LMFDB - Embedded newform 6026.2.a.f.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, 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("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.1178522580$
Analytic rank:	$1$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 5 x^{19} - 17 x^{18} + 115 x^{17} + 78 x^{16} - 1083 x^{15} + 248 x^{14} + 5359 x^{13} + \cdots - 18 $ x^20 - 5x^19 - 17x^18 + 115x^17 + 78x^16 - 1083x^15 + 248x^14 + 5359x^13 - 3723x^12 - 14776x^11 + 14837x^10 + 21886x^9 - 28084x^8 - 14682x^7 + 25315x^6 + 2042x^5 - 9137x^4 + 576x^3 + 1159x^2 - 78*x - 18
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$0.178107$ of defining polynomial
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.178107 q^{3} +1.00000 q^{4} -1.41285 q^{5} -0.178107 q^{6} -1.81585 q^{7} +1.00000 q^{8} -2.96828 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.178107 q^{3} +1.00000 q^{4} -1.41285 q^{5} -0.178107 q^{6} -1.81585 q^{7} +1.00000 q^{8} -2.96828 q^{9} -1.41285 q^{10} +2.27239 q^{11} -0.178107 q^{12} +4.66087 q^{13} -1.81585 q^{14} +0.251639 q^{15} +1.00000 q^{16} -3.31560 q^{17} -2.96828 q^{18} +0.914669 q^{19} -1.41285 q^{20} +0.323416 q^{21} +2.27239 q^{22} +1.00000 q^{23} -0.178107 q^{24} -3.00386 q^{25} +4.66087 q^{26} +1.06299 q^{27} -1.81585 q^{28} -1.00565 q^{29} +0.251639 q^{30} +3.63226 q^{31} +1.00000 q^{32} -0.404728 q^{33} -3.31560 q^{34} +2.56552 q^{35} -2.96828 q^{36} +5.78875 q^{37} +0.914669 q^{38} -0.830134 q^{39} -1.41285 q^{40} -11.9429 q^{41} +0.323416 q^{42} -2.18634 q^{43} +2.27239 q^{44} +4.19373 q^{45} +1.00000 q^{46} +3.07917 q^{47} -0.178107 q^{48} -3.70270 q^{49} -3.00386 q^{50} +0.590532 q^{51} +4.66087 q^{52} +4.22345 q^{53} +1.06299 q^{54} -3.21054 q^{55} -1.81585 q^{56} -0.162909 q^{57} -1.00565 q^{58} -7.70406 q^{59} +0.251639 q^{60} +8.68469 q^{61} +3.63226 q^{62} +5.38994 q^{63} +1.00000 q^{64} -6.58511 q^{65} -0.404728 q^{66} -14.8363 q^{67} -3.31560 q^{68} -0.178107 q^{69} +2.56552 q^{70} +2.58652 q^{71} -2.96828 q^{72} -3.33415 q^{73} +5.78875 q^{74} +0.535009 q^{75} +0.914669 q^{76} -4.12631 q^{77} -0.830134 q^{78} -11.6463 q^{79} -1.41285 q^{80} +8.71551 q^{81} -11.9429 q^{82} -10.0713 q^{83} +0.323416 q^{84} +4.68444 q^{85} -2.18634 q^{86} +0.179113 q^{87} +2.27239 q^{88} +12.9446 q^{89} +4.19373 q^{90} -8.46343 q^{91} +1.00000 q^{92} -0.646931 q^{93} +3.07917 q^{94} -1.29229 q^{95} -0.178107 q^{96} +8.79885 q^{97} -3.70270 q^{98} -6.74507 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 20 q^{2} - 5 q^{3} + 20 q^{4} - 6 q^{5} - 5 q^{6} - 12 q^{7} + 20 q^{8} - q^{9}+O(q^{10}) $ 20 * q + 20 * q^2 - 5 * q^3 + 20 * q^4 - 6 * q^5 - 5 * q^6 - 12 * q^7 + 20 * q^8 - q^9	\( 20 q + 20 q^{2} - 5 q^{3} + 20 q^{4} - 6 q^{5} - 5 q^{6} - 12 q^{7} + 20 q^{8} - q^{9} - 6 q^{10} - 3 q^{11} - 5 q^{12} - 13 q^{13} - 12 q^{14} - 10 q^{15} + 20 q^{16} - 14 q^{17} - q^{18} - 21 q^{19} - 6 q^{20} - 8 q^{21} - 3 q^{22} + 20 q^{23} - 5 q^{24} - 14 q^{25} - 13 q^{26} - 5 q^{27} - 12 q^{28} - 27 q^{29} - 10 q^{30} - 27 q^{31} + 20 q^{32} - 12 q^{33} - 14 q^{34} - 23 q^{35} - q^{36} - 19 q^{37} - 21 q^{38} - 35 q^{39} - 6 q^{40} - 17 q^{41} - 8 q^{42} - 27 q^{43} - 3 q^{44} + 4 q^{45} + 20 q^{46} - 28 q^{47} - 5 q^{48} - 10 q^{49} - 14 q^{50} + 6 q^{51} - 13 q^{52} - 47 q^{53} - 5 q^{54} - 4 q^{55} - 12 q^{56} - 16 q^{57} - 27 q^{58} - 16 q^{59} - 10 q^{60} - 9 q^{61} - 27 q^{62} - 9 q^{63} + 20 q^{64} + 9 q^{65} - 12 q^{66} - 8 q^{67} - 14 q^{68} - 5 q^{69} - 23 q^{70} - 30 q^{71} - q^{72} - 26 q^{73} - 19 q^{74} - 18 q^{75} - 21 q^{76} - 50 q^{77} - 35 q^{78} - 35 q^{79} - 6 q^{80} - 60 q^{81} - 17 q^{82} + 2 q^{83} - 8 q^{84} - 62 q^{85} - 27 q^{86} + q^{87} - 3 q^{88} - 25 q^{89} + 4 q^{90} + 22 q^{91} + 20 q^{92} - 21 q^{93} - 28 q^{94} - 14 q^{95} - 5 q^{96} + 2 q^{97} - 10 q^{98} - 5 q^{99}+O(q^{100}) \) 20 * q + 20 * q^2 - 5 * q^3 + 20 * q^4 - 6 * q^5 - 5 * q^6 - 12 * q^7 + 20 * q^8 - q^9 - 6 * q^10 - 3 * q^11 - 5 * q^12 - 13 * q^13 - 12 * q^14 - 10 * q^15 + 20 * q^16 - 14 * q^17 - q^18 - 21 * q^19 - 6 * q^20 - 8 * q^21 - 3 * q^22 + 20 * q^23 - 5 * q^24 - 14 * q^25 - 13 * q^26 - 5 * q^27 - 12 * q^28 - 27 * q^29 - 10 * q^30 - 27 * q^31 + 20 * q^32 - 12 * q^33 - 14 * q^34 - 23 * q^35 - q^36 - 19 * q^37 - 21 * q^38 - 35 * q^39 - 6 * q^40 - 17 * q^41 - 8 * q^42 - 27 * q^43 - 3 * q^44 + 4 * q^45 + 20 * q^46 - 28 * q^47 - 5 * q^48 - 10 * q^49 - 14 * q^50 + 6 * q^51 - 13 * q^52 - 47 * q^53 - 5 * q^54 - 4 * q^55 - 12 * q^56 - 16 * q^57 - 27 * q^58 - 16 * q^59 - 10 * q^60 - 9 * q^61 - 27 * q^62 - 9 * q^63 + 20 * q^64 + 9 * q^65 - 12 * q^66 - 8 * q^67 - 14 * q^68 - 5 * q^69 - 23 * q^70 - 30 * q^71 - q^72 - 26 * q^73 - 19 * q^74 - 18 * q^75 - 21 * q^76 - 50 * q^77 - 35 * q^78 - 35 * q^79 - 6 * q^80 - 60 * q^81 - 17 * q^82 + 2 * q^83 - 8 * q^84 - 62 * q^85 - 27 * q^86 + q^87 - 3 * q^88 - 25 * q^89 + 4 * q^90 + 22 * q^91 + 20 * q^92 - 21 * q^93 - 28 * q^94 - 14 * q^95 - 5 * q^96 + 2 * q^97 - 10 * q^98 - 5 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−0.178107	−0.102830	−0.0514151	−	0.998677i	$-0.516373\pi$
$3$	−0.178107	−0.102830	−0.0514151	+	0.998677i	$0.516373\pi$
$4$	1.00000	0.500000
$5$	−1.41285	−0.631846	−0.315923	−	0.948785i	$-0.602314\pi$
$5$	−1.41285	−0.631846	−0.315923	+	0.948785i	$0.602314\pi$
$6$	−0.178107	−0.0727120
$7$	−1.81585	−0.686326	−0.343163	−	0.939276i	$-0.611498\pi$
$7$	−1.81585	−0.686326	−0.343163	+	0.939276i	$0.611498\pi$
$8$	1.00000	0.353553
$9$	−2.96828	−0.989426
$10$	−1.41285	−0.446782
$11$	2.27239	0.685150	0.342575	−	0.939490i	$-0.388701\pi$
$11$	2.27239	0.685150	0.342575	+	0.939490i	$0.388701\pi$
$12$	−0.178107	−0.0514151
$13$	4.66087	1.29269	0.646346	−	0.763044i	$-0.276296\pi$
$13$	4.66087	1.29269	0.646346	+	0.763044i	$0.276296\pi$
$14$	−1.81585	−0.485306
$15$	0.251639	0.0649728
$16$	1.00000	0.250000
$17$	−3.31560	−0.804151	−0.402075	−	0.915607i	$-0.631711\pi$
$17$	−3.31560	−0.804151	−0.402075	+	0.915607i	$0.631711\pi$
$18$	−2.96828	−0.699630
$19$	0.914669	0.209840	0.104920	−	0.994481i	$-0.466541\pi$
$19$	0.914669	0.209840	0.104920	+	0.994481i	$0.466541\pi$
$20$	−1.41285	−0.315923
$21$	0.323416	0.0705751
$22$	2.27239	0.484474
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−0.178107	−0.0363560
