LMFDB - Embedded newform 151.2.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [151,2,Mod(1,151)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(151, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("151.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 151 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	151.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:	$1.20574107052$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.257.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 3 $ x^3 - x^2 - 4*x + 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.19869$ of defining polynomial
Character	$\chi$	$=$	151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.83424 q^{2} +2.00000 q^{3} +1.36445 q^{4} -2.03293 q^{5} +3.66849 q^{6} -2.00000 q^{7} -1.16576 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.83424 q^{2} +2.00000 q^{3} +1.36445 q^{4} -2.03293 q^{5} +3.66849 q^{6} -2.00000 q^{7} -1.16576 q^{8} +1.00000 q^{9} -3.72890 q^{10} +1.56314 q^{11} +2.72890 q^{12} -0.728896 q^{13} -3.66849 q^{14} -4.06587 q^{15} -4.86718 q^{16} +1.16576 q^{17} +1.83424 q^{18} +6.59607 q^{19} -2.77383 q^{20} -4.00000 q^{21} +2.86718 q^{22} +3.66849 q^{23} -2.33151 q^{24} -0.867178 q^{25} -1.33697 q^{26} -4.00000 q^{27} -2.72890 q^{28} +10.2646 q^{29} -7.45779 q^{30} -0.364448 q^{31} -6.59607 q^{32} +3.12628 q^{33} +2.13828 q^{34} +4.06587 q^{35} +1.36445 q^{36} -4.50273 q^{37} +12.0988 q^{38} -1.45779 q^{39} +2.36991 q^{40} -7.33697 q^{42} -0.364448 q^{43} +2.13282 q^{44} -2.03293 q^{45} +6.72890 q^{46} -6.19869 q^{47} -9.73436 q^{48} -3.00000 q^{49} -1.59061 q^{50} +2.33151 q^{51} -0.994541 q^{52} -13.1921 q^{53} -7.33697 q^{54} -3.17776 q^{55} +2.33151 q^{56} +13.1921 q^{57} +18.8277 q^{58} +7.63555 q^{59} -5.54767 q^{60} -2.54221 q^{61} -0.668486 q^{62} -2.00000 q^{63} -2.36445 q^{64} +1.48180 q^{65} +5.73436 q^{66} +0.542208 q^{67} +1.59061 q^{68} +7.33697 q^{69} +7.45779 q^{70} -3.66849 q^{71} -1.16576 q^{72} +3.27110 q^{73} -8.25910 q^{74} -1.73436 q^{75} +9.00000 q^{76} -3.12628 q^{77} -2.67395 q^{78} -8.72890 q^{79} +9.89465 q^{80} -11.0000 q^{81} +12.9396 q^{83} -5.45779 q^{84} -2.36991 q^{85} -0.668486 q^{86} +20.5291 q^{87} -1.82224 q^{88} +15.6685 q^{89} -3.72890 q^{90} +1.45779 q^{91} +5.00546 q^{92} -0.728896 q^{93} -11.3699 q^{94} -13.4094 q^{95} -13.1921 q^{96} +15.0593 q^{97} -5.50273 q^{98} +1.56314 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 6 q^{3} + 4 q^{4} + 5 q^{5} - 6 q^{7} - 9 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 6 * q^3 + 4 * q^4 + 5 * q^5 - 6 * q^7 - 9 * q^8 + 3 * q^9	$ 3 q + 6 q^{3} + 4 q^{4} + 5 q^{5} - 6 q^{7} - 9 q^{8} + 3 q^{9} - 11 q^{10} - q^{11} + 8 q^{12} - 2 q^{13} + 10 q^{15} + 2 q^{16} + 9 q^{17} + 3 q^{19} + 8 q^{20} - 12 q^{21} - 8 q^{22} - 18 q^{24} + 14 q^{25} + 18 q^{26} - 12 q^{27} - 8 q^{28} + 3 q^{29} - 22 q^{30} - q^{31} - 3 q^{32} - 2 q^{33} - 10 q^{34} - 10 q^{35} + 4 q^{36} + 3 q^{37} + 3 q^{38} - 4 q^{39} - 26 q^{40} - q^{43} + 23 q^{44} + 5 q^{45} + 20 q^{46} - 13 q^{47} + 4 q^{48} - 9 q^{49} - 21 q^{50} + 18 q^{51} - 36 q^{52} - 6 q^{53} - 10 q^{55} + 18 q^{56} + 6 q^{57} + 23 q^{58} + 23 q^{59} + 16 q^{60} - 8 q^{61} + 9 q^{62} - 6 q^{63} - 7 q^{64} - 6 q^{65} - 16 q^{66} + 2 q^{67} + 21 q^{68} + 22 q^{70} - 9 q^{72} + 10 q^{73} - 30 q^{74} + 28 q^{75} + 27 q^{76} + 2 q^{77} + 36 q^{78} - 26 q^{79} + 35 q^{80} - 33 q^{81} + 28 q^{83} - 16 q^{84} + 26 q^{85} + 9 q^{86} + 6 q^{87} - 5 q^{88} + 36 q^{89} - 11 q^{90} + 4 q^{91} - 18 q^{92} - 2 q^{93} - q^{94} - 24 q^{95} - 6 q^{96} - 5 q^{97} - q^{99}+O(q^{100}) $ 3 * q + 6 * q^3 + 4 * q^4 + 5 * q^5 - 6 * q^7 - 9 * q^8 + 3 * q^9 - 11 * q^10 - q^11 + 8 * q^12 - 2 * q^13 + 10 * q^15 + 2 * q^16 + 9 * q^17 + 3 * q^19 + 8 * q^20 - 12 * q^21 - 8 * q^22 - 18 * q^24 + 14 * q^25 + 18 * q^26 - 12 * q^27 - 8 * q^28 + 3 * q^29 - 22 * q^30 - q^31 - 3 * q^32 - 2 * q^33 - 10 * q^34 - 10 * q^35 + 4 * q^36 + 3 * q^37 + 3 * q^38 - 4 * q^39 - 26 * q^40 - q^43 + 23 * q^44 + 5 * q^45 + 20 * q^46 - 13 * q^47 + 4 * q^48 - 9 * q^49 - 21 * q^50 + 18 * q^51 - 36 * q^52 - 6 * q^53 - 10 * q^55 + 18 * q^56 + 6 * q^57 + 23 * q^58 + 23 * q^59 + 16 * q^60 - 8 * q^61 + 9 * q^62 - 6 * q^63 - 7 * q^64 - 6 * q^65 - 16 * q^66 + 2 * q^67 + 21 * q^68 + 22 * q^70 - 9 * q^72 + 10 * q^73 - 30 * q^74 + 28 * q^75 + 27 * q^76 + 2 * q^77 + 36 * q^78 - 26 * q^79 + 35 * q^80 - 33 * q^81 + 28 * q^83 - 16 * q^84 + 26 * q^85 + 9 * q^86 + 6 * q^87 - 5 * q^88 + 36 * q^89 - 11 * q^90 + 4 * q^91 - 18 * q^92 - 2 * q^93 - q^94 - 24 * q^95 - 6 * q^96 - 5 * q^97 - 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 $

$2$	1.83424	1.29701	0.648503	−	0.761212i	$-0.275395\pi$
$2$	1.83424	1.29701	0.648503	+	0.761212i	$0.275395\pi$
$3$	2.00000	1.15470	0.577350	−	0.816497i	$-0.304087\pi$
$3$	2.00000	1.15470	0.577350	+	0.816497i	$0.304087\pi$
$4$	1.36445	0.682224
$5$	−2.03293	−0.909156	−0.454578	−	0.890707i	$-0.650210\pi$
$5$	−2.03293	−0.909156	−0.454578	+	0.890707i	$0.650210\pi$
$6$	3.66849	1.49765
$7$	−2.00000	−0.755929	−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000	−0.755929	−0.377964	+	0.925820i	$0.623376\pi$
$8$	−1.16576	−0.412157
$9$	1.00000	0.333333
$10$	−3.72890	−1.17918
$11$	1.56314	0.471304	0.235652	−	0.971837i	$-0.424277\pi$
$11$	1.56314	0.471304	0.235652	+	0.971837i	$0.424277\pi$
$12$	2.72890	0.787764
$13$	−0.728896	−0.202159	−0.101080	−	0.994878i	$-0.532230\pi$
$13$	−0.728896	−0.202159	−0.101080	+	0.994878i	$0.532230\pi$
$14$	−3.66849	−0.980444
$15$	−4.06587	−1.04980
$16$	−4.86718	−1.21679
$17$	1.16576	0.282738	0.141369	−	0.989957i	$-0.454850\pi$
$17$	1.16576	0.282738	0.141369	+	0.989957i	$0.454850\pi$
$18$	1.83424	0.432335
$19$	6.59607	1.51324	0.756622	−	0.653853i	$-0.226849\pi$
$19$	6.59607	1.51324	0.756622	+	0.653853i	$0.226849\pi$
$20$	−2.77383	−0.620248
$21$	−4.00000	−0.872872
$22$	2.86718	0.611284
$23$	3.66849	0.764932	0.382466	−	0.923970i	$-0.375075\pi$
$23$	3.66849	0.764932	0.382466	+	0.923970i	$0.375075\pi$
$24$	−2.33151	−0.475918
$25$	−0.867178	−0.173436
$26$	−1.33697	−0.262202
$27$	−4.00000	−0.769800
$28$	−2.72890	−0.515713
