LMFDB - Embedded newform 6014.2.a.k.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6014,2,Mod(1,6014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6014, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6014 = 2 \cdot 31 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6014.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:	$48.0220317756$
Analytic rank:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	6014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.835304 q^{3} +1.00000 q^{4} -3.09750 q^{5} -0.835304 q^{6} +4.05347 q^{7} +1.00000 q^{8} -2.30227 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.835304 q^{3} +1.00000 q^{4} -3.09750 q^{5} -0.835304 q^{6} +4.05347 q^{7} +1.00000 q^{8} -2.30227 q^{9} -3.09750 q^{10} -2.34181 q^{11} -0.835304 q^{12} -6.11497 q^{13} +4.05347 q^{14} +2.58735 q^{15} +1.00000 q^{16} -4.64215 q^{17} -2.30227 q^{18} +7.87506 q^{19} -3.09750 q^{20} -3.38588 q^{21} -2.34181 q^{22} -4.52474 q^{23} -0.835304 q^{24} +4.59450 q^{25} -6.11497 q^{26} +4.42900 q^{27} +4.05347 q^{28} -3.24876 q^{29} +2.58735 q^{30} +1.00000 q^{31} +1.00000 q^{32} +1.95612 q^{33} -4.64215 q^{34} -12.5556 q^{35} -2.30227 q^{36} +10.6704 q^{37} +7.87506 q^{38} +5.10786 q^{39} -3.09750 q^{40} -7.00733 q^{41} -3.38588 q^{42} -6.98779 q^{43} -2.34181 q^{44} +7.13127 q^{45} -4.52474 q^{46} +2.60802 q^{47} -0.835304 q^{48} +9.43061 q^{49} +4.59450 q^{50} +3.87761 q^{51} -6.11497 q^{52} +3.90171 q^{53} +4.42900 q^{54} +7.25376 q^{55} +4.05347 q^{56} -6.57807 q^{57} -3.24876 q^{58} +13.9066 q^{59} +2.58735 q^{60} +2.75610 q^{61} +1.00000 q^{62} -9.33217 q^{63} +1.00000 q^{64} +18.9411 q^{65} +1.95612 q^{66} -14.7840 q^{67} -4.64215 q^{68} +3.77954 q^{69} -12.5556 q^{70} +12.9309 q^{71} -2.30227 q^{72} +13.5595 q^{73} +10.6704 q^{74} -3.83781 q^{75} +7.87506 q^{76} -9.49246 q^{77} +5.10786 q^{78} +3.22670 q^{79} -3.09750 q^{80} +3.20724 q^{81} -7.00733 q^{82} +10.5735 q^{83} -3.38588 q^{84} +14.3791 q^{85} -6.98779 q^{86} +2.71370 q^{87} -2.34181 q^{88} -8.84068 q^{89} +7.13127 q^{90} -24.7868 q^{91} -4.52474 q^{92} -0.835304 q^{93} +2.60802 q^{94} -24.3930 q^{95} -0.835304 q^{96} +1.00000 q^{97} +9.43061 q^{98} +5.39148 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 37 q^{2} + 9 q^{3} + 37 q^{4} + 9 q^{5} + 9 q^{6} + 19 q^{7} + 37 q^{8} + 52 q^{9}+O(q^{10}) $ 37 * q + 37 * q^2 + 9 * q^3 + 37 * q^4 + 9 * q^5 + 9 * q^6 + 19 * q^7 + 37 * q^8 + 52 * q^9	\( 37 q + 37 q^{2} + 9 q^{3} + 37 q^{4} + 9 q^{5} + 9 q^{6} + 19 q^{7} + 37 q^{8} + 52 q^{9} + 9 q^{10} + 5 q^{11} + 9 q^{12} + 16 q^{13} + 19 q^{14} + 22 q^{15} + 37 q^{16} + 3 q^{17} + 52 q^{18} + 36 q^{19} + 9 q^{20} + 6 q^{21} + 5 q^{22} + 11 q^{23} + 9 q^{24} + 58 q^{25} + 16 q^{26} + 24 q^{27} + 19 q^{28} + 5 q^{29} + 22 q^{30} + 37 q^{31} + 37 q^{32} + q^{33} + 3 q^{34} + 28 q^{35} + 52 q^{36} + 21 q^{37} + 36 q^{38} + 38 q^{39} + 9 q^{40} + 21 q^{41} + 6 q^{42} + 14 q^{43} + 5 q^{44} + 55 q^{45} + 11 q^{46} + 59 q^{47} + 9 q^{48} + 82 q^{49} + 58 q^{50} + 46 q^{51} + 16 q^{52} + 8 q^{53} + 24 q^{54} + 25 q^{55} + 19 q^{56} + 5 q^{58} + 41 q^{59} + 22 q^{60} + 16 q^{61} + 37 q^{62} + 23 q^{63} + 37 q^{64} - 46 q^{65} + q^{66} + 45 q^{67} + 3 q^{68} + 68 q^{69} + 28 q^{70} + 55 q^{71} + 52 q^{72} + 29 q^{73} + 21 q^{74} - 12 q^{75} + 36 q^{76} + 30 q^{77} + 38 q^{78} + 25 q^{79} + 9 q^{80} + 73 q^{81} + 21 q^{82} + 70 q^{83} + 6 q^{84} - 21 q^{85} + 14 q^{86} + 37 q^{87} + 5 q^{88} + 55 q^{90} + 18 q^{91} + 11 q^{92} + 9 q^{93} + 59 q^{94} - 9 q^{95} + 9 q^{96} + 37 q^{97} + 82 q^{98} + 33 q^{99}+O(q^{100}) \) 37 * q + 37 * q^2 + 9 * q^3 + 37 * q^4 + 9 * q^5 + 9 * q^6 + 19 * q^7 + 37 * q^8 + 52 * q^9 + 9 * q^10 + 5 * q^11 + 9 * q^12 + 16 * q^13 + 19 * q^14 + 22 * q^15 + 37 * q^16 + 3 * q^17 + 52 * q^18 + 36 * q^19 + 9 * q^20 + 6 * q^21 + 5 * q^22 + 11 * q^23 + 9 * q^24 + 58 * q^25 + 16 * q^26 + 24 * q^27 + 19 * q^28 + 5 * q^29 + 22 * q^30 + 37 * q^31 + 37 * q^32 + q^33 + 3 * q^34 + 28 * q^35 + 52 * q^36 + 21 * q^37 + 36 * q^38 + 38 * q^39 + 9 * q^40 + 21 * q^41 + 6 * q^42 + 14 * q^43 + 5 * q^44 + 55 * q^45 + 11 * q^46 + 59 * q^47 + 9 * q^48 + 82 * q^49 + 58 * q^50 + 46 * q^51 + 16 * q^52 + 8 * q^53 + 24 * q^54 + 25 * q^55 + 19 * q^56 + 5 * q^58 + 41 * q^59 + 22 * q^60 + 16 * q^61 + 37 * q^62 + 23 * q^63 + 37 * q^64 - 46 * q^65 + q^66 + 45 * q^67 + 3 * q^68 + 68 * q^69 + 28 * q^70 + 55 * q^71 + 52 * q^72 + 29 * q^73 + 21 * q^74 - 12 * q^75 + 36 * q^76 + 30 * q^77 + 38 * q^78 + 25 * q^79 + 9 * q^80 + 73 * q^81 + 21 * q^82 + 70 * q^83 + 6 * q^84 - 21 * q^85 + 14 * q^86 + 37 * q^87 + 5 * q^88 + 55 * q^90 + 18 * q^91 + 11 * q^92 + 9 * q^93 + 59 * q^94 - 9 * q^95 + 9 * q^96 + 37 * q^97 + 82 * q^98 + 33 * 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
$3$	−0.835304	−0.482263	−0.241131	−	0.970492i	$-0.577518\pi$
$3$	−0.835304	−0.482263	−0.241131	+	0.970492i	$0.577518\pi$
$4$	1.00000	0.500000
$5$	−3.09750	−1.38524	−0.692622	−	0.721301i	$-0.743545\pi$
$5$	−3.09750	−1.38524	−0.692622	+	0.721301i	$0.743545\pi$
$6$	−0.835304	−0.341011
$7$	4.05347	1.53207	0.766034	−	0.642800i	$-0.222228\pi$
$7$	4.05347	1.53207	0.766034	+	0.642800i	$0.222228\pi$
$8$	1.00000	0.353553
$9$	−2.30227	−0.767422
$10$	−3.09750	−0.979515
$11$	−2.34181	−0.706083	−0.353041	−	0.935608i	$-0.614853\pi$
$11$	−2.34181	−0.706083	−0.353041	+	0.935608i	$0.614853\pi$
$12$	−0.835304	−0.241131
$13$	−6.11497	−1.69599	−0.847993	−	0.530007i	$-0.822189\pi$
$13$	−6.11497	−1.69599	−0.847993	+	0.530007i	$0.822189\pi$
$14$	4.05347	1.08334
$15$	2.58735	0.668052
$16$	1.00000	0.250000
$17$	−4.64215	−1.12589	−0.562943	−	0.826495i	$-0.690331\pi$
$17$	−4.64215	−1.12589	−0.562943	+	0.826495i	$0.690331\pi$
$18$	−2.30227	−0.542650
$19$	7.87506	1.80666	0.903331	−	0.428944i	$-0.141114\pi$
$19$	7.87506	1.80666	0.903331	+	0.428944i	$0.141114\pi$
$20$	−3.09750	−0.692622
$21$	−3.38588	−0.738859
$22$	−2.34181	−0.499276
$23$	−4.52474	−0.943474	−0.471737	−	0.881739i	$-0.656373\pi$
$23$	−4.52474	−0.943474	−0.471737	+	0.881739i	$0.656373\pi$
$24$	−0.835304	−0.170506
$25$	4.59450	0.918900
$26$	−6.11497	−1.19924
$27$	4.42900	0.852362
$28$	4.05347	0.766034
$29$	−3.24876	−0.603280	−0.301640	−	0.953422i	$-0.597534\pi$
