LMFDB - Embedded newform 4034.2.a.d.1.17

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			1.17
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)

$f(q)$	$=$	$q+1.00000 q^{2} -0.909483 q^{3} +1.00000 q^{4} +3.81385 q^{5} -0.909483 q^{6} +4.56339 q^{7} +1.00000 q^{8} -2.17284 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.909483 q^{3} +1.00000 q^{4} +3.81385 q^{5} -0.909483 q^{6} +4.56339 q^{7} +1.00000 q^{8} -2.17284 q^{9} +3.81385 q^{10} -3.92961 q^{11} -0.909483 q^{12} +5.78418 q^{13} +4.56339 q^{14} -3.46863 q^{15} +1.00000 q^{16} -2.17852 q^{17} -2.17284 q^{18} -5.55126 q^{19} +3.81385 q^{20} -4.15033 q^{21} -3.92961 q^{22} -7.56459 q^{23} -0.909483 q^{24} +9.54543 q^{25} +5.78418 q^{26} +4.70461 q^{27} +4.56339 q^{28} +6.68108 q^{29} -3.46863 q^{30} +5.62008 q^{31} +1.00000 q^{32} +3.57392 q^{33} -2.17852 q^{34} +17.4041 q^{35} -2.17284 q^{36} +0.397537 q^{37} -5.55126 q^{38} -5.26062 q^{39} +3.81385 q^{40} +8.48174 q^{41} -4.15033 q^{42} +5.40281 q^{43} -3.92961 q^{44} -8.28688 q^{45} -7.56459 q^{46} -1.01056 q^{47} -0.909483 q^{48} +13.8246 q^{49} +9.54543 q^{50} +1.98133 q^{51} +5.78418 q^{52} +3.74072 q^{53} +4.70461 q^{54} -14.9869 q^{55} +4.56339 q^{56} +5.04878 q^{57} +6.68108 q^{58} -7.17723 q^{59} -3.46863 q^{60} +11.6742 q^{61} +5.62008 q^{62} -9.91552 q^{63} +1.00000 q^{64} +22.0600 q^{65} +3.57392 q^{66} -5.51802 q^{67} -2.17852 q^{68} +6.87987 q^{69} +17.4041 q^{70} -5.97927 q^{71} -2.17284 q^{72} -4.89460 q^{73} +0.397537 q^{74} -8.68141 q^{75} -5.55126 q^{76} -17.9324 q^{77} -5.26062 q^{78} +4.24090 q^{79} +3.81385 q^{80} +2.23975 q^{81} +8.48174 q^{82} +5.78317 q^{83} -4.15033 q^{84} -8.30855 q^{85} +5.40281 q^{86} -6.07634 q^{87} -3.92961 q^{88} +10.4632 q^{89} -8.28688 q^{90} +26.3955 q^{91} -7.56459 q^{92} -5.11137 q^{93} -1.01056 q^{94} -21.1717 q^{95} -0.909483 q^{96} +3.37359 q^{97} +13.8246 q^{98} +8.53842 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.909483	−0.525090	−0.262545	−	0.964920i	$-0.584562\pi$
$3$	−0.909483	−0.525090	−0.262545	+	0.964920i	$0.584562\pi$
$4$	1.00000	0.500000
$5$	3.81385	1.70560	0.852802	−	0.522234i	$-0.174901\pi$
$5$	3.81385	1.70560	0.852802	+	0.522234i	$0.174901\pi$
$6$	−0.909483	−0.371295
$7$	4.56339	1.72480	0.862400	−	0.506227i	$-0.168960\pi$
$7$	4.56339	1.72480	0.862400	+	0.506227i	$0.168960\pi$
$8$	1.00000	0.353553
$9$	−2.17284	−0.724280
$10$	3.81385	1.20604
$11$	−3.92961	−1.18482	−0.592411	−	0.805636i	$-0.701824\pi$
$11$	−3.92961	−1.18482	−0.592411	+	0.805636i	$0.701824\pi$
$12$	−0.909483	−0.262545
$13$	5.78418	1.60424	0.802122	−	0.597160i	$-0.203704\pi$
$13$	5.78418	1.60424	0.802122	+	0.597160i	$0.203704\pi$
$14$	4.56339	1.21962
$15$	−3.46863	−0.895596
$16$	1.00000	0.250000
$17$	−2.17852	−0.528369	−0.264185	−	0.964472i	$-0.585103\pi$
$17$	−2.17852	−0.528369	−0.264185	+	0.964472i	$0.585103\pi$
$18$	−2.17284	−0.512143
$19$	−5.55126	−1.27355	−0.636773	−	0.771051i	$-0.719731\pi$
$19$	−5.55126	−1.27355	−0.636773	+	0.771051i	$0.719731\pi$
$20$	3.81385	0.852802
$21$	−4.15033	−0.905676
$22$	−3.92961	−0.837796
$23$	−7.56459	−1.57733	−0.788663	−	0.614826i	$-0.789226\pi$
$23$	−7.56459	−1.57733	−0.788663	+	0.614826i	$0.789226\pi$
$24$	−0.909483	−0.185648
$25$	9.54543	1.90909
$26$	5.78418	1.13437
$27$	4.70461	0.905403
$28$	4.56339	0.862400
$29$	6.68108	1.24065	0.620323	−	0.784346i	$-0.287001\pi$
$29$	6.68108	1.24065	0.620323	+	0.784346i	$0.287001\pi$
$30$	−3.46863	−0.633282
$31$	5.62008	1.00940	0.504699	−	0.863296i	$-0.331604\pi$
$31$	5.62008	1.00940	0.504699	+	0.863296i	$0.331604\pi$
$32$	1.00000	0.176777
$33$	3.57392	0.622139
$34$	−2.17852	−0.373614
$35$	17.4041	2.94183
$36$	−2.17284	−0.362140
$37$	0.397537	0.0653546	0.0326773	−	0.999466i	$-0.489597\pi$
$37$	0.397537	0.0653546	0.0326773	+	0.999466i	$0.489597\pi$
$38$	−5.55126	−0.900534
$39$	−5.26062	−0.842373
$40$	3.81385	0.603022
$41$	8.48174	1.32462	0.662312	−	0.749228i	$-0.269575\pi$
$41$	8.48174	1.32462	0.662312	+	0.749228i	$0.269575\pi$
$42$	−4.15033	−0.640410
$43$	5.40281	0.823921	0.411961	−	0.911202i	$-0.364844\pi$
$43$	5.40281	0.823921	0.411961	+	0.911202i	$0.364844\pi$
$44$	−3.92961	−0.592411
$45$	−8.28688	−1.23533
$46$	−7.56459	−1.11534
$47$	−1.01056	−0.147405	−0.0737027	−	0.997280i	$-0.523482\pi$
$47$	−1.01056	−0.147405	−0.0737027	+	0.997280i	$0.523482\pi$
$48$	−0.909483	−0.131273
$49$	13.8246	1.97494
$50$	9.54543	1.34993
$51$	1.98133	0.277442
$52$	5.78418	0.802122
$53$	3.74072	0.513828	0.256914	−	0.966434i	$-0.417294\pi$
$53$	3.74072	0.513828	0.256914	+	0.966434i	$0.417294\pi$
$54$	4.70461	0.640217
$55$	−14.9869	−2.02084
$56$	4.56339	0.609809
$57$	5.04878	0.668727
$58$	6.68108	0.877269
$59$	−7.17723	−0.934395	−0.467198	−	0.884153i	$-0.654736\pi$
$59$	−7.17723	−0.934395	−0.467198	+	0.884153i	$0.654736\pi$
$60$	−3.46863	−0.447798
$61$	11.6742	1.49473	0.747366	−	0.664413i	$-0.231318\pi$
$61$	11.6742	1.49473	0.747366	+	0.664413i	$0.231318\pi$
$62$	5.62008	0.713752
$63$	−9.91552	−1.24924
$64$	1.00000	0.125000
$65$	22.0600	2.73620
$66$	3.57392	0.439919
$67$	−5.51802	−0.674133	−0.337066	−	0.941481i	$-0.609435\pi$
$67$	−5.51802	−0.674133	−0.337066	+	0.941481i	$0.609435\pi$
$68$	−2.17852	−0.264185
$69$	6.87987	0.828239
$70$	17.4041	2.08019
$71$	−5.97927	−0.709609	−0.354805	−	0.934941i	$-0.615453\pi$
$71$	−5.97927	−0.709609	−0.354805	+	0.934941i	$0.615453\pi$
$72$	−2.17284	−0.256072
$73$	−4.89460	−0.572870	−0.286435	−	0.958100i	$-0.592470\pi$
$73$	−4.89460	−0.572870	−0.286435	+	0.958100i	$0.592470\pi$
$74$	0.397537	0.0462127
