LMFDB - Embedded newform 6022.2.a.b.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6022,2,Mod(1,6022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6022, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6022 = 2 \cdot 3011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6022.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:	$48.0859120972$
Analytic rank:	$1$
Dimension:	$54$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	6022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.59103 q^{3} +1.00000 q^{4} -2.29870 q^{5} -1.59103 q^{6} -3.52840 q^{7} +1.00000 q^{8} -0.468610 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.59103 q^{3} +1.00000 q^{4} -2.29870 q^{5} -1.59103 q^{6} -3.52840 q^{7} +1.00000 q^{8} -0.468610 q^{9} -2.29870 q^{10} +2.39606 q^{11} -1.59103 q^{12} +2.94967 q^{13} -3.52840 q^{14} +3.65731 q^{15} +1.00000 q^{16} +2.91192 q^{17} -0.468610 q^{18} -8.09922 q^{19} -2.29870 q^{20} +5.61380 q^{21} +2.39606 q^{22} +6.57848 q^{23} -1.59103 q^{24} +0.284016 q^{25} +2.94967 q^{26} +5.51868 q^{27} -3.52840 q^{28} +6.13299 q^{29} +3.65731 q^{30} -3.57511 q^{31} +1.00000 q^{32} -3.81221 q^{33} +2.91192 q^{34} +8.11072 q^{35} -0.468610 q^{36} -3.63362 q^{37} -8.09922 q^{38} -4.69303 q^{39} -2.29870 q^{40} -0.768554 q^{41} +5.61380 q^{42} +5.36279 q^{43} +2.39606 q^{44} +1.07719 q^{45} +6.57848 q^{46} +7.84547 q^{47} -1.59103 q^{48} +5.44958 q^{49} +0.284016 q^{50} -4.63297 q^{51} +2.94967 q^{52} -1.64273 q^{53} +5.51868 q^{54} -5.50781 q^{55} -3.52840 q^{56} +12.8861 q^{57} +6.13299 q^{58} +5.01838 q^{59} +3.65731 q^{60} +2.26215 q^{61} -3.57511 q^{62} +1.65344 q^{63} +1.00000 q^{64} -6.78040 q^{65} -3.81221 q^{66} -5.48145 q^{67} +2.91192 q^{68} -10.4666 q^{69} +8.11072 q^{70} -7.54970 q^{71} -0.468610 q^{72} +5.65480 q^{73} -3.63362 q^{74} -0.451879 q^{75} -8.09922 q^{76} -8.45424 q^{77} -4.69303 q^{78} -16.6607 q^{79} -2.29870 q^{80} -7.37457 q^{81} -0.768554 q^{82} -6.89513 q^{83} +5.61380 q^{84} -6.69363 q^{85} +5.36279 q^{86} -9.75779 q^{87} +2.39606 q^{88} -0.748942 q^{89} +1.07719 q^{90} -10.4076 q^{91} +6.57848 q^{92} +5.68812 q^{93} +7.84547 q^{94} +18.6177 q^{95} -1.59103 q^{96} +18.9271 q^{97} +5.44958 q^{98} -1.12282 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + 54 q^{2} - 22 q^{3} + 54 q^{4} - 14 q^{5} - 22 q^{6} - 20 q^{7} + 54 q^{8} + 32 q^{9}+O(q^{10}) $ 54 * q + 54 * q^2 - 22 * q^3 + 54 * q^4 - 14 * q^5 - 22 * q^6 - 20 * q^7 + 54 * q^8 + 32 * q^9	\( 54 q + 54 q^{2} - 22 q^{3} + 54 q^{4} - 14 q^{5} - 22 q^{6} - 20 q^{7} + 54 q^{8} + 32 q^{9} - 14 q^{10} - 22 q^{11} - 22 q^{12} - 24 q^{13} - 20 q^{14} - 32 q^{15} + 54 q^{16} - 67 q^{17} + 32 q^{18} - 54 q^{19} - 14 q^{20} - 18 q^{21} - 22 q^{22} - 52 q^{23} - 22 q^{24} + 20 q^{25} - 24 q^{26} - 82 q^{27} - 20 q^{28} - 30 q^{29} - 32 q^{30} - 78 q^{31} + 54 q^{32} - 48 q^{33} - 67 q^{34} - 71 q^{35} + 32 q^{36} - 15 q^{37} - 54 q^{38} - 39 q^{39} - 14 q^{40} - 61 q^{41} - 18 q^{42} - 53 q^{43} - 22 q^{44} - 14 q^{45} - 52 q^{46} - 96 q^{47} - 22 q^{48} + 6 q^{49} + 20 q^{50} - 13 q^{51} - 24 q^{52} - 39 q^{53} - 82 q^{54} - 75 q^{55} - 20 q^{56} - 17 q^{57} - 30 q^{58} - 78 q^{59} - 32 q^{60} - 23 q^{61} - 78 q^{62} - 52 q^{63} + 54 q^{64} - 43 q^{65} - 48 q^{66} - 54 q^{67} - 67 q^{68} + 7 q^{69} - 71 q^{70} - 41 q^{71} + 32 q^{72} - 62 q^{73} - 15 q^{74} - 81 q^{75} - 54 q^{76} - 85 q^{77} - 39 q^{78} - 45 q^{79} - 14 q^{80} + 22 q^{81} - 61 q^{82} - 117 q^{83} - 18 q^{84} - 53 q^{86} - 84 q^{87} - 22 q^{88} - 60 q^{89} - 14 q^{90} - 60 q^{91} - 52 q^{92} + 26 q^{93} - 96 q^{94} - 44 q^{95} - 22 q^{96} - 48 q^{97} + 6 q^{98} + 7 q^{99}+O(q^{100}) \) 54 * q + 54 * q^2 - 22 * q^3 + 54 * q^4 - 14 * q^5 - 22 * q^6 - 20 * q^7 + 54 * q^8 + 32 * q^9 - 14 * q^10 - 22 * q^11 - 22 * q^12 - 24 * q^13 - 20 * q^14 - 32 * q^15 + 54 * q^16 - 67 * q^17 + 32 * q^18 - 54 * q^19 - 14 * q^20 - 18 * q^21 - 22 * q^22 - 52 * q^23 - 22 * q^24 + 20 * q^25 - 24 * q^26 - 82 * q^27 - 20 * q^28 - 30 * q^29 - 32 * q^30 - 78 * q^31 + 54 * q^32 - 48 * q^33 - 67 * q^34 - 71 * q^35 + 32 * q^36 - 15 * q^37 - 54 * q^38 - 39 * q^39 - 14 * q^40 - 61 * q^41 - 18 * q^42 - 53 * q^43 - 22 * q^44 - 14 * q^45 - 52 * q^46 - 96 * q^47 - 22 * q^48 + 6 * q^49 + 20 * q^50 - 13 * q^51 - 24 * q^52 - 39 * q^53 - 82 * q^54 - 75 * q^55 - 20 * q^56 - 17 * q^57 - 30 * q^58 - 78 * q^59 - 32 * q^60 - 23 * q^61 - 78 * q^62 - 52 * q^63 + 54 * q^64 - 43 * q^65 - 48 * q^66 - 54 * q^67 - 67 * q^68 + 7 * q^69 - 71 * q^70 - 41 * q^71 + 32 * q^72 - 62 * q^73 - 15 * q^74 - 81 * q^75 - 54 * q^76 - 85 * q^77 - 39 * q^78 - 45 * q^79 - 14 * q^80 + 22 * q^81 - 61 * q^82 - 117 * q^83 - 18 * q^84 - 53 * q^86 - 84 * q^87 - 22 * q^88 - 60 * q^89 - 14 * q^90 - 60 * q^91 - 52 * q^92 + 26 * q^93 - 96 * q^94 - 44 * q^95 - 22 * q^96 - 48 * q^97 + 6 * q^98 + 7 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.59103	−0.918584	−0.459292	−	0.888285i	$-0.651897\pi$
$3$	−1.59103	−0.918584	−0.459292	+	0.888285i	$0.651897\pi$
$4$	1.00000	0.500000
$5$	−2.29870	−1.02801	−0.514005	−	0.857787i	$-0.671839\pi$
$5$	−2.29870	−1.02801	−0.514005	+	0.857787i	$0.671839\pi$
$6$	−1.59103	−0.649537
$7$	−3.52840	−1.33361	−0.666804	−	0.745233i	$-0.732338\pi$
$7$	−3.52840	−1.33361	−0.666804	+	0.745233i	$0.732338\pi$
$8$	1.00000	0.353553
$9$	−0.468610	−0.156203
$10$	−2.29870	−0.726912
$11$	2.39606	0.722438	0.361219	−	0.932481i	$-0.382361\pi$
$11$	2.39606	0.722438	0.361219	+	0.932481i	$0.382361\pi$
$12$	−1.59103	−0.459292
$13$	2.94967	0.818091	0.409046	−	0.912514i	$-0.365862\pi$
$13$	2.94967	0.818091	0.409046	+	0.912514i	$0.365862\pi$
$14$	−3.52840	−0.943004
$15$	3.65731	0.944313
$16$	1.00000	0.250000
$17$	2.91192	0.706245	0.353122	−	0.935577i	$-0.385120\pi$
$17$	2.91192	0.706245	0.353122	+	0.935577i	$0.385120\pi$
$18$	−0.468610	−0.110453
$19$	−8.09922	−1.85809	−0.929045	−	0.369967i	$-0.879369\pi$
$19$	−8.09922	−1.85809	−0.929045	+	0.369967i	$0.879369\pi$
$20$	−2.29870	−0.514005
$21$	5.61380	1.22503
$22$	2.39606	0.510841
$23$	6.57848	1.37171	0.685854	−	0.727739i	$-0.259429\pi$
$23$	6.57848	1.37171	0.685854	+	0.727739i	$0.259429\pi$
$24$	−1.59103	−0.324768
$25$	0.284016	0.0568032
$26$	2.94967	0.578478
$27$	5.51868	1.06207
$28$	−3.52840	−0.666804
