LMFDB - Embedded newform 6033.2.a.b.1.9

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			1.9
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)

$f(q)$	$=$	$q-2.31705 q^{2} +1.00000 q^{3} +3.36871 q^{4} -0.440585 q^{5} -2.31705 q^{6} -0.330548 q^{7} -3.17136 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.31705 q^{2} +1.00000 q^{3} +3.36871 q^{4} -0.440585 q^{5} -2.31705 q^{6} -0.330548 q^{7} -3.17136 q^{8} +1.00000 q^{9} +1.02086 q^{10} -5.06154 q^{11} +3.36871 q^{12} -6.19792 q^{13} +0.765895 q^{14} -0.440585 q^{15} +0.610767 q^{16} +4.97382 q^{17} -2.31705 q^{18} +6.66322 q^{19} -1.48420 q^{20} -0.330548 q^{21} +11.7278 q^{22} -4.08981 q^{23} -3.17136 q^{24} -4.80588 q^{25} +14.3609 q^{26} +1.00000 q^{27} -1.11352 q^{28} +7.11622 q^{29} +1.02086 q^{30} -1.55892 q^{31} +4.92753 q^{32} -5.06154 q^{33} -11.5246 q^{34} +0.145634 q^{35} +3.36871 q^{36} -7.13511 q^{37} -15.4390 q^{38} -6.19792 q^{39} +1.39725 q^{40} +7.41670 q^{41} +0.765895 q^{42} +9.07584 q^{43} -17.0508 q^{44} -0.440585 q^{45} +9.47628 q^{46} +7.71127 q^{47} +0.610767 q^{48} -6.89074 q^{49} +11.1355 q^{50} +4.97382 q^{51} -20.8790 q^{52} -2.47135 q^{53} -2.31705 q^{54} +2.23004 q^{55} +1.04828 q^{56} +6.66322 q^{57} -16.4886 q^{58} +13.1273 q^{59} -1.48420 q^{60} +2.93159 q^{61} +3.61209 q^{62} -0.330548 q^{63} -12.6389 q^{64} +2.73071 q^{65} +11.7278 q^{66} -2.01773 q^{67} +16.7553 q^{68} -4.08981 q^{69} -0.337442 q^{70} +10.8878 q^{71} -3.17136 q^{72} -2.20099 q^{73} +16.5324 q^{74} -4.80588 q^{75} +22.4464 q^{76} +1.67308 q^{77} +14.3609 q^{78} +17.2846 q^{79} -0.269095 q^{80} +1.00000 q^{81} -17.1848 q^{82} +14.2094 q^{83} -1.11352 q^{84} -2.19139 q^{85} -21.0291 q^{86} +7.11622 q^{87} +16.0519 q^{88} -15.6972 q^{89} +1.02086 q^{90} +2.04871 q^{91} -13.7774 q^{92} -1.55892 q^{93} -17.8674 q^{94} -2.93571 q^{95} +4.92753 q^{96} -6.24872 q^{97} +15.9662 q^{98} -5.06154 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.31705	−1.63840	−0.819200	−	0.573508i	$-0.805582\pi$
$2$	−2.31705	−1.63840	−0.819200	+	0.573508i	$0.805582\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.36871	1.68435
$5$	−0.440585	−0.197036	−0.0985178	−	0.995135i	$-0.531410\pi$
$5$	−0.440585	−0.197036	−0.0985178	+	0.995135i	$0.531410\pi$
$6$	−2.31705	−0.945930
$7$	−0.330548	−0.124935	−0.0624677	−	0.998047i	$-0.519897\pi$
$7$	−0.330548	−0.124935	−0.0624677	+	0.998047i	$0.519897\pi$
$8$	−3.17136	−1.12124
$9$	1.00000	0.333333
$10$	1.02086	0.322823
$11$	−5.06154	−1.52611	−0.763055	−	0.646333i	$-0.776302\pi$
$11$	−5.06154	−1.52611	−0.763055	+	0.646333i	$0.776302\pi$
$12$	3.36871	0.972462
$13$	−6.19792	−1.71899	−0.859497	−	0.511141i	$-0.829223\pi$
$13$	−6.19792	−1.71899	−0.859497	+	0.511141i	$0.829223\pi$
$14$	0.765895	0.204694
$15$	−0.440585	−0.113759
$16$	0.610767	0.152692
$17$	4.97382	1.20633	0.603164	−	0.797617i	$-0.293906\pi$
$17$	4.97382	1.20633	0.603164	+	0.797617i	$0.293906\pi$
$18$	−2.31705	−0.546133
$19$	6.66322	1.52865	0.764323	−	0.644833i	$-0.223073\pi$
$19$	6.66322	1.52865	0.764323	+	0.644833i	$0.223073\pi$
$20$	−1.48420	−0.331878
$21$	−0.330548	−0.0721314
$22$	11.7278	2.50038
$23$	−4.08981	−0.852784	−0.426392	−	0.904539i	$-0.640216\pi$
$23$	−4.08981	−0.852784	−0.426392	+	0.904539i	$0.640216\pi$
$24$	−3.17136	−0.647350
$25$	−4.80588	−0.961177
$26$	14.3609	2.81640
$27$	1.00000	0.192450
$28$	−1.11352	−0.210435
$29$	7.11622	1.32145	0.660725	−	0.750628i	$-0.270249\pi$
$29$	7.11622	1.32145	0.660725	+	0.750628i	$0.270249\pi$
$30$	1.02086	0.186382
$31$	−1.55892	−0.279990	−0.139995	−	0.990152i	$-0.544709\pi$
$31$	−1.55892	−0.279990	−0.139995	+	0.990152i	$0.544709\pi$
$32$	4.92753	0.871073
$33$	−5.06154	−0.881101
$34$	−11.5246	−1.97645
$35$	0.145634	0.0246167
$36$	3.36871	0.561451
$37$	−7.13511	−1.17300	−0.586502	−	0.809948i	$-0.699495\pi$
$37$	−7.13511	−1.17300	−0.586502	+	0.809948i	$0.699495\pi$
$38$	−15.4390	−2.50453
$39$	−6.19792	−0.992461
$40$	1.39725	0.220925
$41$	7.41670	1.15829	0.579147	−	0.815223i	$-0.303386\pi$
$41$	7.41670	1.15829	0.579147	+	0.815223i	$0.303386\pi$
$42$	0.765895	0.118180
$43$	9.07584	1.38405	0.692026	−	0.721872i	$-0.256718\pi$
$43$	9.07584	1.38405	0.692026	+	0.721872i	$0.256718\pi$
$44$	−17.0508	−2.57051
$45$	−0.440585	−0.0656786
$46$	9.47628	1.39720
$47$	7.71127	1.12480	0.562402	−	0.826864i	$-0.309877\pi$
$47$	7.71127	1.12480	0.562402	+	0.826864i	$0.309877\pi$
$48$	0.610767	0.0881567
$49$	−6.89074	−0.984391
$50$	11.1355	1.57479
$51$	4.97382	0.696474
$52$	−20.8790	−2.89539
$53$	−2.47135	−0.339466	−0.169733	−	0.985490i	$-0.554291\pi$
$53$	−2.47135	−0.339466	−0.169733	+	0.985490i	$0.554291\pi$
$54$	−2.31705	−0.315310
$55$	2.23004	0.300698
$56$	1.04828	0.140083
$57$	6.66322	0.882564
$58$	−16.4886	−2.16506
$59$	13.1273	1.70903	0.854517	−	0.519424i	$-0.173853\pi$
$59$	13.1273	1.70903	0.854517	+	0.519424i	$0.173853\pi$
$60$	−1.48420	−0.191610
$61$	2.93159	0.375351	0.187676	−	0.982231i	$-0.439905\pi$
$61$	2.93159	0.375351	0.187676	+	0.982231i	$0.439905\pi$
$62$	3.61209	0.458736
$63$	−0.330548	−0.0416451
$64$	−12.6389	−1.57986
$65$	2.73071	0.338703
$66$	11.7278	1.44359
$67$	−2.01773	−0.246505	−0.123253	−	0.992375i	$-0.539333\pi$
$67$	−2.01773	−0.246505	−0.123253	+	0.992375i	$0.539333\pi$
$68$	16.7553	2.03188
$69$	−4.08981	−0.492355
$70$	−0.337442	−0.0403320
$71$	10.8878	1.29215	0.646075	−	0.763274i	$-0.276410\pi$
$71$	10.8878	1.29215	0.646075	+	0.763274i	$0.276410\pi$
$72$	−3.17136	−0.373748
$73$	−2.20099	−0.257606	−0.128803	−	0.991670i	$-0.541114\pi$
$73$	−2.20099	−0.257606	−0.128803	+	0.991670i	$0.541114\pi$
