LMFDB - Embedded newform 5054.2.a.bb.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5054, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("5054.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5054 = 2 \cdot 7 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5054.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$40.3563931816$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.1528713.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 3x^{4} + 7x^{3} + 3x^{2} - 3x - 1 $ x^6 - 3x^5 - 3x^4 + 7x^3 + 3x^2 - 3*x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 266)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-0.725554$ of defining polynomial
Character	$\chi$	$=$	5054.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.11161 q^{3} +1.00000 q^{4} -3.59028 q^{5} -2.11161 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.45891 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.11161 q^{3} +1.00000 q^{4} -3.59028 q^{5} -2.11161 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.45891 q^{9} +3.59028 q^{10} +3.24298 q^{11} +2.11161 q^{12} +0.613941 q^{13} +1.00000 q^{14} -7.58127 q^{15} +1.00000 q^{16} -4.69713 q^{17} -1.45891 q^{18} -3.59028 q^{20} -2.11161 q^{21} -3.24298 q^{22} +4.53089 q^{23} -2.11161 q^{24} +7.89009 q^{25} -0.613941 q^{26} -3.25419 q^{27} -1.00000 q^{28} +4.45024 q^{29} +7.58127 q^{30} -6.48937 q^{31} -1.00000 q^{32} +6.84792 q^{33} +4.69713 q^{34} +3.59028 q^{35} +1.45891 q^{36} +5.34592 q^{37} +1.29641 q^{39} +3.59028 q^{40} -1.08664 q^{41} +2.11161 q^{42} +5.44103 q^{43} +3.24298 q^{44} -5.23789 q^{45} -4.53089 q^{46} +11.6016 q^{47} +2.11161 q^{48} +1.00000 q^{49} -7.89009 q^{50} -9.91851 q^{51} +0.613941 q^{52} -6.12638 q^{53} +3.25419 q^{54} -11.6432 q^{55} +1.00000 q^{56} -4.45024 q^{58} -2.89177 q^{59} -7.58127 q^{60} -13.2269 q^{61} +6.48937 q^{62} -1.45891 q^{63} +1.00000 q^{64} -2.20422 q^{65} -6.84792 q^{66} -6.41158 q^{67} -4.69713 q^{68} +9.56748 q^{69} -3.59028 q^{70} +11.5793 q^{71} -1.45891 q^{72} -16.3204 q^{73} -5.34592 q^{74} +16.6608 q^{75} -3.24298 q^{77} -1.29641 q^{78} -6.43324 q^{79} -3.59028 q^{80} -11.2483 q^{81} +1.08664 q^{82} -8.52076 q^{83} -2.11161 q^{84} +16.8640 q^{85} -5.44103 q^{86} +9.39718 q^{87} -3.24298 q^{88} +1.49287 q^{89} +5.23789 q^{90} -0.613941 q^{91} +4.53089 q^{92} -13.7030 q^{93} -11.6016 q^{94} -2.11161 q^{96} +1.67786 q^{97} -1.00000 q^{98} +4.73121 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 3 q^{3} + 6 q^{4} - 3 q^{5} - 3 q^{6} - 6 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 + 3 * q^3 + 6 * q^4 - 3 * q^5 - 3 * q^6 - 6 * q^7 - 6 * q^8 - 3 * q^9	$ 6 q - 6 q^{2} + 3 q^{3} + 6 q^{4} - 3 q^{5} - 3 q^{6} - 6 q^{7} - 6 q^{8} - 3 q^{9} + 3 q^{10} + 3 q^{11} + 3 q^{12} + 6 q^{13} + 6 q^{14} - 6 q^{15} + 6 q^{16} - 9 q^{17} + 3 q^{18} - 3 q^{20} - 3 q^{21} - 3 q^{22} - 3 q^{24} + 3 q^{25} - 6 q^{26} + 3 q^{27} - 6 q^{28} + 6 q^{29} + 6 q^{30} + 3 q^{31} - 6 q^{32} + 6 q^{33} + 9 q^{34} + 3 q^{35} - 3 q^{36} - 3 q^{37} - 9 q^{39} + 3 q^{40} + 9 q^{41} + 3 q^{42} - 6 q^{43} + 3 q^{44} - 12 q^{45} + 9 q^{47} + 3 q^{48} + 6 q^{49} - 3 q^{50} - 27 q^{51} + 6 q^{52} + 6 q^{53} - 3 q^{54} - 24 q^{55} + 6 q^{56} - 6 q^{58} + 15 q^{59} - 6 q^{60} - 30 q^{61} - 3 q^{62} + 3 q^{63} + 6 q^{64} + 3 q^{65} - 6 q^{66} + 15 q^{67} - 9 q^{68} + 24 q^{69} - 3 q^{70} + 21 q^{71} + 3 q^{72} - 33 q^{73} + 3 q^{74} + 33 q^{75} - 3 q^{77} + 9 q^{78} - 30 q^{79} - 3 q^{80} - 18 q^{81} - 9 q^{82} - 33 q^{83} - 3 q^{84} - 18 q^{85} + 6 q^{86} + 15 q^{87} - 3 q^{88} - 12 q^{89} + 12 q^{90} - 6 q^{91} - 21 q^{93} - 9 q^{94} - 3 q^{96} - 18 q^{97} - 6 q^{98}+O(q^{100}) $ 6 * q - 6 * q^2 + 3 * q^3 + 6 * q^4 - 3 * q^5 - 3 * q^6 - 6 * q^7 - 6 * q^8 - 3 * q^9 + 3 * q^10 + 3 * q^11 + 3 * q^12 + 6 * q^13 + 6 * q^14 - 6 * q^15 + 6 * q^16 - 9 * q^17 + 3 * q^18 - 3 * q^20 - 3 * q^21 - 3 * q^22 - 3 * q^24 + 3 * q^25 - 6 * q^26 + 3 * q^27 - 6 * q^28 + 6 * q^29 + 6 * q^30 + 3 * q^31 - 6 * q^32 + 6 * q^33 + 9 * q^34 + 3 * q^35 - 3 * q^36 - 3 * q^37 - 9 * q^39 + 3 * q^40 + 9 * q^41 + 3 * q^42 - 6 * q^43 + 3 * q^44 - 12 * q^45 + 9 * q^47 + 3 * q^48 + 6 * q^49 - 3 * q^50 - 27 * q^51 + 6 * q^52 + 6 * q^53 - 3 * q^54 - 24 * q^55 + 6 * q^56 - 6 * q^58 + 15 * q^59 - 6 * q^60 - 30 * q^61 - 3 * q^62 + 3 * q^63 + 6 * q^64 + 3 * q^65 - 6 * q^66 + 15 * q^67 - 9 * q^68 + 24 * q^69 - 3 * q^70 + 21 * q^71 + 3 * q^72 - 33 * q^73 + 3 * q^74 + 33 * q^75 - 3 * q^77 + 9 * q^78 - 30 * q^79 - 3 * q^80 - 18 * q^81 - 9 * q^82 - 33 * q^83 - 3 * q^84 - 18 * q^85 + 6 * q^86 + 15 * q^87 - 3 * q^88 - 12 * q^89 + 12 * q^90 - 6 * q^91 - 21 * q^93 - 9 * q^94 - 3 * q^96 - 18 * q^97 - 6 * q^98

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
$3$	2.11161	1.21914	0.609570	−	0.792732i	$-0.291342\pi$
$3$	2.11161	1.21914	0.609570	+	0.792732i	$0.291342\pi$
$4$	1.00000	0.500000
$5$	−3.59028	−1.60562	−0.802810	−	0.596235i	$-0.796663\pi$
$5$	−3.59028	−1.60562	−0.802810	+	0.596235i	$0.796663\pi$
$6$	−2.11161	−0.862062
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	1.45891	0.486303
$10$	3.59028	1.13535
$11$	3.24298	0.977795	0.488898	−	0.872341i	$-0.337399\pi$
$11$	3.24298	0.977795	0.488898	+	0.872341i	$0.337399\pi$
$12$	2.11161	0.609570
$13$	0.613941	0.170277	0.0851383	−	0.996369i	$-0.472867\pi$
$13$	0.613941	0.170277	0.0851383	+	0.996369i	$0.472867\pi$
$14$	1.00000	0.267261
$15$	−7.58127	−1.95748
$16$	1.00000	0.250000
$17$	−4.69713	−1.13922	−0.569610	−	0.821915i	$-0.692906\pi$
$17$	−4.69713	−1.13922	−0.569610	+	0.821915i	$0.692906\pi$
$18$	−1.45891	−0.343868
$19$	0	0
$19$	0	0
$20$	−3.59028	−0.802810
$21$	−2.11161	−0.460792
$22$	−3.24298	−0.691406
$23$	4.53089	0.944756	0.472378	−	0.881396i	$-0.343396\pi$
$23$	4.53089	0.944756	0.472378	+	0.881396i	$0.343396\pi$
$24$	−2.11161	−0.431031
$25$	7.89009	1.57802
$26$	−0.613941	−0.120404
$27$	−3.25419	−0.626269
$28$	−1.00000	−0.188982
$29$	4.45024	0.826388	0.413194	−	0.910643i	$-0.364413\pi$
$29$	4.45024	0.826388	0.413194	+	0.910643i	$0.364413\pi$
$30$	7.58127	1.38415