$29$	10.2646	1.90608	0.953040	−	0.302843i	$-0.0979358\pi$
$29$	10.2646	1.90608	0.953040	+	0.302843i	$0.0979358\pi$
$30$	−7.45779	−1.36160
$31$	−0.364448	−0.0654568	−0.0327284	−	0.999464i	$-0.510420\pi$
$31$	−0.364448	−0.0654568	−0.0327284	+	0.999464i	$0.510420\pi$
$32$	−6.59607	−1.16603
$33$	3.12628	0.544215
$34$	2.13828	0.366712
$35$	4.06587	0.687257
$36$	1.36445	0.227408
$37$	−4.50273	−0.740244	−0.370122	−	0.928983i	$-0.620684\pi$
$37$	−4.50273	−0.740244	−0.370122	+	0.928983i	$0.620684\pi$
$38$	12.0988	1.96269
$39$	−1.45779	−0.233434
$40$	2.36991	0.374715
$41$	0	0		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	−7.33697	−1.13212
$43$	−0.364448	−0.0555778	−0.0277889	−	0.999614i	$-0.508847\pi$
$43$	−0.364448	−0.0555778	−0.0277889	+	0.999614i	$0.508847\pi$
$44$	2.13282	0.321535
$45$	−2.03293	−0.303052
$46$	6.72890	0.992122
$47$	−6.19869	−0.904172	−0.452086	−	0.891974i	$-0.649320\pi$
$47$	−6.19869	−0.904172	−0.452086	+	0.891974i	$0.649320\pi$
$48$	−9.73436	−1.40503
$49$	−3.00000	−0.428571
$50$	−1.59061	−0.224947
$51$	2.33151	0.326477
$52$	−0.994541	−0.137918
$53$	−13.1921	−1.81208	−0.906040	−	0.423191i	$-0.860910\pi$
$53$	−13.1921	−1.81208	−0.906040	+	0.423191i	$0.860910\pi$
$54$	−7.33697	−0.998436
$55$	−3.17776	−0.428489
$56$	2.33151	0.311562
$57$	13.1921	1.74734
$58$	18.8277	2.47220
$59$	7.63555	0.994064	0.497032	−	0.867732i	$-0.334423\pi$
$59$	7.63555	0.994064	0.497032	+	0.867732i	$0.334423\pi$
$60$	−5.54767	−0.716201
$61$	−2.54221	−0.325496	−0.162748	−	0.986668i	$-0.552036\pi$
$61$	−2.54221	−0.325496	−0.162748	+	0.986668i	$0.552036\pi$
$62$	−0.668486	−0.0848979
$63$	−2.00000	−0.251976
$64$	−2.36445	−0.295556
$65$	1.48180	0.183794
$66$	5.73436	0.705850
$67$	0.542208	0.0662412	0.0331206	−	0.999451i	$-0.489455\pi$
$67$	0.542208	0.0662412	0.0331206	+	0.999451i	$0.489455\pi$
$68$	1.59061	0.192890
$69$	7.33697	0.883268
$70$	7.45779	0.891377
$71$	−3.66849	−0.435369	−0.217685	−	0.976019i	$-0.569850\pi$
$71$	−3.66849	−0.435369	−0.217685	+	0.976019i	$0.569850\pi$
$72$	−1.16576	−0.137386
$73$	3.27110	0.382854	0.191427	−	0.981507i	$-0.438689\pi$
$73$	3.27110	0.382854	0.191427	+	0.981507i	$0.438689\pi$
$74$	−8.25910	−0.960101
$75$	−1.73436	−0.200266
$76$	9.00000	1.03237
$77$	−3.12628	−0.356273
$78$	−2.67395	−0.302765
$79$	−8.72890	−0.982078	−0.491039	−	0.871138i	$-0.663383\pi$
$79$	−8.72890	−0.982078	−0.491039	+	0.871138i	$0.663383\pi$
$80$	9.89465	1.10626
$81$	−11.0000	−1.22222
$82$	0	0
$83$	12.9396	1.42030	0.710152	−	0.704048i	$-0.248626\pi$
$83$	12.9396	1.42030	0.710152	+	0.704048i	$0.248626\pi$
$84$	−5.45779	−0.595494
$85$	−2.36991	−0.257053
$86$	−0.668486	−0.0720847
$87$	20.5291	2.20095
$88$	−1.82224	−0.194251
$89$	15.6685	1.66086	0.830428	−	0.557126i	$-0.188096\pi$
$89$	15.6685	1.66086	0.830428	+	0.557126i	$0.188096\pi$
$90$	−3.72890	−0.393060
$91$	1.45779	0.152818
$92$	5.00546	0.521855
$93$	−0.728896	−0.0755830
$94$	−11.3699	−1.17272
$95$	−13.4094	−1.37577
$96$	−13.1921	−1.34642
$97$	15.0593	1.52904	0.764521	−	0.644598i	$-0.222975\pi$
$97$	15.0593	1.52904	0.764521	+	0.644598i	$0.222975\pi$
$98$	−5.50273	−0.555860
$99$	1.56314	0.157101
$100$	−1.18322	−0.118322
$101$	9.52366	0.947640	0.473820	−	0.880622i	$-0.342875\pi$
$101$	9.52366	0.947640	0.473820	+	0.880622i	$0.342875\pi$
$102$	4.27656	0.423443
$103$	−12.6894	−1.25033	−0.625163	−	0.780494i	$-0.714967\pi$
$103$	−12.6894	−1.25033	−0.625163	+	0.780494i	$0.714967\pi$
$104$	0.849716	0.0833215
$105$	8.13174	0.793576
$106$	−24.1976	−2.35028
$107$	−10.4633	−1.01152	−0.505760	−	0.862674i	$-0.668788\pi$
$107$	−10.4633	−1.01152	−0.505760	+	0.862674i	$0.668788\pi$
$108$	−5.45779	−0.525176
$109$	2.00000	0.191565	0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000	0.191565	0.0957826	+	0.995402i	$0.469465\pi$
$110$	−5.82878	−0.555753
$111$	−9.00546	−0.854760
$112$	9.73436	0.919810
$113$	20.5291	1.93122	0.965609	−	0.260000i	$-0.0837226\pi$
$113$	20.5291	1.93122	0.965609	+	0.260000i	$0.0837226\pi$
$114$	24.1976	2.26631
$115$	−7.45779	−0.695443
$116$	14.0055	1.30037
$117$	−0.728896	−0.0673865
$118$	14.0055	1.28931
$119$	−2.33151	−0.213730
$120$	4.73981	0.432684
$121$	−8.55660	−0.777872
$122$	−4.66303	−0.422171
$123$	0	0
$124$	−0.497270	−0.0446562
$125$	11.9276	1.06684
$126$	−3.66849	−0.326815
$127$	−2.90666	−0.257924	−0.128962	−	0.991650i	$-0.541165\pi$
$127$	−2.90666	−0.257924	−0.128962	+	0.991650i	$0.541165\pi$
$128$	8.85517	0.782694
$129$	−0.728896	−0.0641757
$130$	2.71798	0.238382
$131$	−22.4633	−1.96262	−0.981312	−	0.192425i	$-0.938365\pi$
$131$	−22.4633	−1.96262	−0.981312	+	0.192425i	$0.938365\pi$
$132$	4.26564	0.371277
$133$	−13.1921	−1.14390
$134$	0.994541	0.0859152
$135$	8.13174	0.699869
$136$	−1.35899	−0.116532
$137$	6.69596	0.572075	0.286037	−	0.958218i	$-0.407662\pi$
$137$	6.69596	0.572075	0.286037	+	0.958218i	$0.407662\pi$
$138$	13.4578	1.14560
$139$	−11.6805	−0.990726	−0.495363	−	0.868686i	$-0.664965\pi$
$139$	−11.6805	−0.990726	−0.495363	+	0.868686i	$0.664965\pi$
$140$	5.54767	0.468863
$141$	−12.3974	−1.04405
$142$	−6.72890	−0.564676
$143$	−1.13937	−0.0952786
$144$	−4.86718	−0.405598
$145$	−20.8672	−1.73292
$146$	6.00000	0.496564
$147$	−6.00000	−0.494872
$148$	−6.14374	−0.505012
$149$	1.93413	0.158450	0.0792251	−	0.996857i	$-0.474755\pi$
$149$	1.93413	0.158450	0.0792251	+	0.996857i	$0.474755\pi$
$150$	−3.18123	−0.259746
$151$	1.00000	0.0813788
$151$	1.00000	0.0813788
$152$	−7.68942	−0.623694
$153$	1.16576	0.0942459
$154$	−5.73436	−0.462088
$155$	0.740899	0.0595104
$156$	−1.98908	−0.159254
$157$	−3.73436	−0.298034	−0.149017	−	0.988835i	$-0.547611\pi$
$157$	−3.73436	−0.298034	−0.149017	+	0.988835i	$0.547611\pi$
$158$	−16.0109	−1.27376
$159$	−26.3843	−2.09241
$160$	13.4094	1.06010
$161$	−7.33697	−0.578234
$162$	−20.1767	−1.58523
$163$	−13.5477	−1.06114	−0.530568	−	0.847643i	$-0.678021\pi$
$163$	−13.5477	−1.06114	−0.530568	+	0.847643i	$0.678021\pi$
$164$	0	0
$165$	−6.35552	−0.494777
$166$	23.7344	1.84214
$167$	−20.1317	−1.55784	−0.778920	−	0.627123i	$-0.784232\pi$
$167$	−20.1317	−1.55784	−0.778920	+	0.627123i	$0.784232\pi$
$168$	4.66303	0.359760
$169$	−12.4687	−0.959132
$170$	−4.34699	−0.333399
$171$	6.59607	0.504414
$172$	−0.497270	−0.0379165
