LMFDB - Embedded newform 6033.2.a.d.1.6

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:	$84$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
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)

$f(q)$	$=$	$q-2.60855 q^{2} -1.00000 q^{3} +4.80454 q^{4} -1.00742 q^{5} +2.60855 q^{6} +3.22569 q^{7} -7.31578 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.60855 q^{2} -1.00000 q^{3} +4.80454 q^{4} -1.00742 q^{5} +2.60855 q^{6} +3.22569 q^{7} -7.31578 q^{8} +1.00000 q^{9} +2.62791 q^{10} +2.49311 q^{11} -4.80454 q^{12} +1.81154 q^{13} -8.41437 q^{14} +1.00742 q^{15} +9.47451 q^{16} -2.24911 q^{17} -2.60855 q^{18} -0.899840 q^{19} -4.84020 q^{20} -3.22569 q^{21} -6.50341 q^{22} -0.789741 q^{23} +7.31578 q^{24} -3.98510 q^{25} -4.72550 q^{26} -1.00000 q^{27} +15.4979 q^{28} +5.60692 q^{29} -2.62791 q^{30} +3.54799 q^{31} -10.0832 q^{32} -2.49311 q^{33} +5.86691 q^{34} -3.24963 q^{35} +4.80454 q^{36} -0.0621137 q^{37} +2.34728 q^{38} -1.81154 q^{39} +7.37008 q^{40} +0.616081 q^{41} +8.41437 q^{42} +7.26236 q^{43} +11.9783 q^{44} -1.00742 q^{45} +2.06008 q^{46} -4.63227 q^{47} -9.47451 q^{48} +3.40506 q^{49} +10.3953 q^{50} +2.24911 q^{51} +8.70362 q^{52} -10.8738 q^{53} +2.60855 q^{54} -2.51162 q^{55} -23.5984 q^{56} +0.899840 q^{57} -14.6259 q^{58} -11.9467 q^{59} +4.84020 q^{60} -6.82265 q^{61} -9.25512 q^{62} +3.22569 q^{63} +7.35347 q^{64} -1.82499 q^{65} +6.50341 q^{66} -7.33683 q^{67} -10.8059 q^{68} +0.789741 q^{69} +8.47682 q^{70} -7.45870 q^{71} -7.31578 q^{72} -0.691085 q^{73} +0.162027 q^{74} +3.98510 q^{75} -4.32331 q^{76} +8.04200 q^{77} +4.72550 q^{78} +6.52106 q^{79} -9.54483 q^{80} +1.00000 q^{81} -1.60708 q^{82} -4.49461 q^{83} -15.4979 q^{84} +2.26580 q^{85} -18.9442 q^{86} -5.60692 q^{87} -18.2391 q^{88} -2.42347 q^{89} +2.62791 q^{90} +5.84346 q^{91} -3.79434 q^{92} -3.54799 q^{93} +12.0835 q^{94} +0.906518 q^{95} +10.0832 q^{96} -9.37836 q^{97} -8.88228 q^{98} +2.49311 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 13 q^{2} - 84 q^{3} + 81 q^{4} - 10 q^{5} + 13 q^{6} - 32 q^{7} - 39 q^{8} + 84 q^{9}+O(q^{10}) $ 84 * q - 13 * q^2 - 84 * q^3 + 81 * q^4 - 10 * q^5 + 13 * q^6 - 32 * q^7 - 39 * q^8 + 84 * q^9	\( 84 q - 13 q^{2} - 84 q^{3} + 81 q^{4} - 10 q^{5} + 13 q^{6} - 32 q^{7} - 39 q^{8} + 84 q^{9} + 13 q^{10} - 20 q^{11} - 81 q^{12} + 7 q^{13} - 9 q^{14} + 10 q^{15} + 83 q^{16} - 39 q^{17} - 13 q^{18} + 13 q^{19} - 26 q^{20} + 32 q^{21} - 21 q^{22} - 93 q^{23} + 39 q^{24} + 66 q^{25} - 34 q^{26} - 84 q^{27} - 59 q^{28} - 39 q^{29} - 13 q^{30} + 8 q^{31} - 96 q^{32} + 20 q^{33} - 69 q^{35} + 81 q^{36} + 6 q^{37} - 59 q^{38} - 7 q^{39} + 28 q^{40} - 23 q^{41} + 9 q^{42} - 74 q^{43} - 43 q^{44} - 10 q^{45} - 6 q^{46} - 77 q^{47} - 83 q^{48} + 100 q^{49} - 74 q^{50} + 39 q^{51} - 44 q^{52} - 66 q^{53} + 13 q^{54} - 60 q^{55} - 31 q^{56} - 13 q^{57} - 39 q^{58} - 36 q^{59} + 26 q^{60} + 104 q^{61} - 53 q^{62} - 32 q^{63} + 85 q^{64} - 47 q^{65} + 21 q^{66} - 65 q^{67} - 118 q^{68} + 93 q^{69} - 3 q^{70} - 68 q^{71} - 39 q^{72} + 8 q^{73} - 30 q^{74} - 66 q^{75} + 71 q^{76} - 83 q^{77} + 34 q^{78} - 24 q^{79} - 67 q^{80} + 84 q^{81} - 9 q^{82} - 95 q^{83} + 59 q^{84} + 24 q^{85} - 32 q^{86} + 39 q^{87} - 65 q^{88} - 44 q^{89} + 13 q^{90} + 8 q^{91} - 184 q^{92} - 8 q^{93} + 61 q^{94} - 153 q^{95} + 96 q^{96} + 19 q^{97} - 67 q^{98} - 20 q^{99}+O(q^{100}) \) 84 * q - 13 * q^2 - 84 * q^3 + 81 * q^4 - 10 * q^5 + 13 * q^6 - 32 * q^7 - 39 * q^8 + 84 * q^9 + 13 * q^10 - 20 * q^11 - 81 * q^12 + 7 * q^13 - 9 * q^14 + 10 * q^15 + 83 * q^16 - 39 * q^17 - 13 * q^18 + 13 * q^19 - 26 * q^20 + 32 * q^21 - 21 * q^22 - 93 * q^23 + 39 * q^24 + 66 * q^25 - 34 * q^26 - 84 * q^27 - 59 * q^28 - 39 * q^29 - 13 * q^30 + 8 * q^31 - 96 * q^32 + 20 * q^33 - 69 * q^35 + 81 * q^36 + 6 * q^37 - 59 * q^38 - 7 * q^39 + 28 * q^40 - 23 * q^41 + 9 * q^42 - 74 * q^43 - 43 * q^44 - 10 * q^45 - 6 * q^46 - 77 * q^47 - 83 * q^48 + 100 * q^49 - 74 * q^50 + 39 * q^51 - 44 * q^52 - 66 * q^53 + 13 * q^54 - 60 * q^55 - 31 * q^56 - 13 * q^57 - 39 * q^58 - 36 * q^59 + 26 * q^60 + 104 * q^61 - 53 * q^62 - 32 * q^63 + 85 * q^64 - 47 * q^65 + 21 * q^66 - 65 * q^67 - 118 * q^68 + 93 * q^69 - 3 * q^70 - 68 * q^71 - 39 * q^72 + 8 * q^73 - 30 * q^74 - 66 * q^75 + 71 * q^76 - 83 * q^77 + 34 * q^78 - 24 * q^79 - 67 * q^80 + 84 * q^81 - 9 * q^82 - 95 * q^83 + 59 * q^84 + 24 * q^85 - 32 * q^86 + 39 * q^87 - 65 * q^88 - 44 * q^89 + 13 * q^90 + 8 * q^91 - 184 * q^92 - 8 * q^93 + 61 * q^94 - 153 * q^95 + 96 * q^96 + 19 * q^97 - 67 * q^98 - 20 * 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 $

$2$	−2.60855	−1.84452	−0.922262	−	0.386565i	$-0.873661\pi$
$2$	−2.60855	−1.84452	−0.922262	+	0.386565i	$0.873661\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.80454	2.40227
$5$	−1.00742	−0.450533	−0.225266	−	0.974297i	$-0.572325\pi$
$5$	−1.00742	−0.450533	−0.225266	+	0.974297i	$0.572325\pi$
$6$	2.60855	1.06494
$7$	3.22569	1.21920	0.609598	−	0.792711i	$-0.291331\pi$
$7$	3.22569	1.21920	0.609598	+	0.792711i	$0.291331\pi$
$8$	−7.31578	−2.58652
$9$	1.00000	0.333333
$10$	2.62791	0.831019
$11$	2.49311	0.751701	0.375851	−	0.926680i	$-0.377351\pi$
$11$	2.49311	0.751701	0.375851	+	0.926680i	$0.377351\pi$
$12$	−4.80454	−1.38695
$13$	1.81154	0.502431	0.251216	−	0.967931i	$-0.419170\pi$
$13$	1.81154	0.502431	0.251216	+	0.967931i	$0.419170\pi$
$14$	−8.41437	−2.24884
$15$	1.00742	0.260115
$16$	9.47451	2.36863
$17$	−2.24911	−0.545489	−0.272744	−	0.962087i	$-0.587931\pi$
$17$	−2.24911	−0.545489	−0.272744	+	0.962087i	$0.587931\pi$
$18$	−2.60855	−0.614841
$19$	−0.899840	−0.206437	−0.103219	−	0.994659i	$-0.532914\pi$
$19$	−0.899840	−0.206437	−0.103219	+	0.994659i	$0.532914\pi$
$20$	−4.84020	−1.08230
$21$	−3.22569	−0.703903
$22$	−6.50341	−1.38653
$23$	−0.789741	−0.164672	−0.0823362	−	0.996605i	$-0.526238\pi$
$23$	−0.789741	−0.164672	−0.0823362	+	0.996605i	$0.526238\pi$
$24$	7.31578	1.49333
$25$	−3.98510	−0.797020
$26$	−4.72550	−0.926746
$27$	−1.00000	−0.192450
$28$	15.4979	2.92884
$29$	5.60692	1.04118	0.520589	−	0.853807i	$-0.325712\pi$
$29$	5.60692	1.04118	0.520589	+	0.853807i	$0.325712\pi$
$30$	−2.62791	−0.479789
$31$	3.54799	0.637238	0.318619	−	0.947883i	$-0.396781\pi$
