LMFDB - Embedded newform 4034.2.a.d.1.20

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			1.20
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)

$f(q)$	$=$	$q+1.00000 q^{2} -0.550547 q^{3} +1.00000 q^{4} +0.337407 q^{5} -0.550547 q^{6} +1.25225 q^{7} +1.00000 q^{8} -2.69690 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.550547 q^{3} +1.00000 q^{4} +0.337407 q^{5} -0.550547 q^{6} +1.25225 q^{7} +1.00000 q^{8} -2.69690 q^{9} +0.337407 q^{10} +4.84850 q^{11} -0.550547 q^{12} +5.51433 q^{13} +1.25225 q^{14} -0.185759 q^{15} +1.00000 q^{16} +1.55974 q^{17} -2.69690 q^{18} +2.11267 q^{19} +0.337407 q^{20} -0.689425 q^{21} +4.84850 q^{22} -3.60861 q^{23} -0.550547 q^{24} -4.88616 q^{25} +5.51433 q^{26} +3.13641 q^{27} +1.25225 q^{28} -7.56691 q^{29} -0.185759 q^{30} +9.14450 q^{31} +1.00000 q^{32} -2.66933 q^{33} +1.55974 q^{34} +0.422520 q^{35} -2.69690 q^{36} +8.35997 q^{37} +2.11267 q^{38} -3.03590 q^{39} +0.337407 q^{40} -8.23774 q^{41} -0.689425 q^{42} +4.67088 q^{43} +4.84850 q^{44} -0.909953 q^{45} -3.60861 q^{46} +2.43442 q^{47} -0.550547 q^{48} -5.43186 q^{49} -4.88616 q^{50} -0.858711 q^{51} +5.51433 q^{52} +10.2173 q^{53} +3.13641 q^{54} +1.63592 q^{55} +1.25225 q^{56} -1.16313 q^{57} -7.56691 q^{58} -13.2802 q^{59} -0.185759 q^{60} -6.78275 q^{61} +9.14450 q^{62} -3.37720 q^{63} +1.00000 q^{64} +1.86057 q^{65} -2.66933 q^{66} -1.78663 q^{67} +1.55974 q^{68} +1.98671 q^{69} +0.422520 q^{70} +1.41159 q^{71} -2.69690 q^{72} +5.62943 q^{73} +8.35997 q^{74} +2.69006 q^{75} +2.11267 q^{76} +6.07155 q^{77} -3.03590 q^{78} +11.6421 q^{79} +0.337407 q^{80} +6.36395 q^{81} -8.23774 q^{82} +2.29357 q^{83} -0.689425 q^{84} +0.526268 q^{85} +4.67088 q^{86} +4.16594 q^{87} +4.84850 q^{88} -7.46599 q^{89} -0.909953 q^{90} +6.90534 q^{91} -3.60861 q^{92} -5.03448 q^{93} +2.43442 q^{94} +0.712831 q^{95} -0.550547 q^{96} -0.461813 q^{97} -5.43186 q^{98} -13.0759 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.550547	−0.317858	−0.158929	−	0.987290i	$-0.550804\pi$
$3$	−0.550547	−0.317858	−0.158929	+	0.987290i	$0.550804\pi$
$4$	1.00000	0.500000
$5$	0.337407	0.150893	0.0754465	−	0.997150i	$-0.475962\pi$
$5$	0.337407	0.150893	0.0754465	+	0.997150i	$0.475962\pi$
$6$	−0.550547	−0.224760
$7$	1.25225	0.473308	0.236654	−	0.971594i	$-0.423949\pi$
$7$	1.25225	0.473308	0.236654	+	0.971594i	$0.423949\pi$
$8$	1.00000	0.353553
$9$	−2.69690	−0.898966
$10$	0.337407	0.106698
$11$	4.84850	1.46188	0.730939	−	0.682443i	$-0.239082\pi$
$11$	4.84850	1.46188	0.730939	+	0.682443i	$0.239082\pi$
$12$	−0.550547	−0.158929
$13$	5.51433	1.52940	0.764700	−	0.644386i	$-0.222887\pi$
$13$	5.51433	1.52940	0.764700	+	0.644386i	$0.222887\pi$
$14$	1.25225	0.334679
$15$	−0.185759	−0.0479626
$16$	1.00000	0.250000
$17$	1.55974	0.378293	0.189146	−	0.981949i	$-0.439428\pi$
$17$	1.55974	0.378293	0.189146	+	0.981949i	$0.439428\pi$
$18$	−2.69690	−0.635665
$19$	2.11267	0.484680	0.242340	−	0.970191i	$-0.422085\pi$
$19$	2.11267	0.484680	0.242340	+	0.970191i	$0.422085\pi$
$20$	0.337407	0.0754465
$21$	−0.689425	−0.150445
$22$	4.84850	1.03370
$23$	−3.60861	−0.752446	−0.376223	−	0.926529i	$-0.622777\pi$
$23$	−3.60861	−0.752446	−0.376223	+	0.926529i	$0.622777\pi$
$24$	−0.550547	−0.112380
$25$	−4.88616	−0.977231
$26$	5.51433	1.08145
$27$	3.13641	0.603602
$28$	1.25225	0.236654
$29$	−7.56691	−1.40514	−0.702570	−	0.711614i	$-0.747964\pi$
$29$	−7.56691	−1.40514	−0.702570	+	0.711614i	$0.747964\pi$
$30$	−0.185759	−0.0339147
$31$	9.14450	1.64240	0.821200	−	0.570641i	$-0.193305\pi$
$31$	9.14450	1.64240	0.821200	+	0.570641i	$0.193305\pi$
$32$	1.00000	0.176777
$33$	−2.66933	−0.464670
$34$	1.55974	0.267494
$35$	0.422520	0.0714188
$36$	−2.69690	−0.449483
$37$	8.35997	1.37437	0.687185	−	0.726482i	$-0.258846\pi$
$37$	8.35997	1.37437	0.687185	+	0.726482i	$0.258846\pi$
$38$	2.11267	0.342721
$39$	−3.03590	−0.486133
$40$	0.337407	0.0533488
$41$	−8.23774	−1.28652	−0.643259	−	0.765648i	$-0.722418\pi$
$41$	−8.23774	−1.28652	−0.643259	+	0.765648i	$0.722418\pi$
$42$	−0.689425	−0.106381
$43$	4.67088	0.712302	0.356151	−	0.934428i	$-0.384089\pi$
$43$	4.67088	0.712302	0.356151	+	0.934428i	$0.384089\pi$
$44$	4.84850	0.730939
$45$	−0.909953	−0.135648
$46$	−3.60861	−0.532060
$47$	2.43442	0.355096	0.177548	−	0.984112i	$-0.443184\pi$
$47$	2.43442	0.355096	0.177548	+	0.984112i	$0.443184\pi$
$48$	−0.550547	−0.0794646
$49$	−5.43186	−0.775980
$50$	−4.88616	−0.691007
$51$	−0.858711	−0.120244
$52$	5.51433	0.764700
$53$	10.2173	1.40346	0.701728	−	0.712445i	$-0.252412\pi$
$53$	10.2173	1.40346	0.701728	+	0.712445i	$0.252412\pi$
$54$	3.13641	0.426811
$55$	1.63592	0.220587
$56$	1.25225	0.167340
$57$	−1.16313	−0.154060
$58$	−7.56691	−0.993584
$59$	−13.2802	−1.72893	−0.864467	−	0.502689i	$-0.832344\pi$
$59$	−13.2802	−1.72893	−0.864467	+	0.502689i	$0.832344\pi$
$60$	−0.185759	−0.0239813
$61$	−6.78275	−0.868442	−0.434221	−	0.900806i	$-0.642976\pi$
$61$	−6.78275	−0.868442	−0.434221	+	0.900806i	$0.642976\pi$
$62$	9.14450	1.16135
$63$	−3.37720	−0.425487
$64$	1.00000	0.125000
$65$	1.86057	0.230776
$66$	−2.66933	−0.328571
$67$	−1.78663	−0.218272	−0.109136	−	0.994027i	$-0.534808\pi$
$67$	−1.78663	−0.218272	−0.109136	+	0.994027i	$0.534808\pi$
$68$	1.55974	0.189146
$69$	1.98671	0.239171
$70$	0.422520	0.0505007
$71$	1.41159	0.167525	0.0837624	−	0.996486i	$-0.473306\pi$
$71$	1.41159	0.167525	0.0837624	+	0.996486i	$0.473306\pi$
$72$	−2.69690	−0.317832
$73$	5.62943	0.658875	0.329437	−	0.944177i	$-0.393141\pi$
$73$	5.62943	0.658875	0.329437	+	0.944177i	$0.393141\pi$
$74$	8.35997	0.971827
$75$	2.69006	0.310621
