LMFDB - Embedded newform 6047.2.a.a.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6047,2,Mod(1,6047)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6047, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6047.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6047 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6047.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:	$48.2855381023$
Analytic rank:	$1$
Dimension:	$217$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	6047.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.46440 q^{2} -0.383920 q^{3} +4.07326 q^{4} +2.75346 q^{5} +0.946133 q^{6} -1.51513 q^{7} -5.10935 q^{8} -2.85261 q^{9} +O(q^{10})$	\(q-2.46440 q^{2} -0.383920 q^{3} +4.07326 q^{4} +2.75346 q^{5} +0.946133 q^{6} -1.51513 q^{7} -5.10935 q^{8} -2.85261 q^{9} -6.78563 q^{10} -0.490721 q^{11} -1.56381 q^{12} +6.57761 q^{13} +3.73388 q^{14} -1.05711 q^{15} +4.44495 q^{16} +1.76071 q^{17} +7.02996 q^{18} +3.09958 q^{19} +11.2156 q^{20} +0.581688 q^{21} +1.20933 q^{22} +1.97369 q^{23} +1.96158 q^{24} +2.58155 q^{25} -16.2098 q^{26} +2.24693 q^{27} -6.17151 q^{28} -8.69525 q^{29} +2.60514 q^{30} -4.84352 q^{31} -0.735440 q^{32} +0.188398 q^{33} -4.33908 q^{34} -4.17184 q^{35} -11.6194 q^{36} -8.55284 q^{37} -7.63860 q^{38} -2.52528 q^{39} -14.0684 q^{40} -2.34454 q^{41} -1.43351 q^{42} -3.75266 q^{43} -1.99884 q^{44} -7.85454 q^{45} -4.86396 q^{46} +8.55989 q^{47} -1.70651 q^{48} -4.70439 q^{49} -6.36197 q^{50} -0.675971 q^{51} +26.7923 q^{52} -1.97617 q^{53} -5.53734 q^{54} -1.35118 q^{55} +7.74131 q^{56} -1.18999 q^{57} +21.4286 q^{58} -1.53501 q^{59} -4.30589 q^{60} +0.845887 q^{61} +11.9364 q^{62} +4.32206 q^{63} -7.07749 q^{64} +18.1112 q^{65} -0.464288 q^{66} +12.3716 q^{67} +7.17182 q^{68} -0.757740 q^{69} +10.2811 q^{70} -8.60699 q^{71} +14.5750 q^{72} -12.3060 q^{73} +21.0776 q^{74} -0.991109 q^{75} +12.6254 q^{76} +0.743505 q^{77} +6.22329 q^{78} -7.25392 q^{79} +12.2390 q^{80} +7.69517 q^{81} +5.77788 q^{82} -7.67069 q^{83} +2.36937 q^{84} +4.84804 q^{85} +9.24805 q^{86} +3.33828 q^{87} +2.50727 q^{88} +14.8251 q^{89} +19.3567 q^{90} -9.96590 q^{91} +8.03936 q^{92} +1.85953 q^{93} -21.0950 q^{94} +8.53457 q^{95} +0.282351 q^{96} +7.97348 q^{97} +11.5935 q^{98} +1.39983 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 217 q - 20 q^{2} - 27 q^{3} + 184 q^{4} - 19 q^{5} - 17 q^{6} - 48 q^{7} - 57 q^{8} + 152 q^{9}+O(q^{10}) $ 217 * q - 20 * q^2 - 27 * q^3 + 184 * q^4 - 19 * q^5 - 17 * q^6 - 48 * q^7 - 57 * q^8 + 152 * q^9	\( 217 q - 20 q^{2} - 27 q^{3} + 184 q^{4} - 19 q^{5} - 17 q^{6} - 48 q^{7} - 57 q^{8} + 152 q^{9} - 46 q^{10} - 32 q^{11} - 72 q^{12} - 80 q^{13} - 22 q^{14} - 43 q^{15} + 122 q^{16} - 61 q^{17} - 88 q^{18} - 43 q^{19} - 41 q^{20} - 61 q^{21} - 93 q^{22} - 60 q^{23} - 41 q^{24} + 26 q^{25} - 9 q^{26} - 93 q^{27} - 126 q^{28} - 47 q^{29} - 36 q^{30} - 100 q^{31} - 114 q^{32} - 133 q^{33} - 75 q^{34} - 37 q^{35} + 75 q^{36} - 264 q^{37} - 35 q^{38} - 47 q^{39} - 118 q^{40} - 72 q^{41} - 64 q^{42} - 107 q^{43} - 59 q^{44} - 69 q^{45} - 111 q^{46} - 54 q^{47} - 135 q^{48} + 33 q^{49} - 42 q^{50} - 26 q^{51} - 173 q^{52} - 103 q^{53} - 28 q^{54} - 78 q^{55} - 44 q^{56} - 205 q^{57} - 189 q^{58} - 38 q^{59} - 105 q^{60} - 108 q^{61} - 14 q^{62} - 116 q^{63} + 39 q^{64} - 146 q^{65} + 5 q^{66} - 206 q^{67} - 62 q^{68} - 55 q^{69} - 125 q^{70} - 78 q^{71} - 225 q^{72} - 326 q^{73} + 3 q^{74} - 95 q^{75} - 84 q^{76} - 79 q^{77} - 86 q^{78} - 117 q^{79} - 39 q^{80} + q^{81} - 96 q^{82} - 23 q^{83} - 57 q^{84} - 224 q^{85} - 7 q^{86} - 45 q^{87} - 250 q^{88} - 104 q^{89} - 36 q^{90} - 96 q^{91} - 137 q^{92} - 155 q^{93} - 48 q^{94} - 38 q^{95} - 33 q^{96} - 447 q^{97} - 46 q^{98} - 94 q^{99}+O(q^{100}) \) 217 * q - 20 * q^2 - 27 * q^3 + 184 * q^4 - 19 * q^5 - 17 * q^6 - 48 * q^7 - 57 * q^8 + 152 * q^9 - 46 * q^10 - 32 * q^11 - 72 * q^12 - 80 * q^13 - 22 * q^14 - 43 * q^15 + 122 * q^16 - 61 * q^17 - 88 * q^18 - 43 * q^19 - 41 * q^20 - 61 * q^21 - 93 * q^22 - 60 * q^23 - 41 * q^24 + 26 * q^25 - 9 * q^26 - 93 * q^27 - 126 * q^28 - 47 * q^29 - 36 * q^30 - 100 * q^31 - 114 * q^32 - 133 * q^33 - 75 * q^34 - 37 * q^35 + 75 * q^36 - 264 * q^37 - 35 * q^38 - 47 * q^39 - 118 * q^40 - 72 * q^41 - 64 * q^42 - 107 * q^43 - 59 * q^44 - 69 * q^45 - 111 * q^46 - 54 * q^47 - 135 * q^48 + 33 * q^49 - 42 * q^50 - 26 * q^51 - 173 * q^52 - 103 * q^53 - 28 * q^54 - 78 * q^55 - 44 * q^56 - 205 * q^57 - 189 * q^58 - 38 * q^59 - 105 * q^60 - 108 * q^61 - 14 * q^62 - 116 * q^63 + 39 * q^64 - 146 * q^65 + 5 * q^66 - 206 * q^67 - 62 * q^68 - 55 * q^69 - 125 * q^70 - 78 * q^71 - 225 * q^72 - 326 * q^73 + 3 * q^74 - 95 * q^75 - 84 * q^76 - 79 * q^77 - 86 * q^78 - 117 * q^79 - 39 * q^80 + q^81 - 96 * q^82 - 23 * q^83 - 57 * q^84 - 224 * q^85 - 7 * q^86 - 45 * q^87 - 250 * q^88 - 104 * q^89 - 36 * q^90 - 96 * q^91 - 137 * q^92 - 155 * q^93 - 48 * q^94 - 38 * q^95 - 33 * q^96 - 447 * q^97 - 46 * q^98 - 94 * 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 $

$2$	−2.46440	−1.74259	−0.871297	−	0.490756i	$-0.836720\pi$
$2$	−2.46440	−1.74259	−0.871297	+	0.490756i	$0.836720\pi$
$3$	−0.383920	−0.221656	−0.110828	−	0.993840i	$-0.535350\pi$
$3$	−0.383920	−0.221656	−0.110828	+	0.993840i	$0.535350\pi$
$4$	4.07326	2.03663
$5$	2.75346	1.23139	0.615693	−	0.787986i	$-0.288876\pi$
$5$	2.75346	1.23139	0.615693	+	0.787986i	$0.288876\pi$
$6$	0.946133	0.386257
$7$	−1.51513	−0.572664	−0.286332	−	0.958130i	$-0.592436\pi$
$7$	−1.51513	−0.572664	−0.286332	+	0.958130i	$0.592436\pi$
$8$	−5.10935	−1.80643
$9$	−2.85261	−0.950868
$10$	−6.78563	−2.14580
$11$	−0.490721	−0.147958	−0.0739790	−	0.997260i	$-0.523570\pi$
$11$	−0.490721	−0.147958	−0.0739790	+	0.997260i	$0.523570\pi$
$12$	−1.56381	−0.451433
$13$	6.57761	1.82430	0.912150	−	0.409857i	$-0.134421\pi$
$13$	6.57761	1.82430	0.912150	+	0.409857i	$0.134421\pi$
$14$	3.73388	0.997921
$15$	−1.05711	−0.272945
$16$	4.44495	1.11124
$17$	1.76071	0.427034	0.213517	−	0.976939i	$-0.431508\pi$
$17$	1.76071	0.427034	0.213517	+	0.976939i	$0.431508\pi$
$18$	7.02996	1.65698
$19$	3.09958	0.711092	0.355546	−	0.934659i	$-0.384295\pi$
$19$	3.09958	0.711092	0.355546	+	0.934659i	$0.384295\pi$
$20$	11.2156	2.50788
$21$	0.581688	0.126935