$31$	3.54799	0.637238	0.318619	+	0.947883i	$0.396781\pi$
$32$	−10.0832	−1.78247
$33$	−2.49311	−0.433995
$34$	5.86691	1.00617
$35$	−3.24963	−0.549287
$36$	4.80454	0.800756
$37$	−0.0621137	−0.0102114	−0.00510572	−	0.999987i	$-0.501625\pi$
$37$	−0.0621137	−0.0102114	−0.00510572	+	0.999987i	$0.501625\pi$
$38$	2.34728	0.380779
$39$	−1.81154	−0.290079
$40$	7.37008	1.16531
$41$	0.616081	0.0962158	0.0481079	−	0.998842i	$-0.484681\pi$
$41$	0.616081	0.0962158	0.0481079	+	0.998842i	$0.484681\pi$
$42$	8.41437	1.29837
$43$	7.26236	1.10750	0.553750	−	0.832683i	$-0.313196\pi$
$43$	7.26236	1.10750	0.553750	+	0.832683i	$0.313196\pi$
$44$	11.9783	1.80579
$45$	−1.00742	−0.150178
$46$	2.06008	0.303742
$47$	−4.63227	−0.675685	−0.337843	−	0.941203i	$-0.609697\pi$
$47$	−4.63227	−0.675685	−0.337843	+	0.941203i	$0.609697\pi$
$48$	−9.47451	−1.36753
$49$	3.40506	0.486437
$50$	10.3953	1.47012
$51$	2.24911	0.314938
$52$	8.70362	1.20697
$53$	−10.8738	−1.49363	−0.746817	−	0.665029i	$-0.768419\pi$
$53$	−10.8738	−1.49363	−0.746817	+	0.665029i	$0.768419\pi$
$54$	2.60855	0.354979
$55$	−2.51162	−0.338666
$56$	−23.5984	−3.15347
$57$	0.899840	0.119187
$58$	−14.6259	−1.92048
$59$	−11.9467	−1.55533	−0.777664	−	0.628680i	$-0.783596\pi$
$59$	−11.9467	−1.55533	−0.777664	+	0.628680i	$0.783596\pi$
$60$	4.84020	0.624867
$61$	−6.82265	−0.873551	−0.436776	−	0.899570i	$-0.643880\pi$
$61$	−6.82265	−0.873551	−0.436776	+	0.899570i	$0.643880\pi$
$62$	−9.25512	−1.17540
$63$	3.22569	0.406398
$64$	7.35347	0.919184
$65$	−1.82499	−0.226362
$66$	6.50341	0.800514
$67$	−7.33683	−0.896336	−0.448168	−	0.893949i	$-0.647923\pi$
$67$	−7.33683	−0.896336	−0.448168	+	0.893949i	$0.647923\pi$
$68$	−10.8059	−1.31041
$69$	0.789741	0.0950736
$70$	8.47682	1.01317
$71$	−7.45870	−0.885184	−0.442592	−	0.896723i	$-0.645941\pi$
$71$	−7.45870	−0.885184	−0.442592	+	0.896723i	$0.645941\pi$
$72$	−7.31578	−0.862173
$73$	−0.691085	−0.0808854	−0.0404427	−	0.999182i	$-0.512877\pi$
$73$	−0.691085	−0.0808854	−0.0404427	+	0.999182i	$0.512877\pi$
$74$	0.162027	0.0188352
$75$	3.98510	0.460160
$76$	−4.32331	−0.495918
$77$	8.04200	0.916471
$78$	4.72550	0.535057
$79$	6.52106	0.733677	0.366838	−	0.930285i	$-0.380440\pi$
$79$	6.52106	0.733677	0.366838	+	0.930285i	$0.380440\pi$
$80$	−9.54483	−1.06714
$81$	1.00000	0.111111
$82$	−1.60708	−0.177472
$83$	−4.49461	−0.493348	−0.246674	−	0.969099i	$-0.579338\pi$
$83$	−4.49461	−0.493348	−0.246674	+	0.969099i	$0.579338\pi$
$84$	−15.4979	−1.69096
$85$	2.26580	0.245761
$86$	−18.9442	−2.04281
$87$	−5.60692	−0.601124
$88$	−18.2391	−1.94429
$89$	−2.42347	−0.256888	−0.128444	−	0.991717i	$-0.540998\pi$
$89$	−2.42347	−0.256888	−0.128444	+	0.991717i	$0.540998\pi$
$90$	2.62791	0.277006
$91$	5.84346	0.612562
$92$	−3.79434	−0.395587
$93$	−3.54799	−0.367910
$94$	12.0835	1.24632
$95$	0.906518	0.0930068
$96$	10.0832	1.02911
$97$	−9.37836	−0.952228	−0.476114	−	0.879384i	$-0.657955\pi$
$97$	−9.37836	−0.952228	−0.476114	+	0.879384i	$0.657955\pi$
$98$	−8.88228	−0.897245
$99$	2.49311	0.250567
$100$	−19.1466	−1.91466
$101$	−7.85008	−0.781112	−0.390556	−	0.920579i	$-0.627717\pi$
$101$	−7.85008	−0.781112	−0.390556	+	0.920579i	$0.627717\pi$
$102$	−5.86691	−0.580911
$103$	5.00201	0.492862	0.246431	−	0.969160i	$-0.420742\pi$
$103$	5.00201	0.492862	0.246431	+	0.969160i	$0.420742\pi$
$104$	−13.2528	−1.29955
$105$	3.24963	0.317131
$106$	28.3649	2.75505
$107$	−13.1272	−1.26906	−0.634529	−	0.772899i	$-0.718806\pi$
$107$	−13.1272	−1.26906	−0.634529	+	0.772899i	$0.718806\pi$
$108$	−4.80454	−0.462317
$109$	18.8797	1.80835	0.904173	−	0.427166i	$-0.140488\pi$
$109$	18.8797	1.80835	0.904173	+	0.427166i	$0.140488\pi$
$110$	6.55168	0.624678
$111$	0.0621137	0.00589557
$112$	30.5618	2.88782
$113$	−15.4961	−1.45775	−0.728875	−	0.684646i	$-0.759957\pi$
$113$	−15.4961	−1.45775	−0.728875	+	0.684646i	$0.759957\pi$
$114$	−2.34728	−0.219843
$115$	0.795602	0.0741903
$116$	26.9386	2.50119
$117$	1.81154	0.167477
$118$	31.1636	2.86884
$119$	−7.25492	−0.665057
$120$	−7.37008	−0.672793
$121$	−4.78439	−0.434945
$122$	17.7972	1.61129
$123$	−0.616081	−0.0555502
$124$	17.0465	1.53082
$125$	9.05179	0.809616
$126$	−8.41437	−0.749612
$127$	3.53991	0.314117	0.157058	−	0.987589i	$-0.449799\pi$
$127$	3.53991	0.314117	0.157058	+	0.987589i	$0.449799\pi$
$128$	0.984456	0.0870144
$129$	−7.26236	−0.639415
$130$	4.76057	0.417529
$131$	−4.83520	−0.422454	−0.211227	−	0.977437i	$-0.567746\pi$
$131$	−4.83520	−0.422454	−0.211227	+	0.977437i	$0.567746\pi$
$132$	−11.9783	−1.04257
$133$	−2.90260	−0.251687
$134$	19.1385	1.65331
$135$	1.00742	0.0867051
$136$	16.4540	1.41092
$137$	−13.8812	−1.18595	−0.592974	−	0.805222i	$-0.702046\pi$
$137$	−13.8812	−1.18595	−0.592974	+	0.805222i	$0.702046\pi$
$138$	−2.06008	−0.175366
$139$	−5.96634	−0.506058	−0.253029	−	0.967459i	$-0.581427\pi$
$139$	−5.96634	−0.506058	−0.253029	+	0.967459i	$0.581427\pi$
$140$	−15.6130	−1.31954
$141$	4.63227	0.390107
$142$	19.4564	1.63274
$143$	4.51637	0.377678
$144$	9.47451	0.789543
$145$	−5.64853	−0.469085
$146$	1.80273	0.149195
$147$	−3.40506	−0.280845
$148$	−0.298428	−0.0245306
$149$	7.61823	0.624110	0.312055	−	0.950064i	$-0.398983\pi$
$149$	7.61823	0.624110	0.312055	+	0.950064i	$0.398983\pi$
$150$	−10.3953	−0.848776
$151$	9.40150	0.765083	0.382542	−	0.923938i	$-0.375049\pi$
$151$	9.40150	0.765083	0.382542	+	0.923938i	$0.375049\pi$
$152$	6.58303	0.533954
$153$	−2.24911	−0.181830
$154$	−20.9780	−1.69045
$155$	−3.57432	−0.287097
$156$	−8.70362	−0.696847
$157$	−13.2856	−1.06031	−0.530154	−	0.847901i	$-0.677866\pi$
$157$	−13.2856	−1.06031	−0.530154	+	0.847901i	$0.677866\pi$
$158$	−17.0105	−1.35328
$159$	10.8738	0.862350
$160$	10.1580	0.803062
$161$	−2.54746	−0.200768
$162$	−2.60855	−0.204947
$163$	−24.3354	−1.90610	−0.953049	−	0.302817i	$-0.902073\pi$
$163$	−24.3354	−1.90610	−0.953049	+	0.302817i	$0.902073\pi$
$164$	2.95999	0.231136
$165$	2.51162	0.195529
$166$	11.7244	0.909992
$167$	8.19770	0.634357	0.317179	−	0.948366i	$-0.397265\pi$
$167$	8.19770	0.634357	0.317179	+	0.948366i	$0.397265\pi$
$168$	23.5984	1.82066
$169$	−9.71832	−0.747563
$170$	−5.91046	−0.453311
$171$	−0.899840	−0.0688124
$172$	34.8923	2.66051
$173$	22.8731	1.73901	0.869504	−	0.493927i	$-0.164439\pi$