$74$	16.5324	1.92185
$75$	−4.80588	−0.554936
$76$	22.4464	2.57478
$77$	1.67308	0.190665
$78$	14.3609	1.62605
$79$	17.2846	1.94467	0.972335	−	0.233591i	$-0.0750476\pi$
$79$	17.2846	1.94467	0.972335	+	0.233591i	$0.0750476\pi$
$80$	−0.269095	−0.0300857
$81$	1.00000	0.111111
$82$	−17.1848	−1.89775
$83$	14.2094	1.55968	0.779840	−	0.625979i	$-0.215300\pi$
$83$	14.2094	1.55968	0.779840	+	0.625979i	$0.215300\pi$
$84$	−1.11352	−0.121495
$85$	−2.19139	−0.237690
$86$	−21.0291	−2.26763
$87$	7.11622	0.762939
$88$	16.0519	1.71114
$89$	−15.6972	−1.66390	−0.831949	−	0.554853i	$-0.812775\pi$
$89$	−15.6972	−1.66390	−0.831949	+	0.554853i	$0.812775\pi$
$90$	1.02086	0.107608
$91$	2.04871	0.214763
$92$	−13.7774	−1.43639
$93$	−1.55892	−0.161652
$94$	−17.8674	−1.84288
$95$	−2.93571	−0.301198
$96$	4.92753	0.502914
$97$	−6.24872	−0.634461	−0.317230	−	0.948348i	$-0.602753\pi$
$97$	−6.24872	−0.634461	−0.317230	+	0.948348i	$0.602753\pi$
$98$	15.9662	1.61283
$99$	−5.06154	−0.508704
$100$	−16.1896	−1.61896
$101$	2.88842	0.287408	0.143704	−	0.989621i	$-0.454099\pi$
$101$	2.88842	0.287408	0.143704	+	0.989621i	$0.454099\pi$
$102$	−11.5246	−1.14110
$103$	−13.1132	−1.29208	−0.646042	−	0.763302i	$-0.723577\pi$
$103$	−13.1132	−1.29208	−0.646042	+	0.763302i	$0.723577\pi$
$104$	19.6558	1.92741
$105$	0.145634	0.0142125
$106$	5.72623	0.556181
$107$	−13.8350	−1.33748	−0.668741	−	0.743496i	$-0.733166\pi$
$107$	−13.8350	−1.33748	−0.668741	+	0.743496i	$0.733166\pi$
$108$	3.36871	0.324154
$109$	−8.60289	−0.824007	−0.412004	−	0.911182i	$-0.635171\pi$
$109$	−8.60289	−0.824007	−0.412004	+	0.911182i	$0.635171\pi$
$110$	−5.16710	−0.492664
$111$	−7.13511	−0.677234
$112$	−0.201888	−0.0190766
$113$	−17.8562	−1.67977	−0.839884	−	0.542766i	$-0.817377\pi$
$113$	−17.8562	−1.67977	−0.839884	+	0.542766i	$0.817377\pi$
$114$	−15.4390	−1.44599
$115$	1.80191	0.168029
$116$	23.9725	2.22579
$117$	−6.19792	−0.572998
$118$	−30.4167	−2.80008
$119$	−1.64408	−0.150713
$120$	1.39725	0.127551
$121$	14.6192	1.32901
$122$	−6.79262	−0.614975
$123$	7.41670	0.668741
$124$	−5.25154	−0.471602
$125$	4.32033	0.386422
$126$	0.765895	0.0682313
$127$	−11.2185	−0.995478	−0.497739	−	0.867327i	$-0.665836\pi$
$127$	−11.2185	−0.995478	−0.497739	+	0.867327i	$0.665836\pi$
$128$	19.4298	1.71736
$129$	9.07584	0.799083
$130$	−6.32718	−0.554931
$131$	−13.5512	−1.18398	−0.591988	−	0.805947i	$-0.701657\pi$
$131$	−13.5512	−1.18398	−0.591988	+	0.805947i	$0.701657\pi$
$132$	−17.0508	−1.48408
$133$	−2.20251	−0.190982
$134$	4.67518	0.403874
$135$	−0.440585	−0.0379195
$136$	−15.7737	−1.35259
$137$	−13.5964	−1.16162	−0.580810	−	0.814039i	$-0.697264\pi$
$137$	−13.5964	−1.16162	−0.580810	+	0.814039i	$0.697264\pi$
$138$	9.47628	0.806674
$139$	−9.96214	−0.844978	−0.422489	−	0.906368i	$-0.638843\pi$
$139$	−9.96214	−0.844978	−0.422489	+	0.906368i	$0.638843\pi$
$140$	0.490600	0.0414632
$141$	7.71127	0.649406
$142$	−25.2276	−2.11706
$143$	31.3710	2.62337
$144$	0.610767	0.0508973
$145$	−3.13530	−0.260373
$146$	5.09980	0.422062
$147$	−6.89074	−0.568339
$148$	−24.0361	−1.97575
$149$	−22.2689	−1.82434	−0.912169	−	0.409814i	$-0.865594\pi$
$149$	−22.2689	−1.82434	−0.912169	+	0.409814i	$0.865594\pi$
$150$	11.1355	0.909206
$151$	−3.72352	−0.303016	−0.151508	−	0.988456i	$-0.548413\pi$
$151$	−3.72352	−0.303016	−0.151508	+	0.988456i	$0.548413\pi$
$152$	−21.1314	−1.71398
$153$	4.97382	0.402109
$154$	−3.87660	−0.312386
$155$	0.686837	0.0551681
$156$	−20.8790	−1.67166
$157$	7.12524	0.568656	0.284328	−	0.958727i	$-0.408230\pi$
$157$	7.12524	0.568656	0.284328	+	0.958727i	$0.408230\pi$
$158$	−40.0492	−3.18615
$159$	−2.47135	−0.195991
$160$	−2.17100	−0.171632
$161$	1.35188	0.106543
$162$	−2.31705	−0.182044
$163$	11.5674	0.906026	0.453013	−	0.891504i	$-0.350349\pi$
$163$	11.5674	0.906026	0.453013	+	0.891504i	$0.350349\pi$
$164$	24.9847	1.95098
$165$	2.23004	0.173608
$166$	−32.9238	−2.55538
$167$	−5.08370	−0.393389	−0.196694	−	0.980465i	$-0.563021\pi$
$167$	−5.08370	−0.393389	−0.196694	+	0.980465i	$0.563021\pi$
$168$	1.04828	0.0808769
$169$	25.4142	1.95494
$170$	5.07755	0.389431
$171$	6.66322	0.509549
$172$	30.5738	2.33123
$173$	5.22719	0.397416	0.198708	−	0.980059i	$-0.436326\pi$
$173$	5.22719	0.397416	0.198708	+	0.980059i	$0.436326\pi$
$174$	−16.4886	−1.25000
$175$	1.58857	0.120085
$176$	−3.09142	−0.233025
$177$	13.1273	0.986711
$178$	36.3711	2.72613
$179$	3.92749	0.293554	0.146777	−	0.989170i	$-0.453110\pi$
$179$	3.92749	0.293554	0.146777	+	0.989170i	$0.453110\pi$
$180$	−1.48420	−0.110626
$181$	−16.9921	−1.26301	−0.631505	−	0.775372i	$-0.717563\pi$
$181$	−16.9921	−1.26301	−0.631505	+	0.775372i	$0.717563\pi$
$182$	−4.74695	−0.351868
$183$	2.93159	0.216709
$184$	12.9702	0.956178
$185$	3.14362	0.231124
$186$	3.61209	0.264851
$187$	−25.1752	−1.84099
$188$	25.9770	1.89457
$189$	−0.330548	−0.0240438
$190$	6.80219	0.493482
$191$	3.20138	0.231644	0.115822	−	0.993270i	$-0.463050\pi$
$191$	3.20138	0.231644	0.115822	+	0.993270i	$0.463050\pi$
$192$	−12.6389	−0.912131
$193$	6.18165	0.444965	0.222482	−	0.974937i	$-0.428584\pi$
$193$	6.18165	0.444965	0.222482	+	0.974937i	$0.428584\pi$
$194$	14.4786	1.03950
$195$	2.73071	0.195550
$196$	−23.2129	−1.65806
$197$	4.43063	0.315670	0.157835	−	0.987466i	$-0.449549\pi$
$197$	4.43063	0.315670	0.157835	+	0.987466i	$0.449549\pi$
$198$	11.7278	0.833460
$199$	−10.5936	−0.750957	−0.375479	−	0.926831i	$-0.622522\pi$
$199$	−10.5936	−0.750957	−0.375479	+	0.926831i	$0.622522\pi$
$200$	15.2412	1.07771
$201$	−2.01773	−0.142320
$202$	−6.69260	−0.470890
$203$	−2.35225	−0.165096
$204$	16.7553	1.17311
