LMFDB - Embedded newform 6005.2.a.f.1.1

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:	$111$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
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)

$f(q)$	$=$	$q-2.74668 q^{2} +1.63661 q^{3} +5.54423 q^{4} +1.00000 q^{5} -4.49523 q^{6} -2.87647 q^{7} -9.73484 q^{8} -0.321512 q^{9} +O(q^{10})$	\(q-2.74668 q^{2} +1.63661 q^{3} +5.54423 q^{4} +1.00000 q^{5} -4.49523 q^{6} -2.87647 q^{7} -9.73484 q^{8} -0.321512 q^{9} -2.74668 q^{10} +3.16158 q^{11} +9.07373 q^{12} +5.83969 q^{13} +7.90073 q^{14} +1.63661 q^{15} +15.6500 q^{16} +0.860638 q^{17} +0.883089 q^{18} -4.65911 q^{19} +5.54423 q^{20} -4.70765 q^{21} -8.68383 q^{22} +7.59757 q^{23} -15.9321 q^{24} +1.00000 q^{25} -16.0397 q^{26} -5.43602 q^{27} -15.9478 q^{28} -1.34248 q^{29} -4.49523 q^{30} +2.19220 q^{31} -23.5158 q^{32} +5.17427 q^{33} -2.36389 q^{34} -2.87647 q^{35} -1.78253 q^{36} +9.81232 q^{37} +12.7971 q^{38} +9.55729 q^{39} -9.73484 q^{40} +6.94810 q^{41} +12.9304 q^{42} +0.150828 q^{43} +17.5285 q^{44} -0.321512 q^{45} -20.8681 q^{46} +5.04848 q^{47} +25.6129 q^{48} +1.27407 q^{49} -2.74668 q^{50} +1.40853 q^{51} +32.3766 q^{52} +0.317443 q^{53} +14.9310 q^{54} +3.16158 q^{55} +28.0020 q^{56} -7.62514 q^{57} +3.68736 q^{58} -12.4536 q^{59} +9.07373 q^{60} -8.18983 q^{61} -6.02126 q^{62} +0.924819 q^{63} +33.2902 q^{64} +5.83969 q^{65} -14.2120 q^{66} +7.77966 q^{67} +4.77157 q^{68} +12.4342 q^{69} +7.90073 q^{70} +4.90286 q^{71} +3.12987 q^{72} +2.37837 q^{73} -26.9512 q^{74} +1.63661 q^{75} -25.8312 q^{76} -9.09418 q^{77} -26.2508 q^{78} +5.40732 q^{79} +15.6500 q^{80} -7.93209 q^{81} -19.0842 q^{82} -9.00960 q^{83} -26.1003 q^{84} +0.860638 q^{85} -0.414274 q^{86} -2.19711 q^{87} -30.7774 q^{88} -15.7483 q^{89} +0.883089 q^{90} -16.7977 q^{91} +42.1226 q^{92} +3.58777 q^{93} -13.8665 q^{94} -4.65911 q^{95} -38.4861 q^{96} +4.25397 q^{97} -3.49946 q^{98} -1.01649 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 111 q + 20 q^{2} + 40 q^{3} + 136 q^{4} + 111 q^{5} + 3 q^{6} + 39 q^{7} + 45 q^{8} + 139 q^{9}+O(q^{10}) $ 111 * q + 20 * q^2 + 40 * q^3 + 136 * q^4 + 111 * q^5 + 3 * q^6 + 39 * q^7 + 45 * q^8 + 139 * q^9	\( 111 q + 20 q^{2} + 40 q^{3} + 136 q^{4} + 111 q^{5} + 3 q^{6} + 39 q^{7} + 45 q^{8} + 139 q^{9} + 20 q^{10} + 36 q^{11} + 80 q^{12} + 36 q^{13} + 7 q^{14} + 40 q^{15} + 190 q^{16} + 38 q^{17} + 48 q^{18} + 77 q^{19} + 136 q^{20} + 11 q^{21} + 39 q^{22} + 82 q^{23} - 3 q^{24} + 111 q^{25} - 3 q^{26} + 130 q^{27} + 87 q^{28} + 20 q^{29} + 3 q^{30} + 41 q^{31} + 85 q^{32} + 33 q^{33} + 7 q^{34} + 39 q^{35} + 191 q^{36} + 80 q^{37} + 42 q^{38} + 21 q^{39} + 45 q^{40} + 16 q^{41} + 33 q^{42} + 164 q^{43} + 37 q^{44} + 139 q^{45} + 32 q^{46} + 148 q^{47} + 149 q^{48} + 160 q^{49} + 20 q^{50} + 51 q^{51} + 87 q^{52} + 83 q^{53} - 6 q^{54} + 36 q^{55} - 10 q^{56} + 28 q^{57} + 47 q^{58} + 14 q^{59} + 80 q^{60} + 20 q^{61} + 14 q^{62} + 120 q^{63} + 231 q^{64} + 36 q^{65} - 4 q^{66} + 253 q^{67} + 80 q^{68} + 6 q^{69} + 7 q^{70} + 5 q^{71} + 124 q^{72} + 64 q^{73} - 37 q^{74} + 40 q^{75} + 92 q^{76} + 63 q^{77} + 29 q^{78} + 91 q^{79} + 190 q^{80} + 187 q^{81} - 7 q^{82} + 63 q^{83} - 69 q^{84} + 38 q^{85} - 22 q^{86} + 57 q^{87} + 121 q^{88} - 6 q^{89} + 48 q^{90} + 119 q^{91} + 104 q^{92} + 14 q^{93} - q^{94} + 77 q^{95} - 38 q^{96} + 96 q^{97} + 81 q^{98} + 106 q^{99}+O(q^{100}) \) 111 * q + 20 * q^2 + 40 * q^3 + 136 * q^4 + 111 * q^5 + 3 * q^6 + 39 * q^7 + 45 * q^8 + 139 * q^9 + 20 * q^10 + 36 * q^11 + 80 * q^12 + 36 * q^13 + 7 * q^14 + 40 * q^15 + 190 * q^16 + 38 * q^17 + 48 * q^18 + 77 * q^19 + 136 * q^20 + 11 * q^21 + 39 * q^22 + 82 * q^23 - 3 * q^24 + 111 * q^25 - 3 * q^26 + 130 * q^27 + 87 * q^28 + 20 * q^29 + 3 * q^30 + 41 * q^31 + 85 * q^32 + 33 * q^33 + 7 * q^34 + 39 * q^35 + 191 * q^36 + 80 * q^37 + 42 * q^38 + 21 * q^39 + 45 * q^40 + 16 * q^41 + 33 * q^42 + 164 * q^43 + 37 * q^44 + 139 * q^45 + 32 * q^46 + 148 * q^47 + 149 * q^48 + 160 * q^49 + 20 * q^50 + 51 * q^51 + 87 * q^52 + 83 * q^53 - 6 * q^54 + 36 * q^55 - 10 * q^56 + 28 * q^57 + 47 * q^58 + 14 * q^59 + 80 * q^60 + 20 * q^61 + 14 * q^62 + 120 * q^63 + 231 * q^64 + 36 * q^65 - 4 * q^66 + 253 * q^67 + 80 * q^68 + 6 * q^69 + 7 * q^70 + 5 * q^71 + 124 * q^72 + 64 * q^73 - 37 * q^74 + 40 * q^75 + 92 * q^76 + 63 * q^77 + 29 * q^78 + 91 * q^79 + 190 * q^80 + 187 * q^81 - 7 * q^82 + 63 * q^83 - 69 * q^84 + 38 * q^85 - 22 * q^86 + 57 * q^87 + 121 * q^88 - 6 * q^89 + 48 * q^90 + 119 * q^91 + 104 * q^92 + 14 * q^93 - q^94 + 77 * q^95 - 38 * q^96 + 96 * q^97 + 81 * q^98 + 106 * 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 $

$2$	−2.74668	−1.94219	−0.971096	−	0.238688i	$-0.923283\pi$
$2$	−2.74668	−1.94219	−0.971096	+	0.238688i	$0.923283\pi$
$3$	1.63661	0.944896	0.472448	−	0.881358i	$-0.343370\pi$
$3$	1.63661	0.944896	0.472448	+	0.881358i	$0.343370\pi$
$4$	5.54423	2.77211
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−4.49523	−1.83517
$7$	−2.87647	−1.08720	−0.543601	−	0.839343i	$-0.682940\pi$
$7$	−2.87647	−1.08720	−0.543601	+	0.839343i	$0.682940\pi$
$8$	−9.73484	−3.44178
$9$	−0.321512	−0.107171
$10$	−2.74668	−0.868575
$11$	3.16158	0.953252	0.476626	−	0.879106i	$-0.341860\pi$
$11$	3.16158	0.953252	0.476626	+	0.879106i	$0.341860\pi$
$12$	9.07373	2.61936
$13$	5.83969	1.61964	0.809819	−	0.586679i	$-0.199565\pi$
$13$	5.83969	1.61964	0.809819	+	0.586679i	$0.199565\pi$
$14$	7.90073	2.11156
$15$	1.63661	0.422571
$16$	15.6500	3.91250
$17$	0.860638	0.208735	0.104368	−	0.994539i	$-0.466718\pi$
$17$	0.860638	0.208735	0.104368	+	0.994539i	$0.466718\pi$
$18$	0.883089	0.208146
$19$	−4.65911	−1.06887	−0.534437	−	0.845209i	$-0.679476\pi$
$19$	−4.65911	−1.06887	−0.534437	+	0.845209i	$0.679476\pi$
$20$	5.54423	1.23973
$21$	−4.70765	−1.02729
$22$	−8.68383	−1.85140
$23$	7.59757	1.58420	0.792101	−	0.610390i	$-0.208987\pi$
$23$	7.59757	1.58420	0.792101	+	0.610390i	$0.208987\pi$
$24$	−15.9321	−3.25213
$25$	1.00000	0.200000
$26$	−16.0397	−3.14565
$27$	−5.43602	−1.04616
$28$	−15.9478	−3.01385
$29$	−1.34248	−0.249292	−0.124646	−	0.992201i	$-0.539780\pi$
$29$	−1.34248	−0.249292	−0.124646	+	0.992201i	$0.539780\pi$
