LMFDB - Embedded newform 230.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(1,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, 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("230.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.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:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{21}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 5 $ x^2 - x - 5
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.79129$ of defining polynomial
Character	$\chi$	$=$	230.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.79129 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.79129 q^{6} -1.79129 q^{7} -1.00000 q^{8} +4.79129 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.79129 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.79129 q^{6} -1.79129 q^{7} -1.00000 q^{8} +4.79129 q^{9} +1.00000 q^{10} -0.791288 q^{11} -2.79129 q^{12} +5.79129 q^{13} +1.79129 q^{14} +2.79129 q^{15} +1.00000 q^{16} +0.791288 q^{17} -4.79129 q^{18} +5.79129 q^{19} -1.00000 q^{20} +5.00000 q^{21} +0.791288 q^{22} +1.00000 q^{23} +2.79129 q^{24} +1.00000 q^{25} -5.79129 q^{26} -5.00000 q^{27} -1.79129 q^{28} +7.58258 q^{29} -2.79129 q^{30} -3.37386 q^{31} -1.00000 q^{32} +2.20871 q^{33} -0.791288 q^{34} +1.79129 q^{35} +4.79129 q^{36} -4.00000 q^{37} -5.79129 q^{38} -16.1652 q^{39} +1.00000 q^{40} -6.79129 q^{41} -5.00000 q^{42} +11.1652 q^{43} -0.791288 q^{44} -4.79129 q^{45} -1.00000 q^{46} -4.41742 q^{47} -2.79129 q^{48} -3.79129 q^{49} -1.00000 q^{50} -2.20871 q^{51} +5.79129 q^{52} +6.00000 q^{53} +5.00000 q^{54} +0.791288 q^{55} +1.79129 q^{56} -16.1652 q^{57} -7.58258 q^{58} -13.5826 q^{59} +2.79129 q^{60} +10.3739 q^{61} +3.37386 q^{62} -8.58258 q^{63} +1.00000 q^{64} -5.79129 q^{65} -2.20871 q^{66} +11.1652 q^{67} +0.791288 q^{68} -2.79129 q^{69} -1.79129 q^{70} +8.37386 q^{71} -4.79129 q^{72} +12.7477 q^{73} +4.00000 q^{74} -2.79129 q^{75} +5.79129 q^{76} +1.41742 q^{77} +16.1652 q^{78} +8.00000 q^{79} -1.00000 q^{80} -0.417424 q^{81} +6.79129 q^{82} -6.00000 q^{83} +5.00000 q^{84} -0.791288 q^{85} -11.1652 q^{86} -21.1652 q^{87} +0.791288 q^{88} +15.1652 q^{89} +4.79129 q^{90} -10.3739 q^{91} +1.00000 q^{92} +9.41742 q^{93} +4.41742 q^{94} -5.79129 q^{95} +2.79129 q^{96} -7.95644 q^{97} +3.79129 q^{98} -3.79129 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - q^{3} + 2 q^{4} - 2 q^{5} + q^{6} + q^{7} - 2 q^{8} + 5 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - q^3 + 2 * q^4 - 2 * q^5 + q^6 + q^7 - 2 * q^8 + 5 * q^9	\( 2 q - 2 q^{2} - q^{3} + 2 q^{4} - 2 q^{5} + q^{6} + q^{7} - 2 q^{8} + 5 q^{9} + 2 q^{10} + 3 q^{11} - q^{12} + 7 q^{13} - q^{14} + q^{15} + 2 q^{16} - 3 q^{17} - 5 q^{18} + 7 q^{19} - 2 q^{20} + 10 q^{21} - 3 q^{22} + 2 q^{23} + q^{24} + 2 q^{25} - 7 q^{26} - 10 q^{27} + q^{28} + 6 q^{29} - q^{30} + 7 q^{31} - 2 q^{32} + 9 q^{33} + 3 q^{34} - q^{35} + 5 q^{36} - 8 q^{37} - 7 q^{38} - 14 q^{39} + 2 q^{40} - 9 q^{41} - 10 q^{42} + 4 q^{43} + 3 q^{44} - 5 q^{45} - 2 q^{46} - 18 q^{47} - q^{48} - 3 q^{49} - 2 q^{50} - 9 q^{51} + 7 q^{52} + 12 q^{53} + 10 q^{54} - 3 q^{55} - q^{56} - 14 q^{57} - 6 q^{58} - 18 q^{59} + q^{60} + 7 q^{61} - 7 q^{62} - 8 q^{63} + 2 q^{64} - 7 q^{65} - 9 q^{66} + 4 q^{67} - 3 q^{68} - q^{69} + q^{70} + 3 q^{71} - 5 q^{72} - 2 q^{73} + 8 q^{74} - q^{75} + 7 q^{76} + 12 q^{77} + 14 q^{78} + 16 q^{79} - 2 q^{80} - 10 q^{81} + 9 q^{82} - 12 q^{83} + 10 q^{84} + 3 q^{85} - 4 q^{86} - 24 q^{87} - 3 q^{88} + 12 q^{89} + 5 q^{90} - 7 q^{91} + 2 q^{92} + 28 q^{93} + 18 q^{94} - 7 q^{95} + q^{96} + 7 q^{97} + 3 q^{98} - 3 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - q^3 + 2 * q^4 - 2 * q^5 + q^6 + q^7 - 2 * q^8 + 5 * q^9 + 2 * q^10 + 3 * q^11 - q^12 + 7 * q^13 - q^14 + q^15 + 2 * q^16 - 3 * q^17 - 5 * q^18 + 7 * q^19 - 2 * q^20 + 10 * q^21 - 3 * q^22 + 2 * q^23 + q^24 + 2 * q^25 - 7 * q^26 - 10 * q^27 + q^28 + 6 * q^29 - q^30 + 7 * q^31 - 2 * q^32 + 9 * q^33 + 3 * q^34 - q^35 + 5 * q^36 - 8 * q^37 - 7 * q^38 - 14 * q^39 + 2 * q^40 - 9 * q^41 - 10 * q^42 + 4 * q^43 + 3 * q^44 - 5 * q^45 - 2 * q^46 - 18 * q^47 - q^48 - 3 * q^49 - 2 * q^50 - 9 * q^51 + 7 * q^52 + 12 * q^53 + 10 * q^54 - 3 * q^55 - q^56 - 14 * q^57 - 6 * q^58 - 18 * q^59 + q^60 + 7 * q^61 - 7 * q^62 - 8 * q^63 + 2 * q^64 - 7 * q^65 - 9 * q^66 + 4 * q^67 - 3 * q^68 - q^69 + q^70 + 3 * q^71 - 5 * q^72 - 2 * q^73 + 8 * q^74 - q^75 + 7 * q^76 + 12 * q^77 + 14 * q^78 + 16 * q^79 - 2 * q^80 - 10 * q^81 + 9 * q^82 - 12 * q^83 + 10 * q^84 + 3 * q^85 - 4 * q^86 - 24 * q^87 - 3 * q^88 + 12 * q^89 + 5 * q^90 - 7 * q^91 + 2 * q^92 + 28 * q^93 + 18 * q^94 - 7 * q^95 + q^96 + 7 * q^97 + 3 * q^98 - 3 * 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
