LMFDB - Embedded newform 8018.2.a.j.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$0$
Dimension:	$47$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.51480 q^{3} +1.00000 q^{4} -1.33044 q^{5} -1.51480 q^{6} -3.41282 q^{7} +1.00000 q^{8} -0.705394 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.51480 q^{3} +1.00000 q^{4} -1.33044 q^{5} -1.51480 q^{6} -3.41282 q^{7} +1.00000 q^{8} -0.705394 q^{9} -1.33044 q^{10} -1.69974 q^{11} -1.51480 q^{12} -1.37538 q^{13} -3.41282 q^{14} +2.01534 q^{15} +1.00000 q^{16} +3.29766 q^{17} -0.705394 q^{18} -1.00000 q^{19} -1.33044 q^{20} +5.16972 q^{21} -1.69974 q^{22} -9.07443 q^{23} -1.51480 q^{24} -3.22993 q^{25} -1.37538 q^{26} +5.61291 q^{27} -3.41282 q^{28} -4.00309 q^{29} +2.01534 q^{30} -3.30245 q^{31} +1.00000 q^{32} +2.57476 q^{33} +3.29766 q^{34} +4.54054 q^{35} -0.705394 q^{36} -7.04888 q^{37} -1.00000 q^{38} +2.08342 q^{39} -1.33044 q^{40} +3.82702 q^{41} +5.16972 q^{42} -2.87399 q^{43} -1.69974 q^{44} +0.938483 q^{45} -9.07443 q^{46} +0.403746 q^{47} -1.51480 q^{48} +4.64731 q^{49} -3.22993 q^{50} -4.99528 q^{51} -1.37538 q^{52} -3.47236 q^{53} +5.61291 q^{54} +2.26140 q^{55} -3.41282 q^{56} +1.51480 q^{57} -4.00309 q^{58} -4.97524 q^{59} +2.01534 q^{60} +5.81073 q^{61} -3.30245 q^{62} +2.40738 q^{63} +1.00000 q^{64} +1.82986 q^{65} +2.57476 q^{66} +2.62930 q^{67} +3.29766 q^{68} +13.7459 q^{69} +4.54054 q^{70} -1.72879 q^{71} -0.705394 q^{72} -2.94738 q^{73} -7.04888 q^{74} +4.89269 q^{75} -1.00000 q^{76} +5.80091 q^{77} +2.08342 q^{78} -13.6615 q^{79} -1.33044 q^{80} -6.38624 q^{81} +3.82702 q^{82} -13.8574 q^{83} +5.16972 q^{84} -4.38733 q^{85} -2.87399 q^{86} +6.06387 q^{87} -1.69974 q^{88} +0.930086 q^{89} +0.938483 q^{90} +4.69393 q^{91} -9.07443 q^{92} +5.00253 q^{93} +0.403746 q^{94} +1.33044 q^{95} -1.51480 q^{96} +19.0674 q^{97} +4.64731 q^{98} +1.19899 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9}+O(q^{10}) $ 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9} + 15 q^{10} + 17 q^{11} + 10 q^{12} + 27 q^{13} + 10 q^{15} + 47 q^{16} + 16 q^{17} + 69 q^{18} - 47 q^{19} + 15 q^{20} + 26 q^{21} + 17 q^{22} + 24 q^{23} + 10 q^{24} + 86 q^{25} + 27 q^{26} + 43 q^{27} + 58 q^{29} + 10 q^{30} + 21 q^{31} + 47 q^{32} + 18 q^{33} + 16 q^{34} + 24 q^{35} + 69 q^{36} + 78 q^{37} - 47 q^{38} - 4 q^{39} + 15 q^{40} + 53 q^{41} + 26 q^{42} + 47 q^{43} + 17 q^{44} + 23 q^{45} + 24 q^{46} + 16 q^{47} + 10 q^{48} + 93 q^{49} + 86 q^{50} + 28 q^{51} + 27 q^{52} + 43 q^{53} + 43 q^{54} + 23 q^{55} - 10 q^{57} + 58 q^{58} + 3 q^{59} + 10 q^{60} + 12 q^{61} + 21 q^{62} - 5 q^{63} + 47 q^{64} + 62 q^{65} + 18 q^{66} + 68 q^{67} + 16 q^{68} + 12 q^{69} + 24 q^{70} - 13 q^{71} + 69 q^{72} + 35 q^{73} + 78 q^{74} + 22 q^{75} - 47 q^{76} + 26 q^{77} - 4 q^{78} + 21 q^{79} + 15 q^{80} + 123 q^{81} + 53 q^{82} + 23 q^{83} + 26 q^{84} + 38 q^{85} + 47 q^{86} + 39 q^{87} + 17 q^{88} + 24 q^{89} + 23 q^{90} + 49 q^{91} + 24 q^{92} + 91 q^{93} + 16 q^{94} - 15 q^{95} + 10 q^{96} + 88 q^{97} + 93 q^{98} + 26 q^{99}+O(q^{100}) \) 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9 + 15 * q^10 + 17 * q^11 + 10 * q^12 + 27 * q^13 + 10 * q^15 + 47 * q^16 + 16 * q^17 + 69 * q^18 - 47 * q^19 + 15 * q^20 + 26 * q^21 + 17 * q^22 + 24 * q^23 + 10 * q^24 + 86 * q^25 + 27 * q^26 + 43 * q^27 + 58 * q^29 + 10 * q^30 + 21 * q^31 + 47 * q^32 + 18 * q^33 + 16 * q^34 + 24 * q^35 + 69 * q^36 + 78 * q^37 - 47 * q^38 - 4 * q^39 + 15 * q^40 + 53 * q^41 + 26 * q^42 + 47 * q^43 + 17 * q^44 + 23 * q^45 + 24 * q^46 + 16 * q^47 + 10 * q^48 + 93 * q^49 + 86 * q^50 + 28 * q^51 + 27 * q^52 + 43 * q^53 + 43 * q^54 + 23 * q^55 - 10 * q^57 + 58 * q^58 + 3 * q^59 + 10 * q^60 + 12 * q^61 + 21 * q^62 - 5 * q^63 + 47 * q^64 + 62 * q^65 + 18 * q^66 + 68 * q^67 + 16 * q^68 + 12 * q^69 + 24 * q^70 - 13 * q^71 + 69 * q^72 + 35 * q^73 + 78 * q^74 + 22 * q^75 - 47 * q^76 + 26 * q^77 - 4 * q^78 + 21 * q^79 + 15 * q^80 + 123 * q^81 + 53 * q^82 + 23 * q^83 + 26 * q^84 + 38 * q^85 + 47 * q^86 + 39 * q^87 + 17 * q^88 + 24 * q^89 + 23 * q^90 + 49 * q^91 + 24 * q^92 + 91 * q^93 + 16 * q^94 - 15 * q^95 + 10 * q^96 + 88 * q^97 + 93 * q^98 + 26 * 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
$3$	−1.51480	−0.874568	−0.437284	−	0.899324i	$-0.644060\pi$
$3$	−1.51480	−0.874568	−0.437284	+	0.899324i	$0.644060\pi$
$4$	1.00000	0.500000
$5$	−1.33044	−0.594990	−0.297495	−	0.954723i	$-0.596151\pi$
$5$	−1.33044	−0.594990	−0.297495	+	0.954723i	$0.596151\pi$
$6$	−1.51480	−0.618413
$7$	−3.41282	−1.28992	−0.644962	−	0.764215i	$-0.723127\pi$
$7$	−3.41282	−1.28992	−0.644962	+	0.764215i	$0.723127\pi$
$8$	1.00000	0.353553
$9$	−0.705394	−0.235131
$10$	−1.33044	−0.420722
$11$	−1.69974	−0.512491	−0.256246	−	0.966612i	$-0.582486\pi$
$11$	−1.69974	−0.512491	−0.256246	+	0.966612i	$0.582486\pi$
$12$	−1.51480	−0.437284
$13$	−1.37538	−0.381463	−0.190731	−	0.981642i	$-0.561086\pi$
$13$	−1.37538	−0.381463	−0.190731	+	0.981642i	$0.561086\pi$
$14$	−3.41282	−0.912113
$15$	2.01534	0.520359
$16$	1.00000	0.250000
$17$	3.29766	0.799799	0.399900	−	0.916559i	$-0.369045\pi$
$17$	3.29766	0.799799	0.399900	+	0.916559i	$0.369045\pi$
$18$	−0.705394	−0.166263
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−1.33044	−0.297495
$21$	5.16972	1.12813
$22$	−1.69974	−0.362386
$23$	−9.07443	−1.89215	−0.946075	−	0.323948i	$-0.894990\pi$
$23$	−9.07443	−1.89215	−0.946075	+	0.323948i	$0.894990\pi$
$24$	−1.51480	−0.309206
$25$	−3.22993	−0.645987
$26$	−1.37538	−0.269735
$27$	5.61291	1.08021
$28$	−3.41282	−0.644962
$29$	−4.00309	−0.743355	−0.371678	−	0.928362i	$-0.621217\pi$
$29$	−4.00309	−0.743355	−0.371678	+	0.928362i	$0.621217\pi$
$30$	2.01534	0.367950
$31$	−3.30245	−0.593137	−0.296569	−	0.955012i	$-0.595842\pi$
$31$	−3.30245	−0.593137	−0.296569	+	0.955012i	$0.595842\pi$
$32$	1.00000	0.176777
$33$	2.57476	0.448209
$34$	3.29766	0.565543
$35$	4.54054	0.767492
$36$	−0.705394	−0.117566
$37$	−7.04888	−1.15883	−0.579415	−	0.815033i	$-0.696719\pi$
$37$	−7.04888	−1.15883	−0.579415	+	0.815033i	$0.696719\pi$
$38$	−1.00000	−0.162221
$39$	2.08342	0.333615
