LMFDB - Embedded newform 8034.2.a.y.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8034,2,Mod(1,8034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8034, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("8034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8034 = 2 \cdot 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8034.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:	$64.1518129839$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 5 x^{12} - 25 x^{11} + 134 x^{10} + 196 x^{9} - 1151 x^{8} - 801 x^{7} + 4263 x^{6} + \cdots - 180 $ x^13 - 5x^12 - 25x^11 + 134x^10 + 196x^9 - 1151x^8 - 801x^7 + 4263x^6 + 2205x^5 - 6840x^4 - 3579x^3 + 3559x^2 + 1839x - 180
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$2.89547$ of defining polynomial
Character	$\chi$	$=$	8034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.35434 q^{5} -1.00000 q^{6} +2.89547 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.35434 q^{5} -1.00000 q^{6} +2.89547 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.35434 q^{10} +2.23275 q^{11} -1.00000 q^{12} +1.00000 q^{13} +2.89547 q^{14} -3.35434 q^{15} +1.00000 q^{16} -3.39722 q^{17} +1.00000 q^{18} +7.31075 q^{19} +3.35434 q^{20} -2.89547 q^{21} +2.23275 q^{22} -3.61357 q^{23} -1.00000 q^{24} +6.25163 q^{25} +1.00000 q^{26} -1.00000 q^{27} +2.89547 q^{28} -4.47655 q^{29} -3.35434 q^{30} +7.31075 q^{31} +1.00000 q^{32} -2.23275 q^{33} -3.39722 q^{34} +9.71240 q^{35} +1.00000 q^{36} +0.856955 q^{37} +7.31075 q^{38} -1.00000 q^{39} +3.35434 q^{40} -6.78287 q^{41} -2.89547 q^{42} +8.47357 q^{43} +2.23275 q^{44} +3.35434 q^{45} -3.61357 q^{46} -3.31208 q^{47} -1.00000 q^{48} +1.38373 q^{49} +6.25163 q^{50} +3.39722 q^{51} +1.00000 q^{52} +0.133425 q^{53} -1.00000 q^{54} +7.48942 q^{55} +2.89547 q^{56} -7.31075 q^{57} -4.47655 q^{58} -4.10155 q^{59} -3.35434 q^{60} +11.3195 q^{61} +7.31075 q^{62} +2.89547 q^{63} +1.00000 q^{64} +3.35434 q^{65} -2.23275 q^{66} -6.04275 q^{67} -3.39722 q^{68} +3.61357 q^{69} +9.71240 q^{70} -7.81764 q^{71} +1.00000 q^{72} +3.56116 q^{73} +0.856955 q^{74} -6.25163 q^{75} +7.31075 q^{76} +6.46487 q^{77} -1.00000 q^{78} +10.9268 q^{79} +3.35434 q^{80} +1.00000 q^{81} -6.78287 q^{82} -12.9526 q^{83} -2.89547 q^{84} -11.3955 q^{85} +8.47357 q^{86} +4.47655 q^{87} +2.23275 q^{88} +0.160251 q^{89} +3.35434 q^{90} +2.89547 q^{91} -3.61357 q^{92} -7.31075 q^{93} -3.31208 q^{94} +24.5228 q^{95} -1.00000 q^{96} +8.23733 q^{97} +1.38373 q^{98} +2.23275 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 13 q^{2} - 13 q^{3} + 13 q^{4} + 3 q^{5} - 13 q^{6} + 5 q^{7} + 13 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q + 13 * q^2 - 13 * q^3 + 13 * q^4 + 3 * q^5 - 13 * q^6 + 5 * q^7 + 13 * q^8 + 13 * q^9	\( 13 q + 13 q^{2} - 13 q^{3} + 13 q^{4} + 3 q^{5} - 13 q^{6} + 5 q^{7} + 13 q^{8} + 13 q^{9} + 3 q^{10} + 8 q^{11} - 13 q^{12} + 13 q^{13} + 5 q^{14} - 3 q^{15} + 13 q^{16} - q^{17} + 13 q^{18} + 5 q^{19} + 3 q^{20} - 5 q^{21} + 8 q^{22} - 9 q^{23} - 13 q^{24} + 24 q^{25} + 13 q^{26} - 13 q^{27} + 5 q^{28} - q^{29} - 3 q^{30} + 5 q^{31} + 13 q^{32} - 8 q^{33} - q^{34} + 28 q^{35} + 13 q^{36} + 35 q^{37} + 5 q^{38} - 13 q^{39} + 3 q^{40} + 24 q^{41} - 5 q^{42} + 9 q^{43} + 8 q^{44} + 3 q^{45} - 9 q^{46} - 8 q^{47} - 13 q^{48} - 16 q^{49} + 24 q^{50} + q^{51} + 13 q^{52} + 32 q^{53} - 13 q^{54} - 4 q^{55} + 5 q^{56} - 5 q^{57} - q^{58} + 12 q^{59} - 3 q^{60} + 17 q^{61} + 5 q^{62} + 5 q^{63} + 13 q^{64} + 3 q^{65} - 8 q^{66} + 20 q^{67} - q^{68} + 9 q^{69} + 28 q^{70} + 16 q^{71} + 13 q^{72} + 46 q^{73} + 35 q^{74} - 24 q^{75} + 5 q^{76} - 7 q^{77} - 13 q^{78} + 17 q^{79} + 3 q^{80} + 13 q^{81} + 24 q^{82} + 13 q^{83} - 5 q^{84} + 11 q^{85} + 9 q^{86} + q^{87} + 8 q^{88} + 14 q^{89} + 3 q^{90} + 5 q^{91} - 9 q^{92} - 5 q^{93} - 8 q^{94} + 2 q^{95} - 13 q^{96} + 46 q^{97} - 16 q^{98} + 8 q^{99}+O(q^{100}) \) 13 * q + 13 * q^2 - 13 * q^3 + 13 * q^4 + 3 * q^5 - 13 * q^6 + 5 * q^7 + 13 * q^8 + 13 * q^9 + 3 * q^10 + 8 * q^11 - 13 * q^12 + 13 * q^13 + 5 * q^14 - 3 * q^15 + 13 * q^16 - q^17 + 13 * q^18 + 5 * q^19 + 3 * q^20 - 5 * q^21 + 8 * q^22 - 9 * q^23 - 13 * q^24 + 24 * q^25 + 13 * q^26 - 13 * q^27 + 5 * q^28 - q^29 - 3 * q^30 + 5 * q^31 + 13 * q^32 - 8 * q^33 - q^34 + 28 * q^35 + 13 * q^36 + 35 * q^37 + 5 * q^38 - 13 * q^39 + 3 * q^40 + 24 * q^41 - 5 * q^42 + 9 * q^43 + 8 * q^44 + 3 * q^45 - 9 * q^46 - 8 * q^47 - 13 * q^48 - 16 * q^49 + 24 * q^50 + q^51 + 13 * q^52 + 32 * q^53 - 13 * q^54 - 4 * q^55 + 5 * q^56 - 5 * q^57 - q^58 + 12 * q^59 - 3 * q^60 + 17 * q^61 + 5 * q^62 + 5 * q^63 + 13 * q^64 + 3 * q^65 - 8 * q^66 + 20 * q^67 - q^68 + 9 * q^69 + 28 * q^70 + 16 * q^71 + 13 * q^72 + 46 * q^73 + 35 * q^74 - 24 * q^75 + 5 * q^76 - 7 * q^77 - 13 * q^78 + 17 * q^79 + 3 * q^80 + 13 * q^81 + 24 * q^82 + 13 * q^83 - 5 * q^84 + 11 * q^85 + 9 * q^86 + q^87 + 8 * q^88 + 14 * q^89 + 3 * q^90 + 5 * q^91 - 9 * q^92 - 5 * q^93 - 8 * q^94 + 2 * q^95 - 13 * q^96 + 46 * q^97 - 16 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	3.35434	1.50011	0.750054	−	0.661376i	$-0.230027\pi$
$5$	3.35434	1.50011	0.750054	+	0.661376i	$0.230027\pi$
$6$	−1.00000	−0.408248
$7$	2.89547	1.09438	0.547192	−	0.837007i	$-0.315697\pi$
$7$	2.89547	1.09438	0.547192	+	0.837007i	$0.315697\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	3.35434	1.06074
$11$	2.23275	0.673200	0.336600	−	0.941648i	$-0.390723\pi$
$11$	2.23275	0.673200	0.336600	+	0.941648i	$0.390723\pi$
$12$	−1.00000	−0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	2.89547	0.773846
$15$	−3.35434	−0.866088
$16$	1.00000	0.250000
$17$	−3.39722	−0.823947	−0.411974	−	0.911196i	$-0.635160\pi$
$17$	−3.39722	−0.823947	−0.411974	+	0.911196i	$0.635160\pi$
$18$	1.00000	0.235702
$19$	7.31075	1.67720	0.838601	−	0.544746i	$-0.183374\pi$
$19$	7.31075	1.67720	0.838601	+	0.544746i	$0.183374\pi$
$20$	3.35434	0.750054
$21$	−2.89547	−0.631843
$22$	2.23275	0.476025
$23$	−3.61357	−0.753481	−0.376740	−	0.926319i	$-0.622955\pi$
$23$	−3.61357	−0.753481	−0.376740	+	0.926319i	$0.622955\pi$
$24$	−1.00000	−0.204124
$25$	6.25163	1.25033
$26$	1.00000	0.196116
$27$	−1.00000	−0.192450
$28$	2.89547	0.547192
