LMFDB - Embedded newform 2013.2.a.h.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2013,2,Mod(1,2013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2013, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2013 = 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2013.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:	$16.0738859269$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} - 21 x^{12} + 20 x^{11} + 167 x^{10} - 148 x^{9} - 627 x^{8} + 497 x^{7} + 1123 x^{6} + \cdots - 1 $ x^14 - x^13 - 21x^12 + 20x^11 + 167x^10 - 148x^9 - 627x^8 + 497x^7 + 1123x^6 - 745x^5 - 802x^4 + 386x^3 + 74x^2 - 15x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$-1.76637$ of defining polynomial
Character	$\chi$	$=$	2013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.76637 q^{2} -1.00000 q^{3} +1.12006 q^{4} -2.50284 q^{5} -1.76637 q^{6} -4.08919 q^{7} -1.55430 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.76637 q^{2} -1.00000 q^{3} +1.12006 q^{4} -2.50284 q^{5} -1.76637 q^{6} -4.08919 q^{7} -1.55430 q^{8} +1.00000 q^{9} -4.42094 q^{10} -1.00000 q^{11} -1.12006 q^{12} +4.58176 q^{13} -7.22301 q^{14} +2.50284 q^{15} -4.98559 q^{16} -1.68948 q^{17} +1.76637 q^{18} +2.54310 q^{19} -2.80332 q^{20} +4.08919 q^{21} -1.76637 q^{22} +6.64905 q^{23} +1.55430 q^{24} +1.26422 q^{25} +8.09307 q^{26} -1.00000 q^{27} -4.58012 q^{28} +2.87310 q^{29} +4.42094 q^{30} +5.77320 q^{31} -5.69777 q^{32} +1.00000 q^{33} -2.98424 q^{34} +10.2346 q^{35} +1.12006 q^{36} +10.5546 q^{37} +4.49204 q^{38} -4.58176 q^{39} +3.89018 q^{40} -7.50568 q^{41} +7.22301 q^{42} -5.62451 q^{43} -1.12006 q^{44} -2.50284 q^{45} +11.7447 q^{46} +8.24063 q^{47} +4.98559 q^{48} +9.72144 q^{49} +2.23307 q^{50} +1.68948 q^{51} +5.13183 q^{52} -6.73746 q^{53} -1.76637 q^{54} +2.50284 q^{55} +6.35584 q^{56} -2.54310 q^{57} +5.07495 q^{58} +1.44956 q^{59} +2.80332 q^{60} +1.00000 q^{61} +10.1976 q^{62} -4.08919 q^{63} -0.0931904 q^{64} -11.4674 q^{65} +1.76637 q^{66} -2.89684 q^{67} -1.89231 q^{68} -6.64905 q^{69} +18.0780 q^{70} -3.64666 q^{71} -1.55430 q^{72} -1.53009 q^{73} +18.6433 q^{74} -1.26422 q^{75} +2.84841 q^{76} +4.08919 q^{77} -8.09307 q^{78} +6.59373 q^{79} +12.4781 q^{80} +1.00000 q^{81} -13.2578 q^{82} +4.68950 q^{83} +4.58012 q^{84} +4.22850 q^{85} -9.93495 q^{86} -2.87310 q^{87} +1.55430 q^{88} +8.01389 q^{89} -4.42094 q^{90} -18.7357 q^{91} +7.44732 q^{92} -5.77320 q^{93} +14.5560 q^{94} -6.36497 q^{95} +5.69777 q^{96} -8.48718 q^{97} +17.1716 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - q^{2} - 14 q^{3} + 15 q^{4} + q^{5} + q^{6} + 9 q^{7} + 14 q^{9}+O(q^{10}) $ 14 * q - q^2 - 14 * q^3 + 15 * q^4 + q^5 + q^6 + 9 * q^7 + 14 * q^9	\( 14 q - q^{2} - 14 q^{3} + 15 q^{4} + q^{5} + q^{6} + 9 q^{7} + 14 q^{9} + 6 q^{10} - 14 q^{11} - 15 q^{12} + q^{13} - 7 q^{14} - q^{15} + 17 q^{16} - 9 q^{17} - q^{18} + 22 q^{19} + 23 q^{20} - 9 q^{21} + q^{22} + q^{23} + 25 q^{25} + 4 q^{26} - 14 q^{27} + 37 q^{28} - 6 q^{29} - 6 q^{30} + 9 q^{31} + 4 q^{32} + 14 q^{33} + 8 q^{34} + 18 q^{35} + 15 q^{36} + 18 q^{37} + 8 q^{38} - q^{39} + 16 q^{40} - 25 q^{41} + 7 q^{42} + 25 q^{43} - 15 q^{44} + q^{45} + 20 q^{46} + 36 q^{47} - 17 q^{48} + 25 q^{49} + 2 q^{50} + 9 q^{51} - 13 q^{52} + q^{54} - q^{55} - 40 q^{56} - 22 q^{57} + 33 q^{58} + 17 q^{59} - 23 q^{60} + 14 q^{61} - 13 q^{62} + 9 q^{63} - 6 q^{64} - 61 q^{65} - q^{66} + 22 q^{67} + 66 q^{68} - q^{69} + 44 q^{70} - 13 q^{71} + 20 q^{73} - 12 q^{74} - 25 q^{75} + 49 q^{76} - 9 q^{77} - 4 q^{78} + 31 q^{79} + 88 q^{80} + 14 q^{81} + 2 q^{82} + 32 q^{83} - 37 q^{84} + 2 q^{85} - 14 q^{86} + 6 q^{87} - 21 q^{89} + 6 q^{90} + 45 q^{91} - 14 q^{92} - 9 q^{93} - 31 q^{94} + 23 q^{95} - 4 q^{96} + 37 q^{97} - 38 q^{98} - 14 q^{99}+O(q^{100}) \) 14 * q - q^2 - 14 * q^3 + 15 * q^4 + q^5 + q^6 + 9 * q^7 + 14 * q^9 + 6 * q^10 - 14 * q^11 - 15 * q^12 + q^13 - 7 * q^14 - q^15 + 17 * q^16 - 9 * q^17 - q^18 + 22 * q^19 + 23 * q^20 - 9 * q^21 + q^22 + q^23 + 25 * q^25 + 4 * q^26 - 14 * q^27 + 37 * q^28 - 6 * q^29 - 6 * q^30 + 9 * q^31 + 4 * q^32 + 14 * q^33 + 8 * q^34 + 18 * q^35 + 15 * q^36 + 18 * q^37 + 8 * q^38 - q^39 + 16 * q^40 - 25 * q^41 + 7 * q^42 + 25 * q^43 - 15 * q^44 + q^45 + 20 * q^46 + 36 * q^47 - 17 * q^48 + 25 * q^49 + 2 * q^50 + 9 * q^51 - 13 * q^52 + q^54 - q^55 - 40 * q^56 - 22 * q^57 + 33 * q^58 + 17 * q^59 - 23 * q^60 + 14 * q^61 - 13 * q^62 + 9 * q^63 - 6 * q^64 - 61 * q^65 - q^66 + 22 * q^67 + 66 * q^68 - q^69 + 44 * q^70 - 13 * q^71 + 20 * q^73 - 12 * q^74 - 25 * q^75 + 49 * q^76 - 9 * q^77 - 4 * q^78 + 31 * q^79 + 88 * q^80 + 14 * q^81 + 2 * q^82 + 32 * q^83 - 37 * q^84 + 2 * q^85 - 14 * q^86 + 6 * q^87 - 21 * q^89 + 6 * q^90 + 45 * q^91 - 14 * q^92 - 9 * q^93 - 31 * q^94 + 23 * q^95 - 4 * q^96 + 37 * q^97 - 38 * q^98 - 14 * 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 $

$2$	1.76637	1.24901	0.624505	−	0.781020i	$-0.285301\pi$
$2$	1.76637	1.24901	0.624505	+	0.781020i	$0.285301\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.12006	0.560028
$5$	−2.50284	−1.11930	−0.559652	−	0.828727i	$-0.689065\pi$
$5$	−2.50284	−1.11930	−0.559652	+	0.828727i	$0.689065\pi$
$6$	−1.76637	−0.721117
$7$	−4.08919	−1.54557	−0.772784	−	0.634670i	$-0.781136\pi$
$7$	−4.08919	−1.54557	−0.772784	+	0.634670i	$0.781136\pi$
$8$	−1.55430	−0.549530
$9$	1.00000	0.333333
$10$	−4.42094	−1.39802
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−1.12006	−0.323332
$13$	4.58176	1.27075	0.635376	−	0.772203i	$-0.280845\pi$
$13$	4.58176	1.27075	0.635376	+	0.772203i	$0.280845\pi$
$14$	−7.22301	−1.93043
$15$	2.50284	0.646231
$16$	−4.98559	−1.24640
$17$	−1.68948	−0.409759	−0.204879	−	0.978787i	$-0.565680\pi$
$17$	−1.68948	−0.409759	−0.204879	+	0.978787i	$0.565680\pi$
$18$	1.76637	0.416337
$19$	2.54310	0.583426	0.291713	−	0.956506i	$-0.405775\pi$
$19$	2.54310	0.583426	0.291713	+	0.956506i	$0.405775\pi$
$20$	−2.80332	−0.626842
$21$	4.08919	0.892334
$22$	−1.76637	−0.376591
$23$	6.64905	1.38642	0.693212	−	0.720734i	$-0.256195\pi$
$23$	6.64905	1.38642	0.693212	+	0.720734i	$0.256195\pi$
$24$	1.55430	0.317271
$25$	1.26422	0.252844
$26$	8.09307	1.58718
$27$	−1.00000	−0.192450
