LMFDB - Embedded newform 4029.2.a.k.1.18

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			1.18
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)

$f(q)$	$=$	$q+0.617959 q^{2} +1.00000 q^{3} -1.61813 q^{4} +3.16624 q^{5} +0.617959 q^{6} -0.196167 q^{7} -2.23585 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.617959 q^{2} +1.00000 q^{3} -1.61813 q^{4} +3.16624 q^{5} +0.617959 q^{6} -0.196167 q^{7} -2.23585 q^{8} +1.00000 q^{9} +1.95660 q^{10} -1.60281 q^{11} -1.61813 q^{12} -1.04507 q^{13} -0.121223 q^{14} +3.16624 q^{15} +1.85459 q^{16} +1.00000 q^{17} +0.617959 q^{18} -1.16729 q^{19} -5.12337 q^{20} -0.196167 q^{21} -0.990470 q^{22} -0.115056 q^{23} -2.23585 q^{24} +5.02505 q^{25} -0.645810 q^{26} +1.00000 q^{27} +0.317423 q^{28} +6.34232 q^{29} +1.95660 q^{30} -1.71568 q^{31} +5.61777 q^{32} -1.60281 q^{33} +0.617959 q^{34} -0.621110 q^{35} -1.61813 q^{36} +6.10971 q^{37} -0.721338 q^{38} -1.04507 q^{39} -7.07924 q^{40} +3.43821 q^{41} -0.121223 q^{42} +12.5282 q^{43} +2.59355 q^{44} +3.16624 q^{45} -0.0711002 q^{46} -2.31797 q^{47} +1.85459 q^{48} -6.96152 q^{49} +3.10527 q^{50} +1.00000 q^{51} +1.69105 q^{52} +10.5661 q^{53} +0.617959 q^{54} -5.07487 q^{55} +0.438600 q^{56} -1.16729 q^{57} +3.91929 q^{58} +2.43259 q^{59} -5.12337 q^{60} -1.11029 q^{61} -1.06022 q^{62} -0.196167 q^{63} -0.237627 q^{64} -3.30894 q^{65} -0.990470 q^{66} +9.11603 q^{67} -1.61813 q^{68} -0.115056 q^{69} -0.383821 q^{70} +7.31632 q^{71} -2.23585 q^{72} +7.19324 q^{73} +3.77555 q^{74} +5.02505 q^{75} +1.88883 q^{76} +0.314418 q^{77} -0.645810 q^{78} +1.00000 q^{79} +5.87206 q^{80} +1.00000 q^{81} +2.12467 q^{82} +1.78493 q^{83} +0.317423 q^{84} +3.16624 q^{85} +7.74191 q^{86} +6.34232 q^{87} +3.58365 q^{88} -11.2590 q^{89} +1.95660 q^{90} +0.205008 q^{91} +0.186176 q^{92} -1.71568 q^{93} -1.43241 q^{94} -3.69592 q^{95} +5.61777 q^{96} +2.57631 q^{97} -4.30193 q^{98} -1.60281 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.617959	0.436963	0.218481	−	0.975841i	$-0.429890\pi$
$2$	0.617959	0.436963	0.218481	+	0.975841i	$0.429890\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.61813	−0.809063
$5$	3.16624	1.41598	0.707992	−	0.706221i	$-0.249601\pi$
$5$	3.16624	1.41598	0.707992	+	0.706221i	$0.249601\pi$
$6$	0.617959	0.252281
$7$	−0.196167	−0.0741441	−0.0370720	−	0.999313i	$-0.511803\pi$
$7$	−0.196167	−0.0741441	−0.0370720	+	0.999313i	$0.511803\pi$
$8$	−2.23585	−0.790494
$9$	1.00000	0.333333
$10$	1.95660	0.618732
$11$	−1.60281	−0.483265	−0.241632	−	0.970368i	$-0.577683\pi$
$11$	−1.60281	−0.483265	−0.241632	+	0.970368i	$0.577683\pi$
$12$	−1.61813	−0.467113
$13$	−1.04507	−0.289850	−0.144925	−	0.989443i	$-0.546294\pi$
$13$	−1.04507	−0.289850	−0.144925	+	0.989443i	$0.546294\pi$
$14$	−0.121223	−0.0323982
$15$	3.16624	0.817519
$16$	1.85459	0.463647
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	0.617959	0.145654
$19$	−1.16729	−0.267795	−0.133897	−	0.990995i	$-0.542749\pi$
$19$	−1.16729	−0.267795	−0.133897	+	0.990995i	$0.542749\pi$
$20$	−5.12337	−1.14562
$21$	−0.196167	−0.0428071
$22$	−0.990470	−0.211169
$23$	−0.115056	−0.0239909	−0.0119955	−	0.999928i	$-0.503818\pi$
$23$	−0.115056	−0.0239909	−0.0119955	+	0.999928i	$0.503818\pi$
$24$	−2.23585	−0.456392
$25$	5.02505	1.00501
$26$	−0.645810	−0.126654
$27$	1.00000	0.192450
$28$	0.317423	0.0599872
$29$	6.34232	1.17774	0.588869	−	0.808228i	$-0.299573\pi$
$29$	6.34232	1.17774	0.588869	+	0.808228i	$0.299573\pi$
$30$	1.95660	0.357225
$31$	−1.71568	−0.308146	−0.154073	−	0.988060i	$-0.549239\pi$
$31$	−1.71568	−0.308146	−0.154073	+	0.988060i	$0.549239\pi$
$32$	5.61777	0.993090
$33$	−1.60281	−0.279013
$34$	0.617959	0.105979
$35$	−0.621110	−0.104987
$36$	−1.61813	−0.269688
$37$	6.10971	1.00443	0.502215	−	0.864743i	$-0.332519\pi$
$37$	6.10971	1.00443	0.502215	+	0.864743i	$0.332519\pi$
$38$	−0.721338	−0.117016
$39$	−1.04507	−0.167345
$40$	−7.07924	−1.11933
$41$	3.43821	0.536958	0.268479	−	0.963286i	$-0.413479\pi$
$41$	3.43821	0.536958	0.268479	+	0.963286i	$0.413479\pi$
$42$	−0.121223	−0.0187051
$43$	12.5282	1.91053	0.955265	−	0.295750i	$-0.0955694\pi$
$43$	12.5282	1.91053	0.955265	+	0.295750i	$0.0955694\pi$
$44$	2.59355	0.390992
$45$	3.16624	0.471995
$46$	−0.0711002	−0.0104831
$47$	−2.31797	−0.338111	−0.169055	−	0.985607i	$-0.554072\pi$
$47$	−2.31797	−0.338111	−0.169055	+	0.985607i	$0.554072\pi$
$48$	1.85459	0.267687
$49$	−6.96152	−0.994503
$50$	3.10527	0.439152
$51$	1.00000	0.140028
$52$	1.69105	0.234507
$53$	10.5661	1.45136	0.725681	−	0.688031i	$-0.241525\pi$
$53$	10.5661	1.45136	0.725681	+	0.688031i	$0.241525\pi$
$54$	0.617959	0.0840936
$55$	−5.07487	−0.684295
$56$	0.438600	0.0586104
$57$	−1.16729	−0.154612
$58$	3.91929	0.514628
$59$	2.43259	0.316697	0.158348	−	0.987383i	$-0.449383\pi$
$59$	2.43259	0.316697	0.158348	+	0.987383i	$0.449383\pi$
$60$	−5.12337	−0.661424
$61$	−1.11029	−0.142158	−0.0710789	−	0.997471i	$-0.522644\pi$
$61$	−1.11029	−0.142158	−0.0710789	+	0.997471i	$0.522644\pi$
$62$	−1.06022	−0.134648
$63$	−0.196167	−0.0247147
$64$	−0.237627	−0.0297034
$65$	−3.30894	−0.410423
$66$	−0.990470	−0.121918
$67$	9.11603	1.11370	0.556850	−	0.830613i	$-0.312010\pi$
$67$	9.11603	1.11370	0.556850	+	0.830613i	$0.312010\pi$
$68$	−1.61813	−0.196227
$69$	−0.115056	−0.0138512
$70$	−0.383821	−0.0458753
$71$	7.31632	0.868288	0.434144	−	0.900844i	$-0.357051\pi$
$71$	7.31632	0.868288	0.434144	+	0.900844i	$0.357051\pi$
$72$	−2.23585	−0.263498
$73$	7.19324	0.841905	0.420952	−	0.907083i	$-0.361696\pi$
$73$	7.19324	0.841905	0.420952	+	0.907083i	$0.361696\pi$
$74$	3.77555	0.438899
$75$	5.02505	0.580243