$22$	1.20933	0.257831
$23$	1.97369	0.411543	0.205771	−	0.978600i	$-0.434030\pi$
$23$	1.97369	0.411543	0.205771	+	0.978600i	$0.434030\pi$
$24$	1.96158	0.400407
$25$	2.58155	0.516310
$26$	−16.2098	−3.17901
$27$	2.24693	0.432423
$28$	−6.17151	−1.16631
$29$	−8.69525	−1.61467	−0.807334	−	0.590095i	$-0.799090\pi$
$29$	−8.69525	−1.61467	−0.807334	+	0.590095i	$0.799090\pi$
$30$	2.60514	0.475631
$31$	−4.84352	−0.869922	−0.434961	−	0.900449i	$-0.643238\pi$
$31$	−4.84352	−0.869922	−0.434961	+	0.900449i	$0.643238\pi$
$32$	−0.735440	−0.130009
$33$	0.188398	0.0327959
$34$	−4.33908	−0.744147
$35$	−4.17184	−0.705170
$36$	−11.6194	−1.93657
$37$	−8.55284	−1.40608	−0.703039	−	0.711151i	$-0.748174\pi$
$37$	−8.55284	−1.40608	−0.703039	+	0.711151i	$0.748174\pi$
$38$	−7.63860	−1.23914
$39$	−2.52528	−0.404368
$40$	−14.0684	−2.22441
$41$	−2.34454	−0.366155	−0.183078	−	0.983098i	$-0.558606\pi$
$41$	−2.34454	−0.366155	−0.183078	+	0.983098i	$0.558606\pi$
$42$	−1.43351	−0.221196
$43$	−3.75266	−0.572275	−0.286137	−	0.958189i	$-0.592371\pi$
$43$	−3.75266	−0.572275	−0.286137	+	0.958189i	$0.592371\pi$
$44$	−1.99884	−0.301336
$45$	−7.85454	−1.17089
$46$	−4.86396	−0.717152
$47$	8.55989	1.24859	0.624294	−	0.781189i	$-0.285387\pi$
$47$	8.55989	1.24859	0.624294	+	0.781189i	$0.285387\pi$
$48$	−1.70651	−0.246313
$49$	−4.70439	−0.672056
$50$	−6.36197	−0.899718
$51$	−0.675971	−0.0946548
$52$	26.7923	3.71543
$53$	−1.97617	−0.271448	−0.135724	−	0.990747i	$-0.543336\pi$
$53$	−1.97617	−0.271448	−0.135724	+	0.990747i	$0.543336\pi$
$54$	−5.53734	−0.753537
$55$	−1.35118	−0.182193
$56$	7.74131	1.03448
$57$	−1.18999	−0.157618
$58$	21.4286	2.81371
$59$	−1.53501	−0.199841	−0.0999205	−	0.994995i	$-0.531859\pi$
$59$	−1.53501	−0.199841	−0.0999205	+	0.994995i	$0.531859\pi$
$60$	−4.30589	−0.555888
$61$	0.845887	0.108305	0.0541524	−	0.998533i	$-0.482754\pi$
$61$	0.845887	0.108305	0.0541524	+	0.998533i	$0.482754\pi$
$62$	11.9364	1.51592
$63$	4.32206	0.544528
$64$	−7.07749	−0.884686
$65$	18.1112	2.24642
$66$	−0.464288	−0.0571498
$67$	12.3716	1.51143	0.755714	−	0.654901i	$-0.227290\pi$
$67$	12.3716	1.51143	0.755714	+	0.654901i	$0.227290\pi$
$68$	7.17182	0.869711
$69$	−0.757740	−0.0912211
$70$	10.2811	1.22882
$71$	−8.60699	−1.02146	−0.510731	−	0.859741i	$-0.670625\pi$
$71$	−8.60699	−1.02146	−0.510731	+	0.859741i	$0.670625\pi$
$72$	14.5750	1.71768
$73$	−12.3060	−1.44031	−0.720155	−	0.693813i	$-0.755930\pi$
$73$	−12.3060	−1.44031	−0.720155	+	0.693813i	$0.755930\pi$
$74$	21.0776	2.45022
$75$	−0.991109	−0.114443
$76$	12.6254	1.44823
$77$	0.743505	0.0847302
$78$	6.22329	0.704649
$79$	−7.25392	−0.816130	−0.408065	−	0.912953i	$-0.633796\pi$
$79$	−7.25392	−0.816130	−0.408065	+	0.912953i	$0.633796\pi$
$80$	12.2390	1.36836
$81$	7.69517	0.855019
$82$	5.77788	0.638060
$83$	−7.67069	−0.841967	−0.420984	−	0.907068i	$-0.638315\pi$
$83$	−7.67069	−0.841967	−0.420984	+	0.907068i	$0.638315\pi$
$84$	2.36937	0.258519
$85$	4.84804	0.525843
$86$	9.24805	0.997242
$87$	3.33828	0.357901
$88$	2.50727	0.267276
$89$	14.8251	1.57146	0.785729	−	0.618571i	$-0.212288\pi$
$89$	14.8251	1.57146	0.785729	+	0.618571i	$0.212288\pi$
$90$	19.3567	2.04038
$91$	−9.96590	−1.04471
$92$	8.03936	0.838161
$93$	1.85953	0.192824
$94$	−21.0950	−2.17578
$95$	8.53457	0.875629
$96$	0.282351	0.0288173
$97$	7.97348	0.809584	0.404792	−	0.914409i	$-0.367344\pi$
$97$	7.97348	0.809584	0.404792	+	0.914409i	$0.367344\pi$
$98$	11.5935	1.17112
$99$	1.39983	0.140689
$100$	10.5153	1.05153
$101$	−3.35992	−0.334325	−0.167162	−	0.985929i	$-0.553460\pi$
$101$	−3.35992	−0.334325	−0.167162	+	0.985929i	$0.553460\pi$
$102$	1.66586	0.164945
$103$	−13.8547	−1.36515	−0.682573	−	0.730818i	$-0.739139\pi$
$103$	−13.8547	−1.36515	−0.682573	+	0.730818i	$0.739139\pi$
$104$	−33.6073	−3.29547
$105$	1.60165	0.156305
$106$	4.87008	0.473024
$107$	0.443578	0.0428823	0.0214411	−	0.999770i	$-0.493175\pi$
$107$	0.443578	0.0428823	0.0214411	+	0.999770i	$0.493175\pi$
$108$	9.15236	0.880686
$109$	−6.59935	−0.632103	−0.316051	−	0.948742i	$-0.602357\pi$
$109$	−6.59935	−0.632103	−0.316051	+	0.948742i	$0.602357\pi$
$110$	3.32985	0.317489
$111$	3.28361	0.311666
$112$	−6.73467	−0.636366
$113$	−18.5727	−1.74717	−0.873586	−	0.486670i	$-0.838211\pi$
$113$	−18.5727	−1.74717	−0.873586	+	0.486670i	$0.838211\pi$
$114$	2.93261	0.274664
$115$	5.43448	0.506768
$116$	−35.4181	−3.28848
$117$	−18.7633	−1.73467
$118$	3.78287	0.348242
$119$	−2.66769	−0.244547
$120$	5.40114	0.493055
$121$	−10.7592	−0.978108
$122$	−2.08460	−0.188731
$123$	0.900116	0.0811607
$124$	−19.7289	−1.77171
$125$	−6.65911	−0.595609
$126$	−10.6513	−0.948891
$127$	−14.5466	−1.29081	−0.645403	−	0.763842i	$-0.723311\pi$
$127$	−14.5466	−1.29081	−0.645403	+	0.763842i	$0.723311\pi$
$128$	18.9126	1.67166
$129$	1.44072	0.126848
$130$	−44.6332	−3.91459
$131$	16.9749	1.48310	0.741550	−	0.670898i	$-0.234091\pi$
$131$	16.9749	1.48310	0.741550	+	0.670898i	$0.234091\pi$
$132$	0.767394	0.0667931
$133$	−4.69625	−0.407217
$134$	−30.4885	−2.63381
$135$	6.18684	0.532479
$136$	−8.99607	−0.771406
$137$	0.252997	0.0216150	0.0108075	−	0.999942i	$-0.496560\pi$
$137$	0.252997	0.0216150	0.0108075	+	0.999942i	$0.496560\pi$
$138$	1.86737	0.158961
$139$	9.10749	0.772487	0.386243	−	0.922397i	$-0.373772\pi$
$139$	9.10749	0.772487	0.386243	+	0.922397i	$0.373772\pi$
$140$	−16.9930	−1.43617
$141$	−3.28632	−0.276758
$142$	21.2111	1.77999
$143$	−3.22777	−0.269920
$144$	−12.6797	−1.05664
$145$	−23.9420	−1.98828
$146$	30.3270	2.50988
$147$	1.80611	0.148966
$148$	−34.8380	−2.86366
$149$	2.23660	0.183229	0.0916146	−	0.995795i	$-0.470797\pi$
$149$	2.23660	0.183229	0.0916146	+	0.995795i	$0.470797\pi$
$150$	2.44249	0.199428
$151$	5.42668	0.441617	0.220809	−	0.975317i	$-0.429130\pi$
$151$	5.42668	0.441617	0.220809	+	0.975317i	$0.429130\pi$
$152$	−15.8368	−1.28454
$153$	−5.02260	−0.406053
$154$	−1.83229	−0.147650
$155$	−13.3364	−1.07121
$156$	−10.2861	−0.823549
$157$	10.7019	0.854106	0.427053	−	0.904227i	$-0.359552\pi$
$157$	10.7019	0.854106	0.427053	+	0.904227i	$0.359552\pi$
$158$	17.8766	1.42218
$159$	0.758693	0.0601683
$160$	−2.02501	−0.160091
$161$	−2.99039	−0.235676
$162$	−18.9640	−1.48995
$163$	−9.01921	−0.706439	−0.353219	−	0.935541i	$-0.614913\pi$
$163$	−9.01921	−0.706439	−0.353219	+	0.935541i	$0.614913\pi$
$164$	−9.54993	−0.745724
