LMFDB - Embedded newform 4029.2.a.k.1.3

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			1.3
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.41826 q^{2} +1.00000 q^{3} +3.84800 q^{4} +1.43707 q^{5} -2.41826 q^{6} +3.74160 q^{7} -4.46895 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.41826 q^{2} +1.00000 q^{3} +3.84800 q^{4} +1.43707 q^{5} -2.41826 q^{6} +3.74160 q^{7} -4.46895 q^{8} +1.00000 q^{9} -3.47522 q^{10} +4.27025 q^{11} +3.84800 q^{12} +2.58959 q^{13} -9.04818 q^{14} +1.43707 q^{15} +3.11110 q^{16} +1.00000 q^{17} -2.41826 q^{18} -7.71172 q^{19} +5.52985 q^{20} +3.74160 q^{21} -10.3266 q^{22} +3.97190 q^{23} -4.46895 q^{24} -2.93482 q^{25} -6.26230 q^{26} +1.00000 q^{27} +14.3977 q^{28} -2.55730 q^{29} -3.47522 q^{30} -1.53032 q^{31} +1.41444 q^{32} +4.27025 q^{33} -2.41826 q^{34} +5.37695 q^{35} +3.84800 q^{36} -2.68852 q^{37} +18.6490 q^{38} +2.58959 q^{39} -6.42220 q^{40} +8.65508 q^{41} -9.04818 q^{42} -2.21466 q^{43} +16.4319 q^{44} +1.43707 q^{45} -9.60509 q^{46} +2.63011 q^{47} +3.11110 q^{48} +6.99958 q^{49} +7.09717 q^{50} +1.00000 q^{51} +9.96472 q^{52} -0.811178 q^{53} -2.41826 q^{54} +6.13666 q^{55} -16.7210 q^{56} -7.71172 q^{57} +6.18424 q^{58} +8.80098 q^{59} +5.52985 q^{60} +1.53092 q^{61} +3.70072 q^{62} +3.74160 q^{63} -9.64269 q^{64} +3.72142 q^{65} -10.3266 q^{66} +2.18684 q^{67} +3.84800 q^{68} +3.97190 q^{69} -13.0029 q^{70} -1.36413 q^{71} -4.46895 q^{72} +3.33586 q^{73} +6.50156 q^{74} -2.93482 q^{75} -29.6747 q^{76} +15.9776 q^{77} -6.26230 q^{78} +1.00000 q^{79} +4.47087 q^{80} +1.00000 q^{81} -20.9303 q^{82} +0.585100 q^{83} +14.3977 q^{84} +1.43707 q^{85} +5.35564 q^{86} -2.55730 q^{87} -19.0835 q^{88} +10.0870 q^{89} -3.47522 q^{90} +9.68920 q^{91} +15.2839 q^{92} -1.53032 q^{93} -6.36031 q^{94} -11.0823 q^{95} +1.41444 q^{96} +1.60550 q^{97} -16.9268 q^{98} +4.27025 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9}+O(q^{10}) $ 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9	\( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9} + 5 q^{10} + 26 q^{11} + 34 q^{12} + 7 q^{13} + 19 q^{14} + 11 q^{15} + 40 q^{16} + 31 q^{17} + 4 q^{18} + 32 q^{19} + 23 q^{20} + 4 q^{21} + 2 q^{22} + 29 q^{23} + 12 q^{24} + 32 q^{25} + 13 q^{26} + 31 q^{27} - 13 q^{28} + 25 q^{29} + 5 q^{30} + 22 q^{31} + 28 q^{32} + 26 q^{33} + 4 q^{34} + 20 q^{35} + 34 q^{36} - 4 q^{37} + 19 q^{38} + 7 q^{39} - 3 q^{40} + 33 q^{41} + 19 q^{42} + 6 q^{43} + 30 q^{44} + 11 q^{45} - 11 q^{46} + 23 q^{47} + 40 q^{48} + 31 q^{49} + 6 q^{50} + 31 q^{51} - 7 q^{52} + 12 q^{53} + 4 q^{54} + 40 q^{56} + 32 q^{57} + 9 q^{58} + 27 q^{59} + 23 q^{60} - 4 q^{61} + 25 q^{62} + 4 q^{63} + 10 q^{64} + 54 q^{65} + 2 q^{66} + 34 q^{68} + 29 q^{69} - 59 q^{70} + 35 q^{71} + 12 q^{72} + 5 q^{73} + 48 q^{74} + 32 q^{75} + 32 q^{76} + 42 q^{77} + 13 q^{78} + 31 q^{79} + 24 q^{80} + 31 q^{81} + 5 q^{82} + 67 q^{83} - 13 q^{84} + 11 q^{85} - 20 q^{86} + 25 q^{87} - 7 q^{88} + 22 q^{89} + 5 q^{90} + 16 q^{91} + 57 q^{92} + 22 q^{93} + 45 q^{94} + 73 q^{95} + 28 q^{96} - 13 q^{97} - 19 q^{98} + 26 q^{99}+O(q^{100}) \) 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9 + 5 * q^10 + 26 * q^11 + 34 * q^12 + 7 * q^13 + 19 * q^14 + 11 * q^15 + 40 * q^16 + 31 * q^17 + 4 * q^18 + 32 * q^19 + 23 * q^20 + 4 * q^21 + 2 * q^22 + 29 * q^23 + 12 * q^24 + 32 * q^25 + 13 * q^26 + 31 * q^27 - 13 * q^28 + 25 * q^29 + 5 * q^30 + 22 * q^31 + 28 * q^32 + 26 * q^33 + 4 * q^34 + 20 * q^35 + 34 * q^36 - 4 * q^37 + 19 * q^38 + 7 * q^39 - 3 * q^40 + 33 * q^41 + 19 * q^42 + 6 * q^43 + 30 * q^44 + 11 * q^45 - 11 * q^46 + 23 * q^47 + 40 * q^48 + 31 * q^49 + 6 * q^50 + 31 * q^51 - 7 * q^52 + 12 * q^53 + 4 * q^54 + 40 * q^56 + 32 * q^57 + 9 * q^58 + 27 * q^59 + 23 * q^60 - 4 * q^61 + 25 * q^62 + 4 * q^63 + 10 * q^64 + 54 * q^65 + 2 * q^66 + 34 * q^68 + 29 * q^69 - 59 * q^70 + 35 * q^71 + 12 * q^72 + 5 * q^73 + 48 * q^74 + 32 * q^75 + 32 * q^76 + 42 * q^77 + 13 * q^78 + 31 * q^79 + 24 * q^80 + 31 * q^81 + 5 * q^82 + 67 * q^83 - 13 * q^84 + 11 * q^85 - 20 * q^86 + 25 * q^87 - 7 * q^88 + 22 * q^89 + 5 * q^90 + 16 * q^91 + 57 * q^92 + 22 * q^93 + 45 * q^94 + 73 * q^95 + 28 * q^96 - 13 * q^97 - 19 * q^98 + 26 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.41826	−1.70997	−0.854985	−	0.518652i	$-0.826434\pi$
$2$	−2.41826	−1.70997	−0.854985	+	0.518652i	$0.826434\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.84800	1.92400
$5$	1.43707	0.642678	0.321339	−	0.946964i	$-0.395867\pi$
$5$	1.43707	0.642678	0.321339	+	0.946964i	$0.395867\pi$
$6$	−2.41826	−0.987252
$7$	3.74160	1.41419	0.707096	−	0.707117i	$-0.250005\pi$
$7$	3.74160	1.41419	0.707096	+	0.707117i	$0.250005\pi$
$8$	−4.46895	−1.58001
$9$	1.00000	0.333333
$10$	−3.47522	−1.09896
$11$	4.27025	1.28753	0.643765	−	0.765223i	$-0.277372\pi$
$11$	4.27025	1.28753	0.643765	+	0.765223i	$0.277372\pi$
$12$	3.84800	1.11082
$13$	2.58959	0.718222	0.359111	−	0.933295i	$-0.383080\pi$
$13$	2.58959	0.718222	0.359111	+	0.933295i	$0.383080\pi$
$14$	−9.04818	−2.41823
$15$	1.43707	0.371051
$16$	3.11110	0.777775
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.41826	−0.569990
$19$	−7.71172	−1.76919	−0.884595	−	0.466360i	$-0.845565\pi$
$19$	−7.71172	−1.76919	−0.884595	+	0.466360i	$0.845565\pi$
$20$	5.52985	1.23651
$21$	3.74160	0.816484
$22$	−10.3266	−2.20164
$23$	3.97190	0.828198	0.414099	−	0.910232i	$-0.364097\pi$
$23$	3.97190	0.828198	0.414099	+	0.910232i	$0.364097\pi$
$24$	−4.46895	−0.912220
$25$	−2.93482	−0.586964
$26$	−6.26230	−1.22814
$27$	1.00000	0.192450
$28$	14.3977	2.72091
$29$	−2.55730	−0.474880	−0.237440	−	0.971402i	$-0.576308\pi$
$29$	−2.55730	−0.474880	−0.237440	+	0.971402i	$0.576308\pi$
$30$	−3.47522	−0.634486
$31$	−1.53032	−0.274853	−0.137427	−	0.990512i	$-0.543883\pi$
