LMFDB - Embedded newform 4334.2.a.h.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4334,2,Mod(1,4334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4334, 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("4334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4334 = 2 \cdot 11 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4334.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:	$34.6071642360$
Analytic rank:	$0$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	4334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.37214 q^{3} +1.00000 q^{4} +0.332573 q^{5} +1.37214 q^{6} +4.01205 q^{7} -1.00000 q^{8} -1.11723 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.37214 q^{3} +1.00000 q^{4} +0.332573 q^{5} +1.37214 q^{6} +4.01205 q^{7} -1.00000 q^{8} -1.11723 q^{9} -0.332573 q^{10} +1.00000 q^{11} -1.37214 q^{12} -4.10198 q^{13} -4.01205 q^{14} -0.456337 q^{15} +1.00000 q^{16} +6.35398 q^{17} +1.11723 q^{18} -8.37411 q^{19} +0.332573 q^{20} -5.50509 q^{21} -1.00000 q^{22} +8.19416 q^{23} +1.37214 q^{24} -4.88940 q^{25} +4.10198 q^{26} +5.64942 q^{27} +4.01205 q^{28} -7.49574 q^{29} +0.456337 q^{30} +9.05422 q^{31} -1.00000 q^{32} -1.37214 q^{33} -6.35398 q^{34} +1.33430 q^{35} -1.11723 q^{36} -3.32051 q^{37} +8.37411 q^{38} +5.62848 q^{39} -0.332573 q^{40} -11.4011 q^{41} +5.50509 q^{42} +6.07901 q^{43} +1.00000 q^{44} -0.371562 q^{45} -8.19416 q^{46} -1.49985 q^{47} -1.37214 q^{48} +9.09653 q^{49} +4.88940 q^{50} -8.71854 q^{51} -4.10198 q^{52} +8.36249 q^{53} -5.64942 q^{54} +0.332573 q^{55} -4.01205 q^{56} +11.4904 q^{57} +7.49574 q^{58} -3.66299 q^{59} -0.456337 q^{60} +14.2657 q^{61} -9.05422 q^{62} -4.48240 q^{63} +1.00000 q^{64} -1.36421 q^{65} +1.37214 q^{66} +12.9851 q^{67} +6.35398 q^{68} -11.2435 q^{69} -1.33430 q^{70} +1.01796 q^{71} +1.11723 q^{72} -0.874921 q^{73} +3.32051 q^{74} +6.70893 q^{75} -8.37411 q^{76} +4.01205 q^{77} -5.62848 q^{78} -1.41723 q^{79} +0.332573 q^{80} -4.40008 q^{81} +11.4011 q^{82} +9.39387 q^{83} -5.50509 q^{84} +2.11316 q^{85} -6.07901 q^{86} +10.2852 q^{87} -1.00000 q^{88} +4.93644 q^{89} +0.371562 q^{90} -16.4573 q^{91} +8.19416 q^{92} -12.4237 q^{93} +1.49985 q^{94} -2.78501 q^{95} +1.37214 q^{96} -7.05301 q^{97} -9.09653 q^{98} -1.11723 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q - 27 q^{2} + 27 q^{4} + 9 q^{5} + q^{7} - 27 q^{8} + 43 q^{9}+O(q^{10}) $ 27 * q - 27 * q^2 + 27 * q^4 + 9 * q^5 + q^7 - 27 * q^8 + 43 * q^9	$ 27 q - 27 q^{2} + 27 q^{4} + 9 q^{5} + q^{7} - 27 q^{8} + 43 q^{9} - 9 q^{10} + 27 q^{11} + 4 q^{13} - q^{14} + 8 q^{15} + 27 q^{16} + 3 q^{17} - 43 q^{18} + 30 q^{19} + 9 q^{20} + 11 q^{21} - 27 q^{22} + 13 q^{23} + 50 q^{25} - 4 q^{26} - 3 q^{27} + q^{28} + 5 q^{29} - 8 q^{30} + 40 q^{31} - 27 q^{32} - 3 q^{34} - 16 q^{35} + 43 q^{36} + 21 q^{37} - 30 q^{38} + 5 q^{39} - 9 q^{40} + 13 q^{41} - 11 q^{42} + 10 q^{43} + 27 q^{44} + 48 q^{45} - 13 q^{46} + 78 q^{49} - 50 q^{50} + 8 q^{51} + 4 q^{52} + 8 q^{53} + 3 q^{54} + 9 q^{55} - q^{56} - 16 q^{57} - 5 q^{58} + 24 q^{59} + 8 q^{60} + 28 q^{61} - 40 q^{62} - 18 q^{63} + 27 q^{64} - q^{65} + 24 q^{67} + 3 q^{68} - 3 q^{69} + 16 q^{70} - 3 q^{71} - 43 q^{72} + 9 q^{73} - 21 q^{74} + 26 q^{75} + 30 q^{76} + q^{77} - 5 q^{78} + 12 q^{79} + 9 q^{80} + 99 q^{81} - 13 q^{82} - 11 q^{83} + 11 q^{84} + 15 q^{85} - 10 q^{86} - 34 q^{87} - 27 q^{88} + 69 q^{89} - 48 q^{90} + q^{91} + 13 q^{92} - 24 q^{93} - 31 q^{95} + 41 q^{97} - 78 q^{98} + 43 q^{99}+O(q^{100}) $ 27 * q - 27 * q^2 + 27 * q^4 + 9 * q^5 + q^7 - 27 * q^8 + 43 * q^9 - 9 * q^10 + 27 * q^11 + 4 * q^13 - q^14 + 8 * q^15 + 27 * q^16 + 3 * q^17 - 43 * q^18 + 30 * q^19 + 9 * q^20 + 11 * q^21 - 27 * q^22 + 13 * q^23 + 50 * q^25 - 4 * q^26 - 3 * q^27 + q^28 + 5 * q^29 - 8 * q^30 + 40 * q^31 - 27 * q^32 - 3 * q^34 - 16 * q^35 + 43 * q^36 + 21 * q^37 - 30 * q^38 + 5 * q^39 - 9 * q^40 + 13 * q^41 - 11 * q^42 + 10 * q^43 + 27 * q^44 + 48 * q^45 - 13 * q^46 + 78 * q^49 - 50 * q^50 + 8 * q^51 + 4 * q^52 + 8 * q^53 + 3 * q^54 + 9 * q^55 - q^56 - 16 * q^57 - 5 * q^58 + 24 * q^59 + 8 * q^60 + 28 * q^61 - 40 * q^62 - 18 * q^63 + 27 * q^64 - q^65 + 24 * q^67 + 3 * q^68 - 3 * q^69 + 16 * q^70 - 3 * q^71 - 43 * q^72 + 9 * q^73 - 21 * q^74 + 26 * q^75 + 30 * q^76 + q^77 - 5 * q^78 + 12 * q^79 + 9 * q^80 + 99 * q^81 - 13 * q^82 - 11 * q^83 + 11 * q^84 + 15 * q^85 - 10 * q^86 - 34 * q^87 - 27 * q^88 + 69 * q^89 - 48 * q^90 + q^91 + 13 * q^92 - 24 * q^93 - 31 * q^95 + 41 * q^97 - 78 * q^98 + 43 * 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
$3$	−1.37214	−0.792205	−0.396102	−	0.918206i	$-0.629637\pi$
$3$	−1.37214	−0.792205	−0.396102	+	0.918206i	$0.629637\pi$
$4$	1.00000	0.500000
$5$	0.332573	0.148731	0.0743656	−	0.997231i	$-0.476307\pi$
$5$	0.332573	0.148731	0.0743656	+	0.997231i	$0.476307\pi$
$6$	1.37214	0.560173
$7$	4.01205	1.51641	0.758206	−	0.652015i	$-0.226076\pi$
$7$	4.01205	1.51641	0.758206	+	0.652015i	$0.226076\pi$
$8$	−1.00000	−0.353553
$9$	−1.11723	−0.372412
$10$	−0.332573	−0.105169
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.37214	−0.396102
$13$	−4.10198	−1.13768	−0.568842	−	0.822447i	$-0.692608\pi$
$13$	−4.10198	−1.13768	−0.568842	+	0.822447i	$0.692608\pi$
$14$	−4.01205	−1.07227
$15$	−0.456337	−0.117826
$16$	1.00000	0.250000
$17$	6.35398	1.54107	0.770533	−	0.637400i	$-0.219990\pi$
$17$	6.35398	1.54107	0.770533	+	0.637400i	$0.219990\pi$
$18$	1.11723	0.263335
$19$	−8.37411	−1.92115	−0.960577	−	0.278015i	$-0.910323\pi$
$19$	−8.37411	−1.92115	−0.960577	+	0.278015i	$0.910323\pi$
$20$	0.332573	0.0743656
$21$	−5.50509	−1.20131
$22$	−1.00000	−0.213201
$23$	8.19416	1.70860	0.854300	−	0.519781i	$-0.173986\pi$
$23$	8.19416	1.70860	0.854300	+	0.519781i	$0.173986\pi$
$24$	1.37214	0.280087
$25$	−4.88940	−0.977879
$26$	4.10198	0.804464
$27$	5.64942	1.08723
$28$	4.01205	0.758206
$29$	−7.49574	−1.39192	−0.695962	−	0.718079i	$-0.745022\pi$
$29$	−7.49574	−1.39192	−0.695962	+	0.718079i	$0.745022\pi$
$30$	0.456337	0.0833153
$31$	9.05422	1.62619	0.813093	−	0.582134i	$-0.197782\pi$
$31$	9.05422	1.62619	0.813093	+	0.582134i	$0.197782\pi$
$32$	−1.00000	−0.176777