$40$	−1.33044	−0.210361
$41$	3.82702	0.597680	0.298840	−	0.954303i	$-0.403400\pi$
$41$	3.82702	0.597680	0.298840	+	0.954303i	$0.403400\pi$
$42$	5.16972	0.797705
$43$	−2.87399	−0.438279	−0.219140	−	0.975693i	$-0.570325\pi$
$43$	−2.87399	−0.438279	−0.219140	+	0.975693i	$0.570325\pi$
$44$	−1.69974	−0.256246
$45$	0.938483	0.139901
$46$	−9.07443	−1.33795
$47$	0.403746	0.0588924	0.0294462	−	0.999566i	$-0.490626\pi$
$47$	0.403746	0.0588924	0.0294462	+	0.999566i	$0.490626\pi$
$48$	−1.51480	−0.218642
$49$	4.64731	0.663902
$50$	−3.22993	−0.456782
$51$	−4.99528	−0.699479
$52$	−1.37538	−0.190731
$53$	−3.47236	−0.476965	−0.238482	−	0.971147i	$-0.576650\pi$
$53$	−3.47236	−0.476965	−0.238482	+	0.971147i	$0.576650\pi$
$54$	5.61291	0.763821
$55$	2.26140	0.304927
$56$	−3.41282	−0.456057
$57$	1.51480	0.200640
$58$	−4.00309	−0.525632
$59$	−4.97524	−0.647721	−0.323860	−	0.946105i	$-0.604981\pi$
$59$	−4.97524	−0.647721	−0.323860	+	0.946105i	$0.604981\pi$
$60$	2.01534	0.260180
$61$	5.81073	0.743988	0.371994	−	0.928235i	$-0.378674\pi$
$61$	5.81073	0.743988	0.371994	+	0.928235i	$0.378674\pi$
$62$	−3.30245	−0.419411
$63$	2.40738	0.303301
$64$	1.00000	0.125000
$65$	1.82986	0.226967
$66$	2.57476	0.316931
$67$	2.62930	0.321220	0.160610	−	0.987018i	$-0.448654\pi$
$67$	2.62930	0.321220	0.160610	+	0.987018i	$0.448654\pi$
$68$	3.29766	0.399900
$69$	13.7459	1.65481
$70$	4.54054	0.542699
$71$	−1.72879	−0.205170	−0.102585	−	0.994724i	$-0.532711\pi$
$71$	−1.72879	−0.205170	−0.102585	+	0.994724i	$0.532711\pi$
$72$	−0.705394	−0.0831314
$73$	−2.94738	−0.344964	−0.172482	−	0.985013i	$-0.555179\pi$
$73$	−2.94738	−0.344964	−0.172482	+	0.985013i	$0.555179\pi$
$74$	−7.04888	−0.819416
$75$	4.89269	0.564959
$76$	−1.00000	−0.114708
$77$	5.80091	0.661075
$78$	2.08342	0.235901
$79$	−13.6615	−1.53704	−0.768522	−	0.639823i	$-0.779008\pi$
$79$	−13.6615	−1.53704	−0.768522	+	0.639823i	$0.779008\pi$
$80$	−1.33044	−0.148748
$81$	−6.38624	−0.709582
$82$	3.82702	0.422624
$83$	−13.8574	−1.52105	−0.760526	−	0.649308i	$-0.775059\pi$
$83$	−13.8574	−1.52105	−0.760526	+	0.649308i	$0.775059\pi$
$84$	5.16972	0.564063
$85$	−4.38733	−0.475873
$86$	−2.87399	−0.309910
$87$	6.06387	0.650115
$88$	−1.69974	−0.181193
$89$	0.930086	0.0985889	0.0492944	−	0.998784i	$-0.484303\pi$
$89$	0.930086	0.0985889	0.0492944	+	0.998784i	$0.484303\pi$
$90$	0.938483	0.0989248
$91$	4.69393	0.492057
$92$	−9.07443	−0.946075
$93$	5.00253	0.518739
$94$	0.403746	0.0416432
$95$	1.33044	0.136500
$96$	−1.51480	−0.154603
$97$	19.0674	1.93600	0.967999	−	0.250956i	$-0.0807448\pi$
$97$	19.0674	1.93600	0.967999	+	0.250956i	$0.0807448\pi$
$98$	4.64731	0.469449
$99$	1.19899	0.120503
$100$	−3.22993	−0.322993
$101$	−2.12217	−0.211164	−0.105582	−	0.994411i	$-0.533671\pi$
$101$	−2.12217	−0.211164	−0.105582	+	0.994411i	$0.533671\pi$
$102$	−4.99528	−0.494606
$103$	8.09522	0.797645	0.398823	−	0.917028i	$-0.369419\pi$
$103$	8.09522	0.797645	0.398823	+	0.917028i	$0.369419\pi$
$104$	−1.37538	−0.134867
$105$	−6.87799	−0.671223
$106$	−3.47236	−0.337265
$107$	0.314171	0.0303720	0.0151860	−	0.999885i	$-0.495166\pi$
$107$	0.314171	0.0303720	0.0151860	+	0.999885i	$0.495166\pi$
$108$	5.61291	0.540103
$109$	4.65436	0.445806	0.222903	−	0.974841i	$-0.428447\pi$
$109$	4.65436	0.445806	0.222903	+	0.974841i	$0.428447\pi$
$110$	2.26140	0.215616
$111$	10.6776	1.01347
$112$	−3.41282	−0.322481
$113$	6.05343	0.569459	0.284730	−	0.958608i	$-0.408096\pi$
$113$	6.05343	0.569459	0.284730	+	0.958608i	$0.408096\pi$
$114$	1.51480	0.141874
$115$	12.0730	1.12581
$116$	−4.00309	−0.371678
$117$	0.970186	0.0896938
$118$	−4.97524	−0.458008
$119$	−11.2543	−1.03168
$120$	2.01534	0.183975
$121$	−8.11088	−0.737352
$122$	5.81073	0.526079
$123$	−5.79716	−0.522712
$124$	−3.30245	−0.296569
$125$	10.9494	0.979346
$126$	2.40738	0.214466
$127$	−17.2322	−1.52911	−0.764554	−	0.644559i	$-0.777041\pi$
$127$	−17.2322	−1.52911	−0.764554	+	0.644559i	$0.777041\pi$
$128$	1.00000	0.0883883
$129$	4.35351	0.383305
$130$	1.82986	0.160490
$131$	13.8383	1.20905	0.604527	−	0.796585i	$-0.293362\pi$
$131$	13.8383	1.20905	0.604527	+	0.796585i	$0.293362\pi$
$132$	2.57476	0.224104
$133$	3.41282	0.295929
$134$	2.62930	0.227137
$135$	−7.46764	−0.642712
$136$	3.29766	0.282772
$137$	−8.81438	−0.753063	−0.376532	−	0.926404i	$-0.622883\pi$
$137$	−8.81438	−0.753063	−0.376532	+	0.926404i	$0.622883\pi$
$138$	13.7459	1.17013
$139$	−13.5085	−1.14578	−0.572888	−	0.819634i	$-0.694177\pi$
$139$	−13.5085	−1.14578	−0.572888	+	0.819634i	$0.694177\pi$
$140$	4.54054	0.383746
$141$	−0.611592	−0.0515054
$142$	−1.72879	−0.145077
$143$	2.33780	0.195496
$144$	−0.705394	−0.0587828
$145$	5.32587	0.442289
$146$	−2.94738	−0.243927
$147$	−7.03973	−0.580627
$148$	−7.04888	−0.579415
$149$	−8.44192	−0.691589	−0.345795	−	0.938310i	$-0.612391\pi$
$149$	−8.44192	−0.691589	−0.345795	+	0.938310i	$0.612391\pi$
$150$	4.89269	0.399486
$151$	20.4415	1.66351	0.831754	−	0.555145i	$-0.187337\pi$
$151$	20.4415	1.66351	0.831754	+	0.555145i	$0.187337\pi$
$152$	−1.00000	−0.0811107
$153$	−2.32615	−0.188058
$154$	5.80091	0.467450
$155$	4.39370	0.352911
$156$	2.08342	0.166807
$157$	20.3889	1.62721	0.813606	−	0.581416i	$-0.197501\pi$
$157$	20.3889	1.62721	0.813606	+	0.581416i	$0.197501\pi$
$158$	−13.6615	−1.08685
$159$	5.25991	0.417138
$160$	−1.33044	−0.105180
$161$	30.9694	2.44073
$162$	−6.38624	−0.501750
$163$	17.7092	1.38709	0.693544	−	0.720414i	$-0.256048\pi$
$163$	17.7092	1.38709	0.693544	+	0.720414i	$0.256048\pi$
$164$	3.82702	0.298840
$165$	−3.42556	−0.266680
$166$	−13.8574	−1.07555
$167$	12.2727	0.949691	0.474845	−	0.880069i	$-0.342504\pi$
$167$	12.2727	0.949691	0.474845	+	0.880069i	$0.342504\pi$
$168$	5.16972	0.398853
$169$	−11.1083	−0.854486
$170$	−4.38733	−0.336493
$171$	0.705394	0.0539428
$172$	−2.87399	−0.219140
$173$	−6.43453	−0.489208	−0.244604	−	0.969623i	$-0.578658\pi$
$173$	−6.43453	−0.489208	−0.244604	+	0.969623i	$0.578658\pi$
$174$	6.06387	0.459700
$175$	11.0232	0.833273
$176$	−1.69974	−0.128123
$177$	7.53647	0.566476
$178$	0.930086	0.0697129
$179$	3.93151	0.293855	0.146928	−	0.989147i	$-0.453062\pi$