$205$	−3.26769	−0.228225
$206$	30.3839	2.11695
$207$	−4.08981	−0.284261
$208$	−3.78549	−0.262476
$209$	−33.7261	−2.33288
$210$	−0.337442	−0.0232857
$211$	−8.66388	−0.596446	−0.298223	−	0.954496i	$-0.596394\pi$
$211$	−8.66388	−0.596446	−0.298223	+	0.954496i	$0.596394\pi$
$212$	−8.32525	−0.571780
$213$	10.8878	0.746023
$214$	32.0564	2.19133
$215$	−3.99868	−0.272708
$216$	−3.17136	−0.215783
$217$	0.515298	0.0349807
$218$	19.9333	1.35005
$219$	−2.20099	−0.148729
$220$	7.51234	0.506482
$221$	−30.8273	−2.07367
$222$	16.5324	1.10958
$223$	−26.8178	−1.79585	−0.897927	−	0.440145i	$-0.854927\pi$
$223$	−26.8178	−1.79585	−0.897927	+	0.440145i	$0.854927\pi$
$224$	−1.62879	−0.108828
$225$	−4.80588	−0.320392
$226$	41.3736	2.75213
$227$	−25.5689	−1.69707	−0.848535	−	0.529140i	$-0.822515\pi$
$227$	−25.5689	−1.69707	−0.848535	+	0.529140i	$0.822515\pi$
$228$	22.4464	1.48655
$229$	−23.5572	−1.55670	−0.778350	−	0.627830i	$-0.783943\pi$
$229$	−23.5572	−1.55670	−0.778350	+	0.627830i	$0.783943\pi$
$230$	−4.17511	−0.275298
$231$	1.67308	0.110081
$232$	−22.5681	−1.48167
$233$	−15.6734	−1.02680	−0.513401	−	0.858149i	$-0.671615\pi$
$233$	−15.6734	−1.02680	−0.513401	+	0.858149i	$0.671615\pi$
$234$	14.3609	0.938799
$235$	−3.39747	−0.221627
$236$	44.2221	2.87862
$237$	17.2846	1.12276
$238$	3.80942	0.246928
$239$	−14.6399	−0.946977	−0.473489	−	0.880800i	$-0.657005\pi$
$239$	−14.6399	−0.946977	−0.473489	+	0.880800i	$0.657005\pi$
$240$	−0.269095	−0.0173700
$241$	−11.8396	−0.762655	−0.381327	−	0.924440i	$-0.624533\pi$
$241$	−11.8396	−0.762655	−0.381327	+	0.924440i	$0.624533\pi$
$242$	−33.8733	−2.17746
$243$	1.00000	0.0641500
$244$	9.87565	0.632224
$245$	3.03596	0.193960
$246$	−17.1848	−1.09567
$247$	−41.2981	−2.62773
$248$	4.94389	0.313937
$249$	14.2094	0.900482
$250$	−10.0104	−0.633113
$251$	14.6583	0.925223	0.462612	−	0.886561i	$-0.346912\pi$
$251$	14.6583	0.925223	0.462612	+	0.886561i	$0.346912\pi$
$252$	−1.11352	−0.0701451
$253$	20.7007	1.30144
$254$	25.9937	1.63099
$255$	−2.19139	−0.137230
$256$	−19.7420	−1.23387
$257$	20.6156	1.28597	0.642983	−	0.765880i	$-0.277697\pi$
$257$	20.6156	1.28597	0.642983	+	0.765880i	$0.277697\pi$
$258$	−21.0291	−1.30922
$259$	2.35849	0.146550
$260$	9.19896	0.570495
$261$	7.11622	0.440483
$262$	31.3988	1.93983
$263$	−13.0997	−0.807762	−0.403881	−	0.914812i	$-0.632339\pi$
$263$	−13.0997	−0.807762	−0.403881	+	0.914812i	$0.632339\pi$
$264$	16.0519	0.987928
$265$	1.08884	0.0668869
$266$	5.10332	0.312905
$267$	−15.6972	−0.960651
$268$	−6.79715	−0.415202
$269$	−8.50796	−0.518740	−0.259370	−	0.965778i	$-0.583515\pi$
$269$	−8.50796	−0.518740	−0.259370	+	0.965778i	$0.583515\pi$
$270$	1.02086	0.0621273
$271$	−13.5885	−0.825445	−0.412722	−	0.910857i	$-0.635422\pi$
$271$	−13.5885	−0.825445	−0.412722	+	0.910857i	$0.635422\pi$
$272$	3.03785	0.184196
$273$	2.04871	0.123993
$274$	31.5035	1.90320
$275$	24.3252	1.46686
$276$	−13.7774	−0.829300
$277$	−24.8988	−1.49602	−0.748012	−	0.663686i	$-0.768991\pi$
$277$	−24.8988	−1.49602	−0.748012	+	0.663686i	$0.768991\pi$
$278$	23.0827	1.38441
$279$	−1.55892	−0.0933301
$280$	−0.461859	−0.0276013
$281$	22.0381	1.31468	0.657341	−	0.753593i	$-0.271681\pi$
$281$	22.0381	1.31468	0.657341	+	0.753593i	$0.271681\pi$
$282$	−17.8674	−1.06399
$283$	15.8157	0.940149	0.470074	−	0.882627i	$-0.344227\pi$
$283$	15.8157	0.940149	0.470074	+	0.882627i	$0.344227\pi$
$284$	36.6779	2.17644
$285$	−2.93571	−0.173897
$286$	−72.6881	−4.29814
$287$	−2.45157	−0.144712
$288$	4.92753	0.290358
$289$	7.73887	0.455228
$290$	7.26464	0.426594
$291$	−6.24872	−0.366306
$292$	−7.41449	−0.433900
$293$	13.4794	0.787472	0.393736	−	0.919223i	$-0.371182\pi$
$293$	13.4794	0.787472	0.393736	+	0.919223i	$0.371182\pi$
$294$	15.9662	0.931166
$295$	−5.78371	−0.336741
$296$	22.6280	1.31522
$297$	−5.06154	−0.293700
$298$	51.5981	2.98900
$299$	25.3483	1.46593
$300$	−16.1896	−0.934708
$301$	−3.00000	−0.172917
$302$	8.62756	0.496461
$303$	2.88842	0.165935
$304$	4.06967	0.233412
$305$	−1.29161	−0.0739576
$306$	−11.5246	−0.658816
$307$	12.5172	0.714392	0.357196	−	0.934029i	$-0.383733\pi$
$307$	12.5172	0.714392	0.357196	+	0.934029i	$0.383733\pi$
$308$	5.63611	0.321147
$309$	−13.1132	−0.745985
$310$	−1.59143	−0.0903873
$311$	19.4534	1.10310	0.551549	−	0.834142i	$-0.314037\pi$
$311$	19.4534	1.10310	0.551549	+	0.834142i	$0.314037\pi$
$312$	19.6558	1.11279
$313$	28.2165	1.59489	0.797445	−	0.603391i	$-0.206184\pi$
$313$	28.2165	1.59489	0.797445	+	0.603391i	$0.206184\pi$
$314$	−16.5095	−0.931686
$315$	0.145634	0.00820557
$316$	58.2267	3.27551
$317$	26.5395	1.49061	0.745305	−	0.666724i	$-0.232304\pi$
$317$	26.5395	1.49061	0.745305	+	0.666724i	$0.232304\pi$
$318$	5.72623	0.321111
$319$	−36.0190	−2.01668
$320$	5.56849	0.311288
$321$	−13.8350	−0.772195
$322$	−3.13236	−0.174560
$323$	33.1416	1.84405
$324$	3.36871	0.187150
$325$	29.7865	1.65226
$326$	−26.8021	−1.48443
$327$	−8.60289	−0.475741
$328$	−23.5210	−1.29873
$329$	−2.54894	−0.140528
$330$	−5.16710	−0.284440
$331$	−29.3178	−1.61145	−0.805726	−	0.592288i	$-0.798225\pi$
$331$	−29.3178	−1.61145	−0.805726	+	0.592288i	$0.798225\pi$
$332$	47.8672	2.62705
$333$	−7.13511	−0.391001
$334$	11.7792	0.644528
$335$	0.888983	0.0485703
$336$	−0.201888	−0.0110139
$337$	−0.825252	−0.0449543	−0.0224772	−	0.999747i	$-0.507155\pi$
$337$	−0.825252	−0.0449543	−0.0224772	+	0.999747i	$0.507155\pi$
$338$	−58.8859	−3.20297
$339$	−17.8562	−0.969814
$340$	−7.38215	−0.400353
$341$	7.89053	0.427296
$342$	−15.4390	−0.834844
$343$	4.59155	0.247921
$344$	−28.7827	−1.55186
$345$	1.80191	0.0970115