$28$	−4.58012	−0.865561
$29$	2.87310	0.533521	0.266760	−	0.963763i	$-0.414047\pi$
$29$	2.87310	0.533521	0.266760	+	0.963763i	$0.414047\pi$
$30$	4.42094	0.807150
$31$	5.77320	1.03690	0.518449	−	0.855109i	$-0.326510\pi$
$31$	5.77320	1.03690	0.518449	+	0.855109i	$0.326510\pi$
$32$	−5.69777	−1.00723
$33$	1.00000	0.174078
$34$	−2.98424	−0.511793
$35$	10.2346	1.72996
$36$	1.12006	0.186676
$37$	10.5546	1.73516	0.867582	−	0.497293i	$-0.165673\pi$
$37$	10.5546	1.73516	0.867582	+	0.497293i	$0.165673\pi$
$38$	4.49204	0.728706
$39$	−4.58176	−0.733669
$40$	3.89018	0.615091
$41$	−7.50568	−1.17219	−0.586095	−	0.810242i	$-0.699336\pi$
$41$	−7.50568	−1.17219	−0.586095	+	0.810242i	$0.699336\pi$
$42$	7.22301	1.11453
$43$	−5.62451	−0.857729	−0.428865	−	0.903369i	$-0.641086\pi$
$43$	−5.62451	−0.857729	−0.428865	+	0.903369i	$0.641086\pi$
$44$	−1.12006	−0.168855
$45$	−2.50284	−0.373102
$46$	11.7447	1.73166
$47$	8.24063	1.20202	0.601010	−	0.799242i	$-0.294765\pi$
$47$	8.24063	1.20202	0.601010	+	0.799242i	$0.294765\pi$
$48$	4.98559	0.719607
$49$	9.72144	1.38878
$50$	2.23307	0.315804
$51$	1.68948	0.236574
$52$	5.13183	0.711657
$53$	−6.73746	−0.925461	−0.462730	−	0.886499i	$-0.653130\pi$
$53$	−6.73746	−0.925461	−0.462730	+	0.886499i	$0.653130\pi$
$54$	−1.76637	−0.240372
$55$	2.50284	0.337483
$56$	6.35584	0.849335
$57$	−2.54310	−0.336841
$58$	5.07495	0.666373
$59$	1.44956	0.188717	0.0943584	−	0.995538i	$-0.469920\pi$
$59$	1.44956	0.188717	0.0943584	+	0.995538i	$0.469920\pi$
$60$	2.80332	0.361908
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	10.1976	1.29510
$63$	−4.08919	−0.515189
$64$	−0.0931904	−0.0116488
$65$	−11.4674	−1.42236
$66$	1.76637	0.217425
$67$	−2.89684	−0.353905	−0.176953	−	0.984219i	$-0.556624\pi$
$67$	−2.89684	−0.353905	−0.176953	+	0.984219i	$0.556624\pi$
$68$	−1.89231	−0.229477
$69$	−6.64905	−0.800452
$70$	18.0780	2.16074
$71$	−3.64666	−0.432779	−0.216389	−	0.976307i	$-0.569428\pi$
$71$	−3.64666	−0.432779	−0.216389	+	0.976307i	$0.569428\pi$
$72$	−1.55430	−0.183177
$73$	−1.53009	−0.179084	−0.0895419	−	0.995983i	$-0.528540\pi$
$73$	−1.53009	−0.179084	−0.0895419	+	0.995983i	$0.528540\pi$
$74$	18.6433	2.16724
$75$	−1.26422	−0.145979
$76$	2.84841	0.326735
$77$	4.08919	0.466006
$78$	−8.09307	−0.916360
$79$	6.59373	0.741853	0.370926	−	0.928662i	$-0.379040\pi$
$79$	6.59373	0.741853	0.370926	+	0.928662i	$0.379040\pi$
$80$	12.4781	1.39510
$81$	1.00000	0.111111
$82$	−13.2578	−1.46408
$83$	4.68950	0.514739	0.257370	−	0.966313i	$-0.417144\pi$
$83$	4.68950	0.514739	0.257370	+	0.966313i	$0.417144\pi$
$84$	4.58012	0.499732
$85$	4.22850	0.458645
$86$	−9.93495	−1.07131
$87$	−2.87310	−0.308028
$88$	1.55430	0.165689
$89$	8.01389	0.849471	0.424735	−	0.905318i	$-0.360367\pi$
$89$	8.01389	0.849471	0.424735	+	0.905318i	$0.360367\pi$
$90$	−4.42094	−0.466008
$91$	−18.7357	−1.96403
$92$	7.44732	0.776436
$93$	−5.77320	−0.598653
$94$	14.5560	1.50134
$95$	−6.36497	−0.653032
$96$	5.69777	0.581526
$97$	−8.48718	−0.861743	−0.430871	−	0.902413i	$-0.641794\pi$
$97$	−8.48718	−0.861743	−0.430871	+	0.902413i	$0.641794\pi$
$98$	17.1716	1.73460
$99$	−1.00000	−0.100504
$100$	1.41600	0.141600
$101$	−18.2735	−1.81828	−0.909138	−	0.416495i	$-0.863258\pi$
$101$	−18.2735	−1.81828	−0.909138	+	0.416495i	$0.863258\pi$
$102$	2.98424	0.295484
$103$	13.5101	1.33119	0.665594	−	0.746314i	$-0.268178\pi$
$103$	13.5101	1.33119	0.665594	+	0.746314i	$0.268178\pi$
$104$	−7.12145	−0.698315
$105$	−10.2346	−0.998793
$106$	−11.9008	−1.15591
$107$	6.25580	0.604771	0.302385	−	0.953186i	$-0.402217\pi$
$107$	6.25580	0.604771	0.302385	+	0.953186i	$0.402217\pi$
$108$	−1.12006	−0.107777
$109$	9.80803	0.939439	0.469720	−	0.882816i	$-0.344355\pi$
$109$	9.80803	0.939439	0.469720	+	0.882816i	$0.344355\pi$
$110$	4.42094	0.421520
$111$	−10.5546	−1.00180
$112$	20.3870	1.92639
$113$	4.30188	0.404687	0.202343	−	0.979315i	$-0.435144\pi$
$113$	4.30188	0.404687	0.202343	+	0.979315i	$0.435144\pi$
$114$	−4.49204	−0.420718
$115$	−16.6415	−1.55183
$116$	3.21803	0.298787
$117$	4.58176	0.423584
$118$	2.56046	0.235709
$119$	6.90859	0.633310
$120$	−3.89018	−0.355123
$121$	1.00000	0.0909091
$122$	1.76637	0.159919
$123$	7.50568	0.676764
$124$	6.46631	0.580692
$125$	9.35007	0.836296
$126$	−7.22301	−0.643477
$127$	8.95668	0.794776	0.397388	−	0.917651i	$-0.369917\pi$
$127$	8.95668	0.794776	0.397388	+	0.917651i	$0.369917\pi$
$128$	11.2309	0.992684
$129$	5.62451	0.495210
$130$	−20.2557	−1.77654
$131$	16.6930	1.45848	0.729239	−	0.684259i	$-0.239874\pi$
$131$	16.6930	1.45848	0.729239	+	0.684259i	$0.239874\pi$
$132$	1.12006	0.0974884
$133$	−10.3992	−0.901724
$134$	−5.11689	−0.442032
$135$	2.50284	0.215410
$136$	2.62596	0.225175
$137$	1.84979	0.158038	0.0790192	−	0.996873i	$-0.474821\pi$
$137$	1.84979	0.158038	0.0790192	+	0.996873i	$0.474821\pi$
$138$	−11.7447	−0.999773
$139$	−2.09830	−0.177975	−0.0889877	−	0.996033i	$-0.528363\pi$
$139$	−2.09830	−0.177975	−0.0889877	+	0.996033i	$0.528363\pi$
$140$	11.4633	0.968827
$141$	−8.24063	−0.693986
$142$	−6.44134	−0.540545
$143$	−4.58176	−0.383146
$144$	−4.98559	−0.415466
$145$	−7.19091	−0.597172
$146$	−2.70271	−0.223678
$147$	−9.72144	−0.801811
$148$	11.8217	0.971741
$149$	−10.6609	−0.873374	−0.436687	−	0.899614i	$-0.643848\pi$
$149$	−10.6609	−0.873374	−0.436687	+	0.899614i	$0.643848\pi$
$150$	−2.23307	−0.182330
$151$	−15.9563	−1.29850	−0.649252	−	0.760573i	$-0.724918\pi$
$151$	−15.9563	−1.29850	−0.649252	+	0.760573i	$0.724918\pi$
$152$	−3.95274	−0.320610
$153$	−1.68948	−0.136586
$154$	7.22301	0.582047
$155$	−14.4494	−1.16060
$156$	−5.13183	−0.410875
$157$	−12.6000	−1.00559	−0.502795	−	0.864406i	$-0.667695\pi$
$157$	−12.6000	−1.00559	−0.502795	+	0.864406i	$0.667695\pi$
$158$	11.6470	0.926582
$159$	6.73746	0.534315
$160$	14.2606	1.12740
$161$	−27.1892	−2.14281
$162$	1.76637	0.138779
$163$	19.5726	1.53305	0.766523	−	0.642217i	$-0.221985\pi$
$163$	19.5726	1.53305	0.766523	+	0.642217i	$0.221985\pi$
$164$	−8.40679	−0.656460
$165$	−2.50284	−0.194846
$166$	8.28338	0.642915
$167$	−1.21481	−0.0940045	−0.0470023	−	0.998895i	$-0.514967\pi$
$167$	−1.21481	−0.0940045	−0.0470023	+	0.998895i	$0.514967\pi$
$168$	−6.35584	−0.490364
$169$	7.99251	0.614809
