LMFDB - Embedded newform 6005.2.a.g.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6005,2,Mod(1,6005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6005, 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("6005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6005 = 5 \cdot 1201 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6005.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:	$47.9501664138$
Analytic rank:	$0$
Dimension:	$113$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	6005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.21162 q^{2} +0.635696 q^{3} +2.89127 q^{4} -1.00000 q^{5} -1.40592 q^{6} -2.43179 q^{7} -1.97116 q^{8} -2.59589 q^{9} +O(q^{10})$	\(q-2.21162 q^{2} +0.635696 q^{3} +2.89127 q^{4} -1.00000 q^{5} -1.40592 q^{6} -2.43179 q^{7} -1.97116 q^{8} -2.59589 q^{9} +2.21162 q^{10} +0.919331 q^{11} +1.83797 q^{12} -6.48454 q^{13} +5.37820 q^{14} -0.635696 q^{15} -1.42309 q^{16} -4.96365 q^{17} +5.74113 q^{18} +6.76940 q^{19} -2.89127 q^{20} -1.54588 q^{21} -2.03321 q^{22} -6.55458 q^{23} -1.25306 q^{24} +1.00000 q^{25} +14.3414 q^{26} -3.55729 q^{27} -7.03097 q^{28} -0.813970 q^{29} +1.40592 q^{30} +5.48133 q^{31} +7.08965 q^{32} +0.584416 q^{33} +10.9777 q^{34} +2.43179 q^{35} -7.50543 q^{36} -9.59699 q^{37} -14.9713 q^{38} -4.12220 q^{39} +1.97116 q^{40} -2.10271 q^{41} +3.41890 q^{42} -2.89910 q^{43} +2.65804 q^{44} +2.59589 q^{45} +14.4963 q^{46} -4.09097 q^{47} -0.904651 q^{48} -1.08640 q^{49} -2.21162 q^{50} -3.15537 q^{51} -18.7486 q^{52} -2.94884 q^{53} +7.86738 q^{54} -0.919331 q^{55} +4.79344 q^{56} +4.30328 q^{57} +1.80019 q^{58} +0.485840 q^{59} -1.83797 q^{60} -11.5261 q^{61} -12.1226 q^{62} +6.31266 q^{63} -12.8335 q^{64} +6.48454 q^{65} -1.29251 q^{66} +0.598603 q^{67} -14.3513 q^{68} -4.16673 q^{69} -5.37820 q^{70} -2.24024 q^{71} +5.11691 q^{72} +6.45167 q^{73} +21.2249 q^{74} +0.635696 q^{75} +19.5722 q^{76} -2.23562 q^{77} +9.11675 q^{78} -15.3698 q^{79} +1.42309 q^{80} +5.52631 q^{81} +4.65041 q^{82} -11.6899 q^{83} -4.46956 q^{84} +4.96365 q^{85} +6.41170 q^{86} -0.517438 q^{87} -1.81215 q^{88} -11.5903 q^{89} -5.74113 q^{90} +15.7690 q^{91} -18.9511 q^{92} +3.48446 q^{93} +9.04768 q^{94} -6.76940 q^{95} +4.50686 q^{96} +14.2241 q^{97} +2.40270 q^{98} -2.38648 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 113 q - 3 q^{2} + 6 q^{3} + 141 q^{4} - 113 q^{5} + 7 q^{6} + 7 q^{7} - 12 q^{8} + 141 q^{9}+O(q^{10}) $ 113 * q - 3 * q^2 + 6 * q^3 + 141 * q^4 - 113 * q^5 + 7 * q^6 + 7 * q^7 - 12 * q^8 + 141 * q^9	\( 113 q - 3 q^{2} + 6 q^{3} + 141 q^{4} - 113 q^{5} + 7 q^{6} + 7 q^{7} - 12 q^{8} + 141 q^{9} + 3 q^{10} + 38 q^{11} - 4 q^{12} + 17 q^{13} + 23 q^{14} - 6 q^{15} + 193 q^{16} - 11 q^{17} - 3 q^{18} + 76 q^{19} - 141 q^{20} + 19 q^{21} + 41 q^{22} - 28 q^{23} + 29 q^{24} + 113 q^{25} + 21 q^{26} + 18 q^{27} + 29 q^{28} + 24 q^{29} - 7 q^{30} + 59 q^{31} - 22 q^{32} + 3 q^{33} + 55 q^{34} - 7 q^{35} + 232 q^{36} + 41 q^{37} - 6 q^{38} + 55 q^{39} + 12 q^{40} + 24 q^{41} + 17 q^{42} + 136 q^{43} + 85 q^{44} - 141 q^{45} + 84 q^{46} - 91 q^{47} - 19 q^{48} + 198 q^{49} - 3 q^{50} + 97 q^{51} + 45 q^{52} + 9 q^{53} + 54 q^{54} - 38 q^{55} + 98 q^{56} + 22 q^{57} + 69 q^{58} + 59 q^{59} + 4 q^{60} + 51 q^{61} - 30 q^{62} - 22 q^{63} + 298 q^{64} - 17 q^{65} + 76 q^{66} + 201 q^{67} - 34 q^{68} + 42 q^{69} - 23 q^{70} + 69 q^{71} - 7 q^{72} + 30 q^{73} + 35 q^{74} + 6 q^{75} + 170 q^{76} - 37 q^{77} - 11 q^{78} + 143 q^{79} - 193 q^{80} + 197 q^{81} + 55 q^{82} - 15 q^{83} + 83 q^{84} + 11 q^{85} + 78 q^{86} - 51 q^{87} + 113 q^{88} + 53 q^{89} + 3 q^{90} + 217 q^{91} - 40 q^{92} + 36 q^{93} + 81 q^{94} - 76 q^{95} + 66 q^{96} + 63 q^{97} - 62 q^{98} + 184 q^{99}+O(q^{100}) \) 113 * q - 3 * q^2 + 6 * q^3 + 141 * q^4 - 113 * q^5 + 7 * q^6 + 7 * q^7 - 12 * q^8 + 141 * q^9 + 3 * q^10 + 38 * q^11 - 4 * q^12 + 17 * q^13 + 23 * q^14 - 6 * q^15 + 193 * q^16 - 11 * q^17 - 3 * q^18 + 76 * q^19 - 141 * q^20 + 19 * q^21 + 41 * q^22 - 28 * q^23 + 29 * q^24 + 113 * q^25 + 21 * q^26 + 18 * q^27 + 29 * q^28 + 24 * q^29 - 7 * q^30 + 59 * q^31 - 22 * q^32 + 3 * q^33 + 55 * q^34 - 7 * q^35 + 232 * q^36 + 41 * q^37 - 6 * q^38 + 55 * q^39 + 12 * q^40 + 24 * q^41 + 17 * q^42 + 136 * q^43 + 85 * q^44 - 141 * q^45 + 84 * q^46 - 91 * q^47 - 19 * q^48 + 198 * q^49 - 3 * q^50 + 97 * q^51 + 45 * q^52 + 9 * q^53 + 54 * q^54 - 38 * q^55 + 98 * q^56 + 22 * q^57 + 69 * q^58 + 59 * q^59 + 4 * q^60 + 51 * q^61 - 30 * q^62 - 22 * q^63 + 298 * q^64 - 17 * q^65 + 76 * q^66 + 201 * q^67 - 34 * q^68 + 42 * q^69 - 23 * q^70 + 69 * q^71 - 7 * q^72 + 30 * q^73 + 35 * q^74 + 6 * q^75 + 170 * q^76 - 37 * q^77 - 11 * q^78 + 143 * q^79 - 193 * q^80 + 197 * q^81 + 55 * q^82 - 15 * q^83 + 83 * q^84 + 11 * q^85 + 78 * q^86 - 51 * q^87 + 113 * q^88 + 53 * q^89 + 3 * q^90 + 217 * q^91 - 40 * q^92 + 36 * q^93 + 81 * q^94 - 76 * q^95 + 66 * q^96 + 63 * q^97 - 62 * q^98 + 184 * 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 $

$2$	−2.21162	−1.56385	−0.781927	−	0.623371i	$-0.785763\pi$
$2$	−2.21162	−1.56385	−0.781927	+	0.623371i	$0.785763\pi$
$3$	0.635696	0.367020	0.183510	−	0.983018i	$-0.441254\pi$
$3$	0.635696	0.367020	0.183510	+	0.983018i	$0.441254\pi$
$4$	2.89127	1.44564
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.40592	−0.573965
$7$	−2.43179	−0.919130	−0.459565	−	0.888144i	$-0.651995\pi$
$7$	−2.43179	−0.919130	−0.459565	+	0.888144i	$0.651995\pi$
$8$	−1.97116	−0.696910
$9$	−2.59589	−0.865297
$10$	2.21162	0.699376
$11$	0.919331	0.277189	0.138594	−	0.990349i	$-0.455742\pi$
$11$	0.919331	0.277189	0.138594	+	0.990349i	$0.455742\pi$
$12$	1.83797	0.530577
$13$	−6.48454	−1.79849	−0.899244	−	0.437448i	$-0.855882\pi$
$13$	−6.48454	−1.79849	−0.899244	+	0.437448i	$0.855882\pi$
$14$	5.37820	1.43738
$15$	−0.635696	−0.164136
$16$	−1.42309	−0.355772
$17$	−4.96365	−1.20386	−0.601931	−	0.798548i	$-0.705602\pi$
$17$	−4.96365	−1.20386	−0.601931	+	0.798548i	$0.705602\pi$
$18$	5.74113	1.35320
$19$	6.76940	1.55301	0.776503	−	0.630113i	$-0.216992\pi$
$19$	6.76940	1.55301	0.776503	+	0.630113i	$0.216992\pi$
$20$	−2.89127	−0.646508
$21$	−1.54588	−0.337339
$22$	−2.03321	−0.433483
$23$	−6.55458	−1.36673	−0.683363	−	0.730079i	$-0.739483\pi$
