LMFDB - Embedded newform 4029.2.a.k.1.9

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			1.9
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)

$f(q)$	$=$	$q-1.27443 q^{2} +1.00000 q^{3} -0.375837 q^{4} -3.50336 q^{5} -1.27443 q^{6} -0.192219 q^{7} +3.02783 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.27443 q^{2} +1.00000 q^{3} -0.375837 q^{4} -3.50336 q^{5} -1.27443 q^{6} -0.192219 q^{7} +3.02783 q^{8} +1.00000 q^{9} +4.46478 q^{10} +3.68610 q^{11} -0.375837 q^{12} -3.36950 q^{13} +0.244970 q^{14} -3.50336 q^{15} -3.10707 q^{16} +1.00000 q^{17} -1.27443 q^{18} +6.71698 q^{19} +1.31669 q^{20} -0.192219 q^{21} -4.69767 q^{22} +6.93165 q^{23} +3.02783 q^{24} +7.27356 q^{25} +4.29417 q^{26} +1.00000 q^{27} +0.0722432 q^{28} -7.85494 q^{29} +4.46478 q^{30} +6.58645 q^{31} -2.09592 q^{32} +3.68610 q^{33} -1.27443 q^{34} +0.673415 q^{35} -0.375837 q^{36} -4.80266 q^{37} -8.56029 q^{38} -3.36950 q^{39} -10.6076 q^{40} -10.0592 q^{41} +0.244970 q^{42} -12.2298 q^{43} -1.38537 q^{44} -3.50336 q^{45} -8.83388 q^{46} +6.12284 q^{47} -3.10707 q^{48} -6.96305 q^{49} -9.26962 q^{50} +1.00000 q^{51} +1.26638 q^{52} +5.67828 q^{53} -1.27443 q^{54} -12.9138 q^{55} -0.582008 q^{56} +6.71698 q^{57} +10.0105 q^{58} -4.78465 q^{59} +1.31669 q^{60} -8.22716 q^{61} -8.39395 q^{62} -0.192219 q^{63} +8.88525 q^{64} +11.8046 q^{65} -4.69767 q^{66} +9.89341 q^{67} -0.375837 q^{68} +6.93165 q^{69} -0.858218 q^{70} -9.09158 q^{71} +3.02783 q^{72} +14.6430 q^{73} +6.12064 q^{74} +7.27356 q^{75} -2.52449 q^{76} -0.708541 q^{77} +4.29417 q^{78} +1.00000 q^{79} +10.8852 q^{80} +1.00000 q^{81} +12.8197 q^{82} -4.79363 q^{83} +0.0722432 q^{84} -3.50336 q^{85} +15.5860 q^{86} -7.85494 q^{87} +11.1609 q^{88} +18.0558 q^{89} +4.46478 q^{90} +0.647682 q^{91} -2.60517 q^{92} +6.58645 q^{93} -7.80311 q^{94} -23.5320 q^{95} -2.09592 q^{96} -9.13412 q^{97} +8.87390 q^{98} +3.68610 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.27443	−0.901156	−0.450578	−	0.892737i	$-0.648782\pi$
$2$	−1.27443	−0.901156	−0.450578	+	0.892737i	$0.648782\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.375837	−0.187919
$5$	−3.50336	−1.56675	−0.783376	−	0.621548i	$-0.786504\pi$
$5$	−3.50336	−1.56675	−0.783376	+	0.621548i	$0.786504\pi$
$6$	−1.27443	−0.520282
$7$	−0.192219	−0.0726521	−0.0363261	−	0.999340i	$-0.511565\pi$
$7$	−0.192219	−0.0726521	−0.0363261	+	0.999340i	$0.511565\pi$
$8$	3.02783	1.07050
$9$	1.00000	0.333333
$10$	4.46478	1.41189
$11$	3.68610	1.11140	0.555701	−	0.831382i	$-0.312450\pi$
$11$	3.68610	1.11140	0.555701	+	0.831382i	$0.312450\pi$
$12$	−0.375837	−0.108495
$13$	−3.36950	−0.934530	−0.467265	−	0.884117i	$-0.654761\pi$
$13$	−3.36950	−0.934530	−0.467265	+	0.884117i	$0.654761\pi$
$14$	0.244970	0.0654709
$15$	−3.50336	−0.904565
$16$	−3.10707	−0.776768
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.27443	−0.300385
$19$	6.71698	1.54098	0.770490	−	0.637452i	$-0.220012\pi$
$19$	6.71698	1.54098	0.770490	+	0.637452i	$0.220012\pi$
$20$	1.31669	0.294422
$21$	−0.192219	−0.0419457
$22$	−4.69767	−1.00155
$23$	6.93165	1.44535	0.722674	−	0.691189i	$-0.242913\pi$
$23$	6.93165	1.44535	0.722674	+	0.691189i	$0.242913\pi$
$24$	3.02783	0.618053
$25$	7.27356	1.45471
$26$	4.29417	0.842157
$27$	1.00000	0.192450
$28$	0.0722432	0.0136527
$29$	−7.85494	−1.45863	−0.729313	−	0.684180i	$-0.760160\pi$
$29$	−7.85494	−1.45863	−0.729313	+	0.684180i	$0.760160\pi$
$30$	4.46478	0.815154
$31$	6.58645	1.18296	0.591481	−	0.806319i	$-0.298544\pi$
$31$	6.58645	1.18296	0.591481	+	0.806319i	$0.298544\pi$
$32$	−2.09592	−0.370511
$33$	3.68610	0.641668
$34$	−1.27443	−0.218562
$35$	0.673415	0.113828
$36$	−0.375837	−0.0626395
$37$	−4.80266	−0.789553	−0.394776	−	0.918777i	$-0.629178\pi$
$37$	−4.80266	−0.789553	−0.394776	+	0.918777i	$0.629178\pi$
$38$	−8.56029	−1.38866
$39$	−3.36950	−0.539551
$40$	−10.6076	−1.67721
$41$	−10.0592	−1.57098	−0.785492	−	0.618871i	$-0.787590\pi$
$41$	−10.0592	−1.57098	−0.785492	+	0.618871i	$0.787590\pi$
$42$	0.244970	0.0377996
$43$	−12.2298	−1.86503	−0.932513	−	0.361135i	$-0.882389\pi$
$43$	−12.2298	−1.86503	−0.932513	+	0.361135i	$0.882389\pi$
$44$	−1.38537	−0.208853
$45$	−3.50336	−0.522251
$46$	−8.83388	−1.30248
$47$	6.12284	0.893108	0.446554	−	0.894757i	$-0.352651\pi$
$47$	6.12284	0.893108	0.446554	+	0.894757i	$0.352651\pi$
$48$	−3.10707	−0.448467
$49$	−6.96305	−0.994722
$50$	−9.26962	−1.31092
$51$	1.00000	0.140028
$52$	1.26638	0.175615
$53$	5.67828	0.779972	0.389986	−	0.920821i	$-0.372480\pi$
$53$	5.67828	0.779972	0.389986	+	0.920821i	$0.372480\pi$
$54$	−1.27443	−0.173427
$55$	−12.9138	−1.74129
$56$	−0.582008	−0.0777741
$57$	6.71698	0.889685
$58$	10.0105	1.31445
$59$	−4.78465	−0.622908	−0.311454	−	0.950261i	$-0.600816\pi$
$59$	−4.78465	−0.622908	−0.311454	+	0.950261i	$0.600816\pi$
$60$	1.31669	0.169984
$61$	−8.22716	−1.05338	−0.526690	−	0.850058i	$-0.676567\pi$
$61$	−8.22716	−1.05338	−0.526690	+	0.850058i	$0.676567\pi$
$62$	−8.39395	−1.06603
$63$	−0.192219	−0.0242174
$64$	8.88525	1.11066
$65$	11.8046	1.46418
$66$	−4.69767	−0.578243
$67$	9.89341	1.20867	0.604336	−	0.796729i	$-0.293438\pi$
$67$	9.89341	1.20867	0.604336	+	0.796729i	$0.293438\pi$
$68$	−0.375837	−0.0455769
$69$	6.93165	0.834472
$70$	−0.858218	−0.102577
$71$	−9.09158	−1.07897	−0.539486	−	0.841995i	$-0.681381\pi$
$71$	−9.09158	−1.07897	−0.539486	+	0.841995i	$0.681381\pi$
$72$	3.02783	0.356833
$73$	14.6430	1.71383	0.856916	−	0.515456i	$-0.172377\pi$
$73$	14.6430	1.71383	0.856916	+	0.515456i	$0.172377\pi$
$74$	6.12064	0.711510