$173$	18.3963	1.39864	0.699322	−	0.714806i	$-0.253485\pi$
$173$	18.3963	1.39864	0.699322	+	0.714806i	$0.253485\pi$
$174$	37.6554	2.85465
$175$	1.73436	0.131105
$176$	−7.60808	−0.573480
$177$	15.2711	1.14785
$178$	28.7398	2.15414
$179$	16.4633	1.23052	0.615261	−	0.788324i	$-0.289051\pi$
$179$	16.4633	1.23052	0.615261	+	0.788324i	$0.289051\pi$
$180$	−2.77383	−0.206749
$181$	−13.0055	−0.966688	−0.483344	−	0.875430i	$-0.660578\pi$
$181$	−13.0055	−0.966688	−0.483344	+	0.875430i	$0.660578\pi$
$182$	2.67395	0.198206
$183$	−5.08442	−0.375851
$184$	−4.27656	−0.315272
$185$	9.15375	0.672997
$186$	−1.33697	−0.0980316
$187$	1.82224	0.133255
$188$	−8.45779	−0.616848
$189$	8.00000	0.581914
$190$	−24.5961	−1.78439
$191$	13.5357	0.979406	0.489703	−	0.871889i	$-0.337105\pi$
$191$	13.5357	0.979406	0.489703	+	0.871889i	$0.337105\pi$
$192$	−4.72890	−0.341279
$193$	−17.3699	−1.25031	−0.625157	−	0.780499i	$-0.714965\pi$
$193$	−17.3699	−1.25031	−0.625157	+	0.780499i	$0.714965\pi$
$194$	27.6225	1.98318
$195$	2.96360	0.212228
$196$	−4.09334	−0.292382
$197$	6.79476	0.484107	0.242053	−	0.970263i	$-0.422179\pi$
$197$	6.79476	0.484107	0.242053	+	0.970263i	$0.422179\pi$
$198$	2.86718	0.203761
$199$	19.4687	1.38010	0.690050	−	0.723762i	$-0.257588\pi$
$199$	19.4687	1.38010	0.690050	+	0.723762i	$0.257588\pi$
$200$	1.01092	0.0714827
$201$	1.08442	0.0764888
$202$	17.4687	1.22909
$203$	−20.5291	−1.44086
$204$	3.18123	0.222731
$205$	0	0
$206$	−23.2755	−1.62168
$207$	3.66849	0.254977
$208$	3.54767	0.245986
$209$	10.3106	0.713198
$210$	14.9156	1.02927
$211$	−19.1921	−1.32124	−0.660621	−	0.750720i	$-0.729707\pi$
$211$	−19.1921	−1.32124	−0.660621	+	0.750720i	$0.729707\pi$
$212$	−18.0000	−1.23625
$213$	−7.33697	−0.502721
$214$	−19.1921	−1.31195
$215$	0.740899	0.0505289
$216$	4.66303	0.317279
$217$	0.728896	0.0494807
$218$	3.66849	0.248461
$219$	6.54221	0.442081
$220$	−4.33589	−0.292326
$221$	−0.849716	−0.0571581
$222$	−16.5182	−1.10863
$223$	23.2316	1.55570	0.777852	−	0.628447i	$-0.216309\pi$
$223$	23.2316	1.55570	0.777852	+	0.628447i	$0.216309\pi$
$224$	13.1921	0.881437
$225$	−0.867178	−0.0578118
$226$	37.6554	2.50480
$227$	−1.56314	−0.103749	−0.0518746	−	0.998654i	$-0.516520\pi$
$227$	−1.56314	−0.103749	−0.0518746	+	0.998654i	$0.516520\pi$
$228$	18.0000	1.19208
$229$	25.3359	1.67424	0.837121	−	0.547017i	$-0.184237\pi$
$229$	25.3359	1.67424	0.837121	+	0.547017i	$0.184237\pi$
$230$	−13.6794	−0.901993
$231$	−6.25256	−0.411388
$232$	−11.9660	−0.785605
$233$	−0.397382	−0.0260334	−0.0130167	−	0.999915i	$-0.504143\pi$
$233$	−0.397382	−0.0260334	−0.0130167	+	0.999915i	$0.504143\pi$
$234$	−1.33697	−0.0874006
$235$	12.6015	0.822033
$236$	10.4183	0.678174
$237$	−17.4578	−1.13401
$238$	−4.27656	−0.277208
$239$	−4.97907	−0.322069	−0.161035	−	0.986949i	$-0.551483\pi$
$239$	−4.97907	−0.322069	−0.161035	+	0.986949i	$0.551483\pi$
$240$	19.7893	1.27739
$241$	21.5082	1.38546	0.692732	−	0.721195i	$-0.256407\pi$
$241$	21.5082	1.38546	0.692732	+	0.721195i	$0.256407\pi$
$242$	−15.6949	−1.00890
$243$	−10.0000	−0.641500
$244$	−3.46871	−0.222061
$245$	6.09880	0.389638
$246$	0	0
$247$	−4.80785	−0.305916
$248$	0.424858	0.0269785
$249$	25.8792	1.64003
$250$	21.8781	1.38369
$251$	−0.794765	−0.0501651	−0.0250826	−	0.999685i	$-0.507985\pi$
$251$	−0.794765	−0.0501651	−0.0250826	+	0.999685i	$0.507985\pi$
$252$	−2.72890	−0.171904
$253$	5.73436	0.360516
$254$	−5.33151	−0.334529
$255$	−4.73981	−0.296819
$256$	20.9714	1.31072
$257$	19.9869	1.24675	0.623375	−	0.781923i	$-0.285761\pi$
$257$	19.9869	1.24675	0.623375	+	0.781923i	$0.285761\pi$
$258$	−1.33697	−0.0832363
$259$	9.00546	0.559572
$260$	2.02184	0.125389
$261$	10.2646	0.635360
$262$	−41.2031	−2.54553
$263$	−17.8002	−1.09761	−0.548804	−	0.835951i	$-0.684917\pi$
$263$	−17.8002	−1.09761	−0.548804	+	0.835951i	$0.684917\pi$
$264$	−3.64448	−0.224302
$265$	26.8188	1.64746
$266$	−24.1976	−1.48365
$267$	31.3370	1.91779
$268$	0.739814	0.0451914
$269$	2.70251	0.164775	0.0823873	−	0.996600i	$-0.473746\pi$
$269$	2.70251	0.164775	0.0823873	+	0.996600i	$0.473746\pi$
$270$	14.9156	0.907734
$271$	−0.0789564	−0.00479626	−0.00239813	−	0.999997i	$-0.500763\pi$
$271$	−0.0789564	−0.00479626	−0.00239813	+	0.999997i	$0.500763\pi$
$272$	−5.67395	−0.344033
$273$	2.91558	0.176459
$274$	12.2820	0.741984
$275$	−1.35552	−0.0817409
$276$	10.0109	0.602586
$277$	−13.0055	−0.781422	−0.390711	−	0.920513i	$-0.627771\pi$
$277$	−13.0055	−0.781422	−0.390711	+	0.920513i	$0.627771\pi$
$278$	−21.4249	−1.28498
$279$	−0.364448	−0.0218189
$280$	−4.73981	−0.283258
$281$	−15.8661	−0.946492	−0.473246	−	0.880930i	$-0.656918\pi$
$281$	−15.8661	−0.946492	−0.473246	+	0.880930i	$0.656918\pi$
$282$	−22.7398	−1.35414
$283$	21.4687	1.27618	0.638091	−	0.769961i	$-0.279724\pi$
$283$	21.4687	1.27618	0.638091	+	0.769961i	$0.279724\pi$
$284$	−5.00546	−0.297019
$285$	−26.8188	−1.58861
$286$	−2.08987	−0.123577
$287$	0	0
$288$	−6.59607	−0.388677
$289$	−15.6410	−0.920059
$290$	−38.2755	−2.24761
$291$	30.1187	1.76559
$292$	4.46325	0.261192
$293$	−22.4633	−1.31232	−0.656159	−	0.754623i	$-0.727820\pi$
$293$	−22.4633	−1.31232	−0.656159	+	0.754623i	$0.727820\pi$
$294$	−11.0055	−0.641851
$295$	−15.5226	−0.903759
$296$	5.24909	0.305097
$297$	−6.25256	−0.362810
$298$	3.54767	0.205511
$299$	−2.67395	−0.154638
$300$	−2.36644	−0.136626
$301$	0.728896	0.0420129
$302$	1.83424	0.105549
$303$	19.0473	1.09424
$304$	−32.1043	−1.84131
$305$	5.16814	0.295927
$306$	2.13828	0.122237
$307$	−9.77383	−0.557822	−0.278911	−	0.960317i	$-0.589973\pi$
$307$	−9.77383	−0.557822	−0.278911	+	0.960317i	$0.589973\pi$
$308$	−4.26564	−0.243058
$309$	−25.3788	−1.44375
$310$	1.35899	0.0771854
$311$	5.44886	0.308977	0.154488	−	0.987995i	$-0.450627\pi$
$311$	5.44886	0.308977	0.154488	+	0.987995i	$0.450627\pi$
$312$	1.69943	0.0962113
$313$	9.01439	0.509523	0.254762	−	0.967004i	$-0.418003\pi$
$313$	9.01439	0.509523	0.254762	+	0.967004i	$0.418003\pi$
$314$	−6.84972	−0.386552
$315$	4.06587	0.229086
$316$	−11.9101	−0.669997
$317$	−16.8606	−0.946988	−0.473494	−	0.880797i	$-0.657007\pi$
$317$	−16.8606	−0.946988	−0.473494	+	0.880797i	$0.657007\pi$
$318$	−48.3952	−2.71387
$319$	16.0449	0.898344