$3$	−2.79129	−1.61155	−0.805775	−	0.592221i	$-0.798251\pi$
$3$	−2.79129	−1.61155	−0.805775	+	0.592221i	$0.798251\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.79129	1.13954
$7$	−1.79129	−0.677043	−0.338522	−	0.940959i	$-0.609927\pi$
$7$	−1.79129	−0.677043	−0.338522	+	0.940959i	$0.609927\pi$
$8$	−1.00000	−0.353553
$9$	4.79129	1.59710
$10$	1.00000	0.316228
$11$	−0.791288	−0.238582	−0.119291	−	0.992859i	$-0.538062\pi$
$11$	−0.791288	−0.238582	−0.119291	+	0.992859i	$0.538062\pi$
$12$	−2.79129	−0.805775
$13$	5.79129	1.60621	0.803107	−	0.595835i	$-0.203179\pi$
$13$	5.79129	1.60621	0.803107	+	0.595835i	$0.203179\pi$
$14$	1.79129	0.478742
$15$	2.79129	0.720707
$16$	1.00000	0.250000
$17$	0.791288	0.191915	0.0959577	−	0.995385i	$-0.469409\pi$
$17$	0.791288	0.191915	0.0959577	+	0.995385i	$0.469409\pi$
$18$	−4.79129	−1.12932
$19$	5.79129	1.32861	0.664306	−	0.747460i	$-0.268727\pi$
$19$	5.79129	1.32861	0.664306	+	0.747460i	$0.268727\pi$
$20$	−1.00000	−0.223607
$21$	5.00000	1.09109
$22$	0.791288	0.168703
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	2.79129	0.569769
$25$	1.00000	0.200000
$26$	−5.79129	−1.13576
$27$	−5.00000	−0.962250
$28$	−1.79129	−0.338522
$29$	7.58258	1.40805	0.704024	−	0.710176i	$-0.251385\pi$
$29$	7.58258	1.40805	0.704024	+	0.710176i	$0.251385\pi$
$30$	−2.79129	−0.509617
$31$	−3.37386	−0.605964	−0.302982	−	0.952996i	$-0.597982\pi$
$31$	−3.37386	−0.605964	−0.302982	+	0.952996i	$0.597982\pi$
$32$	−1.00000	−0.176777
$33$	2.20871	0.384487
$34$	−0.791288	−0.135705
$35$	1.79129	0.302783
$36$	4.79129	0.798548
$37$	−4.00000	−0.657596	−0.328798	−	0.944400i	$-0.606644\pi$
$37$	−4.00000	−0.657596	−0.328798	+	0.944400i	$0.606644\pi$
$38$	−5.79129	−0.939471
$39$	−16.1652	−2.58850
$40$	1.00000	0.158114
$41$	−6.79129	−1.06062	−0.530310	−	0.847804i	$-0.677925\pi$
$41$	−6.79129	−1.06062	−0.530310	+	0.847804i	$0.677925\pi$
$42$	−5.00000	−0.771517
$43$	11.1652	1.70267	0.851335	−	0.524623i	$-0.175794\pi$
$43$	11.1652	1.70267	0.851335	+	0.524623i	$0.175794\pi$
$44$	−0.791288	−0.119291
$45$	−4.79129	−0.714243
$46$	−1.00000	−0.147442
$47$	−4.41742	−0.644348	−0.322174	−	0.946681i	$-0.604414\pi$
$47$	−4.41742	−0.644348	−0.322174	+	0.946681i	$0.604414\pi$
$48$	−2.79129	−0.402888
$49$	−3.79129	−0.541613
$50$	−1.00000	−0.141421
$51$	−2.20871	−0.309282
$52$	5.79129	0.803107
$53$	6.00000	0.824163	0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000	0.824163	0.412082	+	0.911147i	$0.364802\pi$
$54$	5.00000	0.680414
$55$	0.791288	0.106697
$56$	1.79129	0.239371
$57$	−16.1652	−2.14113
$58$	−7.58258	−0.995641
$59$	−13.5826	−1.76830	−0.884150	−	0.467202i	$-0.845262\pi$
$59$	−13.5826	−1.76830	−0.884150	+	0.467202i	$0.845262\pi$
$60$	2.79129	0.360354
$61$	10.3739	1.32824	0.664119	−	0.747627i	$-0.268807\pi$
$61$	10.3739	1.32824	0.664119	+	0.747627i	$0.268807\pi$
$62$	3.37386	0.428481
$63$	−8.58258	−1.08130
$64$	1.00000	0.125000
$65$	−5.79129	−0.718321
$66$	−2.20871	−0.271874
$67$	11.1652	1.36404	0.682020	−	0.731333i	$-0.261102\pi$
$67$	11.1652	1.36404	0.682020	+	0.731333i	$0.261102\pi$
$68$	0.791288	0.0959577
$69$	−2.79129	−0.336032
$70$	−1.79129	−0.214100
$71$	8.37386	0.993795	0.496897	−	0.867809i	$-0.334473\pi$
$71$	8.37386	0.993795	0.496897	+	0.867809i	$0.334473\pi$
$72$	−4.79129	−0.564659
$73$	12.7477	1.49201	0.746004	−	0.665941i	$-0.231970\pi$
$73$	12.7477	1.49201	0.746004	+	0.665941i	$0.231970\pi$
$74$	4.00000	0.464991
$75$	−2.79129	−0.322310
$76$	5.79129	0.664306
$77$	1.41742	0.161530
$78$	16.1652	1.83034
$79$	8.00000	0.900070	0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000	0.900070	0.450035	+	0.893011i	$0.351411\pi$
$80$	−1.00000	−0.111803
$81$	−0.417424	−0.0463805
$82$	6.79129	0.749972
$83$	−6.00000	−0.658586	−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000	−0.658586	−0.329293	+	0.944228i	$0.606810\pi$
$84$	5.00000	0.545545
$85$	−0.791288	−0.0858272
$86$	−11.1652	−1.20397
$87$	−21.1652	−2.26914
$88$	0.791288	0.0843516
$89$	15.1652	1.60750	0.803751	−	0.594965i	$-0.202834\pi$