$29$	−3.24876	−0.603280	−0.301640	+	0.953422i	$0.597534\pi$
$30$	2.58735	0.472384
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	1.00000	0.176777
$33$	1.95612	0.340518
$34$	−4.64215	−0.796122
$35$	−12.5556	−2.12229
$36$	−2.30227	−0.383711
$37$	10.6704	1.75420	0.877101	−	0.480307i	$-0.159475\pi$
$37$	10.6704	1.75420	0.877101	+	0.480307i	$0.159475\pi$
$38$	7.87506	1.27750
$39$	5.10786	0.817912
$40$	−3.09750	−0.489758
$41$	−7.00733	−1.09436	−0.547181	−	0.837014i	$-0.684299\pi$
$41$	−7.00733	−1.09436	−0.547181	+	0.837014i	$0.684299\pi$
$42$	−3.38588	−0.522452
$43$	−6.98779	−1.06563	−0.532814	−	0.846232i	$-0.678866\pi$
$43$	−6.98779	−1.06563	−0.532814	+	0.846232i	$0.678866\pi$
$44$	−2.34181	−0.353041
$45$	7.13127	1.06307
$46$	−4.52474	−0.667137
$47$	2.60802	0.380418	0.190209	−	0.981744i	$-0.439083\pi$
$47$	2.60802	0.380418	0.190209	+	0.981744i	$0.439083\pi$
$48$	−0.835304	−0.120566
$49$	9.43061	1.34723
$50$	4.59450	0.649761
$51$	3.87761	0.542974
$52$	−6.11497	−0.847993
$53$	3.90171	0.535941	0.267970	−	0.963427i	$-0.413647\pi$
$53$	3.90171	0.535941	0.267970	+	0.963427i	$0.413647\pi$
$54$	4.42900	0.602711
$55$	7.25376	0.978097
$56$	4.05347	0.541668
$57$	−6.57807	−0.871286
$58$	−3.24876	−0.426583
$59$	13.9066	1.81049	0.905245	−	0.424890i	$-0.139687\pi$
$59$	13.9066	1.81049	0.905245	+	0.424890i	$0.139687\pi$
$60$	2.58735	0.334026
$61$	2.75610	0.352882	0.176441	−	0.984311i	$-0.443542\pi$
$61$	2.75610	0.352882	0.176441	+	0.984311i	$0.443542\pi$
$62$	1.00000	0.127000
$63$	−9.33217	−1.17574
$64$	1.00000	0.125000
$65$	18.9411	2.34936
$66$	1.95612	0.240782
$67$	−14.7840	−1.80615	−0.903074	−	0.429485i	$-0.858695\pi$
$67$	−14.7840	−1.80615	−0.903074	+	0.429485i	$0.858695\pi$
$68$	−4.64215	−0.562943
$69$	3.77954	0.455003
$70$	−12.5556	−1.50068
$71$	12.9309	1.53462	0.767310	−	0.641277i	$-0.221595\pi$
$71$	12.9309	1.53462	0.767310	+	0.641277i	$0.221595\pi$
$72$	−2.30227	−0.271325
$73$	13.5595	1.58702	0.793512	−	0.608554i	$-0.208250\pi$
$73$	13.5595	1.58702	0.793512	+	0.608554i	$0.208250\pi$
$74$	10.6704	1.24041
$75$	−3.83781	−0.443152
$76$	7.87506	0.903331
$77$	−9.49246	−1.08177
$78$	5.10786	0.578351
$79$	3.22670	0.363032	0.181516	−	0.983388i	$-0.441900\pi$
$79$	3.22670	0.363032	0.181516	+	0.983388i	$0.441900\pi$
$80$	−3.09750	−0.346311
$81$	3.20724	0.356360
$82$	−7.00733	−0.773831
$83$	10.5735	1.16059	0.580295	−	0.814406i	$-0.302937\pi$
$83$	10.5735	1.16059	0.580295	+	0.814406i	$0.302937\pi$
$84$	−3.38588	−0.369430
$85$	14.3791	1.55963
$86$	−6.98779	−0.753513
$87$	2.71370	0.290940
$88$	−2.34181	−0.249638
$89$	−8.84068	−0.937110	−0.468555	−	0.883434i	$-0.655225\pi$
$89$	−8.84068	−0.937110	−0.468555	+	0.883434i	$0.655225\pi$
$90$	7.13127	0.751702
$91$	−24.7868	−2.59837
$92$	−4.52474	−0.471737
$93$	−0.835304	−0.0866170
$94$	2.60802	0.268996
$95$	−24.3930	−2.50267
$96$	−0.835304	−0.0852528
$97$	1.00000	0.101535
$97$	1.00000	0.101535
$98$	9.43061	0.952636
$99$	5.39148	0.541864
$100$	4.59450	0.459450
$101$	−11.0574	−1.10025	−0.550126	−	0.835082i	$-0.685420\pi$
$101$	−11.0574	−1.10025	−0.550126	+	0.835082i	$0.685420\pi$
$102$	3.87761	0.383940
$103$	−19.2850	−1.90020	−0.950102	−	0.311941i	$-0.899021\pi$
$103$	−19.2850	−1.90020	−0.950102	+	0.311941i	$0.899021\pi$
$104$	−6.11497	−0.599622
$105$	10.4878	1.02350
$106$	3.90171	0.378967
$107$	6.75009	0.652555	0.326278	−	0.945274i	$-0.394206\pi$
$107$	6.75009	0.652555	0.326278	+	0.945274i	$0.394206\pi$
$108$	4.42900	0.426181
$109$	15.7462	1.50821	0.754106	−	0.656753i	$-0.228070\pi$
$109$	15.7462	1.50821	0.754106	+	0.656753i	$0.228070\pi$
$110$	7.25376	0.691619
$111$	−8.91302	−0.845986
$112$	4.05347	0.383017
$113$	12.2985	1.15695	0.578473	−	0.815701i	$-0.303649\pi$
$113$	12.2985	1.15695	0.578473	+	0.815701i	$0.303649\pi$
$114$	−6.57807	−0.616092
$115$	14.0154	1.30694
$116$	−3.24876	−0.301640
$117$	14.0783	1.30154
$118$	13.9066	1.28021
$119$	−18.8168	−1.72493
$120$	2.58735	0.236192
$121$	−5.51592	−0.501447
$122$	2.75610	0.249525
$123$	5.85325	0.527770
$124$	1.00000	0.0898027
$125$	1.25603	0.112343
$126$	−9.33217	−0.831376
$127$	−20.3260	−1.80364	−0.901818	−	0.432115i	$-0.857767\pi$
$127$	−20.3260	−1.80364	−0.901818	+	0.432115i	$0.857767\pi$
$128$	1.00000	0.0883883
$129$	5.83693	0.513913
$130$	18.9411	1.66124
$131$	1.16785	0.102035	0.0510177	−	0.998698i	$-0.483753\pi$
$131$	1.16785	0.102035	0.0510177	+	0.998698i	$0.483753\pi$
$132$	1.95612	0.170259
$133$	31.9213	2.76793
$134$	−14.7840	−1.27714
$135$	−13.7188	−1.18073
$136$	−4.64215	−0.398061
$137$	0.205268	0.0175372	0.00876861	−	0.999962i	$-0.497209\pi$
$137$	0.205268	0.0175372	0.00876861	+	0.999962i	$0.497209\pi$
$138$	3.77954	0.321735
$139$	12.7784	1.08385	0.541925	−	0.840427i	$-0.317696\pi$
$139$	12.7784	1.08385	0.541925	+	0.840427i	$0.317696\pi$
$140$	−12.5556	−1.06114
$141$	−2.17849	−0.183462
$142$	12.9309	1.08514
$143$	14.3201	1.19751
$144$	−2.30227	−0.191856
$145$	10.0630	0.835690
$146$	13.5595	1.12220
$147$	−7.87743	−0.649719
$148$	10.6704	0.877101
$149$	−5.64233	−0.462238	−0.231119	−	0.972926i	$-0.574239\pi$
$149$	−5.64233	−0.462238	−0.231119	+	0.972926i	$0.574239\pi$
$150$	−3.83781	−0.313355
$151$	23.2108	1.88887	0.944433	−	0.328704i	$-0.106612\pi$
$151$	23.2108	1.88887	0.944433	+	0.328704i	$0.106612\pi$
$152$	7.87506	0.638751
$153$	10.6875	0.864031
$154$	−9.49246	−0.764924
$155$	−3.09750	−0.248797
$156$	5.10786	0.408956
$157$	0.932100	0.0743897	0.0371948	−	0.999308i	$-0.488158\pi$
$157$	0.932100	0.0743897	0.0371948	+	0.999308i	$0.488158\pi$
$158$	3.22670	0.256703
$159$	−3.25911	−0.258464
$160$	−3.09750	−0.244879
$161$	−18.3409	−1.44547
$162$	3.20724	0.251984
$163$	0.422707	0.0331089	0.0165545	−	0.999863i	$-0.494730\pi$
$163$	0.422707	0.0331089	0.0165545	+	0.999863i	$0.494730\pi$
$164$	−7.00733	−0.547181
$165$	−6.05909	−0.471700
$166$	10.5735	0.820661
$167$	0.599469	0.0463883	0.0231942	−	0.999731i	$-0.492616\pi$
$167$	0.599469	0.0463883	0.0231942	+	0.999731i	$0.492616\pi$
$168$	−3.38588	−0.261226
$169$	24.3928	1.87637
$170$	14.3791	1.10282
$171$	−18.1305	−1.38647
$172$	−6.98779	−0.532814
$173$	11.5358	0.877053	0.438526	−	0.898718i	$-0.355501\pi$
$173$	11.5358	0.877053	0.438526	+	0.898718i	$0.355501\pi$