$320$	4.80677	0.268706
$321$	−20.9265	−1.16800
$322$	−13.4578	−0.749973
$323$	7.68942	0.427851
$324$	−15.0089	−0.833829
$325$	0.632082	0.0350616
$326$	−24.8497	−1.37630
$327$	4.00000	0.221201
$328$	0	0
$329$	12.3974	0.683490
$330$	−11.6576	−0.641728
$331$	2.30512	0.126701	0.0633505	−	0.997991i	$-0.479821\pi$
$331$	2.30512	0.126701	0.0633505	+	0.997991i	$0.479821\pi$
$332$	17.6554	0.968966
$333$	−4.50273	−0.246748
$334$	−36.9265	−2.02053
$335$	−1.10227	−0.0602236
$336$	19.4687	1.06211
$337$	−21.0055	−1.14424	−0.572120	−	0.820170i	$-0.693879\pi$
$337$	−21.0055	−1.14424	−0.572120	+	0.820170i	$0.693879\pi$
$338$	−22.8706	−1.24400
$339$	41.0582	2.22998
$340$	−3.23362	−0.175367
$341$	−0.569683	−0.0308501
$342$	12.0988	0.654228
$343$	20.0000	1.07990
$344$	0.424858	0.0229068
$345$	−14.9156	−0.803028
$346$	33.7433	1.81405
$347$	−20.1317	−1.08073	−0.540364	−	0.841431i	$-0.681714\pi$
$347$	−20.1317	−1.08073	−0.540364	+	0.841431i	$0.681714\pi$
$348$	28.0109	1.50154
$349$	16.5027	0.883371	0.441685	−	0.897170i	$-0.354381\pi$
$349$	16.5027	0.883371	0.441685	+	0.897170i	$0.354381\pi$
$350$	3.18123	0.170044
$351$	2.91558	0.155622
$352$	−10.3106	−0.549556
$353$	−6.25256	−0.332790	−0.166395	−	0.986059i	$-0.553213\pi$
$353$	−6.25256	−0.332790	−0.166395	+	0.986059i	$0.553213\pi$
$354$	28.0109	1.48876
$355$	7.45779	0.395819
$356$	21.3788	1.13308
$357$	−4.66303	−0.246794
$358$	30.1976	1.59599
$359$	14.9265	0.787791	0.393895	−	0.919155i	$-0.371127\pi$
$359$	14.9265	0.787791	0.393895	+	0.919155i	$0.371127\pi$
$360$	2.36991	0.124905
$361$	24.5082	1.28990
$362$	−23.8552	−1.25380
$363$	−17.1132	−0.898210
$364$	1.98908	0.104256
$365$	−6.64994	−0.348074
$366$	−9.32605	−0.487481
$367$	37.1921	1.94141	0.970707	−	0.240266i	$-0.0772346\pi$
$367$	37.1921	1.94141	0.970707	+	0.240266i	$0.0772346\pi$
$368$	−17.8552	−0.930765
$369$	0	0
$370$	16.7902	0.872881
$371$	26.3843	1.36980
$372$	−0.994541	−0.0515645
$373$	−1.81331	−0.0938897	−0.0469449	−	0.998897i	$-0.514949\pi$
$373$	−1.81331	−0.0938897	−0.0469449	+	0.998897i	$0.514949\pi$
$374$	3.34243	0.172833
$375$	23.8552	1.23188
$376$	7.22617	0.372661
$377$	−7.48180	−0.385332
$378$	14.6739	0.754746
$379$	−20.4633	−1.05113	−0.525563	−	0.850754i	$-0.676145\pi$
$379$	−20.4633	−1.05113	−0.525563	+	0.850754i	$0.676145\pi$
$380$	−18.2964	−0.938586
$381$	−5.81331	−0.297825
$382$	24.8277	1.27030
$383$	−27.9649	−1.42894	−0.714470	−	0.699666i	$-0.753332\pi$
$383$	−27.9649	−1.42894	−0.714470	+	0.699666i	$0.753332\pi$
$384$	17.7103	0.903777
$385$	6.35552	0.323907
$386$	−31.8606	−1.62166
$387$	−0.364448	−0.0185259
$388$	20.5477	1.04315
$389$	24.1976	1.22687	0.613434	−	0.789746i	$-0.289788\pi$
$389$	24.1976	1.22687	0.613434	+	0.789746i	$0.289788\pi$
$390$	5.43596	0.275260
$391$	4.27656	0.216275
$392$	3.49727	0.176639
$393$	−44.9265	−2.26624
$394$	12.4633	0.627890
$395$	17.7453	0.892862
$396$	2.13282	0.107178
$397$	−28.1437	−1.41249	−0.706247	−	0.707966i	$-0.749613\pi$
$397$	−28.1437	−1.41249	−0.706247	+	0.707966i	$0.749613\pi$
$398$	35.7103	1.79000
$399$	−26.3843	−1.32087
$400$	4.22071	0.211035
$401$	19.9880	0.998153	0.499076	−	0.866558i	$-0.333673\pi$
$401$	19.9880	0.998153	0.499076	+	0.866558i	$0.333673\pi$
$402$	1.98908	0.0992064
$403$	0.265645	0.0132327
$404$	12.9945	0.646503
$405$	22.3623	1.11119
$406$	−37.6554	−1.86881
$407$	−7.03839	−0.348880
$408$	−2.71798	−0.134560
$409$	20.3843	1.00794	0.503969	−	0.863722i	$-0.331872\pi$
$409$	20.3843	1.00794	0.503969	+	0.863722i	$0.331872\pi$
$410$	0	0
$411$	13.3919	0.660575
$412$	−17.3141	−0.853002
$413$	−15.2711	−0.751442
$414$	6.72890	0.330707
$415$	−26.3053	−1.29128
$416$	4.80785	0.235724
$417$	−23.3610	−1.14399
$418$	18.9121	0.925022
$419$	−15.6685	−0.765456	−0.382728	−	0.923861i	$-0.625015\pi$
$419$	−15.6685	−0.765456	−0.382728	+	0.923861i	$0.625015\pi$
$420$	11.0953	0.541397
$421$	16.7398	0.815849	0.407924	−	0.913016i	$-0.366253\pi$
$421$	16.7398	0.815849	0.407924	+	0.913016i	$0.366253\pi$
$422$	−35.2031	−1.71366
$423$	−6.19869	−0.301391
$424$	15.3788	0.746862
$425$	−1.01092	−0.0490367
$426$	−13.4578	−0.652032
$427$	5.08442	0.246052
$428$	−14.2766	−0.690084
$429$	−2.27873	−0.110018
$430$	1.35899	0.0655363
$431$	−5.85517	−0.282034	−0.141017	−	0.990007i	$-0.545037\pi$
$431$	−5.85517	−0.282034	−0.141017	+	0.990007i	$0.545037\pi$
$432$	19.4687	0.936689
$433$	−14.1867	−0.681769	−0.340884	−	0.940105i	$-0.610726\pi$
$433$	−14.1867	−0.681769	−0.340884	+	0.940105i	$0.610726\pi$
$434$	1.33697	0.0641767
$435$	−41.7344	−2.00101
$436$	2.72890	0.130690
$437$	24.1976	1.15753
$438$	12.0000	0.573382
$439$	−8.23708	−0.393135	−0.196567	−	0.980490i	$-0.562979\pi$
$439$	−8.23708	−0.393135	−0.196567	+	0.980490i	$0.562979\pi$
$440$	3.70450	0.176605
$441$	−3.00000	−0.142857
$442$	−1.55859	−0.0741343
$443$	9.52366	0.452483	0.226241	−	0.974071i	$-0.427356\pi$
$443$	9.52366	0.452483	0.226241	+	0.974071i	$0.427356\pi$
$444$	−12.2875	−0.583138
$445$	−31.8530	−1.50998
$446$	42.6125	2.01776
$447$	3.86826	0.182963
$448$	4.72890	0.223419
$449$	3.66849	0.173127	0.0865633	−	0.996246i	$-0.472412\pi$
$449$	3.66849	0.173127	0.0865633	+	0.996246i	$0.472412\pi$
$450$	−1.59061	−0.0749823
$451$	0	0
$452$	28.0109	1.31752
$453$	2.00000	0.0939682
$454$	−2.86718	−0.134563
$455$	−2.96360	−0.138936
$456$	−15.3788	−0.720180
$457$	32.6410	1.52688	0.763441	−	0.645878i	$-0.223508\pi$
$457$	32.6410	1.52688	0.763441	+	0.645878i	$0.223508\pi$
$458$	46.4722	2.17150
$459$	−4.66303	−0.217651
$460$	−10.1758	−0.474448
$461$	12.4238	0.578633	0.289316	−	0.957234i	$-0.406572\pi$
$461$	12.4238	0.578633	0.289316	+	0.957234i	$0.406572\pi$
$462$	−11.4687	−0.533573
$463$	24.2371	1.12639	0.563196	−	0.826323i	$-0.309571\pi$
$463$	24.2371	1.12639	0.563196	+	0.826323i	$0.309571\pi$
$464$	−49.9594	−2.31931
$465$	1.48180	0.0687167
$466$	−0.728896	−0.0337655
$467$	−12.9396	−0.598773	−0.299386	−	0.954132i	$-0.596782\pi$
$467$	−12.9396	−0.598773	−0.299386	+	0.954132i	$0.596782\pi$
$468$	−0.994541	−0.0459727
$469$	−1.08442	−0.0500737
$470$	23.1143	1.06618
$471$	−7.46871	−0.344140
$472$	−8.90120	−0.409711
$473$	−0.569683	−0.0261941
$474$	−32.0218	−1.47081
$475$	−5.71997	−0.262450
$476$	−3.18123	−0.145811
