LMFDB - Embedded newform 4034.2.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4034,2,Mod(1,4034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4034, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4034 = 2 \cdot 2017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4034.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:	$32.2116521754$
Analytic rank:	$0$
Dimension:	$52$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	4034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.11260 q^{3} +1.00000 q^{4} -0.160277 q^{5} -3.11260 q^{6} -3.29184 q^{7} +1.00000 q^{8} +6.68830 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.11260 q^{3} +1.00000 q^{4} -0.160277 q^{5} -3.11260 q^{6} -3.29184 q^{7} +1.00000 q^{8} +6.68830 q^{9} -0.160277 q^{10} +3.20139 q^{11} -3.11260 q^{12} +4.98648 q^{13} -3.29184 q^{14} +0.498880 q^{15} +1.00000 q^{16} +0.488669 q^{17} +6.68830 q^{18} +0.517690 q^{19} -0.160277 q^{20} +10.2462 q^{21} +3.20139 q^{22} -0.947329 q^{23} -3.11260 q^{24} -4.97431 q^{25} +4.98648 q^{26} -11.4802 q^{27} -3.29184 q^{28} +3.96026 q^{29} +0.498880 q^{30} -1.55770 q^{31} +1.00000 q^{32} -9.96465 q^{33} +0.488669 q^{34} +0.527608 q^{35} +6.68830 q^{36} -7.26831 q^{37} +0.517690 q^{38} -15.5209 q^{39} -0.160277 q^{40} +6.27157 q^{41} +10.2462 q^{42} -12.1373 q^{43} +3.20139 q^{44} -1.07198 q^{45} -0.947329 q^{46} +1.05047 q^{47} -3.11260 q^{48} +3.83624 q^{49} -4.97431 q^{50} -1.52103 q^{51} +4.98648 q^{52} +2.50350 q^{53} -11.4802 q^{54} -0.513110 q^{55} -3.29184 q^{56} -1.61136 q^{57} +3.96026 q^{58} -6.30857 q^{59} +0.498880 q^{60} +10.7468 q^{61} -1.55770 q^{62} -22.0169 q^{63} +1.00000 q^{64} -0.799220 q^{65} -9.96465 q^{66} -6.07497 q^{67} +0.488669 q^{68} +2.94866 q^{69} +0.527608 q^{70} +15.4790 q^{71} +6.68830 q^{72} +4.28695 q^{73} -7.26831 q^{74} +15.4831 q^{75} +0.517690 q^{76} -10.5385 q^{77} -15.5209 q^{78} +1.98009 q^{79} -0.160277 q^{80} +15.6685 q^{81} +6.27157 q^{82} -2.96501 q^{83} +10.2462 q^{84} -0.0783227 q^{85} -12.1373 q^{86} -12.3267 q^{87} +3.20139 q^{88} +1.13197 q^{89} -1.07198 q^{90} -16.4147 q^{91} -0.947329 q^{92} +4.84849 q^{93} +1.05047 q^{94} -0.0829740 q^{95} -3.11260 q^{96} -3.24444 q^{97} +3.83624 q^{98} +21.4119 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9}+O(q^{10}) $ 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9	\( 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9} + 24 q^{10} + 19 q^{11} + 16 q^{12} + 27 q^{13} + 12 q^{14} + 5 q^{15} + 52 q^{16} + 43 q^{17} + 70 q^{18} + 35 q^{19} + 24 q^{20} + 29 q^{21} + 19 q^{22} + 2 q^{23} + 16 q^{24} + 88 q^{25} + 27 q^{26} + 49 q^{27} + 12 q^{28} + 31 q^{29} + 5 q^{30} + 59 q^{31} + 52 q^{32} + 45 q^{33} + 43 q^{34} + 18 q^{35} + 70 q^{36} + 60 q^{37} + 35 q^{38} + 6 q^{39} + 24 q^{40} + 56 q^{41} + 29 q^{42} + 34 q^{43} + 19 q^{44} + 61 q^{45} + 2 q^{46} - 4 q^{47} + 16 q^{48} + 102 q^{49} + 88 q^{50} + 23 q^{51} + 27 q^{52} + 30 q^{53} + 49 q^{54} + 24 q^{55} + 12 q^{56} + 32 q^{57} + 31 q^{58} + 27 q^{59} + 5 q^{60} + 107 q^{61} + 59 q^{62} - 4 q^{63} + 52 q^{64} + 46 q^{65} + 45 q^{66} + 22 q^{67} + 43 q^{68} + 36 q^{69} + 18 q^{70} + 8 q^{71} + 70 q^{72} + 66 q^{73} + 60 q^{74} + 53 q^{75} + 35 q^{76} + 26 q^{77} + 6 q^{78} + 50 q^{79} + 24 q^{80} + 108 q^{81} + 56 q^{82} + 52 q^{83} + 29 q^{84} + 19 q^{85} + 34 q^{86} - 32 q^{87} + 19 q^{88} + 62 q^{89} + 61 q^{90} + 69 q^{91} + 2 q^{92} + 21 q^{93} - 4 q^{94} - 44 q^{95} + 16 q^{96} + 82 q^{97} + 102 q^{98} + 16 q^{99}+O(q^{100}) \) 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9 + 24 * q^10 + 19 * q^11 + 16 * q^12 + 27 * q^13 + 12 * q^14 + 5 * q^15 + 52 * q^16 + 43 * q^17 + 70 * q^18 + 35 * q^19 + 24 * q^20 + 29 * q^21 + 19 * q^22 + 2 * q^23 + 16 * q^24 + 88 * q^25 + 27 * q^26 + 49 * q^27 + 12 * q^28 + 31 * q^29 + 5 * q^30 + 59 * q^31 + 52 * q^32 + 45 * q^33 + 43 * q^34 + 18 * q^35 + 70 * q^36 + 60 * q^37 + 35 * q^38 + 6 * q^39 + 24 * q^40 + 56 * q^41 + 29 * q^42 + 34 * q^43 + 19 * q^44 + 61 * q^45 + 2 * q^46 - 4 * q^47 + 16 * q^48 + 102 * q^49 + 88 * q^50 + 23 * q^51 + 27 * q^52 + 30 * q^53 + 49 * q^54 + 24 * q^55 + 12 * q^56 + 32 * q^57 + 31 * q^58 + 27 * q^59 + 5 * q^60 + 107 * q^61 + 59 * q^62 - 4 * q^63 + 52 * q^64 + 46 * q^65 + 45 * q^66 + 22 * q^67 + 43 * q^68 + 36 * q^69 + 18 * q^70 + 8 * q^71 + 70 * q^72 + 66 * q^73 + 60 * q^74 + 53 * q^75 + 35 * q^76 + 26 * q^77 + 6 * q^78 + 50 * q^79 + 24 * q^80 + 108 * q^81 + 56 * q^82 + 52 * q^83 + 29 * q^84 + 19 * q^85 + 34 * q^86 - 32 * q^87 + 19 * q^88 + 62 * q^89 + 61 * q^90 + 69 * q^91 + 2 * q^92 + 21 * q^93 - 4 * q^94 - 44 * q^95 + 16 * q^96 + 82 * q^97 + 102 * q^98 + 16 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−3.11260	−1.79706	−0.898531	−	0.438909i	$-0.855365\pi$
$3$	−3.11260	−1.79706	−0.898531	+	0.438909i	$0.855365\pi$
$4$	1.00000	0.500000
$5$	−0.160277	−0.0716782	−0.0358391	−	0.999358i	$-0.511410\pi$
$5$	−0.160277	−0.0716782	−0.0358391	+	0.999358i	$0.511410\pi$
$6$	−3.11260	−1.27072
$7$	−3.29184	−1.24420	−0.622100	−	0.782938i	$-0.713720\pi$
$7$	−3.29184	−1.24420	−0.622100	+	0.782938i	$0.713720\pi$
$8$	1.00000	0.353553
$9$	6.68830	2.22943
$10$	−0.160277	−0.0506842
$11$	3.20139	0.965255	0.482627	−	0.875826i	$-0.339683\pi$
$11$	3.20139	0.965255	0.482627	+	0.875826i	$0.339683\pi$
$12$	−3.11260	−0.898531
$13$	4.98648	1.38300	0.691500	−	0.722376i	$-0.256950\pi$
$13$	4.98648	1.38300	0.691500	+	0.722376i	$0.256950\pi$
$14$	−3.29184	−0.879782
$15$	0.498880	0.128810
$16$	1.00000	0.250000
$17$	0.488669	0.118520	0.0592599	−	0.998243i	$-0.481126\pi$
$17$	0.488669	0.118520	0.0592599	+	0.998243i	$0.481126\pi$
$18$	6.68830	1.57645
$19$	0.517690	0.118766	0.0593831	−	0.998235i	$-0.481087\pi$
$19$	0.517690	0.118766	0.0593831	+	0.998235i	$0.481087\pi$
$20$	−0.160277	−0.0358391
$21$	10.2462	2.23591
$22$	3.20139	0.682538
$23$	−0.947329	−0.197532	−0.0987659	−	0.995111i	$-0.531490\pi$
$23$	−0.947329	−0.197532	−0.0987659	+	0.995111i	$0.531490\pi$
$24$	−3.11260	−0.635358
$25$	−4.97431	−0.994862
$26$	4.98648	0.977929
$27$	−11.4802	−2.20937
$28$	−3.29184	−0.622100
$29$	3.96026	0.735401	0.367701	−	0.929944i	$-0.380145\pi$
$29$	3.96026	0.735401	0.367701	+	0.929944i	$0.380145\pi$
