LMFDB - Embedded newform 6010.2.a.i.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6010,2,Mod(1,6010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6010, 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("6010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6010 = 2 \cdot 5 \cdot 601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6010.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$47.9900916148$
Analytic rank:	$1$
Dimension:	$29$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	6010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.774267 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.774267 q^{6} -0.164549 q^{7} -1.00000 q^{8} -2.40051 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.774267 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.774267 q^{6} -0.164549 q^{7} -1.00000 q^{8} -2.40051 q^{9} +1.00000 q^{10} -4.78058 q^{11} -0.774267 q^{12} +4.61137 q^{13} +0.164549 q^{14} +0.774267 q^{15} +1.00000 q^{16} -7.41168 q^{17} +2.40051 q^{18} +4.67683 q^{19} -1.00000 q^{20} +0.127405 q^{21} +4.78058 q^{22} +1.15268 q^{23} +0.774267 q^{24} +1.00000 q^{25} -4.61137 q^{26} +4.18144 q^{27} -0.164549 q^{28} +3.00453 q^{29} -0.774267 q^{30} -1.28531 q^{31} -1.00000 q^{32} +3.70145 q^{33} +7.41168 q^{34} +0.164549 q^{35} -2.40051 q^{36} +6.29827 q^{37} -4.67683 q^{38} -3.57044 q^{39} +1.00000 q^{40} +7.60067 q^{41} -0.127405 q^{42} -3.54474 q^{43} -4.78058 q^{44} +2.40051 q^{45} -1.15268 q^{46} +3.00410 q^{47} -0.774267 q^{48} -6.97292 q^{49} -1.00000 q^{50} +5.73862 q^{51} +4.61137 q^{52} +4.36922 q^{53} -4.18144 q^{54} +4.78058 q^{55} +0.164549 q^{56} -3.62112 q^{57} -3.00453 q^{58} -2.46714 q^{59} +0.774267 q^{60} +11.9586 q^{61} +1.28531 q^{62} +0.395001 q^{63} +1.00000 q^{64} -4.61137 q^{65} -3.70145 q^{66} -0.921577 q^{67} -7.41168 q^{68} -0.892483 q^{69} -0.164549 q^{70} -4.17902 q^{71} +2.40051 q^{72} +13.4707 q^{73} -6.29827 q^{74} -0.774267 q^{75} +4.67683 q^{76} +0.786639 q^{77} +3.57044 q^{78} -0.511630 q^{79} -1.00000 q^{80} +3.96398 q^{81} -7.60067 q^{82} +1.46299 q^{83} +0.127405 q^{84} +7.41168 q^{85} +3.54474 q^{86} -2.32631 q^{87} +4.78058 q^{88} -4.96160 q^{89} -2.40051 q^{90} -0.758796 q^{91} +1.15268 q^{92} +0.995176 q^{93} -3.00410 q^{94} -4.67683 q^{95} +0.774267 q^{96} -11.5919 q^{97} +6.97292 q^{98} +11.4758 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 29 q - 29 q^{2} - 10 q^{3} + 29 q^{4} - 29 q^{5} + 10 q^{6} - 29 q^{8} + 29 q^{9}+O(q^{10}) $ 29 * q - 29 * q^2 - 10 * q^3 + 29 * q^4 - 29 * q^5 + 10 * q^6 - 29 * q^8 + 29 * q^9	\( 29 q - 29 q^{2} - 10 q^{3} + 29 q^{4} - 29 q^{5} + 10 q^{6} - 29 q^{8} + 29 q^{9} + 29 q^{10} - 10 q^{12} - 4 q^{13} + 10 q^{15} + 29 q^{16} - 23 q^{17} - 29 q^{18} + q^{19} - 29 q^{20} + 2 q^{21} - 9 q^{23} + 10 q^{24} + 29 q^{25} + 4 q^{26} - 43 q^{27} - 5 q^{29} - 10 q^{30} + 21 q^{31} - 29 q^{32} - 19 q^{33} + 23 q^{34} + 29 q^{36} - 6 q^{37} - q^{38} + 18 q^{39} + 29 q^{40} - 17 q^{41} - 2 q^{42} - 19 q^{43} - 29 q^{45} + 9 q^{46} - 21 q^{47} - 10 q^{48} + 45 q^{49} - 29 q^{50} + 11 q^{51} - 4 q^{52} - 53 q^{53} + 43 q^{54} - 16 q^{57} + 5 q^{58} - 30 q^{59} + 10 q^{60} + 16 q^{61} - 21 q^{62} - 17 q^{63} + 29 q^{64} + 4 q^{65} + 19 q^{66} - 35 q^{67} - 23 q^{68} + 13 q^{69} + 2 q^{71} - 29 q^{72} - q^{73} + 6 q^{74} - 10 q^{75} + q^{76} - 50 q^{77} - 18 q^{78} + 26 q^{79} - 29 q^{80} + 33 q^{81} + 17 q^{82} - 54 q^{83} + 2 q^{84} + 23 q^{85} + 19 q^{86} - 56 q^{87} - 2 q^{89} + 29 q^{90} + 27 q^{91} - 9 q^{92} - 26 q^{93} + 21 q^{94} - q^{95} + 10 q^{96} + 15 q^{97} - 45 q^{98} + 27 q^{99}+O(q^{100}) \) 29 * q - 29 * q^2 - 10 * q^3 + 29 * q^4 - 29 * q^5 + 10 * q^6 - 29 * q^8 + 29 * q^9 + 29 * q^10 - 10 * q^12 - 4 * q^13 + 10 * q^15 + 29 * q^16 - 23 * q^17 - 29 * q^18 + q^19 - 29 * q^20 + 2 * q^21 - 9 * q^23 + 10 * q^24 + 29 * q^25 + 4 * q^26 - 43 * q^27 - 5 * q^29 - 10 * q^30 + 21 * q^31 - 29 * q^32 - 19 * q^33 + 23 * q^34 + 29 * q^36 - 6 * q^37 - q^38 + 18 * q^39 + 29 * q^40 - 17 * q^41 - 2 * q^42 - 19 * q^43 - 29 * q^45 + 9 * q^46 - 21 * q^47 - 10 * q^48 + 45 * q^49 - 29 * q^50 + 11 * q^51 - 4 * q^52 - 53 * q^53 + 43 * q^54 - 16 * q^57 + 5 * q^58 - 30 * q^59 + 10 * q^60 + 16 * q^61 - 21 * q^62 - 17 * q^63 + 29 * q^64 + 4 * q^65 + 19 * q^66 - 35 * q^67 - 23 * q^68 + 13 * q^69 + 2 * q^71 - 29 * q^72 - q^73 + 6 * q^74 - 10 * q^75 + q^76 - 50 * q^77 - 18 * q^78 + 26 * q^79 - 29 * q^80 + 33 * q^81 + 17 * q^82 - 54 * q^83 + 2 * q^84 + 23 * q^85 + 19 * q^86 - 56 * q^87 - 2 * q^89 + 29 * q^90 + 27 * q^91 - 9 * q^92 - 26 * q^93 + 21 * q^94 - q^95 + 10 * q^96 + 15 * q^97 - 45 * q^98 + 27 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−0.774267	−0.447023	−0.223512	−	0.974701i	$-0.571752\pi$
$3$	−0.774267	−0.447023	−0.223512	+	0.974701i	$0.571752\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.774267	0.316093
$7$	−0.164549	−0.0621936	−0.0310968	−	0.999516i	$-0.509900\pi$
$7$	−0.164549	−0.0621936	−0.0310968	+	0.999516i	$0.509900\pi$
$8$	−1.00000	−0.353553
$9$	−2.40051	−0.800170
$10$	1.00000	0.316228
$11$	−4.78058	−1.44140	−0.720699	−	0.693248i	$-0.756179\pi$
$11$	−4.78058	−1.44140	−0.720699	+	0.693248i	$0.756179\pi$
$12$	−0.774267	−0.223512
$13$	4.61137	1.27897	0.639483	−	0.768806i	$-0.279149\pi$
$13$	4.61137	1.27897	0.639483	+	0.768806i	$0.279149\pi$
$14$	0.164549	0.0439775
$15$	0.774267	0.199915
$16$	1.00000	0.250000
$17$	−7.41168	−1.79760	−0.898799	−	0.438362i	$-0.855559\pi$
$17$	−7.41168	−1.79760	−0.898799	+	0.438362i	$0.855559\pi$
$18$	2.40051	0.565806
$19$	4.67683	1.07294	0.536470	−	0.843920i	$-0.319758\pi$
$19$	4.67683	1.07294	0.536470	+	0.843920i	$0.319758\pi$
$20$	−1.00000	−0.223607
$21$	0.127405	0.0278020
$22$	4.78058	1.01922
$23$	1.15268	0.240351	0.120175	−	0.992753i	$-0.461654\pi$
$23$	1.15268	0.240351	0.120175	+	0.992753i	$0.461654\pi$
$24$	0.774267	0.158047
$25$	1.00000	0.200000
$26$	−4.61137	−0.904365
$27$	4.18144	0.804718
$28$	−0.164549	−0.0310968
$29$	3.00453	0.557927	0.278963	−	0.960302i	$-0.410009\pi$
$29$	3.00453	0.557927	0.278963	+	0.960302i	$0.410009\pi$
$30$	−0.774267	−0.141361
$31$	−1.28531	−0.230849	−0.115425	−	0.993316i	$-0.536823\pi$
$31$	−1.28531	−0.230849	−0.115425	+	0.993316i	$0.536823\pi$