$173$	22.8731	1.73901	0.869504	+	0.493927i	$0.164439\pi$
$174$	14.6259	1.10879
$175$	−12.8547	−0.971723
$176$	23.6210	1.78050
$177$	11.9467	0.897969
$178$	6.32175	0.473835
$179$	−0.563718	−0.0421343	−0.0210671	−	0.999778i	$-0.506706\pi$
$179$	−0.563718	−0.0421343	−0.0210671	+	0.999778i	$0.506706\pi$
$180$	−4.84020	−0.360767
$181$	−21.4110	−1.59146	−0.795732	−	0.605648i	$-0.792914\pi$
$181$	−21.4110	−1.59146	−0.795732	+	0.605648i	$0.792914\pi$
$182$	−15.2430	−1.12988
$183$	6.82265	0.504345
$184$	5.77757	0.425928
$185$	0.0625747	0.00460059
$186$	9.25512	0.678618
$187$	−5.60728	−0.410045
$188$	−22.2559	−1.62318
$189$	−3.22569	−0.234634
$190$	−2.36470	−0.171553
$191$	1.59040	0.115077	0.0575386	−	0.998343i	$-0.481675\pi$
$191$	1.59040	0.115077	0.0575386	+	0.998343i	$0.481675\pi$
$192$	−7.35347	−0.530691
$193$	−22.5789	−1.62526	−0.812632	−	0.582778i	$-0.801966\pi$
$193$	−22.5789	−1.62526	−0.812632	+	0.582778i	$0.801966\pi$
$194$	24.4639	1.75641
$195$	1.82499	0.130690
$196$	16.3597	1.16855
$197$	1.84814	0.131675	0.0658374	−	0.997830i	$-0.479028\pi$
$197$	1.84814	0.131675	0.0658374	+	0.997830i	$0.479028\pi$
$198$	−6.50341	−0.462177
$199$	21.9084	1.55304	0.776521	−	0.630091i	$-0.216983\pi$
$199$	21.9084	1.55304	0.776521	+	0.630091i	$0.216983\pi$
$200$	29.1541	2.06151
$201$	7.33683	0.517500
$202$	20.4773	1.44078
$203$	18.0862	1.26940
$204$	10.8059	0.756566
$205$	−0.620654	−0.0433484
$206$	−13.0480	−0.909096
$207$	−0.789741	−0.0548908
$208$	17.1635	1.19007
$209$	−2.24340	−0.155179
$210$	−8.47682	−0.584956
$211$	6.93520	0.477439	0.238719	−	0.971089i	$-0.423272\pi$
$211$	6.93520	0.477439	0.238719	+	0.971089i	$0.423272\pi$
$212$	−52.2437	−3.58811
$213$	7.45870	0.511061
$214$	34.2431	2.34081
$215$	−7.31626	−0.498965
$216$	7.31578	0.497776
$217$	11.4447	0.776918
$218$	−49.2486	−3.33554
$219$	0.691085	0.0466992
$220$	−12.0672	−0.813567
$221$	−4.07435	−0.274071
$222$	−0.162027	−0.0108745
$223$	−2.44052	−0.163429	−0.0817146	−	0.996656i	$-0.526040\pi$
$223$	−2.44052	−0.163429	−0.0817146	+	0.996656i	$0.526040\pi$
$224$	−32.5252	−2.17318
$225$	−3.98510	−0.265673
$226$	40.4224	2.68886
$227$	7.06971	0.469233	0.234616	−	0.972088i	$-0.424617\pi$
$227$	7.06971	0.469233	0.234616	+	0.972088i	$0.424617\pi$
$228$	4.32331	0.286318
$229$	−12.6249	−0.834277	−0.417139	−	0.908843i	$-0.636967\pi$
$229$	−12.6249	−0.834277	−0.417139	+	0.908843i	$0.636967\pi$
$230$	−2.07537	−0.136846
$231$	−8.04200	−0.529125
$232$	−41.0190	−2.69303
$233$	−1.53789	−0.100750	−0.0503752	−	0.998730i	$-0.516042\pi$
$233$	−1.53789	−0.100750	−0.0503752	+	0.998730i	$0.516042\pi$
$234$	−4.72550	−0.308915
$235$	4.66665	0.304418
$236$	−57.3984	−3.73632
$237$	−6.52106	−0.423588
$238$	18.9248	1.22671
$239$	−0.859273	−0.0555817	−0.0277909	−	0.999614i	$-0.508847\pi$
$239$	−0.859273	−0.0555817	−0.0277909	+	0.999614i	$0.508847\pi$
$240$	9.54483	0.616116
$241$	2.09352	0.134855	0.0674277	−	0.997724i	$-0.478521\pi$
$241$	2.09352	0.134855	0.0674277	+	0.997724i	$0.478521\pi$
$242$	12.4803	0.802266
$243$	−1.00000	−0.0641500
$244$	−32.7797	−2.09851
$245$	−3.43033	−0.219156
$246$	1.60708	0.102464
$247$	−1.63010	−0.103721
$248$	−25.9563	−1.64823
$249$	4.49461	0.284835
$250$	−23.6120	−1.49336
$251$	16.1642	1.02028	0.510138	−	0.860093i	$-0.329594\pi$
$251$	16.1642	1.02028	0.510138	+	0.860093i	$0.329594\pi$
$252$	15.4979	0.976278
$253$	−1.96891	−0.123784
$254$	−9.23405	−0.579396
$255$	−2.26580	−0.141890
$256$	−17.2749	−1.07968
$257$	19.0940	1.19105	0.595527	−	0.803336i	$-0.296943\pi$
$257$	19.0940	1.19105	0.595527	+	0.803336i	$0.296943\pi$
$258$	18.9442	1.17942
$259$	−0.200360	−0.0124497
$260$	−8.76821	−0.543782
$261$	5.60692	0.347059
$262$	12.6129	0.779226
$263$	24.4878	1.50998	0.754992	−	0.655734i	$-0.227641\pi$
$263$	24.4878	1.50998	0.754992	+	0.655734i	$0.227641\pi$
$264$	18.2391	1.12254
$265$	10.9545	0.672931
$266$	7.57158	0.464244
$267$	2.42347	0.148314
$268$	−35.2501	−2.15324
$269$	4.75643	0.290005	0.145002	−	0.989431i	$-0.453681\pi$
$269$	4.75643	0.290005	0.145002	+	0.989431i	$0.453681\pi$
$270$	−2.62791	−0.159930
$271$	−4.53502	−0.275483	−0.137741	−	0.990468i	$-0.543984\pi$
$271$	−4.53502	−0.275483	−0.137741	+	0.990468i	$0.543984\pi$
$272$	−21.3092	−1.29206
$273$	−5.84346	−0.353663
$274$	36.2097	2.18751
$275$	−9.93530	−0.599121
$276$	3.79434	0.228392
$277$	16.1227	0.968717	0.484358	−	0.874870i	$-0.339053\pi$
$277$	16.1227	0.968717	0.484358	+	0.874870i	$0.339053\pi$
$278$	15.5635	0.933436
$279$	3.54799	0.212413
$280$	23.7736	1.42074
$281$	8.74115	0.521453	0.260727	−	0.965413i	$-0.416038\pi$
$281$	8.74115	0.521453	0.260727	+	0.965413i	$0.416038\pi$
$282$	−12.0835	−0.719562
$283$	−10.6142	−0.630946	−0.315473	−	0.948934i	$-0.602163\pi$
$283$	−10.6142	−0.630946	−0.315473	+	0.948934i	$0.602163\pi$
$284$	−35.8356	−2.12645
$285$	−0.906518	−0.0536975
$286$	−11.7812	−0.696636
$287$	1.98729	0.117306
$288$	−10.0832	−0.594157
$289$	−11.9415	−0.702442
$290$	14.7345	0.865238
$291$	9.37836	0.549769
$292$	−3.32035	−0.194309
$293$	−16.6527	−0.972859	−0.486429	−	0.873720i	$-0.661701\pi$
$293$	−16.6527	−0.972859	−0.486429	+	0.873720i	$0.661701\pi$
$294$	8.88228	0.518025
$295$	12.0354	0.700726
$296$	0.454410	0.0264121
$297$	−2.49311	−0.144665
$298$	−19.8725	−1.15119
$299$	−1.43065	−0.0827365
$300$	19.1466	1.10543
$301$	23.4261	1.35026
$302$	−24.5243	−1.41121
$303$	7.85008	0.450975
$304$	−8.52554	−0.488973
$305$	6.87329	0.393563
$306$	5.86691	0.335389
$307$	28.7746	1.64225	0.821127	−	0.570746i	$-0.193346\pi$
$307$	28.7746	1.64225	0.821127	+	0.570746i	$0.193346\pi$
$308$	38.6381	2.20161
$309$	−5.00201	−0.284554
$310$	9.32381	0.529557
$311$	8.13679	0.461395	0.230698	−	0.973026i	$-0.425899\pi$
$311$	8.13679	0.461395	0.230698	+	0.973026i	$0.425899\pi$
$312$	13.2528	0.750294
$313$	22.5646	1.27543	0.637713	−	0.770274i	$-0.279880\pi$
$313$	22.5646	1.27543	0.637713	+	0.770274i	$0.279880\pi$
$314$	34.6562	1.95576
$315$	−3.24963	−0.183096
$316$	31.3307	1.76249
$317$	0.870068	0.0488679	0.0244339	−	0.999701i	$-0.492222\pi$
$317$	0.870068	0.0488679	0.0244339	+	0.999701i	$0.492222\pi$
$318$	−28.3649	−1.59063
$319$	13.9787	0.782655
$320$	−7.40805	−0.414123
$321$	13.1272	0.732691
$322$	6.64517	0.370321
$323$	2.02384	0.112609
