LMFDB - Embedded newform 4029.2.a.k.1.26

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.26
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.24319 q^{2} +1.00000 q^{3} +3.03191 q^{4} -4.27976 q^{5} +2.24319 q^{6} -0.0653339 q^{7} +2.31477 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.24319 q^{2} +1.00000 q^{3} +3.03191 q^{4} -4.27976 q^{5} +2.24319 q^{6} -0.0653339 q^{7} +2.31477 q^{8} +1.00000 q^{9} -9.60033 q^{10} +3.23018 q^{11} +3.03191 q^{12} -2.88004 q^{13} -0.146556 q^{14} -4.27976 q^{15} -0.871339 q^{16} +1.00000 q^{17} +2.24319 q^{18} +7.45327 q^{19} -12.9759 q^{20} -0.0653339 q^{21} +7.24592 q^{22} -1.14406 q^{23} +2.31477 q^{24} +13.3164 q^{25} -6.46048 q^{26} +1.00000 q^{27} -0.198086 q^{28} +7.28872 q^{29} -9.60033 q^{30} +3.60094 q^{31} -6.58413 q^{32} +3.23018 q^{33} +2.24319 q^{34} +0.279613 q^{35} +3.03191 q^{36} -2.70010 q^{37} +16.7191 q^{38} -2.88004 q^{39} -9.90668 q^{40} +12.7049 q^{41} -0.146556 q^{42} +2.63923 q^{43} +9.79362 q^{44} -4.27976 q^{45} -2.56634 q^{46} +5.16451 q^{47} -0.871339 q^{48} -6.99573 q^{49} +29.8712 q^{50} +1.00000 q^{51} -8.73202 q^{52} -8.09202 q^{53} +2.24319 q^{54} -13.8244 q^{55} -0.151233 q^{56} +7.45327 q^{57} +16.3500 q^{58} +12.2898 q^{59} -12.9759 q^{60} +4.85946 q^{61} +8.07759 q^{62} -0.0653339 q^{63} -13.0268 q^{64} +12.3259 q^{65} +7.24592 q^{66} -7.91890 q^{67} +3.03191 q^{68} -1.14406 q^{69} +0.627227 q^{70} +1.84117 q^{71} +2.31477 q^{72} -2.31371 q^{73} -6.05684 q^{74} +13.3164 q^{75} +22.5976 q^{76} -0.211040 q^{77} -6.46048 q^{78} +1.00000 q^{79} +3.72913 q^{80} +1.00000 q^{81} +28.4996 q^{82} +11.4658 q^{83} -0.198086 q^{84} -4.27976 q^{85} +5.92030 q^{86} +7.28872 q^{87} +7.47714 q^{88} -6.86540 q^{89} -9.60033 q^{90} +0.188164 q^{91} -3.46868 q^{92} +3.60094 q^{93} +11.5850 q^{94} -31.8982 q^{95} -6.58413 q^{96} +8.64709 q^{97} -15.6928 q^{98} +3.23018 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9}+O(q^{10}) $ 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9	\( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9} + 5 q^{10} + 26 q^{11} + 34 q^{12} + 7 q^{13} + 19 q^{14} + 11 q^{15} + 40 q^{16} + 31 q^{17} + 4 q^{18} + 32 q^{19} + 23 q^{20} + 4 q^{21} + 2 q^{22} + 29 q^{23} + 12 q^{24} + 32 q^{25} + 13 q^{26} + 31 q^{27} - 13 q^{28} + 25 q^{29} + 5 q^{30} + 22 q^{31} + 28 q^{32} + 26 q^{33} + 4 q^{34} + 20 q^{35} + 34 q^{36} - 4 q^{37} + 19 q^{38} + 7 q^{39} - 3 q^{40} + 33 q^{41} + 19 q^{42} + 6 q^{43} + 30 q^{44} + 11 q^{45} - 11 q^{46} + 23 q^{47} + 40 q^{48} + 31 q^{49} + 6 q^{50} + 31 q^{51} - 7 q^{52} + 12 q^{53} + 4 q^{54} + 40 q^{56} + 32 q^{57} + 9 q^{58} + 27 q^{59} + 23 q^{60} - 4 q^{61} + 25 q^{62} + 4 q^{63} + 10 q^{64} + 54 q^{65} + 2 q^{66} + 34 q^{68} + 29 q^{69} - 59 q^{70} + 35 q^{71} + 12 q^{72} + 5 q^{73} + 48 q^{74} + 32 q^{75} + 32 q^{76} + 42 q^{77} + 13 q^{78} + 31 q^{79} + 24 q^{80} + 31 q^{81} + 5 q^{82} + 67 q^{83} - 13 q^{84} + 11 q^{85} - 20 q^{86} + 25 q^{87} - 7 q^{88} + 22 q^{89} + 5 q^{90} + 16 q^{91} + 57 q^{92} + 22 q^{93} + 45 q^{94} + 73 q^{95} + 28 q^{96} - 13 q^{97} - 19 q^{98} + 26 q^{99}+O(q^{100}) \) 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9 + 5 * q^10 + 26 * q^11 + 34 * q^12 + 7 * q^13 + 19 * q^14 + 11 * q^15 + 40 * q^16 + 31 * q^17 + 4 * q^18 + 32 * q^19 + 23 * q^20 + 4 * q^21 + 2 * q^22 + 29 * q^23 + 12 * q^24 + 32 * q^25 + 13 * q^26 + 31 * q^27 - 13 * q^28 + 25 * q^29 + 5 * q^30 + 22 * q^31 + 28 * q^32 + 26 * q^33 + 4 * q^34 + 20 * q^35 + 34 * q^36 - 4 * q^37 + 19 * q^38 + 7 * q^39 - 3 * q^40 + 33 * q^41 + 19 * q^42 + 6 * q^43 + 30 * q^44 + 11 * q^45 - 11 * q^46 + 23 * q^47 + 40 * q^48 + 31 * q^49 + 6 * q^50 + 31 * q^51 - 7 * q^52 + 12 * q^53 + 4 * q^54 + 40 * q^56 + 32 * q^57 + 9 * q^58 + 27 * q^59 + 23 * q^60 - 4 * q^61 + 25 * q^62 + 4 * q^63 + 10 * q^64 + 54 * q^65 + 2 * q^66 + 34 * q^68 + 29 * q^69 - 59 * q^70 + 35 * q^71 + 12 * q^72 + 5 * q^73 + 48 * q^74 + 32 * q^75 + 32 * q^76 + 42 * q^77 + 13 * q^78 + 31 * q^79 + 24 * q^80 + 31 * q^81 + 5 * q^82 + 67 * q^83 - 13 * q^84 + 11 * q^85 - 20 * q^86 + 25 * q^87 - 7 * q^88 + 22 * q^89 + 5 * q^90 + 16 * q^91 + 57 * q^92 + 22 * q^93 + 45 * q^94 + 73 * q^95 + 28 * q^96 - 13 * q^97 - 19 * q^98 + 26 * 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 $

$2$	2.24319	1.58618	0.793088	−	0.609107i	$-0.208472\pi$
$2$	2.24319	1.58618	0.793088	+	0.609107i	$0.208472\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.03191	1.51596
$5$	−4.27976	−1.91397	−0.956984	−	0.290140i	$-0.906298\pi$
$5$	−4.27976	−1.91397	−0.956984	+	0.290140i	$0.906298\pi$
$6$	2.24319	0.915779
$7$	−0.0653339	−0.0246939	−0.0123469	−	0.999924i	$-0.503930\pi$
$7$	−0.0653339	−0.0246939	−0.0123469	+	0.999924i	$0.503930\pi$
$8$	2.31477	0.818396
$9$	1.00000	0.333333
$10$	−9.60033	−3.03589
$11$	3.23018	0.973936	0.486968	−	0.873420i	$-0.338103\pi$
$11$	3.23018	0.973936	0.486968	+	0.873420i	$0.338103\pi$
$12$	3.03191	0.875237
$13$	−2.88004	−0.798779	−0.399389	−	0.916781i	$-0.630778\pi$
$13$	−2.88004	−0.798779	−0.399389	+	0.916781i	$0.630778\pi$
$14$	−0.146556	−0.0391688
$15$	−4.27976	−1.10503
$16$	−0.871339	−0.217835
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	2.24319	0.528725
$19$	7.45327	1.70990	0.854948	−	0.518713i	$-0.173589\pi$
$19$	7.45327	1.70990	0.854948	+	0.518713i	$0.173589\pi$
$20$	−12.9759	−2.90149
$21$	−0.0653339	−0.0142570
$22$	7.24592	1.54483
$23$	−1.14406	−0.238552	−0.119276	−	0.992861i	$-0.538057\pi$
$23$	−1.14406	−0.238552	−0.119276	+	0.992861i	$0.538057\pi$
$24$	2.31477	0.472501
$25$	13.3164	2.66328
$26$	−6.46048	−1.26700
$27$	1.00000	0.192450
$28$	−0.198086	−0.0374348
$29$	7.28872	1.35348	0.676740	−	0.736222i	$-0.263392\pi$
$29$	7.28872	1.35348	0.676740	+	0.736222i	$0.263392\pi$
$30$	−9.60033	−1.75277
$31$	3.60094	0.646747	0.323374	−	0.946271i	$-0.395183\pi$
$31$	3.60094	0.646747	0.323374	+	0.946271i	$0.395183\pi$
$32$	−6.58413	−1.16392
$33$	3.23018	0.562302
$34$	2.24319	0.384704
$35$	0.279613	0.0472633
$36$	3.03191	0.505318
$37$	−2.70010	−0.443893	−0.221947	−	0.975059i	$-0.571241\pi$
$37$	−2.70010	−0.443893	−0.221947	+	0.975059i	$0.571241\pi$