$29$	6.13299	1.13887	0.569434	−	0.822037i	$-0.307163\pi$
$29$	6.13299	1.13887	0.569434	+	0.822037i	$0.307163\pi$
$30$	3.65731	0.667730
$31$	−3.57511	−0.642109	−0.321054	−	0.947061i	$-0.604037\pi$
$31$	−3.57511	−0.642109	−0.321054	+	0.947061i	$0.604037\pi$
$32$	1.00000	0.176777
$33$	−3.81221	−0.663620
$34$	2.91192	0.499391
$35$	8.11072	1.37096
$36$	−0.468610	−0.0781017
$37$	−3.63362	−0.597363	−0.298681	−	0.954353i	$-0.596547\pi$
$37$	−3.63362	−0.597363	−0.298681	+	0.954353i	$0.596547\pi$
$38$	−8.09922	−1.31387
$39$	−4.69303	−0.751486
$40$	−2.29870	−0.363456
$41$	−0.768554	−0.120028	−0.0600140	−	0.998198i	$-0.519115\pi$
$41$	−0.768554	−0.120028	−0.0600140	+	0.998198i	$0.519115\pi$
$42$	5.61380	0.866228
$43$	5.36279	0.817817	0.408909	−	0.912575i	$-0.365909\pi$
$43$	5.36279	0.817817	0.408909	+	0.912575i	$0.365909\pi$
$44$	2.39606	0.361219
$45$	1.07719	0.160579
$46$	6.57848	0.969945
$47$	7.84547	1.14438	0.572189	−	0.820121i	$-0.306094\pi$
$47$	7.84547	1.14438	0.572189	+	0.820121i	$0.306094\pi$
$48$	−1.59103	−0.229646
$49$	5.44958	0.778511
$50$	0.284016	0.0401659
$51$	−4.63297	−0.648745
$52$	2.94967	0.409046
$53$	−1.64273	−0.225646	−0.112823	−	0.993615i	$-0.535989\pi$
$53$	−1.64273	−0.225646	−0.112823	+	0.993615i	$0.535989\pi$
$54$	5.51868	0.750997
$55$	−5.50781	−0.742673
$56$	−3.52840	−0.471502
$57$	12.8861	1.70681
$58$	6.13299	0.805301
$59$	5.01838	0.653338	0.326669	−	0.945139i	$-0.394074\pi$
$59$	5.01838	0.653338	0.326669	+	0.945139i	$0.394074\pi$
$60$	3.65731	0.472156
$61$	2.26215	0.289639	0.144819	−	0.989458i	$-0.453740\pi$
$61$	2.26215	0.289639	0.144819	+	0.989458i	$0.453740\pi$
$62$	−3.57511	−0.454040
$63$	1.65344	0.208314
$64$	1.00000	0.125000
$65$	−6.78040	−0.841005
$66$	−3.81221	−0.469250
$67$	−5.48145	−0.669666	−0.334833	−	0.942277i	$-0.608680\pi$
$67$	−5.48145	−0.669666	−0.334833	+	0.942277i	$0.608680\pi$
$68$	2.91192	0.353122
$69$	−10.4666	−1.26003
$70$	8.11072	0.969416
$71$	−7.54970	−0.895984	−0.447992	−	0.894038i	$-0.647861\pi$
$71$	−7.54970	−0.895984	−0.447992	+	0.894038i	$0.647861\pi$
$72$	−0.468610	−0.0552263
$73$	5.65480	0.661844	0.330922	−	0.943658i	$-0.392640\pi$
$73$	5.65480	0.661844	0.330922	+	0.943658i	$0.392640\pi$
$74$	−3.63362	−0.422399
$75$	−0.451879	−0.0521785
$76$	−8.09922	−0.929045
$77$	−8.45424	−0.963450
$78$	−4.69303	−0.531381
$79$	−16.6607	−1.87447	−0.937237	−	0.348692i	$-0.886626\pi$
$79$	−16.6607	−1.87447	−0.937237	+	0.348692i	$0.886626\pi$
$80$	−2.29870	−0.257002
$81$	−7.37457	−0.819397
$82$	−0.768554	−0.0848726
$83$	−6.89513	−0.756839	−0.378419	−	0.925634i	$-0.623532\pi$
$83$	−6.89513	−0.756839	−0.378419	+	0.925634i	$0.623532\pi$
$84$	5.61380	0.612516
$85$	−6.69363	−0.726026
$86$	5.36279	0.578284
$87$	−9.75779	−1.04615
$88$	2.39606	0.255421
$89$	−0.748942	−0.0793877	−0.0396938	−	0.999212i	$-0.512638\pi$
$89$	−0.748942	−0.0793877	−0.0396938	+	0.999212i	$0.512638\pi$
$90$	1.07719	0.113546
$91$	−10.4076	−1.09101
$92$	6.57848	0.685854
$93$	5.68812	0.589831
$94$	7.84547	0.809198
$95$	18.6177	1.91013
$96$	−1.59103	−0.162384
$97$	18.9271	1.92176	0.960878	−	0.276972i	$-0.0893311\pi$
$97$	18.9271	1.92176	0.960878	+	0.276972i	$0.0893311\pi$
$98$	5.44958	0.550491
$99$	−1.12282	−0.112847
$100$	0.284016	0.0284016
$101$	−8.76265	−0.871916	−0.435958	−	0.899967i	$-0.643590\pi$
$101$	−8.76265	−0.871916	−0.435958	+	0.899967i	$0.643590\pi$
$102$	−4.63297	−0.458732
$103$	3.37846	0.332890	0.166445	−	0.986051i	$-0.446771\pi$
$103$	3.37846	0.332890	0.166445	+	0.986051i	$0.446771\pi$
$104$	2.94967	0.289239
$105$	−12.9044	−1.25934
$106$	−1.64273	−0.159556
$107$	17.1275	1.65578	0.827890	−	0.560891i	$-0.189541\pi$
$107$	17.1275	1.65578	0.827890	+	0.560891i	$0.189541\pi$
$108$	5.51868	0.531035
$109$	−6.67328	−0.639184	−0.319592	−	0.947555i	$-0.603546\pi$
$109$	−6.67328	−0.639184	−0.319592	+	0.947555i	$0.603546\pi$
$110$	−5.50781	−0.525149
$111$	5.78121	0.548728
$112$	−3.52840	−0.333402
$113$	−10.2347	−0.962796	−0.481398	−	0.876502i	$-0.659871\pi$
$113$	−10.2347	−0.962796	−0.481398	+	0.876502i	$0.659871\pi$
$114$	12.8861	1.20690
$115$	−15.1220	−1.41013
$116$	6.13299	0.569434
$117$	−1.38225	−0.127789
$118$	5.01838	0.461980
$119$	−10.2744	−0.941854
$120$	3.65731	0.333865
$121$	−5.25891	−0.478083
$122$	2.26215	0.204805
$123$	1.22280	0.110256
$124$	−3.57511	−0.321054
$125$	10.8406	0.969615
$126$	1.65344	0.147300
$127$	−10.2306	−0.907816	−0.453908	−	0.891049i	$-0.649970\pi$
$127$	−10.2306	−0.907816	−0.453908	+	0.891049i	$0.649970\pi$
$128$	1.00000	0.0883883
$129$	−8.53238	−0.751234
$130$	−6.78040	−0.594681
$131$	−11.6320	−1.01629	−0.508147	−	0.861270i	$-0.669669\pi$
$131$	−11.6320	−1.01629	−0.508147	+	0.861270i	$0.669669\pi$
$132$	−3.81221	−0.331810
$133$	28.5773	2.47796
$134$	−5.48145	−0.473525
$135$	−12.6858	−1.09182
$136$	2.91192	0.249695
$137$	20.3355	1.73738	0.868691	−	0.495355i	$-0.164962\pi$
$137$	20.3355	1.73738	0.868691	+	0.495355i	$0.164962\pi$
$138$	−10.4666	−0.890976
$139$	−11.0357	−0.936040	−0.468020	−	0.883718i	$-0.655032\pi$
$139$	−11.0357	−0.936040	−0.468020	+	0.883718i	$0.655032\pi$
$140$	8.11072	0.685481
$141$	−12.4824	−1.05121
$142$	−7.54970	−0.633556
$143$	7.06758	0.591021
$144$	−0.468610	−0.0390509
$145$	−14.0979	−1.17077
$146$	5.65480	0.467994
$147$	−8.67047	−0.715128
$148$	−3.63362	−0.298681
$149$	15.2140	1.24638	0.623192	−	0.782069i	$-0.285836\pi$
$149$	15.2140	1.24638	0.623192	+	0.782069i	$0.285836\pi$
$150$	−0.451879	−0.0368958
$151$	7.88784	0.641903	0.320952	−	0.947096i	$-0.395997\pi$
$151$	7.88784	0.641903	0.320952	+	0.947096i	$0.395997\pi$
$152$	−8.09922	−0.656934
$153$	−1.36456	−0.110318
$154$	−8.45424	−0.681262
$155$	8.21810	0.660094
$156$	−4.69303	−0.375743
$157$	−15.7979	−1.26081	−0.630404	−	0.776268i	$-0.717111\pi$
$157$	−15.7979	−1.26081	−0.630404	+	0.776268i	$0.717111\pi$
$158$	−16.6607	−1.32545
$159$	2.61364	0.207275
$160$	−2.29870	−0.181728
$161$	−23.2115	−1.82932
$162$	−7.37457	−0.579401
$163$	−19.1108	−1.49687	−0.748436	−	0.663207i	$-0.769195\pi$
$163$	−19.1108	−1.49687	−0.748436	+	0.663207i	$0.769195\pi$
$164$	−0.768554	−0.0600140
$165$	8.76312	0.682208
$166$	−6.89513	−0.535166
$167$	−12.9192	−0.999721	−0.499860	−	0.866106i	$-0.666615\pi$
$167$	−12.9192	−0.999721	−0.499860	+	0.866106i	$0.666615\pi$
