LMFDB - Embedded newform 4021.2.a.b.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4021,2,Mod(1,4021)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4021, 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("4021.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4021 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4021.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.1078466528$
Analytic rank:	$1$
Dimension:	$151$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	4021.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.41856 q^{2} -1.61942 q^{3} +3.84946 q^{4} -1.02567 q^{5} +3.91668 q^{6} +2.10305 q^{7} -4.47303 q^{8} -0.377473 q^{9} +O(q^{10})$	\(q-2.41856 q^{2} -1.61942 q^{3} +3.84946 q^{4} -1.02567 q^{5} +3.91668 q^{6} +2.10305 q^{7} -4.47303 q^{8} -0.377473 q^{9} +2.48065 q^{10} -4.37046 q^{11} -6.23389 q^{12} -5.19992 q^{13} -5.08636 q^{14} +1.66099 q^{15} +3.11940 q^{16} -5.84957 q^{17} +0.912942 q^{18} +6.58285 q^{19} -3.94827 q^{20} -3.40573 q^{21} +10.5702 q^{22} +3.51046 q^{23} +7.24372 q^{24} -3.94800 q^{25} +12.5763 q^{26} +5.46955 q^{27} +8.09560 q^{28} +5.73264 q^{29} -4.01722 q^{30} +3.73047 q^{31} +1.40158 q^{32} +7.07762 q^{33} +14.1476 q^{34} -2.15704 q^{35} -1.45306 q^{36} +10.4322 q^{37} -15.9211 q^{38} +8.42087 q^{39} +4.58785 q^{40} -11.2049 q^{41} +8.23697 q^{42} -0.140001 q^{43} -16.8239 q^{44} +0.387162 q^{45} -8.49027 q^{46} +10.9683 q^{47} -5.05163 q^{48} -2.57718 q^{49} +9.54850 q^{50} +9.47291 q^{51} -20.0169 q^{52} -7.39533 q^{53} -13.2285 q^{54} +4.48265 q^{55} -9.40701 q^{56} -10.6604 q^{57} -13.8648 q^{58} -7.00929 q^{59} +6.39392 q^{60} +8.01412 q^{61} -9.02237 q^{62} -0.793844 q^{63} -9.62863 q^{64} +5.33341 q^{65} -17.1177 q^{66} +8.25343 q^{67} -22.5176 q^{68} -5.68491 q^{69} +5.21693 q^{70} +6.75634 q^{71} +1.68845 q^{72} +7.21300 q^{73} -25.2311 q^{74} +6.39348 q^{75} +25.3404 q^{76} -9.19129 q^{77} -20.3664 q^{78} -10.3761 q^{79} -3.19948 q^{80} -7.72510 q^{81} +27.0997 q^{82} -6.10896 q^{83} -13.1102 q^{84} +5.99972 q^{85} +0.338601 q^{86} -9.28357 q^{87} +19.5492 q^{88} -4.09859 q^{89} -0.936377 q^{90} -10.9357 q^{91} +13.5134 q^{92} -6.04120 q^{93} -26.5276 q^{94} -6.75183 q^{95} -2.26975 q^{96} -2.80801 q^{97} +6.23308 q^{98} +1.64973 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 151 q - 16 q^{2} - 29 q^{3} + 120 q^{4} - 27 q^{5} - 18 q^{6} - 18 q^{7} - 48 q^{8} + 98 q^{9}+O(q^{10}) $ 151 * q - 16 * q^2 - 29 * q^3 + 120 * q^4 - 27 * q^5 - 18 * q^6 - 18 * q^7 - 48 * q^8 + 98 * q^9	\( 151 q - 16 q^{2} - 29 q^{3} + 120 q^{4} - 27 q^{5} - 18 q^{6} - 18 q^{7} - 48 q^{8} + 98 q^{9} - 7 q^{10} - 126 q^{11} - 47 q^{12} - 10 q^{13} - 58 q^{14} - 50 q^{15} + 74 q^{16} - 39 q^{17} - 47 q^{18} - 48 q^{19} - 64 q^{20} - 50 q^{21} - 7 q^{22} - 91 q^{23} - 44 q^{24} + 102 q^{25} - 94 q^{26} - 92 q^{27} - 27 q^{28} - 79 q^{29} - 12 q^{30} - 33 q^{31} - 102 q^{32} - 7 q^{33} - 17 q^{34} - 183 q^{35} - 6 q^{36} - 24 q^{37} - 77 q^{38} - 81 q^{39} - 37 q^{40} - 62 q^{41} + 4 q^{42} - 74 q^{43} - 209 q^{44} - 35 q^{45} - 37 q^{46} - 127 q^{47} - 59 q^{48} + 75 q^{49} - 79 q^{50} - 138 q^{51} - 12 q^{52} - 104 q^{53} - 43 q^{54} - 49 q^{55} - 167 q^{56} - 19 q^{57} - 32 q^{58} - 207 q^{59} - 94 q^{60} - 57 q^{61} - 69 q^{62} - 49 q^{63} - 4 q^{64} - 78 q^{65} - 51 q^{66} - 92 q^{67} - 80 q^{68} - 84 q^{69} + 5 q^{70} - 217 q^{71} - 79 q^{72} + 2 q^{73} - 113 q^{74} - 173 q^{75} - 70 q^{76} - 85 q^{77} - 46 q^{78} - 70 q^{79} - 95 q^{80} - 49 q^{81} - 12 q^{82} - 109 q^{83} - 114 q^{84} - 25 q^{85} - 136 q^{86} - 60 q^{87} - 2 q^{88} - 144 q^{89} - 55 q^{90} - 62 q^{91} - 175 q^{92} - 42 q^{93} - 15 q^{94} - 189 q^{95} - 64 q^{96} - 24 q^{97} - 37 q^{98} - 293 q^{99}+O(q^{100}) \) 151 * q - 16 * q^2 - 29 * q^3 + 120 * q^4 - 27 * q^5 - 18 * q^6 - 18 * q^7 - 48 * q^8 + 98 * q^9 - 7 * q^10 - 126 * q^11 - 47 * q^12 - 10 * q^13 - 58 * q^14 - 50 * q^15 + 74 * q^16 - 39 * q^17 - 47 * q^18 - 48 * q^19 - 64 * q^20 - 50 * q^21 - 7 * q^22 - 91 * q^23 - 44 * q^24 + 102 * q^25 - 94 * q^26 - 92 * q^27 - 27 * q^28 - 79 * q^29 - 12 * q^30 - 33 * q^31 - 102 * q^32 - 7 * q^33 - 17 * q^34 - 183 * q^35 - 6 * q^36 - 24 * q^37 - 77 * q^38 - 81 * q^39 - 37 * q^40 - 62 * q^41 + 4 * q^42 - 74 * q^43 - 209 * q^44 - 35 * q^45 - 37 * q^46 - 127 * q^47 - 59 * q^48 + 75 * q^49 - 79 * q^50 - 138 * q^51 - 12 * q^52 - 104 * q^53 - 43 * q^54 - 49 * q^55 - 167 * q^56 - 19 * q^57 - 32 * q^58 - 207 * q^59 - 94 * q^60 - 57 * q^61 - 69 * q^62 - 49 * q^63 - 4 * q^64 - 78 * q^65 - 51 * q^66 - 92 * q^67 - 80 * q^68 - 84 * q^69 + 5 * q^70 - 217 * q^71 - 79 * q^72 + 2 * q^73 - 113 * q^74 - 173 * q^75 - 70 * q^76 - 85 * q^77 - 46 * q^78 - 70 * q^79 - 95 * q^80 - 49 * q^81 - 12 * q^82 - 109 * q^83 - 114 * q^84 - 25 * q^85 - 136 * q^86 - 60 * q^87 - 2 * q^88 - 144 * q^89 - 55 * q^90 - 62 * q^91 - 175 * q^92 - 42 * q^93 - 15 * q^94 - 189 * q^95 - 64 * q^96 - 24 * q^97 - 37 * q^98 - 293 * 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 $

$2$	−2.41856	−1.71018	−0.855092	−	0.518477i	$-0.826499\pi$
$2$	−2.41856	−1.71018	−0.855092	+	0.518477i	$0.826499\pi$
$3$	−1.61942	−0.934974	−0.467487	−	0.884000i	$-0.654840\pi$
$3$	−1.61942	−0.934974	−0.467487	+	0.884000i	$0.654840\pi$
$4$	3.84946	1.92473
$5$	−1.02567	−0.458694	−0.229347	−	0.973345i	$-0.573659\pi$
$5$	−1.02567	−0.458694	−0.229347	+	0.973345i	$0.573659\pi$
$6$	3.91668	1.59898
$7$	2.10305	0.794878	0.397439	−	0.917629i	$-0.369899\pi$
$7$	2.10305	0.794878	0.397439	+	0.917629i	$0.369899\pi$
$8$	−4.47303	−1.58146
$9$	−0.377473	−0.125824
$10$	2.48065	0.784450
$11$	−4.37046	−1.31774	−0.658871	−	0.752256i	$-0.728966\pi$
$11$	−4.37046	−1.31774	−0.658871	+	0.752256i	$0.728966\pi$
$12$	−6.23389	−1.79957
$13$	−5.19992	−1.44220	−0.721099	−	0.692832i	$-0.756363\pi$
$13$	−5.19992	−1.44220	−0.721099	+	0.692832i	$0.756363\pi$
$14$	−5.08636	−1.35939
$15$	1.66099	0.428867
$16$	3.11940	0.779851
$17$	−5.84957	−1.41873	−0.709364	−	0.704842i	$-0.751018\pi$
$17$	−5.84957	−1.41873	−0.709364	+	0.704842i	$0.751018\pi$
$18$	0.912942	0.215182
$19$	6.58285	1.51021	0.755105	−	0.655604i	$-0.227586\pi$
$19$	6.58285	1.51021	0.755105	+	0.655604i	$0.227586\pi$
$20$	−3.94827	−0.882861
$21$	−3.40573	−0.743190
