LMFDB - Embedded newform 6013.2.a.f.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6013,2,Mod(1,6013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6013, 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("6013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6013 = 7 \cdot 859 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6013.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:	$48.0140467354$
Analytic rank:	$0$
Dimension:	$110$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	6013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.63934 q^{2} -1.02733 q^{3} +4.96612 q^{4} -0.539298 q^{5} +2.71147 q^{6} -1.00000 q^{7} -7.82859 q^{8} -1.94460 q^{9} +O(q^{10})$	\(q-2.63934 q^{2} -1.02733 q^{3} +4.96612 q^{4} -0.539298 q^{5} +2.71147 q^{6} -1.00000 q^{7} -7.82859 q^{8} -1.94460 q^{9} +1.42339 q^{10} +4.17920 q^{11} -5.10184 q^{12} +3.02624 q^{13} +2.63934 q^{14} +0.554037 q^{15} +10.7301 q^{16} -5.35366 q^{17} +5.13245 q^{18} -5.68124 q^{19} -2.67822 q^{20} +1.02733 q^{21} -11.0303 q^{22} +1.03217 q^{23} +8.04254 q^{24} -4.70916 q^{25} -7.98727 q^{26} +5.07973 q^{27} -4.96612 q^{28} -2.91329 q^{29} -1.46229 q^{30} -8.03380 q^{31} -12.6631 q^{32} -4.29341 q^{33} +14.1301 q^{34} +0.539298 q^{35} -9.65709 q^{36} -0.364246 q^{37} +14.9947 q^{38} -3.10894 q^{39} +4.22195 q^{40} +2.41121 q^{41} -2.71147 q^{42} +0.729966 q^{43} +20.7544 q^{44} +1.04872 q^{45} -2.72425 q^{46} -0.0565505 q^{47} -11.0233 q^{48} +1.00000 q^{49} +12.4291 q^{50} +5.49997 q^{51} +15.0286 q^{52} +0.843838 q^{53} -13.4071 q^{54} -2.25384 q^{55} +7.82859 q^{56} +5.83650 q^{57} +7.68915 q^{58} +1.99552 q^{59} +2.75141 q^{60} -2.36286 q^{61} +21.2039 q^{62} +1.94460 q^{63} +11.9622 q^{64} -1.63204 q^{65} +11.3318 q^{66} -3.13327 q^{67} -26.5869 q^{68} -1.06038 q^{69} -1.42339 q^{70} -8.01311 q^{71} +15.2234 q^{72} +1.18164 q^{73} +0.961368 q^{74} +4.83785 q^{75} -28.2137 q^{76} -4.17920 q^{77} +8.20555 q^{78} -9.02086 q^{79} -5.78671 q^{80} +0.615236 q^{81} -6.36400 q^{82} +12.3001 q^{83} +5.10184 q^{84} +2.88722 q^{85} -1.92663 q^{86} +2.99290 q^{87} -32.7172 q^{88} -7.36771 q^{89} -2.76792 q^{90} -3.02624 q^{91} +5.12588 q^{92} +8.25336 q^{93} +0.149256 q^{94} +3.06388 q^{95} +13.0092 q^{96} +2.85071 q^{97} -2.63934 q^{98} -8.12685 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9}+O(q^{10}) $ 110 * q + 16 * q^2 + 29 * q^3 + 118 * q^4 + 12 * q^6 - 110 * q^7 + 57 * q^8 + 127 * q^9	\( 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9} + 3 q^{10} + 52 q^{11} + 62 q^{12} - 9 q^{13} - 16 q^{14} + 39 q^{15} + 146 q^{16} + 11 q^{17} + 60 q^{18} + 14 q^{19} + 18 q^{20} - 29 q^{21} + 32 q^{22} + 73 q^{23} + 24 q^{24} + 132 q^{25} - 7 q^{26} + 116 q^{27} - 118 q^{28} + 35 q^{29} + 18 q^{30} + 36 q^{31} + 140 q^{32} + 42 q^{33} - 7 q^{34} + 180 q^{36} + 49 q^{37} + 45 q^{39} + 6 q^{40} - 14 q^{41} - 12 q^{42} + 58 q^{43} + 92 q^{44} + 17 q^{45} + 27 q^{46} + 87 q^{47} + 98 q^{48} + 110 q^{49} + 91 q^{50} + 42 q^{51} + 16 q^{52} + 95 q^{53} + 41 q^{54} + 8 q^{55} - 57 q^{56} + 61 q^{57} + 46 q^{58} + 114 q^{59} + 81 q^{60} - 47 q^{61} + 31 q^{62} - 127 q^{63} + 199 q^{64} + 62 q^{65} + 21 q^{66} + 95 q^{67} + 60 q^{68} - 39 q^{69} - 3 q^{70} + 131 q^{71} + 186 q^{72} + 31 q^{73} + 23 q^{74} + 121 q^{75} + 14 q^{76} - 52 q^{77} + 110 q^{78} + 9 q^{79} + 61 q^{80} + 194 q^{81} + 45 q^{82} + 73 q^{83} - 62 q^{84} + 59 q^{85} + 72 q^{86} + 64 q^{87} + 100 q^{88} - 17 q^{89} + 11 q^{90} + 9 q^{91} + 192 q^{92} + 85 q^{93} - 11 q^{94} + 108 q^{95} + 68 q^{96} + 32 q^{97} + 16 q^{98} + 160 q^{99}+O(q^{100}) \) 110 * q + 16 * q^2 + 29 * q^3 + 118 * q^4 + 12 * q^6 - 110 * q^7 + 57 * q^8 + 127 * q^9 + 3 * q^10 + 52 * q^11 + 62 * q^12 - 9 * q^13 - 16 * q^14 + 39 * q^15 + 146 * q^16 + 11 * q^17 + 60 * q^18 + 14 * q^19 + 18 * q^20 - 29 * q^21 + 32 * q^22 + 73 * q^23 + 24 * q^24 + 132 * q^25 - 7 * q^26 + 116 * q^27 - 118 * q^28 + 35 * q^29 + 18 * q^30 + 36 * q^31 + 140 * q^32 + 42 * q^33 - 7 * q^34 + 180 * q^36 + 49 * q^37 + 45 * q^39 + 6 * q^40 - 14 * q^41 - 12 * q^42 + 58 * q^43 + 92 * q^44 + 17 * q^45 + 27 * q^46 + 87 * q^47 + 98 * q^48 + 110 * q^49 + 91 * q^50 + 42 * q^51 + 16 * q^52 + 95 * q^53 + 41 * q^54 + 8 * q^55 - 57 * q^56 + 61 * q^57 + 46 * q^58 + 114 * q^59 + 81 * q^60 - 47 * q^61 + 31 * q^62 - 127 * q^63 + 199 * q^64 + 62 * q^65 + 21 * q^66 + 95 * q^67 + 60 * q^68 - 39 * q^69 - 3 * q^70 + 131 * q^71 + 186 * q^72 + 31 * q^73 + 23 * q^74 + 121 * q^75 + 14 * q^76 - 52 * q^77 + 110 * q^78 + 9 * q^79 + 61 * q^80 + 194 * q^81 + 45 * q^82 + 73 * q^83 - 62 * q^84 + 59 * q^85 + 72 * q^86 + 64 * q^87 + 100 * q^88 - 17 * q^89 + 11 * q^90 + 9 * q^91 + 192 * q^92 + 85 * q^93 - 11 * q^94 + 108 * q^95 + 68 * q^96 + 32 * q^97 + 16 * q^98 + 160 * 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 $

$2$	−2.63934	−1.86630	−0.933148	−	0.359493i	$-0.882950\pi$
$2$	−2.63934	−1.86630	−0.933148	+	0.359493i	$0.882950\pi$
$3$	−1.02733	−0.593129	−0.296564	−	0.955013i	$-0.595841\pi$
$3$	−1.02733	−0.593129	−0.296564	+	0.955013i	$0.595841\pi$
$4$	4.96612	2.48306
$5$	−0.539298	−0.241182	−0.120591	−	0.992702i	$-0.538479\pi$
$5$	−0.539298	−0.241182	−0.120591	+	0.992702i	$0.538479\pi$
$6$	2.71147	1.10695
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−7.82859	−2.76782
$9$	−1.94460	−0.648198
$10$	1.42339	0.450116
$11$	4.17920	1.26008	0.630038	−	0.776564i	$-0.283039\pi$
$11$	4.17920	1.26008	0.630038	+	0.776564i	$0.283039\pi$
$12$	−5.10184	−1.47277
$13$	3.02624	0.839327	0.419664	−	0.907680i	$-0.362148\pi$
$13$	3.02624	0.839327	0.419664	+	0.907680i	$0.362148\pi$
$14$	2.63934	0.705393
$15$	0.554037	0.143052
$16$	10.7301	2.68252
$17$	−5.35366	−1.29845	−0.649227	−	0.760595i	$-0.724907\pi$
$17$	−5.35366	−1.29845	−0.649227	+	0.760595i	$0.724907\pi$
$18$	5.13245	1.20973
$19$	−5.68124	−1.30337	−0.651683	−	0.758492i	$-0.725937\pi$
$19$	−5.68124	−1.30337	−0.651683	+	0.758492i	$0.725937\pi$
$20$	−2.67822	−0.598868
$21$	1.02733	0.224182
$22$	−11.0303	−2.35167
$23$	1.03217	0.215223	0.107611	−	0.994193i	$-0.465680\pi$
$23$	1.03217	0.215223	0.107611	+	0.994193i	$0.465680\pi$
$24$	8.04254	1.64168
$25$	−4.70916	−0.941831
$26$	−7.98727	−1.56643
$27$	5.07973	0.977594
