LMFDB - Embedded newform 6026.2.a.f.1.19

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			1.19
Root			$-2.02882$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +2.02882 q^{3} +1.00000 q^{4} -0.795313 q^{5} +2.02882 q^{6} -4.29820 q^{7} +1.00000 q^{8} +1.11611 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.02882 q^{3} +1.00000 q^{4} -0.795313 q^{5} +2.02882 q^{6} -4.29820 q^{7} +1.00000 q^{8} +1.11611 q^{9} -0.795313 q^{10} +5.92056 q^{11} +2.02882 q^{12} -3.91438 q^{13} -4.29820 q^{14} -1.61355 q^{15} +1.00000 q^{16} +3.72660 q^{17} +1.11611 q^{18} -8.12011 q^{19} -0.795313 q^{20} -8.72028 q^{21} +5.92056 q^{22} +1.00000 q^{23} +2.02882 q^{24} -4.36748 q^{25} -3.91438 q^{26} -3.82207 q^{27} -4.29820 q^{28} -4.96308 q^{29} -1.61355 q^{30} -0.0401676 q^{31} +1.00000 q^{32} +12.0118 q^{33} +3.72660 q^{34} +3.41842 q^{35} +1.11611 q^{36} +0.836574 q^{37} -8.12011 q^{38} -7.94158 q^{39} -0.795313 q^{40} +2.26685 q^{41} -8.72028 q^{42} -9.32280 q^{43} +5.92056 q^{44} -0.887659 q^{45} +1.00000 q^{46} +0.452233 q^{47} +2.02882 q^{48} +11.4745 q^{49} -4.36748 q^{50} +7.56061 q^{51} -3.91438 q^{52} -11.3556 q^{53} -3.82207 q^{54} -4.70870 q^{55} -4.29820 q^{56} -16.4743 q^{57} -4.96308 q^{58} +2.92995 q^{59} -1.61355 q^{60} +1.58290 q^{61} -0.0401676 q^{62} -4.79728 q^{63} +1.00000 q^{64} +3.11316 q^{65} +12.0118 q^{66} -4.00219 q^{67} +3.72660 q^{68} +2.02882 q^{69} +3.41842 q^{70} -8.40394 q^{71} +1.11611 q^{72} -0.555215 q^{73} +0.836574 q^{74} -8.86083 q^{75} -8.12011 q^{76} -25.4478 q^{77} -7.94158 q^{78} +14.9944 q^{79} -0.795313 q^{80} -11.1026 q^{81} +2.26685 q^{82} -0.959569 q^{83} -8.72028 q^{84} -2.96382 q^{85} -9.32280 q^{86} -10.0692 q^{87} +5.92056 q^{88} +3.11842 q^{89} -0.887659 q^{90} +16.8248 q^{91} +1.00000 q^{92} -0.0814929 q^{93} +0.452233 q^{94} +6.45803 q^{95} +2.02882 q^{96} +17.8474 q^{97} +11.4745 q^{98} +6.60802 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	2.02882	1.17134	0.585670	−	0.810550i	$-0.300831\pi$
$3$	2.02882	1.17134	0.585670	+	0.810550i	$0.300831\pi$
$4$	1.00000	0.500000
$5$	−0.795313	−0.355675	−0.177837	−	0.984060i	$-0.556910\pi$
$5$	−0.795313	−0.355675	−0.177837	+	0.984060i	$0.556910\pi$
$6$	2.02882	0.828263
$7$	−4.29820	−1.62457	−0.812284	−	0.583262i	$-0.801776\pi$
$7$	−4.29820	−1.62457	−0.812284	+	0.583262i	$0.801776\pi$
$8$	1.00000	0.353553
$9$	1.11611	0.372038
$10$	−0.795313	−0.251500
$11$	5.92056	1.78512	0.892558	−	0.450932i	$-0.148908\pi$
$11$	5.92056	1.78512	0.892558	+	0.450932i	$0.148908\pi$
$12$	2.02882	0.585670
$13$	−3.91438	−1.08565	−0.542827	−	0.839844i	$-0.682646\pi$
$13$	−3.91438	−1.08565	−0.542827	+	0.839844i	$0.682646\pi$
$14$	−4.29820	−1.14874
$15$	−1.61355	−0.416616
$16$	1.00000	0.250000
$17$	3.72660	0.903834	0.451917	−	0.892060i	$-0.350740\pi$
$17$	3.72660	0.903834	0.451917	+	0.892060i	$0.350740\pi$
$18$	1.11611	0.263070
$19$	−8.12011	−1.86288	−0.931441	−	0.363893i	$-0.881447\pi$
$19$	−8.12011	−1.86288	−0.931441	+	0.363893i	$0.881447\pi$
$20$	−0.795313	−0.177837
$21$	−8.72028	−1.90292
$22$	5.92056	1.26227
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	2.02882	0.414131
$25$	−4.36748	−0.873495
$26$	−3.91438	−0.767674
$27$	−3.82207	−0.735557
$28$	−4.29820	−0.812284
$29$	−4.96308	−0.921621	−0.460811	−	0.887498i	$-0.652441\pi$
$29$	−4.96308	−0.921621	−0.460811	+	0.887498i	$0.652441\pi$
$30$	−1.61355	−0.294592
$31$	−0.0401676	−0.00721431	−0.00360716	−	0.999993i	$-0.501148\pi$
$31$	−0.0401676	−0.00721431	−0.00360716	+	0.999993i	$0.501148\pi$
$32$	1.00000	0.176777
$33$	12.0118	2.09098
$34$	3.72660	0.639107
$35$	3.41842	0.577818
$36$	1.11611	0.186019
$37$	0.836574	0.137532	0.0687660	−	0.997633i	$-0.478094\pi$
$37$	0.836574	0.137532	0.0687660	+	0.997633i	$0.478094\pi$
$38$	−8.12011	−1.31726
$39$	−7.94158	−1.27167
$40$	−0.795313	−0.125750
$41$	2.26685	0.354022	0.177011	−	0.984209i	$-0.443357\pi$
$41$	2.26685	0.354022	0.177011	+	0.984209i	$0.443357\pi$
$42$	−8.72028	−1.34557
$43$	−9.32280	−1.42171	−0.710857	−	0.703337i	$-0.751693\pi$
$43$	−9.32280	−1.42171	−0.710857	+	0.703337i	$0.751693\pi$
$44$	5.92056	0.892558
$45$	−0.887659	−0.132324
$46$	1.00000	0.147442
$47$	0.452233	0.0659649	0.0329825	−	0.999456i	$-0.489499\pi$
$47$	0.452233	0.0659649	0.0329825	+	0.999456i	$0.489499\pi$
$48$	2.02882	0.292835
$49$	11.4745	1.63922
$50$	−4.36748	−0.617655
$51$	7.56061	1.05870
$52$	−3.91438	−0.542827
$53$	−11.3556	−1.55982	−0.779908	−	0.625894i	$-0.784734\pi$
$53$	−11.3556	−1.55982	−0.779908	+	0.625894i	$0.784734\pi$
$54$	−3.82207	−0.520118
$55$	−4.70870	−0.634921
$56$	−4.29820	−0.574371
$57$	−16.4743	−2.18207
$58$	−4.96308	−0.651685
$59$	2.92995	0.381447	0.190723	−	0.981644i	$-0.438917\pi$
$59$	2.92995	0.381447	0.190723	+	0.981644i	$0.438917\pi$
$60$	−1.61355	−0.208308
$61$	1.58290	0.202669	0.101335	−	0.994852i	$-0.467689\pi$
$61$	1.58290	0.202669	0.101335	+	0.994852i	$0.467689\pi$
$62$	−0.0401676	−0.00510129
$63$	−4.79728	−0.604401
$64$	1.00000	0.125000
$65$	3.11316	0.386140
$66$	12.0118	1.47855
$67$	−4.00219	−0.488945	−0.244473	−	0.969656i	$-0.578615\pi$
$67$	−4.00219	−0.488945	−0.244473	+	0.969656i	$0.578615\pi$
$68$	3.72660	0.451917
$69$	2.02882	0.244241
$70$	3.41842	0.408579
$71$	−8.40394	−0.997364	−0.498682	−	0.866785i	$-0.666182\pi$
$71$	−8.40394	−0.997364	−0.498682	+	0.866785i	$0.666182\pi$
$72$	1.11611	0.131535
$73$	−0.555215	−0.0649830	−0.0324915	−	0.999472i	$-0.510344\pi$
$73$	−0.555215	−0.0649830	−0.0324915	+	0.999472i	$0.510344\pi$
$74$	0.836574	0.0972498
$75$	−8.86083	−1.02316
$76$	−8.12011	−0.931441
