LMFDB - Embedded newform 6026.2.a.f.1.13

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			1.13
Root			$-0.435939$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +0.435939 q^{3} +1.00000 q^{4} -0.796234 q^{5} +0.435939 q^{6} +3.50309 q^{7} +1.00000 q^{8} -2.80996 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.435939 q^{3} +1.00000 q^{4} -0.796234 q^{5} +0.435939 q^{6} +3.50309 q^{7} +1.00000 q^{8} -2.80996 q^{9} -0.796234 q^{10} +3.32161 q^{11} +0.435939 q^{12} -5.74710 q^{13} +3.50309 q^{14} -0.347110 q^{15} +1.00000 q^{16} -5.02257 q^{17} -2.80996 q^{18} -2.58528 q^{19} -0.796234 q^{20} +1.52713 q^{21} +3.32161 q^{22} +1.00000 q^{23} +0.435939 q^{24} -4.36601 q^{25} -5.74710 q^{26} -2.53279 q^{27} +3.50309 q^{28} -1.20814 q^{29} -0.347110 q^{30} +5.64294 q^{31} +1.00000 q^{32} +1.44802 q^{33} -5.02257 q^{34} -2.78928 q^{35} -2.80996 q^{36} -5.90948 q^{37} -2.58528 q^{38} -2.50539 q^{39} -0.796234 q^{40} -8.67527 q^{41} +1.52713 q^{42} -10.6307 q^{43} +3.32161 q^{44} +2.23738 q^{45} +1.00000 q^{46} -7.02860 q^{47} +0.435939 q^{48} +5.27166 q^{49} -4.36601 q^{50} -2.18953 q^{51} -5.74710 q^{52} +1.67208 q^{53} -2.53279 q^{54} -2.64478 q^{55} +3.50309 q^{56} -1.12702 q^{57} -1.20814 q^{58} -8.50760 q^{59} -0.347110 q^{60} +6.06904 q^{61} +5.64294 q^{62} -9.84354 q^{63} +1.00000 q^{64} +4.57604 q^{65} +1.44802 q^{66} +0.567248 q^{67} -5.02257 q^{68} +0.435939 q^{69} -2.78928 q^{70} +10.1319 q^{71} -2.80996 q^{72} +5.84766 q^{73} -5.90948 q^{74} -1.90331 q^{75} -2.58528 q^{76} +11.6359 q^{77} -2.50539 q^{78} +0.978625 q^{79} -0.796234 q^{80} +7.32573 q^{81} -8.67527 q^{82} +1.48384 q^{83} +1.52713 q^{84} +3.99914 q^{85} -10.6307 q^{86} -0.526674 q^{87} +3.32161 q^{88} -14.9323 q^{89} +2.23738 q^{90} -20.1326 q^{91} +1.00000 q^{92} +2.45998 q^{93} -7.02860 q^{94} +2.05849 q^{95} +0.435939 q^{96} +8.30629 q^{97} +5.27166 q^{98} -9.33359 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.435939	0.251690	0.125845	−	0.992050i	$-0.459836\pi$
$3$	0.435939	0.251690	0.125845	+	0.992050i	$0.459836\pi$
$4$	1.00000	0.500000
$5$	−0.796234	−0.356087	−0.178043	−	0.984023i	$-0.556977\pi$
$5$	−0.796234	−0.356087	−0.178043	+	0.984023i	$0.556977\pi$
$6$	0.435939	0.177971
$7$	3.50309	1.32404	0.662022	−	0.749484i	$-0.269698\pi$
$7$	3.50309	1.32404	0.662022	+	0.749484i	$0.269698\pi$
$8$	1.00000	0.353553
$9$	−2.80996	−0.936652
$10$	−0.796234	−0.251791
$11$	3.32161	1.00150	0.500752	−	0.865591i	$-0.333057\pi$
$11$	3.32161	1.00150	0.500752	+	0.865591i	$0.333057\pi$
$12$	0.435939	0.125845
$13$	−5.74710	−1.59396	−0.796980	−	0.604006i	$-0.793570\pi$
$13$	−5.74710	−1.59396	−0.796980	+	0.604006i	$0.793570\pi$
$14$	3.50309	0.936241
$15$	−0.347110	−0.0896233
$16$	1.00000	0.250000
$17$	−5.02257	−1.21815	−0.609076	−	0.793112i	$-0.708460\pi$
$17$	−5.02257	−1.21815	−0.609076	+	0.793112i	$0.708460\pi$
$18$	−2.80996	−0.662313
$19$	−2.58528	−0.593103	−0.296551	−	0.955017i	$-0.595837\pi$
$19$	−2.58528	−0.593103	−0.296551	+	0.955017i	$0.595837\pi$
$20$	−0.796234	−0.178043
$21$	1.52713	0.333248
$22$	3.32161	0.708170
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	0.435939	0.0889857
$25$	−4.36601	−0.873202
$26$	−5.74710	−1.12710
$27$	−2.53279	−0.487435
$28$	3.50309	0.662022
$29$	−1.20814	−0.224345	−0.112173	−	0.993689i	$-0.535781\pi$
$29$	−1.20814	−0.224345	−0.112173	+	0.993689i	$0.535781\pi$
$30$	−0.347110	−0.0633733
$31$	5.64294	1.01350	0.506751	−	0.862093i	$-0.330846\pi$
$31$	5.64294	1.01350	0.506751	+	0.862093i	$0.330846\pi$
$32$	1.00000	0.176777
$33$	1.44802	0.252068
$34$	−5.02257	−0.861364
$35$	−2.78928	−0.471475
$36$	−2.80996	−0.468326
$37$	−5.90948	−0.971512	−0.485756	−	0.874095i	$-0.661456\pi$
$37$	−5.90948	−0.971512	−0.485756	+	0.874095i	$0.661456\pi$
$38$	−2.58528	−0.419387
$39$	−2.50539	−0.401183
$40$	−0.796234	−0.125896
$41$	−8.67527	−1.35485	−0.677425	−	0.735592i	$-0.736904\pi$
$41$	−8.67527	−1.35485	−0.677425	+	0.735592i	$0.736904\pi$
$42$	1.52713	0.235642
$43$	−10.6307	−1.62117	−0.810584	−	0.585622i	$-0.800850\pi$
$43$	−10.6307	−1.62117	−0.810584	+	0.585622i	$0.800850\pi$
$44$	3.32161	0.500752
$45$	2.23738	0.333530
$46$	1.00000	0.147442
$47$	−7.02860	−1.02523	−0.512613	−	0.858620i	$-0.671322\pi$
$47$	−7.02860	−1.02523	−0.512613	+	0.858620i	$0.671322\pi$
$48$	0.435939	0.0629224
$49$	5.27166	0.753094
$50$	−4.36601	−0.617447
$51$	−2.18953	−0.306596
$52$	−5.74710	−0.796980
$53$	1.67208	0.229678	0.114839	−	0.993384i	$-0.463365\pi$
$53$	1.67208	0.229678	0.114839	+	0.993384i	$0.463365\pi$
$54$	−2.53279	−0.344669
$55$	−2.64478	−0.356623
$56$	3.50309	0.468120
$57$	−1.12702	−0.149278
$58$	−1.20814	−0.158636
$59$	−8.50760	−1.10760	−0.553798	−	0.832651i	$-0.686822\pi$
$59$	−8.50760	−1.10760	−0.553798	+	0.832651i	$0.686822\pi$
$60$	−0.347110	−0.0448117
$61$	6.06904	0.777061	0.388531	−	0.921436i	$-0.372983\pi$
$61$	6.06904	0.777061	0.388531	+	0.921436i	$0.372983\pi$
$62$	5.64294	0.716654
$63$	−9.84354	−1.24017
$64$	1.00000	0.125000
$65$	4.57604	0.567588
$66$	1.44802	0.178239
$67$	0.567248	0.0693004	0.0346502	−	0.999400i	$-0.488968\pi$
$67$	0.567248	0.0693004	0.0346502	+	0.999400i	$0.488968\pi$
$68$	−5.02257	−0.609076
$69$	0.435939	0.0524809
$70$	−2.78928	−0.333383
$71$	10.1319	1.20244	0.601218	−	0.799085i	$-0.294682\pi$
$71$	10.1319	1.20244	0.601218	+	0.799085i	$0.294682\pi$
$72$	−2.80996	−0.331157
$73$	5.84766	0.684417	0.342208	−	0.939624i	$-0.388825\pi$
$73$	5.84766	0.684417	0.342208	+	0.939624i	$0.388825\pi$
$74$	−5.90948	−0.686963
$75$	−1.90331	−0.219776
$76$	−2.58528	−0.296551
$77$	11.6359	1.32604