$28$	−4.96612	−0.938508
$29$	−2.91329	−0.540984	−0.270492	−	0.962722i	$-0.587186\pi$
$29$	−2.91329	−0.540984	−0.270492	+	0.962722i	$0.587186\pi$
$30$	−1.46229	−0.266977
$31$	−8.03380	−1.44291	−0.721457	−	0.692460i	$-0.756527\pi$
$31$	−8.03380	−1.44291	−0.721457	+	0.692460i	$0.756527\pi$
$32$	−12.6631	−2.23855
$33$	−4.29341	−0.747387
$34$	14.1301	2.42330
$35$	0.539298	0.0911580
$36$	−9.65709	−1.60951
$37$	−0.364246	−0.0598816	−0.0299408	−	0.999552i	$-0.509532\pi$
$37$	−0.364246	−0.0598816	−0.0299408	+	0.999552i	$0.509532\pi$
$38$	14.9947	2.43246
$39$	−3.10894	−0.497829
$40$	4.22195	0.667548
$41$	2.41121	0.376568	0.188284	−	0.982115i	$-0.439708\pi$
$41$	2.41121	0.376568	0.188284	+	0.982115i	$0.439708\pi$
$42$	−2.71147	−0.418389
$43$	0.729966	0.111319	0.0556594	−	0.998450i	$-0.482274\pi$
$43$	0.729966	0.111319	0.0556594	+	0.998450i	$0.482274\pi$
$44$	20.7544	3.12884
$45$	1.04872	0.156333
$46$	−2.72425	−0.401669
$47$	−0.0565505	−0.00824874	−0.00412437	−	0.999991i	$-0.501313\pi$
$47$	−0.0565505	−0.00824874	−0.00412437	+	0.999991i	$0.501313\pi$
$48$	−11.0233	−1.59108
$49$	1.00000	0.142857
$50$	12.4291	1.75774
$51$	5.49997	0.770150
$52$	15.0286	2.08410
$53$	0.843838	0.115910	0.0579550	−	0.998319i	$-0.481542\pi$
$53$	0.843838	0.115910	0.0579550	+	0.998319i	$0.481542\pi$
$54$	−13.4071	−1.82448
$55$	−2.25384	−0.303907
$56$	7.82859	1.04614
$57$	5.83650	0.773063
$58$	7.68915	1.00964
$59$	1.99552	0.259794	0.129897	−	0.991527i	$-0.458535\pi$
$59$	1.99552	0.259794	0.129897	+	0.991527i	$0.458535\pi$
$60$	2.75141	0.355206
$61$	−2.36286	−0.302533	−0.151266	−	0.988493i	$-0.548335\pi$
$61$	−2.36286	−0.302533	−0.151266	+	0.988493i	$0.548335\pi$
$62$	21.2039	2.69290
$63$	1.94460	0.244996
$64$	11.9622	1.49527
$65$	−1.63204	−0.202430
$66$	11.3318	1.39485
$67$	−3.13327	−0.382790	−0.191395	−	0.981513i	$-0.561301\pi$
$67$	−3.13327	−0.382790	−0.191395	+	0.981513i	$0.561301\pi$
$68$	−26.5869	−3.22414
$69$	−1.06038	−0.127655
$70$	−1.42339	−0.170128
$71$	−8.01311	−0.950981	−0.475490	−	0.879721i	$-0.657729\pi$
$71$	−8.01311	−0.950981	−0.475490	+	0.879721i	$0.657729\pi$
$72$	15.2234	1.79410
$73$	1.18164	0.138301	0.0691504	−	0.997606i	$-0.477971\pi$
$73$	1.18164	0.138301	0.0691504	+	0.997606i	$0.477971\pi$
$74$	0.961368	0.111757
$75$	4.83785	0.558627
$76$	−28.2137	−3.23633
$77$	−4.17920	−0.476264
$78$	8.20555	0.929096
$79$	−9.02086	−1.01493	−0.507463	−	0.861674i	$-0.669417\pi$
$79$	−9.02086	−1.01493	−0.507463	+	0.861674i	$0.669417\pi$
$80$	−5.78671	−0.646974
$81$	0.615236	0.0683596
$82$	−6.36400	−0.702786
$83$	12.3001	1.35011	0.675057	−	0.737766i	$-0.264119\pi$
$83$	12.3001	1.35011	0.675057	+	0.737766i	$0.264119\pi$
$84$	5.10184	0.556656
$85$	2.88722	0.313163
$86$	−1.92663	−0.207754
$87$	2.99290	0.320873
$88$	−32.7172	−3.48767
$89$	−7.36771	−0.780976	−0.390488	−	0.920608i	$-0.627694\pi$
$89$	−7.36771	−0.780976	−0.390488	+	0.920608i	$0.627694\pi$
$90$	−2.76792	−0.291764
$91$	−3.02624	−0.317236
$92$	5.12588	0.534410
$93$	8.25336	0.855833
$94$	0.149256	0.0153946
$95$	3.06388	0.314348
$96$	13.0092	1.32775
$97$	2.85071	0.289446	0.144723	−	0.989472i	$-0.453771\pi$
$97$	2.85071	0.289446	0.144723	+	0.989472i	$0.453771\pi$
$98$	−2.63934	−0.266614
$99$	−8.12685	−0.816779
$100$	−23.3862	−2.33862
$101$	−0.909428	−0.0904915	−0.0452458	−	0.998976i	$-0.514407\pi$
$101$	−0.909428	−0.0904915	−0.0452458	+	0.998976i	$0.514407\pi$
$102$	−14.5163	−1.43733
$103$	−7.77410	−0.766005	−0.383002	−	0.923747i	$-0.625110\pi$
$103$	−7.77410	−0.766005	−0.383002	+	0.923747i	$0.625110\pi$
$104$	−23.6912	−2.32311
$105$	−0.554037	−0.0540684
$106$	−2.22717	−0.216322
$107$	1.19421	0.115449	0.0577243	−	0.998333i	$-0.481616\pi$
$107$	1.19421	0.115449	0.0577243	+	0.998333i	$0.481616\pi$
$108$	25.2265	2.42742
$109$	2.84676	0.272670	0.136335	−	0.990663i	$-0.456468\pi$
$109$	2.84676	0.272670	0.136335	+	0.990663i	$0.456468\pi$
$110$	5.94864	0.567180
$111$	0.374200	0.0355175
$112$	−10.7301	−1.01390
$113$	12.6467	1.18970	0.594852	−	0.803835i	$-0.297211\pi$
$113$	12.6467	1.18970	0.594852	+	0.803835i	$0.297211\pi$
$114$	−15.4045	−1.44276
$115$	−0.556648	−0.0519077
$116$	−14.4677	−1.34329
$117$	−5.88481	−0.544051
$118$	−5.26685	−0.484853
$119$	5.35366	0.490769
$120$	−4.33733	−0.395942
$121$	6.46571	0.587792
$122$	6.23638	0.564615
$123$	−2.47710	−0.223353
$124$	−39.8968	−3.58284
$125$	5.23613	0.468334
$126$	−5.13245	−0.457235
$127$	11.9645	1.06167	0.530837	−	0.847474i	$-0.321878\pi$
$127$	11.9645	1.06167	0.530837	+	0.847474i	$0.321878\pi$
$128$	−6.24601	−0.552075
$129$	−0.749916	−0.0660264
$130$	4.30752	0.377795
$131$	6.46420	0.564779	0.282390	−	0.959300i	$-0.408873\pi$
$131$	6.46420	0.564779	0.282390	+	0.959300i	$0.408873\pi$
$132$	−21.3216	−1.85581
$133$	5.68124	0.492626
$134$	8.26977	0.714400
$135$	−2.73949	−0.235778
$136$	41.9116	3.59389
$137$	13.4902	1.15255	0.576274	−	0.817256i	$-0.304506\pi$
$137$	13.4902	1.15255	0.576274	+	0.817256i	$0.304506\pi$
$138$	2.79870	0.238241
$139$	−18.6832	−1.58469	−0.792345	−	0.610074i	$-0.791140\pi$
$139$	−18.6832	−1.58469	−0.792345	+	0.610074i	$0.791140\pi$
$140$	2.67822	0.226351
$141$	0.0580960	0.00489257
$142$	21.1493	1.77481
$143$	12.6473	1.05762
$144$	−20.8657	−1.73881
$145$	1.57113	0.130475
$146$	−3.11876	−0.258110
$147$	−1.02733	−0.0847327
$148$	−1.80889	−0.148690
$149$	−14.6417	−1.19949	−0.599747	−	0.800190i	$-0.704732\pi$
$149$	−14.6417	−1.19949	−0.599747	+	0.800190i	$0.704732\pi$
$150$	−12.7687	−1.04256
$151$	−12.2563	−0.997404	−0.498702	−	0.866774i	$-0.666190\pi$
$151$	−12.2563	−0.997404	−0.498702	+	0.866774i	$0.666190\pi$
$152$	44.4761	3.60749
$153$	10.4107	0.841655
$154$	11.0303	0.888849
$155$	4.33262	0.348004
$156$	−15.4394	−1.23614
$157$	−4.35888	−0.347877	−0.173938	−	0.984757i	$-0.555649\pi$
$157$	−4.35888	−0.347877	−0.173938	+	0.984757i	$0.555649\pi$
$158$	23.8091	1.89415
$159$	−0.866899	−0.0687496
$160$	6.82921	0.539897
$161$	−1.03217	−0.0813465
$162$	−1.62382	−0.127579
$163$	−8.39914	−0.657871	−0.328936	−	0.944352i	$-0.606690\pi$
$163$	−8.39914	−0.657871	−0.328936	+	0.944352i	$0.606690\pi$
$164$	11.9743	0.935039
$165$	2.31543	0.180256
$166$	−32.4642	−2.51971
$167$	17.0343	1.31815	0.659077	−	0.752076i	$-0.270947\pi$