$324$	4.80454	0.266919
$325$	−7.21917	−0.400448
$326$	63.4802	3.51584
$327$	−18.8797	−1.04405
$328$	−4.50712	−0.248864
$329$	−14.9422	−0.823792
$330$	−6.55168	−0.360658
$331$	12.1701	0.668931	0.334466	−	0.942408i	$-0.391444\pi$
$331$	12.1701	0.668931	0.334466	+	0.942408i	$0.391444\pi$
$332$	−21.5945	−1.18515
$333$	−0.0621137	−0.00340381
$334$	−21.3841	−1.17009
$335$	7.39128	0.403829
$336$	−30.5618	−1.66728
$337$	−9.73969	−0.530555	−0.265277	−	0.964172i	$-0.585464\pi$
$337$	−9.73969	−0.530555	−0.265277	+	0.964172i	$0.585464\pi$
$338$	25.3507	1.37890
$339$	15.4961	0.841633
$340$	10.8861	0.590383
$341$	8.84554	0.479013
$342$	2.34728	0.126926
$343$	−11.5962	−0.626133
$344$	−53.1299	−2.86457
$345$	−0.795602	−0.0428338
$346$	−59.6656	−3.20764
$347$	−8.95872	−0.480929	−0.240465	−	0.970658i	$-0.577300\pi$
$347$	−8.95872	−0.480929	−0.240465	+	0.970658i	$0.577300\pi$
$348$	−26.9386	−1.44406
$349$	30.5491	1.63526	0.817628	−	0.575747i	$-0.195289\pi$
$349$	30.5491	1.63526	0.817628	+	0.575747i	$0.195289\pi$
$350$	33.5321	1.79237
$351$	−1.81154	−0.0966929
$352$	−25.1385	−1.33989
$353$	0.361707	0.0192517	0.00962587	−	0.999954i	$-0.496936\pi$
$353$	0.361707	0.0192517	0.00962587	+	0.999954i	$0.496936\pi$
$354$	−31.1636	−1.65633
$355$	7.51405	0.398805
$356$	−11.6437	−0.617113
$357$	7.25492	0.383971
$358$	1.47049	0.0777177
$359$	20.3133	1.07209	0.536047	−	0.844188i	$-0.319917\pi$
$359$	20.3133	1.07209	0.536047	+	0.844188i	$0.319917\pi$
$360$	7.37008	0.388437
$361$	−18.1903	−0.957384
$362$	55.8516	2.93549
$363$	4.78439	0.251116
$364$	28.0752	1.47154
$365$	0.696214	0.0364415
$366$	−17.7972	−0.930277
$367$	7.55731	0.394488	0.197244	−	0.980354i	$-0.436801\pi$
$367$	7.55731	0.394488	0.197244	+	0.980354i	$0.436801\pi$
$368$	−7.48241	−0.390048
$369$	0.616081	0.0320719
$370$	−0.163229	−0.00848589
$371$	−35.0756	−1.82103
$372$	−17.0465	−0.883818
$373$	−26.9850	−1.39723	−0.698615	−	0.715497i	$-0.746200\pi$
$373$	−26.9850	−1.39723	−0.698615	+	0.715497i	$0.746200\pi$
$374$	14.6269	0.756338
$375$	−9.05179	−0.467432
$376$	33.8886	1.74767
$377$	10.1572	0.523120
$378$	8.41437	0.432789
$379$	1.54201	0.0792077	0.0396038	−	0.999215i	$-0.487390\pi$
$379$	1.54201	0.0792077	0.0396038	+	0.999215i	$0.487390\pi$
$380$	4.35540	0.223427
$381$	−3.53991	−0.181355
$382$	−4.14864	−0.212263
$383$	−0.605510	−0.0309401	−0.0154701	−	0.999880i	$-0.504924\pi$
$383$	−0.605510	−0.0309401	−0.0154701	+	0.999880i	$0.504924\pi$
$384$	−0.984456	−0.0502378
$385$	−8.10169	−0.412900
$386$	58.8982	2.99784
$387$	7.26236	0.369167
$388$	−45.0587	−2.28751
$389$	−21.6972	−1.10009	−0.550046	−	0.835134i	$-0.685390\pi$
$389$	−21.6972	−1.10009	−0.550046	+	0.835134i	$0.685390\pi$
$390$	−4.76057	−0.241061
$391$	1.77621	0.0898269
$392$	−24.9107	−1.25818
$393$	4.83520	0.243904
$394$	−4.82098	−0.242877
$395$	−6.56946	−0.330545
$396$	11.9783	0.601930
$397$	14.4265	0.724046	0.362023	−	0.932169i	$-0.382086\pi$
$397$	14.4265	0.724046	0.362023	+	0.932169i	$0.382086\pi$
$398$	−57.1491	−2.86462
$399$	2.90260	0.145312
$400$	−37.7569	−1.88784
$401$	11.2410	0.561348	0.280674	−	0.959803i	$-0.409442\pi$
$401$	11.2410	0.561348	0.280674	+	0.959803i	$0.409442\pi$
$402$	−19.1385	−0.954541
$403$	6.42733	0.320168
$404$	−37.7160	−1.87644
$405$	−1.00742	−0.0500592
$406$	−47.1787	−2.34144
$407$	−0.154856	−0.00767595
$408$	−16.4540	−0.814594
$409$	−30.0863	−1.48767	−0.743837	−	0.668362i	$-0.766996\pi$
$409$	−30.0863	−1.48767	−0.743837	+	0.668362i	$0.766996\pi$
$410$	1.61901	0.0799571
$411$	13.8812	0.684707
$412$	24.0323	1.18399
$413$	−38.5363	−1.89625
$414$	2.06008	0.101247
$415$	4.52797	0.222269
$416$	−18.2661	−0.895569
$417$	5.96634	0.292173
$418$	5.85202	0.286232
$419$	−6.25997	−0.305819	−0.152910	−	0.988240i	$-0.548864\pi$
$419$	−6.25997	−0.305819	−0.152910	+	0.988240i	$0.548864\pi$
$420$	15.6130	0.761835
$421$	1.33412	0.0650210	0.0325105	−	0.999471i	$-0.489650\pi$
$421$	1.33412	0.0650210	0.0325105	+	0.999471i	$0.489650\pi$
$422$	−18.0908	−0.880648
$423$	−4.63227	−0.225228
$424$	79.5505	3.86331
$425$	8.96292	0.434766
$426$	−19.4564	−0.942665
$427$	−22.0077	−1.06503
$428$	−63.0703	−3.04862
$429$	−4.51637	−0.218053
$430$	19.0848	0.920353
$431$	−9.67104	−0.465838	−0.232919	−	0.972496i	$-0.574828\pi$
$431$	−9.67104	−0.465838	−0.232919	+	0.972496i	$0.574828\pi$
$432$	−9.47451	−0.455843
$433$	3.71721	0.178638	0.0893189	−	0.996003i	$-0.471531\pi$
$433$	3.71721	0.178638	0.0893189	+	0.996003i	$0.471531\pi$
$434$	−29.8541	−1.43304
$435$	5.64853	0.270826
$436$	90.7082	4.34413
$437$	0.710640	0.0339945
$438$	−1.80273	−0.0861378
$439$	−18.7976	−0.897158	−0.448579	−	0.893743i	$-0.648070\pi$
$439$	−18.7976	−0.897158	−0.448579	+	0.893743i	$0.648070\pi$
$440$	18.3744	0.875966
$441$	3.40506	0.162146
$442$	10.6282	0.505530
$443$	−16.3050	−0.774674	−0.387337	−	0.921938i	$-0.626605\pi$
$443$	−16.3050	−0.774674	−0.387337	+	0.921938i	$0.626605\pi$
$444$	0.298428	0.0141628
$445$	2.44146	0.115736
$446$	6.36621	0.301449
$447$	−7.61823	−0.360330
$448$	23.7200	1.12066
$449$	−3.95274	−0.186541	−0.0932706	−	0.995641i	$-0.529732\pi$
$449$	−3.95274	−0.186541	−0.0932706	+	0.995641i	$0.529732\pi$
$450$	10.3953	0.490041
$451$	1.53596	0.0723255
$452$	−74.4516	−3.50191
$453$	−9.40150	−0.441721
$454$	−18.4417	−0.865512
$455$	−5.88683	−0.275979
$456$	−6.58303	−0.308279
$457$	−34.9492	−1.63485	−0.817426	−	0.576033i	$-0.804600\pi$
$457$	−34.9492	−1.63485	−0.817426	+	0.576033i	$0.804600\pi$
$458$	32.9327	1.53884
$459$	2.24911	0.104979
$460$	3.82250	0.178225
$461$	31.9605	1.48855	0.744276	−	0.667873i	$-0.232795\pi$
$461$	31.9605	1.48855	0.744276	+	0.667873i	$0.232795\pi$
$462$	20.9780	0.975983
$463$	−18.9768	−0.881925	−0.440962	−	0.897526i	$-0.645363\pi$
$463$	−18.9768	−0.881925	−0.440962	+	0.897526i	$0.645363\pi$
$464$	53.1228	2.46616
$465$	3.57432	0.165755
$466$	4.01166	0.185836
$467$	1.52641	0.0706336	0.0353168	−	0.999376i	$-0.488756\pi$
$467$	1.52641	0.0706336	0.0353168	+	0.999376i	$0.488756\pi$
$468$	8.70362	0.402325
$469$	−23.6663	−1.09281
$470$	−12.1732	−0.561507
$471$	13.2856	0.612169
$472$	87.3994	4.02289
$473$	18.1059	0.832509
$474$	17.0105	0.781319
$475$	3.58595	0.164535
$476$	−34.8565	−1.59765
$477$	−10.8738	−0.497878
$478$	2.24146	0.102522