$89$	15.1652	1.60750	0.803751	+	0.594965i	$0.202834\pi$
$90$	4.79129	0.505046
$91$	−10.3739	−1.08748
$92$	1.00000	0.104257
$93$	9.41742	0.976541
$94$	4.41742	0.455623
$95$	−5.79129	−0.594174
$96$	2.79129	0.284885
$97$	−7.95644	−0.807854	−0.403927	−	0.914791i	$-0.632355\pi$
$97$	−7.95644	−0.807854	−0.403927	+	0.914791i	$0.632355\pi$
$98$	3.79129	0.382978
$99$	−3.79129	−0.381039
$100$	1.00000	0.100000
$101$	4.41742	0.439550	0.219775	−	0.975551i	$-0.429468\pi$
$101$	4.41742	0.439550	0.219775	+	0.975551i	$0.429468\pi$
$102$	2.20871	0.218695
$103$	−6.37386	−0.628035	−0.314018	−	0.949417i	$-0.601675\pi$
$103$	−6.37386	−0.628035	−0.314018	+	0.949417i	$0.601675\pi$
$104$	−5.79129	−0.567882
$105$	−5.00000	−0.487950
$106$	−6.00000	−0.582772
$107$	4.41742	0.427049	0.213524	−	0.976938i	$-0.431506\pi$
$107$	4.41742	0.427049	0.213524	+	0.976938i	$0.431506\pi$
$108$	−5.00000	−0.481125
$109$	−3.37386	−0.323158	−0.161579	−	0.986860i	$-0.551659\pi$
$109$	−3.37386	−0.323158	−0.161579	+	0.986860i	$0.551659\pi$
$110$	−0.791288	−0.0754463
$111$	11.1652	1.05975
$112$	−1.79129	−0.169261
$113$	6.00000	0.564433	0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000	0.564433	0.282216	+	0.959351i	$0.408930\pi$
$114$	16.1652	1.51401
$115$	−1.00000	−0.0932505
$116$	7.58258	0.704024
$117$	27.7477	2.56528
$118$	13.5826	1.25038
$119$	−1.41742	−0.129935
$120$	−2.79129	−0.254809
$121$	−10.3739	−0.943079
$122$	−10.3739	−0.939205
$123$	18.9564	1.70924
$124$	−3.37386	−0.302982
$125$	−1.00000	−0.0894427
$126$	8.58258	0.764597
$127$	12.7477	1.13118	0.565589	−	0.824687i	$-0.308649\pi$
$127$	12.7477	1.13118	0.565589	+	0.824687i	$0.308649\pi$
$128$	−1.00000	−0.0883883
$129$	−31.1652	−2.74394
$130$	5.79129	0.507930
$131$	−9.16515	−0.800763	−0.400381	−	0.916349i	$-0.631122\pi$
$131$	−9.16515	−0.800763	−0.400381	+	0.916349i	$0.631122\pi$
$132$	2.20871	0.192244
$133$	−10.3739	−0.899528
$134$	−11.1652	−0.964522
$135$	5.00000	0.430331
$136$	−0.791288	−0.0678524
$137$	3.79129	0.323912	0.161956	−	0.986798i	$-0.448220\pi$
$137$	3.79129	0.323912	0.161956	+	0.986798i	$0.448220\pi$
$138$	2.79129	0.237610
$139$	12.7477	1.08125	0.540624	−	0.841264i	$-0.318188\pi$
$139$	12.7477	1.08125	0.540624	+	0.841264i	$0.318188\pi$
$140$	1.79129	0.151391
$141$	12.3303	1.03840
$142$	−8.37386	−0.702719
$143$	−4.58258	−0.383214
$144$	4.79129	0.399274
$145$	−7.58258	−0.629699
$146$	−12.7477	−1.05501
$147$	10.5826	0.872836
$148$	−4.00000	−0.328798
$149$	8.20871	0.672484	0.336242	−	0.941776i	$-0.390844\pi$
$149$	8.20871	0.672484	0.336242	+	0.941776i	$0.390844\pi$
$150$	2.79129	0.227908
$151$	−10.7913	−0.878183	−0.439091	−	0.898442i	$-0.644700\pi$
$151$	−10.7913	−0.878183	−0.439091	+	0.898442i	$0.644700\pi$
$152$	−5.79129	−0.469735
$153$	3.79129	0.306507
$154$	−1.41742	−0.114219
$155$	3.37386	0.270995
$156$	−16.1652	−1.29425
$157$	−14.7477	−1.17700	−0.588498	−	0.808498i	$-0.700281\pi$
$157$	−14.7477	−1.17700	−0.588498	+	0.808498i	$0.700281\pi$
$158$	−8.00000	−0.636446
$159$	−16.7477	−1.32818
$160$	1.00000	0.0790569
$161$	−1.79129	−0.141173
$162$	0.417424	0.0327960
$163$	8.62614	0.675651	0.337826	−	0.941209i	$-0.390309\pi$
$163$	8.62614	0.675651	0.337826	+	0.941209i	$0.390309\pi$
$164$	−6.79129	−0.530310
$165$	−2.20871	−0.171948
$166$	6.00000	0.465690
$167$	18.3303	1.41844	0.709221	−	0.704987i	$-0.249047\pi$
$167$	18.3303	1.41844	0.709221	+	0.704987i	$0.249047\pi$
$168$	−5.00000	−0.385758
$169$	20.5390	1.57992
$170$	0.791288	0.0606890
$171$	27.7477	2.12192
$172$	11.1652	0.851335
$173$	−18.7913	−1.42868	−0.714338	−	0.699801i	$-0.753272\pi$
$173$	−18.7913	−1.42868	−0.714338	+	0.699801i	$0.753272\pi$
$174$	21.1652	1.60453
$175$	−1.79129	−0.135409
$176$	−0.791288	−0.0596456
$177$	37.9129	2.84971
$178$	−15.1652	−1.13668
$179$	10.7477	0.803323	0.401661	−	0.915788i	$-0.368433\pi$
$179$	10.7477	0.803323	0.401661	+	0.915788i	$0.368433\pi$
$180$	−4.79129	−0.357122
$181$	−18.5390	−1.37799	−0.688997	−	0.724764i	$-0.741949\pi$
$181$	−18.5390	−1.37799	−0.688997	+	0.724764i	$0.741949\pi$
$182$	10.3739	0.768962
$183$	−28.9564	−2.14052
$184$	−1.00000	−0.0737210
$185$	4.00000	0.294086
$186$	−9.41742	−0.690519
$187$	−0.626136	−0.0457876
$188$	−4.41742	−0.322174
$189$	8.95644	0.651485
$190$	5.79129	0.420144
$191$	25.5826	1.85109	0.925545	−	0.378637i	$-0.123607\pi$
$191$	25.5826	1.85109	0.925545	+	0.378637i	$0.123607\pi$
$192$	−2.79129	−0.201444