$165$	0.518746	0.0403843
$166$	18.9036	1.46721
$167$	−1.69186	−0.130920	−0.0654602	−	0.997855i	$-0.520852\pi$
$167$	−1.69186	−0.130920	−0.0654602	+	0.997855i	$0.520852\pi$
$168$	−2.97205	−0.229298
$169$	30.2649	2.32807
$170$	−11.9475	−0.916331
$171$	−8.84188	−0.676155
$172$	−15.2856	−1.16551
$173$	8.89462	0.676245	0.338123	−	0.941102i	$-0.390208\pi$
$173$	8.89462	0.676245	0.338123	+	0.941102i	$0.390208\pi$
$174$	−8.22686	−0.623677
$175$	−3.91137	−0.295672
$176$	−2.18123	−0.164417
$177$	0.589321	0.0442960
$178$	−36.5350	−2.73841
$179$	−8.87552	−0.663388	−0.331694	−	0.943387i	$-0.607620\pi$
$179$	−8.87552	−0.663388	−0.331694	+	0.943387i	$0.607620\pi$
$180$	−31.9936	−2.38466
$181$	9.36321	0.695962	0.347981	−	0.937502i	$-0.386867\pi$
$181$	9.36321	0.695962	0.347981	+	0.937502i	$0.386867\pi$
$182$	24.5600	1.82051
$183$	−0.324753	−0.0240065
$184$	−10.0843	−0.743423
$185$	−23.5499	−1.73142
$186$	−4.58261	−0.336014
$187$	−0.864016	−0.0631831
$188$	34.8667	2.54292
$189$	−3.40439	−0.247633
$190$	−21.0326	−1.52586
$191$	1.47014	0.106376	0.0531879	−	0.998585i	$-0.483062\pi$
$191$	1.47014	0.106376	0.0531879	+	0.998585i	$0.483062\pi$
$192$	2.71719	0.196096
$193$	−11.7784	−0.847825	−0.423913	−	0.905703i	$-0.639344\pi$
$193$	−11.7784	−0.847825	−0.423913	+	0.905703i	$0.639344\pi$
$194$	−19.6498	−1.41078
$195$	−6.95325	−0.497933
$196$	−19.1622	−1.36873
$197$	7.30749	0.520637	0.260319	−	0.965523i	$-0.416172\pi$
$197$	7.30749	0.520637	0.260319	+	0.965523i	$0.416172\pi$
$198$	−3.44975	−0.245163
$199$	−8.06238	−0.571527	−0.285763	−	0.958300i	$-0.592247\pi$
$199$	−8.06238	−0.571527	−0.285763	+	0.958300i	$0.592247\pi$
$200$	−13.1900	−0.932677
$201$	−4.74970	−0.335018
$202$	8.28019	0.582592
$203$	13.1744	0.924662
$204$	−2.75341	−0.192777
$205$	−6.45560	−0.450878
$206$	34.1435	2.37889
$207$	−5.63016	−0.391323
$208$	29.2372	2.02723
$209$	−1.52103	−0.105212
$210$	−3.94712	−0.272377
$211$	−9.33441	−0.642607	−0.321304	−	0.946976i	$-0.604121\pi$
$211$	−9.33441	−0.642607	−0.321304	+	0.946976i	$0.604121\pi$
$212$	−8.04948	−0.552840
$213$	3.30440	0.226414
$214$	−1.09315	−0.0747264
$215$	−10.3328	−0.704691
$216$	−11.4804	−0.781141
$217$	7.33855	0.498173
$218$	16.2634	1.10150
$219$	4.72453	0.319254
$220$	−5.50372	−0.371061
$221$	11.5812	0.779038
$222$	−8.09212	−0.543108
$223$	25.2328	1.68971	0.844857	−	0.534993i	$-0.179686\pi$
$223$	25.2328	1.68971	0.844857	+	0.534993i	$0.179686\pi$
$224$	1.11429	0.0744513
$225$	−7.36414	−0.490943
$226$	45.7705	3.04461
$227$	−17.7626	−1.17894	−0.589472	−	0.807789i	$-0.700664\pi$
$227$	−17.7626	−1.17894	−0.589472	+	0.807789i	$0.700664\pi$
$228$	−4.84715	−0.321010
$229$	21.8863	1.44629	0.723144	−	0.690698i	$-0.242696\pi$
$229$	21.8863	1.44629	0.723144	+	0.690698i	$0.242696\pi$
$230$	−13.3927	−0.883090
$231$	−0.285447	−0.0187810
$232$	44.4271	2.91678
$233$	−23.4777	−1.53808	−0.769038	−	0.639203i	$-0.779265\pi$
$233$	−23.4777	−1.53808	−0.769038	+	0.639203i	$0.779265\pi$
$234$	46.2403	3.02282
$235$	23.5693	1.53749
$236$	−6.25249	−0.407003
$237$	2.78493	0.180900
$238$	6.57426	0.426146
$239$	12.4407	0.804725	0.402362	−	0.915480i	$-0.368189\pi$
$239$	12.4407	0.804725	0.402362	+	0.915480i	$0.368189\pi$
$240$	−4.69880	−0.303307
$241$	−12.1085	−0.779975	−0.389987	−	0.920820i	$-0.627521\pi$
$241$	−12.1085	−0.779975	−0.389987	+	0.920820i	$0.627521\pi$
$242$	26.5149	1.70445
$243$	−9.69513	−0.621943
$244$	3.44552	0.220577
$245$	−12.9534	−0.827560
$246$	−2.21825	−0.141430
$247$	20.3878	1.29725
$248$	24.7473	1.57145
$249$	2.94493	0.186627
$250$	16.4107	1.03790
$251$	−25.5974	−1.61569	−0.807847	−	0.589392i	$-0.799367\pi$
$251$	−25.5974	−1.61569	−0.807847	+	0.589392i	$0.799367\pi$
$252$	17.6049	1.10900
$253$	−0.968532	−0.0608911
$254$	35.8488	2.24935
$255$	−1.86126	−0.116557
$256$	−32.4533	−2.02833
$257$	−20.7063	−1.29163	−0.645813	−	0.763495i	$-0.723482\pi$
$257$	−20.7063	−1.29163	−0.645813	+	0.763495i	$0.723482\pi$
$258$	−3.55051	−0.221045
$259$	12.9586	0.805210
$260$	73.7716	4.57512
$261$	24.8041	1.53534
$262$	−41.8328	−2.58444
$263$	0.253673	0.0156422	0.00782108	−	0.999969i	$-0.497510\pi$
$263$	0.253673	0.0156422	0.00782108	+	0.999969i	$0.497510\pi$
$264$	−0.962591	−0.0592434
$265$	−5.44132	−0.334257
$266$	11.5734	0.709614
$267$	−5.69166	−0.348324
$268$	50.3927	3.07822
$269$	9.70811	0.591914	0.295957	−	0.955201i	$-0.404361\pi$
$269$	9.70811	0.591914	0.295957	+	0.955201i	$0.404361\pi$
$270$	−15.2469	−0.927894
$271$	8.51004	0.516948	0.258474	−	0.966018i	$-0.416780\pi$
$271$	8.51004	0.516948	0.258474	+	0.966018i	$0.416780\pi$
$272$	7.82626	0.474537
$273$	3.82611	0.231567
$274$	−0.623486	−0.0376661
$275$	−1.26682	−0.0763922
$276$	−3.08647	−0.185784
$277$	−18.7286	−1.12529	−0.562647	−	0.826697i	$-0.690217\pi$
$277$	−18.7286	−1.12529	−0.562647	+	0.826697i	$0.690217\pi$
$278$	−22.4445	−1.34613
$279$	13.8167	0.827181
$280$	21.3154	1.27384
$281$	23.4720	1.40022	0.700111	−	0.714034i	$-0.253134\pi$
$281$	23.4720	1.40022	0.700111	+	0.714034i	$0.253134\pi$
$282$	8.09879	0.482276
$283$	3.38077	0.200966	0.100483	−	0.994939i	$-0.467961\pi$
$283$	3.38077	0.200966	0.100483	+	0.994939i	$0.467961\pi$
$284$	−35.0585	−2.08034
$285$	−3.27660	−0.194089
$286$	7.95452	0.470360
$287$	3.55227	0.209684
$288$	2.09792	0.123621
$289$	−13.8999	−0.817642
$290$	59.0027	3.46476
$291$	−3.06118	−0.179450
$292$	−50.1257	−2.93338
$293$	24.0072	1.40251	0.701257	−	0.712908i	$-0.252622\pi$
$293$	24.0072	1.40251	0.701257	+	0.712908i	$0.252622\pi$
$294$	−4.45098	−0.259586
$295$	−4.22658	−0.246081
$296$	43.6995	2.53998
$297$	−1.10262	−0.0639804
$298$	−5.51187	−0.319294
$299$	12.9822	0.750777
$300$	−4.03705	−0.233079
$301$	5.68575	0.327721
$302$	−13.3735	−0.769559
$303$	1.28994	0.0741053
$304$	13.7775	0.790193
$305$	2.32912	0.133365
$306$	12.3777	0.707585
$307$	−19.3638	−1.10515	−0.552575	−	0.833463i	$-0.686355\pi$
$307$	−19.3638	−1.10515	−0.552575	+	0.833463i	$0.686355\pi$
$308$	3.02849	0.172564
$309$	5.31910	0.302593
$310$	32.8663	1.86668
$311$	27.0134	1.53179	0.765896	−	0.642965i	$-0.222296\pi$
$311$	27.0134	1.53179	0.765896	+	0.642965i	$0.222296\pi$
$312$	12.9025	0.730462
$313$	5.79613	0.327617	0.163808	−	0.986492i	$-0.447622\pi$
$313$	5.79613	0.327617	0.163808	+	0.986492i	$0.447622\pi$
$314$	−26.3738	−1.48836
$315$	11.9006	0.670524
