LMFDB - Embedded newform 5054.2.a.bk.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5054,2,Mod(1,5054)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5054, 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("5054.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5054 = 2 \cdot 7 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5054.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:	$40.3563931816$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 3x^{8} - 15x^{7} + 40x^{6} + 81x^{5} - 162x^{4} - 205x^{3} + 204x^{2} + 210x + 1 $ x^9 - 3x^8 - 15x^7 + 40x^6 + 81x^5 - 162x^4 - 205x^3 + 204x^2 + 210x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 266)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.81276$ of defining polynomial
Character	$\chi$	$=$	5054.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.81276 q^{3} +1.00000 q^{4} +3.21562 q^{5} -1.81276 q^{6} -1.00000 q^{7} +1.00000 q^{8} +0.286090 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.81276 q^{3} +1.00000 q^{4} +3.21562 q^{5} -1.81276 q^{6} -1.00000 q^{7} +1.00000 q^{8} +0.286090 q^{9} +3.21562 q^{10} +1.13291 q^{11} -1.81276 q^{12} +3.45333 q^{13} -1.00000 q^{14} -5.82914 q^{15} +1.00000 q^{16} +0.980683 q^{17} +0.286090 q^{18} +3.21562 q^{20} +1.81276 q^{21} +1.13291 q^{22} +8.34878 q^{23} -1.81276 q^{24} +5.34022 q^{25} +3.45333 q^{26} +4.91966 q^{27} -1.00000 q^{28} -8.92325 q^{29} -5.82914 q^{30} +2.23416 q^{31} +1.00000 q^{32} -2.05369 q^{33} +0.980683 q^{34} -3.21562 q^{35} +0.286090 q^{36} +0.709571 q^{37} -6.26005 q^{39} +3.21562 q^{40} -5.15565 q^{41} +1.81276 q^{42} +8.69852 q^{43} +1.13291 q^{44} +0.919959 q^{45} +8.34878 q^{46} -7.68237 q^{47} -1.81276 q^{48} +1.00000 q^{49} +5.34022 q^{50} -1.77774 q^{51} +3.45333 q^{52} -7.13209 q^{53} +4.91966 q^{54} +3.64301 q^{55} -1.00000 q^{56} -8.92325 q^{58} -6.68280 q^{59} -5.82914 q^{60} +0.849200 q^{61} +2.23416 q^{62} -0.286090 q^{63} +1.00000 q^{64} +11.1046 q^{65} -2.05369 q^{66} +13.2676 q^{67} +0.980683 q^{68} -15.1343 q^{69} -3.21562 q^{70} +11.0807 q^{71} +0.286090 q^{72} +5.65554 q^{73} +0.709571 q^{74} -9.68053 q^{75} -1.13291 q^{77} -6.26005 q^{78} +4.50556 q^{79} +3.21562 q^{80} -9.77642 q^{81} -5.15565 q^{82} +8.09012 q^{83} +1.81276 q^{84} +3.15351 q^{85} +8.69852 q^{86} +16.1757 q^{87} +1.13291 q^{88} -11.8744 q^{89} +0.919959 q^{90} -3.45333 q^{91} +8.34878 q^{92} -4.04999 q^{93} -7.68237 q^{94} -1.81276 q^{96} +15.8842 q^{97} +1.00000 q^{98} +0.324114 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 9 q^{2} + 3 q^{3} + 9 q^{4} + 3 q^{5} + 3 q^{6} - 9 q^{7} + 9 q^{8} + 12 q^{9}+O(q^{10}) $ 9 * q + 9 * q^2 + 3 * q^3 + 9 * q^4 + 3 * q^5 + 3 * q^6 - 9 * q^7 + 9 * q^8 + 12 * q^9	\( 9 q + 9 q^{2} + 3 q^{3} + 9 q^{4} + 3 q^{5} + 3 q^{6} - 9 q^{7} + 9 q^{8} + 12 q^{9} + 3 q^{10} - 3 q^{11} + 3 q^{12} + 12 q^{13} - 9 q^{14} - 6 q^{15} + 9 q^{16} + 12 q^{17} + 12 q^{18} + 3 q^{20} - 3 q^{21} - 3 q^{22} + 6 q^{23} + 3 q^{24} + 12 q^{26} + 24 q^{27} - 9 q^{28} - 6 q^{29} - 6 q^{30} + 9 q^{31} + 9 q^{32} - 3 q^{33} + 12 q^{34} - 3 q^{35} + 12 q^{36} + 9 q^{37} + 33 q^{39} + 3 q^{40} + 3 q^{41} - 3 q^{42} + 21 q^{43} - 3 q^{44} + 18 q^{45} + 6 q^{46} + 21 q^{47} + 3 q^{48} + 9 q^{49} + 39 q^{51} + 12 q^{52} + 24 q^{54} + 24 q^{55} - 9 q^{56} - 6 q^{58} - 9 q^{59} - 6 q^{60} + 6 q^{61} + 9 q^{62} - 12 q^{63} + 9 q^{64} - 3 q^{65} - 3 q^{66} + 27 q^{67} + 12 q^{68} + 6 q^{69} - 3 q^{70} + 9 q^{71} + 12 q^{72} + 51 q^{73} + 9 q^{74} - 3 q^{75} + 3 q^{77} + 33 q^{78} + 24 q^{79} + 3 q^{80} - 3 q^{81} + 3 q^{82} + 9 q^{83} - 3 q^{84} + 6 q^{85} + 21 q^{86} - 3 q^{87} - 3 q^{88} + 9 q^{89} + 18 q^{90} - 12 q^{91} + 6 q^{92} + 3 q^{93} + 21 q^{94} + 3 q^{96} - 12 q^{97} + 9 q^{98} - 15 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 3 * q^3 + 9 * q^4 + 3 * q^5 + 3 * q^6 - 9 * q^7 + 9 * q^8 + 12 * q^9 + 3 * q^10 - 3 * q^11 + 3 * q^12 + 12 * q^13 - 9 * q^14 - 6 * q^15 + 9 * q^16 + 12 * q^17 + 12 * q^18 + 3 * q^20 - 3 * q^21 - 3 * q^22 + 6 * q^23 + 3 * q^24 + 12 * q^26 + 24 * q^27 - 9 * q^28 - 6 * q^29 - 6 * q^30 + 9 * q^31 + 9 * q^32 - 3 * q^33 + 12 * q^34 - 3 * q^35 + 12 * q^36 + 9 * q^37 + 33 * q^39 + 3 * q^40 + 3 * q^41 - 3 * q^42 + 21 * q^43 - 3 * q^44 + 18 * q^45 + 6 * q^46 + 21 * q^47 + 3 * q^48 + 9 * q^49 + 39 * q^51 + 12 * q^52 + 24 * q^54 + 24 * q^55 - 9 * q^56 - 6 * q^58 - 9 * q^59 - 6 * q^60 + 6 * q^61 + 9 * q^62 - 12 * q^63 + 9 * q^64 - 3 * q^65 - 3 * q^66 + 27 * q^67 + 12 * q^68 + 6 * q^69 - 3 * q^70 + 9 * q^71 + 12 * q^72 + 51 * q^73 + 9 * q^74 - 3 * q^75 + 3 * q^77 + 33 * q^78 + 24 * q^79 + 3 * q^80 - 3 * q^81 + 3 * q^82 + 9 * q^83 - 3 * q^84 + 6 * q^85 + 21 * q^86 - 3 * q^87 - 3 * q^88 + 9 * q^89 + 18 * q^90 - 12 * q^91 + 6 * q^92 + 3 * q^93 + 21 * q^94 + 3 * q^96 - 12 * q^97 + 9 * q^98 - 15 * 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
$3$	−1.81276	−1.04660	−0.523298	−	0.852150i	$-0.675299\pi$
$3$	−1.81276	−1.04660	−0.523298	+	0.852150i	$0.675299\pi$
$4$	1.00000	0.500000
$5$	3.21562	1.43807	0.719035	−	0.694974i	$-0.244584\pi$
$5$	3.21562	1.43807	0.719035	+	0.694974i	$0.244584\pi$
$6$	−1.81276	−0.740055
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	0.286090	0.0953635
$10$	3.21562	1.01687
$11$	1.13291	0.341585	0.170792	−	0.985307i	$-0.445367\pi$
$11$	1.13291	0.341585	0.170792	+	0.985307i	$0.445367\pi$
$12$	−1.81276	−0.523298
$13$	3.45333	0.957781	0.478891	−	0.877875i	$-0.341039\pi$
$13$	3.45333	0.957781	0.478891	+	0.877875i	$0.341039\pi$
$14$	−1.00000	−0.267261
$15$	−5.82914	−1.50508
$16$	1.00000	0.250000
$17$	0.980683	0.237851	0.118925	−	0.992903i	$-0.462055\pi$
$17$	0.980683	0.237851	0.118925	+	0.992903i	$0.462055\pi$
$18$	0.286090	0.0674322
$19$	0	0
$19$	0	0
$20$	3.21562	0.719035
$21$	1.81276	0.395576
$22$	1.13291	0.241537
$23$	8.34878	1.74084	0.870421	−	0.492309i	$-0.163847\pi$
$23$	8.34878	1.74084	0.870421	+	0.492309i	$0.163847\pi$
$24$	−1.81276	−0.370028
$25$	5.34022	1.06804
$26$	3.45333	0.677253
$27$	4.91966	0.946789
$28$	−1.00000	−0.188982
$29$	−8.92325	−1.65701	−0.828503	−	0.559985i	$-0.810807\pi$