$75$	7.27356	0.839879
$76$	−2.52449	−0.289579
$77$	−0.708541	−0.0807457
$78$	4.29417	0.486219
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	10.8852	1.21700
$81$	1.00000	0.111111
$82$	12.8197	1.41570
$83$	−4.79363	−0.526169	−0.263084	−	0.964773i	$-0.584740\pi$
$83$	−4.79363	−0.526169	−0.263084	+	0.964773i	$0.584740\pi$
$84$	0.0722432	0.00788238
$85$	−3.50336	−0.379993
$86$	15.5860	1.68068
$87$	−7.85494	−0.842138
$88$	11.1609	1.18976
$89$	18.0558	1.91391	0.956955	−	0.290236i	$-0.0937339\pi$
$89$	18.0558	1.91391	0.956955	+	0.290236i	$0.0937339\pi$
$90$	4.46478	0.470629
$91$	0.647682	0.0678956
$92$	−2.60517	−0.271608
$93$	6.58645	0.682983
$94$	−7.80311	−0.804829
$95$	−23.5320	−2.41433
$96$	−2.09592	−0.213914
$97$	−9.13412	−0.927430	−0.463715	−	0.885984i	$-0.653484\pi$
$97$	−9.13412	−0.927430	−0.463715	+	0.885984i	$0.653484\pi$
$98$	8.87390	0.896399
$99$	3.68610	0.370467
$100$	−2.73367	−0.273367
$101$	10.5019	1.04497	0.522487	−	0.852647i	$-0.325004\pi$
$101$	10.5019	1.04497	0.522487	+	0.852647i	$0.325004\pi$
$102$	−1.27443	−0.126187
$103$	−10.3810	−1.02287	−0.511437	−	0.859321i	$-0.670887\pi$
$103$	−10.3810	−1.02287	−0.511437	+	0.859321i	$0.670887\pi$
$104$	−10.2023	−1.00041
$105$	0.673415	0.0657186
$106$	−7.23656	−0.702876
$107$	17.8893	1.72943	0.864714	−	0.502264i	$-0.167500\pi$
$107$	17.8893	1.72943	0.864714	+	0.502264i	$0.167500\pi$
$108$	−0.375837	−0.0361649
$109$	−3.37660	−0.323420	−0.161710	−	0.986838i	$-0.551701\pi$
$109$	−3.37660	−0.323420	−0.161710	+	0.986838i	$0.551701\pi$
$110$	16.4576	1.56917
$111$	−4.80266	−0.455848
$112$	0.597240	0.0564338
$113$	17.3123	1.62861	0.814303	−	0.580440i	$-0.197120\pi$
$113$	17.3123	1.62861	0.814303	+	0.580440i	$0.197120\pi$
$114$	−8.56029	−0.801745
$115$	−24.2841	−2.26450
$116$	2.95218	0.274103
$117$	−3.36950	−0.311510
$118$	6.09768	0.561337
$119$	−0.192219	−0.0176207
$120$	−10.6076	−0.968336
$121$	2.58736	0.235215
$122$	10.4849	0.949259
$123$	−10.0592	−0.907008
$124$	−2.47543	−0.222300
$125$	−7.96512	−0.712422
$126$	0.244970	0.0218236
$127$	−17.2313	−1.52903	−0.764515	−	0.644606i	$-0.777021\pi$
$127$	−17.2313	−1.52903	−0.764515	+	0.644606i	$0.777021\pi$
$128$	−7.13175	−0.630363
$129$	−12.2298	−1.07677
$130$	−15.0441	−1.31945
$131$	8.59473	0.750925	0.375463	−	0.926838i	$-0.377484\pi$
$131$	8.59473	0.750925	0.375463	+	0.926838i	$0.377484\pi$
$132$	−1.38537	−0.120581
$133$	−1.29113	−0.111955
$134$	−12.6084	−1.08920
$135$	−3.50336	−0.301522
$136$	3.02783	0.259634
$137$	2.88609	0.246575	0.123288	−	0.992371i	$-0.460656\pi$
$137$	2.88609	0.246575	0.123288	+	0.992371i	$0.460656\pi$
$138$	−8.83388	−0.751990
$139$	19.2120	1.62954	0.814772	−	0.579781i	$-0.196862\pi$
$139$	19.2120	1.62954	0.814772	+	0.579781i	$0.196862\pi$
$140$	−0.253094	−0.0213904
$141$	6.12284	0.515636
$142$	11.5866	0.972322
$143$	−12.4203	−1.03864
$144$	−3.10707	−0.258923
$145$	27.5187	2.28531
$146$	−18.6614	−1.54443
$147$	−6.96305	−0.574303
$148$	1.80502	0.148372
$149$	21.1504	1.73271	0.866354	−	0.499431i	$-0.166457\pi$
$149$	21.1504	1.73271	0.866354	+	0.499431i	$0.166457\pi$
$150$	−9.26962	−0.756862
$151$	−4.95582	−0.403299	−0.201649	−	0.979458i	$-0.564630\pi$
$151$	−4.95582	−0.403299	−0.201649	+	0.979458i	$0.564630\pi$
$152$	20.3379	1.64962
$153$	1.00000	0.0808452
$154$	0.902983	0.0727645
$155$	−23.0747	−1.85341
$156$	1.26638	0.101392
$157$	0.301101	0.0240305	0.0120152	−	0.999928i	$-0.496175\pi$
$157$	0.301101	0.0240305	0.0120152	+	0.999928i	$0.496175\pi$
$158$	−1.27443	−0.101388
$159$	5.67828	0.450317
$160$	7.34279	0.580498
$161$	−1.33240	−0.105008
$162$	−1.27443	−0.100128
$163$	−7.53850	−0.590461	−0.295231	−	0.955426i	$-0.595396\pi$
$163$	−7.53850	−0.590461	−0.295231	+	0.955426i	$0.595396\pi$
$164$	3.78062	0.295217
$165$	−12.9138	−1.00534
$166$	6.10913	0.474160
$167$	6.09009	0.471265	0.235633	−	0.971842i	$-0.424284\pi$
$167$	6.09009	0.471265	0.235633	+	0.971842i	$0.424284\pi$
$168$	−0.582008	−0.0449029
$169$	−1.64650	−0.126654
$170$	4.46478	0.342433
$171$	6.71698	0.513660
$172$	4.59641	0.350473
$173$	4.41379	0.335574	0.167787	−	0.985823i	$-0.446338\pi$
$173$	4.41379	0.335574	0.167787	+	0.985823i	$0.446338\pi$
$174$	10.0105	0.758898
$175$	−1.39812	−0.105688
$176$	−11.4530	−0.863302
$177$	−4.78465	−0.359636
$178$	−23.0108	−1.72473
$179$	19.7257	1.47437	0.737183	−	0.675694i	$-0.236156\pi$
$179$	19.7257	1.47437	0.737183	+	0.675694i	$0.236156\pi$
$180$	1.31669	0.0981406
$181$	9.79219	0.727848	0.363924	−	0.931429i	$-0.381437\pi$
$181$	9.79219	0.727848	0.363924	+	0.931429i	$0.381437\pi$
$182$	−0.825424	−0.0611845
$183$	−8.22716	−0.608169
$184$	20.9879	1.54724
$185$	16.8255	1.23703
$186$	−8.39395	−0.615474
$187$	3.68610	0.269555
$188$	−2.30119	−0.167832
$189$	−0.192219	−0.0139819
$190$	29.9898	2.17569
$191$	−10.1503	−0.734447	−0.367223	−	0.930133i	$-0.619692\pi$
$191$	−10.1503	−0.734447	−0.367223	+	0.930133i	$0.619692\pi$
$192$	8.88525	0.641237
$193$	−13.3311	−0.959592	−0.479796	−	0.877380i	$-0.659289\pi$
$193$	−13.3311	−0.959592	−0.479796	+	0.877380i	$0.659289\pi$
$194$	11.6408	0.835759
$195$	11.8046	0.845343
$196$	2.61697	0.186927
$197$	17.6002	1.25396	0.626982	−	0.779034i	$-0.284290\pi$
$197$	17.6002	1.25396	0.626982	+	0.779034i	$0.284290\pi$
$198$	−4.69767	−0.333849
$199$	−17.3624	−1.23079	−0.615393	−	0.788220i	$-0.711003\pi$
$199$	−17.3624	−1.23079	−0.615393	+	0.788220i	$0.711003\pi$
$200$	22.0231	1.55727
$201$	9.89341	0.697827
$202$	−13.3838	−0.941684
$203$	1.50987	0.105972
$204$	−0.375837	−0.0263139
$205$	35.2411	2.46134
$206$	13.2299	0.921768
$207$	6.93165	0.481783
