LMFDB - Embedded newform 6009.2.a.d.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6009,2,Mod(1,6009)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6009, 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("6009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6009 = 3 \cdot 2003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6009.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:	$47.9821065746$
Analytic rank:	$0$
Dimension:	$93$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	6009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.57633 q^{2} -1.00000 q^{3} +4.63748 q^{4} +2.33581 q^{5} +2.57633 q^{6} -3.18098 q^{7} -6.79503 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.57633 q^{2} -1.00000 q^{3} +4.63748 q^{4} +2.33581 q^{5} +2.57633 q^{6} -3.18098 q^{7} -6.79503 q^{8} +1.00000 q^{9} -6.01782 q^{10} -1.66610 q^{11} -4.63748 q^{12} -2.29429 q^{13} +8.19527 q^{14} -2.33581 q^{15} +8.23128 q^{16} -2.50168 q^{17} -2.57633 q^{18} +6.42910 q^{19} +10.8323 q^{20} +3.18098 q^{21} +4.29242 q^{22} +4.37747 q^{23} +6.79503 q^{24} +0.456004 q^{25} +5.91085 q^{26} -1.00000 q^{27} -14.7518 q^{28} +2.26520 q^{29} +6.01782 q^{30} +5.47236 q^{31} -7.61644 q^{32} +1.66610 q^{33} +6.44516 q^{34} -7.43017 q^{35} +4.63748 q^{36} +4.43691 q^{37} -16.5635 q^{38} +2.29429 q^{39} -15.8719 q^{40} +7.52805 q^{41} -8.19527 q^{42} +4.03482 q^{43} -7.72649 q^{44} +2.33581 q^{45} -11.2778 q^{46} -2.60998 q^{47} -8.23128 q^{48} +3.11866 q^{49} -1.17482 q^{50} +2.50168 q^{51} -10.6397 q^{52} -9.77478 q^{53} +2.57633 q^{54} -3.89168 q^{55} +21.6149 q^{56} -6.42910 q^{57} -5.83589 q^{58} -2.84032 q^{59} -10.8323 q^{60} -6.47199 q^{61} -14.0986 q^{62} -3.18098 q^{63} +3.15991 q^{64} -5.35902 q^{65} -4.29242 q^{66} -14.9818 q^{67} -11.6015 q^{68} -4.37747 q^{69} +19.1426 q^{70} -2.86271 q^{71} -6.79503 q^{72} +11.5817 q^{73} -11.4310 q^{74} -0.456004 q^{75} +29.8148 q^{76} +5.29983 q^{77} -5.91085 q^{78} -3.09782 q^{79} +19.2267 q^{80} +1.00000 q^{81} -19.3948 q^{82} +4.84612 q^{83} +14.7518 q^{84} -5.84345 q^{85} -10.3950 q^{86} -2.26520 q^{87} +11.3212 q^{88} +4.43109 q^{89} -6.01782 q^{90} +7.29809 q^{91} +20.3004 q^{92} -5.47236 q^{93} +6.72419 q^{94} +15.0172 q^{95} +7.61644 q^{96} -0.638668 q^{97} -8.03470 q^{98} -1.66610 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 93 q + 2 q^{2} - 93 q^{3} + 114 q^{4} - 20 q^{5} - 2 q^{6} + 28 q^{7} + 6 q^{8} + 93 q^{9}+O(q^{10}) $ 93 * q + 2 * q^2 - 93 * q^3 + 114 * q^4 - 20 * q^5 - 2 * q^6 + 28 * q^7 + 6 * q^8 + 93 * q^9	\( 93 q + 2 q^{2} - 93 q^{3} + 114 q^{4} - 20 q^{5} - 2 q^{6} + 28 q^{7} + 6 q^{8} + 93 q^{9} + 19 q^{10} + 10 q^{11} - 114 q^{12} + 20 q^{13} + 13 q^{14} + 20 q^{15} + 148 q^{16} - 43 q^{17} + 2 q^{18} + 50 q^{19} - 31 q^{20} - 28 q^{21} + 36 q^{22} + 21 q^{23} - 6 q^{24} + 137 q^{25} + 2 q^{26} - 93 q^{27} + 62 q^{28} - q^{29} - 19 q^{30} + 58 q^{31} + 19 q^{32} - 10 q^{33} + 30 q^{34} + 30 q^{35} + 114 q^{36} + 42 q^{37} - 6 q^{38} - 20 q^{39} + 53 q^{40} - 7 q^{41} - 13 q^{42} + 60 q^{43} + 25 q^{44} - 20 q^{45} + 57 q^{46} + 9 q^{47} - 148 q^{48} + 145 q^{49} + 41 q^{50} + 43 q^{51} + 71 q^{52} - 45 q^{53} - 2 q^{54} + 78 q^{55} + 44 q^{56} - 50 q^{57} + 40 q^{58} + 42 q^{59} + 31 q^{60} + 69 q^{61} - 42 q^{62} + 28 q^{63} + 230 q^{64} - 4 q^{65} - 36 q^{66} + 76 q^{67} - 91 q^{68} - 21 q^{69} + 57 q^{70} + 92 q^{71} + 6 q^{72} + 29 q^{73} + 59 q^{74} - 137 q^{75} + 131 q^{76} - 98 q^{77} - 2 q^{78} + 215 q^{79} - 37 q^{80} + 93 q^{81} + 50 q^{82} - 27 q^{83} - 62 q^{84} + 52 q^{85} + 82 q^{86} + q^{87} + 136 q^{88} - 14 q^{89} + 19 q^{90} + 101 q^{91} - 14 q^{92} - 58 q^{93} + 112 q^{94} + 59 q^{95} - 19 q^{96} + 38 q^{97} - 16 q^{98} + 10 q^{99}+O(q^{100}) \) 93 * q + 2 * q^2 - 93 * q^3 + 114 * q^4 - 20 * q^5 - 2 * q^6 + 28 * q^7 + 6 * q^8 + 93 * q^9 + 19 * q^10 + 10 * q^11 - 114 * q^12 + 20 * q^13 + 13 * q^14 + 20 * q^15 + 148 * q^16 - 43 * q^17 + 2 * q^18 + 50 * q^19 - 31 * q^20 - 28 * q^21 + 36 * q^22 + 21 * q^23 - 6 * q^24 + 137 * q^25 + 2 * q^26 - 93 * q^27 + 62 * q^28 - q^29 - 19 * q^30 + 58 * q^31 + 19 * q^32 - 10 * q^33 + 30 * q^34 + 30 * q^35 + 114 * q^36 + 42 * q^37 - 6 * q^38 - 20 * q^39 + 53 * q^40 - 7 * q^41 - 13 * q^42 + 60 * q^43 + 25 * q^44 - 20 * q^45 + 57 * q^46 + 9 * q^47 - 148 * q^48 + 145 * q^49 + 41 * q^50 + 43 * q^51 + 71 * q^52 - 45 * q^53 - 2 * q^54 + 78 * q^55 + 44 * q^56 - 50 * q^57 + 40 * q^58 + 42 * q^59 + 31 * q^60 + 69 * q^61 - 42 * q^62 + 28 * q^63 + 230 * q^64 - 4 * q^65 - 36 * q^66 + 76 * q^67 - 91 * q^68 - 21 * q^69 + 57 * q^70 + 92 * q^71 + 6 * q^72 + 29 * q^73 + 59 * q^74 - 137 * q^75 + 131 * q^76 - 98 * q^77 - 2 * q^78 + 215 * q^79 - 37 * q^80 + 93 * q^81 + 50 * q^82 - 27 * q^83 - 62 * q^84 + 52 * q^85 + 82 * q^86 + q^87 + 136 * q^88 - 14 * q^89 + 19 * q^90 + 101 * q^91 - 14 * q^92 - 58 * q^93 + 112 * q^94 + 59 * q^95 - 19 * q^96 + 38 * q^97 - 16 * q^98 + 10 * 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 $

$2$	−2.57633	−1.82174	−0.910871	−	0.412692i	$-0.864589\pi$
$2$	−2.57633	−1.82174	−0.910871	+	0.412692i	$0.864589\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.63748	2.31874
$5$	2.33581	1.04461	0.522303	−	0.852760i	$-0.325073\pi$
$5$	2.33581	1.04461	0.522303	+	0.852760i	$0.325073\pi$
$6$	2.57633	1.05178
$7$	−3.18098	−1.20230	−0.601149	−	0.799137i	$-0.705290\pi$
$7$	−3.18098	−1.20230	−0.601149	+	0.799137i	$0.705290\pi$
$8$	−6.79503	−2.40240
$9$	1.00000	0.333333
$10$	−6.01782	−1.90300
$11$	−1.66610	−0.502347	−0.251174	−	0.967942i	$-0.580816\pi$
$11$	−1.66610	−0.502347	−0.251174	+	0.967942i	$0.580816\pi$
$12$	−4.63748	−1.33873
$13$	−2.29429	−0.636321	−0.318160	−	0.948037i	$-0.603065\pi$
$13$	−2.29429	−0.636321	−0.318160	+	0.948037i	$0.603065\pi$
$14$	8.19527	2.19028
$15$	−2.33581	−0.603103
$16$	8.23128	2.05782
$17$	−2.50168	−0.606747	−0.303374	−	0.952872i	$-0.598113\pi$
$17$	−2.50168	−0.606747	−0.303374	+	0.952872i	$0.598113\pi$
$18$	−2.57633	−0.607247
$19$	6.42910	1.47494	0.737468	−	0.675382i	$-0.236021\pi$
$19$	6.42910	1.47494	0.737468	+	0.675382i	$0.236021\pi$
$20$	10.8323	2.42217
$21$	3.18098	0.694148
$22$	4.29242	0.915146
$23$	4.37747	0.912766	0.456383	−	0.889783i	$-0.349145\pi$