$179$	3.93151	0.293855	0.146928	+	0.989147i	$0.453062\pi$
$180$	0.938483	0.0699504
$181$	−12.8893	−0.958054	−0.479027	−	0.877800i	$-0.659010\pi$
$181$	−12.8893	−0.958054	−0.479027	+	0.877800i	$0.659010\pi$
$182$	4.69393	0.347937
$183$	−8.80208	−0.650668
$184$	−9.07443	−0.668976
$185$	9.37811	0.689492
$186$	5.00253	0.366804
$187$	−5.60517	−0.409890
$188$	0.403746	0.0294462
$189$	−19.1558	−1.39338
$190$	1.33044	0.0965202
$191$	14.6660	1.06119	0.530597	−	0.847624i	$-0.321968\pi$
$191$	14.6660	1.06119	0.530597	+	0.847624i	$0.321968\pi$
$192$	−1.51480	−0.109321
$193$	−8.39534	−0.604309	−0.302155	−	0.953259i	$-0.597706\pi$
$193$	−8.39534	−0.604309	−0.302155	+	0.953259i	$0.597706\pi$
$194$	19.0674	1.36896
$195$	−2.77187	−0.198498
$196$	4.64731	0.331951
$197$	21.4394	1.52749	0.763745	−	0.645518i	$-0.223358\pi$
$197$	21.4394	1.52749	0.763745	+	0.645518i	$0.223358\pi$
$198$	1.19899	0.0852083
$199$	3.84538	0.272592	0.136296	−	0.990668i	$-0.456480\pi$
$199$	3.84538	0.272592	0.136296	+	0.990668i	$0.456480\pi$
$200$	−3.22993	−0.228391
$201$	−3.98285	−0.280928
$202$	−2.12217	−0.149316
$203$	13.6618	0.958871
$204$	−4.99528	−0.349739
$205$	−5.09162	−0.355614
$206$	8.09522	0.564020
$207$	6.40104	0.444903
$208$	−1.37538	−0.0953657
$209$	1.69974	0.117574
$210$	−6.87799	−0.474627
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	−3.47236	−0.238482
$213$	2.61877	0.179435
$214$	0.314171	0.0214763
$215$	3.82367	0.260772
$216$	5.61291	0.381910
$217$	11.2706	0.765101
$218$	4.65436	0.315233
$219$	4.46467	0.301695
$220$	2.26140	0.152464
$221$	−4.53554	−0.305094
$222$	10.6776	0.716635
$223$	−25.7019	−1.72113	−0.860564	−	0.509343i	$-0.829888\pi$
$223$	−25.7019	−1.72113	−0.860564	+	0.509343i	$0.829888\pi$
$224$	−3.41282	−0.228028
$225$	2.27837	0.151892
$226$	6.05343	0.402668
$227$	4.95645	0.328971	0.164486	−	0.986379i	$-0.447404\pi$
$227$	4.95645	0.328971	0.164486	+	0.986379i	$0.447404\pi$
$228$	1.51480	0.100320
$229$	−8.83498	−0.583832	−0.291916	−	0.956444i	$-0.594293\pi$
$229$	−8.83498	−0.583832	−0.291916	+	0.956444i	$0.594293\pi$
$230$	12.0730	0.796068
$231$	−8.78719	−0.578155
$232$	−4.00309	−0.262816
$233$	16.3043	1.06813	0.534064	−	0.845444i	$-0.320664\pi$
$233$	16.3043	1.06813	0.534064	+	0.845444i	$0.320664\pi$
$234$	0.970186	0.0634231
$235$	−0.537159	−0.0350404
$236$	−4.97524	−0.323860
$237$	20.6945	1.34425
$238$	−11.2543	−0.729508
$239$	−5.20338	−0.336579	−0.168289	−	0.985738i	$-0.553824\pi$
$239$	−5.20338	−0.336579	−0.168289	+	0.985738i	$0.553824\pi$
$240$	2.01534	0.130090
$241$	25.2116	1.62402	0.812011	−	0.583642i	$-0.198373\pi$
$241$	25.2116	1.62402	0.812011	+	0.583642i	$0.198373\pi$
$242$	−8.11088	−0.521387
$243$	−7.16490	−0.459628
$244$	5.81073	0.371994
$245$	−6.18296	−0.395015
$246$	−5.79716	−0.369613
$247$	1.37538	0.0875135
$248$	−3.30245	−0.209706
$249$	20.9912	1.33026
$250$	10.9494	0.692502
$251$	23.6548	1.49308	0.746538	−	0.665343i	$-0.231715\pi$
$251$	23.6548	1.49308	0.746538	+	0.665343i	$0.231715\pi$
$252$	2.40738	0.151651
$253$	15.4242	0.969710
$254$	−17.2322	−1.08124
$255$	6.64591	0.416183
$256$	1.00000	0.0625000
$257$	−18.4024	−1.14791	−0.573954	−	0.818888i	$-0.694591\pi$
$257$	−18.4024	−1.14791	−0.573954	+	0.818888i	$0.694591\pi$
$258$	4.35351	0.271038
$259$	24.0565	1.49480
$260$	1.82986	0.113483
$261$	2.82375	0.174786
$262$	13.8383	0.854930
$263$	16.7685	1.03399	0.516997	−	0.855987i	$-0.327050\pi$
$263$	16.7685	1.03399	0.516997	+	0.855987i	$0.327050\pi$
$264$	2.57476	0.158466
$265$	4.61976	0.283789
$266$	3.41282	0.209253
$267$	−1.40889	−0.0862227
$268$	2.62930	0.160610
$269$	−25.6422	−1.56343	−0.781715	−	0.623635i	$-0.785655\pi$
$269$	−25.6422	−1.56343	−0.781715	+	0.623635i	$0.785655\pi$
$270$	−7.46764	−0.454466
$271$	−21.3945	−1.29963	−0.649813	−	0.760094i	$-0.725153\pi$
$271$	−21.3945	−1.29963	−0.649813	+	0.760094i	$0.725153\pi$
$272$	3.29766	0.199950
$273$	−7.11034	−0.430338
$274$	−8.81438	−0.532496
$275$	5.49005	0.331063
$276$	13.7459	0.827406
$277$	13.9758	0.839725	0.419862	−	0.907588i	$-0.362078\pi$
$277$	13.9758	0.839725	0.419862	+	0.907588i	$0.362078\pi$
$278$	−13.5085	−0.810186
$279$	2.32953	0.139465
$280$	4.54054	0.271349
$281$	14.4950	0.864698	0.432349	−	0.901706i	$-0.357685\pi$
$281$	14.4950	0.864698	0.432349	+	0.901706i	$0.357685\pi$
$282$	−0.611592	−0.0364198
$283$	−8.77714	−0.521747	−0.260873	−	0.965373i	$-0.584010\pi$
$283$	−8.77714	−0.521747	−0.260873	+	0.965373i	$0.584010\pi$
$284$	−1.72879	−0.102585
$285$	−2.01534	−0.119379
$286$	2.33780	0.138237
$287$	−13.0609	−0.770962
$288$	−0.705394	−0.0415657
$289$	−6.12546	−0.360321
$290$	5.32587	0.312746
$291$	−28.8832	−1.69316
$292$	−2.94738	−0.172482
$293$	9.95726	0.581709	0.290855	−	0.956767i	$-0.406060\pi$
$293$	9.95726	0.581709	0.290855	+	0.956767i	$0.406060\pi$
$294$	−7.03973	−0.410565
$295$	6.61925	0.385388
$296$	−7.04888	−0.409708
$297$	−9.54051	−0.553596
$298$	−8.44192	−0.489028
$299$	12.4808	0.721784
$300$	4.89269	0.282480
$301$	9.80840	0.565347
$302$	20.4415	1.17628
$303$	3.21466	0.184677
$304$	−1.00000	−0.0573539
$305$	−7.73082	−0.442666
$306$	−2.32615	−0.132977
$307$	−25.9108	−1.47881	−0.739404	−	0.673262i	$-0.764893\pi$
$307$	−25.9108	−1.47881	−0.739404	+	0.673262i	$0.764893\pi$
$308$	5.80091	0.330537
$309$	−12.2626	−0.697595
$310$	4.39370	0.249546
$311$	−2.62501	−0.148851	−0.0744254	−	0.997227i	$-0.523712\pi$
$311$	−2.62501	−0.148851	−0.0744254	+	0.997227i	$0.523712\pi$
$312$	2.08342	0.117951
$313$	24.4886	1.38418	0.692088	−	0.721813i	$-0.256691\pi$
$313$	24.4886	1.38418	0.692088	+	0.721813i	$0.256691\pi$
$314$	20.3889	1.15061
$315$	−3.20287	−0.180461
$316$	−13.6615	−0.768522
$317$	23.0562	1.29496	0.647482	−	0.762081i	$-0.275822\pi$
$317$	23.0562	1.29496	0.647482	+	0.762081i	$0.275822\pi$
$318$	5.25991	0.294961
$319$	6.80422	0.380963
$320$	−1.33044	−0.0743738
$321$	−0.475904	−0.0265624
$322$	30.9694	1.72585
$323$	−3.29766	−0.183487
$324$	−6.38624	−0.354791
$325$	4.44240	0.246420
$326$	17.7092	0.980820
$327$	−7.05040	−0.389888
$328$	3.82702	0.211312
$329$	−1.37791	−0.0759666
$330$	−3.42556	−0.188571