$76$	1.88883	0.216663
$77$	0.314418	0.0358312
$78$	−0.645810	−0.0731235
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	5.87206	0.656517
$81$	1.00000	0.111111
$82$	2.12467	0.234631
$83$	1.78493	0.195922	0.0979609	−	0.995190i	$-0.468768\pi$
$83$	1.78493	0.195922	0.0979609	+	0.995190i	$0.468768\pi$
$84$	0.317423	0.0346337
$85$	3.16624	0.343427
$86$	7.74191	0.834831
$87$	6.34232	0.679968
$88$	3.58365	0.382018
$89$	−11.2590	−1.19346	−0.596728	−	0.802443i	$-0.703533\pi$
$89$	−11.2590	−1.19346	−0.596728	+	0.802443i	$0.703533\pi$
$90$	1.95660	0.206244
$91$	0.205008	0.0214907
$92$	0.186176	0.0194102
$93$	−1.71568	−0.177908
$94$	−1.43241	−0.147742
$95$	−3.69592	−0.379193
$96$	5.61777	0.573361
$97$	2.57631	0.261585	0.130792	−	0.991410i	$-0.458248\pi$
$97$	2.57631	0.261585	0.130792	+	0.991410i	$0.458248\pi$
$98$	−4.30193	−0.434561
$99$	−1.60281	−0.161088
$100$	−8.13117	−0.813117
$101$	−16.8118	−1.67284	−0.836421	−	0.548088i	$-0.815356\pi$
$101$	−16.8118	−1.67284	−0.836421	+	0.548088i	$0.815356\pi$
$102$	0.617959	0.0611870
$103$	11.4305	1.12628	0.563142	−	0.826360i	$-0.309592\pi$
$103$	11.4305	1.12628	0.563142	+	0.826360i	$0.309592\pi$
$104$	2.33662	0.229125
$105$	−0.621110	−0.0606142
$106$	6.52940	0.634192
$107$	13.9546	1.34904	0.674521	−	0.738255i	$-0.264350\pi$
$107$	13.9546	1.34904	0.674521	+	0.738255i	$0.264350\pi$
$108$	−1.61813	−0.155704
$109$	−13.9968	−1.34065	−0.670324	−	0.742068i	$-0.733845\pi$
$109$	−13.9968	−1.34065	−0.670324	+	0.742068i	$0.733845\pi$
$110$	−3.13606	−0.299012
$111$	6.10971	0.579908
$112$	−0.363808	−0.0343767
$113$	−14.0417	−1.32093	−0.660465	−	0.750857i	$-0.729641\pi$
$113$	−14.0417	−1.32093	−0.660465	+	0.750857i	$0.729641\pi$
$114$	−0.721338	−0.0675595
$115$	−0.364296	−0.0339708
$116$	−10.2627	−0.952865
$117$	−1.04507	−0.0966167
$118$	1.50324	0.138385
$119$	−0.196167	−0.0179826
$120$	−7.07924	−0.646243
$121$	−8.43100	−0.766455
$122$	−0.686112	−0.0621176
$123$	3.43821	0.310013
$124$	2.77619	0.249309
$125$	0.0793166	0.00709429
$126$	−0.121223	−0.0107994
$127$	8.09640	0.718439	0.359220	−	0.933253i	$-0.383043\pi$
$127$	8.09640	0.718439	0.359220	+	0.933253i	$0.383043\pi$
$128$	−11.3824	−1.00607
$129$	12.5282	1.10305
$130$	−2.04479	−0.179340
$131$	15.2332	1.33093	0.665467	−	0.746427i	$-0.268232\pi$
$131$	15.2332	1.33093	0.665467	+	0.746427i	$0.268232\pi$
$132$	2.59355	0.225739
$133$	0.228984	0.0198554
$134$	5.63333	0.486646
$135$	3.16624	0.272506
$136$	−2.23585	−0.191723
$137$	1.28533	0.109813	0.0549065	−	0.998492i	$-0.482514\pi$
$137$	1.28533	0.109813	0.0549065	+	0.998492i	$0.482514\pi$
$138$	−0.0711002	−0.00605245
$139$	17.5726	1.49049	0.745246	−	0.666790i	$-0.232332\pi$
$139$	17.5726	1.49049	0.745246	+	0.666790i	$0.232332\pi$
$140$	1.00504	0.0849410
$141$	−2.31797	−0.195208
$142$	4.52119	0.379409
$143$	1.67505	0.140074
$144$	1.85459	0.154549
$145$	20.0813	1.66766
$146$	4.44513	0.367881
$147$	−6.96152	−0.574176
$148$	−9.88628	−0.812647
$149$	−6.01942	−0.493130	−0.246565	−	0.969126i	$-0.579302\pi$
$149$	−6.01942	−0.493130	−0.246565	+	0.969126i	$0.579302\pi$
$150$	3.10527	0.253545
$151$	−3.52648	−0.286981	−0.143490	−	0.989652i	$-0.545833\pi$
$151$	−3.52648	−0.286981	−0.143490	+	0.989652i	$0.545833\pi$
$152$	2.60989	0.211690
$153$	1.00000	0.0808452
$154$	0.194297	0.0156569
$155$	−5.43225	−0.436329
$156$	1.69105	0.135393
$157$	17.4114	1.38958	0.694792	−	0.719210i	$-0.255496\pi$
$157$	17.4114	1.38958	0.694792	+	0.719210i	$0.255496\pi$
$158$	0.617959	0.0491622
$159$	10.5661	0.837944
$160$	17.7872	1.40620
$161$	0.0225703	0.00177879
$162$	0.617959	0.0485514
$163$	2.48073	0.194306	0.0971530	−	0.995269i	$-0.469026\pi$
$163$	2.48073	0.194306	0.0971530	+	0.995269i	$0.469026\pi$
$164$	−5.56346	−0.434433
$165$	−5.07487	−0.395078
$166$	1.10302	0.0856106
$167$	11.6166	0.898919	0.449460	−	0.893301i	$-0.351617\pi$
$167$	11.6166	0.898919	0.449460	+	0.893301i	$0.351617\pi$
$168$	0.438600	0.0338387
$169$	−11.9078	−0.915987
$170$	1.95660	0.150065
$171$	−1.16729	−0.0892650
$172$	−20.2722	−1.54574
$173$	−23.0693	−1.75393	−0.876964	−	0.480556i	$-0.840435\pi$
$173$	−23.0693	−1.75393	−0.876964	+	0.480556i	$0.840435\pi$
$174$	3.91929	0.297121
$175$	−0.985748	−0.0745155
$176$	−2.97255	−0.224064
$177$	2.43259	0.182845
$178$	−6.95763	−0.521496
$179$	−17.6162	−1.31670	−0.658349	−	0.752713i	$-0.728745\pi$
$179$	−17.6162	−1.31670	−0.658349	+	0.752713i	$0.728745\pi$
$180$	−5.12337	−0.381874
$181$	−15.5593	−1.15651	−0.578257	−	0.815855i	$-0.696267\pi$
$181$	−15.5593	−1.15651	−0.578257	+	0.815855i	$0.696267\pi$
$182$	0.126686	0.00939062
$183$	−1.11029	−0.0820748
$184$	0.257249	0.0189647
$185$	19.3448	1.42226
$186$	−1.06022	−0.0777392
$187$	−1.60281	−0.117209
$188$	3.75077	0.273553
$189$	−0.196167	−0.0142690
$190$	−2.28393	−0.165693
$191$	2.72217	0.196969	0.0984847	−	0.995139i	$-0.468600\pi$
$191$	2.72217	0.196969	0.0984847	+	0.995139i	$0.468600\pi$
$192$	−0.237627	−0.0171493
$193$	18.4929	1.33115	0.665575	−	0.746331i	$-0.268186\pi$
$193$	18.4929	1.33115	0.665575	+	0.746331i	$0.268186\pi$
$194$	1.59205	0.114303
$195$	−3.30894	−0.236958
$196$	11.2646	0.804616
$197$	−2.56577	−0.182803	−0.0914017	−	0.995814i	$-0.529135\pi$
$197$	−2.56577	−0.182803	−0.0914017	+	0.995814i	$0.529135\pi$
$198$	−0.990470	−0.0703896
$199$	21.8900	1.55174	0.775869	−	0.630894i	$-0.217312\pi$
$199$	21.8900	1.55174	0.775869	+	0.630894i	$0.217312\pi$
$200$	−11.2353	−0.794454
$201$	9.11603	0.642995
$202$	−10.3890	−0.730970
$203$	−1.24415	−0.0873223
$204$	−1.61813	−0.113292
$205$	10.8862	0.760324
$206$	7.06360	0.492144
$207$	−0.115056	−0.00799698
$208$	−1.93817	−0.134388
$209$	1.87094	0.129416
