LMFDB - Embedded newform 6034.2.a.m.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, 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("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$1$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.30616 q^{3} +1.00000 q^{4} -2.85291 q^{5} -2.30616 q^{6} +1.00000 q^{7} +1.00000 q^{8} +2.31835 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.30616 q^{3} +1.00000 q^{4} -2.85291 q^{5} -2.30616 q^{6} +1.00000 q^{7} +1.00000 q^{8} +2.31835 q^{9} -2.85291 q^{10} -1.11641 q^{11} -2.30616 q^{12} +2.44827 q^{13} +1.00000 q^{14} +6.57926 q^{15} +1.00000 q^{16} +1.74072 q^{17} +2.31835 q^{18} -0.0622146 q^{19} -2.85291 q^{20} -2.30616 q^{21} -1.11641 q^{22} -4.67304 q^{23} -2.30616 q^{24} +3.13910 q^{25} +2.44827 q^{26} +1.57199 q^{27} +1.00000 q^{28} -9.83561 q^{29} +6.57926 q^{30} -0.366188 q^{31} +1.00000 q^{32} +2.57460 q^{33} +1.74072 q^{34} -2.85291 q^{35} +2.31835 q^{36} -1.57539 q^{37} -0.0622146 q^{38} -5.64610 q^{39} -2.85291 q^{40} +11.0495 q^{41} -2.30616 q^{42} +1.33962 q^{43} -1.11641 q^{44} -6.61405 q^{45} -4.67304 q^{46} +10.0228 q^{47} -2.30616 q^{48} +1.00000 q^{49} +3.13910 q^{50} -4.01437 q^{51} +2.44827 q^{52} +3.40751 q^{53} +1.57199 q^{54} +3.18501 q^{55} +1.00000 q^{56} +0.143477 q^{57} -9.83561 q^{58} +6.27003 q^{59} +6.57926 q^{60} +2.39900 q^{61} -0.366188 q^{62} +2.31835 q^{63} +1.00000 q^{64} -6.98471 q^{65} +2.57460 q^{66} -13.7231 q^{67} +1.74072 q^{68} +10.7767 q^{69} -2.85291 q^{70} +6.35772 q^{71} +2.31835 q^{72} +3.56320 q^{73} -1.57539 q^{74} -7.23926 q^{75} -0.0622146 q^{76} -1.11641 q^{77} -5.64610 q^{78} +8.90449 q^{79} -2.85291 q^{80} -10.5803 q^{81} +11.0495 q^{82} -10.5291 q^{83} -2.30616 q^{84} -4.96612 q^{85} +1.33962 q^{86} +22.6824 q^{87} -1.11641 q^{88} -6.43133 q^{89} -6.61405 q^{90} +2.44827 q^{91} -4.67304 q^{92} +0.844487 q^{93} +10.0228 q^{94} +0.177493 q^{95} -2.30616 q^{96} -0.643922 q^{97} +1.00000 q^{98} -2.58822 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9}+O(q^{10}) $ 21 * q + 21 * q^2 - 6 * q^3 + 21 * q^4 - 11 * q^5 - 6 * q^6 + 21 * q^7 + 21 * q^8 + 5 * q^9	\( 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9} - 11 q^{10} - 34 q^{11} - 6 q^{12} - 19 q^{13} + 21 q^{14} - 24 q^{15} + 21 q^{16} - 17 q^{17} + 5 q^{18} - 15 q^{19} - 11 q^{20} - 6 q^{21} - 34 q^{22} - 32 q^{23} - 6 q^{24} + 6 q^{25} - 19 q^{26} - 3 q^{27} + 21 q^{28} - 46 q^{29} - 24 q^{30} + 7 q^{31} + 21 q^{32} - 13 q^{33} - 17 q^{34} - 11 q^{35} + 5 q^{36} - 34 q^{37} - 15 q^{38} - 25 q^{39} - 11 q^{40} - 27 q^{41} - 6 q^{42} - 47 q^{43} - 34 q^{44} - 13 q^{45} - 32 q^{46} - 7 q^{47} - 6 q^{48} + 21 q^{49} + 6 q^{50} - 29 q^{51} - 19 q^{52} - 57 q^{53} - 3 q^{54} + 17 q^{55} + 21 q^{56} - 28 q^{57} - 46 q^{58} - 30 q^{59} - 24 q^{60} - 17 q^{61} + 7 q^{62} + 5 q^{63} + 21 q^{64} - 40 q^{65} - 13 q^{66} - 38 q^{67} - 17 q^{68} - 13 q^{69} - 11 q^{70} - 66 q^{71} + 5 q^{72} - 15 q^{73} - 34 q^{74} + 15 q^{75} - 15 q^{76} - 34 q^{77} - 25 q^{78} - 17 q^{79} - 11 q^{80} - 11 q^{81} - 27 q^{82} - 19 q^{83} - 6 q^{84} - 28 q^{85} - 47 q^{86} + 45 q^{87} - 34 q^{88} - 39 q^{89} - 13 q^{90} - 19 q^{91} - 32 q^{92} - 25 q^{93} - 7 q^{94} - 35 q^{95} - 6 q^{96} + 21 q^{98} - 52 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 - 6 * q^3 + 21 * q^4 - 11 * q^5 - 6 * q^6 + 21 * q^7 + 21 * q^8 + 5 * q^9 - 11 * q^10 - 34 * q^11 - 6 * q^12 - 19 * q^13 + 21 * q^14 - 24 * q^15 + 21 * q^16 - 17 * q^17 + 5 * q^18 - 15 * q^19 - 11 * q^20 - 6 * q^21 - 34 * q^22 - 32 * q^23 - 6 * q^24 + 6 * q^25 - 19 * q^26 - 3 * q^27 + 21 * q^28 - 46 * q^29 - 24 * q^30 + 7 * q^31 + 21 * q^32 - 13 * q^33 - 17 * q^34 - 11 * q^35 + 5 * q^36 - 34 * q^37 - 15 * q^38 - 25 * q^39 - 11 * q^40 - 27 * q^41 - 6 * q^42 - 47 * q^43 - 34 * q^44 - 13 * q^45 - 32 * q^46 - 7 * q^47 - 6 * q^48 + 21 * q^49 + 6 * q^50 - 29 * q^51 - 19 * q^52 - 57 * q^53 - 3 * q^54 + 17 * q^55 + 21 * q^56 - 28 * q^57 - 46 * q^58 - 30 * q^59 - 24 * q^60 - 17 * q^61 + 7 * q^62 + 5 * q^63 + 21 * q^64 - 40 * q^65 - 13 * q^66 - 38 * q^67 - 17 * q^68 - 13 * q^69 - 11 * q^70 - 66 * q^71 + 5 * q^72 - 15 * q^73 - 34 * q^74 + 15 * q^75 - 15 * q^76 - 34 * q^77 - 25 * q^78 - 17 * q^79 - 11 * q^80 - 11 * q^81 - 27 * q^82 - 19 * q^83 - 6 * q^84 - 28 * q^85 - 47 * q^86 + 45 * q^87 - 34 * q^88 - 39 * q^89 - 13 * q^90 - 19 * q^91 - 32 * q^92 - 25 * q^93 - 7 * q^94 - 35 * q^95 - 6 * q^96 + 21 * q^98 - 52 * 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
$3$	−2.30616	−1.33146	−0.665730	−	0.746193i	$-0.731880\pi$
$3$	−2.30616	−1.33146	−0.665730	+	0.746193i	$0.731880\pi$
$4$	1.00000	0.500000
$5$	−2.85291	−1.27586	−0.637930	−	0.770094i	$-0.720209\pi$
$5$	−2.85291	−1.27586	−0.637930	+	0.770094i	$0.720209\pi$
$6$	−2.30616	−0.941484
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	2.31835	0.772784
$10$	−2.85291	−0.902170
$11$	−1.11641	−0.336609	−0.168304	−	0.985735i	$-0.553829\pi$
$11$	−1.11641	−0.336609	−0.168304	+	0.985735i	$0.553829\pi$
$12$	−2.30616	−0.665730
$13$	2.44827	0.679029	0.339515	−	0.940601i	$-0.389737\pi$
$13$	2.44827	0.679029	0.339515	+	0.940601i	$0.389737\pi$
$14$	1.00000	0.267261
$15$	6.57926	1.69876
$16$	1.00000	0.250000
$17$	1.74072	0.422187	0.211093	−	0.977466i	$-0.432298\pi$
$17$	1.74072	0.422187	0.211093	+	0.977466i	$0.432298\pi$
$18$	2.31835	0.546441
$19$	−0.0622146	−0.0142730	−0.00713651	−	0.999975i	$-0.502272\pi$
$19$	−0.0622146	−0.0142730	−0.00713651	+	0.999975i	$0.502272\pi$
$20$	−2.85291	−0.637930
$21$	−2.30616	−0.503244
$22$	−1.11641	−0.238018
$23$	−4.67304	−0.974395	−0.487198	−	0.873292i	$-0.661981\pi$
$23$	−4.67304	−0.974395	−0.487198	+	0.873292i	$0.661981\pi$
$24$	−2.30616	−0.470742
$25$	3.13910	0.627821
$26$	2.44827	0.480146
$27$	1.57199	0.302529
$28$	1.00000	0.188982
$29$	−9.83561	−1.82643	−0.913213	−	0.407482i	$-0.866407\pi$
$29$	−9.83561	−1.82643	−0.913213	+	0.407482i	$0.866407\pi$
$30$	6.57926	1.20120
$31$	−0.366188	−0.0657693	−0.0328847	−	0.999459i	$-0.510469\pi$
$31$	−0.366188	−0.0657693	−0.0328847	+	0.999459i	$0.510469\pi$
$32$	1.00000	0.176777
$33$	2.57460	0.448181
$34$	1.74072	0.298531
$35$	−2.85291	−0.482230