$331$	31.1190	1.71045	0.855227	−	0.518253i	$-0.173418\pi$
$331$	31.1190	1.71045	0.855227	+	0.518253i	$0.173418\pi$
$332$	−13.8574	−0.760526
$333$	4.97224	0.272477
$334$	12.2727	0.671533
$335$	−3.49812	−0.191123
$336$	5.16972	0.282031
$337$	23.9576	1.30505	0.652527	−	0.757765i	$-0.273709\pi$
$337$	23.9576	1.30505	0.652527	+	0.757765i	$0.273709\pi$
$338$	−11.1083	−0.604213
$339$	−9.16972	−0.498031
$340$	−4.38733	−0.237936
$341$	5.61331	0.303978
$342$	0.705394	0.0381433
$343$	8.02929	0.433541
$344$	−2.87399	−0.154955
$345$	−18.2881	−0.984597
$346$	−6.43453	−0.345922
$347$	−35.7022	−1.91660	−0.958298	−	0.285771i	$-0.907750\pi$
$347$	−35.7022	−1.91660	−0.958298	+	0.285771i	$0.907750\pi$
$348$	6.06387	0.325057
$349$	4.64600	0.248695	0.124347	−	0.992239i	$-0.460316\pi$
$349$	4.64600	0.248695	0.124347	+	0.992239i	$0.460316\pi$
$350$	11.0232	0.589213
$351$	−7.71991	−0.412058
$352$	−1.69974	−0.0905966
$353$	36.2241	1.92801	0.964006	−	0.265880i	$-0.0856624\pi$
$353$	36.2241	1.92801	0.964006	+	0.265880i	$0.0856624\pi$
$354$	7.53647	0.400559
$355$	2.30005	0.122074
$356$	0.930086	0.0492944
$357$	17.0480	0.902274
$358$	3.93151	0.207787
$359$	25.3870	1.33987	0.669936	−	0.742419i	$-0.266321\pi$
$359$	25.3870	1.33987	0.669936	+	0.742419i	$0.266321\pi$
$360$	0.938483	0.0494624
$361$	1.00000	0.0526316
$362$	−12.8893	−0.677446
$363$	12.2863	0.644865
$364$	4.69393	0.246029
$365$	3.92130	0.205250
$366$	−8.80208	−0.460092
$367$	36.8464	1.92337	0.961684	−	0.274160i	$-0.0883998\pi$
$367$	36.8464	1.92337	0.961684	+	0.274160i	$0.0883998\pi$
$368$	−9.07443	−0.473037
$369$	−2.69956	−0.140533
$370$	9.37811	0.487545
$371$	11.8505	0.615248
$372$	5.00253	0.259369
$373$	17.8694	0.925241	0.462620	−	0.886556i	$-0.346909\pi$
$373$	17.8694	0.925241	0.462620	+	0.886556i	$0.346909\pi$
$374$	−5.60517	−0.289836
$375$	−16.5861	−0.856504
$376$	0.403746	0.0208216
$377$	5.50578	0.283562
$378$	−19.1558	−0.985270
$379$	−8.25938	−0.424256	−0.212128	−	0.977242i	$-0.568039\pi$
$379$	−8.25938	−0.424256	−0.212128	+	0.977242i	$0.568039\pi$
$380$	1.33044	0.0682501
$381$	26.1032	1.33731
$382$	14.6660	0.750377
$383$	−26.7949	−1.36915	−0.684577	−	0.728941i	$-0.740013\pi$
$383$	−26.7949	−1.36915	−0.684577	+	0.728941i	$0.740013\pi$
$384$	−1.51480	−0.0773016
$385$	−7.71775	−0.393333
$386$	−8.39534	−0.427311
$387$	2.02729	0.103053
$388$	19.0674	0.967999
$389$	−37.8046	−1.91677	−0.958384	−	0.285482i	$-0.907846\pi$
$389$	−37.8046	−1.91677	−0.958384	+	0.285482i	$0.907846\pi$
$390$	−2.77187	−0.140359
$391$	−29.9244	−1.51334
$392$	4.64731	0.234725
$393$	−20.9621	−1.05740
$394$	21.4394	1.08010
$395$	18.1759	0.914526
$396$	1.19899	0.0602514
$397$	−24.5588	−1.23257	−0.616285	−	0.787523i	$-0.711363\pi$
$397$	−24.5588	−1.23257	−0.616285	+	0.787523i	$0.711363\pi$
$398$	3.84538	0.192751
$399$	−5.16972	−0.258810
$400$	−3.22993	−0.161497
$401$	1.90144	0.0949536	0.0474768	−	0.998872i	$-0.484882\pi$
$401$	1.90144	0.0949536	0.0474768	+	0.998872i	$0.484882\pi$
$402$	−3.98285	−0.198646
$403$	4.54213	0.226260
$404$	−2.12217	−0.105582
$405$	8.49650	0.422194
$406$	13.6618	0.678024
$407$	11.9813	0.593890
$408$	−4.99528	−0.247303
$409$	3.94505	0.195070	0.0975351	−	0.995232i	$-0.468904\pi$
$409$	3.94505	0.195070	0.0975351	+	0.995232i	$0.468904\pi$
$410$	−5.09162	−0.251457
$411$	13.3520	0.658605
$412$	8.09522	0.398823
$413$	16.9796	0.835510
$414$	6.40104	0.314594
$415$	18.4365	0.905011
$416$	−1.37538	−0.0674337
$417$	20.4626	1.00206
$418$	1.69974	0.0831371
$419$	−7.58752	−0.370674	−0.185337	−	0.982675i	$-0.559338\pi$
$419$	−7.58752	−0.370674	−0.185337	+	0.982675i	$0.559338\pi$
$420$	−6.87799	−0.335612
$421$	2.32906	0.113512	0.0567558	−	0.998388i	$-0.481924\pi$
$421$	2.32906	0.113512	0.0567558	+	0.998388i	$0.481924\pi$
$422$	−1.00000	−0.0486792
$423$	−0.284800	−0.0138474
$424$	−3.47236	−0.168632
$425$	−10.6512	−0.516660
$426$	2.61877	0.126880
$427$	−19.8310	−0.959688
$428$	0.314171	0.0151860
$429$	−3.54128	−0.170975
$430$	3.82367	0.184394
$431$	−32.3917	−1.56025	−0.780127	−	0.625621i	$-0.784846\pi$
$431$	−32.3917	−1.56025	−0.780127	+	0.625621i	$0.784846\pi$
$432$	5.61291	0.270051
$433$	−6.39386	−0.307269	−0.153635	−	0.988128i	$-0.549098\pi$
$433$	−6.39386	−0.307269	−0.153635	+	0.988128i	$0.549098\pi$
$434$	11.2706	0.541008
$435$	−8.06760	−0.386812
$436$	4.65436	0.222903
$437$	9.07443	0.434089
$438$	4.46467	0.213330
$439$	−27.0707	−1.29202	−0.646008	−	0.763331i	$-0.723563\pi$
$439$	−27.0707	−1.29202	−0.646008	+	0.763331i	$0.723563\pi$
$440$	2.26140	0.107808
$441$	−3.27818	−0.156104
$442$	−4.53554	−0.215734
$443$	−26.1683	−1.24329	−0.621647	−	0.783297i	$-0.713536\pi$
$443$	−26.1683	−1.24329	−0.621647	+	0.783297i	$0.713536\pi$
$444$	10.6776	0.506737
$445$	−1.23742	−0.0586594
$446$	−25.7019	−1.21702
$447$	12.7878	0.604842
$448$	−3.41282	−0.161240
$449$	11.6674	0.550619	0.275309	−	0.961356i	$-0.411220\pi$
$449$	11.6674	0.550619	0.275309	+	0.961356i	$0.411220\pi$
$450$	2.27837	0.107404
$451$	−6.50495	−0.306306
$452$	6.05343	0.284730
$453$	−30.9647	−1.45485
$454$	4.95645	0.232618
$455$	−6.24498	−0.292769
$456$	1.51480	0.0709368
$457$	−33.8111	−1.58162	−0.790808	−	0.612064i	$-0.790340\pi$
$457$	−33.8111	−1.58162	−0.790808	+	0.612064i	$0.790340\pi$
$458$	−8.83498	−0.412832
$459$	18.5095	0.863948
$460$	12.0730	0.562905
$461$	2.22299	0.103535	0.0517675	−	0.998659i	$-0.483515\pi$
$461$	2.22299	0.103535	0.0517675	+	0.998659i	$0.483515\pi$
$462$	−8.78719	−0.408817
$463$	−14.0372	−0.652364	−0.326182	−	0.945307i	$-0.605762\pi$
$463$	−14.0372	−0.652364	−0.326182	+	0.945307i	$0.605762\pi$
$464$	−4.00309	−0.185839
$465$	−6.65556	−0.308644
$466$	16.3043	0.755280
$467$	7.36968	0.341028	0.170514	−	0.985355i	$-0.445457\pi$
$467$	7.36968	0.341028	0.170514	+	0.985355i	$0.445457\pi$
$468$	0.970186	0.0448469
$469$	−8.97331	−0.414349
$470$	−0.537159	−0.0247773
$471$	−30.8850	−1.42311
$472$	−4.97524	−0.229004
$473$	4.88504	0.224614
$474$	20.6945	0.950528
$475$	3.22993	0.148200
$476$	−11.2543	−0.515840
$477$	2.44938	0.112149
$478$	−5.20338	−0.237997
$479$	−10.6119	−0.484872	−0.242436	−	0.970167i	$-0.577946\pi$