$33$	−1.37214	−0.238859
$34$	−6.35398	−1.08970
$35$	1.33430	0.225538
$36$	−1.11723	−0.186206
$37$	−3.32051	−0.545888	−0.272944	−	0.962030i	$-0.587997\pi$
$37$	−3.32051	−0.545888	−0.272944	+	0.962030i	$0.587997\pi$
$38$	8.37411	1.35846
$39$	5.62848	0.901279
$40$	−0.332573	−0.0525844
$41$	−11.4011	−1.78055	−0.890273	−	0.455427i	$-0.849486\pi$
$41$	−11.4011	−1.78055	−0.890273	+	0.455427i	$0.849486\pi$
$42$	5.50509	0.849454
$43$	6.07901	0.927041	0.463520	−	0.886086i	$-0.346586\pi$
$43$	6.07901	0.927041	0.463520	+	0.886086i	$0.346586\pi$
$44$	1.00000	0.150756
$45$	−0.371562	−0.0553892
$46$	−8.19416	−1.20816
$47$	−1.49985	−0.218775	−0.109388	−	0.993999i	$-0.534889\pi$
$47$	−1.49985	−0.218775	−0.109388	+	0.993999i	$0.534889\pi$
$48$	−1.37214	−0.198051
$49$	9.09653	1.29950
$50$	4.88940	0.691465
$51$	−8.71854	−1.22084
$52$	−4.10198	−0.568842
$53$	8.36249	1.14868	0.574338	−	0.818618i	$-0.305260\pi$
$53$	8.36249	1.14868	0.574338	+	0.818618i	$0.305260\pi$
$54$	−5.64942	−0.768788
$55$	0.332573	0.0448442
$56$	−4.01205	−0.536133
$57$	11.4904	1.52195
$58$	7.49574	0.984238
$59$	−3.66299	−0.476881	−0.238440	−	0.971157i	$-0.576636\pi$
$59$	−3.66299	−0.476881	−0.238440	+	0.971157i	$0.576636\pi$
$60$	−0.456337	−0.0589128
$61$	14.2657	1.82653	0.913265	−	0.407366i	$-0.133553\pi$
$61$	14.2657	1.82653	0.913265	+	0.407366i	$0.133553\pi$
$62$	−9.05422	−1.14989
$63$	−4.48240	−0.564729
$64$	1.00000	0.125000
$65$	−1.36421	−0.169209
$66$	1.37214	0.168899
$67$	12.9851	1.58639	0.793194	−	0.608970i	$-0.208417\pi$
$67$	12.9851	1.58639	0.793194	+	0.608970i	$0.208417\pi$
$68$	6.35398	0.770533
$69$	−11.2435	−1.35356
$70$	−1.33430	−0.159479
$71$	1.01796	0.120809	0.0604046	−	0.998174i	$-0.480761\pi$
$71$	1.01796	0.120809	0.0604046	+	0.998174i	$0.480761\pi$
$72$	1.11723	0.131667
$73$	−0.874921	−0.102402	−0.0512009	−	0.998688i	$-0.516305\pi$
$73$	−0.874921	−0.102402	−0.0512009	+	0.998688i	$0.516305\pi$
$74$	3.32051	0.386001
$75$	6.70893	0.774680
$76$	−8.37411	−0.960577
$77$	4.01205	0.457215
$78$	−5.62848	−0.637300
$79$	−1.41723	−0.159451	−0.0797254	−	0.996817i	$-0.525404\pi$
$79$	−1.41723	−0.159451	−0.0797254	+	0.996817i	$0.525404\pi$
$80$	0.332573	0.0371828
$81$	−4.40008	−0.488898
$82$	11.4011	1.25904
$83$	9.39387	1.03111	0.515556	−	0.856856i	$-0.327586\pi$
$83$	9.39387	1.03111	0.515556	+	0.856856i	$0.327586\pi$
$84$	−5.50509	−0.600654
$85$	2.11316	0.229205
$86$	−6.07901	−0.655517
$87$	10.2852	1.10269
$88$	−1.00000	−0.106600
$89$	4.93644	0.523261	0.261631	−	0.965168i	$-0.415740\pi$
$89$	4.93644	0.523261	0.261631	+	0.965168i	$0.415740\pi$
$90$	0.371562	0.0391661
$91$	−16.4573	−1.72520
$92$	8.19416	0.854300
$93$	−12.4237	−1.28827
$94$	1.49985	0.154698
$95$	−2.78501	−0.285736
$96$	1.37214	0.140043
$97$	−7.05301	−0.716125	−0.358062	−	0.933698i	$-0.616562\pi$
$97$	−7.05301	−0.716125	−0.358062	+	0.933698i	$0.616562\pi$
$98$	−9.09653	−0.918889
$99$	−1.11723	−0.112286
$100$	−4.88940	−0.488940
$101$	4.24975	0.422866	0.211433	−	0.977393i	$-0.432187\pi$
$101$	4.24975	0.422866	0.211433	+	0.977393i	$0.432187\pi$
$102$	8.71854	0.863264
$103$	8.54607	0.842070	0.421035	−	0.907045i	$-0.361667\pi$
$103$	8.54607	0.842070	0.421035	+	0.907045i	$0.361667\pi$
$104$	4.10198	0.402232
$105$	−1.83085	−0.178672
$106$	−8.36249	−0.812236
$107$	−7.88036	−0.761823	−0.380912	−	0.924611i	$-0.624390\pi$
$107$	−7.88036	−0.761823	−0.380912	+	0.924611i	$0.624390\pi$
$108$	5.64942	0.543616
$109$	−0.744197	−0.0712811	−0.0356406	−	0.999365i	$-0.511347\pi$
$109$	−0.744197	−0.0712811	−0.0356406	+	0.999365i	$0.511347\pi$
$110$	−0.332573	−0.0317096
$111$	4.55620	0.432455
$112$	4.01205	0.379103
$113$	9.33036	0.877726	0.438863	−	0.898554i	$-0.355381\pi$
$113$	9.33036	0.877726	0.438863	+	0.898554i	$0.355381\pi$
$114$	−11.4904	−1.07618
$115$	2.72516	0.254122
$116$	−7.49574	−0.695962
$117$	4.58287	0.423687
$118$	3.66299	0.337206
$119$	25.4925	2.33689
$120$	0.456337	0.0416577
$121$	1.00000	0.0909091
$122$	−14.2657	−1.29155
$123$	15.6438	1.41056
$124$	9.05422	0.813093
$125$	−3.28895	−0.294172
$126$	4.48240	0.399324
$127$	0.750796	0.0666223	0.0333112	−	0.999445i	$-0.489395\pi$
$127$	0.750796	0.0666223	0.0333112	+	0.999445i	$0.489395\pi$
$128$	−1.00000	−0.0883883
$129$	−8.34125	−0.734406
$130$	1.36421	0.119649
$131$	−6.06129	−0.529578	−0.264789	−	0.964306i	$-0.585302\pi$
$131$	−6.06129	−0.529578	−0.264789	+	0.964306i	$0.585302\pi$
$132$	−1.37214	−0.119429
$133$	−33.5974	−2.91326
$134$	−12.9851	−1.12175
$135$	1.87885	0.161705
$136$	−6.35398	−0.544849
$137$	−15.7217	−1.34320	−0.671599	−	0.740915i	$-0.734392\pi$
$137$	−15.7217	−1.34320	−0.671599	+	0.740915i	$0.734392\pi$
$138$	11.2435	0.957112
$139$	−18.8704	−1.60057	−0.800283	−	0.599622i	$-0.795318\pi$
$139$	−18.8704	−1.60057	−0.800283	+	0.599622i	$0.795318\pi$
$140$	1.33430	0.112769
$141$	2.05800	0.173315
$142$	−1.01796	−0.0854250
$143$	−4.10198	−0.343025
$144$	−1.11723	−0.0931029
$145$	−2.49288	−0.207022
$146$	0.874921	0.0724090
$147$	−12.4817	−1.02947
$148$	−3.32051	−0.272944
$149$	−15.8640	−1.29963	−0.649814	−	0.760093i	$-0.725153\pi$
$149$	−15.8640	−1.29963	−0.649814	+	0.760093i	$0.725153\pi$
$150$	−6.70893	−0.547782
$151$	0.363995	0.0296215	0.0148108	−	0.999890i	$-0.495285\pi$
$151$	0.363995	0.0296215	0.0148108	+	0.999890i	$0.495285\pi$
$152$	8.37411	0.679230
$153$	−7.09888	−0.573911
$154$	−4.01205	−0.323300
$155$	3.01119	0.241865
$156$	5.62848	0.450639
$157$	18.3002	1.46052	0.730258	−	0.683171i	$-0.239400\pi$
$157$	18.3002	1.46052	0.730258	+	0.683171i	$0.239400\pi$
$158$	1.41723	0.112749
$159$	−11.4745	−0.909987
$160$	−0.332573	−0.0262922
$161$	32.8754	2.59094
$162$	4.40008	0.345703
$163$	−12.9133	−1.01145	−0.505723	−	0.862696i	$-0.668774\pi$
$163$	−12.9133	−1.01145	−0.505723	+	0.862696i	$0.668774\pi$
$164$	−11.4011	−0.890273
$165$	−0.456337	−0.0355258
$166$	−9.39387	−0.729106
$167$	−3.67679	−0.284518	−0.142259	−	0.989829i	$-0.545437\pi$
$167$	−3.67679	−0.284518	−0.142259	+	0.989829i	$0.545437\pi$
$168$	5.50509	0.424727
$169$	3.82622	0.294325
$170$	−2.11316	−0.162072
$171$	9.35585	0.715460
$172$	6.07901	0.463520
$173$	11.9616	0.909427	0.454713	−	0.890638i	$-0.349742\pi$