$174$	2.71370	0.205725
$175$	18.6237	1.40782
$176$	−2.34181	−0.176521
$177$	−11.6163	−0.873132
$178$	−8.84068	−0.662637
$179$	−15.2761	−1.14179	−0.570895	−	0.821023i	$-0.693404\pi$
$179$	−15.2761	−1.14179	−0.570895	+	0.821023i	$0.693404\pi$
$180$	7.13127	0.531534
$181$	16.4763	1.22468	0.612339	−	0.790596i	$-0.290229\pi$
$181$	16.4763	1.22468	0.612339	+	0.790596i	$0.290229\pi$
$182$	−24.7868	−1.83732
$183$	−2.30218	−0.170182
$184$	−4.52474	−0.333569
$185$	−33.0515	−2.43000
$186$	−0.835304	−0.0612475
$187$	10.8710	0.794970
$188$	2.60802	0.190209
$189$	17.9528	1.30588
$190$	−24.3930	−1.76965
$191$	4.03010	0.291608	0.145804	−	0.989314i	$-0.453423\pi$
$191$	4.03010	0.291608	0.145804	+	0.989314i	$0.453423\pi$
$192$	−0.835304	−0.0602829
$193$	12.4602	0.896908	0.448454	−	0.893806i	$-0.351975\pi$
$193$	12.4602	0.896908	0.448454	+	0.893806i	$0.351975\pi$
$194$	1.00000	0.0717958
$195$	−15.8216	−1.13301
$196$	9.43061	0.673615
$197$	−18.4908	−1.31741	−0.658707	−	0.752400i	$-0.728896\pi$
$197$	−18.4908	−1.31741	−0.658707	+	0.752400i	$0.728896\pi$
$198$	5.39148	0.383156
$199$	10.4042	0.737531	0.368766	−	0.929522i	$-0.379780\pi$
$199$	10.4042	0.737531	0.368766	+	0.929522i	$0.379780\pi$
$200$	4.59450	0.324880
$201$	12.3491	0.871038
$202$	−11.0574	−0.777996
$203$	−13.1688	−0.924265
$204$	3.87761	0.271487
$205$	21.7052	1.51596
$206$	−19.2850	−1.34365
$207$	10.4172	0.724043
$208$	−6.11497	−0.423997
$209$	−18.4419	−1.27565
$210$	10.4878	0.723724
$211$	16.1700	1.11319	0.556593	−	0.830785i	$-0.312108\pi$
$211$	16.1700	1.11319	0.556593	+	0.830785i	$0.312108\pi$
$212$	3.90171	0.267970
$213$	−10.8013	−0.740090
$214$	6.75009	0.461426
$215$	21.6447	1.47616
$216$	4.42900	0.301356
$217$	4.05347	0.275167
$218$	15.7462	1.06647
$219$	−11.3263	−0.765363
$220$	7.25376	0.489048
$221$	28.3866	1.90949
$222$	−8.91302	−0.598203
$223$	−19.8594	−1.32988	−0.664942	−	0.746895i	$-0.731544\pi$
$223$	−19.8594	−1.32988	−0.664942	+	0.746895i	$0.731544\pi$
$224$	4.05347	0.270834
$225$	−10.5778	−0.705185
$226$	12.2985	0.818085
$227$	−9.59660	−0.636949	−0.318474	−	0.947931i	$-0.603170\pi$
$227$	−9.59660	−0.636949	−0.318474	+	0.947931i	$0.603170\pi$
$228$	−6.57807	−0.435643
$229$	0.873800	0.0577423	0.0288712	−	0.999583i	$-0.490809\pi$
$229$	0.873800	0.0577423	0.0288712	+	0.999583i	$0.490809\pi$
$230$	14.0154	0.924148
$231$	7.92909	0.521696
$232$	−3.24876	−0.213292
$233$	20.0414	1.31296	0.656479	−	0.754344i	$-0.272045\pi$
$233$	20.0414	1.31296	0.656479	+	0.754344i	$0.272045\pi$
$234$	14.0783	0.920327
$235$	−8.07833	−0.526972
$236$	13.9066	0.905245
$237$	−2.69528	−0.175077
$238$	−18.8168	−1.21971
$239$	−18.3099	−1.18437	−0.592184	−	0.805803i	$-0.701734\pi$
$239$	−18.3099	−1.18437	−0.592184	+	0.805803i	$0.701734\pi$
$240$	2.58735	0.167013
$241$	13.4431	0.865943	0.432972	−	0.901408i	$-0.357465\pi$
$241$	13.4431	0.865943	0.432972	+	0.901408i	$0.357465\pi$
$242$	−5.51592	−0.354577
$243$	−15.9660	−1.02422
$244$	2.75610	0.176441
$245$	−29.2113	−1.86624
$246$	5.85325	0.373190
$247$	−48.1557	−3.06407
$248$	1.00000	0.0635001
$249$	−8.83206	−0.559709
$250$	1.25603	0.0794383
$251$	10.4067	0.656867	0.328434	−	0.944527i	$-0.393479\pi$
$251$	10.4067	0.656867	0.328434	+	0.944527i	$0.393479\pi$
$252$	−9.33217	−0.587871
$253$	10.5961	0.666171
$254$	−20.3260	−1.27536
$255$	−12.0109	−0.752151
$256$	1.00000	0.0625000
$257$	−5.13238	−0.320149	−0.160075	−	0.987105i	$-0.551173\pi$
$257$	−5.13238	−0.320149	−0.160075	+	0.987105i	$0.551173\pi$
$258$	5.83693	0.363391
$259$	43.2521	2.68755
$260$	18.9411	1.17468
$261$	7.47952	0.462971
$262$	1.16785	0.0721500
$263$	−2.86438	−0.176625	−0.0883127	−	0.996093i	$-0.528147\pi$
$263$	−2.86438	−0.176625	−0.0883127	+	0.996093i	$0.528147\pi$
$264$	1.95612	0.120391
$265$	−12.0855	−0.742409
$266$	31.9213	1.95722
$267$	7.38465	0.451933
$268$	−14.7840	−0.903074
$269$	−1.21418	−0.0740299	−0.0370149	−	0.999315i	$-0.511785\pi$
$269$	−1.21418	−0.0740299	−0.0370149	+	0.999315i	$0.511785\pi$
$270$	−13.7188	−0.834902
$271$	22.5067	1.36718	0.683592	−	0.729865i	$-0.260417\pi$
$271$	22.5067	1.36718	0.683592	+	0.729865i	$0.260417\pi$
$272$	−4.64215	−0.281472
$273$	20.7045	1.25310
$274$	0.205268	0.0124007
$275$	−10.7595	−0.648820
$276$	3.77954	0.227501
$277$	20.4149	1.22661	0.613306	−	0.789845i	$-0.289839\pi$
$277$	20.4149	1.22661	0.613306	+	0.789845i	$0.289839\pi$
$278$	12.7784	0.766397
$279$	−2.30227	−0.137833
$280$	−12.5556	−0.750342
$281$	−17.2209	−1.02731	−0.513655	−	0.857997i	$-0.671709\pi$
$281$	−17.2209	−1.02731	−0.513655	+	0.857997i	$0.671709\pi$
$282$	−2.17849	−0.129727
$283$	20.1675	1.19884	0.599418	−	0.800436i	$-0.295399\pi$
$283$	20.1675	1.19884	0.599418	+	0.800436i	$0.295399\pi$
$284$	12.9309	0.767310
$285$	20.3756	1.20694
$286$	14.3201	0.846765
$287$	−28.4040	−1.67664
$288$	−2.30227	−0.135662
$289$	4.54957	0.267621
$290$	10.0630	0.590922
$291$	−0.835304	−0.0489664
$292$	13.5595	0.793512
$293$	19.0019	1.11010	0.555050	−	0.831817i	$-0.312699\pi$
$293$	19.0019	1.11010	0.555050	+	0.831817i	$0.312699\pi$
$294$	−7.87743	−0.459421
$295$	−43.0758	−2.50797
$296$	10.6704	0.620204
$297$	−10.3719	−0.601838
$298$	−5.64233	−0.326851
$299$	27.6687	1.60012
$300$	−3.83781	−0.221576
$301$	−28.3248	−1.63261
$302$	23.2108	1.33563
$303$	9.23629	0.530611
$304$	7.87506	0.451665
$305$	−8.53701	−0.488828
$306$	10.6875	0.610962
$307$	12.8036	0.730743	0.365371	−	0.930862i	$-0.380942\pi$
$307$	12.8036	0.730743	0.365371	+	0.930862i	$0.380942\pi$
$308$	−9.49246	−0.540883
$309$	16.1088	0.916398
$310$	−3.09750	−0.175926
$311$	−2.97758	−0.168843	−0.0844215	−	0.996430i	$-0.526904\pi$
$311$	−2.97758	−0.168843	−0.0844215	+	0.996430i	$0.526904\pi$
$312$	5.10786	0.289175
$313$	−9.50212	−0.537091	−0.268546	−	0.963267i	$-0.586543\pi$
$313$	−9.50212	−0.537091	−0.268546	+	0.963267i	$0.586543\pi$
$314$	0.932100	0.0526014
$315$	28.9064	1.62869
$316$	3.22670	0.181516
$317$	−8.00085	−0.449373	−0.224686	−	0.974431i	$-0.572136\pi$
$317$	−8.00085	−0.449373	−0.224686	+	0.974431i	$0.572136\pi$
$318$	−3.25911	−0.182762
$319$	7.60799	0.425966
$320$	−3.09750	−0.173155
$321$	−5.63837	−0.314703
$322$	−18.3409	−1.02210
$323$	−36.5572	−2.03410
$324$	3.20724	0.178180
$325$	−28.0952	−1.55844