$170$	7.46909	0.572853
$171$	2.54310	0.194475
$172$	−6.29977	−0.480353
$173$	−16.2092	−1.23236	−0.616180	−	0.787605i	$-0.711321\pi$
$173$	−16.2092	−1.23236	−0.616180	+	0.787605i	$0.711321\pi$
$174$	−5.07495	−0.384731
$175$	−5.16962	−0.390787
$176$	4.98559	0.375803
$177$	−1.44956	−0.108956
$178$	14.1555	1.06100
$179$	−0.460529	−0.0344216	−0.0172108	−	0.999852i	$-0.505479\pi$
$179$	−0.460529	−0.0344216	−0.0172108	+	0.999852i	$0.505479\pi$
$180$	−2.80332	−0.208947
$181$	21.1108	1.56916	0.784578	−	0.620030i	$-0.212879\pi$
$181$	21.1108	1.56916	0.784578	+	0.620030i	$0.212879\pi$
$182$	−33.0941	−2.45310
$183$	−1.00000	−0.0739221
$184$	−10.3347	−0.761881
$185$	−26.4165	−1.94218
$186$	−10.1976	−0.747724
$187$	1.68948	0.123547
$188$	9.22997	0.673165
$189$	4.08919	0.297445
$190$	−11.2429	−0.815644
$191$	20.7120	1.49867	0.749333	−	0.662193i	$-0.230374\pi$
$191$	20.7120	1.49867	0.749333	+	0.662193i	$0.230374\pi$
$192$	0.0931904	0.00672544
$193$	4.36796	0.314413	0.157206	−	0.987566i	$-0.449751\pi$
$193$	4.36796	0.314413	0.157206	+	0.987566i	$0.449751\pi$
$194$	−14.9915	−1.07633
$195$	11.4674	0.821199
$196$	10.8886	0.777755
$197$	−14.9041	−1.06187	−0.530935	−	0.847413i	$-0.678159\pi$
$197$	−14.9041	−1.06187	−0.530935	+	0.847413i	$0.678159\pi$
$198$	−1.76637	−0.125530
$199$	12.3150	0.872990	0.436495	−	0.899707i	$-0.356220\pi$
$199$	12.3150	0.872990	0.436495	+	0.899707i	$0.356220\pi$
$200$	−1.96498	−0.138945
$201$	2.89684	0.204327
$202$	−32.2776	−2.27105
$203$	−11.7486	−0.824592
$204$	1.89231	0.132488
$205$	18.7855	1.31204
$206$	23.8638	1.66267
$207$	6.64905	0.462141
$208$	−22.8428	−1.58386
$209$	−2.54310	−0.175910
$210$	−18.0780	−1.24750
$211$	−0.624271	−0.0429766	−0.0214883	−	0.999769i	$-0.506840\pi$
$211$	−0.624271	−0.0429766	−0.0214883	+	0.999769i	$0.506840\pi$
$212$	−7.54633	−0.518284
$213$	3.64666	0.249865
$214$	11.0500	0.755365
$215$	14.0773	0.960061
$216$	1.55430	0.105757
$217$	−23.6077	−1.60259
$218$	17.3246	1.17337
$219$	1.53009	0.103394
$220$	2.80332	0.189000
$221$	−7.74079	−0.520702
$222$	−18.6433	−1.25126
$223$	1.10168	0.0737740	0.0368870	−	0.999319i	$-0.488256\pi$
$223$	1.10168	0.0737740	0.0368870	+	0.999319i	$0.488256\pi$
$224$	23.2993	1.55675
$225$	1.26422	0.0842812
$226$	7.59871	0.505458
$227$	24.3655	1.61720	0.808599	−	0.588360i	$-0.200226\pi$
$227$	24.3655	1.61720	0.808599	+	0.588360i	$0.200226\pi$
$228$	−2.84841	−0.188641
$229$	−10.0662	−0.665193	−0.332597	−	0.943069i	$-0.607925\pi$
$229$	−10.0662	−0.665193	−0.332597	+	0.943069i	$0.607925\pi$
$230$	−29.3951	−1.93825
$231$	−4.08919	−0.269049
$232$	−4.46567	−0.293185
$233$	−2.64216	−0.173094	−0.0865470	−	0.996248i	$-0.527583\pi$
$233$	−2.64216	−0.173094	−0.0865470	+	0.996248i	$0.527583\pi$
$234$	8.09307	0.529061
$235$	−20.6250	−1.34543
$236$	1.62359	0.105687
$237$	−6.59373	−0.428309
$238$	12.2031	0.791011
$239$	−24.0202	−1.55374	−0.776870	−	0.629662i	$-0.783194\pi$
$239$	−24.0202	−1.55374	−0.776870	+	0.629662i	$0.783194\pi$
$240$	−12.4781	−0.805460
$241$	20.2998	1.30763	0.653813	−	0.756656i	$-0.273168\pi$
$241$	20.2998	1.30763	0.653813	+	0.756656i	$0.273168\pi$
$242$	1.76637	0.113546
$243$	−1.00000	−0.0641500
$244$	1.12006	0.0717043
$245$	−24.3312	−1.55447
$246$	13.2578	0.845286
$247$	11.6518	0.741389
$248$	−8.97331	−0.569806
$249$	−4.68950	−0.297185
$250$	16.5157	1.04454
$251$	−7.85638	−0.495890	−0.247945	−	0.968774i	$-0.579755\pi$
$251$	−7.85638	−0.495890	−0.247945	+	0.968774i	$0.579755\pi$
$252$	−4.58012	−0.288520
$253$	−6.64905	−0.418022
$254$	15.8208	0.992684
$255$	−4.22850	−0.264799
$256$	20.0243	1.25152
$257$	8.43220	0.525986	0.262993	−	0.964798i	$-0.415290\pi$
$257$	8.43220	0.525986	0.262993	+	0.964798i	$0.415290\pi$
$258$	9.93495	0.618523
$259$	−43.1597	−2.68181
$260$	−12.8442	−0.796561
$261$	2.87310	0.177840
$262$	29.4861	1.82165
$263$	−15.8210	−0.975563	−0.487781	−	0.872966i	$-0.662194\pi$
$263$	−15.8210	−0.975563	−0.487781	+	0.872966i	$0.662194\pi$
$264$	−1.55430	−0.0956608
$265$	16.8628	1.03587
$266$	−18.3688	−1.12626
$267$	−8.01389	−0.490442
$268$	−3.24462	−0.198197
$269$	29.6760	1.80938	0.904690	−	0.426070i	$-0.140102\pi$
$269$	29.6760	1.80938	0.904690	+	0.426070i	$0.140102\pi$
$270$	4.42094	0.269050
$271$	13.8327	0.840277	0.420139	−	0.907460i	$-0.361981\pi$
$271$	13.8327	0.840277	0.420139	+	0.907460i	$0.361981\pi$
$272$	8.42304	0.510722
$273$	18.7357	1.13393
$274$	3.26742	0.197392
$275$	−1.26422	−0.0762352
$276$	−7.44732	−0.448276
$277$	10.7545	0.646174	0.323087	−	0.946369i	$-0.395279\pi$
$277$	10.7545	0.646174	0.323087	+	0.946369i	$0.395279\pi$
$278$	−3.70637	−0.222293
$279$	5.77320	0.345632
$280$	−15.9077	−0.950665
$281$	18.7346	1.11761	0.558807	−	0.829298i	$-0.311259\pi$
$281$	18.7346	1.11761	0.558807	+	0.829298i	$0.311259\pi$
$282$	−14.5560	−0.866796
$283$	24.5140	1.45721	0.728603	−	0.684936i	$-0.240170\pi$
$283$	24.5140	1.45721	0.728603	+	0.684936i	$0.240170\pi$
$284$	−4.08446	−0.242368
$285$	6.36497	0.377028
$286$	−8.09307	−0.478553
$287$	30.6921	1.81170
$288$	−5.69777	−0.335744
$289$	−14.1457	−0.832098
$290$	−12.7018	−0.745875
$291$	8.48718	0.497527
$292$	−1.71379	−0.100292
$293$	22.3094	1.30333	0.651665	−	0.758507i	$-0.274071\pi$
$293$	22.3094	1.30333	0.651665	+	0.758507i	$0.274071\pi$
$294$	−17.1716	−1.00147
$295$	−3.62802	−0.211232
$296$	−16.4051	−0.953524
$297$	1.00000	0.0580259
$298$	−18.8310	−1.09085
$299$	30.4644	1.76180
$300$	−1.41600	−0.0817525
$301$	22.9997	1.32568
$302$	−28.1847	−1.62185
$303$	18.2735	1.04978
$304$	−12.6788	−0.727180
$305$	−2.50284	−0.143312
$306$	−2.98424	−0.170598
$307$	9.79575	0.559073	0.279536	−	0.960135i	$-0.409819\pi$
$307$	9.79575	0.559073	0.279536	+	0.960135i	$0.409819\pi$
$308$	4.58012	0.260977
$309$	−13.5101	−0.768562
$310$	−25.5230	−1.44961
$311$	21.0159	1.19170	0.595852	−	0.803094i	$-0.296814\pi$
$311$	21.0159	1.19170	0.595852	+	0.803094i	$0.296814\pi$
$312$	7.12145	0.403173
$313$	−11.8868	−0.671880	−0.335940	−	0.941883i	$-0.609054\pi$
$313$	−11.8868	−0.671880	−0.335940	+	0.941883i	$0.609054\pi$
$314$	−22.2563	−1.25599
$315$	10.2346	0.576654
$316$	7.38535	0.415458
$317$	−20.3584	−1.14344	−0.571720	−	0.820449i	$-0.693723\pi$
$317$	−20.3584	−1.14344	−0.571720	+	0.820449i	$0.693723\pi$