$167$	17.0343	1.31815	0.659077	+	0.752076i	$0.270947\pi$
$168$	−8.04254	−0.620495
$169$	−3.84189	−0.295530
$170$	−7.62036	−0.584455
$171$	11.0477	0.844839
$172$	3.62510	0.276411
$173$	−8.77047	−0.666806	−0.333403	−	0.942784i	$-0.608197\pi$
$173$	−8.77047	−0.666806	−0.333403	+	0.942784i	$0.608197\pi$
$174$	−7.89929	−0.598844
$175$	4.70916	0.355979
$176$	44.8431	3.38018
$177$	−2.05005	−0.154091
$178$	19.4459	1.45753
$179$	5.74291	0.429245	0.214623	−	0.976697i	$-0.431148\pi$
$179$	5.74291	0.429245	0.214623	+	0.976697i	$0.431148\pi$
$180$	5.20805	0.388185
$181$	20.9311	1.55580	0.777899	−	0.628390i	$-0.216286\pi$
$181$	20.9311	1.55580	0.777899	+	0.628390i	$0.216286\pi$
$182$	7.98727	0.592056
$183$	2.42743	0.179441
$184$	−8.08044	−0.595698
$185$	0.196437	0.0144423
$186$	−21.7834	−1.59724
$187$	−22.3740	−1.63615
$188$	−0.280837	−0.0204821
$189$	−5.07973	−0.369496
$190$	−8.08662	−0.586665
$191$	−3.57793	−0.258890	−0.129445	−	0.991587i	$-0.541320\pi$
$191$	−3.57793	−0.258890	−0.129445	+	0.991587i	$0.541320\pi$
$192$	−12.2891	−0.886890
$193$	7.49236	0.539312	0.269656	−	0.962957i	$-0.413090\pi$
$193$	7.49236	0.539312	0.269656	+	0.962957i	$0.413090\pi$
$194$	−7.52399	−0.540191
$195$	1.67665	0.120067
$196$	4.96612	0.354723
$197$	1.05647	0.0752701	0.0376351	−	0.999292i	$-0.488018\pi$
$197$	1.05647	0.0752701	0.0376351	+	0.999292i	$0.488018\pi$
$198$	21.4495	1.52435
$199$	8.02564	0.568923	0.284461	−	0.958687i	$-0.408185\pi$
$199$	8.02564	0.568923	0.284461	+	0.958687i	$0.408185\pi$
$200$	36.8661	2.60682
$201$	3.21890	0.227044
$202$	2.40029	0.168884
$203$	2.91329	0.204473
$204$	27.3135	1.91233
$205$	−1.30036	−0.0908211
$206$	20.5185	1.42959
$207$	−2.00715	−0.139507
$208$	32.4718	2.25151
$209$	−23.7430	−1.64234
$210$	1.46229	0.100908
$211$	8.78398	0.604714	0.302357	−	0.953195i	$-0.402227\pi$
$211$	8.78398	0.604714	0.302357	+	0.953195i	$0.402227\pi$
$212$	4.19060	0.287811
$213$	8.23210	0.564054
$214$	−3.15193	−0.215461
$215$	−0.393670	−0.0268480
$216$	−39.7671	−2.70581
$217$	8.03380	0.545370
$218$	−7.51355	−0.508882
$219$	−1.21394	−0.0820302
$220$	−11.1928	−0.754619
$221$	−16.2014	−1.08983
$222$	−0.987641	−0.0662862
$223$	−7.53063	−0.504289	−0.252144	−	0.967690i	$-0.581136\pi$
$223$	−7.53063	−0.504289	−0.252144	+	0.967690i	$0.581136\pi$
$224$	12.6631	0.846092
$225$	9.15740	0.610494
$226$	−33.3790	−2.22034
$227$	−28.6974	−1.90471	−0.952357	−	0.304985i	$-0.901348\pi$
$227$	−28.6974	−1.90471	−0.952357	+	0.304985i	$0.901348\pi$
$228$	28.9847	1.91956
$229$	−13.4356	−0.887847	−0.443923	−	0.896065i	$-0.646414\pi$
$229$	−13.4356	−0.887847	−0.443923	+	0.896065i	$0.646414\pi$
$230$	1.46918	0.0968751
$231$	4.29341	0.282486
$232$	22.8069	1.49735
$233$	14.2318	0.932358	0.466179	−	0.884690i	$-0.345630\pi$
$233$	14.2318	0.932358	0.466179	+	0.884690i	$0.345630\pi$
$234$	15.5320	1.01536
$235$	0.0304976	0.00198944
$236$	9.90997	0.645084
$237$	9.26739	0.601982
$238$	−14.1301	−0.915920
$239$	9.17582	0.593535	0.296767	−	0.954950i	$-0.404091\pi$
$239$	9.17582	0.593535	0.296767	+	0.954950i	$0.404091\pi$
$240$	5.94486	0.383739
$241$	−10.1567	−0.654252	−0.327126	−	0.944981i	$-0.606080\pi$
$241$	−10.1567	−0.654252	−0.327126	+	0.944981i	$0.606080\pi$
$242$	−17.0652	−1.09699
$243$	−15.8712	−1.01814
$244$	−11.7342	−0.751206
$245$	−0.539298	−0.0344545
$246$	6.53792	0.416843
$247$	−17.1928	−1.09395
$248$	62.8933	3.99373
$249$	−12.6363	−0.800791
$250$	−13.8199	−0.874049
$251$	−14.1760	−0.894779	−0.447390	−	0.894339i	$-0.647646\pi$
$251$	−14.1760	−0.894779	−0.447390	+	0.894339i	$0.647646\pi$
$252$	9.65709	0.608339
$253$	4.31365	0.271197
$254$	−31.5783	−1.98140
$255$	−2.96612	−0.185746
$256$	−7.43905	−0.464940
$257$	4.67637	0.291704	0.145852	−	0.989306i	$-0.453408\pi$
$257$	4.67637	0.291704	0.145852	+	0.989306i	$0.453408\pi$
$258$	1.97928	0.123225
$259$	0.364246	0.0226331
$260$	−8.10492	−0.502646
$261$	5.66516	0.350665
$262$	−17.0612	−1.05405
$263$	14.7988	0.912532	0.456266	−	0.889843i	$-0.349187\pi$
$263$	14.7988	0.912532	0.456266	+	0.889843i	$0.349187\pi$
$264$	33.6114	2.06864
$265$	−0.455080	−0.0279554
$266$	−14.9947	−0.919385
$267$	7.56906	0.463219
$268$	−15.5602	−0.950491
$269$	−17.6102	−1.07371	−0.536857	−	0.843673i	$-0.680389\pi$
$269$	−17.6102	−1.07371	−0.536857	+	0.843673i	$0.680389\pi$
$270$	7.23044	0.440031
$271$	−10.3294	−0.627467	−0.313733	−	0.949511i	$-0.601580\pi$
$271$	−10.3294	−0.627467	−0.313733	+	0.949511i	$0.601580\pi$
$272$	−57.4452	−3.48313
$273$	3.10894	0.188162
$274$	−35.6053	−2.15100
$275$	−19.6805	−1.18678
$276$	−5.26597	−0.316974
$277$	20.0671	1.20572	0.602858	−	0.797849i	$-0.294029\pi$
$277$	20.0671	1.20572	0.602858	+	0.797849i	$0.294029\pi$
$278$	49.3113	2.95750
$279$	15.6225	0.935294
$280$	−4.22195	−0.252309
$281$	−0.372317	−0.0222106	−0.0111053	−	0.999938i	$-0.503535\pi$
$281$	−0.372317	−0.0222106	−0.0111053	+	0.999938i	$0.503535\pi$
$282$	−0.153335	−0.00913097
$283$	9.31474	0.553704	0.276852	−	0.960913i	$-0.410709\pi$
$283$	9.31474	0.553704	0.276852	+	0.960913i	$0.410709\pi$
$284$	−39.7940	−2.36134
$285$	−3.14761	−0.186449
$286$	−33.3804	−1.97382
$287$	−2.41121	−0.142329
$288$	24.6247	1.45102
$289$	11.6617	0.685981
$290$	−4.14675	−0.243505
$291$	−2.92862	−0.171679
$292$	5.86817	0.343409
$293$	−0.787769	−0.0460220	−0.0230110	−	0.999735i	$-0.507325\pi$
$293$	−0.787769	−0.0460220	−0.0230110	+	0.999735i	$0.507325\pi$
$294$	2.71147	0.158136
$295$	−1.07618	−0.0626575
$296$	2.85153	0.165742
$297$	21.2292	1.23184
$298$	38.6444	2.23861
$299$	3.12359	0.180642
$300$	24.0253	1.38710
$301$	−0.729966	−0.0420746
$302$	32.3486	1.86145
$303$	0.934282	0.0536731
$304$	−60.9601	−3.49630
$305$	1.27428	0.0729653
$306$	−27.4774	−1.57078
$307$	−16.8160	−0.959738	−0.479869	−	0.877340i	$-0.659316\pi$
$307$	−16.8160	−0.959738	−0.479869	+	0.877340i	$0.659316\pi$
$308$	−20.7544	−1.18259
$309$	7.98656	0.454339
$310$	−11.4352	−0.649478
$311$	−1.42122	−0.0805901	−0.0402951	−	0.999188i	$-0.512830\pi$
$311$	−1.42122	−0.0805901	−0.0402951	+	0.999188i	$0.512830\pi$
$312$	24.3386	1.37790
$313$	−7.13820	−0.403475	−0.201737	−	0.979440i	$-0.564659\pi$
$313$	−7.13820	−0.403475	−0.201737	+	0.979440i	$0.564659\pi$
$314$	11.5046	0.649241
$315$	−1.04872	−0.0590885
$316$	−44.7986	−2.52012
