LMFDB - Embedded newform 6042.2.a.bd.1.4

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:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 2 x^{10} - 35 x^{9} + 77 x^{8} + 394 x^{7} - 994 x^{6} - 1477 x^{5} + 4683 x^{4} + 563 x^{3} + \cdots + 1534 $ x^11 - 2x^10 - 35x^9 + 77x^8 + 394x^7 - 994x^6 - 1477x^5 + 4683x^4 + 563x^3 - 6194x^2 + 1258x + 1534
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.23681$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.23681 q^{5} +1.00000 q^{6} +2.50061 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.23681 q^{5} +1.00000 q^{6} +2.50061 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.23681 q^{10} +2.68446 q^{11} -1.00000 q^{12} -6.45770 q^{13} -2.50061 q^{14} +1.23681 q^{15} +1.00000 q^{16} +7.36544 q^{17} -1.00000 q^{18} +1.00000 q^{19} -1.23681 q^{20} -2.50061 q^{21} -2.68446 q^{22} -1.51925 q^{23} +1.00000 q^{24} -3.47029 q^{25} +6.45770 q^{26} -1.00000 q^{27} +2.50061 q^{28} -8.34256 q^{29} -1.23681 q^{30} +7.18042 q^{31} -1.00000 q^{32} -2.68446 q^{33} -7.36544 q^{34} -3.09279 q^{35} +1.00000 q^{36} +4.05847 q^{37} -1.00000 q^{38} +6.45770 q^{39} +1.23681 q^{40} -8.17246 q^{41} +2.50061 q^{42} -2.01370 q^{43} +2.68446 q^{44} -1.23681 q^{45} +1.51925 q^{46} -4.36153 q^{47} -1.00000 q^{48} -0.746937 q^{49} +3.47029 q^{50} -7.36544 q^{51} -6.45770 q^{52} +1.00000 q^{53} +1.00000 q^{54} -3.32018 q^{55} -2.50061 q^{56} -1.00000 q^{57} +8.34256 q^{58} -9.31062 q^{59} +1.23681 q^{60} +4.15987 q^{61} -7.18042 q^{62} +2.50061 q^{63} +1.00000 q^{64} +7.98698 q^{65} +2.68446 q^{66} +2.15007 q^{67} +7.36544 q^{68} +1.51925 q^{69} +3.09279 q^{70} +5.63019 q^{71} -1.00000 q^{72} -4.46887 q^{73} -4.05847 q^{74} +3.47029 q^{75} +1.00000 q^{76} +6.71279 q^{77} -6.45770 q^{78} -2.74692 q^{79} -1.23681 q^{80} +1.00000 q^{81} +8.17246 q^{82} +9.55852 q^{83} -2.50061 q^{84} -9.10968 q^{85} +2.01370 q^{86} +8.34256 q^{87} -2.68446 q^{88} -0.527893 q^{89} +1.23681 q^{90} -16.1482 q^{91} -1.51925 q^{92} -7.18042 q^{93} +4.36153 q^{94} -1.23681 q^{95} +1.00000 q^{96} +12.2288 q^{97} +0.746937 q^{98} +2.68446 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 11 q^{2} - 11 q^{3} + 11 q^{4} + 2 q^{5} + 11 q^{6} - 2 q^{7} - 11 q^{8} + 11 q^{9}+O(q^{10}) $ 11 * q - 11 * q^2 - 11 * q^3 + 11 * q^4 + 2 * q^5 + 11 * q^6 - 2 * q^7 - 11 * q^8 + 11 * q^9	\( 11 q - 11 q^{2} - 11 q^{3} + 11 q^{4} + 2 q^{5} + 11 q^{6} - 2 q^{7} - 11 q^{8} + 11 q^{9} - 2 q^{10} - 6 q^{11} - 11 q^{12} - 7 q^{13} + 2 q^{14} - 2 q^{15} + 11 q^{16} - 16 q^{17} - 11 q^{18} + 11 q^{19} + 2 q^{20} + 2 q^{21} + 6 q^{22} - 11 q^{23} + 11 q^{24} + 19 q^{25} + 7 q^{26} - 11 q^{27} - 2 q^{28} - 7 q^{29} + 2 q^{30} + 12 q^{31} - 11 q^{32} + 6 q^{33} + 16 q^{34} - 5 q^{35} + 11 q^{36} + 3 q^{37} - 11 q^{38} + 7 q^{39} - 2 q^{40} + 11 q^{41} - 2 q^{42} + 7 q^{43} - 6 q^{44} + 2 q^{45} + 11 q^{46} - 37 q^{47} - 11 q^{48} + 23 q^{49} - 19 q^{50} + 16 q^{51} - 7 q^{52} + 11 q^{53} + 11 q^{54} - 11 q^{55} + 2 q^{56} - 11 q^{57} + 7 q^{58} - 16 q^{59} - 2 q^{60} + 24 q^{61} - 12 q^{62} - 2 q^{63} + 11 q^{64} - 7 q^{65} - 6 q^{66} - 28 q^{67} - 16 q^{68} + 11 q^{69} + 5 q^{70} + 4 q^{71} - 11 q^{72} - 7 q^{73} - 3 q^{74} - 19 q^{75} + 11 q^{76} - 13 q^{77} - 7 q^{78} + 5 q^{79} + 2 q^{80} + 11 q^{81} - 11 q^{82} - 11 q^{83} + 2 q^{84} - 11 q^{85} - 7 q^{86} + 7 q^{87} + 6 q^{88} - 10 q^{89} - 2 q^{90} - 24 q^{91} - 11 q^{92} - 12 q^{93} + 37 q^{94} + 2 q^{95} + 11 q^{96} - 24 q^{97} - 23 q^{98} - 6 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - 11 * q^3 + 11 * q^4 + 2 * q^5 + 11 * q^6 - 2 * q^7 - 11 * q^8 + 11 * q^9 - 2 * q^10 - 6 * q^11 - 11 * q^12 - 7 * q^13 + 2 * q^14 - 2 * q^15 + 11 * q^16 - 16 * q^17 - 11 * q^18 + 11 * q^19 + 2 * q^20 + 2 * q^21 + 6 * q^22 - 11 * q^23 + 11 * q^24 + 19 * q^25 + 7 * q^26 - 11 * q^27 - 2 * q^28 - 7 * q^29 + 2 * q^30 + 12 * q^31 - 11 * q^32 + 6 * q^33 + 16 * q^34 - 5 * q^35 + 11 * q^36 + 3 * q^37 - 11 * q^38 + 7 * q^39 - 2 * q^40 + 11 * q^41 - 2 * q^42 + 7 * q^43 - 6 * q^44 + 2 * q^45 + 11 * q^46 - 37 * q^47 - 11 * q^48 + 23 * q^49 - 19 * q^50 + 16 * q^51 - 7 * q^52 + 11 * q^53 + 11 * q^54 - 11 * q^55 + 2 * q^56 - 11 * q^57 + 7 * q^58 - 16 * q^59 - 2 * q^60 + 24 * q^61 - 12 * q^62 - 2 * q^63 + 11 * q^64 - 7 * q^65 - 6 * q^66 - 28 * q^67 - 16 * q^68 + 11 * q^69 + 5 * q^70 + 4 * q^71 - 11 * q^72 - 7 * q^73 - 3 * q^74 - 19 * q^75 + 11 * q^76 - 13 * q^77 - 7 * q^78 + 5 * q^79 + 2 * q^80 + 11 * q^81 - 11 * q^82 - 11 * q^83 + 2 * q^84 - 11 * q^85 - 7 * q^86 + 7 * q^87 + 6 * q^88 - 10 * q^89 - 2 * q^90 - 24 * q^91 - 11 * q^92 - 12 * q^93 + 37 * q^94 + 2 * q^95 + 11 * q^96 - 24 * q^97 - 23 * q^98 - 6 * 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
$5$	−1.23681	−0.553120	−0.276560	−	0.960997i	$-0.589195\pi$
$5$	−1.23681	−0.553120	−0.276560	+	0.960997i	$0.589195\pi$
$6$	1.00000	0.408248
$7$	2.50061	0.945143	0.472571	−	0.881292i	$-0.343326\pi$
$7$	2.50061	0.945143	0.472571	+	0.881292i	$0.343326\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.23681	0.391115
$11$	2.68446	0.809395	0.404697	−	0.914451i	$-0.367377\pi$
$11$	2.68446	0.809395	0.404697	+	0.914451i	$0.367377\pi$
$12$	−1.00000	−0.288675
$13$	−6.45770	−1.79104	−0.895522	−	0.445017i	$-0.853198\pi$
$13$	−6.45770	−1.79104	−0.895522	+	0.445017i	$0.853198\pi$
$14$	−2.50061	−0.668317
$15$	1.23681	0.319344
$16$	1.00000	0.250000
$17$	7.36544	1.78638	0.893190	−	0.449679i	$-0.148462\pi$
$17$	7.36544	1.78638	0.893190	+	0.449679i	$0.148462\pi$
$18$	−1.00000	−0.235702
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−1.23681	−0.276560
$21$	−2.50061	−0.545678
$22$	−2.68446	−0.572329
$23$	−1.51925	−0.316786	−0.158393	−	0.987376i	$-0.550631\pi$
$23$	−1.51925	−0.316786	−0.158393	+	0.987376i	$0.550631\pi$
$24$	1.00000	0.204124
$25$	−3.47029	−0.694058
$26$	6.45770	1.26646
$27$	−1.00000	−0.192450
$28$	2.50061	0.472571
$29$	−8.34256	−1.54917	−0.774587	−	0.632467i	$-0.782042\pi$
$29$	−8.34256	−1.54917	−0.774587	+	0.632467i	$0.782042\pi$
$30$	−1.23681	−0.225810
$31$	7.18042	1.28964	0.644821	−	0.764333i	$-0.276932\pi$
$31$	7.18042	1.28964	0.644821	+	0.764333i	$0.276932\pi$
$32$	−1.00000	−0.176777