$32$	−1.00000	−0.176777
$33$	3.70145	0.644339
$34$	7.41168	1.27109
$35$	0.164549	0.0278138
$36$	−2.40051	−0.400085
$37$	6.29827	1.03543	0.517714	−	0.855554i	$-0.326783\pi$
$37$	6.29827	1.03543	0.517714	+	0.855554i	$0.326783\pi$
$38$	−4.67683	−0.758683
$39$	−3.57044	−0.571727
$40$	1.00000	0.158114
$41$	7.60067	1.18703	0.593513	−	0.804824i	$-0.297741\pi$
$41$	7.60067	1.18703	0.593513	+	0.804824i	$0.297741\pi$
$42$	−0.127405	−0.0196590
$43$	−3.54474	−0.540567	−0.270284	−	0.962781i	$-0.587117\pi$
$43$	−3.54474	−0.540567	−0.270284	+	0.962781i	$0.587117\pi$
$44$	−4.78058	−0.720699
$45$	2.40051	0.357847
$46$	−1.15268	−0.169954
$47$	3.00410	0.438193	0.219096	−	0.975703i	$-0.429689\pi$
$47$	3.00410	0.438193	0.219096	+	0.975703i	$0.429689\pi$
$48$	−0.774267	−0.111756
$49$	−6.97292	−0.996132
$50$	−1.00000	−0.141421
$51$	5.73862	0.803568
$52$	4.61137	0.639483
$53$	4.36922	0.600158	0.300079	−	0.953914i	$-0.402987\pi$
$53$	4.36922	0.600158	0.300079	+	0.953914i	$0.402987\pi$
$54$	−4.18144	−0.569022
$55$	4.78058	0.644613
$56$	0.164549	0.0219888
$57$	−3.62112	−0.479629
$58$	−3.00453	−0.394514
$59$	−2.46714	−0.321195	−0.160597	−	0.987020i	$-0.551342\pi$
$59$	−2.46714	−0.321195	−0.160597	+	0.987020i	$0.551342\pi$
$60$	0.774267	0.0999575
$61$	11.9586	1.53115	0.765573	−	0.643349i	$-0.222456\pi$
$61$	11.9586	1.53115	0.765573	+	0.643349i	$0.222456\pi$
$62$	1.28531	0.163235
$63$	0.395001	0.0497655
$64$	1.00000	0.125000
$65$	−4.61137	−0.571971
$66$	−3.70145	−0.455616
$67$	−0.921577	−0.112589	−0.0562943	−	0.998414i	$-0.517928\pi$
$67$	−0.921577	−0.112589	−0.0562943	+	0.998414i	$0.517928\pi$
$68$	−7.41168	−0.898799
$69$	−0.892483	−0.107442
$70$	−0.164549	−0.0196674
$71$	−4.17902	−0.495959	−0.247979	−	0.968765i	$-0.579767\pi$
$71$	−4.17902	−0.495959	−0.247979	+	0.968765i	$0.579767\pi$
$72$	2.40051	0.282903
$73$	13.4707	1.57662	0.788311	−	0.615277i	$-0.210956\pi$
$73$	13.4707	1.57662	0.788311	+	0.615277i	$0.210956\pi$
$74$	−6.29827	−0.732159
$75$	−0.774267	−0.0894047
$76$	4.67683	0.536470
$77$	0.786639	0.0896458
$78$	3.57044	0.404272
$79$	−0.511630	−0.0575629	−0.0287814	−	0.999586i	$-0.509163\pi$
$79$	−0.511630	−0.0575629	−0.0287814	+	0.999586i	$0.509163\pi$
$80$	−1.00000	−0.111803
$81$	3.96398	0.440442
$82$	−7.60067	−0.839354
$83$	1.46299	0.160584	0.0802921	−	0.996771i	$-0.474415\pi$
$83$	1.46299	0.160584	0.0802921	+	0.996771i	$0.474415\pi$
$84$	0.127405	0.0139010
$85$	7.41168	0.803910
$86$	3.54474	0.382239
$87$	−2.32631	−0.249406
$88$	4.78058	0.509611
$89$	−4.96160	−0.525928	−0.262964	−	0.964806i	$-0.584700\pi$
$89$	−4.96160	−0.525928	−0.262964	+	0.964806i	$0.584700\pi$
$90$	−2.40051	−0.253036
$91$	−0.758796	−0.0795435
$92$	1.15268	0.120175
$93$	0.995176	0.103195
$94$	−3.00410	−0.309849
$95$	−4.67683	−0.479833
$96$	0.774267	0.0790233
$97$	−11.5919	−1.17698	−0.588490	−	0.808505i	$-0.700277\pi$
$97$	−11.5919	−1.17698	−0.588490	+	0.808505i	$0.700277\pi$
$98$	6.97292	0.704372
$99$	11.4758	1.15336
$100$	1.00000	0.100000
$101$	−10.0815	−1.00314	−0.501572	−	0.865116i	$-0.667245\pi$
$101$	−10.0815	−1.00314	−0.501572	+	0.865116i	$0.667245\pi$
$102$	−5.73862	−0.568208
$103$	10.8564	1.06971	0.534857	−	0.844943i	$-0.320365\pi$
$103$	10.8564	1.06971	0.534857	+	0.844943i	$0.320365\pi$
$104$	−4.61137	−0.452182
$105$	−0.127405	−0.0124334
$106$	−4.36922	−0.424376
$107$	−7.13914	−0.690166	−0.345083	−	0.938572i	$-0.612149\pi$
$107$	−7.13914	−0.690166	−0.345083	+	0.938572i	$0.612149\pi$
$108$	4.18144	0.402359
$109$	−11.4216	−1.09399	−0.546997	−	0.837134i	$-0.684229\pi$
$109$	−11.4216	−1.09399	−0.546997	+	0.837134i	$0.684229\pi$
$110$	−4.78058	−0.455810
$111$	−4.87654	−0.462861
$112$	−0.164549	−0.0155484
$113$	−16.4516	−1.54763	−0.773817	−	0.633409i	$-0.781655\pi$
$113$	−16.4516	−1.54763	−0.773817	+	0.633409i	$0.781655\pi$
$114$	3.62112	0.339149
$115$	−1.15268	−0.107488
$116$	3.00453	0.278963
$117$	−11.0697	−1.02339
$118$	2.46714	0.227119
$119$	1.21958	0.111799
$120$	−0.774267	−0.0706806
$121$	11.8539	1.07763
$122$	−11.9586	−1.08268
$123$	−5.88495	−0.530628
$124$	−1.28531	−0.115425
$125$	−1.00000	−0.0894427
$126$	−0.395001	−0.0351895
$127$	−17.0063	−1.50907	−0.754533	−	0.656263i	$-0.772136\pi$
$127$	−17.0063	−1.50907	−0.754533	+	0.656263i	$0.772136\pi$
$128$	−1.00000	−0.0883883
$129$	2.74457	0.241646
$130$	4.61137	0.404444
$131$	17.4166	1.52170	0.760848	−	0.648930i	$-0.224783\pi$
$131$	17.4166	1.52170	0.760848	+	0.648930i	$0.224783\pi$
$132$	3.70145	0.322169
$133$	−0.769568	−0.0667300
$134$	0.921577	0.0796121
$135$	−4.18144	−0.359881
$136$	7.41168	0.635547
$137$	−16.6750	−1.42464	−0.712322	−	0.701853i	$-0.752356\pi$
$137$	−16.6750	−1.42464	−0.712322	+	0.701853i	$0.752356\pi$
$138$	0.892483	0.0759732
$139$	10.2898	0.872768	0.436384	−	0.899760i	$-0.356259\pi$
$139$	10.2898	0.872768	0.436384	+	0.899760i	$0.356259\pi$
$140$	0.164549	0.0139069
$141$	−2.32597	−0.195882
$142$	4.17902	0.350696
$143$	−22.0450	−1.84350
$144$	−2.40051	−0.200043
$145$	−3.00453	−0.249512
$146$	−13.4707	−1.11484
$147$	5.39891	0.445294
$148$	6.29827	0.517714
$149$	22.7103	1.86050	0.930250	−	0.366927i	$-0.119590\pi$
$149$	22.7103	1.86050	0.930250	+	0.366927i	$0.119590\pi$
$150$	0.774267	0.0632187
$151$	4.79907	0.390543	0.195271	−	0.980749i	$-0.437441\pi$
$151$	4.79907	0.390543	0.195271	+	0.980749i	$0.437441\pi$
$152$	−4.67683	−0.379341
$153$	17.7918	1.43838
$154$	−0.786639	−0.0633892
$155$	1.28531	0.103239
$156$	−3.57044	−0.285864
$157$	−1.71549	−0.136911	−0.0684554	−	0.997654i	$-0.521807\pi$
$157$	−1.71549	−0.136911	−0.0684554	+	0.997654i	$0.521807\pi$
$158$	0.511630	0.0407031
$159$	−3.38294	−0.268285
$160$	1.00000	0.0790569
$161$	−0.189672	−0.0149483
$162$	−3.96398	−0.311440
$163$	−9.57113	−0.749669	−0.374834	−	0.927092i	$-0.622300\pi$
$163$	−9.57113	−0.749669	−0.374834	+	0.927092i	$0.622300\pi$
$164$	7.60067	0.593513
$165$	−3.70145	−0.288157
$166$	−1.46299	−0.113550
$167$	−17.7724	−1.37527	−0.687633	−	0.726058i	$-0.741350\pi$
$167$	−17.7724	−1.37527	−0.687633	+	0.726058i	$0.741350\pi$
$168$	−0.127405	−0.00982949
$169$	8.26477	0.635752
$170$	−7.41168	−0.568450
$171$	−11.2268	−0.858534
$172$	−3.54474	−0.270284
$173$	6.41269	0.487548	0.243774	−	0.969832i	$-0.421615\pi$
