LMFDB - Embedded newform 6033.2.a.b.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6033,2,Mod(1,6033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6033, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6033 = 3 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6033.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:	$48.1737475394$
Analytic rank:	$1$
Dimension:	$71$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	6033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.64643 q^{2} +1.00000 q^{3} +5.00359 q^{4} +1.18774 q^{5} -2.64643 q^{6} -0.455161 q^{7} -7.94880 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.64643 q^{2} +1.00000 q^{3} +5.00359 q^{4} +1.18774 q^{5} -2.64643 q^{6} -0.455161 q^{7} -7.94880 q^{8} +1.00000 q^{9} -3.14327 q^{10} -2.48515 q^{11} +5.00359 q^{12} -1.48612 q^{13} +1.20455 q^{14} +1.18774 q^{15} +11.0288 q^{16} +2.75097 q^{17} -2.64643 q^{18} -5.13728 q^{19} +5.94296 q^{20} -0.455161 q^{21} +6.57679 q^{22} +6.03852 q^{23} -7.94880 q^{24} -3.58928 q^{25} +3.93291 q^{26} +1.00000 q^{27} -2.27744 q^{28} -1.56027 q^{29} -3.14327 q^{30} -0.248857 q^{31} -13.2893 q^{32} -2.48515 q^{33} -7.28025 q^{34} -0.540612 q^{35} +5.00359 q^{36} +6.10254 q^{37} +13.5955 q^{38} -1.48612 q^{39} -9.44110 q^{40} -8.13089 q^{41} +1.20455 q^{42} -10.3938 q^{43} -12.4347 q^{44} +1.18774 q^{45} -15.9805 q^{46} +9.52089 q^{47} +11.0288 q^{48} -6.79283 q^{49} +9.49878 q^{50} +2.75097 q^{51} -7.43594 q^{52} +3.08790 q^{53} -2.64643 q^{54} -2.95171 q^{55} +3.61799 q^{56} -5.13728 q^{57} +4.12914 q^{58} +9.59010 q^{59} +5.94296 q^{60} +5.64084 q^{61} +0.658583 q^{62} -0.455161 q^{63} +13.1116 q^{64} -1.76512 q^{65} +6.57679 q^{66} +9.40668 q^{67} +13.7647 q^{68} +6.03852 q^{69} +1.43069 q^{70} +1.66349 q^{71} -7.94880 q^{72} -1.51290 q^{73} -16.1500 q^{74} -3.58928 q^{75} -25.7049 q^{76} +1.13115 q^{77} +3.93291 q^{78} -13.1955 q^{79} +13.0993 q^{80} +1.00000 q^{81} +21.5178 q^{82} -4.30146 q^{83} -2.27744 q^{84} +3.26743 q^{85} +27.5065 q^{86} -1.56027 q^{87} +19.7540 q^{88} +16.2657 q^{89} -3.14327 q^{90} +0.676424 q^{91} +30.2143 q^{92} -0.248857 q^{93} -25.1964 q^{94} -6.10175 q^{95} -13.2893 q^{96} -9.57961 q^{97} +17.9767 q^{98} -2.48515 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 71 q - 11 q^{2} + 71 q^{3} + 53 q^{4} - 8 q^{5} - 11 q^{6} - 46 q^{7} - 33 q^{8} + 71 q^{9}+O(q^{10}) $ 71 * q - 11 * q^2 + 71 * q^3 + 53 * q^4 - 8 * q^5 - 11 * q^6 - 46 * q^7 - 33 * q^8 + 71 * q^9	\( 71 q - 11 q^{2} + 71 q^{3} + 53 q^{4} - 8 q^{5} - 11 q^{6} - 46 q^{7} - 33 q^{8} + 71 q^{9} - 41 q^{10} - 18 q^{11} + 53 q^{12} - 67 q^{13} - 7 q^{14} - 8 q^{15} + 21 q^{16} - 25 q^{17} - 11 q^{18} - 43 q^{19} - 8 q^{20} - 46 q^{21} - 49 q^{22} - 75 q^{23} - 33 q^{24} + 19 q^{25} + 71 q^{27} - 89 q^{28} - 35 q^{29} - 41 q^{30} - 82 q^{31} - 62 q^{32} - 18 q^{33} - 28 q^{34} - 51 q^{35} + 53 q^{36} - 66 q^{37} - 29 q^{38} - 67 q^{39} - 102 q^{40} + q^{41} - 7 q^{42} - 112 q^{43} - 25 q^{44} - 8 q^{45} - 36 q^{46} - 67 q^{47} + 21 q^{48} + 7 q^{49} - 24 q^{50} - 25 q^{51} - 134 q^{52} - 40 q^{53} - 11 q^{54} - 112 q^{55} + 9 q^{56} - 43 q^{57} - 47 q^{58} - 18 q^{59} - 8 q^{60} - 144 q^{61} - 19 q^{62} - 46 q^{63} - 17 q^{64} - 31 q^{65} - 49 q^{66} - 85 q^{67} - 22 q^{68} - 75 q^{69} - 11 q^{70} - 44 q^{71} - 33 q^{72} - 98 q^{73} + 6 q^{74} + 19 q^{75} - 85 q^{76} - 39 q^{77} - 126 q^{79} + 21 q^{80} + 71 q^{81} - 69 q^{82} - 43 q^{83} - 89 q^{84} - 112 q^{85} + 32 q^{86} - 35 q^{87} - 85 q^{88} + 8 q^{89} - 41 q^{90} - 40 q^{91} - 96 q^{92} - 82 q^{93} - 99 q^{94} - 103 q^{95} - 62 q^{96} - 67 q^{97} - 11 q^{98} - 18 q^{99}+O(q^{100}) \) 71 * q - 11 * q^2 + 71 * q^3 + 53 * q^4 - 8 * q^5 - 11 * q^6 - 46 * q^7 - 33 * q^8 + 71 * q^9 - 41 * q^10 - 18 * q^11 + 53 * q^12 - 67 * q^13 - 7 * q^14 - 8 * q^15 + 21 * q^16 - 25 * q^17 - 11 * q^18 - 43 * q^19 - 8 * q^20 - 46 * q^21 - 49 * q^22 - 75 * q^23 - 33 * q^24 + 19 * q^25 + 71 * q^27 - 89 * q^28 - 35 * q^29 - 41 * q^30 - 82 * q^31 - 62 * q^32 - 18 * q^33 - 28 * q^34 - 51 * q^35 + 53 * q^36 - 66 * q^37 - 29 * q^38 - 67 * q^39 - 102 * q^40 + q^41 - 7 * q^42 - 112 * q^43 - 25 * q^44 - 8 * q^45 - 36 * q^46 - 67 * q^47 + 21 * q^48 + 7 * q^49 - 24 * q^50 - 25 * q^51 - 134 * q^52 - 40 * q^53 - 11 * q^54 - 112 * q^55 + 9 * q^56 - 43 * q^57 - 47 * q^58 - 18 * q^59 - 8 * q^60 - 144 * q^61 - 19 * q^62 - 46 * q^63 - 17 * q^64 - 31 * q^65 - 49 * q^66 - 85 * q^67 - 22 * q^68 - 75 * q^69 - 11 * q^70 - 44 * q^71 - 33 * q^72 - 98 * q^73 + 6 * q^74 + 19 * q^75 - 85 * q^76 - 39 * q^77 - 126 * q^79 + 21 * q^80 + 71 * q^81 - 69 * q^82 - 43 * q^83 - 89 * q^84 - 112 * q^85 + 32 * q^86 - 35 * q^87 - 85 * q^88 + 8 * q^89 - 41 * q^90 - 40 * q^91 - 96 * q^92 - 82 * q^93 - 99 * q^94 - 103 * q^95 - 62 * q^96 - 67 * q^97 - 11 * q^98 - 18 * 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 $

$2$	−2.64643	−1.87131	−0.935655	−	0.352917i	$-0.885190\pi$
$2$	−2.64643	−1.87131	−0.935655	+	0.352917i	$0.885190\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.00359	2.50180
$5$	1.18774	0.531173	0.265586	−	0.964087i	$-0.414434\pi$
$5$	1.18774	0.531173	0.265586	+	0.964087i	$0.414434\pi$
$6$	−2.64643	−1.08040
$7$	−0.455161	−0.172035	−0.0860174	−	0.996294i	$-0.527414\pi$
$7$	−0.455161	−0.172035	−0.0860174	+	0.996294i	$0.527414\pi$
$8$	−7.94880	−2.81033
$9$	1.00000	0.333333
$10$	−3.14327	−0.993988
$11$	−2.48515	−0.749302	−0.374651	−	0.927166i	$-0.622237\pi$
$11$	−2.48515	−0.749302	−0.374651	+	0.927166i	$0.622237\pi$
$12$	5.00359	1.44441
$13$	−1.48612	−0.412175	−0.206088	−	0.978534i	$-0.566073\pi$
$13$	−1.48612	−0.412175	−0.206088	+	0.978534i	$0.566073\pi$
$14$	1.20455	0.321930
$15$	1.18774	0.306673
$16$	11.0288	2.75719
$17$	2.75097	0.667208	0.333604	−	0.942713i	$-0.391735\pi$
$17$	2.75097	0.667208	0.333604	+	0.942713i	$0.391735\pi$
$18$	−2.64643	−0.623770
$19$	−5.13728	−1.17857	−0.589287	−	0.807924i	$-0.700591\pi$
$19$	−5.13728	−1.17857	−0.589287	+	0.807924i	$0.700591\pi$
$20$	5.94296	1.32889
$21$	−0.455161	−0.0993243
$22$	6.57679	1.40218
$23$	6.03852	1.25912	0.629559	−	0.776953i	$-0.283236\pi$
$23$	6.03852	1.25912	0.629559	+	0.776953i	$0.283236\pi$
$24$	−7.94880	−1.62254
$25$	−3.58928	−0.717856
