LMFDB - Embedded newform 6023.2.a.d.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6023,2,Mod(1,6023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6023, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6023 = 19 \cdot 317 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6023.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:	$48.0938971374$
Analytic rank:	$0$
Dimension:	$140$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	6023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.12238 q^{2} +2.91250 q^{3} +2.50448 q^{4} +1.81666 q^{5} -6.18142 q^{6} +0.226771 q^{7} -1.07071 q^{8} +5.48264 q^{9} +O(q^{10})$	\(q-2.12238 q^{2} +2.91250 q^{3} +2.50448 q^{4} +1.81666 q^{5} -6.18142 q^{6} +0.226771 q^{7} -1.07071 q^{8} +5.48264 q^{9} -3.85564 q^{10} -1.14983 q^{11} +7.29430 q^{12} +5.02940 q^{13} -0.481294 q^{14} +5.29102 q^{15} -2.73652 q^{16} +2.30765 q^{17} -11.6362 q^{18} -1.00000 q^{19} +4.54980 q^{20} +0.660471 q^{21} +2.44037 q^{22} +4.57285 q^{23} -3.11843 q^{24} -1.69975 q^{25} -10.6743 q^{26} +7.23067 q^{27} +0.567946 q^{28} +8.50073 q^{29} -11.2295 q^{30} +1.29540 q^{31} +7.94935 q^{32} -3.34887 q^{33} -4.89771 q^{34} +0.411967 q^{35} +13.7312 q^{36} -1.37103 q^{37} +2.12238 q^{38} +14.6481 q^{39} -1.94511 q^{40} -6.21904 q^{41} -1.40177 q^{42} +1.52813 q^{43} -2.87973 q^{44} +9.96009 q^{45} -9.70532 q^{46} +2.00731 q^{47} -7.97012 q^{48} -6.94857 q^{49} +3.60750 q^{50} +6.72103 q^{51} +12.5961 q^{52} +0.824242 q^{53} -15.3462 q^{54} -2.08885 q^{55} -0.242806 q^{56} -2.91250 q^{57} -18.0417 q^{58} +2.26395 q^{59} +13.2513 q^{60} +8.59437 q^{61} -2.74933 q^{62} +1.24330 q^{63} -11.3985 q^{64} +9.13672 q^{65} +7.10757 q^{66} +4.25792 q^{67} +5.77948 q^{68} +13.3184 q^{69} -0.874349 q^{70} -0.908024 q^{71} -5.87030 q^{72} -5.91665 q^{73} +2.90983 q^{74} -4.95050 q^{75} -2.50448 q^{76} -0.260748 q^{77} -31.0888 q^{78} +9.81411 q^{79} -4.97134 q^{80} +4.61138 q^{81} +13.1992 q^{82} -12.0623 q^{83} +1.65414 q^{84} +4.19222 q^{85} -3.24328 q^{86} +24.7583 q^{87} +1.23113 q^{88} -1.60363 q^{89} -21.1391 q^{90} +1.14053 q^{91} +11.4526 q^{92} +3.77285 q^{93} -4.26028 q^{94} -1.81666 q^{95} +23.1525 q^{96} -0.189887 q^{97} +14.7475 q^{98} -6.30409 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9}+O(q^{10}) $ 140 * q + 4 * q^2 + 3 * q^3 + 162 * q^4 + 13 * q^5 + 12 * q^6 + 25 * q^7 + 12 * q^8 + 181 * q^9	\( 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9} + 8 q^{10} + 19 q^{11} + 17 q^{12} + 28 q^{13} + 5 q^{14} + 14 q^{15} + 202 q^{16} + 38 q^{17} + 26 q^{18} - 140 q^{19} + 36 q^{20} + 4 q^{21} + 53 q^{22} + 58 q^{23} + 47 q^{24} + 279 q^{25} + 29 q^{26} + 21 q^{27} + 69 q^{28} + 18 q^{29} + 50 q^{30} + 20 q^{31} + 13 q^{32} + 47 q^{33} + 6 q^{34} + 35 q^{35} + 230 q^{36} + 88 q^{37} - 4 q^{38} + 32 q^{39} + 32 q^{40} + 24 q^{41} + 75 q^{42} + 100 q^{43} + 63 q^{44} + 87 q^{45} + 23 q^{46} + 35 q^{47} + 46 q^{48} + 255 q^{49} + 11 q^{50} - 6 q^{51} + 47 q^{52} + 77 q^{53} + 16 q^{54} + 63 q^{55} + 21 q^{56} - 3 q^{57} + 165 q^{58} + 18 q^{59} + 28 q^{60} + 99 q^{61} + 34 q^{62} + 89 q^{63} + 298 q^{64} + 78 q^{65} - 3 q^{66} + 28 q^{67} + 93 q^{68} + 19 q^{69} + 16 q^{70} + q^{71} + 43 q^{72} + 201 q^{73} + 32 q^{74} + 22 q^{75} - 162 q^{76} + 86 q^{77} + 122 q^{78} + 58 q^{79} + 92 q^{80} + 288 q^{81} + 143 q^{82} + 57 q^{83} + q^{84} + 136 q^{85} - 6 q^{86} + 43 q^{87} + 198 q^{88} + 46 q^{89} + 30 q^{90} + 26 q^{91} + 129 q^{92} + 111 q^{93} + 44 q^{94} - 13 q^{95} + 32 q^{96} + 110 q^{97} - 34 q^{98} + 62 q^{99}+O(q^{100}) \) 140 * q + 4 * q^2 + 3 * q^3 + 162 * q^4 + 13 * q^5 + 12 * q^6 + 25 * q^7 + 12 * q^8 + 181 * q^9 + 8 * q^10 + 19 * q^11 + 17 * q^12 + 28 * q^13 + 5 * q^14 + 14 * q^15 + 202 * q^16 + 38 * q^17 + 26 * q^18 - 140 * q^19 + 36 * q^20 + 4 * q^21 + 53 * q^22 + 58 * q^23 + 47 * q^24 + 279 * q^25 + 29 * q^26 + 21 * q^27 + 69 * q^28 + 18 * q^29 + 50 * q^30 + 20 * q^31 + 13 * q^32 + 47 * q^33 + 6 * q^34 + 35 * q^35 + 230 * q^36 + 88 * q^37 - 4 * q^38 + 32 * q^39 + 32 * q^40 + 24 * q^41 + 75 * q^42 + 100 * q^43 + 63 * q^44 + 87 * q^45 + 23 * q^46 + 35 * q^47 + 46 * q^48 + 255 * q^49 + 11 * q^50 - 6 * q^51 + 47 * q^52 + 77 * q^53 + 16 * q^54 + 63 * q^55 + 21 * q^56 - 3 * q^57 + 165 * q^58 + 18 * q^59 + 28 * q^60 + 99 * q^61 + 34 * q^62 + 89 * q^63 + 298 * q^64 + 78 * q^65 - 3 * q^66 + 28 * q^67 + 93 * q^68 + 19 * q^69 + 16 * q^70 + q^71 + 43 * q^72 + 201 * q^73 + 32 * q^74 + 22 * q^75 - 162 * q^76 + 86 * q^77 + 122 * q^78 + 58 * q^79 + 92 * q^80 + 288 * q^81 + 143 * q^82 + 57 * q^83 + q^84 + 136 * q^85 - 6 * q^86 + 43 * q^87 + 198 * q^88 + 46 * q^89 + 30 * q^90 + 26 * q^91 + 129 * q^92 + 111 * q^93 + 44 * q^94 - 13 * q^95 + 32 * q^96 + 110 * q^97 - 34 * q^98 + 62 * 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 $

$2$	−2.12238	−1.50075	−0.750374	−	0.661014i	$-0.770126\pi$
$2$	−2.12238	−1.50075	−0.750374	+	0.661014i	$0.770126\pi$
$3$	2.91250	1.68153	0.840765	−	0.541400i	$-0.182105\pi$
$3$	2.91250	1.68153	0.840765	+	0.541400i	$0.182105\pi$
$4$	2.50448	1.25224
$5$	1.81666	0.812435	0.406218	−	0.913776i	$-0.366847\pi$
$5$	1.81666	0.812435	0.406218	+	0.913776i	$0.366847\pi$
$6$	−6.18142	−2.52355
$7$	0.226771	0.0857115	0.0428558	−	0.999081i	$-0.486354\pi$
$7$	0.226771	0.0857115	0.0428558	+	0.999081i	$0.486354\pi$
$8$	−1.07071	−0.378552
$9$	5.48264	1.82755
$10$	−3.85564	−1.21926
$11$	−1.14983	−0.346686	−0.173343	−	0.984861i	$-0.555457\pi$
$11$	−1.14983	−0.346686	−0.173343	+	0.984861i	$0.555457\pi$
$12$	7.29430	2.10568
$13$	5.02940	1.39491	0.697453	−	0.716631i	$-0.254317\pi$
$13$	5.02940	1.39491	0.697453	+	0.716631i	$0.254317\pi$
$14$	−0.481294	−0.128631
$15$	5.29102	1.36613
$16$	−2.73652	−0.684131
$17$	2.30765	0.559688	0.279844	−	0.960045i	$-0.409717\pi$
$17$	2.30765	0.559688	0.279844	+	0.960045i	$0.409717\pi$
$18$	−11.6362	−2.74268
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	4.54980	1.01737
$21$	0.660471	0.144127
$22$	2.44037	0.520289
$23$	4.57285	0.953506	0.476753	−	0.879037i	$-0.341814\pi$
$23$	4.57285	0.953506	0.476753	+	0.879037i	$0.341814\pi$
$24$	−3.11843	−0.636547
$25$	−1.69975	−0.339949
$26$	−10.6743	−2.09340
$27$	7.23067	1.39154
$28$	0.567946	0.107332