$77$	−25.4478	−2.90004
$78$	−7.94158	−0.899207
$79$	14.9944	1.68701	0.843503	−	0.537124i	$-0.180489\pi$
$79$	14.9944	1.68701	0.843503	+	0.537124i	$0.180489\pi$
$80$	−0.795313	−0.0889187
$81$	−11.1026	−1.23363
$82$	2.26685	0.250332
$83$	−0.959569	−0.105326	−0.0526632	−	0.998612i	$-0.516771\pi$
$83$	−0.959569	−0.105326	−0.0526632	+	0.998612i	$0.516771\pi$
$84$	−8.72028	−0.951461
$85$	−2.96382	−0.321471
$86$	−9.32280	−1.00530
$87$	−10.0692	−1.07953
$88$	5.92056	0.631134
$89$	3.11842	0.330552	0.165276	−	0.986247i	$-0.447148\pi$
$89$	3.11842	0.330552	0.165276	+	0.986247i	$0.447148\pi$
$90$	−0.887659	−0.0935675
$91$	16.8248	1.76372
$92$	1.00000	0.104257
$93$	−0.0814929	−0.00845042
$94$	0.452233	0.0466443
$95$	6.45803	0.662580
$96$	2.02882	0.207066
$97$	17.8474	1.81212	0.906062	−	0.423144i	$-0.139074\pi$
$97$	17.8474	1.81212	0.906062	+	0.423144i	$0.139074\pi$
$98$	11.4745	1.15910
$99$	6.60802	0.664131
$100$	−4.36748	−0.436748
$101$	−18.6929	−1.86001	−0.930007	−	0.367543i	$-0.880199\pi$
$101$	−18.6929	−1.86001	−0.930007	+	0.367543i	$0.880199\pi$
$102$	7.56061	0.748612
$103$	−11.0383	−1.08764	−0.543820	−	0.839202i	$-0.683022\pi$
$103$	−11.0383	−1.08764	−0.543820	+	0.839202i	$0.683022\pi$
$104$	−3.91438	−0.383837
$105$	6.93535	0.676821
$106$	−11.3556	−1.10296
$107$	6.59033	0.637111	0.318555	−	0.947904i	$-0.396802\pi$
$107$	6.59033	0.637111	0.318555	+	0.947904i	$0.396802\pi$
$108$	−3.82207	−0.367779
$109$	−18.2870	−1.75158	−0.875788	−	0.482696i	$-0.839658\pi$
$109$	−18.2870	−1.75158	−0.875788	+	0.482696i	$0.839658\pi$
$110$	−4.70870	−0.448957
$111$	1.69726	0.161097
$112$	−4.29820	−0.406142
$113$	−17.2101	−1.61899	−0.809496	−	0.587125i	$-0.800260\pi$
$113$	−17.2101	−1.61899	−0.809496	+	0.587125i	$0.800260\pi$
$114$	−16.4743	−1.54296
$115$	−0.795313	−0.0741633
$116$	−4.96308	−0.460811
$117$	−4.36890	−0.403905
$118$	2.92995	0.269724
$119$	−16.0177	−1.46834
$120$	−1.61355	−0.147296
$121$	24.0531	2.18664
$122$	1.58290	0.143309
$123$	4.59903	0.414681
$124$	−0.0401676	−0.00360716
$125$	7.45008	0.666355
$126$	−4.79728	−0.427376
$127$	3.68421	0.326921	0.163461	−	0.986550i	$-0.447734\pi$
$127$	3.68421	0.326921	0.163461	+	0.986550i	$0.447734\pi$
$128$	1.00000	0.0883883
$129$	−18.9143	−1.66531
$130$	3.11316	0.273042
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	12.0118	1.04549
$133$	34.9019	3.02638
$134$	−4.00219	−0.345737
$135$	3.03974	0.261619
$136$	3.72660	0.319554
$137$	8.77190	0.749434	0.374717	−	0.927139i	$-0.377740\pi$
$137$	8.77190	0.749434	0.374717	+	0.927139i	$0.377740\pi$
$138$	2.02882	0.172705
$139$	9.33851	0.792082	0.396041	−	0.918233i	$-0.370384\pi$
$139$	9.33851	0.792082	0.396041	+	0.918233i	$0.370384\pi$
$140$	3.41842	0.288909
$141$	0.917499	0.0772674
$142$	−8.40394	−0.705243
$143$	−23.1754	−1.93802
$144$	1.11611	0.0930095
$145$	3.94720	0.327797
$146$	−0.555215	−0.0459499
$147$	23.2798	1.92008
$148$	0.836574	0.0687660
$149$	8.17112	0.669404	0.334702	−	0.942324i	$-0.391364\pi$
$149$	8.17112	0.669404	0.334702	+	0.942324i	$0.391364\pi$
$150$	−8.86083	−0.723484
$151$	−13.4865	−1.09752	−0.548759	−	0.835980i	$-0.684900\pi$
$151$	−13.4865	−1.09752	−0.548759	+	0.835980i	$0.684900\pi$
$152$	−8.12011	−0.658628
$153$	4.15931	0.336260
$154$	−25.4478	−2.05064
$155$	0.0319458	0.00256595
$156$	−7.94158	−0.635836
$157$	18.4496	1.47244	0.736220	−	0.676743i	$-0.236609\pi$
$157$	18.4496	1.47244	0.736220	+	0.676743i	$0.236609\pi$
$158$	14.9944	1.19289
$159$	−23.0385	−1.82707
$160$	−0.795313	−0.0628750
$161$	−4.29820	−0.338746
$162$	−11.1026	−0.872305
$163$	20.1763	1.58033	0.790164	−	0.612896i	$-0.209996\pi$
$163$	20.1763	1.58033	0.790164	+	0.612896i	$0.209996\pi$
$164$	2.26685	0.177011
$165$	−9.55311	−0.743708
$166$	−0.959569	−0.0744770
$167$	−19.6484	−1.52044	−0.760219	−	0.649667i	$-0.774908\pi$
$167$	−19.6484	−1.52044	−0.760219	+	0.649667i	$0.774908\pi$
$168$	−8.72028	−0.672784
$169$	2.32240	0.178646
$170$	−2.96382	−0.227314
$171$	−9.06297	−0.693062
$172$	−9.32280	−0.710857
$173$	−10.7808	−0.819652	−0.409826	−	0.912164i	$-0.634411\pi$
$173$	−10.7808	−0.819652	−0.409826	+	0.912164i	$0.634411\pi$
$174$	−10.0692	−0.763345
$175$	18.7723	1.41905
$176$	5.92056	0.446279
$177$	5.94434	0.446804
$178$	3.11842	0.233736
$179$	3.52575	0.263527	0.131764	−	0.991281i	$-0.457936\pi$
$179$	3.52575	0.263527	0.131764	+	0.991281i	$0.457936\pi$
$180$	−0.887659	−0.0661622
$181$	−15.0071	−1.11547	−0.557736	−	0.830018i	$-0.688330\pi$
$181$	−15.0071	−1.11547	−0.557736	+	0.830018i	$0.688330\pi$
$182$	16.8248	1.24714
$183$	3.21141	0.237395
$184$	1.00000	0.0737210
$185$	−0.665338	−0.0489166
$186$	−0.0814929	−0.00597535
$187$	22.0636	1.61345
$188$	0.452233	0.0329825
$189$	16.4280	1.19496
$190$	6.45803	0.468515
$191$	−15.5925	−1.12823	−0.564117	−	0.825695i	$-0.690783\pi$
$191$	−15.5925	−1.12823	−0.564117	+	0.825695i	$0.690783\pi$
$192$	2.02882	0.146418
$193$	−19.8102	−1.42597	−0.712984	−	0.701181i	$-0.752657\pi$
$193$	−19.8102	−1.42597	−0.712984	+	0.701181i	$0.752657\pi$
$194$	17.8474	1.28137
$195$	6.31604	0.452301
$196$	11.4745	0.819610
$197$	24.3354	1.73382	0.866911	−	0.498462i	$-0.166102\pi$
$197$	24.3354	1.73382	0.866911	+	0.498462i	$0.166102\pi$
$198$	6.60802	0.469612
$199$	4.85766	0.344350	0.172175	−	0.985066i	$-0.444920\pi$
$199$	4.85766	0.344350	0.172175	+	0.985066i	$0.444920\pi$
$200$	−4.36748	−0.308827
$201$	−8.11973	−0.572721
$202$	−18.6929	−1.31523
$203$	21.3323	1.49724
$204$	7.56061	0.529349
$205$	−1.80285	−0.125917
$206$	−11.0383	−0.769077
$207$	1.11611	0.0775752
$208$	−3.91438	−0.271414
$209$	−48.0756	−3.32546