$30$	0.498880	0.0910826
$31$	−1.55770	−0.279771	−0.139885	−	0.990168i	$-0.544673\pi$
$31$	−1.55770	−0.279771	−0.139885	+	0.990168i	$0.544673\pi$
$32$	1.00000	0.176777
$33$	−9.96465	−1.73462
$34$	0.488669	0.0838061
$35$	0.527608	0.0891821
$36$	6.68830	1.11472
$37$	−7.26831	−1.19490	−0.597451	−	0.801905i	$-0.703820\pi$
$37$	−7.26831	−1.19490	−0.597451	+	0.801905i	$0.703820\pi$
$38$	0.517690	0.0839804
$39$	−15.5209	−2.48534
$40$	−0.160277	−0.0253421
$41$	6.27157	0.979454	0.489727	−	0.871876i	$-0.337096\pi$
$41$	6.27157	0.979454	0.489727	+	0.871876i	$0.337096\pi$
$42$	10.2462	1.58102
$43$	−12.1373	−1.85092	−0.925458	−	0.378850i	$-0.876320\pi$
$43$	−12.1373	−1.85092	−0.925458	+	0.378850i	$0.876320\pi$
$44$	3.20139	0.482627
$45$	−1.07198	−0.159802
$46$	−0.947329	−0.139676
$47$	1.05047	0.153227	0.0766135	−	0.997061i	$-0.475589\pi$
$47$	1.05047	0.153227	0.0766135	+	0.997061i	$0.475589\pi$
$48$	−3.11260	−0.449266
$49$	3.83624	0.548034
$50$	−4.97431	−0.703474
$51$	−1.52103	−0.212987
$52$	4.98648	0.691500
$53$	2.50350	0.343883	0.171941	−	0.985107i	$-0.444996\pi$
$53$	2.50350	0.343883	0.171941	+	0.985107i	$0.444996\pi$
$54$	−11.4802	−1.56226
$55$	−0.513110	−0.0691877
$56$	−3.29184	−0.439891
$57$	−1.61136	−0.213430
$58$	3.96026	0.520007
$59$	−6.30857	−0.821306	−0.410653	−	0.911792i	$-0.634699\pi$
$59$	−6.30857	−0.821306	−0.410653	+	0.911792i	$0.634699\pi$
$60$	0.498880	0.0644051
$61$	10.7468	1.37599	0.687993	−	0.725717i	$-0.258492\pi$
$61$	10.7468	1.37599	0.687993	+	0.725717i	$0.258492\pi$
$62$	−1.55770	−0.197828
$63$	−22.0169	−2.77386
$64$	1.00000	0.125000
$65$	−0.799220	−0.0991311
$66$	−9.96465	−1.22656
$67$	−6.07497	−0.742176	−0.371088	−	0.928598i	$-0.621015\pi$
$67$	−6.07497	−0.742176	−0.371088	+	0.928598i	$0.621015\pi$
$68$	0.488669	0.0592599
$69$	2.94866	0.354977
$70$	0.527608	0.0630612
$71$	15.4790	1.83702	0.918510	−	0.395398i	$-0.129393\pi$
$71$	15.4790	1.83702	0.918510	+	0.395398i	$0.129393\pi$
$72$	6.68830	0.788224
$73$	4.28695	0.501749	0.250875	−	0.968020i	$-0.419282\pi$
$73$	4.28695	0.501749	0.250875	+	0.968020i	$0.419282\pi$
$74$	−7.26831	−0.844924
$75$	15.4831	1.78783
$76$	0.517690	0.0593831
$77$	−10.5385	−1.20097
$78$	−15.5209	−1.75740
$79$	1.98009	0.222777	0.111389	−	0.993777i	$-0.464470\pi$
$79$	1.98009	0.222777	0.111389	+	0.993777i	$0.464470\pi$
$80$	−0.160277	−0.0179196
$81$	15.6685	1.74095
$82$	6.27157	0.692579
$83$	−2.96501	−0.325452	−0.162726	−	0.986671i	$-0.552029\pi$
$83$	−2.96501	−0.325452	−0.162726	+	0.986671i	$0.552029\pi$
$84$	10.2462	1.11795
$85$	−0.0783227	−0.00849528
$86$	−12.1373	−1.30880
$87$	−12.3267	−1.32156
$88$	3.20139	0.341269
$89$	1.13197	0.119989	0.0599944	−	0.998199i	$-0.480892\pi$
$89$	1.13197	0.119989	0.0599944	+	0.998199i	$0.480892\pi$
$90$	−1.07198	−0.112997
$91$	−16.4147	−1.72073
$92$	−0.947329	−0.0987659
$93$	4.84849	0.502765
$94$	1.05047	0.108348
$95$	−0.0829740	−0.00851295
$96$	−3.11260	−0.317679
$97$	−3.24444	−0.329423	−0.164712	−	0.986342i	$-0.552669\pi$
$97$	−3.24444	−0.329423	−0.164712	+	0.986342i	$0.552669\pi$
$98$	3.83624	0.387518
$99$	21.4119	2.15197
$100$	−4.97431	−0.497431
$101$	15.1039	1.50290	0.751449	−	0.659791i	$-0.229355\pi$
$101$	15.1039	1.50290	0.751449	+	0.659791i	$0.229355\pi$
$102$	−1.52103	−0.150605
$103$	11.1370	1.09736	0.548681	−	0.836032i	$-0.315130\pi$
$103$	11.1370	1.09736	0.548681	+	0.836032i	$0.315130\pi$
$104$	4.98648	0.488965
$105$	−1.64224	−0.160266
$106$	2.50350	0.243162
$107$	11.2403	1.08664	0.543322	−	0.839524i	$-0.317166\pi$
$107$	11.2403	1.08664	0.543322	+	0.839524i	$0.317166\pi$
$108$	−11.4802	−1.10469
$109$	−5.62064	−0.538360	−0.269180	−	0.963090i	$-0.586753\pi$
$109$	−5.62064	−0.538360	−0.269180	+	0.963090i	$0.586753\pi$
$110$	−0.513110	−0.0489231
$111$	22.6234	2.14732
$112$	−3.29184	−0.311050
$113$	12.7698	1.20129	0.600643	−	0.799518i	$-0.294911\pi$
$113$	12.7698	1.20129	0.600643	+	0.799518i	$0.294911\pi$
$114$	−1.61136	−0.150918
$115$	0.151835	0.0141587
$116$	3.96026	0.367701
$117$	33.3511	3.08331
$118$	−6.30857	−0.580751
$119$	−1.60862	−0.147462
$120$	0.498880	0.0455413
$121$	−0.751117	−0.0682834
$122$	10.7468	0.972969
$123$	−19.5209	−1.76014
$124$	−1.55770	−0.139885
$125$	1.59866	0.142988
$126$	−22.0169	−1.96142
$127$	5.63503	0.500028	0.250014	−	0.968242i	$-0.419565\pi$
$127$	5.63503	0.500028	0.250014	+	0.968242i	$0.419565\pi$
$128$	1.00000	0.0883883
$129$	37.7785	3.32621
$130$	−0.799220	−0.0700962
$131$	−5.22061	−0.456127	−0.228063	−	0.973646i	$-0.573239\pi$
$131$	−5.22061	−0.456127	−0.228063	+	0.973646i	$0.573239\pi$
$132$	−9.96465	−0.867312
$133$	−1.70415	−0.147769
$134$	−6.07497	−0.524797
$135$	1.84002	0.158364
$136$	0.488669	0.0419031
$137$	0.799344	0.0682926	0.0341463	−	0.999417i	$-0.489129\pi$
$137$	0.799344	0.0682926	0.0341463	+	0.999417i	$0.489129\pi$
$138$	2.94866	0.251007
$139$	15.0901	1.27993	0.639963	−	0.768406i	$-0.278950\pi$
$139$	15.0901	1.27993	0.639963	+	0.768406i	$0.278950\pi$
$140$	0.527608	0.0445910
$141$	−3.26970	−0.275359
$142$	15.4790	1.29897
$143$	15.9637	1.33495
$144$	6.68830	0.557359
$145$	−0.634739	−0.0527122
$146$	4.28695	0.354790
$147$	−11.9407	−0.984851
$148$	−7.26831	−0.597451
$149$	0.404136	0.0331081	0.0165541	−	0.999863i	$-0.494730\pi$
$149$	0.404136	0.0331081	0.0165541	+	0.999863i	$0.494730\pi$
$150$	15.4831	1.26419
$151$	11.8798	0.966767	0.483383	−	0.875409i	$-0.339408\pi$
$151$	11.8798	0.966767	0.483383	+	0.875409i	$0.339408\pi$
$152$	0.517690	0.0419902
$153$	3.26837	0.264232
$154$	−10.5385	−0.849214
$155$	0.249664	0.0200535
$156$	−15.5209	−1.24267
$157$	5.46056	0.435800	0.217900	−	0.975971i	$-0.430079\pi$
$157$	5.46056	0.435800	0.217900	+	0.975971i	$0.430079\pi$
$158$	1.98009	0.157527
$159$	−7.79241	−0.617979
$160$	−0.160277	−0.0126710
$161$	3.11846	0.245769
$162$	15.6685	1.23103
$163$	6.24694	0.489298	0.244649	−	0.969612i	$-0.421327\pi$
$163$	6.24694	0.489298	0.244649	+	0.969612i	$0.421327\pi$
$164$	6.27157	0.489727
$165$	1.59711	0.124335
$166$	−2.96501	−0.230129
$167$	13.6354	1.05514	0.527571	−	0.849511i	$-0.323103\pi$
$167$	13.6354	1.05514	0.527571	+	0.849511i	$0.323103\pi$
$168$	10.2462	0.790512
$169$	11.8650	0.912692
$170$	−0.0783227	−0.00600707
$171$	3.46247	0.264782
$172$	−12.1373	−0.925458
