LMFDB - Embedded newform 4026.2.a.bc.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4026,2,Mod(1,4026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4026, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4026 = 2 \cdot 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4026.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.1477718538$
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} - x^{8} - 30x^{7} + 7x^{6} + 284x^{5} + 100x^{4} - 777x^{3} - 250x^{2} + 574x - 68 $ x^9 - x^8 - 30x^7 + 7x^6 + 284x^5 + 100x^4 - 777x^3 - 250x^2 + 574*x - 68
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-3.36977$ of defining polynomial
Character	$\chi$	$=$	4026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.36977 q^{5} +1.00000 q^{6} +4.52139 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.36977 q^{5} +1.00000 q^{6} +4.52139 q^{7} +1.00000 q^{8} +1.00000 q^{9} +4.36977 q^{10} +1.00000 q^{11} +1.00000 q^{12} -6.17357 q^{13} +4.52139 q^{14} +4.36977 q^{15} +1.00000 q^{16} +4.36848 q^{17} +1.00000 q^{18} -5.40291 q^{19} +4.36977 q^{20} +4.52139 q^{21} +1.00000 q^{22} -7.65005 q^{23} +1.00000 q^{24} +14.0949 q^{25} -6.17357 q^{26} +1.00000 q^{27} +4.52139 q^{28} -7.78539 q^{29} +4.36977 q^{30} -1.28028 q^{31} +1.00000 q^{32} +1.00000 q^{33} +4.36848 q^{34} +19.7575 q^{35} +1.00000 q^{36} -0.611833 q^{37} -5.40291 q^{38} -6.17357 q^{39} +4.36977 q^{40} +9.12644 q^{41} +4.52139 q^{42} -9.01275 q^{43} +1.00000 q^{44} +4.36977 q^{45} -7.65005 q^{46} -0.764742 q^{47} +1.00000 q^{48} +13.4430 q^{49} +14.0949 q^{50} +4.36848 q^{51} -6.17357 q^{52} -0.479321 q^{53} +1.00000 q^{54} +4.36977 q^{55} +4.52139 q^{56} -5.40291 q^{57} -7.78539 q^{58} +7.96627 q^{59} +4.36977 q^{60} -1.00000 q^{61} -1.28028 q^{62} +4.52139 q^{63} +1.00000 q^{64} -26.9771 q^{65} +1.00000 q^{66} -6.16309 q^{67} +4.36848 q^{68} -7.65005 q^{69} +19.7575 q^{70} +8.06263 q^{71} +1.00000 q^{72} -6.83739 q^{73} -0.611833 q^{74} +14.0949 q^{75} -5.40291 q^{76} +4.52139 q^{77} -6.17357 q^{78} +2.99625 q^{79} +4.36977 q^{80} +1.00000 q^{81} +9.12644 q^{82} -12.1436 q^{83} +4.52139 q^{84} +19.0893 q^{85} -9.01275 q^{86} -7.78539 q^{87} +1.00000 q^{88} +10.2015 q^{89} +4.36977 q^{90} -27.9131 q^{91} -7.65005 q^{92} -1.28028 q^{93} -0.764742 q^{94} -23.6095 q^{95} +1.00000 q^{96} -12.3249 q^{97} +13.4430 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 9 q^{2} + 9 q^{3} + 9 q^{4} + 8 q^{5} + 9 q^{6} + 9 q^{7} + 9 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q + 9 * q^2 + 9 * q^3 + 9 * q^4 + 8 * q^5 + 9 * q^6 + 9 * q^7 + 9 * q^8 + 9 * q^9	\( 9 q + 9 q^{2} + 9 q^{3} + 9 q^{4} + 8 q^{5} + 9 q^{6} + 9 q^{7} + 9 q^{8} + 9 q^{9} + 8 q^{10} + 9 q^{11} + 9 q^{12} + 8 q^{13} + 9 q^{14} + 8 q^{15} + 9 q^{16} + q^{17} + 9 q^{18} + 5 q^{19} + 8 q^{20} + 9 q^{21} + 9 q^{22} - q^{23} + 9 q^{24} + 23 q^{25} + 8 q^{26} + 9 q^{27} + 9 q^{28} - 14 q^{29} + 8 q^{30} + 25 q^{31} + 9 q^{32} + 9 q^{33} + q^{34} + 5 q^{35} + 9 q^{36} + 16 q^{37} + 5 q^{38} + 8 q^{39} + 8 q^{40} + 5 q^{41} + 9 q^{42} + 5 q^{43} + 9 q^{44} + 8 q^{45} - q^{46} + 8 q^{47} + 9 q^{48} + 30 q^{49} + 23 q^{50} + q^{51} + 8 q^{52} + q^{53} + 9 q^{54} + 8 q^{55} + 9 q^{56} + 5 q^{57} - 14 q^{58} + 4 q^{59} + 8 q^{60} - 9 q^{61} + 25 q^{62} + 9 q^{63} + 9 q^{64} - 14 q^{65} + 9 q^{66} - 4 q^{67} + q^{68} - q^{69} + 5 q^{70} + 20 q^{71} + 9 q^{72} + 15 q^{73} + 16 q^{74} + 23 q^{75} + 5 q^{76} + 9 q^{77} + 8 q^{78} - 2 q^{79} + 8 q^{80} + 9 q^{81} + 5 q^{82} + 21 q^{83} + 9 q^{84} - 16 q^{85} + 5 q^{86} - 14 q^{87} + 9 q^{88} + 10 q^{89} + 8 q^{90} - 19 q^{91} - q^{92} + 25 q^{93} + 8 q^{94} - 7 q^{95} + 9 q^{96} + 3 q^{97} + 30 q^{98} + 9 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 9 * q^3 + 9 * q^4 + 8 * q^5 + 9 * q^6 + 9 * q^7 + 9 * q^8 + 9 * q^9 + 8 * q^10 + 9 * q^11 + 9 * q^12 + 8 * q^13 + 9 * q^14 + 8 * q^15 + 9 * q^16 + q^17 + 9 * q^18 + 5 * q^19 + 8 * q^20 + 9 * q^21 + 9 * q^22 - q^23 + 9 * q^24 + 23 * q^25 + 8 * q^26 + 9 * q^27 + 9 * q^28 - 14 * q^29 + 8 * q^30 + 25 * q^31 + 9 * q^32 + 9 * q^33 + q^34 + 5 * q^35 + 9 * q^36 + 16 * q^37 + 5 * q^38 + 8 * q^39 + 8 * q^40 + 5 * q^41 + 9 * q^42 + 5 * q^43 + 9 * q^44 + 8 * q^45 - q^46 + 8 * q^47 + 9 * q^48 + 30 * q^49 + 23 * q^50 + q^51 + 8 * q^52 + q^53 + 9 * q^54 + 8 * q^55 + 9 * q^56 + 5 * q^57 - 14 * q^58 + 4 * q^59 + 8 * q^60 - 9 * q^61 + 25 * q^62 + 9 * q^63 + 9 * q^64 - 14 * q^65 + 9 * q^66 - 4 * q^67 + q^68 - q^69 + 5 * q^70 + 20 * q^71 + 9 * q^72 + 15 * q^73 + 16 * q^74 + 23 * q^75 + 5 * q^76 + 9 * q^77 + 8 * q^78 - 2 * q^79 + 8 * q^80 + 9 * q^81 + 5 * q^82 + 21 * q^83 + 9 * q^84 - 16 * q^85 + 5 * q^86 - 14 * q^87 + 9 * q^88 + 10 * q^89 + 8 * q^90 - 19 * q^91 - q^92 + 25 * q^93 + 8 * q^94 - 7 * q^95 + 9 * q^96 + 3 * q^97 + 30 * q^98 + 9 * 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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	4.36977	1.95422	0.977111	−	0.212729i	$-0.0682352\pi$
$5$	4.36977	1.95422	0.977111	+	0.212729i	$0.0682352\pi$
$6$	1.00000	0.408248
$7$	4.52139	1.70893	0.854463	−	0.519513i	$-0.173886\pi$
$7$	4.52139	1.70893	0.854463	+	0.519513i	$0.173886\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	4.36977	1.38184
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.00000	0.288675
$13$	−6.17357	−1.71224	−0.856121	−	0.516776i	$-0.827132\pi$
$13$	−6.17357	−1.71224	−0.856121	+	0.516776i	$0.827132\pi$
$14$	4.52139	1.20839
$15$	4.36977	1.12827
$16$	1.00000	0.250000
$17$	4.36848	1.05951	0.529756	−	0.848150i	$-0.322283\pi$
$17$	4.36848	1.05951	0.529756	+	0.848150i	$0.322283\pi$
$18$	1.00000	0.235702
$19$	−5.40291	−1.23951	−0.619756	−	0.784794i	$-0.712768\pi$
$19$	−5.40291	−1.23951	−0.619756	+	0.784794i	$0.712768\pi$
$20$	4.36977	0.977111
$21$	4.52139	0.986649
$22$	1.00000	0.213201
$23$	−7.65005	−1.59515	−0.797573	−	0.603222i	$-0.793883\pi$
$23$	−7.65005	−1.59515	−0.797573	+	0.603222i	$0.793883\pi$
$24$	1.00000	0.204124
$25$	14.0949	2.81899
$26$	−6.17357	−1.21074
$27$	1.00000	0.192450
$28$	4.52139	0.854463
$29$	−7.78539	−1.44571	−0.722856	−	0.690999i	$-0.757171\pi$
$29$	−7.78539	−1.44571	−0.722856	+	0.690999i	$0.757171\pi$
