LMFDB - Embedded newform 4029.2.a.g.1.14

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:	$1$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
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)

$f(q)$	$=$	$q+0.977627 q^{2} -1.00000 q^{3} -1.04425 q^{4} +4.02352 q^{5} -0.977627 q^{6} +0.138355 q^{7} -2.97614 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.977627 q^{2} -1.00000 q^{3} -1.04425 q^{4} +4.02352 q^{5} -0.977627 q^{6} +0.138355 q^{7} -2.97614 q^{8} +1.00000 q^{9} +3.93350 q^{10} -4.85148 q^{11} +1.04425 q^{12} +2.81682 q^{13} +0.135260 q^{14} -4.02352 q^{15} -0.821062 q^{16} -1.00000 q^{17} +0.977627 q^{18} -3.91212 q^{19} -4.20154 q^{20} -0.138355 q^{21} -4.74294 q^{22} -0.0160329 q^{23} +2.97614 q^{24} +11.1887 q^{25} +2.75380 q^{26} -1.00000 q^{27} -0.144477 q^{28} -3.77713 q^{29} -3.93350 q^{30} -7.69082 q^{31} +5.14958 q^{32} +4.85148 q^{33} -0.977627 q^{34} +0.556675 q^{35} -1.04425 q^{36} +3.10164 q^{37} -3.82460 q^{38} -2.81682 q^{39} -11.9745 q^{40} +1.60052 q^{41} -0.135260 q^{42} -6.22254 q^{43} +5.06614 q^{44} +4.02352 q^{45} -0.0156742 q^{46} -8.70629 q^{47} +0.821062 q^{48} -6.98086 q^{49} +10.9384 q^{50} +1.00000 q^{51} -2.94145 q^{52} +6.26321 q^{53} -0.977627 q^{54} -19.5200 q^{55} -0.411765 q^{56} +3.91212 q^{57} -3.69262 q^{58} +2.78358 q^{59} +4.20154 q^{60} -7.55238 q^{61} -7.51875 q^{62} +0.138355 q^{63} +6.67649 q^{64} +11.3335 q^{65} +4.74294 q^{66} -8.87257 q^{67} +1.04425 q^{68} +0.0160329 q^{69} +0.544221 q^{70} +7.42016 q^{71} -2.97614 q^{72} -2.37305 q^{73} +3.03224 q^{74} -11.1887 q^{75} +4.08522 q^{76} -0.671229 q^{77} -2.75380 q^{78} -1.00000 q^{79} -3.30356 q^{80} +1.00000 q^{81} +1.56471 q^{82} -13.2800 q^{83} +0.144477 q^{84} -4.02352 q^{85} -6.08333 q^{86} +3.77713 q^{87} +14.4387 q^{88} -12.8483 q^{89} +3.93350 q^{90} +0.389723 q^{91} +0.0167423 q^{92} +7.69082 q^{93} -8.51151 q^{94} -15.7405 q^{95} -5.14958 q^{96} +2.90390 q^{97} -6.82468 q^{98} -4.85148 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 2 q^{2} - 22 q^{3} + 16 q^{4} + 5 q^{5} - 2 q^{6} - 4 q^{7} + 6 q^{8} + 22 q^{9}+O(q^{10}) $ 22 * q + 2 * q^2 - 22 * q^3 + 16 * q^4 + 5 * q^5 - 2 * q^6 - 4 * q^7 + 6 * q^8 + 22 * q^9	\( 22 q + 2 q^{2} - 22 q^{3} + 16 q^{4} + 5 q^{5} - 2 q^{6} - 4 q^{7} + 6 q^{8} + 22 q^{9} - 5 q^{10} - 2 q^{11} - 16 q^{12} - 11 q^{13} - 7 q^{14} - 5 q^{15} - 22 q^{17} + 2 q^{18} - 36 q^{19} + 4 q^{21} - 9 q^{22} + 21 q^{23} - 6 q^{24} + 9 q^{25} - 16 q^{26} - 22 q^{27} - 17 q^{28} - q^{29} + 5 q^{30} - 12 q^{31} - 11 q^{32} + 2 q^{33} - 2 q^{34} - 14 q^{35} + 16 q^{36} - 6 q^{37} + q^{38} + 11 q^{39} - 24 q^{40} - 17 q^{41} + 7 q^{42} - 36 q^{43} + 16 q^{44} + 5 q^{45} - 23 q^{46} - 17 q^{47} - 6 q^{49} - 33 q^{50} + 22 q^{51} - 57 q^{52} - 2 q^{53} - 2 q^{54} - 24 q^{55} - 64 q^{56} + 36 q^{57} - 7 q^{58} - 59 q^{59} - 30 q^{61} - 4 q^{62} - 4 q^{63} - 22 q^{64} + 36 q^{65} + 9 q^{66} - 16 q^{67} - 16 q^{68} - 21 q^{69} - 39 q^{70} - 11 q^{71} + 6 q^{72} - 19 q^{73} - 28 q^{74} - 9 q^{75} - 77 q^{76} + 2 q^{77} + 16 q^{78} - 22 q^{79} - 2 q^{80} + 22 q^{81} + 33 q^{82} - 23 q^{83} + 17 q^{84} - 5 q^{85} + 6 q^{86} + q^{87} - 23 q^{88} + 12 q^{89} - 5 q^{90} - 24 q^{91} + 66 q^{92} + 12 q^{93} - 61 q^{94} - 11 q^{95} + 11 q^{96} - 9 q^{97} + 17 q^{98} - 2 q^{99}+O(q^{100}) \) 22 * q + 2 * q^2 - 22 * q^3 + 16 * q^4 + 5 * q^5 - 2 * q^6 - 4 * q^7 + 6 * q^8 + 22 * q^9 - 5 * q^10 - 2 * q^11 - 16 * q^12 - 11 * q^13 - 7 * q^14 - 5 * q^15 - 22 * q^17 + 2 * q^18 - 36 * q^19 + 4 * q^21 - 9 * q^22 + 21 * q^23 - 6 * q^24 + 9 * q^25 - 16 * q^26 - 22 * q^27 - 17 * q^28 - q^29 + 5 * q^30 - 12 * q^31 - 11 * q^32 + 2 * q^33 - 2 * q^34 - 14 * q^35 + 16 * q^36 - 6 * q^37 + q^38 + 11 * q^39 - 24 * q^40 - 17 * q^41 + 7 * q^42 - 36 * q^43 + 16 * q^44 + 5 * q^45 - 23 * q^46 - 17 * q^47 - 6 * q^49 - 33 * q^50 + 22 * q^51 - 57 * q^52 - 2 * q^53 - 2 * q^54 - 24 * q^55 - 64 * q^56 + 36 * q^57 - 7 * q^58 - 59 * q^59 - 30 * q^61 - 4 * q^62 - 4 * q^63 - 22 * q^64 + 36 * q^65 + 9 * q^66 - 16 * q^67 - 16 * q^68 - 21 * q^69 - 39 * q^70 - 11 * q^71 + 6 * q^72 - 19 * q^73 - 28 * q^74 - 9 * q^75 - 77 * q^76 + 2 * q^77 + 16 * q^78 - 22 * q^79 - 2 * q^80 + 22 * q^81 + 33 * q^82 - 23 * q^83 + 17 * q^84 - 5 * q^85 + 6 * q^86 + q^87 - 23 * q^88 + 12 * q^89 - 5 * q^90 - 24 * q^91 + 66 * q^92 + 12 * q^93 - 61 * q^94 - 11 * q^95 + 11 * q^96 - 9 * q^97 + 17 * q^98 - 2 * 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 $

$2$	0.977627	0.691287	0.345643	−	0.938366i	$-0.387661\pi$
$2$	0.977627	0.691287	0.345643	+	0.938366i	$0.387661\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.04425	−0.522123
$5$	4.02352	1.79937	0.899686	−	0.436538i	$-0.143796\pi$
$5$	4.02352	1.79937	0.899686	+	0.436538i	$0.143796\pi$
$6$	−0.977627	−0.399115
$7$	0.138355	0.0522934	0.0261467	−	0.999658i	$-0.491676\pi$
$7$	0.138355	0.0522934	0.0261467	+	0.999658i	$0.491676\pi$
$8$	−2.97614	−1.05222
$9$	1.00000	0.333333
$10$	3.93350	1.24388
$11$	−4.85148	−1.46278	−0.731389	−	0.681961i	$-0.761127\pi$
$11$	−4.85148	−1.46278	−0.731389	+	0.681961i	$0.761127\pi$
$12$	1.04425	0.301448
$13$	2.81682	0.781246	0.390623	−	0.920551i	$-0.372260\pi$
$13$	2.81682	0.781246	0.390623	+	0.920551i	$0.372260\pi$
$14$	0.135260	0.0361498
$15$	−4.02352	−1.03887
$16$	−0.821062	−0.205266
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	0.977627	0.230429
$19$	−3.91212	−0.897503	−0.448751	−	0.893657i	$-0.648131\pi$
$19$	−3.91212	−0.897503	−0.448751	+	0.893657i	$0.648131\pi$
$20$	−4.20154	−0.939492
$21$	−0.138355	−0.0301916
$22$	−4.74294	−1.01120
$23$	−0.0160329	−0.00334309	−0.00167155	−	0.999999i	$-0.500532\pi$
$23$	−0.0160329	−0.00334309	−0.00167155	+	0.999999i	$0.500532\pi$
$24$	2.97614	0.607501
$25$	11.1887	2.23774
$26$	2.75380	0.540065
$27$	−1.00000	−0.192450
$28$	−0.144477	−0.0273036
$29$	−3.77713	−0.701395	−0.350698	−	0.936489i	$-0.614056\pi$
$29$	−3.77713	−0.701395	−0.350698	+	0.936489i	$0.614056\pi$
$30$	−3.93350	−0.718155
$31$	−7.69082	−1.38131	−0.690656	−	0.723184i	$-0.742678\pi$
$31$	−7.69082	−1.38131	−0.690656	+	0.723184i	$0.742678\pi$
$32$	5.14958	0.910326
$33$	4.85148	0.844535
$34$	−0.977627	−0.167662