$33$	−2.68446	−0.467304
$34$	−7.36544	−1.26316
$35$	−3.09279	−0.522778
$36$	1.00000	0.166667
$37$	4.05847	0.667208	0.333604	−	0.942713i	$-0.391735\pi$
$37$	4.05847	0.667208	0.333604	+	0.942713i	$0.391735\pi$
$38$	−1.00000	−0.162221
$39$	6.45770	1.03406
$40$	1.23681	0.195558
$41$	−8.17246	−1.27632	−0.638162	−	0.769902i	$-0.720305\pi$
$41$	−8.17246	−1.27632	−0.638162	+	0.769902i	$0.720305\pi$
$42$	2.50061	0.385853
$43$	−2.01370	−0.307087	−0.153544	−	0.988142i	$-0.549069\pi$
$43$	−2.01370	−0.307087	−0.153544	+	0.988142i	$0.549069\pi$
$44$	2.68446	0.404697
$45$	−1.23681	−0.184373
$46$	1.51925	0.224002
$47$	−4.36153	−0.636195	−0.318098	−	0.948058i	$-0.603044\pi$
$47$	−4.36153	−0.636195	−0.318098	+	0.948058i	$0.603044\pi$
$48$	−1.00000	−0.144338
$49$	−0.746937	−0.106705
$50$	3.47029	0.490773
$51$	−7.36544	−1.03137
$52$	−6.45770	−0.895522
$53$	1.00000	0.137361
$53$	1.00000	0.137361
$54$	1.00000	0.136083
$55$	−3.32018	−0.447693
$56$	−2.50061	−0.334158
$57$	−1.00000	−0.132453
$58$	8.34256	1.09543
$59$	−9.31062	−1.21214	−0.606070	−	0.795412i	$-0.707255\pi$
$59$	−9.31062	−1.21214	−0.606070	+	0.795412i	$0.707255\pi$
$60$	1.23681	0.159672
$61$	4.15987	0.532617	0.266309	−	0.963888i	$-0.414196\pi$
$61$	4.15987	0.532617	0.266309	+	0.963888i	$0.414196\pi$
$62$	−7.18042	−0.911915
$63$	2.50061	0.315048
$64$	1.00000	0.125000
$65$	7.98698	0.990663
$66$	2.68446	0.330434
$67$	2.15007	0.262673	0.131337	−	0.991338i	$-0.458073\pi$
$67$	2.15007	0.262673	0.131337	+	0.991338i	$0.458073\pi$
$68$	7.36544	0.893190
$69$	1.51925	0.182897
$70$	3.09279	0.369660
$71$	5.63019	0.668181	0.334091	−	0.942541i	$-0.391571\pi$
$71$	5.63019	0.668181	0.334091	+	0.942541i	$0.391571\pi$
$72$	−1.00000	−0.117851
$73$	−4.46887	−0.523041	−0.261521	−	0.965198i	$-0.584224\pi$
$73$	−4.46887	−0.523041	−0.261521	+	0.965198i	$0.584224\pi$
$74$	−4.05847	−0.471787
$75$	3.47029	0.400715
$76$	1.00000	0.114708
$77$	6.71279	0.764994
$78$	−6.45770	−0.731191
$79$	−2.74692	−0.309053	−0.154527	−	0.987989i	$-0.549385\pi$
$79$	−2.74692	−0.309053	−0.154527	+	0.987989i	$0.549385\pi$
$80$	−1.23681	−0.138280
$81$	1.00000	0.111111
$82$	8.17246	0.902497
$83$	9.55852	1.04918	0.524592	−	0.851354i	$-0.324218\pi$
$83$	9.55852	1.04918	0.524592	+	0.851354i	$0.324218\pi$
$84$	−2.50061	−0.272839
$85$	−9.10968	−0.988083
$86$	2.01370	0.217143
$87$	8.34256	0.894416
$88$	−2.68446	−0.286164
$89$	−0.527893	−0.0559565	−0.0279783	−	0.999609i	$-0.508907\pi$
$89$	−0.527893	−0.0559565	−0.0279783	+	0.999609i	$0.508907\pi$
$90$	1.23681	0.130372
$91$	−16.1482	−1.69279
$92$	−1.51925	−0.158393
$93$	−7.18042	−0.744575
$94$	4.36153	0.449858
$95$	−1.23681	−0.126895
$96$	1.00000	0.102062
$97$	12.2288	1.24164	0.620821	−	0.783952i	$-0.286799\pi$
$97$	12.2288	1.24164	0.620821	+	0.783952i	$0.286799\pi$
$98$	0.746937	0.0754520
$99$	2.68446	0.269798
$100$	−3.47029	−0.347029
$101$	−16.8406	−1.67570	−0.837852	−	0.545897i	$-0.816189\pi$
$101$	−16.8406	−1.67570	−0.837852	+	0.545897i	$0.816189\pi$
$102$	7.36544	0.729287
$103$	6.97308	0.687078	0.343539	−	0.939138i	$-0.388374\pi$
$103$	6.97308	0.687078	0.343539	+	0.939138i	$0.388374\pi$
$104$	6.45770	0.633230
$105$	3.09279	0.301826
$106$	−1.00000	−0.0971286
$107$	−9.11050	−0.880746	−0.440373	−	0.897815i	$-0.645154\pi$
$107$	−9.11050	−0.880746	−0.440373	+	0.897815i	$0.645154\pi$
$108$	−1.00000	−0.0962250
$109$	−3.78298	−0.362344	−0.181172	−	0.983451i	$-0.557989\pi$
$109$	−3.78298	−0.362344	−0.181172	+	0.983451i	$0.557989\pi$
$110$	3.32018	0.316567
$111$	−4.05847	−0.385213
$112$	2.50061	0.236286
$113$	−18.2464	−1.71648	−0.858241	−	0.513248i	$-0.828442\pi$
$113$	−18.2464	−1.71648	−0.858241	+	0.513248i	$0.828442\pi$
$114$	1.00000	0.0936586
$115$	1.87903	0.175221
$116$	−8.34256	−0.774587
$117$	−6.45770	−0.597015
$118$	9.31062	0.857112
$119$	18.4181	1.68838
$120$	−1.23681	−0.112905
$121$	−3.79368	−0.344880
$122$	−4.15987	−0.376617
$123$	8.17246	0.736886
$124$	7.18042	0.644821
$125$	10.4762	0.937018
$126$	−2.50061	−0.222772
$127$	4.56305	0.404905	0.202453	−	0.979292i	$-0.435109\pi$
$127$	4.56305	0.404905	0.202453	+	0.979292i	$0.435109\pi$
$128$	−1.00000	−0.0883883
$129$	2.01370	0.177297
$130$	−7.98698	−0.700505
$131$	11.2391	0.981961	0.490980	−	0.871171i	$-0.336639\pi$
$131$	11.2391	0.981961	0.490980	+	0.871171i	$0.336639\pi$
$132$	−2.68446	−0.233652
$133$	2.50061	0.216831
$134$	−2.15007	−0.185738
$135$	1.23681	0.106448
$136$	−7.36544	−0.631581
$137$	−9.46832	−0.808933	−0.404467	−	0.914553i	$-0.632543\pi$
$137$	−9.46832	−0.808933	−0.404467	+	0.914553i	$0.632543\pi$
$138$	−1.51925	−0.129327
$139$	−1.18570	−0.100569	−0.0502847	−	0.998735i	$-0.516013\pi$
$139$	−1.18570	−0.100569	−0.0502847	+	0.998735i	$0.516013\pi$
$140$	−3.09279	−0.261389
$141$	4.36153	0.367307
$142$	−5.63019	−0.472475
$143$	−17.3354	−1.44966
$144$	1.00000	0.0833333
$145$	10.3182	0.856880
$146$	4.46887	0.369846
$147$	0.746937	0.0616063
$148$	4.05847	0.333604
$149$	−13.6650	−1.11948	−0.559741	−	0.828668i	$-0.689099\pi$
$149$	−13.6650	−1.11948	−0.559741	+	0.828668i	$0.689099\pi$
$150$	−3.47029	−0.283348
$151$	8.08814	0.658203	0.329102	−	0.944295i	$-0.393254\pi$
$151$	8.08814	0.658203	0.329102	+	0.944295i	$0.393254\pi$
$152$	−1.00000	−0.0811107
$153$	7.36544	0.595460
$154$	−6.71279	−0.540932
$155$	−8.88086	−0.713327
$156$	6.45770	0.517030
$157$	−6.62674	−0.528871	−0.264436	−	0.964403i	$-0.585186\pi$
$157$	−6.62674	−0.528871	−0.264436	+	0.964403i	$0.585186\pi$
$158$	2.74692	0.218534
$159$	−1.00000	−0.0793052
$160$	1.23681	0.0977788
$161$	−3.79906	−0.299408
$162$	−1.00000	−0.0785674
$163$	4.51646	0.353756	0.176878	−	0.984233i	$-0.443400\pi$
$163$	4.51646	0.353756	0.176878	+	0.984233i	$0.443400\pi$
$164$	−8.17246	−0.638162
$165$	3.32018	0.258476
$166$	−9.55852	−0.741885
$167$	8.78247	0.679608	0.339804	−	0.940496i	$-0.389639\pi$
$167$	8.78247	0.679608	0.339804	+	0.940496i	$0.389639\pi$
$168$	2.50061	0.192926
$169$	28.7019	2.20784
$170$	9.10968	0.698680
$171$	1.00000	0.0764719
$172$	−2.01370	−0.153544
$173$	−23.0007	−1.74871	−0.874355	−	0.485288i	$-0.838715\pi$
$173$	−23.0007	−1.74871	−0.874355	+	0.485288i	$0.838715\pi$
$174$	−8.34256	−0.632448
$175$	−8.67785	−0.655984
$176$	2.68446	0.202349