$208$	10.4693	0.725913
$209$	24.7595	1.71265
$210$	−0.858218	−0.0592226
$211$	7.55215	0.519912	0.259956	−	0.965621i	$-0.416292\pi$
$211$	7.55215	0.519912	0.259956	+	0.965621i	$0.416292\pi$
$212$	−2.13411	−0.146571
$213$	−9.09158	−0.622945
$214$	−22.7987	−1.55848
$215$	42.8454	2.92204
$216$	3.02783	0.206018
$217$	−1.26604	−0.0859446
$218$	4.30323	0.291452
$219$	14.6430	0.989481
$220$	4.85347	0.327221
$221$	−3.36950	−0.226657
$222$	6.12064	0.410790
$223$	1.30002	0.0870556	0.0435278	−	0.999052i	$-0.486140\pi$
$223$	1.30002	0.0870556	0.0435278	+	0.999052i	$0.486140\pi$
$224$	0.402877	0.0269184
$225$	7.27356	0.484904
$226$	−22.0633	−1.46763
$227$	8.80920	0.584687	0.292344	−	0.956313i	$-0.405565\pi$
$227$	8.80920	0.584687	0.292344	+	0.956313i	$0.405565\pi$
$228$	−2.52449	−0.167188
$229$	−19.5184	−1.28981	−0.644905	−	0.764263i	$-0.723103\pi$
$229$	−19.5184	−1.28981	−0.644905	+	0.764263i	$0.723103\pi$
$230$	30.9483	2.04067
$231$	−0.708541	−0.0466186
$232$	−23.7834	−1.56146
$233$	6.28816	0.411951	0.205975	−	0.978557i	$-0.433963\pi$
$233$	6.28816	0.411951	0.205975	+	0.978557i	$0.433963\pi$
$234$	4.29417	0.280719
$235$	−21.4505	−1.39928
$236$	1.79825	0.117056
$237$	1.00000	0.0649570
$238$	0.244970	0.0158790
$239$	5.25186	0.339714	0.169857	−	0.985469i	$-0.445669\pi$
$239$	5.25186	0.339714	0.169857	+	0.985469i	$0.445669\pi$
$240$	10.8852	0.702637
$241$	9.96133	0.641666	0.320833	−	0.947136i	$-0.396037\pi$
$241$	9.96133	0.641666	0.320833	+	0.947136i	$0.396037\pi$
$242$	−3.29740	−0.211965
$243$	1.00000	0.0641500
$244$	3.09207	0.197950
$245$	24.3941	1.55848
$246$	12.8197	0.817356
$247$	−22.6328	−1.44009
$248$	19.9426	1.26636
$249$	−4.79363	−0.303784
$250$	10.1510	0.642003
$251$	0.268213	0.0169295	0.00846473	−	0.999964i	$-0.497306\pi$
$251$	0.268213	0.0169295	0.00846473	+	0.999964i	$0.497306\pi$
$252$	0.0722432	0.00455089
$253$	25.5508	1.60636
$254$	21.9600	1.37789
$255$	−3.50336	−0.219389
$256$	−8.68161	−0.542600
$257$	−30.2087	−1.88437	−0.942184	−	0.335096i	$-0.891231\pi$
$257$	−30.2087	−1.88437	−0.942184	+	0.335096i	$0.891231\pi$
$258$	15.5860	0.970341
$259$	0.923165	0.0573627
$260$	−4.43659	−0.275146
$261$	−7.85494	−0.486209
$262$	−10.9534	−0.676700
$263$	−9.04646	−0.557828	−0.278914	−	0.960316i	$-0.589975\pi$
$263$	−9.04646	−0.557828	−0.278914	+	0.960316i	$0.589975\pi$
$264$	11.1609	0.686906
$265$	−19.8931	−1.22202
$266$	1.64545	0.100889
$267$	18.0558	1.10500
$268$	−3.71831	−0.227132
$269$	23.9856	1.46243	0.731215	−	0.682148i	$-0.238954\pi$
$269$	23.9856	1.46243	0.731215	+	0.682148i	$0.238954\pi$
$270$	4.46478	0.271718
$271$	16.3823	0.995155	0.497577	−	0.867420i	$-0.334223\pi$
$271$	16.3823	0.995155	0.497577	+	0.867420i	$0.334223\pi$
$272$	−3.10707	−0.188394
$273$	0.647682	0.0391995
$274$	−3.67811	−0.222203
$275$	26.8111	1.61677
$276$	−2.60517	−0.156813
$277$	−1.97824	−0.118861	−0.0594306	−	0.998232i	$-0.518928\pi$
$277$	−1.97824	−0.118861	−0.0594306	+	0.998232i	$0.518928\pi$
$278$	−24.4843	−1.46847
$279$	6.58645	0.394320
$280$	2.03899	0.121853
$281$	18.7517	1.11863	0.559315	−	0.828955i	$-0.311064\pi$
$281$	18.7517	1.11863	0.559315	+	0.828955i	$0.311064\pi$
$282$	−7.80311	−0.464668
$283$	14.8609	0.883389	0.441694	−	0.897166i	$-0.354378\pi$
$283$	14.8609	0.883389	0.441694	+	0.897166i	$0.354378\pi$
$284$	3.41695	0.202759
$285$	−23.5320	−1.39392
$286$	15.8288	0.935975
$287$	1.93358	0.114135
$288$	−2.09592	−0.123504
$289$	1.00000	0.0588235
$290$	−35.0706	−2.05942
$291$	−9.13412	−0.535452
$292$	−5.50338	−0.322061
$293$	4.11538	0.240423	0.120212	−	0.992748i	$-0.461643\pi$
$293$	4.11538	0.240423	0.120212	+	0.992748i	$0.461643\pi$
$294$	8.87390	0.517536
$295$	16.7624	0.975943
$296$	−14.5416	−0.845216
$297$	3.68610	0.213889
$298$	−26.9546	−1.56144
$299$	−23.3562	−1.35072
$300$	−2.73367	−0.157829
$301$	2.35080	0.135498
$302$	6.31583	0.363435
$303$	10.5019	0.603316
$304$	−20.8701	−1.19698
$305$	28.8227	1.65038
$306$	−1.27443	−0.0728541
$307$	−0.0476785	−0.00272116	−0.00136058	−	0.999999i	$-0.500433\pi$
$307$	−0.0476785	−0.00272116	−0.00136058	+	0.999999i	$0.500433\pi$
$308$	0.266296	0.0151736
$309$	−10.3810	−0.590556
$310$	29.4071	1.67021
$311$	−29.3859	−1.66632	−0.833162	−	0.553029i	$-0.813472\pi$
$311$	−29.3859	−1.66632	−0.833162	+	0.553029i	$0.813472\pi$
$312$	−10.2023	−0.577589
$313$	−5.04218	−0.285001	−0.142501	−	0.989795i	$-0.545514\pi$
$313$	−5.04218	−0.285001	−0.142501	+	0.989795i	$0.545514\pi$
$314$	−0.383731	−0.0216552
$315$	0.673415	0.0379426
$316$	−0.375837	−0.0211425
$317$	−26.3090	−1.47766	−0.738829	−	0.673893i	$-0.764621\pi$
$317$	−26.3090	−1.47766	−0.738829	+	0.673893i	$0.764621\pi$
$318$	−7.23656	−0.405806
$319$	−28.9541	−1.62112
$320$	−31.1283	−1.74012
$321$	17.8893	0.998486
$322$	1.69804	0.0946282
$323$	6.71698	0.373743
$324$	−0.375837	−0.0208798
$325$	−24.5082	−1.35947
$326$	9.60727	0.532097
$327$	−3.37660	−0.186727
$328$	−30.4576	−1.68174
$329$	−1.17693	−0.0648862
$330$	16.4576	0.905964
$331$	18.3348	1.00777	0.503885	−	0.863771i	$-0.331903\pi$
$331$	18.3348	1.00777	0.503885	+	0.863771i	$0.331903\pi$
$332$	1.80162	0.0988769
$333$	−4.80266	−0.263184
$334$	−7.76137	−0.424683
$335$	−34.6602	−1.89369
$336$	0.597240	0.0325821
$337$	−4.01853	−0.218903	−0.109452	−	0.993992i	$-0.534909\pi$
$337$	−4.01853	−0.218903	−0.109452	+	0.993992i	$0.534909\pi$
$338$	2.09834	0.114135
$339$	17.3123	0.940276
$340$	1.31669	0.0714078
$341$	24.2783	1.31475
$342$	−8.56029	−0.462888
$343$	2.68397	0.144921
$344$	−37.0297	−1.99651
$345$	−24.2841	−1.30741
$346$	−5.62505	−0.302404