$76$	2.11267	0.242340
$77$	6.07155	0.691918
$78$	−3.03590	−0.343748
$79$	11.6421	1.30984	0.654921	−	0.755698i	$-0.272702\pi$
$79$	11.6421	1.30984	0.654921	+	0.755698i	$0.272702\pi$
$80$	0.337407	0.0377233
$81$	6.36395	0.707106
$82$	−8.23774	−0.909706
$83$	2.29357	0.251752	0.125876	−	0.992046i	$-0.459826\pi$
$83$	2.29357	0.251752	0.125876	+	0.992046i	$0.459826\pi$
$84$	−0.689425	−0.0752224
$85$	0.526268	0.0570818
$86$	4.67088	0.503674
$87$	4.16594	0.446636
$88$	4.84850	0.516852
$89$	−7.46599	−0.791393	−0.395696	−	0.918381i	$-0.629497\pi$
$89$	−7.46599	−0.791393	−0.395696	+	0.918381i	$0.629497\pi$
$90$	−0.909953	−0.0959174
$91$	6.90534	0.723877
$92$	−3.60861	−0.376223
$93$	−5.03448	−0.522051
$94$	2.43442	0.251091
$95$	0.712831	0.0731349
$96$	−0.550547	−0.0561900
$97$	−0.461813	−0.0468900	−0.0234450	−	0.999725i	$-0.507463\pi$
$97$	−0.461813	−0.0468900	−0.0234450	+	0.999725i	$0.507463\pi$
$98$	−5.43186	−0.548701
$99$	−13.0759	−1.31418
$100$	−4.88616	−0.488616
$101$	−6.77064	−0.673704	−0.336852	−	0.941558i	$-0.609362\pi$
$101$	−6.77064	−0.673704	−0.336852	+	0.941558i	$0.609362\pi$
$102$	−0.858711	−0.0850251
$103$	4.82410	0.475332	0.237666	−	0.971347i	$-0.423618\pi$
$103$	4.82410	0.475332	0.237666	+	0.971347i	$0.423618\pi$
$104$	5.51433	0.540725
$105$	−0.232617	−0.0227011
$106$	10.2173	0.992393
$107$	−5.68837	−0.549916	−0.274958	−	0.961456i	$-0.588664\pi$
$107$	−5.68837	−0.549916	−0.274958	+	0.961456i	$0.588664\pi$
$108$	3.13641	0.301801
$109$	6.59457	0.631646	0.315823	−	0.948818i	$-0.397719\pi$
$109$	6.59457	0.631646	0.315823	+	0.948818i	$0.397719\pi$
$110$	1.63592	0.155979
$111$	−4.60256	−0.436855
$112$	1.25225	0.118327
$113$	13.6251	1.28175	0.640873	−	0.767647i	$-0.278573\pi$
$113$	13.6251	1.28175	0.640873	+	0.767647i	$0.278573\pi$
$114$	−1.16313	−0.108937
$115$	−1.21757	−0.113539
$116$	−7.56691	−0.702570
$117$	−14.8716	−1.37488
$118$	−13.2802	−1.22254
$119$	1.95319	0.179049
$120$	−0.185759	−0.0169574
$121$	12.5079	1.13709
$122$	−6.78275	−0.614081
$123$	4.53526	0.408931
$124$	9.14450	0.821200
$125$	−3.33566	−0.298351
$126$	−3.37720	−0.300865
$127$	4.41015	0.391338	0.195669	−	0.980670i	$-0.437312\pi$
$127$	4.41015	0.391338	0.195669	+	0.980670i	$0.437312\pi$
$128$	1.00000	0.0883883
$129$	−2.57154	−0.226411
$130$	1.86057	0.163183
$131$	19.6122	1.71352	0.856762	−	0.515712i	$-0.172473\pi$
$131$	19.6122	1.71352	0.856762	+	0.515712i	$0.172473\pi$
$132$	−2.66933	−0.232335
$133$	2.64560	0.229403
$134$	−1.78663	−0.154342
$135$	1.05825	0.0910794
$136$	1.55974	0.133747
$137$	6.30047	0.538285	0.269143	−	0.963100i	$-0.413260\pi$
$137$	6.30047	0.538285	0.269143	+	0.963100i	$0.413260\pi$
$138$	1.98671	0.169120
$139$	2.21497	0.187871	0.0939355	−	0.995578i	$-0.470055\pi$
$139$	2.21497	0.187871	0.0939355	+	0.995578i	$0.470055\pi$
$140$	0.422520	0.0357094
$141$	−1.34026	−0.112870
$142$	1.41159	0.118458
$143$	26.7362	2.23580
$144$	−2.69690	−0.224741
$145$	−2.55313	−0.212026
$146$	5.62943	0.465895
$147$	2.99049	0.246652
$148$	8.35997	0.687185
$149$	−17.5872	−1.44080	−0.720398	−	0.693561i	$-0.756041\pi$
$149$	−17.5872	−1.44080	−0.720398	+	0.693561i	$0.756041\pi$
$150$	2.69006	0.219642
$151$	23.5027	1.91262	0.956310	−	0.292354i	$-0.0944386\pi$
$151$	23.5027	1.91262	0.956310	+	0.292354i	$0.0944386\pi$
$152$	2.11267	0.171360
$153$	−4.20646	−0.340072
$154$	6.07155	0.489260
$155$	3.08542	0.247827
$156$	−3.03590	−0.243066
$157$	19.0240	1.51828	0.759140	−	0.650928i	$-0.225620\pi$
$157$	19.0240	1.51828	0.759140	+	0.650928i	$0.225620\pi$
$158$	11.6421	0.926198
$159$	−5.62511	−0.446100
$160$	0.337407	0.0266744
$161$	−4.51889	−0.356138
$162$	6.36395	0.499999
$163$	−20.1306	−1.57675	−0.788376	−	0.615194i	$-0.789078\pi$
$163$	−20.1306	−1.57675	−0.788376	+	0.615194i	$0.789078\pi$
$164$	−8.23774	−0.643259
$165$	−0.900650	−0.0701155
$166$	2.29357	0.178016
$167$	2.67577	0.207058	0.103529	−	0.994626i	$-0.466987\pi$
$167$	2.67577	0.207058	0.103529	+	0.994626i	$0.466987\pi$
$168$	−0.689425	−0.0531903
$169$	17.4078	1.33907
$170$	0.526268	0.0403629
$171$	−5.69766	−0.435711
$172$	4.67088	0.356151
$173$	−0.473939	−0.0360329	−0.0180165	−	0.999838i	$-0.505735\pi$
$173$	−0.473939	−0.0360329	−0.0180165	+	0.999838i	$0.505735\pi$
$174$	4.16594	0.315819
$175$	−6.11871	−0.462531
$176$	4.84850	0.365469
$177$	7.31137	0.549557
$178$	−7.46599	−0.559599
$179$	−13.3624	−0.998753	−0.499377	−	0.866385i	$-0.666438\pi$
$179$	−13.3624	−0.998753	−0.499377	+	0.866385i	$0.666438\pi$
$180$	−0.909953	−0.0678239
$181$	13.0898	0.972956	0.486478	−	0.873693i	$-0.338281\pi$
$181$	13.0898	0.972956	0.486478	+	0.873693i	$0.338281\pi$
$182$	6.90534	0.511858
$183$	3.73422	0.276042
$184$	−3.60861	−0.266030
$185$	2.82071	0.207383
$186$	−5.03448	−0.369146
$187$	7.56241	0.553018
$188$	2.43442	0.177548
$189$	3.92758	0.285690
$190$	0.712831	0.0517142
$191$	13.8214	1.00008	0.500041	−	0.866002i	$-0.333318\pi$
$191$	13.8214	1.00008	0.500041	+	0.866002i	$0.333318\pi$
$192$	−0.550547	−0.0397323
$193$	1.23168	0.0886582	0.0443291	−	0.999017i	$-0.485885\pi$
$193$	1.23168	0.0886582	0.0443291	+	0.999017i	$0.485885\pi$
$194$	−0.461813	−0.0331563
$195$	−1.02433	−0.0733541
$196$	−5.43186	−0.387990
$197$	8.14270	0.580144	0.290072	−	0.957005i	$-0.406321\pi$
$197$	8.14270	0.580144	0.290072	+	0.957005i	$0.406321\pi$
$198$	−13.0759	−0.929264
$199$	−21.2310	−1.50502	−0.752511	−	0.658579i	$-0.771158\pi$
$199$	−21.2310	−1.50502	−0.752511	+	0.658579i	$0.771158\pi$
$200$	−4.88616	−0.345503
$201$	0.983626	0.0693796
$202$	−6.77064	−0.476381
$203$	−9.47570	−0.665064
$204$	−0.858711	−0.0601218
$205$	−2.77947	−0.194127
