LMFDB - Embedded newform 6026.2.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, 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("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.1178522580$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.73205$ of defining polynomial
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.732051 q^{3} +1.00000 q^{4} -1.73205 q^{5} -0.732051 q^{6} +2.00000 q^{7} +1.00000 q^{8} -2.46410 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.732051 q^{3} +1.00000 q^{4} -1.73205 q^{5} -0.732051 q^{6} +2.00000 q^{7} +1.00000 q^{8} -2.46410 q^{9} -1.73205 q^{10} -1.73205 q^{11} -0.732051 q^{12} +0.732051 q^{13} +2.00000 q^{14} +1.26795 q^{15} +1.00000 q^{16} +1.73205 q^{17} -2.46410 q^{18} +6.73205 q^{19} -1.73205 q^{20} -1.46410 q^{21} -1.73205 q^{22} -1.00000 q^{23} -0.732051 q^{24} -2.00000 q^{25} +0.732051 q^{26} +4.00000 q^{27} +2.00000 q^{28} -9.46410 q^{29} +1.26795 q^{30} +8.00000 q^{31} +1.00000 q^{32} +1.26795 q^{33} +1.73205 q^{34} -3.46410 q^{35} -2.46410 q^{36} -0.535898 q^{37} +6.73205 q^{38} -0.535898 q^{39} -1.73205 q^{40} -0.464102 q^{41} -1.46410 q^{42} -9.19615 q^{43} -1.73205 q^{44} +4.26795 q^{45} -1.00000 q^{46} +11.6603 q^{47} -0.732051 q^{48} -3.00000 q^{49} -2.00000 q^{50} -1.26795 q^{51} +0.732051 q^{52} -3.46410 q^{53} +4.00000 q^{54} +3.00000 q^{55} +2.00000 q^{56} -4.92820 q^{57} -9.46410 q^{58} +7.26795 q^{59} +1.26795 q^{60} -3.19615 q^{61} +8.00000 q^{62} -4.92820 q^{63} +1.00000 q^{64} -1.26795 q^{65} +1.26795 q^{66} +11.1244 q^{67} +1.73205 q^{68} +0.732051 q^{69} -3.46410 q^{70} +7.26795 q^{71} -2.46410 q^{72} +4.19615 q^{73} -0.535898 q^{74} +1.46410 q^{75} +6.73205 q^{76} -3.46410 q^{77} -0.535898 q^{78} -6.53590 q^{79} -1.73205 q^{80} +4.46410 q^{81} -0.464102 q^{82} -2.19615 q^{83} -1.46410 q^{84} -3.00000 q^{85} -9.19615 q^{86} +6.92820 q^{87} -1.73205 q^{88} +9.46410 q^{89} +4.26795 q^{90} +1.46410 q^{91} -1.00000 q^{92} -5.85641 q^{93} +11.6603 q^{94} -11.6603 q^{95} -0.732051 q^{96} -0.535898 q^{97} -3.00000 q^{98} +4.26795 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{6} + 4 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^6 + 4 * q^7 + 2 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{6} + 4 q^{7} + 2 q^{8} + 2 q^{9} + 2 q^{12} - 2 q^{13} + 4 q^{14} + 6 q^{15} + 2 q^{16} + 2 q^{18} + 10 q^{19} + 4 q^{21} - 2 q^{23} + 2 q^{24} - 4 q^{25} - 2 q^{26} + 8 q^{27} + 4 q^{28} - 12 q^{29} + 6 q^{30} + 16 q^{31} + 2 q^{32} + 6 q^{33} + 2 q^{36} - 8 q^{37} + 10 q^{38} - 8 q^{39} + 6 q^{41} + 4 q^{42} - 8 q^{43} + 12 q^{45} - 2 q^{46} + 6 q^{47} + 2 q^{48} - 6 q^{49} - 4 q^{50} - 6 q^{51} - 2 q^{52} + 8 q^{54} + 6 q^{55} + 4 q^{56} + 4 q^{57} - 12 q^{58} + 18 q^{59} + 6 q^{60} + 4 q^{61} + 16 q^{62} + 4 q^{63} + 2 q^{64} - 6 q^{65} + 6 q^{66} - 2 q^{67} - 2 q^{69} + 18 q^{71} + 2 q^{72} - 2 q^{73} - 8 q^{74} - 4 q^{75} + 10 q^{76} - 8 q^{78} - 20 q^{79} + 2 q^{81} + 6 q^{82} + 6 q^{83} + 4 q^{84} - 6 q^{85} - 8 q^{86} + 12 q^{89} + 12 q^{90} - 4 q^{91} - 2 q^{92} + 16 q^{93} + 6 q^{94} - 6 q^{95} + 2 q^{96} - 8 q^{97} - 6 q^{98} + 12 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^6 + 4 * q^7 + 2 * q^8 + 2 * q^9 + 2 * q^12 - 2 * q^13 + 4 * q^14 + 6 * q^15 + 2 * q^16 + 2 * q^18 + 10 * q^19 + 4 * q^21 - 2 * q^23 + 2 * q^24 - 4 * q^25 - 2 * q^26 + 8 * q^27 + 4 * q^28 - 12 * q^29 + 6 * q^30 + 16 * q^31 + 2 * q^32 + 6 * q^33 + 2 * q^36 - 8 * q^37 + 10 * q^38 - 8 * q^39 + 6 * q^41 + 4 * q^42 - 8 * q^43 + 12 * q^45 - 2 * q^46 + 6 * q^47 + 2 * q^48 - 6 * q^49 - 4 * q^50 - 6 * q^51 - 2 * q^52 + 8 * q^54 + 6 * q^55 + 4 * q^56 + 4 * q^57 - 12 * q^58 + 18 * q^59 + 6 * q^60 + 4 * q^61 + 16 * q^62 + 4 * q^63 + 2 * q^64 - 6 * q^65 + 6 * q^66 - 2 * q^67 - 2 * q^69 + 18 * q^71 + 2 * q^72 - 2 * q^73 - 8 * q^74 - 4 * q^75 + 10 * q^76 - 8 * q^78 - 20 * q^79 + 2 * q^81 + 6 * q^82 + 6 * q^83 + 4 * q^84 - 6 * q^85 - 8 * q^86 + 12 * q^89 + 12 * q^90 - 4 * q^91 - 2 * q^92 + 16 * q^93 + 6 * q^94 - 6 * q^95 + 2 * q^96 - 8 * q^97 - 6 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−0.732051	−0.422650	−0.211325	−	0.977416i	$-0.567778\pi$
$3$	−0.732051	−0.422650	−0.211325	+	0.977416i	$0.567778\pi$
$4$	1.00000	0.500000
$5$	−1.73205	−0.774597	−0.387298	−	0.921954i	$-0.626592\pi$
$5$	−1.73205	−0.774597	−0.387298	+	0.921954i	$0.626592\pi$
$6$	−0.732051	−0.298858
$7$	2.00000	0.755929	0.377964	−	0.925820i	$-0.376624\pi$
$7$	2.00000	0.755929	0.377964	+	0.925820i	$0.376624\pi$
$8$	1.00000	0.353553
$9$	−2.46410	−0.821367
$10$	−1.73205	−0.547723
$11$	−1.73205	−0.522233	−0.261116	−	0.965307i	$-0.584091\pi$
$11$	−1.73205	−0.522233	−0.261116	+	0.965307i	$0.584091\pi$
$12$	−0.732051	−0.211325
$13$	0.732051	0.203034	0.101517	−	0.994834i	$-0.467630\pi$
$13$	0.732051	0.203034	0.101517	+	0.994834i	$0.467630\pi$
$14$	2.00000	0.534522
$15$	1.26795	0.327383
$16$	1.00000	0.250000
$17$	1.73205	0.420084	0.210042	−	0.977692i	$-0.432640\pi$
$17$	1.73205	0.420084	0.210042	+	0.977692i	$0.432640\pi$
$18$	−2.46410	−0.580794
$19$	6.73205	1.54444	0.772219	−	0.635356i	$-0.219147\pi$
$19$	6.73205	1.54444	0.772219	+	0.635356i	$0.219147\pi$
$20$	−1.73205	−0.387298
$21$	−1.46410	−0.319493
$22$	−1.73205	−0.369274
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−0.732051	−0.149429
$25$	−2.00000	−0.400000
$26$	0.732051	0.143567
$27$	4.00000	0.769800
$28$	2.00000	0.377964
$29$	−9.46410	−1.75744	−0.878720	−	0.477338i	$-0.841602\pi$
$29$	−9.46410	−1.75744	−0.878720	+	0.477338i	$0.841602\pi$
$30$	1.26795	0.231495
$31$	8.00000	1.43684	0.718421	−	0.695608i	$-0.244865\pi$
$31$	8.00000	1.43684	0.718421	+	0.695608i	$0.244865\pi$
$32$	1.00000	0.176777
$33$	1.26795	0.220722
$34$	1.73205	0.297044
$35$	−3.46410	−0.585540
$36$	−2.46410	−0.410684
$37$	−0.535898	−0.0881012	−0.0440506	−	0.999029i	$-0.514026\pi$
$37$	−0.535898	−0.0881012	−0.0440506	+	0.999029i	$0.514026\pi$
$38$	6.73205	1.09208
$39$	−0.535898	−0.0858124
$40$	−1.73205	−0.273861
$41$	−0.464102	−0.0724805	−0.0362402	−	0.999343i	$-0.511538\pi$
$41$	−0.464102	−0.0724805	−0.0362402	+	0.999343i	$0.511538\pi$
