LMFDB - Embedded newform 6042.2.a.o.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6042,2,Mod(1,6042)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6042, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6042.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6042 = 2 \cdot 3 \cdot 19 \cdot 53 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6042.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:	$48.2456129013$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{33}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 8 $ x^2 - x - 8
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$3.37228$ of defining polynomial
Character	$\chi$	$=$	6042.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.37228 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.37228 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -4.37228 q^{10} -4.00000 q^{11} -1.00000 q^{12} +1.37228 q^{13} +1.00000 q^{14} +4.37228 q^{15} +1.00000 q^{16} +0.627719 q^{17} +1.00000 q^{18} +1.00000 q^{19} -4.37228 q^{20} -1.00000 q^{21} -4.00000 q^{22} +4.37228 q^{23} -1.00000 q^{24} +14.1168 q^{25} +1.37228 q^{26} -1.00000 q^{27} +1.00000 q^{28} +1.74456 q^{29} +4.37228 q^{30} -7.00000 q^{31} +1.00000 q^{32} +4.00000 q^{33} +0.627719 q^{34} -4.37228 q^{35} +1.00000 q^{36} +7.37228 q^{37} +1.00000 q^{38} -1.37228 q^{39} -4.37228 q^{40} -6.00000 q^{41} -1.00000 q^{42} +10.3723 q^{43} -4.00000 q^{44} -4.37228 q^{45} +4.37228 q^{46} -10.1168 q^{47} -1.00000 q^{48} -6.00000 q^{49} +14.1168 q^{50} -0.627719 q^{51} +1.37228 q^{52} -1.00000 q^{53} -1.00000 q^{54} +17.4891 q^{55} +1.00000 q^{56} -1.00000 q^{57} +1.74456 q^{58} +13.7446 q^{59} +4.37228 q^{60} -5.37228 q^{61} -7.00000 q^{62} +1.00000 q^{63} +1.00000 q^{64} -6.00000 q^{65} +4.00000 q^{66} +2.37228 q^{67} +0.627719 q^{68} -4.37228 q^{69} -4.37228 q^{70} -6.62772 q^{71} +1.00000 q^{72} +4.00000 q^{73} +7.37228 q^{74} -14.1168 q^{75} +1.00000 q^{76} -4.00000 q^{77} -1.37228 q^{78} -8.00000 q^{79} -4.37228 q^{80} +1.00000 q^{81} -6.00000 q^{82} +15.3723 q^{83} -1.00000 q^{84} -2.74456 q^{85} +10.3723 q^{86} -1.74456 q^{87} -4.00000 q^{88} -7.62772 q^{89} -4.37228 q^{90} +1.37228 q^{91} +4.37228 q^{92} +7.00000 q^{93} -10.1168 q^{94} -4.37228 q^{95} -1.00000 q^{96} -14.0000 q^{97} -6.00000 q^{98} -4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 3 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 3 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 3 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9} - 3 q^{10} - 8 q^{11} - 2 q^{12} - 3 q^{13} + 2 q^{14} + 3 q^{15} + 2 q^{16} + 7 q^{17} + 2 q^{18} + 2 q^{19} - 3 q^{20} - 2 q^{21} - 8 q^{22} + 3 q^{23} - 2 q^{24} + 11 q^{25} - 3 q^{26} - 2 q^{27} + 2 q^{28} - 8 q^{29} + 3 q^{30} - 14 q^{31} + 2 q^{32} + 8 q^{33} + 7 q^{34} - 3 q^{35} + 2 q^{36} + 9 q^{37} + 2 q^{38} + 3 q^{39} - 3 q^{40} - 12 q^{41} - 2 q^{42} + 15 q^{43} - 8 q^{44} - 3 q^{45} + 3 q^{46} - 3 q^{47} - 2 q^{48} - 12 q^{49} + 11 q^{50} - 7 q^{51} - 3 q^{52} - 2 q^{53} - 2 q^{54} + 12 q^{55} + 2 q^{56} - 2 q^{57} - 8 q^{58} + 16 q^{59} + 3 q^{60} - 5 q^{61} - 14 q^{62} + 2 q^{63} + 2 q^{64} - 12 q^{65} + 8 q^{66} - q^{67} + 7 q^{68} - 3 q^{69} - 3 q^{70} - 19 q^{71} + 2 q^{72} + 8 q^{73} + 9 q^{74} - 11 q^{75} + 2 q^{76} - 8 q^{77} + 3 q^{78} - 16 q^{79} - 3 q^{80} + 2 q^{81} - 12 q^{82} + 25 q^{83} - 2 q^{84} + 6 q^{85} + 15 q^{86} + 8 q^{87} - 8 q^{88} - 21 q^{89} - 3 q^{90} - 3 q^{91} + 3 q^{92} + 14 q^{93} - 3 q^{94} - 3 q^{95} - 2 q^{96} - 28 q^{97} - 12 q^{98} - 8 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 3 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 + 2 * q^9 - 3 * q^10 - 8 * q^11 - 2 * q^12 - 3 * q^13 + 2 * q^14 + 3 * q^15 + 2 * q^16 + 7 * q^17 + 2 * q^18 + 2 * q^19 - 3 * q^20 - 2 * q^21 - 8 * q^22 + 3 * q^23 - 2 * q^24 + 11 * q^25 - 3 * q^26 - 2 * q^27 + 2 * q^28 - 8 * q^29 + 3 * q^30 - 14 * q^31 + 2 * q^32 + 8 * q^33 + 7 * q^34 - 3 * q^35 + 2 * q^36 + 9 * q^37 + 2 * q^38 + 3 * q^39 - 3 * q^40 - 12 * q^41 - 2 * q^42 + 15 * q^43 - 8 * q^44 - 3 * q^45 + 3 * q^46 - 3 * q^47 - 2 * q^48 - 12 * q^49 + 11 * q^50 - 7 * q^51 - 3 * q^52 - 2 * q^53 - 2 * q^54 + 12 * q^55 + 2 * q^56 - 2 * q^57 - 8 * q^58 + 16 * q^59 + 3 * q^60 - 5 * q^61 - 14 * q^62 + 2 * q^63 + 2 * q^64 - 12 * q^65 + 8 * q^66 - q^67 + 7 * q^68 - 3 * q^69 - 3 * q^70 - 19 * q^71 + 2 * q^72 + 8 * q^73 + 9 * q^74 - 11 * q^75 + 2 * q^76 - 8 * q^77 + 3 * q^78 - 16 * q^79 - 3 * q^80 + 2 * q^81 - 12 * q^82 + 25 * q^83 - 2 * q^84 + 6 * q^85 + 15 * q^86 + 8 * q^87 - 8 * q^88 - 21 * q^89 - 3 * q^90 - 3 * q^91 + 3 * q^92 + 14 * q^93 - 3 * q^94 - 3 * q^95 - 2 * q^96 - 28 * q^97 - 12 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−4.37228	−1.95534	−0.977672	−	0.210138i	$-0.932609\pi$
$5$	−4.37228	−1.95534	−0.977672	+	0.210138i	$0.932609\pi$
$6$	−1.00000	−0.408248
$7$	1.00000	0.377964	0.188982	−	0.981981i	$-0.439481\pi$
$7$	1.00000	0.377964	0.188982	+	0.981981i	$0.439481\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−4.37228	−1.38264
$11$	−4.00000	−1.20605	−0.603023	−	0.797724i	$-0.706037\pi$
$11$	−4.00000	−1.20605	−0.603023	+	0.797724i	$0.706037\pi$
$12$	−1.00000	−0.288675
$13$	1.37228	0.380602	0.190301	−	0.981726i	$-0.439054\pi$
$13$	1.37228	0.380602	0.190301	+	0.981726i	$0.439054\pi$
$14$	1.00000	0.267261
$15$	4.37228	1.12892
$16$	1.00000	0.250000
$17$	0.627719	0.152244	0.0761221	−	0.997099i	$-0.475746\pi$
$17$	0.627719	0.152244	0.0761221	+	0.997099i	$0.475746\pi$
$18$	1.00000	0.235702
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−4.37228	−0.977672
$21$	−1.00000	−0.218218
$22$	−4.00000	−0.852803
$23$	4.37228	0.911684	0.455842	−	0.890061i	$-0.349338\pi$
$23$	4.37228	0.911684	0.455842	+	0.890061i	$0.349338\pi$
$24$	−1.00000	−0.204124
$25$	14.1168	2.82337
$26$	1.37228	0.269127
$27$	−1.00000	−0.192450
$28$	1.00000	0.188982
$29$	1.74456	0.323957	0.161979	−	0.986794i	$-0.448212\pi$
$29$	1.74456	0.323957	0.161979	+	0.986794i	$0.448212\pi$
$30$	4.37228	0.798266
$31$	−7.00000	−1.25724	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	−7.00000	−1.25724	−0.628619	+	0.777714i	$0.716379\pi$