$36$	2.31835	0.386392
$37$	−1.57539	−0.258992	−0.129496	−	0.991580i	$-0.541336\pi$
$37$	−1.57539	−0.258992	−0.129496	+	0.991580i	$0.541336\pi$
$38$	−0.0622146	−0.0100925
$39$	−5.64610	−0.904100
$40$	−2.85291	−0.451085
$41$	11.0495	1.72565	0.862825	−	0.505503i	$-0.168693\pi$
$41$	11.0495	1.72565	0.862825	+	0.505503i	$0.168693\pi$
$42$	−2.30616	−0.355847
$43$	1.33962	0.204291	0.102145	−	0.994769i	$-0.467429\pi$
$43$	1.33962	0.204291	0.102145	+	0.994769i	$0.467429\pi$
$44$	−1.11641	−0.168304
$45$	−6.61405	−0.985965
$46$	−4.67304	−0.689002
$47$	10.0228	1.46198	0.730989	−	0.682389i	$-0.239059\pi$
$47$	10.0228	1.46198	0.730989	+	0.682389i	$0.239059\pi$
$48$	−2.30616	−0.332865
$49$	1.00000	0.142857
$50$	3.13910	0.443936
$51$	−4.01437	−0.562125
$52$	2.44827	0.339515
$53$	3.40751	0.468058	0.234029	−	0.972230i	$-0.424809\pi$
$53$	3.40751	0.468058	0.234029	+	0.972230i	$0.424809\pi$
$54$	1.57199	0.213920
$55$	3.18501	0.429466
$56$	1.00000	0.133631
$57$	0.143477	0.0190039
$58$	−9.83561	−1.29148
$59$	6.27003	0.816288	0.408144	−	0.912917i	$-0.366176\pi$
$59$	6.27003	0.816288	0.408144	+	0.912917i	$0.366176\pi$
$60$	6.57926	0.849378
$61$	2.39900	0.307160	0.153580	−	0.988136i	$-0.450920\pi$
$61$	2.39900	0.307160	0.153580	+	0.988136i	$0.450920\pi$
$62$	−0.366188	−0.0465059
$63$	2.31835	0.292085
$64$	1.00000	0.125000
$65$	−6.98471	−0.866347
$66$	2.57460	0.316912
$67$	−13.7231	−1.67654	−0.838270	−	0.545256i	$-0.816433\pi$
$67$	−13.7231	−1.67654	−0.838270	+	0.545256i	$0.816433\pi$
$68$	1.74072	0.211093
$69$	10.7767	1.29737
$70$	−2.85291	−0.340988
$71$	6.35772	0.754522	0.377261	−	0.926107i	$-0.376866\pi$
$71$	6.35772	0.754522	0.377261	+	0.926107i	$0.376866\pi$
$72$	2.31835	0.273220
$73$	3.56320	0.417041	0.208520	−	0.978018i	$-0.433135\pi$
$73$	3.56320	0.417041	0.208520	+	0.978018i	$0.433135\pi$
$74$	−1.57539	−0.183135
$75$	−7.23926	−0.835918
$76$	−0.0622146	−0.00713651
$77$	−1.11641	−0.127226
$78$	−5.64610	−0.639295
$79$	8.90449	1.00183	0.500917	−	0.865495i	$-0.332996\pi$
$79$	8.90449	1.00183	0.500917	+	0.865495i	$0.332996\pi$
$80$	−2.85291	−0.318965
$81$	−10.5803	−1.17559
$82$	11.0495	1.22022
$83$	−10.5291	−1.15572	−0.577861	−	0.816135i	$-0.696112\pi$
$83$	−10.5291	−1.15572	−0.577861	+	0.816135i	$0.696112\pi$
$84$	−2.30616	−0.251622
$85$	−4.96612	−0.538652
$86$	1.33962	0.144455
$87$	22.6824	2.43181
$88$	−1.11641	−0.119009
$89$	−6.43133	−0.681720	−0.340860	−	0.940114i	$-0.610718\pi$
$89$	−6.43133	−0.681720	−0.340860	+	0.940114i	$0.610718\pi$
$90$	−6.61405	−0.697182
$91$	2.44827	0.256649
$92$	−4.67304	−0.487198
$93$	0.844487	0.0875692
$94$	10.0228	1.03377
$95$	0.177493	0.0182104
$96$	−2.30616	−0.235371
$97$	−0.643922	−0.0653804	−0.0326902	−	0.999466i	$-0.510407\pi$
$97$	−0.643922	−0.0653804	−0.0326902	+	0.999466i	$0.510407\pi$
$98$	1.00000	0.101015
$99$	−2.58822	−0.260126
$100$	3.13910	0.313910
$101$	−8.45196	−0.841001	−0.420501	−	0.907292i	$-0.638146\pi$
$101$	−8.45196	−0.841001	−0.420501	+	0.907292i	$0.638146\pi$
$102$	−4.01437	−0.397482
$103$	−11.4959	−1.13272	−0.566362	−	0.824157i	$-0.691650\pi$
$103$	−11.4959	−1.13272	−0.566362	+	0.824157i	$0.691650\pi$
$104$	2.44827	0.240073
$105$	6.57926	0.642070
$106$	3.40751	0.330967
$107$	15.2461	1.47389	0.736947	−	0.675950i	$-0.236267\pi$
$107$	15.2461	1.47389	0.736947	+	0.675950i	$0.236267\pi$
$108$	1.57199	0.151264
$109$	−0.143803	−0.0137739	−0.00688693	−	0.999976i	$-0.502192\pi$
$109$	−0.143803	−0.0137739	−0.00688693	+	0.999976i	$0.502192\pi$
$110$	3.18501	0.303678
$111$	3.63309	0.344838
$112$	1.00000	0.0944911
$113$	19.1507	1.80154	0.900771	−	0.434294i	$-0.143002\pi$
$113$	19.1507	1.80154	0.900771	+	0.434294i	$0.143002\pi$
$114$	0.143477	0.0134378
$115$	13.3318	1.24319
$116$	−9.83561	−0.913213
$117$	5.67596	0.524743
$118$	6.27003	0.577203
$119$	1.74072	0.159572
$120$	6.57926	0.600601
$121$	−9.75364	−0.886694
$122$	2.39900	0.217195
$123$	−25.4820	−2.29763
$124$	−0.366188	−0.0328847
$125$	5.30897	0.474849
$126$	2.31835	0.206535
$127$	−6.28789	−0.557960	−0.278980	−	0.960297i	$-0.589996\pi$
$127$	−6.28789	−0.557960	−0.278980	+	0.960297i	$0.589996\pi$
$128$	1.00000	0.0883883
$129$	−3.08938	−0.272005
$130$	−6.98471	−0.612600
$131$	−18.5132	−1.61751	−0.808755	−	0.588146i	$-0.799858\pi$
$131$	−18.5132	−1.61751	−0.808755	+	0.588146i	$0.799858\pi$
$132$	2.57460	0.224091
$133$	−0.0622146	−0.00539469
$134$	−13.7231	−1.18549
$135$	−4.48474	−0.385985
$136$	1.74072	0.149266
$137$	−16.6271	−1.42055	−0.710273	−	0.703926i	$-0.751429\pi$
$137$	−16.6271	−1.42055	−0.710273	+	0.703926i	$0.751429\pi$
$138$	10.7767	0.917378
$139$	12.0583	1.02277	0.511385	−	0.859352i	$-0.329133\pi$
$139$	12.0583	1.02277	0.511385	+	0.859352i	$0.329133\pi$
$140$	−2.85291	−0.241115
$141$	−23.1142	−1.94656
$142$	6.35772	0.533528
$143$	−2.73327	−0.228567
$144$	2.31835	0.193196
$145$	28.0601	2.33027
$146$	3.56320	0.294892
$147$	−2.30616	−0.190208
$148$	−1.57539	−0.129496
$149$	−6.96165	−0.570320	−0.285160	−	0.958480i	$-0.592047\pi$
$149$	−6.96165	−0.570320	−0.285160	+	0.958480i	$0.592047\pi$
$150$	−7.23926	−0.591083
$151$	21.4849	1.74841	0.874207	−	0.485553i	$-0.161382\pi$
$151$	21.4849	1.74841	0.874207	+	0.485553i	$0.161382\pi$
$152$	−0.0622146	−0.00504627
$153$	4.03560	0.326259
$154$	−1.11641	−0.0899625
$155$	1.04470	0.0839125
$156$	−5.64610	−0.452050
$157$	−23.3500	−1.86353	−0.931766	−	0.363058i	$-0.881733\pi$
$157$	−23.3500	−1.86353	−0.931766	+	0.363058i	$0.881733\pi$
$158$	8.90449	0.708403
$159$	−7.85825	−0.623200
$160$	−2.85291	−0.225542
$161$	−4.67304	−0.368287
$162$	−10.5803	−0.831267
$163$	−7.77446	−0.608943	−0.304471	−	0.952521i	$-0.598480\pi$
$163$	−7.77446	−0.608943	−0.304471	+	0.952521i	$0.598480\pi$
$164$	11.0495	0.862825
$165$	−7.34512	−0.571817
$166$	−10.5291	−0.817219
$167$	−5.23300	−0.404942	−0.202471	−	0.979288i	$-0.564897\pi$
$167$	−5.23300	−0.404942	−0.202471	+	0.979288i	$0.564897\pi$
$168$	−2.30616	−0.177924
$169$	−7.00595	−0.538919
$170$	−4.96612	−0.380884
$171$	−0.144235	−0.0110300
$172$	1.33962	0.102145
$173$	−5.78044	−0.439479	−0.219739	−	0.975559i	$-0.570521\pi$
$173$	−5.78044	−0.439479	−0.219739	+	0.975559i	$0.570521\pi$
$174$	22.6824	1.71955
$175$	3.13910	0.237294