$29$	−4.47655	−0.831274	−0.415637	−	0.909531i	$-0.636441\pi$
$29$	−4.47655	−0.831274	−0.415637	+	0.909531i	$0.636441\pi$
$30$	−3.35434	−0.612417
$31$	7.31075	1.31305	0.656525	−	0.754304i	$-0.272026\pi$
$31$	7.31075	1.31305	0.656525	+	0.754304i	$0.272026\pi$
$32$	1.00000	0.176777
$33$	−2.23275	−0.388672
$34$	−3.39722	−0.582619
$35$	9.71240	1.64169
$36$	1.00000	0.166667
$37$	0.856955	0.140883	0.0704413	−	0.997516i	$-0.477559\pi$
$37$	0.856955	0.140883	0.0704413	+	0.997516i	$0.477559\pi$
$38$	7.31075	1.18596
$39$	−1.00000	−0.160128
$40$	3.35434	0.530368
$41$	−6.78287	−1.05931	−0.529653	−	0.848214i	$-0.677678\pi$
$41$	−6.78287	−1.05931	−0.529653	+	0.848214i	$0.677678\pi$
$42$	−2.89547	−0.446780
$43$	8.47357	1.29221	0.646104	−	0.763250i	$-0.276397\pi$
$43$	8.47357	1.29221	0.646104	+	0.763250i	$0.276397\pi$
$44$	2.23275	0.336600
$45$	3.35434	0.500036
$46$	−3.61357	−0.532791
$47$	−3.31208	−0.483116	−0.241558	−	0.970386i	$-0.577658\pi$
$47$	−3.31208	−0.483116	−0.241558	+	0.970386i	$0.577658\pi$
$48$	−1.00000	−0.144338
$49$	1.38373	0.197676
$50$	6.25163	0.884114
$51$	3.39722	0.475706
$52$	1.00000	0.138675
$53$	0.133425	0.0183273	0.00916367	−	0.999958i	$-0.497083\pi$
$53$	0.133425	0.0183273	0.00916367	+	0.999958i	$0.497083\pi$
$54$	−1.00000	−0.136083
$55$	7.48942	1.00987
$56$	2.89547	0.386923
$57$	−7.31075	−0.968333
$58$	−4.47655	−0.587799
$59$	−4.10155	−0.533976	−0.266988	−	0.963700i	$-0.586028\pi$
$59$	−4.10155	−0.533976	−0.266988	+	0.963700i	$0.586028\pi$
$60$	−3.35434	−0.433044
$61$	11.3195	1.44931	0.724657	−	0.689110i	$-0.241998\pi$
$61$	11.3195	1.44931	0.724657	+	0.689110i	$0.241998\pi$
$62$	7.31075	0.928467
$63$	2.89547	0.364795
$64$	1.00000	0.125000
$65$	3.35434	0.416055
$66$	−2.23275	−0.274833
$67$	−6.04275	−0.738239	−0.369120	−	0.929382i	$-0.620341\pi$
$67$	−6.04275	−0.738239	−0.369120	+	0.929382i	$0.620341\pi$
$68$	−3.39722	−0.411974
$69$	3.61357	0.435022
$70$	9.71240	1.16085
$71$	−7.81764	−0.927784	−0.463892	−	0.885892i	$-0.653547\pi$
$71$	−7.81764	−0.927784	−0.463892	+	0.885892i	$0.653547\pi$
$72$	1.00000	0.117851
$73$	3.56116	0.416802	0.208401	−	0.978043i	$-0.433174\pi$
$73$	3.56116	0.416802	0.208401	+	0.978043i	$0.433174\pi$
$74$	0.856955	0.0996191
$75$	−6.25163	−0.721876
$76$	7.31075	0.838601
$77$	6.46487	0.736740
$78$	−1.00000	−0.113228
$79$	10.9268	1.22936	0.614681	−	0.788776i	$-0.289285\pi$
$79$	10.9268	1.22936	0.614681	+	0.788776i	$0.289285\pi$
$80$	3.35434	0.375027
$81$	1.00000	0.111111
$82$	−6.78287	−0.749043
$83$	−12.9526	−1.42173	−0.710867	−	0.703326i	$-0.751697\pi$
$83$	−12.9526	−1.42173	−0.710867	+	0.703326i	$0.751697\pi$
$84$	−2.89547	−0.315921
$85$	−11.3955	−1.23601
$86$	8.47357	0.913728
$87$	4.47655	0.479936
$88$	2.23275	0.238012
$89$	0.160251	0.0169865	0.00849327	−	0.999964i	$-0.497296\pi$
$89$	0.160251	0.0169865	0.00849327	+	0.999964i	$0.497296\pi$
$90$	3.35434	0.353579
$91$	2.89547	0.303528
$92$	−3.61357	−0.376740
$93$	−7.31075	−0.758090
$94$	−3.31208	−0.341615
$95$	24.5228	2.51599
$96$	−1.00000	−0.102062
$97$	8.23733	0.836375	0.418187	−	0.908361i	$-0.362666\pi$
$97$	8.23733	0.836375	0.418187	+	0.908361i	$0.362666\pi$
$98$	1.38373	0.139778
$99$	2.23275	0.224400
$100$	6.25163	0.625163
$101$	9.30949	0.926329	0.463165	−	0.886272i	$-0.346714\pi$
$101$	9.30949	0.926329	0.463165	+	0.886272i	$0.346714\pi$
$102$	3.39722	0.336375
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	1.00000	0.0980581
$105$	−9.71240	−0.947833
$106$	0.133425	0.0129594
$107$	−8.02589	−0.775892	−0.387946	−	0.921682i	$-0.626815\pi$
$107$	−8.02589	−0.775892	−0.387946	+	0.921682i	$0.626815\pi$
$108$	−1.00000	−0.0962250
$109$	−3.22616	−0.309010	−0.154505	−	0.987992i	$-0.549378\pi$
$109$	−3.22616	−0.309010	−0.154505	+	0.987992i	$0.549378\pi$
$110$	7.48942	0.714089
$111$	−0.856955	−0.0813386
$112$	2.89547	0.273596
$113$	7.38702	0.694912	0.347456	−	0.937696i	$-0.387046\pi$
$113$	7.38702	0.694912	0.347456	+	0.937696i	$0.387046\pi$
$114$	−7.31075	−0.684715
$115$	−12.1211	−1.13030
$116$	−4.47655	−0.415637
$117$	1.00000	0.0924500
$118$	−4.10155	−0.377578
$119$	−9.83655	−0.901715
$120$	−3.35434	−0.306208
$121$	−6.01481	−0.546801
$122$	11.3195	1.02482
$123$	6.78287	0.611591
$124$	7.31075	0.656525
$125$	4.19840	0.375516
$126$	2.89547	0.257949
$127$	2.35703	0.209152	0.104576	−	0.994517i	$-0.466651\pi$
$127$	2.35703	0.209152	0.104576	+	0.994517i	$0.466651\pi$
$128$	1.00000	0.0883883
$129$	−8.47357	−0.746056
$130$	3.35434	0.294196
$131$	−8.54820	−0.746860	−0.373430	−	0.927658i	$-0.621818\pi$
$131$	−8.54820	−0.746860	−0.373430	+	0.927658i	$0.621818\pi$
$132$	−2.23275	−0.194336
$133$	21.1681	1.83550
$134$	−6.04275	−0.522014
$135$	−3.35434	−0.288696
$136$	−3.39722	−0.291309
$137$	−0.950761	−0.0812290	−0.0406145	−	0.999175i	$-0.512932\pi$
$137$	−0.950761	−0.0812290	−0.0406145	+	0.999175i	$0.512932\pi$
$138$	3.61357	0.307607
$139$	10.5451	0.894427	0.447213	−	0.894427i	$-0.352416\pi$
$139$	10.5451	0.894427	0.447213	+	0.894427i	$0.352416\pi$
$140$	9.71240	0.820847
$141$	3.31208	0.278927
$142$	−7.81764	−0.656042
$143$	2.23275	0.186712
$144$	1.00000	0.0833333
$145$	−15.0159	−1.24700
$146$	3.56116	0.294724
$147$	−1.38373	−0.114129
$148$	0.856955	0.0704413
$149$	−2.32059	−0.190110	−0.0950549	−	0.995472i	$-0.530303\pi$
$149$	−2.32059	−0.190110	−0.0950549	+	0.995472i	$0.530303\pi$
$150$	−6.25163	−0.510443
$151$	−10.4459	−0.850076	−0.425038	−	0.905176i	$-0.639739\pi$
$151$	−10.4459	−0.850076	−0.425038	+	0.905176i	$0.639739\pi$
$152$	7.31075	0.592980
$153$	−3.39722	−0.274649
$154$	6.46487	0.520954
$155$	24.5228	1.96972
$156$	−1.00000	−0.0800641
$157$	1.32494	0.105741	0.0528707	−	0.998601i	$-0.483163\pi$
$157$	1.32494	0.105741	0.0528707	+	0.998601i	$0.483163\pi$
$158$	10.9268	0.869290
$159$	−0.133425	−0.0105813
$160$	3.35434	0.265184
$161$	−10.4630	−0.824597
$162$	1.00000	0.0785674
$163$	−0.542471	−0.0424896	−0.0212448	−	0.999774i	$-0.506763\pi$
$163$	−0.542471	−0.0424896	−0.0212448	+	0.999774i	$0.506763\pi$
$164$	−6.78287	−0.529653
$165$	−7.48942	−0.583051
$166$	−12.9526	−1.00532
$167$	8.60095	0.665562	0.332781	−	0.943004i	$-0.392013\pi$
$167$	8.60095	0.665562	0.332781	+	0.943004i	$0.392013\pi$
$168$	−2.89547	−0.223390
$169$	1.00000	0.0769231
$170$	−11.3955	−0.873991