$26$	3.93291	0.771307
$27$	1.00000	0.192450
$28$	−2.27744	−0.430396
$29$	−1.56027	−0.289735	−0.144867	−	0.989451i	$-0.546276\pi$
$29$	−1.56027	−0.289735	−0.144867	+	0.989451i	$0.546276\pi$
$30$	−3.14327	−0.573879
$31$	−0.248857	−0.0446960	−0.0223480	−	0.999750i	$-0.507114\pi$
$31$	−0.248857	−0.0446960	−0.0223480	+	0.999750i	$0.507114\pi$
$32$	−13.2893	−2.34923
$33$	−2.48515	−0.432610
$34$	−7.28025	−1.24855
$35$	−0.540612	−0.0913802
$36$	5.00359	0.833932
$37$	6.10254	1.00325	0.501626	−	0.865085i	$-0.332735\pi$
$37$	6.10254	1.00325	0.501626	+	0.865085i	$0.332735\pi$
$38$	13.5955	2.20548
$39$	−1.48612	−0.237969
$40$	−9.44110	−1.49277
$41$	−8.13089	−1.26983	−0.634916	−	0.772581i	$-0.718965\pi$
$41$	−8.13089	−1.26983	−0.634916	+	0.772581i	$0.718965\pi$
$42$	1.20455	0.185867
$43$	−10.3938	−1.58504	−0.792522	−	0.609844i	$-0.791232\pi$
$43$	−10.3938	−1.58504	−0.792522	+	0.609844i	$0.791232\pi$
$44$	−12.4347	−1.87460
$45$	1.18774	0.177058
$46$	−15.9805	−2.35620
$47$	9.52089	1.38877	0.694383	−	0.719606i	$-0.255678\pi$
$47$	9.52089	1.38877	0.694383	+	0.719606i	$0.255678\pi$
$48$	11.0288	1.59187
$49$	−6.79283	−0.970404
$50$	9.49878	1.34333
$51$	2.75097	0.385213
$52$	−7.43594	−1.03118
$53$	3.08790	0.424156	0.212078	−	0.977253i	$-0.431977\pi$
$53$	3.08790	0.424156	0.212078	+	0.977253i	$0.431977\pi$
$54$	−2.64643	−0.360134
$55$	−2.95171	−0.398009
$56$	3.61799	0.483474
$57$	−5.13728	−0.680450
$58$	4.12914	0.542183
$59$	9.59010	1.24852	0.624262	−	0.781215i	$-0.285400\pi$
$59$	9.59010	1.24852	0.624262	+	0.781215i	$0.285400\pi$
$60$	5.94296	0.767233
$61$	5.64084	0.722236	0.361118	−	0.932520i	$-0.382395\pi$
$61$	5.64084	0.722236	0.361118	+	0.932520i	$0.382395\pi$
$62$	0.658583	0.0836401
$63$	−0.455161	−0.0573449
$64$	13.1116	1.63895
$65$	−1.76512	−0.218936
$66$	6.57679	0.809547
$67$	9.40668	1.14921	0.574604	−	0.818431i	$-0.305156\pi$
$67$	9.40668	1.14921	0.574604	+	0.818431i	$0.305156\pi$
$68$	13.7647	1.66922
$69$	6.03852	0.726952
$70$	1.43069	0.171001
$71$	1.66349	0.197419	0.0987097	−	0.995116i	$-0.468528\pi$
$71$	1.66349	0.197419	0.0987097	+	0.995116i	$0.468528\pi$
$72$	−7.94880	−0.936776
$73$	−1.51290	−0.177072	−0.0885359	−	0.996073i	$-0.528219\pi$
$73$	−1.51290	−0.177072	−0.0885359	+	0.996073i	$0.528219\pi$
$74$	−16.1500	−1.87739
$75$	−3.58928	−0.414454
$76$	−25.7049	−2.94855
$77$	1.13115	0.128906
$78$	3.93291	0.445314
$79$	−13.1955	−1.48461	−0.742307	−	0.670060i	$-0.766268\pi$
$79$	−13.1955	−1.48461	−0.742307	+	0.670060i	$0.766268\pi$
$80$	13.0993	1.46455
$81$	1.00000	0.111111
$82$	21.5178	2.37625
$83$	−4.30146	−0.472147	−0.236073	−	0.971735i	$-0.575861\pi$
$83$	−4.30146	−0.472147	−0.236073	+	0.971735i	$0.575861\pi$
$84$	−2.27744	−0.248489
$85$	3.26743	0.354402
$86$	27.5065	2.96611
$87$	−1.56027	−0.167278
$88$	19.7540	2.10578
$89$	16.2657	1.72416	0.862079	−	0.506774i	$-0.169162\pi$
$89$	16.2657	1.72416	0.862079	+	0.506774i	$0.169162\pi$
$90$	−3.14327	−0.331329
$91$	0.676424	0.0709085
$92$	30.2143	3.15006
$93$	−0.248857	−0.0258053
$94$	−25.1964	−2.59881
$95$	−6.10175	−0.626026
$96$	−13.2893	−1.35633
$97$	−9.57961	−0.972662	−0.486331	−	0.873775i	$-0.661665\pi$
$97$	−9.57961	−0.972662	−0.486331	+	0.873775i	$0.661665\pi$
$98$	17.9767	1.81593
$99$	−2.48515	−0.249767
$100$	−17.9593	−1.79593
$101$	8.68464	0.864154	0.432077	−	0.901837i	$-0.357781\pi$
$101$	8.68464	0.864154	0.432077	+	0.901837i	$0.357781\pi$
$102$	−7.28025	−0.720852
$103$	−10.7270	−1.05697	−0.528484	−	0.848943i	$-0.677239\pi$
$103$	−10.7270	−1.05697	−0.528484	+	0.848943i	$0.677239\pi$
$104$	11.8129	1.15835
$105$	−0.540612	−0.0527584
$106$	−8.17192	−0.793727
$107$	−15.1448	−1.46410	−0.732052	−	0.681249i	$-0.761437\pi$
$107$	−15.1448	−1.46410	−0.732052	+	0.681249i	$0.761437\pi$
$108$	5.00359	0.481471
$109$	6.06286	0.580717	0.290359	−	0.956918i	$-0.406225\pi$
$109$	6.06286	0.580717	0.290359	+	0.956918i	$0.406225\pi$
$110$	7.81150	0.744797
$111$	6.10254	0.579228
$112$	−5.01987	−0.474333
$113$	−11.7406	−1.10446	−0.552231	−	0.833691i	$-0.686223\pi$
$113$	−11.7406	−1.10446	−0.552231	+	0.833691i	$0.686223\pi$
$114$	13.5955	1.27333
$115$	7.17218	0.668809
$116$	−7.80695	−0.724857
$117$	−1.48612	−0.137392
$118$	−25.3795	−2.33638
$119$	−1.25213	−0.114783
$120$	−9.44110	−0.861850
$121$	−4.82401	−0.438546
$122$	−14.9281	−1.35153
$123$	−8.13089	−0.733138
$124$	−1.24518	−0.111820
$125$	−10.2018	−0.912478
$126$	1.20455	0.107310
$127$	1.93262	0.171493	0.0857463	−	0.996317i	$-0.472673\pi$
$127$	1.93262	0.171493	0.0857463	+	0.996317i	$0.472673\pi$
$128$	−8.12035	−0.717744
$129$	−10.3938	−0.915125
$130$	4.67127	0.409697
$131$	−11.3967	−0.995734	−0.497867	−	0.867253i	$-0.665883\pi$
$131$	−11.3967	−0.995734	−0.497867	+	0.867253i	$0.665883\pi$
$132$	−12.4347	−1.08230
$133$	2.33829	0.202756
$134$	−24.8941	−2.15052
$135$	1.18774	0.102224
$136$	−21.8669	−1.87507
$137$	−2.04005	−0.174294	−0.0871468	−	0.996195i	$-0.527775\pi$
$137$	−2.04005	−0.174294	−0.0871468	+	0.996195i	$0.527775\pi$
$138$	−15.9805	−1.36035
$139$	8.85347	0.750942	0.375471	−	0.926834i	$-0.377481\pi$
$139$	8.85347	0.750942	0.375471	+	0.926834i	$0.377481\pi$
$140$	−2.70501	−0.228615
$141$	9.52089	0.801804
$142$	−4.40230	−0.369433
$143$	3.69323	0.308844
$144$	11.0288	0.919064
$145$	−1.85319	−0.153899
$146$	4.00379	0.331356
$147$	−6.79283	−0.560263
$148$	30.5347	2.50993
$149$	−12.1761	−0.997509	−0.498754	−	0.866743i	$-0.666209\pi$
$149$	−12.1761	−0.997509	−0.498754	+	0.866743i	$0.666209\pi$
$150$	9.49878	0.775572
$151$	14.0714	1.14511	0.572556	−	0.819866i	$-0.305952\pi$
$151$	14.0714	1.14511	0.572556	+	0.819866i	$0.305952\pi$
$152$	40.8353	3.31218
$153$	2.75097	0.222403
$154$	−2.99350	−0.241223
$155$	−0.295577	−0.0237413
$156$	−7.43594	−0.595351
$157$	3.11059	0.248252	0.124126	−	0.992266i	$-0.460387\pi$
$157$	3.11059	0.248252	0.124126	+	0.992266i	$0.460387\pi$
$158$	34.9211	2.77817
$159$	3.08790	0.244887
$160$	−15.7842	−1.24785
$161$	−2.74850	−0.216612
$162$	−2.64643	−0.207923
$163$	0.748893	0.0586579	0.0293289	−	0.999570i	$-0.490663\pi$
$163$	0.748893	0.0586579	0.0293289	+	0.999570i	$0.490663\pi$
$164$	−40.6837	−3.17686
$165$	−2.95171	−0.229790
$166$	11.3835	0.883532
$167$	−15.6803	−1.21338	−0.606690	−	0.794938i	$-0.707503\pi$