$173$	11.9616	0.909427	0.454713	+	0.890638i	$0.349742\pi$
$174$	−10.2852	−0.779718
$175$	−19.6165	−1.48287
$176$	1.00000	0.0753778
$177$	5.02613	0.377787
$178$	−4.93644	−0.370002
$179$	0.202304	0.0151209	0.00756045	−	0.999971i	$-0.497593\pi$
$179$	0.202304	0.0151209	0.00756045	+	0.999971i	$0.497593\pi$
$180$	−0.371562	−0.0276946
$181$	−22.4128	−1.66593	−0.832965	−	0.553325i	$-0.813359\pi$
$181$	−22.4128	−1.66593	−0.832965	+	0.553325i	$0.813359\pi$
$182$	16.4573	1.21990
$183$	−19.5745	−1.44699
$184$	−8.19416	−0.604081
$185$	−1.10431	−0.0811906
$186$	12.4237	0.910946
$187$	6.35398	0.464649
$188$	−1.49985	−0.109388
$189$	22.6657	1.64869
$190$	2.78501	0.202046
$191$	20.7339	1.50025	0.750125	−	0.661296i	$-0.229993\pi$
$191$	20.7339	1.50025	0.750125	+	0.661296i	$0.229993\pi$
$192$	−1.37214	−0.0990256
$193$	18.1973	1.30987	0.654936	−	0.755685i	$-0.272696\pi$
$193$	18.1973	1.30987	0.654936	+	0.755685i	$0.272696\pi$
$194$	7.05301	0.506377
$195$	1.87188	0.134048
$196$	9.09653	0.649752
$197$	−1.00000	−0.0712470
$197$	−1.00000	−0.0712470
$198$	1.11723	0.0793984
$199$	17.5970	1.24742	0.623710	−	0.781656i	$-0.285625\pi$
$199$	17.5970	1.24742	0.623710	+	0.781656i	$0.285625\pi$
$200$	4.88940	0.345732
$201$	−17.8174	−1.25674
$202$	−4.24975	−0.299011
$203$	−30.0733	−2.11073
$204$	−8.71854	−0.610420
$205$	−3.79169	−0.264823
$206$	−8.54607	−0.595433
$207$	−9.15479	−0.636302
$208$	−4.10198	−0.284421
$209$	−8.37411	−0.579250
$210$	1.83085	0.126340
$211$	15.2967	1.05307	0.526535	−	0.850154i	$-0.323491\pi$
$211$	15.2967	1.05307	0.526535	+	0.850154i	$0.323491\pi$
$212$	8.36249	0.574338
$213$	−1.39678	−0.0957056
$214$	7.88036	0.538690
$215$	2.02172	0.137880
$216$	−5.64942	−0.384394
$217$	36.3260	2.46597
$218$	0.744197	0.0504034
$219$	1.20051	0.0811231
$220$	0.332573	0.0224221
$221$	−26.0639	−1.75325
$222$	−4.55620	−0.305792
$223$	24.1496	1.61717	0.808587	−	0.588377i	$-0.200233\pi$
$223$	24.1496	1.61717	0.808587	+	0.588377i	$0.200233\pi$
$224$	−4.01205	−0.268066
$225$	5.46260	0.364173
$226$	−9.33036	−0.620646
$227$	8.84732	0.587218	0.293609	−	0.955926i	$-0.405144\pi$
$227$	8.84732	0.587218	0.293609	+	0.955926i	$0.405144\pi$
$228$	11.4904	0.760973
$229$	17.8570	1.18003	0.590013	−	0.807394i	$-0.299123\pi$
$229$	17.8570	1.18003	0.590013	+	0.807394i	$0.299123\pi$
$230$	−2.72516	−0.179692
$231$	−5.50509	−0.362208
$232$	7.49574	0.492119
$233$	−11.8519	−0.776442	−0.388221	−	0.921566i	$-0.626910\pi$
$233$	−11.8519	−0.776442	−0.388221	+	0.921566i	$0.626910\pi$
$234$	−4.58287	−0.299592
$235$	−0.498810	−0.0325388
$236$	−3.66299	−0.238440
$237$	1.94464	0.126318
$238$	−25.4925	−1.65243
$239$	−7.91445	−0.511943	−0.255972	−	0.966684i	$-0.582395\pi$
$239$	−7.91445	−0.511943	−0.255972	+	0.966684i	$0.582395\pi$
$240$	−0.456337	−0.0294564
$241$	8.69160	0.559875	0.279938	−	0.960018i	$-0.409686\pi$
$241$	8.69160	0.559875	0.279938	+	0.960018i	$0.409686\pi$
$242$	−1.00000	−0.0642824
$243$	−10.9107	−0.699924
$244$	14.2657	0.913265
$245$	3.02526	0.193277
$246$	−15.6438	−0.997414
$247$	34.3504	2.18567
$248$	−9.05422	−0.574944
$249$	−12.8897	−0.816851
$250$	3.28895	0.208011
$251$	−11.7638	−0.742525	−0.371262	−	0.928528i	$-0.621075\pi$
$251$	−11.7638	−0.742525	−0.371262	+	0.928528i	$0.621075\pi$
$252$	−4.48240	−0.282365
$253$	8.19416	0.515162
$254$	−0.750796	−0.0471091
$255$	−2.89955	−0.181577
$256$	1.00000	0.0625000
$257$	9.17554	0.572355	0.286177	−	0.958177i	$-0.407615\pi$
$257$	9.17554	0.572355	0.286177	+	0.958177i	$0.407615\pi$
$258$	8.34125	0.519303
$259$	−13.3220	−0.827791
$260$	−1.36421	−0.0846046
$261$	8.37449	0.518368
$262$	6.06129	0.374468
$263$	13.3936	0.825882	0.412941	−	0.910758i	$-0.364501\pi$
$263$	13.3936	0.825882	0.412941	+	0.910758i	$0.364501\pi$
$264$	1.37214	0.0844493
$265$	2.78114	0.170844
$266$	33.5974	2.05999
$267$	−6.77348	−0.414530
$268$	12.9851	0.793194
$269$	5.08009	0.309738	0.154869	−	0.987935i	$-0.450504\pi$
$269$	5.08009	0.309738	0.154869	+	0.987935i	$0.450504\pi$
$270$	−1.87885	−0.114343
$271$	15.1805	0.922151	0.461076	−	0.887361i	$-0.347464\pi$
$271$	15.1805	0.922151	0.461076	+	0.887361i	$0.347464\pi$
$272$	6.35398	0.385267
$273$	22.5817	1.36671
$274$	15.7217	0.949785
$275$	−4.88940	−0.294842
$276$	−11.2435	−0.676780
$277$	26.1333	1.57020	0.785100	−	0.619369i	$-0.212612\pi$
$277$	26.1333	1.57020	0.785100	+	0.619369i	$0.212612\pi$
$278$	18.8704	1.13177
$279$	−10.1157	−0.605611
$280$	−1.33430	−0.0797397
$281$	21.2080	1.26516	0.632581	−	0.774494i	$-0.281996\pi$
$281$	21.2080	1.26516	0.632581	+	0.774494i	$0.281996\pi$
$282$	−2.05800	−0.122552
$283$	−14.7588	−0.877317	−0.438658	−	0.898654i	$-0.644546\pi$
$283$	−14.7588	−0.877317	−0.438658	+	0.898654i	$0.644546\pi$
$284$	1.01796	0.0604046
$285$	3.82142	0.226361
$286$	4.10198	0.242555
$287$	−45.7416	−2.70004
$288$	1.11723	0.0658337
$289$	23.3730	1.37488
$290$	2.49288	0.146387
$291$	9.67771	0.567317
$292$	−0.874921	−0.0512009
$293$	7.77063	0.453965	0.226983	−	0.973899i	$-0.427114\pi$
$293$	7.77063	0.453965	0.226983	+	0.973899i	$0.427114\pi$
$294$	12.4817	0.727948
$295$	−1.21821	−0.0709271
$296$	3.32051	0.193001
$297$	5.64942	0.327812
$298$	15.8640	0.918976
$299$	−33.6122	−1.94385
$300$	6.70893	0.387340
$301$	24.3893	1.40578
$302$	−0.363995	−0.0209456
$303$	−5.83124	−0.334996
$304$	−8.37411	−0.480288
$305$	4.74438	0.271662
$306$	7.09888	0.405816
$307$	26.1080	1.49006	0.745031	−	0.667029i	$-0.232434\pi$
$307$	26.1080	1.49006	0.745031	+	0.667029i	$0.232434\pi$
$308$	4.01205	0.228608
$309$	−11.7264	−0.667092
$310$	−3.01119	−0.171024
$311$	0.543074	0.0307949	0.0153975	−	0.999881i	$-0.495099\pi$
$311$	0.543074	0.0307949	0.0153975	+	0.999881i	$0.495099\pi$
$312$	−5.62848	−0.318650
$313$	−8.58446	−0.485222	−0.242611	−	0.970124i	$-0.578004\pi$
$313$	−8.58446	−0.485222	−0.242611	+	0.970124i	$0.578004\pi$
$314$	−18.3002	−1.03274
$315$	−1.49073	−0.0839929
$316$	−1.41723	−0.0797254
$317$	−0.427380	−0.0240040	−0.0120020	−	0.999928i	$-0.503820\pi$
$317$	−0.427380	−0.0240040	−0.0120020	+	0.999928i	$0.503820\pi$
$318$	11.4745	0.643458
$319$	−7.49574	−0.419681
$320$	0.332573	0.0185914
$321$	10.8130	0.603520
$322$	−32.8754	−1.83207
$323$	−53.2089	−2.96062
$324$	−4.40008	−0.244449