$23$	−6.55458	−1.36673	−0.683363	+	0.730079i	$0.739483\pi$
$24$	−1.25306	−0.255780
$25$	1.00000	0.200000
$26$	14.3414	2.81257
$27$	−3.55729	−0.684600
$28$	−7.03097	−1.32873
$29$	−0.813970	−0.151150	−0.0755752	−	0.997140i	$-0.524079\pi$
$29$	−0.813970	−0.151150	−0.0755752	+	0.997140i	$0.524079\pi$
$30$	1.40592	0.256685
$31$	5.48133	0.984475	0.492238	−	0.870461i	$-0.336179\pi$
$31$	5.48133	0.984475	0.492238	+	0.870461i	$0.336179\pi$
$32$	7.08965	1.25328
$33$	0.584416	0.101734
$34$	10.9777	1.88266
$35$	2.43179	0.411048
$36$	−7.50543	−1.25090
$37$	−9.59699	−1.57774	−0.788868	−	0.614563i	$-0.789333\pi$
$37$	−9.59699	−1.57774	−0.788868	+	0.614563i	$0.789333\pi$
$38$	−14.9713	−2.42867
$39$	−4.12220	−0.660080
$40$	1.97116	0.311668
$41$	−2.10271	−0.328389	−0.164194	−	0.986428i	$-0.552502\pi$
$41$	−2.10271	−0.328389	−0.164194	+	0.986428i	$0.552502\pi$
$42$	3.41890	0.527548
$43$	−2.89910	−0.442108	−0.221054	−	0.975262i	$-0.570950\pi$
$43$	−2.89910	−0.442108	−0.221054	+	0.975262i	$0.570950\pi$
$44$	2.65804	0.400714
$45$	2.59589	0.386972
$46$	14.4963	2.13736
$47$	−4.09097	−0.596729	−0.298365	−	0.954452i	$-0.596441\pi$
$47$	−4.09097	−0.596729	−0.298365	+	0.954452i	$0.596441\pi$
$48$	−0.904651	−0.130575
$49$	−1.08640	−0.155200
$50$	−2.21162	−0.312771
$51$	−3.15537	−0.441841
$52$	−18.7486	−2.59996
$53$	−2.94884	−0.405054	−0.202527	−	0.979277i	$-0.564915\pi$
$53$	−2.94884	−0.405054	−0.202527	+	0.979277i	$0.564915\pi$
$54$	7.86738	1.07061
$55$	−0.919331	−0.123963
$56$	4.79344	0.640551
$57$	4.30328	0.569984
$58$	1.80019	0.236377
$59$	0.485840	0.0632510	0.0316255	−	0.999500i	$-0.489932\pi$
$59$	0.485840	0.0632510	0.0316255	+	0.999500i	$0.489932\pi$
$60$	−1.83797	−0.237281
$61$	−11.5261	−1.47576	−0.737881	−	0.674931i	$-0.764173\pi$
$61$	−11.5261	−1.47576	−0.737881	+	0.674931i	$0.764173\pi$
$62$	−12.1226	−1.53957
$63$	6.31266	0.795320
$64$	−12.8335	−1.60418
$65$	6.48454	0.804308
$66$	−1.29251	−0.159097
$67$	0.598603	0.0731309	0.0365655	−	0.999331i	$-0.488358\pi$
$67$	0.598603	0.0731309	0.0365655	+	0.999331i	$0.488358\pi$
$68$	−14.3513	−1.74035
$69$	−4.16673	−0.501615
$70$	−5.37820	−0.642818
$71$	−2.24024	−0.265868	−0.132934	−	0.991125i	$-0.542440\pi$
$71$	−2.24024	−0.265868	−0.132934	+	0.991125i	$0.542440\pi$
$72$	5.11691	0.603034
$73$	6.45167	0.755110	0.377555	−	0.925987i	$-0.376765\pi$
$73$	6.45167	0.755110	0.377555	+	0.925987i	$0.376765\pi$
$74$	21.2249	2.46735
$75$	0.635696	0.0734039
$76$	19.5722	2.24508
$77$	−2.23562	−0.254773
$78$	9.11675	1.03227
$79$	−15.3698	−1.72924	−0.864621	−	0.502425i	$-0.832441\pi$
$79$	−15.3698	−1.72924	−0.864621	+	0.502425i	$0.832441\pi$
$80$	1.42309	0.159106
$81$	5.52631	0.614035
$82$	4.65041	0.513552
$83$	−11.6899	−1.28313	−0.641565	−	0.767069i	$-0.721714\pi$
$83$	−11.6899	−1.28313	−0.641565	+	0.767069i	$0.721714\pi$
$84$	−4.46956	−0.487669
$85$	4.96365	0.538383
$86$	6.41170	0.691392
$87$	−0.517438	−0.0554752
$88$	−1.81215	−0.193176
$89$	−11.5903	−1.22857	−0.614285	−	0.789084i	$-0.710555\pi$
$89$	−11.5903	−1.22857	−0.614285	+	0.789084i	$0.710555\pi$
$90$	−5.74113	−0.605168
$91$	15.7690	1.65304
$92$	−18.9511	−1.97579
$93$	3.48446	0.361322
$94$	9.04768	0.933197
$95$	−6.76940	−0.694525
$96$	4.50686	0.459980
$97$	14.2241	1.44424	0.722121	−	0.691767i	$-0.243167\pi$
$97$	14.2241	1.44424	0.722121	+	0.691767i	$0.243167\pi$
$98$	2.40270	0.242709
$99$	−2.38648	−0.239851
$100$	2.89127	0.289127
$101$	16.1680	1.60877	0.804386	−	0.594107i	$-0.202495\pi$
$101$	16.1680	1.60877	0.804386	+	0.594107i	$0.202495\pi$
$102$	6.97849	0.690974
$103$	−11.6712	−1.15000	−0.574998	−	0.818155i	$-0.694997\pi$
$103$	−11.6712	−1.15000	−0.574998	+	0.818155i	$0.694997\pi$
$104$	12.7821	1.25338
$105$	1.54588	0.150862
$106$	6.52172	0.633446
$107$	5.03047	0.486314	0.243157	−	0.969987i	$-0.421817\pi$
$107$	5.03047	0.486314	0.243157	+	0.969987i	$0.421817\pi$
$108$	−10.2851	−0.989683
$109$	−5.50840	−0.527609	−0.263804	−	0.964576i	$-0.584977\pi$
$109$	−5.50840	−0.527609	−0.263804	+	0.964576i	$0.584977\pi$
$110$	2.03321	0.193859
$111$	−6.10078	−0.579060
$112$	3.46065	0.327001
$113$	−14.7441	−1.38701	−0.693504	−	0.720453i	$-0.743934\pi$
$113$	−14.7441	−1.38701	−0.693504	+	0.720453i	$0.743934\pi$
$114$	−9.51723	−0.891371
$115$	6.55458	0.611218
$116$	−2.35341	−0.218509
$117$	16.8331	1.55623
$118$	−1.07450	−0.0989153
$119$	12.0705	1.10651
$120$	1.25306	0.114388
$121$	−10.1548	−0.923166
$122$	25.4913	2.30788
$123$	−1.33669	−0.120525
$124$	15.8480	1.42319
$125$	−1.00000	−0.0894427
$126$	−13.9612	−1.24376
$127$	−2.46872	−0.219064	−0.109532	−	0.993983i	$-0.534935\pi$
$127$	−2.46872	−0.219064	−0.109532	+	0.993983i	$0.534935\pi$
$128$	14.2034	1.25542
$129$	−1.84294	−0.162262
$130$	−14.3414	−1.25782
$131$	−11.4764	−1.00270	−0.501350	−	0.865245i	$-0.667163\pi$
$131$	−11.4764	−1.00270	−0.501350	+	0.865245i	$0.667163\pi$
$132$	1.68970	0.147070
$133$	−16.4618	−1.42741
$134$	−1.32388	−0.114366
$135$	3.55729	0.306163
$136$	9.78414	0.838983
$137$	21.3975	1.82811	0.914055	−	0.405590i	$-0.132934\pi$
$137$	21.3975	1.82811	0.914055	+	0.405590i	$0.132934\pi$
$138$	9.21522	0.784452
$139$	−7.66945	−0.650515	−0.325257	−	0.945626i	$-0.605451\pi$
$139$	−7.66945	−0.650515	−0.325257	+	0.945626i	$0.605451\pi$
$140$	7.03097	0.594225
$141$	−2.60061	−0.219011
$142$	4.95457	0.415779
$143$	−5.96144	−0.498521
$144$	3.69418	0.307848
$145$	0.813970	0.0675965
$146$	−14.2686	−1.18088
$147$	−0.690619	−0.0569613
$148$	−27.7475	−2.28083
$149$	4.25014	0.348185	0.174093	−	0.984729i	$-0.444301\pi$
$149$	4.25014	0.348185	0.174093	+	0.984729i	$0.444301\pi$
$150$	−1.40592	−0.114793
$151$	−16.0938	−1.30969	−0.654847	−	0.755762i	$-0.727267\pi$
$151$	−16.0938	−1.30969	−0.654847	+	0.755762i	$0.727267\pi$
$152$	−13.3436	−1.08231
$153$	12.8851	1.04170
$154$	4.94435	0.398427
$155$	−5.48133	−0.440271
$156$	−11.9184	−0.954236
$157$	14.8895	1.18832	0.594158	−	0.804349i	$-0.297486\pi$
$157$	14.8895	1.18832	0.594158	+	0.804349i	$0.297486\pi$
$158$	33.9923	2.70428
$159$	−1.87457	−0.148663
$160$	−7.08965	−0.560486
$161$	15.9394	1.25620
$162$	−12.2221	−0.960260
$163$	5.76416	0.451484	0.225742	−	0.974187i	$-0.427519\pi$
$163$	5.76416	0.451484	0.225742	+	0.974187i	$0.427519\pi$
$164$	−6.07952	−0.474731
$165$	−0.584416	−0.0454967
$166$	25.8536	2.00663