$75$	−8.68141	−1.00244
$76$	−5.55126	−0.636773
$77$	−17.9324	−2.04358
$78$	−5.26062	−0.595648
$79$	4.24090	0.477139	0.238569	−	0.971125i	$-0.423322\pi$
$79$	4.24090	0.477139	0.238569	+	0.971125i	$0.423322\pi$
$80$	3.81385	0.426401
$81$	2.23975	0.248862
$82$	8.48174	0.936651
$83$	5.78317	0.634785	0.317393	−	0.948294i	$-0.397193\pi$
$83$	5.78317	0.634785	0.317393	+	0.948294i	$0.397193\pi$
$84$	−4.15033	−0.452838
$85$	−8.30855	−0.901189
$86$	5.40281	0.582600
$87$	−6.07634	−0.651452
$88$	−3.92961	−0.418898
$89$	10.4632	1.10910	0.554551	−	0.832150i	$-0.312890\pi$
$89$	10.4632	1.10910	0.554551	+	0.832150i	$0.312890\pi$
$90$	−8.28688	−0.873514
$91$	26.3955	2.76700
$92$	−7.56459	−0.788663
$93$	−5.11137	−0.530025
$94$	−1.01056	−0.104231
$95$	−21.1717	−2.17217
$96$	−0.909483	−0.0928238
$97$	3.37359	0.342536	0.171268	−	0.985225i	$-0.445214\pi$
$97$	3.37359	0.342536	0.171268	+	0.985225i	$0.445214\pi$
$98$	13.8246	1.39649
$99$	8.53842	0.858143
$100$	9.54543	0.954543
$101$	−17.8025	−1.77141	−0.885705	−	0.464248i	$-0.846325\pi$
$101$	−17.8025	−1.77141	−0.885705	+	0.464248i	$0.846325\pi$
$102$	1.98133	0.196181
$103$	12.4501	1.22674	0.613370	−	0.789795i	$-0.289813\pi$
$103$	12.4501	1.22674	0.613370	+	0.789795i	$0.289813\pi$
$104$	5.78418	0.567186
$105$	−15.8287	−1.54472
$106$	3.74072	0.363331
$107$	16.3542	1.58102	0.790511	−	0.612448i	$-0.209815\pi$
$107$	16.3542	1.58102	0.790511	+	0.612448i	$0.209815\pi$
$108$	4.70461	0.452701
$109$	−15.9189	−1.52476	−0.762378	−	0.647132i	$-0.775968\pi$
$109$	−15.9189	−1.52476	−0.762378	+	0.647132i	$0.775968\pi$
$110$	−14.9869	−1.42895
$111$	−0.361553	−0.0343171
$112$	4.56339	0.431200
$113$	−13.2343	−1.24498	−0.622488	−	0.782629i	$-0.713878\pi$
$113$	−13.2343	−1.24498	−0.622488	+	0.782629i	$0.713878\pi$
$114$	5.04878	0.472862
$115$	−28.8502	−2.69029
$116$	6.68108	0.620323
$117$	−12.5681	−1.16192
$118$	−7.17723	−0.660717
$119$	−9.94145	−0.911332
$120$	−3.46863	−0.316641
$121$	4.44185	0.403805
$122$	11.6742	1.05693
$123$	−7.71400	−0.695548
$124$	5.62008	0.504699
$125$	17.3356	1.55054
$126$	−9.91552	−0.883345
$127$	−11.0583	−0.981263	−0.490632	−	0.871367i	$-0.663234\pi$
$127$	−11.0583	−0.981263	−0.490632	+	0.871367i	$0.663234\pi$
$128$	1.00000	0.0883883
$129$	−4.91377	−0.432633
$130$	22.0600	1.93479
$131$	−2.89886	−0.253275	−0.126637	−	0.991949i	$-0.540418\pi$
$131$	−2.89886	−0.253275	−0.126637	+	0.991949i	$0.540418\pi$
$132$	3.57392	0.311069
$133$	−25.3326	−2.19661
$134$	−5.51802	−0.476684
$135$	17.9427	1.54426
$136$	−2.17852	−0.186807
$137$	−7.19573	−0.614772	−0.307386	−	0.951585i	$-0.599454\pi$
$137$	−7.19573	−0.614772	−0.307386	+	0.951585i	$0.599454\pi$
$138$	6.87987	0.585653
$139$	−10.6266	−0.901341	−0.450670	−	0.892690i	$-0.648815\pi$
$139$	−10.6266	−0.901341	−0.450670	+	0.892690i	$0.648815\pi$
$140$	17.4041	1.47091
$141$	0.919088	0.0774012
$142$	−5.97927	−0.501769
$143$	−22.7296	−1.90074
$144$	−2.17284	−0.181070
$145$	25.4806	2.11605
$146$	−4.89460	−0.405080
$147$	−12.5732	−1.03702
$148$	0.397537	0.0326773
$149$	−5.00970	−0.410410	−0.205205	−	0.978719i	$-0.565786\pi$
$149$	−5.00970	−0.410410	−0.205205	+	0.978719i	$0.565786\pi$
$150$	−8.68141	−0.708834
$151$	−0.804620	−0.0654790	−0.0327395	−	0.999464i	$-0.510423\pi$
$151$	−0.804620	−0.0654790	−0.0327395	+	0.999464i	$0.510423\pi$
$152$	−5.55126	−0.450267
$153$	4.73358	0.382687
$154$	−17.9324	−1.44503
$155$	21.4341	1.72163
$156$	−5.26062	−0.421187
$157$	5.72338	0.456775	0.228388	−	0.973570i	$-0.426655\pi$
$157$	5.72338	0.456775	0.228388	+	0.973570i	$0.426655\pi$
$158$	4.24090	0.337388
$159$	−3.40213	−0.269806
$160$	3.81385	0.301511
$161$	−34.5202	−2.72057
$162$	2.23975	0.175972
$163$	15.0349	1.17762	0.588811	−	0.808271i	$-0.299596\pi$
$163$	15.0349	1.17762	0.588811	+	0.808271i	$0.299596\pi$
$164$	8.48174	0.662312
$165$	13.6304	1.06112
$166$	5.78317	0.448861
$167$	−12.5980	−0.974866	−0.487433	−	0.873160i	$-0.662067\pi$
$167$	−12.5980	−0.974866	−0.487433	+	0.873160i	$0.662067\pi$
$168$	−4.15033	−0.320205
$169$	20.4568	1.57360
$170$	−8.30855	−0.637237
$171$	12.0620	0.922405
$172$	5.40281	0.411961
$173$	−10.9464	−0.832242	−0.416121	−	0.909309i	$-0.636611\pi$
$173$	−10.9464	−0.832242	−0.416121	+	0.909309i	$0.636611\pi$
$174$	−6.07634	−0.460646
$175$	43.5595	3.29279
$176$	−3.92961	−0.296206
$177$	6.52757	0.490642
$178$	10.4632	0.784253
$179$	−22.3155	−1.66794	−0.833970	−	0.551810i	$-0.813937\pi$
$179$	−22.3155	−1.66794	−0.833970	+	0.551810i	$0.813937\pi$
$180$	−8.28688	−0.617667
$181$	−22.5198	−1.67389	−0.836943	−	0.547290i	$-0.815660\pi$
$181$	−22.5198	−1.67389	−0.836943	+	0.547290i	$0.815660\pi$
$182$	26.3955	1.95656
$183$	−10.6175	−0.784869
$184$	−7.56459	−0.557669
$185$	1.51614	0.111469
$186$	−5.11137	−0.374784
$187$	8.56075	0.626024
$188$	−1.01056	−0.0737027
$189$	21.4690	1.56164
$190$	−21.1717	−1.53595
$191$	14.1797	1.02601	0.513003	−	0.858387i	$-0.328533\pi$
$191$	14.1797	1.02601	0.513003	+	0.858387i	$0.328533\pi$
$192$	−0.909483	−0.0656363
$193$	12.6187	0.908315	0.454157	−	0.890921i	$-0.349940\pi$
$193$	12.6187	0.908315	0.454157	+	0.890921i	$0.349940\pi$
$194$	3.37359	0.242209
$195$	−20.0632	−1.43675
$196$	13.8246	0.987468
$197$	21.6427	1.54198	0.770990	−	0.636847i	$-0.219762\pi$
$197$	21.6427	1.54198	0.770990	+	0.636847i	$0.219762\pi$
$198$	8.53842	0.606799
$199$	−11.1593	−0.791062	−0.395531	−	0.918453i	$-0.629439\pi$
$199$	−11.1593	−0.791062	−0.395531	+	0.918453i	$0.629439\pi$
$200$	9.54543	0.674964
$201$	5.01854	0.353981
$202$	−17.8025	−1.25258
$203$	30.4884	2.13987
