LMFDB - Embedded newform 4641.2.a.ba.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4641,2,Mod(1,4641)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4641, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4641.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4641 = 3 \cdot 7 \cdot 13 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4641.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:	$37.0585715781$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - x^{16} - 29 x^{15} + 26 x^{14} + 339 x^{13} - 266 x^{12} - 2047 x^{11} + 1356 x^{10} + \cdots + 18 $ x^17 - x^16 - 29x^15 + 26x^14 + 339x^13 - 266x^12 - 2047x^11 + 1356x^10 + 6792x^9 - 3573x^8 - 12125x^7 + 4456x^6 + 10521x^5 - 1858x^4 - 3551x^3 + 34x^2 + 323*x + 18
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-1.01973$ of defining polynomial
Character	$\chi$	$=$	4641.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.01973 q^{2} -1.00000 q^{3} -0.960160 q^{4} +3.04739 q^{5} +1.01973 q^{6} -1.00000 q^{7} +3.01855 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.01973 q^{2} -1.00000 q^{3} -0.960160 q^{4} +3.04739 q^{5} +1.01973 q^{6} -1.00000 q^{7} +3.01855 q^{8} +1.00000 q^{9} -3.10751 q^{10} -4.10822 q^{11} +0.960160 q^{12} +1.00000 q^{13} +1.01973 q^{14} -3.04739 q^{15} -1.15777 q^{16} -1.00000 q^{17} -1.01973 q^{18} +5.70877 q^{19} -2.92599 q^{20} +1.00000 q^{21} +4.18926 q^{22} +6.11854 q^{23} -3.01855 q^{24} +4.28661 q^{25} -1.01973 q^{26} -1.00000 q^{27} +0.960160 q^{28} -6.45864 q^{29} +3.10751 q^{30} -4.93096 q^{31} -4.85649 q^{32} +4.10822 q^{33} +1.01973 q^{34} -3.04739 q^{35} -0.960160 q^{36} -6.28527 q^{37} -5.82138 q^{38} -1.00000 q^{39} +9.19872 q^{40} +9.43585 q^{41} -1.01973 q^{42} +4.55242 q^{43} +3.94455 q^{44} +3.04739 q^{45} -6.23923 q^{46} +5.46618 q^{47} +1.15777 q^{48} +1.00000 q^{49} -4.37117 q^{50} +1.00000 q^{51} -0.960160 q^{52} -9.16383 q^{53} +1.01973 q^{54} -12.5194 q^{55} -3.01855 q^{56} -5.70877 q^{57} +6.58604 q^{58} +11.7230 q^{59} +2.92599 q^{60} +12.8471 q^{61} +5.02823 q^{62} -1.00000 q^{63} +7.26783 q^{64} +3.04739 q^{65} -4.18926 q^{66} -9.32671 q^{67} +0.960160 q^{68} -6.11854 q^{69} +3.10751 q^{70} +12.9646 q^{71} +3.01855 q^{72} -6.05786 q^{73} +6.40925 q^{74} -4.28661 q^{75} -5.48133 q^{76} +4.10822 q^{77} +1.01973 q^{78} -8.94458 q^{79} -3.52819 q^{80} +1.00000 q^{81} -9.62198 q^{82} -0.123567 q^{83} -0.960160 q^{84} -3.04739 q^{85} -4.64222 q^{86} +6.45864 q^{87} -12.4009 q^{88} -13.0258 q^{89} -3.10751 q^{90} -1.00000 q^{91} -5.87477 q^{92} +4.93096 q^{93} -5.57400 q^{94} +17.3969 q^{95} +4.85649 q^{96} +7.17879 q^{97} -1.01973 q^{98} -4.10822 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + q^{2} - 17 q^{3} + 25 q^{4} - 4 q^{5} - q^{6} - 17 q^{7} + 6 q^{8} + 17 q^{9}+O(q^{10}) $ 17 * q + q^2 - 17 * q^3 + 25 * q^4 - 4 * q^5 - q^6 - 17 * q^7 + 6 * q^8 + 17 * q^9	\( 17 q + q^{2} - 17 q^{3} + 25 q^{4} - 4 q^{5} - q^{6} - 17 q^{7} + 6 q^{8} + 17 q^{9} - q^{10} + 4 q^{11} - 25 q^{12} + 17 q^{13} - q^{14} + 4 q^{15} + 53 q^{16} - 17 q^{17} + q^{18} + 13 q^{19} - 5 q^{20} + 17 q^{21} + 4 q^{22} + 8 q^{23} - 6 q^{24} + 37 q^{25} + q^{26} - 17 q^{27} - 25 q^{28} - 3 q^{29} + q^{30} + 10 q^{31} + 18 q^{32} - 4 q^{33} - q^{34} + 4 q^{35} + 25 q^{36} - 25 q^{38} - 17 q^{39} - 12 q^{41} + q^{42} + 29 q^{43} + 12 q^{44} - 4 q^{45} + 19 q^{46} - 4 q^{47} - 53 q^{48} + 17 q^{49} + 9 q^{50} + 17 q^{51} + 25 q^{52} - 8 q^{53} - q^{54} + 27 q^{55} - 6 q^{56} - 13 q^{57} + 2 q^{58} + 25 q^{59} + 5 q^{60} - 5 q^{61} - 37 q^{62} - 17 q^{63} + 94 q^{64} - 4 q^{65} - 4 q^{66} + 15 q^{67} - 25 q^{68} - 8 q^{69} + q^{70} + 32 q^{71} + 6 q^{72} - 15 q^{73} + 16 q^{74} - 37 q^{75} + 3 q^{76} - 4 q^{77} - q^{78} + 27 q^{79} + 41 q^{80} + 17 q^{81} - 8 q^{82} - 24 q^{83} + 25 q^{84} + 4 q^{85} + 53 q^{86} + 3 q^{87} - 9 q^{88} - 8 q^{89} - q^{90} - 17 q^{91} + 14 q^{92} - 10 q^{93} + 51 q^{94} - 9 q^{95} - 18 q^{96} - 22 q^{97} + q^{98} + 4 q^{99}+O(q^{100}) \) 17 * q + q^2 - 17 * q^3 + 25 * q^4 - 4 * q^5 - q^6 - 17 * q^7 + 6 * q^8 + 17 * q^9 - q^10 + 4 * q^11 - 25 * q^12 + 17 * q^13 - q^14 + 4 * q^15 + 53 * q^16 - 17 * q^17 + q^18 + 13 * q^19 - 5 * q^20 + 17 * q^21 + 4 * q^22 + 8 * q^23 - 6 * q^24 + 37 * q^25 + q^26 - 17 * q^27 - 25 * q^28 - 3 * q^29 + q^30 + 10 * q^31 + 18 * q^32 - 4 * q^33 - q^34 + 4 * q^35 + 25 * q^36 - 25 * q^38 - 17 * q^39 - 12 * q^41 + q^42 + 29 * q^43 + 12 * q^44 - 4 * q^45 + 19 * q^46 - 4 * q^47 - 53 * q^48 + 17 * q^49 + 9 * q^50 + 17 * q^51 + 25 * q^52 - 8 * q^53 - q^54 + 27 * q^55 - 6 * q^56 - 13 * q^57 + 2 * q^58 + 25 * q^59 + 5 * q^60 - 5 * q^61 - 37 * q^62 - 17 * q^63 + 94 * q^64 - 4 * q^65 - 4 * q^66 + 15 * q^67 - 25 * q^68 - 8 * q^69 + q^70 + 32 * q^71 + 6 * q^72 - 15 * q^73 + 16 * q^74 - 37 * q^75 + 3 * q^76 - 4 * q^77 - q^78 + 27 * q^79 + 41 * q^80 + 17 * q^81 - 8 * q^82 - 24 * q^83 + 25 * q^84 + 4 * q^85 + 53 * q^86 + 3 * q^87 - 9 * q^88 - 8 * q^89 - q^90 - 17 * q^91 + 14 * q^92 - 10 * q^93 + 51 * q^94 - 9 * q^95 - 18 * q^96 - 22 * q^97 + q^98 + 4 * 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 $

$2$	−1.01973	−0.721055	−0.360527	−	0.932749i	$-0.617403\pi$
$2$	−1.01973	−0.721055	−0.360527	+	0.932749i	$0.617403\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.960160	−0.480080
$5$	3.04739	1.36284	0.681418	−	0.731894i	$-0.261364\pi$
$5$	3.04739	1.36284	0.681418	+	0.731894i	$0.261364\pi$
$6$	1.01973	0.416301
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	3.01855	1.06722
$9$	1.00000	0.333333
$10$	−3.10751	−0.982680
$11$	−4.10822	−1.23867	−0.619337	−	0.785125i	$-0.712599\pi$
$11$	−4.10822	−1.23867	−0.619337	+	0.785125i	$0.712599\pi$
$12$	0.960160	0.277174
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	1.01973	0.272533
$15$	−3.04739	−0.786834
$16$	−1.15777	−0.289443
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.01973	−0.240352
$19$	5.70877	1.30968	0.654841	−	0.755767i	$-0.272736\pi$
$19$	5.70877	1.30968	0.654841	+	0.755767i	$0.272736\pi$
$20$	−2.92599	−0.654270
$21$	1.00000	0.218218
$22$	4.18926	0.893152
$23$	6.11854	1.27580	0.637901	−	0.770118i	$-0.279803\pi$
$23$	6.11854	1.27580	0.637901	+	0.770118i	$0.279803\pi$
$24$	−3.01855	−0.616159
$25$	4.28661	0.857323