$78$	−2.50539	−0.283679
$79$	0.978625	0.110104	0.0550519	−	0.998483i	$-0.482468\pi$
$79$	0.978625	0.110104	0.0550519	+	0.998483i	$0.482468\pi$
$80$	−0.796234	−0.0890217
$81$	7.32573	0.813970
$82$	−8.67527	−0.958023
$83$	1.48384	0.162873	0.0814364	−	0.996679i	$-0.474049\pi$
$83$	1.48384	0.162873	0.0814364	+	0.996679i	$0.474049\pi$
$84$	1.52713	0.166624
$85$	3.99914	0.433768
$86$	−10.6307	−1.14634
$87$	−0.526674	−0.0564653
$88$	3.32161	0.354085
$89$	−14.9323	−1.58282	−0.791412	−	0.611283i	$-0.790654\pi$
$89$	−14.9323	−1.58282	−0.791412	+	0.611283i	$0.790654\pi$
$90$	2.23738	0.235841
$91$	−20.1326	−2.11047
$92$	1.00000	0.104257
$93$	2.45998	0.255088
$94$	−7.02860	−0.724944
$95$	2.05849	0.211196
$96$	0.435939	0.0444928
$97$	8.30629	0.843376	0.421688	−	0.906741i	$-0.361438\pi$
$97$	8.30629	0.843376	0.421688	+	0.906741i	$0.361438\pi$
$98$	5.27166	0.532518
$99$	−9.33359	−0.938061
$100$	−4.36601	−0.436601
$101$	14.8732	1.47994	0.739971	−	0.672639i	$-0.234839\pi$
$101$	14.8732	1.47994	0.739971	+	0.672639i	$0.234839\pi$
$102$	−2.18953	−0.216796
$103$	6.09870	0.600922	0.300461	−	0.953794i	$-0.402859\pi$
$103$	6.09870	0.600922	0.300461	+	0.953794i	$0.402859\pi$
$104$	−5.74710	−0.563550
$105$	−1.21596	−0.118665
$106$	1.67208	0.162407
$107$	−1.32271	−0.127871	−0.0639356	−	0.997954i	$-0.520365\pi$
$107$	−1.32271	−0.127871	−0.0639356	+	0.997954i	$0.520365\pi$
$108$	−2.53279	−0.243718
$109$	−10.6216	−1.01736	−0.508681	−	0.860955i	$-0.669867\pi$
$109$	−10.6216	−1.01736	−0.508681	+	0.860955i	$0.669867\pi$
$110$	−2.64478	−0.252170
$111$	−2.57617	−0.244519
$112$	3.50309	0.331011
$113$	−1.11994	−0.105355	−0.0526775	−	0.998612i	$-0.516776\pi$
$113$	−1.11994	−0.105355	−0.0526775	+	0.998612i	$0.516776\pi$
$114$	−1.12702	−0.105555
$115$	−0.796234	−0.0742492
$116$	−1.20814	−0.112173
$117$	16.1491	1.49299
$118$	−8.50760	−0.783188
$119$	−17.5945	−1.61289
$120$	−0.347110	−0.0316866
$121$	0.0331176	0.00301069
$122$	6.06904	0.549465
$123$	−3.78189	−0.341001
$124$	5.64294	0.506751
$125$	7.45754	0.667023
$126$	−9.84354	−0.876932
$127$	−19.1285	−1.69738	−0.848688	−	0.528893i	$-0.822607\pi$
$127$	−19.1285	−1.69738	−0.848688	+	0.528893i	$0.822607\pi$
$128$	1.00000	0.0883883
$129$	−4.63434	−0.408031
$130$	4.57604	0.401345
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	1.44802	0.126034
$133$	−9.05646	−0.785295
$134$	0.567248	0.0490028
$135$	2.01669	0.173569
$136$	−5.02257	−0.430682
$137$	−15.9154	−1.35974	−0.679871	−	0.733331i	$-0.737964\pi$
$137$	−15.9154	−1.35974	−0.679871	+	0.733331i	$0.737964\pi$
$138$	0.435939	0.0371096
$139$	1.77999	0.150977	0.0754886	−	0.997147i	$-0.475948\pi$
$139$	1.77999	0.150977	0.0754886	+	0.997147i	$0.475948\pi$
$140$	−2.78928	−0.235737
$141$	−3.06404	−0.258039
$142$	10.1319	0.850250
$143$	−19.0896	−1.59636
$144$	−2.80996	−0.234163
$145$	0.961959	0.0798864
$146$	5.84766	0.483956
$147$	2.29812	0.189546
$148$	−5.90948	−0.485756
$149$	0.142806	0.0116991	0.00584956	−	0.999983i	$-0.498138\pi$
$149$	0.142806	0.0116991	0.00584956	+	0.999983i	$0.498138\pi$
$150$	−1.90331	−0.155405
$151$	−1.68493	−0.137118	−0.0685590	−	0.997647i	$-0.521840\pi$
$151$	−1.68493	−0.137118	−0.0685590	+	0.997647i	$0.521840\pi$
$152$	−2.58528	−0.209694
$153$	14.1132	1.14099
$154$	11.6359	0.937649
$155$	−4.49310	−0.360895
$156$	−2.50539	−0.200591
$157$	11.1153	0.887096	0.443548	−	0.896251i	$-0.353719\pi$
$157$	11.1153	0.887096	0.443548	+	0.896251i	$0.353719\pi$
$158$	0.978625	0.0778552
$159$	0.728924	0.0578075
$160$	−0.796234	−0.0629479
$161$	3.50309	0.276082
$162$	7.32573	0.575564
$163$	−14.4687	−1.13327	−0.566637	−	0.823967i	$-0.691756\pi$
$163$	−14.4687	−1.13327	−0.566637	+	0.823967i	$0.691756\pi$
$164$	−8.67527	−0.677425
$165$	−1.15296	−0.0897582
$166$	1.48384	0.115168
$167$	17.9373	1.38803	0.694015	−	0.719961i	$-0.255840\pi$
$167$	17.9373	1.38803	0.694015	+	0.719961i	$0.255840\pi$
$168$	1.52713	0.117821
$169$	20.0292	1.54071
$170$	3.99914	0.306720
$171$	7.26451	0.555531
$172$	−10.6307	−0.810584
$173$	19.1917	1.45911	0.729557	−	0.683920i	$-0.239726\pi$
$173$	19.1917	1.45911	0.729557	+	0.683920i	$0.239726\pi$
$174$	−0.526674	−0.0399270
$175$	−15.2945	−1.15616
$176$	3.32161	0.250376
$177$	−3.70880	−0.278770
$178$	−14.9323	−1.11923
$179$	10.8900	0.813955	0.406978	−	0.913438i	$-0.366583\pi$
$179$	10.8900	0.813955	0.406978	+	0.913438i	$0.366583\pi$
$180$	2.23738	0.166765
$181$	8.23674	0.612232	0.306116	−	0.951994i	$-0.400970\pi$
$181$	8.23674	0.612232	0.306116	+	0.951994i	$0.400970\pi$
$182$	−20.1326	−1.49233
$183$	2.64573	0.195578
$184$	1.00000	0.0737210
$185$	4.70533	0.345943
$186$	2.45998	0.180374
$187$	−16.6830	−1.21998
$188$	−7.02860	−0.512613
$189$	−8.87259	−0.645386
$190$	2.05849	0.149338
$191$	−22.8261	−1.65164	−0.825819	−	0.563935i	$-0.809287\pi$
$191$	−22.8261	−1.65164	−0.825819	+	0.563935i	$0.809287\pi$
$192$	0.435939	0.0314612
$193$	−10.8414	−0.780383	−0.390191	−	0.920734i	$-0.627591\pi$
$193$	−10.8414	−0.780383	−0.390191	+	0.920734i	$0.627591\pi$
$194$	8.30629	0.596357
$195$	1.99487	0.142856
$196$	5.27166	0.376547
$197$	2.40350	0.171242	0.0856210	−	0.996328i	$-0.472713\pi$
$197$	2.40350	0.171242	0.0856210	+	0.996328i	$0.472713\pi$
$198$	−9.33359	−0.663310
$199$	4.48419	0.317876	0.158938	−	0.987289i	$-0.449193\pi$
$199$	4.48419	0.317876	0.158938	+	0.987289i	$0.449193\pi$
$200$	−4.36601	−0.308724
$201$	0.247286	0.0174422
$202$	14.8732	1.04648
$203$	−4.23221	−0.297043
$204$	−2.18953	−0.153298
$205$	6.90755	0.482444
$206$	6.09870	0.424916
$207$	−2.80996	−0.195306
$208$	−5.74710	−0.398490
$209$	−8.58729	−0.593995