$168$	5.61380	0.433114
$169$	−4.29945	−0.330727
$170$	−6.69363	−0.513378
$171$	3.79538	0.290240
$172$	5.36279	0.408909
$173$	−18.3400	−1.39436	−0.697182	−	0.716895i	$-0.745563\pi$
$173$	−18.3400	−1.39436	−0.697182	+	0.716895i	$0.745563\pi$
$174$	−9.75779	−0.739736
$175$	−1.00212	−0.0757532
$176$	2.39606	0.180610
$177$	−7.98442	−0.600146
$178$	−0.748942	−0.0561355
$179$	−23.3204	−1.74305	−0.871524	−	0.490353i	$-0.836868\pi$
$179$	−23.3204	−1.74305	−0.871524	+	0.490353i	$0.836868\pi$
$180$	1.07719	0.0802893
$181$	−21.9752	−1.63341	−0.816703	−	0.577059i	$-0.804200\pi$
$181$	−21.9752	−1.63341	−0.816703	+	0.577059i	$0.804200\pi$
$182$	−10.4076	−0.771463
$183$	−3.59916	−0.266057
$184$	6.57848	0.484972
$185$	8.35259	0.614094
$186$	5.68812	0.417073
$187$	6.97713	0.510218
$188$	7.84547	0.572189
$189$	−19.4721	−1.41639
$190$	18.6177	1.35067
$191$	16.1897	1.17145	0.585723	−	0.810511i	$-0.300810\pi$
$191$	16.1897	1.17145	0.585723	+	0.810511i	$0.300810\pi$
$192$	−1.59103	−0.114823
$193$	−26.2414	−1.88890	−0.944449	−	0.328659i	$-0.893403\pi$
$193$	−26.2414	−1.88890	−0.944449	+	0.328659i	$0.893403\pi$
$194$	18.9271	1.35889
$195$	10.7879	0.772534
$196$	5.44958	0.389256
$197$	17.8539	1.27204	0.636020	−	0.771672i	$-0.280579\pi$
$197$	17.8539	1.27204	0.636020	+	0.771672i	$0.280579\pi$
$198$	−1.12282	−0.0797951
$199$	−13.4273	−0.951838	−0.475919	−	0.879489i	$-0.657885\pi$
$199$	−13.4273	−0.951838	−0.475919	+	0.879489i	$0.657885\pi$
$200$	0.284016	0.0200830
$201$	8.72118	0.615145
$202$	−8.76265	−0.616538
$203$	−21.6396	−1.51880
$204$	−4.63297	−0.324373
$205$	1.76667	0.123390
$206$	3.37846	0.235389
$207$	−3.08275	−0.214266
$208$	2.94967	0.204523
$209$	−19.4062	−1.34236
$210$	−12.9044	−0.890490
$211$	8.06904	0.555496	0.277748	−	0.960654i	$-0.410412\pi$
$211$	8.06904	0.555496	0.277748	+	0.960654i	$0.410412\pi$
$212$	−1.64273	−0.112823
$213$	12.0118	0.823037
$214$	17.1275	1.17081
$215$	−12.3274	−0.840724
$216$	5.51868	0.375498
$217$	12.6144	0.856322
$218$	−6.67328	−0.451972
$219$	−8.99698	−0.607959
$220$	−5.50781	−0.371337
$221$	8.58921	0.577773
$222$	5.78121	0.388009
$223$	−22.0743	−1.47820	−0.739102	−	0.673593i	$-0.764750\pi$
$223$	−22.0743	−1.47820	−0.739102	+	0.673593i	$0.764750\pi$
$224$	−3.52840	−0.235751
$225$	−0.133093	−0.00887286
$226$	−10.2347	−0.680800
$227$	4.98025	0.330551	0.165275	−	0.986247i	$-0.447149\pi$
$227$	4.98025	0.330551	0.165275	+	0.986247i	$0.447149\pi$
$228$	12.8861	0.853406
$229$	0.895902	0.0592028	0.0296014	−	0.999562i	$-0.490576\pi$
$229$	0.895902	0.0592028	0.0296014	+	0.999562i	$0.490576\pi$
$230$	−15.1220	−0.997112
$231$	13.4510	0.885010
$232$	6.13299	0.402650
$233$	12.2011	0.799322	0.399661	−	0.916663i	$-0.369128\pi$
$233$	12.2011	0.799322	0.399661	+	0.916663i	$0.369128\pi$
$234$	−1.38225	−0.0903603
$235$	−18.0344	−1.17643
$236$	5.01838	0.326669
$237$	26.5077	1.72186
$238$	−10.2744	−0.665991
$239$	19.0265	1.23072	0.615360	−	0.788246i	$-0.289011\pi$
$239$	19.0265	1.23072	0.615360	+	0.788246i	$0.289011\pi$
$240$	3.65731	0.236078
$241$	−11.8436	−0.762914	−0.381457	−	0.924387i	$-0.624578\pi$
$241$	−11.8436	−0.762914	−0.381457	+	0.924387i	$0.624578\pi$
$242$	−5.25891	−0.338056
$243$	−4.82284	−0.309385
$244$	2.26215	0.144819
$245$	−12.5269	−0.800317
$246$	1.22280	0.0779626
$247$	−23.8900	−1.52009
$248$	−3.57511	−0.227020
$249$	10.9704	0.695220
$250$	10.8406	0.685621
$251$	12.9413	0.816850	0.408425	−	0.912792i	$-0.366078\pi$
$251$	12.9413	0.816850	0.408425	+	0.912792i	$0.366078\pi$
$252$	1.65344	0.104157
$253$	15.7624	0.990975
$254$	−10.2306	−0.641923
$255$	10.6498	0.666916
$256$	1.00000	0.0625000
$257$	−2.69454	−0.168081	−0.0840405	−	0.996462i	$-0.526783\pi$
$257$	−2.69454	−0.168081	−0.0840405	+	0.996462i	$0.526783\pi$
$258$	−8.53238	−0.531203
$259$	12.8208	0.796648
$260$	−6.78040	−0.420503
$261$	−2.87398	−0.177895
$262$	−11.6320	−0.718629
$263$	6.92592	0.427070	0.213535	−	0.976935i	$-0.431502\pi$
$263$	6.92592	0.427070	0.213535	+	0.976935i	$0.431502\pi$
$264$	−3.81221	−0.234625
$265$	3.77614	0.231966
$266$	28.5773	1.75219
$267$	1.19159	0.0729242
$268$	−5.48145	−0.334833
$269$	24.0187	1.46445	0.732223	−	0.681065i	$-0.238483\pi$
$269$	24.0187	1.46445	0.732223	+	0.681065i	$0.238483\pi$
$270$	−12.6858	−0.772032
$271$	−15.6976	−0.953562	−0.476781	−	0.879022i	$-0.658197\pi$
$271$	−15.6976	−0.953562	−0.476781	+	0.879022i	$0.658197\pi$
$272$	2.91192	0.176561
$273$	16.5589	1.00219
$274$	20.3355	1.22851
$275$	0.680518	0.0410368
$276$	−10.4666	−0.630015
$277$	22.6617	1.36161	0.680805	−	0.732465i	$-0.261630\pi$
$277$	22.6617	1.36161	0.680805	+	0.732465i	$0.261630\pi$
$278$	−11.0357	−0.661880
$279$	1.67533	0.100300
$280$	8.11072	0.484708
$281$	−5.51654	−0.329089	−0.164545	−	0.986370i	$-0.552615\pi$
$281$	−5.51654	−0.329089	−0.164545	+	0.986370i	$0.552615\pi$
$282$	−12.4824	−0.743316
$283$	−30.7791	−1.82963	−0.914815	−	0.403874i	$-0.867663\pi$
$283$	−30.7791	−1.82963	−0.914815	+	0.403874i	$0.867663\pi$
$284$	−7.54970	−0.447992
$285$	−29.6214	−1.75462
$286$	7.06758	0.417915
$287$	2.71176	0.160070
$288$	−0.468610	−0.0276131
$289$	−8.52071	−0.501218
$290$	−14.0979	−0.827857
$291$	−30.1137	−1.76529
$292$	5.65480	0.330922
$293$	−11.9132	−0.695978	−0.347989	−	0.937499i	$-0.613135\pi$
$293$	−11.9132	−0.695978	−0.347989	+	0.937499i	$0.613135\pi$
$294$	−8.67047	−0.505672
$295$	−11.5358	−0.671638
$296$	−3.63362	−0.211200
$297$	13.2231	0.767280
$298$	15.2140	0.881326
$299$	19.4044	1.12218
$300$	−0.451879	−0.0260893
$301$	−18.9220	−1.09065
$302$	7.88784	0.453894
$303$	13.9417	0.800928
$304$	−8.09922	−0.464522
$305$	−5.20000	−0.297751
$306$	−1.36456	−0.0780065
$307$	−27.7892	−1.58601	−0.793006	−	0.609214i	$-0.791485\pi$
$307$	−27.7892	−1.58601	−0.793006	+	0.609214i	$0.791485\pi$
$308$	−8.45424	−0.481725
$309$	−5.37525	−0.305787
$310$	8.21810	0.466757
$311$	−32.6301	−1.85028	−0.925141	−	0.379623i	$-0.876054\pi$
$311$	−32.6301	−1.85028	−0.925141	+	0.379623i	$0.876054\pi$
$312$	−4.69303	−0.265690
$313$	−11.4678	−0.648198	−0.324099	−	0.946023i	$-0.605061\pi$
$313$	−11.4678	−0.648198	−0.324099	+	0.946023i	$0.605061\pi$
$314$	−15.7979	−0.891525
$315$	−3.80077	−0.214149
$316$	−16.6607	−0.937237
$317$	16.2674	0.913670	0.456835	−	0.889551i	$-0.348983\pi$
$317$	16.2674	0.913670	0.456835	+	0.889551i	$0.348983\pi$