$38$	16.7191	2.71220
$39$	−2.88004	−0.461175
$40$	−9.90668	−1.56638
$41$	12.7049	1.98418	0.992089	−	0.125533i	$-0.0400641\pi$
$41$	12.7049	1.98418	0.992089	+	0.125533i	$0.0400641\pi$
$42$	−0.146556	−0.0226141
$43$	2.63923	0.402479	0.201239	−	0.979542i	$-0.435503\pi$
$43$	2.63923	0.402479	0.201239	+	0.979542i	$0.435503\pi$
$44$	9.79362	1.47644
$45$	−4.27976	−0.637990
$46$	−2.56634	−0.378386
$47$	5.16451	0.753321	0.376661	−	0.926351i	$-0.377072\pi$
$47$	5.16451	0.753321	0.376661	+	0.926351i	$0.377072\pi$
$48$	−0.871339	−0.125767
$49$	−6.99573	−0.999390
$50$	29.8712	4.22442
$51$	1.00000	0.140028
$52$	−8.73202	−1.21091
$53$	−8.09202	−1.11152	−0.555762	−	0.831341i	$-0.687573\pi$
$53$	−8.09202	−1.11152	−0.555762	+	0.831341i	$0.687573\pi$
$54$	2.24319	0.305260
$55$	−13.8244	−1.86408
$56$	−0.151233	−0.0202094
$57$	7.45327	0.987209
$58$	16.3500	2.14686
$59$	12.2898	1.60000	0.800001	−	0.599999i	$-0.204832\pi$
$59$	12.2898	1.60000	0.800001	+	0.599999i	$0.204832\pi$
$60$	−12.9759	−1.67518
$61$	4.85946	0.622190	0.311095	−	0.950379i	$-0.399304\pi$
$61$	4.85946	0.622190	0.311095	+	0.950379i	$0.399304\pi$
$62$	8.07759	1.02585
$63$	−0.0653339	−0.00823129
$64$	−13.0268	−1.62835
$65$	12.3259	1.52884
$66$	7.24592	0.891911
$67$	−7.91890	−0.967448	−0.483724	−	0.875221i	$-0.660716\pi$
$67$	−7.91890	−0.967448	−0.483724	+	0.875221i	$0.660716\pi$
$68$	3.03191	0.367673
$69$	−1.14406	−0.137728
$70$	0.627227	0.0749679
$71$	1.84117	0.218507	0.109253	−	0.994014i	$-0.465154\pi$
$71$	1.84117	0.218507	0.109253	+	0.994014i	$0.465154\pi$
$72$	2.31477	0.272799
$73$	−2.31371	−0.270799	−0.135400	−	0.990791i	$-0.543232\pi$
$73$	−2.31371	−0.270799	−0.135400	+	0.990791i	$0.543232\pi$
$74$	−6.05684	−0.704093
$75$	13.3164	1.53764
$76$	22.5976	2.59213
$77$	−0.211040	−0.0240503
$78$	−6.46048	−0.731505
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	3.72913	0.416929
$81$	1.00000	0.111111
$82$	28.4996	3.14726
$83$	11.4658	1.25853	0.629265	−	0.777191i	$-0.283356\pi$
$83$	11.4658	1.25853	0.629265	+	0.777191i	$0.283356\pi$
$84$	−0.198086	−0.0216130
$85$	−4.27976	−0.464206
$86$	5.92030	0.638402
$87$	7.28872	0.781432
$88$	7.47714	0.797066
$89$	−6.86540	−0.727731	−0.363866	−	0.931451i	$-0.618543\pi$
$89$	−6.86540	−0.727731	−0.363866	+	0.931451i	$0.618543\pi$
$90$	−9.60033	−1.01196
$91$	0.188164	0.0197249
$92$	−3.46868	−0.361635
$93$	3.60094	0.373400
$94$	11.5850	1.19490
$95$	−31.8982	−3.27269
$96$	−6.58413	−0.671990
$97$	8.64709	0.877979	0.438990	−	0.898492i	$-0.355337\pi$
$97$	8.64709	0.877979	0.438990	+	0.898492i	$0.355337\pi$
$98$	−15.6928	−1.58521
$99$	3.23018	0.324645
$100$	40.3741	4.03741
$101$	−13.6386	−1.35710	−0.678548	−	0.734556i	$-0.737390\pi$
$101$	−13.6386	−1.35710	−0.678548	+	0.734556i	$0.737390\pi$
$102$	2.24319	0.222109
$103$	7.16588	0.706075	0.353038	−	0.935609i	$-0.385149\pi$
$103$	7.16588	0.706075	0.353038	+	0.935609i	$0.385149\pi$
$104$	−6.66663	−0.653717
$105$	0.279613	0.0272875
$106$	−18.1520	−1.76307
$107$	9.38280	0.907070	0.453535	−	0.891238i	$-0.350163\pi$
$107$	9.38280	0.907070	0.453535	+	0.891238i	$0.350163\pi$
$108$	3.03191	0.291746
$109$	8.45836	0.810164	0.405082	−	0.914280i	$-0.367243\pi$
$109$	8.45836	0.810164	0.405082	+	0.914280i	$0.367243\pi$
$110$	−31.0108	−2.95676
$111$	−2.70010	−0.256282
$112$	0.0569280	0.00537919
$113$	−3.94608	−0.371216	−0.185608	−	0.982624i	$-0.559425\pi$
$113$	−3.94608	−0.371216	−0.185608	+	0.982624i	$0.559425\pi$
$114$	16.7191	1.56589
$115$	4.89629	0.456582
$116$	22.0987	2.05182
$117$	−2.88004	−0.266260
$118$	27.5685	2.53789
$119$	−0.0653339	−0.00598914
$120$	−9.90668	−0.904352
$121$	−0.565931	−0.0514483
$122$	10.9007	0.986902
$123$	12.7049	1.14557
$124$	10.9177	0.980440
$125$	−35.5921	−3.18346
$126$	−0.146556	−0.0130563
$127$	−17.7999	−1.57948	−0.789741	−	0.613440i	$-0.789785\pi$
$127$	−17.7999	−1.57948	−0.789741	+	0.613440i	$0.789785\pi$
$128$	−16.0533	−1.41893
$129$	2.63923	0.232371
$130$	27.6493	2.42501
$131$	15.1266	1.32162	0.660809	−	0.750554i	$-0.270213\pi$
$131$	15.1266	1.32162	0.660809	+	0.750554i	$0.270213\pi$
$132$	9.79362	0.852425
$133$	−0.486951	−0.0422240
$134$	−17.7636	−1.53454
$135$	−4.27976	−0.368343
$136$	2.31477	0.198490
$137$	10.9459	0.935168	0.467584	−	0.883949i	$-0.345125\pi$
$137$	10.9459	0.935168	0.467584	+	0.883949i	$0.345125\pi$
$138$	−2.56634	−0.218461
$139$	−5.85835	−0.496898	−0.248449	−	0.968645i	$-0.579921\pi$
$139$	−5.85835	−0.496898	−0.248449	+	0.968645i	$0.579921\pi$
$140$	0.847763	0.0716491
$141$	5.16451	0.434930
$142$	4.13010	0.346590
$143$	−9.30304	−0.777959
$144$	−0.871339	−0.0726116
$145$	−31.1940	−2.59052
$146$	−5.19010	−0.429536
$147$	−6.99573	−0.576998
$148$	−8.18645	−0.672922
$149$	22.3310	1.82943	0.914714	−	0.404103i	$-0.132416\pi$
$149$	22.3310	1.82943	0.914714	+	0.404103i	$0.132416\pi$
$150$	29.8712	2.43897
$151$	−5.35488	−0.435774	−0.217887	−	0.975974i	$-0.569916\pi$
$151$	−5.35488	−0.435774	−0.217887	+	0.975974i	$0.569916\pi$
$152$	17.2526	1.39937
$153$	1.00000	0.0808452
$154$	−0.473404	−0.0381480
$155$	−15.4112	−1.23785
$156$	−8.73202	−0.699121
$157$	−17.8963	−1.42828	−0.714141	−	0.700002i	$-0.753183\pi$
$157$	−17.8963	−1.42828	−0.714141	+	0.700002i	$0.753183\pi$
$158$	2.24319	0.178459
$159$	−8.09202	−0.641739
$160$	28.1785	2.22771
$161$	0.0747457	0.00589078
$162$	2.24319	0.176242
$163$	11.0501	0.865511	0.432756	−	0.901511i	$-0.357541\pi$
$163$	11.0501	0.865511	0.432756	+	0.901511i	$0.357541\pi$
$164$	38.5203	3.00793
$165$	−13.8244	−1.07623
$166$	25.7199	1.99625
$167$	−11.6924	−0.904789	−0.452394	−	0.891818i	$-0.649430\pi$
$167$	−11.6924	−0.904789	−0.452394	+	0.891818i	$0.649430\pi$
$168$	−0.151233	−0.0116679
$169$	−4.70538	−0.361953
$170$	−9.60033	−0.736312
$171$	7.45327	0.569966
$172$	8.00191	0.610140
$173$	−10.3964	−0.790424	−0.395212	−	0.918590i	$-0.629329\pi$
$173$	−10.3964	−0.790424	−0.395212	+	0.918590i	$0.629329\pi$
$174$	16.3500	1.23949
$175$	−0.870010	−0.0657666
$176$	−2.81458	−0.212157
$177$	12.2898	0.923762
$178$	−15.4004	−1.15431
$179$	−26.6599	−1.99265	−0.996326	−	0.0856454i	$-0.972705\pi$