$326$	0.422707	0.0234116
$327$	−13.1529	−0.727355
$328$	−7.00733	−0.386915
$329$	10.5715	0.582826
$330$	−6.05909	−0.333542
$331$	−10.0743	−0.553733	−0.276867	−	0.960908i	$-0.589296\pi$
$331$	−10.0743	−0.553733	−0.276867	+	0.960908i	$0.589296\pi$
$332$	10.5735	0.580295
$333$	−24.5661	−1.34621
$334$	0.599469	0.0328015
$335$	45.7933	2.50196
$336$	−3.38588	−0.184715
$337$	−30.1560	−1.64270	−0.821351	−	0.570423i	$-0.806779\pi$
$337$	−30.1560	−1.64270	−0.821351	+	0.570423i	$0.806779\pi$
$338$	24.3928	1.32679
$339$	−10.2730	−0.557952
$340$	14.3791	0.779814
$341$	−2.34181	−0.126816
$342$	−18.1305	−0.980384
$343$	9.85241	0.531980
$344$	−6.98779	−0.376757
$345$	−11.7071	−0.630290
$346$	11.5358	0.620170
$347$	15.5927	0.837059	0.418530	−	0.908203i	$-0.362546\pi$
$347$	15.5927	0.837059	0.418530	+	0.908203i	$0.362546\pi$
$348$	2.71370	0.145470
$349$	23.3330	1.24899	0.624494	−	0.781029i	$-0.285305\pi$
$349$	23.3330	1.24899	0.624494	+	0.781029i	$0.285305\pi$
$350$	18.6237	0.995477
$351$	−27.0832	−1.44560
$352$	−2.34181	−0.124819
$353$	14.8182	0.788695	0.394347	−	0.918961i	$-0.370971\pi$
$353$	14.8182	0.788695	0.394347	+	0.918961i	$0.370971\pi$
$354$	−11.6163	−0.617398
$355$	−40.0536	−2.12582
$356$	−8.84068	−0.468555
$357$	15.7178	0.831872
$358$	−15.2761	−0.807367
$359$	−2.13424	−0.112641	−0.0563204	−	0.998413i	$-0.517937\pi$
$359$	−2.13424	−0.112641	−0.0563204	+	0.998413i	$0.517937\pi$
$360$	7.13127	0.375851
$361$	43.0165	2.26403
$362$	16.4763	0.865978
$363$	4.60747	0.241829
$364$	−24.7868	−1.29918
$365$	−42.0007	−2.19842
$366$	−2.30218	−0.120337
$367$	1.34060	0.0699786	0.0349893	−	0.999388i	$-0.488860\pi$
$367$	1.34060	0.0699786	0.0349893	+	0.999388i	$0.488860\pi$
$368$	−4.52474	−0.235869
$369$	16.1328	0.839838
$370$	−33.0515	−1.71827
$371$	15.8155	0.821097
$372$	−0.835304	−0.0433085
$373$	10.4050	0.538749	0.269375	−	0.963035i	$-0.413183\pi$
$373$	10.4050	0.538749	0.269375	+	0.963035i	$0.413183\pi$
$374$	10.8710	0.562128
$375$	−1.04917	−0.0541787
$376$	2.60802	0.134498
$377$	19.8661	1.02315
$378$	17.9528	0.923394
$379$	28.0278	1.43969	0.719845	−	0.694135i	$-0.244213\pi$
$379$	28.0278	1.43969	0.719845	+	0.694135i	$0.244213\pi$
$380$	−24.3930	−1.25133
$381$	16.9783	0.869827
$382$	4.03010	0.206198
$383$	20.4175	1.04328	0.521642	−	0.853165i	$-0.325320\pi$
$383$	20.4175	1.04328	0.521642	+	0.853165i	$0.325320\pi$
$384$	−0.835304	−0.0426264
$385$	29.4029	1.49851
$386$	12.4602	0.634210
$387$	16.0878	0.817787
$388$	1.00000	0.0507673
$389$	8.09215	0.410288	0.205144	−	0.978732i	$-0.434234\pi$
$389$	8.09215	0.410288	0.205144	+	0.978732i	$0.434234\pi$
$390$	−15.8216	−0.801157
$391$	21.0045	1.06225
$392$	9.43061	0.476318
$393$	−0.975509	−0.0492079
$394$	−18.4908	−0.931552
$395$	−9.99471	−0.502888
$396$	5.39148	0.270932
$397$	26.6306	1.33655	0.668277	−	0.743913i	$-0.267032\pi$
$397$	26.6306	1.33655	0.668277	+	0.743913i	$0.267032\pi$
$398$	10.4042	0.521513
$399$	−26.6640	−1.33487
$400$	4.59450	0.229725
$401$	21.0551	1.05144	0.525721	−	0.850657i	$-0.323796\pi$
$401$	21.0551	1.05144	0.525721	+	0.850657i	$0.323796\pi$
$402$	12.3491	0.615917
$403$	−6.11497	−0.304608
$404$	−11.0574	−0.550126
$405$	−9.93442	−0.493645
$406$	−13.1688	−0.653554
$407$	−24.9880	−1.23861
$408$	3.87761	0.191970
$409$	−0.162528	−0.00803647	−0.00401824	−	0.999992i	$-0.501279\pi$
$409$	−0.162528	−0.00803647	−0.00401824	+	0.999992i	$0.501279\pi$
$410$	21.7052	1.07194
$411$	−0.171461	−0.00845755
$412$	−19.2850	−0.950102
$413$	56.3701	2.77379
$414$	10.4172	0.511976
$415$	−32.7513	−1.60770
$416$	−6.11497	−0.299811
$417$	−10.6738	−0.522700
$418$	−18.4419	−0.902023
$419$	−22.8882	−1.11816	−0.559082	−	0.829113i	$-0.688846\pi$
$419$	−22.8882	−1.11816	−0.559082	+	0.829113i	$0.688846\pi$
$420$	10.4878	0.511750
$421$	14.9960	0.730860	0.365430	−	0.930839i	$-0.380922\pi$
$421$	14.9960	0.730860	0.365430	+	0.930839i	$0.380922\pi$
$422$	16.1700	0.787142
$423$	−6.00435	−0.291942
$424$	3.90171	0.189484
$425$	−21.3284	−1.03458
$426$	−10.8013	−0.523323
$427$	11.1718	0.540639
$428$	6.75009	0.326278
$429$	−11.9616	−0.577513
$430$	21.6447	1.04380
$431$	−8.26755	−0.398234	−0.199117	−	0.979976i	$-0.563807\pi$
$431$	−8.26755	−0.398234	−0.199117	+	0.979976i	$0.563807\pi$
$432$	4.42900	0.213091
$433$	−30.6741	−1.47410	−0.737051	−	0.675837i	$-0.763782\pi$
$433$	−30.6741	−1.47410	−0.737051	+	0.675837i	$0.763782\pi$
$434$	4.05347	0.194573
$435$	−8.40569	−0.403022
$436$	15.7462	0.754106
$437$	−35.6326	−1.70454
$438$	−11.3263	−0.541194
$439$	−11.2805	−0.538389	−0.269195	−	0.963086i	$-0.586757\pi$
$439$	−11.2805	−0.538389	−0.269195	+	0.963086i	$0.586757\pi$
$440$	7.25376	0.345809
$441$	−21.7118	−1.03389
$442$	28.3866	1.35021
$443$	−3.87963	−0.184327	−0.0921633	−	0.995744i	$-0.529378\pi$
$443$	−3.87963	−0.184327	−0.0921633	+	0.995744i	$0.529378\pi$
$444$	−8.91302	−0.422993
$445$	27.3840	1.29813
$446$	−19.8594	−0.940370
$447$	4.71306	0.222920
$448$	4.05347	0.191508
$449$	−2.00857	−0.0947903	−0.0473952	−	0.998876i	$-0.515092\pi$
$449$	−2.00857	−0.0947903	−0.0473952	+	0.998876i	$0.515092\pi$
$450$	−10.5778	−0.498641
$451$	16.4099	0.772710
$452$	12.2985	0.578473
$453$	−19.3881	−0.910930
$454$	−9.59660	−0.450391
$455$	76.7772	3.59937
$456$	−6.57807	−0.308046
$457$	−17.0979	−0.799807	−0.399904	−	0.916557i	$-0.630956\pi$
$457$	−17.0979	−0.799807	−0.399904	+	0.916557i	$0.630956\pi$
$458$	0.873800	0.0408300
$459$	−20.5601	−0.959664
$460$	14.0154	0.653471
$461$	4.01634	0.187060	0.0935298	−	0.995616i	$-0.470185\pi$
$461$	4.01634	0.187060	0.0935298	+	0.995616i	$0.470185\pi$
$462$	7.92909	0.368895
$463$	−27.1318	−1.26092	−0.630461	−	0.776221i	$-0.717134\pi$
$463$	−27.1318	−1.26092	−0.630461	+	0.776221i	$0.717134\pi$
$464$	−3.24876	−0.150820
$465$	2.58735	0.119986
$466$	20.0414	0.928402
$467$	−27.4419	−1.26986	−0.634930	−	0.772569i	$-0.718971\pi$
$467$	−27.4419	−1.26986	−0.634930	+	0.772569i	$0.718971\pi$
$468$	14.0783	0.650769
$469$	−59.9263	−2.76714
$470$	−8.07833	−0.372626
$471$	−0.778587	−0.0358754
$472$	13.9066	0.640105
$473$	16.3641	0.752422
$474$	−2.69528	−0.123798
$475$	36.1820	1.66014
$476$	−18.8168	−0.862467
$477$	−8.98278	−0.411293
$478$	−18.3099	−0.837474
$479$	7.76912	0.354980	0.177490	−	0.984123i	$-0.443202\pi$