$25$	−3.00386	−0.600771
$26$	4.66087	0.914072
$27$	1.06299	0.204573
$28$	−1.81585	−0.343163
$29$	−1.00565	−0.186744	−0.0933722	−	0.995631i	$-0.529765\pi$
$29$	−1.00565	−0.186744	−0.0933722	+	0.995631i	$0.529765\pi$
$30$	0.251639	0.0459427
$31$	3.63226	0.652373	0.326186	−	0.945305i	$-0.394236\pi$
$31$	3.63226	0.652373	0.326186	+	0.945305i	$0.394236\pi$
$32$	1.00000	0.176777
$33$	−0.404728	−0.0704542
$34$	−3.31560	−0.568621
$35$	2.56552	0.433652
$36$	−2.96828	−0.494713
$37$	5.78875	0.951665	0.475832	−	0.879536i	$-0.342147\pi$
$37$	5.78875	0.951665	0.475832	+	0.879536i	$0.342147\pi$
$38$	0.914669	0.148379
$39$	−0.830134	−0.132928
$40$	−1.41285	−0.223391
$41$	−11.9429	−1.86516	−0.932580	−	0.360962i	$-0.882448\pi$
$41$	−11.9429	−1.86516	−0.932580	+	0.360962i	$0.882448\pi$
$42$	0.323416	0.0499041
$43$	−2.18634	−0.333413	−0.166707	−	0.986007i	$-0.553313\pi$
$43$	−2.18634	−0.333413	−0.166707	+	0.986007i	$0.553313\pi$
$44$	2.27239	0.342575
$45$	4.19373	0.625164
$46$	1.00000	0.147442
$47$	3.07917	0.449143	0.224572	−	0.974458i	$-0.427902\pi$
$47$	3.07917	0.449143	0.224572	+	0.974458i	$0.427902\pi$
$48$	−0.178107	−0.0257076
$49$	−3.70270	−0.528957
$50$	−3.00386	−0.424809
$51$	0.590532	0.0826911
$52$	4.66087	0.646346
$53$	4.22345	0.580136	0.290068	−	0.957006i	$-0.406322\pi$
$53$	4.22345	0.580136	0.290068	+	0.957006i	$0.406322\pi$
$54$	1.06299	0.144655
$55$	−3.21054	−0.432909
$56$	−1.81585	−0.242653
$57$	−0.162909	−0.0215779
$58$	−1.00565	−0.132048
$59$	−7.70406	−1.00298	−0.501491	−	0.865163i	$-0.667215\pi$
$59$	−7.70406	−1.00298	−0.501491	+	0.865163i	$0.667215\pi$
$60$	0.251639	0.0324864
$61$	8.68469	1.11196	0.555980	−	0.831196i	$-0.312343\pi$
$61$	8.68469	1.11196	0.555980	+	0.831196i	$0.312343\pi$
$62$	3.63226	0.461297
$63$	5.38994	0.679069
$64$	1.00000	0.125000
$65$	−6.58511	−0.816782
$66$	−0.404728	−0.0498186
$67$	−14.8363	−1.81254	−0.906270	−	0.422699i	$-0.861083\pi$
$67$	−14.8363	−1.81254	−0.906270	+	0.422699i	$0.861083\pi$
$68$	−3.31560	−0.402075
$69$	−0.178107	−0.0214416
$70$	2.56552	0.306638
$71$	2.58652	0.306964	0.153482	−	0.988151i	$-0.450951\pi$
$71$	2.58652	0.306964	0.153482	+	0.988151i	$0.450951\pi$
$72$	−2.96828	−0.349815
$73$	−3.33415	−0.390232	−0.195116	−	0.980780i	$-0.562508\pi$
$73$	−3.33415	−0.390232	−0.195116	+	0.980780i	$0.562508\pi$
$74$	5.78875	0.672929
$75$	0.535009	0.0617775
$76$	0.914669	0.104920
$77$	−4.12631	−0.470236
$78$	−0.830134	−0.0939942
$79$	−11.6463	−1.31031	−0.655156	−	0.755494i	$-0.727397\pi$
$79$	−11.6463	−1.31031	−0.655156	+	0.755494i	$0.727397\pi$
$80$	−1.41285	−0.157961
$81$	8.71551	0.968390
$82$	−11.9429	−1.31887
$83$	−10.0713	−1.10547	−0.552733	−	0.833359i	$-0.686415\pi$
$83$	−10.0713	−1.10547	−0.552733	+	0.833359i	$0.686415\pi$
$84$	0.323416	0.0352875
$85$	4.68444	0.508099
$86$	−2.18634	−0.235759
$87$	0.179113	0.0192030
$88$	2.27239	0.242237
$89$	12.9446	1.37212	0.686061	−	0.727544i	$-0.259338\pi$
$89$	12.9446	1.37212	0.686061	+	0.727544i	$0.259338\pi$
$90$	4.19373	0.442058
$91$	−8.46343	−0.887208
$92$	1.00000	0.104257
$93$	−0.646931	−0.0670837
$94$	3.07917	0.317592
$95$	−1.29229	−0.132586
$96$	−0.178107	−0.0181780
$97$	8.79885	0.893388	0.446694	−	0.894687i	$-0.352601\pi$
$97$	8.79885	0.893388	0.446694	+	0.894687i	$0.352601\pi$
$98$	−3.70270	−0.374029
$99$	−6.74507	−0.677905
$100$	−3.00386	−0.300386
$101$	1.90855	0.189908	0.0949541	−	0.995482i	$-0.469730\pi$
$101$	1.90855	0.189908	0.0949541	+	0.995482i	$0.469730\pi$
$102$	0.590532	0.0584714
$103$	−20.2832	−1.99857	−0.999284	−	0.0378431i	$-0.987951\pi$
$103$	−20.2832	−1.99857	−0.999284	+	0.0378431i	$0.987951\pi$
$104$	4.66087	0.457036
$105$	−0.456938	−0.0445925
$106$	4.22345	0.410218
$107$	12.8024	1.23766	0.618829	−	0.785526i	$-0.287608\pi$
$107$	12.8024	1.23766	0.618829	+	0.785526i	$0.287608\pi$
$108$	1.06299	0.102287
$109$	−12.8354	−1.22940	−0.614702	−	0.788759i	$-0.710724\pi$
$109$	−12.8354	−1.22940	−0.614702	+	0.788759i	$0.710724\pi$
$110$	−3.21054	−0.306113
$111$	−1.03102	−0.0978599
$112$	−1.81585	−0.171581
$113$	−13.1243	−1.23463	−0.617317	−	0.786714i	$-0.711780\pi$
$113$	−13.1243	−1.23463	−0.617317	+	0.786714i	$0.711780\pi$
$114$	−0.162909	−0.0152578
$115$	−1.41285	−0.131749
$116$	−1.00565	−0.0933722
$117$	−13.8348	−1.27902
$118$	−7.70406	−0.709216
$119$	6.02062	0.551910
$120$	0.251639	0.0229714
$121$	−5.83626	−0.530569
$122$	8.68469	0.786275
$123$	2.12711	0.191795
$124$	3.63226	0.326186
$125$	11.3082	1.01144
$126$	5.38994	0.480174
$127$	1.65390	0.146760	0.0733800	−	0.997304i	$-0.476621\pi$
$127$	1.65390	0.146760	0.0733800	+	0.997304i	$0.476621\pi$
$128$	1.00000	0.0883883
$129$	0.389402	0.0342850
$130$	−6.58511	−0.577552
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	−0.404728	−0.0352271
$133$	−1.66090	−0.144018
$134$	−14.8363	−1.28166
$135$	−1.50185	−0.129259
$136$	−3.31560	−0.284310
$137$	9.64073	0.823663	0.411832	−	0.911260i	$-0.364889\pi$
$137$	9.64073	0.823663	0.411832	+	0.911260i	$0.364889\pi$
$138$	−0.178107	−0.0151615
$139$	−20.5272	−1.74109	−0.870547	−	0.492085i	$-0.836235\pi$
$139$	−20.5272	−1.74109	−0.870547	+	0.492085i	$0.836235\pi$
$140$	2.56552	0.216826
$141$	−0.548422	−0.0461855
$142$	2.58652	0.217056
$143$	10.5913	0.885688
$144$	−2.96828	−0.247356
$145$	1.42083	0.117994
$146$	−3.33415	−0.275936
$147$	0.659477	0.0543928
$148$	5.78875	0.475832
$149$	−10.0701	−0.824971	−0.412485	−	0.910964i	$-0.635339\pi$
$149$	−10.0701	−0.824971	−0.412485	+	0.910964i	$0.635339\pi$
$150$	0.535009	0.0436833
$151$	3.65154	0.297158	0.148579	−	0.988901i	$-0.452530\pi$
$151$	3.65154	0.297158	0.148579	+	0.988901i	$0.452530\pi$
$152$	0.914669	0.0741895
$153$	9.84162	0.795648
$154$	−4.12631	−0.332507
$155$	−5.13183	−0.412199
$156$	−0.830134	−0.0664640
$157$	−16.3207	−1.30253	−0.651267	−	0.758849i	$-0.725762\pi$
$157$	−16.3207	−1.30253	−0.651267	+	0.758849i	$0.725762\pi$
$158$	−11.6463	−0.926530
$159$	−0.752228	−0.0596555
$160$	−1.41285	−0.111696
$161$	−1.81585	−0.143109
$162$	8.71551	0.684755
$163$	−23.4443	−1.83630	−0.918148	−	0.396238i	$-0.870315\pi$
$163$	−23.4443	−1.83630	−0.918148	+	0.396238i	$0.870315\pi$
$164$	−11.9429	−0.932580
$165$	0.571820	0.0445161
$166$	−10.0713	−0.781682
$167$	−1.83425	−0.141938	−0.0709691	−	0.997479i	$-0.522609\pi$
$167$	−1.83425	−0.141938	−0.0709691	+	0.997479i	$0.522609\pi$
