LMFDB - Embedded newform 1805.2.a.q.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1805,2,Mod(1,1805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1805, 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("1805.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1805 = 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1805.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:	$14.4129975648$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.5822000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 8x^{4} + 5x^{3} + 14x^{2} + x - 1 $ x^6 - x^5 - 8x^4 + 5x^3 + 14*x^2 + x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.228906$ of defining polynomial
Character	$\chi$	$=$	1805.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.38913 q^{2} -3.31798 q^{3} -0.0703236 q^{4} -1.00000 q^{5} +4.60910 q^{6} -1.97948 q^{7} +2.87594 q^{8} +8.00899 q^{9} +O(q^{10})$	\(q-1.38913 q^{2} -3.31798 q^{3} -0.0703236 q^{4} -1.00000 q^{5} +4.60910 q^{6} -1.97948 q^{7} +2.87594 q^{8} +8.00899 q^{9} +1.38913 q^{10} +4.53325 q^{11} +0.233332 q^{12} -2.78738 q^{13} +2.74975 q^{14} +3.31798 q^{15} -3.85441 q^{16} +0.944440 q^{17} -11.1255 q^{18} +0.0703236 q^{20} +6.56786 q^{21} -6.29727 q^{22} +6.80836 q^{23} -9.54233 q^{24} +1.00000 q^{25} +3.87203 q^{26} -16.6197 q^{27} +0.139204 q^{28} +2.80184 q^{29} -4.60910 q^{30} -1.55131 q^{31} -0.397624 q^{32} -15.0412 q^{33} -1.31195 q^{34} +1.97948 q^{35} -0.563221 q^{36} -1.67043 q^{37} +9.24847 q^{39} -2.87594 q^{40} -4.34985 q^{41} -9.12360 q^{42} +0.230680 q^{43} -0.318795 q^{44} -8.00899 q^{45} -9.45768 q^{46} -11.4675 q^{47} +12.7888 q^{48} -3.08167 q^{49} -1.38913 q^{50} -3.13363 q^{51} +0.196019 q^{52} -1.87412 q^{53} +23.0869 q^{54} -4.53325 q^{55} -5.69286 q^{56} -3.89211 q^{58} +13.4632 q^{59} -0.233332 q^{60} -8.56805 q^{61} +2.15497 q^{62} -15.8536 q^{63} +8.26117 q^{64} +2.78738 q^{65} +20.8942 q^{66} +3.50898 q^{67} -0.0664164 q^{68} -22.5900 q^{69} -2.74975 q^{70} +1.14205 q^{71} +23.0334 q^{72} -8.60896 q^{73} +2.32044 q^{74} -3.31798 q^{75} -8.97346 q^{77} -12.8473 q^{78} +3.70628 q^{79} +3.85441 q^{80} +31.1170 q^{81} +6.04250 q^{82} +13.1842 q^{83} -0.461876 q^{84} -0.944440 q^{85} -0.320444 q^{86} -9.29644 q^{87} +13.0374 q^{88} -11.7493 q^{89} +11.1255 q^{90} +5.51755 q^{91} -0.478788 q^{92} +5.14722 q^{93} +15.9298 q^{94} +1.31931 q^{96} +4.65308 q^{97} +4.28084 q^{98} +36.3068 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 4 q^{3} + 8 q^{4} - 6 q^{5} + 8 q^{6} + 7 q^{7} + 10 q^{9}+O(q^{10}) $ 6 * q - 2 * q^2 - 4 * q^3 + 8 * q^4 - 6 * q^5 + 8 * q^6 + 7 * q^7 + 10 * q^9	\( 6 q - 2 q^{2} - 4 q^{3} + 8 q^{4} - 6 q^{5} + 8 q^{6} + 7 q^{7} + 10 q^{9} + 2 q^{10} + 15 q^{11} + 20 q^{12} - 6 q^{13} - 20 q^{14} + 4 q^{15} + 20 q^{16} + 5 q^{17} + 8 q^{18} - 8 q^{20} - 7 q^{21} - 14 q^{22} + 18 q^{24} + 6 q^{25} - 22 q^{26} - 28 q^{27} + 10 q^{28} + 20 q^{29} - 8 q^{30} - 12 q^{31} + 8 q^{32} - q^{33} - 7 q^{35} - 14 q^{36} - 20 q^{37} + 16 q^{39} - 8 q^{41} - 30 q^{42} + 27 q^{43} + 46 q^{44} - 10 q^{45} - 16 q^{46} - 8 q^{47} + 24 q^{48} + 11 q^{49} - 2 q^{50} + 11 q^{51} - 4 q^{52} - 19 q^{53} + 30 q^{54} - 15 q^{55} - 62 q^{56} + 20 q^{58} + 41 q^{59} - 20 q^{60} + 6 q^{61} - 30 q^{62} - 18 q^{63} + 48 q^{64} + 6 q^{65} + 46 q^{66} + 15 q^{67} - 14 q^{68} + 10 q^{69} + 20 q^{70} - 2 q^{71} + 68 q^{72} + 8 q^{73} + 2 q^{74} - 4 q^{75} + 21 q^{77} - 46 q^{78} - 18 q^{79} - 20 q^{80} + 50 q^{81} - 18 q^{82} - 10 q^{83} - 4 q^{84} - 5 q^{85} + 10 q^{86} - 14 q^{87} + 52 q^{88} - 17 q^{89} - 8 q^{90} + 23 q^{91} + 28 q^{92} + 10 q^{93} + 28 q^{94} + 26 q^{96} + 4 q^{97} - 50 q^{98} + 58 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 4 * q^3 + 8 * q^4 - 6 * q^5 + 8 * q^6 + 7 * q^7 + 10 * q^9 + 2 * q^10 + 15 * q^11 + 20 * q^12 - 6 * q^13 - 20 * q^14 + 4 * q^15 + 20 * q^16 + 5 * q^17 + 8 * q^18 - 8 * q^20 - 7 * q^21 - 14 * q^22 + 18 * q^24 + 6 * q^25 - 22 * q^26 - 28 * q^27 + 10 * q^28 + 20 * q^29 - 8 * q^30 - 12 * q^31 + 8 * q^32 - q^33 - 7 * q^35 - 14 * q^36 - 20 * q^37 + 16 * q^39 - 8 * q^41 - 30 * q^42 + 27 * q^43 + 46 * q^44 - 10 * q^45 - 16 * q^46 - 8 * q^47 + 24 * q^48 + 11 * q^49 - 2 * q^50 + 11 * q^51 - 4 * q^52 - 19 * q^53 + 30 * q^54 - 15 * q^55 - 62 * q^56 + 20 * q^58 + 41 * q^59 - 20 * q^60 + 6 * q^61 - 30 * q^62 - 18 * q^63 + 48 * q^64 + 6 * q^65 + 46 * q^66 + 15 * q^67 - 14 * q^68 + 10 * q^69 + 20 * q^70 - 2 * q^71 + 68 * q^72 + 8 * q^73 + 2 * q^74 - 4 * q^75 + 21 * q^77 - 46 * q^78 - 18 * q^79 - 20 * q^80 + 50 * q^81 - 18 * q^82 - 10 * q^83 - 4 * q^84 - 5 * q^85 + 10 * q^86 - 14 * q^87 + 52 * q^88 - 17 * q^89 - 8 * q^90 + 23 * q^91 + 28 * q^92 + 10 * q^93 + 28 * q^94 + 26 * q^96 + 4 * q^97 - 50 * q^98 + 58 * 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 $

$2$	−1.38913	−0.982262	−0.491131	−	0.871086i	$-0.663416\pi$
$2$	−1.38913	−0.982262	−0.491131	+	0.871086i	$0.663416\pi$
$3$	−3.31798	−1.91564	−0.957818	−	0.287375i	$-0.907218\pi$
$3$	−3.31798	−1.91564	−0.957818	+	0.287375i	$0.907218\pi$
$4$	−0.0703236	−0.0351618
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	4.60910	1.88166
$7$	−1.97948	−0.748172	−0.374086	−	0.927394i	$-0.622043\pi$
$7$	−1.97948	−0.748172	−0.374086	+	0.927394i	$0.622043\pi$
$8$	2.87594	1.01680
$9$	8.00899	2.66966
$10$	1.38913	0.439281
$11$	4.53325	1.36683	0.683413	−	0.730032i	$-0.260495\pi$
$11$	4.53325	1.36683	0.683413	+	0.730032i	$0.260495\pi$
$12$	0.233332	0.0673573
$13$	−2.78738	−0.773080	−0.386540	−	0.922273i	$-0.626330\pi$
$13$	−2.78738	−0.773080	−0.386540	+	0.922273i	$0.626330\pi$
$14$	2.74975	0.734900
$15$	3.31798	0.856699
$16$	−3.85441	−0.963602
$17$	0.944440	0.229060	0.114530	−	0.993420i	$-0.463464\pi$
$17$	0.944440	0.229060	0.114530	+	0.993420i	$0.463464\pi$
$18$	−11.1255	−2.62231
$19$	0	0
$19$	0	0
$20$	0.0703236	0.0157248
$21$	6.56786	1.43322
$22$	−6.29727	−1.34258
$23$	6.80836	1.41964	0.709820	−	0.704383i	$-0.248776\pi$
$23$	6.80836	1.41964	0.709820	+	0.704383i	$0.248776\pi$
$24$	−9.54233	−1.94782
$25$	1.00000	0.200000
$26$	3.87203	0.759367
$27$	−16.6197	−3.19847
$28$	0.139204	0.0263071
