LMFDB - Embedded newform 6019.2.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6019,2,Mod(1,6019)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6019, 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("6019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6019 = 13 \cdot 463 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6019.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:	$48.0619569766$
Analytic rank:	$1$
Dimension:	$108$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	6019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.73685 q^{2} -2.13610 q^{3} +5.49032 q^{4} -3.88543 q^{5} +5.84618 q^{6} -1.04170 q^{7} -9.55248 q^{8} +1.56292 q^{9} +O(q^{10})$	\(q-2.73685 q^{2} -2.13610 q^{3} +5.49032 q^{4} -3.88543 q^{5} +5.84618 q^{6} -1.04170 q^{7} -9.55248 q^{8} +1.56292 q^{9} +10.6338 q^{10} -4.81178 q^{11} -11.7279 q^{12} -1.00000 q^{13} +2.85096 q^{14} +8.29967 q^{15} +15.1630 q^{16} -2.43895 q^{17} -4.27748 q^{18} -8.54378 q^{19} -21.3323 q^{20} +2.22517 q^{21} +13.1691 q^{22} -5.04586 q^{23} +20.4051 q^{24} +10.0966 q^{25} +2.73685 q^{26} +3.06974 q^{27} -5.71924 q^{28} -7.12604 q^{29} -22.7149 q^{30} -2.50853 q^{31} -22.3939 q^{32} +10.2784 q^{33} +6.67504 q^{34} +4.04744 q^{35} +8.58096 q^{36} +6.71960 q^{37} +23.3830 q^{38} +2.13610 q^{39} +37.1155 q^{40} -0.0878123 q^{41} -6.08993 q^{42} +5.33517 q^{43} -26.4182 q^{44} -6.07264 q^{45} +13.8097 q^{46} -2.03063 q^{47} -32.3897 q^{48} -5.91487 q^{49} -27.6328 q^{50} +5.20985 q^{51} -5.49032 q^{52} -5.73324 q^{53} -8.40140 q^{54} +18.6958 q^{55} +9.95077 q^{56} +18.2504 q^{57} +19.5029 q^{58} -1.84161 q^{59} +45.5679 q^{60} -2.15880 q^{61} +6.86546 q^{62} -1.62809 q^{63} +30.9625 q^{64} +3.88543 q^{65} -28.1305 q^{66} -3.26451 q^{67} -13.3906 q^{68} +10.7785 q^{69} -11.0772 q^{70} +0.628292 q^{71} -14.9298 q^{72} -5.01715 q^{73} -18.3905 q^{74} -21.5673 q^{75} -46.9081 q^{76} +5.01241 q^{77} -5.84618 q^{78} -5.04220 q^{79} -58.9149 q^{80} -11.2460 q^{81} +0.240329 q^{82} +13.1361 q^{83} +12.2169 q^{84} +9.47639 q^{85} -14.6015 q^{86} +15.2219 q^{87} +45.9644 q^{88} +11.0135 q^{89} +16.6199 q^{90} +1.04170 q^{91} -27.7034 q^{92} +5.35847 q^{93} +5.55753 q^{94} +33.1963 q^{95} +47.8356 q^{96} +7.21743 q^{97} +16.1881 q^{98} -7.52045 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9}+O(q^{10}) $ 108 * q - 11 * q^2 + q^3 + 95 * q^4 - 40 * q^5 - 10 * q^6 - 8 * q^7 - 33 * q^8 + 79 * q^9	\( 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9} - q^{10} - 45 q^{11} - 6 q^{12} - 108 q^{13} - 31 q^{14} - 39 q^{15} + 73 q^{16} + 21 q^{17} - 35 q^{18} - 19 q^{19} - 79 q^{20} - 72 q^{21} - 26 q^{23} - 23 q^{24} + 92 q^{25} + 11 q^{26} + 7 q^{27} - 21 q^{28} - 94 q^{29} - 24 q^{30} - 36 q^{31} - 77 q^{32} - 32 q^{33} - 58 q^{34} - 10 q^{35} + 17 q^{36} - 54 q^{37} - 12 q^{38} - q^{39} - 4 q^{40} - 68 q^{41} - 11 q^{42} - 32 q^{43} - 151 q^{44} - 121 q^{45} - 33 q^{46} - 51 q^{47} - 27 q^{48} + 72 q^{49} - 45 q^{50} - 24 q^{51} - 95 q^{52} - 81 q^{53} - 29 q^{54} + 4 q^{55} - 68 q^{56} - 45 q^{57} - 30 q^{58} - 94 q^{59} - 108 q^{60} - 39 q^{61} - 9 q^{62} - 52 q^{63} + 31 q^{64} + 40 q^{65} - 40 q^{66} - 47 q^{67} + 24 q^{68} - 60 q^{69} - 66 q^{70} - 86 q^{71} - 91 q^{72} - 51 q^{73} - 110 q^{74} - 7 q^{75} - 51 q^{76} - 96 q^{77} + 10 q^{78} - 18 q^{79} - 136 q^{80} - 24 q^{81} - 33 q^{82} - 77 q^{83} - 113 q^{84} - 95 q^{85} - 137 q^{86} + 23 q^{87} + 19 q^{88} - 112 q^{89} - 19 q^{90} + 8 q^{91} - 111 q^{92} - 124 q^{93} - 20 q^{94} - 73 q^{95} - 77 q^{96} - 41 q^{97} - 80 q^{98} - 154 q^{99}+O(q^{100}) \) 108 * q - 11 * q^2 + q^3 + 95 * q^4 - 40 * q^5 - 10 * q^6 - 8 * q^7 - 33 * q^8 + 79 * q^9 - q^10 - 45 * q^11 - 6 * q^12 - 108 * q^13 - 31 * q^14 - 39 * q^15 + 73 * q^16 + 21 * q^17 - 35 * q^18 - 19 * q^19 - 79 * q^20 - 72 * q^21 - 26 * q^23 - 23 * q^24 + 92 * q^25 + 11 * q^26 + 7 * q^27 - 21 * q^28 - 94 * q^29 - 24 * q^30 - 36 * q^31 - 77 * q^32 - 32 * q^33 - 58 * q^34 - 10 * q^35 + 17 * q^36 - 54 * q^37 - 12 * q^38 - q^39 - 4 * q^40 - 68 * q^41 - 11 * q^42 - 32 * q^43 - 151 * q^44 - 121 * q^45 - 33 * q^46 - 51 * q^47 - 27 * q^48 + 72 * q^49 - 45 * q^50 - 24 * q^51 - 95 * q^52 - 81 * q^53 - 29 * q^54 + 4 * q^55 - 68 * q^56 - 45 * q^57 - 30 * q^58 - 94 * q^59 - 108 * q^60 - 39 * q^61 - 9 * q^62 - 52 * q^63 + 31 * q^64 + 40 * q^65 - 40 * q^66 - 47 * q^67 + 24 * q^68 - 60 * q^69 - 66 * q^70 - 86 * q^71 - 91 * q^72 - 51 * q^73 - 110 * q^74 - 7 * q^75 - 51 * q^76 - 96 * q^77 + 10 * q^78 - 18 * q^79 - 136 * q^80 - 24 * q^81 - 33 * q^82 - 77 * q^83 - 113 * q^84 - 95 * q^85 - 137 * q^86 + 23 * q^87 + 19 * q^88 - 112 * q^89 - 19 * q^90 + 8 * q^91 - 111 * q^92 - 124 * q^93 - 20 * q^94 - 73 * q^95 - 77 * q^96 - 41 * q^97 - 80 * q^98 - 154 * 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 $

$2$	−2.73685	−1.93524	−0.967621	−	0.252407i	$-0.918778\pi$
$2$	−2.73685	−1.93524	−0.967621	+	0.252407i	$0.918778\pi$
$3$	−2.13610	−1.23328	−0.616639	−	0.787246i	$-0.711506\pi$
$3$	−2.13610	−1.23328	−0.616639	+	0.787246i	$0.711506\pi$
$4$	5.49032	2.74516
$5$	−3.88543	−1.73762	−0.868809	−	0.495147i	$-0.835114\pi$
$5$	−3.88543	−1.73762	−0.868809	+	0.495147i	$0.835114\pi$
$6$	5.84618	2.38669
$7$	−1.04170	−0.393724	−0.196862	−	0.980431i	$-0.563075\pi$
$7$	−1.04170	−0.393724	−0.196862	+	0.980431i	$0.563075\pi$
$8$	−9.55248	−3.37731
$9$	1.56292	0.520975
$10$	10.6338	3.36271
$11$	−4.81178	−1.45081	−0.725403	−	0.688325i	$-0.758347\pi$
$11$	−4.81178	−1.45081	−0.725403	+	0.688325i	$0.758347\pi$
$12$	−11.7279	−3.38555
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	2.85096	0.761951
$15$	8.29967	2.14297
$16$	15.1630	3.79075
$17$	−2.43895	−0.591533	−0.295766	−	0.955260i	$-0.595575\pi$
$17$	−2.43895	−0.591533	−0.295766	+	0.955260i	$0.595575\pi$
$18$	−4.27748	−1.00821
$19$	−8.54378	−1.96008	−0.980038	−	0.198809i	$-0.936293\pi$
$19$	−8.54378	−1.96008	−0.980038	+	0.198809i	$0.936293\pi$
$20$	−21.3323	−4.77004
$21$	2.22517	0.485571
$22$	13.1691	2.80766
$23$	−5.04586	−1.05213	−0.526067	−	0.850443i	$-0.676334\pi$
$23$	−5.04586	−1.05213	−0.526067	+	0.850443i	$0.676334\pi$
$24$	20.4051	4.16516
$25$	10.0966	2.01932