$167$	−15.6803	−1.21338	−0.606690	+	0.794938i	$0.707503\pi$
$168$	3.61799	0.279134
$169$	−10.7915	−0.830112
$170$	−8.64703	−0.663197
$171$	−5.13728	−0.392858
$172$	−52.0065	−3.96546
$173$	8.10776	0.616422	0.308211	−	0.951318i	$-0.400270\pi$
$173$	8.10776	0.616422	0.308211	+	0.951318i	$0.400270\pi$
$174$	4.12914	0.313029
$175$	1.63370	0.123496
$176$	−27.4082	−2.06597
$177$	9.59010	0.720836
$178$	−43.0460	−3.22643
$179$	−16.2762	−1.21654	−0.608270	−	0.793730i	$-0.708136\pi$
$179$	−16.2762	−1.21654	−0.608270	+	0.793730i	$0.708136\pi$
$180$	5.94296	0.442962
$181$	−24.5021	−1.82122	−0.910612	−	0.413262i	$-0.864389\pi$
$181$	−24.5021	−1.82122	−0.910612	+	0.413262i	$0.864389\pi$
$182$	−1.79011	−0.132692
$183$	5.64084	0.416983
$184$	−47.9990	−3.53853
$185$	7.24822	0.532900
$186$	0.658583	0.0482896
$187$	−6.83658	−0.499940
$188$	47.6387	3.47441
$189$	−0.455161	−0.0331081
$190$	16.1478	1.17149
$191$	16.8075	1.21615	0.608073	−	0.793881i	$-0.291943\pi$
$191$	16.8075	1.21615	0.608073	+	0.793881i	$0.291943\pi$
$192$	13.1116	0.946247
$193$	−23.1778	−1.66837	−0.834186	−	0.551484i	$-0.814062\pi$
$193$	−23.1778	−1.66837	−0.834186	+	0.551484i	$0.814062\pi$
$194$	25.3518	1.82015
$195$	−1.76512	−0.126403
$196$	−33.9886	−2.42775
$197$	−21.4777	−1.53022	−0.765111	−	0.643898i	$-0.777316\pi$
$197$	−21.4777	−1.53022	−0.765111	+	0.643898i	$0.777316\pi$
$198$	6.57679	0.467392
$199$	−13.1780	−0.934163	−0.467081	−	0.884214i	$-0.654694\pi$
$199$	−13.1780	−0.934163	−0.467081	+	0.884214i	$0.654694\pi$
$200$	28.5305	2.01741
$201$	9.40668	0.663496
$202$	−22.9833	−1.61710
$203$	0.710174	0.0498444
$204$	13.7647	0.963724
$205$	−9.65737	−0.674500
$206$	28.3884	1.97791
$207$	6.03852	0.419706
$208$	−16.3901	−1.13645
$209$	12.7669	0.883108
$210$	1.43069	0.0987272
$211$	4.95803	0.341325	0.170663	−	0.985330i	$-0.445409\pi$
$211$	4.95803	0.341325	0.170663	+	0.985330i	$0.445409\pi$
$212$	15.4506	1.06115
$213$	1.66349	0.113980
$214$	40.0797	2.73979
$215$	−12.3451	−0.841931
$216$	−7.94880	−0.540848
$217$	0.113270	0.00768927
$218$	−16.0449	−1.08670
$219$	−1.51290	−0.102232
$220$	−14.7692	−0.995737
$221$	−4.08827	−0.275007
$222$	−16.1500	−1.08391
$223$	−16.1127	−1.07899	−0.539493	−	0.841990i	$-0.681384\pi$
$223$	−16.1127	−1.07899	−0.539493	+	0.841990i	$0.681384\pi$
$224$	6.04876	0.404150
$225$	−3.58928	−0.239285
$226$	31.0707	2.06679
$227$	−7.39217	−0.490636	−0.245318	−	0.969443i	$-0.578892\pi$
$227$	−7.39217	−0.490636	−0.245318	+	0.969443i	$0.578892\pi$
$228$	−25.7049	−1.70235
$229$	−15.9338	−1.05294	−0.526468	−	0.850195i	$-0.676484\pi$
$229$	−15.9338	−1.05294	−0.526468	+	0.850195i	$0.676484\pi$
$230$	−18.9807	−1.25155
$231$	1.13115	0.0744240
$232$	12.4023	0.814249
$233$	−19.6871	−1.28975	−0.644873	−	0.764290i	$-0.723090\pi$
$233$	−19.6871	−1.28975	−0.644873	+	0.764290i	$0.723090\pi$
$234$	3.93291	0.257102
$235$	11.3083	0.737674
$236$	47.9850	3.12356
$237$	−13.1955	−0.857142
$238$	3.31369	0.214794
$239$	−0.837010	−0.0541417	−0.0270708	−	0.999634i	$-0.508618\pi$
$239$	−0.837010	−0.0541417	−0.0270708	+	0.999634i	$0.508618\pi$
$240$	13.0993	0.845556
$241$	12.8897	0.830298	0.415149	−	0.909753i	$-0.363729\pi$
$241$	12.8897	0.830298	0.415149	+	0.909753i	$0.363729\pi$
$242$	12.7664	0.820656
$243$	1.00000	0.0641500
$244$	28.2245	1.80689
$245$	−8.06810	−0.515452
$246$	21.5178	1.37193
$247$	7.63461	0.485779
$248$	1.97812	0.125610
$249$	−4.30146	−0.272594
$250$	26.9984	1.70753
$251$	−31.4033	−1.98216	−0.991079	−	0.133274i	$-0.957451\pi$
$251$	−31.4033	−1.98216	−0.991079	+	0.133274i	$0.957451\pi$
$252$	−2.27744	−0.143465
$253$	−15.0067	−0.943460
$254$	−5.11455	−0.320916
$255$	3.26743	0.204614
$256$	−4.73321	−0.295826
$257$	0.267986	0.0167165	0.00835826	−	0.999965i	$-0.497339\pi$
$257$	0.267986	0.0167165	0.00835826	+	0.999965i	$0.497339\pi$
$258$	27.5065	1.71248
$259$	−2.77764	−0.172594
$260$	−8.83194	−0.547734
$261$	−1.56027	−0.0965782
$262$	30.1606	1.86333
$263$	11.0039	0.678528	0.339264	−	0.940691i	$-0.389822\pi$
$263$	11.0039	0.678528	0.339264	+	0.940691i	$0.389822\pi$
$264$	19.7540	1.21578
$265$	3.66762	0.225300
$266$	−6.18813	−0.379419
$267$	16.2657	0.995443
$268$	47.0672	2.87509
$269$	21.2675	1.29670	0.648351	−	0.761342i	$-0.275459\pi$
$269$	21.2675	1.29670	0.648351	+	0.761342i	$0.275459\pi$
$270$	−3.14327	−0.191293
$271$	2.60268	0.158102	0.0790508	−	0.996871i	$-0.474811\pi$
$271$	2.60268	0.158102	0.0790508	+	0.996871i	$0.474811\pi$
$272$	30.3398	1.83962
$273$	0.676424	0.0409390
$274$	5.39886	0.326157
$275$	8.91991	0.537891
$276$	30.2143	1.81869
$277$	0.884326	0.0531340	0.0265670	−	0.999647i	$-0.491542\pi$
$277$	0.884326	0.0531340	0.0265670	+	0.999647i	$0.491542\pi$
$278$	−23.4301	−1.40524
$279$	−0.248857	−0.0148987
$280$	4.29722	0.256808
$281$	18.8719	1.12580	0.562902	−	0.826523i	$-0.309685\pi$
$281$	18.8719	1.12580	0.562902	+	0.826523i	$0.309685\pi$
$282$	−25.1964	−1.50042
$283$	−20.9668	−1.24635	−0.623173	−	0.782084i	$-0.714157\pi$
$283$	−20.9668	−1.24635	−0.623173	+	0.782084i	$0.714157\pi$
$284$	8.32341	0.493904
$285$	−6.10175	−0.361436
$286$	−9.77389	−0.577942
$287$	3.70087	0.218455
$288$	−13.2893	−0.783078
$289$	−9.43217	−0.554834
$290$	4.90434	0.287993
$291$	−9.57961	−0.561567
$292$	−7.56995	−0.442998
$293$	18.0578	1.05495	0.527474	−	0.849571i	$-0.323139\pi$
$293$	18.0578	1.05495	0.527474	+	0.849571i	$0.323139\pi$
$294$	17.9767	1.04843
$295$	11.3905	0.663182
$296$	−48.5079	−2.81947
$297$	−2.48515	−0.144203
$298$	32.2233	1.86665
$299$	−8.97396	−0.518977
$300$	−17.9593	−1.03688
$301$	4.73087	0.272683
$302$	−37.2389	−2.14286
$303$	8.68464	0.498920
$304$	−56.6579	−3.24955
$305$	6.69984	0.383632
$306$	−7.28025	−0.416184
$307$	−23.4552	−1.33866	−0.669330	−	0.742966i	$-0.733419\pi$
$307$	−23.4552	−1.33866	−0.669330	+	0.742966i	$0.733419\pi$
$308$	5.65980	0.322497
$309$	−10.7270	−0.610240
$310$	0.782224	0.0444273
$311$	9.88295	0.560411	0.280205	−	0.959940i	$-0.409597\pi$
$311$	9.88295	0.560411	0.280205	+	0.959940i	$0.409597\pi$
$312$	11.8129	0.668772
$313$	−1.26438	−0.0714671	−0.0357336	−	0.999361i	$-0.511377\pi$
$313$	−1.26438	−0.0714671	−0.0357336	+	0.999361i	$0.511377\pi$
$314$	−8.23197	−0.464557
$315$	−0.540612	−0.0304601
$316$	−66.0251	−3.71420
$317$	−26.8133	−1.50598	−0.752992	−	0.658029i	$-0.771390\pi$