$167$	7.65160	0.592099	0.296049	−	0.955173i	$-0.404331\pi$
$167$	7.65160	0.592099	0.296049	+	0.955173i	$0.404331\pi$
$168$	3.04718	0.235095
$169$	29.0492	2.23456
$170$	−10.9777	−0.841952
$171$	−17.5726	−1.34381
$172$	−8.38208	−0.639127
$173$	−8.32987	−0.633308	−0.316654	−	0.948541i	$-0.602559\pi$
$173$	−8.32987	−0.633308	−0.316654	+	0.948541i	$0.602559\pi$
$174$	1.14438	0.0867550
$175$	−2.43179	−0.183826
$176$	−1.30829	−0.0986160
$177$	0.308847	0.0232144
$178$	25.6334	1.92130
$179$	−8.79463	−0.657342	−0.328671	−	0.944445i	$-0.606601\pi$
$179$	−8.79463	−0.657342	−0.328671	+	0.944445i	$0.606601\pi$
$180$	7.50543	0.559421
$181$	24.5535	1.82505	0.912523	−	0.409025i	$-0.134131\pi$
$181$	24.5535	1.82505	0.912523	+	0.409025i	$0.134131\pi$
$182$	−34.8752	−2.58512
$183$	−7.32708	−0.541634
$184$	12.9201	0.952484
$185$	9.59699	0.705585
$186$	−7.70631	−0.565054
$187$	−4.56324	−0.333697
$188$	−11.8281	−0.862653
$189$	8.65058	0.629237
$190$	14.9713	1.08614
$191$	−12.9355	−0.935977	−0.467989	−	0.883735i	$-0.655021\pi$
$191$	−12.9355	−0.935977	−0.467989	+	0.883735i	$0.655021\pi$
$192$	−8.15818	−0.588766
$193$	22.0612	1.58800	0.794000	−	0.607918i	$-0.207995\pi$
$193$	22.0612	1.58800	0.794000	+	0.607918i	$0.207995\pi$
$194$	−31.4584	−2.25858
$195$	4.12220	0.295197
$196$	−3.14107	−0.224362
$197$	−16.0938	−1.14664	−0.573318	−	0.819333i	$-0.694344\pi$
$197$	−16.0938	−1.14664	−0.573318	+	0.819333i	$0.694344\pi$
$198$	5.27800	0.375091
$199$	−1.06077	−0.0751957	−0.0375978	−	0.999293i	$-0.511971\pi$
$199$	−1.06077	−0.0751957	−0.0375978	+	0.999293i	$0.511971\pi$
$200$	−1.97116	−0.139382
$201$	0.380530	0.0268405
$202$	−35.7574	−2.51588
$203$	1.97940	0.138927
$204$	−9.12305	−0.638741
$205$	2.10271	0.146860
$206$	25.8122	1.79842
$207$	17.0150	1.18262
$208$	9.22806	0.639851
$209$	6.22332	0.430476
$210$	−3.41890	−0.235927
$211$	19.5846	1.34826	0.674129	−	0.738614i	$-0.264519\pi$
$211$	19.5846	1.34826	0.674129	+	0.738614i	$0.264519\pi$
$212$	−8.52590	−0.585562
$213$	−1.42412	−0.0975788
$214$	−11.1255	−0.760523
$215$	2.89910	0.197717
$216$	7.01198	0.477105
$217$	−13.3294	−0.904861
$218$	12.1825	0.825102
$219$	4.10130	0.277140
$220$	−2.65804	−0.179205
$221$	32.1870	2.16513
$222$	13.4926	0.905565
$223$	20.6809	1.38490	0.692449	−	0.721467i	$-0.256532\pi$
$223$	20.6809	1.38490	0.692449	+	0.721467i	$0.256532\pi$
$224$	−17.2405	−1.15193
$225$	−2.59589	−0.173059
$226$	32.6084	2.16908
$227$	−12.3882	−0.822231	−0.411115	−	0.911583i	$-0.634861\pi$
$227$	−12.3882	−0.822231	−0.411115	+	0.911583i	$0.634861\pi$
$228$	12.4420	0.823989
$229$	24.1721	1.59734	0.798670	−	0.601769i	$-0.205537\pi$
$229$	24.1721	1.59734	0.798670	+	0.601769i	$0.205537\pi$
$230$	−14.4963	−0.955855
$231$	−1.42118	−0.0935065
$232$	1.60446	0.105338
$233$	−24.9338	−1.63347	−0.816734	−	0.577015i	$-0.804217\pi$
$233$	−24.9338	−1.63347	−0.816734	+	0.577015i	$0.804217\pi$
$234$	−37.2286	−2.43371
$235$	4.09097	0.266865
$236$	1.40470	0.0914380
$237$	−9.77055	−0.634665
$238$	−26.6955	−1.73041
$239$	13.3402	0.862903	0.431452	−	0.902136i	$-0.358002\pi$
$239$	13.3402	0.862903	0.431452	+	0.902136i	$0.358002\pi$
$240$	0.904651	0.0583950
$241$	−0.391065	−0.0251907	−0.0125953	−	0.999921i	$-0.504009\pi$
$241$	−0.391065	−0.0251907	−0.0125953	+	0.999921i	$0.504009\pi$
$242$	22.4586	1.44370
$243$	14.1849	0.909963
$244$	−33.3250	−2.13342
$245$	1.08640	0.0694074
$246$	2.95625	0.188484
$247$	−43.8964	−2.79306
$248$	−10.8046	−0.686090
$249$	−7.43121	−0.470934
$250$	2.21162	0.139875
$251$	1.29689	0.0818592	0.0409296	−	0.999162i	$-0.486968\pi$
$251$	1.29689	0.0818592	0.0409296	+	0.999162i	$0.486968\pi$
$252$	18.2516	1.14974
$253$	−6.02583	−0.378841
$254$	5.45988	0.342583
$255$	3.15537	0.197597
$256$	−5.74576	−0.359110
$257$	12.0077	0.749017	0.374509	−	0.927223i	$-0.377811\pi$
$257$	12.0077	0.749017	0.374509	+	0.927223i	$0.377811\pi$
$258$	4.07590	0.253754
$259$	23.3379	1.45014
$260$	18.7486	1.16274
$261$	2.11298	0.130790
$262$	25.3815	1.56808
$263$	2.95016	0.181915	0.0909573	−	0.995855i	$-0.471007\pi$
$263$	2.95016	0.181915	0.0909573	+	0.995855i	$0.471007\pi$
$264$	−1.15198	−0.0708992
$265$	2.94884	0.181146
$266$	36.4072	2.23227
$267$	−7.36792	−0.450909
$268$	1.73072	0.105721
$269$	−26.9707	−1.64443	−0.822216	−	0.569175i	$-0.807263\pi$
$269$	−26.9707	−1.64443	−0.822216	+	0.569175i	$0.807263\pi$
$270$	−7.86738	−0.478793
$271$	1.12056	0.0680690	0.0340345	−	0.999421i	$-0.489164\pi$
$271$	1.12056	0.0680690	0.0340345	+	0.999421i	$0.489164\pi$
$272$	7.06370	0.428300
$273$	10.0243	0.606699
$274$	−47.3231	−2.85890
$275$	0.919331	0.0554378
$276$	−12.0471	−0.725153
$277$	−17.9883	−1.08081	−0.540406	−	0.841404i	$-0.681729\pi$
$277$	−17.9883	−1.08081	−0.540406	+	0.841404i	$0.681729\pi$
$278$	16.9619	1.01731
$279$	−14.2289	−0.851863
$280$	−4.79344	−0.286463
$281$	0.831209	0.0495858	0.0247929	−	0.999693i	$-0.492107\pi$
$281$	0.831209	0.0495858	0.0247929	+	0.999693i	$0.492107\pi$
$282$	5.75158	0.342501
$283$	−13.1958	−0.784412	−0.392206	−	0.919877i	$-0.628288\pi$
$283$	−13.1958	−0.784412	−0.392206	+	0.919877i	$0.628288\pi$
$284$	−6.47716	−0.384349
$285$	−4.30328	−0.254904
$286$	13.1845	0.779613
$287$	5.11336	0.301832
$288$	−18.4039	−1.08446
$289$	7.63780	0.449283
$290$	−1.80019	−0.105711
$291$	9.04223	0.530065
$292$	18.6535	1.09162
$293$	17.3865	1.01573	0.507865	−	0.861437i	$-0.330435\pi$
$293$	17.3865	1.01573	0.507865	+	0.861437i	$0.330435\pi$
$294$	1.52739	0.0890791
$295$	−0.485840	−0.0282867
$296$	18.9172	1.09954
$297$	−3.27033	−0.189764
$298$	−9.39971	−0.544510
$299$	42.5035	2.45804
$300$	1.83797	0.106115
$301$	7.04999	0.406355
$302$	35.5934	2.04817
$303$	10.2779	0.590451
$304$	−9.63344	−0.552516
$305$	11.5261	0.659981
$306$	−28.4969	−1.62906
$307$	22.3653	1.27645	0.638227	−	0.769848i	$-0.279668\pi$
$307$	22.3653	1.27645	0.638227	+	0.769848i	$0.279668\pi$
$308$	−6.46379	−0.368309
$309$	−7.41933	−0.422071
$310$	12.1226	0.688519
$311$	−19.9318	−1.13023	−0.565115	−	0.825012i	$-0.691168\pi$
$311$	−19.9318	−1.13023	−0.565115	+	0.825012i	$0.691168\pi$
$312$	8.12551	0.460016
$313$	−26.5132	−1.49861	−0.749307	−	0.662222i	$-0.769613\pi$
$313$	−26.5132	−1.49861	−0.749307	+	0.662222i	$0.769613\pi$
$314$	−32.9301	−1.85835
$315$	−6.31266	−0.355678
$316$	−44.4384	−2.49985