$210$	−0.383821	−0.0264861
$211$	−28.6231	−1.97049	−0.985246	−	0.171143i	$-0.945254\pi$
$211$	−28.6231	−1.97049	−0.985246	+	0.171143i	$0.945254\pi$
$212$	−17.0973	−1.17424
$213$	7.31632	0.501306
$214$	8.62337	0.589482
$215$	39.6672	2.70528
$216$	−2.23585	−0.152131
$217$	0.336560	0.0228472
$218$	−8.64944	−0.585814
$219$	7.19324	0.486074
$220$	8.21178	0.553638
$221$	−1.04507	−0.0702989
$222$	3.77555	0.253398
$223$	21.7230	1.45468	0.727338	−	0.686279i	$-0.240757\pi$
$223$	21.7230	1.45468	0.727338	+	0.686279i	$0.240757\pi$
$224$	−1.10202	−0.0736317
$225$	5.02505	0.335003
$226$	−8.67718	−0.577197
$227$	−7.32807	−0.486381	−0.243191	−	0.969979i	$-0.578194\pi$
$227$	−7.32807	−0.486381	−0.243191	+	0.969979i	$0.578194\pi$
$228$	1.88883	0.125091
$229$	−10.2333	−0.676236	−0.338118	−	0.941104i	$-0.609790\pi$
$229$	−10.2333	−0.676236	−0.338118	+	0.941104i	$0.609790\pi$
$230$	−0.225120	−0.0148440
$231$	0.314418	0.0206872
$232$	−14.1805	−0.930995
$233$	−0.0697658	−0.00457051	−0.00228525	−	0.999997i	$-0.500727\pi$
$233$	−0.0697658	−0.00457051	−0.00228525	+	0.999997i	$0.500727\pi$
$234$	−0.645810	−0.0422179
$235$	−7.33924	−0.478759
$236$	−3.93625	−0.256228
$237$	1.00000	0.0649570
$238$	−0.121223	−0.00785772
$239$	−11.6063	−0.750748	−0.375374	−	0.926873i	$-0.622486\pi$
$239$	−11.6063	−0.750748	−0.375374	+	0.926873i	$0.622486\pi$
$240$	5.87206	0.379040
$241$	−23.1149	−1.48896	−0.744480	−	0.667644i	$-0.767303\pi$
$241$	−23.1149	−1.48896	−0.744480	+	0.667644i	$0.767303\pi$
$242$	−5.21001	−0.334912
$243$	1.00000	0.0641500
$244$	1.79659	0.115015
$245$	−22.0418	−1.40820
$246$	2.12467	0.135464
$247$	1.21990	0.0776204
$248$	3.83601	0.243587
$249$	1.78493	0.113116
$250$	0.0490144	0.00309994
$251$	27.4540	1.73288	0.866439	−	0.499282i	$-0.166403\pi$
$251$	27.4540	1.73288	0.866439	+	0.499282i	$0.166403\pi$
$252$	0.317423	0.0199957
$253$	0.184414	0.0115940
$254$	5.00324	0.313931
$255$	3.16624	0.198277
$256$	−6.55859	−0.409912
$257$	−13.3605	−0.833402	−0.416701	−	0.909044i	$-0.636814\pi$
$257$	−13.3605	−0.833402	−0.416701	+	0.909044i	$0.636814\pi$
$258$	7.74191	0.481990
$259$	−1.19852	−0.0744725
$260$	5.35428	0.332058
$261$	6.34232	0.392580
$262$	9.41351	0.581569
$263$	−1.22433	−0.0754957	−0.0377479	−	0.999287i	$-0.512018\pi$
$263$	−1.22433	−0.0754957	−0.0377479	+	0.999287i	$0.512018\pi$
$264$	3.58365	0.220558
$265$	33.4547	2.05511
$266$	0.141503	0.00867608
$267$	−11.2590	−0.689042
$268$	−14.7509	−0.901054
$269$	−1.59729	−0.0973883	−0.0486941	−	0.998814i	$-0.515506\pi$
$269$	−1.59729	−0.0973883	−0.0486941	+	0.998814i	$0.515506\pi$
$270$	1.95660	0.119075
$271$	−1.26090	−0.0765940	−0.0382970	−	0.999266i	$-0.512193\pi$
$271$	−1.26090	−0.0765940	−0.0382970	+	0.999266i	$0.512193\pi$
$272$	1.85459	0.112451
$273$	0.205008	0.0124076
$274$	0.794280	0.0479842
$275$	−8.05419	−0.485686
$276$	0.186176	0.0112065
$277$	18.8735	1.13400	0.567000	−	0.823718i	$-0.308104\pi$
$277$	18.8735	1.13400	0.567000	+	0.823718i	$0.308104\pi$
$278$	10.8592	0.651290
$279$	−1.71568	−0.102715
$280$	1.38871	0.0829914
$281$	15.7499	0.939562	0.469781	−	0.882783i	$-0.344333\pi$
$281$	15.7499	0.939562	0.469781	+	0.882783i	$0.344333\pi$
$282$	−1.43241	−0.0852988
$283$	−23.4972	−1.39676	−0.698382	−	0.715725i	$-0.746096\pi$
$283$	−23.4972	−1.39676	−0.698382	+	0.715725i	$0.746096\pi$
$284$	−11.8387	−0.702500
$285$	−3.69592	−0.218927
$286$	1.03511	0.0612073
$287$	−0.674462	−0.0398123
$288$	5.61777	0.331030
$289$	1.00000	0.0588235
$290$	12.4094	0.728705
$291$	2.57631	0.151026
$292$	−11.6396	−0.681154
$293$	−1.56352	−0.0913417	−0.0456708	−	0.998957i	$-0.514543\pi$
$293$	−1.56352	−0.0913417	−0.0456708	+	0.998957i	$0.514543\pi$
$294$	−4.30193	−0.250894
$295$	7.70217	0.448438
$296$	−13.6604	−0.793995
$297$	−1.60281	−0.0930044
$298$	−3.71976	−0.215480
$299$	0.120242	0.00695377
$300$	−8.13117	−0.469453
$301$	−2.45761	−0.141655
$302$	−2.17922	−0.125400
$303$	−16.8118	−0.965815
$304$	−2.16484	−0.124162
$305$	−3.51543	−0.201293
$306$	0.617959	0.0353264
$307$	−10.7601	−0.614113	−0.307057	−	0.951691i	$-0.599344\pi$
$307$	−10.7601	−0.614113	−0.307057	+	0.951691i	$0.599344\pi$
$308$	−0.508768	−0.0289897
$309$	11.4305	0.650260
$310$	−3.35691	−0.190660
$311$	2.34771	0.133126	0.0665632	−	0.997782i	$-0.478797\pi$
$311$	2.34771	0.133126	0.0665632	+	0.997782i	$0.478797\pi$
$312$	2.33662	0.132285
$313$	−9.51827	−0.538004	−0.269002	−	0.963140i	$-0.586694\pi$
$313$	−9.51827	−0.538004	−0.269002	+	0.963140i	$0.586694\pi$
$314$	10.7596	0.607197
$315$	−0.621110	−0.0349956
$316$	−1.61813	−0.0910267
$317$	−25.8917	−1.45422	−0.727110	−	0.686521i	$-0.759137\pi$
$317$	−25.8917	−1.45422	−0.727110	+	0.686521i	$0.759137\pi$
$318$	6.52940	0.366151
$319$	−10.1655	−0.569160
$320$	−0.752384	−0.0420595
$321$	13.9546	0.778870
$322$	0.0139475	0.000777263 0
$323$	−1.16729	−0.0649498
$324$	−1.61813	−0.0898959
$325$	−5.25152	−0.291302
$326$	1.53299	0.0849045
$327$	−13.9968	−0.774024
$328$	−7.68733	−0.424462
$329$	0.454709	0.0250689
$330$	−3.13606	−0.172634
$331$	12.2350	0.672499	0.336250	−	0.941773i	$-0.390841\pi$
$331$	12.2350	0.672499	0.336250	+	0.941773i	$0.390841\pi$
$332$	−2.88825	−0.158513
$333$	6.10971	0.334810
$334$	7.17858	0.392794
$335$	28.8635	1.57698
$336$	−0.363808	−0.0198474
$337$	25.4193	1.38468	0.692339	−	0.721573i	$-0.256580\pi$
$337$	25.4193	1.38468	0.692339	+	0.721573i	$0.256580\pi$
$338$	−7.35855	−0.400252
$339$	−14.0417	−0.762639
$340$	−5.12337	−0.277854
$341$	2.74991	0.148916
$342$	−0.721338	−0.0390055
$343$	2.73879	0.147881
$344$	−28.0112	−1.51026
$345$	−0.364296	−0.0196130
$346$	−14.2559	−0.766401
$347$	11.3923	0.611570	0.305785	−	0.952101i	$-0.401081\pi$