$22$	10.5702	2.25358
$23$	3.51046	0.731981	0.365991	−	0.930619i	$-0.380730\pi$
$23$	3.51046	0.731981	0.365991	+	0.930619i	$0.380730\pi$
$24$	7.24372	1.47862
$25$	−3.94800	−0.789600
$26$	12.5763	2.46643
$27$	5.46955	1.05262
$28$	8.09560	1.52992
$29$	5.73264	1.06453	0.532263	−	0.846579i	$-0.321342\pi$
$29$	5.73264	1.06453	0.532263	+	0.846579i	$0.321342\pi$
$30$	−4.01722	−0.733441
$31$	3.73047	0.670011	0.335006	−	0.942216i	$-0.391262\pi$
$31$	3.73047	0.670011	0.335006	+	0.942216i	$0.391262\pi$
$32$	1.40158	0.247767
$33$	7.07762	1.23205
$34$	14.1476	2.42629
$35$	−2.15704	−0.364606
$36$	−1.45306	−0.242177
$37$	10.4322	1.71505	0.857525	−	0.514442i	$-0.172001\pi$
$37$	10.4322	1.71505	0.857525	+	0.514442i	$0.172001\pi$
$38$	−15.9211	−2.58274
$39$	8.42087	1.34842
$40$	4.58785	0.725404
$41$	−11.2049	−1.74991	−0.874955	−	0.484205i	$-0.839109\pi$
$41$	−11.2049	−1.74991	−0.874955	+	0.484205i	$0.839109\pi$
$42$	8.23697	1.27099
$43$	−0.140001	−0.0213499	−0.0106750	−	0.999943i	$-0.503398\pi$
$43$	−0.140001	−0.0213499	−0.0106750	+	0.999943i	$0.503398\pi$
$44$	−16.8239	−2.53630
$45$	0.387162	0.0577148
$46$	−8.49027	−1.25182
$47$	10.9683	1.59989	0.799946	−	0.600072i	$-0.204861\pi$
$47$	10.9683	1.59989	0.799946	+	0.600072i	$0.204861\pi$
$48$	−5.05163	−0.729140
$49$	−2.57718	−0.368168
$50$	9.54850	1.35036
$51$	9.47291	1.32647
$52$	−20.0169	−2.77584
$53$	−7.39533	−1.01583	−0.507913	−	0.861408i	$-0.669583\pi$
$53$	−7.39533	−1.01583	−0.507913	+	0.861408i	$0.669583\pi$
$54$	−13.2285	−1.80017
$55$	4.48265	0.604440
$56$	−9.40701	−1.25706
$57$	−10.6604	−1.41201
$58$	−13.8648	−1.82053
$59$	−7.00929	−0.912532	−0.456266	−	0.889843i	$-0.650813\pi$
$59$	−7.00929	−0.912532	−0.456266	+	0.889843i	$0.650813\pi$
$60$	6.39392	0.825452
$61$	8.01412	1.02610	0.513051	−	0.858358i	$-0.328515\pi$
$61$	8.01412	1.02610	0.513051	+	0.858358i	$0.328515\pi$
$62$	−9.02237	−1.14584
$63$	−0.793844	−0.100015
$64$	−9.62863	−1.20358
$65$	5.33341	0.661528
$66$	−17.1177	−2.10704
$67$	8.25343	1.00832	0.504158	−	0.863611i	$-0.331803\pi$
$67$	8.25343	1.00832	0.504158	+	0.863611i	$0.331803\pi$
$68$	−22.5176	−2.73067
$69$	−5.68491	−0.684383
$70$	5.21693	0.623543
$71$	6.75634	0.801830	0.400915	−	0.916115i	$-0.368692\pi$
$71$	6.75634	0.801830	0.400915	+	0.916115i	$0.368692\pi$
$72$	1.68845	0.198985
$73$	7.21300	0.844218	0.422109	−	0.906545i	$-0.361290\pi$
$73$	7.21300	0.844218	0.422109	+	0.906545i	$0.361290\pi$
$74$	−25.2311	−2.93305
$75$	6.39348	0.738255
$76$	25.3404	2.90674
$77$	−9.19129	−1.04745
$78$	−20.3664	−2.30604
$79$	−10.3761	−1.16740	−0.583700	−	0.811970i	$-0.698395\pi$
$79$	−10.3761	−1.16740	−0.583700	+	0.811970i	$0.698395\pi$
$80$	−3.19948	−0.357713
$81$	−7.72510	−0.858344
$82$	27.0997	2.99267
$83$	−6.10896	−0.670545	−0.335273	−	0.942121i	$-0.608828\pi$
$83$	−6.10896	−0.670545	−0.335273	+	0.942121i	$0.608828\pi$
$84$	−13.1102	−1.43044
$85$	5.99972	0.650762
$86$	0.338601	0.0365123
$87$	−9.28357	−0.995303
$88$	19.5492	2.08395
$89$	−4.09859	−0.434449	−0.217225	−	0.976122i	$-0.569700\pi$
$89$	−4.09859	−0.434449	−0.217225	+	0.976122i	$0.569700\pi$
$90$	−0.936377	−0.0987028
$91$	−10.9357	−1.14637
$92$	13.5134	1.40886
$93$	−6.04120	−0.626443
$94$	−26.5276	−2.73611
$95$	−6.75183	−0.692724
$96$	−2.26975	−0.231656
$97$	−2.80801	−0.285110	−0.142555	−	0.989787i	$-0.545532\pi$
$97$	−2.80801	−0.285110	−0.142555	+	0.989787i	$0.545532\pi$
$98$	6.23308	0.629636
$99$	1.64973	0.165804
$100$	−15.1977	−1.51977
$101$	18.1255	1.80355	0.901777	−	0.432201i	$-0.142263\pi$
$101$	18.1255	1.80355	0.901777	+	0.432201i	$0.142263\pi$
$102$	−22.9109	−2.26851
$103$	12.4449	1.22623	0.613116	−	0.789993i	$-0.289916\pi$
$103$	12.4449	1.22623	0.613116	+	0.789993i	$0.289916\pi$
$104$	23.2594	2.28077
$105$	3.49315	0.340897
$106$	17.8861	1.73725
$107$	11.6653	1.12773	0.563864	−	0.825867i	$-0.309314\pi$
$107$	11.6653	1.12773	0.563864	+	0.825867i	$0.309314\pi$
$108$	21.0548	2.02600
$109$	−16.3584	−1.56685	−0.783424	−	0.621487i	$-0.786529\pi$
$109$	−16.3584	−1.56685	−0.783424	+	0.621487i	$0.786529\pi$
$110$	−10.8416	−1.03370
$111$	−16.8942	−1.60353
$112$	6.56026	0.619886
$113$	−3.80332	−0.357786	−0.178893	−	0.983869i	$-0.557252\pi$
$113$	−3.80332	−0.357786	−0.178893	+	0.983869i	$0.557252\pi$
$114$	25.7829	2.41479
$115$	−3.60057	−0.335755
$116$	22.0676	2.04892
$117$	1.96283	0.181464
$118$	16.9524	1.56060
$119$	−12.3019	−1.12772
$120$	−7.42967	−0.678233
$121$	8.10090	0.736446
$122$	−19.3827	−1.75482
$123$	18.1454	1.63612
$124$	14.3603	1.28959
$125$	9.17770	0.820878
$126$	1.91996	0.171044
$127$	19.1516	1.69943	0.849714	−	0.527245i	$-0.176775\pi$
$127$	19.1516	1.69943	0.849714	+	0.527245i	$0.176775\pi$
$128$	20.4843	1.81057
$129$	0.226720	0.0199616
$130$	−12.8992	−1.13133
$131$	13.5602	1.18476	0.592378	−	0.805660i	$-0.298189\pi$
$131$	13.5602	1.18476	0.592378	+	0.805660i	$0.298189\pi$
$132$	27.2450	2.37137
$133$	13.8441	1.20043
$134$	−19.9615	−1.72441
$135$	−5.60996	−0.482828
$136$	26.1653	2.24365
$137$	6.61367	0.565044	0.282522	−	0.959261i	$-0.408829\pi$
$137$	6.61367	0.565044	0.282522	+	0.959261i	$0.408829\pi$
$138$	13.7493	1.17042
$139$	11.7285	0.994795	0.497397	−	0.867523i	$-0.334289\pi$
$139$	11.7285	0.994795	0.497397	+	0.867523i	$0.334289\pi$
$140$	−8.30342	−0.701767
$141$	−17.7623	−1.49586
$142$	−16.3407	−1.37128
$143$	22.7260	1.90045
$144$	−1.17749	−0.0981241
$145$	−5.87980	−0.488291
$146$	−17.4451	−1.44377
$147$	4.17354	0.344228
$148$	40.1585	3.30101
$149$	−18.2652	−1.49634	−0.748171	−	0.663506i	$-0.769068\pi$
$149$	−18.2652	−1.49634	−0.748171	+	0.663506i	$0.769068\pi$
$150$	−15.4630	−1.26255
$151$	0.264835	0.0215520	0.0107760	−	0.999942i	$-0.496570\pi$
$151$	0.264835	0.0215520	0.0107760	+	0.999942i	$0.496570\pi$
$152$	−29.4453	−2.38833
$153$	2.20805	0.178510
$154$	22.2297	1.79132
$155$	−3.82623	−0.307330
$156$	32.4158	2.59534
$157$	−20.7199	−1.65363	−0.826814	−	0.562475i	$-0.809849\pi$
$157$	−20.7199	−1.65363	−0.826814	+	0.562475i	$0.809849\pi$
$158$	25.0952	1.99647
$159$	11.9762	0.949771
$160$	−1.43756	−0.113649
$161$	7.38267	0.581836
$162$	18.6836	1.46793
$163$	−4.07631	−0.319281	−0.159641	−	0.987175i	$-0.551034\pi$
$163$	−4.07631	−0.319281	−0.159641	+	0.987175i	$0.551034\pi$
$164$	−43.1327	−3.36810
$165$	−7.25930	−0.565136