$176$	−1.11641	−0.0841522
$177$	−14.4597	−1.08685
$178$	−6.43133	−0.482049
$179$	−10.2075	−0.762944	−0.381472	−	0.924380i	$-0.624583\pi$
$179$	−10.2075	−0.762944	−0.381472	+	0.924380i	$0.624583\pi$
$180$	−6.61405	−0.492982
$181$	4.96198	0.368821	0.184411	−	0.982849i	$-0.440962\pi$
$181$	4.96198	0.368821	0.184411	+	0.982849i	$0.440962\pi$
$182$	2.44827	0.181478
$183$	−5.53246	−0.408971
$184$	−4.67304	−0.344501
$185$	4.49444	0.330438
$186$	0.844487	0.0619208
$187$	−1.94335	−0.142112
$188$	10.0228	0.730989
$189$	1.57199	0.114345
$190$	0.177493	0.0128767
$191$	−24.1960	−1.75076	−0.875381	−	0.483434i	$-0.839389\pi$
$191$	−24.1960	−1.75076	−0.875381	+	0.483434i	$0.839389\pi$
$192$	−2.30616	−0.166432
$193$	−12.7960	−0.921077	−0.460538	−	0.887640i	$-0.652344\pi$
$193$	−12.7960	−0.921077	−0.460538	+	0.887640i	$0.652344\pi$
$194$	−0.643922	−0.0462309
$195$	16.1078	1.15351
$196$	1.00000	0.0714286
$197$	−22.6609	−1.61452	−0.807259	−	0.590197i	$-0.799050\pi$
$197$	−22.6609	−1.61452	−0.807259	+	0.590197i	$0.799050\pi$
$198$	−2.58822	−0.183937
$199$	2.94493	0.208760	0.104380	−	0.994537i	$-0.466714\pi$
$199$	2.94493	0.208760	0.104380	+	0.994537i	$0.466714\pi$
$200$	3.13910	0.221968
$201$	31.6475	2.23224
$202$	−8.45196	−0.594678
$203$	−9.83561	−0.690324
$204$	−4.01437	−0.281062
$205$	−31.5234	−2.20169
$206$	−11.4959	−0.800957
$207$	−10.8337	−0.752997
$208$	2.44827	0.169757
$209$	0.0694568	0.00480442
$210$	6.57926	0.454012
$211$	−4.00101	−0.275441	−0.137721	−	0.990471i	$-0.543978\pi$
$211$	−4.00101	−0.275441	−0.137721	+	0.990471i	$0.543978\pi$
$212$	3.40751	0.234029
$213$	−14.6619	−1.00462
$214$	15.2461	1.04220
$215$	−3.82183	−0.260647
$216$	1.57199	0.106960
$217$	−0.366188	−0.0248585
$218$	−0.143803	−0.00973958
$219$	−8.21729	−0.555273
$220$	3.18501	0.214733
$221$	4.26176	0.286677
$222$	3.63309	0.243837
$223$	10.2972	0.689555	0.344777	−	0.938685i	$-0.387954\pi$
$223$	10.2972	0.689555	0.344777	+	0.938685i	$0.387954\pi$
$224$	1.00000	0.0668153
$225$	7.27755	0.485170
$226$	19.1507	1.27388
$227$	−25.9770	−1.72416	−0.862079	−	0.506775i	$-0.830838\pi$
$227$	−25.9770	−1.72416	−0.862079	+	0.506775i	$0.830838\pi$
$228$	0.143477	0.00950197
$229$	17.2712	1.14132	0.570658	−	0.821188i	$-0.306688\pi$
$229$	17.2712	1.14132	0.570658	+	0.821188i	$0.306688\pi$
$230$	13.3318	0.879070
$231$	2.57460	0.169397
$232$	−9.83561	−0.645739
$233$	−24.5892	−1.61089	−0.805447	−	0.592668i	$-0.798074\pi$
$233$	−24.5892	−1.61089	−0.805447	+	0.592668i	$0.798074\pi$
$234$	5.67596	0.371049
$235$	−28.5942	−1.86528
$236$	6.27003	0.408144
$237$	−20.5351	−1.33390
$238$	1.74072	0.112834
$239$	−20.6765	−1.33745	−0.668726	−	0.743509i	$-0.733160\pi$
$239$	−20.6765	−1.33745	−0.668726	+	0.743509i	$0.733160\pi$
$240$	6.57926	0.424689
$241$	30.1422	1.94163	0.970814	−	0.239835i	$-0.0770935\pi$
$241$	30.1422	1.94163	0.970814	+	0.239835i	$0.0770935\pi$
$242$	−9.75364	−0.626988
$243$	19.6839	1.26272
$244$	2.39900	0.153580
$245$	−2.85291	−0.182266
$246$	−25.4820	−1.62467
$247$	−0.152319	−0.00969179
$248$	−0.366188	−0.0232530
$249$	24.2818	1.53880
$250$	5.30897	0.335769
$251$	−11.6646	−0.736262	−0.368131	−	0.929774i	$-0.620002\pi$
$251$	−11.6646	−0.736262	−0.368131	+	0.929774i	$0.620002\pi$
$252$	2.31835	0.146042
$253$	5.21700	0.327990
$254$	−6.28789	−0.394537
$255$	11.4527	0.717193
$256$	1.00000	0.0625000
$257$	0.779329	0.0486132	0.0243066	−	0.999705i	$-0.492262\pi$
$257$	0.779329	0.0486132	0.0243066	+	0.999705i	$0.492262\pi$
$258$	−3.08938	−0.192336
$259$	−1.57539	−0.0978899
$260$	−6.98471	−0.433173
$261$	−22.8024	−1.41143
$262$	−18.5132	−1.14375
$263$	−20.1945	−1.24525	−0.622624	−	0.782521i	$-0.713933\pi$
$263$	−20.1945	−1.24525	−0.622624	+	0.782521i	$0.713933\pi$
$264$	2.57460	0.158456
$265$	−9.72133	−0.597177
$266$	−0.0622146	−0.00381462
$267$	14.8317	0.907682
$268$	−13.7231	−0.838270
$269$	−29.6433	−1.80739	−0.903693	−	0.428181i	$-0.859155\pi$
$269$	−29.6433	−1.80739	−0.903693	+	0.428181i	$0.859155\pi$
$270$	−4.48474	−0.272932
$271$	−19.8498	−1.20579	−0.602894	−	0.797821i	$-0.705986\pi$
$271$	−19.8498	−1.20579	−0.602894	+	0.797821i	$0.705986\pi$
$272$	1.74072	0.105547
$273$	−5.64610	−0.341718
$274$	−16.6271	−1.00448
$275$	−3.50451	−0.211330
$276$	10.7767	0.648684
$277$	6.57812	0.395241	0.197621	−	0.980279i	$-0.436679\pi$
$277$	6.57812	0.395241	0.197621	+	0.980279i	$0.436679\pi$
$278$	12.0583	0.723207
$279$	−0.848953	−0.0508255
$280$	−2.85291	−0.170494
$281$	−28.3013	−1.68832	−0.844158	−	0.536094i	$-0.819899\pi$
$281$	−28.3013	−1.68832	−0.844158	+	0.536094i	$0.819899\pi$
$282$	−23.1142	−1.37643
$283$	−2.17972	−0.129571	−0.0647855	−	0.997899i	$-0.520636\pi$
$283$	−2.17972	−0.129571	−0.0647855	+	0.997899i	$0.520636\pi$
$284$	6.35772	0.377261
$285$	−0.409326	−0.0242464
$286$	−2.73327	−0.161621
$287$	11.0495	0.652234
$288$	2.31835	0.136610
$289$	−13.9699	−0.821758
$290$	28.0601	1.64775
$291$	1.48499	0.0870514
$292$	3.56320	0.208520
$293$	−9.72296	−0.568022	−0.284011	−	0.958821i	$-0.591665\pi$
$293$	−9.72296	−0.568022	−0.284011	+	0.958821i	$0.591665\pi$
$294$	−2.30616	−0.134498
$295$	−17.8878	−1.04147
$296$	−1.57539	−0.0915676
$297$	−1.75497	−0.101834
$298$	−6.96165	−0.403277
$299$	−11.4409	−0.661643
$300$	−7.23926	−0.417959
$301$	1.33962	0.0772147
$302$	21.4849	1.23632
$303$	19.4915	1.11976
$304$	−0.0622146	−0.00356825
$305$	−6.84413	−0.391894
$306$	4.03560	0.230700
$307$	32.6840	1.86537	0.932687	−	0.360687i	$-0.117458\pi$
$307$	32.6840	1.86537	0.932687	+	0.360687i	$0.117458\pi$
$308$	−1.11641	−0.0636131
$309$	26.5113	1.50818
$310$	1.04470	0.0593351
$311$	−8.95524	−0.507805	−0.253903	−	0.967230i	$-0.581714\pi$
$311$	−8.95524	−0.507805	−0.253903	+	0.967230i	$0.581714\pi$
$312$	−5.64610	−0.319648
$313$	−19.5838	−1.10694	−0.553471	−	0.832868i	$-0.686697\pi$
$313$	−19.5838	−1.10694	−0.553471	+	0.832868i	$0.686697\pi$
$314$	−23.3500	−1.31772
$315$	−6.61405	−0.372660
$316$	8.90449	0.500917
$317$	20.5136	1.15216	0.576079	−	0.817394i	$-0.304582\pi$
$317$	20.5136	1.15216	0.576079	+	0.817394i	$0.304582\pi$
$318$	−7.85825	−0.440669
$319$	10.9805	0.614791
$320$	−2.85291	−0.159483
$321$	−35.1598	−1.96243
$322$	−4.67304	−0.260418
$323$	−0.108298	−0.00602588