$31$	−6.48937	−1.16552	−0.582762	−	0.812643i	$-0.698028\pi$
$31$	−6.48937	−1.16552	−0.582762	+	0.812643i	$0.698028\pi$
$32$	−1.00000	−0.176777
$33$	6.84792	1.19207
$34$	4.69713	0.805551
$35$	3.59028	0.606868
$36$	1.45891	0.243152
$37$	5.34592	0.878864	0.439432	−	0.898276i	$-0.355180\pi$
$37$	5.34592	0.878864	0.439432	+	0.898276i	$0.355180\pi$
$38$	0	0
$39$	1.29641	0.207591
$40$	3.59028	0.567673
$41$	−1.08664	−0.169705	−0.0848525	−	0.996394i	$-0.527042\pi$
$41$	−1.08664	−0.169705	−0.0848525	+	0.996394i	$0.527042\pi$
$42$	2.11161	0.325829
$43$	5.44103	0.829750	0.414875	−	0.909878i	$-0.363825\pi$
$43$	5.44103	0.829750	0.414875	+	0.909878i	$0.363825\pi$
$44$	3.24298	0.488898
$45$	−5.23789	−0.780818
$46$	−4.53089	−0.668043
$47$	11.6016	1.69227	0.846133	−	0.532971i	$-0.178925\pi$
$47$	11.6016	1.69227	0.846133	+	0.532971i	$0.178925\pi$
$48$	2.11161	0.304785
$49$	1.00000	0.142857
$50$	−7.89009	−1.11583
$51$	−9.91851	−1.38887
$52$	0.613941	0.0851383
$53$	−6.12638	−0.841523	−0.420762	−	0.907171i	$-0.638237\pi$
$53$	−6.12638	−0.841523	−0.420762	+	0.907171i	$0.638237\pi$
$54$	3.25419	0.442839
$55$	−11.6432	−1.56997
$56$	1.00000	0.133631
$57$	0	0
$58$	−4.45024	−0.584345
$59$	−2.89177	−0.376477	−0.188238	−	0.982123i	$-0.560278\pi$
$59$	−2.89177	−0.376477	−0.188238	+	0.982123i	$0.560278\pi$
$60$	−7.58127	−0.978738
$61$	−13.2269	−1.69353	−0.846764	−	0.531969i	$-0.821452\pi$
$61$	−13.2269	−1.69353	−0.846764	+	0.531969i	$0.821452\pi$
$62$	6.48937	0.824150
$63$	−1.45891	−0.183805
$64$	1.00000	0.125000
$65$	−2.20422	−0.273400
$66$	−6.84792	−0.842921
$67$	−6.41158	−0.783299	−0.391650	−	0.920114i	$-0.628095\pi$
$67$	−6.41158	−0.783299	−0.391650	+	0.920114i	$0.628095\pi$
$68$	−4.69713	−0.569610
$69$	9.56748	1.15179
$70$	−3.59028	−0.429120
$71$	11.5793	1.37421	0.687103	−	0.726560i	$-0.258882\pi$
$71$	11.5793	1.37421	0.687103	+	0.726560i	$0.258882\pi$
$72$	−1.45891	−0.171934
$73$	−16.3204	−1.91015	−0.955077	−	0.296357i	$-0.904228\pi$
$73$	−16.3204	−1.91015	−0.955077	+	0.296357i	$0.904228\pi$
$74$	−5.34592	−0.621451
$75$	16.6608	1.92382
$76$	0	0
$77$	−3.24298	−0.369572
$78$	−1.29641	−0.146789
$79$	−6.43324	−0.723796	−0.361898	−	0.932218i	$-0.617871\pi$
$79$	−6.43324	−0.723796	−0.361898	+	0.932218i	$0.617871\pi$
$80$	−3.59028	−0.401405
$81$	−11.2483	−1.24981
$82$	1.08664	0.120000
$83$	−8.52076	−0.935274	−0.467637	−	0.883921i	$-0.654895\pi$
$83$	−8.52076	−0.935274	−0.467637	+	0.883921i	$0.654895\pi$
$84$	−2.11161	−0.230396
$85$	16.8640	1.82916
$86$	−5.44103	−0.586722
$87$	9.39718	1.00748
$88$	−3.24298	−0.345703
$89$	1.49287	0.158244	0.0791221	−	0.996865i	$-0.474788\pi$
$89$	1.49287	0.158244	0.0791221	+	0.996865i	$0.474788\pi$
$90$	5.23789	0.552122
$91$	−0.613941	−0.0643585
$92$	4.53089	0.472378
$93$	−13.7030	−1.42094
$94$	−11.6016	−1.19661
$95$	0	0
$96$	−2.11161	−0.215516
$97$	1.67786	0.170361	0.0851804	−	0.996366i	$-0.472853\pi$
$97$	1.67786	0.170361	0.0851804	+	0.996366i	$0.472853\pi$
$98$	−1.00000	−0.101015
$99$	4.73121	0.475505
$100$	7.89009	0.789009
$101$	1.86854	0.185927	0.0929636	−	0.995670i	$-0.470366\pi$
$101$	1.86854	0.185927	0.0929636	+	0.995670i	$0.470366\pi$
$102$	9.91851	0.982079
$103$	−20.1263	−1.98310	−0.991550	−	0.129727i	$-0.958590\pi$
$103$	−20.1263	−1.98310	−0.991550	+	0.129727i	$0.958590\pi$
$104$	−0.613941	−0.0602019
$105$	7.58127	0.739857
$106$	6.12638	0.595047
$107$	9.37414	0.906233	0.453116	−	0.891451i	$-0.350312\pi$
$107$	9.37414	0.906233	0.453116	+	0.891451i	$0.350312\pi$
$108$	−3.25419	−0.313134
$109$	−9.28080	−0.888940	−0.444470	−	0.895794i	$-0.646608\pi$
$109$	−9.28080	−0.888940	−0.444470	+	0.895794i	$0.646608\pi$
$110$	11.6432	1.11014
$111$	11.2885	1.07146
$112$	−1.00000	−0.0944911
$113$	−8.67289	−0.815877	−0.407938	−	0.913009i	$-0.633752\pi$
$113$	−8.67289	−0.815877	−0.407938	+	0.913009i	$0.633752\pi$
$114$	0	0
$115$	−16.2671	−1.51692
$116$	4.45024	0.413194
$117$	0.895684	0.0828060
$118$	2.89177	0.266209
$119$	4.69713	0.430585
$120$	7.58127	0.692073
$121$	−0.483078	−0.0439162
$122$	13.2269	1.19750
$123$	−2.29457	−0.206894
$124$	−6.48937	−0.582762
$125$	−10.3762	−0.928077
$126$	1.45891	0.129970
$127$	18.2693	1.62113	0.810567	−	0.585645i	$-0.199159\pi$
$127$	18.2693	1.62113	0.810567	+	0.585645i	$0.199159\pi$
$128$	−1.00000	−0.0883883
$129$	11.4894	1.01158
$130$	2.20422	0.193323
$131$	−8.09149	−0.706957	−0.353478	−	0.935443i	$-0.615001\pi$
$131$	−8.09149	−0.706957	−0.353478	+	0.935443i	$0.615001\pi$
$132$	6.84792	0.596035
$133$	0	0
$134$	6.41158	0.553876
$135$	11.6834	1.00555
$136$	4.69713	0.402775
$137$	4.55482	0.389145	0.194572	−	0.980888i	$-0.437668\pi$
$137$	4.55482	0.389145	0.194572	+	0.980888i	$0.437668\pi$
$138$	−9.56748	−0.814438
$139$	−21.6945	−1.84010	−0.920051	−	0.391799i	$-0.871853\pi$
$139$	−21.6945	−1.84010	−0.920051	+	0.391799i	$0.871853\pi$
$140$	3.59028	0.303434
$141$	24.4981	2.06311
$142$	−11.5793	−0.971710
$143$	1.99100	0.166496
$144$	1.45891	0.121576
$145$	−15.9776	−1.32687
$146$	16.3204	1.35068
$147$	2.11161	0.174163
$148$	5.34592	0.439432
$149$	21.4072	1.75375	0.876874	−	0.480721i	$-0.159625\pi$
$149$	21.4072	1.75375	0.876874	+	0.480721i	$0.159625\pi$
$150$	−16.6608	−1.36035
$151$	5.52022	0.449229	0.224615	−	0.974448i	$-0.427888\pi$
$151$	5.52022	0.449229	0.224615	+	0.974448i	$0.427888\pi$
$152$	0	0
$153$	−6.85268	−0.554007
$154$	3.24298	0.261327
$155$	23.2986	1.87139
$156$	1.29641	0.103796
$157$	−13.5838	−1.08410	−0.542052	−	0.840345i	$-0.682352\pi$
$157$	−13.5838	−1.08410	−0.542052	+	0.840345i	$0.682352\pi$
$158$	6.43324	0.511801
$159$	−12.9365	−1.02594
$160$	3.59028	0.283836
$161$	−4.53089	−0.357084
$162$	11.2483	0.883751
$163$	−6.32223	−0.495195	−0.247598	−	0.968863i	$-0.579641\pi$
$163$	−6.32223	−0.495195	−0.247598	+	0.968863i	$0.579641\pi$
$164$	−1.08664	−0.0848525
$165$	−24.5859	−1.91401
$166$	8.52076	0.661339
$167$	−14.1989	−1.09875	−0.549373	−	0.835577i	$-0.685133\pi$
$167$	−14.1989	−1.09875	−0.549373	+	0.835577i	$0.685133\pi$
$168$	2.11161	0.162914
$169$	−12.6231	−0.971006
$170$	−16.8640	−1.29341
$171$	0	0
$172$	5.44103	0.414875
$173$	7.38609	0.561554	0.280777	−	0.959773i	$-0.409408\pi$