$204$	1.98133	0.138721
$205$	32.3480	2.25929
$206$	12.4501	0.867437
$207$	16.4366	1.14243
$208$	5.78418	0.401061
$209$	21.8143	1.50893
$210$	−15.8287	−1.09229
$211$	7.76198	0.534357	0.267178	−	0.963647i	$-0.413909\pi$
$211$	7.76198	0.534357	0.267178	+	0.963647i	$0.413909\pi$
$212$	3.74072	0.256914
$213$	5.43805	0.372609
$214$	16.3542	1.11795
$215$	20.6055	1.40528
$216$	4.70461	0.320108
$217$	25.6467	1.74101
$218$	−15.9189	−1.07817
$219$	4.45156	0.300808
$220$	−14.9869	−1.01042
$221$	−12.6010	−0.847633
$222$	−0.361553	−0.0242658
$223$	22.9478	1.53670	0.768349	−	0.640031i	$-0.221079\pi$
$223$	22.9478	1.53670	0.768349	+	0.640031i	$0.221079\pi$
$224$	4.56339	0.304904
$225$	−20.7407	−1.38271
$226$	−13.2343	−0.880332
$227$	−20.3165	−1.34846	−0.674228	−	0.738523i	$-0.735524\pi$
$227$	−20.3165	−1.34846	−0.674228	+	0.738523i	$0.735524\pi$
$228$	5.04878	0.334364
$229$	2.34851	0.155194	0.0775971	−	0.996985i	$-0.475275\pi$
$229$	2.34851	0.155194	0.0775971	+	0.996985i	$0.475275\pi$
$230$	−28.8502	−1.90232
$231$	16.3092	1.07307
$232$	6.68108	0.438635
$233$	3.83142	0.251005	0.125502	−	0.992093i	$-0.459946\pi$
$233$	3.83142	0.251005	0.125502	+	0.992093i	$0.459946\pi$
$234$	−12.5681	−0.821603
$235$	−3.85412	−0.251415
$236$	−7.17723	−0.467198
$237$	−3.85703	−0.250541
$238$	−9.94145	−0.644409
$239$	−8.82897	−0.571099	−0.285549	−	0.958364i	$-0.592176\pi$
$239$	−8.82897	−0.571099	−0.285549	+	0.958364i	$0.592176\pi$
$240$	−3.46863	−0.223899
$241$	−19.6095	−1.26316	−0.631580	−	0.775311i	$-0.717593\pi$
$241$	−19.6095	−1.26316	−0.631580	+	0.775311i	$0.717593\pi$
$242$	4.44185	0.285533
$243$	−16.1509	−1.03608
$244$	11.6742	0.747366
$245$	52.7247	3.36846
$246$	−7.71400	−0.491826
$247$	−32.1095	−2.04308
$248$	5.62008	0.356876
$249$	−5.25969	−0.333320
$250$	17.3356	1.09640
$251$	−17.3812	−1.09709	−0.548546	−	0.836121i	$-0.684818\pi$
$251$	−17.3812	−1.09709	−0.548546	+	0.836121i	$0.684818\pi$
$252$	−9.91552	−0.624619
$253$	29.7259	1.86885
$254$	−11.0583	−0.693858
$255$	7.55649	0.473206
$256$	1.00000	0.0625000
$257$	−23.2040	−1.44742	−0.723711	−	0.690103i	$-0.757565\pi$
$257$	−23.2040	−1.44742	−0.723711	+	0.690103i	$0.757565\pi$
$258$	−4.91377	−0.305918
$259$	1.81412	0.112724
$260$	22.0600	1.36810
$261$	−14.5169	−0.898575
$262$	−2.89886	−0.179092
$263$	8.37380	0.516350	0.258175	−	0.966098i	$-0.416879\pi$
$263$	8.37380	0.516350	0.258175	+	0.966098i	$0.416879\pi$
$264$	3.57392	0.219959
$265$	14.2665	0.876387
$266$	−25.3326	−1.55324
$267$	−9.51614	−0.582378
$268$	−5.51802	−0.337066
$269$	−10.3111	−0.628679	−0.314340	−	0.949311i	$-0.601783\pi$
$269$	−10.3111	−0.628679	−0.314340	+	0.949311i	$0.601783\pi$
$270$	17.9427	1.09196
$271$	−6.42045	−0.390014	−0.195007	−	0.980802i	$-0.562473\pi$
$271$	−6.42045	−0.390014	−0.195007	+	0.980802i	$0.562473\pi$
$272$	−2.17852	−0.132092
$273$	−24.0063	−1.45293
$274$	−7.19573	−0.434710
$275$	−37.5098	−2.26193
$276$	6.87987	0.414119
$277$	24.9475	1.49895	0.749474	−	0.662034i	$-0.230306\pi$
$277$	24.9475	1.49895	0.749474	+	0.662034i	$0.230306\pi$
$278$	−10.6266	−0.637344
$279$	−12.2115	−0.731086
$280$	17.4041	1.04009
$281$	−17.1583	−1.02358	−0.511789	−	0.859111i	$-0.671017\pi$
$281$	−17.1583	−1.02358	−0.511789	+	0.859111i	$0.671017\pi$
$282$	0.919088	0.0547309
$283$	15.7896	0.938597	0.469298	−	0.883040i	$-0.344507\pi$
$283$	15.7896	0.938597	0.469298	+	0.883040i	$0.344507\pi$
$284$	−5.97927	−0.354805
$285$	19.2553	1.14058
$286$	−22.7296	−1.34403
$287$	38.7055	2.28471
$288$	−2.17284	−0.128036
$289$	−12.2540	−0.720826
$290$	25.4806	1.49627
$291$	−3.06822	−0.179862
$292$	−4.89460	−0.286435
$293$	−11.7153	−0.684415	−0.342208	−	0.939624i	$-0.611175\pi$
$293$	−11.7153	−0.684415	−0.342208	+	0.939624i	$0.611175\pi$
$294$	−12.5732	−0.733284
$295$	−27.3728	−1.59371
$296$	0.397537	0.0231063
$297$	−18.4873	−1.07274
$298$	−5.00970	−0.290204
$299$	−43.7550	−2.53041
$300$	−8.68141	−0.501221
$301$	24.6552	1.42110
$302$	−0.804620	−0.0463007
$303$	16.1910	0.930151
$304$	−5.55126	−0.318387
$305$	44.5237	2.54942
$306$	4.73358	0.270601
$307$	−10.0457	−0.573336	−0.286668	−	0.958030i	$-0.592548\pi$
$307$	−10.0457	−0.573336	−0.286668	+	0.958030i	$0.592548\pi$
$308$	−17.9324	−1.02179
$309$	−11.3231	−0.644150
$310$	21.4341	1.21738
$311$	11.5924	0.657346	0.328673	−	0.944444i	$-0.393399\pi$
$311$	11.5924	0.657346	0.328673	+	0.944444i	$0.393399\pi$
$312$	−5.26062	−0.297824
$313$	17.2100	0.972769	0.486384	−	0.873745i	$-0.338315\pi$
$313$	17.2100	0.972769	0.486384	+	0.873745i	$0.338315\pi$
$314$	5.72338	0.322989
$315$	−37.8163	−2.13071
$316$	4.24090	0.238569
$317$	13.0661	0.733865	0.366933	−	0.930247i	$-0.380408\pi$
$317$	13.0661	0.733865	0.366933	+	0.930247i	$0.380408\pi$
$318$	−3.40213	−0.190782
$319$	−26.2541	−1.46995
$320$	3.81385	0.213201
$321$	−14.8739	−0.830180
$322$	−34.5202	−1.92373
$323$	12.0935	0.672903
$324$	2.23975	0.124431
$325$	55.2125	3.06264
$326$	15.0349	0.832705
$327$	14.4780	0.800635
$328$	8.48174	0.468326
$329$	−4.61158	−0.254245
$330$	13.6304	0.750327
$331$	10.6184	0.583642	0.291821	−	0.956473i	$-0.405739\pi$
$331$	10.6184	0.583642	0.291821	+	0.956473i	$0.405739\pi$
$332$	5.78317	0.317393
$333$	−0.863784	−0.0473350
$334$	−12.5980	−0.689335
$335$	−21.0449	−1.14980
$336$	−4.15033	−0.226419
$337$	−2.17168	−0.118299	−0.0591495	−	0.998249i	$-0.518839\pi$
$337$	−2.17168	−0.118299	−0.0591495	+	0.998249i	$0.518839\pi$
$338$	20.4568	1.11270
$339$	12.0364	0.653725
$340$	−8.30855	−0.450594
$341$	−22.0848	−1.19596
$342$	12.0620	0.652238
$343$	31.1431	1.68157