$26$	−1.01973	−0.199985
$27$	−1.00000	−0.192450
$28$	0.960160	0.181453
$29$	−6.45864	−1.19934	−0.599670	−	0.800248i	$-0.704701\pi$
$29$	−6.45864	−1.19934	−0.599670	+	0.800248i	$0.704701\pi$
$30$	3.10751	0.567350
$31$	−4.93096	−0.885627	−0.442813	−	0.896614i	$-0.646020\pi$
$31$	−4.93096	−0.885627	−0.442813	+	0.896614i	$0.646020\pi$
$32$	−4.85649	−0.858514
$33$	4.10822	0.715149
$34$	1.01973	0.174881
$35$	−3.04739	−0.515104
$36$	−0.960160	−0.160027
$37$	−6.28527	−1.03329	−0.516646	−	0.856199i	$-0.672820\pi$
$37$	−6.28527	−1.03329	−0.516646	+	0.856199i	$0.672820\pi$
$38$	−5.82138	−0.944352
$39$	−1.00000	−0.160128
$40$	9.19872	1.45444
$41$	9.43585	1.47363	0.736816	−	0.676093i	$-0.236328\pi$
$41$	9.43585	1.47363	0.736816	+	0.676093i	$0.236328\pi$
$42$	−1.01973	−0.157347
$43$	4.55242	0.694238	0.347119	−	0.937821i	$-0.387160\pi$
$43$	4.55242	0.694238	0.347119	+	0.937821i	$0.387160\pi$
$44$	3.94455	0.594663
$45$	3.04739	0.454279
$46$	−6.23923	−0.919924
$47$	5.46618	0.797324	0.398662	−	0.917098i	$-0.369475\pi$
$47$	5.46618	0.797324	0.398662	+	0.917098i	$0.369475\pi$
$48$	1.15777	0.167110
$49$	1.00000	0.142857
$50$	−4.37117	−0.618177
$51$	1.00000	0.140028
$52$	−0.960160	−0.133150
$53$	−9.16383	−1.25875	−0.629374	−	0.777102i	$-0.716689\pi$
$53$	−9.16383	−1.25875	−0.629374	+	0.777102i	$0.716689\pi$
$54$	1.01973	0.138767
$55$	−12.5194	−1.68811
$56$	−3.01855	−0.403371
$57$	−5.70877	−0.756145
$58$	6.58604	0.864790
$59$	11.7230	1.52621	0.763105	−	0.646274i	$-0.223674\pi$
$59$	11.7230	1.52621	0.763105	+	0.646274i	$0.223674\pi$
$60$	2.92599	0.377743
$61$	12.8471	1.64490	0.822451	−	0.568836i	$-0.192606\pi$
$61$	12.8471	1.64490	0.822451	+	0.568836i	$0.192606\pi$
$62$	5.02823	0.638586
$63$	−1.00000	−0.125988
$64$	7.26783	0.908479
$65$	3.04739	0.377983
$66$	−4.18926	−0.515662
$67$	−9.32671	−1.13944	−0.569720	−	0.821839i	$-0.692948\pi$
$67$	−9.32671	−1.13944	−0.569720	+	0.821839i	$0.692948\pi$
$68$	0.960160	0.116436
$69$	−6.11854	−0.736585
$70$	3.10751	0.371418
$71$	12.9646	1.53861	0.769305	−	0.638881i	$-0.220602\pi$
$71$	12.9646	1.53861	0.769305	+	0.638881i	$0.220602\pi$
$72$	3.01855	0.355740
$73$	−6.05786	−0.709019	−0.354510	−	0.935052i	$-0.615352\pi$
$73$	−6.05786	−0.709019	−0.354510	+	0.935052i	$0.615352\pi$
$74$	6.40925	0.745060
$75$	−4.28661	−0.494976
$76$	−5.48133	−0.628752
$77$	4.10822	0.468175
$78$	1.01973	0.115461
$79$	−8.94458	−1.00634	−0.503172	−	0.864186i	$-0.667834\pi$
$79$	−8.94458	−1.00634	−0.503172	+	0.864186i	$0.667834\pi$
$80$	−3.52819	−0.394464
$81$	1.00000	0.111111
$82$	−9.62198	−1.06257
$83$	−0.123567	−0.0135633	−0.00678163	−	0.999977i	$-0.502159\pi$
$83$	−0.123567	−0.0135633	−0.00678163	+	0.999977i	$0.502159\pi$
$84$	−0.960160	−0.104762
$85$	−3.04739	−0.330536
$86$	−4.64222	−0.500584
$87$	6.45864	0.692439
$88$	−12.4009	−1.32194
$89$	−13.0258	−1.38073	−0.690365	−	0.723462i	$-0.742550\pi$
$89$	−13.0258	−1.38073	−0.690365	+	0.723462i	$0.742550\pi$
$90$	−3.10751	−0.327560
$91$	−1.00000	−0.104828
$92$	−5.87477	−0.612487
$93$	4.93096	0.511317
$94$	−5.57400	−0.574914
$95$	17.3969	1.78488
$96$	4.85649	0.495663
$97$	7.17879	0.728895	0.364448	−	0.931224i	$-0.381258\pi$
$97$	7.17879	0.728895	0.364448	+	0.931224i	$0.381258\pi$
$98$	−1.01973	−0.103008
$99$	−4.10822	−0.412892
$100$	−4.11584	−0.411584
$101$	−9.25880	−0.921286	−0.460643	−	0.887586i	$-0.652381\pi$
$101$	−9.25880	−0.921286	−0.460643	+	0.887586i	$0.652381\pi$
$102$	−1.01973	−0.100968
$103$	17.3326	1.70783	0.853917	−	0.520410i	$-0.174221\pi$
$103$	17.3326	1.70783	0.853917	+	0.520410i	$0.174221\pi$
$104$	3.01855	0.295993
$105$	3.04739	0.297395
$106$	9.34459	0.907627
$107$	9.54195	0.922455	0.461228	−	0.887282i	$-0.347409\pi$
$107$	9.54195	0.922455	0.461228	+	0.887282i	$0.347409\pi$
$108$	0.960160	0.0923914
$109$	−11.9550	−1.14508	−0.572540	−	0.819877i	$-0.694042\pi$
$109$	−11.9550	−1.14508	−0.572540	+	0.819877i	$0.694042\pi$
$110$	12.7663	1.21722
$111$	6.28527	0.596571
$112$	1.15777	0.109399
$113$	−0.540671	−0.0508620	−0.0254310	−	0.999677i	$-0.508096\pi$
$113$	−0.540671	−0.0508620	−0.0254310	+	0.999677i	$0.508096\pi$
$114$	5.82138	0.545222
$115$	18.6456	1.73871
$116$	6.20133	0.575779
$117$	1.00000	0.0924500
$118$	−11.9543	−1.10048
$119$	1.00000	0.0916698
$120$	−9.19872	−0.839724
$121$	5.87747	0.534315
$122$	−13.1005	−1.18606
$123$	−9.43585	−0.850802
$124$	4.73451	0.425172
$125$	−2.17397	−0.194445
$126$	1.01973	0.0908444
$127$	14.2356	1.26320	0.631602	−	0.775292i	$-0.282398\pi$
$127$	14.2356	1.26320	0.631602	+	0.775292i	$0.282398\pi$
$128$	2.30179	0.203451
$129$	−4.55242	−0.400818
$130$	−3.10751	−0.272546
$131$	19.2451	1.68145	0.840726	−	0.541461i	$-0.182129\pi$
$131$	19.2451	1.68145	0.840726	+	0.541461i	$0.182129\pi$
$132$	−3.94455	−0.343329
$133$	−5.70877	−0.495013
$134$	9.51069	0.821598
$135$	−3.04739	−0.262278
$136$	−3.01855	−0.258839
$137$	13.3522	1.14076	0.570379	−	0.821381i	$-0.306796\pi$
$137$	13.3522	1.14076	0.570379	+	0.821381i	$0.306796\pi$
$138$	6.23923	0.531118
$139$	−15.5145	−1.31592	−0.657962	−	0.753051i	$-0.728581\pi$
$139$	−15.5145	−1.31592	−0.657962	+	0.753051i	$0.728581\pi$
$140$	2.92599	0.247291
$141$	−5.46618	−0.460335
$142$	−13.2203	−1.10942
$143$	−4.10822	−0.343547
$144$	−1.15777	−0.0964811
$145$	−19.6820	−1.63450
$146$	6.17736	0.511242
$147$	−1.00000	−0.0824786
$148$	6.03486	0.496062
$149$	−8.58234	−0.703093	−0.351546	−	0.936170i	$-0.614344\pi$
$149$	−8.58234	−0.703093	−0.351546	+	0.936170i	$0.614344\pi$
$150$	4.37117	0.356905
$151$	−4.36382	−0.355122	−0.177561	−	0.984110i	$-0.556821\pi$
$151$	−4.36382	−0.355122	−0.177561	+	0.984110i	$0.556821\pi$
$152$	17.2322	1.39772
$153$	−1.00000	−0.0808452
$154$	−4.18926	−0.337580
$155$	−15.0266	−1.20696
$156$	0.960160	0.0768743
$157$	3.37083	0.269022	0.134511	−	0.990912i	$-0.457054\pi$
$157$	3.37083	0.269022	0.134511	+	0.990912i	$0.457054\pi$
$158$	9.12102	0.725629
$159$	9.16383	0.726739
$160$	−14.7996	−1.17001
$161$	−6.11854	−0.482208
$162$	−1.01973	−0.0801172
$163$	−12.9503	−1.01435	−0.507173	−	0.861844i	$-0.669309\pi$
$163$	−12.9503	−1.01435	−0.507173	+	0.861844i	$0.669309\pi$
$164$	−9.05993	−0.707461
$165$	12.5194	0.974631
$166$	0.126005	0.00977986
$167$	−6.89221	−0.533335	−0.266668	−	0.963789i	$-0.585923\pi$