$324$	−10.5803	−0.587794
$325$	7.68539	0.426309
$326$	−7.77446	−0.430588
$327$	0.331633	0.0183393
$328$	11.0495	0.610109
$329$	10.0228	0.552576
$330$	−7.34512	−0.404335
$331$	30.3013	1.66551	0.832754	−	0.553643i	$-0.186763\pi$
$331$	30.3013	1.66551	0.832754	+	0.553643i	$0.186763\pi$
$332$	−10.5291	−0.577861
$333$	−3.65231	−0.200145
$334$	−5.23300	−0.286337
$335$	39.1507	2.13903
$336$	−2.30616	−0.125811
$337$	22.3808	1.21916	0.609581	−	0.792724i	$-0.291338\pi$
$337$	22.3808	1.21916	0.609581	+	0.792724i	$0.291338\pi$
$338$	−7.00595	−0.381074
$339$	−44.1644	−2.39868
$340$	−4.96612	−0.269326
$341$	0.408814	0.0221385
$342$	−0.144235	−0.00779936
$343$	1.00000	0.0539949
$344$	1.33962	0.0722277
$345$	−30.7451	−1.65526
$346$	−5.78044	−0.310758
$347$	3.43112	0.184192	0.0920960	−	0.995750i	$-0.470643\pi$
$347$	3.43112	0.184192	0.0920960	+	0.995750i	$0.470643\pi$
$348$	22.6824	1.21591
$349$	35.3637	1.89298	0.946488	−	0.322738i	$-0.104603\pi$
$349$	35.3637	1.89298	0.946488	+	0.322738i	$0.104603\pi$
$350$	3.13910	0.167792
$351$	3.84865	0.205426
$352$	−1.11641	−0.0595046
$353$	30.9278	1.64612	0.823060	−	0.567954i	$-0.192265\pi$
$353$	30.9278	1.64612	0.823060	+	0.567954i	$0.192265\pi$
$354$	−14.4597	−0.768522
$355$	−18.1380	−0.962666
$356$	−6.43133	−0.340860
$357$	−4.01437	−0.212463
$358$	−10.2075	−0.539483
$359$	6.50892	0.343527	0.171764	−	0.985138i	$-0.445053\pi$
$359$	6.50892	0.343527	0.171764	+	0.985138i	$0.445053\pi$
$360$	−6.61405	−0.348591
$361$	−18.9961	−0.999796
$362$	4.96198	0.260796
$363$	22.4934	1.18060
$364$	2.44827	0.128324
$365$	−10.1655	−0.532086
$366$	−5.53246	−0.289186
$367$	26.6870	1.39305	0.696526	−	0.717531i	$-0.254728\pi$
$367$	26.6870	1.39305	0.696526	+	0.717531i	$0.254728\pi$
$368$	−4.67304	−0.243599
$369$	25.6167	1.33355
$370$	4.49444	0.233655
$371$	3.40751	0.176909
$372$	0.844487	0.0437846
$373$	17.3114	0.896350	0.448175	−	0.893946i	$-0.352074\pi$
$373$	17.3114	0.896350	0.448175	+	0.893946i	$0.352074\pi$
$374$	−1.94335	−0.100488
$375$	−12.2433	−0.632242
$376$	10.0228	0.516887
$377$	−24.0803	−1.24020
$378$	1.57199	0.0808542
$379$	−6.69034	−0.343660	−0.171830	−	0.985127i	$-0.554968\pi$
$379$	−6.69034	−0.343660	−0.171830	+	0.985127i	$0.554968\pi$
$380$	0.177493	0.00910519
$381$	14.5009	0.742901
$382$	−24.1960	−1.23798
$383$	3.32423	0.169860	0.0849300	−	0.996387i	$-0.472933\pi$
$383$	3.32423	0.169860	0.0849300	+	0.996387i	$0.472933\pi$
$384$	−2.30616	−0.117685
$385$	3.18501	0.162323
$386$	−12.7960	−0.651300
$387$	3.10572	0.157873
$388$	−0.643922	−0.0326902
$389$	−15.6491	−0.793442	−0.396721	−	0.917939i	$-0.629852\pi$
$389$	−15.6491	−0.793442	−0.396721	+	0.917939i	$0.629852\pi$
$390$	16.1078	0.815652
$391$	−8.13445	−0.411377
$392$	1.00000	0.0505076
$393$	42.6944	2.15365
$394$	−22.6609	−1.14164
$395$	−25.4037	−1.27820
$396$	−2.58822	−0.130063
$397$	−34.2029	−1.71659	−0.858296	−	0.513155i	$-0.828477\pi$
$397$	−34.2029	−1.71659	−0.858296	+	0.513155i	$0.828477\pi$
$398$	2.94493	0.147616
$399$	0.143477	0.00718281
$400$	3.13910	0.156955
$401$	23.5045	1.17376	0.586879	−	0.809675i	$-0.300356\pi$
$401$	23.5045	1.17376	0.586879	+	0.809675i	$0.300356\pi$
$402$	31.6475	1.57844
$403$	−0.896529	−0.0446593
$404$	−8.45196	−0.420501
$405$	30.1847	1.49989
$406$	−9.83561	−0.488133
$407$	1.75877	0.0871791
$408$	−4.01437	−0.198741
$409$	−34.7273	−1.71715	−0.858577	−	0.512685i	$-0.828651\pi$
$409$	−34.7273	−1.71715	−0.858577	+	0.512685i	$0.828651\pi$
$410$	−31.5234	−1.55683
$411$	38.3446	1.89140
$412$	−11.4959	−0.566362
$413$	6.27003	0.308528
$414$	−10.8337	−0.532449
$415$	30.0387	1.47454
$416$	2.44827	0.120037
$417$	−27.8083	−1.36178
$418$	0.0694568	0.00339724
$419$	3.56794	0.174305	0.0871526	−	0.996195i	$-0.472223\pi$
$419$	3.56794	0.174305	0.0871526	+	0.996195i	$0.472223\pi$
$420$	6.57926	0.321035
$421$	28.7621	1.40178	0.700889	−	0.713270i	$-0.252787\pi$
$421$	28.7621	1.40178	0.700889	+	0.713270i	$0.252787\pi$
$422$	−4.00101	−0.194766
$423$	23.2364	1.12979
$424$	3.40751	0.165483
$425$	5.46431	0.265058
$426$	−14.6619	−0.710371
$427$	2.39900	0.116096
$428$	15.2461	0.736947
$429$	6.30334	0.304328
$430$	−3.82183	−0.184305
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	1.57199	0.0756322
$433$	3.80775	0.182989	0.0914943	−	0.995806i	$-0.470836\pi$
$433$	3.80775	0.182989	0.0914943	+	0.995806i	$0.470836\pi$
$434$	−0.366188	−0.0175776
$435$	−64.7110	−3.10265
$436$	−0.143803	−0.00688693
$437$	0.290731	0.0139076
$438$	−8.21729	−0.392637
$439$	8.53717	0.407457	0.203728	−	0.979027i	$-0.434694\pi$
$439$	8.53717	0.407457	0.203728	+	0.979027i	$0.434694\pi$
$440$	3.18501	0.151839
$441$	2.31835	0.110398
$442$	4.26176	0.202711
$443$	−25.5564	−1.21422	−0.607111	−	0.794617i	$-0.707672\pi$
$443$	−25.5564	−1.21422	−0.607111	+	0.794617i	$0.707672\pi$
$444$	3.63309	0.172419
$445$	18.3480	0.869780
$446$	10.2972	0.487589
$447$	16.0546	0.759358
$448$	1.00000	0.0472456
$449$	12.0113	0.566847	0.283424	−	0.958995i	$-0.408530\pi$
$449$	12.0113	0.566847	0.283424	+	0.958995i	$0.408530\pi$
$450$	7.27755	0.343067
$451$	−12.3358	−0.580869
$452$	19.1507	0.900771
$453$	−49.5474	−2.32794
$454$	−25.9770	−1.21916
$455$	−6.98471	−0.327448
$456$	0.143477	0.00671891
$457$	−2.81543	−0.131700	−0.0658501	−	0.997830i	$-0.520976\pi$
$457$	−2.81543	−0.131700	−0.0658501	+	0.997830i	$0.520976\pi$
$458$	17.2712	0.807032
$459$	2.73639	0.127724
$460$	13.3318	0.621596
$461$	7.64019	0.355839	0.177920	−	0.984045i	$-0.443063\pi$
$461$	7.64019	0.355839	0.177920	+	0.984045i	$0.443063\pi$
$462$	2.57460	0.119781
$463$	2.81964	0.131040	0.0655200	−	0.997851i	$-0.479129\pi$
$463$	2.81964	0.131040	0.0655200	+	0.997851i	$0.479129\pi$
$464$	−9.83561	−0.456607
$465$	−2.40925	−0.111726
$466$	−24.5892	−1.13907
$467$	−22.1228	−1.02372	−0.511862	−	0.859068i	$-0.671044\pi$
$467$	−22.1228	−1.02372	−0.511862	+	0.859068i	$0.671044\pi$
$468$	5.67596	0.262371
$469$	−13.7231	−0.633672
$470$	−28.5942	−1.31895
$471$	53.8487	2.48122
$472$	6.27003	0.288602
$473$	−1.49556	−0.0687661
$474$	−20.5351	−0.943210
$475$	−0.195298	−0.00896090
$476$	1.74072	0.0797858
$477$	7.89982	0.361708
$478$	−20.6765	−0.945721
$479$	33.5466	1.53278	0.766392	−	0.642373i	$-0.222050\pi$
