LMFDB - Embedded newform 4029.2.a.h.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.1717269744$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.743888 q^{2} +1.00000 q^{3} -1.44663 q^{4} +0.602376 q^{5} -0.743888 q^{6} +4.42261 q^{7} +2.56391 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.743888 q^{2} +1.00000 q^{3} -1.44663 q^{4} +0.602376 q^{5} -0.743888 q^{6} +4.42261 q^{7} +2.56391 q^{8} +1.00000 q^{9} -0.448100 q^{10} -2.69724 q^{11} -1.44663 q^{12} -5.35733 q^{13} -3.28992 q^{14} +0.602376 q^{15} +0.986004 q^{16} -1.00000 q^{17} -0.743888 q^{18} +1.87368 q^{19} -0.871415 q^{20} +4.42261 q^{21} +2.00644 q^{22} +1.99116 q^{23} +2.56391 q^{24} -4.63714 q^{25} +3.98525 q^{26} +1.00000 q^{27} -6.39788 q^{28} +1.22981 q^{29} -0.448100 q^{30} -7.92143 q^{31} -5.86129 q^{32} -2.69724 q^{33} +0.743888 q^{34} +2.66407 q^{35} -1.44663 q^{36} -10.9002 q^{37} -1.39380 q^{38} -5.35733 q^{39} +1.54443 q^{40} -10.7059 q^{41} -3.28992 q^{42} +2.98107 q^{43} +3.90191 q^{44} +0.602376 q^{45} -1.48120 q^{46} +0.285756 q^{47} +0.986004 q^{48} +12.5594 q^{49} +3.44951 q^{50} -1.00000 q^{51} +7.75007 q^{52} -9.29966 q^{53} -0.743888 q^{54} -1.62475 q^{55} +11.3391 q^{56} +1.87368 q^{57} -0.914842 q^{58} -12.9236 q^{59} -0.871415 q^{60} +8.80121 q^{61} +5.89265 q^{62} +4.42261 q^{63} +2.38813 q^{64} -3.22712 q^{65} +2.00644 q^{66} +7.66441 q^{67} +1.44663 q^{68} +1.99116 q^{69} -1.98177 q^{70} +1.12524 q^{71} +2.56391 q^{72} -8.28900 q^{73} +8.10852 q^{74} -4.63714 q^{75} -2.71052 q^{76} -11.9288 q^{77} +3.98525 q^{78} +1.00000 q^{79} +0.593945 q^{80} +1.00000 q^{81} +7.96399 q^{82} -3.78822 q^{83} -6.39788 q^{84} -0.602376 q^{85} -2.21758 q^{86} +1.22981 q^{87} -6.91547 q^{88} -5.73835 q^{89} -0.448100 q^{90} -23.6933 q^{91} -2.88047 q^{92} -7.92143 q^{93} -0.212570 q^{94} +1.12866 q^{95} -5.86129 q^{96} +5.52563 q^{97} -9.34282 q^{98} -2.69724 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 7 q^{2} + 25 q^{3} + 21 q^{4} - 12 q^{5} - 7 q^{6} - 4 q^{7} - 21 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q - 7 * q^2 + 25 * q^3 + 21 * q^4 - 12 * q^5 - 7 * q^6 - 4 * q^7 - 21 * q^8 + 25 * q^9	\( 25 q - 7 q^{2} + 25 q^{3} + 21 q^{4} - 12 q^{5} - 7 q^{6} - 4 q^{7} - 21 q^{8} + 25 q^{9} - 9 q^{10} - 19 q^{11} + 21 q^{12} - 12 q^{13} - 15 q^{14} - 12 q^{15} + q^{16} - 25 q^{17} - 7 q^{18} - 35 q^{19} - 11 q^{20} - 4 q^{21} - 2 q^{22} - 16 q^{23} - 21 q^{24} + 19 q^{25} - 5 q^{26} + 25 q^{27} + 3 q^{28} - 37 q^{29} - 9 q^{30} - 28 q^{31} - 19 q^{32} - 19 q^{33} + 7 q^{34} - 42 q^{35} + 21 q^{36} + 8 q^{37} - 35 q^{38} - 12 q^{39} - 9 q^{40} - 34 q^{41} - 15 q^{42} - 19 q^{43} - 56 q^{44} - 12 q^{45} + q^{46} - 25 q^{47} + q^{48} + 25 q^{49} - 7 q^{50} - 25 q^{51} - 37 q^{52} - 44 q^{53} - 7 q^{54} - 11 q^{55} - 18 q^{56} - 35 q^{57} - 3 q^{58} - 47 q^{59} - 11 q^{60} - 28 q^{61} + 11 q^{62} - 4 q^{63} - 9 q^{64} - 63 q^{65} - 2 q^{66} - 28 q^{67} - 21 q^{68} - 16 q^{69} + 5 q^{70} - 27 q^{71} - 21 q^{72} - 21 q^{73} - 18 q^{74} + 19 q^{75} - 50 q^{76} - 58 q^{77} - 5 q^{78} + 25 q^{79} - 56 q^{80} + 25 q^{81} - 5 q^{82} - 61 q^{83} + 3 q^{84} + 12 q^{85} - 28 q^{86} - 37 q^{87} + 15 q^{88} - 34 q^{89} - 9 q^{90} - 30 q^{91} - 31 q^{92} - 28 q^{93} + q^{94} - 32 q^{95} - 19 q^{96} - 11 q^{97} - 66 q^{98} - 19 q^{99}+O(q^{100}) \) 25 * q - 7 * q^2 + 25 * q^3 + 21 * q^4 - 12 * q^5 - 7 * q^6 - 4 * q^7 - 21 * q^8 + 25 * q^9 - 9 * q^10 - 19 * q^11 + 21 * q^12 - 12 * q^13 - 15 * q^14 - 12 * q^15 + q^16 - 25 * q^17 - 7 * q^18 - 35 * q^19 - 11 * q^20 - 4 * q^21 - 2 * q^22 - 16 * q^23 - 21 * q^24 + 19 * q^25 - 5 * q^26 + 25 * q^27 + 3 * q^28 - 37 * q^29 - 9 * q^30 - 28 * q^31 - 19 * q^32 - 19 * q^33 + 7 * q^34 - 42 * q^35 + 21 * q^36 + 8 * q^37 - 35 * q^38 - 12 * q^39 - 9 * q^40 - 34 * q^41 - 15 * q^42 - 19 * q^43 - 56 * q^44 - 12 * q^45 + q^46 - 25 * q^47 + q^48 + 25 * q^49 - 7 * q^50 - 25 * q^51 - 37 * q^52 - 44 * q^53 - 7 * q^54 - 11 * q^55 - 18 * q^56 - 35 * q^57 - 3 * q^58 - 47 * q^59 - 11 * q^60 - 28 * q^61 + 11 * q^62 - 4 * q^63 - 9 * q^64 - 63 * q^65 - 2 * q^66 - 28 * q^67 - 21 * q^68 - 16 * q^69 + 5 * q^70 - 27 * q^71 - 21 * q^72 - 21 * q^73 - 18 * q^74 + 19 * q^75 - 50 * q^76 - 58 * q^77 - 5 * q^78 + 25 * q^79 - 56 * q^80 + 25 * q^81 - 5 * q^82 - 61 * q^83 + 3 * q^84 + 12 * q^85 - 28 * q^86 - 37 * q^87 + 15 * q^88 - 34 * q^89 - 9 * q^90 - 30 * q^91 - 31 * q^92 - 28 * q^93 + q^94 - 32 * q^95 - 19 * q^96 - 11 * q^97 - 66 * q^98 - 19 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.743888	−0.526008	−0.263004	−	0.964795i	$-0.584713\pi$
$2$	−0.743888	−0.526008	−0.263004	+	0.964795i	$0.584713\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.44663	−0.723316
$5$	0.602376	0.269391	0.134695	−	0.990887i	$-0.456994\pi$
$5$	0.602376	0.269391	0.134695	+	0.990887i	$0.456994\pi$
$6$	−0.743888	−0.303691
$7$	4.42261	1.67159	0.835794	−	0.549043i	$-0.185008\pi$
$7$	4.42261	1.67159	0.835794	+	0.549043i	$0.185008\pi$
$8$	2.56391	0.906478
$9$	1.00000	0.333333
$10$	−0.448100	−0.141702
$11$	−2.69724	−0.813249	−0.406624	−	0.913595i	$-0.633294\pi$
$11$	−2.69724	−0.813249	−0.406624	+	0.913595i	$0.633294\pi$
$12$	−1.44663	−0.417606
$13$	−5.35733	−1.48585	−0.742927	−	0.669372i	$-0.766563\pi$
$13$	−5.35733	−1.48585	−0.742927	+	0.669372i	$0.766563\pi$
$14$	−3.28992	−0.879269
$15$	0.602376	0.155533
$16$	0.986004	0.246501
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−0.743888	−0.175336
$19$	1.87368	0.429851	0.214925	−	0.976630i	$-0.431049\pi$
$19$	1.87368	0.429851	0.214925	+	0.976630i	$0.431049\pi$
$20$	−0.871415	−0.194854
$21$	4.42261	0.965092
$22$	2.00644	0.427775
$23$	1.99116	0.415186	0.207593	−	0.978215i	$-0.433437\pi$
$23$	1.99116	0.415186	0.207593	+	0.978215i	$0.433437\pi$
$24$	2.56391	0.523355
$25$	−4.63714	−0.927429
$26$	3.98525	0.781572
$27$	1.00000	0.192450
$28$	−6.39788	−1.20909
$29$	1.22981	0.228370	0.114185	−	0.993459i	$-0.463574\pi$
$29$	1.22981	0.228370	0.114185	+	0.993459i	$0.463574\pi$
$30$	−0.448100	−0.0818115
$31$	−7.92143	−1.42273	−0.711365	−	0.702823i	$-0.751923\pi$
$31$	−7.92143	−1.42273	−0.711365	+	0.702823i	$0.751923\pi$
$32$	−5.86129	−1.03614
$33$	−2.69724	−0.469529
$34$	0.743888	0.127576