$29$	8.50073	1.57855	0.789273	−	0.614043i	$-0.210458\pi$
$29$	8.50073	1.57855	0.789273	+	0.614043i	$0.210458\pi$
$30$	−11.2295	−2.05022
$31$	1.29540	0.232661	0.116331	−	0.993211i	$-0.462887\pi$
$31$	1.29540	0.232661	0.116331	+	0.993211i	$0.462887\pi$
$32$	7.94935	1.40526
$33$	−3.34887	−0.582964
$34$	−4.89771	−0.839951
$35$	0.411967	0.0696351
$36$	13.7312	2.28853
$37$	−1.37103	−0.225395	−0.112698	−	0.993629i	$-0.535949\pi$
$37$	−1.37103	−0.225395	−0.112698	+	0.993629i	$0.535949\pi$
$38$	2.12238	0.344295
$39$	14.6481	2.34558
$40$	−1.94511	−0.307549
$41$	−6.21904	−0.971252	−0.485626	−	0.874167i	$-0.661408\pi$
$41$	−6.21904	−0.971252	−0.485626	+	0.874167i	$0.661408\pi$
$42$	−1.40177	−0.216298
$43$	1.52813	0.233038	0.116519	−	0.993188i	$-0.462826\pi$
$43$	1.52813	0.233038	0.116519	+	0.993188i	$0.462826\pi$
$44$	−2.87973	−0.434135
$45$	9.96009	1.48476
$46$	−9.70532	−1.43097
$47$	2.00731	0.292797	0.146398	−	0.989226i	$-0.453232\pi$
$47$	2.00731	0.292797	0.146398	+	0.989226i	$0.453232\pi$
$48$	−7.97012	−1.15039
$49$	−6.94857	−0.992654
$50$	3.60750	0.510178
$51$	6.72103	0.941133
$52$	12.5961	1.74676
$53$	0.824242	0.113218	0.0566092	−	0.998396i	$-0.481971\pi$
$53$	0.824242	0.113218	0.0566092	+	0.998396i	$0.481971\pi$
$54$	−15.3462	−2.08835
$55$	−2.08885	−0.281660
$56$	−0.242806	−0.0324463
$57$	−2.91250	−0.385770
$58$	−18.0417	−2.36900
$59$	2.26395	0.294741	0.147371	−	0.989081i	$-0.452919\pi$
$59$	2.26395	0.294741	0.147371	+	0.989081i	$0.452919\pi$
$60$	13.2513	1.71073
$61$	8.59437	1.10040	0.550198	−	0.835034i	$-0.314552\pi$
$61$	8.59437	1.10040	0.550198	+	0.835034i	$0.314552\pi$
$62$	−2.74933	−0.349166
$63$	1.24330	0.156642
$64$	−11.3985	−1.42481
$65$	9.13672	1.13327
$66$	7.10757	0.874881
$67$	4.25792	0.520188	0.260094	−	0.965583i	$-0.416246\pi$
$67$	4.25792	0.520188	0.260094	+	0.965583i	$0.416246\pi$
$68$	5.77948	0.700865
$69$	13.3184	1.60335
$70$	−0.874349	−0.104505
$71$	−0.908024	−0.107763	−0.0538813	−	0.998547i	$-0.517159\pi$
$71$	−0.908024	−0.107763	−0.0538813	+	0.998547i	$0.517159\pi$
$72$	−5.87030	−0.691821
$73$	−5.91665	−0.692491	−0.346245	−	0.938144i	$-0.612544\pi$
$73$	−5.91665	−0.692491	−0.346245	+	0.938144i	$0.612544\pi$
$74$	2.90983	0.338261
$75$	−4.95050	−0.571635
$76$	−2.50448	−0.287284
$77$	−0.260748	−0.0297150
$78$	−31.0888	−3.52012
$79$	9.81411	1.10417	0.552087	−	0.833787i	$-0.313832\pi$
$79$	9.81411	1.10417	0.552087	+	0.833787i	$0.313832\pi$
$80$	−4.97134	−0.555812
$81$	4.61138	0.512376
$82$	13.1992	1.45760
$83$	−12.0623	−1.32401	−0.662006	−	0.749499i	$-0.730295\pi$
$83$	−12.0623	−1.32401	−0.662006	+	0.749499i	$0.730295\pi$
$84$	1.65414	0.180481
$85$	4.19222	0.454710
$86$	−3.24328	−0.349731
$87$	24.7583	2.65437
$88$	1.23113	0.131239
$89$	−1.60363	−0.169984	−0.0849920	−	0.996382i	$-0.527086\pi$
$89$	−1.60363	−0.169984	−0.0849920	+	0.996382i	$0.527086\pi$
$90$	−21.1391	−2.22825
$91$	1.14053	0.119560
$92$	11.4526	1.19402
$93$	3.77285	0.391227
$94$	−4.26028	−0.439414
$95$	−1.81666	−0.186385
$96$	23.1525	2.36299
$97$	−0.189887	−0.0192801	−0.00964007	−	0.999954i	$-0.503069\pi$
$97$	−0.189887	−0.0192801	−0.00964007	+	0.999954i	$0.503069\pi$
$98$	14.7475	1.48972
$99$	−6.30409	−0.633585
$100$	−4.25699	−0.425699
$101$	9.19981	0.915415	0.457708	−	0.889103i	$-0.348671\pi$
$101$	9.19981	0.915415	0.457708	+	0.889103i	$0.348671\pi$
$102$	−14.2646	−1.41240
$103$	3.31531	0.326667	0.163334	−	0.986571i	$-0.447775\pi$
$103$	3.31531	0.326667	0.163334	+	0.986571i	$0.447775\pi$
$104$	−5.38502	−0.528045
$105$	1.19985	0.117094
$106$	−1.74935	−0.169912
$107$	1.48089	0.143163	0.0715816	−	0.997435i	$-0.477195\pi$
$107$	1.48089	0.143163	0.0715816	+	0.997435i	$0.477195\pi$
$108$	18.1091	1.74255
$109$	−14.0106	−1.34197	−0.670987	−	0.741469i	$-0.734129\pi$
$109$	−14.0106	−1.34197	−0.670987	+	0.741469i	$0.734129\pi$
$110$	4.43332	0.422701
$111$	−3.99311	−0.379009
$112$	−0.620566	−0.0586379
$113$	−13.0274	−1.22551	−0.612757	−	0.790271i	$-0.709940\pi$
$113$	−13.0274	−1.22551	−0.612757	+	0.790271i	$0.709940\pi$
$114$	6.18142	0.578943
$115$	8.30732	0.774662
$116$	21.2899	1.97672
$117$	27.5744	2.54925
$118$	−4.80496	−0.442332
$119$	0.523310	0.0479717
$120$	−5.66513	−0.517153
$121$	−9.67789	−0.879809
$122$	−18.2405	−1.65142
$123$	−18.1129	−1.63319
$124$	3.24432	0.291348
$125$	−12.1712	−1.08862
$126$	−2.63876	−0.235080
$127$	6.78594	0.602154	0.301077	−	0.953600i	$-0.402654\pi$
$127$	6.78594	0.602154	0.301077	+	0.953600i	$0.402654\pi$
$128$	8.29316	0.733019
$129$	4.45068	0.391861
$130$	−19.3916	−1.70075
$131$	−9.72478	−0.849658	−0.424829	−	0.905274i	$-0.639666\pi$
$131$	−9.72478	−0.849658	−0.424829	+	0.905274i	$0.639666\pi$
$132$	−8.38720	−0.730012
$133$	−0.226771	−0.0196636
$134$	−9.03691	−0.780670
$135$	13.1357	1.13054
$136$	−2.47082	−0.211871
$137$	1.09581	0.0936211	0.0468106	−	0.998904i	$-0.485094\pi$
$137$	1.09581	0.0936211	0.0468106	+	0.998904i	$0.485094\pi$
$138$	−28.2667	−2.40622
$139$	10.9214	0.926343	0.463172	−	0.886269i	$-0.346711\pi$
$139$	10.9214	0.926343	0.463172	+	0.886269i	$0.346711\pi$
$140$	1.03176	0.0872000
$141$	5.84629	0.492347
$142$	1.92717	0.161725
$143$	−5.78295	−0.483595
$144$	−15.0034	−1.25028
$145$	15.4429	1.28247
$146$	12.5574	1.03925
$147$	−20.2377	−1.66918
$148$	−3.43371	−0.282250
$149$	−12.9987	−1.06489	−0.532447	−	0.846463i	$-0.678728\pi$
$149$	−12.9987	−1.06489	−0.532447	+	0.846463i	$0.678728\pi$
$150$	10.5068	0.857879
$151$	3.87657	0.315471	0.157735	−	0.987481i	$-0.449581\pi$
$151$	3.87657	0.315471	0.157735	+	0.987481i	$0.449581\pi$
$152$	1.07071	0.0868458
$153$	12.6520	1.02286
$154$	0.553406	0.0445947
$155$	2.35331	0.189022
$156$	36.6860	2.93723
$157$	−0.430290	−0.0343409	−0.0171704	−	0.999853i	$-0.505466\pi$
$157$	−0.430290	−0.0343409	−0.0171704	+	0.999853i	$0.505466\pi$
$158$	−20.8292	−1.65708
$159$	2.40060	0.190380
$160$	14.4413	1.14168
$161$	1.03699	0.0817265
$162$	−9.78710	−0.768947
$163$	8.46902	0.663345	0.331673	−	0.943395i	$-0.392387\pi$
$163$	8.46902	0.663345	0.331673	+	0.943395i	$0.392387\pi$
$164$	−15.5755	−1.21624
$165$	−6.08376	−0.473620
$166$	25.6008	1.98701
$167$	−0.954402	−0.0738539	−0.0369269	−	0.999318i	$-0.511757\pi$
$167$	−0.954402	−0.0738539	−0.0369269	+	0.999318i	$0.511757\pi$