$210$	−1.21596	−0.0839090
$211$	7.41060	0.510167	0.255083	−	0.966919i	$-0.417897\pi$
$211$	7.41060	0.510167	0.255083	+	0.966919i	$0.417897\pi$
$212$	1.67208	0.114839
$213$	4.41689	0.302641
$214$	−1.32271	−0.0904185
$215$	8.46454	0.577277
$216$	−2.53279	−0.172334
$217$	19.7677	1.34192
$218$	−10.6216	−0.719383
$219$	2.54922	0.172261
$220$	−2.64478	−0.178311
$221$	28.8652	1.94168
$222$	−2.57617	−0.172901
$223$	18.4257	1.23387	0.616937	−	0.787013i	$-0.288373\pi$
$223$	18.4257	1.23387	0.616937	+	0.787013i	$0.288373\pi$
$224$	3.50309	0.234060
$225$	12.2683	0.817887
$226$	−1.11994	−0.0744972
$227$	−9.43138	−0.625983	−0.312991	−	0.949756i	$-0.601331\pi$
$227$	−9.43138	−0.625983	−0.312991	+	0.949756i	$0.601331\pi$
$228$	−1.12702	−0.0746389
$229$	−6.40400	−0.423188	−0.211594	−	0.977358i	$-0.567865\pi$
$229$	−6.40400	−0.423188	−0.211594	+	0.977358i	$0.567865\pi$
$230$	−0.796234	−0.0525021
$231$	5.07255	0.333749
$232$	−1.20814	−0.0793180
$233$	22.1424	1.45059	0.725297	−	0.688436i	$-0.241702\pi$
$233$	22.1424	1.45059	0.725297	+	0.688436i	$0.241702\pi$
$234$	16.1491	1.05570
$235$	5.59641	0.365070
$236$	−8.50760	−0.553798
$237$	0.426621	0.0277120
$238$	−17.5945	−1.14048
$239$	−6.71713	−0.434495	−0.217248	−	0.976117i	$-0.569708\pi$
$239$	−6.71713	−0.434495	−0.217248	+	0.976117i	$0.569708\pi$
$240$	−0.347110	−0.0224058
$241$	−13.7922	−0.888433	−0.444216	−	0.895920i	$-0.646518\pi$
$241$	−13.7922	−0.888433	−0.444216	+	0.895920i	$0.646518\pi$
$242$	0.0331176	0.00212888
$243$	10.7919	0.692303
$244$	6.06904	0.388531
$245$	−4.19747	−0.268167
$246$	−3.78189	−0.241124
$247$	14.8578	0.945382
$248$	5.64294	0.358327
$249$	0.646864	0.0409934
$250$	7.45754	0.471656
$251$	−9.29228	−0.586523	−0.293262	−	0.956032i	$-0.594741\pi$
$251$	−9.29228	−0.586523	−0.293262	+	0.956032i	$0.594741\pi$
$252$	−9.84354	−0.620085
$253$	3.32161	0.208828
$254$	−19.1285	−1.20023
$255$	1.74338	0.109175
$256$	1.00000	0.0625000
$257$	−17.6596	−1.10157	−0.550786	−	0.834646i	$-0.685672\pi$
$257$	−17.6596	−1.10157	−0.550786	+	0.834646i	$0.685672\pi$
$258$	−4.63434	−0.288522
$259$	−20.7014	−1.28632
$260$	4.57604	0.283794
$261$	3.39481	0.210133
$262$	−1.00000	−0.0617802
$263$	−1.14881	−0.0708388	−0.0354194	−	0.999373i	$-0.511277\pi$
$263$	−1.14881	−0.0708388	−0.0354194	+	0.999373i	$0.511277\pi$
$264$	1.44802	0.0891195
$265$	−1.33137	−0.0817852
$266$	−9.05646	−0.555287
$267$	−6.50959	−0.398380
$268$	0.567248	0.0346502
$269$	7.85187	0.478737	0.239368	−	0.970929i	$-0.423060\pi$
$269$	7.85187	0.478737	0.239368	+	0.970929i	$0.423060\pi$
$270$	2.01669	0.122732
$271$	−19.7746	−1.20122	−0.600610	−	0.799542i	$-0.705076\pi$
$271$	−19.7746	−1.20122	−0.600610	+	0.799542i	$0.705076\pi$
$272$	−5.02257	−0.304538
$273$	−8.77660	−0.531184
$274$	−15.9154	−0.961483
$275$	−14.5022	−0.874516
$276$	0.435939	0.0262404
$277$	14.9893	0.900620	0.450310	−	0.892872i	$-0.351314\pi$
$277$	14.9893	0.900620	0.450310	+	0.892872i	$0.351314\pi$
$278$	1.77999	0.106757
$279$	−15.8564	−0.949299
$280$	−2.78928	−0.166692
$281$	−7.43859	−0.443749	−0.221875	−	0.975075i	$-0.571218\pi$
$281$	−7.43859	−0.443749	−0.221875	+	0.975075i	$0.571218\pi$
$282$	−3.06404	−0.182461
$283$	6.89949	0.410132	0.205066	−	0.978748i	$-0.434259\pi$
$283$	6.89949	0.410132	0.205066	+	0.978748i	$0.434259\pi$
$284$	10.1319	0.601218
$285$	0.897374	0.0531559
$286$	−19.0896	−1.12879
$287$	−30.3903	−1.79388
$288$	−2.80996	−0.165578
$289$	8.22621	0.483895
$290$	0.961959	0.0564882
$291$	3.62104	0.212269
$292$	5.84766	0.342208
$293$	14.1166	0.824700	0.412350	−	0.911025i	$-0.364708\pi$
$293$	14.1166	0.824700	0.412350	+	0.911025i	$0.364708\pi$
$294$	2.29812	0.134029
$295$	6.77405	0.394400
$296$	−5.90948	−0.343481
$297$	−8.41294	−0.488168
$298$	0.142806	0.00827252
$299$	−5.74710	−0.332363
$300$	−1.90331	−0.109888
$301$	−37.2404	−2.14650
$302$	−1.68493	−0.0969571
$303$	6.48382	0.372486
$304$	−2.58528	−0.148276
$305$	−4.83238	−0.276701
$306$	14.1132	0.806798
$307$	18.6513	1.06449	0.532244	−	0.846591i	$-0.321349\pi$
$307$	18.6513	1.06449	0.532244	+	0.846591i	$0.321349\pi$
$308$	11.6359	0.663018
$309$	2.65866	0.151246
$310$	−4.49310	−0.255191
$311$	17.9893	1.02008	0.510040	−	0.860151i	$-0.329631\pi$
$311$	17.9893	1.02008	0.510040	+	0.860151i	$0.329631\pi$
$312$	−2.50539	−0.141840
$313$	6.12697	0.346317	0.173158	−	0.984894i	$-0.444603\pi$
$313$	6.12697	0.346317	0.173158	+	0.984894i	$0.444603\pi$
$314$	11.1153	0.627272
$315$	7.83777	0.441608
$316$	0.978625	0.0550519
$317$	−21.8050	−1.22469	−0.612345	−	0.790591i	$-0.709774\pi$
$317$	−21.8050	−1.22469	−0.612345	+	0.790591i	$0.709774\pi$
$318$	0.728924	0.0408761
$319$	−4.01296	−0.224683
$320$	−0.796234	−0.0445109
$321$	−0.576621	−0.0321838
$322$	3.50309	0.195220
$323$	12.9847	0.722490
$324$	7.32573	0.406985
$325$	25.0919	1.39185
$326$	−14.4687	−0.801346
$327$	−4.63036	−0.256059
$328$	−8.67527	−0.479012
$329$	−24.6218	−1.35745
$330$	−1.15296	−0.0634686
$331$	−29.0128	−1.59469	−0.797344	−	0.603525i	$-0.793762\pi$
$331$	−29.0128	−1.59469	−0.797344	+	0.603525i	$0.793762\pi$
$332$	1.48384	0.0814364
$333$	16.6054	0.909969
$334$	17.9373	0.981485
$335$	−0.451663	−0.0246770
$336$	1.52713	0.0833120
$337$	−6.43735	−0.350665	−0.175332	−	0.984509i	$-0.556100\pi$
$337$	−6.43735	−0.350665	−0.175332	+	0.984509i	$0.556100\pi$
$338$	20.0292	1.08944
$339$	−0.488225	−0.0265168
$340$	3.99914	0.216884
$341$	18.7437	1.01503
$342$	7.26451	0.392820
$343$	−6.05455	−0.326915
$344$	−10.6307	−0.573169
$345$	−0.347110	−0.0186878
$346$	19.1917	1.03175
$347$	8.37135	0.449398	0.224699	−	0.974428i	$-0.427860\pi$