$29$	2.80184	0.520288	0.260144	−	0.965570i	$-0.416230\pi$
$29$	2.80184	0.520288	0.260144	+	0.965570i	$0.416230\pi$
$30$	−4.60910	−0.841502
$31$	−1.55131	−0.278624	−0.139312	−	0.990249i	$-0.544489\pi$
$31$	−1.55131	−0.278624	−0.139312	+	0.990249i	$0.544489\pi$
$32$	−0.397624	−0.0702906
$33$	−15.0412	−2.61834
$34$	−1.31195	−0.224997
$35$	1.97948	0.334593
$36$	−0.563221	−0.0938702
$37$	−1.67043	−0.274617	−0.137309	−	0.990528i	$-0.543845\pi$
$37$	−1.67043	−0.274617	−0.137309	+	0.990528i	$0.543845\pi$
$38$	0	0
$39$	9.24847	1.48094
$40$	−2.87594	−0.454727
$41$	−4.34985	−0.679333	−0.339667	−	0.940546i	$-0.610314\pi$
$41$	−4.34985	−0.679333	−0.339667	+	0.940546i	$0.610314\pi$
$42$	−9.12360	−1.40780
$43$	0.230680	0.0351783	0.0175892	−	0.999845i	$-0.494401\pi$
$43$	0.230680	0.0351783	0.0175892	+	0.999845i	$0.494401\pi$
$44$	−0.318795	−0.0480601
$45$	−8.00899	−1.19391
$46$	−9.45768	−1.39446
$47$	−11.4675	−1.67271	−0.836353	−	0.548192i	$-0.815316\pi$
$47$	−11.4675	−1.67271	−0.836353	+	0.548192i	$0.815316\pi$
$48$	12.7888	1.84591
$49$	−3.08167	−0.440239
$50$	−1.38913	−0.196452
$51$	−3.13363	−0.438796
$52$	0.196019	0.0271829
$53$	−1.87412	−0.257430	−0.128715	−	0.991682i	$-0.541085\pi$
$53$	−1.87412	−0.257430	−0.128715	+	0.991682i	$0.541085\pi$
$54$	23.0869	3.14173
$55$	−4.53325	−0.611264
$56$	−5.69286	−0.760741
$57$	0	0
$58$	−3.89211	−0.511059
$59$	13.4632	1.75276	0.876380	−	0.481621i	$-0.159952\pi$
$59$	13.4632	1.75276	0.876380	+	0.481621i	$0.159952\pi$
$60$	−0.233332	−0.0301231
$61$	−8.56805	−1.09703	−0.548513	−	0.836142i	$-0.684806\pi$
$61$	−8.56805	−1.09703	−0.548513	+	0.836142i	$0.684806\pi$
$62$	2.15497	0.273682
$63$	−15.8536	−1.99737
$64$	8.26117	1.03265
$65$	2.78738	0.345732
$66$	20.8942	2.57190
$67$	3.50898	0.428690	0.214345	−	0.976758i	$-0.431238\pi$
$67$	3.50898	0.428690	0.214345	+	0.976758i	$0.431238\pi$
$68$	−0.0664164	−0.00805418
$69$	−22.5900	−2.71952
$70$	−2.74975	−0.328657
$71$	1.14205	0.135536	0.0677679	−	0.997701i	$-0.478412\pi$
$71$	1.14205	0.135536	0.0677679	+	0.997701i	$0.478412\pi$
$72$	23.0334	2.71451
$73$	−8.60896	−1.00760	−0.503802	−	0.863819i	$-0.668066\pi$
$73$	−8.60896	−1.00760	−0.503802	+	0.863819i	$0.668066\pi$
$74$	2.32044	0.269746
$75$	−3.31798	−0.383127
$76$	0	0
$77$	−8.97346	−1.02262
$78$	−12.8473	−1.45467
$79$	3.70628	0.416989	0.208495	−	0.978023i	$-0.433144\pi$
$79$	3.70628	0.416989	0.208495	+	0.978023i	$0.433144\pi$
$80$	3.85441	0.430936
$81$	31.1170	3.45744
$82$	6.04250	0.667283
$83$	13.1842	1.44716	0.723580	−	0.690241i	$-0.242495\pi$
$83$	13.1842	1.44716	0.723580	+	0.690241i	$0.242495\pi$
$84$	−0.461876	−0.0503948
$85$	−0.944440	−0.102439
$86$	−0.320444	−0.0345543
$87$	−9.29644	−0.996683
$88$	13.0374	1.38979
$89$	−11.7493	−1.24542	−0.622712	−	0.782451i	$-0.713969\pi$
$89$	−11.7493	−1.24542	−0.622712	+	0.782451i	$0.713969\pi$
$90$	11.1255	1.17273
$91$	5.51755	0.578397
$92$	−0.478788	−0.0499171
$93$	5.14722	0.533742
$94$	15.9298	1.64303
$95$	0	0
$96$	1.31931	0.134651
$97$	4.65308	0.472449	0.236225	−	0.971699i	$-0.424090\pi$
$97$	4.65308	0.472449	0.236225	+	0.971699i	$0.424090\pi$
$98$	4.28084	0.432430
$99$	36.3068	3.64897
$100$	−0.0703236	−0.00703236
$101$	−2.61248	−0.259951	−0.129976	−	0.991517i	$-0.541490\pi$
$101$	−2.61248	−0.259951	−0.129976	+	0.991517i	$0.541490\pi$
$102$	4.35302	0.431013
$103$	7.75236	0.763862	0.381931	−	0.924191i	$-0.375259\pi$
$103$	7.75236	0.763862	0.381931	+	0.924191i	$0.375259\pi$
$104$	−8.01635	−0.786068
$105$	−6.56786	−0.640958
$106$	2.60339	0.252863
$107$	8.26964	0.799456	0.399728	−	0.916634i	$-0.369105\pi$
$107$	8.26964	0.799456	0.399728	+	0.916634i	$0.369105\pi$
$108$	1.16876	0.112464
$109$	6.35274	0.608483	0.304241	−	0.952595i	$-0.401597\pi$
$109$	6.35274	0.608483	0.304241	+	0.952595i	$0.401597\pi$
$110$	6.29727	0.600421
$111$	5.54246	0.526067
$112$	7.62971	0.720940
$113$	3.24448	0.305215	0.152608	−	0.988287i	$-0.451233\pi$
$113$	3.24448	0.305215	0.152608	+	0.988287i	$0.451233\pi$
$114$	0	0
$115$	−6.80836	−0.634883
$116$	−0.197035	−0.0182943
$117$	−22.3241	−2.06386
$118$	−18.7021	−1.72167
$119$	−1.86950	−0.171376
$120$	9.54233	0.871091
$121$	9.55038	0.868216
$122$	11.9021	1.07757
$123$	14.4327	1.30136
$124$	0.109094	0.00979692
$125$	−1.00000	−0.0894427
$126$	22.0227	1.96194
$127$	4.84540	0.429960	0.214980	−	0.976618i	$-0.431031\pi$
$127$	4.84540	0.429960	0.214980	+	0.976618i	$0.431031\pi$
$128$	−10.6806	−0.944038
$129$	−0.765391	−0.0673889
$130$	−3.87203	−0.339599
$131$	−13.7069	−1.19758	−0.598789	−	0.800907i	$-0.704351\pi$
$131$	−13.7069	−1.19758	−0.598789	+	0.800907i	$0.704351\pi$
$132$	1.05775	0.0920657
$133$	0	0
$134$	−4.87442	−0.421086
$135$	16.6197	1.43040
$136$	2.71616	0.232908
$137$	−4.21003	−0.359688	−0.179844	−	0.983695i	$-0.557559\pi$
$137$	−4.21003	−0.359688	−0.179844	+	0.983695i	$0.557559\pi$
$138$	31.3804	2.67128
$139$	14.1467	1.19990	0.599952	−	0.800036i	$-0.295186\pi$
$139$	14.1467	1.19990	0.599952	+	0.800036i	$0.295186\pi$
$140$	−0.139204	−0.0117649
$141$	38.0489	3.20430
$142$	−1.58645	−0.133132
$143$	−12.6359	−1.05667
$144$	−30.8699	−2.57249
$145$	−2.80184	−0.232680
$146$	11.9590	0.989730
$147$	10.2249	0.843338
$148$	0.117471	0.00965604
$149$	10.8330	0.887477	0.443738	−	0.896156i	$-0.353652\pi$
$149$	10.8330	0.887477	0.443738	+	0.896156i	$0.353652\pi$
$150$	4.60910	0.376331
$151$	−15.5841	−1.26821	−0.634107	−	0.773245i	$-0.718632\pi$
$151$	−15.5841	−1.26821	−0.634107	+	0.773245i	$0.718632\pi$
$152$	0	0
$153$	7.56401	0.611514
$154$	12.4653	1.00448
$155$	1.55131	0.124604
$156$	−0.650386	−0.0520726
$157$	−18.2038	−1.45282	−0.726410	−	0.687261i	$-0.758813\pi$
$157$	−18.2038	−1.45282	−0.726410	+	0.687261i	$0.758813\pi$
$158$	−5.14850	−0.409593
$159$	6.21828	0.493142
$160$	0.397624	0.0314349
$161$	−13.4770	−1.06213
$162$	−43.2254	−3.39611
$163$	15.6518	1.22595	0.612973	−	0.790104i	$-0.289974\pi$
$163$	15.6518	1.22595	0.612973	+	0.790104i	$0.289974\pi$
$164$	0.305898	0.0238866
$165$	15.0412	1.17096
$166$	−18.3146	−1.42149
$167$	−12.0929	−0.935774	−0.467887	−	0.883788i	$-0.654985\pi$
$167$	−12.0929	−0.935774	−0.467887	+	0.883788i	$0.654985\pi$