$206$	4.82410	0.336111
$207$	9.73204	0.676424
$208$	5.51433	0.382350
$209$	10.2433	0.708543
$210$	−0.232617	−0.0160521
$211$	−26.7233	−1.83971	−0.919856	−	0.392257i	$-0.871694\pi$
$211$	−26.7233	−1.83971	−0.919856	+	0.392257i	$0.871694\pi$
$212$	10.2173	0.701728
$213$	−0.777147	−0.0532492
$214$	−5.68837	−0.388849
$215$	1.57599	0.107481
$216$	3.13641	0.213406
$217$	11.4512	0.777360
$218$	6.59457	0.446641
$219$	−3.09927	−0.209429
$220$	1.63592	0.110294
$221$	8.60093	0.578561
$222$	−4.60256	−0.308903
$223$	12.8063	0.857574	0.428787	−	0.903406i	$-0.358941\pi$
$223$	12.8063	0.857574	0.428787	+	0.903406i	$0.358941\pi$
$224$	1.25225	0.0836698
$225$	13.1775	0.878498
$226$	13.6251	0.906331
$227$	−19.0380	−1.26359	−0.631797	−	0.775134i	$-0.717682\pi$
$227$	−19.0380	−1.26359	−0.631797	+	0.775134i	$0.717682\pi$
$228$	−1.16313	−0.0770299
$229$	−0.294814	−0.0194819	−0.00974094	−	0.999953i	$-0.503101\pi$
$229$	−0.294814	−0.0194819	−0.00974094	+	0.999953i	$0.503101\pi$
$230$	−1.21757	−0.0802841
$231$	−3.34268	−0.219932
$232$	−7.56691	−0.496792
$233$	27.3480	1.79163	0.895814	−	0.444429i	$-0.146593\pi$
$233$	27.3480	1.79163	0.895814	+	0.444429i	$0.146593\pi$
$234$	−14.8716	−0.972186
$235$	0.821389	0.0535815
$236$	−13.2802	−0.864467
$237$	−6.40954	−0.416344
$238$	1.95319	0.126607
$239$	−10.0612	−0.650805	−0.325403	−	0.945576i	$-0.605500\pi$
$239$	−10.0612	−0.650805	−0.325403	+	0.945576i	$0.605500\pi$
$240$	−0.185759	−0.0119907
$241$	−17.7231	−1.14165	−0.570823	−	0.821073i	$-0.693376\pi$
$241$	−17.7231	−1.14165	−0.570823	+	0.821073i	$0.693376\pi$
$242$	12.5079	0.804041
$243$	−12.9129	−0.828362
$244$	−6.78275	−0.434221
$245$	−1.83275	−0.117090
$246$	4.53526	0.289158
$247$	11.6500	0.741270
$248$	9.14450	0.580676
$249$	−1.26272	−0.0800216
$250$	−3.33566	−0.210966
$251$	0.608615	0.0384154	0.0192077	−	0.999816i	$-0.493886\pi$
$251$	0.608615	0.0384154	0.0192077	+	0.999816i	$0.493886\pi$
$252$	−3.37720	−0.212744
$253$	−17.4963	−1.09998
$254$	4.41015	0.276718
$255$	−0.289735	−0.0181439
$256$	1.00000	0.0625000
$257$	16.5189	1.03042	0.515212	−	0.857063i	$-0.327713\pi$
$257$	16.5189	1.03042	0.515212	+	0.857063i	$0.327713\pi$
$258$	−2.57154	−0.160097
$259$	10.4688	0.650500
$260$	1.86057	0.115388
$261$	20.4072	1.26317
$262$	19.6122	1.21164
$263$	16.3838	1.01027	0.505134	−	0.863041i	$-0.331443\pi$
$263$	16.3838	1.01027	0.505134	+	0.863041i	$0.331443\pi$
$264$	−2.66933	−0.164286
$265$	3.44739	0.211772
$266$	2.64560	0.162212
$267$	4.11038	0.251551
$268$	−1.78663	−0.109136
$269$	−20.4975	−1.24975	−0.624876	−	0.780724i	$-0.714851\pi$
$269$	−20.4975	−1.24975	−0.624876	+	0.780724i	$0.714851\pi$
$270$	1.05825	0.0644029
$271$	−25.7751	−1.56572	−0.782862	−	0.622195i	$-0.786241\pi$
$271$	−25.7751	−1.56572	−0.782862	+	0.622195i	$0.786241\pi$
$272$	1.55974	0.0945732
$273$	−3.80172	−0.230090
$274$	6.30047	0.380625
$275$	−23.6905	−1.42859
$276$	1.98671	0.119586
$277$	−9.45517	−0.568106	−0.284053	−	0.958809i	$-0.591679\pi$
$277$	−9.45517	−0.568106	−0.284053	+	0.958809i	$0.591679\pi$
$278$	2.21497	0.132845
$279$	−24.6618	−1.47646
$280$	0.422520	0.0252504
$281$	−8.35664	−0.498515	−0.249258	−	0.968437i	$-0.580187\pi$
$281$	−8.35664	−0.498515	−0.249258	+	0.968437i	$0.580187\pi$
$282$	−1.34026	−0.0798113
$283$	12.5174	0.744079	0.372040	−	0.928217i	$-0.378659\pi$
$283$	12.5174	0.744079	0.372040	+	0.928217i	$0.378659\pi$
$284$	1.41159	0.0837624
$285$	−0.392447	−0.0232466
$286$	26.7362	1.58095
$287$	−10.3157	−0.608919
$288$	−2.69690	−0.158916
$289$	−14.5672	−0.856894
$290$	−2.55313	−0.149925
$291$	0.254250	0.0149044
$292$	5.62943	0.329437
$293$	−8.75817	−0.511658	−0.255829	−	0.966722i	$-0.582348\pi$
$293$	−8.75817	−0.511658	−0.255829	+	0.966722i	$0.582348\pi$
$294$	2.99049	0.174409
$295$	−4.48083	−0.260884
$296$	8.35997	0.485913
$297$	15.2069	0.882393
$298$	−17.5872	−1.01880
$299$	−19.8990	−1.15079
$300$	2.69006	0.155311
$301$	5.84912	0.337138
$302$	23.5027	1.35243
$303$	3.72756	0.214143
$304$	2.11267	0.121170
$305$	−2.28855	−0.131042
$306$	−4.20646	−0.240468
$307$	−20.3274	−1.16015	−0.580074	−	0.814564i	$-0.696976\pi$
$307$	−20.3274	−1.16015	−0.580074	+	0.814564i	$0.696976\pi$
$308$	6.07155	0.345959
$309$	−2.65589	−0.151088
$310$	3.08542	0.175240
$311$	19.6769	1.11578	0.557888	−	0.829916i	$-0.311612\pi$
$311$	19.6769	1.11578	0.557888	+	0.829916i	$0.311612\pi$
$312$	−3.03590	−0.171874
$313$	−12.1901	−0.689026	−0.344513	−	0.938782i	$-0.611956\pi$
$313$	−12.1901	−0.689026	−0.344513	+	0.938782i	$0.611956\pi$
$314$	19.0240	1.07359
$315$	−1.13949	−0.0642031
$316$	11.6421	0.654921
$317$	−15.6048	−0.876454	−0.438227	−	0.898864i	$-0.644393\pi$
$317$	−15.6048	−0.876454	−0.438227	+	0.898864i	$0.644393\pi$
$318$	−5.62511	−0.315440
$319$	−36.6882	−2.05414
$320$	0.337407	0.0188616
$321$	3.13172	0.174795
$322$	−4.51889	−0.251828
$323$	3.29522	0.183351
$324$	6.36395	0.353553
$325$	−26.9439	−1.49458
$326$	−20.1306	−1.11493
$327$	−3.63062	−0.200774
$328$	−8.23774	−0.454853
$329$	3.04851	0.168070
$330$	−0.900650	−0.0495792
$331$	2.60334	0.143092	0.0715462	−	0.997437i	$-0.477207\pi$
$331$	2.60334	0.143092	0.0715462	+	0.997437i	$0.477207\pi$
$332$	2.29357	0.125876
$333$	−22.5460	−1.23551
$334$	2.67577	0.146412
$335$	−0.602823	−0.0329358
$336$	−0.689425	−0.0376112
$337$	−12.2376	−0.666624	−0.333312	−	0.942817i	$-0.608166\pi$
$337$	−12.2376	−0.666624	−0.333312	+	0.942817i	$0.608166\pi$
$338$	17.4078	0.946862
$339$	−7.50128	−0.407414
$340$	0.526268	0.0285409
$341$	44.3371	2.40099
$342$	−5.69766	−0.308094
$343$	−15.5678	−0.840585
$344$	4.67088	0.251837
$345$	0.670329	0.0360893