$29$	−8.92325	−1.65701	−0.828503	+	0.559985i	$0.810807\pi$
$30$	−5.82914	−1.06425
$31$	2.23416	0.401267	0.200633	−	0.979666i	$-0.435700\pi$
$31$	2.23416	0.401267	0.200633	+	0.979666i	$0.435700\pi$
$32$	1.00000	0.176777
$33$	−2.05369	−0.357501
$34$	0.980683	0.168186
$35$	−3.21562	−0.543539
$36$	0.286090	0.0476817
$37$	0.709571	0.116653	0.0583264	−	0.998298i	$-0.481424\pi$
$37$	0.709571	0.116653	0.0583264	+	0.998298i	$0.481424\pi$
$38$	0	0
$39$	−6.26005	−1.00241
$40$	3.21562	0.508434
$41$	−5.15565	−0.805177	−0.402589	−	0.915381i	$-0.631889\pi$
$41$	−5.15565	−0.805177	−0.402589	+	0.915381i	$0.631889\pi$
$42$	1.81276	0.279715
$43$	8.69852	1.32651	0.663256	−	0.748393i	$-0.269174\pi$
$43$	8.69852	1.32651	0.663256	+	0.748393i	$0.269174\pi$
$44$	1.13291	0.170792
$45$	0.919959	0.137139
$46$	8.34878	1.23096
$47$	−7.68237	−1.12059	−0.560294	−	0.828294i	$-0.689312\pi$
$47$	−7.68237	−1.12059	−0.560294	+	0.828294i	$0.689312\pi$
$48$	−1.81276	−0.261649
$49$	1.00000	0.142857
$50$	5.34022	0.755222
$51$	−1.77774	−0.248934
$52$	3.45333	0.478891
$53$	−7.13209	−0.979668	−0.489834	−	0.871816i	$-0.662943\pi$
$53$	−7.13209	−0.979668	−0.489834	+	0.871816i	$0.662943\pi$
$54$	4.91966	0.669481
$55$	3.64301	0.491223
$56$	−1.00000	−0.133631
$57$	0	0
$58$	−8.92325	−1.17168
$59$	−6.68280	−0.870026	−0.435013	−	0.900424i	$-0.643256\pi$
$59$	−6.68280	−0.870026	−0.435013	+	0.900424i	$0.643256\pi$
$60$	−5.82914	−0.752539
$61$	0.849200	0.108729	0.0543645	−	0.998521i	$-0.482687\pi$
$61$	0.849200	0.108729	0.0543645	+	0.998521i	$0.482687\pi$
$62$	2.23416	0.283738
$63$	−0.286090	−0.0360440
$64$	1.00000	0.125000
$65$	11.1046	1.37736
$66$	−2.05369	−0.252792
$67$	13.2676	1.62090	0.810448	−	0.585811i	$-0.199224\pi$
$67$	13.2676	1.62090	0.810448	+	0.585811i	$0.199224\pi$
$68$	0.980683	0.118925
$69$	−15.1343	−1.82196
$70$	−3.21562	−0.384340
$71$	11.0807	1.31504	0.657521	−	0.753436i	$-0.271605\pi$
$71$	11.0807	1.31504	0.657521	+	0.753436i	$0.271605\pi$
$72$	0.286090	0.0337161
$73$	5.65554	0.661930	0.330965	−	0.943643i	$-0.392626\pi$
$73$	5.65554	0.661930	0.330965	+	0.943643i	$0.392626\pi$
$74$	0.709571	0.0824860
$75$	−9.68053	−1.11781
$76$	0	0
$77$	−1.13291	−0.129107
$78$	−6.26005	−0.708811
$79$	4.50556	0.506915	0.253458	−	0.967347i	$-0.418432\pi$
$79$	4.50556	0.506915	0.253458	+	0.967347i	$0.418432\pi$
$80$	3.21562	0.359517
$81$	−9.77642	−1.08627
$82$	−5.15565	−0.569346
$83$	8.09012	0.888006	0.444003	−	0.896025i	$-0.353558\pi$
$83$	8.09012	0.888006	0.444003	+	0.896025i	$0.353558\pi$
$84$	1.81276	0.197788
$85$	3.15351	0.342046
$86$	8.69852	0.937986
$87$	16.1757	1.73422
$88$	1.13291	0.120768
$89$	−11.8744	−1.25869	−0.629344	−	0.777127i	$-0.716676\pi$
$89$	−11.8744	−1.25869	−0.629344	+	0.777127i	$0.716676\pi$
$90$	0.919959	0.0969722
$91$	−3.45333	−0.362007
$92$	8.34878	0.870421
$93$	−4.04999	−0.419964
$94$	−7.68237	−0.792376
$95$	0	0
$96$	−1.81276	−0.185014
$97$	15.8842	1.61280	0.806398	−	0.591374i	$-0.201414\pi$
$97$	15.8842	1.61280	0.806398	+	0.591374i	$0.201414\pi$
$98$	1.00000	0.101015
$99$	0.324114	0.0325747
$100$	5.34022	0.534022
$101$	14.3100	1.42390	0.711951	−	0.702229i	$-0.247812\pi$
$101$	14.3100	1.42390	0.711951	+	0.702229i	$0.247812\pi$
$102$	−1.77774	−0.176023
$103$	−5.29425	−0.521658	−0.260829	−	0.965385i	$-0.583996\pi$
$103$	−5.29425	−0.521658	−0.260829	+	0.965385i	$0.583996\pi$
$104$	3.45333	0.338627
$105$	5.82914	0.568866
$106$	−7.13209	−0.692730
$107$	−5.33647	−0.515896	−0.257948	−	0.966159i	$-0.583046\pi$
$107$	−5.33647	−0.515896	−0.257948	+	0.966159i	$0.583046\pi$
$108$	4.91966	0.473395
$109$	1.87677	0.179762	0.0898811	−	0.995953i	$-0.471351\pi$
$109$	1.87677	0.179762	0.0898811	+	0.995953i	$0.471351\pi$
$110$	3.64301	0.347347
$111$	−1.28628	−0.122088
$112$	−1.00000	−0.0944911
$113$	−15.1183	−1.42221	−0.711103	−	0.703088i	$-0.751804\pi$
$113$	−15.1183	−1.42221	−0.711103	+	0.703088i	$0.751804\pi$
$114$	0	0
$115$	26.8465	2.50345
$116$	−8.92325	−0.828503
$117$	0.987964	0.0913373
$118$	−6.68280	−0.615201
$119$	−0.980683	−0.0898991
$120$	−5.82914	−0.532126
$121$	−9.71652	−0.883320
$122$	0.849200	0.0768830
$123$	9.34594	0.842695
$124$	2.23416	0.200633
$125$	1.09403	0.0978532
$126$	−0.286090	−0.0254870
$127$	−7.17004	−0.636238	−0.318119	−	0.948051i	$-0.603051\pi$
$127$	−7.17004	−0.636238	−0.318119	+	0.948051i	$0.603051\pi$
$128$	1.00000	0.0883883
$129$	−15.7683	−1.38832
$130$	11.1046	0.973938
$131$	16.8172	1.46932	0.734661	−	0.678434i	$-0.237341\pi$
$131$	16.8172	1.46932	0.734661	+	0.678434i	$0.237341\pi$
$132$	−2.05369	−0.178751
$133$	0	0
$134$	13.2676	1.14615
$135$	15.8198	1.36155
$136$	0.980683	0.0840929
$137$	10.1526	0.867393	0.433697	−	0.901059i	$-0.357209\pi$
$137$	10.1526	0.867393	0.433697	+	0.901059i	$0.357209\pi$
$138$	−15.1343	−1.28832
$139$	−1.66287	−0.141043	−0.0705216	−	0.997510i	$-0.522466\pi$
$139$	−1.66287	−0.141043	−0.0705216	+	0.997510i	$0.522466\pi$
$140$	−3.21562	−0.271770
$141$	13.9263	1.17280
$142$	11.0807	0.929876
$143$	3.91231	0.327163
$144$	0.286090	0.0238409
$145$	−28.6938	−2.38289
$146$	5.65554	0.468055
$147$	−1.81276	−0.149514
$148$	0.709571	0.0583264
$149$	1.32351	0.108426	0.0542130	−	0.998529i	$-0.482735\pi$
$149$	1.32351	0.108426	0.0542130	+	0.998529i	$0.482735\pi$
$150$	−9.68053	−0.790412
$151$	10.6378	0.865689	0.432844	−	0.901469i	$-0.357510\pi$
$151$	10.6378	0.865689	0.432844	+	0.901469i	$0.357510\pi$
$152$	0	0
$153$	0.280564	0.0226823
$154$	−1.13291	−0.0912924
$155$	7.18421	0.577049
$156$	−6.26005	−0.501205
$157$	16.6290	1.32714	0.663568	−	0.748116i	$-0.269041\pi$
$157$	16.6290	1.32714	0.663568	+	0.748116i	$0.269041\pi$
$158$	4.50556	0.358443
$159$	12.9288	1.02532
$160$	3.21562	0.254217
$161$	−8.34878	−0.657976
$162$	−9.77642	−0.768108
$163$	−8.78895	−0.688403	−0.344202	−	0.938896i	$-0.611850\pi$
$163$	−8.78895	−0.688403	−0.344202	+	0.938896i	$0.611850\pi$
$164$	−5.15565	−0.402589
$165$	−6.60389	−0.514112
$166$	8.09012	0.627915
$167$	−6.97125	−0.539452	−0.269726	−	0.962937i	$-0.586933\pi$
$167$	−6.97125	−0.539452	−0.269726	+	0.962937i	$0.586933\pi$
$168$	1.81276	0.139857
$169$	−1.07452	−0.0826554
$170$	3.15351	0.241863
$171$	0	0