$479$	33.5466	1.53278	0.766392	+	0.642373i	$0.222050\pi$
$480$	6.57926	0.300301
$481$	−3.85698	−0.175863
$482$	30.1422	1.37294
$483$	10.7767	0.490359
$484$	−9.75364	−0.443347
$485$	1.83705	0.0834163
$486$	19.6839	0.892878
$487$	30.4288	1.37886	0.689430	−	0.724352i	$-0.257861\pi$
$487$	30.4288	1.37886	0.689430	+	0.724352i	$0.257861\pi$
$488$	2.39900	0.108598
$489$	17.9291	0.810783
$490$	−2.85291	−0.128881
$491$	1.23396	0.0556880	0.0278440	−	0.999612i	$-0.491136\pi$
$491$	1.23396	0.0556880	0.0278440	+	0.999612i	$0.491136\pi$
$492$	−25.4820	−1.14882
$493$	−17.1210	−0.771093
$494$	−0.152319	−0.00685313
$495$	7.38397	0.331885
$496$	−0.366188	−0.0164423
$497$	6.35772	0.285183
$498$	24.2818	1.08809
$499$	−35.9879	−1.61104	−0.805520	−	0.592568i	$-0.798114\pi$
$499$	−35.9879	−1.61104	−0.805520	+	0.592568i	$0.798114\pi$
$500$	5.30897	0.237424
$501$	12.0681	0.539163
$502$	−11.6646	−0.520616
$503$	2.47621	0.110409	0.0552045	−	0.998475i	$-0.482419\pi$
$503$	2.47621	0.110409	0.0552045	+	0.998475i	$0.482419\pi$
$504$	2.31835	0.103268
$505$	24.1127	1.07300
$506$	5.21700	0.231924
$507$	16.1568	0.717549
$508$	−6.28789	−0.278980
$509$	−4.16050	−0.184411	−0.0922055	−	0.995740i	$-0.529392\pi$
$509$	−4.16050	−0.184411	−0.0922055	+	0.995740i	$0.529392\pi$
$510$	11.4527	0.507132
$511$	3.56320	0.157627
$512$	1.00000	0.0441942
$513$	−0.0978005	−0.00431800
$514$	0.779329	0.0343747
$515$	32.7968	1.44520
$516$	−3.08938	−0.136002
$517$	−11.1895	−0.492115
$518$	−1.57539	−0.0692186
$519$	13.3306	0.585148
$520$	−6.98471	−0.306300
$521$	−33.2387	−1.45621	−0.728106	−	0.685464i	$-0.759599\pi$
$521$	−33.2387	−1.45621	−0.728106	+	0.685464i	$0.759599\pi$
$522$	−22.8024	−0.998034
$523$	−15.5450	−0.679734	−0.339867	−	0.940473i	$-0.610382\pi$
$523$	−15.5450	−0.679734	−0.339867	+	0.940473i	$0.610382\pi$
$524$	−18.5132	−0.808755
$525$	−7.23926	−0.315947
$526$	−20.1945	−0.880523
$527$	−0.637431	−0.0277669
$528$	2.57460	0.112045
$529$	−1.16273	−0.0505536
$530$	−9.72133	−0.422268
$531$	14.5361	0.630815
$532$	−0.0622146	−0.00269735
$533$	27.0523	1.17177
$534$	14.8317	0.641828
$535$	−43.4957	−1.88048
$536$	−13.7231	−0.592746
$537$	23.5401	1.01583
$538$	−29.6433	−1.27802
$539$	−1.11641	−0.0480870
$540$	−4.48474	−0.192992
$541$	−7.44567	−0.320114	−0.160057	−	0.987108i	$-0.551168\pi$
$541$	−7.44567	−0.320114	−0.160057	+	0.987108i	$0.551168\pi$
$542$	−19.8498	−0.852621
$543$	−11.4431	−0.491071
$544$	1.74072	0.0746328
$545$	0.410258	0.0175735
$546$	−5.64610	−0.241631
$547$	13.0053	0.556066	0.278033	−	0.960571i	$-0.410317\pi$
$547$	13.0053	0.556066	0.278033	+	0.960571i	$0.410317\pi$
$548$	−16.6271	−0.710273
$549$	5.56172	0.237369
$550$	−3.50451	−0.149433
$551$	0.611919	0.0260686
$552$	10.7767	0.458689
$553$	8.90449	0.378657
$554$	6.57812	0.279478
$555$	−10.3649	−0.439965
$556$	12.0583	0.511385
$557$	5.82955	0.247006	0.123503	−	0.992344i	$-0.460587\pi$
$557$	5.82955	0.247006	0.123503	+	0.992344i	$0.460587\pi$
$558$	−0.848953	−0.0359390
$559$	3.27977	0.138719
$560$	−2.85291	−0.120558
$561$	4.48167	0.189216
$562$	−28.3013	−1.19382
$563$	−43.3948	−1.82887	−0.914437	−	0.404728i	$-0.867366\pi$
$563$	−43.3948	−1.82887	−0.914437	+	0.404728i	$0.867366\pi$
$564$	−23.1142	−0.973282
$565$	−54.6351	−2.29852
$566$	−2.17972	−0.0916206
$567$	−10.5803	−0.444331
$568$	6.35772	0.266764
$569$	−42.6178	−1.78663	−0.893316	−	0.449429i	$-0.851627\pi$
$569$	−42.6178	−1.78663	−0.893316	+	0.449429i	$0.851627\pi$
$570$	−0.409326	−0.0171448
$571$	−10.4795	−0.438555	−0.219277	−	0.975663i	$-0.570370\pi$
$571$	−10.4795	−0.438555	−0.219277	+	0.975663i	$0.570370\pi$
$572$	−2.73327	−0.114284
$573$	55.7997	2.33107
$574$	11.0495	0.461199
$575$	−14.6692	−0.611746
$576$	2.31835	0.0965980
$577$	−23.1261	−0.962753	−0.481377	−	0.876514i	$-0.659863\pi$
$577$	−23.1261	−0.962753	−0.481377	+	0.876514i	$0.659863\pi$
$578$	−13.9699	−0.581071
$579$	29.5096	1.22638
$580$	28.0601	1.16513
$581$	−10.5291	−0.436822
$582$	1.48499	0.0615546
$583$	−3.80417	−0.157552
$584$	3.56320	0.147446
$585$	−16.1930	−0.669499
$586$	−9.72296	−0.401652
$587$	−34.4648	−1.42251	−0.711257	−	0.702932i	$-0.751874\pi$
$587$	−34.4648	−1.42251	−0.711257	+	0.702932i	$0.751874\pi$
$588$	−2.30616	−0.0951042
$589$	0.0227823	0.000938727 0
$590$	−17.8878	−0.736431
$591$	52.2594	2.14967
$592$	−1.57539	−0.0647481
$593$	−9.77267	−0.401315	−0.200658	−	0.979661i	$-0.564308\pi$
$593$	−9.77267	−0.401315	−0.200658	+	0.979661i	$0.564308\pi$
$594$	−1.75497	−0.0720074
$595$	−4.96612	−0.203591
$596$	−6.96165	−0.285160
$597$	−6.79146	−0.277956
$598$	−11.4409	−0.467852
$599$	18.7807	0.767358	0.383679	−	0.923467i	$-0.374657\pi$
$599$	18.7807	0.767358	0.383679	+	0.923467i	$0.374657\pi$
$600$	−7.23926	−0.295542
$601$	−3.70392	−0.151086	−0.0755429	−	0.997143i	$-0.524069\pi$
$601$	−3.70392	−0.151086	−0.0755429	+	0.997143i	$0.524069\pi$
$602$	1.33962	0.0545990
$603$	−31.8149	−1.29560
$604$	21.4849	0.874207
$605$	27.8263	1.13130
$606$	19.4915	0.791789
$607$	1.82281	0.0739854	0.0369927	−	0.999316i	$-0.488222\pi$
$607$	1.82281	0.0739854	0.0369927	+	0.999316i	$0.488222\pi$
$608$	−0.0622146	−0.00252314
$609$	22.6824	0.919139
$610$	−6.84413	−0.277111
$611$	24.5386	0.992726
$612$	4.03560	0.163130
$613$	−29.0648	−1.17391	−0.586957	−	0.809618i	$-0.699674\pi$
$613$	−29.0648	−1.17391	−0.586957	+	0.809618i	$0.699674\pi$
$614$	32.6840	1.31902
$615$	72.6978	2.93146
$616$	−1.11641	−0.0449813
$617$	−4.50111	−0.181208	−0.0906040	−	0.995887i	$-0.528880\pi$
$617$	−4.50111	−0.181208	−0.0906040	+	0.995887i	$0.528880\pi$
$618$	26.5113	1.06644
$619$	21.2828	0.855429	0.427714	−	0.903914i	$-0.359319\pi$
$619$	21.2828	0.855429	0.427714	+	0.903914i	$0.359319\pi$
$620$	1.04470	0.0419563
$621$	−7.34595	−0.294783
$622$	−8.95524	−0.359073
$623$	−6.43133	−0.257666
$624$	−5.64610	−0.226025
$625$	−30.8415	−1.23366
$626$	−19.5838	−0.782726
$627$	−0.160178	−0.00639690
$628$	−23.3500	−0.931766
$629$	−2.74231	−0.109343
$630$	−6.61405	−0.263510
$631$	37.0250	1.47394	0.736970	−	0.675925i	$-0.236256\pi$
$631$	37.0250	1.47394	0.736970	+	0.675925i	$0.236256\pi$
$632$	8.90449	0.354202
$633$	9.22696	0.366739
$634$	20.5136	0.814698
$635$	17.9388	0.711880