$479$	7.76912	0.354980	0.177490	+	0.984123i	$0.443202\pi$
$480$	2.58735	0.118096
$481$	−65.2491	−2.97510
$482$	13.4431	0.612314
$483$	15.3202	0.697095
$484$	−5.51592	−0.250723
$485$	−3.09750	−0.140650
$486$	−15.9660	−0.724234
$487$	−11.5519	−0.523467	−0.261733	−	0.965140i	$-0.584294\pi$
$487$	−11.5519	−0.523467	−0.261733	+	0.965140i	$0.584294\pi$
$488$	2.75610	0.124763
$489$	−0.353089	−0.0159672
$490$	−29.2113	−1.31963
$491$	23.8013	1.07414	0.537068	−	0.843539i	$-0.319532\pi$
$491$	23.8013	1.07414	0.537068	+	0.843539i	$0.319532\pi$
$492$	5.85325	0.263885
$493$	15.0812	0.679225
$494$	−48.1557	−2.16663
$495$	−16.7001	−0.750614
$496$	1.00000	0.0449013
$497$	52.4151	2.35114
$498$	−8.83206	−0.395774
$499$	−20.6619	−0.924952	−0.462476	−	0.886632i	$-0.653039\pi$
$499$	−20.6619	−0.924952	−0.462476	+	0.886632i	$0.653039\pi$
$500$	1.25603	0.0561714
$501$	−0.500739	−0.0223714
$502$	10.4067	0.464475
$503$	−13.7447	−0.612845	−0.306423	−	0.951896i	$-0.599132\pi$
$503$	−13.7447	−0.612845	−0.306423	+	0.951896i	$0.599132\pi$
$504$	−9.33217	−0.415688
$505$	34.2503	1.52412
$506$	10.5961	0.471054
$507$	−20.3754	−0.904904
$508$	−20.3260	−0.901818
$509$	40.9308	1.81423	0.907114	−	0.420886i	$-0.138281\pi$
$509$	40.9308	1.81423	0.907114	+	0.420886i	$0.138281\pi$
$510$	−12.0109	−0.531851
$511$	54.9632	2.43143
$512$	1.00000	0.0441942
$513$	34.8787	1.53993
$514$	−5.13238	−0.226380
$515$	59.7351	2.63224
$516$	5.83693	0.256957
$517$	−6.10748	−0.268607
$518$	43.2521	1.90039
$519$	−9.63592	−0.422970
$520$	18.9411	0.830622
$521$	−30.6204	−1.34151	−0.670753	−	0.741681i	$-0.734029\pi$
$521$	−30.6204	−1.34151	−0.670753	+	0.741681i	$0.734029\pi$
$522$	7.47952	0.327370
$523$	34.0489	1.48885	0.744426	−	0.667705i	$-0.232723\pi$
$523$	34.0489	1.48885	0.744426	+	0.667705i	$0.232723\pi$
$524$	1.16785	0.0510177
$525$	−15.5564	−0.678938
$526$	−2.86438	−0.124893
$527$	−4.64215	−0.202215
$528$	1.95612	0.0851294
$529$	−2.52669	−0.109856
$530$	−12.0855	−0.524962
$531$	−32.0168	−1.38941
$532$	31.9213	1.38396
$533$	42.8496	1.85602
$534$	7.38465	0.319565
$535$	−20.9084	−0.903948
$536$	−14.7840	−0.638570
$537$	12.7602	0.550643
$538$	−1.21418	−0.0523470
$539$	−22.0847	−0.951256
$540$	−13.7188	−0.590365
$541$	22.0846	0.949491	0.474745	−	0.880123i	$-0.342540\pi$
$541$	22.0846	0.949491	0.474745	+	0.880123i	$0.342540\pi$
$542$	22.5067	0.966745
$543$	−13.7628	−0.590616
$544$	−4.64215	−0.199031
$545$	−48.7738	−2.08924
$546$	20.7045	0.886072
$547$	7.97506	0.340989	0.170495	−	0.985359i	$-0.445463\pi$
$547$	7.97506	0.340989	0.170495	+	0.985359i	$0.445463\pi$
$548$	0.205268	0.00876861
$549$	−6.34527	−0.270810
$550$	−10.7595	−0.458785
$551$	−25.5842	−1.08992
$552$	3.77954	0.160868
$553$	13.0793	0.556190
$554$	20.4149	0.867346
$555$	27.6081	1.17190
$556$	12.7784	0.541925
$557$	−31.2185	−1.32277	−0.661385	−	0.750047i	$-0.730031\pi$
$557$	−31.2185	−1.32277	−0.661385	+	0.750047i	$0.730031\pi$
$558$	−2.30227	−0.0974628
$559$	42.7301	1.80729
$560$	−12.5556	−0.530572
$561$	−9.08063	−0.383384
$562$	−17.2209	−0.726418
$563$	39.3724	1.65935	0.829674	−	0.558248i	$-0.188526\pi$
$563$	39.3724	1.65935	0.829674	+	0.558248i	$0.188526\pi$
$564$	−2.17849	−0.0917308
$565$	−38.0946	−1.60265
$566$	20.1675	0.847705
$567$	13.0004	0.545967
$568$	12.9309	0.542570
$569$	−7.03691	−0.295002	−0.147501	−	0.989062i	$-0.547123\pi$
$569$	−7.03691	−0.295002	−0.147501	+	0.989062i	$0.547123\pi$
$570$	20.3756	0.853438
$571$	−9.93988	−0.415971	−0.207986	−	0.978132i	$-0.566691\pi$
$571$	−9.93988	−0.415971	−0.207986	+	0.978132i	$0.566691\pi$
$572$	14.3201	0.598754
$573$	−3.36636	−0.140632
$574$	−28.4040	−1.18556
$575$	−20.7889	−0.866959
$576$	−2.30227	−0.0959278
$577$	21.6151	0.899849	0.449925	−	0.893067i	$-0.351451\pi$
$577$	21.6151	0.899849	0.449925	+	0.893067i	$0.351451\pi$
$578$	4.54957	0.189237
$579$	−10.4081	−0.432545
$580$	10.0630	0.417845
$581$	42.8593	1.77810
$582$	−0.835304	−0.0346245
$583$	−9.13707	−0.378419
$584$	13.5595	0.561098
$585$	−43.6075	−1.80295
$586$	19.0019	0.784959
$587$	14.4693	0.597210	0.298605	−	0.954377i	$-0.403479\pi$
$587$	14.4693	0.597210	0.298605	+	0.954377i	$0.403479\pi$
$588$	−7.87743	−0.324860
$589$	7.87506	0.324486
$590$	−43.0758	−1.77340
$591$	15.4454	0.635340
$592$	10.6704	0.438550
$593$	37.1467	1.52543	0.762716	−	0.646734i	$-0.223866\pi$
$593$	37.1467	1.52543	0.762716	+	0.646734i	$0.223866\pi$
$594$	−10.3719	−0.425564
$595$	58.2851	2.38945
$596$	−5.64233	−0.231119
$597$	−8.69063	−0.355684
$598$	27.6687	1.13146
$599$	41.0691	1.67804	0.839020	−	0.544101i	$-0.183129\pi$
$599$	41.0691	1.67804	0.839020	+	0.544101i	$0.183129\pi$
$600$	−3.83781	−0.156678
$601$	−14.3463	−0.585198	−0.292599	−	0.956235i	$-0.594520\pi$
$601$	−14.3463	−0.585198	−0.292599	+	0.956235i	$0.594520\pi$
$602$	−28.3248	−1.15443
$603$	34.0366	1.38608
$604$	23.2108	0.944433
$605$	17.0855	0.694626
$606$	9.23629	0.375199
$607$	26.4516	1.07364	0.536818	−	0.843698i	$-0.319626\pi$
$607$	26.4516	1.07364	0.536818	+	0.843698i	$0.319626\pi$
$608$	7.87506	0.319376
$609$	10.9999	0.445739
$610$	−8.53701	−0.345653
$611$	−15.9479	−0.645184
$612$	10.6875	0.432015
$613$	−9.81532	−0.396437	−0.198219	−	0.980158i	$-0.563516\pi$
$613$	−9.81532	−0.396437	−0.198219	+	0.980158i	$0.563516\pi$
$614$	12.8036	0.516713
$615$	−18.1304	−0.731090
$616$	−9.49246	−0.382462
$617$	5.76931	0.232264	0.116132	−	0.993234i	$-0.462950\pi$
$617$	5.76931	0.232264	0.116132	+	0.993234i	$0.462950\pi$
$618$	16.1088	0.647991
$619$	−9.45818	−0.380156	−0.190078	−	0.981769i	$-0.560874\pi$
$619$	−9.45818	−0.380156	−0.190078	+	0.981769i	$0.560874\pi$
$620$	−3.09750	−0.124399
$621$	−20.0401	−0.804182
$622$	−2.97758	−0.119390
$623$	−35.8354	−1.43572
$624$	5.10786	0.204478
$625$	−26.8631	−1.07452
$626$	−9.50212	−0.379781
$627$	15.4046	0.615200
$628$	0.932100	0.0371948
$629$	−49.5336	−1.97503
$630$	28.9064	1.15166
$631$	26.3109	1.04742	0.523711	−	0.851896i	$-0.324547\pi$
$631$	26.3109	1.04742	0.523711	+	0.851896i	$0.324547\pi$
$632$	3.22670	0.128351
$633$	−13.5068	−0.536849
$634$	−8.00085	−0.317754
$635$	62.9596	2.49848
$636$	−3.25911	−0.129232
$637$	−57.6679	−2.28488
$638$	7.60799	0.301203
$639$	−29.7705	−1.17770