$172$	8.69852	0.663256
$173$	9.75988	0.742030	0.371015	−	0.928627i	$-0.379010\pi$
$173$	9.75988	0.742030	0.371015	+	0.928627i	$0.379010\pi$
$174$	16.1757	1.22628
$175$	−5.34022	−0.403683
$176$	1.13291	0.0853962
$177$	12.1143	0.910566
$178$	−11.8744	−0.890027
$179$	−16.0185	−1.19728	−0.598639	−	0.801019i	$-0.704292\pi$
$179$	−16.0185	−1.19728	−0.598639	+	0.801019i	$0.704292\pi$
$180$	0.919959	0.0685697
$181$	−9.54585	−0.709537	−0.354769	−	0.934954i	$-0.615440\pi$
$181$	−9.54585	−0.709537	−0.354769	+	0.934954i	$0.615440\pi$
$182$	−3.45333	−0.255978
$183$	−1.53939	−0.113795
$184$	8.34878	0.615480
$185$	2.28171	0.167755
$186$	−4.04999	−0.296959
$187$	1.11102	0.0812462
$188$	−7.68237	−0.560294
$189$	−4.91966	−0.357853
$190$	0	0
$191$	12.0046	0.868624	0.434312	−	0.900762i	$-0.356991\pi$
$191$	12.0046	0.868624	0.434312	+	0.900762i	$0.356991\pi$
$192$	−1.81276	−0.130825
$193$	13.2181	0.951459	0.475730	−	0.879592i	$-0.342184\pi$
$193$	13.2181	0.951459	0.475730	+	0.879592i	$0.342184\pi$
$194$	15.8842	1.14042
$195$	−20.1299	−1.44154
$196$	1.00000	0.0714286
$197$	−11.6270	−0.828388	−0.414194	−	0.910189i	$-0.635937\pi$
$197$	−11.6270	−0.828388	−0.414194	+	0.910189i	$0.635937\pi$
$198$	0.324114	0.0230338
$199$	9.98653	0.707926	0.353963	−	0.935259i	$-0.384834\pi$
$199$	9.98653	0.707926	0.353963	+	0.935259i	$0.384834\pi$
$200$	5.34022	0.377611
$201$	−24.0509	−1.69642
$202$	14.3100	1.00685
$203$	8.92325	0.626289
$204$	−1.77774	−0.124467
$205$	−16.5786	−1.15790
$206$	−5.29425	−0.368868
$207$	2.38851	0.166013
$208$	3.45333	0.239445
$209$	0	0
$210$	5.82914	0.402249
$211$	−18.6709	−1.28535	−0.642677	−	0.766137i	$-0.722176\pi$
$211$	−18.6709	−1.28535	−0.642677	+	0.766137i	$0.722176\pi$
$212$	−7.13209	−0.489834
$213$	−20.0867	−1.37632
$214$	−5.33647	−0.364794
$215$	27.9712	1.90762
$216$	4.91966	0.334740
$217$	−2.23416	−0.151664
$218$	1.87677	0.127111
$219$	−10.2521	−0.692774
$220$	3.64301	0.245611
$221$	3.38662	0.227809
$222$	−1.28628	−0.0863295
$223$	19.4556	1.30284	0.651421	−	0.758717i	$-0.274173\pi$
$223$	19.4556	1.30284	0.651421	+	0.758717i	$0.274173\pi$
$224$	−1.00000	−0.0668153
$225$	1.52779	0.101852
$226$	−15.1183	−1.00565
$227$	3.32150	0.220456	0.110228	−	0.993906i	$-0.464842\pi$
$227$	3.32150	0.220456	0.110228	+	0.993906i	$0.464842\pi$
$228$	0	0
$229$	−19.0157	−1.25659	−0.628295	−	0.777975i	$-0.716247\pi$
$229$	−19.0157	−1.25659	−0.628295	+	0.777975i	$0.716247\pi$
$230$	26.8465	1.77021
$231$	2.05369	0.135123
$232$	−8.92325	−0.585840
$233$	−27.7929	−1.82077	−0.910386	−	0.413761i	$-0.864215\pi$
$233$	−27.7929	−1.82077	−0.910386	+	0.413761i	$0.864215\pi$
$234$	0.987964	0.0645852
$235$	−24.7036	−1.61148
$236$	−6.68280	−0.435013
$237$	−8.16749	−0.530535
$238$	−0.980683	−0.0635682
$239$	21.3012	1.37786	0.688929	−	0.724829i	$-0.258081\pi$
$239$	21.3012	1.37786	0.688929	+	0.724829i	$0.258081\pi$
$240$	−5.82914	−0.376270
$241$	−0.986833	−0.0635675	−0.0317838	−	0.999495i	$-0.510119\pi$
$241$	−0.986833	−0.0635675	−0.0317838	+	0.999495i	$0.510119\pi$
$242$	−9.71652	−0.624601
$243$	2.96331	0.190096
$244$	0.849200	0.0543645
$245$	3.21562	0.205439
$246$	9.34594	0.595876
$247$	0	0
$248$	2.23416	0.141869
$249$	−14.6654	−0.929384
$250$	1.09403	0.0691927
$251$	2.51135	0.158515	0.0792575	−	0.996854i	$-0.474745\pi$
$251$	2.51135	0.158515	0.0792575	+	0.996854i	$0.474745\pi$
$252$	−0.286090	−0.0180220
$253$	9.45841	0.594645
$254$	−7.17004	−0.449888
$255$	−5.71654	−0.357984
$256$	1.00000	0.0625000
$257$	26.5536	1.65637	0.828183	−	0.560458i	$-0.189375\pi$
$257$	26.5536	1.65637	0.828183	+	0.560458i	$0.189375\pi$
$258$	−15.7683	−0.981692
$259$	−0.709571	−0.0440906
$260$	11.1046	0.688678
$261$	−2.55286	−0.158018
$262$	16.8172	1.03897
$263$	23.3322	1.43873	0.719364	−	0.694634i	$-0.244433\pi$
$263$	23.3322	1.43873	0.719364	+	0.694634i	$0.244433\pi$
$264$	−2.05369	−0.126396
$265$	−22.9341	−1.40883
$266$	0	0
$267$	21.5255	1.31734
$268$	13.2676	0.810448
$269$	24.8757	1.51670	0.758349	−	0.651848i	$-0.226006\pi$
$269$	24.8757	1.51670	0.758349	+	0.651848i	$0.226006\pi$
$270$	15.8198	0.962760
$271$	−4.05400	−0.246263	−0.123132	−	0.992390i	$-0.539294\pi$
$271$	−4.05400	−0.246263	−0.123132	+	0.992390i	$0.539294\pi$
$272$	0.980683	0.0594627
$273$	6.26005	0.378875
$274$	10.1526	0.613340
$275$	6.04999	0.364828
$276$	−15.1343	−0.910979
$277$	1.11550	0.0670240	0.0335120	−	0.999438i	$-0.489331\pi$
$277$	1.11550	0.0670240	0.0335120	+	0.999438i	$0.489331\pi$
$278$	−1.66287	−0.0997326
$279$	0.639171	0.0382662
$280$	−3.21562	−0.192170
$281$	13.5382	0.807619	0.403809	−	0.914843i	$-0.367686\pi$
$281$	13.5382	0.807619	0.403809	+	0.914843i	$0.367686\pi$
$282$	13.9263	0.829297
$283$	20.1172	1.19584	0.597922	−	0.801554i	$-0.295993\pi$
$283$	20.1172	1.19584	0.597922	+	0.801554i	$0.295993\pi$
$284$	11.0807	0.657521
$285$	0	0
$286$	3.91231	0.231340
$287$	5.15565	0.304328
$288$	0.286090	0.0168580
$289$	−16.0383	−0.943427
$290$	−28.6938	−1.68496
$291$	−28.7942	−1.68795
$292$	5.65554	0.330965
$293$	−15.0757	−0.880734	−0.440367	−	0.897818i	$-0.645152\pi$
$293$	−15.0757	−0.880734	−0.440367	+	0.897818i	$0.645152\pi$
$294$	−1.81276	−0.105722
$295$	−21.4893	−1.25116
$296$	0.709571	0.0412430
$297$	5.57353	0.323409
$298$	1.32351	0.0766687
$299$	28.8311	1.66734
$300$	−9.68053	−0.558906
$301$	−8.69852	−0.501374
$302$	10.6378	0.612134
$303$	−25.9406	−1.49025
$304$	0	0
$305$	2.73071	0.156360
$306$	0.280564	0.0160388
$307$	29.7919	1.70031	0.850157	−	0.526529i	$-0.176507\pi$
$307$	29.7919	1.70031	0.850157	+	0.526529i	$0.176507\pi$
$308$	−1.13291	−0.0645535
$309$	9.59720	0.545965
$310$	7.18421	0.408035
$311$	11.9165	0.675720	0.337860	−	0.941196i	$-0.390297\pi$
$311$	11.9165	0.675720	0.337860	+	0.941196i	$0.390297\pi$
$312$	−6.26005	−0.354405
$313$	19.3212	1.09210	0.546049	−	0.837753i	$-0.316131\pi$
$313$	19.3212	1.09210	0.546049	+	0.837753i	$0.316131\pi$
$314$	16.6290	0.938427
$315$	−0.919959	−0.0518338
$316$	4.50556	0.253458
$317$	−9.05969	−0.508843	−0.254422	−	0.967093i	$-0.581885\pi$
$317$	−9.05969	−0.508843	−0.254422	+	0.967093i	$0.581885\pi$
$318$	12.9288	0.725009
$319$	−10.1092	−0.566008
$320$	3.21562	0.179759