$173$	6.41269	0.487548	0.243774	+	0.969832i	$0.421615\pi$
$174$	2.32631	0.176357
$175$	−0.164549	−0.0124387
$176$	−4.78058	−0.360350
$177$	1.91023	0.143581
$178$	4.96160	0.371887
$179$	1.96930	0.147192	0.0735961	−	0.997288i	$-0.476552\pi$
$179$	1.96930	0.147192	0.0735961	+	0.997288i	$0.476552\pi$
$180$	2.40051	0.178923
$181$	−9.86524	−0.733277	−0.366639	−	0.930363i	$-0.619491\pi$
$181$	−9.86524	−0.733277	−0.366639	+	0.930363i	$0.619491\pi$
$182$	0.758796	0.0562457
$183$	−9.25917	−0.684458
$184$	−1.15268	−0.0849768
$185$	−6.29827	−0.463058
$186$	−0.995176	−0.0729699
$187$	35.4321	2.59105
$188$	3.00410	0.219096
$189$	−0.688051	−0.0500483
$190$	4.67683	0.339293
$191$	−14.8961	−1.07784	−0.538922	−	0.842356i	$-0.681168\pi$
$191$	−14.8961	−1.07784	−0.538922	+	0.842356i	$0.681168\pi$
$192$	−0.774267	−0.0558779
$193$	19.9631	1.43698	0.718489	−	0.695538i	$-0.244834\pi$
$193$	19.9631	1.43698	0.718489	+	0.695538i	$0.244834\pi$
$194$	11.5919	0.832250
$195$	3.57044	0.255684
$196$	−6.97292	−0.498066
$197$	−20.2397	−1.44202	−0.721009	−	0.692925i	$-0.756321\pi$
$197$	−20.2397	−1.44202	−0.721009	+	0.692925i	$0.756321\pi$
$198$	−11.4758	−0.815552
$199$	5.11050	0.362274	0.181137	−	0.983458i	$-0.442022\pi$
$199$	5.11050	0.362274	0.181137	+	0.983458i	$0.442022\pi$
$200$	−1.00000	−0.0707107
$201$	0.713547	0.0503297
$202$	10.0815	0.709330
$203$	−0.494391	−0.0346995
$204$	5.73862	0.401784
$205$	−7.60067	−0.530854
$206$	−10.8564	−0.756402
$207$	−2.76702	−0.192321
$208$	4.61137	0.319741
$209$	−22.3580	−1.54653
$210$	0.127405	0.00879177
$211$	2.59733	0.178808	0.0894039	−	0.995995i	$-0.471504\pi$
$211$	2.59733	0.178808	0.0894039	+	0.995995i	$0.471504\pi$
$212$	4.36922	0.300079
$213$	3.23568	0.221705
$214$	7.13914	0.488021
$215$	3.54474	0.241749
$216$	−4.18144	−0.284511
$217$	0.211497	0.0143573
$218$	11.4216	0.773571
$219$	−10.4299	−0.704787
$220$	4.78058	0.322307
$221$	−34.1780	−2.29906
$222$	4.87654	0.327292
$223$	−0.142452	−0.00953926	−0.00476963	−	0.999989i	$-0.501518\pi$
$223$	−0.142452	−0.00953926	−0.00476963	+	0.999989i	$0.501518\pi$
$224$	0.164549	0.0109944
$225$	−2.40051	−0.160034
$226$	16.4516	1.09434
$227$	17.4219	1.15633	0.578167	−	0.815918i	$-0.303768\pi$
$227$	17.4219	1.15633	0.578167	+	0.815918i	$0.303768\pi$
$228$	−3.62112	−0.239815
$229$	−21.1431	−1.39717	−0.698587	−	0.715525i	$-0.746187\pi$
$229$	−21.1431	−1.39717	−0.698587	+	0.715525i	$0.746187\pi$
$230$	1.15268	0.0760055
$231$	−0.609069	−0.0400738
$232$	−3.00453	−0.197257
$233$	−19.7871	−1.29630	−0.648149	−	0.761514i	$-0.724457\pi$
$233$	−19.7871	−1.29630	−0.648149	+	0.761514i	$0.724457\pi$
$234$	11.0697	0.723646
$235$	−3.00410	−0.195966
$236$	−2.46714	−0.160597
$237$	0.396138	0.0257319
$238$	−1.21958	−0.0790539
$239$	−24.4688	−1.58276	−0.791378	−	0.611327i	$-0.790636\pi$
$239$	−24.4688	−1.58276	−0.791378	+	0.611327i	$0.790636\pi$
$240$	0.774267	0.0499787
$241$	−2.76820	−0.178315	−0.0891577	−	0.996018i	$-0.528418\pi$
$241$	−2.76820	−0.178315	−0.0891577	+	0.996018i	$0.528418\pi$
$242$	−11.8539	−0.762000
$243$	−15.6135	−1.00161
$244$	11.9586	0.765573
$245$	6.97292	0.445484
$246$	5.88495	0.375211
$247$	21.5666	1.37225
$248$	1.28531	0.0816175
$249$	−1.13275	−0.0717849
$250$	1.00000	0.0632456
$251$	26.3984	1.66626	0.833128	−	0.553081i	$-0.186548\pi$
$251$	26.3984	1.66626	0.833128	+	0.553081i	$0.186548\pi$
$252$	0.395001	0.0248827
$253$	−5.51048	−0.346441
$254$	17.0063	1.06707
$255$	−5.73862	−0.359367
$256$	1.00000	0.0625000
$257$	23.1405	1.44347	0.721734	−	0.692171i	$-0.243346\pi$
$257$	23.1405	1.44347	0.721734	+	0.692171i	$0.243346\pi$
$258$	−2.74457	−0.170870
$259$	−1.03637	−0.0643971
$260$	−4.61137	−0.285985
$261$	−7.21240	−0.446436
$262$	−17.4166	−1.07600
$263$	14.0399	0.865736	0.432868	−	0.901457i	$-0.357502\pi$
$263$	14.0399	0.865736	0.432868	+	0.901457i	$0.357502\pi$
$264$	−3.70145	−0.227808
$265$	−4.36922	−0.268399
$266$	0.769568	0.0471852
$267$	3.84160	0.235102
$268$	−0.921577	−0.0562943
$269$	22.8151	1.39106	0.695530	−	0.718497i	$-0.255170\pi$
$269$	22.8151	1.39106	0.695530	+	0.718497i	$0.255170\pi$
$270$	4.18144	0.254474
$271$	−17.2988	−1.05083	−0.525415	−	0.850846i	$-0.676090\pi$
$271$	−17.2988	−1.05083	−0.525415	+	0.850846i	$0.676090\pi$
$272$	−7.41168	−0.449399
$273$	0.587511	0.0355578
$274$	16.6750	1.00737
$275$	−4.78058	−0.288280
$276$	−0.892483	−0.0537212
$277$	1.81940	0.109317	0.0546586	−	0.998505i	$-0.482593\pi$
$277$	1.81940	0.109317	0.0546586	+	0.998505i	$0.482593\pi$
$278$	−10.2898	−0.617140
$279$	3.08541	0.184719
$280$	−0.164549	−0.00983368
$281$	30.9714	1.84760	0.923799	−	0.382877i	$-0.125067\pi$
$281$	30.9714	1.84760	0.923799	+	0.382877i	$0.125067\pi$
$282$	2.32597	0.138510
$283$	−27.7266	−1.64817	−0.824087	−	0.566463i	$-0.808312\pi$
$283$	−27.7266	−1.64817	−0.824087	+	0.566463i	$0.808312\pi$
$284$	−4.17902	−0.247979
$285$	3.62112	0.214497
$286$	22.0450	1.30355
$287$	−1.25068	−0.0738254
$288$	2.40051	0.141451
$289$	37.9331	2.23136
$290$	3.00453	0.176432
$291$	8.97523	0.526137
$292$	13.4707	0.788311
$293$	−13.2546	−0.774342	−0.387171	−	0.922008i	$-0.626548\pi$
$293$	−13.2546	−0.774342	−0.387171	+	0.922008i	$0.626548\pi$
$294$	−5.39891	−0.314871
$295$	2.46714	0.143643
$296$	−6.29827	−0.366079
$297$	−19.9897	−1.15992
$298$	−22.7103	−1.31557
$299$	5.31544	0.307400
$300$	−0.774267	−0.0447023
$301$	0.583282	0.0336198
$302$	−4.79907	−0.276156
$303$	7.80575	0.448429
$304$	4.67683	0.268235
$305$	−11.9586	−0.684749
$306$	−17.7918	−1.01709
$307$	−13.4191	−0.765870	−0.382935	−	0.923775i	$-0.625087\pi$
$307$	−13.4191	−0.765870	−0.382935	+	0.923775i	$0.625087\pi$
$308$	0.786639	0.0448229
$309$	−8.40576	−0.478187
$310$	−1.28531	−0.0730009
$311$	−29.1283	−1.65171	−0.825856	−	0.563880i	$-0.809308\pi$
$311$	−29.1283	−1.65171	−0.825856	+	0.563880i	$0.809308\pi$
$312$	3.57044	0.202136
$313$	−6.11913	−0.345874	−0.172937	−	0.984933i	$-0.555326\pi$
$313$	−6.11913	−0.345874	−0.172937	+	0.984933i	$0.555326\pi$
$314$	1.71549	0.0968106
$315$	−0.395001	−0.0222558
$316$	−0.511630	−0.0287814
$317$	−6.16838	−0.346451	−0.173225	−	0.984882i	$-0.555419\pi$
$317$	−6.16838	−0.346451	−0.173225	+	0.984882i	$0.555419\pi$
$318$	3.38294	0.189706
$319$	−14.3634	−0.804195
$320$	−1.00000	−0.0559017