$317$	−17.1534	−0.963431	−0.481716	−	0.876328i	$-0.659986\pi$
$317$	−17.1534	−0.963431	−0.481716	+	0.876328i	$0.659986\pi$
$318$	4.14584	0.232487
$319$	−0.748308	−0.0418972
$320$	12.8335	0.717412
$321$	3.19785	0.178487
$322$	−35.2519	−1.96451
$323$	−33.6009	−1.86960
$324$	15.9781	0.887671
$325$	−6.48454	−0.359697
$326$	−12.7481	−0.706055
$327$	−3.50167	−0.193643
$328$	4.14478	0.228857
$329$	9.94838	0.548472
$330$	1.29251	0.0711501
$331$	−5.79992	−0.318793	−0.159396	−	0.987215i	$-0.550955\pi$
$331$	−5.79992	−0.318793	−0.159396	+	0.987215i	$0.550955\pi$
$332$	−33.7986	−1.85494
$333$	24.9127	1.36521
$334$	−16.9225	−0.925955
$335$	−0.598603	−0.0327052
$336$	2.19992	0.120016
$337$	11.0967	0.604475	0.302238	−	0.953233i	$-0.402266\pi$
$337$	11.0967	0.604475	0.302238	+	0.953233i	$0.402266\pi$
$338$	−64.2460	−3.49452
$339$	−9.37276	−0.509059
$340$	14.3513	0.778306
$341$	5.03915	0.272885
$342$	38.8640	2.10152
$343$	19.6644	1.06178
$344$	5.71458	0.308109
$345$	4.16673	0.224329
$346$	18.4225	0.990401
$347$	28.4666	1.52817	0.764084	−	0.645117i	$-0.223191\pi$
$347$	28.4666	1.52817	0.764084	+	0.645117i	$0.223191\pi$
$348$	−1.49605	−0.0801969
$349$	12.3833	0.662863	0.331431	−	0.943479i	$-0.392468\pi$
$349$	12.3833	0.662863	0.331431	+	0.943479i	$0.392468\pi$
$350$	5.37820	0.287477
$351$	23.0674	1.23125
$352$	6.51774	0.347396
$353$	3.88058	0.206543	0.103271	−	0.994653i	$-0.467069\pi$
$353$	3.88058	0.206543	0.103271	+	0.994653i	$0.467069\pi$
$354$	−0.683053	−0.0363038
$355$	2.24024	0.118900
$356$	−33.5107	−1.77607
$357$	7.67321	0.406109
$358$	19.4504	1.02799
$359$	−21.2297	−1.12046	−0.560231	−	0.828337i	$-0.689288\pi$
$359$	−21.2297	−1.12046	−0.560231	+	0.828337i	$0.689288\pi$
$360$	−5.11691	−0.269685
$361$	26.8247	1.41183
$362$	−54.3030	−2.85410
$363$	−6.45539	−0.338820
$364$	45.5926	2.38970
$365$	−6.45167	−0.337696
$366$	16.2047	0.847035
$367$	−9.38416	−0.489849	−0.244925	−	0.969542i	$-0.578763\pi$
$367$	−9.38416	−0.489849	−0.244925	+	0.969542i	$0.578763\pi$
$368$	9.32774	0.486242
$369$	5.45841	0.284154
$370$	−21.2249	−1.10343
$371$	7.17096	0.372298
$372$	10.0745	0.522340
$373$	−3.45476	−0.178881	−0.0894405	−	0.995992i	$-0.528508\pi$
$373$	−3.45476	−0.178881	−0.0894405	+	0.995992i	$0.528508\pi$
$374$	10.0922	0.521853
$375$	−0.635696	−0.0328272
$376$	8.06395	0.415866
$377$	5.27822	0.271842
$378$	−19.1318	−0.984034
$379$	−10.0837	−0.517965	−0.258983	−	0.965882i	$-0.583387\pi$
$379$	−10.0837	−0.517965	−0.258983	+	0.965882i	$0.583387\pi$
$380$	−19.5722	−1.00403
$381$	−1.56936	−0.0804007
$382$	28.6084	1.46373
$383$	−8.54641	−0.436701	−0.218351	−	0.975870i	$-0.570068\pi$
$383$	−8.54641	−0.436701	−0.218351	+	0.975870i	$0.570068\pi$
$384$	9.02908	0.460763
$385$	2.23562	0.113938
$386$	−48.7910	−2.48340
$387$	7.52573	0.382555
$388$	41.1258	2.08785
$389$	−15.5908	−0.790485	−0.395242	−	0.918577i	$-0.629339\pi$
$389$	−15.5908	−0.790485	−0.395242	+	0.918577i	$0.629339\pi$
$390$	−9.11675	−0.461644
$391$	32.5346	1.64535
$392$	2.14146	0.108160
$393$	−7.29552	−0.368010
$394$	35.5934	1.79317
$395$	15.3698	0.773340
$396$	−6.89997	−0.346737
$397$	−7.56246	−0.379549	−0.189775	−	0.981828i	$-0.560776\pi$
$397$	−7.56246	−0.379549	−0.189775	+	0.981828i	$0.560776\pi$
$398$	2.34601	0.117595
$399$	−10.4647	−0.523889
$400$	−1.42309	−0.0711544
$401$	2.08831	0.104285	0.0521426	−	0.998640i	$-0.483395\pi$
$401$	2.08831	0.104285	0.0521426	+	0.998640i	$0.483395\pi$
$402$	−0.841588	−0.0419746
$403$	−35.5439	−1.77057
$404$	46.7460	2.32570
$405$	−5.52631	−0.274605
$406$	−4.37769	−0.217261
$407$	−8.82282	−0.437331
$408$	6.21974	0.307923
$409$	25.6601	1.26881	0.634404	−	0.773001i	$-0.281245\pi$
$409$	25.6601	1.26881	0.634404	+	0.773001i	$0.281245\pi$
$410$	−4.65041	−0.229667
$411$	13.6023	0.670952
$412$	−33.7446	−1.66248
$413$	−1.18146	−0.0581359
$414$	−37.6307	−1.84945
$415$	11.6899	0.573833
$416$	−45.9731	−2.25402
$417$	−4.87544	−0.238752
$418$	−13.7636	−0.673201
$419$	−20.6241	−1.00756	−0.503778	−	0.863833i	$-0.668057\pi$
$419$	−20.6241	−1.00756	−0.503778	+	0.863833i	$0.668057\pi$
$420$	4.46956	0.218092
$421$	25.3843	1.23716	0.618579	−	0.785723i	$-0.287709\pi$
$421$	25.3843	1.23716	0.618579	+	0.785723i	$0.287709\pi$
$422$	−43.3137	−2.10848
$423$	10.6197	0.516348
$424$	5.81263	0.282286
$425$	−4.96365	−0.240772
$426$	3.14961	0.152599
$427$	28.0290	1.35642
$428$	14.5445	0.703033
$429$	−3.78967	−0.182967
$430$	−6.41170	−0.309200
$431$	25.8447	1.24489	0.622447	−	0.782662i	$-0.286138\pi$
$431$	25.8447	1.24489	0.622447	+	0.782662i	$0.286138\pi$
$432$	5.06233	0.243561
$433$	11.9911	0.576258	0.288129	−	0.957592i	$-0.406967\pi$
$433$	11.9911	0.576258	0.288129	+	0.957592i	$0.406967\pi$
$434$	29.4797	1.41507
$435$	0.517438	0.0248092
$436$	−15.9263	−0.762730
$437$	−44.3706	−2.12253
$438$	−9.07053	−0.433407
$439$	−23.9037	−1.14086	−0.570432	−	0.821345i	$-0.693224\pi$
$439$	−23.9037	−1.14086	−0.570432	+	0.821345i	$0.693224\pi$
$440$	1.81215	0.0863908
$441$	2.82017	0.134294
$442$	−71.1854	−3.38594
$443$	−3.90687	−0.185621	−0.0928105	−	0.995684i	$-0.529585\pi$
$443$	−3.90687	−0.185621	−0.0928105	+	0.995684i	$0.529585\pi$
$444$	−17.6390	−0.837110
$445$	11.5903	0.549433
$446$	−45.7384	−2.16578
$447$	2.70180	0.127791
$448$	31.2083	1.47445
$449$	3.20647	0.151322	0.0756612	−	0.997134i	$-0.475893\pi$
$449$	3.20647	0.151322	0.0756612	+	0.997134i	$0.475893\pi$
$450$	5.74113	0.270639
$451$	−1.93309	−0.0910257
$452$	−42.6292	−2.00511
$453$	−10.2308	−0.480683
$454$	27.3979	1.28585
$455$	−15.7690	−0.739264
$456$	−8.48245	−0.397227
$457$	−13.3253	−0.623330	−0.311665	−	0.950192i	$-0.600887\pi$
$457$	−13.3253	−0.623330	−0.311665	+	0.950192i	$0.600887\pi$
$458$	−53.4597	−2.49801
$459$	17.6571	0.824164
$460$	18.9511	0.883599
$461$	−32.2530	−1.50217	−0.751085	−	0.660205i	$-0.770469\pi$
$461$	−32.2530	−1.50217	−0.751085	+	0.660205i	$0.770469\pi$
$462$	3.14310	0.146230
$463$	−36.3226	−1.68806	−0.844028	−	0.536299i	$-0.819822\pi$
$463$	−36.3226	−1.68806	−0.844028	+	0.536299i	$0.819822\pi$
$464$	1.15835	0.0537751
$465$	−3.48446	−0.161588
$466$	55.1441	2.55450
$467$	−31.7832	−1.47075	−0.735375	−	0.677660i	$-0.762994\pi$
$467$	−31.7832	−1.47075	−0.735375	+	0.677660i	$0.762994\pi$
$468$	48.6692	2.24974
$469$	−1.45568	−0.0672169
$470$	−9.04768	−0.417338