$30$	−4.49523	−0.820713
$31$	2.19220	0.393731	0.196865	−	0.980431i	$-0.436924\pi$
$31$	2.19220	0.393731	0.196865	+	0.980431i	$0.436924\pi$
$32$	−23.5158	−4.15704
$33$	5.17427	0.900724
$34$	−2.36389	−0.405404
$35$	−2.87647	−0.486212
$36$	−1.78253	−0.297089
$37$	9.81232	1.61313	0.806567	−	0.591142i	$-0.201323\pi$
$37$	9.81232	1.61313	0.806567	+	0.591142i	$0.201323\pi$
$38$	12.7971	2.07596
$39$	9.55729	1.53039
$40$	−9.73484	−1.53921
$41$	6.94810	1.08511	0.542555	−	0.840020i	$-0.317457\pi$
$41$	6.94810	1.08511	0.542555	+	0.840020i	$0.317457\pi$
$42$	12.9304	1.99520
$43$	0.150828	0.0230010	0.0115005	−	0.999934i	$-0.496339\pi$
$43$	0.150828	0.0230010	0.0115005	+	0.999934i	$0.496339\pi$
$44$	17.5285	2.64252
$45$	−0.321512	−0.0479282
$46$	−20.8681	−3.07683
$47$	5.04848	0.736396	0.368198	−	0.929747i	$-0.379975\pi$
$47$	5.04848	0.736396	0.368198	+	0.929747i	$0.379975\pi$
$48$	25.6129	3.69690
$49$	1.27407	0.182010
$50$	−2.74668	−0.388439
$51$	1.40853	0.197233
$52$	32.3766	4.48982
$53$	0.317443	0.0436041	0.0218021	−	0.999762i	$-0.493060\pi$
$53$	0.317443	0.0436041	0.0218021	+	0.999762i	$0.493060\pi$
$54$	14.9310	2.03185
$55$	3.16158	0.426307
$56$	28.0020	3.74192
$57$	−7.62514	−1.00997
$58$	3.68736	0.484173
$59$	−12.4536	−1.62132	−0.810659	−	0.585519i	$-0.800891\pi$
$59$	−12.4536	−1.62132	−0.810659	+	0.585519i	$0.800891\pi$
$60$	9.07373	1.17141
$61$	−8.18983	−1.04860	−0.524300	−	0.851533i	$-0.675673\pi$
$61$	−8.18983	−1.04860	−0.524300	+	0.851533i	$0.675673\pi$
$62$	−6.02126	−0.764701
$63$	0.924819	0.116516
$64$	33.2902	4.16127
$65$	5.83969	0.724324
$66$	−14.2120	−1.74938
$67$	7.77966	0.950437	0.475219	−	0.879868i	$-0.342369\pi$
$67$	7.77966	0.950437	0.475219	+	0.879868i	$0.342369\pi$
$68$	4.77157	0.578638
$69$	12.4342	1.49691
$70$	7.90073	0.944317
$71$	4.90286	0.581862	0.290931	−	0.956744i	$-0.406035\pi$
$71$	4.90286	0.581862	0.290931	+	0.956744i	$0.406035\pi$
$72$	3.12987	0.368858
$73$	2.37837	0.278368	0.139184	−	0.990267i	$-0.455552\pi$
$73$	2.37837	0.278368	0.139184	+	0.990267i	$0.455552\pi$
$74$	−26.9512	−3.13302
$75$	1.63661	0.188979
$76$	−25.8312	−2.96304
$77$	−9.09418	−1.03638
$78$	−26.2508	−2.97231
$79$	5.40732	0.608371	0.304186	−	0.952613i	$-0.401616\pi$
$79$	5.40732	0.608371	0.304186	+	0.952613i	$0.401616\pi$
$80$	15.6500	1.74972
$81$	−7.93209	−0.881344
$82$	−19.0842	−2.10749
$83$	−9.00960	−0.988932	−0.494466	−	0.869197i	$-0.664636\pi$
$83$	−9.00960	−0.988932	−0.494466	+	0.869197i	$0.664636\pi$
$84$	−26.1003	−2.84778
$85$	0.860638	0.0933493
$86$	−0.414274	−0.0446723
$87$	−2.19711	−0.235555
$88$	−30.7774	−3.28089
$89$	−15.7483	−1.66932	−0.834659	−	0.550767i	$-0.814335\pi$
$89$	−15.7483	−1.66932	−0.834659	+	0.550767i	$0.814335\pi$
$90$	0.883089	0.0930858
$91$	−16.7977	−1.76088
$92$	42.1226	4.39159
$93$	3.58777	0.372035
$94$	−13.8665	−1.43022
$95$	−4.65911	−0.478015
$96$	−38.4861	−3.92797
$97$	4.25397	0.431926	0.215963	−	0.976402i	$-0.430711\pi$
$97$	4.25397	0.431926	0.215963	+	0.976402i	$0.430711\pi$
$98$	−3.49946	−0.353499
$99$	−1.01649	−0.102161
$100$	5.54423	0.554423
$101$	13.4678	1.34009	0.670047	−	0.742319i	$-0.266274\pi$
$101$	13.4678	1.34009	0.670047	+	0.742319i	$0.266274\pi$
$102$	−3.86877	−0.383065
$103$	16.0372	1.58019	0.790095	−	0.612985i	$-0.210031\pi$
$103$	16.0372	1.58019	0.790095	+	0.612985i	$0.210031\pi$
$104$	−56.8484	−5.57445
$105$	−4.70765	−0.459420
$106$	−0.871912	−0.0846876
$107$	−18.8704	−1.82427	−0.912133	−	0.409894i	$-0.865566\pi$
$107$	−18.8704	−1.82427	−0.912133	+	0.409894i	$0.865566\pi$
$108$	−30.1385	−2.90008
$109$	−15.8764	−1.52068	−0.760342	−	0.649523i	$-0.774968\pi$
$109$	−15.8764	−1.52068	−0.760342	+	0.649523i	$0.774968\pi$
$110$	−8.68383	−0.827970
$111$	16.0589	1.52425
$112$	−45.0167	−4.25368
$113$	0.760618	0.0715529	0.0357765	−	0.999360i	$-0.488610\pi$
$113$	0.760618	0.0715529	0.0357765	+	0.999360i	$0.488610\pi$
$114$	20.9438	1.96157
$115$	7.59757	0.708477
$116$	−7.44301	−0.691066
$117$	−1.87753	−0.173578
$118$	34.2059	3.14891
$119$	−2.47560	−0.226938
$120$	−15.9321	−1.45440
$121$	−1.00443	−0.0913114
$122$	22.4948	2.03658
$123$	11.3713	1.02532
$124$	12.1541	1.09147
$125$	1.00000	0.0894427
$126$	−2.54018	−0.226297
$127$	3.79866	0.337076	0.168538	−	0.985695i	$-0.446095\pi$
$127$	3.79866	0.337076	0.168538	+	0.985695i	$0.446095\pi$
$128$	−44.4058	−3.92495
$129$	0.246846	0.0217335
$130$	−16.0397	−1.40678
$131$	3.13332	0.273759	0.136880	−	0.990588i	$-0.456293\pi$
$131$	3.13332	0.273759	0.136880	+	0.990588i	$0.456293\pi$
$132$	28.6873	2.49691
$133$	13.4018	1.16208
$134$	−21.3682	−1.84593
$135$	−5.43602	−0.467858
$136$	−8.37817	−0.718422
$137$	−14.5452	−1.24268	−0.621341	−	0.783540i	$-0.713412\pi$
$137$	−14.5452	−1.24268	−0.621341	+	0.783540i	$0.713412\pi$
$138$	−34.1528	−2.90728
$139$	8.87899	0.753106	0.376553	−	0.926395i	$-0.377109\pi$
$139$	8.87899	0.753106	0.376553	+	0.926395i	$0.377109\pi$
$140$	−15.9478	−1.34783
$141$	8.26238	0.695818
$142$	−13.4666	−1.13009
$143$	18.4626	1.54392
$144$	−5.03166	−0.419305
$145$	−1.34248	−0.111487
$146$	−6.53262	−0.540644
$147$	2.08516	0.171981
$148$	54.4017	4.47179
$149$	−5.28464	−0.432935	−0.216467	−	0.976290i	$-0.569454\pi$
$149$	−5.28464	−0.432935	−0.216467	+	0.976290i	$0.569454\pi$
$150$	−4.49523	−0.367034
$151$	7.02413	0.571616	0.285808	−	0.958287i	$-0.407738\pi$
$151$	7.02413	0.571616	0.285808	+	0.958287i	$0.407738\pi$
$152$	45.3557	3.67883
$153$	−0.276705	−0.0223703
$154$	24.9788	2.01285
$155$	2.19220	0.176082
$156$	52.9878	4.24242
$157$	16.2479	1.29673	0.648364	−	0.761331i	$-0.275454\pi$
$157$	16.2479	1.29673	0.648364	+	0.761331i	$0.275454\pi$
$158$	−14.8522	−1.18157
$159$	0.519529	0.0412014
$160$	−23.5158	−1.85908
$161$	−21.8542	−1.72235
$162$	21.7869	1.71174
$163$	5.66552	0.443757	0.221879	−	0.975074i	$-0.428781\pi$
$163$	5.66552	0.443757	0.221879	+	0.975074i	$0.428781\pi$
$164$	38.5218	3.00805
$165$	5.17427	0.402816
$166$	24.7464	1.92070
$167$	10.6765	0.826172	0.413086	−	0.910692i	$-0.364451\pi$
$167$	10.6765	0.826172	0.413086	+	0.910692i	$0.364451\pi$
$168$	45.8282	3.53573
$169$	21.1020	1.62323
$170$	−2.36389	−0.181302
$171$	1.49796	0.114552
$172$	0.836222	0.0637613