$173$	−15.2718	−1.16110	−0.580548	−	0.814226i	$-0.697162\pi$
$173$	−15.2718	−1.16110	−0.580548	+	0.814226i	$0.697162\pi$
$174$	−12.3267	−0.934485
$175$	16.3747	1.23781
$176$	3.20139	0.241314
$177$	19.6361	1.47594
$178$	1.13197	0.0848448
$179$	−11.3695	−0.849798	−0.424899	−	0.905241i	$-0.639690\pi$
$179$	−11.3695	−0.849798	−0.424899	+	0.905241i	$0.639690\pi$
$180$	−1.07198	−0.0799010
$181$	0.667110	0.0495859	0.0247929	−	0.999693i	$-0.492107\pi$
$181$	0.667110	0.0495859	0.0247929	+	0.999693i	$0.492107\pi$
$182$	−16.4147	−1.21674
$183$	−33.4505	−2.47273
$184$	−0.947329	−0.0698380
$185$	1.16495	0.0856485
$186$	4.84849	0.355509
$187$	1.56442	0.114402
$188$	1.05047	0.0766135
$189$	37.7911	2.74890
$190$	−0.0829740	−0.00601957
$191$	2.36274	0.170962	0.0854809	−	0.996340i	$-0.472757\pi$
$191$	2.36274	0.170962	0.0854809	+	0.996340i	$0.472757\pi$
$192$	−3.11260	−0.224633
$193$	−27.0198	−1.94493	−0.972463	−	0.233057i	$-0.925127\pi$
$193$	−27.0198	−1.94493	−0.972463	+	0.233057i	$0.925127\pi$
$194$	−3.24444	−0.232937
$195$	2.48766	0.178145
$196$	3.83624	0.274017
$197$	12.5098	0.891288	0.445644	−	0.895210i	$-0.352975\pi$
$197$	12.5098	0.891288	0.445644	+	0.895210i	$0.352975\pi$
$198$	21.4119	1.52167
$199$	4.26521	0.302353	0.151176	−	0.988507i	$-0.451694\pi$
$199$	4.26521	0.302353	0.151176	+	0.988507i	$0.451694\pi$
$200$	−4.97431	−0.351737
$201$	18.9090	1.33374
$202$	15.1039	1.06271
$203$	−13.0365	−0.914986
$204$	−1.52103	−0.106494
$205$	−1.00519	−0.0702055
$206$	11.1370	0.775952
$207$	−6.33603	−0.440384
$208$	4.98648	0.345750
$209$	1.65733	0.114640
$210$	−1.64224	−0.113325
$211$	5.61316	0.386426	0.193213	−	0.981157i	$-0.438109\pi$
$211$	5.61316	0.386426	0.193213	+	0.981157i	$0.438109\pi$
$212$	2.50350	0.171941
$213$	−48.1800	−3.30124
$214$	11.2403	0.768373
$215$	1.94533	0.132670
$216$	−11.4802	−0.781131
$217$	5.12769	0.348091
$218$	−5.62064	−0.380678
$219$	−13.3436	−0.901675
$220$	−0.513110	−0.0345939
$221$	2.43674	0.163913
$222$	22.6234	1.51838
$223$	−19.6956	−1.31891	−0.659456	−	0.751743i	$-0.729213\pi$
$223$	−19.6956	−1.31891	−0.659456	+	0.751743i	$0.729213\pi$
$224$	−3.29184	−0.219946
$225$	−33.2697	−2.21798
$226$	12.7698	0.849437
$227$	−11.2732	−0.748229	−0.374115	−	0.927382i	$-0.622053\pi$
$227$	−11.2732	−0.748229	−0.374115	+	0.927382i	$0.622053\pi$
$228$	−1.61136	−0.106715
$229$	0.466771	0.0308451	0.0154226	−	0.999881i	$-0.495091\pi$
$229$	0.466771	0.0308451	0.0154226	+	0.999881i	$0.495091\pi$
$230$	0.151835	0.0100117
$231$	32.8021	2.15822
$232$	3.96026	0.260004
$233$	8.63571	0.565744	0.282872	−	0.959158i	$-0.408713\pi$
$233$	8.63571	0.565744	0.282872	+	0.959158i	$0.408713\pi$
$234$	33.3511	2.18023
$235$	−0.168367	−0.0109830
$236$	−6.30857	−0.410653
$237$	−6.16323	−0.400345
$238$	−1.60862	−0.104272
$239$	−2.50007	−0.161716	−0.0808579	−	0.996726i	$-0.525766\pi$
$239$	−2.50007	−0.161716	−0.0808579	+	0.996726i	$0.525766\pi$
$240$	0.498880	0.0322026
$241$	12.6794	0.816754	0.408377	−	0.912813i	$-0.366095\pi$
$241$	12.6794	0.816754	0.408377	+	0.912813i	$0.366095\pi$
$242$	−0.751117	−0.0482836
$243$	−14.3292	−0.919216
$244$	10.7468	0.687993
$245$	−0.614862	−0.0392821
$246$	−19.5209	−1.24461
$247$	2.58145	0.164254
$248$	−1.55770	−0.0989138
$249$	9.22890	0.584858
$250$	1.59866	0.101108
$251$	−15.5727	−0.982940	−0.491470	−	0.870895i	$-0.663540\pi$
$251$	−15.5727	−0.982940	−0.491470	+	0.870895i	$0.663540\pi$
$252$	−22.0169	−1.38693
$253$	−3.03277	−0.190669
$254$	5.63503	0.353573
$255$	0.243787	0.0152666
$256$	1.00000	0.0625000
$257$	16.2055	1.01087	0.505436	−	0.862864i	$-0.331332\pi$
$257$	16.2055	1.01087	0.505436	+	0.862864i	$0.331332\pi$
$258$	37.7785	2.35199
$259$	23.9261	1.48670
$260$	−0.799220	−0.0495655
$261$	26.4874	1.63953
$262$	−5.22061	−0.322530
$263$	4.97471	0.306753	0.153377	−	0.988168i	$-0.450985\pi$
$263$	4.97471	0.306753	0.153377	+	0.988168i	$0.450985\pi$
$264$	−9.96465	−0.613282
$265$	−0.401255	−0.0246489
$266$	−1.70415	−0.104488
$267$	−3.52338	−0.215627
$268$	−6.07497	−0.371088
$269$	6.30239	0.384264	0.192132	−	0.981369i	$-0.438460\pi$
$269$	6.30239	0.384264	0.192132	+	0.981369i	$0.438460\pi$
$270$	1.84002	0.111980
$271$	−1.67856	−0.101965	−0.0509826	−	0.998700i	$-0.516235\pi$
$271$	−1.67856	−0.101965	−0.0509826	+	0.998700i	$0.516235\pi$
$272$	0.488669	0.0296299
$273$	51.0925	3.09226
$274$	0.799344	0.0482901
$275$	−15.9247	−0.960295
$276$	2.94866	0.177489
$277$	23.2192	1.39511	0.697553	−	0.716533i	$-0.254272\pi$
$277$	23.2192	1.39511	0.697553	+	0.716533i	$0.254272\pi$
$278$	15.0901	0.905044
$279$	−10.4183	−0.623730
$280$	0.527608	0.0315306
$281$	3.00307	0.179148	0.0895741	−	0.995980i	$-0.471449\pi$
$281$	3.00307	0.179148	0.0895741	+	0.995980i	$0.471449\pi$
$282$	−3.26970	−0.194708
$283$	28.8287	1.71369	0.856845	−	0.515575i	$-0.172422\pi$
$283$	28.8287	1.71369	0.856845	+	0.515575i	$0.172422\pi$
$284$	15.4790	0.918510
$285$	0.258265	0.0152983
$286$	15.9637	0.943951
$287$	−20.6450	−1.21864
$288$	6.68830	0.394112
$289$	−16.7612	−0.985953
$290$	−0.634739	−0.0372732
$291$	10.0987	0.591994
$292$	4.28695	0.250875
$293$	33.1641	1.93747	0.968734	−	0.248102i	$-0.0798068\pi$
$293$	33.1641	1.93747	0.968734	+	0.248102i	$0.0798068\pi$
$294$	−11.9407	−0.696395
$295$	1.01112	0.0588697
$296$	−7.26831	−0.422462
$297$	−36.7527	−2.13261
$298$	0.404136	0.0234110
$299$	−4.72384	−0.273187
$300$	15.4831	0.893915
$301$	39.9540	2.30291
$302$	11.8798	0.683607
$303$	−47.0126	−2.70080
$304$	0.517690	0.0296916
$305$	−1.72247	−0.0986283
$306$	3.26837	0.186840
$307$	−7.74286	−0.441908	−0.220954	−	0.975284i	$-0.570917\pi$
$307$	−7.74286	−0.441908	−0.220954	+	0.975284i	$0.570917\pi$
$308$	−10.5385	−0.600485
$309$	−34.6651	−1.97203
$310$	0.249664	0.0141799
$311$	−3.42237	−0.194065	−0.0970325	−	0.995281i	$-0.530935\pi$
$311$	−3.42237	−0.194065	−0.0970325	+	0.995281i	$0.530935\pi$
$312$	−15.5209	−0.878700
$313$	13.6488	0.771475	0.385738	−	0.922609i	$-0.373947\pi$
$313$	13.6488	0.771475	0.385738	+	0.922609i	$0.373947\pi$
$314$	5.46056	0.308157
$315$	3.52880	0.198826
$316$	1.98009	0.111389
$317$	−4.60548	−0.258669	−0.129335	−	0.991601i	$-0.541284\pi$
$317$	−4.60548	−0.258669	−0.129335	+	0.991601i	$0.541284\pi$
$318$	−7.79241	−0.436977
$319$	12.6783	0.709849