$347$	8.37135	0.449398	0.224699	+	0.974428i	$0.427860\pi$
$348$	−0.526674	−0.0282327
$349$	−18.6824	−1.00005	−0.500023	−	0.866012i	$-0.666675\pi$
$349$	−18.6824	−1.00005	−0.500023	+	0.866012i	$0.666675\pi$
$350$	−15.2945	−0.817527
$351$	14.5562	0.776952
$352$	3.32161	0.177043
$353$	−21.4683	−1.14264	−0.571321	−	0.820726i	$-0.693569\pi$
$353$	−21.4683	−1.14264	−0.571321	+	0.820726i	$0.693569\pi$
$354$	−3.70880	−0.197120
$355$	−8.06737	−0.428172
$356$	−14.9323	−0.791412
$357$	−7.67014	−0.405947
$358$	10.8900	0.575553
$359$	−7.05199	−0.372190	−0.186095	−	0.982532i	$-0.559583\pi$
$359$	−7.05199	−0.372190	−0.186095	+	0.982532i	$0.559583\pi$
$360$	2.23738	0.117921
$361$	−12.3163	−0.648229
$362$	8.23674	0.432913
$363$	0.0144372	0.000757759 0
$364$	−20.1326	−1.05524
$365$	−4.65611	−0.243712
$366$	2.64573	0.138295
$367$	7.10995	0.371136	0.185568	−	0.982631i	$-0.440587\pi$
$367$	7.10995	0.371136	0.185568	+	0.982631i	$0.440587\pi$
$368$	1.00000	0.0521286
$369$	24.3771	1.26902
$370$	4.70533	0.244618
$371$	5.85745	0.304103
$372$	2.45998	0.127544
$373$	−18.8830	−0.977726	−0.488863	−	0.872360i	$-0.662588\pi$
$373$	−18.8830	−0.977726	−0.488863	+	0.872360i	$0.662588\pi$
$374$	−16.6830	−0.862659
$375$	3.25103	0.167883
$376$	−7.02860	−0.362472
$377$	6.94328	0.357597
$378$	−8.87259	−0.456357
$379$	−16.6200	−0.853714	−0.426857	−	0.904319i	$-0.640379\pi$
$379$	−16.6200	−0.853714	−0.426857	+	0.904319i	$0.640379\pi$
$380$	2.05849	0.105598
$381$	−8.33884	−0.427212
$382$	−22.8261	−1.16788
$383$	2.32175	0.118636	0.0593179	−	0.998239i	$-0.481107\pi$
$383$	2.32175	0.118636	0.0593179	+	0.998239i	$0.481107\pi$
$384$	0.435939	0.0222464
$385$	−9.26492	−0.472184
$386$	−10.8414	−0.551814
$387$	29.8718	1.51847
$388$	8.30629	0.421688
$389$	−25.4186	−1.28877	−0.644387	−	0.764699i	$-0.722888\pi$
$389$	−25.4186	−1.28877	−0.644387	+	0.764699i	$0.722888\pi$
$390$	1.99487	0.101014
$391$	−5.02257	−0.254002
$392$	5.27166	0.266259
$393$	−0.435939	−0.0219902
$394$	2.40350	0.121086
$395$	−0.779215	−0.0392065
$396$	−9.33359	−0.469031
$397$	31.1787	1.56482	0.782408	−	0.622766i	$-0.213991\pi$
$397$	31.1787	1.56482	0.782408	+	0.622766i	$0.213991\pi$
$398$	4.48419	0.224772
$399$	−3.94806	−0.197650
$400$	−4.36601	−0.218301
$401$	−2.91378	−0.145507	−0.0727536	−	0.997350i	$-0.523179\pi$
$401$	−2.91378	−0.145507	−0.0727536	+	0.997350i	$0.523179\pi$
$402$	0.247286	0.0123335
$403$	−32.4305	−1.61548
$404$	14.8732	0.739971
$405$	−5.83300	−0.289844
$406$	−4.23221	−0.210041
$407$	−19.6290	−0.972973
$408$	−2.18953	−0.108398
$409$	−14.7713	−0.730391	−0.365196	−	0.930931i	$-0.618998\pi$
$409$	−14.7713	−0.730391	−0.365196	+	0.930931i	$0.618998\pi$
$410$	6.90755	0.341140
$411$	−6.93814	−0.342233
$412$	6.09870	0.300461
$413$	−29.8029	−1.46651
$414$	−2.80996	−0.138102
$415$	−1.18149	−0.0579968
$416$	−5.74710	−0.281775
$417$	0.775969	0.0379994
$418$	−8.58729	−0.420018
$419$	32.7599	1.60043	0.800214	−	0.599715i	$-0.204719\pi$
$419$	32.7599	1.60043	0.800214	+	0.599715i	$0.204719\pi$
$420$	−1.21596	−0.0593326
$421$	26.6453	1.29861	0.649307	−	0.760526i	$-0.275059\pi$
$421$	26.6453	1.29861	0.649307	+	0.760526i	$0.275059\pi$
$422$	7.41060	0.360742
$423$	19.7501	0.960281
$424$	1.67208	0.0812033
$425$	21.9286	1.06369
$426$	4.41689	0.213999
$427$	21.2604	1.02886
$428$	−1.32271	−0.0639356
$429$	−8.32192	−0.401786
$430$	8.46454	0.408196
$431$	−24.5012	−1.18018	−0.590091	−	0.807337i	$-0.700908\pi$
$431$	−24.5012	−1.18018	−0.590091	+	0.807337i	$0.700908\pi$
$432$	−2.53279	−0.121859
$433$	25.1713	1.20966	0.604828	−	0.796356i	$-0.293242\pi$
$433$	25.1713	1.20966	0.604828	+	0.796356i	$0.293242\pi$
$434$	19.7677	0.948882
$435$	0.419356	0.0201066
$436$	−10.6216	−0.508681
$437$	−2.58528	−0.123671
$438$	2.54922	0.121807
$439$	−19.5188	−0.931582	−0.465791	−	0.884895i	$-0.654230\pi$
$439$	−19.5188	−0.931582	−0.465791	+	0.884895i	$0.654230\pi$
$440$	−2.64478	−0.126085
$441$	−14.8131	−0.705387
$442$	28.8652	1.37298
$443$	−8.51186	−0.404410	−0.202205	−	0.979343i	$-0.564811\pi$
$443$	−8.51186	−0.404410	−0.202205	+	0.979343i	$0.564811\pi$
$444$	−2.57617	−0.122260
$445$	11.8896	0.563623
$446$	18.4257	0.872481
$447$	0.0622547	0.00294455
$448$	3.50309	0.165506
$449$	−7.35281	−0.347000	−0.173500	−	0.984834i	$-0.555508\pi$
$449$	−7.35281	−0.347000	−0.173500	+	0.984834i	$0.555508\pi$
$450$	12.2683	0.578333
$451$	−28.8159	−1.35689
$452$	−1.11994	−0.0526775
$453$	−0.734529	−0.0345112
$454$	−9.43138	−0.442637
$455$	16.0303	0.751512
$456$	−1.12702	−0.0527777
$457$	−15.8298	−0.740487	−0.370244	−	0.928935i	$-0.620726\pi$
$457$	−15.8298	−0.740487	−0.370244	+	0.928935i	$0.620726\pi$
$458$	−6.40400	−0.299239
$459$	12.7211	0.593770
$460$	−0.796234	−0.0371246
$461$	12.7326	0.593017	0.296508	−	0.955030i	$-0.404178\pi$
$461$	12.7326	0.593017	0.296508	+	0.955030i	$0.404178\pi$
$462$	5.07255	0.235996
$463$	16.2966	0.757365	0.378683	−	0.925527i	$-0.376377\pi$
$463$	16.2966	0.757365	0.378683	+	0.925527i	$0.376377\pi$
$464$	−1.20814	−0.0560863
$465$	−1.95872	−0.0908334
$466$	22.1424	1.02573
$467$	−19.1898	−0.887996	−0.443998	−	0.896028i	$-0.646440\pi$
$467$	−19.1898	−0.887996	−0.443998	+	0.896028i	$0.646440\pi$
$468$	16.1491	0.746493
$469$	1.98712	0.0917568
$470$	5.59641	0.258143
$471$	4.84559	0.223273
$472$	−8.50760	−0.391594
$473$	−35.3111	−1.62361
$474$	0.426621	0.0195953
$475$	11.2873	0.517899
$476$	−17.5945	−0.806444
$477$	−4.69847	−0.215128
$478$	−6.71713	−0.307234
$479$	−23.8695	−1.09063	−0.545313	−	0.838233i	$-0.683589\pi$
$479$	−23.8695	−1.09063	−0.545313	+	0.838233i	$0.683589\pi$
$480$	−0.347110	−0.0158433
