LMFDB - Embedded newform 8026.2.a.c.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8026,2,Mod(1,8026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8026, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8026 = 2 \cdot 4013 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8026.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:	$64.0879326623$
Analytic rank:	$0$
Dimension:	$86$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	8026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.06398 q^{3} +1.00000 q^{4} -1.63652 q^{5} +2.06398 q^{6} +0.580095 q^{7} -1.00000 q^{8} +1.26000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.06398 q^{3} +1.00000 q^{4} -1.63652 q^{5} +2.06398 q^{6} +0.580095 q^{7} -1.00000 q^{8} +1.26000 q^{9} +1.63652 q^{10} -3.54895 q^{11} -2.06398 q^{12} +0.886296 q^{13} -0.580095 q^{14} +3.37774 q^{15} +1.00000 q^{16} +7.07655 q^{17} -1.26000 q^{18} -7.35734 q^{19} -1.63652 q^{20} -1.19730 q^{21} +3.54895 q^{22} +0.578326 q^{23} +2.06398 q^{24} -2.32181 q^{25} -0.886296 q^{26} +3.59132 q^{27} +0.580095 q^{28} -4.60362 q^{29} -3.37774 q^{30} -1.99169 q^{31} -1.00000 q^{32} +7.32494 q^{33} -7.07655 q^{34} -0.949336 q^{35} +1.26000 q^{36} +10.0064 q^{37} +7.35734 q^{38} -1.82929 q^{39} +1.63652 q^{40} -3.58380 q^{41} +1.19730 q^{42} +10.8843 q^{43} -3.54895 q^{44} -2.06201 q^{45} -0.578326 q^{46} -5.51320 q^{47} -2.06398 q^{48} -6.66349 q^{49} +2.32181 q^{50} -14.6058 q^{51} +0.886296 q^{52} -3.11553 q^{53} -3.59132 q^{54} +5.80792 q^{55} -0.580095 q^{56} +15.1854 q^{57} +4.60362 q^{58} +0.556133 q^{59} +3.37774 q^{60} -14.0553 q^{61} +1.99169 q^{62} +0.730918 q^{63} +1.00000 q^{64} -1.45044 q^{65} -7.32494 q^{66} +2.93561 q^{67} +7.07655 q^{68} -1.19365 q^{69} +0.949336 q^{70} +4.80098 q^{71} -1.26000 q^{72} -15.2142 q^{73} -10.0064 q^{74} +4.79215 q^{75} -7.35734 q^{76} -2.05873 q^{77} +1.82929 q^{78} -13.2416 q^{79} -1.63652 q^{80} -11.1924 q^{81} +3.58380 q^{82} +10.6332 q^{83} -1.19730 q^{84} -11.5809 q^{85} -10.8843 q^{86} +9.50176 q^{87} +3.54895 q^{88} +4.67275 q^{89} +2.06201 q^{90} +0.514136 q^{91} +0.578326 q^{92} +4.11079 q^{93} +5.51320 q^{94} +12.0404 q^{95} +2.06398 q^{96} -12.5355 q^{97} +6.66349 q^{98} -4.47166 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9}+O(q^{10}) $ 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9	\( 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9} - 25 q^{10} + 44 q^{11} + 11 q^{12} - 36 q^{13} + 3 q^{14} + 19 q^{15} + 86 q^{16} + 21 q^{17} - 105 q^{18} + 35 q^{19} + 25 q^{20} + 23 q^{21} - 44 q^{22} + 38 q^{23} - 11 q^{24} + 85 q^{25} + 36 q^{26} + 47 q^{27} - 3 q^{28} + 30 q^{29} - 19 q^{30} + 23 q^{31} - 86 q^{32} + 5 q^{33} - 21 q^{34} + 59 q^{35} + 105 q^{36} - 20 q^{37} - 35 q^{38} + 4 q^{39} - 25 q^{40} + 64 q^{41} - 23 q^{42} + 23 q^{43} + 44 q^{44} + 60 q^{45} - 38 q^{46} + 77 q^{47} + 11 q^{48} + 109 q^{49} - 85 q^{50} + 47 q^{51} - 36 q^{52} + 22 q^{53} - 47 q^{54} + 6 q^{55} + 3 q^{56} - 9 q^{57} - 30 q^{58} + 145 q^{59} + 19 q^{60} - 24 q^{61} - 23 q^{62} + 6 q^{63} + 86 q^{64} + 37 q^{65} - 5 q^{66} + 44 q^{67} + 21 q^{68} + 25 q^{69} - 59 q^{70} + 107 q^{71} - 105 q^{72} - 55 q^{73} + 20 q^{74} + 86 q^{75} + 35 q^{76} + 25 q^{77} - 4 q^{78} + 2 q^{79} + 25 q^{80} + 170 q^{81} - 64 q^{82} + 109 q^{83} + 23 q^{84} - 13 q^{85} - 23 q^{86} + 3 q^{87} - 44 q^{88} + 121 q^{89} - 60 q^{90} + 81 q^{91} + 38 q^{92} + 27 q^{93} - 77 q^{94} + 49 q^{95} - 11 q^{96} - 56 q^{97} - 109 q^{98} + 158 q^{99}+O(q^{100}) \) 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9 - 25 * q^10 + 44 * q^11 + 11 * q^12 - 36 * q^13 + 3 * q^14 + 19 * q^15 + 86 * q^16 + 21 * q^17 - 105 * q^18 + 35 * q^19 + 25 * q^20 + 23 * q^21 - 44 * q^22 + 38 * q^23 - 11 * q^24 + 85 * q^25 + 36 * q^26 + 47 * q^27 - 3 * q^28 + 30 * q^29 - 19 * q^30 + 23 * q^31 - 86 * q^32 + 5 * q^33 - 21 * q^34 + 59 * q^35 + 105 * q^36 - 20 * q^37 - 35 * q^38 + 4 * q^39 - 25 * q^40 + 64 * q^41 - 23 * q^42 + 23 * q^43 + 44 * q^44 + 60 * q^45 - 38 * q^46 + 77 * q^47 + 11 * q^48 + 109 * q^49 - 85 * q^50 + 47 * q^51 - 36 * q^52 + 22 * q^53 - 47 * q^54 + 6 * q^55 + 3 * q^56 - 9 * q^57 - 30 * q^58 + 145 * q^59 + 19 * q^60 - 24 * q^61 - 23 * q^62 + 6 * q^63 + 86 * q^64 + 37 * q^65 - 5 * q^66 + 44 * q^67 + 21 * q^68 + 25 * q^69 - 59 * q^70 + 107 * q^71 - 105 * q^72 - 55 * q^73 + 20 * q^74 + 86 * q^75 + 35 * q^76 + 25 * q^77 - 4 * q^78 + 2 * q^79 + 25 * q^80 + 170 * q^81 - 64 * q^82 + 109 * q^83 + 23 * q^84 - 13 * q^85 - 23 * q^86 + 3 * q^87 - 44 * q^88 + 121 * q^89 - 60 * q^90 + 81 * q^91 + 38 * q^92 + 27 * q^93 - 77 * q^94 + 49 * q^95 - 11 * q^96 - 56 * q^97 - 109 * q^98 + 158 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.06398	−1.19164	−0.595819	−	0.803119i	$-0.703172\pi$
$3$	−2.06398	−1.19164	−0.595819	+	0.803119i	$0.703172\pi$
$4$	1.00000	0.500000
$5$	−1.63652	−0.731874	−0.365937	−	0.930640i	$-0.619251\pi$
$5$	−1.63652	−0.731874	−0.365937	+	0.930640i	$0.619251\pi$
$6$	2.06398	0.842615
$7$	0.580095	0.219255	0.109628	−	0.993973i	$-0.465034\pi$
$7$	0.580095	0.219255	0.109628	+	0.993973i	$0.465034\pi$
$8$	−1.00000	−0.353553
$9$	1.26000	0.419999
$10$	1.63652	0.517513
$11$	−3.54895	−1.07005	−0.535024	−	0.844837i	$-0.679697\pi$
$11$	−3.54895	−1.07005	−0.535024	+	0.844837i	$0.679697\pi$
$12$	−2.06398	−0.595819
$13$	0.886296	0.245814	0.122907	−	0.992418i	$-0.460778\pi$
$13$	0.886296	0.245814	0.122907	+	0.992418i	$0.460778\pi$
$14$	−0.580095	−0.155037
$15$	3.37774	0.872128
$16$	1.00000	0.250000
$17$	7.07655	1.71632	0.858158	−	0.513386i	$-0.171609\pi$
$17$	7.07655	1.71632	0.858158	+	0.513386i	$0.171609\pi$
$18$	−1.26000	−0.296984
$19$	−7.35734	−1.68789	−0.843944	−	0.536431i	$-0.819772\pi$
$19$	−7.35734	−1.68789	−0.843944	+	0.536431i	$0.819772\pi$
$20$	−1.63652	−0.365937
$21$	−1.19730	−0.261273
$22$	3.54895	0.756638
$23$	0.578326	0.120589	0.0602946	−	0.998181i	$-0.480796\pi$
$23$	0.578326	0.120589	0.0602946	+	0.998181i	$0.480796\pi$
$24$	2.06398	0.421307
$25$	−2.32181	−0.464361
$26$	−0.886296	−0.173817
$27$	3.59132	0.691151
$28$	0.580095	0.109628
$29$	−4.60362	−0.854871	−0.427435	−	0.904046i	$-0.640583\pi$
$29$	−4.60362	−0.854871	−0.427435	+	0.904046i	$0.640583\pi$