$344$	5.40281	0.291300
$345$	26.2388	1.41265
$346$	−10.9464	−0.588484
$347$	−36.4191	−1.95508	−0.977541	−	0.210745i	$-0.932411\pi$
$347$	−36.4191	−1.95508	−0.977541	+	0.210745i	$0.932411\pi$
$348$	−6.07634	−0.325726
$349$	−21.3196	−1.14121	−0.570606	−	0.821224i	$-0.693292\pi$
$349$	−21.3196	−1.14121	−0.570606	+	0.821224i	$0.693292\pi$
$350$	43.5595	2.32835
$351$	27.2123	1.45249
$352$	−3.92961	−0.209449
$353$	29.4288	1.56634	0.783168	−	0.621810i	$-0.213602\pi$
$353$	29.4288	1.56634	0.783168	+	0.621810i	$0.213602\pi$
$354$	6.52757	0.346936
$355$	−22.8040	−1.21031
$356$	10.4632	0.554551
$357$	9.04159	0.478531
$358$	−22.3155	−1.17941
$359$	19.7246	1.04103	0.520513	−	0.853853i	$-0.325741\pi$
$359$	19.7246	1.04103	0.520513	+	0.853853i	$0.325741\pi$
$360$	−8.28688	−0.436757
$361$	11.8165	0.621921
$362$	−22.5198	−1.18362
$363$	−4.03979	−0.212034
$364$	26.3955	1.38350
$365$	−18.6673	−0.977089
$366$	−10.6175	−0.554986
$367$	−10.5181	−0.549043	−0.274521	−	0.961581i	$-0.588519\pi$
$367$	−10.5181	−0.549043	−0.274521	+	0.961581i	$0.588519\pi$
$368$	−7.56459	−0.394331
$369$	−18.4295	−0.959399
$370$	1.51614	0.0788206
$371$	17.0704	0.886251
$372$	−5.11137	−0.265012
$373$	13.9858	0.724157	0.362078	−	0.932148i	$-0.382067\pi$
$373$	13.9858	0.724157	0.362078	+	0.932148i	$0.382067\pi$
$374$	8.56075	0.442666
$375$	−15.7664	−0.814173
$376$	−1.01056	−0.0521157
$377$	38.6446	1.99030
$378$	21.4690	1.10425
$379$	−0.336014	−0.0172599	−0.00862994	−	0.999963i	$-0.502747\pi$
$379$	−0.336014	−0.0172599	−0.00862994	+	0.999963i	$0.502747\pi$
$380$	−21.1717	−1.08608
$381$	10.0573	0.515252
$382$	14.1797	0.725496
$383$	−31.9783	−1.63402	−0.817008	−	0.576626i	$-0.804369\pi$
$383$	−31.9783	−1.63402	−0.817008	+	0.576626i	$0.804369\pi$
$384$	−0.909483	−0.0464119
$385$	−68.3913	−3.48554
$386$	12.6187	0.642276
$387$	−11.7394	−0.596750
$388$	3.37359	0.171268
$389$	2.40487	0.121932	0.0609658	−	0.998140i	$-0.480582\pi$
$389$	2.40487	0.121932	0.0609658	+	0.998140i	$0.480582\pi$
$390$	−20.0632	−1.01594
$391$	16.4796	0.833410
$392$	13.8246	0.698245
$393$	2.63646	0.132992
$394$	21.6427	1.09034
$395$	16.1741	0.813809
$396$	8.53842	0.429072
$397$	−27.0505	−1.35763	−0.678814	−	0.734311i	$-0.737506\pi$
$397$	−27.0505	−1.35763	−0.678814	+	0.734311i	$0.737506\pi$
$398$	−11.1593	−0.559365
$399$	23.0396	1.15342
$400$	9.54543	0.477271
$401$	−23.8839	−1.19270	−0.596352	−	0.802723i	$-0.703384\pi$
$401$	−23.8839	−1.19270	−0.596352	+	0.802723i	$0.703384\pi$
$402$	5.01854	0.250302
$403$	32.5076	1.61932
$404$	−17.8025	−0.885705
$405$	8.54208	0.424459
$406$	30.4884	1.51311
$407$	−1.56216	−0.0774336
$408$	1.98133	0.0980904
$409$	−30.0686	−1.48680	−0.743398	−	0.668850i	$-0.766787\pi$
$409$	−30.0686	−1.48680	−0.743398	+	0.668850i	$0.766787\pi$
$410$	32.3480	1.59756
$411$	6.54439	0.322811
$412$	12.4501	0.613370
$413$	−32.7525	−1.61165
$414$	16.4366	0.807817
$415$	22.0561	1.08269
$416$	5.78418	0.283593
$417$	9.66476	0.473285
$418$	21.8143	1.06697
$419$	24.9649	1.21962	0.609809	−	0.792549i	$-0.291246\pi$
$419$	24.9649	1.21962	0.609809	+	0.792549i	$0.291246\pi$
$420$	−15.8287	−0.772362
$421$	−38.4558	−1.87422	−0.937111	−	0.349031i	$-0.886511\pi$
$421$	−38.4558	−1.87422	−0.937111	+	0.349031i	$0.886511\pi$
$422$	7.76198	0.377847
$423$	2.19579	0.106763
$424$	3.74072	0.181666
$425$	−20.7949	−1.00870
$426$	5.43805	0.263474
$427$	53.2741	2.57811
$428$	16.3542	0.790511
$429$	20.6722	0.998063
$430$	20.6055	0.993685
$431$	8.85993	0.426768	0.213384	−	0.976968i	$-0.431551\pi$
$431$	8.85993	0.426768	0.213384	+	0.976968i	$0.431551\pi$
$432$	4.70461	0.226351
$433$	25.2853	1.21513	0.607567	−	0.794269i	$-0.292146\pi$
$433$	25.2853	1.21513	0.607567	+	0.794269i	$0.292146\pi$
$434$	25.6467	1.23108
$435$	−23.1742	−1.11112
$436$	−15.9189	−0.762378
$437$	41.9930	2.00880
$438$	4.45156	0.212704
$439$	20.3042	0.969068	0.484534	−	0.874772i	$-0.338989\pi$
$439$	20.3042	0.969068	0.484534	+	0.874772i	$0.338989\pi$
$440$	−14.9869	−0.714474
$441$	−30.0385	−1.43041
$442$	−12.6010	−0.599367
$443$	−22.8603	−1.08613	−0.543063	−	0.839692i	$-0.682735\pi$
$443$	−22.8603	−1.08613	−0.543063	+	0.839692i	$0.682735\pi$
$444$	−0.361553	−0.0171585
$445$	39.9052	1.89169
$446$	22.9478	1.08661
$447$	4.55624	0.215503
$448$	4.56339	0.215600
$449$	3.91945	0.184970	0.0924852	−	0.995714i	$-0.470519\pi$
$449$	3.91945	0.184970	0.0924852	+	0.995714i	$0.470519\pi$
$450$	−20.7407	−0.977725
$451$	−33.3299	−1.56945
$452$	−13.2343	−0.622488
$453$	0.731788	0.0343824
$454$	−20.3165	−0.953503
$455$	100.668	4.71941
$456$	5.04878	0.236431
$457$	27.2179	1.27320	0.636599	−	0.771195i	$-0.280341\pi$
$457$	27.2179	1.27320	0.636599	+	0.771195i	$0.280341\pi$
$458$	2.34851	0.109739
$459$	−10.2491	−0.478387
$460$	−28.8502	−1.34515
$461$	24.7940	1.15477	0.577385	−	0.816472i	$-0.304073\pi$
$461$	24.7940	1.15477	0.577385	+	0.816472i	$0.304073\pi$
$462$	16.3092	0.758772
$463$	−37.4416	−1.74006	−0.870030	−	0.492998i	$-0.835901\pi$
$463$	−37.4416	−1.74006	−0.870030	+	0.492998i	$0.835901\pi$
$464$	6.68108	0.310162
$465$	−19.4940	−0.904012
$466$	3.83142	0.177487
$467$	9.78265	0.452687	0.226343	−	0.974048i	$-0.427323\pi$
$467$	9.78265	0.452687	0.226343	+	0.974048i	$0.427323\pi$
$468$	−12.5681	−0.580961
$469$	−25.1809	−1.16274
$470$	−3.85412	−0.177777
$471$	−5.20532	−0.239848
$472$	−7.17723	−0.330359
$473$	−21.2310	−0.976201
$474$	−3.85703	−0.177159
$475$	−52.9892	−2.43131
$476$	−9.94145	−0.455666
$477$	−8.12800	−0.372155
$478$	−8.82897	−0.403828
$479$	−36.4494	−1.66542	−0.832708	−	0.553712i	$-0.813211\pi$