$316$	−29.5471	−1.66216
$317$	−34.8756	−1.95881	−0.979403	−	0.201913i	$-0.935284\pi$
$317$	−34.8756	−1.95881	−0.979403	+	0.201913i	$0.935284\pi$
$318$	−1.86972	−0.104849
$319$	4.26694	0.238903
$320$	−19.4876	−1.08939
$321$	−0.170298	−0.00950513
$322$	7.36951	0.410687
$323$	5.45745	0.303661
$324$	31.3445	1.74136
$325$	16.9804	0.941903
$326$	22.2269	1.23104
$327$	2.53362	0.140110
$328$	11.9791	0.661434
$329$	−12.9693	−0.715022
$330$	−1.27840	−0.0703735
$331$	24.1011	1.32472	0.662359	−	0.749187i	$-0.269555\pi$
$331$	24.1011	1.32472	0.662359	+	0.749187i	$0.269555\pi$
$332$	−31.2447	−1.71478
$333$	24.3979	1.33699
$334$	4.16943	0.228141
$335$	34.0647	1.86115
$336$	2.58558	0.141055
$337$	−28.9879	−1.57907	−0.789537	−	0.613703i	$-0.789679\pi$
$337$	−28.9879	−1.57907	−0.789537	+	0.613703i	$0.789679\pi$
$338$	−74.5848	−4.05688
$339$	7.13043	0.387272
$340$	19.7473	1.07095
$341$	2.37682	0.128712
$342$	21.7899	1.17826
$343$	17.7336	0.957526
$344$	19.1736	1.03377
$345$	−2.08641	−0.112328
$346$	−21.9199	−1.17842
$347$	19.0577	1.02307	0.511536	−	0.859262i	$-0.329077\pi$
$347$	19.0577	1.02307	0.511536	+	0.859262i	$0.329077\pi$
$348$	13.5977	0.728914
$349$	−13.2415	−0.708804	−0.354402	−	0.935093i	$-0.615315\pi$
$349$	−13.2415	−0.708804	−0.354402	+	0.935093i	$0.615315\pi$
$350$	9.63918	0.515236
$351$	14.7794	0.788868
$352$	0.360896	0.0192358
$353$	0.242265	0.0128945	0.00644723	−	0.999979i	$-0.497948\pi$
$353$	0.242265	0.0128945	0.00644723	+	0.999979i	$0.497948\pi$
$354$	−1.45232	−0.0771900
$355$	−23.6990	−1.25781
$356$	60.3865	3.20048
$357$	1.02418	0.0542054
$358$	21.8728	1.15601
$359$	−22.7156	−1.19888	−0.599442	−	0.800418i	$-0.704611\pi$
$359$	−22.7156	−1.19888	−0.599442	+	0.800418i	$0.704611\pi$
$360$	40.1316	2.11512
$361$	−9.39261	−0.494348
$362$	−23.0747	−1.21278
$363$	4.13067	0.216804
$364$	−40.5938	−2.12769
$365$	−33.8842	−1.77358
$366$	0.800322	0.0418335
$367$	−11.2808	−0.588853	−0.294426	−	0.955674i	$-0.595129\pi$
$367$	−11.2808	−0.588853	−0.294426	+	0.955674i	$0.595129\pi$
$368$	8.77296	0.457322
$369$	6.68804	0.348166
$370$	58.0364	3.01717
$371$	2.99415	0.155449
$372$	7.57434	0.392711
$373$	4.52292	0.234188	0.117094	−	0.993121i	$-0.462642\pi$
$373$	4.52292	0.234188	0.117094	+	0.993121i	$0.462642\pi$
$374$	2.12928	0.110102
$375$	2.55657	0.132021
$376$	−43.7355	−2.25549
$377$	−57.1939	−2.94564
$378$	8.38977	0.431523
$379$	−18.9674	−0.974288	−0.487144	−	0.873322i	$-0.661961\pi$
$379$	−18.9674	−0.974288	−0.487144	+	0.873322i	$0.661961\pi$
$380$	34.7636	1.78333
$381$	5.58475	0.286116
$382$	−3.62302	−0.185370
$383$	3.48139	0.177891	0.0889455	−	0.996036i	$-0.471650\pi$
$383$	3.48139	0.177891	0.0889455	+	0.996036i	$0.471650\pi$
$384$	−7.26095	−0.370534
$385$	2.04721	0.104336
$386$	29.0266	1.47741
$387$	10.7048	0.544158
$388$	32.4781	1.64883
$389$	16.5741	0.840341	0.420171	−	0.907445i	$-0.361970\pi$
$389$	16.5741	0.840341	0.420171	+	0.907445i	$0.361970\pi$
$390$	17.1356	0.867694
$391$	3.47509	0.175743
$392$	24.0364	1.21402
$393$	−6.51699	−0.328739
$394$	−18.0086	−0.907259
$395$	−19.9734	−1.00497
$396$	5.70189	0.286531
$397$	−32.7913	−1.64575	−0.822874	−	0.568223i	$-0.807631\pi$
$397$	−32.7913	−1.64575	−0.822874	+	0.568223i	$0.807631\pi$
$398$	19.8689	0.995939
$399$	1.80299	0.0902623
$400$	11.4749	0.573743
$401$	10.8159	0.540118	0.270059	−	0.962844i	$-0.412957\pi$
$401$	10.8159	0.540118	0.270059	+	0.962844i	$0.412957\pi$
$402$	11.7052	0.583800
$403$	−31.8588	−1.58700
$404$	−13.6859	−0.680897
$405$	21.1884	1.05286
$406$	−32.4670	−1.61131
$407$	4.19706	0.208040
$408$	3.45377	0.170987
$409$	25.1851	1.24532	0.622661	−	0.782492i	$-0.286052\pi$
$409$	25.1851	1.24532	0.622661	+	0.782492i	$0.286052\pi$
$410$	15.9092	0.785698
$411$	−0.0971307	−0.00479110
$412$	−56.4339	−2.78030
$413$	2.32573	0.114442
$414$	13.8750	0.681917
$415$	−21.1209	−1.03679
$416$	−4.83744	−0.237175
$417$	−3.49655	−0.171227
$418$	3.74842	0.183341
$419$	19.4311	0.949274	0.474637	−	0.880182i	$-0.342579\pi$
$419$	19.4311	0.949274	0.474637	+	0.880182i	$0.342579\pi$
$420$	6.52396	0.318337
$421$	−27.4686	−1.33874	−0.669368	−	0.742931i	$-0.733435\pi$
$421$	−27.4686	−1.33874	−0.669368	+	0.742931i	$0.733435\pi$
$422$	23.0037	1.11980
$423$	−24.4180	−1.18724
$424$	10.0970	0.490352
$425$	4.54535	0.220482
$426$	−8.14336	−0.394547
$427$	−1.28163	−0.0620222
$428$	1.80681	0.0873354
$429$	1.23921	0.0598295
$430$	25.4641	1.22799
$431$	18.3898	0.885804	0.442902	−	0.896570i	$-0.353949\pi$
$431$	18.3898	0.885804	0.442902	+	0.896570i	$0.353949\pi$
$432$	9.98752	0.480525
$433$	−12.9935	−0.624430	−0.312215	−	0.950012i	$-0.601071\pi$
$433$	−12.9935	−0.624430	−0.312215	+	0.950012i	$0.601071\pi$
$434$	−18.0851	−0.868113
$435$	9.19183	0.440715
$436$	−26.8809	−1.28736
$437$	6.11761	0.292645
$438$	−11.6431	−0.556330
$439$	−11.2837	−0.538540	−0.269270	−	0.963065i	$-0.586782\pi$
$439$	−11.2837	−0.538540	−0.269270	+	0.963065i	$0.586782\pi$
$440$	6.90366	0.329119
$441$	13.4198	0.639037
$442$	−28.5408	−1.35755
$443$	−2.81020	−0.133517	−0.0667584	−	0.997769i	$-0.521266\pi$
$443$	−2.81020	−0.133517	−0.0667584	+	0.997769i	$0.521266\pi$
$444$	13.3750	0.634749
$445$	40.8203	1.93507
$446$	−62.1837	−2.94448
$447$	−0.858675	−0.0406139
$448$	10.7233	0.506628
$449$	34.8829	1.64622	0.823112	−	0.567879i	$-0.192236\pi$
$449$	34.8829	1.64622	0.823112	+	0.567879i	$0.192236\pi$
$450$	18.1482	0.855513
$451$	1.15052	0.0541756
$452$	−75.6515	−3.55835
$453$	−2.08341	−0.0978873
$454$	43.7741	2.05442
$455$	−27.4407	−1.28644
$456$	6.08008	0.284726
$457$	−14.4690	−0.676834	−0.338417	−	0.940996i	$-0.609891\pi$
$457$	−14.4690	−0.676834	−0.338417	+	0.940996i	$0.609891\pi$
$458$	−53.9366	−2.52029
$459$	3.95619	0.184659
$460$	22.1361	1.03210
$461$	33.1178	1.54245	0.771225	−	0.636562i	$-0.219644\pi$
$461$	33.1178	1.54245	0.771225	+	0.636562i	$0.219644\pi$
$462$	0.703454	0.0327277
$463$	11.2461	0.522652	0.261326	−	0.965251i	$-0.415840\pi$
$463$	11.2461	0.522652	0.261326	+	0.965251i	$0.415840\pi$
$464$	−38.6500	−1.79428
$465$	5.12013	0.237440
$466$	57.8585	2.68024
$467$	23.4853	1.08677	0.543384	−	0.839484i	$-0.317143\pi$
$467$	23.4853	1.08677	0.543384	+	0.839484i	$0.317143\pi$
$468$	−76.4279	−3.53288
$469$	−18.7445	−0.865541
$470$	−58.0842	−2.67923
$471$	−4.10868	−0.189318
$472$	7.84289	0.360998