$210$	6.93535	0.478585
$211$	−25.9341	−1.78538	−0.892688	−	0.450675i	$-0.851184\pi$
$211$	−25.9341	−1.78538	−0.892688	+	0.450675i	$0.851184\pi$
$212$	−11.3556	−0.779908
$213$	−17.0501	−1.16825
$214$	6.59033	0.450505
$215$	7.41454	0.505668
$216$	−3.82207	−0.260059
$217$	0.172648	0.0117201
$218$	−18.2870	−1.23855
$219$	−1.12643	−0.0761172
$220$	−4.70870	−0.317461
$221$	−14.5874	−0.981252
$222$	1.69726	0.113913
$223$	10.2505	0.686424	0.343212	−	0.939258i	$-0.388485\pi$
$223$	10.2505	0.686424	0.343212	+	0.939258i	$0.388485\pi$
$224$	−4.29820	−0.287186
$225$	−4.87460	−0.324973
$226$	−17.2101	−1.14480
$227$	5.80423	0.385240	0.192620	−	0.981273i	$-0.438302\pi$
$227$	5.80423	0.385240	0.192620	+	0.981273i	$0.438302\pi$
$228$	−16.4743	−1.09103
$229$	5.37100	0.354925	0.177463	−	0.984128i	$-0.443211\pi$
$229$	5.37100	0.354925	0.177463	+	0.984128i	$0.443211\pi$
$230$	−0.795313	−0.0524414
$231$	−51.6290	−3.39694
$232$	−4.96308	−0.325842
$233$	7.31958	0.479521	0.239761	−	0.970832i	$-0.422931\pi$
$233$	7.31958	0.479521	0.239761	+	0.970832i	$0.422931\pi$
$234$	−4.36890	−0.285604
$235$	−0.359667	−0.0234621
$236$	2.92995	0.190723
$237$	30.4210	1.97606
$238$	−16.0177	−1.03827
$239$	−6.56984	−0.424968	−0.212484	−	0.977165i	$-0.568155\pi$
$239$	−6.56984	−0.424968	−0.212484	+	0.977165i	$0.568155\pi$
$240$	−1.61355	−0.104154
$241$	3.81369	0.245661	0.122831	−	0.992428i	$-0.460803\pi$
$241$	3.81369	0.245661	0.122831	+	0.992428i	$0.460803\pi$
$242$	24.0531	1.54619
$243$	−11.0590	−0.709438
$244$	1.58290	0.101335
$245$	−9.12585	−0.583029
$246$	4.59903	0.293224
$247$	31.7852	2.02245
$248$	−0.0401676	−0.00255065
$249$	−1.94679	−0.123373
$250$	7.45008	0.471184
$251$	25.9341	1.63695	0.818474	−	0.574544i	$-0.194820\pi$
$251$	25.9341	1.63695	0.818474	+	0.574544i	$0.194820\pi$
$252$	−4.79728	−0.302200
$253$	5.92056	0.372223
$254$	3.68421	0.231168
$255$	−6.01305	−0.376552
$256$	1.00000	0.0625000
$257$	−16.1954	−1.01024	−0.505122	−	0.863048i	$-0.668552\pi$
$257$	−16.1954	−1.01024	−0.505122	+	0.863048i	$0.668552\pi$
$258$	−18.9143	−1.17755
$259$	−3.59577	−0.223430
$260$	3.11316	0.193070
$261$	−5.53936	−0.342878
$262$	−1.00000	−0.0617802
$263$	−15.4798	−0.954525	−0.477262	−	0.878761i	$-0.658371\pi$
$263$	−15.4798	−0.954525	−0.477262	+	0.878761i	$0.658371\pi$
$264$	12.0118	0.739273
$265$	9.03128	0.554787
$266$	34.9019	2.13997
$267$	6.32672	0.387189
$268$	−4.00219	−0.244473
$269$	−20.9870	−1.27960	−0.639800	−	0.768542i	$-0.720983\pi$
$269$	−20.9870	−1.27960	−0.639800	+	0.768542i	$0.720983\pi$
$270$	3.03974	0.184993
$271$	−29.5766	−1.79665	−0.898326	−	0.439330i	$-0.855216\pi$
$271$	−29.5766	−1.79665	−0.898326	+	0.439330i	$0.855216\pi$
$272$	3.72660	0.225959
$273$	34.1345	2.06592
$274$	8.77190	0.529930
$275$	−25.8579	−1.55929
$276$	2.02882	0.122121
$277$	−9.12809	−0.548454	−0.274227	−	0.961665i	$-0.588422\pi$
$277$	−9.12809	−0.548454	−0.274227	+	0.961665i	$0.588422\pi$
$278$	9.33851	0.560086
$279$	−0.0448316	−0.00268400
$280$	3.41842	0.204289
$281$	−17.9491	−1.07075	−0.535377	−	0.844613i	$-0.679831\pi$
$281$	−17.9491	−1.07075	−0.535377	+	0.844613i	$0.679831\pi$
$282$	0.917499	0.0546363
$283$	−6.67736	−0.396928	−0.198464	−	0.980108i	$-0.563595\pi$
$283$	−6.67736	−0.396928	−0.198464	+	0.980108i	$0.563595\pi$
$284$	−8.40394	−0.498682
$285$	13.1022	0.776107
$286$	−23.1754	−1.37039
$287$	−9.74338	−0.575133
$288$	1.11611	0.0657676
$289$	−3.11243	−0.183084
$290$	3.94720	0.231788
$291$	36.2091	2.12261
$292$	−0.555215	−0.0324915
$293$	11.2903	0.659588	0.329794	−	0.944053i	$-0.393021\pi$
$293$	11.2903	0.659588	0.329794	+	0.944053i	$0.393021\pi$
$294$	23.2798	1.35771
$295$	−2.33023	−0.135671
$296$	0.836574	0.0486249
$297$	−22.6288	−1.31306
$298$	8.17112	0.473340
$299$	−3.91438	−0.226375
$300$	−8.86083	−0.511580
$301$	40.0713	2.30967
$302$	−13.4865	−0.776063
$303$	−37.9245	−2.17871
$304$	−8.12011	−0.465720
$305$	−1.25890	−0.0720843
$306$	4.15931	0.237772
$307$	3.60905	0.205979	0.102990	−	0.994682i	$-0.467159\pi$
$307$	3.60905	0.205979	0.102990	+	0.994682i	$0.467159\pi$
$308$	−25.4478	−1.45002
$309$	−22.3948	−1.27400
$310$	0.0319458	0.00181440
$311$	4.72334	0.267836	0.133918	−	0.990992i	$-0.457244\pi$
$311$	4.72334	0.267836	0.133918	+	0.990992i	$0.457244\pi$
$312$	−7.94158	−0.449604
$313$	17.9138	1.01255	0.506273	−	0.862373i	$-0.331023\pi$
$313$	17.9138	1.01255	0.506273	+	0.862373i	$0.331023\pi$
$314$	18.4496	1.04117
$315$	3.81534	0.214970
$316$	14.9944	0.843503
$317$	33.9501	1.90683	0.953414	−	0.301665i	$-0.0975425\pi$
$317$	33.9501	1.90683	0.953414	+	0.301665i	$0.0975425\pi$
$318$	−23.0385	−1.29194
$319$	−29.3842	−1.64520
$320$	−0.795313	−0.0444593
$321$	13.3706	0.746274
$322$	−4.29820	−0.239529
$323$	−30.2604	−1.68374
$324$	−11.1026	−0.616813
$325$	17.0960	0.948315
$326$	20.1763	1.11746
$327$	−37.1010	−2.05169
$328$	2.26685	0.125166
$329$	−1.94379	−0.107165
$330$	−9.55311	−0.525881
$331$	−5.57755	−0.306570	−0.153285	−	0.988182i	$-0.548985\pi$
$331$	−5.57755	−0.306570	−0.153285	+	0.988182i	$0.548985\pi$
$332$	−0.959569	−0.0526632
$333$	0.933712	0.0511671
$334$	−19.6484	−1.07511
$335$	3.18299	0.173906
$336$	−8.72028	−0.475730
$337$	18.2558	0.994455	0.497228	−	0.867620i	$-0.334351\pi$
$337$	18.2558	0.994455	0.497228	+	0.867620i	$0.334351\pi$
$338$	2.32240	0.126322
$339$	−34.9163	−1.89639
$340$	−2.96382	−0.160735
$341$	−0.237815	−0.0128784
$342$	−9.06297	−0.490069
$343$	−19.2325	−1.03846
$344$	−9.32280	−0.502652
$345$	−1.61355	−0.0868705
$346$	−10.7808	−0.579582
$347$	−23.1066	−1.24043	−0.620215	−	0.784432i	$-0.712954\pi$