$479$	−36.4494	−1.66542	−0.832708	+	0.553712i	$0.813211\pi$
$480$	−3.46863	−0.158321
$481$	2.29942	0.104845
$482$	−19.6095	−0.893189
$483$	31.3955	1.42855
$484$	4.44185	0.201902
$485$	12.8663	0.584230
$486$	−16.1509	−0.732618
$487$	−22.2659	−1.00897	−0.504483	−	0.863422i	$-0.668317\pi$
$487$	−22.2659	−1.00897	−0.504483	+	0.863422i	$0.668317\pi$
$488$	11.6742	0.528467
$489$	−13.6740	−0.618358
$490$	52.7247	2.38186
$491$	9.30011	0.419708	0.209854	−	0.977733i	$-0.432701\pi$
$491$	9.30011	0.419708	0.209854	+	0.977733i	$0.432701\pi$
$492$	−7.71400	−0.347774
$493$	−14.5549	−0.655519
$494$	−32.1095	−1.44468
$495$	32.5642	1.46365
$496$	5.62008	0.252349
$497$	−27.2858	−1.22393
$498$	−5.25969	−0.235693
$499$	15.8834	0.711041	0.355520	−	0.934669i	$-0.384304\pi$
$499$	15.8834	0.711041	0.355520	+	0.934669i	$0.384304\pi$
$500$	17.3356	0.775270
$501$	11.4577	0.511893
$502$	−17.3812	−0.775761
$503$	2.21851	0.0989183	0.0494591	−	0.998776i	$-0.484250\pi$
$503$	2.21851	0.0989183	0.0494591	+	0.998776i	$0.484250\pi$
$504$	−9.91552	−0.441672
$505$	−67.8958	−3.02133
$506$	29.7259	1.32148
$507$	−18.6051	−0.826281
$508$	−11.0583	−0.490632
$509$	−29.3414	−1.30053	−0.650267	−	0.759706i	$-0.725343\pi$
$509$	−29.3414	−1.30053	−0.650267	+	0.759706i	$0.725343\pi$
$510$	7.55649	0.334607
$511$	−22.3360	−0.988086
$512$	1.00000	0.0441942
$513$	−26.1165	−1.15307
$514$	−23.2040	−1.02348
$515$	47.4826	2.09233
$516$	−4.91377	−0.216317
$517$	3.97111	0.174649
$518$	1.81412	0.0797077
$519$	9.95560	0.437002
$520$	22.0600	0.967394
$521$	8.04984	0.352670	0.176335	−	0.984330i	$-0.443576\pi$
$521$	8.04984	0.352670	0.176335	+	0.984330i	$0.443576\pi$
$522$	−14.5169	−0.635389
$523$	1.02636	0.0448795	0.0224397	−	0.999748i	$-0.492857\pi$
$523$	1.02636	0.0448795	0.0224397	+	0.999748i	$0.492857\pi$
$524$	−2.89886	−0.126637
$525$	−39.6167	−1.72901
$526$	8.37380	0.365115
$527$	−12.2435	−0.533334
$528$	3.57392	0.155535
$529$	34.2230	1.48796
$530$	14.2665	0.619699
$531$	15.5950	0.676764
$532$	−25.3326	−1.09831
$533$	49.0599	2.12502
$534$	−9.51614	−0.411804
$535$	62.3725	2.69660
$536$	−5.51802	−0.238342
$537$	20.2956	0.875819
$538$	−10.3111	−0.444543
$539$	−54.3251	−2.33995
$540$	17.9427	0.772129
$541$	−10.1857	−0.437918	−0.218959	−	0.975734i	$-0.570266\pi$
$541$	−10.1857	−0.437918	−0.218959	+	0.975734i	$0.570266\pi$
$542$	−6.42045	−0.275782
$543$	20.4814	0.878942
$544$	−2.17852	−0.0934034
$545$	−60.7123	−2.60063
$546$	−24.0063	−1.02737
$547$	7.79684	0.333369	0.166684	−	0.986010i	$-0.446694\pi$
$547$	7.79684	0.333369	0.166684	+	0.986010i	$0.446694\pi$
$548$	−7.19573	−0.307386
$549$	−25.3662	−1.08260
$550$	−37.5098	−1.59942
$551$	−37.0885	−1.58002
$552$	6.87987	0.292827
$553$	19.3529	0.822969
$554$	24.9475	1.05992
$555$	−1.37891	−0.0585314
$556$	−10.6266	−0.450670
$557$	18.5775	0.787155	0.393578	−	0.919291i	$-0.371237\pi$
$557$	18.5775	0.787155	0.393578	+	0.919291i	$0.371237\pi$
$558$	−12.2115	−0.516956
$559$	31.2509	1.32177
$560$	17.4041	0.735457
$561$	−7.78586	−0.328719
$562$	−17.1583	−0.723779
$563$	35.0113	1.47555	0.737775	−	0.675047i	$-0.235877\pi$
$563$	35.0113	1.47555	0.737775	+	0.675047i	$0.235877\pi$
$564$	0.919088	0.0387006
$565$	−50.4735	−2.12344
$566$	15.7896	0.663688
$567$	10.2209	0.429237
$568$	−5.97927	−0.250885
$569$	18.1945	0.762752	0.381376	−	0.924420i	$-0.375450\pi$
$569$	18.1945	0.762752	0.381376	+	0.924420i	$0.375450\pi$
$570$	19.2553	0.806515
$571$	−39.9862	−1.67337	−0.836685	−	0.547684i	$-0.815510\pi$
$571$	−39.9862	−1.67337	−0.836685	+	0.547684i	$0.815510\pi$
$572$	−22.7296	−0.950372
$573$	−12.8962	−0.538746
$574$	38.7055	1.61554
$575$	−72.2072	−3.01125
$576$	−2.17284	−0.0905350
$577$	−18.4247	−0.767029	−0.383515	−	0.923535i	$-0.625286\pi$
$577$	−18.4247	−0.767029	−0.383515	+	0.923535i	$0.625286\pi$
$578$	−12.2540	−0.509701
$579$	−11.4765	−0.476947
$580$	25.4806	1.05803
$581$	26.3909	1.09488
$582$	−3.06822	−0.127182
$583$	−14.6996	−0.608795
$584$	−4.89460	−0.202540
$585$	−47.9328	−1.98178
$586$	−11.7153	−0.483955
$587$	2.39930	0.0990299	0.0495149	−	0.998773i	$-0.484232\pi$
$587$	2.39930	0.0990299	0.0495149	+	0.998773i	$0.484232\pi$
$588$	−12.5732	−0.518510
$589$	−31.1986	−1.28551
$590$	−27.3728	−1.12692
$591$	−19.6837	−0.809679
$592$	0.397537	0.0163387
$593$	8.83218	0.362694	0.181347	−	0.983419i	$-0.441954\pi$
$593$	8.83218	0.362694	0.181347	+	0.983419i	$0.441954\pi$
$594$	−18.4873	−0.758543
$595$	−37.9152	−1.55437
$596$	−5.00970	−0.205205
$597$	10.1492	0.415379
$598$	−43.7550	−1.78927
$599$	19.5942	0.800597	0.400298	−	0.916385i	$-0.368907\pi$
$599$	19.5942	0.800597	0.400298	+	0.916385i	$0.368907\pi$
$600$	−8.68141	−0.354417
$601$	6.11965	0.249626	0.124813	−	0.992180i	$-0.460167\pi$
$601$	6.11965	0.249626	0.124813	+	0.992180i	$0.460167\pi$
$602$	24.6552	1.00487
$603$	11.9898	0.488261
$604$	−0.804620	−0.0327395
$605$	16.9405	0.688731
$606$	16.1910	0.657716
$607$	−11.9210	−0.483859	−0.241930	−	0.970294i	$-0.577780\pi$
$607$	−11.9210	−0.483859	−0.241930	+	0.970294i	$0.577780\pi$
$608$	−5.55126	−0.225133
$609$	−27.7287	−1.12362
$610$	44.5237	1.80271
$611$	−5.84527	−0.236474
$612$	4.73358	0.191344
$613$	38.5654	1.55764	0.778821	−	0.627246i	$-0.215818\pi$
$613$	38.5654	1.55764	0.778821	+	0.627246i	$0.215818\pi$
$614$	−10.0457	−0.405410
$615$	−29.4200	−1.18633
$616$	−17.9324	−0.722515
$617$	−43.9266	−1.76842	−0.884209	−	0.467091i	$-0.845302\pi$
$617$	−43.9266	−1.76842	−0.884209	+	0.467091i	$0.845302\pi$
$618$	−11.3231	−0.455483
$619$	20.8759	0.839075	0.419537	−	0.907738i	$-0.362192\pi$