$166$	14.7749	1.14676
$167$	−16.5514	−1.28078	−0.640392	−	0.768048i	$-0.721228\pi$
$167$	−16.5514	−1.28078	−0.640392	+	0.768048i	$0.721228\pi$
$168$	15.2339	1.17532
$169$	14.0392	1.07994
$170$	−14.5107	−1.11292
$171$	−2.48485	−0.190021
$172$	−0.538927	−0.0410928
$173$	−10.4382	−0.793600	−0.396800	−	0.917905i	$-0.629879\pi$
$173$	−10.4382	−0.793600	−0.396800	+	0.917905i	$0.629879\pi$
$174$	22.4529	1.70215
$175$	−8.30284	−0.627636
$176$	−13.6332	−1.02764
$177$	11.3510	0.853193
$178$	9.91270	0.742988
$179$	−15.8491	−1.18462	−0.592310	−	0.805710i	$-0.701784\pi$
$179$	−15.8491	−1.18462	−0.592310	+	0.805710i	$0.701784\pi$
$180$	1.49036	0.111085
$181$	−26.3452	−1.95822	−0.979112	−	0.203324i	$-0.934826\pi$
$181$	−26.3452	−1.95822	−0.979112	+	0.203324i	$0.934826\pi$
$182$	26.4487	1.96051
$183$	−12.9782	−0.959379
$184$	−15.7024	−1.15760
$185$	−10.7000	−0.786683
$186$	14.6110	1.07133
$187$	25.5653	1.86952
$188$	42.2220	3.07936
$189$	11.5027	0.836702
$190$	16.3298	1.18468
$191$	4.41380	0.319371	0.159686	−	0.987168i	$-0.448952\pi$
$191$	4.41380	0.319371	0.159686	+	0.987168i	$0.448952\pi$
$192$	15.5928	1.12531
$193$	−8.06629	−0.580624	−0.290312	−	0.956932i	$-0.593759\pi$
$193$	−8.06629	−0.580624	−0.290312	+	0.956932i	$0.593759\pi$
$194$	6.79135	0.487591
$195$	−8.63703	−0.618511
$196$	−9.92074	−0.708624
$197$	−10.7916	−0.768867	−0.384434	−	0.923153i	$-0.625603\pi$
$197$	−10.7916	−0.768867	−0.384434	+	0.923153i	$0.625603\pi$
$198$	−3.98997	−0.283555
$199$	15.0209	1.06480	0.532401	−	0.846492i	$-0.321290\pi$
$199$	15.0209	1.06480	0.532401	+	0.846492i	$0.321290\pi$
$200$	17.6595	1.24872
$201$	−13.3658	−0.942750
$202$	−43.8377	−3.08441
$203$	12.0560	0.846168
$204$	36.4656	2.55310
$205$	11.4925	0.802672
$206$	−30.0988	−2.09708
$207$	−1.32510	−0.0921009
$208$	−16.2207	−1.12470
$209$	−28.7701	−1.99007
$210$	−8.44841	−0.582996
$211$	6.05428	0.416794	0.208397	−	0.978044i	$-0.433175\pi$
$211$	6.05428	0.416794	0.208397	+	0.978044i	$0.433175\pi$
$212$	−28.4680	−1.95519
$213$	−10.9414	−0.749690
$214$	−28.2133	−1.92862
$215$	0.143595	0.00979308
$216$	−24.4655	−1.66467
$217$	7.84536	0.532577
$218$	39.5638	2.67960
$219$	−11.6809	−0.789322
$220$	17.2558	1.16338
$221$	30.4173	2.04609
$222$	40.8597	2.74233
$223$	17.8451	1.19499	0.597497	−	0.801871i	$-0.296162\pi$
$223$	17.8451	1.19499	0.597497	+	0.801871i	$0.296162\pi$
$224$	2.94760	0.196945
$225$	1.49026	0.0993508
$226$	9.19858	0.611880
$227$	−2.47478	−0.164257	−0.0821285	−	0.996622i	$-0.526172\pi$
$227$	−2.47478	−0.164257	−0.0821285	+	0.996622i	$0.526172\pi$
$228$	−41.0368	−2.71773
$229$	−9.48197	−0.626586	−0.313293	−	0.949656i	$-0.601432\pi$
$229$	−9.48197	−0.626586	−0.313293	+	0.949656i	$0.601432\pi$
$230$	8.70822	0.574203
$231$	14.8846	0.979334
$232$	−25.6423	−1.68350
$233$	−2.40567	−0.157601	−0.0788004	−	0.996890i	$-0.525109\pi$
$233$	−2.40567	−0.157601	−0.0788004	+	0.996890i	$0.525109\pi$
$234$	−4.74723	−0.310336
$235$	−11.2499	−0.733860
$236$	−26.9820	−1.75638
$237$	16.8032	1.09149
$238$	29.7530	1.92860
$239$	−8.82866	−0.571079	−0.285539	−	0.958367i	$-0.592173\pi$
$239$	−8.82866	−0.571079	−0.285539	+	0.958367i	$0.592173\pi$
$240$	5.18131	0.334452
$241$	13.9229	0.896851	0.448426	−	0.893820i	$-0.351985\pi$
$241$	13.9229	0.896851	0.448426	+	0.893820i	$0.351985\pi$
$242$	−19.5926	−1.25946
$243$	−3.89847	−0.250087
$244$	30.8500	1.97497
$245$	2.64334	0.168877
$246$	−43.8859	−2.79806
$247$	−34.2303	−2.17802
$248$	−16.6865	−1.05959
$249$	9.89298	0.626942
$250$	−22.1969	−1.40385
$251$	−0.0312357	−0.00197158	−0.000985791	−	1.00000i	$-0.500314\pi$
$251$	−0.0312357	−0.00197158	−0.000985791		1.00000i	$0.500314\pi$
$252$	−3.05587	−0.192502
$253$	−15.3423	−0.964563
$254$	−46.3193	−2.90633
$255$	−9.71609	−0.608445
$256$	−30.2853	−1.89283
$257$	−3.38228	−0.210981	−0.105490	−	0.994420i	$-0.533641\pi$
$257$	−3.38228	−0.210981	−0.105490	+	0.994420i	$0.533641\pi$
$258$	−0.548338	−0.0341380
$259$	21.9395	1.36326
$260$	20.5307	1.27326
$261$	−2.16392	−0.133943
$262$	−32.7961	−2.02615
$263$	17.6679	1.08945	0.544723	−	0.838616i	$-0.316635\pi$
$263$	17.6679	1.08945	0.544723	+	0.838616i	$0.316635\pi$
$264$	−31.6584	−1.94844
$265$	7.58517	0.465953
$266$	−33.4828	−2.05296
$267$	6.63734	0.406199
$268$	31.7712	1.94074
$269$	−5.92612	−0.361322	−0.180661	−	0.983545i	$-0.557824\pi$
$269$	−5.92612	−0.361322	−0.180661	+	0.983545i	$0.557824\pi$
$270$	13.5680	0.825725
$271$	−13.1845	−0.800902	−0.400451	−	0.916318i	$-0.631147\pi$
$271$	−13.1845	−0.800902	−0.400451	+	0.916318i	$0.631147\pi$
$272$	−18.2472	−1.10640
$273$	17.7095	1.07183
$274$	−15.9956	−0.966330
$275$	17.2546	1.04049
$276$	−21.8838	−1.31725
$277$	7.11373	0.427422	0.213711	−	0.976897i	$-0.431445\pi$
$277$	7.11373	0.427422	0.213711	+	0.976897i	$0.431445\pi$
$278$	−28.3660	−1.70128
$279$	−1.40815	−0.0843036
$280$	9.64849	0.576608
$281$	23.1919	1.38351	0.691757	−	0.722131i	$-0.256837\pi$
$281$	23.1919	1.38351	0.691757	+	0.722131i	$0.256837\pi$
$282$	42.9593	2.55819
$283$	30.8222	1.83219	0.916094	−	0.400963i	$-0.131325\pi$
$283$	30.8222	1.83219	0.916094	+	0.400963i	$0.131325\pi$
$284$	26.0083	1.54331
$285$	10.9341	0.647678
$286$	−54.9644	−3.25011
$287$	−23.5644	−1.39097
$288$	−0.529059	−0.0311751
$289$	17.2174	1.01279
$290$	14.2207	0.835067
$291$	4.54735	0.266571
$292$	27.7661	1.62489
$293$	−24.2107	−1.41440	−0.707202	−	0.707011i	$-0.750043\pi$
$293$	−24.2107	−1.41440	−0.707202	+	0.707011i	$0.750043\pi$
$294$	−10.0940	−0.588693
$295$	7.18922	0.418573
$296$	−46.6638	−2.71228
$297$	−23.9045	−1.38708
$298$	44.1755	2.55902
$299$	−18.2541	−1.05566
$300$	24.6114	1.42094
$301$	−0.294429	−0.0169706
$302$	−0.640521	−0.0368578
$303$	−29.3528	−1.68628
$304$	20.5346	1.17774
$305$	−8.21984	−0.470667
$306$	−5.34031	−0.305285
$307$	−17.9722	−1.02573	−0.512865	−	0.858469i	$-0.671416\pi$
$307$	−17.9722	−1.02573	−0.512865	+	0.858469i	$0.671416\pi$
$308$	−35.3815	−2.01605
$309$	−20.1535	−1.14649
$310$	9.25398	0.525591
$311$	−16.9689	−0.962220	−0.481110	−	0.876660i	$-0.659766\pi$
$311$	−16.9689	−0.962220	−0.481110	+	0.876660i	$0.659766\pi$
$312$	−37.6668	−2.13246
$313$	−23.0045	−1.30029	−0.650147	−	0.759809i	$-0.725293\pi$
$313$	−23.0045	−1.30029	−0.650147	+	0.759809i	$0.725293\pi$
$314$	50.1125	2.82801
$315$	0.814222	0.0458762