$173$	23.9895	1.82389	0.911944	−	0.410315i	$-0.134581\pi$
$173$	23.9895	1.82389	0.911944	+	0.410315i	$0.134581\pi$
$174$	6.03476	0.457494
$175$	−2.87647	−0.217441
$176$	49.4786	3.72959
$177$	−20.3816	−1.53198
$178$	43.2555	3.24214
$179$	−13.9417	−1.04205	−0.521024	−	0.853542i	$-0.674450\pi$
$179$	−13.9417	−1.04205	−0.521024	+	0.853542i	$0.674450\pi$
$180$	−1.78253	−0.132862
$181$	0.465869	0.0346278	0.0173139	−	0.999850i	$-0.494489\pi$
$181$	0.465869	0.0346278	0.0173139	+	0.999850i	$0.494489\pi$
$182$	46.1378	3.41996
$183$	−13.4035	−0.990819
$184$	−73.9611	−5.45248
$185$	9.81232	0.721416
$186$	−9.85445	−0.722564
$187$	2.72097	0.198977
$188$	27.9899	2.04137
$189$	15.6365	1.13739
$190$	12.7971	0.928397
$191$	−5.56425	−0.402615	−0.201308	−	0.979528i	$-0.564519\pi$
$191$	−5.56425	−0.402615	−0.201308	+	0.979528i	$0.564519\pi$
$192$	54.4830	3.93197
$193$	−18.0385	−1.29844	−0.649221	−	0.760600i	$-0.724905\pi$
$193$	−18.0385	−1.29844	−0.649221	+	0.760600i	$0.724905\pi$
$194$	−11.6843	−0.838883
$195$	9.55729	0.684412
$196$	7.06374	0.504553
$197$	−18.0036	−1.28270	−0.641351	−	0.767247i	$-0.721626\pi$
$197$	−18.0036	−1.28270	−0.641351	+	0.767247i	$0.721626\pi$
$198$	2.79195	0.198416
$199$	21.5345	1.52654	0.763268	−	0.646082i	$-0.223593\pi$
$199$	21.5345	1.52654	0.763268	+	0.646082i	$0.223593\pi$
$200$	−9.73484	−0.688357
$201$	12.7323	0.898065
$202$	−36.9916	−2.60272
$203$	3.86160	0.271031
$204$	7.80920	0.546753
$205$	6.94810	0.485276
$206$	−44.0489	−3.06903
$207$	−2.44271	−0.169780
$208$	91.3911	6.33683
$209$	−14.7301	−1.01891
$210$	12.9304	0.892282
$211$	7.34563	0.505694	0.252847	−	0.967506i	$-0.418633\pi$
$211$	7.34563	0.505694	0.252847	+	0.967506i	$0.418633\pi$
$212$	1.75997	0.120876
$213$	8.02406	0.549799
$214$	51.8307	3.54308
$215$	0.150828	0.0102864
$216$	52.9187	3.60066
$217$	−6.30580	−0.428065
$218$	43.6073	2.95346
$219$	3.89247	0.263029
$220$	17.5285	1.18177
$221$	5.02586	0.338076
$222$	−44.1086	−2.96038
$223$	19.7664	1.32366	0.661829	−	0.749654i	$-0.269780\pi$
$223$	19.7664	1.32366	0.661829	+	0.749654i	$0.269780\pi$
$224$	67.6423	4.51954
$225$	−0.321512	−0.0214341
$226$	−2.08917	−0.138970
$227$	4.07629	0.270553	0.135276	−	0.990808i	$-0.456808\pi$
$227$	4.07629	0.270553	0.135276	+	0.990808i	$0.456808\pi$
$228$	−42.2755	−2.79976
$229$	4.45819	0.294605	0.147303	−	0.989091i	$-0.452941\pi$
$229$	4.45819	0.294605	0.147303	+	0.989091i	$0.452941\pi$
$230$	−20.8681	−1.37600
$231$	−14.8836	−0.979270
$232$	13.0688	0.858010
$233$	−18.5096	−1.21261	−0.606303	−	0.795234i	$-0.707348\pi$
$233$	−18.5096	−1.21261	−0.606303	+	0.795234i	$0.707348\pi$
$234$	5.15697	0.337121
$235$	5.04848	0.329326
$236$	−69.0455	−4.49448
$237$	8.84967	0.574848
$238$	6.79967	0.440757
$239$	16.7262	1.08192	0.540962	−	0.841047i	$-0.318060\pi$
$239$	16.7262	1.08192	0.540962	+	0.841047i	$0.318060\pi$
$240$	25.6129	1.65331
$241$	−8.84902	−0.570015	−0.285008	−	0.958525i	$-0.591996\pi$
$241$	−8.84902	−0.570015	−0.285008	+	0.958525i	$0.591996\pi$
$242$	2.75883	0.177344
$243$	3.32631	0.213383
$244$	−45.4063	−2.90684
$245$	1.27407	0.0813974
$246$	−31.2333	−1.99136
$247$	−27.2078	−1.73119
$248$	−21.3407	−1.35514
$249$	−14.7452	−0.934438
$250$	−2.74668	−0.173715
$251$	3.66823	0.231537	0.115768	−	0.993276i	$-0.463067\pi$
$251$	3.66823	0.231537	0.115768	+	0.993276i	$0.463067\pi$
$252$	5.12741	0.322996
$253$	24.0203	1.51014
$254$	−10.4337	−0.654667
$255$	1.40853	0.0882054
$256$	55.3879	3.46175
$257$	19.4788	1.21506	0.607528	−	0.794298i	$-0.292161\pi$
$257$	19.4788	1.21506	0.607528	+	0.794298i	$0.292161\pi$
$258$	−0.678005	−0.0422107
$259$	−28.2248	−1.75380
$260$	32.3766	2.00791
$261$	0.431623	0.0267168
$262$	−8.60621	−0.531693
$263$	11.4939	0.708745	0.354372	−	0.935104i	$-0.384695\pi$
$263$	11.4939	0.708745	0.354372	+	0.935104i	$0.384695\pi$
$264$	−50.3706	−3.10010
$265$	0.317443	0.0195004
$266$	−36.8103	−2.25699
$267$	−25.7738	−1.57733
$268$	43.1322	2.63472
$269$	23.0403	1.40479	0.702395	−	0.711787i	$-0.252114\pi$
$269$	23.0403	1.40479	0.702395	+	0.711787i	$0.252114\pi$
$270$	14.9310	0.908670
$271$	10.9227	0.663506	0.331753	−	0.943366i	$-0.392360\pi$
$271$	10.9227	0.663506	0.331753	+	0.943366i	$0.392360\pi$
$272$	13.4690	0.816677
$273$	−27.4912	−1.66385
$274$	39.9510	2.41353
$275$	3.16158	0.190650
$276$	68.9383	4.14960
$277$	13.1283	0.788802	0.394401	−	0.918938i	$-0.370952\pi$
$277$	13.1283	0.788802	0.394401	+	0.918938i	$0.370952\pi$
$278$	−24.3877	−1.46268
$279$	−0.704819	−0.0421964
$280$	28.0020	1.67344
$281$	−18.3296	−1.09345	−0.546726	−	0.837312i	$-0.684126\pi$
$281$	−18.3296	−1.09345	−0.546726	+	0.837312i	$0.684126\pi$
$282$	−22.6941	−1.35141
$283$	29.1124	1.73056	0.865278	−	0.501293i	$-0.167142\pi$
$283$	29.1124	1.73056	0.865278	+	0.501293i	$0.167142\pi$
$284$	27.1825	1.61299
$285$	−7.62514	−0.451674
$286$	−50.7109	−2.99860
$287$	−19.9860	−1.17974
$288$	7.56060	0.445512
$289$	−16.2593	−0.956430
$290$	3.68736	0.216529
$291$	6.96209	0.408125
$292$	13.1862	0.771667
$293$	6.31134	0.368713	0.184356	−	0.982859i	$-0.440980\pi$
$293$	6.31134	0.368713	0.184356	+	0.982859i	$0.440980\pi$
$294$	−5.72725	−0.334020
$295$	−12.4536	−0.725075
$296$	−95.5213	−5.55206
$297$	−17.1864	−0.997255
$298$	14.5152	0.840843
$299$	44.3675	2.56584
$300$	9.07373	0.523872
$301$	−0.433851	−0.0250067
$302$	−19.2930	−1.11019
$303$	22.0415	1.26625
$304$	−72.9150	−4.18196
$305$	−8.18983	−0.468948
$306$	0.760020	0.0434475
$307$	5.62362	0.320957	0.160478	−	0.987039i	$-0.448696\pi$
$307$	5.62362	0.320957	0.160478	+	0.987039i	$0.448696\pi$
$308$	−50.4202	−2.87296
$309$	26.2466	1.49312
$310$	−6.02126	−0.341985
$311$	−25.9746	−1.47288	−0.736441	−	0.676501i	$-0.763495\pi$
$311$	−25.9746	−1.47288	−0.736441	+	0.676501i	$0.763495\pi$
$312$	−93.0386	−5.26728
$313$	22.2530	1.25782	0.628908	−	0.777480i	$-0.283502\pi$
$313$	22.2530	1.25782	0.628908	+	0.777480i	$0.283502\pi$
$314$	−44.6278	−2.51849
$315$	0.924819	0.0521077
$316$	29.9794	1.68647
$317$	16.3300	0.917183	0.458591	−	0.888647i	$-0.348354\pi$
$317$	16.3300	0.917183	0.458591	+	0.888647i	$0.348354\pi$
$318$	−1.42698	−0.0800210
$319$	−4.24435	−0.237638
$320$	33.2902	1.86098
$321$	−30.8834	−1.72374
$322$	60.0263	3.34514