$347$	−23.1066	−1.24043	−0.620215	+	0.784432i	$0.712954\pi$
$348$	−10.0692	−0.539766
$349$	−21.4690	−1.14921	−0.574604	−	0.818432i	$-0.694844\pi$
$349$	−21.4690	−1.14921	−0.574604	+	0.818432i	$0.694844\pi$
$350$	18.7723	1.00342
$351$	14.9610	0.798561
$352$	5.92056	0.315567
$353$	−8.68057	−0.462020	−0.231010	−	0.972951i	$-0.574203\pi$
$353$	−8.68057	−0.462020	−0.231010	+	0.972951i	$0.574203\pi$
$354$	5.94434	0.315938
$355$	6.68376	0.354737
$356$	3.11842	0.165276
$357$	−32.4970	−1.71993
$358$	3.52575	0.186342
$359$	6.08852	0.321340	0.160670	−	0.987008i	$-0.448635\pi$
$359$	6.08852	0.321340	0.160670	+	0.987008i	$0.448635\pi$
$360$	−0.887659	−0.0467838
$361$	46.9362	2.47033
$362$	−15.0071	−0.788758
$363$	48.7994	2.56130
$364$	16.8248	0.881860
$365$	0.441569	0.0231128
$366$	3.21141	0.167863
$367$	−13.4826	−0.703787	−0.351893	−	0.936040i	$-0.614462\pi$
$367$	−13.4826	−0.703787	−0.351893	+	0.936040i	$0.614462\pi$
$368$	1.00000	0.0521286
$369$	2.53006	0.131710
$370$	−0.665338	−0.0345893
$371$	48.8088	2.53403
$372$	−0.0814929	−0.00422521
$373$	25.6318	1.32717	0.663583	−	0.748102i	$-0.269035\pi$
$373$	25.6318	1.32717	0.663583	+	0.748102i	$0.269035\pi$
$374$	22.0636	1.14088
$375$	15.1149	0.780528
$376$	0.452233	0.0233221
$377$	19.4274	1.00056
$378$	16.4280	0.844966
$379$	11.7661	0.604385	0.302192	−	0.953247i	$-0.402282\pi$
$379$	11.7661	0.604385	0.302192	+	0.953247i	$0.402282\pi$
$380$	6.45803	0.331290
$381$	7.47461	0.382936
$382$	−15.5925	−0.797782
$383$	31.7616	1.62294	0.811472	−	0.584391i	$-0.198667\pi$
$383$	31.7616	1.62294	0.811472	+	0.584391i	$0.198667\pi$
$384$	2.02882	0.103533
$385$	20.2389	1.03147
$386$	−19.8102	−1.00831
$387$	−10.4053	−0.528931
$388$	17.8474	0.906062
$389$	33.1424	1.68038	0.840192	−	0.542289i	$-0.182442\pi$
$389$	33.1424	1.68038	0.840192	+	0.542289i	$0.182442\pi$
$390$	6.31604	0.319825
$391$	3.72660	0.188462
$392$	11.4745	0.579552
$393$	−2.02882	−0.102340
$394$	24.3354	1.22600
$395$	−11.9253	−0.600026
$396$	6.60802	0.332066
$397$	−7.46950	−0.374884	−0.187442	−	0.982276i	$-0.560020\pi$
$397$	−7.46950	−0.374884	−0.187442	+	0.982276i	$0.560020\pi$
$398$	4.85766	0.243492
$399$	70.8097	3.54492
$400$	−4.36748	−0.218374
$401$	25.0074	1.24881	0.624406	−	0.781100i	$-0.285341\pi$
$401$	25.0074	1.24881	0.624406	+	0.781100i	$0.285341\pi$
$402$	−8.11973	−0.404975
$403$	0.157231	0.00783226
$404$	−18.6929	−0.930007
$405$	8.83007	0.438769
$406$	21.3323	1.05871
$407$	4.95299	0.245511
$408$	7.56061	0.374306
$409$	6.17897	0.305530	0.152765	−	0.988263i	$-0.451182\pi$
$409$	6.17897	0.305530	0.152765	+	0.988263i	$0.451182\pi$
$410$	−1.80285	−0.0890366
$411$	17.7966	0.877842
$412$	−11.0383	−0.543820
$413$	−12.5935	−0.619686
$414$	1.11611	0.0548540
$415$	0.763157	0.0374619
$416$	−3.91438	−0.191918
$417$	18.9462	0.927797
$418$	−48.0756	−2.35146
$419$	−26.1013	−1.27513	−0.637567	−	0.770395i	$-0.720059\pi$
$419$	−26.1013	−1.27513	−0.637567	+	0.770395i	$0.720059\pi$
$420$	6.93535	0.338411
$421$	21.6188	1.05363	0.526817	−	0.849979i	$-0.323385\pi$
$421$	21.6188	1.05363	0.526817	+	0.849979i	$0.323385\pi$
$422$	−25.9341	−1.26245
$423$	0.504743	0.0245415
$424$	−11.3556	−0.551478
$425$	−16.2759	−0.789495
$426$	−17.0501	−0.826079
$427$	−6.80361	−0.329250
$428$	6.59033	0.318555
$429$	−47.0186	−2.27008
$430$	7.41454	0.357561
$431$	−6.04308	−0.291085	−0.145543	−	0.989352i	$-0.546493\pi$
$431$	−6.04308	−0.291085	−0.145543	+	0.989352i	$0.546493\pi$
$432$	−3.82207	−0.183889
$433$	−18.1908	−0.874195	−0.437098	−	0.899414i	$-0.643994\pi$
$433$	−18.1908	−0.874195	−0.437098	+	0.899414i	$0.643994\pi$
$434$	0.172648	0.00828739
$435$	8.00817	0.383962
$436$	−18.2870	−0.875788
$437$	−8.12011	−0.388438
$438$	−1.12643	−0.0538230
$439$	2.79486	0.133391	0.0666956	−	0.997773i	$-0.478754\pi$
$439$	2.79486	0.133391	0.0666956	+	0.997773i	$0.478754\pi$
$440$	−4.70870	−0.224478
$441$	12.8069	0.609852
$442$	−14.5874	−0.693850
$443$	15.5737	0.739931	0.369966	−	0.929045i	$-0.379369\pi$
$443$	15.5737	0.739931	0.369966	+	0.929045i	$0.379369\pi$
$444$	1.69726	0.0805483
$445$	−2.48012	−0.117569
$446$	10.2505	0.485375
$447$	16.5777	0.784100
$448$	−4.29820	−0.203071
$449$	−26.9582	−1.27223	−0.636117	−	0.771592i	$-0.719461\pi$
$449$	−26.9582	−1.27223	−0.636117	+	0.771592i	$0.719461\pi$
$450$	−4.87460	−0.229791
$451$	13.4210	0.631971
$452$	−17.2101	−0.809496
$453$	−27.3618	−1.28557
$454$	5.80423	0.272406
$455$	−13.3810	−0.627311
$456$	−16.4743	−0.771478
$457$	4.78462	0.223815	0.111908	−	0.993719i	$-0.464304\pi$
$457$	4.78462	0.223815	0.111908	+	0.993719i	$0.464304\pi$
$458$	5.37100	0.250970
$459$	−14.2433	−0.664822
$460$	−0.795313	−0.0370817
$461$	−14.7545	−0.687188	−0.343594	−	0.939118i	$-0.611644\pi$
$461$	−14.7545	−0.687188	−0.343594	+	0.939118i	$0.611644\pi$
$462$	−51.6290	−2.40200
$463$	14.0921	0.654917	0.327459	−	0.944866i	$-0.393808\pi$
$463$	14.0921	0.654917	0.327459	+	0.944866i	$0.393808\pi$
$464$	−4.96308	−0.230405
$465$	0.0648123	0.00300560
$466$	7.31958	0.339073
$467$	2.83911	0.131379	0.0656893	−	0.997840i	$-0.479075\pi$
$467$	2.83911	0.131379	0.0656893	+	0.997840i	$0.479075\pi$
$468$	−4.36890	−0.201952
$469$	17.2022	0.794325
$470$	−0.359667	−0.0165902
$471$	37.4310	1.72473
$472$	2.92995	0.134862
$473$	−55.1962	−2.53793
$474$	30.4210	1.39728
$475$	35.4644	1.62722
$476$	−16.0177	−0.734170
$477$	−12.6742	−0.580310
$478$	−6.56984	−0.300498
$479$	24.2647	1.10868	0.554342	−	0.832289i	$-0.312970\pi$
$479$	24.2647	1.10868	0.554342	+	0.832289i	$0.312970\pi$
$480$	−1.61355	−0.0736480
$481$	−3.27467	−0.149312
$482$	3.81369	0.173709