$42$	−1.46410	−0.225916
$43$	−9.19615	−1.40240	−0.701200	−	0.712965i	$-0.747352\pi$
$43$	−9.19615	−1.40240	−0.701200	+	0.712965i	$0.747352\pi$
$44$	−1.73205	−0.261116
$45$	4.26795	0.636228
$46$	−1.00000	−0.147442
$47$	11.6603	1.70082	0.850411	−	0.526118i	$-0.176353\pi$
$47$	11.6603	1.70082	0.850411	+	0.526118i	$0.176353\pi$
$48$	−0.732051	−0.105662
$49$	−3.00000	−0.428571
$50$	−2.00000	−0.282843
$51$	−1.26795	−0.177548
$52$	0.732051	0.101517
$53$	−3.46410	−0.475831	−0.237915	−	0.971286i	$-0.576464\pi$
$53$	−3.46410	−0.475831	−0.237915	+	0.971286i	$0.576464\pi$
$54$	4.00000	0.544331
$55$	3.00000	0.404520
$56$	2.00000	0.267261
$57$	−4.92820	−0.652756
$58$	−9.46410	−1.24270
$59$	7.26795	0.946206	0.473103	−	0.881007i	$-0.343134\pi$
$59$	7.26795	0.946206	0.473103	+	0.881007i	$0.343134\pi$
$60$	1.26795	0.163692
$61$	−3.19615	−0.409225	−0.204613	−	0.978843i	$-0.565593\pi$
$61$	−3.19615	−0.409225	−0.204613	+	0.978843i	$0.565593\pi$
$62$	8.00000	1.01600
$63$	−4.92820	−0.620895
$64$	1.00000	0.125000
$65$	−1.26795	−0.157270
$66$	1.26795	0.156074
$67$	11.1244	1.35906	0.679528	−	0.733649i	$-0.262185\pi$
$67$	11.1244	1.35906	0.679528	+	0.733649i	$0.262185\pi$
$68$	1.73205	0.210042
$69$	0.732051	0.0881286
$70$	−3.46410	−0.414039
$71$	7.26795	0.862547	0.431273	−	0.902221i	$-0.358064\pi$
$71$	7.26795	0.862547	0.431273	+	0.902221i	$0.358064\pi$
$72$	−2.46410	−0.290397
$73$	4.19615	0.491122	0.245561	−	0.969381i	$-0.421028\pi$
$73$	4.19615	0.491122	0.245561	+	0.969381i	$0.421028\pi$
$74$	−0.535898	−0.0622969
$75$	1.46410	0.169060
$76$	6.73205	0.772219
$77$	−3.46410	−0.394771
$78$	−0.535898	−0.0606785
$79$	−6.53590	−0.735346	−0.367673	−	0.929955i	$-0.619845\pi$
$79$	−6.53590	−0.735346	−0.367673	+	0.929955i	$0.619845\pi$
$80$	−1.73205	−0.193649
$81$	4.46410	0.496011
$82$	−0.464102	−0.0512514
$83$	−2.19615	−0.241059	−0.120530	−	0.992710i	$-0.538459\pi$
$83$	−2.19615	−0.241059	−0.120530	+	0.992710i	$0.538459\pi$
$84$	−1.46410	−0.159747
$85$	−3.00000	−0.325396
$86$	−9.19615	−0.991647
$87$	6.92820	0.742781
$88$	−1.73205	−0.184637
$89$	9.46410	1.00319	0.501596	−	0.865102i	$-0.332746\pi$
$89$	9.46410	1.00319	0.501596	+	0.865102i	$0.332746\pi$
$90$	4.26795	0.449881
$91$	1.46410	0.153480
$92$	−1.00000	−0.104257
$93$	−5.85641	−0.607281
$94$	11.6603	1.20266
$95$	−11.6603	−1.19632
$96$	−0.732051	−0.0747146
$97$	−0.535898	−0.0544122	−0.0272061	−	0.999630i	$-0.508661\pi$
$97$	−0.535898	−0.0544122	−0.0272061	+	0.999630i	$0.508661\pi$
$98$	−3.00000	−0.303046
$99$	4.26795	0.428945
$100$	−2.00000	−0.200000
$101$	−9.46410	−0.941713	−0.470857	−	0.882210i	$-0.656055\pi$
$101$	−9.46410	−0.941713	−0.470857	+	0.882210i	$0.656055\pi$
$102$	−1.26795	−0.125546
$103$	6.26795	0.617599	0.308800	−	0.951127i	$-0.400073\pi$
$103$	6.26795	0.617599	0.308800	+	0.951127i	$0.400073\pi$
$104$	0.732051	0.0717835
$105$	2.53590	0.247478
$106$	−3.46410	−0.336463
$107$	7.73205	0.747486	0.373743	−	0.927532i	$-0.378074\pi$
$107$	7.73205	0.747486	0.373743	+	0.927532i	$0.378074\pi$
$108$	4.00000	0.384900
$109$	1.19615	0.114571	0.0572853	−	0.998358i	$-0.481756\pi$
$109$	1.19615	0.114571	0.0572853	+	0.998358i	$0.481756\pi$
$110$	3.00000	0.286039
$111$	0.392305	0.0372359
$112$	2.00000	0.188982
$113$	2.19615	0.206597	0.103298	−	0.994650i	$-0.467060\pi$
$113$	2.19615	0.206597	0.103298	+	0.994650i	$0.467060\pi$
$114$	−4.92820	−0.461569
$115$	1.73205	0.161515
$116$	−9.46410	−0.878720
$117$	−1.80385	−0.166766
$118$	7.26795	0.669069
$119$	3.46410	0.317554
$120$	1.26795	0.115747
$121$	−8.00000	−0.727273
$122$	−3.19615	−0.289366
$123$	0.339746	0.0306339
$124$	8.00000	0.718421
$125$	12.1244	1.08444
$126$	−4.92820	−0.439039
$127$	16.1962	1.43718	0.718588	−	0.695436i	$-0.244789\pi$
$127$	16.1962	1.43718	0.718588	+	0.695436i	$0.244789\pi$
$128$	1.00000	0.0883883
$129$	6.73205	0.592724
$130$	−1.26795	−0.111207
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	1.26795	0.110361
$133$	13.4641	1.16749
$134$	11.1244	0.960998
$135$	−6.92820	−0.596285
$136$	1.73205	0.148522
$137$	6.12436	0.523239	0.261620	−	0.965171i	$-0.415743\pi$
$137$	6.12436	0.523239	0.261620	+	0.965171i	$0.415743\pi$
$138$	0.732051	0.0623163
$139$	17.0000	1.44192	0.720961	−	0.692976i	$-0.243701\pi$
$139$	17.0000	1.44192	0.720961	+	0.692976i	$0.243701\pi$
$140$	−3.46410	−0.292770
$141$	−8.53590	−0.718852
$142$	7.26795	0.609913
$143$	−1.26795	−0.106031
$144$	−2.46410	−0.205342
$145$	16.3923	1.36131
$146$	4.19615	0.347276
$147$	2.19615	0.181136
$148$	−0.535898	−0.0440506
$149$	3.80385	0.311623	0.155812	−	0.987787i	$-0.450201\pi$
$149$	3.80385	0.311623	0.155812	+	0.987787i	$0.450201\pi$
$150$	1.46410	0.119543
$151$	−4.46410	−0.363283	−0.181642	−	0.983365i	$-0.558141\pi$
$151$	−4.46410	−0.363283	−0.181642	+	0.983365i	$0.558141\pi$
$152$	6.73205	0.546041
$153$	−4.26795	−0.345043
$154$	−3.46410	−0.279145
$155$	−13.8564	−1.11297
$156$	−0.535898	−0.0429062
$157$	14.0000	1.11732	0.558661	−	0.829396i	$-0.311315\pi$
$157$	14.0000	1.11732	0.558661	+	0.829396i	$0.311315\pi$
$158$	−6.53590	−0.519968
$159$	2.53590	0.201110
$160$	−1.73205	−0.136931
$161$	−2.00000	−0.157622
$162$	4.46410	0.350733
$163$	7.53590	0.590257	0.295129	−	0.955458i	$-0.404638\pi$
$163$	7.53590	0.590257	0.295129	+	0.955458i	$0.404638\pi$
$164$	−0.464102	−0.0362402
$165$	−2.19615	−0.170970
$166$	−2.19615	−0.170454
$167$	10.8564	0.840094	0.420047	−	0.907502i	$-0.362014\pi$
$167$	10.8564	0.840094	0.420047	+	0.907502i	$0.362014\pi$
$168$	−1.46410	−0.112958
$169$	−12.4641	−0.958777
$170$	−3.00000	−0.230089
$171$	−16.5885	−1.26855
$172$	−9.19615	−0.701200
$173$	1.39230	0.105855	0.0529275	−	0.998598i	$-0.483145\pi$
$173$	1.39230	0.105855	0.0529275	+	0.998598i	$0.483145\pi$
$174$	6.92820	0.525226
$175$	−4.00000	−0.302372
$176$	−1.73205	−0.130558
$177$	−5.32051	−0.399914
$178$	9.46410	0.709364
$179$	6.92820	0.517838	0.258919	−	0.965899i	$-0.416634\pi$
$179$	6.92820	0.517838	0.258919	+	0.965899i	$0.416634\pi$
$180$	4.26795	0.318114
$181$	10.5359	0.783127	0.391564	−	0.920151i	$-0.371934\pi$