$346$	−12.1116	−0.651125
$347$	−27.3703	−1.46932	−0.734658	−	0.678437i	$-0.762657\pi$
$347$	−27.3703	−1.46932	−0.734658	+	0.678437i	$0.762657\pi$
$348$	23.9725	1.28506
$349$	−1.22011	−0.0653108	−0.0326554	−	0.999467i	$-0.510396\pi$
$349$	−1.22011	−0.0653108	−0.0326554	+	0.999467i	$0.510396\pi$
$350$	−3.68080	−0.196747
$351$	−6.19792	−0.330820
$352$	−24.9409	−1.32935
$353$	−28.7061	−1.52787	−0.763937	−	0.645291i	$-0.776736\pi$
$353$	−28.7061	−1.52787	−0.763937	+	0.645291i	$0.776736\pi$
$354$	−30.4167	−1.61663
$355$	−4.79702	−0.254599
$356$	−52.8792	−2.80259
$357$	−1.64408	−0.0870142
$358$	−9.10018	−0.480959
$359$	22.6956	1.19783	0.598913	−	0.800814i	$-0.295599\pi$
$359$	22.6956	1.19783	0.598913	+	0.800814i	$0.295599\pi$
$360$	1.39725	0.0736416
$361$	25.3984	1.33676
$362$	39.3714	2.06932
$363$	14.6192	0.767307
$364$	6.90150	0.361737
$365$	0.969723	0.0507576
$366$	−6.79262	−0.355056
$367$	11.6820	0.609796	0.304898	−	0.952385i	$-0.401378\pi$
$367$	11.6820	0.609796	0.304898	+	0.952385i	$0.401378\pi$
$368$	−2.49792	−0.130213
$369$	7.41670	0.386098
$370$	−7.28392	−0.378673
$371$	0.816899	0.0424113
$372$	−5.25154	−0.272280
$373$	6.95696	0.360218	0.180109	−	0.983647i	$-0.442355\pi$
$373$	6.95696	0.360218	0.180109	+	0.983647i	$0.442355\pi$
$374$	58.3320	3.01628
$375$	4.32033	0.223101
$376$	−24.4552	−1.26118
$377$	−44.1058	−2.27156
$378$	0.765895	0.0393934
$379$	−8.19780	−0.421093	−0.210546	−	0.977584i	$-0.567524\pi$
$379$	−8.19780	−0.421093	−0.210546	+	0.977584i	$0.567524\pi$
$380$	−9.88955	−0.507323
$381$	−11.2185	−0.574740
$382$	−7.41774	−0.379525
$383$	−11.2127	−0.572945	−0.286472	−	0.958089i	$-0.592483\pi$
$383$	−11.2127	−0.572945	−0.286472	+	0.958089i	$0.592483\pi$
$384$	19.4298	0.991521
$385$	−0.737134	−0.0375678
$386$	−14.3232	−0.729030
$387$	9.07584	0.461351
$388$	−21.0501	−1.06866
$389$	4.87725	0.247286	0.123643	−	0.992327i	$-0.460542\pi$
$389$	4.87725	0.247286	0.123643	+	0.992327i	$0.460542\pi$
$390$	−6.32718	−0.320389
$391$	−20.3420	−1.02874
$392$	21.8530	1.10374
$393$	−13.5512	−0.683569
$394$	−10.2660	−0.517193
$395$	−7.61534	−0.383169
$396$	−17.0508	−0.856836
$397$	−22.3250	−1.12046	−0.560231	−	0.828337i	$-0.689288\pi$
$397$	−22.3250	−1.12046	−0.560231	+	0.828337i	$0.689288\pi$
$398$	24.5458	1.23037
$399$	−2.20251	−0.110263
$400$	−2.93528	−0.146764
$401$	17.3095	0.864394	0.432197	−	0.901779i	$-0.357738\pi$
$401$	17.3095	0.864394	0.432197	+	0.901779i	$0.357738\pi$
$402$	4.67518	0.233177
$403$	9.66206	0.481301
$404$	9.73024	0.484097
$405$	−0.440585	−0.0218929
$406$	5.45028	0.270493
$407$	36.1146	1.79013
$408$	−15.7737	−0.780917
$409$	10.6705	0.527621	0.263811	−	0.964574i	$-0.415021\pi$
$409$	10.6705	0.527621	0.263811	+	0.964574i	$0.415021\pi$
$410$	7.57139	0.373924
$411$	−13.5964	−0.670662
$412$	−44.1746	−2.17632
$413$	−4.33921	−0.213519
$414$	9.47628	0.465734
$415$	−6.26043	−0.307313
$416$	−30.5405	−1.49737
$417$	−9.96214	−0.487848
$418$	78.1450	3.82220
$419$	−38.4894	−1.88033	−0.940166	−	0.340716i	$-0.889330\pi$
$419$	−38.4894	−1.88033	−0.940166	+	0.340716i	$0.889330\pi$
$420$	0.490600	0.0239388
$421$	10.7100	0.521974	0.260987	−	0.965342i	$-0.415952\pi$
$421$	10.7100	0.521974	0.260987	+	0.965342i	$0.415952\pi$
$422$	20.0746	0.977217
$423$	7.71127	0.374935
$424$	7.83753	0.380624
$425$	−23.9036	−1.15949
$426$	−25.2276	−1.22228
$427$	−0.969029	−0.0468946
$428$	−46.6061	−2.25279
$429$	31.3710	1.51461
$430$	9.26513	0.446804
$431$	6.76057	0.325645	0.162823	−	0.986655i	$-0.447940\pi$
$431$	6.76057	0.325645	0.162823	+	0.986655i	$0.447940\pi$
$432$	0.610767	0.0293856
$433$	0.267485	0.0128545	0.00642725	−	0.999979i	$-0.497954\pi$
$433$	0.267485	0.0128545	0.00642725	+	0.999979i	$0.497954\pi$
$434$	−1.19397	−0.0573123
$435$	−3.13530	−0.150326
$436$	−28.9806	−1.38792
$437$	−27.2513	−1.30360
$438$	5.09980	0.243678
$439$	19.5254	0.931897	0.465948	−	0.884812i	$-0.345713\pi$
$439$	19.5254	0.931897	0.465948	+	0.884812i	$0.345713\pi$
$440$	−7.07224	−0.337156
$441$	−6.89074	−0.328130
$442$	71.4284	3.39750
$443$	−19.7984	−0.940652	−0.470326	−	0.882493i	$-0.655864\pi$
$443$	−19.7984	−0.940652	−0.470326	+	0.882493i	$0.655864\pi$
$444$	−24.0361	−1.14070
$445$	6.91594	0.327847
$446$	62.1381	2.94233
$447$	−22.2689	−1.05328
$448$	4.17775	0.197380
$449$	35.4333	1.67220	0.836100	−	0.548577i	$-0.184830\pi$
$449$	35.4333	1.67220	0.836100	+	0.548577i	$0.184830\pi$
$450$	11.1355	0.524931
$451$	−37.5399	−1.76769
$452$	−60.1522	−2.82932
$453$	−3.72352	−0.174946
$454$	59.2444	2.78048
$455$	−0.902630	−0.0423160
$456$	−21.1314	−0.989570
$457$	9.68233	0.452921	0.226460	−	0.974020i	$-0.427285\pi$
$457$	9.68233	0.452921	0.226460	+	0.974020i	$0.427285\pi$
$458$	54.5830	2.55050
$459$	4.97382	0.232158
$460$	6.07010	0.283020
$461$	−26.1592	−1.21836	−0.609178	−	0.793034i	$-0.708500\pi$
$461$	−26.1592	−1.21836	−0.609178	+	0.793034i	$0.708500\pi$
$462$	−3.87660	−0.180356
$463$	−30.3957	−1.41261	−0.706304	−	0.707909i	$-0.749639\pi$
$463$	−30.3957	−1.41261	−0.706304	+	0.707909i	$0.749639\pi$
$464$	4.34636	0.201774
$465$	0.686837	0.0318513
$466$	36.3161	1.68231
$467$	−18.7284	−0.866648	−0.433324	−	0.901238i	$-0.642659\pi$
$467$	−18.7284	−0.866648	−0.433324	+	0.901238i	$0.642659\pi$
$468$	−20.8790	−0.965130
$469$	0.666957	0.0307972
$470$	7.87210	0.363113
$471$	7.12524	0.328314
$472$	−41.6314	−1.91624
$473$	−45.9377	−2.11222
$474$	−40.0492	−1.83952
$475$	−32.0226	−1.46930
$476$	−5.53844	−0.253854
$477$	−2.47135	−0.113155
$478$	33.9214	1.55153
$479$	17.9992	0.822406	0.411203	−	0.911544i	$-0.365109\pi$
$479$	17.9992	0.822406	0.411203	+	0.911544i	$0.365109\pi$