$167$	−6.89221	−0.533335	−0.266668	+	0.963789i	$0.585923\pi$
$168$	3.01855	0.232886
$169$	1.00000	0.0769231
$170$	3.10751	0.238335
$171$	5.70877	0.436560
$172$	−4.37105	−0.333290
$173$	−16.1733	−1.22963	−0.614817	−	0.788670i	$-0.710770\pi$
$173$	−16.1733	−1.22963	−0.614817	+	0.788670i	$0.710770\pi$
$174$	−6.58604	−0.499286
$175$	−4.28661	−0.324038
$176$	4.75639	0.358526
$177$	−11.7230	−0.881158
$178$	13.2827	0.995581
$179$	−6.69912	−0.500716	−0.250358	−	0.968153i	$-0.580548\pi$
$179$	−6.69912	−0.500716	−0.250358	+	0.968153i	$0.580548\pi$
$180$	−2.92599	−0.218090
$181$	16.4953	1.22609	0.613043	−	0.790050i	$-0.289945\pi$
$181$	16.4953	1.22609	0.613043	+	0.790050i	$0.289945\pi$
$182$	1.01973	0.0755871
$183$	−12.8471	−0.949685
$184$	18.4691	1.36156
$185$	−19.1537	−1.40821
$186$	−5.02823	−0.368688
$187$	4.10822	0.300423
$188$	−5.24840	−0.382779
$189$	1.00000	0.0727393
$190$	−17.7400	−1.28700
$191$	−5.58176	−0.403882	−0.201941	−	0.979398i	$-0.564725\pi$
$191$	−5.58176	−0.403882	−0.201941	+	0.979398i	$0.564725\pi$
$192$	−7.26783	−0.524511
$193$	11.9218	0.858149	0.429075	−	0.903269i	$-0.358840\pi$
$193$	11.9218	0.858149	0.429075	+	0.903269i	$0.358840\pi$
$194$	−7.32039	−0.525574
$195$	−3.04739	−0.218228
$196$	−0.960160	−0.0685829
$197$	−6.99400	−0.498302	−0.249151	−	0.968465i	$-0.580152\pi$
$197$	−6.99400	−0.498302	−0.249151	+	0.968465i	$0.580152\pi$
$198$	4.18926	0.297717
$199$	5.26504	0.373229	0.186615	−	0.982433i	$-0.440248\pi$
$199$	5.26504	0.373229	0.186615	+	0.982433i	$0.440248\pi$
$200$	12.9394	0.914951
$201$	9.32671	0.657856
$202$	9.44144	0.664297
$203$	6.45864	0.453308
$204$	−0.960160	−0.0672246
$205$	28.7548	2.00832
$206$	−17.6745	−1.23144
$207$	6.11854	0.425268
$208$	−1.15777	−0.0802771
$209$	−23.4529	−1.62227
$210$	−3.10751	−0.214438
$211$	−6.67798	−0.459731	−0.229865	−	0.973222i	$-0.573829\pi$
$211$	−6.67798	−0.459731	−0.229865	+	0.973222i	$0.573829\pi$
$212$	8.79874	0.604300
$213$	−12.9646	−0.888317
$214$	−9.73017	−0.665141
$215$	13.8730	0.946133
$216$	−3.01855	−0.205386
$217$	4.93096	0.334736
$218$	12.1908	0.825666
$219$	6.05786	0.409353
$220$	12.0206	0.810428
$221$	−1.00000	−0.0672673
$222$	−6.40925	−0.430160
$223$	20.4487	1.36935	0.684674	−	0.728849i	$-0.259944\pi$
$223$	20.4487	1.36935	0.684674	+	0.728849i	$0.259944\pi$
$224$	4.85649	0.324488
$225$	4.28661	0.285774
$226$	0.551336	0.0366743
$227$	20.1081	1.33462	0.667310	−	0.744780i	$-0.267445\pi$
$227$	20.1081	1.33462	0.667310	+	0.744780i	$0.267445\pi$
$228$	5.48133	0.363010
$229$	−1.03161	−0.0681704	−0.0340852	−	0.999419i	$-0.510852\pi$
$229$	−1.03161	−0.0681704	−0.0340852	+	0.999419i	$0.510852\pi$
$230$	−19.0134	−1.25371
$231$	−4.10822	−0.270301
$232$	−19.4957	−1.27996
$233$	−23.1409	−1.51601	−0.758005	−	0.652248i	$-0.773826\pi$
$233$	−23.1409	−1.51601	−0.758005	+	0.652248i	$0.773826\pi$
$234$	−1.01973	−0.0666615
$235$	16.6576	1.08662
$236$	−11.2560	−0.732703
$237$	8.94458	0.581013
$238$	−1.01973	−0.0660990
$239$	−4.56842	−0.295507	−0.147753	−	0.989024i	$-0.547204\pi$
$239$	−4.56842	−0.295507	−0.147753	+	0.989024i	$0.547204\pi$
$240$	3.52819	0.227744
$241$	7.68021	0.494726	0.247363	−	0.968923i	$-0.420436\pi$
$241$	7.68021	0.494726	0.247363	+	0.968923i	$0.420436\pi$
$242$	−5.99340	−0.385271
$243$	−1.00000	−0.0641500
$244$	−12.3353	−0.789685
$245$	3.04739	0.194691
$246$	9.62198	0.613475
$247$	5.70877	0.363240
$248$	−14.8844	−0.945158
$249$	0.123567	0.00783075
$250$	2.21685	0.140206
$251$	20.8813	1.31802	0.659008	−	0.752136i	$-0.270976\pi$
$251$	20.8813	1.31802	0.659008	+	0.752136i	$0.270976\pi$
$252$	0.960160	0.0604844
$253$	−25.1363	−1.58030
$254$	−14.5164	−0.910840
$255$	3.04739	0.190835
$256$	−16.8829	−1.05518
$257$	−8.80412	−0.549186	−0.274593	−	0.961561i	$-0.588543\pi$
$257$	−8.80412	−0.549186	−0.274593	+	0.961561i	$0.588543\pi$
$258$	4.64222	0.289012
$259$	6.28527	0.390547
$260$	−2.92599	−0.181462
$261$	−6.45864	−0.399780
$262$	−19.6247	−1.21242
$263$	7.34625	0.452989	0.226494	−	0.974012i	$-0.427273\pi$
$263$	7.34625	0.452989	0.226494	+	0.974012i	$0.427273\pi$
$264$	12.4009	0.763221
$265$	−27.9258	−1.71547
$266$	5.82138	0.356931
$267$	13.0258	0.797164
$268$	8.95514	0.547022
$269$	−1.25402	−0.0764592	−0.0382296	−	0.999269i	$-0.512172\pi$
$269$	−1.25402	−0.0764592	−0.0382296	+	0.999269i	$0.512172\pi$
$270$	3.10751	0.189117
$271$	29.6442	1.80076	0.900378	−	0.435108i	$-0.143290\pi$
$271$	29.6442	1.80076	0.900378	+	0.435108i	$0.143290\pi$
$272$	1.15777	0.0702003
$273$	1.00000	0.0605228
$274$	−13.6156	−0.822549
$275$	−17.6104	−1.06194
$276$	5.87477	0.353620
$277$	17.7056	1.06383	0.531913	−	0.846799i	$-0.321473\pi$
$277$	17.7056	1.06383	0.531913	+	0.846799i	$0.321473\pi$
$278$	15.8205	0.948853
$279$	−4.93096	−0.295209
$280$	−9.19872	−0.549728
$281$	12.4871	0.744917	0.372459	−	0.928049i	$-0.378515\pi$
$281$	12.4871	0.744917	0.372459	+	0.928049i	$0.378515\pi$
$282$	5.57400	0.331927
$283$	−2.10406	−0.125073	−0.0625367	−	0.998043i	$-0.519919\pi$
$283$	−2.10406	−0.125073	−0.0625367	+	0.998043i	$0.519919\pi$
$284$	−12.4481	−0.738656
$285$	−17.3969	−1.03050
$286$	4.18926	0.247716
$287$	−9.43585	−0.556981
$288$	−4.85649	−0.286171
$289$	1.00000	0.0588235
$290$	20.0703	1.17857
$291$	−7.17879	−0.420828
$292$	5.81652	0.340386
$293$	32.1999	1.88114	0.940569	−	0.339604i	$-0.110293\pi$
$293$	32.1999	1.88114	0.940569	+	0.339604i	$0.110293\pi$
$294$	1.01973	0.0594716
$295$	35.7247	2.07998
$296$	−18.9724	−1.10275
$297$	4.10822	0.238383
$298$	8.75163	0.506968
$299$	6.11854	0.353844
$300$	4.11584	0.237628
$301$	−4.55242	−0.262397
$302$	4.44989	0.256063
$303$	9.25880	0.531904
$304$	−6.60946	−0.379078
$305$	39.1502	2.24173
$306$	1.01973	0.0582938
$307$	9.70581	0.553940	0.276970	−	0.960879i	$-0.410670\pi$
$307$	9.70581	0.553940	0.276970	+	0.960879i	$0.410670\pi$
$308$	−3.94455	−0.224761
$309$	−17.3326	−0.986018
$310$	15.3230	0.870288
$311$	13.1103	0.743419	0.371710	−	0.928349i	$-0.378772\pi$
$311$	13.1103	0.743419	0.371710	+	0.928349i	$0.378772\pi$
$312$	−3.01855	−0.170892
$313$	33.3835	1.88695	0.943474	−	0.331447i	$-0.107537\pi$
$313$	33.3835	1.88695	0.943474	+	0.331447i	$0.107537\pi$
$314$	−3.43732	−0.193979
$315$	−3.04739	−0.171701
$316$	8.58823	0.483126
$317$	13.2897	0.746421	0.373211	−	0.927747i	$-0.378257\pi$