$320$	−0.160277	−0.00895978
$321$	−34.9867	−1.95277
$322$	3.11846	0.173785
$323$	0.252979	0.0140761
$324$	15.6685	0.870473
$325$	−24.8043	−1.37590
$326$	6.24694	0.345986
$327$	17.4948	0.967467
$328$	6.27157	0.346289
$329$	−3.45799	−0.190645
$330$	1.59711	0.0879179
$331$	14.5991	0.802437	0.401218	−	0.915982i	$-0.368587\pi$
$331$	14.5991	0.802437	0.401218	+	0.915982i	$0.368587\pi$
$332$	−2.96501	−0.162726
$333$	−48.6127	−2.66396
$334$	13.6354	0.746099
$335$	0.973680	0.0531978
$336$	10.2462	0.558976
$337$	8.82306	0.480623	0.240311	−	0.970696i	$-0.422750\pi$
$337$	8.82306	0.480623	0.240311	+	0.970696i	$0.422750\pi$
$338$	11.8650	0.645370
$339$	−39.7474	−2.15879
$340$	−0.0783227	−0.00424764
$341$	−4.98679	−0.270050
$342$	3.46247	0.187229
$343$	10.4146	0.562337
$344$	−12.1373	−0.654398
$345$	−0.472604	−0.0254441
$346$	−15.2718	−0.821019
$347$	−13.5206	−0.725826	−0.362913	−	0.931823i	$-0.618218\pi$
$347$	−13.5206	−0.725826	−0.362913	+	0.931823i	$0.618218\pi$
$348$	−12.3267	−0.660781
$349$	28.8668	1.54520	0.772601	−	0.634892i	$-0.218955\pi$
$349$	28.8668	1.54520	0.772601	+	0.634892i	$0.218955\pi$
$350$	16.3747	0.875262
$351$	−57.2460	−3.05556
$352$	3.20139	0.170635
$353$	−4.60265	−0.244974	−0.122487	−	0.992470i	$-0.539087\pi$
$353$	−4.60265	−0.244974	−0.122487	+	0.992470i	$0.539087\pi$
$354$	19.6361	1.04365
$355$	−2.48093	−0.131674
$356$	1.13197	0.0599944
$357$	5.00701	0.264999
$358$	−11.3695	−0.600898
$359$	9.56855	0.505009	0.252504	−	0.967596i	$-0.418746\pi$
$359$	9.56855	0.505009	0.252504	+	0.967596i	$0.418746\pi$
$360$	−1.07198	−0.0564985
$361$	−18.7320	−0.985895
$362$	0.667110	0.0350625
$363$	2.33793	0.122710
$364$	−16.4147	−0.860365
$365$	−0.687101	−0.0359645
$366$	−33.4505	−1.74849
$367$	10.6162	0.554159	0.277079	−	0.960847i	$-0.410634\pi$
$367$	10.6162	0.554159	0.277079	+	0.960847i	$0.410634\pi$
$368$	−0.947329	−0.0493830
$369$	41.9462	2.18363
$370$	1.16495	0.0605626
$371$	−8.24114	−0.427859
$372$	4.84849	0.251383
$373$	4.03275	0.208808	0.104404	−	0.994535i	$-0.466706\pi$
$373$	4.03275	0.208808	0.104404	+	0.994535i	$0.466706\pi$
$374$	1.56442	0.0808942
$375$	−4.97599	−0.256959
$376$	1.05047	0.0541740
$377$	19.7477	1.01706
$378$	37.7911	1.94377
$379$	−14.8074	−0.760603	−0.380301	−	0.924863i	$-0.624180\pi$
$379$	−14.8074	−0.760603	−0.380301	+	0.924863i	$0.624180\pi$
$380$	−0.0829740	−0.00425648
$381$	−17.5396	−0.898581
$382$	2.36274	0.120888
$383$	7.89834	0.403586	0.201793	−	0.979428i	$-0.435323\pi$
$383$	7.89834	0.403586	0.201793	+	0.979428i	$0.435323\pi$
$384$	−3.11260	−0.158839
$385$	1.68908	0.0860834
$386$	−27.0198	−1.37527
$387$	−81.1778	−4.12650
$388$	−3.24444	−0.164712
$389$	31.2093	1.58237	0.791187	−	0.611574i	$-0.209463\pi$
$389$	31.2093	1.58237	0.791187	+	0.611574i	$0.209463\pi$
$390$	2.48766	0.125967
$391$	−0.462931	−0.0234114
$392$	3.83624	0.193759
$393$	16.2497	0.819688
$394$	12.5098	0.630236
$395$	−0.317363	−0.0159683
$396$	21.4119	1.07599
$397$	0.989807	0.0496770	0.0248385	−	0.999691i	$-0.492093\pi$
$397$	0.989807	0.0496770	0.0248385	+	0.999691i	$0.492093\pi$
$398$	4.26521	0.213796
$399$	5.30436	0.265550
$400$	−4.97431	−0.248716
$401$	6.39757	0.319480	0.159740	−	0.987159i	$-0.448934\pi$
$401$	6.39757	0.319480	0.159740	+	0.987159i	$0.448934\pi$
$402$	18.9090	0.943094
$403$	−7.76742	−0.386923
$404$	15.1039	0.751449
$405$	−2.51131	−0.124788
$406$	−13.0365	−0.646993
$407$	−23.2687	−1.15339
$408$	−1.52103	−0.0753024
$409$	−8.57944	−0.424226	−0.212113	−	0.977245i	$-0.568034\pi$
$409$	−8.57944	−0.424226	−0.212113	+	0.977245i	$0.568034\pi$
$410$	−1.00519	−0.0496428
$411$	−2.48804	−0.122726
$412$	11.1370	0.548681
$413$	20.7668	1.02187
$414$	−6.33603	−0.311399
$415$	0.475224	0.0233278
$416$	4.98648	0.244482
$417$	−46.9695	−2.30011
$418$	1.65733	0.0810625
$419$	34.0552	1.66370	0.831852	−	0.554997i	$-0.187281\pi$
$419$	34.0552	1.66370	0.831852	+	0.554997i	$0.187281\pi$
$420$	−1.64224	−0.0801329
$421$	−8.79850	−0.428812	−0.214406	−	0.976745i	$-0.568782\pi$
$421$	−8.79850	−0.428812	−0.214406	+	0.976745i	$0.568782\pi$
$422$	5.61316	0.273245
$423$	7.02588	0.341610
$424$	2.50350	0.121581
$425$	−2.43079	−0.117911
$426$	−48.1800	−2.33433
$427$	−35.3768	−1.71200
$428$	11.2403	0.543322
$429$	−49.6886	−2.39899
$430$	1.94533	0.0938121
$431$	−35.4008	−1.70519	−0.852597	−	0.522568i	$-0.824974\pi$
$431$	−35.4008	−1.70519	−0.852597	+	0.522568i	$0.824974\pi$
$432$	−11.4802	−0.552343
$433$	−1.16111	−0.0557994	−0.0278997	−	0.999611i	$-0.508882\pi$
$433$	−1.16111	−0.0557994	−0.0278997	+	0.999611i	$0.508882\pi$
$434$	5.12769	0.246137
$435$	1.97569	0.0947272
$436$	−5.62064	−0.269180
$437$	−0.490423	−0.0234601
$438$	−13.3436	−0.637580
$439$	−12.5932	−0.601041	−0.300520	−	0.953775i	$-0.597160\pi$
$439$	−12.5932	−0.601041	−0.300520	+	0.953775i	$0.597160\pi$
$440$	−0.513110	−0.0244616
$441$	25.6579	1.22181
$442$	2.43674	0.115904
$443$	12.9800	0.616696	0.308348	−	0.951274i	$-0.400224\pi$
$443$	12.9800	0.616696	0.308348	+	0.951274i	$0.400224\pi$
$444$	22.6234	1.07366
$445$	−0.181429	−0.00860058
$446$	−19.6956	−0.932611
$447$	−1.25792	−0.0594974
$448$	−3.29184	−0.155525
$449$	11.9929	0.565980	0.282990	−	0.959123i	$-0.408674\pi$
$449$	11.9929	0.565980	0.282990	+	0.959123i	$0.408674\pi$
$450$	−33.2697	−1.56835
$451$	20.0777	0.945423
$452$	12.7698	0.600643
$453$	−36.9772	−1.73734
$454$	−11.2732	−0.529078
$455$	2.63091	0.123339
$456$	−1.61136	−0.0754590
$457$	−28.8222	−1.34825	−0.674124	−	0.738619i	$-0.735479\pi$
$457$	−28.8222	−1.34825	−0.674124	+	0.738619i	$0.735479\pi$
$458$	0.466771	0.0218108
$459$	−5.61004	−0.261854
$460$	0.151835	0.00707937
$461$	5.08547	0.236854	0.118427	−	0.992963i	$-0.462215\pi$
$461$	5.08547	0.236854	0.118427	+	0.992963i	$0.462215\pi$
$462$	32.8021	1.52609
$463$	−38.0906	−1.77022	−0.885109	−	0.465383i	$-0.845916\pi$
$463$	−38.0906	−1.77022	−0.885109	+	0.465383i	$0.845916\pi$
$464$	3.96026	0.183850
$465$	−0.777104	−0.0360373
$466$	8.63571	0.400042
$467$	2.24062	0.103684	0.0518418	−	0.998655i	$-0.483491\pi$
$467$	2.24062	0.103684	0.0518418	+	0.998655i	$0.483491\pi$
$468$	33.3511	1.54166
$469$	19.9979	0.923415
$470$	−0.168367	−0.00776619
$471$	−16.9966	−0.783160
$472$	−6.30857	−0.290375
$473$	−38.8561	−1.78661
$474$	−6.16323	−0.283086