$35$	0.556675	0.0940953
$36$	−1.04425	−0.174041
$37$	3.10164	0.509906	0.254953	−	0.966953i	$-0.417940\pi$
$37$	3.10164	0.509906	0.254953	+	0.966953i	$0.417940\pi$
$38$	−3.82460	−0.620432
$39$	−2.81682	−0.451053
$40$	−11.9745	−1.89334
$41$	1.60052	0.249959	0.124979	−	0.992159i	$-0.460114\pi$
$41$	1.60052	0.249959	0.124979	+	0.992159i	$0.460114\pi$
$42$	−0.135260	−0.0208711
$43$	−6.22254	−0.948929	−0.474464	−	0.880275i	$-0.657358\pi$
$43$	−6.22254	−0.948929	−0.474464	+	0.880275i	$0.657358\pi$
$44$	5.06614	0.763749
$45$	4.02352	0.599790
$46$	−0.0156742	−0.00231104
$47$	−8.70629	−1.26994	−0.634972	−	0.772535i	$-0.718988\pi$
$47$	−8.70629	−1.26994	−0.634972	+	0.772535i	$0.718988\pi$
$48$	0.821062	0.118510
$49$	−6.98086	−0.997265
$50$	10.9384	1.54692
$51$	1.00000	0.140028
$52$	−2.94145	−0.407906
$53$	6.26321	0.860318	0.430159	−	0.902753i	$-0.358458\pi$
$53$	6.26321	0.860318	0.430159	+	0.902753i	$0.358458\pi$
$54$	−0.977627	−0.133038
$55$	−19.5200	−2.63208
$56$	−0.411765	−0.0550244
$57$	3.91212	0.518173
$58$	−3.69262	−0.484865
$59$	2.78358	0.362391	0.181196	−	0.983447i	$-0.442003\pi$
$59$	2.78358	0.362391	0.181196	+	0.983447i	$0.442003\pi$
$60$	4.20154	0.542416
$61$	−7.55238	−0.966983	−0.483491	−	0.875349i	$-0.660632\pi$
$61$	−7.55238	−0.966983	−0.483491	+	0.875349i	$0.660632\pi$
$62$	−7.51875	−0.954882
$63$	0.138355	0.0174311
$64$	6.67649	0.834562
$65$	11.3335	1.40575
$66$	4.74294	0.583816
$67$	−8.87257	−1.08396	−0.541978	−	0.840392i	$-0.682325\pi$
$67$	−8.87257	−1.08396	−0.541978	+	0.840392i	$0.682325\pi$
$68$	1.04425	0.126633
$69$	0.0160329	0.00193014
$70$	0.544221	0.0650469
$71$	7.42016	0.880611	0.440305	−	0.897848i	$-0.354870\pi$
$71$	7.42016	0.880611	0.440305	+	0.897848i	$0.354870\pi$
$72$	−2.97614	−0.350741
$73$	−2.37305	−0.277745	−0.138872	−	0.990310i	$-0.544348\pi$
$73$	−2.37305	−0.277745	−0.138872	+	0.990310i	$0.544348\pi$
$74$	3.03224	0.352491
$75$	−11.1887	−1.29196
$76$	4.08522	0.468606
$77$	−0.671229	−0.0764937
$78$	−2.75380	−0.311807
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	−3.30356	−0.369349
$81$	1.00000	0.111111
$82$	1.56471	0.172793
$83$	−13.2800	−1.45767	−0.728835	−	0.684689i	$-0.759938\pi$
$83$	−13.2800	−1.45767	−0.728835	+	0.684689i	$0.759938\pi$
$84$	0.144477	0.0157637
$85$	−4.02352	−0.436412
$86$	−6.08333	−0.655982
$87$	3.77713	0.404951
$88$	14.4387	1.53917
$89$	−12.8483	−1.36192	−0.680960	−	0.732320i	$-0.738437\pi$
$89$	−12.8483	−1.36192	−0.680960	+	0.732320i	$0.738437\pi$
$90$	3.93350	0.414627
$91$	0.389723	0.0408541
$92$	0.0167423	0.00174550
$93$	7.69082	0.797500
$94$	−8.51151	−0.877895
$95$	−15.7405	−1.61494
$96$	−5.14958	−0.525577
$97$	2.90390	0.294847	0.147423	−	0.989073i	$-0.452902\pi$
$97$	2.90390	0.294847	0.147423	+	0.989073i	$0.452902\pi$
$98$	−6.82468	−0.689396
$99$	−4.85148	−0.487592
$100$	−11.6837	−1.16837
$101$	−4.45311	−0.443101	−0.221550	−	0.975149i	$-0.571112\pi$
$101$	−4.45311	−0.443101	−0.221550	+	0.975149i	$0.571112\pi$
$102$	0.977627	0.0967995
$103$	13.9882	1.37830	0.689150	−	0.724619i	$-0.257984\pi$
$103$	13.9882	1.37830	0.689150	+	0.724619i	$0.257984\pi$
$104$	−8.38325	−0.822045
$105$	−0.556675	−0.0543260
$106$	6.12308	0.594726
$107$	4.62338	0.446959	0.223480	−	0.974709i	$-0.428258\pi$
$107$	4.62338	0.446959	0.223480	+	0.974709i	$0.428258\pi$
$108$	1.04425	0.100483
$109$	15.8049	1.51383	0.756916	−	0.653512i	$-0.226705\pi$
$109$	15.8049	1.51383	0.756916	+	0.653512i	$0.226705\pi$
$110$	−19.0833	−1.81952
$111$	−3.10164	−0.294394
$112$	−0.113598	−0.0107340
$113$	−5.98168	−0.562709	−0.281355	−	0.959604i	$-0.590784\pi$
$113$	−5.98168	−0.562709	−0.281355	+	0.959604i	$0.590784\pi$
$114$	3.82460	0.358206
$115$	−0.0645087	−0.00601546
$116$	3.94425	0.366214
$117$	2.81682	0.260415
$118$	2.72130	0.250516
$119$	−0.138355	−0.0126830
$120$	11.9745	1.09312
$121$	12.5369	1.13972
$122$	−7.38341	−0.668463
$123$	−1.60052	−0.144314
$124$	8.03110	0.721214
$125$	24.9003	2.22715
$126$	0.135260	0.0120499
$127$	−15.5609	−1.38081	−0.690403	−	0.723425i	$-0.742567\pi$
$127$	−15.5609	−1.38081	−0.690403	+	0.723425i	$0.742567\pi$
$128$	−3.77204	−0.333404
$129$	6.22254	0.547864
$130$	11.0800	0.971778
$131$	0.319920	0.0279516	0.0139758	−	0.999902i	$-0.495551\pi$
$131$	0.319920	0.0279516	0.0139758	+	0.999902i	$0.495551\pi$
$132$	−5.06614	−0.440951
$133$	−0.541264	−0.0469335
$134$	−8.67406	−0.749325
$135$	−4.02352	−0.346289
$136$	2.97614	0.255202
$137$	16.1378	1.37875	0.689373	−	0.724407i	$-0.257886\pi$
$137$	16.1378	1.37875	0.689373	+	0.724407i	$0.257886\pi$
$138$	0.0156742	0.00133428
$139$	0.985972	0.0836290	0.0418145	−	0.999125i	$-0.486686\pi$
$139$	0.985972	0.0836290	0.0418145	+	0.999125i	$0.486686\pi$
$140$	−0.581306	−0.0491293
$141$	8.70629	0.733202
$142$	7.25415	0.608755
$143$	−13.6658	−1.14279
$144$	−0.821062	−0.0684219
$145$	−15.1973	−1.26207
$146$	−2.31996	−0.192001
$147$	6.98086	0.575771
$148$	−3.23887	−0.266233
$149$	−9.01304	−0.738377	−0.369188	−	0.929355i	$-0.620364\pi$
$149$	−9.01304	−0.738377	−0.369188	+	0.929355i	$0.620364\pi$
$150$	−10.9384	−0.893113
$151$	23.5361	1.91534	0.957672	−	0.287862i	$-0.0929444\pi$
$151$	23.5361	1.91534	0.957672	+	0.287862i	$0.0929444\pi$
$152$	11.6430	0.944373
$153$	−1.00000	−0.0808452
$154$	−0.656212	−0.0528791
$155$	−30.9441	−2.48549
$156$	2.94145	0.235505
$157$	−12.2212	−0.975354	−0.487677	−	0.873024i	$-0.662156\pi$
$157$	−12.2212	−0.975354	−0.487677	+	0.873024i	$0.662156\pi$
$158$	−0.977627	−0.0777758
$159$	−6.26321	−0.496705
$160$	20.7194	1.63801
$161$	−0.00221824	−0.000174822 0
$162$	0.977627	0.0768096
$163$	−1.79216	−0.140373	−0.0701863	−	0.997534i	$-0.522359\pi$
$163$	−1.79216	−0.140373	−0.0701863	+	0.997534i	$0.522359\pi$
$164$	−1.67133	−0.130509
$165$	19.5200	1.51963
$166$	−12.9829	−1.00767
$167$	−20.9380	−1.62023	−0.810116	−	0.586269i	$-0.800596\pi$
$167$	−20.9380	−1.62023	−0.810116	+	0.586269i	$0.800596\pi$
$168$	0.411765	0.0317683
$169$	−5.06551	−0.389654
$170$	−3.93350	−0.301686
$171$	−3.91212	−0.299168
$172$	6.49786	0.495457
$173$	−22.8433	−1.73675	−0.868373	−	0.495911i	$-0.834834\pi$
$173$	−22.8433	−1.73675	−0.868373	+	0.495911i	$0.834834\pi$
$174$	3.69262	0.279937
$175$	1.54802	0.117019
$176$	3.98337	0.300258
$177$	−2.78358	−0.209227