$477$	−13.1921	−0.604027
$478$	−9.13282	−0.417726
$479$	−0.994541	−0.0454417	−0.0227209	−	0.999742i	$-0.507233\pi$
$479$	−0.994541	−0.0454417	−0.0227209	+	0.999742i	$0.507233\pi$
$480$	26.8188	1.22410
$481$	3.28202	0.149647
$482$	39.4512	1.79696
$483$	−14.6739	−0.667688
$484$	−11.6750	−0.530683
$485$	−30.6146	−1.39014
$486$	−18.3424	−0.832030
$487$	23.4148	1.06103	0.530514	−	0.847676i	$-0.321999\pi$
$487$	23.4148	1.06103	0.530514	+	0.847676i	$0.321999\pi$
$488$	2.96360	0.134156
$489$	−27.0953	−1.22529
$490$	11.1867	0.505363
$491$	15.5697	0.702650	0.351325	−	0.936254i	$-0.385731\pi$
$491$	15.5697	0.702650	0.351325	+	0.936254i	$0.385731\pi$
$492$	0	0
$493$	11.9660	0.538921
$494$	−8.81877	−0.396775
$495$	−3.17776	−0.142830
$496$	1.77383	0.0796475
$497$	7.33697	0.329108
$498$	47.4687	2.12712
$499$	−42.5710	−1.90574	−0.952869	−	0.303381i	$-0.901885\pi$
$499$	−42.5710	−1.90574	−0.952869	+	0.303381i	$0.901885\pi$
$500$	16.2746	0.727821
$501$	−40.2635	−1.79884
$502$	−1.45779	−0.0650645
$503$	1.09334	0.0487498	0.0243749	−	0.999703i	$-0.492240\pi$
$503$	1.09334	0.0487498	0.0243749	+	0.999703i	$0.492240\pi$
$504$	2.33151	0.103854
$505$	−19.3610	−0.861552
$506$	10.5182	0.467591
$507$	−24.9374	−1.10751
$508$	−3.96598	−0.175962
$509$	−2.04186	−0.0905040	−0.0452520	−	0.998976i	$-0.514409\pi$
$509$	−2.04186	−0.0905040	−0.0452520	+	0.998976i	$0.514409\pi$
$510$	−8.69397	−0.384976
$511$	−6.54221	−0.289410
$512$	20.7564	0.917311
$513$	−26.3843	−1.16490
$514$	36.6609	1.61704
$515$	25.7968	1.13674
$516$	−0.994541	−0.0437822
$517$	−9.68942	−0.426140
$518$	16.5182	0.725768
$519$	36.7926	1.61502
$520$	−1.72742	−0.0757522
$521$	0.940675	0.0412117	0.0206059	−	0.999788i	$-0.493440\pi$
$521$	0.940675	0.0412117	0.0206059	+	0.999788i	$0.493440\pi$
$522$	18.8277	0.824066
$523$	−11.6554	−0.509655	−0.254828	−	0.966987i	$-0.582019\pi$
$523$	−11.6554	−0.509655	−0.254828	+	0.966987i	$0.582019\pi$
$524$	−30.6499	−1.33895
$525$	3.46871	0.151387
$526$	−32.6499	−1.42361
$527$	−0.424858	−0.0185071
$528$	−15.2162	−0.662198
$529$	−9.54221	−0.414879
$530$	49.1921	2.13677
$531$	7.63555	0.331355
$532$	−18.0000	−0.780399
$533$	0	0
$534$	57.4796	2.48739
$535$	21.2711	0.919630
$536$	−0.632082	−0.0273018
$537$	32.9265	1.42088
$538$	4.95705	0.213714
$539$	−4.68942	−0.201988
$540$	11.0953	0.477467
$541$	3.55660	0.152910	0.0764550	−	0.997073i	$-0.475640\pi$
$541$	3.55660	0.152910	0.0764550	+	0.997073i	$0.475640\pi$
$542$	−0.144825	−0.00622078
$543$	−26.0109	−1.11624
$544$	−7.68942	−0.329681
$545$	−4.06587	−0.174163
$546$	5.34789	0.228869
$547$	18.8617	0.806469	0.403234	−	0.915097i	$-0.367886\pi$
$547$	18.8617	0.806469	0.403234	+	0.915097i	$0.367886\pi$
$548$	9.13629	0.390283
$549$	−2.54221	−0.108499
$550$	−2.48635	−0.106018
$551$	67.7058	2.88436
$552$	−8.55313	−0.364045
$553$	17.4578	0.742381
$554$	−23.8552	−1.01351
$555$	18.3075	0.777110
$556$	−15.9374	−0.675897
$557$	9.21615	0.390501	0.195250	−	0.980753i	$-0.437448\pi$
$557$	9.21615	0.390501	0.195250	+	0.980753i	$0.437448\pi$
$558$	−0.668486	−0.0282993
$559$	0.265645	0.0112356
$560$	−19.7893	−0.836251
$561$	3.64448	0.153870
$562$	−29.1023	−1.22761
$563$	−20.8726	−0.879677	−0.439838	−	0.898077i	$-0.644964\pi$
$563$	−20.8726	−0.879677	−0.439838	+	0.898077i	$0.644964\pi$
$564$	−16.9156	−0.712275
$565$	−41.7344	−1.75578
$566$	39.3788	1.65522
$567$	22.0000	0.923913
$568$	4.27656	0.179441
$569$	31.3084	1.31252	0.656258	−	0.754536i	$-0.272138\pi$
$569$	31.3084	1.31252	0.656258	+	0.754536i	$0.272138\pi$
$570$	−49.1921	−2.06043
$571$	20.5621	0.860495	0.430248	−	0.902711i	$-0.358426\pi$
$571$	20.5621	0.860495	0.430248	+	0.902711i	$0.358426\pi$
$572$	−1.55461	−0.0650013
$573$	27.0713	1.13092
$574$	0	0
$575$	−3.18123	−0.132666
$576$	−2.36445	−0.0985187
$577$	0.675030	0.0281019	0.0140509	−	0.999901i	$-0.495527\pi$
$577$	0.675030	0.0281019	0.0140509	+	0.999901i	$0.495527\pi$
$578$	−28.6894	−1.19332
$579$	−34.7398	−1.44374
$580$	−28.4722	−1.18224
$581$	−25.8792	−1.07365
$582$	55.2449	2.28998
$583$	−20.6212	−0.854041
$584$	−3.81331	−0.157796
$585$	1.48180	0.0612648
$586$	−41.2031	−1.70208
$587$	−25.3370	−1.04577	−0.522884	−	0.852404i	$-0.675144\pi$
$587$	−25.3370	−1.04577	−0.522884	+	0.852404i	$0.675144\pi$
$588$	−8.18669	−0.337613
$589$	−2.40393	−0.0990521
$590$	−28.4722	−1.17218
$591$	13.5895	0.558999
$592$	21.9156	0.900725
$593$	−43.2449	−1.77586	−0.887928	−	0.459982i	$-0.847856\pi$
$593$	−43.2449	−1.77586	−0.887928	+	0.459982i	$0.847856\pi$
$594$	−11.4687	−0.470567
$595$	4.73981	0.194313
$596$	2.63902	0.108099
$597$	38.9374	1.59360
$598$	−4.90467	−0.200567
$599$	10.3184	0.421599	0.210800	−	0.977529i	$-0.432393\pi$
$599$	10.3184	0.421599	0.210800	+	0.977529i	$0.432393\pi$
$600$	2.02184	0.0825411
$601$	31.3808	1.28005	0.640025	−	0.768354i	$-0.278924\pi$
$601$	31.3808	1.28005	0.640025	+	0.768354i	$0.278924\pi$
$602$	1.33697	0.0544909
$603$	0.542208	0.0220804
$604$	1.36445	0.0555186
$605$	17.3950	0.707207
$606$	34.9374	1.41924
$607$	−24.1976	−0.982151	−0.491075	−	0.871117i	$-0.663396\pi$
$607$	−24.1976	−0.982151	−0.491075	+	0.871117i	$0.663396\pi$
$608$	−43.5082	−1.76449
$609$	−41.0582	−1.66376
$610$	9.47963	0.383819
$611$	4.51820	0.182787
$612$	1.59061	0.0642968
$613$	−2.53129	−0.102238	−0.0511189	−	0.998693i	$-0.516279\pi$
$613$	−2.53129	−0.102238	−0.0511189	+	0.998693i	$0.516279\pi$
$614$	−17.9276	−0.723499
$615$	0	0
$616$	3.64448	0.146840
$617$	−15.8661	−0.638745	−0.319372	−	0.947629i	$-0.603472\pi$
$617$	−15.8661	−0.638745	−0.319372	+	0.947629i	$0.603472\pi$
$618$	−46.5510	−1.87255
$619$	−24.2766	−0.975757	−0.487879	−	0.872911i	$-0.662229\pi$
$619$	−24.2766	−0.975757	−0.487879	+	0.872911i	$0.662229\pi$
$620$	1.01092	0.0405995
$621$	−14.6739	−0.588845
$622$	9.99454	0.400745
$623$	−31.3370	−1.25549
$624$	7.09533	0.284041
$625$	−19.9121	−0.796485
$626$	16.5346	0.660855
$627$	20.6212	0.823530
$628$	−5.09533	−0.203326
$629$	−5.24909	−0.209295
$630$	7.45779	0.297126
$631$	19.7344	0.785612	0.392806	−	0.919621i	$-0.371504\pi$
$631$	19.7344	0.785612	0.392806	+	0.919621i	$0.371504\pi$
$632$	10.1758	0.404770
$633$	−38.3843	−1.52564
$634$	−30.9265	−1.22825
$635$	5.90904	0.234493