$475$	−2.57515	−0.118156
$476$	−1.60862	−0.0737311
$477$	16.7442	0.766664
$478$	−2.50007	−0.114350
$479$	0.620140	0.0283349	0.0141675	−	0.999900i	$-0.495490\pi$
$479$	0.620140	0.0283349	0.0141675	+	0.999900i	$0.495490\pi$
$480$	0.498880	0.0227707
$481$	−36.2433	−1.65255
$482$	12.6794	0.577533
$483$	−9.70653	−0.441663
$484$	−0.751117	−0.0341417
$485$	0.520011	0.0236125
$486$	−14.3292	−0.649984
$487$	−1.78683	−0.0809690	−0.0404845	−	0.999180i	$-0.512890\pi$
$487$	−1.78683	−0.0809690	−0.0404845	+	0.999180i	$0.512890\pi$
$488$	10.7468	0.486485
$489$	−19.4442	−0.879299
$490$	−0.614862	−0.0277766
$491$	8.54910	0.385815	0.192908	−	0.981217i	$-0.438208\pi$
$491$	8.54910	0.385815	0.192908	+	0.981217i	$0.438208\pi$
$492$	−19.5209	−0.880070
$493$	1.93526	0.0871595
$494$	2.58145	0.116145
$495$	−3.43184	−0.154250
$496$	−1.55770	−0.0699426
$497$	−50.9545	−2.28562
$498$	9.22890	0.413557
$499$	4.73371	0.211910	0.105955	−	0.994371i	$-0.466210\pi$
$499$	4.73371	0.211910	0.105955	+	0.994371i	$0.466210\pi$
$500$	1.59866	0.0714941
$501$	−42.4418	−1.89616
$502$	−15.5727	−0.695044
$503$	38.9668	1.73745	0.868723	−	0.495299i	$-0.164941\pi$
$503$	38.9668	1.73745	0.868723	+	0.495299i	$0.164941\pi$
$504$	−22.0169	−0.980709
$505$	−2.42082	−0.107725
$506$	−3.03277	−0.134823
$507$	−36.9310	−1.64016
$508$	5.63503	0.250014
$509$	44.2163	1.95985	0.979927	−	0.199355i	$-0.0638848\pi$
$509$	44.2163	1.95985	0.979927	+	0.199355i	$0.0638848\pi$
$510$	0.243787	0.0107951
$511$	−14.1120	−0.624276
$512$	1.00000	0.0441942
$513$	−5.94320	−0.262399
$514$	16.2055	0.714794
$515$	−1.78501	−0.0786569
$516$	37.7785	1.66311
$517$	3.36297	0.147903
$518$	23.9261	1.05125
$519$	47.5352	2.08656
$520$	−0.799220	−0.0350481
$521$	21.3375	0.934814	0.467407	−	0.884042i	$-0.345188\pi$
$521$	21.3375	0.934814	0.467407	+	0.884042i	$0.345188\pi$
$522$	26.4874	1.15932
$523$	−3.94514	−0.172509	−0.0862544	−	0.996273i	$-0.527490\pi$
$523$	−3.94514	−0.172509	−0.0862544	+	0.996273i	$0.527490\pi$
$524$	−5.22061	−0.228063
$525$	−50.9678	−2.22442
$526$	4.97471	0.216907
$527$	−0.761199	−0.0331583
$528$	−9.96465	−0.433656
$529$	−22.1026	−0.960981
$530$	−0.401255	−0.0174294
$531$	−42.1936	−1.83105
$532$	−1.70415	−0.0738845
$533$	31.2731	1.35459
$534$	−3.52338	−0.152471
$535$	−1.80157	−0.0778887
$536$	−6.07497	−0.262399
$537$	35.3888	1.52714
$538$	6.30239	0.271716
$539$	12.2813	0.528992
$540$	1.84002	0.0791819
$541$	−13.3834	−0.575399	−0.287699	−	0.957721i	$-0.592890\pi$
$541$	−13.3834	−0.575399	−0.287699	+	0.957721i	$0.592890\pi$
$542$	−1.67856	−0.0721003
$543$	−2.07645	−0.0891089
$544$	0.488669	0.0209515
$545$	0.900862	0.0385887
$546$	51.0925	2.18656
$547$	29.9084	1.27879	0.639395	−	0.768879i	$-0.279185\pi$
$547$	29.9084	1.27879	0.639395	+	0.768879i	$0.279185\pi$
$548$	0.799344	0.0341463
$549$	71.8779	3.06767
$550$	−15.9247	−0.679031
$551$	2.05019	0.0873408
$552$	2.94866	0.125503
$553$	−6.51814	−0.277179
$554$	23.2192	0.986489
$555$	−3.62602	−0.153916
$556$	15.0901	0.639963
$557$	9.80426	0.415420	0.207710	−	0.978190i	$-0.433399\pi$
$557$	9.80426	0.415420	0.207710	+	0.978190i	$0.433399\pi$
$558$	−10.4183	−0.441044
$559$	−60.5223	−2.55982
$560$	0.527608	0.0222955
$561$	−4.86942	−0.205587
$562$	3.00307	0.126677
$563$	37.9308	1.59859	0.799295	−	0.600938i	$-0.205206\pi$
$563$	37.9308	1.59859	0.799295	+	0.600938i	$0.205206\pi$
$564$	−3.26970	−0.137679
$565$	−2.04672	−0.0861060
$566$	28.8287	1.21176
$567$	−51.5783	−2.16608
$568$	15.4790	0.649485
$569$	−43.0418	−1.80441	−0.902203	−	0.431312i	$-0.858051\pi$
$569$	−43.0418	−1.80441	−0.902203	+	0.431312i	$0.858051\pi$
$570$	0.258265	0.0108175
$571$	24.8342	1.03928	0.519639	−	0.854386i	$-0.326066\pi$
$571$	24.8342	1.03928	0.519639	+	0.854386i	$0.326066\pi$
$572$	15.9637	0.667474
$573$	−7.35427	−0.307229
$574$	−20.6450	−0.861706
$575$	4.71231	0.196517
$576$	6.68830	0.278679
$577$	40.1871	1.67301	0.836505	−	0.547959i	$-0.184595\pi$
$577$	40.1871	1.67301	0.836505	+	0.547959i	$0.184595\pi$
$578$	−16.7612	−0.697174
$579$	84.1019	3.49515
$580$	−0.634739	−0.0263561
$581$	9.76035	0.404927
$582$	10.0987	0.418603
$583$	8.01468	0.331934
$584$	4.28695	0.177395
$585$	−5.34543	−0.221006
$586$	33.1641	1.37000
$587$	12.6772	0.523243	0.261622	−	0.965171i	$-0.415743\pi$
$587$	12.6772	0.523243	0.261622	+	0.965171i	$0.415743\pi$
$588$	−11.9407	−0.492425
$589$	−0.806404	−0.0332273
$590$	1.01112	0.0416272
$591$	−38.9381	−1.60170
$592$	−7.26831	−0.298726
$593$	1.00379	0.0412209	0.0206104	−	0.999788i	$-0.493439\pi$
$593$	1.00379	0.0412209	0.0206104	+	0.999788i	$0.493439\pi$
$594$	−36.7527	−1.50798
$595$	0.257826	0.0105698
$596$	0.404136	0.0165541
$597$	−13.2759	−0.543347
$598$	−4.72384	−0.193172
$599$	−47.6155	−1.94552	−0.972758	−	0.231821i	$-0.925531\pi$
$599$	−47.6155	−1.94552	−0.972758	+	0.231821i	$0.925531\pi$
$600$	15.4831	0.632093
$601$	13.0659	0.532971	0.266485	−	0.963839i	$-0.414138\pi$
$601$	13.0659	0.532971	0.266485	+	0.963839i	$0.414138\pi$
$602$	39.9540	1.62840
$603$	−40.6312	−1.65463
$604$	11.8798	0.483383
$605$	0.120387	0.00489443
$606$	−47.0126	−1.90976
$607$	3.91368	0.158851	0.0794256	−	0.996841i	$-0.474691\pi$
$607$	3.91368	0.158851	0.0794256	+	0.996841i	$0.474691\pi$
$608$	0.517690	0.0209951
$609$	40.5776	1.64429
$610$	−1.72247	−0.0697407
$611$	5.23816	0.211913
$612$	3.26837	0.132116
$613$	23.6657	0.955847	0.477924	−	0.878401i	$-0.341390\pi$
$613$	23.6657	0.955847	0.477924	+	0.878401i	$0.341390\pi$
$614$	−7.74286	−0.312476
$615$	3.12876	0.126164
$616$	−10.5385	−0.424607
$617$	−23.5721	−0.948977	−0.474488	−	0.880262i	$-0.657367\pi$
$617$	−23.5721	−0.948977	−0.474488	+	0.880262i	$0.657367\pi$
$618$	−34.6651	−1.39443
$619$	9.17174	0.368643	0.184322	−	0.982866i	$-0.440991\pi$
$619$	9.17174	0.368643	0.184322	+	0.982866i	$0.440991\pi$
$620$	0.249664	0.0100267
$621$	10.8756	0.436421
$622$	−3.42237	−0.137225
$623$	−3.72627	−0.149290
$624$	−15.5209	−0.621335
$625$	24.6153	0.984613
$626$	13.6488	0.545515
$627$	−5.15860	−0.206015
$628$	5.46056	0.217900
$629$	−3.55180	−0.141620
$630$	3.52880	0.140591
$631$	−17.7627	−0.707121	−0.353561	−	0.935412i	$-0.615029\pi$
$631$	−17.7627	−0.707121	−0.353561	+	0.935412i	$0.615029\pi$
$632$	1.98009	0.0787636
$633$	−17.4716	−0.694432