$193$	−20.7477	−1.49345	−0.746727	−	0.665131i	$-0.768376\pi$
$193$	−20.7477	−1.49345	−0.746727	+	0.665131i	$0.768376\pi$
$194$	7.95644	0.571239
$195$	16.1652	1.15761
$196$	−3.79129	−0.270806
$197$	−11.5390	−0.822121	−0.411060	−	0.911608i	$-0.634841\pi$
$197$	−11.5390	−0.822121	−0.411060	+	0.911608i	$0.634841\pi$
$198$	3.79129	0.269435
$199$	−16.3303	−1.15762	−0.578812	−	0.815461i	$-0.696484\pi$
$199$	−16.3303	−1.15762	−0.578812	+	0.815461i	$0.696484\pi$
$200$	−1.00000	−0.0707107
$201$	−31.1652	−2.19822
$202$	−4.41742	−0.310809
$203$	−13.5826	−0.953310
$204$	−2.20871	−0.154641
$205$	6.79129	0.474324
$206$	6.37386	0.444088
$207$	4.79129	0.333018
$208$	5.79129	0.401554
$209$	−4.58258	−0.316983
$210$	5.00000	0.345033
$211$	−10.0000	−0.688428	−0.344214	−	0.938891i	$-0.611855\pi$
$211$	−10.0000	−0.688428	−0.344214	+	0.938891i	$0.611855\pi$
$212$	6.00000	0.412082
$213$	−23.3739	−1.60155
$214$	−4.41742	−0.301969
$215$	−11.1652	−0.761457
$216$	5.00000	0.340207
$217$	6.04356	0.410264
$218$	3.37386	0.228507
$219$	−35.5826	−2.40445
$220$	0.791288	0.0533486
$221$	4.58258	0.308257
$222$	−11.1652	−0.749356
$223$	−7.16515	−0.479814	−0.239907	−	0.970796i	$-0.577117\pi$
$223$	−7.16515	−0.479814	−0.239907	+	0.970796i	$0.577117\pi$
$224$	1.79129	0.119685
$225$	4.79129	0.319419
$226$	−6.00000	−0.399114
$227$	−22.7477	−1.50982	−0.754910	−	0.655829i	$-0.772319\pi$
$227$	−22.7477	−1.50982	−0.754910	+	0.655829i	$0.772319\pi$
$228$	−16.1652	−1.07056
$229$	20.3303	1.34346	0.671732	−	0.740794i	$-0.265551\pi$
$229$	20.3303	1.34346	0.671732	+	0.740794i	$0.265551\pi$
$230$	1.00000	0.0659380
$231$	−3.95644	−0.260315
$232$	−7.58258	−0.497820
$233$	−1.58258	−0.103678	−0.0518390	−	0.998655i	$-0.516508\pi$
$233$	−1.58258	−0.103678	−0.0518390	+	0.998655i	$0.516508\pi$
$234$	−27.7477	−1.81393
$235$	4.41742	0.288161
$236$	−13.5826	−0.884150
$237$	−22.3303	−1.45051
$238$	1.41742	0.0918780
$239$	−15.1652	−0.980952	−0.490476	−	0.871455i	$-0.663177\pi$
$239$	−15.1652	−0.980952	−0.490476	+	0.871455i	$0.663177\pi$
$240$	2.79129	0.180177
$241$	−28.0000	−1.80364	−0.901819	−	0.432113i	$-0.857768\pi$
$241$	−28.0000	−1.80364	−0.901819	+	0.432113i	$0.857768\pi$
$242$	10.3739	0.666857
$243$	16.1652	1.03699
$244$	10.3739	0.664119
$245$	3.79129	0.242216
$246$	−18.9564	−1.20862
$247$	33.5390	2.13404
$248$	3.37386	0.214241
$249$	16.7477	1.06134
$250$	1.00000	0.0632456
$251$	26.2087	1.65428	0.827140	−	0.561996i	$-0.189967\pi$
$251$	26.2087	1.65428	0.827140	+	0.561996i	$0.189967\pi$
$252$	−8.58258	−0.540651
$253$	−0.791288	−0.0497478
$254$	−12.7477	−0.799864
$255$	2.20871	0.138315
$256$	1.00000	0.0625000
$257$	−4.74773	−0.296155	−0.148078	−	0.988976i	$-0.547309\pi$
$257$	−4.74773	−0.296155	−0.148078	+	0.988976i	$0.547309\pi$
$258$	31.1652	1.94026
$259$	7.16515	0.445221
$260$	−5.79129	−0.359160
$261$	36.3303	2.24879
$262$	9.16515	0.566225
$263$	11.2087	0.691159	0.345579	−	0.938390i	$-0.387682\pi$
$263$	11.2087	0.691159	0.345579	+	0.938390i	$0.387682\pi$
$264$	−2.20871	−0.135937
$265$	−6.00000	−0.368577
$266$	10.3739	0.636062
$267$	−42.3303	−2.59057
$268$	11.1652	0.682020
$269$	−10.7477	−0.655300	−0.327650	−	0.944799i	$-0.606257\pi$
$269$	−10.7477	−0.655300	−0.327650	+	0.944799i	$0.606257\pi$
$270$	−5.00000	−0.304290
$271$	18.1216	1.10081	0.550404	−	0.834898i	$-0.314474\pi$
$271$	18.1216	1.10081	0.550404	+	0.834898i	$0.314474\pi$
$272$	0.791288	0.0479789
$273$	28.9564	1.75252
$274$	−3.79129	−0.229040
$275$	−0.791288	−0.0477165
$276$	−2.79129	−0.168016
$277$	17.1652	1.03135	0.515677	−	0.856783i	$-0.327540\pi$
$277$	17.1652	1.03135	0.515677	+	0.856783i	$0.327540\pi$
$278$	−12.7477	−0.764558
$279$	−16.1652	−0.967782
$280$	−1.79129	−0.107050
$281$	10.7477	0.641156	0.320578	−	0.947222i	$-0.396123\pi$
$281$	10.7477	0.641156	0.320578	+	0.947222i	$0.396123\pi$
$282$	−12.3303	−0.734259
$283$	8.33030	0.495185	0.247593	−	0.968864i	$-0.420361\pi$
$283$	8.33030	0.495185	0.247593	+	0.968864i	$0.420361\pi$
$284$	8.37386	0.496897
$285$	16.1652	0.957541
$286$	4.58258	0.270973
$287$	12.1652	0.718086
$288$	−4.79129	−0.282329
$289$	−16.3739	−0.963168
$290$	7.58258	0.445264
$291$	22.2087	1.30190
$292$	12.7477	0.746004
$293$	27.4955	1.60630	0.803151	−	0.595776i	$-0.203155\pi$
$293$	27.4955	1.60630	0.803151	+	0.595776i	$0.203155\pi$
$294$	−10.5826	−0.617188
$295$	13.5826	0.790808
$296$	4.00000	0.232495
$297$	3.95644	0.229576