$168$	0.323416	0.0249521
$169$	8.72370	0.671054
$170$	4.68444	0.359280
$171$	−2.71499	−0.207621
$172$	−2.18634	−0.166707
$173$	−21.0765	−1.60242	−0.801210	−	0.598383i	$-0.795810\pi$
$173$	−21.0765	−1.60242	−0.801210	+	0.598383i	$0.795810\pi$
$174$	0.179113	0.0135786
$175$	5.45455	0.412325
$176$	2.27239	0.171288
$177$	1.37215	0.103137
$178$	12.9446	0.970237
$179$	4.86009	0.363260	0.181630	−	0.983367i	$-0.441863\pi$
$179$	4.86009	0.363260	0.181630	+	0.983367i	$0.441863\pi$
$180$	4.19373	0.312582
$181$	10.9821	0.816294	0.408147	−	0.912916i	$-0.366175\pi$
$181$	10.9821	0.816294	0.408147	+	0.912916i	$0.366175\pi$
$182$	−8.46343	−0.627351
$183$	−1.54681	−0.114343
$184$	1.00000	0.0737210
$185$	−8.17863	−0.601305
$186$	−0.646931	−0.0474353
$187$	−7.53432	−0.550964
$188$	3.07917	0.224572
$189$	−1.93023	−0.140404
$190$	−1.29229	−0.0937526
$191$	1.23419	0.0893025	0.0446512	−	0.999003i	$-0.485782\pi$
$191$	1.23419	0.0893025	0.0446512	+	0.999003i	$0.485782\pi$
$192$	−0.178107	−0.0128538
$193$	2.25761	0.162506	0.0812530	−	0.996694i	$-0.474108\pi$
$193$	2.25761	0.162506	0.0812530	+	0.996694i	$0.474108\pi$
$194$	8.79885	0.631721
$195$	1.17286	0.0839899
$196$	−3.70270	−0.264478
$197$	−0.492305	−0.0350753	−0.0175377	−	0.999846i	$-0.505583\pi$
$197$	−0.492305	−0.0350753	−0.0175377	+	0.999846i	$0.505583\pi$
$198$	−6.74507	−0.479351
$199$	−11.5653	−0.819843	−0.409921	−	0.912121i	$-0.634444\pi$
$199$	−11.5653	−0.819843	−0.409921	+	0.912121i	$0.634444\pi$
$200$	−3.00386	−0.212405
$201$	2.64245	0.186384
$202$	1.90855	0.134285
$203$	1.82611	0.128168
$204$	0.590532	0.0413455
$205$	16.8735	1.17849
$206$	−20.2832	−1.41320
$207$	−2.96828	−0.206310
$208$	4.66087	0.323173
$209$	2.07848	0.143772
$210$	−0.456938	−0.0315317
$211$	−16.5537	−1.13960	−0.569801	−	0.821783i	$-0.692980\pi$
$211$	−16.5537	−1.13960	−0.569801	+	0.821783i	$0.692980\pi$
$212$	4.22345	0.290068
$213$	−0.460678	−0.0315652
$214$	12.8024	0.875156
$215$	3.08896	0.210666
$216$	1.06299	0.0723275
$217$	−6.59563	−0.447740
$218$	−12.8354	−0.869320
$219$	0.593836	0.0401277
$220$	−3.21054	−0.216454
$221$	−15.4536	−1.03952
$222$	−1.03102	−0.0691974
$223$	2.60117	0.174188	0.0870938	−	0.996200i	$-0.472242\pi$
$223$	2.60117	0.174188	0.0870938	+	0.996200i	$0.472242\pi$
$224$	−1.81585	−0.121326
$225$	8.91628	0.594419
$226$	−13.1243	−0.873018
$227$	−8.91823	−0.591924	−0.295962	−	0.955200i	$-0.595640\pi$
$227$	−8.91823	−0.591924	−0.295962	+	0.955200i	$0.595640\pi$
$228$	−0.162909	−0.0107889
$229$	−5.46562	−0.361178	−0.180589	−	0.983559i	$-0.557800\pi$
$229$	−5.46562	−0.361178	−0.180589	+	0.983559i	$0.557800\pi$
$230$	−1.41285	−0.0931605
$231$	0.734925	0.0483545
$232$	−1.00565	−0.0660241
$233$	−6.70773	−0.439438	−0.219719	−	0.975563i	$-0.570514\pi$
$233$	−6.70773	−0.439438	−0.219719	+	0.975563i	$0.570514\pi$
$234$	−13.8348	−0.904406
$235$	−4.35040	−0.283789
$236$	−7.70406	−0.501491
$237$	2.07429	0.134740
$238$	6.02062	0.390259
$239$	13.5108	0.873938	0.436969	−	0.899477i	$-0.356052\pi$
$239$	13.5108	0.873938	0.436969	+	0.899477i	$0.356052\pi$
$240$	0.251639	0.0162432
$241$	6.75844	0.435350	0.217675	−	0.976021i	$-0.430153\pi$
$241$	6.75844	0.435350	0.217675	+	0.976021i	$0.430153\pi$
$242$	−5.83626	−0.375169
$243$	−4.74128	−0.304153
$244$	8.68469	0.555980
$245$	5.23135	0.334219
$246$	2.12711	0.135620
$247$	4.26315	0.271258
$248$	3.63226	0.230649
$249$	1.79377	0.113675
$250$	11.3082	0.715196
$251$	−8.07671	−0.509798	−0.254899	−	0.966968i	$-0.582042\pi$
$251$	−8.07671	−0.509798	−0.254899	+	0.966968i	$0.582042\pi$
$252$	5.38994	0.339534
$253$	2.27239	0.142864
$254$	1.65390	0.103775
$255$	−0.834333	−0.0522480
$256$	1.00000	0.0625000
$257$	−12.9540	−0.808046	−0.404023	−	0.914749i	$-0.632388\pi$
$257$	−12.9540	−0.808046	−0.404023	+	0.914749i	$0.632388\pi$
$258$	0.389402	0.0242431
$259$	−10.5115	−0.653152
$260$	−6.58511	−0.408391
$261$	2.98505	0.184770
$262$	−1.00000	−0.0617802
$263$	12.7361	0.785342	0.392671	−	0.919679i	$-0.371551\pi$
$263$	12.7361	0.785342	0.392671	+	0.919679i	$0.371551\pi$
$264$	−0.404728	−0.0249093
$265$	−5.96710	−0.366556
$266$	−1.66090	−0.101836
$267$	−2.30552	−0.141096
$268$	−14.8363	−0.906270
$269$	2.96979	0.181071	0.0905357	−	0.995893i	$-0.471142\pi$
$269$	2.96979	0.181071	0.0905357	+	0.995893i	$0.471142\pi$
$270$	−1.50185	−0.0913997
$271$	29.4507	1.78900	0.894500	−	0.447067i	$-0.147531\pi$
$271$	29.4507	1.78900	0.894500	+	0.447067i	$0.147531\pi$
$272$	−3.31560	−0.201038
$273$	1.50740	0.0912319
$274$	9.64073	0.582418
$275$	−6.82592	−0.411618
$276$	−0.178107	−0.0107208
$277$	−7.23226	−0.434544	−0.217272	−	0.976111i	$-0.569716\pi$
$277$	−7.23226	−0.434544	−0.217272	+	0.976111i	$0.569716\pi$
$278$	−20.5272	−1.23114
$279$	−10.7816	−0.645475
$280$	2.56552	0.153319
$281$	−10.9868	−0.655417	−0.327709	−	0.944779i	$-0.606276\pi$
$281$	−10.9868	−0.655417	−0.327709	+	0.944779i	$0.606276\pi$
$282$	−0.548422	−0.0326581
$283$	4.48327	0.266503	0.133251	−	0.991082i	$-0.457458\pi$
$283$	4.48327	0.266503	0.133251	+	0.991082i	$0.457458\pi$
$284$	2.58652	0.153482
$285$	0.230166	0.0136339
$286$	10.5913	0.626276
$287$	21.6864	1.28011
$288$	−2.96828	−0.174907
$289$	−6.00680	−0.353341
$290$	1.42083	0.0834341
$291$	−1.56714	−0.0918673
$292$	−3.33415	−0.195116
$293$	−31.2586	−1.82615	−0.913075	−	0.407792i	$-0.866299\pi$
$293$	−31.2586	−1.82615	−0.913075	+	0.407792i	$0.866299\pi$
$294$	0.659477	0.0384615
$295$	10.8847	0.633730
$296$	5.78875	0.336464
$297$	2.41553	0.140163
$298$	−10.0701	−0.583343
$299$	4.66087	0.269545
$300$	0.535009	0.0308887
$301$	3.97005	0.228830
$302$	3.65154	0.210123
$303$	−0.339927	−0.0195283
$304$	0.914669	0.0524599
$305$	−12.2702	−0.702587
$306$	9.84162	0.562608
$307$	0.617623	0.0352496	0.0176248	−	0.999845i	$-0.494390\pi$
$307$	0.617623	0.0352496	0.0176248	+	0.999845i	$0.494390\pi$
$308$	−4.12631	−0.235118
$309$	3.61259	0.205513
$310$	−5.13183	−0.291469
$311$	16.6115	0.941953	0.470977	−	0.882146i	$-0.343902\pi$
$311$	16.6115	0.941953	0.470977	+	0.882146i	$0.343902\pi$
$312$	−0.830134	−0.0469971
$313$	−26.7093	−1.50970	−0.754849	−	0.655898i	$-0.772290\pi$
$313$	−26.7093	−1.50970	−0.754849	+	0.655898i	$0.772290\pi$
$314$	−16.3207	−0.921031
$315$	−7.61517	−0.429066
$316$	−11.6463	−0.655156
$317$	21.6922	1.21835	0.609177	−	0.793034i	$-0.291500\pi$