$347$	11.3923	0.611570	0.305785	+	0.952101i	$0.401081\pi$
$348$	−10.2627	−0.550137
$349$	20.4374	1.09399	0.546994	−	0.837136i	$-0.315772\pi$
$349$	20.4374	1.09399	0.546994	+	0.837136i	$0.315772\pi$
$350$	−0.609152	−0.0325605
$351$	−1.04507	−0.0557817
$352$	−9.00420	−0.479926
$353$	29.5110	1.57071	0.785356	−	0.619044i	$-0.212480\pi$
$353$	29.5110	1.57071	0.785356	+	0.619044i	$0.212480\pi$
$354$	1.50324	0.0798965
$355$	23.1652	1.22948
$356$	18.2186	0.965582
$357$	−0.196167	−0.0103822
$358$	−10.8861	−0.575348
$359$	−0.532636	−0.0281114	−0.0140557	−	0.999901i	$-0.504474\pi$
$359$	−0.532636	−0.0281114	−0.0140557	+	0.999901i	$0.504474\pi$
$360$	−7.07924	−0.373109
$361$	−17.6374	−0.928286
$362$	−9.61501	−0.505354
$363$	−8.43100	−0.442513
$364$	−0.331729	−0.0173873
$365$	22.7755	1.19212
$366$	−0.686112	−0.0358636
$367$	16.1291	0.841930	0.420965	−	0.907077i	$-0.361692\pi$
$367$	16.1291	0.841930	0.420965	+	0.907077i	$0.361692\pi$
$368$	−0.213382	−0.0111233
$369$	3.43821	0.178986
$370$	11.9543	0.621473
$371$	−2.07271	−0.107610
$372$	2.77619	0.143939
$373$	−14.0079	−0.725302	−0.362651	−	0.931925i	$-0.618128\pi$
$373$	−14.0079	−0.725302	−0.362651	+	0.931925i	$0.618128\pi$
$374$	−0.990470	−0.0512160
$375$	0.0793166	0.00409589
$376$	5.18264	0.267274
$377$	−6.62816	−0.341368
$378$	−0.121223	−0.00623504
$379$	−19.6415	−1.00892	−0.504458	−	0.863436i	$-0.668308\pi$
$379$	−19.6415	−1.00892	−0.504458	+	0.863436i	$0.668308\pi$
$380$	5.98047	0.306791
$381$	8.09640	0.414791
$382$	1.68219	0.0860684
$383$	18.6096	0.950906	0.475453	−	0.879741i	$-0.342284\pi$
$383$	18.6096	0.950906	0.475453	+	0.879741i	$0.342284\pi$
$384$	−11.3824	−0.580854
$385$	0.995521	0.0507364
$386$	11.4279	0.581663
$387$	12.5282	0.636844
$388$	−4.16880	−0.211639
$389$	−19.0565	−0.966205	−0.483102	−	0.875564i	$-0.660490\pi$
$389$	−19.0565	−0.966205	−0.483102	+	0.875564i	$0.660490\pi$
$390$	−2.04479	−0.103542
$391$	−0.115056	−0.00581866
$392$	15.5649	0.786148
$393$	15.2332	0.768415
$394$	−1.58554	−0.0798783
$395$	3.16624	0.159311
$396$	2.59355	0.130331
$397$	−28.2679	−1.41872	−0.709362	−	0.704844i	$-0.751017\pi$
$397$	−28.2679	−1.41872	−0.709362	+	0.704844i	$0.751017\pi$
$398$	13.5271	0.678052
$399$	0.228984	0.0114635
$400$	9.31940	0.465970
$401$	30.5463	1.52541	0.762704	−	0.646747i	$-0.223871\pi$
$401$	30.5463	1.52541	0.762704	+	0.646747i	$0.223871\pi$
$402$	5.63333	0.280965
$403$	1.79301	0.0893160
$404$	27.2037	1.35343
$405$	3.16624	0.157332
$406$	−0.768835	−0.0381566
$407$	−9.79269	−0.485406
$408$	−2.23585	−0.110691
$409$	16.4649	0.814136	0.407068	−	0.913398i	$-0.366551\pi$
$409$	16.4649	0.814136	0.407068	+	0.913398i	$0.366551\pi$
$410$	6.72721	0.332233
$411$	1.28533	0.0634006
$412$	−18.4960	−0.911235
$413$	−0.477194	−0.0234812
$414$	−0.0711002	−0.00349438
$415$	5.65152	0.277422
$416$	−5.87095	−0.287847
$417$	17.5726	0.860536
$418$	1.15617	0.0565500
$419$	−18.6467	−0.910952	−0.455476	−	0.890248i	$-0.650531\pi$
$419$	−18.6467	−0.910952	−0.455476	+	0.890248i	$0.650531\pi$
$420$	1.00504	0.0490407
$421$	31.5927	1.53973	0.769867	−	0.638204i	$-0.220322\pi$
$421$	31.5927	1.53973	0.769867	+	0.638204i	$0.220322\pi$
$422$	−17.6879	−0.861032
$423$	−2.31797	−0.112704
$424$	−23.6242	−1.14729
$425$	5.02505	0.243751
$426$	4.52119	0.219052
$427$	0.217801	0.0105401
$428$	−22.5803	−1.09146
$429$	1.67505	0.0808720
$430$	24.5127	1.18211
$431$	5.08958	0.245156	0.122578	−	0.992459i	$-0.460884\pi$
$431$	5.08958	0.245156	0.122578	+	0.992459i	$0.460884\pi$
$432$	1.85459	0.0892289
$433$	−25.4887	−1.22491	−0.612455	−	0.790505i	$-0.709818\pi$
$433$	−25.4887	−1.22491	−0.612455	+	0.790505i	$0.709818\pi$
$434$	0.207980	0.00998336
$435$	20.0813	0.962823
$436$	22.6486	1.08467
$437$	0.134304	0.00642465
$438$	4.44513	0.212396
$439$	−4.28434	−0.204480	−0.102240	−	0.994760i	$-0.532601\pi$
$439$	−4.28434	−0.204480	−0.102240	+	0.994760i	$0.532601\pi$
$440$	11.3467	0.540931
$441$	−6.96152	−0.331501
$442$	−0.645810	−0.0307180
$443$	28.2386	1.34166	0.670828	−	0.741613i	$-0.265939\pi$
$443$	28.2386	1.34166	0.670828	+	0.741613i	$0.265939\pi$
$444$	−9.88628	−0.469182
$445$	−35.6488	−1.68992
$446$	13.4239	0.635640
$447$	−6.01942	−0.284709
$448$	0.0466146	0.00220233
$449$	−8.37226	−0.395111	−0.197556	−	0.980292i	$-0.563300\pi$
$449$	−8.37226	−0.395111	−0.197556	+	0.980292i	$0.563300\pi$
$450$	3.10527	0.146384
$451$	−5.51079	−0.259493
$452$	22.7212	1.06872
$453$	−3.52648	−0.165689
$454$	−4.52845	−0.212531
$455$	0.649103	0.0304304
$456$	2.60989	0.122219
$457$	−15.6571	−0.732409	−0.366204	−	0.930534i	$-0.619343\pi$
$457$	−15.6571	−0.732409	−0.366204	+	0.930534i	$0.619343\pi$
$458$	−6.32376	−0.295490
$459$	1.00000	0.0466760
$460$	0.589477	0.0274845
$461$	0.739633	0.0344482	0.0172241	−	0.999852i	$-0.494517\pi$
$461$	0.739633	0.0344482	0.0172241	+	0.999852i	$0.494517\pi$
$462$	0.194297	0.00903953
$463$	−5.41429	−0.251623	−0.125812	−	0.992054i	$-0.540153\pi$
$463$	−5.41429	−0.251623	−0.125812	+	0.992054i	$0.540153\pi$
$464$	11.7624	0.546055
$465$	−5.43225	−0.251915
$466$	−0.0431124	−0.00199714
$467$	−9.91253	−0.458697	−0.229348	−	0.973344i	$-0.573660\pi$
$467$	−9.91253	−0.458697	−0.229348	+	0.973344i	$0.573660\pi$
$468$	1.69105	0.0781690
$469$	−1.78826	−0.0825742
$470$	−4.53535	−0.209200
$471$	17.4114	0.802277
$472$	−5.43893	−0.250347
$473$	−20.0803	−0.923293
$474$	0.617959	0.0283838
$475$	−5.86570	−0.269137
$476$	0.317423	0.0145490
$477$	10.5661	0.483787
$478$	−7.17220	−0.328049
$479$	−5.53695	−0.252989	−0.126495	−	0.991967i	$-0.540373\pi$
$479$	−5.53695	−0.252989	−0.126495	+	0.991967i	$0.540373\pi$
$480$	17.7872	0.811870