$30$	4.36977	0.797808
$31$	−1.28028	−0.229945	−0.114972	−	0.993369i	$-0.536678\pi$
$31$	−1.28028	−0.229945	−0.114972	+	0.993369i	$0.536678\pi$
$32$	1.00000	0.176777
$33$	1.00000	0.174078
$34$	4.36848	0.749189
$35$	19.7575	3.33962
$36$	1.00000	0.166667
$37$	−0.611833	−0.100585	−0.0502924	−	0.998735i	$-0.516015\pi$
$37$	−0.611833	−0.100585	−0.0502924	+	0.998735i	$0.516015\pi$
$38$	−5.40291	−0.876468
$39$	−6.17357	−0.988563
$40$	4.36977	0.690922
$41$	9.12644	1.42531	0.712655	−	0.701515i	$-0.247492\pi$
$41$	9.12644	1.42531	0.712655	+	0.701515i	$0.247492\pi$
$42$	4.52139	0.697666
$43$	−9.01275	−1.37443	−0.687215	−	0.726454i	$-0.741167\pi$
$43$	−9.01275	−1.37443	−0.687215	+	0.726454i	$0.741167\pi$
$44$	1.00000	0.150756
$45$	4.36977	0.651407
$46$	−7.65005	−1.12794
$47$	−0.764742	−0.111549	−0.0557746	−	0.998443i	$-0.517763\pi$
$47$	−0.764742	−0.111549	−0.0557746	+	0.998443i	$0.517763\pi$
$48$	1.00000	0.144338
$49$	13.4430	1.92043
$50$	14.0949	1.99332
$51$	4.36848	0.611710
$52$	−6.17357	−0.856121
$53$	−0.479321	−0.0658398	−0.0329199	−	0.999458i	$-0.510481\pi$
$53$	−0.479321	−0.0658398	−0.0329199	+	0.999458i	$0.510481\pi$
$54$	1.00000	0.136083
$55$	4.36977	0.589220
$56$	4.52139	0.604196
$57$	−5.40291	−0.715633
$58$	−7.78539	−1.02227
$59$	7.96627	1.03712	0.518560	−	0.855041i	$-0.326468\pi$
$59$	7.96627	1.03712	0.518560	+	0.855041i	$0.326468\pi$
$60$	4.36977	0.564135
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	−1.28028	−0.162596
$63$	4.52139	0.569642
$64$	1.00000	0.125000
$65$	−26.9771	−3.34610
$66$	1.00000	0.123091
$67$	−6.16309	−0.752941	−0.376470	−	0.926429i	$-0.622862\pi$
$67$	−6.16309	−0.752941	−0.376470	+	0.926429i	$0.622862\pi$
$68$	4.36848	0.529756
$69$	−7.65005	−0.920958
$70$	19.7575	2.36147
$71$	8.06263	0.956858	0.478429	−	0.878126i	$-0.341206\pi$
$71$	8.06263	0.956858	0.478429	+	0.878126i	$0.341206\pi$
$72$	1.00000	0.117851
$73$	−6.83739	−0.800256	−0.400128	−	0.916459i	$-0.631034\pi$
$73$	−6.83739	−0.800256	−0.400128	+	0.916459i	$0.631034\pi$
$74$	−0.611833	−0.0711242
$75$	14.0949	1.62754
$76$	−5.40291	−0.619756
$77$	4.52139	0.515260
$78$	−6.17357	−0.699019
$79$	2.99625	0.337104	0.168552	−	0.985693i	$-0.446091\pi$
$79$	2.99625	0.337104	0.168552	+	0.985693i	$0.446091\pi$
$80$	4.36977	0.488556
$81$	1.00000	0.111111
$82$	9.12644	1.00785
$83$	−12.1436	−1.33294	−0.666469	−	0.745533i	$-0.732195\pi$
$83$	−12.1436	−1.33294	−0.666469	+	0.745533i	$0.732195\pi$
$84$	4.52139	0.493324
$85$	19.0893	2.07052
$86$	−9.01275	−0.971869
$87$	−7.78539	−0.834682
$88$	1.00000	0.106600
$89$	10.2015	1.08136	0.540680	−	0.841228i	$-0.318167\pi$
$89$	10.2015	1.08136	0.540680	+	0.841228i	$0.318167\pi$
$90$	4.36977	0.460615
$91$	−27.9131	−2.92609
$92$	−7.65005	−0.797573
$93$	−1.28028	−0.132759
$94$	−0.764742	−0.0788771
$95$	−23.6095	−2.42228
$96$	1.00000	0.102062
$97$	−12.3249	−1.25140	−0.625701	−	0.780063i	$-0.715187\pi$
$97$	−12.3249	−1.25140	−0.625701	+	0.780063i	$0.715187\pi$
$98$	13.4430	1.35795
$99$	1.00000	0.100504
$100$	14.0949	1.40949
$101$	−15.7838	−1.57055	−0.785273	−	0.619150i	$-0.787477\pi$
$101$	−15.7838	−1.57055	−0.785273	+	0.619150i	$0.787477\pi$
$102$	4.36848	0.432544
$103$	−3.21980	−0.317256	−0.158628	−	0.987338i	$-0.550707\pi$
$103$	−3.21980	−0.317256	−0.158628	+	0.987338i	$0.550707\pi$
$104$	−6.17357	−0.605369
$105$	19.7575	1.92813
$106$	−0.479321	−0.0465557
$107$	1.80234	0.174239	0.0871195	−	0.996198i	$-0.472234\pi$
$107$	1.80234	0.174239	0.0871195	+	0.996198i	$0.472234\pi$
$108$	1.00000	0.0962250
$109$	4.31978	0.413760	0.206880	−	0.978366i	$-0.433669\pi$
$109$	4.31978	0.413760	0.206880	+	0.978366i	$0.433669\pi$
$110$	4.36977	0.416642
$111$	−0.611833	−0.0580727
$112$	4.52139	0.427231
$113$	6.52957	0.614250	0.307125	−	0.951669i	$-0.400633\pi$
$113$	6.52957	0.614250	0.307125	+	0.951669i	$0.400633\pi$
$114$	−5.40291	−0.506029
$115$	−33.4290	−3.11727
$116$	−7.78539	−0.722856
$117$	−6.17357	−0.570747
$118$	7.96627	0.733354
$119$	19.7516	1.81063
$120$	4.36977	0.398904
$121$	1.00000	0.0909091
$122$	−1.00000	−0.0905357
$123$	9.12644	0.822903
$124$	−1.28028	−0.114972
$125$	39.7428	3.55470
$126$	4.52139	0.402798
$127$	6.04195	0.536137	0.268068	−	0.963400i	$-0.413615\pi$
$127$	6.04195	0.536137	0.268068	+	0.963400i	$0.413615\pi$
$128$	1.00000	0.0883883
$129$	−9.01275	−0.793528
$130$	−26.9771	−2.36605
$131$	−0.440775	−0.0385107	−0.0192553	−	0.999815i	$-0.506130\pi$
$131$	−0.440775	−0.0385107	−0.0192553	+	0.999815i	$0.506130\pi$
$132$	1.00000	0.0870388
$133$	−24.4287	−2.11823
$134$	−6.16309	−0.532410
$135$	4.36977	0.376090
$136$	4.36848	0.374594
$137$	−23.2581	−1.98707	−0.993535	−	0.113524i	$-0.963786\pi$
$137$	−23.2581	−1.98707	−0.993535	+	0.113524i	$0.963786\pi$
$138$	−7.65005	−0.651216
$139$	−16.3664	−1.38818	−0.694088	−	0.719890i	$-0.744192\pi$
$139$	−16.3664	−1.38818	−0.694088	+	0.719890i	$0.744192\pi$
$140$	19.7575	1.66981
$141$	−0.764742	−0.0644029
$142$	8.06263	0.676601
$143$	−6.17357	−0.516260
$144$	1.00000	0.0833333
$145$	−34.0204	−2.82524
$146$	−6.83739	−0.565866
$147$	13.4430	1.10876
$148$	−0.611833	−0.0502924
$149$	7.80061	0.639051	0.319526	−	0.947578i	$-0.396476\pi$
$149$	7.80061	0.639051	0.319526	+	0.947578i	$0.396476\pi$
$150$	14.0949	1.15085
$151$	20.5763	1.67447	0.837236	−	0.546842i	$-0.184170\pi$
$151$	20.5763	1.67447	0.837236	+	0.546842i	$0.184170\pi$
$152$	−5.40291	−0.438234
$153$	4.36848	0.353171
$154$	4.52139	0.364344
$155$	−5.59453	−0.449363
$156$	−6.17357	−0.494281
$157$	8.51977	0.679952	0.339976	−	0.940434i	$-0.389581\pi$
$157$	8.51977	0.679952	0.339976	+	0.940434i	$0.389581\pi$
$158$	2.99625	0.238369
$159$	−0.479321	−0.0380126
$160$	4.36977	0.345461
$161$	−34.5889	−2.72599
$162$	1.00000	0.0785674
$163$	−15.6757	−1.22782	−0.613909	−	0.789377i	$-0.710404\pi$
$163$	−15.6757	−1.22782	−0.613909	+	0.789377i	$0.710404\pi$
$164$	9.12644	0.712655
$165$	4.36977	0.340186
$166$	−12.1436	−0.942529
$167$	−3.55356	−0.274982	−0.137491	−	0.990503i	$-0.543904\pi$
$167$	−3.55356	−0.274982	−0.137491	+	0.990503i	$0.543904\pi$
$168$	4.52139	0.348833
$169$	25.1130	1.93177
$170$	19.0893	1.46408
$171$	−5.40291	−0.413171
$172$	−9.01275	−0.687215