$317$	−26.8133	−1.50598	−0.752992	+	0.658029i	$0.771390\pi$
$318$	−8.17192	−0.458259
$319$	3.87751	0.217099
$320$	15.5731	0.870564
$321$	−15.1448	−0.845301
$322$	7.27372	0.405348
$323$	−14.1325	−0.786354
$324$	5.00359	0.277977
$325$	5.33409	0.295882
$326$	−1.98189	−0.109767
$327$	6.06286	0.335277
$328$	64.6309	3.56864
$329$	−4.33354	−0.238916
$330$	7.81150	0.430009
$331$	13.0072	0.714943	0.357471	−	0.933924i	$-0.383639\pi$
$331$	13.0072	0.714943	0.357471	+	0.933924i	$0.383639\pi$
$332$	−21.5228	−1.18122
$333$	6.10254	0.334417
$334$	41.4969	2.27061
$335$	11.1727	0.610428
$336$	−5.01987	−0.273856
$337$	5.89112	0.320910	0.160455	−	0.987043i	$-0.448704\pi$
$337$	5.89112	0.320910	0.160455	+	0.987043i	$0.448704\pi$
$338$	28.5588	1.55340
$339$	−11.7406	−0.637662
$340$	16.3489	0.886643
$341$	0.618448	0.0334908
$342$	13.5955	0.735158
$343$	6.27796	0.338978
$344$	82.6185	4.45449
$345$	7.17218	0.386137
$346$	−21.4566	−1.15352
$347$	6.77046	0.363457	0.181729	−	0.983349i	$-0.441831\pi$
$347$	6.77046	0.363457	0.181729	+	0.983349i	$0.441831\pi$
$348$	−7.80695	−0.418497
$349$	13.0051	0.696149	0.348074	−	0.937467i	$-0.386836\pi$
$349$	13.0051	0.696149	0.348074	+	0.937467i	$0.386836\pi$
$350$	−4.32348	−0.231100
$351$	−1.48612	−0.0793231
$352$	33.0259	1.76029
$353$	23.6575	1.25916	0.629581	−	0.776935i	$-0.283226\pi$
$353$	23.6575	1.25916	0.629581	+	0.776935i	$0.283226\pi$
$354$	−25.3795	−1.34891
$355$	1.97579	0.104864
$356$	81.3869	4.31349
$357$	−1.25213	−0.0662700
$358$	43.0738	2.27652
$359$	11.7598	0.620657	0.310328	−	0.950629i	$-0.399561\pi$
$359$	11.7598	0.620657	0.310328	+	0.950629i	$0.399561\pi$
$360$	−9.44110	−0.497590
$361$	7.39168	0.389036
$362$	64.8430	3.40807
$363$	−4.82401	−0.253195
$364$	3.38455	0.177399
$365$	−1.79693	−0.0940557
$366$	−14.9281	−0.780304
$367$	25.5181	1.33203	0.666017	−	0.745936i	$-0.267998\pi$
$367$	25.5181	1.33203	0.666017	+	0.745936i	$0.267998\pi$
$368$	66.5974	3.47163
$369$	−8.13089	−0.423277
$370$	−19.1819	−0.997220
$371$	−1.40549	−0.0729696
$372$	−1.24518	−0.0645596
$373$	29.3813	1.52131	0.760654	−	0.649158i	$-0.224879\pi$
$373$	29.3813	1.52131	0.760654	+	0.649158i	$0.224879\pi$
$374$	18.0925	0.935543
$375$	−10.2018	−0.526819
$376$	−75.6797	−3.90288
$377$	2.31874	0.119421
$378$	1.20455	0.0619555
$379$	−27.7873	−1.42734	−0.713668	−	0.700484i	$-0.752967\pi$
$379$	−27.7873	−1.42734	−0.713668	+	0.700484i	$0.752967\pi$
$380$	−30.5307	−1.56619
$381$	1.93262	0.0990113
$382$	−44.4798	−2.27578
$383$	−14.4016	−0.735887	−0.367943	−	0.929848i	$-0.619938\pi$
$383$	−14.4016	−0.735887	−0.367943	+	0.929848i	$0.619938\pi$
$384$	−8.12035	−0.414390
$385$	1.34351	0.0684714
$386$	61.3383	3.12204
$387$	−10.3938	−0.528348
$388$	−47.9325	−2.43340
$389$	18.7978	0.953086	0.476543	−	0.879151i	$-0.341890\pi$
$389$	18.7978	0.953086	0.476543	+	0.879151i	$0.341890\pi$
$390$	4.67127	0.236539
$391$	16.6118	0.840094
$392$	53.9949	2.72715
$393$	−11.3967	−0.574887
$394$	56.8392	2.86352
$395$	−15.6728	−0.788586
$396$	−12.4347	−0.624867
$397$	1.21878	0.0611689	0.0305844	−	0.999532i	$-0.490263\pi$
$397$	1.21878	0.0611689	0.0305844	+	0.999532i	$0.490263\pi$
$398$	34.8746	1.74811
$399$	2.33829	0.117061
$400$	−39.5853	−1.97927
$401$	38.3386	1.91454	0.957268	−	0.289202i	$-0.0933900\pi$
$401$	38.3386	1.91454	0.957268	+	0.289202i	$0.0933900\pi$
$402$	−24.8941	−1.24161
$403$	0.369831	0.0184226
$404$	43.4544	2.16194
$405$	1.18774	0.0590192
$406$	−1.87943	−0.0932743
$407$	−15.1658	−0.751739
$408$	−21.8669	−1.08257
$409$	5.22092	0.258158	0.129079	−	0.991634i	$-0.458798\pi$
$409$	5.22092	0.258158	0.129079	+	0.991634i	$0.458798\pi$
$410$	25.5575	1.26220
$411$	−2.04005	−0.100628
$412$	−53.6738	−2.64432
$413$	−4.36504	−0.214790
$414$	−15.9805	−0.785400
$415$	−5.10901	−0.250791
$416$	19.7494	0.968295
$417$	8.85347	0.433556
$418$	−33.7868	−1.65257
$419$	−30.3443	−1.48242	−0.741208	−	0.671276i	$-0.765747\pi$
$419$	−30.3443	−1.48242	−0.741208	+	0.671276i	$0.765747\pi$
$420$	−2.70501	−0.131991
$421$	13.6771	0.666581	0.333290	−	0.942824i	$-0.391841\pi$
$421$	13.6771	0.666581	0.333290	+	0.942824i	$0.391841\pi$
$422$	−13.1211	−0.638725
$423$	9.52089	0.462922
$424$	−24.5451	−1.19202
$425$	−9.87399	−0.478959
$426$	−4.40230	−0.213292
$427$	−2.56749	−0.124250
$428$	−75.7785	−3.66289
$429$	3.69323	0.178311
$430$	32.6706	1.57551
$431$	4.34735	0.209404	0.104702	−	0.994504i	$-0.466611\pi$
$431$	4.34735	0.209404	0.104702	+	0.994504i	$0.466611\pi$
$432$	11.0288	0.530622
$433$	−32.1646	−1.54573	−0.772865	−	0.634570i	$-0.781177\pi$
$433$	−32.1646	−1.54573	−0.772865	+	0.634570i	$0.781177\pi$
$434$	−0.299761	−0.0143890
$435$	−1.85319	−0.0888537
$436$	30.3361	1.45284
$437$	−31.0216	−1.48396
$438$	4.00379	0.191309
$439$	19.8869	0.949148	0.474574	−	0.880216i	$-0.342602\pi$
$439$	19.8869	0.949148	0.474574	+	0.880216i	$0.342602\pi$
$440$	23.4626	1.11853
$441$	−6.79283	−0.323468
$442$	10.8193	0.514622
$443$	−19.4239	−0.922857	−0.461428	−	0.887178i	$-0.652663\pi$
$443$	−19.4239	−0.922857	−0.461428	+	0.887178i	$0.652663\pi$
$444$	30.5347	1.44911
$445$	19.3194	0.915826
$446$	42.6412	2.01912
$447$	−12.1761	−0.575912
$448$	−5.96788	−0.281956
$449$	−1.04659	−0.0493918	−0.0246959	−	0.999695i	$-0.507862\pi$
$449$	−1.04659	−0.0493918	−0.0246959	+	0.999695i	$0.507862\pi$
$450$	9.49878	0.447777
$451$	20.2065	0.951488
$452$	−58.7452	−2.76314
$453$	14.0714	0.661131
$454$	19.5629	0.918131
$455$	0.803414	0.0376646
$456$	40.8353	1.91229
$457$	−10.3378	−0.483580	−0.241790	−	0.970329i	$-0.577734\pi$
$457$	−10.3378	−0.483580	−0.241790	+	0.970329i	$0.577734\pi$
$458$	42.1677	1.97037
$459$	2.75097	0.128404
$460$	35.8867	1.67322
$461$	32.5635	1.51663	0.758316	−	0.651887i	$-0.226023\pi$
$461$	32.5635	1.51663	0.758316	+	0.651887i	$0.226023\pi$
$462$	−2.99350	−0.139270
$463$	−33.0659	−1.53670	−0.768352	−	0.640027i	$-0.778923\pi$
$463$	−33.0659	−1.53670	−0.768352	+	0.640027i	$0.778923\pi$
$464$	−17.2078	−0.798854
$465$	−0.295577	−0.0137071
$466$	52.1006	2.41351
$467$	−37.1780	−1.72039	−0.860197	−	0.509962i	$-0.829659\pi$
$467$	−37.1780	−1.72039	−0.860197	+	0.509962i	$0.829659\pi$
$468$	−7.43594	−0.343726
$469$	−4.28156	−0.197704
$470$	−29.9267	−1.38042
$471$	3.11059	0.143329
$472$	−76.2298	−3.50876
$473$	25.8303	1.18768