$318$	11.9008	0.667365
$319$	−2.87310	−0.160863
$320$	0.233241	0.0130386
$321$	−6.25580	−0.349164
$322$	−48.0262	−2.67639
$323$	−4.29651	−0.239064
$324$	1.12006	0.0622254
$325$	5.79234	0.321301
$326$	34.5725	1.91479
$327$	−9.80803	−0.542385
$328$	11.6661	0.644153
$329$	−33.6975	−1.85780
$330$	−4.42094	−0.243365
$331$	−18.5600	−1.02015	−0.510074	−	0.860130i	$-0.670382\pi$
$331$	−18.5600	−1.02015	−0.510074	+	0.860130i	$0.670382\pi$
$332$	5.25250	0.288268
$333$	10.5546	0.578388
$334$	−2.14579	−0.117413
$335$	7.25033	0.396128
$336$	−20.3870	−1.11220
$337$	10.9967	0.599029	0.299515	−	0.954092i	$-0.403175\pi$
$337$	10.9967	0.599029	0.299515	+	0.954092i	$0.403175\pi$
$338$	14.1177	0.767903
$339$	−4.30188	−0.233646
$340$	4.73616	0.256854
$341$	−5.77320	−0.312636
$342$	4.49204	0.242902
$343$	−11.1285	−0.600882
$344$	8.74220	0.471348
$345$	16.6415	0.895950
$346$	−28.6314	−1.53923
$347$	−6.33081	−0.339856	−0.169928	−	0.985457i	$-0.554353\pi$
$347$	−6.33081	−0.339856	−0.169928	+	0.985457i	$0.554353\pi$
$348$	−3.21803	−0.172505
$349$	−14.8101	−0.792766	−0.396383	−	0.918085i	$-0.629735\pi$
$349$	−14.8101	−0.792766	−0.396383	+	0.918085i	$0.629735\pi$
$350$	−9.13146	−0.488097
$351$	−4.58176	−0.244556
$352$	5.69777	0.303692
$353$	18.2039	0.968897	0.484448	−	0.874820i	$-0.339020\pi$
$353$	18.2039	0.968897	0.484448	+	0.874820i	$0.339020\pi$
$354$	−2.56046	−0.136087
$355$	9.12701	0.484411
$356$	8.97601	0.475728
$357$	−6.90859	−0.365642
$358$	−0.813464	−0.0429929
$359$	−31.9112	−1.68421	−0.842105	−	0.539313i	$-0.818684\pi$
$359$	−31.9112	−1.68421	−0.842105	+	0.539313i	$0.818684\pi$
$360$	3.89018	0.205030
$361$	−12.5327	−0.659614
$362$	37.2895	1.95989
$363$	−1.00000	−0.0524864
$364$	−20.9850	−1.09991
$365$	3.82958	0.200449
$366$	−1.76637	−0.0923295
$367$	27.3610	1.42823	0.714117	−	0.700026i	$-0.246828\pi$
$367$	27.3610	1.42823	0.714117	+	0.700026i	$0.246828\pi$
$368$	−33.1494	−1.72803
$369$	−7.50568	−0.390730
$370$	−46.6612	−2.42580
$371$	27.5507	1.43036
$372$	−6.46631	−0.335263
$373$	−10.8401	−0.561279	−0.280639	−	0.959813i	$-0.590546\pi$
$373$	−10.8401	−0.561279	−0.280639	+	0.959813i	$0.590546\pi$
$374$	2.98424	0.154311
$375$	−9.35007	−0.482836
$376$	−12.8084	−0.660545
$377$	13.1638	0.677972
$378$	7.22301	0.371511
$379$	28.1412	1.44552	0.722758	−	0.691101i	$-0.242874\pi$
$379$	28.1412	1.44552	0.722758	+	0.691101i	$0.242874\pi$
$380$	−7.12912	−0.365716
$381$	−8.95668	−0.458864
$382$	36.5850	1.87185
$383$	12.3294	0.630003	0.315002	−	0.949091i	$-0.397995\pi$
$383$	12.3294	0.630003	0.315002	+	0.949091i	$0.397995\pi$
$384$	−11.2309	−0.573126
$385$	−10.2346	−0.521603
$386$	7.71543	0.392705
$387$	−5.62451	−0.285910
$388$	−9.50612	−0.482600
$389$	2.35013	0.119156	0.0595782	−	0.998224i	$-0.481024\pi$
$389$	2.35013	0.119156	0.0595782	+	0.998224i	$0.481024\pi$
$390$	20.2557	1.02569
$391$	−11.2334	−0.568099
$392$	−15.1101	−0.763174
$393$	−16.6930	−0.842052
$394$	−26.3261	−1.32629
$395$	−16.5031	−0.830359
$396$	−1.12006	−0.0562850
$397$	7.28324	0.365535	0.182768	−	0.983156i	$-0.441494\pi$
$397$	7.28324	0.365535	0.182768	+	0.983156i	$0.441494\pi$
$398$	21.7529	1.09037
$399$	10.3992	0.520611
$400$	−6.30287	−0.315143
$401$	−5.92148	−0.295704	−0.147852	−	0.989009i	$-0.547236\pi$
$401$	−5.92148	−0.295704	−0.147852	+	0.989009i	$0.547236\pi$
$402$	5.11689	0.255207
$403$	26.4514	1.31764
$404$	−20.4673	−1.01829
$405$	−2.50284	−0.124367
$406$	−20.7524	−1.02992
$407$	−10.5546	−0.523172
$408$	−2.62596	−0.130005
$409$	37.5868	1.85855	0.929273	−	0.369395i	$-0.120435\pi$
$409$	37.5868	1.85855	0.929273	+	0.369395i	$0.120435\pi$
$410$	33.1822	1.63875
$411$	−1.84979	−0.0912436
$412$	15.1321	0.745503
$413$	−5.92753	−0.291675
$414$	11.7447	0.577219
$415$	−11.7371	−0.576150
$416$	−26.1058	−1.27994
$417$	2.09830	0.102754
$418$	−4.49204	−0.219713
$419$	2.49710	0.121991	0.0609957	−	0.998138i	$-0.480572\pi$
$419$	2.49710	0.121991	0.0609957	+	0.998138i	$0.480572\pi$
$420$	−11.4633	−0.559352
$421$	−4.42273	−0.215551	−0.107775	−	0.994175i	$-0.534373\pi$
$421$	−4.42273	−0.215551	−0.107775	+	0.994175i	$0.534373\pi$
$422$	−1.10269	−0.0536783
$423$	8.24063	0.400673
$424$	10.4721	0.508568
$425$	−2.13587	−0.103605
$426$	6.44134	0.312084
$427$	−4.08919	−0.197890
$428$	7.00684	0.338689
$429$	4.58176	0.221209
$430$	24.8656	1.19913
$431$	−9.88068	−0.475936	−0.237968	−	0.971273i	$-0.576481\pi$
$431$	−9.88068	−0.475936	−0.237968	+	0.971273i	$0.576481\pi$
$432$	4.98559	0.239869
$433$	−39.0060	−1.87451	−0.937254	−	0.348648i	$-0.886641\pi$
$433$	−39.0060	−1.87451	−0.937254	+	0.348648i	$0.886641\pi$
$434$	−41.6999	−2.00166
$435$	7.19091	0.344778
$436$	10.9855	0.526112
$437$	16.9092	0.808876
$438$	2.70271	0.129140
$439$	20.6364	0.984924	0.492462	−	0.870334i	$-0.336097\pi$
$439$	20.6364	0.984924	0.492462	+	0.870334i	$0.336097\pi$
$440$	−3.89018	−0.185457
$441$	9.72144	0.462926
$442$	−13.6731	−0.650362
$443$	−32.1706	−1.52847	−0.764235	−	0.644938i	$-0.776883\pi$
$443$	−32.1706	−1.52847	−0.764235	+	0.644938i	$0.776883\pi$
$444$	−11.8217	−0.561035
$445$	−20.0575	−0.950817
$446$	1.94597	0.0921445
$447$	10.6609	0.504242
$448$	0.381073	0.0180040
$449$	−5.85730	−0.276423	−0.138212	−	0.990403i	$-0.544135\pi$
$449$	−5.85730	−0.276423	−0.138212	+	0.990403i	$0.544135\pi$
$450$	2.23307	0.105268
$451$	7.50568	0.353429
$452$	4.81835	0.226636
$453$	15.9563	0.749692
$454$	43.0385	2.01990
$455$	46.8924	2.19835
$456$	3.95274	0.185104
$457$	−1.68219	−0.0786896	−0.0393448	−	0.999226i	$-0.512527\pi$
$457$	−1.68219	−0.0786896	−0.0393448	+	0.999226i	$0.512527\pi$
$458$	−17.7806	−0.830833
$459$	1.68948	0.0788581
$460$	−18.6395	−0.869069
$461$	−6.22874	−0.290101	−0.145051	−	0.989424i	$-0.546335\pi$
$461$	−6.22874	−0.290101	−0.145051	+	0.989424i	$0.546335\pi$
$462$	−7.22301	−0.336045
$463$	20.0233	0.930560	0.465280	−	0.885163i	$-0.345954\pi$
$463$	20.0233	0.930560	0.465280	+	0.885163i	$0.345954\pi$
$464$	−14.3241	−0.664978
$465$	14.4494	0.670075
$466$	−4.66704	−0.216196
$467$	11.2040	0.518457	0.259229	−	0.965816i	$-0.416532\pi$
$467$	11.2040	0.518457	0.259229	+	0.965816i	$0.416532\pi$
$468$	5.13183	0.237219
$469$	11.8457	0.546985
$470$	−36.4313	−1.68045
$471$	12.6000	0.580578