$26$	2.73685	0.536740
$27$	3.06974	0.590771
$28$	−5.71924	−1.08084
$29$	−7.12604	−1.32327	−0.661636	−	0.749825i	$-0.730138\pi$
$29$	−7.12604	−1.32327	−0.661636	+	0.749825i	$0.730138\pi$
$30$	−22.7149	−4.14716
$31$	−2.50853	−0.450545	−0.225273	−	0.974296i	$-0.572327\pi$
$31$	−2.50853	−0.450545	−0.225273	+	0.974296i	$0.572327\pi$
$32$	−22.3939	−3.95871
$33$	10.2784	1.78925
$34$	6.67504	1.14476
$35$	4.04744	0.684142
$36$	8.58096	1.43016
$37$	6.71960	1.10470	0.552348	−	0.833614i	$-0.313732\pi$
$37$	6.71960	1.10470	0.552348	+	0.833614i	$0.313732\pi$
$38$	23.3830	3.79322
$39$	2.13610	0.342050
$40$	37.1155	5.86848
$41$	−0.0878123	−0.0137140	−0.00685699	−	0.999976i	$-0.502183\pi$
$41$	−0.0878123	−0.0137140	−0.00685699	+	0.999976i	$0.502183\pi$
$42$	−6.08993	−0.939697
$43$	5.33517	0.813605	0.406803	−	0.913516i	$-0.366644\pi$
$43$	5.33517	0.813605	0.406803	+	0.913516i	$0.366644\pi$
$44$	−26.4182	−3.98270
$45$	−6.07264	−0.905256
$46$	13.8097	2.03613
$47$	−2.03063	−0.296198	−0.148099	−	0.988973i	$-0.547315\pi$
$47$	−2.03063	−0.296198	−0.148099	+	0.988973i	$0.547315\pi$
$48$	−32.3897	−4.67505
$49$	−5.91487	−0.844982
$50$	−27.6328	−3.90787
$51$	5.20985	0.729525
$52$	−5.49032	−0.761371
$53$	−5.73324	−0.787521	−0.393761	−	0.919213i	$-0.628826\pi$
$53$	−5.73324	−0.787521	−0.393761	+	0.919213i	$0.628826\pi$
$54$	−8.40140	−1.14329
$55$	18.6958	2.52095
$56$	9.95077	1.32973
$57$	18.2504	2.41732
$58$	19.5029	2.56085
$59$	−1.84161	−0.239757	−0.119879	−	0.992789i	$-0.538251\pi$
$59$	−1.84161	−0.239757	−0.119879	+	0.992789i	$0.538251\pi$
$60$	45.5679	5.88279
$61$	−2.15880	−0.276406	−0.138203	−	0.990404i	$-0.544133\pi$
$61$	−2.15880	−0.276406	−0.138203	+	0.990404i	$0.544133\pi$
$62$	6.86546	0.871914
$63$	−1.62809	−0.205120
$64$	30.9625	3.87032
$65$	3.88543	0.481929
$66$	−28.1305	−3.46263
$67$	−3.26451	−0.398824	−0.199412	−	0.979916i	$-0.563903\pi$
$67$	−3.26451	−0.398824	−0.199412	+	0.979916i	$0.563903\pi$
$68$	−13.3906	−1.62385
$69$	10.7785	1.29757
$70$	−11.0772	−1.32398
$71$	0.628292	0.0745646	0.0372823	−	0.999305i	$-0.488130\pi$
$71$	0.628292	0.0745646	0.0372823	+	0.999305i	$0.488130\pi$
$72$	−14.9298	−1.75949
$73$	−5.01715	−0.587213	−0.293607	−	0.955926i	$-0.594856\pi$
$73$	−5.01715	−0.587213	−0.293607	+	0.955926i	$0.594856\pi$
$74$	−18.3905	−2.13785
$75$	−21.5673	−2.49038
$76$	−46.9081	−5.38073
$77$	5.01241	0.571217
$78$	−5.84618	−0.661949
$79$	−5.04220	−0.567292	−0.283646	−	0.958929i	$-0.591544\pi$
$79$	−5.04220	−0.567292	−0.283646	+	0.958929i	$0.591544\pi$
$80$	−58.9149	−6.58688
$81$	−11.2460	−1.24956
$82$	0.240329	0.0265399
$83$	13.1361	1.44187	0.720936	−	0.693002i	$-0.243712\pi$
$83$	13.1361	1.44187	0.720936	+	0.693002i	$0.243712\pi$
$84$	12.2169	1.33297
$85$	9.47639	1.02786
$86$	−14.6015	−1.57452
$87$	15.2219	1.63196
$88$	45.9644	4.89982
$89$	11.0135	1.16742	0.583712	−	0.811961i	$-0.301600\pi$
$89$	11.0135	1.16742	0.583712	+	0.811961i	$0.301600\pi$
$90$	16.6199	1.75189
$91$	1.04170	0.109199
$92$	−27.7034	−2.88828
$93$	5.35847	0.555648
$94$	5.55753	0.573215
$95$	33.1963	3.40586
$96$	47.8356	4.88220
$97$	7.21743	0.732819	0.366410	−	0.930454i	$-0.380587\pi$
$97$	7.21743	0.732819	0.366410	+	0.930454i	$0.380587\pi$
$98$	16.1881	1.63524
$99$	−7.52045	−0.755833
$100$	55.4335	5.54335
$101$	−2.30728	−0.229583	−0.114791	−	0.993390i	$-0.536620\pi$
$101$	−2.30728	−0.229583	−0.114791	+	0.993390i	$0.536620\pi$
$102$	−14.2585	−1.41181
$103$	2.09318	0.206247	0.103123	−	0.994669i	$-0.467116\pi$
$103$	2.09318	0.206247	0.103123	+	0.994669i	$0.467116\pi$
$104$	9.55248	0.936698
$105$	−8.64573	−0.843737
$106$	15.6910	1.52404
$107$	14.7454	1.42549	0.712744	−	0.701425i	$-0.247452\pi$
$107$	14.7454	1.42549	0.712744	+	0.701425i	$0.247452\pi$
$108$	16.8539	1.62176
$109$	−16.1087	−1.54294	−0.771468	−	0.636268i	$-0.780477\pi$
$109$	−16.1087	−1.54294	−0.771468	+	0.636268i	$0.780477\pi$
$110$	−51.1676	−4.87864
$111$	−14.3537	−1.36240
$112$	−15.7952	−1.49251
$113$	6.01998	0.566312	0.283156	−	0.959074i	$-0.408619\pi$
$113$	6.01998	0.566312	0.283156	+	0.959074i	$0.408619\pi$
$114$	−49.9484	−4.67810
$115$	19.6053	1.82821
$116$	−39.1243	−3.63260
$117$	−1.56292	−0.144492
$118$	5.04021	0.463989
$119$	2.54065	0.232901
$120$	−79.2825	−7.23747
$121$	12.1532	1.10484
$122$	5.90830	0.534912
$123$	0.187576	0.0169131
$124$	−13.7726	−1.23682
$125$	−19.8024	−1.77118
$126$	4.45583	0.396957
$127$	0.243216	0.0215820	0.0107910	−	0.999942i	$-0.496565\pi$
$127$	0.243216	0.0215820	0.0107910	+	0.999942i	$0.496565\pi$
$128$	−39.9520	−3.53129
$129$	−11.3965	−1.00340
$130$	−10.6338	−0.932649
$131$	19.3749	1.69279	0.846397	−	0.532552i	$-0.178767\pi$
$131$	19.3749	1.69279	0.846397	+	0.532552i	$0.178767\pi$
$132$	56.4320	4.91177
$133$	8.90001	0.771729
$134$	8.93447	0.771821
$135$	−11.9273	−1.02653
$136$	23.2980	1.99779
$137$	−6.89862	−0.589389	−0.294695	−	0.955591i	$-0.595218\pi$
$137$	−6.89862	−0.589389	−0.294695	+	0.955591i	$0.595218\pi$
$138$	−29.4990	−2.51112
$139$	−1.50039	−0.127261	−0.0636305	−	0.997974i	$-0.520268\pi$
$139$	−1.50039	−0.127261	−0.0636305	+	0.997974i	$0.520268\pi$
$140$	22.2217	1.87808
$141$	4.33764	0.365295
$142$	−1.71954	−0.144301
$143$	4.81178	0.402381
$144$	23.6987	1.97489
$145$	27.6877	2.29934
$146$	13.7312	1.13640
$147$	12.6348	1.04210
$148$	36.8928	3.03257
$149$	−17.0457	−1.39643	−0.698217	−	0.715886i	$-0.746023\pi$
$149$	−17.0457	−1.39643	−0.698217	+	0.715886i	$0.746023\pi$
$150$	59.0264	4.81949
$151$	−20.8041	−1.69301	−0.846507	−	0.532377i	$-0.821299\pi$
$151$	−20.8041	−1.69301	−0.846507	+	0.532377i	$0.821299\pi$
$152$	81.6142	6.61979
$153$	−3.81190	−0.308174
$154$	−13.7182	−1.10544
$155$	9.74672	0.782876
$156$	11.7279	0.938982
$157$	−14.5062	−1.15772	−0.578861	−	0.815426i	$-0.696503\pi$
$157$	−14.5062	−1.15772	−0.578861	+	0.815426i	$0.696503\pi$
$158$	13.7997	1.09785
$159$	12.2468	0.971233
$160$	87.0099	6.87873
$161$	5.25625	0.414250
$162$	30.7787	2.41820
$163$	2.54841	0.199607	0.0998034	−	0.995007i	$-0.468179\pi$
$163$	2.54841	0.199607	0.0998034	+	0.995007i	$0.468179\pi$
$164$	−0.482118	−0.0376471
$165$	−39.9362	−3.10903
$166$	−35.9514	−2.79037
$167$	−14.1168	−1.09239	−0.546194	−	0.837659i	$-0.683924\pi$