$479$	−10.6119	−0.484872	−0.242436	+	0.970167i	$0.577946\pi$
$480$	2.01534	0.0919874
$481$	9.69491	0.442050
$482$	25.2116	1.14836
$483$	−46.9123	−2.13458
$484$	−8.11088	−0.368676
$485$	−25.3680	−1.15190
$486$	−7.16490	−0.325006
$487$	−30.9772	−1.40371	−0.701856	−	0.712319i	$-0.747645\pi$
$487$	−30.9772	−1.40371	−0.701856	+	0.712319i	$0.747645\pi$
$488$	5.81073	0.263040
$489$	−26.8258	−1.21310
$490$	−6.18296	−0.279318
$491$	−11.8094	−0.532951	−0.266476	−	0.963842i	$-0.585859\pi$
$491$	−11.8094	−0.532951	−0.266476	+	0.963842i	$0.585859\pi$
$492$	−5.79716	−0.261356
$493$	−13.2008	−0.594535
$494$	1.37538	0.0618814
$495$	−1.59518	−0.0716979
$496$	−3.30245	−0.148284
$497$	5.90005	0.264653
$498$	20.9912	0.940638
$499$	−4.86110	−0.217613	−0.108806	−	0.994063i	$-0.534703\pi$
$499$	−4.86110	−0.217613	−0.108806	+	0.994063i	$0.534703\pi$
$500$	10.9494	0.489673
$501$	−18.5907	−0.830569
$502$	23.6548	1.05576
$503$	−10.8269	−0.482749	−0.241375	−	0.970432i	$-0.577598\pi$
$503$	−10.8269	−0.482749	−0.241375	+	0.970432i	$0.577598\pi$
$504$	2.40738	0.107233
$505$	2.82342	0.125641
$506$	15.4242	0.685689
$507$	16.8268	0.747306
$508$	−17.2322	−0.764554
$509$	4.47330	0.198275	0.0991377	−	0.995074i	$-0.468392\pi$
$509$	4.47330	0.198275	0.0991377	+	0.995074i	$0.468392\pi$
$510$	6.64591	0.294286
$511$	10.0589	0.444977
$512$	1.00000	0.0441942
$513$	−5.61291	−0.247816
$514$	−18.4024	−0.811693
$515$	−10.7702	−0.474591
$516$	4.35351	0.191653
$517$	−0.686264	−0.0301818
$518$	24.0565	1.05698
$519$	9.74699	0.427845
$520$	1.82986	0.0802448
$521$	−10.9369	−0.479154	−0.239577	−	0.970877i	$-0.577009\pi$
$521$	−10.9369	−0.479154	−0.239577	+	0.970877i	$0.577009\pi$
$522$	2.82375	0.123592
$523$	−33.9413	−1.48415	−0.742076	−	0.670316i	$-0.766158\pi$
$523$	−33.9413	−1.48415	−0.742076	+	0.670316i	$0.766158\pi$
$524$	13.8383	0.604527
$525$	−16.6978	−0.728754
$526$	16.7685	0.731144
$527$	−10.8903	−0.474391
$528$	2.57476	0.112052
$529$	59.3453	2.58023
$530$	4.61976	0.200669
$531$	3.50950	0.152299
$532$	3.41282	0.147964
$533$	−5.26362	−0.227993
$534$	−1.40889	−0.0609686
$535$	−0.417985	−0.0180710
$536$	2.62930	0.113568
$537$	−5.95544	−0.256996
$538$	−25.6422	−1.10551
$539$	−7.89923	−0.340244
$540$	−7.46764	−0.321356
$541$	−21.9795	−0.944972	−0.472486	−	0.881338i	$-0.656643\pi$
$541$	−21.9795	−0.944972	−0.472486	+	0.881338i	$0.656643\pi$
$542$	−21.3945	−0.918974
$543$	19.5247	0.837883
$544$	3.29766	0.141386
$545$	−6.19233	−0.265250
$546$	−7.11034	−0.304295
$547$	7.50662	0.320960	0.160480	−	0.987039i	$-0.448696\pi$
$547$	7.50662	0.320960	0.160480	+	0.987039i	$0.448696\pi$
$548$	−8.81438	−0.376532
$549$	−4.09885	−0.174935
$550$	5.49005	0.234097
$551$	4.00309	0.170537
$552$	13.7459	0.585065
$553$	46.6244	1.98267
$554$	13.9758	0.593775
$555$	−14.2059	−0.603008
$556$	−13.5085	−0.572888
$557$	18.3852	0.779005	0.389503	−	0.921025i	$-0.372647\pi$
$557$	18.3852	0.779005	0.389503	+	0.921025i	$0.372647\pi$
$558$	2.32953	0.0986167
$559$	3.95284	0.167187
$560$	4.54054	0.191873
$561$	8.49068	0.358477
$562$	14.4950	0.611434
$563$	38.1339	1.60715	0.803576	−	0.595203i	$-0.202928\pi$
$563$	38.1339	1.60715	0.803576	+	0.595203i	$0.202928\pi$
$564$	−0.611592	−0.0257527
$565$	−8.05372	−0.338823
$566$	−8.77714	−0.368931
$567$	21.7951	0.915306
$568$	−1.72879	−0.0725385
$569$	−19.8800	−0.833412	−0.416706	−	0.909041i	$-0.636815\pi$
$569$	−19.8800	−0.833412	−0.416706	+	0.909041i	$0.636815\pi$
$570$	−2.01534	−0.0844134
$571$	36.9444	1.54607	0.773037	−	0.634362i	$-0.218737\pi$
$571$	36.9444	1.54607	0.773037	+	0.634362i	$0.218737\pi$
$572$	2.33780	0.0977482
$573$	−22.2160	−0.928086
$574$	−13.0609	−0.545152
$575$	29.3098	1.22230
$576$	−0.705394	−0.0293914
$577$	30.2144	1.25784	0.628921	−	0.777469i	$-0.283497\pi$
$577$	30.2144	1.25784	0.628921	+	0.777469i	$0.283497\pi$
$578$	−6.12546	−0.254786
$579$	12.7172	0.528510
$580$	5.32587	0.221145
$581$	47.2929	1.96204
$582$	−28.8832	−1.19725
$583$	5.90211	0.244440
$584$	−2.94738	−0.121963
$585$	−1.29077	−0.0533669
$586$	9.95726	0.411331
$587$	8.57185	0.353798	0.176899	−	0.984229i	$-0.443393\pi$
$587$	8.57185	0.353798	0.176899	+	0.984229i	$0.443393\pi$
$588$	−7.03973	−0.290314
$589$	3.30245	0.136075
$590$	6.61925	0.272510
$591$	−32.4762	−1.33589
$592$	−7.04888	−0.289707
$593$	−10.9435	−0.449397	−0.224699	−	0.974428i	$-0.572140\pi$
$593$	−10.9435	−0.449397	−0.224699	+	0.974428i	$0.572140\pi$
$594$	−9.54051	−0.391452
$595$	14.9731	0.613839
$596$	−8.44192	−0.345795
$597$	−5.82496	−0.238400
$598$	12.4808	0.510379
$599$	−24.7178	−1.00994	−0.504972	−	0.863136i	$-0.668497\pi$
$599$	−24.7178	−1.00994	−0.504972	+	0.863136i	$0.668497\pi$
$600$	4.89269	0.199743
$601$	−10.4790	−0.427449	−0.213725	−	0.976894i	$-0.568559\pi$
$601$	−10.4790	−0.427449	−0.213725	+	0.976894i	$0.568559\pi$
$602$	9.80840	0.399761
$603$	−1.85469	−0.0755288
$604$	20.4415	0.831754
$605$	10.7910	0.438717
$606$	3.21466	0.130587
$607$	−18.2506	−0.740768	−0.370384	−	0.928879i	$-0.620774\pi$
$607$	−18.2506	−0.740768	−0.370384	+	0.928879i	$0.620774\pi$
$608$	−1.00000	−0.0405554
$609$	−20.6949	−0.838598
$610$	−7.73082	−0.313012
$611$	−0.555305	−0.0224652
$612$	−2.32615	−0.0940289
$613$	30.7226	1.24087	0.620437	−	0.784256i	$-0.286955\pi$
$613$	30.7226	1.24087	0.620437	+	0.784256i	$0.286955\pi$
$614$	−25.9108	−1.04568
$615$	7.71276	0.311009
$616$	5.80091	0.233725
$617$	18.7514	0.754901	0.377451	−	0.926030i	$-0.376801\pi$
$617$	18.7514	0.754901	0.377451	+	0.926030i	$0.376801\pi$
$618$	−12.2626	−0.493274
$619$	30.2250	1.21485	0.607424	−	0.794378i	$-0.292203\pi$
$619$	30.2250	1.21485	0.607424	+	0.794378i	$0.292203\pi$
$620$	4.39370	0.176455
$621$	−50.9340	−2.04391
$622$	−2.62501	−0.105253
$623$	−3.17421	−0.127172
$624$	2.08342	0.0834037
$625$	1.58214	0.0632855
$626$	24.4886	0.978760
$627$	−2.57476	−0.102826
$628$	20.3889	0.813606
$629$	−23.2448	−0.926831
$630$	−3.20287	−0.127605
$631$	−36.3344	−1.44645	−0.723225	−	0.690612i	$-0.757341\pi$
$631$	−36.3344	−1.44645	−0.723225	+	0.690612i	$0.757341\pi$
$632$	−13.6615	−0.543427
$633$	1.51480	0.0602077
$634$	23.0562	0.915678
$635$	22.9264	0.909805
$636$	5.25991	0.208569
