LMFDB - Embedded newform 6018.2.a.q.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6018,2,Mod(1,6018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6018, 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("6018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6018 = 2 \cdot 3 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6018.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:	$48.0539719364$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.5173625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 8x^{4} + 8x^{3} + 10x^{2} - 7x + 1 $ x^6 - x^5 - 8x^4 + 8x^3 + 10x^2 - 7x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.16459$ of defining polynomial
Character	$\chi$	$=$	6018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.16459 q^{5} -1.00000 q^{6} -4.86606 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.16459 q^{5} -1.00000 q^{6} -4.86606 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.16459 q^{10} +1.96039 q^{11} -1.00000 q^{12} +1.04699 q^{13} -4.86606 q^{14} +2.16459 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} +3.22234 q^{19} -2.16459 q^{20} +4.86606 q^{21} +1.96039 q^{22} +0.557869 q^{23} -1.00000 q^{24} -0.314531 q^{25} +1.04699 q^{26} -1.00000 q^{27} -4.86606 q^{28} +6.75162 q^{29} +2.16459 q^{30} +7.16937 q^{31} +1.00000 q^{32} -1.96039 q^{33} -1.00000 q^{34} +10.5330 q^{35} +1.00000 q^{36} -1.93788 q^{37} +3.22234 q^{38} -1.04699 q^{39} -2.16459 q^{40} -2.72957 q^{41} +4.86606 q^{42} -2.43213 q^{43} +1.96039 q^{44} -2.16459 q^{45} +0.557869 q^{46} +0.360309 q^{47} -1.00000 q^{48} +16.6785 q^{49} -0.314531 q^{50} +1.00000 q^{51} +1.04699 q^{52} -4.44569 q^{53} -1.00000 q^{54} -4.24346 q^{55} -4.86606 q^{56} -3.22234 q^{57} +6.75162 q^{58} +1.00000 q^{59} +2.16459 q^{60} -0.336402 q^{61} +7.16937 q^{62} -4.86606 q^{63} +1.00000 q^{64} -2.26632 q^{65} -1.96039 q^{66} +8.27684 q^{67} -1.00000 q^{68} -0.557869 q^{69} +10.5330 q^{70} -10.4047 q^{71} +1.00000 q^{72} -10.5494 q^{73} -1.93788 q^{74} +0.314531 q^{75} +3.22234 q^{76} -9.53938 q^{77} -1.04699 q^{78} -13.0929 q^{79} -2.16459 q^{80} +1.00000 q^{81} -2.72957 q^{82} -9.08951 q^{83} +4.86606 q^{84} +2.16459 q^{85} -2.43213 q^{86} -6.75162 q^{87} +1.96039 q^{88} +10.1515 q^{89} -2.16459 q^{90} -5.09474 q^{91} +0.557869 q^{92} -7.16937 q^{93} +0.360309 q^{94} -6.97505 q^{95} -1.00000 q^{96} -3.92641 q^{97} +16.6785 q^{98} +1.96039 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} - 6 q^{3} + 6 q^{4} - 5 q^{5} - 6 q^{6} - q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 - 6 * q^3 + 6 * q^4 - 5 * q^5 - 6 * q^6 - q^7 + 6 * q^8 + 6 * q^9	$ 6 q + 6 q^{2} - 6 q^{3} + 6 q^{4} - 5 q^{5} - 6 q^{6} - q^{7} + 6 q^{8} + 6 q^{9} - 5 q^{10} - 6 q^{12} + 2 q^{13} - q^{14} + 5 q^{15} + 6 q^{16} - 6 q^{17} + 6 q^{18} - 5 q^{20} + q^{21} - 10 q^{23} - 6 q^{24} - 9 q^{25} + 2 q^{26} - 6 q^{27} - q^{28} - 3 q^{29} + 5 q^{30} - 7 q^{31} + 6 q^{32} - 6 q^{34} + 6 q^{35} + 6 q^{36} - 23 q^{37} - 2 q^{39} - 5 q^{40} - 12 q^{41} + q^{42} - 18 q^{43} - 5 q^{45} - 10 q^{46} - 14 q^{47} - 6 q^{48} + 9 q^{49} - 9 q^{50} + 6 q^{51} + 2 q^{52} + 21 q^{53} - 6 q^{54} + 4 q^{55} - q^{56} - 3 q^{58} + 6 q^{59} + 5 q^{60} - 2 q^{61} - 7 q^{62} - q^{63} + 6 q^{64} - 6 q^{65} + q^{67} - 6 q^{68} + 10 q^{69} + 6 q^{70} + 4 q^{71} + 6 q^{72} - 38 q^{73} - 23 q^{74} + 9 q^{75} - 22 q^{77} - 2 q^{78} - 30 q^{79} - 5 q^{80} + 6 q^{81} - 12 q^{82} + 23 q^{83} + q^{84} + 5 q^{85} - 18 q^{86} + 3 q^{87} - 7 q^{89} - 5 q^{90} - 5 q^{91} - 10 q^{92} + 7 q^{93} - 14 q^{94} - 7 q^{95} - 6 q^{96} - 10 q^{97} + 9 q^{98}+O(q^{100}) $ 6 * q + 6 * q^2 - 6 * q^3 + 6 * q^4 - 5 * q^5 - 6 * q^6 - q^7 + 6 * q^8 + 6 * q^9 - 5 * q^10 - 6 * q^12 + 2 * q^13 - q^14 + 5 * q^15 + 6 * q^16 - 6 * q^17 + 6 * q^18 - 5 * q^20 + q^21 - 10 * q^23 - 6 * q^24 - 9 * q^25 + 2 * q^26 - 6 * q^27 - q^28 - 3 * q^29 + 5 * q^30 - 7 * q^31 + 6 * q^32 - 6 * q^34 + 6 * q^35 + 6 * q^36 - 23 * q^37 - 2 * q^39 - 5 * q^40 - 12 * q^41 + q^42 - 18 * q^43 - 5 * q^45 - 10 * q^46 - 14 * q^47 - 6 * q^48 + 9 * q^49 - 9 * q^50 + 6 * q^51 + 2 * q^52 + 21 * q^53 - 6 * q^54 + 4 * q^55 - q^56 - 3 * q^58 + 6 * q^59 + 5 * q^60 - 2 * q^61 - 7 * q^62 - q^63 + 6 * q^64 - 6 * q^65 + q^67 - 6 * q^68 + 10 * q^69 + 6 * q^70 + 4 * q^71 + 6 * q^72 - 38 * q^73 - 23 * q^74 + 9 * q^75 - 22 * q^77 - 2 * q^78 - 30 * q^79 - 5 * q^80 + 6 * q^81 - 12 * q^82 + 23 * q^83 + q^84 + 5 * q^85 - 18 * q^86 + 3 * q^87 - 7 * q^89 - 5 * q^90 - 5 * q^91 - 10 * q^92 + 7 * q^93 - 14 * q^94 - 7 * q^95 - 6 * q^96 - 10 * q^97 + 9 * q^98

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
$5$	−2.16459	−0.968036	−0.484018	−	0.875058i	$-0.660823\pi$
$5$	−2.16459	−0.968036	−0.484018	+	0.875058i	$0.660823\pi$
$6$	−1.00000	−0.408248
$7$	−4.86606	−1.83920	−0.919598	−	0.392860i	$-0.871486\pi$
$7$	−4.86606	−1.83920	−0.919598	+	0.392860i	$0.871486\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−2.16459	−0.684505
$11$	1.96039	0.591081	0.295540	−	0.955330i	$-0.404500\pi$
$11$	1.96039	0.591081	0.295540	+	0.955330i	$0.404500\pi$
$12$	−1.00000	−0.288675
$13$	1.04699	0.290384	0.145192	−	0.989403i	$-0.453620\pi$
$13$	1.04699	0.290384	0.145192	+	0.989403i	$0.453620\pi$
$14$	−4.86606	−1.30051
$15$	2.16459	0.558896
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.00000	0.235702
$19$	3.22234	0.739255	0.369627	−	0.929180i	$-0.379485\pi$
$19$	3.22234	0.739255	0.369627	+	0.929180i	$0.379485\pi$
$20$	−2.16459	−0.484018
$21$	4.86606	1.06186
$22$	1.96039	0.417957
$23$	0.557869	0.116324	0.0581619	−	0.998307i	$-0.481476\pi$
$23$	0.557869	0.116324	0.0581619	+	0.998307i	$0.481476\pi$
$24$	−1.00000	−0.204124
$25$	−0.314531	−0.0629061
$26$	1.04699	0.205333
$27$	−1.00000	−0.192450
$28$	−4.86606	−0.919598
$29$	6.75162	1.25374	0.626872	−	0.779122i	$-0.284335\pi$
$29$	6.75162	1.25374	0.626872	+	0.779122i	$0.284335\pi$
$30$	2.16459	0.395199
$31$	7.16937	1.28766	0.643828	−	0.765170i	$-0.277345\pi$
$31$	7.16937	1.28766	0.643828	+	0.765170i	$0.277345\pi$
$32$	1.00000	0.176777
$33$	−1.96039	−0.341261
$34$	−1.00000	−0.171499
$35$	10.5330	1.78041
$36$	1.00000	0.166667