$321$	9.67373	0.539935
$322$	−8.34878	−0.465259
$323$	0	0
$324$	−9.77642	−0.543135
$325$	18.4415	1.02295
$326$	−8.78895	−0.486775
$327$	−3.40213	−0.188138
$328$	−5.15565	−0.284673
$329$	7.68237	0.423543
$330$	−6.60389	−0.363532
$331$	12.3504	0.678841	0.339421	−	0.940635i	$-0.389769\pi$
$331$	12.3504	0.678841	0.339421	+	0.940635i	$0.389769\pi$
$332$	8.09012	0.444003
$333$	0.203001	0.0111244
$334$	−6.97125	−0.381450
$335$	42.6636	2.33096
$336$	1.81276	0.0988940
$337$	17.1079	0.931927	0.465964	−	0.884804i	$-0.345708\pi$
$337$	17.1079	0.931927	0.465964	+	0.884804i	$0.345708\pi$
$338$	−1.07452	−0.0584462
$339$	27.4057	1.48848
$340$	3.15351	0.171023
$341$	2.53110	0.137067
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	8.69852	0.468993
$345$	−48.6662	−2.62010
$346$	9.75988	0.524695
$347$	−29.3712	−1.57673	−0.788364	−	0.615209i	$-0.789072\pi$
$347$	−29.3712	−1.57673	−0.788364	+	0.615209i	$0.789072\pi$
$348$	16.1757	0.867108
$349$	14.6169	0.782422	0.391211	−	0.920301i	$-0.372056\pi$
$349$	14.6169	0.782422	0.391211	+	0.920301i	$0.372056\pi$
$350$	−5.34022	−0.285447
$351$	16.9892	0.906817
$352$	1.13291	0.0603842
$353$	16.2848	0.866754	0.433377	−	0.901213i	$-0.357322\pi$
$353$	16.2848	0.866754	0.433377	+	0.901213i	$0.357322\pi$
$354$	12.1143	0.643867
$355$	35.6315	1.89112
$356$	−11.8744	−0.629344
$357$	1.77774	0.0940880
$358$	−16.0185	−0.846604
$359$	−8.33535	−0.439923	−0.219962	−	0.975509i	$-0.570593\pi$
$359$	−8.33535	−0.439923	−0.219962	+	0.975509i	$0.570593\pi$
$360$	0.919959	0.0484861
$361$	0	0
$362$	−9.54585	−0.501719
$363$	17.6137	0.924479
$364$	−3.45333	−0.181004
$365$	18.1861	0.951902
$366$	−1.53939	−0.0804654
$367$	−28.8703	−1.50702	−0.753510	−	0.657437i	$-0.771641\pi$
$367$	−28.8703	−1.50702	−0.753510	+	0.657437i	$0.771641\pi$
$368$	8.34878	0.435210
$369$	−1.47498	−0.0767845
$370$	2.28171	0.118621
$371$	7.13209	0.370280
$372$	−4.04999	−0.209982
$373$	−20.4623	−1.05950	−0.529750	−	0.848154i	$-0.677714\pi$
$373$	−20.4623	−1.05950	−0.529750	+	0.848154i	$0.677714\pi$
$374$	1.11102	0.0574497
$375$	−1.98322	−0.102413
$376$	−7.68237	−0.396188
$377$	−30.8149	−1.58705
$378$	−4.91966	−0.253040
$379$	32.0182	1.64467	0.822333	−	0.569007i	$-0.192672\pi$
$379$	32.0182	1.64467	0.822333	+	0.569007i	$0.192672\pi$
$380$	0	0
$381$	12.9975	0.665884
$382$	12.0046	0.614210
$383$	28.5167	1.45714	0.728569	−	0.684973i	$-0.240186\pi$
$383$	28.5167	1.45714	0.728569	+	0.684973i	$0.240186\pi$
$384$	−1.81276	−0.0925069
$385$	−3.64301	−0.185665
$386$	13.2181	0.672783
$387$	2.48856	0.126501
$388$	15.8842	0.806398
$389$	−24.0734	−1.22057	−0.610285	−	0.792182i	$-0.708945\pi$
$389$	−24.0734	−1.22057	−0.610285	+	0.792182i	$0.708945\pi$
$390$	−20.1299	−1.01932
$391$	8.18751	0.414060
$392$	1.00000	0.0505076
$393$	−30.4854	−1.53779
$394$	−11.6270	−0.585759
$395$	14.4882	0.728979
$396$	0.324114	0.0162874
$397$	36.9192	1.85292	0.926461	−	0.376392i	$-0.122835\pi$
$397$	36.9192	1.85292	0.926461	+	0.376392i	$0.122835\pi$
$398$	9.98653	0.500579
$399$	0	0
$400$	5.34022	0.267011
$401$	−22.3797	−1.11759	−0.558794	−	0.829306i	$-0.688736\pi$
$401$	−22.3797	−1.11759	−0.558794	+	0.829306i	$0.688736\pi$
$402$	−24.0509	−1.19955
$403$	7.71528	0.384325
$404$	14.3100	0.711951
$405$	−31.4373	−1.56213
$406$	8.92325	0.442853
$407$	0.803879	0.0398468
$408$	−1.77774	−0.0880113
$409$	−1.54331	−0.0763117	−0.0381558	−	0.999272i	$-0.512148\pi$
$409$	−1.54331	−0.0763117	−0.0381558	+	0.999272i	$0.512148\pi$
$410$	−16.5786	−0.818760
$411$	−18.4042	−0.907810
$412$	−5.29425	−0.260829
$413$	6.68280	0.328839
$414$	2.38851	0.117389
$415$	26.0148	1.27702
$416$	3.45333	0.169313
$417$	3.01439	0.147615
$418$	0	0
$419$	−6.91279	−0.337712	−0.168856	−	0.985641i	$-0.554007\pi$
$419$	−6.91279	−0.337712	−0.168856	+	0.985641i	$0.554007\pi$
$420$	5.82914	0.284433
$421$	6.34362	0.309169	0.154585	−	0.987980i	$-0.450596\pi$
$421$	6.34362	0.309169	0.154585	+	0.987980i	$0.450596\pi$
$422$	−18.6709	−0.908883
$423$	−2.19785	−0.106863
$424$	−7.13209	−0.346365
$425$	5.23707	0.254035
$426$	−20.0867	−0.973204
$427$	−0.849200	−0.0410957
$428$	−5.33647	−0.257948
$429$	−7.09206	−0.342408
$430$	27.9712	1.34889
$431$	5.07140	0.244281	0.122140	−	0.992513i	$-0.461024\pi$
$431$	5.07140	0.244281	0.122140	+	0.992513i	$0.461024\pi$
$432$	4.91966	0.236697
$433$	−40.0076	−1.92264	−0.961322	−	0.275427i	$-0.911181\pi$
$433$	−40.0076	−1.92264	−0.961322	+	0.275427i	$0.911181\pi$
$434$	−2.23416	−0.107243
$435$	52.0149	2.49392
$436$	1.87677	0.0898811
$437$	0	0
$438$	−10.2521	−0.489865
$439$	−20.1943	−0.963819	−0.481910	−	0.876221i	$-0.660057\pi$
$439$	−20.1943	−0.963819	−0.481910	+	0.876221i	$0.660057\pi$
$440$	3.64301	0.173673
$441$	0.286090	0.0136234
$442$	3.38662	0.161085
$443$	−40.3071	−1.91505	−0.957523	−	0.288356i	$-0.906891\pi$
$443$	−40.3071	−1.91505	−0.957523	+	0.288356i	$0.906891\pi$
$444$	−1.28628	−0.0610442
$445$	−38.1837	−1.81008
$446$	19.4556	0.921248
$447$	−2.39920	−0.113478
$448$	−1.00000	−0.0472456
$449$	23.7357	1.12016	0.560080	−	0.828439i	$-0.310771\pi$
$449$	23.7357	1.12016	0.560080	+	0.828439i	$0.310771\pi$
$450$	1.52779	0.0720206
$451$	−5.84088	−0.275036
$452$	−15.1183	−0.711103
$453$	−19.2837	−0.906026
$454$	3.32150	0.155886
$455$	−11.1046	−0.520592
$456$	0	0
$457$	−15.8083	−0.739481	−0.369741	−	0.929135i	$-0.620553\pi$
$457$	−15.8083	−0.739481	−0.369741	+	0.929135i	$0.620553\pi$
$458$	−19.0157	−0.888543
$459$	4.82463	0.225194
$460$	26.8465	1.25173
$461$	−17.0288	−0.793109	−0.396555	−	0.918011i	$-0.629794\pi$
$461$	−17.0288	−0.793109	−0.396555	+	0.918011i	$0.629794\pi$
$462$	2.05369	0.0955463
$463$	−41.8119	−1.94316	−0.971581	−	0.236707i	$-0.923932\pi$
$463$	−41.8119	−1.94316	−0.971581	+	0.236707i	$0.923932\pi$
$464$	−8.92325	−0.414251
$465$	−13.0232	−0.603938
$466$	−27.7929	−1.28748
$467$	−8.42744	−0.389975	−0.194988	−	0.980806i	$-0.562467\pi$
$467$	−8.42744	−0.389975	−0.194988	+	0.980806i	$0.562467\pi$
$468$	0.987964	0.0456687
$469$	−13.2676	−0.612641
$470$	−24.7036	−1.13949
$471$	−30.1443	−1.38898
$472$	−6.68280	−0.307601
$473$	9.85463	0.453116
$474$	−8.16749	−0.375145
$475$	0	0