$317$	13.2897	0.746421	0.373211	+	0.927747i	$0.378257\pi$
$318$	−9.34459	−0.524019
$319$	26.5335	1.48559
$320$	22.1480	1.23811
$321$	−9.54195	−0.532580
$322$	6.23923	0.347699
$323$	−5.70877	−0.317644
$324$	−0.960160	−0.0533422
$325$	4.28661	0.237779
$326$	13.2057	0.731399
$327$	11.9550	0.661112
$328$	28.4826	1.57269
$329$	−5.46618	−0.301360
$330$	−12.7663	−0.702763
$331$	14.9511	0.821786	0.410893	−	0.911684i	$-0.365217\pi$
$331$	14.9511	0.821786	0.410893	+	0.911684i	$0.365217\pi$
$332$	0.118644	0.00651145
$333$	−6.28527	−0.344430
$334$	7.02816	0.384564
$335$	−28.4222	−1.55287
$336$	−1.15777	−0.0631617
$337$	16.9812	0.925023	0.462512	−	0.886613i	$-0.346948\pi$
$337$	16.9812	0.925023	0.462512	+	0.886613i	$0.346948\pi$
$338$	−1.01973	−0.0554658
$339$	0.540671	0.0293652
$340$	2.92599	0.158684
$341$	20.2575	1.09700
$342$	−5.82138	−0.314784
$343$	−1.00000	−0.0539949
$344$	13.7417	0.740904
$345$	−18.6456	−1.00385
$346$	16.4923	0.886633
$347$	−10.1452	−0.544622	−0.272311	−	0.962209i	$-0.587788\pi$
$347$	−10.1452	−0.544622	−0.272311	+	0.962209i	$0.587788\pi$
$348$	−6.20133	−0.332426
$349$	27.2791	1.46022	0.730108	−	0.683332i	$-0.239470\pi$
$349$	27.2791	1.46022	0.730108	+	0.683332i	$0.239470\pi$
$350$	4.37117	0.233649
$351$	−1.00000	−0.0533761
$352$	19.9515	1.06342
$353$	19.9598	1.06236	0.531178	−	0.847261i	$-0.321750\pi$
$353$	19.9598	1.06236	0.531178	+	0.847261i	$0.321750\pi$
$354$	11.9543	0.635363
$355$	39.5081	2.09687
$356$	12.5068	0.662860
$357$	−1.00000	−0.0529256
$358$	6.83127	0.361044
$359$	−8.05467	−0.425109	−0.212555	−	0.977149i	$-0.568178\pi$
$359$	−8.05467	−0.425109	−0.212555	+	0.977149i	$0.568178\pi$
$360$	9.19872	0.484815
$361$	13.5900	0.715264
$362$	−16.8207	−0.884075
$363$	−5.87747	−0.308487
$364$	0.960160	0.0503261
$365$	−18.4607	−0.966277
$366$	13.1005	0.684775
$367$	1.73120	0.0903680	0.0451840	−	0.998979i	$-0.485613\pi$
$367$	1.73120	0.0903680	0.0451840	+	0.998979i	$0.485613\pi$
$368$	−7.08388	−0.369273
$369$	9.43585	0.491211
$370$	19.5315	1.01539
$371$	9.16383	0.475762
$372$	−4.73451	−0.245473
$373$	−15.5159	−0.803384	−0.401692	−	0.915775i	$-0.631578\pi$
$373$	−15.5159	−0.803384	−0.401692	+	0.915775i	$0.631578\pi$
$374$	−4.18926	−0.216621
$375$	2.17397	0.112263
$376$	16.4999	0.850919
$377$	−6.45864	−0.332637
$378$	−1.01973	−0.0524490
$379$	−10.6211	−0.545569	−0.272785	−	0.962075i	$-0.587945\pi$
$379$	−10.6211	−0.545569	−0.272785	+	0.962075i	$0.587945\pi$
$380$	−16.7038	−0.856886
$381$	−14.2356	−0.729312
$382$	5.69187	0.291221
$383$	22.6067	1.15515	0.577574	−	0.816338i	$-0.303999\pi$
$383$	22.6067	1.15515	0.577574	+	0.816338i	$0.303999\pi$
$384$	−2.30179	−0.117463
$385$	12.5194	0.638046
$386$	−12.1570	−0.618773
$387$	4.55242	0.231413
$388$	−6.89278	−0.349928
$389$	−9.82773	−0.498286	−0.249143	−	0.968467i	$-0.580149\pi$
$389$	−9.82773	−0.498286	−0.249143	+	0.968467i	$0.580149\pi$
$390$	3.10751	0.157355
$391$	−6.11854	−0.309428
$392$	3.01855	0.152460
$393$	−19.2451	−0.970786
$394$	7.13196	0.359303
$395$	−27.2577	−1.37148
$396$	3.94455	0.198221
$397$	23.3690	1.17286	0.586429	−	0.810001i	$-0.300533\pi$
$397$	23.3690	1.17286	0.586429	+	0.810001i	$0.300533\pi$
$398$	−5.36890	−0.269119
$399$	5.70877	0.285796
$400$	−4.96293	−0.248146
$401$	−34.3941	−1.71756	−0.858780	−	0.512344i	$-0.828777\pi$
$401$	−34.3941	−1.71756	−0.858780	+	0.512344i	$0.828777\pi$
$402$	−9.51069	−0.474350
$403$	−4.93096	−0.245629
$404$	8.88993	0.442291
$405$	3.04739	0.151426
$406$	−6.58604	−0.326860
$407$	25.8213	1.27991
$408$	3.01855	0.149441
$409$	18.5712	0.918285	0.459143	−	0.888363i	$-0.348157\pi$
$409$	18.5712	0.918285	0.459143	+	0.888363i	$0.348157\pi$
$410$	−29.3220	−1.44811
$411$	−13.3522	−0.658617
$412$	−16.6421	−0.819897
$413$	−11.7230	−0.576853
$414$	−6.23923	−0.306641
$415$	−0.376558	−0.0184845
$416$	−4.85649	−0.238109
$417$	15.5145	0.759749
$418$	23.9155	1.16974
$419$	−12.8450	−0.627518	−0.313759	−	0.949503i	$-0.601588\pi$
$419$	−12.8450	−0.627518	−0.313759	+	0.949503i	$0.601588\pi$
$420$	−2.92599	−0.142774
$421$	15.5465	0.757691	0.378846	−	0.925460i	$-0.376321\pi$
$421$	15.5465	0.757691	0.378846	+	0.925460i	$0.376321\pi$
$422$	6.80970	0.331491
$423$	5.46618	0.265775
$424$	−27.6615	−1.34336
$425$	−4.28661	−0.207931
$426$	13.2203	0.640525
$427$	−12.8471	−0.621715
$428$	−9.16180	−0.442852
$429$	4.10822	0.198347
$430$	−14.1467	−0.682214
$431$	−12.0405	−0.579970	−0.289985	−	0.957031i	$-0.593650\pi$
$431$	−12.0405	−0.579970	−0.289985	+	0.957031i	$0.593650\pi$
$432$	1.15777	0.0557034
$433$	16.6994	0.802521	0.401261	−	0.915964i	$-0.368572\pi$
$433$	16.6994	0.802521	0.401261	+	0.915964i	$0.368572\pi$
$434$	−5.02823	−0.241363
$435$	19.6820	0.943681
$436$	11.4787	0.549730
$437$	34.9293	1.67089
$438$	−6.17736	−0.295166
$439$	24.1717	1.15365	0.576826	−	0.816867i	$-0.304291\pi$
$439$	24.1717	1.15365	0.576826	+	0.816867i	$0.304291\pi$
$440$	−37.7903	−1.80158
$441$	1.00000	0.0476190
$442$	1.01973	0.0485034
$443$	6.08535	0.289124	0.144562	−	0.989496i	$-0.453823\pi$
$443$	6.08535	0.289124	0.144562	+	0.989496i	$0.453823\pi$
$444$	−6.03486	−0.286402
$445$	−39.6947	−1.88171
$446$	−20.8521	−0.987375
$447$	8.58234	0.405931
$448$	−7.26783	−0.343373
$449$	13.8408	0.653188	0.326594	−	0.945165i	$-0.394099\pi$
$449$	13.8408	0.653188	0.326594	+	0.945165i	$0.394099\pi$
$450$	−4.37117	−0.206059
$451$	−38.7645	−1.82535
$452$	0.519131	0.0244178
$453$	4.36382	0.205030
$454$	−20.5047	−0.962335
$455$	−3.04739	−0.142864
$456$	−17.2322	−0.806972
$457$	2.79873	0.130919	0.0654596	−	0.997855i	$-0.479149\pi$
$457$	2.79873	0.130919	0.0654596	+	0.997855i	$0.479149\pi$
$458$	1.05195	0.0491546
$459$	1.00000	0.0466760
$460$	−17.9028	−0.834720
$461$	0.284953	0.0132716	0.00663578	−	0.999978i	$-0.497888\pi$
$461$	0.284953	0.0132716	0.00663578	+	0.999978i	$0.497888\pi$
$462$	4.18926	0.194902
$463$	23.1113	1.07407	0.537036	−	0.843559i	$-0.319544\pi$
$463$	23.1113	1.07407	0.537036	+	0.843559i	$0.319544\pi$
$464$	7.47764	0.347141
$465$	15.0266	0.696841
$466$	23.5974	1.09313
$467$	−40.4090	−1.86990	−0.934952	−	0.354774i	$-0.884558\pi$
$467$	−40.4090	−1.86990	−0.934952	+	0.354774i	$0.884558\pi$
$468$	−0.960160	−0.0443834
$469$	9.32671	0.430668
$470$	−16.9862	−0.783514