$168$	−0.707171	−0.0545594
$169$	12.2949	0.945762
$170$	−8.89748	−0.682405
$171$	−5.48264	−0.419268
$172$	3.82719	0.291820
$173$	17.5950	1.33773	0.668863	−	0.743385i	$-0.266781\pi$
$173$	17.5950	1.33773	0.668863	+	0.743385i	$0.266781\pi$
$174$	−52.5465	−3.98354
$175$	−0.385454	−0.0291376
$176$	3.14653	0.237179
$177$	6.59375	0.495617
$178$	3.40350	0.255103
$179$	−4.82018	−0.360277	−0.180138	−	0.983641i	$-0.557655\pi$
$179$	−4.82018	−0.360277	−0.180138	+	0.983641i	$0.557655\pi$
$180$	24.9449	1.85928
$181$	9.30990	0.692000	0.346000	−	0.938235i	$-0.387540\pi$
$181$	9.30990	0.692000	0.346000	+	0.938235i	$0.387540\pi$
$182$	−2.42062	−0.179429
$183$	25.0311	1.85035
$184$	−4.89619	−0.360952
$185$	−2.49069	−0.183119
$186$	−8.00742	−0.587132
$187$	−2.65341	−0.194036
$188$	5.02728	0.366652
$189$	1.63971	0.119271
$190$	3.85564	0.279717
$191$	4.79495	0.346951	0.173475	−	0.984838i	$-0.444500\pi$
$191$	4.79495	0.346951	0.173475	+	0.984838i	$0.444500\pi$
$192$	−33.1980	−2.39586
$193$	−19.7761	−1.42352	−0.711759	−	0.702424i	$-0.752101\pi$
$193$	−19.7761	−1.42352	−0.711759	+	0.702424i	$0.752101\pi$
$194$	0.403013	0.0289346
$195$	26.6107	1.90563
$196$	−17.4026	−1.24304
$197$	3.55307	0.253146	0.126573	−	0.991957i	$-0.459602\pi$
$197$	3.55307	0.253146	0.126573	+	0.991957i	$0.459602\pi$
$198$	13.3797	0.950851
$199$	26.7320	1.89498	0.947492	−	0.319778i	$-0.103608\pi$
$199$	26.7320	1.89498	0.947492	+	0.319778i	$0.103608\pi$
$200$	1.81993	0.128688
$201$	12.4012	0.874712
$202$	−19.5255	−1.37381
$203$	1.92772	0.135300
$204$	16.8327	1.17853
$205$	−11.2979	−0.789079
$206$	−7.03634	−0.490245
$207$	25.0713	1.74258
$208$	−13.7631	−0.954299
$209$	1.14983	0.0795353
$210$	−2.54654	−0.175728
$211$	2.48341	0.170965	0.0854826	−	0.996340i	$-0.472757\pi$
$211$	2.48341	0.170965	0.0854826	+	0.996340i	$0.472757\pi$
$212$	2.06430	0.141777
$213$	−2.64462	−0.181206
$214$	−3.14301	−0.214852
$215$	2.77610	0.189328
$216$	−7.74193	−0.526771
$217$	0.293760	0.0199417
$218$	29.7358	2.01396
$219$	−17.2322	−1.16444
$220$	−5.23149	−0.352707
$221$	11.6061	0.780712
$222$	8.47488	0.568797
$223$	15.3756	1.02963	0.514815	−	0.857302i	$-0.327861\pi$
$223$	15.3756	1.02963	0.514815	+	0.857302i	$0.327861\pi$
$224$	1.80269	0.120447
$225$	−9.31908	−0.621272
$226$	27.6490	1.83919
$227$	−11.0376	−0.732592	−0.366296	−	0.930498i	$-0.619374\pi$
$227$	−11.0376	−0.732592	−0.366296	+	0.930498i	$0.619374\pi$
$228$	−7.29430	−0.483077
$229$	16.9947	1.12304	0.561520	−	0.827463i	$-0.310217\pi$
$229$	16.9947	1.12304	0.561520	+	0.827463i	$0.310217\pi$
$230$	−17.6313	−1.16257
$231$	−0.759428	−0.0499667
$232$	−9.10179	−0.597562
$233$	−24.9966	−1.63758	−0.818791	−	0.574092i	$-0.805355\pi$
$233$	−24.9966	−1.63758	−0.818791	+	0.574092i	$0.805355\pi$
$234$	−58.5233	−3.82578
$235$	3.64661	0.237878
$236$	5.67003	0.369088
$237$	28.5835	1.85670
$238$	−1.11066	−0.0719935
$239$	3.25781	0.210730	0.105365	−	0.994434i	$-0.466399\pi$
$239$	3.25781	0.210730	0.105365	+	0.994434i	$0.466399\pi$
$240$	−14.4790	−0.934615
$241$	5.04698	0.325104	0.162552	−	0.986700i	$-0.448027\pi$
$241$	5.04698	0.325104	0.162552	+	0.986700i	$0.448027\pi$
$242$	20.5401	1.32037
$243$	−8.26136	−0.529967
$244$	21.5245	1.37796
$245$	−12.6232	−0.806467
$246$	38.4425	2.45100
$247$	−5.02940	−0.320013
$248$	−1.38700	−0.0880744
$249$	−35.1315	−2.22637
$250$	25.8318	1.63375
$251$	7.27635	0.459279	0.229640	−	0.973276i	$-0.426245\pi$
$251$	7.27635	0.459279	0.229640	+	0.973276i	$0.426245\pi$
$252$	3.11384	0.196153
$253$	−5.25800	−0.330568
$254$	−14.4023	−0.903682
$255$	12.2098	0.764609
$256$	5.19574	0.324734
$257$	14.4657	0.902344	0.451172	−	0.892437i	$-0.351006\pi$
$257$	14.4657	0.902344	0.451172	+	0.892437i	$0.351006\pi$
$258$	−9.44603	−0.588084
$259$	−0.310910	−0.0193190
$260$	22.8828	1.41913
$261$	46.6064	2.88486
$262$	20.6397	1.27512
$263$	−19.8095	−1.22151	−0.610753	−	0.791821i	$-0.709133\pi$
$263$	−19.8095	−1.22151	−0.610753	+	0.791821i	$0.709133\pi$
$264$	3.58566	0.220682
$265$	1.49737	0.0919826
$266$	0.481294	0.0295101
$267$	−4.67056	−0.285833
$268$	10.6639	0.651401
$269$	19.0356	1.16062	0.580312	−	0.814394i	$-0.302931\pi$
$269$	19.0356	1.16062	0.580312	+	0.814394i	$0.302931\pi$
$270$	−27.8788	−1.69665
$271$	−2.46043	−0.149460	−0.0747302	−	0.997204i	$-0.523810\pi$
$271$	−2.46043	−0.149460	−0.0747302	+	0.997204i	$0.523810\pi$
$272$	−6.31495	−0.382900
$273$	3.32178	0.201043
$274$	−2.32572	−0.140502
$275$	1.95442	0.117856
$276$	33.3558	2.00778
$277$	−1.61703	−0.0971577	−0.0485789	−	0.998819i	$-0.515469\pi$
$277$	−1.61703	−0.0971577	−0.0485789	+	0.998819i	$0.515469\pi$
$278$	−23.1794	−1.39021
$279$	7.10222	0.425199
$280$	−0.441096	−0.0263605
$281$	−16.4918	−0.983816	−0.491908	−	0.870647i	$-0.663700\pi$
$281$	−16.4918	−0.983816	−0.491908	+	0.870647i	$0.663700\pi$
$282$	−12.4080	−0.738888
$283$	−1.24914	−0.0742536	−0.0371268	−	0.999311i	$-0.511821\pi$
$283$	−1.24914	−0.0742536	−0.0371268	+	0.999311i	$0.511821\pi$
$284$	−2.27413	−0.134945
$285$	−5.29102	−0.313413
$286$	12.2736	0.725753
$287$	−1.41030	−0.0832475
$288$	43.5834	2.56818
$289$	−11.6747	−0.686749
$290$	−32.7757	−1.92466
$291$	−0.553047	−0.0324202
$292$	−14.8181	−0.867167
$293$	12.5600	0.733760	0.366880	−	0.930268i	$-0.380426\pi$
$293$	12.5600	0.733760	0.366880	+	0.930268i	$0.380426\pi$
$294$	42.9520	2.50501
$295$	4.11283	0.239458
$296$	1.46797	0.0853239
$297$	−8.31403	−0.482429
$298$	27.5881	1.59814
$299$	22.9987	1.33005
$300$	−12.3985	−0.715825
$301$	0.346537	0.0199741
$302$	−8.22754	−0.473442
$303$	26.7944	1.53930
$304$	2.73652	0.156950
$305$	15.6130	0.894000
$306$	−26.8524	−1.53505
$307$	2.31137	0.131917	0.0659585	−	0.997822i	$-0.478990\pi$
$307$	2.31137	0.131917	0.0659585	+	0.997822i	$0.478990\pi$
$308$	−0.653040	−0.0372104
$309$	9.65583	0.549301
$310$	−4.99460	−0.283674
$311$	−13.1104	−0.743422	−0.371711	−	0.928349i	$-0.621229\pi$
$311$	−13.1104	−0.743422	−0.371711	+	0.928349i	$0.621229\pi$
$312$	−15.6839	−0.887923
$313$	−1.51504	−0.0856350	−0.0428175	−	0.999083i	$-0.513633\pi$
$313$	−1.51504	−0.0856350	−0.0428175	+	0.999083i	$0.513633\pi$
$314$	0.913238	0.0515370
$315$	2.25866	0.127261
$316$	24.5793	1.38269
$317$	1.00000	0.0561656
$317$	1.00000	0.0561656
$318$	−5.09498	−0.285713