$173$	7.38609	0.561554	0.280777	+	0.959773i	$0.409408\pi$
$174$	−9.39718	−0.712398
$175$	−7.89009	−0.596435
$176$	3.24298	0.244449
$177$	−6.10631	−0.458978
$178$	−1.49287	−0.111895
$179$	−6.37886	−0.476778	−0.238389	−	0.971170i	$-0.576619\pi$
$179$	−6.37886	−0.476778	−0.238389	+	0.971170i	$0.576619\pi$
$180$	−5.23789	−0.390409
$181$	22.2731	1.65555	0.827774	−	0.561062i	$-0.189607\pi$
$181$	22.2731	1.65555	0.827774	+	0.561062i	$0.189607\pi$
$182$	0.613941	0.0455083
$183$	−27.9300	−2.06465
$184$	−4.53089	−0.334022
$185$	−19.1933	−1.41112
$186$	13.7030	1.00475
$187$	−15.2327	−1.11392
$188$	11.6016	0.846133
$189$	3.25419	0.236707
$190$	0	0
$191$	−23.4129	−1.69410	−0.847048	−	0.531516i	$-0.821623\pi$
$191$	−23.4129	−1.69410	−0.847048	+	0.531516i	$0.821623\pi$
$192$	2.11161	0.152393
$193$	−15.1577	−1.09107	−0.545537	−	0.838087i	$-0.683674\pi$
$193$	−15.1577	−1.09107	−0.545537	+	0.838087i	$0.683674\pi$
$194$	−1.67786	−0.120463
$195$	−4.65445	−0.333312
$196$	1.00000	0.0714286
$197$	−14.5729	−1.03828	−0.519138	−	0.854691i	$-0.673747\pi$
$197$	−14.5729	−1.03828	−0.519138	+	0.854691i	$0.673747\pi$
$198$	−4.73121	−0.336233
$199$	7.05899	0.500398	0.250199	−	0.968194i	$-0.419504\pi$
$199$	7.05899	0.500398	0.250199	+	0.968194i	$0.419504\pi$
$200$	−7.89009	−0.557913
$201$	−13.5388	−0.954952
$202$	−1.86854	−0.131470
$203$	−4.45024	−0.312345
$204$	−9.91851	−0.694435
$205$	3.90134	0.272482
$206$	20.1263	1.40226
$207$	6.61016	0.459438
$208$	0.613941	0.0425691
$209$	0	0
$210$	−7.58127	−0.523158
$211$	−5.69557	−0.392099	−0.196050	−	0.980594i	$-0.562811\pi$
$211$	−5.69557	−0.392099	−0.196050	+	0.980594i	$0.562811\pi$
$212$	−6.12638	−0.420762
$213$	24.4509	1.67535
$214$	−9.37414	−0.640803
$215$	−19.5348	−1.33226
$216$	3.25419	0.221419
$217$	6.48937	0.440527
$218$	9.28080	0.628575
$219$	−34.4623	−2.32875
$220$	−11.6432	−0.784984
$221$	−2.88376	−0.193983
$222$	−11.2885	−0.757636
$223$	18.5836	1.24445	0.622226	−	0.782838i	$-0.286228\pi$
$223$	18.5836	1.24445	0.622226	+	0.782838i	$0.286228\pi$
$224$	1.00000	0.0668153
$225$	11.5109	0.767395
$226$	8.67289	0.576912
$227$	0.527433	0.0350070	0.0175035	−	0.999847i	$-0.494428\pi$
$227$	0.527433	0.0350070	0.0175035	+	0.999847i	$0.494428\pi$
$228$	0	0
$229$	−11.9310	−0.788426	−0.394213	−	0.919019i	$-0.628983\pi$
$229$	−11.9310	−0.788426	−0.394213	+	0.919019i	$0.628983\pi$
$230$	16.2671	1.07262
$231$	−6.84792	−0.450560
$232$	−4.45024	−0.292172
$233$	−6.00187	−0.393195	−0.196598	−	0.980484i	$-0.562989\pi$
$233$	−6.00187	−0.393195	−0.196598	+	0.980484i	$0.562989\pi$
$234$	−0.895684	−0.0585527
$235$	−41.6529	−2.71714
$236$	−2.89177	−0.188238
$237$	−13.5845	−0.882409
$238$	−4.69713	−0.304470
$239$	−22.2435	−1.43882	−0.719408	−	0.694588i	$-0.755587\pi$
$239$	−22.2435	−1.43882	−0.719408	+	0.694588i	$0.755587\pi$
$240$	−7.58127	−0.489369
$241$	19.8067	1.27586	0.637932	−	0.770093i	$-0.279790\pi$
$241$	19.8067	1.27586	0.637932	+	0.770093i	$0.279790\pi$
$242$	0.483078	0.0310534
$243$	−13.9895	−0.897428
$244$	−13.2269	−0.846764
$245$	−3.59028	−0.229374
$246$	2.29457	0.146296
$247$	0	0
$248$	6.48937	0.412075
$249$	−17.9925	−1.14023
$250$	10.3762	0.656249
$251$	6.27968	0.396370	0.198185	−	0.980165i	$-0.436495\pi$
$251$	6.27968	0.396370	0.198185	+	0.980165i	$0.436495\pi$
$252$	−1.45891	−0.0919026
$253$	14.6936	0.923778
$254$	−18.2693	−1.14632
$255$	35.6102	2.23000
$256$	1.00000	0.0625000
$257$	−11.4959	−0.717096	−0.358548	−	0.933511i	$-0.616728\pi$
$257$	−11.4959	−0.717096	−0.358548	+	0.933511i	$0.616728\pi$
$258$	−11.4894	−0.715296
$259$	−5.34592	−0.332179
$260$	−2.20422	−0.136700
$261$	6.49249	0.401875
$262$	8.09149	0.499894
$263$	4.04284	0.249292	0.124646	−	0.992201i	$-0.460220\pi$
$263$	4.04284	0.249292	0.124646	+	0.992201i	$0.460220\pi$
$264$	−6.84792	−0.421460
$265$	21.9954	1.35117
$266$	0	0
$267$	3.15237	0.192922
$268$	−6.41158	−0.391650
$269$	−15.2503	−0.929826	−0.464913	−	0.885356i	$-0.653914\pi$
$269$	−15.2503	−0.929826	−0.464913	+	0.885356i	$0.653914\pi$
$270$	−11.6834	−0.711031
$271$	−17.9249	−1.08886	−0.544429	−	0.838807i	$-0.683254\pi$
$271$	−17.9249	−1.08886	−0.544429	+	0.838807i	$0.683254\pi$
$272$	−4.69713	−0.284805
$273$	−1.29641	−0.0784620
$274$	−4.55482	−0.275167
$275$	25.5874	1.54298
$276$	9.56748	0.575895
$277$	−3.58168	−0.215202	−0.107601	−	0.994194i	$-0.534317\pi$
$277$	−3.58168	−0.215202	−0.107601	+	0.994194i	$0.534317\pi$
$278$	21.6945	1.30115
$279$	−9.46740	−0.566798
$280$	−3.59028	−0.214560
$281$	−7.09159	−0.423049	−0.211524	−	0.977373i	$-0.567843\pi$
$281$	−7.09159	−0.423049	−0.211524	+	0.977373i	$0.567843\pi$
$282$	−24.4981	−1.45884
$283$	−14.0809	−0.837021	−0.418511	−	0.908212i	$-0.637448\pi$
$283$	−14.0809	−0.837021	−0.418511	+	0.908212i	$0.637448\pi$
$284$	11.5793	0.687103
$285$	0	0
$286$	−1.99100	−0.117730
$287$	1.08664	0.0641424
$288$	−1.45891	−0.0859671
$289$	5.06300	0.297824
$290$	15.9776	0.938236
$291$	3.54299	0.207694
$292$	−16.3204	−0.955077
$293$	22.8960	1.33760	0.668798	−	0.743444i	$-0.266809\pi$
$293$	22.8960	1.33760	0.668798	+	0.743444i	$0.266809\pi$
$294$	−2.11161	−0.123152
$295$	10.3823	0.604479
$296$	−5.34592	−0.310725
$297$	−10.5533	−0.612363
$298$	−21.4072	−1.24009
$299$	2.78170	0.160870
$300$	16.6608	0.961912
$301$	−5.44103	−0.313616
$302$	−5.52022	−0.317653
$303$	3.94564	0.226671
$304$	0	0
$305$	47.4881	2.71916
$306$	6.85268	0.391742
$307$	−32.8057	−1.87232	−0.936161	−	0.351572i	$-0.885647\pi$
$307$	−32.8057	−1.87232	−0.936161	+	0.351572i	$0.885647\pi$
$308$	−3.24298	−0.184786
$309$	−42.4989	−2.41768
$310$	−23.2986	−1.32327
$311$	13.6967	0.776671	0.388336	−	0.921518i	$-0.373050\pi$
$311$	13.6967	0.776671	0.388336	+	0.921518i	$0.373050\pi$
$312$	−1.29641	−0.0733945
$313$	7.88847	0.445883	0.222941	−	0.974832i	$-0.428434\pi$
$313$	7.88847	0.445883	0.222941	+	0.974832i	$0.428434\pi$
$314$	13.5838	0.766577
$315$	5.23789	0.295122
$316$	−6.43324	−0.361898
$317$	28.0164	1.57356	0.786780	−	0.617234i	$-0.211747\pi$
$317$	28.0164	1.57356	0.786780	+	0.617234i	$0.211747\pi$
$318$	12.9365	0.725446
$319$	14.4320	0.808039
$320$	−3.59028	−0.200703