$171$	7.31075	0.559067
$172$	8.47357	0.646104
$173$	−10.4070	−0.791233	−0.395617	−	0.918416i	$-0.629469\pi$
$173$	−10.4070	−0.791233	−0.395617	+	0.918416i	$0.629469\pi$
$174$	4.47655	0.339366
$175$	18.1014	1.36834
$176$	2.23275	0.168300
$177$	4.10155	0.308291
$178$	0.160251	0.0120113
$179$	−5.38352	−0.402383	−0.201192	−	0.979552i	$-0.564481\pi$
$179$	−5.38352	−0.402383	−0.201192	+	0.979552i	$0.564481\pi$
$180$	3.35434	0.250018
$181$	−24.2610	−1.80331	−0.901655	−	0.432457i	$-0.857647\pi$
$181$	−24.2610	−1.80331	−0.901655	+	0.432457i	$0.857647\pi$
$182$	2.89547	0.214626
$183$	−11.3195	−0.836761
$184$	−3.61357	−0.266396
$185$	2.87452	0.211339
$186$	−7.31075	−0.536051
$187$	−7.58516	−0.554682
$188$	−3.31208	−0.241558
$189$	−2.89547	−0.210614
$190$	24.5228	1.77907
$191$	−12.3723	−0.895225	−0.447613	−	0.894228i	$-0.647726\pi$
$191$	−12.3723	−0.895225	−0.447613	+	0.894228i	$0.647726\pi$
$192$	−1.00000	−0.0721688
$193$	−5.72454	−0.412062	−0.206031	−	0.978545i	$-0.566055\pi$
$193$	−5.72454	−0.412062	−0.206031	+	0.978545i	$0.566055\pi$
$194$	8.23733	0.591406
$195$	−3.35434	−0.240210
$196$	1.38373	0.0988382
$197$	−13.2494	−0.943979	−0.471990	−	0.881604i	$-0.656464\pi$
$197$	−13.2494	−0.943979	−0.471990	+	0.881604i	$0.656464\pi$
$198$	2.23275	0.158675
$199$	1.19933	0.0850179	0.0425090	−	0.999096i	$-0.486465\pi$
$199$	1.19933	0.0850179	0.0425090	+	0.999096i	$0.486465\pi$
$200$	6.25163	0.442057
$201$	6.04275	0.426223
$202$	9.30949	0.655014
$203$	−12.9617	−0.909733
$204$	3.39722	0.237853
$205$	−22.7521	−1.58908
$206$	1.00000	0.0696733
$207$	−3.61357	−0.251160
$208$	1.00000	0.0693375
$209$	16.3231	1.12909
$210$	−9.71240	−0.670219
$211$	−0.158374	−0.0109029	−0.00545145	−	0.999985i	$-0.501735\pi$
$211$	−0.158374	−0.0109029	−0.00545145	+	0.999985i	$0.501735\pi$
$212$	0.133425	0.00916367
$213$	7.81764	0.535656
$214$	−8.02589	−0.548638
$215$	28.4233	1.93845
$216$	−1.00000	−0.0680414
$217$	21.1681	1.43698
$218$	−3.22616	−0.218503
$219$	−3.56116	−0.240641
$220$	7.48942	0.504937
$221$	−3.39722	−0.228522
$222$	−0.856955	−0.0575151
$223$	−11.2410	−0.752752	−0.376376	−	0.926467i	$-0.622830\pi$
$223$	−11.2410	−0.752752	−0.376376	+	0.926467i	$0.622830\pi$
$224$	2.89547	0.193462
$225$	6.25163	0.416775
$226$	7.38702	0.491377
$227$	8.66975	0.575431	0.287716	−	0.957716i	$-0.407104\pi$
$227$	8.66975	0.575431	0.287716	+	0.957716i	$0.407104\pi$
$228$	−7.31075	−0.484167
$229$	10.0151	0.661814	0.330907	−	0.943663i	$-0.392645\pi$
$229$	10.0151	0.661814	0.330907	+	0.943663i	$0.392645\pi$
$230$	−12.1211	−0.799245
$231$	−6.46487	−0.425357
$232$	−4.47655	−0.293900
$233$	−20.2982	−1.32978	−0.664891	−	0.746940i	$-0.731522\pi$
$233$	−20.2982	−1.32978	−0.664891	+	0.746940i	$0.731522\pi$
$234$	1.00000	0.0653720
$235$	−11.1098	−0.724726
$236$	−4.10155	−0.266988
$237$	−10.9268	−0.709773
$238$	−9.83655	−0.637609
$239$	4.77489	0.308862	0.154431	−	0.988004i	$-0.450646\pi$
$239$	4.77489	0.308862	0.154431	+	0.988004i	$0.450646\pi$
$240$	−3.35434	−0.216522
$241$	−19.2803	−1.24195	−0.620976	−	0.783829i	$-0.713264\pi$
$241$	−19.2803	−1.24195	−0.620976	+	0.783829i	$0.713264\pi$
$242$	−6.01481	−0.386647
$243$	−1.00000	−0.0641500
$244$	11.3195	0.724657
$245$	4.64152	0.296536
$246$	6.78287	0.432460
$247$	7.31075	0.465172
$248$	7.31075	0.464233
$249$	12.9526	0.820839
$250$	4.19840	0.265530
$251$	−13.2074	−0.833643	−0.416822	−	0.908988i	$-0.636856\pi$
$251$	−13.2074	−0.833643	−0.416822	+	0.908988i	$0.636856\pi$
$252$	2.89547	0.182397
$253$	−8.06820	−0.507244
$254$	2.35703	0.147893
$255$	11.3955	0.713611
$256$	1.00000	0.0625000
$257$	13.0988	0.817080	0.408540	−	0.912741i	$-0.366038\pi$
$257$	13.0988	0.817080	0.408540	+	0.912741i	$0.366038\pi$
$258$	−8.47357	−0.527541
$259$	2.48129	0.154180
$260$	3.35434	0.208028
$261$	−4.47655	−0.277091
$262$	−8.54820	−0.528110
$263$	0.849962	0.0524109	0.0262054	−	0.999657i	$-0.491658\pi$
$263$	0.849962	0.0524109	0.0262054	+	0.999657i	$0.491658\pi$
$264$	−2.23275	−0.137416
$265$	0.447554	0.0274930
$266$	21.1681	1.29790
$267$	−0.160251	−0.00980718
$268$	−6.04275	−0.369120
$269$	24.2292	1.47728	0.738641	−	0.674099i	$-0.235468\pi$
$269$	24.2292	1.47728	0.738641	+	0.674099i	$0.235468\pi$
$270$	−3.35434	−0.204139
$271$	−5.02862	−0.305467	−0.152734	−	0.988267i	$-0.548808\pi$
$271$	−5.02862	−0.305467	−0.152734	+	0.988267i	$0.548808\pi$
$272$	−3.39722	−0.205987
$273$	−2.89547	−0.175242
$274$	−0.950761	−0.0574376
$275$	13.9583	0.841720
$276$	3.61357	0.217511
$277$	12.4334	0.747050	0.373525	−	0.927620i	$-0.378149\pi$
$277$	12.4334	0.747050	0.373525	+	0.927620i	$0.378149\pi$
$278$	10.5451	0.632455
$279$	7.31075	0.437683
$280$	9.71240	0.580427
$281$	27.6456	1.64920	0.824599	−	0.565718i	$-0.191401\pi$
$281$	27.6456	1.64920	0.824599	+	0.565718i	$0.191401\pi$
$282$	3.31208	0.197231
$283$	−23.6779	−1.40751	−0.703754	−	0.710444i	$-0.748494\pi$
$283$	−23.6779	−1.40751	−0.703754	+	0.710444i	$0.748494\pi$
$284$	−7.81764	−0.463892
$285$	−24.5228	−1.45260
$286$	2.23275	0.132025
$287$	−19.6396	−1.15929
$288$	1.00000	0.0589256
$289$	−5.45888	−0.321111
$290$	−15.0159	−0.881763
$291$	−8.23733	−0.482881
$292$	3.56116	0.208401
$293$	8.69413	0.507917	0.253958	−	0.967215i	$-0.418267\pi$
$293$	8.69413	0.507917	0.253958	+	0.967215i	$0.418267\pi$
$294$	−1.38373	−0.0807011
$295$	−13.7580	−0.801022
$296$	0.856955	0.0498095
$297$	−2.23275	−0.129557
$298$	−2.32059	−0.134428
$299$	−3.61357	−0.208978
$300$	−6.25163	−0.360938
$301$	24.5349	1.41417
$302$	−10.4459	−0.601094
$303$	−9.30949	−0.534816
$304$	7.31075	0.419301
$305$	37.9695	2.17413
$306$	−3.39722	−0.194206
$307$	−0.525067	−0.0299672	−0.0149836	−	0.999888i	$-0.504770\pi$
$307$	−0.525067	−0.0299672	−0.0149836	+	0.999888i	$0.504770\pi$
$308$	6.46487	0.368370
$309$	−1.00000	−0.0568880
$310$	24.5228	1.39280
$311$	28.6465	1.62439	0.812197	−	0.583383i	$-0.198271\pi$
$311$	28.6465	1.62439	0.812197	+	0.583383i	$0.198271\pi$
$312$	−1.00000	−0.0566139
$313$	−26.0708	−1.47361	−0.736804	−	0.676106i	$-0.763666\pi$
$313$	−26.0708	−1.47361	−0.736804	+	0.676106i	$0.763666\pi$
$314$	1.32494	0.0747704
$315$	9.71240	0.547232
$316$	10.9268	0.614681
$317$	−20.8187	−1.16930	−0.584648	−	0.811287i	$-0.698767\pi$
$317$	−20.8187	−1.16930	−0.584648	+	0.811287i	$0.698767\pi$