$636$	−7.85825	−0.311600
$637$	2.44827	0.0970042
$638$	10.9805	0.434723
$639$	14.7394	0.583083
$640$	−2.85291	−0.112771
$641$	−36.9930	−1.46113	−0.730567	−	0.682841i	$-0.760744\pi$
$641$	−36.9930	−1.46113	−0.730567	+	0.682841i	$0.760744\pi$
$642$	−35.1598	−1.38765
$643$	−4.83761	−0.190777	−0.0953884	−	0.995440i	$-0.530409\pi$
$643$	−4.83761	−0.190777	−0.0953884	+	0.995440i	$0.530409\pi$
$644$	−4.67304	−0.184143
$645$	8.81373	0.347040
$646$	−0.108298	−0.00426094
$647$	46.9247	1.84480	0.922401	−	0.386234i	$-0.126224\pi$
$647$	46.9247	1.84480	0.922401	+	0.386234i	$0.126224\pi$
$648$	−10.5803	−0.415633
$649$	−6.99990	−0.274770
$650$	7.68539	0.301446
$651$	0.844487	0.0330980
$652$	−7.77446	−0.304471
$653$	−0.853442	−0.0333978	−0.0166989	−	0.999861i	$-0.505316\pi$
$653$	−0.853442	−0.0333978	−0.0166989	+	0.999861i	$0.505316\pi$
$654$	0.331633	0.0129679
$655$	52.8166	2.06372
$656$	11.0495	0.431412
$657$	8.26075	0.322282
$658$	10.0228	0.390730
$659$	−14.3987	−0.560893	−0.280446	−	0.959870i	$-0.590483\pi$
$659$	−14.3987	−0.560893	−0.280446	+	0.959870i	$0.590483\pi$
$660$	−7.34512	−0.285908
$661$	−24.1679	−0.940022	−0.470011	−	0.882661i	$-0.655750\pi$
$661$	−24.1679	−0.940022	−0.470011	+	0.882661i	$0.655750\pi$
$662$	30.3013	1.17769
$663$	−9.82829	−0.381699
$664$	−10.5291	−0.408609
$665$	0.177493	0.00688288
$666$	−3.65231	−0.141524
$667$	45.9621	1.77966
$668$	−5.23300	−0.202471
$669$	−23.7470	−0.918114
$670$	39.1507	1.51252
$671$	−2.67825	−0.103393
$672$	−2.30616	−0.0889619
$673$	−36.7733	−1.41751	−0.708754	−	0.705455i	$-0.750742\pi$
$673$	−36.7733	−1.41751	−0.708754	+	0.705455i	$0.750742\pi$
$674$	22.3808	0.862077
$675$	4.93463	0.189934
$676$	−7.00595	−0.269460
$677$	3.29864	0.126777	0.0633885	−	0.997989i	$-0.479809\pi$
$677$	3.29864	0.126777	0.0633885	+	0.997989i	$0.479809\pi$
$678$	−44.1644	−1.69612
$679$	−0.643922	−0.0247115
$680$	−4.96612	−0.190442
$681$	59.9071	2.29565
$682$	0.408814	0.0156543
$683$	26.2678	1.00511	0.502554	−	0.864546i	$-0.332394\pi$
$683$	26.2678	1.00511	0.502554	+	0.864546i	$0.332394\pi$
$684$	−0.144235	−0.00551498
$685$	47.4356	1.81242
$686$	1.00000	0.0381802
$687$	−39.8302	−1.51962
$688$	1.33962	0.0510727
$689$	8.34253	0.317825
$690$	−30.7451	−1.17045
$691$	2.89971	0.110310	0.0551551	−	0.998478i	$-0.482435\pi$
$691$	2.89971	0.110310	0.0551551	+	0.998478i	$0.482435\pi$
$692$	−5.78044	−0.219739
$693$	−2.58822	−0.0983184
$694$	3.43112	0.130243
$695$	−34.4012	−1.30491
$696$	22.6824	0.859775
$697$	19.2342	0.728547
$698$	35.3637	1.33854
$699$	56.7065	2.14484
$700$	3.13910	0.118647
$701$	−20.1627	−0.761535	−0.380767	−	0.924671i	$-0.624340\pi$
$701$	−20.1627	−0.761535	−0.380767	+	0.924671i	$0.624340\pi$
$702$	3.84865	0.145258
$703$	0.0980122	0.00369660
$704$	−1.11641	−0.0420761
$705$	65.9427	2.48354
$706$	30.9278	1.16398
$707$	−8.45196	−0.317869
$708$	−14.4597	−0.543427
$709$	−45.2207	−1.69830	−0.849150	−	0.528152i	$-0.822885\pi$
$709$	−45.2207	−1.69830	−0.849150	+	0.528152i	$0.822885\pi$
$710$	−18.1380	−0.680707
$711$	20.6437	0.774201
$712$	−6.43133	−0.241024
$713$	1.71121	0.0640853
$714$	−4.01437	−0.150234
$715$	7.79777	0.291620
$716$	−10.2075	−0.381472
$717$	47.6832	1.78076
$718$	6.50892	0.242911
$719$	−7.08748	−0.264319	−0.132159	−	0.991228i	$-0.542191\pi$
$719$	−7.08748	−0.264319	−0.132159	+	0.991228i	$0.542191\pi$
$720$	−6.61405	−0.246491
$721$	−11.4959	−0.428129
$722$	−18.9961	−0.706963
$723$	−69.5125	−2.58520
$724$	4.96198	0.184411
$725$	−30.8750	−1.14667
$726$	22.4934	0.834809
$727$	−4.84114	−0.179548	−0.0897741	−	0.995962i	$-0.528614\pi$
$727$	−4.84114	−0.179548	−0.0897741	+	0.995962i	$0.528614\pi$
$728$	2.44827	0.0907391
$729$	−13.6531	−0.505671
$730$	−10.1655	−0.376242
$731$	2.33191	0.0862489
$732$	−5.53246	−0.204486
$733$	−25.3622	−0.936775	−0.468388	−	0.883523i	$-0.655165\pi$
$733$	−25.3622	−0.936775	−0.468388	+	0.883523i	$0.655165\pi$
$734$	26.6870	0.985037
$735$	6.57926	0.242680
$736$	−4.67304	−0.172250
$737$	15.3205	0.564338
$738$	25.6167	0.942965
$739$	20.8124	0.765595	0.382797	−	0.923832i	$-0.374961\pi$
$739$	20.8124	0.765595	0.382797	+	0.923832i	$0.374961\pi$
$740$	4.49444	0.165219
$741$	0.351270	0.0129042
$742$	3.40751	0.125094
$743$	−22.3985	−0.821722	−0.410861	−	0.911698i	$-0.634772\pi$
$743$	−22.3985	−0.821722	−0.410861	+	0.911698i	$0.634772\pi$
$744$	0.844487	0.0309604
$745$	19.8610	0.727649
$746$	17.3114	0.633815
$747$	−24.4102	−0.893123
$748$	−1.94335	−0.0710559
$749$	15.2461	0.557080
$750$	−12.2433	−0.447062
$751$	50.4296	1.84020	0.920101	−	0.391682i	$-0.128107\pi$
$751$	50.4296	1.84020	0.920101	+	0.391682i	$0.128107\pi$
$752$	10.0228	0.365494
$753$	26.9003	0.980302
$754$	−24.0803	−0.876951
$755$	−61.2944	−2.23073
$756$	1.57199	0.0571726
$757$	44.3722	1.61274	0.806368	−	0.591414i	$-0.201430\pi$
$757$	44.3722	1.61274	0.806368	+	0.591414i	$0.201430\pi$
$758$	−6.69034	−0.243004
$759$	−12.0312	−0.436706
$760$	0.177493	0.00643834
$761$	−43.8499	−1.58956	−0.794779	−	0.606899i	$-0.792413\pi$
$761$	−43.8499	−1.58956	−0.794779	+	0.606899i	$0.792413\pi$
$762$	14.5009	0.525311
$763$	−0.143803	−0.00520603
$764$	−24.1960	−0.875381
$765$	−11.5132	−0.416261
$766$	3.32423	0.120109
$767$	15.3508	0.554284
$768$	−2.30616	−0.0832162
$769$	19.4438	0.701163	0.350581	−	0.936532i	$-0.385984\pi$
$769$	19.4438	0.701163	0.350581	+	0.936532i	$0.385984\pi$
$770$	3.18501	0.114780
$771$	−1.79725	−0.0647265
$772$	−12.7960	−0.460538
$773$	−4.35033	−0.156471	−0.0782353	−	0.996935i	$-0.524929\pi$
$773$	−4.35033	−0.156471	−0.0782353	+	0.996935i	$0.524929\pi$
$774$	3.10572	0.111633
$775$	−1.14950	−0.0412914
$776$	−0.643922	−0.0231155
$777$	3.63309	0.130336
$778$	−15.6491	−0.561048
$779$	−0.687444	−0.0246302
$780$	16.1078	0.576753
$781$	−7.09779	−0.253979
$782$	−8.13445	−0.290887
$783$	−15.4614	−0.552547
$784$	1.00000	0.0357143
$785$	66.6155	2.37761
$786$	42.6944	1.52286
$787$	53.3313	1.90106	0.950528	−	0.310638i	$-0.100543\pi$
$787$	53.3313	1.90106	0.950528	+	0.310638i	$0.100543\pi$
$788$	−22.6609	−0.807259
$789$	46.5717	1.65800
$790$	−25.4037	−0.903824
$791$	19.1507	0.680919
$792$	−2.58822	−0.0919684
$793$	5.87341	0.208571
$794$	−34.2029	−1.21381
$795$	22.4189	0.795117