$325$	20.0562	1.11252
$326$	12.9133	0.715200
$327$	1.02114	0.0564693
$328$	11.4011	0.629518
$329$	−6.01747	−0.331754
$330$	0.456337	0.0251205
$331$	30.5950	1.68165	0.840826	−	0.541305i	$-0.182070\pi$
$331$	30.5950	1.68165	0.840826	+	0.541305i	$0.182070\pi$
$332$	9.39387	0.515556
$333$	3.70979	0.203295
$334$	3.67679	0.201185
$335$	4.31851	0.235945
$336$	−5.50509	−0.300327
$337$	−11.1362	−0.606627	−0.303314	−	0.952891i	$-0.598093\pi$
$337$	−11.1362	−0.606627	−0.303314	+	0.952891i	$0.598093\pi$
$338$	−3.82622	−0.208119
$339$	−12.8025	−0.695339
$340$	2.11316	0.114602
$341$	9.05422	0.490314
$342$	−9.35585	−0.505906
$343$	8.41140	0.454173
$344$	−6.07901	−0.327758
$345$	−3.73929	−0.201317
$346$	−11.9616	−0.643062
$347$	16.6680	0.894783	0.447392	−	0.894338i	$-0.352353\pi$
$347$	16.6680	0.894783	0.447392	+	0.894338i	$0.352353\pi$
$348$	10.2852	0.551344
$349$	22.4775	1.20320	0.601598	−	0.798799i	$-0.294531\pi$
$349$	22.4775	1.20320	0.601598	+	0.798799i	$0.294531\pi$
$350$	19.6165	1.04855
$351$	−23.1738	−1.23693
$352$	−1.00000	−0.0533002
$353$	14.3008	0.761153	0.380577	−	0.924749i	$-0.375726\pi$
$353$	14.3008	0.761153	0.380577	+	0.924749i	$0.375726\pi$
$354$	−5.02613	−0.267136
$355$	0.338545	0.0179681
$356$	4.93644	0.261631
$357$	−34.9792	−1.85130
$358$	−0.202304	−0.0106921
$359$	28.2845	1.49280	0.746400	−	0.665497i	$-0.231780\pi$
$359$	28.2845	1.49280	0.746400	+	0.665497i	$0.231780\pi$
$360$	0.371562	0.0195831
$361$	51.1258	2.69083
$362$	22.4128	1.17799
$363$	−1.37214	−0.0720186
$364$	−16.4573	−0.862599
$365$	−0.290975	−0.0152303
$366$	19.5745	1.02317
$367$	14.2526	0.743982	0.371991	−	0.928236i	$-0.378675\pi$
$367$	14.2526	0.743982	0.371991	+	0.928236i	$0.378675\pi$
$368$	8.19416	0.427150
$369$	12.7377	0.663096
$370$	1.10431	0.0574105
$371$	33.5507	1.74187
$372$	−12.4237	−0.644136
$373$	5.66199	0.293167	0.146583	−	0.989198i	$-0.453172\pi$
$373$	5.66199	0.293167	0.146583	+	0.989198i	$0.453172\pi$
$374$	−6.35398	−0.328556
$375$	4.51289	0.233045
$376$	1.49985	0.0773488
$377$	30.7473	1.58357
$378$	−22.6657	−1.16580
$379$	−32.2040	−1.65421	−0.827104	−	0.562049i	$-0.810013\pi$
$379$	−32.2040	−1.65421	−0.827104	+	0.562049i	$0.810013\pi$
$380$	−2.78501	−0.142868
$381$	−1.03020	−0.0527785
$382$	−20.7339	−1.06084
$383$	−14.4227	−0.736964	−0.368482	−	0.929635i	$-0.620122\pi$
$383$	−14.4227	−0.736964	−0.368482	+	0.929635i	$0.620122\pi$
$384$	1.37214	0.0700217
$385$	1.33430	0.0680022
$386$	−18.1973	−0.926219
$387$	−6.79168	−0.345241
$388$	−7.05301	−0.358062
$389$	−2.64449	−0.134081	−0.0670405	−	0.997750i	$-0.521356\pi$
$389$	−2.64449	−0.134081	−0.0670405	+	0.997750i	$0.521356\pi$
$390$	−1.87188	−0.0947865
$391$	52.0655	2.63306
$392$	−9.09653	−0.459444
$393$	8.31694	0.419534
$394$	1.00000	0.0503793
$395$	−0.471333	−0.0237153
$396$	−1.11723	−0.0561432
$397$	12.6111	0.632935	0.316467	−	0.948603i	$-0.397503\pi$
$397$	12.6111	0.632935	0.316467	+	0.948603i	$0.397503\pi$
$398$	−17.5970	−0.882059
$399$	46.1002	2.30790
$400$	−4.88940	−0.244470
$401$	9.13246	0.456053	0.228027	−	0.973655i	$-0.426773\pi$
$401$	9.13246	0.456053	0.228027	+	0.973655i	$0.426773\pi$
$402$	17.8174	0.888652
$403$	−37.1402	−1.85009
$404$	4.24975	0.211433
$405$	−1.46335	−0.0727144
$406$	30.0733	1.49251
$407$	−3.32051	−0.164591
$408$	8.71854	0.431632
$409$	22.5356	1.11432	0.557158	−	0.830407i	$-0.311892\pi$
$409$	22.5356	1.11432	0.557158	+	0.830407i	$0.311892\pi$
$410$	3.79169	0.187258
$411$	21.5724	1.06409
$412$	8.54607	0.421035
$413$	−14.6961	−0.723148
$414$	9.15479	0.449934
$415$	3.12415	0.153359
$416$	4.10198	0.201116
$417$	25.8928	1.26798
$418$	8.37411	0.409591
$419$	−21.1302	−1.03228	−0.516139	−	0.856505i	$-0.672631\pi$
$419$	−21.1302	−1.03228	−0.516139	+	0.856505i	$0.672631\pi$
$420$	−1.83085	−0.0893361
$421$	−9.85027	−0.480073	−0.240036	−	0.970764i	$-0.577159\pi$
$421$	−9.85027	−0.480073	−0.240036	+	0.970764i	$0.577159\pi$
$422$	−15.2967	−0.744633
$423$	1.67568	0.0814745
$424$	−8.36249	−0.406118
$425$	−31.0671	−1.50698
$426$	1.39678	0.0676741
$427$	57.2345	2.76977
$428$	−7.88036	−0.380912
$429$	5.62848	0.271746
$430$	−2.02172	−0.0974958
$431$	6.28111	0.302551	0.151275	−	0.988492i	$-0.451662\pi$
$431$	6.28111	0.302551	0.151275	+	0.988492i	$0.451662\pi$
$432$	5.64942	0.271808
$433$	11.8615	0.570028	0.285014	−	0.958523i	$-0.408002\pi$
$433$	11.8615	0.570028	0.285014	+	0.958523i	$0.408002\pi$
$434$	−36.3260	−1.74370
$435$	3.42058	0.164004
$436$	−0.744197	−0.0356406
$437$	−68.6188	−3.28248
$438$	−1.20051	−0.0573627
$439$	−12.7096	−0.606595	−0.303297	−	0.952896i	$-0.598088\pi$
$439$	−12.7096	−0.606595	−0.303297	+	0.952896i	$0.598088\pi$
$440$	−0.332573	−0.0158548
$441$	−10.1630	−0.483951
$442$	26.0639	1.23973
$443$	−32.3739	−1.53813	−0.769066	−	0.639170i	$-0.779278\pi$
$443$	−32.3739	−1.53813	−0.769066	+	0.639170i	$0.779278\pi$
$444$	4.55620	0.216228
$445$	1.64173	0.0778253
$446$	−24.1496	−1.14351
$447$	21.7676	1.02957
$448$	4.01205	0.189551
$449$	−25.7239	−1.21399	−0.606993	−	0.794707i	$-0.707624\pi$
$449$	−25.7239	−1.21399	−0.606993	+	0.794707i	$0.707624\pi$
$450$	−5.46260	−0.257510
$451$	−11.4011	−0.536855
$452$	9.33036	0.438863
$453$	−0.499452	−0.0234663
$454$	−8.84732	−0.415225
$455$	−5.47327	−0.256591
$456$	−11.4904	−0.538090
$457$	−33.4105	−1.56288	−0.781439	−	0.623981i	$-0.785514\pi$
$457$	−33.4105	−1.56288	−0.781439	+	0.623981i	$0.785514\pi$
$458$	−17.8570	−0.834404
$459$	35.8963	1.67549
$460$	2.72516	0.127061
$461$	−11.3714	−0.529618	−0.264809	−	0.964301i	$-0.585309\pi$
$461$	−11.3714	−0.529618	−0.264809	+	0.964301i	$0.585309\pi$
$462$	5.50509	0.256120
$463$	17.1572	0.797365	0.398683	−	0.917089i	$-0.369468\pi$
$463$	17.1572	0.797365	0.398683	+	0.917089i	$0.369468\pi$
$464$	−7.49574	−0.347981
$465$	−4.13177	−0.191606
$466$	11.8519	0.549028
$467$	1.09579	0.0507073	0.0253537	−	0.999679i	$-0.491929\pi$
$467$	1.09579	0.0507073	0.0253537	+	0.999679i	$0.491929\pi$
$468$	4.58287	0.211843
$469$	52.0970	2.40562
$470$	0.498810	0.0230084
$471$	−25.1104	−1.15703
$472$	3.66299	0.168603
$473$	6.07901	0.279513
$474$	−1.94464	−0.0893201
$475$	40.9443	1.87866
$476$	25.4925	1.16845
$477$	−9.34286	−0.427780