$35$	2.66407	0.450310
$36$	−1.44663	−0.241105
$37$	−10.9002	−1.79198	−0.895991	−	0.444073i	$-0.853533\pi$
$37$	−10.9002	−1.79198	−0.895991	+	0.444073i	$0.853533\pi$
$38$	−1.39380	−0.226105
$39$	−5.35733	−0.857859
$40$	1.54443	0.244197
$41$	−10.7059	−1.67198	−0.835990	−	0.548744i	$-0.815106\pi$
$41$	−10.7059	−1.67198	−0.835990	+	0.548744i	$0.815106\pi$
$42$	−3.28992	−0.507646
$43$	2.98107	0.454608	0.227304	−	0.973824i	$-0.427009\pi$
$43$	2.98107	0.454608	0.227304	+	0.973824i	$0.427009\pi$
$44$	3.90191	0.588236
$45$	0.602376	0.0897968
$46$	−1.48120	−0.218391
$47$	0.285756	0.0416818	0.0208409	−	0.999783i	$-0.493366\pi$
$47$	0.285756	0.0416818	0.0208409	+	0.999783i	$0.493366\pi$
$48$	0.986004	0.142317
$49$	12.5594	1.79421
$50$	3.44951	0.487835
$51$	−1.00000	−0.140028
$52$	7.75007	1.07474
$53$	−9.29966	−1.27741	−0.638703	−	0.769453i	$-0.720529\pi$
$53$	−9.29966	−1.27741	−0.638703	+	0.769453i	$0.720529\pi$
$54$	−0.743888	−0.101230
$55$	−1.62475	−0.219082
$56$	11.3391	1.51526
$57$	1.87368	0.248174
$58$	−0.914842	−0.120125
$59$	−12.9236	−1.68251	−0.841257	−	0.540636i	$-0.818184\pi$
$59$	−12.9236	−1.68251	−0.841257	+	0.540636i	$0.818184\pi$
$60$	−0.871415	−0.112499
$61$	8.80121	1.12688	0.563440	−	0.826157i	$-0.309478\pi$
$61$	8.80121	1.12688	0.563440	+	0.826157i	$0.309478\pi$
$62$	5.89265	0.748367
$63$	4.42261	0.557196
$64$	2.38813	0.298517
$65$	−3.22712	−0.400275
$66$	2.00644	0.246976
$67$	7.66441	0.936357	0.468179	−	0.883634i	$-0.344910\pi$
$67$	7.66441	0.936357	0.468179	+	0.883634i	$0.344910\pi$
$68$	1.44663	0.175430
$69$	1.99116	0.239707
$70$	−1.98177	−0.236867
$71$	1.12524	0.133542	0.0667708	−	0.997768i	$-0.478730\pi$
$71$	1.12524	0.133542	0.0667708	+	0.997768i	$0.478730\pi$
$72$	2.56391	0.302159
$73$	−8.28900	−0.970154	−0.485077	−	0.874471i	$-0.661208\pi$
$73$	−8.28900	−0.970154	−0.485077	+	0.874471i	$0.661208\pi$
$74$	8.10852	0.942597
$75$	−4.63714	−0.535451
$76$	−2.71052	−0.310918
$77$	−11.9288	−1.35942
$78$	3.98525	0.451241
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	0.593945	0.0664050
$81$	1.00000	0.111111
$82$	7.96399	0.879475
$83$	−3.78822	−0.415811	−0.207906	−	0.978149i	$-0.566665\pi$
$83$	−3.78822	−0.415811	−0.207906	+	0.978149i	$0.566665\pi$
$84$	−6.39788	−0.698066
$85$	−0.602376	−0.0653368
$86$	−2.21758	−0.239128
$87$	1.22981	0.131850
$88$	−6.91547	−0.737192
$89$	−5.73835	−0.608264	−0.304132	−	0.952630i	$-0.598366\pi$
$89$	−5.73835	−0.608264	−0.304132	+	0.952630i	$0.598366\pi$
$90$	−0.448100	−0.0472339
$91$	−23.6933	−2.48374
$92$	−2.88047	−0.300310
$93$	−7.92143	−0.821414
$94$	−0.212570	−0.0219250
$95$	1.12866	0.115798
$96$	−5.86129	−0.598215
$97$	5.52563	0.561043	0.280521	−	0.959848i	$-0.409493\pi$
$97$	5.52563	0.561043	0.280521	+	0.959848i	$0.409493\pi$
$98$	−9.34282	−0.943767
$99$	−2.69724	−0.271083
$100$	6.70824	0.670824
$101$	−2.21251	−0.220153	−0.110076	−	0.993923i	$-0.535110\pi$
$101$	−2.21251	−0.220153	−0.110076	+	0.993923i	$0.535110\pi$
$102$	0.743888	0.0736559
$103$	−0.244038	−0.0240458	−0.0120229	−	0.999928i	$-0.503827\pi$
$103$	−0.244038	−0.0240458	−0.0120229	+	0.999928i	$0.503827\pi$
$104$	−13.7357	−1.34689
$105$	2.66407	0.259987
$106$	6.91790	0.671926
$107$	13.1184	1.26821	0.634104	−	0.773248i	$-0.281369\pi$
$107$	13.1184	1.26821	0.634104	+	0.773248i	$0.281369\pi$
$108$	−1.44663	−0.139202
$109$	−3.03919	−0.291102	−0.145551	−	0.989351i	$-0.546495\pi$
$109$	−3.03919	−0.291102	−0.145551	+	0.989351i	$0.546495\pi$
$110$	1.20863	0.115239
$111$	−10.9002	−1.03460
$112$	4.36071	0.412048
$113$	5.25564	0.494409	0.247205	−	0.968963i	$-0.420488\pi$
$113$	5.25564	0.494409	0.247205	+	0.968963i	$0.420488\pi$
$114$	−1.39380	−0.130542
$115$	1.19943	0.111847
$116$	−1.77908	−0.165184
$117$	−5.35733	−0.495285
$118$	9.61373	0.885016
$119$	−4.42261	−0.405420
$120$	1.54443	0.140987
$121$	−3.72489	−0.338626
$122$	−6.54711	−0.592748
$123$	−10.7059	−0.965318
$124$	11.4594	1.02908
$125$	−5.80518	−0.519231
$126$	−3.28992	−0.293090
$127$	6.44713	0.572090	0.286045	−	0.958216i	$-0.407659\pi$
$127$	6.44713	0.572090	0.286045	+	0.958216i	$0.407659\pi$
$128$	9.94607	0.879117
$129$	2.98107	0.262468
$130$	2.40062	0.210548
$131$	0.938440	0.0819919	0.0409960	−	0.999159i	$-0.486947\pi$
$131$	0.938440	0.0819919	0.0409960	+	0.999159i	$0.486947\pi$
$132$	3.90191	0.339618
$133$	8.28653	0.718533
$134$	−5.70146	−0.492531
$135$	0.602376	0.0518442
$136$	−2.56391	−0.219853
$137$	−9.26167	−0.791278	−0.395639	−	0.918406i	$-0.629477\pi$
$137$	−9.26167	−0.791278	−0.395639	+	0.918406i	$0.629477\pi$
$138$	−1.48120	−0.126088
$139$	15.8032	1.34041	0.670204	−	0.742177i	$-0.266207\pi$
$139$	15.8032	1.34041	0.670204	+	0.742177i	$0.266207\pi$
$140$	−3.85393	−0.325716
$141$	0.285756	0.0240650
$142$	−0.837053	−0.0702439
$143$	14.4500	1.20837
$144$	0.986004	0.0821670
$145$	0.740809	0.0615208
$146$	6.16609	0.510309
$147$	12.5594	1.03589
$148$	15.7686	1.29617
$149$	−3.27381	−0.268201	−0.134101	−	0.990968i	$-0.542815\pi$
$149$	−3.27381	−0.268201	−0.134101	+	0.990968i	$0.542815\pi$
$150$	3.44951	0.281652
$151$	5.22283	0.425028	0.212514	−	0.977158i	$-0.431835\pi$
$151$	5.22283	0.425028	0.212514	+	0.977158i	$0.431835\pi$
$152$	4.80393	0.389650
$153$	−1.00000	−0.0808452
$154$	8.87372	0.715064
$155$	−4.77167	−0.383270
$156$	7.75007	0.620503
$157$	−9.06767	−0.723679	−0.361840	−	0.932240i	$-0.617851\pi$
$157$	−9.06767	−0.723679	−0.361840	+	0.932240i	$0.617851\pi$
$158$	−0.743888	−0.0591805
$159$	−9.29966	−0.737511
$160$	−3.53070	−0.279126
$161$	8.80612	0.694019
$162$	−0.743888	−0.0584453
$163$	2.82673	0.221407	0.110703	−	0.993853i	$-0.464690\pi$
$163$	2.82673	0.221407	0.110703	+	0.993853i	$0.464690\pi$
$164$	15.4875	1.20937
$165$	−1.62475	−0.126487
$166$	2.81801	0.218720
$167$	19.8948	1.53951	0.769753	−	0.638342i	$-0.220380\pi$
$167$	19.8948	1.53951	0.769753	+	0.638342i	$0.220380\pi$
$168$	11.3391	0.874834
$169$	15.7009	1.20776
$170$	0.448100	0.0343677
$171$	1.87368	0.143284
$172$	−4.31250	−0.328825
$173$	−2.08076	−0.158197	−0.0790987	−	0.996867i	$-0.525204\pi$
$173$	−2.08076	−0.158197	−0.0790987	+	0.996867i	$0.525204\pi$
$174$	−0.914842	−0.0693540
$175$	−20.5083	−1.55028
$176$	−2.65949	−0.200467
$177$	−12.9236	−0.971400