$796$	2.94493	0.104380
$797$	9.26963	0.328347	0.164174	−	0.986431i	$-0.447504\pi$
$797$	9.26963	0.328347	0.164174	+	0.986431i	$0.447504\pi$
$798$	0.143477	0.00507902
$799$	17.4469	0.617228
$800$	3.13910	0.110984
$801$	−14.9101	−0.526822
$802$	23.5045	0.829972
$803$	−3.97797	−0.140380
$804$	31.6475	1.11612
$805$	13.3318	0.469883
$806$	−0.896529	−0.0315789
$807$	68.3621	2.40646
$808$	−8.45196	−0.297339
$809$	39.3826	1.38462	0.692309	−	0.721601i	$-0.256594\pi$
$809$	39.3826	1.38462	0.692309	+	0.721601i	$0.256594\pi$
$810$	30.1847	1.06058
$811$	−37.7972	−1.32724	−0.663620	−	0.748070i	$-0.730981\pi$
$811$	−37.7972	−1.32724	−0.663620	+	0.748070i	$0.730981\pi$
$812$	−9.83561	−0.345162
$813$	45.7767	1.60546
$814$	1.75877	0.0616449
$815$	22.1799	0.776927
$816$	−4.01437	−0.140531
$817$	−0.0833442	−0.00291585
$818$	−34.7273	−1.21421
$819$	5.67596	0.198334
$820$	−31.5234	−1.10084
$821$	−30.9543	−1.08031	−0.540156	−	0.841565i	$-0.681635\pi$
$821$	−30.9543	−1.08031	−0.540156	+	0.841565i	$0.681635\pi$
$822$	38.3446	1.33742
$823$	−31.2635	−1.08978	−0.544888	−	0.838509i	$-0.683428\pi$
$823$	−31.2635	−1.08978	−0.544888	+	0.838509i	$0.683428\pi$
$824$	−11.4959	−0.400478
$825$	8.08195	0.281377
$826$	6.27003	0.218162
$827$	37.2643	1.29581	0.647904	−	0.761722i	$-0.275646\pi$
$827$	37.2643	1.29581	0.647904	+	0.761722i	$0.275646\pi$
$828$	−10.8337	−0.376499
$829$	21.7847	0.756614	0.378307	−	0.925680i	$-0.376506\pi$
$829$	21.7847	0.756614	0.378307	+	0.925680i	$0.376506\pi$
$830$	30.0387	1.04266
$831$	−15.1702	−0.526248
$832$	2.44827	0.0848786
$833$	1.74072	0.0603124
$834$	−27.8083	−0.962921
$835$	14.9293	0.516649
$836$	0.0694568	0.00240221
$837$	−0.575643	−0.0198971
$838$	3.56794	0.123252
$839$	16.7692	0.578936	0.289468	−	0.957188i	$-0.406522\pi$
$839$	16.7692	0.578936	0.289468	+	0.957188i	$0.406522\pi$
$840$	6.57926	0.227006
$841$	67.7391	2.33583
$842$	28.7621	0.991207
$843$	65.2673	2.24793
$844$	−4.00101	−0.137721
$845$	19.9874	0.687586
$846$	23.2364	0.798884
$847$	−9.75364	−0.335139
$848$	3.40751	0.117014
$849$	5.02678	0.172519
$850$	5.46431	0.187424
$851$	7.36185	0.252361
$852$	−14.6619	−0.502308
$853$	−38.2901	−1.31103	−0.655513	−	0.755184i	$-0.727548\pi$
$853$	−38.2901	−1.31103	−0.655513	+	0.755184i	$0.727548\pi$
$854$	2.39900	0.0820920
$855$	0.411491	0.0140727
$856$	15.2461	0.521100
$857$	27.7078	0.946481	0.473241	−	0.880933i	$-0.343084\pi$
$857$	27.7078	0.946481	0.473241	+	0.880933i	$0.343084\pi$
$858$	6.30334	0.215192
$859$	−29.2029	−0.996390	−0.498195	−	0.867065i	$-0.666004\pi$
$859$	−29.2029	−0.996390	−0.498195	+	0.867065i	$0.666004\pi$
$860$	−3.82183	−0.130323
$861$	−25.4820	−0.868423
$862$	−1.00000	−0.0340601
$863$	−4.67867	−0.159264	−0.0796319	−	0.996824i	$-0.525374\pi$
$863$	−4.67867	−0.159264	−0.0796319	+	0.996824i	$0.525374\pi$
$864$	1.57199	0.0534800
$865$	16.4911	0.560714
$866$	3.80775	0.129393
$867$	32.2167	1.09414
$868$	−0.366188	−0.0124292
$869$	−9.94102	−0.337226
$870$	−64.7110	−2.19391
$871$	−33.5978	−1.13842
$872$	−0.143803	−0.00486979
$873$	−1.49284	−0.0505249
$874$	0.290731	0.00983413
$875$	5.30897	0.179476
$876$	−8.21729	−0.277636
$877$	34.2464	1.15642	0.578210	−	0.815888i	$-0.303752\pi$
$877$	34.2464	1.15642	0.578210	+	0.815888i	$0.303752\pi$
$878$	8.53717	0.288116
$879$	22.4227	0.756298
$880$	3.18501	0.107367
$881$	14.1983	0.478354	0.239177	−	0.970976i	$-0.423122\pi$
$881$	14.1983	0.478354	0.239177	+	0.970976i	$0.423122\pi$
$882$	2.31835	0.0780630
$883$	−29.6181	−0.996727	−0.498364	−	0.866968i	$-0.666066\pi$
$883$	−29.6181	−0.996727	−0.498364	+	0.866968i	$0.666066\pi$
$884$	4.26176	0.143339
$885$	41.2521	1.38668
$886$	−25.5564	−0.858584
$887$	−4.87367	−0.163642	−0.0818209	−	0.996647i	$-0.526074\pi$
$887$	−4.87367	−0.163642	−0.0818209	+	0.996647i	$0.526074\pi$
$888$	3.63309	0.121919
$889$	−6.28789	−0.210889
$890$	18.3480	0.615027
$891$	11.8119	0.395714
$892$	10.2972	0.344777
$893$	−0.623566	−0.0208668
$894$	16.0546	0.536947
$895$	29.1211	0.973410
$896$	1.00000	0.0334077
$897$	26.3844	0.880951
$898$	12.0113	0.400822
$899$	3.60168	0.120123
$900$	7.27755	0.242585
$901$	5.93153	0.197608
$902$	−12.3358	−0.410736
$903$	−3.08938	−0.102808
$904$	19.1507	0.636942
$905$	−14.1561	−0.470565
$906$	−49.5474	−1.64610
$907$	15.3551	0.509857	0.254929	−	0.966960i	$-0.417948\pi$
$907$	15.3551	0.509857	0.254929	+	0.966960i	$0.417948\pi$
$908$	−25.9770	−0.862079
$909$	−19.5946	−0.649912
$910$	−6.98471	−0.231541
$911$	−43.7447	−1.44933	−0.724664	−	0.689102i	$-0.758005\pi$
$911$	−43.7447	−1.44933	−0.724664	+	0.689102i	$0.758005\pi$
$912$	0.143477	0.00475098
$913$	11.7548	0.389026
$914$	−2.81543	−0.0931261
$915$	15.7836	0.521791
$916$	17.2712	0.570658
$917$	−18.5132	−0.611361
$918$	2.73639	0.0903143
$919$	−16.5680	−0.546527	−0.273263	−	0.961939i	$-0.588103\pi$
$919$	−16.5680	−0.546527	−0.273263	+	0.961939i	$0.588103\pi$
$920$	13.3318	0.439535
$921$	−75.3744	−2.48367
$922$	7.64019	0.251616
$923$	15.5654	0.512343
$924$	2.57460	0.0846983
$925$	−4.94531	−0.162601
$926$	2.81964	0.0926593
$927$	−26.6515	−0.875351
$928$	−9.83561	−0.322870
$929$	−38.3284	−1.25751	−0.628757	−	0.777602i	$-0.716436\pi$
$929$	−38.3284	−1.25751	−0.628757	+	0.777602i	$0.716436\pi$
$930$	−2.40925	−0.0790023
$931$	−0.0622146	−0.00203900
$932$	−24.5892	−0.805447
$933$	20.6522	0.676122
$934$	−22.1228	−0.723882
$935$	5.54421	0.181315
$936$	5.67596	0.185525
$937$	−40.4110	−1.32017	−0.660084	−	0.751192i	$-0.729479\pi$
$937$	−40.4110	−1.32017	−0.660084	+	0.751192i	$0.729479\pi$
$938$	−13.7231	−0.448074
$939$	45.1633	1.47385
$940$	−28.5942	−0.932640
$941$	−19.2147	−0.626381	−0.313190	−	0.949690i	$-0.601398\pi$
$941$	−19.2147	−0.626381	−0.313190	+	0.949690i	$0.601398\pi$
$942$	53.8487	1.75449
$943$	−51.6349	−1.68147
$944$	6.27003	0.204072
$945$	−4.48474	−0.145889
$946$	−1.49556	−0.0486250
$947$	−9.44861	−0.307039	−0.153519	−	0.988146i	$-0.549061\pi$
$947$	−9.44861	−0.307039	−0.153519	+	0.988146i	$0.549061\pi$
$948$	−20.5351	−0.666950
$949$	8.72368	0.283183
$950$	−0.195298	−0.00633631
$951$	−47.3075	−1.53405
$952$	1.74072	0.0564171
$953$	−37.9813	−1.23033	−0.615167	−	0.788397i	$-0.710912\pi$