$30$	−3.37774	−0.616687
$31$	−1.99169	−0.357717	−0.178859	−	0.983875i	$-0.557240\pi$
$31$	−1.99169	−0.357717	−0.178859	+	0.983875i	$0.557240\pi$
$32$	−1.00000	−0.176777
$33$	7.32494	1.27511
$34$	−7.07655	−1.21362
$35$	−0.949336	−0.160467
$36$	1.26000	0.209999
$37$	10.0064	1.64504	0.822519	−	0.568737i	$-0.192568\pi$
$37$	10.0064	1.64504	0.822519	+	0.568737i	$0.192568\pi$
$38$	7.35734	1.19352
$39$	−1.82929	−0.292921
$40$	1.63652	0.258756
$41$	−3.58380	−0.559695	−0.279847	−	0.960044i	$-0.590284\pi$
$41$	−3.58380	−0.559695	−0.279847	+	0.960044i	$0.590284\pi$
$42$	1.19730	0.184748
$43$	10.8843	1.65984	0.829921	−	0.557881i	$-0.188385\pi$
$43$	10.8843	1.65984	0.829921	+	0.557881i	$0.188385\pi$
$44$	−3.54895	−0.535024
$45$	−2.06201	−0.307386
$46$	−0.578326	−0.0852695
$47$	−5.51320	−0.804182	−0.402091	−	0.915600i	$-0.631717\pi$
$47$	−5.51320	−0.804182	−0.402091	+	0.915600i	$0.631717\pi$
$48$	−2.06398	−0.297909
$49$	−6.66349	−0.951927
$50$	2.32181	0.328353
$51$	−14.6058	−2.04523
$52$	0.886296	0.122907
$53$	−3.11553	−0.427951	−0.213975	−	0.976839i	$-0.568641\pi$
$53$	−3.11553	−0.427951	−0.213975	+	0.976839i	$0.568641\pi$
$54$	−3.59132	−0.488717
$55$	5.80792	0.783139
$56$	−0.580095	−0.0775185
$57$	15.1854	2.01135
$58$	4.60362	0.604485
$59$	0.556133	0.0724024	0.0362012	−	0.999345i	$-0.488474\pi$
$59$	0.556133	0.0724024	0.0362012	+	0.999345i	$0.488474\pi$
$60$	3.37774	0.436064
$61$	−14.0553	−1.79959	−0.899796	−	0.436312i	$-0.856285\pi$
$61$	−14.0553	−1.79959	−0.899796	+	0.436312i	$0.856285\pi$
$62$	1.99169	0.252944
$63$	0.730918	0.0920870
$64$	1.00000	0.125000
$65$	−1.45044	−0.179905
$66$	−7.32494	−0.901638
$67$	2.93561	0.358642	0.179321	−	0.983791i	$-0.442610\pi$
$67$	2.93561	0.358642	0.179321	+	0.983791i	$0.442610\pi$
$68$	7.07655	0.858158
$69$	−1.19365	−0.143699
$70$	0.949336	0.113467
$71$	4.80098	0.569772	0.284886	−	0.958561i	$-0.408044\pi$
$71$	4.80098	0.569772	0.284886	+	0.958561i	$0.408044\pi$
$72$	−1.26000	−0.148492
$73$	−15.2142	−1.78068	−0.890342	−	0.455292i	$-0.849535\pi$
$73$	−15.2142	−1.78068	−0.890342	+	0.455292i	$0.849535\pi$
$74$	−10.0064	−1.16322
$75$	4.79215	0.553350
$76$	−7.35734	−0.843944
$77$	−2.05873	−0.234614
$78$	1.82929	0.207127
$79$	−13.2416	−1.48980	−0.744900	−	0.667176i	$-0.767503\pi$
$79$	−13.2416	−1.48980	−0.744900	+	0.667176i	$0.767503\pi$
$80$	−1.63652	−0.182968
$81$	−11.1924	−1.24360
$82$	3.58380	0.395764
$83$	10.6332	1.16714	0.583571	−	0.812062i	$-0.301655\pi$
$83$	10.6332	1.16714	0.583571	+	0.812062i	$0.301655\pi$
$84$	−1.19730	−0.130636
$85$	−11.5809	−1.25613
$86$	−10.8843	−1.17369
$87$	9.50176	1.01870
$88$	3.54895	0.378319
$89$	4.67275	0.495311	0.247656	−	0.968848i	$-0.420340\pi$
$89$	4.67275	0.495311	0.247656	+	0.968848i	$0.420340\pi$
$90$	2.06201	0.217355
$91$	0.514136	0.0538961
$92$	0.578326	0.0602946
$93$	4.11079	0.426269
$94$	5.51320	0.568643
$95$	12.0404	1.23532
$96$	2.06398	0.210654
$97$	−12.5355	−1.27279	−0.636394	−	0.771364i	$-0.719575\pi$
$97$	−12.5355	−1.27279	−0.636394	+	0.771364i	$0.719575\pi$
$98$	6.66349	0.673114
$99$	−4.47166	−0.449419
$100$	−2.32181	−0.232181
$101$	13.9965	1.39270	0.696350	−	0.717703i	$-0.254806\pi$
$101$	13.9965	1.39270	0.696350	+	0.717703i	$0.254806\pi$
$102$	14.6058	1.44619
$103$	12.6899	1.25037	0.625187	−	0.780475i	$-0.285023\pi$
$103$	12.6899	1.25037	0.625187	+	0.780475i	$0.285023\pi$
$104$	−0.886296	−0.0869084
$105$	1.95941	0.191219
$106$	3.11553	0.302607
$107$	18.0426	1.74425	0.872123	−	0.489287i	$-0.162743\pi$
$107$	18.0426	1.74425	0.872123	+	0.489287i	$0.162743\pi$
$108$	3.59132	0.345575
$109$	3.38255	0.323989	0.161995	−	0.986792i	$-0.448207\pi$
$109$	3.38255	0.323989	0.161995	+	0.986792i	$0.448207\pi$
$110$	−5.80792	−0.553763
$111$	−20.6529	−1.96029
$112$	0.580095	0.0548138
$113$	−8.56600	−0.805822	−0.402911	−	0.915239i	$-0.632002\pi$
$113$	−8.56600	−0.805822	−0.402911	+	0.915239i	$0.632002\pi$
$114$	−15.1854	−1.42224
$115$	−0.946441	−0.0882561
$116$	−4.60362	−0.427435
$117$	1.11673	0.103242
$118$	−0.556133	−0.0511962
$119$	4.10507	0.376311
$120$	−3.37774	−0.308344
$121$	1.59501	0.145001
$122$	14.0553	1.27250
$123$	7.39687	0.666953
$124$	−1.99169	−0.178859
$125$	11.9823	1.07173
$126$	−0.730918	−0.0651153
$127$	−15.2144	−1.35006	−0.675030	−	0.737790i	$-0.735869\pi$
$127$	−15.2144	−1.35006	−0.675030	+	0.737790i	$0.735869\pi$
$128$	−1.00000	−0.0883883
$129$	−22.4650	−1.97793
$130$	1.45044	0.127212
$131$	−21.8752	−1.91125	−0.955623	−	0.294593i	$-0.904816\pi$
$131$	−21.8752	−1.91125	−0.955623	+	0.294593i	$0.904816\pi$
$132$	7.32494	0.637554
$133$	−4.26795	−0.370079
$134$	−2.93561	−0.253598
$135$	−5.87727	−0.505835
$136$	−7.07655	−0.606809
$137$	−14.8111	−1.26540	−0.632699	−	0.774398i	$-0.718053\pi$
$137$	−14.8111	−1.26540	−0.632699	+	0.774398i	$0.718053\pi$
$138$	1.19365	0.101610
$139$	19.4273	1.64780	0.823901	−	0.566734i	$-0.191793\pi$
$139$	19.4273	1.64780	0.823901	+	0.566734i	$0.191793\pi$
$140$	−0.949336	−0.0802336
$141$	11.3791	0.958293
$142$	−4.80098	−0.402890
$143$	−3.14542	−0.263033
$144$	1.26000	0.105000
$145$	7.53391	0.625657
$146$	15.2142	1.25913
$147$	13.7533	1.13435
$148$	10.0064	0.822519
$149$	−23.2174	−1.90205	−0.951023	−	0.309119i	$-0.899966\pi$
$149$	−23.2174	−1.90205	−0.951023	+	0.309119i	$0.899966\pi$
$150$	−4.79215	−0.391277
$151$	0.268548	0.0218542	0.0109271	−	0.999940i	$-0.496522\pi$
$151$	0.268548	0.0218542	0.0109271	+	0.999940i	$0.496522\pi$
$152$	7.35734	0.596759
$153$	8.91643	0.720851
$154$	2.05873	0.165897
$155$	3.25943	0.261804
$156$	−1.82929	−0.146461
$157$	−7.54517	−0.602170	−0.301085	−	0.953597i	$-0.597349\pi$
$157$	−7.54517	−0.602170	−0.301085	+	0.953597i	$0.597349\pi$
$158$	13.2416	1.05345
$159$	6.43037	0.509962
$160$	1.63652	0.129378
$161$	0.335484	0.0264398
$162$	11.1924	0.879358
$163$	−19.8990	−1.55861	−0.779303	−	0.626647i	$-0.784427\pi$
$163$	−19.8990	−1.55861	−0.779303	+	0.626647i	$0.784427\pi$
$164$	−3.58380	−0.279847
$165$	−11.9874	−0.933218
$166$	−10.6332	−0.825295
$167$	20.0497	1.55149	0.775747	−	0.631044i	$-0.217373\pi$
$167$	20.0497	1.55149	0.775747	+	0.631044i	$0.217373\pi$
$168$	1.19730	0.0923739
$169$	−12.2145	−0.939575
$170$	11.5809	0.888215
$171$	−9.27022	−0.708912