$634$	−4.60548	−0.182907
$635$	−0.903167	−0.0358411
$636$	−7.79241	−0.308989
$637$	19.1293	0.757931
$638$	12.6783	0.501939
$639$	103.528	4.09552
$640$	−0.160277	−0.00633552
$641$	31.6626	1.25060	0.625300	−	0.780385i	$-0.284977\pi$
$641$	31.6626	1.25060	0.625300	+	0.780385i	$0.284977\pi$
$642$	−34.9867	−1.38082
$643$	14.5630	0.574309	0.287154	−	0.957884i	$-0.407291\pi$
$643$	14.5630	0.574309	0.287154	+	0.957884i	$0.407291\pi$
$644$	3.11846	0.122885
$645$	−6.05504	−0.238417
$646$	0.252979	0.00995334
$647$	−29.4305	−1.15703	−0.578517	−	0.815670i	$-0.696368\pi$
$647$	−29.4305	−1.15703	−0.578517	+	0.815670i	$0.696368\pi$
$648$	15.6685	0.615517
$649$	−20.1962	−0.792769
$650$	−24.8043	−0.972905
$651$	−15.9605	−0.625541
$652$	6.24694	0.244649
$653$	−16.3568	−0.640092	−0.320046	−	0.947402i	$-0.603698\pi$
$653$	−16.3568	−0.640092	−0.320046	+	0.947402i	$0.603698\pi$
$654$	17.4948	0.684102
$655$	0.836746	0.0326944
$656$	6.27157	0.244864
$657$	28.6724	1.11862
$658$	−3.45799	−0.134806
$659$	7.36925	0.287065	0.143533	−	0.989646i	$-0.454154\pi$
$659$	7.36925	0.287065	0.143533	+	0.989646i	$0.454154\pi$
$660$	1.59711	0.0621674
$661$	−29.1846	−1.13515	−0.567575	−	0.823322i	$-0.692118\pi$
$661$	−29.1846	−1.13515	−0.567575	+	0.823322i	$0.692118\pi$
$662$	14.5991	0.567409
$663$	−7.58461	−0.294562
$664$	−2.96501	−0.115065
$665$	0.273137	0.0105918
$666$	−48.6127	−1.88370
$667$	−3.75167	−0.145265
$668$	13.6354	0.527571
$669$	61.3045	2.37017
$670$	0.973680	0.0376166
$671$	34.4047	1.32818
$672$	10.2462	0.395256
$673$	30.4599	1.17414	0.587072	−	0.809534i	$-0.300280\pi$
$673$	30.4599	1.17414	0.587072	+	0.809534i	$0.300280\pi$
$674$	8.82306	0.339852
$675$	57.1062	2.19802
$676$	11.8650	0.456346
$677$	−29.9505	−1.15109	−0.575545	−	0.817770i	$-0.695210\pi$
$677$	−29.9505	−1.15109	−0.575545	+	0.817770i	$0.695210\pi$
$678$	−39.7474	−1.52649
$679$	10.6802	0.409868
$680$	−0.0783227	−0.00300354
$681$	35.0890	1.34462
$682$	−4.98679	−0.190954
$683$	−15.9331	−0.609662	−0.304831	−	0.952406i	$-0.598600\pi$
$683$	−15.9331	−0.609662	−0.304831	+	0.952406i	$0.598600\pi$
$684$	3.46247	0.132391
$685$	−0.128117	−0.00489509
$686$	10.4146	0.397632
$687$	−1.45287	−0.0554306
$688$	−12.1373	−0.462729
$689$	12.4837	0.475590
$690$	−0.472604	−0.0179917
$691$	−7.29236	−0.277415	−0.138707	−	0.990333i	$-0.544295\pi$
$691$	−7.29236	−0.277415	−0.138707	+	0.990333i	$0.544295\pi$
$692$	−15.2718	−0.580548
$693$	−70.4845	−2.67748
$694$	−13.5206	−0.513236
$695$	−2.41860	−0.0917428
$696$	−12.3267	−0.467243
$697$	3.06472	0.116085
$698$	28.8668	1.09262
$699$	−26.8796	−1.01668
$700$	16.3747	0.618904
$701$	−15.1196	−0.571059	−0.285530	−	0.958370i	$-0.592170\pi$
$701$	−15.1196	−0.571059	−0.285530	+	0.958370i	$0.592170\pi$
$702$	−57.2460	−2.16061
$703$	−3.76273	−0.141914
$704$	3.20139	0.120657
$705$	0.524059	0.0197372
$706$	−4.60265	−0.173223
$707$	−49.7198	−1.86991
$708$	19.6361	0.737969
$709$	−39.8102	−1.49510	−0.747552	−	0.664203i	$-0.768771\pi$
$709$	−39.8102	−1.49510	−0.747552	+	0.664203i	$0.768771\pi$
$710$	−2.48093	−0.0931078
$711$	13.2434	0.496667
$712$	1.13197	0.0424224
$713$	1.47565	0.0552636
$714$	5.00701	0.187383
$715$	−2.55861	−0.0956867
$716$	−11.3695	−0.424899
$717$	7.78171	0.290613
$718$	9.56855	0.357095
$719$	22.3383	0.833079	0.416540	−	0.909118i	$-0.363243\pi$
$719$	22.3383	0.833079	0.416540	+	0.909118i	$0.363243\pi$
$720$	−1.07198	−0.0399505
$721$	−36.6613	−1.36534
$722$	−18.7320	−0.697133
$723$	−39.4661	−1.46776
$724$	0.667110	0.0247929
$725$	−19.6995	−0.731623
$726$	2.33793	0.0867687
$727$	5.32897	0.197641	0.0988203	−	0.995105i	$-0.468493\pi$
$727$	5.32897	0.197641	0.0988203	+	0.995105i	$0.468493\pi$
$728$	−16.4147	−0.608370
$729$	−2.40452	−0.0890562
$730$	−0.687101	−0.0254307
$731$	−5.93111	−0.219370
$732$	−33.4505	−1.23637
$733$	−20.9782	−0.774848	−0.387424	−	0.921902i	$-0.626635\pi$
$733$	−20.9782	−0.774848	−0.387424	+	0.921902i	$0.626635\pi$
$734$	10.6162	0.391849
$735$	1.91382	0.0705924
$736$	−0.947329	−0.0349190
$737$	−19.4483	−0.716389
$738$	41.9462	1.54406
$739$	20.9156	0.769392	0.384696	−	0.923043i	$-0.374306\pi$
$739$	20.9156	0.769392	0.384696	+	0.923043i	$0.374306\pi$
$740$	1.16495	0.0428243
$741$	−8.03504	−0.295174
$742$	−8.24114	−0.302542
$743$	−3.26107	−0.119637	−0.0598184	−	0.998209i	$-0.519052\pi$
$743$	−3.26107	−0.119637	−0.0598184	+	0.998209i	$0.519052\pi$
$744$	4.84849	0.177754
$745$	−0.0647739	−0.00237313
$746$	4.03275	0.147650
$747$	−19.8309	−0.725574
$748$	1.56442	0.0572009
$749$	−37.0014	−1.35200
$750$	−4.97599	−0.181697
$751$	52.5853	1.91886	0.959432	−	0.281939i	$-0.0909776\pi$
$751$	52.5853	1.91886	0.959432	+	0.281939i	$0.0909776\pi$
$752$	1.05047	0.0383068
$753$	48.4716	1.76640
$754$	19.7477	0.719170
$755$	−1.90407	−0.0692961
$756$	37.7911	1.37445
$757$	−20.7214	−0.753132	−0.376566	−	0.926390i	$-0.622895\pi$
$757$	−20.7214	−0.753132	−0.376566	+	0.926390i	$0.622895\pi$
$758$	−14.8074	−0.537828
$759$	9.43981	0.342643
$760$	−0.0829740	−0.00300978
$761$	5.06622	0.183650	0.0918251	−	0.995775i	$-0.470730\pi$
$761$	5.06622	0.183650	0.0918251	+	0.995775i	$0.470730\pi$
$762$	−17.5396	−0.635393
$763$	18.5023	0.669828
$764$	2.36274	0.0854809
$765$	−0.523846	−0.0189397
$766$	7.89834	0.285379
$767$	−31.4576	−1.13587
$768$	−3.11260	−0.112316
$769$	0.561057	0.0202322	0.0101161	−	0.999949i	$-0.496780\pi$
$769$	0.561057	0.0202322	0.0101161	+	0.999949i	$0.496780\pi$
$770$	1.68908	0.0608702
$771$	−50.4413	−1.81660
$772$	−27.0198	−0.972463
$773$	34.4338	1.23850	0.619248	−	0.785195i	$-0.287438\pi$
$773$	34.4338	1.23850	0.619248	+	0.785195i	$0.287438\pi$
$774$	−81.1778	−2.91787
$775$	7.74847	0.278333
$776$	−3.24444	−0.116469
$777$	−74.4726	−2.67169
$778$	31.2093	1.11891
$779$	3.24673	0.116326
$780$	2.48766	0.0890724
$781$	49.5543	1.77319
$782$	−0.462931	−0.0165544
$783$	−45.4647	−1.62477
$784$	3.83624	0.137008
$785$	−0.875204	−0.0312374
$786$	16.2497	0.579607
$787$	−51.3908	−1.83189	−0.915943	−	0.401309i	$-0.868556\pi$
$787$	−51.3908	−1.83189	−0.915943	+	0.401309i	$0.868556\pi$
$788$	12.5098	0.445644
$789$	−15.4843	−0.551255
$790$	−0.317363	−0.0112913
$791$	−42.0363	−1.49464
$792$	21.4119	0.760837
$793$	53.5887	1.90299
$794$	0.989807	0.0351269
$795$	1.24895	0.0442956