$478$	7.91445	0.361998
$479$	39.9682	1.82619	0.913097	−	0.407742i	$-0.133684\pi$
$479$	39.9682	1.82619	0.913097	+	0.407742i	$0.133684\pi$
$480$	0.456337	0.0208288
$481$	13.6206	0.621048
$482$	−8.69160	−0.395892
$483$	−45.1096	−2.05256
$484$	1.00000	0.0454545
$485$	−2.34564	−0.106510
$486$	10.9107	0.494921
$487$	3.53781	0.160314	0.0801568	−	0.996782i	$-0.474458\pi$
$487$	3.53781	0.160314	0.0801568	+	0.996782i	$0.474458\pi$
$488$	−14.2657	−0.645776
$489$	17.7188	0.801272
$490$	−3.02526	−0.136668
$491$	20.0700	0.905746	0.452873	−	0.891575i	$-0.350399\pi$
$491$	20.0700	0.905746	0.452873	+	0.891575i	$0.350399\pi$
$492$	15.6438	0.705278
$493$	−47.6277	−2.14505
$494$	−34.3504	−1.54550
$495$	−0.371562	−0.0167005
$496$	9.05422	0.406547
$497$	4.08409	0.183197
$498$	12.8897	0.577601
$499$	43.3124	1.93893	0.969464	−	0.245235i	$-0.0788652\pi$
$499$	43.3124	1.93893	0.969464	+	0.245235i	$0.0788652\pi$
$500$	−3.28895	−0.147086
$501$	5.04506	0.225397
$502$	11.7638	0.525044
$503$	−10.4660	−0.466655	−0.233328	−	0.972398i	$-0.574961\pi$
$503$	−10.4660	−0.466655	−0.233328	+	0.972398i	$0.574961\pi$
$504$	4.48240	0.199662
$505$	1.41335	0.0628934
$506$	−8.19416	−0.364275
$507$	−5.25011	−0.233165
$508$	0.750796	0.0333112
$509$	−36.7098	−1.62713	−0.813566	−	0.581472i	$-0.802477\pi$
$509$	−36.7098	−1.62713	−0.813566	+	0.581472i	$0.802477\pi$
$510$	2.89955	0.128394
$511$	−3.51022	−0.155283
$512$	−1.00000	−0.0441942
$513$	−47.3089	−2.08874
$514$	−9.17554	−0.404716
$515$	2.84219	0.125242
$516$	−8.34125	−0.367203
$517$	−1.49985	−0.0659633
$518$	13.3220	0.585337
$519$	−16.4130	−0.720452
$520$	1.36421	0.0598245
$521$	40.5993	1.77869	0.889343	−	0.457240i	$-0.151162\pi$
$521$	40.5993	1.77869	0.889343	+	0.457240i	$0.151162\pi$
$522$	−8.37449	−0.366542
$523$	7.03382	0.307567	0.153784	−	0.988105i	$-0.450854\pi$
$523$	7.03382	0.307567	0.153784	+	0.988105i	$0.450854\pi$
$524$	−6.06129	−0.264789
$525$	26.9166	1.17473
$526$	−13.3936	−0.583987
$527$	57.5303	2.50606
$528$	−1.37214	−0.0597147
$529$	44.1442	1.91931
$530$	−2.78114	−0.120805
$531$	4.09242	0.177596
$532$	−33.5974	−1.45663
$533$	46.7669	2.02570
$534$	6.77348	0.293117
$535$	−2.62080	−0.113307
$536$	−12.9851	−0.560873
$537$	−0.277589	−0.0119788
$538$	−5.08009	−0.219018
$539$	9.09653	0.391815
$540$	1.87885	0.0808526
$541$	−20.7737	−0.893131	−0.446565	−	0.894751i	$-0.647353\pi$
$541$	−20.7737	−0.893131	−0.446565	+	0.894751i	$0.647353\pi$
$542$	−15.1805	−0.652060
$543$	30.7535	1.31976
$544$	−6.35398	−0.272425
$545$	−0.247500	−0.0106017
$546$	−22.5817	−0.966410
$547$	−6.95411	−0.297336	−0.148668	−	0.988887i	$-0.547499\pi$
$547$	−6.95411	−0.297336	−0.148668	+	0.988887i	$0.547499\pi$
$548$	−15.7217	−0.671599
$549$	−15.9381	−0.680221
$550$	4.88940	0.208485
$551$	62.7701	2.67410
$552$	11.2435	0.478556
$553$	−5.68599	−0.241793
$554$	−26.1333	−1.11030
$555$	1.51527	0.0643196
$556$	−18.8704	−0.800283
$557$	15.3781	0.651593	0.325796	−	0.945440i	$-0.394368\pi$
$557$	15.3781	0.651593	0.325796	+	0.945440i	$0.394368\pi$
$558$	10.1157	0.428231
$559$	−24.9360	−1.05468
$560$	1.33430	0.0563845
$561$	−8.71854	−0.368097
$562$	−21.2080	−0.894604
$563$	−35.7308	−1.50587	−0.752936	−	0.658094i	$-0.771363\pi$
$563$	−35.7308	−1.50587	−0.752936	+	0.658094i	$0.771363\pi$
$564$	2.05800	0.0866575
$565$	3.10303	0.130545
$566$	14.7588	0.620357
$567$	−17.6533	−0.741371
$568$	−1.01796	−0.0427125
$569$	−44.5699	−1.86847	−0.934235	−	0.356659i	$-0.883916\pi$
$569$	−44.5699	−1.86847	−0.934235	+	0.356659i	$0.883916\pi$
$570$	−3.82142	−0.160061
$571$	−46.6521	−1.95233	−0.976165	−	0.217028i	$-0.930364\pi$
$571$	−46.6521	−1.95233	−0.976165	+	0.217028i	$0.930364\pi$
$572$	−4.10198	−0.171512
$573$	−28.4497	−1.18851
$574$	45.7416	1.90922
$575$	−40.0645	−1.67080
$576$	−1.11723	−0.0465514
$577$	33.5577	1.39703	0.698513	−	0.715598i	$-0.253846\pi$
$577$	33.5577	1.39703	0.698513	+	0.715598i	$0.253846\pi$
$578$	−23.3730	−0.972190
$579$	−24.9692	−1.03769
$580$	−2.49288	−0.103511
$581$	37.6887	1.56359
$582$	−9.67771	−0.401154
$583$	8.36249	0.346339
$584$	0.874921	0.0362045
$585$	1.52414	0.0630155
$586$	−7.77063	−0.321002
$587$	−10.9767	−0.453058	−0.226529	−	0.974004i	$-0.572738\pi$
$587$	−10.9767	−0.453058	−0.226529	+	0.974004i	$0.572738\pi$
$588$	−12.4817	−0.514737
$589$	−75.8211	−3.12415
$590$	1.21821	0.0501530
$591$	1.37214	0.0564423
$592$	−3.32051	−0.136472
$593$	6.64348	0.272815	0.136408	−	0.990653i	$-0.456444\pi$
$593$	6.64348	0.272815	0.136408	+	0.990653i	$0.456444\pi$
$594$	−5.64942	−0.231798
$595$	8.47811	0.347569
$596$	−15.8640	−0.649814
$597$	−24.1456	−0.988212
$598$	33.6122	1.37451
$599$	−29.3586	−1.19956	−0.599781	−	0.800164i	$-0.704745\pi$
$599$	−29.3586	−1.19956	−0.599781	+	0.800164i	$0.704745\pi$
$600$	−6.70893	−0.273891
$601$	−23.2339	−0.947732	−0.473866	−	0.880597i	$-0.657142\pi$
$601$	−23.2339	−0.947732	−0.473866	+	0.880597i	$0.657142\pi$
$602$	−24.3893	−0.994033
$603$	−14.5074	−0.590789
$604$	0.363995	0.0148108
$605$	0.332573	0.0135210
$606$	5.83124	0.236878
$607$	−2.69770	−0.109496	−0.0547482	−	0.998500i	$-0.517436\pi$
$607$	−2.69770	−0.109496	−0.0547482	+	0.998500i	$0.517436\pi$
$608$	8.37411	0.339615
$609$	41.2647	1.67213
$610$	−4.74438	−0.192094
$611$	6.15235	0.248897
$612$	−7.09888	−0.286955
$613$	30.4186	1.22860	0.614298	−	0.789074i	$-0.289439\pi$
$613$	30.4186	1.22860	0.614298	+	0.789074i	$0.289439\pi$
$614$	−26.1080	−1.05363
$615$	5.20272	0.209794
$616$	−4.01205	−0.161650
$617$	0.230065	0.00926208	0.00463104	−	0.999989i	$-0.498526\pi$
$617$	0.230065	0.00926208	0.00463104	+	0.999989i	$0.498526\pi$
$618$	11.7264	0.471705
$619$	6.80694	0.273594	0.136797	−	0.990599i	$-0.456319\pi$
$619$	6.80694	0.273594	0.136797	+	0.990599i	$0.456319\pi$
$620$	3.01119	0.120932
$621$	46.2922	1.85764
$622$	−0.543074	−0.0217753
$623$	19.8052	0.793480
$624$	5.62848	0.225320
$625$	23.3532	0.934126
$626$	8.58446	0.343104
$627$	11.4904	0.458884
$628$	18.3002	0.730258
$629$	−21.0984	−0.841250
$630$	1.49073	0.0593920
$631$	23.3052	0.927765	0.463883	−	0.885897i	$-0.346456\pi$
$631$	23.3052	0.927765	0.463883	+	0.885897i	$0.346456\pi$
$632$	1.41723	0.0563744
$633$	−20.9892	−0.834247
$634$	0.427380	0.0169734