$316$	−39.9422	−2.24693
$317$	−0.567344	−0.0318652	−0.0159326	−	0.999873i	$-0.505072\pi$
$317$	−0.567344	−0.0318652	−0.0159326	+	0.999873i	$0.505072\pi$
$318$	−28.9651	−1.62428
$319$	−25.0543	−1.40277
$320$	9.87579	0.552074
$321$	−18.8911	−1.05440
$322$	−17.8555	−0.995046
$323$	−38.5068	−2.14258
$324$	−29.7374	−1.65208
$325$	20.5293	1.13876
$326$	9.85883	0.546030
$327$	26.4911	1.46496
$328$	50.1198	2.76740
$329$	23.0669	1.27172
$330$	17.5571	0.966486
$331$	0.476696	0.0262016	0.0131008	−	0.999914i	$-0.495830\pi$
$331$	0.476696	0.0262016	0.0131008	+	0.999914i	$0.495830\pi$
$332$	−23.5162	−1.29062
$333$	−3.93789	−0.215795
$334$	40.0306	2.19038
$335$	−8.46529	−0.462508
$336$	−10.6238	−0.579578
$337$	29.3099	1.59661	0.798305	−	0.602254i	$-0.205730\pi$
$337$	29.3099	1.59661	0.798305	+	0.602254i	$0.205730\pi$
$338$	−33.9547	−1.84689
$339$	6.15918	0.334521
$340$	23.0957	1.25254
$341$	−16.3038	−0.882903
$342$	6.00976	0.324971
$343$	−20.1413	−1.08753
$344$	0.626228	0.0337640
$345$	5.83085	0.313922
$346$	25.2454	1.35720
$347$	8.97196	0.481640	0.240820	−	0.970570i	$-0.422584\pi$
$347$	8.97196	0.481640	0.240820	+	0.970570i	$0.422584\pi$
$348$	−35.7367	−1.91569
$349$	−1.39297	−0.0745638	−0.0372819	−	0.999305i	$-0.511870\pi$
$349$	−1.39297	−0.0745638	−0.0372819	+	0.999305i	$0.511870\pi$
$350$	20.0810	1.07337
$351$	−28.4413	−1.51808
$352$	−6.12556	−0.326493
$353$	1.24544	0.0662879	0.0331440	−	0.999451i	$-0.489448\pi$
$353$	1.24544	0.0662879	0.0331440	+	0.999451i	$0.489448\pi$
$354$	−27.4531	−1.45912
$355$	−6.92978	−0.367795
$356$	−15.7773	−0.836197
$357$	19.9220	1.05438
$358$	38.3322	2.02592
$359$	22.0714	1.16489	0.582443	−	0.812871i	$-0.302097\pi$
$359$	22.0714	1.16489	0.582443	+	0.812871i	$0.302097\pi$
$360$	−1.73179	−0.0912733
$361$	24.3339	1.28073
$362$	63.7176	3.34892
$363$	−13.1188	−0.688557
$364$	−42.0965	−2.20646
$365$	−7.39816	−0.387238
$366$	31.3887	1.64071
$367$	15.8842	0.829146	0.414573	−	0.910016i	$-0.363931\pi$
$367$	15.8842	0.829146	0.414573	+	0.910016i	$0.363931\pi$
$368$	10.9505	0.570836
$369$	4.22954	0.220181
$370$	25.8788	1.34537
$371$	−15.5528	−0.807459
$372$	−23.2553	−1.20573
$373$	−4.46970	−0.231432	−0.115716	−	0.993282i	$-0.536916\pi$
$373$	−4.46970	−0.231432	−0.115716	+	0.993282i	$0.536916\pi$
$374$	−61.8313	−3.19722
$375$	−14.8626	−0.767500
$376$	−49.0616	−2.53016
$377$	−29.8093	−1.53526
$378$	−27.8201	−1.43091
$379$	−20.8436	−1.07066	−0.535332	−	0.844642i	$-0.679813\pi$
$379$	−20.8436	−1.07066	−0.535332	+	0.844642i	$0.679813\pi$
$380$	−25.9909	−1.33330
$381$	−31.0145	−1.58892
$382$	−10.6751	−0.546183
$383$	5.92671	0.302841	0.151420	−	0.988469i	$-0.451615\pi$
$383$	5.92671	0.302841	0.151420	+	0.988469i	$0.451615\pi$
$384$	−33.1727	−1.69284
$385$	9.42724	0.480456
$386$	19.5089	0.992974
$387$	0.0528465	0.00268634
$388$	−10.8093	−0.548760
$389$	−28.6996	−1.45513	−0.727565	−	0.686039i	$-0.759348\pi$
$389$	−28.6996	−1.45513	−0.727565	+	0.686039i	$0.759348\pi$
$390$	20.8892	1.05777
$391$	−20.5347	−1.03848
$392$	11.5278	0.582242
$393$	−21.9596	−1.10772
$394$	26.1001	1.31490
$395$	10.6424	0.535479
$396$	6.35056	0.319127
$397$	6.48639	0.325543	0.162771	−	0.986664i	$-0.447957\pi$
$397$	6.48639	0.325543	0.162771	+	0.986664i	$0.447957\pi$
$398$	−36.3290	−1.82101
$399$	−22.4194	−1.12237
$400$	−12.3154	−0.615770
$401$	9.79443	0.489110	0.244555	−	0.969635i	$-0.421358\pi$
$401$	9.79443	0.489110	0.244555	+	0.969635i	$0.421358\pi$
$402$	32.3260	1.61227
$403$	−19.3981	−0.966290
$404$	69.7733	3.47135
$405$	7.92340	0.393717
$406$	−29.1583	−1.44710
$407$	−45.5937	−2.26000
$408$	−42.3726	−2.09776
$409$	20.5482	1.01605	0.508023	−	0.861344i	$-0.330377\pi$
$409$	20.5482	1.01605	0.508023	+	0.861344i	$0.330377\pi$
$410$	−27.7954	−1.37272
$411$	−10.7103	−0.528302
$412$	47.9061	2.36016
$413$	−14.7409	−0.725352
$414$	3.20484	0.157510
$415$	6.26578	0.307575
$416$	−7.28812	−0.357330
$417$	−18.9933	−0.930107
$418$	69.5823	3.40338
$419$	0.660989	0.0322914	0.0161457	−	0.999870i	$-0.494860\pi$
$419$	0.660989	0.0322914	0.0161457	+	0.999870i	$0.494860\pi$
$420$	13.4467	0.656133
$421$	−2.66326	−0.129800	−0.0648998	−	0.997892i	$-0.520673\pi$
$421$	−2.66326	−0.129800	−0.0648998	+	0.997892i	$0.520673\pi$
$422$	−14.6427	−0.712795
$423$	−4.14024	−0.201305
$424$	33.0795	1.60648
$425$	23.0941	1.12023
$426$	26.4624	1.28211
$427$	16.8541	0.815627
$428$	44.9051	2.17057
$429$	−36.8031	−1.77687
$430$	−0.347293	−0.0167480
$431$	9.98243	0.480837	0.240418	−	0.970669i	$-0.422715\pi$
$431$	9.98243	0.480837	0.240418	+	0.970669i	$0.422715\pi$
$432$	17.0617	0.820883
$433$	11.8659	0.570239	0.285120	−	0.958492i	$-0.407967\pi$
$433$	11.8659	0.570239	0.285120	+	0.958492i	$0.407967\pi$
$434$	−18.9745	−0.910805
$435$	9.52188	0.456539
$436$	−62.9709	−3.01576
$437$	23.1088	1.10545
$438$	28.2510	1.34989
$439$	−28.8584	−1.37734	−0.688669	−	0.725076i	$-0.741805\pi$
$439$	−28.8584	−1.37734	−0.688669	+	0.725076i	$0.741805\pi$
$440$	−20.0510	−0.955895
$441$	0.972815	0.0463245
$442$	−73.5662	−3.49919
$443$	14.1430	0.671954	0.335977	−	0.941870i	$-0.390934\pi$
$443$	14.1430	0.671954	0.335977	+	0.941870i	$0.390934\pi$
$444$	−65.0335	−3.08635
$445$	4.20380	0.199279
$446$	−43.1594	−2.04366
$447$	29.5790	1.39904
$448$	−20.2495	−0.956698
$449$	−12.6676	−0.597819	−0.298910	−	0.954281i	$-0.596623\pi$
$449$	−12.6676	−0.597819	−0.298910	+	0.954281i	$0.596623\pi$
$450$	−3.60430	−0.169908
$451$	48.9705	2.30593
$452$	−14.6407	−0.688642
$453$	−0.428880	−0.0201505
$454$	5.98542	0.280909
$455$	11.2164	0.525834
$456$	47.6844	2.23302
$457$	4.61030	0.215661	0.107830	−	0.994169i	$-0.465610\pi$
$457$	4.61030	0.215661	0.107830	+	0.994169i	$0.465610\pi$
$458$	22.9328	1.07158
$459$	−31.9945	−1.49338
$460$	−13.8602	−0.646237
$461$	27.2357	1.26849	0.634246	−	0.773131i	$-0.281311\pi$
$461$	27.2357	1.26849	0.634246	+	0.773131i	$0.281311\pi$
$462$	−35.9993	−1.67484
$463$	−25.9044	−1.20388	−0.601939	−	0.798542i	$-0.705605\pi$
$463$	−25.9044	−1.20388	−0.601939	+	0.798542i	$0.705605\pi$
$464$	17.8824	0.830171
$465$	6.19628	0.287345
$466$	5.81827	0.269526
$467$	10.4143	0.481916	0.240958	−	0.970536i	$-0.422538\pi$
$467$	10.4143	0.481916	0.240958	+	0.970536i	$0.422538\pi$
$468$	7.55582	0.349268
$469$	17.3574	0.801489
$470$	27.2085	1.25504