$471$	−3.37083	−0.155320
$472$	35.3866	1.62880
$473$	−18.7024	−0.859935
$474$	−9.12102	−0.418942
$475$	24.4713	1.12282
$476$	−0.960160	−0.0440089
$477$	−9.16383	−0.419583
$478$	4.65854	0.213077
$479$	27.2984	1.24729	0.623647	−	0.781706i	$-0.285650\pi$
$479$	27.2984	1.24729	0.623647	+	0.781706i	$0.285650\pi$
$480$	14.7996	0.675508
$481$	−6.28527	−0.286583
$482$	−7.83170	−0.356724
$483$	6.11854	0.278403
$484$	−5.64331	−0.256514
$485$	21.8766	0.993365
$486$	1.01973	0.0462557
$487$	10.5024	0.475910	0.237955	−	0.971276i	$-0.423523\pi$
$487$	10.5024	0.475910	0.237955	+	0.971276i	$0.423523\pi$
$488$	38.7796	1.75547
$489$	12.9503	0.585633
$490$	−3.10751	−0.140383
$491$	17.4075	0.785591	0.392795	−	0.919626i	$-0.371508\pi$
$491$	17.4075	0.785591	0.392795	+	0.919626i	$0.371508\pi$
$492$	9.05993	0.408453
$493$	6.45864	0.290883
$494$	−5.82138	−0.261916
$495$	−12.5194	−0.562704
$496$	5.70894	0.256339
$497$	−12.9646	−0.581540
$498$	−0.126005	−0.00564640
$499$	−13.8948	−0.622016	−0.311008	−	0.950407i	$-0.600667\pi$
$499$	−13.8948	−0.622016	−0.311008	+	0.950407i	$0.600667\pi$
$500$	2.08736	0.0933494
$501$	6.89221	0.307921
$502$	−21.2932	−0.950362
$503$	−15.5633	−0.693932	−0.346966	−	0.937878i	$-0.612788\pi$
$503$	−15.5633	−0.693932	−0.346966	+	0.937878i	$0.612788\pi$
$504$	−3.01855	−0.134457
$505$	−28.2152	−1.25556
$506$	25.6321	1.13949
$507$	−1.00000	−0.0444116
$508$	−13.6684	−0.606439
$509$	28.2171	1.25070	0.625350	−	0.780344i	$-0.284956\pi$
$509$	28.2171	1.25070	0.625350	+	0.780344i	$0.284956\pi$
$510$	−3.10751	−0.137603
$511$	6.05786	0.267984
$512$	12.6123	0.557390
$513$	−5.70877	−0.252048
$514$	8.97779	0.395993
$515$	52.8193	2.32750
$516$	4.37105	0.192425
$517$	−22.4563	−0.987625
$518$	−6.40925	−0.281606
$519$	16.1733	0.709929
$520$	9.19872	0.403390
$521$	−5.50530	−0.241192	−0.120596	−	0.992702i	$-0.538481\pi$
$521$	−5.50530	−0.241192	−0.120596	+	0.992702i	$0.538481\pi$
$522$	6.58604	0.288263
$523$	−8.69041	−0.380005	−0.190003	−	0.981784i	$-0.560850\pi$
$523$	−8.69041	−0.380005	−0.190003	+	0.981784i	$0.560850\pi$
$524$	−18.4784	−0.807231
$525$	4.28661	0.187083
$526$	−7.49116	−0.326630
$527$	4.93096	0.214796
$528$	−4.75639	−0.206995
$529$	14.4365	0.627673
$530$	28.4767	1.23695
$531$	11.7230	0.508737
$532$	5.48133	0.237646
$533$	9.43585	0.408712
$534$	−13.2827	−0.574799
$535$	29.0781	1.25716
$536$	−28.1532	−1.21603
$537$	6.69912	0.289088
$538$	1.27876	0.0551312
$539$	−4.10822	−0.176954
$540$	2.92599	0.125914
$541$	−17.4991	−0.752343	−0.376172	−	0.926550i	$-0.622760\pi$
$541$	−17.4991	−0.752343	−0.376172	+	0.926550i	$0.622760\pi$
$542$	−30.2289	−1.29844
$543$	−16.4953	−0.707881
$544$	4.85649	0.208220
$545$	−36.4316	−1.56056
$546$	−1.01973	−0.0436402
$547$	30.0404	1.28443	0.642217	−	0.766523i	$-0.278015\pi$
$547$	30.0404	1.28443	0.642217	+	0.766523i	$0.278015\pi$
$548$	−12.8203	−0.547655
$549$	12.8471	0.548301
$550$	17.9577	0.765720
$551$	−36.8709	−1.57075
$552$	−18.4691	−0.786098
$553$	8.94458	0.380362
$554$	−18.0548	−0.767076
$555$	19.1537	0.813029
$556$	14.8964	0.631748
$557$	−35.3695	−1.49865	−0.749326	−	0.662201i	$-0.769622\pi$
$557$	−35.3695	−1.49865	−0.749326	+	0.662201i	$0.769622\pi$
$558$	5.02823	0.212862
$559$	4.55242	0.192547
$560$	3.52819	0.149093
$561$	−4.10822	−0.173449
$562$	−12.7334	−0.537126
$563$	34.6086	1.45858	0.729289	−	0.684206i	$-0.239851\pi$
$563$	34.6086	1.45858	0.729289	+	0.684206i	$0.239851\pi$
$564$	5.24840	0.220998
$565$	−1.64764	−0.0693166
$566$	2.14556	0.0901847
$567$	−1.00000	−0.0419961
$568$	39.1342	1.64203
$569$	−2.96706	−0.124385	−0.0621927	−	0.998064i	$-0.519809\pi$
$569$	−2.96706	−0.124385	−0.0621927	+	0.998064i	$0.519809\pi$
$570$	17.7400	0.743048
$571$	43.4647	1.81894	0.909471	−	0.415768i	$-0.136487\pi$
$571$	43.4647	1.81894	0.909471	+	0.415768i	$0.136487\pi$
$572$	3.94455	0.164930
$573$	5.58176	0.233182
$574$	9.62198	0.401614
$575$	26.2278	1.09378
$576$	7.26783	0.302826
$577$	−22.9148	−0.953957	−0.476979	−	0.878915i	$-0.658268\pi$
$577$	−22.9148	−0.953957	−0.476979	+	0.878915i	$0.658268\pi$
$578$	−1.01973	−0.0424150
$579$	−11.9218	−0.495453
$580$	18.8979	0.784692
$581$	0.123567	0.00512643
$582$	7.32039	0.303440
$583$	37.6470	1.55918
$584$	−18.2860	−0.756679
$585$	3.04739	0.125994
$586$	−32.8350	−1.35640
$587$	−27.7721	−1.14628	−0.573138	−	0.819459i	$-0.694274\pi$
$587$	−27.7721	−1.14628	−0.573138	+	0.819459i	$0.694274\pi$
$588$	0.960160	0.0395963
$589$	−28.1497	−1.15989
$590$	−36.4294	−1.49978
$591$	6.99400	0.287695
$592$	7.27691	0.299079
$593$	15.8803	0.652124	0.326062	−	0.945348i	$-0.394278\pi$
$593$	15.8803	0.652124	0.326062	+	0.945348i	$0.394278\pi$
$594$	−4.18926	−0.171887
$595$	3.04739	0.124931
$596$	8.24042	0.337541
$597$	−5.26504	−0.215484
$598$	−6.23923	−0.255141
$599$	44.5535	1.82041	0.910204	−	0.414161i	$-0.135925\pi$
$599$	44.5535	1.82041	0.910204	+	0.414161i	$0.135925\pi$
$600$	−12.9394	−0.528247
$601$	−4.67478	−0.190688	−0.0953441	−	0.995444i	$-0.530395\pi$
$601$	−4.67478	−0.190688	−0.0953441	+	0.995444i	$0.530395\pi$
$602$	4.64222	0.189203
$603$	−9.32671	−0.379813
$604$	4.18996	0.170487
$605$	17.9110	0.728184
$606$	−9.44144	−0.383532
$607$	−1.37975	−0.0560023	−0.0280012	−	0.999608i	$-0.508914\pi$
$607$	−1.37975	−0.0560023	−0.0280012	+	0.999608i	$0.508914\pi$
$608$	−27.7246	−1.12438
$609$	−6.45864	−0.261717
$610$	−39.9224	−1.61641
$611$	5.46618	0.221138
$612$	0.960160	0.0388122
$613$	11.3704	0.459247	0.229624	−	0.973279i	$-0.426250\pi$
$613$	11.3704	0.459247	0.229624	+	0.973279i	$0.426250\pi$
$614$	−9.89727	−0.399421
$615$	−28.7548	−1.15950
$616$	12.4009	0.499645
$617$	−16.4096	−0.660625	−0.330312	−	0.943872i	$-0.607154\pi$
$617$	−16.4096	−0.660625	−0.330312	+	0.943872i	$0.607154\pi$
$618$	17.6745	0.710973
$619$	−3.97555	−0.159791	−0.0798953	−	0.996803i	$-0.525459\pi$
$619$	−3.97555	−0.159791	−0.0798953	+	0.996803i	$0.525459\pi$
$620$	14.4279	0.579440
$621$	−6.11854	−0.245528
$622$	−13.3690	−0.536046
$623$	13.0258	0.521867
$624$	1.15777	0.0463480
$625$	−28.0580	−1.12232
$626$	−34.0420	−1.36059
$627$	23.4529	0.936617
$628$	−3.23654	−0.129152
$629$	6.28527	0.250610
$630$	3.10751	0.123806
$631$	34.2923	1.36515	0.682577	−	0.730814i	$-0.260859\pi$
$631$	34.2923	1.36515	0.682577	+	0.730814i	$0.260859\pi$