$177$	9.31062	0.699829
$178$	0.527893	0.0395672
$179$	14.8460	1.10965	0.554823	−	0.831968i	$-0.312786\pi$
$179$	14.8460	1.10965	0.554823	+	0.831968i	$0.312786\pi$
$180$	−1.23681	−0.0921867
$181$	10.6239	0.789670	0.394835	−	0.918752i	$-0.370802\pi$
$181$	10.6239	0.789670	0.394835	+	0.918752i	$0.370802\pi$
$182$	16.1482	1.19698
$183$	−4.15987	−0.307507
$184$	1.51925	0.112001
$185$	−5.01957	−0.369046
$186$	7.18042	0.526494
$187$	19.7722	1.44589
$188$	−4.36153	−0.318098
$189$	−2.50061	−0.181893
$190$	1.23681	0.0897280
$191$	3.59388	0.260044	0.130022	−	0.991511i	$-0.458495\pi$
$191$	3.59388	0.260044	0.130022	+	0.991511i	$0.458495\pi$
$192$	−1.00000	−0.0721688
$193$	−11.6896	−0.841439	−0.420720	−	0.907191i	$-0.638222\pi$
$193$	−11.6896	−0.841439	−0.420720	+	0.907191i	$0.638222\pi$
$194$	−12.2288	−0.877974
$195$	−7.98698	−0.571960
$196$	−0.746937	−0.0533526
$197$	6.30783	0.449414	0.224707	−	0.974426i	$-0.427857\pi$
$197$	6.30783	0.449414	0.224707	+	0.974426i	$0.427857\pi$
$198$	−2.68446	−0.190776
$199$	16.3443	1.15862	0.579309	−	0.815108i	$-0.303322\pi$
$199$	16.3443	1.15862	0.579309	+	0.815108i	$0.303322\pi$
$200$	3.47029	0.245387
$201$	−2.15007	−0.151654
$202$	16.8406	1.18490
$203$	−20.8615	−1.46419
$204$	−7.36544	−0.515684
$205$	10.1078	0.705961
$206$	−6.97308	−0.485838
$207$	−1.51925	−0.105595
$208$	−6.45770	−0.447761
$209$	2.68446	0.185688
$210$	−3.09279	−0.213423
$211$	18.1841	1.25185	0.625924	−	0.779884i	$-0.284722\pi$
$211$	18.1841	1.25185	0.625924	+	0.779884i	$0.284722\pi$
$212$	1.00000	0.0686803
$213$	−5.63019	−0.385775
$214$	9.11050	0.622781
$215$	2.49058	0.169856
$216$	1.00000	0.0680414
$217$	17.9555	1.21890
$218$	3.78298	0.256216
$219$	4.46887	0.301978
$220$	−3.32018	−0.223846
$221$	−47.5638	−3.19949
$222$	4.05847	0.272386
$223$	−1.59565	−0.106853	−0.0534263	−	0.998572i	$-0.517014\pi$
$223$	−1.59565	−0.106853	−0.0534263	+	0.998572i	$0.517014\pi$
$224$	−2.50061	−0.167079
$225$	−3.47029	−0.231353
$226$	18.2464	1.21374
$227$	−27.9395	−1.85441	−0.927206	−	0.374552i	$-0.877797\pi$
$227$	−27.9395	−1.85441	−0.927206	+	0.374552i	$0.877797\pi$
$228$	−1.00000	−0.0662266
$229$	2.68484	0.177420	0.0887098	−	0.996058i	$-0.471726\pi$
$229$	2.68484	0.177420	0.0887098	+	0.996058i	$0.471726\pi$
$230$	−1.87903	−0.123900
$231$	−6.71279	−0.441669
$232$	8.34256	0.547716
$233$	12.4330	0.814510	0.407255	−	0.913314i	$-0.366486\pi$
$233$	12.4330	0.814510	0.407255	+	0.913314i	$0.366486\pi$
$234$	6.45770	0.422153
$235$	5.39441	0.351892
$236$	−9.31062	−0.606070
$237$	2.74692	0.178432
$238$	−18.4181	−1.19387
$239$	0.256780	0.0166097	0.00830485	−	0.999966i	$-0.497356\pi$
$239$	0.256780	0.0166097	0.00830485	+	0.999966i	$0.497356\pi$
$240$	1.23681	0.0798360
$241$	−20.8924	−1.34580	−0.672898	−	0.739735i	$-0.734951\pi$
$241$	−20.8924	−1.34580	−0.672898	+	0.739735i	$0.734951\pi$
$242$	3.79368	0.243867
$243$	−1.00000	−0.0641500
$244$	4.15987	0.266309
$245$	0.923822	0.0590208
$246$	−8.17246	−0.521057
$247$	−6.45770	−0.410894
$248$	−7.18042	−0.455957
$249$	−9.55852	−0.605747
$250$	−10.4762	−0.662572
$251$	1.11998	0.0706926	0.0353463	−	0.999375i	$-0.488747\pi$
$251$	1.11998	0.0706926	0.0353463	+	0.999375i	$0.488747\pi$
$252$	2.50061	0.157524
$253$	−4.07837	−0.256405
$254$	−4.56305	−0.286311
$255$	9.10968	0.570470
$256$	1.00000	0.0625000
$257$	−12.3181	−0.768380	−0.384190	−	0.923254i	$-0.625519\pi$
$257$	−12.3181	−0.768380	−0.384190	+	0.923254i	$0.625519\pi$
$258$	−2.01370	−0.125368
$259$	10.1487	0.630607
$260$	7.98698	0.495331
$261$	−8.34256	−0.516392
$262$	−11.2391	−0.694351
$263$	−15.1112	−0.931794	−0.465897	−	0.884839i	$-0.654268\pi$
$263$	−15.1112	−0.931794	−0.465897	+	0.884839i	$0.654268\pi$
$264$	2.68446	0.165217
$265$	−1.23681	−0.0759769
$266$	−2.50061	−0.153322
$267$	0.527893	0.0323065
$268$	2.15007	0.131337
$269$	1.56889	0.0956570	0.0478285	−	0.998856i	$-0.484770\pi$
$269$	1.56889	0.0956570	0.0478285	+	0.998856i	$0.484770\pi$
$270$	−1.23681	−0.0752701
$271$	16.0601	0.975584	0.487792	−	0.872960i	$-0.337802\pi$
$271$	16.0601	0.975584	0.487792	+	0.872960i	$0.337802\pi$
$272$	7.36544	0.446595
$273$	16.1482	0.977334
$274$	9.46832	0.572002
$275$	−9.31585	−0.561767
$276$	1.51925	0.0914483
$277$	−2.75686	−0.165644	−0.0828219	−	0.996564i	$-0.526393\pi$
$277$	−2.75686	−0.165644	−0.0828219	+	0.996564i	$0.526393\pi$
$278$	1.18570	0.0711133
$279$	7.18042	0.429881
$280$	3.09279	0.184830
$281$	−26.7999	−1.59875	−0.799373	−	0.600835i	$-0.794835\pi$
$281$	−26.7999	−1.59875	−0.799373	+	0.600835i	$0.794835\pi$
$282$	−4.36153	−0.259726
$283$	−13.8300	−0.822108	−0.411054	−	0.911611i	$-0.634839\pi$
$283$	−13.8300	−0.822108	−0.411054	+	0.911611i	$0.634839\pi$
$284$	5.63019	0.334091
$285$	1.23681	0.0732626
$286$	17.3354	1.02507
$287$	−20.4362	−1.20631
$288$	−1.00000	−0.0589256
$289$	37.2496	2.19116
$290$	−10.3182	−0.605906
$291$	−12.2288	−0.716863
$292$	−4.46887	−0.261521
$293$	−8.04316	−0.469887	−0.234943	−	0.972009i	$-0.575490\pi$
$293$	−8.04316	−0.469887	−0.234943	+	0.972009i	$0.575490\pi$
$294$	−0.746937	−0.0435622
$295$	11.5155	0.670459
$296$	−4.05847	−0.235894
$297$	−2.68446	−0.155768
$298$	13.6650	0.791593
$299$	9.81088	0.567378
$300$	3.47029	0.200357
$301$	−5.03550	−0.290241
$302$	−8.08814	−0.465420
$303$	16.8406	0.967469
$304$	1.00000	0.0573539
$305$	−5.14499	−0.294601
$306$	−7.36544	−0.421054
$307$	−31.2900	−1.78581	−0.892906	−	0.450243i	$-0.851338\pi$
$307$	−31.2900	−1.78581	−0.892906	+	0.450243i	$0.851338\pi$
$308$	6.71279	0.382497
$309$	−6.97308	−0.396685
$310$	8.88086	0.504399
$311$	30.1020	1.70693	0.853463	−	0.521153i	$-0.174498\pi$
$311$	30.1020	1.70693	0.853463	+	0.521153i	$0.174498\pi$
$312$	−6.45770	−0.365595
$313$	−9.20181	−0.520117	−0.260058	−	0.965593i	$-0.583742\pi$
$313$	−9.20181	−0.520117	−0.260058	+	0.965593i	$0.583742\pi$
$314$	6.62674	0.373969
$315$	−3.09279	−0.174259
$316$	−2.74692	−0.154527
$317$	−6.23926	−0.350432	−0.175216	−	0.984530i	$-0.556062\pi$
$317$	−6.23926	−0.350432	−0.175216	+	0.984530i	$0.556062\pi$
$318$	1.00000	0.0560772
$319$	−22.3953	−1.25389
$320$	−1.23681	−0.0691400
$321$	9.11050	0.508499
$322$	3.79906	0.211713
$323$	7.36544	0.409824
$324$	1.00000	0.0555556
$325$	22.4101	1.24309
