LMFDB - Embedded newform 6045.2.a.bi.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6045,2,Mod(1,6045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6045, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 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("6045.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6045 = 3 \cdot 5 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6045.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:	$48.2695680219$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 4 x^{17} - 21 x^{16} + 97 x^{15} + 156 x^{14} - 935 x^{13} - 411 x^{12} + 4582 x^{11} + \cdots - 112 $ x^18 - 4x^17 - 21x^16 + 97x^15 + 156x^14 - 935x^13 - 411x^12 + 4582x^11 - 446x^10 - 12159x^9 + 4398x^8 + 17347x^7 - 7839x^6 - 12832x^5 + 4744x^4 + 5064x^3 - 746x^2 - 892*x - 112
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.62138$ of defining polynomial
Character	$\chi$	$=$	6045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.62138 q^{2} +1.00000 q^{3} +4.87165 q^{4} +1.00000 q^{5} -2.62138 q^{6} +2.00076 q^{7} -7.52769 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.62138 q^{2} +1.00000 q^{3} +4.87165 q^{4} +1.00000 q^{5} -2.62138 q^{6} +2.00076 q^{7} -7.52769 q^{8} +1.00000 q^{9} -2.62138 q^{10} +3.21776 q^{11} +4.87165 q^{12} -1.00000 q^{13} -5.24475 q^{14} +1.00000 q^{15} +9.98967 q^{16} +5.50306 q^{17} -2.62138 q^{18} -6.01274 q^{19} +4.87165 q^{20} +2.00076 q^{21} -8.43499 q^{22} +1.21368 q^{23} -7.52769 q^{24} +1.00000 q^{25} +2.62138 q^{26} +1.00000 q^{27} +9.74699 q^{28} +0.468628 q^{29} -2.62138 q^{30} +1.00000 q^{31} -11.1314 q^{32} +3.21776 q^{33} -14.4256 q^{34} +2.00076 q^{35} +4.87165 q^{36} -1.12116 q^{37} +15.7617 q^{38} -1.00000 q^{39} -7.52769 q^{40} +3.57423 q^{41} -5.24475 q^{42} +5.38707 q^{43} +15.6758 q^{44} +1.00000 q^{45} -3.18151 q^{46} -10.9077 q^{47} +9.98967 q^{48} -2.99697 q^{49} -2.62138 q^{50} +5.50306 q^{51} -4.87165 q^{52} +8.83326 q^{53} -2.62138 q^{54} +3.21776 q^{55} -15.0611 q^{56} -6.01274 q^{57} -1.22845 q^{58} +3.38591 q^{59} +4.87165 q^{60} +1.44074 q^{61} -2.62138 q^{62} +2.00076 q^{63} +9.20023 q^{64} -1.00000 q^{65} -8.43499 q^{66} +7.98350 q^{67} +26.8090 q^{68} +1.21368 q^{69} -5.24475 q^{70} +2.93868 q^{71} -7.52769 q^{72} -5.98034 q^{73} +2.93900 q^{74} +1.00000 q^{75} -29.2920 q^{76} +6.43796 q^{77} +2.62138 q^{78} -1.23428 q^{79} +9.98967 q^{80} +1.00000 q^{81} -9.36943 q^{82} +3.96349 q^{83} +9.74699 q^{84} +5.50306 q^{85} -14.1216 q^{86} +0.468628 q^{87} -24.2223 q^{88} +2.49608 q^{89} -2.62138 q^{90} -2.00076 q^{91} +5.91260 q^{92} +1.00000 q^{93} +28.5934 q^{94} -6.01274 q^{95} -11.1314 q^{96} +9.03718 q^{97} +7.85619 q^{98} +3.21776 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 4 q^{2} + 18 q^{3} + 22 q^{4} + 18 q^{5} + 4 q^{6} + 8 q^{7} + 9 q^{8} + 18 q^{9}+O(q^{10}) $ 18 * q + 4 * q^2 + 18 * q^3 + 22 * q^4 + 18 * q^5 + 4 * q^6 + 8 * q^7 + 9 * q^8 + 18 * q^9	\( 18 q + 4 q^{2} + 18 q^{3} + 22 q^{4} + 18 q^{5} + 4 q^{6} + 8 q^{7} + 9 q^{8} + 18 q^{9} + 4 q^{10} + 6 q^{11} + 22 q^{12} - 18 q^{13} + 5 q^{14} + 18 q^{15} + 30 q^{16} + 18 q^{17} + 4 q^{18} + 12 q^{19} + 22 q^{20} + 8 q^{21} + 7 q^{22} + 32 q^{23} + 9 q^{24} + 18 q^{25} - 4 q^{26} + 18 q^{27} + 10 q^{28} + 7 q^{29} + 4 q^{30} + 18 q^{31} + 22 q^{32} + 6 q^{33} + 15 q^{34} + 8 q^{35} + 22 q^{36} + 3 q^{37} + 32 q^{38} - 18 q^{39} + 9 q^{40} + 4 q^{41} + 5 q^{42} + 14 q^{43} - 5 q^{44} + 18 q^{45} + 10 q^{46} + 23 q^{47} + 30 q^{48} + 28 q^{49} + 4 q^{50} + 18 q^{51} - 22 q^{52} + 35 q^{53} + 4 q^{54} + 6 q^{55} - 7 q^{56} + 12 q^{57} - 6 q^{58} + 28 q^{59} + 22 q^{60} + 19 q^{61} + 4 q^{62} + 8 q^{63} + 43 q^{64} - 18 q^{65} + 7 q^{66} + 34 q^{67} + 55 q^{68} + 32 q^{69} + 5 q^{70} - 8 q^{71} + 9 q^{72} + 22 q^{74} + 18 q^{75} + 2 q^{76} + 21 q^{77} - 4 q^{78} + 4 q^{79} + 30 q^{80} + 18 q^{81} + 29 q^{82} + 11 q^{83} + 10 q^{84} + 18 q^{85} - 22 q^{86} + 7 q^{87} - 31 q^{88} + 17 q^{89} + 4 q^{90} - 8 q^{91} + 33 q^{92} + 18 q^{93} - 14 q^{94} + 12 q^{95} + 22 q^{96} + 32 q^{97} + 20 q^{98} + 6 q^{99}+O(q^{100}) \) 18 * q + 4 * q^2 + 18 * q^3 + 22 * q^4 + 18 * q^5 + 4 * q^6 + 8 * q^7 + 9 * q^8 + 18 * q^9 + 4 * q^10 + 6 * q^11 + 22 * q^12 - 18 * q^13 + 5 * q^14 + 18 * q^15 + 30 * q^16 + 18 * q^17 + 4 * q^18 + 12 * q^19 + 22 * q^20 + 8 * q^21 + 7 * q^22 + 32 * q^23 + 9 * q^24 + 18 * q^25 - 4 * q^26 + 18 * q^27 + 10 * q^28 + 7 * q^29 + 4 * q^30 + 18 * q^31 + 22 * q^32 + 6 * q^33 + 15 * q^34 + 8 * q^35 + 22 * q^36 + 3 * q^37 + 32 * q^38 - 18 * q^39 + 9 * q^40 + 4 * q^41 + 5 * q^42 + 14 * q^43 - 5 * q^44 + 18 * q^45 + 10 * q^46 + 23 * q^47 + 30 * q^48 + 28 * q^49 + 4 * q^50 + 18 * q^51 - 22 * q^52 + 35 * q^53 + 4 * q^54 + 6 * q^55 - 7 * q^56 + 12 * q^57 - 6 * q^58 + 28 * q^59 + 22 * q^60 + 19 * q^61 + 4 * q^62 + 8 * q^63 + 43 * q^64 - 18 * q^65 + 7 * q^66 + 34 * q^67 + 55 * q^68 + 32 * q^69 + 5 * q^70 - 8 * q^71 + 9 * q^72 + 22 * q^74 + 18 * q^75 + 2 * q^76 + 21 * q^77 - 4 * q^78 + 4 * q^79 + 30 * q^80 + 18 * q^81 + 29 * q^82 + 11 * q^83 + 10 * q^84 + 18 * q^85 - 22 * q^86 + 7 * q^87 - 31 * q^88 + 17 * q^89 + 4 * q^90 - 8 * q^91 + 33 * q^92 + 18 * q^93 - 14 * q^94 + 12 * q^95 + 22 * q^96 + 32 * q^97 + 20 * q^98 + 6 * 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 $

$2$	−2.62138	−1.85360	−0.926799	−	0.375558i	$-0.877451\pi$
$2$	−2.62138	−1.85360	−0.926799	+	0.375558i	$0.877451\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.87165	2.43582
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.62138	−1.07018
$7$	2.00076	0.756216	0.378108	−	0.925762i	$-0.376575\pi$
$7$	2.00076	0.756216	0.378108	+	0.925762i	$0.376575\pi$
$8$	−7.52769	−2.66144
$9$	1.00000	0.333333
$10$	−2.62138	−0.828954
$11$	3.21776	0.970192	0.485096	−	0.874461i	$-0.338785\pi$
$11$	3.21776	0.970192	0.485096	+	0.874461i	$0.338785\pi$
$12$	4.87165	1.40632
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−5.24475	−1.40172
$15$	1.00000	0.258199
$16$	9.98967	2.49742
$17$	5.50306	1.33469	0.667344	−	0.744750i	$-0.267431\pi$
$17$	5.50306	1.33469	0.667344	+	0.744750i	$0.267431\pi$
$18$	−2.62138	−0.617866
$19$	−6.01274	−1.37942	−0.689709	−	0.724087i	$-0.742261\pi$
$19$	−6.01274	−1.37942	−0.689709	+	0.724087i	$0.742261\pi$