$167$	−14.1168	−1.09239	−0.546194	+	0.837659i	$0.683924\pi$
$168$	−21.2558	−1.63992
$169$	1.00000	0.0769231
$170$	−25.9354	−1.98915
$171$	−13.3533	−1.02115
$172$	29.2918	2.23348
$173$	−3.31480	−0.252020	−0.126010	−	0.992029i	$-0.540217\pi$
$173$	−3.31480	−0.252020	−0.126010	+	0.992029i	$0.540217\pi$
$174$	−41.6601	−3.15824
$175$	−10.5176	−0.795053
$176$	−72.9611	−5.49965
$177$	3.93387	0.295688
$178$	−30.1421	−2.25925
$179$	−7.34557	−0.549034	−0.274517	−	0.961582i	$-0.588518\pi$
$179$	−7.34557	−0.549034	−0.274517	+	0.961582i	$0.588518\pi$
$180$	−33.3408	−2.48507
$181$	−6.80415	−0.505749	−0.252874	−	0.967499i	$-0.581376\pi$
$181$	−6.80415	−0.505749	−0.252874	+	0.967499i	$0.581376\pi$
$182$	−2.85096	−0.211327
$183$	4.61141	0.340885
$184$	48.2004	3.55338
$185$	−26.1086	−1.91954
$186$	−14.6653	−1.07531
$187$	11.7357	0.858199
$188$	−11.1488	−0.813112
$189$	−3.19773	−0.232601
$190$	−90.8531	−6.59117
$191$	25.3409	1.83361	0.916803	−	0.399340i	$-0.130761\pi$
$191$	25.3409	1.83361	0.916803	+	0.399340i	$0.130761\pi$
$192$	−66.1391	−4.77318
$193$	20.8841	1.50327	0.751634	−	0.659581i	$-0.229266\pi$
$193$	20.8841	1.50327	0.751634	+	0.659581i	$0.229266\pi$
$194$	−19.7530	−1.41818
$195$	−8.29967	−0.594352
$196$	−32.4746	−2.31961
$197$	−10.4203	−0.742414	−0.371207	−	0.928550i	$-0.621056\pi$
$197$	−10.4203	−0.742414	−0.371207	+	0.928550i	$0.621056\pi$
$198$	20.5823	1.46272
$199$	24.7080	1.75150	0.875751	−	0.482762i	$-0.160367\pi$
$199$	24.7080	1.75150	0.875751	+	0.482762i	$0.160367\pi$
$200$	−96.4474	−6.81986
$201$	6.97333	0.491861
$202$	6.31466	0.444298
$203$	7.42316	0.521004
$204$	28.6038	2.00266
$205$	0.341189	0.0238297
$206$	−5.72870	−0.399138
$207$	−7.88630	−0.548135
$208$	−15.1630	−1.05137
$209$	41.1108	2.84369
$210$	23.6620	1.63284
$211$	12.3077	0.847299	0.423649	−	0.905826i	$-0.360749\pi$
$211$	12.3077	0.847299	0.423649	+	0.905826i	$0.360749\pi$
$212$	−31.4774	−2.16187
$213$	−1.34210	−0.0919589
$214$	−40.3558	−2.75866
$215$	−20.7294	−1.41374
$216$	−29.3236	−1.99522
$217$	2.61312	0.177390
$218$	44.0871	2.98596
$219$	10.7171	0.724197
$220$	102.646	6.92041
$221$	2.43895	0.164062
$222$	39.2840	2.63657
$223$	−2.10609	−0.141034	−0.0705170	−	0.997511i	$-0.522465\pi$
$223$	−2.10609	−0.141034	−0.0705170	+	0.997511i	$0.522465\pi$
$224$	23.3276	1.55864
$225$	15.7802	1.05201
$226$	−16.4758	−1.09595
$227$	19.0185	1.26230	0.631150	−	0.775661i	$-0.282583\pi$
$227$	19.0185	1.26230	0.631150	+	0.775661i	$0.282583\pi$
$228$	100.200	6.63593
$229$	−19.0552	−1.25920	−0.629600	−	0.776919i	$-0.716781\pi$
$229$	−19.0552	−1.25920	−0.629600	+	0.776919i	$0.716781\pi$
$230$	−53.6568	−3.53802
$231$	−10.7070	−0.704469
$232$	68.0713	4.46910
$233$	20.6972	1.35592	0.677960	−	0.735099i	$-0.262864\pi$
$233$	20.6972	1.35592	0.677960	+	0.735099i	$0.262864\pi$
$234$	4.27748	0.279628
$235$	7.88989	0.514679
$236$	−10.1110	−0.658173
$237$	10.7707	0.699629
$238$	−6.95335	−0.450719
$239$	29.0535	1.87931	0.939657	−	0.342118i	$-0.111144\pi$
$239$	29.0535	1.87931	0.939657	+	0.342118i	$0.111144\pi$
$240$	125.848	8.12346
$241$	−10.1928	−0.656574	−0.328287	−	0.944578i	$-0.606471\pi$
$241$	−10.1928	−0.656574	−0.328287	+	0.944578i	$0.606471\pi$
$242$	−33.2615	−2.13813
$243$	14.8135	0.950284
$244$	−11.8525	−0.758779
$245$	22.9818	1.46826
$246$	−0.513366	−0.0327310
$247$	8.54378	0.543627
$248$	23.9627	1.52163
$249$	−28.0600	−1.77823
$250$	54.1962	3.42767
$251$	1.24427	0.0785375	0.0392687	−	0.999229i	$-0.487497\pi$
$251$	1.24427	0.0785375	0.0392687	+	0.999229i	$0.487497\pi$
$252$	−8.93875	−0.563088
$253$	24.2795	1.52644
$254$	−0.665646	−0.0417663
$255$	−20.2425	−1.26764
$256$	47.4173	2.96358
$257$	9.81600	0.612306	0.306153	−	0.951982i	$-0.400958\pi$
$257$	9.81600	0.612306	0.306153	+	0.951982i	$0.400958\pi$
$258$	31.1903	1.94183
$259$	−6.99978	−0.434945
$260$	21.3323	1.32297
$261$	−11.1375	−0.689392
$262$	−53.0262	−3.27597
$263$	19.2664	1.18802	0.594010	−	0.804458i	$-0.297544\pi$
$263$	19.2664	1.18802	0.594010	+	0.804458i	$0.297544\pi$
$264$	−98.1846	−6.04284
$265$	22.2761	1.36841
$266$	−24.3580	−1.49348
$267$	−23.5259	−1.43976
$268$	−17.9232	−1.09484
$269$	17.9430	1.09401	0.547003	−	0.837130i	$-0.315768\pi$
$269$	17.9430	1.09401	0.547003	+	0.837130i	$0.315768\pi$
$270$	32.6431	1.98659
$271$	15.2724	0.927733	0.463867	−	0.885905i	$-0.346462\pi$
$271$	15.2724	0.927733	0.463867	+	0.885905i	$0.346462\pi$
$272$	−36.9819	−2.24236
$273$	−2.22517	−0.134673
$274$	18.8805	1.14061
$275$	−48.5825	−2.92964
$276$	59.1772	3.56205
$277$	−15.9268	−0.956947	−0.478473	−	0.878102i	$-0.658810\pi$
$277$	−15.9268	−0.956947	−0.478473	+	0.878102i	$0.658810\pi$
$278$	4.10632	0.246281
$279$	−3.92064	−0.234723
$280$	−38.6631	−2.31056
$281$	31.8854	1.90212	0.951061	−	0.309004i	$-0.0999958\pi$
$281$	31.8854	1.90212	0.951061	+	0.309004i	$0.0999958\pi$
$282$	−11.8714	−0.706934
$283$	31.9100	1.89685	0.948427	−	0.316995i	$-0.102674\pi$
$283$	31.9100	1.89685	0.948427	+	0.316995i	$0.102674\pi$
$284$	3.44953	0.204692
$285$	−70.9106	−4.20038
$286$	−13.1691	−0.778705
$287$	0.0914736	0.00539952
$288$	−34.9999	−2.06239
$289$	−11.0515	−0.650089
$290$	−75.7771	−4.44978
$291$	−15.4172	−0.903770
$292$	−27.5458	−1.61200
$293$	31.8826	1.86260	0.931302	−	0.364249i	$-0.118674\pi$
$293$	31.8826	1.86260	0.931302	+	0.364249i	$0.118674\pi$
$294$	−34.5794	−2.01671
$295$	7.15546	0.416607
$296$	−64.1889	−3.73090
$297$	−14.7709	−0.857094
$298$	46.6513	2.70244
$299$	5.04586	0.291809
$300$	−118.412	−6.83650
$301$	−5.55762	−0.320336
$302$	56.9376	3.27639
$303$	4.92858	0.283139
$304$	−129.549	−7.43017
$305$	8.38787	0.480288
$306$	10.4326	0.596391
$307$	−25.3407	−1.44627	−0.723135	−	0.690707i	$-0.757299\pi$
$307$	−25.3407	−1.44627	−0.723135	+	0.690707i	$0.757299\pi$
$308$	27.5197	1.56808
$309$	−4.47124	−0.254360
$310$	−26.6753	−1.51505
$311$	−26.9588	−1.52870	−0.764348	−	0.644804i	$-0.776939\pi$
$311$	−26.9588	−1.52870	−0.764348	+	0.644804i	$0.776939\pi$
$312$	−20.4051	−1.15521
$313$	5.22590	0.295385	0.147693	−	0.989033i	$-0.452815\pi$
$313$	5.22590	0.295385	0.147693	+	0.989033i	$0.452815\pi$
$314$	39.7013	2.24047
$315$	6.32584	0.356421
$316$	−27.6833	−1.55731
$317$	−33.4451	−1.87846	−0.939232	−	0.343284i	$-0.888461\pi$