$479$	−22.3998	−1.02348	−0.511738	−	0.859142i	$-0.670998\pi$
$479$	−22.3998	−1.02348	−0.511738	+	0.859142i	$0.670998\pi$
$480$	−10.1580	−0.463648
$481$	−0.112522	−0.00513054
$482$	−5.46105	−0.248744
$483$	2.54746	0.115913
$484$	−22.9868	−1.04485
$485$	9.44796	0.429010
$486$	2.60855	0.118326
$487$	−32.3296	−1.46499	−0.732497	−	0.680771i	$-0.761645\pi$
$487$	−32.3296	−1.46499	−0.732497	+	0.680771i	$0.761645\pi$
$488$	49.9130	2.25946
$489$	24.3354	1.10049
$490$	8.94820	0.404238
$491$	24.0187	1.08395	0.541975	−	0.840394i	$-0.317677\pi$
$491$	24.0187	1.08395	0.541975	+	0.840394i	$0.317677\pi$
$492$	−2.95999	−0.133447
$493$	−12.6106	−0.567951
$494$	4.25219	0.191315
$495$	−2.51162	−0.112889
$496$	33.6155	1.50938
$497$	−24.0594	−1.07921
$498$	−11.7244	−0.525384
$499$	−1.61019	−0.0720820	−0.0360410	−	0.999350i	$-0.511475\pi$
$499$	−1.61019	−0.0720820	−0.0360410	+	0.999350i	$0.511475\pi$
$500$	43.4897	1.94492
$501$	−8.19770	−0.366246
$502$	−42.1651	−1.88192
$503$	19.7672	0.881377	0.440689	−	0.897660i	$-0.354734\pi$
$503$	19.7672	0.881377	0.440689	+	0.897660i	$0.354734\pi$
$504$	−23.5984	−1.05116
$505$	7.90834	0.351917
$506$	5.13601	0.228323
$507$	9.71832	0.431606
$508$	17.0077	0.754593
$509$	24.4700	1.08461	0.542306	−	0.840181i	$-0.317551\pi$
$509$	24.4700	1.08461	0.542306	+	0.840181i	$0.317551\pi$
$510$	5.91046	0.261719
$511$	−2.22923	−0.0986151
$512$	43.0937	1.90449
$513$	0.899840	0.0397289
$514$	−49.8078	−2.19693
$515$	−5.03913	−0.222051
$516$	−34.8923	−1.53605
$517$	−11.5488	−0.507914
$518$	0.522648	0.0229638
$519$	−22.8731	−1.00402
$520$	13.3512	0.585489
$521$	3.58573	0.157094	0.0785468	−	0.996910i	$-0.474972\pi$
$521$	3.58573	0.157094	0.0785468	+	0.996910i	$0.474972\pi$
$522$	−14.6259	−0.640159
$523$	−26.1423	−1.14312	−0.571561	−	0.820560i	$-0.693662\pi$
$523$	−26.1423	−1.14312	−0.571561	+	0.820560i	$0.693662\pi$
$524$	−23.2309	−1.01485
$525$	12.8547	0.561025
$526$	−63.8777	−2.78520
$527$	−7.97982	−0.347606
$528$	−23.6210	−1.02797
$529$	−22.3763	−0.972883
$530$	−28.5754	−1.24124
$531$	−11.9467	−0.518443
$532$	−13.9457	−0.604621
$533$	1.11606	0.0483418
$534$	−6.32175	−0.273569
$535$	13.2247	0.571752
$536$	53.6746	2.31839
$537$	0.563718	0.0243262
$538$	−12.4074	−0.534920
$539$	8.48920	0.365656
$540$	4.84020	0.208289
$541$	10.6504	0.457897	0.228949	−	0.973438i	$-0.426471\pi$
$541$	10.6504	0.457897	0.228949	+	0.973438i	$0.426471\pi$
$542$	11.8298	0.508135
$543$	21.4110	0.918833
$544$	22.6782	0.972318
$545$	−19.0198	−0.814719
$546$	15.2430	0.652339
$547$	−15.0286	−0.642577	−0.321289	−	0.946981i	$-0.604116\pi$
$547$	−15.0286	−0.642577	−0.321289	+	0.946981i	$0.604116\pi$
$548$	−66.6926	−2.84897
$549$	−6.82265	−0.291184
$550$	25.9167	1.10509
$551$	−5.04532	−0.214938
$552$	−5.77757	−0.245910
$553$	21.0349	0.894495
$554$	−42.0568	−1.78682
$555$	−0.0625747	−0.00265615
$556$	−28.6655	−1.21569
$557$	−40.9555	−1.73534	−0.867671	−	0.497139i	$-0.834384\pi$
$557$	−40.9555	−1.73534	−0.867671	+	0.497139i	$0.834384\pi$
$558$	−9.25512	−0.391800
$559$	13.1561	0.556442
$560$	−30.7886	−1.30106
$561$	5.60728	0.236739
$562$	−22.8017	−0.961833
$563$	−1.11620	−0.0470421	−0.0235211	−	0.999723i	$-0.507488\pi$
$563$	−1.11620	−0.0470421	−0.0235211	+	0.999723i	$0.507488\pi$
$564$	22.2559	0.937142
$565$	15.6111	0.656764
$566$	27.6876	1.16380
$567$	3.22569	0.135466
$568$	54.5662	2.28955
$569$	3.08259	0.129229	0.0646145	−	0.997910i	$-0.479418\pi$
$569$	3.08259	0.129229	0.0646145	+	0.997910i	$0.479418\pi$
$570$	2.36470	0.0990463
$571$	26.6485	1.11521	0.557603	−	0.830108i	$-0.311721\pi$
$571$	26.6485	1.11521	0.557603	+	0.830108i	$0.311721\pi$
$572$	21.6991	0.907285
$573$	−1.59040	−0.0664399
$574$	−5.18394	−0.216373
$575$	3.14720	0.131247
$576$	7.35347	0.306395
$577$	−5.05486	−0.210437	−0.105218	−	0.994449i	$-0.533554\pi$
$577$	−5.05486	−0.210437	−0.105218	+	0.994449i	$0.533554\pi$
$578$	31.1500	1.29567
$579$	22.5789	0.938346
$580$	−27.1386	−1.12687
$581$	−14.4982	−0.601487
$582$	−24.4639	−1.01406
$583$	−27.1097	−1.12277
$584$	5.05583	0.209212
$585$	−1.82499	−0.0754539
$586$	43.4393	1.79446
$587$	13.5440	0.559020	0.279510	−	0.960143i	$-0.409828\pi$
$587$	13.5440	0.559020	0.279510	+	0.960143i	$0.409828\pi$
$588$	−16.3597	−0.674665
$589$	−3.19262	−0.131550
$590$	−31.3949	−1.29251
$591$	−1.84814	−0.0760225
$592$	−0.588497	−0.0241871
$593$	14.7122	0.604157	0.302079	−	0.953283i	$-0.402319\pi$
$593$	14.7122	0.604157	0.302079	+	0.953283i	$0.402319\pi$
$594$	6.50341	0.266838
$595$	7.30877	0.299630
$596$	36.6021	1.49928
$597$	−21.9084	−0.896649
$598$	3.73192	0.152609
$599$	10.2422	0.418486	0.209243	−	0.977864i	$-0.432900\pi$
$599$	10.2422	0.418486	0.209243	+	0.977864i	$0.432900\pi$
$600$	−29.1541	−1.19021
$601$	39.3041	1.60325	0.801624	−	0.597829i	$-0.203970\pi$
$601$	39.3041	1.60325	0.801624	+	0.597829i	$0.203970\pi$
$602$	−61.1082	−2.49058
$603$	−7.33683	−0.298779
$604$	45.1699	1.83794
$605$	4.81990	0.195957
$606$	−20.4773	−0.831835
$607$	−44.4311	−1.80340	−0.901701	−	0.432361i	$-0.857681\pi$
$607$	−44.4311	−1.80340	−0.901701	+	0.432361i	$0.857681\pi$
$608$	9.07325	0.367969
$609$	−18.0862	−0.732888
$610$	−17.9293	−0.725937
$611$	−8.39154	−0.339485
$612$	−10.8059	−0.436804
$613$	−26.4974	−1.07022	−0.535110	−	0.844783i	$-0.679730\pi$
$613$	−26.4974	−1.07022	−0.535110	+	0.844783i	$0.679730\pi$
$614$	−75.0600	−3.02918
$615$	0.620654	0.0250272
$616$	−58.8335	−2.37047
$617$	−17.7185	−0.713321	−0.356660	−	0.934234i	$-0.616085\pi$
$617$	−17.7185	−0.713321	−0.356660	+	0.934234i	$0.616085\pi$
$618$	13.0480	0.524867
$619$	−4.81349	−0.193471	−0.0967353	−	0.995310i	$-0.530840\pi$
$619$	−4.81349	−0.193471	−0.0967353	+	0.995310i	$0.530840\pi$
$620$	−17.1730	−0.689683
$621$	0.789741	0.0316912
$622$	−21.2252	−0.851054
$623$	−7.81737	−0.313196
$624$	−17.1635	−0.687088
$625$	10.8065	0.432261
$626$	−58.8609	−2.35256
$627$	2.24340	0.0895928
$628$	−63.8313	−2.54715
$629$	0.139701	0.00557022
$630$	8.47682	0.337725
$631$	−29.9812	−1.19353	−0.596767	−	0.802415i	$-0.703548\pi$
$631$	−29.9812	−1.19353	−0.596767	+	0.802415i	$0.703548\pi$
$632$	−47.7067	−1.89767
$633$	−6.93520	−0.275650
$634$	−2.26962	−0.0901380
$635$	−3.56619	−0.141520
$636$	52.2437	2.07160
$637$	6.16841	0.244401