$619$	20.8759	0.839075	0.419537	+	0.907738i	$0.362192\pi$
$620$	21.4341	0.860816
$621$	−35.5884	−1.42812
$622$	11.5924	0.464814
$623$	47.7479	1.91298
$624$	−5.26062	−0.210593
$625$	18.3880	0.735521
$626$	17.2100	0.687851
$627$	−19.8397	−0.792323
$628$	5.72338	0.228388
$629$	−0.866043	−0.0345314
$630$	−37.8163	−1.50664
$631$	15.6536	0.623159	0.311580	−	0.950220i	$-0.399142\pi$
$631$	15.6536	0.623159	0.311580	+	0.950220i	$0.399142\pi$
$632$	4.24090	0.168694
$633$	−7.05939	−0.280586
$634$	13.0661	0.518921
$635$	−42.1746	−1.67365
$636$	−3.40213	−0.134903
$637$	79.9637	3.16828
$638$	−26.2541	−1.03941
$639$	12.9920	0.513956
$640$	3.81385	0.150756
$641$	−19.6541	−0.776291	−0.388146	−	0.921598i	$-0.626884\pi$
$641$	−19.6541	−0.776291	−0.388146	+	0.921598i	$0.626884\pi$
$642$	−14.8739	−0.587026
$643$	−33.3120	−1.31370	−0.656849	−	0.754022i	$-0.728111\pi$
$643$	−33.3120	−1.31370	−0.656849	+	0.754022i	$0.728111\pi$
$644$	−34.5202	−1.36029
$645$	−18.7404	−0.737901
$646$	12.0935	0.475814
$647$	−31.6708	−1.24511	−0.622555	−	0.782576i	$-0.713905\pi$
$647$	−31.6708	−1.24511	−0.622555	+	0.782576i	$0.713905\pi$
$648$	2.23975	0.0879859
$649$	28.2037	1.10709
$650$	55.2125	2.16561
$651$	−23.3252	−0.914187
$652$	15.0349	0.588811
$653$	12.2492	0.479349	0.239674	−	0.970853i	$-0.422959\pi$
$653$	12.2492	0.479349	0.239674	+	0.970853i	$0.422959\pi$
$654$	14.4780	0.566134
$655$	−11.0558	−0.431986
$656$	8.48174	0.331156
$657$	10.6352	0.414918
$658$	−4.61158	−0.179778
$659$	4.75684	0.185300	0.0926501	−	0.995699i	$-0.470466\pi$
$659$	4.75684	0.185300	0.0926501	+	0.995699i	$0.470466\pi$
$660$	13.6304	0.530561
$661$	2.45392	0.0954464	0.0477232	−	0.998861i	$-0.484803\pi$
$661$	2.45392	0.0954464	0.0477232	+	0.998861i	$0.484803\pi$
$662$	10.6184	0.412697
$663$	11.4604	0.445084
$664$	5.78317	0.224430
$665$	−96.6146	−3.74655
$666$	−0.863784	−0.0334709
$667$	−50.5397	−1.95690
$668$	−12.5980	−0.487433
$669$	−20.8706	−0.806905
$670$	−21.0449	−0.813034
$671$	−45.8752	−1.77099
$672$	−4.15033	−0.160102
$673$	18.0457	0.695610	0.347805	−	0.937567i	$-0.386927\pi$
$673$	18.0457	0.695610	0.347805	+	0.937567i	$0.386927\pi$
$674$	−2.17168	−0.0836500
$675$	44.9075	1.72849
$676$	20.4568	0.786799
$677$	26.6094	1.02268	0.511341	−	0.859378i	$-0.329149\pi$
$677$	26.6094	1.02268	0.511341	+	0.859378i	$0.329149\pi$
$678$	12.0364	0.462254
$679$	15.3950	0.590806
$680$	−8.30855	−0.318618
$681$	18.4776	0.708062
$682$	−22.0848	−0.845669
$683$	−28.3101	−1.08326	−0.541628	−	0.840618i	$-0.682192\pi$
$683$	−28.3101	−1.08326	−0.541628	+	0.840618i	$0.682192\pi$
$684$	12.0620	0.461202
$685$	−27.4434	−1.04856
$686$	31.1431	1.18905
$687$	−2.13593	−0.0814910
$688$	5.40281	0.205980
$689$	21.6370	0.824305
$690$	26.2388	0.998892
$691$	−17.2270	−0.655346	−0.327673	−	0.944791i	$-0.606264\pi$
$691$	−17.2270	−0.655346	−0.327673	+	0.944791i	$0.606264\pi$
$692$	−10.9464	−0.416121
$693$	38.9642	1.48013
$694$	−36.4191	−1.38245
$695$	−40.5284	−1.53733
$696$	−6.07634	−0.230323
$697$	−18.4777	−0.699891
$698$	−21.3196	−0.806959
$699$	−3.48462	−0.131800
$700$	43.5595	1.64640
$701$	2.10923	0.0796645	0.0398322	−	0.999206i	$-0.487318\pi$
$701$	2.10923	0.0796645	0.0398322	+	0.999206i	$0.487318\pi$
$702$	27.2123	1.02706
$703$	−2.20683	−0.0832322
$704$	−3.92961	−0.148103
$705$	3.50526	0.132016
$706$	29.4288	1.10757
$707$	−81.2396	−3.05533
$708$	6.52757	0.245321
$709$	−48.2100	−1.81057	−0.905283	−	0.424810i	$-0.860341\pi$
$709$	−48.2100	−1.81057	−0.905283	+	0.424810i	$0.860341\pi$
$710$	−22.8040	−0.855820
$711$	−9.21480	−0.345582
$712$	10.4632	0.392126
$713$	−42.5136	−1.59215
$714$	9.04159	0.338373
$715$	−86.6872	−3.24192
$716$	−22.3155	−0.833970
$717$	8.02980	0.299878
$718$	19.7246	0.736117
$719$	40.8658	1.52404	0.762019	−	0.647554i	$-0.224208\pi$
$719$	40.8658	1.52404	0.762019	+	0.647554i	$0.224208\pi$
$720$	−8.28688	−0.308834
$721$	56.8145	2.11588
$722$	11.8165	0.439765
$723$	17.8345	0.663273
$724$	−22.5198	−0.836943
$725$	63.7738	2.36850
$726$	−4.03979	−0.149931
$727$	−34.1774	−1.26757	−0.633785	−	0.773509i	$-0.718500\pi$
$727$	−34.1774	−1.26757	−0.633785	+	0.773509i	$0.718500\pi$
$728$	26.3955	0.978282
$729$	7.96967	0.295173
$730$	−18.6673	−0.690906
$731$	−11.7702	−0.435335
$732$	−10.6175	−0.392434
$733$	14.8200	0.547389	0.273694	−	0.961817i	$-0.411754\pi$
$733$	14.8200	0.547389	0.273694	+	0.961817i	$0.411754\pi$
$734$	−10.5181	−0.388232
$735$	−47.9523	−1.76875
$736$	−7.56459	−0.278834
$737$	21.6837	0.798728
$738$	−18.4295	−0.678398
$739$	−6.06416	−0.223074	−0.111537	−	0.993760i	$-0.535577\pi$
$739$	−6.06416	−0.223074	−0.111537	+	0.993760i	$0.535577\pi$
$740$	1.51614	0.0557346
$741$	29.2031	1.07280
$742$	17.0704	0.626674
$743$	−13.9719	−0.512578	−0.256289	−	0.966600i	$-0.582500\pi$
$743$	−13.9719	−0.512578	−0.256289	+	0.966600i	$0.582500\pi$
$744$	−5.11137	−0.187392
$745$	−19.1062	−0.699998
$746$	13.9858	0.512056
$747$	−12.5659	−0.459762
$748$	8.56075	0.313012
$749$	74.6307	2.72695
$750$	−15.7664	−0.575707
$751$	5.72999	0.209090	0.104545	−	0.994520i	$-0.466661\pi$
$751$	5.72999	0.209090	0.104545	+	0.994520i	$0.466661\pi$
$752$	−1.01056	−0.0368514
$753$	15.8079	0.576072
$754$	38.6446	1.40735
$755$	−3.06870	−0.111681
$756$	21.4690	0.780820
$757$	−2.04940	−0.0744867	−0.0372433	−	0.999306i	$-0.511858\pi$
$757$	−2.04940	−0.0744867	−0.0372433	+	0.999306i	$0.511858\pi$
$758$	−0.336014	−0.0122046
$759$	−27.0352	−0.981316
$760$	−21.1717	−0.767977
$761$	29.5508	1.07122	0.535608	−	0.844467i	$-0.320083\pi$