$173$	10.0811	0.766451	0.383225	−	0.923655i	$-0.374813\pi$
$173$	10.0811	0.766451	0.383225	+	0.923655i	$0.374813\pi$
$174$	−7.78539	−0.590209
$175$	63.7287	4.81744
$176$	1.00000	0.0753778
$177$	7.96627	0.598781
$178$	10.2015	0.764638
$179$	16.8091	1.25637	0.628187	−	0.778063i	$-0.283797\pi$
$179$	16.8091	1.25637	0.628187	+	0.778063i	$0.283797\pi$
$180$	4.36977	0.325704
$181$	−12.7394	−0.946915	−0.473457	−	0.880817i	$-0.656994\pi$
$181$	−12.7394	−0.946915	−0.473457	+	0.880817i	$0.656994\pi$
$182$	−27.9131	−2.06906
$183$	−1.00000	−0.0739221
$184$	−7.65005	−0.563969
$185$	−2.67357	−0.196565
$186$	−1.28028	−0.0938746
$187$	4.36848	0.319455
$188$	−0.764742	−0.0557746
$189$	4.52139	0.328883
$190$	−23.6095	−1.71281
$191$	−11.0407	−0.798877	−0.399439	−	0.916760i	$-0.630795\pi$
$191$	−11.0407	−0.798877	−0.399439	+	0.916760i	$0.630795\pi$
$192$	1.00000	0.0721688
$193$	2.31091	0.166343	0.0831715	−	0.996535i	$-0.473495\pi$
$193$	2.31091	0.166343	0.0831715	+	0.996535i	$0.473495\pi$
$194$	−12.3249	−0.884875
$195$	−26.9771	−1.93187
$196$	13.4430	0.960213
$197$	−19.4329	−1.38453	−0.692267	−	0.721641i	$-0.743388\pi$
$197$	−19.4329	−1.38453	−0.692267	+	0.721641i	$0.743388\pi$
$198$	1.00000	0.0710669
$199$	9.49175	0.672853	0.336426	−	0.941710i	$-0.390782\pi$
$199$	9.49175	0.672853	0.336426	+	0.941710i	$0.390782\pi$
$200$	14.0949	0.996662
$201$	−6.16309	−0.434711
$202$	−15.7838	−1.11054
$203$	−35.2008	−2.47061
$204$	4.36848	0.305855
$205$	39.8805	2.78537
$206$	−3.21980	−0.224334
$207$	−7.65005	−0.531715
$208$	−6.17357	−0.428060
$209$	−5.40291	−0.373727
$210$	19.7575	1.36339
$211$	−14.2323	−0.979791	−0.489895	−	0.871781i	$-0.662965\pi$
$211$	−14.2323	−0.979791	−0.489895	+	0.871781i	$0.662965\pi$
$212$	−0.479321	−0.0329199
$213$	8.06263	0.552442
$214$	1.80234	0.123206
$215$	−39.3837	−2.68594
$216$	1.00000	0.0680414
$217$	−5.78864	−0.392959
$218$	4.31978	0.292573
$219$	−6.83739	−0.462028
$220$	4.36977	0.294610
$221$	−26.9691	−1.81414
$222$	−0.611833	−0.0410636
$223$	−6.11859	−0.409731	−0.204865	−	0.978790i	$-0.565676\pi$
$223$	−6.11859	−0.409731	−0.204865	+	0.978790i	$0.565676\pi$
$224$	4.52139	0.302098
$225$	14.0949	0.939662
$226$	6.52957	0.434340
$227$	11.2276	0.745201	0.372600	−	0.927992i	$-0.378466\pi$
$227$	11.2276	0.745201	0.372600	+	0.927992i	$0.378466\pi$
$228$	−5.40291	−0.357816
$229$	19.3616	1.27945	0.639724	−	0.768605i	$-0.279049\pi$
$229$	19.3616	1.27945	0.639724	+	0.768605i	$0.279049\pi$
$230$	−33.4290	−2.20424
$231$	4.52139	0.297486
$232$	−7.78539	−0.511136
$233$	5.77018	0.378017	0.189009	−	0.981975i	$-0.439473\pi$
$233$	5.77018	0.378017	0.189009	+	0.981975i	$0.439473\pi$
$234$	−6.17357	−0.403579
$235$	−3.34175	−0.217992
$236$	7.96627	0.518560
$237$	2.99625	0.194627
$238$	19.7516	1.28031
$239$	21.9886	1.42232	0.711162	−	0.703028i	$-0.248169\pi$
$239$	21.9886	1.42232	0.711162	+	0.703028i	$0.248169\pi$
$240$	4.36977	0.282068
$241$	7.82691	0.504176	0.252088	−	0.967704i	$-0.418883\pi$
$241$	7.82691	0.504176	0.252088	+	0.967704i	$0.418883\pi$
$242$	1.00000	0.0642824
$243$	1.00000	0.0641500
$244$	−1.00000	−0.0640184
$245$	58.7428	3.75294
$246$	9.12644	0.581880
$247$	33.3553	2.12234
$248$	−1.28028	−0.0812978
$249$	−12.1436	−0.769572
$250$	39.7428	2.51355
$251$	−14.2970	−0.902420	−0.451210	−	0.892418i	$-0.649007\pi$
$251$	−14.2970	−0.902420	−0.451210	+	0.892418i	$0.649007\pi$
$252$	4.52139	0.284821
$253$	−7.65005	−0.480955
$254$	6.04195	0.379106
$255$	19.0893	1.19542
$256$	1.00000	0.0625000
$257$	−11.8679	−0.740298	−0.370149	−	0.928972i	$-0.620693\pi$
$257$	−11.8679	−0.740298	−0.370149	+	0.928972i	$0.620693\pi$
$258$	−9.01275	−0.561109
$259$	−2.76634	−0.171892
$260$	−26.9771	−1.67305
$261$	−7.78539	−0.481904
$262$	−0.440775	−0.0272312
$263$	−0.830033	−0.0511820	−0.0255910	−	0.999672i	$-0.508147\pi$
$263$	−0.830033	−0.0511820	−0.0255910	+	0.999672i	$0.508147\pi$
$264$	1.00000	0.0615457
$265$	−2.09452	−0.128666
$266$	−24.4287	−1.49782
$267$	10.2015	0.624324
$268$	−6.16309	−0.376470
$269$	2.06778	0.126075	0.0630375	−	0.998011i	$-0.479921\pi$
$269$	2.06778	0.126075	0.0630375	+	0.998011i	$0.479921\pi$
$270$	4.36977	0.265936
$271$	18.7718	1.14031	0.570154	−	0.821538i	$-0.306883\pi$
$271$	18.7718	1.14031	0.570154	+	0.821538i	$0.306883\pi$
$272$	4.36848	0.264878
$273$	−27.9131	−1.68938
$274$	−23.2581	−1.40507
$275$	14.0949	0.849956
$276$	−7.65005	−0.460479
$277$	−23.7427	−1.42656	−0.713280	−	0.700880i	$-0.752791\pi$
$277$	−23.7427	−1.42656	−0.713280	+	0.700880i	$0.752791\pi$
$278$	−16.3664	−0.981589
$279$	−1.28028	−0.0766483
$280$	19.7575	1.18073
$281$	15.2565	0.910126	0.455063	−	0.890459i	$-0.349617\pi$
$281$	15.2565	0.910126	0.455063	+	0.890459i	$0.349617\pi$
$282$	−0.764742	−0.0455397
$283$	10.0897	0.599770	0.299885	−	0.953975i	$-0.403052\pi$
$283$	10.0897	0.599770	0.299885	+	0.953975i	$0.403052\pi$
$284$	8.06263	0.478429
$285$	−23.6095	−1.39851
$286$	−6.17357	−0.365051
$287$	41.2642	2.43575
$288$	1.00000	0.0589256
$289$	2.08364	0.122567
$290$	−34.0204	−1.99775
$291$	−12.3249	−0.722497
$292$	−6.83739	−0.400128
$293$	−22.1467	−1.29382	−0.646911	−	0.762565i	$-0.723940\pi$
$293$	−22.1467	−1.29382	−0.646911	+	0.762565i	$0.723940\pi$
$294$	13.4430	0.784011
$295$	34.8108	2.02676
$296$	−0.611833	−0.0355621
$297$	1.00000	0.0580259
$298$	7.80061	0.451877
$299$	47.2282	2.73127
$300$	14.0949	0.813771
$301$	−40.7502	−2.34880
$302$	20.5763	1.18403
$303$	−15.7838	−0.906755
$304$	−5.40291	−0.309878
$305$	−4.36977	−0.250213
$306$	4.36848	0.249730
$307$	2.13389	0.121788	0.0608939	−	0.998144i	$-0.480605\pi$
$307$	2.13389	0.121788	0.0608939	+	0.998144i	$0.480605\pi$
$308$	4.52139	0.257630
$309$	−3.21980	−0.183168
$310$	−5.59453	−0.317748
$311$	13.5648	0.769190	0.384595	−	0.923085i	$-0.374341\pi$
$311$	13.5648	0.769190	0.384595	+	0.923085i	$0.374341\pi$
$312$	−6.17357	−0.349510
$313$	6.44538	0.364315	0.182157	−	0.983269i	$-0.441692\pi$
$313$	6.44538	0.364315	0.182157	+	0.983269i	$0.441692\pi$
$314$	8.51977	0.480799
$315$	19.7575	1.11321
$316$	2.99625	0.168552
$317$	28.0311	1.57438	0.787191	−	0.616709i	$-0.211535\pi$
$317$	28.0311	1.57438	0.787191	+	0.616709i	$0.211535\pi$
$318$	−0.479321	−0.0268790