$323$	−4.00981	−0.223112
$324$	−43.9773	−2.44318
$325$	5.83969	0.323928
$326$	−15.5613	−0.861862
$327$	−25.9835	−1.43689
$328$	−67.6386	−3.73472
$329$	−14.5218	−0.800612
$330$	−14.2120	−0.782346
$331$	17.0369	0.936434	0.468217	−	0.883614i	$-0.344897\pi$
$331$	17.0369	0.936434	0.468217	+	0.883614i	$0.344897\pi$
$332$	−49.9512	−2.74143
$333$	−3.15478	−0.172881
$334$	−29.3249	−1.60459
$335$	7.77966	0.425048
$336$	−73.6747	−4.01928
$337$	−0.863435	−0.0470343	−0.0235172	−	0.999723i	$-0.507486\pi$
$337$	−0.863435	−0.0470343	−0.0235172	+	0.999723i	$0.507486\pi$
$338$	−57.9603	−3.15263
$339$	1.24483	0.0676101
$340$	4.77157	0.258775
$341$	6.93081	0.375325
$342$	−4.11441	−0.222482
$343$	16.4705	0.889321
$344$	−1.46828	−0.0791644
$345$	12.4342	0.669437
$346$	−65.8914	−3.54234
$347$	−17.6469	−0.947338	−0.473669	−	0.880703i	$-0.657071\pi$
$347$	−17.6469	−0.947338	−0.473669	+	0.880703i	$0.657071\pi$
$348$	−12.1813	−0.652986
$349$	5.25433	0.281258	0.140629	−	0.990062i	$-0.455088\pi$
$349$	5.25433	0.281258	0.140629	+	0.990062i	$0.455088\pi$
$350$	7.90073	0.422312
$351$	−31.7446	−1.69440
$352$	−74.3469	−3.96270
$353$	16.1862	0.861503	0.430752	−	0.902471i	$-0.358248\pi$
$353$	16.1862	0.861503	0.430752	+	0.902471i	$0.358248\pi$
$354$	55.9817	2.97540
$355$	4.90286	0.260217
$356$	−87.3122	−4.62754
$357$	−4.05159	−0.214433
$358$	38.2932	2.02386
$359$	−19.5690	−1.03281	−0.516405	−	0.856345i	$-0.672730\pi$
$359$	−19.5690	−1.03281	−0.516405	+	0.856345i	$0.672730\pi$
$360$	3.12987	0.164958
$361$	2.70731	0.142490
$362$	−1.27959	−0.0672538
$363$	−1.64385	−0.0862799
$364$	−93.1302	−4.88135
$365$	2.37837	0.124490
$366$	36.8152	1.92436
$367$	−8.32539	−0.434582	−0.217291	−	0.976107i	$-0.569722\pi$
$367$	−8.32539	−0.434582	−0.217291	+	0.976107i	$0.569722\pi$
$368$	118.902	6.19819
$369$	−2.23390	−0.116292
$370$	−26.9512	−1.40113
$371$	−0.913114	−0.0474065
$372$	19.8914	1.03132
$373$	−27.9868	−1.44910	−0.724552	−	0.689221i	$-0.757953\pi$
$373$	−27.9868	−1.44910	−0.724552	+	0.689221i	$0.757953\pi$
$374$	−7.47363	−0.386452
$375$	1.63661	0.0845141
$376$	−49.1461	−2.53452
$377$	−7.83966	−0.403763
$378$	−42.9485	−2.20903
$379$	33.2067	1.70572	0.852858	−	0.522143i	$-0.174867\pi$
$379$	33.2067	1.70572	0.852858	+	0.522143i	$0.174867\pi$
$380$	−25.8312	−1.32511
$381$	6.21692	0.318502
$382$	15.2832	0.781956
$383$	−19.4187	−0.992250	−0.496125	−	0.868251i	$-0.665244\pi$
$383$	−19.4187	−0.992250	−0.496125	+	0.868251i	$0.665244\pi$
$384$	−72.6749	−3.70868
$385$	−9.09418	−0.463482
$386$	49.5460	2.52183
$387$	−0.0484929	−0.00246503
$388$	23.5850	1.19735
$389$	8.14657	0.413048	0.206524	−	0.978442i	$-0.433785\pi$
$389$	8.14657	0.413048	0.206524	+	0.978442i	$0.433785\pi$
$390$	−26.2508	−1.32926
$391$	6.53876	0.330679
$392$	−12.4029	−0.626440
$393$	5.12802	0.258674
$394$	49.4500	2.49126
$395$	5.40732	0.272072
$396$	−5.63562	−0.283201
$397$	−31.7909	−1.59554	−0.797770	−	0.602962i	$-0.793987\pi$
$397$	−31.7909	−1.59554	−0.797770	+	0.602962i	$0.793987\pi$
$398$	−59.1481	−2.96483
$399$	21.9335	1.09805
$400$	15.6500	0.782499
$401$	24.5100	1.22397	0.611986	−	0.790868i	$-0.290371\pi$
$401$	24.5100	1.22397	0.611986	+	0.790868i	$0.290371\pi$
$402$	−34.9714	−1.74422
$403$	12.8018	0.637702
$404$	74.6683	3.71489
$405$	−7.93209	−0.394149
$406$	−10.6066	−0.526395
$407$	31.0224	1.53772
$408$	−13.7118	−0.678835
$409$	9.92068	0.490546	0.245273	−	0.969454i	$-0.421122\pi$
$409$	9.92068	0.490546	0.245273	+	0.969454i	$0.421122\pi$
$410$	−19.0842	−0.942500
$411$	−23.8048	−1.17421
$412$	88.9137	4.38046
$413$	35.8223	1.76270
$414$	6.70933	0.329746
$415$	−9.00960	−0.442264
$416$	−137.325	−6.73290
$417$	14.5314	0.711607
$418$	40.4589	1.97891
$419$	36.4673	1.78154	0.890772	−	0.454451i	$-0.150164\pi$
$419$	36.4673	1.78154	0.890772	+	0.454451i	$0.150164\pi$
$420$	−26.1003	−1.27356
$421$	−32.3880	−1.57849	−0.789247	−	0.614075i	$-0.789529\pi$
$421$	−32.3880	−1.57849	−0.789247	+	0.614075i	$0.789529\pi$
$422$	−20.1761	−0.982155
$423$	−1.62315	−0.0789201
$424$	−3.09025	−0.150076
$425$	0.860638	0.0417471
$426$	−22.0395	−1.06782
$427$	23.5578	1.14004
$428$	−104.622	−5.05707
$429$	30.2161	1.45885
$430$	−0.414274	−0.0199781
$431$	20.4219	0.983690	0.491845	−	0.870683i	$-0.336323\pi$
$431$	20.4219	0.983690	0.491845	+	0.870683i	$0.336323\pi$
$432$	−85.0736	−4.09310
$433$	16.1734	0.777246	0.388623	−	0.921397i	$-0.372951\pi$
$433$	16.1734	0.777246	0.388623	+	0.921397i	$0.372951\pi$
$434$	17.3200	0.831385
$435$	−2.19711	−0.105344
$436$	−88.0223	−4.21551
$437$	−35.3979	−1.69331
$438$	−10.6913	−0.510852
$439$	−33.7258	−1.60965	−0.804823	−	0.593515i	$-0.797740\pi$
$439$	−33.7258	−1.60965	−0.804823	+	0.593515i	$0.797740\pi$
$440$	−30.7774	−1.46726
$441$	−0.409629	−0.0195062
$442$	−13.8044	−0.656609
$443$	14.2629	0.677650	0.338825	−	0.940849i	$-0.389970\pi$
$443$	14.2629	0.677650	0.338825	+	0.940849i	$0.389970\pi$
$444$	89.0343	4.22538
$445$	−15.7483	−0.746542
$446$	−54.2920	−2.57080
$447$	−8.64890	−0.409079
$448$	−95.7581	−4.52415
$449$	−24.5250	−1.15741	−0.578703	−	0.815539i	$-0.696441\pi$
$449$	−24.5250	−1.15741	−0.578703	+	0.815539i	$0.696441\pi$
$450$	0.883089	0.0416292
$451$	21.9669	1.03438
$452$	4.21704	0.198353
$453$	11.4958	0.540118
$454$	−11.1962	−0.525466
$455$	−16.7977	−0.787488
$456$	74.2295	3.47611
$457$	33.5886	1.57121	0.785605	−	0.618728i	$-0.212352\pi$
$457$	33.5886	1.57121	0.785605	+	0.618728i	$0.212352\pi$
$458$	−12.2452	−0.572180
$459$	−4.67844	−0.218371
$460$	42.1226	1.96398
$461$	30.7413	1.43177	0.715883	−	0.698221i	$-0.246024\pi$
$461$	30.7413	1.43177	0.715883	+	0.698221i	$0.246024\pi$
$462$	40.8805	1.90193
$463$	−40.7050	−1.89172	−0.945861	−	0.324573i	$-0.894779\pi$
$463$	−40.7050	−1.89172	−0.945861	+	0.324573i	$0.894779\pi$
$464$	−21.0098	−0.975355
$465$	3.58777	0.166379
$466$	50.8399	2.35511
$467$	−16.0613	−0.743230	−0.371615	−	0.928387i	$-0.621196\pi$
$467$	−16.0613	−0.743230	−0.371615	+	0.928387i	$0.621196\pi$
$468$	−10.4095	−0.481177
$469$	−22.3780	−1.03332
$470$	−13.8665	−0.639615
$471$	26.5915	1.22527
$472$	121.234	5.58023
$473$	0.476853	0.0219257
$474$	−24.3072	−1.11647
$475$	−4.65911	−0.213775
$476$	−13.7253	−0.629097
$477$	−0.102062	−0.00467308