$640$	−3.09750	−0.122439
$641$	−7.54838	−0.298143	−0.149072	−	0.988826i	$-0.547628\pi$
$641$	−7.54838	−0.298143	−0.149072	+	0.988826i	$0.547628\pi$
$642$	−5.63837	−0.222529
$643$	−7.26533	−0.286517	−0.143258	−	0.989685i	$-0.545758\pi$
$643$	−7.26533	−0.286517	−0.143258	+	0.989685i	$0.545758\pi$
$644$	−18.3409	−0.722733
$645$	−18.0799	−0.711895
$646$	−36.5572	−1.43832
$647$	21.6839	0.852482	0.426241	−	0.904610i	$-0.359838\pi$
$647$	21.6839	0.852482	0.426241	+	0.904610i	$0.359838\pi$
$648$	3.20724	0.125992
$649$	−32.5667	−1.27836
$650$	−28.0952	−1.10199
$651$	−3.38588	−0.132703
$652$	0.422707	0.0165545
$653$	−18.8522	−0.737743	−0.368871	−	0.929480i	$-0.620256\pi$
$653$	−18.8522	−0.737743	−0.368871	+	0.929480i	$0.620256\pi$
$654$	−13.1529	−0.514318
$655$	−3.61741	−0.141344
$656$	−7.00733	−0.273590
$657$	−31.2177	−1.21792
$658$	10.5715	0.412121
$659$	20.8516	0.812262	0.406131	−	0.913815i	$-0.366878\pi$
$659$	20.8516	0.812262	0.406131	+	0.913815i	$0.366878\pi$
$660$	−6.05909	−0.235850
$661$	−31.8799	−1.23998	−0.619992	−	0.784608i	$-0.712864\pi$
$661$	−31.8799	−1.23998	−0.619992	+	0.784608i	$0.712864\pi$
$662$	−10.0743	−0.391548
$663$	−23.7114	−0.920876
$664$	10.5735	0.410330
$665$	−98.8762	−3.83425
$666$	−24.5661	−0.951917
$667$	14.6998	0.569179
$668$	0.599469	0.0231942
$669$	16.5886	0.641354
$670$	45.7933	1.76915
$671$	−6.45426	−0.249164
$672$	−3.38588	−0.130613
$673$	−5.07593	−0.195663	−0.0978314	−	0.995203i	$-0.531191\pi$
$673$	−5.07593	−0.195663	−0.0978314	+	0.995203i	$0.531191\pi$
$674$	−30.1560	−1.16157
$675$	20.3491	0.783236
$676$	24.3928	0.938186
$677$	−35.3585	−1.35894	−0.679468	−	0.733705i	$-0.737789\pi$
$677$	−35.3585	−1.35894	−0.679468	+	0.733705i	$0.737789\pi$
$678$	−10.2730	−0.394532
$679$	4.05347	0.155558
$680$	14.3791	0.551412
$681$	8.01608	0.307177
$682$	−2.34181	−0.0896726
$683$	18.5453	0.709618	0.354809	−	0.934939i	$-0.384546\pi$
$683$	18.5453	0.709618	0.354809	+	0.934939i	$0.384546\pi$
$684$	−18.1305	−0.693236
$685$	−0.635817	−0.0242933
$686$	9.85241	0.376167
$687$	−0.729889	−0.0278470
$688$	−6.98779	−0.266407
$689$	−23.8588	−0.908949
$690$	−11.7071	−0.445682
$691$	−41.2391	−1.56881	−0.784405	−	0.620249i	$-0.787032\pi$
$691$	−41.2391	−1.56881	−0.784405	+	0.620249i	$0.787032\pi$
$692$	11.5358	0.438526
$693$	21.8542	0.830172
$694$	15.5927	0.591890
$695$	−39.5811	−1.50140
$696$	2.71370	0.102863
$697$	32.5291	1.23213
$698$	23.3330	0.883169
$699$	−16.7407	−0.633191
$700$	18.6237	0.703909
$701$	−35.5573	−1.34298	−0.671491	−	0.741013i	$-0.734346\pi$
$701$	−35.5573	−1.34298	−0.671491	+	0.741013i	$0.734346\pi$
$702$	−27.0832	−1.02219
$703$	84.0299	3.16925
$704$	−2.34181	−0.0882604
$705$	6.74786	0.254139
$706$	14.8182	0.557691
$707$	−44.8208	−1.68566
$708$	−11.6163	−0.436566
$709$	−16.8918	−0.634386	−0.317193	−	0.948361i	$-0.602740\pi$
$709$	−16.8918	−0.634386	−0.317193	+	0.948361i	$0.602740\pi$
$710$	−40.0536	−1.50318
$711$	−7.42873	−0.278599
$712$	−8.84068	−0.331318
$713$	−4.52474	−0.169453
$714$	15.7178	0.588222
$715$	−44.3565	−1.65884
$716$	−15.2761	−0.570895
$717$	15.2943	0.571176
$718$	−2.13424	−0.0796491
$719$	18.5975	0.693571	0.346786	−	0.937944i	$-0.387273\pi$
$719$	18.5975	0.693571	0.346786	+	0.937944i	$0.387273\pi$
$720$	7.13127	0.265767
$721$	−78.1710	−2.91124
$722$	43.0165	1.60091
$723$	−11.2290	−0.417612
$724$	16.4763	0.612339
$725$	−14.9264	−0.554354
$726$	4.60747	0.170999
$727$	−20.7394	−0.769181	−0.384590	−	0.923087i	$-0.625657\pi$
$727$	−20.7394	−0.769181	−0.384590	+	0.923087i	$0.625657\pi$
$728$	−24.7868	−0.918661
$729$	3.71478	0.137584
$730$	−42.0007	−1.55452
$731$	32.4384	1.19978
$732$	−2.30218	−0.0850910
$733$	4.65935	0.172097	0.0860484	−	0.996291i	$-0.472576\pi$
$733$	4.65935	0.172097	0.0860484	+	0.996291i	$0.472576\pi$
$734$	1.34060	0.0494823
$735$	24.4003	0.900019
$736$	−4.52474	−0.166784
$737$	34.6213	1.27529
$738$	16.1328	0.593855
$739$	−47.5206	−1.74807	−0.874036	−	0.485861i	$-0.838506\pi$
$739$	−47.5206	−1.74807	−0.874036	+	0.485861i	$0.838506\pi$
$740$	−33.0515	−1.21500
$741$	40.2247	1.47769
$742$	15.8155	0.580604
$743$	−8.06290	−0.295799	−0.147900	−	0.989002i	$-0.547251\pi$
$743$	−8.06290	−0.295799	−0.147900	+	0.989002i	$0.547251\pi$
$744$	−0.835304	−0.0306237
$745$	17.4771	0.640312
$746$	10.4050	0.380953
$747$	−24.3430	−0.890663
$748$	10.8710	0.397485
$749$	27.3613	0.999759
$750$	−1.04917	−0.0383102
$751$	−7.57375	−0.276370	−0.138185	−	0.990406i	$-0.544127\pi$
$751$	−7.57375	−0.276370	−0.138185	+	0.990406i	$0.544127\pi$
$752$	2.60802	0.0951046
$753$	−8.69279	−0.316783
$754$	19.8661	0.723480
$755$	−71.8954	−2.61654
$756$	17.9528	0.652938
$757$	−0.690376	−0.0250922	−0.0125461	−	0.999921i	$-0.503994\pi$
$757$	−0.690376	−0.0250922	−0.0125461	+	0.999921i	$0.503994\pi$
$758$	28.0278	1.01801
$759$	−8.85096	−0.321270
$760$	−24.3930	−0.884826
$761$	5.96308	0.216161	0.108081	−	0.994142i	$-0.465530\pi$
$761$	5.96308	0.216161	0.108081	+	0.994142i	$0.465530\pi$
$762$	16.9783	0.615061
$763$	63.8267	2.31068
$764$	4.03010	0.145804
$765$	−33.1044	−1.19689
$766$	20.4175	0.737713
$767$	−85.0386	−3.07057
$768$	−0.835304	−0.0301414
$769$	34.9273	1.25951	0.629755	−	0.776794i	$-0.283155\pi$
$769$	34.9273	1.25951	0.629755	+	0.776794i	$0.283155\pi$
$770$	29.4029	1.05961
$771$	4.28710	0.154396
$772$	12.4602	0.448454
$773$	3.32589	0.119624	0.0598120	−	0.998210i	$-0.480950\pi$
$773$	3.32589	0.119624	0.0598120	+	0.998210i	$0.480950\pi$
$774$	16.0878	0.578263
$775$	4.59450	0.165039
$776$	1.00000	0.0358979
$777$	−36.1286	−1.29611
$778$	8.09215	0.290118
$779$	−55.1831	−1.97714
$780$	−15.8216	−0.566503
$781$	−30.2818	−1.08357
$782$	21.0045	0.751121
$783$	−14.3888	−0.514213
$784$	9.43061	0.336808
$785$	−2.88718	−0.103048
$786$	−0.975509	−0.0347953
$787$	−25.3696	−0.904327	−0.452164	−	0.891935i	$-0.649348\pi$
$787$	−25.3696	−0.904327	−0.452164	+	0.891935i	$0.649348\pi$
$788$	−18.4908	−0.658707
$789$	2.39263	0.0851799
$790$	−9.99471	−0.355596
$791$	49.8516	1.77252
$792$	5.39148	0.191578
$793$	−16.8534	−0.598483
$794$	26.6306	0.945086
$795$	10.0951	0.358036
$796$	10.4042	0.368766
$797$	−4.49648	−0.159273	−0.0796367	−	0.996824i	$-0.525376\pi$
$797$	−4.49648	−0.159273	−0.0796367	+	0.996824i	$0.525376\pi$