$172$	10.8843	0.829921
$173$	−5.82014	−0.442497	−0.221248	−	0.975217i	$-0.571013\pi$
$173$	−5.82014	−0.442497	−0.221248	+	0.975217i	$0.571013\pi$
$174$	−9.50176	−0.720327
$175$	−1.34687	−0.101814
$176$	−3.54895	−0.267512
$177$	−1.14785	−0.0862774
$178$	−4.67275	−0.350238
$179$	−1.45393	−0.108672	−0.0543360	−	0.998523i	$-0.517304\pi$
$179$	−1.45393	−0.108672	−0.0543360	+	0.998523i	$0.517304\pi$
$180$	−2.06201	−0.153693
$181$	−8.41969	−0.625831	−0.312915	−	0.949781i	$-0.601306\pi$
$181$	−8.41969	−0.625831	−0.312915	+	0.949781i	$0.601306\pi$
$182$	−0.514136	−0.0381103
$183$	29.0097	2.14446
$184$	−0.578326	−0.0426347
$185$	−16.3756	−1.20396
$186$	−4.11079	−0.301418
$187$	−25.1143	−1.83654
$188$	−5.51320	−0.402091
$189$	2.08331	0.151538
$190$	−12.0404	−0.873504
$191$	−10.4040	−0.752807	−0.376403	−	0.926456i	$-0.622839\pi$
$191$	−10.4040	−0.752807	−0.376403	+	0.926456i	$0.622839\pi$
$192$	−2.06398	−0.148955
$193$	14.4951	1.04338	0.521688	−	0.853136i	$-0.325302\pi$
$193$	14.4951	1.04338	0.521688	+	0.853136i	$0.325302\pi$
$194$	12.5355	0.899997
$195$	2.99367	0.214381
$196$	−6.66349	−0.475964
$197$	−2.10073	−0.149671	−0.0748355	−	0.997196i	$-0.523843\pi$
$197$	−2.10073	−0.149671	−0.0748355	+	0.997196i	$0.523843\pi$
$198$	4.47166	0.317787
$199$	−8.51886	−0.603886	−0.301943	−	0.953326i	$-0.597635\pi$
$199$	−8.51886	−0.603886	−0.301943	+	0.953326i	$0.597635\pi$
$200$	2.32181	0.164176
$201$	−6.05903	−0.427371
$202$	−13.9965	−0.984787
$203$	−2.67054	−0.187435
$204$	−14.6058	−1.02261
$205$	5.86495	0.409626
$206$	−12.6899	−0.884147
$207$	0.728689	0.0506474
$208$	0.886296	0.0614536
$209$	26.1108	1.80612
$210$	−1.95941	−0.135212
$211$	−6.01330	−0.413972	−0.206986	−	0.978344i	$-0.566366\pi$
$211$	−6.01330	−0.413972	−0.206986	+	0.978344i	$0.566366\pi$
$212$	−3.11553	−0.213975
$213$	−9.90911	−0.678961
$214$	−18.0426	−1.23337
$215$	−17.8124	−1.21479
$216$	−3.59132	−0.244359
$217$	−1.15537	−0.0784314
$218$	−3.38255	−0.229095
$219$	31.4017	2.12193
$220$	5.80792	0.391570
$221$	6.27192	0.421895
$222$	20.6529	1.38613
$223$	0.468926	0.0314016	0.0157008	−	0.999877i	$-0.495002\pi$
$223$	0.468926	0.0314016	0.0157008	+	0.999877i	$0.495002\pi$
$224$	−0.580095	−0.0387592
$225$	−2.92547	−0.195031
$226$	8.56600	0.569802
$227$	26.4649	1.75654	0.878270	−	0.478166i	$-0.158698\pi$
$227$	26.4649	1.75654	0.878270	+	0.478166i	$0.158698\pi$
$228$	15.1854	1.00568
$229$	13.3509	0.882251	0.441126	−	0.897445i	$-0.354579\pi$
$229$	13.3509	0.882251	0.441126	+	0.897445i	$0.354579\pi$
$230$	0.946441	0.0624065
$231$	4.24916	0.279574
$232$	4.60362	0.302243
$233$	−12.7064	−0.832425	−0.416212	−	0.909267i	$-0.636643\pi$
$233$	−12.7064	−0.832425	−0.416212	+	0.909267i	$0.636643\pi$
$234$	−1.11673	−0.0730029
$235$	9.02245	0.588560
$236$	0.556133	0.0362012
$237$	27.3304	1.77530
$238$	−4.10507	−0.266092
$239$	23.0565	1.49140	0.745701	−	0.666281i	$-0.232115\pi$
$239$	23.0565	1.49140	0.745701	+	0.666281i	$0.232115\pi$
$240$	3.37774	0.218032
$241$	−23.1288	−1.48986	−0.744929	−	0.667144i	$-0.767517\pi$
$241$	−23.1288	−1.48986	−0.744929	+	0.667144i	$0.767517\pi$
$242$	−1.59501	−0.102531
$243$	12.3269	0.790769
$244$	−14.0553	−0.899796
$245$	10.9049	0.696690
$246$	−7.39687	−0.471607
$247$	−6.52078	−0.414907
$248$	1.99169	0.126472
$249$	−21.9466	−1.39081
$250$	−11.9823	−0.757826
$251$	6.45395	0.407370	0.203685	−	0.979037i	$-0.434708\pi$
$251$	6.45395	0.407370	0.203685	+	0.979037i	$0.434708\pi$
$252$	0.730918	0.0460435
$253$	−2.05245	−0.129036
$254$	15.2144	0.954636
$255$	23.9027	1.49685
$256$	1.00000	0.0625000
$257$	−14.8905	−0.928844	−0.464422	−	0.885614i	$-0.653738\pi$
$257$	−14.8905	−0.928844	−0.464422	+	0.885614i	$0.653738\pi$
$258$	22.4650	1.39861
$259$	5.80465	0.360683
$260$	−1.45044	−0.0899525
$261$	−5.80055	−0.359045
$262$	21.8752	1.35145
$263$	−13.7096	−0.845368	−0.422684	−	0.906277i	$-0.638912\pi$
$263$	−13.7096	−0.845368	−0.422684	+	0.906277i	$0.638912\pi$
$264$	−7.32494	−0.450819
$265$	5.09862	0.313206
$266$	4.26795	0.261685
$267$	−9.64445	−0.590231
$268$	2.93561	0.179321
$269$	−11.7222	−0.714717	−0.357358	−	0.933967i	$-0.616322\pi$
$269$	−11.7222	−0.714717	−0.357358	+	0.933967i	$0.616322\pi$
$270$	5.87727	0.357679
$271$	15.4815	0.940434	0.470217	−	0.882551i	$-0.344176\pi$
$271$	15.4815	0.940434	0.470217	+	0.882551i	$0.344176\pi$
$272$	7.07655	0.429079
$273$	−1.06116	−0.0642246
$274$	14.8111	0.894771
$275$	8.23996	0.496888
$276$	−1.19365	−0.0718493
$277$	−30.0761	−1.80710	−0.903548	−	0.428488i	$-0.859047\pi$
$277$	−30.0761	−1.80710	−0.903548	+	0.428488i	$0.859047\pi$
$278$	−19.4273	−1.16517
$279$	−2.50952	−0.150241
$280$	0.949336	0.0567337
$281$	1.98841	0.118619	0.0593094	−	0.998240i	$-0.481110\pi$
$281$	1.98841	0.118619	0.0593094	+	0.998240i	$0.481110\pi$
$282$	−11.3791	−0.677616
$283$	29.9209	1.77861	0.889307	−	0.457311i	$-0.151187\pi$
$283$	29.9209	1.77861	0.889307	+	0.457311i	$0.151187\pi$
$284$	4.80098	0.284886
$285$	−24.8511	−1.47205
$286$	3.14542	0.185992
$287$	−2.07894	−0.122716
$288$	−1.26000	−0.0742460
$289$	33.0776	1.94574
$290$	−7.53391	−0.442407
$291$	25.8730	1.51670
$292$	−15.2142	−0.890342
$293$	11.1357	0.650556	0.325278	−	0.945619i	$-0.394542\pi$
$293$	11.1357	0.650556	0.325278	+	0.945619i	$0.394542\pi$
$294$	−13.7533	−0.802108
$295$	−0.910123	−0.0529894
$296$	−10.0064	−0.581609
$297$	−12.7454	−0.739564
$298$	23.2174	1.34495
$299$	0.512568	0.0296426
$300$	4.79215	0.276675
$301$	6.31394	0.363929
$302$	−0.268548	−0.0154532
$303$	−28.8884	−1.65959
$304$	−7.35734	−0.421972
$305$	23.0017	1.31707
$306$	−8.91643	−0.509718
$307$	−18.5541	−1.05894	−0.529470	−	0.848329i	$-0.677609\pi$
$307$	−18.5541	−1.05894	−0.529470	+	0.848329i	$0.677609\pi$
$308$	−2.05873	−0.117307
$309$	−26.1917	−1.48999
$310$	−3.25943	−0.185123
$311$	−6.98601	−0.396140	−0.198070	−	0.980188i	$-0.563467\pi$
$311$	−6.98601	−0.396140	−0.198070	+	0.980188i	$0.563467\pi$
$312$	1.82929	0.103563
$313$	5.17135	0.292302	0.146151	−	0.989262i	$-0.453311\pi$
$313$	5.17135	0.292302	0.146151	+	0.989262i	$0.453311\pi$
$314$	7.54517	0.425799
$315$	−1.19616	−0.0673960
$316$	−13.2416	−0.744900
$317$	8.51799	0.478418	0.239209	−	0.970968i	$-0.423112\pi$
$317$	8.51799	0.478418	0.239209	+	0.970968i	$0.423112\pi$