$317$	−33.4451	−1.87846	−0.939232	+	0.343284i	$0.888461\pi$
$318$	−33.5175	−1.87957
$319$	34.2889	1.91981
$320$	−120.303	−6.72513
$321$	−31.4976	−1.75802
$322$	−14.3855	−0.801674
$323$	20.8379	1.15945
$324$	−61.7444	−3.43025
$325$	−10.0966	−0.560058
$326$	−6.97460	−0.386287
$327$	34.4099	1.90287
$328$	0.838825	0.0463164
$329$	2.11530	0.116620
$330$	109.299	6.01672
$331$	−16.7547	−0.920923	−0.460462	−	0.887680i	$-0.652316\pi$
$331$	−16.7547	−0.920923	−0.460462	+	0.887680i	$0.652316\pi$
$332$	72.1213	3.95817
$333$	10.5022	0.575519
$334$	38.6354	2.11404
$335$	12.6840	0.693004
$336$	33.7402	1.84068
$337$	−3.19255	−0.173909	−0.0869546	−	0.996212i	$-0.527713\pi$
$337$	−3.19255	−0.173909	−0.0869546	+	0.996212i	$0.527713\pi$
$338$	−2.73685	−0.148865
$339$	−12.8593	−0.698420
$340$	52.0284	2.82164
$341$	12.0705	0.653654
$342$	36.5459	1.97617
$343$	13.4534	0.726413
$344$	−50.9641	−2.74780
$345$	−41.8790	−2.25469
$346$	9.07210	0.487719
$347$	5.06081	0.271678	0.135839	−	0.990731i	$-0.456627\pi$
$347$	5.06081	0.271678	0.135839	+	0.990731i	$0.456627\pi$
$348$	83.5734	4.48000
$349$	35.2229	1.88544	0.942720	−	0.333584i	$-0.108258\pi$
$349$	35.2229	1.88544	0.942720	+	0.333584i	$0.108258\pi$
$350$	28.7850	1.53862
$351$	−3.06974	−0.163850
$352$	107.754	5.74333
$353$	−6.28219	−0.334367	−0.167184	−	0.985926i	$-0.553467\pi$
$353$	−6.28219	−0.334367	−0.167184	+	0.985926i	$0.553467\pi$
$354$	−10.7664	−0.572227
$355$	−2.44119	−0.129565
$356$	60.4675	3.20477
$357$	−5.42707	−0.287231
$358$	20.1037	1.06251
$359$	−30.4132	−1.60515	−0.802575	−	0.596551i	$-0.796537\pi$
$359$	−30.4132	−1.60515	−0.802575	+	0.596551i	$0.796537\pi$
$360$	58.0088	3.05733
$361$	53.9961	2.84190
$362$	18.6219	0.978746
$363$	−25.9605	−1.36257
$364$	5.71924	0.299770
$365$	19.4938	1.02035
$366$	−12.6207	−0.659696
$367$	7.29088	0.380581	0.190290	−	0.981728i	$-0.439057\pi$
$367$	7.29088	0.380581	0.190290	+	0.981728i	$0.439057\pi$
$368$	−76.5104	−3.98838
$369$	−0.137244	−0.00714464
$370$	71.4551	3.71477
$371$	5.97229	0.310066
$372$	29.4197	1.52534
$373$	−12.4891	−0.646661	−0.323331	−	0.946286i	$-0.604803\pi$
$373$	−12.4891	−0.646661	−0.323331	+	0.946286i	$0.604803\pi$
$374$	−32.1188	−1.66082
$375$	42.3000	2.18436
$376$	19.3976	1.00035
$377$	7.12604	0.367010
$378$	8.75169	0.450139
$379$	−12.4662	−0.640344	−0.320172	−	0.947359i	$-0.603741\pi$
$379$	−12.4662	−0.640344	−0.320172	+	0.947359i	$0.603741\pi$
$380$	182.258	9.34965
$381$	−0.519535	−0.0266166
$382$	−69.3542	−3.54847
$383$	−1.93620	−0.0989354	−0.0494677	−	0.998776i	$-0.515752\pi$
$383$	−1.93620	−0.0989354	−0.0494677	+	0.998776i	$0.515752\pi$
$384$	85.3414	4.35506
$385$	−19.4754	−0.992557
$386$	−57.1564	−2.90919
$387$	8.33846	0.423868
$388$	39.6261	2.01171
$389$	−34.5307	−1.75078	−0.875388	−	0.483421i	$-0.839394\pi$
$389$	−34.5307	−1.75078	−0.875388	+	0.483421i	$0.839394\pi$
$390$	22.7149	1.15022
$391$	12.3066	0.622372
$392$	56.5017	2.85377
$393$	−41.3868	−2.08769
$394$	28.5187	1.43675
$395$	19.5911	0.985738
$396$	−41.2897	−2.07489
$397$	27.6361	1.38702	0.693508	−	0.720449i	$-0.256064\pi$
$397$	27.6361	1.38702	0.693508	+	0.720449i	$0.256064\pi$
$398$	−67.6219	−3.38958
$399$	−19.0113	−0.951756
$400$	153.095	7.65473
$401$	2.15291	0.107511	0.0537557	−	0.998554i	$-0.482881\pi$
$401$	2.15291	0.107511	0.0537557	+	0.998554i	$0.482881\pi$
$402$	−19.0849	−0.951869
$403$	2.50853	0.124959
$404$	−12.6677	−0.630242
$405$	43.6957	2.17126
$406$	−20.3160	−1.00827
$407$	−32.3332	−1.60270
$408$	−49.7670	−2.46383
$409$	8.39495	0.415103	0.207552	−	0.978224i	$-0.433450\pi$
$409$	8.39495	0.415103	0.207552	+	0.978224i	$0.433450\pi$
$410$	−0.933781	−0.0461162
$411$	14.7362	0.726881
$412$	11.4922	0.566181
$413$	1.91840	0.0943982
$414$	21.5836	1.06077
$415$	−51.0393	−2.50542
$416$	22.3939	1.09795
$417$	3.20497	0.156948
$418$	−112.514	−5.50323
$419$	−10.3148	−0.503913	−0.251957	−	0.967739i	$-0.581074\pi$
$419$	−10.3148	−0.503913	−0.251957	+	0.967739i	$0.581074\pi$
$420$	−47.4679	−2.31619
$421$	17.6791	0.861628	0.430814	−	0.902441i	$-0.358226\pi$
$421$	17.6791	0.861628	0.430814	+	0.902441i	$0.358226\pi$
$422$	−33.6843	−1.63973
$423$	−3.17373	−0.154312
$424$	54.7667	2.65970
$425$	−24.6251	−1.19449
$426$	3.67311	0.177963
$427$	2.24881	0.108828
$428$	80.9568	3.91319
$429$	−10.2784	−0.496248
$430$	56.7333	2.73592
$431$	30.3188	1.46040	0.730202	−	0.683232i	$-0.239426\pi$
$431$	30.3188	1.46040	0.730202	+	0.683232i	$0.239426\pi$
$432$	46.5465	2.23947
$433$	4.82589	0.231917	0.115959	−	0.993254i	$-0.463006\pi$
$433$	4.82589	0.231917	0.115959	+	0.993254i	$0.463006\pi$
$434$	−7.15172	−0.343293
$435$	−59.1438	−2.83573
$436$	−88.4422	−4.23561
$437$	43.1107	2.06226
$438$	−29.3312	−1.40150
$439$	−10.7155	−0.511422	−0.255711	−	0.966753i	$-0.582310\pi$
$439$	−10.7155	−0.511422	−0.255711	+	0.966753i	$0.582310\pi$
$440$	−178.592	−8.51402
$441$	−9.24450	−0.440214
$442$	−6.67504	−0.317499
$443$	−36.8263	−1.74967	−0.874836	−	0.484419i	$-0.839031\pi$
$443$	−36.8263	−1.74967	−0.874836	+	0.484419i	$0.839031\pi$
$444$	−78.8067	−3.74000
$445$	−42.7921	−2.02854
$446$	5.76403	0.272935
$447$	36.4112	1.72219
$448$	−32.2535	−1.52384
$449$	−15.6406	−0.738124	−0.369062	−	0.929405i	$-0.620321\pi$
$449$	−15.6406	−0.738124	−0.369062	+	0.929405i	$0.620321\pi$
$450$	−43.1880	−2.03590
$451$	0.422533	0.0198963
$452$	33.0516	1.55462
$453$	44.4397	2.08796
$454$	−52.0506	−2.44286
$455$	−4.04744	−0.189747
$456$	−174.336	−8.16404
$457$	1.26029	0.0589541	0.0294771	−	0.999565i	$-0.490616\pi$
$457$	1.26029	0.0589541	0.0294771	+	0.999565i	$0.490616\pi$
$458$	52.1511	2.43686
$459$	−7.48694	−0.349461
$460$	107.640	5.01873
$461$	−14.3915	−0.670280	−0.335140	−	0.942168i	$-0.608784\pi$
$461$	−14.3915	−0.670280	−0.335140	+	0.942168i	$0.608784\pi$
$462$	29.3034	1.36332
$463$	−1.00000	−0.0464739
$463$	−1.00000	−0.0464739
$464$	−108.052	−5.01620
$465$	−20.8200	−0.965503
$466$	−56.6451	−2.62403
$467$	−0.539807	−0.0249793	−0.0124896	−	0.999922i	$-0.503976\pi$
$467$	−0.539807	−0.0249793	−0.0124896	+	0.999922i	$0.503976\pi$
$468$	−8.58096	−0.396655
$469$	3.40063	0.157026
$470$	−21.5934	−0.996029
$471$	30.9867	1.42779
$472$	17.5920	0.809736