$318$	2.61364	0.146565
$319$	14.6950	0.822761
$320$	−2.29870	−0.128501
$321$	−27.2505	−1.52097
$322$	−23.2115	−1.29353
$323$	−23.5843	−1.31227
$324$	−7.37457	−0.409698
$325$	0.837753	0.0464702
$326$	−19.1108	−1.05845
$327$	10.6174	0.587145
$328$	−0.768554	−0.0424363
$329$	−27.6819	−1.52615
$330$	8.76312	0.482394
$331$	0.692333	0.0380541	0.0190270	−	0.999819i	$-0.493943\pi$
$331$	0.692333	0.0380541	0.0190270	+	0.999819i	$0.493943\pi$
$332$	−6.89513	−0.378419
$333$	1.70275	0.0933101
$334$	−12.9192	−0.706909
$335$	12.6002	0.688423
$336$	5.61380	0.306258
$337$	−4.08012	−0.222259	−0.111129	−	0.993806i	$-0.535447\pi$
$337$	−4.08012	−0.222259	−0.111129	+	0.993806i	$0.535447\pi$
$338$	−4.29945	−0.233859
$339$	16.2837	0.884409
$340$	−6.69363	−0.363013
$341$	−8.56617	−0.463884
$342$	3.79538	0.205231
$343$	5.47050	0.295379
$344$	5.36279	0.289142
$345$	24.0595	1.29532
$346$	−18.3400	−0.985964
$347$	−3.96824	−0.213026	−0.106513	−	0.994311i	$-0.533969\pi$
$347$	−3.96824	−0.213026	−0.106513	+	0.994311i	$0.533969\pi$
$348$	−9.75779	−0.523073
$349$	35.8237	1.91760	0.958798	−	0.284087i	$-0.0916906\pi$
$349$	35.8237	1.91760	0.958798	+	0.284087i	$0.0916906\pi$
$350$	−1.00212	−0.0535656
$351$	16.2783	0.868870
$352$	2.39606	0.127710
$353$	−28.7479	−1.53010	−0.765049	−	0.643972i	$-0.777285\pi$
$353$	−28.7479	−1.53010	−0.765049	+	0.643972i	$0.777285\pi$
$354$	−7.98442	−0.424367
$355$	17.3545	0.921080
$356$	−0.748942	−0.0396938
$357$	16.3469	0.865172
$358$	−23.3204	−1.23252
$359$	20.3175	1.07231	0.536157	−	0.844118i	$-0.319875\pi$
$359$	20.3175	1.07231	0.536157	+	0.844118i	$0.319875\pi$
$360$	1.07719	0.0567731
$361$	46.5974	2.45250
$362$	−21.9752	−1.15499
$363$	8.36711	0.439159
$364$	−10.4076	−0.545507
$365$	−12.9987	−0.680382
$366$	−3.59916	−0.188131
$367$	−23.5086	−1.22714	−0.613569	−	0.789641i	$-0.710267\pi$
$367$	−23.5086	−1.22714	−0.613569	+	0.789641i	$0.710267\pi$
$368$	6.57848	0.342927
$369$	0.360152	0.0187488
$370$	8.35259	0.434230
$371$	5.79619	0.300923
$372$	5.68812	0.294915
$373$	−18.7974	−0.973293	−0.486646	−	0.873599i	$-0.661780\pi$
$373$	−18.7974	−0.973293	−0.486646	+	0.873599i	$0.661780\pi$
$374$	6.97713	0.360779
$375$	−17.2478	−0.890673
$376$	7.84547	0.404599
$377$	18.0903	0.931698
$378$	−19.4721	−1.00154
$379$	34.9265	1.79405	0.897026	−	0.441978i	$-0.145723\pi$
$379$	34.9265	1.79405	0.897026	+	0.441978i	$0.145723\pi$
$380$	18.6177	0.955067
$381$	16.2772	0.833905
$382$	16.1897	0.828338
$383$	−23.4562	−1.19856	−0.599278	−	0.800541i	$-0.704546\pi$
$383$	−23.4562	−1.19856	−0.599278	+	0.800541i	$0.704546\pi$
$384$	−1.59103	−0.0811921
$385$	19.4337	0.990435
$386$	−26.2414	−1.33565
$387$	−2.51306	−0.127746
$388$	18.9271	0.960878
$389$	−7.74727	−0.392802	−0.196401	−	0.980524i	$-0.562925\pi$
$389$	−7.74727	−0.392802	−0.196401	+	0.980524i	$0.562925\pi$
$390$	10.7879	0.546264
$391$	19.1560	0.968762
$392$	5.44958	0.275245
$393$	18.5070	0.933552
$394$	17.8539	0.899468
$395$	38.2979	1.92698
$396$	−1.12282	−0.0564237
$397$	−6.11523	−0.306914	−0.153457	−	0.988155i	$-0.549041\pi$
$397$	−6.11523	−0.306914	−0.153457	+	0.988155i	$0.549041\pi$
$398$	−13.4273	−0.673051
$399$	−45.4674	−2.27622
$400$	0.284016	0.0142008
$401$	5.68897	0.284094	0.142047	−	0.989860i	$-0.454632\pi$
$401$	5.68897	0.284094	0.142047	+	0.989860i	$0.454632\pi$
$402$	8.72118	0.434973
$403$	−10.5454	−0.525304
$404$	−8.76265	−0.435958
$405$	16.9519	0.842348
$406$	−21.6396	−1.07396
$407$	−8.70635	−0.431558
$408$	−4.63297	−0.229366
$409$	29.1072	1.43926	0.719630	−	0.694358i	$-0.244311\pi$
$409$	29.1072	1.43926	0.719630	+	0.694358i	$0.244311\pi$
$410$	1.76667	0.0872498
$411$	−32.3545	−1.59593
$412$	3.37846	0.166445
$413$	−17.7069	−0.871297
$414$	−3.08275	−0.151509
$415$	15.8498	0.778037
$416$	2.94967	0.144619
$417$	17.5583	0.859831
$418$	−19.4062	−0.949188
$419$	23.3953	1.14293	0.571467	−	0.820625i	$-0.306375\pi$
$419$	23.3953	1.14293	0.571467	+	0.820625i	$0.306375\pi$
$420$	−12.9044	−0.629672
$421$	26.0643	1.27029	0.635147	−	0.772391i	$-0.280939\pi$
$421$	26.0643	1.27029	0.635147	+	0.772391i	$0.280939\pi$
$422$	8.06904	0.392795
$423$	−3.67647	−0.178756
$424$	−1.64273	−0.0797779
$425$	0.827032	0.0401170
$426$	12.0118	0.581975
$427$	−7.98176	−0.386265
$428$	17.1275	0.827890
$429$	−11.2448	−0.542902
$430$	−12.3274	−0.594482
$431$	1.62227	0.0781420	0.0390710	−	0.999236i	$-0.487560\pi$
$431$	1.62227	0.0781420	0.0390710	+	0.999236i	$0.487560\pi$
$432$	5.51868	0.265517
$433$	13.7452	0.660553	0.330276	−	0.943884i	$-0.392858\pi$
$433$	13.7452	0.660553	0.330276	+	0.943884i	$0.392858\pi$
$434$	12.6144	0.605511
$435$	22.4302	1.07545
$436$	−6.67328	−0.319592
$437$	−53.2806	−2.54876
$438$	−8.99698	−0.429892
$439$	16.5465	0.789720	0.394860	−	0.918741i	$-0.370793\pi$
$439$	16.5465	0.789720	0.394860	+	0.918741i	$0.370793\pi$
$440$	−5.50781	−0.262575
$441$	−2.55373	−0.121606
$442$	8.58921	0.408547
$443$	−0.671762	−0.0319164	−0.0159582	−	0.999873i	$-0.505080\pi$
$443$	−0.671762	−0.0319164	−0.0159582	+	0.999873i	$0.505080\pi$
$444$	5.78121	0.274364
$445$	1.72159	0.0816113
$446$	−22.0743	−1.04525
$447$	−24.2061	−1.14491
$448$	−3.52840	−0.166701
$449$	22.9504	1.08309	0.541547	−	0.840670i	$-0.317839\pi$
$449$	22.9504	1.08309	0.541547	+	0.840670i	$0.317839\pi$
$450$	−0.133093	−0.00627406
$451$	−1.84150	−0.0867128
$452$	−10.2347	−0.481398
$453$	−12.5498	−0.589642
$454$	4.98025	0.233735
$455$	23.9239	1.12157
$456$	12.8861	0.603449
$457$	−15.5691	−0.728290	−0.364145	−	0.931342i	$-0.618639\pi$
$457$	−15.5691	−0.728290	−0.364145	+	0.931342i	$0.618639\pi$
$458$	0.895902	0.0418627
$459$	16.0700	0.750082
$460$	−15.1220	−0.705065
$461$	−41.1432	−1.91623	−0.958115	−	0.286384i	$-0.907547\pi$
$461$	−41.1432	−1.91623	−0.958115	+	0.286384i	$0.907547\pi$
$462$	13.4510	0.625796
$463$	10.0633	0.467682	0.233841	−	0.972275i	$-0.424870\pi$
$463$	10.0633	0.467682	0.233841	+	0.972275i	$0.424870\pi$
$464$	6.13299	0.284717
$465$	−13.0753	−0.606352
$466$	12.2011	0.565206
$467$	−4.97040	−0.230003	−0.115001	−	0.993365i	$-0.536687\pi$
$467$	−4.97040	−0.230003	−0.115001	+	0.993365i	$0.536687\pi$
$468$	−1.38225	−0.0638944
$469$	19.3407	0.893072
$470$	−18.0344	−0.831863
$471$	25.1349	1.15816
$472$	5.01838	0.230990
$473$	12.8495	0.590823