$473$	1.84151	0.0846727
$474$	−6.86317	−0.315236
$475$	8.00171	0.367144
$476$	−10.8662	−0.498052
$477$	5.63724	0.258112
$478$	−30.6590	−1.40231
$479$	−23.7888	−1.08694	−0.543469	−	0.839429i	$-0.682889\pi$
$479$	−23.7888	−1.08694	−0.543469	+	0.839429i	$0.682889\pi$
$480$	0.777441	0.0354852
$481$	−56.2572	−2.56511
$482$	29.8401	1.35918
$483$	1.14807	0.0522390
$484$	−43.8250	−1.99205
$485$	21.9547	0.996910
$486$	23.8927	1.08379
$487$	10.7009	0.484906	0.242453	−	0.970163i	$-0.422048\pi$
$487$	10.7009	0.484906	0.242453	+	0.970163i	$0.422048\pi$
$488$	−4.32194	−0.195645
$489$	3.46266	0.156587
$490$	31.9223	1.44210
$491$	−32.6989	−1.47568	−0.737841	−	0.674974i	$-0.764155\pi$
$491$	−32.6989	−1.47568	−0.737841	+	0.674974i	$0.764155\pi$
$492$	3.66641	0.165295
$493$	−15.3098	−0.689518
$494$	−50.2437	−2.26057
$495$	3.85439	0.173242
$496$	−21.5292	−0.966691
$497$	13.0407	0.584954
$498$	−7.25749	−0.325216
$499$	−39.4925	−1.76793	−0.883963	−	0.467557i	$-0.845134\pi$
$499$	−39.4925	−1.76793	−0.883963	+	0.467557i	$0.845134\pi$
$500$	−27.1243	−1.21304
$501$	0.649541	0.0290193
$502$	63.0823	2.81550
$503$	34.9015	1.55618	0.778091	−	0.628151i	$-0.216188\pi$
$503$	34.9015	1.55618	0.778091	+	0.628151i	$0.216188\pi$
$504$	−22.0829	−0.983651
$505$	−9.25142	−0.411683
$506$	2.38685	0.106108
$507$	−11.6193	−0.516032
$508$	−59.2523	−2.62890
$509$	−31.1087	−1.37887	−0.689434	−	0.724348i	$-0.742141\pi$
$509$	−31.1087	−1.37887	−0.689434	+	0.724348i	$0.742141\pi$
$510$	4.58689	0.203111
$511$	18.6452	0.824814
$512$	42.1527	1.86290
$513$	6.96455	0.307492
$514$	51.0287	2.25078
$515$	−38.1484	−1.68102
$516$	5.86844	0.258344
$517$	−4.20052	−0.184739
$518$	−31.9352	−1.40315
$519$	−3.41482	−0.149894
$520$	−92.5364	−4.05799
$521$	−8.85774	−0.388064	−0.194032	−	0.980995i	$-0.562157\pi$
$521$	−8.85774	−0.388064	−0.194032	+	0.980995i	$0.562157\pi$
$522$	−61.1272	−2.67547
$523$	36.3920	1.59131	0.795655	−	0.605750i	$-0.207127\pi$
$523$	36.3920	1.59131	0.795655	+	0.605750i	$0.207127\pi$
$524$	69.1431	3.02053
$525$	1.50166	0.0655376
$526$	−0.625152	−0.0272579
$527$	−8.52802	−0.371486
$528$	0.837420	0.0364440
$529$	−19.1045	−0.830633
$530$	13.4096	0.582475
$531$	4.37877	0.190022
$532$	−19.1291	−0.829351
$533$	−15.4215	−0.667977
$534$	14.0265	0.606987
$535$	1.22137	0.0528046
$536$	−63.2107	−2.73029
$537$	3.40749	0.147044
$538$	−23.9247	−1.03147
$539$	2.30855	0.0994361
$540$	25.2007	1.08446
$541$	−26.6181	−1.14440	−0.572201	−	0.820113i	$-0.693910\pi$
$541$	−26.6181	−1.14440	−0.572201	+	0.820113i	$0.693910\pi$
$542$	−20.9721	−0.900830
$543$	−3.59472	−0.154264
$544$	−1.29489	−0.0555181
$545$	−18.1711	−0.778362
$546$	−9.42907	−0.403527
$547$	−28.7520	−1.22935	−0.614674	−	0.788781i	$-0.710713\pi$
$547$	−28.7520	−1.22935	−0.614674	+	0.788781i	$0.710713\pi$
$548$	1.03052	0.0440218
$549$	−2.41298	−0.102984
$550$	3.12195	0.133120
$551$	−26.9516	−1.14818
$552$	3.87156	0.164784
$553$	10.9906	0.467368
$554$	46.1548	1.96093
$555$	9.04128	0.383781
$556$	37.0972	1.57327
$557$	−32.1673	−1.36297	−0.681486	−	0.731831i	$-0.738666\pi$
$557$	−32.1673	−1.36297	−0.681486	+	0.731831i	$0.738666\pi$
$558$	−34.0497	−1.44144
$559$	−24.6835	−1.04400
$560$	−18.5436	−0.783612
$561$	0.331713	0.0140049
$562$	−57.8444	−2.44002
$563$	37.9128	1.59783	0.798916	−	0.601442i	$-0.205407\pi$
$563$	37.9128	1.59783	0.798916	+	0.601442i	$0.205407\pi$
$564$	−13.3860	−0.563654
$565$	−51.1392	−2.15144
$566$	−8.33157	−0.350202
$567$	−11.6592	−0.489639
$568$	43.9761	1.84520
$569$	5.85738	0.245554	0.122777	−	0.992434i	$-0.460820\pi$
$569$	5.85738	0.245554	0.122777	+	0.992434i	$0.460820\pi$
$570$	8.07484	0.338218
$571$	37.3153	1.56160	0.780799	−	0.624782i	$-0.214812\pi$
$571$	37.3153	1.56160	0.780799	+	0.624782i	$0.214812\pi$
$572$	−13.1476	−0.549727
$573$	−0.564417	−0.0235789
$574$	−8.75422	−0.365394
$575$	5.09518	0.212484
$576$	20.1893	0.841220
$577$	−34.7013	−1.44463	−0.722317	−	0.691562i	$-0.756923\pi$
$577$	−34.7013	−1.44463	−0.722317	+	0.691562i	$0.756923\pi$
$578$	34.2549	1.42482
$579$	4.52195	0.187926
$580$	−97.5222	−4.04939
$581$	11.6221	0.482164
$582$	7.54397	0.312708
$583$	0.969750	0.0401630
$584$	62.8758	2.60182
$585$	−51.6641	−2.13605
$586$	−59.1633	−2.44401
$587$	37.5599	1.55026	0.775131	−	0.631800i	$-0.217684\pi$
$587$	37.5599	1.55026	0.775131	+	0.631800i	$0.217684\pi$
$588$	7.35677	0.303388
$589$	−15.0129	−0.618595
$590$	10.4160	0.428820
$591$	−2.80549	−0.115403
$592$	−38.0170	−1.56249
$593$	−14.0043	−0.575087	−0.287544	−	0.957768i	$-0.592839\pi$
$593$	−14.0043	−0.575087	−0.287544	+	0.957768i	$0.592839\pi$
$594$	2.71729	0.111492
$595$	−7.34539	−0.301132
$596$	9.11026	0.373171
$597$	3.09531	0.126683
$598$	−31.9932	−1.30830
$599$	11.3086	0.462058	0.231029	−	0.972947i	$-0.425791\pi$
$599$	11.3086	0.462058	0.231029	+	0.972947i	$0.425791\pi$
$600$	5.06392	0.206734
$601$	9.94851	0.405808	0.202904	−	0.979199i	$-0.434962\pi$
$601$	9.94851	0.405808	0.202904	+	0.979199i	$0.434962\pi$
$602$	−14.0120	−0.571085
$603$	−35.2912	−1.43717
$604$	22.1043	0.899412
$605$	−29.6250	−1.20443
$606$	−3.17893	−0.129135
$607$	−12.7104	−0.515901	−0.257950	−	0.966158i	$-0.583047\pi$
$607$	−12.7104	−0.515901	−0.257950	+	0.966158i	$0.583047\pi$
$608$	−2.27956	−0.0924482
$609$	−5.05792	−0.204957
$610$	−5.73988	−0.232401
$611$	56.3036	2.27780
$612$	−20.4584	−0.826981
$613$	−13.1924	−0.532837	−0.266418	−	0.963857i	$-0.585840\pi$
$613$	−13.1924	−0.532837	−0.266418	+	0.963857i	$0.585840\pi$
$614$	47.7201	1.92583
$615$	2.47843	0.0999401
$616$	−3.79883	−0.153059
$617$	−29.9611	−1.20619	−0.603094	−	0.797670i	$-0.706065\pi$
$617$	−29.9611	−1.20619	−0.603094	+	0.797670i	$0.706065\pi$
$618$	−13.1084	−0.527297
$619$	−14.7338	−0.592201	−0.296100	−	0.955157i	$-0.595686\pi$
$619$	−14.7338	−0.592201	−0.296100	+	0.955157i	$0.595686\pi$
$620$	−54.3229	−2.18166
$621$	4.43475	0.177960
$622$	−66.5719	−2.66929
$623$	−22.4619	−0.899917
$624$	−11.2247	−0.449349
$625$	−31.2433	−1.24973
$626$	−14.2840	−0.570903
$627$	0.583954	0.0233209
$628$	43.5917	1.73950
$629$	−15.0590	−0.600443
$630$	−29.3279	−1.16845
$631$	−2.01127	−0.0800674	−0.0400337	−	0.999198i	$-0.512747\pi$
$631$	−2.01127	−0.0800674	−0.0400337	+	0.999198i	$0.512747\pi$
$632$	37.0628	1.47428
$633$	3.58367	0.142438
$634$	85.9473	3.41340
$635$	−40.0536	−1.58948