$638$	−36.4641	−1.44363
$639$	−7.45870	−0.295061
$640$	−0.991763	−0.0392029
$641$	−0.0586919	−0.00231819	−0.00115910	−	0.999999i	$-0.500369\pi$
$641$	−0.0586919	−0.00231819	−0.00115910	+	0.999999i	$0.500369\pi$
$642$	−34.2431	−1.35147
$643$	1.18513	0.0467368	0.0233684	−	0.999727i	$-0.492561\pi$
$643$	1.18513	0.0467368	0.0233684	+	0.999727i	$0.492561\pi$
$644$	−12.2394	−0.482298
$645$	7.31626	0.288078
$646$	−5.27928	−0.207711
$647$	−33.2640	−1.30774	−0.653870	−	0.756607i	$-0.726856\pi$
$647$	−33.2640	−1.30774	−0.653870	+	0.756607i	$0.726856\pi$
$648$	−7.31578	−0.287391
$649$	−29.7845	−1.16914
$650$	18.8316	0.738635
$651$	−11.4447	−0.448554
$652$	−116.920	−4.57896
$653$	−21.6421	−0.846923	−0.423461	−	0.905914i	$-0.639185\pi$
$653$	−21.6421	−0.846923	−0.423461	+	0.905914i	$0.639185\pi$
$654$	49.2486	1.92577
$655$	4.87109	0.190329
$656$	5.83707	0.227899
$657$	−0.691085	−0.0269618
$658$	38.9776	1.51951
$659$	25.0704	0.976605	0.488303	−	0.872674i	$-0.337616\pi$
$659$	25.0704	0.976605	0.488303	+	0.872674i	$0.337616\pi$
$660$	12.0672	0.469713
$661$	19.3893	0.754156	0.377078	−	0.926182i	$-0.376929\pi$
$661$	19.3893	0.754156	0.377078	+	0.926182i	$0.376929\pi$
$662$	−31.7464	−1.23386
$663$	4.07435	0.158235
$664$	32.8816	1.27605
$665$	2.92414	0.113393
$666$	0.162027	0.00627841
$667$	−4.42801	−0.171453
$668$	39.3862	1.52390
$669$	2.44052	0.0943559
$670$	−19.2805	−0.744872
$671$	−17.0096	−0.656650
$672$	32.5252	1.25469
$673$	−8.29648	−0.319806	−0.159903	−	0.987133i	$-0.551118\pi$
$673$	−8.29648	−0.319806	−0.159903	+	0.987133i	$0.551118\pi$
$674$	25.4065	0.978621
$675$	3.98510	0.153387
$676$	−46.6920	−1.79585
$677$	5.39266	0.207257	0.103628	−	0.994616i	$-0.466955\pi$
$677$	5.39266	0.207257	0.103628	+	0.994616i	$0.466955\pi$
$678$	−40.4224	−1.55241
$679$	−30.2517	−1.16095
$680$	−16.5761	−0.635664
$681$	−7.06971	−0.270912
$682$	−23.0740	−0.883551
$683$	−10.9276	−0.418133	−0.209067	−	0.977901i	$-0.567043\pi$
$683$	−10.9276	−0.418133	−0.209067	+	0.977901i	$0.567043\pi$
$684$	−4.32331	−0.165306
$685$	13.9842	0.534308
$686$	30.2491	1.15492
$687$	12.6249	0.481670
$688$	68.8073	2.62325
$689$	−19.6984	−0.750448
$690$	2.07537	0.0790080
$691$	−23.4172	−0.890831	−0.445415	−	0.895324i	$-0.646944\pi$
$691$	−23.4172	−0.890831	−0.445415	+	0.895324i	$0.646944\pi$
$692$	109.895	4.17756
$693$	8.04200	0.305490
$694$	23.3693	0.887086
$695$	6.01062	0.227996
$696$	41.0190	1.55482
$697$	−1.38563	−0.0524846
$698$	−79.6889	−3.01627
$699$	1.53789	0.0581682
$700$	−61.7609	−2.33434
$701$	−14.6062	−0.551670	−0.275835	−	0.961205i	$-0.588954\pi$
$701$	−14.6062	−0.551670	−0.275835	+	0.961205i	$0.588954\pi$
$702$	4.72550	0.178352
$703$	0.0558924	0.00210802
$704$	18.3330	0.690952
$705$	−4.66665	−0.175756
$706$	−0.943532	−0.0355103
$707$	−25.3219	−0.952328
$708$	57.3984	2.15716
$709$	32.7419	1.22965	0.614824	−	0.788664i	$-0.289227\pi$
$709$	32.7419	1.22965	0.614824	+	0.788664i	$0.289227\pi$
$710$	−19.6008	−0.735605
$711$	6.52106	0.244559
$712$	17.7296	0.664445
$713$	−2.80199	−0.104936
$714$	−18.9248	−0.708244
$715$	−4.54989	−0.170156
$716$	−2.70840	−0.101218
$717$	0.859273	0.0320901
$718$	−52.9883	−1.97750
$719$	−1.48771	−0.0554823	−0.0277411	−	0.999615i	$-0.508831\pi$
$719$	−1.48771	−0.0554823	−0.0277411	+	0.999615i	$0.508831\pi$
$720$	−9.54483	−0.355715
$721$	16.1349	0.600895
$722$	47.4503	1.76592
$723$	−2.09352	−0.0778588
$724$	−102.870	−3.82313
$725$	−22.3441	−0.829840
$726$	−12.4803	−0.463189
$727$	14.1778	0.525826	0.262913	−	0.964820i	$-0.415317\pi$
$727$	14.1778	0.525826	0.262913	+	0.964820i	$0.415317\pi$
$728$	−42.7495	−1.58440
$729$	1.00000	0.0370370
$730$	−1.81611	−0.0672173
$731$	−16.3338	−0.604129
$732$	32.7797	1.21157
$733$	−21.9113	−0.809313	−0.404656	−	0.914469i	$-0.632609\pi$
$733$	−21.9113	−0.809313	−0.404656	+	0.914469i	$0.632609\pi$
$734$	−19.7136	−0.727643
$735$	3.43033	0.126530
$736$	7.96310	0.293524
$737$	−18.2915	−0.673777
$738$	−1.60708	−0.0591574
$739$	−24.6010	−0.904964	−0.452482	−	0.891774i	$-0.649461\pi$
$739$	−24.6010	−0.904964	−0.452482	+	0.891774i	$0.649461\pi$
$740$	0.300643	0.0110518
$741$	1.63010	0.0598831
$742$	91.4964	3.35894
$743$	−12.5129	−0.459055	−0.229528	−	0.973302i	$-0.573718\pi$
$743$	−12.5129	−0.459055	−0.229528	+	0.973302i	$0.573718\pi$
$744$	25.9563	0.951605
$745$	−7.67477	−0.281182
$746$	70.3918	2.57723
$747$	−4.49461	−0.164449
$748$	−26.9404	−0.985038
$749$	−42.3443	−1.54723
$750$	23.6120	0.862190
$751$	24.0236	0.876635	0.438318	−	0.898820i	$-0.355575\pi$
$751$	24.0236	0.876635	0.438318	+	0.898820i	$0.355575\pi$
$752$	−43.8884	−1.60045
$753$	−16.1642	−0.589056
$754$	−26.4955	−0.964908
$755$	−9.47128	−0.344695
$756$	−15.4979	−0.563655
$757$	7.16239	0.260322	0.130161	−	0.991493i	$-0.458451\pi$
$757$	7.16239	0.260322	0.130161	+	0.991493i	$0.458451\pi$
$758$	−4.02241	−0.146100
$759$	1.96891	0.0714670
$760$	−6.63189	−0.240564
$761$	−6.13323	−0.222330	−0.111165	−	0.993802i	$-0.535458\pi$
$761$	−6.13323	−0.222330	−0.111165	+	0.993802i	$0.535458\pi$
$762$	9.23405	0.334514
$763$	60.9000	2.20473
$764$	7.64114	0.276447
$765$	2.26580	0.0819202
$766$	1.57950	0.0570698
$767$	−21.6419	−0.781445
$768$	17.2749	0.623356
$769$	−2.02045	−0.0728591	−0.0364296	−	0.999336i	$-0.511598\pi$
$769$	−2.02045	−0.0728591	−0.0364296	+	0.999336i	$0.511598\pi$
$770$	21.1337	0.761604
$771$	−19.0940	−0.687655
$772$	−108.481	−3.90432
$773$	3.77872	0.135911	0.0679556	−	0.997688i	$-0.478352\pi$
$773$	3.77872	0.135911	0.0679556	+	0.997688i	$0.478352\pi$
$774$	−18.9442	−0.680937
$775$	−14.1391	−0.507892
$776$	68.6100	2.46296
$777$	0.200360	0.00718786
$778$	56.5983	2.02915
$779$	−0.554374	−0.0198625
$780$	8.76821	0.313952
$781$	−18.5954	−0.665394
$782$	−4.63334	−0.165688
$783$	−5.60692	−0.200375
$784$	32.2613	1.15219
$785$	13.3842	0.477704
$786$	−12.6129	−0.449886
$787$	−8.01836	−0.285824	−0.142912	−	0.989735i	$-0.545647\pi$
$787$	−8.01836	−0.285824	−0.142912	+	0.989735i	$0.545647\pi$
$788$	8.87948	0.316318
$789$	−24.4878	−0.871789
$790$	17.1368	0.609699
$791$	−49.9856	−1.77728
$792$	−18.2391	−0.648097
$793$	−12.3595	−0.438899
$794$	−37.6323	−1.33552
$795$	−10.9545	−0.388517
$796$	105.260	3.73082
$797$	5.58369	0.197784	0.0988922	−	0.995098i	$-0.468470\pi$