$298$	−8.20871	−0.475518
$299$	5.79129	0.334919
$300$	−2.79129	−0.161155
$301$	−20.0000	−1.15278
$302$	10.7913	0.620969
$303$	−12.3303	−0.708357
$304$	5.79129	0.332153
$305$	−10.3739	−0.594006
$306$	−3.79129	−0.216734
$307$	−15.5390	−0.886858	−0.443429	−	0.896309i	$-0.646238\pi$
$307$	−15.5390	−0.886858	−0.443429	+	0.896309i	$0.646238\pi$
$308$	1.41742	0.0807652
$309$	17.7913	1.01211
$310$	−3.37386	−0.191623
$311$	12.0000	0.680458	0.340229	−	0.940343i	$-0.389495\pi$
$311$	12.0000	0.680458	0.340229	+	0.940343i	$0.389495\pi$
$312$	16.1652	0.915171
$313$	−4.62614	−0.261485	−0.130742	−	0.991416i	$-0.541736\pi$
$313$	−4.62614	−0.261485	−0.130742	+	0.991416i	$0.541736\pi$
$314$	14.7477	0.832262
$315$	8.58258	0.483573
$316$	8.00000	0.450035
$317$	9.79129	0.549934	0.274967	−	0.961454i	$-0.411333\pi$
$317$	9.79129	0.549934	0.274967	+	0.961454i	$0.411333\pi$
$318$	16.7477	0.939166
$319$	−6.00000	−0.335936
$320$	−1.00000	−0.0559017
$321$	−12.3303	−0.688210
$322$	1.79129	0.0998246
$323$	4.58258	0.254981
$324$	−0.417424	−0.0231902
$325$	5.79129	0.321243
$326$	−8.62614	−0.477758
$327$	9.41742	0.520785
$328$	6.79129	0.374986
$329$	7.91288	0.436251
$330$	2.20871	0.121586
$331$	−20.7477	−1.14040	−0.570199	−	0.821507i	$-0.693134\pi$
$331$	−20.7477	−1.14040	−0.570199	+	0.821507i	$0.693134\pi$
$332$	−6.00000	−0.329293
$333$	−19.1652	−1.05024
$334$	−18.3303	−1.00299
$335$	−11.1652	−0.610017
$336$	5.00000	0.272772
$337$	−12.2087	−0.665051	−0.332525	−	0.943094i	$-0.607901\pi$
$337$	−12.2087	−0.665051	−0.332525	+	0.943094i	$0.607901\pi$
$338$	−20.5390	−1.11718
$339$	−16.7477	−0.909612
$340$	−0.791288	−0.0429136
$341$	2.66970	0.144572
$342$	−27.7477	−1.50043
$343$	19.3303	1.04374
$344$	−11.1652	−0.601985
$345$	2.79129	0.150278
$346$	18.7913	1.01023
$347$	5.20871	0.279618	0.139809	−	0.990178i	$-0.455351\pi$
$347$	5.20871	0.279618	0.139809	+	0.990178i	$0.455351\pi$
$348$	−21.1652	−1.13457
$349$	26.0000	1.39175	0.695874	−	0.718164i	$-0.255017\pi$
$349$	26.0000	1.39175	0.695874	+	0.718164i	$0.255017\pi$
$350$	1.79129	0.0957484
$351$	−28.9564	−1.54558
$352$	0.791288	0.0421758
$353$	3.16515	0.168464	0.0842320	−	0.996446i	$-0.473156\pi$
$353$	3.16515	0.168464	0.0842320	+	0.996446i	$0.473156\pi$
$354$	−37.9129	−2.01505
$355$	−8.37386	−0.444439
$356$	15.1652	0.803751
$357$	3.95644	0.209397
$358$	−10.7477	−0.568035
$359$	9.16515	0.483718	0.241859	−	0.970311i	$-0.422243\pi$
$359$	9.16515	0.483718	0.241859	+	0.970311i	$0.422243\pi$
$360$	4.79129	0.252523
$361$	14.5390	0.765211
$362$	18.5390	0.974389
$363$	28.9564	1.51982
$364$	−10.3739	−0.543738
$365$	−12.7477	−0.667247
$366$	28.9564	1.51358
$367$	−19.1652	−1.00041	−0.500206	−	0.865906i	$-0.666743\pi$
$367$	−19.1652	−1.00041	−0.500206	+	0.865906i	$0.666743\pi$
$368$	1.00000	0.0521286
$369$	−32.5390	−1.69391
$370$	−4.00000	−0.207950
$371$	−10.7477	−0.557994
$372$	9.41742	0.488271
$373$	12.7477	0.660052	0.330026	−	0.943972i	$-0.392942\pi$
$373$	12.7477	0.660052	0.330026	+	0.943972i	$0.392942\pi$
$374$	0.626136	0.0323767
$375$	2.79129	0.144141
$376$	4.41742	0.227811
$377$	43.9129	2.26163
$378$	−8.95644	−0.460670
$379$	−6.37386	−0.327403	−0.163702	−	0.986510i	$-0.552343\pi$
$379$	−6.37386	−0.327403	−0.163702	+	0.986510i	$0.552343\pi$
$380$	−5.79129	−0.297087
$381$	−35.5826	−1.82295
$382$	−25.5826	−1.30892
$383$	−24.0000	−1.22634	−0.613171	−	0.789950i	$-0.710106\pi$
$383$	−24.0000	−1.22634	−0.613171	+	0.789950i	$0.710106\pi$
$384$	2.79129	0.142442
$385$	−1.41742	−0.0722386
$386$	20.7477	1.05603
$387$	53.4955	2.71933
$388$	−7.95644	−0.403927
$389$	−20.7042	−1.04974	−0.524871	−	0.851182i	$-0.675887\pi$
$389$	−20.7042	−1.04974	−0.524871	+	0.851182i	$0.675887\pi$
$390$	−16.1652	−0.818554
$391$	0.791288	0.0400171
$392$	3.79129	0.191489
$393$	25.5826	1.29047
$394$	11.5390	0.581327
$395$	−8.00000	−0.402524
$396$	−3.79129	−0.190519
$397$	−15.5390	−0.779881	−0.389940	−	0.920840i	$-0.627504\pi$
$397$	−15.5390	−0.779881	−0.389940	+	0.920840i	$0.627504\pi$
$398$	16.3303	0.818564
$399$	28.9564	1.44964
$400$	1.00000	0.0500000
$401$	−4.74773	−0.237090	−0.118545	−	0.992949i	$-0.537823\pi$
$401$	−4.74773	−0.237090	−0.118545	+	0.992949i	$0.537823\pi$
$402$	31.1652	1.55438
$403$	−19.5390	−0.973308
$404$	4.41742	0.219775
$405$	0.417424	0.0207420
$406$	13.5826	0.674092
$407$	3.16515	0.156891
$408$	2.20871	0.109348
$409$	−18.2087	−0.900363	−0.450181	−	0.892937i	$-0.648641\pi$