$318$	−6.43037	−0.360597
$319$	16.3380	0.914752
$320$	−1.63652	−0.0914842
$321$	−37.2395	−2.07851
$322$	−0.335484	−0.0186958
$323$	−52.0646	−2.89695
$324$	−11.1924	−0.621800
$325$	−2.05781	−0.114147
$326$	19.8990	1.10210
$327$	−6.98150	−0.386078
$328$	3.58380	0.197882
$329$	−3.19818	−0.176321
$330$	11.9874	0.659885
$331$	9.30553	0.511478	0.255739	−	0.966746i	$-0.417681\pi$
$331$	9.30553	0.511478	0.255739	+	0.966746i	$0.417681\pi$
$332$	10.6332	0.583571
$333$	12.6080	0.690914
$334$	−20.0497	−1.09707
$335$	−4.80418	−0.262480
$336$	−1.19730	−0.0653182
$337$	−5.91973	−0.322468	−0.161234	−	0.986916i	$-0.551547\pi$
$337$	−5.91973	−0.322468	−0.161234	+	0.986916i	$0.551547\pi$
$338$	12.2145	0.664380
$339$	17.6800	0.960247
$340$	−11.5809	−0.628063
$341$	7.06838	0.382774
$342$	9.27022	0.501276
$343$	−7.92612	−0.427970
$344$	−10.8843	−0.586843
$345$	1.95343	0.105169
$346$	5.82014	0.312892
$347$	34.1656	1.83411	0.917054	−	0.398764i	$-0.130561\pi$
$347$	34.1656	1.83411	0.917054	+	0.398764i	$0.130561\pi$
$348$	9.50176	0.509348
$349$	14.9410	0.799775	0.399887	−	0.916564i	$-0.369049\pi$
$349$	14.9410	0.799775	0.399887	+	0.916564i	$0.369049\pi$
$350$	1.34687	0.0719931
$351$	3.18298	0.169895
$352$	3.54895	0.189159
$353$	10.8111	0.575417	0.287708	−	0.957718i	$-0.407107\pi$
$353$	10.8111	0.575417	0.287708	+	0.957718i	$0.407107\pi$
$354$	1.14785	0.0610073
$355$	−7.85690	−0.417001
$356$	4.67275	0.247656
$357$	−8.47277	−0.448426
$358$	1.45393	0.0768428
$359$	−1.35529	−0.0715293	−0.0357647	−	0.999360i	$-0.511387\pi$
$359$	−1.35529	−0.0715293	−0.0357647	+	0.999360i	$0.511387\pi$
$360$	2.06201	0.108677
$361$	35.1304	1.84897
$362$	8.41969	0.442529
$363$	−3.29207	−0.172789
$364$	0.514136	0.0269480
$365$	24.8983	1.30324
$366$	−29.0097	−1.51636
$367$	−33.3341	−1.74002	−0.870012	−	0.493030i	$-0.835889\pi$
$367$	−33.3341	−1.74002	−0.870012	+	0.493030i	$0.835889\pi$
$368$	0.578326	0.0301473
$369$	−4.51557	−0.235071
$370$	16.3756	0.851328
$371$	−1.80730	−0.0938304
$372$	4.11079	0.213135
$373$	19.3902	1.00399	0.501993	−	0.864872i	$-0.332600\pi$
$373$	19.3902	1.00399	0.501993	+	0.864872i	$0.332600\pi$
$374$	25.1143	1.29863
$375$	−24.7311	−1.27711
$376$	5.51320	0.284321
$377$	−4.08017	−0.210139
$378$	−2.08331	−0.107154
$379$	−15.0260	−0.771836	−0.385918	−	0.922533i	$-0.626115\pi$
$379$	−15.0260	−0.771836	−0.385918	+	0.922533i	$0.626115\pi$
$380$	12.0404	0.617661
$381$	31.4022	1.60878
$382$	10.4040	0.532315
$383$	19.0690	0.974380	0.487190	−	0.873296i	$-0.338022\pi$
$383$	19.0690	0.974380	0.487190	+	0.873296i	$0.338022\pi$
$384$	2.06398	0.105327
$385$	3.36914	0.171707
$386$	−14.4951	−0.737779
$387$	13.7142	0.697132
$388$	−12.5355	−0.636394
$389$	29.7584	1.50881	0.754405	−	0.656409i	$-0.227925\pi$
$389$	29.7584	1.50881	0.754405	+	0.656409i	$0.227925\pi$
$390$	−2.99367	−0.151591
$391$	4.09255	0.206969
$392$	6.66349	0.336557
$393$	45.1499	2.27751
$394$	2.10073	0.105833
$395$	21.6702	1.09035
$396$	−4.47166	−0.224709
$397$	−9.46210	−0.474889	−0.237445	−	0.971401i	$-0.576310\pi$
$397$	−9.46210	−0.474889	−0.237445	+	0.971401i	$0.576310\pi$
$398$	8.51886	0.427012
$399$	8.80896	0.440999
$400$	−2.32181	−0.116090
$401$	19.0247	0.950047	0.475023	−	0.879973i	$-0.342440\pi$
$401$	19.0247	0.950047	0.475023	+	0.879973i	$0.342440\pi$
$402$	6.05903	0.302197
$403$	−1.76522	−0.0879320
$404$	13.9965	0.696350
$405$	18.3166	0.910158
$406$	2.67054	0.132537
$407$	−35.5121	−1.76027
$408$	14.6058	0.723096
$409$	−22.5419	−1.11462	−0.557312	−	0.830303i	$-0.688167\pi$
$409$	−22.5419	−1.11462	−0.557312	+	0.830303i	$0.688167\pi$
$410$	−5.86495	−0.289649
$411$	30.5697	1.50789
$412$	12.6899	0.625187
$413$	0.322610	0.0158746
$414$	−0.728689	−0.0358131
$415$	−17.4014	−0.854201
$416$	−0.886296	−0.0434542
$417$	−40.0975	−1.96358
$418$	−26.1108	−1.27712
$419$	1.55625	0.0760278	0.0380139	−	0.999277i	$-0.487897\pi$
$419$	1.55625	0.0760278	0.0380139	+	0.999277i	$0.487897\pi$
$420$	1.95941	0.0956093
$421$	20.2645	0.987629	0.493815	−	0.869567i	$-0.335602\pi$
$421$	20.2645	0.987629	0.493815	+	0.869567i	$0.335602\pi$
$422$	6.01330	0.292723
$423$	−6.94661	−0.337756
$424$	3.11553	0.151303
$425$	−16.4304	−0.796990
$426$	9.90911	0.480098
$427$	−8.15338	−0.394570
$428$	18.0426	0.872123
$429$	6.49206	0.313440
$430$	17.8124	0.858990
$431$	−37.4088	−1.80192	−0.900960	−	0.433901i	$-0.857137\pi$
$431$	−37.4088	−1.80192	−0.900960	+	0.433901i	$0.857137\pi$
$432$	3.59132	0.172788
$433$	18.2561	0.877333	0.438666	−	0.898650i	$-0.355451\pi$
$433$	18.2561	0.877333	0.438666	+	0.898650i	$0.355451\pi$
$434$	1.15537	0.0554594
$435$	−15.5498	−0.745557
$436$	3.38255	0.161995
$437$	−4.25494	−0.203541
$438$	−31.4017	−1.50043
$439$	−20.4118	−0.974203	−0.487102	−	0.873345i	$-0.661946\pi$
$439$	−20.4118	−0.974203	−0.487102	+	0.873345i	$0.661946\pi$
$440$	−5.80792	−0.276882
$441$	−8.39598	−0.399808
$442$	−6.27192	−0.298325
$443$	8.87416	0.421624	0.210812	−	0.977527i	$-0.432389\pi$
$443$	8.87416	0.421624	0.210812	+	0.977527i	$0.432389\pi$
$444$	−20.6529	−0.980144
$445$	−7.64705	−0.362505
$446$	−0.468926	−0.0222043
$447$	47.9202	2.26655
$448$	0.580095	0.0274069
$449$	17.7701	0.838621	0.419311	−	0.907843i	$-0.362272\pi$
$449$	17.7701	0.838621	0.419311	+	0.907843i	$0.362272\pi$
$450$	2.92547	0.137908
$451$	12.7187	0.598900
$452$	−8.56600	−0.402911
$453$	−0.554278	−0.0260422
$454$	−26.4649	−1.24206
$455$	−0.841393	−0.0394451
$456$	−15.1854	−0.711120
$457$	1.28600	0.0601566	0.0300783	−	0.999548i	$-0.490424\pi$
$457$	1.28600	0.0601566	0.0300783	+	0.999548i	$0.490424\pi$
$458$	−13.3509	−0.623846
$459$	25.4142	1.18623
$460$	−0.946441	−0.0441281
$461$	−30.5617	−1.42340	−0.711700	−	0.702484i	$-0.752074\pi$
$461$	−30.5617	−1.42340	−0.711700	+	0.702484i	$0.752074\pi$
$462$	−4.24916	−0.197689
$463$	−16.0653	−0.746616	−0.373308	−	0.927708i	$-0.621776\pi$
$463$	−16.0653	−0.746616	−0.373308	+	0.927708i	$0.621776\pi$
$464$	−4.60362	−0.213718
$465$	−6.72739	−0.311975
$466$	12.7064	0.588613
$467$	−34.1135	−1.57858	−0.789291	−	0.614019i	$-0.789552\pi$
$467$	−34.1135	−1.57858	−0.789291	+	0.614019i	$0.789552\pi$
$468$	1.11673	0.0516209
$469$	1.70293	0.0786341
$470$	−9.02245	−0.416175
$471$	15.5731	0.717568
$472$	−0.556133	−0.0255981