$346$	−0.473939	−0.0254791
$347$	−4.04370	−0.217077	−0.108539	−	0.994092i	$-0.534617\pi$
$347$	−4.04370	−0.217077	−0.108539	+	0.994092i	$0.534617\pi$
$348$	4.16594	0.223318
$349$	15.3758	0.823048	0.411524	−	0.911399i	$-0.364997\pi$
$349$	15.3758	0.823048	0.411524	+	0.911399i	$0.364997\pi$
$350$	−6.11871	−0.327059
$351$	17.2952	0.923150
$352$	4.84850	0.258426
$353$	−14.9998	−0.798358	−0.399179	−	0.916873i	$-0.630705\pi$
$353$	−14.9998	−0.798358	−0.399179	+	0.916873i	$0.630705\pi$
$354$	7.31137	0.388595
$355$	0.476281	0.0252783
$356$	−7.46599	−0.395696
$357$	−1.07532	−0.0569122
$358$	−13.3624	−0.706225
$359$	4.12956	0.217950	0.108975	−	0.994045i	$-0.465243\pi$
$359$	4.12956	0.217950	0.108975	+	0.994045i	$0.465243\pi$
$360$	−0.909953	−0.0479587
$361$	−14.5366	−0.765085
$362$	13.0898	0.687984
$363$	−6.88621	−0.361432
$364$	6.90534	0.361938
$365$	1.89941	0.0994196
$366$	3.73422	0.195191
$367$	14.5734	0.760726	0.380363	−	0.924837i	$-0.375799\pi$
$367$	14.5734	0.760726	0.380363	+	0.924837i	$0.375799\pi$
$368$	−3.60861	−0.188112
$369$	22.2163	1.15654
$370$	2.82071	0.146642
$371$	12.7947	0.664266
$372$	−5.03448	−0.261025
$373$	−6.71870	−0.347881	−0.173941	−	0.984756i	$-0.555650\pi$
$373$	−6.71870	−0.347881	−0.173941	+	0.984756i	$0.555650\pi$
$374$	7.56241	0.391043
$375$	1.83644	0.0948332
$376$	2.43442	0.125545
$377$	−41.7265	−2.14902
$378$	3.92758	0.202013
$379$	25.4733	1.30847	0.654237	−	0.756290i	$-0.272990\pi$
$379$	25.4733	1.30847	0.654237	+	0.756290i	$0.272990\pi$
$380$	0.712831	0.0365675
$381$	−2.42800	−0.124390
$382$	13.8214	0.707165
$383$	5.23057	0.267270	0.133635	−	0.991031i	$-0.457335\pi$
$383$	5.23057	0.267270	0.133635	+	0.991031i	$0.457335\pi$
$384$	−0.550547	−0.0280950
$385$	2.04859	0.104406
$386$	1.23168	0.0626908
$387$	−12.5969	−0.640335
$388$	−0.461813	−0.0234450
$389$	38.7922	1.96684	0.983421	−	0.181339i	$-0.0580431\pi$
$389$	38.7922	1.96684	0.983421	+	0.181339i	$0.0580431\pi$
$390$	−1.02433	−0.0518692
$391$	−5.62849	−0.284645
$392$	−5.43186	−0.274350
$393$	−10.7974	−0.544658
$394$	8.14270	0.410223
$395$	3.92814	0.197646
$396$	−13.0759	−0.657089
$397$	17.6872	0.887694	0.443847	−	0.896102i	$-0.353613\pi$
$397$	17.6872	0.887694	0.443847	+	0.896102i	$0.353613\pi$
$398$	−21.2310	−1.06421
$399$	−1.45653	−0.0729177
$400$	−4.88616	−0.244308
$401$	−11.6282	−0.580683	−0.290341	−	0.956923i	$-0.593769\pi$
$401$	−11.6282	−0.580683	−0.290341	+	0.956923i	$0.593769\pi$
$402$	0.983626	0.0490588
$403$	50.4258	2.51189
$404$	−6.77064	−0.336852
$405$	2.14724	0.106697
$406$	−9.47570	−0.470271
$407$	40.5333	2.00916
$408$	−0.858711	−0.0425125
$409$	34.0010	1.68124	0.840620	−	0.541626i	$-0.182191\pi$
$409$	34.0010	1.68124	0.840620	+	0.541626i	$0.182191\pi$
$410$	−2.77947	−0.137268
$411$	−3.46870	−0.171099
$412$	4.82410	0.237666
$413$	−16.6302	−0.818318
$414$	9.73204	0.478304
$415$	0.773868	0.0379877
$416$	5.51433	0.270362
$417$	−1.21944	−0.0597164
$418$	10.2433	0.501016
$419$	−11.2359	−0.548910	−0.274455	−	0.961600i	$-0.588497\pi$
$419$	−11.2359	−0.548910	−0.274455	+	0.961600i	$0.588497\pi$
$420$	−0.232617	−0.0113505
$421$	17.3951	0.847786	0.423893	−	0.905712i	$-0.360663\pi$
$421$	17.3951	0.847786	0.423893	+	0.905712i	$0.360663\pi$
$422$	−26.7233	−1.30087
$423$	−6.56537	−0.319219
$424$	10.2173	0.496196
$425$	−7.62114	−0.369680
$426$	−0.777147	−0.0376529
$427$	−8.49373	−0.411040
$428$	−5.68837	−0.274958
$429$	−14.7196	−0.710667
$430$	1.57599	0.0760009
$431$	−31.9272	−1.53788	−0.768940	−	0.639320i	$-0.779216\pi$
$431$	−31.9272	−1.53788	−0.768940	+	0.639320i	$0.779216\pi$
$432$	3.13641	0.150901
$433$	−9.32710	−0.448232	−0.224116	−	0.974562i	$-0.571949\pi$
$433$	−9.32710	−0.448232	−0.224116	+	0.974562i	$0.571949\pi$
$434$	11.4512	0.549677
$435$	1.40562	0.0673943
$436$	6.59457	0.315823
$437$	−7.62380	−0.364696
$438$	−3.09927	−0.148089
$439$	−16.0384	−0.765470	−0.382735	−	0.923858i	$-0.625018\pi$
$439$	−16.0384	−0.765470	−0.382735	+	0.923858i	$0.625018\pi$
$440$	1.63592	0.0779894
$441$	14.6492	0.697580
$442$	8.60093	0.409105
$443$	17.1746	0.815992	0.407996	−	0.912984i	$-0.366228\pi$
$443$	17.1746	0.815992	0.407996	+	0.912984i	$0.366228\pi$
$444$	−4.60256	−0.218428
$445$	−2.51908	−0.119416
$446$	12.8063	0.606397
$447$	9.68256	0.457969
$448$	1.25225	0.0591634
$449$	−10.1810	−0.480473	−0.240236	−	0.970714i	$-0.577225\pi$
$449$	−10.1810	−0.480473	−0.240236	+	0.970714i	$0.577225\pi$
$450$	13.1775	0.621192
$451$	−39.9407	−1.88073
$452$	13.6251	0.640873
$453$	−12.9393	−0.607943
$454$	−19.0380	−0.893496
$455$	2.32991	0.109228
$456$	−1.16313	−0.0544684
$457$	5.69689	0.266489	0.133245	−	0.991083i	$-0.457460\pi$
$457$	5.69689	0.266489	0.133245	+	0.991083i	$0.457460\pi$
$458$	−0.294814	−0.0137758
$459$	4.89199	0.228339
$460$	−1.21757	−0.0567695
$461$	−27.1797	−1.26589	−0.632943	−	0.774198i	$-0.718153\pi$
$461$	−27.1797	−1.26589	−0.632943	+	0.774198i	$0.718153\pi$
$462$	−3.34268	−0.155515
$463$	−32.8499	−1.52666	−0.763332	−	0.646006i	$-0.776438\pi$
$463$	−32.8499	−1.52666	−0.763332	+	0.646006i	$0.776438\pi$
$464$	−7.56691	−0.351285
$465$	−1.69867	−0.0787738
$466$	27.3480	1.26687
$467$	6.79244	0.314316	0.157158	−	0.987573i	$-0.449767\pi$
$467$	6.79244	0.314316	0.157158	+	0.987573i	$0.449767\pi$
$468$	−14.8716	−0.687439
$469$	−2.23732	−0.103310
$470$	0.821389	0.0378879
$471$	−10.4736	−0.482598
$472$	−13.2802	−0.611271
$473$	22.6467	1.04130
$474$	−6.40954	−0.294400
$475$	−10.3228	−0.473645
$476$	1.95319	0.0895245
$477$	−27.5550	−1.26166
$478$	−10.0612	−0.460189
$479$	−20.5432	−0.938641	−0.469320	−	0.883028i	$-0.655501\pi$