$473$	−25.6716	−1.18038
$474$	−29.4776	−1.35395
$475$	−86.2630	−3.95802
$476$	13.9490	0.639350
$477$	−8.96062	−0.410279
$478$	−79.5149	−3.63693
$479$	12.7481	0.582476	0.291238	−	0.956651i	$-0.405933\pi$
$479$	12.7481	0.582476	0.291238	+	0.956651i	$0.405933\pi$
$480$	−185.862	−8.48339
$481$	−6.71960	−0.306388
$482$	27.8961	1.27063
$483$	−11.2279	−0.510886
$484$	66.7251	3.03296
$485$	−28.0429	−1.27336
$486$	−40.5422	−1.83903
$487$	−41.6084	−1.88546	−0.942728	−	0.333562i	$-0.891749\pi$
$487$	−41.6084	−1.88546	−0.942728	+	0.333562i	$0.891749\pi$
$488$	20.6219	0.933509
$489$	−5.44366	−0.246171
$490$	−62.8977	−2.84143
$491$	−18.0035	−0.812489	−0.406244	−	0.913764i	$-0.633162\pi$
$491$	−18.0035	−0.812489	−0.406244	+	0.913764i	$0.633162\pi$
$492$	1.02985	0.0464293
$493$	17.3801	0.782759
$494$	−23.3830	−1.05205
$495$	29.2202	1.31335
$496$	−38.0369	−1.70791
$497$	−0.654489	−0.0293578
$498$	76.7958	3.44130
$499$	3.67993	0.164736	0.0823681	−	0.996602i	$-0.473752\pi$
$499$	3.67993	0.164736	0.0823681	+	0.996602i	$0.473752\pi$
$500$	−108.722	−4.86219
$501$	30.1548	1.34722
$502$	−3.40537	−0.151989
$503$	8.84749	0.394490	0.197245	−	0.980354i	$-0.436801\pi$
$503$	8.84749	0.394490	0.197245	+	0.980354i	$0.436801\pi$
$504$	15.5523	0.692755
$505$	8.96477	0.398927
$506$	−66.4494	−2.95403
$507$	−2.13610	−0.0948675
$508$	1.33534	0.0592460
$509$	−7.25431	−0.321541	−0.160771	−	0.986992i	$-0.551398\pi$
$509$	−7.25431	−0.321541	−0.160771	+	0.986992i	$0.551398\pi$
$510$	55.4006	2.45318
$511$	5.22634	0.231200
$512$	−49.8698	−2.20395
$513$	−26.2271	−1.15796
$514$	−26.8649	−1.18496
$515$	−8.13290	−0.358378
$516$	−62.5702	−2.75450
$517$	9.77096	0.429726
$518$	19.1573	0.841724
$519$	7.08075	0.310810
$520$	−37.1155	−1.62762
$521$	−38.6762	−1.69443	−0.847217	−	0.531247i	$-0.821723\pi$
$521$	−38.6762	−1.69443	−0.847217	+	0.531247i	$0.821723\pi$
$522$	30.4815	1.33414
$523$	15.3399	0.670768	0.335384	−	0.942082i	$-0.391134\pi$
$523$	15.3399	0.670768	0.335384	+	0.942082i	$0.391134\pi$
$524$	106.375	4.64700
$525$	22.4666	0.980522
$526$	−52.7293	−2.29911
$527$	6.11819	0.266512
$528$	155.852	6.78259
$529$	2.46068	0.106986
$530$	−60.9663	−2.64821
$531$	−2.87830	−0.124908
$532$	48.8639	2.11852
$533$	0.0878123	0.00380357
$534$	64.3866	2.78628
$535$	−57.2921	−2.47695
$536$	31.1842	1.34695
$537$	15.6909	0.677111
$538$	−49.1073	−2.11717
$539$	28.4610	1.22590
$540$	−65.4845	−2.81800
$541$	5.15144	0.221478	0.110739	−	0.993850i	$-0.464678\pi$
$541$	5.15144	0.221478	0.110739	+	0.993850i	$0.464678\pi$
$542$	−41.7983	−1.79539
$543$	14.5344	0.623729
$544$	54.6176	2.34171
$545$	62.5894	2.68104
$546$	6.08993	0.260625
$547$	24.4581	1.04575	0.522876	−	0.852409i	$-0.324859\pi$
$547$	24.4581	1.04575	0.522876	+	0.852409i	$0.324859\pi$
$548$	−37.8757	−1.61797
$549$	−3.37404	−0.144001
$550$	132.963	5.66956
$551$	60.8833	2.59372
$552$	−102.961	−4.38231
$553$	5.25244	0.223356
$554$	43.5891	1.85192
$555$	55.7705	2.36733
$556$	−8.23760	−0.349352
$557$	−10.7088	−0.453747	−0.226874	−	0.973924i	$-0.572850\pi$
$557$	−10.7088	−0.453747	−0.226874	+	0.973924i	$0.572850\pi$
$558$	10.7302	0.454245
$559$	−5.33517	−0.225654
$560$	61.3713	2.59341
$561$	−25.0686	−1.05840
$562$	−87.2653	−3.68107
$563$	−31.4244	−1.32438	−0.662189	−	0.749337i	$-0.730373\pi$
$563$	−31.4244	−1.32438	−0.662189	+	0.749337i	$0.730373\pi$
$564$	23.8150	1.00279
$565$	−23.3902	−0.984034
$566$	−87.3328	−3.67087
$567$	11.7149	0.491982
$568$	−6.00175	−0.251828
$569$	−28.2959	−1.18623	−0.593114	−	0.805119i	$-0.702102\pi$
$569$	−28.2959	−1.18623	−0.593114	+	0.805119i	$0.702102\pi$
$570$	194.071	8.12875
$571$	−13.4088	−0.561139	−0.280569	−	0.959834i	$-0.590523\pi$
$571$	−13.4088	−0.561139	−0.280569	+	0.959834i	$0.590523\pi$
$572$	26.4182	1.10460
$573$	−54.1308	−2.26135
$574$	−0.250349	−0.0104494
$575$	−50.9459	−2.12459
$576$	48.3921	2.01634
$577$	−0.176938	−0.00736601	−0.00368301	−	0.999993i	$-0.501172\pi$
$577$	−0.176938	−0.00736601	−0.00368301	+	0.999993i	$0.501172\pi$
$578$	30.2463	1.25808
$579$	−44.6104	−1.85395
$580$	152.015	6.31207
$581$	−13.6838	−0.567699
$582$	42.1944	1.74901
$583$	27.5871	1.14254
$584$	47.9263	1.98320
$585$	6.07264	0.251073
$586$	−87.2578	−3.60459
$587$	−16.6182	−0.685905	−0.342952	−	0.939353i	$-0.611427\pi$
$587$	−16.6182	−0.685905	−0.342952	+	0.939353i	$0.611427\pi$
$588$	69.3689	2.86073
$589$	21.4323	0.883103
$590$	−19.5834	−0.806235
$591$	22.2588	0.915603
$592$	101.889	4.18763
$593$	−4.24910	−0.174490	−0.0872449	−	0.996187i	$-0.527806\pi$
$593$	−4.24910	−0.174490	−0.0872449	+	0.996187i	$0.527806\pi$
$594$	40.4257	1.65868
$595$	−9.87151	−0.404692
$596$	−93.5862	−3.83344
$597$	−52.7787	−2.16009
$598$	−13.8097	−0.564722
$599$	10.8399	0.442905	0.221452	−	0.975171i	$-0.428920\pi$
$599$	10.8399	0.442905	0.221452	+	0.975171i	$0.428920\pi$
$600$	206.021	8.41079
$601$	29.5201	1.20415	0.602075	−	0.798440i	$-0.294341\pi$
$601$	29.5201	1.20415	0.602075	+	0.798440i	$0.294341\pi$
$602$	15.2103	0.619927
$603$	−5.10219	−0.207777
$604$	−114.221	−4.64760
$605$	−47.2205	−1.91979
$606$	−13.4888	−0.547943
$607$	38.4945	1.56244	0.781221	−	0.624254i	$-0.214597\pi$
$607$	38.4945	1.56244	0.781221	+	0.624254i	$0.214597\pi$
$608$	191.328	7.75938
$609$	−15.8566	−0.642543
$610$	−22.9563	−0.929474
$611$	2.03063	0.0821506
$612$	−20.9286	−0.845987
$613$	−36.7654	−1.48494	−0.742471	−	0.669878i	$-0.766346\pi$
$613$	−36.7654	−1.48494	−0.742471	+	0.669878i	$0.766346\pi$
$614$	69.3535	2.79888
$615$	−0.728813	−0.0293886
$616$	−47.8809	−1.92918
$617$	−17.1088	−0.688773	−0.344386	−	0.938828i	$-0.611913\pi$
$617$	−17.1088	−0.688773	−0.344386	+	0.938828i	$0.611913\pi$
$618$	12.2371	0.492248
$619$	−42.9464	−1.72616	−0.863080	−	0.505067i	$-0.831468\pi$
$619$	−42.9464	−1.72616	−0.863080	+	0.505067i	$0.831468\pi$
$620$	53.5127	2.14912
$621$	−15.4895	−0.621570
$622$	73.7822	2.95840
$623$	−11.4727	−0.459643
$624$	32.3897	1.29663
$625$	26.4581	1.05832
$626$	−14.3025	−0.571642
$627$	−87.8167	−3.50706
$628$	−79.6438	−3.17813
$629$	−16.3888	−0.653464
$630$	−17.3128	−0.689760
$631$	22.5845	0.899077	0.449538	−	0.893261i	$-0.351589\pi$
$631$	22.5845	0.899077	0.449538	+	0.893261i	$0.351589\pi$