$409$	−18.2087	−0.900363	−0.450181	+	0.892937i	$0.648641\pi$
$410$	−6.79129	−0.335398
$411$	−10.5826	−0.522000
$412$	−6.37386	−0.314018
$413$	24.3303	1.19722
$414$	−4.79129	−0.235479
$415$	6.00000	0.294528
$416$	−5.79129	−0.283941
$417$	−35.5826	−1.74249
$418$	4.58258	0.224141
$419$	20.8348	1.01785	0.508924	−	0.860811i	$-0.330043\pi$
$419$	20.8348	1.01785	0.508924	+	0.860811i	$0.330043\pi$
$420$	−5.00000	−0.243975
$421$	18.1216	0.883192	0.441596	−	0.897214i	$-0.354412\pi$
$421$	18.1216	0.883192	0.441596	+	0.897214i	$0.354412\pi$
$422$	10.0000	0.486792
$423$	−21.1652	−1.02908
$424$	−6.00000	−0.291386
$425$	0.791288	0.0383831
$426$	23.3739	1.13247
$427$	−18.5826	−0.899274
$428$	4.41742	0.213524
$429$	12.7913	0.617569
$430$	11.1652	0.538431
$431$	25.9129	1.24818	0.624090	−	0.781353i	$-0.285470\pi$
$431$	25.9129	1.24818	0.624090	+	0.781353i	$0.285470\pi$
$432$	−5.00000	−0.240563
$433$	−30.5390	−1.46761	−0.733806	−	0.679359i	$-0.762258\pi$
$433$	−30.5390	−1.46761	−0.733806	+	0.679359i	$0.762258\pi$
$434$	−6.04356	−0.290100
$435$	21.1652	1.01479
$436$	−3.37386	−0.161579
$437$	5.79129	0.277035
$438$	35.5826	1.70020
$439$	−6.53901	−0.312090	−0.156045	−	0.987750i	$-0.549875\pi$
$439$	−6.53901	−0.312090	−0.156045	+	0.987750i	$0.549875\pi$
$440$	−0.791288	−0.0377232
$441$	−18.1652	−0.865007
$442$	−4.58258	−0.217971
$443$	−39.7913	−1.89054	−0.945271	−	0.326288i	$-0.894202\pi$
$443$	−39.7913	−1.89054	−0.945271	+	0.326288i	$0.894202\pi$
$444$	11.1652	0.529875
$445$	−15.1652	−0.718897
$446$	7.16515	0.339280
$447$	−22.9129	−1.08374
$448$	−1.79129	−0.0846304
$449$	−16.1216	−0.760825	−0.380412	−	0.924817i	$-0.624218\pi$
$449$	−16.1216	−0.760825	−0.380412	+	0.924817i	$0.624218\pi$
$450$	−4.79129	−0.225863
$451$	5.37386	0.253045
$452$	6.00000	0.282216
$453$	30.1216	1.41524
$454$	22.7477	1.06760
$455$	10.3739	0.486334
$456$	16.1652	0.757003
$457$	−10.0000	−0.467780	−0.233890	−	0.972263i	$-0.575146\pi$
$457$	−10.0000	−0.467780	−0.233890	+	0.972263i	$0.575146\pi$
$458$	−20.3303	−0.949973
$459$	−3.95644	−0.184671
$460$	−1.00000	−0.0466252
$461$	−28.7477	−1.33892	−0.669458	−	0.742850i	$-0.733473\pi$
$461$	−28.7477	−1.33892	−0.669458	+	0.742850i	$0.733473\pi$
$462$	3.95644	0.184070
$463$	−10.0000	−0.464739	−0.232370	−	0.972628i	$-0.574648\pi$
$463$	−10.0000	−0.464739	−0.232370	+	0.972628i	$0.574648\pi$
$464$	7.58258	0.352012
$465$	−9.41742	−0.436723
$466$	1.58258	0.0733114
$467$	−19.9129	−0.921458	−0.460729	−	0.887541i	$-0.652412\pi$
$467$	−19.9129	−0.921458	−0.460729	+	0.887541i	$0.652412\pi$
$468$	27.7477	1.28264
$469$	−20.0000	−0.923514
$470$	−4.41742	−0.203761
$471$	41.1652	1.89679
$472$	13.5826	0.625189
$473$	−8.83485	−0.406227
$474$	22.3303	1.02566
$475$	5.79129	0.265723
$476$	−1.41742	−0.0649675
$477$	28.7477	1.31627
$478$	15.1652	0.693638
$479$	15.4955	0.708005	0.354003	−	0.935244i	$-0.384820\pi$
$479$	15.4955	0.708005	0.354003	+	0.935244i	$0.384820\pi$
$480$	−2.79129	−0.127404
$481$	−23.1652	−1.05624
$482$	28.0000	1.27537
$483$	5.00000	0.227508
$484$	−10.3739	−0.471539
$485$	7.95644	0.361283
$486$	−16.1652	−0.733266
$487$	6.41742	0.290801	0.145401	−	0.989373i	$-0.453553\pi$
$487$	6.41742	0.290801	0.145401	+	0.989373i	$0.453553\pi$
$488$	−10.3739	−0.469603
$489$	−24.0780	−1.08885
$490$	−3.79129	−0.171273
$491$	10.7477	0.485038	0.242519	−	0.970147i	$-0.422026\pi$
$491$	10.7477	0.485038	0.242519	+	0.970147i	$0.422026\pi$
$492$	18.9564	0.854622
$493$	6.00000	0.270226
$494$	−33.5390	−1.50899
$495$	3.79129	0.170406
$496$	−3.37386	−0.151491
$497$	−15.0000	−0.672842
$498$	−16.7477	−0.750484
$499$	4.83485	0.216438	0.108219	−	0.994127i	$-0.465485\pi$
$499$	4.83485	0.216438	0.108219	+	0.994127i	$0.465485\pi$
$500$	−1.00000	−0.0447214
$501$	−51.1652	−2.28589
$502$	−26.2087	−1.16975
$503$	14.2087	0.633535	0.316768	−	0.948503i	$-0.397402\pi$
$503$	14.2087	0.633535	0.316768	+	0.948503i	$0.397402\pi$
$504$	8.58258	0.382298
$505$	−4.41742	−0.196573
$506$	0.791288	0.0351770
$507$	−57.3303	−2.54613
$508$	12.7477	0.565589
$509$	34.7477	1.54017	0.770083	−	0.637944i	$-0.220215\pi$
$509$	34.7477	1.54017	0.770083	+	0.637944i	$0.220215\pi$
$510$	−2.20871	−0.0978034
$511$	−22.8348	−1.01015
$512$	−1.00000	−0.0441942
$513$	−28.9564	−1.27846
$514$	4.74773	0.209413
$515$	6.37386	0.280866
$516$	−31.1652	−1.37197
$517$	3.49545	0.153730
$518$	−7.16515	−0.314819
$519$	52.4519	2.30238