$32$	1.00000	0.176777
$33$	4.00000	0.696311
$34$	0.627719	0.107653
$35$	−4.37228	−0.739050
$36$	1.00000	0.166667
$37$	7.37228	1.21200	0.605998	−	0.795466i	$-0.292774\pi$
$37$	7.37228	1.21200	0.605998	+	0.795466i	$0.292774\pi$
$38$	1.00000	0.162221
$39$	−1.37228	−0.219741
$40$	−4.37228	−0.691318
$41$	−6.00000	−0.937043	−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000	−0.937043	−0.468521	+	0.883452i	$0.655213\pi$
$42$	−1.00000	−0.154303
$43$	10.3723	1.58176	0.790879	−	0.611973i	$-0.209624\pi$
$43$	10.3723	1.58176	0.790879	+	0.611973i	$0.209624\pi$
$44$	−4.00000	−0.603023
$45$	−4.37228	−0.651781
$46$	4.37228	0.644658
$47$	−10.1168	−1.47569	−0.737847	−	0.674968i	$-0.764157\pi$
$47$	−10.1168	−1.47569	−0.737847	+	0.674968i	$0.764157\pi$
$48$	−1.00000	−0.144338
$49$	−6.00000	−0.857143
$50$	14.1168	1.99642
$51$	−0.627719	−0.0878982
$52$	1.37228	0.190301
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	−1.00000	−0.136083
$55$	17.4891	2.35823
$56$	1.00000	0.133631
$57$	−1.00000	−0.132453
$58$	1.74456	0.229072
$59$	13.7446	1.78939	0.894695	−	0.446678i	$-0.147393\pi$
$59$	13.7446	1.78939	0.894695	+	0.446678i	$0.147393\pi$
$60$	4.37228	0.564459
$61$	−5.37228	−0.687850	−0.343925	−	0.938997i	$-0.611757\pi$
$61$	−5.37228	−0.687850	−0.343925	+	0.938997i	$0.611757\pi$
$62$	−7.00000	−0.889001
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	−6.00000	−0.744208
$66$	4.00000	0.492366
$67$	2.37228	0.289820	0.144910	−	0.989445i	$-0.453711\pi$
$67$	2.37228	0.289820	0.144910	+	0.989445i	$0.453711\pi$
$68$	0.627719	0.0761221
$69$	−4.37228	−0.526361
$70$	−4.37228	−0.522588
$71$	−6.62772	−0.786565	−0.393283	−	0.919418i	$-0.628661\pi$
$71$	−6.62772	−0.786565	−0.393283	+	0.919418i	$0.628661\pi$
$72$	1.00000	0.117851
$73$	4.00000	0.468165	0.234082	−	0.972217i	$-0.424791\pi$
$73$	4.00000	0.468165	0.234082	+	0.972217i	$0.424791\pi$
$74$	7.37228	0.857010
$75$	−14.1168	−1.63007
$76$	1.00000	0.114708
$77$	−4.00000	−0.455842
$78$	−1.37228	−0.155380
$79$	−8.00000	−0.900070	−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000	−0.900070	−0.450035	+	0.893011i	$0.648589\pi$
$80$	−4.37228	−0.488836
$81$	1.00000	0.111111
$82$	−6.00000	−0.662589
$83$	15.3723	1.68733	0.843664	−	0.536872i	$-0.180394\pi$
$83$	15.3723	1.68733	0.843664	+	0.536872i	$0.180394\pi$
$84$	−1.00000	−0.109109
$85$	−2.74456	−0.297690
$86$	10.3723	1.11847
$87$	−1.74456	−0.187037
$88$	−4.00000	−0.426401
$89$	−7.62772	−0.808537	−0.404268	−	0.914640i	$-0.632474\pi$
$89$	−7.62772	−0.808537	−0.404268	+	0.914640i	$0.632474\pi$
$90$	−4.37228	−0.460879
$91$	1.37228	0.143854
$92$	4.37228	0.455842
$93$	7.00000	0.725866
$94$	−10.1168	−1.04347
$95$	−4.37228	−0.448587
$96$	−1.00000	−0.102062
$97$	−14.0000	−1.42148	−0.710742	−	0.703452i	$-0.751641\pi$
$97$	−14.0000	−1.42148	−0.710742	+	0.703452i	$0.751641\pi$
$98$	−6.00000	−0.606092
$99$	−4.00000	−0.402015
$100$	14.1168	1.41168
$101$	−14.4891	−1.44172	−0.720861	−	0.693080i	$-0.756253\pi$
$101$	−14.4891	−1.44172	−0.720861	+	0.693080i	$0.756253\pi$
$102$	−0.627719	−0.0621534
$103$	15.1168	1.48951	0.744753	−	0.667340i	$-0.232567\pi$
$103$	15.1168	1.48951	0.744753	+	0.667340i	$0.232567\pi$
$104$	1.37228	0.134563
$105$	4.37228	0.426691
$106$	−1.00000	−0.0971286
$107$	−0.255437	−0.0246941	−0.0123470	−	0.999924i	$-0.503930\pi$
$107$	−0.255437	−0.0246941	−0.0123470	+	0.999924i	$0.503930\pi$
$108$	−1.00000	−0.0962250
$109$	15.8614	1.51925	0.759624	−	0.650363i	$-0.225383\pi$
$109$	15.8614	1.51925	0.759624	+	0.650363i	$0.225383\pi$
$110$	17.4891	1.66752
$111$	−7.37228	−0.699746
$112$	1.00000	0.0944911
$113$	3.62772	0.341267	0.170634	−	0.985335i	$-0.445419\pi$
$113$	3.62772	0.341267	0.170634	+	0.985335i	$0.445419\pi$
$114$	−1.00000	−0.0936586
$115$	−19.1168	−1.78265
$116$	1.74456	0.161979
$117$	1.37228	0.126867
$118$	13.7446	1.26529
$119$	0.627719	0.0575429
$120$	4.37228	0.399133
$121$	5.00000	0.454545
$122$	−5.37228	−0.486383
$123$	6.00000	0.541002
$124$	−7.00000	−0.628619
$125$	−39.8614	−3.56531
$126$	1.00000	0.0890871
$127$	−21.2337	−1.88419	−0.942093	−	0.335353i	$-0.891144\pi$
$127$	−21.2337	−1.88419	−0.942093	+	0.335353i	$0.891144\pi$
$128$	1.00000	0.0883883
$129$	−10.3723	−0.913228
$130$	−6.00000	−0.526235
$131$	−19.4891	−1.70277	−0.851386	−	0.524539i	$-0.824238\pi$
$131$	−19.4891	−1.70277	−0.851386	+	0.524539i	$0.824238\pi$
$132$	4.00000	0.348155
$133$	1.00000	0.0867110
$134$	2.37228	0.204934
$135$	4.37228	0.376306
$136$	0.627719	0.0538264
$137$	−4.37228	−0.373549	−0.186775	−	0.982403i	$-0.559803\pi$
$137$	−4.37228	−0.373549	−0.186775	+	0.982403i	$0.559803\pi$
$138$	−4.37228	−0.372193
$139$	−12.1168	−1.02774	−0.513869	−	0.857869i	$-0.671788\pi$
$139$	−12.1168	−1.02774	−0.513869	+	0.857869i	$0.671788\pi$
$140$	−4.37228	−0.369525
$141$	10.1168	0.851992
$142$	−6.62772	−0.556186
$143$	−5.48913	−0.459024
$144$	1.00000	0.0833333
$145$	−7.62772	−0.633448
$146$	4.00000	0.331042
$147$	6.00000	0.494872
$148$	7.37228	0.605998
$149$	0	0		−	1.00000i	$-0.5\pi$
$149$	0	0			1.00000i	$0.5\pi$
$150$	−14.1168	−1.15264
$151$	−15.7446	−1.28127	−0.640637	−	0.767844i	$-0.721330\pi$
$151$	−15.7446	−1.28127	−0.640637	+	0.767844i	$0.721330\pi$
$152$	1.00000	0.0811107
$153$	0.627719	0.0507480
$154$	−4.00000	−0.322329
$155$	30.6060	2.45833
$156$	−1.37228	−0.109870
$157$	6.62772	0.528950	0.264475	−	0.964393i	$-0.414801\pi$
$157$	6.62772	0.528950	0.264475	+	0.964393i	$0.414801\pi$
$158$	−8.00000	−0.636446
$159$	1.00000	0.0793052
$160$	−4.37228	−0.345659
$161$	4.37228	0.344584
$162$	1.00000	0.0785674
$163$	5.62772	0.440797	0.220398	−	0.975410i	$-0.429264\pi$
$163$	5.62772	0.440797	0.220398	+	0.975410i	$0.429264\pi$
$164$	−6.00000	−0.468521
$165$	−17.4891	−1.36153
$166$	15.3723	1.19312
$167$	−14.8614	−1.15001	−0.575005	−	0.818150i	$-0.695000\pi$
$167$	−14.8614	−1.15001	−0.575005	+	0.818150i	$0.695000\pi$
$168$	−1.00000	−0.0771517
$169$	−11.1168	−0.855142
$170$	−2.74456	−0.210498
$171$	1.00000	0.0764719
$172$	10.3723	0.790879
$173$	−18.7446	−1.42512	−0.712561	−	0.701610i	$-0.752465\pi$
$173$	−18.7446	−1.42512	−0.712561	+	0.701610i	$0.752465\pi$
$174$	−1.74456	−0.132255