$480$	−2.17100	−0.0990921
$481$	44.2228	2.01639
$482$	27.4329	1.24953
$483$	1.35188	0.0615125
$484$	49.2477	2.23853
$485$	2.75309	0.125011
$486$	−2.31705	−0.105103
$487$	7.33936	0.332578	0.166289	−	0.986077i	$-0.446822\pi$
$487$	7.33936	0.332578	0.166289	+	0.986077i	$0.446822\pi$
$488$	−9.29710	−0.420860
$489$	11.5674	0.523094
$490$	−7.03445	−0.317784
$491$	−1.74738	−0.0788582	−0.0394291	−	0.999222i	$-0.512554\pi$
$491$	−1.74738	−0.0788582	−0.0394291	+	0.999222i	$0.512554\pi$
$492$	24.9847	1.12640
$493$	35.3948	1.59410
$494$	95.6895	4.30528
$495$	2.23004	0.100233
$496$	−0.952137	−0.0427522
$497$	−3.59895	−0.161435
$498$	−32.9238	−1.47535
$499$	2.61371	0.117006	0.0585029	−	0.998287i	$-0.481367\pi$
$499$	2.61371	0.117006	0.0585029	+	0.998287i	$0.481367\pi$
$500$	14.5539	0.650871
$501$	−5.08370	−0.227123
$502$	−33.9639	−1.51589
$503$	7.85676	0.350316	0.175158	−	0.984540i	$-0.443956\pi$
$503$	7.85676	0.350316	0.175158	+	0.984540i	$0.443956\pi$
$504$	1.04828	0.0466943
$505$	−1.27259	−0.0566297
$506$	−47.9645	−2.13228
$507$	25.4142	1.12868
$508$	−37.7917	−1.67674
$509$	32.9424	1.46014	0.730072	−	0.683370i	$-0.239486\pi$
$509$	32.9424	1.46014	0.730072	+	0.683370i	$0.239486\pi$
$510$	5.07755	0.224838
$511$	0.727532	0.0321841
$512$	6.88350	0.304210
$513$	6.66322	0.294188
$514$	−47.7673	−2.10693
$515$	5.77749	0.254586
$516$	30.5738	1.34594
$517$	−39.0309	−1.71658
$518$	−5.46474	−0.240107
$519$	5.22719	0.229448
$520$	−8.66005	−0.379769
$521$	−8.50414	−0.372573	−0.186286	−	0.982495i	$-0.559645\pi$
$521$	−8.50414	−0.372573	−0.186286	+	0.982495i	$0.559645\pi$
$522$	−16.4886	−0.721687
$523$	29.7695	1.30173	0.650864	−	0.759194i	$-0.274407\pi$
$523$	29.7695	1.30173	0.650864	+	0.759194i	$0.274407\pi$
$524$	−45.6501	−1.99423
$525$	1.58857	0.0693311
$526$	30.3526	1.32344
$527$	−7.75379	−0.337760
$528$	−3.09142	−0.134537
$529$	−6.27347	−0.272760
$530$	−2.52289	−0.109587
$531$	13.1273	0.569678
$532$	−7.41961	−0.321681
$533$	−45.9681	−1.99110
$534$	36.3711	1.57393
$535$	6.09550	0.263532
$536$	6.39895	0.276392
$537$	3.92749	0.169484
$538$	19.7133	0.849903
$539$	34.8777	1.50229
$540$	−1.48420	−0.0638699
$541$	−7.36980	−0.316852	−0.158426	−	0.987371i	$-0.550642\pi$
$541$	−7.36980	−0.316852	−0.158426	+	0.987371i	$0.550642\pi$
$542$	31.4853	1.35241
$543$	−16.9921	−0.729199
$544$	24.5087	1.05080
$545$	3.79030	0.162359
$546$	−4.74695	−0.203151
$547$	−8.73826	−0.373621	−0.186811	−	0.982396i	$-0.559815\pi$
$547$	−8.73826	−0.373621	−0.186811	+	0.982396i	$0.559815\pi$
$548$	−45.8023	−1.95658
$549$	2.93159	0.125117
$550$	−56.3625	−2.40331
$551$	47.4169	2.02003
$552$	12.9702	0.552050
$553$	−5.71339	−0.242958
$554$	57.6917	2.45108
$555$	3.14362	0.133439
$556$	−33.5595	−1.42324
$557$	15.0936	0.639537	0.319768	−	0.947496i	$-0.396395\pi$
$557$	15.0936	0.639537	0.319768	+	0.947496i	$0.396395\pi$
$558$	3.61209	0.152912
$559$	−56.2513	−2.37918
$560$	0.0889487	0.00375877
$561$	−25.1752	−1.06290
$562$	−51.0633	−2.15398
$563$	8.01676	0.337866	0.168933	−	0.985628i	$-0.445968\pi$
$563$	8.01676	0.337866	0.168933	+	0.985628i	$0.445968\pi$
$564$	25.9770	1.09383
$565$	7.86717	0.330974
$566$	−36.6458	−1.54034
$567$	−0.330548	−0.0138817
$568$	−34.5292	−1.44881
$569$	33.0559	1.38578	0.692888	−	0.721045i	$-0.256338\pi$
$569$	33.0559	1.38578	0.692888	+	0.721045i	$0.256338\pi$
$570$	6.80219	0.284912
$571$	−24.8120	−1.03835	−0.519176	−	0.854667i	$-0.673761\pi$
$571$	−24.8120	−1.03835	−0.519176	+	0.854667i	$0.673761\pi$
$572$	105.680	4.41869
$573$	3.20138	0.133739
$574$	5.68041	0.237096
$575$	19.6551	0.819676
$576$	−12.6389	−0.526619
$577$	15.3780	0.640197	0.320098	−	0.947384i	$-0.396284\pi$
$577$	15.3780	0.640197	0.320098	+	0.947384i	$0.396284\pi$
$578$	−17.9313	−0.745845
$579$	6.18165	0.256901
$580$	−10.5619	−0.438559
$581$	−4.69687	−0.194859
$582$	14.4786	0.600156
$583$	12.5088	0.518063
$584$	6.98012	0.288839
$585$	2.73071	0.112901
$586$	−31.2323	−1.29019
$587$	37.0675	1.52994	0.764969	−	0.644067i	$-0.222754\pi$
$587$	37.0675	1.52994	0.764969	+	0.644067i	$0.222754\pi$
$588$	−23.2129	−0.957283
$589$	−10.3874	−0.428006
$590$	13.4011	0.551716
$591$	4.43063	0.182252
$592$	−4.35789	−0.179108
$593$	2.75118	0.112978	0.0564888	−	0.998403i	$-0.482009\pi$
$593$	2.75118	0.112978	0.0564888	+	0.998403i	$0.482009\pi$
$594$	11.7278	0.481198
$595$	0.724359	0.0296958
$596$	−75.0173	−3.07283
$597$	−10.5936	−0.433565
$598$	−58.7332	−2.40178
$599$	−31.4750	−1.28603	−0.643017	−	0.765852i	$-0.722318\pi$
$599$	−31.4750	−1.28603	−0.643017	+	0.765852i	$0.722318\pi$
$600$	15.2412	0.622218
$601$	−14.7948	−0.603491	−0.301745	−	0.953389i	$-0.597569\pi$
$601$	−14.7948	−0.603491	−0.301745	+	0.953389i	$0.597569\pi$
$602$	6.95114	0.283307
$603$	−2.01773	−0.0821684
$604$	−12.5434	−0.510385
$605$	−6.44099	−0.261863
$606$	−6.69260	−0.271868
$607$	−35.1152	−1.42528	−0.712642	−	0.701528i	$-0.752501\pi$
$607$	−35.1152	−1.42528	−0.712642	+	0.701528i	$0.752501\pi$
$608$	32.8332	1.33156
$609$	−2.35225	−0.0953180
$610$	2.99273	0.121172
$611$	−47.7938	−1.93353
$612$	16.7553	0.677294
$613$	−21.2543	−0.858452	−0.429226	−	0.903197i	$-0.641214\pi$
$613$	−21.2543	−0.858452	−0.429226	+	0.903197i	$0.641214\pi$
$614$	−29.0029	−1.17046
$615$	−3.26769	−0.131766
$616$	−5.30593	−0.213782
$617$	−1.04491	−0.0420665	−0.0210332	−	0.999779i	$-0.506696\pi$
$617$	−1.04491	−0.0420665	−0.0210332	+	0.999779i	$0.506696\pi$
$618$	30.3839	1.22222
$619$	−37.2833	−1.49854	−0.749270	−	0.662264i	$-0.769596\pi$
$619$	−37.2833	−1.49854	−0.749270	+	0.662264i	$0.769596\pi$
$620$	2.31375	0.0929225