$798$	−26.6640	−0.943895
$799$	−12.1068	−0.428308
$800$	4.59450	0.162440
$801$	20.3536	0.719159
$802$	21.0551	0.743482
$803$	−31.7539	−1.12057
$804$	12.3491	0.435519
$805$	56.8110	2.00232
$806$	−6.11497	−0.215391
$807$	1.01421	0.0357019
$808$	−11.0574	−0.388998
$809$	−31.6897	−1.11415	−0.557075	−	0.830462i	$-0.688076\pi$
$809$	−31.6897	−1.11415	−0.557075	+	0.830462i	$0.688076\pi$
$810$	−9.93442	−0.349060
$811$	−38.4003	−1.34842	−0.674209	−	0.738540i	$-0.735515\pi$
$811$	−38.4003	−1.34842	−0.674209	+	0.738540i	$0.735515\pi$
$812$	−13.1688	−0.462133
$813$	−18.7999	−0.659342
$814$	−24.9880	−0.875830
$815$	−1.30933	−0.0458640
$816$	3.87761	0.135743
$817$	−55.0293	−1.92523
$818$	−0.162528	−0.00568264
$819$	57.0659	1.99404
$820$	21.7052	0.757979
$821$	−28.1464	−0.982318	−0.491159	−	0.871070i	$-0.663427\pi$
$821$	−28.1464	−0.982318	−0.491159	+	0.871070i	$0.663427\pi$
$822$	−0.171461	−0.00598039
$823$	−16.5345	−0.576355	−0.288177	−	0.957577i	$-0.593049\pi$
$823$	−16.5345	−0.576355	−0.288177	+	0.957577i	$0.593049\pi$
$824$	−19.2850	−0.671823
$825$	8.98742	0.312902
$826$	56.3701	1.96137
$827$	16.0966	0.559734	0.279867	−	0.960039i	$-0.409710\pi$
$827$	16.0966	0.559734	0.279867	+	0.960039i	$0.409710\pi$
$828$	10.4172	0.362022
$829$	−1.95423	−0.0678733	−0.0339367	−	0.999424i	$-0.510804\pi$
$829$	−1.95423	−0.0678733	−0.0339367	+	0.999424i	$0.510804\pi$
$830$	−32.7513	−1.13682
$831$	−17.0526	−0.591550
$832$	−6.11497	−0.211998
$833$	−43.7783	−1.51683
$834$	−10.6738	−0.369605
$835$	−1.85686	−0.0642591
$836$	−18.4419	−0.637826
$837$	4.42900	0.153089
$838$	−22.8882	−0.790661
$839$	−39.2515	−1.35511	−0.677557	−	0.735471i	$-0.736961\pi$
$839$	−39.2515	−1.35511	−0.677557	+	0.735471i	$0.736961\pi$
$840$	10.4878	0.361862
$841$	−18.4455	−0.636053
$842$	14.9960	0.516796
$843$	14.3847	0.495434
$844$	16.1700	0.556593
$845$	−75.5568	−2.59923
$846$	−6.00435	−0.206434
$847$	−22.3586	−0.768251
$848$	3.90171	0.133985
$849$	−16.8460	−0.578154
$850$	−21.3284	−0.731557
$851$	−48.2808	−1.65504
$852$	−10.8013	−0.370045
$853$	38.3541	1.31322	0.656609	−	0.754231i	$-0.271990\pi$
$853$	38.3541	1.31322	0.656609	+	0.754231i	$0.271990\pi$
$854$	11.1718	0.382290
$855$	56.1592	1.92060
$856$	6.75009	0.230713
$857$	−33.3507	−1.13924	−0.569619	−	0.821909i	$-0.692909\pi$
$857$	−33.3507	−1.13924	−0.569619	+	0.821909i	$0.692909\pi$
$858$	−11.9616	−0.408364
$859$	24.5338	0.837084	0.418542	−	0.908197i	$-0.362541\pi$
$859$	24.5338	0.837084	0.418542	+	0.908197i	$0.362541\pi$
$860$	21.6447	0.738078
$861$	23.7260	0.808579
$862$	−8.26755	−0.281594
$863$	−36.1785	−1.23153	−0.615765	−	0.787929i	$-0.711153\pi$
$863$	−36.1785	−1.23153	−0.615765	+	0.787929i	$0.711153\pi$
$864$	4.42900	0.150678
$865$	−35.7322	−1.21493
$866$	−30.6741	−1.04235
$867$	−3.80027	−0.129064
$868$	4.05347	0.137584
$869$	−7.55633	−0.256331
$870$	−8.40569	−0.284980
$871$	90.4034	3.06320
$872$	15.7462	0.533234
$873$	−2.30227	−0.0779199
$874$	−35.6326	−1.20529
$875$	5.09128	0.172117
$876$	−11.3263	−0.382682
$877$	−27.1238	−0.915905	−0.457953	−	0.888977i	$-0.651417\pi$
$877$	−27.1238	−0.915905	−0.457953	+	0.888977i	$0.651417\pi$
$878$	−11.2805	−0.380699
$879$	−15.8723	−0.535360
$880$	7.25376	0.244524
$881$	36.5468	1.23129	0.615646	−	0.788023i	$-0.288895\pi$
$881$	36.5468	1.23129	0.615646	+	0.788023i	$0.288895\pi$
$882$	−21.7118	−0.731074
$883$	−51.4293	−1.73073	−0.865367	−	0.501138i	$-0.832915\pi$
$883$	−51.4293	−1.73073	−0.865367	+	0.501138i	$0.832915\pi$
$884$	28.3866	0.954745
$885$	35.9814	1.20950
$886$	−3.87963	−0.130339
$887$	−19.8733	−0.667282	−0.333641	−	0.942700i	$-0.608277\pi$
$887$	−19.8733	−0.667282	−0.333641	+	0.942700i	$0.608277\pi$
$888$	−8.91302	−0.299101
$889$	−82.3906	−2.76329
$890$	27.3840	0.917914
$891$	−7.51075	−0.251620
$892$	−19.8594	−0.664942
$893$	20.5383	0.687287
$894$	4.71306	0.157628
$895$	47.3177	1.58166
$896$	4.05347	0.135417
$897$	−23.1117	−0.771679
$898$	−2.00857	−0.0670269
$899$	−3.24876	−0.108352
$900$	−10.5778	−0.352592
$901$	−18.1123	−0.603409
$902$	16.4099	0.546388
$903$	23.6598	0.787349
$904$	12.2985	0.409042
$905$	−51.0355	−1.69648
$906$	−19.3881	−0.644125
$907$	22.5360	0.748297	0.374148	−	0.927369i	$-0.377935\pi$
$907$	22.5360	0.748297	0.374148	+	0.927369i	$0.377935\pi$
$908$	−9.59660	−0.318474
$909$	25.4571	0.844358
$910$	76.7772	2.54514
$911$	25.6261	0.849031	0.424516	−	0.905421i	$-0.360444\pi$
$911$	25.6261	0.849031	0.424516	+	0.905421i	$0.360444\pi$
$912$	−6.57807	−0.217822
$913$	−24.7611	−0.819472
$914$	−17.0979	−0.565549
$915$	7.13100	0.235743
$916$	0.873800	0.0288712
$917$	4.73384	0.156325
$918$	−20.5601	−0.678585
$919$	2.82419	0.0931613	0.0465807	−	0.998915i	$-0.485168\pi$
$919$	2.82419	0.0931613	0.0465807	+	0.998915i	$0.485168\pi$
$920$	14.0154	0.462074
$921$	−10.6949	−0.352410
$922$	4.01634	0.132271
$923$	−79.0722	−2.60269
$924$	7.92909	0.260848
$925$	49.0251	1.61194
$926$	−27.1318	−0.891606
$927$	44.3991	1.45826
$928$	−3.24876	−0.106646
$929$	−5.79201	−0.190030	−0.0950148	−	0.995476i	$-0.530290\pi$
$929$	−5.79201	−0.190030	−0.0950148	+	0.995476i	$0.530290\pi$
$930$	2.58735	0.0848427
$931$	74.2666	2.43399
$932$	20.0414	0.656479
$933$	2.48718	0.0814267
$934$	−27.4419	−0.897927
$935$	−33.6731	−1.10123
$936$	14.0783	0.460163
$937$	30.4651	0.995250	0.497625	−	0.867392i	$-0.334206\pi$
$937$	30.4651	0.995250	0.497625	+	0.867392i	$0.334206\pi$
$938$	−59.9263	−1.95666
$939$	7.93716	0.259019
$940$	−8.07833	−0.263486
$941$	−20.1333	−0.656326	−0.328163	−	0.944621i	$-0.606430\pi$
$941$	−20.1333	−0.656326	−0.328163	+	0.944621i	$0.606430\pi$
$942$	−0.778587	−0.0253677
$943$	31.7064	1.03250
$944$	13.9066	0.452622
$945$	−55.6089	−1.80896
$946$	16.3641	0.532043
$947$	−29.1497	−0.947239	−0.473620	−	0.880729i	$-0.657053\pi$
$947$	−29.1497	−0.947239	−0.473620	+	0.880729i	$0.657053\pi$
$948$	−2.69528	−0.0875385
$949$	−82.9162	−2.69157
$950$	36.1820	1.17390
$951$	6.68314	0.216716
$952$	−18.8168	−0.609856
$953$	−11.0726	−0.358677	−0.179338	−	0.983787i	$-0.557396\pi$
$953$	−11.0726	−0.358677	−0.179338	+	0.983787i	$0.557396\pi$
$954$	−8.98278	−0.290828
$955$	−12.4832	−0.403948
$956$	−18.3099	−0.592184
$957$	−6.35498	−0.205427
$958$	7.76912	0.251009
$959$	0.832047	0.0268682