$481$	33.9624	1.54855
$482$	−13.7922	−0.628217
$483$	1.52713	0.0694870
$484$	0.0331176	0.00150534
$485$	−6.61376	−0.300315
$486$	10.7919	0.489532
$487$	5.81510	0.263507	0.131754	−	0.991282i	$-0.457939\pi$
$487$	5.81510	0.263507	0.131754	+	0.991282i	$0.457939\pi$
$488$	6.06904	0.274733
$489$	−6.30746	−0.285233
$490$	−4.19747	−0.189623
$491$	39.3804	1.77721	0.888605	−	0.458672i	$-0.151675\pi$
$491$	39.3804	1.77721	0.888605	+	0.458672i	$0.151675\pi$
$492$	−3.78189	−0.170501
$493$	6.06795	0.273287
$494$	14.8578	0.668486
$495$	7.43173	0.334031
$496$	5.64294	0.253375
$497$	35.4930	1.59208
$498$	0.646864	0.0289867
$499$	−31.5640	−1.41300	−0.706499	−	0.707714i	$-0.749726\pi$
$499$	−31.5640	−1.41300	−0.706499	+	0.707714i	$0.749726\pi$
$500$	7.45754	0.333511
$501$	7.81957	0.349352
$502$	−9.29228	−0.414735
$503$	24.9853	1.11404	0.557019	−	0.830500i	$-0.311945\pi$
$503$	24.9853	1.11404	0.557019	+	0.830500i	$0.311945\pi$
$504$	−9.84354	−0.438466
$505$	−11.8426	−0.526988
$506$	3.32161	0.147664
$507$	8.73150	0.387779
$508$	−19.1285	−0.848688
$509$	−18.2822	−0.810344	−0.405172	−	0.914241i	$-0.632788\pi$
$509$	−18.2822	−0.810344	−0.405172	+	0.914241i	$0.632788\pi$
$510$	1.74338	0.0771983
$511$	20.4849	0.906198
$512$	1.00000	0.0441942
$513$	6.54795	0.289099
$514$	−17.6596	−0.778930
$515$	−4.85599	−0.213981
$516$	−4.63434	−0.204016
$517$	−23.3463	−1.02677
$518$	−20.7014	−0.909569
$519$	8.36639	0.367244
$520$	4.57604	0.200673
$521$	−9.31383	−0.408046	−0.204023	−	0.978966i	$-0.565402\pi$
$521$	−9.31383	−0.408046	−0.204023	+	0.978966i	$0.565402\pi$
$522$	3.39481	0.148587
$523$	32.0899	1.40319	0.701596	−	0.712575i	$-0.252471\pi$
$523$	32.0899	1.40319	0.701596	+	0.712575i	$0.252471\pi$
$524$	−1.00000	−0.0436852
$525$	−6.66749	−0.290993
$526$	−1.14881	−0.0500906
$527$	−28.3421	−1.23460
$528$	1.44802	0.0630170
$529$	1.00000	0.0434783
$530$	−1.33137	−0.0578309
$531$	23.9060	1.03743
$532$	−9.05646	−0.392647
$533$	49.8576	2.15957
$534$	−6.50959	−0.281697
$535$	1.05319	0.0455332
$536$	0.567248	0.0245014
$537$	4.74737	0.204864
$538$	7.85187	0.338518
$539$	17.5104	0.754227
$540$	2.01669	0.0867846
$541$	−27.6319	−1.18799	−0.593995	−	0.804469i	$-0.702450\pi$
$541$	−27.6319	−1.18799	−0.593995	+	0.804469i	$0.702450\pi$
$542$	−19.7746	−0.849391
$543$	3.59072	0.154092
$544$	−5.02257	−0.215341
$545$	8.45726	0.362269
$546$	−8.77660	−0.375604
$547$	−26.0649	−1.11445	−0.557227	−	0.830360i	$-0.688135\pi$
$547$	−26.0649	−1.11445	−0.557227	+	0.830360i	$0.688135\pi$
$548$	−15.9154	−0.679871
$549$	−17.0538	−0.727836
$550$	−14.5022	−0.618376
$551$	3.12336	0.133060
$552$	0.435939	0.0185548
$553$	3.42821	0.145782
$554$	14.9893	0.636834
$555$	2.05124	0.0870701
$556$	1.77999	0.0754886
$557$	14.0664	0.596013	0.298006	−	0.954564i	$-0.403678\pi$
$557$	14.0664	0.596013	0.298006	+	0.954564i	$0.403678\pi$
$558$	−15.8564	−0.671256
$559$	61.0958	2.58408
$560$	−2.78928	−0.117869
$561$	−7.27279	−0.307057
$562$	−7.43859	−0.313778
$563$	41.3410	1.74231	0.871157	−	0.491004i	$-0.163370\pi$
$563$	41.3410	1.74231	0.871157	+	0.491004i	$0.163370\pi$
$564$	−3.06404	−0.129019
$565$	0.891734	0.0375155
$566$	6.89949	0.290007
$567$	25.6627	1.07773
$568$	10.1319	0.425125
$569$	−8.02844	−0.336570	−0.168285	−	0.985738i	$-0.553823\pi$
$569$	−8.02844	−0.336570	−0.168285	+	0.985738i	$0.553823\pi$
$570$	0.897374	0.0375869
$571$	−2.90090	−0.121399	−0.0606995	−	0.998156i	$-0.519333\pi$
$571$	−2.90090	−0.121399	−0.0606995	+	0.998156i	$0.519333\pi$
$572$	−19.0896	−0.798178
$573$	−9.95079	−0.415700
$574$	−30.3903	−1.26847
$575$	−4.36601	−0.182075
$576$	−2.80996	−0.117082
$577$	−16.3257	−0.679649	−0.339824	−	0.940489i	$-0.610368\pi$
$577$	−16.3257	−0.679649	−0.339824	+	0.940489i	$0.610368\pi$
$578$	8.22621	0.342165
$579$	−4.72620	−0.196414
$580$	0.961959	0.0399432
$581$	5.19803	0.215651
$582$	3.62104	0.150097
$583$	5.55400	0.230023
$584$	5.84766	0.241978
$585$	−12.8585	−0.531633
$586$	14.1166	0.583151
$587$	4.08819	0.168738	0.0843689	−	0.996435i	$-0.473113\pi$
$587$	4.08819	0.168738	0.0843689	+	0.996435i	$0.473113\pi$
$588$	2.29812	0.0947729
$589$	−14.5886	−0.601111
$590$	6.77405	0.278883
$591$	1.04778	0.0430998
$592$	−5.90948	−0.242878
$593$	22.9795	0.943653	0.471827	−	0.881691i	$-0.343595\pi$
$593$	22.9795	0.943653	0.471827	+	0.881691i	$0.343595\pi$
$594$	−8.41294	−0.345187
$595$	14.0094	0.574328
$596$	0.142806	0.00584956
$597$	1.95483	0.0800061
$598$	−5.74710	−0.235016
$599$	−39.7070	−1.62239	−0.811193	−	0.584779i	$-0.801181\pi$
$599$	−39.7070	−1.62239	−0.811193	+	0.584779i	$0.801181\pi$
$600$	−1.90331	−0.0777025
$601$	−22.8958	−0.933941	−0.466970	−	0.884273i	$-0.654655\pi$
$601$	−22.8958	−0.933941	−0.466970	+	0.884273i	$0.654655\pi$
$602$	−37.2404	−1.51780
$603$	−1.59394	−0.0649104
$604$	−1.68493	−0.0685590
$605$	−0.0263693	−0.00107207
$606$	6.48382	0.263387
$607$	−1.83789	−0.0745977	−0.0372989	−	0.999304i	$-0.511875\pi$
$607$	−1.83789	−0.0745977	−0.0372989	+	0.999304i	$0.511875\pi$
$608$	−2.58528	−0.104847
$609$	−1.84499	−0.0747626
$610$	−4.83238	−0.195657
$611$	40.3941	1.63417
$612$	14.1132	0.570493
$613$	−6.62972	−0.267772	−0.133886	−	0.990997i	$-0.542746\pi$
$613$	−6.62972	−0.267772	−0.133886	+	0.990997i	$0.542746\pi$
$614$	18.6513	0.752707
$615$	3.01127	0.121426
$616$	11.6359	0.468825
$617$	18.3463	0.738595	0.369298	−	0.929311i	$-0.379598\pi$
$617$	18.3463	0.738595	0.369298	+	0.929311i	$0.379598\pi$
$618$	2.65866	0.106947
$619$	−29.8652	−1.20039	−0.600193	−	0.799855i	$-0.704909\pi$
$619$	−29.8652	−1.20039	−0.600193	+	0.799855i	$0.704909\pi$
$620$	−4.49310	−0.180447