$481$	−6.38507	−0.291134
$482$	−14.2841	−0.650621
$483$	0.0225703	0.00102698
$484$	13.6424	0.620111
$485$	8.15720	0.370400
$486$	0.617959	0.0280312
$487$	−23.9481	−1.08519	−0.542596	−	0.839994i	$-0.682558\pi$
$487$	−23.9481	−1.08519	−0.542596	+	0.839994i	$0.682558\pi$
$488$	2.48244	0.112375
$489$	2.48073	0.112183
$490$	−13.6209	−0.615331
$491$	−29.3370	−1.32396	−0.661980	−	0.749521i	$-0.730284\pi$
$491$	−29.3370	−1.32396	−0.661980	+	0.749521i	$0.730284\pi$
$492$	−5.56346	−0.250820
$493$	6.34232	0.285644
$494$	0.753848	0.0339172
$495$	−5.07487	−0.228098
$496$	−3.18188	−0.142871
$497$	−1.43522	−0.0643784
$498$	1.10302	0.0494273
$499$	−26.7345	−1.19680	−0.598400	−	0.801197i	$-0.704197\pi$
$499$	−26.7345	−1.19680	−0.598400	+	0.801197i	$0.704197\pi$
$500$	−0.128344	−0.00573973
$501$	11.6166	0.518991
$502$	16.9654	0.757204
$503$	−4.75319	−0.211934	−0.105967	−	0.994370i	$-0.533794\pi$
$503$	−4.75319	−0.211934	−0.105967	+	0.994370i	$0.533794\pi$
$504$	0.438600	0.0195368
$505$	−53.2303	−2.36872
$506$	0.113960	0.00506614
$507$	−11.9078	−0.528845
$508$	−13.1010	−0.581263
$509$	−0.0359670	−0.00159421	−0.000797104	−	1.00000i	$-0.500254\pi$
$509$	−0.0359670	−0.00159421	−0.000797104		1.00000i	$0.500254\pi$
$510$	1.95660	0.0866399
$511$	−1.41107	−0.0624222
$512$	18.7118	0.826953
$513$	−1.16729	−0.0515372
$514$	−8.25621	−0.364166
$515$	36.1918	1.59480
$516$	−20.2722	−0.892434
$517$	3.71526	0.163397
$518$	−0.740637	−0.0325417
$519$	−23.0693	−1.01263
$520$	7.39829	0.324437
$521$	30.0519	1.31660	0.658298	−	0.752757i	$-0.271277\pi$
$521$	30.0519	1.31660	0.658298	+	0.752757i	$0.271277\pi$
$522$	3.91929	0.171543
$523$	7.94136	0.347251	0.173626	−	0.984812i	$-0.444452\pi$
$523$	7.94136	0.347251	0.173626	+	0.984812i	$0.444452\pi$
$524$	−24.6493	−1.07681
$525$	−0.985748	−0.0430216
$526$	−0.756589	−0.0329888
$527$	−1.71568	−0.0747363
$528$	−2.97255	−0.129364
$529$	−22.9868	−0.999424
$530$	20.6736	0.898005
$531$	2.43259	0.105566
$532$	−0.370525	−0.0160643
$533$	−3.59317	−0.155637
$534$	−6.95763	−0.301086
$535$	44.1836	1.91022
$536$	−20.3821	−0.880373
$537$	−17.6162	−0.760196
$538$	−0.987057	−0.0425551
$539$	11.1580	0.480608
$540$	−5.12337	−0.220475
$541$	36.4884	1.56876	0.784380	−	0.620281i	$-0.212981\pi$
$541$	36.4884	1.56876	0.784380	+	0.620281i	$0.212981\pi$
$542$	−0.779182	−0.0334687
$543$	−15.5593	−0.667713
$544$	5.61777	0.240860
$545$	−44.3171	−1.89834
$546$	0.126686	0.00542168
$547$	−26.7293	−1.14286	−0.571431	−	0.820650i	$-0.693611\pi$
$547$	−26.7293	−1.14286	−0.571431	+	0.820650i	$0.693611\pi$
$548$	−2.07982	−0.0888457
$549$	−1.11029	−0.0473859
$550$	−4.97716	−0.212227
$551$	−7.40333	−0.315392
$552$	0.257249	0.0109493
$553$	−0.196167	−0.00834186
$554$	11.6631	0.495516
$555$	19.3448	0.821140
$556$	−28.4348	−1.20590
$557$	−4.77334	−0.202253	−0.101126	−	0.994874i	$-0.532245\pi$
$557$	−4.77334	−0.202253	−0.101126	+	0.994874i	$0.532245\pi$
$558$	−1.06022	−0.0448827
$559$	−13.0928	−0.553767
$560$	−1.15190	−0.0486768
$561$	−1.60281	−0.0676706
$562$	9.73281	0.410554
$563$	12.4910	0.526431	0.263215	−	0.964737i	$-0.415217\pi$
$563$	12.4910	0.526431	0.263215	+	0.964737i	$0.415217\pi$
$564$	3.75077	0.157936
$565$	−44.4592	−1.87041
$566$	−14.5203	−0.610334
$567$	−0.196167	−0.00823823
$568$	−16.3582	−0.686376
$569$	35.7826	1.50008	0.750042	−	0.661390i	$-0.230033\pi$
$569$	35.7826	1.50008	0.750042	+	0.661390i	$0.230033\pi$
$570$	−2.28393	−0.0956632
$571$	−4.08656	−0.171017	−0.0855086	−	0.996337i	$-0.527252\pi$
$571$	−4.08656	−0.171017	−0.0855086	+	0.996337i	$0.527252\pi$
$572$	−2.71044	−0.113329
$573$	2.72217	0.113720
$574$	−0.416790	−0.0173965
$575$	−0.578165	−0.0241111
$576$	−0.237627	−0.00990113
$577$	20.0692	0.835492	0.417746	−	0.908564i	$-0.362820\pi$
$577$	20.0692	0.835492	0.417746	+	0.908564i	$0.362820\pi$
$578$	0.617959	0.0257037
$579$	18.4929	0.768540
$580$	−32.4940	−1.34924
$581$	−0.350145	−0.0145264
$582$	1.59205	0.0659927
$583$	−16.9354	−0.701393
$584$	−16.0830	−0.665520
$585$	−3.30894	−0.136808
$586$	−0.966189	−0.0399129
$587$	28.7936	1.18844	0.594220	−	0.804303i	$-0.297461\pi$
$587$	28.7936	1.18844	0.594220	+	0.804303i	$0.297461\pi$
$588$	11.2646	0.464545
$589$	2.00270	0.0825198
$590$	4.75962	0.195951
$591$	−2.56577	−0.105542
$592$	11.3310	0.465701
$593$	−22.7560	−0.934475	−0.467238	−	0.884132i	$-0.654751\pi$
$593$	−22.7560	−0.934475	−0.467238	+	0.884132i	$0.654751\pi$
$594$	−0.990470	−0.0406395
$595$	−0.621110	−0.0254630
$596$	9.74019	0.398974
$597$	21.8900	0.895896
$598$	0.0743046	0.00303854
$599$	6.68465	0.273127	0.136564	−	0.990631i	$-0.456394\pi$
$599$	6.68465	0.273127	0.136564	+	0.990631i	$0.456394\pi$
$600$	−11.2353	−0.458678
$601$	−44.0129	−1.79532	−0.897661	−	0.440687i	$-0.854735\pi$
$601$	−44.0129	−1.79532	−0.897661	+	0.440687i	$0.854735\pi$
$602$	−1.51870	−0.0618978
$603$	9.11603	0.371233
$604$	5.70629	0.232186
$605$	−26.6946	−1.08529
$606$	−10.3890	−0.422026
$607$	−3.01812	−0.122502	−0.0612508	−	0.998122i	$-0.519509\pi$
$607$	−3.01812	−0.122502	−0.0612508	+	0.998122i	$0.519509\pi$
$608$	−6.55757	−0.265945
$609$	−1.24415	−0.0504156
$610$	−2.17239	−0.0879576
$611$	2.42244	0.0980014
$612$	−1.61813	−0.0654089
$613$	−4.26320	−0.172189	−0.0860946	−	0.996287i	$-0.527439\pi$
$613$	−4.26320	−0.172189	−0.0860946	+	0.996287i	$0.527439\pi$
$614$	−6.64932	−0.268345
$615$	10.8862	0.438973
$616$	−0.702992	−0.0283244
$617$	−48.7716	−1.96347	−0.981736	−	0.190250i	$-0.939070\pi$
$617$	−48.7716	−1.96347	−0.981736	+	0.190250i	$0.939070\pi$
$618$	7.06360	0.284140
$619$	−35.7957	−1.43875	−0.719376	−	0.694621i	$-0.755572\pi$
$619$	−35.7957	−1.43875	−0.719376	+	0.694621i	$0.755572\pi$