$473$	−38.6278	−1.77611
$474$	−27.3304	−1.25533
$475$	17.0823	0.783790
$476$	4.10507	0.188156
$477$	−3.92555	−0.179739
$478$	−23.0565	−1.05458
$479$	34.8139	1.59069	0.795343	−	0.606159i	$-0.207291\pi$
$479$	34.8139	1.59069	0.795343	+	0.606159i	$0.207291\pi$
$480$	−3.37774	−0.154172
$481$	8.86861	0.404374
$482$	23.1288	1.05349
$483$	−0.692431	−0.0315067
$484$	1.59501	0.0725007
$485$	20.5146	0.931519
$486$	−12.3269	−0.559158
$487$	28.0533	1.27122	0.635608	−	0.772012i	$-0.280750\pi$
$487$	28.0533	1.27122	0.635608	+	0.772012i	$0.280750\pi$
$488$	14.0553	0.636252
$489$	41.0710	1.85729
$490$	−10.9049	−0.492634
$491$	−10.1644	−0.458714	−0.229357	−	0.973342i	$-0.573662\pi$
$491$	−10.1644	−0.458714	−0.229357	+	0.973342i	$0.573662\pi$
$492$	7.39687	0.333477
$493$	−32.5778	−1.46723
$494$	6.52078	0.293384
$495$	7.31796	0.328918
$496$	−1.99169	−0.0894293
$497$	2.78503	0.124926
$498$	21.9466	0.983452
$499$	15.4814	0.693041	0.346521	−	0.938042i	$-0.387363\pi$
$499$	15.4814	0.693041	0.346521	+	0.938042i	$0.387363\pi$
$500$	11.9823	0.535864
$501$	−41.3821	−1.84882
$502$	−6.45395	−0.288054
$503$	−15.1627	−0.676070	−0.338035	−	0.941134i	$-0.609762\pi$
$503$	−15.1627	−0.676070	−0.338035	+	0.941134i	$0.609762\pi$
$504$	−0.730918	−0.0325577
$505$	−22.9055	−1.01928
$506$	2.05245	0.0912424
$507$	25.2104	1.11963
$508$	−15.2144	−0.675030
$509$	−21.1340	−0.936750	−0.468375	−	0.883530i	$-0.655160\pi$
$509$	−21.1340	−0.936750	−0.468375	+	0.883530i	$0.655160\pi$
$510$	−23.9027	−1.05843
$511$	−8.82567	−0.390425
$512$	−1.00000	−0.0441942
$513$	−26.4226	−1.16659
$514$	14.8905	0.656792
$515$	−20.7673	−0.915115
$516$	−22.4650	−0.988965
$517$	19.5660	0.860513
$518$	−5.80465	−0.255042
$519$	12.0126	0.527295
$520$	1.45044	0.0636060
$521$	2.20280	0.0965064	0.0482532	−	0.998835i	$-0.484635\pi$
$521$	2.20280	0.0965064	0.0482532	+	0.998835i	$0.484635\pi$
$522$	5.80055	0.253883
$523$	19.6181	0.857838	0.428919	−	0.903343i	$-0.358895\pi$
$523$	19.6181	0.857838	0.428919	+	0.903343i	$0.358895\pi$
$524$	−21.8752	−0.955623
$525$	2.77990	0.121325
$526$	13.7096	0.597765
$527$	−14.0943	−0.613956
$528$	7.32494	0.318777
$529$	−22.6655	−0.985458
$530$	−5.09862	−0.221470
$531$	0.700726	0.0304089
$532$	−4.26795	−0.185039
$533$	−3.17630	−0.137581
$534$	9.64445	0.417356
$535$	−29.5271	−1.27657
$536$	−2.93561	−0.126799
$537$	3.00088	0.129498
$538$	11.7222	0.505381
$539$	23.6484	1.01861
$540$	−5.87727	−0.252917
$541$	32.4187	1.39379	0.696894	−	0.717174i	$-0.254565\pi$
$541$	32.4187	1.39379	0.696894	+	0.717174i	$0.254565\pi$
$542$	−15.4815	−0.664987
$543$	17.3780	0.745763
$544$	−7.07655	−0.303405
$545$	−5.53560	−0.237119
$546$	1.06116	0.0454136
$547$	43.6343	1.86567	0.932835	−	0.360304i	$-0.117327\pi$
$547$	43.6343	1.86567	0.932835	+	0.360304i	$0.117327\pi$
$548$	−14.8111	−0.632699
$549$	−17.7096	−0.755826
$550$	−8.23996	−0.351353
$551$	33.8704	1.44293
$552$	1.19365	0.0508051
$553$	−7.68141	−0.326647
$554$	30.0761	1.27781
$555$	33.7989	1.43468
$556$	19.4273	0.823901
$557$	19.6954	0.834520	0.417260	−	0.908787i	$-0.362991\pi$
$557$	19.6954	0.834520	0.417260	+	0.908787i	$0.362991\pi$
$558$	2.50952	0.106236
$559$	9.64672	0.408013
$560$	−0.949336	−0.0401168
$561$	51.8353	2.18849
$562$	−1.98841	−0.0838762
$563$	13.5532	0.571201	0.285600	−	0.958349i	$-0.407807\pi$
$563$	13.5532	0.571201	0.285600	+	0.958349i	$0.407807\pi$
$564$	11.3791	0.479147
$565$	14.0184	0.589760
$566$	−29.9209	−1.25767
$567$	−6.49265	−0.272666
$568$	−4.80098	−0.201445
$569$	−1.63078	−0.0683658	−0.0341829	−	0.999416i	$-0.510883\pi$
$569$	−1.63078	−0.0683658	−0.0341829	+	0.999416i	$0.510883\pi$
$570$	24.8511	1.04090
$571$	−26.3214	−1.10151	−0.550757	−	0.834665i	$-0.685661\pi$
$571$	−26.3214	−1.10151	−0.550757	+	0.834665i	$0.685661\pi$
$572$	−3.14542	−0.131516
$573$	21.4736	0.897073
$574$	2.07894	0.0867734
$575$	−1.34276	−0.0559970
$576$	1.26000	0.0524999
$577$	10.4295	0.434188	0.217094	−	0.976151i	$-0.430342\pi$
$577$	10.4295	0.434188	0.217094	+	0.976151i	$0.430342\pi$
$578$	−33.0776	−1.37584
$579$	−29.9174	−1.24333
$580$	7.53391	0.312829
$581$	6.16825	0.255902
$582$	−25.8730	−1.07247
$583$	11.0568	0.457927
$584$	15.2142	0.629567
$585$	−1.82755	−0.0755599
$586$	−11.1357	−0.460012
$587$	35.8322	1.47895	0.739476	−	0.673183i	$-0.235073\pi$
$587$	35.8322	1.47895	0.739476	+	0.673183i	$0.235073\pi$
$588$	13.7533	0.567176
$589$	14.6535	0.603787
$590$	0.910123	0.0374692
$591$	4.33586	0.178353
$592$	10.0064	0.411260
$593$	−5.36185	−0.220185	−0.110092	−	0.993921i	$-0.535115\pi$
$593$	−5.36185	−0.220185	−0.110092	+	0.993921i	$0.535115\pi$
$594$	12.7454	0.522951
$595$	−6.71803	−0.275412
$596$	−23.2174	−0.951023
$597$	17.5827	0.719613
$598$	−0.512568	−0.0209605
$599$	34.6350	1.41515	0.707573	−	0.706640i	$-0.249790\pi$
$599$	34.6350	1.41515	0.707573	+	0.706640i	$0.249790\pi$
$600$	−4.79215	−0.195639
$601$	−8.43148	−0.343927	−0.171964	−	0.985103i	$-0.555011\pi$
$601$	−8.43148	−0.343927	−0.171964	+	0.985103i	$0.555011\pi$
$602$	−6.31394	−0.257337
$603$	3.69886	0.150629
$604$	0.268548	0.0109271
$605$	−2.61027	−0.106123
$606$	28.8884	1.17351
$607$	3.38534	0.137407	0.0687034	−	0.997637i	$-0.478114\pi$
$607$	3.38534	0.137407	0.0687034	+	0.997637i	$0.478114\pi$
$608$	7.35734	0.298379
$609$	5.51192	0.223354
$610$	−23.0017	−0.931311
$611$	−4.88632	−0.197679
$612$	8.91643	0.360425
$613$	34.4560	1.39167	0.695833	−	0.718204i	$-0.255035\pi$
$613$	34.4560	1.39167	0.695833	+	0.718204i	$0.255035\pi$
$614$	18.5541	0.748783
$615$	−12.1051	−0.488125
$616$	2.05873	0.0829484
$617$	4.46033	0.179566	0.0897830	−	0.995961i	$-0.471383\pi$
$617$	4.46033	0.179566	0.0897830	+	0.995961i	$0.471383\pi$
$618$	26.1917	1.05358
$619$	21.4026	0.860245	0.430123	−	0.902771i	$-0.358470\pi$
$619$	21.4026	0.860245	0.430123	+	0.902771i	$0.358470\pi$
$620$	3.25943	0.130902
$621$	2.07696	0.0833454
$622$	6.98601	0.280114
$623$	2.71064	0.108600
$624$	−1.82929	−0.0732303
$625$	−8.00019	−0.320008
$626$	−5.17135	−0.206689
$627$	−53.8920	−2.15224
$628$	−7.54517	−0.301085
$629$	70.8106	2.82340
$630$	1.19616	0.0476562
$631$	−32.5941	−1.29755	−0.648775	−	0.760981i	$-0.724718\pi$
$631$	−32.5941	−1.29755	−0.648775	+	0.760981i	$0.724718\pi$
$632$	13.2416	0.526724