$636$	−36.0000	−1.42749
$637$	2.18669	0.0866397
$638$	29.4303	1.16516
$639$	−3.66849	−0.145123
$640$	−18.0020	−0.711591
$641$	15.1173	0.597099	0.298550	−	0.954394i	$-0.403497\pi$
$641$	15.1173	0.597099	0.298550	+	0.954394i	$0.403497\pi$
$642$	−38.3843	−1.51491
$643$	40.4491	1.59516	0.797578	−	0.603216i	$-0.206114\pi$
$643$	40.4491	1.59516	0.797578	+	0.603216i	$0.206114\pi$
$644$	−10.0109	−0.394485
$645$	1.48180	0.0583457
$646$	14.1043	0.554925
$647$	28.2899	1.11219	0.556095	−	0.831119i	$-0.312299\pi$
$647$	28.2899	1.11219	0.556095	+	0.831119i	$0.312299\pi$
$648$	12.8233	0.503748
$649$	11.9354	0.468507
$650$	1.15939	0.0454751
$651$	1.45779	0.0571354
$652$	−18.4851	−0.723932
$653$	−47.3479	−1.85287	−0.926433	−	0.376459i	$-0.877141\pi$
$653$	−47.3479	−1.85287	−0.926433	+	0.376459i	$0.877141\pi$
$654$	7.33697	0.286898
$655$	45.6663	1.78433
$656$	0	0
$657$	3.27110	0.127618
$658$	22.7398	0.886490
$659$	−25.8881	−1.00846	−0.504229	−	0.863570i	$-0.668223\pi$
$659$	−25.8881	−1.00846	−0.504229	+	0.863570i	$0.668223\pi$
$660$	−8.67178	−0.337548
$661$	−12.7398	−0.495521	−0.247761	−	0.968821i	$-0.579695\pi$
$661$	−12.7398	−0.495521	−0.247761	+	0.968821i	$0.579695\pi$
$662$	4.22816	0.164332
$663$	−1.69943	−0.0660004
$664$	−15.0844	−0.585389
$665$	26.8188	1.03999
$666$	−8.25910	−0.320034
$667$	37.6554	1.45802
$668$	−27.4687	−1.06280
$669$	46.4633	1.79637
$670$	−2.02184	−0.0781104
$671$	−3.97382	−0.153408
$672$	26.3843	1.01780
$673$	7.12389	0.274606	0.137303	−	0.990529i	$-0.456157\pi$
$673$	7.12389	0.274606	0.137303	+	0.990529i	$0.456157\pi$
$674$	−38.5291	−1.48409
$675$	3.46871	0.133511
$676$	−17.0129	−0.654343
$677$	−31.9869	−1.22936	−0.614678	−	0.788778i	$-0.710714\pi$
$677$	−31.9869	−1.22936	−0.614678	+	0.788778i	$0.710714\pi$
$678$	75.3108	2.89229
$679$	−30.1187	−1.15585
$680$	2.76274	0.105946
$681$	−3.12628	−0.119799
$682$	−1.04494	−0.0400127
$683$	−18.1976	−0.696312	−0.348156	−	0.937437i	$-0.613192\pi$
$683$	−18.1976	−0.696312	−0.348156	+	0.937437i	$0.613192\pi$
$684$	9.00000	0.344124
$685$	−13.6125	−0.520105
$686$	36.6849	1.40063
$687$	50.6718	1.93325
$688$	1.77383	0.0676268
$689$	9.61571	0.366329
$690$	−27.3588	−1.04153
$691$	−27.1132	−1.03143	−0.515717	−	0.856759i	$-0.672474\pi$
$691$	−27.1132	−1.03143	−0.515717	+	0.856759i	$0.672474\pi$
$692$	25.1008	0.954189
$693$	−3.12628	−0.118758
$694$	−36.9265	−1.40171
$695$	23.7457	0.900725
$696$	−23.9320	−0.907139
$697$	0	0
$698$	30.2700	1.14574
$699$	−0.794765	−0.0300608
$700$	2.36644	0.0894429
$701$	40.7069	1.53748	0.768739	−	0.639563i	$-0.220885\pi$
$701$	40.7069	1.53748	0.768739	+	0.639563i	$0.220885\pi$
$702$	5.34789	0.201843
$703$	−29.7003	−1.12017
$704$	−3.69596	−0.139297
$705$	25.2031	0.949202
$706$	−11.4687	−0.431631
$707$	−19.0473	−0.716348
$708$	20.8366	0.783088
$709$	−26.8870	−1.00976	−0.504882	−	0.863189i	$-0.668464\pi$
$709$	−26.8870	−1.00976	−0.504882	+	0.863189i	$0.668464\pi$
$710$	13.6794	0.513379
$711$	−8.72890	−0.327359
$712$	−18.2656	−0.684534
$713$	−1.33697	−0.0500700
$714$	−8.55313	−0.320093
$715$	2.31626	0.0866231
$716$	22.4633	0.839491
$717$	−9.95814	−0.371893
$718$	27.3788	1.02177
$719$	−17.9450	−0.669237	−0.334619	−	0.942354i	$-0.608608\pi$
$719$	−17.9450	−0.669237	−0.334619	+	0.942354i	$0.608608\pi$
$720$	9.89465	0.368752
$721$	25.3788	0.945157
$722$	44.9540	1.67301
$723$	43.0164	1.59980
$724$	−17.7453	−0.659498
$725$	−8.90120	−0.330582
$726$	−31.3898	−1.16498
$727$	−12.0000	−0.445055	−0.222528	−	0.974926i	$-0.571431\pi$
$727$	−12.0000	−0.445055	−0.222528	+	0.974926i	$0.571431\pi$
$728$	−1.69943	−0.0629851
$729$	13.0000	0.481481
$730$	−12.1976	−0.451454
$731$	−0.424858	−0.0157139
$732$	−6.93742	−0.256414
$733$	−2.08987	−0.0771913	−0.0385956	−	0.999255i	$-0.512288\pi$
$733$	−2.08987	−0.0771913	−0.0385956	+	0.999255i	$0.512288\pi$
$734$	68.2194	2.51803
$735$	12.1976	0.449915
$736$	−24.1976	−0.891936
$737$	0.847546	0.0312198
$738$	0	0
$739$	−48.4742	−1.78315	−0.891576	−	0.452872i	$-0.850399\pi$
$739$	−48.4742	−1.78315	−0.891576	+	0.452872i	$0.850399\pi$
$740$	12.4898	0.459135
$741$	−9.61571	−0.353242
$742$	48.3952	1.77664
$743$	30.1163	1.10486	0.552429	−	0.833560i	$-0.313701\pi$
$743$	30.1163	1.10486	0.552429	+	0.833560i	$0.313701\pi$
$744$	0.849716	0.0311521
$745$	−3.93196	−0.144056
$746$	−3.32605	−0.121776
$747$	12.9396	0.473435
$748$	2.48635	0.0909100
$749$	20.9265	0.764638
$750$	43.7562	1.59775
$751$	−15.6554	−0.571274	−0.285637	−	0.958338i	$-0.592205\pi$
$751$	−15.6554	−0.571274	−0.285637	+	0.958338i	$0.592205\pi$
$752$	30.1701	1.10019
$753$	−1.58953	−0.0579257
$754$	−13.7234	−0.499778
$755$	−2.03293	−0.0739861
$756$	10.9156	0.396996
$757$	−45.2120	−1.64326	−0.821629	−	0.570023i	$-0.806934\pi$
$757$	−45.2120	−1.64326	−0.821629	+	0.570023i	$0.806934\pi$
$758$	−37.5346	−1.36332
$759$	11.4687	0.416288
$760$	15.6321	0.567035
$761$	14.4763	0.524767	0.262383	−	0.964964i	$-0.415491\pi$
$761$	14.4763	0.524767	0.262383	+	0.964964i	$0.415491\pi$
$762$	−10.6630	−0.386281
$763$	−4.00000	−0.144810
$764$	18.4687	0.668174
$765$	−2.36991	−0.0856842
$766$	−51.2944	−1.85334
$767$	−5.56552	−0.200959
$768$	41.9429	1.51348
$769$	12.8188	0.462257	0.231128	−	0.972923i	$-0.425758\pi$
$769$	12.8188	0.462257	0.231128	+	0.972923i	$0.425758\pi$
$770$	11.6576	0.420110
$771$	39.9738	1.43962
$772$	−23.7003	−0.852994
$773$	37.0473	1.33250	0.666250	−	0.745729i	$-0.267898\pi$
$773$	37.0473	1.33250	0.666250	+	0.745729i	$0.267898\pi$
$774$	−0.668486	−0.0240282
$775$	0.316041	0.0113525
$776$	−17.5555	−0.630206
$777$	18.0109	0.646138
$778$	44.3843	1.59125
$779$	0	0
$780$	4.04367	0.144787
$781$	−5.73436	−0.205191
$782$	7.84426	0.280510
$783$	−41.0582	−1.46730
$784$	14.6015	0.521483
$785$	7.59170	0.270959
$786$	−82.4061	−2.93933
$787$	−27.7058	−0.987605	−0.493802	−	0.869574i	$-0.664393\pi$
$787$	−27.7058	−0.987605	−0.493802	+	0.869574i	$0.664393\pi$
$788$	9.27110	0.330269
$789$	−35.6004	−1.26741
$790$	32.5491	1.15805
$791$	−41.0582	−1.45986
$792$	−1.82224	−0.0647505
$793$	1.85301	0.0658022
$794$	−51.6225	−1.83201
$795$	53.6375	1.90233
$796$	26.5640	0.941538
$797$	7.48071	0.264980	0.132490	−	0.991184i	$-0.457703\pi$