$347$	17.8880	0.960277	0.480138	−	0.877193i	$-0.340586\pi$
$347$	17.8880	0.960277	0.480138	+	0.877193i	$0.340586\pi$
$348$	2.95218	0.158253
$349$	28.6959	1.53606	0.768029	−	0.640415i	$-0.221238\pi$
$349$	28.6959	1.53606	0.768029	+	0.640415i	$0.221238\pi$
$350$	1.78180	0.0952413
$351$	−3.36950	−0.179850
$352$	−7.72579	−0.411786
$353$	8.25538	0.439389	0.219695	−	0.975569i	$-0.429494\pi$
$353$	8.25538	0.439389	0.219695	+	0.975569i	$0.429494\pi$
$354$	6.09768	0.324088
$355$	31.8511	1.69048
$356$	−6.78604	−0.359659
$357$	−0.192219	−0.0101733
$358$	−25.1389	−1.32863
$359$	18.9600	1.00067	0.500334	−	0.865832i	$-0.333211\pi$
$359$	18.9600	1.00067	0.500334	+	0.865832i	$0.333211\pi$
$360$	−10.6076	−0.559069
$361$	26.1178	1.37462
$362$	−12.4794	−0.655904
$363$	2.58736	0.135801
$364$	−0.243423	−0.0127588
$365$	−51.2997	−2.68515
$366$	10.4849	0.548055
$367$	21.7468	1.13517	0.567586	−	0.823314i	$-0.307877\pi$
$367$	21.7468	1.13517	0.567586	+	0.823314i	$0.307877\pi$
$368$	−21.5371	−1.12270
$369$	−10.0592	−0.523662
$370$	−21.4428	−1.11476
$371$	−1.09148	−0.0566666
$372$	−2.47543	−0.128345
$373$	13.3769	0.692630	0.346315	−	0.938118i	$-0.387433\pi$
$373$	13.3769	0.692630	0.346315	+	0.938118i	$0.387433\pi$
$374$	−4.69767	−0.242911
$375$	−7.96512	−0.411317
$376$	18.5389	0.956072
$377$	26.4672	1.36313
$378$	0.244970	0.0125999
$379$	24.5327	1.26016	0.630079	−	0.776531i	$-0.283023\pi$
$379$	24.5327	1.26016	0.630079	+	0.776531i	$0.283023\pi$
$380$	8.84420	0.453698
$381$	−17.2313	−0.882786
$382$	12.9358	0.661851
$383$	−0.818733	−0.0418353	−0.0209176	−	0.999781i	$-0.506659\pi$
$383$	−0.818733	−0.0418353	−0.0209176	+	0.999781i	$0.506659\pi$
$384$	−7.13175	−0.363940
$385$	2.48228	0.126509
$386$	16.9895	0.864742
$387$	−12.2298	−0.621676
$388$	3.43294	0.174281
$389$	17.8825	0.906679	0.453340	−	0.891338i	$-0.350233\pi$
$389$	17.8825	0.906679	0.453340	+	0.891338i	$0.350233\pi$
$390$	−15.0441	−0.761785
$391$	6.93165	0.350549
$392$	−21.0829	−1.06485
$393$	8.59473	0.433547
$394$	−22.4302	−1.13002
$395$	−3.50336	−0.176273
$396$	−1.38537	−0.0696177
$397$	12.0334	0.603937	0.301968	−	0.953318i	$-0.402356\pi$
$397$	12.0334	0.603937	0.301968	+	0.953318i	$0.402356\pi$
$398$	22.1271	1.10913
$399$	−1.29113	−0.0646375
$400$	−22.5995	−1.12997
$401$	−25.7019	−1.28349	−0.641745	−	0.766918i	$-0.721789\pi$
$401$	−25.7019	−1.28349	−0.641745	+	0.766918i	$0.721789\pi$
$402$	−12.6084	−0.628851
$403$	−22.1930	−1.10551
$404$	−3.94699	−0.196370
$405$	−3.50336	−0.174084
$406$	−1.92422	−0.0954975
$407$	−17.7031	−0.877511
$408$	3.02783	0.149900
$409$	3.19789	0.158125	0.0790627	−	0.996870i	$-0.474807\pi$
$409$	3.19789	0.158125	0.0790627	+	0.996870i	$0.474807\pi$
$410$	−44.9122	−2.21805
$411$	2.88609	0.142360
$412$	3.90158	0.192217
$413$	0.919702	0.0452556
$414$	−8.83388	−0.434161
$415$	16.7938	0.824376
$416$	7.06221	0.346253
$417$	19.2120	0.940818
$418$	−31.5541	−1.54336
$419$	25.9647	1.26846	0.634230	−	0.773145i	$-0.281317\pi$
$419$	25.9647	1.26846	0.634230	+	0.773145i	$0.281317\pi$
$420$	−0.253094	−0.0123497
$421$	14.7904	0.720839	0.360420	−	0.932790i	$-0.382633\pi$
$421$	14.7904	0.720839	0.360420	+	0.932790i	$0.382633\pi$
$422$	−9.62466	−0.468521
$423$	6.12284	0.297703
$424$	17.1929	0.834960
$425$	7.27356	0.352820
$426$	11.5866	0.561370
$427$	1.58142	0.0765302
$428$	−6.72348	−0.324992
$429$	−12.4203	−0.599658
$430$	−54.6034	−2.63321
$431$	−37.9041	−1.82578	−0.912889	−	0.408209i	$-0.866153\pi$
$431$	−37.9041	−1.82578	−0.912889	+	0.408209i	$0.866153\pi$
$432$	−3.10707	−0.149489
$433$	−27.5366	−1.32332	−0.661662	−	0.749802i	$-0.730149\pi$
$433$	−27.5366	−1.32332	−0.661662	+	0.749802i	$0.730149\pi$
$434$	1.61348	0.0774495
$435$	27.5187	1.31942
$436$	1.26905	0.0607766
$437$	46.5597	2.22725
$438$	−18.6614	−0.891677
$439$	−9.45115	−0.451079	−0.225539	−	0.974234i	$-0.572414\pi$
$439$	−9.45115	−0.451079	−0.225539	+	0.974234i	$0.572414\pi$
$440$	−39.1007	−1.86405
$441$	−6.96305	−0.331574
$442$	4.29417	0.204253
$443$	−14.2238	−0.675795	−0.337898	−	0.941183i	$-0.609716\pi$
$443$	−14.2238	−0.675795	−0.337898	+	0.941183i	$0.609716\pi$
$444$	1.80502	0.0856624
$445$	−63.2560	−2.99862
$446$	−1.65678	−0.0784507
$447$	21.1504	1.00038
$448$	−1.70792	−0.0806915
$449$	16.9095	0.798009	0.399004	−	0.916949i	$-0.369356\pi$
$449$	16.9095	0.798009	0.399004	+	0.916949i	$0.369356\pi$
$450$	−9.26962	−0.436974
$451$	−37.0793	−1.74600
$452$	−6.50661	−0.306045
$453$	−4.95582	−0.232845
$454$	−11.2267	−0.526894
$455$	−2.26907	−0.106376
$456$	20.3379	0.952408
$457$	−18.0421	−0.843975	−0.421987	−	0.906602i	$-0.638667\pi$
$457$	−18.0421	−0.843975	−0.421987	+	0.906602i	$0.638667\pi$
$458$	24.8747	1.16232
$459$	1.00000	0.0466760
$460$	9.12686	0.425542
$461$	26.3375	1.22666	0.613330	−	0.789827i	$-0.289830\pi$
$461$	26.3375	1.22666	0.613330	+	0.789827i	$0.289830\pi$
$462$	0.902983	0.0420106
$463$	10.7625	0.500177	0.250088	−	0.968223i	$-0.419540\pi$
$463$	10.7625	0.500177	0.250088	+	0.968223i	$0.419540\pi$
$464$	24.4059	1.13301
$465$	−23.0747	−1.07007
$466$	−8.01380	−0.371232
$467$	−3.25445	−0.150598	−0.0752990	−	0.997161i	$-0.523991\pi$
$467$	−3.25445	−0.150598	−0.0752990	+	0.997161i	$0.523991\pi$
$468$	1.26638	0.0585385
$469$	−1.90171	−0.0878126
$470$	27.3371	1.26097
$471$	0.301101	0.0138740
$472$	−14.4871	−0.666823
$473$	−45.0803	−2.07279
$474$	−1.27443	−0.0585363
$475$	48.8564	2.24168
$476$	0.0722432	0.00331126
$477$	5.67828	0.259991
$478$	−6.69310	−0.306135
$479$	−29.8212	−1.36256	−0.681282	−	0.732021i	$-0.738577\pi$
$479$	−29.8212	−1.36256	−0.681282	+	0.732021i	$0.738577\pi$