$179$	−26.6599	−1.99265	−0.996326	+	0.0856454i	$0.972705\pi$
$180$	−12.9759	−0.967164
$181$	−14.5419	−1.08089	−0.540446	−	0.841379i	$-0.681744\pi$
$181$	−14.5419	−1.08089	−0.540446	+	0.841379i	$0.681744\pi$
$182$	0.422088	0.0312872
$183$	4.85946	0.359221
$184$	−2.64823	−0.195230
$185$	11.5558	0.849598
$186$	8.07759	0.592278
$187$	3.23018	0.236214
$188$	15.6583	1.14200
$189$	−0.0653339	−0.00475234
$190$	−71.5538	−5.19106
$191$	10.3079	0.745853	0.372927	−	0.927861i	$-0.378354\pi$
$191$	10.3079	0.745853	0.372927	+	0.927861i	$0.378354\pi$
$192$	−13.0268	−0.940127
$193$	1.90532	0.137148	0.0685741	−	0.997646i	$-0.478155\pi$
$193$	1.90532	0.137148	0.0685741	+	0.997646i	$0.478155\pi$
$194$	19.3971	1.39263
$195$	12.3259	0.882675
$196$	−21.2104	−1.51503
$197$	5.83384	0.415644	0.207822	−	0.978167i	$-0.433363\pi$
$197$	5.83384	0.415644	0.207822	+	0.978167i	$0.433363\pi$
$198$	7.24592	0.514945
$199$	5.83516	0.413643	0.206822	−	0.978379i	$-0.433688\pi$
$199$	5.83516	0.413643	0.206822	+	0.978379i	$0.433688\pi$
$200$	30.8244	2.17961
$201$	−7.91890	−0.558556
$202$	−30.5941	−2.15259
$203$	−0.476200	−0.0334227
$204$	3.03191	0.212276
$205$	−54.3742	−3.79766
$206$	16.0744	1.11996
$207$	−1.14406	−0.0795175
$208$	2.50949	0.174002
$209$	24.0754	1.66533
$210$	0.627227	0.0432828
$211$	−7.24857	−0.499012	−0.249506	−	0.968373i	$-0.580268\pi$
$211$	−7.24857	−0.499012	−0.249506	+	0.968373i	$0.580268\pi$
$212$	−24.5343	−1.68502
$213$	1.84117	0.126155
$214$	21.0474	1.43877
$215$	−11.2953	−0.770331
$216$	2.31477	0.157500
$217$	−0.235263	−0.0159707
$218$	18.9737	1.28506
$219$	−2.31371	−0.156346
$220$	−41.9144	−2.82587
$221$	−2.88004	−0.193732
$222$	−6.05684	−0.406508
$223$	−15.7699	−1.05603	−0.528014	−	0.849235i	$-0.677063\pi$
$223$	−15.7699	−1.05603	−0.528014	+	0.849235i	$0.677063\pi$
$224$	0.430167	0.0287417
$225$	13.3164	0.887759
$226$	−8.85181	−0.588813
$227$	−11.1561	−0.740457	−0.370228	−	0.928941i	$-0.620721\pi$
$227$	−11.1561	−0.740457	−0.370228	+	0.928941i	$0.620721\pi$
$228$	22.5976	1.49657
$229$	−2.46171	−0.162674	−0.0813370	−	0.996687i	$-0.525919\pi$
$229$	−2.46171	−0.162674	−0.0813370	+	0.996687i	$0.525919\pi$
$230$	10.9833	0.724219
$231$	−0.211040	−0.0138854
$232$	16.8717	1.10768
$233$	6.94093	0.454716	0.227358	−	0.973811i	$-0.426991\pi$
$233$	6.94093	0.454716	0.227358	+	0.973811i	$0.426991\pi$
$234$	−6.46048	−0.422335
$235$	−22.1029	−1.44183
$236$	37.2617	2.42553
$237$	1.00000	0.0649570
$238$	−0.146556	−0.00949984
$239$	10.5045	0.679479	0.339739	−	0.940520i	$-0.389661\pi$
$239$	10.5045	0.679479	0.339739	+	0.940520i	$0.389661\pi$
$240$	3.72913	0.240714
$241$	25.0266	1.61210	0.806052	−	0.591844i	$-0.201600\pi$
$241$	25.0266	1.61210	0.806052	+	0.591844i	$0.201600\pi$
$242$	−1.26949	−0.0816061
$243$	1.00000	0.0641500
$244$	14.7334	0.943212
$245$	29.9401	1.91280
$246$	28.4996	1.81707
$247$	−21.4657	−1.36583
$248$	8.33535	0.529295
$249$	11.4658	0.726612
$250$	−79.8400	−5.04952
$251$	−17.4686	−1.10261	−0.551303	−	0.834305i	$-0.685869\pi$
$251$	−17.4686	−1.10261	−0.551303	+	0.834305i	$0.685869\pi$
$252$	−0.198086	−0.0124783
$253$	−3.69551	−0.232335
$254$	−39.9285	−2.50534
$255$	−4.27976	−0.268009
$256$	−9.95712	−0.622320
$257$	16.5472	1.03219	0.516094	−	0.856532i	$-0.327386\pi$
$257$	16.5472	1.03219	0.516094	+	0.856532i	$0.327386\pi$
$258$	5.92030	0.368582
$259$	0.176408	0.0109614
$260$	37.3710	2.31765
$261$	7.28872	0.451160
$262$	33.9319	2.09632
$263$	1.84760	0.113928	0.0569640	−	0.998376i	$-0.481858\pi$
$263$	1.84760	0.113928	0.0569640	+	0.998376i	$0.481858\pi$
$264$	7.47714	0.460186
$265$	34.6319	2.12742
$266$	−1.09232	−0.0669747
$267$	−6.86540	−0.420156
$268$	−24.0094	−1.46661
$269$	25.0351	1.52642	0.763209	−	0.646152i	$-0.223623\pi$
$269$	25.0351	1.52642	0.763209	+	0.646152i	$0.223623\pi$
$270$	−9.60033	−0.584258
$271$	−0.0889911	−0.00540583	−0.00270291	−	0.999996i	$-0.500860\pi$
$271$	−0.0889911	−0.00540583	−0.00270291	+	0.999996i	$0.500860\pi$
$272$	−0.871339	−0.0528327
$273$	0.188164	0.0113882
$274$	24.5537	1.48334
$275$	43.0143	2.59386
$276$	−3.46868	−0.208790
$277$	3.46495	0.208189	0.104094	−	0.994567i	$-0.466806\pi$
$277$	3.46495	0.208189	0.104094	+	0.994567i	$0.466806\pi$
$278$	−13.1414	−0.788168
$279$	3.60094	0.215582
$280$	0.647242	0.0386801
$281$	−20.4218	−1.21826	−0.609131	−	0.793070i	$-0.708482\pi$
$281$	−20.4218	−1.21826	−0.609131	+	0.793070i	$0.708482\pi$
$282$	11.5850	0.689876
$283$	10.7287	0.637755	0.318878	−	0.947796i	$-0.396694\pi$
$283$	10.7287	0.637755	0.318878	+	0.947796i	$0.396694\pi$
$284$	5.58227	0.331247
$285$	−31.8982	−1.88949
$286$	−20.8685	−1.23398
$287$	−0.830063	−0.0489971
$288$	−6.58413	−0.387974
$289$	1.00000	0.0588235
$290$	−69.9741	−4.10902
$291$	8.64709	0.506901
$292$	−7.01497	−0.410520
$293$	31.7647	1.85571	0.927857	−	0.372937i	$-0.121649\pi$
$293$	31.7647	1.85571	0.927857	+	0.372937i	$0.121649\pi$
$294$	−15.6928	−0.915221
$295$	−52.5977	−3.06235
$296$	−6.25011	−0.363281
$297$	3.23018	0.187434
$298$	50.0927	2.90179
$299$	3.29493	0.190551
$300$	40.3741	2.33100
$301$	−0.172431	−0.00993876
$302$	−12.0120	−0.691214
$303$	−13.6386	−0.783520
$304$	−6.49432	−0.372475
$305$	−20.7973	−1.19085
$306$	2.24319	0.128235
$307$	−24.8838	−1.42019	−0.710097	−	0.704104i	$-0.751349\pi$
$307$	−24.8838	−1.42019	−0.710097	+	0.704104i	$0.751349\pi$
$308$	−0.639855	−0.0364591
$309$	7.16588	0.407653
$310$	−34.5702	−1.96345
$311$	1.31464	0.0745465	0.0372732	−	0.999305i	$-0.488133\pi$
$311$	1.31464	0.0745465	0.0372732	+	0.999305i	$0.488133\pi$
$312$	−6.66663	−0.377424
$313$	−25.5573	−1.44459	−0.722293	−	0.691588i	$-0.756912\pi$
$313$	−25.5573	−1.44459	−0.722293	+	0.691588i	$0.756912\pi$
$314$	−40.1449	−2.26551
$315$	0.279613	0.0157544
$316$	3.03191	0.170558
$317$	−15.9302	−0.894730	−0.447365	−	0.894351i	$-0.647638\pi$
$317$	−15.9302	−0.894730	−0.447365	+	0.894351i	$0.647638\pi$
$318$	−18.1520	−1.01791
$319$	23.5439	1.31820
$320$	55.7516	3.11661
$321$	9.38280	0.523697
$322$	0.167669	0.00934382
$323$	7.45327	0.414711
$324$	3.03191	0.168439
$325$	−38.3517	−2.12737
$326$	24.7875	1.37285
$327$	8.45836	0.467748
$328$	29.4091	1.62384
$329$	−0.337417	−0.0186024