$168$	18.8888	1.45730
$169$	−5.23051	−0.402347
$170$	1.31195	0.100622
$171$	0	0
$172$	−0.0162222	−0.00123693
$173$	9.75337	0.741535	0.370767	−	0.928726i	$-0.379095\pi$
$173$	9.75337	0.741535	0.370767	+	0.928726i	$0.379095\pi$
$174$	12.9139	0.979004
$175$	−1.97948	−0.149634
$176$	−17.4730	−1.31708
$177$	−44.6706	−3.35765
$178$	16.3213	1.22333
$179$	2.21400	0.165482	0.0827409	−	0.996571i	$-0.473633\pi$
$179$	2.21400	0.165482	0.0827409	+	0.996571i	$0.473633\pi$
$180$	0.563221	0.0419800
$181$	13.1722	0.979081	0.489540	−	0.871981i	$-0.337165\pi$
$181$	13.1722	0.979081	0.489540	+	0.871981i	$0.337165\pi$
$182$	−7.66459	−0.568137
$183$	28.4286	2.10150
$184$	19.5805	1.44349
$185$	1.67043	0.122813
$186$	−7.15015	−0.524274
$187$	4.28138	0.313086
$188$	0.806436	0.0588154
$189$	32.8984	2.39300
$190$	0	0
$191$	−23.2330	−1.68108	−0.840539	−	0.541751i	$-0.817762\pi$
$191$	−23.2330	−1.68108	−0.840539	+	0.541751i	$0.817762\pi$
$192$	−27.4104	−1.97817
$193$	−19.3773	−1.39481	−0.697404	−	0.716678i	$-0.745662\pi$
$193$	−19.3773	−1.39481	−0.697404	+	0.716678i	$0.745662\pi$
$194$	−6.46373	−0.464069
$195$	−9.24847	−0.662297
$196$	0.216714	0.0154796
$197$	−5.98403	−0.426344	−0.213172	−	0.977015i	$-0.568380\pi$
$197$	−5.98403	−0.426344	−0.213172	+	0.977015i	$0.568380\pi$
$198$	−50.4348	−3.58424
$199$	−7.76803	−0.550661	−0.275331	−	0.961350i	$-0.588787\pi$
$199$	−7.76803	−0.550661	−0.275331	+	0.961350i	$0.588787\pi$
$200$	2.87594	0.203360
$201$	−11.6427	−0.821214
$202$	3.62907	0.255340
$203$	−5.54617	−0.389265
$204$	0.220368	0.0154289
$205$	4.34985	0.303807
$206$	−10.7690	−0.750313
$207$	54.5281	3.78996
$208$	10.7437	0.744941
$209$	0	0
$210$	9.12360	0.629588
$211$	2.87539	0.197950	0.0989749	−	0.995090i	$-0.468444\pi$
$211$	2.87539	0.197950	0.0989749	+	0.995090i	$0.468444\pi$
$212$	0.131795	0.00905169
$213$	−3.78928	−0.259637
$214$	−11.4876	−0.785275
$215$	−0.230680	−0.0157322
$216$	−47.7974	−3.25220
$217$	3.07079	0.208459
$218$	−8.82477	−0.597689
$219$	28.5644	1.93020
$220$	0.318795	0.0214931
$221$	−2.63251	−0.177082
$222$	−7.69919	−0.516735
$223$	25.9702	1.73909	0.869546	−	0.493852i	$-0.164412\pi$
$223$	25.9702	1.73909	0.869546	+	0.493852i	$0.164412\pi$
$224$	0.787087	0.0525895
$225$	8.00899	0.533933
$226$	−4.50700	−0.299801
$227$	−17.5702	−1.16617	−0.583087	−	0.812410i	$-0.698155\pi$
$227$	−17.5702	−1.16617	−0.583087	+	0.812410i	$0.698155\pi$
$228$	0	0
$229$	14.5751	0.963147	0.481574	−	0.876406i	$-0.340065\pi$
$229$	14.5751	0.963147	0.481574	+	0.876406i	$0.340065\pi$
$230$	9.45768	0.623621
$231$	29.7738	1.95897
$232$	8.05793	0.529029
$233$	22.7458	1.49013	0.745063	−	0.666994i	$-0.232419\pi$
$233$	22.7458	1.49013	0.745063	+	0.666994i	$0.232419\pi$
$234$	31.0110	2.02725
$235$	11.4675	0.748057
$236$	−0.946781	−0.0616302
$237$	−12.2974	−0.798800
$238$	2.59697	0.168337
$239$	3.29374	0.213054	0.106527	−	0.994310i	$-0.466027\pi$
$239$	3.29374	0.213054	0.106527	+	0.994310i	$0.466027\pi$
$240$	−12.7888	−0.825516
$241$	10.6159	0.683829	0.341915	−	0.939731i	$-0.388925\pi$
$241$	10.6159	0.683829	0.341915	+	0.939731i	$0.388925\pi$
$242$	−13.2667	−0.852815
$243$	−53.3862	−3.42473
$244$	0.602536	0.0385734
$245$	3.08167	0.196881
$246$	−20.0489	−1.27827
$247$	0	0
$248$	−4.46149	−0.283305
$249$	−43.7451	−2.77223
$250$	1.38913	0.0878562
$251$	24.2672	1.53173	0.765865	−	0.643002i	$-0.222311\pi$
$251$	24.2672	1.53173	0.765865	+	0.643002i	$0.222311\pi$
$252$	1.11488	0.0702310
$253$	30.8640	1.94040
$254$	−6.73089	−0.422333
$255$	3.13363	0.196236
$256$	−1.68566	−0.105353
$257$	27.7297	1.72973	0.864864	−	0.502006i	$-0.167404\pi$
$257$	27.7297	1.72973	0.864864	+	0.502006i	$0.167404\pi$
$258$	1.06323	0.0661935
$259$	3.30658	0.205461
$260$	−0.196019	−0.0121566
$261$	22.4399	1.38899
$262$	19.0407	1.17634
$263$	−31.6408	−1.95105	−0.975527	−	0.219879i	$-0.929434\pi$
$263$	−31.6408	−1.95105	−0.975527	+	0.219879i	$0.929434\pi$
$264$	−43.2578	−2.66233
$265$	1.87412	0.115126
$266$	0	0
$267$	38.9840	2.38578
$268$	−0.246764	−0.0150735
$269$	−9.74892	−0.594402	−0.297201	−	0.954815i	$-0.596053\pi$
$269$	−9.74892	−0.594402	−0.297201	+	0.954815i	$0.596053\pi$
$270$	−23.0869	−1.40503
$271$	28.0561	1.70429	0.852144	−	0.523308i	$-0.175302\pi$
$271$	28.0561	1.70429	0.852144	+	0.523308i	$0.175302\pi$
$272$	−3.64026	−0.220723
$273$	−18.3071	−1.10800
$274$	5.84828	0.353307
$275$	4.53325	0.273365
$276$	1.58861	0.0956231
$277$	20.3444	1.22238	0.611189	−	0.791484i	$-0.290691\pi$
$277$	20.3444	1.22238	0.611189	+	0.791484i	$0.290691\pi$
$278$	−19.6515	−1.17862
$279$	−12.4244	−0.743832
$280$	5.69286	0.340214
$281$	−17.6557	−1.05325	−0.526625	−	0.850098i	$-0.676543\pi$
$281$	−17.6557	−1.05325	−0.526625	+	0.850098i	$0.676543\pi$
$282$	−52.8548	−3.14746
$283$	−1.84090	−0.109430	−0.0547150	−	0.998502i	$-0.517425\pi$
$283$	−1.84090	−0.109430	−0.0547150	+	0.998502i	$0.517425\pi$
$284$	−0.0803128	−0.00476569
$285$	0	0
$286$	17.5529	1.03792
$287$	8.61043	0.508258
$288$	−3.18457	−0.187652
$289$	−16.1080	−0.947531
$290$	3.89211	0.228553
$291$	−15.4388	−0.905041
$292$	0.605414	0.0354291
$293$	13.5178	0.789720	0.394860	−	0.918741i	$-0.370793\pi$
$293$	13.5178	0.789720	0.394860	+	0.918741i	$0.370793\pi$
$294$	−14.2037	−0.828379
$295$	−13.4632	−0.783858
$296$	−4.80407	−0.279231
$297$	−75.3414	−4.37175
$298$	−15.0485	−0.871735
$299$	−18.9775	−1.09750
$300$	0.233332	0.0134715
$301$	−0.456625	−0.0263194
$302$	21.6483	1.24572
$303$	8.66815	0.497972
$304$	0	0
$305$	8.56805	0.490605
$306$	−10.5074	−0.600667
$307$	23.4950	1.34093	0.670466	−	0.741940i	$-0.266094\pi$
$307$	23.4950	1.34093	0.670466	+	0.741940i	$0.266094\pi$
$308$	0.631047	0.0359572
$309$	−25.7222	−1.46328
$310$	−2.15497	−0.122394
$311$	−2.59318	−0.147046	−0.0735229	−	0.997294i	$-0.523424\pi$
$311$	−2.59318	−0.147046	−0.0735229	+	0.997294i	$0.523424\pi$
$312$	26.5981	1.50582
$313$	0.288688	0.0163176	0.00815881	−	0.999967i	$-0.497403\pi$
$313$	0.288688	0.0163176	0.00815881	+	0.999967i	$0.497403\pi$
$314$	25.2874	1.42705
$315$	15.8536	0.893249
$316$	−0.260639	−0.0146621
$317$	−16.6475	−0.935016	−0.467508	−	0.883989i	$-0.654848\pi$