$472$	−2.25306	−0.103705
$473$	5.62451	0.258615
$474$	−11.6470	−0.534962
$475$	3.21503	0.147516
$476$	7.73802	0.354671
$477$	−6.73746	−0.308487
$478$	−42.4286	−1.94064
$479$	−36.8757	−1.68490	−0.842448	−	0.538778i	$-0.818886\pi$
$479$	−36.8757	−1.68490	−0.842448	+	0.538778i	$0.818886\pi$
$480$	−14.2606	−0.650905
$481$	48.3586	2.20496
$482$	35.8569	1.63324
$483$	27.1892	1.23715
$484$	1.12006	0.0509117
$485$	21.2421	0.964553
$486$	−1.76637	−0.0801241
$487$	−27.2350	−1.23414	−0.617069	−	0.786909i	$-0.711680\pi$
$487$	−27.2350	−1.23414	−0.617069	+	0.786909i	$0.711680\pi$
$488$	−1.55430	−0.0703601
$489$	−19.5726	−0.885104
$490$	−42.9779	−1.94154
$491$	−9.95507	−0.449266	−0.224633	−	0.974443i	$-0.572118\pi$
$491$	−9.95507	−0.449266	−0.224633	+	0.974443i	$0.572118\pi$
$492$	8.40679	0.379007
$493$	−4.85404	−0.218615
$494$	20.5815	0.926003
$495$	2.50284	0.112494
$496$	−28.7828	−1.29239
$497$	14.9119	0.668888
$498$	−8.28338	−0.371187
$499$	−24.8590	−1.11284	−0.556421	−	0.830901i	$-0.687826\pi$
$499$	−24.8590	−1.11284	−0.556421	+	0.830901i	$0.687826\pi$
$500$	10.4726	0.468349
$501$	1.21481	0.0542735
$502$	−13.8773	−0.619372
$503$	−7.90956	−0.352670	−0.176335	−	0.984330i	$-0.556424\pi$
$503$	−7.90956	−0.352670	−0.176335	+	0.984330i	$0.556424\pi$
$504$	6.35584	0.283112
$505$	45.7356	2.03521
$506$	−11.7447	−0.522115
$507$	−7.99251	−0.354960
$508$	10.0320	0.445097
$509$	−26.7176	−1.18423	−0.592117	−	0.805852i	$-0.701708\pi$
$509$	−26.7176	−1.18423	−0.592117	+	0.805852i	$0.701708\pi$
$510$	−7.46909	−0.330737
$511$	6.25683	0.276786
$512$	12.9085	0.570480
$513$	−2.54310	−0.112280
$514$	14.8944	0.656963
$515$	−33.8136	−1.49001
$516$	6.29977	0.277332
$517$	−8.24063	−0.362422
$518$	−76.2359	−3.34961
$519$	16.2092	0.711503
$520$	17.8239	0.781628
$521$	−44.3858	−1.94458	−0.972288	−	0.233788i	$-0.924888\pi$
$521$	−44.3858	−1.94458	−0.972288	+	0.233788i	$0.924888\pi$
$522$	5.07495	0.222124
$523$	−9.29556	−0.406466	−0.203233	−	0.979130i	$-0.565145\pi$
$523$	−9.29556	−0.406466	−0.203233	+	0.979130i	$0.565145\pi$
$524$	18.6971	0.816789
$525$	5.16962	0.225621
$526$	−27.9457	−1.21849
$527$	−9.75370	−0.424878
$528$	−4.98559	−0.216970
$529$	21.2099	0.922171
$530$	29.7859	1.29382
$531$	1.44956	0.0629056
$532$	−11.6477	−0.504991
$533$	−34.3892	−1.48956
$534$	−14.1555	−0.612568
$535$	−15.6573	−0.676923
$536$	4.50257	0.194481
$537$	0.460529	0.0198733
$538$	52.4188	2.25994
$539$	−9.72144	−0.418732
$540$	2.80332	0.120636
$541$	−12.2230	−0.525508	−0.262754	−	0.964863i	$-0.584631\pi$
$541$	−12.2230	−0.525508	−0.262754	+	0.964863i	$0.584631\pi$
$542$	24.4337	1.04952
$543$	−21.1108	−0.905953
$544$	9.62627	0.412723
$545$	−24.5480	−1.05152
$546$	33.0941	1.41630
$547$	41.0194	1.75386	0.876932	−	0.480615i	$-0.159587\pi$
$547$	41.0194	1.75386	0.876932	+	0.480615i	$0.159587\pi$
$548$	2.07187	0.0885060
$549$	1.00000	0.0426790
$550$	−2.23307	−0.0952186
$551$	7.30656	0.311270
$552$	10.3347	0.439872
$553$	−26.9630	−1.14658
$554$	18.9964	0.807079
$555$	26.4165	1.12132
$556$	−2.35021	−0.0996713
$557$	37.2860	1.57986	0.789930	−	0.613197i	$-0.210117\pi$
$557$	37.2860	1.57986	0.789930	+	0.613197i	$0.210117\pi$
$558$	10.1976	0.431699
$559$	−25.7701	−1.08996
$560$	−51.0254	−2.15622
$561$	−1.68948	−0.0713299
$562$	33.0922	1.39591
$563$	−21.0358	−0.886553	−0.443276	−	0.896385i	$-0.646184\pi$
$563$	−21.0358	−0.886553	−0.443276	+	0.896385i	$0.646184\pi$
$564$	−9.22997	−0.388652
$565$	−10.7669	−0.452968
$566$	43.3007	1.82007
$567$	−4.08919	−0.171730
$568$	5.66802	0.237825
$569$	−14.9610	−0.627198	−0.313599	−	0.949556i	$-0.601535\pi$
$569$	−14.9610	−0.627198	−0.313599	+	0.949556i	$0.601535\pi$
$570$	11.2429	0.470912
$571$	22.6822	0.949220	0.474610	−	0.880196i	$-0.342589\pi$
$571$	22.6822	0.949220	0.474610	+	0.880196i	$0.342589\pi$
$572$	−5.13183	−0.214573
$573$	−20.7120	−0.865256
$574$	54.2136	2.26283
$575$	8.40585	0.350548
$576$	−0.0931904	−0.00388293
$577$	16.8414	0.701115	0.350558	−	0.936541i	$-0.385992\pi$
$577$	16.8414	0.701115	0.350558	+	0.936541i	$0.385992\pi$
$578$	−24.9864	−1.03930
$579$	−4.36796	−0.181526
$580$	−8.05422	−0.334433
$581$	−19.1762	−0.795564
$582$	14.9915	0.621417
$583$	6.73746	0.279037
$584$	2.37823	0.0984118
$585$	−11.4674	−0.474119
$586$	39.4067	1.62787
$587$	24.6219	1.01625	0.508127	−	0.861282i	$-0.330338\pi$
$587$	24.6219	1.01625	0.508127	+	0.861282i	$0.330338\pi$
$588$	−10.8886	−0.449037
$589$	14.6818	0.604953
$590$	−6.40843	−0.263831
$591$	14.9041	0.613071
$592$	−52.6208	−2.16270
$593$	−29.1431	−1.19676	−0.598381	−	0.801212i	$-0.704189\pi$
$593$	−29.1431	−1.19676	−0.598381	+	0.801212i	$0.704189\pi$
$594$	1.76637	0.0724750
$595$	−17.2911	−0.708867
$596$	−11.9408	−0.489114
$597$	−12.3150	−0.504021
$598$	53.8113	2.20051
$599$	−13.0824	−0.534533	−0.267266	−	0.963623i	$-0.586120\pi$
$599$	−13.0824	−0.534533	−0.267266	+	0.963623i	$0.586120\pi$
$600$	1.96498	0.0802200
$601$	23.1391	0.943864	0.471932	−	0.881635i	$-0.343557\pi$
$601$	23.1391	0.943864	0.471932	+	0.881635i	$0.343557\pi$
$602$	40.6259	1.65579
$603$	−2.89684	−0.117968
$604$	−17.8719	−0.727199
$605$	−2.50284	−0.101755
$606$	32.2776	1.31119
$607$	8.61728	0.349765	0.174882	−	0.984589i	$-0.444046\pi$
$607$	8.61728	0.349765	0.174882	+	0.984589i	$0.444046\pi$
$608$	−14.4900	−0.587646
$609$	11.7486	0.476078
$610$	−4.42094	−0.178999
$611$	37.7566	1.52747
$612$	−1.89231	−0.0764922
$613$	41.9165	1.69299	0.846496	−	0.532396i	$-0.178708\pi$
$613$	41.9165	1.69299	0.846496	+	0.532396i	$0.178708\pi$
$614$	17.3029	0.698288
$615$	−18.7855	−0.757506
$616$	−6.35584	−0.256084
$617$	40.7094	1.63890	0.819449	−	0.573152i	$-0.194279\pi$
$617$	40.7094	1.63890	0.819449	+	0.573152i	$0.194279\pi$
$618$	−23.8638	−0.959942
$619$	38.7050	1.55569	0.777843	−	0.628459i	$-0.216314\pi$
$619$	38.7050	1.55569	0.777843	+	0.628459i	$0.216314\pi$
$620$	−16.1842	−0.649971
$621$	−6.64905	−0.266817
$622$	37.1219	1.48845
$623$	−32.7703	−1.31291
$624$	22.8428	0.914442
$625$	−29.7228	−1.18891
$626$	−20.9964	−0.839186
$627$	2.54310	0.101561
$628$	−14.1127	−0.563159
$629$	−17.8318	−0.710999
$630$	18.0780	0.720247
$631$	2.44555	0.0973560	0.0486780	−	0.998815i	$-0.484499\pi$
$631$	2.44555	0.0973560	0.0486780	+	0.998815i	$0.484499\pi$