$37$	−1.93788	−0.318586	−0.159293	−	0.987231i	$-0.550921\pi$
$37$	−1.93788	−0.318586	−0.159293	+	0.987231i	$0.550921\pi$
$38$	3.22234	0.522732
$39$	−1.04699	−0.167653
$40$	−2.16459	−0.342252
$41$	−2.72957	−0.426287	−0.213144	−	0.977021i	$-0.568370\pi$
$41$	−2.72957	−0.426287	−0.213144	+	0.977021i	$0.568370\pi$
$42$	4.86606	0.750849
$43$	−2.43213	−0.370896	−0.185448	−	0.982654i	$-0.559374\pi$
$43$	−2.43213	−0.370896	−0.185448	+	0.982654i	$0.559374\pi$
$44$	1.96039	0.295540
$45$	−2.16459	−0.322679
$46$	0.557869	0.0822533
$47$	0.360309	0.0525565	0.0262783	−	0.999655i	$-0.491634\pi$
$47$	0.360309	0.0525565	0.0262783	+	0.999655i	$0.491634\pi$
$48$	−1.00000	−0.144338
$49$	16.6785	2.38264
$50$	−0.314531	−0.0444813
$51$	1.00000	0.140028
$52$	1.04699	0.145192
$53$	−4.44569	−0.610662	−0.305331	−	0.952246i	$-0.598767\pi$
$53$	−4.44569	−0.610662	−0.305331	+	0.952246i	$0.598767\pi$
$54$	−1.00000	−0.136083
$55$	−4.24346	−0.572187
$56$	−4.86606	−0.650254
$57$	−3.22234	−0.426809
$58$	6.75162	0.886531
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	2.16459	0.279448
$61$	−0.336402	−0.0430718	−0.0215359	−	0.999768i	$-0.506856\pi$
$61$	−0.336402	−0.0430718	−0.0215359	+	0.999768i	$0.506856\pi$
$62$	7.16937	0.910511
$63$	−4.86606	−0.613065
$64$	1.00000	0.125000
$65$	−2.26632	−0.281102
$66$	−1.96039	−0.241308
$67$	8.27684	1.01118	0.505588	−	0.862775i	$-0.331276\pi$
$67$	8.27684	1.01118	0.505588	+	0.862775i	$0.331276\pi$
$68$	−1.00000	−0.121268
$69$	−0.557869	−0.0671596
$70$	10.5330	1.25894
$71$	−10.4047	−1.23481	−0.617405	−	0.786646i	$-0.711816\pi$
$71$	−10.4047	−1.23481	−0.617405	+	0.786646i	$0.711816\pi$
$72$	1.00000	0.117851
$73$	−10.5494	−1.23471	−0.617356	−	0.786684i	$-0.711796\pi$
$73$	−10.5494	−1.23471	−0.617356	+	0.786684i	$0.711796\pi$
$74$	−1.93788	−0.225274
$75$	0.314531	0.0363189
$76$	3.22234	0.369627
$77$	−9.53938	−1.08711
$78$	−1.04699	−0.118549
$79$	−13.0929	−1.47306	−0.736532	−	0.676403i	$-0.763538\pi$
$79$	−13.0929	−1.47306	−0.736532	+	0.676403i	$0.763538\pi$
$80$	−2.16459	−0.242009
$81$	1.00000	0.111111
$82$	−2.72957	−0.301431
$83$	−9.08951	−0.997703	−0.498852	−	0.866687i	$-0.666245\pi$
$83$	−9.08951	−0.997703	−0.498852	+	0.866687i	$0.666245\pi$
$84$	4.86606	0.530930
$85$	2.16459	0.234783
$86$	−2.43213	−0.262263
$87$	−6.75162	−0.723849
$88$	1.96039	0.208979
$89$	10.1515	1.07606	0.538030	−	0.842926i	$-0.319169\pi$
$89$	10.1515	1.07606	0.538030	+	0.842926i	$0.319169\pi$
$90$	−2.16459	−0.228168
$91$	−5.09474	−0.534073
$92$	0.557869	0.0581619
$93$	−7.16937	−0.743429
$94$	0.360309	0.0371631
$95$	−6.97505	−0.715625
$96$	−1.00000	−0.102062
$97$	−3.92641	−0.398667	−0.199333	−	0.979932i	$-0.563878\pi$
$97$	−3.92641	−0.398667	−0.199333	+	0.979932i	$0.563878\pi$
$98$	16.6785	1.68478
$99$	1.96039	0.197027
$100$	−0.314531	−0.0314531
$101$	1.77755	0.176872	0.0884362	−	0.996082i	$-0.471813\pi$
$101$	1.77755	0.176872	0.0884362	+	0.996082i	$0.471813\pi$
$102$	1.00000	0.0990148
$103$	7.25793	0.715145	0.357573	−	0.933885i	$-0.383604\pi$
$103$	7.25793	0.715145	0.357573	+	0.933885i	$0.383604\pi$
$104$	1.04699	0.102666
$105$	−10.5330	−1.02792
$106$	−4.44569	−0.431804
$107$	−1.52404	−0.147334	−0.0736670	−	0.997283i	$-0.523470\pi$
$107$	−1.52404	−0.147334	−0.0736670	+	0.997283i	$0.523470\pi$
$108$	−1.00000	−0.0962250
$109$	−8.65902	−0.829384	−0.414692	−	0.909962i	$-0.636111\pi$
$109$	−8.65902	−0.829384	−0.414692	+	0.909962i	$0.636111\pi$
$110$	−4.24346	−0.404598
$111$	1.93788	0.183936
$112$	−4.86606	−0.459799
$113$	−9.26644	−0.871713	−0.435857	−	0.900016i	$-0.643554\pi$
$113$	−9.26644	−0.871713	−0.435857	+	0.900016i	$0.643554\pi$
$114$	−3.22234	−0.301799
$115$	−1.20756	−0.112606
$116$	6.75162	0.626872
$117$	1.04699	0.0967947
$118$	1.00000	0.0920575
$119$	4.86606	0.446071
$120$	2.16459	0.197600
$121$	−7.15686	−0.650624
$122$	−0.336402	−0.0304564
$123$	2.72957	0.246117
$124$	7.16937	0.643828
$125$	11.5038	1.02893
$126$	−4.86606	−0.433503
$127$	6.39303	0.567290	0.283645	−	0.958929i	$-0.408456\pi$
$127$	6.39303	0.567290	0.283645	+	0.958929i	$0.408456\pi$
$128$	1.00000	0.0883883
$129$	2.43213	0.214137
$130$	−2.26632	−0.198769
$131$	−3.21102	−0.280548	−0.140274	−	0.990113i	$-0.544798\pi$
$131$	−3.21102	−0.280548	−0.140274	+	0.990113i	$0.544798\pi$
$132$	−1.96039	−0.170630
$133$	−15.6801	−1.35963
$134$	8.27684	0.715010
$135$	2.16459	0.186299
$136$	−1.00000	−0.0857493
$137$	−6.71342	−0.573567	−0.286783	−	0.957995i	$-0.592586\pi$
$137$	−6.71342	−0.573567	−0.286783	+	0.957995i	$0.592586\pi$
$138$	−0.557869	−0.0474890
$139$	−10.3361	−0.876697	−0.438349	−	0.898805i	$-0.644436\pi$
$139$	−10.3361	−0.876697	−0.438349	+	0.898805i	$0.644436\pi$
$140$	10.5330	0.890204
$141$	−0.360309	−0.0303435
$142$	−10.4047	−0.873142
$143$	2.05252	0.171640
$144$	1.00000	0.0833333
$145$	−14.6145	−1.21367
$146$	−10.5494	−0.873073
$147$	−16.6785	−1.37562
$148$	−1.93788	−0.159293
$149$	−4.79384	−0.392726	−0.196363	−	0.980531i	$-0.562913\pi$
$149$	−4.79384	−0.392726	−0.196363	+	0.980531i	$0.562913\pi$
$150$	0.314531	0.0256813
$151$	0.670341	0.0545516	0.0272758	−	0.999628i	$-0.491317\pi$
$151$	0.670341	0.0545516	0.0272758	+	0.999628i	$0.491317\pi$
$152$	3.22234	0.261366
$153$	−1.00000	−0.0808452
$154$	−9.53938	−0.768705
$155$	−15.5188	−1.24650
$156$	−1.04699	−0.0838267
$157$	0.300682	0.0239970	0.0119985	−	0.999928i	$-0.496181\pi$
$157$	0.300682	0.0239970	0.0119985	+	0.999928i	$0.496181\pi$
$158$	−13.0929	−1.04161
$159$	4.44569	0.352566
$160$	−2.16459	−0.171126
$161$	−2.71462	−0.213942
$162$	1.00000	0.0785674
$163$	3.85466	0.301920	0.150960	−	0.988540i	$-0.451764\pi$
$163$	3.85466	0.301920	0.150960	+	0.988540i	$0.451764\pi$
$164$	−2.72957	−0.213144
$165$	4.24346	0.330353
$166$	−9.08951	−0.705483
$167$	−20.6483	−1.59781	−0.798906	−	0.601456i	$-0.794587\pi$
$167$	−20.6483	−1.59781	−0.798906	+	0.601456i	$0.794587\pi$
$168$	4.86606	0.375424
$169$	−11.9038	−0.915677
$170$	2.16459	0.166017
$171$	3.22234	0.246418
$172$	−2.43213	−0.185448
$173$	0.353487	0.0268751	0.0134375	−	0.999910i	$-0.495723\pi$
$173$	0.353487	0.0268751	0.0134375	+	0.999910i	$0.495723\pi$
$174$	−6.75162	−0.511839
$175$	1.53052	0.115697