$326$	−4.51646	−0.250143
$327$	3.78298	0.209199
$328$	8.17246	0.451249
$329$	−10.9065	−0.601295
$330$	−3.32018	−0.182770
$331$	−9.64534	−0.530156	−0.265078	−	0.964227i	$-0.585398\pi$
$331$	−9.64534	−0.530156	−0.265078	+	0.964227i	$0.585398\pi$
$332$	9.55852	0.524592
$333$	4.05847	0.222403
$334$	−8.78247	−0.480556
$335$	−2.65924	−0.145290
$336$	−2.50061	−0.136420
$337$	25.9410	1.41310	0.706549	−	0.707664i	$-0.250251\pi$
$337$	25.9410	1.41310	0.706549	+	0.707664i	$0.250251\pi$
$338$	−28.7019	−1.56118
$339$	18.2464	0.991011
$340$	−9.10968	−0.494042
$341$	19.2756	1.04383
$342$	−1.00000	−0.0540738
$343$	−19.3721	−1.04599
$344$	2.01370	0.108572
$345$	−1.87903	−0.101164
$346$	23.0007	1.23652
$347$	−10.8051	−0.580050	−0.290025	−	0.957019i	$-0.593664\pi$
$347$	−10.8051	−0.580050	−0.290025	+	0.957019i	$0.593664\pi$
$348$	8.34256	0.447208
$349$	12.9413	0.692731	0.346365	−	0.938100i	$-0.387416\pi$
$349$	12.9413	0.692731	0.346365	+	0.938100i	$0.387416\pi$
$350$	8.67785	0.463851
$351$	6.45770	0.344687
$352$	−2.68446	−0.143082
$353$	−30.5593	−1.62651	−0.813253	−	0.581910i	$-0.802305\pi$
$353$	−30.5593	−1.62651	−0.813253	+	0.581910i	$0.802305\pi$
$354$	−9.31062	−0.494854
$355$	−6.96351	−0.369585
$356$	−0.527893	−0.0279783
$357$	−18.4181	−0.974789
$358$	−14.8460	−0.784638
$359$	10.5010	0.554221	0.277110	−	0.960838i	$-0.410623\pi$
$359$	10.5010	0.554221	0.277110	+	0.960838i	$0.410623\pi$
$360$	1.23681	0.0651859
$361$	1.00000	0.0526316
$362$	−10.6239	−0.558381
$363$	3.79368	0.199116
$364$	−16.1482	−0.846396
$365$	5.52716	0.289305
$366$	4.15987	0.217440
$367$	−17.3586	−0.906110	−0.453055	−	0.891483i	$-0.649666\pi$
$367$	−17.3586	−0.906110	−0.453055	+	0.891483i	$0.649666\pi$
$368$	−1.51925	−0.0791965
$369$	−8.17246	−0.425441
$370$	5.01957	0.260955
$371$	2.50061	0.129825
$372$	−7.18042	−0.372288
$373$	−15.1475	−0.784310	−0.392155	−	0.919899i	$-0.628270\pi$
$373$	−15.1475	−0.784310	−0.392155	+	0.919899i	$0.628270\pi$
$374$	−19.7722	−1.02240
$375$	−10.4762	−0.540988
$376$	4.36153	0.224929
$377$	53.8738	2.77464
$378$	2.50061	0.128618
$379$	−18.9798	−0.974927	−0.487464	−	0.873143i	$-0.662078\pi$
$379$	−18.9798	−0.974927	−0.487464	+	0.873143i	$0.662078\pi$
$380$	−1.23681	−0.0634473
$381$	−4.56305	−0.233772
$382$	−3.59388	−0.183879
$383$	−30.3136	−1.54895	−0.774476	−	0.632603i	$-0.781987\pi$
$383$	−30.3136	−1.54895	−0.774476	+	0.632603i	$0.781987\pi$
$384$	1.00000	0.0510310
$385$	−8.30248	−0.423134
$386$	11.6896	0.594987
$387$	−2.01370	−0.102362
$388$	12.2288	0.620821
$389$	16.6599	0.844692	0.422346	−	0.906435i	$-0.361207\pi$
$389$	16.6599	0.844692	0.422346	+	0.906435i	$0.361207\pi$
$390$	7.98698	0.404436
$391$	−11.1900	−0.565900
$392$	0.746937	0.0377260
$393$	−11.2391	−0.566935
$394$	−6.30783	−0.317784
$395$	3.39744	0.170944
$396$	2.68446	0.134899
$397$	28.7380	1.44232	0.721159	−	0.692769i	$-0.243610\pi$
$397$	28.7380	1.44232	0.721159	+	0.692769i	$0.243610\pi$
$398$	−16.3443	−0.819267
$399$	−2.50061	−0.125187
$400$	−3.47029	−0.173514
$401$	25.6345	1.28013	0.640064	−	0.768322i	$-0.278908\pi$
$401$	25.6345	1.28013	0.640064	+	0.768322i	$0.278908\pi$
$402$	2.15007	0.107236
$403$	−46.3690	−2.30981
$404$	−16.8406	−0.837852
$405$	−1.23681	−0.0614578
$406$	20.8615	1.03534
$407$	10.8948	0.540035
$408$	7.36544	0.364643
$409$	−15.4846	−0.765662	−0.382831	−	0.923818i	$-0.625051\pi$
$409$	−15.4846	−0.765662	−0.382831	+	0.923818i	$0.625051\pi$
$410$	−10.1078	−0.499189
$411$	9.46832	0.467038
$412$	6.97308	0.343539
$413$	−23.2822	−1.14564
$414$	1.51925	0.0746672
$415$	−11.8221	−0.580325
$416$	6.45770	0.316615
$417$	1.18570	0.0580638
$418$	−2.68446	−0.131301
$419$	−39.1461	−1.91241	−0.956206	−	0.292694i	$-0.905448\pi$
$419$	−39.1461	−1.91241	−0.956206	+	0.292694i	$0.905448\pi$
$420$	3.09279	0.150913
$421$	−14.8866	−0.725531	−0.362765	−	0.931881i	$-0.618167\pi$
$421$	−14.8866	−0.725531	−0.362765	+	0.931881i	$0.618167\pi$
$422$	−18.1841	−0.885190
$423$	−4.36153	−0.212065
$424$	−1.00000	−0.0485643
$425$	−25.5602	−1.23985
$426$	5.63019	0.272784
$427$	10.4022	0.503399
$428$	−9.11050	−0.440373
$429$	17.3354	0.836963
$430$	−2.49058	−0.120106
$431$	−11.3919	−0.548728	−0.274364	−	0.961626i	$-0.588467\pi$
$431$	−11.3919	−0.548728	−0.274364	+	0.961626i	$0.588467\pi$
$432$	−1.00000	−0.0481125
$433$	9.21500	0.442845	0.221422	−	0.975178i	$-0.428930\pi$
$433$	9.21500	0.442845	0.221422	+	0.975178i	$0.428930\pi$
$434$	−17.9555	−0.861890
$435$	−10.3182	−0.494720
$436$	−3.78298	−0.181172
$437$	−1.51925	−0.0726757
$438$	−4.46887	−0.213531
$439$	4.01667	0.191705	0.0958526	−	0.995396i	$-0.469442\pi$
$439$	4.01667	0.191705	0.0958526	+	0.995396i	$0.469442\pi$
$440$	3.32018	0.158283
$441$	−0.746937	−0.0355684
$442$	47.5638	2.26238
$443$	−11.6944	−0.555619	−0.277809	−	0.960636i	$-0.589608\pi$
$443$	−11.6944	−0.555619	−0.277809	+	0.960636i	$0.589608\pi$
$444$	−4.05847	−0.192606
$445$	0.652906	0.0309507
$446$	1.59565	0.0755562
$447$	13.6650	0.646333
$448$	2.50061	0.118143
$449$	6.14205	0.289861	0.144931	−	0.989442i	$-0.453704\pi$
$449$	6.14205	0.289861	0.144931	+	0.989442i	$0.453704\pi$
$450$	3.47029	0.163591
$451$	−21.9386	−1.03305
$452$	−18.2464	−0.858241
$453$	−8.08814	−0.380014
$454$	27.9395	1.31127
$455$	19.9723	0.936318
$456$	1.00000	0.0468293
$457$	−13.0751	−0.611625	−0.305813	−	0.952092i	$-0.598928\pi$
$457$	−13.0751	−0.611625	−0.305813	+	0.952092i	$0.598928\pi$
$458$	−2.68484	−0.125455
$459$	−7.36544	−0.343789
$460$	1.87903	0.0876104
$461$	−18.0466	−0.840514	−0.420257	−	0.907405i	$-0.638060\pi$
$461$	−18.0466	−0.840514	−0.420257	+	0.907405i	$0.638060\pi$
$462$	6.71279	0.312307
$463$	−24.6912	−1.14750	−0.573748	−	0.819032i	$-0.694511\pi$
$463$	−24.6912	−1.14750	−0.573748	+	0.819032i	$0.694511\pi$
$464$	−8.34256	−0.387294
$465$	8.88086	0.411840
$466$	−12.4330	−0.575946
$467$	−38.4518	−1.77934	−0.889668	−	0.456608i	$-0.849064\pi$
$467$	−38.4518	−1.77934	−0.889668	+	0.456608i	$0.849064\pi$
$468$	−6.45770	−0.298507
$469$	5.37650	0.248264
$470$	−5.39441	−0.248826
$471$	6.62674	0.305344
$472$	9.31062	0.428556
$473$	−5.40571	−0.248555
$474$	−2.74692	−0.126170
$475$	−3.47029	−0.159228
$476$	18.4181	0.844192
$477$	1.00000	0.0457869