$471$	33.5543	1.54610
$472$	31.3528	1.44313
$473$	0.611868	0.0281337
$474$	−40.6397	−1.86664
$475$	−25.9891	−1.19246
$476$	−47.3557	−2.17055
$477$	2.79153	0.127816
$478$	21.3527	0.976649
$479$	−33.9084	−1.54931	−0.774657	−	0.632381i	$-0.782078\pi$
$479$	−33.9084	−1.54931	−0.774657	+	0.632381i	$0.782078\pi$
$480$	2.32802	0.106259
$481$	−54.2469	−2.47344
$482$	−33.6734	−1.53378
$483$	−11.9557	−0.544001
$484$	31.1841	1.41746
$485$	2.88009	0.130778
$486$	9.42870	0.427695
$487$	−15.5183	−0.703203	−0.351602	−	0.936150i	$-0.614363\pi$
$487$	−15.5183	−0.703203	−0.351602	+	0.936150i	$0.614363\pi$
$488$	−35.8474	−1.62274
$489$	6.60127	0.298520
$490$	−6.39308	−0.288810
$491$	−26.5885	−1.19992	−0.599961	−	0.800029i	$-0.704817\pi$
$491$	−26.5885	−1.19992	−0.599961	+	0.800029i	$0.704817\pi$
$492$	69.8501	3.14909
$493$	−33.5335	−1.51027
$494$	82.7882	3.72482
$495$	−1.69208	−0.0760532
$496$	11.6368	0.522509
$497$	14.2089	0.637358
$498$	−23.9268	−1.07219
$499$	−43.5408	−1.94916	−0.974578	−	0.224050i	$-0.928072\pi$
$499$	−43.5408	−1.94916	−0.974578	+	0.224050i	$0.928072\pi$
$500$	35.3291	1.57997
$501$	26.8037	1.19750
$502$	0.0755457	0.00337177
$503$	1.16963	0.0521511	0.0260755	−	0.999660i	$-0.491699\pi$
$503$	1.16963	0.0521511	0.0260755	+	0.999660i	$0.491699\pi$
$504$	3.55089	0.158169
$505$	−18.5908	−0.827279
$506$	37.1064	1.64958
$507$	−22.7354	−1.00971
$508$	73.7231	3.27094
$509$	−5.36033	−0.237593	−0.118796	−	0.992919i	$-0.537904\pi$
$509$	−5.36033	−0.237593	−0.118796	+	0.992919i	$0.537904\pi$
$510$	23.4990	1.04055
$511$	15.1693	0.671051
$512$	32.2785	1.42652
$513$	36.0053	1.58967
$514$	8.18027	0.360816
$515$	−12.7644	−0.562465
$516$	0.872750	0.0384207
$517$	−47.9365	−2.10825
$518$	−53.0622	−2.33142
$519$	16.9038	0.741995
$520$	−23.8565	−1.04618
$521$	−11.5287	−0.505082	−0.252541	−	0.967586i	$-0.581266\pi$
$521$	−11.5287	−0.505082	−0.252541	+	0.967586i	$0.581266\pi$
$522$	5.23357	0.229067
$523$	−29.7992	−1.30303	−0.651513	−	0.758637i	$-0.725866\pi$
$523$	−29.7992	−1.30303	−0.651513	+	0.758637i	$0.725866\pi$
$524$	52.1992	2.28033
$525$	13.4458	0.586823
$526$	−42.7309	−1.86315
$527$	−21.8216	−0.950564
$528$	22.0779	0.960819
$529$	−10.6767	−0.464204
$530$	−18.3452	−0.796866
$531$	2.64581	0.114819
$532$	53.2921	2.31051
$533$	58.2645	2.52372
$534$	−16.0528	−0.694674
$535$	−11.9648	−0.517282
$536$	−36.9178	−1.59461
$537$	25.6665	1.10759
$538$	14.3327	0.617927
$539$	11.2635	0.485151
$540$	−21.5953	−0.929313
$541$	−21.0385	−0.904517	−0.452259	−	0.891887i	$-0.649382\pi$
$541$	−21.0385	−0.904517	−0.452259	+	0.891887i	$0.649382\pi$
$542$	31.8876	1.36969
$543$	42.6640	1.83089
$544$	−8.19865	−0.351514
$545$	16.7783	0.718704
$546$	−42.8316	−1.83302
$547$	14.5248	0.621036	0.310518	−	0.950568i	$-0.399498\pi$
$547$	14.5248	0.621036	0.310518	+	0.950568i	$0.399498\pi$
$548$	25.4591	1.08756
$549$	−3.02511	−0.129109
$550$	−41.7313	−1.77943
$551$	37.7371	1.60766
$552$	25.4288	1.08232
$553$	−21.8214	−0.927940
$554$	−17.2050	−0.730971
$555$	17.3279	0.735528
$556$	45.1482	1.91471
$557$	−40.4214	−1.71271	−0.856355	−	0.516387i	$-0.827277\pi$
$557$	−40.4214	−1.71271	−0.856355	+	0.516387i	$0.827277\pi$
$558$	3.40570	0.144175
$559$	0.727993	0.0307908
$560$	−6.72866	−0.284338
$561$	−41.4010	−1.74795
$562$	−56.0911	−2.36606
$563$	14.7657	0.622301	0.311151	−	0.950361i	$-0.399286\pi$
$563$	14.7657	0.622301	0.311151	+	0.950361i	$0.399286\pi$
$564$	−68.3753	−2.87912
$565$	3.90095	0.164114
$566$	−74.5454	−3.13338
$567$	−16.2463	−0.682279
$568$	−30.2213	−1.26806
$569$	33.6900	1.41236	0.706179	−	0.708033i	$-0.250417\pi$
$569$	33.6900	1.41236	0.706179	+	0.708033i	$0.250417\pi$
$570$	−26.4448	−1.10765
$571$	4.91494	0.205684	0.102842	−	0.994698i	$-0.467206\pi$
$571$	4.91494	0.205684	0.102842	+	0.994698i	$0.467206\pi$
$572$	87.4829	3.65784
$573$	−7.14780	−0.298604
$574$	56.9921	2.37881
$575$	−13.8593	−0.577972
$576$	3.63454	0.151439
$577$	0.161571	0.00672628	0.00336314	−	0.999994i	$-0.498929\pi$
$577$	0.161571	0.00672628	0.00336314	+	0.999994i	$0.498929\pi$
$578$	−41.6414	−1.73206
$579$	13.0627	0.542869
$580$	−22.6340	−0.939827
$581$	−12.8474	−0.533002
$582$	−10.9981	−0.455885
$583$	32.3210	1.33860
$584$	−32.2640	−1.33509
$585$	−2.01321	−0.0832362
$586$	58.5552	2.41889
$587$	19.5287	0.806036	0.403018	−	0.915192i	$-0.367961\pi$
$587$	19.5287	0.806036	0.403018	+	0.915192i	$0.367961\pi$
$588$	16.0659	0.662545
$589$	24.5571	1.01186
$590$	−17.3876	−0.715836
$591$	17.4761	0.718871
$592$	32.5424	1.33748
$593$	−34.2456	−1.40630	−0.703149	−	0.711043i	$-0.748223\pi$
$593$	−34.2456	−1.40630	−0.703149	+	0.711043i	$0.748223\pi$
$594$	57.8145	2.37216
$595$	12.6177	0.517276
$596$	−70.3111	−2.88005
$597$	−24.3252	−0.995562
$598$	44.1488	1.80538
$599$	−33.2334	−1.35788	−0.678939	−	0.734194i	$-0.737560\pi$
$599$	−33.2334	−1.35788	−0.678939	+	0.734194i	$0.737560\pi$
$600$	−28.5982	−1.16752
$601$	−16.2586	−0.663202	−0.331601	−	0.943420i	$-0.607589\pi$
$601$	−16.2586	−0.663202	−0.331601	+	0.943420i	$0.607589\pi$
$602$	0.712095	0.0290228
$603$	−3.11544	−0.126871
$604$	1.01947	0.0414817
$605$	−8.30886	−0.337803
$606$	70.9917	2.88384
$607$	−32.3207	−1.31186	−0.655929	−	0.754823i	$-0.727723\pi$
$607$	−32.3207	−1.31186	−0.655929	+	0.754823i	$0.727723\pi$
$608$	9.22641	0.374180
$609$	−19.5238	−0.791145
$610$	19.8802	0.804927
$611$	−57.0344	−2.30736
$612$	8.49979	0.343584
$613$	−18.7137	−0.755839	−0.377919	−	0.925839i	$-0.623360\pi$
$613$	−18.7137	−0.755839	−0.377919	+	0.925839i	$0.623360\pi$
$614$	43.4671	1.75419
$615$	−18.6112	−0.750478
$616$	41.1129	1.65649
$617$	17.3233	0.697409	0.348704	−	0.937233i	$-0.386622\pi$
$617$	17.3233	0.697409	0.348704	+	0.937233i	$0.386622\pi$
$618$	48.7426	1.96072
$619$	1.47323	0.0592140	0.0296070	−	0.999562i	$-0.490574\pi$
$619$	1.47323	0.0592140	0.0296070	+	0.999562i	$0.490574\pi$
$620$	−14.7289	−0.591527
$621$	19.2006	0.770495
$622$	41.0405	1.64557
$623$	−8.61953	−0.345334
$624$	26.2681	1.05156
$625$	10.3267	0.413068
$626$	55.6380	2.22374
$627$	46.5909	1.86066
$628$	−79.7604	−3.18279
$629$	−61.0241	−2.43319
$630$	−1.96925	−0.0784568
$631$	−33.2992	−1.32562	−0.662811	−	0.748787i	$-0.730637\pi$
$631$	−33.2992	−1.32562	−0.662811	+	0.748787i	$0.730637\pi$
$632$	46.4125	1.84619
$633$	−9.80444	−0.389692