$637$	−6.39184	−0.253254
$638$	6.80422	0.269382
$639$	1.21948	0.0482418
$640$	−1.33044	−0.0525902
$641$	17.2843	0.682688	0.341344	−	0.939938i	$-0.389118\pi$
$641$	17.2843	0.682688	0.341344	+	0.939938i	$0.389118\pi$
$642$	−0.475904	−0.0187824
$643$	22.9355	0.904486	0.452243	−	0.891895i	$-0.350624\pi$
$643$	22.9355	0.904486	0.452243	+	0.891895i	$0.350624\pi$
$644$	30.9694	1.22036
$645$	−5.79208	−0.228063
$646$	−3.29766	−0.129745
$647$	−20.3085	−0.798408	−0.399204	−	0.916862i	$-0.630713\pi$
$647$	−20.3085	−0.798408	−0.399204	+	0.916862i	$0.630713\pi$
$648$	−6.38624	−0.250875
$649$	8.45662	0.331951
$650$	4.44240	0.174245
$651$	−17.0727	−0.669133
$652$	17.7092	0.693544
$653$	18.7836	0.735060	0.367530	−	0.930012i	$-0.380203\pi$
$653$	18.7836	0.735060	0.367530	+	0.930012i	$0.380203\pi$
$654$	−7.05040	−0.275692
$655$	−18.4109	−0.719375
$656$	3.82702	0.149420
$657$	2.07906	0.0811119
$658$	−1.37791	−0.0537165
$659$	4.56516	0.177833	0.0889167	−	0.996039i	$-0.471659\pi$
$659$	4.56516	0.177833	0.0889167	+	0.996039i	$0.471659\pi$
$660$	−3.42556	−0.133340
$661$	−9.42639	−0.366644	−0.183322	−	0.983053i	$-0.558685\pi$
$661$	−9.42639	−0.366644	−0.183322	+	0.983053i	$0.558685\pi$
$662$	31.1190	1.20947
$663$	6.87042	0.266825
$664$	−13.8574	−0.537773
$665$	−4.54054	−0.176075
$666$	4.97224	0.192670
$667$	36.3258	1.40654
$668$	12.2727	0.474845
$669$	38.9331	1.50524
$670$	−3.49812	−0.135144
$671$	−9.87675	−0.381288
$672$	5.16972	0.199426
$673$	26.5563	1.02367	0.511835	−	0.859084i	$-0.328966\pi$
$673$	26.5563	1.02367	0.511835	+	0.859084i	$0.328966\pi$
$674$	23.9576	0.922813
$675$	−18.1293	−0.697799
$676$	−11.1083	−0.427243
$677$	−1.64399	−0.0631835	−0.0315918	−	0.999501i	$-0.510058\pi$
$677$	−1.64399	−0.0631835	−0.0315918	+	0.999501i	$0.510058\pi$
$678$	−9.16972	−0.352161
$679$	−65.0734	−2.49729
$680$	−4.38733	−0.168246
$681$	−7.50802	−0.287708
$682$	5.61331	0.214945
$683$	−3.20287	−0.122555	−0.0612773	−	0.998121i	$-0.519517\pi$
$683$	−3.20287	−0.122555	−0.0612773	+	0.998121i	$0.519517\pi$
$684$	0.705394	0.0269714
$685$	11.7270	0.448065
$686$	8.02929	0.306560
$687$	13.3832	0.510601
$688$	−2.87399	−0.109570
$689$	4.77582	0.181944
$690$	−18.2881	−0.696216
$691$	−35.1314	−1.33646	−0.668231	−	0.743954i	$-0.732948\pi$
$691$	−35.1314	−1.33646	−0.668231	+	0.743954i	$0.732948\pi$
$692$	−6.43453	−0.244604
$693$	−4.09192	−0.155439
$694$	−35.7022	−1.35524
$695$	17.9722	0.681725
$696$	6.06387	0.229850
$697$	12.6202	0.478024
$698$	4.64600	0.175854
$699$	−24.6976	−0.934150
$700$	11.0232	0.416637
$701$	−40.6089	−1.53378	−0.766889	−	0.641780i	$-0.778196\pi$
$701$	−40.6089	−1.53378	−0.766889	+	0.641780i	$0.778196\pi$
$702$	−7.71991	−0.291369
$703$	7.04888	0.265854
$704$	−1.69974	−0.0640614
$705$	0.813686	0.0306452
$706$	36.2241	1.36331
$707$	7.24258	0.272385
$708$	7.53647	0.283238
$709$	6.61864	0.248568	0.124284	−	0.992247i	$-0.460337\pi$
$709$	6.61864	0.248568	0.124284	+	0.992247i	$0.460337\pi$
$710$	2.30005	0.0863194
$711$	9.63677	0.361407
$712$	0.930086	0.0348564
$713$	29.9678	1.12230
$714$	17.0480	0.638004
$715$	−3.11029	−0.116318
$716$	3.93151	0.146928
$717$	7.88206	0.294361
$718$	25.3870	0.947433
$719$	−6.02280	−0.224613	−0.112306	−	0.993674i	$-0.535824\pi$
$719$	−6.02280	−0.224613	−0.112306	+	0.993674i	$0.535824\pi$
$720$	0.938483	0.0349752
$721$	−27.6275	−1.02890
$722$	1.00000	0.0372161
$723$	−38.1904	−1.42032
$724$	−12.8893	−0.479027
$725$	12.9297	0.480198
$726$	12.2863	0.455988
$727$	−30.5647	−1.13358	−0.566791	−	0.823862i	$-0.691815\pi$
$727$	−30.5647	−1.13358	−0.566791	+	0.823862i	$0.691815\pi$
$728$	4.69393	0.173969
$729$	30.0121	1.11156
$730$	3.92130	0.145134
$731$	−9.47743	−0.350536
$732$	−8.80208	−0.325334
$733$	−2.54785	−0.0941068	−0.0470534	−	0.998892i	$-0.514983\pi$
$733$	−2.54785	−0.0941068	−0.0470534	+	0.998892i	$0.514983\pi$
$734$	36.8464	1.36003
$735$	9.36593	0.345467
$736$	−9.07443	−0.334488
$737$	−4.46913	−0.164622
$738$	−2.69956	−0.0993721
$739$	47.3283	1.74100	0.870499	−	0.492170i	$-0.163796\pi$
$739$	47.3283	1.74100	0.870499	+	0.492170i	$0.163796\pi$
$740$	9.37811	0.344746
$741$	−2.08342	−0.0765365
$742$	11.8505	0.435046
$743$	6.21476	0.227997	0.113999	−	0.993481i	$-0.463634\pi$
$743$	6.21476	0.227997	0.113999	+	0.993481i	$0.463634\pi$
$744$	5.00253	0.183402
$745$	11.2315	0.411489
$746$	17.8694	0.654244
$747$	9.77495	0.357647
$748$	−5.60517	−0.204945
$749$	−1.07221	−0.0391776
$750$	−16.5861	−0.605640
$751$	−14.1073	−0.514783	−0.257391	−	0.966307i	$-0.582863\pi$
$751$	−14.1073	−0.514783	−0.257391	+	0.966307i	$0.582863\pi$
$752$	0.403746	0.0147231
$753$	−35.8321	−1.30580
$754$	5.50578	0.200509
$755$	−27.1962	−0.989770
$756$	−19.1558	−0.696691
$757$	47.9900	1.74423	0.872113	−	0.489304i	$-0.162749\pi$
$757$	47.9900	1.74423	0.872113	+	0.489304i	$0.162749\pi$
$758$	−8.25938	−0.299994
$759$	−23.3645	−0.848078
$760$	1.33044	0.0482601
$761$	−43.1871	−1.56553	−0.782766	−	0.622316i	$-0.786192\pi$
$761$	−43.1871	−1.56553	−0.782766	+	0.622316i	$0.786192\pi$
$762$	26.1032	0.945620
$763$	−15.8845	−0.575056
$764$	14.6660	0.530597
$765$	3.09479	0.111893
$766$	−26.7949	−0.968138
$767$	6.84286	0.247081
$768$	−1.51480	−0.0546605
$769$	−26.4903	−0.955263	−0.477632	−	0.878560i	$-0.658505\pi$
$769$	−26.4903	−0.955263	−0.477632	+	0.878560i	$0.658505\pi$
$770$	−7.71775	−0.278128
$771$	27.8758	1.00392
$772$	−8.39534	−0.302155
$773$	−32.5049	−1.16912	−0.584560	−	0.811351i	$-0.698733\pi$
$773$	−32.5049	−1.16912	−0.584560	+	0.811351i	$0.698733\pi$
$774$	2.02729	0.0728696
$775$	10.6667	0.383159
$776$	19.0674	0.684478
$777$	−36.4407	−1.30730
$778$	−37.8046	−1.35536
$779$	−3.82702	−0.137117
$780$	−2.77187	−0.0992488
$781$	2.93850	0.105148
$782$	−29.9244	−1.07009
$783$	−22.4690	−0.802977
$784$	4.64731	0.165975
$785$	−27.1262	−0.968176
$786$	−20.9621	−0.747694
$787$	−8.97760	−0.320017	−0.160008	−	0.987116i	$-0.551152\pi$
$787$	−8.97760	−0.320017	−0.160008	+	0.987116i	$0.551152\pi$
$788$	21.4394	0.763745
$789$	−25.4009	−0.904297
$790$	18.1759	0.646668
$791$	−20.6593	−0.734559
$792$	1.19899	0.0426042
$793$	−7.99199	−0.283804
$794$	−24.5588	−0.871559