$178$	−12.5609	−0.941478
$179$	11.4898	0.858787	0.429393	−	0.903118i	$-0.358727\pi$
$179$	11.4898	0.858787	0.429393	+	0.903118i	$0.358727\pi$
$180$	−4.20154	−0.313164
$181$	−6.08102	−0.451999	−0.225999	−	0.974127i	$-0.572565\pi$
$181$	−6.08102	−0.451999	−0.225999	+	0.974127i	$0.572565\pi$
$182$	0.381004	0.0282419
$183$	7.55238	0.558288
$184$	0.0477161	0.00351768
$185$	12.4795	0.917510
$186$	7.51875	0.551302
$187$	4.85148	0.354776
$188$	9.09150	0.663066
$189$	−0.138355	−0.0100639
$190$	−15.3883	−1.11639
$191$	0.665354	0.0481433	0.0240717	−	0.999710i	$-0.492337\pi$
$191$	0.665354	0.0481433	0.0240717	+	0.999710i	$0.492337\pi$
$192$	−6.67649	−0.481835
$193$	−16.7912	−1.20866	−0.604330	−	0.796734i	$-0.706559\pi$
$193$	−16.7912	−1.20866	−0.604330	+	0.796734i	$0.706559\pi$
$194$	2.83894	0.203824
$195$	−11.3335	−0.811611
$196$	7.28973	0.520695
$197$	8.87917	0.632615	0.316307	−	0.948657i	$-0.397557\pi$
$197$	8.87917	0.632615	0.316307	+	0.948657i	$0.397557\pi$
$198$	−4.74294	−0.337066
$199$	−1.94946	−0.138194	−0.0690968	−	0.997610i	$-0.522012\pi$
$199$	−1.94946	−0.138194	−0.0690968	+	0.997610i	$0.522012\pi$
$200$	−33.2991	−2.35460
$201$	8.87257	0.625823
$202$	−4.35348	−0.306310
$203$	−0.522586	−0.0366784
$204$	−1.04425	−0.0731118
$205$	6.43970	0.449768
$206$	13.6753	0.952800
$207$	−0.0160329	−0.00111436
$208$	−2.31279	−0.160363
$209$	18.9796	1.31285
$210$	−0.544221	−0.0375548
$211$	−12.7393	−0.877011	−0.438505	−	0.898729i	$-0.644492\pi$
$211$	−12.7393	−0.877011	−0.438505	+	0.898729i	$0.644492\pi$
$212$	−6.54032	−0.449191
$213$	−7.42016	−0.508421
$214$	4.51994	0.308977
$215$	−25.0365	−1.70747
$216$	2.97614	0.202500
$217$	−1.06407	−0.0722335
$218$	15.4513	1.04649
$219$	2.37305	0.160356
$220$	20.3837	1.37427
$221$	−2.81682	−0.189480
$222$	−3.03224	−0.203511
$223$	−11.1497	−0.746641	−0.373321	−	0.927702i	$-0.621781\pi$
$223$	−11.1497	−0.746641	−0.373321	+	0.927702i	$0.621781\pi$
$224$	0.712473	0.0476041
$225$	11.1887	0.745912
$226$	−5.84786	−0.388994
$227$	−4.68991	−0.311280	−0.155640	−	0.987814i	$-0.549744\pi$
$227$	−4.68991	−0.311280	−0.155640	+	0.987814i	$0.549744\pi$
$228$	−4.08522	−0.270550
$229$	−15.8696	−1.04870	−0.524348	−	0.851504i	$-0.675691\pi$
$229$	−15.8696	−1.04870	−0.524348	+	0.851504i	$0.675691\pi$
$230$	−0.0630654	−0.00415841
$231$	0.671229	0.0441636
$232$	11.2413	0.738025
$233$	−22.3730	−1.46571	−0.732853	−	0.680387i	$-0.761812\pi$
$233$	−22.3730	−1.46571	−0.732853	+	0.680387i	$0.761812\pi$
$234$	2.75380	0.180022
$235$	−35.0299	−2.28510
$236$	−2.90674	−0.189213
$237$	1.00000	0.0649570
$238$	−0.135260	−0.00876761
$239$	14.3196	0.926259	0.463129	−	0.886291i	$-0.346726\pi$
$239$	14.3196	0.926259	0.463129	+	0.886291i	$0.346726\pi$
$240$	3.30356	0.213244
$241$	−18.7706	−1.20912	−0.604561	−	0.796559i	$-0.706651\pi$
$241$	−18.7706	−1.20912	−0.604561	+	0.796559i	$0.706651\pi$
$242$	12.2564	0.787871
$243$	−1.00000	−0.0641500
$244$	7.88653	0.504884
$245$	−28.0876	−1.79445
$246$	−1.56471	−0.0997622
$247$	−11.0198	−0.701171
$248$	22.8889	1.45345
$249$	13.2800	0.841586
$250$	24.3432	1.53960
$251$	−7.58732	−0.478907	−0.239454	−	0.970908i	$-0.576968\pi$
$251$	−7.58732	−0.478907	−0.239454	+	0.970908i	$0.576968\pi$
$252$	−0.144477	−0.00910119
$253$	0.0777834	0.00489020
$254$	−15.2128	−0.954533
$255$	4.02352	0.251962
$256$	−17.0406	−1.06504
$257$	−14.2866	−0.891176	−0.445588	−	0.895238i	$-0.647005\pi$
$257$	−14.2866	−0.891176	−0.445588	+	0.895238i	$0.647005\pi$
$258$	6.08333	0.378731
$259$	0.429128	0.0266647
$260$	−11.8350	−0.733975
$261$	−3.77713	−0.233798
$262$	0.312763	0.0193225
$263$	−2.93240	−0.180820	−0.0904098	−	0.995905i	$-0.528818\pi$
$263$	−2.93240	−0.180820	−0.0904098	+	0.995905i	$0.528818\pi$
$264$	−14.4387	−0.888639
$265$	25.2001	1.54803
$266$	−0.529154	−0.0324445
$267$	12.8483	0.786305
$268$	9.26513	0.565958
$269$	13.1659	0.802739	0.401370	−	0.915916i	$-0.368534\pi$
$269$	13.1659	0.802739	0.401370	+	0.915916i	$0.368534\pi$
$270$	−3.93350	−0.239385
$271$	−1.75013	−0.106313	−0.0531564	−	0.998586i	$-0.516928\pi$
$271$	−1.75013	−0.106313	−0.0531564	+	0.998586i	$0.516928\pi$
$272$	0.821062	0.0497842
$273$	−0.389723	−0.0235871
$274$	15.7768	0.953109
$275$	−54.2817	−3.27331
$276$	−0.0167423	−0.00100777
$277$	15.8049	0.949627	0.474813	−	0.880087i	$-0.342516\pi$
$277$	15.8049	0.949627	0.474813	+	0.880087i	$0.342516\pi$
$278$	0.963913	0.0578117
$279$	−7.69082	−0.460437
$280$	−1.65674	−0.0990093
$281$	15.0483	0.897704	0.448852	−	0.893606i	$-0.351833\pi$
$281$	15.0483	0.897704	0.448852	+	0.893606i	$0.351833\pi$
$282$	8.51151	0.506853
$283$	7.56553	0.449724	0.224862	−	0.974391i	$-0.427807\pi$
$283$	7.56553	0.449724	0.224862	+	0.974391i	$0.427807\pi$
$284$	−7.74846	−0.459787
$285$	15.7405	0.932386
$286$	−13.3600	−0.789995
$287$	0.221440	0.0130712
$288$	5.14958	0.303442
$289$	1.00000	0.0588235
$290$	−14.8573	−0.872453
$291$	−2.90390	−0.170230
$292$	2.47805	0.145017
$293$	−14.9496	−0.873368	−0.436684	−	0.899615i	$-0.643847\pi$
$293$	−14.9496	−0.873368	−0.436684	+	0.899615i	$0.643847\pi$
$294$	6.82468	0.398023
$295$	11.1998	0.652076
$296$	−9.23090	−0.536535
$297$	4.85148	0.281512
$298$	−8.81139	−0.510430
$299$	−0.0451619	−0.00261178
$300$	11.6837	0.674560
$301$	−0.860922	−0.0496227
$302$	23.0096	1.32405
$303$	4.45311	0.255824
$304$	3.21210	0.184226
$305$	−30.3871	−1.73996
$306$	−0.977627	−0.0558872
$307$	25.9795	1.48273	0.741364	−	0.671104i	$-0.234179\pi$
$307$	25.9795	1.48273	0.741364	+	0.671104i	$0.234179\pi$
$308$	0.700928	0.0399391
$309$	−13.9882	−0.795762
$310$	−30.2518	−1.71819
$311$	9.75837	0.553347	0.276673	−	0.960964i	$-0.410768\pi$
$311$	9.75837	0.553347	0.276673	+	0.960964i	$0.410768\pi$
$312$	8.38325	0.474608
$313$	6.23165	0.352234	0.176117	−	0.984369i	$-0.443646\pi$
$313$	6.23165	0.352234	0.176117	+	0.984369i	$0.443646\pi$
$314$	−11.9477	−0.674250
$315$	0.556675	0.0313651
$316$	1.04425	0.0587434
$317$	31.8592	1.78939	0.894695	−	0.446678i	$-0.147393\pi$
$317$	31.8592	1.78939	0.894695	+	0.446678i	$0.147393\pi$
$318$	−6.12308	−0.343365
$319$	18.3247	1.02599
$320$	26.8630	1.50169
$321$	−4.62338	−0.258052
$322$	−0.00216861	−0.000120852 0
$323$	3.91212	0.217676
$324$	−1.04425	−0.0580136