$23$	4.37747	0.912766	0.456383	+	0.889783i	$0.349145\pi$
$24$	6.79503	1.38703
$25$	0.456004	0.0912007
$26$	5.91085	1.15921
$27$	−1.00000	−0.192450
$28$	−14.7518	−2.78782
$29$	2.26520	0.420636	0.210318	−	0.977633i	$-0.432550\pi$
$29$	2.26520	0.420636	0.210318	+	0.977633i	$0.432550\pi$
$30$	6.01782	1.09870
$31$	5.47236	0.982865	0.491432	−	0.870916i	$-0.336473\pi$
$31$	5.47236	0.982865	0.491432	+	0.870916i	$0.336473\pi$
$32$	−7.61644	−1.34641
$33$	1.66610	0.290030
$34$	6.44516	1.10534
$35$	−7.43017	−1.25593
$36$	4.63748	0.772914
$37$	4.43691	0.729424	0.364712	−	0.931120i	$-0.381167\pi$
$37$	4.43691	0.729424	0.364712	+	0.931120i	$0.381167\pi$
$38$	−16.5635	−2.68695
$39$	2.29429	0.367380
$40$	−15.8719	−2.50957
$41$	7.52805	1.17568	0.587842	−	0.808976i	$-0.299978\pi$
$41$	7.52805	1.17568	0.587842	+	0.808976i	$0.299978\pi$
$42$	−8.19527	−1.26456
$43$	4.03482	0.615305	0.307652	−	0.951499i	$-0.400457\pi$
$43$	4.03482	0.615305	0.307652	+	0.951499i	$0.400457\pi$
$44$	−7.72649	−1.16481
$45$	2.33581	0.348202
$46$	−11.2778	−1.66282
$47$	−2.60998	−0.380705	−0.190353	−	0.981716i	$-0.560963\pi$
$47$	−2.60998	−0.380705	−0.190353	+	0.981716i	$0.560963\pi$
$48$	−8.23128	−1.18808
$49$	3.11866	0.445523
$50$	−1.17482	−0.166144
$51$	2.50168	0.350306
$52$	−10.6397	−1.47546
$53$	−9.77478	−1.34267	−0.671334	−	0.741155i	$-0.734279\pi$
$53$	−9.77478	−1.34267	−0.671334	+	0.741155i	$0.734279\pi$
$54$	2.57633	0.350594
$55$	−3.89168	−0.524755
$56$	21.6149	2.88841
$57$	−6.42910	−0.851555
$58$	−5.83589	−0.766290
$59$	−2.84032	−0.369778	−0.184889	−	0.982759i	$-0.559193\pi$
$59$	−2.84032	−0.369778	−0.184889	+	0.982759i	$0.559193\pi$
$60$	−10.8323	−1.39844
$61$	−6.47199	−0.828653	−0.414327	−	0.910128i	$-0.635983\pi$
$61$	−6.47199	−0.828653	−0.414327	+	0.910128i	$0.635983\pi$
$62$	−14.0986	−1.79053
$63$	−3.18098	−0.400766
$64$	3.15991	0.394989
$65$	−5.35902	−0.664704
$66$	−4.29242	−0.528360
$67$	−14.9818	−1.83032	−0.915159	−	0.403094i	$-0.867935\pi$
$67$	−14.9818	−1.83032	−0.915159	+	0.403094i	$0.867935\pi$
$68$	−11.6015	−1.40689
$69$	−4.37747	−0.526986
$70$	19.1426	2.28798
$71$	−2.86271	−0.339741	−0.169870	−	0.985466i	$-0.554335\pi$
$71$	−2.86271	−0.339741	−0.169870	+	0.985466i	$0.554335\pi$
$72$	−6.79503	−0.800802
$73$	11.5817	1.35554	0.677771	−	0.735273i	$-0.262946\pi$
$73$	11.5817	1.35554	0.677771	+	0.735273i	$0.262946\pi$
$74$	−11.4310	−1.32882
$75$	−0.456004	−0.0526548
$76$	29.8148	3.42000
$77$	5.29983	0.603971
$78$	−5.91085	−0.669271
$79$	−3.09782	−0.348532	−0.174266	−	0.984699i	$-0.555755\pi$
$79$	−3.09782	−0.348532	−0.174266	+	0.984699i	$0.555755\pi$
$80$	19.2267	2.14961
$81$	1.00000	0.111111
$82$	−19.3948	−2.14179
$83$	4.84612	0.531931	0.265965	−	0.963983i	$-0.414309\pi$
$83$	4.84612	0.531931	0.265965	+	0.963983i	$0.414309\pi$
$84$	14.7518	1.60955
$85$	−5.84345	−0.633811
$86$	−10.3950	−1.12093
$87$	−2.26520	−0.242854
$88$	11.3212	1.20684
$89$	4.43109	0.469695	0.234848	−	0.972032i	$-0.424541\pi$
$89$	4.43109	0.469695	0.234848	+	0.972032i	$0.424541\pi$
$90$	−6.01782	−0.634334
$91$	7.29809	0.765048
$92$	20.3004	2.11647
$93$	−5.47236	−0.567457
$94$	6.72419	0.693547
$95$	15.0172	1.54073
$96$	7.61644	0.777349
$97$	−0.638668	−0.0648469	−0.0324234	−	0.999474i	$-0.510323\pi$
$97$	−0.638668	−0.0648469	−0.0324234	+	0.999474i	$0.510323\pi$
$98$	−8.03470	−0.811627
$99$	−1.66610	−0.167449
$100$	2.11471	0.211471
$101$	−13.0297	−1.29650	−0.648250	−	0.761427i	$-0.724499\pi$
$101$	−13.0297	−1.29650	−0.648250	+	0.761427i	$0.724499\pi$
$102$	−6.44516	−0.638166
$103$	3.93468	0.387695	0.193848	−	0.981032i	$-0.437903\pi$
$103$	3.93468	0.387695	0.193848	+	0.981032i	$0.437903\pi$
$104$	15.5897	1.52870
$105$	7.43017	0.725110
$106$	25.1831	2.44599
$107$	−18.5917	−1.79733	−0.898665	−	0.438636i	$-0.855462\pi$
$107$	−18.5917	−1.79733	−0.898665	+	0.438636i	$0.855462\pi$
$108$	−4.63748	−0.446242
$109$	6.24424	0.598089	0.299045	−	0.954239i	$-0.403332\pi$
$109$	6.24424	0.598089	0.299045	+	0.954239i	$0.403332\pi$
$110$	10.0263	0.955967
$111$	−4.43691	−0.421133
$112$	−26.1836	−2.47411
$113$	−17.5468	−1.65066	−0.825332	−	0.564647i	$-0.809012\pi$
$113$	−17.5468	−1.65066	−0.825332	+	0.564647i	$0.809012\pi$
$114$	16.5635	1.55131
$115$	10.2249	0.953480
$116$	10.5048	0.975346
$117$	−2.29429	−0.212107
$118$	7.31761	0.673641
$119$	7.95781	0.729491
$120$	15.8719	1.44890
$121$	−8.22412	−0.747647
$122$	16.6740	1.50959
$123$	−7.52805	−0.678782
$124$	25.3780	2.27901
$125$	−10.6139	−0.949337
$126$	8.19527	0.730092
$127$	7.98011	0.708120	0.354060	−	0.935223i	$-0.384801\pi$
$127$	7.98011	0.708120	0.354060	+	0.935223i	$0.384801\pi$
$128$	7.09189	0.626841
$129$	−4.03482	−0.355246
$130$	13.8066	1.21092
$131$	8.51764	0.744189	0.372095	−	0.928195i	$-0.378640\pi$
$131$	8.51764	0.744189	0.372095	+	0.928195i	$0.378640\pi$
$132$	7.72649	0.672505
$133$	−20.4509	−1.77331
$134$	38.5981	3.33436
$135$	−2.33581	−0.201034
$136$	16.9990	1.45765
$137$	11.8158	1.00949	0.504744	−	0.863269i	$-0.331587\pi$
$137$	11.8158	1.00949	0.504744	+	0.863269i	$0.331587\pi$
$138$	11.2778	0.960032
$139$	23.3034	1.97657	0.988283	−	0.152632i	$-0.0487750\pi$
$139$	23.3034	1.97657	0.988283	+	0.152632i	$0.0487750\pi$
$140$	−34.4573	−2.91217
$141$	2.60998	0.219800
$142$	7.37528	0.618920
$143$	3.82251	0.319654
$144$	8.23128	0.685940
$145$	5.29106	0.439399
$146$	−29.8384	−2.46945
$147$	−3.11866	−0.257223
$148$	20.5761	1.69134
$149$	−10.5987	−0.868279	−0.434140	−	0.900846i	$-0.642948\pi$
$149$	−10.5987	−0.868279	−0.434140	+	0.900846i	$0.642948\pi$
$150$	1.17482	0.0959234
$151$	20.5912	1.67569	0.837845	−	0.545908i	$-0.183815\pi$
$151$	20.5912	1.67569	0.837845	+	0.545908i	$0.183815\pi$
$152$	−43.6859	−3.54340
$153$	−2.50168	−0.202249
$154$	−13.6541	−1.10028
$155$	12.7824	1.02671
$156$	10.6397	0.851859
$157$	10.5260	0.840064	0.420032	−	0.907509i	$-0.362019\pi$
$157$	10.5260	0.840064	0.420032	+	0.907509i	$0.362019\pi$
$158$	7.98102	0.634935
$159$	9.77478	0.775190
$160$	−17.7905	−1.40647
$161$	−13.9247	−1.09742
$162$	−2.57633	−0.202416
$163$	−5.89229	−0.461520	−0.230760	−	0.973011i	$-0.574121\pi$
$163$	−5.89229	−0.461520	−0.230760	+	0.973011i	$0.574121\pi$
$164$	34.9112	2.72611
$165$	3.89168	0.302967
$166$	−12.4852	−0.969040