$319$	−9.77438	−0.547260
$320$	−20.7072	−1.15757
$321$	4.31309	0.240733
$322$	−2.20089	−0.122651
$323$	−2.30765	−0.128401
$324$	11.5491	0.641619
$325$	−8.54870	−0.474197
$326$	−17.9745	−0.995513
$327$	−40.8059	−2.25657
$328$	6.65878	0.367669
$329$	0.455201	0.0250961
$330$	12.9120	0.710784
$331$	−0.424605	−0.0233384	−0.0116692	−	0.999932i	$-0.503715\pi$
$331$	−0.424605	−0.0233384	−0.0116692	+	0.999932i	$0.503715\pi$
$332$	−30.2099	−1.65798
$333$	−7.51684	−0.411920
$334$	2.02560	0.110836
$335$	7.73520	0.422619
$336$	−1.80740	−0.0986015
$337$	−15.8961	−0.865915	−0.432958	−	0.901414i	$-0.642530\pi$
$337$	−15.8961	−0.865915	−0.432958	+	0.901414i	$0.642530\pi$
$338$	−26.0944	−1.41935
$339$	−37.9422	−2.06074
$340$	10.4994	0.569408
$341$	−1.48949	−0.0806604
$342$	11.6362	0.629215
$343$	−3.16314	−0.170793
$344$	−1.63618	−0.0882171
$345$	24.1951	1.30262
$346$	−37.3433	−2.00759
$347$	−21.2726	−1.14197	−0.570986	−	0.820960i	$-0.693439\pi$
$347$	−21.2726	−1.14197	−0.570986	+	0.820960i	$0.693439\pi$
$348$	62.0069	3.32392
$349$	2.29534	0.122867	0.0614335	−	0.998111i	$-0.480433\pi$
$349$	2.29534	0.122867	0.0614335	+	0.998111i	$0.480433\pi$
$350$	0.818078	0.0437281
$351$	36.3659	1.94107
$352$	−9.14039	−0.487185
$353$	−0.177187	−0.00943073	−0.00471537	−	0.999989i	$-0.501501\pi$
$353$	−0.177187	−0.00943073	−0.00471537	+	0.999989i	$0.501501\pi$
$354$	−13.9944	−0.743795
$355$	−1.64957	−0.0875502
$356$	−4.01626	−0.212861
$357$	1.52414	0.0806659
$358$	10.2302	0.540685
$359$	−12.7399	−0.672386	−0.336193	−	0.941793i	$-0.609139\pi$
$359$	−12.7399	−0.672386	−0.336193	+	0.941793i	$0.609139\pi$
$360$	−10.6643	−0.562060
$361$	1.00000	0.0526316
$362$	−19.7591	−1.03852
$363$	−28.1868	−1.47943
$364$	2.85643	0.149718
$365$	−10.7485	−0.562604
$366$	−53.1254	−2.77691
$367$	−5.80343	−0.302937	−0.151468	−	0.988462i	$-0.548400\pi$
$367$	−5.80343	−0.302937	−0.151468	+	0.988462i	$0.548400\pi$
$368$	−12.5137	−0.652323
$369$	−34.0968	−1.77501
$370$	5.28618	0.274815
$371$	0.186915	0.00970412
$372$	9.44906	0.489911
$373$	−35.1962	−1.82239	−0.911196	−	0.411973i	$-0.864840\pi$
$373$	−35.1962	−1.82239	−0.911196	+	0.411973i	$0.864840\pi$
$374$	5.63153	0.291199
$375$	−35.4485	−1.83055
$376$	−2.14924	−0.110839
$377$	42.7536	2.20192
$378$	−3.48008	−0.178996
$379$	−13.5713	−0.697109	−0.348554	−	0.937289i	$-0.613327\pi$
$379$	−13.5713	−0.697109	−0.348554	+	0.937289i	$0.613327\pi$
$380$	−4.54980	−0.233400
$381$	19.7640	1.01254
$382$	−10.1767	−0.520685
$383$	−22.4170	−1.14546	−0.572728	−	0.819746i	$-0.694115\pi$
$383$	−22.4170	−1.14546	−0.572728	+	0.819746i	$0.694115\pi$
$384$	24.1538	1.23259
$385$	−0.473691	−0.0241415
$386$	41.9724	2.13634
$387$	8.37820	0.425888
$388$	−0.475570	−0.0241434
$389$	19.9597	1.01200	0.505999	−	0.862534i	$-0.331124\pi$
$389$	19.9597	1.01200	0.505999	+	0.862534i	$0.331124\pi$
$390$	−56.4779	−2.85987
$391$	10.5526	0.533666
$392$	7.43989	0.375771
$393$	−28.3234	−1.42873
$394$	−7.54095	−0.379908
$395$	17.8289	0.897069
$396$	−15.7885	−0.793402
$397$	26.9966	1.35492	0.677462	−	0.735558i	$-0.263080\pi$
$397$	26.9966	1.35492	0.677462	+	0.735558i	$0.263080\pi$
$398$	−56.7355	−2.84389
$399$	−0.660471	−0.0330649
$400$	4.65139	0.232570
$401$	20.4591	1.02168	0.510839	−	0.859676i	$-0.329335\pi$
$401$	20.4591	1.02168	0.510839	+	0.859676i	$0.329335\pi$
$402$	−26.3200	−1.31272
$403$	6.51510	0.324540
$404$	23.0408	1.14632
$405$	8.37732	0.416272
$406$	−4.09135	−0.203050
$407$	1.57644	0.0781415
$408$	−7.19626	−0.356268
$409$	34.2477	1.69344	0.846719	−	0.532041i	$-0.178575\pi$
$409$	34.2477	1.69344	0.846719	+	0.532041i	$0.178575\pi$
$410$	23.9784	1.18421
$411$	3.19153	0.157427
$412$	8.30315	0.409067
$413$	0.513399	0.0252627
$414$	−53.2107	−2.61517
$415$	−21.9131	−1.07567
$416$	39.9805	1.96021
$417$	31.8086	1.55767
$418$	−2.44037	−0.119362
$419$	−9.83393	−0.480419	−0.240209	−	0.970721i	$-0.577216\pi$
$419$	−9.83393	−0.480419	−0.240209	+	0.970721i	$0.577216\pi$
$420$	3.00501	0.146629
$421$	2.19567	0.107010	0.0535052	−	0.998568i	$-0.482961\pi$
$421$	2.19567	0.107010	0.0535052	+	0.998568i	$0.482961\pi$
$422$	−5.27074	−0.256576
$423$	11.0054	0.535099
$424$	−0.882522	−0.0428591
$425$	−3.92242	−0.190265
$426$	5.61288	0.271945
$427$	1.94896	0.0943166
$428$	3.70887	0.179275
$429$	−16.8428	−0.813179
$430$	−5.89193	−0.284134
$431$	−17.4221	−0.839193	−0.419597	−	0.907711i	$-0.637828\pi$
$431$	−17.4221	−0.839193	−0.419597	+	0.907711i	$0.637828\pi$
$432$	−19.7869	−0.951998
$433$	13.1942	0.634071	0.317035	−	0.948414i	$-0.397313\pi$
$433$	13.1942	0.634071	0.317035	+	0.948414i	$0.397313\pi$
$434$	−0.623470	−0.0299275
$435$	44.9775	2.15651
$436$	−35.0894	−1.68048
$437$	−4.57285	−0.218749
$438$	36.5732	1.74754
$439$	−16.6737	−0.795794	−0.397897	−	0.917430i	$-0.630260\pi$
$439$	−16.6737	−0.795794	−0.397897	+	0.917430i	$0.630260\pi$
$440$	2.23654	0.106623
$441$	−38.0965	−1.81412
$442$	−24.6326	−1.17165
$443$	31.1221	1.47866	0.739328	−	0.673346i	$-0.235143\pi$
$443$	31.1221	1.47866	0.739328	+	0.673346i	$0.235143\pi$
$444$	−10.0007	−0.474611
$445$	−2.91324	−0.138101
$446$	−32.6329	−1.54521
$447$	−37.8587	−1.79065
$448$	−2.58485	−0.122123
$449$	18.6473	0.880021	0.440011	−	0.897993i	$-0.354975\pi$
$449$	18.6473	0.880021	0.440011	+	0.897993i	$0.354975\pi$
$450$	19.7786	0.932373
$451$	7.15083	0.336720
$452$	−32.6269	−1.53464
$453$	11.2905	0.530473
$454$	23.4260	1.09944
$455$	2.07195	0.0971344
$456$	3.11843	0.146034
$457$	6.74608	0.315568	0.157784	−	0.987474i	$-0.449565\pi$
$457$	6.74608	0.315568	0.157784	+	0.987474i	$0.449565\pi$
$458$	−36.0691	−1.68540
$459$	16.6859	0.778830
$460$	20.8056	0.970065
$461$	−14.5768	−0.678907	−0.339454	−	0.940623i	$-0.610242\pi$
$461$	−14.5768	−0.678907	−0.339454	+	0.940623i	$0.610242\pi$
$462$	1.61179	0.0749874
$463$	−10.7183	−0.498120	−0.249060	−	0.968488i	$-0.580122\pi$
$463$	−10.7183	−0.498120	−0.249060	+	0.968488i	$0.580122\pi$
$464$	−23.2625	−1.07993
$465$	6.85399	0.317846
$466$	53.0522	2.45760
$467$	−33.9392	−1.57052	−0.785260	−	0.619166i	$-0.787471\pi$
$467$	−33.9392	−1.57052	−0.785260	+	0.619166i	$0.787471\pi$
$468$	69.0596	3.19228
$469$	0.965575	0.0445861
$470$	−7.73947	−0.356995
$471$	−1.25322	−0.0577452
$472$	−2.42403	−0.111575