$621$	−2.53279	−0.101637
$622$	17.9893	0.721305
$623$	−52.3093	−2.09573
$624$	−2.50539	−0.100296
$625$	15.8921	0.635684
$626$	6.12697	0.244883
$627$	−3.74353	−0.149502
$628$	11.1153	0.443548
$629$	29.6808	1.18345
$630$	7.83777	0.312264
$631$	−5.67566	−0.225944	−0.112972	−	0.993598i	$-0.536037\pi$
$631$	−5.67566	−0.225944	−0.112972	+	0.993598i	$0.536037\pi$
$632$	0.978625	0.0389276
$633$	3.23057	0.128404
$634$	−21.8050	−0.865986
$635$	15.2307	0.604414
$636$	0.728924	0.0289037
$637$	−30.2967	−1.20040
$638$	−4.01296	−0.158875
$639$	−28.4702	−1.12626
$640$	−0.796234	−0.0314739
$641$	17.1644	0.677953	0.338976	−	0.940795i	$-0.389919\pi$
$641$	17.1644	0.677953	0.338976	+	0.940795i	$0.389919\pi$
$642$	−0.576621	−0.0227574
$643$	−40.1492	−1.58333	−0.791665	−	0.610956i	$-0.790785\pi$
$643$	−40.1492	−1.58333	−0.791665	+	0.610956i	$0.790785\pi$
$644$	3.50309	0.138041
$645$	3.69002	0.145295
$646$	12.9847	0.510877
$647$	−21.0670	−0.828228	−0.414114	−	0.910225i	$-0.635908\pi$
$647$	−21.0670	−0.828228	−0.414114	+	0.910225i	$0.635908\pi$
$648$	7.32573	0.287782
$649$	−28.2590	−1.10926
$650$	25.0919	0.984185
$651$	8.61753	0.337748
$652$	−14.4687	−0.566637
$653$	−19.8467	−0.776662	−0.388331	−	0.921520i	$-0.626948\pi$
$653$	−19.8467	−0.776662	−0.388331	+	0.921520i	$0.626948\pi$
$654$	−4.63036	−0.181061
$655$	0.796234	0.0311115
$656$	−8.67527	−0.338712
$657$	−16.4317	−0.641060
$658$	−24.6218	−0.959859
$659$	−6.07746	−0.236744	−0.118372	−	0.992969i	$-0.537768\pi$
$659$	−6.07746	−0.236744	−0.118372	+	0.992969i	$0.537768\pi$
$660$	−1.15296	−0.0448791
$661$	16.6269	0.646713	0.323356	−	0.946277i	$-0.395189\pi$
$661$	16.6269	0.646713	0.323356	+	0.946277i	$0.395189\pi$
$662$	−29.0128	−1.12761
$663$	12.5835	0.488702
$664$	1.48384	0.0575842
$665$	7.21107	0.279633
$666$	16.6054	0.643445
$667$	−1.20814	−0.0467792
$668$	17.9373	0.694015
$669$	8.03247	0.310553
$670$	−0.451663	−0.0174492
$671$	20.1590	0.778230
$672$	1.52713	0.0589105
$673$	30.0087	1.15675	0.578375	−	0.815771i	$-0.303687\pi$
$673$	30.0087	1.15675	0.578375	+	0.815771i	$0.303687\pi$
$674$	−6.43735	−0.247957
$675$	11.0582	0.425629
$676$	20.0292	0.770353
$677$	42.7109	1.64151	0.820756	−	0.571279i	$-0.193552\pi$
$677$	42.7109	1.64151	0.820756	+	0.571279i	$0.193552\pi$
$678$	−0.488225	−0.0187502
$679$	29.0977	1.11667
$680$	3.99914	0.153360
$681$	−4.11151	−0.157553
$682$	18.7437	0.717732
$683$	−14.1756	−0.542416	−0.271208	−	0.962521i	$-0.587423\pi$
$683$	−14.1756	−0.542416	−0.271208	+	0.962521i	$0.587423\pi$
$684$	7.26451	0.277766
$685$	12.6724	0.484187
$686$	−6.05455	−0.231164
$687$	−2.79175	−0.106512
$688$	−10.6307	−0.405292
$689$	−9.60960	−0.366097
$690$	−0.347110	−0.0132142
$691$	−15.1731	−0.577212	−0.288606	−	0.957448i	$-0.593192\pi$
$691$	−15.1731	−0.577212	−0.288606	+	0.957448i	$0.593192\pi$
$692$	19.1917	0.729557
$693$	−32.6964	−1.24203
$694$	8.37135	0.317772
$695$	−1.41729	−0.0537610
$696$	−0.526674	−0.0199635
$697$	43.5722	1.65041
$698$	−18.6824	−0.707139
$699$	9.65272	0.365099
$700$	−15.2945	−0.578079
$701$	−13.3277	−0.503380	−0.251690	−	0.967808i	$-0.580986\pi$
$701$	−13.3277	−0.503380	−0.251690	+	0.967808i	$0.580986\pi$
$702$	14.5562	0.549388
$703$	15.2776	0.576207
$704$	3.32161	0.125188
$705$	2.43969	0.0918842
$706$	−21.4683	−0.807970
$707$	52.1023	1.95951
$708$	−3.70880	−0.139385
$709$	21.7257	0.815927	0.407964	−	0.912998i	$-0.366239\pi$
$709$	21.7257	0.815927	0.407964	+	0.912998i	$0.366239\pi$
$710$	−8.06737	−0.302763
$711$	−2.74989	−0.103129
$712$	−14.9323	−0.559613
$713$	5.64294	0.211330
$714$	−7.67014	−0.287048
$715$	15.1998	0.568442
$716$	10.8900	0.406978
$717$	−2.92826	−0.109358
$718$	−7.05199	−0.263178
$719$	15.7367	0.586880	0.293440	−	0.955978i	$-0.405200\pi$
$719$	15.7367	0.586880	0.293440	+	0.955978i	$0.405200\pi$
$720$	2.23738	0.0833824
$721$	21.3643	0.795648
$722$	−12.3163	−0.458367
$723$	−6.01255	−0.223609
$724$	8.23674	0.306116
$725$	5.27473	0.195899
$726$	0.0144372	0.000535816 0
$727$	−17.2753	−0.640704	−0.320352	−	0.947299i	$-0.603801\pi$
$727$	−17.2753	−0.640704	−0.320352	+	0.947299i	$0.603801\pi$
$728$	−20.1326	−0.746165
$729$	−17.2726	−0.639725
$730$	−4.65611	−0.172330
$731$	53.3935	1.97483
$732$	2.64573	0.0977891
$733$	−35.1193	−1.29716	−0.648581	−	0.761145i	$-0.724637\pi$
$733$	−35.1193	−1.29716	−0.648581	+	0.761145i	$0.724637\pi$
$734$	7.10995	0.262433
$735$	−1.82984	−0.0674948
$736$	1.00000	0.0368605
$737$	1.88418	0.0694046
$738$	24.3771	0.897335
$739$	3.64792	0.134191	0.0670955	−	0.997747i	$-0.478627\pi$
$739$	3.64792	0.134191	0.0670955	+	0.997747i	$0.478627\pi$
$740$	4.70533	0.172971
$741$	6.47711	0.237943
$742$	5.85745	0.215034
$743$	32.8960	1.20684	0.603419	−	0.797424i	$-0.293805\pi$
$743$	32.8960	1.20684	0.603419	+	0.797424i	$0.293805\pi$
$744$	2.45998	0.0901871
$745$	−0.113707	−0.00416590
$746$	−18.8830	−0.691357
$747$	−4.16953	−0.152555
$748$	−16.6830	−0.609992
$749$	−4.63357	−0.169307
$750$	3.25103	0.118711
$751$	53.4905	1.95190	0.975948	−	0.218002i	$-0.0699540\pi$
$751$	53.4905	1.95190	0.975948	+	0.218002i	$0.0699540\pi$
$752$	−7.02860	−0.256307
$753$	−4.05087	−0.147622
$754$	6.94328	0.252859
$755$	1.34160	0.0488259
$756$	−8.87259	−0.322693
$757$	2.41791	0.0878806	0.0439403	−	0.999034i	$-0.486009\pi$
$757$	2.41791	0.0878806	0.0439403	+	0.999034i	$0.486009\pi$
$758$	−16.6200	−0.603667
$759$	1.44802	0.0525598
$760$	2.05849	0.0746691
$761$	47.0819	1.70672	0.853360	−	0.521323i	$-0.174561\pi$
$761$	47.0819	1.70672	0.853360	+	0.521323i	$0.174561\pi$
$762$	−8.33884	−0.302084
$763$	−37.2083	−1.34703
$764$	−22.8261	−0.825819