$632$	48.1656	1.91592
$633$	−26.2905	−1.04495
$634$	91.5340	3.63528
$635$	−0.945001	−0.0375012
$636$	67.2388	2.66619
$637$	5.91487	0.234356
$638$	−93.8435	−3.71530
$639$	0.981974	0.0388463
$640$	155.231	6.13603
$641$	−37.6168	−1.48578	−0.742888	−	0.669416i	$-0.766544\pi$
$641$	−37.6168	−1.48578	−0.742888	+	0.669416i	$0.766544\pi$
$642$	86.2040	3.40220
$643$	29.2487	1.15346	0.576728	−	0.816936i	$-0.304329\pi$
$643$	29.2487	1.15346	0.576728	+	0.816936i	$0.304329\pi$
$644$	28.8585	1.13718
$645$	44.2801	1.74353
$646$	−57.0300	−2.24382
$647$	−4.90081	−0.192671	−0.0963353	−	0.995349i	$-0.530712\pi$
$647$	−4.90081	−0.192671	−0.0963353	+	0.995349i	$0.530712\pi$
$648$	107.428	4.22015
$649$	8.86143	0.347841
$650$	27.6328	1.08385
$651$	−5.58189	−0.218772
$652$	13.9916	0.547953
$653$	−3.49216	−0.136659	−0.0683293	−	0.997663i	$-0.521767\pi$
$653$	−3.49216	−0.136659	−0.0683293	+	0.997663i	$0.521767\pi$
$654$	−94.1745	−3.68251
$655$	−75.2799	−2.94143
$656$	−1.33150	−0.0519863
$657$	−7.84143	−0.305923
$658$	−5.78925	−0.225689
$659$	8.49550	0.330938	0.165469	−	0.986215i	$-0.447086\pi$
$659$	8.49550	0.330938	0.165469	+	0.986215i	$0.447086\pi$
$660$	−219.263	−8.53479
$661$	−22.6587	−0.881321	−0.440661	−	0.897674i	$-0.645256\pi$
$661$	−22.6587	−0.881321	−0.440661	+	0.897674i	$0.645256\pi$
$662$	45.8551	1.78221
$663$	−5.20985	−0.202334
$664$	−125.482	−4.86965
$665$	−34.5804	−1.34097
$666$	−28.7430	−1.11377
$667$	35.9570	1.39226
$668$	−77.5056	−2.99878
$669$	4.49881	0.173934
$670$	−34.7143	−1.34113
$671$	10.3877	0.401011
$672$	−49.8301	−1.92224
$673$	−0.317076	−0.0122224	−0.00611119	−	0.999981i	$-0.501945\pi$
$673$	−0.317076	−0.0122224	−0.00611119	+	0.999981i	$0.501945\pi$
$674$	8.73751	0.336556
$675$	30.9939	1.19295
$676$	5.49032	0.211166
$677$	−11.9933	−0.460941	−0.230471	−	0.973079i	$-0.574027\pi$
$677$	−11.9933	−0.460941	−0.230471	+	0.973079i	$0.574027\pi$
$678$	35.1939	1.35161
$679$	−7.51837	−0.288528
$680$	−90.5230	−3.47140
$681$	−40.6253	−1.55677
$682$	−33.0351	−1.26498
$683$	−26.6880	−1.02119	−0.510594	−	0.859822i	$-0.670575\pi$
$683$	−26.6880	−1.02119	−0.510594	+	0.859822i	$0.670575\pi$
$684$	−73.3138	−2.80322
$685$	26.8041	1.02413
$686$	−36.8198	−1.40579
$687$	40.7038	1.55294
$688$	80.8972	3.08418
$689$	5.73324	0.218419
$690$	114.616	4.36337
$691$	−38.3242	−1.45792	−0.728960	−	0.684556i	$-0.759996\pi$
$691$	−38.3242	−1.45792	−0.728960	+	0.684556i	$0.759996\pi$
$692$	−18.1993	−0.691835
$693$	7.83401	0.297590
$694$	−13.8507	−0.525764
$695$	5.82965	0.221131
$696$	−145.407	−5.51165
$697$	0.214170	0.00811227
$698$	−96.3997	−3.64878
$699$	−44.2114	−1.67223
$700$	−57.7448	−2.18255
$701$	−41.1072	−1.55260	−0.776298	−	0.630366i	$-0.782905\pi$
$701$	−41.1072	−1.55260	−0.776298	+	0.630366i	$0.782905\pi$
$702$	8.40140	0.317090
$703$	−57.4108	−2.16529
$704$	−148.985	−5.61508
$705$	−16.8536	−0.634743
$706$	17.1934	0.647082
$707$	2.40348	0.0903922
$708$	21.5982	0.811711
$709$	44.6891	1.67833	0.839167	−	0.543874i	$-0.183043\pi$
$709$	44.6891	1.67833	0.839167	+	0.543874i	$0.183043\pi$
$710$	6.68115	0.250739
$711$	−7.88059	−0.295545
$712$	−105.206	−3.94276
$713$	12.6577	0.474034
$714$	14.8531	0.555862
$715$	−18.6958	−0.699185
$716$	−40.3296	−1.50719
$717$	−62.0612	−2.31772
$718$	83.2364	3.10635
$719$	41.6442	1.55307	0.776533	−	0.630076i	$-0.216976\pi$
$719$	41.6442	1.55307	0.776533	+	0.630076i	$0.216976\pi$
$720$	−92.0795	−3.43160
$721$	−2.18045	−0.0812043
$722$	−147.779	−5.49977
$723$	21.7728	0.809739
$724$	−37.3570	−1.38836
$725$	−71.9487	−2.67211
$726$	71.0498	2.63691
$727$	44.5943	1.65391	0.826955	−	0.562268i	$-0.190071\pi$
$727$	44.5943	1.65391	0.826955	+	0.562268i	$0.190071\pi$
$728$	−9.95077	−0.368800
$729$	2.09508	0.0775956
$730$	−53.3516	−1.97463
$731$	−13.0122	−0.481274
$732$	25.3181	0.935786
$733$	−17.6837	−0.653161	−0.326580	−	0.945169i	$-0.605896\pi$
$733$	−17.6837	−0.653161	−0.326580	+	0.945169i	$0.605896\pi$
$734$	−19.9540	−0.736516
$735$	−49.0915	−1.81077
$736$	112.996	4.16510
$737$	15.7081	0.578616
$738$	0.375616	0.0138266
$739$	35.7787	1.31614	0.658071	−	0.752956i	$-0.271373\pi$
$739$	35.7787	1.31614	0.658071	+	0.752956i	$0.271373\pi$
$740$	−143.344	−5.26945
$741$	−18.2504	−0.670444
$742$	−16.3452	−0.600052
$743$	−20.1591	−0.739566	−0.369783	−	0.929118i	$-0.620568\pi$
$743$	−20.1591	−0.739566	−0.369783	+	0.929118i	$0.620568\pi$
$744$	−51.1867	−1.87660
$745$	66.2297	2.42647
$746$	34.1808	1.25145
$747$	20.5307	0.751179
$748$	64.4328	2.35590
$749$	−15.3602	−0.561248
$750$	−115.769	−4.22727
$751$	22.0890	0.806039	0.403019	−	0.915191i	$-0.367961\pi$
$751$	22.0890	0.806039	0.403019	+	0.915191i	$0.367961\pi$
$752$	−30.7905	−1.12281
$753$	−2.65788	−0.0968586
$754$	−19.5029	−0.710253
$755$	80.8330	2.94181
$756$	−17.5566	−0.638526
$757$	−3.88367	−0.141154	−0.0705772	−	0.997506i	$-0.522484\pi$
$757$	−3.88367	−0.141154	−0.0705772	+	0.997506i	$0.522484\pi$
$758$	34.1180	1.23922
$759$	−51.8635	−1.88253
$760$	−317.107	−11.5027
$761$	0.756438	0.0274209	0.0137104	−	0.999906i	$-0.495636\pi$
$761$	0.756438	0.0274209	0.0137104	+	0.999906i	$0.495636\pi$
$762$	1.42189	0.0515095
$763$	16.7804	0.607491
$764$	139.130	5.03355
$765$	14.8109	0.535488
$766$	5.29909	0.191464
$767$	1.84161	0.0664968
$768$	−101.288	−3.65492
$769$	31.5753	1.13864	0.569318	−	0.822118i	$-0.307208\pi$
$769$	31.5753	1.13864	0.569318	+	0.822118i	$0.307208\pi$
$770$	53.3011	1.92084
$771$	−20.9680	−0.755143
$772$	114.660	4.12671
$773$	−6.87968	−0.247445	−0.123722	−	0.992317i	$-0.539483\pi$
$773$	−6.87968	−0.247445	−0.123722	+	0.992317i	$0.539483\pi$
$774$	−22.8211	−0.820287
$775$	−25.3276	−0.909794
$776$	−68.9444	−2.47496
$777$	14.9522	0.536408
$778$	94.5052	3.38818
$779$	0.750249	0.0268804
$780$	−45.5679	−1.63159
$781$	−3.02320	−0.108179
$782$	−33.6813	−1.20444
$783$	−21.8751	−0.781751
$784$	−89.6873	−3.20312
$785$	56.3629	2.01168
$786$	113.269	4.04018
$787$	−19.5276	−0.696083	−0.348042	−	0.937479i	$-0.613153\pi$
$787$	−19.5276	−0.696083	−0.348042	+	0.937479i	$0.613153\pi$
$788$	−57.2107	−2.03805
$789$	−41.1551	−1.46516
$790$	−53.6179	−1.90764
$791$	−6.27098	−0.222971
$792$	71.8389	2.55268
$793$	2.15880	0.0766612
$794$	−75.6357	−2.68421