$181$	10.5359	0.783127	0.391564	+	0.920151i	$0.371934\pi$
$182$	1.46410	0.108526
$183$	2.33975	0.172959
$184$	−1.00000	−0.0737210
$185$	0.928203	0.0682429
$186$	−5.85641	−0.429413
$187$	−3.00000	−0.219382
$188$	11.6603	0.850411
$189$	8.00000	0.581914
$190$	−11.6603	−0.845924
$191$	19.5167	1.41218	0.706088	−	0.708124i	$-0.250458\pi$
$191$	19.5167	1.41218	0.706088	+	0.708124i	$0.250458\pi$
$192$	−0.732051	−0.0528312
$193$	10.3205	0.742886	0.371443	−	0.928456i	$-0.378863\pi$
$193$	10.3205	0.742886	0.371443	+	0.928456i	$0.378863\pi$
$194$	−0.535898	−0.0384753
$195$	0.928203	0.0664700
$196$	−3.00000	−0.214286
$197$	−21.0000	−1.49619	−0.748094	−	0.663593i	$-0.769031\pi$
$197$	−21.0000	−1.49619	−0.748094	+	0.663593i	$0.769031\pi$
$198$	4.26795	0.303310
$199$	18.2679	1.29498	0.647490	−	0.762074i	$-0.275819\pi$
$199$	18.2679	1.29498	0.647490	+	0.762074i	$0.275819\pi$
$200$	−2.00000	−0.141421
$201$	−8.14359	−0.574405
$202$	−9.46410	−0.665892
$203$	−18.9282	−1.32850
$204$	−1.26795	−0.0887742
$205$	0.803848	0.0561432
$206$	6.26795	0.436709
$207$	2.46410	0.171267
$208$	0.732051	0.0507586
$209$	−11.6603	−0.806557
$210$	2.53590	0.174994
$211$	12.0526	0.829732	0.414866	−	0.909882i	$-0.363828\pi$
$211$	12.0526	0.829732	0.414866	+	0.909882i	$0.363828\pi$
$212$	−3.46410	−0.237915
$213$	−5.32051	−0.364555
$214$	7.73205	0.528552
$215$	15.9282	1.08629
$216$	4.00000	0.272166
$217$	16.0000	1.08615
$218$	1.19615	0.0810137
$219$	−3.07180	−0.207573
$220$	3.00000	0.202260
$221$	1.26795	0.0852915
$222$	0.392305	0.0263298
$223$	26.0000	1.74109	0.870544	−	0.492090i	$-0.163767\pi$
$223$	26.0000	1.74109	0.870544	+	0.492090i	$0.163767\pi$
$224$	2.00000	0.133631
$225$	4.92820	0.328547
$226$	2.19615	0.146086
$227$	−6.00000	−0.398234	−0.199117	−	0.979976i	$-0.563807\pi$
$227$	−6.00000	−0.398234	−0.199117	+	0.979976i	$0.563807\pi$
$228$	−4.92820	−0.326378
$229$	28.7846	1.90214	0.951070	−	0.308975i	$-0.0999858\pi$
$229$	28.7846	1.90214	0.951070	+	0.308975i	$0.0999858\pi$
$230$	1.73205	0.114208
$231$	2.53590	0.166850
$232$	−9.46410	−0.621349
$233$	13.3923	0.877359	0.438680	−	0.898644i	$-0.355446\pi$
$233$	13.3923	0.877359	0.438680	+	0.898644i	$0.355446\pi$
$234$	−1.80385	−0.117921
$235$	−20.1962	−1.31745
$236$	7.26795	0.473103
$237$	4.78461	0.310794
$238$	3.46410	0.224544
$239$	−10.3923	−0.672222	−0.336111	−	0.941822i	$-0.609112\pi$
$239$	−10.3923	−0.672222	−0.336111	+	0.941822i	$0.609112\pi$
$240$	1.26795	0.0818458
$241$	−2.26795	−0.146091	−0.0730457	−	0.997329i	$-0.523272\pi$
$241$	−2.26795	−0.146091	−0.0730457	+	0.997329i	$0.523272\pi$
$242$	−8.00000	−0.514259
$243$	−15.2679	−0.979439
$244$	−3.19615	−0.204613
$245$	5.19615	0.331970
$246$	0.339746	0.0216614
$247$	4.92820	0.313574
$248$	8.00000	0.508001
$249$	1.60770	0.101884
$250$	12.1244	0.766812
$251$	−13.5167	−0.853164	−0.426582	−	0.904449i	$-0.640282\pi$
$251$	−13.5167	−0.853164	−0.426582	+	0.904449i	$0.640282\pi$
$252$	−4.92820	−0.310448
$253$	1.73205	0.108893
$254$	16.1962	1.01624
$255$	2.19615	0.137528
$256$	1.00000	0.0625000
$257$	−23.3205	−1.45469	−0.727347	−	0.686270i	$-0.759247\pi$
$257$	−23.3205	−1.45469	−0.727347	+	0.686270i	$0.759247\pi$
$258$	6.73205	0.419119
$259$	−1.07180	−0.0665982
$260$	−1.26795	−0.0786349
$261$	23.3205	1.44350
$262$	−1.00000	−0.0617802
$263$	−27.1244	−1.67256	−0.836280	−	0.548303i	$-0.815274\pi$
$263$	−27.1244	−1.67256	−0.836280	+	0.548303i	$0.815274\pi$
$264$	1.26795	0.0780369
$265$	6.00000	0.368577
$266$	13.4641	0.825537
$267$	−6.92820	−0.423999
$268$	11.1244	0.679528
$269$	−9.80385	−0.597751	−0.298876	−	0.954292i	$-0.596612\pi$
$269$	−9.80385	−0.597751	−0.298876	+	0.954292i	$0.596612\pi$
$270$	−6.92820	−0.421637
$271$	19.5359	1.18672	0.593361	−	0.804937i	$-0.297801\pi$
$271$	19.5359	1.18672	0.593361	+	0.804937i	$0.297801\pi$
$272$	1.73205	0.105021
$273$	−1.07180	−0.0648681
$274$	6.12436	0.369986
$275$	3.46410	0.208893
$276$	0.732051	0.0440643
$277$	6.39230	0.384076	0.192038	−	0.981387i	$-0.438490\pi$
$277$	6.39230	0.384076	0.192038	+	0.981387i	$0.438490\pi$
$278$	17.0000	1.01959
$279$	−19.7128	−1.18018
$280$	−3.46410	−0.207020
$281$	−9.58846	−0.571999	−0.286000	−	0.958230i	$-0.592326\pi$
$281$	−9.58846	−0.571999	−0.286000	+	0.958230i	$0.592326\pi$
$282$	−8.53590	−0.508305
$283$	18.3923	1.09331	0.546655	−	0.837358i	$-0.315901\pi$
$283$	18.3923	1.09331	0.546655	+	0.837358i	$0.315901\pi$
$284$	7.26795	0.431273
$285$	8.53590	0.505623
$286$	−1.26795	−0.0749754
$287$	−0.928203	−0.0547901
$288$	−2.46410	−0.145199
$289$	−14.0000	−0.823529
$290$	16.3923	0.962589
$291$	0.392305	0.0229973
$292$	4.19615	0.245561
$293$	−17.6603	−1.03172	−0.515862	−	0.856672i	$-0.672528\pi$
$293$	−17.6603	−1.03172	−0.515862	+	0.856672i	$0.672528\pi$
$294$	2.19615	0.128082
$295$	−12.5885	−0.732928
$296$	−0.535898	−0.0311485
$297$	−6.92820	−0.402015
$298$	3.80385	0.220351
$299$	−0.732051	−0.0423356
$300$	1.46410	0.0845299
$301$	−18.3923	−1.06011
$302$	−4.46410	−0.256880
$303$	6.92820	0.398015
$304$	6.73205	0.386110
$305$	5.53590	0.316985
$306$	−4.26795	−0.243982
$307$	−1.80385	−0.102951	−0.0514755	−	0.998674i	$-0.516392\pi$
$307$	−1.80385	−0.102951	−0.0514755	+	0.998674i	$0.516392\pi$
$308$	−3.46410	−0.197386
$309$	−4.58846	−0.261028
$310$	−13.8564	−0.786991
$311$	9.00000	0.510343	0.255172	−	0.966896i	$-0.417868\pi$
$311$	9.00000	0.510343	0.255172	+	0.966896i	$0.417868\pi$
$312$	−0.535898	−0.0303393
$313$	8.92820	0.504652	0.252326	−	0.967642i	$-0.418804\pi$
$313$	8.92820	0.504652	0.252326	+	0.967642i	$0.418804\pi$
$314$	14.0000	0.790066
$315$	8.53590	0.480943
$316$	−6.53590	−0.367673
$317$	−3.80385	−0.213645	−0.106823	−	0.994278i	$-0.534068\pi$
$317$	−3.80385	−0.213645	−0.106823	+	0.994278i	$0.534068\pi$
$318$	2.53590	0.142206
$319$	16.3923	0.917793
$320$	−1.73205	−0.0968246
$321$	−5.66025	−0.315925
$322$	−2.00000	−0.111456
$323$	11.6603	0.648794
$324$	4.46410	0.248006
$325$	−1.46410	−0.0812137
$326$	7.53590	0.417375
$327$	−0.875644	−0.0484232
$328$	−0.464102	−0.0256257
$329$	23.3205	1.28570
$330$	−2.19615	−0.120894
$331$	−14.3923	−0.791073	−0.395536	−	0.918450i	$-0.629441\pi$