$621$	−4.08981	−0.164118
$622$	−45.0743	−1.80732
$623$	5.18867	0.207880
$624$	−3.78549	−0.151541
$625$	22.1260	0.885038
$626$	−65.3790	−2.61307
$627$	−33.7261	−1.34689
$628$	24.0028	0.957818
$629$	−35.4887	−1.41503
$630$	−0.337442	−0.0134440
$631$	22.5697	0.898487	0.449244	−	0.893409i	$-0.351693\pi$
$631$	22.5697	0.898487	0.449244	+	0.893409i	$0.351693\pi$
$632$	−54.8156	−2.18045
$633$	−8.66388	−0.344358
$634$	−61.4934	−2.44221
$635$	4.94269	0.196145
$636$	−8.32525	−0.330118
$637$	42.7082	1.69216
$638$	83.4578	3.30412
$639$	10.8878	0.430716
$640$	−8.56047	−0.338382
$641$	−2.95099	−0.116557	−0.0582786	−	0.998300i	$-0.518561\pi$
$641$	−2.95099	−0.116557	−0.0582786	+	0.998300i	$0.518561\pi$
$642$	32.0564	1.26516
$643$	9.40757	0.370998	0.185499	−	0.982644i	$-0.440610\pi$
$643$	9.40757	0.370998	0.185499	+	0.982644i	$0.440610\pi$
$644$	4.55408	0.179456
$645$	−3.99868	−0.157448
$646$	−76.7907	−3.02129
$647$	−14.1367	−0.555772	−0.277886	−	0.960614i	$-0.589634\pi$
$647$	−14.1367	−0.555772	−0.277886	+	0.960614i	$0.589634\pi$
$648$	−3.17136	−0.124583
$649$	−66.4445	−2.60817
$650$	−69.0167	−2.70706
$651$	0.515298	0.0201961
$652$	38.9671	1.52607
$653$	−14.0604	−0.550227	−0.275114	−	0.961412i	$-0.588715\pi$
$653$	−14.0604	−0.550227	−0.275114	+	0.961412i	$0.588715\pi$
$654$	19.9333	0.779453
$655$	5.97047	0.233286
$656$	4.52988	0.176862
$657$	−2.20099	−0.0858688
$658$	5.90602	0.230241
$659$	−17.8504	−0.695353	−0.347677	−	0.937614i	$-0.613029\pi$
$659$	−17.8504	−0.695353	−0.347677	+	0.937614i	$0.613029\pi$
$660$	7.51234	0.292418
$661$	1.53033	0.0595229	0.0297615	−	0.999557i	$-0.490525\pi$
$661$	1.53033	0.0595229	0.0297615	+	0.999557i	$0.490525\pi$
$662$	67.9307	2.64020
$663$	−30.8273	−1.19723
$664$	−45.0629	−1.74878
$665$	0.970394	0.0376302
$666$	16.5324	0.640616
$667$	−29.1040	−1.12691
$668$	−17.1255	−0.662605
$669$	−26.8178	−1.03684
$670$	−2.05982	−0.0795776
$671$	−14.8383	−0.572828
$672$	−1.62879	−0.0628318
$673$	−6.78025	−0.261359	−0.130680	−	0.991425i	$-0.541716\pi$
$673$	−6.78025	−0.261359	−0.130680	+	0.991425i	$0.541716\pi$
$674$	1.91215	0.0736531
$675$	−4.80588	−0.184979
$676$	85.6129	3.29281
$677$	−51.7333	−1.98827	−0.994135	−	0.108144i	$-0.965509\pi$
$677$	−51.7333	−1.98827	−0.994135	+	0.108144i	$0.965509\pi$
$678$	41.3736	1.58894
$679$	2.06550	0.0792666
$680$	6.94968	0.266508
$681$	−25.5689	−0.979804
$682$	−18.2827	−0.700082
$683$	37.4686	1.43370	0.716848	−	0.697230i	$-0.245584\pi$
$683$	37.4686	1.43370	0.716848	+	0.697230i	$0.245584\pi$
$684$	22.4464	0.858260
$685$	5.99038	0.228881
$686$	−10.6388	−0.406193
$687$	−23.5572	−0.898761
$688$	5.54323	0.211334
$689$	15.3172	0.583540
$690$	−4.17511	−0.158944
$691$	41.2769	1.57025	0.785123	−	0.619340i	$-0.212600\pi$
$691$	41.2769	1.57025	0.785123	+	0.619340i	$0.212600\pi$
$692$	17.6088	0.669388
$693$	1.67308	0.0635551
$694$	63.4183	2.40733
$695$	4.38917	0.166491
$696$	−22.5681	−0.855440
$697$	36.8893	1.39728
$698$	2.82704	0.107005
$699$	−15.6734	−0.592824
$700$	5.35144	0.202265
$701$	16.4043	0.619582	0.309791	−	0.950805i	$-0.399741\pi$
$701$	16.4043	0.619582	0.309791	+	0.950805i	$0.399741\pi$
$702$	14.3609	0.542016
$703$	−47.5427	−1.79311
$704$	63.9721	2.41104
$705$	−3.39747	−0.127956
$706$	66.5134	2.50327
$707$	−0.954761	−0.0359075
$708$	44.2221	1.66197
$709$	25.8302	0.970073	0.485036	−	0.874494i	$-0.338806\pi$
$709$	25.8302	0.970073	0.485036	+	0.874494i	$0.338806\pi$
$710$	11.1149	0.417136
$711$	17.2846	0.648223
$712$	49.7813	1.86563
$713$	6.37568	0.238771
$714$	3.80942	0.142564
$715$	−13.8216	−0.516898
$716$	13.2306	0.494449
$717$	−14.6399	−0.546737
$718$	−52.5867	−1.96252
$719$	−3.82712	−0.142728	−0.0713638	−	0.997450i	$-0.522735\pi$
$719$	−3.82712	−0.142728	−0.0713638	+	0.997450i	$0.522735\pi$
$720$	−0.269095	−0.0100286
$721$	4.33454	0.161427
$722$	−58.8494	−2.19015
$723$	−11.8396	−0.440319
$724$	−57.2413	−2.12736
$725$	−34.1997	−1.27015
$726$	−33.8733	−1.25716
$727$	−36.2317	−1.34376	−0.671879	−	0.740661i	$-0.734513\pi$
$727$	−36.2317	−1.34376	−0.671879	+	0.740661i	$0.734513\pi$
$728$	−6.49718	−0.240802
$729$	1.00000	0.0370370
$730$	−2.24689	−0.0831613
$731$	45.1416	1.66962
$732$	9.87565	0.365015
$733$	−43.1643	−1.59431	−0.797155	−	0.603774i	$-0.793663\pi$
$733$	−43.1643	−1.59431	−0.797155	+	0.603774i	$0.793663\pi$
$734$	−27.0677	−0.999089
$735$	3.03596	0.111983
$736$	−20.1527	−0.742837
$737$	10.2128	0.376194
$738$	−17.1848	−0.632583
$739$	−14.7787	−0.543643	−0.271822	−	0.962348i	$-0.587626\pi$
$739$	−14.7787	−0.543643	−0.271822	+	0.962348i	$0.587626\pi$
$740$	10.5899	0.389294
$741$	−41.2981	−1.51712
$742$	−1.89279	−0.0694866
$743$	−53.3537	−1.95736	−0.978679	−	0.205395i	$-0.934152\pi$
$743$	−53.3537	−1.95736	−0.978679	+	0.205395i	$0.934152\pi$
$744$	4.94389	0.181252
$745$	9.81134	0.359460
$746$	−16.1196	−0.590181
$747$	14.2094	0.519893
$748$	−84.8077	−3.10088
$749$	4.57313	0.167099
$750$	−10.0104	−0.365528
$751$	8.61685	0.314433	0.157217	−	0.987564i	$-0.449748\pi$
$751$	8.61685	0.314433	0.157217	+	0.987564i	$0.449748\pi$
$752$	4.70979	0.171748
$753$	14.6583	0.534178
$754$	102.195	3.72173
$755$	1.64053	0.0597049
$756$	−1.11352	−0.0404983
$757$	−2.50706	−0.0911208	−0.0455604	−	0.998962i	$-0.514507\pi$
$757$	−2.50706	−0.0911208	−0.0455604	+	0.998962i	$0.514507\pi$
$758$	18.9947	0.689918
$759$	20.7007	0.751388
$760$	9.31019	0.337716
$761$	−5.24789	−0.190236	−0.0951180	−	0.995466i	$-0.530323\pi$
$761$	−5.24789	−0.190236	−0.0951180	+	0.995466i	$0.530323\pi$
$762$	25.9937	0.941653
$763$	2.84367	0.102948
$764$	10.7845	0.390170
$765$	−2.19139	−0.0792299