$476$	−0.980683	−0.0449495
$477$	−2.04042	−0.0934246
$478$	21.3012	0.974293
$479$	−32.7224	−1.49512	−0.747562	−	0.664192i	$-0.768776\pi$
$479$	−32.7224	−1.49512	−0.747562	+	0.664192i	$0.768776\pi$
$480$	−5.82914	−0.266063
$481$	2.45038	0.111728
$482$	−0.986833	−0.0449490
$483$	15.1343	0.688635
$484$	−9.71652	−0.441660
$485$	51.0775	2.31931
$486$	2.96331	0.134418
$487$	−0.832868	−0.0377409	−0.0188704	−	0.999822i	$-0.506007\pi$
$487$	−0.832868	−0.0377409	−0.0188704	+	0.999822i	$0.506007\pi$
$488$	0.849200	0.0384415
$489$	15.9322	0.720480
$490$	3.21562	0.145267
$491$	6.07853	0.274320	0.137160	−	0.990549i	$-0.456202\pi$
$491$	6.07853	0.274320	0.137160	+	0.990549i	$0.456202\pi$
$492$	9.34594	0.421348
$493$	−8.75088	−0.394120
$494$	0	0
$495$	1.04223	0.0468447
$496$	2.23416	0.100317
$497$	−11.0807	−0.497039
$498$	−14.6654	−0.657174
$499$	6.24888	0.279738	0.139869	−	0.990170i	$-0.455332\pi$
$499$	6.24888	0.279738	0.139869	+	0.990170i	$0.455332\pi$
$500$	1.09403	0.0489266
$501$	12.6372	0.564588
$502$	2.51135	0.112087
$503$	−8.71977	−0.388795	−0.194398	−	0.980923i	$-0.562275\pi$
$503$	−8.71977	−0.388795	−0.194398	+	0.980923i	$0.562275\pi$
$504$	−0.286090	−0.0127435
$505$	46.0157	2.04767
$506$	9.45841	0.420477
$507$	1.94785	0.0865069
$508$	−7.17004	−0.318119
$509$	−42.5864	−1.88761	−0.943805	−	0.330502i	$-0.892782\pi$
$509$	−42.5864	−1.88761	−0.943805	+	0.330502i	$0.892782\pi$
$510$	−5.71654	−0.253133
$511$	−5.65554	−0.250186
$512$	1.00000	0.0441942
$513$	0	0
$514$	26.5536	1.17123
$515$	−17.0243	−0.750181
$516$	−15.7683	−0.694161
$517$	−8.70342	−0.382776
$518$	−0.709571	−0.0311768
$519$	−17.6923	−0.776606
$520$	11.1046	0.486969
$521$	5.32471	0.233280	0.116640	−	0.993174i	$-0.462788\pi$
$521$	5.32471	0.233280	0.116640	+	0.993174i	$0.462788\pi$
$522$	−2.55286	−0.111735
$523$	−27.7416	−1.21305	−0.606527	−	0.795063i	$-0.707438\pi$
$523$	−27.7416	−1.21305	−0.606527	+	0.795063i	$0.707438\pi$
$524$	16.8172	0.734661
$525$	9.68053	0.422493
$526$	23.3322	1.01733
$527$	2.19100	0.0954415
$528$	−2.05369	−0.0893753
$529$	46.7021	2.03053
$530$	−22.9341	−0.996194
$531$	−1.91188	−0.0829687
$532$	0	0
$533$	−17.8042	−0.771184
$534$	21.5255	0.931498
$535$	−17.1601	−0.741895
$536$	13.2676	0.573073
$537$	29.0376	1.25307
$538$	24.8757	1.07247
$539$	1.13291	0.0487978
$540$	15.8198	0.680774
$541$	−17.9800	−0.773019	−0.386509	−	0.922285i	$-0.626319\pi$
$541$	−17.9800	−0.773019	−0.386509	+	0.922285i	$0.626319\pi$
$542$	−4.05400	−0.174134
$543$	17.3043	0.742599
$544$	0.980683	0.0420464
$545$	6.03499	0.258511
$546$	6.26005	0.267905
$547$	−9.93522	−0.424799	−0.212400	−	0.977183i	$-0.568128\pi$
$547$	−9.93522	−0.424799	−0.212400	+	0.977183i	$0.568128\pi$
$548$	10.1526	0.433697
$549$	0.242948	0.0103688
$550$	6.04999	0.257972
$551$	0	0
$552$	−15.1343	−0.644159
$553$	−4.50556	−0.191596
$554$	1.11550	0.0473931
$555$	−4.13619	−0.175572
$556$	−1.66287	−0.0705216
$557$	1.46867	0.0622295	0.0311147	−	0.999516i	$-0.490094\pi$
$557$	1.46867	0.0622295	0.0311147	+	0.999516i	$0.490094\pi$
$558$	0.639171	0.0270583
$559$	30.0389	1.27051
$560$	−3.21562	−0.135885
$561$	−2.01402	−0.0850319
$562$	13.5382	0.571073
$563$	9.34957	0.394037	0.197019	−	0.980400i	$-0.436874\pi$
$563$	9.34957	0.394037	0.197019	+	0.980400i	$0.436874\pi$
$564$	13.9263	0.586402
$565$	−48.6146	−2.04523
$566$	20.1172	0.845589
$567$	9.77642	0.410571
$568$	11.0807	0.464938
$569$	−36.1711	−1.51637	−0.758185	−	0.652039i	$-0.773914\pi$
$569$	−36.1711	−1.51637	−0.758185	+	0.652039i	$0.773914\pi$
$570$	0	0
$571$	−28.6109	−1.19733	−0.598665	−	0.801000i	$-0.704302\pi$
$571$	−28.6109	−1.19733	−0.598665	+	0.801000i	$0.704302\pi$
$572$	3.91231	0.163582
$573$	−21.7615	−0.909099
$574$	5.15565	0.215193
$575$	44.5844	1.85930
$576$	0.286090	0.0119204
$577$	−7.62210	−0.317312	−0.158656	−	0.987334i	$-0.550716\pi$
$577$	−7.62210	−0.317312	−0.158656	+	0.987334i	$0.550716\pi$
$578$	−16.0383	−0.667104
$579$	−23.9612	−0.995794
$580$	−28.6938	−1.19144
$581$	−8.09012	−0.335635
$582$	−28.7942	−1.19356
$583$	−8.08001	−0.334640
$584$	5.65554	0.234028
$585$	3.17692	0.131349
$586$	−15.0757	−0.622773
$587$	29.2446	1.20705	0.603527	−	0.797342i	$-0.293761\pi$
$587$	29.2446	1.20705	0.603527	+	0.797342i	$0.293761\pi$
$588$	−1.81276	−0.0747569
$589$	0	0
$590$	−21.4893	−0.884702
$591$	21.0769	0.866988
$592$	0.709571	0.0291632
$593$	42.1707	1.73174	0.865871	−	0.500267i	$-0.166765\pi$
$593$	42.1707	1.73174	0.865871	+	0.500267i	$0.166765\pi$
$594$	5.57353	0.228685
$595$	−3.15351	−0.129281
$596$	1.32351	0.0542130
$597$	−18.1032	−0.740913
$598$	28.8311	1.17899
$599$	24.1460	0.986581	0.493290	−	0.869865i	$-0.335794\pi$
$599$	24.1460	0.986581	0.493290	+	0.869865i	$0.335794\pi$
$600$	−9.68053	−0.395206
$601$	10.0723	0.410859	0.205429	−	0.978672i	$-0.434141\pi$
$601$	10.0723	0.410859	0.205429	+	0.978672i	$0.434141\pi$
$602$	−8.69852	−0.354525
$603$	3.79573	0.154574
$604$	10.6378	0.432844
$605$	−31.2446	−1.27028
$606$	−25.9406	−1.05377
$607$	24.9744	1.01368	0.506839	−	0.862040i	$-0.330814\pi$
$607$	24.9744	1.01368	0.506839	+	0.862040i	$0.330814\pi$
$608$	0	0
$609$	−16.1757	−0.655472
$610$	2.73071	0.110563
$611$	−26.5297	−1.07328
$612$	0.280564	0.0113411
$613$	6.71068	0.271042	0.135521	−	0.990774i	$-0.456729\pi$
$613$	6.71068	0.271042	0.135521	+	0.990774i	$0.456729\pi$
$614$	29.7919	1.20230
$615$	30.0530	1.21185
$616$	−1.13291	−0.0456462
$617$	29.0107	1.16793	0.583964	−	0.811780i	$-0.301501\pi$
$617$	29.0107	1.16793	0.583964	+	0.811780i	$0.301501\pi$
$618$	9.59720	0.386056
$619$	14.0910	0.566365	0.283183	−	0.959066i	$-0.408610\pi$
$619$	14.0910	0.566365	0.283183	+	0.959066i	$0.408610\pi$
$620$	7.18421	0.288525
$621$	41.0732	1.64821
$622$	11.9165	0.477806
$623$	11.8744	0.475739
$624$	−6.26005	−0.250602
$625$	−23.1831	−0.927325
$626$	19.3212	0.772230
$627$	0	0
$628$	16.6290	0.663568
$629$	0.695864	0.0277459
$630$	−0.919959	−0.0366520
$631$	29.6980	1.18226	0.591130	−	0.806576i	$-0.298682\pi$
$631$	29.6980	1.18226	0.591130	+	0.806576i	$0.298682\pi$
$632$	4.50556	0.179222
$633$	33.8457	1.34525
$634$	−9.05969	−0.359806
$635$	−23.0561	−0.914955
$636$	12.9288	0.512658