$175$	14.1168	1.06713
$176$	−4.00000	−0.301511
$177$	−13.7446	−1.03310
$178$	−7.62772	−0.571722
$179$	5.48913	0.410276	0.205138	−	0.978733i	$-0.434236\pi$
$179$	5.48913	0.410276	0.205138	+	0.978733i	$0.434236\pi$
$180$	−4.37228	−0.325891
$181$	−24.6060	−1.82895	−0.914474	−	0.404645i	$-0.867395\pi$
$181$	−24.6060	−1.82895	−0.914474	+	0.404645i	$0.867395\pi$
$182$	1.37228	0.101720
$183$	5.37228	0.397130
$184$	4.37228	0.322329
$185$	−32.2337	−2.36987
$186$	7.00000	0.513265
$187$	−2.51087	−0.183613
$188$	−10.1168	−0.737847
$189$	−1.00000	−0.0727393
$190$	−4.37228	−0.317199
$191$	−26.7446	−1.93517	−0.967584	−	0.252548i	$-0.918731\pi$
$191$	−26.7446	−1.93517	−0.967584	+	0.252548i	$0.918731\pi$
$192$	−1.00000	−0.0721688
$193$	6.86141	0.493895	0.246947	−	0.969029i	$-0.420573\pi$
$193$	6.86141	0.493895	0.246947	+	0.969029i	$0.420573\pi$
$194$	−14.0000	−1.00514
$195$	6.00000	0.429669
$196$	−6.00000	−0.428571
$197$	15.4891	1.10355	0.551777	−	0.833992i	$-0.313950\pi$
$197$	15.4891	1.10355	0.551777	+	0.833992i	$0.313950\pi$
$198$	−4.00000	−0.284268
$199$	16.4891	1.16888	0.584442	−	0.811436i	$-0.301314\pi$
$199$	16.4891	1.16888	0.584442	+	0.811436i	$0.301314\pi$
$200$	14.1168	0.998212
$201$	−2.37228	−0.167328
$202$	−14.4891	−1.01945
$203$	1.74456	0.122444
$204$	−0.627719	−0.0439491
$205$	26.2337	1.83224
$206$	15.1168	1.05324
$207$	4.37228	0.303895
$208$	1.37228	0.0951506
$209$	−4.00000	−0.276686
$210$	4.37228	0.301716
$211$	−26.3505	−1.81405	−0.907023	−	0.421082i	$-0.861651\pi$
$211$	−26.3505	−1.81405	−0.907023	+	0.421082i	$0.861651\pi$
$212$	−1.00000	−0.0686803
$213$	6.62772	0.454124
$214$	−0.255437	−0.0174613
$215$	−45.3505	−3.09288
$216$	−1.00000	−0.0680414
$217$	−7.00000	−0.475191
$218$	15.8614	1.07427
$219$	−4.00000	−0.270295
$220$	17.4891	1.17912
$221$	0.861407	0.0579445
$222$	−7.37228	−0.494795
$223$	10.0000	0.669650	0.334825	−	0.942280i	$-0.391323\pi$
$223$	10.0000	0.669650	0.334825	+	0.942280i	$0.391323\pi$
$224$	1.00000	0.0668153
$225$	14.1168	0.941123
$226$	3.62772	0.241312
$227$	1.62772	0.108035	0.0540177	−	0.998540i	$-0.482797\pi$
$227$	1.62772	0.108035	0.0540177	+	0.998540i	$0.482797\pi$
$228$	−1.00000	−0.0662266
$229$	20.6060	1.36168	0.680840	−	0.732432i	$-0.261615\pi$
$229$	20.6060	1.36168	0.680840	+	0.732432i	$0.261615\pi$
$230$	−19.1168	−1.26053
$231$	4.00000	0.263181
$232$	1.74456	0.114536
$233$	10.0000	0.655122	0.327561	−	0.944830i	$-0.393773\pi$
$233$	10.0000	0.655122	0.327561	+	0.944830i	$0.393773\pi$
$234$	1.37228	0.0897088
$235$	44.2337	2.88549
$236$	13.7446	0.894695
$237$	8.00000	0.519656
$238$	0.627719	0.0406890
$239$	29.7228	1.92261	0.961304	−	0.275488i	$-0.0888395\pi$
$239$	29.7228	1.92261	0.961304	+	0.275488i	$0.0888395\pi$
$240$	4.37228	0.282230
$241$	1.48913	0.0959230	0.0479615	−	0.998849i	$-0.484728\pi$
$241$	1.48913	0.0959230	0.0479615	+	0.998849i	$0.484728\pi$
$242$	5.00000	0.321412
$243$	−1.00000	−0.0641500
$244$	−5.37228	−0.343925
$245$	26.2337	1.67601
$246$	6.00000	0.382546
$247$	1.37228	0.0873162
$248$	−7.00000	−0.444500
$249$	−15.3723	−0.974179
$250$	−39.8614	−2.52106
$251$	−11.6060	−0.732562	−0.366281	−	0.930504i	$-0.619369\pi$
$251$	−11.6060	−0.732562	−0.366281	+	0.930504i	$0.619369\pi$
$252$	1.00000	0.0629941
$253$	−17.4891	−1.09953
$254$	−21.2337	−1.33232
$255$	2.74456	0.171871
$256$	1.00000	0.0625000
$257$	9.37228	0.584627	0.292313	−	0.956323i	$-0.405575\pi$
$257$	9.37228	0.584627	0.292313	+	0.956323i	$0.405575\pi$
$258$	−10.3723	−0.645750
$259$	7.37228	0.458091
$260$	−6.00000	−0.372104
$261$	1.74456	0.107986
$262$	−19.4891	−1.20404
$263$	−22.3723	−1.37953	−0.689767	−	0.724031i	$-0.742287\pi$
$263$	−22.3723	−1.37953	−0.689767	+	0.724031i	$0.742287\pi$
$264$	4.00000	0.246183
$265$	4.37228	0.268587
$266$	1.00000	0.0613139
$267$	7.62772	0.466809
$268$	2.37228	0.144910
$269$	−19.6277	−1.19672	−0.598362	−	0.801226i	$-0.704181\pi$
$269$	−19.6277	−1.19672	−0.598362	+	0.801226i	$0.704181\pi$
$270$	4.37228	0.266089
$271$	23.1168	1.40425	0.702124	−	0.712055i	$-0.252235\pi$
$271$	23.1168	1.40425	0.702124	+	0.712055i	$0.252235\pi$
$272$	0.627719	0.0380610
$273$	−1.37228	−0.0830542
$274$	−4.37228	−0.264139
$275$	−56.4674	−3.40511
$276$	−4.37228	−0.263180
$277$	−15.4891	−0.930651	−0.465326	−	0.885140i	$-0.654063\pi$
$277$	−15.4891	−0.930651	−0.465326	+	0.885140i	$0.654063\pi$
$278$	−12.1168	−0.726720
$279$	−7.00000	−0.419079
$280$	−4.37228	−0.261294
$281$	−13.8614	−0.826902	−0.413451	−	0.910526i	$-0.635677\pi$
$281$	−13.8614	−0.826902	−0.413451	+	0.910526i	$0.635677\pi$
$282$	10.1168	0.602449
$283$	8.62772	0.512865	0.256432	−	0.966562i	$-0.417453\pi$
$283$	8.62772	0.512865	0.256432	+	0.966562i	$0.417453\pi$
$284$	−6.62772	−0.393283
$285$	4.37228	0.258992
$286$	−5.48913	−0.324579
$287$	−6.00000	−0.354169
$288$	1.00000	0.0589256
$289$	−16.6060	−0.976822
$290$	−7.62772	−0.447915
$291$	14.0000	0.820695
$292$	4.00000	0.234082
$293$	−28.1168	−1.64260	−0.821302	−	0.570494i	$-0.806752\pi$
$293$	−28.1168	−1.64260	−0.821302	+	0.570494i	$0.806752\pi$
$294$	6.00000	0.349927
$295$	−60.0951	−3.49887
$296$	7.37228	0.428505
$297$	4.00000	0.232104
$298$	0	0
$299$	6.00000	0.346989
$300$	−14.1168	−0.815036
$301$	10.3723	0.597848
$302$	−15.7446	−0.905998
$303$	14.4891	0.832378
$304$	1.00000	0.0573539
$305$	23.4891	1.34498
$306$	0.627719	0.0358843
$307$	11.8832	0.678208	0.339104	−	0.940749i	$-0.389876\pi$
$307$	11.8832	0.678208	0.339104	+	0.940749i	$0.389876\pi$
$308$	−4.00000	−0.227921
$309$	−15.1168	−0.859967
$310$	30.6060	1.73830
$311$	24.3505	1.38079	0.690396	−	0.723432i	$-0.257436\pi$
$311$	24.3505	1.38079	0.690396	+	0.723432i	$0.257436\pi$
$312$	−1.37228	−0.0776901
$313$	−11.2554	−0.636195	−0.318097	−	0.948058i	$-0.603044\pi$
$313$	−11.2554	−0.636195	−0.318097	+	0.948058i	$0.603044\pi$
$314$	6.62772	0.374024
$315$	−4.37228	−0.246350
$316$	−8.00000	−0.450035
$317$	14.0000	0.786318	0.393159	−	0.919470i	$-0.371382\pi$
$317$	14.0000	0.786318	0.393159	+	0.919470i	$0.371382\pi$
$318$	1.00000	0.0560772
$319$	−6.97825	−0.390707
$320$	−4.37228	−0.244418
$321$	0.255437	0.0142571
$322$	4.37228	0.243658
$323$	0.627719	0.0349272
$324$	1.00000	0.0555556