$479$	−20.5432	−0.938641	−0.469320	+	0.883028i	$0.655501\pi$
$480$	−0.185759	−0.00847868
$481$	46.0997	2.10196
$482$	−17.7231	−0.807265
$483$	2.48786	0.113202
$484$	12.5079	0.568543
$485$	−0.155819	−0.00707538
$486$	−12.9129	−0.585740
$487$	22.7661	1.03163	0.515815	−	0.856700i	$-0.327489\pi$
$487$	22.7661	1.03163	0.515815	+	0.856700i	$0.327489\pi$
$488$	−6.78275	−0.307041
$489$	11.0828	0.501184
$490$	−1.83275	−0.0827951
$491$	−5.22516	−0.235808	−0.117904	−	0.993025i	$-0.537618\pi$
$491$	−5.22516	−0.235808	−0.117904	+	0.993025i	$0.537618\pi$
$492$	4.53526	0.204465
$493$	−11.8024	−0.531555
$494$	11.6500	0.524157
$495$	−4.41191	−0.198300
$496$	9.14450	0.410600
$497$	1.76767	0.0792908
$498$	−1.26272	−0.0565838
$499$	18.4894	0.827698	0.413849	−	0.910346i	$-0.364184\pi$
$499$	18.4894	0.827698	0.413849	+	0.910346i	$0.364184\pi$
$500$	−3.33566	−0.149175
$501$	−1.47314	−0.0658150
$502$	0.608615	0.0271638
$503$	1.09184	0.0486829	0.0243414	−	0.999704i	$-0.492251\pi$
$503$	1.09184	0.0486829	0.0243414	+	0.999704i	$0.492251\pi$
$504$	−3.37720	−0.150433
$505$	−2.28446	−0.101657
$506$	−17.4963	−0.777806
$507$	−9.58384	−0.425633
$508$	4.41015	0.195669
$509$	25.9973	1.15231	0.576156	−	0.817340i	$-0.304552\pi$
$509$	25.9973	1.15231	0.576156	+	0.817340i	$0.304552\pi$
$510$	−0.289735	−0.0128297
$511$	7.04948	0.311850
$512$	1.00000	0.0441942
$513$	6.62621	0.292554
$514$	16.5189	0.728620
$515$	1.62768	0.0717244
$516$	−2.57154	−0.113206
$517$	11.8033	0.519107
$518$	10.4688	0.459973
$519$	0.260926	0.0114534
$520$	1.86057	0.0815916
$521$	34.7337	1.52171	0.760856	−	0.648921i	$-0.224780\pi$
$521$	34.7337	1.52171	0.760856	+	0.648921i	$0.224780\pi$
$522$	20.4072	0.893199
$523$	−44.2351	−1.93427	−0.967133	−	0.254270i	$-0.918165\pi$
$523$	−44.2351	−1.93427	−0.967133	+	0.254270i	$0.918165\pi$
$524$	19.6122	0.856762
$525$	3.36864	0.147019
$526$	16.3838	0.714367
$527$	14.2631	0.621308
$528$	−2.66933	−0.116168
$529$	−9.97797	−0.433825
$530$	3.44739	0.149745
$531$	35.8153	1.55425
$532$	2.64560	0.114701
$533$	−45.4256	−1.96760
$534$	4.11038	0.177873
$535$	−1.91930	−0.0829784
$536$	−1.78663	−0.0771709
$537$	7.35663	0.317462
$538$	−20.4975	−0.883709
$539$	−26.3364	−1.13439
$540$	1.05825	0.0455397
$541$	−8.12889	−0.349488	−0.174744	−	0.984614i	$-0.555910\pi$
$541$	−8.12889	−0.349488	−0.174744	+	0.984614i	$0.555910\pi$
$542$	−25.7751	−1.10713
$543$	−7.20654	−0.309262
$544$	1.55974	0.0668734
$545$	2.22506	0.0953110
$546$	−3.80172	−0.162698
$547$	−15.0891	−0.645162	−0.322581	−	0.946542i	$-0.604550\pi$
$547$	−15.0891	−0.645162	−0.322581	+	0.946542i	$0.604550\pi$
$548$	6.30047	0.269143
$549$	18.2924	0.780700
$550$	−23.6905	−1.01017
$551$	−15.9864	−0.681044
$552$	1.98671	0.0845599
$553$	14.5789	0.619958
$554$	−9.45517	−0.401712
$555$	−1.55294	−0.0659185
$556$	2.21497	0.0939355
$557$	−21.5853	−0.914599	−0.457299	−	0.889313i	$-0.651183\pi$
$557$	−21.5853	−0.914599	−0.457299	+	0.889313i	$0.651183\pi$
$558$	−24.6618	−1.04402
$559$	25.7568	1.08939
$560$	0.422520	0.0178547
$561$	−4.16346	−0.175781
$562$	−8.35664	−0.352504
$563$	4.61429	0.194469	0.0972345	−	0.995261i	$-0.469000\pi$
$563$	4.61429	0.194469	0.0972345	+	0.995261i	$0.469000\pi$
$564$	−1.34026	−0.0564351
$565$	4.59722	0.193407
$566$	12.5174	0.526143
$567$	7.96929	0.334679
$568$	1.41159	0.0592290
$569$	−34.1658	−1.43231	−0.716153	−	0.697943i	$-0.754099\pi$
$569$	−34.1658	−1.43231	−0.716153	+	0.697943i	$0.754099\pi$
$570$	−0.392447	−0.0164378
$571$	−1.96679	−0.0823077	−0.0411539	−	0.999153i	$-0.513103\pi$
$571$	−1.96679	−0.0823077	−0.0411539	+	0.999153i	$0.513103\pi$
$572$	26.7362	1.11790
$573$	−7.60934	−0.317885
$574$	−10.3157	−0.430571
$575$	17.6322	0.735314
$576$	−2.69690	−0.112371
$577$	−27.6219	−1.14991	−0.574957	−	0.818183i	$-0.694981\pi$
$577$	−27.6219	−1.14991	−0.574957	+	0.818183i	$0.694981\pi$
$578$	−14.5672	−0.605916
$579$	−0.678097	−0.0281808
$580$	−2.55313	−0.106013
$581$	2.87214	0.119156
$582$	0.254250	0.0105390
$583$	49.5386	2.05168
$584$	5.62943	0.232947
$585$	−5.01778	−0.207460
$586$	−8.75817	−0.361797
$587$	−3.81882	−0.157620	−0.0788098	−	0.996890i	$-0.525112\pi$
$587$	−3.81882	−0.157620	−0.0788098	+	0.996890i	$0.525112\pi$
$588$	2.99049	0.123326
$589$	19.3193	0.796039
$590$	−4.48083	−0.184473
$591$	−4.48294	−0.184404
$592$	8.35997	0.343593
$593$	−20.4216	−0.838613	−0.419306	−	0.907845i	$-0.637727\pi$
$593$	−20.4216	−0.838613	−0.419306	+	0.907845i	$0.637727\pi$
$594$	15.2069	0.623946
$595$	0.659021	0.0270172
$596$	−17.5872	−0.720398
$597$	11.6886	0.478384
$598$	−19.8990	−0.813732
$599$	5.99768	0.245059	0.122529	−	0.992465i	$-0.460899\pi$
$599$	5.99768	0.245059	0.122529	+	0.992465i	$0.460899\pi$
$600$	2.69006	0.109821
$601$	27.9369	1.13957	0.569785	−	0.821794i	$-0.307027\pi$
$601$	27.9369	1.13957	0.569785	+	0.821794i	$0.307027\pi$
$602$	5.84912	0.238393
$603$	4.81837	0.196219
$604$	23.5027	0.956310
$605$	4.22027	0.171578
$606$	3.72756	0.151422
$607$	−34.4916	−1.39997	−0.699985	−	0.714158i	$-0.746810\pi$
$607$	−34.4916	−1.39997	−0.699985	+	0.714158i	$0.746810\pi$
$608$	2.11267	0.0856802
$609$	5.21682	0.211396
$610$	−2.28855	−0.0926606
$611$	13.4242	0.543084
$612$	−4.20646	−0.170036
$613$	−2.53509	−0.102391	−0.0511957	−	0.998689i	$-0.516303\pi$
$613$	−2.53509	−0.102391	−0.0511957	+	0.998689i	$0.516303\pi$
$614$	−20.3274	−0.820348
$615$	1.53023	0.0617048
$616$	6.07155	0.244630
$617$	−7.17482	−0.288847	−0.144424	−	0.989516i	$-0.546133\pi$
$617$	−7.17482	−0.288847	−0.144424	+	0.989516i	$0.546133\pi$
$618$	−2.65589	−0.106836
$619$	25.1926	1.01258	0.506289	−	0.862364i	$-0.331017\pi$