$634$	1.37216	0.0544954
$635$	−19.6432	−0.779516
$636$	46.1017	1.82805
$637$	13.4011	0.530972
$638$	60.5954	2.39899
$639$	−2.55033	−0.100890
$640$	−21.0101	−0.830498
$641$	4.98610	0.196939	0.0984695	−	0.995140i	$-0.468605\pi$
$641$	4.98610	0.196939	0.0984695	+	0.995140i	$0.468605\pi$
$642$	45.6893	1.80321
$643$	−12.9348	−0.510099	−0.255050	−	0.966928i	$-0.582092\pi$
$643$	−12.9348	−0.510099	−0.255050	+	0.966928i	$0.582092\pi$
$644$	28.4193	1.11988
$645$	−0.232540	−0.00915627
$646$	93.1312	3.66420
$647$	22.8403	0.897944	0.448972	−	0.893546i	$-0.351790\pi$
$647$	22.8403	0.897944	0.448972	+	0.893546i	$0.351790\pi$
$648$	34.5546	1.35743
$649$	30.6338	1.20248
$650$	−49.6514	−1.94749
$651$	−12.7049	−0.497946
$652$	−15.6916	−0.614530
$653$	31.0062	1.21337	0.606684	−	0.794943i	$-0.292499\pi$
$653$	31.0062	1.21337	0.606684	+	0.794943i	$0.292499\pi$
$654$	−64.0705	−2.50535
$655$	−13.9082	−0.543440
$656$	−34.9526	−1.36467
$657$	−2.72271	−0.106223
$658$	−55.7888	−2.17487
$659$	−39.1128	−1.52362	−0.761810	−	0.647801i	$-0.775689\pi$
$659$	−39.1128	−1.52362	−0.761810	+	0.647801i	$0.775689\pi$
$660$	−27.9444	−1.08773
$661$	−1.40983	−0.0548359	−0.0274180	−	0.999624i	$-0.508729\pi$
$661$	−1.40983	−0.0548359	−0.0274180	+	0.999624i	$0.508729\pi$
$662$	−1.15292	−0.0448095
$663$	−49.2584	−1.91304
$664$	27.3256	1.06044
$665$	−14.1994	−0.550631
$666$	9.52404	0.369049
$667$	20.1242	0.779212
$668$	−63.7138	−2.46516
$669$	−28.8987	−1.11729
$670$	20.4739	0.790974
$671$	−35.0254	−1.35214
$672$	−4.77341	−0.184138
$673$	15.6911	0.604847	0.302424	−	0.953174i	$-0.402204\pi$
$673$	15.6911	0.604847	0.302424	+	0.953174i	$0.402204\pi$
$674$	−70.8878	−2.73050
$675$	−21.5938	−0.831146
$676$	54.0433	2.07859
$677$	−40.3431	−1.55051	−0.775256	−	0.631647i	$-0.782379\pi$
$677$	−40.3431	−1.55051	−0.775256	+	0.631647i	$0.782379\pi$
$678$	−14.8964	−0.572092
$679$	−5.90539	−0.226628
$680$	−26.8370	−1.02915
$681$	4.00771	0.153576
$682$	39.4319	1.50993
$683$	8.44320	0.323070	0.161535	−	0.986867i	$-0.448356\pi$
$683$	8.44320	0.323070	0.161535	+	0.986867i	$0.448356\pi$
$684$	−9.56531	−0.365739
$685$	−6.78345	−0.259182
$686$	48.7130	1.85987
$687$	15.3553	0.585842
$688$	−0.436719	−0.0166498
$689$	38.4551	1.46502
$690$	−14.1023	−0.536865
$691$	−9.19990	−0.349981	−0.174990	−	0.984570i	$-0.555989\pi$
$691$	−9.19990	−0.349981	−0.174990	+	0.984570i	$0.555989\pi$
$692$	−40.1813	−1.52747
$693$	3.46946	0.131794
$694$	−21.6993	−0.823693
$695$	−12.0295	−0.456306
$696$	41.5257	1.57403
$697$	65.5437	2.48265
$698$	3.36898	0.127518
$699$	3.89580	0.147353
$700$	−31.9614	−1.20803
$701$	−24.2382	−0.915465	−0.457732	−	0.889090i	$-0.651338\pi$
$701$	−24.2382	−0.915465	−0.457732	+	0.889090i	$0.651338\pi$
$702$	68.7870	2.59620
$703$	68.6739	2.59009
$704$	42.0815	1.58601
$705$	18.2183	0.686140
$706$	−3.01217	−0.113364
$707$	38.1188	1.43361
$708$	43.6952	1.64217
$709$	−18.3479	−0.689068	−0.344534	−	0.938774i	$-0.611963\pi$
$709$	−18.3479	−0.689068	−0.344534	+	0.938774i	$0.611963\pi$
$710$	16.7601	0.628996
$711$	3.91668	0.146887
$712$	18.3331	0.687062
$713$	13.0956	0.490436
$714$	−48.1827	−1.80319
$715$	−23.3094	−0.871723
$716$	−61.0106	−2.28007
$717$	14.2973	0.533943
$718$	−53.3812	−1.99217
$719$	24.3758	0.909063	0.454531	−	0.890731i	$-0.349807\pi$
$719$	24.3758	0.909063	0.454531	+	0.890731i	$0.349807\pi$
$720$	1.20772	0.0450089
$721$	26.1722	0.974705
$722$	−58.8532	−2.19029
$723$	−22.5470	−0.838532
$724$	−101.415	−3.76905
$725$	−22.6325	−0.840549
$726$	31.7286	1.17756
$727$	36.8485	1.36664	0.683318	−	0.730121i	$-0.260536\pi$
$727$	36.8485	1.36664	0.683318	+	0.730121i	$0.260536\pi$
$728$	48.9157	1.81294
$729$	29.4886	1.09217
$730$	17.8929	0.662247
$731$	0.818944	0.0302897
$732$	−49.9592	−1.84654
$733$	−8.83828	−0.326449	−0.163225	−	0.986589i	$-0.552190\pi$
$733$	−8.83828	−0.326449	−0.163225	+	0.986589i	$0.552190\pi$
$734$	−38.4169	−1.41799
$735$	−4.28068	−0.157895
$736$	4.92020	0.181361
$737$	−36.0713	−1.32870
$738$	−10.2294	−0.376550
$739$	3.23491	0.118998	0.0594991	−	0.998228i	$-0.481050\pi$
$739$	3.23491	0.118998	0.0594991	+	0.998228i	$0.481050\pi$
$740$	−41.1894	−1.51415
$741$	55.4333	2.03639
$742$	37.6153	1.38090
$743$	−33.2195	−1.21871	−0.609353	−	0.792899i	$-0.708571\pi$
$743$	−33.2195	−1.21871	−0.609353	+	0.792899i	$0.708571\pi$
$744$	27.0225	0.990692
$745$	18.7341	0.686363
$746$	10.8103	0.395792
$747$	2.30596	0.0843708
$748$	98.4124	3.59831
$749$	24.5328	0.896407
$750$	35.9461	1.31257
$751$	−3.45207	−0.125968	−0.0629840	−	0.998015i	$-0.520062\pi$
$751$	−3.45207	−0.125968	−0.0629840	+	0.998015i	$0.520062\pi$
$752$	34.2146	1.24768
$753$	0.0505838	0.00184338
$754$	72.0957	2.62557
$755$	−0.271633	−0.00988575
$756$	44.2793	1.61042
$757$	−5.07455	−0.184438	−0.0922189	−	0.995739i	$-0.529396\pi$
$757$	−5.07455	−0.184438	−0.0922189	+	0.995739i	$0.529396\pi$
$758$	50.4116	1.83103
$759$	24.8457	0.901841
$760$	30.2012	1.09551
$761$	25.7027	0.931722	0.465861	−	0.884858i	$-0.345745\pi$
$761$	25.7027	0.931722	0.465861	+	0.884858i	$0.345745\pi$
$762$	75.0105	2.71734
$763$	−34.4025	−1.24545
$764$	16.9907	0.614703
$765$	−2.26473	−0.0818815
$766$	−14.3341	−0.517913
$767$	36.4478	1.31605
$768$	49.0447	1.76975
$769$	−24.5659	−0.885868	−0.442934	−	0.896554i	$-0.646062\pi$
$769$	−24.5659	−0.885868	−0.442934	+	0.896554i	$0.646062\pi$
$770$	−22.8004	−0.821669
$771$	5.47734	0.197262
$772$	−31.0508	−1.11754
$773$	42.6336	1.53342	0.766712	−	0.641991i	$-0.221891\pi$
$773$	42.6336	1.53342	0.766712	+	0.641991i	$0.221891\pi$
$774$	−0.127813	−0.00459413
$775$	−14.7279	−0.529041
$776$	12.5603	0.450889
$777$	−35.5294	−1.27461
$778$	69.4119	2.48854
$779$	−73.7601	−2.64273
$780$	−33.2479	−1.19047
$781$	−29.5283	−1.05661
$782$	49.6644	1.77600
$783$	31.3550	1.12054
$784$	−8.03926	−0.287116
$785$	21.2518	0.758509
$786$	53.1107	1.89440
$787$	15.7332	0.560829	0.280415	−	0.959879i	$-0.409528\pi$
$787$	15.7332	0.560829	0.280415	+	0.959879i	$0.409528\pi$
$788$	−41.5417	−1.47986
$789$	−28.6117	−1.01860
$790$	−25.7394	−0.915767
$791$	−7.99858	−0.284397
$792$	−7.37929	−0.262211
$793$	−41.6728	−1.47984
$794$	−15.6878	−0.556738
$795$	−12.2836	−0.435654
$796$	57.8222	2.04946
$797$	−42.3500	−1.50011	−0.750057	−	0.661373i	$-0.769974\pi$