$797$	7.48071	0.264980	0.132490	+	0.991184i	$0.457703\pi$
$798$	−48.3952	−1.71317
$799$	−7.22617	−0.255643
$800$	5.71997	0.202231
$801$	15.6685	0.553619
$802$	36.6628	1.29461
$803$	5.11319	0.180441
$804$	1.47963	0.0521825
$805$	14.9156	0.525705
$806$	0.487257	0.0171629
$807$	5.40501	0.190265
$808$	−11.1023	−0.390577
$809$	21.6135	0.759891	0.379946	−	0.925009i	$-0.375943\pi$
$809$	21.6135	0.759891	0.379946	+	0.925009i	$0.375943\pi$
$810$	41.0179	1.44122
$811$	−3.26019	−0.114481	−0.0572403	−	0.998360i	$-0.518230\pi$
$811$	−3.26019	−0.114481	−0.0572403	+	0.998360i	$0.518230\pi$
$812$	−28.0109	−0.982991
$813$	−0.157913	−0.00553825
$814$	−12.9101	−0.452500
$815$	27.5415	0.964737
$816$	−11.3479	−0.397256
$817$	−2.40393	−0.0841027
$818$	37.3898	1.30730
$819$	1.45779	0.0509394
$820$	0	0
$821$	−49.5346	−1.72877	−0.864384	−	0.502832i	$-0.832292\pi$
$821$	−49.5346	−1.72877	−0.864384	+	0.502832i	$0.832292\pi$
$822$	24.5640	0.856769
$823$	−3.52258	−0.122789	−0.0613946	−	0.998114i	$-0.519555\pi$
$823$	−3.52258	−0.122789	−0.0613946	+	0.998114i	$0.519555\pi$
$824$	14.7928	0.515331
$825$	−2.71104	−0.0943863
$826$	−28.0109	−0.974624
$827$	−19.8421	−0.689977	−0.344988	−	0.938607i	$-0.612117\pi$
$827$	−19.8421	−0.689977	−0.344988	+	0.938607i	$0.612117\pi$
$828$	5.00546	0.173952
$829$	4.16883	0.144789	0.0723947	−	0.997376i	$-0.476936\pi$
$829$	4.16883	0.144789	0.0723947	+	0.997376i	$0.476936\pi$
$830$	−48.2504	−1.67480
$831$	−26.0109	−0.902309
$832$	1.72344	0.0597494
$833$	−3.49727	−0.121173
$834$	−42.8497	−1.48376
$835$	40.9265	1.41632
$836$	14.0683	0.486561
$837$	1.45779	0.0503887
$838$	−28.7398	−0.992800
$839$	5.51166	0.190284	0.0951418	−	0.995464i	$-0.469670\pi$
$839$	5.51166	0.190284	0.0951418	+	0.995464i	$0.469670\pi$
$840$	−9.47963	−0.327078
$841$	76.3612	2.63314
$842$	30.7049	1.05816
$843$	−31.7322	−1.09291
$844$	−26.1867	−0.901383
$845$	25.3481	0.872000
$846$	−11.3699	−0.390905
$847$	17.1132	0.588016
$848$	64.2085	2.20493
$849$	42.9374	1.47361
$850$	−1.85427	−0.0636009
$851$	−16.5182	−0.566237
$852$	−10.0109	−0.342968
$853$	48.8386	1.67220	0.836101	−	0.548575i	$-0.184830\pi$
$853$	48.8386	1.67220	0.836101	+	0.548575i	$0.184830\pi$
$854$	9.32605	0.319131
$855$	−13.4094	−0.458591
$856$	12.1976	0.416906
$857$	−43.0473	−1.47047	−0.735234	−	0.677813i	$-0.762928\pi$
$857$	−43.0473	−1.47047	−0.735234	+	0.677813i	$0.762928\pi$
$858$	−4.17975	−0.142694
$859$	20.4633	0.698197	0.349099	−	0.937086i	$-0.386488\pi$
$859$	20.4633	0.698197	0.349099	+	0.937086i	$0.386488\pi$
$860$	1.01092	0.0344720
$861$	0	0
$862$	−10.7398	−0.365800
$863$	53.0582	1.80612	0.903062	−	0.429511i	$-0.141314\pi$
$863$	53.0582	1.80612	0.903062	+	0.429511i	$0.141314\pi$
$864$	26.3843	0.897612
$865$	−37.3985	−1.27159
$866$	−26.0218	−0.884258
$867$	−31.2820	−1.06239
$868$	0.994541	0.0337569
$869$	−13.6445	−0.462857
$870$	−76.5510	−2.59532
$871$	−0.395213	−0.0133913
$872$	−2.33151	−0.0789550
$873$	15.0593	0.509681
$874$	44.3843	1.50132
$875$	−23.8552	−0.806452
$876$	8.92650	0.301599
$877$	−21.1132	−0.712942	−0.356471	−	0.934306i	$-0.616020\pi$
$877$	−21.1132	−0.712942	−0.356471	+	0.934306i	$0.616020\pi$
$878$	−15.1088	−0.509898
$879$	−44.9265	−1.51533
$880$	15.4667	0.521383
$881$	−26.6190	−0.896817	−0.448408	−	0.893829i	$-0.648009\pi$
$881$	−26.6190	−0.896817	−0.448408	+	0.893829i	$0.648009\pi$
$882$	−5.50273	−0.185287
$883$	−34.6214	−1.16510	−0.582551	−	0.812794i	$-0.697945\pi$
$883$	−34.6214	−1.16510	−0.582551	+	0.812794i	$0.697945\pi$
$884$	−1.15939	−0.0389946
$885$	−31.0452	−1.04357
$886$	17.4687	0.586873
$887$	0.994541	0.0333934	0.0166967	−	0.999861i	$-0.494685\pi$
$887$	0.994541	0.0333934	0.0166967	+	0.999861i	$0.494685\pi$
$888$	10.4982	0.352296
$889$	5.81331	0.194972
$890$	−58.4262	−1.95845
$891$	−17.1945	−0.576039
$892$	31.6983	1.06134
$893$	−40.8870	−1.36823
$894$	7.09533	0.237303
$895$	−33.4687	−1.11874
$896$	−17.7103	−0.591661
$897$	−5.34789	−0.178561
$898$	6.72890	0.224546
$899$	−3.74090	−0.124766
$900$	−1.18322	−0.0394406
$901$	−15.3788	−0.512343
$902$	0	0
$903$	1.45779	0.0485123
$904$	−23.9320	−0.795965
$905$	26.4392	0.878870
$906$	3.66849	0.121877
$907$	54.8836	1.82238	0.911189	−	0.411988i	$-0.135165\pi$
$907$	54.8836	1.82238	0.911189	+	0.411988i	$0.135165\pi$
$908$	−2.13282	−0.0707802
$909$	9.52366	0.315880
$910$	−5.43596	−0.180200
$911$	−28.7169	−0.951433	−0.475717	−	0.879599i	$-0.657811\pi$
$911$	−28.7169	−0.951433	−0.475717	+	0.879599i	$0.657811\pi$
$912$	−64.2085	−2.12616
$913$	20.2264	0.669396
$914$	59.8716	1.98037
$915$	10.3363	0.341707
$916$	34.5695	1.14221
$917$	44.9265	1.48360
$918$	−8.55313	−0.282295
$919$	−15.5477	−0.512870	−0.256435	−	0.966561i	$-0.582548\pi$
$919$	−15.5477	−0.512870	−0.256435	+	0.966561i	$0.582548\pi$
$920$	8.69397	0.286632
$921$	−19.5477	−0.644118
$922$	22.7882	0.750490
$923$	2.67395	0.0880140
$924$	−8.53129	−0.280659
$925$	3.90467	0.128385
$926$	44.4567	1.46094
$927$	−12.6894	−0.416775
$928$	−67.7058	−2.22255
$929$	−2.42139	−0.0794432	−0.0397216	−	0.999211i	$-0.512647\pi$
$929$	−2.42139	−0.0794432	−0.0397216	+	0.999211i	$0.512647\pi$
$930$	2.71798	0.0891260
$931$	−19.7882	−0.648533
$932$	−0.542208	−0.0177606
$933$	10.8977	0.356776
$934$	−23.7344	−0.776612
$935$	−3.70450	−0.121150
$936$	0.849716	0.0277738
$937$	−29.4436	−0.961881	−0.480941	−	0.876753i	$-0.659705\pi$
$937$	−29.4436	−0.961881	−0.480941	+	0.876753i	$0.659705\pi$
$938$	−1.98908	−0.0649458
$939$	18.0288	0.588347
$940$	17.1941	0.560811
$941$	−20.6739	−0.673951	−0.336976	−	0.941513i	$-0.609404\pi$
$941$	−20.6739	−0.673951	−0.336976	+	0.941513i	$0.609404\pi$
$942$	−13.6994	−0.446352
$943$	0	0
$944$	−37.1636	−1.20957
$945$	−16.2635	−0.529051
$946$	−1.04494	−0.0339738
$947$	40.6609	1.32130	0.660650	−	0.750694i	$-0.270281\pi$
$947$	40.6609	1.32130	0.660650	+	0.750694i	$0.270281\pi$
$948$	−23.8203	−0.773646
$949$	−2.38429	−0.0773975
$950$	−10.4918	−0.340399
$951$	−33.7213	−1.09349
$952$	2.71798	0.0880902
$953$	−35.4567	−1.14856	−0.574278	−	0.818661i	$-0.694717\pi$
$953$	−35.4567	−1.14856	−0.574278	+	0.818661i	$0.694717\pi$
$954$	−24.1976	−0.783426
$955$	−27.5171	−0.890433
$956$	−6.79368	−0.219723
$957$	32.0899	1.03732
$958$	−1.82423	−0.0589382