$637$	3.45333	0.136826
$638$	−10.1092	−0.400228
$639$	3.17010	0.125407
$640$	3.21562	0.127109
$641$	−44.1466	−1.74368	−0.871842	−	0.489787i	$-0.837074\pi$
$641$	−44.1466	−1.74368	−0.871842	+	0.489787i	$0.837074\pi$
$642$	9.67373	0.381792
$643$	−42.0797	−1.65946	−0.829731	−	0.558163i	$-0.811506\pi$
$643$	−42.0797	−1.65946	−0.829731	+	0.558163i	$0.811506\pi$
$644$	−8.34878	−0.328988
$645$	−50.7049	−1.99650
$646$	0	0
$647$	−18.4723	−0.726222	−0.363111	−	0.931746i	$-0.618285\pi$
$647$	−18.4723	−0.726222	−0.363111	+	0.931746i	$0.618285\pi$
$648$	−9.77642	−0.384054
$649$	−7.57100	−0.297188
$650$	18.4415	0.723337
$651$	4.04999	0.158731
$652$	−8.78895	−0.344202
$653$	−3.81769	−0.149398	−0.0746990	−	0.997206i	$-0.523800\pi$
$653$	−3.81769	−0.149398	−0.0746990	+	0.997206i	$0.523800\pi$
$654$	−3.40213	−0.133034
$655$	54.0776	2.11299
$656$	−5.15565	−0.201294
$657$	1.61799	0.0631240
$658$	7.68237	0.299490
$659$	−37.2252	−1.45009	−0.725043	−	0.688704i	$-0.758180\pi$
$659$	−37.2252	−1.45009	−0.725043	+	0.688704i	$0.758180\pi$
$660$	−6.60389	−0.257056
$661$	27.9177	1.08587	0.542935	−	0.839774i	$-0.317313\pi$
$661$	27.9177	1.08587	0.542935	+	0.839774i	$0.317313\pi$
$662$	12.3504	0.480013
$663$	−6.13912	−0.238424
$664$	8.09012	0.313958
$665$	0	0
$666$	0.203001	0.00786615
$667$	−74.4983	−2.88458
$668$	−6.97125	−0.269726
$669$	−35.2682	−1.36355
$670$	42.6636	1.64824
$671$	0.962066	0.0371402
$672$	1.81276	0.0699286
$673$	10.6858	0.411908	0.205954	−	0.978562i	$-0.433970\pi$
$673$	10.6858	0.411908	0.205954	+	0.978562i	$0.433970\pi$
$674$	17.1079	0.658972
$675$	26.2721	1.01121
$676$	−1.07452	−0.0413277
$677$	−40.5951	−1.56020	−0.780098	−	0.625658i	$-0.784831\pi$
$677$	−40.5951	−1.56020	−0.780098	+	0.625658i	$0.784831\pi$
$678$	27.4057	1.05251
$679$	−15.8842	−0.609579
$680$	3.15351	0.120931
$681$	−6.02107	−0.230728
$682$	2.53110	0.0969207
$683$	14.8494	0.568196	0.284098	−	0.958795i	$-0.408306\pi$
$683$	14.8494	0.568196	0.284098	+	0.958795i	$0.408306\pi$
$684$	0	0
$685$	32.6469	1.24737
$686$	−1.00000	−0.0381802
$687$	34.4708	1.31514
$688$	8.69852	0.331628
$689$	−24.6295	−0.938308
$690$	−48.6662	−1.85269
$691$	−8.41334	−0.320059	−0.160029	−	0.987112i	$-0.551159\pi$
$691$	−8.41334	−0.320059	−0.160029	+	0.987112i	$0.551159\pi$
$692$	9.75988	0.371015
$693$	−0.324114	−0.0123121
$694$	−29.3712	−1.11492
$695$	−5.34718	−0.202830
$696$	16.1757	0.613138
$697$	−5.05606	−0.191512
$698$	14.6169	0.553256
$699$	50.3817	1.90561
$700$	−5.34022	−0.201842
$701$	−31.9013	−1.20489	−0.602447	−	0.798159i	$-0.705808\pi$
$701$	−31.9013	−1.20489	−0.602447	+	0.798159i	$0.705808\pi$
$702$	16.9892	0.641216
$703$	0	0
$704$	1.13291	0.0426981
$705$	44.7816	1.68657
$706$	16.2848	0.612887
$707$	−14.3100	−0.538185
$708$	12.1143	0.455283
$709$	16.2546	0.610455	0.305227	−	0.952279i	$-0.401268\pi$
$709$	16.2546	0.610455	0.305227	+	0.952279i	$0.401268\pi$
$710$	35.6315	1.33723
$711$	1.28900	0.0483412
$712$	−11.8744	−0.445013
$713$	18.6525	0.698541
$714$	1.77774	0.0665303
$715$	12.5805	0.470484
$716$	−16.0185	−0.598639
$717$	−38.6139	−1.44206
$718$	−8.33535	−0.311073
$719$	−23.8877	−0.890862	−0.445431	−	0.895316i	$-0.646950\pi$
$719$	−23.8877	−0.890862	−0.445431	+	0.895316i	$0.646950\pi$
$720$	0.919959	0.0342848
$721$	5.29425	0.197168
$722$	0	0
$723$	1.78889	0.0665295
$724$	−9.54585	−0.354769
$725$	−47.6521	−1.76976
$726$	17.6137	0.653705
$727$	−29.3069	−1.08693	−0.543467	−	0.839431i	$-0.682889\pi$
$727$	−29.3069	−1.08693	−0.543467	+	0.839431i	$0.682889\pi$
$728$	−3.45333	−0.127989
$729$	23.9575	0.887315
$730$	18.1861	0.673096
$731$	8.53049	0.315512
$732$	−1.53939	−0.0568976
$733$	−2.36168	−0.0872307	−0.0436153	−	0.999048i	$-0.513888\pi$
$733$	−2.36168	−0.0872307	−0.0436153	+	0.999048i	$0.513888\pi$
$734$	−28.8703	−1.06562
$735$	−5.82914	−0.215011
$736$	8.34878	0.307740
$737$	15.0310	0.553673
$738$	−1.47498	−0.0542948
$739$	−13.3374	−0.490626	−0.245313	−	0.969444i	$-0.578891\pi$
$739$	−13.3374	−0.490626	−0.245313	+	0.969444i	$0.578891\pi$
$740$	2.28171	0.0838774
$741$	0	0
$742$	7.13209	0.261827
$743$	−0.297376	−0.0109097	−0.00545483	−	0.999985i	$-0.501736\pi$
$743$	−0.297376	−0.0109097	−0.00545483	+	0.999985i	$0.501736\pi$
$744$	−4.04999	−0.148480
$745$	4.25590	0.155924
$746$	−20.4623	−0.749180
$747$	2.31451	0.0846834
$748$	1.11102	0.0406231
$749$	5.33647	0.194990
$750$	−1.98322	−0.0724168
$751$	−11.4751	−0.418734	−0.209367	−	0.977837i	$-0.567140\pi$
$751$	−11.4751	−0.418734	−0.209367	+	0.977837i	$0.567140\pi$
$752$	−7.68237	−0.280147
$753$	−4.55247	−0.165901
$754$	−30.8149	−1.12221
$755$	34.2070	1.24492
$756$	−4.91966	−0.178926
$757$	−22.6508	−0.823257	−0.411628	−	0.911352i	$-0.635040\pi$
$757$	−22.6508	−0.823257	−0.411628	+	0.911352i	$0.635040\pi$
$758$	32.0182	1.16295
$759$	−17.1458	−0.622353
$760$	0	0
$761$	−22.8349	−0.827765	−0.413883	−	0.910330i	$-0.635828\pi$
$761$	−22.8349	−0.827765	−0.413883	+	0.910330i	$0.635828\pi$
$762$	12.9975	0.470851
$763$	−1.87677	−0.0679437
$764$	12.0046	0.434312
$765$	0.902188	0.0326187
$766$	28.5167	1.03035
$767$	−23.0779	−0.833294
$768$	−1.81276	−0.0654123
$769$	22.4858	0.810860	0.405430	−	0.914126i	$-0.367122\pi$
$769$	22.4858	0.810860	0.405430	+	0.914126i	$0.367122\pi$
$770$	−3.64301	−0.131285
$771$	−48.1352	−1.73355
$772$	13.2181	0.475730
$773$	27.7302	0.997384	0.498692	−	0.866779i	$-0.333814\pi$
$773$	27.7302	0.997384	0.498692	+	0.866779i	$0.333814\pi$
$774$	2.48856	0.0894496
$775$	11.9309	0.428571
$776$	15.8842	0.570209
$777$	1.28628	0.0461450
$778$	−24.0734	−0.863074
$779$	0	0
$780$	−20.1299	−0.720768
$781$	12.5535	0.449199
$782$	8.18751	0.292785
$783$	−43.8994	−1.56883
$784$	1.00000	0.0357143
$785$	53.4725	1.90851
$786$	−30.4854	−1.08738
$787$	−1.03483	−0.0368878	−0.0184439	−	0.999830i	$-0.505871\pi$
$787$	−1.03483	−0.0368878	−0.0184439	+	0.999830i	$0.505871\pi$
$788$	−11.6270	−0.414194
$789$	−42.2957	−1.50577
$790$	14.4882	0.515466
$791$	15.1183	0.537544
$792$	0.324114	0.0115169
$793$	2.93257	0.104139
$794$	36.9192	1.31021
$795$	41.5740	1.47448
$796$	9.98653	0.353963
$797$	18.8956	0.669317	0.334659	−	0.942339i	$-0.391379\pi$