$480$	7.34279	0.335151
$481$	16.1825	0.737861
$482$	−12.6950	−0.578241
$483$	−1.33240	−0.0606262
$484$	−0.972426	−0.0442012
$485$	32.0002	1.45305
$486$	−1.27443	−0.0578092
$487$	34.8281	1.57821	0.789107	−	0.614256i	$-0.210544\pi$
$487$	34.8281	1.57821	0.789107	+	0.614256i	$0.210544\pi$
$488$	−24.9104	−1.12764
$489$	−7.53850	−0.340903
$490$	−31.0885	−1.40444
$491$	−42.7565	−1.92957	−0.964787	−	0.263032i	$-0.915278\pi$
$491$	−42.7565	−1.92957	−0.964787	+	0.263032i	$0.915278\pi$
$492$	3.78062	0.170444
$493$	−7.85494	−0.353769
$494$	28.8439	1.29775
$495$	−12.9138	−0.580431
$496$	−20.4646	−0.918886
$497$	1.74758	0.0783896
$498$	6.10913	0.273756
$499$	35.7840	1.60191	0.800957	−	0.598722i	$-0.204325\pi$
$499$	35.7840	1.60191	0.800957	+	0.598722i	$0.204325\pi$
$500$	2.99359	0.133877
$501$	6.09009	0.272085
$502$	−0.341818	−0.0152561
$503$	4.57535	0.204005	0.102002	−	0.994784i	$-0.467475\pi$
$503$	4.57535	0.204005	0.102002	+	0.994784i	$0.467475\pi$
$504$	−0.582008	−0.0259247
$505$	−36.7918	−1.63722
$506$	−32.5626	−1.44758
$507$	−1.64650	−0.0731237
$508$	6.47616	0.287333
$509$	−10.3504	−0.458773	−0.229387	−	0.973335i	$-0.573672\pi$
$509$	−10.3504	−0.458773	−0.229387	+	0.973335i	$0.573672\pi$
$510$	4.46478	0.197704
$511$	−2.81467	−0.124514
$512$	25.3276	1.11933
$513$	6.71698	0.296562
$514$	38.4988	1.69811
$515$	36.3685	1.60259
$516$	4.59641	0.202346
$517$	22.5694	0.992602
$518$	−1.17651	−0.0516927
$519$	4.41379	0.193744
$520$	35.7422	1.56740
$521$	−8.66459	−0.379602	−0.189801	−	0.981823i	$-0.560784\pi$
$521$	−8.66459	−0.379602	−0.189801	+	0.981823i	$0.560784\pi$
$522$	10.0105	0.438150
$523$	30.5072	1.33399	0.666993	−	0.745064i	$-0.267581\pi$
$523$	30.5072	1.33399	0.666993	+	0.745064i	$0.267581\pi$
$524$	−3.23022	−0.141113
$525$	−1.39812	−0.0610190
$526$	11.5290	0.502690
$527$	6.58645	0.286910
$528$	−11.4530	−0.498427
$529$	25.0477	1.08903
$530$	25.3523	1.10123
$531$	−4.78465	−0.207636
$532$	0.485256	0.0210385
$533$	33.8945	1.46813
$534$	−23.0108	−0.995774
$535$	−62.6729	−2.70959
$536$	29.9556	1.29388
$537$	19.7257	0.851225
$538$	−30.5679	−1.31788
$539$	−25.6665	−1.10554
$540$	1.31669	0.0566615
$541$	9.90014	0.425640	0.212820	−	0.977091i	$-0.431735\pi$
$541$	9.90014	0.425640	0.212820	+	0.977091i	$0.431735\pi$
$542$	−20.8781	−0.896789
$543$	9.79219	0.420223
$544$	−2.09592	−0.0898620
$545$	11.8295	0.506719
$546$	−0.825424	−0.0353249
$547$	20.0729	0.858255	0.429128	−	0.903244i	$-0.358821\pi$
$547$	20.0729	0.858255	0.429128	+	0.903244i	$0.358821\pi$
$548$	−1.08470	−0.0463360
$549$	−8.22716	−0.351126
$550$	−34.1688	−1.45696
$551$	−52.7615	−2.24771
$552$	20.9879	0.893302
$553$	−0.192219	−0.00817400
$554$	2.52113	0.107112
$555$	16.8255	0.714202
$556$	−7.22060	−0.306222
$557$	15.6393	0.662660	0.331330	−	0.943515i	$-0.392503\pi$
$557$	15.6393	0.662660	0.331330	+	0.943515i	$0.392503\pi$
$558$	−8.39395	−0.355344
$559$	41.2082	1.74292
$560$	−2.09235	−0.0884179
$561$	3.68610	0.155627
$562$	−23.8976	−1.00806
$563$	12.0160	0.506416	0.253208	−	0.967412i	$-0.418514\pi$
$563$	12.0160	0.506416	0.253208	+	0.967412i	$0.418514\pi$
$564$	−2.30119	−0.0968976
$565$	−60.6513	−2.55162
$566$	−18.9391	−0.796071
$567$	−0.192219	−0.00807246
$568$	−27.5278	−1.15504
$569$	21.2291	0.889971	0.444985	−	0.895538i	$-0.353209\pi$
$569$	21.2291	0.889971	0.444985	+	0.895538i	$0.353209\pi$
$570$	29.9898	1.25614
$571$	1.25416	0.0524850	0.0262425	−	0.999656i	$-0.491646\pi$
$571$	1.25416	0.0524850	0.0262425	+	0.999656i	$0.491646\pi$
$572$	4.66801	0.195179
$573$	−10.1503	−0.424033
$574$	−2.46420	−0.102854
$575$	50.4178	2.10257
$576$	8.88525	0.370219
$577$	−2.40212	−0.100002	−0.0500008	−	0.998749i	$-0.515922\pi$
$577$	−2.40212	−0.100002	−0.0500008	+	0.998749i	$0.515922\pi$
$578$	−1.27443	−0.0530092
$579$	−13.3311	−0.554021
$580$	−10.3426	−0.429451
$581$	0.921428	0.0382273
$582$	11.6408	0.482525
$583$	20.9307	0.866863
$584$	44.3365	1.83466
$585$	11.8046	0.488059
$586$	−5.24475	−0.216659
$587$	−4.88794	−0.201747	−0.100873	−	0.994899i	$-0.532164\pi$
$587$	−4.88794	−0.201747	−0.100873	+	0.994899i	$0.532164\pi$
$588$	2.61697	0.107922
$589$	44.2410	1.82292
$590$	−21.3624	−0.879476
$591$	17.6002	0.723977
$592$	14.9222	0.613299
$593$	−12.4675	−0.511979	−0.255989	−	0.966680i	$-0.582401\pi$
$593$	−12.4675	−0.511979	−0.255989	+	0.966680i	$0.582401\pi$
$594$	−4.69767	−0.192748
$595$	0.673415	0.0276073
$596$	−7.94910	−0.325608
$597$	−17.3624	−0.710595
$598$	29.7657	1.21721
$599$	35.9305	1.46808	0.734040	−	0.679107i	$-0.237633\pi$
$599$	35.9305	1.46808	0.734040	+	0.679107i	$0.237633\pi$
$600$	22.0231	0.899090
$601$	−2.80054	−0.114236	−0.0571182	−	0.998367i	$-0.518191\pi$
$601$	−2.80054	−0.114236	−0.0571182	+	0.998367i	$0.518191\pi$
$602$	−2.99593	−0.122105
$603$	9.89341	0.402891
$604$	1.86258	0.0757873
$605$	−9.06447	−0.368523
$606$	−13.3838	−0.543682
$607$	−5.06541	−0.205599	−0.102799	−	0.994702i	$-0.532780\pi$
$607$	−5.06541	−0.205599	−0.102799	+	0.994702i	$0.532780\pi$
$608$	−14.0783	−0.570949
$609$	1.50987	0.0611831
$610$	−36.7325	−1.48725
$611$	−20.6309	−0.834636
$612$	−0.375837	−0.0151923
$613$	26.8378	1.08397	0.541985	−	0.840388i	$-0.317673\pi$
$613$	26.8378	1.08397	0.541985	+	0.840388i	$0.317673\pi$
$614$	0.0607627	0.00245218
$615$	35.2411	1.42106
$616$	−2.14534	−0.0864382
$617$	−3.70256	−0.149060	−0.0745298	−	0.997219i	$-0.523746\pi$
$617$	−3.70256	−0.149060	−0.0745298	+	0.997219i	$0.523746\pi$
$618$	13.2299	0.532183
$619$	−14.2237	−0.571697	−0.285849	−	0.958275i	$-0.592275\pi$
$619$	−14.2237	−0.571697	−0.285849	+	0.958275i	$0.592275\pi$