$176$	1.96039	0.147770
$177$	−1.00000	−0.0751646
$178$	10.1515	0.760889
$179$	−7.03446	−0.525780	−0.262890	−	0.964826i	$-0.584676\pi$
$179$	−7.03446	−0.525780	−0.262890	+	0.964826i	$0.584676\pi$
$180$	−2.16459	−0.161339
$181$	17.1018	1.27117	0.635584	−	0.772032i	$-0.280759\pi$
$181$	17.1018	1.27117	0.635584	+	0.772032i	$0.280759\pi$
$182$	−5.09474	−0.377647
$183$	0.336402	0.0248675
$184$	0.557869	0.0411267
$185$	4.19473	0.308403
$186$	−7.16937	−0.525684
$187$	−1.96039	−0.143358
$188$	0.360309	0.0262783
$189$	4.86606	0.353953
$190$	−6.97505	−0.506023
$191$	14.7544	1.06759	0.533795	−	0.845614i	$-0.320765\pi$
$191$	14.7544	1.06759	0.533795	+	0.845614i	$0.320765\pi$
$192$	−1.00000	−0.0721688
$193$	−18.7746	−1.35143	−0.675714	−	0.737164i	$-0.736164\pi$
$193$	−18.7746	−1.35143	−0.675714	+	0.737164i	$0.736164\pi$
$194$	−3.92641	−0.281900
$195$	2.26632	0.162295
$196$	16.6785	1.19132
$197$	12.6810	0.903486	0.451743	−	0.892148i	$-0.350802\pi$
$197$	12.6810	0.903486	0.451743	+	0.892148i	$0.350802\pi$
$198$	1.96039	0.139319
$199$	12.9312	0.916670	0.458335	−	0.888780i	$-0.348446\pi$
$199$	12.9312	0.916670	0.458335	+	0.888780i	$0.348446\pi$
$200$	−0.314531	−0.0222407
$201$	−8.27684	−0.583803
$202$	1.77755	0.125068
$203$	−32.8537	−2.30588
$204$	1.00000	0.0700140
$205$	5.90841	0.412661
$206$	7.25793	0.505684
$207$	0.557869	0.0387746
$208$	1.04699	0.0725960
$209$	6.31705	0.436959
$210$	−10.5330	−0.726849
$211$	−22.2928	−1.53470	−0.767350	−	0.641228i	$-0.778425\pi$
$211$	−22.2928	−1.53470	−0.767350	+	0.641228i	$0.778425\pi$
$212$	−4.44569	−0.305331
$213$	10.4047	0.712917
$214$	−1.52404	−0.104181
$215$	5.26458	0.359041
$216$	−1.00000	−0.0680414
$217$	−34.8866	−2.36825
$218$	−8.65902	−0.586463
$219$	10.5494	0.712861
$220$	−4.24346	−0.286094
$221$	−1.04699	−0.0704285
$222$	1.93788	0.130062
$223$	17.9156	1.19972	0.599858	−	0.800106i	$-0.295224\pi$
$223$	17.9156	1.19972	0.599858	+	0.800106i	$0.295224\pi$
$224$	−4.86606	−0.325127
$225$	−0.314531	−0.0209687
$226$	−9.26644	−0.616394
$227$	3.58551	0.237979	0.118989	−	0.992896i	$-0.462035\pi$
$227$	3.58551	0.237979	0.118989	+	0.992896i	$0.462035\pi$
$228$	−3.22234	−0.213404
$229$	−3.15147	−0.208255	−0.104128	−	0.994564i	$-0.533205\pi$
$229$	−3.15147	−0.208255	−0.104128	+	0.994564i	$0.533205\pi$
$230$	−1.20756	−0.0796242
$231$	9.53938	0.627645
$232$	6.75162	0.443265
$233$	−9.58028	−0.627625	−0.313812	−	0.949485i	$-0.601606\pi$
$233$	−9.58028	−0.627625	−0.313812	+	0.949485i	$0.601606\pi$
$234$	1.04699	0.0684442
$235$	−0.779924	−0.0508766
$236$	1.00000	0.0650945
$237$	13.0929	0.850474
$238$	4.86606	0.315420
$239$	−29.5344	−1.91042	−0.955211	−	0.295926i	$-0.904372\pi$
$239$	−29.5344	−1.91042	−0.955211	+	0.295926i	$0.904372\pi$
$240$	2.16459	0.139724
$241$	−19.9977	−1.28816	−0.644081	−	0.764957i	$-0.722760\pi$
$241$	−19.9977	−1.28816	−0.644081	+	0.764957i	$0.722760\pi$
$242$	−7.15686	−0.460060
$243$	−1.00000	−0.0641500
$244$	−0.336402	−0.0215359
$245$	−36.1022	−2.30648
$246$	2.72957	0.174031
$247$	3.37377	0.214668
$248$	7.16937	0.455255
$249$	9.08951	0.576024
$250$	11.5038	0.727564
$251$	11.1525	0.703940	0.351970	−	0.936011i	$-0.385512\pi$
$251$	11.1525	0.703940	0.351970	+	0.936011i	$0.385512\pi$
$252$	−4.86606	−0.306533
$253$	1.09364	0.0687567
$254$	6.39303	0.401134
$255$	−2.16459	−0.135552
$256$	1.00000	0.0625000
$257$	−26.5822	−1.65815	−0.829077	−	0.559135i	$-0.811133\pi$
$257$	−26.5822	−1.65815	−0.829077	+	0.559135i	$0.811133\pi$
$258$	2.43213	0.151418
$259$	9.42984	0.585942
$260$	−2.26632	−0.140551
$261$	6.75162	0.417915
$262$	−3.21102	−0.198377
$263$	−21.5223	−1.32712	−0.663561	−	0.748122i	$-0.730956\pi$
$263$	−21.5223	−1.32712	−0.663561	+	0.748122i	$0.730956\pi$
$264$	−1.96039	−0.120654
$265$	9.62312	0.591143
$266$	−15.6801	−0.961407
$267$	−10.1515	−0.621263
$268$	8.27684	0.505588
$269$	−12.2228	−0.745239	−0.372619	−	0.927984i	$-0.621540\pi$
$269$	−12.2228	−0.745239	−0.372619	+	0.927984i	$0.621540\pi$
$270$	2.16459	0.131733
$271$	8.87974	0.539406	0.269703	−	0.962944i	$-0.413075\pi$
$271$	8.87974	0.539406	0.269703	+	0.962944i	$0.413075\pi$
$272$	−1.00000	−0.0606339
$273$	5.09474	0.308347
$274$	−6.71342	−0.405573
$275$	−0.616603	−0.0371826
$276$	−0.557869	−0.0335798
$277$	−14.8539	−0.892487	−0.446243	−	0.894912i	$-0.647238\pi$
$277$	−14.8539	−0.892487	−0.446243	+	0.894912i	$0.647238\pi$
$278$	−10.3361	−0.619919
$279$	7.16937	0.429219
$280$	10.5330	0.629469
$281$	4.93967	0.294676	0.147338	−	0.989086i	$-0.452929\pi$
$281$	4.93967	0.294676	0.147338	+	0.989086i	$0.452929\pi$
$282$	−0.360309	−0.0214561
$283$	15.1791	0.902306	0.451153	−	0.892447i	$-0.351013\pi$
$283$	15.1791	0.902306	0.451153	+	0.892447i	$0.351013\pi$
$284$	−10.4047	−0.617405
$285$	6.97505	0.413166
$286$	2.05252	0.121368
$287$	13.2822	0.784026
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	−14.6145	−0.858194
$291$	3.92641	0.230170
$292$	−10.5494	−0.617356
$293$	18.3574	1.07245	0.536226	−	0.844074i	$-0.319849\pi$
$293$	18.3574	1.07245	0.536226	+	0.844074i	$0.319849\pi$
$294$	−16.6785	−0.972710
$295$	−2.16459	−0.126028
$296$	−1.93788	−0.112637
$297$	−1.96039	−0.113754
$298$	−4.79384	−0.277699
$299$	0.584086	0.0337786
$300$	0.314531	0.0181594
$301$	11.8349	0.682151
$302$	0.670341	0.0385738
$303$	−1.77755	−0.102117
$304$	3.22234	0.184814
$305$	0.728173	0.0416951
$306$	−1.00000	−0.0571662
$307$	−22.3229	−1.27403	−0.637016	−	0.770850i	$-0.719832\pi$
$307$	−22.3229	−1.27403	−0.637016	+	0.770850i	$0.719832\pi$
$308$	−9.53938	−0.543557
$309$	−7.25793	−0.412889
$310$	−15.5188	−0.881407
$311$	27.9250	1.58348	0.791741	−	0.610857i	$-0.209175\pi$
$311$	27.9250	1.58348	0.791741	+	0.610857i	$0.209175\pi$
$312$	−1.04699	−0.0592744
$313$	−26.2584	−1.48421	−0.742106	−	0.670282i	$-0.766173\pi$
$313$	−26.2584	−1.48421	−0.742106	+	0.670282i	$0.766173\pi$
$314$	0.300682	0.0169684
$315$	10.5330	0.593469
$316$	−13.0929	−0.736532
$317$	21.7424	1.22117	0.610587	−	0.791949i	$-0.290934\pi$
$317$	21.7424	1.22117	0.610587	+	0.791949i	$0.290934\pi$
$318$	4.44569	0.249302
$319$	13.2358	0.741064
$320$	−2.16459	−0.121005
$321$	1.52404	0.0850633
$322$	−2.71462	−0.151280