$317$	−21.0305	−1.18119	−0.590596	−	0.806967i	$-0.701107\pi$
$317$	−21.0305	−1.18119	−0.590596	+	0.806967i	$0.701107\pi$
$318$	2.28804	0.128307
$319$	−12.1752	−0.681681
$320$	−6.45119	−0.360633
$321$	−1.22685	−0.0684759
$322$	2.72425	0.151817
$323$	30.4154	1.69236
$324$	3.05534	0.169741
$325$	−14.2510	−0.790505
$326$	22.1682	1.22778
$327$	−2.92455	−0.161728
$328$	−18.8764	−1.04227
$329$	0.0565505	0.00311773
$330$	−6.11121	−0.336411
$331$	22.4631	1.23468	0.617341	−	0.786696i	$-0.288210\pi$
$331$	22.4631	1.23468	0.617341	+	0.786696i	$0.288210\pi$
$332$	61.0838	3.35241
$333$	0.708310	0.0388152
$334$	−44.9593	−2.46006
$335$	1.68977	0.0923219
$336$	11.0233	0.601371
$337$	−21.5526	−1.17405	−0.587024	−	0.809570i	$-0.699700\pi$
$337$	−21.5526	−1.17405	−0.587024	+	0.809570i	$0.699700\pi$
$338$	10.1400	0.551546
$339$	−12.9923	−0.705647
$340$	14.3383	0.777602
$341$	−33.5749	−1.81818
$342$	−29.1587	−1.57672
$343$	−1.00000	−0.0539949
$344$	−5.71461	−0.308111
$345$	0.571861	0.0307879
$346$	23.1483	1.24446
$347$	−16.8165	−0.902757	−0.451378	−	0.892333i	$-0.649067\pi$
$347$	−16.8165	−0.902757	−0.451378	+	0.892333i	$0.649067\pi$
$348$	14.8631	0.796746
$349$	−18.2521	−0.977015	−0.488507	−	0.872560i	$-0.662458\pi$
$349$	−18.2521	−0.977015	−0.488507	+	0.872560i	$0.662458\pi$
$350$	−12.4291	−0.664362
$351$	15.3725	0.820521
$352$	−52.9218	−2.82074
$353$	16.3031	0.867725	0.433862	−	0.900979i	$-0.357150\pi$
$353$	16.3031	0.867725	0.433862	+	0.900979i	$0.357150\pi$
$354$	5.41078	0.287580
$355$	4.32145	0.229359
$356$	−36.5889	−1.93921
$357$	−5.49997	−0.291089
$358$	−15.1575	−0.801098
$359$	33.7852	1.78311	0.891557	−	0.452908i	$-0.149613\pi$
$359$	33.7852	1.78311	0.891557	+	0.452908i	$0.149613\pi$
$360$	−8.20997	−0.432704
$361$	13.2764	0.698760
$362$	−55.2443	−2.90358
$363$	−6.64241	−0.348636
$364$	−15.0286	−0.787715
$365$	−0.637258	−0.0333556
$366$	−6.40681	−0.334890
$367$	−28.3033	−1.47742	−0.738711	−	0.674022i	$-0.764565\pi$
$367$	−28.3033	−1.47742	−0.738711	+	0.674022i	$0.764565\pi$
$368$	11.0753	0.577339
$369$	−4.68883	−0.244091
$370$	−0.518464	−0.0269537
$371$	−0.843838	−0.0438099
$372$	40.9871	2.12508
$373$	−11.8198	−0.612004	−0.306002	−	0.952031i	$-0.598991\pi$
$373$	−11.8198	−0.612004	−0.306002	+	0.952031i	$0.598991\pi$
$374$	59.0526	3.05354
$375$	−5.37923	−0.277782
$376$	0.442711	0.0228311
$377$	−8.81630	−0.454062
$378$	13.4071	0.689588
$379$	14.7023	0.755207	0.377603	−	0.925967i	$-0.376748\pi$
$379$	14.7023	0.755207	0.377603	+	0.925967i	$0.376748\pi$
$380$	15.2156	0.780543
$381$	−12.2914	−0.629709
$382$	9.44338	0.483166
$383$	−1.40006	−0.0715396	−0.0357698	−	0.999360i	$-0.511388\pi$
$383$	−1.40006	−0.0715396	−0.0357698	+	0.999360i	$0.511388\pi$
$384$	6.41671	0.327451
$385$	2.25384	0.114866
$386$	−19.7749	−1.00652
$387$	−1.41949	−0.0721567
$388$	14.1570	0.718711
$389$	16.0301	0.812761	0.406380	−	0.913704i	$-0.366791\pi$
$389$	16.0301	0.812761	0.406380	+	0.913704i	$0.366791\pi$
$390$	−4.42524	−0.224081
$391$	−5.52589	−0.279456
$392$	−7.82859	−0.395404
$393$	−6.64086	−0.334987
$394$	−2.78837	−0.140476
$395$	4.86493	0.244781
$396$	−40.3589	−2.02811
$397$	−11.9866	−0.601592	−0.300796	−	0.953688i	$-0.597252\pi$
$397$	−11.9866	−0.601592	−0.300796	+	0.953688i	$0.597252\pi$
$398$	−21.1824	−1.06178
$399$	−5.83650	−0.292190
$400$	−50.5296	−2.52648
$401$	28.5087	1.42366	0.711828	−	0.702354i	$-0.247867\pi$
$401$	28.5087	1.42366	0.711828	+	0.702354i	$0.247867\pi$
$402$	−8.49578	−0.423731
$403$	−24.3122	−1.21108
$404$	−4.51633	−0.224696
$405$	−0.331796	−0.0164871
$406$	−7.68915	−0.381606
$407$	−1.52226	−0.0754554
$408$	−43.0570	−2.13164
$409$	14.8281	0.733203	0.366601	−	0.930378i	$-0.380521\pi$
$409$	14.8281	0.733203	0.366601	+	0.930378i	$0.380521\pi$
$410$	3.43209	0.169499
$411$	−13.8589	−0.683609
$412$	−38.6071	−1.90203
$413$	−1.99552	−0.0981929
$414$	5.29756	0.260361
$415$	−6.63343	−0.325622
$416$	−38.3217	−1.87888
$417$	19.1938	0.939925
$418$	62.6659	3.06509
$419$	11.4835	0.561007	0.280504	−	0.959853i	$-0.409499\pi$
$419$	11.4835	0.561007	0.280504	+	0.959853i	$0.409499\pi$
$420$	−2.75141	−0.134255
$421$	34.2758	1.67050	0.835251	−	0.549869i	$-0.185322\pi$
$421$	34.2758	1.67050	0.835251	+	0.549869i	$0.185322\pi$
$422$	−23.1839	−1.12858
$423$	0.109968	0.00534682
$424$	−6.60606	−0.320819
$425$	25.2112	1.22292
$426$	−21.7273	−1.05269
$427$	2.36286	0.114347
$428$	5.93058	0.286666
$429$	−12.9929	−0.627303
$430$	1.03903	0.0501064
$431$	34.3490	1.65453	0.827266	−	0.561810i	$-0.189895\pi$
$431$	34.3490	1.65453	0.827266	+	0.561810i	$0.189895\pi$
$432$	54.5059	2.62241
$433$	21.4448	1.03057	0.515287	−	0.857018i	$-0.327685\pi$
$433$	21.4448	1.03057	0.515287	+	0.857018i	$0.327685\pi$
$434$	−21.2039	−1.01782
$435$	−1.61407	−0.0773886
$436$	14.1373	0.677055
$437$	−5.86401	−0.280514
$438$	3.20399	0.153093
$439$	−0.854042	−0.0407612	−0.0203806	−	0.999792i	$-0.506488\pi$
$439$	−0.854042	−0.0407612	−0.0203806	+	0.999792i	$0.506488\pi$
$440$	17.6444	0.841162
$441$	−1.94460	−0.0925998
$442$	42.7611	2.03394
$443$	12.2705	0.582991	0.291495	−	0.956572i	$-0.405847\pi$
$443$	12.2705	0.582991	0.291495	+	0.956572i	$0.405847\pi$
$444$	1.85832	0.0881920
$445$	3.97339	0.188357
$446$	19.8759	0.941151
$447$	15.0418	0.711454
$448$	−11.9622	−0.565161
$449$	25.8133	1.21820	0.609102	−	0.793092i	$-0.291530\pi$
$449$	25.8133	1.21820	0.609102	+	0.793092i	$0.291530\pi$
$450$	−24.1695	−1.13936
$451$	10.0769	0.474504
$452$	62.8051	2.95410
$453$	12.5913	0.591589
$454$	75.7422	3.55476
$455$	1.63204	0.0765114
$456$	−45.6916	−2.13970
$457$	−21.1581	−0.989735	−0.494868	−	0.868968i	$-0.664783\pi$
$457$	−21.1581	−0.989735	−0.494868	+	0.868968i	$0.664783\pi$
$458$	35.4610	1.65698
$459$	−27.1951	−1.26936
$460$	−2.76438	−0.128890
$461$	−20.9387	−0.975212	−0.487606	−	0.873064i	$-0.662130\pi$
$461$	−20.9387	−0.975212	−0.487606	+	0.873064i	$0.662130\pi$
$462$	−11.3318	−0.527202
$463$	−10.9014	−0.506632	−0.253316	−	0.967384i	$-0.581521\pi$
$463$	−10.9014	−0.506632	−0.253316	+	0.967384i	$0.581521\pi$
$464$	−31.2598	−1.45120
$465$	−4.45102	−0.206411
$466$	−37.5627	−1.74006
$467$	13.3908	0.619654	0.309827	−	0.950793i	$-0.399729\pi$
$467$	13.3908	0.619654	0.309827	+	0.950793i	$0.399729\pi$