$766$	25.9805	0.938712
$767$	−81.3622	−2.93782
$768$	−19.7420	−0.712376
$769$	32.8298	1.18387	0.591936	−	0.805985i	$-0.298364\pi$
$769$	32.8298	1.18387	0.591936	+	0.805985i	$0.298364\pi$
$770$	1.70797	0.0615511
$771$	20.6156	0.742453
$772$	20.8242	0.749478
$773$	−42.6611	−1.53441	−0.767207	−	0.641400i	$-0.778354\pi$
$773$	−42.6611	−1.53441	−0.767207	+	0.641400i	$0.778354\pi$
$774$	−21.0291	−0.755877
$775$	7.49199	0.269120
$776$	19.8169	0.711385
$777$	2.35849	0.0846105
$778$	−11.3008	−0.405154
$779$	49.4191	1.77062
$780$	9.19896	0.329376
$781$	−55.1092	−1.97196
$782$	47.1333	1.68548
$783$	7.11622	0.254313
$784$	−4.20864	−0.150308
$785$	−3.13927	−0.112046
$786$	31.3988	1.11996
$787$	14.1635	0.504873	0.252437	−	0.967613i	$-0.418768\pi$
$787$	14.1635	0.504873	0.252437	+	0.967613i	$0.418768\pi$
$788$	14.9255	0.531699
$789$	−13.0997	−0.466362
$790$	17.6451	0.627784
$791$	5.90232	0.209862
$792$	16.0519	0.570381
$793$	−18.1697	−0.645226
$794$	51.7282	1.83576
$795$	1.08884	0.0386172
$796$	−35.6866	−1.26488
$797$	−35.2440	−1.24841	−0.624204	−	0.781262i	$-0.714577\pi$
$797$	−35.2440	−1.24841	−0.624204	+	0.781262i	$0.714577\pi$
$798$	5.10332	0.180656
$799$	38.3545	1.35688
$800$	−23.6812	−0.837256
$801$	−15.6972	−0.554632
$802$	−40.1069	−1.41622
$803$	11.1404	0.393136
$804$	−6.79715	−0.239717
$805$	−0.595617	−0.0209927
$806$	−22.3874	−0.788564
$807$	−8.50796	−0.299494
$808$	−9.16020	−0.322255
$809$	−4.77051	−0.167722	−0.0838611	−	0.996477i	$-0.526725\pi$
$809$	−4.77051	−0.167722	−0.0838611	+	0.996477i	$0.526725\pi$
$810$	1.02086	0.0358692
$811$	6.96888	0.244711	0.122355	−	0.992486i	$-0.460955\pi$
$811$	6.96888	0.244711	0.122355	+	0.992486i	$0.460955\pi$
$812$	−7.92404	−0.278079
$813$	−13.5885	−0.476571
$814$	−83.6792	−2.93296
$815$	−5.09641	−0.178519
$816$	3.03785	0.106346
$817$	60.4743	2.11573
$818$	−24.7240	−0.864455
$819$	2.04871	0.0715877
$820$	−11.0079	−0.384412
$821$	−20.4342	−0.713157	−0.356579	−	0.934265i	$-0.616057\pi$
$821$	−20.4342	−0.713157	−0.356579	+	0.934265i	$0.616057\pi$
$822$	31.5035	1.09881
$823$	−27.3201	−0.952320	−0.476160	−	0.879359i	$-0.657972\pi$
$823$	−27.3201	−0.952320	−0.476160	+	0.879359i	$0.657972\pi$
$824$	41.5867	1.44874
$825$	24.3252	0.846894
$826$	10.0542	0.349829
$827$	−14.9833	−0.521021	−0.260510	−	0.965471i	$-0.583891\pi$
$827$	−14.9833	−0.521021	−0.260510	+	0.965471i	$0.583891\pi$
$828$	−13.7774	−0.478796
$829$	−36.0239	−1.25116	−0.625581	−	0.780159i	$-0.715138\pi$
$829$	−36.0239	−1.25116	−0.625581	+	0.780159i	$0.715138\pi$
$830$	14.5057	0.503501
$831$	−24.8988	−0.863729
$832$	78.3346	2.71577
$833$	−34.2733	−1.18750
$834$	23.0827	0.799290
$835$	2.23980	0.0775116
$836$	−113.613	−3.92940
$837$	−1.55892	−0.0538842
$838$	89.1818	3.08074
$839$	2.18052	0.0752798	0.0376399	−	0.999291i	$-0.488016\pi$
$839$	2.18052	0.0752798	0.0376399	+	0.999291i	$0.488016\pi$
$840$	−0.461859	−0.0159356
$841$	21.6406	0.746228
$842$	−24.8156	−0.855202
$843$	22.0381	0.759032
$844$	−29.1861	−1.00463
$845$	−11.1971	−0.385193
$846$	−17.8674	−0.614293
$847$	−4.83233	−0.166041
$848$	−1.50942	−0.0518337
$849$	15.8157	0.542795
$850$	55.3858	1.89972
$851$	29.1812	1.00032
$852$	36.6779	1.25657
$853$	50.1032	1.71550	0.857750	−	0.514067i	$-0.171862\pi$
$853$	50.1032	1.71550	0.857750	+	0.514067i	$0.171862\pi$
$854$	2.24529	0.0768321
$855$	−2.93571	−0.100399
$856$	43.8758	1.49964
$857$	−0.786403	−0.0268630	−0.0134315	−	0.999910i	$-0.504276\pi$
$857$	−0.786403	−0.0268630	−0.0134315	+	0.999910i	$0.504276\pi$
$858$	−72.6881	−2.48153
$859$	−26.0804	−0.889852	−0.444926	−	0.895567i	$-0.646770\pi$
$859$	−26.0804	−0.889852	−0.444926	+	0.895567i	$0.646770\pi$
$860$	−13.4704	−0.459336
$861$	−2.45157	−0.0835494
$862$	−15.6646	−0.533537
$863$	6.16745	0.209942	0.104971	−	0.994475i	$-0.466525\pi$
$863$	6.16745	0.209942	0.104971	+	0.994475i	$0.466525\pi$
$864$	4.92753	0.167638
$865$	−2.30302	−0.0783050
$866$	−0.619775	−0.0210608
$867$	7.73887	0.262826
$868$	1.73589	0.0589198
$869$	−87.4867	−2.96778
$870$	7.26464	0.246294
$871$	12.5057	0.423741
$872$	27.2828	0.923913
$873$	−6.24872	−0.211487
$874$	63.1425	2.13583
$875$	−1.42807	−0.0482777
$876$	−7.41449	−0.250512
$877$	−4.33357	−0.146334	−0.0731672	−	0.997320i	$-0.523311\pi$
$877$	−4.33357	−0.146334	−0.0731672	+	0.997320i	$0.523311\pi$
$878$	−45.2413	−1.52682
$879$	13.4794	0.454647
$880$	1.36203	0.0459142
$881$	19.6579	0.662290	0.331145	−	0.943580i	$-0.392565\pi$
$881$	19.6579	0.662290	0.331145	+	0.943580i	$0.392565\pi$
$882$	15.9662	0.537609
$883$	−14.2296	−0.478864	−0.239432	−	0.970913i	$-0.576961\pi$
$883$	−14.2296	−0.478864	−0.239432	+	0.970913i	$0.576961\pi$
$884$	−103.848	−3.49279
$885$	−5.78371	−0.194417
$886$	45.8739	1.54116
$887$	−34.2313	−1.14937	−0.574687	−	0.818373i	$-0.694876\pi$
$887$	−34.2313	−1.14937	−0.574687	+	0.818373i	$0.694876\pi$
$888$	22.6280	0.759344
$889$	3.70824	0.124370
$890$	−16.0246	−0.537144
$891$	−5.06154	−0.169568
$892$	−90.3413	−3.02485
$893$	51.3819	1.71943
$894$	51.5981	1.72570
$895$	−1.73039	−0.0578407
$896$	−6.42247	−0.214560
$897$	25.3483	0.846355
$898$	−82.1006	−2.73973
$899$	−11.0936	−0.369993
$900$	−16.1896	−0.539654
$901$	−12.2920	−0.409507
$902$	86.9817	2.89617
$903$	−3.00000	−0.0998337
$904$	56.6283	1.88343
$905$	7.48645	0.248858
$906$	8.62756	0.286632
$907$	54.9210	1.82362	0.911810	−	0.410611i	$-0.134685\pi$
$907$	54.9210	1.82362	0.911810	+	0.410611i	$0.134685\pi$
$908$	−86.1342	−2.85846
$909$	2.88842	0.0958028
$910$	2.09144	0.0693305
$911$	7.73674	0.256330	0.128165	−	0.991753i	$-0.459091\pi$