$178$	4.26869	0.319952
$179$	−6.95109	−0.519549	−0.259775	−	0.965669i	$-0.583648\pi$
$179$	−6.95109	−0.519549	−0.259775	+	0.965669i	$0.583648\pi$
$180$	−0.871415	−0.0649515
$181$	−26.6039	−1.97745	−0.988727	−	0.149730i	$-0.952159\pi$
$181$	−26.6039	−1.97745	−0.988727	+	0.149730i	$0.952159\pi$
$182$	17.6252	1.30647
$183$	8.80121	0.650604
$184$	5.10515	0.376356
$185$	−6.56601	−0.482743
$186$	5.89265	0.432070
$187$	2.69724	0.197242
$188$	−0.413383	−0.0301491
$189$	4.42261	0.321697
$190$	−0.839594	−0.0609105
$191$	2.02876	0.146796	0.0733980	−	0.997303i	$-0.476616\pi$
$191$	2.02876	0.146796	0.0733980	+	0.997303i	$0.476616\pi$
$192$	2.38813	0.172349
$193$	9.47415	0.681964	0.340982	−	0.940070i	$-0.389240\pi$
$193$	9.47415	0.681964	0.340982	+	0.940070i	$0.389240\pi$
$194$	−4.11045	−0.295113
$195$	−3.22712	−0.231099
$196$	−18.1689	−1.29778
$197$	6.98007	0.497309	0.248655	−	0.968592i	$-0.420012\pi$
$197$	6.98007	0.497309	0.248655	+	0.968592i	$0.420012\pi$
$198$	2.00644	0.142592
$199$	9.39916	0.666289	0.333145	−	0.942876i	$-0.391890\pi$
$199$	9.39916	0.666289	0.333145	+	0.942876i	$0.391890\pi$
$200$	−11.8892	−0.840694
$201$	7.66441	0.540606
$202$	1.64586	0.115802
$203$	5.43898	0.381741
$204$	1.44663	0.101284
$205$	−6.44897	−0.450416
$206$	0.181537	0.0126483
$207$	1.99116	0.138395
$208$	−5.28234	−0.366265
$209$	−5.05376	−0.349576
$210$	−1.98177	−0.136755
$211$	−14.5935	−1.00466	−0.502329	−	0.864677i	$-0.667523\pi$
$211$	−14.5935	−1.00466	−0.502329	+	0.864677i	$0.667523\pi$
$212$	13.4532	0.923968
$213$	1.12524	0.0771003
$214$	−9.75865	−0.667088
$215$	1.79572	0.122467
$216$	2.56391	0.174452
$217$	−35.0333	−2.37822
$218$	2.26082	0.153122
$219$	−8.28900	−0.560119
$220$	2.35042	0.158465
$221$	5.35733	0.360373
$222$	8.10852	0.544208
$223$	19.9160	1.33367	0.666836	−	0.745204i	$-0.267648\pi$
$223$	19.9160	1.33367	0.666836	+	0.745204i	$0.267648\pi$
$224$	−25.9222	−1.73200
$225$	−4.63714	−0.309143
$226$	−3.90961	−0.260063
$227$	−17.3772	−1.15337	−0.576683	−	0.816968i	$-0.695653\pi$
$227$	−17.3772	−1.15337	−0.576683	+	0.816968i	$0.695653\pi$
$228$	−2.71052	−0.179508
$229$	−2.04644	−0.135233	−0.0676164	−	0.997711i	$-0.521539\pi$
$229$	−2.04644	−0.135233	−0.0676164	+	0.997711i	$0.521539\pi$
$230$	−0.892238	−0.0588325
$231$	−11.9288	−0.784860
$232$	3.15312	0.207013
$233$	−17.5577	−1.15024	−0.575121	−	0.818068i	$-0.695045\pi$
$233$	−17.5577	−1.15024	−0.575121	+	0.818068i	$0.695045\pi$
$234$	3.98525	0.260524
$235$	0.172132	0.0112287
$236$	18.6957	1.21699
$237$	1.00000	0.0649570
$238$	3.28992	0.213254
$239$	17.4639	1.12964	0.564822	−	0.825213i	$-0.308945\pi$
$239$	17.4639	1.12964	0.564822	+	0.825213i	$0.308945\pi$
$240$	0.593945	0.0383390
$241$	−14.0988	−0.908183	−0.454091	−	0.890955i	$-0.650036\pi$
$241$	−14.0988	−0.908183	−0.454091	+	0.890955i	$0.650036\pi$
$242$	2.77090	0.178120
$243$	1.00000	0.0641500
$244$	−12.7321	−0.815090
$245$	7.56550	0.483342
$246$	7.96399	0.507765
$247$	−10.0379	−0.638696
$248$	−20.3098	−1.28967
$249$	−3.78822	−0.240069
$250$	4.31840	0.273120
$251$	−2.62859	−0.165915	−0.0829575	−	0.996553i	$-0.526437\pi$
$251$	−2.62859	−0.165915	−0.0829575	+	0.996553i	$0.526437\pi$
$252$	−6.39788	−0.403029
$253$	−5.37064	−0.337649
$254$	−4.79594	−0.300924
$255$	−0.602376	−0.0377222
$256$	−12.1750	−0.760939
$257$	−30.0110	−1.87203	−0.936017	−	0.351956i	$-0.885517\pi$
$257$	−30.0110	−1.87203	−0.936017	+	0.351956i	$0.885517\pi$
$258$	−2.21758	−0.138060
$259$	−48.2073	−2.99546
$260$	4.66846	0.289525
$261$	1.22981	0.0761235
$262$	−0.698094	−0.0431284
$263$	−23.0822	−1.42331	−0.711656	−	0.702528i	$-0.752055\pi$
$263$	−23.0822	−1.42331	−0.711656	+	0.702528i	$0.752055\pi$
$264$	−6.91547	−0.425618
$265$	−5.60189	−0.344121
$266$	−6.16425	−0.377954
$267$	−5.73835	−0.351182
$268$	−11.0876	−0.677282
$269$	−16.6421	−1.01469	−0.507345	−	0.861743i	$-0.669373\pi$
$269$	−16.6421	−1.01469	−0.507345	+	0.861743i	$0.669373\pi$
$270$	−0.448100	−0.0272705
$271$	32.0713	1.94820	0.974098	−	0.226127i	$-0.0726065\pi$
$271$	32.0713	1.94820	0.974098	+	0.226127i	$0.0726065\pi$
$272$	−0.986004	−0.0597853
$273$	−23.6933	−1.43399
$274$	6.88964	0.416218
$275$	12.5075	0.754230
$276$	−2.88047	−0.173384
$277$	−18.8771	−1.13421	−0.567107	−	0.823644i	$-0.691937\pi$
$277$	−18.8771	−1.13421	−0.567107	+	0.823644i	$0.691937\pi$
$278$	−11.7558	−0.705065
$279$	−7.92143	−0.474243
$280$	6.83043	0.408196
$281$	24.6086	1.46803	0.734014	−	0.679135i	$-0.237645\pi$
$281$	24.6086	1.46803	0.734014	+	0.679135i	$0.237645\pi$
$282$	−0.212570	−0.0126584
$283$	26.3133	1.56417	0.782083	−	0.623174i	$-0.214157\pi$
$283$	26.3133	1.56417	0.782083	+	0.623174i	$0.214157\pi$
$284$	−1.62781	−0.0965927
$285$	1.12866	0.0668559
$286$	−10.7492	−0.635612
$287$	−47.3480	−2.79486
$288$	−5.86129	−0.345380
$289$	1.00000	0.0588235
$290$	−0.551079	−0.0323605
$291$	5.52563	0.323918
$292$	11.9911	0.701728
$293$	−20.0684	−1.17241	−0.586204	−	0.810163i	$-0.699378\pi$
$293$	−20.0684	−1.17241	−0.586204	+	0.810163i	$0.699378\pi$
$294$	−9.34282	−0.544884
$295$	−7.78488	−0.453253
$296$	−27.9471	−1.62439
$297$	−2.69724	−0.156510
$298$	2.43535	0.141076
$299$	−10.6673	−0.616905
$300$	6.70824	0.387300
$301$	13.1841	0.759918
$302$	−3.88520	−0.223568
$303$	−2.21251	−0.127105
$304$	1.84745	0.105959
$305$	5.30164	0.303571
$306$	0.743888	0.0425252
$307$	−14.2402	−0.812731	−0.406366	−	0.913711i	$-0.633204\pi$
$307$	−14.2402	−0.812731	−0.406366	+	0.913711i	$0.633204\pi$
$308$	17.2566	0.983288
$309$	−0.244038	−0.0138829
$310$	3.54959	0.201603
$311$	−28.0937	−1.59305	−0.796523	−	0.604609i	$-0.793329\pi$
$311$	−28.0937	−1.59305	−0.796523	+	0.604609i	$0.793329\pi$
$312$	−13.7357	−0.777630
$313$	−2.30396	−0.130228	−0.0651138	−	0.997878i	$-0.520741\pi$
$313$	−2.30396	−0.130228	−0.0651138	+	0.997878i	$0.520741\pi$
$314$	6.74533	0.380661
$315$	2.66407	0.150103
$316$	−1.44663	−0.0813794
$317$	15.1488	0.850839	0.425420	−	0.904996i	$-0.360126\pi$
$317$	15.1488	0.850839	0.425420	+	0.904996i	$0.360126\pi$
$318$	6.91790	0.387937
$319$	−3.31710	−0.185722
$320$	1.43855	0.0804176
$321$	13.1184	0.732200
$322$	−6.55076	−0.365060
$323$	−1.87368	−0.104254
$324$	−1.44663	−0.0803684
$325$	24.8427	1.37802
$326$	−2.10277	−0.116462