$317$	−16.6475	−0.935016	−0.467508	+	0.883989i	$0.654848\pi$
$318$	−8.63799	−0.484394
$319$	12.7014	0.711144
$320$	−8.26117	−0.461813
$321$	−27.4385	−1.53147
$322$	18.7212	1.04329
$323$	0	0
$324$	−2.18826	−0.121570
$325$	−2.78738	−0.154616
$326$	−21.7424	−1.20420
$327$	−21.0783	−1.16563
$328$	−12.5099	−0.690746
$329$	22.6996	1.25147
$330$	−20.8942	−1.15019
$331$	−28.0338	−1.54088	−0.770439	−	0.637514i	$-0.779963\pi$
$331$	−28.0338	−1.54088	−0.770439	+	0.637514i	$0.779963\pi$
$332$	−0.927164	−0.0508847
$333$	−13.3785	−0.733136
$334$	16.7985	0.919175
$335$	−3.50898	−0.191716
$336$	−25.3152	−1.38106
$337$	−3.69334	−0.201189	−0.100595	−	0.994928i	$-0.532074\pi$
$337$	−3.69334	−0.201189	−0.100595	+	0.994928i	$0.532074\pi$
$338$	7.26585	0.395210
$339$	−10.7651	−0.584681
$340$	0.0664164	0.00360194
$341$	−7.03249	−0.380831
$342$	0	0
$343$	19.9564	1.07755
$344$	0.663422	0.0357693
$345$	22.5900	1.21620
$346$	−13.5487	−0.728381
$347$	−15.1641	−0.814050	−0.407025	−	0.913417i	$-0.633434\pi$
$347$	−15.1641	−0.814050	−0.407025	+	0.913417i	$0.633434\pi$
$348$	0.653760	0.0350452
$349$	0.559671	0.0299585	0.0149792	−	0.999888i	$-0.495232\pi$
$349$	0.559671	0.0299585	0.0149792	+	0.999888i	$0.495232\pi$
$350$	2.74975	0.146980
$351$	46.3255	2.47267
$352$	−1.80253	−0.0960751
$353$	15.5815	0.829321	0.414660	−	0.909976i	$-0.363900\pi$
$353$	15.5815	0.829321	0.414660	+	0.909976i	$0.363900\pi$
$354$	62.0532	3.29809
$355$	−1.14205	−0.0606135
$356$	0.826254	0.0437914
$357$	6.20295	0.328295
$358$	−3.07552	−0.162546
$359$	13.2737	0.700561	0.350281	−	0.936645i	$-0.386086\pi$
$359$	13.2737	0.700561	0.350281	+	0.936645i	$0.386086\pi$
$360$	−23.0334	−1.21397
$361$	0	0
$362$	−18.2979	−0.961714
$363$	−31.6880	−1.66319
$364$	−0.388014	−0.0203375
$365$	8.60896	0.450614
$366$	−39.4910	−2.06423
$367$	−7.33366	−0.382814	−0.191407	−	0.981511i	$-0.561305\pi$
$367$	−7.33366	−0.382814	−0.191407	+	0.981511i	$0.561305\pi$
$368$	−26.2422	−1.36797
$369$	−34.8379	−1.81359
$370$	−2.32044	−0.120634
$371$	3.70977	0.192602
$372$	−0.361971	−0.0187673
$373$	−10.4747	−0.542358	−0.271179	−	0.962529i	$-0.587413\pi$
$373$	−10.4747	−0.542358	−0.271179	+	0.962529i	$0.587413\pi$
$374$	−5.94739	−0.307532
$375$	3.31798	0.171340
$376$	−32.9799	−1.70081
$377$	−7.80979	−0.402225
$378$	−45.7000	−2.35056
$379$	11.9934	0.616061	0.308030	−	0.951377i	$-0.400330\pi$
$379$	11.9934	0.616061	0.308030	+	0.951377i	$0.400330\pi$
$380$	0	0
$381$	−16.0770	−0.823647
$382$	32.2736	1.65126
$383$	16.7338	0.855058	0.427529	−	0.904002i	$-0.359384\pi$
$383$	16.7338	0.855058	0.427529	+	0.904002i	$0.359384\pi$
$384$	35.4379	1.80843
$385$	8.97346	0.457330
$386$	26.9175	1.37007
$387$	1.84751	0.0939143
$388$	−0.327222	−0.0166122
$389$	8.50476	0.431209	0.215604	−	0.976481i	$-0.430828\pi$
$389$	8.50476	0.431209	0.215604	+	0.976481i	$0.430828\pi$
$390$	12.8473	0.650549
$391$	6.43008	0.325183
$392$	−8.86272	−0.447635
$393$	45.4793	2.29413
$394$	8.31258	0.418782
$395$	−3.70628	−0.186483
$396$	−2.55322	−0.128304
$397$	−11.6504	−0.584715	−0.292358	−	0.956309i	$-0.594440\pi$
$397$	−11.6504	−0.584715	−0.292358	+	0.956309i	$0.594440\pi$
$398$	10.7908	0.540893
$399$	0	0
$400$	−3.85441	−0.192720
$401$	13.5374	0.676023	0.338012	−	0.941142i	$-0.390246\pi$
$401$	13.5374	0.676023	0.338012	+	0.941142i	$0.390246\pi$
$402$	16.1732	0.806648
$403$	4.32410	0.215399
$404$	0.183719	0.00914036
$405$	−31.1170	−1.54621
$406$	7.70434	0.382360
$407$	−7.57249	−0.375354
$408$	−9.01215	−0.446168
$409$	−30.8146	−1.52369	−0.761843	−	0.647762i	$-0.775705\pi$
$409$	−30.8146	−1.52369	−0.761843	+	0.647762i	$0.775705\pi$
$410$	−6.04250	−0.298418
$411$	13.9688	0.689031
$412$	−0.545174	−0.0268588
$413$	−26.6501	−1.31136
$414$	−75.7464	−3.72273
$415$	−13.1842	−0.647189
$416$	1.10833	0.0543403
$417$	−46.9383	−2.29858
$418$	0	0
$419$	−19.6831	−0.961581	−0.480791	−	0.876835i	$-0.659650\pi$
$419$	−19.6831	−0.961581	−0.480791	+	0.876835i	$0.659650\pi$
$420$	0.461876	0.0225372
$421$	22.1714	1.08057	0.540285	−	0.841482i	$-0.318316\pi$
$421$	22.1714	1.08057	0.540285	+	0.841482i	$0.318316\pi$
$422$	−3.99428	−0.194438
$423$	−91.8430	−4.46556
$424$	−5.38985	−0.261754
$425$	0.944440	0.0458121
$426$	5.26380	0.255032
$427$	16.9603	0.820764
$428$	−0.581551	−0.0281103
$429$	41.9257	2.02419
$430$	0.320444	0.0154532
$431$	36.9642	1.78050	0.890250	−	0.455472i	$-0.150529\pi$
$431$	36.9642	1.78050	0.890250	+	0.455472i	$0.150529\pi$
$432$	64.0592	3.08205
$433$	7.58604	0.364562	0.182281	−	0.983246i	$-0.441652\pi$
$433$	7.58604	0.364562	0.182281	+	0.983246i	$0.441652\pi$
$434$	−4.26571	−0.204761
$435$	9.29644	0.445730
$436$	−0.446748	−0.0213954
$437$	0	0
$438$	−39.6796	−1.89596
$439$	0.835408	0.0398719	0.0199359	−	0.999801i	$-0.493654\pi$
$439$	0.835408	0.0398719	0.0199359	+	0.999801i	$0.493654\pi$
$440$	−13.0374	−0.621533
$441$	−24.6811	−1.17529
$442$	3.65690	0.173941
$443$	0.928844	0.0441307	0.0220654	−	0.999757i	$-0.492976\pi$
$443$	0.928844	0.0441307	0.0220654	+	0.999757i	$0.492976\pi$
$444$	−0.389766	−0.0184975
$445$	11.7493	0.556971
$446$	−36.0759	−1.70824
$447$	−35.9438	−1.70008
$448$	−16.3528	−0.772596
$449$	10.3325	0.487622	0.243811	−	0.969823i	$-0.421602\pi$
$449$	10.3325	0.487622	0.243811	+	0.969823i	$0.421602\pi$
$450$	−11.1255	−0.524462
$451$	−19.7190	−0.928531
$452$	−0.228164	−0.0107319
$453$	51.7077	2.42944
$454$	24.4072	1.14549
$455$	−5.51755	−0.258667
$456$	0	0
$457$	27.8563	1.30307	0.651533	−	0.758621i	$-0.274126\pi$
$457$	27.8563	1.30307	0.651533	+	0.758621i	$0.274126\pi$
$458$	−20.2466	−0.946063
$459$	−15.6963	−0.732642
$460$	0.478788	0.0223236
$461$	4.44189	0.206879	0.103440	−	0.994636i	$-0.467015\pi$
$461$	4.44189	0.206879	0.103440	+	0.994636i	$0.467015\pi$
$462$	−41.3596	−1.92422
$463$	16.4427	0.764155	0.382078	−	0.924130i	$-0.375209\pi$
$463$	16.4427	0.764155	0.382078	+	0.924130i	$0.375209\pi$
$464$	−10.7994	−0.501351
$465$	−5.14722	−0.238697
$466$	−31.5968	−1.46369
$467$	16.1255	0.746201	0.373100	−	0.927791i	$-0.378295\pi$
$467$	16.1255	0.746201	0.373100	+	0.927791i	$0.378295\pi$
$468$	1.56991	0.0725692
$469$	−6.94594	−0.320734
$470$	−15.9298	−0.734788
$471$	60.3998	2.78308