$323$	−3.22234	−0.179296
$324$	1.00000	0.0555556
$325$	−0.329312	−0.0182669
$326$	3.85466	0.213490
$327$	8.65902	0.478845
$328$	−2.72957	−0.150715
$329$	−1.75329	−0.0966618
$330$	4.24346	0.233595
$331$	10.4552	0.574671	0.287335	−	0.957830i	$-0.407231\pi$
$331$	10.4552	0.574671	0.287335	+	0.957830i	$0.407231\pi$
$332$	−9.08951	−0.498852
$333$	−1.93788	−0.106195
$334$	−20.6483	−1.12982
$335$	−17.9160	−0.978855
$336$	4.86606	0.265465
$337$	5.91275	0.322088	0.161044	−	0.986947i	$-0.448514\pi$
$337$	5.91275	0.322088	0.161044	+	0.986947i	$0.448514\pi$
$338$	−11.9038	−0.647481
$339$	9.26644	0.503284
$340$	2.16459	0.117392
$341$	14.0548	0.761109
$342$	3.22234	0.174244
$343$	−47.0961	−2.54295
$344$	−2.43213	−0.131132
$345$	1.20756	0.0650129
$346$	0.353487	0.0190036
$347$	−12.5603	−0.674270	−0.337135	−	0.941456i	$-0.609458\pi$
$347$	−12.5603	−0.674270	−0.337135	+	0.941456i	$0.609458\pi$
$348$	−6.75162	−0.361925
$349$	−14.0306	−0.751039	−0.375520	−	0.926814i	$-0.622536\pi$
$349$	−14.0306	−0.751039	−0.375520	+	0.926814i	$0.622536\pi$
$350$	1.53052	0.0818099
$351$	−1.04699	−0.0558845
$352$	1.96039	0.104489
$353$	−14.1189	−0.751471	−0.375735	−	0.926727i	$-0.622610\pi$
$353$	−14.1189	−0.751471	−0.375735	+	0.926727i	$0.622610\pi$
$354$	−1.00000	−0.0531494
$355$	22.5219	1.19534
$356$	10.1515	0.538030
$357$	−4.86606	−0.257539
$358$	−7.03446	−0.371783
$359$	13.7220	0.724220	0.362110	−	0.932135i	$-0.382056\pi$
$359$	13.7220	0.724220	0.362110	+	0.932135i	$0.382056\pi$
$360$	−2.16459	−0.114084
$361$	−8.61655	−0.453503
$362$	17.1018	0.898852
$363$	7.15686	0.375638
$364$	−5.09474	−0.267037
$365$	22.8351	1.19525
$366$	0.336402	0.0175840
$367$	1.76159	0.0919543	0.0459771	−	0.998942i	$-0.485360\pi$
$367$	1.76159	0.0919543	0.0459771	+	0.998942i	$0.485360\pi$
$368$	0.557869	0.0290809
$369$	−2.72957	−0.142096
$370$	4.19473	0.218074
$371$	21.6330	1.12313
$372$	−7.16937	−0.371714
$373$	−17.8969	−0.926668	−0.463334	−	0.886184i	$-0.653347\pi$
$373$	−17.8969	−0.926668	−0.463334	+	0.886184i	$0.653347\pi$
$374$	−1.96039	−0.101370
$375$	−11.5038	−0.594054
$376$	0.360309	0.0185815
$377$	7.06891	0.364067
$378$	4.86606	0.250283
$379$	18.1966	0.934695	0.467347	−	0.884074i	$-0.345210\pi$
$379$	18.1966	0.934695	0.467347	+	0.884074i	$0.345210\pi$
$380$	−6.97505	−0.357813
$381$	−6.39303	−0.327525
$382$	14.7544	0.754901
$383$	17.2449	0.881172	0.440586	−	0.897710i	$-0.354771\pi$
$383$	17.2449	0.881172	0.440586	+	0.897710i	$0.354771\pi$
$384$	−1.00000	−0.0510310
$385$	20.6489	1.05237
$386$	−18.7746	−0.955604
$387$	−2.43213	−0.123632
$388$	−3.92641	−0.199333
$389$	−16.6600	−0.844697	−0.422349	−	0.906434i	$-0.638794\pi$
$389$	−16.6600	−0.844697	−0.422349	+	0.906434i	$0.638794\pi$
$390$	2.26632	0.114760
$391$	−0.557869	−0.0282127
$392$	16.6785	0.842391
$393$	3.21102	0.161974
$394$	12.6810	0.638861
$395$	28.3408	1.42598
$396$	1.96039	0.0985135
$397$	−7.48104	−0.375463	−0.187731	−	0.982220i	$-0.560113\pi$
$397$	−7.48104	−0.375463	−0.187731	+	0.982220i	$0.560113\pi$
$398$	12.9312	0.648183
$399$	15.6801	0.784985
$400$	−0.314531	−0.0157265
$401$	−11.5774	−0.578147	−0.289074	−	0.957307i	$-0.593347\pi$
$401$	−11.5774	−0.578147	−0.289074	+	0.957307i	$0.593347\pi$
$402$	−8.27684	−0.412811
$403$	7.50629	0.373915
$404$	1.77755	0.0884362
$405$	−2.16459	−0.107560
$406$	−32.8537	−1.63050
$407$	−3.79901	−0.188310
$408$	1.00000	0.0495074
$409$	−9.36414	−0.463027	−0.231514	−	0.972832i	$-0.574368\pi$
$409$	−9.36414	−0.463027	−0.231514	+	0.972832i	$0.574368\pi$
$410$	5.90841	0.291796
$411$	6.71342	0.331149
$412$	7.25793	0.357573
$413$	−4.86606	−0.239443
$414$	0.557869	0.0274178
$415$	19.6751	0.965813
$416$	1.04699	0.0513332
$417$	10.3361	0.506161
$418$	6.31705	0.308977
$419$	23.6957	1.15761	0.578806	−	0.815465i	$-0.303519\pi$
$419$	23.6957	1.15761	0.578806	+	0.815465i	$0.303519\pi$
$420$	−10.5330	−0.513960
$421$	9.45732	0.460922	0.230461	−	0.973082i	$-0.425977\pi$
$421$	9.45732	0.460922	0.230461	+	0.973082i	$0.425977\pi$
$422$	−22.2928	−1.08520
$423$	0.360309	0.0175188
$424$	−4.44569	−0.215902
$425$	0.314531	0.0152570
$426$	10.4047	0.504109
$427$	1.63695	0.0792175
$428$	−1.52404	−0.0736670
$429$	−2.05252	−0.0990967
$430$	5.26458	0.253880
$431$	24.3135	1.17114	0.585571	−	0.810621i	$-0.300870\pi$
$431$	24.3135	1.17114	0.585571	+	0.810621i	$0.300870\pi$
$432$	−1.00000	−0.0481125
$433$	2.75148	0.132228	0.0661138	−	0.997812i	$-0.478940\pi$
$433$	2.75148	0.132228	0.0661138	+	0.997812i	$0.478940\pi$
$434$	−34.8866	−1.67461
$435$	14.6145	0.700712
$436$	−8.65902	−0.414692
$437$	1.79764	0.0859929
$438$	10.5494	0.504069
$439$	−27.8372	−1.32860	−0.664300	−	0.747466i	$-0.731270\pi$
$439$	−27.8372	−1.32860	−0.664300	+	0.747466i	$0.731270\pi$
$440$	−4.24346	−0.202299
$441$	16.6785	0.794214
$442$	−1.04699	−0.0498005
$443$	12.3721	0.587816	0.293908	−	0.955834i	$-0.405044\pi$
$443$	12.3721	0.587816	0.293908	+	0.955834i	$0.405044\pi$
$444$	1.93788	0.0919678
$445$	−21.9739	−1.04166
$446$	17.9156	0.848328
$447$	4.79384	0.226741
$448$	−4.86606	−0.229900
$449$	−7.82637	−0.369349	−0.184675	−	0.982800i	$-0.559123\pi$
$449$	−7.82637	−0.369349	−0.184675	+	0.982800i	$0.559123\pi$
$450$	−0.314531	−0.0148271
$451$	−5.35103	−0.251970
$452$	−9.26644	−0.435857
$453$	−0.670341	−0.0314954
$454$	3.58551	0.168276
$455$	11.0280	0.517002
$456$	−3.22234	−0.150900
$457$	−19.3997	−0.907481	−0.453740	−	0.891134i	$-0.649911\pi$
$457$	−19.3997	−0.907481	−0.453740	+	0.891134i	$0.649911\pi$
$458$	−3.15147	−0.147259
$459$	1.00000	0.0466760
$460$	−1.20756	−0.0563028
$461$	6.82880	0.318049	0.159025	−	0.987275i	$-0.449165\pi$
$461$	6.82880	0.318049	0.159025	+	0.987275i	$0.449165\pi$
$462$	9.53938	0.443812
$463$	−6.88302	−0.319881	−0.159940	−	0.987127i	$-0.551130\pi$
$463$	−6.88302	−0.319881	−0.159940	+	0.987127i	$0.551130\pi$
$464$	6.75162	0.313436
$465$	15.5188	0.719666
$466$	−9.58028	−0.443798
$467$	−24.2443	−1.12189	−0.560945	−	0.827853i	$-0.689562\pi$
$467$	−24.2443	−1.12189	−0.560945	+	0.827853i	$0.689562\pi$
$468$	1.04699	0.0483974
$469$	−40.2755	−1.85975
$470$	−0.779924	−0.0359752
$471$	−0.300682	−0.0138547
$472$	1.00000	0.0460287