$325$	19.3723	1.07458
$326$	5.62772	0.311691
$327$	−15.8614	−0.877138
$328$	−6.00000	−0.331295
$329$	−10.1168	−0.557760
$330$	−17.4891	−0.962745
$331$	−35.7228	−1.96350	−0.981752	−	0.190167i	$-0.939097\pi$
$331$	−35.7228	−1.96350	−0.981752	+	0.190167i	$0.939097\pi$
$332$	15.3723	0.843664
$333$	7.37228	0.403999
$334$	−14.8614	−0.813180
$335$	−10.3723	−0.566698
$336$	−1.00000	−0.0545545
$337$	20.4891	1.11611	0.558057	−	0.829803i	$-0.311547\pi$
$337$	20.4891	1.11611	0.558057	+	0.829803i	$0.311547\pi$
$338$	−11.1168	−0.604677
$339$	−3.62772	−0.197031
$340$	−2.74456	−0.148845
$341$	28.0000	1.51629
$342$	1.00000	0.0540738
$343$	−13.0000	−0.701934
$344$	10.3723	0.559236
$345$	19.1168	1.02922
$346$	−18.7446	−1.00771
$347$	16.9783	0.911440	0.455720	−	0.890123i	$-0.349382\pi$
$347$	16.9783	0.911440	0.455720	+	0.890123i	$0.349382\pi$
$348$	−1.74456	−0.0935184
$349$	5.60597	0.300081	0.150040	−	0.988680i	$-0.452060\pi$
$349$	5.60597	0.300081	0.150040	+	0.988680i	$0.452060\pi$
$350$	14.1168	0.754577
$351$	−1.37228	−0.0732470
$352$	−4.00000	−0.213201
$353$	−0.510875	−0.0271911	−0.0135956	−	0.999908i	$-0.504328\pi$
$353$	−0.510875	−0.0271911	−0.0135956	+	0.999908i	$0.504328\pi$
$354$	−13.7446	−0.730515
$355$	28.9783	1.53801
$356$	−7.62772	−0.404268
$357$	−0.627719	−0.0332224
$358$	5.48913	0.290109
$359$	−17.8614	−0.942689	−0.471344	−	0.881949i	$-0.656231\pi$
$359$	−17.8614	−0.942689	−0.471344	+	0.881949i	$0.656231\pi$
$360$	−4.37228	−0.230439
$361$	1.00000	0.0526316
$362$	−24.6060	−1.29326
$363$	−5.00000	−0.262432
$364$	1.37228	0.0719271
$365$	−17.4891	−0.915423
$366$	5.37228	0.280814
$367$	−4.62772	−0.241565	−0.120782	−	0.992679i	$-0.538540\pi$
$367$	−4.62772	−0.241565	−0.120782	+	0.992679i	$0.538540\pi$
$368$	4.37228	0.227921
$369$	−6.00000	−0.312348
$370$	−32.2337	−1.67575
$371$	−1.00000	−0.0519174
$372$	7.00000	0.362933
$373$	17.6277	0.912729	0.456364	−	0.889793i	$-0.349151\pi$
$373$	17.6277	0.912729	0.456364	+	0.889793i	$0.349151\pi$
$374$	−2.51087	−0.129834
$375$	39.8614	2.05843
$376$	−10.1168	−0.521736
$377$	2.39403	0.123299
$378$	−1.00000	−0.0514344
$379$	−8.23369	−0.422936	−0.211468	−	0.977385i	$-0.567824\pi$
$379$	−8.23369	−0.422936	−0.211468	+	0.977385i	$0.567824\pi$
$380$	−4.37228	−0.224293
$381$	21.2337	1.08783
$382$	−26.7446	−1.36837
$383$	1.76631	0.0902543	0.0451272	−	0.998981i	$-0.485631\pi$
$383$	1.76631	0.0902543	0.0451272	+	0.998981i	$0.485631\pi$
$384$	−1.00000	−0.0510310
$385$	17.4891	0.891328
$386$	6.86141	0.349236
$387$	10.3723	0.527253
$388$	−14.0000	−0.710742
$389$	−20.2554	−1.02699	−0.513496	−	0.858092i	$-0.671650\pi$
$389$	−20.2554	−1.02699	−0.513496	+	0.858092i	$0.671650\pi$
$390$	6.00000	0.303822
$391$	2.74456	0.138798
$392$	−6.00000	−0.303046
$393$	19.4891	0.983096
$394$	15.4891	0.780331
$395$	34.9783	1.75995
$396$	−4.00000	−0.201008
$397$	−0.627719	−0.0315043	−0.0157521	−	0.999876i	$-0.505014\pi$
$397$	−0.627719	−0.0315043	−0.0157521	+	0.999876i	$0.505014\pi$
$398$	16.4891	0.826525
$399$	−1.00000	−0.0500626
$400$	14.1168	0.705842
$401$	14.8614	0.742143	0.371072	−	0.928604i	$-0.378990\pi$
$401$	14.8614	0.742143	0.371072	+	0.928604i	$0.378990\pi$
$402$	−2.37228	−0.118319
$403$	−9.60597	−0.478507
$404$	−14.4891	−0.720861
$405$	−4.37228	−0.217260
$406$	1.74456	0.0865812
$407$	−29.4891	−1.46172
$408$	−0.627719	−0.0310767
$409$	−21.4891	−1.06257	−0.531284	−	0.847194i	$-0.678290\pi$
$409$	−21.4891	−1.06257	−0.531284	+	0.847194i	$0.678290\pi$
$410$	26.2337	1.29559
$411$	4.37228	0.215669
$412$	15.1168	0.744753
$413$	13.7446	0.676326
$414$	4.37228	0.214886
$415$	−67.2119	−3.29930
$416$	1.37228	0.0672816
$417$	12.1168	0.593364
$418$	−4.00000	−0.195646
$419$	−25.4891	−1.24523	−0.622613	−	0.782530i	$-0.713929\pi$
$419$	−25.4891	−1.24523	−0.622613	+	0.782530i	$0.713929\pi$
$420$	4.37228	0.213345
$421$	16.6060	0.809325	0.404663	−	0.914466i	$-0.367389\pi$
$421$	16.6060	0.809325	0.404663	+	0.914466i	$0.367389\pi$
$422$	−26.3505	−1.28272
$423$	−10.1168	−0.491898
$424$	−1.00000	−0.0485643
$425$	8.86141	0.429841
$426$	6.62772	0.321114
$427$	−5.37228	−0.259983
$428$	−0.255437	−0.0123470
$429$	5.48913	0.265017
$430$	−45.3505	−2.18700
$431$	−16.6060	−0.799881	−0.399941	−	0.916541i	$-0.630969\pi$
$431$	−16.6060	−0.799881	−0.399941	+	0.916541i	$0.630969\pi$
$432$	−1.00000	−0.0481125
$433$	32.9783	1.58483	0.792417	−	0.609980i	$-0.208823\pi$
$433$	32.9783	1.58483	0.792417	+	0.609980i	$0.208823\pi$
$434$	−7.00000	−0.336011
$435$	7.62772	0.365721
$436$	15.8614	0.759624
$437$	4.37228	0.209155
$438$	−4.00000	−0.191127
$439$	17.7228	0.845864	0.422932	−	0.906161i	$-0.361001\pi$
$439$	17.7228	0.845864	0.422932	+	0.906161i	$0.361001\pi$
$440$	17.4891	0.833761
$441$	−6.00000	−0.285714
$442$	0.861407	0.0409729
$443$	−8.60597	−0.408882	−0.204441	−	0.978879i	$-0.565538\pi$
$443$	−8.60597	−0.408882	−0.204441	+	0.978879i	$0.565538\pi$
$444$	−7.37228	−0.349873
$445$	33.3505	1.58097
$446$	10.0000	0.473514
$447$	0	0
$448$	1.00000	0.0472456
$449$	−10.0000	−0.471929	−0.235965	−	0.971762i	$-0.575825\pi$
$449$	−10.0000	−0.471929	−0.235965	+	0.971762i	$0.575825\pi$
$450$	14.1168	0.665474
$451$	24.0000	1.13012
$452$	3.62772	0.170634
$453$	15.7446	0.739744
$454$	1.62772	0.0763926
$455$	−6.00000	−0.281284
$456$	−1.00000	−0.0468293
$457$	−14.2337	−0.665824	−0.332912	−	0.942958i	$-0.608031\pi$
$457$	−14.2337	−0.665824	−0.332912	+	0.942958i	$0.608031\pi$
$458$	20.6060	0.962854
$459$	−0.627719	−0.0292994
$460$	−19.1168	−0.891327
$461$	−8.23369	−0.383481	−0.191741	−	0.981446i	$-0.561413\pi$
$461$	−8.23369	−0.383481	−0.191741	+	0.981446i	$0.561413\pi$
$462$	4.00000	0.186097
$463$	18.2337	0.847391	0.423696	−	0.905805i	$-0.360733\pi$
$463$	18.2337	0.847391	0.423696	+	0.905805i	$0.360733\pi$
$464$	1.74456	0.0809893
$465$	−30.6060	−1.41932
$466$	10.0000	0.463241
$467$	−9.25544	−0.428291	−0.214145	−	0.976802i	$-0.568697\pi$
$467$	−9.25544	−0.428291	−0.214145	+	0.976802i	$0.568697\pi$
$468$	1.37228	0.0634337
$469$	2.37228	0.109542
$470$	44.2337	2.04035
$471$	−6.62772	−0.305389
$472$	13.7446	0.632645
$473$	−41.4891	−1.90767
$474$	8.00000	0.367452
$475$	14.1168	0.647725