$474$	26.5077	1.21754
$475$	−2.30031	−0.105545
$476$	−10.2744	−0.470927
$477$	0.769799	0.0352467
$478$	19.0265	0.870251
$479$	−16.9883	−0.776215	−0.388107	−	0.921614i	$-0.626871\pi$
$479$	−16.9883	−0.776215	−0.388107	+	0.921614i	$0.626871\pi$
$480$	3.65731	0.166933
$481$	−10.7180	−0.488697
$482$	−11.8436	−0.539462
$483$	36.9303	1.68039
$484$	−5.25891	−0.239041
$485$	−43.5077	−1.97558
$486$	−4.82284	−0.218768
$487$	22.9281	1.03897	0.519487	−	0.854479i	$-0.326123\pi$
$487$	22.9281	1.03897	0.519487	+	0.854479i	$0.326123\pi$
$488$	2.26215	0.102403
$489$	30.4059	1.37500
$490$	−12.5269	−0.565910
$491$	−18.0451	−0.814362	−0.407181	−	0.913347i	$-0.633488\pi$
$491$	−18.0451	−0.814362	−0.407181	+	0.913347i	$0.633488\pi$
$492$	1.22280	0.0551279
$493$	17.8588	0.804319
$494$	−23.8900	−1.07486
$495$	2.58102	0.116008
$496$	−3.57511	−0.160527
$497$	26.6383	1.19489
$498$	10.9704	0.491595
$499$	−0.619732	−0.0277430	−0.0138715	−	0.999904i	$-0.504416\pi$
$499$	−0.619732	−0.0277430	−0.0138715	+	0.999904i	$0.504416\pi$
$500$	10.8406	0.484808
$501$	20.5550	0.918328
$502$	12.9413	0.577600
$503$	26.0175	1.16006	0.580031	−	0.814594i	$-0.303040\pi$
$503$	26.0175	1.16006	0.580031	+	0.814594i	$0.303040\pi$
$504$	1.65344	0.0736502
$505$	20.1427	0.896338
$506$	15.7624	0.700725
$507$	6.84057	0.303800
$508$	−10.2306	−0.453908
$509$	−23.3465	−1.03482	−0.517408	−	0.855739i	$-0.673103\pi$
$509$	−23.3465	−1.03482	−0.517408	+	0.855739i	$0.673103\pi$
$510$	10.6498	0.471581
$511$	−19.9524	−0.882641
$512$	1.00000	0.0441942
$513$	−44.6970	−1.97342
$514$	−2.69454	−0.118851
$515$	−7.76607	−0.342214
$516$	−8.53238	−0.375617
$517$	18.7982	0.826743
$518$	12.8208	0.563315
$519$	29.1795	1.28084
$520$	−6.78040	−0.297340
$521$	31.8960	1.39739	0.698696	−	0.715419i	$-0.253764\pi$
$521$	31.8960	1.39739	0.698696	+	0.715419i	$0.253764\pi$
$522$	−2.87398	−0.125791
$523$	−25.5058	−1.11529	−0.557645	−	0.830080i	$-0.688295\pi$
$523$	−25.5058	−1.11529	−0.557645	+	0.830080i	$0.688295\pi$
$524$	−11.6320	−0.508147
$525$	1.59441	0.0695857
$526$	6.92592	0.301984
$527$	−10.4104	−0.453486
$528$	−3.81221	−0.165905
$529$	20.2765	0.881585
$530$	3.77614	0.164025
$531$	−2.35167	−0.102054
$532$	28.5773	1.23898
$533$	−2.26698	−0.0981939
$534$	1.19159	0.0515652
$535$	−39.3710	−1.70216
$536$	−5.48145	−0.236763
$537$	37.1035	1.60114
$538$	24.0187	1.03552
$539$	13.0575	0.562427
$540$	−12.6858	−0.545909
$541$	24.6495	1.05977	0.529883	−	0.848071i	$-0.322236\pi$
$541$	24.6495	1.05977	0.529883	+	0.848071i	$0.322236\pi$
$542$	−15.6976	−0.674270
$543$	34.9633	1.50042
$544$	2.91192	0.124848
$545$	15.3399	0.657088
$546$	16.5589	0.708654
$547$	−24.0867	−1.02987	−0.514937	−	0.857228i	$-0.672185\pi$
$547$	−24.0867	−1.02987	−0.514937	+	0.857228i	$0.672185\pi$
$548$	20.3355	0.868691
$549$	−1.06007	−0.0452426
$550$	0.680518	0.0290174
$551$	−49.6725	−2.11612
$552$	−10.4666	−0.445488
$553$	58.7855	2.49982
$554$	22.6617	0.962804
$555$	−13.2893	−0.564097
$556$	−11.0357	−0.468020
$557$	12.6359	0.535402	0.267701	−	0.963502i	$-0.413736\pi$
$557$	12.6359	0.535402	0.267701	+	0.963502i	$0.413736\pi$
$558$	1.67533	0.0709226
$559$	15.8185	0.669049
$560$	8.11072	0.342740
$561$	−11.1009	−0.468678
$562$	−5.51654	−0.232701
$563$	20.4978	0.863879	0.431939	−	0.901903i	$-0.357829\pi$
$563$	20.4978	0.863879	0.431939	+	0.901903i	$0.357829\pi$
$564$	−12.4824	−0.525604
$565$	23.5264	0.989763
$566$	−30.7791	−1.29374
$567$	26.0204	1.09275
$568$	−7.54970	−0.316778
$569$	−37.6982	−1.58039	−0.790196	−	0.612855i	$-0.790021\pi$
$569$	−37.6982	−1.58039	−0.790196	+	0.612855i	$0.790021\pi$
$570$	−29.6214	−1.24070
$571$	−34.5121	−1.44429	−0.722144	−	0.691743i	$-0.756843\pi$
$571$	−34.5121	−1.44429	−0.722144	+	0.691743i	$0.756843\pi$
$572$	7.06758	0.295510
$573$	−25.7584	−1.07607
$574$	2.71176	0.113187
$575$	1.86839	0.0779174
$576$	−0.468610	−0.0195254
$577$	−24.9576	−1.03900	−0.519500	−	0.854471i	$-0.673882\pi$
$577$	−24.9576	−1.03900	−0.519500	+	0.854471i	$0.673882\pi$
$578$	−8.52071	−0.354415
$579$	41.7510	1.73511
$580$	−14.0979	−0.585383
$581$	24.3287	1.00933
$582$	−30.1137	−1.24825
$583$	−3.93607	−0.163015
$584$	5.65480	0.233997
$585$	3.17737	0.131368
$586$	−11.9132	−0.492131
$587$	31.4468	1.29795	0.648974	−	0.760811i	$-0.275199\pi$
$587$	31.4468	1.29795	0.648974	+	0.760811i	$0.275199\pi$
$588$	−8.67047	−0.357564
$589$	28.9556	1.19310
$590$	−11.5358	−0.474920
$591$	−28.4062	−1.16848
$592$	−3.63362	−0.149341
$593$	−18.6386	−0.765397	−0.382699	−	0.923873i	$-0.625005\pi$
$593$	−18.6386	−0.765397	−0.382699	+	0.923873i	$0.625005\pi$
$594$	13.2231	0.542549
$595$	23.6178	0.968235
$596$	15.2140	0.623192
$597$	21.3633	0.874343
$598$	19.4044	0.793503
$599$	30.2581	1.23631	0.618156	−	0.786055i	$-0.287880\pi$
$599$	30.2581	1.23631	0.618156	+	0.786055i	$0.287880\pi$
$600$	−0.451879	−0.0184479
$601$	−7.26666	−0.296413	−0.148207	−	0.988956i	$-0.547350\pi$
$601$	−7.26666	−0.296413	−0.148207	+	0.988956i	$0.547350\pi$
$602$	−18.9220	−0.771205
$603$	2.56867	0.104604
$604$	7.88784	0.320952
$605$	12.0887	0.491474
$606$	13.9417	0.566342
$607$	−33.8431	−1.37365	−0.686825	−	0.726823i	$-0.740996\pi$
$607$	−33.8431	−1.37365	−0.686825	+	0.726823i	$0.740996\pi$
$608$	−8.09922	−0.328467
$609$	34.4294	1.39515
$610$	−5.20000	−0.210542
$611$	23.1415	0.936206
$612$	−1.36456	−0.0551590
$613$	−38.6318	−1.56032	−0.780162	−	0.625577i	$-0.784863\pi$
$613$	−38.6318	−1.56032	−0.780162	+	0.625577i	$0.784863\pi$
$614$	−27.7892	−1.12148
$615$	−2.81084	−0.113344
$616$	−8.45424	−0.340631
$617$	−2.09119	−0.0841883	−0.0420941	−	0.999114i	$-0.513403\pi$
$617$	−2.09119	−0.0841883	−0.0420941	+	0.999114i	$0.513403\pi$
$618$	−5.37525	−0.216224
$619$	−20.0233	−0.804806	−0.402403	−	0.915463i	$-0.631825\pi$
$619$	−20.0233	−0.804806	−0.402403	+	0.915463i	$0.631825\pi$
$620$	8.21810	0.330047
$621$	36.3045	1.45685
$622$	−32.6301	−1.30835
$623$	2.64256	0.105872
$624$	−4.69303	−0.187871
$625$	−26.3394	−1.05358
$626$	−11.4678	−0.458345
$627$	30.8759	1.23307
$628$	−15.7979	−0.630404
$629$	−10.5808	−0.421884
$630$	−3.80077	−0.151426
$631$	32.5107	1.29423	0.647115	−	0.762392i	$-0.275975\pi$
$631$	32.5107	1.29423	0.647115	+	0.762392i	$0.275975\pi$
$632$	−16.6607	−0.662727
$633$	−12.8381	−0.510270
$634$	16.2674	0.646062
$635$	23.5170	0.933243