$478$	−0.256780	−0.0117448
$479$	−4.18272	−0.191113	−0.0955567	−	0.995424i	$-0.530463\pi$
$479$	−4.18272	−0.191113	−0.0955567	+	0.995424i	$0.530463\pi$
$480$	−1.23681	−0.0564526
$481$	−26.2084	−1.19500
$482$	20.8924	0.951622
$483$	3.79906	0.172863
$484$	−3.79368	−0.172440
$485$	−15.1247	−0.686778
$486$	1.00000	0.0453609
$487$	−36.6014	−1.65857	−0.829284	−	0.558827i	$-0.811252\pi$
$487$	−36.6014	−1.65857	−0.829284	+	0.558827i	$0.811252\pi$
$488$	−4.15987	−0.188309
$489$	−4.51646	−0.204241
$490$	−0.923822	−0.0417340
$491$	−22.3241	−1.00747	−0.503737	−	0.863857i	$-0.668042\pi$
$491$	−22.3241	−1.00747	−0.503737	+	0.863857i	$0.668042\pi$
$492$	8.17246	0.368443
$493$	−61.4466	−2.76742
$494$	6.45770	0.290546
$495$	−3.32018	−0.149231
$496$	7.18042	0.322411
$497$	14.0789	0.631527
$498$	9.55852	0.428328
$499$	−9.11240	−0.407927	−0.203963	−	0.978978i	$-0.565382\pi$
$499$	−9.11240	−0.407927	−0.203963	+	0.978978i	$0.565382\pi$
$500$	10.4762	0.468509
$501$	−8.78247	−0.392372
$502$	−1.11998	−0.0499872
$503$	9.60383	0.428214	0.214107	−	0.976810i	$-0.431316\pi$
$503$	9.60383	0.428214	0.214107	+	0.976810i	$0.431316\pi$
$504$	−2.50061	−0.111386
$505$	20.8287	0.926866
$506$	4.07837	0.181306
$507$	−28.7019	−1.27470
$508$	4.56305	0.202453
$509$	1.57432	0.0697806	0.0348903	−	0.999391i	$-0.488892\pi$
$509$	1.57432	0.0697806	0.0348903	+	0.999391i	$0.488892\pi$
$510$	−9.10968	−0.403383
$511$	−11.1749	−0.494349
$512$	−1.00000	−0.0441942
$513$	−1.00000	−0.0441511
$514$	12.3181	0.543327
$515$	−8.62441	−0.380037
$516$	2.01370	0.0886484
$517$	−11.7084	−0.514933
$518$	−10.1487	−0.445906
$519$	23.0007	1.00962
$520$	−7.98698	−0.350252
$521$	−7.22126	−0.316369	−0.158185	−	0.987410i	$-0.550564\pi$
$521$	−7.22126	−0.316369	−0.158185	+	0.987410i	$0.550564\pi$
$522$	8.34256	0.365144
$523$	−33.6530	−1.47154	−0.735772	−	0.677229i	$-0.763181\pi$
$523$	−33.6530	−1.47154	−0.735772	+	0.677229i	$0.763181\pi$
$524$	11.2391	0.490980
$525$	8.67785	0.378732
$526$	15.1112	0.658878
$527$	52.8870	2.30379
$528$	−2.68446	−0.116826
$529$	−20.6919	−0.899647
$530$	1.23681	0.0537238
$531$	−9.31062	−0.404046
$532$	2.50061	0.108415
$533$	52.7753	2.28595
$534$	−0.527893	−0.0228442
$535$	11.2680	0.487158
$536$	−2.15007	−0.0928690
$537$	−14.8460	−0.640654
$538$	−1.56889	−0.0676397
$539$	−2.00512	−0.0863667
$540$	1.23681	0.0532240
$541$	0.660587	0.0284008	0.0142004	−	0.999899i	$-0.495480\pi$
$541$	0.660587	0.0284008	0.0142004	+	0.999899i	$0.495480\pi$
$542$	−16.0601	−0.689842
$543$	−10.6239	−0.455916
$544$	−7.36544	−0.315790
$545$	4.67884	0.200420
$546$	−16.1482	−0.691080
$547$	14.3337	0.612865	0.306432	−	0.951892i	$-0.400865\pi$
$547$	14.3337	0.612865	0.306432	+	0.951892i	$0.400865\pi$
$548$	−9.46832	−0.404467
$549$	4.15987	0.177539
$550$	9.31585	0.397229
$551$	−8.34256	−0.355405
$552$	−1.51925	−0.0646637
$553$	−6.86899	−0.292099
$554$	2.75686	0.117128
$555$	5.01957	0.213069
$556$	−1.18570	−0.0502847
$557$	11.5341	0.488714	0.244357	−	0.969685i	$-0.421423\pi$
$557$	11.5341	0.488714	0.244357	+	0.969685i	$0.421423\pi$
$558$	−7.18042	−0.303972
$559$	13.0039	0.550007
$560$	−3.09279	−0.130694
$561$	−19.7722	−0.834783
$562$	26.7999	1.13048
$563$	3.33692	0.140634	0.0703172	−	0.997525i	$-0.477599\pi$
$563$	3.33692	0.140634	0.0703172	+	0.997525i	$0.477599\pi$
$564$	4.36153	0.183654
$565$	22.5675	0.949421
$566$	13.8300	0.581318
$567$	2.50061	0.105016
$568$	−5.63019	−0.236238
$569$	4.05900	0.170162	0.0850810	−	0.996374i	$-0.472885\pi$
$569$	4.05900	0.170162	0.0850810	+	0.996374i	$0.472885\pi$
$570$	−1.23681	−0.0518045
$571$	31.6372	1.32398	0.661988	−	0.749514i	$-0.269713\pi$
$571$	31.6372	1.32398	0.661988	+	0.749514i	$0.269713\pi$
$572$	−17.3354	−0.724831
$573$	−3.59388	−0.150137
$574$	20.4362	0.852988
$575$	5.27225	0.219868
$576$	1.00000	0.0416667
$577$	13.5768	0.565209	0.282604	−	0.959237i	$-0.408802\pi$
$577$	13.5768	0.565209	0.282604	+	0.959237i	$0.408802\pi$
$578$	−37.2496	−1.54938
$579$	11.6896	0.485805
$580$	10.3182	0.428440
$581$	23.9022	0.991629
$582$	12.2288	0.506898
$583$	2.68446	0.111179
$584$	4.46887	0.184923
$585$	7.98698	0.330221
$586$	8.04316	0.332260
$587$	4.94153	0.203959	0.101979	−	0.994787i	$-0.467482\pi$
$587$	4.94153	0.203959	0.101979	+	0.994787i	$0.467482\pi$
$588$	0.746937	0.0308032
$589$	7.18042	0.295864
$590$	−11.5155	−0.474086
$591$	−6.30783	−0.259469
$592$	4.05847	0.166802
$593$	−24.5074	−1.00640	−0.503198	−	0.864171i	$-0.667843\pi$
$593$	−24.5074	−1.00640	−0.503198	+	0.864171i	$0.667843\pi$
$594$	2.68446	0.110145
$595$	−22.7798	−0.933880
$596$	−13.6650	−0.559741
$597$	−16.3443	−0.668929
$598$	−9.81088	−0.401197
$599$	−46.7339	−1.90950	−0.954748	−	0.297416i	$-0.903875\pi$
$599$	−46.7339	−1.90950	−0.954748	+	0.297416i	$0.903875\pi$
$600$	−3.47029	−0.141674
$601$	−9.72331	−0.396622	−0.198311	−	0.980139i	$-0.563546\pi$
$601$	−9.72331	−0.396622	−0.198311	+	0.980139i	$0.563546\pi$
$602$	5.03550	0.205231
$603$	2.15007	0.0875577
$604$	8.08814	0.329102
$605$	4.69208	0.190760
$606$	−16.8406	−0.684104
$607$	2.04569	0.0830318	0.0415159	−	0.999138i	$-0.486781\pi$
$607$	2.04569	0.0830318	0.0415159	+	0.999138i	$0.486781\pi$
$608$	−1.00000	−0.0405554
$609$	20.8615	0.845351
$610$	5.14499	0.208315
$611$	28.1655	1.13945
$612$	7.36544	0.297730
$613$	−35.0969	−1.41755	−0.708775	−	0.705435i	$-0.750752\pi$
$613$	−35.0969	−1.41755	−0.708775	+	0.705435i	$0.750752\pi$
$614$	31.2900	1.26276
$615$	−10.1078	−0.407586
$616$	−6.71279	−0.270466
$617$	−7.65858	−0.308323	−0.154161	−	0.988046i	$-0.549268\pi$
$617$	−7.65858	−0.308323	−0.154161	+	0.988046i	$0.549268\pi$
$618$	6.97308	0.280499
$619$	−46.4249	−1.86597	−0.932987	−	0.359909i	$-0.882808\pi$
$619$	−46.4249	−1.86597	−0.932987	+	0.359909i	$0.882808\pi$
$620$	−8.88086	−0.356664
$621$	1.51925	0.0609655
$622$	−30.1020	−1.20698
$623$	−1.32006	−0.0528869
$624$	6.45770	0.258515
$625$	4.39436	0.175774
$626$	9.20181	0.367778
$627$	−2.68446	−0.107207
$628$	−6.62674	−0.264436
$629$	29.8924	1.19189
$630$	3.09279	0.123220
$631$	27.3181	1.08752	0.543759	−	0.839242i	$-0.317001\pi$
$631$	27.3181	1.08752	0.543759	+	0.839242i	$0.317001\pi$
$632$	2.74692	0.109267
$633$	−18.1841	−0.722755
$634$	6.23926	0.247793