$167$	9.06531	0.701495	0.350747	−	0.936470i	$-0.385928\pi$
$167$	9.06531	0.701495	0.350747	+	0.936470i	$0.385928\pi$
$168$	−21.6149	−1.66762
$169$	−7.73624	−0.595096
$170$	15.0547	1.15464
$171$	6.42910	0.491646
$172$	18.7114	1.42673
$173$	−3.62616	−0.275692	−0.137846	−	0.990454i	$-0.544018\pi$
$173$	−3.62616	−0.275692	−0.137846	+	0.990454i	$0.544018\pi$
$174$	5.83589	0.442418
$175$	−1.45054	−0.109651
$176$	−13.7141	−1.03374
$177$	2.84032	0.213492
$178$	−11.4160	−0.855663
$179$	−5.28335	−0.394896	−0.197448	−	0.980313i	$-0.563265\pi$
$179$	−5.28335	−0.394896	−0.197448	+	0.980313i	$0.563265\pi$
$180$	10.8323	0.807390
$181$	4.79521	0.356425	0.178213	−	0.983992i	$-0.442969\pi$
$181$	4.79521	0.356425	0.178213	+	0.983992i	$0.442969\pi$
$182$	−18.8023	−1.39372
$183$	6.47199	0.478423
$184$	−29.7450	−2.19283
$185$	10.3638	0.761960
$186$	14.0986	1.03376
$187$	4.16805	0.304798
$188$	−12.1038	−0.882757
$189$	3.18098	0.231383
$190$	−38.6892	−2.80681
$191$	−8.28765	−0.599673	−0.299837	−	0.953991i	$-0.596932\pi$
$191$	−8.28765	−0.599673	−0.299837	+	0.953991i	$0.596932\pi$
$192$	−3.15991	−0.228047
$193$	12.0670	0.868601	0.434300	−	0.900768i	$-0.356996\pi$
$193$	12.0670	0.868601	0.434300	+	0.900768i	$0.356996\pi$
$194$	1.64542	0.118134
$195$	5.35902	0.383767
$196$	14.4627	1.03305
$197$	−17.1695	−1.22328	−0.611638	−	0.791138i	$-0.709489\pi$
$197$	−17.1695	−1.22328	−0.611638	+	0.791138i	$0.709489\pi$
$198$	4.29242	0.305049
$199$	1.41081	0.100009	0.0500047	−	0.998749i	$-0.484076\pi$
$199$	1.41081	0.100009	0.0500047	+	0.998749i	$0.484076\pi$
$200$	−3.09856	−0.219101
$201$	14.9818	1.05673
$202$	33.5687	2.36189
$203$	−7.20555	−0.505730
$204$	11.6015	0.812268
$205$	17.5841	1.22813
$206$	−10.1370	−0.706281
$207$	4.37747	0.304255
$208$	−18.8849	−1.30943
$209$	−10.7115	−0.740930
$210$	−19.1426	−1.32096
$211$	11.4146	0.785816	0.392908	−	0.919578i	$-0.371469\pi$
$211$	11.4146	0.785816	0.392908	+	0.919578i	$0.371469\pi$
$212$	−45.3303	−3.11330
$213$	2.86271	0.196149
$214$	47.8984	3.27427
$215$	9.42457	0.642751
$216$	6.79503	0.462343
$217$	−17.4075	−1.18170
$218$	−16.0872	−1.08956
$219$	−11.5817	−0.782622
$220$	−18.0476	−1.21677
$221$	5.73958	0.386086
$222$	11.4310	0.767195
$223$	23.8528	1.59730	0.798651	−	0.601794i	$-0.205547\pi$
$223$	23.8528	1.59730	0.798651	+	0.601794i	$0.205547\pi$
$224$	24.2278	1.61879
$225$	0.456004	0.0304002
$226$	45.2064	3.00708
$227$	−0.752756	−0.0499621	−0.0249811	−	0.999688i	$-0.507953\pi$
$227$	−0.752756	−0.0499621	−0.0249811	+	0.999688i	$0.507953\pi$
$228$	−29.8148	−1.97454
$229$	−16.6711	−1.10166	−0.550830	−	0.834618i	$-0.685689\pi$
$229$	−16.6711	−1.10166	−0.550830	+	0.834618i	$0.685689\pi$
$230$	−26.3428	−1.73699
$231$	−5.29983	−0.348703
$232$	−15.3921	−1.01054
$233$	4.00936	0.262662	0.131331	−	0.991339i	$-0.458075\pi$
$233$	4.00936	0.262662	0.131331	+	0.991339i	$0.458075\pi$
$234$	5.91085	0.386404
$235$	−6.09643	−0.397687
$236$	−13.1719	−0.857420
$237$	3.09782	0.201225
$238$	−20.5020	−1.32894
$239$	1.29004	0.0834460	0.0417230	−	0.999129i	$-0.486715\pi$
$239$	1.29004	0.0834460	0.0417230	+	0.999129i	$0.486715\pi$
$240$	−19.2267	−1.24108
$241$	21.5922	1.39088	0.695439	−	0.718585i	$-0.255210\pi$
$241$	21.5922	1.39088	0.695439	+	0.718585i	$0.255210\pi$
$242$	21.1881	1.36202
$243$	−1.00000	−0.0641500
$244$	−30.0137	−1.92143
$245$	7.28459	0.465395
$246$	19.3948	1.23656
$247$	−14.7502	−0.938533
$248$	−37.1848	−2.36124
$249$	−4.84612	−0.307110
$250$	27.3449	1.72945
$251$	−1.74737	−0.110293	−0.0551466	−	0.998478i	$-0.517563\pi$
$251$	−1.74737	−0.110293	−0.0551466	+	0.998478i	$0.517563\pi$
$252$	−14.7518	−0.929273
$253$	−7.29329	−0.458525
$254$	−20.5594	−1.29001
$255$	5.84345	0.365931
$256$	−24.5909	−1.53693
$257$	−22.1877	−1.38403	−0.692017	−	0.721882i	$-0.743278\pi$
$257$	−22.1877	−1.38403	−0.692017	+	0.721882i	$0.743278\pi$
$258$	10.3950	0.647167
$259$	−14.1137	−0.876985
$260$	−24.8524	−1.54128
$261$	2.26520	0.140212
$262$	−21.9443	−1.35572
$263$	−2.58064	−0.159129	−0.0795644	−	0.996830i	$-0.525353\pi$
$263$	−2.58064	−0.159129	−0.0795644	+	0.996830i	$0.525353\pi$
$264$	−11.3212	−0.696770
$265$	−22.8320	−1.40256
$266$	52.6882	3.23052
$267$	−4.43109	−0.271179
$268$	−69.4778	−4.24403
$269$	−6.05174	−0.368981	−0.184491	−	0.982834i	$-0.559064\pi$
$269$	−6.05174	−0.368981	−0.184491	+	0.982834i	$0.559064\pi$
$270$	6.01782	0.366233
$271$	22.5804	1.37166	0.685831	−	0.727760i	$-0.259439\pi$
$271$	22.5804	1.37166	0.685831	+	0.727760i	$0.259439\pi$
$272$	−20.5920	−1.24858
$273$	−7.29809	−0.441701
$274$	−30.4413	−1.83903
$275$	−0.759746	−0.0458144
$276$	−20.3004	−1.22194
$277$	20.4695	1.22989	0.614947	−	0.788569i	$-0.289178\pi$
$277$	20.4695	1.22989	0.614947	+	0.788569i	$0.289178\pi$
$278$	−60.0372	−3.60079
$279$	5.47236	0.327622
$280$	50.4882	3.01725
$281$	17.3313	1.03390	0.516949	−	0.856016i	$-0.327068\pi$
$281$	17.3313	1.03390	0.516949	+	0.856016i	$0.327068\pi$
$282$	−6.72419	−0.400419
$283$	4.89735	0.291117	0.145559	−	0.989350i	$-0.453502\pi$
$283$	4.89735	0.291117	0.145559	+	0.989350i	$0.453502\pi$
$284$	−13.2758	−0.787771
$285$	−15.0172	−0.889539
$286$	−9.84804	−0.582327
$287$	−23.9466	−1.41352
$288$	−7.61644	−0.448803
$289$	−10.7416	−0.631858
$290$	−13.6315	−0.800471
$291$	0.638668	0.0374394
$292$	53.7102	3.14315
$293$	19.4610	1.13692	0.568462	−	0.822709i	$-0.307539\pi$
$293$	19.4610	1.13692	0.568462	+	0.822709i	$0.307539\pi$
$294$	8.03470	0.468593
$295$	−6.63445	−0.386273
$296$	−30.1489	−1.75237
$297$	1.66610	0.0966767
$298$	27.3058	1.58178
$299$	−10.0432	−0.580812
$300$	−2.11471	−0.122093
$301$	−12.8347	−0.739780
$302$	−53.0498	−3.05267
$303$	13.0297	0.748535
$304$	52.9197	3.03515
$305$	−15.1173	−0.865616
$306$	6.44516	0.368445
$307$	−33.1603	−1.89256	−0.946281	−	0.323347i	$-0.895192\pi$
$307$	−33.1603	−1.89256	−0.946281	+	0.323347i	$0.895192\pi$
$308$	24.5779	1.40045
$309$	−3.93468	−0.223836
$310$	−32.9317	−1.87039
$311$	4.27333	0.242318	0.121159	−	0.992633i	$-0.461339\pi$
$311$	4.27333	0.242318	0.121159	+	0.992633i	$0.461339\pi$
$312$	−15.5897	−0.882596
$313$	6.29780	0.355973	0.177986	−	0.984033i	$-0.443042\pi$
$313$	6.29780	0.355973	0.177986	+	0.984033i	$0.443042\pi$
$314$	−27.1184	−1.53038
$315$	−7.43017	−0.418643
$316$	−14.3661	−0.808156