$765$	−11.2374	−0.406290
$766$	2.32175	0.0838881
$767$	48.8941	1.76546
$768$	0.435939	0.0157306
$769$	12.8096	0.461925	0.230963	−	0.972963i	$-0.425812\pi$
$769$	12.8096	0.461925	0.230963	+	0.972963i	$0.425812\pi$
$770$	−9.26492	−0.333885
$771$	−7.69849	−0.277254
$772$	−10.8414	−0.390191
$773$	−4.28153	−0.153996	−0.0769979	−	0.997031i	$-0.524533\pi$
$773$	−4.28153	−0.153996	−0.0769979	+	0.997031i	$0.524533\pi$
$774$	29.8718	1.07372
$775$	−24.6371	−0.884992
$776$	8.30629	0.298179
$777$	−9.02457	−0.323755
$778$	−25.4186	−0.911301
$779$	22.4280	0.803565
$780$	1.99487	0.0714280
$781$	33.6543	1.20424
$782$	−5.02257	−0.179607
$783$	3.05995	0.109354
$784$	5.27166	0.188273
$785$	−8.85037	−0.315883
$786$	−0.435939	−0.0155494
$787$	15.8083	0.563506	0.281753	−	0.959487i	$-0.409084\pi$
$787$	15.8083	0.563506	0.281753	+	0.959487i	$0.409084\pi$
$788$	2.40350	0.0856210
$789$	−0.500812	−0.0178294
$790$	−0.779215	−0.0277232
$791$	−3.92325	−0.139495
$792$	−9.33359	−0.331655
$793$	−34.8794	−1.23860
$794$	31.1787	1.10649
$795$	−0.580395	−0.0205845
$796$	4.48419	0.158938
$797$	4.60067	0.162964	0.0814820	−	0.996675i	$-0.474035\pi$
$797$	4.60067	0.162964	0.0814820	+	0.996675i	$0.474035\pi$
$798$	−3.94806	−0.139760
$799$	35.3016	1.24888
$800$	−4.36601	−0.154362
$801$	41.9592	1.48256
$802$	−2.91378	−0.102889
$803$	19.4237	0.685446
$804$	0.247286	0.00872109
$805$	−2.78928	−0.0983093
$806$	−32.4305	−1.14232
$807$	3.42294	0.120493
$808$	14.8732	0.523238
$809$	23.3713	0.821691	0.410846	−	0.911705i	$-0.365234\pi$
$809$	23.3713	0.821691	0.410846	+	0.911705i	$0.365234\pi$
$810$	−5.83300	−0.204951
$811$	−12.5688	−0.441350	−0.220675	−	0.975347i	$-0.570826\pi$
$811$	−12.5688	−0.441350	−0.220675	+	0.975347i	$0.570826\pi$
$812$	−4.23221	−0.148521
$813$	−8.62051	−0.302335
$814$	−19.6290	−0.687996
$815$	11.5205	0.403544
$816$	−2.18953	−0.0766490
$817$	27.4833	0.961520
$818$	−14.7713	−0.516465
$819$	56.5718	1.97678
$820$	6.90755	0.241222
$821$	−51.0824	−1.78279	−0.891394	−	0.453228i	$-0.850272\pi$
$821$	−51.0824	−1.78279	−0.891394	+	0.453228i	$0.850272\pi$
$822$	−6.93814	−0.241995
$823$	−53.9419	−1.88030	−0.940149	−	0.340765i	$-0.889314\pi$
$823$	−53.9419	−1.88030	−0.940149	+	0.340765i	$0.889314\pi$
$824$	6.09870	0.212458
$825$	−6.32208	−0.220106
$826$	−29.8029	−1.03698
$827$	−48.6105	−1.69035	−0.845177	−	0.534487i	$-0.820505\pi$
$827$	−48.6105	−1.69035	−0.845177	+	0.534487i	$0.820505\pi$
$828$	−2.80996	−0.0976528
$829$	11.2814	0.391819	0.195910	−	0.980622i	$-0.437234\pi$
$829$	11.2814	0.391819	0.195910	+	0.980622i	$0.437234\pi$
$830$	−1.18149	−0.0410100
$831$	6.53442	0.226677
$832$	−5.74710	−0.199245
$833$	−26.4773	−0.917383
$834$	0.775969	0.0268696
$835$	−14.2823	−0.494259
$836$	−8.58729	−0.296998
$837$	−14.2924	−0.494016
$838$	32.7599	1.13167
$839$	21.2399	0.733283	0.366641	−	0.930362i	$-0.380508\pi$
$839$	21.2399	0.733283	0.366641	+	0.930362i	$0.380508\pi$
$840$	−1.21596	−0.0419545
$841$	−27.5404	−0.949669
$842$	26.6453	0.918259
$843$	−3.24277	−0.111687
$844$	7.41060	0.255083
$845$	−15.9479	−0.548625
$846$	19.7501	0.679021
$847$	0.116014	0.00398628
$848$	1.67208	0.0574194
$849$	3.00776	0.103226
$850$	21.9286	0.752145
$851$	−5.90948	−0.202574
$852$	4.41689	0.151320
$853$	42.6520	1.46038	0.730189	−	0.683245i	$-0.239432\pi$
$853$	42.6520	1.46038	0.730189	+	0.683245i	$0.239432\pi$
$854$	21.2604	0.727517
$855$	−5.78426	−0.197817
$856$	−1.32271	−0.0452093
$857$	−2.27554	−0.0777311	−0.0388655	−	0.999244i	$-0.512374\pi$
$857$	−2.27554	−0.0777311	−0.0388655	+	0.999244i	$0.512374\pi$
$858$	−8.32192	−0.284106
$859$	2.54447	0.0868162	0.0434081	−	0.999057i	$-0.486178\pi$
$859$	2.54447	0.0868162	0.0434081	+	0.999057i	$0.486178\pi$
$860$	8.46454	0.288638
$861$	−13.2483	−0.451501
$862$	−24.5012	−0.834514
$863$	−3.84548	−0.130902	−0.0654509	−	0.997856i	$-0.520849\pi$
$863$	−3.84548	−0.130902	−0.0654509	+	0.997856i	$0.520849\pi$
$864$	−2.53279	−0.0861672
$865$	−15.2811	−0.519572
$866$	25.1713	0.855356
$867$	3.58613	0.121791
$868$	19.7677	0.670961
$869$	3.25061	0.110269
$870$	0.419356	0.0142175
$871$	−3.26003	−0.110462
$872$	−10.6216	−0.359692
$873$	−23.3403	−0.789950
$874$	−2.58528	−0.0874483
$875$	26.1245	0.883168
$876$	2.54922	0.0861303
$877$	6.18831	0.208964	0.104482	−	0.994527i	$-0.466681\pi$
$877$	6.18831	0.208964	0.104482	+	0.994527i	$0.466681\pi$
$878$	−19.5188	−0.658728
$879$	6.15398	0.207568
$880$	−2.64478	−0.0891556
$881$	14.8509	0.500338	0.250169	−	0.968202i	$-0.419514\pi$
$881$	14.8509	0.500338	0.250169	+	0.968202i	$0.419514\pi$
$882$	−14.8131	−0.498784
$883$	51.5087	1.73341	0.866704	−	0.498823i	$-0.166234\pi$
$883$	51.5087	1.73341	0.866704	+	0.498823i	$0.166234\pi$
$884$	28.8652	0.970842
$885$	2.95307	0.0992664
$886$	−8.51186	−0.285961
$887$	12.3989	0.416314	0.208157	−	0.978095i	$-0.433253\pi$
$887$	12.3989	0.416314	0.208157	+	0.978095i	$0.433253\pi$
$888$	−2.57617	−0.0864507
$889$	−67.0088	−2.24740
$890$	11.8896	0.398542
$891$	24.3332	0.815194
$892$	18.4257	0.616937
$893$	18.1709	0.608065
$894$	0.0622547	0.00208211
$895$	−8.67098	−0.289839
$896$	3.50309	0.117030
$897$	−2.50539	−0.0836524
$898$	−7.35281	−0.245366
$899$	−6.81744	−0.227374
$900$	12.2683	0.408943
$901$	−8.39813	−0.279782
$902$	−28.8159	−0.959464
$903$	−16.2345	−0.540251
$904$	−1.11994	−0.0372486
$905$	−6.55838	−0.218008
$906$	−0.734529	−0.0244031
$907$	27.6327	0.917530	0.458765	−	0.888558i	$-0.348292\pi$
$907$	27.6327	0.917530	0.458765	+	0.888558i	$0.348292\pi$
$908$	−9.43138	−0.312991
$909$	−41.7931	−1.38619
$910$	16.0303	0.531399