$330$	−31.0108	−1.70709
$331$	14.8737	0.817534	0.408767	−	0.912639i	$-0.365959\pi$
$331$	14.8737	0.817534	0.408767	+	0.912639i	$0.365959\pi$
$332$	34.7631	1.90787
$333$	−2.70010	−0.147964
$334$	−26.2284	−1.43515
$335$	33.8910	1.85166
$336$	0.0569280	0.00310567
$337$	−1.91722	−0.104437	−0.0522187	−	0.998636i	$-0.516629\pi$
$337$	−1.91722	−0.104437	−0.0522187	+	0.998636i	$0.516629\pi$
$338$	−10.5551	−0.574121
$339$	−3.94608	−0.214321
$340$	−12.9759	−0.703715
$341$	11.6317	0.629890
$342$	16.7191	0.904066
$343$	0.914395	0.0493727
$344$	6.10922	0.329387
$345$	4.89629	0.263608
$346$	−23.3211	−1.25375
$347$	−23.3849	−1.25537	−0.627685	−	0.778468i	$-0.715997\pi$
$347$	−23.3849	−1.25537	−0.627685	+	0.778468i	$0.715997\pi$
$348$	22.0987	1.18462
$349$	24.9527	1.33569	0.667844	−	0.744301i	$-0.267217\pi$
$349$	24.9527	1.33569	0.667844	+	0.744301i	$0.267217\pi$
$350$	−1.95160	−0.104317
$351$	−2.88004	−0.153725
$352$	−21.2679	−1.13358
$353$	13.0410	0.694102	0.347051	−	0.937846i	$-0.387183\pi$
$353$	13.0410	0.694102	0.347051	+	0.937846i	$0.387183\pi$
$354$	27.5685	1.46525
$355$	−7.87978	−0.418215
$356$	−20.8153	−1.10321
$357$	−0.0653339	−0.00345783
$358$	−59.8032	−3.16070
$359$	−21.4840	−1.13388	−0.566941	−	0.823758i	$-0.691873\pi$
$359$	−21.4840	−1.13388	−0.566941	+	0.823758i	$0.691873\pi$
$360$	−9.90668	−0.522128
$361$	36.5512	1.92375
$362$	−32.6203	−1.71449
$363$	−0.565931	−0.0297037
$364$	0.570496	0.0299021
$365$	9.90214	0.518302
$366$	10.9007	0.569788
$367$	−10.7360	−0.560415	−0.280208	−	0.959939i	$-0.590403\pi$
$367$	−10.7360	−0.560415	−0.280208	+	0.959939i	$0.590403\pi$
$368$	0.996862	0.0519650
$369$	12.7049	0.661393
$370$	25.9218	1.34761
$371$	0.528683	0.0274478
$372$	10.9177	0.566057
$373$	−19.7906	−1.02472	−0.512359	−	0.858772i	$-0.671228\pi$
$373$	−19.7906	−1.02472	−0.512359	+	0.858772i	$0.671228\pi$
$374$	7.24592	0.374677
$375$	−35.5921	−1.83797
$376$	11.9547	0.616515
$377$	−20.9918	−1.08113
$378$	−0.146556	−0.00753805
$379$	3.13241	0.160901	0.0804505	−	0.996759i	$-0.474364\pi$
$379$	3.13241	0.160901	0.0804505	+	0.996759i	$0.474364\pi$
$380$	−96.7125	−4.96125
$381$	−17.7999	−0.911915
$382$	23.1226	1.18305
$383$	22.7645	1.16321	0.581606	−	0.813471i	$-0.302425\pi$
$383$	22.7645	1.16321	0.581606	+	0.813471i	$0.302425\pi$
$384$	−16.0533	−0.819218
$385$	0.903202	0.0460314
$386$	4.27401	0.217541
$387$	2.63923	0.134160
$388$	26.2172	1.33098
$389$	28.5165	1.44584	0.722921	−	0.690931i	$-0.242799\pi$
$389$	28.5165	1.44584	0.722921	+	0.690931i	$0.242799\pi$
$390$	27.6493	1.40008
$391$	−1.14406	−0.0578575
$392$	−16.1935	−0.817897
$393$	15.1266	0.763037
$394$	13.0864	0.659285
$395$	−4.27976	−0.215338
$396$	9.79362	0.492148
$397$	36.9626	1.85510	0.927550	−	0.373699i	$-0.121911\pi$
$397$	36.9626	1.85510	0.927550	+	0.373699i	$0.121911\pi$
$398$	13.0894	0.656111
$399$	−0.486951	−0.0243780
$400$	−11.6031	−0.580154
$401$	−14.5668	−0.727430	−0.363715	−	0.931510i	$-0.618492\pi$
$401$	−14.5668	−0.727430	−0.363715	+	0.931510i	$0.618492\pi$
$402$	−17.7636	−0.885969
$403$	−10.3708	−0.516608
$404$	−41.3512	−2.05730
$405$	−4.27976	−0.212663
$406$	−1.06821	−0.0530143
$407$	−8.72180	−0.432324
$408$	2.31477	0.114598
$409$	−37.0354	−1.83128	−0.915640	−	0.401998i	$-0.868316\pi$
$409$	−37.0354	−1.83128	−0.915640	+	0.401998i	$0.868316\pi$
$410$	−121.972	−6.02375
$411$	10.9459	0.539919
$412$	21.7263	1.07038
$413$	−0.802943	−0.0395103
$414$	−2.56634	−0.126129
$415$	−49.0707	−2.40879
$416$	18.9625	0.929715
$417$	−5.85835	−0.286884
$418$	54.0057	2.64151
$419$	38.5543	1.88350	0.941751	−	0.336311i	$-0.109179\pi$
$419$	38.5543	1.88350	0.941751	+	0.336311i	$0.109179\pi$
$420$	0.847763	0.0413666
$421$	11.8642	0.578223	0.289112	−	0.957295i	$-0.406640\pi$
$421$	11.8642	0.578223	0.289112	+	0.957295i	$0.406640\pi$
$422$	−16.2599	−0.791522
$423$	5.16451	0.251107
$424$	−18.7312	−0.909667
$425$	13.3164	0.645939
$426$	4.13010	0.200104
$427$	−0.317487	−0.0153643
$428$	28.4478	1.37508
$429$	−9.30304	−0.449155
$430$	−25.3375	−1.22188
$431$	−36.6782	−1.76672	−0.883362	−	0.468691i	$-0.844726\pi$
$431$	−36.6782	−1.76672	−0.883362	+	0.468691i	$0.844726\pi$
$432$	−0.871339	−0.0419223
$433$	5.95020	0.285948	0.142974	−	0.989726i	$-0.454333\pi$
$433$	5.95020	0.285948	0.142974	+	0.989726i	$0.454333\pi$
$434$	−0.527740	−0.0253323
$435$	−31.1940	−1.49564
$436$	25.6450	1.22817
$437$	−8.52696	−0.407900
$438$	−5.19010	−0.247993
$439$	8.10451	0.386807	0.193404	−	0.981119i	$-0.438047\pi$
$439$	8.10451	0.386807	0.193404	+	0.981119i	$0.438047\pi$
$440$	−32.0004	−1.52556
$441$	−6.99573	−0.333130
$442$	−6.46048	−0.307294
$443$	−7.36079	−0.349722	−0.174861	−	0.984593i	$-0.555948\pi$
$443$	−7.36079	−0.349722	−0.174861	+	0.984593i	$0.555948\pi$
$444$	−8.18645	−0.388512
$445$	29.3823	1.39285
$446$	−35.3749	−1.67505
$447$	22.3310	1.05622
$448$	0.851090	0.0402102
$449$	7.87811	0.371791	0.185895	−	0.982570i	$-0.440481\pi$
$449$	7.87811	0.371791	0.185895	+	0.982570i	$0.440481\pi$
$450$	29.8712	1.40814
$451$	41.0393	1.93246
$452$	−11.9642	−0.562746
$453$	−5.35488	−0.251594
$454$	−25.0253	−1.17450
$455$	−0.805297	−0.0377529
$456$	17.2526	0.807928
$457$	−29.7161	−1.39006	−0.695030	−	0.718981i	$-0.744609\pi$
$457$	−29.7161	−1.39006	−0.695030	+	0.718981i	$0.744609\pi$
$458$	−5.52208	−0.258030
$459$	1.00000	0.0466760
$460$	14.8451	0.692158
$461$	29.8469	1.39011	0.695053	−	0.718958i	$-0.255381\pi$
$461$	29.8469	1.39011	0.695053	+	0.718958i	$0.255381\pi$
$462$	−0.473404	−0.0220247
$463$	−21.1974	−0.985126	−0.492563	−	0.870277i	$-0.663940\pi$
$463$	−21.1974	−0.985126	−0.492563	+	0.870277i	$0.663940\pi$
$464$	−6.35095	−0.294835
$465$	−15.4112	−0.714675
$466$	15.5698	0.721259
$467$	−35.0045	−1.61982	−0.809908	−	0.586557i	$-0.800483\pi$
$467$	−35.0045	−1.61982	−0.809908	+	0.586557i	$0.800483\pi$
$468$	−8.73202	−0.403638
$469$	0.517372	0.0238900
$470$	−49.5810	−2.28700
$471$	−17.8963	−0.824619
$472$	28.4482	1.30944
$473$	8.52519	0.391988
$474$	2.24319	0.103033
$475$	99.2505	4.55393
$476$	−0.198086	−0.00907928
$477$	−8.09202	−0.370508
$478$	23.5636	1.07777
$479$	−9.11379	−0.416419	−0.208210	−	0.978084i	$-0.566764\pi$