$478$	−45.9413	−2.10131
$479$	15.2093	0.694930	0.347465	−	0.937693i	$-0.387042\pi$
$479$	15.2093	0.694930	0.347465	+	0.937693i	$0.387042\pi$
$480$	−38.4861	−1.75664
$481$	57.3009	2.61270
$482$	24.3054	1.10708
$483$	−35.7667	−1.62744
$484$	−5.56876	−0.253126
$485$	4.25397	0.193163
$486$	−9.13630	−0.414431
$487$	−0.395192	−0.0179079	−0.00895394	−	0.999960i	$-0.502850\pi$
$487$	−0.395192	−0.0179079	−0.00895394	+	0.999960i	$0.502850\pi$
$488$	79.7267	3.60906
$489$	9.27223	0.419305
$490$	−3.49946	−0.158090
$491$	38.2412	1.72580	0.862901	−	0.505373i	$-0.168645\pi$
$491$	38.2412	1.72580	0.862901	+	0.505373i	$0.168645\pi$
$492$	63.0451	2.84229
$493$	−1.15539	−0.0520361
$494$	74.7309	3.36230
$495$	−1.01649	−0.0456876
$496$	34.3079	1.54047
$497$	−14.1029	−0.632602
$498$	40.5002	1.81486
$499$	26.2228	1.17389	0.586946	−	0.809626i	$-0.300330\pi$
$499$	26.2228	1.17389	0.586946	+	0.809626i	$0.300330\pi$
$500$	5.54423	0.247945
$501$	17.4733	0.780647
$502$	−10.0754	−0.449689
$503$	3.88802	0.173358	0.0866791	−	0.996236i	$-0.472375\pi$
$503$	3.88802	0.173358	0.0866791	+	0.996236i	$0.472375\pi$
$504$	−9.00296	−0.401024
$505$	13.4678	0.599308
$506$	−65.9760	−2.93299
$507$	34.5357	1.53378
$508$	21.0606	0.934414
$509$	−15.9415	−0.706593	−0.353297	−	0.935511i	$-0.614939\pi$
$509$	−15.9415	−0.706593	−0.353297	+	0.935511i	$0.614939\pi$
$510$	−3.86877	−0.171312
$511$	−6.84132	−0.302642
$512$	−63.3211	−2.79842
$513$	25.3270	1.11821
$514$	−53.5020	−2.35987
$515$	16.0372	0.706682
$516$	1.36857	0.0602478
$517$	15.9612	0.701971
$518$	77.5244	3.40623
$519$	39.2614	1.72339
$520$	−56.8484	−2.49297
$521$	28.9158	1.26683	0.633413	−	0.773814i	$-0.281654\pi$
$521$	28.9158	1.26683	0.633413	+	0.773814i	$0.281654\pi$
$522$	−1.18553	−0.0518892
$523$	36.3440	1.58921	0.794605	−	0.607127i	$-0.207678\pi$
$523$	36.3440	1.58921	0.794605	+	0.607127i	$0.207678\pi$
$524$	17.3718	0.758892
$525$	−4.70765	−0.205459
$526$	−31.5700	−1.37652
$527$	1.88669	0.0821856
$528$	80.9772	3.52408
$529$	34.7231	1.50970
$530$	−0.871912	−0.0378734
$531$	4.00397	0.173758
$532$	74.3025	3.22142
$533$	40.5747	1.75749
$534$	70.7923	3.06348
$535$	−18.8704	−0.815837
$536$	−75.7338	−3.27120
$537$	−22.8170	−0.984628
$538$	−63.2842	−2.72837
$539$	4.02808	0.173502
$540$	−30.1385	−1.29695
$541$	−7.04655	−0.302955	−0.151477	−	0.988461i	$-0.548403\pi$
$541$	−7.04655	−0.302955	−0.151477	+	0.988461i	$0.548403\pi$
$542$	−30.0011	−1.28866
$543$	0.762445	0.0327197
$544$	−20.2386	−0.867721
$545$	−15.8764	−0.680070
$546$	75.5095	3.23151
$547$	16.9415	0.724367	0.362184	−	0.932107i	$-0.382031\pi$
$547$	16.9415	0.724367	0.362184	+	0.932107i	$0.382031\pi$
$548$	−80.6420	−3.44486
$549$	2.63313	0.112379
$550$	−8.68383	−0.370280
$551$	6.25476	0.266462
$552$	−121.045	−5.15203
$553$	−15.5540	−0.661423
$554$	−36.0591	−1.53201
$555$	16.0589	0.681663
$556$	49.2271	2.08769
$557$	−23.3117	−0.987750	−0.493875	−	0.869533i	$-0.664420\pi$
$557$	−23.3117	−0.987750	−0.493875	+	0.869533i	$0.664420\pi$
$558$	1.93591	0.0819535
$559$	0.880786	0.0372533
$560$	−45.0167	−1.90230
$561$	4.45317	0.188013
$562$	50.3454	2.12369
$563$	−34.4371	−1.45135	−0.725675	−	0.688037i	$-0.758473\pi$
$563$	−34.4371	−1.45135	−0.725675	+	0.688037i	$0.758473\pi$
$564$	45.8085	1.92889
$565$	0.760618	0.0319994
$566$	−79.9624	−3.36107
$567$	22.8164	0.958200
$568$	−47.7285	−2.00264
$569$	−32.9189	−1.38003	−0.690017	−	0.723793i	$-0.742397\pi$
$569$	−32.9189	−1.38003	−0.690017	+	0.723793i	$0.742397\pi$
$570$	20.9438	0.877239
$571$	2.77025	0.115931	0.0579657	−	0.998319i	$-0.481539\pi$
$571$	2.77025	0.115931	0.0579657	+	0.998319i	$0.481539\pi$
$572$	102.361	4.27993
$573$	−9.10650	−0.380430
$574$	54.8950	2.29127
$575$	7.59757	0.316841
$576$	−10.7032	−0.445966
$577$	−3.15241	−0.131237	−0.0656183	−	0.997845i	$-0.520902\pi$
$577$	−3.15241	−0.131237	−0.0656183	+	0.997845i	$0.520902\pi$
$578$	44.6590	1.85757
$579$	−29.5220	−1.22689
$580$	−7.44301	−0.309054
$581$	25.9158	1.07517
$582$	−19.1226	−0.792658
$583$	1.00362	0.0415657
$584$	−23.1531	−0.958082
$585$	−1.87753	−0.0776263
$586$	−17.3352	−0.716111
$587$	−30.4208	−1.25560	−0.627801	−	0.778374i	$-0.716045\pi$
$587$	−30.4208	−1.25560	−0.627801	+	0.778374i	$0.716045\pi$
$588$	11.5606	0.476750
$589$	−10.2137	−0.420848
$590$	34.2059	1.40824
$591$	−29.4648	−1.21202
$592$	153.563	6.31138
$593$	−5.63633	−0.231456	−0.115728	−	0.993281i	$-0.536920\pi$
$593$	−5.63633	−0.231456	−0.115728	+	0.993281i	$0.536920\pi$
$594$	47.2054	1.93686
$595$	−2.47560	−0.101490
$596$	−29.2993	−1.20014
$597$	35.2435	1.44242
$598$	−121.863	−4.98335
$599$	−14.9851	−0.612275	−0.306138	−	0.951987i	$-0.599037\pi$
$599$	−14.9851	−0.612275	−0.306138	+	0.951987i	$0.599037\pi$
$600$	−15.9321	−0.650426
$601$	8.27171	0.337410	0.168705	−	0.985667i	$-0.446041\pi$
$601$	8.27171	0.337410	0.168705	+	0.985667i	$0.446041\pi$
$602$	1.19165	0.0485679
$603$	−2.50126	−0.101859
$604$	38.9434	1.58458
$605$	−1.00443	−0.0408357
$606$	−60.5408	−2.45930
$607$	−15.1951	−0.616748	−0.308374	−	0.951265i	$-0.599785\pi$
$607$	−15.1951	−0.616748	−0.308374	+	0.951265i	$0.599785\pi$
$608$	109.562	4.44335
$609$	6.31993	0.256096
$610$	22.4948	0.910788
$611$	29.4816	1.19270
$612$	−1.53412	−0.0620130
$613$	7.39942	0.298860	0.149430	−	0.988772i	$-0.452256\pi$
$613$	7.39942	0.298860	0.149430	+	0.988772i	$0.452256\pi$
$614$	−15.4463	−0.623360
$615$	11.3713	0.458536
$616$	88.5303	3.56699
$617$	−23.3100	−0.938425	−0.469212	−	0.883085i	$-0.655462\pi$
$617$	−23.3100	−0.938425	−0.469212	+	0.883085i	$0.655462\pi$
$618$	−72.0908	−2.89992
$619$	46.3938	1.86472	0.932362	−	0.361525i	$-0.117744\pi$
$619$	46.3938	1.86472	0.932362	+	0.361525i	$0.117744\pi$
$620$	12.1541	0.488119
$621$	−41.3005	−1.65733
$622$	71.3437	2.86062
$623$	45.2995	1.81489
$624$	149.571	5.98765
$625$	1.00000	0.0400000
$626$	−61.1218	−2.44292
$627$	−24.1075	−0.962760
$628$	90.0823	3.59467
$629$	8.44485	0.336718
$630$	−2.54018	−0.101203
$631$	3.81606	0.151915	0.0759574	−	0.997111i	$-0.475799\pi$
$631$	3.81606	0.151915	0.0759574	+	0.997111i	$0.475799\pi$
$632$	−52.6394	−2.09388
$633$	12.0219	0.477828
$634$	−44.8531	−1.78135
$635$	3.79866	0.150745
$636$	2.88039	0.114215
$637$	7.44018	0.294791