$472$	38.7194	1.78221
$473$	1.04573	0.0480827
$474$	17.0826	0.784631
$475$	0	0
$476$	0.131470	0.00602591
$477$	−15.0098	−0.687251
$478$	−4.57542	−0.209275
$479$	29.6697	1.35564	0.677822	−	0.735226i	$-0.262924\pi$
$479$	29.6697	1.35564	0.677822	+	0.735226i	$0.262924\pi$
$480$	−1.31931	−0.0602179
$481$	4.65613	0.212301
$482$	−14.7468	−0.671699
$483$	44.7163	2.03466
$484$	−0.671617	−0.0305280
$485$	−4.65308	−0.211286
$486$	74.1603	3.36398
$487$	−20.9383	−0.948807	−0.474403	−	0.880308i	$-0.657336\pi$
$487$	−20.9383	−0.948807	−0.474403	+	0.880308i	$0.657336\pi$
$488$	−24.6412	−1.11546
$489$	−51.9324	−2.34847
$490$	−4.28084	−0.193389
$491$	9.31115	0.420206	0.210103	−	0.977679i	$-0.432620\pi$
$491$	9.31115	0.420206	0.210103	+	0.977679i	$0.432620\pi$
$492$	−1.01496	−0.0457580
$493$	2.64617	0.119177
$494$	0	0
$495$	−36.3068	−1.63187
$496$	5.97939	0.268482
$497$	−2.26065	−0.101404
$498$	60.7675	2.72306
$499$	33.9143	1.51821	0.759107	−	0.650966i	$-0.225636\pi$
$499$	33.9143	1.51821	0.759107	+	0.650966i	$0.225636\pi$
$500$	0.0703236	0.00314497
$501$	40.1239	1.79260
$502$	−33.7102	−1.50456
$503$	3.23623	0.144296	0.0721481	−	0.997394i	$-0.477015\pi$
$503$	3.23623	0.144296	0.0721481	+	0.997394i	$0.477015\pi$
$504$	−45.5941	−2.03092
$505$	2.61248	0.116254
$506$	−42.8740	−1.90598
$507$	17.3547	0.770751
$508$	−0.340746	−0.0151182
$509$	−6.46485	−0.286549	−0.143275	−	0.989683i	$-0.545763\pi$
$509$	−6.46485	−0.286549	−0.143275	+	0.989683i	$0.545763\pi$
$510$	−4.35302	−0.192755
$511$	17.0412	0.753860
$512$	23.7027	1.04752
$513$	0	0
$514$	−38.5200	−1.69905
$515$	−7.75236	−0.341610
$516$	0.0538251	0.00236952
$517$	−51.9850	−2.28630
$518$	−4.59326	−0.201816
$519$	−32.3615	−1.42051
$520$	8.01635	0.351540
$521$	4.24031	0.185771	0.0928857	−	0.995677i	$-0.470391\pi$
$521$	4.24031	0.185771	0.0928857	+	0.995677i	$0.470391\pi$
$522$	−31.1719	−1.36436
$523$	37.8951	1.65704	0.828519	−	0.559961i	$-0.189184\pi$
$523$	37.8951	1.65704	0.828519	+	0.559961i	$0.189184\pi$
$524$	0.963920	0.0421090
$525$	6.56786	0.286645
$526$	43.9531	1.91645
$527$	−1.46512	−0.0638217
$528$	57.9751	2.52304
$529$	23.3537	1.01538
$530$	−2.60339	−0.113084
$531$	107.827	4.67928
$532$	0	0
$533$	12.1247	0.525179
$534$	−54.1537	−2.34346
$535$	−8.26964	−0.357528
$536$	10.0916	0.435892
$537$	−7.34599	−0.317003
$538$	13.5425	0.583859
$539$	−13.9700	−0.601731
$540$	−1.16876	−0.0502954
$541$	−18.9844	−0.816204	−0.408102	−	0.912936i	$-0.633809\pi$
$541$	−18.9844	−0.816204	−0.408102	+	0.912936i	$0.633809\pi$
$542$	−38.9735	−1.67406
$543$	−43.7050	−1.87556
$544$	−0.375532	−0.0161008
$545$	−6.35274	−0.272122
$546$	25.4309	1.08834
$547$	18.7562	0.801957	0.400978	−	0.916088i	$-0.368670\pi$
$547$	18.7562	0.801957	0.400978	+	0.916088i	$0.368670\pi$
$548$	0.296065	0.0126473
$549$	−68.6214	−2.92869
$550$	−6.29727	−0.268516
$551$	0	0
$552$	−64.9676	−2.76520
$553$	−7.33650	−0.311980
$554$	−28.2610	−1.20070
$555$	−5.54246	−0.235264
$556$	−0.994845	−0.0421908
$557$	6.19811	0.262622	0.131311	−	0.991341i	$-0.458081\pi$
$557$	6.19811	0.262622	0.131311	+	0.991341i	$0.458081\pi$
$558$	17.2591	0.730638
$559$	−0.642992	−0.0271957
$560$	−7.62971	−0.322414
$561$	−14.2055	−0.599759
$562$	24.5260	1.03457
$563$	27.6199	1.16404	0.582020	−	0.813174i	$-0.302262\pi$
$563$	27.6199	1.16404	0.582020	+	0.813174i	$0.302262\pi$
$564$	−2.67574	−0.112669
$565$	−3.24448	−0.136496
$566$	2.55724	0.107489
$567$	−61.5953	−2.58676
$568$	3.28446	0.137813
$569$	−44.6852	−1.87330	−0.936651	−	0.350264i	$-0.886092\pi$
$569$	−44.6852	−1.87330	−0.936651	+	0.350264i	$0.886092\pi$
$570$	0	0
$571$	15.2049	0.636304	0.318152	−	0.948040i	$-0.396938\pi$
$571$	15.2049	0.636304	0.318152	+	0.948040i	$0.396938\pi$
$572$	0.888602	0.0371543
$573$	77.0865	3.22033
$574$	−11.9610	−0.499242
$575$	6.80836	0.283928
$576$	66.1636	2.75682
$577$	1.06337	0.0442686	0.0221343	−	0.999755i	$-0.492954\pi$
$577$	1.06337	0.0442686	0.0221343	+	0.999755i	$0.492954\pi$
$578$	22.3761	0.930724
$579$	64.2934	2.67194
$580$	0.197035	0.00818145
$581$	−26.0979	−1.08272
$582$	21.4465	0.888987
$583$	−8.49584	−0.351862
$584$	−24.7589	−1.02453
$585$	22.3241	0.922988
$586$	−18.7780	−0.775712
$587$	−7.90131	−0.326122	−0.163061	−	0.986616i	$-0.552137\pi$
$587$	−7.90131	−0.326122	−0.163061	+	0.986616i	$0.552137\pi$
$588$	−0.719054	−0.0296533
$589$	0	0
$590$	18.7021	0.769954
$591$	19.8549	0.816721
$592$	6.43853	0.264622
$593$	47.1481	1.93614	0.968070	−	0.250682i	$-0.0806548\pi$
$593$	47.1481	1.93614	0.968070	+	0.250682i	$0.0806548\pi$
$594$	104.659	4.29421
$595$	1.86950	0.0766419
$596$	−0.761818	−0.0312053
$597$	25.7742	1.05487
$598$	26.3621	1.07803
$599$	9.90013	0.404509	0.202254	−	0.979333i	$-0.435173\pi$
$599$	9.90013	0.404509	0.202254	+	0.979333i	$0.435173\pi$
$600$	−9.54233	−0.389564
$601$	4.43255	0.180808	0.0904038	−	0.995905i	$-0.471184\pi$
$601$	4.43255	0.180808	0.0904038	+	0.995905i	$0.471184\pi$
$602$	0.634311	0.0258526
$603$	28.1034	1.14446
$604$	1.09593	0.0445927
$605$	−9.55038	−0.388278
$606$	−12.0412	−0.489139
$607$	28.5533	1.15894	0.579472	−	0.814992i	$-0.303259\pi$
$607$	28.5533	1.15894	0.579472	+	0.814992i	$0.303259\pi$
$608$	0	0
$609$	18.4021	0.745690
$610$	−11.9021	−0.481903
$611$	31.9643	1.29314
$612$	−0.531929	−0.0215019
$613$	23.6705	0.956044	0.478022	−	0.878348i	$-0.341354\pi$
$613$	23.6705	0.956044	0.478022	+	0.878348i	$0.341354\pi$
$614$	−32.6376	−1.31715
$615$	−14.4327	−0.581984
$616$	−25.8072	−1.03980
$617$	−12.7935	−0.515046	−0.257523	−	0.966272i	$-0.582906\pi$
$617$	−12.7935	−0.515046	−0.257523	+	0.966272i	$0.582906\pi$
$618$	35.7314	1.43733
$619$	18.9938	0.763424	0.381712	−	0.924281i	$-0.375335\pi$
$619$	18.9938	0.763424	0.381712	+	0.924281i	$0.375335\pi$
$620$	−0.109094	−0.00438132
$621$	−113.153	−4.54067
$622$	3.60226	0.144438
$623$	23.2575	0.931791
$624$	−35.6474	−1.42704
$625$	1.00000	0.0400000
$626$	−0.401025	−0.0160282
$627$	0	0
$628$	1.28016	0.0510838
$629$	−1.57762	−0.0629039
$630$	−22.0227	−0.877405
$631$	−2.88795	−0.114967	−0.0574837	−	0.998346i	$-0.518308\pi$
$631$	−2.88795	−0.114967	−0.0574837	+	0.998346i	$0.518308\pi$
$632$	10.6591	0.423995