$636$	2.61364	0.103637
$637$	16.0745	0.636893
$638$	14.6950	0.581780
$639$	3.53787	0.139956
$640$	−2.29870	−0.0908640
$641$	0.676729	0.0267292	0.0133646	−	0.999911i	$-0.495746\pi$
$641$	0.676729	0.0267292	0.0133646	+	0.999911i	$0.495746\pi$
$642$	−27.2505	−1.07549
$643$	15.9129	0.627543	0.313771	−	0.949499i	$-0.398407\pi$
$643$	15.9129	0.627543	0.313771	+	0.949499i	$0.398407\pi$
$644$	−23.2115	−0.914661
$645$	19.6134	0.772276
$646$	−23.5843	−0.927912
$647$	−40.7202	−1.60088	−0.800438	−	0.599416i	$-0.795400\pi$
$647$	−40.7202	−1.60088	−0.800438	+	0.599416i	$0.795400\pi$
$648$	−7.37457	−0.289701
$649$	12.0243	0.471996
$650$	0.837753	0.0328594
$651$	−20.0700	−0.786604
$652$	−19.1108	−0.748436
$653$	4.59925	0.179982	0.0899912	−	0.995943i	$-0.471316\pi$
$653$	4.59925	0.179982	0.0899912	+	0.995943i	$0.471316\pi$
$654$	10.6174	0.415174
$655$	26.7385	1.04476
$656$	−0.768554	−0.0300070
$657$	−2.64990	−0.103382
$658$	−27.6819	−1.07915
$659$	−22.4572	−0.874808	−0.437404	−	0.899265i	$-0.644102\pi$
$659$	−22.4572	−0.874808	−0.437404	+	0.899265i	$0.644102\pi$
$660$	8.76312	0.341104
$661$	14.2044	0.552488	0.276244	−	0.961088i	$-0.410910\pi$
$661$	14.2044	0.552488	0.276244	+	0.961088i	$0.410910\pi$
$662$	0.692333	0.0269083
$663$	−13.6657	−0.530733
$664$	−6.89513	−0.267583
$665$	−65.6905	−2.54737
$666$	1.70275	0.0659802
$667$	40.3458	1.56219
$668$	−12.9192	−0.499860
$669$	35.1210	1.35786
$670$	12.6002	0.486789
$671$	5.42024	0.209246
$672$	5.61380	0.216557
$673$	24.9460	0.961600	0.480800	−	0.876830i	$-0.340346\pi$
$673$	24.9460	0.961600	0.480800	+	0.876830i	$0.340346\pi$
$674$	−4.08012	−0.157161
$675$	1.56739	0.0603290
$676$	−4.29945	−0.165363
$677$	7.32708	0.281602	0.140801	−	0.990038i	$-0.455032\pi$
$677$	7.32708	0.281602	0.140801	+	0.990038i	$0.455032\pi$
$678$	16.2837	0.625372
$679$	−66.7823	−2.56287
$680$	−6.69363	−0.256689
$681$	−7.92374	−0.303639
$682$	−8.56617	−0.328016
$683$	−51.9198	−1.98666	−0.993328	−	0.115327i	$-0.963208\pi$
$683$	−51.9198	−1.98666	−0.993328	+	0.115327i	$0.963208\pi$
$684$	3.79538	0.145120
$685$	−46.7453	−1.78604
$686$	5.47050	0.208865
$687$	−1.42541	−0.0543828
$688$	5.36279	0.204454
$689$	−4.84551	−0.184599
$690$	24.0595	0.915931
$691$	−24.6432	−0.937472	−0.468736	−	0.883338i	$-0.655290\pi$
$691$	−24.6432	−0.937472	−0.468736	+	0.883338i	$0.655290\pi$
$692$	−18.3400	−0.697182
$693$	3.96174	0.150494
$694$	−3.96824	−0.150632
$695$	25.3679	0.962258
$696$	−9.75779	−0.369868
$697$	−2.23797	−0.0847692
$698$	35.8237	1.35595
$699$	−19.4124	−0.734245
$700$	−1.00212	−0.0378766
$701$	−4.85160	−0.183243	−0.0916213	−	0.995794i	$-0.529205\pi$
$701$	−4.85160	−0.183243	−0.0916213	+	0.995794i	$0.529205\pi$
$702$	16.2783	0.614384
$703$	29.4295	1.10995
$704$	2.39606	0.0903048
$705$	28.6933	1.08065
$706$	−28.7479	−1.08194
$707$	30.9181	1.16279
$708$	−7.98442	−0.300073
$709$	−21.4704	−0.806339	−0.403170	−	0.915125i	$-0.632092\pi$
$709$	−21.4704	−0.806339	−0.403170	+	0.915125i	$0.632092\pi$
$710$	17.3545	0.651302
$711$	7.80738	0.292799
$712$	−0.748942	−0.0280678
$713$	−23.5188	−0.880786
$714$	16.3469	0.611769
$715$	−16.2462	−0.607575
$716$	−23.3204	−0.871524
$717$	−30.2718	−1.13052
$718$	20.3175	0.758241
$719$	−38.4938	−1.43558	−0.717789	−	0.696261i	$-0.754846\pi$
$719$	−38.4938	−1.43558	−0.717789	+	0.696261i	$0.754846\pi$
$720$	1.07719	0.0401447
$721$	−11.9206	−0.443945
$722$	46.5974	1.73418
$723$	18.8436	0.700801
$724$	−21.9752	−0.816703
$725$	1.74187	0.0646913
$726$	8.36711	0.310532
$727$	−22.7612	−0.844165	−0.422082	−	0.906557i	$-0.638701\pi$
$727$	−22.7612	−0.844165	−0.422082	+	0.906557i	$0.638701\pi$
$728$	−10.4076	−0.385732
$729$	29.7970	1.10359
$730$	−12.9987	−0.481103
$731$	15.6160	0.577579
$732$	−3.59916	−0.133029
$733$	1.87190	0.0691401	0.0345700	−	0.999402i	$-0.488994\pi$
$733$	1.87190	0.0691401	0.0345700	+	0.999402i	$0.488994\pi$
$734$	−23.5086	−0.867718
$735$	19.9308	0.735158
$736$	6.57848	0.242486
$737$	−13.1339	−0.483793
$738$	0.360152	0.0132574
$739$	40.3264	1.48343	0.741716	−	0.670714i	$-0.234012\pi$
$739$	40.3264	1.48343	0.741716	+	0.670714i	$0.234012\pi$
$740$	8.35259	0.307047
$741$	38.0099	1.39633
$742$	5.79619	0.212785
$743$	20.4225	0.749229	0.374615	−	0.927181i	$-0.377775\pi$
$743$	20.4225	0.749229	0.374615	+	0.927181i	$0.377775\pi$
$744$	5.68812	0.208537
$745$	−34.9725	−1.28129
$746$	−18.7974	−0.688222
$747$	3.23113	0.118221
$748$	6.97713	0.255109
$749$	−60.4327	−2.20816
$750$	−17.2478	−0.629801
$751$	12.3434	0.450415	0.225208	−	0.974311i	$-0.427694\pi$
$751$	12.3434	0.450415	0.225208	+	0.974311i	$0.427694\pi$
$752$	7.84547	0.286095
$753$	−20.5901	−0.750346
$754$	18.0903	0.658810
$755$	−18.1318	−0.659883
$756$	−19.4721	−0.708193
$757$	4.54786	0.165295	0.0826473	−	0.996579i	$-0.473662\pi$
$757$	4.54786	0.165295	0.0826473	+	0.996579i	$0.473662\pi$
$758$	34.9265	1.26859
$759$	−25.0786	−0.910294
$760$	18.6177	0.675334
$761$	8.96232	0.324884	0.162442	−	0.986718i	$-0.448063\pi$
$761$	8.96232	0.324884	0.162442	+	0.986718i	$0.448063\pi$
$762$	16.2772	0.589660
$763$	23.5460	0.852422
$764$	16.1897	0.585723
$765$	3.13671	0.113408
$766$	−23.4562	−0.847508
$767$	14.8026	0.534490
$768$	−1.59103	−0.0574115
$769$	0.940397	0.0339116	0.0169558	−	0.999856i	$-0.494603\pi$
$769$	0.940397	0.0339116	0.0169558	+	0.999856i	$0.494603\pi$
$770$	19.4337	0.700344
$771$	4.28711	0.154397
$772$	−26.2414	−0.944449
$773$	−1.86556	−0.0670996	−0.0335498	−	0.999437i	$-0.510681\pi$
$773$	−1.86556	−0.0670996	−0.0335498	+	0.999437i	$0.510681\pi$
$774$	−2.51306	−0.0903300
$775$	−1.01539	−0.0364738
$776$	18.9271	0.679443
$777$	−20.3984	−0.731788
$778$	−7.74727	−0.277753
$779$	6.22469	0.223023
$780$	10.7879	0.386267
$781$	−18.0895	−0.647293
$782$	19.1560	0.685018
$783$	33.8460	1.20956
$784$	5.44958	0.194628
$785$	36.3145	1.29612
$786$	18.5070	0.660121
$787$	27.5023	0.980350	0.490175	−	0.871624i	$-0.336933\pi$
$787$	27.5023	0.980350	0.490175	+	0.871624i	$0.336933\pi$
$788$	17.8539	0.636020
$789$	−11.0194	−0.392300
$790$	38.2979	1.36258
$791$	36.1119	1.28399
$792$	−1.12282	−0.0398976
$793$	6.67260	0.236951
$794$	−6.11523	−0.217021
$795$	−6.00796	−0.213080
$796$	−13.4273	−0.475919
$797$	4.47863	0.158641	0.0793206	−	0.996849i	$-0.474725\pi$
$797$	4.47863	0.158641	0.0793206	+	0.996849i	$0.474725\pi$