$795$	−6.99799	−0.248193
$796$	3.84538	0.136296
$797$	−36.7219	−1.30076	−0.650379	−	0.759610i	$-0.725390\pi$
$797$	−36.7219	−1.30076	−0.650379	+	0.759610i	$0.725390\pi$
$798$	−5.16972	−0.183006
$799$	1.33142	0.0471021
$800$	−3.22993	−0.114195
$801$	−0.656077	−0.0231813
$802$	1.90144	0.0671423
$803$	5.00978	0.176791
$804$	−3.98285	−0.140464
$805$	−41.2028	−1.45221
$806$	4.54213	0.159990
$807$	38.8427	1.36733
$808$	−2.12217	−0.0746578
$809$	13.5360	0.475901	0.237950	−	0.971277i	$-0.423524\pi$
$809$	13.5360	0.475901	0.237950	+	0.971277i	$0.423524\pi$
$810$	8.49650	0.298537
$811$	45.7810	1.60759	0.803794	−	0.594907i	$-0.202811\pi$
$811$	45.7810	1.60759	0.803794	+	0.594907i	$0.202811\pi$
$812$	13.6618	0.479436
$813$	32.4084	1.13661
$814$	11.9813	0.419944
$815$	−23.5609	−0.825304
$816$	−4.99528	−0.174870
$817$	2.87399	0.100548
$818$	3.94505	0.137935
$819$	−3.31107	−0.115698
$820$	−5.09162	−0.177807
$821$	6.08793	0.212470	0.106235	−	0.994341i	$-0.466120\pi$
$821$	6.08793	0.212470	0.106235	+	0.994341i	$0.466120\pi$
$822$	13.3520	0.465704
$823$	−24.5573	−0.856014	−0.428007	−	0.903775i	$-0.640784\pi$
$823$	−24.5573	−0.856014	−0.428007	+	0.903775i	$0.640784\pi$
$824$	8.09522	0.282010
$825$	−8.31631	−0.289537
$826$	16.9796	0.590795
$827$	44.1891	1.53661	0.768303	−	0.640086i	$-0.221101\pi$
$827$	44.1891	1.53661	0.768303	+	0.640086i	$0.221101\pi$
$828$	6.40104	0.222452
$829$	43.4526	1.50917	0.754586	−	0.656201i	$-0.227838\pi$
$829$	43.4526	1.50917	0.754586	+	0.656201i	$0.227838\pi$
$830$	18.4365	0.639939
$831$	−21.1705	−0.734396
$832$	−1.37538	−0.0476828
$833$	15.3252	0.530988
$834$	20.4626	0.708562
$835$	−16.3281	−0.565057
$836$	1.69974	0.0587868
$837$	−18.5364	−0.640710
$838$	−7.58752	−0.262106
$839$	−3.59994	−0.124284	−0.0621419	−	0.998067i	$-0.519793\pi$
$839$	−3.59994	−0.124284	−0.0621419	+	0.998067i	$0.519793\pi$
$840$	−6.87799	−0.237313
$841$	−12.9753	−0.447423
$842$	2.32906	0.0802648
$843$	−21.9569	−0.756237
$844$	−1.00000	−0.0344214
$845$	14.7789	0.508411
$846$	−0.284800	−0.00979162
$847$	27.6809	0.951128
$848$	−3.47236	−0.119241
$849$	13.2956	0.456303
$850$	−10.6512	−0.365334
$851$	63.9646	2.19268
$852$	2.61877	0.0897175
$853$	10.9039	0.373343	0.186672	−	0.982422i	$-0.440230\pi$
$853$	10.9039	0.373343	0.186672	+	0.982422i	$0.440230\pi$
$854$	−19.8310	−0.678602
$855$	−0.938483	−0.0320954
$856$	0.314171	0.0107381
$857$	−32.4946	−1.10999	−0.554997	−	0.831852i	$-0.687281\pi$
$857$	−32.4946	−1.10999	−0.554997	+	0.831852i	$0.687281\pi$
$858$	−3.54128	−0.120897
$859$	−22.5303	−0.768725	−0.384363	−	0.923182i	$-0.625579\pi$
$859$	−22.5303	−0.768725	−0.384363	+	0.923182i	$0.625579\pi$
$860$	3.82367	0.130386
$861$	19.7846	0.674258
$862$	−32.3917	−1.10327
$863$	48.2969	1.64404	0.822022	−	0.569455i	$-0.192846\pi$
$863$	48.2969	1.64404	0.822022	+	0.569455i	$0.192846\pi$
$864$	5.61291	0.190955
$865$	8.56074	0.291074
$866$	−6.39386	−0.217272
$867$	9.27882	0.315125
$868$	11.2706	0.382551
$869$	23.2211	0.787722
$870$	−8.06760	−0.273517
$871$	−3.61629	−0.122533
$872$	4.65436	0.157616
$873$	−13.4500	−0.455213
$874$	9.07443	0.306947
$875$	−37.3684	−1.26328
$876$	4.46467	0.150847
$877$	−50.3611	−1.70058	−0.850288	−	0.526318i	$-0.823572\pi$
$877$	−50.3611	−1.70058	−0.850288	+	0.526318i	$0.823572\pi$
$878$	−27.0707	−0.913593
$879$	−15.0832	−0.508744
$880$	2.26140	0.0762318
$881$	53.6654	1.80803	0.904016	−	0.427498i	$-0.140605\pi$
$881$	53.6654	1.80803	0.904016	+	0.427498i	$0.140605\pi$
$882$	−3.27818	−0.110382
$883$	16.8234	0.566153	0.283077	−	0.959097i	$-0.408645\pi$
$883$	16.8234	0.566153	0.283077	+	0.959097i	$0.408645\pi$
$884$	−4.53554	−0.152547
$885$	−10.0268	−0.337048
$886$	−26.1683	−0.879142
$887$	−34.5624	−1.16049	−0.580246	−	0.814441i	$-0.697044\pi$
$887$	−34.5624	−1.16049	−0.580246	+	0.814441i	$0.697044\pi$
$888$	10.6776	0.358317
$889$	58.8103	1.97243
$890$	−1.23742	−0.0414785
$891$	10.8550	0.363655
$892$	−25.7019	−0.860564
$893$	−0.403746	−0.0135108
$894$	12.7878	0.427688
$895$	−5.23064	−0.174841
$896$	−3.41282	−0.114014
$897$	−18.9059	−0.631249
$898$	11.6674	0.389346
$899$	13.2200	0.440912
$900$	2.27837	0.0759458
$901$	−11.4506	−0.381476
$902$	−6.50495	−0.216591
$903$	−14.8577	−0.494434
$904$	6.05343	0.201334
$905$	17.1484	0.570033
$906$	−30.9647	−1.02873
$907$	−3.97159	−0.131875	−0.0659373	−	0.997824i	$-0.521004\pi$
$907$	−3.97159	−0.131875	−0.0659373	+	0.997824i	$0.521004\pi$
$908$	4.95645	0.164486
$909$	1.49697	0.0496513
$910$	−6.24498	−0.207019
$911$	−16.7147	−0.553784	−0.276892	−	0.960901i	$-0.589304\pi$
$911$	−16.7147	−0.553784	−0.276892	+	0.960901i	$0.589304\pi$
$912$	1.51480	0.0501599
$913$	23.5541	0.779526
$914$	−33.8111	−1.11837
$915$	11.7106	0.387141
$916$	−8.83498	−0.291916
$917$	−47.2274	−1.55959
$918$	18.5095	0.610903
$919$	45.0691	1.48669	0.743346	−	0.668907i	$-0.233237\pi$
$919$	45.0691	1.48669	0.743346	+	0.668907i	$0.233237\pi$
$920$	12.0730	0.398034
$921$	39.2496	1.29332
$922$	2.22299	0.0732102
$923$	2.37775	0.0782647
$924$	−8.78719	−0.289077
$925$	22.7674	0.748588
$926$	−14.0372	−0.461291
$927$	−5.71031	−0.187551
$928$	−4.00309	−0.131408
$929$	16.2331	0.532590	0.266295	−	0.963892i	$-0.414200\pi$
$929$	16.2331	0.532590	0.266295	+	0.963892i	$0.414200\pi$
$930$	−6.65556	−0.218245
$931$	−4.64731	−0.152310
$932$	16.3043	0.534064
$933$	3.97636	0.130180
$934$	7.36968	0.241143
$935$	7.45733	0.243881
$936$	0.970186	0.0317115
$937$	−47.8440	−1.56299	−0.781497	−	0.623909i	$-0.785544\pi$
$937$	−47.8440	−1.56299	−0.781497	+	0.623909i	$0.785544\pi$
$938$	−8.97331	−0.292989
$939$	−37.0952	−1.21056
$940$	−0.537159	−0.0175202
$941$	−37.5434	−1.22388	−0.611941	−	0.790904i	$-0.709611\pi$
$941$	−37.5434	−1.22388	−0.611941	+	0.790904i	$0.709611\pi$
$942$	−30.8850	−1.00629
$943$	−34.7280	−1.13090
$944$	−4.97524	−0.161930
$945$	25.4857	0.829049
$946$	4.88504	0.158826
$947$	5.96089	0.193703	0.0968515	−	0.995299i	$-0.469123\pi$
$947$	5.96089	0.193703	0.0968515	+	0.995299i	$0.469123\pi$
$948$	20.6945	0.672125
$949$	4.05377	0.131591
$950$	3.22993	0.104793
$951$	−34.9254	−1.13253
$952$	−11.2543	−0.364754