$797$	5.58369	0.197784	0.0988922	+	0.995098i	$0.468470\pi$
$798$	−7.57158	−0.268031
$799$	10.4185	0.368579
$800$	40.1825	1.42067
$801$	−2.42347	−0.0856292
$802$	−29.3227	−1.03542
$803$	−1.72295	−0.0608017
$804$	35.2501	1.24317
$805$	2.56636	0.0904525
$806$	−16.7660	−0.590558
$807$	−4.75643	−0.167434
$808$	57.4295	2.02036
$809$	17.3287	0.609245	0.304622	−	0.952473i	$-0.401470\pi$
$809$	17.3287	0.609245	0.304622	+	0.952473i	$0.401470\pi$
$810$	2.62791	0.0923354
$811$	0.788826	0.0276994	0.0138497	−	0.999904i	$-0.495591\pi$
$811$	0.788826	0.0276994	0.0138497	+	0.999904i	$0.495591\pi$
$812$	86.8956	3.04944
$813$	4.53502	0.159050
$814$	0.403951	0.0141585
$815$	24.5160	0.858759
$816$	21.3092	0.745971
$817$	−6.53496	−0.228629
$818$	78.4817	2.74405
$819$	5.84346	0.204187
$820$	−2.98196	−0.104134
$821$	−32.5767	−1.13694	−0.568468	−	0.822705i	$-0.692464\pi$
$821$	−32.5767	−1.13694	−0.568468	+	0.822705i	$0.692464\pi$
$822$	−36.2097	−1.26296
$823$	−18.0003	−0.627452	−0.313726	−	0.949514i	$-0.601577\pi$
$823$	−18.0003	−0.627452	−0.313726	+	0.949514i	$0.601577\pi$
$824$	−36.5936	−1.27480
$825$	9.93530	0.345903
$826$	100.524	3.49768
$827$	−10.9199	−0.379724	−0.189862	−	0.981811i	$-0.560804\pi$
$827$	−10.9199	−0.379724	−0.189862	+	0.981811i	$0.560804\pi$
$828$	−3.79434	−0.131862
$829$	3.23451	0.112339	0.0561696	−	0.998421i	$-0.482111\pi$
$829$	3.23451	0.112339	0.0561696	+	0.998421i	$0.482111\pi$
$830$	−11.8114	−0.409981
$831$	−16.1227	−0.559289
$832$	13.3211	0.461827
$833$	−7.65835	−0.265346
$834$	−15.5635	−0.538920
$835$	−8.25854	−0.285799
$836$	−10.7785	−0.372782
$837$	−3.54799	−0.122637
$838$	16.3294	0.564091
$839$	16.8523	0.581805	0.290902	−	0.956753i	$-0.406045\pi$
$839$	16.8523	0.581805	0.290902	+	0.956753i	$0.406045\pi$
$840$	−23.7736	−0.820266
$841$	2.43750	0.0840516
$842$	−3.48012	−0.119933
$843$	−8.74115	−0.301061
$844$	33.3204	1.14694
$845$	9.79045	0.336802
$846$	12.0835	0.415439
$847$	−15.4330	−0.530283
$848$	−103.024	−3.53786
$849$	10.6142	0.364277
$850$	−23.3802	−0.801936
$851$	0.0490538	0.00168154
$852$	35.8356	1.22771
$853$	−30.1898	−1.03368	−0.516839	−	0.856082i	$-0.672892\pi$
$853$	−30.1898	−1.03368	−0.516839	+	0.856082i	$0.672892\pi$
$854$	57.4083	1.96447
$855$	0.906518	0.0310023
$856$	96.0359	3.28244
$857$	−46.0321	−1.57243	−0.786214	−	0.617955i	$-0.787962\pi$
$857$	−46.0321	−1.57243	−0.786214	+	0.617955i	$0.787962\pi$
$858$	11.7812	0.402203
$859$	2.23543	0.0762718	0.0381359	−	0.999273i	$-0.487858\pi$
$859$	2.23543	0.0762718	0.0381359	+	0.999273i	$0.487858\pi$
$860$	−35.1513	−1.19865
$861$	−1.98729	−0.0677265
$862$	25.2274	0.859248
$863$	5.75964	0.196060	0.0980302	−	0.995183i	$-0.468746\pi$
$863$	5.75964	0.196060	0.0980302	+	0.995183i	$0.468746\pi$
$864$	10.0832	0.343037
$865$	−23.0428	−0.783480
$866$	−9.69654	−0.329502
$867$	11.9415	0.405555
$868$	54.9866	1.86637
$869$	16.2577	0.551506
$870$	−14.7345	−0.499546
$871$	−13.2910	−0.450347
$872$	−138.120	−4.67732
$873$	−9.37836	−0.317409
$874$	−1.85374	−0.0627037
$875$	29.1982	0.987081
$876$	3.32035	0.112184
$877$	48.7376	1.64575	0.822877	−	0.568220i	$-0.192368\pi$
$877$	48.7376	1.64575	0.822877	+	0.568220i	$0.192368\pi$
$878$	49.0344	1.65483
$879$	16.6527	0.561680
$880$	−23.7963	−0.802174
$881$	18.0537	0.608243	0.304121	−	0.952633i	$-0.401637\pi$
$881$	18.0537	0.608243	0.304121	+	0.952633i	$0.401637\pi$
$882$	−8.88228	−0.299082
$883$	−37.1105	−1.24887	−0.624434	−	0.781078i	$-0.714670\pi$
$883$	−37.1105	−1.24887	−0.624434	+	0.781078i	$0.714670\pi$
$884$	−19.5754	−0.658391
$885$	−12.0354	−0.404564
$886$	42.5324	1.42891
$887$	12.6680	0.425351	0.212676	−	0.977123i	$-0.431782\pi$
$887$	12.6680	0.425351	0.212676	+	0.977123i	$0.431782\pi$
$888$	−0.454410	−0.0152490
$889$	11.4187	0.382969
$890$	−6.36867	−0.213478
$891$	2.49311	0.0835224
$892$	−11.7256	−0.392601
$893$	4.16830	0.139487
$894$	19.8725	0.664637
$895$	0.567902	0.0189829
$896$	3.17555	0.106088
$897$	1.43065	0.0477679
$898$	10.3109	0.344080
$899$	19.8933	0.663478
$900$	−19.1466	−0.638219
$901$	24.4564	0.814761
$902$	−4.00663	−0.133406
$903$	−23.4261	−0.779572
$904$	113.366	3.77050
$905$	21.5699	0.717007
$906$	24.5243	0.814765
$907$	38.9880	1.29458	0.647288	−	0.762245i	$-0.275903\pi$
$907$	38.9880	1.29458	0.647288	+	0.762245i	$0.275903\pi$
$908$	33.9667	1.12722
$909$	−7.85008	−0.260371
$910$	15.3561	0.509050
$911$	−23.6953	−0.785059	−0.392530	−	0.919739i	$-0.628400\pi$
$911$	−23.6953	−0.785059	−0.392530	+	0.919739i	$0.628400\pi$
$912$	8.52554	0.282309
$913$	−11.2056	−0.370850
$914$	91.1667	3.01552
$915$	−6.87329	−0.227224
$916$	−60.6568	−2.00416
$917$	−15.5969	−0.515054
$918$	−5.86691	−0.193637
$919$	4.90688	0.161863	0.0809315	−	0.996720i	$-0.474211\pi$
$919$	4.90688	0.161863	0.0809315	+	0.996720i	$0.474211\pi$
$920$	−5.82045	−0.191895
$921$	−28.7746	−0.948156
$922$	−83.3707	−2.74567
$923$	−13.5117	−0.444744
$924$	−38.6381	−1.27110
$925$	0.247530	0.00813872
$926$	49.5018	1.62673
$927$	5.00201	0.164287
$928$	−56.5355	−1.85587
$929$	−45.4470	−1.49107	−0.745534	−	0.666467i	$-0.767806\pi$
$929$	−45.4470	−1.49107	−0.745534	+	0.666467i	$0.767806\pi$
$930$	−9.32381	−0.305740
$931$	−3.06401	−0.100419
$932$	−7.38884	−0.242029
$933$	−8.13679	−0.266387
$934$	−3.98171	−0.130285
$935$	5.64889	0.184739
$936$	−13.2528	−0.433182
$937$	47.1105	1.53903	0.769516	−	0.638627i	$-0.220497\pi$
$937$	47.1105	1.53903	0.769516	+	0.638627i	$0.220497\pi$
$938$	61.7348	2.01571
$939$	−22.5646	−0.736368
$940$	22.4211	0.731295
$941$	42.5676	1.38766	0.693832	−	0.720137i	$-0.255921\pi$
$941$	42.5676	1.38766	0.693832	+	0.720137i	$0.255921\pi$
$942$	−34.6562	−1.12916
$943$	−0.486545	−0.0158441
$944$	−113.189	−3.68399
$945$	3.24963	0.105710
$946$	−47.2301	−1.53558
$947$	−48.7632	−1.58459	−0.792295	−	0.610138i	$-0.791114\pi$
$947$	−48.7632	−1.58459	−0.792295	+	0.610138i	$0.791114\pi$
$948$	−31.3307	−1.01757
$949$	−1.25193	−0.0406393
$950$	−9.35414	−0.303488
$951$	−0.870068	−0.0282139
$952$	53.0754	1.72018
$953$	0.0521077	0.00168793	0.000843967	−	1.00000i	$-0.499731\pi$
$953$	0.0521077	0.00168793	0.000843967		1.00000i	$0.499731\pi$
$954$	28.3649	0.918348
$955$	−1.60220	−0.0518461
$956$	−4.12841	−0.133522
$957$	−13.9787	−0.451866
$958$	58.4311	1.88782