$321$	5.52760	0.308521
$322$	0.189672	0.0105700
$323$	−34.6632	−1.92871
$324$	3.96398	0.220221
$325$	4.61137	0.255793
$326$	9.57113	0.530096
$327$	8.84340	0.489041
$328$	−7.60067	−0.419677
$329$	−0.494321	−0.0272528
$330$	3.70145	0.203758
$331$	−7.14184	−0.392551	−0.196276	−	0.980549i	$-0.562885\pi$
$331$	−7.14184	−0.392551	−0.196276	+	0.980549i	$0.562885\pi$
$332$	1.46299	0.0802921
$333$	−15.1191	−0.828519
$334$	17.7724	0.972461
$335$	0.921577	0.0503511
$336$	0.127405	0.00695050
$337$	−32.2925	−1.75908	−0.879541	−	0.475822i	$-0.842150\pi$
$337$	−32.2925	−1.75908	−0.879541	+	0.475822i	$0.842150\pi$
$338$	−8.26477	−0.449544
$339$	12.7379	0.691829
$340$	7.41168	0.401955
$341$	6.14454	0.332746
$342$	11.2268	0.607075
$343$	2.29923	0.124147
$344$	3.54474	0.191119
$345$	0.892483	0.0480497
$346$	−6.41269	−0.344748
$347$	32.2463	1.73107	0.865536	−	0.500847i	$-0.166978\pi$
$347$	32.2463	1.73107	0.865536	+	0.500847i	$0.166978\pi$
$348$	−2.32631	−0.124703
$349$	22.6325	1.21149	0.605744	−	0.795659i	$-0.292875\pi$
$349$	22.6325	1.21149	0.605744	+	0.795659i	$0.292875\pi$
$350$	0.164549	0.00879551
$351$	19.2822	1.02921
$352$	4.78058	0.254806
$353$	−14.8738	−0.791654	−0.395827	−	0.918325i	$-0.629542\pi$
$353$	−14.8738	−0.791654	−0.395827	+	0.918325i	$0.629542\pi$
$354$	−1.91023	−0.101527
$355$	4.17902	0.221799
$356$	−4.96160	−0.262964
$357$	−0.944284	−0.0499768
$358$	−1.96930	−0.104081
$359$	11.5764	0.610981	0.305491	−	0.952195i	$-0.401180\pi$
$359$	11.5764	0.610981	0.305491	+	0.952195i	$0.401180\pi$
$360$	−2.40051	−0.126518
$361$	2.87278	0.151199
$362$	9.86524	0.518505
$363$	−9.17811	−0.481726
$364$	−0.758796	−0.0397717
$365$	−13.4707	−0.705087
$366$	9.25917	0.483985
$367$	−20.5272	−1.07151	−0.535756	−	0.844373i	$-0.679973\pi$
$367$	−20.5272	−1.07151	−0.535756	+	0.844373i	$0.679973\pi$
$368$	1.15268	0.0600877
$369$	−18.2455	−0.949822
$370$	6.29827	0.327431
$371$	−0.718950	−0.0373260
$372$	0.995176	0.0515975
$373$	−6.55114	−0.339205	−0.169603	−	0.985513i	$-0.554248\pi$
$373$	−6.55114	−0.339205	−0.169603	+	0.985513i	$0.554248\pi$
$374$	−35.4321	−1.83215
$375$	0.774267	0.0399830
$376$	−3.00410	−0.154924
$377$	13.8550	0.713569
$378$	0.688051	0.0353895
$379$	27.0047	1.38714	0.693569	−	0.720391i	$-0.256037\pi$
$379$	27.0047	1.38714	0.693569	+	0.720391i	$0.256037\pi$
$380$	−4.67683	−0.239917
$381$	13.1674	0.674587
$382$	14.8961	0.762150
$383$	−22.3458	−1.14182	−0.570908	−	0.821014i	$-0.693409\pi$
$383$	−22.3458	−1.14182	−0.570908	+	0.821014i	$0.693409\pi$
$384$	0.774267	0.0395117
$385$	−0.786639	−0.0400908
$386$	−19.9631	−1.01610
$387$	8.50917	0.432546
$388$	−11.5919	−0.588490
$389$	−5.31295	−0.269377	−0.134689	−	0.990888i	$-0.543003\pi$
$389$	−5.31295	−0.269377	−0.134689	+	0.990888i	$0.543003\pi$
$390$	−3.57044	−0.180796
$391$	−8.54331	−0.432054
$392$	6.97292	0.352186
$393$	−13.4851	−0.680234
$394$	20.2397	1.01966
$395$	0.511630	0.0257429
$396$	11.4758	0.576682
$397$	6.87369	0.344981	0.172490	−	0.985011i	$-0.444819\pi$
$397$	6.87369	0.344981	0.172490	+	0.985011i	$0.444819\pi$
$398$	−5.11050	−0.256166
$399$	0.595851	0.0298299
$400$	1.00000	0.0500000
$401$	14.3004	0.714128	0.357064	−	0.934080i	$-0.383778\pi$
$401$	14.3004	0.714128	0.357064	+	0.934080i	$0.383778\pi$
$402$	−0.713547	−0.0355885
$403$	−5.92706	−0.295248
$404$	−10.0815	−0.501572
$405$	−3.96398	−0.196972
$406$	0.494391	0.0245362
$407$	−30.1094	−1.49247
$408$	−5.73862	−0.284104
$409$	35.1127	1.73621	0.868105	−	0.496380i	$-0.165338\pi$
$409$	35.1127	1.73621	0.868105	+	0.496380i	$0.165338\pi$
$410$	7.60067	0.375371
$411$	12.9109	0.636849
$412$	10.8564	0.534857
$413$	0.405965	0.0199763
$414$	2.76702	0.135992
$415$	−1.46299	−0.0718154
$416$	−4.61137	−0.226091
$417$	−7.96705	−0.390148
$418$	22.3580	1.09356
$419$	−8.79841	−0.429831	−0.214915	−	0.976633i	$-0.568948\pi$
$419$	−8.79841	−0.429831	−0.214915	+	0.976633i	$0.568948\pi$
$420$	−0.127405	−0.00621672
$421$	−24.8368	−1.21047	−0.605235	−	0.796047i	$-0.706921\pi$
$421$	−24.8368	−1.21047	−0.605235	+	0.796047i	$0.706921\pi$
$422$	−2.59733	−0.126436
$423$	−7.21137	−0.350629
$424$	−4.36922	−0.212188
$425$	−7.41168	−0.359519
$426$	−3.23568	−0.156769
$427$	−1.96778	−0.0952275
$428$	−7.13914	−0.345083
$429$	17.0688	0.824087
$430$	−3.54474	−0.170942
$431$	−7.45585	−0.359136	−0.179568	−	0.983746i	$-0.557470\pi$
$431$	−7.45585	−0.359136	−0.179568	+	0.983746i	$0.557470\pi$
$432$	4.18144	0.201180
$433$	26.3699	1.26726	0.633629	−	0.773637i	$-0.281564\pi$
$433$	26.3699	1.26726	0.633629	+	0.773637i	$0.281564\pi$
$434$	−0.211497	−0.0101522
$435$	2.32631	0.111538
$436$	−11.4216	−0.546997
$437$	5.39090	0.257882
$438$	10.4299	0.498360
$439$	−0.991460	−0.0473198	−0.0236599	−	0.999720i	$-0.507532\pi$
$439$	−0.991460	−0.0473198	−0.0236599	+	0.999720i	$0.507532\pi$
$440$	−4.78058	−0.227905
$441$	16.7386	0.797075
$442$	34.1780	1.62568
$443$	2.91008	0.138262	0.0691311	−	0.997608i	$-0.477977\pi$
$443$	2.91008	0.138262	0.0691311	+	0.997608i	$0.477977\pi$
$444$	−4.87654	−0.231430
$445$	4.96160	0.235202
$446$	0.142452	0.00674528
$447$	−17.5838	−0.831687
$448$	−0.164549	−0.00777420
$449$	−31.7499	−1.49837	−0.749184	−	0.662361i	$-0.769554\pi$
$449$	−31.7499	−1.49837	−0.749184	+	0.662361i	$0.769554\pi$
$450$	2.40051	0.113161
$451$	−36.3356	−1.71098
$452$	−16.4516	−0.773817
$453$	−3.71576	−0.174582
$454$	−17.4219	−0.817652
$455$	0.758796	0.0355729
$456$	3.62112	0.169574
$457$	−3.29008	−0.153903	−0.0769517	−	0.997035i	$-0.524519\pi$
$457$	−3.29008	−0.153903	−0.0769517	+	0.997035i	$0.524519\pi$
$458$	21.1431	0.987951
$459$	−30.9915	−1.44656
$460$	−1.15268	−0.0537440
$461$	16.7443	0.779858	0.389929	−	0.920845i	$-0.372500\pi$
$461$	16.7443	0.779858	0.389929	+	0.920845i	$0.372500\pi$
$462$	0.609069	0.0283364
$463$	−35.7570	−1.66177	−0.830883	−	0.556447i	$-0.812164\pi$
$463$	−35.7570	−1.66177	−0.830883	+	0.556447i	$0.812164\pi$
$464$	3.00453	0.139482
$465$	−0.995176	−0.0461502
$466$	19.7871	0.916621
$467$	−8.66827	−0.401120	−0.200560	−	0.979681i	$-0.564276\pi$
$467$	−8.66827	−0.401120	−0.200560	+	0.979681i	$0.564276\pi$
$468$	−11.0697	−0.511695
$469$	0.151644	0.00700229
$470$	3.00410	0.138569
$471$	1.32825	0.0612024
$472$	2.46714	0.113559
$473$	16.9459	0.779173