$620$	8.67234	0.348290
$621$	6.93165	0.278157
$622$	37.4502	1.50162
$623$	−3.47067	−0.139050
$624$	10.4693	0.419106
$625$	−8.46309	−0.338523
$626$	6.42589	0.256830
$627$	24.7595	0.988798
$628$	−0.113165	−0.00451577
$629$	−4.80266	−0.191495
$630$	−0.858218	−0.0341922
$631$	−24.8511	−0.989308	−0.494654	−	0.869090i	$-0.664705\pi$
$631$	−24.8511	−0.989308	−0.494654	+	0.869090i	$0.664705\pi$
$632$	3.02783	0.120441
$633$	7.55215	0.300171
$634$	33.5288	1.33160
$635$	60.3675	2.39561
$636$	−2.13411	−0.0846229
$637$	23.4620	0.929597
$638$	36.8999	1.46088
$639$	−9.09158	−0.359657
$640$	24.9851	0.987623
$641$	7.66504	0.302751	0.151376	−	0.988476i	$-0.451630\pi$
$641$	7.66504	0.302751	0.151376	+	0.988476i	$0.451630\pi$
$642$	−22.7987	−0.899791
$643$	−46.7401	−1.84325	−0.921625	−	0.388083i	$-0.873138\pi$
$643$	−46.7401	−1.84325	−0.921625	+	0.388083i	$0.873138\pi$
$644$	0.500764	0.0197329
$645$	42.8454	1.68704
$646$	−8.56029	−0.336800
$647$	45.5047	1.78897	0.894487	−	0.447094i	$-0.147541\pi$
$647$	45.5047	1.78897	0.894487	+	0.447094i	$0.147541\pi$
$648$	3.02783	0.118944
$649$	−17.6367	−0.692301
$650$	31.2340	1.22510
$651$	−1.26604	−0.0496202
$652$	2.83325	0.110959
$653$	21.2324	0.830886	0.415443	−	0.909619i	$-0.363627\pi$
$653$	21.2324	0.830886	0.415443	+	0.909619i	$0.363627\pi$
$654$	4.30323	0.168270
$655$	−30.1105	−1.17651
$656$	31.2547	1.22029
$657$	14.6430	0.571277
$658$	1.49991	0.0584725
$659$	13.8010	0.537610	0.268805	−	0.963195i	$-0.413371\pi$
$659$	13.8010	0.537610	0.268805	+	0.963195i	$0.413371\pi$
$660$	4.85347	0.188921
$661$	10.5103	0.408801	0.204401	−	0.978887i	$-0.434475\pi$
$661$	10.5103	0.408801	0.204401	+	0.978887i	$0.434475\pi$
$662$	−23.3663	−0.908158
$663$	−3.36950	−0.130860
$664$	−14.5143	−0.563264
$665$	4.52331	0.175406
$666$	6.12064	0.237170
$667$	−54.4477	−2.10822
$668$	−2.28888	−0.0885595
$669$	1.30002	0.0502616
$670$	44.1719	1.70651
$671$	−30.3262	−1.17073
$672$	0.402877	0.0155413
$673$	3.06801	0.118263	0.0591316	−	0.998250i	$-0.481167\pi$
$673$	3.06801	0.118263	0.0591316	+	0.998250i	$0.481167\pi$
$674$	5.12132	0.197266
$675$	7.27356	0.279960
$676$	0.618816	0.0238006
$677$	−23.9732	−0.921363	−0.460682	−	0.887565i	$-0.652395\pi$
$677$	−23.9732	−0.921363	−0.460682	+	0.887565i	$0.652395\pi$
$678$	−22.0633	−0.847335
$679$	1.75576	0.0673797
$680$	−10.6076	−0.406783
$681$	8.80920	0.337569
$682$	−30.9410	−1.18479
$683$	23.1851	0.887154	0.443577	−	0.896236i	$-0.353709\pi$
$683$	23.1851	0.887154	0.443577	+	0.896236i	$0.353709\pi$
$684$	−2.52449	−0.0965262
$685$	−10.1110	−0.386322
$686$	−3.42052	−0.130596
$687$	−19.5184	−0.744672
$688$	37.9989	1.44869
$689$	−19.1330	−0.728907
$690$	30.9483	1.17818
$691$	2.11309	0.0803858	0.0401929	−	0.999192i	$-0.487203\pi$
$691$	2.11309	0.0803858	0.0401929	+	0.999192i	$0.487203\pi$
$692$	−1.65886	−0.0630606
$693$	−0.708541	−0.0269152
$694$	−22.7969	−0.865359
$695$	−67.3068	−2.55309
$696$	−23.7834	−0.901509
$697$	−10.0592	−0.381020
$698$	−36.5709	−1.38423
$699$	6.28816	0.237840
$700$	0.525465	0.0198607
$701$	−25.2892	−0.955160	−0.477580	−	0.878588i	$-0.658486\pi$
$701$	−25.2892	−0.955160	−0.477580	+	0.878588i	$0.658486\pi$
$702$	4.29417	0.162073
$703$	−32.2594	−1.21669
$704$	32.7519	1.23439
$705$	−21.4505	−0.807874
$706$	−10.5209	−0.395958
$707$	−2.01866	−0.0759196
$708$	1.79825	0.0675823
$709$	13.8230	0.519135	0.259567	−	0.965725i	$-0.416420\pi$
$709$	13.8230	0.519135	0.259567	+	0.965725i	$0.416420\pi$
$710$	−40.5919	−1.52339
$711$	1.00000	0.0375029
$712$	54.6699	2.04884
$713$	45.6549	1.70979
$714$	0.244970	0.00916775
$715$	43.5129	1.62729
$716$	−7.41363	−0.277061
$717$	5.25186	0.196134
$718$	−24.1631	−0.901758
$719$	−20.1596	−0.751827	−0.375913	−	0.926655i	$-0.622671\pi$
$719$	−20.1596	−0.751827	−0.375913	+	0.926655i	$0.622671\pi$
$720$	10.8852	0.405668
$721$	1.99544	0.0743139
$722$	−33.2852	−1.23875
$723$	9.96133	0.370466
$724$	−3.68027	−0.136776
$725$	−57.1334	−2.12188
$726$	−3.29740	−0.122378
$727$	−36.7454	−1.36281	−0.681406	−	0.731906i	$-0.738631\pi$
$727$	−36.7454	−1.36281	−0.681406	+	0.731906i	$0.738631\pi$
$728$	1.96107	0.0726822
$729$	1.00000	0.0370370
$730$	65.3777	2.41974
$731$	−12.2298	−0.452335
$732$	3.09207	0.114286
$733$	33.0162	1.21948	0.609740	−	0.792601i	$-0.291274\pi$
$733$	33.0162	1.21948	0.609740	+	0.792601i	$0.291274\pi$
$734$	−27.7147	−1.02297
$735$	24.3941	0.899790
$736$	−14.5282	−0.535517
$737$	36.4681	1.34332
$738$	12.8197	0.471901
$739$	30.9725	1.13934	0.569671	−	0.821873i	$-0.307070\pi$
$739$	30.9725	1.13934	0.569671	+	0.821873i	$0.307070\pi$
$740$	−6.32364	−0.232462
$741$	−22.6328	−0.831438
$742$	1.39101	0.0510655
$743$	0.433176	0.0158917	0.00794584	−	0.999968i	$-0.497471\pi$
$743$	0.433176	0.0158917	0.00794584	+	0.999968i	$0.497471\pi$
$744$	19.9426	0.731133
$745$	−74.0975	−2.71472
$746$	−17.0479	−0.624168
$747$	−4.79363	−0.175390
$748$	−1.38537	−0.0506543
$749$	−3.43868	−0.125647
$750$	10.1510	0.370661
$751$	44.6061	1.62770	0.813849	−	0.581076i	$-0.197368\pi$
$751$	44.6061	1.62770	0.813849	+	0.581076i	$0.197368\pi$
$752$	−19.0241	−0.693738
$753$	0.268213	0.00977423
$754$	−33.7305	−1.22839
$755$	17.3620	0.631869
$756$	0.0722432	0.00262746
$757$	−22.7667	−0.827471	−0.413735	−	0.910397i	$-0.635776\pi$
$757$	−22.7667	−0.827471	−0.413735	+	0.910397i	$0.635776\pi$
$758$	−31.2651	−1.13560
$759$	25.5508	0.927434
$760$	−71.2509	−2.58454
$761$	30.9874	1.12329	0.561647	−	0.827377i	$-0.310168\pi$
$761$	30.9874	1.12329	0.561647	+	0.827377i	$0.310168\pi$
$762$	21.9600	0.795527
$763$	0.649049	0.0234972