$471$	9.46523	0.436135
$472$	−0.957668	−0.0440803
$473$	−2.66523	−0.122547
$474$	21.6088	0.992523
$475$	6.76940	0.310601
$476$	34.8993	1.59960
$477$	7.65487	0.350492
$478$	−29.5034	−1.34945
$479$	−25.1126	−1.14742	−0.573712	−	0.819057i	$-0.694497\pi$
$479$	−25.1126	−1.14742	−0.573712	+	0.819057i	$0.694497\pi$
$480$	−4.50686	−0.205709
$481$	62.2321	2.83754
$482$	0.864888	0.0393946
$483$	10.1326	0.461049
$484$	−29.3604	−1.33456
$485$	−14.2241	−0.645885
$486$	−31.3717	−1.42305
$487$	41.6192	1.88595	0.942973	−	0.332869i	$-0.108017\pi$
$487$	41.6192	1.88595	0.942973	+	0.332869i	$0.108017\pi$
$488$	22.7197	1.02847
$489$	3.66426	0.165703
$490$	−2.40270	−0.108543
$491$	34.0256	1.53555	0.767776	−	0.640718i	$-0.221363\pi$
$491$	34.0256	1.53555	0.767776	+	0.640718i	$0.221363\pi$
$492$	−3.86473	−0.174235
$493$	4.04026	0.181964
$494$	97.0823	4.36794
$495$	2.38648	0.107264
$496$	−7.80040	−0.350248
$497$	5.44780	0.244367
$498$	16.4350	0.736471
$499$	−29.3012	−1.31170	−0.655852	−	0.754890i	$-0.727690\pi$
$499$	−29.3012	−1.31170	−0.655852	+	0.754890i	$0.727690\pi$
$500$	−2.89127	−0.129302
$501$	4.86410	0.217312
$502$	−2.86824	−0.128016
$503$	10.5247	0.469271	0.234635	−	0.972083i	$-0.424610\pi$
$503$	10.5247	0.469271	0.234635	+	0.972083i	$0.424610\pi$
$504$	−12.4433	−0.554267
$505$	−16.1680	−0.719465
$506$	13.3269	0.592451
$507$	18.4665	0.820126
$508$	−7.13775	−0.316686
$509$	−5.52735	−0.244995	−0.122498	−	0.992469i	$-0.539090\pi$
$509$	−5.52735	−0.244995	−0.122498	+	0.992469i	$0.539090\pi$
$510$	−6.97849	−0.309013
$511$	−15.6891	−0.694045
$512$	−15.6994	−0.693824
$513$	−24.0807	−1.06319
$514$	−26.5564	−1.17135
$515$	11.6712	0.514294
$516$	−5.32846	−0.234572
$517$	−3.76095	−0.165407
$518$	−51.6146	−2.26781
$519$	−5.29527	−0.232436
$520$	−12.7821	−0.560530
$521$	5.64107	0.247140	0.123570	−	0.992336i	$-0.460566\pi$
$521$	5.64107	0.247140	0.123570	+	0.992336i	$0.460566\pi$
$522$	−4.67311	−0.204536
$523$	−27.2602	−1.19200	−0.596002	−	0.802983i	$-0.703245\pi$
$523$	−27.2602	−1.19200	−0.596002	+	0.802983i	$0.703245\pi$
$524$	−33.1815	−1.44954
$525$	−1.54588	−0.0674677
$526$	−6.52464	−0.284488
$527$	−27.2074	−1.18517
$528$	−0.831674	−0.0361940
$529$	19.9626	0.867938
$530$	−6.52172	−0.283286
$531$	−1.26119	−0.0547309
$532$	−47.5954	−2.06352
$533$	13.6351	0.590603
$534$	16.2950	0.705156
$535$	−5.03047	−0.217486
$536$	−1.17994	−0.0509657
$537$	−5.59072	−0.241257
$538$	59.6490	2.57165
$539$	−0.998759	−0.0430196
$540$	10.2851	0.442600
$541$	42.6505	1.83369	0.916845	−	0.399244i	$-0.130727\pi$
$541$	42.6505	1.83369	0.916845	+	0.399244i	$0.130727\pi$
$542$	−2.47825	−0.106450
$543$	15.6086	0.669828
$544$	−35.1905	−1.50878
$545$	5.50840	0.235954
$546$	−22.1700	−0.948789
$547$	−14.4699	−0.618686	−0.309343	−	0.950951i	$-0.600109\pi$
$547$	−14.4699	−0.618686	−0.309343	+	0.950951i	$0.600109\pi$
$548$	61.8660	2.64278
$549$	29.9204	1.27697
$550$	−2.03321	−0.0866965
$551$	−5.51009	−0.234738
$552$	8.21328	0.349580
$553$	37.3762	1.58940
$554$	39.7833	1.69023
$555$	6.10078	0.258963
$556$	−22.1745	−0.940407
$557$	13.4912	0.571641	0.285821	−	0.958283i	$-0.407734\pi$
$557$	13.4912	0.571641	0.285821	+	0.958283i	$0.407734\pi$
$558$	31.4690	1.33219
$559$	18.7993	0.795126
$560$	−3.46065	−0.146239
$561$	−2.90083	−0.122473
$562$	−1.83832	−0.0775448
$563$	39.0604	1.64620	0.823100	−	0.567897i	$-0.192243\pi$
$563$	39.0604	1.64620	0.823100	+	0.567897i	$0.192243\pi$
$564$	−7.51908	−0.316611
$565$	14.7441	0.620288
$566$	29.1842	1.22670
$567$	−13.4388	−0.564378
$568$	4.41588	0.185286
$569$	−6.90068	−0.289292	−0.144646	−	0.989483i	$-0.546204\pi$
$569$	−6.90068	−0.289292	−0.144646	+	0.989483i	$0.546204\pi$
$570$	9.51723	0.398633
$571$	37.7271	1.57883	0.789415	−	0.613860i	$-0.210384\pi$
$571$	37.7271	1.57883	0.789415	+	0.613860i	$0.210384\pi$
$572$	−17.2361	−0.720679
$573$	−8.22303	−0.343522
$574$	−11.3088	−0.472021
$575$	−6.55458	−0.273345
$576$	33.3142	1.38809
$577$	30.9936	1.29028	0.645141	−	0.764064i	$-0.276799\pi$
$577$	30.9936	1.29028	0.645141	+	0.764064i	$0.276799\pi$
$578$	−16.8919	−0.702612
$579$	14.0242	0.582827
$580$	2.35341	0.0977200
$581$	28.4273	1.17936
$582$	−19.9980	−0.828944
$583$	−2.71096	−0.112277
$584$	−12.7173	−0.526244
$585$	−16.8331	−0.695965
$586$	−38.4523	−1.58845
$587$	−1.31555	−0.0542984	−0.0271492	−	0.999631i	$-0.508643\pi$
$587$	−1.31555	−0.0542984	−0.0271492	+	0.999631i	$0.508643\pi$
$588$	−1.99677	−0.0823453
$589$	37.1053	1.52890
$590$	1.07450	0.0442363
$591$	−10.2308	−0.420838
$592$	13.6574	0.561314
$593$	17.9958	0.738999	0.369499	−	0.929231i	$-0.379529\pi$
$593$	17.9958	0.738999	0.369499	+	0.929231i	$0.379529\pi$
$594$	7.23272	0.296762
$595$	−12.0705	−0.494844
$596$	12.2883	0.503349
$597$	−0.674325	−0.0275983
$598$	−94.0016	−3.84401
$599$	15.2768	0.624194	0.312097	−	0.950050i	$-0.398969\pi$
$599$	15.2768	0.624194	0.312097	+	0.950050i	$0.398969\pi$
$600$	−1.25306	−0.0511559
$601$	24.1756	0.986142	0.493071	−	0.869989i	$-0.335874\pi$
$601$	24.1756	0.986142	0.493071	+	0.869989i	$0.335874\pi$
$602$	−15.5919	−0.635479
$603$	−1.55391	−0.0632800
$604$	−46.5315	−1.89334
$605$	10.1548	0.412853
$606$	−22.7309	−0.923378
$607$	7.50834	0.304754	0.152377	−	0.988322i	$-0.451307\pi$
$607$	7.50834	0.304754	0.152377	+	0.988322i	$0.451307\pi$
$608$	47.9926	1.94636
$609$	1.25830	0.0509889
$610$	−25.4913	−1.03211
$611$	26.5280	1.07321
$612$	37.2543	1.50592
$613$	−27.8792	−1.12603	−0.563015	−	0.826446i	$-0.690359\pi$
$613$	−27.8792	−1.12603	−0.563015	+	0.826446i	$0.690359\pi$
$614$	−49.4636	−1.99619
$615$	1.33669	0.0539005
$616$	4.40676	0.177554
$617$	22.1700	0.892532	0.446266	−	0.894900i	$-0.352753\pi$
$617$	22.1700	0.892532	0.446266	+	0.894900i	$0.352753\pi$
$618$	16.4088	0.660057
$619$	16.3381	0.656683	0.328342	−	0.944559i	$-0.393510\pi$
$619$	16.3381	0.656683	0.328342	+	0.944559i	$0.393510\pi$
$620$	−15.8480	−0.636471
$621$	23.3165	0.935660
$622$	44.0817	1.76751
$623$	28.1852	1.12922
$624$	5.86625	0.234838
$625$	1.00000	0.0400000
$626$	58.6372	2.34361
$627$	3.95614	0.157993
$628$	43.0497	1.71787
$629$	47.6361	1.89938
$630$	13.9612	0.556228
$631$	−14.2868	−0.568749	−0.284375	−	0.958713i	$-0.591786\pi$
$631$	−14.2868	−0.568749	−0.284375	+	0.958713i	$0.591786\pi$
$632$	30.2964	1.20513