$474$	−0.396138	−0.0181952
$475$	4.67683	0.214588
$476$	1.21958	0.0558995
$477$	−10.4884	−0.480229
$478$	24.4688	1.11918
$479$	−9.22950	−0.421706	−0.210853	−	0.977518i	$-0.567624\pi$
$479$	−9.22950	−0.421706	−0.210853	+	0.977518i	$0.567624\pi$
$480$	−0.774267	−0.0353403
$481$	29.0437	1.32428
$482$	2.76820	0.126088
$483$	0.146857	0.00668223
$484$	11.8539	0.538815
$485$	11.5919	0.526361
$486$	15.6135	0.708243
$487$	−4.10840	−0.186169	−0.0930847	−	0.995658i	$-0.529673\pi$
$487$	−4.10840	−0.186169	−0.0930847	+	0.995658i	$0.529673\pi$
$488$	−11.9586	−0.541342
$489$	7.41061	0.335120
$490$	−6.97292	−0.315005
$491$	−36.7664	−1.65925	−0.829623	−	0.558324i	$-0.811445\pi$
$491$	−36.7664	−1.65925	−0.829623	+	0.558324i	$0.811445\pi$
$492$	−5.88495	−0.265314
$493$	−22.2686	−1.00293
$494$	−21.5666	−0.970329
$495$	−11.4758	−0.515800
$496$	−1.28531	−0.0577123
$497$	0.687653	0.0308455
$498$	1.13275	0.0507596
$499$	−23.6466	−1.05857	−0.529283	−	0.848445i	$-0.677539\pi$
$499$	−23.6466	−1.05857	−0.529283	+	0.848445i	$0.677539\pi$
$500$	−1.00000	−0.0447214
$501$	13.7606	0.614777
$502$	−26.3984	−1.17822
$503$	−16.4459	−0.733288	−0.366644	−	0.930361i	$-0.619493\pi$
$503$	−16.4459	−0.733288	−0.366644	+	0.930361i	$0.619493\pi$
$504$	−0.395001	−0.0175948
$505$	10.0815	0.448620
$506$	5.51048	0.244971
$507$	−6.39914	−0.284196
$508$	−17.0063	−0.754533
$509$	19.1060	0.846859	0.423430	−	0.905929i	$-0.360826\pi$
$509$	19.1060	0.846859	0.423430	+	0.905929i	$0.360826\pi$
$510$	5.73862	0.254111
$511$	−2.21658	−0.0980559
$512$	−1.00000	−0.0441942
$513$	19.5559	0.863414
$514$	−23.1405	−1.02069
$515$	−10.8564	−0.478391
$516$	2.74457	0.120823
$517$	−14.3613	−0.631610
$518$	1.03637	0.0455356
$519$	−4.96514	−0.217945
$520$	4.61137	0.202222
$521$	−3.74146	−0.163916	−0.0819581	−	0.996636i	$-0.526117\pi$
$521$	−3.74146	−0.163916	−0.0819581	+	0.996636i	$0.526117\pi$
$522$	7.21240	0.315678
$523$	−11.8797	−0.519464	−0.259732	−	0.965681i	$-0.583634\pi$
$523$	−11.8797	−0.519464	−0.259732	+	0.965681i	$0.583634\pi$
$524$	17.4166	0.760848
$525$	0.127405	0.00556040
$526$	−14.0399	−0.612168
$527$	9.52634	0.414974
$528$	3.70145	0.161085
$529$	−21.6713	−0.942232
$530$	4.36922	0.189787
$531$	5.92240	0.257010
$532$	−0.769568	−0.0333650
$533$	35.0496	1.51816
$534$	−3.84160	−0.166242
$535$	7.13914	0.308652
$536$	0.921577	0.0398060
$537$	−1.52476	−0.0657983
$538$	−22.8151	−0.983628
$539$	33.3346	1.43582
$540$	−4.18144	−0.179940
$541$	7.25392	0.311870	0.155935	−	0.987767i	$-0.450161\pi$
$541$	7.25392	0.311870	0.155935	+	0.987767i	$0.450161\pi$
$542$	17.2988	0.743049
$543$	7.63833	0.327792
$544$	7.41168	0.317773
$545$	11.4216	0.489249
$546$	−0.587511	−0.0251432
$547$	−43.4980	−1.85984	−0.929919	−	0.367764i	$-0.880123\pi$
$547$	−43.4980	−1.85984	−0.929919	+	0.367764i	$0.880123\pi$
$548$	−16.6750	−0.712322
$549$	−28.7068	−1.22518
$550$	4.78058	0.203845
$551$	14.0517	0.598621
$552$	0.892483	0.0379866
$553$	0.0841881	0.00358004
$554$	−1.81940	−0.0772990
$555$	4.87654	0.206998
$556$	10.2898	0.436384
$557$	−26.8322	−1.13692	−0.568459	−	0.822711i	$-0.692460\pi$
$557$	−26.8322	−1.13692	−0.568459	+	0.822711i	$0.692460\pi$
$558$	−3.08541	−0.130616
$559$	−16.3461	−0.691366
$560$	0.164549	0.00695346
$561$	−27.4339	−1.15826
$562$	−30.9714	−1.30645
$563$	0.259526	0.0109377	0.00546886	−	0.999985i	$-0.498259\pi$
$563$	0.259526	0.0109377	0.00546886	+	0.999985i	$0.498259\pi$
$564$	−2.32597	−0.0979412
$565$	16.4516	0.692123
$566$	27.7266	1.16544
$567$	−0.652268	−0.0273927
$568$	4.17902	0.175348
$569$	18.5226	0.776508	0.388254	−	0.921552i	$-0.373078\pi$
$569$	18.5226	0.776508	0.388254	+	0.921552i	$0.373078\pi$
$570$	−3.62112	−0.151672
$571$	−36.5188	−1.52827	−0.764133	−	0.645059i	$-0.776833\pi$
$571$	−36.5188	−1.52827	−0.764133	+	0.645059i	$0.776833\pi$
$572$	−22.0450	−0.921749
$573$	11.5336	0.481821
$574$	1.25068	0.0522025
$575$	1.15268	0.0480701
$576$	−2.40051	−0.100021
$577$	−34.4326	−1.43345	−0.716725	−	0.697356i	$-0.754360\pi$
$577$	−34.4326	−1.43345	−0.716725	+	0.697356i	$0.754360\pi$
$578$	−37.9331	−1.57781
$579$	−15.4568	−0.642363
$580$	−3.00453	−0.124756
$581$	−0.240734	−0.00998731
$582$	−8.97523	−0.372035
$583$	−20.8874	−0.865068
$584$	−13.4707	−0.557420
$585$	11.0697	0.457674
$586$	13.2546	0.547542
$587$	−15.9194	−0.657066	−0.328533	−	0.944493i	$-0.606554\pi$
$587$	−15.9194	−0.657066	−0.328533	+	0.944493i	$0.606554\pi$
$588$	5.39891	0.222647
$589$	−6.01120	−0.247687
$590$	−2.46714	−0.101571
$591$	15.6709	0.644616
$592$	6.29827	0.258857
$593$	−48.4462	−1.98945	−0.994723	−	0.102598i	$-0.967284\pi$
$593$	−48.4462	−1.98945	−0.994723	+	0.102598i	$0.967284\pi$
$594$	19.9897	0.820187
$595$	−1.21958	−0.0499981
$596$	22.7103	0.930250
$597$	−3.95690	−0.161945
$598$	−5.31544	−0.217365
$599$	12.4560	0.508937	0.254468	−	0.967081i	$-0.418099\pi$
$599$	12.4560	0.508937	0.254468	+	0.967081i	$0.418099\pi$
$600$	0.774267	0.0316093
$601$	−1.00000	−0.0407909
$601$	−1.00000	−0.0407909
$602$	−0.583282	−0.0237728
$603$	2.21225	0.0900900
$604$	4.79907	0.195271
$605$	−11.8539	−0.481931
$606$	−7.80575	−0.317087
$607$	43.9001	1.78185	0.890924	−	0.454152i	$-0.150058\pi$
$607$	43.9001	1.78185	0.890924	+	0.454152i	$0.150058\pi$
$608$	−4.67683	−0.189671
$609$	0.382791	0.0155115
$610$	11.9586	0.484191
$611$	13.8530	0.560433
$612$	17.7918	0.719192
$613$	3.80144	0.153539	0.0767694	−	0.997049i	$-0.475539\pi$
$613$	3.80144	0.153539	0.0767694	+	0.997049i	$0.475539\pi$
$614$	13.4191	0.541552
$615$	5.88495	0.237304
$616$	−0.786639	−0.0316946
$617$	19.8629	0.799649	0.399824	−	0.916592i	$-0.369071\pi$
$617$	19.8629	0.799649	0.399824	+	0.916592i	$0.369071\pi$
$618$	8.40576	0.338129
$619$	28.8323	1.15887	0.579435	−	0.815019i	$-0.303273\pi$
$619$	28.8323	1.15887	0.579435	+	0.815019i	$0.303273\pi$
$620$	1.28531	0.0516194
$621$	4.81986	0.193415
$622$	29.1283	1.16794
$623$	0.816425	0.0327094
$624$	−3.57044	−0.142932
$625$	1.00000	0.0400000
$626$	6.11913	0.244570
$627$	17.3110	0.691337
$628$	−1.71549	−0.0684554
$629$	−46.6808	−1.86128
$630$	0.395001	0.0157372
$631$	−4.76085	−0.189526	−0.0947631	−	0.995500i	$-0.530209\pi$
$631$	−4.76085	−0.189526	−0.0947631	+	0.995500i	$0.530209\pi$
$632$	0.511630	0.0203515