$473$	−4.76793	−0.219230
$474$	13.0929	0.601376
$475$	−1.01352	−0.0465036
$476$	4.86606	0.223035
$477$	−4.44569	−0.203554
$478$	−29.5344	−1.35087
$479$	21.3104	0.973698	0.486849	−	0.873486i	$-0.338146\pi$
$479$	21.3104	0.973698	0.486849	+	0.873486i	$0.338146\pi$
$480$	2.16459	0.0987998
$481$	−2.02895	−0.0925123
$482$	−19.9977	−0.910869
$483$	2.71462	0.123520
$484$	−7.15686	−0.325312
$485$	8.49909	0.385924
$486$	−1.00000	−0.0453609
$487$	−11.8898	−0.538780	−0.269390	−	0.963031i	$-0.586822\pi$
$487$	−11.8898	−0.538780	−0.269390	+	0.963031i	$0.586822\pi$
$488$	−0.336402	−0.0152282
$489$	−3.85466	−0.174314
$490$	−36.1022	−1.63093
$491$	25.8542	1.16678	0.583391	−	0.812192i	$-0.301726\pi$
$491$	25.8542	1.16678	0.583391	+	0.812192i	$0.301726\pi$
$492$	2.72957	0.123059
$493$	−6.75162	−0.304078
$494$	3.37377	0.151793
$495$	−4.24346	−0.190729
$496$	7.16937	0.321914
$497$	50.6298	2.27106
$498$	9.08951	0.407311
$499$	−29.6593	−1.32773	−0.663866	−	0.747851i	$-0.731086\pi$
$499$	−29.6593	−1.32773	−0.663866	+	0.747851i	$0.731086\pi$
$500$	11.5038	0.514466
$501$	20.6483	0.922497
$502$	11.1525	0.497761
$503$	−30.5752	−1.36328	−0.681640	−	0.731688i	$-0.738733\pi$
$503$	−30.5752	−1.36328	−0.681640	+	0.731688i	$0.738733\pi$
$504$	−4.86606	−0.216751
$505$	−3.84767	−0.171219
$506$	1.09364	0.0486183
$507$	11.9038	0.528666
$508$	6.39303	0.283645
$509$	32.2948	1.43144	0.715722	−	0.698385i	$-0.246098\pi$
$509$	32.2948	1.43144	0.715722	+	0.698385i	$0.246098\pi$
$510$	−2.16459	−0.0958499
$511$	51.3339	2.27088
$512$	1.00000	0.0441942
$513$	−3.22234	−0.142270
$514$	−26.5822	−1.17249
$515$	−15.7105	−0.692287
$516$	2.43213	0.107069
$517$	0.706348	0.0310652
$518$	9.42984	0.414323
$519$	−0.353487	−0.0155163
$520$	−2.26632	−0.0993847
$521$	12.5389	0.549339	0.274670	−	0.961539i	$-0.411432\pi$
$521$	12.5389	0.549339	0.274670	+	0.961539i	$0.411432\pi$
$522$	6.75162	0.295510
$523$	21.7811	0.952420	0.476210	−	0.879332i	$-0.342010\pi$
$523$	21.7811	0.952420	0.476210	+	0.879332i	$0.342010\pi$
$524$	−3.21102	−0.140274
$525$	−1.53052	−0.0667975
$526$	−21.5223	−0.938417
$527$	−7.16937	−0.312303
$528$	−1.96039	−0.0853152
$529$	−22.6888	−0.986469
$530$	9.62312	0.418001
$531$	1.00000	0.0433963
$532$	−15.6801	−0.679817
$533$	−2.85785	−0.123787
$534$	−10.1515	−0.439300
$535$	3.29892	0.142625
$536$	8.27684	0.357505
$537$	7.03446	0.303559
$538$	−12.2228	−0.526963
$539$	32.6964	1.40833
$540$	2.16459	0.0931493
$541$	−35.8162	−1.53986	−0.769930	−	0.638128i	$-0.779709\pi$
$541$	−35.8162	−1.53986	−0.769930	+	0.638128i	$0.779709\pi$
$542$	8.87974	0.381417
$543$	−17.1018	−0.733909
$544$	−1.00000	−0.0428746
$545$	18.7433	0.802874
$546$	5.09474	0.218035
$547$	−25.4110	−1.08650	−0.543249	−	0.839572i	$-0.682806\pi$
$547$	−25.4110	−1.08650	−0.543249	+	0.839572i	$0.682806\pi$
$548$	−6.71342	−0.286783
$549$	−0.336402	−0.0143573
$550$	−0.616603	−0.0262921
$551$	21.7560	0.926836
$552$	−0.557869	−0.0237445
$553$	63.7107	2.70925
$554$	−14.8539	−0.631084
$555$	−4.19473	−0.178056
$556$	−10.3361	−0.438349
$557$	8.01861	0.339760	0.169880	−	0.985465i	$-0.445662\pi$
$557$	8.01861	0.339760	0.169880	+	0.985465i	$0.445662\pi$
$558$	7.16937	0.303504
$559$	−2.54643	−0.107702
$560$	10.5330	0.445102
$561$	1.96039	0.0827679
$562$	4.93967	0.208367
$563$	26.9447	1.13558	0.567792	−	0.823172i	$-0.307798\pi$
$563$	26.9447	1.13558	0.567792	+	0.823172i	$0.307798\pi$
$564$	−0.360309	−0.0151718
$565$	20.0581	0.843850
$566$	15.1791	0.638027
$567$	−4.86606	−0.204355
$568$	−10.4047	−0.436571
$569$	−42.9950	−1.80245	−0.901223	−	0.433356i	$-0.857329\pi$
$569$	−42.9950	−1.80245	−0.901223	+	0.433356i	$0.857329\pi$
$570$	6.97505	0.292153
$571$	8.65569	0.362229	0.181115	−	0.983462i	$-0.442029\pi$
$571$	8.65569	0.362229	0.181115	+	0.983462i	$0.442029\pi$
$572$	2.05252	0.0858202
$573$	−14.7544	−0.616374
$574$	13.2822	0.554390
$575$	−0.175467	−0.00731747
$576$	1.00000	0.0416667
$577$	42.9811	1.78933	0.894664	−	0.446740i	$-0.147415\pi$
$577$	42.9811	1.78933	0.894664	+	0.446740i	$0.147415\pi$
$578$	1.00000	0.0415945
$579$	18.7746	0.780247
$580$	−14.6145	−0.606835
$581$	44.2301	1.83497
$582$	3.92641	0.162755
$583$	−8.71530	−0.360951
$584$	−10.5494	−0.436537
$585$	−2.26632	−0.0937008
$586$	18.3574	0.758338
$587$	8.43017	0.347950	0.173975	−	0.984750i	$-0.444339\pi$
$587$	8.43017	0.347950	0.173975	+	0.984750i	$0.444339\pi$
$588$	−16.6785	−0.687810
$589$	23.1021	0.951906
$590$	−2.16459	−0.0891149
$591$	−12.6810	−0.521628
$592$	−1.93788	−0.0796465
$593$	−4.85091	−0.199203	−0.0996015	−	0.995027i	$-0.531757\pi$
$593$	−4.85091	−0.199203	−0.0996015	+	0.995027i	$0.531757\pi$
$594$	−1.96039	−0.0804359
$595$	−10.5330	−0.431812
$596$	−4.79384	−0.196363
$597$	−12.9312	−0.529239
$598$	0.584086	0.0238851
$599$	35.1939	1.43798	0.718992	−	0.695019i	$-0.244604\pi$
$599$	35.1939	1.43798	0.718992	+	0.695019i	$0.244604\pi$
$600$	0.314531	0.0128407
$601$	4.37817	0.178589	0.0892947	−	0.996005i	$-0.471539\pi$
$601$	4.37817	0.178589	0.0892947	+	0.996005i	$0.471539\pi$
$602$	11.8349	0.482354
$603$	8.27684	0.337059
$604$	0.670341	0.0272758
$605$	15.4917	0.629827
$606$	−1.77755	−0.0722079
$607$	17.1010	0.694109	0.347054	−	0.937845i	$-0.387182\pi$
$607$	17.1010	0.694109	0.347054	+	0.937845i	$0.387182\pi$
$608$	3.22234	0.130683
$609$	32.8537	1.33130
$610$	0.728173	0.0294829
$611$	0.377242	0.0152616
$612$	−1.00000	−0.0404226
$613$	−45.7232	−1.84674	−0.923371	−	0.383908i	$-0.874578\pi$
$613$	−45.7232	−1.84674	−0.923371	+	0.383908i	$0.874578\pi$
$614$	−22.3229	−0.900877
$615$	−5.90841	−0.238250
$616$	−9.53938	−0.384353
$617$	9.58008	0.385680	0.192840	−	0.981230i	$-0.438230\pi$
$617$	9.58008	0.385680	0.192840	+	0.981230i	$0.438230\pi$
$618$	−7.25793	−0.291957
$619$	−25.6216	−1.02982	−0.514910	−	0.857244i	$-0.672175\pi$
$619$	−25.6216	−1.02982	−0.514910	+	0.857244i	$0.672175\pi$
$620$	−15.5188	−0.623249
$621$	−0.557869	−0.0223865
$622$	27.9250	1.11969
$623$	−49.3979	−1.97909
$624$	−1.04699	−0.0419133
$625$	−23.3284	−0.933137
$626$	−26.2584	−1.04950
$627$	−6.31705	−0.252278
$628$	0.300682	0.0119985
$629$	1.93788	0.0772684
$630$	10.5330	0.419646
$631$	−1.35737	−0.0540359	−0.0270180	−	0.999635i	$-0.508601\pi$