$797$	18.8956	0.669317	0.334659	+	0.942339i	$0.391379\pi$
$798$	0	0
$799$	−7.53397	−0.266533
$800$	5.34022	0.188805
$801$	−3.39716	−0.120033
$802$	−22.3797	−0.790254
$803$	6.40721	0.226105
$804$	−24.0509	−0.848211
$805$	−26.8465	−0.946216
$806$	7.71528	0.271759
$807$	−45.0936	−1.58737
$808$	14.3100	0.503426
$809$	−35.3889	−1.24421	−0.622104	−	0.782934i	$-0.713722\pi$
$809$	−35.3889	−1.24421	−0.622104	+	0.782934i	$0.713722\pi$
$810$	−31.4373	−1.10459
$811$	−27.9254	−0.980595	−0.490297	−	0.871555i	$-0.663112\pi$
$811$	−27.9254	−0.980595	−0.490297	+	0.871555i	$0.663112\pi$
$812$	8.92325	0.313145
$813$	7.34893	0.257738
$814$	0.803879	0.0281759
$815$	−28.2619	−0.989972
$816$	−1.77774	−0.0622334
$817$	0	0
$818$	−1.54331	−0.0539605
$819$	−0.987964	−0.0345223
$820$	−16.5786	−0.578951
$821$	36.8675	1.28668	0.643342	−	0.765579i	$-0.277547\pi$
$821$	36.8675	1.28668	0.643342	+	0.765579i	$0.277547\pi$
$822$	−18.4042	−0.641919
$823$	−39.8289	−1.38835	−0.694175	−	0.719807i	$-0.744230\pi$
$823$	−39.8289	−1.38835	−0.694175	+	0.719807i	$0.744230\pi$
$824$	−5.29425	−0.184434
$825$	−10.9672	−0.381827
$826$	6.68280	0.232524
$827$	36.4123	1.26618	0.633090	−	0.774078i	$-0.281786\pi$
$827$	36.4123	1.26618	0.633090	+	0.774078i	$0.281786\pi$
$828$	2.38851	0.0830063
$829$	8.09318	0.281088	0.140544	−	0.990074i	$-0.455115\pi$
$829$	8.09318	0.281088	0.140544	+	0.990074i	$0.455115\pi$
$830$	26.0148	0.902986
$831$	−2.02213	−0.0701470
$832$	3.45333	0.119723
$833$	0.980683	0.0339787
$834$	3.01439	0.104380
$835$	−22.4169	−0.775769
$836$	0	0
$837$	10.9913	0.379915
$838$	−6.91279	−0.238798
$839$	4.52138	0.156095	0.0780476	−	0.996950i	$-0.475131\pi$
$839$	4.52138	0.156095	0.0780476	+	0.996950i	$0.475131\pi$
$840$	5.82914	0.201125
$841$	50.6244	1.74567
$842$	6.34362	0.218616
$843$	−24.5414	−0.845250
$844$	−18.6709	−0.642677
$845$	−3.45525	−0.118864
$846$	−2.19785	−0.0755637
$847$	9.71652	0.333864
$848$	−7.13209	−0.244917
$849$	−36.4676	−1.25157
$850$	5.23707	0.179630
$851$	5.92405	0.203074
$852$	−20.0867	−0.688159
$853$	−30.3891	−1.04050	−0.520252	−	0.854013i	$-0.674162\pi$
$853$	−30.3891	−1.04050	−0.520252	+	0.854013i	$0.674162\pi$
$854$	−0.849200	−0.0290590
$855$	0	0
$856$	−5.33647	−0.182397
$857$	−28.1300	−0.960901	−0.480451	−	0.877022i	$-0.659527\pi$
$857$	−28.1300	−0.960901	−0.480451	+	0.877022i	$0.659527\pi$
$858$	−7.09206	−0.242119
$859$	−23.9143	−0.815946	−0.407973	−	0.912994i	$-0.633764\pi$
$859$	−23.9143	−0.815946	−0.407973	+	0.912994i	$0.633764\pi$
$860$	27.9712	0.953808
$861$	−9.34594	−0.318509
$862$	5.07140	0.172733
$863$	9.97260	0.339471	0.169736	−	0.985490i	$-0.445709\pi$
$863$	9.97260	0.339471	0.169736	+	0.985490i	$0.445709\pi$
$864$	4.91966	0.167370
$865$	31.3841	1.06709
$866$	−40.0076	−1.35951
$867$	29.0735	0.987387
$868$	−2.23416	−0.0758322
$869$	5.10439	0.173154
$870$	52.0149	1.76347
$871$	45.8174	1.55246
$872$	1.87677	0.0635555
$873$	4.54431	0.153802
$874$	0	0
$875$	−1.09403	−0.0369850
$876$	−10.2521	−0.346387
$877$	−23.8061	−0.803876	−0.401938	−	0.915667i	$-0.631663\pi$
$877$	−23.8061	−0.803876	−0.401938	+	0.915667i	$0.631663\pi$
$878$	−20.1943	−0.681523
$879$	27.3287	0.921773
$880$	3.64301	0.122806
$881$	0.713107	0.0240252	0.0120126	−	0.999928i	$-0.496176\pi$
$881$	0.713107	0.0240252	0.0120126	+	0.999928i	$0.496176\pi$
$882$	0.286090	0.00963317
$883$	−25.2152	−0.848558	−0.424279	−	0.905532i	$-0.639472\pi$
$883$	−25.2152	−0.848558	−0.424279	+	0.905532i	$0.639472\pi$
$884$	3.38662	0.113904
$885$	38.9550	1.30946
$886$	−40.3071	−1.35414
$887$	−27.0108	−0.906935	−0.453468	−	0.891273i	$-0.649813\pi$
$887$	−27.0108	−0.906935	−0.453468	+	0.891273i	$0.649813\pi$
$888$	−1.28628	−0.0431647
$889$	7.17004	0.240475
$890$	−38.1837	−1.27992
$891$	−11.0758	−0.371053
$892$	19.4556	0.651421
$893$	0	0
$894$	−2.39920	−0.0802412
$895$	−51.5094	−1.72177
$896$	−1.00000	−0.0334077
$897$	−52.2638	−1.74504
$898$	23.7357	0.792072
$899$	−19.9359	−0.664901
$900$	1.52779	0.0509262
$901$	−6.99432	−0.233015
$902$	−5.84088	−0.194480
$903$	15.7683	0.524737
$904$	−15.1183	−0.502826
$905$	−30.6958	−1.02036
$906$	−19.2837	−0.640657
$907$	−40.3001	−1.33814	−0.669071	−	0.743198i	$-0.733308\pi$
$907$	−40.3001	−1.33814	−0.669071	+	0.743198i	$0.733308\pi$
$908$	3.32150	0.110228
$909$	4.09397	0.135788
$910$	−11.1046	−0.368114
$911$	12.4904	0.413825	0.206913	−	0.978359i	$-0.433658\pi$
$911$	12.4904	0.413825	0.206913	+	0.978359i	$0.433658\pi$
$912$	0	0
$913$	9.16537	0.303329
$914$	−15.8083	−0.522892
$915$	−4.95011	−0.163646
$916$	−19.0157	−0.628295
$917$	−16.8172	−0.555352
$918$	4.82463	0.159236
$919$	−27.8474	−0.918603	−0.459301	−	0.888281i	$-0.651900\pi$
$919$	−27.8474	−0.918603	−0.459301	+	0.888281i	$0.651900\pi$
$920$	26.8465	0.885104
$921$	−54.0055	−1.77954
$922$	−17.0288	−0.560813
$923$	38.2655	1.25952
$924$	2.05369	0.0675614
$925$	3.78927	0.124590
$926$	−41.8119	−1.37402
$927$	−1.51463	−0.0497471
$928$	−8.92325	−0.292920
$929$	19.1870	0.629504	0.314752	−	0.949174i	$-0.398079\pi$
$929$	19.1870	0.629504	0.314752	+	0.949174i	$0.398079\pi$
$930$	−13.0232	−0.427048
$931$	0	0
$932$	−27.7929	−0.910386
$933$	−21.6017	−0.707206
$934$	−8.42744	−0.275754
$935$	3.57263	0.116838
$936$	0.987964	0.0322926
$937$	25.2937	0.826308	0.413154	−	0.910661i	$-0.364427\pi$
$937$	25.2937	0.826308	0.413154	+	0.910661i	$0.364427\pi$
$938$	−13.2676	−0.433202
$939$	−35.0246	−1.14299
$940$	−24.7036	−0.805742
$941$	−5.46589	−0.178183	−0.0890915	−	0.996023i	$-0.528396\pi$
$941$	−5.46589	−0.178183	−0.0890915	+	0.996023i	$0.528396\pi$
$942$	−30.1443	−0.982154
$943$	−43.0434	−1.40169
$944$	−6.68280	−0.217506
$945$	−15.8198	−0.514617
$946$	9.85463	0.320402
$947$	−47.4546	−1.54207	−0.771033	−	0.636795i	$-0.780260\pi$
$947$	−47.4546	−1.54207	−0.771033	+	0.636795i	$0.780260\pi$
$948$	−8.16749	−0.265268
$949$	19.5304	0.633984
$950$	0	0
$951$	16.4230	0.532553
$952$	−0.980683	−0.0317841
$953$	1.78076	0.0576844	0.0288422	−	0.999584i	$-0.490818\pi$
$953$	1.78076	0.0576844	0.0288422	+	0.999584i	$0.490818\pi$
$954$	−2.04042	−0.0660611
$955$	38.6023	1.24914
$956$	21.3012	0.688929
$957$	18.3256	0.592382
$958$	−32.7224	−1.05721