$633$	12.4498	0.494837
$634$	37.9369	1.50666
$635$	2.46872	0.0979683
$636$	−5.41989	−0.214913
$637$	7.04479	0.279125
$638$	1.65497	0.0655211
$639$	5.81543	0.230055
$640$	−14.2034	−0.561440
$641$	−36.7381	−1.45107	−0.725534	−	0.688187i	$-0.758407\pi$
$641$	−36.7381	−1.45107	−0.725534	+	0.688187i	$0.758407\pi$
$642$	−7.07244	−0.279127
$643$	41.4328	1.63395	0.816976	−	0.576672i	$-0.195649\pi$
$643$	41.4328	1.63395	0.816976	+	0.576672i	$0.195649\pi$
$644$	46.0851	1.81601
$645$	1.84294	0.0725659
$646$	74.3125	2.92379
$647$	−5.49622	−0.216079	−0.108039	−	0.994147i	$-0.534457\pi$
$647$	−5.49622	−0.216079	−0.108039	+	0.994147i	$0.534457\pi$
$648$	−10.8932	−0.427927
$649$	0.446648	0.0175325
$650$	14.3414	0.562514
$651$	−8.47347	−0.332102
$652$	16.6658	0.652682
$653$	−15.3780	−0.601788	−0.300894	−	0.953658i	$-0.597285\pi$
$653$	−15.3780	−0.601788	−0.300894	+	0.953658i	$0.597285\pi$
$654$	7.74437	0.302829
$655$	11.4764	0.448421
$656$	2.99235	0.116831
$657$	−16.7478	−0.653395
$658$	−22.0020	−0.857729
$659$	19.2705	0.750673	0.375336	−	0.926889i	$-0.377527\pi$
$659$	19.2705	0.750673	0.375336	+	0.926889i	$0.377527\pi$
$660$	−1.68970	−0.0657717
$661$	−26.9927	−1.04989	−0.524946	−	0.851135i	$-0.675915\pi$
$661$	−26.9927	−1.04989	−0.524946	+	0.851135i	$0.675915\pi$
$662$	12.8272	0.498545
$663$	20.4611	0.794645
$664$	23.0426	0.894226
$665$	16.4618	0.638359
$666$	−55.0976	−2.13499
$667$	5.33523	0.206581
$668$	22.1229	0.855959
$669$	13.1468	0.508285
$670$	1.32388	0.0511461
$671$	−10.5963	−0.409065
$672$	−10.9597	−0.422781
$673$	−28.9332	−1.11529	−0.557646	−	0.830079i	$-0.688296\pi$
$673$	−28.9332	−1.11529	−0.557646	+	0.830079i	$0.688296\pi$
$674$	−24.5417	−0.945311
$675$	−3.55729	−0.136920
$676$	83.9893	3.23036
$677$	−27.0398	−1.03922	−0.519612	−	0.854402i	$-0.673924\pi$
$677$	−27.0398	−1.03922	−0.519612	+	0.854402i	$0.673924\pi$
$678$	20.7290	0.796093
$679$	−34.5901	−1.32745
$680$	−9.78414	−0.375205
$681$	−7.87511	−0.301775
$682$	−11.1447	−0.426753
$683$	26.5074	1.01428	0.507138	−	0.861865i	$-0.330703\pi$
$683$	26.5074	1.01428	0.507138	+	0.861865i	$0.330703\pi$
$684$	−50.8072	−1.94266
$685$	−21.3975	−0.817556
$686$	−43.4903	−1.66047
$687$	15.3661	0.586255
$688$	4.12567	0.157290
$689$	19.1219	0.728485
$690$	−9.21522	−0.350818
$691$	7.83872	0.298199	0.149100	−	0.988822i	$-0.452363\pi$
$691$	7.83872	0.298199	0.149100	+	0.988822i	$0.452363\pi$
$692$	−24.0839	−0.915533
$693$	5.80342	0.220454
$694$	−62.9574	−2.38983
$695$	7.66945	0.290919
$696$	1.01995	0.0386612
$697$	10.4371	0.395335
$698$	−27.3872	−1.03662
$699$	−15.8503	−0.599514
$700$	−7.03097	−0.265746
$701$	29.8475	1.12732	0.563661	−	0.826006i	$-0.309392\pi$
$701$	29.8475	1.12732	0.563661	+	0.826006i	$0.309392\pi$
$702$	−51.0163	−1.92549
$703$	−64.9659	−2.45023
$704$	−11.7982	−0.444661
$705$	2.60061	0.0979448
$706$	−8.58238	−0.323002
$707$	−39.3171	−1.47867
$708$	0.892961	0.0335595
$709$	−29.7066	−1.11565	−0.557827	−	0.829957i	$-0.688365\pi$
$709$	−29.7066	−1.11565	−0.557827	+	0.829957i	$0.688365\pi$
$710$	−4.95457	−0.185942
$711$	39.8984	1.49631
$712$	22.8463	0.856203
$713$	−35.9278	−1.34551
$714$	−16.9702	−0.635095
$715$	5.96144	0.222945
$716$	−25.4277	−0.950277
$717$	8.48029	0.316702
$718$	46.9521	1.75224
$719$	−25.9434	−0.967527	−0.483764	−	0.875199i	$-0.660731\pi$
$719$	−25.9434	−0.967527	−0.483764	+	0.875199i	$0.660731\pi$
$720$	−3.69418	−0.137674
$721$	28.3819	1.05700
$722$	−59.3262	−2.20789
$723$	−0.248599	−0.00924548
$724$	70.9908	2.63835
$725$	−0.813970	−0.0302301
$726$	14.2769	0.529865
$727$	47.4260	1.75893	0.879466	−	0.475962i	$-0.157900\pi$
$727$	47.4260	1.75893	0.879466	+	0.475962i	$0.157900\pi$
$728$	−31.0833	−1.15202
$729$	−7.56164	−0.280061
$730$	14.2686	0.528106
$731$	14.3901	0.532237
$732$	−21.1846	−0.783005
$733$	33.1996	1.22625	0.613127	−	0.789984i	$-0.289911\pi$
$733$	33.1996	1.22625	0.613127	+	0.789984i	$0.289911\pi$
$734$	20.7542	0.766052
$735$	0.690619	0.0254739
$736$	−46.4697	−1.71290
$737$	0.550314	0.0202711
$738$	−12.0720	−0.444375
$739$	−10.4867	−0.385761	−0.192881	−	0.981222i	$-0.561783\pi$
$739$	−10.4867	−0.385761	−0.192881	+	0.981222i	$0.561783\pi$
$740$	27.7475	1.02002
$741$	−27.9048	−1.02511
$742$	−15.8595	−0.582219
$743$	−27.1997	−0.997861	−0.498930	−	0.866642i	$-0.666274\pi$
$743$	−27.1997	−0.997861	−0.498930	+	0.866642i	$0.666274\pi$
$744$	−6.86842	−0.251809
$745$	−4.25014	−0.155713
$746$	7.64063	0.279743
$747$	30.3456	1.11029
$748$	−13.1936	−0.482404
$749$	−12.2330	−0.446986
$750$	1.40592	0.0513370
$751$	46.5733	1.69948	0.849742	−	0.527198i	$-0.176758\pi$
$751$	46.5733	1.69948	0.849742	+	0.527198i	$0.176758\pi$
$752$	5.82180	0.212299
$753$	0.824430	0.0300439
$754$	−11.6734	−0.425121
$755$	16.0938	0.585713
$756$	25.0112	0.909648
$757$	44.1975	1.60639	0.803193	−	0.595718i	$-0.203133\pi$
$757$	44.1975	1.60639	0.803193	+	0.595718i	$0.203133\pi$
$758$	22.3014	0.810022
$759$	−3.83060	−0.139042
$760$	13.3436	0.484022
$761$	6.21439	0.225272	0.112636	−	0.993636i	$-0.464071\pi$
$761$	6.21439	0.225272	0.112636	+	0.993636i	$0.464071\pi$
$762$	3.47083	0.125735
$763$	13.3953	0.484941
$764$	−37.3999	−1.35308
$765$	−12.8851	−0.465861
$766$	18.9014	0.682936
$767$	−3.15045	−0.113756
$768$	−3.65256	−0.131800
$769$	−7.44635	−0.268522	−0.134261	−	0.990946i	$-0.542866\pi$
$769$	−7.44635	−0.268522	−0.134261	+	0.990946i	$0.542866\pi$
$770$	−4.94435	−0.178182
$771$	7.63323	0.274904
$772$	63.7850	2.29567
$773$	−51.8270	−1.86409	−0.932043	−	0.362347i	$-0.881975\pi$
$773$	−51.8270	−1.86409	−0.932043	+	0.362347i	$0.881975\pi$
$774$	−16.6441	−0.598259
$775$	5.48133	0.196895
$776$	−28.0380	−1.00651
$777$	14.8358	0.532231
$778$	34.4810	1.23620
$779$	−14.2341	−0.509990
$780$	11.9184	0.426747
$781$	−2.05953	−0.0736957
$782$	−71.9543	−2.57308
$783$	2.89553	0.103478
$784$	1.54604	0.0552157
$785$	−14.8895	−0.531431
$786$	16.1349	0.575514
$787$	27.5594	0.982386	0.491193	−	0.871051i	$-0.336561\pi$
$787$	27.5594	0.982386	0.491193	+	0.871051i	$0.336561\pi$
$788$	−46.5316	−1.65762
$789$	1.87541	0.0667662
$790$	−33.9923	−1.20939
$791$	35.8545	1.27484
$792$	4.70414	0.167154
$793$	74.7413	2.65414
$794$	16.7253	0.593559
$795$	1.87457	0.0664841
$796$	−3.06696	−0.108706
$797$	24.5243	0.868695	0.434348	−	0.900745i	$-0.356979\pi$