$479$	−9.11379	−0.416419	−0.208210	+	0.978084i	$0.566764\pi$
$480$	28.1785	1.28617
$481$	7.77638	0.354572
$482$	56.1395	2.55708
$483$	0.0747457	0.00340105
$484$	−1.71585	−0.0779933
$485$	−37.0075	−1.68042
$486$	2.24319	0.101753
$487$	8.56392	0.388068	0.194034	−	0.980995i	$-0.437843\pi$
$487$	8.56392	0.388068	0.194034	+	0.980995i	$0.437843\pi$
$488$	11.2485	0.509197
$489$	11.0501	0.499703
$490$	67.1613	3.03404
$491$	−13.8472	−0.624917	−0.312458	−	0.949931i	$-0.601152\pi$
$491$	−13.8472	−0.624917	−0.312458	+	0.949931i	$0.601152\pi$
$492$	38.5203	1.73663
$493$	7.28872	0.328267
$494$	−48.1517	−2.16645
$495$	−13.8244	−0.621361
$496$	−3.13764	−0.140884
$497$	−0.120291	−0.00539578
$498$	25.7199	1.15254
$499$	−41.5122	−1.85834	−0.929171	−	0.369650i	$-0.879478\pi$
$499$	−41.5122	−1.85834	−0.929171	+	0.369650i	$0.879478\pi$
$500$	−107.912	−4.82598
$501$	−11.6924	−0.522380
$502$	−39.1853	−1.74893
$503$	17.2207	0.767833	0.383917	−	0.923368i	$-0.374575\pi$
$503$	17.2207	0.767833	0.383917	+	0.923368i	$0.374575\pi$
$504$	−0.151233	−0.00673646
$505$	58.3702	2.59744
$506$	−8.28974	−0.368524
$507$	−4.70538	−0.208973
$508$	−53.9676	−2.39442
$509$	−33.8186	−1.49898	−0.749491	−	0.662014i	$-0.769702\pi$
$509$	−33.8186	−1.49898	−0.749491	+	0.662014i	$0.769702\pi$
$510$	−9.60033	−0.425110
$511$	0.151164	0.00668709
$512$	9.77092	0.431818
$513$	7.45327	0.329070
$514$	37.1186	1.63723
$515$	−30.6683	−1.35141
$516$	8.00191	0.352264
$517$	16.6823	0.733687
$518$	0.395717	0.0173868
$519$	−10.3964	−0.456351
$520$	28.5316	1.25119
$521$	1.22209	0.0535409	0.0267705	−	0.999642i	$-0.491478\pi$
$521$	1.22209	0.0535409	0.0267705	+	0.999642i	$0.491478\pi$
$522$	16.3500	0.715620
$523$	−16.2375	−0.710017	−0.355009	−	0.934863i	$-0.615522\pi$
$523$	−16.2375	−0.710017	−0.355009	+	0.934863i	$0.615522\pi$
$524$	45.8626	2.00351
$525$	−0.870010	−0.0379704
$526$	4.14453	0.180710
$527$	3.60094	0.156859
$528$	−2.81458	−0.122489
$529$	−21.6911	−0.943093
$530$	77.6861	3.37447
$531$	12.2898	0.533334
$532$	−1.47639	−0.0640097
$533$	−36.5907	−1.58492
$534$	−15.4004	−0.666441
$535$	−40.1562	−1.73610
$536$	−18.3305	−0.791755
$537$	−26.6599	−1.15046
$538$	56.1586	2.42117
$539$	−22.5975	−0.973342
$540$	−12.9759	−0.558392
$541$	−31.0112	−1.33328	−0.666638	−	0.745382i	$-0.732267\pi$
$541$	−31.0112	−1.33328	−0.666638	+	0.745382i	$0.732267\pi$
$542$	−0.199624	−0.00857459
$543$	−14.5419	−0.624053
$544$	−6.58413	−0.282292
$545$	−36.1998	−1.55063
$546$	0.422088	0.0180637
$547$	−7.23456	−0.309328	−0.154664	−	0.987967i	$-0.549429\pi$
$547$	−7.23456	−0.309328	−0.154664	+	0.987967i	$0.549429\pi$
$548$	33.1869	1.41767
$549$	4.85946	0.207397
$550$	96.4894	4.11432
$551$	54.3247	2.31431
$552$	−2.64823	−0.112716
$553$	−0.0653339	−0.00277828
$554$	7.77255	0.330224
$555$	11.5558	0.490516
$556$	−17.7620	−0.753276
$557$	16.7212	0.708501	0.354250	−	0.935151i	$-0.384736\pi$
$557$	16.7212	0.708501	0.354250	+	0.935151i	$0.384736\pi$
$558$	8.07759	0.341952
$559$	−7.60108	−0.321491
$560$	−0.243638	−0.0102956
$561$	3.23018	0.136378
$562$	−45.8100	−1.93238
$563$	8.37738	0.353064	0.176532	−	0.984295i	$-0.443512\pi$
$563$	8.37738	0.353064	0.176532	+	0.984295i	$0.443512\pi$
$564$	15.6583	0.659335
$565$	16.8883	0.710495
$566$	24.0665	1.01159
$567$	−0.0653339	−0.00274376
$568$	4.26189	0.178825
$569$	−6.47451	−0.271426	−0.135713	−	0.990748i	$-0.543332\pi$
$569$	−6.47451	−0.271426	−0.135713	+	0.990748i	$0.543332\pi$
$570$	−71.5538	−2.99706
$571$	−5.08808	−0.212930	−0.106465	−	0.994316i	$-0.533953\pi$
$571$	−5.08808	−0.212930	−0.106465	+	0.994316i	$0.533953\pi$
$572$	−28.2060	−1.17935
$573$	10.3079	0.430619
$574$	−1.86199	−0.0777180
$575$	−15.2347	−0.635331
$576$	−13.0268	−0.542783
$577$	26.9593	1.12233	0.561166	−	0.827703i	$-0.310353\pi$
$577$	26.9593	1.12233	0.561166	+	0.827703i	$0.310353\pi$
$578$	2.24319	0.0933045
$579$	1.90532	0.0791825
$580$	−94.5774	−3.92711
$581$	−0.749102	−0.0310780
$582$	19.3971	0.804035
$583$	−26.1387	−1.08255
$584$	−5.35572	−0.221621
$585$	12.3259	0.509612
$586$	71.2543	2.94349
$587$	−7.56818	−0.312372	−0.156186	−	0.987728i	$-0.549920\pi$
$587$	−7.56818	−0.312372	−0.156186	+	0.987728i	$0.549920\pi$
$588$	−21.2104	−0.874703
$589$	26.8387	1.10587
$590$	−117.987	−4.85743
$591$	5.83384	0.239972
$592$	2.35270	0.0966954
$593$	33.8791	1.39125	0.695624	−	0.718406i	$-0.255128\pi$
$593$	33.8791	1.39125	0.695624	+	0.718406i	$0.255128\pi$
$594$	7.24592	0.297304
$595$	0.279613	0.0114630
$596$	67.7056	2.77333
$597$	5.83516	0.238817
$598$	7.39115	0.302247
$599$	−30.1074	−1.23015	−0.615077	−	0.788467i	$-0.710875\pi$
$599$	−30.1074	−1.23015	−0.615077	+	0.788467i	$0.710875\pi$
$600$	30.8244	1.25840
$601$	−5.03682	−0.205456	−0.102728	−	0.994709i	$-0.532757\pi$
$601$	−5.03682	−0.205456	−0.102728	+	0.994709i	$0.532757\pi$
$602$	−0.386796	−0.0157646
$603$	−7.91890	−0.322483
$604$	−16.2355	−0.660614
$605$	2.42205	0.0984705
$606$	−30.5941	−1.24280
$607$	−10.2109	−0.414448	−0.207224	−	0.978294i	$-0.566443\pi$
$607$	−10.2109	−0.414448	−0.207224	+	0.978294i	$0.566443\pi$
$608$	−49.0733	−1.99018
$609$	−0.476200	−0.0192966
$610$	−46.6524	−1.88890
$611$	−14.8740	−0.601737
$612$	3.03191	0.122558
$613$	5.75216	0.232328	0.116164	−	0.993230i	$-0.462940\pi$
$613$	5.75216	0.232328	0.116164	+	0.993230i	$0.462940\pi$
$614$	−55.8192	−2.25268
$615$	−54.3742	−2.19258
$616$	−0.488510	−0.0196826
$617$	−40.0191	−1.61111	−0.805555	−	0.592521i	$-0.798133\pi$
$617$	−40.0191	−1.61111	−0.805555	+	0.592521i	$0.798133\pi$
$618$	16.0744	0.646609
$619$	6.83554	0.274744	0.137372	−	0.990520i	$-0.456134\pi$
$619$	6.83554	0.274744	0.137372	+	0.990520i	$0.456134\pi$
$620$	−46.7252	−1.87653
$621$	−1.14406	−0.0459094
$622$	2.94899	0.118244
$623$	0.448543	0.0179705
$624$	2.50949	0.100460
$625$	85.7440	3.42976
$626$	−57.3300	−2.29137
$627$	24.0754	0.961479
$628$	−54.2601	−2.16521
$629$	−2.70010	−0.107660
$630$	0.627227	0.0249893
$631$	11.9665	0.476378	0.238189	−	0.971219i	$-0.423446\pi$
$631$	11.9665	0.476378	0.238189	+	0.971219i	$0.423446\pi$
$632$	2.31477	0.0920767
$633$	−7.24857	−0.288105
$634$	−35.7345	−1.41920
$635$	76.1792	3.02308