$635$	−5.64364	−0.223961
$636$	−1.00000	−0.0396526
$637$	4.82349	0.191114
$638$	22.3953	0.886637
$639$	5.63019	0.222727
$640$	1.23681	0.0488894
$641$	27.9903	1.10555	0.552776	−	0.833330i	$-0.313569\pi$
$641$	27.9903	1.10555	0.552776	+	0.833330i	$0.313569\pi$
$642$	−9.11050	−0.359563
$643$	−33.6845	−1.32839	−0.664194	−	0.747560i	$-0.731225\pi$
$643$	−33.6845	−1.32839	−0.664194	+	0.747560i	$0.731225\pi$
$644$	−3.79906	−0.149704
$645$	−2.49058	−0.0980665
$646$	−7.36544	−0.289789
$647$	40.9530	1.61003	0.805015	−	0.593255i	$-0.202157\pi$
$647$	40.9530	1.61003	0.805015	+	0.593255i	$0.202157\pi$
$648$	−1.00000	−0.0392837
$649$	−24.9940	−0.981099
$650$	−22.4101	−0.878996
$651$	−17.9555	−0.703730
$652$	4.51646	0.176878
$653$	25.7820	1.00893	0.504463	−	0.863433i	$-0.331691\pi$
$653$	25.7820	1.00893	0.504463	+	0.863433i	$0.331691\pi$
$654$	−3.78298	−0.147926
$655$	−13.9006	−0.543142
$656$	−8.17246	−0.319081
$657$	−4.46887	−0.174347
$658$	10.9065	0.425180
$659$	16.6368	0.648078	0.324039	−	0.946044i	$-0.394959\pi$
$659$	16.6368	0.648078	0.324039	+	0.946044i	$0.394959\pi$
$660$	3.32018	0.129238
$661$	−18.9800	−0.738238	−0.369119	−	0.929382i	$-0.620341\pi$
$661$	−18.9800	−0.738238	−0.369119	+	0.929382i	$0.620341\pi$
$662$	9.64534	0.374877
$663$	47.5638	1.84722
$664$	−9.55852	−0.370943
$665$	−3.09279	−0.119933
$666$	−4.05847	−0.157262
$667$	12.6745	0.490757
$668$	8.78247	0.339804
$669$	1.59565	0.0616914
$670$	2.65924	0.102735
$671$	11.1670	0.431098
$672$	2.50061	0.0964632
$673$	13.3009	0.512711	0.256355	−	0.966583i	$-0.417478\pi$
$673$	13.3009	0.512711	0.256355	+	0.966583i	$0.417478\pi$
$674$	−25.9410	−0.999212
$675$	3.47029	0.133572
$676$	28.7019	1.10392
$677$	−19.0295	−0.731363	−0.365682	−	0.930740i	$-0.619164\pi$
$677$	−19.0295	−0.731363	−0.365682	+	0.930740i	$0.619164\pi$
$678$	−18.2464	−0.700750
$679$	30.5794	1.17353
$680$	9.10968	0.349340
$681$	27.9395	1.07065
$682$	−19.2756	−0.738099
$683$	−36.3692	−1.39163	−0.695814	−	0.718222i	$-0.744956\pi$
$683$	−36.3692	−1.39163	−0.695814	+	0.718222i	$0.744956\pi$
$684$	1.00000	0.0382360
$685$	11.7106	0.447437
$686$	19.3721	0.739630
$687$	−2.68484	−0.102433
$688$	−2.01370	−0.0767718
$689$	−6.45770	−0.246019
$690$	1.87903	0.0715336
$691$	−20.8260	−0.792257	−0.396128	−	0.918195i	$-0.629647\pi$
$691$	−20.8260	−0.792257	−0.396128	+	0.918195i	$0.629647\pi$
$692$	−23.0007	−0.874355
$693$	6.71279	0.254998
$694$	10.8051	0.410157
$695$	1.46649	0.0556270
$696$	−8.34256	−0.316224
$697$	−60.1937	−2.28000
$698$	−12.9413	−0.489835
$699$	−12.4330	−0.470258
$700$	−8.67785	−0.327992
$701$	−50.9515	−1.92441	−0.962206	−	0.272324i	$-0.912208\pi$
$701$	−50.9515	−1.92441	−0.962206	+	0.272324i	$0.912208\pi$
$702$	−6.45770	−0.243730
$703$	4.05847	0.153068
$704$	2.68446	0.101174
$705$	−5.39441	−0.203165
$706$	30.5593	1.15011
$707$	−42.1119	−1.58378
$708$	9.31062	0.349914
$709$	13.9215	0.522832	0.261416	−	0.965226i	$-0.415811\pi$
$709$	13.9215	0.522832	0.261416	+	0.965226i	$0.415811\pi$
$710$	6.96351	0.261336
$711$	−2.74692	−0.103018
$712$	0.527893	0.0197836
$713$	−10.9089	−0.408541
$714$	18.4181	0.689280
$715$	21.4407	0.801838
$716$	14.8460	0.554823
$717$	−0.256780	−0.00958962
$718$	−10.5010	−0.391893
$719$	42.1583	1.57224	0.786120	−	0.618074i	$-0.212087\pi$
$719$	42.1583	1.57224	0.786120	+	0.618074i	$0.212087\pi$
$720$	−1.23681	−0.0460934
$721$	17.4370	0.649387
$722$	−1.00000	−0.0372161
$723$	20.8924	0.776996
$724$	10.6239	0.394835
$725$	28.9511	1.07522
$726$	−3.79368	−0.140797
$727$	0.754452	0.0279811	0.0139905	−	0.999902i	$-0.495547\pi$
$727$	0.754452	0.0279811	0.0139905	+	0.999902i	$0.495547\pi$
$728$	16.1482	0.598492
$729$	1.00000	0.0370370
$730$	−5.52716	−0.204569
$731$	−14.8318	−0.548574
$732$	−4.15987	−0.153753
$733$	−44.2822	−1.63560	−0.817800	−	0.575502i	$-0.804807\pi$
$733$	−44.2822	−1.63560	−0.817800	+	0.575502i	$0.804807\pi$
$734$	17.3586	0.640716
$735$	−0.923822	−0.0340757
$736$	1.51925	0.0560004
$737$	5.77178	0.212606
$738$	8.17246	0.300832
$739$	18.2303	0.670613	0.335306	−	0.942109i	$-0.391160\pi$
$739$	18.2303	0.670613	0.335306	+	0.942109i	$0.391160\pi$
$740$	−5.01957	−0.184523
$741$	6.45770	0.237230
$742$	−2.50061	−0.0918004
$743$	−5.63682	−0.206795	−0.103397	−	0.994640i	$-0.532971\pi$
$743$	−5.63682	−0.206795	−0.103397	+	0.994640i	$0.532971\pi$
$744$	7.18042	0.263247
$745$	16.9011	0.619208
$746$	15.1475	0.554591
$747$	9.55852	0.349728
$748$	19.7722	0.722944
$749$	−22.7818	−0.832430
$750$	10.4762	0.382536
$751$	26.8720	0.980574	0.490287	−	0.871561i	$-0.336892\pi$
$751$	26.8720	0.980574	0.490287	+	0.871561i	$0.336892\pi$
$752$	−4.36153	−0.159049
$753$	−1.11998	−0.0408144
$754$	−53.8738	−1.96197
$755$	−10.0035	−0.364066
$756$	−2.50061	−0.0909464
$757$	−10.4668	−0.380421	−0.190210	−	0.981743i	$-0.560917\pi$
$757$	−10.4668	−0.380421	−0.190210	+	0.981743i	$0.560917\pi$
$758$	18.9798	0.689378
$759$	4.07837	0.148036
$760$	1.23681	0.0448640
$761$	20.1790	0.731488	0.365744	−	0.930716i	$-0.380815\pi$
$761$	20.1790	0.731488	0.365744	+	0.930716i	$0.380815\pi$
$762$	4.56305	0.165302
$763$	−9.45976	−0.342466
$764$	3.59388	0.130022
$765$	−9.10968	−0.329361
$766$	30.3136	1.09528
$767$	60.1252	2.17099
$768$	−1.00000	−0.0360844
$769$	23.2726	0.839231	0.419615	−	0.907702i	$-0.362165\pi$
$769$	23.2726	0.839231	0.419615	+	0.907702i	$0.362165\pi$
$770$	8.30248	0.299201
$771$	12.3181	0.443624
$772$	−11.6896	−0.420720
$773$	47.1422	1.69559	0.847794	−	0.530325i	$-0.177930\pi$
$773$	47.1422	1.69559	0.847794	+	0.530325i	$0.177930\pi$
$774$	2.01370	0.0723811
$775$	−24.9182	−0.895086
$776$	−12.2288	−0.438987
$777$	−10.1487	−0.364081
$778$	−16.6599	−0.597288
$779$	−8.17246	−0.292809
$780$	−7.98698	−0.285980
$781$	15.1140	0.540822
$782$	11.1900	0.400152
$783$	8.34256	0.298139
$784$	−0.746937	−0.0266763
$785$	8.19605	0.292530
$786$	11.2391	0.400884
$787$	51.0697	1.82044	0.910219	−	0.414126i	$-0.135913\pi$
$787$	51.0697	1.82044	0.910219	+	0.414126i	$0.135913\pi$
$788$	6.30783	0.224707
$789$	15.1112	0.537971
$790$	−3.39744	−0.120875
$791$	−45.6273	−1.62232
$792$	−2.68446	−0.0953881
$793$	−26.8632	−0.953941
$794$	−28.7380	−1.01987
$795$	1.23681	0.0438653
$796$	16.3443	0.579309