$638$	11.6579	0.461539
$639$	−1.57633	−0.0623585
$640$	−44.4058	−1.75529
$641$	−30.0008	−1.18496	−0.592479	−	0.805586i	$-0.701851\pi$
$641$	−30.0008	−1.18496	−0.592479	+	0.805586i	$0.701851\pi$
$642$	84.8266	3.34784
$643$	18.7416	0.739096	0.369548	−	0.929212i	$-0.379513\pi$
$643$	18.7416	0.739096	0.369548	+	0.929212i	$0.379513\pi$
$644$	−121.164	−4.77455
$645$	0.246846	0.00971954
$646$	11.0136	0.433326
$647$	10.5323	0.414067	0.207033	−	0.978334i	$-0.433619\pi$
$647$	10.5323	0.414067	0.207033	+	0.978334i	$0.433619\pi$
$648$	77.2176	3.03340
$649$	−39.3730	−1.54552
$650$	−16.0397	−0.629130
$651$	−10.3201	−0.404477
$652$	31.4109	1.23015
$653$	−42.9859	−1.68217	−0.841085	−	0.540904i	$-0.818082\pi$
$653$	−42.9859	−1.68217	−0.841085	+	0.540904i	$0.818082\pi$
$654$	71.3681	2.79071
$655$	3.13332	0.122429
$656$	108.738	4.24549
$657$	−0.764676	−0.0298329
$658$	39.8866	1.55494
$659$	−16.4393	−0.640385	−0.320193	−	0.947352i	$-0.603748\pi$
$659$	−16.4393	−0.640385	−0.320193	+	0.947352i	$0.603748\pi$
$660$	28.6873	1.11665
$661$	8.03521	0.312533	0.156267	−	0.987715i	$-0.450054\pi$
$661$	8.03521	0.312533	0.156267	+	0.987715i	$0.450054\pi$
$662$	−46.7949	−1.81873
$663$	8.22537	0.319447
$664$	87.7069	3.40369
$665$	13.4018	0.519699
$666$	8.66515	0.335768
$667$	−10.1996	−0.394929
$668$	59.1929	2.29024
$669$	32.3499	1.25072
$670$	−21.3682	−0.825526
$671$	−25.8928	−0.999580
$672$	110.704	4.27050
$673$	19.3479	0.745805	0.372902	−	0.927871i	$-0.378363\pi$
$673$	19.3479	0.745805	0.372902	+	0.927871i	$0.378363\pi$
$674$	2.37158	0.0913497
$675$	−5.43602	−0.209232
$676$	116.994	4.49978
$677$	−39.9809	−1.53659	−0.768295	−	0.640096i	$-0.778895\pi$
$677$	−39.9809	−1.53659	−0.768295	+	0.640096i	$0.778895\pi$
$678$	−3.41915	−0.131312
$679$	−12.2364	−0.469591
$680$	−8.37817	−0.321288
$681$	6.67129	0.255644
$682$	−19.0367	−0.728953
$683$	−22.0437	−0.843479	−0.421740	−	0.906717i	$-0.638580\pi$
$683$	−22.0437	−0.843479	−0.421740	+	0.906717i	$0.638580\pi$
$684$	8.30503	0.317551
$685$	−14.5452	−0.555745
$686$	−45.2390	−1.72723
$687$	7.29631	0.278371
$688$	2.36045	0.0899913
$689$	1.85377	0.0706229
$690$	−34.1528	−1.30018
$691$	−27.7031	−1.05388	−0.526938	−	0.849904i	$-0.676660\pi$
$691$	−27.7031	−1.05388	−0.526938	+	0.849904i	$0.676660\pi$
$692$	133.003	5.05602
$693$	2.92389	0.111069
$694$	48.4704	1.83991
$695$	8.87899	0.336799
$696$	21.3885	0.810731
$697$	5.97980	0.226501
$698$	−14.4319	−0.546257
$699$	−30.2930	−1.14579
$700$	−15.9478	−0.602770
$701$	−4.71440	−0.178061	−0.0890303	−	0.996029i	$-0.528377\pi$
$701$	−4.71440	−0.178061	−0.0890303	+	0.996029i	$0.528377\pi$
$702$	87.1922	3.29086
$703$	−45.7167	−1.72424
$704$	105.249	3.96674
$705$	8.26238	0.311179
$706$	−44.4582	−1.67321
$707$	−38.7396	−1.45695
$708$	−113.000	−4.24681
$709$	−33.3227	−1.25146	−0.625730	−	0.780040i	$-0.715199\pi$
$709$	−33.3227	−1.25146	−0.625730	+	0.780040i	$0.715199\pi$
$710$	−13.4666	−0.505391
$711$	−1.73852	−0.0651995
$712$	153.307	5.74543
$713$	16.6554	0.623750
$714$	11.1284	0.416470
$715$	18.4626	0.690463
$716$	−77.2957	−2.88868
$717$	27.3742	1.02231
$718$	53.7496	2.00592
$719$	36.8008	1.37244	0.686218	−	0.727396i	$-0.259270\pi$
$719$	36.8008	1.37244	0.686218	+	0.727396i	$0.259270\pi$
$720$	−5.03166	−0.187519
$721$	−46.1304	−1.71799
$722$	−7.43609	−0.276743
$723$	−14.4824	−0.538606
$724$	2.58288	0.0959921
$725$	−1.34248	−0.0498584
$726$	4.51513	0.167572
$727$	27.4233	1.01707	0.508537	−	0.861040i	$-0.330186\pi$
$727$	27.4233	1.01707	0.508537	+	0.861040i	$0.330186\pi$
$728$	163.523	6.06056
$729$	29.2402	1.08297
$730$	−6.53262	−0.241783
$731$	0.129808	0.00480112
$732$	−74.3123	−2.74666
$733$	−9.74025	−0.359764	−0.179882	−	0.983688i	$-0.557572\pi$
$733$	−9.74025	−0.359764	−0.179882	+	0.983688i	$0.557572\pi$
$734$	22.8671	0.844041
$735$	2.08516	0.0769121
$736$	−178.663	−6.58559
$737$	24.5960	0.906006
$738$	6.13579	0.225861
$739$	−19.9226	−0.732866	−0.366433	−	0.930444i	$-0.619421\pi$
$739$	−19.9226	−0.732866	−0.366433	+	0.930444i	$0.619421\pi$
$740$	54.4017	1.99985
$741$	−44.5285	−1.63579
$742$	2.50803	0.0920726
$743$	29.6709	1.08852	0.544260	−	0.838916i	$-0.316810\pi$
$743$	29.6709	1.08852	0.544260	+	0.838916i	$0.316810\pi$
$744$	−34.9264	−1.28046
$745$	−5.28464	−0.193614
$746$	76.8707	2.81444
$747$	2.89669	0.105984
$748$	15.0857	0.551588
$749$	54.2800	1.98335
$750$	−4.49523	−0.164143
$751$	1.66576	0.0607845	0.0303923	−	0.999538i	$-0.490324\pi$
$751$	1.66576	0.0607845	0.0303923	+	0.999538i	$0.490324\pi$
$752$	79.0086	2.88115
$753$	6.00346	0.218778
$754$	21.5330	0.784186
$755$	7.02413	0.255634
$756$	86.6924	3.15297
$757$	52.2146	1.89777	0.948886	−	0.315619i	$-0.102212\pi$
$757$	52.2146	1.89777	0.948886	+	0.315619i	$0.102212\pi$
$758$	−91.2082	−3.31283
$759$	39.3118	1.42693
$760$	45.3557	1.64522
$761$	−45.7260	−1.65757	−0.828783	−	0.559570i	$-0.810966\pi$
$761$	−45.7260	−1.65757	−0.828783	+	0.559570i	$0.810966\pi$
$762$	−17.0758	−0.618593
$763$	45.6680	1.65329
$764$	−30.8495	−1.11609
$765$	−0.276705	−0.0100043
$766$	53.3369	1.92714
$767$	−72.7251	−2.62595
$768$	90.6484	3.27099
$769$	−32.2772	−1.16395	−0.581973	−	0.813208i	$-0.697719\pi$
$769$	−32.2772	−1.16395	−0.581973	+	0.813208i	$0.697719\pi$
$770$	24.9788	0.900172
$771$	31.8792	1.14810
$772$	−100.010	−3.59943
$773$	−24.0611	−0.865416	−0.432708	−	0.901534i	$-0.642442\pi$
$773$	−24.0611	−0.865416	−0.432708	+	0.901534i	$0.642442\pi$
$774$	0.133194	0.00478756
$775$	2.19220	0.0787462
$776$	−41.4117	−1.48660
$777$	−46.1930	−1.65716
$778$	−22.3760	−0.802218
$779$	−32.3719	−1.15985
$780$	52.9878	1.89727
$781$	15.5008	0.554661
$782$	−17.9598	−0.642243
$783$	7.29774	0.260800
$784$	19.9392	0.712114
$785$	16.2479	0.579914
$786$	−14.0850	−0.502395
$787$	0.577700	0.0205928	0.0102964	−	0.999947i	$-0.496722\pi$
$787$	0.577700	0.0205928	0.0102964	+	0.999947i	$0.496722\pi$
$788$	−99.8160	−3.55580
$789$	18.8110	0.669690
$790$	−14.8522	−0.528416
$791$	−2.18789	−0.0777925
$792$	9.89532	0.351615
$793$	−47.8261	−1.69835
$794$	87.3193	3.09885
$795$	0.519529	0.0184258
$796$	119.392	4.23173
$797$	35.7267	1.26551	0.632753	−	0.774354i	$-0.281925\pi$
$797$	35.7267	1.26551	0.632753	+	0.774354i	$0.281925\pi$