$474$	34.9211	1.60398
$475$	18.4391	0.846046
$476$	−6.26517	−0.287164
$477$	3.08790	0.141385
$478$	2.21509	0.101316
$479$	−30.3970	−1.38887	−0.694436	−	0.719554i	$-0.744346\pi$
$479$	−30.3970	−1.38887	−0.694436	+	0.719554i	$0.744346\pi$
$480$	−15.7842	−0.720445
$481$	−9.06910	−0.413516
$482$	−34.1117	−1.55374
$483$	−2.74850	−0.125061
$484$	−24.1374	−1.09715
$485$	−11.3781	−0.516652
$486$	−2.64643	−0.120045
$487$	−0.602996	−0.0273244	−0.0136622	−	0.999907i	$-0.504349\pi$
$487$	−0.602996	−0.0273244	−0.0136622	+	0.999907i	$0.504349\pi$
$488$	−44.8380	−2.02972
$489$	0.748893	0.0338661
$490$	21.3517	0.964570
$491$	5.62471	0.253840	0.126920	−	0.991913i	$-0.459491\pi$
$491$	5.62471	0.253840	0.126920	+	0.991913i	$0.459491\pi$
$492$	−40.6837	−1.83416
$493$	−4.29225	−0.193313
$494$	−20.2045	−0.909042
$495$	−2.95171	−0.132670
$496$	−2.74459	−0.123236
$497$	−0.757155	−0.0339630
$498$	11.3835	0.510108
$499$	32.8564	1.47085	0.735427	−	0.677603i	$-0.236981\pi$
$499$	32.8564	1.47085	0.735427	+	0.677603i	$0.236981\pi$
$500$	−51.0457	−2.28283
$501$	−15.6803	−0.700545
$502$	83.1066	3.70923
$503$	2.66060	0.118630	0.0593152	−	0.998239i	$-0.481108\pi$
$503$	2.66060	0.118630	0.0593152	+	0.998239i	$0.481108\pi$
$504$	3.61799	0.161158
$505$	10.3151	0.459015
$506$	39.7141	1.76551
$507$	−10.7915	−0.479265
$508$	9.67006	0.429040
$509$	1.11879	0.0495894	0.0247947	−	0.999693i	$-0.492107\pi$
$509$	1.11879	0.0495894	0.0247947	+	0.999693i	$0.492107\pi$
$510$	−8.64703	−0.382897
$511$	0.688615	0.0304625
$512$	28.7668	1.27133
$513$	−5.13728	−0.226817
$514$	−0.709207	−0.0312818
$515$	−12.7409	−0.561432
$516$	−52.0065	−2.28946
$517$	−23.6609	−1.04060
$518$	7.35084	0.322977
$519$	8.10776	0.355891
$520$	14.0306	0.615282
$521$	−27.0452	−1.18487	−0.592435	−	0.805618i	$-0.701833\pi$
$521$	−27.0452	−1.18487	−0.592435	+	0.805618i	$0.701833\pi$
$522$	4.12914	0.180728
$523$	−35.2747	−1.54245	−0.771227	−	0.636560i	$-0.780357\pi$
$523$	−35.2747	−1.54245	−0.771227	+	0.636560i	$0.780357\pi$
$524$	−57.0244	−2.49112
$525$	1.63370	0.0713006
$526$	−29.1210	−1.26974
$527$	−0.684598	−0.0298215
$528$	−27.4082	−1.19279
$529$	13.4637	0.585379
$530$	−9.70610	−0.421606
$531$	9.59010	0.416175
$532$	11.6999	0.507254
$533$	12.0835	0.523393
$534$	−43.0460	−1.86278
$535$	−17.9881	−0.777692
$536$	−74.7719	−3.22965
$537$	−16.2762	−0.702370
$538$	−56.2830	−2.42653
$539$	16.8812	0.727126
$540$	5.94296	0.255744
$541$	31.0076	1.33312	0.666560	−	0.745451i	$-0.267766\pi$
$541$	31.0076	1.33312	0.666560	+	0.745451i	$0.267766\pi$
$542$	−6.88781	−0.295857
$543$	−24.5021	−1.05148
$544$	−36.5584	−1.56743
$545$	7.20109	0.308461
$546$	−1.79011	−0.0766096
$547$	−27.2204	−1.16386	−0.581931	−	0.813238i	$-0.697703\pi$
$547$	−27.2204	−1.16386	−0.581931	+	0.813238i	$0.697703\pi$
$548$	−10.2076	−0.436047
$549$	5.64084	0.240745
$550$	−23.6059	−1.00656
$551$	8.01554	0.341474
$552$	−47.9990	−2.04297
$553$	6.00610	0.255405
$554$	−2.34031	−0.0994302
$555$	7.24822	0.307670
$556$	44.2992	1.87870
$557$	33.9359	1.43791	0.718955	−	0.695057i	$-0.244621\pi$
$557$	33.9359	1.43791	0.718955	+	0.695057i	$0.244621\pi$
$558$	0.658583	0.0278800
$559$	15.4465	0.653315
$560$	−5.96229	−0.251953
$561$	−6.83658	−0.288641
$562$	−49.9432	−2.10673
$563$	−17.6638	−0.744439	−0.372219	−	0.928145i	$-0.621403\pi$
$563$	−17.6638	−0.744439	−0.372219	+	0.928145i	$0.621403\pi$
$564$	47.6387	2.00595
$565$	−13.9447	−0.586660
$566$	55.4872	2.33230
$567$	−0.455161	−0.0191150
$568$	−13.2227	−0.554813
$569$	−46.9013	−1.96620	−0.983102	−	0.183061i	$-0.941399\pi$
$569$	−46.9013	−1.96620	−0.983102	+	0.183061i	$0.941399\pi$
$570$	16.1478	0.676359
$571$	8.68373	0.363403	0.181701	−	0.983354i	$-0.441840\pi$
$571$	8.68373	0.363403	0.181701	+	0.983354i	$0.441840\pi$
$572$	18.4794	0.772664
$573$	16.8075	0.702142
$574$	−9.79409	−0.408797
$575$	−21.6739	−0.903865
$576$	13.1116	0.546316
$577$	−31.2885	−1.30256	−0.651279	−	0.758838i	$-0.725767\pi$
$577$	−31.2885	−1.30256	−0.651279	+	0.758838i	$0.725767\pi$
$578$	24.9616	1.03827
$579$	−23.1778	−0.963235
$580$	−9.27261	−0.385024
$581$	1.95786	0.0812257
$582$	25.3518	1.05087
$583$	−7.67392	−0.317821
$584$	12.0258	0.497630
$585$	−1.76512	−0.0729787
$586$	−47.7887	−1.97413
$587$	−30.3766	−1.25378	−0.626888	−	0.779109i	$-0.715672\pi$
$587$	−30.3766	−1.25378	−0.626888	+	0.779109i	$0.715672\pi$
$588$	−33.9886	−1.40166
$589$	1.27845	0.0526776
$590$	−30.1442	−1.24102
$591$	−21.4777	−0.883475
$592$	67.3035	2.76616
$593$	14.1386	0.580604	0.290302	−	0.956935i	$-0.406244\pi$
$593$	14.1386	0.580604	0.290302	+	0.956935i	$0.406244\pi$
$594$	6.57679	0.269849
$595$	−1.48721	−0.0609696
$596$	−60.9245	−2.49556
$597$	−13.1780	−0.539339
$598$	23.7490	0.971167
$599$	22.9202	0.936493	0.468247	−	0.883598i	$-0.344886\pi$
$599$	22.9202	0.936493	0.468247	+	0.883598i	$0.344886\pi$
$600$	28.5305	1.16475
$601$	13.5778	0.553851	0.276926	−	0.960891i	$-0.410684\pi$
$601$	13.5778	0.553851	0.276926	+	0.960891i	$0.410684\pi$
$602$	−12.5199	−0.510273
$603$	9.40668	0.383070
$604$	70.4075	2.86484
$605$	−5.72966	−0.232944
$606$	−22.9833	−0.933633
$607$	−20.4216	−0.828889	−0.414445	−	0.910075i	$-0.636024\pi$
$607$	−20.4216	−0.828889	−0.414445	+	0.910075i	$0.636024\pi$
$608$	68.2707	2.76874
$609$	0.710174	0.0287777
$610$	−17.7307	−0.717894
$611$	−14.1492	−0.572414
$612$	13.7647	0.556406
$613$	−16.3852	−0.661792	−0.330896	−	0.943667i	$-0.607351\pi$
$613$	−16.3852	−0.661792	−0.330896	+	0.943667i	$0.607351\pi$
$614$	62.0726	2.50505
$615$	−9.65737	−0.389423
$616$	−8.99126	−0.362268
$617$	−38.9694	−1.56885	−0.784424	−	0.620225i	$-0.787041\pi$
$617$	−38.9694	−1.56885	−0.784424	+	0.620225i	$0.787041\pi$
$618$	28.3884	1.14195
$619$	45.6322	1.83411	0.917056	−	0.398757i	$-0.130558\pi$
$619$	45.6322	1.83411	0.917056	+	0.398757i	$0.130558\pi$
$620$	−1.47895	−0.0593959
$621$	6.03852	0.242317
$622$	−26.1545	−1.04870
$623$	−7.40351	−0.296615
$624$	−16.3901	−0.656128
$625$	5.82931	0.233173
$626$	3.34610	0.133737
$627$	12.7669	0.509862
$628$	15.5641	0.621077
$629$	16.7879	0.669378
$630$	1.43069	0.0570002
$631$	−32.1916	−1.28153	−0.640764	−	0.767738i	$-0.721382\pi$
$631$	−32.1916	−1.28153	−0.640764	+	0.767738i	$0.721382\pi$
$632$	104.889	4.17225
$633$	4.95803	0.197064