$317$	−21.2019	−1.19082	−0.595408	−	0.803424i	$-0.703009\pi$
$317$	−21.2019	−1.19082	−0.595408	+	0.803424i	$0.703009\pi$
$318$	−25.1831	−1.41220
$319$	−3.77403	−0.211305
$320$	7.38096	0.412608
$321$	18.5917	1.03769
$322$	35.8746	1.99921
$323$	−16.0836	−0.894914
$324$	4.63748	0.257638
$325$	−1.04620	−0.0580329
$326$	15.1805	0.840770
$327$	−6.24424	−0.345307
$328$	−51.1533	−2.82447
$329$	8.30232	0.457722
$330$	−10.0263	−0.551928
$331$	12.6046	0.692811	0.346405	−	0.938085i	$-0.387402\pi$
$331$	12.6046	0.692811	0.346405	+	0.938085i	$0.387402\pi$
$332$	22.4738	1.23341
$333$	4.43691	0.243141
$334$	−23.3552	−1.27794
$335$	−34.9946	−1.91196
$336$	26.1836	1.42843
$337$	16.6565	0.907339	0.453669	−	0.891170i	$-0.350115\pi$
$337$	16.6565	0.907339	0.453669	+	0.891170i	$0.350115\pi$
$338$	19.9311	1.08411
$339$	17.5468	0.953012
$340$	−27.0989	−1.46964
$341$	−9.11748	−0.493739
$342$	−16.5635	−0.895651
$343$	12.3465	0.666648
$344$	−27.4167	−1.47821
$345$	−10.2249	−0.550492
$346$	9.34219	0.502239
$347$	7.41315	0.397959	0.198979	−	0.980004i	$-0.436237\pi$
$347$	7.41315	0.397959	0.198979	+	0.980004i	$0.436237\pi$
$348$	−10.5048	−0.563117
$349$	35.2887	1.88896	0.944481	−	0.328566i	$-0.106565\pi$
$349$	35.2887	1.88896	0.944481	+	0.328566i	$0.106565\pi$
$350$	3.73707	0.199755
$351$	2.29429	0.122460
$352$	12.6897	0.676364
$353$	18.3699	0.977730	0.488865	−	0.872359i	$-0.337411\pi$
$353$	18.3699	0.977730	0.488865	+	0.872359i	$0.337411\pi$
$354$	−7.31761	−0.388927
$355$	−6.68674	−0.354895
$356$	20.5491	1.08910
$357$	−7.95781	−0.421172
$358$	13.6117	0.719398
$359$	−19.9754	−1.05426	−0.527132	−	0.849783i	$-0.676733\pi$
$359$	−19.9754	−1.05426	−0.527132	+	0.849783i	$0.676733\pi$
$360$	−15.8719	−0.836522
$361$	22.3333	1.17544
$362$	−12.3540	−0.649314
$363$	8.22412	0.431654
$364$	33.8448	1.77395
$365$	27.0528	1.41601
$366$	−16.6740	−0.871563
$367$	8.94209	0.466773	0.233387	−	0.972384i	$-0.425019\pi$
$367$	8.94209	0.466773	0.233387	+	0.972384i	$0.425019\pi$
$368$	36.0322	1.87831
$369$	7.52805	0.391895
$370$	−26.7005	−1.38809
$371$	31.0934	1.61429
$372$	−25.3780	−1.31579
$373$	−10.9754	−0.568283	−0.284142	−	0.958782i	$-0.591709\pi$
$373$	−10.9754	−0.568283	−0.284142	+	0.958782i	$0.591709\pi$
$374$	−10.7383	−0.555262
$375$	10.6139	0.548100
$376$	17.7349	0.914609
$377$	−5.19701	−0.267660
$378$	−8.19527	−0.421519
$379$	−6.44708	−0.331164	−0.165582	−	0.986196i	$-0.552950\pi$
$379$	−6.44708	−0.331164	−0.165582	+	0.986196i	$0.552950\pi$
$380$	69.6418	3.57255
$381$	−7.98011	−0.408833
$382$	21.3517	1.09245
$383$	6.05062	0.309172	0.154586	−	0.987979i	$-0.450596\pi$
$383$	6.05062	0.309172	0.154586	+	0.987979i	$0.450596\pi$
$384$	−7.09189	−0.361907
$385$	12.3794	0.630912
$386$	−31.0886	−1.58237
$387$	4.03482	0.205102
$388$	−2.96181	−0.150363
$389$	20.6327	1.04612	0.523058	−	0.852297i	$-0.324791\pi$
$389$	20.6327	1.04612	0.523058	+	0.852297i	$0.324791\pi$
$390$	−13.8066	−0.699125
$391$	−10.9510	−0.553818
$392$	−21.1914	−1.07033
$393$	−8.51764	−0.429658
$394$	44.2343	2.22849
$395$	−7.23592	−0.364079
$396$	−7.72649	−0.388271
$397$	4.19853	0.210718	0.105359	−	0.994434i	$-0.466401\pi$
$397$	4.19853	0.210718	0.105359	+	0.994434i	$0.466401\pi$
$398$	−3.63470	−0.182191
$399$	20.4509	1.02382
$400$	3.75349	0.187675
$401$	−4.87077	−0.243235	−0.121617	−	0.992577i	$-0.538808\pi$
$401$	−4.87077	−0.243235	−0.121617	+	0.992577i	$0.538808\pi$
$402$	−38.5981	−1.92510
$403$	−12.5552	−0.625418
$404$	−60.4248	−3.00625
$405$	2.33581	0.116067
$406$	18.5639	0.921310
$407$	−7.39233	−0.366424
$408$	−16.9990	−0.841576
$409$	−35.0062	−1.73095	−0.865473	−	0.500956i	$-0.832982\pi$
$409$	−35.0062	−1.73095	−0.865473	+	0.500956i	$0.832982\pi$
$410$	−45.3025	−2.23733
$411$	−11.8158	−0.582828
$412$	18.2470	0.898965
$413$	9.03502	0.444584
$414$	−11.2778	−0.554275
$415$	11.3196	0.555658
$416$	17.4743	0.856748
$417$	−23.3034	−1.14117
$418$	27.5964	1.34978
$419$	23.6875	1.15721	0.578604	−	0.815609i	$-0.303598\pi$
$419$	23.6875	1.15721	0.578604	+	0.815609i	$0.303598\pi$
$420$	34.4573	1.68134
$421$	−21.0159	−1.02425	−0.512127	−	0.858910i	$-0.671142\pi$
$421$	−21.0159	−1.02425	−0.512127	+	0.858910i	$0.671142\pi$
$422$	−29.4079	−1.43155
$423$	−2.60998	−0.126902
$424$	66.4199	3.22563
$425$	−1.14078	−0.0553358
$426$	−7.37528	−0.357334
$427$	20.5873	0.996289
$428$	−86.2188	−4.16754
$429$	−3.82251	−0.184552
$430$	−24.2808	−1.17093
$431$	−1.94930	−0.0938946	−0.0469473	−	0.998897i	$-0.514949\pi$
$431$	−1.94930	−0.0938946	−0.0469473	+	0.998897i	$0.514949\pi$
$432$	−8.23128	−0.396027
$433$	14.4218	0.693067	0.346533	−	0.938038i	$-0.387359\pi$
$433$	14.4218	0.693067	0.346533	+	0.938038i	$0.387359\pi$
$434$	44.8475	2.15275
$435$	−5.29106	−0.253687
$436$	28.9575	1.38681
$437$	28.1432	1.34627
$438$	29.8384	1.42573
$439$	31.2988	1.49381	0.746906	−	0.664930i	$-0.231539\pi$
$439$	31.2988	1.49381	0.746906	+	0.664930i	$0.231539\pi$
$440$	26.4441	1.26067
$441$	3.11866	0.148508
$442$	−14.7871	−0.703349
$443$	20.8068	0.988561	0.494280	−	0.869303i	$-0.335432\pi$
$443$	20.8068	0.988561	0.494280	+	0.869303i	$0.335432\pi$
$444$	−20.5761	−0.976498
$445$	10.3502	0.490646
$446$	−61.4528	−2.90987
$447$	10.5987	0.501301
$448$	−10.0516	−0.474895
$449$	22.3188	1.05329	0.526645	−	0.850086i	$-0.323450\pi$
$449$	22.3188	1.05329	0.526645	+	0.850086i	$0.323450\pi$
$450$	−1.17482	−0.0553814
$451$	−12.5425	−0.590602
$452$	−81.3730	−3.82746
$453$	−20.5912	−0.967460
$454$	1.93935	0.0910181
$455$	17.0469	0.799173
$456$	43.6859	2.04578
$457$	−29.2500	−1.36826	−0.684128	−	0.729362i	$-0.739817\pi$
$457$	−29.2500	−1.36826	−0.684128	+	0.729362i	$0.739817\pi$
$458$	42.9503	2.00694
$459$	2.50168	0.116769
$460$	47.4180	2.21087
$461$	33.0499	1.53929	0.769644	−	0.638473i	$-0.220434\pi$
$461$	33.0499	1.53929	0.769644	+	0.638473i	$0.220434\pi$
$462$	13.6541	0.635247
$463$	4.18745	0.194607	0.0973037	−	0.995255i	$-0.468978\pi$
$463$	4.18745	0.194607	0.0973037	+	0.995255i	$0.468978\pi$
$464$	18.6454	0.865593
$465$	−12.7824	−0.592769
$466$	−10.3294	−0.478502
$467$	23.7169	1.09749	0.548743	−	0.835991i	$-0.315107\pi$
$467$	23.7169	1.09749	0.548743	+	0.835991i	$0.315107\pi$
$468$	−10.6397	−0.491821
$469$	47.6568	2.20059
$470$	15.7064	0.724483
$471$	−10.5260	−0.485011
$472$	19.3001	0.888358