$468$	−29.2246	−1.35091
$469$	3.13327	0.144681
$470$	−0.0804936	−0.00371289
$471$	4.47801	0.206336
$472$	−15.6221	−0.719064
$473$	3.05068	0.140270
$474$	−24.4598	−1.12348
$475$	26.7538	1.22755
$476$	26.5869	1.21861
$477$	−1.64092	−0.0751327
$478$	−24.2181	−1.10771
$479$	−6.39004	−0.291968	−0.145984	−	0.989287i	$-0.546635\pi$
$479$	−6.39004	−0.291968	−0.145984	+	0.989287i	$0.546635\pi$
$480$	−7.01585	−0.320228
$481$	−1.10229	−0.0502603
$482$	26.8070	1.22103
$483$	1.06038	0.0482489
$484$	32.1095	1.45952
$485$	−1.53738	−0.0698090
$486$	41.8896	1.90015
$487$	0.604546	0.0273946	0.0136973	−	0.999906i	$-0.495640\pi$
$487$	0.604546	0.0273946	0.0136973	+	0.999906i	$0.495640\pi$
$488$	18.4978	0.837358
$489$	8.62867	0.390202
$490$	1.42339	0.0643023
$491$	−39.1523	−1.76692	−0.883459	−	0.468508i	$-0.844792\pi$
$491$	−39.1523	−1.76692	−0.883459	+	0.468508i	$0.844792\pi$
$492$	−12.3016	−0.554599
$493$	15.5967	0.702442
$494$	45.3776	2.04163
$495$	4.38280	0.196992
$496$	−86.2033	−3.87064
$497$	8.01311	0.359437
$498$	33.3514	1.49451
$499$	−14.1272	−0.632418	−0.316209	−	0.948689i	$-0.602410\pi$
$499$	−14.1272	−0.632418	−0.316209	+	0.948689i	$0.602410\pi$
$500$	26.0032	1.16290
$501$	−17.4998	−0.781834
$502$	37.4152	1.66992
$503$	3.72408	0.166049	0.0830243	−	0.996548i	$-0.473542\pi$
$503$	3.72408	0.166049	0.0830243	+	0.996548i	$0.473542\pi$
$504$	−15.2234	−0.678106
$505$	0.490453	0.0218249
$506$	−11.3852	−0.506133
$507$	3.94688	0.175287
$508$	59.4169	2.63620
$509$	−0.145577	−0.00645260	−0.00322630	−	0.999995i	$-0.501027\pi$
$509$	−0.145577	−0.00645260	−0.00322630	+	0.999995i	$0.501027\pi$
$510$	7.82861	0.346657
$511$	−1.18164	−0.0522728
$512$	32.1262	1.41979
$513$	−28.8591	−1.27416
$514$	−12.3425	−0.544406
$515$	4.19256	0.184746
$516$	−3.72417	−0.163947
$517$	−0.236336	−0.0103940
$518$	−0.961368	−0.0422401
$519$	9.01016	0.395502
$520$	12.7766	0.560291
$521$	26.0609	1.14175	0.570873	−	0.821038i	$-0.306605\pi$
$521$	26.0609	1.14175	0.570873	+	0.821038i	$0.306605\pi$
$522$	−14.9523	−0.654444
$523$	38.0924	1.66566	0.832832	−	0.553525i	$-0.186718\pi$
$523$	38.0924	1.66566	0.832832	+	0.553525i	$0.186718\pi$
$524$	32.1019	1.40238
$525$	−4.83785	−0.211141
$526$	−39.0590	−1.70305
$527$	43.0102	1.87356
$528$	−46.0687	−2.00488
$529$	−21.9346	−0.953679
$530$	1.20111	0.0521730
$531$	−3.88047	−0.168398
$532$	28.2137	1.22322
$533$	7.29689	0.316063
$534$	−19.9773	−0.864503
$535$	−0.644035	−0.0278441
$536$	24.5291	1.05950
$537$	−5.89986	−0.254598
$538$	46.4794	2.00387
$539$	4.17920	0.180011
$540$	−13.6046	−0.585449
$541$	10.2065	0.438810	0.219405	−	0.975634i	$-0.429588\pi$
$541$	10.2065	0.438810	0.219405	+	0.975634i	$0.429588\pi$
$542$	27.2628	1.17104
$543$	−21.5031	−0.922788
$544$	67.7942	2.90665
$545$	−1.53525	−0.0657629
$546$	−8.20555	−0.351165
$547$	−23.6600	−1.01163	−0.505814	−	0.862643i	$-0.668808\pi$
$547$	−23.6600	−1.01163	−0.505814	+	0.862643i	$0.668808\pi$
$548$	66.9941	2.86184
$549$	4.59480	0.196101
$550$	51.9436	2.21488
$551$	16.5511	0.705099
$552$	8.30127	0.353326
$553$	9.02086	0.383606
$554$	−52.9639	−2.25022
$555$	−0.201805	−0.00856617
$556$	−92.7830	−3.93488
$557$	−25.8088	−1.09355	−0.546777	−	0.837278i	$-0.684145\pi$
$557$	−25.8088	−1.09355	−0.546777	+	0.837278i	$0.684145\pi$
$558$	−41.2331	−1.74554
$559$	2.20905	0.0934329
$560$	5.78671	0.244533
$561$	22.9855	0.970448
$562$	0.982672	0.0414515
$563$	13.1483	0.554136	0.277068	−	0.960850i	$-0.410637\pi$
$563$	13.1483	0.554136	0.277068	+	0.960850i	$0.410637\pi$
$564$	0.288511	0.0121485
$565$	−6.82036	−0.286935
$566$	−24.5848	−1.03337
$567$	−0.615236	−0.0258375
$568$	62.7313	2.63215
$569$	−34.2971	−1.43781	−0.718905	−	0.695108i	$-0.755356\pi$
$569$	−34.2971	−1.43781	−0.718905	+	0.695108i	$0.755356\pi$
$570$	8.30762	0.347968
$571$	29.1544	1.22007	0.610036	−	0.792374i	$-0.291155\pi$
$571$	29.1544	1.22007	0.610036	+	0.792374i	$0.291155\pi$
$572$	62.8077	2.62612
$573$	3.67571	0.153555
$574$	6.36400	0.265628
$575$	−4.86066	−0.202703
$576$	−23.2616	−0.969235
$577$	28.3930	1.18202	0.591009	−	0.806665i	$-0.298730\pi$
$577$	28.3930	1.18202	0.591009	+	0.806665i	$0.298730\pi$
$578$	−30.7791	−1.28024
$579$	−7.69712	−0.319881
$580$	7.80242	0.323978
$581$	−12.3001	−0.510295
$582$	7.72962	0.320403
$583$	3.52657	0.146055
$584$	−9.25060	−0.382792
$585$	3.17367	0.131215
$586$	2.07919	0.0858906
$587$	29.3087	1.20970	0.604851	−	0.796339i	$-0.293233\pi$
$587$	29.3087	1.20970	0.604851	+	0.796339i	$0.293233\pi$
$588$	−5.10184	−0.210396
$589$	45.6419	1.88064
$590$	2.84040	0.116937
$591$	−1.08534	−0.0446449
$592$	−3.90838	−0.160634
$593$	8.51224	0.349556	0.174778	−	0.984608i	$-0.444079\pi$
$593$	8.51224	0.349556	0.174778	+	0.984608i	$0.444079\pi$
$594$	−56.0311	−2.29898
$595$	−2.88722	−0.118364
$596$	−72.7123	−2.97841
$597$	−8.24498	−0.337444
$598$	−8.24423	−0.337132
$599$	40.5777	1.65796	0.828980	−	0.559278i	$-0.188921\pi$
$599$	40.5777	1.65796	0.828980	+	0.559278i	$0.188921\pi$
$600$	−37.8736	−1.54618
$601$	−14.1173	−0.575856	−0.287928	−	0.957652i	$-0.592966\pi$
$601$	−14.1173	−0.575856	−0.287928	+	0.957652i	$0.592966\pi$
$602$	1.92663	0.0785236
$603$	6.09295	0.248124
$604$	−60.8662	−2.47661
$605$	−3.48695	−0.141765
$606$	−2.46589	−0.100170
$607$	4.60522	0.186920	0.0934600	−	0.995623i	$-0.470207\pi$
$607$	4.60522	0.186920	0.0934600	+	0.995623i	$0.470207\pi$
$608$	71.9423	2.91765
$609$	−2.99290	−0.121279
$610$	−3.36327	−0.136175
$611$	−0.171135	−0.00692340
$612$	51.7008	2.08988
$613$	−6.03353	−0.243692	−0.121846	−	0.992549i	$-0.538881\pi$
$613$	−6.03353	−0.243692	−0.121846	+	0.992549i	$0.538881\pi$
$614$	44.3831	1.79116
$615$	1.33590	0.0538686
$616$	32.7172	1.31822
$617$	18.6465	0.750681	0.375340	−	0.926887i	$-0.377526\pi$
$617$	18.6465	0.750681	0.375340	+	0.926887i	$0.377526\pi$
$618$	−21.0792	−0.847931
$619$	12.8200	0.515280	0.257640	−	0.966241i	$-0.417055\pi$
$619$	12.8200	0.515280	0.257640	+	0.966241i	$0.417055\pi$
$620$	21.5163	0.864114
$621$	5.24315	0.210400
$622$	3.75109	0.150405
$623$	7.36771	0.295181
$624$	−33.3592	−1.33544
$625$	20.7219	0.828878
$626$	18.8401	0.753003
$627$	24.3919	0.974118
$628$	−21.6467	−0.863798
$629$	1.95005	0.0777535
$630$	2.76792	0.110277
$631$	5.18193	0.206289	0.103145	−	0.994666i	$-0.467110\pi$