$473$	−1.75709	−0.0807911
$474$	−60.6651	−2.78644
$475$	1.69975	0.0779897
$476$	1.31062	0.0600722
$477$	4.51902	0.206912
$478$	−6.91430	−0.316253
$479$	−41.9550	−1.91697	−0.958486	−	0.285138i	$-0.907960\pi$
$479$	−41.9550	−1.91697	−0.958486	+	0.285138i	$0.907960\pi$
$480$	42.0602	1.91977
$481$	−6.89545	−0.314405
$482$	−10.7116	−0.487900
$483$	3.02024	0.137426
$484$	−24.2381	−1.10173
$485$	−0.344961	−0.0156639
$486$	17.5337	0.795346
$487$	−28.6227	−1.29702	−0.648509	−	0.761207i	$-0.724607\pi$
$487$	−28.6227	−1.29702	−0.648509	+	0.761207i	$0.724607\pi$
$488$	−9.20205	−0.416557
$489$	24.6660	1.11544
$490$	26.7912	1.21030
$491$	12.4202	0.560516	0.280258	−	0.959925i	$-0.409580\pi$
$491$	12.4202	0.560516	0.280258	+	0.959925i	$0.409580\pi$
$492$	−45.3636	−2.04515
$493$	19.6167	0.883493
$494$	10.6743	0.480259
$495$	−11.4524	−0.514747
$496$	−3.54490	−0.159171
$497$	−0.205914	−0.00923650
$498$	74.5622	3.34121
$499$	−1.49014	−0.0667079	−0.0333539	−	0.999444i	$-0.510619\pi$
$499$	−1.49014	−0.0667079	−0.0333539	+	0.999444i	$0.510619\pi$
$500$	−30.4825	−1.36322
$501$	−2.77969	−0.124188
$502$	−15.4432	−0.689262
$503$	−33.4401	−1.49102	−0.745510	−	0.666495i	$-0.767794\pi$
$503$	−33.4401	−1.49102	−0.745510	+	0.666495i	$0.767794\pi$
$504$	−1.33122	−0.0592971
$505$	16.7129	0.743716
$506$	11.1595	0.496098
$507$	35.8089	1.59033
$508$	16.9953	0.754043
$509$	5.16012	0.228718	0.114359	−	0.993439i	$-0.463519\pi$
$509$	5.16012	0.228718	0.114359	+	0.993439i	$0.463519\pi$
$510$	−25.9139	−1.14749
$511$	−1.34173	−0.0593545
$512$	−27.6136	−1.22036
$513$	−7.23067	−0.319242
$514$	−30.7016	−1.35419
$515$	6.02280	0.265396
$516$	11.1467	0.490705
$517$	−2.30807	−0.101509
$518$	0.659867	0.0289929
$519$	51.2455	2.24943
$520$	−9.78275	−0.429002
$521$	23.4127	1.02573	0.512865	−	0.858469i	$-0.328584\pi$
$521$	23.4127	1.02573	0.512865	+	0.858469i	$0.328584\pi$
$522$	−98.9163	−4.32945
$523$	31.4200	1.37390	0.686950	−	0.726705i	$-0.258949\pi$
$523$	31.4200	1.37390	0.686950	+	0.726705i	$0.258949\pi$
$524$	−24.3556	−1.06398
$525$	−1.12263	−0.0489957
$526$	42.0432	1.83317
$527$	2.98934	0.130218
$528$	9.16427	0.398824
$529$	−2.08900	−0.0908261
$530$	−3.17798	−0.138043
$531$	12.4124	0.538653
$532$	−0.567946	−0.0246236
$533$	−31.2781	−1.35480
$534$	9.91268	0.428964
$535$	2.69028	0.116311
$536$	−4.55899	−0.196918
$537$	−14.0387	−0.605817
$538$	−40.4008	−1.74180
$539$	7.98967	0.344139
$540$	32.8981	1.41571
$541$	10.0222	0.430887	0.215444	−	0.976516i	$-0.430880\pi$
$541$	10.0222	0.430887	0.215444	+	0.976516i	$0.430880\pi$
$542$	5.22196	0.224302
$543$	27.1151	1.16362
$544$	18.3444	0.786508
$545$	−25.4525	−1.09027
$546$	−7.05006	−0.301715
$547$	−34.0026	−1.45385	−0.726924	−	0.686718i	$-0.759051\pi$
$547$	−34.0026	−1.45385	−0.726924	+	0.686718i	$0.759051\pi$
$548$	2.74443	0.117236
$549$	47.1198	2.01102
$550$	−4.14801	−0.176872
$551$	−8.50073	−0.362143
$552$	−14.2601	−0.606952
$553$	2.22556	0.0946404
$554$	3.43194	0.145809
$555$	−7.25412	−0.307920
$556$	27.3525	1.16001
$557$	16.8216	0.712755	0.356377	−	0.934342i	$-0.384012\pi$
$557$	16.8216	0.712755	0.356377	+	0.934342i	$0.384012\pi$
$558$	−15.0736	−0.638116
$559$	7.68560	0.325066
$560$	−1.12736	−0.0476395
$561$	−7.72803	−0.326278
$562$	35.0017	1.47646
$563$	−27.0564	−1.14029	−0.570146	−	0.821543i	$-0.693113\pi$
$563$	−27.0564	−1.14029	−0.570146	+	0.821543i	$0.693113\pi$
$564$	14.6419	0.616537
$565$	−23.6663	−0.995651
$566$	2.65114	0.111436
$567$	1.04573	0.0439165
$568$	0.972228	0.0407938
$569$	−43.7649	−1.83472	−0.917360	−	0.398059i	$-0.869684\pi$
$569$	−43.7649	−1.83472	−0.917360	+	0.398059i	$0.869684\pi$
$570$	11.2295	0.470353
$571$	−2.92084	−0.122233	−0.0611167	−	0.998131i	$-0.519466\pi$
$571$	−2.92084	−0.122233	−0.0611167	+	0.998131i	$0.519466\pi$
$572$	−14.4833	−0.605578
$573$	13.9653	0.583408
$574$	2.99319	0.124933
$575$	−7.77269	−0.324143
$576$	−62.4937	−2.60390
$577$	21.3279	0.887892	0.443946	−	0.896053i	$-0.353578\pi$
$577$	21.3279	0.887892	0.443946	+	0.896053i	$0.353578\pi$
$578$	24.7782	1.03064
$579$	−57.5980	−2.39369
$580$	38.6766	1.60596
$581$	−2.73539	−0.113483
$582$	1.17377	0.0486545
$583$	−0.947737	−0.0392513
$584$	6.33500	0.262144
$585$	50.0933	2.07110
$586$	−26.6570	−1.10119
$587$	−7.19420	−0.296936	−0.148468	−	0.988917i	$-0.547434\pi$
$587$	−7.19420	−0.296936	−0.148468	+	0.988917i	$0.547434\pi$
$588$	−50.6850	−2.09021
$589$	−1.29540	−0.0533761
$590$	−8.72898	−0.359366
$591$	10.3483	0.425672
$592$	3.75185	0.154200
$593$	−6.28352	−0.258033	−0.129017	−	0.991642i	$-0.541182\pi$
$593$	−6.28352	−0.258033	−0.129017	+	0.991642i	$0.541182\pi$
$594$	17.6455	0.724004
$595$	0.950676	0.0389739
$596$	−32.5550	−1.33351
$597$	77.8570	3.18647
$598$	−48.8120	−1.99607
$599$	−6.79541	−0.277653	−0.138826	−	0.990317i	$-0.544333\pi$
$599$	−6.79541	−0.277653	−0.138826	+	0.990317i	$0.544333\pi$
$600$	5.30054	0.216394
$601$	−10.8715	−0.443457	−0.221728	−	0.975108i	$-0.571170\pi$
$601$	−10.8715	−0.443457	−0.221728	+	0.975108i	$0.571170\pi$
$602$	−0.735482	−0.0299760
$603$	23.3446	0.950667
$604$	9.70881	0.395046
$605$	−17.5814	−0.714787
$606$	−56.8679	−2.31010
$607$	−14.4936	−0.588279	−0.294140	−	0.955762i	$-0.595033\pi$
$607$	−14.4936	−0.588279	−0.294140	+	0.955762i	$0.595033\pi$
$608$	−7.94935	−0.322389
$609$	5.61448	0.227510
$610$	−33.1368	−1.34167
$611$	10.0956	0.408424
$612$	31.6868	1.28086
$613$	32.6018	1.31678	0.658388	−	0.752679i	$-0.271239\pi$
$613$	32.6018	1.31678	0.658388	+	0.752679i	$0.271239\pi$
$614$	−4.90560	−0.197974
$615$	−32.9051	−1.32686
$616$	0.279185	0.0112487
$617$	0.477157	0.0192096	0.00960482	−	0.999954i	$-0.496943\pi$
$617$	0.477157	0.0192096	0.00960482	+	0.999954i	$0.496943\pi$
$618$	−20.4933	−0.824362
$619$	35.1168	1.41146	0.705731	−	0.708480i	$-0.250619\pi$
$619$	35.1168	1.41146	0.705731	+	0.708480i	$0.250619\pi$
$620$	5.89382	0.236701
$621$	33.0648	1.32684
$622$	27.8252	1.11569
$623$	−0.363657	−0.0145696
$624$	−40.0850	−1.60468
$625$	−13.6121	−0.544486
$626$	3.21548	0.128517
$627$	3.34887	0.133741
$628$	−1.07765	−0.0430031
$629$	−3.16385	−0.126151
$630$	−4.79373	−0.190987
$631$	16.5367	0.658316	0.329158	−	0.944275i	$-0.393235\pi$
$631$	16.5367	0.658316	0.329158	+	0.944275i	$0.393235\pi$
$632$	−10.5080	−0.417987