$635$	0.249695	0.00990882
$636$	−11.4745	−0.454993
$637$	−37.3138	−1.47843
$638$	7.49574	0.296759
$639$	−1.13730	−0.0449907
$640$	−0.332573	−0.0131461
$641$	−30.9639	−1.22300	−0.611501	−	0.791244i	$-0.709434\pi$
$641$	−30.9639	−1.22300	−0.611501	+	0.791244i	$0.709434\pi$
$642$	−10.8130	−0.426753
$643$	−19.8625	−0.783302	−0.391651	−	0.920114i	$-0.628096\pi$
$643$	−19.8625	−0.783302	−0.391651	+	0.920114i	$0.628096\pi$
$644$	32.8754	1.29547
$645$	−2.77408	−0.109229
$646$	53.2089	2.09348
$647$	−38.7828	−1.52471	−0.762354	−	0.647160i	$-0.775957\pi$
$647$	−38.7828	−1.52471	−0.762354	+	0.647160i	$0.775957\pi$
$648$	4.40008	0.172852
$649$	−3.66299	−0.143785
$650$	−20.0562	−0.786668
$651$	−49.8443	−1.95355
$652$	−12.9133	−0.505723
$653$	4.44419	0.173914	0.0869572	−	0.996212i	$-0.472286\pi$
$653$	4.44419	0.173914	0.0869572	+	0.996212i	$0.472286\pi$
$654$	−1.02114	−0.0399298
$655$	−2.01582	−0.0787648
$656$	−11.4011	−0.445136
$657$	0.977492	0.0381356
$658$	6.01747	0.234585
$659$	−9.69469	−0.377651	−0.188826	−	0.982011i	$-0.560468\pi$
$659$	−9.69469	−0.377651	−0.188826	+	0.982011i	$0.560468\pi$
$660$	−0.456337	−0.0177629
$661$	11.4849	0.446713	0.223356	−	0.974737i	$-0.428299\pi$
$661$	11.4849	0.446713	0.223356	+	0.974737i	$0.428299\pi$
$662$	−30.5950	−1.18911
$663$	35.7633	1.38893
$664$	−9.39387	−0.364553
$665$	−11.1736	−0.433293
$666$	−3.70979	−0.143751
$667$	−61.4212	−2.37824
$668$	−3.67679	−0.142259
$669$	−33.1365	−1.28113
$670$	−4.31851	−0.166839
$671$	14.2657	0.550720
$672$	5.50509	0.212363
$673$	11.1177	0.428556	0.214278	−	0.976773i	$-0.431260\pi$
$673$	11.1177	0.428556	0.214278	+	0.976773i	$0.431260\pi$
$674$	11.1362	0.428950
$675$	−27.6222	−1.06318
$676$	3.82622	0.147162
$677$	4.86140	0.186839	0.0934193	−	0.995627i	$-0.470220\pi$
$677$	4.86140	0.186839	0.0934193	+	0.995627i	$0.470220\pi$
$678$	12.8025	0.491679
$679$	−28.2970	−1.08594
$680$	−2.11316	−0.0810361
$681$	−12.1398	−0.465197
$682$	−9.05422	−0.346704
$683$	−13.8652	−0.530535	−0.265268	−	0.964175i	$-0.585460\pi$
$683$	−13.8652	−0.530535	−0.265268	+	0.964175i	$0.585460\pi$
$684$	9.35585	0.357730
$685$	−5.22863	−0.199776
$686$	−8.41140	−0.321149
$687$	−24.5023	−0.934822
$688$	6.07901	0.231760
$689$	−34.3027	−1.30683
$690$	3.73929	0.142352
$691$	18.0808	0.687827	0.343914	−	0.939001i	$-0.388247\pi$
$691$	18.0808	0.687827	0.343914	+	0.939001i	$0.388247\pi$
$692$	11.9616	0.454713
$693$	−4.48240	−0.170272
$694$	−16.6680	−0.632707
$695$	−6.27579	−0.238054
$696$	−10.2852	−0.389859
$697$	−72.4421	−2.74394
$698$	−22.4775	−0.850788
$699$	16.2624	0.615101
$700$	−19.6165	−0.741434
$701$	−3.64052	−0.137501	−0.0687503	−	0.997634i	$-0.521901\pi$
$701$	−3.64052	−0.137501	−0.0687503	+	0.997634i	$0.521901\pi$
$702$	23.1738	0.874638
$703$	27.8063	1.04873
$704$	1.00000	0.0376889
$705$	0.684436	0.0257774
$706$	−14.3008	−0.538217
$707$	17.0502	0.641239
$708$	5.02613	0.188894
$709$	−0.768652	−0.0288673	−0.0144337	−	0.999896i	$-0.504595\pi$
$709$	−0.768652	−0.0288673	−0.0144337	+	0.999896i	$0.504595\pi$
$710$	−0.338545	−0.0127054
$711$	1.58338	0.0593813
$712$	−4.93644	−0.185001
$713$	74.1917	2.77850
$714$	34.9792	1.30906
$715$	−1.36421	−0.0510185
$716$	0.202304	0.00756045
$717$	10.8597	0.405564
$718$	−28.2845	−1.05557
$719$	28.4959	1.06272	0.531358	−	0.847147i	$-0.321682\pi$
$719$	28.4959	1.06272	0.531358	+	0.847147i	$0.321682\pi$
$720$	−0.371562	−0.0138473
$721$	34.2873	1.27692
$722$	−51.1258	−1.90270
$723$	−11.9261	−0.443536
$724$	−22.4128	−0.832965
$725$	36.6496	1.36113
$726$	1.37214	0.0509249
$727$	9.66551	0.358474	0.179237	−	0.983806i	$-0.442637\pi$
$727$	9.66551	0.358474	0.179237	+	0.983806i	$0.442637\pi$
$728$	16.4573	0.609949
$729$	28.1713	1.04338
$730$	0.290975	0.0107695
$731$	38.6259	1.42863
$732$	−19.5745	−0.723493
$733$	21.7958	0.805045	0.402522	−	0.915410i	$-0.368134\pi$
$733$	21.7958	0.805045	0.402522	+	0.915410i	$0.368134\pi$
$734$	−14.2526	−0.526075
$735$	−4.15108	−0.153115
$736$	−8.19416	−0.302041
$737$	12.9851	0.478314
$738$	−12.7377	−0.468880
$739$	−12.7427	−0.468749	−0.234375	−	0.972146i	$-0.575304\pi$
$739$	−12.7427	−0.468749	−0.234375	+	0.972146i	$0.575304\pi$
$740$	−1.10431	−0.0405953
$741$	−47.1336	−1.73149
$742$	−33.5507	−1.23169
$743$	29.9330	1.09814	0.549068	−	0.835778i	$-0.314983\pi$
$743$	29.9330	1.09814	0.549068	+	0.835778i	$0.314983\pi$
$744$	12.4237	0.455473
$745$	−5.27594	−0.193295
$746$	−5.66199	−0.207300
$747$	−10.4952	−0.383998
$748$	6.35398	0.232324
$749$	−31.6164	−1.15524
$750$	−4.51289	−0.164788
$751$	31.1019	1.13492	0.567461	−	0.823400i	$-0.307926\pi$
$751$	31.1019	1.13492	0.567461	+	0.823400i	$0.307926\pi$
$752$	−1.49985	−0.0546939
$753$	16.1416	0.588232
$754$	−30.7473	−1.11975
$755$	0.121055	0.00440565
$756$	22.6657	0.824345
$757$	29.8797	1.08600	0.542999	−	0.839734i	$-0.317289\pi$
$757$	29.8797	1.08600	0.542999	+	0.839734i	$0.317289\pi$
$758$	32.2040	1.16970
$759$	−11.2435	−0.408114
$760$	2.78501	0.101023
$761$	10.8945	0.394925	0.197463	−	0.980310i	$-0.436730\pi$
$761$	10.8945	0.394925	0.197463	+	0.980310i	$0.436730\pi$
$762$	1.03020	0.0373201
$763$	−2.98575	−0.108092
$764$	20.7339	0.750125
$765$	−2.36090	−0.0853585
$766$	14.4227	0.521112
$767$	15.0255	0.542540
$768$	−1.37214	−0.0495128
$769$	−12.2533	−0.441867	−0.220933	−	0.975289i	$-0.570910\pi$
$769$	−12.2533	−0.441867	−0.220933	+	0.975289i	$0.570910\pi$
$770$	−1.33430	−0.0480848
$771$	−12.5901	−0.453422
$772$	18.1973	0.654936
$773$	21.4673	0.772125	0.386063	−	0.922473i	$-0.373835\pi$
$773$	21.4673	0.772125	0.386063	+	0.922473i	$0.373835\pi$
$774$	6.79168	0.244122
$775$	−44.2697	−1.59021
$776$	7.05301	0.253188
$777$	18.2797	0.655780
$778$	2.64449	0.0948096
$779$	95.4737	3.42070
$780$	1.87188	0.0670242
$781$	1.01796	0.0364253
$782$	−52.0655	−1.86186
$783$	−42.3465	−1.51334
$784$	9.09653	0.324876
$785$	6.08616	0.217224
$786$	−8.31694	−0.296655
$787$	30.5997	1.09076	0.545380	−	0.838189i	$-0.316385\pi$
$787$	30.5997	1.09076	0.545380	+	0.838189i	$0.316385\pi$
$788$	−1.00000	−0.0356235
$789$	−18.3778	−0.654268
$790$	0.471333	0.0167693
$791$	37.4338	1.33099
$792$	1.11723	0.0396992
$793$	−58.5174	−2.07801
$794$	−12.6111	−0.447552