$632$	−10.2487	−0.407670
$633$	0.624271	0.0248126
$634$	−35.9604	−1.42817
$635$	−22.4171	−0.889597
$636$	7.54633	0.299231
$637$	44.5413	1.76479
$638$	−5.07495	−0.200919
$639$	−3.64666	−0.144260
$640$	−28.1093	−1.11112
$641$	−3.52047	−0.139050	−0.0695250	−	0.997580i	$-0.522148\pi$
$641$	−3.52047	−0.139050	−0.0695250	+	0.997580i	$0.522148\pi$
$642$	−11.0500	−0.436110
$643$	12.7865	0.504250	0.252125	−	0.967695i	$-0.418871\pi$
$643$	12.7865	0.504250	0.252125	+	0.967695i	$0.418871\pi$
$644$	−30.4535	−1.20003
$645$	−14.0773	−0.554291
$646$	−7.58921	−0.298594
$647$	7.00044	0.275216	0.137608	−	0.990487i	$-0.456059\pi$
$647$	7.00044	0.275216	0.137608	+	0.990487i	$0.456059\pi$
$648$	−1.55430	−0.0610588
$649$	−1.44956	−0.0569003
$650$	10.2314	0.401309
$651$	23.6077	0.925258
$652$	21.9224	0.858549
$653$	−13.6757	−0.535171	−0.267586	−	0.963534i	$-0.586226\pi$
$653$	−13.6757	−0.535171	−0.267586	+	0.963534i	$0.586226\pi$
$654$	−17.3246	−0.677445
$655$	−41.7800	−1.63248
$656$	37.4202	1.46101
$657$	−1.53009	−0.0596946
$658$	−59.5221	−2.32041
$659$	−44.0565	−1.71620	−0.858099	−	0.513484i	$-0.828355\pi$
$659$	−44.0565	−1.71620	−0.858099	+	0.513484i	$0.828355\pi$
$660$	−2.80332	−0.109119
$661$	−1.47619	−0.0574170	−0.0287085	−	0.999588i	$-0.509139\pi$
$661$	−1.47619	−0.0574170	−0.0287085	+	0.999588i	$0.509139\pi$
$662$	−32.7837	−1.27418
$663$	7.74079	0.300627
$664$	−7.28891	−0.282864
$665$	26.0275	1.00930
$666$	18.6433	0.722413
$667$	19.1034	0.739686
$668$	−1.36065	−0.0526452
$669$	−1.10168	−0.0425934
$670$	12.8068	0.494768
$671$	−1.00000	−0.0386046
$672$	−23.2993	−0.898788
$673$	24.3555	0.938836	0.469418	−	0.882976i	$-0.344464\pi$
$673$	24.3555	0.938836	0.469418	+	0.882976i	$0.344464\pi$
$674$	19.4243	0.748194
$675$	−1.26422	−0.0486598
$676$	8.95207	0.344310
$677$	−23.0375	−0.885403	−0.442701	−	0.896669i	$-0.645980\pi$
$677$	−23.0375	−0.885403	−0.442701	+	0.896669i	$0.645980\pi$
$678$	−7.59871	−0.291827
$679$	34.7057	1.33188
$680$	−6.57238	−0.252039
$681$	−24.3655	−0.933690
$682$	−10.1976	−0.390486
$683$	−48.5599	−1.85809	−0.929047	−	0.369962i	$-0.879371\pi$
$683$	−48.5599	−1.85809	−0.929047	+	0.369962i	$0.879371\pi$
$684$	2.84841	0.108912
$685$	−4.62974	−0.176893
$686$	−19.6570	−0.750508
$687$	10.0662	0.384049
$688$	28.0415	1.06907
$689$	−30.8694	−1.17603
$690$	29.3951	1.11905
$691$	21.8077	0.829606	0.414803	−	0.909911i	$-0.363851\pi$
$691$	21.8077	0.829606	0.414803	+	0.909911i	$0.363851\pi$
$692$	−18.1552	−0.690156
$693$	4.08919	0.155335
$694$	−11.1825	−0.424483
$695$	5.25171	0.199209
$696$	4.46567	0.169271
$697$	12.6807	0.480315
$698$	−26.1601	−0.990173
$699$	2.64216	0.0999359
$700$	−5.79027	−0.218852
$701$	12.3112	0.464988	0.232494	−	0.972598i	$-0.425311\pi$
$701$	12.3112	0.464988	0.232494	+	0.972598i	$0.425311\pi$
$702$	−8.09307	−0.305453
$703$	26.8413	1.01234
$704$	0.0931904	0.00351224
$705$	20.6250	0.776782
$706$	32.1548	1.21016
$707$	74.7235	2.81027
$708$	−1.62359	−0.0610183
$709$	7.64608	0.287155	0.143577	−	0.989639i	$-0.454139\pi$
$709$	7.64608	0.287155	0.143577	+	0.989639i	$0.454139\pi$
$710$	16.1217	0.605035
$711$	6.59373	0.247284
$712$	−12.4560	−0.466809
$713$	38.3863	1.43758
$714$	−12.2031	−0.456690
$715$	11.4674	0.428857
$716$	−0.515819	−0.0192771
$717$	24.0202	0.897052
$718$	−56.3670	−2.10360
$719$	−19.7235	−0.735564	−0.367782	−	0.929912i	$-0.619883\pi$
$719$	−19.7235	−0.735564	−0.367782	+	0.929912i	$0.619883\pi$
$720$	12.4781	0.465033
$721$	−55.2452	−2.05744
$722$	−22.1373	−0.823865
$723$	−20.2998	−0.754958
$724$	23.6453	0.878772
$725$	3.63222	0.134897
$726$	−1.76637	−0.0655561
$727$	−12.7551	−0.473061	−0.236531	−	0.971624i	$-0.576010\pi$
$727$	−12.7551	−0.473061	−0.236531	+	0.971624i	$0.576010\pi$
$728$	29.1209	1.07929
$729$	1.00000	0.0370370
$730$	6.76445	0.250363
$731$	9.50249	0.351462
$732$	−1.12006	−0.0413985
$733$	40.2693	1.48738	0.743690	−	0.668524i	$-0.233074\pi$
$733$	40.2693	1.48738	0.743690	+	0.668524i	$0.233074\pi$
$734$	48.3297	1.78388
$735$	24.3312	0.897471
$736$	−37.8848	−1.39645
$737$	2.89684	0.106706
$738$	−13.2578	−0.488026
$739$	13.7457	0.505644	0.252822	−	0.967513i	$-0.418641\pi$
$739$	13.7457	0.505644	0.252822	+	0.967513i	$0.418641\pi$
$740$	−29.5880	−1.08767
$741$	−11.6518	−0.428041
$742$	48.6647	1.78654
$743$	44.8666	1.64599	0.822997	−	0.568045i	$-0.192300\pi$
$743$	44.8666	1.64599	0.822997	+	0.568045i	$0.192300\pi$
$744$	8.97331	0.328978
$745$	26.6825	0.977571
$746$	−19.1476	−0.701043
$747$	4.68950	0.171580
$748$	1.89231	0.0691898
$749$	−25.5811	−0.934713
$750$	−16.5157	−0.603067
$751$	−23.6834	−0.864219	−0.432109	−	0.901821i	$-0.642231\pi$
$751$	−23.6834	−0.864219	−0.432109	+	0.901821i	$0.642231\pi$
$752$	−41.0844	−1.49819
$753$	7.85638	0.286302
$754$	23.2522	0.846794
$755$	39.9361	1.45342
$756$	4.58012	0.166577
$757$	23.5395	0.855557	0.427778	−	0.903884i	$-0.359296\pi$
$757$	23.5395	0.855557	0.427778	+	0.903884i	$0.359296\pi$
$758$	49.7077	1.80546
$759$	6.64905	0.241345
$760$	9.89309	0.358860
$761$	14.0136	0.507992	0.253996	−	0.967205i	$-0.418255\pi$
$761$	14.0136	0.507992	0.253996	+	0.967205i	$0.418255\pi$
$762$	−15.8208	−0.573127
$763$	−40.1069	−1.45197
$764$	23.1986	0.839296
$765$	4.22850	0.152882
$766$	21.7783	0.786881
$767$	6.64154	0.239812
$768$	−20.0243	−0.722566
$769$	44.6655	1.61068	0.805339	−	0.592814i	$-0.201983\pi$
$769$	44.6655	1.61068	0.805339	+	0.592814i	$0.201983\pi$
$770$	−18.0780	−0.651488
$771$	−8.43220	−0.303678
$772$	4.89237	0.176080
$773$	36.4789	1.31205	0.656027	−	0.754737i	$-0.272236\pi$
$773$	36.4789	1.31205	0.656027	+	0.754737i	$0.272236\pi$
$774$	−9.93495	−0.357104
$775$	7.29858	0.262173
$776$	13.1917	0.473553
$777$	43.1597	1.54835
$778$	4.15120	0.148828
$779$	−19.0877	−0.683886
$780$	12.8442	0.459895
$781$	3.64666	0.130488
$782$	−19.8424	−0.709562
$783$	−2.87310	−0.102676
$784$	−48.4671	−1.73097
$785$	31.5358	1.12556
$786$	−29.4861	−1.05173
$787$	41.9161	1.49415	0.747075	−	0.664740i	$-0.231458\pi$
$787$	41.9161	1.49415	0.747075	+	0.664740i	$0.231458\pi$
$788$	−16.6934	−0.594677
$789$	15.8210	0.563242
$790$	−29.1505	−1.03713
$791$	−17.5912	−0.625471
$792$	1.55430	0.0552298
$793$	4.58176	0.162703
$794$	12.8649	0.456558