$631$	5.18193	0.206289	0.103145	+	0.994666i	$0.467110\pi$
$632$	70.6206	2.80914
$633$	−9.02404	−0.358673
$634$	55.5067	2.20445
$635$	−6.45241	−0.256056
$636$	−4.30512	−0.170709
$637$	3.02624	0.119904
$638$	32.1345	1.27222
$639$	15.5822	0.616424
$640$	3.36846	0.133150
$641$	7.56894	0.298955	0.149478	−	0.988765i	$-0.452241\pi$
$641$	7.56894	0.298955	0.149478	+	0.988765i	$0.452241\pi$
$642$	3.23806	0.127796
$643$	25.6155	1.01018	0.505089	−	0.863067i	$-0.331460\pi$
$643$	25.6155	1.01018	0.505089	+	0.863067i	$0.331460\pi$
$644$	−5.12588	−0.201988
$645$	0.404428	0.0159243
$646$	−80.2766	−3.15844
$647$	33.8912	1.33240	0.666200	−	0.745773i	$-0.267920\pi$
$647$	33.8912	1.33240	0.666200	+	0.745773i	$0.267920\pi$
$648$	−4.81643	−0.189207
$649$	8.33966	0.327360
$650$	37.6133	1.47532
$651$	−8.25336	−0.323475
$652$	−41.7111	−1.63353
$653$	−1.34172	−0.0525057	−0.0262529	−	0.999655i	$-0.508358\pi$
$653$	−1.34172	−0.0525057	−0.0262529	+	0.999655i	$0.508358\pi$
$654$	7.71889	0.301833
$655$	−3.48613	−0.136214
$656$	25.8725	1.01015
$657$	−2.29782	−0.0896464
$658$	−0.149256	−0.00581861
$659$	5.02651	0.195805	0.0979026	−	0.995196i	$-0.468787\pi$
$659$	5.02651	0.195805	0.0979026	+	0.995196i	$0.468787\pi$
$660$	11.4987	0.447586
$661$	−24.0906	−0.937017	−0.468509	−	0.883459i	$-0.655209\pi$
$661$	−24.0906	−0.937017	−0.468509	+	0.883459i	$0.655209\pi$
$662$	−59.2876	−2.30428
$663$	16.6442	0.646408
$664$	−96.2926	−3.73688
$665$	−3.06388	−0.118812
$666$	−1.86947	−0.0724406
$667$	−3.00701	−0.116432
$668$	84.5943	3.27305
$669$	7.73644	0.299108
$670$	−4.45988	−0.172300
$671$	−9.87485	−0.381214
$672$	−13.0092	−0.501842
$673$	41.8407	1.61284	0.806421	−	0.591342i	$-0.201402\pi$
$673$	41.8407	1.61284	0.806421	+	0.591342i	$0.201402\pi$
$674$	56.8848	2.19112
$675$	−23.9212	−0.920729
$676$	−19.0793	−0.733817
$677$	34.0974	1.31047	0.655235	−	0.755425i	$-0.272570\pi$
$677$	34.0974	1.31047	0.655235	+	0.755425i	$0.272570\pi$
$678$	34.2912	1.31695
$679$	−2.85071	−0.109400
$680$	−22.6029	−0.866780
$681$	29.4817	1.12974
$682$	88.6155	3.39326
$683$	−22.3754	−0.856170	−0.428085	−	0.903738i	$-0.640812\pi$
$683$	−22.3754	−0.856170	−0.428085	+	0.903738i	$0.640812\pi$
$684$	54.8642	2.09778
$685$	−7.27526	−0.277973
$686$	2.63934	0.100770
$687$	13.8027	0.526607
$688$	7.83260	0.298615
$689$	2.55365	0.0972865
$690$	−1.50933	−0.0574594
$691$	42.1790	1.60457	0.802283	−	0.596944i	$-0.203618\pi$
$691$	42.1790	1.60457	0.802283	+	0.596944i	$0.203618\pi$
$692$	−43.5552	−1.65572
$693$	8.12685	0.308714
$694$	44.3844	1.68481
$695$	10.0758	0.382198
$696$	−23.4302	−0.888120
$697$	−12.9088	−0.488955
$698$	48.1736	1.82340
$699$	−14.6208	−0.553008
$700$	23.3862	0.883916
$701$	−32.0734	−1.21139	−0.605697	−	0.795695i	$-0.707106\pi$
$701$	−32.0734	−1.21139	−0.605697	+	0.795695i	$0.707106\pi$
$702$	−40.5731	−1.53133
$703$	2.06937	0.0780476
$704$	49.9924	1.88416
$705$	−0.0313311	−0.00118000
$706$	−43.0293	−1.61943
$707$	0.909428	0.0342026
$708$	−10.1808	−0.382618
$709$	4.69473	0.176314	0.0881571	−	0.996107i	$-0.471902\pi$
$709$	4.69473	0.176314	0.0881571	+	0.996107i	$0.471902\pi$
$710$	−11.4058	−0.428052
$711$	17.5419	0.657873
$712$	57.6788	2.16160
$713$	−8.29226	−0.310547
$714$	14.5163	0.543259
$715$	−6.82064	−0.255078
$716$	28.5200	1.06584
$717$	−9.42659	−0.352042
$718$	−89.1706	−3.32782
$719$	39.8687	1.48685	0.743426	−	0.668818i	$-0.233200\pi$
$719$	39.8687	1.48685	0.743426	+	0.668818i	$0.233200\pi$
$720$	11.2528	0.419368
$721$	7.77410	0.289523
$722$	−35.0411	−1.30409
$723$	10.4343	0.388056
$724$	103.946	3.86314
$725$	13.7191	0.509516
$726$	17.5316	0.650658
$727$	19.7320	0.731820	0.365910	−	0.930650i	$-0.380758\pi$
$727$	19.7320	0.731820	0.365910	+	0.930650i	$0.380758\pi$
$728$	23.6912	0.878053
$729$	14.4593	0.535528
$730$	1.68194	0.0622514
$731$	−3.90799	−0.144542
$732$	12.0549	0.445562
$733$	50.5514	1.86716	0.933578	−	0.358373i	$-0.116668\pi$
$733$	50.5514	1.86716	0.933578	+	0.358373i	$0.116668\pi$
$734$	74.7021	2.75731
$735$	0.554037	0.0204360
$736$	−13.0705	−0.481786
$737$	−13.0946	−0.482345
$738$	12.3754	0.455545
$739$	32.6976	1.20280	0.601401	−	0.798948i	$-0.294610\pi$
$739$	32.6976	1.20280	0.601401	+	0.798948i	$0.294610\pi$
$740$	0.975529	0.0358612
$741$	17.6626	0.648853
$742$	2.22717	0.0817622
$743$	10.1432	0.372118	0.186059	−	0.982539i	$-0.440428\pi$
$743$	10.1432	0.372118	0.186059	+	0.982539i	$0.440428\pi$
$744$	−64.6121	−2.36880
$745$	7.89624	0.289296
$746$	31.1964	1.14218
$747$	−23.9188	−0.875141
$748$	−111.112	−4.06266
$749$	−1.19421	−0.0436355
$750$	14.1976	0.518424
$751$	1.98119	0.0722945	0.0361473	−	0.999346i	$-0.488491\pi$
$751$	1.98119	0.0722945	0.0361473	+	0.999346i	$0.488491\pi$
$752$	−0.606792	−0.0221274
$753$	14.5634	0.530719
$754$	23.2692	0.847415
$755$	6.60980	0.240555
$756$	−25.2265	−0.917479
$757$	53.9534	1.96097	0.980485	−	0.196592i	$-0.0629873\pi$
$757$	53.9534	1.96097	0.980485	+	0.196592i	$0.0629873\pi$
$758$	−38.8044	−1.40944
$759$	−4.43154	−0.160855
$760$	−23.9859	−0.870059
$761$	−27.6398	−1.00194	−0.500970	−	0.865464i	$-0.667023\pi$
$761$	−27.6398	−1.00194	−0.500970	+	0.865464i	$0.667023\pi$
$762$	32.4413	1.17522
$763$	−2.84676	−0.103059
$764$	−17.7684	−0.642839
$765$	−5.61447	−0.202992
$766$	3.69523	0.133514
$767$	6.03891	0.218052
$768$	7.64235	0.275769
$769$	−0.608429	−0.0219405	−0.0109703	−	0.999940i	$-0.503492\pi$
$769$	−0.608429	−0.0219405	−0.0109703	+	0.999940i	$0.503492\pi$
$770$	−5.94864	−0.214374
$771$	−4.80418	−0.173018
$772$	37.2079	1.33914
$773$	−25.1056	−0.902985	−0.451492	−	0.892275i	$-0.649108\pi$
$773$	−25.1056	−0.902985	−0.451492	+	0.892275i	$0.649108\pi$
$774$	3.74651	0.134666
$775$	37.8324	1.35898
$776$	−22.3170	−0.801135
$777$	−0.374200	−0.0134244
$778$	−42.3090	−1.51685
$779$	−13.6986	−0.490805
$780$	8.32642	0.298134
$781$	−33.4884	−1.19831
$782$	14.5847	0.521548
$783$	−14.7987	−0.528862
$784$	10.7301	0.383217
$785$	2.35074	0.0839015
$786$	17.5275	0.625184
$787$	−7.68707	−0.274014	−0.137007	−	0.990570i	$-0.543748\pi$
$787$	−7.68707	−0.274014	−0.137007	+	0.990570i	$0.543748\pi$
$788$	5.24654	0.186900
$789$	−15.2032	−0.541249
$790$	−12.8402	−0.456834
$791$	−12.6467	−0.449666
$792$	63.6218	2.26070
$793$	−7.15056	−0.253924