$633$	7.23293	0.287483
$634$	−2.12238	−0.0842904
$635$	12.3277	0.489211
$636$	6.01227	0.238402
$637$	−34.9472	−1.38466
$638$	20.7449	0.821299
$639$	−4.97837	−0.196941
$640$	15.0659	0.595530
$641$	33.6016	1.32718	0.663591	−	0.748096i	$-0.269032\pi$
$641$	33.6016	1.32718	0.663591	+	0.748096i	$0.269032\pi$
$642$	−9.15401	−0.361280
$643$	−27.4190	−1.08130	−0.540650	−	0.841248i	$-0.681821\pi$
$643$	−27.4190	−1.08130	−0.540650	+	0.841248i	$0.681821\pi$
$644$	2.59713	0.102341
$645$	8.08538	0.318362
$646$	4.89771	0.192698
$647$	26.1667	1.02872	0.514359	−	0.857575i	$-0.328030\pi$
$647$	26.1667	1.02872	0.514359	+	0.857575i	$0.328030\pi$
$648$	−4.93744	−0.193961
$649$	−2.60316	−0.102183
$650$	18.1436	0.711650
$651$	0.855575	0.0335326
$652$	21.2105	0.830669
$653$	−2.36493	−0.0925469	−0.0462734	−	0.998929i	$-0.514735\pi$
$653$	−2.36493	−0.0925469	−0.0462734	+	0.998929i	$0.514735\pi$
$654$	86.6055	3.38654
$655$	−17.6666	−0.690292
$656$	17.0186	0.664464
$657$	−32.4388	−1.26556
$658$	−0.966109	−0.0376628
$659$	2.35706	0.0918182	0.0459091	−	0.998946i	$-0.485382\pi$
$659$	2.35706	0.0918182	0.0459091	+	0.998946i	$0.485382\pi$
$660$	−15.2367	−0.593087
$661$	−5.67247	−0.220633	−0.110317	−	0.993896i	$-0.535187\pi$
$661$	−5.67247	−0.220633	−0.110317	+	0.993896i	$0.535187\pi$
$662$	0.901172	0.0350250
$663$	33.8028	1.31279
$664$	12.9152	0.501208
$665$	−0.411967	−0.0159754
$666$	15.9536	0.618188
$667$	38.8726	1.50515
$668$	−2.39029	−0.0924830
$669$	44.7815	1.73135
$670$	−16.4170	−0.634244
$671$	−9.88205	−0.381492
$672$	5.25032	0.202535
$673$	11.6108	0.447562	0.223781	−	0.974639i	$-0.428160\pi$
$673$	11.6108	0.447562	0.223781	+	0.974639i	$0.428160\pi$
$674$	33.7375	1.29952
$675$	−12.2903	−0.473053
$676$	30.7924	1.18432
$677$	−11.1816	−0.429743	−0.214872	−	0.976642i	$-0.568933\pi$
$677$	−11.1816	−0.429743	−0.214872	+	0.976642i	$0.568933\pi$
$678$	80.5277	3.09265
$679$	−0.0430610	−0.00165253
$680$	−4.48864	−0.172132
$681$	−32.1470	−1.23188
$682$	3.16126	0.121051
$683$	33.3249	1.27514	0.637571	−	0.770391i	$-0.279939\pi$
$683$	33.3249	1.27514	0.637571	+	0.770391i	$0.279939\pi$
$684$	−13.7312	−0.525025
$685$	1.99071	0.0760611
$686$	6.71337	0.256318
$687$	49.4970	1.88843
$688$	−4.18178	−0.159429
$689$	4.14545	0.157929
$690$	−51.3510	−1.95490
$691$	26.3948	1.00411	0.502053	−	0.864837i	$-0.332578\pi$
$691$	26.3948	1.00411	0.502053	+	0.864837i	$0.332578\pi$
$692$	44.0665	1.67516
$693$	−1.42959	−0.0543055
$694$	45.1485	1.71381
$695$	19.8405	0.752594
$696$	−26.5089	−1.00482
$697$	−14.3514	−0.543598
$698$	−4.87159	−0.184392
$699$	−72.8025	−2.75364
$700$	−0.965363	−0.0364873
$701$	45.2216	1.70800	0.853998	−	0.520276i	$-0.174171\pi$
$701$	45.2216	1.70800	0.853998	+	0.520276i	$0.174171\pi$
$702$	−77.1822	−2.91306
$703$	1.37103	0.0517092
$704$	13.1063	0.493962
$705$	10.6207	0.400000
$706$	0.376059	0.0141531
$707$	2.08625	0.0784617
$708$	16.5139	0.620632
$709$	−14.9836	−0.562719	−0.281360	−	0.959602i	$-0.590785\pi$
$709$	−14.9836	−0.562719	−0.281360	+	0.959602i	$0.590785\pi$
$710$	3.50101	0.131391
$711$	53.8072	2.01793
$712$	1.71701	0.0643478
$713$	5.92369	0.221844
$714$	−3.23480	−0.121059
$715$	−10.5057	−0.392889
$716$	−12.0721	−0.451154
$717$	9.48836	0.354349
$718$	27.0389	1.00908
$719$	−15.7174	−0.586160	−0.293080	−	0.956088i	$-0.594680\pi$
$719$	−15.7174	−0.586160	−0.293080	+	0.956088i	$0.594680\pi$
$720$	−27.2560	−1.01577
$721$	0.751818	0.0279992
$722$	−2.12238	−0.0789867
$723$	14.6993	0.546673
$724$	23.3165	0.866551
$725$	−14.4491	−0.536625
$726$	59.8231	2.22024
$727$	−11.6554	−0.432274	−0.216137	−	0.976363i	$-0.569346\pi$
$727$	−11.6554	−0.432274	−0.216137	+	0.976363i	$0.569346\pi$
$728$	−1.22117	−0.0452595
$729$	−37.8953	−1.40353
$730$	22.8124	0.844326
$731$	3.52640	0.130429
$732$	62.6899	2.31709
$733$	48.4402	1.78918	0.894589	−	0.446889i	$-0.147468\pi$
$733$	48.4402	1.78918	0.894589	+	0.446889i	$0.147468\pi$
$734$	12.3171	0.454631
$735$	−36.7650	−1.35610
$736$	36.3512	1.33992
$737$	−4.89588	−0.180342
$738$	72.3662	2.66384
$739$	−27.3408	−1.00575	−0.502874	−	0.864360i	$-0.667724\pi$
$739$	−27.3408	−1.00575	−0.502874	+	0.864360i	$0.667724\pi$
$740$	−6.23789	−0.229310
$741$	−14.6481	−0.538112
$742$	−0.396703	−0.0145634
$743$	−28.1786	−1.03377	−0.516886	−	0.856054i	$-0.672909\pi$
$743$	−28.1786	−1.03377	−0.516886	+	0.856054i	$0.672909\pi$
$744$	−4.03962	−0.148100
$745$	−23.6142	−0.865158
$746$	74.6997	2.73495
$747$	−66.1333	−2.41969
$748$	−6.64541	−0.242980
$749$	0.335824	0.0122707
$750$	75.2350	2.74719
$751$	13.2023	0.481760	0.240880	−	0.970555i	$-0.422564\pi$
$751$	13.2023	0.481760	0.240880	+	0.970555i	$0.422564\pi$
$752$	−5.49306	−0.200311
$753$	21.1924	0.772292
$754$	−90.7392	−3.30453
$755$	7.04241	0.256299
$756$	4.10662	0.149357
$757$	45.6627	1.65964	0.829819	−	0.558032i	$-0.188443\pi$
$757$	45.6627	1.65964	0.829819	+	0.558032i	$0.188443\pi$
$758$	28.8033	1.04618
$759$	−15.3139	−0.555859
$760$	1.94511	0.0705566
$761$	41.0732	1.48890	0.744452	−	0.667676i	$-0.232711\pi$
$761$	41.0732	1.48890	0.744452	+	0.667676i	$0.232711\pi$
$762$	−41.9467	−1.51957
$763$	−3.17721	−0.115023
$764$	12.0089	0.434466
$765$	22.9844	0.831004
$766$	47.5774	1.71904
$767$	11.3863	0.411136
$768$	15.1326	0.546050
$769$	14.3467	0.517354	0.258677	−	0.965964i	$-0.416714\pi$
$769$	14.3467	0.517354	0.258677	+	0.965964i	$0.416714\pi$
$770$	1.00535	0.0362303
$771$	42.1312	1.51732
$772$	−49.5291	−1.78259
$773$	−21.7172	−0.781112	−0.390556	−	0.920579i	$-0.627717\pi$
$773$	−21.7172	−0.781112	−0.390556	+	0.920579i	$0.627717\pi$
$774$	−17.7817	−0.639150
$775$	−2.20185	−0.0790929
$776$	0.203314	0.00729854
$777$	−0.905523	−0.0324855
$778$	−42.3620	−1.51875
$779$	6.21904	0.222820
$780$	66.6460	2.38631
$781$	1.04407	0.0373598
$782$	−22.3965	−0.800898
$783$	61.4659	2.19661
$784$	19.0149	0.679105
$785$	−0.781691	−0.0278997
$786$	60.1129	2.14416
$787$	38.1119	1.35854	0.679271	−	0.733887i	$-0.262296\pi$
$787$	38.1119	1.35854	0.679271	+	0.733887i	$0.262296\pi$
$788$	8.89861	0.317000
$789$	−57.6951	−2.05400
$790$	−37.8396	−1.34627
$791$	−2.95424	−0.105041
$792$	6.74984	0.239845
$793$	43.2245	1.53495
$794$	−57.2971	−2.03340
$795$	4.36108	0.154672
$796$	66.9500	2.37298