$619$	25.1926	1.01258	0.506289	+	0.862364i	$0.331017\pi$
$620$	3.08542	0.123913
$621$	−11.3181	−0.454178
$622$	19.6769	0.788972
$623$	−9.34931	−0.374572
$624$	−3.03590	−0.121533
$625$	23.3053	0.932212
$626$	−12.1901	−0.487215
$627$	−5.63941	−0.225217
$628$	19.0240	0.759140
$629$	13.0394	0.519915
$630$	−1.13949	−0.0453985
$631$	−33.9314	−1.35079	−0.675395	−	0.737456i	$-0.736027\pi$
$631$	−33.9314	−1.35079	−0.675395	+	0.737456i	$0.736027\pi$
$632$	11.6421	0.463099
$633$	14.7125	0.584768
$634$	−15.6048	−0.619747
$635$	1.48802	0.0590502
$636$	−5.62511	−0.223050
$637$	−29.9531	−1.18678
$638$	−36.6882	−1.45250
$639$	−3.80691	−0.150599
$640$	0.337407	0.0133372
$641$	−40.7304	−1.60875	−0.804377	−	0.594120i	$-0.797501\pi$
$641$	−40.7304	−1.60875	−0.804377	+	0.594120i	$0.797501\pi$
$642$	3.13172	0.123599
$643$	16.9992	0.670383	0.335192	−	0.942150i	$-0.391199\pi$
$643$	16.9992	0.670383	0.335192	+	0.942150i	$0.391199\pi$
$644$	−4.51889	−0.178069
$645$	−0.867655	−0.0341639
$646$	3.29522	0.129649
$647$	−13.1064	−0.515265	−0.257633	−	0.966243i	$-0.582942\pi$
$647$	−13.1064	−0.515265	−0.257633	+	0.966243i	$0.582942\pi$
$648$	6.36395	0.250000
$649$	−64.3890	−2.52749
$650$	−26.9439	−1.05683
$651$	−6.30444	−0.247091
$652$	−20.1306	−0.788376
$653$	−39.3898	−1.54144	−0.770720	−	0.637174i	$-0.780103\pi$
$653$	−39.3898	−1.54144	−0.770720	+	0.637174i	$0.780103\pi$
$654$	−3.63062	−0.141969
$655$	6.61729	0.258559
$656$	−8.23774	−0.321630
$657$	−15.1820	−0.592306
$658$	3.04851	0.118843
$659$	−31.5228	−1.22795	−0.613976	−	0.789325i	$-0.710431\pi$
$659$	−31.5228	−1.22795	−0.613976	+	0.789325i	$0.710431\pi$
$660$	−0.900650	−0.0350578
$661$	13.6555	0.531138	0.265569	−	0.964092i	$-0.414440\pi$
$661$	13.6555	0.531138	0.265569	+	0.964092i	$0.414440\pi$
$662$	2.60334	0.101182
$663$	−4.73522	−0.183901
$664$	2.29357	0.0890079
$665$	0.892646	0.0346153
$666$	−22.5460	−0.873639
$667$	27.3060	1.05729
$668$	2.67577	0.103529
$669$	−7.05048	−0.272587
$670$	−0.602823	−0.0232891
$671$	−32.8862	−1.26956
$672$	−0.689425	−0.0265951
$673$	34.0736	1.31344	0.656721	−	0.754134i	$-0.271943\pi$
$673$	34.0736	1.31344	0.656721	+	0.754134i	$0.271943\pi$
$674$	−12.2376	−0.471374
$675$	−15.3250	−0.589859
$676$	17.4078	0.669533
$677$	21.5980	0.830080	0.415040	−	0.909803i	$-0.363768\pi$
$677$	21.5980	0.830080	0.415040	+	0.909803i	$0.363768\pi$
$678$	−7.50128	−0.288085
$679$	−0.578308	−0.0221934
$680$	0.526268	0.0201815
$681$	10.4813	0.401644
$682$	44.3371	1.69775
$683$	16.8192	0.643568	0.321784	−	0.946813i	$-0.395718\pi$
$683$	16.8192	0.643568	0.321784	+	0.946813i	$0.395718\pi$
$684$	−5.69766	−0.217856
$685$	2.12582	0.0812235
$686$	−15.5678	−0.594383
$687$	0.162309	0.00619248
$688$	4.67088	0.178075
$689$	56.3416	2.14644
$690$	0.670329	0.0255190
$691$	−16.0690	−0.611292	−0.305646	−	0.952145i	$-0.598872\pi$
$691$	−16.0690	−0.611292	−0.305646	+	0.952145i	$0.598872\pi$
$692$	−0.473939	−0.0180165
$693$	−16.3744	−0.622010
$694$	−4.04370	−0.153497
$695$	0.747346	0.0283484
$696$	4.16594	0.157910
$697$	−12.8487	−0.486681
$698$	15.3758	0.581983
$699$	−15.0564	−0.569484
$700$	−6.11871	−0.231265
$701$	−23.8503	−0.900814	−0.450407	−	0.892823i	$-0.648721\pi$
$701$	−23.8503	−0.900814	−0.450407	+	0.892823i	$0.648721\pi$
$702$	17.2952	0.652765
$703$	17.6619	0.666131
$704$	4.84850	0.182735
$705$	−0.452213	−0.0170313
$706$	−14.9998	−0.564524
$707$	−8.47857	−0.318869
$708$	7.31137	0.274778
$709$	−12.9237	−0.485359	−0.242679	−	0.970107i	$-0.578026\pi$
$709$	−12.9237	−0.485359	−0.242679	+	0.970107i	$0.578026\pi$
$710$	0.476281	0.0178745
$711$	−31.3976	−1.17750
$712$	−7.46599	−0.279800
$713$	−32.9989	−1.23582
$714$	−1.07532	−0.0402430
$715$	9.02100	0.337366
$716$	−13.3624	−0.499377
$717$	5.53917	0.206864
$718$	4.12956	0.154114
$719$	−26.7455	−0.997438	−0.498719	−	0.866764i	$-0.666196\pi$
$719$	−26.7455	−0.997438	−0.498719	+	0.866764i	$0.666196\pi$
$720$	−0.909953	−0.0339119
$721$	6.04099	0.224978
$722$	−14.5366	−0.540997
$723$	9.75740	0.362882
$724$	13.0898	0.486478
$725$	36.9731	1.37315
$726$	−6.88621	−0.255571
$727$	−41.2347	−1.52931	−0.764656	−	0.644439i	$-0.777091\pi$
$727$	−41.2347	−1.52931	−0.764656	+	0.644439i	$0.777091\pi$
$728$	6.90534	0.255929
$729$	−11.9827	−0.443804
$730$	1.89941	0.0703003
$731$	7.28536	0.269459
$732$	3.73422	0.138021
$733$	26.2755	0.970506	0.485253	−	0.874374i	$-0.338727\pi$
$733$	26.2755	0.970506	0.485253	+	0.874374i	$0.338727\pi$
$734$	14.5734	0.537914
$735$	1.00901	0.0372181
$736$	−3.60861	−0.133015
$737$	−8.66250	−0.319087
$738$	22.2163	0.817795
$739$	−14.3012	−0.526078	−0.263039	−	0.964785i	$-0.584725\pi$
$739$	−14.3012	−0.526078	−0.263039	+	0.964785i	$0.584725\pi$
$740$	2.82071	0.103692
$741$	−6.41386	−0.235619
$742$	12.7947	0.469707
$743$	−36.9983	−1.35734	−0.678668	−	0.734445i	$-0.737443\pi$
$743$	−36.9983	−1.35734	−0.678668	+	0.734445i	$0.737443\pi$
$744$	−5.03448	−0.184573
$745$	−5.93403	−0.217406
$746$	−6.71870	−0.245989
$747$	−6.18553	−0.226317
$748$	7.56241	0.276509
$749$	−7.12329	−0.260279
$750$	1.83644	0.0670572
$751$	−18.4352	−0.672709	−0.336355	−	0.941735i	$-0.609194\pi$
$751$	−18.4352	−0.672709	−0.336355	+	0.941735i	$0.609194\pi$
$752$	2.43442	0.0887740
$753$	−0.335071	−0.0122107
$754$	−41.7265	−1.51959
$755$	7.92997	0.288601
$756$	3.92758	0.142845
$757$	−44.0789	−1.60207	−0.801037	−	0.598614i	$-0.795718\pi$
$757$	−44.0789	−1.60207	−0.801037	+	0.598614i	$0.795718\pi$
$758$	25.4733	0.925230
$759$	9.63255	0.349639
$760$	0.712831	0.0258571
$761$	−33.0802	−1.19916	−0.599578	−	0.800316i	$-0.704665\pi$
$761$	−33.0802	−1.19916	−0.599578	+	0.800316i	$0.704665\pi$