$794$	31.6368	1.12275
$795$	0.467517	0.0165811
$796$	39.8563	1.41267
$797$	10.1116	0.358171	0.179085	−	0.983834i	$-0.442686\pi$
$797$	10.1116	0.358171	0.179085	+	0.983834i	$0.442686\pi$
$798$	15.4045	0.545314
$799$	0.302752	0.0107106
$800$	59.6328	2.10834
$801$	14.3272	0.506227
$802$	−75.2442	−2.65696
$803$	4.93832	0.174270
$804$	15.9854	0.563763
$805$	0.556648	0.0196193
$806$	64.1681	2.26023
$807$	18.0915	0.636851
$808$	7.11954	0.250465
$809$	22.5905	0.794239	0.397120	−	0.917767i	$-0.370010\pi$
$809$	22.5905	0.794239	0.397120	+	0.917767i	$0.370010\pi$
$810$	0.875722	0.0307697
$811$	−7.71155	−0.270789	−0.135394	−	0.990792i	$-0.543230\pi$
$811$	−7.71155	−0.270789	−0.135394	+	0.990792i	$0.543230\pi$
$812$	14.4677	0.507717
$813$	10.6117	0.372168
$814$	4.01775	0.140822
$815$	4.52964	0.158666
$816$	59.0151	2.06594
$817$	−4.14711	−0.145089
$818$	−39.1364	−1.36837
$819$	5.88481	0.205632
$820$	−6.45774	−0.225514
$821$	12.6310	0.440826	0.220413	−	0.975407i	$-0.429260\pi$
$821$	12.6310	0.440826	0.220413	+	0.975407i	$0.429260\pi$
$822$	36.5784	1.27582
$823$	−10.1703	−0.354514	−0.177257	−	0.984165i	$-0.556722\pi$
$823$	−10.1703	−0.354514	−0.177257	+	0.984165i	$0.556722\pi$
$824$	60.8602	2.12017
$825$	20.2184	0.703913
$826$	5.26685	0.183257
$827$	−18.2949	−0.636177	−0.318088	−	0.948061i	$-0.603041\pi$
$827$	−18.2949	−0.636177	−0.318088	+	0.948061i	$0.603041\pi$
$828$	−9.96776	−0.346404
$829$	50.9213	1.76857	0.884284	−	0.466949i	$-0.154647\pi$
$829$	50.9213	1.76857	0.884284	+	0.466949i	$0.154647\pi$
$830$	17.5079	0.607708
$831$	−20.6155	−0.715145
$832$	36.2005	1.25502
$833$	−5.35366	−0.185493
$834$	−50.6590	−1.75418
$835$	−9.18657	−0.317914
$836$	−117.911	−4.07802
$837$	−40.8095	−1.41058
$838$	−30.3089	−1.04700
$839$	−34.8510	−1.20319	−0.601596	−	0.798801i	$-0.705468\pi$
$839$	−34.8510	−1.20319	−0.601596	+	0.798801i	$0.705468\pi$
$840$	4.33733	0.149652
$841$	−20.5128	−0.707337
$842$	−90.4656	−3.11765
$843$	0.382492	0.0131737
$844$	43.6223	1.50154
$845$	2.07192	0.0712763
$846$	−0.290243	−0.00997875
$847$	−6.46571	−0.222165
$848$	9.05445	0.310931
$849$	−9.56930	−0.328418
$850$	−66.5410	−2.28234
$851$	−0.375964	−0.0128879
$852$	40.8816	1.40058
$853$	10.7520	0.368140	0.184070	−	0.982913i	$-0.441073\pi$
$853$	10.7520	0.368140	0.184070	+	0.982913i	$0.441073\pi$
$854$	−6.23638	−0.213405
$855$	−5.95801	−0.203760
$856$	−9.34898	−0.319541
$857$	−2.76567	−0.0944733	−0.0472367	−	0.998884i	$-0.515041\pi$
$857$	−2.76567	−0.0944733	−0.0472367	+	0.998884i	$0.515041\pi$
$858$	34.2927	1.17073
$859$	1.00000	0.0341196
$859$	1.00000	0.0341196
$860$	−1.95501	−0.0666653
$861$	2.47710	0.0844195
$862$	−90.6586	−3.08785
$863$	30.8444	1.04996	0.524978	−	0.851116i	$-0.324074\pi$
$863$	30.8444	1.04996	0.524978	+	0.851116i	$0.324074\pi$
$864$	−64.3253	−2.18839
$865$	4.72990	0.160821
$866$	−56.6002	−1.92335
$867$	−11.9804	−0.406875
$868$	39.8968	1.35419
$869$	−37.7000	−1.27888
$870$	4.26007	0.144430
$871$	−9.48203	−0.321286
$872$	−22.2861	−0.754702
$873$	−5.54348	−0.187618
$874$	15.4771	0.523521
$875$	−5.23613	−0.177014
$876$	−6.02855	−0.203686
$877$	−2.91132	−0.0983082	−0.0491541	−	0.998791i	$-0.515653\pi$
$877$	−2.91132	−0.0983082	−0.0491541	+	0.998791i	$0.515653\pi$
$878$	2.25411	0.0760725
$879$	0.809298	0.0272969
$880$	−24.1838	−0.815237
$881$	−30.8287	−1.03865	−0.519323	−	0.854578i	$-0.673816\pi$
$881$	−30.8287	−1.03865	−0.519323	+	0.854578i	$0.673816\pi$
$882$	5.13245	0.172819
$883$	0.851044	0.0286399	0.0143199	−	0.999897i	$-0.495442\pi$
$883$	0.851044	0.0286399	0.0143199	+	0.999897i	$0.495442\pi$
$884$	−80.4583	−2.70610
$885$	1.10559	0.0371640
$886$	−32.3861	−1.08803
$887$	−23.4160	−0.786232	−0.393116	−	0.919489i	$-0.628603\pi$
$887$	−23.4160	−0.786232	−0.393116	+	0.919489i	$0.628603\pi$
$888$	−2.92946	−0.0983062
$889$	−11.9645	−0.401275
$890$	−10.4871	−0.351530
$891$	2.57120	0.0861383
$892$	−37.3980	−1.25218
$893$	0.321277	0.0107511
$894$	−39.7005	−1.32778
$895$	−3.09714	−0.103526
$896$	6.24601	0.208665
$897$	−3.20896	−0.107144
$898$	−68.1300	−2.27353
$899$	23.4048	0.780593
$900$	45.4767	1.51589
$901$	−4.51762	−0.150504
$902$	−26.5964	−0.885564
$903$	0.749916	0.0249556
$904$	−99.0060	−3.29289
$905$	−11.2881	−0.375230
$906$	−33.2326	−1.10408
$907$	2.48428	0.0824891	0.0412446	−	0.999149i	$-0.486868\pi$
$907$	2.48428	0.0824891	0.0412446	+	0.999149i	$0.486868\pi$
$908$	−142.515	−4.72952
$909$	1.76847	0.0586565
$910$	−4.30752	−0.142793
$911$	18.1710	0.602031	0.301015	−	0.953619i	$-0.402674\pi$
$911$	18.1710	0.602031	0.301015	+	0.953619i	$0.402674\pi$
$912$	62.6261	2.07376
$913$	51.4047	1.70125
$914$	55.8435	1.84714
$915$	−1.30911	−0.0432778
$916$	−66.7226	−2.20458
$917$	−6.46420	−0.213467
$918$	71.7772	2.36900
$919$	−19.2585	−0.635279	−0.317640	−	0.948212i	$-0.602890\pi$
$919$	−19.2585	−0.635279	−0.317640	+	0.948212i	$0.602890\pi$
$920$	4.35777	0.143671
$921$	17.2755	0.569248
$922$	55.2643	1.82003
$923$	−24.2496	−0.798184
$924$	21.3216	0.701429
$925$	1.71529	0.0563984
$926$	28.7725	0.945524
$927$	15.1175	0.496523
$928$	36.8914	1.21102
$929$	−28.0241	−0.919442	−0.459721	−	0.888063i	$-0.652051\pi$
$929$	−28.0241	−0.919442	−0.459721	+	0.888063i	$0.652051\pi$
$930$	11.7478	0.385224
$931$	−5.68124	−0.186195
$932$	70.6769	2.31510
$933$	1.46006	0.0478003
$934$	−35.3430	−1.15646
$935$	12.0663	0.394609
$936$	46.0697	1.50584
$937$	19.4636	0.635848	0.317924	−	0.948116i	$-0.397014\pi$
$937$	19.4636	0.635848	0.317924	+	0.948116i	$0.397014\pi$
$938$	−8.26977	−0.270018
$939$	7.33328	0.239312
$940$	0.151455	0.00493991
$941$	43.6092	1.42162	0.710810	−	0.703385i	$-0.248329\pi$
$941$	43.6092	1.42162	0.710810	+	0.703385i	$0.248329\pi$
$942$	−11.8190	−0.385083
$943$	2.48878	0.0810458
$944$	21.4120	0.696903
$945$	2.73949	0.0891155
$946$	−8.05177	−0.261786
$947$	18.4222	0.598641	0.299321	−	0.954153i	$-0.403240\pi$
$947$	18.4222	0.598641	0.299321	+	0.954153i	$0.403240\pi$
$948$	46.0229	1.49476
$949$	3.57593	0.116080
$950$	−70.6125	−2.29097
$951$	21.6053	0.700599
$952$	−41.9116	−1.35836
$953$	30.6041	0.991365	0.495682	−	0.868504i	$-0.334918\pi$
$953$	30.6041	0.991365	0.495682	+	0.868504i	$0.334918\pi$
$954$	4.33095	0.140220
$955$	1.92957	0.0624395
$956$	45.5682	1.47378