$632$	−26.9997	−1.07399
$633$	6.67798	0.265426
$634$	−13.5518	−0.538211
$635$	43.3815	1.72154
$636$	−8.79874	−0.348893
$637$	1.00000	0.0396214
$638$	−27.0569	−1.07119
$639$	12.9646	0.512870
$640$	7.01445	0.277270
$641$	−14.9030	−0.588632	−0.294316	−	0.955708i	$-0.595092\pi$
$641$	−14.9030	−0.588632	−0.294316	+	0.955708i	$0.595092\pi$
$642$	9.73017	0.384019
$643$	−20.5684	−0.811139	−0.405570	−	0.914064i	$-0.632927\pi$
$643$	−20.5684	−0.811139	−0.405570	+	0.914064i	$0.632927\pi$
$644$	5.87477	0.231498
$645$	−13.8730	−0.546250
$646$	5.82138	0.229039
$647$	−16.7497	−0.658500	−0.329250	−	0.944243i	$-0.606796\pi$
$647$	−16.7497	−0.658500	−0.329250	+	0.944243i	$0.606796\pi$
$648$	3.01855	0.118580
$649$	−48.1608	−1.89048
$650$	−4.37117	−0.171451
$651$	−4.93096	−0.193260
$652$	12.4344	0.486967
$653$	−38.6239	−1.51147	−0.755734	−	0.654879i	$-0.772720\pi$
$653$	−38.6239	−1.51147	−0.755734	+	0.654879i	$0.772720\pi$
$654$	−12.1908	−0.476698
$655$	58.6474	2.29154
$656$	−10.9246	−0.426533
$657$	−6.05786	−0.236340
$658$	5.57400	0.217297
$659$	0.593370	0.0231144	0.0115572	−	0.999933i	$-0.496321\pi$
$659$	0.593370	0.0231144	0.0115572	+	0.999933i	$0.496321\pi$
$660$	−12.0206	−0.467901
$661$	19.7601	0.768578	0.384289	−	0.923213i	$-0.374447\pi$
$661$	19.7601	0.768578	0.384289	+	0.923213i	$0.374447\pi$
$662$	−15.2460	−0.592552
$663$	1.00000	0.0388368
$664$	−0.372994	−0.0144750
$665$	−17.3969	−0.674622
$666$	6.40925	0.248353
$667$	−39.5174	−1.53012
$668$	6.61762	0.256043
$669$	−20.4487	−0.790594
$670$	28.9828	1.11970
$671$	−52.7787	−2.03750
$672$	−4.85649	−0.187343
$673$	−13.8157	−0.532557	−0.266279	−	0.963896i	$-0.585794\pi$
$673$	−13.8157	−0.532557	−0.266279	+	0.963896i	$0.585794\pi$
$674$	−17.3161	−0.666992
$675$	−4.28661	−0.164992
$676$	−0.960160	−0.0369292
$677$	13.4668	0.517572	0.258786	−	0.965935i	$-0.416678\pi$
$677$	13.4668	0.517572	0.258786	+	0.965935i	$0.416678\pi$
$678$	−0.551336	−0.0211739
$679$	−7.17879	−0.275497
$680$	−9.19872	−0.352755
$681$	−20.1081	−0.770544
$682$	−20.6571	−0.791000
$683$	34.9511	1.33737	0.668684	−	0.743547i	$-0.266858\pi$
$683$	34.9511	1.33737	0.668684	+	0.743547i	$0.266858\pi$
$684$	−5.48133	−0.209584
$685$	40.6895	1.55467
$686$	1.01973	0.0389333
$687$	1.03161	0.0393582
$688$	−5.27067	−0.200943
$689$	−9.16383	−0.349114
$690$	19.0134	0.723827
$691$	−16.3504	−0.621997	−0.310998	−	0.950410i	$-0.600663\pi$
$691$	−16.3504	−0.621997	−0.310998	+	0.950410i	$0.600663\pi$
$692$	15.5290	0.590323
$693$	4.10822	0.156058
$694$	10.3453	0.392702
$695$	−47.2788	−1.79339
$696$	19.4957	0.738984
$697$	−9.43585	−0.357408
$698$	−27.8172	−1.05290
$699$	23.1409	0.875269
$700$	4.11584	0.155564
$701$	51.1292	1.93112	0.965562	−	0.260174i	$-0.0837799\pi$
$701$	51.1292	1.93112	0.965562	+	0.260174i	$0.0837799\pi$
$702$	1.01973	0.0384871
$703$	−35.8811	−1.35328
$704$	−29.8579	−1.12531
$705$	−16.6576	−0.627362
$706$	−20.3536	−0.766016
$707$	9.25880	0.348213
$708$	11.2560	0.423026
$709$	−2.52444	−0.0948072	−0.0474036	−	0.998876i	$-0.515095\pi$
$709$	−2.52444	−0.0948072	−0.0474036	+	0.998876i	$0.515095\pi$
$710$	−40.2875	−1.51196
$711$	−8.94458	−0.335448
$712$	−39.3190	−1.47354
$713$	−30.1703	−1.12989
$714$	1.01973	0.0381623
$715$	−12.5194	−0.468198
$716$	6.43223	0.240384
$717$	4.56842	0.170611
$718$	8.21355	0.306527
$719$	−11.4799	−0.428127	−0.214063	−	0.976820i	$-0.568670\pi$
$719$	−11.4799	−0.428127	−0.214063	+	0.976820i	$0.568670\pi$
$720$	−3.52819	−0.131488
$721$	−17.3326	−0.645500
$722$	−13.8581	−0.515745
$723$	−7.68021	−0.285630
$724$	−15.8381	−0.588619
$725$	−27.6857	−1.02822
$726$	5.99340	0.222436
$727$	10.8951	0.404075	0.202038	−	0.979378i	$-0.435244\pi$
$727$	10.8951	0.404075	0.202038	+	0.979378i	$0.435244\pi$
$728$	−3.01855	−0.111875
$729$	1.00000	0.0370370
$730$	18.8248	0.696739
$731$	−4.55242	−0.168377
$732$	12.3353	0.455925
$733$	−29.2015	−1.07858	−0.539290	−	0.842120i	$-0.681307\pi$
$733$	−29.2015	−1.07858	−0.539290	+	0.842120i	$0.681307\pi$
$734$	−1.76535	−0.0651603
$735$	−3.04739	−0.112405
$736$	−29.7146	−1.09530
$737$	38.3162	1.41139
$738$	−9.62198	−0.354190
$739$	14.9488	0.549901	0.274950	−	0.961458i	$-0.411339\pi$
$739$	14.9488	0.549901	0.274950	+	0.961458i	$0.411339\pi$
$740$	18.3906	0.676052
$741$	−5.70877	−0.209717
$742$	−9.34459	−0.343051
$743$	20.4695	0.750954	0.375477	−	0.926832i	$-0.377479\pi$
$743$	20.4695	0.750954	0.375477	+	0.926832i	$0.377479\pi$
$744$	14.8844	0.545687
$745$	−26.1538	−0.958200
$746$	15.8220	0.579284
$747$	−0.123567	−0.00452109
$748$	−3.94455	−0.144227
$749$	−9.54195	−0.348655
$750$	−2.21685	−0.0809479
$751$	7.92734	0.289273	0.144636	−	0.989485i	$-0.453799\pi$
$751$	7.92734	0.289273	0.144636	+	0.989485i	$0.453799\pi$
$752$	−6.32859	−0.230780
$753$	−20.8813	−0.760957
$754$	6.58604	0.239849
$755$	−13.2983	−0.483974
$756$	−0.960160	−0.0349207
$757$	29.9446	1.08835	0.544177	−	0.838970i	$-0.316842\pi$
$757$	29.9446	1.08835	0.544177	+	0.838970i	$0.316842\pi$
$758$	10.8306	0.393385
$759$	25.1363	0.912389
$760$	52.5133	1.90486
$761$	−47.9792	−1.73924	−0.869622	−	0.493718i	$-0.835638\pi$
$761$	−47.9792	−1.73924	−0.869622	+	0.493718i	$0.835638\pi$
$762$	14.5164	0.525874
$763$	11.9550	0.432800
$764$	5.35939	0.193896
$765$	−3.04739	−0.110179
$766$	−23.0526	−0.832925
$767$	11.7230	0.423295
$768$	16.8829	0.609208
$769$	19.0369	0.686489	0.343245	−	0.939246i	$-0.388474\pi$
$769$	19.0369	0.686489	0.343245	+	0.939246i	$0.388474\pi$
$770$	−12.7663	−0.460066
$771$	8.80412	0.317073
$772$	−11.4468	−0.411980
$773$	−48.9945	−1.76221	−0.881106	−	0.472920i	$-0.843200\pi$
$773$	−48.9945	−1.76221	−0.881106	+	0.472920i	$0.843200\pi$
$774$	−4.64222	−0.166861
$775$	−21.1371	−0.759268
$776$	21.6695	0.777891
$777$	−6.28527	−0.225483
$778$	10.0216	0.359291
$779$	53.8671	1.92999
$780$	2.92599	0.104767
$781$	−53.2613	−1.90584
$782$	6.23923	0.223114
$783$	6.45864	0.230813
$784$	−1.15777	−0.0413490
$785$	10.2723	0.366633
$786$	19.6247	0.699990
$787$	24.8504	0.885820	0.442910	−	0.896566i	$-0.353946\pi$
$787$	24.8504	0.885820	0.442910	+	0.896566i	$0.353946\pi$
$788$	6.71536	0.239225
$789$	−7.34625	−0.261533
$790$	27.7953	0.988914
$791$	0.540671	0.0192240
$792$	−12.4009	−0.440646
$793$	12.8471	0.456214
$794$	−23.8300	−0.845695
$795$	27.9258	0.990426