$331$	−14.3923	−0.791073	−0.395536	+	0.918450i	$0.629441\pi$
$332$	−2.19615	−0.120530
$333$	1.32051	0.0723634
$334$	10.8564	0.594036
$335$	−19.2679	−1.05272
$336$	−1.46410	−0.0798733
$337$	10.1962	0.555420	0.277710	−	0.960665i	$-0.410425\pi$
$337$	10.1962	0.555420	0.277710	+	0.960665i	$0.410425\pi$
$338$	−12.4641	−0.677958
$339$	−1.60770	−0.0873180
$340$	−3.00000	−0.162698
$341$	−13.8564	−0.750366
$342$	−16.5885	−0.897001
$343$	−20.0000	−1.07990
$344$	−9.19615	−0.495823
$345$	−1.26795	−0.0682641
$346$	1.39230	0.0748508
$347$	16.8564	0.904899	0.452450	−	0.891790i	$-0.350550\pi$
$347$	16.8564	0.904899	0.452450	+	0.891790i	$0.350550\pi$
$348$	6.92820	0.371391
$349$	6.14359	0.328859	0.164430	−	0.986389i	$-0.447422\pi$
$349$	6.14359	0.328859	0.164430	+	0.986389i	$0.447422\pi$
$350$	−4.00000	−0.213809
$351$	2.92820	0.156296
$352$	−1.73205	−0.0923186
$353$	−8.32051	−0.442856	−0.221428	−	0.975177i	$-0.571072\pi$
$353$	−8.32051	−0.442856	−0.221428	+	0.975177i	$0.571072\pi$
$354$	−5.32051	−0.282782
$355$	−12.5885	−0.668126
$356$	9.46410	0.501596
$357$	−2.53590	−0.134214
$358$	6.92820	0.366167
$359$	−3.58846	−0.189392	−0.0946958	−	0.995506i	$-0.530188\pi$
$359$	−3.58846	−0.189392	−0.0946958	+	0.995506i	$0.530188\pi$
$360$	4.26795	0.224941
$361$	26.3205	1.38529
$362$	10.5359	0.553755
$363$	5.85641	0.307382
$364$	1.46410	0.0767398
$365$	−7.26795	−0.380422
$366$	2.33975	0.122300
$367$	−3.41154	−0.178081	−0.0890405	−	0.996028i	$-0.528380\pi$
$367$	−3.41154	−0.178081	−0.0890405	+	0.996028i	$0.528380\pi$
$368$	−1.00000	−0.0521286
$369$	1.14359	0.0595331
$370$	0.928203	0.0482550
$371$	−6.92820	−0.359694
$372$	−5.85641	−0.303641
$373$	−20.0526	−1.03828	−0.519141	−	0.854689i	$-0.673748\pi$
$373$	−20.0526	−1.03828	−0.519141	+	0.854689i	$0.673748\pi$
$374$	−3.00000	−0.155126
$375$	−8.87564	−0.458336
$376$	11.6603	0.601332
$377$	−6.92820	−0.356821
$378$	8.00000	0.411476
$379$	−16.1244	−0.828253	−0.414126	−	0.910219i	$-0.635913\pi$
$379$	−16.1244	−0.828253	−0.414126	+	0.910219i	$0.635913\pi$
$380$	−11.6603	−0.598158
$381$	−11.8564	−0.607422
$382$	19.5167	0.998559
$383$	−22.3923	−1.14419	−0.572097	−	0.820186i	$-0.693870\pi$
$383$	−22.3923	−1.14419	−0.572097	+	0.820186i	$0.693870\pi$
$384$	−0.732051	−0.0373573
$385$	6.00000	0.305788
$386$	10.3205	0.525300
$387$	22.6603	1.15189
$388$	−0.535898	−0.0272061
$389$	−16.7321	−0.848349	−0.424174	−	0.905581i	$-0.639436\pi$
$389$	−16.7321	−0.848349	−0.424174	+	0.905581i	$0.639436\pi$
$390$	0.928203	0.0470014
$391$	−1.73205	−0.0875936
$392$	−3.00000	−0.151523
$393$	0.732051	0.0369271
$394$	−21.0000	−1.05796
$395$	11.3205	0.569597
$396$	4.26795	0.214473
$397$	−0.196152	−0.00984461	−0.00492230	−	0.999988i	$-0.501567\pi$
$397$	−0.196152	−0.00984461	−0.00492230	+	0.999988i	$0.501567\pi$
$398$	18.2679	0.915690
$399$	−9.85641	−0.493438
$400$	−2.00000	−0.100000
$401$	15.7128	0.784660	0.392330	−	0.919824i	$-0.371669\pi$
$401$	15.7128	0.784660	0.392330	+	0.919824i	$0.371669\pi$
$402$	−8.14359	−0.406166
$403$	5.85641	0.291728
$404$	−9.46410	−0.470857
$405$	−7.73205	−0.384209
$406$	−18.9282	−0.939391
$407$	0.928203	0.0460093
$408$	−1.26795	−0.0627728
$409$	35.2487	1.74294	0.871468	−	0.490452i	$-0.163168\pi$
$409$	35.2487	1.74294	0.871468	+	0.490452i	$0.163168\pi$
$410$	0.803848	0.0396992
$411$	−4.48334	−0.221147
$412$	6.26795	0.308800
$413$	14.5359	0.715265
$414$	2.46410	0.121104
$415$	3.80385	0.186724
$416$	0.732051	0.0358917
$417$	−12.4449	−0.609428
$418$	−11.6603	−0.570322
$419$	−11.6603	−0.569641	−0.284820	−	0.958581i	$-0.591934\pi$
$419$	−11.6603	−0.569641	−0.284820	+	0.958581i	$0.591934\pi$
$420$	2.53590	0.123739
$421$	−29.8564	−1.45511	−0.727556	−	0.686048i	$-0.759344\pi$
$421$	−29.8564	−1.45511	−0.727556	+	0.686048i	$0.759344\pi$
$422$	12.0526	0.586709
$423$	−28.7321	−1.39700
$424$	−3.46410	−0.168232
$425$	−3.46410	−0.168034
$426$	−5.32051	−0.257779
$427$	−6.39230	−0.309345
$428$	7.73205	0.373743
$429$	0.928203	0.0448141
$430$	15.9282	0.768126
$431$	22.9808	1.10694	0.553472	−	0.832868i	$-0.313303\pi$
$431$	22.9808	1.10694	0.553472	+	0.832868i	$0.313303\pi$
$432$	4.00000	0.192450
$433$	5.58846	0.268564	0.134282	−	0.990943i	$-0.457127\pi$
$433$	5.58846	0.268564	0.134282	+	0.990943i	$0.457127\pi$
$434$	16.0000	0.768025
$435$	−12.0000	−0.575356
$436$	1.19615	0.0572853
$437$	−6.73205	−0.322038
$438$	−3.07180	−0.146776
$439$	−9.78461	−0.466994	−0.233497	−	0.972358i	$-0.575017\pi$
$439$	−9.78461	−0.466994	−0.233497	+	0.972358i	$0.575017\pi$
$440$	3.00000	0.143019
$441$	7.39230	0.352015
$442$	1.26795	0.0603102
$443$	27.4641	1.30486	0.652429	−	0.757849i	$-0.273750\pi$
$443$	27.4641	1.30486	0.652429	+	0.757849i	$0.273750\pi$
$444$	0.392305	0.0186180
$445$	−16.3923	−0.777070
$446$	26.0000	1.23114
$447$	−2.78461	−0.131708
$448$	2.00000	0.0944911
$449$	−15.4641	−0.729796	−0.364898	−	0.931047i	$-0.618896\pi$
$449$	−15.4641	−0.729796	−0.364898	+	0.931047i	$0.618896\pi$
$450$	4.92820	0.232318
$451$	0.803848	0.0378517
$452$	2.19615	0.103298
$453$	3.26795	0.153542
$454$	−6.00000	−0.281594
$455$	−2.53590	−0.118885
$456$	−4.92820	−0.230784
$457$	−12.7846	−0.598039	−0.299019	−	0.954247i	$-0.596660\pi$
$457$	−12.7846	−0.598039	−0.299019	+	0.954247i	$0.596660\pi$
$458$	28.7846	1.34502
$459$	6.92820	0.323381
$460$	1.73205	0.0807573
$461$	5.53590	0.257832	0.128916	−	0.991655i	$-0.458850\pi$
$461$	5.53590	0.257832	0.128916	+	0.991655i	$0.458850\pi$
$462$	2.53590	0.117981
$463$	7.32051	0.340213	0.170106	−	0.985426i	$-0.445589\pi$
$463$	7.32051	0.340213	0.170106	+	0.985426i	$0.445589\pi$
$464$	−9.46410	−0.439360
$465$	10.1436	0.470398
$466$	13.3923	0.620387
$467$	11.8756	0.549539	0.274770	−	0.961510i	$-0.411398\pi$
$467$	11.8756	0.549539	0.274770	+	0.961510i	$0.411398\pi$
$468$	−1.80385	−0.0833829
$469$	22.2487	1.02735
$470$	−20.1962	−0.931579
$471$	−10.2487	−0.472236
$472$	7.26795	0.334534
$473$	15.9282	0.732380
$474$	4.78461	0.219764
$475$	−13.4641	−0.617775
$476$	3.46410	0.158777
$477$	8.53590	0.390832
$478$	−10.3923	−0.475333
$479$	−22.5167	−1.02881	−0.514406	−	0.857547i	$-0.671988\pi$