$633$	−2.01103	−0.0799313
$634$	6.16838	0.244978
$635$	17.0063	0.674874
$636$	−3.38294	−0.134142
$637$	−32.1548	−1.27402
$638$	14.3634	0.568651
$639$	10.0318	0.396851
$640$	1.00000	0.0395285
$641$	−31.4069	−1.24050	−0.620248	−	0.784405i	$-0.712968\pi$
$641$	−31.4069	−1.24050	−0.620248	+	0.784405i	$0.712968\pi$
$642$	−5.52760	−0.218157
$643$	−21.2181	−0.836760	−0.418380	−	0.908272i	$-0.637402\pi$
$643$	−21.2181	−0.836760	−0.418380	+	0.908272i	$0.637402\pi$
$644$	−0.189672	−0.00747414
$645$	−2.74457	−0.108067
$646$	34.6632	1.36381
$647$	−16.2275	−0.637969	−0.318985	−	0.947760i	$-0.603342\pi$
$647$	−16.2275	−0.637969	−0.318985	+	0.947760i	$0.603342\pi$
$648$	−3.96398	−0.155720
$649$	11.7944	0.462969
$650$	−4.61137	−0.180873
$651$	−0.163755	−0.00641807
$652$	−9.57113	−0.374834
$653$	−27.5924	−1.07977	−0.539886	−	0.841738i	$-0.681533\pi$
$653$	−27.5924	−1.07977	−0.539886	+	0.841738i	$0.681533\pi$
$654$	−8.84340	−0.345804
$655$	−17.4166	−0.680523
$656$	7.60067	0.296756
$657$	−32.3365	−1.26157
$658$	0.494321	0.0192706
$659$	38.2558	1.49023	0.745117	−	0.666934i	$-0.232394\pi$
$659$	38.2558	1.49023	0.745117	+	0.666934i	$0.232394\pi$
$660$	−3.70145	−0.144079
$661$	−1.66557	−0.0647832	−0.0323916	−	0.999475i	$-0.510312\pi$
$661$	−1.66557	−0.0647832	−0.0323916	+	0.999475i	$0.510312\pi$
$662$	7.14184	0.277576
$663$	26.4629	1.02774
$664$	−1.46299	−0.0567751
$665$	0.769568	0.0298426
$666$	15.1191	0.585851
$667$	3.46326	0.134098
$668$	−17.7724	−0.687633
$669$	0.110296	0.00426427
$670$	−0.921577	−0.0356036
$671$	−57.1692	−2.20699
$672$	−0.127405	−0.00491475
$673$	−16.7514	−0.645720	−0.322860	−	0.946447i	$-0.604644\pi$
$673$	−16.7514	−0.645720	−0.322860	+	0.946447i	$0.604644\pi$
$674$	32.2925	1.24386
$675$	4.18144	0.160944
$676$	8.26477	0.317876
$677$	49.0769	1.88618	0.943090	−	0.332537i	$-0.107905\pi$
$677$	49.0769	1.88618	0.943090	+	0.332537i	$0.107905\pi$
$678$	−12.7379	−0.489197
$679$	1.90743	0.0732006
$680$	−7.41168	−0.284225
$681$	−13.4892	−0.516909
$682$	−6.14454	−0.235287
$683$	−6.32867	−0.242160	−0.121080	−	0.992643i	$-0.538636\pi$
$683$	−6.32867	−0.242160	−0.121080	+	0.992643i	$0.538636\pi$
$684$	−11.2268	−0.429267
$685$	16.6750	0.637120
$686$	−2.29923	−0.0877850
$687$	16.3704	0.624569
$688$	−3.54474	−0.135142
$689$	20.1481	0.767582
$690$	−0.892483	−0.0339763
$691$	−43.6693	−1.66126	−0.830629	−	0.556827i	$-0.812019\pi$
$691$	−43.6693	−1.66126	−0.830629	+	0.556827i	$0.812019\pi$
$692$	6.41269	0.243774
$693$	−1.88833	−0.0717319
$694$	−32.2463	−1.22405
$695$	−10.2898	−0.390314
$696$	2.32631	0.0881784
$697$	−56.3338	−2.13379
$698$	−22.6325	−0.856652
$699$	15.3205	0.579475
$700$	−0.164549	−0.00621936
$701$	37.1000	1.40125	0.700623	−	0.713532i	$-0.252905\pi$
$701$	37.1000	1.40125	0.700623	+	0.713532i	$0.252905\pi$
$702$	−19.2822	−0.727759
$703$	29.4560	1.11095
$704$	−4.78058	−0.180175
$705$	2.32597	0.0876013
$706$	14.8738	0.559784
$707$	1.65889	0.0623892
$708$	1.91023	0.0717907
$709$	24.5204	0.920883	0.460441	−	0.887690i	$-0.347691\pi$
$709$	24.5204	0.920883	0.460441	+	0.887690i	$0.347691\pi$
$710$	−4.17902	−0.156836
$711$	1.22817	0.0460601
$712$	4.96160	0.185944
$713$	−1.48156	−0.0554847
$714$	0.944284	0.0353389
$715$	22.0450	0.824438
$716$	1.96930	0.0735961
$717$	18.9454	0.707529
$718$	−11.5764	−0.432029
$719$	31.3246	1.16821	0.584105	−	0.811678i	$-0.301446\pi$
$719$	31.3246	1.16821	0.584105	+	0.811678i	$0.301446\pi$
$720$	2.40051	0.0894617
$721$	−1.78641	−0.0665294
$722$	−2.87278	−0.106914
$723$	2.14333	0.0797111
$724$	−9.86524	−0.366639
$725$	3.00453	0.111585
$726$	9.17811	0.340632
$727$	−45.1396	−1.67413	−0.837067	−	0.547101i	$-0.815732\pi$
$727$	−45.1396	−1.67413	−0.837067	+	0.547101i	$0.815732\pi$
$728$	0.758796	0.0281229
$729$	0.197079	0.00729921
$730$	13.4707	0.498572
$731$	26.2725	0.971722
$732$	−9.25917	−0.342229
$733$	37.8781	1.39906	0.699529	−	0.714604i	$-0.253393\pi$
$733$	37.8781	1.39906	0.699529	+	0.714604i	$0.253393\pi$
$734$	20.5272	0.757674
$735$	−5.39891	−0.199142
$736$	−1.15268	−0.0424884
$737$	4.40567	0.162285
$738$	18.2455	0.671626
$739$	1.39993	0.0514972	0.0257486	−	0.999668i	$-0.491803\pi$
$739$	1.39993	0.0514972	0.0257486	+	0.999668i	$0.491803\pi$
$740$	−6.29827	−0.231529
$741$	−16.6983	−0.613429
$742$	0.718950	0.0263935
$743$	−8.87420	−0.325563	−0.162781	−	0.986662i	$-0.552047\pi$
$743$	−8.87420	−0.325563	−0.162781	+	0.986662i	$0.552047\pi$
$744$	−0.995176	−0.0364849
$745$	−22.7103	−0.832041
$746$	6.55114	0.239854
$747$	−3.51193	−0.128495
$748$	35.4321	1.29553
$749$	1.17474	0.0429240
$750$	−0.774267	−0.0282722
$751$	−49.5467	−1.80799	−0.903993	−	0.427547i	$-0.859378\pi$
$751$	−49.5467	−1.80799	−0.903993	+	0.427547i	$0.859378\pi$
$752$	3.00410	0.109548
$753$	−20.4395	−0.744855
$754$	−13.8550	−0.504569
$755$	−4.79907	−0.174656
$756$	−0.688051	−0.0250242
$757$	−41.5712	−1.51093	−0.755465	−	0.655189i	$-0.772589\pi$
$757$	−41.5712	−1.51093	−0.755465	+	0.655189i	$0.772589\pi$
$758$	−27.0047	−0.980854
$759$	4.26659	0.154867
$760$	4.67683	0.169647
$761$	−14.2855	−0.517850	−0.258925	−	0.965897i	$-0.583368\pi$
$761$	−14.2855	−0.517850	−0.258925	+	0.965897i	$0.583368\pi$
$762$	−13.1674	−0.477005
$763$	1.87942	0.0680395
$764$	−14.8961	−0.538922
$765$	−17.7918	−0.643265
$766$	22.3458	0.807385
$767$	−11.3769	−0.410797
$768$	−0.774267	−0.0279390
$769$	23.5030	0.847538	0.423769	−	0.905770i	$-0.360707\pi$
$769$	23.5030	0.847538	0.423769	+	0.905770i	$0.360707\pi$
$770$	0.786639	0.0283485
$771$	−17.9170	−0.645264
$772$	19.9631	0.718489
$773$	6.65882	0.239501	0.119751	−	0.992804i	$-0.461791\pi$
$773$	6.65882	0.239501	0.119751	+	0.992804i	$0.461791\pi$
$774$	−8.50917	−0.305856
$775$	−1.28531	−0.0461698
$776$	11.5919	0.416125
$777$	0.802429	0.0287870
$778$	5.31295	0.190479
$779$	35.5471	1.27361
$780$	3.57044	0.127842
$781$	19.9781	0.714874
$782$	8.54331	0.305508
$783$	12.5632	0.448974
$784$	−6.97292	−0.249033
$785$	1.71549	0.0612284
$786$	13.4851	0.480998
$787$	−15.0640	−0.536974	−0.268487	−	0.963283i	$-0.586524\pi$
$787$	−15.0640	−0.536974	−0.268487	+	0.963283i	$0.586524\pi$
$788$	−20.2397	−0.721009
$789$	−10.8706	−0.387004
$790$	−0.511630	−0.0182030
$791$	2.70709	0.0962530
$792$	−11.4758	−0.407776
$793$	55.1457	1.95828