$797$	−42.3500	−1.50011	−0.750057	+	0.661373i	$0.769974\pi$
$798$	54.2227	1.91946
$799$	−64.1598	−2.26981
$800$	−5.53345	−0.195637
$801$	1.54710	0.0546642
$802$	−23.6885	−0.836468
$803$	−31.5241	−1.11246
$804$	−51.4510	−1.81454
$805$	−7.57219	−0.266884
$806$	46.9156	1.65253
$807$	9.59688	0.337826
$808$	−81.0759	−2.85224
$809$	−31.8593	−1.12011	−0.560057	−	0.828454i	$-0.689221\pi$
$809$	−31.8593	−1.12011	−0.560057	+	0.828454i	$0.689221\pi$
$810$	−19.1633	−0.673328
$811$	9.64059	0.338527	0.169263	−	0.985571i	$-0.445861\pi$
$811$	9.64059	0.338527	0.169263	+	0.985571i	$0.445861\pi$
$812$	46.4092	1.62864
$813$	21.3513	0.748822
$814$	110.271	3.86501
$815$	4.18095	0.146452
$816$	29.5498	1.03445
$817$	−0.921605	−0.0322429
$818$	−49.6973	−1.73762
$819$	4.12793	0.144241
$820$	44.2400	1.54493
$821$	−25.2933	−0.882742	−0.441371	−	0.897325i	$-0.645508\pi$
$821$	−25.2933	−0.882742	−0.441371	+	0.897325i	$0.645508\pi$
$822$	25.9036	0.903493
$823$	−16.5822	−0.578019	−0.289010	−	0.957326i	$-0.593326\pi$
$823$	−16.5822	−0.578019	−0.289010	+	0.957326i	$0.593326\pi$
$824$	−55.6664	−1.93923
$825$	−27.9424	−0.972831
$826$	35.6518	1.24048
$827$	−17.1943	−0.597903	−0.298952	−	0.954268i	$-0.596637\pi$
$827$	−17.1943	−0.597903	−0.298952	+	0.954268i	$0.596637\pi$
$828$	−5.10092	−0.177269
$829$	−19.8279	−0.688650	−0.344325	−	0.938851i	$-0.611892\pi$
$829$	−19.8279	−0.688650	−0.344325	+	0.938851i	$0.611892\pi$
$830$	−15.1542	−0.526009
$831$	−11.5201	−0.399629
$832$	50.0681	1.73580
$833$	15.0754	0.522331
$834$	45.9366	1.59065
$835$	16.9763	0.587488
$836$	−110.749	−3.83034
$837$	20.4040	0.705265
$838$	−1.59865	−0.0552243
$839$	−39.3895	−1.35988	−0.679938	−	0.733270i	$-0.737993\pi$
$839$	−39.3895	−1.35988	−0.679938	+	0.733270i	$0.737993\pi$
$840$	−15.6250	−0.539113
$841$	3.86319	0.133214
$842$	6.44128	0.221981
$843$	−37.5575	−1.29355
$844$	23.3057	0.802216
$845$	−14.3996	−0.495361
$846$	10.0134	0.344269
$847$	17.0366	0.585385
$848$	−23.0690	−0.792193
$849$	−49.9141	−1.71305
$850$	−55.8545	−1.91580
$851$	36.6220	1.25538
$852$	−42.1183	−1.44295
$853$	−4.49379	−0.153865	−0.0769323	−	0.997036i	$-0.524513\pi$
$853$	−4.49379	−0.153865	−0.0769323	+	0.997036i	$0.524513\pi$
$854$	−40.7627	−1.39487
$855$	2.54863	0.0871614
$856$	−52.1793	−1.78345
$857$	33.6803	1.15050	0.575249	−	0.817978i	$-0.304905\pi$
$857$	33.6803	1.15050	0.575249	+	0.817978i	$0.304905\pi$
$858$	89.0106	3.03877
$859$	−7.71313	−0.263169	−0.131584	−	0.991305i	$-0.542006\pi$
$859$	−7.71313	−0.263169	−0.131584	+	0.991305i	$0.542006\pi$
$860$	0.552761	0.0188490
$861$	38.1608	1.30052
$862$	−24.1432	−0.822319
$863$	6.07938	0.206944	0.103472	−	0.994632i	$-0.467005\pi$
$863$	6.07938	0.206944	0.103472	+	0.994632i	$0.467005\pi$
$864$	7.66603	0.260804
$865$	10.7061	0.364019
$866$	−28.6985	−0.975214
$867$	−27.8823	−0.946931
$868$	30.2004	1.02507
$869$	45.3482	1.53833
$870$	−23.0293	−0.780766
$871$	−42.9172	−1.45419
$872$	73.1716	2.47790
$873$	1.05995	0.0358738
$874$	−55.8902	−1.89051
$875$	19.3012	0.652498
$876$	−44.9651	−1.51923
$877$	5.87542	0.198399	0.0991994	−	0.995068i	$-0.468372\pi$
$877$	5.87542	0.198399	0.0991994	+	0.995068i	$0.468372\pi$
$878$	69.7960	2.35550
$879$	39.2074	1.32243
$880$	13.9832	0.471373
$881$	−4.30133	−0.144915	−0.0724577	−	0.997371i	$-0.523084\pi$
$881$	−4.30133	−0.144915	−0.0724577	+	0.997371i	$0.523084\pi$
$882$	−2.35282	−0.0792234
$883$	9.69350	0.326212	0.163106	−	0.986609i	$-0.447849\pi$
$883$	9.69350	0.326212	0.163106	+	0.986609i	$0.447849\pi$
$884$	117.090	3.93816
$885$	−11.6424	−0.391354
$886$	−34.2057	−1.14916
$887$	47.7437	1.60308	0.801539	−	0.597943i	$-0.204015\pi$
$887$	47.7437	1.60308	0.801539	+	0.597943i	$0.204015\pi$
$888$	75.5683	2.53591
$889$	40.2767	1.35084
$890$	−10.1672	−0.340804
$891$	33.7622	1.13108
$892$	68.6938	2.30004
$893$	72.2027	2.41617
$894$	−71.5389	−2.39262
$895$	16.2560	0.543378
$896$	43.0795	1.43918
$897$	29.5611	0.987017
$898$	30.6373	1.02238
$899$	21.3854	0.713244
$900$	5.73670	0.191223
$901$	43.2595	1.44118
$902$	−118.438	−3.94356
$903$	0.476804	0.0158671
$904$	17.0124	0.565823
$905$	27.0215	0.898225
$906$	1.03727	0.0344611
$907$	−46.9881	−1.56022	−0.780108	−	0.625645i	$-0.784836\pi$
$907$	−46.9881	−1.56022	−0.780108	+	0.625645i	$0.784836\pi$
$908$	−9.52656	−0.316150
$909$	−6.84188	−0.226931
$910$	−27.1276	−0.899273
$911$	53.6332	1.77695	0.888474	−	0.458926i	$-0.151766\pi$
$911$	53.6332	1.77695	0.888474	+	0.458926i	$0.151766\pi$
$912$	−33.2541	−1.10115
$913$	26.6989	0.883606
$914$	−11.1503	−0.368819
$915$	13.3114	0.440061
$916$	−36.5004	−1.20601
$917$	28.5177	0.941737
$918$	77.3808	2.55395
$919$	−44.5231	−1.46868	−0.734340	−	0.678781i	$-0.762508\pi$
$919$	−44.5231	−1.46868	−0.734340	+	0.678781i	$0.762508\pi$
$920$	16.1055	0.530982
$921$	29.1047	0.959031
$922$	−65.8713	−2.16936
$923$	−35.1325	−1.15640
$924$	57.2976	1.88495
$925$	−41.1865	−1.35420
$926$	62.6514	2.05885
$927$	−4.69761	−0.154290
$928$	8.03477	0.263754
$929$	−1.57288	−0.0516045	−0.0258022	−	0.999667i	$-0.508214\pi$
$929$	−1.57288	−0.0516045	−0.0258022	+	0.999667i	$0.508214\pi$
$930$	−14.9861	−0.491413
$931$	−16.9652	−0.556012
$932$	−9.26053	−0.303339
$933$	27.4799	0.899650
$934$	−25.1876	−0.824164
$935$	−26.2215	−0.857536
$936$	−8.77979	−0.286976
$937$	16.1967	0.529124	0.264562	−	0.964369i	$-0.414773\pi$
$937$	16.1967	0.529124	0.264562	+	0.964369i	$0.414773\pi$
$938$	−41.9799	−1.37069
$939$	37.2541	1.21574
$940$	−43.3059	−1.41248
$941$	50.2359	1.63764	0.818822	−	0.574047i	$-0.194627\pi$
$941$	50.2359	1.63764	0.818822	+	0.574047i	$0.194627\pi$
$942$	−81.1532	−2.64411
$943$	−39.3343	−1.28090
$944$	−21.8648	−0.711639
$945$	−11.7980	−0.383790
$946$	−1.47984	−0.0481138
$947$	4.23677	0.137676	0.0688382	−	0.997628i	$-0.478071\pi$
$947$	4.23677	0.137676	0.0688382	+	0.997628i	$0.478071\pi$
$948$	64.6833	2.10082
$949$	−37.5071	−1.21753
$950$	62.8563	2.03933
$951$	0.918769	0.0297931
$952$	55.0269	1.78343
$953$	−10.0061	−0.324129	−0.162065	−	0.986780i	$-0.551815\pi$
$953$	−10.0061	−0.324129	−0.162065	+	0.986780i	$0.551815\pi$
$954$	−6.75151	−0.218588
$955$	−4.52710	−0.146493
$956$	−33.9855	−1.09917
$957$	40.5734	1.31155
$958$	82.0097	2.64961
$959$	13.9089	0.449141
$960$	−15.9931	−0.516174
$961$	−17.0836	−0.551085
$962$	131.200	4.23004