$479$	−22.5167	−1.02881	−0.514406	+	0.857547i	$0.671988\pi$
$480$	1.26795	0.0578737
$481$	−0.392305	−0.0178876
$482$	−2.26795	−0.103302
$483$	1.46410	0.0666189
$484$	−8.00000	−0.363636
$485$	0.928203	0.0421475
$486$	−15.2679	−0.692568
$487$	37.7846	1.71218	0.856092	−	0.516823i	$-0.172886\pi$
$487$	37.7846	1.71218	0.856092	+	0.516823i	$0.172886\pi$
$488$	−3.19615	−0.144683
$489$	−5.51666	−0.249472
$490$	5.19615	0.234738
$491$	21.0000	0.947717	0.473858	−	0.880601i	$-0.342861\pi$
$491$	21.0000	0.947717	0.473858	+	0.880601i	$0.342861\pi$
$492$	0.339746	0.0153169
$493$	−16.3923	−0.738272
$494$	4.92820	0.221730
$495$	−7.39230	−0.332259
$496$	8.00000	0.359211
$497$	14.5359	0.652024
$498$	1.60770	0.0720425
$499$	−26.1769	−1.17184	−0.585920	−	0.810369i	$-0.699267\pi$
$499$	−26.1769	−1.17184	−0.585920	+	0.810369i	$0.699267\pi$
$500$	12.1244	0.542218
$501$	−7.94744	−0.355065
$502$	−13.5167	−0.603278
$503$	−0.124356	−0.00554474	−0.00277237	−	0.999996i	$-0.500882\pi$
$503$	−0.124356	−0.00554474	−0.00277237	+	0.999996i	$0.500882\pi$
$504$	−4.92820	−0.219520
$505$	16.3923	0.729448
$506$	1.73205	0.0769991
$507$	9.12436	0.405227
$508$	16.1962	0.718588
$509$	−2.07180	−0.0918308	−0.0459154	−	0.998945i	$-0.514620\pi$
$509$	−2.07180	−0.0918308	−0.0459154	+	0.998945i	$0.514620\pi$
$510$	2.19615	0.0972473
$511$	8.39230	0.371254
$512$	1.00000	0.0441942
$513$	26.9282	1.18891
$514$	−23.3205	−1.02862
$515$	−10.8564	−0.478390
$516$	6.73205	0.296362
$517$	−20.1962	−0.888226
$518$	−1.07180	−0.0470920
$519$	−1.01924	−0.0447396
$520$	−1.26795	−0.0556033
$521$	−3.58846	−0.157213	−0.0786066	−	0.996906i	$-0.525047\pi$
$521$	−3.58846	−0.157213	−0.0786066	+	0.996906i	$0.525047\pi$
$522$	23.3205	1.02071
$523$	18.7321	0.819095	0.409548	−	0.912289i	$-0.365687\pi$
$523$	18.7321	0.819095	0.409548	+	0.912289i	$0.365687\pi$
$524$	−1.00000	−0.0436852
$525$	2.92820	0.127797
$526$	−27.1244	−1.18268
$527$	13.8564	0.603595
$528$	1.26795	0.0551804
$529$	1.00000	0.0434783
$530$	6.00000	0.260623
$531$	−17.9090	−0.777183
$532$	13.4641	0.583743
$533$	−0.339746	−0.0147160
$534$	−6.92820	−0.299813
$535$	−13.3923	−0.579000
$536$	11.1244	0.480499
$537$	−5.07180	−0.218864
$538$	−9.80385	−0.422674
$539$	5.19615	0.223814
$540$	−6.92820	−0.298142
$541$	−14.8564	−0.638727	−0.319363	−	0.947632i	$-0.603469\pi$
$541$	−14.8564	−0.638727	−0.319363	+	0.947632i	$0.603469\pi$
$542$	19.5359	0.839139
$543$	−7.71281	−0.330988
$544$	1.73205	0.0742611
$545$	−2.07180	−0.0887460
$546$	−1.07180	−0.0458687
$547$	−7.92820	−0.338985	−0.169493	−	0.985531i	$-0.554213\pi$
$547$	−7.92820	−0.338985	−0.169493	+	0.985531i	$0.554213\pi$
$548$	6.12436	0.261620
$549$	7.87564	0.336124
$550$	3.46410	0.147710
$551$	−63.7128	−2.71426
$552$	0.732051	0.0311582
$553$	−13.0718	−0.555869
$554$	6.39230	0.271583
$555$	−0.679492	−0.0288428
$556$	17.0000	0.720961
$557$	37.9808	1.60930	0.804648	−	0.593752i	$-0.202354\pi$
$557$	37.9808	1.60930	0.804648	+	0.593752i	$0.202354\pi$
$558$	−19.7128	−0.834510
$559$	−6.73205	−0.284735
$560$	−3.46410	−0.146385
$561$	2.19615	0.0927216
$562$	−9.58846	−0.404465
$563$	3.46410	0.145994	0.0729972	−	0.997332i	$-0.476744\pi$
$563$	3.46410	0.145994	0.0729972	+	0.997332i	$0.476744\pi$
$564$	−8.53590	−0.359426
$565$	−3.80385	−0.160029
$566$	18.3923	0.773086
$567$	8.92820	0.374949
$568$	7.26795	0.304956
$569$	23.3205	0.977647	0.488823	−	0.872383i	$-0.337426\pi$
$569$	23.3205	0.977647	0.488823	+	0.872383i	$0.337426\pi$
$570$	8.53590	0.357529
$571$	−32.3923	−1.35558	−0.677788	−	0.735257i	$-0.737061\pi$
$571$	−32.3923	−1.35558	−0.677788	+	0.735257i	$0.737061\pi$
$572$	−1.26795	−0.0530156
$573$	−14.2872	−0.596856
$574$	−0.928203	−0.0387425
$575$	2.00000	0.0834058
$576$	−2.46410	−0.102671
$577$	25.7846	1.07343	0.536714	−	0.843764i	$-0.319666\pi$
$577$	25.7846	1.07343	0.536714	+	0.843764i	$0.319666\pi$
$578$	−14.0000	−0.582323
$579$	−7.55514	−0.313981
$580$	16.3923	0.680653
$581$	−4.39230	−0.182224
$582$	0.392305	0.0162616
$583$	6.00000	0.248495
$584$	4.19615	0.173638
$585$	3.12436	0.129176
$586$	−17.6603	−0.729538
$587$	40.6410	1.67743	0.838717	−	0.544567i	$-0.183306\pi$
$587$	40.6410	1.67743	0.838717	+	0.544567i	$0.183306\pi$
$588$	2.19615	0.0905678
$589$	53.8564	2.21911
$590$	−12.5885	−0.518259
$591$	15.3731	0.632363
$592$	−0.535898	−0.0220253
$593$	28.9808	1.19010	0.595049	−	0.803690i	$-0.297133\pi$
$593$	28.9808	1.19010	0.595049	+	0.803690i	$0.297133\pi$
$594$	−6.92820	−0.284268
$595$	−6.00000	−0.245976
$596$	3.80385	0.155812
$597$	−13.3731	−0.547323
$598$	−0.732051	−0.0299358
$599$	4.60770	0.188265	0.0941327	−	0.995560i	$-0.469992\pi$
$599$	4.60770	0.188265	0.0941327	+	0.995560i	$0.469992\pi$
$600$	1.46410	0.0597717
$601$	30.1769	1.23094	0.615471	−	0.788160i	$-0.288966\pi$
$601$	30.1769	1.23094	0.615471	+	0.788160i	$0.288966\pi$
$602$	−18.3923	−0.749614
$603$	−27.4115	−1.11628
$604$	−4.46410	−0.181642
$605$	13.8564	0.563343
$606$	6.92820	0.281439
$607$	2.58846	0.105062	0.0525311	−	0.998619i	$-0.483271\pi$
$607$	2.58846	0.105062	0.0525311	+	0.998619i	$0.483271\pi$
$608$	6.73205	0.273021
$609$	13.8564	0.561490
$610$	5.53590	0.224142
$611$	8.53590	0.345325
$612$	−4.26795	−0.172522
$613$	−23.9808	−0.968574	−0.484287	−	0.874909i	$-0.660921\pi$
$613$	−23.9808	−0.968574	−0.484287	+	0.874909i	$0.660921\pi$
$614$	−1.80385	−0.0727974
$615$	−0.588457	−0.0237289
$616$	−3.46410	−0.139573
$617$	15.3397	0.617555	0.308777	−	0.951134i	$-0.400080\pi$
$617$	15.3397	0.617555	0.308777	+	0.951134i	$0.400080\pi$
$618$	−4.58846	−0.184575
$619$	41.3731	1.66292	0.831462	−	0.555582i	$-0.187504\pi$
$619$	41.3731	1.66292	0.831462	+	0.555582i	$0.187504\pi$
$620$	−13.8564	−0.556487
$621$	−4.00000	−0.160514
$622$	9.00000	0.360867
$623$	18.9282	0.758342
$624$	−0.535898	−0.0214531
$625$	−11.0000	−0.440000
$626$	8.92820	0.356843
$627$	8.53590	0.340891
$628$	14.0000	0.558661
$629$	−0.928203	−0.0370099
$630$	8.53590	0.340078
$631$	36.6410	1.45866	0.729328	−	0.684164i	$-0.239833\pi$
$631$	36.6410	1.45866	0.729328	+	0.684164i	$0.239833\pi$
$632$	−6.53590	−0.259984
$633$	−8.82309	−0.350686