$764$	3.81484	0.138016
$765$	−3.50336	−0.126664
$766$	1.04341	0.0377001
$767$	16.1218	0.582126
$768$	−8.68161	−0.313270
$769$	18.2462	0.657975	0.328987	−	0.944334i	$-0.393293\pi$
$769$	18.2462	0.657975	0.328987	+	0.944334i	$0.393293\pi$
$770$	−3.16348	−0.114004
$771$	−30.2087	−1.08794
$772$	5.01031	0.180325
$773$	−3.93680	−0.141597	−0.0707985	−	0.997491i	$-0.522555\pi$
$773$	−3.93680	−0.141597	−0.0707985	+	0.997491i	$0.522555\pi$
$774$	15.5860	0.560226
$775$	47.9070	1.72087
$776$	−27.6566	−0.992813
$777$	0.923165	0.0331184
$778$	−22.7899	−0.817059
$779$	−67.5675	−2.42086
$780$	−4.43659	−0.158856
$781$	−33.5125	−1.19917
$782$	−8.83388	−0.315899
$783$	−7.85494	−0.280713
$784$	21.6347	0.772668
$785$	−1.05487	−0.0376498
$786$	−10.9534	−0.390693
$787$	13.8283	0.492925	0.246462	−	0.969152i	$-0.420732\pi$
$787$	13.8283	0.492925	0.246462	+	0.969152i	$0.420732\pi$
$788$	−6.61482	−0.235643
$789$	−9.04646	−0.322062
$790$	4.46478	0.158850
$791$	−3.32776	−0.118322
$792$	11.1609	0.396585
$793$	27.7214	0.984415
$794$	−15.3356	−0.544241
$795$	−19.8931	−0.705536
$796$	6.52543	0.231288
$797$	−5.82441	−0.206311	−0.103156	−	0.994665i	$-0.532894\pi$
$797$	−5.82441	−0.206311	−0.103156	+	0.994665i	$0.532894\pi$
$798$	1.64545	0.0582485
$799$	6.12284	0.216610
$800$	−15.2448	−0.538986
$801$	18.0558	0.637970
$802$	32.7552	1.15663
$803$	53.9756	1.90476
$804$	−3.71831	−0.131135
$805$	4.66787	0.164521
$806$	28.2834	0.996239
$807$	23.9856	0.844334
$808$	31.7978	1.11864
$809$	17.6814	0.621644	0.310822	−	0.950468i	$-0.399396\pi$
$809$	17.6814	0.621644	0.310822	+	0.950468i	$0.399396\pi$
$810$	4.46478	0.156876
$811$	−24.4341	−0.857998	−0.428999	−	0.903305i	$-0.641134\pi$
$811$	−24.4341	−0.857998	−0.428999	+	0.903305i	$0.641134\pi$
$812$	−0.567466	−0.0199142
$813$	16.3823	0.574553
$814$	22.5613	0.790774
$815$	26.4101	0.925106
$816$	−3.10707	−0.108769
$817$	−82.1473	−2.87397
$818$	−4.07547	−0.142496
$819$	0.647682	0.0226319
$820$	−13.2449	−0.462532
$821$	27.7877	0.969796	0.484898	−	0.874571i	$-0.338857\pi$
$821$	27.7877	0.969796	0.484898	+	0.874571i	$0.338857\pi$
$822$	−3.67811	−0.128289
$823$	16.9990	0.592548	0.296274	−	0.955103i	$-0.404256\pi$
$823$	16.9990	0.592548	0.296274	+	0.955103i	$0.404256\pi$
$824$	−31.4320	−1.09499
$825$	26.8111	0.933443
$826$	−1.17209	−0.0407823
$827$	−54.9541	−1.91094	−0.955470	−	0.295089i	$-0.904651\pi$
$827$	−54.9541	−1.91094	−0.955470	+	0.295089i	$0.904651\pi$
$828$	−2.60517	−0.0905359
$829$	−14.9631	−0.519689	−0.259844	−	0.965651i	$-0.583671\pi$
$829$	−14.9631	−0.519689	−0.259844	+	0.965651i	$0.583671\pi$
$830$	−21.4025	−0.742891
$831$	−1.97824	−0.0686245
$832$	−29.9388	−1.03794
$833$	−6.96305	−0.241255
$834$	−24.4843	−0.847824
$835$	−21.3358	−0.738356
$836$	−9.30553	−0.321838
$837$	6.58645	0.227661
$838$	−33.0901	−1.14308
$839$	6.51771	0.225016	0.112508	−	0.993651i	$-0.464112\pi$
$839$	6.51771	0.225016	0.112508	+	0.993651i	$0.464112\pi$
$840$	2.03899	0.0703517
$841$	32.7001	1.12759
$842$	−18.8493	−0.649589
$843$	18.7517	0.645841
$844$	−2.83838	−0.0977010
$845$	5.76829	0.198435
$846$	−7.80311	−0.268276
$847$	−0.497341	−0.0170888
$848$	−17.6428	−0.605858
$849$	14.8609	0.510025
$850$	−9.26962	−0.317945
$851$	−33.2904	−1.14118
$852$	3.41695	0.117063
$853$	17.5861	0.602138	0.301069	−	0.953602i	$-0.402657\pi$
$853$	17.5861	0.602138	0.301069	+	0.953602i	$0.402657\pi$
$854$	−2.01540	−0.0689657
$855$	−23.5320	−0.804778
$856$	54.1659	1.85135
$857$	−26.9995	−0.922286	−0.461143	−	0.887326i	$-0.652560\pi$
$857$	−26.9995	−0.922286	−0.461143	+	0.887326i	$0.652560\pi$
$858$	15.8288	0.540385
$859$	5.78527	0.197391	0.0986954	−	0.995118i	$-0.468533\pi$
$859$	5.78527	0.197391	0.0986954	+	0.995118i	$0.468533\pi$
$860$	−16.1029	−0.549105
$861$	1.93358	0.0658961
$862$	48.3060	1.64531
$863$	−14.9079	−0.507469	−0.253735	−	0.967274i	$-0.581659\pi$
$863$	−14.9079	−0.507469	−0.253735	+	0.967274i	$0.581659\pi$
$864$	−2.09592	−0.0713048
$865$	−15.4631	−0.525761
$866$	35.0934	1.19252
$867$	1.00000	0.0339618
$868$	0.475826	0.0161506
$869$	3.68610	0.125043
$870$	−35.0706	−1.18900
$871$	−33.3358	−1.12954
$872$	−10.2238	−0.346221
$873$	−9.13412	−0.309143
$874$	−59.3369	−2.00710
$875$	1.53105	0.0517590
$876$	−5.50338	−0.185942
$877$	−22.3909	−0.756088	−0.378044	−	0.925788i	$-0.623403\pi$
$877$	−22.3909	−0.756088	−0.378044	+	0.925788i	$0.623403\pi$
$878$	12.0448	0.406492
$879$	4.11538	0.138808
$880$	40.1240	1.35258
$881$	35.8257	1.20700	0.603499	−	0.797364i	$-0.293773\pi$
$881$	35.8257	1.20700	0.603499	+	0.797364i	$0.293773\pi$
$882$	8.87390	0.298800
$883$	−36.6604	−1.23372	−0.616860	−	0.787073i	$-0.711595\pi$
$883$	−36.6604	−1.23372	−0.616860	+	0.787073i	$0.711595\pi$
$884$	1.26638	0.0425930
$885$	16.7624	0.563461
$886$	18.1273	0.608997
$887$	43.6684	1.46624	0.733120	−	0.680099i	$-0.238063\pi$
$887$	43.6684	1.46624	0.733120	+	0.680099i	$0.238063\pi$
$888$	−14.5416	−0.487986
$889$	3.31219	0.111087
$890$	80.6152	2.70223
$891$	3.68610	0.123489
$892$	−0.488595	−0.0163594
$893$	41.1270	1.37626
$894$	−26.9546	−0.901497
$895$	−69.1062	−2.30997
$896$	1.37086	0.0457972
$897$	−23.3562	−0.779839
$898$	−21.5499	−0.719130
$899$	−51.7362	−1.72550
$900$	−2.73367	−0.0911225
$901$	5.67828	0.189171
$902$	47.2548	1.57341
$903$	2.35080	0.0782299
$904$	52.4187	1.74342
$905$	−34.3056	−1.14036
$906$	6.31583	0.209829
$907$	−35.9109	−1.19240	−0.596202	−	0.802835i	$-0.703324\pi$
$907$	−35.9109	−1.19240	−0.596202	+	0.802835i	$0.703324\pi$
$908$	−3.31082	−0.109874
$909$	10.5019	0.348325
$910$	2.89176	0.0958609