$318$	−0.133425	−0.00748211
$319$	−9.99502	−0.559614
$320$	3.35434	0.187514
$321$	8.02589	0.447961
$322$	−10.4630	−0.583078
$323$	−24.8363	−1.38193
$324$	1.00000	0.0555556
$325$	6.25163	0.346778
$326$	−0.542471	−0.0300447
$327$	3.22616	0.178407
$328$	−6.78287	−0.374521
$329$	−9.59001	−0.528714
$330$	−7.48942	−0.412279
$331$	12.8194	0.704620	0.352310	−	0.935883i	$-0.385396\pi$
$331$	12.8194	0.704620	0.352310	+	0.935883i	$0.385396\pi$
$332$	−12.9526	−0.710867
$333$	0.856955	0.0469609
$334$	8.60095	0.470623
$335$	−20.2695	−1.10744
$336$	−2.89547	−0.157961
$337$	12.5888	0.685754	0.342877	−	0.939380i	$-0.388599\pi$
$337$	12.5888	0.685754	0.342877	+	0.939380i	$0.388599\pi$
$338$	1.00000	0.0543928
$339$	−7.38702	−0.401208
$340$	−11.3955	−0.618005
$341$	16.3231	0.883946
$342$	7.31075	0.395320
$343$	−16.2617	−0.878050
$344$	8.47357	0.456864
$345$	12.1211	0.652581
$346$	−10.4070	−0.559486
$347$	−35.2932	−1.89464	−0.947320	−	0.320290i	$-0.896220\pi$
$347$	−35.2932	−1.89464	−0.947320	+	0.320290i	$0.896220\pi$
$348$	4.47655	0.239968
$349$	−6.51378	−0.348674	−0.174337	−	0.984686i	$-0.555778\pi$
$349$	−6.51378	−0.348674	−0.174337	+	0.984686i	$0.555778\pi$
$350$	18.1014	0.967560
$351$	−1.00000	−0.0533761
$352$	2.23275	0.119006
$353$	9.00142	0.479097	0.239549	−	0.970884i	$-0.423001\pi$
$353$	9.00142	0.479097	0.239549	+	0.970884i	$0.423001\pi$
$354$	4.10155	0.217995
$355$	−26.2231	−1.39178
$356$	0.160251	0.00849327
$357$	9.83655	0.520605
$358$	−5.38352	−0.284528
$359$	25.0319	1.32113	0.660566	−	0.750768i	$-0.270316\pi$
$359$	25.0319	1.32113	0.660566	+	0.750768i	$0.270316\pi$
$360$	3.35434	0.176789
$361$	34.4471	1.81301
$362$	−24.2610	−1.27513
$363$	6.01481	0.315696
$364$	2.89547	0.151764
$365$	11.9454	0.625248
$366$	−11.3195	−0.591680
$367$	11.7544	0.613574	0.306787	−	0.951778i	$-0.400746\pi$
$367$	11.7544	0.613574	0.306787	+	0.951778i	$0.400746\pi$
$368$	−3.61357	−0.188370
$369$	−6.78287	−0.353102
$370$	2.87452	0.149439
$371$	0.386328	0.0200572
$372$	−7.31075	−0.379045
$373$	2.42429	0.125525	0.0627625	−	0.998028i	$-0.480009\pi$
$373$	2.42429	0.125525	0.0627625	+	0.998028i	$0.480009\pi$
$374$	−7.58516	−0.392219
$375$	−4.19840	−0.216804
$376$	−3.31208	−0.170807
$377$	−4.47655	−0.230554
$378$	−2.89547	−0.148927
$379$	−13.6771	−0.702547	−0.351274	−	0.936273i	$-0.614251\pi$
$379$	−13.6771	−0.702547	−0.351274	+	0.936273i	$0.614251\pi$
$380$	24.5228	1.25799
$381$	−2.35703	−0.120754
$382$	−12.3723	−0.633020
$383$	8.61426	0.440168	0.220084	−	0.975481i	$-0.429367\pi$
$383$	8.61426	0.440168	0.220084	+	0.975481i	$0.429367\pi$
$384$	−1.00000	−0.0510310
$385$	21.6854	1.10519
$386$	−5.72454	−0.291372
$387$	8.47357	0.430736
$388$	8.23733	0.418187
$389$	−3.68944	−0.187062	−0.0935309	−	0.995616i	$-0.529815\pi$
$389$	−3.68944	−0.187062	−0.0935309	+	0.995616i	$0.529815\pi$
$390$	−3.35434	−0.169854
$391$	12.2761	0.620829
$392$	1.38373	0.0698892
$393$	8.54820	0.431200
$394$	−13.2494	−0.667494
$395$	36.6523	1.84418
$396$	2.23275	0.112200
$397$	18.6268	0.934853	0.467427	−	0.884032i	$-0.345181\pi$
$397$	18.6268	0.934853	0.467427	+	0.884032i	$0.345181\pi$
$398$	1.19933	0.0601168
$399$	−21.1681	−1.05973
$400$	6.25163	0.312581
$401$	37.9224	1.89376	0.946878	−	0.321592i	$-0.104218\pi$
$401$	37.9224	1.89376	0.946878	+	0.321592i	$0.104218\pi$
$402$	6.04275	0.301385
$403$	7.31075	0.364175
$404$	9.30949	0.463165
$405$	3.35434	0.166679
$406$	−12.9617	−0.643278
$407$	1.91337	0.0948422
$408$	3.39722	0.168188
$409$	12.7746	0.631662	0.315831	−	0.948815i	$-0.397717\pi$
$409$	12.7746	0.631662	0.315831	+	0.948815i	$0.397717\pi$
$410$	−22.7521	−1.12365
$411$	0.950761	0.0468976
$412$	1.00000	0.0492665
$413$	−11.8759	−0.584375
$414$	−3.61357	−0.177597
$415$	−43.4476	−2.13276
$416$	1.00000	0.0490290
$417$	−10.5451	−0.516398
$418$	16.3231	0.798389
$419$	−5.72215	−0.279545	−0.139773	−	0.990184i	$-0.544637\pi$
$419$	−5.72215	−0.279545	−0.139773	+	0.990184i	$0.544637\pi$
$420$	−9.71240	−0.473916
$421$	16.7182	0.814798	0.407399	−	0.913250i	$-0.366436\pi$
$421$	16.7182	0.814798	0.407399	+	0.913250i	$0.366436\pi$
$422$	−0.158374	−0.00770951
$423$	−3.31208	−0.161039
$424$	0.133425	0.00647970
$425$	−21.2382	−1.03020
$426$	7.81764	0.378766
$427$	32.7752	1.58611
$428$	−8.02589	−0.387946
$429$	−2.23275	−0.107798
$430$	28.4233	1.37069
$431$	−0.938685	−0.0452148	−0.0226074	−	0.999744i	$-0.507197\pi$
$431$	−0.938685	−0.0452148	−0.0226074	+	0.999744i	$0.507197\pi$
$432$	−1.00000	−0.0481125
$433$	6.11345	0.293793	0.146897	−	0.989152i	$-0.453072\pi$
$433$	6.11345	0.293793	0.146897	+	0.989152i	$0.453072\pi$
$434$	21.1681	1.01610
$435$	15.0159	0.719956
$436$	−3.22616	−0.154505
$437$	−26.4179	−1.26374
$438$	−3.56116	−0.170159
$439$	−1.40875	−0.0672357	−0.0336179	−	0.999435i	$-0.510703\pi$
$439$	−1.40875	−0.0672357	−0.0336179	+	0.999435i	$0.510703\pi$
$440$	7.48942	0.357044
$441$	1.38373	0.0658921
$442$	−3.39722	−0.161589
$443$	10.3412	0.491326	0.245663	−	0.969355i	$-0.420994\pi$
$443$	10.3412	0.491326	0.245663	+	0.969355i	$0.420994\pi$
$444$	−0.856955	−0.0406693
$445$	0.537536	0.0254816
$446$	−11.2410	−0.532276
$447$	2.32059	0.109760
$448$	2.89547	0.136798
$449$	35.6419	1.68204	0.841022	−	0.541001i	$-0.181954\pi$
$449$	35.6419	1.68204	0.841022	+	0.541001i	$0.181954\pi$
$450$	6.25163	0.294705
$451$	−15.1445	−0.713126
$452$	7.38702	0.347456
$453$	10.4459	0.490791
$454$	8.66975	0.406892
$455$	9.71240	0.455324
$456$	−7.31075	−0.342357
$457$	−8.76921	−0.410206	−0.205103	−	0.978740i	$-0.565753\pi$
$457$	−8.76921	−0.410206	−0.205103	+	0.978740i	$0.565753\pi$
$458$	10.0151	0.467973
$459$	3.39722	0.158569
$460$	−12.1211	−0.565151
$461$	−0.392215	−0.0182673	−0.00913365	−	0.999958i	$-0.502907\pi$
$461$	−0.392215	−0.0182673	−0.00913365	+	0.999958i	$0.502907\pi$
$462$	−6.46487	−0.300773
$463$	17.3559	0.806595	0.403298	−	0.915069i	$-0.367864\pi$
$463$	17.3559	0.806595	0.403298	+	0.915069i	$0.367864\pi$
$464$	−4.47655	−0.207818
$465$	−24.5228	−1.13722
$466$	−20.2982	−0.940298
$467$	−24.8716	−1.15092	−0.575461	−	0.817829i	$-0.695177\pi$
$467$	−24.8716	−1.15092	−0.575461	+	0.817829i	$0.695177\pi$
$468$	1.00000	0.0462250
$469$	−17.4966	−0.807917
$470$	−11.1098	−0.512459