$634$	−3.80385	−0.151070
$635$	−28.0526	−1.11323
$636$	2.53590	0.100555
$637$	−2.19615	−0.0870147
$638$	16.3923	0.648978
$639$	−17.9090	−0.708468
$640$	−1.73205	−0.0684653
$641$	−32.4449	−1.28150	−0.640748	−	0.767752i	$-0.721375\pi$
$641$	−32.4449	−1.28150	−0.640748	+	0.767752i	$0.721375\pi$
$642$	−5.66025	−0.223392
$643$	−23.6077	−0.930997	−0.465498	−	0.885049i	$-0.654125\pi$
$643$	−23.6077	−0.930997	−0.465498	+	0.885049i	$0.654125\pi$
$644$	−2.00000	−0.0788110
$645$	−11.6603	−0.459122
$646$	11.6603	0.458767
$647$	−4.85641	−0.190925	−0.0954625	−	0.995433i	$-0.530433\pi$
$647$	−4.85641	−0.190925	−0.0954625	+	0.995433i	$0.530433\pi$
$648$	4.46410	0.175366
$649$	−12.5885	−0.494140
$650$	−1.46410	−0.0574268
$651$	−11.7128	−0.459061
$652$	7.53590	0.295129
$653$	−30.9282	−1.21031	−0.605157	−	0.796106i	$-0.706890\pi$
$653$	−30.9282	−1.21031	−0.605157	+	0.796106i	$0.706890\pi$
$654$	−0.875644	−0.0342404
$655$	1.73205	0.0676768
$656$	−0.464102	−0.0181201
$657$	−10.3397	−0.403392
$658$	23.3205	0.909128
$659$	2.66025	0.103629	0.0518144	−	0.998657i	$-0.483500\pi$
$659$	2.66025	0.103629	0.0518144	+	0.998657i	$0.483500\pi$
$660$	−2.19615	−0.0854851
$661$	29.8038	1.15924	0.579618	−	0.814889i	$-0.303202\pi$
$661$	29.8038	1.15924	0.579618	+	0.814889i	$0.303202\pi$
$662$	−14.3923	−0.559373
$663$	−0.928203	−0.0360484
$664$	−2.19615	−0.0852272
$665$	−23.3205	−0.904331
$666$	1.32051	0.0511686
$667$	9.46410	0.366451
$668$	10.8564	0.420047
$669$	−19.0333	−0.735871
$670$	−19.2679	−0.744386
$671$	5.53590	0.213711
$672$	−1.46410	−0.0564789
$673$	−16.3397	−0.629851	−0.314925	−	0.949116i	$-0.601980\pi$
$673$	−16.3397	−0.629851	−0.314925	+	0.949116i	$0.601980\pi$
$674$	10.1962	0.392741
$675$	−8.00000	−0.307920
$676$	−12.4641	−0.479389
$677$	36.5885	1.40621	0.703104	−	0.711087i	$-0.251797\pi$
$677$	36.5885	1.40621	0.703104	+	0.711087i	$0.251797\pi$
$678$	−1.60770	−0.0617432
$679$	−1.07180	−0.0411318
$680$	−3.00000	−0.115045
$681$	4.39230	0.168313
$682$	−13.8564	−0.530589
$683$	−50.1962	−1.92070	−0.960351	−	0.278793i	$-0.910066\pi$
$683$	−50.1962	−1.92070	−0.960351	+	0.278793i	$0.910066\pi$
$684$	−16.5885	−0.634276
$685$	−10.6077	−0.405299
$686$	−20.0000	−0.763604
$687$	−21.0718	−0.803939
$688$	−9.19615	−0.350600
$689$	−2.53590	−0.0966100
$690$	−1.26795	−0.0482700
$691$	20.0000	0.760836	0.380418	−	0.924815i	$-0.375780\pi$
$691$	20.0000	0.760836	0.380418	+	0.924815i	$0.375780\pi$
$692$	1.39230	0.0529275
$693$	8.53590	0.324252
$694$	16.8564	0.639860
$695$	−29.4449	−1.11691
$696$	6.92820	0.262613
$697$	−0.803848	−0.0304479
$698$	6.14359	0.232538
$699$	−9.80385	−0.370816
$700$	−4.00000	−0.151186
$701$	13.6077	0.513956	0.256978	−	0.966417i	$-0.417273\pi$
$701$	13.6077	0.513956	0.256978	+	0.966417i	$0.417273\pi$
$702$	2.92820	0.110518
$703$	−3.60770	−0.136067
$704$	−1.73205	−0.0652791
$705$	14.7846	0.556821
$706$	−8.32051	−0.313146
$707$	−18.9282	−0.711868
$708$	−5.32051	−0.199957
$709$	−15.0718	−0.566033	−0.283017	−	0.959115i	$-0.591335\pi$
$709$	−15.0718	−0.566033	−0.283017	+	0.959115i	$0.591335\pi$
$710$	−12.5885	−0.472436
$711$	16.1051	0.603989
$712$	9.46410	0.354682
$713$	−8.00000	−0.299602
$714$	−2.53590	−0.0949036
$715$	2.19615	0.0821314
$716$	6.92820	0.258919
$717$	7.60770	0.284115
$718$	−3.58846	−0.133920
$719$	−39.2487	−1.46373	−0.731865	−	0.681450i	$-0.761350\pi$
$719$	−39.2487	−1.46373	−0.731865	+	0.681450i	$0.761350\pi$
$720$	4.26795	0.159057
$721$	12.5359	0.466861
$722$	26.3205	0.979548
$723$	1.66025	0.0617455
$724$	10.5359	0.391564
$725$	18.9282	0.702976
$726$	5.85641	0.217352
$727$	41.5885	1.54243	0.771215	−	0.636574i	$-0.219649\pi$
$727$	41.5885	1.54243	0.771215	+	0.636574i	$0.219649\pi$
$728$	1.46410	0.0542632
$729$	−2.21539	−0.0820515
$730$	−7.26795	−0.268999
$731$	−15.9282	−0.589126
$732$	2.33975	0.0864795
$733$	−12.7846	−0.472210	−0.236105	−	0.971728i	$-0.575871\pi$
$733$	−12.7846	−0.472210	−0.236105	+	0.971728i	$0.575871\pi$
$734$	−3.41154	−0.125922
$735$	−3.80385	−0.140307
$736$	−1.00000	−0.0368605
$737$	−19.2679	−0.709744
$738$	1.14359	0.0420963
$739$	−38.9808	−1.43393	−0.716965	−	0.697109i	$-0.754469\pi$
$739$	−38.9808	−1.43393	−0.716965	+	0.697109i	$0.754469\pi$
$740$	0.928203	0.0341214
$741$	−3.60770	−0.132532
$742$	−6.92820	−0.254342
$743$	−0.803848	−0.0294903	−0.0147452	−	0.999891i	$-0.504694\pi$
$743$	−0.803848	−0.0294903	−0.0147452	+	0.999891i	$0.504694\pi$
$744$	−5.85641	−0.214706
$745$	−6.58846	−0.241382
$746$	−20.0526	−0.734176
$747$	5.41154	0.197998
$748$	−3.00000	−0.109691
$749$	15.4641	0.565046
$750$	−8.87564	−0.324093
$751$	4.41154	0.160979	0.0804897	−	0.996755i	$-0.474352\pi$
$751$	4.41154	0.160979	0.0804897	+	0.996755i	$0.474352\pi$
$752$	11.6603	0.425206
$753$	9.89488	0.360590
$754$	−6.92820	−0.252310
$755$	7.73205	0.281398
$756$	8.00000	0.290957
$757$	−22.3731	−0.813163	−0.406581	−	0.913615i	$-0.633279\pi$
$757$	−22.3731	−0.813163	−0.406581	+	0.913615i	$0.633279\pi$
$758$	−16.1244	−0.585663
$759$	−1.26795	−0.0460236
$760$	−11.6603	−0.422962
$761$	−53.3205	−1.93287	−0.966433	−	0.256917i	$-0.917293\pi$
$761$	−53.3205	−1.93287	−0.966433	+	0.256917i	$0.917293\pi$
$762$	−11.8564	−0.429512
$763$	2.39230	0.0866073
$764$	19.5167	0.706088
$765$	7.39230	0.267269
$766$	−22.3923	−0.809067
$767$	5.32051	0.192112
$768$	−0.732051	−0.0264156
$769$	−41.1769	−1.48488	−0.742439	−	0.669914i	$-0.766331\pi$
$769$	−41.1769	−1.48488	−0.742439	+	0.669914i	$0.766331\pi$
$770$	6.00000	0.216225
$771$	17.0718	0.614826
$772$	10.3205	0.371443
$773$	−23.0718	−0.829835	−0.414917	−	0.909859i	$-0.636190\pi$
$773$	−23.0718	−0.829835	−0.414917	+	0.909859i	$0.636190\pi$
$774$	22.6603	0.814506
$775$	−16.0000	−0.574737
$776$	−0.535898	−0.0192376
$777$	0.784610	0.0281477
$778$	−16.7321	−0.599873
$779$	−3.12436	−0.111942
$780$	0.928203	0.0332350
$781$	−12.5885	−0.450450
$782$	−1.73205	−0.0619380
$783$	−37.8564	−1.35288
$784$	−3.00000	−0.107143
$785$	−24.2487	−0.865474
$786$	0.732051	0.0261114
$787$	44.8038	1.59708	0.798542	−	0.601939i	$-0.205605\pi$
$787$	44.8038	1.59708	0.798542	+	0.601939i	$0.205605\pi$