$798$	−45.4674	−1.60953
$799$	22.8454	0.808212
$800$	0.284016	0.0100415
$801$	0.350962	0.0124006
$802$	5.68897	0.200885
$803$	13.5492	0.478142
$804$	8.72118	0.307572
$805$	53.3562	1.88056
$806$	−10.5454	−0.371446
$807$	−38.2146	−1.34522
$808$	−8.76265	−0.308269
$809$	−15.8553	−0.557443	−0.278721	−	0.960372i	$-0.589911\pi$
$809$	−15.8553	−0.557443	−0.278721	+	0.960372i	$0.589911\pi$
$810$	16.9519	0.595630
$811$	44.7266	1.57056	0.785281	−	0.619139i	$-0.212518\pi$
$811$	44.7266	1.57056	0.785281	+	0.619139i	$0.212518\pi$
$812$	−21.6396	−0.759402
$813$	24.9754	0.875927
$814$	−8.70635	−0.305157
$815$	43.9300	1.53880
$816$	−4.63297	−0.162186
$817$	−43.4344	−1.51958
$818$	29.1072	1.01771
$819$	4.87711	0.170420
$820$	1.76667	0.0616949
$821$	−52.7146	−1.83975	−0.919875	−	0.392211i	$-0.871710\pi$
$821$	−52.7146	−1.83975	−0.919875	+	0.392211i	$0.871710\pi$
$822$	−32.3545	−1.12849
$823$	6.78952	0.236668	0.118334	−	0.992974i	$-0.462245\pi$
$823$	6.78952	0.236668	0.118334	+	0.992974i	$0.462245\pi$
$824$	3.37846	0.117694
$825$	−1.08273	−0.0376958
$826$	−17.7069	−0.616100
$827$	−3.98776	−0.138668	−0.0693340	−	0.997594i	$-0.522087\pi$
$827$	−3.98776	−0.138668	−0.0693340	+	0.997594i	$0.522087\pi$
$828$	−3.08275	−0.107133
$829$	−2.38213	−0.0827349	−0.0413675	−	0.999144i	$-0.513171\pi$
$829$	−2.38213	−0.0827349	−0.0413675	+	0.999144i	$0.513171\pi$
$830$	15.8498	0.550155
$831$	−36.0555	−1.25075
$832$	2.94967	0.102261
$833$	15.8688	0.549820
$834$	17.5583	0.607993
$835$	29.6974	1.02772
$836$	−19.4062	−0.671178
$837$	−19.7299	−0.681965
$838$	23.3953	0.808176
$839$	9.20771	0.317886	0.158943	−	0.987288i	$-0.449191\pi$
$839$	9.20771	0.317886	0.158943	+	0.987288i	$0.449191\pi$
$840$	−12.9044	−0.445245
$841$	8.61355	0.297019
$842$	26.0643	0.898234
$843$	8.77701	0.302296
$844$	8.06904	0.277748
$845$	9.88313	0.339990
$846$	−3.67647	−0.126400
$847$	18.5555	0.637575
$848$	−1.64273	−0.0564115
$849$	48.9706	1.68067
$850$	0.827032	0.0283670
$851$	−23.9037	−0.819408
$852$	12.0118	0.411518
$853$	−12.2375	−0.419005	−0.209503	−	0.977808i	$-0.567184\pi$
$853$	−12.2375	−0.419005	−0.209503	+	0.977808i	$0.567184\pi$
$854$	−7.98176	−0.273130
$855$	−8.72444	−0.298369
$856$	17.1275	0.585407
$857$	−6.66107	−0.227538	−0.113769	−	0.993507i	$-0.536292\pi$
$857$	−6.66107	−0.227538	−0.113769	+	0.993507i	$0.536292\pi$
$858$	−11.2448	−0.383890
$859$	−47.0300	−1.60464	−0.802322	−	0.596892i	$-0.796402\pi$
$859$	−47.0300	−1.60464	−0.802322	+	0.596892i	$0.796402\pi$
$860$	−12.3274	−0.420362
$861$	−4.31451	−0.147038
$862$	1.62227	0.0552548
$863$	−29.8456	−1.01596	−0.507979	−	0.861370i	$-0.669607\pi$
$863$	−29.8456	−1.01596	−0.507979	+	0.861370i	$0.669607\pi$
$864$	5.51868	0.187749
$865$	42.1581	1.43342
$866$	13.7452	0.467081
$867$	13.5567	0.460411
$868$	12.6144	0.428161
$869$	−39.9200	−1.35419
$870$	22.4302	0.760456
$871$	−16.1685	−0.547848
$872$	−6.67328	−0.225986
$873$	−8.86944	−0.300185
$874$	−53.2806	−1.80224
$875$	−38.2500	−1.29309
$876$	−8.99698	−0.303980
$877$	−25.6324	−0.865544	−0.432772	−	0.901503i	$-0.642464\pi$
$877$	−25.6324	−0.865544	−0.432772	+	0.901503i	$0.642464\pi$
$878$	16.5465	0.558416
$879$	18.9544	0.639314
$880$	−5.50781	−0.185668
$881$	46.2066	1.55674	0.778370	−	0.627806i	$-0.216047\pi$
$881$	46.2066	1.55674	0.778370	+	0.627806i	$0.216047\pi$
$882$	−2.55373	−0.0859886
$883$	38.8930	1.30885	0.654426	−	0.756126i	$-0.272910\pi$
$883$	38.8930	1.30885	0.654426	+	0.756126i	$0.272910\pi$
$884$	8.58921	0.288886
$885$	18.3538	0.616956
$886$	−0.671762	−0.0225683
$887$	−38.9855	−1.30901	−0.654503	−	0.756059i	$-0.727122\pi$
$887$	−38.9855	−1.30901	−0.654503	+	0.756059i	$0.727122\pi$
$888$	5.78121	0.194005
$889$	36.0975	1.21067
$890$	1.72159	0.0577079
$891$	−17.6699	−0.591964
$892$	−22.0743	−0.739102
$893$	−63.5422	−2.12636
$894$	−24.2061	−0.809572
$895$	53.6065	1.79187
$896$	−3.52840	−0.117875
$897$	−30.8730	−1.03082
$898$	22.9504	0.765863
$899$	−21.9261	−0.731277
$900$	−0.133093	−0.00443643
$901$	−4.78350	−0.159361
$902$	−1.84150	−0.0613152
$903$	30.1056	1.00185
$904$	−10.2347	−0.340400
$905$	50.5144	1.67916
$906$	−12.5498	−0.416940
$907$	−40.1051	−1.33167	−0.665834	−	0.746100i	$-0.731924\pi$
$907$	−40.1051	−1.33167	−0.665834	+	0.746100i	$0.731924\pi$
$908$	4.98025	0.165275
$909$	4.10627	0.136196
$910$	23.9239	0.793071
$911$	−14.6854	−0.486549	−0.243275	−	0.969957i	$-0.578222\pi$
$911$	−14.6854	−0.486549	−0.243275	+	0.969957i	$0.578222\pi$
$912$	12.8861	0.426703
$913$	−16.5211	−0.546769
$914$	−15.5691	−0.514979
$915$	8.27338	0.273510
$916$	0.895902	0.0296014
$917$	41.0424	1.35534
$918$	16.0700	0.530388
$919$	−36.7707	−1.21295	−0.606477	−	0.795101i	$-0.707418\pi$
$919$	−36.7707	−1.21295	−0.606477	+	0.795101i	$0.707418\pi$
$920$	−15.1220	−0.498556
$921$	44.2135	1.45688
$922$	−41.1432	−1.35498
$923$	−22.2691	−0.732997
$924$	13.4510	0.442505
$925$	−1.03200	−0.0339321
$926$	10.0633	0.330701
$927$	−1.58318	−0.0519985
$928$	6.13299	0.201325
$929$	27.7480	0.910384	0.455192	−	0.890393i	$-0.349571\pi$
$929$	27.7480	0.910384	0.455192	+	0.890393i	$0.349571\pi$
$930$	−13.0753	−0.428755
$931$	−44.1374	−1.44654
$932$	12.2011	0.399661
$933$	51.9156	1.69964
$934$	−4.97040	−0.162636
$935$	−16.0383	−0.524509
$936$	−1.38225	−0.0451801
$937$	13.4450	0.439230	0.219615	−	0.975587i	$-0.429520\pi$
$937$	13.4450	0.439230	0.219615	+	0.975587i	$0.429520\pi$
$938$	19.3407	0.631498
$939$	18.2456	0.595424
$940$	−18.0344	−0.588216
$941$	−13.9645	−0.455231	−0.227615	−	0.973751i	$-0.573093\pi$
$941$	−13.9645	−0.455231	−0.227615	+	0.973751i	$0.573093\pi$
$942$	25.1349	0.818941
$943$	−5.05592	−0.164643
$944$	5.01838	0.163335
$945$	44.7604	1.45606
$946$	12.8495	0.417775
$947$	49.0700	1.59456	0.797280	−	0.603609i	$-0.206271\pi$
$947$	49.0700	1.59456	0.797280	+	0.603609i	$0.206271\pi$
$948$	26.5077	0.860931
$949$	16.6798	0.541449
$950$	−2.30031	−0.0746319
$951$	−25.8820	−0.839282
$952$	−10.2744	−0.332996
$953$	−27.8971	−0.903676	−0.451838	−	0.892100i	$-0.649232\pi$
$953$	−27.8971	−0.903676	−0.451838	+	0.892100i	$0.649232\pi$
$954$	0.769799	0.0249232
$955$	−37.2153	−1.20426
$956$	19.0265	0.615360
$957$	−23.3802	−0.755776
$958$	−16.9883	−0.548867
$959$	−71.7518	−2.31699
$960$	3.65731	0.118039
$961$	−18.2186	−0.587696