$483$	−8.72028	−0.396787
$484$	24.0531	1.09332
$485$	−14.1942	−0.644527
$486$	−11.0590	−0.501648
$487$	−5.26989	−0.238802	−0.119401	−	0.992846i	$-0.538097\pi$
$487$	−5.26989	−0.238802	−0.119401	+	0.992846i	$0.538097\pi$
$488$	1.58290	0.0716544
$489$	40.9340	1.85110
$490$	−9.12585	−0.412264
$491$	16.2026	0.731214	0.365607	−	0.930769i	$-0.380861\pi$
$491$	16.2026	0.731214	0.365607	+	0.930769i	$0.380861\pi$
$492$	4.59903	0.207340
$493$	−18.4954	−0.832993
$494$	31.7852	1.43009
$495$	−5.25544	−0.236215
$496$	−0.0401676	−0.00180358
$497$	36.1218	1.62029
$498$	−1.94679	−0.0872379
$499$	−30.4465	−1.36297	−0.681486	−	0.731831i	$-0.738666\pi$
$499$	−30.4465	−1.36297	−0.681486	+	0.731831i	$0.738666\pi$
$500$	7.45008	0.333178
$501$	−39.8631	−1.78095
$502$	25.9341	1.15750
$503$	29.5804	1.31893	0.659463	−	0.751737i	$-0.270784\pi$
$503$	29.5804	1.31893	0.659463	+	0.751737i	$0.270784\pi$
$504$	−4.79728	−0.213688
$505$	14.8667	0.661560
$506$	5.92056	0.263201
$507$	4.71174	0.209256
$508$	3.68421	0.163461
$509$	28.7398	1.27387	0.636935	−	0.770918i	$-0.280202\pi$
$509$	28.7398	1.27387	0.636935	+	0.770918i	$0.280202\pi$
$510$	−6.01305	−0.266262
$511$	2.38643	0.105569
$512$	1.00000	0.0441942
$513$	31.0356	1.37026
$514$	−16.1954	−0.714350
$515$	8.77893	0.386846
$516$	−18.9143	−0.832655
$517$	2.67747	0.117755
$518$	−3.59577	−0.157989
$519$	−21.8724	−0.960092
$520$	3.11316	0.136521
$521$	−25.6433	−1.12345	−0.561727	−	0.827323i	$-0.689863\pi$
$521$	−25.6433	−1.12345	−0.561727	+	0.827323i	$0.689863\pi$
$522$	−5.53936	−0.242451
$523$	−7.02257	−0.307076	−0.153538	−	0.988143i	$-0.549067\pi$
$523$	−7.02257	−0.307076	−0.153538	+	0.988143i	$0.549067\pi$
$524$	−1.00000	−0.0436852
$525$	38.0856	1.66219
$526$	−15.4798	−0.674951
$527$	−0.149689	−0.00652054
$528$	12.0118	0.522745
$529$	1.00000	0.0434783
$530$	9.03128	0.392294
$531$	3.27016	0.141913
$532$	34.9019	1.51319
$533$	−8.87332	−0.384346
$534$	6.32672	0.273784
$535$	−5.24137	−0.226604
$536$	−4.00219	−0.172868
$537$	7.15312	0.308680
$538$	−20.9870	−0.904814
$539$	67.9358	2.92620
$540$	3.03974	0.130810
$541$	1.29832	0.0558193	0.0279097	−	0.999610i	$-0.491115\pi$
$541$	1.29832	0.0558193	0.0279097	+	0.999610i	$0.491115\pi$
$542$	−29.5766	−1.27042
$543$	−30.4468	−1.30660
$544$	3.72660	0.159777
$545$	14.5439	0.622991
$546$	34.1345	1.46082
$547$	37.9641	1.62323	0.811613	−	0.584195i	$-0.198590\pi$
$547$	37.9641	1.62323	0.811613	+	0.584195i	$0.198590\pi$
$548$	8.77190	0.374717
$549$	1.76669	0.0754006
$550$	−25.8579	−1.10259
$551$	40.3008	1.71687
$552$	2.02882	0.0863523
$553$	−64.4492	−2.74066
$554$	−9.12809	−0.387815
$555$	−1.34985	−0.0572980
$556$	9.33851	0.396041
$557$	14.8559	0.629463	0.314731	−	0.949181i	$-0.398086\pi$
$557$	14.8559	0.629463	0.314731	+	0.949181i	$0.398086\pi$
$558$	−0.0448316	−0.00189787
$559$	36.4930	1.54349
$560$	3.41842	0.144454
$561$	44.7631	1.88990
$562$	−17.9491	−0.757138
$563$	30.9306	1.30357	0.651785	−	0.758403i	$-0.274020\pi$
$563$	30.9306	1.30357	0.651785	+	0.758403i	$0.274020\pi$
$564$	0.917499	0.0386337
$565$	13.6874	0.575835
$566$	−6.67736	−0.280670
$567$	47.7214	2.00411
$568$	−8.40394	−0.352621
$569$	−31.4435	−1.31818	−0.659091	−	0.752063i	$-0.729059\pi$
$569$	−31.4435	−1.31818	−0.659091	+	0.752063i	$0.729059\pi$
$570$	13.1022	0.548790
$571$	23.7804	0.995181	0.497590	−	0.867412i	$-0.334218\pi$
$571$	23.7804	0.995181	0.497590	+	0.867412i	$0.334218\pi$
$572$	−23.1754	−0.969010
$573$	−31.6344	−1.32155
$574$	−9.74338	−0.406681
$575$	−4.36748	−0.182136
$576$	1.11611	0.0465047
$577$	30.7129	1.27860	0.639298	−	0.768959i	$-0.279225\pi$
$577$	30.7129	1.27860	0.639298	+	0.768959i	$0.279225\pi$
$578$	−3.11243	−0.129460
$579$	−40.1913	−1.67029
$580$	3.94720	0.163899
$581$	4.12442	0.171110
$582$	36.2091	1.50091
$583$	−67.2317	−2.78445
$584$	−0.555215	−0.0229750
$585$	3.47464	0.143659
$586$	11.2903	0.466399
$587$	−4.67541	−0.192975	−0.0964874	−	0.995334i	$-0.530761\pi$
$587$	−4.67541	−0.192975	−0.0964874	+	0.995334i	$0.530761\pi$
$588$	23.2798	0.960042
$589$	0.326165	0.0134394
$590$	−2.33023	−0.0959339
$591$	49.3721	2.03090
$592$	0.836574	0.0343830
$593$	−26.1758	−1.07491	−0.537455	−	0.843293i	$-0.680614\pi$
$593$	−26.1758	−1.07491	−0.537455	+	0.843293i	$0.680614\pi$
$594$	−22.6288	−0.928471
$595$	12.7391	0.522251
$596$	8.17112	0.334702
$597$	9.85532	0.403351
$598$	−3.91438	−0.160071
$599$	21.4588	0.876785	0.438392	−	0.898784i	$-0.355548\pi$
$599$	21.4588	0.876785	0.438392	+	0.898784i	$0.355548\pi$
$600$	−8.86083	−0.361742
$601$	5.01186	0.204438	0.102219	−	0.994762i	$-0.467406\pi$
$601$	5.01186	0.204438	0.102219	+	0.994762i	$0.467406\pi$
$602$	40.0713	1.63318
$603$	−4.46690	−0.181906
$604$	−13.4865	−0.548759
$605$	−19.1297	−0.777734
$606$	−37.9245	−1.54058
$607$	38.1255	1.54746	0.773732	−	0.633513i	$-0.218387\pi$
$607$	38.1255	1.54746	0.773732	+	0.633513i	$0.218387\pi$
$608$	−8.12011	−0.329314
$609$	43.2795	1.75377
$610$	−1.25890	−0.0509713
$611$	−1.77021	−0.0716152
$612$	4.15931	0.168130
$613$	31.9742	1.29143	0.645714	−	0.763580i	$-0.276560\pi$
$613$	31.9742	1.29143	0.645714	+	0.763580i	$0.276560\pi$
$614$	3.60905	0.145649
$615$	−3.65767	−0.147491
$616$	−25.4478	−1.02532
$617$	0.272662	0.0109770	0.00548848	−	0.999985i	$-0.498253\pi$
$617$	0.272662	0.0109770	0.00548848	+	0.999985i	$0.498253\pi$
$618$	−22.3948	−0.900851
$619$	12.6082	0.506766	0.253383	−	0.967366i	$-0.418457\pi$
$619$	12.6082	0.506766	0.253383	+	0.967366i	$0.418457\pi$
$620$	0.0319458	0.00128297
$621$	−3.82207	−0.153374
$622$	4.72334	0.189389
$623$	−13.4036	−0.537004