$20$	4.87165	1.08933
$21$	2.00076	0.436601
$22$	−8.43499	−1.79835
$23$	1.21368	0.253069	0.126534	−	0.991962i	$-0.459615\pi$
$23$	1.21368	0.253069	0.126534	+	0.991962i	$0.459615\pi$
$24$	−7.52769	−1.53658
$25$	1.00000	0.200000
$26$	2.62138	0.514096
$27$	1.00000	0.192450
$28$	9.74699	1.84201
$29$	0.468628	0.0870220	0.0435110	−	0.999053i	$-0.486146\pi$
$29$	0.468628	0.0870220	0.0435110	+	0.999053i	$0.486146\pi$
$30$	−2.62138	−0.478597
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−11.1314	−1.96777
$33$	3.21776	0.560140
$34$	−14.4256	−2.47398
$35$	2.00076	0.338190
$36$	4.87165	0.811942
$37$	−1.12116	−0.184318	−0.0921590	−	0.995744i	$-0.529377\pi$
$37$	−1.12116	−0.184318	−0.0921590	+	0.995744i	$0.529377\pi$
$38$	15.7617	2.55689
$39$	−1.00000	−0.160128
$40$	−7.52769	−1.19023
$41$	3.57423	0.558201	0.279101	−	0.960262i	$-0.409964\pi$
$41$	3.57423	0.558201	0.279101	+	0.960262i	$0.409964\pi$
$42$	−5.24475	−0.809283
$43$	5.38707	0.821520	0.410760	−	0.911743i	$-0.365263\pi$
$43$	5.38707	0.821520	0.410760	+	0.911743i	$0.365263\pi$
$44$	15.6758	2.36322
$45$	1.00000	0.149071
$46$	−3.18151	−0.469088
$47$	−10.9077	−1.59106	−0.795529	−	0.605916i	$-0.792807\pi$
$47$	−10.9077	−1.59106	−0.795529	+	0.605916i	$0.792807\pi$
$48$	9.98967	1.44188
$49$	−2.99697	−0.428138
$50$	−2.62138	−0.370720
$51$	5.50306	0.770583
$52$	−4.87165	−0.675576
$53$	8.83326	1.21334	0.606671	−	0.794953i	$-0.292505\pi$
$53$	8.83326	1.21334	0.606671	+	0.794953i	$0.292505\pi$
$54$	−2.62138	−0.356725
$55$	3.21776	0.433883
$56$	−15.0611	−2.01262
$57$	−6.01274	−0.796407
$58$	−1.22845	−0.161304
$59$	3.38591	0.440807	0.220404	−	0.975409i	$-0.429263\pi$
$59$	3.38591	0.440807	0.220404	+	0.975409i	$0.429263\pi$
$60$	4.87165	0.628927
$61$	1.44074	0.184467	0.0922337	−	0.995737i	$-0.470599\pi$
$61$	1.44074	0.184467	0.0922337	+	0.995737i	$0.470599\pi$
$62$	−2.62138	−0.332916
$63$	2.00076	0.252072
$64$	9.20023	1.15003
$65$	−1.00000	−0.124035
$66$	−8.43499	−1.03828
$67$	7.98350	0.975340	0.487670	−	0.873028i	$-0.337847\pi$
$67$	7.98350	0.975340	0.487670	+	0.873028i	$0.337847\pi$
$68$	26.8090	3.25107
$69$	1.21368	0.146109
$70$	−5.24475	−0.626868
$71$	2.93868	0.348758	0.174379	−	0.984679i	$-0.444208\pi$
$71$	2.93868	0.348758	0.174379	+	0.984679i	$0.444208\pi$
$72$	−7.52769	−0.887147
$73$	−5.98034	−0.699946	−0.349973	−	0.936760i	$-0.613809\pi$
$73$	−5.98034	−0.699946	−0.349973	+	0.936760i	$0.613809\pi$
$74$	2.93900	0.341651
$75$	1.00000	0.115470
$76$	−29.2920	−3.36002
$77$	6.43796	0.733674
$78$	2.62138	0.296813
$79$	−1.23428	−0.138868	−0.0694339	−	0.997587i	$-0.522119\pi$
$79$	−1.23428	−0.138868	−0.0694339	+	0.997587i	$0.522119\pi$
$80$	9.98967	1.11688
$81$	1.00000	0.111111
$82$	−9.36943	−1.03468
$83$	3.96349	0.435050	0.217525	−	0.976055i	$-0.430202\pi$
$83$	3.96349	0.435050	0.217525	+	0.976055i	$0.430202\pi$
$84$	9.74699	1.06348
$85$	5.50306	0.596891
$86$	−14.1216	−1.52277
$87$	0.468628	0.0502422
$88$	−24.2223	−2.58211
$89$	2.49608	0.264584	0.132292	−	0.991211i	$-0.457766\pi$
$89$	2.49608	0.264584	0.132292	+	0.991211i	$0.457766\pi$
$90$	−2.62138	−0.276318
$91$	−2.00076	−0.209736
$92$	5.91260	0.616431
$93$	1.00000	0.103695
$94$	28.5934	2.94918
$95$	−6.01274	−0.616894
$96$	−11.1314	−1.13609
$97$	9.03718	0.917587	0.458794	−	0.888543i	$-0.348282\pi$
$97$	9.03718	0.917587	0.458794	+	0.888543i	$0.348282\pi$
$98$	7.85619	0.793595
$99$	3.21776	0.323397
$100$	4.87165	0.487165
$101$	−0.869474	−0.0865159	−0.0432580	−	0.999064i	$-0.513774\pi$
$101$	−0.869474	−0.0865159	−0.0432580	+	0.999064i	$0.513774\pi$
$102$	−14.4256	−1.42835
$103$	−2.36745	−0.233272	−0.116636	−	0.993175i	$-0.537211\pi$
$103$	−2.36745	−0.233272	−0.116636	+	0.993175i	$0.537211\pi$
$104$	7.52769	0.738151
$105$	2.00076	0.195254
$106$	−23.1554	−2.24905
$107$	15.1321	1.46288	0.731438	−	0.681908i	$-0.238849\pi$
$107$	15.1321	1.46288	0.731438	+	0.681908i	$0.238849\pi$
$108$	4.87165	0.468775
$109$	−19.1180	−1.83117	−0.915585	−	0.402125i	$-0.868272\pi$
$109$	−19.1180	−1.83117	−0.915585	+	0.402125i	$0.868272\pi$
$110$	−8.43499	−0.804244
$111$	−1.12116	−0.106416
$112$	19.9869	1.88859
$113$	3.71940	0.349892	0.174946	−	0.984578i	$-0.444025\pi$
$113$	3.71940	0.349892	0.174946	+	0.984578i	$0.444025\pi$
$114$	15.7617	1.47622
$115$	1.21368	0.113176
$116$	2.28299	0.211970
$117$	−1.00000	−0.0924500
$118$	−8.87576	−0.817080
$119$	11.0103	1.00931
$120$	−7.52769	−0.687181
$121$	−0.646009	−0.0587280
$122$	−3.77672	−0.341928
$123$	3.57423	0.322278
$124$	4.87165	0.437487
$125$	1.00000	0.0894427
$126$	−5.24475	−0.467240
$127$	−13.7818	−1.22294	−0.611470	−	0.791268i	$-0.709422\pi$
$127$	−13.7818	−1.22294	−0.611470	+	0.791268i	$0.709422\pi$
$128$	−1.85460	−0.163925
$129$	5.38707	0.474305
$130$	2.62138	0.229911
$131$	9.78085	0.854557	0.427278	−	0.904120i	$-0.359472\pi$
$131$	9.78085	0.854557	0.427278	+	0.904120i	$0.359472\pi$
$132$	15.6758	1.36440
$133$	−12.0300	−1.04314
$134$	−20.9278	−1.80789
$135$	1.00000	0.0860663
$136$	−41.4253	−3.55219
$137$	19.8513	1.69601	0.848005	−	0.529989i	$-0.177804\pi$
$137$	19.8513	1.69601	0.848005	+	0.529989i	$0.177804\pi$
$138$	−3.18151	−0.270828
$139$	8.53364	0.723814	0.361907	−	0.932214i	$-0.382126\pi$
$139$	8.53364	0.723814	0.361907	+	0.932214i	$0.382126\pi$
$140$	9.74699	0.823771
$141$	−10.9077	−0.918597
$142$	−7.70342	−0.646456
$143$	−3.21776	−0.269083
$144$	9.98967	0.832472
$145$	0.468628	0.0389174
$146$	15.6768	1.29742
$147$	−2.99697	−0.247186
$148$	−5.46191	−0.448966
$149$	−9.24370	−0.757273	−0.378637	−	0.925545i	$-0.623607\pi$
$149$	−9.24370	−0.757273	−0.378637	+	0.925545i	$0.623607\pi$
$150$	−2.62138	−0.214035
$151$	−8.66771	−0.705368	−0.352684	−	0.935742i	$-0.614731\pi$
$151$	−8.66771	−0.705368	−0.352684	+	0.935742i	$0.614731\pi$
$152$	45.2621	3.67124
$153$	5.50306	0.444896
$154$	−16.8764	−1.35994
$155$	1.00000	0.0803219
$156$	−4.87165	−0.390044
$157$	14.6011	1.16530	0.582648	−	0.812725i	$-0.302017\pi$
$157$	14.6011	1.16530	0.582648	+	0.812725i	$0.302017\pi$
$158$	3.23553	0.257405
$159$	8.83326	0.700523
$160$	−11.1314	−0.880011
$161$	2.42827	0.191375
$162$	−2.62138	−0.205955
$163$	7.88038	0.617239	0.308620	−	0.951186i	$-0.400133\pi$
$163$	7.88038	0.617239	0.308620	+	0.951186i	$0.400133\pi$
$164$	17.4124	1.35968