$327$	−3.03919	−0.168068
$328$	−27.4489	−1.51561
$329$	1.26379	0.0696748
$330$	1.20863	0.0665331
$331$	23.7680	1.30641	0.653203	−	0.757183i	$-0.273425\pi$
$331$	23.7680	1.30641	0.653203	+	0.757183i	$0.273425\pi$
$332$	5.48015	0.300763
$333$	−10.9002	−0.597327
$334$	−14.7995	−0.809792
$335$	4.61685	0.252246
$336$	4.36071	0.237896
$337$	27.2314	1.48339	0.741694	−	0.670738i	$-0.234022\pi$
$337$	27.2314	1.48339	0.741694	+	0.670738i	$0.234022\pi$
$338$	−11.6797	−0.635294
$339$	5.25564	0.285447
$340$	0.871415	0.0472591
$341$	21.3660	1.15703
$342$	−1.39380	−0.0753683
$343$	24.5872	1.32759
$344$	7.64318	0.412092
$345$	1.19943	0.0645749
$346$	1.54785	0.0832131
$347$	−34.3975	−1.84655	−0.923277	−	0.384136i	$-0.874499\pi$
$347$	−34.3975	−1.84655	−0.923277	+	0.384136i	$0.874499\pi$
$348$	−1.77908	−0.0953690
$349$	−3.42647	−0.183415	−0.0917073	−	0.995786i	$-0.529232\pi$
$349$	−3.42647	−0.183415	−0.0917073	+	0.995786i	$0.529232\pi$
$350$	15.2558	0.815459
$351$	−5.35733	−0.285953
$352$	15.8093	0.842639
$353$	−10.2319	−0.544587	−0.272293	−	0.962214i	$-0.587782\pi$
$353$	−10.2319	−0.544587	−0.272293	+	0.962214i	$0.587782\pi$
$354$	9.61373	0.510964
$355$	0.677818	0.0359748
$356$	8.30128	0.439967
$357$	−4.42261	−0.234069
$358$	5.17083	0.273287
$359$	−18.6717	−0.985453	−0.492726	−	0.870184i	$-0.664000\pi$
$359$	−18.6717	−0.985453	−0.492726	+	0.870184i	$0.664000\pi$
$360$	1.54443	0.0813989
$361$	−15.4893	−0.815228
$362$	19.7903	1.04016
$363$	−3.72489	−0.195506
$364$	34.2755	1.79653
$365$	−4.99309	−0.261350
$366$	−6.54711	−0.342223
$367$	−18.4375	−0.962431	−0.481215	−	0.876602i	$-0.659804\pi$
$367$	−18.4375	−0.962431	−0.481215	+	0.876602i	$0.659804\pi$
$368$	1.96329	0.102344
$369$	−10.7059	−0.557327
$370$	4.88438	0.253927
$371$	−41.1287	−2.13530
$372$	11.4594	0.594141
$373$	13.2516	0.686143	0.343072	−	0.939309i	$-0.388533\pi$
$373$	13.2516	0.686143	0.343072	+	0.939309i	$0.388533\pi$
$374$	−2.00644	−0.103751
$375$	−5.80518	−0.299778
$376$	0.732651	0.0377836
$377$	−6.58851	−0.339325
$378$	−3.28992	−0.169215
$379$	17.3139	0.889355	0.444678	−	0.895691i	$-0.353318\pi$
$379$	17.3139	0.889355	0.444678	+	0.895691i	$0.353318\pi$
$380$	−1.63275	−0.0837583
$381$	6.44713	0.330297
$382$	−1.50917	−0.0772159
$383$	−16.6854	−0.852584	−0.426292	−	0.904586i	$-0.640180\pi$
$383$	−16.6854	−0.852584	−0.426292	+	0.904586i	$0.640180\pi$
$384$	9.94607	0.507559
$385$	−7.18564	−0.366214
$386$	−7.04770	−0.358719
$387$	2.98107	0.151536
$388$	−7.99355	−0.405811
$389$	−5.62560	−0.285229	−0.142615	−	0.989778i	$-0.545551\pi$
$389$	−5.62560	−0.285229	−0.142615	+	0.989778i	$0.545551\pi$
$390$	2.40062	0.121560
$391$	−1.99116	−0.100697
$392$	32.2012	1.62641
$393$	0.938440	0.0473380
$394$	−5.19239	−0.261589
$395$	0.602376	0.0303088
$396$	3.90191	0.196079
$397$	−17.2656	−0.866536	−0.433268	−	0.901265i	$-0.642640\pi$
$397$	−17.2656	−0.866536	−0.433268	+	0.901265i	$0.642640\pi$
$398$	−6.99192	−0.350473
$399$	8.28653	0.414845
$400$	−4.57224	−0.228612
$401$	−12.3497	−0.616717	−0.308358	−	0.951270i	$-0.599780\pi$
$401$	−12.3497	−0.616717	−0.308358	+	0.951270i	$0.599780\pi$
$402$	−5.70146	−0.284363
$403$	42.4377	2.11397
$404$	3.20068	0.159240
$405$	0.602376	0.0299323
$406$	−4.04599	−0.200799
$407$	29.4005	1.45733
$408$	−2.56391	−0.126932
$409$	9.54061	0.471753	0.235876	−	0.971783i	$-0.424204\pi$
$409$	9.54061	0.471753	0.235876	+	0.971783i	$0.424204\pi$
$410$	4.79731	0.236922
$411$	−9.26167	−0.456844
$412$	0.353034	0.0173927
$413$	−57.1561	−2.81247
$414$	−1.48120	−0.0727970
$415$	−2.28193	−0.112016
$416$	31.4008	1.53955
$417$	15.8032	0.773885
$418$	3.75943	0.183880
$419$	13.2627	0.647925	0.323963	−	0.946070i	$-0.394985\pi$
$419$	13.2627	0.647925	0.323963	+	0.946070i	$0.394985\pi$
$420$	−3.85393	−0.188052
$421$	9.07132	0.442109	0.221054	−	0.975261i	$-0.429050\pi$
$421$	9.07132	0.442109	0.221054	+	0.975261i	$0.429050\pi$
$422$	10.8559	0.528458
$423$	0.285756	0.0138939
$424$	−23.8435	−1.15794
$425$	4.63714	0.224935
$426$	−0.837053	−0.0405554
$427$	38.9243	1.88368
$428$	−18.9776	−0.917315
$429$	14.4500	0.697653
$430$	−1.33582	−0.0644187
$431$	−1.84729	−0.0889810	−0.0444905	−	0.999010i	$-0.514166\pi$
$431$	−1.84729	−0.0889810	−0.0444905	+	0.999010i	$0.514166\pi$
$432$	0.986004	0.0474391
$433$	−14.3857	−0.691334	−0.345667	−	0.938357i	$-0.612347\pi$
$433$	−14.3857	−0.691334	−0.345667	+	0.938357i	$0.612347\pi$
$434$	26.0609	1.25096
$435$	0.740809	0.0355191
$436$	4.39659	0.210559
$437$	3.73079	0.178468
$438$	6.16609	0.294627
$439$	31.1219	1.48537	0.742683	−	0.669643i	$-0.233553\pi$
$439$	31.1219	1.48537	0.742683	+	0.669643i	$0.233553\pi$
$440$	−4.16571	−0.198593
$441$	12.5594	0.598069
$442$	−3.98525	−0.189559
$443$	−8.28672	−0.393714	−0.196857	−	0.980432i	$-0.563073\pi$
$443$	−8.28672	−0.393714	−0.196857	+	0.980432i	$0.563073\pi$
$444$	15.7686	0.748343
$445$	−3.45664	−0.163861
$446$	−14.8152	−0.701522
$447$	−3.27381	−0.154846
$448$	10.5618	0.498997
$449$	−12.1115	−0.571579	−0.285789	−	0.958292i	$-0.592256\pi$
$449$	−12.1115	−0.571579	−0.285789	+	0.958292i	$0.592256\pi$
$450$	3.44951	0.162612
$451$	28.8764	1.35974
$452$	−7.60297	−0.357614
$453$	5.22283	0.245390
$454$	12.9267	0.606680
$455$	−14.2723	−0.669095
$456$	4.80393	0.224965
$457$	−26.6019	−1.24439	−0.622193	−	0.782864i	$-0.713758\pi$
$457$	−26.6019	−1.24439	−0.622193	+	0.782864i	$0.713758\pi$
$458$	1.52232	0.0711336
$459$	−1.00000	−0.0466760
$460$	−1.73513	−0.0809007
$461$	0.509887	0.0237478	0.0118739	−	0.999930i	$-0.496220\pi$
$461$	0.509887	0.0237478	0.0118739	+	0.999930i	$0.496220\pi$
$462$	8.87372	0.412843
$463$	23.2395	1.08003	0.540016	−	0.841654i	$-0.318418\pi$
$463$	23.2395	1.08003	0.540016	+	0.841654i	$0.318418\pi$
$464$	1.21260	0.0562935
$465$	−4.77167	−0.221281
$466$	13.0609	0.605037
$467$	−28.5438	−1.32085	−0.660426	−	0.750891i	$-0.729624\pi$
$467$	−28.5438	−1.32085	−0.660426	+	0.750891i	$0.729624\pi$
$468$	7.75007	0.358247
$469$	33.8967	1.56520
$470$	−0.128047	−0.00590637
$471$	−9.06767	−0.417816
$472$	−33.1350	−1.52516
$473$	−8.04066	−0.369710
$474$	−0.743888	−0.0341679
$475$	−8.68851	−0.398656
$476$	6.39788	0.293246
$477$	−9.29966	−0.425802
$478$	−12.9912	−0.594201
$479$	−3.22830	−0.147505	−0.0737524	−	0.997277i	$-0.523497\pi$