$476$	0.627719	0.0287714
$477$	−1.00000	−0.0457869
$478$	29.7228	1.35949
$479$	−29.6277	−1.35373	−0.676863	−	0.736109i	$-0.736661\pi$
$479$	−29.6277	−1.35373	−0.676863	+	0.736109i	$0.736661\pi$
$480$	4.37228	0.199566
$481$	10.1168	0.461288
$482$	1.48913	0.0678278
$483$	−4.37228	−0.198946
$484$	5.00000	0.227273
$485$	61.2119	2.77949
$486$	−1.00000	−0.0453609
$487$	−28.2337	−1.27939	−0.639695	−	0.768629i	$-0.720939\pi$
$487$	−28.2337	−1.27939	−0.639695	+	0.768629i	$0.720939\pi$
$488$	−5.37228	−0.243192
$489$	−5.62772	−0.254494
$490$	26.2337	1.18512
$491$	20.6060	0.929934	0.464967	−	0.885328i	$-0.346066\pi$
$491$	20.6060	0.929934	0.464967	+	0.885328i	$0.346066\pi$
$492$	6.00000	0.270501
$493$	1.09509	0.0493206
$494$	1.37228	0.0617419
$495$	17.4891	0.786078
$496$	−7.00000	−0.314309
$497$	−6.62772	−0.297294
$498$	−15.3723	−0.688848
$499$	−7.13859	−0.319567	−0.159784	−	0.987152i	$-0.551080\pi$
$499$	−7.13859	−0.319567	−0.159784	+	0.987152i	$0.551080\pi$
$500$	−39.8614	−1.78266
$501$	14.8614	0.663959
$502$	−11.6060	−0.518000
$503$	−10.3723	−0.462477	−0.231239	−	0.972897i	$-0.574278\pi$
$503$	−10.3723	−0.462477	−0.231239	+	0.972897i	$0.574278\pi$
$504$	1.00000	0.0445435
$505$	63.3505	2.81906
$506$	−17.4891	−0.777486
$507$	11.1168	0.493716
$508$	−21.2337	−0.942093
$509$	24.0000	1.06378	0.531891	−	0.846813i	$-0.321482\pi$
$509$	24.0000	1.06378	0.531891	+	0.846813i	$0.321482\pi$
$510$	2.74456	0.121531
$511$	4.00000	0.176950
$512$	1.00000	0.0441942
$513$	−1.00000	−0.0441511
$514$	9.37228	0.413394
$515$	−66.0951	−2.91250
$516$	−10.3723	−0.456614
$517$	40.4674	1.77975
$518$	7.37228	0.323919
$519$	18.7446	0.822795
$520$	−6.00000	−0.263117
$521$	−26.2337	−1.14932	−0.574659	−	0.818393i	$-0.694865\pi$
$521$	−26.2337	−1.14932	−0.574659	+	0.818393i	$0.694865\pi$
$522$	1.74456	0.0763574
$523$	−38.3505	−1.67695	−0.838476	−	0.544939i	$-0.816553\pi$
$523$	−38.3505	−1.67695	−0.838476	+	0.544939i	$0.816553\pi$
$524$	−19.4891	−0.851386
$525$	−14.1168	−0.616110
$526$	−22.3723	−0.975478
$527$	−4.39403	−0.191407
$528$	4.00000	0.174078
$529$	−3.88316	−0.168833
$530$	4.37228	0.189920
$531$	13.7446	0.596463
$532$	1.00000	0.0433555
$533$	−8.23369	−0.356641
$534$	7.62772	0.330084
$535$	1.11684	0.0482854
$536$	2.37228	0.102467
$537$	−5.48913	−0.236873
$538$	−19.6277	−0.846211
$539$	24.0000	1.03375
$540$	4.37228	0.188153
$541$	−17.8614	−0.767922	−0.383961	−	0.923349i	$-0.625440\pi$
$541$	−17.8614	−0.767922	−0.383961	+	0.923349i	$0.625440\pi$
$542$	23.1168	0.992953
$543$	24.6060	1.05594
$544$	0.627719	0.0269132
$545$	−69.3505	−2.97065
$546$	−1.37228	−0.0587282
$547$	−17.8832	−0.764629	−0.382314	−	0.924032i	$-0.624873\pi$
$547$	−17.8832	−0.764629	−0.382314	+	0.924032i	$0.624873\pi$
$548$	−4.37228	−0.186775
$549$	−5.37228	−0.229283
$550$	−56.4674	−2.40778
$551$	1.74456	0.0743209
$552$	−4.37228	−0.186097
$553$	−8.00000	−0.340195
$554$	−15.4891	−0.658070
$555$	32.2337	1.36824
$556$	−12.1168	−0.513869
$557$	−14.7228	−0.623826	−0.311913	−	0.950111i	$-0.600970\pi$
$557$	−14.7228	−0.623826	−0.311913	+	0.950111i	$0.600970\pi$
$558$	−7.00000	−0.296334
$559$	14.2337	0.602021
$560$	−4.37228	−0.184763
$561$	2.51087	0.106009
$562$	−13.8614	−0.584708
$563$	24.9783	1.05271	0.526354	−	0.850266i	$-0.323559\pi$
$563$	24.9783	1.05271	0.526354	+	0.850266i	$0.323559\pi$
$564$	10.1168	0.425996
$565$	−15.8614	−0.667294
$566$	8.62772	0.362650
$567$	1.00000	0.0419961
$568$	−6.62772	−0.278093
$569$	−33.8397	−1.41863	−0.709316	−	0.704891i	$-0.750996\pi$
$569$	−33.8397	−1.41863	−0.709316	+	0.704891i	$0.750996\pi$
$570$	4.37228	0.183135
$571$	−26.9783	−1.12900	−0.564502	−	0.825431i	$-0.690932\pi$
$571$	−26.9783	−1.12900	−0.564502	+	0.825431i	$0.690932\pi$
$572$	−5.48913	−0.229512
$573$	26.7446	1.11727
$574$	−6.00000	−0.250435
$575$	61.7228	2.57402
$576$	1.00000	0.0416667
$577$	−10.8614	−0.452166	−0.226083	−	0.974108i	$-0.572592\pi$
$577$	−10.8614	−0.452166	−0.226083	+	0.974108i	$0.572592\pi$
$578$	−16.6060	−0.690717
$579$	−6.86141	−0.285150
$580$	−7.62772	−0.316724
$581$	15.3723	0.637750
$582$	14.0000	0.580319
$583$	4.00000	0.165663
$584$	4.00000	0.165521
$585$	−6.00000	−0.248069
$586$	−28.1168	−1.16150
$587$	41.4891	1.71244	0.856220	−	0.516612i	$-0.172807\pi$
$587$	41.4891	1.71244	0.856220	+	0.516612i	$0.172807\pi$
$588$	6.00000	0.247436
$589$	−7.00000	−0.288430
$590$	−60.0951	−2.47408
$591$	−15.4891	−0.637137
$592$	7.37228	0.302999
$593$	7.60597	0.312340	0.156170	−	0.987730i	$-0.450085\pi$
$593$	7.60597	0.312340	0.156170	+	0.987730i	$0.450085\pi$
$594$	4.00000	0.164122
$595$	−2.74456	−0.112516
$596$	0	0
$597$	−16.4891	−0.674855
$598$	6.00000	0.245358
$599$	30.9783	1.26574	0.632869	−	0.774259i	$-0.281877\pi$
$599$	30.9783	1.26574	0.632869	+	0.774259i	$0.281877\pi$
$600$	−14.1168	−0.576318
$601$	−5.74456	−0.234326	−0.117163	−	0.993113i	$-0.537380\pi$
$601$	−5.74456	−0.234326	−0.117163	+	0.993113i	$0.537380\pi$
$602$	10.3723	0.422743
$603$	2.37228	0.0966068
$604$	−15.7446	−0.640637
$605$	−21.8614	−0.888793
$606$	14.4891	0.588580
$607$	6.23369	0.253018	0.126509	−	0.991965i	$-0.459623\pi$
$607$	6.23369	0.253018	0.126509	+	0.991965i	$0.459623\pi$
$608$	1.00000	0.0405554
$609$	−1.74456	−0.0706932
$610$	23.4891	0.951047
$611$	−13.8832	−0.561652
$612$	0.627719	0.0253740
$613$	14.1168	0.570174	0.285087	−	0.958502i	$-0.407978\pi$
$613$	14.1168	0.570174	0.285087	+	0.958502i	$0.407978\pi$
$614$	11.8832	0.479565
$615$	−26.2337	−1.05784
$616$	−4.00000	−0.161165
$617$	12.9783	0.522485	0.261242	−	0.965273i	$-0.415868\pi$
$617$	12.9783	0.522485	0.261242	+	0.965273i	$0.415868\pi$
$618$	−15.1168	−0.608089
$619$	17.6277	0.708518	0.354259	−	0.935147i	$-0.384733\pi$
$619$	17.6277	0.708518	0.354259	+	0.935147i	$0.384733\pi$
$620$	30.6060	1.22917
$621$	−4.37228	−0.175454
$622$	24.3505	0.976367
$623$	−7.62772	−0.305598
$624$	−1.37228	−0.0549352
$625$	103.701	4.14804
$626$	−11.2554	−0.449858
$627$	4.00000	0.159745
$628$	6.62772	0.264475
$629$	4.62772	0.184519
$630$	−4.37228	−0.174196
$631$	−35.7228	−1.42210	−0.711051	−	0.703140i	$-0.751781\pi$
$631$	−35.7228	−1.42210	−0.711051	+	0.703140i	$0.751781\pi$
$632$	−8.00000	−0.318223