$798$	−60.2441	−2.13262
$799$	4.34491	0.153712
$800$	−23.5158	−0.831407
$801$	5.06327	0.178902
$802$	−67.3211	−2.37719
$803$	7.51942	0.265354
$804$	70.5906	2.48954
$805$	−21.8542	−0.770258
$806$	−35.1623	−1.23854
$807$	37.7079	1.32738
$808$	−131.107	−4.61231
$809$	42.3459	1.48880	0.744402	−	0.667732i	$-0.232735\pi$
$809$	42.3459	1.48880	0.744402	+	0.667732i	$0.232735\pi$
$810$	21.7869	0.765513
$811$	1.63113	0.0572768	0.0286384	−	0.999590i	$-0.490883\pi$
$811$	1.63113	0.0572768	0.0286384	+	0.999590i	$0.490883\pi$
$812$	21.4096	0.751329
$813$	17.8762	0.626945
$814$	−85.2085	−2.98656
$815$	5.66552	0.198454
$816$	22.0434	0.771675
$817$	−0.702722	−0.0245851
$818$	−27.2489	−0.952735
$819$	5.40066	0.188714
$820$	38.5218	1.34524
$821$	21.0869	0.735938	0.367969	−	0.929838i	$-0.380053\pi$
$821$	21.0869	0.735938	0.367969	+	0.929838i	$0.380053\pi$
$822$	65.3842	2.28054
$823$	5.81798	0.202802	0.101401	−	0.994846i	$-0.467667\pi$
$823$	5.81798	0.202802	0.101401	+	0.994846i	$0.467667\pi$
$824$	−156.119	−5.43867
$825$	5.17427	0.180145
$826$	−98.3923	−3.42351
$827$	−34.5644	−1.20192	−0.600961	−	0.799279i	$-0.705215\pi$
$827$	−34.5644	−1.20192	−0.600961	+	0.799279i	$0.705215\pi$
$828$	−13.5429	−0.470649
$829$	−22.0944	−0.767371	−0.383685	−	0.923464i	$-0.625345\pi$
$829$	−22.0944	−0.767371	−0.383685	+	0.923464i	$0.625345\pi$
$830$	24.7464	0.858961
$831$	21.4859	0.745337
$832$	194.404	6.73976
$833$	1.09651	0.0379920
$834$	−39.9131	−1.38208
$835$	10.6765	0.369475
$836$	−81.6672	−2.82452
$837$	−11.9168	−0.411906
$838$	−100.164	−3.46010
$839$	15.8358	0.546713	0.273356	−	0.961913i	$-0.411866\pi$
$839$	15.8358	0.546713	0.273356	+	0.961913i	$0.411866\pi$
$840$	45.8282	1.58122
$841$	−27.1977	−0.937853
$842$	88.9593	3.06574
$843$	−29.9984	−1.03320
$844$	40.7258	1.40184
$845$	21.1020	0.725930
$846$	4.45826	0.153278
$847$	2.88920	0.0992741
$848$	4.96797	0.170601
$849$	47.6457	1.63520
$850$	−2.36389	−0.0810809
$851$	74.5498	2.55553
$852$	44.4872	1.52411
$853$	−37.0221	−1.26761	−0.633806	−	0.773492i	$-0.718508\pi$
$853$	−37.0221	−1.26761	−0.633806	+	0.773492i	$0.718508\pi$
$854$	−64.7056	−2.21418
$855$	1.49796	0.0512291
$856$	183.700	6.27873
$857$	51.9102	1.77322	0.886610	−	0.462518i	$-0.153054\pi$
$857$	51.9102	1.77322	0.886610	+	0.462518i	$0.153054\pi$
$858$	−82.9938	−2.83336
$859$	3.21578	0.109721	0.0548605	−	0.998494i	$-0.482529\pi$
$859$	3.21578	0.109721	0.0548605	+	0.998494i	$0.482529\pi$
$860$	0.836222	0.0285149
$861$	−32.7092	−1.11473
$862$	−56.0924	−1.91052
$863$	−0.219252	−0.00746343	−0.00373171	−	0.999993i	$-0.501188\pi$
$863$	−0.219252	−0.00746343	−0.00373171	+	0.999993i	$0.501188\pi$
$864$	127.832	4.34893
$865$	23.9895	0.815667
$866$	−44.4232	−1.50956
$867$	−26.6101	−0.903727
$868$	−34.9608	−1.18665
$869$	17.0957	0.579931
$870$	6.03476	0.204597
$871$	45.4308	1.53937
$872$	154.554	5.23386
$873$	−1.36770	−0.0462898
$874$	97.2266	3.28874
$875$	−2.87647	−0.0972424
$876$	21.5807	0.729145
$877$	42.1346	1.42279	0.711393	−	0.702795i	$-0.248065\pi$
$877$	42.1346	1.42279	0.711393	+	0.702795i	$0.248065\pi$
$878$	92.6339	3.12624
$879$	10.3292	0.348395
$880$	49.4786	1.66792
$881$	8.60661	0.289964	0.144982	−	0.989434i	$-0.453688\pi$
$881$	8.60661	0.289964	0.144982	+	0.989434i	$0.453688\pi$
$882$	1.12512	0.0378847
$883$	−6.52805	−0.219686	−0.109843	−	0.993949i	$-0.535035\pi$
$883$	−6.52805	−0.219686	−0.109843	+	0.993949i	$0.535035\pi$
$884$	27.8645	0.937185
$885$	−20.3816	−0.685121
$886$	−39.1755	−1.31613
$887$	8.89766	0.298754	0.149377	−	0.988780i	$-0.452273\pi$
$887$	8.89766	0.298754	0.149377	+	0.988780i	$0.452273\pi$
$888$	−156.331	−5.24612
$889$	−10.9267	−0.366470
$890$	43.2555	1.44993
$891$	−25.0779	−0.840142
$892$	109.590	3.66933
$893$	−23.5214	−0.787114
$894$	23.7557	0.794510
$895$	−13.9417	−0.466018
$896$	127.732	4.26722
$897$	72.6122	2.42445
$898$	67.3622	2.24790
$899$	−2.94298	−0.0981540
$900$	−1.78253	−0.0594178
$901$	0.273203	0.00910172
$902$	−60.3361	−2.00897
$903$	−0.710044	−0.0236288
$904$	−7.40449	−0.246270
$905$	0.465869	0.0154860
$906$	−31.5751	−1.04901
$907$	−4.21305	−0.139892	−0.0699460	−	0.997551i	$-0.522283\pi$
$907$	−4.21305	−0.139892	−0.0699460	+	0.997551i	$0.522283\pi$
$908$	22.5999	0.750003
$909$	−4.33005	−0.143619
$910$	46.1378	1.52945
$911$	−6.83870	−0.226576	−0.113288	−	0.993562i	$-0.536138\pi$
$911$	−6.83870	−0.226576	−0.113288	+	0.993562i	$0.536138\pi$
$912$	−119.333	−3.95152
$913$	−28.4845	−0.942701
$914$	−92.2571	−3.05159
$915$	−13.4035	−0.443108
$916$	24.7172	0.816679
$917$	−9.01289	−0.297632
$918$	12.8502	0.424119
$919$	−23.6211	−0.779189	−0.389594	−	0.920987i	$-0.627385\pi$
$919$	−23.6211	−0.779189	−0.389594	+	0.920987i	$0.627385\pi$
$920$	−73.9611	−2.43843
$921$	9.20366	0.303271
$922$	−84.4364	−2.78076
$923$	28.6312	0.942406
$924$	−82.5181	−2.71465
$925$	9.81232	0.322627
$926$	111.803	3.67409
$927$	−5.15614	−0.169350
$928$	31.5694	1.03632
$929$	−45.8529	−1.50438	−0.752192	−	0.658944i	$-0.771004\pi$
$929$	−45.8529	−1.50438	−0.752192	+	0.658944i	$0.771004\pi$
$930$	−9.85445	−0.323140
$931$	−5.93604	−0.194546
$932$	−102.622	−3.36148
$933$	−42.5102	−1.39172
$934$	44.1153	1.44350
$935$	2.72097	0.0889854
$936$	18.2775	0.597417
$937$	31.2182	1.01985	0.509927	−	0.860217i	$-0.329672\pi$
$937$	31.2182	1.01985	0.509927	+	0.860217i	$0.329672\pi$
$938$	61.4650	2.00690
$939$	36.4195	1.18851
$940$	27.9899	0.912930
$941$	−9.66631	−0.315113	−0.157556	−	0.987510i	$-0.550362\pi$
$941$	−9.66631	−0.315113	−0.157556	+	0.987510i	$0.550362\pi$
$942$	−73.0383	−2.37972
$943$	52.7886	1.71903
$944$	−194.898	−6.34340
$945$	15.6365	0.508656
$946$	−1.30976	−0.0425840
$947$	−33.9703	−1.10389	−0.551943	−	0.833882i	$-0.686113\pi$
$947$	−33.9703	−1.10389	−0.551943	+	0.833882i	$0.686113\pi$
$948$	49.0646	1.59354
$949$	13.8890	0.450855
$950$	12.7971	0.415192
$951$	26.7258	0.866643
$952$	24.0995	0.781071
$953$	29.9985	0.971747	0.485873	−	0.874029i	$-0.338502\pi$
$953$	29.9985	0.971747	0.485873	+	0.874029i	$0.338502\pi$
$954$	0.280330	0.00907602
$955$	−5.56425	−0.180055
$956$	92.7336	2.99922
$957$	−6.94635	−0.224543
$958$	−41.7750	−1.34969
$959$	41.8389	1.35105
$960$	54.4830	1.75843
$961$	−26.1943	−0.844976