$317$	21.6922	1.21835	0.609177	+	0.793034i	$0.291500\pi$
$318$	−0.752228	−0.0421828
$319$	−2.28522	−0.127948
$320$	−1.41285	−0.0789807
$321$	−2.28020	−0.127269
$322$	−1.81585	−0.101193
$323$	−3.03268	−0.168743
$324$	8.71551	0.484195
$325$	−14.0006	−0.776612
$326$	−23.4443	−1.29846
$327$	2.28607	0.126420
$328$	−11.9429	−0.659434
$329$	−5.59130	−0.308258
$330$	0.571820	0.0314777
$331$	−14.4767	−0.795713	−0.397857	−	0.917448i	$-0.630246\pi$
$331$	−14.4767	−0.795713	−0.397857	+	0.917448i	$0.630246\pi$
$332$	−10.0713	−0.552733
$333$	−17.1826	−0.941602
$334$	−1.83425	−0.100365
$335$	20.9614	1.14525
$336$	0.323416	0.0176438
$337$	−13.5900	−0.740296	−0.370148	−	0.928973i	$-0.620693\pi$
$337$	−13.5900	−0.740296	−0.370148	+	0.928973i	$0.620693\pi$
$338$	8.72370	0.474507
$339$	2.33754	0.126958
$340$	4.68444	0.254050
$341$	8.25389	0.446973
$342$	−2.71499	−0.146810
$343$	19.4345	1.04936
$344$	−2.18634	−0.117879
$345$	0.251639	0.0135478
$346$	−21.0765	−1.13308
$347$	−14.6933	−0.788778	−0.394389	−	0.918944i	$-0.629044\pi$
$347$	−14.6933	−0.788778	−0.394389	+	0.918944i	$0.629044\pi$
$348$	0.179113	0.00960149
$349$	−14.6842	−0.786027	−0.393013	−	0.919533i	$-0.628567\pi$
$349$	−14.6842	−0.786027	−0.393013	+	0.919533i	$0.628567\pi$
$350$	5.45455	0.291558
$351$	4.95447	0.264450
$352$	2.27239	0.121119
$353$	−12.5224	−0.666500	−0.333250	−	0.942838i	$-0.608145\pi$
$353$	−12.5224	−0.666500	−0.333250	+	0.942838i	$0.608145\pi$
$354$	1.37215	0.0729288
$355$	−3.65437	−0.193954
$356$	12.9446	0.686061
$357$	−1.07232	−0.0567530
$358$	4.86009	0.256864
$359$	−8.82817	−0.465933	−0.232967	−	0.972485i	$-0.574843\pi$
$359$	−8.82817	−0.465933	−0.232967	+	0.972485i	$0.574843\pi$
$360$	4.19373	0.221029
$361$	−18.1634	−0.955967
$362$	10.9821	0.577207
$363$	1.03948	0.0545586
$364$	−8.46343	−0.443604
$365$	4.71065	0.246567
$366$	−1.54681	−0.0808528
$367$	30.3961	1.58666	0.793331	−	0.608791i	$-0.208345\pi$
$367$	30.3961	1.58666	0.793331	+	0.608791i	$0.208345\pi$
$368$	1.00000	0.0521286
$369$	35.4497	1.84544
$370$	−8.17863	−0.425187
$371$	−7.66915	−0.398162
$372$	−0.646931	−0.0335418
$373$	6.13144	0.317474	0.158737	−	0.987321i	$-0.449258\pi$
$373$	6.13144	0.317474	0.158737	+	0.987321i	$0.449258\pi$
$374$	−7.53432	−0.389590
$375$	−2.01408	−0.104007
$376$	3.07917	0.158796
$377$	−4.68720	−0.241403
$378$	−1.93023	−0.0992805
$379$	8.13702	0.417971	0.208985	−	0.977919i	$-0.432984\pi$
$379$	8.13702	0.417971	0.208985	+	0.977919i	$0.432984\pi$
$380$	−1.29229	−0.0662931
$381$	−0.294572	−0.0150914
$382$	1.23419	0.0631464
$383$	31.7073	1.62017	0.810085	−	0.586313i	$-0.199421\pi$
$383$	31.7073	1.62017	0.810085	+	0.586313i	$0.199421\pi$
$384$	−0.178107	−0.00908900
$385$	5.82985	0.297117
$386$	2.25761	0.114909
$387$	6.48965	0.329888
$388$	8.79885	0.446694
$389$	21.5461	1.09243	0.546216	−	0.837645i	$-0.316068\pi$
$389$	21.5461	1.09243	0.546216	+	0.837645i	$0.316068\pi$
$390$	1.17286	0.0593898
$391$	−3.31560	−0.167677
$392$	−3.70270	−0.187014
$393$	0.178107	0.00898432
$394$	−0.492305	−0.0248020
$395$	16.4545	0.827914
$396$	−6.74507	−0.338953
$397$	−4.30313	−0.215968	−0.107984	−	0.994153i	$-0.534440\pi$
$397$	−4.30313	−0.215968	−0.107984	+	0.994153i	$0.534440\pi$
$398$	−11.5653	−0.579716
$399$	0.295818	0.0148094
$400$	−3.00386	−0.150193
$401$	−8.63112	−0.431017	−0.215509	−	0.976502i	$-0.569141\pi$
$401$	−8.63112	−0.431017	−0.215509	+	0.976502i	$0.569141\pi$
$402$	2.64245	0.131793
$403$	16.9295	0.843317
$404$	1.90855	0.0949541
$405$	−12.3137	−0.611873
$406$	1.82611	0.0906281
$407$	13.1543	0.652033
$408$	0.590532	0.0292357
$409$	−3.05113	−0.150869	−0.0754343	−	0.997151i	$-0.524034\pi$
$409$	−3.05113	−0.150869	−0.0754343	+	0.997151i	$0.524034\pi$
$410$	16.8735	0.833321
$411$	−1.71708	−0.0846975
$412$	−20.2832	−0.999284
$413$	13.9894	0.688373
$414$	−2.96828	−0.145883
$415$	14.2292	0.698483
$416$	4.66087	0.228518
$417$	3.65604	0.179037
$418$	2.07848	0.101662
$419$	15.9054	0.777028	0.388514	−	0.921443i	$-0.372988\pi$
$419$	15.9054	0.777028	0.388514	+	0.921443i	$0.372988\pi$
$420$	−0.456938	−0.0222963
$421$	38.2315	1.86329	0.931645	−	0.363370i	$-0.118374\pi$
$421$	38.2315	1.86329	0.931645	+	0.363370i	$0.118374\pi$
$422$	−16.5537	−0.805820
$423$	−9.13983	−0.444394
$424$	4.22345	0.205109
$425$	9.95958	0.483111
$426$	−0.460678	−0.0223199
$427$	−15.7701	−0.763167
$428$	12.8024	0.618829
$429$	−1.88639	−0.0910756
$430$	3.08896	0.148963
$431$	16.9963	0.818684	0.409342	−	0.912381i	$-0.365758\pi$
$431$	16.9963	0.818684	0.409342	+	0.912381i	$0.365758\pi$
$432$	1.06299	0.0511433
$433$	17.0249	0.818163	0.409081	−	0.912498i	$-0.365849\pi$
$433$	17.0249	0.818163	0.409081	+	0.912498i	$0.365849\pi$
$434$	−6.59563	−0.316600
$435$	−0.253060	−0.0121333
$436$	−12.8354	−0.614702
$437$	0.914669	0.0437546
$438$	0.593836	0.0283746
$439$	26.6398	1.27145	0.635724	−	0.771917i	$-0.280702\pi$
$439$	26.6398	1.27145	0.635724	+	0.771917i	$0.280702\pi$
$440$	−3.21054	−0.153056
$441$	10.9906	0.523364
$442$	−15.4536	−0.735051
$443$	−17.2678	−0.820420	−0.410210	−	0.911991i	$-0.634545\pi$
$443$	−17.2678	−0.820420	−0.410210	+	0.911991i	$0.634545\pi$
$444$	−1.03102	−0.0489300
$445$	−18.2887	−0.866969
$446$	2.60117	0.123169
$447$	1.79355	0.0848320
$448$	−1.81585	−0.0857907
$449$	−11.6935	−0.551852	−0.275926	−	0.961179i	$-0.588984\pi$
$449$	−11.6935	−0.551852	−0.275926	+	0.961179i	$0.588984\pi$
$450$	8.91628	0.420317
$451$	−27.1388	−1.27791
$452$	−13.1243	−0.617317
$453$	−0.650366	−0.0305569
$454$	−8.91823	−0.418553
$455$	11.9575	0.560579
$456$	−0.162909	−0.00762892
$457$	41.9709	1.96332	0.981658	−	0.190650i	$-0.0610595\pi$
$457$	41.9709	1.96332	0.981658	+	0.190650i	$0.0610595\pi$
$458$	−5.46562	−0.255392
$459$	−3.52446	−0.164508
$460$	−1.41285	−0.0658744
$461$	−9.05281	−0.421631	−0.210816	−	0.977526i	$-0.567612\pi$
$461$	−9.05281	−0.421631	−0.210816	+	0.977526i	$0.567612\pi$
$462$	0.734925	0.0341918
$463$	−15.8265	−0.735518	−0.367759	−	0.929921i	$-0.619875\pi$
$463$	−15.8265	−0.735518	−0.367759	+	0.929921i	$0.619875\pi$
$464$	−1.00565	−0.0466861
$465$	0.914017	0.0423865
$466$	−6.70773	−0.310729
$467$	34.3648	1.59021	0.795106	−	0.606470i	$-0.207415\pi$
$467$	34.3648	1.59021	0.795106	+	0.606470i	$0.207415\pi$
$468$	−13.8348	−0.639512
$469$	26.9404	1.24399
$470$	−4.35040	−0.200669