$633$	26.3505	1.04734
$634$	14.0000	0.556011
$635$	92.8397	3.68423
$636$	1.00000	0.0396526
$637$	−8.23369	−0.326231
$638$	−6.97825	−0.276272
$639$	−6.62772	−0.262188
$640$	−4.37228	−0.172830
$641$	34.4674	1.36138	0.680690	−	0.732572i	$-0.261680\pi$
$641$	34.4674	1.36138	0.680690	+	0.732572i	$0.261680\pi$
$642$	0.255437	0.0100813
$643$	−45.5842	−1.79767	−0.898833	−	0.438291i	$-0.855584\pi$
$643$	−45.5842	−1.79767	−0.898833	+	0.438291i	$0.855584\pi$
$644$	4.37228	0.172292
$645$	45.3505	1.78568
$646$	0.627719	0.0246973
$647$	2.97825	0.117087	0.0585436	−	0.998285i	$-0.481354\pi$
$647$	2.97825	0.117087	0.0585436	+	0.998285i	$0.481354\pi$
$648$	1.00000	0.0392837
$649$	−54.9783	−2.15809
$650$	19.3723	0.759843
$651$	7.00000	0.274352
$652$	5.62772	0.220398
$653$	−0.978251	−0.0382819	−0.0191410	−	0.999817i	$-0.506093\pi$
$653$	−0.978251	−0.0382819	−0.0191410	+	0.999817i	$0.506093\pi$
$654$	−15.8614	−0.620230
$655$	85.2119	3.32951
$656$	−6.00000	−0.234261
$657$	4.00000	0.156055
$658$	−10.1168	−0.394396
$659$	8.23369	0.320739	0.160369	−	0.987057i	$-0.448731\pi$
$659$	8.23369	0.320739	0.160369	+	0.987057i	$0.448731\pi$
$660$	−17.4891	−0.680763
$661$	−13.7228	−0.533756	−0.266878	−	0.963730i	$-0.585992\pi$
$661$	−13.7228	−0.533756	−0.266878	+	0.963730i	$0.585992\pi$
$662$	−35.7228	−1.38841
$663$	−0.861407	−0.0334543
$664$	15.3723	0.596560
$665$	−4.37228	−0.169550
$666$	7.37228	0.285670
$667$	7.62772	0.295346
$668$	−14.8614	−0.575005
$669$	−10.0000	−0.386622
$670$	−10.3723	−0.400716
$671$	21.4891	0.829578
$672$	−1.00000	−0.0385758
$673$	6.00000	0.231283	0.115642	−	0.993291i	$-0.463108\pi$
$673$	6.00000	0.231283	0.115642	+	0.993291i	$0.463108\pi$
$674$	20.4891	0.789212
$675$	−14.1168	−0.543358
$676$	−11.1168	−0.427571
$677$	−20.9783	−0.806260	−0.403130	−	0.915143i	$-0.632078\pi$
$677$	−20.9783	−0.806260	−0.403130	+	0.915143i	$0.632078\pi$
$678$	−3.62772	−0.139322
$679$	−14.0000	−0.537271
$680$	−2.74456	−0.105249
$681$	−1.62772	−0.0623743
$682$	28.0000	1.07218
$683$	44.8614	1.71657	0.858287	−	0.513170i	$-0.171529\pi$
$683$	44.8614	1.71657	0.858287	+	0.513170i	$0.171529\pi$
$684$	1.00000	0.0382360
$685$	19.1168	0.730417
$686$	−13.0000	−0.496342
$687$	−20.6060	−0.786167
$688$	10.3723	0.395440
$689$	−1.37228	−0.0522798
$690$	19.1168	0.727766
$691$	31.3723	1.19346	0.596729	−	0.802443i	$-0.296467\pi$
$691$	31.3723	1.19346	0.596729	+	0.802443i	$0.296467\pi$
$692$	−18.7446	−0.712561
$693$	−4.00000	−0.151947
$694$	16.9783	0.644486
$695$	52.9783	2.00958
$696$	−1.74456	−0.0661275
$697$	−3.76631	−0.142659
$698$	5.60597	0.212189
$699$	−10.0000	−0.378235
$700$	14.1168	0.533567
$701$	−37.9783	−1.43442	−0.717209	−	0.696858i	$-0.754581\pi$
$701$	−37.9783	−1.43442	−0.717209	+	0.696858i	$0.754581\pi$
$702$	−1.37228	−0.0517934
$703$	7.37228	0.278051
$704$	−4.00000	−0.150756
$705$	−44.2337	−1.66594
$706$	−0.510875	−0.0192270
$707$	−14.4891	−0.544920
$708$	−13.7446	−0.516552
$709$	24.3505	0.914503	0.457252	−	0.889337i	$-0.348834\pi$
$709$	24.3505	0.914503	0.457252	+	0.889337i	$0.348834\pi$
$710$	28.9783	1.08753
$711$	−8.00000	−0.300023
$712$	−7.62772	−0.285861
$713$	−30.6060	−1.14620
$714$	−0.627719	−0.0234918
$715$	24.0000	0.897549
$716$	5.48913	0.205138
$717$	−29.7228	−1.11002
$718$	−17.8614	−0.666582
$719$	−26.3723	−0.983520	−0.491760	−	0.870731i	$-0.663646\pi$
$719$	−26.3723	−0.983520	−0.491760	+	0.870731i	$0.663646\pi$
$720$	−4.37228	−0.162945
$721$	15.1168	0.562981
$722$	1.00000	0.0372161
$723$	−1.48913	−0.0553812
$724$	−24.6060	−0.914474
$725$	24.6277	0.914651
$726$	−5.00000	−0.185567
$727$	−34.9783	−1.29727	−0.648636	−	0.761099i	$-0.724660\pi$
$727$	−34.9783	−1.29727	−0.648636	+	0.761099i	$0.724660\pi$
$728$	1.37228	0.0508601
$729$	1.00000	0.0370370
$730$	−17.4891	−0.647302
$731$	6.51087	0.240813
$732$	5.37228	0.198565
$733$	5.39403	0.199233	0.0996165	−	0.995026i	$-0.468238\pi$
$733$	5.39403	0.199233	0.0996165	+	0.995026i	$0.468238\pi$
$734$	−4.62772	−0.170812
$735$	−26.2337	−0.967644
$736$	4.37228	0.161164
$737$	−9.48913	−0.349536
$738$	−6.00000	−0.220863
$739$	40.0000	1.47142	0.735712	−	0.677295i	$-0.236848\pi$
$739$	40.0000	1.47142	0.735712	+	0.677295i	$0.236848\pi$
$740$	−32.2337	−1.18493
$741$	−1.37228	−0.0504120
$742$	−1.00000	−0.0367112
$743$	38.7446	1.42140	0.710700	−	0.703495i	$-0.248378\pi$
$743$	38.7446	1.42140	0.710700	+	0.703495i	$0.248378\pi$
$744$	7.00000	0.256632
$745$	0	0
$746$	17.6277	0.645397
$747$	15.3723	0.562442
$748$	−2.51087	−0.0918067
$749$	−0.255437	−0.00933348
$750$	39.8614	1.45553
$751$	38.0000	1.38664	0.693320	−	0.720630i	$-0.256147\pi$
$751$	38.0000	1.38664	0.693320	+	0.720630i	$0.256147\pi$
$752$	−10.1168	−0.368923
$753$	11.6060	0.422945
$754$	2.39403	0.0871855
$755$	68.8397	2.50533
$756$	−1.00000	−0.0363696
$757$	−31.1168	−1.13096	−0.565480	−	0.824762i	$-0.691309\pi$
$757$	−31.1168	−1.13096	−0.565480	+	0.824762i	$0.691309\pi$
$758$	−8.23369	−0.299061
$759$	17.4891	0.634815
$760$	−4.37228	−0.158599
$761$	−8.74456	−0.316990	−0.158495	−	0.987360i	$-0.550664\pi$
$761$	−8.74456	−0.316990	−0.158495	+	0.987360i	$0.550664\pi$
$762$	21.2337	0.769215
$763$	15.8614	0.574221
$764$	−26.7446	−0.967584
$765$	−2.74456	−0.0992299
$766$	1.76631	0.0638194
$767$	18.8614	0.681046
$768$	−1.00000	−0.0360844
$769$	−37.4891	−1.35189	−0.675946	−	0.736951i	$-0.736265\pi$
$769$	−37.4891	−1.35189	−0.675946	+	0.736951i	$0.736265\pi$
$770$	17.4891	0.630264
$771$	−9.37228	−0.337534
$772$	6.86141	0.246947
$773$	22.9783	0.826470	0.413235	−	0.910624i	$-0.364399\pi$
$773$	22.9783	0.826470	0.413235	+	0.910624i	$0.364399\pi$
$774$	10.3723	0.372824
$775$	−98.8179	−3.54964
$776$	−14.0000	−0.502571
$777$	−7.37228	−0.264479
$778$	−20.2554	−0.726193
$779$	−6.00000	−0.214972
$780$	6.00000	0.214834
$781$	26.5109	0.948634
$782$	2.74456	0.0981454
$783$	−1.74456	−0.0623456
$784$	−6.00000	−0.214286
$785$	−28.9783	−1.03428
$786$	19.4891	0.695154
$787$	45.8614	1.63478	0.817391	−	0.576083i	$-0.195419\pi$
$787$	45.8614	1.63478	0.817391	+	0.576083i	$0.195419\pi$
$788$	15.4891	0.551777
$789$	22.3723	0.796474
$790$	34.9783	1.24447
$791$	3.62772	0.128987
$792$	−4.00000	−0.142134
$793$	−7.37228	−0.261797