$631$	−1.35737	−0.0540359	−0.0270180	+	0.999635i	$0.508601\pi$
$632$	−13.0929	−0.520807
$633$	22.2928	0.886060
$634$	21.7424	0.863500
$635$	−13.8383	−0.549157
$636$	4.44569	0.176283
$637$	17.4623	0.691882
$638$	13.2358	0.524011
$639$	−10.4047	−0.411603
$640$	−2.16459	−0.0855631
$641$	12.7306	0.502830	0.251415	−	0.967879i	$-0.419104\pi$
$641$	12.7306	0.502830	0.251415	+	0.967879i	$0.419104\pi$
$642$	1.52404	0.0601489
$643$	11.5232	0.454432	0.227216	−	0.973844i	$-0.427038\pi$
$643$	11.5232	0.454432	0.227216	+	0.973844i	$0.427038\pi$
$644$	−2.71462	−0.106971
$645$	−5.26458	−0.207292
$646$	−3.22234	−0.126781
$647$	−29.2555	−1.15015	−0.575076	−	0.818100i	$-0.695028\pi$
$647$	−29.2555	−1.15015	−0.575076	+	0.818100i	$0.695028\pi$
$648$	1.00000	0.0392837
$649$	1.96039	0.0769522
$650$	−0.329312	−0.0129167
$651$	34.8866	1.36731
$652$	3.85466	0.150960
$653$	8.57205	0.335450	0.167725	−	0.985834i	$-0.446358\pi$
$653$	8.57205	0.335450	0.167725	+	0.985834i	$0.446358\pi$
$654$	8.65902	0.338595
$655$	6.95055	0.271581
$656$	−2.72957	−0.106572
$657$	−10.5494	−0.411571
$658$	−1.75329	−0.0683502
$659$	34.1989	1.33220	0.666099	−	0.745863i	$-0.267963\pi$
$659$	34.1989	1.33220	0.666099	+	0.745863i	$0.267963\pi$
$660$	4.24346	0.165176
$661$	12.5362	0.487603	0.243801	−	0.969825i	$-0.421605\pi$
$661$	12.5362	0.487603	0.243801	+	0.969825i	$0.421605\pi$
$662$	10.4552	0.406354
$663$	1.04699	0.0406619
$664$	−9.08951	−0.352741
$665$	33.9410	1.31618
$666$	−1.93788	−0.0750914
$667$	3.76652	0.145840
$668$	−20.6483	−0.798906
$669$	−17.9156	−0.692657
$670$	−17.9160	−0.692155
$671$	−0.659479	−0.0254589
$672$	4.86606	0.187712
$673$	5.84032	0.225128	0.112564	−	0.993644i	$-0.464094\pi$
$673$	5.84032	0.225128	0.112564	+	0.993644i	$0.464094\pi$
$674$	5.91275	0.227750
$675$	0.314531	0.0121063
$676$	−11.9038	−0.457839
$677$	−14.6680	−0.563737	−0.281869	−	0.959453i	$-0.590954\pi$
$677$	−14.6680	−0.563737	−0.281869	+	0.959453i	$0.590954\pi$
$678$	9.26644	0.355875
$679$	19.1061	0.733226
$680$	2.16459	0.0830084
$681$	−3.58551	−0.137397
$682$	14.0548	0.538185
$683$	−26.0000	−0.994861	−0.497430	−	0.867504i	$-0.665723\pi$
$683$	−26.0000	−0.994861	−0.497430	+	0.867504i	$0.665723\pi$
$684$	3.22234	0.123209
$685$	14.5318	0.555233
$686$	−47.0961	−1.79814
$687$	3.15147	0.120236
$688$	−2.43213	−0.0927241
$689$	−4.65461	−0.177327
$690$	1.20756	0.0459710
$691$	6.07597	0.231141	0.115570	−	0.993299i	$-0.463130\pi$
$691$	6.07597	0.231141	0.115570	+	0.993299i	$0.463130\pi$
$692$	0.353487	0.0134375
$693$	−9.53938	−0.362371
$694$	−12.5603	−0.476781
$695$	22.3735	0.848674
$696$	−6.75162	−0.255919
$697$	2.72957	0.103390
$698$	−14.0306	−0.531065
$699$	9.58028	0.362359
$700$	1.53052	0.0578483
$701$	24.7325	0.934133	0.467067	−	0.884222i	$-0.345311\pi$
$701$	24.7325	0.934133	0.467067	+	0.884222i	$0.345311\pi$
$702$	−1.04699	−0.0395163
$703$	−6.24451	−0.235516
$704$	1.96039	0.0738851
$705$	0.779924	0.0293736
$706$	−14.1189	−0.531370
$707$	−8.64964	−0.325303
$708$	−1.00000	−0.0375823
$709$	−41.6645	−1.56474	−0.782371	−	0.622812i	$-0.785990\pi$
$709$	−41.6645	−1.56474	−0.782371	+	0.622812i	$0.785990\pi$
$710$	22.5219	0.845233
$711$	−13.0929	−0.491021
$712$	10.1515	0.380445
$713$	3.99957	0.149785
$714$	−4.86606	−0.182108
$715$	−4.44288	−0.166154
$716$	−7.03446	−0.262890
$717$	29.5344	1.10298
$718$	13.7220	0.512101
$719$	29.5069	1.10042	0.550211	−	0.835025i	$-0.314547\pi$
$719$	29.5069	1.10042	0.550211	+	0.835025i	$0.314547\pi$
$720$	−2.16459	−0.0806697
$721$	−35.3175	−1.31529
$722$	−8.61655	−0.320675
$723$	19.9977	0.743721
$724$	17.1018	0.635584
$725$	−2.12359	−0.0788681
$726$	7.15686	0.265616
$727$	−31.6141	−1.17250	−0.586250	−	0.810130i	$-0.699396\pi$
$727$	−31.6141	−1.17250	−0.586250	+	0.810130i	$0.699396\pi$
$728$	−5.09474	−0.188823
$729$	1.00000	0.0370370
$730$	22.8351	0.845166
$731$	2.43213	0.0899556
$732$	0.336402	0.0124338
$733$	−23.9585	−0.884927	−0.442464	−	0.896787i	$-0.645895\pi$
$733$	−23.9585	−0.884927	−0.442464	+	0.896787i	$0.645895\pi$
$734$	1.76159	0.0650215
$735$	36.1022	1.33165
$736$	0.557869	0.0205633
$737$	16.2259	0.597687
$738$	−2.72957	−0.100477
$739$	14.1986	0.522304	0.261152	−	0.965298i	$-0.415898\pi$
$739$	14.1986	0.522304	0.261152	+	0.965298i	$0.415898\pi$
$740$	4.19473	0.154201
$741$	−3.37377	−0.123939
$742$	21.6330	0.794172
$743$	37.0295	1.35848	0.679241	−	0.733915i	$-0.262309\pi$
$743$	37.0295	1.35848	0.679241	+	0.733915i	$0.262309\pi$
$744$	−7.16937	−0.262842
$745$	10.3767	0.380173
$746$	−17.8969	−0.655253
$747$	−9.08951	−0.332568
$748$	−1.96039	−0.0716791
$749$	7.41604	0.270976
$750$	−11.5038	−0.420060
$751$	33.2533	1.21343	0.606716	−	0.794919i	$-0.292487\pi$
$751$	33.2533	1.21343	0.606716	+	0.794919i	$0.292487\pi$
$752$	0.360309	0.0131391
$753$	−11.1525	−0.406420
$754$	7.06891	0.257434
$755$	−1.45102	−0.0528079
$756$	4.86606	0.176977
$757$	8.97894	0.326345	0.163173	−	0.986598i	$-0.447827\pi$
$757$	8.97894	0.326345	0.163173	+	0.986598i	$0.447827\pi$
$758$	18.1966	0.660929
$759$	−1.09364	−0.0396967
$760$	−6.97505	−0.253012
$761$	−26.7272	−0.968860	−0.484430	−	0.874830i	$-0.660973\pi$
$761$	−26.7272	−0.968860	−0.484430	+	0.874830i	$0.660973\pi$
$762$	−6.39303	−0.231595
$763$	42.1353	1.52540
$764$	14.7544	0.533795
$765$	2.16459	0.0782611
$766$	17.2449	0.623083
$767$	1.04699	0.0378048
$768$	−1.00000	−0.0360844
$769$	10.7203	0.386584	0.193292	−	0.981141i	$-0.438084\pi$
$769$	10.7203	0.386584	0.193292	+	0.981141i	$0.438084\pi$
$770$	20.6489	0.744134
$771$	26.5822	0.957335
$772$	−18.7746	−0.675714
$773$	20.3177	0.730776	0.365388	−	0.930855i	$-0.380936\pi$
$773$	20.3177	0.730776	0.365388	+	0.930855i	$0.380936\pi$
$774$	−2.43213	−0.0874211
$775$	−2.25499	−0.0810015
$776$	−3.92641	−0.140950
$777$	−9.42984	−0.338294
$778$	−16.6600	−0.597291
$779$	−8.79559	−0.315135
$780$	2.26632	0.0811473
$781$	−20.3973	−0.729872
$782$	−0.557869	−0.0199494
$783$	−6.75162	−0.241283
$784$	16.6785	0.595661
$785$	−0.650854	−0.0232300
$786$	3.21102	0.114533
$787$	−7.56051	−0.269503	−0.134752	−	0.990879i	$-0.543024\pi$
$787$	−7.56051	−0.269503	−0.134752	+	0.990879i	$0.543024\pi$