$796$	4.26521	0.151176
$797$	−33.7133	−1.19419	−0.597093	−	0.802172i	$-0.703678\pi$
$797$	−33.7133	−1.19419	−0.597093	+	0.802172i	$0.703678\pi$
$798$	5.30436	0.187772
$799$	0.513333	0.0181604
$800$	−4.97431	−0.175868
$801$	7.57097	0.267507
$802$	6.39757	0.225906
$803$	13.7242	0.484316
$804$	18.9090	0.666868
$805$	−0.499819	−0.0176163
$806$	−7.76742	−0.273596
$807$	−19.6169	−0.690546
$808$	15.1039	0.531355
$809$	0.446423	0.0156954	0.00784769	−	0.999969i	$-0.497502\pi$
$809$	0.446423	0.0156954	0.00784769	+	0.999969i	$0.497502\pi$
$810$	−2.51131	−0.0882383
$811$	42.6692	1.49832	0.749159	−	0.662390i	$-0.230458\pi$
$811$	42.6692	1.49832	0.749159	+	0.662390i	$0.230458\pi$
$812$	−13.0365	−0.457493
$813$	5.22469	0.183238
$814$	−23.2687	−0.815567
$815$	−1.00124	−0.0350720
$816$	−1.52103	−0.0532469
$817$	−6.28334	−0.219826
$818$	−8.57944	−0.299973
$819$	−109.787	−3.83626
$820$	−1.00519	−0.0351028
$821$	−33.1380	−1.15652	−0.578262	−	0.815851i	$-0.696269\pi$
$821$	−33.1380	−1.15652	−0.578262	+	0.815851i	$0.696269\pi$
$822$	−2.48804	−0.0867804
$823$	−20.2623	−0.706300	−0.353150	−	0.935567i	$-0.614889\pi$
$823$	−20.2623	−0.706300	−0.353150	+	0.935567i	$0.614889\pi$
$824$	11.1370	0.387976
$825$	49.5673	1.72571
$826$	20.7668	0.722570
$827$	3.87129	0.134618	0.0673090	−	0.997732i	$-0.478559\pi$
$827$	3.87129	0.134618	0.0673090	+	0.997732i	$0.478559\pi$
$828$	−6.33603	−0.220192
$829$	−33.7407	−1.17186	−0.585932	−	0.810361i	$-0.699271\pi$
$829$	−33.7407	−1.17186	−0.585932	+	0.810361i	$0.699271\pi$
$830$	0.475224	0.0164953
$831$	−72.2721	−2.50709
$832$	4.98648	0.172875
$833$	1.87465	0.0649528
$834$	−46.9695	−1.62642
$835$	−2.18545	−0.0756308
$836$	1.65733	0.0573198
$837$	17.8827	0.618117
$838$	34.0552	1.17642
$839$	−24.7102	−0.853092	−0.426546	−	0.904466i	$-0.640270\pi$
$839$	−24.7102	−0.853092	−0.426546	+	0.904466i	$0.640270\pi$
$840$	−1.64224	−0.0566625
$841$	−13.3164	−0.459185
$842$	−8.79850	−0.303216
$843$	−9.34737	−0.321941
$844$	5.61316	0.193213
$845$	−1.90169	−0.0654201
$846$	7.02588	0.241555
$847$	2.47256	0.0849582
$848$	2.50350	0.0859706
$849$	−89.7324	−3.07961
$850$	−2.43079	−0.0833755
$851$	6.88548	0.236031
$852$	−48.1800	−1.65062
$853$	−19.9384	−0.682677	−0.341339	−	0.939940i	$-0.610880\pi$
$853$	−19.9384	−0.682677	−0.341339	+	0.939940i	$0.610880\pi$
$854$	−35.3768	−1.21057
$855$	−0.554955	−0.0189791
$856$	11.2403	0.384187
$857$	−41.8180	−1.42848	−0.714239	−	0.699902i	$-0.753227\pi$
$857$	−41.8180	−1.42848	−0.714239	+	0.699902i	$0.753227\pi$
$858$	−49.6886	−1.69634
$859$	15.9195	0.543166	0.271583	−	0.962415i	$-0.412453\pi$
$859$	15.9195	0.543166	0.271583	+	0.962415i	$0.412453\pi$
$860$	1.94533	0.0663352
$861$	64.2598	2.18997
$862$	−35.4008	−1.20575
$863$	−38.0834	−1.29637	−0.648187	−	0.761481i	$-0.724472\pi$
$863$	−38.0834	−1.29637	−0.648187	+	0.761481i	$0.724472\pi$
$864$	−11.4802	−0.390565
$865$	2.44773	0.0832253
$866$	−1.16111	−0.0394561
$867$	52.1710	1.77182
$868$	5.12769	0.174045
$869$	6.33902	0.215037
$870$	1.97569	0.0669823
$871$	−30.2927	−1.02643
$872$	−5.62064	−0.190339
$873$	−21.6998	−0.734428
$874$	−0.490423	−0.0165888
$875$	−5.26253	−0.177906
$876$	−13.3436	−0.450837
$877$	36.1361	1.22023	0.610116	−	0.792312i	$-0.291123\pi$
$877$	36.1361	1.22023	0.610116	+	0.792312i	$0.291123\pi$
$878$	−12.5932	−0.425000
$879$	−103.227	−3.48175
$880$	−0.513110	−0.0172969
$881$	19.9859	0.673343	0.336671	−	0.941622i	$-0.390699\pi$
$881$	19.9859	0.673343	0.336671	+	0.941622i	$0.390699\pi$
$882$	25.6579	0.863947
$883$	38.1099	1.28250	0.641250	−	0.767332i	$-0.278416\pi$
$883$	38.1099	1.28250	0.641250	+	0.767332i	$0.278416\pi$
$884$	2.43674	0.0819565
$885$	−3.14722	−0.105793
$886$	12.9800	0.436070
$887$	−0.582164	−0.0195472	−0.00977358	−	0.999952i	$-0.503111\pi$
$887$	−0.582164	−0.0195472	−0.00977358	+	0.999952i	$0.503111\pi$
$888$	22.6234	0.759191
$889$	−18.5496	−0.622134
$890$	−0.181429	−0.00608153
$891$	50.1610	1.68046
$892$	−19.6956	−0.659456
$893$	0.543819	0.0181982
$894$	−1.25792	−0.0420710
$895$	1.82228	0.0609120
$896$	−3.29184	−0.109973
$897$	14.7034	0.490934
$898$	11.9929	0.400208
$899$	−6.16888	−0.205744
$900$	−33.2697	−1.10899
$901$	1.22339	0.0407569
$902$	20.0777	0.668515
$903$	−124.361	−4.13847
$904$	12.7698	0.424718
$905$	−0.106923	−0.00355423
$906$	−36.9772	−1.22849
$907$	31.1954	1.03583	0.517914	−	0.855433i	$-0.326709\pi$
$907$	31.1954	1.03583	0.517914	+	0.855433i	$0.326709\pi$
$908$	−11.2732	−0.374115
$909$	101.020	3.35061
$910$	2.63091	0.0872137
$911$	−20.7522	−0.687551	−0.343776	−	0.939052i	$-0.611706\pi$
$911$	−20.7522	−0.687551	−0.343776	+	0.939052i	$0.611706\pi$
$912$	−1.61136	−0.0533576
$913$	−9.49214	−0.314144
$914$	−28.8222	−0.953355
$915$	5.36136	0.177241
$916$	0.466771	0.0154226
$917$	17.1854	0.567513
$918$	−5.61004	−0.185159
$919$	−52.5064	−1.73203	−0.866013	−	0.500022i	$-0.833325\pi$
$919$	−52.5064	−1.73203	−0.866013	+	0.500022i	$0.833325\pi$
$920$	0.151835	0.00500587
$921$	24.1005	0.794137
$922$	5.08547	0.167481
$923$	77.1858	2.54060
$924$	32.8021	1.07911
$925$	36.1548	1.18876
$926$	−38.0906	−1.25173
$927$	74.4877	2.44650
$928$	3.96026	0.130002
$929$	19.7558	0.648166	0.324083	−	0.946029i	$-0.394944\pi$
$929$	19.7558	0.648166	0.324083	+	0.946029i	$0.394944\pi$
$930$	−0.777104	−0.0254822
$931$	1.98598	0.0650879
$932$	8.63571	0.282872
$933$	10.6525	0.348747
$934$	2.24062	0.0733154
$935$	−0.250741	−0.00820011
$936$	33.3511	1.09011
$937$	32.4835	1.06119	0.530595	−	0.847625i	$-0.321968\pi$
$937$	32.4835	1.06119	0.530595	+	0.847625i	$0.321968\pi$
$938$	19.9979	0.652953
$939$	−42.4833	−1.38639
$940$	−0.168367	−0.00549152
$941$	30.4657	0.993155	0.496577	−	0.867992i	$-0.334590\pi$
$941$	30.4657	0.993155	0.496577	+	0.867992i	$0.334590\pi$
$942$	−16.9966	−0.553778
$943$	−5.94124	−0.193473
$944$	−6.30857	−0.205326
$945$	−6.05706	−0.197036
$946$	−38.8561	−1.26332
$947$	−35.8060	−1.16354	−0.581770	−	0.813353i	$-0.697640\pi$
$947$	−35.8060	−1.16354	−0.581770	+	0.813353i	$0.697640\pi$
$948$	−6.16323	−0.200172
$949$	21.3768	0.693920
$950$	−2.57515	−0.0835489
$951$	14.3350	0.464845
$952$	−1.60862	−0.0521358
$953$	−13.5482	−0.438868	−0.219434	−	0.975627i	$-0.570421\pi$
$953$	−13.5482	−0.438868	−0.219434	+	0.975627i	$0.570421\pi$