$325$	31.5165	1.74822
$326$	−1.75206	−0.0970377
$327$	−15.8049	−0.874012
$328$	−4.76336	−0.263012
$329$	−1.20456	−0.0664097
$330$	19.0833	1.05050
$331$	8.98036	0.493605	0.246803	−	0.969066i	$-0.420620\pi$
$331$	8.98036	0.493605	0.246803	+	0.969066i	$0.420620\pi$
$332$	13.8676	0.761082
$333$	3.10164	0.169969
$334$	−20.4696	−1.12005
$335$	−35.6989	−1.95044
$336$	0.113598	0.00619730
$337$	−34.1011	−1.85760	−0.928802	−	0.370577i	$-0.879160\pi$
$337$	−34.1011	−1.85760	−0.928802	+	0.370577i	$0.879160\pi$
$338$	−4.95218	−0.269363
$339$	5.98168	0.324880
$340$	4.20154	0.227860
$341$	37.3119	2.02055
$342$	−3.82460	−0.206811
$343$	−1.93433	−0.104444
$344$	18.5191	0.998485
$345$	0.0645087	0.00347303
$346$	−22.3323	−1.20059
$347$	−19.4120	−1.04209	−0.521045	−	0.853529i	$-0.674458\pi$
$347$	−19.4120	−1.04209	−0.521045	+	0.853529i	$0.674458\pi$
$348$	−3.94425	−0.211434
$349$	−14.6684	−0.785180	−0.392590	−	0.919714i	$-0.628421\pi$
$349$	−14.6684	−0.785180	−0.392590	+	0.919714i	$0.628421\pi$
$350$	1.51338	0.0808937
$351$	−2.81682	−0.150351
$352$	−24.9831	−1.33160
$353$	18.7496	0.997943	0.498972	−	0.866618i	$-0.333711\pi$
$353$	18.7496	0.997943	0.498972	+	0.866618i	$0.333711\pi$
$354$	−2.72130	−0.144636
$355$	29.8551	1.58455
$356$	13.4168	0.711089
$357$	0.138355	0.00732255
$358$	11.2327	0.593668
$359$	13.7317	0.724734	0.362367	−	0.932036i	$-0.381969\pi$
$359$	13.7317	0.724734	0.362367	+	0.932036i	$0.381969\pi$
$360$	−11.9745	−0.631113
$361$	−3.69529	−0.194489
$362$	−5.94497	−0.312461
$363$	−12.5369	−0.658016
$364$	−0.406966	−0.0213308
$365$	−9.54802	−0.499766
$366$	7.38341	0.385937
$367$	11.6507	0.608162	0.304081	−	0.952646i	$-0.401651\pi$
$367$	11.6507	0.608162	0.304081	+	0.952646i	$0.401651\pi$
$368$	0.0131640	0.000686222 0
$369$	1.60052	0.0833196
$370$	12.2003	0.634263
$371$	0.866549	0.0449890
$372$	−8.03110	−0.416393
$373$	−6.53865	−0.338558	−0.169279	−	0.985568i	$-0.554144\pi$
$373$	−6.53865	−0.338558	−0.169279	+	0.985568i	$0.554144\pi$
$374$	4.74294	0.245252
$375$	−24.9003	−1.28584
$376$	25.9111	1.33626
$377$	−10.6395	−0.547962
$378$	−0.135260	−0.00695703
$379$	16.7661	0.861215	0.430607	−	0.902539i	$-0.358299\pi$
$379$	16.7661	0.861215	0.430607	+	0.902539i	$0.358299\pi$
$380$	16.4369	0.843197
$381$	15.5609	0.797209
$382$	0.650468	0.0332809
$383$	29.1054	1.48722	0.743608	−	0.668616i	$-0.233113\pi$
$383$	29.1054	1.48722	0.743608	+	0.668616i	$0.233113\pi$
$384$	3.77204	0.192491
$385$	−2.70070	−0.137640
$386$	−16.4156	−0.835530
$387$	−6.22254	−0.316310
$388$	−3.03239	−0.153946
$389$	8.36150	0.423945	0.211972	−	0.977276i	$-0.432011\pi$
$389$	8.36150	0.423945	0.211972	+	0.977276i	$0.432011\pi$
$390$	−11.0800	−0.561056
$391$	0.0160329	0.000810819 0
$392$	20.7760	1.04935
$393$	−0.319920	−0.0161378
$394$	8.68052	0.437318
$395$	−4.02352	−0.202445
$396$	5.06614	0.254583
$397$	−4.15020	−0.208293	−0.104146	−	0.994562i	$-0.533211\pi$
$397$	−4.15020	−0.208293	−0.104146	+	0.994562i	$0.533211\pi$
$398$	−1.90584	−0.0955314
$399$	0.541264	0.0270971
$400$	−9.18660	−0.459330
$401$	−27.5851	−1.37753	−0.688767	−	0.724983i	$-0.741848\pi$
$401$	−27.5851	−1.37753	−0.688767	+	0.724983i	$0.741848\pi$
$402$	8.67406	0.432623
$403$	−21.6637	−1.07914
$404$	4.65014	0.231353
$405$	4.02352	0.199930
$406$	−0.510895	−0.0253553
$407$	−15.0475	−0.745879
$408$	−2.97614	−0.147341
$409$	−3.27036	−0.161709	−0.0808544	−	0.996726i	$-0.525765\pi$
$409$	−3.27036	−0.161709	−0.0808544	+	0.996726i	$0.525765\pi$
$410$	6.29563	0.310919
$411$	−16.1378	−0.796019
$412$	−14.6071	−0.719641
$413$	0.385123	0.0189507
$414$	−0.0156742	−0.000770345 0
$415$	−53.4323	−2.62289
$416$	14.5055	0.711189
$417$	−0.985972	−0.0482832
$418$	18.5550	0.907553
$419$	21.1433	1.03292	0.516458	−	0.856313i	$-0.327250\pi$
$419$	21.1433	1.03292	0.516458	+	0.856313i	$0.327250\pi$
$420$	0.581306	0.0283648
$421$	−8.52801	−0.415630	−0.207815	−	0.978168i	$-0.566635\pi$
$421$	−8.52801	−0.415630	−0.207815	+	0.978168i	$0.566635\pi$
$422$	−12.4543	−0.606266
$423$	−8.70629	−0.423314
$424$	−18.6402	−0.905246
$425$	−11.1887	−0.542731
$426$	−7.25415	−0.351465
$427$	−1.04491	−0.0505669
$428$	−4.82794	−0.233367
$429$	13.6658	0.659790
$430$	−24.4764	−1.18035
$431$	17.0379	0.820689	0.410344	−	0.911931i	$-0.365408\pi$
$431$	17.0379	0.820689	0.410344	+	0.911931i	$0.365408\pi$
$432$	0.821062	0.0395034
$433$	33.2932	1.59997	0.799985	−	0.600020i	$-0.204841\pi$
$433$	33.2932	1.59997	0.799985	+	0.600020i	$0.204841\pi$
$434$	−1.04026	−0.0499341
$435$	15.1973	0.728657
$436$	−16.5042	−0.790406
$437$	0.0627227	0.00300043
$438$	2.31996	0.110852
$439$	23.9282	1.14203	0.571016	−	0.820939i	$-0.306549\pi$
$439$	23.9282	1.14203	0.571016	+	0.820939i	$0.306549\pi$
$440$	58.0943	2.76953
$441$	−6.98086	−0.332422
$442$	−2.75380	−0.130985
$443$	−31.5490	−1.49894	−0.749469	−	0.662039i	$-0.769691\pi$
$443$	−31.5490	−1.49894	−0.749469	+	0.662039i	$0.769691\pi$
$444$	3.23887	0.153710
$445$	−51.6955	−2.45060
$446$	−10.9003	−0.516143
$447$	9.01304	0.426302
$448$	0.923729	0.0436421
$449$	6.54071	0.308675	0.154338	−	0.988018i	$-0.450676\pi$
$449$	6.54071	0.308675	0.154338	+	0.988018i	$0.450676\pi$
$450$	10.9384	0.515639
$451$	−7.76488	−0.365634
$452$	6.24634	0.293803
$453$	−23.5361	−1.10582
$454$	−4.58498	−0.215184
$455$	1.56806	0.0735116
$456$	−11.6430	−0.545234
$457$	26.6219	1.24532	0.622660	−	0.782493i	$-0.286052\pi$
$457$	26.6219	1.24532	0.622660	+	0.782493i	$0.286052\pi$
$458$	−15.5146	−0.724949
$459$	1.00000	0.0466760
$460$	0.0673628	0.00314081
$461$	7.89703	0.367801	0.183901	−	0.982945i	$-0.441128\pi$
$461$	7.89703	0.367801	0.183901	+	0.982945i	$0.441128\pi$
$462$	0.656212	0.0305297
$463$	−23.9245	−1.11187	−0.555933	−	0.831227i	$-0.687639\pi$
$463$	−23.9245	−1.11187	−0.555933	+	0.831227i	$0.687639\pi$
$464$	3.10126	0.143972
$465$	30.9441	1.43500
$466$	−21.8725	−1.01322
$467$	−11.0328	−0.510538	−0.255269	−	0.966870i	$-0.582164\pi$
$467$	−11.0328	−0.510538	−0.255269	+	0.966870i	$0.582164\pi$
$468$	−2.94145	−0.135969
$469$	−1.22757	−0.0566838
$470$	−34.2462	−1.57966
$471$	12.2212	0.563121
$472$	−8.28431	−0.381316
$473$	30.1886	1.38807
$474$	0.977627	0.0449039
$475$	−43.7715	−2.00837
$476$	0.144477	0.00662209
$477$	6.26321	0.286773