$911$	−48.1793	−1.59625	−0.798126	−	0.602491i	$-0.794175\pi$
$911$	−48.1793	−1.59625	−0.798126	+	0.602491i	$0.794175\pi$
$912$	−20.8701	−0.691079
$913$	−17.6698	−0.584785
$914$	22.9934	0.760553
$915$	28.8227	0.952850
$916$	7.33572	0.242379
$917$	−1.65207	−0.0545563
$918$	−1.27443	−0.0420623
$919$	−29.3369	−0.967734	−0.483867	−	0.875142i	$-0.660768\pi$
$919$	−29.3369	−0.967734	−0.483867	+	0.875142i	$0.660768\pi$
$920$	−73.5281	−2.42415
$921$	−0.0476785	−0.00157106
$922$	−33.5652	−1.10541
$923$	30.6340	1.00833
$924$	0.266296	0.00876049
$925$	−34.9325	−1.14857
$926$	−13.7160	−0.450737
$927$	−10.3810	−0.340958
$928$	16.4634	0.540436
$929$	−10.9329	−0.358696	−0.179348	−	0.983786i	$-0.557399\pi$
$929$	−10.9329	−0.358696	−0.179348	+	0.983786i	$0.557399\pi$
$930$	29.4071	0.964295
$931$	−46.7707	−1.53285
$932$	−2.36332	−0.0774132
$933$	−29.3859	−0.962053
$934$	4.14756	0.135712
$935$	−12.9138	−0.422325
$936$	−10.2023	−0.333471
$937$	−10.5590	−0.344947	−0.172473	−	0.985014i	$-0.555176\pi$
$937$	−10.5590	−0.344947	−0.172473	+	0.985014i	$0.555176\pi$
$938$	2.42358	0.0791328
$939$	−5.04218	−0.164545
$940$	8.06191	0.262950
$941$	−6.95161	−0.226616	−0.113308	−	0.993560i	$-0.536145\pi$
$941$	−6.95161	−0.226616	−0.113308	+	0.993560i	$0.536145\pi$
$942$	−0.383731	−0.0125026
$943$	−69.7269	−2.27062
$944$	14.8662	0.483855
$945$	0.673415	0.0219062
$946$	57.4515	1.86791
$947$	35.0177	1.13792	0.568962	−	0.822364i	$-0.307345\pi$
$947$	35.0177	1.13792	0.568962	+	0.822364i	$0.307345\pi$
$948$	−0.375837	−0.0122066
$949$	−49.3395	−1.60163
$950$	−62.2638	−2.02011
$951$	−26.3090	−0.853126
$952$	−0.582008	−0.0188630
$953$	22.4256	0.726436	0.363218	−	0.931704i	$-0.381678\pi$
$953$	22.4256	0.726436	0.363218	+	0.931704i	$0.381678\pi$
$954$	−7.23656	−0.234292
$955$	35.5600	1.15070
$956$	−1.97384	−0.0638386
$957$	−28.9541	−0.935954
$958$	38.0049	1.22788
$959$	−0.554762	−0.0179142
$960$	−31.1283	−1.00466
$961$	12.3813	0.399397
$962$	−20.6235	−0.664927
$963$	17.8893	0.576476
$964$	−3.74384	−0.120581
$965$	46.7036	1.50344
$966$	1.69804	0.0546336
$967$	−48.3180	−1.55380	−0.776900	−	0.629624i	$-0.783209\pi$
$967$	−48.3180	−1.55380	−0.776900	+	0.629624i	$0.783209\pi$
$968$	7.83409	0.251797
$969$	6.71698	0.215780
$970$	−40.7819	−1.30943
$971$	9.95294	0.319405	0.159703	−	0.987165i	$-0.448947\pi$
$971$	9.95294	0.319405	0.159703	+	0.987165i	$0.448947\pi$
$972$	−0.375837	−0.0120550
$973$	−3.69293	−0.118390
$974$	−44.3859	−1.42222
$975$	−24.5082	−0.784892
$976$	25.5624	0.818232
$977$	8.22102	0.263014	0.131507	−	0.991315i	$-0.458018\pi$
$977$	8.22102	0.263014	0.131507	+	0.991315i	$0.458018\pi$
$978$	9.60727	0.307207
$979$	66.5555	2.12712
$980$	−9.16821	−0.292868
$981$	−3.37660	−0.107807
$982$	54.4900	1.73885
$983$	36.5641	1.16621	0.583106	−	0.812396i	$-0.301837\pi$
$983$	36.5641	1.16621	0.583106	+	0.812396i	$0.301837\pi$
$984$	−30.4576	−0.970952
$985$	−61.6600	−1.96465
$986$	10.0105	0.318801
$987$	−1.17693	−0.0374621
$988$	8.50625	0.270620
$989$	−84.7727	−2.69561
$990$	16.4576	0.523058
$991$	12.1880	0.387165	0.193583	−	0.981084i	$-0.437989\pi$
$991$	12.1880	0.387165	0.193583	+	0.981084i	$0.437989\pi$
$992$	−13.8047	−0.438300
$993$	18.3348	0.581836
$994$	−2.22716	−0.0706412
$995$	60.8268	1.92834
$996$	1.80162	0.0570866
$997$	44.3151	1.40347	0.701737	−	0.712436i	$-0.252408\pi$
$997$	44.3151	1.40347	0.701737	+	0.712436i	$0.252408\pi$
$998$	−45.6041	−1.44357
$999$	−4.80266	−0.151949

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.k.1.9	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.k.1.9	✓	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)

\(f(q)\)	\(=\)	\(q-1.27443 q^{2} +1.00000 q^{3} -0.375837 q^{4} -3.50336 q^{5} -1.27443 q^{6} -0.192219 q^{7} +3.02783 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.27443 q^{2} +1.00000 q^{3} -0.375837 q^{4} -3.50336 q^{5} -1.27443 q^{6} -0.192219 q^{7} +3.02783 q^{8} +1.00000 q^{9} +4.46478 q^{10} +3.68610 q^{11} -0.375837 q^{12} -3.36950 q^{13} +0.244970 q^{14} -3.50336 q^{15} -3.10707 q^{16} +1.00000 q^{17} -1.27443 q^{18} +6.71698 q^{19} +1.31669 q^{20} -0.192219 q^{21} -4.69767 q^{22} +6.93165 q^{23} +3.02783 q^{24} +7.27356 q^{25} +4.29417 q^{26} +1.00000 q^{27} +0.0722432 q^{28} -7.85494 q^{29} +4.46478 q^{30} +6.58645 q^{31} -2.09592 q^{32} +3.68610 q^{33} -1.27443 q^{34} +0.673415 q^{35} -0.375837 q^{36} -4.80266 q^{37} -8.56029 q^{38} -3.36950 q^{39} -10.6076 q^{40} -10.0592 q^{41} +0.244970 q^{42} -12.2298 q^{43} -1.38537 q^{44} -3.50336 q^{45} -8.83388 q^{46} +6.12284 q^{47} -3.10707 q^{48} -6.96305 q^{49} -9.26962 q^{50} +1.00000 q^{51} +1.26638 q^{52} +5.67828 q^{53} -1.27443 q^{54} -12.9138 q^{55} -0.582008 q^{56} +6.71698 q^{57} +10.0105 q^{58} -4.78465 q^{59} +1.31669 q^{60} -8.22716 q^{61} -8.39395 q^{62} -0.192219 q^{63} +8.88525 q^{64} +11.8046 q^{65} -4.69767 q^{66} +9.89341 q^{67} -0.375837 q^{68} +6.93165 q^{69} -0.858218 q^{70} -9.09158 q^{71} +3.02783 q^{72} +14.6430 q^{73} +6.12064 q^{74} +7.27356 q^{75} -2.52449 q^{76} -0.708541 q^{77} +4.29417 q^{78} +1.00000 q^{79} +10.8852 q^{80} +1.00000 q^{81} +12.8197 q^{82} -4.79363 q^{83} +0.0722432 q^{84} -3.50336 q^{85} +15.5860 q^{86} -7.85494 q^{87} +11.1609 q^{88} +18.0558 q^{89} +4.46478 q^{90} +0.647682 q^{91} -2.60517 q^{92} +6.58645 q^{93} -7.80311 q^{94} -23.5320 q^{95} -2.09592 q^{96} -9.13412 q^{97} +8.87390 q^{98} +3.68610 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9}+O(q^{10}) \) 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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