$959$	−10.1526	−0.327844
$960$	−5.82914	−0.188135
$961$	−26.0085	−0.838985
$962$	2.45038	0.0790035
$963$	−1.52671	−0.0491977
$964$	−0.986833	−0.0317838
$965$	42.5044	1.36826
$966$	15.1343	0.486939
$967$	−35.8285	−1.15217	−0.576083	−	0.817391i	$-0.695420\pi$
$967$	−35.8285	−1.15217	−0.576083	+	0.817391i	$0.695420\pi$
$968$	−9.71652	−0.312301
$969$	0	0
$970$	51.0775	1.64000
$971$	−20.7705	−0.666558	−0.333279	−	0.942828i	$-0.608155\pi$
$971$	−20.7705	−0.666558	−0.333279	+	0.942828i	$0.608155\pi$
$972$	2.96331	0.0950481
$973$	1.66287	0.0533093
$974$	−0.832868	−0.0266868
$975$	−33.4301	−1.07062
$976$	0.849200	0.0271822
$977$	29.6771	0.949455	0.474728	−	0.880133i	$-0.342547\pi$
$977$	29.6771	0.949455	0.474728	+	0.880133i	$0.342547\pi$
$978$	15.9322	0.509457
$979$	−13.4527	−0.429949
$980$	3.21562	0.102719
$981$	0.536926	0.0171427
$982$	6.07853	0.193974
$983$	25.4481	0.811669	0.405834	−	0.913947i	$-0.366981\pi$
$983$	25.4481	0.811669	0.405834	+	0.913947i	$0.366981\pi$
$984$	9.34594	0.297938
$985$	−37.3880	−1.19128
$986$	−8.75088	−0.278685
$987$	−13.9263	−0.443278
$988$	0	0
$989$	72.6221	2.30925
$990$	1.04223	0.0331242
$991$	6.59967	0.209646	0.104823	−	0.994491i	$-0.466572\pi$
$991$	6.59967	0.209646	0.104823	+	0.994491i	$0.466572\pi$
$992$	2.23416	0.0709346
$993$	−22.3883	−0.710473
$994$	−11.0807	−0.351460
$995$	32.1129	1.01805
$996$	−14.6654	−0.464692
$997$	−34.7578	−1.10079	−0.550396	−	0.834904i	$-0.685523\pi$
$997$	−34.7578	−1.10079	−0.550396	+	0.834904i	$0.685523\pi$
$998$	6.24888	0.197805
$999$	3.49085	0.110446

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5054.2.a.bk.1.2		9
19.4	even	9		266.2.u.c.225.3	✓	18
19.5	even	9		266.2.u.c.253.3	yes	18
19.18	odd	2		5054.2.a.bj.1.8		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
266.2.u.c.225.3	✓	18	19.4	even	9
266.2.u.c.253.3	yes	18	19.5	even	9
5054.2.a.bj.1.8		9	19.18	odd	2
5054.2.a.bk.1.2		9	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:	\( N \)	\(=\)	\( 5054 = 2 \cdot 7 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5054.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.81276 q^{3} +1.00000 q^{4} +3.21562 q^{5} -1.81276 q^{6} -1.00000 q^{7} +1.00000 q^{8} +0.286090 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.81276 q^{3} +1.00000 q^{4} +3.21562 q^{5} -1.81276 q^{6} -1.00000 q^{7} +1.00000 q^{8} +0.286090 q^{9} +3.21562 q^{10} +1.13291 q^{11} -1.81276 q^{12} +3.45333 q^{13} -1.00000 q^{14} -5.82914 q^{15} +1.00000 q^{16} +0.980683 q^{17} +0.286090 q^{18} +3.21562 q^{20} +1.81276 q^{21} +1.13291 q^{22} +8.34878 q^{23} -1.81276 q^{24} +5.34022 q^{25} +3.45333 q^{26} +4.91966 q^{27} -1.00000 q^{28} -8.92325 q^{29} -5.82914 q^{30} +2.23416 q^{31} +1.00000 q^{32} -2.05369 q^{33} +0.980683 q^{34} -3.21562 q^{35} +0.286090 q^{36} +0.709571 q^{37} -6.26005 q^{39} +3.21562 q^{40} -5.15565 q^{41} +1.81276 q^{42} +8.69852 q^{43} +1.13291 q^{44} +0.919959 q^{45} +8.34878 q^{46} -7.68237 q^{47} -1.81276 q^{48} +1.00000 q^{49} +5.34022 q^{50} -1.77774 q^{51} +3.45333 q^{52} -7.13209 q^{53} +4.91966 q^{54} +3.64301 q^{55} -1.00000 q^{56} -8.92325 q^{58} -6.68280 q^{59} -5.82914 q^{60} +0.849200 q^{61} +2.23416 q^{62} -0.286090 q^{63} +1.00000 q^{64} +11.1046 q^{65} -2.05369 q^{66} +13.2676 q^{67} +0.980683 q^{68} -15.1343 q^{69} -3.21562 q^{70} +11.0807 q^{71} +0.286090 q^{72} +5.65554 q^{73} +0.709571 q^{74} -9.68053 q^{75} -1.13291 q^{77} -6.26005 q^{78} +4.50556 q^{79} +3.21562 q^{80} -9.77642 q^{81} -5.15565 q^{82} +8.09012 q^{83} +1.81276 q^{84} +3.15351 q^{85} +8.69852 q^{86} +16.1757 q^{87} +1.13291 q^{88} -11.8744 q^{89} +0.919959 q^{90} -3.45333 q^{91} +8.34878 q^{92} -4.04999 q^{93} -7.68237 q^{94} -1.81276 q^{96} +15.8842 q^{97} +1.00000 q^{98} +0.324114 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} + 3 q^{3} + 9 q^{4} + 3 q^{5} + 3 q^{6} - 9 q^{7} + 9 q^{8} + 12 q^{9}+O(q^{10}) \) 9 * q + 9 * q^2 + 3 * q^3 + 9 * q^4 + 3 * q^5 + 3 * q^6 - 9 * q^7 + 9 * q^8 + 12 * q^9	\( 9 q + 9 q^{2} + 3 q^{3} + 9 q^{4} + 3 q^{5} + 3 q^{6} - 9 q^{7} + 9 q^{8} + 12 q^{9} + 3 q^{10} - 3 q^{11} + 3 q^{12} + 12 q^{13} - 9 q^{14} - 6 q^{15} + 9 q^{16} + 12 q^{17} + 12 q^{18} + 3 q^{20} - 3 q^{21} - 3 q^{22} + 6 q^{23} + 3 q^{24} + 12 q^{26} + 24 q^{27} - 9 q^{28} - 6 q^{29} - 6 q^{30} + 9 q^{31} + 9 q^{32} - 3 q^{33} + 12 q^{34} - 3 q^{35} + 12 q^{36} + 9 q^{37} + 33 q^{39} + 3 q^{40} + 3 q^{41} - 3 q^{42} + 21 q^{43} - 3 q^{44} + 18 q^{45} + 6 q^{46} + 21 q^{47} + 3 q^{48} + 9 q^{49} + 39 q^{51} + 12 q^{52} + 24 q^{54} + 24 q^{55} - 9 q^{56} - 6 q^{58} - 9 q^{59} - 6 q^{60} + 6 q^{61} + 9 q^{62} - 12 q^{63} + 9 q^{64} - 3 q^{65} - 3 q^{66} + 27 q^{67} + 12 q^{68} + 6 q^{69} - 3 q^{70} + 9 q^{71} + 12 q^{72} + 51 q^{73} + 9 q^{74} - 3 q^{75} + 3 q^{77} + 33 q^{78} + 24 q^{79} + 3 q^{80} - 3 q^{81} + 3 q^{82} + 9 q^{83} - 3 q^{84} + 6 q^{85} + 21 q^{86} - 3 q^{87} - 3 q^{88} + 9 q^{89} + 18 q^{90} - 12 q^{91} + 6 q^{92} + 3 q^{93} + 21 q^{94} + 3 q^{96} - 12 q^{97} + 9 q^{98} - 15 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 3 * q^3 + 9 * q^4 + 3 * q^5 + 3 * q^6 - 9 * q^7 + 9 * q^8 + 12 * q^9 + 3 * q^10 - 3 * q^11 + 3 * q^12 + 12 * q^13 - 9 * q^14 - 6 * q^15 + 9 * q^16 + 12 * q^17 + 12 * q^18 + 3 * q^20 - 3 * q^21 - 3 * q^22 + 6 * q^23 + 3 * q^24 + 12 * q^26 + 24 * q^27 - 9 * q^28 - 6 * q^29 - 6 * q^30 + 9 * q^31 + 9 * q^32 - 3 * q^33 + 12 * q^34 - 3 * q^35 + 12 * q^36 + 9 * q^37 + 33 * q^39 + 3 * q^40 + 3 * q^41 - 3 * q^42 + 21 * q^43 - 3 * q^44 + 18 * q^45 + 6 * q^46 + 21 * q^47 + 3 * q^48 + 9 * q^49 + 39 * q^51 + 12 * q^52 + 24 * q^54 + 24 * q^55 - 9 * q^56 - 6 * q^58 - 9 * q^59 - 6 * q^60 + 6 * q^61 + 9 * q^62 - 12 * q^63 + 9 * q^64 - 3 * q^65 - 3 * q^66 + 27 * q^67 + 12 * q^68 + 6 * q^69 - 3 * q^70 + 9 * q^71 + 12 * q^72 + 51 * q^73 + 9 * q^74 - 3 * q^75 + 3 * q^77 + 33 * q^78 + 24 * q^79 + 3 * q^80 - 3 * q^81 + 3 * q^82 + 9 * q^83 - 3 * q^84 + 6 * q^85 + 21 * q^86 - 3 * q^87 - 3 * q^88 + 9 * q^89 + 18 * q^90 - 12 * q^91 + 6 * q^92 + 3 * q^93 + 21 * q^94 + 3 * q^96 - 12 * q^97 + 9 * q^98 - 15 * q^99

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