$520$	5.79129	0.253965
$521$	18.0000	0.788594	0.394297	−	0.918983i	$-0.370988\pi$
$521$	18.0000	0.788594	0.394297	+	0.918983i	$0.370988\pi$
$522$	−36.3303	−1.59013
$523$	17.1652	0.750580	0.375290	−	0.926908i	$-0.377543\pi$
$523$	17.1652	0.750580	0.375290	+	0.926908i	$0.377543\pi$
$524$	−9.16515	−0.400381
$525$	5.00000	0.218218
$526$	−11.2087	−0.488723
$527$	−2.66970	−0.116294
$528$	2.20871	0.0961219
$529$	1.00000	0.0434783
$530$	6.00000	0.260623
$531$	−65.0780	−2.82415
$532$	−10.3739	−0.449764
$533$	−39.3303	−1.70358
$534$	42.3303	1.83181
$535$	−4.41742	−0.190982
$536$	−11.1652	−0.482261
$537$	−30.0000	−1.29460
$538$	10.7477	0.463367
$539$	3.00000	0.129219
$540$	5.00000	0.215166
$541$	1.66970	0.0717859	0.0358929	−	0.999356i	$-0.488572\pi$
$541$	1.66970	0.0717859	0.0358929	+	0.999356i	$0.488572\pi$
$542$	−18.1216	−0.778389
$543$	51.7477	2.22071
$544$	−0.791288	−0.0339262
$545$	3.37386	0.144520
$546$	−28.9564	−1.23922
$547$	−26.1216	−1.11688	−0.558439	−	0.829545i	$-0.688600\pi$
$547$	−26.1216	−1.11688	−0.558439	+	0.829545i	$0.688600\pi$
$548$	3.79129	0.161956
$549$	49.7042	2.12132
$550$	0.791288	0.0337406
$551$	43.9129	1.87075
$552$	2.79129	0.118805
$553$	−14.3303	−0.609386
$554$	−17.1652	−0.729277
$555$	−11.1652	−0.473934
$556$	12.7477	0.540624
$557$	−6.33030	−0.268224	−0.134112	−	0.990966i	$-0.542818\pi$
$557$	−6.33030	−0.268224	−0.134112	+	0.990966i	$0.542818\pi$
$558$	16.1652	0.684325
$559$	64.6606	2.73485
$560$	1.79129	0.0756957
$561$	1.74773	0.0737891
$562$	−10.7477	−0.453366
$563$	−15.1652	−0.639135	−0.319567	−	0.947564i	$-0.603538\pi$
$563$	−15.1652	−0.639135	−0.319567	+	0.947564i	$0.603538\pi$
$564$	12.3303	0.519199
$565$	−6.00000	−0.252422
$566$	−8.33030	−0.350149
$567$	0.747727	0.0314016
$568$	−8.37386	−0.351360
$569$	−39.4955	−1.65574	−0.827868	−	0.560923i	$-0.810446\pi$
$569$	−39.4955	−1.65574	−0.827868	+	0.560923i	$0.810446\pi$
$570$	−16.1652	−0.677084
$571$	−11.1216	−0.465424	−0.232712	−	0.972546i	$-0.574760\pi$
$571$	−11.1216	−0.465424	−0.232712	+	0.972546i	$0.574760\pi$
$572$	−4.58258	−0.191607
$573$	−71.4083	−2.98313
$574$	−12.1652	−0.507764
$575$	1.00000	0.0417029
$576$	4.79129	0.199637
$577$	41.1652	1.71373	0.856864	−	0.515543i	$-0.172410\pi$
$577$	41.1652	1.71373	0.856864	+	0.515543i	$0.172410\pi$
$578$	16.3739	0.681063
$579$	57.9129	2.40678
$580$	−7.58258	−0.314849
$581$	10.7477	0.445891
$582$	−22.2087	−0.920581
$583$	−4.74773	−0.196631
$584$	−12.7477	−0.527505
$585$	−27.7477	−1.14723
$586$	−27.4955	−1.13583
$587$	−30.7913	−1.27089	−0.635446	−	0.772145i	$-0.719184\pi$
$587$	−30.7913	−1.27089	−0.635446	+	0.772145i	$0.719184\pi$
$588$	10.5826	0.436418
$589$	−19.5390	−0.805091
$590$	−13.5826	−0.559186
$591$	32.2087	1.32489
$592$	−4.00000	−0.164399
$593$	−31.9129	−1.31050	−0.655252	−	0.755410i	$-0.727438\pi$
$593$	−31.9129	−1.31050	−0.655252	+	0.755410i	$0.727438\pi$
$594$	−3.95644	−0.162335
$595$	1.41742	0.0581087
$596$	8.20871	0.336242
$597$	45.5826	1.86557
$598$	−5.79129	−0.236823
$599$	1.12159	0.0458270	0.0229135	−	0.999737i	$-0.492706\pi$
$599$	1.12159	0.0458270	0.0229135	+	0.999737i	$0.492706\pi$
$600$	2.79129	0.113954
$601$	−18.2087	−0.742749	−0.371374	−	0.928483i	$-0.621113\pi$
$601$	−18.2087	−0.742749	−0.371374	+	0.928483i	$0.621113\pi$
$602$	20.0000	0.815139
$603$	53.4955	2.17850
$604$	−10.7913	−0.439091
$605$	10.3739	0.421758
$606$	12.3303	0.500884
$607$	−28.0000	−1.13648	−0.568242	−	0.822861i	$-0.692376\pi$
$607$	−28.0000	−1.13648	−0.568242	+	0.822861i	$0.692376\pi$
$608$	−5.79129	−0.234868
$609$	37.9129	1.53631
$610$	10.3739	0.420025
$611$	−25.5826	−1.03496
$612$	3.79129	0.153254
$613$	14.0000	0.565455	0.282727	−	0.959200i	$-0.408761\pi$
$613$	14.0000	0.565455	0.282727	+	0.959200i	$0.408761\pi$
$614$	15.5390	0.627104
$615$	−18.9564	−0.764397
$616$	−1.41742	−0.0571097
$617$	−23.8693	−0.960943	−0.480471	−	0.877010i	$-0.659534\pi$
$617$	−23.8693	−0.960943	−0.480471	+	0.877010i	$0.659534\pi$
$618$	−17.7913	−0.715671
$619$	−1.79129	−0.0719979	−0.0359990	−	0.999352i	$-0.511461\pi$
$619$	−1.79129	−0.0719979	−0.0359990	+	0.999352i	$0.511461\pi$
$620$	3.37386	0.135498
$621$	−5.00000	−0.200643
$622$	−12.0000	−0.481156
$623$	−27.1652	−1.08835
$624$	−16.1652	−0.647124
$625$	1.00000	0.0400000
$626$	4.62614	0.184898
$627$	12.7913	0.510835
$628$	−14.7477	−0.588498
$629$	−3.16515	−0.126203
$630$	−8.58258	−0.341938
$631$	27.9129	1.11119	0.555597	−	0.831452i	$-0.312490\pi$