$634$	70.9595	2.81816
$635$	2.29545	0.0910922
$636$	15.4506	0.612657
$637$	10.0949	0.399976
$638$	−10.2616	−0.406259
$639$	1.66349	0.0658065
$640$	−9.64485	−0.381246
$641$	21.2497	0.839312	0.419656	−	0.907683i	$-0.362151\pi$
$641$	21.2497	0.839312	0.419656	+	0.907683i	$0.362151\pi$
$642$	40.0797	1.58182
$643$	15.9741	0.629957	0.314979	−	0.949099i	$-0.398003\pi$
$643$	15.9741	0.629957	0.314979	+	0.949099i	$0.398003\pi$
$644$	−13.7524	−0.541920
$645$	−12.3451	−0.486089
$646$	37.4007	1.47151
$647$	−38.8043	−1.52555	−0.762776	−	0.646662i	$-0.776164\pi$
$647$	−38.8043	−1.52555	−0.762776	+	0.646662i	$0.776164\pi$
$648$	−7.94880	−0.312259
$649$	−23.8329	−0.935522
$650$	−14.1163	−0.553687
$651$	0.113270	0.00443940
$652$	3.74716	0.146750
$653$	0.0315837	0.00123597	0.000617983	−	1.00000i	$-0.499803\pi$
$653$	0.0315837	0.00123597	0.000617983		1.00000i	$0.499803\pi$
$654$	−16.0449	−0.627407
$655$	−13.5363	−0.528906
$656$	−89.6737	−3.50117
$657$	−1.51290	−0.0590240
$658$	11.4684	0.447086
$659$	7.89729	0.307635	0.153817	−	0.988099i	$-0.450843\pi$
$659$	7.89729	0.307635	0.153817	+	0.988099i	$0.450843\pi$
$660$	−14.7692	−0.574889
$661$	11.4147	0.443981	0.221991	−	0.975049i	$-0.428745\pi$
$661$	11.4147	0.443981	0.221991	+	0.975049i	$0.428745\pi$
$662$	−34.4228	−1.33788
$663$	−4.08827	−0.158775
$664$	34.1915	1.32689
$665$	2.77728	0.107698
$666$	−16.1500	−0.625798
$667$	−9.42171	−0.364810
$668$	−78.4580	−3.03563
$669$	−16.1127	−0.622953
$670$	−29.5677	−1.14230
$671$	−14.0184	−0.541173
$672$	6.04876	0.233336
$673$	7.14631	0.275470	0.137735	−	0.990469i	$-0.456018\pi$
$673$	7.14631	0.275470	0.137735	+	0.990469i	$0.456018\pi$
$674$	−15.5904	−0.600521
$675$	−3.58928	−0.138151
$676$	−53.9960	−2.07677
$677$	32.8051	1.26080	0.630402	−	0.776269i	$-0.282890\pi$
$677$	32.8051	1.26080	0.630402	+	0.776269i	$0.282890\pi$
$678$	31.0707	1.19326
$679$	4.36027	0.167332
$680$	−25.9722	−0.995987
$681$	−7.39217	−0.283269
$682$	−1.63668	−0.0626717
$683$	1.31269	0.0502285	0.0251143	−	0.999685i	$-0.492005\pi$
$683$	1.31269	0.0502285	0.0251143	+	0.999685i	$0.492005\pi$
$684$	−25.7049	−0.982851
$685$	−2.42305	−0.0925800
$686$	−16.6142	−0.634333
$687$	−15.9338	−0.607912
$688$	−114.631	−4.37027
$689$	−4.58899	−0.174827
$690$	−18.9807	−0.722582
$691$	−26.3102	−1.00089	−0.500444	−	0.865769i	$-0.666830\pi$
$691$	−26.3102	−1.00089	−0.500444	+	0.865769i	$0.666830\pi$
$692$	40.5680	1.54216
$693$	1.13115	0.0429687
$694$	−17.9175	−0.680141
$695$	10.5156	0.398880
$696$	12.4023	0.470107
$697$	−22.3678	−0.847242
$698$	−34.4172	−1.30271
$699$	−19.6871	−0.744635
$700$	8.17438	0.308962
$701$	−24.8921	−0.940161	−0.470080	−	0.882624i	$-0.655775\pi$
$701$	−24.8921	−0.940161	−0.470080	+	0.882624i	$0.655775\pi$
$702$	3.93291	0.148438
$703$	−31.3505	−1.18241
$704$	−32.5843	−1.22807
$705$	11.3083	0.425896
$706$	−62.6080	−2.35628
$707$	−3.95291	−0.148665
$708$	47.9850	1.80339
$709$	39.7566	1.49309	0.746545	−	0.665335i	$-0.231711\pi$
$709$	39.7566	1.49309	0.746545	+	0.665335i	$0.231711\pi$
$710$	−5.22878	−0.196233
$711$	−13.1955	−0.494871
$712$	−129.293	−4.84545
$713$	−1.50273	−0.0562776
$714$	3.31369	0.124012
$715$	4.38659	0.164049
$716$	−81.4395	−3.04354
$717$	−0.837010	−0.0312587
$718$	−31.1214	−1.16144
$719$	1.59327	0.0594190	0.0297095	−	0.999559i	$-0.490542\pi$
$719$	1.59327	0.0594190	0.0297095	+	0.999559i	$0.490542\pi$
$720$	13.0993	0.488182
$721$	4.88254	0.181835
$722$	−19.5616	−0.728006
$723$	12.8897	0.479373
$724$	−122.598	−4.55633
$725$	5.60024	0.207988
$726$	12.7664	0.473806
$727$	26.0000	0.964287	0.482143	−	0.876092i	$-0.339858\pi$
$727$	26.0000	0.964287	0.482143	+	0.876092i	$0.339858\pi$
$728$	−5.37676	−0.199276
$729$	1.00000	0.0370370
$730$	4.75546	0.176007
$731$	−28.5931	−1.05755
$732$	28.2245	1.04321
$733$	11.1181	0.410657	0.205328	−	0.978693i	$-0.434174\pi$
$733$	11.1181	0.410657	0.205328	+	0.978693i	$0.434174\pi$
$734$	−67.5319	−2.49265
$735$	−8.06810	−0.297596
$736$	−80.2475	−2.95796
$737$	−23.3770	−0.861105
$738$	21.5178	0.792082
$739$	−14.1289	−0.519739	−0.259869	−	0.965644i	$-0.583679\pi$
$739$	−14.1289	−0.519739	−0.259869	+	0.965644i	$0.583679\pi$
$740$	36.2672	1.33321
$741$	7.63461	0.280465
$742$	3.71954	0.136549
$743$	1.30251	0.0477844	0.0238922	−	0.999715i	$-0.492394\pi$
$743$	1.30251	0.0477844	0.0238922	+	0.999715i	$0.492394\pi$
$744$	1.97812	0.0725212
$745$	−14.4621	−0.529849
$746$	−77.7556	−2.84684
$747$	−4.30146	−0.157382
$748$	−34.2075	−1.25075
$749$	6.89333	0.251877
$750$	26.9984	0.985842
$751$	−15.3881	−0.561519	−0.280759	−	0.959778i	$-0.590586\pi$
$751$	−15.3881	−0.561519	−0.280759	+	0.959778i	$0.590586\pi$
$752$	105.004	3.82909
$753$	−31.4033	−1.14440
$754$	−6.13640	−0.223474
$755$	16.7131	0.608252
$756$	−2.27744	−0.0828298
$757$	39.5072	1.43591	0.717957	−	0.696088i	$-0.245078\pi$
$757$	39.5072	1.43591	0.717957	+	0.696088i	$0.245078\pi$
$758$	73.5370	2.67099
$759$	−15.0067	−0.544707
$760$	48.5016	1.75934
$761$	−29.8898	−1.08350	−0.541751	−	0.840539i	$-0.682239\pi$
$761$	−29.8898	−1.08350	−0.541751	+	0.840539i	$0.682239\pi$
$762$	−5.11455	−0.185281
$763$	−2.75958	−0.0999036
$764$	84.0977	3.04255
$765$	3.26743	0.118134
$766$	38.1128	1.37707
$767$	−14.2520	−0.514611
$768$	−4.73321	−0.170795
$769$	−6.57468	−0.237089	−0.118545	−	0.992949i	$-0.537823\pi$
$769$	−6.57468	−0.237089	−0.118545	+	0.992949i	$0.537823\pi$
$770$	−3.55549	−0.128131
$771$	0.267986	0.00965129
$772$	−115.972	−4.17393
$773$	−0.215592	−0.00775430	−0.00387715	−	0.999992i	$-0.501234\pi$
$773$	−0.215592	−0.00775430	−0.00387715	+	0.999992i	$0.501234\pi$
$774$	27.5065	0.988702
$775$	0.893217	0.0320853
$776$	76.1465	2.73350
$777$	−2.77764	−0.0996473
$778$	−49.7470	−1.78352
$779$	41.7707	1.49659
$780$	−8.83194	−0.316234
$781$	−4.13402	−0.147927
$782$	−43.9619	−1.57207
$783$	−1.56027	−0.0557594
$784$	−74.9165	−2.67559
$785$	3.69457	0.131865
$786$	30.1606	1.07579
$787$	30.8012	1.09794	0.548972	−	0.835841i	$-0.315019\pi$
$787$	30.8012	1.09794	0.548972	+	0.835841i	$0.315019\pi$
$788$	−107.466	−3.82831
$789$	11.0039	0.391748
$790$	41.4771	1.47569
$791$	5.34386	0.190006
$792$	19.7540	0.701928
$793$	−8.38296	−0.297688
$794$	−3.22542	−0.114466
$795$	3.66762	0.130077
$796$	−65.9373	−2.33709