$796$	−5.05528	−0.179180
$797$	−50.0128	−1.77155	−0.885773	−	0.464119i	$-0.846371\pi$
$797$	−50.0128	−1.77155	−0.885773	+	0.464119i	$0.846371\pi$
$798$	−5.82138	−0.206074
$799$	−5.46618	−0.193379
$800$	−20.8179	−0.736024
$801$	−13.0258	−0.460243
$802$	35.0726	1.23845
$803$	24.8870	0.878244
$804$	−8.95514	−0.315823
$805$	−18.6456	−0.657171
$806$	5.02823	0.177112
$807$	1.25402	0.0441437
$808$	−27.9482	−0.983213
$809$	25.3897	0.892655	0.446328	−	0.894870i	$-0.352732\pi$
$809$	25.3897	0.892655	0.446328	+	0.894870i	$0.352732\pi$
$810$	−3.10751	−0.109187
$811$	49.8521	1.75054	0.875271	−	0.483632i	$-0.160683\pi$
$811$	49.8521	1.75054	0.875271	+	0.483632i	$0.160683\pi$
$812$	−6.20133	−0.217624
$813$	−29.6442	−1.03967
$814$	−26.3306	−0.922887
$815$	−39.4647	−1.38239
$816$	−1.15777	−0.0405302
$817$	25.9887	0.909230
$818$	−18.9375	−0.662134
$819$	−1.00000	−0.0349428
$820$	−27.6092	−0.964154
$821$	−9.45571	−0.330007	−0.165003	−	0.986293i	$-0.552763\pi$
$821$	−9.45571	−0.330007	−0.165003	+	0.986293i	$0.552763\pi$
$822$	13.6156	0.474899
$823$	−3.14006	−0.109456	−0.0547278	−	0.998501i	$-0.517429\pi$
$823$	−3.14006	−0.109456	−0.0547278	+	0.998501i	$0.517429\pi$
$824$	52.3194	1.82263
$825$	17.6104	0.613114
$826$	11.9543	0.415943
$827$	−23.8379	−0.828926	−0.414463	−	0.910066i	$-0.636031\pi$
$827$	−23.8379	−0.828926	−0.414463	+	0.910066i	$0.636031\pi$
$828$	−5.87477	−0.204162
$829$	−12.2046	−0.423884	−0.211942	−	0.977282i	$-0.567979\pi$
$829$	−12.2046	−0.423884	−0.211942	+	0.977282i	$0.567979\pi$
$830$	0.383986	0.0133283
$831$	−17.7056	−0.614200
$832$	7.26783	0.251967
$833$	−1.00000	−0.0346479
$834$	−15.8205	−0.547821
$835$	−21.0033	−0.726848
$836$	22.5185	0.778819
$837$	4.93096	0.170439
$838$	13.0983	0.452475
$839$	−21.1222	−0.729219	−0.364609	−	0.931161i	$-0.618797\pi$
$839$	−21.1222	−0.729219	−0.364609	+	0.931161i	$0.618797\pi$
$840$	9.19872	0.317386
$841$	12.7140	0.438415
$842$	−15.8532	−0.546337
$843$	−12.4871	−0.430078
$844$	6.41192	0.220708
$845$	3.04739	0.104834
$846$	−5.57400	−0.191638
$847$	−5.87747	−0.201952
$848$	10.6096	0.364336
$849$	2.10406	0.0722111
$850$	4.37117	0.149930
$851$	−38.4566	−1.31828
$852$	12.4481	0.426463
$853$	5.42457	0.185734	0.0928669	−	0.995679i	$-0.470397\pi$
$853$	5.42457	0.185734	0.0928669	+	0.995679i	$0.470397\pi$
$854$	13.1005	0.448290
$855$	17.3969	0.594960
$856$	28.8029	0.984462
$857$	−24.2252	−0.827517	−0.413758	−	0.910387i	$-0.635784\pi$
$857$	−24.2252	−0.827517	−0.413758	+	0.910387i	$0.635784\pi$
$858$	−4.18926	−0.143019
$859$	21.2706	0.725743	0.362872	−	0.931839i	$-0.381796\pi$
$859$	21.2706	0.725743	0.362872	+	0.931839i	$0.381796\pi$
$860$	−13.3203	−0.454219
$861$	9.43585	0.321573
$862$	12.2780	0.418190
$863$	−33.9498	−1.15566	−0.577832	−	0.816156i	$-0.696101\pi$
$863$	−33.9498	−1.15566	−0.577832	+	0.816156i	$0.696101\pi$
$864$	4.85649	0.165221
$865$	−49.2865	−1.67579
$866$	−17.0288	−0.578662
$867$	−1.00000	−0.0339618
$868$	−4.73451	−0.160700
$869$	36.7463	1.24653
$870$	−20.0703	−0.680446
$871$	−9.32671	−0.316024
$872$	−36.0867	−1.22205
$873$	7.17879	0.242965
$874$	−35.6183	−1.20481
$875$	2.17397	0.0734935
$876$	−5.81652	−0.196522
$877$	−29.7781	−1.00554	−0.502768	−	0.864421i	$-0.667685\pi$
$877$	−29.7781	−1.00554	−0.502768	+	0.864421i	$0.667685\pi$
$878$	−24.6485	−0.831847
$879$	−32.1999	−1.08608
$880$	14.4946	0.488612
$881$	44.7059	1.50618	0.753090	−	0.657918i	$-0.228563\pi$
$881$	44.7059	1.50618	0.753090	+	0.657918i	$0.228563\pi$
$882$	−1.01973	−0.0343359
$883$	−53.9398	−1.81522	−0.907609	−	0.419817i	$-0.862094\pi$
$883$	−53.9398	−1.81522	−0.907609	+	0.419817i	$0.862094\pi$
$884$	0.960160	0.0322937
$885$	−35.7247	−1.20087
$886$	−6.20539	−0.208474
$887$	−28.2212	−0.947575	−0.473787	−	0.880639i	$-0.657113\pi$
$887$	−28.2212	−0.947575	−0.473787	+	0.880639i	$0.657113\pi$
$888$	18.9724	0.636672
$889$	−14.2356	−0.477447
$890$	40.4777	1.35681
$891$	−4.10822	−0.137631
$892$	−19.6341	−0.657397
$893$	31.2051	1.04424
$894$	−8.75163	−0.292698
$895$	−20.4149	−0.682394
$896$	−2.30179	−0.0768973
$897$	−6.11854	−0.204292
$898$	−14.1138	−0.470985
$899$	31.8473	1.06217
$900$	−4.11584	−0.137195
$901$	9.16383	0.305291
$902$	39.5292	1.31618
$903$	4.55242	0.151495
$904$	−1.63204	−0.0542809
$905$	50.2677	1.67095
$906$	−4.44989	−0.147838
$907$	−57.8856	−1.92206	−0.961030	−	0.276444i	$-0.910844\pi$
$907$	−57.8856	−1.92206	−0.961030	+	0.276444i	$0.910844\pi$
$908$	−19.3070	−0.640725
$909$	−9.25880	−0.307095
$910$	3.10751	0.103013
$911$	9.43535	0.312607	0.156303	−	0.987709i	$-0.450042\pi$
$911$	9.43535	0.312607	0.156303	+	0.987709i	$0.450042\pi$
$912$	6.60946	0.218861
$913$	0.507641	0.0168005
$914$	−2.85394	−0.0943998
$915$	−39.1502	−1.29427
$916$	0.990506	0.0327272
$917$	−19.2451	−0.635529
$918$	−1.01973	−0.0336560
$919$	−34.1980	−1.12809	−0.564044	−	0.825745i	$-0.690755\pi$
$919$	−34.1980	−1.12809	−0.564044	+	0.825745i	$0.690755\pi$
$920$	56.2827	1.85558
$921$	−9.70581	−0.319817
$922$	−0.290573	−0.00956952
$923$	12.9646	0.426734
$924$	3.94455	0.129766
$925$	−26.9425	−0.885864
$926$	−23.5672	−0.774465
$927$	17.3326	0.569278
$928$	31.3663	1.02965
$929$	−47.0160	−1.54254	−0.771272	−	0.636505i	$-0.780379\pi$
$929$	−47.0160	−1.54254	−0.771272	+	0.636505i	$0.780379\pi$
$930$	−15.3230	−0.502461
$931$	5.70877	0.187097
$932$	22.2190	0.727806
$933$	−13.1103	−0.429213
$934$	41.2061	1.34830
$935$	12.5194	0.409427
$936$	3.01855	0.0986644
$937$	20.4248	0.667249	0.333624	−	0.942706i	$-0.391728\pi$
$937$	20.4248	0.667249	0.333624	+	0.942706i	$0.391728\pi$
$938$	−9.51069	−0.310535
$939$	−33.3835	−1.08943
$940$	−15.9940	−0.521665
$941$	35.5226	1.15800	0.579002	−	0.815326i	$-0.303442\pi$
$941$	35.5226	1.15800	0.579002	+	0.815326i	$0.303442\pi$
$942$	3.43732	0.111994
$943$	57.7336	1.88006
$944$	−13.5726	−0.441751
$945$	3.04739	0.0991318
$946$	19.0713	0.620060
$947$	−51.3600	−1.66898	−0.834488	−	0.551026i	$-0.814236\pi$
$947$	−51.3600	−1.66898	−0.834488	+	0.551026i	$0.814236\pi$
$948$	−8.58823	−0.278933
$949$	−6.05786	−0.196647
$950$	−24.9540	−0.809614
$951$	−13.2897	−0.430947
$952$	3.01855	0.0978318
$953$	−34.0937	−1.10440	−0.552201	−	0.833711i	$-0.686212\pi$
$953$	−34.0937	−1.10440	−0.552201	+	0.833711i	$0.686212\pi$
$954$	9.34459	0.302542