$762$	−2.42800	−0.0879571
$763$	8.25808	0.298963
$764$	13.8214	0.500041
$765$	−1.41929	−0.0513146
$766$	5.23057	0.188988
$767$	−73.2314	−2.64423
$768$	−0.550547	−0.0198662
$769$	23.4076	0.844100	0.422050	−	0.906572i	$-0.361311\pi$
$769$	23.4076	0.844100	0.422050	+	0.906572i	$0.361311\pi$
$770$	2.04859	0.0738259
$771$	−9.09446	−0.327529
$772$	1.23168	0.0443291
$773$	31.9992	1.15093	0.575465	−	0.817826i	$-0.304821\pi$
$773$	31.9992	1.15093	0.575465	+	0.817826i	$0.304821\pi$
$774$	−12.5969	−0.452785
$775$	−44.6814	−1.60500
$776$	−0.461813	−0.0165781
$777$	−5.76357	−0.206767
$778$	38.7922	1.39077
$779$	−17.4036	−0.623550
$780$	−1.02433	−0.0366770
$781$	6.84409	0.244901
$782$	−5.62849	−0.201274
$783$	−23.7329	−0.848146
$784$	−5.43186	−0.193995
$785$	6.41883	0.229098
$786$	−10.7974	−0.385131
$787$	−27.2060	−0.969791	−0.484895	−	0.874572i	$-0.661142\pi$
$787$	−27.2060	−0.969791	−0.484895	+	0.874572i	$0.661142\pi$
$788$	8.14270	0.290072
$789$	−9.02004	−0.321122
$790$	3.92814	0.139757
$791$	17.0621	0.606660
$792$	−13.0759	−0.464632
$793$	−37.4023	−1.32820
$794$	17.6872	0.627695
$795$	−1.89795	−0.0673134
$796$	−21.2310	−0.752511
$797$	23.6122	0.836389	0.418194	−	0.908358i	$-0.362663\pi$
$797$	23.6122	0.836389	0.418194	+	0.908358i	$0.362663\pi$
$798$	−1.45653	−0.0515606
$799$	3.79706	0.134330
$800$	−4.88616	−0.172752
$801$	20.1350	0.711435
$802$	−11.6282	−0.410605
$803$	27.2943	0.963194
$804$	0.983626	0.0346898
$805$	−1.52471	−0.0537388
$806$	50.4258	1.77617
$807$	11.2848	0.397245
$808$	−6.77064	−0.238190
$809$	30.3474	1.06696	0.533479	−	0.845814i	$-0.320884\pi$
$809$	30.3474	1.06696	0.533479	+	0.845814i	$0.320884\pi$
$810$	2.14724	0.0754464
$811$	36.4711	1.28068	0.640338	−	0.768094i	$-0.278794\pi$
$811$	36.4711	1.28068	0.640338	+	0.768094i	$0.278794\pi$
$812$	−9.47570	−0.332532
$813$	14.1904	0.497679
$814$	40.5333	1.42069
$815$	−6.79221	−0.237921
$816$	−0.858711	−0.0300609
$817$	9.86803	0.345239
$818$	34.0010	1.18882
$819$	−18.6230	−0.650741
$820$	−2.77947	−0.0970634
$821$	56.5535	1.97373	0.986866	−	0.161541i	$-0.0516465\pi$
$821$	56.5535	1.97373	0.986866	+	0.161541i	$0.0516465\pi$
$822$	−3.46870	−0.120985
$823$	−14.2150	−0.495504	−0.247752	−	0.968824i	$-0.579692\pi$
$823$	−14.2150	−0.495504	−0.247752	+	0.968824i	$0.579692\pi$
$824$	4.82410	0.168055
$825$	13.0427	0.454090
$826$	−16.6302	−0.578638
$827$	−37.1401	−1.29149	−0.645744	−	0.763554i	$-0.723453\pi$
$827$	−37.1401	−1.29149	−0.645744	+	0.763554i	$0.723453\pi$
$828$	9.73204	0.338212
$829$	−44.5883	−1.54862	−0.774309	−	0.632808i	$-0.781902\pi$
$829$	−44.5883	−1.54862	−0.774309	+	0.632808i	$0.781902\pi$
$830$	0.773868	0.0268614
$831$	5.20552	0.180577
$832$	5.51433	0.191175
$833$	−8.47230	−0.293548
$834$	−1.21944	−0.0422259
$835$	0.902825	0.0312436
$836$	10.2433	0.354272
$837$	28.6809	0.991357
$838$	−11.2359	−0.388138
$839$	−11.0768	−0.382414	−0.191207	−	0.981550i	$-0.561240\pi$
$839$	−11.0768	−0.382414	−0.191207	+	0.981550i	$0.561240\pi$
$840$	−0.232617	−0.00802605
$841$	28.2582	0.974420
$842$	17.3951	0.599476
$843$	4.60072	0.158457
$844$	−26.7233	−0.919856
$845$	5.87353	0.202056
$846$	−6.56537	−0.225722
$847$	15.6631	0.538191
$848$	10.2173	0.350864
$849$	−6.89139	−0.236512
$850$	−7.62114	−0.261403
$851$	−30.1678	−1.03414
$852$	−0.777147	−0.0266246
$853$	−31.5878	−1.08155	−0.540773	−	0.841168i	$-0.681868\pi$
$853$	−31.5878	−1.08155	−0.540773	+	0.841168i	$0.681868\pi$
$854$	−8.49373	−0.290649
$855$	−1.92243	−0.0657458
$856$	−5.68837	−0.194425
$857$	51.4898	1.75886	0.879429	−	0.476030i	$-0.157925\pi$
$857$	51.4898	1.75886	0.879429	+	0.476030i	$0.157925\pi$
$858$	−14.7196	−0.502517
$859$	−0.804777	−0.0274587	−0.0137293	−	0.999906i	$-0.504370\pi$
$859$	−0.804777	−0.0274587	−0.0137293	+	0.999906i	$0.504370\pi$
$860$	1.57599	0.0537407
$861$	5.67930	0.193550
$862$	−31.9272	−1.08745
$863$	−21.7710	−0.741092	−0.370546	−	0.928814i	$-0.620829\pi$
$863$	−21.7710	−0.741092	−0.370546	+	0.928814i	$0.620829\pi$
$864$	3.13641	0.106703
$865$	−0.159910	−0.00543712
$866$	−9.32710	−0.316948
$867$	8.01993	0.272371
$868$	11.4512	0.388680
$869$	56.4468	1.91483
$870$	1.40562	0.0476549
$871$	−9.85209	−0.333825
$872$	6.59457	0.223320
$873$	1.24546	0.0421525
$874$	−7.62380	−0.257879
$875$	−4.17709	−0.141212
$876$	−3.09927	−0.104714
$877$	−14.4418	−0.487666	−0.243833	−	0.969817i	$-0.578405\pi$
$877$	−14.4418	−0.487666	−0.243833	+	0.969817i	$0.578405\pi$
$878$	−16.0384	−0.541269
$879$	4.82178	0.162635
$880$	1.63592	0.0551468
$881$	−18.4984	−0.623229	−0.311614	−	0.950209i	$-0.600870\pi$
$881$	−18.4984	−0.623229	−0.311614	+	0.950209i	$0.600870\pi$
$882$	14.6492	0.493263
$883$	−22.3161	−0.750997	−0.375499	−	0.926823i	$-0.622528\pi$
$883$	−22.3161	−0.750997	−0.375499	+	0.926823i	$0.622528\pi$
$884$	8.60093	0.289281
$885$	2.46691	0.0829243
$886$	17.1746	0.576994
$887$	−42.6558	−1.43224	−0.716120	−	0.697977i	$-0.754084\pi$
$887$	−42.6558	−1.43224	−0.716120	+	0.697977i	$0.754084\pi$
$888$	−4.60256	−0.154452
$889$	5.52263	0.185223
$890$	−2.51908	−0.0844397
$891$	30.8556	1.03370
$892$	12.8063	0.428787
$893$	5.14312	0.172108
$894$	9.68256	0.323833
$895$	−4.50857	−0.150705
$896$	1.25225	0.0418349
$897$	10.9554	0.365789
$898$	−10.1810	−0.339746
$899$	−69.1956	−2.30780
$900$	13.1775	0.439249
$901$	15.9364	0.530917
$902$	−39.9407	−1.32988
$903$	−3.22022	−0.107162
$904$	13.6251	0.453166
$905$	4.41659	0.146812
$906$	−12.9393	−0.429880
$907$	−14.8392	−0.492729	−0.246365	−	0.969177i	$-0.579236\pi$
$907$	−14.8392	−0.492729	−0.246365	+	0.969177i	$0.579236\pi$
$908$	−19.0380	−0.631797