$633$	12.4113	0.493305
$634$	−8.51799	−0.338293
$635$	24.8987	0.988073
$636$	6.43037	0.254981
$637$	−5.90582	−0.233997
$638$	−16.3380	−0.646828
$639$	6.04922	0.239304
$640$	1.63652	0.0646891
$641$	42.5099	1.67904	0.839520	−	0.543328i	$-0.182836\pi$
$641$	42.5099	1.67904	0.839520	+	0.543328i	$0.182836\pi$
$642$	37.2395	1.46973
$643$	12.2811	0.484319	0.242159	−	0.970236i	$-0.422144\pi$
$643$	12.2811	0.484319	0.242159	+	0.970236i	$0.422144\pi$
$644$	0.335484	0.0132199
$645$	36.7643	1.44759
$646$	52.0646	2.04845
$647$	27.6649	1.08762	0.543809	−	0.839209i	$-0.316982\pi$
$647$	27.6649	1.08762	0.543809	+	0.839209i	$0.316982\pi$
$648$	11.1924	0.439679
$649$	−1.97369	−0.0774740
$650$	2.05781	0.0807138
$651$	2.38465	0.0934618
$652$	−19.8990	−0.779303
$653$	37.7337	1.47663	0.738317	−	0.674454i	$-0.235621\pi$
$653$	37.7337	1.47663	0.738317	+	0.674454i	$0.235621\pi$
$654$	6.98150	0.272998
$655$	35.7992	1.39879
$656$	−3.58380	−0.139924
$657$	−19.1698	−0.747886
$658$	3.19818	0.124678
$659$	33.0208	1.28631	0.643154	−	0.765737i	$-0.277626\pi$
$659$	33.0208	1.28631	0.643154	+	0.765737i	$0.277626\pi$
$660$	−11.9874	−0.466609
$661$	6.76166	0.262998	0.131499	−	0.991316i	$-0.458021\pi$
$661$	6.76166	0.262998	0.131499	+	0.991316i	$0.458021\pi$
$662$	−9.30553	−0.361670
$663$	−12.9451	−0.502745
$664$	−10.6332	−0.412647
$665$	6.98459	0.270851
$666$	−12.6080	−0.488550
$667$	−2.66239	−0.103088
$668$	20.0497	0.775747
$669$	−0.967852	−0.0374193
$670$	4.80418	0.185602
$671$	49.8813	1.92565
$672$	1.19730	0.0461869
$673$	8.86041	0.341544	0.170772	−	0.985311i	$-0.445374\pi$
$673$	8.86041	0.341544	0.170772	+	0.985311i	$0.445374\pi$
$674$	5.91973	0.228019
$675$	−8.33836	−0.320944
$676$	−12.2145	−0.469788
$677$	3.50774	0.134813	0.0674066	−	0.997726i	$-0.478528\pi$
$677$	3.50774	0.134813	0.0674066	+	0.997726i	$0.478528\pi$
$678$	−17.6800	−0.678997
$679$	−7.27178	−0.279065
$680$	11.5809	0.444108
$681$	−54.6230	−2.09316
$682$	−7.06838	−0.270662
$683$	6.99027	0.267475	0.133738	−	0.991017i	$-0.457302\pi$
$683$	6.99027	0.267475	0.133738	+	0.991017i	$0.457302\pi$
$684$	−9.27022	−0.354456
$685$	24.2386	0.926111
$686$	7.92612	0.302621
$687$	−27.5559	−1.05132
$688$	10.8843	0.414961
$689$	−2.76128	−0.105196
$690$	−1.95343	−0.0743659
$691$	−28.8446	−1.09730	−0.548651	−	0.836052i	$-0.684858\pi$
$691$	−28.8446	−1.09730	−0.548651	+	0.836052i	$0.684858\pi$
$692$	−5.82014	−0.221248
$693$	−2.59399	−0.0985374
$694$	−34.1656	−1.29691
$695$	−31.7931	−1.20598
$696$	−9.50176	−0.360163
$697$	−25.3609	−0.960613
$698$	−14.9410	−0.565526
$699$	26.2257	0.991948
$700$	−1.34687	−0.0509068
$701$	0.128202	0.00484214	0.00242107	−	0.999997i	$-0.499229\pi$
$701$	0.128202	0.00484214	0.00242107	+	0.999997i	$0.499229\pi$
$702$	−3.18298	−0.120134
$703$	−73.6203	−2.77664
$704$	−3.54895	−0.133756
$705$	−18.6221	−0.701350
$706$	−10.8111	−0.406881
$707$	8.11928	0.305357
$708$	−1.14785	−0.0431387
$709$	48.8473	1.83450	0.917249	−	0.398314i	$-0.130404\pi$
$709$	48.8473	1.83450	0.917249	+	0.398314i	$0.130404\pi$
$710$	7.85690	0.294864
$711$	−16.6844	−0.625715
$712$	−4.67275	−0.175119
$713$	−1.15184	−0.0431369
$714$	8.47277	0.317085
$715$	5.14753	0.192507
$716$	−1.45393	−0.0543360
$717$	−47.5881	−1.77721
$718$	1.35529	0.0505789
$719$	16.1131	0.600918	0.300459	−	0.953795i	$-0.402860\pi$
$719$	16.1131	0.600918	0.300459	+	0.953795i	$0.402860\pi$
$720$	−2.06201	−0.0768465
$721$	7.36135	0.274151
$722$	−35.1304	−1.30742
$723$	47.7373	1.77537
$724$	−8.41969	−0.312915
$725$	10.6887	0.396969
$726$	3.29207	0.122180
$727$	38.3930	1.42392	0.711959	−	0.702221i	$-0.247808\pi$
$727$	38.3930	1.42392	0.711959	+	0.702221i	$0.247808\pi$
$728$	−0.514136	−0.0190551
$729$	8.13484	0.301290
$730$	−24.8983	−0.921527
$731$	77.0234	2.84881
$732$	29.0097	1.07223
$733$	−7.76343	−0.286749	−0.143374	−	0.989669i	$-0.545795\pi$
$733$	−7.76343	−0.286749	−0.143374	+	0.989669i	$0.545795\pi$
$734$	33.3341	1.23038
$735$	−22.5075	−0.830202
$736$	−0.578326	−0.0213174
$737$	−10.4183	−0.383764
$738$	4.51557	0.166220
$739$	−18.2426	−0.671065	−0.335533	−	0.942029i	$-0.608916\pi$
$739$	−18.2426	−0.671065	−0.335533	+	0.942029i	$0.608916\pi$
$740$	−16.3756	−0.601980
$741$	13.4587	0.494419
$742$	1.80730	0.0663481
$743$	36.0693	1.32326	0.661628	−	0.749832i	$-0.269866\pi$
$743$	36.0693	1.32326	0.661628	+	0.749832i	$0.269866\pi$
$744$	−4.11079	−0.150709
$745$	37.9958	1.39206
$746$	−19.3902	−0.709925
$747$	13.3978	0.490199
$748$	−25.1143	−0.918269
$749$	10.4664	0.382435
$750$	24.7311	0.903053
$751$	−11.9477	−0.435977	−0.217989	−	0.975951i	$-0.569950\pi$
$751$	−11.9477	−0.435977	−0.217989	+	0.975951i	$0.569950\pi$
$752$	−5.51320	−0.201046
$753$	−13.3208	−0.485437
$754$	4.08017	0.148591
$755$	−0.439485	−0.0159945
$756$	2.08331	0.0757692
$757$	−11.0711	−0.402386	−0.201193	−	0.979552i	$-0.564482\pi$
$757$	−11.0711	−0.402386	−0.201193	+	0.979552i	$0.564482\pi$
$758$	15.0260	0.545770
$759$	4.23620	0.153764
$760$	−12.0404	−0.436752
$761$	41.1837	1.49291	0.746453	−	0.665438i	$-0.231755\pi$
$761$	41.1837	1.49291	0.746453	+	0.665438i	$0.231755\pi$
$762$	−31.4022	−1.13758
$763$	1.96220	0.0710364
$764$	−10.4040	−0.376403
$765$	−14.5919	−0.527571
$766$	−19.0690	−0.688990
$767$	0.492899	0.0177975
$768$	−2.06398	−0.0744773
$769$	3.50895	0.126536	0.0632680	−	0.997997i	$-0.479848\pi$
$769$	3.50895	0.126536	0.0632680	+	0.997997i	$0.479848\pi$
$770$	−3.36914	−0.121416
$771$	30.7336	1.10685
$772$	14.4951	0.521688
$773$	16.6590	0.599181	0.299590	−	0.954068i	$-0.403150\pi$
$773$	16.6590	0.599181	0.299590	+	0.954068i	$0.403150\pi$
$774$	−13.7142	−0.492947
$775$	4.62431	0.166110
$776$	12.5355	0.449998
$777$	−11.9807	−0.429804
$778$	−29.7584	−1.06689
$779$	26.3672	0.944703
$780$	2.99367	0.107191
$781$	−17.0384	−0.609683
$782$	−4.09255	−0.146349
$783$	−16.5331	−0.590845
$784$	−6.66349	−0.237982
$785$	12.3478	0.440712
$786$	−45.1499	−1.61044
$787$	20.9581	0.747077	0.373539	−	0.927615i	$-0.378144\pi$
$787$	20.9581	0.747077	0.373539	+	0.927615i	$0.378144\pi$
$788$	−2.10073	−0.0748355
$789$	28.2962	1.00737
$790$	−21.6702	−0.770991
$791$	−4.96909	−0.176681
$792$	4.47166	0.158894
$793$	−12.4571	−0.442365
$794$	9.46210	0.335797
$795$	−10.5234	−0.373228
$796$	−8.51886	−0.301943