$788$	12.6810	0.451743
$789$	21.5223	0.766215
$790$	28.3408	1.00832
$791$	45.0910	1.60325
$792$	1.96039	0.0696595
$793$	−0.352211	−0.0125074
$794$	−7.48104	−0.265492
$795$	−9.62312	−0.341297
$796$	12.9312	0.458335
$797$	−16.3480	−0.579075	−0.289538	−	0.957167i	$-0.593502\pi$
$797$	−16.3480	−0.579075	−0.289538	+	0.957167i	$0.593502\pi$
$798$	15.6801	0.555068
$799$	−0.360309	−0.0127468
$800$	−0.314531	−0.0111203
$801$	10.1515	0.358687
$802$	−11.5774	−0.408812
$803$	−20.6809	−0.729814
$804$	−8.27684	−0.291902
$805$	5.87606	0.207104
$806$	7.50629	0.264398
$807$	12.2228	0.430264
$808$	1.77755	0.0625339
$809$	−25.4694	−0.895458	−0.447729	−	0.894169i	$-0.647767\pi$
$809$	−25.4694	−0.895458	−0.447729	+	0.894169i	$0.647767\pi$
$810$	−2.16459	−0.0760561
$811$	−24.3649	−0.855566	−0.427783	−	0.903882i	$-0.640705\pi$
$811$	−24.3649	−0.855566	−0.427783	+	0.903882i	$0.640705\pi$
$812$	−32.8537	−1.15294
$813$	−8.87974	−0.311426
$814$	−3.79901	−0.133155
$815$	−8.34377	−0.292270
$816$	1.00000	0.0350070
$817$	−7.83714	−0.274187
$818$	−9.36414	−0.327410
$819$	−5.09474	−0.178024
$820$	5.90841	0.206331
$821$	−1.62941	−0.0568668	−0.0284334	−	0.999596i	$-0.509052\pi$
$821$	−1.62941	−0.0568668	−0.0284334	+	0.999596i	$0.509052\pi$
$822$	6.71342	0.234158
$823$	17.8183	0.621108	0.310554	−	0.950556i	$-0.399485\pi$
$823$	17.8183	0.621108	0.310554	+	0.950556i	$0.399485\pi$
$824$	7.25793	0.252842
$825$	0.616603	0.0214674
$826$	−4.86606	−0.169312
$827$	−52.0304	−1.80927	−0.904637	−	0.426183i	$-0.859858\pi$
$827$	−52.0304	−1.80927	−0.904637	+	0.426183i	$0.859858\pi$
$828$	0.557869	0.0193873
$829$	−46.5673	−1.61735	−0.808675	−	0.588256i	$-0.799815\pi$
$829$	−46.5673	−1.61735	−0.808675	+	0.588256i	$0.799815\pi$
$830$	19.6751	0.682933
$831$	14.8539	0.515278
$832$	1.04699	0.0362980
$833$	−16.6785	−0.577876
$834$	10.3361	0.357910
$835$	44.6951	1.54674
$836$	6.31705	0.218480
$837$	−7.16937	−0.247810
$838$	23.6957	0.818556
$839$	−44.1776	−1.52518	−0.762589	−	0.646883i	$-0.776072\pi$
$839$	−44.1776	−1.52518	−0.762589	+	0.646883i	$0.776072\pi$
$840$	−10.5330	−0.363424
$841$	16.5843	0.571873
$842$	9.45732	0.325921
$843$	−4.93967	−0.170131
$844$	−22.2928	−0.767350
$845$	25.7669	0.886408
$846$	0.360309	0.0123877
$847$	34.8257	1.19662
$848$	−4.44569	−0.152666
$849$	−15.1791	−0.520947
$850$	0.314531	0.0107883
$851$	−1.08108	−0.0370591
$852$	10.4047	0.356459
$853$	−10.0387	−0.343720	−0.171860	−	0.985121i	$-0.554978\pi$
$853$	−10.0387	−0.343720	−0.171860	+	0.985121i	$0.554978\pi$
$854$	1.63695	0.0560152
$855$	−6.97505	−0.238542
$856$	−1.52404	−0.0520904
$857$	−50.4890	−1.72467	−0.862335	−	0.506338i	$-0.830999\pi$
$857$	−50.4890	−1.72467	−0.862335	+	0.506338i	$0.830999\pi$
$858$	−2.05252	−0.0700719
$859$	−52.5188	−1.79192	−0.895959	−	0.444136i	$-0.853511\pi$
$859$	−52.5188	−1.79192	−0.895959	+	0.444136i	$0.853511\pi$
$860$	5.26458	0.179521
$861$	−13.2822	−0.452658
$862$	24.3135	0.828122
$863$	−23.6344	−0.804526	−0.402263	−	0.915524i	$-0.631776\pi$
$863$	−23.6344	−0.804526	−0.402263	+	0.915524i	$0.631776\pi$
$864$	−1.00000	−0.0340207
$865$	−0.765155	−0.0260161
$866$	2.75148	0.0934990
$867$	−1.00000	−0.0339618
$868$	−34.8866	−1.18413
$869$	−25.6672	−0.870699
$870$	14.6145	0.495478
$871$	8.66581	0.293630
$872$	−8.65902	−0.293232
$873$	−3.92641	−0.132889
$874$	1.79764	0.0608061
$875$	−55.9782	−1.89241
$876$	10.5494	0.356431
$877$	31.7149	1.07094	0.535468	−	0.844555i	$-0.320135\pi$
$877$	31.7149	1.07094	0.535468	+	0.844555i	$0.320135\pi$
$878$	−27.8372	−0.939462
$879$	−18.3574	−0.619180
$880$	−4.24346	−0.143047
$881$	11.9165	0.401478	0.200739	−	0.979645i	$-0.435666\pi$
$881$	11.9165	0.401478	0.200739	+	0.979645i	$0.435666\pi$
$882$	16.6785	0.561594
$883$	−25.5366	−0.859376	−0.429688	−	0.902977i	$-0.641376\pi$
$883$	−25.5366	−0.859376	−0.429688	+	0.902977i	$0.641376\pi$
$884$	−1.04699	−0.0352143
$885$	2.16459	0.0727620
$886$	12.3721	0.415649
$887$	−8.88205	−0.298230	−0.149115	−	0.988820i	$-0.547642\pi$
$887$	−8.88205	−0.298230	−0.149115	+	0.988820i	$0.547642\pi$
$888$	1.93788	0.0650311
$889$	−31.1088	−1.04336
$890$	−21.9739	−0.736568
$891$	1.96039	0.0656756
$892$	17.9156	0.599858
$893$	1.16104	0.0388527
$894$	4.79384	0.160330
$895$	15.2268	0.508974
$896$	−4.86606	−0.162564
$897$	−0.584086	−0.0195021
$898$	−7.82637	−0.261169
$899$	48.4048	1.61439
$900$	−0.314531	−0.0104844
$901$	4.44569	0.148107
$902$	−5.35103	−0.178170
$903$	−11.8349	−0.393840
$904$	−9.26644	−0.308197
$905$	−37.0185	−1.23054
$906$	−0.670341	−0.0222706
$907$	22.4490	0.745406	0.372703	−	0.927951i	$-0.378431\pi$
$907$	22.4490	0.745406	0.372703	+	0.927951i	$0.378431\pi$
$908$	3.58551	0.118989
$909$	1.77755	0.0589575
$910$	11.0280	0.365576
$911$	4.38582	0.145309	0.0726544	−	0.997357i	$-0.476853\pi$
$911$	4.38582	0.145309	0.0726544	+	0.997357i	$0.476853\pi$
$912$	−3.22234	−0.106702
$913$	−17.8190	−0.589723
$914$	−19.3997	−0.641686
$915$	−0.728173	−0.0240727
$916$	−3.15147	−0.104128
$917$	15.6250	0.515983
$918$	1.00000	0.0330049
$919$	−59.5435	−1.96416	−0.982080	−	0.188465i	$-0.939649\pi$
$919$	−59.5435	−1.96416	−0.982080	+	0.188465i	$0.939649\pi$
$920$	−1.20756	−0.0398121
$921$	22.3229	0.735563
$922$	6.82880	0.224895
$923$	−10.8937	−0.358569
$924$	9.53938	0.313823
$925$	0.609523	0.0200410
$926$	−6.88302	−0.226190
$927$	7.25793	0.238382
$928$	6.75162	0.221633
$929$	15.1210	0.496104	0.248052	−	0.968747i	$-0.420210\pi$
$929$	15.1210	0.496104	0.248052	+	0.968747i	$0.420210\pi$
$930$	15.5188	0.508881
$931$	53.7437	1.76138
$932$	−9.58028	−0.313812
$933$	−27.9250	−0.914223
$934$	−24.2443	−0.793296
$935$	4.24346	0.138776
$936$	1.04699	0.0342221
$937$	−10.2370	−0.334428	−0.167214	−	0.985921i	$-0.553477\pi$
$937$	−10.2370	−0.334428	−0.167214	+	0.985921i	$0.553477\pi$
$938$	−40.2755	−1.31504
$939$	26.2584	0.856911
$940$	−0.779924	−0.0254383
$941$	−38.9752	−1.27055	−0.635277	−	0.772284i	$-0.719114\pi$
$941$	−38.9752	−1.27055	−0.635277	+	0.772284i	$0.719114\pi$
$942$	−0.300682	−0.00979673
$943$	−1.52274	−0.0495873
$944$	1.00000	0.0325472
$945$	−10.5330	−0.342640
$946$	−4.76793	−0.155019
$947$	22.1295	0.719113	0.359557	−	0.933123i	$-0.382928\pi$