$624$	−7.94158	−0.317918
$625$	15.9122	0.636490
$626$	17.9138	0.715978
$627$	−97.5369	−3.89525
$628$	18.4496	0.736220
$629$	3.11758	0.124306
$630$	3.81534	0.152007
$631$	−2.22513	−0.0885809	−0.0442904	−	0.999019i	$-0.514103\pi$
$631$	−2.22513	−0.0885809	−0.0442904	+	0.999019i	$0.514103\pi$
$632$	14.9944	0.596447
$633$	−52.6156	−2.09128
$634$	33.9501	1.34833
$635$	−2.93010	−0.116278
$636$	−23.0385	−0.913537
$637$	−44.9158	−1.77963
$638$	−29.3842	−1.16333
$639$	−9.37975	−0.371057
$640$	−0.795313	−0.0314375
$641$	3.84445	0.151847	0.0759234	−	0.997114i	$-0.475810\pi$
$641$	3.84445	0.151847	0.0759234	+	0.997114i	$0.475810\pi$
$642$	13.3706	0.527695
$643$	−16.9938	−0.670171	−0.335086	−	0.942188i	$-0.608765\pi$
$643$	−16.9938	−0.670171	−0.335086	+	0.942188i	$0.608765\pi$
$644$	−4.29820	−0.169373
$645$	15.0428	0.592309
$646$	−30.2604	−1.19058
$647$	22.2600	0.875129	0.437565	−	0.899187i	$-0.355841\pi$
$647$	22.2600	0.875129	0.437565	+	0.899187i	$0.355841\pi$
$648$	−11.1026	−0.436153
$649$	17.3469	0.680927
$650$	17.0960	0.670560
$651$	0.350273	0.0137283
$652$	20.1763	0.790164
$653$	4.56812	0.178764	0.0893821	−	0.995997i	$-0.471511\pi$
$653$	4.56812	0.178764	0.0893821	+	0.995997i	$0.471511\pi$
$654$	−37.1010	−1.45076
$655$	0.795313	0.0310754
$656$	2.26685	0.0885056
$657$	−0.619683	−0.0241761
$658$	−1.94379	−0.0757768
$659$	21.4480	0.835496	0.417748	−	0.908563i	$-0.362820\pi$
$659$	21.4480	0.835496	0.417748	+	0.908563i	$0.362820\pi$
$660$	−9.55311	−0.371854
$661$	−12.3975	−0.482208	−0.241104	−	0.970499i	$-0.577509\pi$
$661$	−12.3975	−0.482208	−0.241104	+	0.970499i	$0.577509\pi$
$662$	−5.57755	−0.216778
$663$	−29.5951	−1.14938
$664$	−0.959569	−0.0372385
$665$	−27.7579	−1.07641
$666$	0.933712	0.0361806
$667$	−4.96308	−0.192171
$668$	−19.6484	−0.760219
$669$	20.7964	0.804037
$670$	3.18299	0.122970
$671$	9.37164	0.361788
$672$	−8.72028	−0.336392
$673$	16.2571	0.626667	0.313333	−	0.949643i	$-0.398554\pi$
$673$	16.2571	0.626667	0.313333	+	0.949643i	$0.398554\pi$
$674$	18.2558	0.703186
$675$	16.6928	0.642506
$676$	2.32240	0.0893232
$677$	46.8368	1.80008	0.900042	−	0.435804i	$-0.143536\pi$
$677$	46.8368	1.80008	0.900042	+	0.435804i	$0.143536\pi$
$678$	−34.9163	−1.34095
$679$	−76.7116	−2.94392
$680$	−2.96382	−0.113657
$681$	11.7757	0.451247
$682$	−0.237815	−0.00910640
$683$	−6.64796	−0.254377	−0.127189	−	0.991879i	$-0.540595\pi$
$683$	−6.64796	−0.254377	−0.127189	+	0.991879i	$0.540595\pi$
$684$	−9.06297	−0.346531
$685$	−6.97640	−0.266555
$686$	−19.2325	−0.734300
$687$	10.8968	0.415738
$688$	−9.32280	−0.355428
$689$	44.4503	1.69342
$690$	−1.61355	−0.0614267
$691$	25.7381	0.979123	0.489561	−	0.871969i	$-0.337157\pi$
$691$	25.7381	0.979123	0.489561	+	0.871969i	$0.337157\pi$
$692$	−10.7808	−0.409826
$693$	−28.4026	−1.07893
$694$	−23.1066	−0.877116
$695$	−7.42703	−0.281723
$696$	−10.0692	−0.381672
$697$	8.44765	0.319978
$698$	−21.4690	−0.812612
$699$	14.8501	0.561683
$700$	18.7723	0.709526
$701$	−34.0473	−1.28595	−0.642974	−	0.765888i	$-0.722300\pi$
$701$	−34.0473	−1.28595	−0.642974	+	0.765888i	$0.722300\pi$
$702$	14.9610	0.564668
$703$	−6.79308	−0.256206
$704$	5.92056	0.223140
$705$	−0.729699	−0.0274821
$706$	−8.68057	−0.326697
$707$	80.3459	3.02172
$708$	5.94434	0.223402
$709$	−43.5014	−1.63373	−0.816866	−	0.576828i	$-0.804290\pi$
$709$	−43.5014	−1.63373	−0.816866	+	0.576828i	$0.804290\pi$
$710$	6.68376	0.250837
$711$	16.7355	0.627630
$712$	3.11842	0.116868
$713$	−0.0401676	−0.00150429
$714$	−32.4970	−1.21617
$715$	18.4317	0.689305
$716$	3.52575	0.131764
$717$	−13.3290	−0.497782
$718$	6.08852	0.227221
$719$	1.06658	0.0397766	0.0198883	−	0.999802i	$-0.493669\pi$
$719$	1.06658	0.0397766	0.0198883	+	0.999802i	$0.493669\pi$
$720$	−0.887659	−0.0330811
$721$	47.4450	1.76694
$722$	46.9362	1.74679
$723$	7.73729	0.287753
$724$	−15.0071	−0.557736
$725$	21.6762	0.805032
$726$	48.7994	1.81111
$727$	−37.5680	−1.39332	−0.696660	−	0.717402i	$-0.745331\pi$
$727$	−37.5680	−1.39332	−0.696660	+	0.717402i	$0.745331\pi$
$728$	16.8248	0.623569
$729$	10.8711	0.402632
$730$	0.441569	0.0163432
$731$	−34.7424	−1.28499
$732$	3.21141	0.118697
$733$	−10.2037	−0.376881	−0.188441	−	0.982085i	$-0.560343\pi$
$733$	−10.2037	−0.376881	−0.188441	+	0.982085i	$0.560343\pi$
$734$	−13.4826	−0.497652
$735$	−18.5147	−0.682926
$736$	1.00000	0.0368605
$737$	−23.6952	−0.872825
$738$	2.53006	0.0931328
$739$	−14.1087	−0.518997	−0.259498	−	0.965744i	$-0.583557\pi$
$739$	−14.1087	−0.518997	−0.259498	+	0.965744i	$0.583557\pi$
$740$	−0.665338	−0.0244583
$741$	64.4866	2.36897
$742$	48.8088	1.79183
$743$	−12.7317	−0.467080	−0.233540	−	0.972347i	$-0.575031\pi$
$743$	−12.7317	−0.467080	−0.233540	+	0.972347i	$0.575031\pi$
$744$	−0.0814929	−0.00298767
$745$	−6.49860	−0.238090
$746$	25.6318	0.938448
$747$	−1.07099	−0.0391854
$748$	22.0636	0.806725
$749$	−28.3266	−1.03503
$750$	15.1149	0.551917
$751$	−9.69616	−0.353818	−0.176909	−	0.984227i	$-0.556610\pi$
$751$	−9.69616	−0.353818	−0.176909	+	0.984227i	$0.556610\pi$
$752$	0.452233	0.0164912
$753$	52.6157	1.91742
$754$	19.4274	0.707505
$755$	10.7260	0.390360
$756$	16.4280	0.597481
$757$	−3.59109	−0.130520	−0.0652601	−	0.997868i	$-0.520788\pi$
$757$	−3.59109	−0.130520	−0.0652601	+	0.997868i	$0.520788\pi$
$758$	11.7661	0.427365
$759$	12.0118	0.435999
$760$	6.45803	0.234257
$761$	−3.78562	−0.137228	−0.0686142	−	0.997643i	$-0.521858\pi$
$761$	−3.78562	−0.137228	−0.0686142	+	0.997643i	$0.521858\pi$
$762$	7.47461	0.270776
$763$	78.6012	2.84555
$764$	−15.5925	−0.564117
$765$	−3.30795	−0.119599
$766$	31.7616	1.14759