$794$	−0.627719	−0.0222769
$795$	−4.37228	−0.155069
$796$	16.4891	0.584442
$797$	33.7228	1.19452	0.597262	−	0.802046i	$-0.296255\pi$
$797$	33.7228	1.19452	0.597262	+	0.802046i	$0.296255\pi$
$798$	−1.00000	−0.0353996
$799$	−6.35053	−0.224666
$800$	14.1168	0.499106
$801$	−7.62772	−0.269512
$802$	14.8614	0.524775
$803$	−16.0000	−0.564628
$804$	−2.37228	−0.0836639
$805$	−19.1168	−0.673780
$806$	−9.60597	−0.338356
$807$	19.6277	0.690928
$808$	−14.4891	−0.509726
$809$	7.11684	0.250215	0.125107	−	0.992143i	$-0.460072\pi$
$809$	7.11684	0.250215	0.125107	+	0.992143i	$0.460072\pi$
$810$	−4.37228	−0.153626
$811$	12.3940	0.435213	0.217607	−	0.976037i	$-0.430175\pi$
$811$	12.3940	0.435213	0.217607	+	0.976037i	$0.430175\pi$
$812$	1.74456	0.0612221
$813$	−23.1168	−0.810743
$814$	−29.4891	−1.03359
$815$	−24.6060	−0.861910
$816$	−0.627719	−0.0219745
$817$	10.3723	0.362880
$818$	−21.4891	−0.751350
$819$	1.37228	0.0479514
$820$	26.2337	0.916120
$821$	25.9783	0.906647	0.453324	−	0.891346i	$-0.350238\pi$
$821$	25.9783	0.906647	0.453324	+	0.891346i	$0.350238\pi$
$822$	4.37228	0.152501
$823$	−27.3723	−0.954138	−0.477069	−	0.878866i	$-0.658301\pi$
$823$	−27.3723	−0.954138	−0.477069	+	0.878866i	$0.658301\pi$
$824$	15.1168	0.526620
$825$	56.4674	1.96594
$826$	13.7446	0.478234
$827$	−9.76631	−0.339608	−0.169804	−	0.985478i	$-0.554313\pi$
$827$	−9.76631	−0.339608	−0.169804	+	0.985478i	$0.554313\pi$
$828$	4.37228	0.151947
$829$	−21.3505	−0.741535	−0.370767	−	0.928726i	$-0.620905\pi$
$829$	−21.3505	−0.741535	−0.370767	+	0.928726i	$0.620905\pi$
$830$	−67.2119	−2.33296
$831$	15.4891	0.537312
$832$	1.37228	0.0475753
$833$	−3.76631	−0.130495
$834$	12.1168	0.419572
$835$	64.9783	2.24867
$836$	−4.00000	−0.138343
$837$	7.00000	0.241955
$838$	−25.4891	−0.880507
$839$	−19.1168	−0.659987	−0.329993	−	0.943983i	$-0.607047\pi$
$839$	−19.1168	−0.659987	−0.329993	+	0.943983i	$0.607047\pi$
$840$	4.37228	0.150858
$841$	−25.9565	−0.895052
$842$	16.6060	0.572279
$843$	13.8614	0.477412
$844$	−26.3505	−0.907023
$845$	48.6060	1.67210
$846$	−10.1168	−0.347824
$847$	5.00000	0.171802
$848$	−1.00000	−0.0343401
$849$	−8.62772	−0.296103
$850$	8.86141	0.303944
$851$	32.2337	1.10496
$852$	6.62772	0.227062
$853$	7.37228	0.252422	0.126211	−	0.992003i	$-0.459718\pi$
$853$	7.37228	0.252422	0.126211	+	0.992003i	$0.459718\pi$
$854$	−5.37228	−0.183836
$855$	−4.37228	−0.149529
$856$	−0.255437	−0.00873067
$857$	52.3723	1.78900	0.894502	−	0.447065i	$-0.147531\pi$
$857$	52.3723	1.78900	0.894502	+	0.447065i	$0.147531\pi$
$858$	5.48913	0.187396
$859$	49.4891	1.68855	0.844274	−	0.535912i	$-0.180032\pi$
$859$	49.4891	1.68855	0.844274	+	0.535912i	$0.180032\pi$
$860$	−45.3505	−1.54644
$861$	6.00000	0.204479
$862$	−16.6060	−0.565602
$863$	40.0951	1.36485	0.682426	−	0.730954i	$-0.260925\pi$
$863$	40.0951	1.36485	0.682426	+	0.730954i	$0.260925\pi$
$864$	−1.00000	−0.0340207
$865$	81.9565	2.78660
$866$	32.9783	1.12065
$867$	16.6060	0.563968
$868$	−7.00000	−0.237595
$869$	32.0000	1.08553
$870$	7.62772	0.258604
$871$	3.25544	0.110306
$872$	15.8614	0.537135
$873$	−14.0000	−0.473828
$874$	4.37228	0.147895
$875$	−39.8614	−1.34756
$876$	−4.00000	−0.135147
$877$	−17.3723	−0.586620	−0.293310	−	0.956017i	$-0.594757\pi$
$877$	−17.3723	−0.586620	−0.293310	+	0.956017i	$0.594757\pi$
$878$	17.7228	0.598116
$879$	28.1168	0.948358
$880$	17.4891	0.589558
$881$	−52.6060	−1.77234	−0.886170	−	0.463360i	$-0.846644\pi$
$881$	−52.6060	−1.77234	−0.886170	+	0.463360i	$0.846644\pi$
$882$	−6.00000	−0.202031
$883$	50.2337	1.69050	0.845249	−	0.534372i	$-0.179452\pi$
$883$	50.2337	1.69050	0.845249	+	0.534372i	$0.179452\pi$
$884$	0.861407	0.0289722
$885$	60.0951	2.02007
$886$	−8.60597	−0.289123
$887$	1.64947	0.0553837	0.0276919	−	0.999617i	$-0.491184\pi$
$887$	1.64947	0.0553837	0.0276919	+	0.999617i	$0.491184\pi$
$888$	−7.37228	−0.247398
$889$	−21.2337	−0.712155
$890$	33.3505	1.11791
$891$	−4.00000	−0.134005
$892$	10.0000	0.334825
$893$	−10.1168	−0.338547
$894$	0	0
$895$	−24.0000	−0.802232
$896$	1.00000	0.0334077
$897$	−6.00000	−0.200334
$898$	−10.0000	−0.333704
$899$	−12.2119	−0.407291
$900$	14.1168	0.470561
$901$	−0.627719	−0.0209123
$902$	24.0000	0.799113
$903$	−10.3723	−0.345168
$904$	3.62772	0.120656
$905$	107.584	3.57622
$906$	15.7446	0.523078
$907$	−1.02175	−0.0339266	−0.0169633	−	0.999856i	$-0.505400\pi$
$907$	−1.02175	−0.0339266	−0.0169633	+	0.999856i	$0.505400\pi$
$908$	1.62772	0.0540177
$909$	−14.4891	−0.480574
$910$	−6.00000	−0.198898
$911$	38.6060	1.27907	0.639536	−	0.768761i	$-0.279126\pi$
$911$	38.6060	1.27907	0.639536	+	0.768761i	$0.279126\pi$
$912$	−1.00000	−0.0331133
$913$	−61.4891	−2.03499
$914$	−14.2337	−0.470809
$915$	−23.4891	−0.776527
$916$	20.6060	0.680840
$917$	−19.4891	−0.643588
$918$	−0.627719	−0.0207178
$919$	24.5109	0.808539	0.404270	−	0.914640i	$-0.367526\pi$
$919$	24.5109	0.808539	0.404270	+	0.914640i	$0.367526\pi$
$920$	−19.1168	−0.630264
$921$	−11.8832	−0.391563
$922$	−8.23369	−0.271162
$923$	−9.09509	−0.299369
$924$	4.00000	0.131590
$925$	104.073	3.42191
$926$	18.2337	0.599196
$927$	15.1168	0.496502
$928$	1.74456	0.0572681
$929$	21.0951	0.692108	0.346054	−	0.938215i	$-0.387521\pi$
$929$	21.0951	0.692108	0.346054	+	0.938215i	$0.387521\pi$
$930$	−30.6060	−1.00361
$931$	−6.00000	−0.196642
$932$	10.0000	0.327561
$933$	−24.3505	−0.797201
$934$	−9.25544	−0.302847
$935$	10.9783	0.359027
$936$	1.37228	0.0448544
$937$	−45.4674	−1.48535	−0.742677	−	0.669650i	$-0.766444\pi$
$937$	−45.4674	−1.48535	−0.742677	+	0.669650i	$0.766444\pi$
$938$	2.37228	0.0774577
$939$	11.2554	0.367307
$940$	44.2337	1.44274
$941$	36.0951	1.17667	0.588333	−	0.808619i	$-0.299784\pi$
$941$	36.0951	1.17667	0.588333	+	0.808619i	$0.299784\pi$
$942$	−6.62772	−0.215943
$943$	−26.2337	−0.854286
$944$	13.7446	0.447347
$945$	4.37228	0.142230
$946$	−41.4891	−1.34893
$947$	−5.02175	−0.163185	−0.0815925	−	0.996666i	$-0.526001\pi$
$947$	−5.02175	−0.163185	−0.0815925	+	0.996666i	$0.526001\pi$
$948$	8.00000	0.259828
$949$	5.48913	0.178185
$950$	14.1168	0.458011
$951$	−14.0000	−0.453981
$952$	0.627719	0.0203445
$953$	−9.35053	−0.302893	−0.151447	−	0.988465i	$-0.548393\pi$