$797$	45.1398	1.59893	0.799467	−	0.600709i	$-0.205115\pi$
$797$	45.1398	1.59893	0.799467	+	0.600709i	$0.205115\pi$
$798$	1.40177	0.0496221
$799$	4.63218	0.163875
$800$	−13.5119	−0.477717
$801$	−8.79210	−0.310654
$802$	−43.4219	−1.53328
$803$	6.80313	0.240077
$804$	31.0586	1.09535
$805$	1.88386	0.0663975
$806$	−13.8275	−0.487053
$807$	55.4413	1.95162
$808$	−9.85030	−0.346532
$809$	−39.4919	−1.38846	−0.694231	−	0.719752i	$-0.744255\pi$
$809$	−39.4919	−1.38846	−0.694231	+	0.719752i	$0.744255\pi$
$810$	−17.7798	−0.624719
$811$	−32.7941	−1.15156	−0.575779	−	0.817606i	$-0.695301\pi$
$811$	−32.7941	−1.15156	−0.575779	+	0.817606i	$0.695301\pi$
$812$	4.82795	0.169428
$813$	−7.16599	−0.251322
$814$	−3.34581	−0.117271
$815$	15.3853	0.538925
$816$	−18.3923	−0.643858
$817$	−1.52813	−0.0534626
$818$	−72.6864	−2.54142
$819$	6.25308	0.218500
$820$	−28.2954	−0.988118
$821$	2.31735	0.0808761	0.0404380	−	0.999182i	$-0.487125\pi$
$821$	2.31735	0.0808761	0.0404380	+	0.999182i	$0.487125\pi$
$822$	−6.77364	−0.236258
$823$	5.88824	0.205251	0.102626	−	0.994720i	$-0.467276\pi$
$823$	5.88824	0.205251	0.102626	+	0.994720i	$0.467276\pi$
$824$	−3.54973	−0.123661
$825$	5.69223	0.198178
$826$	−1.08963	−0.0379130
$827$	−35.0419	−1.21853	−0.609263	−	0.792969i	$-0.708534\pi$
$827$	−35.0419	−1.21853	−0.609263	+	0.792969i	$0.708534\pi$
$828$	62.7907	2.18213
$829$	16.2004	0.562661	0.281331	−	0.959611i	$-0.409224\pi$
$829$	16.2004	0.562661	0.281331	+	0.959611i	$0.409224\pi$
$830$	46.5079	1.61431
$831$	−4.70958	−0.163374
$832$	−57.3275	−1.98747
$833$	−16.0349	−0.555576
$834$	−67.5099	−2.33768
$835$	−1.73383	−0.0600015
$836$	2.87973	0.0995975
$837$	9.36662	0.323758
$838$	20.8713	0.720987
$839$	−21.3311	−0.736431	−0.368216	−	0.929740i	$-0.620031\pi$
$839$	−21.3311	−0.736431	−0.368216	+	0.929740i	$0.620031\pi$
$840$	−1.28469	−0.0443260
$841$	43.2624	1.49181
$842$	−4.66004	−0.160595
$843$	−48.0322	−1.65432
$844$	6.21967	0.214090
$845$	22.3357	0.768370
$846$	−23.3575	−0.803049
$847$	−2.19467	−0.0754097
$848$	−2.25556	−0.0774562
$849$	−3.63811	−0.124860
$850$	8.32486	0.285540
$851$	−6.26950	−0.214916
$852$	−6.62340	−0.226914
$853$	44.1458	1.51152	0.755761	−	0.654847i	$-0.227267\pi$
$853$	44.1458	1.51152	0.755761	+	0.654847i	$0.227267\pi$
$854$	−4.13642	−0.141545
$855$	−9.96009	−0.340628
$856$	−1.58560	−0.0541947
$857$	7.91760	0.270460	0.135230	−	0.990814i	$-0.456823\pi$
$857$	7.91760	0.270460	0.135230	+	0.990814i	$0.456823\pi$
$858$	35.7468	1.22038
$859$	−6.06036	−0.206777	−0.103388	−	0.994641i	$-0.532968\pi$
$859$	−6.06036	−0.206777	−0.103388	+	0.994641i	$0.532968\pi$
$860$	6.95270	0.237085
$861$	−4.10750	−0.139983
$862$	36.9763	1.25942
$863$	8.39821	0.285878	0.142939	−	0.989731i	$-0.454345\pi$
$863$	8.39821	0.285878	0.142939	+	0.989731i	$0.454345\pi$
$864$	57.4791	1.95548
$865$	31.9642	1.08682
$866$	−28.0030	−0.951580
$867$	−34.0026	−1.15479
$868$	0.735718	0.0249719
$869$	−11.2845	−0.382802
$870$	−95.4592	−3.23637
$871$	21.4148	0.725613
$872$	15.0013	0.508007
$873$	−1.04108	−0.0352353
$874$	9.70532	0.328287
$875$	−2.76007	−0.0933074
$876$	−43.1578	−1.45817
$877$	−13.4640	−0.454647	−0.227324	−	0.973819i	$-0.572997\pi$
$877$	−13.4640	−0.454647	−0.227324	+	0.973819i	$0.572997\pi$
$878$	35.3879	1.19429
$879$	36.5808	1.23384
$880$	5.71618	0.192693
$881$	18.2038	0.613301	0.306651	−	0.951822i	$-0.400792\pi$
$881$	18.2038	0.613301	0.306651	+	0.951822i	$0.400792\pi$
$882$	80.8551	2.72253
$883$	−3.16864	−0.106633	−0.0533166	−	0.998578i	$-0.516979\pi$
$883$	−3.16864	−0.106633	−0.0533166	+	0.998578i	$0.516979\pi$
$884$	29.0674	0.977641
$885$	11.9786	0.402656
$886$	−66.0528	−2.21909
$887$	21.8611	0.734023	0.367011	−	0.930216i	$-0.380381\pi$
$887$	21.8611	0.734023	0.367011	+	0.930216i	$0.380381\pi$
$888$	4.27545	0.143475
$889$	1.53886	0.0516116
$890$	6.18300	0.207255
$891$	−5.30230	−0.177634
$892$	38.5081	1.28935
$893$	−2.00731	−0.0671722
$894$	80.3503	2.68732
$895$	−8.75662	−0.292702
$896$	1.88065	0.0628281
$897$	66.9837	2.23652
$898$	−39.5766	−1.32069
$899$	11.0119	0.367266
$900$	−23.3395	−0.777983
$901$	1.90207	0.0633670
$902$	−15.1768	−0.505331
$903$	1.00929	0.0335870
$904$	13.9485	0.463921
$905$	16.9129	0.562205
$906$	−23.9627	−0.796107
$907$	1.57827	0.0524056	0.0262028	−	0.999657i	$-0.491658\pi$
$907$	1.57827	0.0524056	0.0262028	+	0.999657i	$0.491658\pi$
$908$	−27.6435	−0.917383
$909$	50.4392	1.67296
$910$	−4.39745	−0.145774
$911$	2.95023	0.0977455	0.0488727	−	0.998805i	$-0.484437\pi$
$911$	2.95023	0.0977455	0.0488727	+	0.998805i	$0.484437\pi$
$912$	7.97012	0.263917
$913$	13.8696	0.459017
$914$	−14.3177	−0.473588
$915$	45.4729	1.50329
$916$	42.5630	1.40632
$917$	−2.20530	−0.0728255
$918$	−35.4137	−1.16883
$919$	26.9270	0.888239	0.444119	−	0.895968i	$-0.353517\pi$
$919$	26.9270	0.888239	0.444119	+	0.895968i	$0.353517\pi$
$920$	−8.89471	−0.293250
$921$	6.73186	0.221822
$922$	30.9374	1.01887
$923$	−4.56682	−0.150319
$924$	−1.90198	−0.0625704
$925$	2.33040	0.0766229
$926$	22.7482	0.747553
$927$	18.1766	0.596999
$928$	67.5753	2.21827
$929$	−15.8190	−0.519005	−0.259503	−	0.965742i	$-0.583559\pi$
$929$	−15.8190	−0.519005	−0.259503	+	0.965742i	$0.583559\pi$
$930$	−14.5468	−0.477007
$931$	6.94857	0.227730
$932$	−62.6036	−2.05065
$933$	−38.1840	−1.25009
$934$	72.0318	2.35695
$935$	−4.82034	−0.157642
$936$	−29.5241	−0.965025
$937$	−30.1057	−0.983509	−0.491755	−	0.870734i	$-0.663644\pi$
$937$	−30.1057	−0.983509	−0.491755	+	0.870734i	$0.663644\pi$
$938$	−2.04931	−0.0669125
$939$	−4.41254	−0.143998
$940$	9.13287	0.297881
$941$	15.3687	0.501006	0.250503	−	0.968116i	$-0.419404\pi$
$941$	15.3687	0.501006	0.250503	+	0.968116i	$0.419404\pi$
$942$	2.65980	0.0866610
$943$	−28.4388	−0.926094
$944$	−6.19536	−0.201642
$945$	2.97879	0.0969002
$946$	3.72921	0.121247
$947$	34.9854	1.13687	0.568437	−	0.822727i	$-0.307548\pi$
$947$	34.9854	1.13687	0.568437	+	0.822727i	$0.307548\pi$
$948$	71.5871	2.32504
$949$	−29.7572	−0.965960
$950$	−3.60750	−0.117043
$951$	2.91250	0.0944442
$952$	−0.560312	−0.0181598
$953$	−18.4503	−0.597665	−0.298832	−	0.954306i	$-0.596597\pi$
$953$	−18.4503	−0.597665	−0.298832	+	0.954306i	$0.596597\pi$
$954$	−9.59107	−0.310522
$955$	8.71080	0.281875
$956$	8.15914	0.263885