$319$	−7.78539	−0.435898
$320$	4.36977	0.244278
$321$	1.80234	0.100597
$322$	−34.5889	−1.92756
$323$	−23.6025	−1.31328
$324$	1.00000	0.0555556
$325$	−87.0161	−4.82678
$326$	−15.6757	−0.868198
$327$	4.31978	0.238885
$328$	9.12644	0.503923
$329$	−3.45770	−0.190629
$330$	4.36977	0.240548
$331$	11.8382	0.650685	0.325342	−	0.945596i	$-0.394520\pi$
$331$	11.8382	0.650685	0.325342	+	0.945596i	$0.394520\pi$
$332$	−12.1436	−0.666469
$333$	−0.611833	−0.0335283
$334$	−3.55356	−0.194442
$335$	−26.9313	−1.47141
$336$	4.52139	0.246662
$337$	1.26199	0.0687449	0.0343724	−	0.999409i	$-0.489057\pi$
$337$	1.26199	0.0687449	0.0343724	+	0.999409i	$0.489057\pi$
$338$	25.1130	1.36597
$339$	6.52957	0.354638
$340$	19.0893	1.03526
$341$	−1.28028	−0.0693310
$342$	−5.40291	−0.292156
$343$	29.1313	1.57294
$344$	−9.01275	−0.485935
$345$	−33.4290	−1.79976
$346$	10.0811	0.541962
$347$	−8.59566	−0.461439	−0.230720	−	0.973020i	$-0.574108\pi$
$347$	−8.59566	−0.461439	−0.230720	+	0.973020i	$0.574108\pi$
$348$	−7.78539	−0.417341
$349$	15.7282	0.841912	0.420956	−	0.907081i	$-0.361695\pi$
$349$	15.7282	0.841912	0.420956	+	0.907081i	$0.361695\pi$
$350$	63.7287	3.40644
$351$	−6.17357	−0.329521
$352$	1.00000	0.0533002
$353$	34.0373	1.81163	0.905813	−	0.423678i	$-0.139261\pi$
$353$	34.0373	1.81163	0.905813	+	0.423678i	$0.139261\pi$
$354$	7.96627	0.423402
$355$	35.2319	1.86991
$356$	10.2015	0.540680
$357$	19.7516	1.04537
$358$	16.8091	0.888390
$359$	−27.7906	−1.46673	−0.733366	−	0.679834i	$-0.762052\pi$
$359$	−27.7906	−1.46673	−0.733366	+	0.679834i	$0.762052\pi$
$360$	4.36977	0.230307
$361$	10.1914	0.536391
$362$	−12.7394	−0.669570
$363$	1.00000	0.0524864
$364$	−27.9131	−1.46305
$365$	−29.8778	−1.56388
$366$	−1.00000	−0.0522708
$367$	18.3450	0.957601	0.478801	−	0.877924i	$-0.341072\pi$
$367$	18.3450	0.957601	0.478801	+	0.877924i	$0.341072\pi$
$368$	−7.65005	−0.398787
$369$	9.12644	0.475103
$370$	−2.67357	−0.138992
$371$	−2.16720	−0.112515
$372$	−1.28028	−0.0663794
$373$	32.5317	1.68443	0.842214	−	0.539143i	$-0.181252\pi$
$373$	32.5317	1.68443	0.842214	+	0.539143i	$0.181252\pi$
$374$	4.36848	0.225889
$375$	39.7428	2.05231
$376$	−0.764742	−0.0394386
$377$	48.0637	2.47541
$378$	4.52139	0.232555
$379$	15.5430	0.798393	0.399196	−	0.916865i	$-0.369289\pi$
$379$	15.5430	0.798393	0.399196	+	0.916865i	$0.369289\pi$
$380$	−23.6095	−1.21114
$381$	6.04195	0.309539
$382$	−11.0407	−0.564892
$383$	22.9515	1.17277	0.586383	−	0.810034i	$-0.300551\pi$
$383$	22.9515	1.17277	0.586383	+	0.810034i	$0.300551\pi$
$384$	1.00000	0.0510310
$385$	19.7575	1.00693
$386$	2.31091	0.117622
$387$	−9.01275	−0.458144
$388$	−12.3249	−0.625701
$389$	13.3563	0.677189	0.338595	−	0.940932i	$-0.390048\pi$
$389$	13.3563	0.677189	0.338595	+	0.940932i	$0.390048\pi$
$390$	−26.9771	−1.36604
$391$	−33.4191	−1.69008
$392$	13.4430	0.678973
$393$	−0.440775	−0.0222342
$394$	−19.4329	−0.979014
$395$	13.0929	0.658777
$396$	1.00000	0.0502519
$397$	−8.33191	−0.418167	−0.209083	−	0.977898i	$-0.567048\pi$
$397$	−8.33191	−0.418167	−0.209083	+	0.977898i	$0.567048\pi$
$398$	9.49175	0.475779
$399$	−24.4287	−1.22296
$400$	14.0949	0.704746
$401$	21.1298	1.05517	0.527585	−	0.849502i	$-0.323097\pi$
$401$	21.1298	1.05517	0.527585	+	0.849502i	$0.323097\pi$
$402$	−6.16309	−0.307387
$403$	7.90389	0.393721
$404$	−15.7838	−0.785273
$405$	4.36977	0.217136
$406$	−35.2008	−1.74699
$407$	−0.611833	−0.0303275
$408$	4.36848	0.216272
$409$	−21.2533	−1.05091	−0.525454	−	0.850822i	$-0.676104\pi$
$409$	−21.2533	−1.05091	−0.525454	+	0.850822i	$0.676104\pi$
$410$	39.8805	1.96956
$411$	−23.2581	−1.14724
$412$	−3.21980	−0.158628
$413$	36.0186	1.77236
$414$	−7.65005	−0.375980
$415$	−53.0650	−2.60486
$416$	−6.17357	−0.302684
$417$	−16.3664	−0.801464
$418$	−5.40291	−0.264265
$419$	3.08019	0.150477	0.0752385	−	0.997166i	$-0.476028\pi$
$419$	3.08019	0.150477	0.0752385	+	0.997166i	$0.476028\pi$
$420$	19.7575	0.964065
$421$	−16.1588	−0.787533	−0.393766	−	0.919211i	$-0.628828\pi$
$421$	−16.1588	−0.787533	−0.393766	+	0.919211i	$0.628828\pi$
$422$	−14.2323	−0.692817
$423$	−0.764742	−0.0371830
$424$	−0.479321	−0.0232779
$425$	61.5734	2.98675
$426$	8.06263	0.390636
$427$	−4.52139	−0.218805
$428$	1.80234	0.0871195
$429$	−6.17357	−0.298063
$430$	−39.3837	−1.89925
$431$	−5.91170	−0.284757	−0.142378	−	0.989812i	$-0.545475\pi$
$431$	−5.91170	−0.284757	−0.142378	+	0.989812i	$0.545475\pi$
$432$	1.00000	0.0481125
$433$	5.07766	0.244017	0.122008	−	0.992529i	$-0.461067\pi$
$433$	5.07766	0.244017	0.122008	+	0.992529i	$0.461067\pi$
$434$	−5.78864	−0.277864
$435$	−34.0204	−1.63115
$436$	4.31978	0.206880
$437$	41.3325	1.97720
$438$	−6.83739	−0.326703
$439$	15.8377	0.755892	0.377946	−	0.925828i	$-0.376630\pi$
$439$	15.8377	0.755892	0.377946	+	0.925828i	$0.376630\pi$
$440$	4.36977	0.208321
$441$	13.4430	0.640142
$442$	−26.9691	−1.28279
$443$	−14.2435	−0.676730	−0.338365	−	0.941015i	$-0.609874\pi$
$443$	−14.2435	−0.676730	−0.338365	+	0.941015i	$0.609874\pi$
$444$	−0.611833	−0.0290363
$445$	44.5784	2.11322
$446$	−6.11859	−0.289724
$447$	7.80061	0.368956
$448$	4.52139	0.213616
$449$	5.96861	0.281676	0.140838	−	0.990033i	$-0.455020\pi$
$449$	5.96861	0.281676	0.140838	+	0.990033i	$0.455020\pi$
$450$	14.0949	0.664441
$451$	9.12644	0.429747
$452$	6.52957	0.307125
$453$	20.5763	0.966757
$454$	11.2276	0.526937
$455$	−121.974	−5.71824
$456$	−5.40291	−0.253014
$457$	17.9080	0.837699	0.418850	−	0.908056i	$-0.362433\pi$
$457$	17.9080	0.837699	0.418850	+	0.908056i	$0.362433\pi$
$458$	19.3616	0.904706
$459$	4.36848	0.203903
$460$	−33.4290	−1.55864
$461$	−31.1703	−1.45175	−0.725873	−	0.687829i	$-0.758564\pi$
$461$	−31.1703	−1.45175	−0.725873	+	0.687829i	$0.758564\pi$
$462$	4.52139	0.210354
$463$	−23.2553	−1.08077	−0.540383	−	0.841419i	$-0.681721\pi$
$463$	−23.2553	−1.08077	−0.540383	+	0.841419i	$0.681721\pi$
$464$	−7.78539	−0.361428
$465$	−5.59453	−0.259440
$466$	5.77018	0.267298
$467$	−35.0717	−1.62292	−0.811462	−	0.584405i	$-0.801328\pi$
$467$	−35.0717	−1.62292	−0.811462	+	0.584405i	$0.801328\pi$
$468$	−6.17357	−0.285374
$469$	−27.8657	−1.28672
$470$	−3.34175	−0.154143
$471$	8.51977	0.392570
$472$	7.96627	0.366677
$473$	−9.01275	−0.414407