$620$	8.79008	0.353018
$621$	−0.115056	−0.00461706
$622$	1.45079	0.0581713
$623$	2.20865	0.0884877
$624$	−1.93817	−0.0775890
$625$	−24.8741	−0.994965
$626$	−5.88190	−0.235088
$627$	1.87094	0.0747183
$628$	−28.1739	−1.12426
$629$	6.10971	0.243610
$630$	−0.383821	−0.0152918
$631$	0.772760	0.0307631	0.0153815	−	0.999882i	$-0.495104\pi$
$631$	0.772760	0.0307631	0.0153815	+	0.999882i	$0.495104\pi$
$632$	−2.23585	−0.0889375
$633$	−28.6231	−1.13766
$634$	−16.0000	−0.635440
$635$	25.6351	1.01730
$636$	−17.0973	−0.677950
$637$	7.27527	0.288257
$638$	−6.28187	−0.248702
$639$	7.31632	0.289429
$640$	−36.0393	−1.42458
$641$	5.09923	0.201407	0.100704	−	0.994916i	$-0.467891\pi$
$641$	5.09923	0.201407	0.100704	+	0.994916i	$0.467891\pi$
$642$	8.62337	0.340337
$643$	−8.23208	−0.324642	−0.162321	−	0.986738i	$-0.551898\pi$
$643$	−8.23208	−0.324642	−0.162321	+	0.986738i	$0.551898\pi$
$644$	−0.0365215	−0.00143915
$645$	39.6672	1.56189
$646$	−0.721338	−0.0283807
$647$	38.8970	1.52920	0.764599	−	0.644506i	$-0.222937\pi$
$647$	38.8970	1.52920	0.764599	+	0.644506i	$0.222937\pi$
$648$	−2.23585	−0.0878326
$649$	−3.89898	−0.153048
$650$	−3.24523	−0.127288
$651$	0.336560	0.0131908
$652$	−4.01414	−0.157206
$653$	−6.42336	−0.251365	−0.125683	−	0.992070i	$-0.540112\pi$
$653$	−6.42336	−0.251365	−0.125683	+	0.992070i	$0.540112\pi$
$654$	−8.64944	−0.338220
$655$	48.2320	1.88458
$656$	6.37646	0.248959
$657$	7.19324	0.280635
$658$	0.280991	0.0109542
$659$	−3.79696	−0.147909	−0.0739543	−	0.997262i	$-0.523562\pi$
$659$	−3.79696	−0.147909	−0.0739543	+	0.997262i	$0.523562\pi$
$660$	8.21178	0.319643
$661$	−17.2634	−0.671468	−0.335734	−	0.941957i	$-0.608984\pi$
$661$	−17.2634	−0.671468	−0.335734	+	0.941957i	$0.608984\pi$
$662$	7.56076	0.293857
$663$	−1.04507	−0.0405871
$664$	−3.99085	−0.154875
$665$	0.725017	0.0281149
$666$	3.77555	0.146300
$667$	−0.729725	−0.0282551
$668$	−18.7971	−0.727282
$669$	21.7230	0.839858
$670$	17.8365	0.689082
$671$	1.77958	0.0686998
$672$	−1.10202	−0.0425113
$673$	−12.6941	−0.489320	−0.244660	−	0.969609i	$-0.578676\pi$
$673$	−12.6941	−0.489320	−0.244660	+	0.969609i	$0.578676\pi$
$674$	15.7081	0.605053
$675$	5.02505	0.193414
$676$	19.2684	0.741092
$677$	−6.23783	−0.239739	−0.119870	−	0.992790i	$-0.538248\pi$
$677$	−6.23783	−0.239739	−0.119870	+	0.992790i	$0.538248\pi$
$678$	−8.67718	−0.333245
$679$	−0.505386	−0.0193949
$680$	−7.07924	−0.271476
$681$	−7.32807	−0.280812
$682$	1.69933	0.0650707
$683$	−16.4951	−0.631166	−0.315583	−	0.948898i	$-0.602200\pi$
$683$	−16.4951	−0.631166	−0.315583	+	0.948898i	$0.602200\pi$
$684$	1.88883	0.0722210
$685$	4.06965	0.155493
$686$	1.69246	0.0646183
$687$	−10.2333	−0.390425
$688$	23.2346	0.885812
$689$	−11.0423	−0.420677
$690$	−0.225120	−0.00857017
$691$	6.37863	0.242654	0.121327	−	0.992613i	$-0.461285\pi$
$691$	6.37863	0.242654	0.121327	+	0.992613i	$0.461285\pi$
$692$	37.3291	1.41904
$693$	0.314418	0.0119437
$694$	7.03996	0.267233
$695$	55.6391	2.11051
$696$	−14.1805	−0.537510
$697$	3.43821	0.130231
$698$	12.6295	0.478032
$699$	−0.0697658	−0.00263878
$700$	1.59507	0.0602878
$701$	−40.4775	−1.52882	−0.764408	−	0.644733i	$-0.776969\pi$
$701$	−40.4775	−1.52882	−0.764408	+	0.644733i	$0.776969\pi$
$702$	−0.645810	−0.0243745
$703$	−7.13181	−0.268981
$704$	0.380871	0.0143546
$705$	−7.33924	−0.276412
$706$	18.2366	0.686343
$707$	3.29793	0.124031
$708$	−3.93625	−0.147933
$709$	45.2526	1.69950	0.849749	−	0.527188i	$-0.176754\pi$
$709$	45.2526	1.69950	0.849749	+	0.527188i	$0.176754\pi$
$710$	14.3151	0.537238
$711$	1.00000	0.0375029
$712$	25.1736	0.943420
$713$	0.197400	0.00739270
$714$	−0.121223	−0.00453666
$715$	5.30359	0.198343
$716$	28.5053	1.06529
$717$	−11.6063	−0.433445
$718$	−0.329147	−0.0122837
$719$	−15.9816	−0.596015	−0.298007	−	0.954564i	$-0.596322\pi$
$719$	−15.9816	−0.596015	−0.298007	+	0.954564i	$0.596322\pi$
$720$	5.87206	0.218839
$721$	−2.24229	−0.0835072
$722$	−10.8992	−0.405626
$723$	−23.1149	−0.859652
$724$	25.1769	0.935693
$725$	31.8705	1.18364
$726$	−5.21001	−0.193362
$727$	−12.7681	−0.473541	−0.236771	−	0.971566i	$-0.576089\pi$
$727$	−12.7681	−0.473541	−0.236771	+	0.971566i	$0.576089\pi$
$728$	−0.458367	−0.0169882
$729$	1.00000	0.0370370
$730$	14.0743	0.520914
$731$	12.5282	0.463372
$732$	1.79659	0.0664037
$733$	−49.2623	−1.81955	−0.909773	−	0.415107i	$-0.863744\pi$
$733$	−49.2623	−1.81955	−0.909773	+	0.415107i	$0.863744\pi$
$734$	9.96710	0.367892
$735$	−22.0418	−0.813024
$736$	−0.646360	−0.0238252
$737$	−14.6112	−0.538212
$738$	2.12467	0.0782103
$739$	−37.0887	−1.36433	−0.682165	−	0.731198i	$-0.738961\pi$
$739$	−37.0887	−1.36433	−0.682165	+	0.731198i	$0.738961\pi$
$740$	−31.3023	−1.15070
$741$	1.21990	0.0448141
$742$	−1.28085	−0.0470215
$743$	−43.6284	−1.60057	−0.800286	−	0.599618i	$-0.795319\pi$
$743$	−43.6284	−1.60057	−0.800286	+	0.599618i	$0.795319\pi$
$744$	3.83601	0.140635
$745$	−19.0589	−0.698265
$746$	−8.65632	−0.316930
$747$	1.78493	0.0653073
$748$	2.59355	0.0948295
$749$	−2.73743	−0.100024
$750$	0.0490144	0.00178975
$751$	−46.0139	−1.67907	−0.839535	−	0.543305i	$-0.817173\pi$
$751$	−46.0139	−1.67907	−0.839535	+	0.543305i	$0.817173\pi$
$752$	−4.29888	−0.156764
$753$	27.4540	1.00048
$754$	−4.09593	−0.149165
$755$	−11.1657	−0.406360
$756$	0.317423	0.0115446
$757$	9.17048	0.333307	0.166653	−	0.986016i	$-0.446704\pi$
$757$	9.17048	0.333307	0.166653	+	0.986016i	$0.446704\pi$
$758$	−12.1376	−0.440859
$759$	0.184414	0.00669379
$760$	8.26354	0.299750
$761$	23.7141	0.859636	0.429818	−	0.902916i	$-0.358578\pi$
$761$	23.7141	0.859636	0.429818	+	0.902916i	$0.358578\pi$
$762$	5.00324	0.181248