$911$	7.73674	0.256330	0.128165	+	0.991753i	$0.459091\pi$
$912$	4.06967	0.134760
$913$	−71.9212	−2.38024
$914$	−22.4344	−0.742065
$915$	−1.29161	−0.0426994
$916$	−79.3571	−2.62203
$917$	4.47933	0.147920
$918$	−11.5246	−0.380368
$919$	−9.98868	−0.329496	−0.164748	−	0.986336i	$-0.552681\pi$
$919$	−9.98868	−0.329496	−0.164748	+	0.986336i	$0.552681\pi$
$920$	−5.71449	−0.188401
$921$	12.5172	0.412455
$922$	60.6121	1.99615
$923$	−67.4820	−2.22120
$924$	5.63611	0.185415
$925$	34.2905	1.12746
$926$	70.4282	2.31441
$927$	−13.1132	−0.430694
$928$	35.0654	1.15108
$929$	−9.08245	−0.297985	−0.148993	−	0.988838i	$-0.547603\pi$
$929$	−9.08245	−0.297985	−0.148993	+	0.988838i	$0.547603\pi$
$930$	−1.59143	−0.0521852
$931$	−45.9145	−1.50479
$932$	−52.7992	−1.72950
$933$	19.4534	0.636874
$934$	43.3946	1.41992
$935$	11.0918	0.362741
$936$	19.6558	0.642470
$937$	12.8047	0.418312	0.209156	−	0.977882i	$-0.432928\pi$
$937$	12.8047	0.418312	0.209156	+	0.977882i	$0.432928\pi$
$938$	−1.54537	−0.0504581
$939$	28.2165	0.920811
$940$	−11.4451	−0.373297
$941$	−34.6515	−1.12961	−0.564803	−	0.825226i	$-0.691048\pi$
$941$	−34.6515	−1.12961	−0.564803	+	0.825226i	$0.691048\pi$
$942$	−16.5095	−0.537909
$943$	−30.3329	−0.987774
$944$	8.01775	0.260955
$945$	0.145634	0.00473749
$946$	106.440	3.46066
$947$	−40.4228	−1.31357	−0.656783	−	0.754080i	$-0.728083\pi$
$947$	−40.4228	−1.31357	−0.656783	+	0.754080i	$0.728083\pi$
$948$	58.2267	1.89112
$949$	13.6416	0.442824
$950$	74.1980	2.40730
$951$	26.5395	0.860604
$952$	5.21398	0.168986
$953$	16.3026	0.528094	0.264047	−	0.964510i	$-0.414943\pi$
$953$	16.3026	0.528094	0.264047	+	0.964510i	$0.414943\pi$
$954$	5.72623	0.185394
$955$	−1.41048	−0.0456420
$956$	−49.3175	−1.59504
$957$	−36.0190	−1.16433
$958$	−41.7050	−1.34743
$959$	4.49426	0.145127
$960$	5.56849	0.179722
$961$	−28.5698	−0.921605
$962$	−102.466	−3.30365
$963$	−13.8350	−0.445827
$964$	−39.8841	−1.28458
$965$	−2.72354	−0.0876739
$966$	−3.13236	−0.100782
$967$	−18.6732	−0.600488	−0.300244	−	0.953862i	$-0.597068\pi$
$967$	−18.6732	−0.600488	−0.300244	+	0.953862i	$0.597068\pi$
$968$	−46.3626	−1.49015
$969$	33.1416	1.06466
$970$	−6.37904	−0.204819
$971$	−14.8189	−0.475561	−0.237780	−	0.971319i	$-0.576420\pi$
$971$	−14.8189	−0.475561	−0.237780	+	0.971319i	$0.576420\pi$
$972$	3.36871	0.108051
$973$	3.29296	0.105568
$974$	−17.0056	−0.544896
$975$	29.7865	0.953931
$976$	1.79052	0.0573131
$977$	19.8097	0.633768	0.316884	−	0.948464i	$-0.397363\pi$
$977$	19.8097	0.633768	0.316884	+	0.948464i	$0.397363\pi$
$978$	−26.8021	−0.857038
$979$	79.4518	2.53929
$980$	10.2272	0.326697
$981$	−8.60289	−0.274669
$982$	4.04876	0.129201
$983$	29.9810	0.956246	0.478123	−	0.878293i	$-0.341317\pi$
$983$	29.9810	0.956246	0.478123	+	0.878293i	$0.341317\pi$
$984$	−23.5210	−0.749822
$985$	−1.95207	−0.0621982
$986$	−82.0114	−2.61178
$987$	−2.54894	−0.0811338
$988$	−139.121	−4.42603
$989$	−37.1184	−1.18030
$990$	−5.16710	−0.164221
$991$	−12.3454	−0.392164	−0.196082	−	0.980588i	$-0.562822\pi$
$991$	−12.3454	−0.392164	−0.196082	+	0.980588i	$0.562822\pi$
$992$	−7.68163	−0.243892
$993$	−29.3178	−0.930373
$994$	8.33894	0.264495
$995$	4.66736	0.147965
$996$	47.8672	1.51673
$997$	48.1349	1.52445	0.762224	−	0.647313i	$-0.224107\pi$
$997$	48.1349	1.52445	0.762224	+	0.647313i	$0.224107\pi$
$998$	−6.05609	−0.191702
$999$	−7.13511	−0.225745

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6033.2.a.b.1.9	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6033.2.a.b.1.9	✓	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)

\(f(q)\)	\(=\)	\(q-2.31705 q^{2} +1.00000 q^{3} +3.36871 q^{4} -0.440585 q^{5} -2.31705 q^{6} -0.330548 q^{7} -3.17136 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.31705 q^{2} +1.00000 q^{3} +3.36871 q^{4} -0.440585 q^{5} -2.31705 q^{6} -0.330548 q^{7} -3.17136 q^{8} +1.00000 q^{9} +1.02086 q^{10} -5.06154 q^{11} +3.36871 q^{12} -6.19792 q^{13} +0.765895 q^{14} -0.440585 q^{15} +0.610767 q^{16} +4.97382 q^{17} -2.31705 q^{18} +6.66322 q^{19} -1.48420 q^{20} -0.330548 q^{21} +11.7278 q^{22} -4.08981 q^{23} -3.17136 q^{24} -4.80588 q^{25} +14.3609 q^{26} +1.00000 q^{27} -1.11352 q^{28} +7.11622 q^{29} +1.02086 q^{30} -1.55892 q^{31} +4.92753 q^{32} -5.06154 q^{33} -11.5246 q^{34} +0.145634 q^{35} +3.36871 q^{36} -7.13511 q^{37} -15.4390 q^{38} -6.19792 q^{39} +1.39725 q^{40} +7.41670 q^{41} +0.765895 q^{42} +9.07584 q^{43} -17.0508 q^{44} -0.440585 q^{45} +9.47628 q^{46} +7.71127 q^{47} +0.610767 q^{48} -6.89074 q^{49} +11.1355 q^{50} +4.97382 q^{51} -20.8790 q^{52} -2.47135 q^{53} -2.31705 q^{54} +2.23004 q^{55} +1.04828 q^{56} +6.66322 q^{57} -16.4886 q^{58} +13.1273 q^{59} -1.48420 q^{60} +2.93159 q^{61} +3.61209 q^{62} -0.330548 q^{63} -12.6389 q^{64} +2.73071 q^{65} +11.7278 q^{66} -2.01773 q^{67} +16.7553 q^{68} -4.08981 q^{69} -0.337442 q^{70} +10.8878 q^{71} -3.17136 q^{72} -2.20099 q^{73} +16.5324 q^{74} -4.80588 q^{75} +22.4464 q^{76} +1.67308 q^{77} +14.3609 q^{78} +17.2846 q^{79} -0.269095 q^{80} +1.00000 q^{81} -17.1848 q^{82} +14.2094 q^{83} -1.11352 q^{84} -2.19139 q^{85} -21.0291 q^{86} +7.11622 q^{87} +16.0519 q^{88} -15.6972 q^{89} +1.02086 q^{90} +2.04871 q^{91} -13.7774 q^{92} -1.55892 q^{93} -17.8674 q^{94} -2.93571 q^{95} +4.92753 q^{96} -6.24872 q^{97} +15.9662 q^{98} -5.06154 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q - 11 q^{2} + 71 q^{3} + 53 q^{4} - 8 q^{5} - 11 q^{6} - 46 q^{7} - 33 q^{8} + 71 q^{9}+O(q^{10}) \) 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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