$31$	−1.53032	−0.274853	−0.137427	+	0.990512i	$0.543883\pi$
$32$	1.41444	0.250040
$33$	4.27025	0.743355
$34$	−2.41826	−0.414729
$35$	5.37695	0.908871
$36$	3.84800	0.641333
$37$	−2.68852	−0.441990	−0.220995	−	0.975275i	$-0.570931\pi$
$37$	−2.68852	−0.441990	−0.220995	+	0.975275i	$0.570931\pi$
$38$	18.6490	3.02526
$39$	2.58959	0.414666
$40$	−6.42220	−1.01544
$41$	8.65508	1.35170	0.675848	−	0.737041i	$-0.263778\pi$
$41$	8.65508	1.35170	0.675848	+	0.737041i	$0.263778\pi$
$42$	−9.04818	−1.39616
$43$	−2.21466	−0.337733	−0.168867	−	0.985639i	$-0.554011\pi$
$43$	−2.21466	−0.337733	−0.168867	+	0.985639i	$0.554011\pi$
$44$	16.4319	2.47721
$45$	1.43707	0.214226
$46$	−9.60509	−1.41619
$47$	2.63011	0.383642	0.191821	−	0.981430i	$-0.438561\pi$
$47$	2.63011	0.383642	0.191821	+	0.981430i	$0.438561\pi$
$48$	3.11110	0.449048
$49$	6.99958	0.999940
$50$	7.09717	1.00369
$51$	1.00000	0.140028
$52$	9.96472	1.38186
$53$	−0.811178	−0.111424	−0.0557119	−	0.998447i	$-0.517743\pi$
$53$	−0.811178	−0.111424	−0.0557119	+	0.998447i	$0.517743\pi$
$54$	−2.41826	−0.329084
$55$	6.13666	0.827467
$56$	−16.7210	−2.23444
$57$	−7.71172	−1.02144
$58$	6.18424	0.812030
$59$	8.80098	1.14579	0.572895	−	0.819629i	$-0.305820\pi$
$59$	8.80098	1.14579	0.572895	+	0.819629i	$0.305820\pi$
$60$	5.52985	0.713901
$61$	1.53092	0.196014	0.0980069	−	0.995186i	$-0.468753\pi$
$61$	1.53092	0.196014	0.0980069	+	0.995186i	$0.468753\pi$
$62$	3.70072	0.469991
$63$	3.74160	0.471397
$64$	−9.64269	−1.20534
$65$	3.72142	0.461586
$66$	−10.3266	−1.27112
$67$	2.18684	0.267166	0.133583	−	0.991038i	$-0.457352\pi$
$67$	2.18684	0.267166	0.133583	+	0.991038i	$0.457352\pi$
$68$	3.84800	0.466638
$69$	3.97190	0.478160
$70$	−13.0029	−1.55414
$71$	−1.36413	−0.161893	−0.0809465	−	0.996718i	$-0.525794\pi$
$71$	−1.36413	−0.161893	−0.0809465	+	0.996718i	$0.525794\pi$
$72$	−4.46895	−0.526671
$73$	3.33586	0.390433	0.195217	−	0.980760i	$-0.437459\pi$
$73$	3.33586	0.390433	0.195217	+	0.980760i	$0.437459\pi$
$74$	6.50156	0.755791
$75$	−2.93482	−0.338884
$76$	−29.6747	−3.40392
$77$	15.9776	1.82081
$78$	−6.26230	−0.709066
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	4.47087	0.499859
$81$	1.00000	0.111111
$82$	−20.9303	−2.31136
$83$	0.585100	0.0642231	0.0321115	−	0.999484i	$-0.489777\pi$
$83$	0.585100	0.0642231	0.0321115	+	0.999484i	$0.489777\pi$
$84$	14.3977	1.57092
$85$	1.43707	0.155872
$86$	5.35564	0.577514
$87$	−2.55730	−0.274172
$88$	−19.0835	−2.03431
$89$	10.0870	1.06922	0.534610	−	0.845099i	$-0.320458\pi$
$89$	10.0870	1.06922	0.534610	+	0.845099i	$0.320458\pi$
$90$	−3.47522	−0.366320
$91$	9.68920	1.01570
$92$	15.2839	1.59345
$93$	−1.53032	−0.158687
$94$	−6.36031	−0.656016
$95$	−11.0823	−1.13702
$96$	1.41444	0.144361
$97$	1.60550	0.163014	0.0815068	−	0.996673i	$-0.474027\pi$
$97$	1.60550	0.163014	0.0815068	+	0.996673i	$0.474027\pi$
$98$	−16.9268	−1.70987
$99$	4.27025	0.429176
$100$	−11.2932	−1.12932
$101$	−16.1021	−1.60221	−0.801107	−	0.598521i	$-0.795755\pi$
$101$	−16.1021	−1.60221	−0.801107	+	0.598521i	$0.795755\pi$
$102$	−2.41826	−0.239444
$103$	−2.66118	−0.262214	−0.131107	−	0.991368i	$-0.541853\pi$
$103$	−2.66118	−0.262214	−0.131107	+	0.991368i	$0.541853\pi$
$104$	−11.5727	−1.13480
$105$	5.37695	0.524737
$106$	1.96164	0.190532
$107$	10.4918	1.01428	0.507138	−	0.861865i	$-0.330703\pi$
$107$	10.4918	1.01428	0.507138	+	0.861865i	$0.330703\pi$
$108$	3.84800	0.370274
$109$	10.1201	0.969326	0.484663	−	0.874701i	$-0.338942\pi$
$109$	10.1201	0.969326	0.484663	+	0.874701i	$0.338942\pi$
$110$	−14.8401	−1.41495
$111$	−2.68852	−0.255183
$112$	11.6405	1.09992
$113$	17.0041	1.59961	0.799803	−	0.600262i	$-0.204937\pi$
$113$	17.0041	1.59961	0.799803	+	0.600262i	$0.204937\pi$
$114$	18.6490	1.74664
$115$	5.70791	0.532265
$116$	−9.84050	−0.913668
$117$	2.58959	0.239407
$118$	−21.2831	−1.95927
$119$	3.74160	0.342992
$120$	−6.42220	−0.586264
$121$	7.23505	0.657732
$122$	−3.70216	−0.335178
$123$	8.65508	0.780402
$124$	−5.88867	−0.528818
$125$	−11.4029	−1.01991
$126$	−9.04818	−0.806076
$127$	11.1393	0.988455	0.494227	−	0.869333i	$-0.335451\pi$
$127$	11.1393	0.988455	0.494227	+	0.869333i	$0.335451\pi$
$128$	20.4897	1.81105
$129$	−2.21466	−0.194990
$130$	−8.99938	−0.789298
$131$	−2.37479	−0.207486	−0.103743	−	0.994604i	$-0.533082\pi$
$131$	−2.37479	−0.207486	−0.103743	+	0.994604i	$0.533082\pi$
$132$	16.4319	1.43022
$133$	−28.8542	−2.50198
$134$	−5.28837	−0.456845
$135$	1.43707	0.123684
$136$	−4.46895	−0.383209
$137$	−14.8950	−1.27257	−0.636284	−	0.771455i	$-0.719529\pi$
$137$	−14.8950	−1.27257	−0.636284	+	0.771455i	$0.719529\pi$
$138$	−9.60509	−0.817640
$139$	21.2326	1.80093	0.900463	−	0.434932i	$-0.143228\pi$
$139$	21.2326	1.80093	0.900463	+	0.434932i	$0.143228\pi$
$140$	20.6905	1.74867
$141$	2.63011	0.221496
$142$	3.29884	0.276832
$143$	11.0582	0.924732
$144$	3.11110	0.259258
$145$	−3.67503	−0.305195
$146$	−8.06699	−0.667629
$147$	6.99958	0.577316
$148$	−10.3454	−0.850389
$149$	4.30985	0.353076	0.176538	−	0.984294i	$-0.443510\pi$
$149$	4.30985	0.353076	0.176538	+	0.984294i	$0.443510\pi$
$150$	7.09717	0.579482
$151$	−19.7238	−1.60510	−0.802550	−	0.596585i	$-0.796524\pi$
$151$	−19.7238	−1.60510	−0.802550	+	0.596585i	$0.796524\pi$
$152$	34.4633	2.79534
$153$	1.00000	0.0808452
$154$	−38.6380	−3.11354
$155$	−2.19918	−0.176642
$156$	9.96472	0.797816
$157$	14.6968	1.17293	0.586467	−	0.809973i	$-0.300518\pi$
$157$	14.6968	1.17293	0.586467	+	0.809973i	$0.300518\pi$
$158$	−2.41826	−0.192387
$159$	−0.811178	−0.0643306
$160$	2.03266	0.160696
$161$	14.8613	1.17123
$162$	−2.41826	−0.189997
$163$	0.0695570	0.00544813	0.00272406	−	0.999996i	$-0.499133\pi$
$163$	0.0695570	0.00544813	0.00272406	+	0.999996i	$0.499133\pi$
$164$	33.3047	2.60066
$165$	6.13666	0.477739
$166$	−1.41493	−0.109820
$167$	−0.744912	−0.0576430	−0.0288215	−	0.999585i	$-0.509175\pi$