$797$	−5.33116	−0.188839	−0.0944197	−	0.995532i	$-0.530100\pi$
$797$	−5.33116	−0.188839	−0.0944197	+	0.995532i	$0.530100\pi$
$798$	−6.18813	−0.219057
$799$	26.1917	0.926595
$800$	47.6989	1.68641
$801$	16.2657	0.574719
$802$	−101.460	−3.58269
$803$	3.75980	0.132680
$804$	47.0672	1.65993
$805$	−3.26450	−0.115058
$806$	−0.978732	−0.0344744
$807$	21.2675	0.748651
$808$	−69.0325	−2.42856
$809$	9.69980	0.341027	0.170513	−	0.985355i	$-0.445457\pi$
$809$	9.69980	0.341027	0.170513	+	0.985355i	$0.445457\pi$
$810$	−3.14327	−0.110443
$811$	−27.1473	−0.953271	−0.476635	−	0.879101i	$-0.658144\pi$
$811$	−27.1473	−0.953271	−0.476635	+	0.879101i	$0.658144\pi$
$812$	3.55342	0.124701
$813$	2.60268	0.0912800
$814$	40.1351	1.40674
$815$	0.889489	0.0311574
$816$	30.3398	1.06211
$817$	53.3960	1.86809
$818$	−13.8168	−0.483093
$819$	0.676424	0.0236362
$820$	−48.3215	−1.68746
$821$	−45.9834	−1.60483	−0.802416	−	0.596765i	$-0.796452\pi$
$821$	−45.9834	−1.60483	−0.802416	+	0.596765i	$0.796452\pi$
$822$	5.39886	0.188307
$823$	−14.9233	−0.520194	−0.260097	−	0.965583i	$-0.583754\pi$
$823$	−14.9233	−0.520194	−0.260097	+	0.965583i	$0.583754\pi$
$824$	85.2672	2.97042
$825$	8.91991	0.310551
$826$	11.5518	0.401938
$827$	−22.1194	−0.769167	−0.384583	−	0.923090i	$-0.625655\pi$
$827$	−22.1194	−0.769167	−0.384583	+	0.923090i	$0.625655\pi$
$828$	30.2143	1.05002
$829$	−24.1057	−0.837226	−0.418613	−	0.908165i	$-0.637484\pi$
$829$	−24.1057	−0.837226	−0.418613	+	0.908165i	$0.637484\pi$
$830$	13.5206	0.469308
$831$	0.884326	0.0306769
$832$	−19.4854	−0.675533
$833$	−18.6869	−0.647461
$834$	−23.4301	−0.811318
$835$	−18.6241	−0.644514
$836$	63.8806	2.20936
$837$	−0.248857	−0.00860176
$838$	80.3040	2.77406
$839$	−21.6261	−0.746616	−0.373308	−	0.927707i	$-0.621777\pi$
$839$	−21.6261	−0.746616	−0.373308	+	0.927707i	$0.621777\pi$
$840$	4.29722	0.148268
$841$	−26.5656	−0.916054
$842$	−36.1955	−1.24738
$843$	18.8719	0.649984
$844$	24.8080	0.853926
$845$	−12.8174	−0.440933
$846$	−25.1964	−0.866269
$847$	2.19570	0.0754452
$848$	34.0558	1.16948
$849$	−20.9668	−0.719579
$850$	26.1308	0.896280
$851$	36.8503	1.26321
$852$	8.32341	0.285155
$853$	−16.0867	−0.550797	−0.275399	−	0.961330i	$-0.588810\pi$
$853$	−16.0867	−0.550797	−0.275399	+	0.961330i	$0.588810\pi$
$854$	6.79469	0.232510
$855$	−6.10175	−0.208675
$856$	120.383	4.11461
$857$	38.2482	1.30653	0.653267	−	0.757128i	$-0.273398\pi$
$857$	38.2482	1.30653	0.653267	+	0.757128i	$0.273398\pi$
$858$	−9.77389	−0.333675
$859$	15.6915	0.535387	0.267693	−	0.963504i	$-0.413739\pi$
$859$	15.6915	0.535387	0.267693	+	0.963504i	$0.413739\pi$
$860$	−61.7701	−2.10634
$861$	3.70087	0.126125
$862$	−11.5050	−0.391860
$863$	21.9309	0.746537	0.373268	−	0.927723i	$-0.378237\pi$
$863$	21.9309	0.746537	0.373268	+	0.927723i	$0.378237\pi$
$864$	−13.2893	−0.452110
$865$	9.62990	0.327426
$866$	85.1213	2.89254
$867$	−9.43217	−0.320333
$868$	0.566758	0.0192370
$869$	32.7930	1.11242
$870$	4.90434	0.166273
$871$	−13.9794	−0.473675
$872$	−48.1925	−1.63200
$873$	−9.57961	−0.324221
$874$	82.0965	2.77695
$875$	4.64347	0.156978
$876$	−7.56995	−0.255765
$877$	14.6525	0.494780	0.247390	−	0.968916i	$-0.420427\pi$
$877$	14.6525	0.494780	0.247390	+	0.968916i	$0.420427\pi$
$878$	−52.6292	−1.77615
$879$	18.0578	0.609074
$880$	−32.5538	−1.09739
$881$	−33.4132	−1.12572	−0.562859	−	0.826553i	$-0.690299\pi$
$881$	−33.4132	−1.12572	−0.562859	+	0.826553i	$0.690299\pi$
$882$	17.9767	0.605309
$883$	−4.91807	−0.165506	−0.0827532	−	0.996570i	$-0.526371\pi$
$883$	−4.91807	−0.165506	−0.0827532	+	0.996570i	$0.526371\pi$
$884$	−20.4560	−0.688011
$885$	11.3905	0.382888
$886$	51.4040	1.72695
$887$	0.106487	0.00357547	0.00178773	−	0.999998i	$-0.499431\pi$
$887$	0.106487	0.00357547	0.00178773	+	0.999998i	$0.499431\pi$
$888$	−48.5079	−1.62782
$889$	−0.879655	−0.0295027
$890$	−51.1273	−1.71379
$891$	−2.48515	−0.0832558
$892$	−80.6214	−2.69941
$893$	−48.9115	−1.63676
$894$	32.2233	1.07771
$895$	−19.3319	−0.646193
$896$	3.69607	0.123477
$897$	−8.97396	−0.299632
$898$	2.76974	0.0924273
$899$	0.388284	0.0129500
$900$	−17.9593	−0.598643
$901$	8.49472	0.283000
$902$	−53.4751	−1.78053
$903$	4.73087	0.157433
$904$	93.3237	3.10390
$905$	−29.1020	−0.967384
$906$	−37.2389	−1.23718
$907$	−45.2538	−1.50263	−0.751314	−	0.659945i	$-0.770579\pi$
$907$	−45.2538	−1.50263	−0.751314	+	0.659945i	$0.770579\pi$
$908$	−36.9874	−1.22747
$909$	8.68464	0.288051
$910$	−2.12618	−0.0704822
$911$	43.1931	1.43105	0.715526	−	0.698586i	$-0.246187\pi$
$911$	43.1931	1.43105	0.715526	+	0.698586i	$0.246187\pi$
$912$	−56.6579	−1.87613
$913$	10.6898	0.353780
$914$	27.3581	0.904927
$915$	6.69984	0.221490
$916$	−79.7263	−2.63423
$917$	5.18733	0.171301
$918$	−7.28025	−0.240284
$919$	−4.41885	−0.145764	−0.0728822	−	0.997341i	$-0.523220\pi$
$919$	−4.41885	−0.145764	−0.0728822	+	0.997341i	$0.523220\pi$
$920$	−57.0103	−1.87957
$921$	−23.4552	−0.772875
$922$	−86.1769	−2.83809
$923$	−2.47214	−0.0813714
$924$	5.65980	0.186194
$925$	−21.9037	−0.720190
$926$	87.5067	2.87565
$927$	−10.7270	−0.352322
$928$	20.7348	0.680654
$929$	42.0784	1.38055	0.690273	−	0.723549i	$-0.257490\pi$
$929$	42.0784	1.38055	0.690273	+	0.723549i	$0.257490\pi$
$930$	0.782224	0.0256501
$931$	34.8967	1.14369
$932$	−98.5064	−3.22668
$933$	9.88295	0.323553
$934$	98.3890	3.21939
$935$	−8.12007	−0.265555
$936$	11.8129	0.386116
$937$	−17.7065	−0.578445	−0.289223	−	0.957262i	$-0.593397\pi$
$937$	−17.7065	−0.578445	−0.289223	+	0.957262i	$0.593397\pi$
$938$	11.3308	0.369965
$939$	−1.26438	−0.0412616
$940$	56.5823	1.84551
$941$	60.1604	1.96117	0.980587	−	0.196084i	$-0.0628226\pi$
$941$	60.1604	1.96117	0.980587	+	0.196084i	$0.0628226\pi$
$942$	−8.23197	−0.268212
$943$	−49.0985	−1.59887
$944$	105.767	3.44242
$945$	−0.540612	−0.0175861
$946$	−68.3580	−2.22251
$947$	55.7621	1.81203	0.906013	−	0.423250i	$-0.139111\pi$
$947$	55.7621	1.81203	0.906013	+	0.423250i	$0.139111\pi$
$948$	−66.0251	−2.14440
$949$	2.24835	0.0729846
$950$	−48.7979	−1.58321
$951$	−26.8133	−0.869481
$952$	9.95297	0.322578
$953$	32.9392	1.06700	0.533502	−	0.845799i	$-0.320876\pi$
$953$	32.9392	1.06700	0.533502	+	0.845799i	$0.320876\pi$
$954$	−8.17192	−0.264576
$955$	19.9629	0.645983
$956$	−4.18806	−0.135452
$957$	3.87751	0.125342
$958$	80.4434	2.59901