$947$	22.1295	0.719113	0.359557	+	0.933123i	$0.382928\pi$
$948$	13.0929	0.425237
$949$	−11.0452	−0.358541
$950$	−1.01352	−0.0328830
$951$	−21.7424	−0.705045
$952$	4.86606	0.157710
$953$	13.2994	0.430811	0.215406	−	0.976525i	$-0.430893\pi$
$953$	13.2994	0.430811	0.215406	+	0.976525i	$0.430893\pi$
$954$	−4.44569	−0.143935
$955$	−31.9373	−1.03347
$956$	−29.5344	−0.955211
$957$	−13.2358	−0.427853
$958$	21.3104	0.688509
$959$	32.6679	1.05490
$960$	2.16459	0.0698620
$961$	20.3999	0.658060
$962$	−2.02895	−0.0654161
$963$	−1.52404	−0.0491113
$964$	−19.9977	−0.644081
$965$	40.6395	1.30823
$966$	2.71462	0.0873415
$967$	−10.4481	−0.335990	−0.167995	−	0.985788i	$-0.553729\pi$
$967$	−10.4481	−0.335990	−0.167995	+	0.985788i	$0.553729\pi$
$968$	−7.15686	−0.230030
$969$	3.22234	0.103516
$970$	8.49909	0.272889
$971$	−53.1018	−1.70412	−0.852059	−	0.523446i	$-0.824646\pi$
$971$	−53.1018	−1.70412	−0.852059	+	0.523446i	$0.824646\pi$
$972$	−1.00000	−0.0320750
$973$	50.2961	1.61242
$974$	−11.8898	−0.380975
$975$	0.329312	0.0105464
$976$	−0.336402	−0.0107680
$977$	26.3978	0.844539	0.422270	−	0.906470i	$-0.361234\pi$
$977$	26.3978	0.844539	0.422270	+	0.906470i	$0.361234\pi$
$978$	−3.85466	−0.123258
$979$	19.9010	0.636038
$980$	−36.1022	−1.15324
$981$	−8.65902	−0.276461
$982$	25.8542	0.825039
$983$	21.2308	0.677158	0.338579	−	0.940938i	$-0.390054\pi$
$983$	21.2308	0.677158	0.338579	+	0.940938i	$0.390054\pi$
$984$	2.72957	0.0870155
$985$	−27.4493	−0.874607
$986$	−6.75162	−0.215015
$987$	1.75329	0.0558077
$988$	3.37377	0.107334
$989$	−1.35681	−0.0431441
$990$	−4.24346	−0.134866
$991$	−47.6248	−1.51285	−0.756426	−	0.654079i	$-0.773056\pi$
$991$	−47.6248	−1.51285	−0.756426	+	0.654079i	$0.773056\pi$
$992$	7.16937	0.227628
$993$	−10.4552	−0.331786
$994$	50.6298	1.60588
$995$	−27.9908	−0.887369
$996$	9.08951	0.288012
$997$	−17.6687	−0.559574	−0.279787	−	0.960062i	$-0.590264\pi$
$997$	−17.6687	−0.559574	−0.279787	+	0.960062i	$0.590264\pi$
$998$	−29.6593	−0.938849
$999$	1.93788	0.0613119

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.q.1.2	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.q.1.2	✓	6	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:	\( N \)	\(=\)	\( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.16459 q^{5} -1.00000 q^{6} -4.86606 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.16459 q^{5} -1.00000 q^{6} -4.86606 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.16459 q^{10} +1.96039 q^{11} -1.00000 q^{12} +1.04699 q^{13} -4.86606 q^{14} +2.16459 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} +3.22234 q^{19} -2.16459 q^{20} +4.86606 q^{21} +1.96039 q^{22} +0.557869 q^{23} -1.00000 q^{24} -0.314531 q^{25} +1.04699 q^{26} -1.00000 q^{27} -4.86606 q^{28} +6.75162 q^{29} +2.16459 q^{30} +7.16937 q^{31} +1.00000 q^{32} -1.96039 q^{33} -1.00000 q^{34} +10.5330 q^{35} +1.00000 q^{36} -1.93788 q^{37} +3.22234 q^{38} -1.04699 q^{39} -2.16459 q^{40} -2.72957 q^{41} +4.86606 q^{42} -2.43213 q^{43} +1.96039 q^{44} -2.16459 q^{45} +0.557869 q^{46} +0.360309 q^{47} -1.00000 q^{48} +16.6785 q^{49} -0.314531 q^{50} +1.00000 q^{51} +1.04699 q^{52} -4.44569 q^{53} -1.00000 q^{54} -4.24346 q^{55} -4.86606 q^{56} -3.22234 q^{57} +6.75162 q^{58} +1.00000 q^{59} +2.16459 q^{60} -0.336402 q^{61} +7.16937 q^{62} -4.86606 q^{63} +1.00000 q^{64} -2.26632 q^{65} -1.96039 q^{66} +8.27684 q^{67} -1.00000 q^{68} -0.557869 q^{69} +10.5330 q^{70} -10.4047 q^{71} +1.00000 q^{72} -10.5494 q^{73} -1.93788 q^{74} +0.314531 q^{75} +3.22234 q^{76} -9.53938 q^{77} -1.04699 q^{78} -13.0929 q^{79} -2.16459 q^{80} +1.00000 q^{81} -2.72957 q^{82} -9.08951 q^{83} +4.86606 q^{84} +2.16459 q^{85} -2.43213 q^{86} -6.75162 q^{87} +1.96039 q^{88} +10.1515 q^{89} -2.16459 q^{90} -5.09474 q^{91} +0.557869 q^{92} -7.16937 q^{93} +0.360309 q^{94} -6.97505 q^{95} -1.00000 q^{96} -3.92641 q^{97} +16.6785 q^{98} +1.96039 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} - 6 q^{3} + 6 q^{4} - 5 q^{5} - 6 q^{6} - q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 - 6 * q^3 + 6 * q^4 - 5 * q^5 - 6 * q^6 - q^7 + 6 * q^8 + 6 * q^9	\( 6 q + 6 q^{2} - 6 q^{3} + 6 q^{4} - 5 q^{5} - 6 q^{6} - q^{7} + 6 q^{8} + 6 q^{9} - 5 q^{10} - 6 q^{12} + 2 q^{13} - q^{14} + 5 q^{15} + 6 q^{16} - 6 q^{17} + 6 q^{18} - 5 q^{20} + q^{21} - 10 q^{23} - 6 q^{24} - 9 q^{25} + 2 q^{26} - 6 q^{27} - q^{28} - 3 q^{29} + 5 q^{30} - 7 q^{31} + 6 q^{32} - 6 q^{34} + 6 q^{35} + 6 q^{36} - 23 q^{37} - 2 q^{39} - 5 q^{40} - 12 q^{41} + q^{42} - 18 q^{43} - 5 q^{45} - 10 q^{46} - 14 q^{47} - 6 q^{48} + 9 q^{49} - 9 q^{50} + 6 q^{51} + 2 q^{52} + 21 q^{53} - 6 q^{54} + 4 q^{55} - q^{56} - 3 q^{58} + 6 q^{59} + 5 q^{60} - 2 q^{61} - 7 q^{62} - q^{63} + 6 q^{64} - 6 q^{65} + q^{67} - 6 q^{68} + 10 q^{69} + 6 q^{70} + 4 q^{71} + 6 q^{72} - 38 q^{73} - 23 q^{74} + 9 q^{75} - 22 q^{77} - 2 q^{78} - 30 q^{79} - 5 q^{80} + 6 q^{81} - 12 q^{82} + 23 q^{83} + q^{84} + 5 q^{85} - 18 q^{86} + 3 q^{87} - 7 q^{89} - 5 q^{90} - 5 q^{91} - 10 q^{92} + 7 q^{93} - 14 q^{94} - 7 q^{95} - 6 q^{96} - 10 q^{97} + 9 q^{98}+O(q^{100}) \) 6 * q + 6 * q^2 - 6 * q^3 + 6 * q^4 - 5 * q^5 - 6 * q^6 - q^7 + 6 * q^8 + 6 * q^9 - 5 * q^10 - 6 * q^12 + 2 * q^13 - q^14 + 5 * q^15 + 6 * q^16 - 6 * q^17 + 6 * q^18 - 5 * q^20 + q^21 - 10 * q^23 - 6 * q^24 - 9 * q^25 + 2 * q^26 - 6 * q^27 - q^28 - 3 * q^29 + 5 * q^30 - 7 * q^31 + 6 * q^32 - 6 * q^34 + 6 * q^35 + 6 * q^36 - 23 * q^37 - 2 * q^39 - 5 * q^40 - 12 * q^41 + q^42 - 18 * q^43 - 5 * q^45 - 10 * q^46 - 14 * q^47 - 6 * q^48 + 9 * q^49 - 9 * q^50 + 6 * q^51 + 2 * q^52 + 21 * q^53 - 6 * q^54 + 4 * q^55 - q^56 - 3 * q^58 + 6 * q^59 + 5 * q^60 - 2 * q^61 - 7 * q^62 - q^63 + 6 * q^64 - 6 * q^65 + q^67 - 6 * q^68 + 10 * q^69 + 6 * q^70 + 4 * q^71 + 6 * q^72 - 38 * q^73 - 23 * q^74 + 9 * q^75 - 22 * q^77 - 2 * q^78 - 30 * q^79 - 5 * q^80 + 6 * q^81 - 12 * q^82 + 23 * q^83 + q^84 + 5 * q^85 - 18 * q^86 + 3 * q^87 - 7 * q^89 - 5 * q^90 - 5 * q^91 - 10 * q^92 + 7 * q^93 - 14 * q^94 - 7 * q^95 - 6 * q^96 - 10 * q^97 + 9 * q^98

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