$471$	2.90684	0.133940
$472$	−7.70406	−0.354608
$473$	−4.96820	−0.228438
$474$	2.07429	0.0952753
$475$	−2.74753	−0.126066
$476$	6.02062	0.275955
$477$	−12.5364	−0.574002
$478$	13.5108	0.617967
$479$	−15.4641	−0.706571	−0.353286	−	0.935515i	$-0.614936\pi$
$479$	−15.4641	−0.706571	−0.353286	+	0.935515i	$0.614936\pi$
$480$	0.251639	0.0114857
$481$	26.9806	1.23021
$482$	6.75844	0.307839
$483$	0.323416	0.0147159
$484$	−5.83626	−0.265285
$485$	−12.4315	−0.564483
$486$	−4.74128	−0.215069
$487$	−12.8984	−0.584480	−0.292240	−	0.956345i	$-0.594401\pi$
$487$	−12.8984	−0.584480	−0.292240	+	0.956345i	$0.594401\pi$
$488$	8.68469	0.393137
$489$	4.17559	0.188827
$490$	5.23135	0.236328
$491$	30.6064	1.38125	0.690624	−	0.723214i	$-0.257336\pi$
$491$	30.6064	1.38125	0.690624	+	0.723214i	$0.257336\pi$
$492$	2.12711	0.0958975
$493$	3.33433	0.150171
$494$	4.26315	0.191808
$495$	9.52977	0.428331
$496$	3.63226	0.163093
$497$	−4.69673	−0.210677
$498$	1.79377	0.0803806
$499$	8.34998	0.373797	0.186898	−	0.982379i	$-0.440157\pi$
$499$	8.34998	0.373797	0.186898	+	0.982379i	$0.440157\pi$
$500$	11.3082	0.505720
$501$	0.326692	0.0145955
$502$	−8.07671	−0.360481
$503$	−20.6265	−0.919691	−0.459846	−	0.887999i	$-0.652095\pi$
$503$	−20.6265	−0.919691	−0.459846	+	0.887999i	$0.652095\pi$
$504$	5.38994	0.240087
$505$	−2.69650	−0.119993
$506$	2.27239	0.101020
$507$	−1.55375	−0.0690046
$508$	1.65390	0.0733800
$509$	7.34048	0.325361	0.162681	−	0.986679i	$-0.447986\pi$
$509$	7.34048	0.325361	0.162681	+	0.986679i	$0.447986\pi$
$510$	−0.834333	−0.0369449
$511$	6.05430	0.267827
$512$	1.00000	0.0441942
$513$	0.972287	0.0429275
$514$	−12.9540	−0.571375
$515$	28.6572	1.26279
$516$	0.389402	0.0171425
$517$	6.99706	0.307730
$518$	−10.5115	−0.461848
$519$	3.75389	0.164777
$520$	−6.58511	−0.288776
$521$	35.9443	1.57475	0.787374	−	0.616475i	$-0.211440\pi$
$521$	35.9443	1.57475	0.787374	+	0.616475i	$0.211440\pi$
$522$	2.98505	0.130652
$523$	−6.09667	−0.266589	−0.133294	−	0.991076i	$-0.542556\pi$
$523$	−6.09667	−0.266589	−0.133294	+	0.991076i	$0.542556\pi$
$524$	−1.00000	−0.0436852
$525$	−0.971494	−0.0423995
$526$	12.7361	0.555321
$527$	−12.0431	−0.524606
$528$	−0.404728	−0.0176135
$529$	1.00000	0.0434783
$530$	−5.96710	−0.259194
$531$	22.8678	0.992377
$532$	−1.66090	−0.0720091
$533$	−55.6641	−2.41108
$534$	−2.30552	−0.0997697
$535$	−18.0879	−0.782008
$536$	−14.8363	−0.640830
$537$	−0.865617	−0.0373541
$538$	2.96979	0.128037
$539$	−8.41396	−0.362415
$540$	−1.50185	−0.0646293
$541$	−8.09018	−0.347824	−0.173912	−	0.984761i	$-0.555641\pi$
$541$	−8.09018	−0.347824	−0.173912	+	0.984761i	$0.555641\pi$
$542$	29.4507	1.26501
$543$	−1.95599	−0.0839397
$544$	−3.31560	−0.142155
$545$	18.1344	0.776794
$546$	1.50740	0.0645107
$547$	38.0739	1.62792	0.813960	−	0.580920i	$-0.197307\pi$
$547$	38.0739	1.62792	0.813960	+	0.580920i	$0.197307\pi$
$548$	9.64073	0.411832
$549$	−25.7786	−1.10020
$550$	−6.82592	−0.291058
$551$	−0.919837	−0.0391864
$552$	−0.178107	−0.00758075
$553$	21.1479	0.899301
$554$	−7.23226	−0.307269
$555$	1.45667	0.0618324
$556$	−20.5272	−0.870547
$557$	32.7347	1.38701	0.693507	−	0.720450i	$-0.256065\pi$
$557$	32.7347	1.38701	0.693507	+	0.720450i	$0.256065\pi$
$558$	−10.7816	−0.456419
$559$	−10.1902	−0.431001
$560$	2.56552	0.108413
$561$	1.34192	0.0566558
$562$	−10.9868	−0.463450
$563$	−41.2219	−1.73729	−0.868647	−	0.495432i	$-0.835010\pi$
$563$	−41.2219	−1.73729	−0.868647	+	0.495432i	$0.835010\pi$
$564$	−0.548422	−0.0230927
$565$	18.5427	0.780098
$566$	4.48327	0.188446
$567$	−15.8260	−0.664631
$568$	2.58652	0.108528
$569$	20.3883	0.854723	0.427362	−	0.904081i	$-0.359443\pi$
$569$	20.3883	0.854723	0.427362	+	0.904081i	$0.359443\pi$
$570$	0.230166	0.00964060
$571$	−44.7901	−1.87441	−0.937204	−	0.348781i	$-0.886596\pi$
$571$	−44.7901	−1.87441	−0.937204	+	0.348781i	$0.886596\pi$
$572$	10.5913	0.442844
$573$	−0.219817	−0.00918300
$574$	21.6864	0.905173
$575$	−3.00386	−0.125269
$576$	−2.96828	−0.123678
$577$	44.7937	1.86479	0.932393	−	0.361445i	$-0.117717\pi$
$577$	44.7937	1.86479	0.932393	+	0.361445i	$0.117717\pi$
$578$	−6.00680	−0.249850
$579$	−0.402096	−0.0167105
$580$	1.42083	0.0589968
$581$	18.2879	0.758710
$582$	−1.56714	−0.0649600
$583$	9.59731	0.397480
$584$	−3.33415	−0.137968
$585$	19.5464	0.808145
$586$	−31.2586	−1.29128
$587$	11.0519	0.456159	0.228080	−	0.973643i	$-0.426755\pi$
$587$	11.0519	0.456159	0.228080	+	0.973643i	$0.426755\pi$
$588$	0.659477	0.0271964
$589$	3.32231	0.136894
$590$	10.8847	0.448115
$591$	0.0876832	0.00360680
$592$	5.78875	0.237916
$593$	−30.4008	−1.24841	−0.624205	−	0.781260i	$-0.714577\pi$
$593$	−30.4008	−1.24841	−0.624205	+	0.781260i	$0.714577\pi$
$594$	2.41553	0.0991104
$595$	−8.50623	−0.348722
$596$	−10.0701	−0.412485
$597$	2.05986	0.0843046
$598$	4.66087	0.190597
$599$	16.5244	0.675171	0.337585	−	0.941295i	$-0.390390\pi$
$599$	16.5244	0.675171	0.337585	+	0.941295i	$0.390390\pi$
$600$	0.535009	0.0218416
$601$	−29.7955	−1.21538	−0.607691	−	0.794173i	$-0.707904\pi$
$601$	−29.7955	−1.21538	−0.607691	+	0.794173i	$0.707904\pi$
$602$	3.97005	0.161807
$603$	44.0382	1.79337
$604$	3.65154	0.148579
$605$	8.24576	0.335238
$606$	−0.339927	−0.0138086
$607$	−27.4983	−1.11612	−0.558060	−	0.829801i	$-0.688454\pi$
$607$	−27.4983	−1.11612	−0.558060	+	0.829801i	$0.688454\pi$
$608$	0.914669	0.0370947
$609$	−0.325243	−0.0131795
$610$	−12.2702	−0.496804
$611$	14.3516	0.580604
$612$	9.84162	0.397824
$613$	−22.2087	−0.897003	−0.448501	−	0.893782i	$-0.648042\pi$
$613$	−22.2087	−0.897003	−0.448501	+	0.893782i	$0.648042\pi$
$614$	0.617623	0.0249252
$615$	−3.00529	−0.121185
$616$	−4.12631	−0.166254
$617$	6.49797	0.261598	0.130799	−	0.991409i	$-0.458246\pi$
$617$	6.49797	0.261598	0.130799	+	0.991409i	$0.458246\pi$
$618$	3.61259	0.145320
$619$	49.2839	1.98089	0.990444	−	0.137917i	$-0.0440407\pi$
$619$	49.2839	1.98089	0.990444	+	0.137917i	$0.0440407\pi$
$620$	−5.13183	−0.206099
$621$	1.06299	0.0426565
$622$	16.6115	0.666061
$623$	−23.5054	−0.941723
$624$	−0.830134	−0.0332320
$625$	−0.957567	−0.0383027
$626$	−26.7093	−1.06752
$627$	−0.370193	−0.0147841
$628$	−16.3207	−0.651267
$629$	−19.1932	−0.765282
$630$	−7.61517	−0.303396
$631$	15.9559	0.635195	0.317597	−	0.948226i	$-0.397124\pi$
$631$	15.9559	0.635195	0.317597	+	0.948226i	$0.397124\pi$