$797$	24.5243	0.868695	0.434348	+	0.900745i	$0.356979\pi$
$798$	23.1439	0.819286
$799$	20.3061	0.718379
$800$	7.08965	0.250657
$801$	30.0872	1.06308
$802$	−4.61855	−0.163087
$803$	5.93122	0.209308
$804$	1.10021	0.0388016
$805$	−15.9394	−0.561789
$806$	78.6096	2.76891
$807$	−17.1452	−0.603539
$808$	−31.8696	−1.12117
$809$	7.22086	0.253872	0.126936	−	0.991911i	$-0.459486\pi$
$809$	7.22086	0.253872	0.126936	+	0.991911i	$0.459486\pi$
$810$	12.2221	0.429442
$811$	29.8818	1.04929	0.524646	−	0.851321i	$-0.324198\pi$
$811$	29.8818	1.04929	0.524646	+	0.851321i	$0.324198\pi$
$812$	5.72300	0.200838
$813$	0.712334	0.0249826
$814$	19.5127	0.683921
$815$	−5.76416	−0.201910
$816$	4.49037	0.157194
$817$	−19.6251	−0.686596
$818$	−56.7504	−1.98423
$819$	−40.9347	−1.43037
$820$	6.07952	0.212306
$821$	−14.3831	−0.501975	−0.250987	−	0.967990i	$-0.580755\pi$
$821$	−14.3831	−0.501975	−0.250987	+	0.967990i	$0.580755\pi$
$822$	−30.0832	−1.04927
$823$	42.6978	1.48835	0.744176	−	0.667984i	$-0.232843\pi$
$823$	42.6978	1.48835	0.744176	+	0.667984i	$0.232843\pi$
$824$	23.0058	0.801443
$825$	0.584416	0.0203467
$826$	2.61295	0.0909160
$827$	−54.6517	−1.90042	−0.950212	−	0.311604i	$-0.899134\pi$
$827$	−54.6517	−1.90042	−0.950212	+	0.311604i	$0.899134\pi$
$828$	49.1949	1.70964
$829$	−32.1242	−1.11572	−0.557860	−	0.829935i	$-0.688377\pi$
$829$	−32.1242	−1.11572	−0.557860	+	0.829935i	$0.688377\pi$
$830$	−25.8536	−0.897391
$831$	−11.4351	−0.396679
$832$	83.2190	2.88510
$833$	5.39250	0.186839
$834$	10.7826	0.373372
$835$	−7.65160	−0.264795
$836$	17.9933	0.622312
$837$	−19.4987	−0.673972
$838$	45.6128	1.57567
$839$	−7.35442	−0.253903	−0.126951	−	0.991909i	$-0.540519\pi$
$839$	−7.35442	−0.253903	−0.126951	+	0.991909i	$0.540519\pi$
$840$	−3.04718	−0.105138
$841$	−28.3375	−0.977154
$842$	−56.1406	−1.93473
$843$	0.528396	0.0181989
$844$	56.6243	1.94909
$845$	−29.0492	−0.999324
$846$	−23.4868	−0.807492
$847$	24.6944	0.848510
$848$	4.19646	0.144107
$849$	−8.38855	−0.287894
$850$	10.9777	0.376533
$851$	62.9043	2.15633
$852$	−4.11751	−0.141063
$853$	14.5543	0.498329	0.249165	−	0.968461i	$-0.419844\pi$
$853$	14.5543	0.498329	0.249165	+	0.968461i	$0.419844\pi$
$854$	−61.9895	−2.12124
$855$	17.5726	0.600971
$856$	−9.91585	−0.338917
$857$	−21.0470	−0.718951	−0.359476	−	0.933154i	$-0.617044\pi$
$857$	−21.0470	−0.718951	−0.359476	+	0.933154i	$0.617044\pi$
$858$	8.38131	0.286133
$859$	29.2597	0.998327	0.499163	−	0.866508i	$-0.333641\pi$
$859$	29.2597	0.998327	0.499163	+	0.866508i	$0.333641\pi$
$860$	8.38208	0.285826
$861$	3.25054	0.110778
$862$	−57.1587	−1.94683
$863$	4.77946	0.162695	0.0813473	−	0.996686i	$-0.474078\pi$
$863$	4.77946	0.162695	0.0813473	+	0.996686i	$0.474078\pi$
$864$	−25.2199	−0.857999
$865$	8.32987	0.283224
$866$	−26.5199	−0.901182
$867$	4.85532	0.164895
$868$	−38.5390	−1.30810
$869$	−14.1300	−0.479326
$870$	−1.14438	−0.0387980
$871$	−3.88166	−0.131525
$872$	10.8579	0.367696
$873$	−36.9243	−1.24970
$874$	98.1310	3.31933
$875$	2.43179	0.0822095
$876$	11.8580	0.400644
$877$	−45.1947	−1.52612	−0.763059	−	0.646329i	$-0.776303\pi$
$877$	−45.1947	−1.52612	−0.763059	+	0.646329i	$0.776303\pi$
$878$	52.8660	1.78414
$879$	11.0525	0.372793
$880$	1.30829	0.0441024
$881$	14.4732	0.487613	0.243807	−	0.969824i	$-0.421604\pi$
$881$	14.4732	0.487613	0.243807	+	0.969824i	$0.421604\pi$
$882$	−6.23715	−0.210016
$883$	5.29485	0.178186	0.0890929	−	0.996023i	$-0.471603\pi$
$883$	5.29485	0.178186	0.0890929	+	0.996023i	$0.471603\pi$
$884$	93.0613	3.12999
$885$	−0.308847	−0.0103818
$886$	8.64052	0.290284
$887$	35.2961	1.18513	0.592564	−	0.805523i	$-0.298116\pi$
$887$	35.2961	1.18513	0.592564	+	0.805523i	$0.298116\pi$
$888$	12.0256	0.403553
$889$	6.00341	0.201348
$890$	−25.6334	−0.859233
$891$	5.08051	0.170204
$892$	59.7943	2.00206
$893$	−27.6934	−0.926724
$894$	−5.97536	−0.199846
$895$	8.79463	0.293972
$896$	−34.5398	−1.15389
$897$	27.0193	0.902148
$898$	−7.09149	−0.236646
$899$	−4.46163	−0.148804
$900$	−7.50543	−0.250181
$901$	14.6370	0.487629
$902$	4.27527	0.142351
$903$	4.48165	0.149140
$904$	29.0629	0.966619
$905$	−24.5535	−0.816186
$906$	22.6266	0.751718
$907$	−24.5736	−0.815952	−0.407976	−	0.912993i	$-0.633765\pi$
$907$	−24.5736	−0.815952	−0.407976	+	0.912993i	$0.633765\pi$
$908$	−35.8175	−1.18865
$909$	−41.9702	−1.39206
$910$	34.8752	1.15610
$911$	23.8786	0.791132	0.395566	−	0.918438i	$-0.370548\pi$
$911$	23.8786	0.791132	0.395566	+	0.918438i	$0.370548\pi$
$912$	−6.12395	−0.202784
$913$	−10.7469	−0.355669
$914$	29.4705	0.974796
$915$	7.32708	0.242226
$916$	69.8883	2.30917
$917$	27.9083	0.921612
$918$	−39.0509	−1.28887
$919$	10.1340	0.334290	0.167145	−	0.985932i	$-0.446545\pi$
$919$	10.1340	0.334290	0.167145	+	0.985932i	$0.446545\pi$
$920$	−12.9201	−0.425964
$921$	14.2175	0.468484
$922$	71.3314	2.34917
$923$	14.5270	0.478161
$924$	−4.10901	−0.135176
$925$	−9.59699	−0.315547
$926$	80.3319	2.63987
$927$	30.2971	0.995088
$928$	−5.77076	−0.189435
$929$	23.8846	0.783630	0.391815	−	0.920044i	$-0.371847\pi$
$929$	23.8846	0.783630	0.391815	+	0.920044i	$0.371847\pi$
$930$	7.70631	0.252700
$931$	−7.35426	−0.241026
$932$	−72.0904	−2.36140
$933$	−12.6706	−0.414816
$934$	70.2924	2.30004
$935$	4.56324	0.149234
$936$	−33.1808	−1.08455
$937$	14.8340	0.484607	0.242303	−	0.970201i	$-0.422097\pi$
$937$	14.8340	0.484607	0.242303	+	0.970201i	$0.422097\pi$
$938$	3.21940	0.105117
$939$	−16.8543	−0.550021
$940$	11.8281	0.385790
$941$	11.6821	0.380826	0.190413	−	0.981704i	$-0.439017\pi$
$941$	11.6821	0.380826	0.190413	+	0.981704i	$0.439017\pi$
$942$	−20.9335	−0.682051
$943$	13.7824	0.448817
$944$	−0.691393	−0.0225029
$945$	−8.65058	−0.281403
$946$	5.89448	0.191646
$947$	−48.2141	−1.56675	−0.783375	−	0.621550i	$-0.786503\pi$
$947$	−48.2141	−1.56675	−0.783375	+	0.621550i	$0.786503\pi$
$948$	−28.2493	−0.917495
$949$	−41.8361	−1.35806
$950$	−14.9713	−0.485735
$951$	−10.9044	−0.353598
$952$	−23.7930	−0.771135
$953$	34.6630	1.12284	0.561422	−	0.827530i	$-0.310254\pi$
$953$	34.6630	1.12284	0.561422	+	0.827530i	$0.310254\pi$
$954$	−16.9297	−0.548118
$955$	12.9355	0.418582
$956$	38.5700	1.24744
$957$	−0.475697	−0.0153771
$958$	55.5396	1.79440
$959$	−52.0342	−1.68027
$960$	8.15818	0.263304
$961$	−0.955069	−0.0308087
$962$	−137.634	−4.43749