$963$	−4.40334	−0.141896
$964$	53.5955	1.72620
$965$	8.27336	0.266329
$966$	28.9155	0.930342
$967$	54.1896	1.74262	0.871310	−	0.490732i	$-0.163271\pi$
$967$	54.1896	1.74262	0.871310	+	0.490732i	$0.163271\pi$
$968$	−36.2356	−1.16466
$969$	62.3588	2.00325
$970$	−6.96569	−0.223655
$971$	−44.2016	−1.41850	−0.709248	−	0.704959i	$-0.750965\pi$
$971$	−44.2016	−1.41850	−0.709248	+	0.704959i	$0.750965\pi$
$972$	−15.0070	−0.481349
$973$	24.6655	0.790741
$974$	37.5321	1.20261
$975$	−33.2456	−1.06471
$976$	24.9993	0.800207
$977$	52.4286	1.67734	0.838670	−	0.544640i	$-0.183334\pi$
$977$	52.4286	1.67734	0.838670	+	0.544640i	$0.183334\pi$
$978$	−15.9656	−0.510524
$979$	17.9127	0.572492
$980$	10.1754	0.325041
$981$	6.17484	0.197148
$982$	64.3060	2.05209
$983$	13.7094	0.437262	0.218631	−	0.975808i	$-0.429841\pi$
$983$	13.7094	0.437262	0.218631	+	0.975808i	$0.429841\pi$
$984$	−81.1651	−2.58745
$985$	11.0686	0.352675
$986$	81.1029	2.58284
$987$	−37.3551	−1.18902
$988$	−131.768	−4.19210
$989$	−0.491467	−0.0156277
$990$	4.09240	0.130065
$991$	−38.7628	−1.23134	−0.615670	−	0.788004i	$-0.711115\pi$
$991$	−38.7628	−1.23134	−0.615670	+	0.788004i	$0.711115\pi$
$992$	5.22856	0.166007
$993$	−0.771971	−0.0244978
$994$	−34.3652	−1.09000
$995$	−15.4065	−0.488418
$996$	38.0826	1.20669
$997$	41.0966	1.30154	0.650771	−	0.759274i	$-0.274446\pi$
$997$	41.0966	1.30154	0.650771	+	0.759274i	$0.274446\pi$
$998$	105.306	3.33341
$999$	57.0597	1.80529

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4021.2.a.b.1.14	✓	151

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4021.2.a.b.1.14	✓	151	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:	\( N \)	\(=\)	\( 4021 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4021.a (trivial)

\(f(q)\)	\(=\)	\(q-2.41856 q^{2} -1.61942 q^{3} +3.84946 q^{4} -1.02567 q^{5} +3.91668 q^{6} +2.10305 q^{7} -4.47303 q^{8} -0.377473 q^{9} +O(q^{10})\)	\(q-2.41856 q^{2} -1.61942 q^{3} +3.84946 q^{4} -1.02567 q^{5} +3.91668 q^{6} +2.10305 q^{7} -4.47303 q^{8} -0.377473 q^{9} +2.48065 q^{10} -4.37046 q^{11} -6.23389 q^{12} -5.19992 q^{13} -5.08636 q^{14} +1.66099 q^{15} +3.11940 q^{16} -5.84957 q^{17} +0.912942 q^{18} +6.58285 q^{19} -3.94827 q^{20} -3.40573 q^{21} +10.5702 q^{22} +3.51046 q^{23} +7.24372 q^{24} -3.94800 q^{25} +12.5763 q^{26} +5.46955 q^{27} +8.09560 q^{28} +5.73264 q^{29} -4.01722 q^{30} +3.73047 q^{31} +1.40158 q^{32} +7.07762 q^{33} +14.1476 q^{34} -2.15704 q^{35} -1.45306 q^{36} +10.4322 q^{37} -15.9211 q^{38} +8.42087 q^{39} +4.58785 q^{40} -11.2049 q^{41} +8.23697 q^{42} -0.140001 q^{43} -16.8239 q^{44} +0.387162 q^{45} -8.49027 q^{46} +10.9683 q^{47} -5.05163 q^{48} -2.57718 q^{49} +9.54850 q^{50} +9.47291 q^{51} -20.0169 q^{52} -7.39533 q^{53} -13.2285 q^{54} +4.48265 q^{55} -9.40701 q^{56} -10.6604 q^{57} -13.8648 q^{58} -7.00929 q^{59} +6.39392 q^{60} +8.01412 q^{61} -9.02237 q^{62} -0.793844 q^{63} -9.62863 q^{64} +5.33341 q^{65} -17.1177 q^{66} +8.25343 q^{67} -22.5176 q^{68} -5.68491 q^{69} +5.21693 q^{70} +6.75634 q^{71} +1.68845 q^{72} +7.21300 q^{73} -25.2311 q^{74} +6.39348 q^{75} +25.3404 q^{76} -9.19129 q^{77} -20.3664 q^{78} -10.3761 q^{79} -3.19948 q^{80} -7.72510 q^{81} +27.0997 q^{82} -6.10896 q^{83} -13.1102 q^{84} +5.99972 q^{85} +0.338601 q^{86} -9.28357 q^{87} +19.5492 q^{88} -4.09859 q^{89} -0.936377 q^{90} -10.9357 q^{91} +13.5134 q^{92} -6.04120 q^{93} -26.5276 q^{94} -6.75183 q^{95} -2.26975 q^{96} -2.80801 q^{97} +6.23308 q^{98} +1.64973 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 151 q - 16 q^{2} - 29 q^{3} + 120 q^{4} - 27 q^{5} - 18 q^{6} - 18 q^{7} - 48 q^{8} + 98 q^{9}+O(q^{10}) \) 151 * q - 16 * q^2 - 29 * q^3 + 120 * q^4 - 27 * q^5 - 18 * q^6 - 18 * q^7 - 48 * q^8 + 98 * q^9	\( 151 q - 16 q^{2} - 29 q^{3} + 120 q^{4} - 27 q^{5} - 18 q^{6} - 18 q^{7} - 48 q^{8} + 98 q^{9} - 7 q^{10} - 126 q^{11} - 47 q^{12} - 10 q^{13} - 58 q^{14} - 50 q^{15} + 74 q^{16} - 39 q^{17} - 47 q^{18} - 48 q^{19} - 64 q^{20} - 50 q^{21} - 7 q^{22} - 91 q^{23} - 44 q^{24} + 102 q^{25} - 94 q^{26} - 92 q^{27} - 27 q^{28} - 79 q^{29} - 12 q^{30} - 33 q^{31} - 102 q^{32} - 7 q^{33} - 17 q^{34} - 183 q^{35} - 6 q^{36} - 24 q^{37} - 77 q^{38} - 81 q^{39} - 37 q^{40} - 62 q^{41} + 4 q^{42} - 74 q^{43} - 209 q^{44} - 35 q^{45} - 37 q^{46} - 127 q^{47} - 59 q^{48} + 75 q^{49} - 79 q^{50} - 138 q^{51} - 12 q^{52} - 104 q^{53} - 43 q^{54} - 49 q^{55} - 167 q^{56} - 19 q^{57} - 32 q^{58} - 207 q^{59} - 94 q^{60} - 57 q^{61} - 69 q^{62} - 49 q^{63} - 4 q^{64} - 78 q^{65} - 51 q^{66} - 92 q^{67} - 80 q^{68} - 84 q^{69} + 5 q^{70} - 217 q^{71} - 79 q^{72} + 2 q^{73} - 113 q^{74} - 173 q^{75} - 70 q^{76} - 85 q^{77} - 46 q^{78} - 70 q^{79} - 95 q^{80} - 49 q^{81} - 12 q^{82} - 109 q^{83} - 114 q^{84} - 25 q^{85} - 136 q^{86} - 60 q^{87} - 2 q^{88} - 144 q^{89} - 55 q^{90} - 62 q^{91} - 175 q^{92} - 42 q^{93} - 15 q^{94} - 189 q^{95} - 64 q^{96} - 24 q^{97} - 37 q^{98} - 293 q^{99}+O(q^{100}) \) 151 * q - 16 * q^2 - 29 * q^3 + 120 * q^4 - 27 * q^5 - 18 * q^6 - 18 * q^7 - 48 * q^8 + 98 * q^9 - 7 * q^10 - 126 * q^11 - 47 * q^12 - 10 * q^13 - 58 * q^14 - 50 * q^15 + 74 * q^16 - 39 * q^17 - 47 * q^18 - 48 * q^19 - 64 * q^20 - 50 * q^21 - 7 * q^22 - 91 * q^23 - 44 * q^24 + 102 * q^25 - 94 * q^26 - 92 * q^27 - 27 * q^28 - 79 * q^29 - 12 * q^30 - 33 * q^31 - 102 * q^32 - 7 * q^33 - 17 * q^34 - 183 * q^35 - 6 * q^36 - 24 * q^37 - 77 * q^38 - 81 * q^39 - 37 * q^40 - 62 * q^41 + 4 * q^42 - 74 * q^43 - 209 * q^44 - 35 * q^45 - 37 * q^46 - 127 * q^47 - 59 * q^48 + 75 * q^49 - 79 * q^50 - 138 * q^51 - 12 * q^52 - 104 * q^53 - 43 * q^54 - 49 * q^55 - 167 * q^56 - 19 * q^57 - 32 * q^58 - 207 * q^59 - 94 * q^60 - 57 * q^61 - 69 * q^62 - 49 * q^63 - 4 * q^64 - 78 * q^65 - 51 * q^66 - 92 * q^67 - 80 * q^68 - 84 * q^69 + 5 * q^70 - 217 * q^71 - 79 * q^72 + 2 * q^73 - 113 * q^74 - 173 * q^75 - 70 * q^76 - 85 * q^77 - 46 * q^78 - 70 * q^79 - 95 * q^80 - 49 * q^81 - 12 * q^82 - 109 * q^83 - 114 * q^84 - 25 * q^85 - 136 * q^86 - 60 * q^87 - 2 * q^88 - 144 * q^89 - 55 * q^90 - 62 * q^91 - 175 * q^92 - 42 * q^93 - 15 * q^94 - 189 * q^95 - 64 * q^96 - 24 * q^97 - 37 * q^98 - 293 * q^99

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