$636$	3.09036	0.122541
$637$	−30.9436	−1.22603
$638$	−10.5155	−0.416311
$639$	24.5523	0.971276
$640$	52.0752	2.05845
$641$	−12.8645	−0.508116	−0.254058	−	0.967189i	$-0.581765\pi$
$641$	−12.8645	−0.508116	−0.254058	+	0.967189i	$0.581765\pi$
$642$	0.419683	0.0165636
$643$	19.7336	0.778219	0.389109	−	0.921192i	$-0.372783\pi$
$643$	19.7336	0.778219	0.389109	+	0.921192i	$0.372783\pi$
$644$	−12.1806	−0.479985
$645$	3.96697	0.156199
$646$	−13.4493	−0.529157
$647$	12.0645	0.474303	0.237152	−	0.971473i	$-0.423786\pi$
$647$	12.0645	0.474303	0.237152	+	0.971473i	$0.423786\pi$
$648$	−39.3173	−1.54453
$649$	0.753261	0.0295681
$650$	−41.8465	−1.64135
$651$	−2.81742	−0.110423
$652$	−36.7376	−1.43876
$653$	−18.5800	−0.727091	−0.363545	−	0.931576i	$-0.618434\pi$
$653$	−18.5800	−0.727091	−0.363545	+	0.931576i	$0.618434\pi$
$654$	−6.24386	−0.244154
$655$	46.7396	1.82627
$656$	−10.4214	−0.406886
$657$	35.1042	1.36955
$658$	31.9616	1.24599
$659$	32.5260	1.26703	0.633516	−	0.773730i	$-0.281611\pi$
$659$	32.5260	1.26703	0.633516	+	0.773730i	$0.281611\pi$
$660$	2.11299	0.0822480
$661$	−16.2296	−0.631258	−0.315629	−	0.948883i	$-0.602216\pi$
$661$	−16.2296	−0.631258	−0.315629	+	0.948883i	$0.602216\pi$
$662$	−59.3948	−2.30845
$663$	−4.44627	−0.172679
$664$	39.1922	1.52095
$665$	−12.9310	−0.501441
$666$	−60.1261	−2.32984
$667$	−17.1617	−0.664505
$668$	−6.89141	−0.266637
$669$	−9.68738	−0.374536
$670$	−83.9489	−3.24323
$671$	−0.415095	−0.0160246
$672$	−0.427797	−0.0165026
$673$	4.23575	0.163276	0.0816381	−	0.996662i	$-0.473985\pi$
$673$	4.23575	0.163276	0.0816381	+	0.996662i	$0.473985\pi$
$674$	71.4379	2.75168
$675$	5.80057	0.223264
$676$	123.277	4.74142
$677$	−6.04484	−0.232322	−0.116161	−	0.993230i	$-0.537059\pi$
$677$	−6.04484	−0.232322	−0.116161	+	0.993230i	$0.537059\pi$
$678$	−17.5722	−0.674858
$679$	−12.0808	−0.463620
$680$	−24.7703	−0.949898
$681$	6.81942	0.261321
$682$	−5.85743	−0.224293
$683$	46.9061	1.79481	0.897406	−	0.441205i	$-0.145449\pi$
$683$	46.9061	1.79481	0.897406	+	0.441205i	$0.145449\pi$
$684$	−36.0153	−1.37708
$685$	0.696617	0.0266164
$686$	−43.7028	−1.66858
$687$	−8.40259	−0.320579
$688$	−16.6804	−0.635934
$689$	−12.9985	−0.495203
$690$	5.14174	0.195743
$691$	3.02295	0.114998	0.0574992	−	0.998346i	$-0.481687\pi$
$691$	3.02295	0.114998	0.0574992	+	0.998346i	$0.481687\pi$
$692$	36.2301	1.37726
$693$	−2.12093	−0.0805673
$694$	−46.9659	−1.78280
$695$	25.0771	0.951229
$696$	−17.0565	−0.646523
$697$	−4.12804	−0.156361
$698$	32.6325	1.23516
$699$	9.01357	0.340925
$700$	−15.9321	−0.602175
$701$	17.4390	0.658661	0.329331	−	0.944215i	$-0.393177\pi$
$701$	17.4390	0.658661	0.329331	+	0.944215i	$0.393177\pi$
$702$	−36.4225	−1.37468
$703$	−26.5102	−0.999851
$704$	3.47308	0.130896
$705$	−9.04874	−0.340795
$706$	−0.597038	−0.0224698
$707$	5.09071	0.191456
$708$	2.40046	0.0902148
$709$	−41.1828	−1.54665	−0.773325	−	0.634009i	$-0.781408\pi$
$709$	−41.1828	−1.54665	−0.773325	+	0.634009i	$0.781408\pi$
$710$	58.4038	2.19186
$711$	20.6926	0.776032
$712$	−75.7466	−2.83873
$713$	−9.55961	−0.358010
$714$	−2.52399	−0.0944580
$715$	−8.88754	−0.332375
$716$	−36.1523	−1.35108
$717$	−4.77625	−0.178372
$718$	55.9804	2.08917
$719$	−4.28286	−0.159724	−0.0798618	−	0.996806i	$-0.525448\pi$
$719$	−4.28286	−0.159724	−0.0798618	+	0.996806i	$0.525448\pi$
$720$	−34.9131	−1.30113
$721$	20.9916	0.781770
$722$	23.1471	0.861447
$723$	4.64868	0.172886
$724$	38.1388	1.41742
$725$	−22.4472	−0.833668
$726$	−10.1796	−0.377801
$727$	−25.3185	−0.939010	−0.469505	−	0.882930i	$-0.655568\pi$
$727$	−25.3185	−0.939010	−0.469505	+	0.882930i	$0.655568\pi$
$728$	50.9193	1.88720
$729$	−19.3634	−0.717161
$730$	83.5041	3.09062
$731$	−6.60733	−0.244381
$732$	−1.32281	−0.0488923
$733$	−42.6912	−1.57684	−0.788418	−	0.615139i	$-0.789100\pi$
$733$	−42.6912	−1.57684	−0.788418	+	0.615139i	$0.789100\pi$
$734$	27.8004	1.02613
$735$	4.97306	0.183434
$736$	−1.45153	−0.0535042
$737$	−6.07100	−0.223628
$738$	−16.4820	−0.606711
$739$	9.90573	0.364388	0.182194	−	0.983263i	$-0.441680\pi$
$739$	9.90573	0.364388	0.182194	+	0.983263i	$0.441680\pi$
$740$	−95.9250	−3.52627
$741$	−7.82729	−0.287543
$742$	−7.37879	−0.270884
$743$	5.06666	0.185878	0.0929388	−	0.995672i	$-0.470374\pi$
$743$	5.06666	0.185878	0.0929388	+	0.995672i	$0.470374\pi$
$744$	−9.50097	−0.348322
$745$	6.15839	0.225626
$746$	−11.1463	−0.408094
$747$	21.8814	0.800600
$748$	−3.51937	−0.128681
$749$	−0.672076	−0.0245571
$750$	−6.30041	−0.230058
$751$	−38.1075	−1.39056	−0.695281	−	0.718738i	$-0.744720\pi$
$751$	−38.1075	−1.39056	−0.695281	+	0.718738i	$0.744720\pi$
$752$	38.0483	1.38748
$753$	9.82737	0.358129
$754$	140.949	5.13305
$755$	14.9422	0.543801
$756$	−13.8670	−0.504337
$757$	5.80484	0.210980	0.105490	−	0.994420i	$-0.466359\pi$
$757$	5.80484	0.210980	0.105490	+	0.994420i	$0.466359\pi$
$758$	46.7432	1.69779
$759$	0.371839	0.0134969
$760$	−43.6061	−1.58176
$761$	40.6473	1.47346	0.736731	−	0.676186i	$-0.236368\pi$
$761$	40.6473	1.47346	0.736731	+	0.676186i	$0.236368\pi$
$762$	−13.7631	−0.498583
$763$	9.99885	0.361983
$764$	5.98828	0.216648
$765$	−13.8295	−0.500008
$766$	−8.57955	−0.309992
$767$	−10.0967	−0.364570
$768$	12.4595	0.449593
$769$	3.68035	0.132717	0.0663584	−	0.997796i	$-0.478862\pi$
$769$	3.68035	0.132717	0.0663584	+	0.997796i	$0.478862\pi$
$770$	−5.04515	−0.181814
$771$	7.94959	0.286297
$772$	−47.9764	−1.72671
$773$	−1.43706	−0.0516874	−0.0258437	−	0.999666i	$-0.508227\pi$
$773$	−1.43706	−0.0516874	−0.0258437	+	0.999666i	$0.508227\pi$
$774$	−26.3810	−0.948246
$775$	−12.5038	−0.449149
$776$	−40.7393	−1.46246
$777$	−4.97508	−0.178480
$778$	−40.8453	−1.46437
$779$	−7.26708	−0.260370
$780$	−28.3224	−1.01411
$781$	4.22363	0.151133
$782$	−8.56400	−0.306248
$783$	−19.5377	−0.698219
$784$	−20.9108	−0.746815
$785$	29.4673	1.05173
$786$	16.0605	0.572858
$787$	−37.7835	−1.34683	−0.673417	−	0.739262i	$-0.735174\pi$
$787$	−37.7835	−1.34683	−0.673417	+	0.739262i	$0.735174\pi$
$788$	29.7654	1.06035
$789$	−0.0973903	−0.00346719
$790$	49.2224	1.75125
$791$	28.1400	1.00054
$792$	−7.15225	−0.254144
$793$	5.56391	0.197580
$794$	80.8109	2.86787
$795$	2.08903	0.0740903
$796$	−32.8402	−1.16399
$797$	−29.5725	−1.04751	−0.523755	−	0.851869i	$-0.675469\pi$
$797$	−29.5725	−1.04751	−0.523755	+	0.851869i	$0.675469\pi$