$165$	3.21776	0.250502
$166$	−10.3898	−0.806407
$167$	23.4934	1.81798	0.908989	−	0.416821i	$-0.136856\pi$
$167$	23.4934	1.81798	0.908989	+	0.416821i	$0.136856\pi$
$168$	−15.0611	−1.16199
$169$	1.00000	0.0769231
$170$	−14.4256	−1.10640
$171$	−6.01274	−0.459806
$172$	26.2439	2.00108
$173$	−9.24360	−0.702778	−0.351389	−	0.936230i	$-0.614291\pi$
$173$	−9.24360	−0.702778	−0.351389	+	0.936230i	$0.614291\pi$
$174$	−1.22845	−0.0931287
$175$	2.00076	0.151243
$176$	32.1444	2.42297
$177$	3.38591	0.254500
$178$	−6.54319	−0.490433
$179$	6.83541	0.510903	0.255451	−	0.966822i	$-0.417776\pi$
$179$	6.83541	0.510903	0.255451	+	0.966822i	$0.417776\pi$
$180$	4.87165	0.363111
$181$	8.06930	0.599786	0.299893	−	0.953973i	$-0.403049\pi$
$181$	8.06930	0.599786	0.299893	+	0.953973i	$0.403049\pi$
$182$	5.24475	0.388767
$183$	1.44074	0.106502
$184$	−9.13618	−0.673528
$185$	−1.12116	−0.0824295
$186$	−2.62138	−0.192209
$187$	17.7075	1.29490
$188$	−53.1387	−3.87554
$189$	2.00076	0.145534
$190$	15.7617	1.14347
$191$	15.3270	1.10902	0.554512	−	0.832175i	$-0.312905\pi$
$191$	15.3270	1.10902	0.554512	+	0.832175i	$0.312905\pi$
$192$	9.20023	0.663969
$193$	13.8443	0.996535	0.498268	−	0.867023i	$-0.333970\pi$
$193$	13.8443	0.996535	0.498268	+	0.867023i	$0.333970\pi$
$194$	−23.6899	−1.70084
$195$	−1.00000	−0.0716115
$196$	−14.6002	−1.04287
$197$	1.52437	0.108607	0.0543035	−	0.998524i	$-0.482706\pi$
$197$	1.52437	0.108607	0.0543035	+	0.998524i	$0.482706\pi$
$198$	−8.43499	−0.599448
$199$	−7.70371	−0.546102	−0.273051	−	0.962000i	$-0.588033\pi$
$199$	−7.70371	−0.546102	−0.273051	+	0.962000i	$0.588033\pi$
$200$	−7.52769	−0.532288
$201$	7.98350	0.563113
$202$	2.27923	0.160366
$203$	0.937611	0.0658074
$204$	26.8090	1.87700
$205$	3.57423	0.249635
$206$	6.20599	0.432392
$207$	1.21368	0.0843563
$208$	−9.98967	−0.692659
$209$	−19.3476	−1.33830
$210$	−5.24475	−0.361922
$211$	−7.10591	−0.489191	−0.244596	−	0.969625i	$-0.578655\pi$
$211$	−7.10591	−0.489191	−0.244596	+	0.969625i	$0.578655\pi$
$212$	43.0326	2.95549
$213$	2.93868	0.201355
$214$	−39.6671	−2.71158
$215$	5.38707	0.367395
$216$	−7.52769	−0.512195
$217$	2.00076	0.135820
$218$	50.1155	3.39425
$219$	−5.98034	−0.404114
$220$	15.6758	1.05686
$221$	−5.50306	−0.370176
$222$	2.93900	0.197252
$223$	4.94437	0.331100	0.165550	−	0.986201i	$-0.447060\pi$
$223$	4.94437	0.331100	0.165550	+	0.986201i	$0.447060\pi$
$224$	−22.2712	−1.48806
$225$	1.00000	0.0666667
$226$	−9.74997	−0.648558
$227$	−9.82644	−0.652204	−0.326102	−	0.945335i	$-0.605735\pi$
$227$	−9.82644	−0.652204	−0.326102	+	0.945335i	$0.605735\pi$
$228$	−29.2920	−1.93991
$229$	5.15273	0.340502	0.170251	−	0.985401i	$-0.445542\pi$
$229$	5.15273	0.340502	0.170251	+	0.985401i	$0.445542\pi$
$230$	−3.18151	−0.209783
$231$	6.43796	0.423587
$232$	−3.52768	−0.231604
$233$	16.2247	1.06291	0.531457	−	0.847085i	$-0.321645\pi$
$233$	16.2247	1.06291	0.531457	+	0.847085i	$0.321645\pi$
$234$	2.62138	0.171365
$235$	−10.9077	−0.711542
$236$	16.4949	1.07373
$237$	−1.23428	−0.0801754
$238$	−28.8622	−1.87086
$239$	20.7271	1.34072	0.670362	−	0.742035i	$-0.266139\pi$
$239$	20.7271	1.34072	0.670362	+	0.742035i	$0.266139\pi$
$240$	9.98967	0.644830
$241$	−0.852370	−0.0549060	−0.0274530	−	0.999623i	$-0.508740\pi$
$241$	−0.852370	−0.0549060	−0.0274530	+	0.999623i	$0.508740\pi$
$242$	1.69344	0.108858
$243$	1.00000	0.0641500
$244$	7.01876	0.449330
$245$	−2.99697	−0.191469
$246$	−9.36943	−0.597373
$247$	6.01274	0.382582
$248$	−7.52769	−0.478009
$249$	3.96349	0.251176
$250$	−2.62138	−0.165791
$251$	−14.8354	−0.936404	−0.468202	−	0.883621i	$-0.655098\pi$
$251$	−14.8354	−0.936404	−0.468202	+	0.883621i	$0.655098\pi$
$252$	9.74699	0.614003
$253$	3.90532	0.245525
$254$	36.1275	2.26684
$255$	5.50306	0.344615
$256$	−13.5388	−0.846178
$257$	−14.7994	−0.923161	−0.461581	−	0.887098i	$-0.652717\pi$
$257$	−14.7994	−0.923161	−0.461581	+	0.887098i	$0.652717\pi$
$258$	−14.1216	−0.879171
$259$	−2.24317	−0.139384
$260$	−4.87165	−0.302127
$261$	0.468628	0.0290073
$262$	−25.6394	−1.58400
$263$	−11.6988	−0.721380	−0.360690	−	0.932686i	$-0.617459\pi$
$263$	−11.6988	−0.721380	−0.360690	+	0.932686i	$0.617459\pi$
$264$	−24.2223	−1.49078
$265$	8.83326	0.542623
$266$	31.5354	1.93356
$267$	2.49608	0.152758
$268$	38.8928	2.37576
$269$	−10.3023	−0.628145	−0.314073	−	0.949399i	$-0.601694\pi$
$269$	−10.3023	−0.628145	−0.314073	+	0.949399i	$0.601694\pi$
$270$	−2.62138	−0.159532
$271$	−1.75996	−0.106910	−0.0534549	−	0.998570i	$-0.517023\pi$
$271$	−1.75996	−0.106910	−0.0534549	+	0.998570i	$0.517023\pi$
$272$	54.9737	3.33327
$273$	−2.00076	−0.121091
$274$	−52.0378	−3.14372
$275$	3.21776	0.194038
$276$	5.91260	0.355897
$277$	4.92214	0.295743	0.147871	−	0.989007i	$-0.452758\pi$
$277$	4.92214	0.295743	0.147871	+	0.989007i	$0.452758\pi$
$278$	−22.3699	−1.34166
$279$	1.00000	0.0598684
$280$	−15.0611	−0.900073
$281$	−26.0945	−1.55667	−0.778333	−	0.627852i	$-0.783934\pi$
$281$	−26.0945	−1.55667	−0.778333	+	0.627852i	$0.783934\pi$
$282$	28.5934	1.70271
$283$	14.4458	0.858713	0.429357	−	0.903135i	$-0.358740\pi$
$283$	14.4458	0.858713	0.429357	+	0.903135i	$0.358740\pi$
$284$	14.3162	0.849512
$285$	−6.01274	−0.356164
$286$	8.43499	0.498771
$287$	7.15117	0.422120
$288$	−11.1314	−0.655922
$289$	13.2837	0.781392
$290$	−1.22845	−0.0721372
$291$	9.03718	0.529769
$292$	−29.1341	−1.70495
$293$	−32.7703	−1.91446	−0.957230	−	0.289327i	$-0.906568\pi$
$293$	−32.7703	−1.91446	−0.957230	+	0.289327i	$0.906568\pi$
$294$	7.85619	0.458183
$295$	3.38591	0.197135
$296$	8.43976	0.490551
$297$	3.21776	0.186713
$298$	24.2313	1.40368
$299$	−1.21368	−0.0701887
$300$	4.87165	0.281265
$301$	10.7782	0.621247
$302$	22.7214	1.30747
$303$	−0.869474	−0.0499500
$304$	−60.0653	−3.44498
$305$	1.44074	0.0824963
$306$	−14.4256	−0.824658
$307$	−18.6258	−1.06303	−0.531516	−	0.847048i	$-0.678377\pi$
$307$	−18.6258	−1.06303	−0.531516	+	0.847048i	$0.678377\pi$
$308$	31.3635	1.78710
$309$	−2.36745	−0.134679
$310$	−2.62138	−0.148885
$311$	−0.445063	−0.0252372	−0.0126186	−	0.999920i	$-0.504017\pi$
$311$	−0.445063	−0.0252372	−0.0126186	+	0.999920i	$0.504017\pi$
$312$	7.52769	0.426172
$313$	24.6379	1.39261	0.696307	−	0.717744i	$-0.254825\pi$
$313$	24.6379	1.39261	0.696307	+	0.717744i	$0.254825\pi$
$314$	−38.2751	−2.15999