$795$	−47.5840	−1.68763
$796$	135.655	4.80816
$797$	−19.2931	−0.683395	−0.341698	−	0.939810i	$-0.611002\pi$
$797$	−19.2931	−0.683395	−0.341698	+	0.939810i	$0.611002\pi$
$798$	52.0310	1.84188
$799$	4.95262	0.175211
$800$	−226.102	−7.99390
$801$	17.2132	0.608199
$802$	−5.89219	−0.208061
$803$	24.1414	0.851932
$804$	38.2858	1.35024
$805$	−20.4228	−0.719809
$806$	−6.86546	−0.241825
$807$	−38.3281	−1.34921
$808$	22.0402	0.775372
$809$	24.6762	0.867569	0.433784	−	0.901017i	$-0.357178\pi$
$809$	24.6762	0.867569	0.433784	+	0.901017i	$0.357178\pi$
$810$	−119.588	−4.20191
$811$	−7.72451	−0.271244	−0.135622	−	0.990761i	$-0.543303\pi$
$811$	−7.72451	−0.271244	−0.135622	+	0.990761i	$0.543303\pi$
$812$	40.7556	1.43024
$813$	−32.6234	−1.14415
$814$	88.4911	3.10161
$815$	−9.90167	−0.346840
$816$	78.9970	2.76545
$817$	−45.5825	−1.59473
$818$	−22.9757	−0.803326
$819$	1.62809	0.0568901
$820$	1.87324	0.0654163
$821$	27.6647	0.965504	0.482752	−	0.875757i	$-0.339637\pi$
$821$	27.6647	0.965504	0.482752	+	0.875757i	$0.339637\pi$
$822$	−40.3306	−1.40669
$823$	−11.9498	−0.416544	−0.208272	−	0.978071i	$-0.566784\pi$
$823$	−11.9498	−0.416544	−0.208272	+	0.978071i	$0.566784\pi$
$824$	−19.9950	−0.696560
$825$	103.777	3.61306
$826$	−5.25036	−0.182683
$827$	−30.1918	−1.04987	−0.524936	−	0.851142i	$-0.675911\pi$
$827$	−30.1918	−1.04987	−0.524936	+	0.851142i	$0.675911\pi$
$828$	−43.2983	−1.50472
$829$	−46.8562	−1.62738	−0.813692	−	0.581297i	$-0.802546\pi$
$829$	−46.8562	−1.62738	−0.813692	+	0.581297i	$0.802546\pi$
$830$	139.687	4.84860
$831$	34.0212	1.18018
$832$	−30.9625	−1.07343
$833$	14.4261	0.499834
$834$	−8.77152	−0.303733
$835$	54.8498	1.89815
$836$	225.711	7.80639
$837$	−7.70053	−0.266169
$838$	28.2301	0.975194
$839$	40.2013	1.38790	0.693952	−	0.720021i	$-0.255868\pi$
$839$	40.2013	1.38790	0.693952	+	0.720021i	$0.255868\pi$
$840$	82.5882	2.84956
$841$	21.7804	0.751050
$842$	−48.3851	−1.66746
$843$	−68.1103	−2.34584
$844$	67.5734	2.32597
$845$	−3.88543	−0.133663
$846$	8.68600	0.298631
$847$	−12.6599	−0.435001
$848$	−86.9332	−2.98530
$849$	−68.1630	−2.33935
$850$	67.3951	2.31163
$851$	−33.9062	−1.16229
$852$	−7.36854	−0.252442
$853$	41.9603	1.43669	0.718347	−	0.695685i	$-0.244899\pi$
$853$	41.9603	1.43669	0.718347	+	0.695685i	$0.244899\pi$
$854$	−6.15465	−0.210608
$855$	51.8833	1.77437
$856$	−140.855	−4.81431
$857$	−29.4403	−1.00566	−0.502830	−	0.864385i	$-0.667708\pi$
$857$	−29.4403	−1.00566	−0.502830	+	0.864385i	$0.667708\pi$
$858$	28.1305	0.960360
$859$	−49.8410	−1.70055	−0.850277	−	0.526336i	$-0.823565\pi$
$859$	−49.8410	−1.70055	−0.850277	+	0.526336i	$0.823565\pi$
$860$	−113.811	−3.88093
$861$	−0.195397	−0.00665911
$862$	−82.9778	−2.82623
$863$	−12.5205	−0.426203	−0.213101	−	0.977030i	$-0.568356\pi$
$863$	−12.5205	−0.426203	−0.213101	+	0.977030i	$0.568356\pi$
$864$	−68.7433	−2.33869
$865$	12.8794	0.437914
$866$	−13.2077	−0.448816
$867$	23.6071	0.801740
$868$	14.3469	0.486965
$869$	24.2620	0.823031
$870$	161.867	5.48782
$871$	3.26451	0.110614
$872$	153.878	5.21098
$873$	11.2803	0.381781
$874$	−117.987	−3.99098
$875$	20.6281	0.697357
$876$	58.8406	1.98804
$877$	−12.6586	−0.427450	−0.213725	−	0.976894i	$-0.568560\pi$
$877$	−12.6586	−0.427450	−0.213725	+	0.976894i	$0.568560\pi$
$878$	29.3266	0.989726
$879$	−68.1045	−2.29711
$880$	283.485	9.55629
$881$	−35.2375	−1.18718	−0.593591	−	0.804767i	$-0.702290\pi$
$881$	−35.2375	−1.18718	−0.593591	+	0.804767i	$0.702290\pi$
$882$	25.3008	0.851921
$883$	−45.9961	−1.54789	−0.773946	−	0.633252i	$-0.781720\pi$
$883$	−45.9961	−1.54789	−0.773946	+	0.633252i	$0.781720\pi$
$884$	13.3906	0.450376
$885$	−15.2848	−0.513792
$886$	100.788	3.38604
$887$	20.9057	0.701946	0.350973	−	0.936386i	$-0.385851\pi$
$887$	20.9057	0.701946	0.350973	+	0.936386i	$0.385851\pi$
$888$	137.114	4.60124
$889$	−0.253357	−0.00849733
$890$	117.115	3.92571
$891$	54.1135	1.81287
$892$	−11.5631	−0.387161
$893$	17.3493	0.580571
$894$	−99.6519	−3.33286
$895$	28.5407	0.954011
$896$	41.6178	1.39035
$897$	−10.7785	−0.359882
$898$	42.8058	1.42845
$899$	17.8759	0.596194
$900$	86.6384	2.88795
$901$	13.9831	0.465845
$902$	−1.15641	−0.0385042
$903$	11.8716	0.395063
$904$	−57.5057	−1.91261
$905$	26.4371	0.878798
$906$	−121.625	−4.04070
$907$	−11.6071	−0.385406	−0.192703	−	0.981257i	$-0.561725\pi$
$907$	−11.6071	−0.385406	−0.192703	+	0.981257i	$0.561725\pi$
$908$	104.418	3.46522
$909$	−3.60610	−0.119607
$910$	11.0772	0.367206
$911$	−20.8849	−0.691948	−0.345974	−	0.938244i	$-0.612451\pi$
$911$	−20.8849	−0.691948	−0.345974	+	0.938244i	$0.612451\pi$
$912$	276.731	9.16346
$913$	−63.2079	−2.09187
$914$	−3.44923	−0.114090
$915$	−17.9173	−0.592329
$916$	−104.619	−3.45671
$917$	−20.1828	−0.666493
$918$	20.4906	0.676291
$919$	−22.5935	−0.745291	−0.372646	−	0.927974i	$-0.621549\pi$
$919$	−22.5935	−0.745291	−0.372646	+	0.927974i	$0.621549\pi$
$920$	−187.280	−6.17443
$921$	54.1302	1.78365
$922$	39.3874	1.29715
$923$	−0.628292	−0.0206805
$924$	−58.7849	−1.93388
$925$	67.8451	2.23073
$926$	2.73685	0.0899383
$927$	3.27148	0.107449
$928$	159.580	5.23846
$929$	52.7057	1.72922	0.864610	−	0.502444i	$-0.167566\pi$
$929$	52.7057	1.72922	0.864610	+	0.502444i	$0.167566\pi$
$930$	56.9811	1.86848
$931$	50.5353	1.65623
$932$	113.635	3.72222
$933$	57.5868	1.88531
$934$	1.47737	0.0483409
$935$	−45.5983	−1.49122
$936$	14.9298	0.487996
$937$	−30.0882	−0.982940	−0.491470	−	0.870895i	$-0.663540\pi$
$937$	−30.0882	−0.982940	−0.491470	+	0.870895i	$0.663540\pi$
$938$	−9.30699	−0.303884
$939$	−11.1630	−0.364292
$940$	43.3180	1.41288
$941$	8.54893	0.278687	0.139344	−	0.990244i	$-0.455501\pi$
$941$	8.54893	0.278687	0.139344	+	0.990244i	$0.455501\pi$
$942$	−84.8059	−2.76313
$943$	0.443088	0.0144289
$944$	−27.9244	−0.908861
$945$	12.4246	0.404171
$946$	70.2593	2.28433
$947$	−37.9812	−1.23422	−0.617111	−	0.786876i	$-0.711697\pi$
$947$	−37.9812	−1.23422	−0.617111	+	0.786876i	$0.711697\pi$
$948$	59.1344	1.92060
$949$	5.01715	0.162864
$950$	236.088	7.65972
$951$	71.4421	2.31667
$952$	−24.2695	−0.786578
$953$	40.4039	1.30881	0.654405	−	0.756144i	$-0.272919\pi$
$953$	40.4039	1.30881	0.654405	+	0.756144i	$0.272919\pi$
$954$	24.5238	0.793989