$471$	−1.32494	−0.0610498
$472$	−4.10155	−0.188789
$473$	18.9194	0.869914
$474$	−10.9268	−0.501885
$475$	45.7041	2.09705
$476$	−9.83655	−0.450857
$477$	0.133425	0.00610912
$478$	4.77489	0.218398
$479$	−37.4571	−1.71146	−0.855729	−	0.517425i	$-0.826891\pi$
$479$	−37.4571	−1.71146	−0.855729	+	0.517425i	$0.826891\pi$
$480$	−3.35434	−0.153104
$481$	0.856955	0.0390738
$482$	−19.2803	−0.878193
$483$	10.4630	0.476081
$484$	−6.01481	−0.273401
$485$	27.6309	1.25465
$486$	−1.00000	−0.0453609
$487$	−29.0283	−1.31540	−0.657700	−	0.753280i	$-0.728470\pi$
$487$	−29.0283	−1.31540	−0.657700	+	0.753280i	$0.728470\pi$
$488$	11.3195	0.512410
$489$	0.542471	0.0245314
$490$	4.64152	0.209683
$491$	−38.9785	−1.75908	−0.879538	−	0.475828i	$-0.842148\pi$
$491$	−38.9785	−1.75908	−0.879538	+	0.475828i	$0.842148\pi$
$492$	6.78287	0.305795
$493$	15.2078	0.684926
$494$	7.31075	0.328926
$495$	7.48942	0.336625
$496$	7.31075	0.328263
$497$	−22.6357	−1.01535
$498$	12.9526	0.580421
$499$	−3.11970	−0.139657	−0.0698285	−	0.997559i	$-0.522245\pi$
$499$	−3.11970	−0.139657	−0.0698285	+	0.997559i	$0.522245\pi$
$500$	4.19840	0.187758
$501$	−8.60095	−0.384262
$502$	−13.2074	−0.589475
$503$	26.0145	1.15993	0.579964	−	0.814642i	$-0.303067\pi$
$503$	26.0145	1.15993	0.579964	+	0.814642i	$0.303067\pi$
$504$	2.89547	0.128974
$505$	31.2273	1.38959
$506$	−8.06820	−0.358675
$507$	−1.00000	−0.0444116
$508$	2.35703	0.104576
$509$	18.1043	0.802461	0.401231	−	0.915977i	$-0.368583\pi$
$509$	18.1043	0.802461	0.401231	+	0.915977i	$0.368583\pi$
$510$	11.3955	0.504599
$511$	10.3112	0.456142
$512$	1.00000	0.0441942
$513$	−7.31075	−0.322778
$514$	13.0988	0.577762
$515$	3.35434	0.147810
$516$	−8.47357	−0.373028
$517$	−7.39505	−0.325234
$518$	2.48129	0.109022
$519$	10.4070	0.456819
$520$	3.35434	0.147098
$521$	35.2007	1.54217	0.771085	−	0.636732i	$-0.219714\pi$
$521$	35.2007	1.54217	0.771085	+	0.636732i	$0.219714\pi$
$522$	−4.47655	−0.195933
$523$	−3.18523	−0.139280	−0.0696401	−	0.997572i	$-0.522185\pi$
$523$	−3.18523	−0.139280	−0.0696401	+	0.997572i	$0.522185\pi$
$524$	−8.54820	−0.373430
$525$	−18.1014	−0.790010
$526$	0.849962	0.0370601
$527$	−24.8363	−1.08188
$528$	−2.23275	−0.0971681
$529$	−9.94213	−0.432267
$530$	0.447554	0.0194405
$531$	−4.10155	−0.177992
$532$	21.1681	0.917752
$533$	−6.78287	−0.293799
$534$	−0.160251	−0.00693472
$535$	−26.9216	−1.16392
$536$	−6.04275	−0.261007
$537$	5.38352	0.232316
$538$	24.2292	1.04460
$539$	3.08954	0.133076
$540$	−3.35434	−0.144348
$541$	17.4863	0.751794	0.375897	−	0.926662i	$-0.377335\pi$
$541$	17.4863	0.751794	0.375897	+	0.926662i	$0.377335\pi$
$542$	−5.02862	−0.215998
$543$	24.2610	1.04114
$544$	−3.39722	−0.145655
$545$	−10.8216	−0.463548
$546$	−2.89547	−0.123915
$547$	−3.08773	−0.132022	−0.0660108	−	0.997819i	$-0.521027\pi$
$547$	−3.08773	−0.132022	−0.0660108	+	0.997819i	$0.521027\pi$
$548$	−0.950761	−0.0406145
$549$	11.3195	0.483104
$550$	13.9583	0.595186
$551$	−32.7269	−1.39421
$552$	3.61357	0.153804
$553$	31.6382	1.34539
$554$	12.4334	0.528244
$555$	−2.87452	−0.122017
$556$	10.5451	0.447213
$557$	4.28716	0.181653	0.0908263	−	0.995867i	$-0.471049\pi$
$557$	4.28716	0.181653	0.0908263	+	0.995867i	$0.471049\pi$
$558$	7.31075	0.309489
$559$	8.47357	0.358394
$560$	9.71240	0.410424
$561$	7.58516	0.320246
$562$	27.6456	1.16616
$563$	−7.61796	−0.321059	−0.160529	−	0.987031i	$-0.551320\pi$
$563$	−7.61796	−0.321059	−0.160529	+	0.987031i	$0.551320\pi$
$564$	3.31208	0.139464
$565$	24.7786	1.04244
$566$	−23.6779	−0.995258
$567$	2.89547	0.121598
$568$	−7.81764	−0.328021
$569$	8.73712	0.366279	0.183139	−	0.983087i	$-0.441374\pi$
$569$	8.73712	0.366279	0.183139	+	0.983087i	$0.441374\pi$
$570$	−24.5228	−1.02715
$571$	31.2656	1.30842	0.654212	−	0.756311i	$-0.273000\pi$
$571$	31.2656	1.30842	0.654212	+	0.756311i	$0.273000\pi$
$572$	2.23275	0.0933561
$573$	12.3723	0.516859
$574$	−19.6396	−0.819741
$575$	−22.5907	−0.942096
$576$	1.00000	0.0416667
$577$	−38.4071	−1.59891	−0.799454	−	0.600728i	$-0.794878\pi$
$577$	−38.4071	−1.59891	−0.799454	+	0.600728i	$0.794878\pi$
$578$	−5.45888	−0.227060
$579$	5.72454	0.237904
$580$	−15.0159	−0.623500
$581$	−37.5039	−1.55592
$582$	−8.23733	−0.341449
$583$	0.297905	0.0123380
$584$	3.56116	0.147362
$585$	3.35434	0.138685
$586$	8.69413	0.359151
$587$	32.1687	1.32774	0.663872	−	0.747847i	$-0.268912\pi$
$587$	32.1687	1.32774	0.663872	+	0.747847i	$0.268912\pi$
$588$	−1.38373	−0.0570643
$589$	53.4471	2.20225
$590$	−13.7580	−0.566408
$591$	13.2494	0.545007
$592$	0.856955	0.0352207
$593$	18.5716	0.762646	0.381323	−	0.924442i	$-0.375469\pi$
$593$	18.5716	0.762646	0.381323	+	0.924442i	$0.375469\pi$
$594$	−2.23275	−0.0916110
$595$	−32.9952	−1.35267
$596$	−2.32059	−0.0950549
$597$	−1.19933	−0.0490851
$598$	−3.61357	−0.147770
$599$	−5.96060	−0.243543	−0.121772	−	0.992558i	$-0.538858\pi$
$599$	−5.96060	−0.243543	−0.121772	+	0.992558i	$0.538858\pi$
$600$	−6.25163	−0.255222
$601$	15.2506	0.622085	0.311042	−	0.950396i	$-0.399322\pi$
$601$	15.2506	0.622085	0.311042	+	0.950396i	$0.399322\pi$
$602$	24.5349	0.999970
$603$	−6.04275	−0.246080
$604$	−10.4459	−0.425038
$605$	−20.1758	−0.820261
$606$	−9.30949	−0.378172
$607$	−2.19470	−0.0890800	−0.0445400	−	0.999008i	$-0.514182\pi$
$607$	−2.19470	−0.0890800	−0.0445400	+	0.999008i	$0.514182\pi$
$608$	7.31075	0.296490
$609$	12.9617	0.525234
$610$	37.9695	1.53734
$611$	−3.31208	−0.133992
$612$	−3.39722	−0.137325
$613$	35.9430	1.45172	0.725862	−	0.687840i	$-0.241441\pi$
$613$	35.9430	1.45172	0.725862	+	0.687840i	$0.241441\pi$
$614$	−0.525067	−0.0211900
$615$	22.7521	0.917453
$616$	6.46487	0.260477
$617$	27.6197	1.11193	0.555964	−	0.831206i	$-0.312349\pi$
$617$	27.6197	1.11193	0.555964	+	0.831206i	$0.312349\pi$
$618$	−1.00000	−0.0402259
$619$	23.9683	0.963368	0.481684	−	0.876345i	$-0.340025\pi$
$619$	23.9683	0.963368	0.481684	+	0.876345i	$0.340025\pi$
$620$	24.5228	0.984859
$621$	3.61357	0.145007
$622$	28.6465	1.14862
$623$	0.464001	0.0185898
$624$	−1.00000	−0.0400320
$625$	−17.1753	−0.687011
$626$	−26.0708	−1.04200
$627$	−16.3231	−0.651882
$628$	1.32494	0.0528707
$629$	−2.91127	−0.116080
$630$	9.71240	0.386951
$631$	−18.7754	−0.747438	−0.373719	−	0.927542i	$-0.621918\pi$