$797$	39.2309	1.38963	0.694815	−	0.719188i	$-0.255486\pi$
$797$	39.2309	1.38963	0.694815	+	0.719188i	$0.255486\pi$
$798$	−8.80896	−0.311834
$799$	−39.0144	−1.38023
$800$	2.32181	0.0820882
$801$	5.88766	0.208030
$802$	−19.0247	−0.671784
$803$	53.9943	1.90542
$804$	−6.05903	−0.213685
$805$	−0.549026	−0.0193506
$806$	1.76522	0.0621773
$807$	24.1944	0.851683
$808$	−13.9965	−0.492394
$809$	−17.6706	−0.621264	−0.310632	−	0.950530i	$-0.600541\pi$
$809$	−17.6706	−0.621264	−0.310632	+	0.950530i	$0.600541\pi$
$810$	−18.3166	−0.643579
$811$	−21.9218	−0.769779	−0.384889	−	0.922963i	$-0.625760\pi$
$811$	−21.9218	−0.769779	−0.384889	+	0.922963i	$0.625760\pi$
$812$	−2.67054	−0.0937175
$813$	−31.9534	−1.12066
$814$	35.5121	1.24470
$815$	32.5650	1.14070
$816$	−14.6058	−0.511306
$817$	−80.0796	−2.80163
$818$	22.5419	0.788158
$819$	0.647809	0.0226363
$820$	5.86495	0.204813
$821$	−15.7495	−0.549663	−0.274831	−	0.961492i	$-0.588622\pi$
$821$	−15.7495	−0.549663	−0.274831	+	0.961492i	$0.588622\pi$
$822$	−30.5697	−1.06624
$823$	14.8321	0.517015	0.258508	−	0.966009i	$-0.416769\pi$
$823$	14.8321	0.517015	0.258508	+	0.966009i	$0.416769\pi$
$824$	−12.6899	−0.442074
$825$	−17.0071	−0.592111
$826$	−0.322610	−0.0112250
$827$	25.7520	0.895486	0.447743	−	0.894162i	$-0.352228\pi$
$827$	25.7520	0.895486	0.447743	+	0.894162i	$0.352228\pi$
$828$	0.728689	0.0253237
$829$	−3.06235	−0.106360	−0.0531799	−	0.998585i	$-0.516936\pi$
$829$	−3.06235	−0.106360	−0.0531799	+	0.998585i	$0.516936\pi$
$830$	17.4014	0.604011
$831$	62.0763	2.15340
$832$	0.886296	0.0307268
$833$	−47.1545	−1.63381
$834$	40.0975	1.38846
$835$	−32.8117	−1.13550
$836$	26.1108	0.903061
$837$	−7.15279	−0.247237
$838$	−1.55625	−0.0537597
$839$	−24.5276	−0.846786	−0.423393	−	0.905946i	$-0.639161\pi$
$839$	−24.5276	−0.846786	−0.423393	+	0.905946i	$0.639161\pi$
$840$	−1.95941	−0.0676060
$841$	−7.80668	−0.269196
$842$	−20.2645	−0.698359
$843$	−4.10404	−0.141351
$844$	−6.01330	−0.206986
$845$	19.9892	0.687650
$846$	6.94661	0.238829
$847$	0.925260	0.0317923
$848$	−3.11553	−0.106988
$849$	−61.7560	−2.11946
$850$	16.4304	0.563557
$851$	5.78695	0.198374
$852$	−9.90911	−0.339481
$853$	16.1547	0.553128	0.276564	−	0.960996i	$-0.410804\pi$
$853$	16.1547	0.553128	0.276564	+	0.960996i	$0.410804\pi$
$854$	8.15338	0.279003
$855$	15.1709	0.518834
$856$	−18.0426	−0.616684
$857$	−39.3885	−1.34549	−0.672743	−	0.739876i	$-0.734884\pi$
$857$	−39.3885	−1.34549	−0.672743	+	0.739876i	$0.734884\pi$
$858$	−6.49206	−0.221635
$859$	32.6720	1.11475	0.557377	−	0.830260i	$-0.311808\pi$
$859$	32.6720	1.11475	0.557377	+	0.830260i	$0.311808\pi$
$860$	−17.8124	−0.607397
$861$	4.29089	0.146233
$862$	37.4088	1.27415
$863$	0.727083	0.0247502	0.0123751	−	0.999923i	$-0.496061\pi$
$863$	0.727083	0.0247502	0.0123751	+	0.999923i	$0.496061\pi$
$864$	−3.59132	−0.122179
$865$	9.52476	0.323852
$866$	−18.2561	−0.620368
$867$	−68.2713	−2.31861
$868$	−1.15537	−0.0392157
$869$	46.9938	1.59416
$870$	15.5498	0.527188
$871$	2.60182	0.0881592
$872$	−3.38255	−0.114547
$873$	−15.7947	−0.534569
$874$	4.25494	0.143925
$875$	6.95086	0.234982
$876$	31.4017	1.06096
$877$	−14.3756	−0.485430	−0.242715	−	0.970098i	$-0.578038\pi$
$877$	−14.3756	−0.485430	−0.242715	+	0.970098i	$0.578038\pi$
$878$	20.4118	0.688866
$879$	−22.9839	−0.775226
$880$	5.80792	0.195785
$881$	0.375440	0.0126489	0.00632446	−	0.999980i	$-0.497987\pi$
$881$	0.375440	0.0126489	0.00632446	+	0.999980i	$0.497987\pi$
$882$	8.39598	0.282707
$883$	−43.2463	−1.45536	−0.727678	−	0.685919i	$-0.759400\pi$
$883$	−43.2463	−1.45536	−0.727678	+	0.685919i	$0.759400\pi$
$884$	6.27192	0.210947
$885$	1.87847	0.0631441
$886$	−8.87416	−0.298133
$887$	−21.4600	−0.720556	−0.360278	−	0.932845i	$-0.617318\pi$
$887$	−21.4600	−0.720556	−0.360278	+	0.932845i	$0.617318\pi$
$888$	20.6529	0.693067
$889$	−8.82580	−0.296008
$890$	7.64705	0.256330
$891$	39.7212	1.33071
$892$	0.468926	0.0157008
$893$	40.5624	1.35737
$894$	−47.9202	−1.60269
$895$	2.37939	0.0795342
$896$	−0.580095	−0.0193796
$897$	−1.05793	−0.0353232
$898$	−17.7701	−0.592995
$899$	9.16897	0.305802
$900$	−2.92547	−0.0975156
$901$	−22.0472	−0.734498
$902$	−12.7187	−0.423486
$903$	−13.0318	−0.433672
$904$	8.56600	0.284901
$905$	13.7790	0.458029
$906$	0.554278	0.0184146
$907$	24.4614	0.812229	0.406114	−	0.913822i	$-0.366883\pi$
$907$	24.4614	0.812229	0.406114	+	0.913822i	$0.366883\pi$
$908$	26.4649	0.878270
$909$	17.6355	0.584932
$910$	0.841393	0.0278919
$911$	−26.6311	−0.882329	−0.441164	−	0.897426i	$-0.645434\pi$
$911$	−26.6311	−0.882329	−0.441164	+	0.897426i	$0.645434\pi$
$912$	15.1854	0.502838
$913$	−37.7366	−1.24890
$914$	−1.28600	−0.0425372
$915$	−47.4749	−1.56947
$916$	13.3509	0.441126
$917$	−12.6897	−0.419051
$918$	−25.4142	−0.838793
$919$	20.3921	0.672672	0.336336	−	0.941742i	$-0.390812\pi$
$919$	20.3921	0.672672	0.336336	+	0.941742i	$0.390812\pi$
$920$	0.946441	0.0312032
$921$	38.2953	1.26187
$922$	30.5617	1.00650
$923$	4.25509	0.140058
$924$	4.24916	0.139787
$925$	−23.2329	−0.763892
$926$	16.0653	0.527937
$927$	15.9892	0.525155
$928$	4.60362	0.151121
$929$	23.8756	0.783334	0.391667	−	0.920107i	$-0.371898\pi$
$929$	23.8756	0.783334	0.391667	+	0.920107i	$0.371898\pi$
$930$	6.72739	0.220600
$931$	49.0255	1.60675
$932$	−12.7064	−0.416212
$933$	14.4190	0.472055
$934$	34.1135	1.11623
$935$	41.1000	1.34411
$936$	−1.11673	−0.0365015
$937$	23.6248	0.771789	0.385894	−	0.922543i	$-0.373893\pi$
$937$	23.6248	0.771789	0.385894	+	0.922543i	$0.373893\pi$
$938$	−1.70293	−0.0556027
$939$	−10.6735	−0.348318
$940$	9.02245	0.294280
$941$	1.21747	0.0396885	0.0198442	−	0.999803i	$-0.493683\pi$
$941$	1.21747	0.0396885	0.0198442	+	0.999803i	$0.493683\pi$
$942$	−15.5731	−0.507397
$943$	−2.07260	−0.0674932
$944$	0.556133	0.0181006
$945$	−3.40938	−0.110907
$946$	38.6278	1.25590
$947$	18.7484	0.609242	0.304621	−	0.952474i	$-0.401470\pi$
$947$	18.7484	0.609242	0.304621	+	0.952474i	$0.401470\pi$
$948$	27.3304	0.887651
$949$	−13.4843	−0.437718
$950$	−17.0823	−0.554223
$951$	−17.5809	−0.570101
$952$	−4.10507	−0.133046
$953$	28.7090	0.929976	0.464988	−	0.885317i	$-0.346059\pi$
$953$	28.7090	0.929976	0.464988	+	0.885317i	$0.346059\pi$
$954$	3.92555	0.127095
$955$	17.0263	0.550960