$474$	2.99625	0.137622
$475$	−76.1536	−3.49417
$476$	19.7516	0.905314
$477$	−0.479321	−0.0219466
$478$	21.9886	1.00574
$479$	−13.2527	−0.605533	−0.302767	−	0.953065i	$-0.597910\pi$
$479$	−13.2527	−0.605533	−0.302767	+	0.953065i	$0.597910\pi$
$480$	4.36977	0.199452
$481$	3.77720	0.172225
$482$	7.82691	0.356506
$483$	−34.5889	−1.57385
$484$	1.00000	0.0454545
$485$	−53.8569	−2.44552
$486$	1.00000	0.0453609
$487$	25.7716	1.16782	0.583911	−	0.811818i	$-0.301522\pi$
$487$	25.7716	1.16782	0.583911	+	0.811818i	$0.301522\pi$
$488$	−1.00000	−0.0452679
$489$	−15.6757	−0.708881
$490$	58.7428	2.65373
$491$	−25.1818	−1.13644	−0.568220	−	0.822876i	$-0.692368\pi$
$491$	−25.1818	−1.13644	−0.568220	+	0.822876i	$0.692368\pi$
$492$	9.12644	0.411452
$493$	−34.0104	−1.53175
$494$	33.3553	1.50072
$495$	4.36977	0.196407
$496$	−1.28028	−0.0574862
$497$	36.4543	1.63520
$498$	−12.1436	−0.544170
$499$	−7.95322	−0.356035	−0.178017	−	0.984027i	$-0.556968\pi$
$499$	−7.95322	−0.356035	−0.178017	+	0.984027i	$0.556968\pi$
$500$	39.7428	1.77735
$501$	−3.55356	−0.158761
$502$	−14.2970	−0.638107
$503$	4.39401	0.195919	0.0979596	−	0.995190i	$-0.468768\pi$
$503$	4.39401	0.195919	0.0979596	+	0.995190i	$0.468768\pi$
$504$	4.52139	0.201399
$505$	−68.9716	−3.06920
$506$	−7.65005	−0.340086
$507$	25.1130	1.11531
$508$	6.04195	0.268068
$509$	18.2141	0.807326	0.403663	−	0.914908i	$-0.367737\pi$
$509$	18.2141	0.807326	0.403663	+	0.914908i	$0.367737\pi$
$510$	19.0893	0.845288
$511$	−30.9145	−1.36758
$512$	1.00000	0.0441942
$513$	−5.40291	−0.238544
$514$	−11.8679	−0.523469
$515$	−14.0698	−0.619990
$516$	−9.01275	−0.396764
$517$	−0.764742	−0.0336333
$518$	−2.76634	−0.121546
$519$	10.0811	0.442510
$520$	−26.9771	−1.18302
$521$	31.0861	1.36190	0.680952	−	0.732328i	$-0.261566\pi$
$521$	31.0861	1.36190	0.680952	+	0.732328i	$0.261566\pi$
$522$	−7.78539	−0.340757
$523$	1.81995	0.0795810	0.0397905	−	0.999208i	$-0.487331\pi$
$523$	1.81995	0.0795810	0.0397905	+	0.999208i	$0.487331\pi$
$524$	−0.440775	−0.0192553
$525$	63.7287	2.78135
$526$	−0.830033	−0.0361912
$527$	−5.59288	−0.243629
$528$	1.00000	0.0435194
$529$	35.5233	1.54449
$530$	−2.09452	−0.0909803
$531$	7.96627	0.345706
$532$	−24.4287	−1.05912
$533$	−56.3427	−2.44047
$534$	10.2015	0.441464
$535$	7.87583	0.340502
$536$	−6.16309	−0.266205
$537$	16.8091	0.725367
$538$	2.06778	0.0891485
$539$	13.4430	0.579030
$540$	4.36977	0.188045
$541$	20.5675	0.884266	0.442133	−	0.896949i	$-0.354222\pi$
$541$	20.5675	0.884266	0.442133	+	0.896949i	$0.354222\pi$
$542$	18.7718	0.806320
$543$	−12.7394	−0.546701
$544$	4.36848	0.187297
$545$	18.8765	0.808579
$546$	−27.9131	−1.19457
$547$	−13.9930	−0.598297	−0.299148	−	0.954207i	$-0.596703\pi$
$547$	−13.9930	−0.598297	−0.299148	+	0.954207i	$0.596703\pi$
$548$	−23.2581	−0.993535
$549$	−1.00000	−0.0426790
$550$	14.0949	0.601010
$551$	42.0638	1.79198
$552$	−7.65005	−0.325608
$553$	13.5472	0.576086
$554$	−23.7427	−1.00873
$555$	−2.67357	−0.113487
$556$	−16.3664	−0.694088
$557$	40.4315	1.71314	0.856569	−	0.516033i	$-0.172592\pi$
$557$	40.4315	1.71314	0.856569	+	0.516033i	$0.172592\pi$
$558$	−1.28028	−0.0541985
$559$	55.6408	2.35336
$560$	19.7575	0.834905
$561$	4.36848	0.184437
$562$	15.2565	0.643556
$563$	−39.7403	−1.67486	−0.837428	−	0.546548i	$-0.815942\pi$
$563$	−39.7403	−1.67486	−0.837428	+	0.546548i	$0.815942\pi$
$564$	−0.764742	−0.0322015
$565$	28.5327	1.20038
$566$	10.0897	0.424102
$567$	4.52139	0.189881
$568$	8.06263	0.338300
$569$	−22.6884	−0.951148	−0.475574	−	0.879676i	$-0.657760\pi$
$569$	−22.6884	−0.951148	−0.475574	+	0.879676i	$0.657760\pi$
$570$	−23.6095	−0.988893
$571$	13.6282	0.570323	0.285161	−	0.958480i	$-0.407953\pi$
$571$	13.6282	0.570323	0.285161	+	0.958480i	$0.407953\pi$
$572$	−6.17357	−0.258130
$573$	−11.0407	−0.461232
$574$	41.2642	1.72233
$575$	−107.827	−4.49669
$576$	1.00000	0.0416667
$577$	6.80917	0.283469	0.141735	−	0.989905i	$-0.454732\pi$
$577$	6.80917	0.283469	0.141735	+	0.989905i	$0.454732\pi$
$578$	2.08364	0.0866682
$579$	2.31091	0.0960382
$580$	−34.0204	−1.41262
$581$	−54.9062	−2.27789
$582$	−12.3249	−0.510883
$583$	−0.479321	−0.0198514
$584$	−6.83739	−0.282933
$585$	−26.9771	−1.11537
$586$	−22.1467	−0.914871
$587$	−44.8600	−1.85157	−0.925785	−	0.378052i	$-0.876594\pi$
$587$	−44.8600	−1.85157	−0.925785	+	0.378052i	$0.876594\pi$
$588$	13.4430	0.554379
$589$	6.91723	0.285019
$590$	34.8108	1.43314
$591$	−19.4329	−0.799362
$592$	−0.611833	−0.0251462
$593$	−33.2409	−1.36504	−0.682519	−	0.730868i	$-0.739116\pi$
$593$	−33.2409	−1.36504	−0.682519	+	0.730868i	$0.739116\pi$
$594$	1.00000	0.0410305
$595$	86.3101	3.53837
$596$	7.80061	0.319526
$597$	9.49175	0.388472
$598$	47.2282	1.93130
$599$	−23.0587	−0.942153	−0.471076	−	0.882092i	$-0.656134\pi$
$599$	−23.0587	−0.942153	−0.471076	+	0.882092i	$0.656134\pi$
$600$	14.0949	0.575423
$601$	8.33698	0.340072	0.170036	−	0.985438i	$-0.445612\pi$
$601$	8.33698	0.340072	0.170036	+	0.985438i	$0.445612\pi$
$602$	−40.7502	−1.66085
$603$	−6.16309	−0.250980
$604$	20.5763	0.837236
$605$	4.36977	0.177657
$606$	−15.7838	−0.641173
$607$	37.4407	1.51967	0.759837	−	0.650114i	$-0.225279\pi$
$607$	37.4407	1.51967	0.759837	+	0.650114i	$0.225279\pi$
$608$	−5.40291	−0.219117
$609$	−35.2008	−1.42641
$610$	−4.36977	−0.176927
$611$	4.72119	0.190999
$612$	4.36848	0.176585
$613$	−13.4997	−0.545247	−0.272623	−	0.962121i	$-0.587891\pi$
$613$	−13.4997	−0.545247	−0.272623	+	0.962121i	$0.587891\pi$
$614$	2.13389	0.0861169
$615$	39.8805	1.60814
$616$	4.52139	0.182172
$617$	14.8163	0.596482	0.298241	−	0.954491i	$-0.403600\pi$
$617$	14.8163	0.596482	0.298241	+	0.954491i	$0.403600\pi$
$618$	−3.21980	−0.129519
$619$	−13.9425	−0.560395	−0.280197	−	0.959942i	$-0.590400\pi$
$619$	−13.9425	−0.560395	−0.280197	+	0.959942i	$0.590400\pi$
$620$	−5.59453	−0.224682
$621$	−7.65005	−0.306986
$622$	13.5648	0.543899
$623$	46.1251	1.84797
$624$	−6.17357	−0.247141
$625$	103.192	4.12769
$626$	6.44538	0.257609
$627$	−5.40291	−0.215771
$628$	8.51977	0.339976
$629$	−2.67278	−0.106571
$630$	19.7575	0.787156
$631$	−22.8178	−0.908361	−0.454180	−	0.890910i	$-0.650068\pi$
$631$	−22.8178	−0.908361	−0.454180	+	0.890910i	$0.650068\pi$