$960$	2.58735	0.0835065
$961$	1.00000	0.0322581
$962$	−65.2491	−2.10371
$963$	−15.5405	−0.500786
$964$	13.4431	0.432972
$965$	−38.5956	−1.24244
$966$	15.3202	0.492920
$967$	13.7732	0.442916	0.221458	−	0.975170i	$-0.428918\pi$
$967$	13.7732	0.442916	0.221458	+	0.975170i	$0.428918\pi$
$968$	−5.51592	−0.177288
$969$	30.5364	0.980970
$970$	−3.09750	−0.0994547
$971$	−0.758569	−0.0243436	−0.0121718	−	0.999926i	$-0.503875\pi$
$971$	−0.758569	−0.0243436	−0.0121718	+	0.999926i	$0.503875\pi$
$972$	−15.9660	−0.512111
$973$	51.7968	1.66053
$974$	−11.5519	−0.370147
$975$	23.4681	0.751579
$976$	2.75610	0.0882205
$977$	20.2286	0.647171	0.323585	−	0.946199i	$-0.395112\pi$
$977$	20.2286	0.647171	0.323585	+	0.946199i	$0.395112\pi$
$978$	−0.353089	−0.0112905
$979$	20.7032	0.661677
$980$	−29.2113	−0.933121
$981$	−36.2520	−1.15744
$982$	23.8013	0.759529
$983$	15.8609	0.505885	0.252942	−	0.967481i	$-0.418602\pi$
$983$	15.8609	0.505885	0.252942	+	0.967481i	$0.418602\pi$
$984$	5.85325	0.186595
$985$	57.2752	1.82494
$986$	15.0812	0.480285
$987$	−8.83043	−0.281076
$988$	−48.1557	−1.53204
$989$	31.6180	1.00539
$990$	−16.7001	−0.530764
$991$	−30.9033	−0.981676	−0.490838	−	0.871251i	$-0.663309\pi$
$991$	−30.9033	−0.981676	−0.490838	+	0.871251i	$0.663309\pi$
$992$	1.00000	0.0317500
$993$	8.41509	0.267045
$994$	52.4151	1.66251
$995$	−32.2269	−1.02166
$996$	−8.83206	−0.279855
$997$	−3.41311	−0.108094	−0.0540471	−	0.998538i	$-0.517212\pi$
$997$	−3.41311	−0.108094	−0.0540471	+	0.998538i	$0.517212\pi$
$998$	−20.6619	−0.654040
$999$	47.2592	1.49521

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.k.1.13	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.k.1.13	✓	37	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:	\( N \)	\(=\)	\( 6014 = 2 \cdot 31 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6014.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.835304 q^{3} +1.00000 q^{4} -3.09750 q^{5} -0.835304 q^{6} +4.05347 q^{7} +1.00000 q^{8} -2.30227 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.835304 q^{3} +1.00000 q^{4} -3.09750 q^{5} -0.835304 q^{6} +4.05347 q^{7} +1.00000 q^{8} -2.30227 q^{9} -3.09750 q^{10} -2.34181 q^{11} -0.835304 q^{12} -6.11497 q^{13} +4.05347 q^{14} +2.58735 q^{15} +1.00000 q^{16} -4.64215 q^{17} -2.30227 q^{18} +7.87506 q^{19} -3.09750 q^{20} -3.38588 q^{21} -2.34181 q^{22} -4.52474 q^{23} -0.835304 q^{24} +4.59450 q^{25} -6.11497 q^{26} +4.42900 q^{27} +4.05347 q^{28} -3.24876 q^{29} +2.58735 q^{30} +1.00000 q^{31} +1.00000 q^{32} +1.95612 q^{33} -4.64215 q^{34} -12.5556 q^{35} -2.30227 q^{36} +10.6704 q^{37} +7.87506 q^{38} +5.10786 q^{39} -3.09750 q^{40} -7.00733 q^{41} -3.38588 q^{42} -6.98779 q^{43} -2.34181 q^{44} +7.13127 q^{45} -4.52474 q^{46} +2.60802 q^{47} -0.835304 q^{48} +9.43061 q^{49} +4.59450 q^{50} +3.87761 q^{51} -6.11497 q^{52} +3.90171 q^{53} +4.42900 q^{54} +7.25376 q^{55} +4.05347 q^{56} -6.57807 q^{57} -3.24876 q^{58} +13.9066 q^{59} +2.58735 q^{60} +2.75610 q^{61} +1.00000 q^{62} -9.33217 q^{63} +1.00000 q^{64} +18.9411 q^{65} +1.95612 q^{66} -14.7840 q^{67} -4.64215 q^{68} +3.77954 q^{69} -12.5556 q^{70} +12.9309 q^{71} -2.30227 q^{72} +13.5595 q^{73} +10.6704 q^{74} -3.83781 q^{75} +7.87506 q^{76} -9.49246 q^{77} +5.10786 q^{78} +3.22670 q^{79} -3.09750 q^{80} +3.20724 q^{81} -7.00733 q^{82} +10.5735 q^{83} -3.38588 q^{84} +14.3791 q^{85} -6.98779 q^{86} +2.71370 q^{87} -2.34181 q^{88} -8.84068 q^{89} +7.13127 q^{90} -24.7868 q^{91} -4.52474 q^{92} -0.835304 q^{93} +2.60802 q^{94} -24.3930 q^{95} -0.835304 q^{96} +1.00000 q^{97} +9.43061 q^{98} +5.39148 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 37 q^{2} + 9 q^{3} + 37 q^{4} + 9 q^{5} + 9 q^{6} + 19 q^{7} + 37 q^{8} + 52 q^{9}+O(q^{10}) \) 37 * q + 37 * q^2 + 9 * q^3 + 37 * q^4 + 9 * q^5 + 9 * q^6 + 19 * q^7 + 37 * q^8 + 52 * q^9	\( 37 q + 37 q^{2} + 9 q^{3} + 37 q^{4} + 9 q^{5} + 9 q^{6} + 19 q^{7} + 37 q^{8} + 52 q^{9} + 9 q^{10} + 5 q^{11} + 9 q^{12} + 16 q^{13} + 19 q^{14} + 22 q^{15} + 37 q^{16} + 3 q^{17} + 52 q^{18} + 36 q^{19} + 9 q^{20} + 6 q^{21} + 5 q^{22} + 11 q^{23} + 9 q^{24} + 58 q^{25} + 16 q^{26} + 24 q^{27} + 19 q^{28} + 5 q^{29} + 22 q^{30} + 37 q^{31} + 37 q^{32} + q^{33} + 3 q^{34} + 28 q^{35} + 52 q^{36} + 21 q^{37} + 36 q^{38} + 38 q^{39} + 9 q^{40} + 21 q^{41} + 6 q^{42} + 14 q^{43} + 5 q^{44} + 55 q^{45} + 11 q^{46} + 59 q^{47} + 9 q^{48} + 82 q^{49} + 58 q^{50} + 46 q^{51} + 16 q^{52} + 8 q^{53} + 24 q^{54} + 25 q^{55} + 19 q^{56} + 5 q^{58} + 41 q^{59} + 22 q^{60} + 16 q^{61} + 37 q^{62} + 23 q^{63} + 37 q^{64} - 46 q^{65} + q^{66} + 45 q^{67} + 3 q^{68} + 68 q^{69} + 28 q^{70} + 55 q^{71} + 52 q^{72} + 29 q^{73} + 21 q^{74} - 12 q^{75} + 36 q^{76} + 30 q^{77} + 38 q^{78} + 25 q^{79} + 9 q^{80} + 73 q^{81} + 21 q^{82} + 70 q^{83} + 6 q^{84} - 21 q^{85} + 14 q^{86} + 37 q^{87} + 5 q^{88} + 55 q^{90} + 18 q^{91} + 11 q^{92} + 9 q^{93} + 59 q^{94} - 9 q^{95} + 9 q^{96} + 37 q^{97} + 82 q^{98} + 33 q^{99}+O(q^{100}) \) 37 * q + 37 * q^2 + 9 * q^3 + 37 * q^4 + 9 * q^5 + 9 * q^6 + 19 * q^7 + 37 * q^8 + 52 * q^9 + 9 * q^10 + 5 * q^11 + 9 * q^12 + 16 * q^13 + 19 * q^14 + 22 * q^15 + 37 * q^16 + 3 * q^17 + 52 * q^18 + 36 * q^19 + 9 * q^20 + 6 * q^21 + 5 * q^22 + 11 * q^23 + 9 * q^24 + 58 * q^25 + 16 * q^26 + 24 * q^27 + 19 * q^28 + 5 * q^29 + 22 * q^30 + 37 * q^31 + 37 * q^32 + q^33 + 3 * q^34 + 28 * q^35 + 52 * q^36 + 21 * q^37 + 36 * q^38 + 38 * q^39 + 9 * q^40 + 21 * q^41 + 6 * q^42 + 14 * q^43 + 5 * q^44 + 55 * q^45 + 11 * q^46 + 59 * q^47 + 9 * q^48 + 82 * q^49 + 58 * q^50 + 46 * q^51 + 16 * q^52 + 8 * q^53 + 24 * q^54 + 25 * q^55 + 19 * q^56 + 5 * q^58 + 41 * q^59 + 22 * q^60 + 16 * q^61 + 37 * q^62 + 23 * q^63 + 37 * q^64 - 46 * q^65 + q^66 + 45 * q^67 + 3 * q^68 + 68 * q^69 + 28 * q^70 + 55 * q^71 + 52 * q^72 + 29 * q^73 + 21 * q^74 - 12 * q^75 + 36 * q^76 + 30 * q^77 + 38 * q^78 + 25 * q^79 + 9 * q^80 + 73 * q^81 + 21 * q^82 + 70 * q^83 + 6 * q^84 - 21 * q^85 + 14 * q^86 + 37 * q^87 + 5 * q^88 + 55 * q^90 + 18 * q^91 + 11 * q^92 + 9 * q^93 + 59 * q^94 - 9 * q^95 + 9 * q^96 + 37 * q^97 + 82 * q^98 + 33 * q^99

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