$167$	−0.744912	−0.0576430	−0.0288215	+	0.999585i	$0.509175\pi$
$168$	−16.7210	−1.29006
$169$	−6.29405	−0.484157
$170$	−3.47522	−0.266537
$171$	−7.71172	−0.589730
$172$	−8.52202	−0.649798
$173$	7.23891	0.550364	0.275182	−	0.961392i	$-0.411262\pi$
$173$	7.23891	0.550364	0.275182	+	0.961392i	$0.411262\pi$
$174$	6.18424	0.468826
$175$	−10.9809	−0.830081
$176$	13.2852	1.00141
$177$	8.80098	0.661522
$178$	−24.3930	−1.82834
$179$	−13.5003	−1.00906	−0.504528	−	0.863395i	$-0.668334\pi$
$179$	−13.5003	−1.00906	−0.504528	+	0.863395i	$0.668334\pi$
$180$	5.52985	0.412171
$181$	−19.2944	−1.43414	−0.717070	−	0.697001i	$-0.754517\pi$
$181$	−19.2944	−1.43414	−0.717070	+	0.697001i	$0.754517\pi$
$182$	−23.4310	−1.73682
$183$	1.53092	0.113169
$184$	−17.7502	−1.30856
$185$	−3.86360	−0.284058
$186$	3.70072	0.271350
$187$	4.27025	0.312272
$188$	10.1207	0.738126
$189$	3.74160	0.272161
$190$	26.7999	1.94427
$191$	−20.7925	−1.50449	−0.752247	−	0.658882i	$-0.771030\pi$
$191$	−20.7925	−1.50449	−0.752247	+	0.658882i	$0.771030\pi$
$192$	−9.64269	−0.695901
$193$	4.40761	0.317267	0.158633	−	0.987338i	$-0.449291\pi$
$193$	4.40761	0.317267	0.158633	+	0.987338i	$0.449291\pi$
$194$	−3.88252	−0.278749
$195$	3.72142	0.266497
$196$	26.9344	1.92388
$197$	10.7014	0.762441	0.381221	−	0.924484i	$-0.375504\pi$
$197$	10.7014	0.762441	0.381221	+	0.924484i	$0.375504\pi$
$198$	−10.3266	−0.733879
$199$	12.1396	0.860550	0.430275	−	0.902698i	$-0.358417\pi$
$199$	12.1396	0.860550	0.430275	+	0.902698i	$0.358417\pi$
$200$	13.1156	0.927411
$201$	2.18684	0.154248
$202$	38.9390	2.73974
$203$	−9.56841	−0.671571
$204$	3.84800	0.269414
$205$	12.4380	0.868706
$206$	6.43544	0.448378
$207$	3.97190	0.276066
$208$	8.05646	0.558615
$209$	−32.9310	−2.27788
$210$	−13.0029	−0.897285
$211$	−9.19535	−0.633034	−0.316517	−	0.948587i	$-0.602513\pi$
$211$	−9.19535	−0.633034	−0.316517	+	0.948587i	$0.602513\pi$
$212$	−3.12141	−0.214379
$213$	−1.36413	−0.0934690
$214$	−25.3718	−1.73438
$215$	−3.18263	−0.217054
$216$	−4.46895	−0.304073
$217$	−5.72584	−0.388696
$218$	−24.4730	−1.65752
$219$	3.33586	0.225417
$220$	23.6139	1.59205
$221$	2.58959	0.174194
$222$	6.50156	0.436356
$223$	−4.41708	−0.295790	−0.147895	−	0.989003i	$-0.547250\pi$
$223$	−4.41708	−0.295790	−0.147895	+	0.989003i	$0.547250\pi$
$224$	5.29228	0.353605
$225$	−2.93482	−0.195655
$226$	−41.1203	−2.73528
$227$	9.11347	0.604882	0.302441	−	0.953168i	$-0.402198\pi$
$227$	9.11347	0.604882	0.302441	+	0.953168i	$0.402198\pi$
$228$	−29.6747	−1.96525
$229$	15.4085	1.01822	0.509110	−	0.860701i	$-0.329975\pi$
$229$	15.4085	1.01822	0.509110	+	0.860701i	$0.329975\pi$
$230$	−13.8032	−0.910157
$231$	15.9776	1.05125
$232$	11.4285	0.750315
$233$	−6.27810	−0.411292	−0.205646	−	0.978626i	$-0.565930\pi$
$233$	−6.27810	−0.411292	−0.205646	+	0.978626i	$0.565930\pi$
$234$	−6.26230	−0.409379
$235$	3.77967	0.246558
$236$	33.8662	2.20450
$237$	1.00000	0.0649570
$238$	−9.04818	−0.586506
$239$	−10.1095	−0.653932	−0.326966	−	0.945036i	$-0.606026\pi$
$239$	−10.1095	−0.653932	−0.326966	+	0.945036i	$0.606026\pi$
$240$	4.47087	0.288594
$241$	−17.0269	−1.09680	−0.548399	−	0.836217i	$-0.684763\pi$
$241$	−17.0269	−1.09680	−0.548399	+	0.836217i	$0.684763\pi$
$242$	−17.4963	−1.12470
$243$	1.00000	0.0641500
$244$	5.89097	0.377130
$245$	10.0589	0.642640
$246$	−20.9303	−1.33446
$247$	−19.9702	−1.27067
$248$	6.83892	0.434272
$249$	0.585100	0.0370792
$250$	27.5753	1.74401
$251$	−19.8391	−1.25223	−0.626117	−	0.779729i	$-0.715357\pi$
$251$	−19.8391	−1.25223	−0.626117	+	0.779729i	$0.715357\pi$
$252$	14.3977	0.906969
$253$	16.9610	1.06633
$254$	−26.9378	−1.69023
$255$	1.43707	0.0899930
$256$	−30.2641	−1.89150
$257$	8.49648	0.529996	0.264998	−	0.964249i	$-0.414629\pi$
$257$	8.49648	0.529996	0.264998	+	0.964249i	$0.414629\pi$
$258$	5.35564	0.333428
$259$	−10.0594	−0.625060
$260$	14.3200	0.888091
$261$	−2.55730	−0.158293
$262$	5.74287	0.354796
$263$	−16.5873	−1.02281	−0.511407	−	0.859339i	$-0.670876\pi$
$263$	−16.5873	−1.02281	−0.511407	+	0.859339i	$0.670876\pi$
$264$	−19.0835	−1.17451
$265$	−1.16572	−0.0716097
$266$	69.7770	4.27830
$267$	10.0870	0.617315
$268$	8.41498	0.514027
$269$	−3.01940	−0.184096	−0.0920480	−	0.995755i	$-0.529341\pi$
$269$	−3.01940	−0.184096	−0.0920480	+	0.995755i	$0.529341\pi$
$270$	−3.47522	−0.211495
$271$	10.0368	0.609694	0.304847	−	0.952401i	$-0.401395\pi$
$271$	10.0368	0.609694	0.304847	+	0.952401i	$0.401395\pi$
$272$	3.11110	0.188638
$273$	9.68920	0.586417
$274$	36.0201	2.17605
$275$	−12.5324	−0.755734
$276$	15.2839	0.919980
$277$	−28.7577	−1.72788	−0.863940	−	0.503594i	$-0.832011\pi$
$277$	−28.7577	−1.72788	−0.863940	+	0.503594i	$0.832011\pi$
$278$	−51.3460	−3.07953
$279$	−1.53032	−0.0916178
$280$	−24.0293	−1.43603
$281$	−0.250260	−0.0149293	−0.00746464	−	0.999972i	$-0.502376\pi$
$281$	−0.250260	−0.0149293	−0.00746464	+	0.999972i	$0.502376\pi$
$282$	−6.36031	−0.378751
$283$	−18.1370	−1.07813	−0.539067	−	0.842263i	$-0.681223\pi$
$283$	−18.1370	−1.07813	−0.539067	+	0.842263i	$0.681223\pi$
$284$	−5.24919	−0.311482
$285$	−11.0823	−0.656459
$286$	−26.7416	−1.58126
$287$	32.3839	1.91156
$288$	1.41444	0.0833468
$289$	1.00000	0.0588235
$290$	8.88720	0.521874
$291$	1.60550	0.0941160
$292$	12.8364	0.751193
$293$	8.82213	0.515394	0.257697	−	0.966226i	$-0.417036\pi$
$293$	8.82213	0.515394	0.257697	+	0.966226i	$0.417036\pi$
$294$	−16.9268	−0.987193
$295$	12.6477	0.736375
$296$	12.0149	0.698350
$297$	4.27025	0.247785
$298$	−10.4223	−0.603750
$299$	10.2856	0.594830
$300$	−11.2932	−0.652013
$301$	−8.28639	−0.477619
$302$	47.6973	2.74467
$303$	−16.1021	−0.925039
$304$	−23.9919	−1.37603
$305$	2.20004	0.125974
$306$	−2.41826	−0.138243
$307$	−14.0933	−0.804346	−0.402173	−	0.915564i	$-0.631745\pi$
$307$	−14.0933	−0.804346	−0.402173	+	0.915564i	$0.631745\pi$