$636$	−24.5343	−0.972847
$637$	20.1480	0.798292
$638$	52.8134	2.09090
$639$	1.84117	0.0728356
$640$	68.7044	2.71578
$641$	20.3054	0.802017	0.401008	−	0.916074i	$-0.368660\pi$
$641$	20.3054	0.802017	0.401008	+	0.916074i	$0.368660\pi$
$642$	21.0474	0.830676
$643$	−6.76980	−0.266975	−0.133487	−	0.991051i	$-0.542618\pi$
$643$	−6.76980	−0.266975	−0.133487	+	0.991051i	$0.542618\pi$
$644$	0.226622	0.00893016
$645$	−11.2953	−0.444751
$646$	16.7191	0.657804
$647$	−10.7095	−0.421034	−0.210517	−	0.977590i	$-0.567515\pi$
$647$	−10.7095	−0.421034	−0.210517	+	0.977590i	$0.567515\pi$
$648$	2.31477	0.0909329
$649$	39.6984	1.55830
$650$	−86.0302	−3.37438
$651$	−0.235263	−0.00922068
$652$	33.5029	1.31208
$653$	32.8301	1.28474	0.642371	−	0.766393i	$-0.277951\pi$
$653$	32.8301	1.28474	0.642371	+	0.766393i	$0.277951\pi$
$654$	18.9737	0.741932
$655$	−64.7383	−2.52954
$656$	−11.0703	−0.432223
$657$	−2.31371	−0.0902665
$658$	−0.756892	−0.0295067
$659$	27.9870	1.09022	0.545110	−	0.838365i	$-0.316488\pi$
$659$	27.9870	1.09022	0.545110	+	0.838365i	$0.316488\pi$
$660$	−41.9144	−1.63151
$661$	3.39998	0.132244	0.0661219	−	0.997812i	$-0.478937\pi$
$661$	3.39998	0.132244	0.0661219	+	0.997812i	$0.478937\pi$
$662$	33.3646	1.29675
$663$	−2.88004	−0.111851
$664$	26.5406	1.02998
$665$	2.08403	0.0808154
$666$	−6.05684	−0.234698
$667$	−8.33871	−0.322876
$668$	−35.4504	−1.37162
$669$	−15.7699	−0.609699
$670$	76.0241	2.93707
$671$	15.6969	0.605973
$672$	0.430167	0.0165940
$673$	−34.9002	−1.34530	−0.672651	−	0.739960i	$-0.734845\pi$
$673$	−34.9002	−1.34530	−0.672651	+	0.739960i	$0.734845\pi$
$674$	−4.30069	−0.165656
$675$	13.3164	0.512548
$676$	−14.2663	−0.548704
$677$	44.6542	1.71620	0.858100	−	0.513482i	$-0.171645\pi$
$677$	44.6542	1.71620	0.858100	+	0.513482i	$0.171645\pi$
$678$	−8.85181	−0.339952
$679$	−0.564948	−0.0216807
$680$	−9.90668	−0.379904
$681$	−11.1561	−0.427503
$682$	26.0921	0.999117
$683$	0.715961	0.0273955	0.0136978	−	0.999906i	$-0.495640\pi$
$683$	0.715961	0.0273955	0.0136978	+	0.999906i	$0.495640\pi$
$684$	22.5976	0.864042
$685$	−46.8457	−1.78988
$686$	2.05116	0.0783138
$687$	−2.46171	−0.0939199
$688$	−2.29966	−0.0876739
$689$	23.3053	0.887862
$690$	10.9833	0.418128
$691$	11.3132	0.430375	0.215187	−	0.976573i	$-0.430964\pi$
$691$	11.3132	0.430375	0.215187	+	0.976573i	$0.430964\pi$
$692$	−31.5210	−1.19825
$693$	−0.211040	−0.00801675
$694$	−52.4569	−1.99124
$695$	25.0723	0.951048
$696$	16.8717	0.639521
$697$	12.7049	0.481234
$698$	55.9737	2.11864
$699$	6.94093	0.262530
$700$	−2.63779	−0.0996992
$701$	39.4997	1.49188	0.745942	−	0.666011i	$-0.231999\pi$
$701$	39.4997	1.49188	0.745942	+	0.666011i	$0.231999\pi$
$702$	−6.46048	−0.243835
$703$	−20.1245	−0.759012
$704$	−42.0789	−1.58591
$705$	−22.1029	−0.832443
$706$	29.2535	1.10097
$707$	0.891065	0.0335120
$708$	37.2617	1.40038
$709$	7.83441	0.294227	0.147114	−	0.989120i	$-0.453002\pi$
$709$	7.83441	0.294227	0.147114	+	0.989120i	$0.453002\pi$
$710$	−17.6759	−0.663363
$711$	1.00000	0.0375029
$712$	−15.8919	−0.595572
$713$	−4.11968	−0.154283
$714$	−0.146556	−0.00548473
$715$	39.8148	1.48899
$716$	−80.8303	−3.02077
$717$	10.5045	0.392297
$718$	−48.1928	−1.79854
$719$	0.919912	0.0343069	0.0171535	−	0.999853i	$-0.494540\pi$
$719$	0.919912	0.0343069	0.0171535	+	0.999853i	$0.494540\pi$
$720$	3.72913	0.138976
$721$	−0.468175	−0.0174357
$722$	81.9913	3.05140
$723$	25.0266	0.930749
$724$	−44.0898	−1.63858
$725$	97.0593	3.60469
$726$	−1.26949	−0.0471153
$727$	18.6452	0.691511	0.345756	−	0.938325i	$-0.387623\pi$
$727$	18.6452	0.691511	0.345756	+	0.938325i	$0.387623\pi$
$728$	0.435557	0.0161428
$729$	1.00000	0.0370370
$730$	22.2124	0.822118
$731$	2.63923	0.0976154
$732$	14.7334	0.544563
$733$	−42.2388	−1.56013	−0.780064	−	0.625700i	$-0.784813\pi$
$733$	−42.2388	−1.56013	−0.780064	+	0.625700i	$0.784813\pi$
$734$	−24.0829	−0.888917
$735$	29.9401	1.10436
$736$	7.53262	0.277656
$737$	−25.5795	−0.942232
$738$	28.4996	1.04909
$739$	−42.2571	−1.55445	−0.777227	−	0.629221i	$-0.783374\pi$
$739$	−42.2571	−1.55445	−0.777227	+	0.629221i	$0.783374\pi$
$740$	35.0361	1.28795
$741$	−21.4657	−0.788562
$742$	1.18594	0.0435371
$743$	2.82361	0.103588	0.0517941	−	0.998658i	$-0.483506\pi$
$743$	2.82361	0.103588	0.0517941	+	0.998658i	$0.483506\pi$
$744$	8.33535	0.305589
$745$	−95.5714	−3.50147
$746$	−44.3941	−1.62538
$747$	11.4658	0.419510
$748$	9.79362	0.358090
$749$	−0.613015	−0.0223991
$750$	−79.8400	−2.91534
$751$	40.7594	1.48733	0.743665	−	0.668552i	$-0.233086\pi$
$751$	40.7594	1.48733	0.743665	+	0.668552i	$0.233086\pi$
$752$	−4.50004	−0.164100
$753$	−17.4686	−0.636590
$754$	−47.0886	−1.71487
$755$	22.9176	0.834058
$756$	−0.198086	−0.00720433
$757$	16.7162	0.607560	0.303780	−	0.952742i	$-0.401751\pi$
$757$	16.7162	0.607560	0.303780	+	0.952742i	$0.401751\pi$
$758$	7.02660	0.255217
$759$	−3.69551	−0.134139
$760$	−73.8372	−2.67836
$761$	−31.3212	−1.13539	−0.567696	−	0.823238i	$-0.692165\pi$
$761$	−31.3212	−1.13539	−0.567696	+	0.823238i	$0.692165\pi$
$762$	−39.9285	−1.44646
$763$	−0.552617	−0.0200061
$764$	31.2526	1.13068
$765$	−4.27976	−0.154735
$766$	51.0651	1.84506
$767$	−35.3952	−1.27805
$768$	−9.95712	−0.359297
$769$	55.1421	1.98848	0.994238	−	0.107199i	$-0.0341883\pi$
$769$	55.1421	1.98848	0.994238	+	0.107199i	$0.0341883\pi$
$770$	2.02606	0.0730140
$771$	16.5472	0.595934
$772$	5.77677	0.207910
$773$	−20.2070	−0.726795	−0.363397	−	0.931634i	$-0.618383\pi$
$773$	−20.2070	−0.726795	−0.363397	+	0.931634i	$0.618383\pi$
$774$	5.92030	0.212801
$775$	47.9514	1.72247
$776$	20.0161	0.718535
$777$	0.176408	0.00632859
$778$	63.9679	2.29336
$779$	94.6933	3.39274
$780$	37.3710	1.33810
$781$	5.94732	0.212812
$782$	−2.56634	−0.0917721
$783$	7.28872	0.260477
$784$	6.09566	0.217702
$785$	76.5920	2.73369
$786$	33.9319	1.21031
$787$	−20.9602	−0.747151	−0.373576	−	0.927600i	$-0.621868\pi$
$787$	−20.9602	−0.747151	−0.373576	+	0.927600i	$0.621868\pi$
$788$	17.6877	0.630098
$789$	1.84760	0.0657764
$790$	−9.60033	−0.341564
$791$	0.257812	0.00916675
$792$	7.47714	0.265689
$793$	−13.9954	−0.496992
$794$	82.9142	2.94252
$795$	34.6319	1.22827