$321$	19.7946	1.10482
$322$	4.53089	0.252497
$323$	0	0
$324$	−11.2483	−0.624906
$325$	4.84405	0.268699
$326$	6.32223	0.350156
$327$	−19.5975	−1.08374
$328$	1.08664	0.0599998
$329$	−11.6016	−0.639617
$330$	24.5859	1.35341
$331$	−13.6501	−0.750278	−0.375139	−	0.926969i	$-0.622405\pi$
$331$	−13.6501	−0.750278	−0.375139	+	0.926969i	$0.622405\pi$
$332$	−8.52076	−0.467637
$333$	7.79921	0.427394
$334$	14.1989	0.776931
$335$	23.0194	1.25768
$336$	−2.11161	−0.115198
$337$	−17.2621	−0.940324	−0.470162	−	0.882580i	$-0.655805\pi$
$337$	−17.2621	−0.940324	−0.470162	+	0.882580i	$0.655805\pi$
$338$	12.6231	0.686605
$339$	−18.3138	−0.994668
$340$	16.8640	0.914578
$341$	−21.0449	−1.13964
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	−5.44103	−0.293361
$345$	−34.3499	−1.84934
$346$	−7.38609	−0.397078
$347$	−2.69423	−0.144634	−0.0723170	−	0.997382i	$-0.523039\pi$
$347$	−2.69423	−0.144634	−0.0723170	+	0.997382i	$0.523039\pi$
$348$	9.39718	0.503742
$349$	−5.06542	−0.271145	−0.135573	−	0.990767i	$-0.543287\pi$
$349$	−5.06542	−0.271145	−0.135573	+	0.990767i	$0.543287\pi$
$350$	7.89009	0.421743
$351$	−1.99788	−0.106639
$352$	−3.24298	−0.172851
$353$	−21.7080	−1.15540	−0.577701	−	0.816249i	$-0.696050\pi$
$353$	−21.7080	−1.15540	−0.577701	+	0.816249i	$0.696050\pi$
$354$	6.10631	0.324547
$355$	−41.5728	−2.20645
$356$	1.49287	0.0791221
$357$	9.91851	0.524943
$358$	6.37886	0.337133
$359$	5.02083	0.264989	0.132495	−	0.991184i	$-0.457701\pi$
$359$	5.02083	0.264989	0.132495	+	0.991184i	$0.457701\pi$
$360$	5.23789	0.276061
$361$	0	0
$362$	−22.2731	−1.17065
$363$	−1.02007	−0.0535400
$364$	−0.613941	−0.0321792
$365$	58.5946	3.06698
$366$	27.9300	1.45993
$367$	−7.51570	−0.392316	−0.196158	−	0.980572i	$-0.562847\pi$
$367$	−7.51570	−0.392316	−0.196158	+	0.980572i	$0.562847\pi$
$368$	4.53089	0.236189
$369$	−1.58531	−0.0825280
$370$	19.1933	0.997814
$371$	6.12638	0.318066
$372$	−13.7030	−0.710469
$373$	14.0820	0.729137	0.364569	−	0.931177i	$-0.381216\pi$
$373$	14.0820	0.729137	0.364569	+	0.931177i	$0.381216\pi$
$374$	15.2327	0.787664
$375$	−21.9105	−1.13146
$376$	−11.6016	−0.598307
$377$	2.73218	0.140715
$378$	−3.25419	−0.167377
$379$	6.46372	0.332019	0.166010	−	0.986124i	$-0.446912\pi$
$379$	6.46372	0.332019	0.166010	+	0.986124i	$0.446912\pi$
$380$	0	0
$381$	38.5776	1.97639
$382$	23.4129	1.19791
$383$	−18.5181	−0.946229	−0.473115	−	0.881001i	$-0.656870\pi$
$383$	−18.5181	−0.946229	−0.473115	+	0.881001i	$0.656870\pi$
$384$	−2.11161	−0.107758
$385$	11.6432	0.593392
$386$	15.1577	0.771506
$387$	7.93797	0.403510
$388$	1.67786	0.0851804
$389$	−37.2070	−1.88647	−0.943234	−	0.332128i	$-0.892233\pi$
$389$	−37.2070	−1.88647	−0.943234	+	0.332128i	$0.892233\pi$
$390$	4.65445	0.235687
$391$	−21.2822	−1.07629
$392$	−1.00000	−0.0505076
$393$	−17.0861	−0.861880
$394$	14.5729	0.734172
$395$	23.0971	1.16214
$396$	4.73121	0.237752
$397$	34.3856	1.72576	0.862881	−	0.505407i	$-0.168658\pi$
$397$	34.3856	1.72576	0.862881	+	0.505407i	$0.168658\pi$
$398$	−7.05899	−0.353835
$399$	0	0
$400$	7.89009	0.394504
$401$	24.7614	1.23653	0.618263	−	0.785971i	$-0.287837\pi$
$401$	24.7614	1.23653	0.618263	+	0.785971i	$0.287837\pi$
$402$	13.5388	0.675253
$403$	−3.98409	−0.198462
$404$	1.86854	0.0929636
$405$	40.3846	2.00672
$406$	4.45024	0.220862
$407$	17.3367	0.859349
$408$	9.91851	0.491040
$409$	8.46451	0.418543	0.209271	−	0.977858i	$-0.432891\pi$
$409$	8.46451	0.418543	0.209271	+	0.977858i	$0.432891\pi$
$410$	−3.90134	−0.192674
$411$	9.61802	0.474422
$412$	−20.1263	−0.991550
$413$	2.89177	0.142295
$414$	−6.61016	−0.324871
$415$	30.5919	1.50170
$416$	−0.613941	−0.0301009
$417$	−45.8103	−2.24334
$418$	0	0
$419$	−10.9702	−0.535929	−0.267964	−	0.963429i	$-0.586351\pi$
$419$	−10.9702	−0.535929	−0.267964	+	0.963429i	$0.586351\pi$
$420$	7.58127	0.369928
$421$	32.1234	1.56560	0.782800	−	0.622273i	$-0.213791\pi$
$421$	32.1234	1.56560	0.782800	+	0.622273i	$0.213791\pi$
$422$	5.69557	0.277256
$423$	16.9257	0.822955
$424$	6.12638	0.297523
$425$	−37.0607	−1.79771
$426$	−24.4509	−1.18465
$427$	13.2269	0.640093
$428$	9.37414	0.453116
$429$	4.20422	0.202982
$430$	19.5348	0.942052
$431$	−7.26547	−0.349966	−0.174983	−	0.984571i	$-0.555987\pi$
$431$	−7.26547	−0.349966	−0.174983	+	0.984571i	$0.555987\pi$
$432$	−3.25419	−0.156567
$433$	18.2307	0.876111	0.438056	−	0.898948i	$-0.355667\pi$
$433$	18.2307	0.876111	0.438056	+	0.898948i	$0.355667\pi$
$434$	−6.48937	−0.311500
$435$	−33.7385	−1.61764
$436$	−9.28080	−0.444470
$437$	0	0
$438$	34.4623	1.64667
$439$	−32.5406	−1.55308	−0.776539	−	0.630069i	$-0.783027\pi$
$439$	−32.5406	−1.55308	−0.776539	+	0.630069i	$0.783027\pi$
$440$	11.6432	0.555068
$441$	1.45891	0.0694719
$442$	2.88376	0.137166
$443$	−0.0189181	−0.000898825 0	−0.000449412	−	1.00000i	$-0.500143\pi$
$443$	−0.0189181	−0.000898825 0	−0.000449412		1.00000i	$0.500143\pi$
$444$	11.2885	0.535729
$445$	−5.35982	−0.254080
$446$	−18.5836	−0.879961
$447$	45.2037	2.13806
$448$	−1.00000	−0.0472456
$449$	4.85684	0.229209	0.114604	−	0.993411i	$-0.463440\pi$
$449$	4.85684	0.229209	0.114604	+	0.993411i	$0.463440\pi$
$450$	−11.5109	−0.542630
$451$	−3.52396	−0.165937
$452$	−8.67289	−0.407938
$453$	11.6566	0.547673
$454$	−0.527433	−0.0247537
$455$	2.20422	0.103335
$456$	0	0
$457$	30.2842	1.41663	0.708317	−	0.705895i	$-0.249455\pi$
$457$	30.2842	1.41663	0.708317	+	0.705895i	$0.249455\pi$
$458$	11.9310	0.557501
$459$	15.2853	0.713458
$460$	−16.2671	−0.758460
$461$	20.6428	0.961432	0.480716	−	0.876876i	$-0.340377\pi$
$461$	20.6428	0.961432	0.480716	+	0.876876i	$0.340377\pi$
$462$	6.84792	0.318594
$463$	21.7134	1.00911	0.504554	−	0.863380i	$-0.331657\pi$
$463$	21.7134	1.00911	0.504554	+	0.863380i	$0.331657\pi$
$464$	4.45024	0.206597
$465$	49.1977	2.28149
$466$	6.00187	0.278031
$467$	18.9511	0.876952	0.438476	−	0.898743i	$-0.355518\pi$
$467$	18.9511	0.876952	0.438476	+	0.898743i	$0.355518\pi$
$468$	0.895684	0.0414030
$469$	6.41158	0.296059
$470$	41.6529	1.92131
$471$	−28.6837	−1.32167
$472$	2.89177	0.133105
$473$	17.6452	0.811325
$474$	13.5845	0.623958
$475$	0	0
$476$	4.69713	0.215292