$632$	−11.6463	−0.463265
$633$	2.94833	0.117186
$634$	21.6922	0.861506
$635$	−2.33671	−0.0927297
$636$	−0.752228	−0.0298278
$637$	−17.2578	−0.683778
$638$	−2.28522	−0.0904729
$639$	−7.67752	−0.303718
$640$	−1.41285	−0.0558478
$641$	3.26044	0.128780	0.0643898	−	0.997925i	$-0.479490\pi$
$641$	3.26044	0.128780	0.0643898	+	0.997925i	$0.479490\pi$
$642$	−2.28020	−0.0899925
$643$	33.9210	1.33771	0.668856	−	0.743392i	$-0.266784\pi$
$643$	33.9210	1.33771	0.668856	+	0.743392i	$0.266784\pi$
$644$	−1.81585	−0.0715544
$645$	−0.550167	−0.0216628
$646$	−3.03268	−0.119319
$647$	−6.34726	−0.249537	−0.124768	−	0.992186i	$-0.539819\pi$
$647$	−6.34726	−0.249537	−0.124768	+	0.992186i	$0.539819\pi$
$648$	8.71551	0.342377
$649$	−17.5066	−0.687193
$650$	−14.0006	−0.549148
$651$	1.17473	0.0460413
$652$	−23.4443	−0.918148
$653$	0.115073	0.00450315	0.00225158	−	0.999997i	$-0.499283\pi$
$653$	0.115073	0.00450315	0.00225158	+	0.999997i	$0.499283\pi$
$654$	2.28607	0.0893925
$655$	1.41285	0.0552046
$656$	−11.9429	−0.466290
$657$	9.89667	0.386106
$658$	−5.59130	−0.217972
$659$	−10.1561	−0.395626	−0.197813	−	0.980240i	$-0.563384\pi$
$659$	−10.1561	−0.395626	−0.197813	+	0.980240i	$0.563384\pi$
$660$	0.571820	0.0222581
$661$	−1.96665	−0.0764937	−0.0382469	−	0.999268i	$-0.512177\pi$
$661$	−1.96665	−0.0764937	−0.0382469	+	0.999268i	$0.512177\pi$
$662$	−14.4767	−0.562654
$663$	2.75239	0.106894
$664$	−10.0713	−0.390841
$665$	2.34660	0.0909973
$666$	−17.1826	−0.665813
$667$	−1.00565	−0.0389389
$668$	−1.83425	−0.0709691
$669$	−0.463288	−0.0179118
$670$	20.9614	0.809811
$671$	19.7350	0.761860
$672$	0.323416	0.0124760
$673$	−42.4032	−1.63452	−0.817262	−	0.576266i	$-0.804509\pi$
$673$	−42.4032	−1.63452	−0.817262	+	0.576266i	$0.804509\pi$
$674$	−13.5900	−0.523468
$675$	−3.19308	−0.122902
$676$	8.72370	0.335527
$677$	48.6053	1.86805	0.934026	−	0.357205i	$-0.116270\pi$
$677$	48.6053	1.86805	0.934026	+	0.357205i	$0.116270\pi$
$678$	2.33754	0.0897727
$679$	−15.9774	−0.613155
$680$	4.68444	0.179640
$681$	1.58840	0.0608677
$682$	8.25389	0.316058
$683$	−35.0014	−1.33929	−0.669646	−	0.742680i	$-0.733554\pi$
$683$	−35.0014	−1.33929	−0.669646	+	0.742680i	$0.733554\pi$
$684$	−2.71499	−0.103810
$685$	−13.6209	−0.520428
$686$	19.4345	0.742011
$687$	0.973467	0.0371401
$688$	−2.18634	−0.0833533
$689$	19.6850	0.749937
$690$	0.251639	0.00957972
$691$	−0.173654	−0.00660612	−0.00330306	−	0.999995i	$-0.501051\pi$
$691$	−0.173654	−0.00660612	−0.00330306	+	0.999995i	$0.501051\pi$
$692$	−21.0765	−0.801210
$693$	12.2480	0.465264
$694$	−14.6933	−0.557751
$695$	29.0018	1.10010
$696$	0.179113	0.00678928
$697$	39.5977	1.49987
$698$	−14.6842	−0.555805
$699$	1.19469	0.0451875
$700$	5.45455	0.206162
$701$	−31.2022	−1.17849	−0.589246	−	0.807953i	$-0.700575\pi$
$701$	−31.2022	−1.17849	−0.589246	+	0.807953i	$0.700575\pi$
$702$	4.95447	0.186995
$703$	5.29479	0.199697
$704$	2.27239	0.0856438
$705$	0.774838	0.0291821
$706$	−12.5224	−0.471287
$707$	−3.46564	−0.130339
$708$	1.37215	0.0515685
$709$	−34.9165	−1.31132	−0.655658	−	0.755058i	$-0.727609\pi$
$709$	−34.9165	−1.31132	−0.655658	+	0.755058i	$0.727609\pi$
$710$	−3.65437	−0.137146
$711$	34.5695	1.29646
$712$	12.9446	0.485118
$713$	3.63226	0.136029
$714$	−1.07232	−0.0401304
$715$	−14.9639	−0.559618
$716$	4.86009	0.181630
$717$	−2.40636	−0.0898673
$718$	−8.82817	−0.329465
$719$	−36.5981	−1.36488	−0.682440	−	0.730942i	$-0.739081\pi$
$719$	−36.5981	−1.36488	−0.682440	+	0.730942i	$0.739081\pi$
$720$	4.19373	0.156291
$721$	36.8313	1.37167
$722$	−18.1634	−0.675971
$723$	−1.20373	−0.0447671
$724$	10.9821	0.408147
$725$	3.02083	0.112191
$726$	1.03948	0.0385788
$727$	−16.2356	−0.602146	−0.301073	−	0.953601i	$-0.597345\pi$
$727$	−16.2356	−0.602146	−0.301073	+	0.953601i	$0.597345\pi$
$728$	−8.46343	−0.313675
$729$	−25.3021	−0.937113
$730$	4.71065	0.174349
$731$	7.24902	0.268115
$732$	−1.54681	−0.0571716
$733$	33.1568	1.22468	0.612338	−	0.790596i	$-0.290229\pi$
$733$	33.1568	1.22468	0.612338	+	0.790596i	$0.290229\pi$
$734$	30.3961	1.12194
$735$	−0.931742	−0.0343678
$736$	1.00000	0.0368605
$737$	−33.7137	−1.24186
$738$	35.4497	1.30492
$739$	−21.4215	−0.788004	−0.394002	−	0.919110i	$-0.628910\pi$
$739$	−21.4215	−0.788004	−0.394002	+	0.919110i	$0.628910\pi$
$740$	−8.17863	−0.300653
$741$	−0.759298	−0.0278935
$742$	−7.66915	−0.281543
$743$	11.1302	0.408327	0.204164	−	0.978937i	$-0.434553\pi$
$743$	11.1302	0.408327	0.204164	+	0.978937i	$0.434553\pi$
$744$	−0.646931	−0.0237177
$745$	14.2275	0.521254
$746$	6.13144	0.224488
$747$	29.8943	1.09378
$748$	−7.53432	−0.275482
$749$	−23.2473	−0.849436
$750$	−2.01408	−0.0735438
$751$	−8.28255	−0.302235	−0.151117	−	0.988516i	$-0.548287\pi$
$751$	−8.28255	−0.302235	−0.151117	+	0.988516i	$0.548287\pi$
$752$	3.07917	0.112286
$753$	1.43852	0.0524226
$754$	−4.68720	−0.170698
$755$	−5.15908	−0.187758
$756$	−1.93023	−0.0702019
$757$	−9.63793	−0.350297	−0.175148	−	0.984542i	$-0.556040\pi$
$757$	−9.63793	−0.350297	−0.175148	+	0.984542i	$0.556040\pi$
$758$	8.13702	0.295550
$759$	−0.404728	−0.0146907
$760$	−1.29229	−0.0468763
$761$	−36.7195	−1.33108	−0.665541	−	0.746362i	$-0.731799\pi$
$761$	−36.7195	−1.33108	−0.665541	+	0.746362i	$0.731799\pi$
$762$	−0.294572	−0.0106712
$763$	23.3071	0.843772
$764$	1.23419	0.0446512
$765$	−13.9047	−0.502726
$766$	31.7073	1.14563
$767$	−35.9076	−1.29655
$768$	−0.178107	−0.00642689
$769$	−31.6641	−1.14184	−0.570918	−	0.821007i	$-0.693412\pi$
$769$	−31.6641	−1.14184	−0.570918	+	0.821007i	$0.693412\pi$
$770$	5.82985	0.210093
$771$	2.30720	0.0830916
$772$	2.25761	0.0812530
$773$	36.4327	1.31039	0.655196	−	0.755459i	$-0.272586\pi$
$773$	36.4327	1.31039	0.655196	+	0.755459i	$0.272586\pi$
$774$	6.48965	0.233266
$775$	−10.9108	−0.391927
$776$	8.79885	0.315860
$777$	1.87217	0.0671638
$778$	21.5461	0.772466
$779$	−10.9238	−0.391384
$780$	1.17286	0.0419949
$781$	5.87757	0.210316
$782$	−3.31560	−0.118566
$783$	−1.06900	−0.0382029
$784$	−3.70270	−0.132239
$785$	23.0587	0.823000
$786$	0.178107	0.00635288
$787$	−14.3395	−0.511146	−0.255573	−	0.966790i	$-0.582264\pi$
$787$	−14.3395	−0.511146	−0.255573	+	0.966790i	$0.582264\pi$
$788$	−0.492305	−0.0175377
$789$	−2.26839	−0.0807569
$790$	16.4545	0.585424
$791$	23.8318	0.847362
$792$	−6.74507	−0.239676