$955$	−17.0098	−0.550426
$956$	4.38642	0.141867
$957$	−26.5335	−0.857707
$958$	−27.8368	−0.899367
$959$	−13.3522	−0.431166
$960$	−22.1480	−0.714822
$961$	−6.68561	−0.215665
$962$	6.40925	0.206642
$963$	9.54195	0.307485
$964$	−7.37423	−0.237508
$965$	36.3304	1.16952
$966$	−6.23923	−0.200744
$967$	−28.8577	−0.928002	−0.464001	−	0.885835i	$-0.653587\pi$
$967$	−28.8577	−0.928002	−0.464001	+	0.885835i	$0.653587\pi$
$968$	17.7414	0.570231
$969$	5.70877	0.183392
$970$	−22.3081	−0.716271
$971$	−27.4754	−0.881728	−0.440864	−	0.897574i	$-0.645328\pi$
$971$	−27.4754	−0.881728	−0.440864	+	0.897574i	$0.645328\pi$
$972$	0.960160	0.0307971
$973$	15.5145	0.497372
$974$	−10.7096	−0.343157
$975$	−4.28661	−0.137282
$976$	−14.8740	−0.476106
$977$	12.5465	0.401398	0.200699	−	0.979653i	$-0.435679\pi$
$977$	12.5465	0.401398	0.200699	+	0.979653i	$0.435679\pi$
$978$	−13.2057	−0.422273
$979$	53.5127	1.71027
$980$	−2.92599	−0.0934672
$981$	−11.9550	−0.381693
$982$	−17.7509	−0.566454
$983$	−6.04770	−0.192892	−0.0964458	−	0.995338i	$-0.530747\pi$
$983$	−6.04770	−0.192892	−0.0964458	+	0.995338i	$0.530747\pi$
$984$	−28.4826	−0.907992
$985$	−21.3135	−0.679104
$986$	−6.58604	−0.209742
$987$	5.46618	0.173990
$988$	−5.48133	−0.174384
$989$	27.8542	0.885711
$990$	12.7663	0.405740
$991$	39.9693	1.26967	0.634833	−	0.772649i	$-0.281069\pi$
$991$	39.9693	1.26967	0.634833	+	0.772649i	$0.281069\pi$
$992$	23.9472	0.760323
$993$	−14.9511	−0.474458
$994$	13.2203	0.419322
$995$	16.0447	0.508650
$996$	−0.118644	−0.00375939
$997$	0.564468	0.0178769	0.00893844	−	0.999960i	$-0.497155\pi$
$997$	0.564468	0.0178769	0.00893844	+	0.999960i	$0.497155\pi$
$998$	14.1689	0.448507
$999$	6.28527	0.198857

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4641.2.a.ba.1.6	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4641.2.a.ba.1.6	✓	17	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:	\( N \)	\(=\)	\( 4641 = 3 \cdot 7 \cdot 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4641.a (trivial)

\(f(q)\)	\(=\)	\(q-1.01973 q^{2} -1.00000 q^{3} -0.960160 q^{4} +3.04739 q^{5} +1.01973 q^{6} -1.00000 q^{7} +3.01855 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.01973 q^{2} -1.00000 q^{3} -0.960160 q^{4} +3.04739 q^{5} +1.01973 q^{6} -1.00000 q^{7} +3.01855 q^{8} +1.00000 q^{9} -3.10751 q^{10} -4.10822 q^{11} +0.960160 q^{12} +1.00000 q^{13} +1.01973 q^{14} -3.04739 q^{15} -1.15777 q^{16} -1.00000 q^{17} -1.01973 q^{18} +5.70877 q^{19} -2.92599 q^{20} +1.00000 q^{21} +4.18926 q^{22} +6.11854 q^{23} -3.01855 q^{24} +4.28661 q^{25} -1.01973 q^{26} -1.00000 q^{27} +0.960160 q^{28} -6.45864 q^{29} +3.10751 q^{30} -4.93096 q^{31} -4.85649 q^{32} +4.10822 q^{33} +1.01973 q^{34} -3.04739 q^{35} -0.960160 q^{36} -6.28527 q^{37} -5.82138 q^{38} -1.00000 q^{39} +9.19872 q^{40} +9.43585 q^{41} -1.01973 q^{42} +4.55242 q^{43} +3.94455 q^{44} +3.04739 q^{45} -6.23923 q^{46} +5.46618 q^{47} +1.15777 q^{48} +1.00000 q^{49} -4.37117 q^{50} +1.00000 q^{51} -0.960160 q^{52} -9.16383 q^{53} +1.01973 q^{54} -12.5194 q^{55} -3.01855 q^{56} -5.70877 q^{57} +6.58604 q^{58} +11.7230 q^{59} +2.92599 q^{60} +12.8471 q^{61} +5.02823 q^{62} -1.00000 q^{63} +7.26783 q^{64} +3.04739 q^{65} -4.18926 q^{66} -9.32671 q^{67} +0.960160 q^{68} -6.11854 q^{69} +3.10751 q^{70} +12.9646 q^{71} +3.01855 q^{72} -6.05786 q^{73} +6.40925 q^{74} -4.28661 q^{75} -5.48133 q^{76} +4.10822 q^{77} +1.01973 q^{78} -8.94458 q^{79} -3.52819 q^{80} +1.00000 q^{81} -9.62198 q^{82} -0.123567 q^{83} -0.960160 q^{84} -3.04739 q^{85} -4.64222 q^{86} +6.45864 q^{87} -12.4009 q^{88} -13.0258 q^{89} -3.10751 q^{90} -1.00000 q^{91} -5.87477 q^{92} +4.93096 q^{93} -5.57400 q^{94} +17.3969 q^{95} +4.85649 q^{96} +7.17879 q^{97} -1.01973 q^{98} -4.10822 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + q^{2} - 17 q^{3} + 25 q^{4} - 4 q^{5} - q^{6} - 17 q^{7} + 6 q^{8} + 17 q^{9}+O(q^{10}) \) 17 * q + q^2 - 17 * q^3 + 25 * q^4 - 4 * q^5 - q^6 - 17 * q^7 + 6 * q^8 + 17 * q^9	\( 17 q + q^{2} - 17 q^{3} + 25 q^{4} - 4 q^{5} - q^{6} - 17 q^{7} + 6 q^{8} + 17 q^{9} - q^{10} + 4 q^{11} - 25 q^{12} + 17 q^{13} - q^{14} + 4 q^{15} + 53 q^{16} - 17 q^{17} + q^{18} + 13 q^{19} - 5 q^{20} + 17 q^{21} + 4 q^{22} + 8 q^{23} - 6 q^{24} + 37 q^{25} + q^{26} - 17 q^{27} - 25 q^{28} - 3 q^{29} + q^{30} + 10 q^{31} + 18 q^{32} - 4 q^{33} - q^{34} + 4 q^{35} + 25 q^{36} - 25 q^{38} - 17 q^{39} - 12 q^{41} + q^{42} + 29 q^{43} + 12 q^{44} - 4 q^{45} + 19 q^{46} - 4 q^{47} - 53 q^{48} + 17 q^{49} + 9 q^{50} + 17 q^{51} + 25 q^{52} - 8 q^{53} - q^{54} + 27 q^{55} - 6 q^{56} - 13 q^{57} + 2 q^{58} + 25 q^{59} + 5 q^{60} - 5 q^{61} - 37 q^{62} - 17 q^{63} + 94 q^{64} - 4 q^{65} - 4 q^{66} + 15 q^{67} - 25 q^{68} - 8 q^{69} + q^{70} + 32 q^{71} + 6 q^{72} - 15 q^{73} + 16 q^{74} - 37 q^{75} + 3 q^{76} - 4 q^{77} - q^{78} + 27 q^{79} + 41 q^{80} + 17 q^{81} - 8 q^{82} - 24 q^{83} + 25 q^{84} + 4 q^{85} + 53 q^{86} + 3 q^{87} - 9 q^{88} - 8 q^{89} - q^{90} - 17 q^{91} + 14 q^{92} - 10 q^{93} + 51 q^{94} - 9 q^{95} - 18 q^{96} - 22 q^{97} + q^{98} + 4 q^{99}+O(q^{100}) \) 17 * q + q^2 - 17 * q^3 + 25 * q^4 - 4 * q^5 - q^6 - 17 * q^7 + 6 * q^8 + 17 * q^9 - q^10 + 4 * q^11 - 25 * q^12 + 17 * q^13 - q^14 + 4 * q^15 + 53 * q^16 - 17 * q^17 + q^18 + 13 * q^19 - 5 * q^20 + 17 * q^21 + 4 * q^22 + 8 * q^23 - 6 * q^24 + 37 * q^25 + q^26 - 17 * q^27 - 25 * q^28 - 3 * q^29 + q^30 + 10 * q^31 + 18 * q^32 - 4 * q^33 - q^34 + 4 * q^35 + 25 * q^36 - 25 * q^38 - 17 * q^39 - 12 * q^41 + q^42 + 29 * q^43 + 12 * q^44 - 4 * q^45 + 19 * q^46 - 4 * q^47 - 53 * q^48 + 17 * q^49 + 9 * q^50 + 17 * q^51 + 25 * q^52 - 8 * q^53 - q^54 + 27 * q^55 - 6 * q^56 - 13 * q^57 + 2 * q^58 + 25 * q^59 + 5 * q^60 - 5 * q^61 - 37 * q^62 - 17 * q^63 + 94 * q^64 - 4 * q^65 - 4 * q^66 + 15 * q^67 - 25 * q^68 - 8 * q^69 + q^70 + 32 * q^71 + 6 * q^72 - 15 * q^73 + 16 * q^74 - 37 * q^75 + 3 * q^76 - 4 * q^77 - q^78 + 27 * q^79 + 41 * q^80 + 17 * q^81 - 8 * q^82 - 24 * q^83 + 25 * q^84 + 4 * q^85 + 53 * q^86 + 3 * q^87 - 9 * q^88 - 8 * q^89 - q^90 - 17 * q^91 + 14 * q^92 - 10 * q^93 + 51 * q^94 - 9 * q^95 - 18 * q^96 - 22 * q^97 + q^98 + 4 * q^99

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