$788$	−21.0000	−0.748094
$789$	19.8564	0.706907
$790$	11.3205	0.402766
$791$	4.39230	0.156172
$792$	4.26795	0.151655
$793$	−2.33975	−0.0830868
$794$	−0.196152	−0.00696119
$795$	−4.39230	−0.155779
$796$	18.2679	0.647490
$797$	−36.8038	−1.30366	−0.651830	−	0.758365i	$-0.725998\pi$
$797$	−36.8038	−1.30366	−0.651830	+	0.758365i	$0.725998\pi$
$798$	−9.85641	−0.348913
$799$	20.1962	0.714489
$800$	−2.00000	−0.0707107
$801$	−23.3205	−0.823990
$802$	15.7128	0.554839
$803$	−7.26795	−0.256480
$804$	−8.14359	−0.287202
$805$	3.46410	0.122094
$806$	5.85641	0.206283
$807$	7.17691	0.252639
$808$	−9.46410	−0.332946
$809$	−32.1962	−1.13196	−0.565978	−	0.824420i	$-0.691501\pi$
$809$	−32.1962	−1.13196	−0.565978	+	0.824420i	$0.691501\pi$
$810$	−7.73205	−0.271677
$811$	−18.7846	−0.659617	−0.329808	−	0.944048i	$-0.606984\pi$
$811$	−18.7846	−0.659617	−0.329808	+	0.944048i	$0.606984\pi$
$812$	−18.9282	−0.664250
$813$	−14.3013	−0.501567
$814$	0.928203	0.0325335
$815$	−13.0526	−0.457211
$816$	−1.26795	−0.0443871
$817$	−61.9090	−2.16592
$818$	35.2487	1.23244
$819$	−3.60770	−0.126063
$820$	0.803848	0.0280716
$821$	−30.5885	−1.06754	−0.533772	−	0.845628i	$-0.679226\pi$
$821$	−30.5885	−1.06754	−0.533772	+	0.845628i	$0.679226\pi$
$822$	−4.48334	−0.156374
$823$	−36.1962	−1.26172	−0.630859	−	0.775897i	$-0.717297\pi$
$823$	−36.1962	−1.26172	−0.630859	+	0.775897i	$0.717297\pi$
$824$	6.26795	0.218354
$825$	−2.53590	−0.0882886
$826$	14.5359	0.505769
$827$	−20.7846	−0.722752	−0.361376	−	0.932420i	$-0.617693\pi$
$827$	−20.7846	−0.722752	−0.361376	+	0.932420i	$0.617693\pi$
$828$	2.46410	0.0856335
$829$	12.0526	0.418603	0.209301	−	0.977851i	$-0.432881\pi$
$829$	12.0526	0.418603	0.209301	+	0.977851i	$0.432881\pi$
$830$	3.80385	0.132033
$831$	−4.67949	−0.162330
$832$	0.732051	0.0253793
$833$	−5.19615	−0.180036
$834$	−12.4449	−0.430930
$835$	−18.8038	−0.650734
$836$	−11.6603	−0.403278
$837$	32.0000	1.10608
$838$	−11.6603	−0.402797
$839$	4.14359	0.143053	0.0715264	−	0.997439i	$-0.477213\pi$
$839$	4.14359	0.143053	0.0715264	+	0.997439i	$0.477213\pi$
$840$	2.53590	0.0874968
$841$	60.5692	2.08859
$842$	−29.8564	−1.02892
$843$	7.01924	0.241755
$844$	12.0526	0.414866
$845$	21.5885	0.742666
$846$	−28.7321	−0.987828
$847$	−16.0000	−0.549767
$848$	−3.46410	−0.118958
$849$	−13.4641	−0.462087
$850$	−3.46410	−0.118818
$851$	0.535898	0.0183704
$852$	−5.32051	−0.182278
$853$	−13.4641	−0.461002	−0.230501	−	0.973072i	$-0.574037\pi$
$853$	−13.4641	−0.461002	−0.230501	+	0.973072i	$0.574037\pi$
$854$	−6.39230	−0.218740
$855$	28.7321	0.982615
$856$	7.73205	0.264276
$857$	−32.1051	−1.09669	−0.548345	−	0.836252i	$-0.684742\pi$
$857$	−32.1051	−1.09669	−0.548345	+	0.836252i	$0.684742\pi$
$858$	0.928203	0.0316883
$859$	−40.0000	−1.36478	−0.682391	−	0.730987i	$-0.739060\pi$
$859$	−40.0000	−1.36478	−0.682391	+	0.730987i	$0.739060\pi$
$860$	15.9282	0.543147
$861$	0.679492	0.0231570
$862$	22.9808	0.782728
$863$	23.0718	0.785373	0.392687	−	0.919672i	$-0.371546\pi$
$863$	23.0718	0.785373	0.392687	+	0.919672i	$0.371546\pi$
$864$	4.00000	0.136083
$865$	−2.41154	−0.0819949
$866$	5.58846	0.189904
$867$	10.2487	0.348064
$868$	16.0000	0.543075
$869$	11.3205	0.384022
$870$	−12.0000	−0.406838
$871$	8.14359	0.275935
$872$	1.19615	0.0405068
$873$	1.32051	0.0446924
$874$	−6.73205	−0.227715
$875$	24.2487	0.819756
$876$	−3.07180	−0.103786
$877$	14.2487	0.481145	0.240572	−	0.970631i	$-0.422665\pi$
$877$	14.2487	0.481145	0.240572	+	0.970631i	$0.422665\pi$
$878$	−9.78461	−0.330215
$879$	12.9282	0.436057
$880$	3.00000	0.101130
$881$	−18.0000	−0.606435	−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000	−0.606435	−0.303218	+	0.952921i	$0.598061\pi$
$882$	7.39230	0.248912
$883$	3.14359	0.105790	0.0528952	−	0.998600i	$-0.483155\pi$
$883$	3.14359	0.105790	0.0528952	+	0.998600i	$0.483155\pi$
$884$	1.26795	0.0426457
$885$	9.21539	0.309772
$886$	27.4641	0.922675
$887$	16.1769	0.543168	0.271584	−	0.962415i	$-0.412453\pi$
$887$	16.1769	0.543168	0.271584	+	0.962415i	$0.412453\pi$
$888$	0.392305	0.0131649
$889$	32.3923	1.08640
$890$	−16.3923	−0.549471
$891$	−7.73205	−0.259033
$892$	26.0000	0.870544
$893$	78.4974	2.62682
$894$	−2.78461	−0.0931313
$895$	−12.0000	−0.401116
$896$	2.00000	0.0668153
$897$	0.535898	0.0178931
$898$	−15.4641	−0.516044
$899$	−75.7128	−2.52516
$900$	4.92820	0.164273
$901$	−6.00000	−0.199889
$902$	0.803848	0.0267652
$903$	13.4641	0.448057
$904$	2.19615	0.0730429
$905$	−18.2487	−0.606608
$906$	3.26795	0.108570
$907$	−48.9090	−1.62400	−0.811998	−	0.583661i	$-0.801620\pi$
$907$	−48.9090	−1.62400	−0.811998	+	0.583661i	$0.801620\pi$
$908$	−6.00000	−0.199117
$909$	23.3205	0.773492
$910$	−2.53590	−0.0840642
$911$	−45.9615	−1.52277	−0.761387	−	0.648298i	$-0.775481\pi$
$911$	−45.9615	−1.52277	−0.761387	+	0.648298i	$0.775481\pi$
$912$	−4.92820	−0.163189
$913$	3.80385	0.125889
$914$	−12.7846	−0.422877
$915$	−4.05256	−0.133973
$916$	28.7846	0.951070
$917$	−2.00000	−0.0660458
$918$	6.92820	0.228665
$919$	−11.9808	−0.395209	−0.197604	−	0.980282i	$-0.563316\pi$
$919$	−11.9808	−0.395209	−0.197604	+	0.980282i	$0.563316\pi$
$920$	1.73205	0.0571040
$921$	1.32051	0.0435122
$922$	5.53590	0.182315
$923$	5.32051	0.175127
$924$	2.53590	0.0834249
$925$	1.07180	0.0352405
$926$	7.32051	0.240567
$927$	−15.4449	−0.507276
$928$	−9.46410	−0.310674
$929$	−13.1436	−0.431227	−0.215614	−	0.976479i	$-0.569175\pi$
$929$	−13.1436	−0.431227	−0.215614	+	0.976479i	$0.569175\pi$
$930$	10.1436	0.332622
$931$	−20.1962	−0.661902
$932$	13.3923	0.438680
$933$	−6.58846	−0.215696
$934$	11.8756	0.388583
$935$	5.19615	0.169932
$936$	−1.80385	−0.0589606
$937$	3.85641	0.125983	0.0629917	−	0.998014i	$-0.479936\pi$
$937$	3.85641	0.125983	0.0629917	+	0.998014i	$0.479936\pi$
$938$	22.2487	0.726446
$939$	−6.53590	−0.213291
$940$	−20.1962	−0.658726
$941$	−25.2679	−0.823712	−0.411856	−	0.911249i	$-0.635119\pi$
$941$	−25.2679	−0.823712	−0.411856	+	0.911249i	$0.635119\pi$
$942$	−10.2487	−0.333921
$943$	0.464102	0.0151132
$944$	7.26795	0.236552
$945$	−13.8564	−0.450749
$946$	15.9282	0.517871