$797$	36.6064	1.29666	0.648332	−	0.761358i	$-0.275467\pi$
$797$	36.6064	1.29666	0.648332	+	0.761358i	$0.275467\pi$
$798$	2.50061	0.0885207
$799$	−32.1246	−1.13649
$800$	3.47029	0.122693
$801$	−0.527893	−0.0186522
$802$	−25.6345	−0.905187
$803$	−11.9965	−0.423347
$804$	−2.15007	−0.0758272
$805$	4.69874	0.165609
$806$	46.3690	1.63328
$807$	−1.56889	−0.0552276
$808$	16.8406	0.592451
$809$	−14.3064	−0.502988	−0.251494	−	0.967859i	$-0.580922\pi$
$809$	−14.3064	−0.502988	−0.251494	+	0.967859i	$0.580922\pi$
$810$	1.23681	0.0434572
$811$	−19.6024	−0.688333	−0.344166	−	0.938909i	$-0.611838\pi$
$811$	−19.6024	−0.688333	−0.344166	+	0.938909i	$0.611838\pi$
$812$	−20.8615	−0.732096
$813$	−16.0601	−0.563254
$814$	−10.8948	−0.381862
$815$	−5.58602	−0.195670
$816$	−7.36544	−0.257842
$817$	−2.01370	−0.0704506
$818$	15.4846	0.541405
$819$	−16.1482	−0.564264
$820$	10.1078	0.352980
$821$	−12.4931	−0.436013	−0.218006	−	0.975947i	$-0.569955\pi$
$821$	−12.4931	−0.436013	−0.218006	+	0.975947i	$0.569955\pi$
$822$	−9.46832	−0.330246
$823$	53.7861	1.87487	0.937433	−	0.348166i	$-0.113196\pi$
$823$	53.7861	1.87487	0.937433	+	0.348166i	$0.113196\pi$
$824$	−6.97308	−0.242919
$825$	9.31585	0.324336
$826$	23.2822	0.810093
$827$	−2.79666	−0.0972494	−0.0486247	−	0.998817i	$-0.515484\pi$
$827$	−2.79666	−0.0972494	−0.0486247	+	0.998817i	$0.515484\pi$
$828$	−1.51925	−0.0527977
$829$	1.11829	0.0388400	0.0194200	−	0.999811i	$-0.493818\pi$
$829$	1.11829	0.0388400	0.0194200	+	0.999811i	$0.493818\pi$
$830$	11.8221	0.410352
$831$	2.75686	0.0956345
$832$	−6.45770	−0.223881
$833$	−5.50151	−0.190616
$834$	−1.18570	−0.0410573
$835$	−10.8623	−0.375905
$836$	2.68446	0.0928440
$837$	−7.18042	−0.248192
$838$	39.1461	1.35228
$839$	−5.17785	−0.178759	−0.0893796	−	0.995998i	$-0.528488\pi$
$839$	−5.17785	−0.178759	−0.0893796	+	0.995998i	$0.528488\pi$
$840$	−3.09279	−0.106712
$841$	40.5983	1.39994
$842$	14.8866	0.513028
$843$	26.7999	0.923036
$844$	18.1841	0.625924
$845$	−35.4989	−1.22120
$846$	4.36153	0.149953
$847$	−9.48652	−0.325961
$848$	1.00000	0.0343401
$849$	13.8300	0.474644
$850$	25.5602	0.876707
$851$	−6.16583	−0.211362
$852$	−5.63019	−0.192887
$853$	37.5164	1.28454	0.642269	−	0.766479i	$-0.277993\pi$
$853$	37.5164	1.28454	0.642269	+	0.766479i	$0.277993\pi$
$854$	−10.4022	−0.355957
$855$	−1.23681	−0.0422982
$856$	9.11050	0.311391
$857$	−40.8580	−1.39568	−0.697842	−	0.716252i	$-0.745856\pi$
$857$	−40.8580	−1.39568	−0.697842	+	0.716252i	$0.745856\pi$
$858$	−17.3354	−0.591822
$859$	−6.83739	−0.233289	−0.116644	−	0.993174i	$-0.537214\pi$
$859$	−6.83739	−0.233289	−0.116644	+	0.993174i	$0.537214\pi$
$860$	2.49058	0.0849281
$861$	20.4362	0.696462
$862$	11.3919	0.388009
$863$	0.347088	0.0118150	0.00590751	−	0.999983i	$-0.498120\pi$
$863$	0.347088	0.0118150	0.00590751	+	0.999983i	$0.498120\pi$
$864$	1.00000	0.0340207
$865$	28.4476	0.967247
$866$	−9.21500	−0.313138
$867$	−37.2496	−1.26506
$868$	17.9555	0.609448
$869$	−7.37401	−0.250146
$870$	10.3182	0.349820
$871$	−13.8845	−0.470459
$872$	3.78298	0.128108
$873$	12.2288	0.413881
$874$	1.51925	0.0513895
$875$	26.1969	0.885616
$876$	4.46887	0.150989
$877$	47.8974	1.61738	0.808690	−	0.588236i	$-0.200177\pi$
$877$	47.8974	1.61738	0.808690	+	0.588236i	$0.200177\pi$
$878$	−4.01667	−0.135556
$879$	8.04316	0.271289
$880$	−3.32018	−0.111923
$881$	−45.2423	−1.52425	−0.762126	−	0.647429i	$-0.775844\pi$
$881$	−45.2423	−1.52425	−0.762126	+	0.647429i	$0.775844\pi$
$882$	0.746937	0.0251507
$883$	−13.9959	−0.471000	−0.235500	−	0.971874i	$-0.575673\pi$
$883$	−13.9959	−0.471000	−0.235500	+	0.971874i	$0.575673\pi$
$884$	−47.5638	−1.59974
$885$	−11.5155	−0.387090
$886$	11.6944	0.392882
$887$	−14.7761	−0.496132	−0.248066	−	0.968743i	$-0.579795\pi$
$887$	−14.7761	−0.496132	−0.248066	+	0.968743i	$0.579795\pi$
$888$	4.05847	0.136193
$889$	11.4104	0.382693
$890$	−0.652906	−0.0218854
$891$	2.68446	0.0899328
$892$	−1.59565	−0.0534263
$893$	−4.36153	−0.145953
$894$	−13.6650	−0.457026
$895$	−18.3618	−0.613768
$896$	−2.50061	−0.0835396
$897$	−9.81088	−0.327576
$898$	−6.14205	−0.204963
$899$	−59.9031	−1.99788
$900$	−3.47029	−0.115676
$901$	7.36544	0.245378
$902$	21.9386	0.730477
$903$	5.03550	0.167571
$904$	18.2464	0.606868
$905$	−13.1398	−0.436783
$906$	8.08814	0.268710
$907$	−10.4190	−0.345958	−0.172979	−	0.984926i	$-0.555339\pi$
$907$	−10.4190	−0.345958	−0.172979	+	0.984926i	$0.555339\pi$
$908$	−27.9395	−0.927206
$909$	−16.8406	−0.558568
$910$	−19.9723	−0.662077
$911$	59.2967	1.96459	0.982294	−	0.187348i	$-0.0599892\pi$
$911$	59.2967	1.96459	0.982294	+	0.187348i	$0.0599892\pi$
$912$	−1.00000	−0.0331133
$913$	25.6595	0.849204
$914$	13.0751	0.432484
$915$	5.14499	0.170088
$916$	2.68484	0.0887098
$917$	28.1045	0.928093
$918$	7.36544	0.243096
$919$	12.0456	0.397348	0.198674	−	0.980066i	$-0.436337\pi$
$919$	12.0456	0.397348	0.198674	+	0.980066i	$0.436337\pi$
$920$	−1.87903	−0.0619499
$921$	31.2900	1.03104
$922$	18.0466	0.594333
$923$	−36.3581	−1.19674
$924$	−6.71279	−0.220835
$925$	−14.0841	−0.463081
$926$	24.6912	0.811402
$927$	6.97308	0.229026
$928$	8.34256	0.273858
$929$	−32.8823	−1.07883	−0.539416	−	0.842039i	$-0.681355\pi$
$929$	−32.8823	−1.07883	−0.539416	+	0.842039i	$0.681355\pi$
$930$	−8.88086	−0.291215
$931$	−0.746937	−0.0244799
$932$	12.4330	0.407255
$933$	−30.1020	−0.985494
$934$	38.4518	1.25818
$935$	−24.4546	−0.799750
$936$	6.45770	0.211077
$937$	−45.9635	−1.50156	−0.750780	−	0.660552i	$-0.770322\pi$
$937$	−45.9635	−1.50156	−0.750780	+	0.660552i	$0.770322\pi$
$938$	−5.37650	−0.175549
$939$	9.20181	0.300290
$940$	5.39441	0.175946
$941$	−52.6230	−1.71546	−0.857730	−	0.514101i	$-0.828126\pi$
$941$	−52.6230	−1.71546	−0.857730	+	0.514101i	$0.828126\pi$
$942$	−6.62674	−0.215911
$943$	12.4160	0.404321
$944$	−9.31062	−0.303035
$945$	3.09279	0.100609
$946$	5.40571	0.175755
$947$	18.4333	0.599002	0.299501	−	0.954096i	$-0.403180\pi$
$947$	18.4333	0.599002	0.299501	+	0.954096i	$0.403180\pi$
$948$	2.74692	0.0892159
$949$	28.8586	0.936790
$950$	3.47029	0.112591
$951$	6.23926	0.202322
$952$	−18.4181	−0.596934
$953$	23.7783	0.770253	0.385127	−	0.922864i	$-0.374158\pi$
$953$	23.7783	0.770253	0.385127	+	0.922864i	$0.374158\pi$