$963$	−13.0585	−0.420806
$964$	−1.13068	−0.0364166
$965$	−22.0612	−0.710175
$966$	−22.4095	−0.721013
$967$	−22.7162	−0.730504	−0.365252	−	0.930909i	$-0.619017\pi$
$967$	−22.7162	−0.730504	−0.365252	+	0.930909i	$0.619017\pi$
$968$	20.0168	0.643364
$969$	−21.3600	−0.686181
$970$	31.4584	1.01007
$971$	−28.9394	−0.928709	−0.464355	−	0.885649i	$-0.653714\pi$
$971$	−28.9394	−0.928709	−0.464355	+	0.885649i	$0.653714\pi$
$972$	41.0125	1.31548
$973$	18.6505	0.597908
$974$	−92.0460	−2.94934
$975$	−4.12220	−0.132016
$976$	16.4026	0.525035
$977$	−46.6592	−1.49276	−0.746380	−	0.665520i	$-0.768210\pi$
$977$	−46.6592	−1.49276	−0.746380	+	0.665520i	$0.768210\pi$
$978$	−8.10395	−0.259136
$979$	−10.6553	−0.340546
$980$	3.14107	0.100338
$981$	14.2992	0.456538
$982$	−75.2517	−2.40138
$983$	43.4659	1.38635	0.693174	−	0.720771i	$-0.256212\pi$
$983$	43.4659	1.38635	0.693174	+	0.720771i	$0.256212\pi$
$984$	2.63482	0.0839951
$985$	16.0938	0.512791
$986$	−8.93553	−0.284565
$987$	6.32415	0.201300
$988$	−126.917	−4.03775
$989$	19.0024	0.604240
$990$	−5.27800	−0.167746
$991$	−15.2516	−0.484483	−0.242241	−	0.970216i	$-0.577883\pi$
$991$	−15.2516	−0.484483	−0.242241	+	0.970216i	$0.577883\pi$
$992$	38.8607	1.23383
$993$	−3.68699	−0.117003
$994$	−12.0485	−0.382155
$995$	1.06077	0.0336285
$996$	−21.4856	−0.680799
$997$	−48.1860	−1.52607	−0.763033	−	0.646359i	$-0.776291\pi$
$997$	−48.1860	−1.52607	−0.763033	+	0.646359i	$0.776291\pi$
$998$	64.8033	2.05131
$999$	34.1393	1.08012

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6005.2.a.g.1.16	✓	113

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6005.2.a.g.1.16	✓	113	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:	\( N \)	\(=\)	\( 6005 = 5 \cdot 1201 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6005.a (trivial)

\(f(q)\)	\(=\)	\(q-2.21162 q^{2} +0.635696 q^{3} +2.89127 q^{4} -1.00000 q^{5} -1.40592 q^{6} -2.43179 q^{7} -1.97116 q^{8} -2.59589 q^{9} +O(q^{10})\)	\(q-2.21162 q^{2} +0.635696 q^{3} +2.89127 q^{4} -1.00000 q^{5} -1.40592 q^{6} -2.43179 q^{7} -1.97116 q^{8} -2.59589 q^{9} +2.21162 q^{10} +0.919331 q^{11} +1.83797 q^{12} -6.48454 q^{13} +5.37820 q^{14} -0.635696 q^{15} -1.42309 q^{16} -4.96365 q^{17} +5.74113 q^{18} +6.76940 q^{19} -2.89127 q^{20} -1.54588 q^{21} -2.03321 q^{22} -6.55458 q^{23} -1.25306 q^{24} +1.00000 q^{25} +14.3414 q^{26} -3.55729 q^{27} -7.03097 q^{28} -0.813970 q^{29} +1.40592 q^{30} +5.48133 q^{31} +7.08965 q^{32} +0.584416 q^{33} +10.9777 q^{34} +2.43179 q^{35} -7.50543 q^{36} -9.59699 q^{37} -14.9713 q^{38} -4.12220 q^{39} +1.97116 q^{40} -2.10271 q^{41} +3.41890 q^{42} -2.89910 q^{43} +2.65804 q^{44} +2.59589 q^{45} +14.4963 q^{46} -4.09097 q^{47} -0.904651 q^{48} -1.08640 q^{49} -2.21162 q^{50} -3.15537 q^{51} -18.7486 q^{52} -2.94884 q^{53} +7.86738 q^{54} -0.919331 q^{55} +4.79344 q^{56} +4.30328 q^{57} +1.80019 q^{58} +0.485840 q^{59} -1.83797 q^{60} -11.5261 q^{61} -12.1226 q^{62} +6.31266 q^{63} -12.8335 q^{64} +6.48454 q^{65} -1.29251 q^{66} +0.598603 q^{67} -14.3513 q^{68} -4.16673 q^{69} -5.37820 q^{70} -2.24024 q^{71} +5.11691 q^{72} +6.45167 q^{73} +21.2249 q^{74} +0.635696 q^{75} +19.5722 q^{76} -2.23562 q^{77} +9.11675 q^{78} -15.3698 q^{79} +1.42309 q^{80} +5.52631 q^{81} +4.65041 q^{82} -11.6899 q^{83} -4.46956 q^{84} +4.96365 q^{85} +6.41170 q^{86} -0.517438 q^{87} -1.81215 q^{88} -11.5903 q^{89} -5.74113 q^{90} +15.7690 q^{91} -18.9511 q^{92} +3.48446 q^{93} +9.04768 q^{94} -6.76940 q^{95} +4.50686 q^{96} +14.2241 q^{97} +2.40270 q^{98} -2.38648 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 113 q - 3 q^{2} + 6 q^{3} + 141 q^{4} - 113 q^{5} + 7 q^{6} + 7 q^{7} - 12 q^{8} + 141 q^{9}+O(q^{10}) \) 113 * q - 3 * q^2 + 6 * q^3 + 141 * q^4 - 113 * q^5 + 7 * q^6 + 7 * q^7 - 12 * q^8 + 141 * q^9	\( 113 q - 3 q^{2} + 6 q^{3} + 141 q^{4} - 113 q^{5} + 7 q^{6} + 7 q^{7} - 12 q^{8} + 141 q^{9} + 3 q^{10} + 38 q^{11} - 4 q^{12} + 17 q^{13} + 23 q^{14} - 6 q^{15} + 193 q^{16} - 11 q^{17} - 3 q^{18} + 76 q^{19} - 141 q^{20} + 19 q^{21} + 41 q^{22} - 28 q^{23} + 29 q^{24} + 113 q^{25} + 21 q^{26} + 18 q^{27} + 29 q^{28} + 24 q^{29} - 7 q^{30} + 59 q^{31} - 22 q^{32} + 3 q^{33} + 55 q^{34} - 7 q^{35} + 232 q^{36} + 41 q^{37} - 6 q^{38} + 55 q^{39} + 12 q^{40} + 24 q^{41} + 17 q^{42} + 136 q^{43} + 85 q^{44} - 141 q^{45} + 84 q^{46} - 91 q^{47} - 19 q^{48} + 198 q^{49} - 3 q^{50} + 97 q^{51} + 45 q^{52} + 9 q^{53} + 54 q^{54} - 38 q^{55} + 98 q^{56} + 22 q^{57} + 69 q^{58} + 59 q^{59} + 4 q^{60} + 51 q^{61} - 30 q^{62} - 22 q^{63} + 298 q^{64} - 17 q^{65} + 76 q^{66} + 201 q^{67} - 34 q^{68} + 42 q^{69} - 23 q^{70} + 69 q^{71} - 7 q^{72} + 30 q^{73} + 35 q^{74} + 6 q^{75} + 170 q^{76} - 37 q^{77} - 11 q^{78} + 143 q^{79} - 193 q^{80} + 197 q^{81} + 55 q^{82} - 15 q^{83} + 83 q^{84} + 11 q^{85} + 78 q^{86} - 51 q^{87} + 113 q^{88} + 53 q^{89} + 3 q^{90} + 217 q^{91} - 40 q^{92} + 36 q^{93} + 81 q^{94} - 76 q^{95} + 66 q^{96} + 63 q^{97} - 62 q^{98} + 184 q^{99}+O(q^{100}) \) 113 * q - 3 * q^2 + 6 * q^3 + 141 * q^4 - 113 * q^5 + 7 * q^6 + 7 * q^7 - 12 * q^8 + 141 * q^9 + 3 * q^10 + 38 * q^11 - 4 * q^12 + 17 * q^13 + 23 * q^14 - 6 * q^15 + 193 * q^16 - 11 * q^17 - 3 * q^18 + 76 * q^19 - 141 * q^20 + 19 * q^21 + 41 * q^22 - 28 * q^23 + 29 * q^24 + 113 * q^25 + 21 * q^26 + 18 * q^27 + 29 * q^28 + 24 * q^29 - 7 * q^30 + 59 * q^31 - 22 * q^32 + 3 * q^33 + 55 * q^34 - 7 * q^35 + 232 * q^36 + 41 * q^37 - 6 * q^38 + 55 * q^39 + 12 * q^40 + 24 * q^41 + 17 * q^42 + 136 * q^43 + 85 * q^44 - 141 * q^45 + 84 * q^46 - 91 * q^47 - 19 * q^48 + 198 * q^49 - 3 * q^50 + 97 * q^51 + 45 * q^52 + 9 * q^53 + 54 * q^54 - 38 * q^55 + 98 * q^56 + 22 * q^57 + 69 * q^58 + 59 * q^59 + 4 * q^60 + 51 * q^61 - 30 * q^62 - 22 * q^63 + 298 * q^64 - 17 * q^65 + 76 * q^66 + 201 * q^67 - 34 * q^68 + 42 * q^69 - 23 * q^70 + 69 * q^71 - 7 * q^72 + 30 * q^73 + 35 * q^74 + 6 * q^75 + 170 * q^76 - 37 * q^77 - 11 * q^78 + 143 * q^79 - 193 * q^80 + 197 * q^81 + 55 * q^82 - 15 * q^83 + 83 * q^84 + 11 * q^85 + 78 * q^86 - 51 * q^87 + 113 * q^88 + 53 * q^89 + 3 * q^90 + 217 * q^91 - 40 * q^92 + 36 * q^93 + 81 * q^94 - 76 * q^95 + 66 * q^96 + 63 * q^97 - 62 * q^98 + 184 * q^99

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