$795$	−16.8628	−0.598061
$796$	13.7935	0.488899
$797$	7.04587	0.249577	0.124789	−	0.992183i	$-0.460175\pi$
$797$	7.04587	0.249577	0.124789	+	0.992183i	$0.460175\pi$
$798$	18.3688	0.650248
$799$	−13.9224	−0.492538
$800$	−7.20323	−0.254673
$801$	8.01389	0.283157
$802$	−10.4595	−0.369338
$803$	1.53009	0.0539958
$804$	3.24462	0.114429
$805$	68.0503	2.39846
$806$	46.7229	1.64575
$807$	−29.6760	−1.04465
$808$	28.4025	0.999197
$809$	−37.9979	−1.33594	−0.667968	−	0.744190i	$-0.732836\pi$
$809$	−37.9979	−1.33594	−0.667968	+	0.744190i	$0.732836\pi$
$810$	−4.42094	−0.155336
$811$	−54.3212	−1.90748	−0.953738	−	0.300641i	$-0.902800\pi$
$811$	−54.3212	−1.90748	−0.953738	+	0.300641i	$0.902800\pi$
$812$	−13.1591	−0.461795
$813$	−13.8327	−0.485134
$814$	−18.6433	−0.653447
$815$	−48.9872	−1.71595
$816$	−8.42304	−0.294866
$817$	−14.3037	−0.500422
$818$	66.3920	2.32134
$819$	−18.7357	−0.654677
$820$	21.0409	0.734779
$821$	0.336067	0.0117288	0.00586440	−	0.999983i	$-0.498133\pi$
$821$	0.336067	0.0117288	0.00586440	+	0.999983i	$0.498133\pi$
$822$	−3.26742	−0.113964
$823$	−26.5549	−0.925646	−0.462823	−	0.886451i	$-0.653163\pi$
$823$	−26.5549	−0.925646	−0.462823	+	0.886451i	$0.653163\pi$
$824$	−20.9988	−0.731527
$825$	1.26422	0.0440144
$826$	−10.4702	−0.364305
$827$	28.7699	1.00043	0.500214	−	0.865902i	$-0.333255\pi$
$827$	28.7699	1.00043	0.500214	+	0.865902i	$0.333255\pi$
$828$	7.44732	0.258812
$829$	36.5733	1.27024	0.635122	−	0.772412i	$-0.280950\pi$
$829$	36.5733	1.27024	0.635122	+	0.772412i	$0.280950\pi$
$830$	−20.7320	−0.719618
$831$	−10.7545	−0.373069
$832$	−0.426976	−0.0148027
$833$	−16.4242	−0.569064
$834$	3.70637	0.128341
$835$	3.04047	0.105220
$836$	−2.84841	−0.0985143
$837$	−5.77320	−0.199551
$838$	4.41080	0.152369
$839$	−36.5200	−1.26081	−0.630405	−	0.776267i	$-0.717111\pi$
$839$	−36.5200	−1.26081	−0.630405	+	0.776267i	$0.717111\pi$
$840$	15.9077	0.548867
$841$	−20.7453	−0.715356
$842$	−7.81217	−0.269225
$843$	−18.7346	−0.645255
$844$	−0.699219	−0.0240681
$845$	−20.0040	−0.688159
$846$	14.5560	0.500445
$847$	−4.08919	−0.140506
$848$	33.5902	1.15349
$849$	−24.5140	−0.841318
$850$	−3.77273	−0.129404
$851$	70.1781	2.40567
$852$	4.08446	0.139931
$853$	−30.1362	−1.03184	−0.515922	−	0.856635i	$-0.672551\pi$
$853$	−30.1362	−1.03184	−0.515922	+	0.856635i	$0.672551\pi$
$854$	−7.22301	−0.247166
$855$	−6.36497	−0.217677
$856$	−9.72341	−0.332339
$857$	−31.6160	−1.07998	−0.539991	−	0.841671i	$-0.681572\pi$
$857$	−31.6160	−1.07998	−0.539991	+	0.841671i	$0.681572\pi$
$858$	8.09307	0.276293
$859$	44.5621	1.52044	0.760219	−	0.649667i	$-0.225092\pi$
$859$	44.5621	1.52044	0.760219	+	0.649667i	$0.225092\pi$
$860$	15.7673	0.537661
$861$	−30.6921	−1.04598
$862$	−17.4529	−0.594449
$863$	15.9335	0.542382	0.271191	−	0.962526i	$-0.412583\pi$
$863$	15.9335	0.542382	0.271191	+	0.962526i	$0.412583\pi$
$864$	5.69777	0.193842
$865$	40.5690	1.37939
$866$	−68.8989	−2.34128
$867$	14.1457	0.480412
$868$	−26.4419	−0.897498
$869$	−6.59373	−0.223677
$870$	12.7018	0.430631
$871$	−13.2726	−0.449726
$872$	−15.2447	−0.516250
$873$	−8.48718	−0.287248
$874$	29.8678	1.01029
$875$	−38.2342	−1.29255
$876$	1.71379	0.0579036
$877$	−19.4169	−0.655662	−0.327831	−	0.944736i	$-0.606318\pi$
$877$	−19.4169	−0.655662	−0.327831	+	0.944736i	$0.606318\pi$
$878$	36.4516	1.23018
$879$	−22.3094	−0.752478
$880$	−12.4781	−0.420638
$881$	−37.0820	−1.24932	−0.624661	−	0.780896i	$-0.714763\pi$
$881$	−37.0820	−1.24932	−0.624661	+	0.780896i	$0.714763\pi$
$882$	17.1716	0.578200
$883$	9.54777	0.321308	0.160654	−	0.987011i	$-0.448640\pi$
$883$	9.54777	0.321308	0.160654	+	0.987011i	$0.448640\pi$
$884$	−8.67012	−0.291608
$885$	3.62802	0.121955
$886$	−56.8251	−1.90908
$887$	34.6540	1.16357	0.581783	−	0.813344i	$-0.302355\pi$
$887$	34.6540	1.16357	0.581783	+	0.813344i	$0.302355\pi$
$888$	16.4051	0.550518
$889$	−36.6255	−1.22838
$890$	−35.4289	−1.18758
$891$	−1.00000	−0.0335013
$892$	1.23394	0.0413155
$893$	20.9567	0.701289
$894$	18.8310	0.629804
$895$	1.15263	0.0385282
$896$	−45.9254	−1.53426
$897$	−30.4644	−1.01718
$898$	−10.3462	−0.345256
$899$	16.5870	0.553206
$900$	1.41600	0.0471998
$901$	11.3828	0.379216
$902$	13.2578	0.441436
$903$	−22.9997	−0.765381
$904$	−6.68643	−0.222387
$905$	−52.8371	−1.75636
$906$	28.1847	0.936374
$907$	39.5498	1.31323	0.656614	−	0.754227i	$-0.271988\pi$
$907$	39.5498	1.31323	0.656614	+	0.754227i	$0.271988\pi$
$908$	27.2908	0.905677
$909$	−18.2735	−0.606092
$910$	82.8293	2.74576
$911$	57.7089	1.91198	0.955991	−	0.293395i	$-0.0947851\pi$
$911$	57.7089	1.91198	0.955991	+	0.293395i	$0.0947851\pi$
$912$	12.6788	0.419838
$913$	−4.68950	−0.155200
$914$	−2.97137	−0.0982842
$915$	2.50284	0.0827414
$916$	−11.2747	−0.372527
$917$	−68.2610	−2.25418
$918$	2.98424	0.0984947
$919$	−36.0033	−1.18764	−0.593820	−	0.804598i	$-0.702381\pi$
$919$	−36.0033	−1.18764	−0.593820	+	0.804598i	$0.702381\pi$
$920$	25.8660	0.852777
$921$	−9.79575	−0.322781
$922$	−11.0022	−0.362340
$923$	−16.7081	−0.549954
$924$	−4.58012	−0.150675
$925$	13.3433	0.438725
$926$	35.3685	1.16228
$927$	13.5101	0.443729
$928$	−16.3702	−0.537380
$929$	−5.93686	−0.194782	−0.0973910	−	0.995246i	$-0.531050\pi$
$929$	−5.93686	−0.194782	−0.0973910	+	0.995246i	$0.531050\pi$
$930$	25.5230	0.836931
$931$	24.7226	0.810249
$932$	−2.95937	−0.0969375
$933$	−21.0159	−0.688031
$934$	19.7903	0.647559
$935$	−4.22850	−0.138287
$936$	−7.12145	−0.232772
$937$	31.8437	1.04029	0.520145	−	0.854078i	$-0.325878\pi$
$937$	31.8437	1.04029	0.520145	+	0.854078i	$0.325878\pi$
$938$	20.9239	0.683190
$939$	11.8868	0.387910
$940$	−23.1012	−0.753477
$941$	39.0802	1.27398	0.636989	−	0.770873i	$-0.280180\pi$
$941$	39.0802	1.27398	0.636989	+	0.770873i	$0.280180\pi$
$942$	22.2563	0.725148
$943$	−49.9057	−1.62515
$944$	−7.22691	−0.235216
$945$	−10.2346	−0.332931
$946$	9.93495	0.323013
$947$	24.9953	0.812237	0.406119	−	0.913820i	$-0.366882\pi$
$947$	24.9953	0.812237	0.406119	+	0.913820i	$0.366882\pi$
$948$	−7.38535	−0.239865
$949$	−7.01051	−0.227571
$950$	5.67892	0.184249
$951$	20.3584	0.660165
$952$	−10.7381	−0.348023
$953$	20.1451	0.652564	0.326282	−	0.945273i	$-0.394204\pi$
$953$	20.1451	0.652564	0.326282	+	0.945273i	$0.394204\pi$