$473$	−6.72241	−0.309097
$474$	−7.98102	−0.366580
$475$	2.93169	0.134515
$476$	36.9042	1.69150
$477$	−9.77478	−0.447556
$478$	−3.32358	−0.152017
$479$	7.60097	0.347297	0.173649	−	0.984808i	$-0.444444\pi$
$479$	7.60097	0.347297	0.173649	+	0.984808i	$0.444444\pi$
$480$	17.7905	0.812024
$481$	−10.1796	−0.464148
$482$	−55.6287	−2.53382
$483$	13.9247	0.633594
$484$	−38.1392	−1.73360
$485$	−1.49181	−0.0677394
$486$	2.57633	0.116865
$487$	25.1754	1.14081	0.570404	−	0.821364i	$-0.306787\pi$
$487$	25.1754	1.14081	0.570404	+	0.821364i	$0.306787\pi$
$488$	43.9773	1.99076
$489$	5.89229	0.266459
$490$	−18.7675	−0.847830
$491$	26.4507	1.19370	0.596851	−	0.802352i	$-0.296418\pi$
$491$	26.4507	1.19370	0.596851	+	0.802352i	$0.296418\pi$
$492$	−34.9112	−1.57392
$493$	−5.66680	−0.255220
$494$	38.0014	1.70976
$495$	−3.89168	−0.174918
$496$	45.0445	2.02256
$497$	9.10622	0.408470
$498$	12.4852	0.559476
$499$	−37.3933	−1.67396	−0.836978	−	0.547237i	$-0.815680\pi$
$499$	−37.3933	−1.67396	−0.836978	+	0.547237i	$0.815680\pi$
$500$	−49.2218	−2.20127
$501$	−9.06531	−0.405008
$502$	4.50181	0.200926
$503$	8.56130	0.381729	0.190865	−	0.981616i	$-0.438871\pi$
$503$	8.56130	0.381729	0.190865	+	0.981616i	$0.438871\pi$
$504$	21.6149	0.962803
$505$	−30.4348	−1.35433
$506$	18.7899	0.835315
$507$	7.73624	0.343579
$508$	37.0076	1.64195
$509$	25.8688	1.14661	0.573307	−	0.819340i	$-0.305660\pi$
$509$	25.8688	1.14661	0.573307	+	0.819340i	$0.305660\pi$
$510$	−15.0547	−0.666632
$511$	−36.8414	−1.62977
$512$	49.1705	2.17305
$513$	−6.42910	−0.283852
$514$	57.1630	2.52135
$515$	9.19066	0.404989
$516$	−18.7114	−0.823724
$517$	4.34849	0.191246
$518$	36.3617	1.59764
$519$	3.62616	0.159171
$520$	36.4147	1.59689
$521$	−3.27797	−0.143610	−0.0718052	−	0.997419i	$-0.522876\pi$
$521$	−3.27797	−0.143610	−0.0718052	+	0.997419i	$0.522876\pi$
$522$	−5.83589	−0.255430
$523$	28.5870	1.25002	0.625010	−	0.780616i	$-0.285095\pi$
$523$	28.5870	1.25002	0.625010	+	0.780616i	$0.285095\pi$
$524$	39.5004	1.72558
$525$	1.45054	0.0633068
$526$	6.64857	0.289891
$527$	−13.6901	−0.596350
$528$	13.7141	0.596830
$529$	−3.83774	−0.166858
$530$	58.8228	2.55510
$531$	−2.84032	−0.123259
$532$	−94.8405	−4.11186
$533$	−17.2715	−0.748113
$534$	11.4160	0.494017
$535$	−43.4267	−1.87750
$536$	101.802	4.39716
$537$	5.28335	0.227993
$538$	15.5913	0.672188
$539$	−5.19599	−0.223807
$540$	−10.8323	−0.466147
$541$	−38.8740	−1.67132	−0.835662	−	0.549244i	$-0.814916\pi$
$541$	−38.8740	−1.67132	−0.835662	+	0.549244i	$0.814916\pi$
$542$	−58.1746	−2.49881
$543$	−4.79521	−0.205782
$544$	19.0539	0.816930
$545$	14.5853	0.624767
$546$	18.8023	0.804664
$547$	1.12306	0.0480186	0.0240093	−	0.999712i	$-0.492357\pi$
$547$	1.12306	0.0480186	0.0240093	+	0.999712i	$0.492357\pi$
$548$	54.7954	2.34074
$549$	−6.47199	−0.276218
$550$	1.95736	0.0834620
$551$	14.5632	0.620412
$552$	29.7450	1.26603
$553$	9.85412	0.419040
$554$	−52.7362	−2.24055
$555$	−10.3638	−0.439918
$556$	108.069	4.58314
$557$	23.2107	0.983471	0.491735	−	0.870745i	$-0.336363\pi$
$557$	23.2107	0.983471	0.491735	+	0.870745i	$0.336363\pi$
$558$	−14.0986	−0.596842
$559$	−9.25704	−0.391531
$560$	−61.1598	−2.58447
$561$	−4.16805	−0.175975
$562$	−44.6512	−1.88350
$563$	41.7079	1.75778	0.878890	−	0.477025i	$-0.158285\pi$
$563$	41.7079	1.75778	0.878890	+	0.477025i	$0.158285\pi$
$564$	12.1038	0.509660
$565$	−40.9860	−1.72429
$566$	−12.6172	−0.530340
$567$	−3.18098	−0.133589
$568$	19.4522	0.816195
$569$	40.2643	1.68797	0.843983	−	0.536370i	$-0.180205\pi$
$569$	40.2643	1.68797	0.843983	+	0.536370i	$0.180205\pi$
$570$	38.6892	1.62051
$571$	14.7394	0.616823	0.308411	−	0.951253i	$-0.400203\pi$
$571$	14.7394	0.616823	0.308411	+	0.951253i	$0.400203\pi$
$572$	17.7268	0.741195
$573$	8.28765	0.346221
$574$	61.6944	2.57508
$575$	1.99614	0.0832449
$576$	3.15991	0.131663
$577$	12.2465	0.509830	0.254915	−	0.966963i	$-0.417952\pi$
$577$	12.2465	0.509830	0.254915	+	0.966963i	$0.417952\pi$
$578$	27.6739	1.15108
$579$	−12.0670	−0.501487
$580$	24.5372	1.01885
$581$	−15.4154	−0.639540
$582$	−1.64542	−0.0682048
$583$	16.2857	0.674486
$584$	−78.6983	−3.25656
$585$	−5.35902	−0.221568
$586$	−50.1380	−2.07118
$587$	5.62241	0.232062	0.116031	−	0.993246i	$-0.462983\pi$
$587$	5.62241	0.232062	0.116031	+	0.993246i	$0.462983\pi$
$588$	−14.4627	−0.596433
$589$	35.1824	1.44966
$590$	17.0925	0.703689
$591$	17.1695	0.706259
$592$	36.5214	1.50102
$593$	−34.4466	−1.41455	−0.707276	−	0.706937i	$-0.750076\pi$
$593$	−34.4466	−1.41455	−0.707276	+	0.706937i	$0.750076\pi$
$594$	−4.29242	−0.176120
$595$	18.5879	0.762031
$596$	−49.1513	−2.01331
$597$	−1.41081	−0.0577404
$598$	25.8746	1.05809
$599$	−16.1235	−0.658788	−0.329394	−	0.944193i	$-0.606844\pi$
$599$	−16.1235	−0.658788	−0.329394	+	0.944193i	$0.606844\pi$
$600$	3.09856	0.126498
$601$	−5.29136	−0.215839	−0.107919	−	0.994160i	$-0.534419\pi$
$601$	−5.29136	−0.215839	−0.107919	+	0.994160i	$0.534419\pi$
$602$	33.0665	1.34769
$603$	−14.9818	−0.610106
$604$	95.4915	3.88549
$605$	−19.2100	−0.780997
$606$	−33.5687	−1.36364
$607$	31.7942	1.29049	0.645243	−	0.763977i	$-0.276756\pi$
$607$	31.7942	1.29049	0.645243	+	0.763977i	$0.276756\pi$
$608$	−48.9668	−1.98587
$609$	7.20555	0.291984
$610$	38.9472	1.57693
$611$	5.98806	0.242251
$612$	−11.6015	−0.468963
$613$	−25.7281	−1.03915	−0.519575	−	0.854425i	$-0.673910\pi$
$613$	−25.7281	−1.03915	−0.519575	+	0.854425i	$0.673910\pi$
$614$	85.4320	3.44776
$615$	−17.5841	−0.709059
$616$	−36.0125	−1.45098
$617$	−0.957594	−0.0385513	−0.0192756	−	0.999814i	$-0.506136\pi$
$617$	−0.957594	−0.0385513	−0.0192756	+	0.999814i	$0.506136\pi$
$618$	10.1370	0.407771
$619$	15.0231	0.603831	0.301915	−	0.953335i	$-0.402374\pi$
$619$	15.0231	0.603831	0.301915	+	0.953335i	$0.402374\pi$
$620$	59.2781	2.38067
$621$	−4.37747	−0.175662
$622$	−11.0095	−0.441441
$623$	−14.0952	−0.564714
$624$	18.8849	0.756002
$625$	−27.0721	−1.08288
$626$	−16.2252	−0.648491
$627$	10.7115	0.427776
$628$	48.8140	1.94789
$629$	−11.0997	−0.442576
$630$	19.1426	0.762659
$631$	17.1459	0.682566	0.341283	−	0.939961i	$-0.389139\pi$
$631$	17.1459	0.682566	0.341283	+	0.939961i	$0.389139\pi$
$632$	21.0498	0.837315
$633$	−11.4146	−0.453691
$634$	54.6230	2.16936
$635$	18.6400	0.739706