$479$	−3.22830	−0.147505	−0.0737524	+	0.997277i	$0.523497\pi$
$480$	−3.53070	−0.161154
$481$	58.3959	2.66262
$482$	10.4879	0.477711
$483$	8.80612	0.400692
$484$	5.38854	0.244934
$485$	3.32850	0.151140
$486$	−0.743888	−0.0337434
$487$	−4.21092	−0.190815	−0.0954074	−	0.995438i	$-0.530415\pi$
$487$	−4.21092	−0.190815	−0.0954074	+	0.995438i	$0.530415\pi$
$488$	22.5655	1.02149
$489$	2.82673	0.127829
$490$	−5.62789	−0.254242
$491$	8.50109	0.383649	0.191824	−	0.981429i	$-0.438560\pi$
$491$	8.50109	0.383649	0.191824	+	0.981429i	$0.438560\pi$
$492$	15.4875	0.698230
$493$	−1.22981	−0.0553880
$494$	7.46707	0.335959
$495$	−1.62475	−0.0730272
$496$	−7.81055	−0.350704
$497$	4.97650	0.223227
$498$	2.81801	0.126278
$499$	2.35554	0.105449	0.0527243	−	0.998609i	$-0.483210\pi$
$499$	2.35554	0.105449	0.0527243	+	0.998609i	$0.483210\pi$
$500$	8.39795	0.375568
$501$	19.8948	0.888834
$502$	1.95538	0.0872727
$503$	10.7265	0.478273	0.239137	−	0.970986i	$-0.423136\pi$
$503$	10.7265	0.478273	0.239137	+	0.970986i	$0.423136\pi$
$504$	11.3391	0.505086
$505$	−1.33276	−0.0593070
$506$	3.99515	0.177606
$507$	15.7009	0.697303
$508$	−9.32662	−0.413802
$509$	38.7098	1.71578	0.857890	−	0.513833i	$-0.171775\pi$
$509$	38.7098	1.71578	0.857890	+	0.513833i	$0.171775\pi$
$510$	0.448100	0.0198422
$511$	−36.6590	−1.62170
$512$	−10.8353	−0.478857
$513$	1.87368	0.0827248
$514$	22.3248	0.984704
$515$	−0.147003	−0.00647772
$516$	−4.31250	−0.189847
$517$	−0.770753	−0.0338977
$518$	35.8608	1.57563
$519$	−2.08076	−0.0913353
$520$	−8.27404	−0.362841
$521$	−14.2507	−0.624333	−0.312167	−	0.950027i	$-0.601055\pi$
$521$	−14.2507	−0.624333	−0.312167	+	0.950027i	$0.601055\pi$
$522$	−0.914842	−0.0400416
$523$	24.9112	1.08929	0.544646	−	0.838666i	$-0.316664\pi$
$523$	24.9112	1.08929	0.544646	+	0.838666i	$0.316664\pi$
$524$	−1.35758	−0.0593060
$525$	−20.5083	−0.895054
$526$	17.1706	0.748674
$527$	7.92143	0.345063
$528$	−2.65949	−0.115739
$529$	−19.0353	−0.827621
$530$	4.16718	0.181011
$531$	−12.9236	−0.560838
$532$	−11.9876	−0.519726
$533$	57.3550	2.48432
$534$	4.26869	0.184724
$535$	7.90223	0.341643
$536$	19.6508	0.848787
$537$	−6.95109	−0.299962
$538$	12.3799	0.533735
$539$	−33.8759	−1.45914
$540$	−0.871415	−0.0374997
$541$	−35.8127	−1.53971	−0.769854	−	0.638220i	$-0.779671\pi$
$541$	−35.8127	−1.53971	−0.769854	+	0.638220i	$0.779671\pi$
$542$	−23.8575	−1.02477
$543$	−26.6039	−1.14168
$544$	5.86129	0.251301
$545$	−1.83074	−0.0784201
$546$	17.6252	0.754288
$547$	7.15771	0.306041	0.153021	−	0.988223i	$-0.451100\pi$
$547$	7.15771	0.306041	0.153021	+	0.988223i	$0.451100\pi$
$548$	13.3982	0.572343
$549$	8.80121	0.375627
$550$	−9.30417	−0.396731
$551$	2.30427	0.0981652
$552$	5.10515	0.217290
$553$	4.42261	0.188068
$554$	14.0424	0.596606
$555$	−6.56601	−0.278712
$556$	−22.8614	−0.969538
$557$	−42.5321	−1.80214	−0.901072	−	0.433670i	$-0.857218\pi$
$557$	−42.5321	−1.80214	−0.901072	+	0.433670i	$0.857218\pi$
$558$	5.89265	0.249456
$559$	−15.9705	−0.675482
$560$	2.62678	0.111002
$561$	2.69724	0.113878
$562$	−18.3060	−0.772194
$563$	−11.4668	−0.483267	−0.241634	−	0.970368i	$-0.577683\pi$
$563$	−11.4668	−0.483267	−0.241634	+	0.970368i	$0.577683\pi$
$564$	−0.413383	−0.0174066
$565$	3.16587	0.133189
$566$	−19.5742	−0.822764
$567$	4.42261	0.185732
$568$	2.88501	0.121052
$569$	18.1421	0.760558	0.380279	−	0.924872i	$-0.375828\pi$
$569$	18.1421	0.760558	0.380279	+	0.924872i	$0.375828\pi$
$570$	−0.839594	−0.0351667
$571$	28.5793	1.19601	0.598004	−	0.801493i	$-0.295961\pi$
$571$	28.5793	1.19601	0.598004	+	0.801493i	$0.295961\pi$
$572$	−20.9038	−0.874033
$573$	2.02876	0.0847527
$574$	35.2216	1.47012
$575$	−9.23329	−0.385055
$576$	2.38813	0.0995056
$577$	36.9996	1.54031	0.770157	−	0.637854i	$-0.220178\pi$
$577$	36.9996	1.54031	0.770157	+	0.637854i	$0.220178\pi$
$578$	−0.743888	−0.0309416
$579$	9.47415	0.393732
$580$	−1.07168	−0.0444990
$581$	−16.7538	−0.695065
$582$	−4.11045	−0.170384
$583$	25.0834	1.03885
$584$	−21.2522	−0.879423
$585$	−3.22712	−0.133425
$586$	14.9286	0.616696
$587$	29.4378	1.21503	0.607515	−	0.794308i	$-0.292167\pi$
$587$	29.4378	1.21503	0.607515	+	0.794308i	$0.292167\pi$
$588$	−18.1689	−0.749272
$589$	−14.8422	−0.611562
$590$	5.79108	0.238415
$591$	6.98007	0.287122
$592$	−10.7476	−0.441725
$593$	9.49431	0.389885	0.194942	−	0.980815i	$-0.437548\pi$
$593$	9.49431	0.389885	0.194942	+	0.980815i	$0.437548\pi$
$594$	2.00644	0.0823254
$595$	−2.66407	−0.109216
$596$	4.73600	0.193994
$597$	9.39916	0.384682
$598$	7.93527	0.324497
$599$	19.8511	0.811092	0.405546	−	0.914075i	$-0.367081\pi$
$599$	19.8511	0.811092	0.405546	+	0.914075i	$0.367081\pi$
$600$	−11.8892	−0.485375
$601$	29.3314	1.19645	0.598226	−	0.801327i	$-0.295872\pi$
$601$	29.3314	1.19645	0.598226	+	0.801327i	$0.295872\pi$
$602$	−9.80748	−0.399723
$603$	7.66441	0.312119
$604$	−7.55551	−0.307429
$605$	−2.24378	−0.0912227
$606$	1.64586	0.0668584
$607$	−28.3069	−1.14894	−0.574470	−	0.818526i	$-0.694792\pi$
$607$	−28.3069	−1.14894	−0.574470	+	0.818526i	$0.694792\pi$
$608$	−10.9822	−0.445385
$609$	5.43898	0.220398
$610$	−3.94382	−0.159681
$611$	−1.53089	−0.0619331
$612$	1.44663	0.0584766
$613$	10.4264	0.421117	0.210558	−	0.977581i	$-0.432472\pi$
$613$	10.4264	0.421117	0.210558	+	0.977581i	$0.432472\pi$
$614$	10.5931	0.427503
$615$	−6.44897	−0.260048
$616$	−30.5844	−1.23228
$617$	17.0766	0.687480	0.343740	−	0.939065i	$-0.388306\pi$
$617$	17.0766	0.687480	0.343740	+	0.939065i	$0.388306\pi$
$618$	0.181537	0.00730250
$619$	−9.29477	−0.373588	−0.186794	−	0.982399i	$-0.559810\pi$
$619$	−9.29477	−0.373588	−0.186794	+	0.982399i	$0.559810\pi$
$620$	6.90285	0.277225
$621$	1.99116	0.0799025
$622$	20.8985	0.837955
$623$	−25.3785	−1.01677
$624$	−5.28234	−0.211463
$625$	19.6888	0.787553
$626$	1.71389	0.0685008
$627$	−5.05376	−0.201828
$628$	13.1176	0.523448
$629$	10.9002	0.434619
$630$	−1.98177	−0.0789556
$631$	20.0837	0.799519	0.399760	−	0.916620i	$-0.369094\pi$
$631$	20.0837	0.799519	0.399760	+	0.916620i	$0.369094\pi$
$632$	2.56391	0.101987
$633$	−14.5935	−0.580039
$634$	−11.2690	−0.447548
$635$	3.88359	0.154116
$636$	13.4532	0.533453
$637$	−67.2850	−2.66593
$638$	2.46755	0.0976913
$639$	1.12524	0.0445139