$793$	40.4782	1.43742
$794$	−4.30313	−0.152712
$795$	1.06278	0.0376931
$796$	−11.5653	−0.409921
$797$	6.00843	0.212830	0.106415	−	0.994322i	$-0.466063\pi$
$797$	6.00843	0.212830	0.106415	+	0.994322i	$0.466063\pi$
$798$	0.295818	0.0104719
$799$	−10.2093	−0.361179
$800$	−3.00386	−0.106202
$801$	−38.4231	−1.35761
$802$	−8.63112	−0.304775
$803$	−7.57647	−0.267368
$804$	2.64245	0.0931920
$805$	2.56552	0.0904227
$806$	16.9295	0.596315
$807$	−0.528941	−0.0186196
$808$	1.90855	0.0671427
$809$	−15.6256	−0.549366	−0.274683	−	0.961535i	$-0.588573\pi$
$809$	−15.6256	−0.549366	−0.274683	+	0.961535i	$0.588573\pi$
$810$	−12.3137	−0.432659
$811$	51.8949	1.82228	0.911138	−	0.412102i	$-0.135205\pi$
$811$	51.8949	1.82228	0.911138	+	0.412102i	$0.135205\pi$
$812$	1.82611	0.0640838
$813$	−5.24538	−0.183963
$814$	13.1543	0.461057
$815$	33.1232	1.16026
$816$	0.590532	0.0206728
$817$	−1.99977	−0.0699633
$818$	−3.05113	−0.106680
$819$	25.1218	0.877827
$820$	16.8735	0.589247
$821$	−39.4479	−1.37674	−0.688371	−	0.725359i	$-0.741674\pi$
$821$	−39.4479	−1.37674	−0.688371	+	0.725359i	$0.741674\pi$
$822$	−1.71708	−0.0598902
$823$	−42.0781	−1.46675	−0.733374	−	0.679825i	$-0.762056\pi$
$823$	−42.0781	−1.46675	−0.733374	+	0.679825i	$0.762056\pi$
$824$	−20.2832	−0.706600
$825$	1.21575	0.0423268
$826$	13.9894	0.486753
$827$	−27.9102	−0.970534	−0.485267	−	0.874366i	$-0.661278\pi$
$827$	−27.9102	−0.970534	−0.485267	+	0.874366i	$0.661278\pi$
$828$	−2.96828	−0.103155
$829$	−42.1896	−1.46530	−0.732652	−	0.680603i	$-0.761718\pi$
$829$	−42.1896	−1.46530	−0.732652	+	0.680603i	$0.761718\pi$
$830$	14.2292	0.493902
$831$	1.28812	0.0446843
$832$	4.66087	0.161587
$833$	12.2767	0.425361
$834$	3.65604	0.126598
$835$	2.59151	0.0896830
$836$	2.07848	0.0718858
$837$	3.86107	0.133458
$838$	15.9054	0.549442
$839$	−5.95824	−0.205701	−0.102851	−	0.994697i	$-0.532796\pi$
$839$	−5.95824	−0.205701	−0.102851	+	0.994697i	$0.532796\pi$
$840$	−0.456938	−0.0157658
$841$	−27.9887	−0.965127
$842$	38.2315	1.31754
$843$	1.95683	0.0673967
$844$	−16.5537	−0.569801
$845$	−12.3253	−0.424002
$846$	−9.13983	−0.314234
$847$	10.5978	0.364144
$848$	4.22345	0.145034
$849$	−0.798503	−0.0274045
$850$	9.95958	0.341611
$851$	5.78875	0.198436
$852$	−0.460678	−0.0157826
$853$	9.18417	0.314460	0.157230	−	0.987562i	$-0.449744\pi$
$853$	9.18417	0.314460	0.157230	+	0.987562i	$0.449744\pi$
$854$	−15.7701	−0.539641
$855$	3.83588	0.131184
$856$	12.8024	0.437578
$857$	48.5626	1.65887	0.829433	−	0.558606i	$-0.188664\pi$
$857$	48.5626	1.65887	0.829433	+	0.558606i	$0.188664\pi$
$858$	−1.88639	−0.0644001
$859$	30.8860	1.05382	0.526909	−	0.849922i	$-0.323351\pi$
$859$	30.8860	1.05382	0.526909	+	0.849922i	$0.323351\pi$
$860$	3.08896	0.105333
$861$	−3.86251	−0.131634
$862$	16.9963	0.578897
$863$	−13.0395	−0.443868	−0.221934	−	0.975062i	$-0.571237\pi$
$863$	−13.0395	−0.443868	−0.221934	+	0.975062i	$0.571237\pi$
$864$	1.06299	0.0361638
$865$	29.7780	1.01248
$866$	17.0249	0.578529
$867$	1.06985	0.0363342
$868$	−6.59563	−0.223870
$869$	−26.4649	−0.897760
$870$	−0.253060	−0.00857955
$871$	−69.1499	−2.34306
$872$	−12.8354	−0.434660
$873$	−26.1174	−0.883941
$874$	0.914669	0.0309391
$875$	−20.5340	−0.694178
$876$	0.593836	0.0200638
$877$	26.5095	0.895162	0.447581	−	0.894243i	$-0.352286\pi$
$877$	26.5095	0.895162	0.447581	+	0.894243i	$0.352286\pi$
$878$	26.6398	0.899049
$879$	5.56739	0.187783
$880$	−3.21054	−0.108227
$881$	−16.0033	−0.539164	−0.269582	−	0.962977i	$-0.586886\pi$
$881$	−16.0033	−0.539164	−0.269582	+	0.962977i	$0.586886\pi$
$882$	10.9906	0.370074
$883$	2.52302	0.0849064	0.0424532	−	0.999098i	$-0.486483\pi$
$883$	2.52302	0.0849064	0.0424532	+	0.999098i	$0.486483\pi$
$884$	−15.4536	−0.519760
$885$	−1.93864	−0.0651666
$886$	−17.2678	−0.580125
$887$	51.7172	1.73649	0.868246	−	0.496134i	$-0.165248\pi$
$887$	51.7172	1.73649	0.868246	+	0.496134i	$0.165248\pi$
$888$	−1.03102	−0.0345987
$889$	−3.00323	−0.100725
$890$	−18.2887	−0.613040
$891$	19.8050	0.663492
$892$	2.60117	0.0870938
$893$	2.81642	0.0942479
$894$	1.79355	0.0599853
$895$	−6.86657	−0.229524
$896$	−1.81585	−0.0606632
$897$	−0.830134	−0.0277174
$898$	−11.6935	−0.390218
$899$	−3.65278	−0.121827
$900$	8.91628	0.297209
$901$	−14.0033	−0.466517
$902$	−27.1388	−0.903622
$903$	−0.707095	−0.0235307
$904$	−13.1243	−0.436509
$905$	−15.5161	−0.515772
$906$	−0.650366	−0.0216070
$907$	−3.05299	−0.101373	−0.0506865	−	0.998715i	$-0.516141\pi$
$907$	−3.05299	−0.101373	−0.0506865	+	0.998715i	$0.516141\pi$
$908$	−8.91823	−0.295962
$909$	−5.66512	−0.187900
$910$	11.9575	0.396389
$911$	−8.57834	−0.284213	−0.142107	−	0.989851i	$-0.545388\pi$
$911$	−8.57834	−0.284213	−0.142107	+	0.989851i	$0.545388\pi$
$912$	−0.162909	−0.00539446
$913$	−22.8858	−0.757410
$914$	41.9709	1.38827
$915$	2.18540	0.0722472
$916$	−5.46562	−0.180589
$917$	1.81585	0.0599646
$918$	−3.52446	−0.116325
$919$	14.2122	0.468817	0.234409	−	0.972138i	$-0.424685\pi$
$919$	14.2122	0.468817	0.234409	+	0.972138i	$0.424685\pi$
$920$	−1.41285	−0.0465803
$921$	−0.110003	−0.00362473
$922$	−9.05281	−0.298138
$923$	12.0554	0.396810
$924$	0.734925	0.0241773
$925$	−17.3886	−0.571733
$926$	−15.8265	−0.520090
$927$	60.2063	1.97743
$928$	−1.00565	−0.0330121
$929$	27.2679	0.894630	0.447315	−	0.894376i	$-0.352380\pi$
$929$	27.2679	0.894630	0.447315	+	0.894376i	$0.352380\pi$
$930$	0.914017	0.0299718
$931$	−3.38674	−0.110996
$932$	−6.70773	−0.219719
$933$	−2.95863	−0.0968613
$934$	34.3648	1.12445
$935$	10.6449	0.348124
$936$	−13.8348	−0.452203
$937$	−8.01674	−0.261896	−0.130948	−	0.991389i	$-0.541802\pi$
$937$	−8.01674	−0.261896	−0.130948	+	0.991389i	$0.541802\pi$
$938$	26.9404	0.879636
$939$	4.75712	0.155243
$940$	−4.35040	−0.141895
$941$	−26.8377	−0.874886	−0.437443	−	0.899246i	$-0.644116\pi$
$941$	−26.8377	−0.874886	−0.437443	+	0.899246i	$0.644116\pi$
$942$	2.90684	0.0947098
$943$	−11.9429	−0.388913
$944$	−7.70406	−0.250746
$945$	2.72713	0.0887136
$946$	−4.96820	−0.161530
$947$	29.8389	0.969634	0.484817	−	0.874616i	$-0.338886\pi$
$947$	29.8389	0.969634	0.484817	+	0.874616i	$0.338886\pi$
$948$	2.07429	0.0673698
$949$	−15.5400	−0.504450
$950$	−2.74753	−0.0891418
$951$	−3.86353	−0.125284
$952$	6.02062	0.195130
$953$	−18.2779	−0.592078	−0.296039	−	0.955176i	$-0.595666\pi$