$962$	−157.387	−5.07436
$963$	6.06705	0.195508
$964$	−49.0610	−1.58015
$965$	−18.0385	−0.580681
$966$	98.2396	3.16081
$967$	−39.0096	−1.25446	−0.627232	−	0.778833i	$-0.715812\pi$
$967$	−39.0096	−1.25446	−0.627232	+	0.778833i	$0.715812\pi$
$968$	9.77792	0.314274
$969$	−6.56249	−0.210817
$970$	−11.6843	−0.375160
$971$	−29.7710	−0.955398	−0.477699	−	0.878523i	$-0.658529\pi$
$971$	−29.7710	−0.955398	−0.477699	+	0.878523i	$0.658529\pi$
$972$	18.4418	0.591522
$973$	−25.5401	−0.818779
$974$	1.08547	0.0347805
$975$	9.55729	0.306078
$976$	−128.171	−4.10265
$977$	50.1198	1.60347	0.801737	−	0.597678i	$-0.203910\pi$
$977$	50.1198	1.60347	0.801737	+	0.597678i	$0.203910\pi$
$978$	−25.4678	−0.814371
$979$	−49.7895	−1.59128
$980$	7.06374	0.225643
$981$	5.10445	0.162973
$982$	−105.036	−3.35184
$983$	−17.6542	−0.563082	−0.281541	−	0.959549i	$-0.590846\pi$
$983$	−17.6542	−0.563082	−0.281541	+	0.959549i	$0.590846\pi$
$984$	−110.698	−3.52892
$985$	−18.0036	−0.573642
$986$	3.17348	0.101064
$987$	−23.7665	−0.756496
$988$	−150.846	−4.79905
$989$	1.14592	0.0364382
$990$	2.79195	0.0887341
$991$	34.1879	1.08601	0.543007	−	0.839728i	$-0.317286\pi$
$991$	34.1879	1.08601	0.543007	+	0.839728i	$0.317286\pi$
$992$	−51.5513	−1.63675
$993$	27.8828	0.884833
$994$	38.7361	1.22864
$995$	21.5345	0.682688
$996$	−81.7506	−2.59037
$997$	15.0013	0.475096	0.237548	−	0.971376i	$-0.423656\pi$
$997$	15.0013	0.475096	0.237548	+	0.971376i	$0.423656\pi$
$998$	−72.0255	−2.27993
$999$	−53.3399	−1.68760

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6005.2.a.f.1.1	✓	111

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6005.2.a.f.1.1	✓	111	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)

\(f(q)\)	\(=\)	\(q-2.74668 q^{2} +1.63661 q^{3} +5.54423 q^{4} +1.00000 q^{5} -4.49523 q^{6} -2.87647 q^{7} -9.73484 q^{8} -0.321512 q^{9} +O(q^{10})\)	\(q-2.74668 q^{2} +1.63661 q^{3} +5.54423 q^{4} +1.00000 q^{5} -4.49523 q^{6} -2.87647 q^{7} -9.73484 q^{8} -0.321512 q^{9} -2.74668 q^{10} +3.16158 q^{11} +9.07373 q^{12} +5.83969 q^{13} +7.90073 q^{14} +1.63661 q^{15} +15.6500 q^{16} +0.860638 q^{17} +0.883089 q^{18} -4.65911 q^{19} +5.54423 q^{20} -4.70765 q^{21} -8.68383 q^{22} +7.59757 q^{23} -15.9321 q^{24} +1.00000 q^{25} -16.0397 q^{26} -5.43602 q^{27} -15.9478 q^{28} -1.34248 q^{29} -4.49523 q^{30} +2.19220 q^{31} -23.5158 q^{32} +5.17427 q^{33} -2.36389 q^{34} -2.87647 q^{35} -1.78253 q^{36} +9.81232 q^{37} +12.7971 q^{38} +9.55729 q^{39} -9.73484 q^{40} +6.94810 q^{41} +12.9304 q^{42} +0.150828 q^{43} +17.5285 q^{44} -0.321512 q^{45} -20.8681 q^{46} +5.04848 q^{47} +25.6129 q^{48} +1.27407 q^{49} -2.74668 q^{50} +1.40853 q^{51} +32.3766 q^{52} +0.317443 q^{53} +14.9310 q^{54} +3.16158 q^{55} +28.0020 q^{56} -7.62514 q^{57} +3.68736 q^{58} -12.4536 q^{59} +9.07373 q^{60} -8.18983 q^{61} -6.02126 q^{62} +0.924819 q^{63} +33.2902 q^{64} +5.83969 q^{65} -14.2120 q^{66} +7.77966 q^{67} +4.77157 q^{68} +12.4342 q^{69} +7.90073 q^{70} +4.90286 q^{71} +3.12987 q^{72} +2.37837 q^{73} -26.9512 q^{74} +1.63661 q^{75} -25.8312 q^{76} -9.09418 q^{77} -26.2508 q^{78} +5.40732 q^{79} +15.6500 q^{80} -7.93209 q^{81} -19.0842 q^{82} -9.00960 q^{83} -26.1003 q^{84} +0.860638 q^{85} -0.414274 q^{86} -2.19711 q^{87} -30.7774 q^{88} -15.7483 q^{89} +0.883089 q^{90} -16.7977 q^{91} +42.1226 q^{92} +3.58777 q^{93} -13.8665 q^{94} -4.65911 q^{95} -38.4861 q^{96} +4.25397 q^{97} -3.49946 q^{98} -1.01649 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 111 q + 20 q^{2} + 40 q^{3} + 136 q^{4} + 111 q^{5} + 3 q^{6} + 39 q^{7} + 45 q^{8} + 139 q^{9}+O(q^{10}) \) 111 * q + 20 * q^2 + 40 * q^3 + 136 * q^4 + 111 * q^5 + 3 * q^6 + 39 * q^7 + 45 * q^8 + 139 * q^9	\( 111 q + 20 q^{2} + 40 q^{3} + 136 q^{4} + 111 q^{5} + 3 q^{6} + 39 q^{7} + 45 q^{8} + 139 q^{9} + 20 q^{10} + 36 q^{11} + 80 q^{12} + 36 q^{13} + 7 q^{14} + 40 q^{15} + 190 q^{16} + 38 q^{17} + 48 q^{18} + 77 q^{19} + 136 q^{20} + 11 q^{21} + 39 q^{22} + 82 q^{23} - 3 q^{24} + 111 q^{25} - 3 q^{26} + 130 q^{27} + 87 q^{28} + 20 q^{29} + 3 q^{30} + 41 q^{31} + 85 q^{32} + 33 q^{33} + 7 q^{34} + 39 q^{35} + 191 q^{36} + 80 q^{37} + 42 q^{38} + 21 q^{39} + 45 q^{40} + 16 q^{41} + 33 q^{42} + 164 q^{43} + 37 q^{44} + 139 q^{45} + 32 q^{46} + 148 q^{47} + 149 q^{48} + 160 q^{49} + 20 q^{50} + 51 q^{51} + 87 q^{52} + 83 q^{53} - 6 q^{54} + 36 q^{55} - 10 q^{56} + 28 q^{57} + 47 q^{58} + 14 q^{59} + 80 q^{60} + 20 q^{61} + 14 q^{62} + 120 q^{63} + 231 q^{64} + 36 q^{65} - 4 q^{66} + 253 q^{67} + 80 q^{68} + 6 q^{69} + 7 q^{70} + 5 q^{71} + 124 q^{72} + 64 q^{73} - 37 q^{74} + 40 q^{75} + 92 q^{76} + 63 q^{77} + 29 q^{78} + 91 q^{79} + 190 q^{80} + 187 q^{81} - 7 q^{82} + 63 q^{83} - 69 q^{84} + 38 q^{85} - 22 q^{86} + 57 q^{87} + 121 q^{88} - 6 q^{89} + 48 q^{90} + 119 q^{91} + 104 q^{92} + 14 q^{93} - q^{94} + 77 q^{95} - 38 q^{96} + 96 q^{97} + 81 q^{98} + 106 q^{99}+O(q^{100}) \) 111 * q + 20 * q^2 + 40 * q^3 + 136 * q^4 + 111 * q^5 + 3 * q^6 + 39 * q^7 + 45 * q^8 + 139 * q^9 + 20 * q^10 + 36 * q^11 + 80 * q^12 + 36 * q^13 + 7 * q^14 + 40 * q^15 + 190 * q^16 + 38 * q^17 + 48 * q^18 + 77 * q^19 + 136 * q^20 + 11 * q^21 + 39 * q^22 + 82 * q^23 - 3 * q^24 + 111 * q^25 - 3 * q^26 + 130 * q^27 + 87 * q^28 + 20 * q^29 + 3 * q^30 + 41 * q^31 + 85 * q^32 + 33 * q^33 + 7 * q^34 + 39 * q^35 + 191 * q^36 + 80 * q^37 + 42 * q^38 + 21 * q^39 + 45 * q^40 + 16 * q^41 + 33 * q^42 + 164 * q^43 + 37 * q^44 + 139 * q^45 + 32 * q^46 + 148 * q^47 + 149 * q^48 + 160 * q^49 + 20 * q^50 + 51 * q^51 + 87 * q^52 + 83 * q^53 - 6 * q^54 + 36 * q^55 - 10 * q^56 + 28 * q^57 + 47 * q^58 + 14 * q^59 + 80 * q^60 + 20 * q^61 + 14 * q^62 + 120 * q^63 + 231 * q^64 + 36 * q^65 - 4 * q^66 + 253 * q^67 + 80 * q^68 + 6 * q^69 + 7 * q^70 + 5 * q^71 + 124 * q^72 + 64 * q^73 - 37 * q^74 + 40 * q^75 + 92 * q^76 + 63 * q^77 + 29 * q^78 + 91 * q^79 + 190 * q^80 + 187 * q^81 - 7 * q^82 + 63 * q^83 - 69 * q^84 + 38 * q^85 - 22 * q^86 + 57 * q^87 + 121 * q^88 - 6 * q^89 + 48 * q^90 + 119 * q^91 + 104 * q^92 + 14 * q^93 - q^94 + 77 * q^95 - 38 * q^96 + 96 * q^97 + 81 * q^98 + 106 * q^99

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