$308$	61.4817	3.50325
$309$	−2.66118	−0.151389
$310$	5.31820	0.302053
$311$	8.54992	0.484822	0.242411	−	0.970174i	$-0.422062\pi$
$311$	8.54992	0.484822	0.242411	+	0.970174i	$0.422062\pi$
$312$	−11.5727	−0.655177
$313$	−20.4335	−1.15497	−0.577484	−	0.816402i	$-0.695966\pi$
$313$	−20.4335	−1.15497	−0.577484	+	0.816402i	$0.695966\pi$
$314$	−35.5408	−2.00568
$315$	5.37695	0.302957
$316$	3.84800	0.216467
$317$	18.3470	1.03047	0.515236	−	0.857048i	$-0.327704\pi$
$317$	18.3470	1.03047	0.515236	+	0.857048i	$0.327704\pi$
$318$	1.96164	0.110003
$319$	−10.9203	−0.611421
$320$	−13.8572	−0.774644
$321$	10.4918	0.585593
$322$	−35.9384	−2.00277
$323$	−7.71172	−0.429092
$324$	3.84800	0.213778
$325$	−7.59997	−0.421571
$326$	−0.168207	−0.00931614
$327$	10.1201	0.559641
$328$	−38.6791	−2.13570
$329$	9.84084	0.542543
$330$	−14.8401	−0.816919
$331$	29.2454	1.60747	0.803736	−	0.594987i	$-0.202843\pi$
$331$	29.2454	1.60747	0.803736	+	0.594987i	$0.202843\pi$
$332$	2.25146	0.123565
$333$	−2.68852	−0.147330
$334$	1.80139	0.0985679
$335$	3.14266	0.171702
$336$	11.6405	0.635041
$337$	−16.2320	−0.884212	−0.442106	−	0.896963i	$-0.645769\pi$
$337$	−16.2320	−0.884212	−0.442106	+	0.896963i	$0.645769\pi$
$338$	15.2207	0.827895
$339$	17.0041	0.923533
$340$	5.52985	0.299898
$341$	−6.53485	−0.353882
$342$	18.6490	1.00842
$343$	−0.00156242	−8.43626e−5 0
$344$	9.89722	0.533622
$345$	5.70791	0.307303
$346$	−17.5056	−0.941106
$347$	−8.67217	−0.465546	−0.232773	−	0.972531i	$-0.574780\pi$
$347$	−8.67217	−0.465546	−0.232773	+	0.972531i	$0.574780\pi$
$348$	−9.84050	−0.527506
$349$	6.54812	0.350513	0.175256	−	0.984523i	$-0.443925\pi$
$349$	6.54812	0.350513	0.175256	+	0.984523i	$0.443925\pi$
$350$	26.5548	1.41941
$351$	2.58959	0.138222
$352$	6.04002	0.321934
$353$	−16.5315	−0.879883	−0.439941	−	0.898026i	$-0.645001\pi$
$353$	−16.5315	−0.879883	−0.439941	+	0.898026i	$0.645001\pi$
$354$	−21.2831	−1.13118
$355$	−1.96036	−0.104045
$356$	38.8148	2.05718
$357$	3.74160	0.198027
$358$	32.6472	1.72546
$359$	27.4632	1.44945	0.724725	−	0.689038i	$-0.241967\pi$
$359$	27.4632	1.44945	0.724725	+	0.689038i	$0.241967\pi$
$360$	−6.42220	−0.338480
$361$	40.4706	2.13003
$362$	46.6589	2.45234
$363$	7.23505	0.379742
$364$	37.2840	1.95421
$365$	4.79388	0.250923
$366$	−3.70216	−0.193515
$367$	1.16447	0.0607850	0.0303925	−	0.999538i	$-0.490324\pi$
$367$	1.16447	0.0607850	0.0303925	+	0.999538i	$0.490324\pi$
$368$	12.3570	0.644151
$369$	8.65508	0.450565
$370$	9.34321	0.485730
$371$	−3.03510	−0.157575
$372$	−5.88867	−0.305313
$373$	26.0396	1.34828	0.674141	−	0.738603i	$-0.264514\pi$
$373$	26.0396	1.34828	0.674141	+	0.738603i	$0.264514\pi$
$374$	−10.3266	−0.533976
$375$	−11.4029	−0.588844
$376$	−11.7538	−0.606158
$377$	−6.62236	−0.341069
$378$	−9.04818	−0.465388
$379$	20.2683	1.04111	0.520557	−	0.853827i	$-0.325724\pi$
$379$	20.2683	1.04111	0.520557	+	0.853827i	$0.325724\pi$
$380$	−42.6447	−2.18763
$381$	11.1393	0.570685
$382$	50.2818	2.57264
$383$	−30.1723	−1.54173	−0.770867	−	0.636996i	$-0.780177\pi$
$383$	−30.1723	−1.54173	−0.770867	+	0.636996i	$0.780177\pi$
$384$	20.4897	1.04561
$385$	22.9609	1.17020
$386$	−10.6588	−0.542517
$387$	−2.21466	−0.112578
$388$	6.17796	0.313638
$389$	34.9455	1.77181	0.885903	−	0.463871i	$-0.153540\pi$
$389$	34.9455	1.77181	0.885903	+	0.463871i	$0.153540\pi$
$390$	−8.99938	−0.455701
$391$	3.97190	0.200867
$392$	−31.2808	−1.57992
$393$	−2.37479	−0.119792
$394$	−25.8787	−1.30375
$395$	1.43707	0.0723070
$396$	16.4319	0.825735
$397$	−22.0369	−1.10600	−0.552999	−	0.833182i	$-0.686517\pi$
$397$	−22.0369	−1.10600	−0.552999	+	0.833182i	$0.686517\pi$
$398$	−29.3566	−1.47152
$399$	−28.8542	−1.44452
$400$	−9.13052	−0.456526
$401$	5.52505	0.275908	0.137954	−	0.990439i	$-0.455947\pi$
$401$	5.52505	0.275908	0.137954	+	0.990439i	$0.455947\pi$
$402$	−5.28837	−0.263760
$403$	−3.96289	−0.197406
$404$	−61.9607	−3.08266
$405$	1.43707	0.0714087
$406$	23.1389	1.14837
$407$	−11.4807	−0.569076
$408$	−4.46895	−0.221246
$409$	−23.9969	−1.18657	−0.593286	−	0.804992i	$-0.702170\pi$
$409$	−23.9969	−1.18657	−0.593286	+	0.804992i	$0.702170\pi$
$410$	−30.0783	−1.48546
$411$	−14.8950	−0.734717
$412$	−10.2402	−0.504499
$413$	32.9298	1.62037
$414$	−9.60509	−0.472065
$415$	0.840831	0.0412748
$416$	3.66282	0.179584
$417$	21.2326	1.03977
$418$	79.6358	3.89512
$419$	−8.62002	−0.421115	−0.210558	−	0.977581i	$-0.567528\pi$
$419$	−8.62002	−0.421115	−0.210558	+	0.977581i	$0.567528\pi$
$420$	20.6905	1.00959
$421$	−14.8641	−0.724433	−0.362217	−	0.932094i	$-0.617980\pi$
$421$	−14.8641	−0.724433	−0.362217	+	0.932094i	$0.617980\pi$
$422$	22.2368	1.08247
$423$	2.63011	0.127881
$424$	3.62511	0.176051
$425$	−2.93482	−0.142360
$426$	3.29884	0.159829
$427$	5.72808	0.277201
$428$	40.3723	1.95147
$429$	11.0582	0.533894
$430$	7.69644	0.371156
$431$	17.4944	0.842676	0.421338	−	0.906904i	$-0.361561\pi$
$431$	17.4944	0.842676	0.421338	+	0.906904i	$0.361561\pi$
$432$	3.11110	0.149683
$433$	−6.42272	−0.308656	−0.154328	−	0.988020i	$-0.549321\pi$
$433$	−6.42272	−0.308656	−0.154328	+	0.988020i	$0.549321\pi$
$434$	13.8466	0.664658
$435$	−3.67503	−0.176204
$436$	38.9420	1.86498
$437$	−30.6302	−1.46524
$438$	−8.06699	−0.385456
$439$	11.2816	0.538441	0.269220	−	0.963079i	$-0.413234\pi$
$439$	11.2816	0.538441	0.269220	+	0.963079i	$0.413234\pi$
$440$	−27.4244	−1.30741
$441$	6.99958	0.333313
$442$	−6.26230	−0.297867
$443$	18.6312	0.885195	0.442598	−	0.896720i	$-0.354057\pi$
$443$	18.6312	0.885195	0.442598	+	0.896720i	$0.354057\pi$
$444$	−10.3454	−0.490973
$445$	14.4958	0.687165
$446$	10.6817	0.505792
$447$	4.30985	0.203849
$448$	−36.0791	−1.70458
$449$	−28.6311	−1.35118	−0.675592	−	0.737276i	$-0.736112\pi$
$449$	−28.6311	−1.35118	−0.675592	+	0.737276i	$0.736112\pi$
$450$	7.09717	0.334564
$451$	36.9594	1.74035