$478$	13.9992	0.640311
$479$	1.94630	0.0889289	0.0444644	−	0.999011i	$-0.485842\pi$
$479$	1.94630	0.0889289	0.0444644	+	0.999011i	$0.485842\pi$
$480$	−20.7194	−0.945708
$481$	8.73676	0.398362
$482$	−18.3507	−0.835850
$483$	0.00221824	0.000100933 0
$484$	−13.0916	−0.595072
$485$	11.6839	0.530539
$486$	−0.977627	−0.0443461
$487$	25.3693	1.14959	0.574797	−	0.818296i	$-0.305081\pi$
$487$	25.3693	1.14959	0.574797	+	0.818296i	$0.305081\pi$
$488$	22.4769	1.01748
$489$	1.79216	0.0810441
$490$	−27.4592	−1.24048
$491$	−18.5482	−0.837071	−0.418535	−	0.908201i	$-0.637456\pi$
$491$	−18.5482	−0.837071	−0.418535	+	0.908201i	$0.637456\pi$
$492$	1.67133	0.0753494
$493$	3.77713	0.170113
$494$	−10.7732	−0.484710
$495$	−19.5200	−0.877360
$496$	6.31464	0.283536
$497$	1.02662	0.0460502
$498$	12.9829	0.581777
$499$	31.2133	1.39730	0.698649	−	0.715464i	$-0.253785\pi$
$499$	31.2133	1.39730	0.698649	+	0.715464i	$0.253785\pi$
$500$	−26.0020	−1.16284
$501$	20.9380	0.935442
$502$	−7.41757	−0.331062
$503$	−6.08671	−0.271393	−0.135696	−	0.990750i	$-0.543327\pi$
$503$	−6.08671	−0.271393	−0.135696	+	0.990750i	$0.543327\pi$
$504$	−0.411765	−0.0183415
$505$	−17.9172	−0.797303
$506$	0.0760431	0.00338053
$507$	5.06551	0.224967
$508$	16.2494	0.720950
$509$	−35.1086	−1.55616	−0.778080	−	0.628165i	$-0.783806\pi$
$509$	−35.1086	−1.55616	−0.778080	+	0.628165i	$0.783806\pi$
$510$	3.93350	0.174178
$511$	−0.328325	−0.0145242
$512$	−9.11531	−0.402844
$513$	3.91212	0.172724
$514$	−13.9670	−0.616058
$515$	56.2818	2.48007
$516$	−6.49786	−0.286052
$517$	42.2384	1.85764
$518$	0.419528	0.0184330
$519$	22.8433	1.00271
$520$	−33.7301	−1.47916
$521$	−2.98501	−0.130775	−0.0653877	−	0.997860i	$-0.520828\pi$
$521$	−2.98501	−0.130775	−0.0653877	+	0.997860i	$0.520828\pi$
$522$	−3.69262	−0.161622
$523$	0.636687	0.0278404	0.0139202	−	0.999903i	$-0.495569\pi$
$523$	0.636687	0.0278404	0.0139202	+	0.999903i	$0.495569\pi$
$524$	−0.334075	−0.0145941
$525$	−1.54802	−0.0675609
$526$	−2.86679	−0.124998
$527$	7.69082	0.335017
$528$	−3.98337	−0.173354
$529$	−22.9997	−0.999989
$530$	24.6363	1.07013
$531$	2.78358	0.120797
$532$	0.565212	0.0245050
$533$	4.50837	0.195279
$534$	12.5609	0.543562
$535$	18.6022	0.804245
$536$	26.4060	1.14056
$537$	−11.4898	−0.495821
$538$	12.8713	0.554923
$539$	33.8675	1.45878
$540$	4.20154	0.180805
$541$	−4.16830	−0.179209	−0.0896046	−	0.995977i	$-0.528560\pi$
$541$	−4.16830	−0.179209	−0.0896046	+	0.995977i	$0.528560\pi$
$542$	−1.71097	−0.0734927
$543$	6.08102	0.260962
$544$	−5.14958	−0.220786
$545$	63.5912	2.72395
$546$	−0.381004	−0.0163055
$547$	−0.246551	−0.0105418	−0.00527089	−	0.999986i	$-0.501678\pi$
$547$	−0.246551	−0.0105418	−0.00527089	+	0.999986i	$0.501678\pi$
$548$	−16.8518	−0.719874
$549$	−7.55238	−0.322328
$550$	−53.0673	−2.26280
$551$	14.7766	0.629504
$552$	−0.0477161	−0.00203093
$553$	−0.138355	−0.00588347
$554$	15.4513	0.656464
$555$	−12.4795	−0.529725
$556$	−1.02960	−0.0436646
$557$	−15.0093	−0.635964	−0.317982	−	0.948097i	$-0.603005\pi$
$557$	−15.0093	−0.635964	−0.317982	+	0.948097i	$0.603005\pi$
$558$	−7.51875	−0.318294
$559$	−17.5278	−0.741347
$560$	−0.457065	−0.0193145
$561$	−4.85148	−0.204830
$562$	14.7116	0.620571
$563$	12.2707	0.517148	0.258574	−	0.965991i	$-0.416747\pi$
$563$	12.2707	0.517148	0.258574	+	0.965991i	$0.416747\pi$
$564$	−9.09150	−0.382821
$565$	−24.0674	−1.01252
$566$	7.39627	0.310888
$567$	0.138355	0.00581038
$568$	−22.0834	−0.926599
$569$	38.8515	1.62874	0.814370	−	0.580346i	$-0.197083\pi$
$569$	38.8515	1.62874	0.814370	+	0.580346i	$0.197083\pi$
$570$	15.3883	0.644546
$571$	34.7866	1.45578	0.727888	−	0.685696i	$-0.240502\pi$
$571$	34.7866	1.45578	0.727888	+	0.685696i	$0.240502\pi$
$572$	14.2704	0.596676
$573$	−0.665354	−0.0277956
$574$	0.216486	0.00903595
$575$	−0.179387	−0.00748096
$576$	6.67649	0.278187
$577$	−39.3652	−1.63880	−0.819398	−	0.573225i	$-0.805692\pi$
$577$	−39.3652	−1.63880	−0.819398	+	0.573225i	$0.805692\pi$
$578$	0.977627	0.0406639
$579$	16.7912	0.697820
$580$	15.8697	0.658955
$581$	−1.83736	−0.0762266
$582$	−2.83894	−0.117678
$583$	−30.3858	−1.25845
$584$	7.06253	0.292250
$585$	11.3335	0.468584
$586$	−14.6152	−0.603748
$587$	34.9765	1.44363	0.721817	−	0.692084i	$-0.243307\pi$
$587$	34.9765	1.44363	0.721817	+	0.692084i	$0.243307\pi$
$588$	−7.28973	−0.300623
$589$	30.0874	1.23973
$590$	10.9492	0.450772
$591$	−8.87917	−0.365240
$592$	−2.54664	−0.104666
$593$	−18.9931	−0.779951	−0.389976	−	0.920825i	$-0.627517\pi$
$593$	−18.9931	−0.779951	−0.389976	+	0.920825i	$0.627517\pi$
$594$	4.74294	0.194605
$595$	−0.556675	−0.0228215
$596$	9.41182	0.385523
$597$	1.94946	0.0797861
$598$	−0.0441515	−0.00180549
$599$	4.39995	0.179777	0.0898885	−	0.995952i	$-0.471349\pi$
$599$	4.39995	0.179777	0.0898885	+	0.995952i	$0.471349\pi$
$600$	33.2991	1.35943
$601$	27.7647	1.13255	0.566273	−	0.824217i	$-0.308385\pi$
$601$	27.7647	1.13255	0.566273	+	0.824217i	$0.308385\pi$
$602$	−0.841661	−0.0343036
$603$	−8.87257	−0.361319
$604$	−24.5775	−1.00004
$605$	50.4424	2.05077
$606$	4.35348	0.176848
$607$	−20.0249	−0.812784	−0.406392	−	0.913699i	$-0.633213\pi$
$607$	−20.0249	−0.812784	−0.406392	+	0.913699i	$0.633213\pi$
$608$	−20.1458	−0.817020
$609$	0.522586	0.0211763
$610$	−29.7073	−1.20281
$611$	−24.5241	−0.992138
$612$	1.04425	0.0422111
$613$	−24.2666	−0.980118	−0.490059	−	0.871689i	$-0.663025\pi$
$613$	−24.2666	−0.980118	−0.490059	+	0.871689i	$0.663025\pi$
$614$	25.3982	1.02499
$615$	−6.43970	−0.259674
$616$	1.99767	0.0804884
$617$	−34.4794	−1.38809	−0.694044	−	0.719933i	$-0.744173\pi$
$617$	−34.4794	−1.38809	−0.694044	+	0.719933i	$0.744173\pi$
$618$	−13.6753	−0.550100
$619$	2.39232	0.0961554	0.0480777	−	0.998844i	$-0.484690\pi$
$619$	2.39232	0.0961554	0.0480777	+	0.998844i	$0.484690\pi$
$620$	32.3132	1.29773
$621$	0.0160329	0.000643378 0
$622$	9.54005	0.382521
$623$	−1.77764	−0.0712195
$624$	2.31279	0.0925856
$625$	44.2432	1.76973
$626$	6.09223	0.243495
$627$	−18.9796	−0.757972
$628$	12.7619	0.509254
$629$	−3.10164	−0.123670
$630$	0.544221	0.0216823
$631$	27.4885	1.09430	0.547150	−	0.837035i	$-0.315713\pi$
$631$	27.4885	1.09430	0.547150	+	0.837035i	$0.315713\pi$
$632$	2.97614	0.118384
$633$	12.7393	0.506343