$954$	−1.00000	−0.0323762
$955$	−4.44497	−0.143836
$956$	0.256780	0.00830485
$957$	22.3953	0.723936
$958$	4.18272	0.135138
$959$	−23.6766	−0.764557
$960$	1.23681	0.0399180
$961$	20.5585	0.663178
$962$	26.2084	0.844992
$963$	−9.11050	−0.293582
$964$	−20.8924	−0.672898
$965$	14.4579	0.465417
$966$	−3.79906	−0.122233
$967$	−26.3740	−0.848130	−0.424065	−	0.905632i	$-0.639397\pi$
$967$	−26.3740	−0.848130	−0.424065	+	0.905632i	$0.639397\pi$
$968$	3.79368	0.121933
$969$	−7.36544	−0.236612
$970$	15.1247	0.485625
$971$	−24.3805	−0.782409	−0.391204	−	0.920304i	$-0.627941\pi$
$971$	−24.3805	−0.782409	−0.391204	+	0.920304i	$0.627941\pi$
$972$	−1.00000	−0.0320750
$973$	−2.96497	−0.0950525
$974$	36.6014	1.17278
$975$	−22.4101	−0.717697
$976$	4.15987	0.133154
$977$	27.8870	0.892186	0.446093	−	0.894987i	$-0.352815\pi$
$977$	27.8870	0.892186	0.446093	+	0.894987i	$0.352815\pi$
$978$	4.51646	0.144420
$979$	−1.41711	−0.0452909
$980$	0.923822	0.0295104
$981$	−3.78298	−0.120781
$982$	22.3241	0.712391
$983$	36.4266	1.16183	0.580914	−	0.813965i	$-0.302695\pi$
$983$	36.4266	1.16183	0.580914	+	0.813965i	$0.302695\pi$
$984$	−8.17246	−0.260528
$985$	−7.80162	−0.248580
$986$	61.4466	1.95686
$987$	10.9065	0.347158
$988$	−6.45770	−0.205447
$989$	3.05933	0.0972809
$990$	3.32018	0.105522
$991$	3.19358	0.101447	0.0507237	−	0.998713i	$-0.483847\pi$
$991$	3.19358	0.101447	0.0507237	+	0.998713i	$0.483847\pi$
$992$	−7.18042	−0.227979
$993$	9.64534	0.306086
$994$	−14.0789	−0.446557
$995$	−20.2149	−0.640856
$996$	−9.55852	−0.302873
$997$	−36.9482	−1.17016	−0.585080	−	0.810975i	$-0.698937\pi$
$997$	−36.9482	−1.17016	−0.585080	+	0.810975i	$0.698937\pi$
$998$	9.11240	0.288448
$999$	−4.05847	−0.128404

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6042.2.a.bd.1.4	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6042.2.a.bd.1.4	✓	11	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.23681 q^{5} +1.00000 q^{6} +2.50061 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.23681 q^{5} +1.00000 q^{6} +2.50061 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.23681 q^{10} +2.68446 q^{11} -1.00000 q^{12} -6.45770 q^{13} -2.50061 q^{14} +1.23681 q^{15} +1.00000 q^{16} +7.36544 q^{17} -1.00000 q^{18} +1.00000 q^{19} -1.23681 q^{20} -2.50061 q^{21} -2.68446 q^{22} -1.51925 q^{23} +1.00000 q^{24} -3.47029 q^{25} +6.45770 q^{26} -1.00000 q^{27} +2.50061 q^{28} -8.34256 q^{29} -1.23681 q^{30} +7.18042 q^{31} -1.00000 q^{32} -2.68446 q^{33} -7.36544 q^{34} -3.09279 q^{35} +1.00000 q^{36} +4.05847 q^{37} -1.00000 q^{38} +6.45770 q^{39} +1.23681 q^{40} -8.17246 q^{41} +2.50061 q^{42} -2.01370 q^{43} +2.68446 q^{44} -1.23681 q^{45} +1.51925 q^{46} -4.36153 q^{47} -1.00000 q^{48} -0.746937 q^{49} +3.47029 q^{50} -7.36544 q^{51} -6.45770 q^{52} +1.00000 q^{53} +1.00000 q^{54} -3.32018 q^{55} -2.50061 q^{56} -1.00000 q^{57} +8.34256 q^{58} -9.31062 q^{59} +1.23681 q^{60} +4.15987 q^{61} -7.18042 q^{62} +2.50061 q^{63} +1.00000 q^{64} +7.98698 q^{65} +2.68446 q^{66} +2.15007 q^{67} +7.36544 q^{68} +1.51925 q^{69} +3.09279 q^{70} +5.63019 q^{71} -1.00000 q^{72} -4.46887 q^{73} -4.05847 q^{74} +3.47029 q^{75} +1.00000 q^{76} +6.71279 q^{77} -6.45770 q^{78} -2.74692 q^{79} -1.23681 q^{80} +1.00000 q^{81} +8.17246 q^{82} +9.55852 q^{83} -2.50061 q^{84} -9.10968 q^{85} +2.01370 q^{86} +8.34256 q^{87} -2.68446 q^{88} -0.527893 q^{89} +1.23681 q^{90} -16.1482 q^{91} -1.51925 q^{92} -7.18042 q^{93} +4.36153 q^{94} -1.23681 q^{95} +1.00000 q^{96} +12.2288 q^{97} +0.746937 q^{98} +2.68446 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 11 q^{2} - 11 q^{3} + 11 q^{4} + 2 q^{5} + 11 q^{6} - 2 q^{7} - 11 q^{8} + 11 q^{9}+O(q^{10}) \) 11 * q - 11 * q^2 - 11 * q^3 + 11 * q^4 + 2 * q^5 + 11 * q^6 - 2 * q^7 - 11 * q^8 + 11 * q^9	\( 11 q - 11 q^{2} - 11 q^{3} + 11 q^{4} + 2 q^{5} + 11 q^{6} - 2 q^{7} - 11 q^{8} + 11 q^{9} - 2 q^{10} - 6 q^{11} - 11 q^{12} - 7 q^{13} + 2 q^{14} - 2 q^{15} + 11 q^{16} - 16 q^{17} - 11 q^{18} + 11 q^{19} + 2 q^{20} + 2 q^{21} + 6 q^{22} - 11 q^{23} + 11 q^{24} + 19 q^{25} + 7 q^{26} - 11 q^{27} - 2 q^{28} - 7 q^{29} + 2 q^{30} + 12 q^{31} - 11 q^{32} + 6 q^{33} + 16 q^{34} - 5 q^{35} + 11 q^{36} + 3 q^{37} - 11 q^{38} + 7 q^{39} - 2 q^{40} + 11 q^{41} - 2 q^{42} + 7 q^{43} - 6 q^{44} + 2 q^{45} + 11 q^{46} - 37 q^{47} - 11 q^{48} + 23 q^{49} - 19 q^{50} + 16 q^{51} - 7 q^{52} + 11 q^{53} + 11 q^{54} - 11 q^{55} + 2 q^{56} - 11 q^{57} + 7 q^{58} - 16 q^{59} - 2 q^{60} + 24 q^{61} - 12 q^{62} - 2 q^{63} + 11 q^{64} - 7 q^{65} - 6 q^{66} - 28 q^{67} - 16 q^{68} + 11 q^{69} + 5 q^{70} + 4 q^{71} - 11 q^{72} - 7 q^{73} - 3 q^{74} - 19 q^{75} + 11 q^{76} - 13 q^{77} - 7 q^{78} + 5 q^{79} + 2 q^{80} + 11 q^{81} - 11 q^{82} - 11 q^{83} + 2 q^{84} - 11 q^{85} - 7 q^{86} + 7 q^{87} + 6 q^{88} - 10 q^{89} - 2 q^{90} - 24 q^{91} - 11 q^{92} - 12 q^{93} + 37 q^{94} + 2 q^{95} + 11 q^{96} - 24 q^{97} - 23 q^{98} - 6 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - 11 * q^3 + 11 * q^4 + 2 * q^5 + 11 * q^6 - 2 * q^7 - 11 * q^8 + 11 * q^9 - 2 * q^10 - 6 * q^11 - 11 * q^12 - 7 * q^13 + 2 * q^14 - 2 * q^15 + 11 * q^16 - 16 * q^17 - 11 * q^18 + 11 * q^19 + 2 * q^20 + 2 * q^21 + 6 * q^22 - 11 * q^23 + 11 * q^24 + 19 * q^25 + 7 * q^26 - 11 * q^27 - 2 * q^28 - 7 * q^29 + 2 * q^30 + 12 * q^31 - 11 * q^32 + 6 * q^33 + 16 * q^34 - 5 * q^35 + 11 * q^36 + 3 * q^37 - 11 * q^38 + 7 * q^39 - 2 * q^40 + 11 * q^41 - 2 * q^42 + 7 * q^43 - 6 * q^44 + 2 * q^45 + 11 * q^46 - 37 * q^47 - 11 * q^48 + 23 * q^49 - 19 * q^50 + 16 * q^51 - 7 * q^52 + 11 * q^53 + 11 * q^54 - 11 * q^55 + 2 * q^56 - 11 * q^57 + 7 * q^58 - 16 * q^59 - 2 * q^60 + 24 * q^61 - 12 * q^62 - 2 * q^63 + 11 * q^64 - 7 * q^65 - 6 * q^66 - 28 * q^67 - 16 * q^68 + 11 * q^69 + 5 * q^70 + 4 * q^71 - 11 * q^72 - 7 * q^73 - 3 * q^74 - 19 * q^75 + 11 * q^76 - 13 * q^77 - 7 * q^78 + 5 * q^79 + 2 * q^80 + 11 * q^81 - 11 * q^82 - 11 * q^83 + 2 * q^84 - 11 * q^85 - 7 * q^86 + 7 * q^87 + 6 * q^88 - 10 * q^89 - 2 * q^90 - 24 * q^91 - 11 * q^92 - 12 * q^93 + 37 * q^94 + 2 * q^95 + 11 * q^96 - 24 * q^97 - 23 * q^98 - 6 * q^99

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