$452$	65.4316	3.07764
$453$	−19.7238	−0.926704
$454$	−22.0388	−1.03433
$455$	13.9241	0.652771
$456$	34.4633	1.61389
$457$	−18.8263	−0.880657	−0.440329	−	0.897837i	$-0.645138\pi$
$457$	−18.8263	−0.880657	−0.440329	+	0.897837i	$0.645138\pi$
$458$	−37.2617	−1.74113
$459$	1.00000	0.0466760
$460$	21.9640	1.02408
$461$	18.7948	0.875363	0.437681	−	0.899130i	$-0.355800\pi$
$461$	18.7948	0.875363	0.437681	+	0.899130i	$0.355800\pi$
$462$	−38.6380	−1.79760
$463$	28.4842	1.32377	0.661886	−	0.749605i	$-0.269756\pi$
$463$	28.4842	1.32377	0.661886	+	0.749605i	$0.269756\pi$
$464$	−7.95603	−0.369349
$465$	−2.19918	−0.101985
$466$	15.1821	0.703297
$467$	−30.7207	−1.42159	−0.710793	−	0.703402i	$-0.751664\pi$
$467$	−30.7207	−1.42159	−0.710793	+	0.703402i	$0.751664\pi$
$468$	9.96472	0.460620
$469$	8.18230	0.377824
$470$	−9.14023	−0.421607
$471$	14.6968	0.677194
$472$	−39.3311	−1.81036
$473$	−9.45717	−0.434841
$474$	−2.41826	−0.111075
$475$	22.6325	1.03845
$476$	14.3977	0.659917
$477$	−0.811178	−0.0371413
$478$	24.4476	1.11821
$479$	23.9174	1.09281	0.546407	−	0.837520i	$-0.315995\pi$
$479$	23.9174	1.09281	0.546407	+	0.837520i	$0.315995\pi$
$480$	2.03266	0.0927776
$481$	−6.96216	−0.317447
$482$	41.1755	1.87549
$483$	14.8613	0.676211
$484$	27.8405	1.26548
$485$	2.30722	0.104765
$486$	−2.41826	−0.109695
$487$	7.44745	0.337476	0.168738	−	0.985661i	$-0.446031\pi$
$487$	7.44745	0.337476	0.168738	+	0.985661i	$0.446031\pi$
$488$	−6.84159	−0.309704
$489$	0.0695570	0.00314548
$490$	−24.3251	−1.09890
$491$	12.6240	0.569713	0.284856	−	0.958570i	$-0.408054\pi$
$491$	12.6240	0.569713	0.284856	+	0.958570i	$0.408054\pi$
$492$	33.3047	1.50149
$493$	−2.55730	−0.115175
$494$	48.2931	2.17281
$495$	6.13666	0.275822
$496$	−4.76097	−0.213774
$497$	−5.10405	−0.228948
$498$	−1.41493	−0.0634044
$499$	31.3716	1.40439	0.702193	−	0.711987i	$-0.252204\pi$
$499$	31.3716	1.40439	0.702193	+	0.711987i	$0.252204\pi$
$500$	−43.8784	−1.96230
$501$	−0.744912	−0.0332802
$502$	47.9762	2.14128
$503$	−18.1364	−0.808661	−0.404331	−	0.914613i	$-0.632495\pi$
$503$	−18.1364	−0.808661	−0.404331	+	0.914613i	$0.632495\pi$
$504$	−16.7210	−0.744814
$505$	−23.1398	−1.02971
$506$	−41.0162	−1.82339
$507$	−6.29405	−0.279528
$508$	42.8641	1.90179
$509$	20.9859	0.930182	0.465091	−	0.885263i	$-0.346022\pi$
$509$	20.9859	0.930182	0.465091	+	0.885263i	$0.346022\pi$
$510$	−3.47522	−0.153885
$511$	12.4815	0.552148
$512$	32.2071	1.42337
$513$	−7.71172	−0.340481
$514$	−20.5467	−0.906278
$515$	−3.82431	−0.168519
$516$	−8.52202	−0.375161
$517$	11.2312	0.493950
$518$	24.3262	1.06883
$519$	7.23891	0.317753
$520$	−16.6309	−0.729311
$521$	1.66328	0.0728696	0.0364348	−	0.999336i	$-0.488400\pi$
$521$	1.66328	0.0728696	0.0364348	+	0.999336i	$0.488400\pi$
$522$	6.18424	0.270677
$523$	0.533569	0.0233313	0.0116657	−	0.999932i	$-0.496287\pi$
$523$	0.533569	0.0233313	0.0116657	+	0.999932i	$0.496287\pi$
$524$	−9.13819	−0.399204
$525$	−10.9809	−0.479247
$526$	40.1124	1.74898
$527$	−1.53032	−0.0666617
$528$	13.2852	0.578163
$529$	−7.22403	−0.314088
$530$	2.81902	0.122451
$531$	8.80098	0.381930
$532$	−111.031	−4.81380
$533$	22.4131	0.970818
$534$	−24.3930	−1.05559
$535$	15.0774	0.651854
$536$	−9.77290	−0.422125
$537$	−13.5003	−0.582579
$538$	7.30170	0.314799
$539$	29.8900	1.28745
$540$	5.52985	0.237967
$541$	13.1043	0.563399	0.281700	−	0.959503i	$-0.409102\pi$
$541$	13.1043	0.563399	0.281700	+	0.959503i	$0.409102\pi$
$542$	−24.2717	−1.04256
$543$	−19.2944	−0.828001
$544$	1.41444	0.0606437
$545$	14.5433	0.622965
$546$	−23.4310	−1.00276
$547$	−39.8637	−1.70445	−0.852224	−	0.523178i	$-0.824746\pi$
$547$	−39.8637	−1.70445	−0.852224	+	0.523178i	$0.824746\pi$
$548$	−57.3160	−2.44842
$549$	1.53092	0.0653379
$550$	30.3067	1.29228
$551$	19.7212	0.840152
$552$	−17.7502	−0.755499
$553$	3.74160	0.159109
$554$	69.5436	2.95462
$555$	−3.86360	−0.164001
$556$	81.7031	3.46498
$557$	16.0410	0.679678	0.339839	−	0.940484i	$-0.389627\pi$
$557$	16.0410	0.679678	0.339839	+	0.940484i	$0.389627\pi$
$558$	3.70072	0.156664
$559$	−5.73506	−0.242567
$560$	16.7282	0.706897
$561$	4.27025	0.180290
$562$	0.605195	0.0255286
$563$	9.05973	0.381822	0.190911	−	0.981607i	$-0.438856\pi$
$563$	9.05973	0.381822	0.190911	+	0.981607i	$0.438856\pi$
$564$	10.1207	0.426157
$565$	24.4361	1.02803
$566$	43.8601	1.84358
$567$	3.74160	0.157132
$568$	6.09625	0.255793
$569$	2.60152	0.109062	0.0545308	−	0.998512i	$-0.482634\pi$
$569$	2.60152	0.109062	0.0545308	+	0.998512i	$0.482634\pi$
$570$	26.7999	1.12253
$571$	−25.1548	−1.05270	−0.526349	−	0.850269i	$-0.676439\pi$
$571$	−25.1548	−1.05270	−0.526349	+	0.850269i	$0.676439\pi$
$572$	42.5519	1.77918
$573$	−20.7925	−0.868620
$574$	−78.3127	−3.26871
$575$	−11.6568	−0.486123
$576$	−9.64269	−0.401779
$577$	−35.3344	−1.47099	−0.735495	−	0.677530i	$-0.763050\pi$
$577$	−35.3344	−1.47099	−0.735495	+	0.677530i	$0.763050\pi$
$578$	−2.41826	−0.100587
$579$	4.40761	0.183174
$580$	−14.1415	−0.587195
$581$	2.18921	0.0908238
$582$	−3.88252	−0.160936
$583$	−3.46393	−0.143461
$584$	−14.9078	−0.616889
$585$	3.72142	0.153862
$586$	−21.3342	−0.881309
$587$	−36.0425	−1.48763	−0.743816	−	0.668384i	$-0.766986\pi$
$587$	−36.0425	−1.48763	−0.743816	+	0.668384i	$0.766986\pi$
$588$	26.9344	1.11076
$589$	11.8014	0.486268
$590$	−30.5854	−1.25918
$591$	10.7014	0.440196
$592$	−8.36426	−0.343769
$593$	15.7996	0.648813	0.324406	−	0.945918i	$-0.394836\pi$
$593$	15.7996	0.648813	0.324406	+	0.945918i	$0.394836\pi$
$594$	−10.3266	−0.423705
$595$	5.37695	0.220434
$596$	16.5843	0.679319
$597$	12.1396	0.496839
$598$	−24.8732	−1.01714
$599$	32.9095	1.34465	0.672323	−	0.740258i	$-0.265297\pi$
$599$	32.9095	1.34465	0.672323	+	0.740258i	$0.265297\pi$
$600$	13.1156	0.535441
$601$	−4.42825	−0.180632	−0.0903160	−	0.995913i	$-0.528788\pi$
$601$	−4.42825	−0.180632	−0.0903160	+	0.995913i	$0.528788\pi$