$634$	31.1464	1.23698
$635$	−62.6095	−2.48458
$636$	6.54032	0.259341
$637$	−19.6638	−0.779110
$638$	17.9147	0.709250
$639$	7.42016	0.293537
$640$	−15.1769	−0.599918
$641$	42.1315	1.66409	0.832047	−	0.554705i	$-0.187169\pi$
$641$	42.1315	1.66409	0.832047	+	0.554705i	$0.187169\pi$
$642$	−4.51994	−0.178388
$643$	−38.7011	−1.52622	−0.763112	−	0.646266i	$-0.776329\pi$
$643$	−38.7011	−1.52622	−0.763112	+	0.646266i	$0.776329\pi$
$644$	0.00231639	9.12784e−5 0
$645$	25.0365	0.985811
$646$	3.82460	0.150477
$647$	43.6307	1.71530	0.857650	−	0.514233i	$-0.171923\pi$
$647$	43.6307	1.71530	0.857650	+	0.514233i	$0.171923\pi$
$648$	−2.97614	−0.116914
$649$	−13.5045	−0.530098
$650$	30.8114	1.20852
$651$	1.06407	0.0417040
$652$	1.87145	0.0732917
$653$	7.25440	0.283887	0.141943	−	0.989875i	$-0.454665\pi$
$653$	7.25440	0.283887	0.141943	+	0.989875i	$0.454665\pi$
$654$	−15.4513	−0.604193
$655$	1.28720	0.0502952
$656$	−1.31412	−0.0513079
$657$	−2.37305	−0.0925816
$658$	−1.17761	−0.0459082
$659$	−4.26462	−0.166126	−0.0830629	−	0.996544i	$-0.526470\pi$
$659$	−4.26462	−0.166126	−0.0830629	+	0.996544i	$0.526470\pi$
$660$	−20.3837	−0.793434
$661$	−14.5051	−0.564181	−0.282091	−	0.959388i	$-0.591028\pi$
$661$	−14.5051	−0.564181	−0.282091	+	0.959388i	$0.591028\pi$
$662$	8.77944	0.341223
$663$	2.81682	0.109396
$664$	39.5231	1.53379
$665$	−2.17778	−0.0844508
$666$	3.03224	0.117497
$667$	0.0605584	0.00234483
$668$	21.8644	0.845960
$669$	11.1497	0.431074
$670$	−34.9002	−1.34831
$671$	36.6402	1.41448
$672$	−0.712473	−0.0274842
$673$	19.7460	0.761151	0.380575	−	0.924750i	$-0.375726\pi$
$673$	19.7460	0.761151	0.380575	+	0.924750i	$0.375726\pi$
$674$	−33.3381	−1.28414
$675$	−11.1887	−0.430653
$676$	5.28963	0.203447
$677$	29.2003	1.12226	0.561129	−	0.827729i	$-0.310367\pi$
$677$	29.2003	1.12226	0.561129	+	0.827729i	$0.310367\pi$
$678$	5.84786	0.224586
$679$	0.401771	0.0154186
$680$	11.9745	0.459202
$681$	4.68991	0.179718
$682$	36.4771	1.39678
$683$	24.1507	0.924100	0.462050	−	0.886854i	$-0.347114\pi$
$683$	24.1507	0.924100	0.462050	+	0.886854i	$0.347114\pi$
$684$	4.08522	0.156202
$685$	64.9307	2.48088
$686$	−1.89105	−0.0722007
$687$	15.8696	0.605465
$688$	5.10909	0.194782
$689$	17.6423	0.672120
$690$	0.0630654	0.00240086
$691$	−39.7091	−1.51060	−0.755302	−	0.655377i	$-0.772510\pi$
$691$	−39.7091	−1.51060	−0.755302	+	0.655377i	$0.772510\pi$
$692$	23.8540	0.906795
$693$	−0.671229	−0.0254979
$694$	−18.9777	−0.720383
$695$	3.96707	0.150480
$696$	−11.2413	−0.426099
$697$	−1.60052	−0.0606239
$698$	−14.3402	−0.542785
$699$	22.3730	0.846226
$700$	−1.61651	−0.0610982
$701$	−13.6136	−0.514177	−0.257088	−	0.966388i	$-0.582763\pi$
$701$	−13.6136	−0.514177	−0.257088	+	0.966388i	$0.582763\pi$
$702$	−2.75380	−0.103936
$703$	−12.1340	−0.457642
$704$	−32.3909	−1.22078
$705$	35.0299	1.31930
$706$	18.3302	0.689865
$707$	−0.616112	−0.0231713
$708$	2.90674	0.109242
$709$	25.2382	0.947842	0.473921	−	0.880567i	$-0.342838\pi$
$709$	25.2382	0.947842	0.473921	+	0.880567i	$0.342838\pi$
$710$	29.1872	1.09538
$711$	−1.00000	−0.0375029
$712$	38.2384	1.43304
$713$	0.123306	0.00461785
$714$	0.135260	0.00506198
$715$	−54.9845	−2.05630
$716$	−11.9981	−0.448392
$717$	−14.3196	−0.534776
$718$	13.4245	0.500999
$719$	14.5523	0.542711	0.271356	−	0.962479i	$-0.412528\pi$
$719$	14.5523	0.542711	0.271356	+	0.962479i	$0.412528\pi$
$720$	−3.30356	−0.123116
$721$	1.93535	0.0720760
$722$	−3.61262	−0.134448
$723$	18.7706	0.698087
$724$	6.35008	0.235999
$725$	−42.2611	−1.56954
$726$	−12.2564	−0.454878
$727$	53.7450	1.99329	0.996645	−	0.0818401i	$-0.0260797\pi$
$727$	53.7450	1.99329	0.996645	+	0.0818401i	$0.0260797\pi$
$728$	−1.15987	−0.0429876
$729$	1.00000	0.0370370
$730$	−9.33440	−0.345482
$731$	6.22254	0.230149
$732$	−7.88653	−0.291495
$733$	25.9434	0.958240	0.479120	−	0.877749i	$-0.340956\pi$
$733$	25.9434	0.958240	0.479120	+	0.877749i	$0.340956\pi$
$734$	11.3901	0.420415
$735$	28.0876	1.03603
$736$	−0.0825627	−0.00304330
$737$	43.0451	1.58559
$738$	1.56471	0.0575977
$739$	−43.6163	−1.60445	−0.802225	−	0.597021i	$-0.796351\pi$
$739$	−43.6163	−1.60445	−0.802225	+	0.597021i	$0.796351\pi$
$740$	−13.0316	−0.479053
$741$	11.0198	0.404821
$742$	0.847162	0.0311003
$743$	23.3947	0.858266	0.429133	−	0.903241i	$-0.358819\pi$
$743$	23.3947	0.858266	0.429133	+	0.903241i	$0.358819\pi$
$744$	−22.8889	−0.839148
$745$	−36.2641	−1.32861
$746$	−6.39236	−0.234041
$747$	−13.2800	−0.485890
$748$	−5.06614	−0.185236
$749$	0.639670	0.0233730
$750$	−24.3432	−0.888887
$751$	−41.5109	−1.51475	−0.757377	−	0.652978i	$-0.773519\pi$
$751$	−41.5109	−1.51475	−0.757377	+	0.652978i	$0.773519\pi$
$752$	7.14841	0.260676
$753$	7.58732	0.276497
$754$	−10.4015	−0.378799
$755$	94.6980	3.44641
$756$	0.144477	0.00525458
$757$	4.52732	0.164548	0.0822741	−	0.996610i	$-0.473782\pi$
$757$	4.52732	0.164548	0.0822741	+	0.996610i	$0.473782\pi$
$758$	16.3910	0.595346
$759$	−0.0777834	−0.00282336
$760$	46.8459	1.69928
$761$	34.2988	1.24333	0.621666	−	0.783282i	$-0.286456\pi$
$761$	34.2988	1.24333	0.621666	+	0.783282i	$0.286456\pi$
$762$	15.2128	0.551100
$763$	2.18669	0.0791635
$764$	−0.694793	−0.0251367
$765$	−4.02352	−0.145471
$766$	28.4542	1.02809
$767$	7.84085	0.283117
$768$	17.0406	0.614901
$769$	6.07216	0.218968	0.109484	−	0.993989i	$-0.465080\pi$
$769$	6.07216	0.218968	0.109484	+	0.993989i	$0.465080\pi$
$770$	−2.64028	−0.0951491
$771$	14.2866	0.514521
$772$	17.5342	0.631068
$773$	32.4521	1.16722	0.583611	−	0.812033i	$-0.301639\pi$
$773$	32.4521	1.16722	0.583611	+	0.812033i	$0.301639\pi$
$774$	−6.08333	−0.218661
$775$	−86.0501	−3.09101
$776$	−8.64241	−0.310245
$777$	−0.429128	−0.0153949
$778$	8.17443	0.293068
$779$	−6.26142	−0.224339
$780$	11.8350	0.423761
$781$	−35.9988	−1.28814
$782$	0.0156742	0.000560508 0
$783$	3.77713	0.134984
$784$	5.73172	0.204704
$785$	−49.1720	−1.75502
$786$	−0.312763	−0.0111559
$787$	−19.7637	−0.704499	−0.352250	−	0.935906i	$-0.614583\pi$
$787$	−19.7637	−0.704499	−0.352250	+	0.935906i	$0.614583\pi$
$788$	−9.27203	−0.330302
$789$	2.93240	0.104396
$790$	−3.93350	−0.139948
$791$	−0.827598	−0.0294260
$792$	14.4387	0.513056
$793$	−21.2737	−0.755452
$794$	−4.05735	−0.143990
$795$	−25.2001	−0.893756