$633$	−9.54047	−0.379200
$634$	23.1255	0.918430
$635$	−4.84540	−0.192284
$636$	−0.437292	−0.0173398
$637$	8.58980	0.340340
$638$	−17.6439	−0.698530
$639$	9.14663	0.361835
$640$	10.6806	0.422186
$641$	43.1374	1.70382	0.851912	−	0.523684i	$-0.175443\pi$
$641$	43.1374	1.70382	0.851912	+	0.523684i	$0.175443\pi$
$642$	38.1156	1.50430
$643$	−7.96510	−0.314113	−0.157056	−	0.987590i	$-0.550200\pi$
$643$	−7.96510	−0.314113	−0.157056	+	0.987590i	$0.550200\pi$
$644$	0.947750	0.0373466
$645$	0.765391	0.0301372
$646$	0	0
$647$	−10.5042	−0.412961	−0.206481	−	0.978451i	$-0.566201\pi$
$647$	−10.5042	−0.412961	−0.206481	+	0.978451i	$0.566201\pi$
$648$	89.4906	3.51552
$649$	61.0321	2.39572
$650$	3.87203	0.151873
$651$	−10.1888	−0.399331
$652$	−1.10069	−0.0431065
$653$	−44.7572	−1.75148	−0.875741	−	0.482781i	$-0.839627\pi$
$653$	−44.7572	−1.75148	−0.875741	+	0.482781i	$0.839627\pi$
$654$	29.2804	1.14496
$655$	13.7069	0.535574
$656$	16.7661	0.654607
$657$	−68.9491	−2.68996
$658$	−31.5327	−1.22927
$659$	9.24530	0.360146	0.180073	−	0.983653i	$-0.442367\pi$
$659$	9.24530	0.360146	0.180073	+	0.983653i	$0.442367\pi$
$660$	−1.05775	−0.0411730
$661$	−5.16653	−0.200955	−0.100477	−	0.994939i	$-0.532037\pi$
$661$	−5.16653	−0.200955	−0.100477	+	0.994939i	$0.532037\pi$
$662$	38.9426	1.51355
$663$	8.73462	0.339225
$664$	37.9172	1.47147
$665$	0	0
$666$	18.5844	0.720131
$667$	19.0759	0.738622
$668$	0.850414	0.0329035
$669$	−86.1685	−3.33147
$670$	4.87442	0.188315
$671$	−38.8411	−1.49945
$672$	−2.61154	−0.100742
$673$	−13.9059	−0.536035	−0.268017	−	0.963414i	$-0.586368\pi$
$673$	−13.9059	−0.536035	−0.268017	+	0.963414i	$0.586368\pi$
$674$	5.13052	0.197620
$675$	−16.6197	−0.639694
$676$	0.367829	0.0141473
$677$	37.9793	1.45966	0.729832	−	0.683626i	$-0.239598\pi$
$677$	37.9793	1.45966	0.729832	+	0.683626i	$0.239598\pi$
$678$	14.9541	0.574310
$679$	−9.21067	−0.353473
$680$	−2.71616	−0.104160
$681$	58.2975	2.23396
$682$	9.76903	0.374075
$683$	29.9782	1.14708	0.573542	−	0.819176i	$-0.305569\pi$
$683$	29.9782	1.14708	0.573542	+	0.819176i	$0.305569\pi$
$684$	0	0
$685$	4.21003	0.160857
$686$	−27.7220	−1.05843
$687$	−48.3598	−1.84504
$688$	−0.889134	−0.0338979
$689$	5.22387	0.199014
$690$	−31.3804	−1.19463
$691$	18.8053	0.715387	0.357693	−	0.933839i	$-0.383563\pi$
$691$	18.8053	0.715387	0.357693	+	0.933839i	$0.383563\pi$
$692$	−0.685892	−0.0260737
$693$	−71.8684	−2.73005
$694$	21.0648	0.799610
$695$	−14.1467	−0.536614
$696$	−26.7361	−1.01343
$697$	−4.10818	−0.155608
$698$	−0.777454	−0.0294271
$699$	−75.4701	−2.85454
$700$	0.139204	0.00526141
$701$	4.34733	0.164196	0.0820981	−	0.996624i	$-0.473838\pi$
$701$	4.34733	0.164196	0.0820981	+	0.996624i	$0.473838\pi$
$702$	−64.3520	−2.42881
$703$	0	0
$704$	37.4499	1.41145
$705$	−38.0489	−1.43300
$706$	−21.6447	−0.814610
$707$	5.17134	0.194488
$708$	3.14140	0.118061
$709$	−46.5408	−1.74788	−0.873938	−	0.486037i	$-0.838442\pi$
$709$	−46.5408	−1.74788	−0.873938	+	0.486037i	$0.838442\pi$
$710$	1.58645	0.0595383
$711$	29.6836	1.11322
$712$	−33.7904	−1.26635
$713$	−10.5619	−0.395546
$714$	−8.61669	−0.322472
$715$	12.6359	0.472556
$716$	−0.155696	−0.00581864
$717$	−10.9286	−0.408134
$718$	−18.4389	−0.688134
$719$	−6.50124	−0.242455	−0.121228	−	0.992625i	$-0.538683\pi$
$719$	−6.50124	−0.242455	−0.121228	+	0.992625i	$0.538683\pi$
$720$	30.8699	1.15045
$721$	−15.3456	−0.571500
$722$	0	0
$723$	−35.2233	−1.30997
$724$	−0.926316	−0.0344263
$725$	2.80184	0.104058
$726$	44.0186	1.63368
$727$	−3.47765	−0.128979	−0.0644894	−	0.997918i	$-0.520542\pi$
$727$	−3.47765	−0.128979	−0.0644894	+	0.997918i	$0.520542\pi$
$728$	15.8682	0.588114
$729$	83.7836	3.10310
$730$	−11.9590	−0.442621
$731$	0.217863	0.00805796
$732$	−1.99920	−0.0738927
$733$	22.8754	0.844922	0.422461	−	0.906381i	$-0.361166\pi$
$733$	22.8754	0.844922	0.422461	+	0.906381i	$0.361166\pi$
$734$	10.1874	0.376023
$735$	−10.2249	−0.377152
$736$	−2.70716	−0.0997874
$737$	15.9071	0.585945
$738$	48.3944	1.78142
$739$	−19.3982	−0.713575	−0.356788	−	0.934186i	$-0.616128\pi$
$739$	−19.3982	−0.713575	−0.356788	+	0.934186i	$0.616128\pi$
$740$	−0.117471	−0.00431831
$741$	0	0
$742$	−5.15334	−0.189185
$743$	20.6598	0.757936	0.378968	−	0.925410i	$-0.376279\pi$
$743$	20.6598	0.757936	0.378968	+	0.925410i	$0.376279\pi$
$744$	14.8031	0.542709
$745$	−10.8330	−0.396892
$746$	14.5506	0.532737
$747$	105.593	3.86343
$748$	−0.301082	−0.0110087
$749$	−16.3695	−0.598130
$750$	−4.60910	−0.168300
$751$	−45.2262	−1.65033	−0.825164	−	0.564893i	$-0.808918\pi$
$751$	−45.2262	−1.65033	−0.825164	+	0.564893i	$0.808918\pi$
$752$	44.2004	1.61182
$753$	−80.5180	−2.93424
$754$	10.8488	0.395090
$755$	15.5841	0.567163
$756$	−2.31353	−0.0841423
$757$	−2.76494	−0.100494	−0.0502468	−	0.998737i	$-0.516001\pi$
$757$	−2.76494	−0.100494	−0.0502468	+	0.998737i	$0.516001\pi$
$758$	−16.6604	−0.605133
$759$	−102.406	−3.71711
$760$	0	0
$761$	−10.1029	−0.366231	−0.183115	−	0.983091i	$-0.558618\pi$
$761$	−10.1029	−0.366231	−0.183115	+	0.983091i	$0.558618\pi$
$762$	22.3329	0.809037
$763$	−12.5751	−0.455249
$764$	1.63383	0.0591098
$765$	−7.56401	−0.273477
$766$	−23.2454	−0.839891
$767$	−37.5271	−1.35502
$768$	5.59297	0.201819
$769$	5.27876	0.190357	0.0951785	−	0.995460i	$-0.469658\pi$
$769$	5.27876	0.190357	0.0951785	+	0.995460i	$0.469658\pi$
$770$	−12.4653	−0.449218
$771$	−92.0064	−3.31353
$772$	1.36268	0.0490440
$773$	−30.4554	−1.09540	−0.547701	−	0.836674i	$-0.684497\pi$
$773$	−30.4554	−1.09540	−0.547701	+	0.836674i	$0.684497\pi$
$774$	−2.56643	−0.0922484
$775$	−1.55131	−0.0557248
$776$	13.3820	0.480386
$777$	−10.9712	−0.393588
$778$	−11.8142	−0.423560
$779$	0	0
$780$	0.650386	0.0232876
$781$	5.17718	0.185254
$782$	−8.93221	−0.319415
$783$	−46.5658	−1.66413
$784$	11.8780	0.424215
$785$	18.2038	0.649721
$786$	−63.1765	−2.25343
$787$	−30.2322	−1.07766	−0.538831	−	0.842414i	$-0.681134\pi$
$787$	−30.2322	−1.07766	−0.538831	+	0.842414i	$0.681134\pi$
$788$	0.420818	0.0149910
$789$	104.983	3.73751
$790$	5.14850	0.183175
$791$	−6.42237	−0.228353
$792$	104.416	3.71027
$793$	23.8824	0.848089
$794$	16.1839	0.574344
$795$	−6.21828	−0.220540