$955$	−98.4605	−3.18611
$956$	159.513	5.15902
$957$	−73.2446	−2.36766
$958$	−34.8896	−1.12723
$959$	7.18626	0.232057
$960$	256.979	8.29396
$961$	−24.7073	−0.797009
$962$	18.3905	0.592934
$963$	23.0459	0.742643
$964$	−55.9616	−1.80240
$965$	−81.1436	−2.61210
$966$	30.7289	0.988687
$967$	20.1013	0.646413	0.323206	−	0.946328i	$-0.395239\pi$
$967$	20.1013	0.646413	0.323206	+	0.946328i	$0.395239\pi$
$968$	−116.093	−3.73138
$969$	−44.5118	−1.42992
$970$	76.7490	2.46426
$971$	42.9791	1.37927	0.689633	−	0.724159i	$-0.257772\pi$
$971$	42.9791	1.37927	0.689633	+	0.724159i	$0.257772\pi$
$972$	81.3307	2.60868
$973$	1.56294	0.0501057
$974$	113.876	3.64881
$975$	21.5673	0.690707
$976$	−32.7339	−1.04779
$977$	36.1430	1.15632	0.578159	−	0.815924i	$-0.303771\pi$
$977$	36.1430	1.15632	0.578159	+	0.815924i	$0.303771\pi$
$978$	14.8984	0.476400
$979$	−52.9943	−1.69371
$980$	126.178	4.03060
$981$	−25.1767	−0.803831
$982$	49.2729	1.57236
$983$	−11.6382	−0.371201	−0.185600	−	0.982625i	$-0.559423\pi$
$983$	−11.6382	−0.371201	−0.185600	+	0.982625i	$0.559423\pi$
$984$	−1.79181	−0.0571210
$985$	40.4873	1.29003
$986$	−47.5666	−1.51483
$987$	−4.51849	−0.143825
$988$	46.9081	1.49235
$989$	−26.9205	−0.856022
$990$	−79.9712	−2.54165
$991$	−49.3534	−1.56776	−0.783880	−	0.620912i	$-0.786763\pi$
$991$	−49.3534	−1.56776	−0.783880	+	0.620912i	$0.786763\pi$
$992$	56.1757	1.78358
$993$	35.7898	1.13575
$994$	1.79124	0.0568145
$995$	−96.0012	−3.04344
$996$	−154.058	−4.88152
$997$	28.2173	0.893651	0.446825	−	0.894621i	$-0.352554\pi$
$997$	28.2173	0.893651	0.446825	+	0.894621i	$0.352554\pi$
$998$	−10.0714	−0.318805
$999$	20.6274	0.652622

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.c.1.2	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.c.1.2	✓	108	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:	\( N \)	\(=\)	\( 6019 = 13 \cdot 463 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.73685 q^{2} -2.13610 q^{3} +5.49032 q^{4} -3.88543 q^{5} +5.84618 q^{6} -1.04170 q^{7} -9.55248 q^{8} +1.56292 q^{9} +O(q^{10})\)	\(q-2.73685 q^{2} -2.13610 q^{3} +5.49032 q^{4} -3.88543 q^{5} +5.84618 q^{6} -1.04170 q^{7} -9.55248 q^{8} +1.56292 q^{9} +10.6338 q^{10} -4.81178 q^{11} -11.7279 q^{12} -1.00000 q^{13} +2.85096 q^{14} +8.29967 q^{15} +15.1630 q^{16} -2.43895 q^{17} -4.27748 q^{18} -8.54378 q^{19} -21.3323 q^{20} +2.22517 q^{21} +13.1691 q^{22} -5.04586 q^{23} +20.4051 q^{24} +10.0966 q^{25} +2.73685 q^{26} +3.06974 q^{27} -5.71924 q^{28} -7.12604 q^{29} -22.7149 q^{30} -2.50853 q^{31} -22.3939 q^{32} +10.2784 q^{33} +6.67504 q^{34} +4.04744 q^{35} +8.58096 q^{36} +6.71960 q^{37} +23.3830 q^{38} +2.13610 q^{39} +37.1155 q^{40} -0.0878123 q^{41} -6.08993 q^{42} +5.33517 q^{43} -26.4182 q^{44} -6.07264 q^{45} +13.8097 q^{46} -2.03063 q^{47} -32.3897 q^{48} -5.91487 q^{49} -27.6328 q^{50} +5.20985 q^{51} -5.49032 q^{52} -5.73324 q^{53} -8.40140 q^{54} +18.6958 q^{55} +9.95077 q^{56} +18.2504 q^{57} +19.5029 q^{58} -1.84161 q^{59} +45.5679 q^{60} -2.15880 q^{61} +6.86546 q^{62} -1.62809 q^{63} +30.9625 q^{64} +3.88543 q^{65} -28.1305 q^{66} -3.26451 q^{67} -13.3906 q^{68} +10.7785 q^{69} -11.0772 q^{70} +0.628292 q^{71} -14.9298 q^{72} -5.01715 q^{73} -18.3905 q^{74} -21.5673 q^{75} -46.9081 q^{76} +5.01241 q^{77} -5.84618 q^{78} -5.04220 q^{79} -58.9149 q^{80} -11.2460 q^{81} +0.240329 q^{82} +13.1361 q^{83} +12.2169 q^{84} +9.47639 q^{85} -14.6015 q^{86} +15.2219 q^{87} +45.9644 q^{88} +11.0135 q^{89} +16.6199 q^{90} +1.04170 q^{91} -27.7034 q^{92} +5.35847 q^{93} +5.55753 q^{94} +33.1963 q^{95} +47.8356 q^{96} +7.21743 q^{97} +16.1881 q^{98} -7.52045 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9}+O(q^{10}) \) 108 * q - 11 * q^2 + q^3 + 95 * q^4 - 40 * q^5 - 10 * q^6 - 8 * q^7 - 33 * q^8 + 79 * q^9	\( 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9} - q^{10} - 45 q^{11} - 6 q^{12} - 108 q^{13} - 31 q^{14} - 39 q^{15} + 73 q^{16} + 21 q^{17} - 35 q^{18} - 19 q^{19} - 79 q^{20} - 72 q^{21} - 26 q^{23} - 23 q^{24} + 92 q^{25} + 11 q^{26} + 7 q^{27} - 21 q^{28} - 94 q^{29} - 24 q^{30} - 36 q^{31} - 77 q^{32} - 32 q^{33} - 58 q^{34} - 10 q^{35} + 17 q^{36} - 54 q^{37} - 12 q^{38} - q^{39} - 4 q^{40} - 68 q^{41} - 11 q^{42} - 32 q^{43} - 151 q^{44} - 121 q^{45} - 33 q^{46} - 51 q^{47} - 27 q^{48} + 72 q^{49} - 45 q^{50} - 24 q^{51} - 95 q^{52} - 81 q^{53} - 29 q^{54} + 4 q^{55} - 68 q^{56} - 45 q^{57} - 30 q^{58} - 94 q^{59} - 108 q^{60} - 39 q^{61} - 9 q^{62} - 52 q^{63} + 31 q^{64} + 40 q^{65} - 40 q^{66} - 47 q^{67} + 24 q^{68} - 60 q^{69} - 66 q^{70} - 86 q^{71} - 91 q^{72} - 51 q^{73} - 110 q^{74} - 7 q^{75} - 51 q^{76} - 96 q^{77} + 10 q^{78} - 18 q^{79} - 136 q^{80} - 24 q^{81} - 33 q^{82} - 77 q^{83} - 113 q^{84} - 95 q^{85} - 137 q^{86} + 23 q^{87} + 19 q^{88} - 112 q^{89} - 19 q^{90} + 8 q^{91} - 111 q^{92} - 124 q^{93} - 20 q^{94} - 73 q^{95} - 77 q^{96} - 41 q^{97} - 80 q^{98} - 154 q^{99}+O(q^{100}) \) 108 * q - 11 * q^2 + q^3 + 95 * q^4 - 40 * q^5 - 10 * q^6 - 8 * q^7 - 33 * q^8 + 79 * q^9 - q^10 - 45 * q^11 - 6 * q^12 - 108 * q^13 - 31 * q^14 - 39 * q^15 + 73 * q^16 + 21 * q^17 - 35 * q^18 - 19 * q^19 - 79 * q^20 - 72 * q^21 - 26 * q^23 - 23 * q^24 + 92 * q^25 + 11 * q^26 + 7 * q^27 - 21 * q^28 - 94 * q^29 - 24 * q^30 - 36 * q^31 - 77 * q^32 - 32 * q^33 - 58 * q^34 - 10 * q^35 + 17 * q^36 - 54 * q^37 - 12 * q^38 - q^39 - 4 * q^40 - 68 * q^41 - 11 * q^42 - 32 * q^43 - 151 * q^44 - 121 * q^45 - 33 * q^46 - 51 * q^47 - 27 * q^48 + 72 * q^49 - 45 * q^50 - 24 * q^51 - 95 * q^52 - 81 * q^53 - 29 * q^54 + 4 * q^55 - 68 * q^56 - 45 * q^57 - 30 * q^58 - 94 * q^59 - 108 * q^60 - 39 * q^61 - 9 * q^62 - 52 * q^63 + 31 * q^64 + 40 * q^65 - 40 * q^66 - 47 * q^67 + 24 * q^68 - 60 * q^69 - 66 * q^70 - 86 * q^71 - 91 * q^72 - 51 * q^73 - 110 * q^74 - 7 * q^75 - 51 * q^76 - 96 * q^77 + 10 * q^78 - 18 * q^79 - 136 * q^80 - 24 * q^81 - 33 * q^82 - 77 * q^83 - 113 * q^84 - 95 * q^85 - 137 * q^86 + 23 * q^87 + 19 * q^88 - 112 * q^89 - 19 * q^90 + 8 * q^91 - 111 * q^92 - 124 * q^93 - 20 * q^94 - 73 * q^95 - 77 * q^96 - 41 * q^97 - 80 * q^98 - 154 * q^99

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