$632$	2.99625	0.119184
$633$	−14.2323	−0.565682
$634$	28.0311	1.11326
$635$	26.4020	1.04773
$636$	−0.479321	−0.0190063
$637$	−82.9912	−3.28823
$638$	−7.78539	−0.308227
$639$	8.06263	0.318953
$640$	4.36977	0.172730
$641$	3.55614	0.140459	0.0702295	−	0.997531i	$-0.477627\pi$
$641$	3.55614	0.140459	0.0702295	+	0.997531i	$0.477627\pi$
$642$	1.80234	0.0711328
$643$	−33.1329	−1.30664	−0.653318	−	0.757084i	$-0.726623\pi$
$643$	−33.1329	−1.30664	−0.653318	+	0.757084i	$0.726623\pi$
$644$	−34.5889	−1.36299
$645$	−39.3837	−1.55073
$646$	−23.6025	−0.928629
$647$	−47.9054	−1.88335	−0.941677	−	0.336517i	$-0.890751\pi$
$647$	−47.9054	−1.88335	−0.941677	+	0.336517i	$0.890751\pi$
$648$	1.00000	0.0392837
$649$	7.96627	0.312703
$650$	−87.0161	−3.41305
$651$	−5.78864	−0.226875
$652$	−15.6757	−0.613909
$653$	24.6014	0.962728	0.481364	−	0.876521i	$-0.340142\pi$
$653$	24.6014	0.962728	0.481364	+	0.876521i	$0.340142\pi$
$654$	4.31978	0.168917
$655$	−1.92609	−0.0752584
$656$	9.12644	0.356328
$657$	−6.83739	−0.266752
$658$	−3.45770	−0.134795
$659$	−4.11041	−0.160119	−0.0800594	−	0.996790i	$-0.525511\pi$
$659$	−4.11041	−0.160119	−0.0800594	+	0.996790i	$0.525511\pi$
$660$	4.36977	0.170093
$661$	34.2325	1.33149	0.665744	−	0.746180i	$-0.268114\pi$
$661$	34.2325	1.33149	0.665744	+	0.746180i	$0.268114\pi$
$662$	11.8382	0.460104
$663$	−26.9691	−1.04739
$664$	−12.1436	−0.471265
$665$	−106.748	−4.13950
$666$	−0.611833	−0.0237081
$667$	59.5587	2.30612
$668$	−3.55356	−0.137491
$669$	−6.11859	−0.236558
$670$	−26.9313	−1.04045
$671$	−1.00000	−0.0386046
$672$	4.52139	0.174416
$673$	21.9016	0.844246	0.422123	−	0.906539i	$-0.361285\pi$
$673$	21.9016	0.844246	0.422123	+	0.906539i	$0.361285\pi$
$674$	1.26199	0.0486100
$675$	14.0949	0.542514
$676$	25.1130	0.965885
$677$	43.4742	1.67085	0.835425	−	0.549605i	$-0.185222\pi$
$677$	43.4742	1.67085	0.835425	+	0.549605i	$0.185222\pi$
$678$	6.52957	0.250767
$679$	−55.7256	−2.13855
$680$	19.0893	0.732041
$681$	11.2276	0.430242
$682$	−1.28028	−0.0490244
$683$	−8.33634	−0.318981	−0.159491	−	0.987199i	$-0.550985\pi$
$683$	−8.33634	−0.318981	−0.159491	+	0.987199i	$0.550985\pi$
$684$	−5.40291	−0.206585
$685$	−101.632	−3.88318
$686$	29.1313	1.11224
$687$	19.3616	0.738690
$688$	−9.01275	−0.343608
$689$	2.95912	0.112734
$690$	−33.4290	−1.27262
$691$	9.30293	0.353900	0.176950	−	0.984220i	$-0.443377\pi$
$691$	9.30293	0.353900	0.176950	+	0.984220i	$0.443377\pi$
$692$	10.0811	0.383225
$693$	4.52139	0.171753
$694$	−8.59566	−0.326287
$695$	−71.5173	−2.71280
$696$	−7.78539	−0.295105
$697$	39.8687	1.51013
$698$	15.7282	0.595322
$699$	5.77018	0.218248
$700$	63.7287	2.40872
$701$	−14.6044	−0.551601	−0.275800	−	0.961215i	$-0.588943\pi$
$701$	−14.6044	−0.551601	−0.275800	+	0.961215i	$0.588943\pi$
$702$	−6.17357	−0.233006
$703$	3.30568	0.124676
$704$	1.00000	0.0376889
$705$	−3.34175	−0.125858
$706$	34.0373	1.28101
$707$	−71.3647	−2.68395
$708$	7.96627	0.299391
$709$	25.6703	0.964067	0.482034	−	0.876153i	$-0.339898\pi$
$709$	25.6703	0.964067	0.482034	+	0.876153i	$0.339898\pi$
$710$	35.2319	1.32223
$711$	2.99625	0.112368
$712$	10.2015	0.382319
$713$	9.79420	0.366796
$714$	19.7516	0.739186
$715$	−26.9771	−1.00889
$716$	16.8091	0.628187
$717$	21.9886	0.821180
$718$	−27.7906	−1.03714
$719$	−32.1358	−1.19846	−0.599231	−	0.800576i	$-0.704527\pi$
$719$	−32.1358	−1.19846	−0.599231	+	0.800576i	$0.704527\pi$
$720$	4.36977	0.162852
$721$	−14.5580	−0.542168
$722$	10.1914	0.379286
$723$	7.82691	0.291086
$724$	−12.7394	−0.473457
$725$	−109.735	−4.07544
$726$	1.00000	0.0371135
$727$	30.2279	1.12109	0.560545	−	0.828124i	$-0.310592\pi$
$727$	30.2279	1.12109	0.560545	+	0.828124i	$0.310592\pi$
$728$	−27.9131	−1.03453
$729$	1.00000	0.0370370
$730$	−29.8778	−1.10583
$731$	−39.3720	−1.45623
$732$	−1.00000	−0.0369611
$733$	30.7308	1.13507	0.567533	−	0.823350i	$-0.307898\pi$
$733$	30.7308	1.13507	0.567533	+	0.823350i	$0.307898\pi$
$734$	18.3450	0.677126
$735$	58.7428	2.16676
$736$	−7.65005	−0.281985
$737$	−6.16309	−0.227020
$738$	9.12644	0.335949
$739$	13.4294	0.494009	0.247005	−	0.969014i	$-0.420554\pi$
$739$	13.4294	0.494009	0.247005	+	0.969014i	$0.420554\pi$
$740$	−2.67357	−0.0982825
$741$	33.3553	1.22534
$742$	−2.16720	−0.0795603
$743$	0.0383888	0.00140835	0.000704174	−	1.00000i	$-0.499776\pi$
$743$	0.0383888	0.00140835	0.000704174		1.00000i	$0.499776\pi$
$744$	−1.28028	−0.0469373
$745$	34.0869	1.24885
$746$	32.5317	1.19107
$747$	−12.1436	−0.444313
$748$	4.36848	0.159728
$749$	8.14909	0.297761
$750$	39.7428	1.45120
$751$	−2.62026	−0.0956147	−0.0478073	−	0.998857i	$-0.515223\pi$
$751$	−2.62026	−0.0956147	−0.0478073	+	0.998857i	$0.515223\pi$
$752$	−0.764742	−0.0278873
$753$	−14.2970	−0.521012
$754$	48.0637	1.75038
$755$	89.9136	3.27229
$756$	4.52139	0.164441
$757$	5.00749	0.182000	0.0910002	−	0.995851i	$-0.470994\pi$
$757$	5.00749	0.182000	0.0910002	+	0.995851i	$0.470994\pi$
$758$	15.5430	0.564549
$759$	−7.65005	−0.277679
$760$	−23.6095	−0.856406
$761$	−45.7775	−1.65943	−0.829716	−	0.558186i	$-0.811497\pi$
$761$	−45.7775	−1.65943	−0.829716	+	0.558186i	$0.811497\pi$
$762$	6.04195	0.218877
$763$	19.5314	0.707085
$764$	−11.0407	−0.399439
$765$	19.0893	0.690175
$766$	22.9515	0.829270
$767$	−49.1803	−1.77580
$768$	1.00000	0.0360844
$769$	−2.43051	−0.0876465	−0.0438232	−	0.999039i	$-0.513954\pi$
$769$	−2.43051	−0.0876465	−0.0438232	+	0.999039i	$0.513954\pi$
$770$	19.7575	0.712009
$771$	−11.8679	−0.427411
$772$	2.31091	0.0831715
$773$	−29.1472	−1.04835	−0.524176	−	0.851610i	$-0.675627\pi$
$773$	−29.1472	−1.04835	−0.524176	+	0.851610i	$0.675627\pi$
$774$	−9.01275	−0.323956
$775$	−18.0454	−0.648211
$776$	−12.3249	−0.442437
$777$	−2.76634	−0.0992418
$778$	13.3563	0.478845
$779$	−49.3093	−1.76669
$780$	−26.9771	−0.965936
$781$	8.06263	0.288504
$782$	−33.4191	−1.19507
$783$	−7.78539	−0.278227
$784$	13.4430	0.480107
$785$	37.2295	1.32878
$786$	−0.440775	−0.0157219
$787$	−9.04595	−0.322453	−0.161227	−	0.986917i	$-0.551545\pi$
$787$	−9.04595	−0.322453	−0.161227	+	0.986917i	$0.551545\pi$
$788$	−19.4329	−0.692267
$789$	−0.830033	−0.0295500
$790$	13.0929	0.465825
$791$	29.5227	1.04971
$792$	1.00000	0.0355335