$909$	18.2597	0.605637
$910$	2.32991	0.0772359
$911$	8.86624	0.293752	0.146876	−	0.989155i	$-0.453078\pi$
$911$	8.86624	0.293752	0.146876	+	0.989155i	$0.453078\pi$
$912$	−1.16313	−0.0385149
$913$	11.1204	0.368031
$914$	5.69689	0.188436
$915$	1.25995	0.0416528
$916$	−0.294814	−0.00974094
$917$	24.5594	0.811024
$918$	4.89199	0.161460
$919$	10.7955	0.356111	0.178056	−	0.984020i	$-0.443019\pi$
$919$	10.7955	0.356111	0.178056	+	0.984020i	$0.443019\pi$
$920$	−1.21757	−0.0401421
$921$	11.1912	0.368763
$922$	−27.1797	−0.895117
$923$	7.78397	0.256213
$924$	−3.34268	−0.109966
$925$	−40.8481	−1.34308
$926$	−32.8499	−1.07951
$927$	−13.0101	−0.427308
$928$	−7.56691	−0.248396
$929$	−24.4091	−0.800836	−0.400418	−	0.916333i	$-0.631135\pi$
$929$	−24.4091	−0.800836	−0.400418	+	0.916333i	$0.631135\pi$
$930$	−1.69867	−0.0557015
$931$	−11.4757	−0.376102
$932$	27.3480	0.895814
$933$	−10.8331	−0.354659
$934$	6.79244	0.222255
$935$	2.55161	0.0834466
$936$	−14.8716	−0.486093
$937$	−1.04534	−0.0341499	−0.0170749	−	0.999854i	$-0.505435\pi$
$937$	−1.04534	−0.0341499	−0.0170749	+	0.999854i	$0.505435\pi$
$938$	−2.23732	−0.0730511
$939$	6.71123	0.219013
$940$	0.821389	0.0267908
$941$	22.3454	0.728438	0.364219	−	0.931313i	$-0.381336\pi$
$941$	22.3454	0.728438	0.364219	+	0.931313i	$0.381336\pi$
$942$	−10.4736	−0.341248
$943$	29.7267	0.968036
$944$	−13.2802	−0.432234
$945$	1.32519	0.0431086
$946$	22.6467	0.736309
$947$	−12.4898	−0.405865	−0.202932	−	0.979193i	$-0.565047\pi$
$947$	−12.4898	−0.405865	−0.202932	+	0.979193i	$0.565047\pi$
$948$	−6.40954	−0.208172
$949$	31.0425	1.00768
$950$	−10.3228	−0.334917
$951$	8.59119	0.278588
$952$	1.95319	0.0633034
$953$	5.23263	0.169501	0.0847507	−	0.996402i	$-0.472991\pi$
$953$	5.23263	0.169501	0.0847507	+	0.996402i	$0.472991\pi$
$954$	−27.5550	−0.892127
$955$	4.66345	0.150906
$956$	−10.0612	−0.325403
$957$	20.1986	0.652927
$958$	−20.5432	−0.663719
$959$	7.88979	0.254774
$960$	−0.185759	−0.00599533
$961$	52.6218	1.69748
$962$	46.0997	1.48631
$963$	15.3410	0.494355
$964$	−17.7231	−0.570823
$965$	0.415577	0.0133779
$966$	2.48786	0.0800456
$967$	15.5371	0.499640	0.249820	−	0.968292i	$-0.419628\pi$
$967$	15.5371	0.499640	0.249820	+	0.968292i	$0.419628\pi$
$968$	12.5079	0.402021
$969$	−1.81418	−0.0582797
$970$	−0.155819	−0.00500305
$971$	−14.9060	−0.478356	−0.239178	−	0.970976i	$-0.576878\pi$
$971$	−14.9060	−0.478356	−0.239178	+	0.970976i	$0.576878\pi$
$972$	−12.9129	−0.414181
$973$	2.77370	0.0889208
$974$	22.7661	0.729473
$975$	14.8339	0.475064
$976$	−6.78275	−0.217111
$977$	−32.1486	−1.02852	−0.514262	−	0.857633i	$-0.671934\pi$
$977$	−32.1486	−1.02852	−0.514262	+	0.857633i	$0.671934\pi$
$978$	11.0828	0.354390
$979$	−36.1988	−1.15692
$980$	−1.83275	−0.0585450
$981$	−17.7849	−0.567828
$982$	−5.22516	−0.166742
$983$	−48.0732	−1.53330	−0.766648	−	0.642068i	$-0.778077\pi$
$983$	−48.0732	−1.53330	−0.766648	+	0.642068i	$0.778077\pi$
$984$	4.53526	0.144579
$985$	2.74741	0.0875396
$986$	−11.8024	−0.375866
$987$	−1.67835	−0.0534224
$988$	11.6500	0.370635
$989$	−16.8553	−0.535969
$990$	−4.41191	−0.140220
$991$	41.4866	1.31787	0.658933	−	0.752202i	$-0.271008\pi$
$991$	41.4866	1.31787	0.658933	+	0.752202i	$0.271008\pi$
$992$	9.14450	0.290338
$993$	−1.43326	−0.0454831
$994$	1.76767	0.0560671
$995$	−7.16348	−0.227097
$996$	−1.26272	−0.0400108
$997$	43.9090	1.39061	0.695306	−	0.718714i	$-0.255269\pi$
$997$	43.9090	1.39061	0.695306	+	0.718714i	$0.255269\pi$
$998$	18.4894	0.585271
$999$	26.2203	0.829574

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.d.1.20	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.d.1.20	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.550547 q^{3} +1.00000 q^{4} +0.337407 q^{5} -0.550547 q^{6} +1.25225 q^{7} +1.00000 q^{8} -2.69690 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.550547 q^{3} +1.00000 q^{4} +0.337407 q^{5} -0.550547 q^{6} +1.25225 q^{7} +1.00000 q^{8} -2.69690 q^{9} +0.337407 q^{10} +4.84850 q^{11} -0.550547 q^{12} +5.51433 q^{13} +1.25225 q^{14} -0.185759 q^{15} +1.00000 q^{16} +1.55974 q^{17} -2.69690 q^{18} +2.11267 q^{19} +0.337407 q^{20} -0.689425 q^{21} +4.84850 q^{22} -3.60861 q^{23} -0.550547 q^{24} -4.88616 q^{25} +5.51433 q^{26} +3.13641 q^{27} +1.25225 q^{28} -7.56691 q^{29} -0.185759 q^{30} +9.14450 q^{31} +1.00000 q^{32} -2.66933 q^{33} +1.55974 q^{34} +0.422520 q^{35} -2.69690 q^{36} +8.35997 q^{37} +2.11267 q^{38} -3.03590 q^{39} +0.337407 q^{40} -8.23774 q^{41} -0.689425 q^{42} +4.67088 q^{43} +4.84850 q^{44} -0.909953 q^{45} -3.60861 q^{46} +2.43442 q^{47} -0.550547 q^{48} -5.43186 q^{49} -4.88616 q^{50} -0.858711 q^{51} +5.51433 q^{52} +10.2173 q^{53} +3.13641 q^{54} +1.63592 q^{55} +1.25225 q^{56} -1.16313 q^{57} -7.56691 q^{58} -13.2802 q^{59} -0.185759 q^{60} -6.78275 q^{61} +9.14450 q^{62} -3.37720 q^{63} +1.00000 q^{64} +1.86057 q^{65} -2.66933 q^{66} -1.78663 q^{67} +1.55974 q^{68} +1.98671 q^{69} +0.422520 q^{70} +1.41159 q^{71} -2.69690 q^{72} +5.62943 q^{73} +8.35997 q^{74} +2.69006 q^{75} +2.11267 q^{76} +6.07155 q^{77} -3.03590 q^{78} +11.6421 q^{79} +0.337407 q^{80} +6.36395 q^{81} -8.23774 q^{82} +2.29357 q^{83} -0.689425 q^{84} +0.526268 q^{85} +4.67088 q^{86} +4.16594 q^{87} +4.84850 q^{88} -7.46599 q^{89} -0.909953 q^{90} +6.90534 q^{91} -3.60861 q^{92} -5.03448 q^{93} +2.43442 q^{94} +0.712831 q^{95} -0.550547 q^{96} -0.461813 q^{97} -5.43186 q^{98} -13.0759 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9}+O(q^{10}) \) 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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