$631$	−18.7754	−0.747438	−0.373719	+	0.927542i	$0.621918\pi$
$632$	10.9268	0.434645
$633$	0.158374	0.00629479
$634$	−20.8187	−0.826817
$635$	7.90628	0.313751
$636$	−0.133425	−0.00529065
$637$	1.38373	0.0548256
$638$	−9.99502	−0.395707
$639$	−7.81764	−0.309261
$640$	3.35434	0.132592
$641$	1.72360	0.0680779	0.0340390	−	0.999421i	$-0.489163\pi$
$641$	1.72360	0.0680779	0.0340390	+	0.999421i	$0.489163\pi$
$642$	8.02589	0.316757
$643$	12.3057	0.485290	0.242645	−	0.970115i	$-0.421985\pi$
$643$	12.3057	0.485290	0.242645	+	0.970115i	$0.421985\pi$
$644$	−10.4630	−0.412299
$645$	−28.4233	−1.11917
$646$	−24.8363	−0.977169
$647$	−24.7132	−0.971577	−0.485788	−	0.874076i	$-0.661467\pi$
$647$	−24.7132	−0.971577	−0.485788	+	0.874076i	$0.661467\pi$
$648$	1.00000	0.0392837
$649$	−9.15775	−0.359473
$650$	6.25163	0.245209
$651$	−21.1681	−0.829642
$652$	−0.542471	−0.0212448
$653$	−29.2454	−1.14446	−0.572231	−	0.820093i	$-0.693922\pi$
$653$	−29.2454	−1.14446	−0.572231	+	0.820093i	$0.693922\pi$
$654$	3.22616	0.126153
$655$	−28.6736	−1.12037
$656$	−6.78287	−0.264827
$657$	3.56116	0.138934
$658$	−9.59001	−0.373858
$659$	16.9868	0.661712	0.330856	−	0.943681i	$-0.392663\pi$
$659$	16.9868	0.661712	0.330856	+	0.943681i	$0.392663\pi$
$660$	−7.48942	−0.291525
$661$	0.384996	0.0149746	0.00748731	−	0.999972i	$-0.497617\pi$
$661$	0.384996	0.0149746	0.00748731	+	0.999972i	$0.497617\pi$
$662$	12.8194	0.498241
$663$	3.39722	0.131937
$664$	−12.9526	−0.502659
$665$	71.0050	2.75345
$666$	0.856955	0.0332064
$667$	16.1763	0.626349
$668$	8.60095	0.332781
$669$	11.2410	0.434601
$670$	−20.2695	−0.783078
$671$	25.2736	0.975678
$672$	−2.89547	−0.111695
$673$	32.3479	1.24692	0.623460	−	0.781855i	$-0.285726\pi$
$673$	32.3479	1.24692	0.623460	+	0.781855i	$0.285726\pi$
$674$	12.5888	0.484901
$675$	−6.25163	−0.240625
$676$	1.00000	0.0384615
$677$	17.9284	0.689043	0.344521	−	0.938778i	$-0.388041\pi$
$677$	17.9284	0.689043	0.344521	+	0.938778i	$0.388041\pi$
$678$	−7.38702	−0.283697
$679$	23.8509	0.915315
$680$	−11.3955	−0.436996
$681$	−8.66975	−0.332226
$682$	16.3231	0.625044
$683$	−6.99201	−0.267542	−0.133771	−	0.991012i	$-0.542709\pi$
$683$	−6.99201	−0.267542	−0.133771	+	0.991012i	$0.542709\pi$
$684$	7.31075	0.279534
$685$	−3.18918	−0.121852
$686$	−16.2617	−0.620875
$687$	−10.0151	−0.382098
$688$	8.47357	0.323052
$689$	0.133425	0.00508309
$690$	12.1211	0.461444
$691$	23.5818	0.897093	0.448546	−	0.893760i	$-0.351942\pi$
$691$	23.5818	0.897093	0.448546	+	0.893760i	$0.351942\pi$
$692$	−10.4070	−0.395617
$693$	6.46487	0.245580
$694$	−35.2932	−1.33971
$695$	35.3720	1.34174
$696$	4.47655	0.169683
$697$	23.0429	0.872813
$698$	−6.51378	−0.246550
$699$	20.2982	0.767750
$700$	18.1014	0.684168
$701$	−15.6148	−0.589761	−0.294881	−	0.955534i	$-0.595280\pi$
$701$	−15.6148	−0.589761	−0.294881	+	0.955534i	$0.595280\pi$
$702$	−1.00000	−0.0377426
$703$	6.26499	0.236289
$704$	2.23275	0.0841501
$705$	11.1098	0.418421
$706$	9.00142	0.338773
$707$	26.9553	1.01376
$708$	4.10155	0.154146
$709$	−48.1429	−1.80805	−0.904023	−	0.427484i	$-0.859400\pi$
$709$	−48.1429	−1.80805	−0.904023	+	0.427484i	$0.859400\pi$
$710$	−26.2231	−0.984134
$711$	10.9268	0.409787
$712$	0.160251	0.00600565
$713$	−26.4179	−0.989358
$714$	9.83655	0.368124
$715$	7.48942	0.280089
$716$	−5.38352	−0.201192
$717$	−4.77489	−0.178321
$718$	25.0319	0.934182
$719$	−32.3978	−1.20823	−0.604117	−	0.796895i	$-0.706474\pi$
$719$	−32.3978	−1.20823	−0.604117	+	0.796895i	$0.706474\pi$
$720$	3.35434	0.125009
$721$	2.89547	0.107833
$722$	34.4471	1.28199
$723$	19.2803	0.717042
$724$	−24.2610	−0.901655
$725$	−27.9857	−1.03936
$726$	6.01481	0.223231
$727$	−51.1911	−1.89857	−0.949286	−	0.314413i	$-0.898192\pi$
$727$	−51.1911	−1.89857	−0.949286	+	0.314413i	$0.898192\pi$
$728$	2.89547	0.107313
$729$	1.00000	0.0370370
$730$	11.9454	0.442117
$731$	−28.7866	−1.06471
$732$	−11.3195	−0.418381
$733$	−51.8874	−1.91650	−0.958252	−	0.285924i	$-0.907699\pi$
$733$	−51.8874	−1.91650	−0.958252	+	0.285924i	$0.907699\pi$
$734$	11.7544	0.433862
$735$	−4.64152	−0.171205
$736$	−3.61357	−0.133198
$737$	−13.4920	−0.496983
$738$	−6.78287	−0.249681
$739$	−32.3216	−1.18897	−0.594485	−	0.804107i	$-0.702644\pi$
$739$	−32.3216	−1.18897	−0.594485	+	0.804107i	$0.702644\pi$
$740$	2.87452	0.105670
$741$	−7.31075	−0.268567
$742$	0.386328	0.0141826
$743$	11.8311	0.434040	0.217020	−	0.976167i	$-0.430366\pi$
$743$	11.8311	0.434040	0.217020	+	0.976167i	$0.430366\pi$
$744$	−7.31075	−0.268025
$745$	−7.78405	−0.285185
$746$	2.42429	0.0887595
$747$	−12.9526	−0.473912
$748$	−7.58516	−0.277341
$749$	−23.2387	−0.849124
$750$	−4.19840	−0.153304
$751$	−32.0436	−1.16929	−0.584644	−	0.811290i	$-0.698766\pi$
$751$	−32.0436	−1.16929	−0.584644	+	0.811290i	$0.698766\pi$
$752$	−3.31208	−0.120779
$753$	13.2074	0.481304
$754$	−4.47655	−0.163026
$755$	−35.0392	−1.27521
$756$	−2.89547	−0.105307
$757$	−35.3978	−1.28655	−0.643277	−	0.765633i	$-0.722426\pi$
$757$	−35.3978	−1.28655	−0.643277	+	0.765633i	$0.722426\pi$
$758$	−13.6771	−0.496776
$759$	8.06820	0.292857
$760$	24.5228	0.889535
$761$	3.40881	0.123569	0.0617846	−	0.998090i	$-0.480321\pi$
$761$	3.40881	0.123569	0.0617846	+	0.998090i	$0.480321\pi$
$762$	−2.35703	−0.0853861
$763$	−9.34123	−0.338175
$764$	−12.3723	−0.447613
$765$	−11.3955	−0.412004
$766$	8.61426	0.311246
$767$	−4.10155	−0.148098
$768$	−1.00000	−0.0360844
$769$	28.6803	1.03424	0.517119	−	0.855913i	$-0.327004\pi$
$769$	28.6803	1.03424	0.517119	+	0.855913i	$0.327004\pi$
$770$	21.6854	0.781487
$771$	−13.0988	−0.471741
$772$	−5.72454	−0.206031
$773$	10.2147	0.367397	0.183699	−	0.982983i	$-0.441193\pi$
$773$	10.2147	0.367397	0.183699	+	0.982983i	$0.441193\pi$
$774$	8.47357	0.304576
$775$	45.7041	1.64174
$776$	8.23733	0.295703
$777$	−2.48129	−0.0890157
$778$	−3.68944	−0.132273
$779$	−49.5879	−1.77667
$780$	−3.35434	−0.120105
$781$	−17.4549	−0.624584
$782$	12.2761	0.438992
$783$	4.47655	0.159979
$784$	1.38373	0.0494191
$785$	4.44429	0.158623
$786$	8.54820	0.304904
$787$	−44.6423	−1.59133	−0.795663	−	0.605740i	$-0.792877\pi$
$787$	−44.6423	−1.59133	−0.795663	+	0.605740i	$0.792877\pi$
$788$	−13.2494	−0.471990
$789$	−0.849962	−0.0302594
$790$	36.6523	1.30403
$791$	21.3889	0.760501
$792$	2.23275	0.0793374