$477$	−8.93784	−0.409235
$478$	22.2435	1.01740
$479$	20.3473	0.929690	0.464845	−	0.885392i	$-0.346110\pi$
$479$	20.3473	0.929690	0.464845	+	0.885392i	$0.346110\pi$
$480$	7.58127	0.346036
$481$	3.28208	0.149650
$482$	−19.8067	−0.902171
$483$	−9.56748	−0.435336
$484$	−0.483078	−0.0219581
$485$	−6.02398	−0.273535
$486$	13.9895	0.634577
$487$	0.582139	0.0263793	0.0131896	−	0.999913i	$-0.495801\pi$
$487$	0.582139	0.0263793	0.0131896	+	0.999913i	$0.495801\pi$
$488$	13.2269	0.598752
$489$	−13.3501	−0.603713
$490$	3.59028	0.162192
$491$	−33.5615	−1.51461	−0.757304	−	0.653063i	$-0.773484\pi$
$491$	−33.5615	−1.51461	−0.757304	+	0.653063i	$0.773484\pi$
$492$	−2.29457	−0.103447
$493$	−20.9033	−0.941439
$494$	0	0
$495$	−16.9864	−0.763481
$496$	−6.48937	−0.291381
$497$	−11.5793	−0.519401
$498$	17.9925	0.806265
$499$	−7.71505	−0.345373	−0.172687	−	0.984977i	$-0.555245\pi$
$499$	−7.71505	−0.345373	−0.172687	+	0.984977i	$0.555245\pi$
$500$	−10.3762	−0.464038
$501$	−29.9826	−1.33953
$502$	−6.27968	−0.280276
$503$	17.1560	0.764949	0.382475	−	0.923966i	$-0.375072\pi$
$503$	17.1560	0.764949	0.382475	+	0.923966i	$0.375072\pi$
$504$	1.45891	0.0649850
$505$	−6.70859	−0.298528
$506$	−14.6936	−0.653209
$507$	−26.6551	−1.18379
$508$	18.2693	0.810567
$509$	−25.9509	−1.15025	−0.575126	−	0.818065i	$-0.695047\pi$
$509$	−25.9509	−1.15025	−0.575126	+	0.818065i	$0.695047\pi$
$510$	−35.6102	−1.57685
$511$	16.3204	0.721971
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	11.4959	0.507064
$515$	72.2588	3.18411
$516$	11.4894	0.505791
$517$	37.6238	1.65469
$518$	5.34592	0.234886
$519$	15.5966	0.684613
$520$	2.20422	0.0966613
$521$	−19.9715	−0.874969	−0.437485	−	0.899226i	$-0.644131\pi$
$521$	−19.9715	−0.874969	−0.437485	+	0.899226i	$0.644131\pi$
$522$	−6.49249	−0.284169
$523$	8.44182	0.369135	0.184568	−	0.982820i	$-0.440912\pi$
$523$	8.44182	0.369135	0.184568	+	0.982820i	$0.440912\pi$
$524$	−8.09149	−0.353478
$525$	−16.6608	−0.727137
$526$	−4.04284	−0.176276
$527$	30.4814	1.32779
$528$	6.84792	0.298017
$529$	−2.47105	−0.107437
$530$	−21.9954	−0.955419
$531$	−4.21884	−0.183082
$532$	0	0
$533$	−0.667134	−0.0288968
$534$	−3.15237	−0.136416
$535$	−33.6558	−1.45507
$536$	6.41158	0.276938
$537$	−13.4697	−0.581260
$538$	15.2503	0.657486
$539$	3.24298	0.139685
$540$	11.6834	0.502775
$541$	−39.3246	−1.69070	−0.845349	−	0.534214i	$-0.820608\pi$
$541$	−39.3246	−1.69070	−0.845349	+	0.534214i	$0.820608\pi$
$542$	17.9249	0.769939
$543$	47.0322	2.01834
$544$	4.69713	0.201388
$545$	33.3206	1.42730
$546$	1.29641	0.0554810
$547$	−20.7275	−0.886245	−0.443122	−	0.896461i	$-0.646129\pi$
$547$	−20.7275	−0.886245	−0.443122	+	0.896461i	$0.646129\pi$
$548$	4.55482	0.194572
$549$	−19.2968	−0.823568
$550$	−25.5874	−1.09105
$551$	0	0
$552$	−9.56748	−0.407219
$553$	6.43324	0.273569
$554$	3.58168	0.152171
$555$	−40.5289	−1.72036
$556$	−21.6945	−0.920051
$557$	−30.6400	−1.29826	−0.649130	−	0.760677i	$-0.724867\pi$
$557$	−30.6400	−1.29826	−0.649130	+	0.760677i	$0.724867\pi$
$558$	9.46740	0.400787
$559$	3.34047	0.141287
$560$	3.59028	0.151717
$561$	−32.1655	−1.35803
$562$	7.09159	0.299141
$563$	−19.3305	−0.814682	−0.407341	−	0.913276i	$-0.633544\pi$
$563$	−19.3305	−0.814682	−0.407341	+	0.913276i	$0.633544\pi$
$564$	24.4981	1.03156
$565$	31.1381	1.30999
$566$	14.0809	0.591863
$567$	11.2483	0.472385
$568$	−11.5793	−0.485855
$569$	−18.0853	−0.758174	−0.379087	−	0.925361i	$-0.623762\pi$
$569$	−18.0853	−0.758174	−0.379087	+	0.925361i	$0.623762\pi$
$570$	0	0
$571$	1.49157	0.0624203	0.0312102	−	0.999513i	$-0.490064\pi$
$571$	1.49157	0.0624203	0.0312102	+	0.999513i	$0.490064\pi$
$572$	1.99100	0.0832478
$573$	−49.4390	−2.06534
$574$	−1.08664	−0.0453555
$575$	35.7491	1.49084
$576$	1.45891	0.0607879
$577$	26.2740	1.09380	0.546900	−	0.837198i	$-0.315808\pi$
$577$	26.2740	1.09380	0.546900	+	0.837198i	$0.315808\pi$
$578$	−5.06300	−0.210593
$579$	−32.0072	−1.33017
$580$	−15.9776	−0.663433
$581$	8.52076	0.353500
$582$	−3.54299	−0.146862
$583$	−19.8677	−0.822838
$584$	16.3204	0.675342
$585$	−3.21575	−0.132955
$586$	−22.8960	−0.945823
$587$	14.2560	0.588408	0.294204	−	0.955743i	$-0.404946\pi$
$587$	14.2560	0.588408	0.294204	+	0.955743i	$0.404946\pi$
$588$	2.11161	0.0870815
$589$	0	0
$590$	−10.3823	−0.427431
$591$	−30.7723	−1.26580
$592$	5.34592	0.219716
$593$	26.0203	1.06852	0.534262	−	0.845319i	$-0.320589\pi$
$593$	26.0203	1.06852	0.534262	+	0.845319i	$0.320589\pi$
$594$	10.5533	0.433006
$595$	−16.8640	−0.691356
$596$	21.4072	0.876874
$597$	14.9058	0.610056
$598$	−2.78170	−0.113752
$599$	−26.0530	−1.06450	−0.532248	−	0.846589i	$-0.678653\pi$
$599$	−26.0530	−1.06450	−0.532248	+	0.846589i	$0.678653\pi$
$600$	−16.6608	−0.680175
$601$	26.5798	1.08421	0.542106	−	0.840310i	$-0.317627\pi$
$601$	26.5798	1.08421	0.542106	+	0.840310i	$0.317627\pi$
$602$	5.44103	0.221760
$603$	−9.35392	−0.380921
$604$	5.52022	0.224615
$605$	1.73438	0.0705127
$606$	−3.94564	−0.160281
$607$	10.3567	0.420367	0.210184	−	0.977662i	$-0.432594\pi$
$607$	10.3567	0.420367	0.210184	+	0.977662i	$0.432594\pi$
$608$	0	0
$609$	−9.39718	−0.380793
$610$	−47.4881	−1.92274
$611$	7.12270	0.288153
$612$	−6.85268	−0.277003
$613$	−13.1694	−0.531908	−0.265954	−	0.963986i	$-0.585687\pi$
$613$	−13.1694	−0.531908	−0.265954	+	0.963986i	$0.585687\pi$
$614$	32.8057	1.32393
$615$	8.23813	0.332193
$616$	3.24298	0.130663
$617$	6.28250	0.252924	0.126462	−	0.991971i	$-0.459638\pi$
$617$	6.28250	0.252924	0.126462	+	0.991971i	$0.459638\pi$
$618$	42.4989	1.70956
$619$	−6.86393	−0.275885	−0.137942	−	0.990440i	$-0.544049\pi$
$619$	−6.86393	−0.275885	−0.137942	+	0.990440i	$0.544049\pi$
$620$	23.2986	0.935695
$621$	−14.7444	−0.591671
$622$	−13.6967	−0.549190
$623$	−1.49287	−0.0598107
$624$	1.29641	0.0518978
$625$	−2.19696	−0.0878784
$626$	−7.88847	−0.315287
$627$	0	0
$628$	−13.5838	−0.542052
$629$	−25.1105	−1.00122
$630$	−5.23789	−0.208682
$631$	−34.6486	−1.37934	−0.689669	−	0.724125i	$-0.742244\pi$
$631$	−34.6486	−1.37934	−0.689669	+	0.724125i	$0.742244\pi$
$632$	6.43324	0.255901
$633$	−12.0268	−0.478024
$634$	−28.0164	−1.11267
$635$	−65.5917	−2.60293