$953$	−37.9813	−1.23033	−0.615167	+	0.788397i	$0.710912\pi$
$954$	7.89982	0.255766
$955$	69.0291	2.23373
$956$	−20.6765	−0.668726
$957$	−25.3228	−0.818570
$958$	33.5466	1.08384
$959$	−16.6271	−0.536916
$960$	6.57926	0.212345
$961$	−30.8659	−0.995674
$962$	−3.85698	−0.124354
$963$	35.3458	1.13900
$964$	30.1422	0.970814
$965$	36.5059	1.17517
$966$	10.7767	0.346736
$967$	26.5889	0.855043	0.427521	−	0.904005i	$-0.359387\pi$
$967$	26.5889	0.855043	0.427521	+	0.904005i	$0.359387\pi$
$968$	−9.75364	−0.313494
$969$	0.249753	0.00802321
$970$	1.83705	0.0589842
$971$	12.3210	0.395399	0.197699	−	0.980263i	$-0.436653\pi$
$971$	12.3210	0.395399	0.197699	+	0.980263i	$0.436653\pi$
$972$	19.6839	0.631360
$973$	12.0583	0.386571
$974$	30.4288	0.975002
$975$	−17.7237	−0.567613
$976$	2.39900	0.0767901
$977$	−9.73459	−0.311437	−0.155719	−	0.987801i	$-0.549769\pi$
$977$	−9.73459	−0.311437	−0.155719	+	0.987801i	$0.549769\pi$
$978$	17.9291	0.573310
$979$	7.17997	0.229473
$980$	−2.85291	−0.0911329
$981$	−0.333387	−0.0106442
$982$	1.23396	0.0393773
$983$	30.7178	0.979744	0.489872	−	0.871794i	$-0.337043\pi$
$983$	30.7178	0.979744	0.489872	+	0.871794i	$0.337043\pi$
$984$	−25.4820	−0.812336
$985$	64.6494	2.05990
$986$	−17.1210	−0.545245
$987$	−23.1142	−0.735732
$988$	−0.152319	−0.00484590
$989$	−6.26011	−0.199060
$990$	7.38397	0.234678
$991$	41.5314	1.31929	0.659644	−	0.751578i	$-0.270707\pi$
$991$	41.5314	1.31929	0.659644	+	0.751578i	$0.270707\pi$
$992$	−0.366188	−0.0116265
$993$	−69.8794	−2.21756
$994$	6.35772	0.201655
$995$	−8.40161	−0.266349
$996$	24.2818	0.769398
$997$	−20.0947	−0.636405	−0.318202	−	0.948023i	$-0.603079\pi$
$997$	−20.0947	−0.636405	−0.318202	+	0.948023i	$0.603079\pi$
$998$	−35.9879	−1.13918
$999$	−2.47649	−0.0783526

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.m.1.3	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.m.1.3	✓	21	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.30616 q^{3} +1.00000 q^{4} -2.85291 q^{5} -2.30616 q^{6} +1.00000 q^{7} +1.00000 q^{8} +2.31835 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.30616 q^{3} +1.00000 q^{4} -2.85291 q^{5} -2.30616 q^{6} +1.00000 q^{7} +1.00000 q^{8} +2.31835 q^{9} -2.85291 q^{10} -1.11641 q^{11} -2.30616 q^{12} +2.44827 q^{13} +1.00000 q^{14} +6.57926 q^{15} +1.00000 q^{16} +1.74072 q^{17} +2.31835 q^{18} -0.0622146 q^{19} -2.85291 q^{20} -2.30616 q^{21} -1.11641 q^{22} -4.67304 q^{23} -2.30616 q^{24} +3.13910 q^{25} +2.44827 q^{26} +1.57199 q^{27} +1.00000 q^{28} -9.83561 q^{29} +6.57926 q^{30} -0.366188 q^{31} +1.00000 q^{32} +2.57460 q^{33} +1.74072 q^{34} -2.85291 q^{35} +2.31835 q^{36} -1.57539 q^{37} -0.0622146 q^{38} -5.64610 q^{39} -2.85291 q^{40} +11.0495 q^{41} -2.30616 q^{42} +1.33962 q^{43} -1.11641 q^{44} -6.61405 q^{45} -4.67304 q^{46} +10.0228 q^{47} -2.30616 q^{48} +1.00000 q^{49} +3.13910 q^{50} -4.01437 q^{51} +2.44827 q^{52} +3.40751 q^{53} +1.57199 q^{54} +3.18501 q^{55} +1.00000 q^{56} +0.143477 q^{57} -9.83561 q^{58} +6.27003 q^{59} +6.57926 q^{60} +2.39900 q^{61} -0.366188 q^{62} +2.31835 q^{63} +1.00000 q^{64} -6.98471 q^{65} +2.57460 q^{66} -13.7231 q^{67} +1.74072 q^{68} +10.7767 q^{69} -2.85291 q^{70} +6.35772 q^{71} +2.31835 q^{72} +3.56320 q^{73} -1.57539 q^{74} -7.23926 q^{75} -0.0622146 q^{76} -1.11641 q^{77} -5.64610 q^{78} +8.90449 q^{79} -2.85291 q^{80} -10.5803 q^{81} +11.0495 q^{82} -10.5291 q^{83} -2.30616 q^{84} -4.96612 q^{85} +1.33962 q^{86} +22.6824 q^{87} -1.11641 q^{88} -6.43133 q^{89} -6.61405 q^{90} +2.44827 q^{91} -4.67304 q^{92} +0.844487 q^{93} +10.0228 q^{94} +0.177493 q^{95} -2.30616 q^{96} -0.643922 q^{97} +1.00000 q^{98} -2.58822 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9}+O(q^{10}) \) 21 * q + 21 * q^2 - 6 * q^3 + 21 * q^4 - 11 * q^5 - 6 * q^6 + 21 * q^7 + 21 * q^8 + 5 * q^9	\( 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9} - 11 q^{10} - 34 q^{11} - 6 q^{12} - 19 q^{13} + 21 q^{14} - 24 q^{15} + 21 q^{16} - 17 q^{17} + 5 q^{18} - 15 q^{19} - 11 q^{20} - 6 q^{21} - 34 q^{22} - 32 q^{23} - 6 q^{24} + 6 q^{25} - 19 q^{26} - 3 q^{27} + 21 q^{28} - 46 q^{29} - 24 q^{30} + 7 q^{31} + 21 q^{32} - 13 q^{33} - 17 q^{34} - 11 q^{35} + 5 q^{36} - 34 q^{37} - 15 q^{38} - 25 q^{39} - 11 q^{40} - 27 q^{41} - 6 q^{42} - 47 q^{43} - 34 q^{44} - 13 q^{45} - 32 q^{46} - 7 q^{47} - 6 q^{48} + 21 q^{49} + 6 q^{50} - 29 q^{51} - 19 q^{52} - 57 q^{53} - 3 q^{54} + 17 q^{55} + 21 q^{56} - 28 q^{57} - 46 q^{58} - 30 q^{59} - 24 q^{60} - 17 q^{61} + 7 q^{62} + 5 q^{63} + 21 q^{64} - 40 q^{65} - 13 q^{66} - 38 q^{67} - 17 q^{68} - 13 q^{69} - 11 q^{70} - 66 q^{71} + 5 q^{72} - 15 q^{73} - 34 q^{74} + 15 q^{75} - 15 q^{76} - 34 q^{77} - 25 q^{78} - 17 q^{79} - 11 q^{80} - 11 q^{81} - 27 q^{82} - 19 q^{83} - 6 q^{84} - 28 q^{85} - 47 q^{86} + 45 q^{87} - 34 q^{88} - 39 q^{89} - 13 q^{90} - 19 q^{91} - 32 q^{92} - 25 q^{93} - 7 q^{94} - 35 q^{95} - 6 q^{96} + 21 q^{98} - 52 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 - 6 * q^3 + 21 * q^4 - 11 * q^5 - 6 * q^6 + 21 * q^7 + 21 * q^8 + 5 * q^9 - 11 * q^10 - 34 * q^11 - 6 * q^12 - 19 * q^13 + 21 * q^14 - 24 * q^15 + 21 * q^16 - 17 * q^17 + 5 * q^18 - 15 * q^19 - 11 * q^20 - 6 * q^21 - 34 * q^22 - 32 * q^23 - 6 * q^24 + 6 * q^25 - 19 * q^26 - 3 * q^27 + 21 * q^28 - 46 * q^29 - 24 * q^30 + 7 * q^31 + 21 * q^32 - 13 * q^33 - 17 * q^34 - 11 * q^35 + 5 * q^36 - 34 * q^37 - 15 * q^38 - 25 * q^39 - 11 * q^40 - 27 * q^41 - 6 * q^42 - 47 * q^43 - 34 * q^44 - 13 * q^45 - 32 * q^46 - 7 * q^47 - 6 * q^48 + 21 * q^49 + 6 * q^50 - 29 * q^51 - 19 * q^52 - 57 * q^53 - 3 * q^54 + 17 * q^55 + 21 * q^56 - 28 * q^57 - 46 * q^58 - 30 * q^59 - 24 * q^60 - 17 * q^61 + 7 * q^62 + 5 * q^63 + 21 * q^64 - 40 * q^65 - 13 * q^66 - 38 * q^67 - 17 * q^68 - 13 * q^69 - 11 * q^70 - 66 * q^71 + 5 * q^72 - 15 * q^73 - 34 * q^74 + 15 * q^75 - 15 * q^76 - 34 * q^77 - 25 * q^78 - 17 * q^79 - 11 * q^80 - 11 * q^81 - 27 * q^82 - 19 * q^83 - 6 * q^84 - 28 * q^85 - 47 * q^86 + 45 * q^87 - 34 * q^88 - 39 * q^89 - 13 * q^90 - 19 * q^91 - 32 * q^92 - 25 * q^93 - 7 * q^94 - 35 * q^95 - 6 * q^96 + 21 * q^98 - 52 * q^99

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