$793$	11.3195	0.401967
$794$	18.6268	0.661041
$795$	−0.447554	−0.0158731
$796$	1.19933	0.0425090
$797$	33.0469	1.17058	0.585291	−	0.810824i	$-0.300980\pi$
$797$	33.0469	1.17058	0.585291	+	0.810824i	$0.300980\pi$
$798$	−21.1681	−0.749341
$799$	11.2519	0.398062
$800$	6.25163	0.221028
$801$	0.160251	0.00566218
$802$	37.9224	1.33909
$803$	7.95119	0.280591
$804$	6.04275	0.213111
$805$	−35.0964	−1.23699
$806$	7.31075	0.257510
$807$	−24.2292	−0.852909
$808$	9.30949	0.327507
$809$	−37.6013	−1.32199	−0.660996	−	0.750390i	$-0.729866\pi$
$809$	−37.6013	−1.32199	−0.660996	+	0.750390i	$0.729866\pi$
$810$	3.35434	0.117860
$811$	−38.1435	−1.33940	−0.669699	−	0.742633i	$-0.733577\pi$
$811$	−38.1435	−1.33940	−0.669699	+	0.742633i	$0.733577\pi$
$812$	−12.9617	−0.454866
$813$	5.02862	0.176361
$814$	1.91337	0.0670636
$815$	−1.81964	−0.0637390
$816$	3.39722	0.118927
$817$	61.9482	2.16729
$818$	12.7746	0.446652
$819$	2.89547	0.101176
$820$	−22.7521	−0.794538
$821$	17.9648	0.626977	0.313489	−	0.949592i	$-0.398502\pi$
$821$	17.9648	0.626977	0.313489	+	0.949592i	$0.398502\pi$
$822$	0.950761	0.0331616
$823$	19.1125	0.666219	0.333109	−	0.942888i	$-0.391902\pi$
$823$	19.1125	0.666219	0.333109	+	0.942888i	$0.391902\pi$
$824$	1.00000	0.0348367
$825$	−13.9583	−0.485967
$826$	−11.8759	−0.413216
$827$	12.6256	0.439034	0.219517	−	0.975609i	$-0.429552\pi$
$827$	12.6256	0.439034	0.219517	+	0.975609i	$0.429552\pi$
$828$	−3.61357	−0.125580
$829$	51.6003	1.79215	0.896076	−	0.443901i	$-0.146406\pi$
$829$	51.6003	1.79215	0.896076	+	0.443901i	$0.146406\pi$
$830$	−43.4476	−1.50809
$831$	−12.4334	−0.431310
$832$	1.00000	0.0346688
$833$	−4.70086	−0.162875
$834$	−10.5451	−0.365148
$835$	28.8506	0.998415
$836$	16.3231	0.564547
$837$	−7.31075	−0.252697
$838$	−5.72215	−0.197669
$839$	−17.1416	−0.591795	−0.295897	−	0.955220i	$-0.595619\pi$
$839$	−17.1416	−0.591795	−0.295897	+	0.955220i	$0.595619\pi$
$840$	−9.71240	−0.335110
$841$	−8.96054	−0.308984
$842$	16.7182	0.576149
$843$	−27.6456	−0.952165
$844$	−0.158374	−0.00545145
$845$	3.35434	0.115393
$846$	−3.31208	−0.113872
$847$	−17.4157	−0.598410
$848$	0.133425	0.00458184
$849$	23.6779	0.812625
$850$	−21.2382	−0.728463
$851$	−3.09667	−0.106152
$852$	7.81764	0.267828
$853$	−0.706926	−0.0242047	−0.0121023	−	0.999927i	$-0.503852\pi$
$853$	−0.706926	−0.0242047	−0.0121023	+	0.999927i	$0.503852\pi$
$854$	32.7752	1.12155
$855$	24.5228	0.838662
$856$	−8.02589	−0.274319
$857$	42.8475	1.46364	0.731822	−	0.681496i	$-0.238670\pi$
$857$	42.8475	1.46364	0.731822	+	0.681496i	$0.238670\pi$
$858$	−2.23275	−0.0762249
$859$	3.08796	0.105360	0.0526800	−	0.998611i	$-0.483224\pi$
$859$	3.08796	0.105360	0.0526800	+	0.998611i	$0.483224\pi$
$860$	28.4233	0.969226
$861$	19.6396	0.669315
$862$	−0.938685	−0.0319717
$863$	−16.6224	−0.565833	−0.282917	−	0.959144i	$-0.591302\pi$
$863$	−16.6224	−0.565833	−0.282917	+	0.959144i	$0.591302\pi$
$864$	−1.00000	−0.0340207
$865$	−34.9088	−1.18694
$866$	6.11345	0.207743
$867$	5.45888	0.185393
$868$	21.1681	0.718491
$869$	24.3969	0.827607
$870$	15.0159	0.509086
$871$	−6.04275	−0.204751
$872$	−3.22616	−0.109251
$873$	8.23733	0.278792
$874$	−26.4179	−0.893599
$875$	12.1563	0.410959
$876$	−3.56116	−0.120320
$877$	−57.4127	−1.93869	−0.969345	−	0.245703i	$-0.920981\pi$
$877$	−57.4127	−1.93869	−0.969345	+	0.245703i	$0.920981\pi$
$878$	−1.40875	−0.0475428
$879$	−8.69413	−0.293246
$880$	7.48942	0.252468
$881$	34.0975	1.14877	0.574387	−	0.818584i	$-0.305241\pi$
$881$	34.0975	1.14877	0.574387	+	0.818584i	$0.305241\pi$
$882$	1.38373	0.0465928
$883$	20.3201	0.683825	0.341912	−	0.939732i	$-0.388925\pi$
$883$	20.3201	0.683825	0.341912	+	0.939732i	$0.388925\pi$
$884$	−3.39722	−0.114261
$885$	13.7580	0.462470
$886$	10.3412	0.347420
$887$	14.0480	0.471685	0.235842	−	0.971791i	$-0.424215\pi$
$887$	14.0480	0.471685	0.235842	+	0.971791i	$0.424215\pi$
$888$	−0.856955	−0.0287575
$889$	6.82470	0.228893
$890$	0.537536	0.0180182
$891$	2.23275	0.0748001
$892$	−11.2410	−0.376376
$893$	−24.2138	−0.810283
$894$	2.32059	0.0776120
$895$	−18.0582	−0.603618
$896$	2.89547	0.0967308
$897$	3.61357	0.120653
$898$	35.6419	1.18938
$899$	−32.7269	−1.09150
$900$	6.25163	0.208388
$901$	−0.453275	−0.0151008
$902$	−15.1445	−0.504256
$903$	−24.5349	−0.816472
$904$	7.38702	0.245689
$905$	−81.3799	−2.70516
$906$	10.4459	0.347042
$907$	32.2833	1.07195	0.535974	−	0.844234i	$-0.319944\pi$
$907$	32.2833	1.07195	0.535974	+	0.844234i	$0.319944\pi$
$908$	8.66975	0.287716
$909$	9.30949	0.308776
$910$	9.71240	0.321963
$911$	−3.15357	−0.104482	−0.0522412	−	0.998634i	$-0.516636\pi$
$911$	−3.15357	−0.104482	−0.0522412	+	0.998634i	$0.516636\pi$
$912$	−7.31075	−0.242083
$913$	−28.9200	−0.957113
$914$	−8.76921	−0.290060
$915$	−37.9695	−1.25523
$916$	10.0151	0.330907
$917$	−24.7510	−0.817351
$918$	3.39722	0.112125
$919$	−31.0528	−1.02434	−0.512169	−	0.858884i	$-0.671158\pi$
$919$	−31.0528	−1.02434	−0.512169	+	0.858884i	$0.671158\pi$
$920$	−12.1211	−0.399622
$921$	0.525067	0.0173015
$922$	−0.392215	−0.0129169
$923$	−7.81764	−0.257321
$924$	−6.46487	−0.212678
$925$	5.35737	0.176149
$926$	17.3559	0.570349
$927$	1.00000	0.0328443
$928$	−4.47655	−0.146950
$929$	−24.4257	−0.801382	−0.400691	−	0.916213i	$-0.631230\pi$
$929$	−24.4257	−0.801382	−0.400691	+	0.916213i	$0.631230\pi$
$930$	−24.5228	−0.804134
$931$	10.1161	0.331543
$932$	−20.2982	−0.664891
$933$	−28.6465	−0.937844
$934$	−24.8716	−0.813825
$935$	−25.4432	−0.832083
$936$	1.00000	0.0326860
$937$	−43.1496	−1.40964	−0.704818	−	0.709388i	$-0.748971\pi$
$937$	−43.1496	−1.40964	−0.704818	+	0.709388i	$0.748971\pi$
$938$	−17.4966	−0.571284
$939$	26.0708	0.850788
$940$	−11.1098	−0.362363
$941$	6.83421	0.222789	0.111394	−	0.993776i	$-0.464468\pi$
$941$	6.83421	0.222789	0.111394	+	0.993776i	$0.464468\pi$
$942$	−1.32494	−0.0431687
$943$	24.5104	0.798167
$944$	−4.10155	−0.133494
$945$	−9.71240	−0.315944
$946$	18.9194	0.615122
$947$	−30.0480	−0.976430	−0.488215	−	0.872723i	$-0.662352\pi$
$947$	−30.0480	−0.976430	−0.488215	+	0.872723i	$0.662352\pi$
$948$	−10.9268	−0.354886
$949$	3.56116	0.115600
$950$	45.7041	1.48284
$951$	20.8187	0.675093
$952$	−9.83655	−0.318804
$953$	28.9498	0.937774	0.468887	−	0.883258i	$-0.344655\pi$