$763$	2.74570	0.0994011
$764$	−4.40482	−0.159361
$765$	3.16624	0.114476
$766$	11.5000	0.415511
$767$	−2.54223	−0.0917946
$768$	−6.55859	−0.236663
$769$	−24.5122	−0.883932	−0.441966	−	0.897032i	$-0.645719\pi$
$769$	−24.5122	−0.883932	−0.441966	+	0.897032i	$0.645719\pi$
$770$	0.615191	0.0221699
$771$	−13.3605	−0.481165
$772$	−29.9239	−1.07698
$773$	3.47380	0.124944	0.0624720	−	0.998047i	$-0.480102\pi$
$773$	3.47380	0.124944	0.0624720	+	0.998047i	$0.480102\pi$
$774$	7.74191	0.278277
$775$	−8.62139	−0.309689
$776$	−5.76025	−0.206781
$777$	−1.19852	−0.0429967
$778$	−11.7762	−0.422196
$779$	−4.01339	−0.143795
$780$	5.35428	0.191714
$781$	−11.7267	−0.419613
$782$	−0.0711002	−0.00254254
$783$	6.34232	0.226656
$784$	−12.9107	−0.461098
$785$	55.1287	1.96763
$786$	9.41351	0.335769
$787$	9.55063	0.340443	0.170222	−	0.985406i	$-0.445552\pi$
$787$	9.55063	0.340443	0.170222	+	0.985406i	$0.445552\pi$
$788$	4.15174	0.147899
$789$	−1.22433	−0.0435875
$790$	1.95660	0.0696128
$791$	2.75451	0.0979391
$792$	3.58365	0.127339
$793$	1.16033	0.0412044
$794$	−17.4684	−0.619930
$795$	33.4547	1.18652
$796$	−35.4207	−1.25545
$797$	8.61101	0.305018	0.152509	−	0.988302i	$-0.451265\pi$
$797$	8.61101	0.305018	0.152509	+	0.988302i	$0.451265\pi$
$798$	0.141503	0.00500914
$799$	−2.31797	−0.0820039
$800$	28.2296	0.998066
$801$	−11.2590	−0.397819
$802$	18.8763	0.666547
$803$	−11.5294	−0.406863
$804$	−14.7509	−0.520224
$805$	0.0714628	0.00251873
$806$	1.10800	0.0390278
$807$	−1.59729	−0.0562271
$808$	37.5888	1.32237
$809$	50.6875	1.78208	0.891039	−	0.453927i	$-0.149977\pi$
$809$	50.6875	1.78208	0.891039	+	0.453927i	$0.149977\pi$
$810$	1.95660	0.0687480
$811$	−40.5563	−1.42412	−0.712062	−	0.702116i	$-0.752239\pi$
$811$	−40.5563	−1.42412	−0.712062	+	0.702116i	$0.752239\pi$
$812$	2.01320	0.0706493
$813$	−1.26090	−0.0442216
$814$	−6.05148	−0.212104
$815$	7.85459	0.275134
$816$	1.85459	0.0649236
$817$	−14.6240	−0.511631
$818$	10.1746	0.355747
$819$	0.205008	0.00716355
$820$	−17.6152	−0.615150
$821$	37.6706	1.31471	0.657356	−	0.753580i	$-0.271675\pi$
$821$	37.6706	1.31471	0.657356	+	0.753580i	$0.271675\pi$
$822$	0.794280	0.0277037
$823$	−19.2670	−0.671606	−0.335803	−	0.941932i	$-0.609008\pi$
$823$	−19.2670	−0.671606	−0.335803	+	0.941932i	$0.609008\pi$
$824$	−25.5570	−0.890320
$825$	−8.05419	−0.280411
$826$	−0.294886	−0.0102604
$827$	37.2925	1.29679	0.648393	−	0.761306i	$-0.275441\pi$
$827$	37.2925	1.29679	0.648393	+	0.761306i	$0.275441\pi$
$828$	0.186176	0.00647006
$829$	−24.0886	−0.836631	−0.418316	−	0.908302i	$-0.637379\pi$
$829$	−24.0886	−0.836631	−0.418316	+	0.908302i	$0.637379\pi$
$830$	3.49241	0.121223
$831$	18.8735	0.654715
$832$	0.248337	0.00860953
$833$	−6.96152	−0.241202
$834$	10.8592	0.376022
$835$	36.7809	1.27285
$836$	−3.02743	−0.104706
$837$	−1.71568	−0.0593026
$838$	−11.5229	−0.398052
$839$	−17.7381	−0.612388	−0.306194	−	0.951969i	$-0.599056\pi$
$839$	−17.7381	−0.612388	−0.306194	+	0.951969i	$0.599056\pi$
$840$	1.38871	0.0479151
$841$	11.2250	0.387068
$842$	19.5230	0.672807
$843$	15.7499	0.542456
$844$	46.3157	1.59425
$845$	−37.7030	−1.29702
$846$	−1.43241	−0.0492473
$847$	1.65388	0.0568281
$848$	19.5957	0.672920
$849$	−23.4972	−0.806422
$850$	3.10527	0.106510
$851$	−0.702961	−0.0240972
$852$	−11.8387	−0.405588
$853$	−4.87180	−0.166807	−0.0834037	−	0.996516i	$-0.526579\pi$
$853$	−4.87180	−0.166807	−0.0834037	+	0.996516i	$0.526579\pi$
$854$	0.134592	0.00460565
$855$	−3.69592	−0.126398
$856$	−31.2005	−1.06641
$857$	42.5821	1.45458	0.727289	−	0.686331i	$-0.240780\pi$
$857$	42.5821	1.45458	0.727289	+	0.686331i	$0.240780\pi$
$858$	1.03511	0.0353380
$859$	37.0814	1.26520	0.632600	−	0.774479i	$-0.281988\pi$
$859$	37.0814	1.26520	0.632600	+	0.774479i	$0.281988\pi$
$860$	−64.1866	−2.18874
$861$	−0.674462	−0.0229856
$862$	3.14515	0.107124
$863$	9.01460	0.306861	0.153430	−	0.988159i	$-0.450968\pi$
$863$	9.01460	0.306861	0.153430	+	0.988159i	$0.450968\pi$
$864$	5.61777	0.191120
$865$	−73.0429	−2.48353
$866$	−15.7510	−0.535240
$867$	1.00000	0.0339618
$868$	−0.544596	−0.0184848
$869$	−1.60281	−0.0543716
$870$	12.4094	0.420718
$871$	−9.52688	−0.322806
$872$	31.2948	1.05977
$873$	2.57631	0.0871949
$874$	0.0829946	0.00280733
$875$	−0.0155593	−0.000526000 0
$876$	−11.6396	−0.393265
$877$	−56.1196	−1.89503	−0.947513	−	0.319718i	$-0.896412\pi$
$877$	−56.1196	−1.89503	−0.947513	+	0.319718i	$0.896412\pi$
$878$	−2.64754	−0.0893503
$879$	−1.56352	−0.0527361
$880$	−9.41179	−0.317271
$881$	−16.2482	−0.547415	−0.273707	−	0.961813i	$-0.588250\pi$
$881$	−16.2482	−0.547415	−0.273707	+	0.961813i	$0.588250\pi$
$882$	−4.30193	−0.144854
$883$	−45.5590	−1.53318	−0.766591	−	0.642136i	$-0.778049\pi$
$883$	−45.5590	−1.53318	−0.766591	+	0.642136i	$0.778049\pi$
$884$	1.69105	0.0568763
$885$	7.70217	0.258906
$886$	17.4503	0.586254
$887$	27.7332	0.931188	0.465594	−	0.884998i	$-0.345841\pi$
$887$	27.7332	0.931188	0.465594	+	0.884998i	$0.345841\pi$
$888$	−13.6604	−0.458413
$889$	−1.58824	−0.0532680
$890$	−22.0295	−0.738430
$891$	−1.60281	−0.0536961
$892$	−35.1505	−1.17693
$893$	2.70575	0.0905443
$894$	−3.71976	−0.124407
$895$	−55.7771	−1.86442
$896$	2.23284	0.0745941
$897$	0.120242	0.00401476
$898$	−5.17371	−0.172649
$899$	−10.8814	−0.362915
$900$	−8.13117	−0.271039
$901$	10.5661	0.352007
$902$	−3.40544	−0.113389
$903$	−2.45761	−0.0817843
$904$	31.3951	1.04419
$905$	−49.2644	−1.63760
$906$	−2.17922	−0.0723998
$907$	−38.9730	−1.29408	−0.647038	−	0.762458i	$-0.723993\pi$
$907$	−38.9730	−1.29408	−0.647038	+	0.762458i	$0.723993\pi$
$908$	11.8577	0.393513
$909$	−16.8118	−0.557614
$910$	0.401119	0.0132970