$602$	20.0387	0.816715
$603$	2.18684	0.0890552
$604$	−75.8971	−3.08821
$605$	10.3973	0.422710
$606$	38.9390	1.58179
$607$	−4.34059	−0.176179	−0.0880896	−	0.996113i	$-0.528076\pi$
$607$	−4.34059	−0.176179	−0.0880896	+	0.996113i	$0.528076\pi$
$608$	−10.9078	−0.442369
$609$	−9.56841	−0.387732
$610$	−5.32027	−0.215412
$611$	6.81091	0.275540
$612$	3.84800	0.155546
$613$	26.5860	1.07380	0.536898	−	0.843647i	$-0.319596\pi$
$613$	26.5860	1.07380	0.536898	+	0.843647i	$0.319596\pi$
$614$	34.0813	1.37541
$615$	12.4380	0.501548
$616$	−71.4030	−2.87691
$617$	14.5692	0.586533	0.293266	−	0.956031i	$-0.405258\pi$
$617$	14.5692	0.586533	0.293266	+	0.956031i	$0.405258\pi$
$618$	6.43544	0.258871
$619$	−26.1438	−1.05081	−0.525404	−	0.850853i	$-0.676086\pi$
$619$	−26.1438	−1.05081	−0.525404	+	0.850853i	$0.676086\pi$
$620$	−8.46244	−0.339860
$621$	3.97190	0.159387
$622$	−20.6760	−0.829031
$623$	37.7416	1.51208
$624$	8.05646	0.322516
$625$	−1.71271	−0.0685085
$626$	49.4136	1.97496
$627$	−32.9310	−1.31514
$628$	56.5534	2.25672
$629$	−2.68852	−0.107198
$630$	−13.0029	−0.518048
$631$	−44.3335	−1.76489	−0.882444	−	0.470417i	$-0.844103\pi$
$631$	−44.3335	−1.76489	−0.882444	+	0.470417i	$0.844103\pi$
$632$	−4.46895	−0.177765
$633$	−9.19535	−0.365483
$634$	−44.3679	−1.76208
$635$	16.0080	0.635259
$636$	−3.12141	−0.123772
$637$	18.1260	0.718179
$638$	26.4082	1.04551
$639$	−1.36413	−0.0539643
$640$	29.4452	1.16392
$641$	−9.00144	−0.355536	−0.177768	−	0.984072i	$-0.556888\pi$
$641$	−9.00144	−0.355536	−0.177768	+	0.984072i	$0.556888\pi$
$642$	−25.3718	−1.00135
$643$	−22.9213	−0.903929	−0.451965	−	0.892036i	$-0.649277\pi$
$643$	−22.9213	−0.903929	−0.451965	+	0.892036i	$0.649277\pi$
$644$	57.1861	2.25345
$645$	−3.18263	−0.125316
$646$	18.6490	0.733734
$647$	−45.1176	−1.77376	−0.886879	−	0.462002i	$-0.847131\pi$
$647$	−45.1176	−1.77376	−0.886879	+	0.462002i	$0.847131\pi$
$648$	−4.46895	−0.175557
$649$	37.5824	1.47524
$650$	18.3787	0.720873
$651$	−5.72584	−0.224414
$652$	0.267655	0.0104822
$653$	48.0075	1.87868	0.939338	−	0.342992i	$-0.111440\pi$
$653$	48.0075	1.87868	0.939338	+	0.342992i	$0.111440\pi$
$654$	−24.4730	−0.956969
$655$	−3.41275	−0.133347
$656$	26.9268	1.05132
$657$	3.33586	0.130144
$658$	−23.7977	−0.927733
$659$	34.3792	1.33922	0.669612	−	0.742711i	$-0.266460\pi$
$659$	34.3792	1.33922	0.669612	+	0.742711i	$0.266460\pi$
$660$	23.6139	0.919169
$661$	19.7035	0.766378	0.383189	−	0.923670i	$-0.374826\pi$
$661$	19.7035	0.766378	0.383189	+	0.923670i	$0.374826\pi$
$662$	−70.7230	−2.74873
$663$	2.58959	0.100571
$664$	−2.61478	−0.101473
$665$	−41.4656	−1.60797
$666$	6.50156	0.251930
$667$	−10.1574	−0.393294
$668$	−2.86642	−0.110905
$669$	−4.41708	−0.170774
$670$	−7.59977	−0.293605
$671$	6.53740	0.252374
$672$	5.29228	0.204154
$673$	43.1029	1.66150	0.830748	−	0.556648i	$-0.187913\pi$
$673$	43.1029	1.66150	0.830748	+	0.556648i	$0.187913\pi$
$674$	39.2532	1.51198
$675$	−2.93482	−0.112961
$676$	−24.2195	−0.931519
$677$	46.8286	1.79977	0.899886	−	0.436126i	$-0.143650\pi$
$677$	46.8286	1.79977	0.899886	+	0.436126i	$0.143650\pi$
$678$	−41.1203	−1.57922
$679$	6.00714	0.230533
$680$	−6.42220	−0.246280
$681$	9.11347	0.349229
$682$	15.8030	0.605128
$683$	−35.4834	−1.35774	−0.678868	−	0.734261i	$-0.737529\pi$
$683$	−35.4834	−1.35774	−0.678868	+	0.734261i	$0.737529\pi$
$684$	−29.6747	−1.13464
$685$	−21.4052	−0.817851
$686$	0.00377834	0.000144258 0
$687$	15.4085	0.587870
$688$	−6.89004	−0.262680
$689$	−2.10061	−0.0800271
$690$	−13.8032	−0.525480
$691$	−1.16284	−0.0442365	−0.0221183	−	0.999755i	$-0.507041\pi$
$691$	−1.16284	−0.0442365	−0.0221183	+	0.999755i	$0.507041\pi$
$692$	27.8553	1.05890
$693$	15.9776	0.606938
$694$	20.9716	0.796070
$695$	30.5128	1.15742
$696$	11.4285	0.433195
$697$	8.65508	0.327834
$698$	−15.8351	−0.599367
$699$	−6.27810	−0.237459
$700$	−42.2546	−1.59707
$701$	−2.68744	−0.101503	−0.0507516	−	0.998711i	$-0.516162\pi$
$701$	−2.68744	−0.101503	−0.0507516	+	0.998711i	$0.516162\pi$
$702$	−6.26230	−0.236355
$703$	20.7331	0.781965
$704$	−41.1767	−1.55191
$705$	3.77967	0.142350
$706$	39.9775	1.50457
$707$	−60.2475	−2.26584
$708$	33.8662	1.27277
$709$	−28.8031	−1.08172	−0.540862	−	0.841111i	$-0.681902\pi$
$709$	−28.8031	−1.08172	−0.540862	+	0.841111i	$0.681902\pi$
$710$	4.74067	0.177914
$711$	1.00000	0.0375029
$712$	−45.0783	−1.68938
$713$	−6.07827	−0.227633
$714$	−9.04818	−0.338620
$715$	15.8914	0.594305
$716$	−51.9490	−1.94142
$717$	−10.1095	−0.377548
$718$	−66.4132	−2.47852
$719$	−2.22656	−0.0830368	−0.0415184	−	0.999138i	$-0.513220\pi$
$719$	−2.22656	−0.0830368	−0.0415184	+	0.999138i	$0.513220\pi$
$720$	4.47087	0.166620
$721$	−9.95708	−0.370821
$722$	−97.8686	−3.64229
$723$	−17.0269	−0.633237
$724$	−74.2448	−2.75929
$725$	7.50523	0.278737
$726$	−17.4963	−0.649347
$727$	−11.9538	−0.443341	−0.221671	−	0.975122i	$-0.571151\pi$
$727$	−11.9538	−0.443341	−0.221671	+	0.975122i	$0.571151\pi$
$728$	−43.3005	−1.60482
$729$	1.00000	0.0370370
$730$	−11.5929	−0.429071
$731$	−2.21466	−0.0819123
$732$	5.89097	0.217736
$733$	33.3616	1.23224	0.616120	−	0.787652i	$-0.288704\pi$
$733$	33.3616	1.23224	0.616120	+	0.787652i	$0.288704\pi$
$734$	−2.81600	−0.103941
$735$	10.0589	0.371028
$736$	5.61802	0.207083
$737$	9.33838	0.343984
$738$	−20.9303	−0.770454
$739$	29.3361	1.07915	0.539573	−	0.841939i	$-0.318586\pi$
$739$	29.3361	1.07915	0.539573	+	0.841939i	$0.318586\pi$
$740$	−14.8671	−0.546527
$741$	−19.9702	−0.733622
$742$	7.33968	0.269448
$743$	−22.9459	−0.841804	−0.420902	−	0.907106i	$-0.638286\pi$
$743$	−22.9459	−0.841804	−0.420902	+	0.907106i	$0.638286\pi$
$744$	6.83892	0.250727
$745$	6.19356	0.226915
$746$	−62.9707	−2.30552
$747$	0.585100	0.0214077
$748$	16.4319	0.600811
$749$	39.2560	1.43438
$750$	27.5753	1.00691