$636$	45.3303	1.79747
$637$	−7.15510	−0.283495
$638$	9.72316	0.384944
$639$	−2.86271	−0.113247
$640$	16.5653	0.654801
$641$	4.01737	0.158676	0.0793382	−	0.996848i	$-0.474719\pi$
$641$	4.01737	0.158676	0.0793382	+	0.996848i	$0.474719\pi$
$642$	−47.8984	−1.89040
$643$	8.75833	0.345395	0.172697	−	0.984975i	$-0.444752\pi$
$643$	8.75833	0.345395	0.172697	+	0.984975i	$0.444752\pi$
$644$	−64.5754	−2.54463
$645$	−9.42457	−0.371092
$646$	41.4366	1.63030
$647$	−20.8147	−0.818312	−0.409156	−	0.912464i	$-0.634177\pi$
$647$	−20.8147	−0.818312	−0.409156	+	0.912464i	$0.634177\pi$
$648$	−6.79503	−0.266934
$649$	4.73225	0.185757
$650$	2.69537	0.105721
$651$	17.4075	0.682253
$652$	−27.3254	−1.07015
$653$	36.0137	1.40933	0.704663	−	0.709542i	$-0.251098\pi$
$653$	36.0137	1.40933	0.704663	+	0.709542i	$0.251098\pi$
$654$	16.0872	0.629060
$655$	19.8956	0.777384
$656$	61.9655	2.41935
$657$	11.5817	0.451847
$658$	−21.3895	−0.833851
$659$	−21.5404	−0.839094	−0.419547	−	0.907734i	$-0.637811\pi$
$659$	−21.5404	−0.839094	−0.419547	+	0.907734i	$0.637811\pi$
$660$	18.0476	0.702502
$661$	−10.1932	−0.396468	−0.198234	−	0.980155i	$-0.563521\pi$
$661$	−10.1932	−0.396468	−0.198234	+	0.980155i	$0.563521\pi$
$662$	−32.4736	−1.26212
$663$	−5.73958	−0.222907
$664$	−32.9295	−1.27791
$665$	−47.7693	−1.85241
$666$	−11.4310	−0.442940
$667$	9.91583	0.383942
$668$	42.0402	1.62658
$669$	−23.8528	−0.922203
$670$	90.1577	3.48310
$671$	10.7830	0.416271
$672$	−24.2278	−0.934606
$673$	18.6893	0.720420	0.360210	−	0.932871i	$-0.382705\pi$
$673$	18.6893	0.720420	0.360210	+	0.932871i	$0.382705\pi$
$674$	−42.9127	−1.65294
$675$	−0.456004	−0.0175516
$676$	−35.8767	−1.37987
$677$	−18.0135	−0.692316	−0.346158	−	0.938176i	$-0.612514\pi$
$677$	−18.0135	−0.692316	−0.346158	+	0.938176i	$0.612514\pi$
$678$	−45.2064	−1.73614
$679$	2.03159	0.0779653
$680$	39.7064	1.52267
$681$	0.752756	0.0288457
$682$	23.4897	0.899465
$683$	−6.34825	−0.242909	−0.121455	−	0.992597i	$-0.538756\pi$
$683$	−6.34825	−0.242909	−0.121455	+	0.992597i	$0.538756\pi$
$684$	29.8148	1.14000
$685$	27.5994	1.05452
$686$	−31.8086	−1.21446
$687$	16.6711	0.636043
$688$	33.2117	1.26619
$689$	22.4261	0.854368
$690$	26.3428	1.00285
$691$	4.76765	0.181370	0.0906850	−	0.995880i	$-0.471094\pi$
$691$	4.76765	0.181370	0.0906850	+	0.995880i	$0.471094\pi$
$692$	−16.8163	−0.639258
$693$	5.29983	0.201324
$694$	−19.0987	−0.724978
$695$	54.4322	2.06473
$696$	15.3921	0.583435
$697$	−18.8328	−0.713343
$698$	−90.9154	−3.44120
$699$	−4.00936	−0.151648
$700$	−6.72685	−0.254251
$701$	−27.8004	−1.05001	−0.525003	−	0.851100i	$-0.675936\pi$
$701$	−27.8004	−1.05001	−0.525003	+	0.851100i	$0.675936\pi$
$702$	−5.91085	−0.223090
$703$	28.5254	1.07585
$704$	−5.26472	−0.198422
$705$	6.09643	0.229605
$706$	−47.3269	−1.78117
$707$	41.4472	1.55878
$708$	13.1719	0.495032
$709$	9.51974	0.357521	0.178761	−	0.983893i	$-0.442791\pi$
$709$	9.51974	0.357521	0.178761	+	0.983893i	$0.442791\pi$
$710$	17.2272	0.646527
$711$	−3.09782	−0.116177
$712$	−30.1094	−1.12840
$713$	23.9551	0.897126
$714$	20.5020	0.767266
$715$	8.92864	0.333912
$716$	−24.5014	−0.915661
$717$	−1.29004	−0.0481776
$718$	51.4634	1.92060
$719$	−51.6356	−1.92568	−0.962842	−	0.270065i	$-0.912955\pi$
$719$	−51.6356	−1.92568	−0.962842	+	0.270065i	$0.912955\pi$
$720$	19.2267	0.716536
$721$	−12.5161	−0.466126
$722$	−57.5381	−2.14135
$723$	−21.5922	−0.803023
$724$	22.2377	0.826457
$725$	1.03294	0.0383623
$726$	−21.1881	−0.786363
$727$	12.3876	0.459430	0.229715	−	0.973258i	$-0.426221\pi$
$727$	12.3876	0.459430	0.229715	+	0.973258i	$0.426221\pi$
$728$	−49.5907	−1.83795
$729$	1.00000	0.0370370
$730$	−69.6968	−2.57960
$731$	−10.0938	−0.373334
$732$	30.0137	1.10934
$733$	24.6936	0.912077	0.456039	−	0.889960i	$-0.349268\pi$
$733$	24.6936	0.912077	0.456039	+	0.889960i	$0.349268\pi$
$734$	−23.0378	−0.850340
$735$	−7.28459	−0.268696
$736$	−33.3407	−1.22896
$737$	24.9611	0.919455
$738$	−19.3948	−0.713931
$739$	16.5868	0.610155	0.305077	−	0.952328i	$-0.401318\pi$
$739$	16.5868	0.610155	0.305077	+	0.952328i	$0.401318\pi$
$740$	48.0618	1.76679
$741$	14.7502	0.541862
$742$	−80.1069	−2.94082
$743$	31.7023	1.16304	0.581522	−	0.813531i	$-0.302457\pi$
$743$	31.7023	1.16304	0.581522	+	0.813531i	$0.302457\pi$
$744$	37.1848	1.36326
$745$	−24.7565	−0.907009
$746$	28.2762	1.03527
$747$	4.84612	0.177310
$748$	19.3292	0.706747
$749$	59.1400	2.16093
$750$	−27.3449	−0.998496
$751$	46.4068	1.69341	0.846703	−	0.532065i	$-0.178584\pi$
$751$	46.4068	1.69341	0.846703	+	0.532065i	$0.178584\pi$
$752$	−21.4835	−0.783423
$753$	1.74737	0.0636778
$754$	13.3892	0.487607
$755$	48.0972	1.75044
$756$	14.7518	0.536516
$757$	−46.6439	−1.69530	−0.847650	−	0.530556i	$-0.821983\pi$
$757$	−46.6439	−1.69530	−0.847650	+	0.530556i	$0.821983\pi$
$758$	16.6098	0.603295
$759$	7.29329	0.264730
$760$	−102.042	−3.70145
$761$	−2.90175	−0.105188	−0.0525942	−	0.998616i	$-0.516749\pi$
$761$	−2.90175	−0.105188	−0.0525942	+	0.998616i	$0.516749\pi$
$762$	20.5594	0.744788
$763$	−19.8628	−0.719082
$764$	−38.4338	−1.39049
$765$	−5.84345	−0.211270
$766$	−15.5884	−0.563232
$767$	6.51652	0.235298
$768$	24.5909	0.887347
$769$	24.0393	0.866879	0.433439	−	0.901183i	$-0.357300\pi$
$769$	24.0393	0.866879	0.433439	+	0.901183i	$0.357300\pi$
$770$	−31.8934	−1.14936
$771$	22.1877	0.799072
$772$	55.9605	2.01406
$773$	−26.3063	−0.946170	−0.473085	−	0.881017i	$-0.656860\pi$
$773$	−26.3063	−0.946170	−0.473085	+	0.881017i	$0.656860\pi$
$774$	−10.3950	−0.373642
$775$	2.49542	0.0896380
$776$	4.33976	0.155788
$777$	14.1137	0.506328
$778$	−53.1565	−1.90575
$779$	48.3986	1.73406
$780$	24.8524	0.889857
$781$	4.76955	0.170668
$782$	28.2135	1.00891
$783$	−2.26520	−0.0809515
$784$	25.6705	0.916805
$785$	24.5867	0.877536
$786$	21.9443	0.782726
$787$	−13.6677	−0.487199	−0.243600	−	0.969876i	$-0.578328\pi$
$787$	−13.6677	−0.487199	−0.243600	+	0.969876i	$0.578328\pi$
$788$	−79.6233	−2.83646
$789$	2.58064	0.0918730
$790$	18.6421	0.663257
$791$	55.8161	1.98459
$792$	11.3212	0.402280
$793$	14.8486	0.527289
$794$	−10.8168	−0.383874
$795$	22.8320	0.809768
$796$	6.54258	0.231896
$797$	−10.5126	−0.372375	−0.186187	−	0.982514i	$-0.559613\pi$
$797$	−10.5126	−0.372375	−0.186187	+	0.982514i	$0.559613\pi$
