224865

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.k.1.20	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.k.1.20	✓	37	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:	\( N \)	\(=\)	\( 6014 = 2 \cdot 31 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6014.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.452250 q^{3} +1.00000 q^{4} -3.58205 q^{5} +0.452250 q^{6} -1.19090 q^{7} +1.00000 q^{8} -2.79547 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.452250 q^{3} +1.00000 q^{4} -3.58205 q^{5} +0.452250 q^{6} -1.19090 q^{7} +1.00000 q^{8} -2.79547 q^{9} -3.58205 q^{10} -5.76974 q^{11} +0.452250 q^{12} -3.35699 q^{13} -1.19090 q^{14} -1.61999 q^{15} +1.00000 q^{16} +5.21054 q^{17} -2.79547 q^{18} +0.755101 q^{19} -3.58205 q^{20} -0.538583 q^{21} -5.76974 q^{22} -5.86733 q^{23} +0.452250 q^{24} +7.83111 q^{25} -3.35699 q^{26} -2.62100 q^{27} -1.19090 q^{28} +1.17674 q^{29} -1.61999 q^{30} +1.00000 q^{31} +1.00000 q^{32} -2.60936 q^{33} +5.21054 q^{34} +4.26585 q^{35} -2.79547 q^{36} +2.71167 q^{37} +0.755101 q^{38} -1.51820 q^{39} -3.58205 q^{40} -5.57683 q^{41} -0.538583 q^{42} +6.91476 q^{43} -5.76974 q^{44} +10.0135 q^{45} -5.86733 q^{46} -2.93655 q^{47} +0.452250 q^{48} -5.58177 q^{49} +7.83111 q^{50} +2.35647 q^{51} -3.35699 q^{52} -2.05863 q^{53} -2.62100 q^{54} +20.6675 q^{55} -1.19090 q^{56} +0.341495 q^{57} +1.17674 q^{58} -9.58199 q^{59} -1.61999 q^{60} +11.8770 q^{61} +1.00000 q^{62} +3.32911 q^{63} +1.00000 q^{64} +12.0249 q^{65} -2.60936 q^{66} +15.3278 q^{67} +5.21054 q^{68} -2.65350 q^{69} +4.26585 q^{70} -1.09647 q^{71} -2.79547 q^{72} -6.36693 q^{73} +2.71167 q^{74} +3.54162 q^{75} +0.755101 q^{76} +6.87115 q^{77} -1.51820 q^{78} -7.74805 q^{79} -3.58205 q^{80} +7.20106 q^{81} -5.57683 q^{82} +17.6387 q^{83} -0.538583 q^{84} -18.6645 q^{85} +6.91476 q^{86} +0.532181 q^{87} -5.76974 q^{88} -3.03239 q^{89} +10.0135 q^{90} +3.99783 q^{91} -5.86733 q^{92} +0.452250 q^{93} -2.93655 q^{94} -2.70481 q^{95} +0.452250 q^{96} +1.00000 q^{97} -5.58177 q^{98} +16.1291 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 37 q^{2} + 9 q^{3} + 37 q^{4} + 9 q^{5} + 9 q^{6} + 19 q^{7} + 37 q^{8} + 52 q^{9}+O(q^{10}) \) 37 * q + 37 * q^2 + 9 * q^3 + 37 * q^4 + 9 * q^5 + 9 * q^6 + 19 * q^7 + 37 * q^8 + 52 * q^9	\( 37 q + 