$751$	−40.3686	−1.47307	−0.736536	−	0.676399i	$-0.763540\pi$
$751$	−40.3686	−1.47307	−0.736536	+	0.676399i	$0.763540\pi$
$752$	8.18254	0.298387
$753$	−19.8391	−0.722977
$754$	16.0146	0.583218
$755$	−28.3445	−1.03156
$756$	14.3977	0.523639
$757$	−20.5814	−0.748043	−0.374022	−	0.927420i	$-0.622021\pi$
$757$	−20.5814	−0.748043	−0.374022	+	0.927420i	$0.622021\pi$
$758$	−49.0142	−1.78027
$759$	16.9610	0.615645
$760$	49.5262	1.79651
$761$	14.3261	0.519320	0.259660	−	0.965700i	$-0.416389\pi$
$761$	14.3261	0.519320	0.259660	+	0.965700i	$0.416389\pi$
$762$	−26.9378	−0.975854
$763$	37.8653	1.37081
$764$	−80.0096	−2.89464
$765$	1.43707	0.0519575
$766$	72.9647	2.63632
$767$	22.7909	0.822932
$768$	−30.2641	−1.09206
$769$	29.3853	1.05966	0.529830	−	0.848104i	$-0.322256\pi$
$769$	29.3853	1.05966	0.529830	+	0.848104i	$0.322256\pi$
$770$	−55.5256	−2.00100
$771$	8.49648	0.305993
$772$	16.9605	0.610421
$773$	−43.7678	−1.57422	−0.787108	−	0.616815i	$-0.788423\pi$
$773$	−43.7678	−1.57422	−0.787108	+	0.616815i	$0.788423\pi$
$774$	5.35564	0.192505
$775$	4.49121	0.161329
$776$	−7.17489	−0.257564
$777$	−10.0594	−0.360878
$778$	−84.5074	−3.02974
$779$	−66.7455	−2.39141
$780$	14.3200	0.512739
$781$	−5.82520	−0.208442
$782$	−9.60509	−0.343477
$783$	−2.55730	−0.0913906
$784$	21.7764	0.777728
$785$	21.1204	0.753820
$786$	5.74287	0.204841
$787$	−1.53726	−0.0547975	−0.0273988	−	0.999625i	$-0.508722\pi$
$787$	−1.53726	−0.0547975	−0.0273988	+	0.999625i	$0.508722\pi$
$788$	41.1789	1.46694
$789$	−16.5873	−0.590522
$790$	−3.47522	−0.123643
$791$	63.6224	2.26215
$792$	−19.0835	−0.678104
$793$	3.96444	0.140781
$794$	53.2910	1.89123
$795$	−1.16572	−0.0413439
$796$	46.7130	1.65570
$797$	−52.3005	−1.85258	−0.926290	−	0.376811i	$-0.877021\pi$
$797$	−52.3005	−1.85258	−0.926290	+	0.376811i	$0.877021\pi$
$798$	69.7770	2.47008
$799$	2.63011	0.0930467
$800$	−4.15113	−0.146765
$801$	10.0870	0.356407
$802$	−13.3610	−0.471794
$803$	14.2450	0.502694
$804$	8.41498	0.296773
$805$	21.3567	0.752725
$806$	9.58332	0.337558
$807$	−3.01940	−0.106288
$808$	71.9593	2.53152
$809$	21.7755	0.765585	0.382792	−	0.923834i	$-0.374962\pi$
$809$	21.7755	0.765585	0.382792	+	0.923834i	$0.374962\pi$
$810$	−3.47522	−0.122107
$811$	−7.72144	−0.271136	−0.135568	−	0.990768i	$-0.543286\pi$
$811$	−7.72144	−0.271136	−0.135568	+	0.990768i	$0.543286\pi$
$812$	−36.8192	−1.29210
$813$	10.0368	0.352007
$814$	27.7633	0.973103
$815$	0.0999585	0.00350139
$816$	3.11110	0.108910
$817$	17.0789	0.597514
$818$	58.0309	2.02900
$819$	9.68920	0.338568
$820$	47.8613	1.67139
$821$	−51.1834	−1.78631	−0.893157	−	0.449746i	$-0.851515\pi$
$821$	−51.1834	−1.78631	−0.893157	+	0.449746i	$0.851515\pi$
$822$	36.0201	1.25634
$823$	−41.6829	−1.45298	−0.726488	−	0.687179i	$-0.758849\pi$
$823$	−41.6829	−1.45298	−0.726488	+	0.687179i	$0.758849\pi$
$824$	11.8927	0.414301
$825$	−12.5324	−0.436323
$826$	−79.6329	−2.77078
$827$	−33.8667	−1.17766	−0.588830	−	0.808257i	$-0.700411\pi$
$827$	−33.8667	−1.17766	−0.588830	+	0.808257i	$0.700411\pi$
$828$	15.2839	0.531151
$829$	−26.7372	−0.928622	−0.464311	−	0.885672i	$-0.653698\pi$
$829$	−26.7372	−0.928622	−0.464311	+	0.885672i	$0.653698\pi$
$830$	−2.03335	−0.0705787
$831$	−28.7577	−0.997592
$832$	−24.9706	−0.865699
$833$	6.99958	0.242521
$834$	−51.3460	−1.77797
$835$	−1.07049	−0.0370459
$836$	−126.718	−4.38265
$837$	−1.53032	−0.0528956
$838$	20.8455	0.720095
$839$	−16.8465	−0.581605	−0.290803	−	0.956783i	$-0.593922\pi$
$839$	−16.8465	−0.581605	−0.290803	+	0.956783i	$0.593922\pi$
$840$	−24.0293	−0.829091
$841$	−22.4602	−0.774489
$842$	35.9454	1.23876
$843$	−0.250260	−0.00861942
$844$	−35.3837	−1.21796
$845$	−9.04500	−0.311158
$846$	−6.36031	−0.218672
$847$	27.0707	0.930160
$848$	−2.52365	−0.0866626
$849$	−18.1370	−0.622461
$850$	7.09717	0.243431
$851$	−10.6785	−0.366056
$852$	−5.24919	−0.179834
$853$	−22.6295	−0.774818	−0.387409	−	0.921908i	$-0.626630\pi$
$853$	−22.6295	−0.774818	−0.387409	+	0.921908i	$0.626630\pi$
$854$	−13.8520	−0.474006
$855$	−11.0823	−0.379007
$856$	−46.8871	−1.60257
$857$	−35.5254	−1.21353	−0.606763	−	0.794883i	$-0.707532\pi$
$857$	−35.5254	−1.21353	−0.606763	+	0.794883i	$0.707532\pi$
$858$	−26.7416	−0.912943
$859$	38.9522	1.32903	0.664516	−	0.747274i	$-0.268638\pi$
$859$	38.9522	1.32903	0.664516	+	0.747274i	$0.268638\pi$
$860$	−12.2468	−0.417611
$861$	32.3839	1.10364
$862$	−42.3061	−1.44095
$863$	−40.9279	−1.39320	−0.696601	−	0.717458i	$-0.745305\pi$
$863$	−40.9279	−1.39320	−0.696601	+	0.717458i	$0.745305\pi$
$864$	1.41444	0.0481203
$865$	10.4028	0.353707
$866$	15.5318	0.527793
$867$	1.00000	0.0339618
$868$	−22.0330	−0.747850
$869$	4.27025	0.144858
$870$	8.88720	0.301304
$871$	5.66302	0.191884
$872$	−45.2261	−1.53155
$873$	1.60550	0.0543379
$874$	74.0718	2.50552
$875$	−42.6652	−1.44235
$876$	12.8364	0.433702
$877$	−30.4423	−1.02797	−0.513983	−	0.857801i	$-0.671830\pi$
$877$	−30.4423	−1.02797	−0.513983	+	0.857801i	$0.671830\pi$
$878$	−27.2818	−0.920717
$879$	8.82213	0.297563
$880$	19.0918	0.643583
$881$	−44.4180	−1.49648	−0.748241	−	0.663427i	$-0.769101\pi$
$881$	−44.4180	−1.49648	−0.748241	+	0.663427i	$0.769101\pi$
$882$	−16.9268	−0.569956
$883$	2.84344	0.0956892	0.0478446	−	0.998855i	$-0.484765\pi$
$883$	2.84344	0.0956892	0.0478446	+	0.998855i	$0.484765\pi$
$884$	9.96472	0.335150
$885$	12.6477	0.425146
$886$	−45.0552	−1.51366
$887$	−12.0071	−0.403159	−0.201580	−	0.979472i	$-0.564608\pi$
$887$	−12.0071	−0.403159	−0.201580	+	0.979472i	$0.564608\pi$
$888$	12.0149	0.403193
$889$	41.6789	1.39787
$890$	−35.0546	−1.17503
$891$	4.27025	0.143059
$892$	−16.9969	−0.569099
$893$	−20.2827	−0.678735
$894$	−10.4223	−0.348575
$895$	−19.4008	−0.648499
$896$	76.6642	2.56117
$897$	10.2856	0.343425
$898$	69.2374	2.31048
$899$	3.91349	0.130522
$900$	−11.2932	−0.376440
$901$	−0.811178	−0.0270243
$902$	−89.3775	−2.97595