$798$	−52.6882	−1.86514
$799$	6.52935	0.230992
$800$	−3.47312	−0.122793
$801$	4.43109	0.156565
$802$	12.5487	0.443111
$803$	−19.2963	−0.680952
$804$	69.4778	2.45029
$805$	−32.5254	−1.14637
$806$	32.3463	1.13935
$807$	6.05174	0.213031
$808$	88.5369	3.11472
$809$	−6.63725	−0.233353	−0.116677	−	0.993170i	$-0.537224\pi$
$809$	−6.63725	−0.233353	−0.116677	+	0.993170i	$0.537224\pi$
$810$	−6.01782	−0.211445
$811$	−1.78966	−0.0628433	−0.0314217	−	0.999506i	$-0.510003\pi$
$811$	−1.78966	−0.0628433	−0.0314217	+	0.999506i	$0.510003\pi$
$812$	−33.4156	−1.17266
$813$	−22.5804	−0.791930
$814$	19.0451	0.667530
$815$	−13.7633	−0.482106
$816$	20.5920	0.720866
$817$	25.9403	0.907536
$818$	90.1876	3.15333
$819$	7.29809	0.255016
$820$	81.5459	2.84771
$821$	23.7856	0.830124	0.415062	−	0.909793i	$-0.363760\pi$
$821$	23.7856	0.830124	0.415062	+	0.909793i	$0.363760\pi$
$822$	30.4413	1.06176
$823$	22.6368	0.789070	0.394535	−	0.918881i	$-0.370906\pi$
$823$	22.6368	0.789070	0.394535	+	0.918881i	$0.370906\pi$
$824$	−26.7363	−0.931401
$825$	0.759746	0.0264510
$826$	−23.2772	−0.809917
$827$	2.99295	0.104075	0.0520376	−	0.998645i	$-0.483428\pi$
$827$	2.99295	0.104075	0.0520376	+	0.998645i	$0.483428\pi$
$828$	20.3004	0.705489
$829$	42.3919	1.47233	0.736167	−	0.676800i	$-0.236634\pi$
$829$	42.3919	1.47233	0.736167	+	0.676800i	$0.236634\pi$
$830$	−29.1631	−1.01226
$831$	−20.4695	−0.710079
$832$	−7.24975	−0.251340
$833$	−7.80189	−0.270320
$834$	60.0372	2.07892
$835$	21.1748	0.732785
$836$	−49.6744	−1.71803
$837$	−5.47236	−0.189152
$838$	−61.0267	−2.10813
$839$	4.57336	0.157890	0.0789450	−	0.996879i	$-0.474845\pi$
$839$	4.57336	0.157890	0.0789450	+	0.996879i	$0.474845\pi$
$840$	−50.4882	−1.74201
$841$	−23.8689	−0.823065
$842$	54.1440	1.86593
$843$	−17.3313	−0.596921
$844$	52.9352	1.82210
$845$	−18.0704	−0.621640
$846$	6.72419	0.231182
$847$	26.1608	0.898896
$848$	−80.4589	−2.76297
$849$	−4.89735	−0.168077
$850$	2.93902	0.100807
$851$	19.4225	0.665793
$852$	13.2758	0.454820
$853$	17.3240	0.593163	0.296582	−	0.955008i	$-0.404153\pi$
$853$	17.3240	0.593163	0.296582	+	0.955008i	$0.404153\pi$
$854$	−53.0397	−1.81498
$855$	15.0172	0.513576
$856$	126.331	4.31791
$857$	−8.94411	−0.305525	−0.152763	−	0.988263i	$-0.548817\pi$
$857$	−8.94411	−0.305525	−0.152763	+	0.988263i	$0.548817\pi$
$858$	9.84804	0.336207
$859$	−0.825174	−0.0281546	−0.0140773	−	0.999901i	$-0.504481\pi$
$859$	−0.825174	−0.0281546	−0.0140773	+	0.999901i	$0.504481\pi$
$860$	43.7063	1.49037
$861$	23.9466	0.816099
$862$	5.02205	0.171052
$863$	34.0289	1.15836	0.579179	−	0.815201i	$-0.303373\pi$
$863$	34.0289	1.15836	0.579179	+	0.815201i	$0.303373\pi$
$864$	7.61644	0.259116
$865$	−8.47002	−0.287989
$866$	−37.1553	−1.26259
$867$	10.7416	0.364803
$868$	−80.7269	−2.74005
$869$	5.16127	0.175084
$870$	13.6315	0.462152
$871$	34.3725	1.16467
$872$	−42.4298	−1.43685
$873$	−0.638668	−0.0216156
$874$	−72.5062	−2.45256
$875$	33.7627	1.14139
$876$	−53.7102	−1.81470
$877$	−39.9155	−1.34785	−0.673925	−	0.738800i	$-0.735393\pi$
$877$	−39.9155	−1.34785	−0.673925	+	0.738800i	$0.735393\pi$
$878$	−80.6362	−2.72134
$879$	−19.4610	−0.656404
$880$	−32.0335	−1.07985
$881$	9.69606	0.326669	0.163334	−	0.986571i	$-0.447775\pi$
$881$	9.69606	0.326669	0.163334	+	0.986571i	$0.447775\pi$
$882$	−8.03470	−0.270542
$883$	4.97212	0.167325	0.0836626	−	0.996494i	$-0.473338\pi$
$883$	4.97212	0.167325	0.0836626	+	0.996494i	$0.473338\pi$
$884$	26.6172	0.895233
$885$	6.63445	0.223015
$886$	−53.6052	−1.80090
$887$	−13.0580	−0.438445	−0.219222	−	0.975675i	$-0.570352\pi$
$887$	−13.0580	−0.438445	−0.219222	+	0.975675i	$0.570352\pi$
$888$	30.1489	1.01173
$889$	−25.3846	−0.851372
$890$	−26.6655	−0.893830
$891$	−1.66610	−0.0558163
$892$	110.617	3.70373
$893$	−16.7799	−0.561516
$894$	−27.3058	−0.913241
$895$	−12.3409	−0.412511
$896$	−22.5592	−0.753650
$897$	10.0432	0.335332
$898$	−57.5006	−1.91882
$899$	12.3960	0.413429
$900$	2.11471	0.0704903
$901$	24.4534	0.814660
$902$	32.3135	1.07592
$903$	12.8347	0.427112
$904$	119.231	3.96557
$905$	11.2007	0.372324
$906$	53.0498	1.76246
$907$	37.0674	1.23080	0.615402	−	0.788213i	$-0.288994\pi$
$907$	37.0674	1.23080	0.615402	+	0.788213i	$0.288994\pi$
$908$	−3.49089	−0.115849
$909$	−13.0297	−0.432167
$910$	−43.9186	−1.45589
$911$	45.2797	1.50018	0.750092	−	0.661333i	$-0.230009\pi$
$911$	45.2797	1.50018	0.750092	+	0.661333i	$0.230009\pi$
$912$	−52.9197	−1.75235
$913$	−8.07411	−0.267214
$914$	75.3576	2.49261
$915$	15.1173	0.499763
$916$	−77.3121	−2.55446
$917$	−27.0945	−0.894738
$918$	−6.44516	−0.212722
$919$	−52.5549	−1.73363	−0.866813	−	0.498634i	$-0.833835\pi$
$919$	−52.5549	−1.73363	−0.866813	+	0.498634i	$0.833835\pi$
$920$	−69.4787	−2.29065
$921$	33.1603	1.09267
$922$	−85.1476	−2.80419
$923$	6.56787	0.216184
$924$	−24.5779	−0.808552
$925$	2.02325	0.0665240
$926$	−10.7883	−0.354524
$927$	3.93468	0.129232
$928$	−17.2527	−0.566348
$929$	−26.4763	−0.868660	−0.434330	−	0.900754i	$-0.643015\pi$
$929$	−26.4763	−0.868660	−0.434330	+	0.900754i	$0.643015\pi$
$930$	32.9317	1.07987
$931$	20.0502	0.657118
$932$	18.5933	0.609045
$933$	−4.27333	−0.139903
$934$	−61.1025	−1.99934
$935$	9.73576	0.318393
$936$	15.5897	0.509567
$937$	−18.7193	−0.611532	−0.305766	−	0.952107i	$-0.598912\pi$
$937$	−18.7193	−0.611532	−0.305766	+	0.952107i	$0.598912\pi$
$938$	−122.780	−4.00890
$939$	−6.29780	−0.205521
$940$	−28.2721	−0.922133
$941$	−5.21199	−0.169906	−0.0849531	−	0.996385i	$-0.527074\pi$
$941$	−5.21199	−0.169906	−0.0849531	+	0.996385i	$0.527074\pi$
$942$	27.1184	0.883565
$943$	32.9538	1.07312
$944$	−23.3795	−0.760937
$945$	7.43017	0.241703
$946$	17.3191	0.563094
$947$	27.3975	0.890301	0.445150	−	0.895456i	$-0.353150\pi$
$947$	27.3975	0.890301	0.445150	+	0.895456i	$0.353150\pi$
$948$	14.3661	0.466589
$949$	−26.5719	−0.862559
$950$	−7.55301	−0.245052
$951$	21.2019	0.687517
$952$	−54.0735	−1.75253
$953$	48.4883	1.57069	0.785344	−	0.619059i	$-0.212486\pi$
$953$	48.4883	1.57069	0.785344	+	0.619059i	$0.212486\pi$
$954$	25.1831	0.815332
$955$	−19.3584	−0.626422
$956$	5.98256	0.193490
$957$	3.77403	0.121997
$958$	−19.5826	−0.632686
$959$	−37.5857	−1.21371
$960$	−7.38096	−0.238219
$961$	−1.05328	−0.0339766
$962$	26.2259	0.845557
$963$	−18.5917	−0.599110