$315$	2.00076	0.112730
$316$	−6.01300	−0.338258
$317$	−22.1549	−1.24434	−0.622171	−	0.782881i	$-0.713749\pi$
$317$	−22.1549	−1.24434	−0.622171	+	0.782881i	$0.713749\pi$
$318$	−23.1554	−1.29849
$319$	1.50793	0.0844280
$320$	9.20023	0.514308
$321$	15.1321	0.844592
$322$	−6.36543	−0.354732
$323$	−33.0885	−1.84109
$324$	4.87165	0.270647
$325$	−1.00000	−0.0554700
$326$	−20.6575	−1.14411
$327$	−19.1180	−1.05723
$328$	−26.9057	−1.48562
$329$	−21.8238	−1.20318
$330$	−8.43499	−0.464331
$331$	−16.4836	−0.906019	−0.453009	−	0.891506i	$-0.649650\pi$
$331$	−16.4836	−0.906019	−0.453009	+	0.891506i	$0.649650\pi$
$332$	19.3087	1.05970
$333$	−1.12116	−0.0614393
$334$	−61.5853	−3.36980
$335$	7.98350	0.436185
$336$	19.9869	1.09038
$337$	−1.42245	−0.0774860	−0.0387430	−	0.999249i	$-0.512335\pi$
$337$	−1.42245	−0.0774860	−0.0387430	+	0.999249i	$0.512335\pi$
$338$	−2.62138	−0.142584
$339$	3.71940	0.202010
$340$	26.8090	1.45392
$341$	3.21776	0.174252
$342$	15.7617	0.852295
$343$	−20.0015	−1.07998
$344$	−40.5522	−2.18643
$345$	1.21368	0.0653421
$346$	24.2310	1.30267
$347$	13.7835	0.739936	0.369968	−	0.929045i	$-0.379369\pi$
$347$	13.7835	0.739936	0.369968	+	0.929045i	$0.379369\pi$
$348$	2.28299	0.122381
$349$	−14.0294	−0.750976	−0.375488	−	0.926827i	$-0.622525\pi$
$349$	−14.0294	−0.750976	−0.375488	+	0.926827i	$0.622525\pi$
$350$	−5.24475	−0.280344
$351$	−1.00000	−0.0533761
$352$	−35.8181	−1.90911
$353$	−3.60041	−0.191631	−0.0958154	−	0.995399i	$-0.530546\pi$
$353$	−3.60041	−0.191631	−0.0958154	+	0.995399i	$0.530546\pi$
$354$	−8.87576	−0.471741
$355$	2.93868	0.155969
$356$	12.1600	0.644481
$357$	11.0103	0.582727
$358$	−17.9182	−0.947008
$359$	3.38091	0.178438	0.0892188	−	0.996012i	$-0.471563\pi$
$359$	3.38091	0.178438	0.0892188	+	0.996012i	$0.471563\pi$
$360$	−7.52769	−0.396744
$361$	17.1531	0.902793
$362$	−21.1527	−1.11176
$363$	−0.646009	−0.0339067
$364$	−9.74699	−0.510881
$365$	−5.98034	−0.313025
$366$	−3.77672	−0.197412
$367$	34.8055	1.81683	0.908415	−	0.418069i	$-0.137293\pi$
$367$	34.8055	1.81683	0.908415	+	0.418069i	$0.137293\pi$
$368$	12.1242	0.632019
$369$	3.57423	0.186067
$370$	2.93900	0.152791
$371$	17.6732	0.917548
$372$	4.87165	0.252583
$373$	−7.31658	−0.378838	−0.189419	−	0.981896i	$-0.560660\pi$
$373$	−7.31658	−0.378838	−0.189419	+	0.981896i	$0.560660\pi$
$374$	−46.4182	−2.40023
$375$	1.00000	0.0516398
$376$	82.1101	4.23451
$377$	−0.468628	−0.0241356
$378$	−5.24475	−0.269761
$379$	−26.0722	−1.33924	−0.669618	−	0.742705i	$-0.733542\pi$
$379$	−26.0722	−1.33924	−0.669618	+	0.742705i	$0.733542\pi$
$380$	−29.2920	−1.50265
$381$	−13.7818	−0.706065
$382$	−40.1780	−2.05569
$383$	−23.0120	−1.17586	−0.587930	−	0.808912i	$-0.700057\pi$
$383$	−23.0120	−1.17586	−0.587930	+	0.808912i	$0.700057\pi$
$384$	−1.85460	−0.0946420
$385$	6.43796	0.328109
$386$	−36.2912	−1.84718
$387$	5.38707	0.273840
$388$	44.0260	2.23508
$389$	4.61579	0.234030	0.117015	−	0.993130i	$-0.462667\pi$
$389$	4.61579	0.234030	0.117015	+	0.993130i	$0.462667\pi$
$390$	2.62138	0.132739
$391$	6.67893	0.337768
$392$	22.5602	1.13946
$393$	9.78085	0.493379
$394$	−3.99596	−0.201314
$395$	−1.23428	−0.0621036
$396$	15.6758	0.787739
$397$	−15.2026	−0.762998	−0.381499	−	0.924369i	$-0.624592\pi$
$397$	−15.2026	−0.762998	−0.381499	+	0.924369i	$0.624592\pi$
$398$	20.1944	1.01225
$399$	−12.0300	−0.602256
$400$	9.98967	0.499483
$401$	1.98888	0.0993200	0.0496600	−	0.998766i	$-0.484186\pi$
$401$	1.98888	0.0993200	0.0496600	+	0.998766i	$0.484186\pi$
$402$	−20.9278	−1.04378
$403$	−1.00000	−0.0498135
$404$	−4.23577	−0.210738
$405$	1.00000	0.0496904
$406$	−2.45784	−0.121980
$407$	−3.60763	−0.178824
$408$	−41.4253	−2.05086
$409$	−9.34351	−0.462007	−0.231004	−	0.972953i	$-0.574201\pi$
$409$	−9.34351	−0.462007	−0.231004	+	0.972953i	$0.574201\pi$
$410$	−9.36943	−0.462723
$411$	19.8513	0.979192
$412$	−11.5334	−0.568209
$413$	6.77438	0.333346
$414$	−3.18151	−0.156363
$415$	3.96349	0.194560
$416$	11.1314	0.545760
$417$	8.53364	0.417894
$418$	50.7174	2.48067
$419$	−9.84667	−0.481041	−0.240521	−	0.970644i	$-0.577318\pi$
$419$	−9.84667	−0.481041	−0.240521	+	0.970644i	$0.577318\pi$
$420$	9.74699	0.475605
$421$	15.8820	0.774044	0.387022	−	0.922071i	$-0.373504\pi$
$421$	15.8820	0.774044	0.387022	+	0.922071i	$0.373504\pi$
$422$	18.6273	0.906764
$423$	−10.9077	−0.530352
$424$	−66.4941	−3.22924
$425$	5.50306	0.266938
$426$	−7.70342	−0.373232
$427$	2.88257	0.139497
$428$	73.7183	3.56331
$429$	−3.21776	−0.155355
$430$	−14.1216	−0.681003
$431$	−15.7082	−0.756638	−0.378319	−	0.925675i	$-0.623498\pi$
$431$	−15.7082	−0.756638	−0.378319	+	0.925675i	$0.623498\pi$
$432$	9.98967	0.480628
$433$	−0.353612	−0.0169935	−0.00849675	−	0.999964i	$-0.502705\pi$
$433$	−0.353612	−0.0169935	−0.00849675	+	0.999964i	$0.502705\pi$
$434$	−5.24475	−0.251756
$435$	0.468628	0.0224690
$436$	−93.1360	−4.46041
$437$	−7.29752	−0.349088
$438$	15.6768	0.749065
$439$	13.9235	0.664530	0.332265	−	0.943186i	$-0.392187\pi$
$439$	13.9235	0.664530	0.332265	+	0.943186i	$0.392187\pi$
$440$	−24.2223	−1.15475
$441$	−2.99697	−0.142713
$442$	14.4256	0.686157
$443$	29.8297	1.41725	0.708625	−	0.705585i	$-0.249316\pi$
$443$	29.8297	1.41725	0.708625	+	0.705585i	$0.249316\pi$
$444$	−5.46191	−0.259211
$445$	2.49608	0.118326
$446$	−12.9611	−0.613726
$447$	−9.24370	−0.437212
$448$	18.4074	0.869670
$449$	−23.8208	−1.12417	−0.562086	−	0.827079i	$-0.690001\pi$
$449$	−23.8208	−1.12417	−0.562086	+	0.827079i	$0.690001\pi$
$450$	−2.62138	−0.123573
$451$	11.5010	0.541562
$452$	18.1196	0.852274
$453$	−8.66771	−0.407244
$454$	25.7589	1.20892
$455$	−2.00076	−0.0937970
$456$	45.2621	2.11959
$457$	−20.7921	−0.972611	−0.486306	−	0.873789i	$-0.661656\pi$
$457$	−20.7921	−0.972611	−0.486306	+	0.873789i	$0.661656\pi$
$458$	−13.5073	−0.631154
$459$	5.50306	0.256861
$460$	5.91260	0.275677
$461$	24.5890	1.14522	0.572612	−	0.819826i	$-0.305930\pi$
$461$	24.5890	1.14522	0.572612	+	0.819826i	$0.305930\pi$
$462$	−16.8764	−0.785160
$463$	22.3272	1.03763	0.518817	−	0.854885i	$-0.326373\pi$
$463$	22.3272	1.03763	0.518817	+	0.854885i	$0.326373\pi$
$464$	4.68143	0.217330
$465$	1.00000	0.0463739
$466$	−42.5311	−1.97022
$467$	17.6998	0.819050	0.409525	−	0.912299i	$-0.365694\pi$
$467$	17.6998	0.819050	0.409525	+	0.912299i	$0.365694\pi$