$953$	−21.8039	−0.706298	−0.353149	−	0.935567i	$-0.614889\pi$
$953$	−21.8039	−0.706298	−0.353149	+	0.935567i	$0.614889\pi$
$954$	2.44938	0.0793015
$955$	−19.5122	−0.631400
$956$	−5.20338	−0.168289
$957$	−10.3070	−0.333178
$958$	−10.6119	−0.342856
$959$	30.0819	0.971394
$960$	2.01534	0.0650449
$961$	−20.0938	−0.648188
$962$	9.69491	0.312577
$963$	−0.221614	−0.00714141
$964$	25.2116	0.812011
$965$	11.1695	0.359558
$966$	−46.9123	−1.50938
$967$	52.0431	1.67359	0.836796	−	0.547514i	$-0.184426\pi$
$967$	52.0431	1.67359	0.836796	+	0.547514i	$0.184426\pi$
$968$	−8.11088	−0.260693
$969$	4.99528	0.160471
$970$	−25.3680	−0.814516
$971$	−41.5607	−1.33375	−0.666873	−	0.745172i	$-0.732367\pi$
$971$	−41.5607	−1.33375	−0.666873	+	0.745172i	$0.732367\pi$
$972$	−7.16490	−0.229814
$973$	46.1020	1.47796
$974$	−30.9772	−0.992575
$975$	−6.72932	−0.215511
$976$	5.81073	0.185997
$977$	−44.8146	−1.43375	−0.716873	−	0.697204i	$-0.754427\pi$
$977$	−44.8146	−1.43375	−0.716873	+	0.697204i	$0.754427\pi$
$978$	−26.8258	−0.857793
$979$	−1.58091	−0.0505260
$980$	−6.18296	−0.197508
$981$	−3.28315	−0.104823
$982$	−11.8094	−0.376853
$983$	59.9488	1.91207	0.956034	−	0.293254i	$-0.0947382\pi$
$983$	59.9488	1.91207	0.956034	+	0.293254i	$0.0947382\pi$
$984$	−5.79716	−0.184807
$985$	−28.5237	−0.908842
$986$	−13.2008	−0.420400
$987$	2.08725	0.0664380
$988$	1.37538	0.0437568
$989$	26.0798	0.829290
$990$	−1.59518	−0.0506981
$991$	45.1889	1.43547	0.717737	−	0.696315i	$-0.245178\pi$
$991$	45.1889	1.43547	0.717737	+	0.696315i	$0.245178\pi$
$992$	−3.30245	−0.104853
$993$	−47.1389	−1.49591
$994$	5.90005	0.187138
$995$	−5.11604	−0.162189
$996$	20.9912	0.665131
$997$	−37.9300	−1.20126	−0.600628	−	0.799529i	$-0.705083\pi$
$997$	−37.9300	−1.20126	−0.600628	+	0.799529i	$0.705083\pi$
$998$	−4.86110	−0.153876
$999$	−39.5648	−1.25177

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.j.1.12	✓	47

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.j.1.12	✓	47	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.51480 q^{3} +1.00000 q^{4} -1.33044 q^{5} -1.51480 q^{6} -3.41282 q^{7} +1.00000 q^{8} -0.705394 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.51480 q^{3} +1.00000 q^{4} -1.33044 q^{5} -1.51480 q^{6} -3.41282 q^{7} +1.00000 q^{8} -0.705394 q^{9} -1.33044 q^{10} -1.69974 q^{11} -1.51480 q^{12} -1.37538 q^{13} -3.41282 q^{14} +2.01534 q^{15} +1.00000 q^{16} +3.29766 q^{17} -0.705394 q^{18} -1.00000 q^{19} -1.33044 q^{20} +5.16972 q^{21} -1.69974 q^{22} -9.07443 q^{23} -1.51480 q^{24} -3.22993 q^{25} -1.37538 q^{26} +5.61291 q^{27} -3.41282 q^{28} -4.00309 q^{29} +2.01534 q^{30} -3.30245 q^{31} +1.00000 q^{32} +2.57476 q^{33} +3.29766 q^{34} +4.54054 q^{35} -0.705394 q^{36} -7.04888 q^{37} -1.00000 q^{38} +2.08342 q^{39} -1.33044 q^{40} +3.82702 q^{41} +5.16972 q^{42} -2.87399 q^{43} -1.69974 q^{44} +0.938483 q^{45} -9.07443 q^{46} +0.403746 q^{47} -1.51480 q^{48} +4.64731 q^{49} -3.22993 q^{50} -4.99528 q^{51} -1.37538 q^{52} -3.47236 q^{53} +5.61291 q^{54} +2.26140 q^{55} -3.41282 q^{56} +1.51480 q^{57} -4.00309 q^{58} -4.97524 q^{59} +2.01534 q^{60} +5.81073 q^{61} -3.30245 q^{62} +2.40738 q^{63} +1.00000 q^{64} +1.82986 q^{65} +2.57476 q^{66} +2.62930 q^{67} +3.29766 q^{68} +13.7459 q^{69} +4.54054 q^{70} -1.72879 q^{71} -0.705394 q^{72} -2.94738 q^{73} -7.04888 q^{74} +4.89269 q^{75} -1.00000 q^{76} +5.80091 q^{77} +2.08342 q^{78} -13.6615 q^{79} -1.33044 q^{80} -6.38624 q^{81} +3.82702 q^{82} -13.8574 q^{83} +5.16972 q^{84} -4.38733 q^{85} -2.87399 q^{86} +6.06387 q^{87} -1.69974 q^{88} +0.930086 q^{89} +0.938483 q^{90} +4.69393 q^{91} -9.07443 q^{92} +5.00253 q^{93} +0.403746 q^{94} +1.33044 q^{95} -1.51480 q^{96} +19.0674 q^{97} +4.64731 q^{98} +1.19899 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9}+O(q^{10}) \) 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9} + 15 q^{10} + 17 q^{11} + 10 q^{12} + 27 q^{13} + 10 q^{15} + 47 q^{16} + 16 q^{17} + 69 q^{18} - 47 q^{19} + 15 q^{20} + 26 q^{21} + 17 q^{22} + 24 q^{23} + 10 q^{24} + 86 q^{25} + 27 q^{26} + 43 q^{27} + 58 q^{29} + 10 q^{30} + 21 q^{31} + 47 q^{32} + 18 q^{33} + 16 q^{34} + 24 q^{35} + 69 q^{36} + 78 q^{37} - 47 q^{38} - 4 q^{39} + 15 q^{40} + 53 q^{41} + 26 q^{42} + 47 q^{43} + 17 q^{44} + 23 q^{45} + 24 q^{46} + 16 q^{47} + 10 q^{48} + 93 q^{49} + 86 q^{50} + 28 q^{51} + 27 q^{52} + 43 q^{53} + 43 q^{54} + 23 q^{55} - 10 q^{57} + 58 q^{58} + 3 q^{59} + 10 q^{60} + 12 q^{61} + 21 q^{62} - 5 q^{63} + 47 q^{64} + 62 q^{65} + 18 q^{66} + 68 q^{67} + 16 q^{68} + 12 q^{69} + 24 q^{70} - 13 q^{71} + 69 q^{72} + 35 q^{73} + 78 q^{74} + 22 q^{75} - 47 q^{76} + 26 q^{77} - 4 q^{78} + 21 q^{79} + 15 q^{80} + 123 q^{81} + 53 q^{82} + 23 q^{83} + 26 q^{84} + 38 q^{85} + 47 q^{86} + 39 q^{87} + 17 q^{88} + 24 q^{89} + 23 q^{90} + 49 q^{91} + 24 q^{92} + 91 q^{93} + 16 q^{94} - 15 q^{95} + 10 q^{96} + 88 q^{97} + 93 q^{98} + 26 q^{99}+O(q^{100}) \) 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9 + 15 * q^10 + 17 * q^11 + 10 * q^12 + 27 * q^13 + 10 * q^15 + 47 * q^16 + 16 * q^17 + 69 * q^18 - 47 * q^19 + 15 * q^20 + 26 * q^21 + 17 * q^22 + 24 * q^23 + 10 * q^24 + 86 * q^25 + 27 * q^26 + 43 * q^27 + 58 * q^29 + 10 * q^30 + 21 * q^31 + 47 * q^32 + 18 * q^33 + 16 * q^34 + 24 * q^35 + 69 * q^36 + 78 * q^37 - 47 * q^38 - 4 * q^39 + 15 * q^40 + 53 * q^41 + 26 * q^42 + 47 * q^43 + 17 * q^44 + 23 * q^45 + 24 * q^46 + 16 * q^47 + 10 * q^48 + 93 * q^49 + 86 * q^50 + 28 * q^51 + 27 * q^52 + 43 * q^53 + 43 * q^54 + 23 * q^55 - 10 * q^57 + 58 * q^58 + 3 * q^59 + 10 * q^60 + 12 * q^61 + 21 * q^62 - 5 * q^63 + 47 * q^64 + 62 * q^65 + 18 * q^66 + 68 * q^67 + 16 * q^68 + 12 * q^69 + 24 * q^70 - 13 * q^71 + 69 * q^72 + 35 * q^73 + 78 * q^74 + 22 * q^75 - 47 * q^76 + 26 * q^77 - 4 * q^78 + 21 * q^79 + 15 * q^80 + 123 * q^81 + 53 * q^82 + 23 * q^83 + 26 * q^84 + 38 * q^85 + 47 * q^86 + 39 * q^87 + 17 * q^88 + 24 * q^89 + 23 * q^90 + 49 * q^91 + 24 * q^92 + 91 * q^93 + 16 * q^94 - 15 * q^95 + 10 * q^96 + 88 * q^97 + 93 * q^98 + 26 * q^99

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