$903$	−8.28639	−0.275754
$904$	−75.9903	−2.52740
$905$	−27.7274	−0.921691
$906$	47.6973	1.58464
$907$	56.4484	1.87434	0.937168	−	0.348877i	$-0.113437\pi$
$907$	56.4484	1.87434	0.937168	+	0.348877i	$0.113437\pi$
$908$	35.0686	1.16379
$909$	−16.1021	−0.534072
$910$	−33.6721	−1.11622
$911$	20.1045	0.666091	0.333045	−	0.942911i	$-0.391924\pi$
$911$	20.1045	0.666091	0.333045	+	0.942911i	$0.391924\pi$
$912$	−23.9919	−0.794452
$913$	2.49852	0.0826891
$914$	45.5270	1.50590
$915$	2.20004	0.0727310
$916$	59.2918	1.95905
$917$	−8.88552	−0.293426
$918$	−2.41826	−0.0798146
$919$	28.2551	0.932049	0.466025	−	0.884772i	$-0.345686\pi$
$919$	28.2551	0.932049	0.466025	+	0.884772i	$0.345686\pi$
$920$	−25.5083	−0.840985
$921$	−14.0933	−0.464390
$922$	−45.4509	−1.49684
$923$	−3.53254	−0.116275
$924$	61.4817	2.02260
$925$	7.89034	0.259433
$926$	−68.8822	−2.26361
$927$	−2.66118	−0.0874046
$928$	−3.61716	−0.118739
$929$	−4.72062	−0.154878	−0.0774392	−	0.996997i	$-0.524674\pi$
$929$	−4.72062	−0.154878	−0.0774392	+	0.996997i	$0.524674\pi$
$930$	5.31820	0.174391
$931$	−53.9788	−1.76908
$932$	−24.1581	−0.791325
$933$	8.54992	0.279912
$934$	74.2908	2.43087
$935$	6.13666	0.200690
$936$	−11.5727	−0.378266
$937$	2.14740	0.0701524	0.0350762	−	0.999385i	$-0.488833\pi$
$937$	2.14740	0.0701524	0.0350762	+	0.999385i	$0.488833\pi$
$938$	−19.7870	−0.646067
$939$	−20.4335	−0.666822
$940$	14.5441	0.474378
$941$	13.0863	0.426603	0.213301	−	0.976986i	$-0.431578\pi$
$941$	13.0863	0.426603	0.213301	+	0.976986i	$0.431578\pi$
$942$	−35.5408	−1.15798
$943$	34.3771	1.11947
$944$	27.3807	0.891167
$945$	5.37695	0.174912
$946$	22.8699	0.743566
$947$	−3.34712	−0.108767	−0.0543834	−	0.998520i	$-0.517319\pi$
$947$	−3.34712	−0.108767	−0.0543834	+	0.998520i	$0.517319\pi$
$948$	3.84800	0.124977
$949$	8.63850	0.280418
$950$	−54.7314	−1.77572
$951$	18.3470	0.594943
$952$	−16.7210	−0.541932
$953$	15.9799	0.517640	0.258820	−	0.965926i	$-0.416666\pi$
$953$	15.9799	0.517640	0.258820	+	0.965926i	$0.416666\pi$
$954$	1.96164	0.0635105
$955$	−29.8804	−0.966905
$956$	−38.9015	−1.25817
$957$	−10.9203	−0.353004
$958$	−57.8386	−1.86868
$959$	−55.7312	−1.79965
$960$	−13.8572	−0.447241
$961$	−28.6581	−0.924456
$962$	16.8363	0.542825
$963$	10.4918	0.338092
$964$	−65.5195	−2.11024
$965$	6.33406	0.203901
$966$	−35.9384	−1.15630
$967$	−38.5404	−1.23938	−0.619688	−	0.784848i	$-0.712741\pi$
$967$	−38.5404	−1.23938	−0.619688	+	0.784848i	$0.712741\pi$
$968$	−32.3331	−1.03922
$969$	−7.71172	−0.247736
$970$	−5.57946	−0.179146
$971$	34.7449	1.11502	0.557508	−	0.830171i	$-0.311757\pi$
$971$	34.7449	1.11502	0.557508	+	0.830171i	$0.311757\pi$
$972$	3.84800	0.123425
$973$	79.4440	2.54686
$974$	−18.0099	−0.577074
$975$	−7.59997	−0.243394
$976$	4.76283	0.152455
$977$	−31.7248	−1.01497	−0.507484	−	0.861661i	$-0.669424\pi$
$977$	−31.7248	−1.01497	−0.507484	+	0.861661i	$0.669424\pi$
$978$	−0.168207	−0.00537868
$979$	43.0741	1.37665
$980$	38.7067	1.23644
$981$	10.1201	0.323109
$982$	−30.5281	−0.974192
$983$	16.5416	0.527594	0.263797	−	0.964578i	$-0.415025\pi$
$983$	16.5416	0.527594	0.263797	+	0.964578i	$0.415025\pi$
$984$	−38.6791	−1.23304
$985$	15.3787	0.490005
$986$	6.18424	0.196946
$987$	9.84084	0.313237
$988$	−76.8452	−2.44477
$989$	−8.79642	−0.279710
$990$	−14.8401	−0.471648
$991$	10.7711	0.342157	0.171078	−	0.985257i	$-0.445275\pi$
$991$	10.7711	0.342157	0.171078	+	0.985257i	$0.445275\pi$
$992$	−2.16455	−0.0687244
$993$	29.2454	0.928074
$994$	12.3429	0.391494
$995$	17.4454	0.553057
$996$	2.25146	0.0713404
$997$	−17.2258	−0.545546	−0.272773	−	0.962078i	$-0.587941\pi$
$997$	−17.2258	−0.545546	−0.272773	+	0.962078i	$0.587941\pi$
$998$	−75.8648	−2.40146
$999$	−2.68852	−0.0850611

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.k.1.3	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.k.1.3	✓	31	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q-2.41826 q^{2} +1.00000 q^{3} +3.84800 q^{4} +1.43707 q^{5} -2.41826 q^{6} +3.74160 q^{7} -4.46895 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.41826 q^{2} +1.00000 q^{3} +3.84800 q^{4} +1.43707 q^{5} -2.41826 q^{6} +3.74160 q^{7} -4.46895 q^{8} +1.00000 q^{9} -3.47522 q^{10} +4.27025 q^{11} +3.84800 q^{12} +2.58959 q^{13} -9.04818 q^{14} +1.43707 q^{15} +3.11110 q^{16} +1.00000 q^{17} -2.41826 q^{18} -7.71172 q^{19} +5.52985 q^{20} +3.74160 q^{21} -10.3266 q^{22} +3.97190 q^{23} -4.46895 q^{24} -2.93482 q^{25} -6.26230 q^{26} +1.00000 q^{27} +14.3977 q^{28} -2.55730 q^{29} -3.47522 q^{30} -1.53032 q^{31} +1.41444 q^{32} +4.27025 q^{33} -2.41826 q^{34} +5.37695 q^{35} +3.84800 q^{36} -2.68852 q^{37} +18.6490 q^{38} +2.58959 q^{39} -6.42220 q^{40} +8.65508 q^{41} -9.04818 q^{42} -2.21466 q^{43} +16.4319 q^{44} +1.43707 q^{45} -9.60509 q^{46} +2.63011 q^{47} +3.11110 q^{48} +6.99958 q^{49} +7.09717 q^{50} +1.00000 q^{51} +9.96472 q^{52} -0.811178 q^{53} -2.41826 q^{54} +6.13666 q^{55} -16.7210 q^{56} -7.71172 q^{57} +6.18424 q^{58} +8.80098 q^{59} +5.52985 q^{60} +1.53092 q^{61} +3.70072 q^{62} +3.74160 q^{63} -9.64269 q^{64} +3.72142 q^{65} -10.3266 q^{66} +2.18684 q^{67} +3.84800 q^{68} +3.97190 q^{69} -13.0029 q^{70} -1.36413 q^{71} -4.46895 q^{72} +3.33586 q^{73} +6.50156 q^{74} -2.93482 q^{75} -29.6747 q^{76} +15.9776 q^{77} -6.26230 q^{78} +1.00000 q^{79} +4.47087 q^{80} +1.00000 q^{81} -20.9303 q^{82} +0.585100 q^{83} +14.3977 q^{84} +1.43707 q^{85} +5.35564 q^{86} -2.55730 q^{87} -19.0835 q^{88} +10.0870 q^{89} -3.47522 q^{90} +9.68920 q^{91} +15.2839 q^{92} -1.53032 q^{93} -6.36031 q^{94} -11.0823 q^{95} +1.41444 q^{96} +1.60550 q^{97} -16.9268 q^{98} +4.27025 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9}+O(q^{10}) \) 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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