$796$	0.546276	0.0193622
$797$	−26.4088	−0.935447	−0.467724	−	0.883875i	$-0.654926\pi$
$797$	−26.4088	−0.935447	−0.467724	+	0.883875i	$0.654926\pi$
$798$	0	0
$799$	−10.8304	−0.383150
$800$	−0.397624	−0.0140581
$801$	−94.1001	−3.32486
$802$	−18.8051	−0.664032
$803$	−39.0266	−1.37722
$804$	0.818759	0.0288754
$805$	13.4770	0.475001
$806$	−6.00672	−0.211578
$807$	32.3467	1.13866
$808$	−7.51334	−0.264318
$809$	−19.5554	−0.687533	−0.343766	−	0.939055i	$-0.611703\pi$
$809$	−19.5554	−0.687533	−0.343766	+	0.939055i	$0.611703\pi$
$810$	43.2254	1.51879
$811$	52.8975	1.85748	0.928740	−	0.370731i	$-0.120893\pi$
$811$	52.8975	1.85748	0.928740	+	0.370731i	$0.120893\pi$
$812$	0.390027	0.0136873
$813$	−93.0896	−3.26480
$814$	10.5192	0.368696
$815$	−15.6518	−0.548259
$816$	12.0783	0.422825
$817$	0	0
$818$	42.8055	1.49666
$819$	44.1900	1.54412
$820$	−0.305898	−0.0106824
$821$	17.8930	0.624469	0.312234	−	0.950005i	$-0.398923\pi$
$821$	17.8930	0.624469	0.312234	+	0.950005i	$0.398923\pi$
$822$	−19.4045	−0.676808
$823$	42.0480	1.46570	0.732851	−	0.680390i	$-0.238189\pi$
$823$	42.0480	1.46570	0.732851	+	0.680390i	$0.238189\pi$
$824$	22.2953	0.776695
$825$	−15.0412	−0.523669
$826$	37.0204	1.28810
$827$	20.2598	0.704503	0.352252	−	0.935905i	$-0.385416\pi$
$827$	20.2598	0.704503	0.352252	+	0.935905i	$0.385416\pi$
$828$	−3.83461	−0.133262
$829$	38.6409	1.34205	0.671027	−	0.741433i	$-0.265854\pi$
$829$	38.6409	1.34205	0.671027	+	0.741433i	$0.265854\pi$
$830$	18.3146	0.635709
$831$	−67.5024	−2.34163
$832$	−23.0270	−0.798318
$833$	−2.91046	−0.100841
$834$	65.2034	2.25781
$835$	12.0929	0.418491
$836$	0	0
$837$	25.7824	0.891170
$838$	27.3423	0.944525
$839$	6.08588	0.210108	0.105054	−	0.994467i	$-0.466498\pi$
$839$	6.08588	0.210108	0.105054	+	0.994467i	$0.466498\pi$
$840$	−18.8888	−0.651726
$841$	−21.1497	−0.729300
$842$	−30.7990	−1.06140
$843$	58.5812	2.01764
$844$	−0.202208	−0.00696027
$845$	5.23051	0.179935
$846$	127.582	4.38635
$847$	−18.9047	−0.649575
$848$	7.22361	0.248060
$849$	6.10806	0.209628
$850$	−1.31195	−0.0449994
$851$	−11.3729	−0.389858
$852$	0.266476	0.00912932
$853$	24.3234	0.832818	0.416409	−	0.909177i	$-0.363288\pi$
$853$	24.3234	0.832818	0.416409	+	0.909177i	$0.363288\pi$
$854$	−23.5600	−0.806205
$855$	0	0
$856$	23.7830	0.812887
$857$	9.37273	0.320166	0.160083	−	0.987104i	$-0.448824\pi$
$857$	9.37273	0.320166	0.160083	+	0.987104i	$0.448824\pi$
$858$	−58.2401	−1.98828
$859$	23.5126	0.802241	0.401120	−	0.916025i	$-0.368621\pi$
$859$	23.5126	0.802241	0.401120	+	0.916025i	$0.368621\pi$
$860$	0.0162222	0.000553174 0
$861$	−28.5692	−0.973637
$862$	−51.3479	−1.74892
$863$	8.41440	0.286430	0.143215	−	0.989692i	$-0.454256\pi$
$863$	8.41440	0.286430	0.143215	+	0.989692i	$0.454256\pi$
$864$	6.60840	0.224822
$865$	−9.75337	−0.331625
$866$	−10.5380	−0.358095
$867$	53.4461	1.81513
$868$	−0.215949	−0.00732978
$869$	16.8015	0.569952
$870$	−12.9139	−0.437824
$871$	−9.78086	−0.331412
$872$	18.2701	0.618705
$873$	37.2665	1.26128
$874$	0	0
$875$	1.97948	0.0669185
$876$	−2.00875	−0.0678694
$877$	−21.5002	−0.726011	−0.363006	−	0.931787i	$-0.618249\pi$
$877$	−21.5002	−0.726011	−0.363006	+	0.931787i	$0.618249\pi$
$878$	−1.16049	−0.0391646
$879$	−44.8519	−1.51282
$880$	17.4730	0.589015
$881$	44.9937	1.51588	0.757938	−	0.652327i	$-0.226207\pi$
$881$	44.9937	1.51588	0.757938	+	0.652327i	$0.226207\pi$
$882$	34.2852	1.15444
$883$	38.7617	1.30443	0.652217	−	0.758032i	$-0.273839\pi$
$883$	38.7617	1.30443	0.652217	+	0.758032i	$0.273839\pi$
$884$	0.185128	0.00622652
$885$	44.6706	1.50159
$886$	−1.29028	−0.0433479
$887$	−8.70502	−0.292286	−0.146143	−	0.989263i	$-0.546686\pi$
$887$	−8.70502	−0.292286	−0.146143	+	0.989263i	$0.546686\pi$
$888$	15.9398	0.534905
$889$	−9.59136	−0.321684
$890$	−16.3213	−0.547091
$891$	141.061	4.72572
$892$	−1.82632	−0.0611496
$893$	0	0
$894$	49.9305	1.66993
$895$	−2.21400	−0.0740057
$896$	21.1419	0.706302
$897$	62.9669	2.10240
$898$	−14.3532	−0.478973
$899$	−4.34653	−0.144965
$900$	−0.563221	−0.0187740
$901$	−1.76999	−0.0589669
$902$	27.3922	0.912060
$903$	1.51507	0.0504185
$904$	9.33095	0.310343
$905$	−13.1722	−0.437858
$906$	−71.8285	−2.38634
$907$	47.4596	1.57587	0.787936	−	0.615758i	$-0.211150\pi$
$907$	47.4596	1.57587	0.787936	+	0.615758i	$0.211150\pi$
$908$	1.23560	0.0410048
$909$	−20.9233	−0.693982
$910$	7.66459	0.254079
$911$	−39.6247	−1.31283	−0.656413	−	0.754402i	$-0.727927\pi$
$911$	−39.6247	−1.31283	−0.656413	+	0.754402i	$0.727927\pi$
$912$	0	0
$913$	59.7675	1.97802
$914$	−38.6960	−1.27995
$915$	−28.4286	−0.939821
$916$	−1.02497	−0.0338660
$917$	27.1325	0.895995
$918$	21.8042	0.719646
$919$	−28.0347	−0.924781	−0.462391	−	0.886676i	$-0.653008\pi$
$919$	−28.0347	−0.924781	−0.462391	+	0.886676i	$0.653008\pi$
$920$	−19.5805	−0.645548
$921$	−77.9561	−2.56874
$922$	−6.17035	−0.203210
$923$	−3.18331	−0.104780
$924$	−2.09380	−0.0688810
$925$	−1.67043	−0.0549235
$926$	−22.8410	−0.750600
$927$	62.0885	2.03926
$928$	−1.11408	−0.0365714
$929$	23.9498	0.785769	0.392884	−	0.919588i	$-0.371477\pi$
$929$	23.9498	0.785769	0.392884	+	0.919588i	$0.371477\pi$
$930$	7.15015	0.234463
$931$	0	0
$932$	−1.59957	−0.0523955
$933$	8.60412	0.281686
$934$	−22.4004	−0.732964
$935$	−4.28138	−0.140016
$936$	−64.2029	−2.09854
$937$	49.9950	1.63326	0.816632	−	0.577158i	$-0.195838\pi$
$937$	49.9950	1.63326	0.816632	+	0.577158i	$0.195838\pi$
$938$	9.64880	0.315045
$939$	−0.957862	−0.0312586
$940$	−0.806436	−0.0263030
$941$	−19.8648	−0.647575	−0.323788	−	0.946130i	$-0.604956\pi$
$941$	−19.8648	−0.647575	−0.323788	+	0.946130i	$0.604956\pi$
$942$	−83.9031	−2.73371
$943$	−29.6154	−0.964409
$944$	−51.8927	−1.68896
$945$	−32.8984	−1.07018
$946$	−1.45265	−0.0472298
$947$	18.1829	0.590863	0.295432	−	0.955364i	$-0.404537\pi$
$947$	18.1829	0.590863	0.295432	+	0.955364i	$0.404537\pi$
$948$	0.864796	0.0280873
$949$	23.9965	0.778958
$950$	0	0
$951$	55.2360	1.79115
$952$	−5.37657	−0.174256
$953$	14.8620	0.481427	0.240713	−	0.970596i	$-0.422619\pi$
$953$	14.8620	0.481427	0.240713	+	0.970596i	$0.422619\pi$
$954$	20.8505	0.675060
$955$	23.2330	0.751801
$956$	−0.231628	−0.00749137