$953$	−9.35053	−0.302893	−0.151447	+	0.988465i	$0.548393\pi$
$954$	−1.00000	−0.0323762
$955$	116.935	3.78392
$956$	29.7228	0.961304
$957$	6.97825	0.225575
$958$	−29.6277	−0.957228
$959$	−4.37228	−0.141188
$960$	4.37228	0.141115
$961$	18.0000	0.580645
$962$	10.1168	0.326180
$963$	−0.255437	−0.00823135
$964$	1.48913	0.0479615
$965$	−30.0000	−0.965734
$966$	−4.37228	−0.140676
$967$	−55.6060	−1.78817	−0.894084	−	0.447900i	$-0.852172\pi$
$967$	−55.6060	−1.78817	−0.894084	+	0.447900i	$0.852172\pi$
$968$	5.00000	0.160706
$969$	−0.627719	−0.0201652
$970$	61.2119	1.96540
$971$	41.7446	1.33965	0.669823	−	0.742520i	$-0.266370\pi$
$971$	41.7446	1.33965	0.669823	+	0.742520i	$0.266370\pi$
$972$	−1.00000	−0.0320750
$973$	−12.1168	−0.388448
$974$	−28.2337	−0.904666
$975$	−19.3723	−0.620410
$976$	−5.37228	−0.171963
$977$	−58.8179	−1.88175	−0.940876	−	0.338752i	$-0.889995\pi$
$977$	−58.8179	−1.88175	−0.940876	+	0.338752i	$0.889995\pi$
$978$	−5.62772	−0.179955
$979$	30.5109	0.975132
$980$	26.2337	0.838004
$981$	15.8614	0.506416
$982$	20.6060	0.657563
$983$	0.138593	0.00442044	0.00221022	−	0.999998i	$-0.499296\pi$
$983$	0.138593	0.00442044	0.00221022	+	0.999998i	$0.499296\pi$
$984$	6.00000	0.191273
$985$	−67.7228	−2.15783
$986$	1.09509	0.0348749
$987$	10.1168	0.322023
$988$	1.37228	0.0436581
$989$	45.3505	1.44206
$990$	17.4891	0.555841
$991$	−43.7228	−1.38890	−0.694450	−	0.719541i	$-0.744352\pi$
$991$	−43.7228	−1.38890	−0.694450	+	0.719541i	$0.744352\pi$
$992$	−7.00000	−0.222250
$993$	35.7228	1.13363
$994$	−6.62772	−0.210218
$995$	−72.0951	−2.28557
$996$	−15.3723	−0.487089
$997$	−57.5842	−1.82371	−0.911855	−	0.410512i	$-0.865350\pi$
$997$	−57.5842	−1.82371	−0.911855	+	0.410512i	$0.865350\pi$
$998$	−7.13859	−0.225968
$999$	−7.37228	−0.233249

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6042.2.a.o.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6042.2.a.o.1.1	✓	2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6042 = 2 \cdot 3 \cdot 19 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6042.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.37228 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.37228 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -4.37228 q^{10} -4.00000 q^{11} -1.00000 q^{12} +1.37228 q^{13} +1.00000 q^{14} +4.37228 q^{15} +1.00000 q^{16} +0.627719 q^{17} +1.00000 q^{18} +1.00000 q^{19} -4.37228 q^{20} -1.00000 q^{21} -4.00000 q^{22} +4.37228 q^{23} -1.00000 q^{24} +14.1168 q^{25} +1.37228 q^{26} -1.00000 q^{27} +1.00000 q^{28} +1.74456 q^{29} +4.37228 q^{30} -7.00000 q^{31} +1.00000 q^{32} +4.00000 q^{33} +0.627719 q^{34} -4.37228 q^{35} +1.00000 q^{36} +7.37228 q^{37} +1.00000 q^{38} -1.37228 q^{39} -4.37228 q^{40} -6.00000 q^{41} -1.00000 q^{42} +10.3723 q^{43} -4.00000 q^{44} -4.37228 q^{45} +4.37228 q^{46} -10.1168 q^{47} -1.00000 q^{48} -6.00000 q^{49} +14.1168 q^{50} -0.627719 q^{51} +1.37228 q^{52} -1.00000 q^{53} -1.00000 q^{54} +17.4891 q^{55} +1.00000 q^{56} -1.00000 q^{57} +1.74456 q^{58} +13.7446 q^{59} +4.37228 q^{60} -5.37228 q^{61} -7.00000 q^{62} +1.00000 q^{63} +1.00000 q^{64} -6.00000 q^{65} +4.00000 q^{66} +2.37228 q^{67} +0.627719 q^{68} -4.37228 q^{69} -4.37228 q^{70} -6.62772 q^{71} +1.00000 q^{72} +4.00000 q^{73} +7.37228 q^{74} -14.1168 q^{75} +1.00000 q^{76} -4.00000 q^{77} -1.37228 q^{78} -8.00000 q^{79} -4.37228 q^{80} +1.00000 q^{81} -6.00000 q^{82} +15.3723 q^{83} -1.00000 q^{84} -2.74456 q^{85} +10.3723 q^{86} -1.74456 q^{87} -4.00000 q^{88} -7.62772 q^{89} -4.37228 q^{90} +1.37228 q^{91} +4.37228 q^{92} +7.00000 q^{93} -10.1168 q^{94} -4.37228 q^{95} -1.00000 q^{96} -14.0000 q^{97} -6.00000 q^{98} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 3 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 3 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 3 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9} - 3 q^{10} - 8 q^{11} - 2 q^{12} - 3 q^{13} + 2 q^{14} + 3 q^{15} + 2 q^{16} + 7 q^{17} + 2 q^{18} + 2 q^{19} - 3 q^{20} - 2 q^{21} - 8 q^{22} + 3 q^{23} - 2 q^{24} + 11 q^{25} - 3 q^{26} - 2 q^{27} + 2 q^{28} - 8 q^{29} + 3 q^{30} - 14 q^{31} + 2 q^{32} + 8 q^{33} + 7 q^{34} - 3 q^{35} + 2 q^{36} + 9 q^{37} + 2 q^{38} + 3 q^{39} - 3 q^{40} - 12 q^{41} - 2 q^{42} + 15 q^{43} - 8 q^{44} - 3 q^{45} + 3 q^{46} - 3 q^{47} - 2 q^{48} - 12 q^{49} + 11 q^{50} - 7 q^{51} - 3 q^{52} - 2 q^{53} - 2 q^{54} + 12 q^{55} + 2 q^{56} - 2 q^{57} - 8 q^{58} + 16 q^{59} + 3 q^{60} - 5 q^{61} - 14 q^{62} + 2 q^{63} + 2 q^{64} - 12 q^{65} + 8 q^{66} - q^{67} + 7 q^{68} - 3 q^{69} - 3 q^{70} - 19 q^{71} + 2 q^{72} + 8 q^{73} + 9 q^{74} - 11 q^{75} + 2 q^{76} - 8 q^{77} + 3 q^{78} - 16 q^{79} - 3 q^{80} + 2 q^{81} - 12 q^{82} + 25 q^{83} - 2 q^{84} + 6 q^{85} + 15 q^{86} + 8 q^{87} - 8 q^{88} - 21 q^{89} - 3 q^{90} - 3 q^{91} + 3 q^{92} + 14 q^{93} - 3 q^{94} - 3 q^{95} - 2 q^{96} - 28 q^{97} - 12 q^{98} - 8 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 3 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 + 2 * q^9 - 3 * q^10 - 8 * q^11 - 2 * q^12 - 3 * q^13 + 2 * q^14 + 3 * q^15 + 2 * q^16 + 7 * q^17 + 2 * q^18 + 2 * q^19 - 3 * q^20 - 2 * q^21 - 8 * q^22 + 3 * q^23 - 2 * q^24 + 11 * q^25 - 3 * q^26 - 2 * q^27 + 2 * q^28 - 8 * q^29 + 3 * q^30 - 14 * q^31 + 2 * q^32 + 8 * q^33 + 7 * q^34 - 3 * q^35 + 2 * q^36 + 9 * q^37 + 2 * q^38 + 3 * q^39 - 3 * q^40 - 12 * q^41 - 2 * q^42 + 15 * q^43 - 8 * q^44 - 3 * q^45 + 3 * q^46 - 3 * q^47 - 2 * q^48 - 12 * q^49 + 11 * q^50 - 7 * q^51 - 3 * q^52 - 2 * q^53 - 2 * q^54 + 12 * q^55 + 2 * q^56 - 2 * q^57 - 8 * q^58 + 16 * q^59 + 3 * q^60 - 5 * q^61 - 14 * q^62 + 2 * q^63 + 2 * q^64 - 12 * q^65 + 8 * q^66 - q^67 + 7 * q^68 - 3 * q^69 - 3 * q^70 - 19 * q^71 + 2 * q^72 + 8 * q^73 + 9 * q^74 - 11 * q^75 + 2 * q^76 - 8 * q^77 + 3 * q^78 - 16 * q^79 - 3 * q^80 + 2 * q^81 - 12 * q^82 + 25 * q^83 - 2 * q^84 + 6 * q^85 + 15 * q^86 + 8 * q^87 - 8 * q^88 - 21 * q^89 - 3 * q^90 - 3 * q^91 + 3 * q^92 + 14 * q^93 - 3 * q^94 - 3 * q^95 - 2 * q^96 - 28 * q^97 - 12 * q^98 - 8 * q^99

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