$636$	−12.9365	−0.512968
$637$	0.613941	0.0243252
$638$	−14.4320	−0.571370
$639$	16.8931	0.668280
$640$	3.59028	0.141918
$641$	−2.33296	−0.0921463	−0.0460732	−	0.998938i	$-0.514671\pi$
$641$	−2.33296	−0.0921463	−0.0460732	+	0.998938i	$0.514671\pi$
$642$	−19.7946	−0.781229
$643$	−42.1217	−1.66112	−0.830559	−	0.556931i	$-0.811979\pi$
$643$	−42.1217	−1.66112	−0.830559	+	0.556931i	$0.811979\pi$
$644$	−4.53089	−0.178542
$645$	−41.2500	−1.62422
$646$	0	0
$647$	18.7499	0.737133	0.368566	−	0.929601i	$-0.379849\pi$
$647$	18.7499	0.737133	0.368566	+	0.929601i	$0.379849\pi$
$648$	11.2483	0.441875
$649$	−9.37797	−0.368117
$650$	−4.84405	−0.189999
$651$	13.7030	0.537064
$652$	−6.32223	−0.247598
$653$	12.8937	0.504569	0.252285	−	0.967653i	$-0.418818\pi$
$653$	12.8937	0.504569	0.252285	+	0.967653i	$0.418818\pi$
$654$	19.5975	0.766321
$655$	29.0507	1.13510
$656$	−1.08664	−0.0424262
$657$	−23.8099	−0.928914
$658$	11.6016	0.452277
$659$	18.6966	0.728318	0.364159	−	0.931337i	$-0.381357\pi$
$659$	18.6966	0.728318	0.364159	+	0.931337i	$0.381357\pi$
$660$	−24.5859	−0.957006
$661$	34.7384	1.35117	0.675584	−	0.737283i	$-0.263892\pi$
$661$	34.7384	1.35117	0.675584	+	0.737283i	$0.263892\pi$
$662$	13.6501	0.530526
$663$	−6.08938	−0.236492
$664$	8.52076	0.330669
$665$	0	0
$666$	−7.79921	−0.302213
$667$	20.1635	0.780735
$668$	−14.1989	−0.549373
$669$	39.2414	1.51716
$670$	−23.0194	−0.889315
$671$	−42.8945	−1.65592
$672$	2.11161	0.0814572
$673$	−32.2228	−1.24210	−0.621049	−	0.783771i	$-0.713293\pi$
$673$	−32.2228	−1.24210	−0.621049	+	0.783771i	$0.713293\pi$
$674$	17.2621	0.664910
$675$	−25.6758	−0.988263
$676$	−12.6231	−0.485503
$677$	−25.6438	−0.985570	−0.492785	−	0.870151i	$-0.664021\pi$
$677$	−25.6438	−0.985570	−0.492785	+	0.870151i	$0.664021\pi$
$678$	18.3138	0.703337
$679$	−1.67786	−0.0643903
$680$	−16.8640	−0.646704
$681$	1.11373	0.0426784
$682$	21.0449	0.805850
$683$	−3.96087	−0.151558	−0.0757792	−	0.997125i	$-0.524144\pi$
$683$	−3.96087	−0.151558	−0.0757792	+	0.997125i	$0.524144\pi$
$684$	0	0
$685$	−16.3531	−0.624819
$686$	1.00000	0.0381802
$687$	−25.1938	−0.961202
$688$	5.44103	0.207437
$689$	−3.76124	−0.143292
$690$	34.3499	1.30768
$691$	16.9238	0.643811	0.321905	−	0.946772i	$-0.395677\pi$
$691$	16.9238	0.643811	0.321905	+	0.946772i	$0.395677\pi$
$692$	7.38609	0.280777
$693$	−4.73121	−0.179724
$694$	2.69423	0.102272
$695$	77.8892	2.95450
$696$	−9.39718	−0.356199
$697$	5.10409	0.193331
$698$	5.06542	0.191729
$699$	−12.6736	−0.479360
$700$	−7.89009	−0.298217
$701$	16.8434	0.636166	0.318083	−	0.948063i	$-0.396961\pi$
$701$	16.8434	0.636166	0.318083	+	0.948063i	$0.396961\pi$
$702$	1.99788	0.0754051
$703$	0	0
$704$	3.24298	0.122224
$705$	−87.9549	−3.31257
$706$	21.7080	0.816992
$707$	−1.86854	−0.0702739
$708$	−6.10631	−0.229489
$709$	−28.7267	−1.07885	−0.539426	−	0.842033i	$-0.681359\pi$
$709$	−28.7267	−1.07885	−0.539426	+	0.842033i	$0.681359\pi$
$710$	41.5728	1.56020
$711$	−9.38552	−0.351984
$712$	−1.49287	−0.0559477
$713$	−29.4026	−1.10114
$714$	−9.91851	−0.371191
$715$	−7.14823	−0.267329
$716$	−6.37886	−0.238389
$717$	−46.9698	−1.75412
$718$	−5.02083	−0.187376
$719$	−32.2712	−1.20351	−0.601757	−	0.798679i	$-0.705532\pi$
$719$	−32.2712	−1.20351	−0.601757	+	0.798679i	$0.705532\pi$
$720$	−5.23789	−0.195205
$721$	20.1263	0.749541
$722$	0	0
$723$	41.8241	1.55546
$724$	22.2731	0.827774
$725$	35.1128	1.30406
$726$	1.02007	0.0378585
$727$	6.48738	0.240604	0.120302	−	0.992737i	$-0.461614\pi$
$727$	6.48738	0.240604	0.120302	+	0.992737i	$0.461614\pi$
$728$	0.613941	0.0227542
$729$	4.20448	0.155722
$730$	−58.5946	−2.16868
$731$	−25.5572	−0.945268
$732$	−27.9300	−1.03232
$733$	−15.0737	−0.556758	−0.278379	−	0.960471i	$-0.589797\pi$
$733$	−15.0737	−0.556758	−0.278379	+	0.960471i	$0.589797\pi$
$734$	7.51570	0.277410
$735$	−7.58127	−0.279640
$736$	−4.53089	−0.167011
$737$	−20.7926	−0.765906
$738$	1.58531	0.0583561
$739$	−21.8502	−0.803772	−0.401886	−	0.915690i	$-0.631645\pi$
$739$	−21.8502	−0.803772	−0.401886	+	0.915690i	$0.631645\pi$
$740$	−19.1933	−0.705561
$741$	0	0
$742$	−6.12638	−0.224907
$743$	41.7004	1.52984	0.764919	−	0.644127i	$-0.222779\pi$
$743$	41.7004	1.52984	0.764919	+	0.644127i	$0.222779\pi$
$744$	13.7030	0.502377
$745$	−76.8578	−2.81585
$746$	−14.0820	−0.515578
$747$	−12.4310	−0.454827
$748$	−15.2327	−0.556962
$749$	−9.37414	−0.342524
$750$	21.9105	0.800060
$751$	−36.4048	−1.32843	−0.664215	−	0.747542i	$-0.731234\pi$
$751$	−36.4048	−1.32843	−0.664215	+	0.747542i	$0.731234\pi$
$752$	11.6016	0.423067
$753$	13.2603	0.483230
$754$	−2.73218	−0.0995002
$755$	−19.8191	−0.721292
$756$	3.25419	0.118354
$757$	4.98234	0.181086	0.0905431	−	0.995893i	$-0.471140\pi$
$757$	4.98234	0.181086	0.0905431	+	0.995893i	$0.471140\pi$
$758$	−6.46372	−0.234773
$759$	31.0272	1.12621
$760$	0	0
$761$	16.1769	0.586412	0.293206	−	0.956049i	$-0.405278\pi$
$761$	16.1769	0.586412	0.293206	+	0.956049i	$0.405278\pi$
$762$	−38.5776	−1.39752
$763$	9.28080	0.335988
$764$	−23.4129	−0.847048
$765$	24.6030	0.889524
$766$	18.5181	0.669085
$767$	−1.77538	−0.0641052
$768$	2.11161	0.0761963
$769$	29.6375	1.06876	0.534378	−	0.845246i	$-0.320546\pi$
$769$	29.6375	1.06876	0.534378	+	0.845246i	$0.320546\pi$
$770$	−11.6432	−0.419592
$771$	−24.2749	−0.874241
$772$	−15.1577	−0.545537
$773$	35.2879	1.26922	0.634608	−	0.772834i	$-0.281161\pi$
$773$	35.2879	1.26922	0.634608	+	0.772834i	$0.281161\pi$
$774$	−7.93797	−0.285325
$775$	−51.2017	−1.83922
$776$	−1.67786	−0.0602316
$777$	−11.2885	−0.404973
$778$	37.2070	1.33393
$779$	0	0
$780$	−4.65445	−0.166656
$781$	37.5513	1.34369
$782$	21.2822	0.761048
$783$	−14.4819	−0.517541
$784$	1.00000	0.0357143
$785$	48.7695	1.74066
$786$	17.0861	0.609441
$787$	48.1868	1.71767	0.858836	−	0.512250i	$-0.171188\pi$
$787$	48.1868	1.71767	0.858836	+	0.512250i	$0.171188\pi$
$788$	−14.5729	−0.519138
$789$	8.53691	0.303922
$790$	−23.0971	−0.821759
$791$	8.67289	0.308372
$792$	−4.73121	−0.168116
$793$	−8.12052	−0.288368
$794$	−34.3856	−1.22030
$795$	46.4458	1.64726
$796$	7.05899	0.250199
$797$	10.0767	0.356934	0.178467	−	0.983946i	$-0.442886\pi$