$957$	12.5079	0.404324
$958$	16.8655	0.544899
$959$	−13.4902	−0.435622
$960$	6.62750	0.213902
$961$	33.5420	1.08200
$962$	2.90933	0.0938005
$963$	−2.32225	−0.0748336
$964$	−50.4395	−1.62455
$965$	−4.04062	−0.130072
$966$	−2.79870	−0.0900467
$967$	33.6416	1.08184	0.540921	−	0.841073i	$-0.318076\pi$
$967$	33.6416	1.08184	0.540921	+	0.841073i	$0.318076\pi$
$968$	−50.6174	−1.62691
$969$	−31.2466	−1.00379
$970$	4.05768	0.130284
$971$	−52.5930	−1.68779	−0.843895	−	0.536508i	$-0.819743\pi$
$971$	−52.5930	−1.68779	−0.843895	+	0.536508i	$0.819743\pi$
$972$	−78.8184	−2.52810
$973$	18.6832	0.598956
$974$	−1.59560	−0.0511264
$975$	14.6405	0.468871
$976$	−25.3536	−0.811550
$977$	−16.1564	−0.516890	−0.258445	−	0.966026i	$-0.583210\pi$
$977$	−16.1564	−0.516890	−0.258445	+	0.966026i	$0.583210\pi$
$978$	−22.7740	−0.728232
$979$	−30.7911	−0.984089
$980$	−2.67822	−0.0855525
$981$	−5.53579	−0.176744
$982$	103.336	3.29759
$983$	−22.9699	−0.732625	−0.366313	−	0.930492i	$-0.619380\pi$
$983$	−22.9699	−0.732625	−0.366313	+	0.930492i	$0.619380\pi$
$984$	19.3922	0.618202
$985$	−0.569751	−0.0181538
$986$	−41.1651	−1.31096
$987$	−0.0580960	−0.00184922
$988$	−85.3813	−2.71634
$989$	0.753450	0.0239583
$990$	−11.5677	−0.367645
$991$	49.7379	1.57998	0.789989	−	0.613121i	$-0.210086\pi$
$991$	49.7379	1.57998	0.789989	+	0.613121i	$0.210086\pi$
$992$	101.733	3.23003
$993$	−23.0769	−0.732325
$994$	−21.1493	−0.670816
$995$	−4.32822	−0.137214
$996$	−62.7532	−1.98841
$997$	−19.1503	−0.606497	−0.303248	−	0.952912i	$-0.598071\pi$
$997$	−19.1503	−0.606497	−0.303248	+	0.952912i	$0.598071\pi$
$998$	37.2864	1.18028
$999$	−1.85027	−0.0585399

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6013.2.a.f.1.4	✓	110

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6013.2.a.f.1.4	✓	110	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:	\( N \)	\(=\)	\( 6013 = 7 \cdot 859 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.63934 q^{2} -1.02733 q^{3} +4.96612 q^{4} -0.539298 q^{5} +2.71147 q^{6} -1.00000 q^{7} -7.82859 q^{8} -1.94460 q^{9} +O(q^{10})\)	\(q-2.63934 q^{2} -1.02733 q^{3} +4.96612 q^{4} -0.539298 q^{5} +2.71147 q^{6} -1.00000 q^{7} -7.82859 q^{8} -1.94460 q^{9} +1.42339 q^{10} +4.17920 q^{11} -5.10184 q^{12} +3.02624 q^{13} +2.63934 q^{14} +0.554037 q^{15} +10.7301 q^{16} -5.35366 q^{17} +5.13245 q^{18} -5.68124 q^{19} -2.67822 q^{20} +1.02733 q^{21} -11.0303 q^{22} +1.03217 q^{23} +8.04254 q^{24} -4.70916 q^{25} -7.98727 q^{26} +5.07973 q^{27} -4.96612 q^{28} -2.91329 q^{29} -1.46229 q^{30} -8.03380 q^{31} -12.6631 q^{32} -4.29341 q^{33} +14.1301 q^{34} +0.539298 q^{35} -9.65709 q^{36} -0.364246 q^{37} +14.9947 q^{38} -3.10894 q^{39} +4.22195 q^{40} +2.41121 q^{41} -2.71147 q^{42} +0.729966 q^{43} +20.7544 q^{44} +1.04872 q^{45} -2.72425 q^{46} -0.0565505 q^{47} -11.0233 q^{48} +1.00000 q^{49} +12.4291 q^{50} +5.49997 q^{51} +15.0286 q^{52} +0.843838 q^{53} -13.4071 q^{54} -2.25384 q^{55} +7.82859 q^{56} +5.83650 q^{57} +7.68915 q^{58} +1.99552 q^{59} +2.75141 q^{60} -2.36286 q^{61} +21.2039 q^{62} +1.94460 q^{63} +11.9622 q^{64} -1.63204 q^{65} +11.3318 q^{66} -3.13327 q^{67} -26.5869 q^{68} -1.06038 q^{69} -1.42339 q^{70} -8.01311 q^{71} +15.2234 q^{72} +1.18164 q^{73} +0.961368 q^{74} +4.83785 q^{75} -28.2137 q^{76} -4.17920 q^{77} +8.20555 q^{78} -9.02086 q^{79} -5.78671 q^{80} +0.615236 q^{81} -6.36400 q^{82} +12.3001 q^{83} +5.10184 q^{84} +2.88722 q^{85} -1.92663 q^{86} +2.99290 q^{87} -32.7172 q^{88} -7.36771 q^{89} -2.76792 q^{90} -3.02624 q^{91} +5.12588 q^{92} +8.25336 q^{93} +0.149256 q^{94} +3.06388 q^{95} +13.0092 q^{96} +2.85071 q^{97} -2.63934 q^{98} -8.12685 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9}+O(q^{10}) \) 110 * q + 16 * q^2 + 29 * q^3 + 118 * q^4 + 12 * q^6 - 110 * q^7 + 57 * q^8 + 127 * q^9	\( 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9} + 3 q^{10} + 52 q^{11} + 62 q^{12} - 9 q^{13} - 16 q^{14} + 39 q^{15} + 146 q^{16} + 11 q^{17} + 60 q^{18} + 14 q^{19} + 18 q^{20} - 29 q^{21} + 32 q^{22} + 73 q^{23} + 24 q^{24} + 132 q^{25} - 7 q^{26} + 116 q^{27} - 118 q^{28} + 35 q^{29} + 18 q^{30} + 36 q^{31} + 140 q^{32} + 42 q^{33} - 7 q^{34} + 180 q^{36} + 49 q^{37} + 45 q^{39} + 6 q^{40} - 14 q^{41} - 12 q^{42} + 58 q^{43} + 92 q^{44} + 17 q^{45} + 27 q^{46} + 87 q^{47} + 98 q^{48} + 110 q^{49} + 91 q^{50} + 42 q^{51} + 16 q^{52} + 95 q^{53} + 41 q^{54} + 8 q^{55} - 57 q^{56} + 61 q^{57} + 46 q^{58} + 114 q^{59} + 81 q^{60} - 47 q^{61} + 31 q^{62} - 127 q^{63} + 199 q^{64} + 62 q^{65} + 21 q^{66} + 95 q^{67} + 60 q^{68} - 39 q^{69} - 3 q^{70} + 131 q^{71} + 186 q^{72} + 31 q^{73} + 23 q^{74} + 121 q^{75} + 14 q^{76} - 52 q^{77} + 110 q^{78} + 9 q^{79} + 61 q^{80} + 194 q^{81} + 45 q^{82} + 73 q^{83} - 62 q^{84} + 59 q^{85} + 72 q^{86} + 64 q^{87} + 100 q^{88} - 17 q^{89} + 11 q^{90} + 9 q^{91} + 192 q^{92} + 85 q^{93} - 11 q^{94} + 108 q^{95} + 68 q^{96} + 32 q^{97} + 16 q^{98} + 160 q^{99}+O(q^{100}) \) 110 * q + 16 * q^2 + 29 * q^3 + 118 * q^4 + 12 * q^6 - 110 * q^7 + 57 * q^8 + 127 * q^9 + 3 * q^10 + 52 * q^11 + 62 * q^12 - 9 * q^13 - 16 * q^14 + 39 * q^15 + 146 * q^16 + 11 * q^17 + 60 * q^18 + 14 * q^19 + 18 * q^20 - 29 * q^21 + 32 * q^22 + 73 * q^23 + 24 * q^24 + 132 * q^25 - 7 * q^26 + 116 * q^27 - 118 * q^28 + 35 * q^29 + 18 * q^30 + 36 * q^31 + 140 * q^32 + 42 * q^33 - 7 * q^34 + 180 * q^36 + 49 * q^37 + 45 * q^39 + 6 * q^40 - 14 * q^41 - 12 * q^42 + 58 * q^43 + 92 * q^44 + 17 * q^45 + 27 * q^46 + 87 * q^47 + 98 * q^48 + 110 * q^49 + 91 * q^50 + 42 * q^51 + 16 * q^52 + 95 * q^53 + 41 * q^54 + 8 * q^55 - 57 * q^56 + 61 * q^57 + 46 * q^58 + 114 * q^59 + 81 * q^60 - 47 * q^61 + 31 * q^62 - 127 * q^63 + 199 * q^64 + 62 * q^65 + 21 * q^66 + 95 * q^67 + 60 * q^68 - 39 * q^69 - 3 * q^70 + 131 * q^71 + 186 * q^72 + 31 * q^73 + 23 * q^74 + 121 * q^75 + 14 * q^76 - 52 * q^77 + 110 * q^78 + 9 * q^79 + 61 * q^80 + 194 * q^81 + 45 * q^82 + 73 * q^83 - 62 * q^84 + 59 * q^85 + 72 * q^86 + 64 * q^87 + 100 * q^88 - 17 * q^89 + 11 * q^90 + 9 * q^91 + 192 * q^92 + 85 * q^93 - 11 * q^94 + 108 * q^95 + 68 * q^96 + 32 * q^97 + 16 * q^98 + 160 * q^99

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