$795$	−3.81611	−0.135343
$796$	17.5970	0.623710
$797$	27.0832	0.959335	0.479667	−	0.877450i	$-0.340757\pi$
$797$	27.0832	0.959335	0.479667	+	0.877450i	$0.340757\pi$
$798$	−46.1002	−1.63193
$799$	−9.53001	−0.337147
$800$	4.88940	0.172866
$801$	−5.51516	−0.194869
$802$	−9.13246	−0.322478
$803$	−0.874921	−0.0308753
$804$	−17.8174	−0.628372
$805$	10.9335	0.385354
$806$	37.1402	1.30821
$807$	−6.97059	−0.245376
$808$	−4.24975	−0.149506
$809$	−43.2266	−1.51977	−0.759883	−	0.650060i	$-0.774744\pi$
$809$	−43.2266	−1.51977	−0.759883	+	0.650060i	$0.774744\pi$
$810$	1.46335	0.0514169
$811$	49.4473	1.73633	0.868165	−	0.496276i	$-0.165300\pi$
$811$	49.4473	1.73633	0.868165	+	0.496276i	$0.165300\pi$
$812$	−30.0733	−1.05536
$813$	−20.8298	−0.730533
$814$	3.32051	0.116384
$815$	−4.29461	−0.150434
$816$	−8.71854	−0.305210
$817$	−50.9063	−1.78099
$818$	−22.5356	−0.787940
$819$	18.3867	0.642483
$820$	−3.79169	−0.132411
$821$	−12.9558	−0.452160	−0.226080	−	0.974109i	$-0.572591\pi$
$821$	−12.9558	−0.452160	−0.226080	+	0.974109i	$0.572591\pi$
$822$	−21.5724	−0.752424
$823$	30.5510	1.06494	0.532470	−	0.846449i	$-0.321264\pi$
$823$	30.5510	1.06494	0.532470	+	0.846449i	$0.321264\pi$
$824$	−8.54607	−0.297717
$825$	6.70893	0.233575
$826$	14.6961	0.511343
$827$	−41.4251	−1.44049	−0.720245	−	0.693719i	$-0.755971\pi$
$827$	−41.4251	−1.44049	−0.720245	+	0.693719i	$0.755971\pi$
$828$	−9.15479	−0.318151
$829$	27.9151	0.969530	0.484765	−	0.874644i	$-0.338905\pi$
$829$	27.9151	0.969530	0.484765	+	0.874644i	$0.338905\pi$
$830$	−3.12415	−0.108441
$831$	−35.8586	−1.24392
$832$	−4.10198	−0.142210
$833$	57.7992	2.00262
$834$	−25.8928	−0.896595
$835$	−1.22280	−0.0423168
$836$	−8.37411	−0.289625
$837$	51.1511	1.76804
$838$	21.1302	0.729931
$839$	−10.5229	−0.363293	−0.181646	−	0.983364i	$-0.558143\pi$
$839$	−10.5229	−0.363293	−0.181646	+	0.983364i	$0.558143\pi$
$840$	1.83085	0.0631702
$841$	27.1860	0.937450
$842$	9.85027	0.339463
$843$	−29.1003	−1.00227
$844$	15.2967	0.526535
$845$	1.27250	0.0437753
$846$	−1.67568	−0.0576112
$847$	4.01205	0.137856
$848$	8.36249	0.287169
$849$	20.2511	0.695015
$850$	31.0671	1.06559
$851$	−27.2088	−0.932704
$852$	−1.39678	−0.0478528
$853$	−0.179536	−0.00614720	−0.00307360	−	0.999995i	$-0.500978\pi$
$853$	−0.179536	−0.00614720	−0.00307360	+	0.999995i	$0.500978\pi$
$854$	−57.2345	−1.95852
$855$	3.11151	0.106411
$856$	7.88036	0.269345
$857$	−46.7630	−1.59739	−0.798697	−	0.601733i	$-0.794477\pi$
$857$	−46.7630	−1.59739	−0.798697	+	0.601733i	$0.794477\pi$
$858$	−5.62848	−0.192153
$859$	−27.1531	−0.926450	−0.463225	−	0.886241i	$-0.653308\pi$
$859$	−27.1531	−0.926450	−0.463225	+	0.886241i	$0.653308\pi$
$860$	2.02172	0.0689400
$861$	62.7638	2.13899
$862$	−6.28111	−0.213936
$863$	−3.02382	−0.102932	−0.0514660	−	0.998675i	$-0.516389\pi$
$863$	−3.02382	−0.102932	−0.0514660	+	0.998675i	$0.516389\pi$
$864$	−5.64942	−0.192197
$865$	3.97812	0.135260
$866$	−11.8615	−0.403071
$867$	−32.0711	−1.08919
$868$	36.3260	1.23298
$869$	−1.41723	−0.0480762
$870$	−3.42058	−0.115968
$871$	−53.2648	−1.80481
$872$	0.744197	0.0252017
$873$	7.87987	0.266693
$874$	68.6188	2.32107
$875$	−13.1954	−0.446087
$876$	1.20051	0.0405616
$877$	22.1336	0.747399	0.373699	−	0.927550i	$-0.378089\pi$
$877$	22.1336	0.747399	0.373699	+	0.927550i	$0.378089\pi$
$878$	12.7096	0.428927
$879$	−10.6624	−0.359633
$880$	0.332573	0.0112110
$881$	3.80208	0.128095	0.0640476	−	0.997947i	$-0.479599\pi$
$881$	3.80208	0.128095	0.0640476	+	0.997947i	$0.479599\pi$
$882$	10.1630	0.342205
$883$	−27.6666	−0.931054	−0.465527	−	0.885034i	$-0.654135\pi$
$883$	−27.6666	−0.931054	−0.465527	+	0.885034i	$0.654135\pi$
$884$	−26.0639	−0.876623
$885$	1.67156	0.0561888
$886$	32.3739	1.08762
$887$	−17.3534	−0.582672	−0.291336	−	0.956621i	$-0.594100\pi$
$887$	−17.3534	−0.582672	−0.291336	+	0.956621i	$0.594100\pi$
$888$	−4.55620	−0.152896
$889$	3.01223	0.101027
$890$	−1.64173	−0.0550308
$891$	−4.40008	−0.147408
$892$	24.1496	0.808587
$893$	12.5599	0.420301
$894$	−21.7676	−0.728017
$895$	0.0672808	0.00224895
$896$	−4.01205	−0.134033
$897$	46.1207	1.53992
$898$	25.7239	0.858417
$899$	−67.8680	−2.26353
$900$	5.46260	0.182087
$901$	53.1351	1.77019
$902$	11.4011	0.379614
$903$	−33.4655	−1.11366
$904$	−9.33036	−0.310323
$905$	−7.45390	−0.247776
$906$	0.499452	0.0165932
$907$	−56.7604	−1.88470	−0.942349	−	0.334632i	$-0.891388\pi$
$907$	−56.7604	−1.88470	−0.942349	+	0.334632i	$0.891388\pi$
$908$	8.84732	0.293609
$909$	−4.74797	−0.157480
$910$	5.47327	0.181437
$911$	4.58691	0.151971	0.0759856	−	0.997109i	$-0.475790\pi$
$911$	4.58691	0.151971	0.0759856	+	0.997109i	$0.475790\pi$
$912$	11.4904	0.380487
$913$	9.39387	0.310892
$914$	33.4105	1.10512
$915$	−6.50994	−0.215212
$916$	17.8570	0.590013
$917$	−24.3182	−0.803058
$918$	−35.8963	−1.18475
$919$	7.49363	0.247192	0.123596	−	0.992333i	$-0.460557\pi$
$919$	7.49363	0.247192	0.123596	+	0.992333i	$0.460557\pi$
$920$	−2.72516	−0.0898458
$921$	−35.8238	−1.18043
$922$	11.3714	0.374496
$923$	−4.17563	−0.137443
$924$	−5.50509	−0.181104
$925$	16.2353	0.533813
$926$	−17.1572	−0.563822
$927$	−9.54797	−0.313596
$928$	7.49574	0.246060
$929$	37.9733	1.24586	0.622932	−	0.782276i	$-0.285941\pi$
$929$	37.9733	1.24586	0.622932	+	0.782276i	$0.285941\pi$
$930$	4.13177	0.135486
$931$	−76.1754	−2.49655
$932$	−11.8519	−0.388221
$933$	−0.745173	−0.0243959
$934$	−1.09579	−0.0358555
$935$	2.11316	0.0691078
$936$	−4.58287	−0.149796
$937$	−9.78855	−0.319778	−0.159889	−	0.987135i	$-0.551114\pi$
$937$	−9.78855	−0.319778	−0.159889	+	0.987135i	$0.551114\pi$
$938$	−52.0970	−1.70103
$939$	11.7791	0.384396
$940$	−0.498810	−0.0162694
$941$	−28.3107	−0.922903	−0.461452	−	0.887165i	$-0.652671\pi$
$941$	−28.3107	−0.922903	−0.461452	+	0.887165i	$0.652671\pi$
$942$	25.1104	0.818142
$943$	−93.4220	−3.04224
$944$	−3.66299	−0.119220
$945$	7.53802	0.245212
$946$	−6.07901	−0.197646
$947$	−15.5327	−0.504746	−0.252373	−	0.967630i	$-0.581211\pi$
$947$	−15.5327	−0.504746	−0.252373	+	0.967630i	$0.581211\pi$
$948$	1.94464	0.0631588
$949$	3.58891	0.116501
$950$	−40.9443	−1.32841
$951$	0.586425	0.0190161
$952$	−25.4925	−0.826216