$797$	10.0767	0.356934	0.178467	+	0.983946i	$0.442886\pi$
$798$	0	0
$799$	−54.4942	−1.92787
$800$	−7.89009	−0.278957
$801$	2.17797	0.0769546
$802$	−24.7614	−0.874356
$803$	−52.9266	−1.86774
$804$	−13.5388	−0.477476
$805$	16.2671	0.573342
$806$	3.98409	0.140333
$807$	−32.2027	−1.13359
$808$	−1.86854	−0.0657352
$809$	37.6152	1.32248	0.661240	−	0.750174i	$-0.270030\pi$
$809$	37.6152	1.32248	0.661240	+	0.750174i	$0.270030\pi$
$810$	−40.3846	−1.41897
$811$	−1.02897	−0.0361321	−0.0180661	−	0.999837i	$-0.505751\pi$
$811$	−1.02897	−0.0361321	−0.0180661	+	0.999837i	$0.505751\pi$
$812$	−4.45024	−0.156173
$813$	−37.8504	−1.32747
$814$	−17.3367	−0.607652
$815$	22.6986	0.795096
$816$	−9.91851	−0.347217
$817$	0	0
$818$	−8.46451	−0.295954
$819$	−0.895684	−0.0312977
$820$	3.90134	0.136241
$821$	−29.6164	−1.03362	−0.516809	−	0.856101i	$-0.672880\pi$
$821$	−29.6164	−1.03362	−0.516809	+	0.856101i	$0.672880\pi$
$822$	−9.61802	−0.335467
$823$	−29.6541	−1.03368	−0.516839	−	0.856083i	$-0.672891\pi$
$823$	−29.6541	−1.03368	−0.516839	+	0.856083i	$0.672891\pi$
$824$	20.1263	0.701132
$825$	54.0307	1.88111
$826$	−2.89177	−0.100618
$827$	5.98622	0.208161	0.104081	−	0.994569i	$-0.466810\pi$
$827$	5.98622	0.208161	0.104081	+	0.994569i	$0.466810\pi$
$828$	6.61016	0.229719
$829$	3.97321	0.137995	0.0689976	−	0.997617i	$-0.478020\pi$
$829$	3.97321	0.137995	0.0689976	+	0.997617i	$0.478020\pi$
$830$	−30.5919	−1.06186
$831$	−7.56312	−0.262362
$832$	0.613941	0.0212846
$833$	−4.69713	−0.162746
$834$	45.8103	1.58628
$835$	50.9781	1.76417
$836$	0	0
$837$	21.1176	0.729931
$838$	10.9702	0.378959
$839$	44.1324	1.52362	0.761810	−	0.647801i	$-0.224311\pi$
$839$	44.1324	1.52362	0.761810	+	0.647801i	$0.224311\pi$
$840$	−7.58127	−0.261579
$841$	−9.19539	−0.317082
$842$	−32.1234	−1.10705
$843$	−14.9747	−0.515756
$844$	−5.69557	−0.196050
$845$	45.3203	1.55907
$846$	−16.9257	−0.581917
$847$	0.483078	0.0165988
$848$	−6.12638	−0.210381
$849$	−29.7334	−1.02045
$850$	37.0607	1.27117
$851$	24.2218	0.830312
$852$	24.4509	0.837675
$853$	1.76629	0.0604767	0.0302384	−	0.999543i	$-0.490373\pi$
$853$	1.76629	0.0604767	0.0302384	+	0.999543i	$0.490373\pi$
$854$	−13.2269	−0.452614
$855$	0	0
$856$	−9.37414	−0.320402
$857$	−42.8844	−1.46490	−0.732451	−	0.680819i	$-0.761624\pi$
$857$	−42.8844	−1.46490	−0.732451	+	0.680819i	$0.761624\pi$
$858$	−4.20422	−0.143530
$859$	3.86858	0.131994	0.0659971	−	0.997820i	$-0.478977\pi$
$859$	3.86858	0.131994	0.0659971	+	0.997820i	$0.478977\pi$
$860$	−19.5348	−0.666132
$861$	2.29457	0.0781986
$862$	7.26547	0.247463
$863$	32.7259	1.11400	0.557001	−	0.830512i	$-0.311952\pi$
$863$	32.7259	1.11400	0.557001	+	0.830512i	$0.311952\pi$
$864$	3.25419	0.110710
$865$	−26.5181	−0.901642
$866$	−18.2307	−0.619504
$867$	10.6911	0.363089
$868$	6.48937	0.220263
$869$	−20.8629	−0.707725
$870$	33.7385	1.14384
$871$	−3.93633	−0.133378
$872$	9.28080	0.314288
$873$	2.44784	0.0828470
$874$	0	0
$875$	10.3762	0.350780
$876$	−34.4623	−1.16437
$877$	−11.6549	−0.393559	−0.196779	−	0.980448i	$-0.563048\pi$
$877$	−11.6549	−0.393559	−0.196779	+	0.980448i	$0.563048\pi$
$878$	32.5406	1.09819
$879$	48.3474	1.63072
$880$	−11.6432	−0.392492
$881$	52.9550	1.78410	0.892050	−	0.451937i	$-0.149267\pi$
$881$	52.9550	1.78410	0.892050	+	0.451937i	$0.149267\pi$
$882$	−1.45891	−0.0491240
$883$	−0.838696	−0.0282244	−0.0141122	−	0.999900i	$-0.504492\pi$
$883$	−0.838696	−0.0282244	−0.0141122	+	0.999900i	$0.504492\pi$
$884$	−2.88376	−0.0969913
$885$	21.9233	0.736945
$886$	0.0189181	0.000635565 0
$887$	48.3051	1.62193	0.810963	−	0.585097i	$-0.198944\pi$
$887$	48.3051	1.62193	0.810963	+	0.585097i	$0.198944\pi$
$888$	−11.2885	−0.378818
$889$	−18.2693	−0.612731
$890$	5.35982	0.179662
$891$	−36.4781	−1.22206
$892$	18.5836	0.622226
$893$	0	0
$894$	−45.2037	−1.51184
$895$	22.9019	0.765525
$896$	1.00000	0.0334077
$897$	5.87387	0.196123
$898$	−4.85684	−0.162075
$899$	−28.8792	−0.963176
$900$	11.5109	0.383697
$901$	28.7764	0.958681
$902$	3.52396	0.117335
$903$	−11.4894	−0.382342
$904$	8.67289	0.288456
$905$	−79.9667	−2.65818
$906$	−11.6566	−0.387264
$907$	−39.8456	−1.32305	−0.661526	−	0.749922i	$-0.730091\pi$
$907$	−39.8456	−1.32305	−0.661526	+	0.749922i	$0.730091\pi$
$908$	0.527433	0.0175035
$909$	2.72604	0.0904170
$910$	−2.20422	−0.0730691
$911$	33.9742	1.12562	0.562808	−	0.826587i	$-0.309721\pi$
$911$	33.9742	1.12562	0.562808	+	0.826587i	$0.309721\pi$
$912$	0	0
$913$	−27.6326	−0.914507
$914$	−30.2842	−1.00171
$915$	100.277	3.31504
$916$	−11.9310	−0.394213
$917$	8.09149	0.267205
$918$	−15.2853	−0.504491
$919$	23.7930	0.784858	0.392429	−	0.919782i	$-0.371635\pi$
$919$	23.7930	0.784858	0.392429	+	0.919782i	$0.371635\pi$
$920$	16.2671	0.536312
$921$	−69.2730	−2.28262
$922$	−20.6428	−0.679835
$923$	7.10898	0.233995
$924$	−6.84792	−0.225280
$925$	42.1798	1.38686
$926$	−21.7134	−0.713547
$927$	−29.3624	−0.964387
$928$	−4.45024	−0.146086
$929$	−6.90591	−0.226575	−0.113288	−	0.993562i	$-0.536138\pi$
$929$	−6.90591	−0.226575	−0.113288	+	0.993562i	$0.536138\pi$
$930$	−49.1977	−1.61326
$931$	0	0
$932$	−6.00187	−0.196598
$933$	28.9222	0.946871
$934$	−18.9511	−0.620099
$935$	54.6896	1.78854
$936$	−0.895684	−0.0292763
$937$	0.663778	0.0216847	0.0108423	−	0.999941i	$-0.496549\pi$
$937$	0.663778	0.0216847	0.0108423	+	0.999941i	$0.496549\pi$
$938$	−6.41158	−0.209346
$939$	16.6574	0.543593
$940$	−41.6529	−1.35857
$941$	1.97654	0.0644334	0.0322167	−	0.999481i	$-0.489743\pi$
$941$	1.97654	0.0644334	0.0322167	+	0.999481i	$0.489743\pi$
$942$	28.6837	0.934564
$943$	−4.92345	−0.160330
$944$	−2.89177	−0.0941192
$945$	−11.6834	−0.380062
$946$	−17.6452	−0.573694
$947$	42.1283	1.36899	0.684493	−	0.729020i	$-0.260024\pi$
$947$	42.1283	1.36899	0.684493	+	0.729020i	$0.260024\pi$
$948$	−13.5845	−0.441205
$949$	−10.0197	−0.325255
$950$	0	0
$951$	59.1599	1.91839
$952$	−4.69713	−0.152235
$953$	50.5277	1.63675	0.818376	−	0.574683i	$-0.194875\pi$
$953$	50.5277	1.63675	0.818376	+	0.574683i	$0.194875\pi$
$954$	8.93784	0.289373
$955$	84.0587	2.72008
$956$	−22.2435	−0.719408
$957$	30.4749	0.985112