$957$	−28.4678	−0.920235
$958$	89.0443	2.87689
$959$	0.248498	0.00802441
$960$	−60.3095	−1.94648
$961$	−29.3219	−0.945869
$962$	14.6347	0.471843
$963$	8.11919	0.261637
$964$	12.6401	0.407110
$965$	−35.9265	−1.15652
$966$	−6.41008	−0.206241
$967$	12.0560	0.387695	0.193847	−	0.981032i	$-0.437903\pi$
$967$	12.0560	0.387695	0.193847	+	0.981032i	$0.437903\pi$
$968$	10.3622	0.333054
$969$	−6.72103	−0.215911
$970$	0.732137	0.0235075
$971$	−38.0103	−1.21981	−0.609904	−	0.792475i	$-0.708792\pi$
$971$	−38.0103	−1.21981	−0.609904	+	0.792475i	$0.708792\pi$
$972$	−20.6905	−0.663647
$973$	2.47667	0.0793983
$974$	60.7482	1.94650
$975$	−24.8981	−0.797376
$976$	−23.5187	−0.752815
$977$	3.19986	0.102372	0.0511862	−	0.998689i	$-0.483700\pi$
$977$	3.19986	0.102372	0.0511862	+	0.998689i	$0.483700\pi$
$978$	−52.3506	−1.67399
$979$	1.84390	0.0589311
$980$	−31.6146	−1.00989
$981$	−76.8151	−2.45252
$982$	−26.3604	−0.841193
$983$	−54.7497	−1.74625	−0.873123	−	0.487500i	$-0.837909\pi$
$983$	−54.7497	−1.74625	−0.873123	+	0.487500i	$0.837909\pi$
$984$	19.3937	0.618247
$985$	6.45472	0.205665
$986$	−41.6341	−1.32590
$987$	1.32577	0.0421998
$988$	−12.5961	−0.400734
$989$	6.98793	0.222203
$990$	24.3063	0.772505
$991$	5.80962	0.184549	0.0922743	−	0.995734i	$-0.470586\pi$
$991$	5.80962	0.184549	0.0922743	+	0.995734i	$0.470586\pi$
$992$	10.2976	0.326949
$993$	−1.23666	−0.0392442
$994$	0.437027	0.0138617
$995$	48.5631	1.53955
$996$	−87.9862	−2.78795
$997$	−1.28820	−0.0407978	−0.0203989	−	0.999792i	$-0.506494\pi$
$997$	−1.28820	−0.0407978	−0.0203989	+	0.999792i	$0.506494\pi$
$998$	3.16264	0.100112
$999$	−9.91343	−0.313647

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.d.1.20	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.d.1.20	✓	140	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:	\( N \)	\(=\)	\( 6023 = 19 \cdot 317 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.12238 q^{2} +2.91250 q^{3} +2.50448 q^{4} +1.81666 q^{5} -6.18142 q^{6} +0.226771 q^{7} -1.07071 q^{8} +5.48264 q^{9} +O(q^{10})\)	\(q-2.12238 q^{2} +2.91250 q^{3} +2.50448 q^{4} +1.81666 q^{5} -6.18142 q^{6} +0.226771 q^{7} -1.07071 q^{8} +5.48264 q^{9} -3.85564 q^{10} -1.14983 q^{11} +7.29430 q^{12} +5.02940 q^{13} -0.481294 q^{14} +5.29102 q^{15} -2.73652 q^{16} +2.30765 q^{17} -11.6362 q^{18} -1.00000 q^{19} +4.54980 q^{20} +0.660471 q^{21} +2.44037 q^{22} +4.57285 q^{23} -3.11843 q^{24} -1.69975 q^{25} -10.6743 q^{26} +7.23067 q^{27} +0.567946 q^{28} +8.50073 q^{29} -11.2295 q^{30} +1.29540 q^{31} +7.94935 q^{32} -3.34887 q^{33} -4.89771 q^{34} +0.411967 q^{35} +13.7312 q^{36} -1.37103 q^{37} +2.12238 q^{38} +14.6481 q^{39} -1.94511 q^{40} -6.21904 q^{41} -1.40177 q^{42} +1.52813 q^{43} -2.87973 q^{44} +9.96009 q^{45} -9.70532 q^{46} +2.00731 q^{47} -7.97012 q^{48} -6.94857 q^{49} +3.60750 q^{50} +6.72103 q^{51} +12.5961 q^{52} +0.824242 q^{53} -15.3462 q^{54} -2.08885 q^{55} -0.242806 q^{56} -2.91250 q^{57} -18.0417 q^{58} +2.26395 q^{59} +13.2513 q^{60} +8.59437 q^{61} -2.74933 q^{62} +1.24330 q^{63} -11.3985 q^{64} +9.13672 q^{65} +7.10757 q^{66} +4.25792 q^{67} +5.77948 q^{68} +13.3184 q^{69} -0.874349 q^{70} -0.908024 q^{71} -5.87030 q^{72} -5.91665 q^{73} +2.90983 q^{74} -4.95050 q^{75} -2.50448 q^{76} -0.260748 q^{77} -31.0888 q^{78} +9.81411 q^{79} -4.97134 q^{80} +4.61138 q^{81} +13.1992 q^{82} -12.0623 q^{83} +1.65414 q^{84} +4.19222 q^{85} -3.24328 q^{86} +24.7583 q^{87} +1.23113 q^{88} -1.60363 q^{89} -21.1391 q^{90} +1.14053 q^{91} +11.4526 q^{92} +3.77285 q^{93} -4.26028 q^{94} -1.81666 q^{95} +23.1525 q^{96} -0.189887 q^{97} +14.7475 q^{98} -6.30409 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9}+O(q^{10}) \) 140 * q + 4 * q^2 + 3 * q^3 + 162 * q^4 + 13 * q^5 + 12 * q^6 + 25 * q^7 + 12 * q^8 + 181 * q^9	\( 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9} + 8 q^{10} + 19 q^{11} + 17 q^{12} + 28 q^{13} + 5 q^{14} + 14 q^{15} + 202 q^{16} + 38 q^{17} + 26 q^{18} - 140 q^{19} + 36 q^{20} + 4 q^{21} + 53 q^{22} + 58 q^{23} + 47 q^{24} + 279 q^{25} + 29 q^{26} + 21 q^{27} + 69 q^{28} + 18 q^{29} + 50 q^{30} + 20 q^{31} + 13 q^{32} + 47 q^{33} + 6 q^{34} + 35 q^{35} + 230 q^{36} + 88 q^{37} - 4 q^{38} + 32 q^{39} + 32 q^{40} + 24 q^{41} + 75 q^{42} + 100 q^{43} + 63 q^{44} + 87 q^{45} + 23 q^{46} + 35 q^{47} + 46 q^{48} + 255 q^{49} + 11 q^{50} - 6 q^{51} + 47 q^{52} + 77 q^{53} + 16 q^{54} + 63 q^{55} + 21 q^{56} - 3 q^{57} + 165 q^{58} + 18 q^{59} + 28 q^{60} + 99 q^{61} + 34 q^{62} + 89 q^{63} + 298 q^{64} + 78 q^{65} - 3 q^{66} + 28 q^{67} + 93 q^{68} + 19 q^{69} + 16 q^{70} + q^{71} + 43 q^{72} + 201 q^{73} + 32 q^{74} + 22 q^{75} - 162 q^{76} + 86 q^{77} + 122 q^{78} + 58 q^{79} + 92 q^{80} + 288 q^{81} + 143 q^{82} + 57 q^{83} + q^{84} + 136 q^{85} - 6 q^{86} + 43 q^{87} + 198 q^{88} + 46 q^{89} + 30 q^{90} + 26 q^{91} + 129 q^{92} + 111 q^{93} + 44 q^{94} - 13 q^{95} + 32 q^{96} + 110 q^{97} - 34 q^{98} + 62 q^{99}+O(q^{100}) \) 140 * q + 4 * q^2 + 3 * q^3 + 162 * q^4 + 13 * q^5 + 12 * q^6 + 25 * q^7 + 12 * q^8 + 181 * q^9 + 8 * q^10 + 19 * q^11 + 17 * q^12 + 28 * q^13 + 5 * q^14 + 14 * q^15 + 202 * q^16 + 38 * q^17 + 26 * q^18 - 140 * q^19 + 36 * q^20 + 4 * q^21 + 53 * q^22 + 58 * q^23 + 47 * q^24 + 279 * q^25 + 29 * q^26 + 21 * q^27 + 69 * q^28 + 18 * q^29 + 50 * q^30 + 20 * q^31 + 13 * q^32 + 47 * q^33 + 6 * q^34 + 35 * q^35 + 230 * q^36 + 88 * q^37 - 4 * q^38 + 32 * q^39 + 32 * q^40 + 24 * q^41 + 75 * q^42 + 100 * q^43 + 63 * q^44 + 87 * q^45 + 23 * q^46 + 35 * q^47 + 46 * q^48 + 255 * q^49 + 11 * q^50 - 6 * q^51 + 47 * q^52 + 77 * q^53 + 16 * q^54 + 63 * q^55 + 21 * q^56 - 3 * q^57 + 165 * q^58 + 18 * q^59 + 28 * q^60 + 99 * q^61 + 34 * q^62 + 89 * q^63 + 298 * q^64 + 78 * q^65 - 3 * q^66 + 28 * q^67 + 93 * q^68 + 19 * q^69 + 16 * q^70 + q^71 + 43 * q^72 + 201 * q^73 + 32 * q^74 + 22 * q^75 - 162 * q^76 + 86 * q^77 + 122 * q^78 + 58 * q^79 + 92 * q^80 + 288 * q^81 + 143 * q^82 + 57 * q^83 + q^84 + 136 * q^85 - 6 * q^86 + 43 * q^87 + 198 * q^88 + 46 * q^89 + 30 * q^90 + 26 * q^91 + 129 * q^92 + 111 * q^93 + 44 * q^94 - 13 * q^95 + 32 * q^96 + 110 * q^97 - 34 * q^98 + 62 * q^99

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