$953$	28.9498	0.937774	0.468887	+	0.883258i	$0.344655\pi$
$954$	0.133425	0.00431980
$955$	−41.5008	−1.34294
$956$	4.77489	0.154431
$957$	9.99502	0.323093
$958$	−37.4571	−1.21018
$959$	−2.75290	−0.0888957
$960$	−3.35434	−0.108261
$961$	22.4471	0.724101
$962$	0.856955	0.0276294
$963$	−8.02589	−0.258631
$964$	−19.2803	−0.620976
$965$	−19.2021	−0.618137
$966$	10.4630	0.336640
$967$	38.3597	1.23356	0.616782	−	0.787134i	$-0.288436\pi$
$967$	38.3597	1.23356	0.616782	+	0.787134i	$0.288436\pi$
$968$	−6.01481	−0.193323
$969$	24.8363	0.797856
$970$	27.6309	0.887173
$971$	15.6463	0.502115	0.251058	−	0.967972i	$-0.419222\pi$
$971$	15.6463	0.502115	0.251058	+	0.967972i	$0.419222\pi$
$972$	−1.00000	−0.0320750
$973$	30.5331	0.978847
$974$	−29.0283	−0.930128
$975$	−6.25163	−0.200212
$976$	11.3195	0.362328
$977$	−4.97351	−0.159117	−0.0795584	−	0.996830i	$-0.525351\pi$
$977$	−4.97351	−0.159117	−0.0795584	+	0.996830i	$0.525351\pi$
$978$	0.542471	0.0173463
$979$	0.357800	0.0114353
$980$	4.64152	0.148268
$981$	−3.22616	−0.103003
$982$	−38.9785	−1.24385
$983$	4.38744	0.139938	0.0699689	−	0.997549i	$-0.477710\pi$
$983$	4.38744	0.139938	0.0699689	+	0.997549i	$0.477710\pi$
$984$	6.78287	0.216230
$985$	−44.4430	−1.41607
$986$	15.2078	0.484316
$987$	9.59001	0.305253
$988$	7.31075	0.232586
$989$	−30.6198	−0.973653
$990$	7.48942	0.238030
$991$	22.1705	0.704270	0.352135	−	0.935949i	$-0.385456\pi$
$991$	22.1705	0.704270	0.352135	+	0.935949i	$0.385456\pi$
$992$	7.31075	0.232117
$993$	−12.8194	−0.406812
$994$	−22.6357	−0.717962
$995$	4.02295	0.127536
$996$	12.9526	0.410420
$997$	7.90025	0.250203	0.125102	−	0.992144i	$-0.460074\pi$
$997$	7.90025	0.250203	0.125102	+	0.992144i	$0.460074\pi$
$998$	−3.11970	−0.0987524
$999$	−0.856955	−0.0271129

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.y.1.11	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.y.1.11	✓	13	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:	\( N \)	\(=\)	\( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.35434 q^{5} -1.00000 q^{6} +2.89547 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.35434 q^{5} -1.00000 q^{6} +2.89547 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.35434 q^{10} +2.23275 q^{11} -1.00000 q^{12} +1.00000 q^{13} +2.89547 q^{14} -3.35434 q^{15} +1.00000 q^{16} -3.39722 q^{17} +1.00000 q^{18} +7.31075 q^{19} +3.35434 q^{20} -2.89547 q^{21} +2.23275 q^{22} -3.61357 q^{23} -1.00000 q^{24} +6.25163 q^{25} +1.00000 q^{26} -1.00000 q^{27} +2.89547 q^{28} -4.47655 q^{29} -3.35434 q^{30} +7.31075 q^{31} +1.00000 q^{32} -2.23275 q^{33} -3.39722 q^{34} +9.71240 q^{35} +1.00000 q^{36} +0.856955 q^{37} +7.31075 q^{38} -1.00000 q^{39} +3.35434 q^{40} -6.78287 q^{41} -2.89547 q^{42} +8.47357 q^{43} +2.23275 q^{44} +3.35434 q^{45} -3.61357 q^{46} -3.31208 q^{47} -1.00000 q^{48} +1.38373 q^{49} +6.25163 q^{50} +3.39722 q^{51} +1.00000 q^{52} +0.133425 q^{53} -1.00000 q^{54} +7.48942 q^{55} +2.89547 q^{56} -7.31075 q^{57} -4.47655 q^{58} -4.10155 q^{59} -3.35434 q^{60} +11.3195 q^{61} +7.31075 q^{62} +2.89547 q^{63} +1.00000 q^{64} +3.35434 q^{65} -2.23275 q^{66} -6.04275 q^{67} -3.39722 q^{68} +3.61357 q^{69} +9.71240 q^{70} -7.81764 q^{71} +1.00000 q^{72} +3.56116 q^{73} +0.856955 q^{74} -6.25163 q^{75} +7.31075 q^{76} +6.46487 q^{77} -1.00000 q^{78} +10.9268 q^{79} +3.35434 q^{80} +1.00000 q^{81} -6.78287 q^{82} -12.9526 q^{83} -2.89547 q^{84} -11.3955 q^{85} +8.47357 q^{86} +4.47655 q^{87} +2.23275 q^{88} +0.160251 q^{89} +3.35434 q^{90} +2.89547 q^{91} -3.61357 q^{92} -7.31075 q^{93} -3.31208 q^{94} +24.5228 q^{95} -1.00000 q^{96} +8.23733 q^{97} +1.38373 q^{98} +2.23275 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 13 q^{2} - 13 q^{3} + 13 q^{4} + 3 q^{5} - 13 q^{6} + 5 q^{7} + 13 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q + 13 * q^2 - 13 * q^3 + 13 * q^4 + 3 * q^5 - 13 * q^6 + 5 * q^7 + 13 * q^8 + 13 * q^9	\( 13 q + 13 q^{2} - 13 q^{3} + 13 q^{4} + 3 q^{5} - 13 q^{6} + 5 q^{7} + 13 q^{8} + 13 q^{9} + 3 q^{10} + 8 q^{11} - 13 q^{12} + 13 q^{13} + 5 q^{14} - 3 q^{15} + 13 q^{16} - q^{17} + 13 q^{18} + 5 q^{19} + 3 q^{20} - 5 q^{21} + 8 q^{22} - 9 q^{23} - 13 q^{24} + 24 q^{25} + 13 q^{26} - 13 q^{27} + 5 q^{28} - q^{29} - 3 q^{30} + 5 q^{31} + 13 q^{32} - 8 q^{33} - q^{34} + 28 q^{35} + 13 q^{36} + 35 q^{37} + 5 q^{38} - 13 q^{39} + 3 q^{40} + 24 q^{41} - 5 q^{42} + 9 q^{43} + 8 q^{44} + 3 q^{45} - 9 q^{46} - 8 q^{47} - 13 q^{48} - 16 q^{49} + 24 q^{50} + q^{51} + 13 q^{52} + 32 q^{53} - 13 q^{54} - 4 q^{55} + 5 q^{56} - 5 q^{57} - q^{58} + 12 q^{59} - 3 q^{60} + 17 q^{61} + 5 q^{62} + 5 q^{63} + 13 q^{64} + 3 q^{65} - 8 q^{66} + 20 q^{67} - q^{68} + 9 q^{69} + 28 q^{70} + 16 q^{71} + 13 q^{72} + 46 q^{73} + 35 q^{74} - 24 q^{75} + 5 q^{76} - 7 q^{77} - 13 q^{78} + 17 q^{79} + 3 q^{80} + 13 q^{81} + 24 q^{82} + 13 q^{83} - 5 q^{84} + 11 q^{85} + 9 q^{86} + q^{87} + 8 q^{88} + 14 q^{89} + 3 q^{90} + 5 q^{91} - 9 q^{92} - 5 q^{93} - 8 q^{94} + 2 q^{95} - 13 q^{96} + 46 q^{97} - 16 q^{98} + 8 q^{99}+O(q^{100}) \) 13 * q + 13 * q^2 - 13 * q^3 + 13 * q^4 + 3 * q^5 - 13 * q^6 + 5 * q^7 + 13 * q^8 + 13 * q^9 + 3 * q^10 + 8 * q^11 - 13 * q^12 + 13 * q^13 + 5 * q^14 - 3 * q^15 + 13 * q^16 - q^17 + 13 * q^18 + 5 * q^19 + 3 * q^20 - 5 * q^21 + 8 * q^22 - 9 * q^23 - 13 * q^24 + 24 * q^25 + 13 * q^26 - 13 * q^27 + 5 * q^28 - q^29 - 3 * q^30 + 5 * q^31 + 13 * q^32 - 8 * q^33 - q^34 + 28 * q^35 + 13 * q^36 + 35 * q^37 + 5 * q^38 - 13 * q^39 + 3 * q^40 + 24 * q^41 - 5 * q^42 + 9 * q^43 + 8 * q^44 + 3 * q^45 - 9 * q^46 - 8 * q^47 - 13 * q^48 - 16 * q^49 + 24 * q^50 + q^51 + 13 * q^52 + 32 * q^53 - 13 * q^54 - 4 * q^55 + 5 * q^56 - 5 * q^57 - q^58 + 12 * q^59 - 3 * q^60 + 17 * q^61 + 5 * q^62 + 5 * q^63 + 13 * q^64 + 3 * q^65 - 8 * q^66 + 20 * q^67 - q^68 + 9 * q^69 + 28 * q^70 + 16 * q^71 + 13 * q^72 + 46 * q^73 + 35 * q^74 - 24 * q^75 + 5 * q^76 - 7 * q^77 - 13 * q^78 + 17 * q^79 + 3 * q^80 + 13 * q^81 + 24 * q^82 + 13 * q^83 - 5 * q^84 + 11 * q^85 + 9 * q^86 + q^87 + 8 * q^88 + 14 * q^89 + 3 * q^90 + 5 * q^91 - 9 * q^92 - 5 * q^93 - 8 * q^94 + 2 * q^95 - 13 * q^96 + 46 * q^97 - 16 * q^98 + 8 * q^99

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