$958$	−20.3473	−0.657390
$959$	−4.55482	−0.147083
$960$	−7.58127	−0.244685
$961$	11.1119	0.358447
$962$	−3.28208	−0.105818
$963$	13.6760	0.440704
$964$	19.8067	0.637932
$965$	54.4203	1.75185
$966$	9.56748	0.307829
$967$	−38.8196	−1.24835	−0.624176	−	0.781284i	$-0.714565\pi$
$967$	−38.8196	−1.24835	−0.624176	+	0.781284i	$0.714565\pi$
$968$	0.483078	0.0155267
$969$	0	0
$970$	6.02398	0.193418
$971$	1.81105	0.0581194	0.0290597	−	0.999578i	$-0.490749\pi$
$971$	1.81105	0.0581194	0.0290597	+	0.999578i	$0.490749\pi$
$972$	−13.9895	−0.448714
$973$	21.6945	0.695493
$974$	−0.582139	−0.0186530
$975$	10.2288	0.327582
$976$	−13.2269	−0.423382
$977$	−19.1940	−0.614069	−0.307035	−	0.951698i	$-0.599337\pi$
$977$	−19.1940	−0.614069	−0.307035	+	0.951698i	$0.599337\pi$
$978$	13.3501	0.426889
$979$	4.84136	0.154730
$980$	−3.59028	−0.114687
$981$	−13.5398	−0.432294
$982$	33.5615	1.07099
$983$	4.19927	0.133936	0.0669680	−	0.997755i	$-0.478667\pi$
$983$	4.19927	0.133936	0.0669680	+	0.997755i	$0.478667\pi$
$984$	2.29457	0.0731481
$985$	52.3207	1.66708
$986$	20.9033	0.665698
$987$	−24.4981	−0.779783
$988$	0	0
$989$	24.6527	0.783911
$990$	16.9864	0.539862
$991$	9.13292	0.290117	0.145058	−	0.989423i	$-0.453663\pi$
$991$	9.13292	0.290117	0.145058	+	0.989423i	$0.453663\pi$
$992$	6.48937	0.206038
$993$	−28.8237	−0.914694
$994$	11.5793	0.367272
$995$	−25.3437	−0.803450
$996$	−17.9925	−0.570115
$997$	−23.2862	−0.737482	−0.368741	−	0.929532i	$-0.620211\pi$
$997$	−23.2862	−0.737482	−0.368741	+	0.929532i	$0.620211\pi$
$998$	7.71505	0.244216
$999$	−17.3966	−0.550405

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5054.2.a.bb.1.5		6
19.9	even	9		266.2.u.b.43.2	✓	12
19.17	even	9		266.2.u.b.99.2	yes	12
19.18	odd	2		5054.2.a.bc.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
266.2.u.b.43.2	✓	12	19.9	even	9
266.2.u.b.99.2	yes	12	19.17	even	9
5054.2.a.bb.1.5		6	1.1	even	1	trivial
5054.2.a.bc.1.2		6	19.18	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 5054 = 2 \cdot 7 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5054.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.11161 q^{3} +1.00000 q^{4} -3.59028 q^{5} -2.11161 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.45891 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.11161 q^{3} +1.00000 q^{4} -3.59028 q^{5} -2.11161 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.45891 q^{9} +3.59028 q^{10} +3.24298 q^{11} +2.11161 q^{12} +0.613941 q^{13} +1.00000 q^{14} -7.58127 q^{15} +1.00000 q^{16} -4.69713 q^{17} -1.45891 q^{18} -3.59028 q^{20} -2.11161 q^{21} -3.24298 q^{22} +4.53089 q^{23} -2.11161 q^{24} +7.89009 q^{25} -0.613941 q^{26} -3.25419 q^{27} -1.00000 q^{28} +4.45024 q^{29} +7.58127 q^{30} -6.48937 q^{31} -1.00000 q^{32} +6.84792 q^{33} +4.69713 q^{34} +3.59028 q^{35} +1.45891 q^{36} +5.34592 q^{37} +1.29641 q^{39} +3.59028 q^{40} -1.08664 q^{41} +2.11161 q^{42} +5.44103 q^{43} +3.24298 q^{44} -5.23789 q^{45} -4.53089 q^{46} +11.6016 q^{47} +2.11161 q^{48} +1.00000 q^{49} -7.89009 q^{50} -9.91851 q^{51} +0.613941 q^{52} -6.12638 q^{53} +3.25419 q^{54} -11.6432 q^{55} +1.00000 q^{56} -4.45024 q^{58} -2.89177 q^{59} -7.58127 q^{60} -13.2269 q^{61} +6.48937 q^{62} -1.45891 q^{63} +1.00000 q^{64} -2.20422 q^{65} -6.84792 q^{66} -6.41158 q^{67} -4.69713 q^{68} +9.56748 q^{69} -3.59028 q^{70} +11.5793 q^{71} -1.45891 q^{72} -16.3204 q^{73} -5.34592 q^{74} +16.6608 q^{75} -3.24298 q^{77} -1.29641 q^{78} -6.43324 q^{79} -3.59028 q^{80} -11.2483 q^{81} +1.08664 q^{82} -8.52076 q^{83} -2.11161 q^{84} +16.8640 q^{85} -5.44103 q^{86} +9.39718 q^{87} -3.24298 q^{88} +1.49287 q^{89} +5.23789 q^{90} -0.613941 q^{91} +4.53089 q^{92} -13.7030 q^{93} -11.6016 q^{94} -2.11161 q^{96} +1.67786 q^{97} -1.00000 q^{98} +4.73121 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 3 q^{3} + 6 q^{4} - 3 q^{5} - 3 q^{6} - 6 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 + 3 * q^3 + 6 * q^4 - 3 * q^5 - 3 * q^6 - 6 * q^7 - 6 * q^8 - 3 * q^9	\( 6 q - 6 q^{2} + 3 q^{3} + 6 q^{4} - 3 q^{5} - 3 q^{6} - 6 q^{7} - 6 q^{8} - 3 q^{9} + 3 q^{10} + 3 q^{11} + 3 q^{12} + 6 q^{13} + 6 q^{14} - 6 q^{15} + 6 q^{16} - 9 q^{17} + 3 q^{18} - 3 q^{20} - 3 q^{21} - 3 q^{22} - 3 q^{24} + 3 q^{25} - 6 q^{26} + 3 q^{27} - 6 q^{28} + 6 q^{29} + 6 q^{30} + 3 q^{31} - 6 q^{32} + 6 q^{33} + 9 q^{34} + 3 q^{35} - 3 q^{36} - 3 q^{37} - 9 q^{39} + 3 q^{40} + 9 q^{41} + 3 q^{42} - 6 q^{43} + 3 q^{44} - 12 q^{45} + 9 q^{47} + 3 q^{48} + 6 q^{49} - 3 q^{50} - 27 q^{51} + 6 q^{52} + 6 q^{53} - 3 q^{54} - 24 q^{55} + 6 q^{56} - 6 q^{58} + 15 q^{59} - 6 q^{60} - 30 q^{61} - 3 q^{62} + 3 q^{63} + 6 q^{64} + 3 q^{65} - 6 q^{66} + 15 q^{67} - 9 q^{68} + 24 q^{69} - 3 q^{70} + 21 q^{71} + 3 q^{72} - 33 q^{73} + 3 q^{74} + 33 q^{75} - 3 q^{77} + 9 q^{78} - 30 q^{79} - 3 q^{80} - 18 q^{81} - 9 q^{82} - 33 q^{83} - 3 q^{84} - 18 q^{85} + 6 q^{86} + 15 q^{87} - 3 q^{88} - 12 q^{89} + 12 q^{90} - 6 q^{91} - 21 q^{93} - 9 q^{94} - 3 q^{96} - 18 q^{97} - 6 q^{98}+O(q^{100}) \) 6 * q - 6 * q^2 + 3 * q^3 + 6 * q^4 - 3 * q^5 - 3 * q^6 - 6 * q^7 - 6 * q^8 - 3 * q^9 + 3 * q^10 + 3 * q^11 + 3 * q^12 + 6 * q^13 + 6 * q^14 - 6 * q^15 + 6 * q^16 - 9 * q^17 + 3 * q^18 - 3 * q^20 - 3 * q^21 - 3 * q^22 - 3 * q^24 + 3 * q^25 - 6 * q^26 + 3 * q^27 - 6 * q^28 + 6 * q^29 + 6 * q^30 + 3 * q^31 - 6 * q^32 + 6 * q^33 + 9 * q^34 + 3 * q^35 - 3 * q^36 - 3 * q^37 - 9 * q^39 + 3 * q^40 + 9 * q^41 + 3 * q^42 - 6 * q^43 + 3 * q^44 - 12 * q^45 + 9 * q^47 + 3 * q^48 + 6 * q^49 - 3 * q^50 - 27 * q^51 + 6 * q^52 + 6 * q^53 - 3 * q^54 - 24 * q^55 + 6 * q^56 - 6 * q^58 + 15 * q^59 - 6 * q^60 - 30 * q^61 - 3 * q^62 + 3 * q^63 + 6 * q^64 + 3 * q^65 - 6 * q^66 + 15 * q^67 - 9 * q^68 + 24 * q^69 - 3 * q^70 + 21 * q^71 + 3 * q^72 - 33 * q^73 + 3 * q^74 + 33 * q^75 - 3 * q^77 + 9 * q^78 - 30 * q^79 - 3 * q^80 - 18 * q^81 - 9 * q^82 - 33 * q^83 - 3 * q^84 - 18 * q^85 + 6 * q^86 + 15 * q^87 - 3 * q^88 - 12 * q^89 + 12 * q^90 - 6 * q^91 - 21 * q^93 - 9 * q^94 - 3 * q^96 - 18 * q^97 - 6 * q^98

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