$468$	−4.87165	−0.225192
$469$	15.9731	0.737567
$470$	28.5934	1.31891
$471$	14.6011	0.672784
$472$	−25.4881	−1.17318
$473$	17.3343	0.797032
$474$	3.23553	0.148613
$475$	−6.01274	−0.275884
$476$	53.6383	2.45851
$477$	8.83326	0.404447
$478$	−54.3336	−2.48516
$479$	−20.9809	−0.958643	−0.479322	−	0.877639i	$-0.659117\pi$
$479$	−20.9809	−0.958643	−0.479322	+	0.877639i	$0.659117\pi$
$480$	−11.1314	−0.508075
$481$	1.12116	0.0511206
$482$	2.23439	0.101774
$483$	2.42827	0.110490
$484$	−3.14713	−0.143051
$485$	9.03718	0.410357
$486$	−2.62138	−0.118908
$487$	−10.8988	−0.493871	−0.246935	−	0.969032i	$-0.579424\pi$
$487$	−10.8988	−0.493871	−0.246935	+	0.969032i	$0.579424\pi$
$488$	−10.8454	−0.490949
$489$	7.88038	0.356363
$490$	7.85619	0.354907
$491$	4.97040	0.224311	0.112155	−	0.993691i	$-0.464225\pi$
$491$	4.97040	0.224311	0.112155	+	0.993691i	$0.464225\pi$
$492$	17.4124	0.785012
$493$	2.57889	0.116147
$494$	−15.7617	−0.709153
$495$	3.21776	0.144628
$496$	9.98967	0.448549
$497$	5.87960	0.263736
$498$	−10.3898	−0.465579
$499$	−42.2595	−1.89180	−0.945898	−	0.324464i	$-0.894816\pi$
$499$	−42.2595	−1.89180	−0.945898	+	0.324464i	$0.894816\pi$
$500$	4.87165	0.217867
$501$	23.4934	1.04961
$502$	38.8894	1.73572
$503$	−2.92602	−0.130465	−0.0652324	−	0.997870i	$-0.520779\pi$
$503$	−2.92602	−0.130465	−0.0652324	+	0.997870i	$0.520779\pi$
$504$	−15.0611	−0.670875
$505$	−0.869474	−0.0386911
$506$	−10.2373	−0.455105
$507$	1.00000	0.0444116
$508$	−67.1403	−2.97887
$509$	7.01138	0.310774	0.155387	−	0.987854i	$-0.450338\pi$
$509$	7.01138	0.310774	0.155387	+	0.987854i	$0.450338\pi$
$510$	−14.4256	−0.638778
$511$	−11.9652	−0.529310
$512$	39.1997	1.73240
$513$	−6.01274	−0.265469
$514$	38.7949	1.71117
$515$	−2.36745	−0.104322
$516$	26.2439	1.15532
$517$	−35.0985	−1.54363
$518$	5.88022	0.258362
$519$	−9.24360	−0.405749
$520$	7.52769	0.330111
$521$	19.1352	0.838326	0.419163	−	0.907911i	$-0.362324\pi$
$521$	19.1352	0.838326	0.419163	+	0.907911i	$0.362324\pi$
$522$	−1.22845	−0.0537679
$523$	23.0846	1.00942	0.504710	−	0.863289i	$-0.331599\pi$
$523$	23.0846	1.00942	0.504710	+	0.863289i	$0.331599\pi$
$524$	47.6489	2.08155
$525$	2.00076	0.0873203
$526$	30.6671	1.33715
$527$	5.50306	0.239717
$528$	32.1444	1.39890
$529$	−21.5270	−0.935956
$530$	−23.1554	−1.00580
$531$	3.38591	0.146936
$532$	−58.6062	−2.54090
$533$	−3.57423	−0.154817
$534$	−6.54319	−0.283152
$535$	15.1321	0.654218
$536$	−60.0974	−2.59581
$537$	6.83541	0.294970
$538$	27.0064	1.16433
$539$	−9.64352	−0.415376
$540$	4.87165	0.209642
$541$	10.2859	0.442223	0.221112	−	0.975248i	$-0.429031\pi$
$541$	10.2859	0.442223	0.221112	+	0.975248i	$0.429031\pi$
$542$	4.61352	0.198168
$543$	8.06930	0.346287
$544$	−61.2566	−2.62635
$545$	−19.1180	−0.818924
$546$	5.24475	0.224455
$547$	7.15162	0.305781	0.152891	−	0.988243i	$-0.451142\pi$
$547$	7.15162	0.305781	0.152891	+	0.988243i	$0.451142\pi$
$548$	96.7085	4.13118
$549$	1.44074	0.0614891
$550$	−8.43499	−0.359669
$551$	−2.81774	−0.120040
$552$	−9.13618	−0.388862
$553$	−2.46950	−0.105014
$554$	−12.9028	−0.548188
$555$	−1.12116	−0.0475907
$556$	41.5729	1.76308
$557$	−23.5370	−0.997294	−0.498647	−	0.866805i	$-0.666170\pi$
$557$	−23.5370	−0.997294	−0.498647	+	0.866805i	$0.666170\pi$
$558$	−2.62138	−0.110972
$559$	−5.38707	−0.227849
$560$	19.9869	0.844601
$561$	17.7075	0.747613
$562$	68.4036	2.88543
$563$	−36.6770	−1.54575	−0.772875	−	0.634558i	$-0.781182\pi$
$563$	−36.6770	−1.54575	−0.772875	+	0.634558i	$0.781182\pi$
$564$	−53.1387	−2.23754
$565$	3.71940	0.156476
$566$	−37.8680	−1.59171
$567$	2.00076	0.0840240
$568$	−22.1215	−0.928198
$569$	37.0758	1.55430	0.777149	−	0.629316i	$-0.216665\pi$
$569$	37.0758	1.55430	0.777149	+	0.629316i	$0.216665\pi$
$570$	15.7617	0.660185
$571$	26.1175	1.09298	0.546492	−	0.837465i	$-0.315963\pi$
$571$	26.1175	1.09298	0.546492	+	0.837465i	$0.315963\pi$
$572$	−15.6758	−0.655438
$573$	15.3270	0.640296
$574$	−18.7460	−0.782442
$575$	1.21368	0.0506138
$576$	9.20023	0.383343
$577$	13.7930	0.574209	0.287104	−	0.957899i	$-0.407307\pi$
$577$	13.7930	0.574209	0.287104	+	0.957899i	$0.407307\pi$
$578$	−34.8216	−1.44839
$579$	13.8443	0.575350
$580$	2.28299	0.0947960
$581$	7.92999	0.328991
$582$	−23.6899	−0.981979
$583$	28.4233	1.17717
$584$	45.0182	1.86287
$585$	−1.00000	−0.0413449
$586$	85.9035	3.54864
$587$	−11.9609	−0.493677	−0.246839	−	0.969057i	$-0.579392\pi$
$587$	−11.9609	−0.493677	−0.246839	+	0.969057i	$0.579392\pi$
$588$	−14.6002	−0.602101
$589$	−6.01274	−0.247751
$590$	−8.87576	−0.365409
$591$	1.52437	0.0627043
$592$	−11.2000	−0.460319
$593$	24.1733	0.992678	0.496339	−	0.868129i	$-0.334677\pi$
$593$	24.1733	0.992678	0.496339	+	0.868129i	$0.334677\pi$
$594$	−8.43499	−0.346092
$595$	11.0103	0.451378
$596$	−45.0321	−1.84459
$597$	−7.70371	−0.315292
$598$	3.18151	0.130102
$599$	−37.2539	−1.52215	−0.761077	−	0.648661i	$-0.775329\pi$
$599$	−37.2539	−1.52215	−0.761077	+	0.648661i	$0.775329\pi$
$600$	−7.52769	−0.307317
$601$	26.7231	1.09006	0.545030	−	0.838417i	$-0.316518\pi$
$601$	26.7231	1.09006	0.545030	+	0.838417i	$0.316518\pi$
$602$	−28.2539	−1.15154
$603$	7.98350	0.325113
$604$	−42.2260	−1.71815
$605$	−0.646009	−0.0262640
$606$	2.27923	0.0925872
$607$	39.6921	1.61105	0.805527	−	0.592560i	$-0.201883\pi$
$607$	39.6921	1.61105	0.805527	+	0.592560i	$0.201883\pi$
$608$	66.9300	2.71437
$609$	0.937611	0.0379939
$610$	−3.77672	−0.152915
$611$	10.9077	0.441280
$612$	26.8090	1.08369
$613$	−2.70259	−0.109156	−0.0545782	−	0.998509i	$-0.517381\pi$
$613$	−2.70259	−0.109156	−0.0545782	+	0.998509i	$0.517381\pi$
$614$	48.8254	1.97043
$615$	3.57423	0.144127
$616$	−48.4630	−1.95263
$617$	14.2453	0.573495	0.286748	−	0.958006i	$-0.407426\pi$
$617$	14.2453	0.573495	0.286748	+	0.958006i	$0.407426\pi$
$618$	6.20599	0.249642
$619$	9.82486	0.394895	0.197447	−	0.980314i	$-0.436735\pi$
$619$	9.82486	0.394895	0.197447	+	0.980314i	$0.436735\pi$
$620$	4.87165	0.195650
$621$	1.21368	0.0487031
$622$	1.16668	0.0467796
$623$	4.99406	0.200083
$624$	−9.98967	−0.399907
$625$	1.00000	0.0400000
$626$	−64.5853	−2.58135
$627$	−19.3476	−0.772668
$628$	71.1315	2.83846
$629$	−6.16982	−0.246007
$630$	−5.24475	−0.208956
$631$	10.8270	0.431016	0.215508	−	0.976502i	$-0.430859\pi$