$964$	100.134	3.22508
$965$	28.1862	0.907345
$966$	−35.8746	−1.15424
$967$	−35.2675	−1.13413	−0.567064	−	0.823674i	$-0.691921\pi$
$967$	−35.2675	−1.13413	−0.567064	+	0.823674i	$0.691921\pi$
$968$	55.8831	1.79615
$969$	16.0836	0.516679
$970$	3.84338	0.123404
$971$	−23.6091	−0.757653	−0.378826	−	0.925468i	$-0.623672\pi$
$971$	−23.6091	−0.757653	−0.378826	+	0.925468i	$0.623672\pi$
$972$	−4.63748	−0.148747
$973$	−74.1276	−2.37642
$974$	−64.8602	−2.07826
$975$	1.04620	0.0335053
$976$	−53.2727	−1.70522
$977$	−38.3297	−1.22628	−0.613138	−	0.789976i	$-0.710093\pi$
$977$	−38.3297	−1.22628	−0.613138	+	0.789976i	$0.710093\pi$
$978$	−15.1805	−0.485419
$979$	−7.38263	−0.235950
$980$	33.7822	1.07913
$981$	6.24424	0.199363
$982$	−68.1457	−2.17462
$983$	−1.40369	−0.0447708	−0.0223854	−	0.999749i	$-0.507126\pi$
$983$	−1.40369	−0.0447708	−0.0223854	+	0.999749i	$0.507126\pi$
$984$	51.1533	1.63071
$985$	−40.1047	−1.27784
$986$	14.5996	0.464944
$987$	−8.30232	−0.264266
$988$	−68.4038	−2.17622
$989$	17.6623	0.561629
$990$	10.0263	0.318656
$991$	20.1123	0.638889	0.319444	−	0.947605i	$-0.396504\pi$
$991$	20.1123	0.638889	0.319444	+	0.947605i	$0.396504\pi$
$992$	−41.6799	−1.32334
$993$	−12.6046	−0.399994
$994$	−23.4607	−0.744127
$995$	3.29537	0.104470
$996$	−22.4738	−0.712109
$997$	−35.8613	−1.13574	−0.567870	−	0.823119i	$-0.692232\pi$
$997$	−35.8613	−1.13574	−0.567870	+	0.823119i	$0.692232\pi$
$998$	96.3376	3.04951
$999$	−4.43691	−0.140378

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6009.2.a.d.1.8	✓	93

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6009.2.a.d.1.8	✓	93	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:	\( N \)	\(=\)	\( 6009 = 3 \cdot 2003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6009.a (trivial)

\(f(q)\)	\(=\)	\(q-2.57633 q^{2} -1.00000 q^{3} +4.63748 q^{4} +2.33581 q^{5} +2.57633 q^{6} -3.18098 q^{7} -6.79503 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.57633 q^{2} -1.00000 q^{3} +4.63748 q^{4} +2.33581 q^{5} +2.57633 q^{6} -3.18098 q^{7} -6.79503 q^{8} +1.00000 q^{9} -6.01782 q^{10} -1.66610 q^{11} -4.63748 q^{12} -2.29429 q^{13} +8.19527 q^{14} -2.33581 q^{15} +8.23128 q^{16} -2.50168 q^{17} -2.57633 q^{18} +6.42910 q^{19} +10.8323 q^{20} +3.18098 q^{21} +4.29242 q^{22} +4.37747 q^{23} +6.79503 q^{24} +0.456004 q^{25} +5.91085 q^{26} -1.00000 q^{27} -14.7518 q^{28} +2.26520 q^{29} +6.01782 q^{30} +5.47236 q^{31} -7.61644 q^{32} +1.66610 q^{33} +6.44516 q^{34} -7.43017 q^{35} +4.63748 q^{36} +4.43691 q^{37} -16.5635 q^{38} +2.29429 q^{39} -15.8719 q^{40} +7.52805 q^{41} -8.19527 q^{42} +4.03482 q^{43} -7.72649 q^{44} +2.33581 q^{45} -11.2778 q^{46} -2.60998 q^{47} -8.23128 q^{48} +3.11866 q^{49} -1.17482 q^{50} +2.50168 q^{51} -10.6397 q^{52} -9.77478 q^{53} +2.57633 q^{54} -3.89168 q^{55} +21.6149 q^{56} -6.42910 q^{57} -5.83589 q^{58} -2.84032 q^{59} -10.8323 q^{60} -6.47199 q^{61} -14.0986 q^{62} -3.18098 q^{63} +3.15991 q^{64} -5.35902 q^{65} -4.29242 q^{66} -14.9818 q^{67} -11.6015 q^{68} -4.37747 q^{69} +19.1426 q^{70} -2.86271 q^{71} -6.79503 q^{72} +11.5817 q^{73} -11.4310 q^{74} -0.456004 q^{75} +29.8148 q^{76} +5.29983 q^{77} -5.91085 q^{78} -3.09782 q^{79} +19.2267 q^{80} +1.00000 q^{81} -19.3948 q^{82} +4.84612 q^{83} +14.7518 q^{84} -5.84345 q^{85} -10.3950 q^{86} -2.26520 q^{87} +11.3212 q^{88} +4.43109 q^{89} -6.01782 q^{90} +7.29809 q^{91} +20.3004 q^{92} -5.47236 q^{93} +6.72419 q^{94} +15.0172 q^{95} +7.61644 q^{96} -0.638668 q^{97} -8.03470 q^{98} -1.66610 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 93 q + 2 q^{2} - 93 q^{3} + 114 q^{4} - 20 q^{5} - 2 q^{6} + 28 q^{7} + 6 q^{8} + 93 q^{9}+O(q^{10}) \) 93 * q + 2 * q^2 - 93 * q^3 + 114 * q^4 - 20 * q^5 - 2 * q^6 + 28 * q^7 + 6 * q^8 + 93 * q^9	\( 93 q + 2 q^{2} - 93 q^{3} + 114 q^{4} - 20 q^{5} - 2 q^{6} + 28 q^{7} + 6 q^{8} + 93 q^{9} + 19 q^{10} + 10 q^{11} - 114 q^{12} + 20 q^{13} + 13 q^{14} + 20 q^{15} + 148 q^{16} - 43 q^{17} + 2 q^{18} + 50 q^{19} - 31 q^{20} - 28 q^{21} + 36 q^{22} + 21 q^{23} - 6 q^{24} + 137 q^{25} + 2 q^{26} - 93 q^{27} + 62 q^{28} - q^{29} - 19 q^{30} + 58 q^{31} + 19 q^{32} - 10 q^{33} + 30 q^{34} + 30 q^{35} + 114 q^{36} + 42 q^{37} - 6 q^{38} - 20 q^{39} + 53 q^{40} - 7 q^{41} - 13 q^{42} + 60 q^{43} + 25 q^{44} - 20 q^{45} + 57 q^{46} + 9 q^{47} - 148 q^{48} + 145 q^{49} + 41 q^{50} + 43 q^{51} + 71 q^{52} - 45 q^{53} - 2 q^{54} + 78 q^{55} + 44 q^{56} - 50 q^{57} + 40 q^{58} + 42 q^{59} + 31 q^{60} + 69 q^{61} - 42 q^{62} + 28 q^{63} + 230 q^{64} - 4 q^{65} - 36 q^{66} + 76 q^{67} - 91 q^{68} - 21 q^{69} + 57 q^{70} + 92 q^{71} + 6 q^{72} + 29 q^{73} + 59 q^{74} - 137 q^{75} + 131 q^{76} - 98 q^{77} - 2 q^{78} + 215 q^{79} - 37 q^{80} + 93 q^{81} + 50 q^{82} - 27 q^{83} - 62 q^{84} + 52 q^{85} + 82 q^{86} + q^{87} + 136 q^{88} - 14 q^{89} + 19 q^{90} + 101 q^{91} - 14 q^{92} - 58 q^{93} + 112 q^{94} + 59 q^{95} - 19 q^{96} + 38 q^{97} - 16 q^{98} + 10 q^{99}+O(q^{100}) \) 93 * q + 2 * q^2 - 93 * q^3 + 114 * q^4 - 20 * q^5 - 2 * q^6 + 28 * q^7 + 6 * q^8 + 93 * q^9 + 19 * q^10 + 10 * q^11 - 114 * q^12 + 20 * q^13 + 13 * q^14 + 20 * q^15 + 148 * q^16 - 43 * q^17 + 2 * q^18 + 50 * q^19 - 31 * q^20 - 28 * q^21 + 36 * q^22 + 21 * q^23 - 6 * q^24 + 137 * q^25 + 2 * q^26 - 93 * q^27 + 62 * q^28 - q^29 - 19 * q^30 + 58 * q^31 + 19 * q^32 - 10 * q^33 + 30 * q^34 + 30 * q^35 + 114 * q^36 + 42 * q^37 - 6 * q^38 - 20 * q^39 + 53 * q^40 - 7 * q^41 - 13 * q^42 + 60 * q^43 + 25 * q^44 - 20 * q^45 + 57 * q^46 + 9 * q^47 - 148 * q^48 + 145 * q^49 + 41 * q^50 + 43 * q^51 + 71 * q^52 - 45 * q^53 - 2 * q^54 + 78 * q^55 + 44 * q^56 - 50 * q^57 + 40 * q^58 + 42 * q^59 + 31 * q^60 + 69 * q^61 - 42 * q^62 + 28 * q^63 + 230 * q^64 - 4 * q^65 - 36 * q^66 + 76 * q^67 - 91 * q^68 - 21 * q^69 + 57 * q^70 + 92 * q^71 + 6 * q^72 + 29 * q^73 + 59 * q^74 - 137 * q^75 + 131 * q^76 - 98 * q^77 - 2 * q^78 + 215 * q^79 - 37 * q^80 + 93 * q^81 + 50 * q^82 - 27 * q^83 - 62 * q^84 + 52 * q^85 + 82 * q^86 + q^87 + 136 * q^88 - 14 * q^89 + 19 * q^90 + 101 * q^91 - 14 * q^92 - 58 * q^93 + 112 * q^94 + 59 * q^95 - 19 * q^96 + 38 * q^97 - 16 * q^98 + 10 * q^99

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