$947$	−20.7846	−0.675409	−0.337705	−	0.941252i	$-0.609650\pi$
$947$	−20.7846	−0.675409	−0.337705	+	0.941252i	$0.609650\pi$
$948$	4.78461	0.155397
$949$	3.07180	0.0997147
$950$	−13.4641	−0.436833
$951$	2.78461	0.0902972
$952$	3.46410	0.112272
$953$	24.6795	0.799447	0.399724	−	0.916636i	$-0.369106\pi$
$953$	24.6795	0.799447	0.399724	+	0.916636i	$0.369106\pi$
$954$	8.53590	0.276360
$955$	−33.8038	−1.09387
$956$	−10.3923	−0.336111
$957$	−12.0000	−0.387905
$958$	−22.5167	−0.727480
$959$	12.2487	0.395532
$960$	1.26795	0.0409229
$961$	33.0000	1.06452
$962$	−0.392305	−0.0126484
$963$	−19.0526	−0.613960
$964$	−2.26795	−0.0730457
$965$	−17.8756	−0.575437
$966$	1.46410	0.0471067
$967$	0.392305	0.0126157	0.00630784	−	0.999980i	$-0.497992\pi$
$967$	0.392305	0.0126157	0.00630784	+	0.999980i	$0.497992\pi$
$968$	−8.00000	−0.257130
$969$	−8.53590	−0.274213
$970$	0.928203	0.0298028
$971$	28.3923	0.911152	0.455576	−	0.890197i	$-0.349433\pi$
$971$	28.3923	0.911152	0.455576	+	0.890197i	$0.349433\pi$
$972$	−15.2679	−0.489720
$973$	34.0000	1.08999
$974$	37.7846	1.21070
$975$	1.07180	0.0343250
$976$	−3.19615	−0.102306
$977$	22.0526	0.705524	0.352762	−	0.935713i	$-0.385243\pi$
$977$	22.0526	0.705524	0.352762	+	0.935713i	$0.385243\pi$
$978$	−5.51666	−0.176403
$979$	−16.3923	−0.523900
$980$	5.19615	0.165985
$981$	−2.94744	−0.0941046
$982$	21.0000	0.670137
$983$	−36.2487	−1.15615	−0.578077	−	0.815982i	$-0.696197\pi$
$983$	−36.2487	−1.15615	−0.578077	+	0.815982i	$0.696197\pi$
$984$	0.339746	0.0108307
$985$	36.3731	1.15894
$986$	−16.3923	−0.522037
$987$	−17.0718	−0.543401
$988$	4.92820	0.156787
$989$	9.19615	0.292421
$990$	−7.39230	−0.234943
$991$	−11.1769	−0.355046	−0.177523	−	0.984117i	$-0.556808\pi$
$991$	−11.1769	−0.355046	−0.177523	+	0.984117i	$0.556808\pi$
$992$	8.00000	0.254000
$993$	10.5359	0.334347
$994$	14.5359	0.461051
$995$	−31.6410	−1.00309
$996$	1.60770	0.0509418
$997$	−22.5885	−0.715384	−0.357692	−	0.933840i	$-0.616436\pi$
$997$	−22.5885	−0.715384	−0.357692	+	0.933840i	$0.616436\pi$
$998$	−26.1769	−0.828616
$999$	−2.14359	−0.0678203

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.e.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.e.1.1	✓	2	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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.732051 q^{3} +1.00000 q^{4} -1.73205 q^{5} -0.732051 q^{6} +2.00000 q^{7} +1.00000 q^{8} -2.46410 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.732051 q^{3} +1.00000 q^{4} -1.73205 q^{5} -0.732051 q^{6} +2.00000 q^{7} +1.00000 q^{8} -2.46410 q^{9} -1.73205 q^{10} -1.73205 q^{11} -0.732051 q^{12} +0.732051 q^{13} +2.00000 q^{14} +1.26795 q^{15} +1.00000 q^{16} +1.73205 q^{17} -2.46410 q^{18} +6.73205 q^{19} -1.73205 q^{20} -1.46410 q^{21} -1.73205 q^{22} -1.00000 q^{23} -0.732051 q^{24} -2.00000 q^{25} +0.732051 q^{26} +4.00000 q^{27} +2.00000 q^{28} -9.46410 q^{29} +1.26795 q^{30} +8.00000 q^{31} +1.00000 q^{32} +1.26795 q^{33} +1.73205 q^{34} -3.46410 q^{35} -2.46410 q^{36} -0.535898 q^{37} +6.73205 q^{38} -0.535898 q^{39} -1.73205 q^{40} -0.464102 q^{41} -1.46410 q^{42} -9.19615 q^{43} -1.73205 q^{44} +4.26795 q^{45} -1.00000 q^{46} +11.6603 q^{47} -0.732051 q^{48} -3.00000 q^{49} -2.00000 q^{50} -1.26795 q^{51} +0.732051 q^{52} -3.46410 q^{53} +4.00000 q^{54} +3.00000 q^{55} +2.00000 q^{56} -4.92820 q^{57} -9.46410 q^{58} +7.26795 q^{59} +1.26795 q^{60} -3.19615 q^{61} +8.00000 q^{62} -4.92820 q^{63} +1.00000 q^{64} -1.26795 q^{65} +1.26795 q^{66} +11.1244 q^{67} +1.73205 q^{68} +0.732051 q^{69} -3.46410 q^{70} +7.26795 q^{71} -2.46410 q^{72} +4.19615 q^{73} -0.535898 q^{74} +1.46410 q^{75} +6.73205 q^{76} -3.46410 q^{77} -0.535898 q^{78} -6.53590 q^{79} -1.73205 q^{80} +4.46410 q^{81} -0.464102 q^{82} -2.19615 q^{83} -1.46410 q^{84} -3.00000 q^{85} -9.19615 q^{86} +6.92820 q^{87} -1.73205 q^{88} +9.46410 q^{89} +4.26795 q^{90} +1.46410 q^{91} -1.00000 q^{92} -5.85641 q^{93} +11.6603 q^{94} -11.6603 q^{95} -0.732051 q^{96} -0.535898 q^{97} -3.00000 q^{98} +4.26795 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{6} + 4 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^6 + 4 * q^7 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{6} + 4 q^{7} + 2 q^{8} + 2 q^{9} + 2 q^{12} - 2 q^{13} + 4 q^{14} + 6 q^{15} + 2 q^{16} + 2 q^{18} + 10 q^{19} + 4 q^{21} - 2 q^{23} + 2 q^{24} - 4 q^{25} - 2 q^{26} + 8 q^{27} + 4 q^{28} - 12 q^{29} + 6 q^{30} + 16 q^{31} + 2 q^{32} + 6 q^{33} + 2 q^{36} - 8 q^{37} + 10 q^{38} - 8 q^{39} + 6 q^{41} + 4 q^{42} - 8 q^{43} + 12 q^{45} - 2 q^{46} + 6 q^{47} + 2 q^{48} - 6 q^{49} - 4 q^{50} - 6 q^{51} - 2 q^{52} + 8 q^{54} + 6 q^{55} + 4 q^{56} + 4 q^{57} - 12 q^{58} + 18 q^{59} + 6 q^{60} + 4 q^{61} + 16 q^{62} + 4 q^{63} + 2 q^{64} - 6 q^{65} + 6 q^{66} - 2 q^{67} - 2 q^{69} + 18 q^{71} + 2 q^{72} - 2 q^{73} - 8 q^{74} - 4 q^{75} + 10 q^{76} - 8 q^{78} - 20 q^{79} + 2 q^{81} + 6 q^{82} + 6 q^{83} + 4 q^{84} - 6 q^{85} - 8 q^{86} + 12 q^{89} + 12 q^{90} - 4 q^{91} - 2 q^{92} + 16 q^{93} + 6 q^{94} - 6 q^{95} + 2 q^{96} - 8 q^{97} - 6 q^{98} + 12 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^6 + 4 * q^7 + 2 * q^8 + 2 * q^9 + 2 * q^12 - 2 * q^13 + 4 * q^14 + 6 * q^15 + 2 * q^16 + 2 * q^18 + 10 * q^19 + 4 * q^21 - 2 * q^23 + 2 * q^24 - 4 * q^25 - 2 * q^26 + 8 * q^27 + 4 * q^28 - 12 * q^29 + 6 * q^30 + 16 * q^31 + 2 * q^32 + 6 * q^33 + 2 * q^36 - 8 * q^37 + 10 * q^38 - 8 * q^39 + 6 * q^41 + 4 * q^42 - 8 * q^43 + 12 * q^45 - 2 * q^46 + 6 * q^47 + 2 * q^48 - 6 * q^49 - 4 * q^50 - 6 * q^51 - 2 * q^52 + 8 * q^54 + 6 * q^55 + 4 * q^56 + 4 * q^57 - 12 * q^58 + 18 * q^59 + 6 * q^60 + 4 * q^61 + 16 * q^62 + 4 * q^63 + 2 * q^64 - 6 * q^65 + 6 * q^66 - 2 * q^67 - 2 * q^69 + 18 * q^71 + 2 * q^72 - 2 * q^73 - 8 * q^74 - 4 * q^75 + 10 * q^76 - 8 * q^78 - 20 * q^79 + 2 * q^81 + 6 * q^82 + 6 * q^83 + 4 * q^84 - 6 * q^85 - 8 * q^86 + 12 * q^89 + 12 * q^90 - 4 * q^91 - 2 * q^92 + 16 * q^93 + 6 * q^94 - 6 * q^95 + 2 * q^96 - 8 * q^97 - 6 * q^98 + 12 * q^99

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