$911$	−11.6704	−0.386657	−0.193328	−	0.981134i	$-0.561928\pi$
$911$	−11.6704	−0.386657	−0.193328	+	0.981134i	$0.561928\pi$
$912$	−2.16484	−0.0716852
$913$	−2.86091	−0.0946822
$914$	−9.67545	−0.320035
$915$	−3.51543	−0.116217
$916$	16.5588	0.547118
$917$	−2.98825	−0.0986808
$918$	0.617959	0.0203957
$919$	−35.4366	−1.16895	−0.584473	−	0.811413i	$-0.698699\pi$
$919$	−35.4366	−1.16895	−0.584473	+	0.811413i	$0.698699\pi$
$920$	0.814513	0.0268537
$921$	−10.7601	−0.354558
$922$	0.457063	0.0150526
$923$	−7.64606	−0.251673
$924$	−0.508768	−0.0167372
$925$	30.7016	1.00946
$926$	−3.34581	−0.109950
$927$	11.4305	0.375428
$928$	35.6297	1.16960
$929$	−1.07006	−0.0351076	−0.0175538	−	0.999846i	$-0.505588\pi$
$929$	−1.07006	−0.0351076	−0.0175538	+	0.999846i	$0.505588\pi$
$930$	−3.35691	−0.110077
$931$	8.12612	0.266323
$932$	0.112890	0.00369783
$933$	2.34771	0.0768605
$934$	−6.12553	−0.200434
$935$	−5.07487	−0.165966
$936$	2.33662	0.0763749
$937$	34.7158	1.13412	0.567058	−	0.823678i	$-0.308081\pi$
$937$	34.7158	1.13412	0.567058	+	0.823678i	$0.308081\pi$
$938$	−1.10507	−0.0360819
$939$	−9.51827	−0.310617
$940$	11.8758	0.387347
$941$	26.9717	0.879253	0.439627	−	0.898181i	$-0.355111\pi$
$941$	26.9717	0.879253	0.439627	+	0.898181i	$0.355111\pi$
$942$	10.7596	0.350565
$943$	−0.395588	−0.0128821
$944$	4.51146	0.146836
$945$	−0.621110	−0.0202047
$946$	−12.4088	−0.403445
$947$	3.65450	0.118755	0.0593776	−	0.998236i	$-0.481088\pi$
$947$	3.65450	0.118755	0.0593776	+	0.998236i	$0.481088\pi$
$948$	−1.61813	−0.0525543
$949$	−7.51743	−0.244026
$950$	−3.62476	−0.117603
$951$	−25.8917	−0.839594
$952$	0.438600	0.0142151
$953$	−18.3292	−0.593742	−0.296871	−	0.954918i	$-0.595943\pi$
$953$	−18.3292	−0.593742	−0.296871	+	0.954918i	$0.595943\pi$
$954$	6.52940	0.211397
$955$	8.61904	0.278906
$956$	18.7804	0.607403
$957$	−10.1655	−0.328605
$958$	−3.42160	−0.110547
$959$	−0.252139	−0.00814198
$960$	−0.752384	−0.0242831
$961$	−28.0564	−0.905046
$962$	−3.94571	−0.127215
$963$	13.9546	0.449681
$964$	37.4028	1.20466
$965$	58.5530	1.88489
$966$	0.0139475	0.000448753 0
$967$	15.2000	0.488798	0.244399	−	0.969675i	$-0.421409\pi$
$967$	15.2000	0.488798	0.244399	+	0.969675i	$0.421409\pi$
$968$	18.8505	0.605878
$969$	−1.16729	−0.0374988
$970$	5.04082	0.161851
$971$	21.3639	0.685599	0.342800	−	0.939409i	$-0.388625\pi$
$971$	21.3639	0.685599	0.342800	+	0.939409i	$0.388625\pi$
$972$	−1.61813	−0.0519014
$973$	−3.44717	−0.110511
$974$	−14.7989	−0.474189
$975$	−5.25152	−0.168183
$976$	−2.05913	−0.0659110
$977$	0.662290	0.0211885	0.0105943	−	0.999944i	$-0.496628\pi$
$977$	0.662290	0.0211885	0.0105943	+	0.999944i	$0.496628\pi$
$978$	1.53299	0.0490196
$979$	18.0461	0.576756
$980$	35.6664	1.13932
$981$	−13.9968	−0.446883
$982$	−18.1291	−0.578522
$983$	−51.8503	−1.65377	−0.826883	−	0.562373i	$-0.809888\pi$
$983$	−51.8503	−1.65377	−0.826883	+	0.562373i	$0.809888\pi$
$984$	−7.68733	−0.245063
$985$	−8.12382	−0.258847
$986$	3.91929	0.124816
$987$	0.454709	0.0144735
$988$	−1.97395	−0.0627998
$989$	−1.44145	−0.0458354
$990$	−3.13606	−0.0996706
$991$	34.0048	1.08020	0.540099	−	0.841601i	$-0.318387\pi$
$991$	34.0048	1.08020	0.540099	+	0.841601i	$0.318387\pi$
$992$	−9.63830	−0.306016
$993$	12.2350	0.388268
$994$	−0.886906	−0.0281310
$995$	69.3088	2.19724
$996$	−2.88825	−0.0915176
$997$	−10.8324	−0.343064	−0.171532	−	0.985179i	$-0.554872\pi$
$997$	−10.8324	−0.343064	−0.171532	+	0.985179i	$0.554872\pi$
$998$	−16.5208	−0.522957
$999$	6.10971	0.193303

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.k.1.18	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.k.1.18	✓	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)

\(f(q)\)	\(=\)	\(q+0.617959 q^{2} +1.00000 q^{3} -1.61813 q^{4} +3.16624 q^{5} +0.617959 q^{6} -0.196167 q^{7} -2.23585 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.617959 q^{2} +1.00000 q^{3} -1.61813 q^{4} +3.16624 q^{5} +0.617959 q^{6} -0.196167 q^{7} -2.23585 q^{8} +1.00000 q^{9} +1.95660 q^{10} -1.60281 q^{11} -1.61813 q^{12} -1.04507 q^{13} -0.121223 q^{14} +3.16624 q^{15} +1.85459 q^{16} +1.00000 q^{17} +0.617959 q^{18} -1.16729 q^{19} -5.12337 q^{20} -0.196167 q^{21} -0.990470 q^{22} -0.115056 q^{23} -2.23585 q^{24} +5.02505 q^{25} -0.645810 q^{26} +1.00000 q^{27} +0.317423 q^{28} +6.34232 q^{29} +1.95660 q^{30} -1.71568 q^{31} +5.61777 q^{32} -1.60281 q^{33} +0.617959 q^{34} -0.621110 q^{35} -1.61813 q^{36} +6.10971 q^{37} -0.721338 q^{38} -1.04507 q^{39} -7.07924 q^{40} +3.43821 q^{41} -0.121223 q^{42} +12.5282 q^{43} +2.59355 q^{44} +3.16624 q^{45} -0.0711002 q^{46} -2.31797 q^{47} +1.85459 q^{48} -6.96152 q^{49} +3.10527 q^{50} +1.00000 q^{51} +1.69105 q^{52} +10.5661 q^{53} +0.617959 q^{54} -5.07487 q^{55} +0.438600 q^{56} -1.16729 q^{57} +3.91929 q^{58} +2.43259 q^{59} -5.12337 q^{60} -1.11029 q^{61} -1.06022 q^{62} -0.196167 q^{63} -0.237627 q^{64} -3.30894 q^{65} -0.990470 q^{66} +9.11603 q^{67} -1.61813 q^{68} -0.115056 q^{69} -0.383821 q^{70} +7.31632 q^{71} -2.23585 q^{72} +7.19324 q^{73} +3.77555 q^{74} +5.02505 q^{75} +1.88883 q^{76} +0.314418 q^{77} -0.645810 q^{78} +1.00000 q^{79} +5.87206 q^{80} +1.00000 q^{81} +2.12467 q^{82} +1.78493 q^{83} +0.317423 q^{84} +3.16624 q^{85} +7.74191 q^{86} +6.34232 q^{87} +3.58365 q^{88} -11.2590 q^{89} +1.95660 q^{90} +0.205008 q^{91} +0.186176 q^{92} -1.71568 q^{93} -1.43241 q^{94} -3.69592 q^{95} +5.61777 q^{96} +2.57631 q^{97} -4.30193 q^{98} -1.60281 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9}+O(q^{10}) \) 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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