$761$	29.5508	1.07122	0.535608	+	0.844467i	$0.320083\pi$
$762$	10.0573	0.364338
$763$	−72.6443	−2.62990
$764$	14.1797	0.513003
$765$	18.0532	0.652713
$766$	−31.9783	−1.15542
$767$	−41.5144	−1.49900
$768$	−0.909483	−0.0328182
$769$	−27.5950	−0.995101	−0.497550	−	0.867435i	$-0.665767\pi$
$769$	−27.5950	−0.995101	−0.497550	+	0.867435i	$0.665767\pi$
$770$	−68.3913	−2.46465
$771$	21.1036	0.760028
$772$	12.6187	0.454157
$773$	37.3104	1.34196	0.670980	−	0.741475i	$-0.265874\pi$
$773$	37.3104	1.34196	0.670980	+	0.741475i	$0.265874\pi$
$774$	−11.7394	−0.421966
$775$	53.6461	1.92702
$776$	3.37359	0.121105
$777$	−1.64991	−0.0591901
$778$	2.40487	0.0862187
$779$	−47.0843	−1.68697
$780$	−20.0632	−0.718377
$781$	23.4962	0.840761
$782$	16.4796	0.589310
$783$	31.4319	1.12328
$784$	13.8246	0.493734
$785$	21.8281	0.779078
$786$	2.63646	0.0940396
$787$	−45.2340	−1.61242	−0.806208	−	0.591632i	$-0.798484\pi$
$787$	−45.2340	−1.61242	−0.806208	+	0.591632i	$0.798484\pi$
$788$	21.6427	0.770990
$789$	−7.61583	−0.271131
$790$	16.1741	0.575450
$791$	−60.3932	−2.14734
$792$	8.53842	0.303399
$793$	67.5258	2.39791
$794$	−27.0505	−0.959987
$795$	−12.9752	−0.460182
$796$	−11.1593	−0.395531
$797$	−0.224719	−0.00795995	−0.00397997	−	0.999992i	$-0.501267\pi$
$797$	−0.224719	−0.00795995	−0.00397997	+	0.999992i	$0.501267\pi$
$798$	23.0396	0.815592
$799$	2.20153	0.0778845
$800$	9.54543	0.337482
$801$	−22.7349	−0.803300
$802$	−23.8839	−0.843369
$803$	19.2339	0.678749
$804$	5.01854	0.176990
$805$	−131.655	−4.64022
$806$	32.5076	1.14503
$807$	9.37778	0.330113
$808$	−17.8025	−0.626288
$809$	36.8667	1.29616	0.648081	−	0.761571i	$-0.275572\pi$
$809$	36.8667	1.29616	0.648081	+	0.761571i	$0.275572\pi$
$810$	8.54208	0.300138
$811$	16.8995	0.593422	0.296711	−	0.954967i	$-0.404110\pi$
$811$	16.8995	0.593422	0.296711	+	0.954967i	$0.404110\pi$
$812$	30.4884	1.06993
$813$	5.83929	0.204793
$814$	−1.56216	−0.0547538
$815$	57.3407	2.00856
$816$	1.98133	0.0693604
$817$	−29.9924	−1.04930
$818$	−30.0686	−1.05132
$819$	−57.3532	−2.00408
$820$	32.3480	1.12964
$821$	54.0454	1.88620	0.943099	−	0.332511i	$-0.107896\pi$
$821$	54.0454	1.88620	0.943099	+	0.332511i	$0.107896\pi$
$822$	6.54439	0.228262
$823$	35.7657	1.24671	0.623356	−	0.781938i	$-0.285769\pi$
$823$	35.7657	1.24671	0.623356	+	0.781938i	$0.285769\pi$
$824$	12.4501	0.433718
$825$	34.1146	1.18772
$826$	−32.7525	−1.13961
$827$	25.8396	0.898529	0.449265	−	0.893399i	$-0.351686\pi$
$827$	25.8396	0.898529	0.449265	+	0.893399i	$0.351686\pi$
$828$	16.4366	0.571213
$829$	4.81028	0.167068	0.0835340	−	0.996505i	$-0.473379\pi$
$829$	4.81028	0.167068	0.0835340	+	0.996505i	$0.473379\pi$
$830$	22.0561	0.765579
$831$	−22.6893	−0.787083
$832$	5.78418	0.200530
$833$	−30.1171	−1.04350
$834$	9.66476	0.334663
$835$	−48.0470	−1.66274
$836$	21.8143	0.754463
$837$	26.4403	0.913911
$838$	24.9649	0.862400
$839$	−47.9438	−1.65520	−0.827602	−	0.561316i	$-0.810295\pi$
$839$	−47.9438	−1.65520	−0.827602	+	0.561316i	$0.810295\pi$
$840$	−15.8287	−0.546143
$841$	15.6369	0.539203
$842$	−38.4558	−1.32528
$843$	15.6052	0.537471
$844$	7.76198	0.267178
$845$	78.0190	2.68394
$846$	2.19579	0.0754927
$847$	20.2699	0.696482
$848$	3.74072	0.128457
$849$	−14.3604	−0.492848
$850$	−20.7949	−0.713260
$851$	−3.00720	−0.103086
$852$	5.43805	0.186304
$853$	−7.81110	−0.267447	−0.133723	−	0.991019i	$-0.542693\pi$
$853$	−7.81110	−0.267447	−0.133723	+	0.991019i	$0.542693\pi$
$854$	53.2741	1.82300
$855$	46.0026	1.57326
$856$	16.3542	0.558976
$857$	−47.2741	−1.61485	−0.807427	−	0.589968i	$-0.799140\pi$
$857$	−47.2741	−1.61485	−0.807427	+	0.589968i	$0.799140\pi$
$858$	20.6722	0.705737
$859$	9.76098	0.333040	0.166520	−	0.986038i	$-0.446747\pi$
$859$	9.76098	0.333040	0.166520	+	0.986038i	$0.446747\pi$
$860$	20.6055	0.702642
$861$	−35.2020	−1.19968
$862$	8.85993	0.301770
$863$	15.4772	0.526849	0.263424	−	0.964680i	$-0.415148\pi$
$863$	15.4772	0.526849	0.263424	+	0.964680i	$0.415148\pi$
$864$	4.70461	0.160054
$865$	−41.7480	−1.41948
$866$	25.2853	0.859229
$867$	11.1448	0.378499
$868$	25.6467	0.870504
$869$	−16.6651	−0.565325
$870$	−23.1742	−0.785679
$871$	−31.9172	−1.08147
$872$	−15.9189	−0.539083
$873$	−7.33026	−0.248092
$874$	41.9930	1.42043
$875$	79.1089	2.67437
$876$	4.45156	0.150404
$877$	21.5246	0.726833	0.363416	−	0.931627i	$-0.381610\pi$
$877$	21.5246	0.726833	0.363416	+	0.931627i	$0.381610\pi$
$878$	20.3042	0.685234
$879$	10.6549	0.359380
$880$	−14.9869	−0.505210
$881$	13.7560	0.463452	0.231726	−	0.972781i	$-0.425563\pi$
$881$	13.7560	0.463452	0.231726	+	0.972781i	$0.425563\pi$
$882$	−30.0385	−1.01145
$883$	−28.8034	−0.969313	−0.484657	−	0.874705i	$-0.661055\pi$
$883$	−28.8034	−0.969313	−0.484657	+	0.874705i	$0.661055\pi$
$884$	−12.6010	−0.423817
$885$	24.8951	0.836841
$886$	−22.8603	−0.768007
$887$	18.0592	0.606368	0.303184	−	0.952932i	$-0.401950\pi$
$887$	18.0592	0.606368	0.303184	+	0.952932i	$0.401950\pi$
$888$	−0.361553	−0.0121329
$889$	−50.4632	−1.69248
$890$	39.9052	1.33762
$891$	−8.80137	−0.294857
$892$	22.9478	0.768349
$893$	5.60989	0.187728
$894$	4.55624	0.152383
$895$	−85.1079	−2.84484
$896$	4.56339	0.152452
$897$	39.7944	1.32870
$898$	3.91945	0.130794
$899$	37.5483	1.25230
$900$	−20.7407	−0.691356
$901$	−8.14925	−0.271491
$902$	−33.3299	−1.10977
$903$	−22.4235	−0.746206
$904$	−13.2343	−0.440166
$905$	−85.8872	−2.85499
$906$	0.731788	0.0243120
$907$	−12.0731	−0.400882	−0.200441	−	0.979706i	$-0.564238\pi$
$907$	−12.0731	−0.400882	−0.200441	+	0.979706i	$0.564238\pi$
$908$	−20.3165	−0.674228
$909$	38.6819	1.28300