$954$	16.7442	0.542113
$955$	−0.378694	−0.0122542
$956$	−2.50007	−0.0808579
$957$	−39.4626	−1.27564
$958$	0.620140	0.0200358
$959$	−2.63132	−0.0849696
$960$	0.498880	0.0161013
$961$	−28.5736	−0.921728
$962$	−36.2433	−1.16853
$963$	75.1788	2.42260
$964$	12.6794	0.408377
$965$	4.33066	0.139409
$966$	−9.70653	−0.312303
$967$	19.8765	0.639187	0.319593	−	0.947555i	$-0.396454\pi$
$967$	19.8765	0.639187	0.319593	+	0.947555i	$0.396454\pi$
$968$	−0.751117	−0.0241418
$969$	−0.787424	−0.0252957
$970$	0.520011	0.0166965
$971$	21.2457	0.681807	0.340904	−	0.940098i	$-0.389267\pi$
$971$	21.2457	0.681807	0.340904	+	0.940098i	$0.389267\pi$
$972$	−14.3292	−0.459608
$973$	−49.6743	−1.59248
$974$	−1.78683	−0.0572537
$975$	77.2060	2.47257
$976$	10.7468	0.343997
$977$	18.8849	0.604182	0.302091	−	0.953279i	$-0.402315\pi$
$977$	18.8849	0.604182	0.302091	+	0.953279i	$0.402315\pi$
$978$	−19.4442	−0.621759
$979$	3.62388	0.115820
$980$	−0.614862	−0.0196410
$981$	−37.5926	−1.20024
$982$	8.54910	0.272813
$983$	−37.7172	−1.20299	−0.601496	−	0.798876i	$-0.705428\pi$
$983$	−37.7172	−1.20299	−0.601496	+	0.798876i	$0.705428\pi$
$984$	−19.5209	−0.622304
$985$	−2.00504	−0.0638860
$986$	1.93526	0.0616311
$987$	10.7634	0.342601
$988$	2.58145	0.0821269
$989$	11.4980	0.365615
$990$	−3.43184	−0.109071
$991$	−57.6759	−1.83213	−0.916067	−	0.401025i	$-0.868654\pi$
$991$	−57.6759	−1.83213	−0.916067	+	0.401025i	$0.868654\pi$
$992$	−1.55770	−0.0494569
$993$	−45.4411	−1.44203
$994$	−50.9545	−1.61618
$995$	−0.683617	−0.0216721
$996$	9.22890	0.292429
$997$	−40.1605	−1.27190	−0.635948	−	0.771732i	$-0.719391\pi$
$997$	−40.1605	−1.27190	−0.635948	+	0.771732i	$0.719391\pi$
$998$	4.73371	0.149843
$999$	83.4419	2.63998

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.d.1.2	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.d.1.2	✓	52	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:	\( N \)	\(=\)	\( 4034 = 2 \cdot 2017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.11260 q^{3} +1.00000 q^{4} -0.160277 q^{5} -3.11260 q^{6} -3.29184 q^{7} +1.00000 q^{8} +6.68830 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.11260 q^{3} +1.00000 q^{4} -0.160277 q^{5} -3.11260 q^{6} -3.29184 q^{7} +1.00000 q^{8} +6.68830 q^{9} -0.160277 q^{10} +3.20139 q^{11} -3.11260 q^{12} +4.98648 q^{13} -3.29184 q^{14} +0.498880 q^{15} +1.00000 q^{16} +0.488669 q^{17} +6.68830 q^{18} +0.517690 q^{19} -0.160277 q^{20} +10.2462 q^{21} +3.20139 q^{22} -0.947329 q^{23} -3.11260 q^{24} -4.97431 q^{25} +4.98648 q^{26} -11.4802 q^{27} -3.29184 q^{28} +3.96026 q^{29} +0.498880 q^{30} -1.55770 q^{31} +1.00000 q^{32} -9.96465 q^{33} +0.488669 q^{34} +0.527608 q^{35} +6.68830 q^{36} -7.26831 q^{37} +0.517690 q^{38} -15.5209 q^{39} -0.160277 q^{40} +6.27157 q^{41} +10.2462 q^{42} -12.1373 q^{43} +3.20139 q^{44} -1.07198 q^{45} -0.947329 q^{46} +1.05047 q^{47} -3.11260 q^{48} +3.83624 q^{49} -4.97431 q^{50} -1.52103 q^{51} +4.98648 q^{52} +2.50350 q^{53} -11.4802 q^{54} -0.513110 q^{55} -3.29184 q^{56} -1.61136 q^{57} +3.96026 q^{58} -6.30857 q^{59} +0.498880 q^{60} +10.7468 q^{61} -1.55770 q^{62} -22.0169 q^{63} +1.00000 q^{64} -0.799220 q^{65} -9.96465 q^{66} -6.07497 q^{67} +0.488669 q^{68} +2.94866 q^{69} +0.527608 q^{70} +15.4790 q^{71} +6.68830 q^{72} +4.28695 q^{73} -7.26831 q^{74} +15.4831 q^{75} +0.517690 q^{76} -10.5385 q^{77} -15.5209 q^{78} +1.98009 q^{79} -0.160277 q^{80} +15.6685 q^{81} +6.27157 q^{82} -2.96501 q^{83} +10.2462 q^{84} -0.0783227 q^{85} -12.1373 q^{86} -12.3267 q^{87} +3.20139 q^{88} +1.13197 q^{89} -1.07198 q^{90} -16.4147 q^{91} -0.947329 q^{92} +4.84849 q^{93} +1.05047 q^{94} -0.0829740 q^{95} -3.11260 q^{96} -3.24444 q^{97} +3.83624 q^{98} +21.4119 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9}+O(q^{10}) \) 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9	\( 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9} + 24 q^{10} + 19 q^{11} + 16 q^{12} + 27 q^{13} + 12 q^{14} + 5 q^{15} + 52 q^{16} + 43 q^{17} + 70 q^{18} + 35 q^{19} + 24 q^{20} + 29 q^{21} + 19 q^{22} + 2 q^{23} + 16 q^{24} + 88 q^{25} + 27 q^{26} + 49 q^{27} + 12 q^{28} + 31 q^{29} + 5 q^{30} + 59 q^{31} + 52 q^{32} + 45 q^{33} + 43 q^{34} + 18 q^{35} + 70 q^{36} + 60 q^{37} + 35 q^{38} + 6 q^{39} + 24 q^{40} + 56 q^{41} + 29 q^{42} + 34 q^{43} + 19 q^{44} + 61 q^{45} + 2 q^{46} - 4 q^{47} + 16 q^{48} + 102 q^{49} + 88 q^{50} + 23 q^{51} + 27 q^{52} + 30 q^{53} + 49 q^{54} + 24 q^{55} + 12 q^{56} + 32 q^{57} + 31 q^{58} + 27 q^{59} + 5 q^{60} + 107 q^{61} + 59 q^{62} - 4 q^{63} + 52 q^{64} + 46 q^{65} + 45 q^{66} + 22 q^{67} + 43 q^{68} + 36 q^{69} + 18 q^{70} + 8 q^{71} + 70 q^{72} + 66 q^{73} + 60 q^{74} + 53 q^{75} + 35 q^{76} + 26 q^{77} + 6 q^{78} + 50 q^{79} + 24 q^{80} + 108 q^{81} + 56 q^{82} + 52 q^{83} + 29 q^{84} + 19 q^{85} + 34 q^{86} - 32 q^{87} + 19 q^{88} + 62 q^{89} + 61 q^{90} + 69 q^{91} + 2 q^{92} + 21 q^{93} - 4 q^{94} - 44 q^{95} + 16 q^{96} + 82 q^{97} + 102 q^{98} + 16 q^{99}+O(q^{100}) \) 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9 + 24 * q^10 + 19 * q^11 + 16 * q^12 + 27 * q^13 + 12 * q^14 + 5 * q^15 + 52 * q^16 + 43 * q^17 + 70 * q^18 + 35 * q^19 + 24 * q^20 + 29 * q^21 + 19 * q^22 + 2 * q^23 + 16 * q^24 + 88 * q^25 + 27 * q^26 + 49 * q^27 + 12 * q^28 + 31 * q^29 + 5 * q^30 + 59 * q^31 + 52 * q^32 + 45 * q^33 + 43 * q^34 + 18 * q^35 + 70 * q^36 + 60 * q^37 + 35 * q^38 + 6 * q^39 + 24 * q^40 + 56 * q^41 + 29 * q^42 + 34 * q^43 + 19 * q^44 + 61 * q^45 + 2 * q^46 - 4 * q^47 + 16 * q^48 + 102 * q^49 + 88 * q^50 + 23 * q^51 + 27 * q^52 + 30 * q^53 + 49 * q^54 + 24 * q^55 + 12 * q^56 + 32 * q^57 + 31 * q^58 + 27 * q^59 + 5 * q^60 + 107 * q^61 + 59 * q^62 - 4 * q^63 + 52 * q^64 + 46 * q^65 + 45 * q^66 + 22 * q^67 + 43 * q^68 + 36 * q^69 + 18 * q^70 + 8 * q^71 + 70 * q^72 + 66 * q^73 + 60 * q^74 + 53 * q^75 + 35 * q^76 + 26 * q^77 + 6 * q^78 + 50 * q^79 + 24 * q^80 + 108 * q^81 + 56 * q^82 + 52 * q^83 + 29 * q^84 + 19 * q^85 + 34 * q^86 - 32 * q^87 + 19 * q^88 + 62 * q^89 + 61 * q^90 + 69 * q^91 + 2 * q^92 + 21 * q^93 - 4 * q^94 - 44 * q^95 + 16 * q^96 + 82 * q^97 + 102 * q^98 + 16 * q^99

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