$953$	−18.2779	−0.592078	−0.296039	+	0.955176i	$0.595666\pi$
$954$	−12.5364	−0.405880
$955$	−1.74372	−0.0564254
$956$	13.5108	0.436969
$957$	0.407015	0.0131569
$958$	−15.4641	−0.499621
$959$	−17.5061	−0.565301
$960$	0.251639	0.00812161
$961$	−17.8067	−0.574410
$962$	26.9806	0.869890
$963$	−38.0012	−1.22457
$964$	6.75844	0.217675
$965$	−3.18966	−0.102679
$966$	0.323416	0.0104057
$967$	8.70219	0.279844	0.139922	−	0.990163i	$-0.455315\pi$
$967$	8.70219	0.279844	0.139922	+	0.990163i	$0.455315\pi$
$968$	−5.83626	−0.187585
$969$	0.540142	0.0173519
$970$	−12.4315	−0.399150
$971$	9.77007	0.313536	0.156768	−	0.987635i	$-0.449892\pi$
$971$	9.77007	0.313536	0.156768	+	0.987635i	$0.449892\pi$
$972$	−4.74128	−0.152076
$973$	37.2743	1.19496
$974$	−12.8984	−0.413290
$975$	2.49360	0.0798593
$976$	8.68469	0.277990
$977$	20.8151	0.665933	0.332967	−	0.942939i	$-0.391950\pi$
$977$	20.8151	0.665933	0.332967	+	0.942939i	$0.391950\pi$
$978$	4.17559	0.133521
$979$	29.4151	0.940109
$980$	5.23135	0.167109
$981$	38.0989	1.21641
$982$	30.6064	0.976690
$983$	3.71622	0.118529	0.0592645	−	0.998242i	$-0.481124\pi$
$983$	3.71622	0.118529	0.0592645	+	0.998242i	$0.481124\pi$
$984$	2.12711	0.0678098
$985$	0.695553	0.0221622
$986$	3.33433	0.106187
$987$	0.995851	0.0316983
$988$	4.26315	0.135629
$989$	−2.18634	−0.0695215
$990$	9.52977	0.302876
$991$	3.74015	0.118810	0.0594049	−	0.998234i	$-0.481080\pi$
$991$	3.74015	0.118810	0.0594049	+	0.998234i	$0.481080\pi$
$992$	3.63226	0.115324
$993$	2.57841	0.0818234
$994$	−4.69673	−0.148971
$995$	16.3400	0.518014
$996$	1.79377	0.0568377
$997$	32.0518	1.01509	0.507545	−	0.861625i	$-0.330553\pi$
$997$	32.0518	1.01509	0.507545	+	0.861625i	$0.330553\pi$
$998$	8.34998	0.264314
$999$	6.15340	0.194685

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.f.1.11	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.f.1.11	✓	20	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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.178107 q^{3} +1.00000 q^{4} -1.41285 q^{5} -0.178107 q^{6} -1.81585 q^{7} +1.00000 q^{8} -2.96828 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.178107 q^{3} +1.00000 q^{4} -1.41285 q^{5} -0.178107 q^{6} -1.81585 q^{7} +1.00000 q^{8} -2.96828 q^{9} -1.41285 q^{10} +2.27239 q^{11} -0.178107 q^{12} +4.66087 q^{13} -1.81585 q^{14} +0.251639 q^{15} +1.00000 q^{16} -3.31560 q^{17} -2.96828 q^{18} +0.914669 q^{19} -1.41285 q^{20} +0.323416 q^{21} +2.27239 q^{22} +1.00000 q^{23} -0.178107 q^{24} -3.00386 q^{25} +4.66087 q^{26} +1.06299 q^{27} -1.81585 q^{28} -1.00565 q^{29} +0.251639 q^{30} +3.63226 q^{31} +1.00000 q^{32} -0.404728 q^{33} -3.31560 q^{34} +2.56552 q^{35} -2.96828 q^{36} +5.78875 q^{37} +0.914669 q^{38} -0.830134 q^{39} -1.41285 q^{40} -11.9429 q^{41} +0.323416 q^{42} -2.18634 q^{43} +2.27239 q^{44} +4.19373 q^{45} +1.00000 q^{46} +3.07917 q^{47} -0.178107 q^{48} -3.70270 q^{49} -3.00386 q^{50} +0.590532 q^{51} +4.66087 q^{52} +4.22345 q^{53} +1.06299 q^{54} -3.21054 q^{55} -1.81585 q^{56} -0.162909 q^{57} -1.00565 q^{58} -7.70406 q^{59} +0.251639 q^{60} +8.68469 q^{61} +3.63226 q^{62} +5.38994 q^{63} +1.00000 q^{64} -6.58511 q^{65} -0.404728 q^{66} -14.8363 q^{67} -3.31560 q^{68} -0.178107 q^{69} +2.56552 q^{70} +2.58652 q^{71} -2.96828 q^{72} -3.33415 q^{73} +5.78875 q^{74} +0.535009 q^{75} +0.914669 q^{76} -4.12631 q^{77} -0.830134 q^{78} -11.6463 q^{79} -1.41285 q^{80} +8.71551 q^{81} -11.9429 q^{82} -10.0713 q^{83} +0.323416 q^{84} +4.68444 q^{85} -2.18634 q^{86} +0.179113 q^{87} +2.27239 q^{88} +12.9446 q^{89} +4.19373 q^{90} -8.46343 q^{91} +1.00000 q^{92} -0.646931 q^{93} +3.07917 q^{94} -1.29229 q^{95} -0.178107 q^{96} +8.79885 q^{97} -3.70270 q^{98} -6.74507 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{2} - 5 q^{3} + 20 q^{4} - 6 q^{5} - 5 q^{6} - 12 q^{7} + 20 q^{8} - q^{9}+O(q^{10}) \) 20 * q + 20 * q^2 - 5 * q^3 + 20 * q^4 - 6 * q^5 - 5 * q^6 - 12 * q^7 + 20 * q^8 - q^9	\( 20 q + 20 q^{2} - 5 q^{3} + 20 q^{4} - 6 q^{5} - 5 q^{6} - 12 q^{7} + 20 q^{8} - q^{9} - 6 q^{10} - 3 q^{11} - 5 q^{12} - 13 q^{13} - 12 q^{14} - 10 q^{15} + 20 q^{16} - 14 q^{17} - q^{18} - 21 q^{19} - 6 q^{20} - 8 q^{21} - 3 q^{22} + 20 q^{23} - 5 q^{24} - 14 q^{25} - 13 q^{26} - 5 q^{27} - 12 q^{28} - 27 q^{29} - 10 q^{30} - 27 q^{31} + 20 q^{32} - 12 q^{33} - 14 q^{34} - 23 q^{35} - q^{36} - 19 q^{37} - 21 q^{38} - 35 q^{39} - 6 q^{40} - 17 q^{41} - 8 q^{42} - 27 q^{43} - 3 q^{44} + 4 q^{45} + 20 q^{46} - 28 q^{47} - 5 q^{48} - 10 q^{49} - 14 q^{50} + 6 q^{51} - 13 q^{52} - 47 q^{53} - 5 q^{54} - 4 q^{55} - 12 q^{56} - 16 q^{57} - 27 q^{58} - 16 q^{59} - 10 q^{60} - 9 q^{61} - 27 q^{62} - 9 q^{63} + 20 q^{64} + 9 q^{65} - 12 q^{66} - 8 q^{67} - 14 q^{68} - 5 q^{69} - 23 q^{70} - 30 q^{71} - q^{72} - 26 q^{73} - 19 q^{74} - 18 q^{75} - 21 q^{76} - 50 q^{77} - 35 q^{78} - 35 q^{79} - 6 q^{80} - 60 q^{81} - 17 q^{82} + 2 q^{83} - 8 q^{84} - 62 q^{85} - 27 q^{86} + q^{87} - 3 q^{88} - 25 q^{89} + 4 q^{90} + 22 q^{91} + 20 q^{92} - 21 q^{93} - 28 q^{94} - 14 q^{95} - 5 q^{96} + 2 q^{97} - 10 q^{98} - 5 q^{99}+O(q^{100}) \) 20 * q + 20 * q^2 - 5 * q^3 + 20 * q^4 - 6 * q^5 - 5 * q^6 - 12 * q^7 + 20 * q^8 - q^9 - 6 * q^10 - 3 * q^11 - 5 * q^12 - 13 * q^13 - 12 * q^14 - 10 * q^15 + 20 * q^16 - 14 * q^17 - q^18 - 21 * q^19 - 6 * q^20 - 8 * q^21 - 3 * q^22 + 20 * q^23 - 5 * q^24 - 14 * q^25 - 13 * q^26 - 5 * q^27 - 12 * q^28 - 27 * q^29 - 10 * q^30 - 27 * q^31 + 20 * q^32 - 12 * q^33 - 14 * q^34 - 23 * q^35 - q^36 - 19 * q^37 - 21 * q^38 - 35 * q^39 - 6 * q^40 - 17 * q^41 - 8 * q^42 - 27 * q^43 - 3 * q^44 + 4 * q^45 + 20 * q^46 - 28 * q^47 - 5 * q^48 - 10 * q^49 - 14 * q^50 + 6 * q^51 - 13 * q^52 - 47 * q^53 - 5 * q^54 - 4 * q^55 - 12 * q^56 - 16 * q^57 - 27 * q^58 - 16 * q^59 - 10 * q^60 - 9 * q^61 - 27 * q^62 - 9 * q^63 + 20 * q^64 + 9 * q^65 - 12 * q^66 - 8 * q^67 - 14 * q^68 - 5 * q^69 - 23 * q^70 - 30 * q^71 - q^72 - 26 * q^73 - 19 * q^74 - 18 * q^75 - 21 * q^76 - 50 * q^77 - 35 * q^78 - 35 * q^79 - 6 * q^80 - 60 * q^81 - 17 * q^82 + 2 * q^83 - 8 * q^84 - 62 * q^85 - 27 * q^86 + q^87 - 3 * q^88 - 25 * q^89 + 4 * q^90 + 22 * q^91 + 20 * q^92 - 21 * q^93 - 28 * q^94 - 14 * q^95 - 5 * q^96 + 2 * q^97 - 10 * q^98 - 5 * q^99

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