$796$	17.6917	0.627065
$797$	−16.4859	−0.583962	−0.291981	−	0.956424i	$-0.594314\pi$
$797$	−16.4859	−0.583962	−0.291981	+	0.956424i	$0.594314\pi$
$798$	−1.09232	−0.0386678
$799$	5.16451	0.182707
$800$	−87.6768	−3.09984
$801$	−6.86540	−0.242577
$802$	−32.6761	−1.15383
$803$	−7.47371	−0.263741
$804$	−24.0094	−0.846746
$805$	−0.319894	−0.0112748
$806$	−23.2638	−0.819431
$807$	25.0351	0.881278
$808$	−31.5704	−1.11064
$809$	3.19727	0.112410	0.0562050	−	0.998419i	$-0.482100\pi$
$809$	3.19727	0.112410	0.0562050	+	0.998419i	$0.482100\pi$
$810$	−9.60033	−0.337321
$811$	52.9353	1.85881	0.929404	−	0.369064i	$-0.120322\pi$
$811$	52.9353	1.85881	0.929404	+	0.369064i	$0.120322\pi$
$812$	−1.44380	−0.0506673
$813$	−0.0889911	−0.00312106
$814$	−19.5647	−0.685742
$815$	−47.2919	−1.65656
$816$	−0.871339	−0.0305030
$817$	19.6709	0.688197
$818$	−83.0774	−2.90473
$819$	0.188164	0.00657498
$820$	−164.858	−5.75708
$821$	−10.3302	−0.360528	−0.180264	−	0.983618i	$-0.557695\pi$
$821$	−10.3302	−0.360528	−0.180264	+	0.983618i	$0.557695\pi$
$822$	24.5537	0.856407
$823$	−20.5023	−0.714665	−0.357333	−	0.933977i	$-0.616314\pi$
$823$	−20.5023	−0.714665	−0.357333	+	0.933977i	$0.616314\pi$
$824$	16.5874	0.577849
$825$	43.0143	1.49757
$826$	−1.80116	−0.0626702
$827$	16.2558	0.565271	0.282636	−	0.959227i	$-0.408791\pi$
$827$	16.2558	0.565271	0.282636	+	0.959227i	$0.408791\pi$
$828$	−3.46868	−0.120545
$829$	44.2832	1.53802	0.769010	−	0.639237i	$-0.220750\pi$
$829$	44.2832	1.53802	0.769010	+	0.639237i	$0.220750\pi$
$830$	−110.075	−3.82076
$831$	3.46495	0.120198
$832$	37.5176	1.30069
$833$	−6.99573	−0.242388
$834$	−13.1414	−0.455049
$835$	50.0409	1.73174
$836$	72.9945	2.52457
$837$	3.60094	0.124467
$838$	86.4847	2.98757
$839$	−3.09167	−0.106736	−0.0533681	−	0.998575i	$-0.516996\pi$
$839$	−3.09167	−0.106736	−0.0533681	+	0.998575i	$0.516996\pi$
$840$	0.647242	0.0223320
$841$	24.1254	0.831910
$842$	26.6136	0.917164
$843$	−20.4218	−0.703364
$844$	−21.9770	−0.756480
$845$	20.1379	0.692766
$846$	11.5850	0.398300
$847$	0.0369745	0.00127046
$848$	7.05089	0.242129
$849$	10.7287	0.368208
$850$	29.8712	1.02457
$851$	3.08907	0.105892
$852$	5.58227	0.191245
$853$	−54.8783	−1.87900	−0.939499	−	0.342551i	$-0.888709\pi$
$853$	−54.8783	−1.87900	−0.939499	+	0.342551i	$0.888709\pi$
$854$	−0.712184	−0.0243704
$855$	−31.8982	−1.09090
$856$	21.7191	0.742343
$857$	1.62498	0.0555083	0.0277541	−	0.999615i	$-0.491164\pi$
$857$	1.62498	0.0555083	0.0277541	+	0.999615i	$0.491164\pi$
$858$	−20.8685	−0.712439
$859$	−8.63692	−0.294688	−0.147344	−	0.989085i	$-0.547072\pi$
$859$	−8.63692	−0.294688	−0.147344	+	0.989085i	$0.547072\pi$
$860$	−34.2463	−1.16779
$861$	−0.830063	−0.0282885
$862$	−82.2761	−2.80234
$863$	−37.1114	−1.26329	−0.631643	−	0.775259i	$-0.717619\pi$
$863$	−37.1114	−1.26329	−0.631643	+	0.775259i	$0.717619\pi$
$864$	−6.58413	−0.223997
$865$	44.4941	1.51285
$866$	13.3474	0.453565
$867$	1.00000	0.0339618
$868$	−0.713296	−0.0242109
$869$	3.23018	0.109576
$870$	−69.9741	−2.37234
$871$	22.8067	0.772777
$872$	19.5792	0.663035
$873$	8.64709	0.292660
$874$	−19.1276	−0.647001
$875$	2.32537	0.0786119
$876$	−7.01497	−0.237014
$877$	9.62427	0.324989	0.162494	−	0.986709i	$-0.448046\pi$
$877$	9.62427	0.324989	0.162494	+	0.986709i	$0.448046\pi$
$878$	18.1800	0.613544
$879$	31.7647	1.07140
$880$	12.0458	0.406062
$881$	16.4726	0.554977	0.277489	−	0.960729i	$-0.410498\pi$
$881$	16.4726	0.554977	0.277489	+	0.960729i	$0.410498\pi$
$882$	−15.6928	−0.528403
$883$	23.4669	0.789724	0.394862	−	0.918741i	$-0.370792\pi$
$883$	23.4669	0.789724	0.394862	+	0.918741i	$0.370792\pi$
$884$	−8.73202	−0.293689
$885$	−52.5977	−1.76805
$886$	−16.5117	−0.554720
$887$	46.3409	1.55598	0.777988	−	0.628279i	$-0.216240\pi$
$887$	46.3409	1.55598	0.777988	+	0.628279i	$0.216240\pi$
$888$	−6.25011	−0.209740
$889$	1.16293	0.0390035
$890$	65.9101	2.20931
$891$	3.23018	0.108215
$892$	−47.8129	−1.60089
$893$	38.4925	1.28810
$894$	50.0927	1.67535
$895$	114.098	3.81387
$896$	1.04883	0.0350388
$897$	3.29493	0.110014
$898$	17.6721	0.589726
$899$	26.2462	0.875360
$900$	40.3741	1.34580
$901$	−8.09202	−0.269584
$902$	92.0590	3.06523
$903$	−0.172431	−0.00573814
$904$	−9.13427	−0.303801
$905$	62.2360	2.06879
$906$	−12.0120	−0.399073
$907$	18.7815	0.623631	0.311815	−	0.950143i	$-0.399063\pi$
$907$	18.7815	0.623631	0.311815	+	0.950143i	$0.399063\pi$
$908$	−33.8243	−1.12250
$909$	−13.6386	−0.452365
$910$	−1.80644	−0.0598828
$911$	10.9307	0.362152	0.181076	−	0.983469i	$-0.442042\pi$
$911$	10.9307	0.362152	0.181076	+	0.983469i	$0.442042\pi$
$912$	−6.49432	−0.215049
$913$	37.0365	1.22573
$914$	−66.6589	−2.20488
$915$	−20.7973	−0.687538
$916$	−7.46367	−0.246607
$917$	−0.988280	−0.0326359
$918$	2.24319	0.0740364
$919$	18.8356	0.621330	0.310665	−	0.950519i	$-0.399448\pi$
$919$	18.8356	0.621330	0.310665	+	0.950519i	$0.399448\pi$
$920$	11.3338	0.373665
$921$	−24.8838	−0.819949
$922$	66.9522	2.20495
$923$	−5.30264	−0.174539
$924$	−0.639855	−0.0210497
$925$	−35.9555	−1.18221
$926$	−47.5498	−1.56258
$927$	7.16588	0.235358
$928$	−47.9899	−1.57534
$929$	13.5613	0.444933	0.222466	−	0.974940i	$-0.428589\pi$
$929$	13.5613	0.444933	0.222466	+	0.974940i	$0.428589\pi$
$930$	−34.5702	−1.13360
$931$	−52.1410	−1.70885
$932$	21.0443	0.689328
$933$	1.31464	0.0430394
$934$	−78.5218	−2.56931
$935$	−13.8244	−0.452107
$936$	−6.66663	−0.217906
$937$	−37.2320	−1.21632	−0.608158	−	0.793816i	$-0.708091\pi$
$937$	−37.2320	−1.21632	−0.608158	+	0.793816i	$0.708091\pi$
$938$	1.16057	0.0378938
$939$	−25.5573	−0.834032
$940$	−67.0140	−2.18575
$941$	52.2433	1.70308	0.851542	−	0.524287i	$-0.175668\pi$
$941$	52.2433	1.70308	0.851542	+	0.524287i	$0.175668\pi$
$942$	−40.1449	−1.30799
$943$	−14.5352	−0.473331
$944$	−10.7086	−0.348536
$945$	0.279613	0.00909583
$946$	19.1236	0.621763
$947$	−23.1081	−0.750912	−0.375456	−	0.926840i	$-0.622514\pi$
$947$	−23.1081	−0.750912	−0.375456	+	0.926840i	$0.622514\pi$
$948$	3.03191	0.0984719
$949$	6.66357	0.216309
$950$	222.638	7.22333
$951$	−15.9302	−0.516573
$952$	−0.151233	−0.00490149
$953$	−30.5266	−0.988855	−0.494427	−	0.869219i	$-0.664622\pi$