$796$	2.03571	0.0721540
$797$	26.9442	0.954412	0.477206	−	0.878792i	$-0.341650\pi$
$797$	26.9442	0.954412	0.477206	+	0.878792i	$0.341650\pi$
$798$	0.529154	0.0187318
$799$	8.70629	0.308007
$800$	57.6170	2.03707
$801$	−12.8483	−0.453973
$802$	−26.9679	−0.952271
$803$	11.5128	0.406279
$804$	−9.26513	−0.326756
$805$	−0.00892512	−0.000314569 0
$806$	−21.1790	−0.745998
$807$	−13.1659	−0.463462
$808$	13.2531	0.466241
$809$	15.3530	0.539783	0.269892	−	0.962891i	$-0.413012\pi$
$809$	15.3530	0.539783	0.269892	+	0.962891i	$0.413012\pi$
$810$	3.93350	0.138209
$811$	−22.6949	−0.796926	−0.398463	−	0.917185i	$-0.630456\pi$
$811$	−22.6949	−0.796926	−0.398463	+	0.917185i	$0.630456\pi$
$812$	0.545708	0.0191506
$813$	1.75013	0.0613797
$814$	−14.7109	−0.515616
$815$	−7.21077	−0.252582
$816$	−0.821062	−0.0287429
$817$	24.3433	0.851666
$818$	−3.19719	−0.111787
$819$	0.389723	0.0136180
$820$	−6.72463	−0.234834
$821$	30.7872	1.07448	0.537241	−	0.843429i	$-0.319467\pi$
$821$	30.7872	1.07448	0.537241	+	0.843429i	$0.319467\pi$
$822$	−15.7768	−0.550278
$823$	39.0157	1.36000	0.680001	−	0.733211i	$-0.261979\pi$
$823$	39.0157	1.36000	0.680001	+	0.733211i	$0.261979\pi$
$824$	−41.6308	−1.45028
$825$	54.2817	1.88985
$826$	0.376507	0.0131004
$827$	1.64150	0.0570807	0.0285404	−	0.999593i	$-0.490914\pi$
$827$	1.64150	0.0570807	0.0285404	+	0.999593i	$0.490914\pi$
$828$	0.0167423	0.000581835 0
$829$	38.1613	1.32540	0.662698	−	0.748887i	$-0.269411\pi$
$829$	38.1613	1.32540	0.662698	+	0.748887i	$0.269411\pi$
$830$	−52.2369	−1.81317
$831$	−15.8049	−0.548267
$832$	18.8065	0.651998
$833$	6.98086	0.241872
$834$	−0.963913	−0.0333776
$835$	−84.2445	−2.91540
$836$	−19.8194	−0.685467
$837$	7.69082	0.265833
$838$	20.6702	0.714041
$839$	−37.4156	−1.29173	−0.645865	−	0.763452i	$-0.723503\pi$
$839$	−37.4156	−1.29173	−0.645865	+	0.763452i	$0.723503\pi$
$840$	1.65674	0.0571630
$841$	−14.7333	−0.508045
$842$	−8.33721	−0.287319
$843$	−15.0483	−0.518290
$844$	13.3030	0.457907
$845$	−20.3811	−0.701133
$846$	−8.51151	−0.292632
$847$	1.73455	0.0595997
$848$	−5.14248	−0.176594
$849$	−7.56553	−0.259648
$850$	−10.9384	−0.375183
$851$	−0.0497283	−0.00170466
$852$	7.74846	0.265458
$853$	−18.9844	−0.650013	−0.325007	−	0.945712i	$-0.605367\pi$
$853$	−18.9844	−0.650013	−0.325007	+	0.945712i	$0.605367\pi$
$854$	−1.02153	−0.0349562
$855$	−15.7405	−0.538313
$856$	−13.7598	−0.470301
$857$	37.3836	1.27700	0.638500	−	0.769622i	$-0.279555\pi$
$857$	37.3836	1.27700	0.638500	+	0.769622i	$0.279555\pi$
$858$	13.3600	0.456104
$859$	7.98691	0.272510	0.136255	−	0.990674i	$-0.456493\pi$
$859$	7.98691	0.272510	0.136255	+	0.990674i	$0.456493\pi$
$860$	26.1442	0.891511
$861$	−0.221440	−0.00754666
$862$	16.6568	0.567331
$863$	−46.3934	−1.57925	−0.789625	−	0.613589i	$-0.789725\pi$
$863$	−46.3934	−1.57925	−0.789625	+	0.613589i	$0.789725\pi$
$864$	−5.14958	−0.175192
$865$	−91.9105	−3.12505
$866$	32.5484	1.10604
$867$	−1.00000	−0.0339618
$868$	1.11115	0.0377147
$869$	4.85148	0.164575
$870$	14.8573	0.503711
$871$	−24.9925	−0.846837
$872$	−47.0375	−1.59289
$873$	2.90390	0.0982823
$874$	0.0613194	0.00207416
$875$	3.44509	0.116465
$876$	−2.47805	−0.0837255
$877$	−7.03515	−0.237560	−0.118780	−	0.992921i	$-0.537898\pi$
$877$	−7.03515	−0.237560	−0.118780	+	0.992921i	$0.537898\pi$
$878$	23.3929	0.789472
$879$	14.9496	0.504239
$880$	16.0272	0.540275
$881$	−8.14336	−0.274357	−0.137178	−	0.990546i	$-0.543803\pi$
$881$	−8.14336	−0.274357	−0.137178	+	0.990546i	$0.543803\pi$
$882$	−6.82468	−0.229799
$883$	31.3775	1.05594	0.527968	−	0.849264i	$-0.322954\pi$
$883$	31.3775	1.05594	0.527968	+	0.849264i	$0.322954\pi$
$884$	2.94145	0.0989318
$885$	−11.1998	−0.376476
$886$	−30.8432	−1.03620
$887$	−20.3418	−0.683011	−0.341505	−	0.939880i	$-0.610937\pi$
$887$	−20.3418	−0.683011	−0.341505	+	0.939880i	$0.610937\pi$
$888$	9.23090	0.309769
$889$	−2.15293	−0.0722071
$890$	−50.5389	−1.69407
$891$	−4.85148	−0.162531
$892$	11.6431	0.389838
$893$	34.0601	1.13978
$894$	8.81139	0.294697
$895$	46.2293	1.54528
$896$	−0.521882	−0.0174349
$897$	0.0451619	0.00150791
$898$	6.39438	0.213383
$899$	29.0492	0.968845
$900$	−11.6837	−0.389458
$901$	−6.26321	−0.208658
$902$	−7.59116	−0.252758
$903$	0.860922	0.0286497
$904$	17.8023	0.592096
$905$	−24.4671	−0.813314
$906$	−23.0096	−0.764442
$907$	43.1365	1.43232	0.716161	−	0.697935i	$-0.245897\pi$
$907$	43.1365	1.43232	0.716161	+	0.697935i	$0.245897\pi$
$908$	4.89742	0.162526
$909$	−4.45311	−0.147700
$910$	1.53297	0.0508176
$911$	33.9292	1.12412	0.562062	−	0.827095i	$-0.310008\pi$
$911$	33.9292	1.12412	0.562062	+	0.827095i	$0.310008\pi$
$912$	−3.21210	−0.106363
$913$	64.4277	2.13225
$914$	26.0263	0.860873
$915$	30.3871	1.00457
$916$	16.5718	0.547547
$917$	0.0442627	0.00146168
$918$	0.977627	0.0322665
$919$	10.0728	0.332271	0.166136	−	0.986103i	$-0.446871\pi$
$919$	10.0728	0.332271	0.166136	+	0.986103i	$0.446871\pi$
$920$	0.191987	0.00632961
$921$	−25.9795	−0.856053
$922$	7.72035	0.254256
$923$	20.9013	0.687974
$924$	−0.700928	−0.0230588
$925$	34.7032	1.14104
$926$	−23.3893	−0.768618
$927$	13.9882	0.459433
$928$	−19.4506	−0.638498
$929$	−6.55194	−0.214962	−0.107481	−	0.994207i	$-0.534278\pi$
$929$	−6.55194	−0.214962	−0.107481	+	0.994207i	$0.534278\pi$
$930$	30.2518	0.991996
$931$	27.3100	0.895048
$932$	23.3629	0.765278
$933$	−9.75837	−0.319475
$934$	−10.7860	−0.352928
$935$	19.5200	0.638373
$936$	−8.38325	−0.274015
$937$	−32.4546	−1.06025	−0.530123	−	0.847921i	$-0.677854\pi$
$937$	−32.4546	−1.06025	−0.530123	+	0.847921i	$0.677854\pi$
$938$	−1.20010	−0.0391848
$939$	−6.23165	−0.203362
$940$	36.5798	1.19310
$941$	−57.3931	−1.87096	−0.935481	−	0.353377i	$-0.885033\pi$
$941$	−57.3931	−1.87096	−0.935481	+	0.353377i	$0.885033\pi$
$942$	11.9477	0.389278
$943$	−0.0256609	−0.000835635 0
$944$	−2.28549	−0.0743864
$945$	−0.556675	−0.0181087
$946$	29.5132	0.959555
$947$	24.0396	0.781182	0.390591	−	0.920564i	$-0.372271\pi$
$947$	24.0396	0.781182	0.390591	+	0.920564i	$0.372271\pi$
$948$	−1.04425	−0.0339155
$949$	−6.68447	−0.216987
$950$	−42.7922	−1.38836
$951$	−31.8592	−1.03310
$952$	0.411765	0.0133454
$953$	33.7222	1.09237	0.546185	−	0.837665i	$-0.316080\pi$