$793$	6.17357	0.219230
$794$	−8.33191	−0.295688
$795$	−2.09452	−0.0742851
$796$	9.49175	0.336426
$797$	9.03872	0.320168	0.160084	−	0.987103i	$-0.448824\pi$
$797$	9.03872	0.320168	0.160084	+	0.987103i	$0.448824\pi$
$798$	−24.4287	−0.864765
$799$	−3.34076	−0.118188
$800$	14.0949	0.498331
$801$	10.2015	0.360454
$802$	21.1298	0.746118
$803$	−6.83739	−0.241286
$804$	−6.16309	−0.217355
$805$	−151.146	−5.32718
$806$	7.90389	0.278403
$807$	2.06778	0.0727895
$808$	−15.7838	−0.555272
$809$	6.99022	0.245763	0.122882	−	0.992421i	$-0.460786\pi$
$809$	6.99022	0.245763	0.122882	+	0.992421i	$0.460786\pi$
$810$	4.36977	0.153538
$811$	13.4533	0.472409	0.236205	−	0.971703i	$-0.424096\pi$
$811$	13.4533	0.472409	0.236205	+	0.971703i	$0.424096\pi$
$812$	−35.2008	−1.23531
$813$	18.7718	0.658357
$814$	−0.611833	−0.0214447
$815$	−68.4994	−2.39943
$816$	4.36848	0.152927
$817$	48.6950	1.70362
$818$	−21.2533	−0.743104
$819$	−27.9131	−0.975364
$820$	39.8805	1.39269
$821$	−33.5662	−1.17147	−0.585734	−	0.810503i	$-0.699194\pi$
$821$	−33.5662	−1.17147	−0.585734	+	0.810503i	$0.699194\pi$
$822$	−23.2581	−0.811218
$823$	−0.780631	−0.0272111	−0.0136055	−	0.999907i	$-0.504331\pi$
$823$	−0.780631	−0.0272111	−0.0136055	+	0.999907i	$0.504331\pi$
$824$	−3.21980	−0.112167
$825$	14.0949	0.490722
$826$	36.0186	1.25325
$827$	−26.9147	−0.935916	−0.467958	−	0.883751i	$-0.655010\pi$
$827$	−26.9147	−0.935916	−0.467958	+	0.883751i	$0.655010\pi$
$828$	−7.65005	−0.265858
$829$	−32.4821	−1.12815	−0.564074	−	0.825724i	$-0.690767\pi$
$829$	−32.4821	−1.12815	−0.564074	+	0.825724i	$0.690767\pi$
$830$	−53.0650	−1.84191
$831$	−23.7427	−0.823624
$832$	−6.17357	−0.214030
$833$	58.7254	2.03472
$834$	−16.3664	−0.566720
$835$	−15.5282	−0.537377
$836$	−5.40291	−0.186864
$837$	−1.28028	−0.0442529
$838$	3.08019	0.106403
$839$	−2.68221	−0.0926002	−0.0463001	−	0.998928i	$-0.514743\pi$
$839$	−2.68221	−0.0926002	−0.0463001	+	0.998928i	$0.514743\pi$
$840$	19.7575	0.681697
$841$	31.6123	1.09008
$842$	−16.1588	−0.556870
$843$	15.2565	0.525462
$844$	−14.2323	−0.489895
$845$	109.738	3.77511
$846$	−0.764742	−0.0262924
$847$	4.52139	0.155357
$848$	−0.479321	−0.0164599
$849$	10.0897	0.346278
$850$	61.5734	2.11195
$851$	4.68056	0.160447
$852$	8.06263	0.276221
$853$	−17.0441	−0.583577	−0.291789	−	0.956483i	$-0.594250\pi$
$853$	−17.0441	−0.583577	−0.291789	+	0.956483i	$0.594250\pi$
$854$	−4.52139	−0.154719
$855$	−23.6095	−0.807428
$856$	1.80234	0.0616028
$857$	−38.8172	−1.32597	−0.662985	−	0.748633i	$-0.730711\pi$
$857$	−38.8172	−1.32597	−0.662985	+	0.748633i	$0.730711\pi$
$858$	−6.17357	−0.210762
$859$	17.5011	0.597130	0.298565	−	0.954389i	$-0.403492\pi$
$859$	17.5011	0.597130	0.298565	+	0.954389i	$0.403492\pi$
$860$	−39.3837	−1.34297
$861$	41.2642	1.40628
$862$	−5.91170	−0.201353
$863$	24.5863	0.836928	0.418464	−	0.908233i	$-0.362569\pi$
$863$	24.5863	0.836928	0.418464	+	0.908233i	$0.362569\pi$
$864$	1.00000	0.0340207
$865$	44.0521	1.49781
$866$	5.07766	0.172546
$867$	2.08364	0.0707642
$868$	−5.78864	−0.196479
$869$	2.99625	0.101641
$870$	−34.0204	−1.15340
$871$	38.0483	1.28922
$872$	4.31978	0.146286
$873$	−12.3249	−0.417134
$874$	41.3325	1.39809
$875$	179.693	6.07472
$876$	−6.83739	−0.231014
$877$	−46.5387	−1.57150	−0.785749	−	0.618545i	$-0.787722\pi$
$877$	−46.5387	−1.57150	−0.785749	+	0.618545i	$0.787722\pi$
$878$	15.8377	0.534497
$879$	−22.1467	−0.746989
$880$	4.36977	0.147305
$881$	−4.66697	−0.157234	−0.0786171	−	0.996905i	$-0.525050\pi$
$881$	−4.66697	−0.157234	−0.0786171	+	0.996905i	$0.525050\pi$
$882$	13.4430	0.452649
$883$	30.6222	1.03052	0.515259	−	0.857034i	$-0.327696\pi$
$883$	30.6222	1.03052	0.515259	+	0.857034i	$0.327696\pi$
$884$	−26.9691	−0.907071
$885$	34.8108	1.17015
$886$	−14.2435	−0.478520
$887$	−30.6653	−1.02964	−0.514820	−	0.857298i	$-0.672141\pi$
$887$	−30.6653	−1.02964	−0.514820	+	0.857298i	$0.672141\pi$
$888$	−0.611833	−0.0205318
$889$	27.3180	0.916218
$890$	44.5784	1.49427
$891$	1.00000	0.0335013
$892$	−6.11859	−0.204865
$893$	4.13183	0.138267
$894$	7.80061	0.260892
$895$	73.4521	2.45523
$896$	4.52139	0.151049
$897$	47.2282	1.57690
$898$	5.96861	0.199175
$899$	9.96747	0.332434
$900$	14.0949	0.469831
$901$	−2.09390	−0.0697581
$902$	9.12644	0.303877
$903$	−40.7502	−1.35608
$904$	6.52957	0.217170
$905$	−55.6684	−1.85048
$906$	20.5763	0.683600
$907$	11.2629	0.373978	0.186989	−	0.982362i	$-0.440127\pi$
$907$	11.2629	0.373978	0.186989	+	0.982362i	$0.440127\pi$
$908$	11.2276	0.372600
$909$	−15.7838	−0.523515
$910$	−121.974	−4.04340
$911$	−32.0029	−1.06030	−0.530152	−	0.847903i	$-0.677865\pi$
$911$	−32.0029	−1.06030	−0.530152	+	0.847903i	$0.677865\pi$
$912$	−5.40291	−0.178908
$913$	−12.1436	−0.401896
$914$	17.9080	0.592343
$915$	−4.36977	−0.144460
$916$	19.3616	0.639724
$917$	−1.99292	−0.0658119
$918$	4.36848	0.144181
$919$	−18.3317	−0.604708	−0.302354	−	0.953196i	$-0.597773\pi$
$919$	−18.3317	−0.604708	−0.302354	+	0.953196i	$0.597773\pi$
$920$	−33.4290	−1.10212
$921$	2.13389	0.0703142
$922$	−31.1703	−1.02654
$923$	−49.7752	−1.63837
$924$	4.52139	0.148743
$925$	−8.62375	−0.283547
$926$	−23.2553	−0.764217
$927$	−3.21980	−0.105752
$928$	−7.78539	−0.255568
$929$	55.9316	1.83506	0.917528	−	0.397672i	$-0.130182\pi$
$929$	55.9316	1.83506	0.917528	+	0.397672i	$0.130182\pi$
$930$	−5.59453	−0.183452
$931$	−72.6312	−2.38039
$932$	5.77018	0.189009
$933$	13.5648	0.444092
$934$	−35.0717	−1.14758
$935$	19.0893	0.624286
$936$	−6.17357	−0.201790
$937$	−36.6902	−1.19862	−0.599309	−	0.800518i	$-0.704558\pi$
$937$	−36.6902	−1.19862	−0.599309	+	0.800518i	$0.704558\pi$
$938$	−27.8657	−0.909848
$939$	6.44538	0.210337
$940$	−3.34175	−0.108996
$941$	52.2649	1.70379	0.851893	−	0.523716i	$-0.175455\pi$
$941$	52.2649	1.70379	0.851893	+	0.523716i	$0.175455\pi$
$942$	8.51977	0.277589
$943$	−69.8177	−2.27358
$944$	7.96627	0.259280
$945$	19.7575	0.642710
$946$	−9.01275	−0.293030
$947$	−28.7089	−0.932915	−0.466457	−	0.884544i	$-0.654470\pi$
$947$	−28.7089	−0.932915	−0.466457	+	0.884544i	$0.654470\pi$
$948$	2.99625	0.0973136
$949$	42.2111	1.37023
$950$	−76.1536	−2.47075
$951$	28.0311	0.908970
$952$	19.7516	0.640154