$767$	−11.4689	−0.414120
$768$	2.02882	0.0732088
$769$	10.2667	0.370227	0.185114	−	0.982717i	$-0.440735\pi$
$769$	10.2667	0.370227	0.185114	+	0.982717i	$0.440735\pi$
$770$	20.2389	0.729361
$771$	−32.8576	−1.18334
$772$	−19.8102	−0.712984
$773$	−16.2107	−0.583058	−0.291529	−	0.956562i	$-0.594164\pi$
$773$	−16.2107	−0.583058	−0.291529	+	0.956562i	$0.594164\pi$
$774$	−10.4053	−0.374011
$775$	0.175431	0.00630167
$776$	17.8474	0.640683
$777$	−7.29516	−0.261713
$778$	33.1424	1.18821
$779$	−18.4071	−0.659502
$780$	6.31604	0.226151
$781$	−49.7560	−1.78041
$782$	3.72660	0.133263
$783$	18.9692	0.677905
$784$	11.4745	0.409805
$785$	−14.6732	−0.523710
$786$	−2.02882	−0.0723656
$787$	−8.85482	−0.315640	−0.157820	−	0.987468i	$-0.550447\pi$
$787$	−8.85482	−0.315640	−0.157820	+	0.987468i	$0.550447\pi$
$788$	24.3354	0.866911
$789$	−31.4057	−1.11807
$790$	−11.9253	−0.424282
$791$	73.9726	2.63016
$792$	6.60802	0.234806
$793$	−6.19607	−0.220029
$794$	−7.46950	−0.265083
$795$	18.3228	0.649844
$796$	4.85766	0.172175
$797$	−3.51774	−0.124605	−0.0623023	−	0.998057i	$-0.519844\pi$
$797$	−3.51774	−0.124605	−0.0623023	+	0.998057i	$0.519844\pi$
$798$	70.8097	2.50664
$799$	1.68529	0.0596214
$800$	−4.36748	−0.154414
$801$	3.48051	0.122978
$802$	25.0074	0.883043
$803$	−3.28718	−0.116002
$804$	−8.11973	−0.286361
$805$	3.41842	0.120483
$806$	0.157231	0.00553824
$807$	−42.5788	−1.49885
$808$	−18.6929	−0.657614
$809$	−24.7004	−0.868420	−0.434210	−	0.900812i	$-0.642972\pi$
$809$	−24.7004	−0.868420	−0.434210	+	0.900812i	$0.642972\pi$
$810$	8.83007	0.310257
$811$	−3.57073	−0.125385	−0.0626926	−	0.998033i	$-0.519969\pi$
$811$	−3.57073	−0.125385	−0.0626926	+	0.998033i	$0.519969\pi$
$812$	21.3323	0.748618
$813$	−60.0057	−2.10449
$814$	4.95299	0.173602
$815$	−16.0464	−0.562082
$816$	7.56061	0.264674
$817$	75.7022	2.64848
$818$	6.17897	0.216042
$819$	18.7784	0.656171
$820$	−1.80285	−0.0629584
$821$	−35.9983	−1.25635	−0.628174	−	0.778073i	$-0.716197\pi$
$821$	−35.9983	−1.25635	−0.628174	+	0.778073i	$0.716197\pi$
$822$	17.7966	0.620728
$823$	−54.8683	−1.91259	−0.956294	−	0.292408i	$-0.905543\pi$
$823$	−54.8683	−1.91259	−0.956294	+	0.292408i	$0.905543\pi$
$824$	−11.0383	−0.384538
$825$	−52.4611	−1.82646
$826$	−12.5935	−0.438184
$827$	−4.23664	−0.147322	−0.0736612	−	0.997283i	$-0.523468\pi$
$827$	−4.23664	−0.147322	−0.0736612	+	0.997283i	$0.523468\pi$
$828$	1.11611	0.0387876
$829$	19.2748	0.669442	0.334721	−	0.942317i	$-0.391358\pi$
$829$	19.2748	0.669442	0.334721	+	0.942317i	$0.391358\pi$
$830$	0.763157	0.0264896
$831$	−18.5193	−0.642426
$832$	−3.91438	−0.135707
$833$	42.7611	1.48158
$834$	18.9462	0.656052
$835$	15.6266	0.540781
$836$	−48.0756	−1.66273
$837$	0.153523	0.00530654
$838$	−26.1013	−0.901655
$839$	−38.2821	−1.32164	−0.660822	−	0.750543i	$-0.729792\pi$
$839$	−38.2821	−1.32164	−0.660822	+	0.750543i	$0.729792\pi$
$840$	6.93535	0.239292
$841$	−4.36781	−0.150614
$842$	21.6188	0.745032
$843$	−36.4155	−1.25422
$844$	−25.9341	−0.892688
$845$	−1.84704	−0.0635400
$846$	0.504743	0.0173534
$847$	−103.385	−3.55235
$848$	−11.3556	−0.389954
$849$	−13.5472	−0.464938
$850$	−16.2759	−0.558257
$851$	0.836574	0.0286774
$852$	−17.0501	−0.584126
$853$	−46.9744	−1.60837	−0.804187	−	0.594377i	$-0.797399\pi$
$853$	−46.9744	−1.60837	−0.804187	+	0.594377i	$0.797399\pi$
$854$	−6.80361	−0.232815
$855$	7.20789	0.246505
$856$	6.59033	0.225253
$857$	7.75104	0.264770	0.132385	−	0.991198i	$-0.457736\pi$
$857$	7.75104	0.264770	0.132385	+	0.991198i	$0.457736\pi$
$858$	−47.0186	−1.60519
$859$	21.7747	0.742942	0.371471	−	0.928445i	$-0.378854\pi$
$859$	21.7747	0.742942	0.371471	+	0.928445i	$0.378854\pi$
$860$	7.41454	0.252834
$861$	−19.7676	−0.673677
$862$	−6.04308	−0.205828
$863$	−42.6048	−1.45028	−0.725142	−	0.688599i	$-0.758226\pi$
$863$	−42.6048	−1.45028	−0.725142	+	0.688599i	$0.758226\pi$
$864$	−3.82207	−0.130029
$865$	8.57414	0.291530
$866$	−18.1908	−0.618150
$867$	−6.31455	−0.214453
$868$	0.172648	0.00586007
$869$	88.7756	3.01150
$870$	8.00817	0.271502
$871$	15.6661	0.530826
$872$	−18.2870	−0.619276
$873$	19.9197	0.674179
$874$	−8.12011	−0.274667
$875$	−32.0219	−1.08254
$876$	−1.12643	−0.0380586
$877$	−50.5307	−1.70630	−0.853149	−	0.521667i	$-0.825311\pi$
$877$	−50.5307	−1.70630	−0.853149	+	0.521667i	$0.825311\pi$
$878$	2.79486	0.0943218
$879$	22.9060	0.772602
$880$	−4.70870	−0.158730
$881$	−12.3857	−0.417284	−0.208642	−	0.977992i	$-0.566904\pi$
$881$	−12.3857	−0.417284	−0.208642	+	0.977992i	$0.566904\pi$
$882$	12.8069	0.431231
$883$	−17.7850	−0.598512	−0.299256	−	0.954173i	$-0.596738\pi$
$883$	−17.7850	−0.598512	−0.299256	+	0.954173i	$0.596738\pi$
$884$	−14.5874	−0.490626
$885$	−4.72761	−0.158917
$886$	15.5737	0.523210
$887$	−26.2558	−0.881582	−0.440791	−	0.897610i	$-0.645302\pi$
$887$	−26.2558	−0.881582	−0.440791	+	0.897610i	$0.645302\pi$
$888$	1.69726	0.0569563
$889$	−15.8355	−0.531105
$890$	−2.48012	−0.0831339
$891$	−65.7338	−2.20217
$892$	10.2505	0.343212
$893$	−3.67218	−0.122885
$894$	16.5777	0.554443
$895$	−2.80408	−0.0937300
$896$	−4.29820	−0.143593
$897$	−7.94158	−0.265162
$898$	−26.9582	−0.899606
$899$	0.199355	0.00664887
$900$	−4.87460	−0.162487
$901$	−42.3179	−1.40981
$902$	13.4210	0.446871
$903$	81.2975	2.70541
$904$	−17.2101	−0.572400
$905$	11.9354	0.396745
$906$	−27.3618	−0.909034
$907$	0.380440	0.0126323	0.00631616	−	0.999980i	$-0.497989\pi$
$907$	0.380440	0.0126323	0.00631616	+	0.999980i	$0.497989\pi$
$908$	5.80423	0.192620
$909$	−20.8634	−0.691995
$910$	−13.3810	−0.443576
$911$	−26.8517	−0.889635	−0.444818	−	0.895621i	$-0.646732\pi$