$962$	−10.7180	−0.345561
$963$	−8.02613	−0.258639
$964$	−11.8436	−0.381457
$965$	60.3211	1.94180
$966$	36.9303	1.18821
$967$	−3.75286	−0.120684	−0.0603420	−	0.998178i	$-0.519219\pi$
$967$	−3.75286	−0.120684	−0.0603420	+	0.998178i	$0.519219\pi$
$968$	−5.25891	−0.169028
$969$	37.5234	1.20543
$970$	−43.5077	−1.39695
$971$	−29.3870	−0.943073	−0.471536	−	0.881847i	$-0.656300\pi$
$971$	−29.3870	−0.943073	−0.471536	+	0.881847i	$0.656300\pi$
$972$	−4.82284	−0.154693
$973$	38.9385	1.24831
$974$	22.9281	0.734665
$975$	−1.33289	−0.0426868
$976$	2.26215	0.0724097
$977$	25.7354	0.823349	0.411675	−	0.911331i	$-0.364944\pi$
$977$	25.7354	0.823349	0.411675	+	0.911331i	$0.364944\pi$
$978$	30.4059	0.972274
$979$	−1.79451	−0.0573527
$980$	−12.5269	−0.400159
$981$	3.12717	0.0998428
$982$	−18.0451	−0.575841
$983$	7.44977	0.237611	0.118805	−	0.992918i	$-0.462094\pi$
$983$	7.44977	0.237611	0.118805	+	0.992918i	$0.462094\pi$
$984$	1.22280	0.0389813
$985$	−41.0408	−1.30767
$986$	17.8588	0.568740
$987$	44.0429	1.40190
$988$	−23.8900	−0.760043
$989$	35.2790	1.12181
$990$	2.58102	0.0820302
$991$	−26.2995	−0.835430	−0.417715	−	0.908578i	$-0.637169\pi$
$991$	−26.2995	−0.835430	−0.417715	+	0.908578i	$0.637169\pi$
$992$	−3.57511	−0.113510
$993$	−1.10153	−0.0349559
$994$	26.6383	0.844916
$995$	30.8654	0.978499
$996$	10.9704	0.347610
$997$	34.1369	1.08113	0.540563	−	0.841303i	$-0.318211\pi$
$997$	34.1369	1.08113	0.540563	+	0.841303i	$0.318211\pi$
$998$	−0.619732	−0.0196173
$999$	−20.0528	−0.634441

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6022.2.a.b.1.18	✓	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6022.2.a.b.1.18	✓	54	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:	\( N \)	\(=\)	\( 6022 = 2 \cdot 3011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6022.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.59103 q^{3} +1.00000 q^{4} -2.29870 q^{5} -1.59103 q^{6} -3.52840 q^{7} +1.00000 q^{8} -0.468610 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.59103 q^{3} +1.00000 q^{4} -2.29870 q^{5} -1.59103 q^{6} -3.52840 q^{7} +1.00000 q^{8} -0.468610 q^{9} -2.29870 q^{10} +2.39606 q^{11} -1.59103 q^{12} +2.94967 q^{13} -3.52840 q^{14} +3.65731 q^{15} +1.00000 q^{16} +2.91192 q^{17} -0.468610 q^{18} -8.09922 q^{19} -2.29870 q^{20} +5.61380 q^{21} +2.39606 q^{22} +6.57848 q^{23} -1.59103 q^{24} +0.284016 q^{25} +2.94967 q^{26} +5.51868 q^{27} -3.52840 q^{28} +6.13299 q^{29} +3.65731 q^{30} -3.57511 q^{31} +1.00000 q^{32} -3.81221 q^{33} +2.91192 q^{34} +8.11072 q^{35} -0.468610 q^{36} -3.63362 q^{37} -8.09922 q^{38} -4.69303 q^{39} -2.29870 q^{40} -0.768554 q^{41} +5.61380 q^{42} +5.36279 q^{43} +2.39606 q^{44} +1.07719 q^{45} +6.57848 q^{46} +7.84547 q^{47} -1.59103 q^{48} +5.44958 q^{49} +0.284016 q^{50} -4.63297 q^{51} +2.94967 q^{52} -1.64273 q^{53} +5.51868 q^{54} -5.50781 q^{55} -3.52840 q^{56} +12.8861 q^{57} +6.13299 q^{58} +5.01838 q^{59} +3.65731 q^{60} +2.26215 q^{61} -3.57511 q^{62} +1.65344 q^{63} +1.00000 q^{64} -6.78040 q^{65} -3.81221 q^{66} -5.48145 q^{67} +2.91192 q^{68} -10.4666 q^{69} +8.11072 q^{70} -7.54970 q^{71} -0.468610 q^{72} +5.65480 q^{73} -3.63362 q^{74} -0.451879 q^{75} -8.09922 q^{76} -8.45424 q^{77} -4.69303 q^{78} -16.6607 q^{79} -2.29870 q^{80} -7.37457 q^{81} -0.768554 q^{82} -6.89513 q^{83} +5.61380 q^{84} -6.69363 q^{85} +5.36279 q^{86} -9.75779 q^{87} +2.39606 q^{88} -0.748942 q^{89} +1.07719 q^{90} -10.4076 q^{91} +6.57848 q^{92} +5.68812 q^{93} +7.84547 q^{94} +18.6177 q^{95} -1.59103 q^{96} +18.9271 q^{97} +5.44958 q^{98} -1.12282 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 54 q^{2} - 22 q^{3} + 54 q^{4} - 14 q^{5} - 22 q^{6} - 20 q^{7} + 54 q^{8} + 32 q^{9}+O(q^{10}) \) 54 * q + 54 * q^2 - 22 * q^3 + 54 * q^4 - 14 * q^5 - 22 * q^6 - 20 * q^7 + 54 * q^8 + 32 * q^9	\( 54 q + 54 q^{2} - 22 q^{3} + 54 q^{4} - 14 q^{5} - 22 q^{6} - 20 q^{7} + 54 q^{8} + 32 q^{9} - 14 q^{10} - 22 q^{11} - 22 q^{12} - 24 q^{13} - 20 q^{14} - 32 q^{15} + 54 q^{16} - 67 q^{17} + 32 q^{18} - 54 q^{19} - 14 q^{20} - 18 q^{21} - 22 q^{22} - 52 q^{23} - 22 q^{24} + 20 q^{25} - 24 q^{26} - 82 q^{27} - 20 q^{28} - 30 q^{29} - 32 q^{30} - 78 q^{31} + 54 q^{32} - 48 q^{33} - 67 q^{34} - 71 q^{35} + 32 q^{36} - 15 q^{37} - 54 q^{38} - 39 q^{39} - 14 q^{40} - 61 q^{41} - 18 q^{42} - 53 q^{43} - 22 q^{44} - 14 q^{45} - 52 q^{46} - 96 q^{47} - 22 q^{48} + 6 q^{49} + 20 q^{50} - 13 q^{51} - 24 q^{52} - 39 q^{53} - 82 q^{54} - 75 q^{55} - 20 q^{56} - 17 q^{57} - 30 q^{58} - 78 q^{59} - 32 q^{60} - 23 q^{61} - 78 q^{62} - 52 q^{63} + 54 q^{64} - 43 q^{65} - 48 q^{66} - 54 q^{67} - 67 q^{68} + 7 q^{69} - 71 q^{70} - 41 q^{71} + 32 q^{72} - 62 q^{73} - 15 q^{74} - 81 q^{75} - 54 q^{76} - 85 q^{77} - 39 q^{78} - 45 q^{79} - 14 q^{80} + 22 q^{81} - 61 q^{82} - 117 q^{83} - 18 q^{84} - 53 q^{86} - 84 q^{87} - 22 q^{88} - 60 q^{89} - 14 q^{90} - 60 q^{91} - 52 q^{92} + 26 q^{93} - 96 q^{94} - 44 q^{95} - 22 q^{96} - 48 q^{97} + 6 q^{98} + 7 q^{99}+O(q^{100}) \) 54 * q + 54 * q^2 - 22 * q^3 + 54 * q^4 - 14 * q^5 - 22 * q^6 - 20 * q^7 + 54 * q^8 + 32 * q^9 - 14 * q^10 - 22 * q^11 - 22 * q^12 - 24 * q^13 - 20 * q^14 - 32 * q^15 + 54 * q^16 - 67 * q^17 + 32 * q^18 - 54 * q^19 - 14 * q^20 - 18 * q^21 - 22 * q^22 - 52 * q^23 - 22 * q^24 + 20 * q^25 - 24 * q^26 - 82 * q^27 - 20 * q^28 - 30 * q^29 - 32 * q^30 - 78 * q^31 + 54 * q^32 - 48 * q^33 - 67 * q^34 - 71 * q^35 + 32 * q^36 - 15 * q^37 - 54 * q^38 - 39 * q^39 - 14 * q^40 - 61 * q^41 - 18 * q^42 - 53 * q^43 - 22 * q^44 - 14 * q^45 - 52 * q^46 - 96 * q^47 - 22 * q^48 + 6 * q^49 + 20 * q^50 - 13 * q^51 - 24 * q^52 - 39 * q^53 - 82 * q^54 - 75 * q^55 - 20 * q^56 - 17 * q^57 - 30 * q^58 - 78 * q^59 - 32 * q^60 - 23 * q^61 - 78 * q^62 - 52 * q^63 + 54 * q^64 - 43 * q^65 - 48 * q^66 - 54 * q^67 - 67 * q^68 + 7 * q^69 - 71 * q^70 - 41 * q^71 + 32 * q^72 - 62 * q^73 - 15 * q^74 - 81 * q^75 - 54 * q^76 - 85 * q^77 - 39 * q^78 - 45 * q^79 - 14 * q^80 + 22 * q^81 - 61 * q^82 - 117 * q^83 - 18 * q^84 - 53 * q^86 - 84 * q^87 - 22 * q^88 - 60 * q^89 - 14 * q^90 - 60 * q^91 - 52 * q^92 + 26 * q^93 - 96 * q^94 - 44 * q^95 - 22 * q^96 - 48 * q^97 + 6 * q^98 + 7 * q^99

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