37 q^{2} + 9 q^{3} + 37 q^{4} + 9 q^{5} + 9 q^{6} + 19 q^{7} + 37 q^{8} + 52 q^{9} + 9 q^{10} + 5 q^{11} + 9 q^{12} + 16 q^{13} + 19 q^{14} + 22 q^{15} + 37 q^{16} + 3 q^{17} + 52 q^{18} + 36 q^{19} + 9 q^{20} + 6 q^{21} + 5 q^{22} + 11 q^{23} + 9 q^{24} + 58 q^{25} + 16 q^{26} + 24 q^{27} + 19 q^{28} + 5 q^{29} + 22 q^{30} + 37 q^{31} + 37 q^{32} + q^{33} + 3 q^{34} + 28 q^{35} + 52 q^{36} + 21 q^{37} + 36 q^{38} + 38 q^{39} + 9 q^{40} + 21 q^{41} + 6 q^{42} + 14 q^{43} + 5 q^{44} + 55 q^{45} + 11 q^{46} + 59 q^{47} + 9 q^{48} + 82 q^{49} + 58 q^{50} + 46 q^{51} + 16 q^{52} + 8 q^{53} + 24 q^{54} + 25 q^{55} + 19 q^{56} + 5 q^{58} + 41 q^{59} + 22 q^{60} + 16 q^{61} + 37 q^{62} + 23 q^{63} + 37 q^{64} - 46 q^{65} + q^{66} + 45 q^{67} + 3 q^{68} + 68 q^{69} + 28 q^{70} + 55 q^{71} + 52 q^{72} + 29 q^{73} + 21 q^{74} - 12 q^{75} + 36 q^{76} + 30 q^{77} + 38 q^{78} + 25 q^{79} + 9 q^{80} + 73 q^{81} + 21 q^{82} + 70 q^{83} + 6 q^{84} - 21 q^{85} + 14 q^{86} + 37 q^{87} + 5 q^{88} + 55 q^{90} + 18 q^{91} + 11 q^{92} + 9 q^{93} + 59 q^{94} - 9 q^{95} + 9 q^{96} + 37 q^{97} + 82 q^{98} + 33 q^{99}+O(q^{100}) \) 37 * q + 37 * q^2 + 9 * q^3 + 37 * q^4 + 9 * q^5 + 9 * q^6 + 19 * q^7 + 37 * q^8 + 52 * q^9 + 9 * q^10 + 5 * q^11 + 9 * q^12 + 16 * q^13 + 19 * q^14 + 22 * q^15 + 37 * q^16 + 3 * q^17 + 52 * q^18 + 36 * q^19 + 9 * q^20 + 6 * q^21 + 5 * q^22 + 11 * q^23 + 9 * q^24 + 58 * q^25 + 16 * q^26 + 24 * q^27 + 19 * q^28 + 5 * q^29 + 22 * q^30 + 37 * q^31 + 37 * q^32 + q^33 + 3 * q^34 + 28 * q^35 + 52 * q^36 + 21 * q^37 + 36 * q^38 + 38 * q^39 + 9 * q^40 + 21 * q^41 + 6 * q^42 + 14 * q^43 + 5 * q^44 + 55 * q^45 + 11 * q^46 + 59 * q^47 + 9 * q^48 + 82 * q^49 + 58 * q^50 + 46 * q^51 + 16 * q^52 + 8 * q^53 + 24 * q^54 + 25 * q^55 + 19 * q^56 + 5 * q^58 + 41 * q^59 + 22 * q^60 + 16 * q^61 + 37 * q^62 + 23 * q^63 + 37 * q^64 - 46 * q^65 + q^66 + 45 * q^67 + 3 * q^68 + 68 * q^69 + 28 * q^70 + 55 * q^71 + 52 * q^72 + 29 * q^73 + 21 * q^74 - 12 * q^75 + 36 * q^76 + 30 * q^77 + 38 * q^78 + 25 * q^79 + 9 * q^80 + 73 * q^81 + 21 * q^82 + 70 * q^83 + 6 * q^84 - 21 * q^85 + 14 * q^86 + 37 * q^87 + 5 * q^88 + 55 * q^90 + 18 * q^91 + 11 * q^92 + 9 * q^93 + 59 * q^94 - 9 * q^95 + 9 * q^96 + 37 * q^97 + 82 * q^98 + 33 * q^99

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