$959$	0.928554	0.0299846
$960$	15.5731	0.502620
$961$	−30.9381	−0.998002
$962$	24.0008	0.773815
$963$	−15.1448	−0.488034
$964$	64.4948	2.07724
$965$	−27.5291	−0.886193
$966$	7.27372	0.234028
$967$	33.3272	1.07173	0.535865	−	0.844304i	$-0.319986\pi$
$967$	33.3272	1.07173	0.535865	+	0.844304i	$0.319986\pi$
$968$	38.3451	1.23246
$969$	−14.1325	−0.454001
$970$	30.1113	0.966815
$971$	21.3060	0.683742	0.341871	−	0.939747i	$-0.388939\pi$
$971$	21.3060	0.683742	0.341871	+	0.939747i	$0.388939\pi$
$972$	5.00359	0.160490
$973$	−4.02976	−0.129188
$974$	1.59579	0.0511323
$975$	5.33409	0.170828
$976$	62.2116	1.99134
$977$	−8.97932	−0.287274	−0.143637	−	0.989630i	$-0.545880\pi$
$977$	−8.97932	−0.287274	−0.143637	+	0.989630i	$0.545880\pi$
$978$	−1.98189	−0.0633740
$979$	−40.4227	−1.29192
$980$	−40.3695	−1.28956
$981$	6.06286	0.193572
$982$	−14.8854	−0.475012
$983$	27.4493	0.875495	0.437748	−	0.899098i	$-0.355776\pi$
$983$	27.4493	0.875495	0.437748	+	0.899098i	$0.355776\pi$
$984$	64.6309	2.06036
$985$	−25.5099	−0.812812
$986$	11.3591	0.361749
$987$	−4.33354	−0.137938
$988$	38.2005	1.21532
$989$	−62.7633	−1.99576
$990$	7.81150	0.248266
$991$	−44.7952	−1.42297	−0.711484	−	0.702703i	$-0.751976\pi$
$991$	−44.7952	−1.42297	−0.711484	+	0.702703i	$0.751976\pi$
$992$	3.30713	0.105001
$993$	13.0072	0.412772
$994$	2.00376	0.0635553
$995$	−15.6520	−0.496202
$996$	−21.5228	−0.681975
$997$	−22.6036	−0.715863	−0.357931	−	0.933748i	$-0.616518\pi$
$997$	−22.6036	−0.715863	−0.357931	+	0.933748i	$0.616518\pi$
$998$	−86.9522	−2.75242
$999$	6.10254	0.193076

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6033.2.a.b.1.4	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6033.2.a.b.1.4	✓	71	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:	\( N \)	\(=\)	\( 6033 = 3 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.64643 q^{2} +1.00000 q^{3} +5.00359 q^{4} +1.18774 q^{5} -2.64643 q^{6} -0.455161 q^{7} -7.94880 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.64643 q^{2} +1.00000 q^{3} +5.00359 q^{4} +1.18774 q^{5} -2.64643 q^{6} -0.455161 q^{7} -7.94880 q^{8} +1.00000 q^{9} -3.14327 q^{10} -2.48515 q^{11} +5.00359 q^{12} -1.48612 q^{13} +1.20455 q^{14} +1.18774 q^{15} +11.0288 q^{16} +2.75097 q^{17} -2.64643 q^{18} -5.13728 q^{19} +5.94296 q^{20} -0.455161 q^{21} +6.57679 q^{22} +6.03852 q^{23} -7.94880 q^{24} -3.58928 q^{25} +3.93291 q^{26} +1.00000 q^{27} -2.27744 q^{28} -1.56027 q^{29} -3.14327 q^{30} -0.248857 q^{31} -13.2893 q^{32} -2.48515 q^{33} -7.28025 q^{34} -0.540612 q^{35} +5.00359 q^{36} +6.10254 q^{37} +13.5955 q^{38} -1.48612 q^{39} -9.44110 q^{40} -8.13089 q^{41} +1.20455 q^{42} -10.3938 q^{43} -12.4347 q^{44} +1.18774 q^{45} -15.9805 q^{46} +9.52089 q^{47} +11.0288 q^{48} -6.79283 q^{49} +9.49878 q^{50} +2.75097 q^{51} -7.43594 q^{52} +3.08790 q^{53} -2.64643 q^{54} -2.95171 q^{55} +3.61799 q^{56} -5.13728 q^{57} +4.12914 q^{58} +9.59010 q^{59} +5.94296 q^{60} +5.64084 q^{61} +0.658583 q^{62} -0.455161 q^{63} +13.1116 q^{64} -1.76512 q^{65} +6.57679 q^{66} +9.40668 q^{67} +13.7647 q^{68} +6.03852 q^{69} +1.43069 q^{70} +1.66349 q^{71} -7.94880 q^{72} -1.51290 q^{73} -16.1500 q^{74} -3.58928 q^{75} -25.7049 q^{76} +1.13115 q^{77} +3.93291 q^{78} -13.1955 q^{79} +13.0993 q^{80} +1.00000 q^{81} +21.5178 q^{82} -4.30146 q^{83} -2.27744 q^{84} +3.26743 q^{85} +27.5065 q^{86} -1.56027 q^{87} +19.7540 q^{88} +16.2657 q^{89} -3.14327 q^{90} +0.676424 q^{91} +30.2143 q^{92} -0.248857 q^{93} -25.1964 q^{94} -6.10175 q^{95} -13.2893 q^{96} -9.57961 q^{97} +17.9767 q^{98} -2.48515 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q - 11 q^{2} + 71 q^{3} + 53 q^{4} - 8 q^{5} - 11 q^{6} - 46 q^{7} - 33 q^{8} + 71 q^{9}+O(q^{10}) \) 71 * q - 11 * q^2 + 71 * q^3 + 53 * q^4 - 8 * q^5 - 11 * q^6 - 46 * q^7 - 33 * q^8 + 71 * q^9	\( 71 q - 11 q^{2} + 71 q^{3} + 53 q^{4} - 8 q^{5} - 11 q^{6} - 46 q^{7} - 33 q^{8} + 71 q^{9} - 41 q^{10} - 18 q^{11} + 53 q^{12} - 67 q^{13} - 7 q^{14} - 8 q^{15} + 21 q^{16} - 25 q^{17} - 11 q^{18} - 43 q^{19} - 8 q^{20} - 46 q^{21} - 49 q^{22} - 75 q^{23} - 33 q^{24} + 19 q^{25} + 71 q^{27} - 89 q^{28} - 35 q^{29} - 41 q^{30} - 82 q^{31} - 62 q^{32} - 18 q^{33} - 28 q^{34} - 51 q^{35} + 53 q^{36} - 66 q^{37} - 29 q^{38} - 67 q^{39} - 102 q^{40} + q^{41} - 7 q^{42} - 112 q^{43} - 25 q^{44} - 8 q^{45} - 36 q^{46} - 67 q^{47} + 21 q^{48} + 7 q^{49} - 24 q^{50} - 25 q^{51} - 134 q^{52} - 40 q^{53} - 11 q^{54} - 112 q^{55} + 9 q^{56} - 43 q^{57} - 47 q^{58} - 18 q^{59} - 8 q^{60} - 144 q^{61} - 19 q^{62} - 46 q^{63} - 17 q^{64} - 31 q^{65} - 49 q^{66} - 85 q^{67} - 22 q^{68} - 75 q^{69} - 11 q^{70} - 44 q^{71} - 33 q^{72} - 98 q^{73} + 6 q^{74} + 19 q^{75} - 85 q^{76} - 39 q^{77} - 126 q^{79} + 21 q^{80} + 71 q^{81} - 69 q^{82} - 43 q^{83} - 89 q^{84} - 112 q^{85} + 32 q^{86} - 35 q^{87} - 85 q^{88} + 8 q^{89} - 41 q^{90} - 40 q^{91} - 96 q^{92} - 82 q^{93} - 99 q^{94} - 103 q^{95} - 62 q^{96} - 67 q^{97} - 11 q^{98} - 18 q^{99}+O(q^{100}) \) 71 * q - 11 * q^2 + 71 * q^3 + 53 * q^4 - 8 * q^5 - 11 * q^6 - 46 * q^7 - 33 * q^8 + 71 * q^9 - 41 * q^10 - 18 * q^11 + 53 * q^12 - 67 * q^13 - 7 * q^14 - 8 * q^15 + 21 * q^16 - 25 * q^17 - 11 * q^18 - 43 * q^19 - 8 * q^20 - 46 * q^21 - 49 * q^22 - 75 * q^23 - 33 * q^24 + 19 * q^25 + 71 * q^27 - 89 * q^28 - 35 * q^29 - 41 * q^30 - 82 * q^31 - 62 * q^32 - 18 * q^33 - 28 * q^34 - 51 * q^35 + 53 * q^36 - 66 * q^37 - 29 * q^38 - 67 * q^39 - 102 * q^40 + q^41 - 7 * q^42 - 112 * q^43 - 25 * q^44 - 8 * q^45 - 36 * q^46 - 67 * q^47 + 21 * q^48 + 7 * q^49 - 24 * q^50 - 25 * q^51 - 134 * q^52 - 40 * q^53 - 11 * q^54 - 112 * q^55 + 9 * q^56 - 43 * q^57 - 47 * q^58 - 18 * q^59 - 8 * q^60 - 144 * q^61 - 19 * q^62 - 46 * q^63 - 17 * q^64 - 31 * q^65 - 49 * q^66 - 85 * q^67 - 22 * q^68 - 75 * q^69 - 11 * q^70 - 44 * q^71 - 33 * q^72 - 98 * q^73 + 6 * q^74 + 19 * q^75 - 85 * q^76 - 39 * q^77 - 126 * q^79 + 21 * q^80 + 71 * q^81 - 69 * q^82 - 43 * q^83 - 89 * q^84 - 112 * q^85 + 32 * q^86 - 35 * q^87 - 85 * q^88 + 8 * q^89 - 41 * q^90 - 40 * q^91 - 96 * q^92 - 82 * q^93 - 99 * q^94 - 103 * q^95 - 62 * q^96 - 67 * q^97 - 11 * q^98 - 18 * q^99

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