$954$	−11.9008	−0.385304
$955$	−51.8388	−1.67747
$956$	−26.9040	−0.870138
$957$	2.87310	0.0928740
$958$	−65.1361	−2.10445
$959$	−7.56415	−0.244259
$960$	−0.233241	−0.00752781
$961$	2.32984	0.0751562
$962$	85.4191	2.75402
$963$	6.25580	0.201590
$964$	22.7369	0.732307
$965$	−10.9323	−0.351924
$966$	48.0262	1.54522
$967$	−19.5208	−0.627746	−0.313873	−	0.949465i	$-0.601627\pi$
$967$	−19.5208	−0.627746	−0.313873	+	0.949465i	$0.601627\pi$
$968$	−1.55430	−0.0499572
$969$	4.29651	0.138024
$970$	37.5213	1.20474
$971$	−23.1778	−0.743811	−0.371905	−	0.928271i	$-0.621295\pi$
$971$	−23.1778	−0.743811	−0.371905	+	0.928271i	$0.621295\pi$
$972$	−1.12006	−0.0359258
$973$	8.58034	0.275073
$974$	−48.1071	−1.54145
$975$	−5.79234	−0.185503
$976$	−4.98559	−0.159585
$977$	25.0807	0.802401	0.401201	−	0.915990i	$-0.368593\pi$
$977$	25.0807	0.802401	0.401201	+	0.915990i	$0.368593\pi$
$978$	−34.5725	−1.10551
$979$	−8.01389	−0.256125
$980$	−27.2524	−0.870545
$981$	9.80803	0.313146
$982$	−17.5843	−0.561138
$983$	23.1549	0.738527	0.369263	−	0.929325i	$-0.379610\pi$
$983$	23.1549	0.738527	0.369263	+	0.929325i	$0.379610\pi$
$984$	−11.6661	−0.371902
$985$	37.3025	1.18856
$986$	−8.57402	−0.273052
$987$	33.6975	1.07260
$988$	13.0507	0.415199
$989$	−37.3977	−1.18918
$990$	4.42094	0.140507
$991$	−20.3916	−0.647762	−0.323881	−	0.946098i	$-0.604988\pi$
$991$	−20.3916	−0.647762	−0.323881	+	0.946098i	$0.604988\pi$
$992$	−32.8944	−1.04440
$993$	18.5600	0.588983
$994$	26.3398	0.835449
$995$	−30.8226	−0.977142
$996$	−5.25250	−0.166432
$997$	−37.9430	−1.20167	−0.600834	−	0.799374i	$-0.705165\pi$
$997$	−37.9430	−1.20167	−0.600834	+	0.799374i	$0.705165\pi$
$998$	−43.9101	−1.38995
$999$	−10.5546	−0.333933

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.2.a.h.1.12	✓	14
3.2	odd	2		6039.2.a.j.1.3		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.2.a.h.1.12	✓	14	1.1	even	1	trivial
6039.2.a.j.1.3		14	3.2	odd	2

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:	\( N \)	\(=\)	\( 2013 = 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2013.a (trivial)

\(f(q)\)	\(=\)	\(q+1.76637 q^{2} -1.00000 q^{3} +1.12006 q^{4} -2.50284 q^{5} -1.76637 q^{6} -4.08919 q^{7} -1.55430 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.76637 q^{2} -1.00000 q^{3} +1.12006 q^{4} -2.50284 q^{5} -1.76637 q^{6} -4.08919 q^{7} -1.55430 q^{8} +1.00000 q^{9} -4.42094 q^{10} -1.00000 q^{11} -1.12006 q^{12} +4.58176 q^{13} -7.22301 q^{14} +2.50284 q^{15} -4.98559 q^{16} -1.68948 q^{17} +1.76637 q^{18} +2.54310 q^{19} -2.80332 q^{20} +4.08919 q^{21} -1.76637 q^{22} +6.64905 q^{23} +1.55430 q^{24} +1.26422 q^{25} +8.09307 q^{26} -1.00000 q^{27} -4.58012 q^{28} +2.87310 q^{29} +4.42094 q^{30} +5.77320 q^{31} -5.69777 q^{32} +1.00000 q^{33} -2.98424 q^{34} +10.2346 q^{35} +1.12006 q^{36} +10.5546 q^{37} +4.49204 q^{38} -4.58176 q^{39} +3.89018 q^{40} -7.50568 q^{41} +7.22301 q^{42} -5.62451 q^{43} -1.12006 q^{44} -2.50284 q^{45} +11.7447 q^{46} +8.24063 q^{47} +4.98559 q^{48} +9.72144 q^{49} +2.23307 q^{50} +1.68948 q^{51} +5.13183 q^{52} -6.73746 q^{53} -1.76637 q^{54} +2.50284 q^{55} +6.35584 q^{56} -2.54310 q^{57} +5.07495 q^{58} +1.44956 q^{59} +2.80332 q^{60} +1.00000 q^{61} +10.1976 q^{62} -4.08919 q^{63} -0.0931904 q^{64} -11.4674 q^{65} +1.76637 q^{66} -2.89684 q^{67} -1.89231 q^{68} -6.64905 q^{69} +18.0780 q^{70} -3.64666 q^{71} -1.55430 q^{72} -1.53009 q^{73} +18.6433 q^{74} -1.26422 q^{75} +2.84841 q^{76} +4.08919 q^{77} -8.09307 q^{78} +6.59373 q^{79} +12.4781 q^{80} +1.00000 q^{81} -13.2578 q^{82} +4.68950 q^{83} +4.58012 q^{84} +4.22850 q^{85} -9.93495 q^{86} -2.87310 q^{87} +1.55430 q^{88} +8.01389 q^{89} -4.42094 q^{90} -18.7357 q^{91} +7.44732 q^{92} -5.77320 q^{93} +14.5560 q^{94} -6.36497 q^{95} +5.69777 q^{96} -8.48718 q^{97} +17.1716 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - q^{2} - 14 q^{3} + 15 q^{4} + q^{5} + q^{6} + 9 q^{7} + 14 q^{9}+O(q^{10}) \) 14 * q - q^2 - 14 * q^3 + 15 * q^4 + q^5 + q^6 + 9 * q^7 + 14 * q^9	\( 14 q - q^{2} - 14 q^{3} + 15 q^{4} + q^{5} + q^{6} + 9 q^{7} + 14 q^{9} + 6 q^{10} - 14 q^{11} - 15 q^{12} + q^{13} - 7 q^{14} - q^{15} + 17 q^{16} - 9 q^{17} - q^{18} + 22 q^{19} + 23 q^{20} - 9 q^{21} + q^{22} + q^{23} + 25 q^{25} + 4 q^{26} - 14 q^{27} + 37 q^{28} - 6 q^{29} - 6 q^{30} + 9 q^{31} + 4 q^{32} + 14 q^{33} + 8 q^{34} + 18 q^{35} + 15 q^{36} + 18 q^{37} + 8 q^{38} - q^{39} + 16 q^{40} - 25 q^{41} + 7 q^{42} + 25 q^{43} - 15 q^{44} + q^{45} + 20 q^{46} + 36 q^{47} - 17 q^{48} + 25 q^{49} + 2 q^{50} + 9 q^{51} - 13 q^{52} + q^{54} - q^{55} - 40 q^{56} - 22 q^{57} + 33 q^{58} + 17 q^{59} - 23 q^{60} + 14 q^{61} - 13 q^{62} + 9 q^{63} - 6 q^{64} - 61 q^{65} - q^{66} + 22 q^{67} + 66 q^{68} - q^{69} + 44 q^{70} - 13 q^{71} + 20 q^{73} - 12 q^{74} - 25 q^{75} + 49 q^{76} - 9 q^{77} - 4 q^{78} + 31 q^{79} + 88 q^{80} + 14 q^{81} + 2 q^{82} + 32 q^{83} - 37 q^{84} + 2 q^{85} - 14 q^{86} + 6 q^{87} - 21 q^{89} + 6 q^{90} + 45 q^{91} - 14 q^{92} - 9 q^{93} - 31 q^{94} + 23 q^{95} - 4 q^{96} + 37 q^{97} - 38 q^{98} - 14 q^{99}+O(q^{100}) \) 14 * q - q^2 - 14 * q^3 + 15 * q^4 + q^5 + q^6 + 9 * q^7 + 14 * q^9 + 6 * q^10 - 14 * q^11 - 15 * q^12 + q^13 - 7 * q^14 - q^15 + 17 * q^16 - 9 * q^17 - q^18 + 22 * q^19 + 23 * q^20 - 9 * q^21 + q^22 + q^23 + 25 * q^25 + 4 * q^26 - 14 * q^27 + 37 * q^28 - 6 * q^29 - 6 * q^30 + 9 * q^31 + 4 * q^32 + 14 * q^33 + 8 * q^34 + 18 * q^35 + 15 * q^36 + 18 * q^37 + 8 * q^38 - q^39 + 16 * q^40 - 25 * q^41 + 7 * q^42 + 25 * q^43 - 15 * q^44 + q^45 + 20 * q^46 + 36 * q^47 - 17 * q^48 + 25 * q^49 + 2 * q^50 + 9 * q^51 - 13 * q^52 + q^54 - q^55 - 40 * q^56 - 22 * q^57 + 33 * q^58 + 17 * q^59 - 23 * q^60 + 14 * q^61 - 13 * q^62 + 9 * q^63 - 6 * q^64 - 61 * q^65 - q^66 + 22 * q^67 + 66 * q^68 - q^69 + 44 * q^70 - 13 * q^71 + 20 * q^73 - 12 * q^74 - 25 * q^75 + 49 * q^76 - 9 * q^77 - 4 * q^78 + 31 * q^79 + 88 * q^80 + 14 * q^81 + 2 * q^82 + 32 * q^83 - 37 * q^84 + 2 * q^85 - 14 * q^86 + 6 * q^87 - 21 * q^89 + 6 * q^90 + 45 * q^91 - 14 * q^92 - 9 * q^93 - 31 * q^94 + 23 * q^95 - 4 * q^96 + 37 * q^97 - 38 * q^98 - 14 * q^99

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