$953$	−5.26980	−0.170705	−0.0853527	−	0.996351i	$-0.527202\pi$
$953$	−5.26980	−0.170705	−0.0853527	+	0.996351i	$0.527202\pi$
$954$	9.34286	0.302486
$955$	6.89553	0.223134
$956$	−7.91445	−0.255972
$957$	10.2852	0.332473
$958$	−39.9682	−1.29131
$959$	−63.0764	−2.03684
$960$	−0.456337	−0.0147282
$961$	50.9789	1.64448
$962$	−13.6206	−0.439147
$963$	8.80421	0.283712
$964$	8.69160	0.279938
$965$	6.05194	0.194819
$966$	45.1096	1.45138
$967$	48.9619	1.57451	0.787255	−	0.616627i	$-0.211502\pi$
$967$	48.9619	1.57451	0.787255	+	0.616627i	$0.211502\pi$
$968$	−1.00000	−0.0321412
$969$	73.0101	2.34542
$970$	2.34564	0.0753140
$971$	17.9834	0.577114	0.288557	−	0.957463i	$-0.406824\pi$
$971$	17.9834	0.577114	0.288557	+	0.957463i	$0.406824\pi$
$972$	−10.9107	−0.349962
$973$	−75.7090	−2.42712
$974$	−3.53781	−0.113359
$975$	−27.5199	−0.881341
$976$	14.2657	0.456632
$977$	43.5225	1.39241	0.696204	−	0.717844i	$-0.254871\pi$
$977$	43.5225	1.39241	0.696204	+	0.717844i	$0.254871\pi$
$978$	−17.7188	−0.566585
$979$	4.93644	0.157769
$980$	3.02526	0.0966385
$981$	0.831442	0.0265459
$982$	−20.0700	−0.640459
$983$	−3.65101	−0.116449	−0.0582246	−	0.998304i	$-0.518544\pi$
$983$	−3.65101	−0.116449	−0.0582246	+	0.998304i	$0.518544\pi$
$984$	−15.6438	−0.498707
$985$	−0.332573	−0.0105967
$986$	47.6277	1.51678
$987$	8.25680	0.262817
$988$	34.3504	1.09283
$989$	49.8124	1.58394
$990$	0.371562	0.0118090
$991$	−59.3819	−1.88633	−0.943165	−	0.332326i	$-0.892167\pi$
$991$	−59.3819	−1.88633	−0.943165	+	0.332326i	$0.892167\pi$
$992$	−9.05422	−0.287472
$993$	−41.9806	−1.33221
$994$	−4.08409	−0.129539
$995$	5.85230	0.185530
$996$	−12.8897	−0.408426
$997$	−10.3464	−0.327675	−0.163837	−	0.986487i	$-0.552387\pi$
$997$	−10.3464	−0.327675	−0.163837	+	0.986487i	$0.552387\pi$
$998$	−43.3124	−1.37103
$999$	−18.7589	−0.593507

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.h.1.8	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.h.1.8	✓	27	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:	\( N \)	\(=\)	\( 4334 = 2 \cdot 11 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4334.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.37214 q^{3} +1.00000 q^{4} +0.332573 q^{5} +1.37214 q^{6} +4.01205 q^{7} -1.00000 q^{8} -1.11723 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.37214 q^{3} +1.00000 q^{4} +0.332573 q^{5} +1.37214 q^{6} +4.01205 q^{7} -1.00000 q^{8} -1.11723 q^{9} -0.332573 q^{10} +1.00000 q^{11} -1.37214 q^{12} -4.10198 q^{13} -4.01205 q^{14} -0.456337 q^{15} +1.00000 q^{16} +6.35398 q^{17} +1.11723 q^{18} -8.37411 q^{19} +0.332573 q^{20} -5.50509 q^{21} -1.00000 q^{22} +8.19416 q^{23} +1.37214 q^{24} -4.88940 q^{25} +4.10198 q^{26} +5.64942 q^{27} +4.01205 q^{28} -7.49574 q^{29} +0.456337 q^{30} +9.05422 q^{31} -1.00000 q^{32} -1.37214 q^{33} -6.35398 q^{34} +1.33430 q^{35} -1.11723 q^{36} -3.32051 q^{37} +8.37411 q^{38} +5.62848 q^{39} -0.332573 q^{40} -11.4011 q^{41} +5.50509 q^{42} +6.07901 q^{43} +1.00000 q^{44} -0.371562 q^{45} -8.19416 q^{46} -1.49985 q^{47} -1.37214 q^{48} +9.09653 q^{49} +4.88940 q^{50} -8.71854 q^{51} -4.10198 q^{52} +8.36249 q^{53} -5.64942 q^{54} +0.332573 q^{55} -4.01205 q^{56} +11.4904 q^{57} +7.49574 q^{58} -3.66299 q^{59} -0.456337 q^{60} +14.2657 q^{61} -9.05422 q^{62} -4.48240 q^{63} +1.00000 q^{64} -1.36421 q^{65} +1.37214 q^{66} +12.9851 q^{67} +6.35398 q^{68} -11.2435 q^{69} -1.33430 q^{70} +1.01796 q^{71} +1.11723 q^{72} -0.874921 q^{73} +3.32051 q^{74} +6.70893 q^{75} -8.37411 q^{76} +4.01205 q^{77} -5.62848 q^{78} -1.41723 q^{79} +0.332573 q^{80} -4.40008 q^{81} +11.4011 q^{82} +9.39387 q^{83} -5.50509 q^{84} +2.11316 q^{85} -6.07901 q^{86} +10.2852 q^{87} -1.00000 q^{88} +4.93644 q^{89} +0.371562 q^{90} -16.4573 q^{91} +8.19416 q^{92} -12.4237 q^{93} +1.49985 q^{94} -2.78501 q^{95} +1.37214 q^{96} -7.05301 q^{97} -9.09653 q^{98} -1.11723 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 27 q^{2} + 27 q^{4} + 9 q^{5} + q^{7} - 27 q^{8} + 43 q^{9}+O(q^{10}) \) 27 * q - 27 * q^2 + 27 * q^4 + 9 * q^5 + q^7 - 27 * q^8 + 43 * q^9	\( 27 q - 27 q^{2} + 27 q^{4} + 9 q^{5} + q^{7} - 27 q^{8} + 43 q^{9} - 9 q^{10} + 27 q^{11} + 4 q^{13} - q^{14} + 8 q^{15} + 27 q^{16} + 3 q^{17} - 43 q^{18} + 30 q^{19} + 9 q^{20} + 11 q^{21} - 27 q^{22} + 13 q^{23} + 50 q^{25} - 4 q^{26} - 3 q^{27} + q^{28} + 5 q^{29} - 8 q^{30} + 40 q^{31} - 27 q^{32} - 3 q^{34} - 16 q^{35} + 43 q^{36} + 21 q^{37} - 30 q^{38} + 5 q^{39} - 9 q^{40} + 13 q^{41} - 11 q^{42} + 10 q^{43} + 27 q^{44} + 48 q^{45} - 13 q^{46} + 78 q^{49} - 50 q^{50} + 8 q^{51} + 4 q^{52} + 8 q^{53} + 3 q^{54} + 9 q^{55} - q^{56} - 16 q^{57} - 5 q^{58} + 24 q^{59} + 8 q^{60} + 28 q^{61} - 40 q^{62} - 18 q^{63} + 27 q^{64} - q^{65} + 24 q^{67} + 3 q^{68} - 3 q^{69} + 16 q^{70} - 3 q^{71} - 43 q^{72} + 9 q^{73} - 21 q^{74} + 26 q^{75} + 30 q^{76} + q^{77} - 5 q^{78} + 12 q^{79} + 9 q^{80} + 99 q^{81} - 13 q^{82} - 11 q^{83} + 11 q^{84} + 15 q^{85} - 10 q^{86} - 34 q^{87} - 27 q^{88} + 69 q^{89} - 48 q^{90} + q^{91} + 13 q^{92} - 24 q^{93} - 31 q^{95} + 41 q^{97} - 78 q^{98} + 43 q^{99}+O(q^{100}) \) 27 * q - 27 * q^2 + 27 * q^4 + 9 * q^5 + q^7 - 27 * q^8 + 43 * q^9 - 9 * q^10 + 27 * q^11 + 4 * q^13 - q^14 + 8 * q^15 + 27 * q^16 + 3 * q^17 - 43 * q^18 + 30 * q^19 + 9 * q^20 + 11 * q^21 - 27 * q^22 + 13 * q^23 + 50 * q^25 - 4 * q^26 - 3 * q^27 + q^28 + 5 * q^29 - 8 * q^30 + 40 * q^31 - 27 * q^32 - 3 * q^34 - 16 * q^35 + 43 * q^36 + 21 * q^37 - 30 * q^38 + 5 * q^39 - 9 * q^40 + 13 * q^41 - 11 * q^42 + 10 * q^43 + 27 * q^44 + 48 * q^45 - 13 * q^46 + 78 * q^49 - 50 * q^50 + 8 * q^51 + 4 * q^52 + 8 * q^53 + 3 * q^54 + 9 * q^55 - q^56 - 16 * q^57 - 5 * q^58 + 24 * q^59 + 8 * q^60 + 28 * q^61 - 40 * q^62 - 18 * q^63 + 27 * q^64 - q^65 + 24 * q^67 + 3 * q^68 - 3 * q^69 + 16 * q^70 - 3 * q^71 - 43 * q^72 + 9 * q^73 - 21 * q^74 + 26 * q^75 + 30 * q^76 + q^77 - 5 * q^78 + 12 * q^79 + 9 * q^80 + 99 * q^81 - 13 * q^82 - 11 * q^83 + 11 * q^84 + 15 * q^85 - 10 * q^86 - 34 * q^87 - 27 * q^88 + 69 * q^89 - 48 * q^90 + q^91 + 13 * q^92 - 24 * q^93 - 31 * q^95 + 41 * q^97 - 78 * q^98 + 43 * q^99

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