$956$	23.0565	0.745701
$957$	−33.7212	−1.09005
$958$	−34.8139	−1.12479
$959$	−8.59184	−0.277445
$960$	3.37774	0.109016
$961$	−27.0332	−0.872038
$962$	−8.86861	−0.285935
$963$	22.7336	0.732581
$964$	−23.1288	−0.744929
$965$	−23.7214	−0.763620
$966$	0.692431	0.0222786
$967$	−1.21791	−0.0391653	−0.0195826	−	0.999808i	$-0.506234\pi$
$967$	−1.21791	−0.0391653	−0.0195826	+	0.999808i	$0.506234\pi$
$968$	−1.59501	−0.0512657
$969$	107.460	3.45211
$970$	−20.5146	−0.658684
$971$	−23.6957	−0.760430	−0.380215	−	0.924898i	$-0.624150\pi$
$971$	−23.6957	−0.760430	−0.380215	+	0.924898i	$0.624150\pi$
$972$	12.3269	0.395384
$973$	11.2697	0.361289
$974$	−28.0533	−0.898885
$975$	4.24726	0.136021
$976$	−14.0553	−0.449898
$977$	−19.4644	−0.622722	−0.311361	−	0.950292i	$-0.600785\pi$
$977$	−19.4644	−0.622722	−0.311361	+	0.950292i	$0.600785\pi$
$978$	−41.0710	−1.31330
$979$	−16.5834	−0.530006
$980$	10.9049	0.348345
$981$	4.26200	0.136075
$982$	10.1644	0.324360
$983$	29.2353	0.932460	0.466230	−	0.884663i	$-0.345612\pi$
$983$	29.2353	0.932460	0.466230	+	0.884663i	$0.345612\pi$
$984$	−7.39687	−0.235804
$985$	3.43789	0.109540
$986$	32.5778	1.03749
$987$	6.60096	0.210111
$988$	−6.52078	−0.207454
$989$	6.29468	0.200159
$990$	−7.31796	−0.232580
$991$	−40.9951	−1.30225	−0.651126	−	0.758970i	$-0.725703\pi$
$991$	−40.9951	−1.30225	−0.651126	+	0.758970i	$0.725703\pi$
$992$	1.99169	0.0632361
$993$	−19.2064	−0.609497
$994$	−2.78503	−0.0883357
$995$	13.9413	0.441968
$996$	−21.9466	−0.695405
$997$	−49.2156	−1.55867	−0.779337	−	0.626605i	$-0.784444\pi$
$997$	−49.2156	−1.55867	−0.779337	+	0.626605i	$0.784444\pi$
$998$	−15.4814	−0.490054
$999$	35.9362	1.13697

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8026.2.a.c.1.17	✓	86

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8026.2.a.c.1.17	✓	86	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:	\( N \)	\(=\)	\( 8026 = 2 \cdot 4013 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.06398 q^{3} +1.00000 q^{4} -1.63652 q^{5} +2.06398 q^{6} +0.580095 q^{7} -1.00000 q^{8} +1.26000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.06398 q^{3} +1.00000 q^{4} -1.63652 q^{5} +2.06398 q^{6} +0.580095 q^{7} -1.00000 q^{8} +1.26000 q^{9} +1.63652 q^{10} -3.54895 q^{11} -2.06398 q^{12} +0.886296 q^{13} -0.580095 q^{14} +3.37774 q^{15} +1.00000 q^{16} +7.07655 q^{17} -1.26000 q^{18} -7.35734 q^{19} -1.63652 q^{20} -1.19730 q^{21} +3.54895 q^{22} +0.578326 q^{23} +2.06398 q^{24} -2.32181 q^{25} -0.886296 q^{26} +3.59132 q^{27} +0.580095 q^{28} -4.60362 q^{29} -3.37774 q^{30} -1.99169 q^{31} -1.00000 q^{32} +7.32494 q^{33} -7.07655 q^{34} -0.949336 q^{35} +1.26000 q^{36} +10.0064 q^{37} +7.35734 q^{38} -1.82929 q^{39} +1.63652 q^{40} -3.58380 q^{41} +1.19730 q^{42} +10.8843 q^{43} -3.54895 q^{44} -2.06201 q^{45} -0.578326 q^{46} -5.51320 q^{47} -2.06398 q^{48} -6.66349 q^{49} +2.32181 q^{50} -14.6058 q^{51} +0.886296 q^{52} -3.11553 q^{53} -3.59132 q^{54} +5.80792 q^{55} -0.580095 q^{56} +15.1854 q^{57} +4.60362 q^{58} +0.556133 q^{59} +3.37774 q^{60} -14.0553 q^{61} +1.99169 q^{62} +0.730918 q^{63} +1.00000 q^{64} -1.45044 q^{65} -7.32494 q^{66} +2.93561 q^{67} +7.07655 q^{68} -1.19365 q^{69} +0.949336 q^{70} +4.80098 q^{71} -1.26000 q^{72} -15.2142 q^{73} -10.0064 q^{74} +4.79215 q^{75} -7.35734 q^{76} -2.05873 q^{77} +1.82929 q^{78} -13.2416 q^{79} -1.63652 q^{80} -11.1924 q^{81} +3.58380 q^{82} +10.6332 q^{83} -1.19730 q^{84} -11.5809 q^{85} -10.8843 q^{86} +9.50176 q^{87} +3.54895 q^{88} +4.67275 q^{89} +2.06201 q^{90} +0.514136 q^{91} +0.578326 q^{92} +4.11079 q^{93} +5.51320 q^{94} +12.0404 q^{95} +2.06398 q^{96} -12.5355 q^{97} +6.66349 q^{98} -4.47166 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9}+O(q^{10}) \) 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9	\( 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9} - 25 q^{10} + 44 q^{11} + 11 q^{12} - 36 q^{13} + 3 q^{14} + 19 q^{15} + 86 q^{16} + 21 q^{17} - 105 q^{18} + 35 q^{19} + 25 q^{20} + 23 q^{21} - 44 q^{22} + 38 q^{23} - 11 q^{24} + 85 q^{25} + 36 q^{26} + 47 q^{27} - 3 q^{28} + 30 q^{29} - 19 q^{30} + 23 q^{31} - 86 q^{32} + 5 q^{33} - 21 q^{34} + 59 q^{35} + 105 q^{36} - 20 q^{37} - 35 q^{38} + 4 q^{39} - 25 q^{40} + 64 q^{41} - 23 q^{42} + 23 q^{43} + 44 q^{44} + 60 q^{45} - 38 q^{46} + 77 q^{47} + 11 q^{48} + 109 q^{49} - 85 q^{50} + 47 q^{51} - 36 q^{52} + 22 q^{53} - 47 q^{54} + 6 q^{55} + 3 q^{56} - 9 q^{57} - 30 q^{58} + 145 q^{59} + 19 q^{60} - 24 q^{61} - 23 q^{62} + 6 q^{63} + 86 q^{64} + 37 q^{65} - 5 q^{66} + 44 q^{67} + 21 q^{68} + 25 q^{69} - 59 q^{70} + 107 q^{71} - 105 q^{72} - 55 q^{73} + 20 q^{74} + 86 q^{75} + 35 q^{76} + 25 q^{77} - 4 q^{78} + 2 q^{79} + 25 q^{80} + 170 q^{81} - 64 q^{82} + 109 q^{83} + 23 q^{84} - 13 q^{85} - 23 q^{86} + 3 q^{87} - 44 q^{88} + 121 q^{89} - 60 q^{90} + 81 q^{91} + 38 q^{92} + 27 q^{93} - 77 q^{94} + 49 q^{95} - 11 q^{96} - 56 q^{97} - 109 q^{98} + 158 q^{99}+O(q^{100}) \) 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9 - 25 * q^10 + 44 * q^11 + 11 * q^12 - 36 * q^13 + 3 * q^14 + 19 * q^15 + 86 * q^16 + 21 * q^17 - 105 * q^18 + 35 * q^19 + 25 * q^20 + 23 * q^21 - 44 * q^22 + 38 * q^23 - 11 * q^24 + 85 * q^25 + 36 * q^26 + 47 * q^27 - 3 * q^28 + 30 * q^29 - 19 * q^30 + 23 * q^31 - 86 * q^32 + 5 * q^33 - 21 * q^34 + 59 * q^35 + 105 * q^36 - 20 * q^37 - 35 * q^38 + 4 * q^39 - 25 * q^40 + 64 * q^41 - 23 * q^42 + 23 * q^43 + 44 * q^44 + 60 * q^45 - 38 * q^46 + 77 * q^47 + 11 * q^48 + 109 * q^49 - 85 * q^50 + 47 * q^51 - 36 * q^52 + 22 * q^53 - 47 * q^54 + 6 * q^55 + 3 * q^56 - 9 * q^57 - 30 * q^58 + 145 * q^59 + 19 * q^60 - 24 * q^61 - 23 * q^62 + 6 * q^63 + 86 * q^64 + 37 * q^65 - 5 * q^66 + 44 * q^67 + 21 * q^68 + 25 * q^69 - 59 * q^70 + 107 * q^71 - 105 * q^72 - 55 * q^73 + 20 * q^74 + 86 * q^75 + 35 * q^76 + 25 * q^77 - 4 * q^78 + 2 * q^79 + 25 * q^80 + 170 * q^81 - 64 * q^82 + 109 * q^83 + 23 * q^84 - 13 * q^85 - 23 * q^86 + 3 * q^87 - 44 * q^88 + 121 * q^89 - 60 * q^90 + 81 * q^91 + 38 * q^92 + 27 * q^93 - 77 * q^94 + 49 * q^95 - 11 * q^96 - 56 * q^97 - 109 * q^98 + 158 * q^99

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