$794$	−6.87369	−0.243938
$795$	3.38294	0.119981
$796$	5.11050	0.181137
$797$	43.0167	1.52373	0.761866	−	0.647735i	$-0.224284\pi$
$797$	43.0167	1.52373	0.761866	+	0.647735i	$0.224284\pi$
$798$	−0.595851	−0.0210929
$799$	−22.2654	−0.787694
$800$	−1.00000	−0.0353553
$801$	11.9104	0.420832
$802$	−14.3004	−0.504965
$803$	−64.3976	−2.27254
$804$	0.713547	0.0251648
$805$	0.189672	0.00668507
$806$	5.92706	0.208772
$807$	−17.6650	−0.621836
$808$	10.0815	0.354665
$809$	4.79410	0.168552	0.0842759	−	0.996442i	$-0.473142\pi$
$809$	4.79410	0.168552	0.0842759	+	0.996442i	$0.473142\pi$
$810$	3.96398	0.139280
$811$	−10.3877	−0.364760	−0.182380	−	0.983228i	$-0.558380\pi$
$811$	−10.3877	−0.364760	−0.182380	+	0.983228i	$0.558380\pi$
$812$	−0.494391	−0.0173497
$813$	13.3939	0.469745
$814$	30.1094	1.05533
$815$	9.57113	0.335262
$816$	5.73862	0.200892
$817$	−16.5781	−0.579996
$818$	−35.1127	−1.22769
$819$	1.82150	0.0636483
$820$	−7.60067	−0.265427
$821$	−9.29883	−0.324531	−0.162266	−	0.986747i	$-0.551880\pi$
$821$	−9.29883	−0.324531	−0.162266	+	0.986747i	$0.551880\pi$
$822$	−12.9109	−0.450320
$823$	−48.3979	−1.68705	−0.843523	−	0.537093i	$-0.819522\pi$
$823$	−48.3979	−1.68705	−0.843523	+	0.537093i	$0.819522\pi$
$824$	−10.8564	−0.378201
$825$	3.70145	0.128868
$826$	−0.405965	−0.0141253
$827$	−37.1246	−1.29095	−0.645474	−	0.763782i	$-0.723340\pi$
$827$	−37.1246	−1.29095	−0.645474	+	0.763782i	$0.723340\pi$
$828$	−2.76702	−0.0961607
$829$	−3.22706	−0.112080	−0.0560402	−	0.998429i	$-0.517848\pi$
$829$	−3.22706	−0.112080	−0.0560402	+	0.998429i	$0.517848\pi$
$830$	1.46299	0.0507812
$831$	−1.40870	−0.0488674
$832$	4.61137	0.159871
$833$	51.6811	1.79064
$834$	7.96705	0.275876
$835$	17.7724	0.615038
$836$	−22.3580	−0.773267
$837$	−5.37446	−0.185768
$838$	8.79841	0.303936
$839$	38.5764	1.33180	0.665902	−	0.746039i	$-0.268047\pi$
$839$	38.5764	1.33180	0.665902	+	0.746039i	$0.268047\pi$
$840$	0.127405	0.00439588
$841$	−19.9728	−0.688718
$842$	24.8368	0.855932
$843$	−23.9801	−0.825920
$844$	2.59733	0.0894039
$845$	−8.26477	−0.284317
$846$	7.21137	0.247932
$847$	−1.95055	−0.0670217
$848$	4.36922	0.150040
$849$	21.4678	0.736773
$850$	7.41168	0.254219
$851$	7.25989	0.248866
$852$	3.23568	0.110853
$853$	−14.0457	−0.480916	−0.240458	−	0.970659i	$-0.577298\pi$
$853$	−14.0457	−0.480916	−0.240458	+	0.970659i	$0.577298\pi$
$854$	1.96778	0.0673360
$855$	11.2268	0.383948
$856$	7.13914	0.244011
$857$	7.91519	0.270378	0.135189	−	0.990820i	$-0.456836\pi$
$857$	7.91519	0.270378	0.135189	+	0.990820i	$0.456836\pi$
$858$	−17.0688	−0.582718
$859$	36.0078	1.22857	0.614285	−	0.789085i	$-0.289445\pi$
$859$	36.0078	1.22857	0.614285	+	0.789085i	$0.289445\pi$
$860$	3.54474	0.120874
$861$	0.968362	0.0330017
$862$	7.45585	0.253947
$863$	−47.4297	−1.61453	−0.807264	−	0.590191i	$-0.799052\pi$
$863$	−47.4297	−1.61453	−0.807264	+	0.590191i	$0.799052\pi$
$864$	−4.18144	−0.142255
$865$	−6.41269	−0.218038
$866$	−26.3699	−0.896087
$867$	−29.3703	−0.997468
$868$	0.211497	0.00717867
$869$	2.44589	0.0829710
$870$	−2.32631	−0.0788692
$871$	−4.24973	−0.143997
$872$	11.4216	0.386786
$873$	27.8265	0.941784
$874$	−5.39090	−0.182350
$875$	0.164549	0.00556277
$876$	−10.4299	−0.352394
$877$	2.70543	0.0913558	0.0456779	−	0.998956i	$-0.485455\pi$
$877$	2.70543	0.0913558	0.0456779	+	0.998956i	$0.485455\pi$
$878$	0.991460	0.0334601
$879$	10.2626	0.346149
$880$	4.78058	0.161153
$881$	19.1469	0.645074	0.322537	−	0.946557i	$-0.395464\pi$
$881$	19.1469	0.645074	0.322537	+	0.946557i	$0.395464\pi$
$882$	−16.7386	−0.563617
$883$	24.2381	0.815677	0.407838	−	0.913054i	$-0.366283\pi$
$883$	24.2381	0.815677	0.407838	+	0.913054i	$0.366283\pi$
$884$	−34.1780	−1.14953
$885$	−1.91023	−0.0642116
$886$	−2.91008	−0.0977661
$887$	−1.57315	−0.0528213	−0.0264106	−	0.999651i	$-0.508408\pi$
$887$	−1.57315	−0.0528213	−0.0264106	+	0.999651i	$0.508408\pi$
$888$	4.87654	0.163646
$889$	2.79837	0.0938542
$890$	−4.96160	−0.166313
$891$	−18.9501	−0.634853
$892$	−0.142452	−0.00476963
$893$	14.0497	0.470154
$894$	17.5838	0.588091
$895$	−1.96930	−0.0658263
$896$	0.164549	0.00549719
$897$	−4.11557	−0.137415
$898$	31.7499	1.05951
$899$	−3.86176	−0.128797
$900$	−2.40051	−0.0800170
$901$	−32.3833	−1.07884
$902$	36.3356	1.20984
$903$	−0.451616	−0.0150288
$904$	16.4516	0.547171
$905$	9.86524	0.327932
$906$	3.71576	0.123448
$907$	48.2608	1.60247	0.801237	−	0.598348i	$-0.204176\pi$
$907$	48.2608	1.60247	0.801237	+	0.598348i	$0.204176\pi$
$908$	17.4219	0.578167
$909$	24.2007	0.802686
$910$	−0.758796	−0.0251539
$911$	8.39894	0.278269	0.139135	−	0.990273i	$-0.455568\pi$
$911$	8.39894	0.278269	0.139135	+	0.990273i	$0.455568\pi$
$912$	−3.62112	−0.119907
$913$	−6.99395	−0.231466
$914$	3.29008	0.108826
$915$	9.25917	0.306099
$916$	−21.1431	−0.698587
$917$	−2.86588	−0.0946398
$918$	30.9915	1.02287
$919$	−58.5880	−1.93264	−0.966320	−	0.257343i	$-0.917153\pi$
$919$	−58.5880	−1.93264	−0.966320	+	0.257343i	$0.917153\pi$
$920$	1.15268	0.0380028
$921$	10.3900	0.342362
$922$	−16.7443	−0.551443
$923$	−19.2710	−0.634314
$924$	−0.609069	−0.0200369
$925$	6.29827	0.207086
$926$	35.7570	1.17505
$927$	−26.0609	−0.855953
$928$	−3.00453	−0.0986284
$929$	40.2963	1.32208	0.661040	−	0.750351i	$-0.270115\pi$
$929$	40.2963	1.32208	0.661040	+	0.750351i	$0.270115\pi$
$930$	0.995176	0.0326331
$931$	−32.6112	−1.06879
$932$	−19.7871	−0.648149
$933$	22.5531	0.738354
$934$	8.66827	0.283634
$935$	−35.4321	−1.15875
$936$	11.0697	0.361823
$937$	39.3302	1.28486	0.642430	−	0.766344i	$-0.277926\pi$
$937$	39.3302	1.28486	0.642430	+	0.766344i	$0.277926\pi$
$938$	−0.151644	−0.00495136
$939$	4.73784	0.154614
$940$	−3.00410	−0.0979828
$941$	−10.7647	−0.350919	−0.175459	−	0.984487i	$-0.556141\pi$
$941$	−10.7647	−0.350919	−0.175459	+	0.984487i	$0.556141\pi$
$942$	−1.32825	−0.0432766
$943$	8.76115	0.285302
$944$	−2.46714	−0.0802986
$945$	0.688051	0.0223823
$946$	−16.9459	−0.550958
$947$	1.46076	0.0474684	0.0237342	−	0.999718i	$-0.492444\pi$
$947$	1.46076	0.0474684	0.0237342	+	0.999718i	$0.492444\pi$
$948$	0.396138	0.0128660
$949$	62.1183	2.01644
$950$	−4.67683	−0.151737
$951$	4.77597	0.154872
$952$	−1.21958	−0.0395269
$953$	34.2141	1.10830	0.554152	−	0.832415i	$-0.313043\pi$