$953$	33.7222	1.09237	0.546185	+	0.837665i	$0.316080\pi$
$954$	6.12308	0.198242
$955$	2.67706	0.0866277
$956$	−14.9532	−0.483621
$957$	−18.3247	−0.592353
$958$	1.90276	0.0614754
$959$	2.23275	0.0720994
$960$	−26.8630	−0.866999
$961$	28.1486	0.908021
$962$	8.54130	0.275382
$963$	4.62338	0.148986
$964$	19.6011	0.631310
$965$	−67.5598	−2.17483
$966$	0.00216861	6.97739e−5 0
$967$	−8.72815	−0.280678	−0.140339	−	0.990103i	$-0.544819\pi$
$967$	−8.72815	−0.280678	−0.140339	+	0.990103i	$0.544819\pi$
$968$	−37.3115	−1.19924
$969$	−3.91212	−0.125676
$970$	11.4225	0.366754
$971$	7.85405	0.252048	0.126024	−	0.992027i	$-0.459778\pi$
$971$	7.85405	0.252048	0.126024	+	0.992027i	$0.459778\pi$
$972$	1.04425	0.0334942
$973$	0.136415	0.00437325
$974$	24.8018	0.794699
$975$	−31.5165	−1.00934
$976$	6.20097	0.198488
$977$	12.3966	0.396604	0.198302	−	0.980141i	$-0.436457\pi$
$977$	12.3966	0.396604	0.198302	+	0.980141i	$0.436457\pi$
$978$	1.75206	0.0560248
$979$	62.3335	1.99219
$980$	29.3303	0.936923
$981$	15.8049	0.504611
$982$	−18.1333	−0.578656
$983$	57.5505	1.83557	0.917787	−	0.397073i	$-0.129974\pi$
$983$	57.5505	1.83557	0.917787	+	0.397073i	$0.129974\pi$
$984$	4.76336	0.151850
$985$	35.7255	1.13831
$986$	3.69262	0.117597
$987$	1.20456	0.0383417
$988$	11.5073	0.366097
$989$	0.0997654	0.00317236
$990$	−19.0833	−0.606507
$991$	−30.2575	−0.961160	−0.480580	−	0.876951i	$-0.659574\pi$
$991$	−30.2575	−0.961160	−0.480580	+	0.876951i	$0.659574\pi$
$992$	−39.6045	−1.25744
$993$	−8.98036	−0.284983
$994$	1.00365	0.0318339
$995$	−7.84368	−0.248661
$996$	−13.8676	−0.439411
$997$	47.4868	1.50392	0.751961	−	0.659208i	$-0.229108\pi$
$997$	47.4868	1.50392	0.751961	+	0.659208i	$0.229108\pi$
$998$	30.5150	0.965934
$999$	−3.10164	−0.0981314

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.g.1.14	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.g.1.14	✓	22	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)

\(f(q)\)	\(=\)	\(q+0.977627 q^{2} -1.00000 q^{3} -1.04425 q^{4} +4.02352 q^{5} -0.977627 q^{6} +0.138355 q^{7} -2.97614 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.977627 q^{2} -1.00000 q^{3} -1.04425 q^{4} +4.02352 q^{5} -0.977627 q^{6} +0.138355 q^{7} -2.97614 q^{8} +1.00000 q^{9} +3.93350 q^{10} -4.85148 q^{11} +1.04425 q^{12} +2.81682 q^{13} +0.135260 q^{14} -4.02352 q^{15} -0.821062 q^{16} -1.00000 q^{17} +0.977627 q^{18} -3.91212 q^{19} -4.20154 q^{20} -0.138355 q^{21} -4.74294 q^{22} -0.0160329 q^{23} +2.97614 q^{24} +11.1887 q^{25} +2.75380 q^{26} -1.00000 q^{27} -0.144477 q^{28} -3.77713 q^{29} -3.93350 q^{30} -7.69082 q^{31} +5.14958 q^{32} +4.85148 q^{33} -0.977627 q^{34} +0.556675 q^{35} -1.04425 q^{36} +3.10164 q^{37} -3.82460 q^{38} -2.81682 q^{39} -11.9745 q^{40} +1.60052 q^{41} -0.135260 q^{42} -6.22254 q^{43} +5.06614 q^{44} +4.02352 q^{45} -0.0156742 q^{46} -8.70629 q^{47} +0.821062 q^{48} -6.98086 q^{49} +10.9384 q^{50} +1.00000 q^{51} -2.94145 q^{52} +6.26321 q^{53} -0.977627 q^{54} -19.5200 q^{55} -0.411765 q^{56} +3.91212 q^{57} -3.69262 q^{58} +2.78358 q^{59} +4.20154 q^{60} -7.55238 q^{61} -7.51875 q^{62} +0.138355 q^{63} +6.67649 q^{64} +11.3335 q^{65} +4.74294 q^{66} -8.87257 q^{67} +1.04425 q^{68} +0.0160329 q^{69} +0.544221 q^{70} +7.42016 q^{71} -2.97614 q^{72} -2.37305 q^{73} +3.03224 q^{74} -11.1887 q^{75} +4.08522 q^{76} -0.671229 q^{77} -2.75380 q^{78} -1.00000 q^{79} -3.30356 q^{80} +1.00000 q^{81} +1.56471 q^{82} -13.2800 q^{83} +0.144477 q^{84} -4.02352 q^{85} -6.08333 q^{86} +3.77713 q^{87} +14.4387 q^{88} -12.8483 q^{89} +3.93350 q^{90} +0.389723 q^{91} +0.0167423 q^{92} +7.69082 q^{93} -8.51151 q^{94} -15.7405 q^{95} -5.14958 q^{96} +2.90390 q^{97} -6.82468 q^{98} -4.85148 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{2} - 22 q^{3} + 16 q^{4} + 5 q^{5} - 2 q^{6} - 4 q^{7} + 6 q^{8} + 22 q^{9}+O(q^{10}) \) 22 * q + 2 * q^2 - 22 * q^3 + 16 * q^4 + 5 * q^5 - 2 * q^6 - 4 * q^7 + 6 * q^8 + 22 * q^9	\( 22 q + 2 q^{2} - 22 q^{3} + 16 q^{4} + 5 q^{5} - 2 q^{6} - 4 q^{7} + 6 q^{8} + 22 q^{9} - 5 q^{10} - 2 q^{11} - 16 q^{12} - 11 q^{13} - 7 q^{14} - 5 q^{15} - 22 q^{17} + 2 q^{18} - 36 q^{19} + 4 q^{21} - 9 q^{22} + 21 q^{23} - 6 q^{24} + 9 q^{25} - 16 q^{26} - 22 q^{27} - 17 q^{28} - q^{29} + 5 q^{30} - 12 q^{31} - 11 q^{32} + 2 q^{33} - 2 q^{34} - 14 q^{35} + 16 q^{36} - 6 q^{37} + q^{38} + 11 q^{39} - 24 q^{40} - 17 q^{41} + 7 q^{42} - 36 q^{43} + 16 q^{44} + 5 q^{45} - 23 q^{46} - 17 q^{47} - 6 q^{49} - 33 q^{50} + 22 q^{51} - 57 q^{52} - 2 q^{53} - 2 q^{54} - 24 q^{55} - 64 q^{56} + 36 q^{57} - 7 q^{58} - 59 q^{59} - 30 q^{61} - 4 q^{62} - 4 q^{63} - 22 q^{64} + 36 q^{65} + 9 q^{66} - 16 q^{67} - 16 q^{68} - 21 q^{69} - 39 q^{70} - 11 q^{71} + 6 q^{72} - 19 q^{73} - 28 q^{74} - 9 q^{75} - 77 q^{76} + 2 q^{77} + 16 q^{78} - 22 q^{79} - 2 q^{80} + 22 q^{81} + 33 q^{82} - 23 q^{83} + 17 q^{84} - 5 q^{85} + 6 q^{86} + q^{87} - 23 q^{88} + 12 q^{89} - 5 q^{90} - 24 q^{91} + 66 q^{92} + 12 q^{93} - 61 q^{94} - 11 q^{95} + 11 q^{96} - 9 q^{97} + 17 q^{98} - 2 q^{99}+O(q^{100}) \) 22 * q + 2 * q^2 - 22 * q^3 + 16 * q^4 + 5 * q^5 - 2 * q^6 - 4 * q^7 + 6 * q^8 + 22 * q^9 - 5 * q^10 - 2 * q^11 - 16 * q^12 - 11 * q^13 - 7 * q^14 - 5 * q^15 - 22 * q^17 + 2 * q^18 - 36 * q^19 + 4 * q^21 - 9 * q^22 + 21 * q^23 - 6 * q^24 + 9 * q^25 - 16 * q^26 - 22 * q^27 - 17 * q^28 - q^29 + 5 * q^30 - 12 * q^31 - 11 * q^32 + 2 * q^33 - 2 * q^34 - 14 * q^35 + 16 * q^36 - 6 * q^37 + q^38 + 11 * q^39 - 24 * q^40 - 17 * q^41 + 7 * q^42 - 36 * q^43 + 16 * q^44 + 5 * q^45 - 23 * q^46 - 17 * q^47 - 6 * q^49 - 33 * q^50 + 22 * q^51 - 57 * q^52 - 2 * q^53 - 2 * q^54 - 24 * q^55 - 64 * q^56 + 36 * q^57 - 7 * q^58 - 59 * q^59 - 30 * q^61 - 4 * q^62 - 4 * q^63 - 22 * q^64 + 36 * q^65 + 9 * q^66 - 16 * q^67 - 16 * q^68 - 21 * q^69 - 39 * q^70 - 11 * q^71 + 6 * q^72 - 19 * q^73 - 28 * q^74 - 9 * q^75 - 77 * q^76 + 2 * q^77 + 16 * q^78 - 22 * q^79 - 2 * q^80 + 22 * q^81 + 33 * q^82 - 23 * q^83 + 17 * q^84 - 5 * q^85 + 6 * q^86 + q^87 - 23 * q^88 + 12 * q^89 - 5 * q^90 - 24 * q^91 + 66 * q^92 + 12 * q^93 - 61 * q^94 - 11 * q^95 + 11 * q^96 - 9 * q^97 + 17 * q^98 - 2 * q^99

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