$911$	40.9013	1.35512	0.677560	−	0.735468i	$-0.263038\pi$
$911$	40.9013	1.35512	0.677560	+	0.735468i	$0.263038\pi$
$912$	−1.12702	−0.0373195
$913$	4.92875	0.163118
$914$	−15.8298	−0.523604
$915$	−2.10662	−0.0696428
$916$	−6.40400	−0.211594
$917$	−3.50309	−0.115682
$918$	12.7211	0.419859
$919$	−26.8073	−0.884292	−0.442146	−	0.896943i	$-0.645783\pi$
$919$	−26.8073	−0.884292	−0.442146	+	0.896943i	$0.645783\pi$
$920$	−0.796234	−0.0262511
$921$	8.13085	0.267921
$922$	12.7326	0.419326
$923$	−58.2291	−1.91663
$924$	5.07255	0.166875
$925$	25.8008	0.848326
$926$	16.2966	0.535538
$927$	−17.1371	−0.562855
$928$	−1.20814	−0.0396590
$929$	54.0942	1.77477	0.887387	−	0.461025i	$-0.152518\pi$
$929$	54.0942	1.77477	0.887387	+	0.461025i	$0.152518\pi$
$930$	−1.95872	−0.0642289
$931$	−13.6287	−0.446662
$932$	22.1424	0.725297
$933$	7.84224	0.256743
$934$	−19.1898	−0.627908
$935$	13.2836	0.434421
$936$	16.1491	0.527850
$937$	−26.8561	−0.877352	−0.438676	−	0.898645i	$-0.644552\pi$
$937$	−26.8561	−0.877352	−0.438676	+	0.898645i	$0.644552\pi$
$938$	1.98712	0.0648819
$939$	2.67098	0.0871643
$940$	5.59641	0.182535
$941$	25.4717	0.830355	0.415177	−	0.909740i	$-0.363720\pi$
$941$	25.4717	0.830355	0.415177	+	0.909740i	$0.363720\pi$
$942$	4.84559	0.157878
$943$	−8.67527	−0.282506
$944$	−8.50760	−0.276899
$945$	7.06466	0.229813
$946$	−35.3111	−1.14806
$947$	−1.45569	−0.0473036	−0.0236518	−	0.999720i	$-0.507529\pi$
$947$	−1.45569	−0.0473036	−0.0236518	+	0.999720i	$0.507529\pi$
$948$	0.426621	0.0138560
$949$	−33.6071	−1.09093
$950$	11.2873	0.366210
$951$	−9.50564	−0.308242
$952$	−17.5945	−0.570242
$953$	21.6060	0.699886	0.349943	−	0.936771i	$-0.386201\pi$
$953$	21.6060	0.699886	0.349943	+	0.936771i	$0.386201\pi$
$954$	−4.69847	−0.152119
$955$	18.1749	0.588127
$956$	−6.71713	−0.217248
$957$	−1.74941	−0.0565503
$958$	−23.8695	−0.771189
$959$	−55.7530	−1.80036
$960$	−0.347110	−0.0112029
$961$	0.842753	0.0271856
$962$	33.9624	1.09499
$963$	3.71676	0.119771
$964$	−13.7922	−0.444216
$965$	8.63232	0.277884
$966$	1.52713	0.0491348
$967$	44.6257	1.43507	0.717534	−	0.696524i	$-0.245271\pi$
$967$	44.6257	1.43507	0.717534	+	0.696524i	$0.245271\pi$
$968$	0.0331176	0.00106444
$969$	5.66055	0.181843
$970$	−6.61376	−0.212355
$971$	−20.5797	−0.660434	−0.330217	−	0.943905i	$-0.607122\pi$
$971$	−20.5797	−0.660434	−0.330217	+	0.943905i	$0.607122\pi$
$972$	10.7919	0.346151
$973$	6.23548	0.199900
$974$	5.81510	0.186328
$975$	10.9385	0.350314
$976$	6.06904	0.194265
$977$	39.4620	1.26250	0.631251	−	0.775578i	$-0.282542\pi$
$977$	39.4620	1.26250	0.631251	+	0.775578i	$0.282542\pi$
$978$	−6.30746	−0.201690
$979$	−49.5994	−1.58520
$980$	−4.19747	−0.134083
$981$	29.8461	0.952914
$982$	39.3804	1.25668
$983$	53.4795	1.70573	0.852866	−	0.522129i	$-0.174862\pi$
$983$	53.4795	1.70573	0.852866	+	0.522129i	$0.174862\pi$
$984$	−3.78189	−0.120562
$985$	−1.91375	−0.0609771
$986$	6.06795	0.193243
$987$	−10.7336	−0.341655
$988$	14.8578	0.472691
$989$	−10.6307	−0.338037
$990$	7.43173	0.236196
$991$	32.4320	1.03024	0.515118	−	0.857119i	$-0.327748\pi$
$991$	32.4320	1.03024	0.515118	+	0.857119i	$0.327748\pi$
$992$	5.64294	0.179163
$993$	−12.6478	−0.401366
$994$	35.4930	1.12577
$995$	−3.57047	−0.113191
$996$	0.646864	0.0204967
$997$	−13.8187	−0.437642	−0.218821	−	0.975765i	$-0.570221\pi$
$997$	−13.8187	−0.437642	−0.218821	+	0.975765i	$0.570221\pi$
$998$	−31.5640	−0.999140
$999$	14.9674	0.473549

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.f.1.13	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.f.1.13	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.435939 q^{3} +1.00000 q^{4} -0.796234 q^{5} +0.435939 q^{6} +3.50309 q^{7} +1.00000 q^{8} -2.80996 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.435939 q^{3} +1.00000 q^{4} -0.796234 q^{5} +0.435939 q^{6} +3.50309 q^{7} +1.00000 q^{8} -2.80996 q^{9} -0.796234 q^{10} +3.32161 q^{11} +0.435939 q^{12} -5.74710 q^{13} +3.50309 q^{14} -0.347110 q^{15} +1.00000 q^{16} -5.02257 q^{17} -2.80996 q^{18} -2.58528 q^{19} -0.796234 q^{20} +1.52713 q^{21} +3.32161 q^{22} +1.00000 q^{23} +0.435939 q^{24} -4.36601 q^{25} -5.74710 q^{26} -2.53279 q^{27} +3.50309 q^{28} -1.20814 q^{29} -0.347110 q^{30} +5.64294 q^{31} +1.00000 q^{32} +1.44802 q^{33} -5.02257 q^{34} -2.78928 q^{35} -2.80996 q^{36} -5.90948 q^{37} -2.58528 q^{38} -2.50539 q^{39} -0.796234 q^{40} -8.67527 q^{41} +1.52713 q^{42} -10.6307 q^{43} +3.32161 q^{44} +2.23738 q^{45} +1.00000 q^{46} -7.02860 q^{47} +0.435939 q^{48} +5.27166 q^{49} -4.36601 q^{50} -2.18953 q^{51} -5.74710 q^{52} +1.67208 q^{53} -2.53279 q^{54} -2.64478 q^{55} +3.50309 q^{56} -1.12702 q^{57} -1.20814 q^{58} -8.50760 q^{59} -0.347110 q^{60} +6.06904 q^{61} +5.64294 q^{62} -9.84354 q^{63} +1.00000 q^{64} +4.57604 q^{65} +1.44802 q^{66} +0.567248 q^{67} -5.02257 q^{68} +0.435939 q^{69} -2.78928 q^{70} +10.1319 q^{71} -2.80996 q^{72} +5.84766 q^{73} -5.90948 q^{74} -1.90331 q^{75} -2.58528 q^{76} +11.6359 q^{77} -2.50539 q^{78} +0.978625 q^{79} -0.796234 q^{80} +7.32573 q^{81} -8.67527 q^{82} +1.48384 q^{83} +1.52713 q^{84} +3.99914 q^{85} -10.6307 q^{86} -0.526674 q^{87} +3.32161 q^{88} -14.9323 q^{89} +2.23738 q^{90} -20.1326 q^{91} +1.00000 q^{92} +2.45998 q^{93} -7.02860 q^{94} +2.05849 q^{95} +0.435939 q^{96} +8.30629 q^{97} +5.27166 q^{98} -9.33359 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{2} - 5 q^{3} + 20 q^{4} - 6 q^{5} - 5 q^{6} - 12 q^{7} + 20 q^{8} - q^{9}+O(q^{10}) \) 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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