$640$	5.99127	0.236826
$641$	−9.26570	−0.365973	−0.182987	−	0.983115i	$-0.558577\pi$
$641$	−9.26570	−0.365973	−0.182987	+	0.983115i	$0.558577\pi$
$642$	−9.75865	−0.385143
$643$	−29.8971	−1.17903	−0.589513	−	0.807759i	$-0.700680\pi$
$643$	−29.8971	−1.17903	−0.589513	+	0.807759i	$0.700680\pi$
$644$	−12.7392	−0.501995
$645$	1.79572	0.0707065
$646$	1.39380	0.0548385
$647$	22.2182	0.873488	0.436744	−	0.899586i	$-0.356132\pi$
$647$	22.2182	0.873488	0.436744	+	0.899586i	$0.356132\pi$
$648$	2.56391	0.100720
$649$	34.8582	1.36830
$650$	−18.4802	−0.724852
$651$	−35.0333	−1.37307
$652$	−4.08924	−0.160147
$653$	−8.13489	−0.318343	−0.159171	−	0.987251i	$-0.550882\pi$
$653$	−8.13489	−0.318343	−0.159171	+	0.987251i	$0.550882\pi$
$654$	2.26082	0.0884050
$655$	0.565293	0.0220878
$656$	−10.5561	−0.412145
$657$	−8.28900	−0.323385
$658$	−0.940115	−0.0366495
$659$	−2.75929	−0.107487	−0.0537434	−	0.998555i	$-0.517115\pi$
$659$	−2.75929	−0.107487	−0.0537434	+	0.998555i	$0.517115\pi$
$660$	2.35042	0.0914899
$661$	−21.3366	−0.829898	−0.414949	−	0.909845i	$-0.636200\pi$
$661$	−21.3366	−0.829898	−0.414949	+	0.909845i	$0.636200\pi$
$662$	−17.6807	−0.687180
$663$	5.35733	0.208061
$664$	−9.71264	−0.376923
$665$	4.99160	0.193566
$666$	8.10852	0.314199
$667$	2.44875	0.0948161
$668$	−28.7804	−1.11355
$669$	19.9160	0.769996
$670$	−3.43442	−0.132683
$671$	−23.7390	−0.916434
$672$	−25.9222	−0.999970
$673$	−11.5487	−0.445168	−0.222584	−	0.974914i	$-0.571449\pi$
$673$	−11.5487	−0.445168	−0.222584	+	0.974914i	$0.571449\pi$
$674$	−20.2571	−0.780274
$675$	−4.63714	−0.178484
$676$	−22.7135	−0.873595
$677$	9.86018	0.378958	0.189479	−	0.981885i	$-0.439320\pi$
$677$	9.86018	0.378958	0.189479	+	0.981885i	$0.439320\pi$
$678$	−3.90961	−0.150148
$679$	24.4377	0.937832
$680$	−1.54443	−0.0592264
$681$	−17.3772	−0.665896
$682$	−15.8939	−0.608609
$683$	51.6404	1.97597	0.987983	−	0.154560i	$-0.0493959\pi$
$683$	51.6404	1.97597	0.987983	+	0.154560i	$0.0493959\pi$
$684$	−2.71052	−0.103639
$685$	−5.57900	−0.213163
$686$	−18.2901	−0.698321
$687$	−2.04644	−0.0780767
$688$	2.93934	0.112061
$689$	49.8213	1.89804
$690$	−0.892238	−0.0339669
$691$	−11.2853	−0.429313	−0.214657	−	0.976690i	$-0.568863\pi$
$691$	−11.2853	−0.429313	−0.214657	+	0.976690i	$0.568863\pi$
$692$	3.01009	0.114427
$693$	−11.9288	−0.453139
$694$	25.5879	0.971302
$695$	9.51945	0.361093
$696$	3.15312	0.119519
$697$	10.7059	0.405515
$698$	2.54891	0.0964775
$699$	−17.5577	−0.664093
$700$	29.6679	1.12134
$701$	24.8493	0.938546	0.469273	−	0.883053i	$-0.344516\pi$
$701$	24.8493	0.938546	0.469273	+	0.883053i	$0.344516\pi$
$702$	3.98525	0.150414
$703$	−20.4234	−0.770285
$704$	−6.44137	−0.242768
$705$	0.172132	0.00648288
$706$	7.61135	0.286457
$707$	−9.78505	−0.368005
$708$	18.6957	0.702628
$709$	−13.3378	−0.500911	−0.250455	−	0.968128i	$-0.580580\pi$
$709$	−13.3378	−0.500911	−0.250455	+	0.968128i	$0.580580\pi$
$710$	−0.504220	−0.0189231
$711$	1.00000	0.0375029
$712$	−14.7126	−0.551378
$713$	−15.7728	−0.590697
$714$	3.28992	0.123122
$715$	8.70433	0.325523
$716$	10.0557	0.375798
$717$	17.4639	0.652200
$718$	13.8896	0.518356
$719$	−0.130171	−0.00485455	−0.00242728	−	0.999997i	$-0.500773\pi$
$719$	−0.130171	−0.00485455	−0.00242728	+	0.999997i	$0.500773\pi$
$720$	0.593945	0.0221350
$721$	−1.07929	−0.0401947
$722$	11.5223	0.428817
$723$	−14.0988	−0.524340
$724$	38.4861	1.43032
$725$	−5.70282	−0.211797
$726$	2.77090	0.102838
$727$	36.7819	1.36416	0.682082	−	0.731276i	$-0.261075\pi$
$727$	36.7819	1.36416	0.682082	+	0.731276i	$0.261075\pi$
$728$	−60.7475	−2.25145
$729$	1.00000	0.0370370
$730$	3.71430	0.137472
$731$	−2.98107	−0.110259
$732$	−12.7321	−0.470592
$733$	12.1125	0.447385	0.223693	−	0.974660i	$-0.428189\pi$
$733$	12.1125	0.447385	0.223693	+	0.974660i	$0.428189\pi$
$734$	13.7154	0.506246
$735$	7.56550	0.279058
$736$	−11.6708	−0.430190
$737$	−20.6728	−0.761491
$738$	7.96399	0.293158
$739$	46.4714	1.70948	0.854739	−	0.519058i	$-0.173717\pi$
$739$	46.4714	1.70948	0.854739	+	0.519058i	$0.173717\pi$
$740$	9.49860	0.349175
$741$	−10.0379	−0.368751
$742$	30.5952	1.12318
$743$	−52.5346	−1.92731	−0.963654	−	0.267154i	$-0.913917\pi$
$743$	−52.5346	−1.92731	−0.963654	+	0.267154i	$0.913917\pi$
$744$	−20.3098	−0.744593
$745$	−1.97206	−0.0722508
$746$	−9.85772	−0.360917
$747$	−3.78822	−0.138604
$748$	−3.90191	−0.142668
$749$	58.0177	2.11992
$750$	4.31840	0.157686
$751$	1.02818	0.0375187	0.0187594	−	0.999824i	$-0.494028\pi$
$751$	1.02818	0.0375187	0.0187594	+	0.999824i	$0.494028\pi$
$752$	0.281756	0.0102746
$753$	−2.62859	−0.0957911
$754$	4.90111	0.178488
$755$	3.14610	0.114498
$756$	−6.39788	−0.232689
$757$	−3.16343	−0.114977	−0.0574885	−	0.998346i	$-0.518309\pi$
$757$	−3.16343	−0.114977	−0.0574885	+	0.998346i	$0.518309\pi$
$758$	−12.8796	−0.467808
$759$	−5.37064	−0.194942
$760$	2.89377	0.104968
$761$	16.8857	0.612108	0.306054	−	0.952014i	$-0.400991\pi$
$761$	16.8857	0.612108	0.306054	+	0.952014i	$0.400991\pi$
$762$	−4.79594	−0.173739
$763$	−13.4412	−0.486603
$764$	−2.93487	−0.106180
$765$	−0.602376	−0.0217789
$766$	12.4121	0.448466
$767$	69.2361	2.49997
$768$	−12.1750	−0.439329
$769$	−23.1440	−0.834592	−0.417296	−	0.908771i	$-0.637022\pi$
$769$	−23.1440	−0.834592	−0.417296	+	0.908771i	$0.637022\pi$
$770$	5.34531	0.192632
$771$	−30.0110	−1.08082
$772$	−13.7056	−0.493275
$773$	−9.16759	−0.329735	−0.164868	−	0.986316i	$-0.552720\pi$
$773$	−9.16759	−0.329735	−0.164868	+	0.986316i	$0.552720\pi$
$774$	−2.21758	−0.0797092
$775$	36.7328	1.31948
$776$	14.1672	0.508573
$777$	−48.2073	−1.72943
$778$	4.18481	0.150033
$779$	−20.0594	−0.718702
$780$	4.66846	0.167158
$781$	−3.03505	−0.108603
$782$	1.48120	0.0529676
$783$	1.22981	0.0439499
$784$	12.3837	0.442274
$785$	−5.46214	−0.194952
$786$	−0.698094	−0.0249002
$787$	24.1143	0.859582	0.429791	−	0.902928i	$-0.358587\pi$
$787$	24.1143	0.859582	0.429791	+	0.902928i	$0.358587\pi$
$788$	−10.0976	−0.359712
$789$	−23.0822	−0.821750
$790$	−0.448100	−0.0159427
$791$	23.2436	0.826448
$792$	−6.91547	−0.245731
$793$	−47.1510	−1.67438
$794$	12.8437	0.455805
$795$	−5.60189	−0.198679
$796$	−13.5971	−0.481937
$797$	−17.6614	−0.625600	−0.312800	−	0.949819i	$-0.601267\pi$