$910$	100.668	3.33712
$911$	24.8199	0.822318	0.411159	−	0.911564i	$-0.365124\pi$
$911$	24.8199	0.822318	0.411159	+	0.911564i	$0.365124\pi$
$912$	5.04878	0.167182
$913$	−22.7256	−0.752108
$914$	27.2179	0.900287
$915$	−40.4936	−1.33868
$916$	2.34851	0.0775971
$917$	−13.2286	−0.436848
$918$	−10.2491	−0.338271
$919$	−11.5691	−0.381630	−0.190815	−	0.981626i	$-0.561113\pi$
$919$	−11.5691	−0.381630	−0.190815	+	0.981626i	$0.561113\pi$
$920$	−28.8502	−0.951162
$921$	9.13635	0.301053
$922$	24.7940	0.816545
$923$	−34.5852	−1.13839
$924$	16.3092	0.536533
$925$	3.79466	0.124768
$926$	−37.4416	−1.23041
$927$	−27.0520	−0.888504
$928$	6.68108	0.219317
$929$	−38.6469	−1.26796	−0.633981	−	0.773348i	$-0.718580\pi$
$929$	−38.6469	−1.26796	−0.633981	+	0.773348i	$0.718580\pi$
$930$	−19.4940	−0.639233
$931$	−76.7437	−2.51517
$932$	3.83142	0.125502
$933$	−10.5431	−0.345166
$934$	9.78265	0.320098
$935$	32.6494	1.06775
$936$	−12.5681	−0.410801
$937$	32.3885	1.05809	0.529044	−	0.848595i	$-0.322551\pi$
$937$	32.3885	1.05809	0.529044	+	0.848595i	$0.322551\pi$
$938$	−25.1809	−0.822185
$939$	−15.6522	−0.510792
$940$	−3.85412	−0.125708
$941$	18.1171	0.590600	0.295300	−	0.955405i	$-0.404580\pi$
$941$	18.1171	0.590600	0.295300	+	0.955405i	$0.404580\pi$
$942$	−5.20532	−0.169598
$943$	−64.1608	−2.08936
$944$	−7.17723	−0.233599
$945$	81.8794	2.66354
$946$	−21.2310	−0.690278
$947$	29.7221	0.965838	0.482919	−	0.875665i	$-0.339577\pi$
$947$	29.7221	0.965838	0.482919	+	0.875665i	$0.339577\pi$
$948$	−3.85703	−0.125270
$949$	−28.3113	−0.919023
$950$	−52.9892	−1.71920
$951$	−11.8834	−0.385346
$952$	−9.94145	−0.322204
$953$	−10.2263	−0.331262	−0.165631	−	0.986188i	$-0.552966\pi$
$953$	−10.2263	−0.331262	−0.165631	+	0.986188i	$0.552966\pi$
$954$	−8.12800	−0.263154
$955$	54.0792	1.74996
$956$	−8.82897	−0.285549
$957$	23.8776	0.771854
$958$	−36.4494	−1.17763
$959$	−32.8369	−1.06036
$960$	−3.46863	−0.111950
$961$	0.585355	0.0188824
$962$	2.29942	0.0741364
$963$	−35.5351	−1.14510
$964$	−19.6095	−0.631580
$965$	48.1258	1.54923
$966$	31.3955	1.01013
$967$	24.6241	0.791859	0.395929	−	0.918281i	$-0.370423\pi$
$967$	24.6241	0.791859	0.395929	+	0.918281i	$0.370423\pi$
$968$	4.44185	0.142766
$969$	−10.9989	−0.353335
$970$	12.8663	0.413113
$971$	−7.14985	−0.229450	−0.114725	−	0.993397i	$-0.536599\pi$
$971$	−7.14985	−0.229450	−0.114725	+	0.993397i	$0.536599\pi$
$972$	−16.1509	−0.518039
$973$	−48.4936	−1.55463
$974$	−22.2659	−0.713447
$975$	−50.2148	−1.60816
$976$	11.6742	0.373683
$977$	−34.0124	−1.08815	−0.544076	−	0.839036i	$-0.683120\pi$
$977$	−34.0124	−1.08815	−0.544076	+	0.839036i	$0.683120\pi$
$978$	−13.6740	−0.437245
$979$	−41.1165	−1.31409
$980$	52.7247	1.68423
$981$	34.5893	1.10435
$982$	9.30011	0.296779
$983$	19.8462	0.632996	0.316498	−	0.948593i	$-0.397493\pi$
$983$	19.8462	0.632996	0.316498	+	0.948593i	$0.397493\pi$
$984$	−7.71400	−0.245913
$985$	82.5420	2.63001
$986$	−14.5549	−0.463522
$987$	4.19416	0.133502
$988$	−32.1095	−1.02154
$989$	−40.8701	−1.29959
$990$	32.5642	1.03496
$991$	2.96887	0.0943094	0.0471547	−	0.998888i	$-0.484985\pi$
$991$	2.96887	0.0943094	0.0471547	+	0.998888i	$0.484985\pi$
$992$	5.62008	0.178438
$993$	−9.65729	−0.306465
$994$	−27.2858	−0.865452
$995$	−42.5599	−1.34924
$996$	−5.25969	−0.166660
$997$	−43.3553	−1.37308	−0.686538	−	0.727094i	$-0.740871\pi$
$997$	−43.3553	−1.37308	−0.686538	+	0.727094i	$0.740871\pi$
$998$	15.8834	0.502782
$999$	1.87026	0.0591723

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.d.1.17	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.d.1.17	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.909483 q^{3} +1.00000 q^{4} +3.81385 q^{5} -0.909483 q^{6} +4.56339 q^{7} +1.00000 q^{8} -2.17284 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.909483 q^{3} +1.00000 q^{4} +3.81385 q^{5} -0.909483 q^{6} +4.56339 q^{7} +1.00000 q^{8} -2.17284 q^{9} +3.81385 q^{10} -3.92961 q^{11} -0.909483 q^{12} +5.78418 q^{13} +4.56339 q^{14} -3.46863 q^{15} +1.00000 q^{16} -2.17852 q^{17} -2.17284 q^{18} -5.55126 q^{19} +3.81385 q^{20} -4.15033 q^{21} -3.92961 q^{22} -7.56459 q^{23} -0.909483 q^{24} +9.54543 q^{25} +5.78418 q^{26} +4.70461 q^{27} +4.56339 q^{28} +6.68108 q^{29} -3.46863 q^{30} +5.62008 q^{31} +1.00000 q^{32} +3.57392 q^{33} -2.17852 q^{34} +17.4041 q^{35} -2.17284 q^{36} +0.397537 q^{37} -5.55126 q^{38} -5.26062 q^{39} +3.81385 q^{40} +8.48174 q^{41} -4.15033 q^{42} +5.40281 q^{43} -3.92961 q^{44} -8.28688 q^{45} -7.56459 q^{46} -1.01056 q^{47} -0.909483 q^{48} +13.8246 q^{49} +9.54543 q^{50} +1.98133 q^{51} +5.78418 q^{52} +3.74072 q^{53} +4.70461 q^{54} -14.9869 q^{55} +4.56339 q^{56} +5.04878 q^{57} +6.68108 q^{58} -7.17723 q^{59} -3.46863 q^{60} +11.6742 q^{61} +5.62008 q^{62} -9.91552 q^{63} +1.00000 q^{64} +22.0600 q^{65} +3.57392 q^{66} -5.51802 q^{67} -2.17852 q^{68} +6.87987 q^{69} +17.4041 q^{70} -5.97927 q^{71} -2.17284 q^{72} -4.89460 q^{73} +0.397537 q^{74} -8.68141 q^{75} -5.55126 q^{76} -17.9324 q^{77} -5.26062 q^{78} +4.24090 q^{79} +3.81385 q^{80} +2.23975 q^{81} +8.48174 q^{82} +5.78317 q^{83} -4.15033 q^{84} -8.30855 q^{85} +5.40281 q^{86} -6.07634 q^{87} -3.92961 q^{88} +10.4632 q^{89} -8.28688 q^{90} +26.3955 q^{91} -7.56459 q^{92} -5.11137 q^{93} -1.01056 q^{94} -21.1717 q^{95} -0.909483 q^{96} +3.37359 q^{97} +13.8246 q^{98} +8.53842 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9}+O(q^{10}) \) 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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