$953$	34.2141	1.10830	0.554152	+	0.832415i	$0.313043\pi$
$954$	10.4884	0.339573
$955$	14.8961	0.482026
$956$	−24.4688	−0.791378
$957$	11.1211	0.359494
$958$	9.22950	0.298191
$959$	2.74386	0.0886037
$960$	0.774267	0.0249894
$961$	−29.3480	−0.946709
$962$	−29.0437	−0.936405
$963$	17.1376	0.552251
$964$	−2.76820	−0.0891577
$965$	−19.9631	−0.642636
$966$	−0.146857	−0.00472505
$967$	44.2393	1.42264	0.711320	−	0.702868i	$-0.248098\pi$
$967$	44.2393	1.42264	0.711320	+	0.702868i	$0.248098\pi$
$968$	−11.8539	−0.381000
$969$	26.8386	0.862180
$970$	−11.5919	−0.372194
$971$	1.61985	0.0519835	0.0259917	−	0.999662i	$-0.491726\pi$
$971$	1.61985	0.0519835	0.0259917	+	0.999662i	$0.491726\pi$
$972$	−15.6135	−0.500803
$973$	−1.69317	−0.0542806
$974$	4.10840	0.131642
$975$	−3.57044	−0.114345
$976$	11.9586	0.382786
$977$	−32.5759	−1.04220	−0.521098	−	0.853497i	$-0.674477\pi$
$977$	−32.5759	−1.04220	−0.521098	+	0.853497i	$0.674477\pi$
$978$	−7.41061	−0.236965
$979$	23.7193	0.758072
$980$	6.97292	0.222742
$981$	27.4178	0.875382
$982$	36.7664	1.17326
$983$	48.2197	1.53797	0.768984	−	0.639268i	$-0.220762\pi$
$983$	48.2197	1.53797	0.768984	+	0.639268i	$0.220762\pi$
$984$	5.88495	0.187605
$985$	20.2397	0.644890
$986$	22.2686	0.709177
$987$	0.382736	0.0121826
$988$	21.5666	0.686126
$989$	−4.08595	−0.129926
$990$	11.4758	0.364726
$991$	56.4236	1.79235	0.896177	−	0.443697i	$-0.146333\pi$
$991$	56.4236	1.79235	0.896177	+	0.443697i	$0.146333\pi$
$992$	1.28531	0.0408087
$993$	5.52970	0.175480
$994$	−0.687653	−0.0218110
$995$	−5.11050	−0.162014
$996$	−1.13275	−0.0358925
$997$	−5.04046	−0.159633	−0.0798165	−	0.996810i	$-0.525433\pi$
$997$	−5.04046	−0.159633	−0.0798165	+	0.996810i	$0.525433\pi$
$998$	23.6466	0.748519
$999$	26.3358	0.833228

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.i.1.14	✓	29

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.i.1.14	✓	29	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:	\( N \)	\(=\)	\( 6010 = 2 \cdot 5 \cdot 601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6010.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.774267 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.774267 q^{6} -0.164549 q^{7} -1.00000 q^{8} -2.40051 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.774267 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.774267 q^{6} -0.164549 q^{7} -1.00000 q^{8} -2.40051 q^{9} +1.00000 q^{10} -4.78058 q^{11} -0.774267 q^{12} +4.61137 q^{13} +0.164549 q^{14} +0.774267 q^{15} +1.00000 q^{16} -7.41168 q^{17} +2.40051 q^{18} +4.67683 q^{19} -1.00000 q^{20} +0.127405 q^{21} +4.78058 q^{22} +1.15268 q^{23} +0.774267 q^{24} +1.00000 q^{25} -4.61137 q^{26} +4.18144 q^{27} -0.164549 q^{28} +3.00453 q^{29} -0.774267 q^{30} -1.28531 q^{31} -1.00000 q^{32} +3.70145 q^{33} +7.41168 q^{34} +0.164549 q^{35} -2.40051 q^{36} +6.29827 q^{37} -4.67683 q^{38} -3.57044 q^{39} +1.00000 q^{40} +7.60067 q^{41} -0.127405 q^{42} -3.54474 q^{43} -4.78058 q^{44} +2.40051 q^{45} -1.15268 q^{46} +3.00410 q^{47} -0.774267 q^{48} -6.97292 q^{49} -1.00000 q^{50} +5.73862 q^{51} +4.61137 q^{52} +4.36922 q^{53} -4.18144 q^{54} +4.78058 q^{55} +0.164549 q^{56} -3.62112 q^{57} -3.00453 q^{58} -2.46714 q^{59} +0.774267 q^{60} +11.9586 q^{61} +1.28531 q^{62} +0.395001 q^{63} +1.00000 q^{64} -4.61137 q^{65} -3.70145 q^{66} -0.921577 q^{67} -7.41168 q^{68} -0.892483 q^{69} -0.164549 q^{70} -4.17902 q^{71} +2.40051 q^{72} +13.4707 q^{73} -6.29827 q^{74} -0.774267 q^{75} +4.67683 q^{76} +0.786639 q^{77} +3.57044 q^{78} -0.511630 q^{79} -1.00000 q^{80} +3.96398 q^{81} -7.60067 q^{82} +1.46299 q^{83} +0.127405 q^{84} +7.41168 q^{85} +3.54474 q^{86} -2.32631 q^{87} +4.78058 q^{88} -4.96160 q^{89} -2.40051 q^{90} -0.758796 q^{91} +1.15268 q^{92} +0.995176 q^{93} -3.00410 q^{94} -4.67683 q^{95} +0.774267 q^{96} -11.5919 q^{97} +6.97292 q^{98} +11.4758 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 29 q - 29 q^{2} - 10 q^{3} + 29 q^{4} - 29 q^{5} + 10 q^{6} - 29 q^{8} + 29 q^{9}+O(q^{10}) \) 29 * q - 29 * q^2 - 10 * q^3 + 29 * q^4 - 29 * q^5 + 10 * q^6 - 29 * q^8 + 29 * q^9	\( 29 q - 29 q^{2} - 10 q^{3} + 29 q^{4} - 29 q^{5} + 10 q^{6} - 29 q^{8} + 29 q^{9} + 29 q^{10} - 10 q^{12} - 4 q^{13} + 10 q^{15} + 29 q^{16} - 23 q^{17} - 29 q^{18} + q^{19} - 29 q^{20} + 2 q^{21} - 9 q^{23} + 10 q^{24} + 29 q^{25} + 4 q^{26} - 43 q^{27} - 5 q^{29} - 10 q^{30} + 21 q^{31} - 29 q^{32} - 19 q^{33} + 23 q^{34} + 29 q^{36} - 6 q^{37} - q^{38} + 18 q^{39} + 29 q^{40} - 17 q^{41} - 2 q^{42} - 19 q^{43} - 29 q^{45} + 9 q^{46} - 21 q^{47} - 10 q^{48} + 45 q^{49} - 29 q^{50} + 11 q^{51} - 4 q^{52} - 53 q^{53} + 43 q^{54} - 16 q^{57} + 5 q^{58} - 30 q^{59} + 10 q^{60} + 16 q^{61} - 21 q^{62} - 17 q^{63} + 29 q^{64} + 4 q^{65} + 19 q^{66} - 35 q^{67} - 23 q^{68} + 13 q^{69} + 2 q^{71} - 29 q^{72} - q^{73} + 6 q^{74} - 10 q^{75} + q^{76} - 50 q^{77} - 18 q^{78} + 26 q^{79} - 29 q^{80} + 33 q^{81} + 17 q^{82} - 54 q^{83} + 2 q^{84} + 23 q^{85} + 19 q^{86} - 56 q^{87} - 2 q^{89} + 29 q^{90} + 27 q^{91} - 9 q^{92} - 26 q^{93} + 21 q^{94} - q^{95} + 10 q^{96} + 15 q^{97} - 45 q^{98} + 27 q^{99}+O(q^{100}) \) 29 * q - 29 * q^2 - 10 * q^3 + 29 * q^4 - 29 * q^5 + 10 * q^6 - 29 * q^8 + 29 * q^9 + 29 * q^10 - 10 * q^12 - 4 * q^13 + 10 * q^15 + 29 * q^16 - 23 * q^17 - 29 * q^18 + q^19 - 29 * q^20 + 2 * q^21 - 9 * q^23 + 10 * q^24 + 29 * q^25 + 4 * q^26 - 43 * q^27 - 5 * q^29 - 10 * q^30 + 21 * q^31 - 29 * q^32 - 19 * q^33 + 23 * q^34 + 29 * q^36 - 6 * q^37 - q^38 + 18 * q^39 + 29 * q^40 - 17 * q^41 - 2 * q^42 - 19 * q^43 - 29 * q^45 + 9 * q^46 - 21 * q^47 - 10 * q^48 + 45 * q^49 - 29 * q^50 + 11 * q^51 - 4 * q^52 - 53 * q^53 + 43 * q^54 - 16 * q^57 + 5 * q^58 - 30 * q^59 + 10 * q^60 + 16 * q^61 - 21 * q^62 - 17 * q^63 + 29 * q^64 + 4 * q^65 + 19 * q^66 - 35 * q^67 - 23 * q^68 + 13 * q^69 + 2 * q^71 - 29 * q^72 - q^73 + 6 * q^74 - 10 * q^75 + q^76 - 50 * q^77 - 18 * q^78 + 26 * q^79 - 29 * q^80 + 33 * q^81 + 17 * q^82 - 54 * q^83 + 2 * q^84 + 23 * q^85 + 19 * q^86 - 56 * q^87 - 2 * q^89 + 29 * q^90 + 27 * q^91 - 9 * q^92 - 26 * q^93 + 21 * q^94 - q^95 + 10 * q^96 + 15 * q^97 - 45 * q^98 + 27 * q^99

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