$631$	10.8270	0.431016	0.215508	+	0.976502i	$0.430859\pi$
$632$	9.29131	0.369589
$633$	−7.10591	−0.282435
$634$	58.0764	2.30651
$635$	−13.7818	−0.546915
$636$	43.0326	1.70635
$637$	2.99697	0.118744
$638$	−3.95287	−0.156496
$639$	2.93868	0.116253
$640$	−1.85460	−0.0733094
$641$	−6.63354	−0.262009	−0.131005	−	0.991382i	$-0.541820\pi$
$641$	−6.63354	−0.262009	−0.131005	+	0.991382i	$0.541820\pi$
$642$	−39.6671	−1.56553
$643$	−38.6301	−1.52342	−0.761710	−	0.647918i	$-0.775640\pi$
$643$	−38.6301	−1.52342	−0.761710	+	0.647918i	$0.775640\pi$
$644$	11.8297	0.466155
$645$	5.38707	0.212116
$646$	86.7376	3.41265
$647$	39.6576	1.55910	0.779551	−	0.626339i	$-0.215447\pi$
$647$	39.6576	1.55910	0.779551	+	0.626339i	$0.215447\pi$
$648$	−7.52769	−0.295716
$649$	10.8950	0.427668
$650$	2.62138	0.102819
$651$	2.00076	0.0784159
$652$	38.3905	1.50349
$653$	−39.4743	−1.54475	−0.772375	−	0.635167i	$-0.780931\pi$
$653$	−39.4743	−1.54475	−0.772375	+	0.635167i	$0.780931\pi$
$654$	50.1155	1.95967
$655$	9.78085	0.382169
$656$	35.7054	1.39406
$657$	−5.98034	−0.233315
$658$	57.2084	2.23022
$659$	−15.6051	−0.607889	−0.303945	−	0.952690i	$-0.598304\pi$
$659$	−15.6051	−0.607889	−0.303945	+	0.952690i	$0.598304\pi$
$660$	15.6758	0.610180
$661$	11.9292	0.463992	0.231996	−	0.972717i	$-0.425474\pi$
$661$	11.9292	0.463992	0.231996	+	0.972717i	$0.425474\pi$
$662$	43.2097	1.67939
$663$	−5.50306	−0.213721
$664$	−29.8359	−1.15786
$665$	−12.0300	−0.466505
$666$	2.93900	0.113884
$667$	0.568762	0.0220226
$668$	114.452	4.42827
$669$	4.94437	0.191161
$670$	−20.9278	−0.808512
$671$	4.63595	0.178969
$672$	−22.2712	−0.859129
$673$	−11.0346	−0.425354	−0.212677	−	0.977123i	$-0.568218\pi$
$673$	−11.0346	−0.425354	−0.212677	+	0.977123i	$0.568218\pi$
$674$	3.72880	0.143628
$675$	1.00000	0.0384900
$676$	4.87165	0.187371
$677$	28.4318	1.09272	0.546362	−	0.837549i	$-0.316012\pi$
$677$	28.4318	1.09272	0.546362	+	0.837549i	$0.316012\pi$
$678$	−9.74997	−0.374445
$679$	18.0812	0.693894
$680$	−41.4253	−1.58859
$681$	−9.82644	−0.376550
$682$	−8.43499	−0.322992
$683$	18.2863	0.699706	0.349853	−	0.936805i	$-0.386232\pi$
$683$	18.2863	0.699706	0.349853	+	0.936805i	$0.386232\pi$
$684$	−29.2920	−1.12001
$685$	19.8513	0.758479
$686$	52.4316	2.00185
$687$	5.15273	0.196589
$688$	53.8150	2.05168
$689$	−8.83326	−0.336521
$690$	−3.18151	−0.121118
$691$	48.6359	1.85020	0.925099	−	0.379727i	$-0.123982\pi$
$691$	48.6359	1.85020	0.925099	+	0.379727i	$0.123982\pi$
$692$	−45.0316	−1.71184
$693$	6.43796	0.244558
$694$	−36.1318	−1.37154
$695$	8.53364	0.323699
$696$	−3.52768	−0.133717
$697$	19.6692	0.745024
$698$	36.7764	1.39201
$699$	16.2247	0.613674
$700$	9.74699	0.368402
$701$	30.8679	1.16587	0.582933	−	0.812521i	$-0.301905\pi$
$701$	30.8679	1.16587	0.582933	+	0.812521i	$0.301905\pi$
$702$	2.62138	0.0989377
$703$	6.74126	0.254251
$704$	29.6041	1.11575
$705$	−10.9077	−0.410809
$706$	9.43807	0.355206
$707$	−1.73961	−0.0654247
$708$	16.4949	0.619918
$709$	36.7008	1.37833	0.689164	−	0.724606i	$-0.257978\pi$
$709$	36.7008	1.37833	0.689164	+	0.724606i	$0.257978\pi$
$710$	−7.70342	−0.289104
$711$	−1.23428	−0.0462893
$712$	−18.7897	−0.704176
$713$	1.21368	0.0454525
$714$	−28.8622	−1.08014
$715$	−3.21776	−0.120337
$716$	33.2997	1.24447
$717$	20.7271	0.774067
$718$	−8.86266	−0.330751
$719$	35.4387	1.32164	0.660820	−	0.750545i	$-0.270209\pi$
$719$	35.4387	1.32164	0.660820	+	0.750545i	$0.270209\pi$
$720$	9.98967	0.372293
$721$	−4.73669	−0.176404
$722$	−44.9648	−1.67342
$723$	−0.852370	−0.0317000
$724$	39.3108	1.46097
$725$	0.468628	0.0174044
$726$	1.69344	0.0628493
$727$	−25.4842	−0.945158	−0.472579	−	0.881288i	$-0.656677\pi$
$727$	−25.4842	−0.945158	−0.472579	+	0.881288i	$0.656677\pi$
$728$	15.0611	0.558201
$729$	1.00000	0.0370370
$730$	15.6768	0.580223
$731$	29.6454	1.09647
$732$	7.01876	0.259421
$733$	12.4718	0.460655	0.230327	−	0.973113i	$-0.426020\pi$
$733$	12.4718	0.460655	0.230327	+	0.973113i	$0.426020\pi$
$734$	−91.2384	−3.36767
$735$	−2.99697	−0.110545
$736$	−13.5099	−0.497980
$737$	25.6890	0.946267
$738$	−9.36943	−0.344893
$739$	−0.0549631	−0.00202185	−0.00101092	−	0.999999i	$-0.500322\pi$
$739$	−0.0549631	−0.00202185	−0.00101092	+	0.999999i	$0.500322\pi$
$740$	−5.46191	−0.200784
$741$	6.01274	0.220884
$742$	−46.3283	−1.70077
$743$	−22.0361	−0.808427	−0.404213	−	0.914665i	$-0.632455\pi$
$743$	−22.0361	−0.808427	−0.404213	+	0.914665i	$0.632455\pi$
$744$	−7.52769	−0.275979
$745$	−9.24370	−0.338663
$746$	19.1796	0.702213
$747$	3.96349	0.145017
$748$	86.2649	3.15416
$749$	30.2757	1.10625
$750$	−2.62138	−0.0957194
$751$	−14.9731	−0.546376	−0.273188	−	0.961961i	$-0.588078\pi$
$751$	−14.9731	−0.546376	−0.273188	+	0.961961i	$0.588078\pi$
$752$	−108.965	−3.97353
$753$	−14.8354	−0.540633
$754$	1.22845	0.0447376
$755$	−8.66771	−0.315450
$756$	9.74699	0.354495
$757$	−28.1380	−1.02269	−0.511346	−	0.859375i	$-0.670853\pi$
$757$	−28.1380	−1.02269	−0.511346	+	0.859375i	$0.670853\pi$
$758$	68.3451	2.48241
$759$	3.90532	0.141754
$760$	45.2621	1.64183
$761$	13.1318	0.476029	0.238014	−	0.971262i	$-0.423503\pi$
$761$	13.1318	0.476029	0.238014	+	0.971262i	$0.423503\pi$
$762$	36.1275	1.30876
$763$	−38.2504	−1.38476
$764$	74.6679	2.70139
$765$	5.50306	0.198964
$766$	60.3234	2.17957
$767$	−3.38591	−0.122258
$768$	−13.5388	−0.488541
$769$	−6.90885	−0.249139	−0.124570	−	0.992211i	$-0.539755\pi$
$769$	−6.90885	−0.249139	−0.124570	+	0.992211i	$0.539755\pi$
$770$	−16.8764	−0.608182
$771$	−14.7994	−0.532987
$772$	67.4446	2.42738
$773$	48.1519	1.73190	0.865952	−	0.500127i	$-0.166713\pi$
$773$	48.1519	1.73190	0.865952	+	0.500127i	$0.166713\pi$
$774$	−14.1216	−0.507589
$775$	1.00000	0.0359211
$776$	−68.0292	−2.44210
$777$	−2.24317	−0.0804734
$778$	−12.0998	−0.433797
$779$	−21.4909	−0.769993
$780$	−4.87165	−0.174433
$781$	9.45599	0.338362
$782$	−17.5080	−0.626086
$783$	0.468628	0.0167474
$784$	−29.9387	−1.06924
$785$	14.6011	0.521136
$786$	−25.6394	−0.914525
$787$	18.1959	0.648614	0.324307	−	0.945952i	$-0.394869\pi$
$787$	18.1959	0.648614	0.324307	+	0.945952i	$0.394869\pi$
$788$	7.42621	0.264548
$789$	−11.6988	−0.416489
$790$	3.23553	0.115115
$791$	7.44162	0.264593
$792$	−24.2223	−0.860703
$793$	−1.44074	−0.0511621
$794$	39.8519	1.41429
$795$	8.83326	0.313284
$796$	−37.5298	−1.33021