$959$	−44.7763	−1.44590
$960$	7.40805	0.239094
$961$	−18.4118	−0.593928
$962$	0.293518	0.00946341
$963$	−13.1272	−0.423019
$964$	10.0584	0.323959
$965$	22.7465	0.732234
$966$	−6.64517	−0.213805
$967$	54.0687	1.73873	0.869366	−	0.494169i	$-0.164528\pi$
$967$	54.0687	1.73873	0.869366	+	0.494169i	$0.164528\pi$
$968$	35.0016	1.12499
$969$	−2.02384	−0.0650150
$970$	−24.6455	−0.791319
$971$	13.6610	0.438403	0.219202	−	0.975680i	$-0.429655\pi$
$971$	13.6610	0.438403	0.219202	+	0.975680i	$0.429655\pi$
$972$	−4.80454	−0.154106
$973$	−19.2455	−0.616983
$974$	84.3334	2.70222
$975$	7.21917	0.231199
$976$	−64.6413	−2.06912
$977$	−1.64226	−0.0525405	−0.0262702	−	0.999655i	$-0.508363\pi$
$977$	−1.64226	−0.0525405	−0.0262702	+	0.999655i	$0.508363\pi$
$978$	−63.4802	−2.02987
$979$	−6.04199	−0.193103
$980$	−16.4812	−0.526472
$981$	18.8797	0.602782
$982$	−62.6541	−1.99937
$983$	−20.9143	−0.667063	−0.333532	−	0.942739i	$-0.608240\pi$
$983$	−20.9143	−0.667063	−0.333532	+	0.942739i	$0.608240\pi$
$984$	4.50712	0.143682
$985$	−1.86186	−0.0593238
$986$	32.8953	1.04760
$987$	14.9422	0.475617
$988$	−7.83186	−0.249165
$989$	−5.73539	−0.182375
$990$	6.55168	0.208226
$991$	−42.6589	−1.35511	−0.677553	−	0.735474i	$-0.736960\pi$
$991$	−42.6589	−1.35511	−0.677553	+	0.735474i	$0.736960\pi$
$992$	−35.7750	−1.13586
$993$	−12.1701	−0.386208
$994$	62.7602	1.99063
$995$	−22.0710	−0.699696
$996$	21.5945	0.684249
$997$	−5.65744	−0.179173	−0.0895865	−	0.995979i	$-0.528555\pi$
$997$	−5.65744	−0.179173	−0.0895865	+	0.995979i	$0.528555\pi$
$998$	4.20026	0.132957
$999$	0.0621137	0.00196519

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6033.2.a.d.1.6	✓	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6033.2.a.d.1.6	✓	84	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)

\(f(q)\)	\(=\)	\(q-2.60855 q^{2} -1.00000 q^{3} +4.80454 q^{4} -1.00742 q^{5} +2.60855 q^{6} +3.22569 q^{7} -7.31578 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.60855 q^{2} -1.00000 q^{3} +4.80454 q^{4} -1.00742 q^{5} +2.60855 q^{6} +3.22569 q^{7} -7.31578 q^{8} +1.00000 q^{9} +2.62791 q^{10} +2.49311 q^{11} -4.80454 q^{12} +1.81154 q^{13} -8.41437 q^{14} +1.00742 q^{15} +9.47451 q^{16} -2.24911 q^{17} -2.60855 q^{18} -0.899840 q^{19} -4.84020 q^{20} -3.22569 q^{21} -6.50341 q^{22} -0.789741 q^{23} +7.31578 q^{24} -3.98510 q^{25} -4.72550 q^{26} -1.00000 q^{27} +15.4979 q^{28} +5.60692 q^{29} -2.62791 q^{30} +3.54799 q^{31} -10.0832 q^{32} -2.49311 q^{33} +5.86691 q^{34} -3.24963 q^{35} +4.80454 q^{36} -0.0621137 q^{37} +2.34728 q^{38} -1.81154 q^{39} +7.37008 q^{40} +0.616081 q^{41} +8.41437 q^{42} +7.26236 q^{43} +11.9783 q^{44} -1.00742 q^{45} +2.06008 q^{46} -4.63227 q^{47} -9.47451 q^{48} +3.40506 q^{49} +10.3953 q^{50} +2.24911 q^{51} +8.70362 q^{52} -10.8738 q^{53} +2.60855 q^{54} -2.51162 q^{55} -23.5984 q^{56} +0.899840 q^{57} -14.6259 q^{58} -11.9467 q^{59} +4.84020 q^{60} -6.82265 q^{61} -9.25512 q^{62} +3.22569 q^{63} +7.35347 q^{64} -1.82499 q^{65} +6.50341 q^{66} -7.33683 q^{67} -10.8059 q^{68} +0.789741 q^{69} +8.47682 q^{70} -7.45870 q^{71} -7.31578 q^{72} -0.691085 q^{73} +0.162027 q^{74} +3.98510 q^{75} -4.32331 q^{76} +8.04200 q^{77} +4.72550 q^{78} +6.52106 q^{79} -9.54483 q^{80} +1.00000 q^{81} -1.60708 q^{82} -4.49461 q^{83} -15.4979 q^{84} +2.26580 q^{85} -18.9442 q^{86} -5.60692 q^{87} -18.2391 q^{88} -2.42347 q^{89} +2.62791 q^{90} +5.84346 q^{91} -3.79434 q^{92} -3.54799 q^{93} +12.0835 q^{94} +0.906518 q^{95} +10.0832 q^{96} -9.37836 q^{97} -8.88228 q^{98} +2.49311 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 13 q^{2} - 84 q^{3} + 81 q^{4} - 10 q^{5} + 13 q^{6} - 32 q^{7} - 39 q^{8} + 84 q^{9}+O(q^{10}) \) 84 * q - 13 * q^2 - 84 * q^3 + 81 * q^4 - 10 * q^5 + 13 * q^6 - 32 * q^7 - 39 * q^8 + 84 * q^9	\( 84 q - 13 q^{2} - 84 q^{3} + 81 q^{4} - 10 q^{5} + 13 q^{6} - 32 q^{7} - 39 q^{8} + 84 q^{9} + 13 q^{10} - 20 q^{11} - 81 q^{12} + 7 q^{13} - 9 q^{14} + 10 q^{15} + 83 q^{16} - 39 q^{17} - 13 q^{18} + 13 q^{19} - 26 q^{20} + 32 q^{21} - 21 q^{22} - 93 q^{23} + 39 q^{24} + 66 q^{25} - 34 q^{26} - 84 q^{27} - 59 q^{28} - 39 q^{29} - 13 q^{30} + 8 q^{31} - 96 q^{32} + 20 q^{33} - 69 q^{35} + 81 q^{36} + 6 q^{37} - 59 q^{38} - 7 q^{39} + 28 q^{40} - 23 q^{41} + 9 q^{42} - 74 q^{43} - 43 q^{44} - 10 q^{45} - 6 q^{46} - 77 q^{47} - 83 q^{48} + 100 q^{49} - 74 q^{50} + 39 q^{51} - 44 q^{52} - 66 q^{53} + 13 q^{54} - 60 q^{55} - 31 q^{56} - 13 q^{57} - 39 q^{58} - 36 q^{59} + 26 q^{60} + 104 q^{61} - 53 q^{62} - 32 q^{63} + 85 q^{64} - 47 q^{65} + 21 q^{66} - 65 q^{67} - 118 q^{68} + 93 q^{69} - 3 q^{70} - 68 q^{71} - 39 q^{72} + 8 q^{73} - 30 q^{74} - 66 q^{75} + 71 q^{76} - 83 q^{77} + 34 q^{78} - 24 q^{79} - 67 q^{80} + 84 q^{81} - 9 q^{82} - 95 q^{83} + 59 q^{84} + 24 q^{85} - 32 q^{86} + 39 q^{87} - 65 q^{88} - 44 q^{89} + 13 q^{90} + 8 q^{91} - 184 q^{92} - 8 q^{93} + 61 q^{94} - 153 q^{95} + 96 q^{96} + 19 q^{97} - 67 q^{98} - 20 q^{99}+O(q^{100}) \) 84 * q - 13 * q^2 - 84 * q^3 + 81 * q^4 - 10 * q^5 + 13 * q^6 - 32 * q^7 - 39 * q^8 + 84 * q^9 + 13 * q^10 - 20 * q^11 - 81 * q^12 + 7 * q^13 - 9 * q^14 + 10 * q^15 + 83 * q^16 - 39 * q^17 - 13 * q^18 + 13 * q^19 - 26 * q^20 + 32 * q^21 - 21 * q^22 - 93 * q^23 + 39 * q^24 + 66 * q^25 - 34 * q^26 - 84 * q^27 - 59 * q^28 - 39 * q^29 - 13 * q^30 + 8 * q^31 - 96 * q^32 + 20 * q^33 - 69 * q^35 + 81 * q^36 + 6 * q^37 - 59 * q^38 - 7 * q^39 + 28 * q^40 - 23 * q^41 + 9 * q^42 - 74 * q^43 - 43 * q^44 - 10 * q^45 - 6 * q^46 - 77 * q^47 - 83 * q^48 + 100 * q^49 - 74 * q^50 + 39 * q^51 - 44 * q^52 - 66 * q^53 + 13 * q^54 - 60 * q^55 - 31 * q^56 - 13 * q^57 - 39 * q^58 - 36 * q^59 + 26 * q^60 + 104 * q^61 - 53 * q^62 - 32 * q^63 + 85 * q^64 - 47 * q^65 + 21 * q^66 - 65 * q^67 - 118 * q^68 + 93 * q^69 - 3 * q^70 - 68 * q^71 - 39 * q^72 + 8 * q^73 - 30 * q^74 - 66 * q^75 + 71 * q^76 - 83 * q^77 + 34 * q^78 - 24 * q^79 - 67 * q^80 + 84 * q^81 - 9 * q^82 - 95 * q^83 + 59 * q^84 + 24 * q^85 - 32 * q^86 + 39 * q^87 - 65 * q^88 - 44 * q^89 + 13 * q^90 + 8 * q^91 - 184 * q^92 - 8 * q^93 + 61 * q^94 - 153 * q^95 + 96 * q^96 + 19 * q^97 - 67 * q^98 - 20 * q^99

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