$953$	−54.9641	−1.78046	−0.890230	−	0.455511i	$-0.849457\pi$
$953$	−54.9641	−1.78046	−0.890230	+	0.455511i	$0.849457\pi$
$954$	−0.479321	−0.0155186
$955$	−48.2454	−1.56118
$956$	21.9886	0.711162
$957$	−7.78539	−0.251666
$958$	−13.2527	−0.428177
$959$	−105.159	−3.39576
$960$	4.36977	0.141034
$961$	−29.3609	−0.947125
$962$	3.77720	0.121782
$963$	1.80234	0.0580797
$964$	7.82691	0.252088
$965$	10.0982	0.325071
$966$	−34.5889	−1.11288
$967$	−11.7674	−0.378415	−0.189208	−	0.981937i	$-0.560592\pi$
$967$	−11.7674	−0.378415	−0.189208	+	0.981937i	$0.560592\pi$
$968$	1.00000	0.0321412
$969$	−23.6025	−0.758222
$970$	−53.8569	−1.72924
$971$	26.4661	0.849338	0.424669	−	0.905349i	$-0.360391\pi$
$971$	26.4661	0.849338	0.424669	+	0.905349i	$0.360391\pi$
$972$	1.00000	0.0320750
$973$	−73.9987	−2.37229
$974$	25.7716	0.825774
$975$	−87.0161	−2.78674
$976$	−1.00000	−0.0320092
$977$	27.5807	0.882386	0.441193	−	0.897412i	$-0.354555\pi$
$977$	27.5807	0.882386	0.441193	+	0.897412i	$0.354555\pi$
$978$	−15.6757	−0.501255
$979$	10.2015	0.326043
$980$	58.7428	1.87647
$981$	4.31978	0.137920
$982$	−25.1818	−0.803585
$983$	7.46974	0.238248	0.119124	−	0.992879i	$-0.461991\pi$
$983$	7.46974	0.238248	0.119124	+	0.992879i	$0.461991\pi$
$984$	9.12644	0.290940
$985$	−84.9173	−2.70569
$986$	−34.0104	−1.08311
$987$	−3.45770	−0.110060
$988$	33.3553	1.06117
$989$	68.9480	2.19242
$990$	4.36977	0.138881
$991$	6.76266	0.214823	0.107412	−	0.994215i	$-0.465744\pi$
$991$	6.76266	0.214823	0.107412	+	0.994215i	$0.465744\pi$
$992$	−1.28028	−0.0406489
$993$	11.8382	0.375673
$994$	36.4543	1.15626
$995$	41.4768	1.31490
$996$	−12.1436	−0.384786
$997$	50.8630	1.61085	0.805423	−	0.592700i	$-0.201938\pi$
$997$	50.8630	1.61085	0.805423	+	0.592700i	$0.201938\pi$
$998$	−7.95322	−0.251755
$999$	−0.611833	−0.0193576

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.bc.1.9	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.bc.1.9	✓	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:	\( N \)	\(=\)	\( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.36977 q^{5} +1.00000 q^{6} +4.52139 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.36977 q^{5} +1.00000 q^{6} +4.52139 q^{7} +1.00000 q^{8} +1.00000 q^{9} +4.36977 q^{10} +1.00000 q^{11} +1.00000 q^{12} -6.17357 q^{13} +4.52139 q^{14} +4.36977 q^{15} +1.00000 q^{16} +4.36848 q^{17} +1.00000 q^{18} -5.40291 q^{19} +4.36977 q^{20} +4.52139 q^{21} +1.00000 q^{22} -7.65005 q^{23} +1.00000 q^{24} +14.0949 q^{25} -6.17357 q^{26} +1.00000 q^{27} +4.52139 q^{28} -7.78539 q^{29} +4.36977 q^{30} -1.28028 q^{31} +1.00000 q^{32} +1.00000 q^{33} +4.36848 q^{34} +19.7575 q^{35} +1.00000 q^{36} -0.611833 q^{37} -5.40291 q^{38} -6.17357 q^{39} +4.36977 q^{40} +9.12644 q^{41} +4.52139 q^{42} -9.01275 q^{43} +1.00000 q^{44} +4.36977 q^{45} -7.65005 q^{46} -0.764742 q^{47} +1.00000 q^{48} +13.4430 q^{49} +14.0949 q^{50} +4.36848 q^{51} -6.17357 q^{52} -0.479321 q^{53} +1.00000 q^{54} +4.36977 q^{55} +4.52139 q^{56} -5.40291 q^{57} -7.78539 q^{58} +7.96627 q^{59} +4.36977 q^{60} -1.00000 q^{61} -1.28028 q^{62} +4.52139 q^{63} +1.00000 q^{64} -26.9771 q^{65} +1.00000 q^{66} -6.16309 q^{67} +4.36848 q^{68} -7.65005 q^{69} +19.7575 q^{70} +8.06263 q^{71} +1.00000 q^{72} -6.83739 q^{73} -0.611833 q^{74} +14.0949 q^{75} -5.40291 q^{76} +4.52139 q^{77} -6.17357 q^{78} +2.99625 q^{79} +4.36977 q^{80} +1.00000 q^{81} +9.12644 q^{82} -12.1436 q^{83} +4.52139 q^{84} +19.0893 q^{85} -9.01275 q^{86} -7.78539 q^{87} +1.00000 q^{88} +10.2015 q^{89} +4.36977 q^{90} -27.9131 q^{91} -7.65005 q^{92} -1.28028 q^{93} -0.764742 q^{94} -23.6095 q^{95} +1.00000 q^{96} -12.3249 q^{97} +13.4430 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} + 9 q^{3} + 9 q^{4} + 8 q^{5} + 9 q^{6} + 9 q^{7} + 9 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q + 9 * q^2 + 9 * q^3 + 9 * q^4 + 8 * q^5 + 9 * q^6 + 9 * q^7 + 9 * q^8 + 9 * q^9	\( 9 q + 9 q^{2} + 9 q^{3} + 9 q^{4} + 8 q^{5} + 9 q^{6} + 9 q^{7} + 9 q^{8} + 9 q^{9} + 8 q^{10} + 9 q^{11} + 9 q^{12} + 8 q^{13} + 9 q^{14} + 8 q^{15} + 9 q^{16} + q^{17} + 9 q^{18} + 5 q^{19} + 8 q^{20} + 9 q^{21} + 9 q^{22} - q^{23} + 9 q^{24} + 23 q^{25} + 8 q^{26} + 9 q^{27} + 9 q^{28} - 14 q^{29} + 8 q^{30} + 25 q^{31} + 9 q^{32} + 9 q^{33} + q^{34} + 5 q^{35} + 9 q^{36} + 16 q^{37} + 5 q^{38} + 8 q^{39} + 8 q^{40} + 5 q^{41} + 9 q^{42} + 5 q^{43} + 9 q^{44} + 8 q^{45} - q^{46} + 8 q^{47} + 9 q^{48} + 30 q^{49} + 23 q^{50} + q^{51} + 8 q^{52} + q^{53} + 9 q^{54} + 8 q^{55} + 9 q^{56} + 5 q^{57} - 14 q^{58} + 4 q^{59} + 8 q^{60} - 9 q^{61} + 25 q^{62} + 9 q^{63} + 9 q^{64} - 14 q^{65} + 9 q^{66} - 4 q^{67} + q^{68} - q^{69} + 5 q^{70} + 20 q^{71} + 9 q^{72} + 15 q^{73} + 16 q^{74} + 23 q^{75} + 5 q^{76} + 9 q^{77} + 8 q^{78} - 2 q^{79} + 8 q^{80} + 9 q^{81} + 5 q^{82} + 21 q^{83} + 9 q^{84} - 16 q^{85} + 5 q^{86} - 14 q^{87} + 9 q^{88} + 10 q^{89} + 8 q^{90} - 19 q^{91} - q^{92} + 25 q^{93} + 8 q^{94} - 7 q^{95} + 9 q^{96} + 3 q^{97} + 30 q^{98} + 9 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 9 * q^3 + 9 * q^4 + 8 * q^5 + 9 * q^6 + 9 * q^7 + 9 * q^8 + 9 * q^9 + 8 * q^10 + 9 * q^11 + 9 * q^12 + 8 * q^13 + 9 * q^14 + 8 * q^15 + 9 * q^16 + q^17 + 9 * q^18 + 5 * q^19 + 8 * q^20 + 9 * q^21 + 9 * q^22 - q^23 + 9 * q^24 + 23 * q^25 + 8 * q^26 + 9 * q^27 + 9 * q^28 - 14 * q^29 + 8 * q^30 + 25 * q^31 + 9 * q^32 + 9 * q^33 + q^34 + 5 * q^35 + 9 * q^36 + 16 * q^37 + 5 * q^38 + 8 * q^39 + 8 * q^40 + 5 * q^41 + 9 * q^42 + 5 * q^43 + 9 * q^44 + 8 * q^45 - q^46 + 8 * q^47 + 9 * q^48 + 30 * q^49 + 23 * q^50 + q^51 + 8 * q^52 + q^53 + 9 * q^54 + 8 * q^55 + 9 * q^56 + 5 * q^57 - 14 * q^58 + 4 * q^59 + 8 * q^60 - 9 * q^61 + 25 * q^62 + 9 * q^63 + 9 * q^64 - 14 * q^65 + 9 * q^66 - 4 * q^67 + q^68 - q^69 + 5 * q^70 + 20 * q^71 + 9 * q^72 + 15 * q^73 + 16 * q^74 + 23 * q^75 + 5 * q^76 + 9 * q^77 + 8 * q^78 - 2 * q^79 + 8 * q^80 + 9 * q^81 + 5 * q^82 + 21 * q^83 + 9 * q^84 - 16 * q^85 + 5 * q^86 - 14 * q^87 + 9 * q^88 + 10 * q^89 + 8 * q^90 - 19 * q^91 - q^92 + 25 * q^93 + 8 * q^94 - 7 * q^95 + 9 * q^96 + 3 * q^97 + 30 * q^98 + 9 * q^99

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