$797$	14.7482	0.522407	0.261203	−	0.965284i	$-0.415881\pi$
$797$	14.7482	0.522407	0.261203	+	0.965284i	$0.415881\pi$
$798$	31.5354	1.11634
$799$	−60.0260	−2.12357
$800$	−11.1314	−0.393553
$801$	2.49608	0.0881948
$802$	−5.21362	−0.184099
$803$	−19.2433	−0.679082
$804$	38.8928	1.37164
$805$	2.42827	0.0855854
$806$	2.62138	0.0923343
$807$	−10.3023	−0.362660
$808$	6.54514	0.230257
$809$	−46.7014	−1.64193	−0.820967	−	0.570975i	$-0.806565\pi$
$809$	−46.7014	−1.64193	−0.820967	+	0.570975i	$0.806565\pi$
$810$	−2.62138	−0.0921060
$811$	−18.9812	−0.666520	−0.333260	−	0.942835i	$-0.608149\pi$
$811$	−18.9812	−0.666520	−0.333260	+	0.942835i	$0.608149\pi$
$812$	4.56771	0.160295
$813$	−1.75996	−0.0617244
$814$	9.45699	0.331467
$815$	7.88038	0.276038
$816$	54.9737	1.92447
$817$	−32.3911	−1.13322
$818$	24.4929	0.856375
$819$	−2.00076	−0.0699122
$820$	17.4124	0.608067
$821$	−18.1277	−0.632660	−0.316330	−	0.948649i	$-0.602451\pi$
$821$	−18.1277	−0.632660	−0.316330	+	0.948649i	$0.602451\pi$
$822$	−52.0378	−1.81503
$823$	−15.0811	−0.525694	−0.262847	−	0.964838i	$-0.584661\pi$
$823$	−15.0811	−0.525694	−0.262847	+	0.964838i	$0.584661\pi$
$824$	17.8214	0.620839
$825$	3.21776	0.112028
$826$	−17.7582	−0.617889
$827$	12.9934	0.451825	0.225912	−	0.974148i	$-0.427464\pi$
$827$	12.9934	0.451825	0.225912	+	0.974148i	$0.427464\pi$
$828$	5.91260	0.205477
$829$	28.4679	0.988730	0.494365	−	0.869254i	$-0.335401\pi$
$829$	28.4679	0.988730	0.494365	+	0.869254i	$0.335401\pi$
$830$	−10.3898	−0.360636
$831$	4.92214	0.170747
$832$	−9.20023	−0.318961
$833$	−16.4925	−0.571431
$834$	−22.3699	−0.774608
$835$	23.4934	0.813024
$836$	−94.2546	−3.25986
$837$	1.00000	0.0345651
$838$	25.8119	0.891657
$839$	−3.95917	−0.136686	−0.0683429	−	0.997662i	$-0.521771\pi$
$839$	−3.95917	−0.136686	−0.0683429	+	0.997662i	$0.521771\pi$
$840$	−15.0611	−0.519657
$841$	−28.7804	−0.992427
$842$	−41.6329	−1.43477
$843$	−26.0945	−0.898741
$844$	−34.6175	−1.19158
$845$	1.00000	0.0344010
$846$	28.5934	0.983060
$847$	−1.29251	−0.0444111
$848$	88.2414	3.03022
$849$	14.4458	0.495778
$850$	−14.4256	−0.494795
$851$	−1.36073	−0.0466451
$852$	14.3162	0.490466
$853$	−22.5617	−0.772499	−0.386250	−	0.922394i	$-0.626230\pi$
$853$	−22.5617	−0.772499	−0.386250	+	0.922394i	$0.626230\pi$
$854$	−7.55631	−0.258572
$855$	−6.01274	−0.205631
$856$	−113.910	−3.89336
$857$	−40.1907	−1.37289	−0.686445	−	0.727182i	$-0.740830\pi$
$857$	−40.1907	−1.37289	−0.686445	+	0.727182i	$0.740830\pi$
$858$	8.43499	0.287966
$859$	−12.6271	−0.430830	−0.215415	−	0.976523i	$-0.569110\pi$
$859$	−12.6271	−0.430830	−0.215415	+	0.976523i	$0.569110\pi$
$860$	26.2439	0.894910
$861$	7.15117	0.243711
$862$	41.1772	1.40250
$863$	32.4457	1.10447	0.552233	−	0.833690i	$-0.313776\pi$
$863$	32.4457	1.10447	0.552233	+	0.833690i	$0.313776\pi$
$864$	−11.1314	−0.378697
$865$	−9.24360	−0.314292
$866$	0.926952	0.0314991
$867$	13.2837	0.451137
$868$	9.74699	0.330835
$869$	−3.97163	−0.134728
$870$	−1.22845	−0.0416484
$871$	−7.98350	−0.270511
$872$	143.914	4.87355
$873$	9.03718	0.305862
$874$	19.1296	0.647068
$875$	2.00076	0.0676380
$876$	−29.1341	−0.984351
$877$	6.00566	0.202797	0.101398	−	0.994846i	$-0.467668\pi$
$877$	6.00566	0.202797	0.101398	+	0.994846i	$0.467668\pi$
$878$	−36.4987	−1.23177
$879$	−32.7703	−1.10531
$880$	32.1444	1.08359
$881$	−12.4168	−0.418333	−0.209167	−	0.977880i	$-0.567075\pi$
$881$	−12.4168	−0.418333	−0.209167	+	0.977880i	$0.567075\pi$
$882$	7.85619	0.264532
$883$	6.35649	0.213913	0.106956	−	0.994264i	$-0.465889\pi$
$883$	6.35649	0.213913	0.106956	+	0.994264i	$0.465889\pi$
$884$	−26.8090	−0.901684
$885$	3.38591	0.113816
$886$	−78.1950	−2.62701
$887$	−12.3085	−0.413280	−0.206640	−	0.978417i	$-0.566253\pi$
$887$	−12.3085	−0.413280	−0.206640	+	0.978417i	$0.566253\pi$
$888$	8.43976	0.283220
$889$	−27.5741	−0.924806
$890$	−6.54319	−0.219328
$891$	3.21776	0.107799
$892$	24.0873	0.806501
$893$	65.5854	2.19473
$894$	24.2313	0.810415
$895$	6.83541	0.228483
$896$	−3.71060	−0.123963
$897$	−1.21368	−0.0405235
$898$	62.4434	2.08376
$899$	0.468628	0.0156296
$900$	4.87165	0.162388
$901$	48.6100	1.61943
$902$	−30.1486	−1.00384
$903$	10.7782	0.358677
$904$	−27.9985	−0.931216
$905$	8.06930	0.268233
$906$	22.7214	0.754867
$907$	49.5455	1.64513	0.822565	−	0.568671i	$-0.192542\pi$
$907$	49.5455	1.64513	0.822565	+	0.568671i	$0.192542\pi$
$908$	−47.8710	−1.58865
$909$	−0.869474	−0.0288386
$910$	5.24475	0.173862
$911$	48.3644	1.60238	0.801192	−	0.598408i	$-0.204200\pi$
$911$	48.3644	1.60238	0.801192	+	0.598408i	$0.204200\pi$
$912$	−60.0653	−1.98896
$913$	12.7536	0.422082
$914$	54.5039	1.80283
$915$	1.44074	0.0476293
$916$	25.1023	0.829403
$917$	19.5691	0.646229
$918$	−14.4256	−0.476117
$919$	−38.2735	−1.26253	−0.631263	−	0.775569i	$-0.717463\pi$
$919$	−38.2735	−1.26253	−0.631263	+	0.775569i	$0.717463\pi$
$920$	−9.13618	−0.301211
$921$	−18.6258	−0.613741
$922$	−64.4572	−2.12279
$923$	−2.93868	−0.0967280
$924$	31.3635	1.03178
$925$	−1.12116	−0.0368636
$926$	−58.5282	−1.92336
$927$	−2.36745	−0.0777572
$928$	−5.21646	−0.171239
$929$	25.1900	0.826457	0.413229	−	0.910627i	$-0.364401\pi$
$929$	25.1900	0.826457	0.413229	+	0.910627i	$0.364401\pi$
$930$	−2.62138	−0.0859585
$931$	18.0200	0.590581
$932$	79.0409	2.58907
$933$	−0.445063	−0.0145707
$934$	−46.3980	−1.51819
$935$	17.7075	0.579098
$936$	7.52769	0.246050
$937$	33.7569	1.10279	0.551395	−	0.834244i	$-0.314096\pi$
$937$	33.7569	1.10279	0.551395	+	0.834244i	$0.314096\pi$
$938$	−41.8715	−1.36715
$939$	24.6379	0.804026
$940$	−53.1387	−1.73319
$941$	7.35679	0.239825	0.119912	−	0.992784i	$-0.461739\pi$
$941$	7.35679	0.239825	0.119912	+	0.992784i	$0.461739\pi$
$942$	−38.2751	−1.24707
$943$	4.33796	0.141263
$944$	33.8241	1.10088
$945$	2.00076	0.0650847
$946$	−45.4399	−1.47738
$947$	6.87635	0.223451	0.111726	−	0.993739i	$-0.464362\pi$
$947$	6.87635	0.223451	0.111726	+	0.993739i	$0.464362\pi$
$948$	−6.01300	−0.195293
$949$	5.98034	0.194130
$950$	15.7617	0.511377
$951$	−22.1549	−0.718421
$952$	−82.8821	−2.68623
$953$	−35.9509	−1.16457	−0.582283	−	0.812986i	$-0.697840\pi$
$953$	−35.9509	−1.16457	−0.582283	+	0.812986i	$0.697840\pi$
$954$	−23.1554	−0.749683
$955$	15.3270	0.495971
$956$	100.975	3.26577
$957$	1.50793	0.0487445
$958$	54.9991	1.77694