$959$	−13.3919	−0.432448
$960$	9.61354	0.310276
$961$	−30.8672	−0.995715
$962$	6.02003	0.194093
$963$	−10.4633	−0.337174
$964$	29.3468	0.945197
$965$	35.3119	1.13673
$966$	−26.9156	−0.865995
$967$	43.1132	1.38643	0.693213	−	0.720732i	$-0.256194\pi$
$967$	43.1132	1.38643	0.693213	+	0.720732i	$0.256194\pi$
$968$	9.97491	0.320606
$969$	15.3788	0.494039
$970$	−56.1547	−1.80302
$971$	−41.3657	−1.32749	−0.663745	−	0.747959i	$-0.731034\pi$
$971$	−41.3657	−1.32749	−0.663745	+	0.747959i	$0.731034\pi$
$972$	−13.6445	−0.437647
$973$	23.3610	0.748919
$974$	42.9485	1.37616
$975$	1.26416	0.0404857
$976$	12.3734	0.396062
$977$	47.0033	1.50377	0.751884	−	0.659295i	$-0.229145\pi$
$977$	47.0033	1.50377	0.751884	+	0.659295i	$0.229145\pi$
$978$	−49.6994	−1.58921
$979$	24.4920	0.782769
$980$	8.32150	0.265821
$981$	2.00000	0.0638551
$982$	28.5586	0.911341
$983$	3.03640	0.0968462	0.0484231	−	0.998827i	$-0.484580\pi$
$983$	3.03640	0.0968462	0.0484231	+	0.998827i	$0.484580\pi$
$984$	0	0
$985$	−13.8133	−0.440129
$986$	21.9485	0.698983
$987$	24.7948	0.789226
$988$	−6.56007	−0.208703
$989$	−1.33697	−0.0425133
$990$	−5.82878	−0.185251
$991$	59.8960	1.90266	0.951329	−	0.308178i	$-0.0997191\pi$
$991$	59.8960	1.90266	0.951329	+	0.308178i	$0.0997191\pi$
$992$	2.40393	0.0763247
$993$	4.61025	0.146302
$994$	13.4578	0.426855
$995$	−39.5786	−1.25473
$996$	35.3108	1.11887
$997$	−14.4129	−0.456460	−0.228230	−	0.973607i	$-0.573294\pi$
$997$	−14.4129	−0.456460	−0.228230	+	0.973607i	$0.573294\pi$
$998$	−78.0855	−2.47175
$999$	18.0109	0.569840

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	151.2.a.b.1.3	✓	3
3.2	odd	2		1359.2.a.e.1.1		3
4.3	odd	2		2416.2.a.f.1.1		3
5.4	even	2		3775.2.a.j.1.1		3
7.6	odd	2		7399.2.a.c.1.3		3
8.3	odd	2		9664.2.a.v.1.3		3
8.5	even	2		9664.2.a.m.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
151.2.a.b.1.3	✓	3	1.1	even	1	trivial
1359.2.a.e.1.1		3	3.2	odd	2
2416.2.a.f.1.1		3	4.3	odd	2
3775.2.a.j.1.1		3	5.4	even	2
7399.2.a.c.1.3		3	7.6	odd	2
9664.2.a.m.1.3		3	8.5	even	2
9664.2.a.v.1.3		3	8.3	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:	\( N \)	\(=\)	\( 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	151.a (trivial)

\(f(q)\)	\(=\)	\(q+1.83424 q^{2} +2.00000 q^{3} +1.36445 q^{4} -2.03293 q^{5} +3.66849 q^{6} -2.00000 q^{7} -1.16576 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.83424 q^{2} +2.00000 q^{3} +1.36445 q^{4} -2.03293 q^{5} +3.66849 q^{6} -2.00000 q^{7} -1.16576 q^{8} +1.00000 q^{9} -3.72890 q^{10} +1.56314 q^{11} +2.72890 q^{12} -0.728896 q^{13} -3.66849 q^{14} -4.06587 q^{15} -4.86718 q^{16} +1.16576 q^{17} +1.83424 q^{18} +6.59607 q^{19} -2.77383 q^{20} -4.00000 q^{21} +2.86718 q^{22} +3.66849 q^{23} -2.33151 q^{24} -0.867178 q^{25} -1.33697 q^{26} -4.00000 q^{27} -2.72890 q^{28} +10.2646 q^{29} -7.45779 q^{30} -0.364448 q^{31} -6.59607 q^{32} +3.12628 q^{33} +2.13828 q^{34} +4.06587 q^{35} +1.36445 q^{36} -4.50273 q^{37} +12.0988 q^{38} -1.45779 q^{39} +2.36991 q^{40} -7.33697 q^{42} -0.364448 q^{43} +2.13282 q^{44} -2.03293 q^{45} +6.72890 q^{46} -6.19869 q^{47} -9.73436 q^{48} -3.00000 q^{49} -1.59061 q^{50} +2.33151 q^{51} -0.994541 q^{52} -13.1921 q^{53} -7.33697 q^{54} -3.17776 q^{55} +2.33151 q^{56} +13.1921 q^{57} +18.8277 q^{58} +7.63555 q^{59} -5.54767 q^{60} -2.54221 q^{61} -0.668486 q^{62} -2.00000 q^{63} -2.36445 q^{64} +1.48180 q^{65} +5.73436 q^{66} +0.542208 q^{67} +1.59061 q^{68} +7.33697 q^{69} +7.45779 q^{70} -3.66849 q^{71} -1.16576 q^{72} +3.27110 q^{73} -8.25910 q^{74} -1.73436 q^{75} +9.00000 q^{76} -3.12628 q^{77} -2.67395 q^{78} -8.72890 q^{79} +9.89465 q^{80} -11.0000 q^{81} +12.9396 q^{83} -5.45779 q^{84} -2.36991 q^{85} -0.668486 q^{86} +20.5291 q^{87} -1.82224 q^{88} +15.6685 q^{89} -3.72890 q^{90} +1.45779 q^{91} +5.00546 q^{92} -0.728896 q^{93} -11.3699 q^{94} -13.4094 q^{95} -13.1921 q^{96} +15.0593 q^{97} -5.50273 q^{98} +1.56314 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 6 q^{3} + 4 q^{4} + 5 q^{5} - 6 q^{7} - 9 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 6 * q^3 + 4 * q^4 + 5 * q^5 - 6 * q^7 - 9 * q^8 + 3 * q^9	\( 3 q + 6 q^{3} + 4 q^{4} + 5 q^{5} - 6 q^{7} - 9 q^{8} + 3 q^{9} - 11 q^{10} - q^{11} + 8 q^{12} - 2 q^{13} + 10 q^{15} + 2 q^{16} + 9 q^{17} + 3 q^{19} + 8 q^{20} - 12 q^{21} - 8 q^{22} - 18 q^{24} + 14 q^{25} + 18 q^{26} - 12 q^{27} - 8 q^{28} + 3 q^{29} - 22 q^{30} - q^{31} - 3 q^{32} - 2 q^{33} - 10 q^{34} - 10 q^{35} + 4 q^{36} + 3 q^{37} + 3 q^{38} - 4 q^{39} - 26 q^{40} - q^{43} + 23 q^{44} + 5 q^{45} + 20 q^{46} - 13 q^{47} + 4 q^{48} - 9 q^{49} - 21 q^{50} + 18 q^{51} - 36 q^{52} - 6 q^{53} - 10 q^{55} + 18 q^{56} + 6 q^{57} + 23 q^{58} + 23 q^{59} + 16 q^{60} - 8 q^{61} + 9 q^{62} - 6 q^{63} - 7 q^{64} - 6 q^{65} - 16 q^{66} + 2 q^{67} + 21 q^{68} + 22 q^{70} - 9 q^{72} + 10 q^{73} - 30 q^{74} + 28 q^{75} + 27 q^{76} + 2 q^{77} + 36 q^{78} - 26 q^{79} + 35 q^{80} - 33 q^{81} + 28 q^{83} - 16 q^{84} + 26 q^{85} + 9 q^{86} + 6 q^{87} - 5 q^{88} + 36 q^{89} - 11 q^{90} + 4 q^{91} - 18 q^{92} - 2 q^{93} - q^{94} - 24 q^{95} - 6 q^{96} - 5 q^{97} - q^{99}+O(q^{100}) \) 3 * q + 6 * q^3 + 4 * q^4 + 5 * q^5 - 6 * q^7 - 9 * q^8 + 3 * q^9 - 11 * q^10 - q^11 + 8 * q^12 - 2 * q^13 + 10 * q^15 + 2 * q^16 + 9 * q^17 + 3 * q^19 + 8 * q^20 - 12 * q^21 - 8 * q^22 - 18 * q^24 + 14 * q^25 + 18 * q^26 - 12 * q^27 - 8 * q^28 + 3 * q^29 - 22 * q^30 - q^31 - 3 * q^32 - 2 * q^33 - 10 * q^34 - 10 * q^35 + 4 * q^36 + 3 * q^37 + 3 * q^38 - 4 * q^39 - 26 * q^40 - q^43 + 23 * q^44 + 5 * q^45 + 20 * q^46 - 13 * q^47 + 4 * q^48 - 9 * q^49 - 21 * q^50 + 18 * q^51 - 36 * q^52 - 6 * q^53 - 10 * q^55 + 18 * q^56 + 6 * q^57 + 23 * q^58 + 23 * q^59 + 16 * q^60 - 8 * q^61 + 9 * q^62 - 6 * q^63 - 7 * q^64 - 6 * q^65 - 16 * q^66 + 2 * q^67 + 21 * q^68 + 22 * q^70 - 9 * q^72 + 10 * q^73 - 30 * q^74 + 28 * q^75 + 27 * q^76 + 2 * q^77 + 36 * q^78 - 26 * q^79 + 35 * q^80 - 33 * q^81 + 28 * q^83 - 16 * q^84 + 26 * q^85 + 9 * q^86 + 6 * q^87 - 5 * q^88 + 36 * q^89 - 11 * q^90 + 4 * q^91 - 18 * q^92 - 2 * q^93 - q^94 - 24 * q^95 - 6 * q^96 - 5 * q^97 - q^99

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