$797$	−17.6614	−0.625600	−0.312800	+	0.949819i	$0.601267\pi$
$798$	−6.16425	−0.218212
$799$	−0.285756	−0.0101093
$800$	27.1796	0.960945
$801$	−5.73835	−0.202755
$802$	9.18682	0.324398
$803$	22.3574	0.788977
$804$	−11.0876	−0.391029
$805$	5.30459	0.186962
$806$	−31.5689	−1.11197
$807$	−16.6421	−0.585831
$808$	−5.67266	−0.199564
$809$	19.9511	0.701442	0.350721	−	0.936480i	$-0.385937\pi$
$809$	19.9511	0.701442	0.350721	+	0.936480i	$0.385937\pi$
$810$	−0.448100	−0.0157446
$811$	36.2160	1.27171	0.635857	−	0.771807i	$-0.280647\pi$
$811$	36.2160	1.27171	0.635857	+	0.771807i	$0.280647\pi$
$812$	−7.86819	−0.276119
$813$	32.0713	1.12479
$814$	−21.8706	−0.766566
$815$	1.70275	0.0596449
$816$	−0.986004	−0.0345170
$817$	5.58555	0.195414
$818$	−7.09714	−0.248146
$819$	−23.6933	−0.827912
$820$	9.32928	0.325793
$821$	37.8244	1.32008	0.660040	−	0.751231i	$-0.270539\pi$
$821$	37.8244	1.32008	0.660040	+	0.751231i	$0.270539\pi$
$822$	6.88964	0.240304
$823$	48.8477	1.70272	0.851362	−	0.524579i	$-0.175777\pi$
$823$	48.8477	1.70272	0.851362	+	0.524579i	$0.175777\pi$
$824$	−0.625692	−0.0217970
$825$	12.5075	0.435455
$826$	42.5177	1.47938
$827$	−10.7005	−0.372093	−0.186046	−	0.982541i	$-0.559567\pi$
$827$	−10.7005	−0.372093	−0.186046	+	0.982541i	$0.559567\pi$
$828$	−2.88047	−0.100103
$829$	−48.0595	−1.66918	−0.834588	−	0.550874i	$-0.814294\pi$
$829$	−48.0595	−1.66918	−0.834588	+	0.550874i	$0.814294\pi$
$830$	1.69750	0.0589211
$831$	−18.8771	−0.654839
$832$	−12.7940	−0.443552
$833$	−12.5594	−0.435159
$834$	−11.7558	−0.407070
$835$	11.9841	0.414728
$836$	7.31092	0.252854
$837$	−7.92143	−0.273805
$838$	−9.86596	−0.340814
$839$	−22.7583	−0.785703	−0.392852	−	0.919602i	$-0.628511\pi$
$839$	−22.7583	−0.785703	−0.392852	+	0.919602i	$0.628511\pi$
$840$	6.83043	0.235672
$841$	−27.4876	−0.947847
$842$	−6.74804	−0.232553
$843$	24.6086	0.847566
$844$	21.1114	0.726684
$845$	9.45786	0.325360
$846$	−0.212570	−0.00730832
$847$	−16.4737	−0.566044
$848$	−9.16950	−0.314882
$849$	26.3133	0.903072
$850$	−3.44951	−0.118317
$851$	−21.7040	−0.744005
$852$	−1.62781	−0.0557678
$853$	−13.9479	−0.477568	−0.238784	−	0.971073i	$-0.576749\pi$
$853$	−13.9479	−0.477568	−0.238784	+	0.971073i	$0.576749\pi$
$854$	−28.9553	−0.990830
$855$	1.12866	0.0385992
$856$	33.6345	1.14960
$857$	−34.1794	−1.16755	−0.583774	−	0.811916i	$-0.698425\pi$
$857$	−34.1794	−1.16755	−0.583774	+	0.811916i	$0.698425\pi$
$858$	−10.7492	−0.366971
$859$	−25.3038	−0.863355	−0.431678	−	0.902028i	$-0.642078\pi$
$859$	−25.3038	−0.863355	−0.431678	+	0.902028i	$0.642078\pi$
$860$	−2.59775	−0.0885824
$861$	−47.3480	−1.61361
$862$	1.37418	0.0468047
$863$	−14.6453	−0.498533	−0.249267	−	0.968435i	$-0.580190\pi$
$863$	−14.6453	−0.498533	−0.249267	+	0.968435i	$0.580190\pi$
$864$	−5.86129	−0.199405
$865$	−1.25340	−0.0426169
$866$	10.7014	0.363647
$867$	1.00000	0.0339618
$868$	50.6803	1.72020
$869$	−2.69724	−0.0914976
$870$	−0.551079	−0.0186833
$871$	−41.0608	−1.39129
$872$	−7.79221	−0.263878
$873$	5.52563	0.187014
$874$	−2.77529	−0.0938755
$875$	−25.6740	−0.867940
$876$	11.9911	0.405143
$877$	23.8305	0.804700	0.402350	−	0.915486i	$-0.368193\pi$
$877$	23.8305	0.804700	0.402350	+	0.915486i	$0.368193\pi$
$878$	−23.1512	−0.781315
$879$	−20.0684	−0.676890
$880$	−1.60201	−0.0540038
$881$	0.317357	0.0106920	0.00534602	−	0.999986i	$-0.498298\pi$
$881$	0.317357	0.0106920	0.00534602	+	0.999986i	$0.498298\pi$
$882$	−9.34282	−0.314589
$883$	5.58030	0.187792	0.0938960	−	0.995582i	$-0.470068\pi$
$883$	5.58030	0.187792	0.0938960	+	0.995582i	$0.470068\pi$
$884$	−7.75007	−0.260663
$885$	−7.78488	−0.261686
$886$	6.16439	0.207097
$887$	−32.7845	−1.10080	−0.550398	−	0.834902i	$-0.685524\pi$
$887$	−32.7845	−1.10080	−0.550398	+	0.834902i	$0.685524\pi$
$888$	−27.9471	−0.937843
$889$	28.5131	0.956300
$890$	2.57135	0.0861920
$891$	−2.69724	−0.0903610
$892$	−28.8111	−0.964666
$893$	0.535414	0.0179169
$894$	2.43535	0.0814502
$895$	−4.18717	−0.139962
$896$	43.9876	1.46952
$897$	−10.6673	−0.356171
$898$	9.00962	0.300655
$899$	−9.74187	−0.324909
$900$	6.70824	0.223608
$901$	9.29966	0.309817
$902$	−21.4808	−0.715232
$903$	13.1841	0.438739
$904$	13.4750	0.448171
$905$	−16.0256	−0.532707
$906$	−3.88520	−0.129077
$907$	−20.5568	−0.682576	−0.341288	−	0.939959i	$-0.610863\pi$
$907$	−20.5568	−0.682576	−0.341288	+	0.939959i	$0.610863\pi$
$908$	25.1384	0.834247
$909$	−2.21251	−0.0733842
$910$	10.6170	0.351950
$911$	55.5054	1.83898	0.919489	−	0.393116i	$-0.128603\pi$
$911$	55.5054	1.83898	0.919489	+	0.393116i	$0.128603\pi$
$912$	1.84745	0.0611752
$913$	10.2177	0.338158
$914$	19.7888	0.654557
$915$	5.30164	0.175267
$916$	2.96045	0.0978160
$917$	4.15035	0.137057
$918$	0.743888	0.0245520
$919$	−29.0375	−0.957859	−0.478929	−	0.877853i	$-0.658975\pi$
$919$	−29.0375	−0.957859	−0.478929	+	0.877853i	$0.658975\pi$
$920$	3.07522	0.101387
$921$	−14.2402	−0.469231
$922$	−0.379299	−0.0124915
$923$	−6.02829	−0.198423
$924$	17.2566	0.567701
$925$	50.5458	1.66194
$926$	−17.2876	−0.568106
$927$	−0.244038	−0.00801528
$928$	−7.20829	−0.236624
$929$	54.3335	1.78262	0.891312	−	0.453391i	$-0.149786\pi$
$929$	54.3335	1.78262	0.891312	+	0.453391i	$0.149786\pi$
$930$	3.54959	0.116396
$931$	23.5323	0.771241
$932$	25.3995	0.831988
$933$	−28.0937	−0.919745
$934$	21.2334	0.694779
$935$	1.62475	0.0531351
$936$	−13.7357	−0.448965
$937$	26.5975	0.868901	0.434451	−	0.900696i	$-0.356943\pi$
$937$	26.5975	0.868901	0.434451	+	0.900696i	$0.356943\pi$
$938$	−25.2153	−0.823310
$939$	−2.30396	−0.0751870
$940$	−0.249012	−0.00812188
$941$	9.20971	0.300228	0.150114	−	0.988669i	$-0.452036\pi$
$941$	9.20971	0.300228	0.150114	+	0.988669i	$0.452036\pi$
$942$	6.74533	0.219775
$943$	−21.3172	−0.694182
$944$	−12.7427	−0.414741
$945$	2.66407	0.0866622
$946$	5.98134	0.194470
$947$	−37.3269	−1.21296	−0.606481	−	0.795098i	$-0.707419\pi$
$947$	−37.3269	−1.21296	−0.606481	+	0.795098i	$0.707419\pi$
$948$	−1.44663	−0.0469844
$949$	44.4069	1.44151
$950$	6.46327	0.209696
$951$	15.1488	0.491232
$952$	−11.3391	−0.367504
$953$	35.1837	1.13971	0.569856	−	0.821745i	$-0.306999\pi$
$953$	35.1837	1.13971	0.569856	+	0.821745i	$0.306999\pi$
$954$	6.91790	0.223975
$955$	1.22208	0.0395455
$956$	−25.2638	−0.817089