$959$	39.7176	1.28255
$960$	9.20023	0.296936
$961$	1.00000	0.0322581
$962$	−2.93900	−0.0947570
$963$	15.1321	0.487625
$964$	−4.15245	−0.133741
$965$	13.8443	0.445664
$966$	−6.36543	−0.204804
$967$	9.84704	0.316660	0.158330	−	0.987386i	$-0.449389\pi$
$967$	9.84704	0.316660	0.158330	+	0.987386i	$0.449389\pi$
$968$	4.86295	0.156301
$969$	−33.0885	−1.06296
$970$	−23.6899	−0.760638
$971$	12.7219	0.408267	0.204133	−	0.978943i	$-0.434562\pi$
$971$	12.7219	0.408267	0.204133	+	0.978943i	$0.434562\pi$
$972$	4.87165	0.156258
$973$	17.0738	0.547359
$974$	28.5699	0.915438
$975$	−1.00000	−0.0320256
$976$	14.3925	0.460692
$977$	−13.4991	−0.431876	−0.215938	−	0.976407i	$-0.569281\pi$
$977$	−13.4991	−0.431876	−0.215938	+	0.976407i	$0.569281\pi$
$978$	−20.6575	−0.660554
$979$	8.03180	0.256697
$980$	−14.6002	−0.466385
$981$	−19.1180	−0.610390
$982$	−13.0293	−0.415782
$983$	−19.5913	−0.624865	−0.312433	−	0.949940i	$-0.601144\pi$
$983$	−19.5913	−0.624865	−0.312433	+	0.949940i	$0.601144\pi$
$984$	−26.9057	−0.857723
$985$	1.52437	0.0485705
$986$	−6.76025	−0.215290
$987$	−21.8238	−0.694658
$988$	29.2920	0.931902
$989$	6.53816	0.207901
$990$	−8.43499	−0.268081
$991$	40.6649	1.29176	0.645882	−	0.763437i	$-0.276490\pi$
$991$	40.6649	1.29176	0.645882	+	0.763437i	$0.276490\pi$
$992$	−11.1314	−0.353421
$993$	−16.4836	−0.523090
$994$	−15.4127	−0.488860
$995$	−7.70371	−0.244224
$996$	19.3087	0.611821
$997$	−1.17169	−0.0371078	−0.0185539	−	0.999828i	$-0.505906\pi$
$997$	−1.17169	−0.0371078	−0.0185539	+	0.999828i	$0.505906\pi$
$998$	110.778	3.50663
$999$	−1.12116	−0.0354720

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6045.2.a.bi.1.1	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6045.2.a.bi.1.1	✓	18	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:	\( N \)	\(=\)	\( 6045 = 3 \cdot 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6045.a (trivial)

\(f(q)\)	\(=\)	\(q-2.62138 q^{2} +1.00000 q^{3} +4.87165 q^{4} +1.00000 q^{5} -2.62138 q^{6} +2.00076 q^{7} -7.52769 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.62138 q^{2} +1.00000 q^{3} +4.87165 q^{4} +1.00000 q^{5} -2.62138 q^{6} +2.00076 q^{7} -7.52769 q^{8} +1.00000 q^{9} -2.62138 q^{10} +3.21776 q^{11} +4.87165 q^{12} -1.00000 q^{13} -5.24475 q^{14} +1.00000 q^{15} +9.98967 q^{16} +5.50306 q^{17} -2.62138 q^{18} -6.01274 q^{19} +4.87165 q^{20} +2.00076 q^{21} -8.43499 q^{22} +1.21368 q^{23} -7.52769 q^{24} +1.00000 q^{25} +2.62138 q^{26} +1.00000 q^{27} +9.74699 q^{28} +0.468628 q^{29} -2.62138 q^{30} +1.00000 q^{31} -11.1314 q^{32} +3.21776 q^{33} -14.4256 q^{34} +2.00076 q^{35} +4.87165 q^{36} -1.12116 q^{37} +15.7617 q^{38} -1.00000 q^{39} -7.52769 q^{40} +3.57423 q^{41} -5.24475 q^{42} +5.38707 q^{43} +15.6758 q^{44} +1.00000 q^{45} -3.18151 q^{46} -10.9077 q^{47} +9.98967 q^{48} -2.99697 q^{49} -2.62138 q^{50} +5.50306 q^{51} -4.87165 q^{52} +8.83326 q^{53} -2.62138 q^{54} +3.21776 q^{55} -15.0611 q^{56} -6.01274 q^{57} -1.22845 q^{58} +3.38591 q^{59} +4.87165 q^{60} +1.44074 q^{61} -2.62138 q^{62} +2.00076 q^{63} +9.20023 q^{64} -1.00000 q^{65} -8.43499 q^{66} +7.98350 q^{67} +26.8090 q^{68} +1.21368 q^{69} -5.24475 q^{70} +2.93868 q^{71} -7.52769 q^{72} -5.98034 q^{73} +2.93900 q^{74} +1.00000 q^{75} -29.2920 q^{76} +6.43796 q^{77} +2.62138 q^{78} -1.23428 q^{79} +9.98967 q^{80} +1.00000 q^{81} -9.36943 q^{82} +3.96349 q^{83} +9.74699 q^{84} +5.50306 q^{85} -14.1216 q^{86} +0.468628 q^{87} -24.2223 q^{88} +2.49608 q^{89} -2.62138 q^{90} -2.00076 q^{91} +5.91260 q^{92} +1.00000 q^{93} +28.5934 q^{94} -6.01274 q^{95} -11.1314 q^{96} +9.03718 q^{97} +7.85619 q^{98} +3.21776 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 4 q^{2} + 18 q^{3} + 22 q^{4} + 18 q^{5} + 4 q^{6} + 8 q^{7} + 9 q^{8} + 18 q^{9}+O(q^{10}) \) 18 * q + 4 * q^2 + 18 * q^3 + 22 * q^4 + 18 * q^5 + 4 * q^6 + 8 * q^7 + 9 * q^8 + 18 * q^9	\( 18 q + 4 q^{2} + 18 q^{3} + 22 q^{4} + 18 q^{5} + 4 q^{6} + 8 q^{7} + 9 q^{8} + 18 q^{9} + 4 q^{10} + 6 q^{11} + 22 q^{12} - 18 q^{13} + 5 q^{14} + 18 q^{15} + 30 q^{16} + 18 q^{17} + 4 q^{18} + 12 q^{19} + 22 q^{20} + 8 q^{21} + 7 q^{22} + 32 q^{23} + 9 q^{24} + 18 q^{25} - 4 q^{26} + 18 q^{27} + 10 q^{28} + 7 q^{29} + 4 q^{30} + 18 q^{31} + 22 q^{32} + 6 q^{33} + 15 q^{34} + 8 q^{35} + 22 q^{36} + 3 q^{37} + 32 q^{38} - 18 q^{39} + 9 q^{40} + 4 q^{41} + 5 q^{42} + 14 q^{43} - 5 q^{44} + 18 q^{45} + 10 q^{46} + 23 q^{47} + 30 q^{48} + 28 q^{49} + 4 q^{50} + 18 q^{51} - 22 q^{52} + 35 q^{53} + 4 q^{54} + 6 q^{55} - 7 q^{56} + 12 q^{57} - 6 q^{58} + 28 q^{59} + 22 q^{60} + 19 q^{61} + 4 q^{62} + 8 q^{63} + 43 q^{64} - 18 q^{65} + 7 q^{66} + 34 q^{67} + 55 q^{68} + 32 q^{69} + 5 q^{70} - 8 q^{71} + 9 q^{72} + 22 q^{74} + 18 q^{75} + 2 q^{76} + 21 q^{77} - 4 q^{78} + 4 q^{79} + 30 q^{80} + 18 q^{81} + 29 q^{82} + 11 q^{83} + 10 q^{84} + 18 q^{85} - 22 q^{86} + 7 q^{87} - 31 q^{88} + 17 q^{89} + 4 q^{90} - 8 q^{91} + 33 q^{92} + 18 q^{93} - 14 q^{94} + 12 q^{95} + 22 q^{96} + 32 q^{97} + 20 q^{98} + 6 q^{99}+O(q^{100}) \) 18 * q + 4 * q^2 + 18 * q^3 + 22 * q^4 + 18 * q^5 + 4 * q^6 + 8 * q^7 + 9 * q^8 + 18 * q^9 + 4 * q^10 + 6 * q^11 + 22 * q^12 - 18 * q^13 + 5 * q^14 + 18 * q^15 + 30 * q^16 + 18 * q^17 + 4 * q^18 + 12 * q^19 + 22 * q^20 + 8 * q^21 + 7 * q^22 + 32 * q^23 + 9 * q^24 + 18 * q^25 - 4 * q^26 + 18 * q^27 + 10 * q^28 + 7 * q^29 + 4 * q^30 + 18 * q^31 + 22 * q^32 + 6 * q^33 + 15 * q^34 + 8 * q^35 + 22 * q^36 + 3 * q^37 + 32 * q^38 - 18 * q^39 + 9 * q^40 + 4 * q^41 + 5 * q^42 + 14 * q^43 - 5 * q^44 + 18 * q^45 + 10 * q^46 + 23 * q^47 + 30 * q^48 + 28 * q^49 + 4 * q^50 + 18 * q^51 - 22 * q^52 + 35 * q^53 + 4 * q^54 + 6 * q^55 - 7 * q^56 + 12 * q^57 - 6 * q^58 + 28 * q^59 + 22 * q^60 + 19 * q^61 + 4 * q^62 + 8 * q^63 + 43 * q^64 - 18 * q^65 + 7 * q^66 + 34 * q^67 + 55 * q^68 + 32 * q^69 + 5 * q^70 - 8 * q^71 + 9 * q^72 + 22 * q^74 + 18 * q^75 + 2 * q^76 + 21 * q^77 - 4 * q^78 + 4 * q^79 + 30 * q^80 + 18 * q^81 + 29 * q^82 + 11 * q^83 + 10 * q^84 + 18 * q^85 - 22 * q^86 + 7 * q^87 - 31 * q^88 + 17 * q^89 + 4 * q^90 - 8 * q^91 + 33 * q^92 + 18 * q^93 - 14 * q^94 + 12 * q^95 + 22 * q^96 + 32 * q^97 + 20 * q^98 + 6 * q^99

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