$957$	−42.1431	−1.36229
$958$	−41.2150	−1.33160
$959$	8.33366	0.269108
$960$	27.4104	0.884666
$961$	−28.5934	−0.922369
$962$	−6.46796	−0.208535
$963$	66.2314	2.13428
$964$	−0.746548	−0.0240447
$965$	19.3773	0.623777
$966$	−62.1167	−1.99857
$967$	14.8074	0.476172	0.238086	−	0.971244i	$-0.423480\pi$
$967$	14.8074	0.476172	0.238086	+	0.971244i	$0.423480\pi$
$968$	27.4664	0.882802
$969$	0	0
$970$	6.46373	0.207538
$971$	−48.0131	−1.54081	−0.770407	−	0.637553i	$-0.779947\pi$
$971$	−48.0131	−1.54081	−0.770407	+	0.637553i	$0.779947\pi$
$972$	3.75431	0.120420
$973$	−28.0030	−0.897734
$974$	29.0860	0.931977
$975$	9.24847	0.296188
$976$	33.0248	1.05710
$977$	34.8560	1.11514	0.557571	−	0.830129i	$-0.311733\pi$
$977$	34.8560	1.11514	0.557571	+	0.830129i	$0.311733\pi$
$978$	72.1408	2.30681
$979$	−53.2626	−1.70228
$980$	−0.216714	−0.00692269
$981$	50.8791	1.62444
$982$	−12.9344	−0.412752
$983$	25.6787	0.819023	0.409512	−	0.912305i	$-0.365699\pi$
$983$	25.6787	0.819023	0.409512	+	0.912305i	$0.365699\pi$
$984$	41.5077	1.32322
$985$	5.98403	0.190667
$986$	−3.67587	−0.117063
$987$	−75.3169	−2.39736
$988$	0	0
$989$	1.57055	0.0499406
$990$	50.4348	1.60292
$991$	−41.7630	−1.32665	−0.663323	−	0.748333i	$-0.730855\pi$
$991$	−41.7630	−1.32665	−0.663323	+	0.748333i	$0.730855\pi$
$992$	0.616839	0.0195846
$993$	93.0156	2.95176
$994$	3.14033	0.0996053
$995$	7.76803	0.246263
$996$	3.07631	0.0974767
$997$	49.7927	1.57695	0.788475	−	0.615067i	$-0.210871\pi$
$997$	49.7927	1.57695	0.788475	+	0.615067i	$0.210871\pi$
$998$	−47.1113	−1.49128
$999$	27.7621	0.878355

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.a.q.1.3	✓	6
5.4	even	2		9025.2.a.ca.1.4		6
19.18	odd	2		1805.2.a.r.1.4	yes	6
95.94	odd	2		9025.2.a.bq.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1805.2.a.q.1.3	✓	6	1.1	even	1	trivial
1805.2.a.r.1.4	yes	6	19.18	odd	2
9025.2.a.bq.1.3		6	95.94	odd	2
9025.2.a.ca.1.4		6	5.4	even	2

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:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1805.a (trivial)

\(f(q)\)	\(=\)	\(q-1.38913 q^{2} -3.31798 q^{3} -0.0703236 q^{4} -1.00000 q^{5} +4.60910 q^{6} -1.97948 q^{7} +2.87594 q^{8} +8.00899 q^{9} +O(q^{10})\)	\(q-1.38913 q^{2} -3.31798 q^{3} -0.0703236 q^{4} -1.00000 q^{5} +4.60910 q^{6} -1.97948 q^{7} +2.87594 q^{8} +8.00899 q^{9} +1.38913 q^{10} +4.53325 q^{11} +0.233332 q^{12} -2.78738 q^{13} +2.74975 q^{14} +3.31798 q^{15} -3.85441 q^{16} +0.944440 q^{17} -11.1255 q^{18} +0.0703236 q^{20} +6.56786 q^{21} -6.29727 q^{22} +6.80836 q^{23} -9.54233 q^{24} +1.00000 q^{25} +3.87203 q^{26} -16.6197 q^{27} +0.139204 q^{28} +2.80184 q^{29} -4.60910 q^{30} -1.55131 q^{31} -0.397624 q^{32} -15.0412 q^{33} -1.31195 q^{34} +1.97948 q^{35} -0.563221 q^{36} -1.67043 q^{37} +9.24847 q^{39} -2.87594 q^{40} -4.34985 q^{41} -9.12360 q^{42} +0.230680 q^{43} -0.318795 q^{44} -8.00899 q^{45} -9.45768 q^{46} -11.4675 q^{47} +12.7888 q^{48} -3.08167 q^{49} -1.38913 q^{50} -3.13363 q^{51} +0.196019 q^{52} -1.87412 q^{53} +23.0869 q^{54} -4.53325 q^{55} -5.69286 q^{56} -3.89211 q^{58} +13.4632 q^{59} -0.233332 q^{60} -8.56805 q^{61} +2.15497 q^{62} -15.8536 q^{63} +8.26117 q^{64} +2.78738 q^{65} +20.8942 q^{66} +3.50898 q^{67} -0.0664164 q^{68} -22.5900 q^{69} -2.74975 q^{70} +1.14205 q^{71} +23.0334 q^{72} -8.60896 q^{73} +2.32044 q^{74} -3.31798 q^{75} -8.97346 q^{77} -12.8473 q^{78} +3.70628 q^{79} +3.85441 q^{80} +31.1170 q^{81} +6.04250 q^{82} +13.1842 q^{83} -0.461876 q^{84} -0.944440 q^{85} -0.320444 q^{86} -9.29644 q^{87} +13.0374 q^{88} -11.7493 q^{89} +11.1255 q^{90} +5.51755 q^{91} -0.478788 q^{92} +5.14722 q^{93} +15.9298 q^{94} +1.31931 q^{96} +4.65308 q^{97} +4.28084 q^{98} +36.3068 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 4 q^{3} + 8 q^{4} - 6 q^{5} + 8 q^{6} + 7 q^{7} + 10 q^{9}+O(q^{10}) \) 6 * q - 2 * q^2 - 4 * q^3 + 8 * q^4 - 6 * q^5 + 8 * q^6 + 7 * q^7 + 10 * q^9	\( 6 q - 2 q^{2} - 4 q^{3} + 8 q^{4} - 6 q^{5} + 8 q^{6} + 7 q^{7} + 10 q^{9} + 2 q^{10} + 15 q^{11} + 20 q^{12} - 6 q^{13} - 20 q^{14} + 4 q^{15} + 20 q^{16} + 5 q^{17} + 8 q^{18} - 8 q^{20} - 7 q^{21} - 14 q^{22} + 18 q^{24} + 6 q^{25} - 22 q^{26} - 28 q^{27} + 10 q^{28} + 20 q^{29} - 8 q^{30} - 12 q^{31} + 8 q^{32} - q^{33} - 7 q^{35} - 14 q^{36} - 20 q^{37} + 16 q^{39} - 8 q^{41} - 30 q^{42} + 27 q^{43} + 46 q^{44} - 10 q^{45} - 16 q^{46} - 8 q^{47} + 24 q^{48} + 11 q^{49} - 2 q^{50} + 11 q^{51} - 4 q^{52} - 19 q^{53} + 30 q^{54} - 15 q^{55} - 62 q^{56} + 20 q^{58} + 41 q^{59} - 20 q^{60} + 6 q^{61} - 30 q^{62} - 18 q^{63} + 48 q^{64} + 6 q^{65} + 46 q^{66} + 15 q^{67} - 14 q^{68} + 10 q^{69} + 20 q^{70} - 2 q^{71} + 68 q^{72} + 8 q^{73} + 2 q^{74} - 4 q^{75} + 21 q^{77} - 46 q^{78} - 18 q^{79} - 20 q^{80} + 50 q^{81} - 18 q^{82} - 10 q^{83} - 4 q^{84} - 5 q^{85} + 10 q^{86} - 14 q^{87} + 52 q^{88} - 17 q^{89} - 8 q^{90} + 23 q^{91} + 28 q^{92} + 10 q^{93} + 28 q^{94} + 26 q^{96} + 4 q^{97} - 50 q^{98} + 58 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 4 * q^3 + 8 * q^4 - 6 * q^5 + 8 * q^6 + 7 * q^7 + 10 * q^9 + 2 * q^10 + 15 * q^11 + 20 * q^12 - 6 * q^13 - 20 * q^14 + 4 * q^15 + 20 * q^16 + 5 * q^17 + 8 * q^18 - 8 * q^20 - 7 * q^21 - 14 * q^22 + 18 * q^24 + 6 * q^25 - 22 * q^26 - 28 * q^27 + 10 * q^28 + 20 * q^29 - 8 * q^30 - 12 * q^31 + 8 * q^32 - q^33 - 7 * q^35 - 14 * q^36 - 20 * q^37 + 16 * q^39 - 8 * q^41 - 30 * q^42 + 27 * q^43 + 46 * q^44 - 10 * q^45 - 16 * q^46 - 8 * q^47 + 24 * q^48 + 11 * q^49 - 2 * q^50 + 11 * q^51 - 4 * q^52 - 19 * q^53 + 30 * q^54 - 15 * q^55 - 62 * q^56 + 20 * q^58 + 41 * q^59 - 20 * q^60 + 6 * q^61 - 30 * q^62 - 18 * q^63 + 48 * q^64 + 6 * q^65 + 46 * q^66 + 15 * q^67 - 14 * q^68 + 10 * q^69 + 20 * q^70 - 2 * q^71 + 68 * q^72 + 8 * q^73 + 2 * q^74 - 4 * q^75 + 21 * q^77 - 46 * q^78 - 18 * q^79 - 20 * q^80 + 50 * q^81 - 18 * q^82 - 10 * q^83 - 4 * q^84 - 5 * q^85 + 10 * q^86 - 14 * q^87 + 52 * q^88 - 17 * q^89 - 8 * q^90 + 23 * q^91 + 28 * q^92 + 10 * q^93 + 28 * q^94 + 26 * q^96 + 4 * q^97 - 50 * q^98 + 58 * q^99

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