$957$	−3.31710	−0.107227
$958$	2.40149	0.0775887
$959$	−40.9607	−1.32269
$960$	1.43855	0.0464291
$961$	31.7490	1.02416
$962$	−43.4400	−1.40056
$963$	13.1184	0.422736
$964$	20.3957	0.656903
$965$	5.70700	0.183715
$966$	−6.55076	−0.210767
$967$	47.2033	1.51796	0.758978	−	0.651117i	$-0.225699\pi$
$967$	47.2033	1.51796	0.758978	+	0.651117i	$0.225699\pi$
$968$	−9.55027	−0.306957
$969$	−1.87368	−0.0601911
$970$	−2.47603	−0.0795007
$971$	29.6524	0.951591	0.475796	−	0.879556i	$-0.342160\pi$
$971$	29.6524	0.951591	0.475796	+	0.879556i	$0.342160\pi$
$972$	−1.44663	−0.0464007
$973$	69.8912	2.24061
$974$	3.13245	0.100370
$975$	24.8427	0.795603
$976$	8.67803	0.277777
$977$	16.5917	0.530815	0.265408	−	0.964136i	$-0.414493\pi$
$977$	16.5917	0.530815	0.265408	+	0.964136i	$0.414493\pi$
$978$	−2.10277	−0.0672392
$979$	15.4777	0.494670
$980$	−10.9445	−0.349609
$981$	−3.03919	−0.0970340
$982$	−6.32386	−0.201802
$983$	32.5709	1.03885	0.519426	−	0.854516i	$-0.326146\pi$
$983$	32.5709	1.03885	0.519426	+	0.854516i	$0.326146\pi$
$984$	−27.4489	−0.875040
$985$	4.20462	0.133970
$986$	0.914842	0.0291345
$987$	1.26379	0.0402267
$988$	14.5211	0.461979
$989$	5.93578	0.188747
$990$	1.20863	0.0384129
$991$	−32.3282	−1.02694	−0.513470	−	0.858108i	$-0.671640\pi$
$991$	−32.3282	−1.02694	−0.513470	+	0.858108i	$0.671640\pi$
$992$	46.4298	1.47415
$993$	23.7680	0.754254
$994$	−3.70196	−0.117419
$995$	5.66183	0.179492
$996$	5.48015	0.173645
$997$	−9.00173	−0.285088	−0.142544	−	0.989788i	$-0.545528\pi$
$997$	−9.00173	−0.285088	−0.142544	+	0.989788i	$0.545528\pi$
$998$	−1.75226	−0.0554668
$999$	−10.9002	−0.344867

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.h.1.11	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.h.1.11	✓	25	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-0.743888 q^{2} +1.00000 q^{3} -1.44663 q^{4} +0.602376 q^{5} -0.743888 q^{6} +4.42261 q^{7} +2.56391 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.743888 q^{2} +1.00000 q^{3} -1.44663 q^{4} +0.602376 q^{5} -0.743888 q^{6} +4.42261 q^{7} +2.56391 q^{8} +1.00000 q^{9} -0.448100 q^{10} -2.69724 q^{11} -1.44663 q^{12} -5.35733 q^{13} -3.28992 q^{14} +0.602376 q^{15} +0.986004 q^{16} -1.00000 q^{17} -0.743888 q^{18} +1.87368 q^{19} -0.871415 q^{20} +4.42261 q^{21} +2.00644 q^{22} +1.99116 q^{23} +2.56391 q^{24} -4.63714 q^{25} +3.98525 q^{26} +1.00000 q^{27} -6.39788 q^{28} +1.22981 q^{29} -0.448100 q^{30} -7.92143 q^{31} -5.86129 q^{32} -2.69724 q^{33} +0.743888 q^{34} +2.66407 q^{35} -1.44663 q^{36} -10.9002 q^{37} -1.39380 q^{38} -5.35733 q^{39} +1.54443 q^{40} -10.7059 q^{41} -3.28992 q^{42} +2.98107 q^{43} +3.90191 q^{44} +0.602376 q^{45} -1.48120 q^{46} +0.285756 q^{47} +0.986004 q^{48} +12.5594 q^{49} +3.44951 q^{50} -1.00000 q^{51} +7.75007 q^{52} -9.29966 q^{53} -0.743888 q^{54} -1.62475 q^{55} +11.3391 q^{56} +1.87368 q^{57} -0.914842 q^{58} -12.9236 q^{59} -0.871415 q^{60} +8.80121 q^{61} +5.89265 q^{62} +4.42261 q^{63} +2.38813 q^{64} -3.22712 q^{65} +2.00644 q^{66} +7.66441 q^{67} +1.44663 q^{68} +1.99116 q^{69} -1.98177 q^{70} +1.12524 q^{71} +2.56391 q^{72} -8.28900 q^{73} +8.10852 q^{74} -4.63714 q^{75} -2.71052 q^{76} -11.9288 q^{77} +3.98525 q^{78} +1.00000 q^{79} +0.593945 q^{80} +1.00000 q^{81} +7.96399 q^{82} -3.78822 q^{83} -6.39788 q^{84} -0.602376 q^{85} -2.21758 q^{86} +1.22981 q^{87} -6.91547 q^{88} -5.73835 q^{89} -0.448100 q^{90} -23.6933 q^{91} -2.88047 q^{92} -7.92143 q^{93} -0.212570 q^{94} +1.12866 q^{95} -5.86129 q^{96} +5.52563 q^{97} -9.34282 q^{98} -2.69724 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 7 q^{2} + 25 q^{3} + 21 q^{4} - 12 q^{5} - 7 q^{6} - 4 q^{7} - 21 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q - 7 * q^2 + 25 * q^3 + 21 * q^4 - 12 * q^5 - 7 * q^6 - 4 * q^7 - 21 * q^8 + 25 * q^9	\( 25 q - 7 q^{2} + 25 q^{3} + 21 q^{4} - 12 q^{5} - 7 q^{6} - 4 q^{7} - 21 q^{8} + 25 q^{9} - 9 q^{10} - 19 q^{11} + 21 q^{12} - 12 q^{13} - 15 q^{14} - 12 q^{15} + q^{16} - 25 q^{17} - 7 q^{18} - 35 q^{19} - 11 q^{20} - 4 q^{21} - 2 q^{22} - 16 q^{23} - 21 q^{24} + 19 q^{25} - 5 q^{26} + 25 q^{27} + 3 q^{28} - 37 q^{29} - 9 q^{30} - 28 q^{31} - 19 q^{32} - 19 q^{33} + 7 q^{34} - 42 q^{35} + 21 q^{36} + 8 q^{37} - 35 q^{38} - 12 q^{39} - 9 q^{40} - 34 q^{41} - 15 q^{42} - 19 q^{43} - 56 q^{44} - 12 q^{45} + q^{46} - 25 q^{47} + q^{48} + 25 q^{49} - 7 q^{50} - 25 q^{51} - 37 q^{52} - 44 q^{53} - 7 q^{54} - 11 q^{55} - 18 q^{56} - 35 q^{57} - 3 q^{58} - 47 q^{59} - 11 q^{60} - 28 q^{61} + 11 q^{62} - 4 q^{63} - 9 q^{64} - 63 q^{65} - 2 q^{66} - 28 q^{67} - 21 q^{68} - 16 q^{69} + 5 q^{70} - 27 q^{71} - 21 q^{72} - 21 q^{73} - 18 q^{74} + 19 q^{75} - 50 q^{76} - 58 q^{77} - 5 q^{78} + 25 q^{79} - 56 q^{80} + 25 q^{81} - 5 q^{82} - 61 q^{83} + 3 q^{84} + 12 q^{85} - 28 q^{86} - 37 q^{87} + 15 q^{88} - 34 q^{89} - 9 q^{90} - 30 q^{91} - 31 q^{92} - 28 q^{93} + q^{94} - 32 q^{95} - 19 q^{96} - 11 q^{97} - 66 q^{98} - 19 q^{99}+O(q^{100}) \) 25 * q - 7 * q^2 + 25 * q^3 + 21 * q^4 - 12 * q^5 - 7 * q^6 - 4 * q^7 - 21 * q^8 + 25 * q^9 - 9 * q^10 - 19 * q^11 + 21 * q^12 - 12 * q^13 - 15 * q^14 - 12 * q^15 + q^16 - 25 * q^17 - 7 * q^18 - 35 * q^19 - 11 * q^20 - 4 * q^21 - 2 * q^22 - 16 * q^23 - 21 * q^24 + 19 * q^25 - 5 * q^26 + 25 * q^27 + 3 * q^28 - 37 * q^29 - 9 * q^30 - 28 * q^31 - 19 * q^32 - 19 * q^33 + 7 * q^34 - 42 * q^35 + 21 * q^36 + 8 * q^37 - 35 * q^38 - 12 * q^39 - 9 * q^40 - 34 * q^41 - 15 * q^42 - 19 * q^43 - 56 * q^44 - 12 * q^45 + q^46 - 25 * q^47 + q^48 + 25 * q^49 - 7 * q^50 - 25 * q^51 - 37 * q^52 - 44 * q^53 - 7 * q^54 - 11 * q^55 - 18 * q^56 - 35 * q^57 - 3 * q^58 - 47 * q^59 - 11 * q^60 - 28 * q^61 + 11 * q^62 - 4 * q^63 - 9 * q^64 - 63 * q^65 - 2 * q^66 - 28 * q^67 - 21 * q^68 - 16 * q^69 + 5 * q^70 - 27 * q^71 - 21 * q^72 - 21 * q^73 - 18 * q^74 + 19 * q^75 - 50 * q^76 - 58 * q^77 - 5 * q^78 + 25 * q^79 - 56 * q^80 + 25 * q^81 - 5 * q^82 - 61 * q^83 + 3 * q^84 + 12 * q^85 - 28 * q^86 - 37 * q^87 + 15 * q^88 - 34 * q^89 - 9 * q^90 - 30 * q^91 - 31 * q^92 - 28 * q^93 + q^94 - 32 * q^95 - 19 * q^96 - 11 * q^97 - 66 * q^98 - 19 * q^99

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