$953$	−30.5266	−0.988855	−0.494427	+	0.869219i	$0.664622\pi$
$954$	−18.1520	−0.587691
$955$	−44.1154	−1.42754
$956$	31.8487	1.03006
$957$	23.5439	0.761065
$958$	−20.4440	−0.660515
$959$	−0.715135	−0.0230929
$960$	55.7516	1.79937
$961$	−18.0333	−0.581718
$962$	17.4439	0.562414
$963$	9.38280	0.302357
$964$	75.8784	2.44388
$965$	−8.15433	−0.262497
$966$	0.167669	0.00539466
$967$	−28.5510	−0.918137	−0.459069	−	0.888401i	$-0.651817\pi$
$967$	−28.5510	−0.918137	−0.459069	+	0.888401i	$0.651817\pi$
$968$	−1.31000	−0.0421051
$969$	7.45327	0.239433
$970$	−83.0150	−2.66545
$971$	−57.0453	−1.83067	−0.915336	−	0.402691i	$-0.868075\pi$
$971$	−57.0453	−1.83067	−0.915336	+	0.402691i	$0.868075\pi$
$972$	3.03191	0.0972486
$973$	0.382748	0.0122703
$974$	19.2105	0.615545
$975$	−38.3517	−1.22824
$976$	−4.23424	−0.135535
$977$	13.8746	0.443889	0.221945	−	0.975059i	$-0.428760\pi$
$977$	13.8746	0.443889	0.221945	+	0.975059i	$0.428760\pi$
$978$	24.7875	0.792617
$979$	−22.1765	−0.708764
$980$	90.7756	2.89972
$981$	8.45836	0.270055
$982$	−31.0620	−0.991228
$983$	−24.8229	−0.791728	−0.395864	−	0.918309i	$-0.629555\pi$
$983$	−24.8229	−0.791728	−0.395864	+	0.918309i	$0.629555\pi$
$984$	29.4091	0.937527
$985$	−24.9675	−0.795530
$986$	16.3500	0.520690
$987$	−0.337417	−0.0107401
$988$	−65.0820	−2.07054
$989$	−3.01943	−0.0960122
$990$	−31.0108	−0.985588
$991$	38.1462	1.21175	0.605877	−	0.795558i	$-0.292822\pi$
$991$	38.1462	1.21175	0.605877	+	0.795558i	$0.292822\pi$
$992$	−23.7090	−0.752762
$993$	14.8737	0.472003
$994$	−0.269835	−0.00855866
$995$	−24.9731	−0.791701
$996$	34.7631	1.10151
$997$	−7.97553	−0.252588	−0.126294	−	0.991993i	$-0.540308\pi$
$997$	−7.97553	−0.252588	−0.126294	+	0.991993i	$0.540308\pi$
$998$	−93.1199	−2.94766
$999$	−2.70010	−0.0854273

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.k.1.26	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.k.1.26	✓	31	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q+2.24319 q^{2} +1.00000 q^{3} +3.03191 q^{4} -4.27976 q^{5} +2.24319 q^{6} -0.0653339 q^{7} +2.31477 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.24319 q^{2} +1.00000 q^{3} +3.03191 q^{4} -4.27976 q^{5} +2.24319 q^{6} -0.0653339 q^{7} +2.31477 q^{8} +1.00000 q^{9} -9.60033 q^{10} +3.23018 q^{11} +3.03191 q^{12} -2.88004 q^{13} -0.146556 q^{14} -4.27976 q^{15} -0.871339 q^{16} +1.00000 q^{17} +2.24319 q^{18} +7.45327 q^{19} -12.9759 q^{20} -0.0653339 q^{21} +7.24592 q^{22} -1.14406 q^{23} +2.31477 q^{24} +13.3164 q^{25} -6.46048 q^{26} +1.00000 q^{27} -0.198086 q^{28} +7.28872 q^{29} -9.60033 q^{30} +3.60094 q^{31} -6.58413 q^{32} +3.23018 q^{33} +2.24319 q^{34} +0.279613 q^{35} +3.03191 q^{36} -2.70010 q^{37} +16.7191 q^{38} -2.88004 q^{39} -9.90668 q^{40} +12.7049 q^{41} -0.146556 q^{42} +2.63923 q^{43} +9.79362 q^{44} -4.27976 q^{45} -2.56634 q^{46} +5.16451 q^{47} -0.871339 q^{48} -6.99573 q^{49} +29.8712 q^{50} +1.00000 q^{51} -8.73202 q^{52} -8.09202 q^{53} +2.24319 q^{54} -13.8244 q^{55} -0.151233 q^{56} +7.45327 q^{57} +16.3500 q^{58} +12.2898 q^{59} -12.9759 q^{60} +4.85946 q^{61} +8.07759 q^{62} -0.0653339 q^{63} -13.0268 q^{64} +12.3259 q^{65} +7.24592 q^{66} -7.91890 q^{67} +3.03191 q^{68} -1.14406 q^{69} +0.627227 q^{70} +1.84117 q^{71} +2.31477 q^{72} -2.31371 q^{73} -6.05684 q^{74} +13.3164 q^{75} +22.5976 q^{76} -0.211040 q^{77} -6.46048 q^{78} +1.00000 q^{79} +3.72913 q^{80} +1.00000 q^{81} +28.4996 q^{82} +11.4658 q^{83} -0.198086 q^{84} -4.27976 q^{85} +5.92030 q^{86} +7.28872 q^{87} +7.47714 q^{88} -6.86540 q^{89} -9.60033 q^{90} +0.188164 q^{91} -3.46868 q^{92} +3.60094 q^{93} +11.5850 q^{94} -31.8982 q^{95} -6.58413 q^{96} +8.64709 q^{97} -15.6928 q^{98} +3.23018 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9}+O(q^{10}) \) 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9	\( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9} + 5 q^{10} + 26 q^{11} + 34 q^{12} + 7 q^{13} + 19 q^{14} + 11 q^{15} + 40 q^{16} + 31 q^{17} + 4 q^{18} + 32 q^{19} + 23 q^{20} + 4 q^{21} + 2 q^{22} + 29 q^{23} + 12 q^{24} + 32 q^{25} + 13 q^{26} + 31 q^{27} - 13 q^{28} + 25 q^{29} + 5 q^{30} + 22 q^{31} + 28 q^{32} + 26 q^{33} + 4 q^{34} + 20 q^{35} + 34 q^{36} - 4 q^{37} + 19 q^{38} + 7 q^{39} - 3 q^{40} + 33 q^{41} + 19 q^{42} + 6 q^{43} + 30 q^{44} + 11 q^{45} - 11 q^{46} + 23 q^{47} + 40 q^{48} + 31 q^{49} + 6 q^{50} + 31 q^{51} - 7 q^{52} + 12 q^{53} + 4 q^{54} + 40 q^{56} + 32 q^{57} + 9 q^{58} + 27 q^{59} + 23 q^{60} - 4 q^{61} + 25 q^{62} + 4 q^{63} + 10 q^{64} + 54 q^{65} + 2 q^{66} + 34 q^{68} + 29 q^{69} - 59 q^{70} + 35 q^{71} + 12 q^{72} + 5 q^{73} + 48 q^{74} + 32 q^{75} + 32 q^{76} + 42 q^{77} + 13 q^{78} + 31 q^{79} + 24 q^{80} + 31 q^{81} + 5 q^{82} + 67 q^{83} - 13 q^{84} + 11 q^{85} - 20 q^{86} + 25 q^{87} - 7 q^{88} + 22 q^{89} + 5 q^{90} + 16 q^{91} + 57 q^{92} + 22 q^{93} + 45 q^{94} + 73 q^{95} + 28 q^{96} - 13 q^{97} - 19 q^{98} + 26 q^{99}+O(q^{100}) \) 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9 + 5 * q^10 + 26 * q^11 + 34 * q^12 + 7 * q^13 + 19 * q^14 + 11 * q^15 + 40 * q^16 + 31 * q^17 + 4 * q^18 + 32 * q^19 + 23 * q^20 + 4 * q^21 + 2 * q^22 + 29 * q^23 + 12 * q^24 + 32 * q^25 + 13 * q^26 + 31 * q^27 - 13 * q^28 + 25 * q^29 + 5 * q^30 + 22 * q^31 + 28 * q^32 + 26 * q^33 + 4 * q^34 + 20 * q^35 + 34 * q^36 - 4 * q^37 + 19 * q^38 + 7 * q^39 - 3 * q^40 + 33 * q^41 + 19 * q^42 + 6 * q^43 + 30 * q^44 + 11 * q^45 - 11 * q^46 + 23 * q^47 + 40 * q^48 + 31 * q^49 + 6 * q^50 + 31 * q^51 - 7 * q^52 + 12 * q^53 + 4 * q^54 + 40 * q^56 + 32 * q^57 + 9 * q^58 + 27 * q^59 + 23 * q^60 - 4 * q^61 + 25 * q^62 + 4 * q^63 + 10 * q^64 + 54 * q^65 + 2 * q^66 + 34 * q^68 + 29 * q^69 - 59 * q^70 + 35 * q^71 + 12 * q^72 + 5 * q^73 + 48 * q^74 + 32 * q^75 + 32 * q^76 + 42 * q^77 + 13 * q^78 + 31 * q^79 + 24 * q^80 + 31 * q^81 + 5 * q^82 + 67 * q^83 - 13 * q^84 + 11 * q^85 - 20 * q^86 + 25 * q^87 - 7 * q^88 + 22 * q^89 + 5 * q^90 + 16 * q^91 + 57 * q^92 + 22 * q^93 + 45 * q^94 + 73 * q^95 + 28 * q^96 - 13 * q^97 - 19 * q^98 + 26 * q^99

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