$798$	−4.44328	−0.157290
$799$	15.0715	0.533190
$800$	−1.89858	−0.0671248
$801$	−42.2902	−1.49425
$802$	−26.6546	−0.941207
$803$	6.03883	0.213106
$804$	−19.3468	−0.682308
$805$	−8.23392	−0.290208
$806$	78.5127	2.76549
$807$	−3.72714	−0.131202
$808$	17.1670	0.603934
$809$	−39.2331	−1.37936	−0.689680	−	0.724114i	$-0.742249\pi$
$809$	−39.2331	−1.37936	−0.689680	+	0.724114i	$0.742249\pi$
$810$	−52.2166	−1.83470
$811$	−34.8404	−1.22341	−0.611705	−	0.791086i	$-0.709516\pi$
$811$	−34.8404	−1.22341	−0.611705	+	0.791086i	$0.709516\pi$
$812$	53.6628	1.88320
$813$	−3.26718	−0.114585
$814$	−10.3432	−0.362530
$815$	−24.8340	−0.869898
$816$	−3.00466	−0.105184
$817$	−11.6317	−0.406940
$818$	−62.0661	−2.17009
$819$	28.4288	0.993382
$820$	−26.2953	−0.918273
$821$	−28.5486	−0.996352	−0.498176	−	0.867076i	$-0.665997\pi$
$821$	−28.5486	−0.996352	−0.498176	+	0.867076i	$0.665997\pi$
$822$	0.239369	0.00834894
$823$	45.5139	1.58652	0.793258	−	0.608886i	$-0.208383\pi$
$823$	45.5139	1.58652	0.793258	+	0.608886i	$0.208383\pi$
$824$	70.7886	2.46604
$825$	0.486358	0.0169328
$826$	−5.73153	−0.199425
$827$	29.7716	1.03526	0.517630	−	0.855605i	$-0.326814\pi$
$827$	29.7716	1.03526	0.517630	+	0.855605i	$0.326814\pi$
$828$	−22.9331	−0.796981
$829$	6.09594	0.211721	0.105860	−	0.994381i	$-0.466240\pi$
$829$	6.09594	0.211721	0.105860	+	0.994381i	$0.466240\pi$
$830$	52.0504	1.80670
$831$	7.19030	0.249429
$832$	−46.5529	−1.61393
$833$	−8.28305	−0.286991
$834$	8.61689	0.298379
$835$	−4.65848	−0.161213
$836$	−6.19556	−0.214278
$837$	−10.8831	−0.376174
$838$	−47.8861	−1.65420
$839$	−31.1384	−1.07502	−0.537509	−	0.843258i	$-0.680634\pi$
$839$	−31.1384	−1.07502	−0.537509	+	0.843258i	$0.680634\pi$
$840$	−8.18342	−0.282355
$841$	46.6074	1.60715
$842$	67.6936	2.33287
$843$	−9.01138	−0.310368
$844$	−38.0215	−1.30875
$845$	83.3332	2.86675
$846$	60.1757	2.06888
$847$	16.3015	0.560127
$848$	−8.78400	−0.301644
$849$	−1.29795	−0.0445454
$850$	−11.2016	−0.384210
$851$	−16.8806	−0.578661
$852$	13.4597	0.461121
$853$	−53.5520	−1.83359	−0.916793	−	0.399362i	$-0.869232\pi$
$853$	−53.5520	−1.83359	−0.916793	+	0.399362i	$0.869232\pi$
$854$	3.15844	0.108080
$855$	−24.3458	−0.832608
$856$	−2.26639	−0.0774638
$857$	0.768297	0.0262445	0.0131223	−	0.999914i	$-0.495823\pi$
$857$	0.768297	0.0262445	0.0131223	+	0.999914i	$0.495823\pi$
$858$	−3.05390	−0.104258
$859$	−48.3896	−1.65103	−0.825516	−	0.564379i	$-0.809116\pi$
$859$	−48.3896	−1.65103	−0.825516	+	0.564379i	$0.809116\pi$
$860$	−42.0882	−1.43520
$861$	−1.36379	−0.0464778
$862$	−45.3197	−1.54360
$863$	−36.0238	−1.22627	−0.613133	−	0.789980i	$-0.710091\pi$
$863$	−36.0238	−1.22627	−0.613133	+	0.789980i	$0.710091\pi$
$864$	−1.65249	−0.0562187
$865$	24.4910	0.832718
$866$	32.0213	1.08813
$867$	5.33646	0.181236
$868$	29.8918	1.01460
$869$	3.55965	0.120753
$870$	−22.6523	−0.767986
$871$	81.3754	2.75730
$872$	33.7184	1.14185
$873$	−22.7452	−0.769808
$874$	−15.0762	−0.509961
$875$	10.0894	0.341084
$876$	19.2443	0.650203
$877$	50.3964	1.70177	0.850883	−	0.525355i	$-0.176067\pi$
$877$	50.3964	1.70177	0.850883	+	0.525355i	$0.176067\pi$
$878$	27.8075	0.938457
$879$	−9.21685	−0.310876
$880$	−6.00594	−0.202460
$881$	−0.288305	−0.00971323	−0.00485661	−	0.999988i	$-0.501546\pi$
$881$	−0.288305	−0.00971323	−0.00485661	+	0.999988i	$0.501546\pi$
$882$	−33.0717	−1.11358
$883$	−11.8874	−0.400042	−0.200021	−	0.979792i	$-0.564101\pi$
$883$	−11.8874	−0.400042	−0.200021	+	0.979792i	$0.564101\pi$
$884$	47.1734	1.58661
$885$	1.62267	0.0545455
$886$	6.92546	0.232665
$887$	−49.8737	−1.67460	−0.837298	−	0.546747i	$-0.815866\pi$
$887$	−49.8737	−1.67460	−0.837298	+	0.546747i	$0.815866\pi$
$888$	−16.7771	−0.563003
$889$	22.0400	0.739198
$890$	−100.598	−3.37204
$891$	−3.77618	−0.126507
$892$	102.780	3.44132
$893$	26.5321	0.887862
$894$	2.11612	0.0707736
$895$	−24.4384	−0.816886
$896$	−28.6550	−0.957298
$897$	−4.98411	−0.166415
$898$	−85.9653	−2.86870
$899$	42.1156	1.40463
$900$	−29.9961	−0.999869
$901$	−3.47946	−0.115918
$902$	−2.83533	−0.0944061
$903$	−2.18287	−0.0726415
$904$	94.8944	3.15614
$905$	25.7812	0.856997
$906$	5.13436	0.170578
$907$	−46.5713	−1.54638	−0.773188	−	0.634177i	$-0.781339\pi$
$907$	−46.5713	−1.54638	−0.773188	+	0.634177i	$0.781339\pi$
$908$	−72.3517	−2.40108
$909$	9.58453	0.317899
$910$	67.6249	2.24174
$911$	−29.3891	−0.973704	−0.486852	−	0.873484i	$-0.661855\pi$
$911$	−29.3891	−0.973704	−0.486852	+	0.873484i	$0.661855\pi$
$912$	−5.28946	−0.175151
$913$	3.76417	0.124576
$914$	35.6575	1.17945
$915$	−0.894196	−0.0295612
$916$	89.1487	2.94555
$917$	−25.7190	−0.849318
$918$	−9.74963	−0.321786
$919$	37.4374	1.23495	0.617473	−	0.786592i	$-0.288157\pi$
$919$	37.4374	1.23495	0.617473	+	0.786592i	$0.288157\pi$
$920$	−27.7667	−0.915440
$921$	7.43415	0.244964
$922$	−81.6156	−2.68787
$923$	−56.6134	−1.86345
$924$	−1.16270	−0.0382500
$925$	−22.0796	−0.725971
$926$	−27.7149	−0.910769
$927$	39.5220	1.29807
$928$	6.39484	0.209921
$929$	23.2733	0.763572	0.381786	−	0.924251i	$-0.375309\pi$
$929$	23.2733	0.763572	0.381786	+	0.924251i	$0.375309\pi$
$930$	−12.6180	−0.413762
$931$	−14.5816	−0.477894
$932$	−95.6310	−3.13250
$933$	−10.3710	−0.339531
$934$	−57.8771	−1.89380
$935$	−2.37903	−0.0778027
$936$	95.8684	3.13356
$937$	−13.5879	−0.443896	−0.221948	−	0.975059i	$-0.571242\pi$
$937$	−13.5879	−0.443896	−0.221948	+	0.975059i	$0.571242\pi$
$938$	46.1939	1.50829
$939$	−2.22525	−0.0726184
$940$	96.0041	3.13131
$941$	−2.37562	−0.0774431	−0.0387216	−	0.999250i	$-0.512329\pi$
$941$	−2.37562	−0.0774431	−0.0387216	+	0.999250i	$0.512329\pi$
$942$	10.1254	0.329905
$943$	−4.62739	−0.150689
$944$	−6.82304	−0.222071
$945$	−9.37385	−0.304931
$946$	−4.53821	−0.147550
$947$	58.0115	1.88512	0.942561	−	0.334034i	$-0.108410\pi$
$947$	58.0115	1.88512	0.942561	+	0.334034i	$0.108410\pi$
$948$	11.3437	0.368428
$949$	−80.9442	−2.62756
$950$	−19.7194	−0.639782
$951$	13.3894	0.434182
$952$	13.6302	0.441757
$953$	−19.2010	−0.621983	−0.310991	−	0.950413i	$-0.600661\pi$
$953$	−19.2010	−0.621983	−0.310991	+	0.950413i	$0.600661\pi$
$954$	−13.8924	−0.449784
$955$	4.04798	0.130990
$956$	50.6744	1.63893
$957$	−1.63817	−0.0529544
$958$	58.6251	1.89409
$959$	−0.383322	−0.0123781
$960$	7.48168	0.241470
$961$	−7.54031	−0.243236
$962$	138.640	4.46994