$911$	−26.8517	−0.889635	−0.444818	+	0.895621i	$0.646732\pi$
$912$	−16.4743	−0.545517
$913$	−5.68119	−0.188020
$914$	4.78462	0.158261
$915$	−2.55408	−0.0844352
$916$	5.37100	0.177463
$917$	4.29820	0.141939
$918$	−14.2433	−0.470100
$919$	−51.3777	−1.69479	−0.847397	−	0.530960i	$-0.821831\pi$
$919$	−51.3777	−1.69479	−0.847397	+	0.530960i	$0.821831\pi$
$920$	−0.795313	−0.0262207
$921$	7.32211	0.241272
$922$	−14.7545	−0.485915
$923$	32.8962	1.08279
$924$	−51.6290	−1.69847
$925$	−3.65372	−0.120134
$926$	14.0921	0.463096
$927$	−12.3200	−0.404643
$928$	−4.96308	−0.162921
$929$	15.1054	0.495591	0.247795	−	0.968812i	$-0.420294\pi$
$929$	15.1054	0.495591	0.247795	+	0.968812i	$0.420294\pi$
$930$	0.0648123	0.00212528
$931$	−93.1746	−3.05367
$932$	7.31958	0.239761
$933$	9.58281	0.313727
$934$	2.83911	0.0928987
$935$	−17.5475	−0.573863
$936$	−4.36890	−0.142802
$937$	−24.1531	−0.789046	−0.394523	−	0.918886i	$-0.629090\pi$
$937$	−24.1531	−0.789046	−0.394523	+	0.918886i	$0.629090\pi$
$938$	17.2022	0.561673
$939$	36.3438	1.18604
$940$	−0.359667	−0.0117310
$941$	4.90434	0.159877	0.0799385	−	0.996800i	$-0.474528\pi$
$941$	4.90434	0.159877	0.0799385	+	0.996800i	$0.474528\pi$
$942$	37.4310	1.21957
$943$	2.26685	0.0738188
$944$	2.92995	0.0953617
$945$	−13.0654	−0.425018
$946$	−55.1962	−1.79458
$947$	−23.3201	−0.757802	−0.378901	−	0.925437i	$-0.623698\pi$
$947$	−23.3201	−0.757802	−0.378901	+	0.925437i	$0.623698\pi$
$948$	30.4210	0.988029
$949$	2.17332	0.0705491
$950$	35.4644	1.15062
$951$	68.8787	2.23354
$952$	−16.0177	−0.519137
$953$	5.94695	0.192641	0.0963203	−	0.995350i	$-0.469293\pi$
$953$	5.94695	0.192641	0.0963203	+	0.995350i	$0.469293\pi$
$954$	−12.6742	−0.410341
$955$	12.4009	0.401284
$956$	−6.56984	−0.212484
$957$	−59.6154	−1.92709
$958$	24.2647	0.783958
$959$	−37.7034	−1.21751
$960$	−1.61355	−0.0520770
$961$	−30.9984	−0.999948
$962$	−3.27467	−0.105580
$963$	7.35555	0.237029
$964$	3.81369	0.122831
$965$	15.7553	0.507181
$966$	−8.72028	−0.280570
$967$	25.4776	0.819306	0.409653	−	0.912241i	$-0.365650\pi$
$967$	25.4776	0.819306	0.409653	+	0.912241i	$0.365650\pi$
$968$	24.0531	0.773095
$969$	−61.3930	−1.97223
$970$	−14.1942	−0.455749
$971$	25.9708	0.833441	0.416721	−	0.909035i	$-0.363179\pi$
$971$	25.9708	0.833441	0.416721	+	0.909035i	$0.363179\pi$
$972$	−11.0590	−0.354719
$973$	−40.1388	−1.28679
$974$	−5.26989	−0.168858
$975$	34.6847	1.11080
$976$	1.58290	0.0506673
$977$	−48.1151	−1.53934	−0.769670	−	0.638442i	$-0.779579\pi$
$977$	−48.1151	−1.53934	−0.769670	+	0.638442i	$0.779579\pi$
$978$	40.9340	1.30893
$979$	18.4628	0.590074
$980$	−9.12585	−0.291515
$981$	−20.4104	−0.651653
$982$	16.2026	0.517046
$983$	−44.7786	−1.42822	−0.714108	−	0.700035i	$-0.753168\pi$
$983$	−44.7786	−1.42822	−0.714108	+	0.700035i	$0.753168\pi$
$984$	4.59903	0.146612
$985$	−19.3542	−0.616677
$986$	−18.4954	−0.589015
$987$	−3.94360	−0.125526
$988$	31.7852	1.01122
$989$	−9.32280	−0.296448
$990$	−5.25544	−0.167029
$991$	13.8569	0.440180	0.220090	−	0.975480i	$-0.429365\pi$
$991$	13.8569	0.440180	0.220090	+	0.975480i	$0.429365\pi$
$992$	−0.0401676	−0.00127532
$993$	−11.3159	−0.359098
$994$	36.1218	1.14571
$995$	−3.86336	−0.122477
$996$	−1.94679	−0.0616865
$997$	36.7627	1.16429	0.582144	−	0.813086i	$-0.302214\pi$
$997$	36.7627	1.16429	0.582144	+	0.813086i	$0.302214\pi$
$998$	−30.4465	−0.963767
$999$	−3.19744	−0.101163

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.f.1.19	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.f.1.19	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.02882 q^{3} +1.00000 q^{4} -0.795313 q^{5} +2.02882 q^{6} -4.29820 q^{7} +1.00000 q^{8} +1.11611 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.02882 q^{3} +1.00000 q^{4} -0.795313 q^{5} +2.02882 q^{6} -4.29820 q^{7} +1.00000 q^{8} +1.11611 q^{9} -0.795313 q^{10} +5.92056 q^{11} +2.02882 q^{12} -3.91438 q^{13} -4.29820 q^{14} -1.61355 q^{15} +1.00000 q^{16} +3.72660 q^{17} +1.11611 q^{18} -8.12011 q^{19} -0.795313 q^{20} -8.72028 q^{21} +5.92056 q^{22} +1.00000 q^{23} +2.02882 q^{24} -4.36748 q^{25} -3.91438 q^{26} -3.82207 q^{27} -4.29820 q^{28} -4.96308 q^{29} -1.61355 q^{30} -0.0401676 q^{31} +1.00000 q^{32} +12.0118 q^{33} +3.72660 q^{34} +3.41842 q^{35} +1.11611 q^{36} +0.836574 q^{37} -8.12011 q^{38} -7.94158 q^{39} -0.795313 q^{40} +2.26685 q^{41} -8.72028 q^{42} -9.32280 q^{43} +5.92056 q^{44} -0.887659 q^{45} +1.00000 q^{46} +0.452233 q^{47} +2.02882 q^{48} +11.4745 q^{49} -4.36748 q^{50} +7.56061 q^{51} -3.91438 q^{52} -11.3556 q^{53} -3.82207 q^{54} -4.70870 q^{55} -4.29820 q^{56} -16.4743 q^{57} -4.96308 q^{58} +2.92995 q^{59} -1.61355 q^{60} +1.58290 q^{61} -0.0401676 q^{62} -4.79728 q^{63} +1.00000 q^{64} +3.11316 q^{65} +12.0118 q^{66} -4.00219 q^{67} +3.72660 q^{68} +2.02882 q^{69} +3.41842 q^{70} -8.40394 q^{71} +1.11611 q^{72} -0.555215 q^{73} +0.836574 q^{74} -8.86083 q^{75} -8.12011 q^{76} -25.4478 q^{77} -7.94158 q^{78} +14.9944 q^{79} -0.795313 q^{80} -11.1026 q^{81} +2.26685 q^{82} -0.959569 q^{83} -8.72028 q^{84} -2.96382 q^{85} -9.32280 q^{86} -10.0692 q^{87} +5.92056 q^{88} +3.11842 q^{89} -0.887659 q^{90} +16.8248 q^{91} +1.00000 q^{92} -0.0814929 q^{93} +0.452233 q^{94} +6.45803 q^{95} +2.02882 q^{96} +17.8474 q^{97} +11.4745 q^{98} +6.60802 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{2} - 5 q^{3} + 20 q^{4} - 6 q^{5} - 5 q^{6} - 12 q^{7} + 20 q^{8} - q^{9}+O(q^{10}) \) 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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