$963$	−1.26535	−0.0407754
$964$	−49.3210	−1.58852
$965$	−32.4313	−1.04400
$966$	−2.82931	−0.0910314
$967$	55.0032	1.76878	0.884392	−	0.466745i	$-0.154573\pi$
$967$	55.0032	1.76878	0.884392	+	0.466745i	$0.154573\pi$
$968$	54.9725	1.76688
$969$	−2.09522	−0.0673083
$970$	−54.1051	−1.73721
$971$	−15.0193	−0.481991	−0.240995	−	0.970526i	$-0.577474\pi$
$971$	−15.0193	−0.481991	−0.240995	+	0.970526i	$0.577474\pi$
$972$	−39.4908	−1.26667
$973$	−13.7990	−0.442375
$974$	−26.3714	−0.844994
$975$	−6.51912	−0.208779
$976$	3.75993	0.120352
$977$	−38.4411	−1.22984	−0.614920	−	0.788590i	$-0.710812\pi$
$977$	−38.4411	−1.22984	−0.614920	+	0.788590i	$0.710812\pi$
$978$	−8.53337	−0.272867
$979$	−7.27499	−0.232510
$980$	−52.7625	−1.68544
$981$	18.8253	0.601047
$982$	80.5832	2.57151
$983$	20.0840	0.640581	0.320291	−	0.947319i	$-0.396219\pi$
$983$	20.0840	0.640581	0.320291	+	0.947319i	$0.396219\pi$
$984$	−4.59901	−0.146611
$985$	20.1209	0.641105
$986$	37.7294	1.20155
$987$	4.97918	0.158489
$988$	83.0449	2.64201
$989$	−7.40658	−0.235516
$990$	−9.49875	−0.301890
$991$	13.8875	0.441151	0.220575	−	0.975370i	$-0.429207\pi$
$991$	13.8875	0.441151	0.220575	+	0.975370i	$0.429207\pi$
$992$	3.56212	0.113097
$993$	−9.25291	−0.293632
$994$	−32.1374	−1.01934
$995$	−22.1994	−0.703770
$996$	11.9955	0.380091
$997$	12.3506	0.391147	0.195573	−	0.980689i	$-0.437343\pi$
$997$	12.3506	0.391147	0.195573	+	0.980689i	$0.437343\pi$
$998$	97.3252	3.08078
$999$	−19.2177	−0.608020

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6047.2.a.a.1.17	✓	217

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6047.2.a.a.1.17	✓	217	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:	\( N \)	\(=\)	\( 6047 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6047.a (trivial)

\(f(q)\)	\(=\)	\(q-2.46440 q^{2} -0.383920 q^{3} +4.07326 q^{4} +2.75346 q^{5} +0.946133 q^{6} -1.51513 q^{7} -5.10935 q^{8} -2.85261 q^{9} +O(q^{10})\)	\(q-2.46440 q^{2} -0.383920 q^{3} +4.07326 q^{4} +2.75346 q^{5} +0.946133 q^{6} -1.51513 q^{7} -5.10935 q^{8} -2.85261 q^{9} -6.78563 q^{10} -0.490721 q^{11} -1.56381 q^{12} +6.57761 q^{13} +3.73388 q^{14} -1.05711 q^{15} +4.44495 q^{16} +1.76071 q^{17} +7.02996 q^{18} +3.09958 q^{19} +11.2156 q^{20} +0.581688 q^{21} +1.20933 q^{22} +1.97369 q^{23} +1.96158 q^{24} +2.58155 q^{25} -16.2098 q^{26} +2.24693 q^{27} -6.17151 q^{28} -8.69525 q^{29} +2.60514 q^{30} -4.84352 q^{31} -0.735440 q^{32} +0.188398 q^{33} -4.33908 q^{34} -4.17184 q^{35} -11.6194 q^{36} -8.55284 q^{37} -7.63860 q^{38} -2.52528 q^{39} -14.0684 q^{40} -2.34454 q^{41} -1.43351 q^{42} -3.75266 q^{43} -1.99884 q^{44} -7.85454 q^{45} -4.86396 q^{46} +8.55989 q^{47} -1.70651 q^{48} -4.70439 q^{49} -6.36197 q^{50} -0.675971 q^{51} +26.7923 q^{52} -1.97617 q^{53} -5.53734 q^{54} -1.35118 q^{55} +7.74131 q^{56} -1.18999 q^{57} +21.4286 q^{58} -1.53501 q^{59} -4.30589 q^{60} +0.845887 q^{61} +11.9364 q^{62} +4.32206 q^{63} -7.07749 q^{64} +18.1112 q^{65} -0.464288 q^{66} +12.3716 q^{67} +7.17182 q^{68} -0.757740 q^{69} +10.2811 q^{70} -8.60699 q^{71} +14.5750 q^{72} -12.3060 q^{73} +21.0776 q^{74} -0.991109 q^{75} +12.6254 q^{76} +0.743505 q^{77} +6.22329 q^{78} -7.25392 q^{79} +12.2390 q^{80} +7.69517 q^{81} +5.77788 q^{82} -7.67069 q^{83} +2.36937 q^{84} +4.84804 q^{85} +9.24805 q^{86} +3.33828 q^{87} +2.50727 q^{88} +14.8251 q^{89} +19.3567 q^{90} -9.96590 q^{91} +8.03936 q^{92} +1.85953 q^{93} -21.0950 q^{94} +8.53457 q^{95} +0.282351 q^{96} +7.97348 q^{97} +11.5935 q^{98} +1.39983 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 217 q - 20 q^{2} - 27 q^{3} + 184 q^{4} - 19 q^{5} - 17 q^{6} - 48 q^{7} - 57 q^{8} + 152 q^{9}+O(q^{10}) \) 217 * q - 20 * q^2 - 27 * q^3 + 184 * q^4 - 19 * q^5 - 17 * q^6 - 48 * q^7 - 57 * q^8 + 152 * q^9	\( 217 q - 20 q^{2} - 27 q^{3} + 184 q^{4} - 19 q^{5} - 17 q^{6} - 48 q^{7} - 57 q^{8} + 152 q^{9} - 46 q^{10} - 32 q^{11} - 72 q^{12} - 80 q^{13} - 22 q^{14} - 43 q^{15} + 122 q^{16} - 61 q^{17} - 88 q^{18} - 43 q^{19} - 41 q^{20} - 61 q^{21} - 93 q^{22} - 60 q^{23} - 41 q^{24} + 26 q^{25} - 9 q^{26} - 93 q^{27} - 126 q^{28} - 47 q^{29} - 36 q^{30} - 100 q^{31} - 114 q^{32} - 133 q^{33} - 75 q^{34} - 37 q^{35} + 75 q^{36} - 264 q^{37} - 35 q^{38} - 47 q^{39} - 118 q^{40} - 72 q^{41} - 64 q^{42} - 107 q^{43} - 59 q^{44} - 69 q^{45} - 111 q^{46} - 54 q^{47} - 135 q^{48} + 33 q^{49} - 42 q^{50} - 26 q^{51} - 173 q^{52} - 103 q^{53} - 28 q^{54} - 78 q^{55} - 44 q^{56} - 205 q^{57} - 189 q^{58} - 38 q^{59} - 105 q^{60} - 108 q^{61} - 14 q^{62} - 116 q^{63} + 39 q^{64} - 146 q^{65} + 5 q^{66} - 206 q^{67} - 62 q^{68} - 55 q^{69} - 125 q^{70} - 78 q^{71} - 225 q^{72} - 326 q^{73} + 3 q^{74} - 95 q^{75} - 84 q^{76} - 79 q^{77} - 86 q^{78} - 117 q^{79} - 39 q^{80} + q^{81} - 96 q^{82} - 23 q^{83} - 57 q^{84} - 224 q^{85} - 7 q^{86} - 45 q^{87} - 250 q^{88} - 104 q^{89} - 36 q^{90} - 96 q^{91} - 137 q^{92} - 155 q^{93} - 48 q^{94} - 38 q^{95} - 33 q^{96} - 447 q^{97} - 46 q^{98} - 94 q^{99}+O(q^{100}) \) 217 * q - 20 * q^2 - 27 * q^3 + 184 * q^4 - 19 * q^5 - 17 * q^6 - 48 * q^7 - 57 * q^8 + 152 * q^9 - 46 * q^10 - 32 * q^11 - 72 * q^12 - 80 * q^13 - 22 * q^14 - 43 * q^15 + 122 * q^16 - 61 * q^17 - 88 * q^18 - 43 * q^19 - 41 * q^20 - 61 * q^21 - 93 * q^22 - 60 * q^23 - 41 * q^24 + 26 * q^25 - 9 * q^26 - 93 * q^27 - 126 * q^28 - 47 * q^29 - 36 * q^30 - 100 * q^31 - 114 * q^32 - 133 * q^33 - 75 * q^34 - 37 * q^35 + 75 * q^36 - 264 * q^37 - 35 * q^38 - 47 * q^39 - 118 * q^40 - 72 * q^41 - 64 * q^42 - 107 * q^43 - 59 * q^44 - 69 * q^45 - 111 * q^46 - 54 * q^47 - 135 * q^48 + 33 * q^49 - 42 * q^50 - 26 * q^51 - 173 * q^52 - 103 * q^53 - 28 * q^54 - 78 * q^55 - 44 * q^56 - 205 * q^57 - 189 * q^58 - 38 * q^59 - 105 * q^60 - 108 * q^61 - 14 * q^62 - 116 * q^63 + 39 * q^64 - 146 * q^65 + 5 * q^66 - 206 * q^67 - 62 * q^68 - 55 * q^69 - 125 * q^70 - 78 * q^71 - 225 * q^72 - 326 * q^73 + 3 * q^74 - 95 * q^75 - 84 * q^76 - 79 * q^77 - 86 * q^78 - 117 * q^79 - 39 * q^80 + q^81 - 96 * q^82 - 23 * q^83 - 57 * q^84 - 224 * q^85 - 7 * q^86 - 45 * q^87 - 250 * q^88 - 104 * q^89 - 36 * q^90 - 96 * q^91 - 137 * q^92 - 155 * q^93 - 48 * q^94 - 38 * q^95 - 33 * q^96 - 447 * q^97 - 46 * q^98 - 94 * q^99

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