$631$	27.9129	1.11119	0.555597	+	0.831452i	$0.312490\pi$
$632$	−8.00000	−0.318223
$633$	27.9129	1.10944
$634$	−9.79129	−0.388862
$635$	−12.7477	−0.505878
$636$	−16.7477	−0.664091
$637$	−21.9564	−0.869946
$638$	6.00000	0.237542
$639$	40.1216	1.58719
$640$	1.00000	0.0395285
$641$	15.1652	0.598987	0.299494	−	0.954098i	$-0.403182\pi$
$641$	15.1652	0.598987	0.299494	+	0.954098i	$0.403182\pi$
$642$	12.3303	0.486638
$643$	6.74773	0.266104	0.133052	−	0.991109i	$-0.457522\pi$
$643$	6.74773	0.266104	0.133052	+	0.991109i	$0.457522\pi$
$644$	−1.79129	−0.0705866
$645$	31.1652	1.22713
$646$	−4.58258	−0.180299
$647$	21.1652	0.832088	0.416044	−	0.909344i	$-0.363416\pi$
$647$	21.1652	0.832088	0.416044	+	0.909344i	$0.363416\pi$
$648$	0.417424	0.0163980
$649$	10.7477	0.421885
$650$	−5.79129	−0.227153
$651$	−16.8693	−0.661161
$652$	8.62614	0.337826
$653$	3.46099	0.135439	0.0677194	−	0.997704i	$-0.478428\pi$
$653$	3.46099	0.135439	0.0677194	+	0.997704i	$0.478428\pi$
$654$	−9.41742	−0.368250
$655$	9.16515	0.358112
$656$	−6.79129	−0.265155
$657$	61.0780	2.38288
$658$	−7.91288	−0.308476
$659$	−8.83485	−0.344157	−0.172078	−	0.985083i	$-0.555048\pi$
$659$	−8.83485	−0.344157	−0.172078	+	0.985083i	$0.555048\pi$
$660$	−2.20871	−0.0859740
$661$	−25.6261	−0.996741	−0.498371	−	0.866964i	$-0.666068\pi$
$661$	−25.6261	−0.996741	−0.498371	+	0.866964i	$0.666068\pi$
$662$	20.7477	0.806383
$663$	−12.7913	−0.496772
$664$	6.00000	0.232845
$665$	10.3739	0.402281
$666$	19.1652	0.742635
$667$	7.58258	0.293599
$668$	18.3303	0.709221
$669$	20.0000	0.773245
$670$	11.1652	0.431347
$671$	−8.20871	−0.316894
$672$	−5.00000	−0.192879
$673$	38.0000	1.46479	0.732396	−	0.680879i	$-0.238402\pi$
$673$	38.0000	1.46479	0.732396	+	0.680879i	$0.238402\pi$
$674$	12.2087	0.470262
$675$	−5.00000	−0.192450
$676$	20.5390	0.789962
$677$	42.6606	1.63958	0.819790	−	0.572664i	$-0.194090\pi$
$677$	42.6606	1.63958	0.819790	+	0.572664i	$0.194090\pi$
$678$	16.7477	0.643193
$679$	14.2523	0.546952
$680$	0.791288	0.0303445
$681$	63.4955	2.43315
$682$	−2.66970	−0.102228
$683$	−11.3739	−0.435209	−0.217604	−	0.976037i	$-0.569824\pi$
$683$	−11.3739	−0.435209	−0.217604	+	0.976037i	$0.569824\pi$
$684$	27.7477	1.06096
$685$	−3.79129	−0.144858
$686$	−19.3303	−0.738034
$687$	−56.7477	−2.16506
$688$	11.1652	0.425667
$689$	34.7477	1.32378
$690$	−2.79129	−0.106263
$691$	42.7477	1.62620	0.813100	−	0.582124i	$-0.197778\pi$
$691$	42.7477	1.62620	0.813100	+	0.582124i	$0.197778\pi$
$692$	−18.7913	−0.714338
$693$	6.79129	0.257980
$694$	−5.20871	−0.197720
$695$	−12.7477	−0.483549
$696$	21.1652	0.802263
$697$	−5.37386	−0.203550
$698$	−26.0000	−0.984115
$699$	4.41742	0.167082
$700$	−1.79129	−0.0677043
$701$	23.3739	0.882819	0.441409	−	0.897306i	$-0.354479\pi$
$701$	23.3739	0.882819	0.441409	+	0.897306i	$0.354479\pi$
$702$	28.9564	1.09289
$703$	−23.1652	−0.873690
$704$	−0.791288	−0.0298228
$705$	−12.3303	−0.464386
$706$	−3.16515	−0.119122
$707$	−7.91288	−0.297594
$708$	37.9129	1.42485
$709$	2.46099	0.0924242	0.0462121	−	0.998932i	$-0.485285\pi$
$709$	2.46099	0.0924242	0.0462121	+	0.998932i	$0.485285\pi$
$710$	8.37386	0.314265
$711$	38.3303	1.43750
$712$	−15.1652	−0.568338
$713$	−3.37386	−0.126352
$714$	−3.95644	−0.148066
$715$	4.58258	0.171379
$716$	10.7477	0.401661
$717$	42.3303	1.58085
$718$	−9.16515	−0.342040
$719$	2.53901	0.0946893	0.0473446	−	0.998879i	$-0.484924\pi$
$719$	2.53901	0.0946893	0.0473446	+	0.998879i	$0.484924\pi$
$720$	−4.79129	−0.178561
$721$	11.4174	0.425207
$722$	−14.5390	−0.541086
$723$	78.1561	2.90666
$724$	−18.5390	−0.688997
$725$	7.58258	0.281610
$726$	−28.9564	−1.07467
$727$	39.1216	1.45094	0.725470	−	0.688254i	$-0.241623\pi$
$727$	39.1216	1.45094	0.725470	+	0.688254i	$0.241623\pi$
$728$	10.3739	0.384481
$729$	−43.8693	−1.62479
$730$	12.7477	0.471815
$731$	8.83485	0.326769
$732$	−28.9564	−1.07026
$733$	26.0000	0.960332	0.480166	−	0.877178i	$-0.340576\pi$
$733$	26.0000	0.960332	0.480166	+	0.877178i	$0.340576\pi$
$734$	19.1652	0.707399
$735$	−10.5826	−0.390344
$736$	−1.00000	−0.0368605
$737$	−8.83485	−0.325436
$738$	32.5390	1.19778
$739$	8.00000	0.294285	0.147142	−	0.989115i	$-0.452992\pi$
$739$	8.00000	0.294285	0.147142	+	0.989115i	$0.452992\pi$
$740$	4.00000	0.147043
$741$	−93.6170	−3.43911
$742$	10.7477	0.394561
$743$	−12.9564	−0.475326	−0.237663	−	0.971348i	$-0.576381\pi$
$743$	−12.9564	−0.475326	−0.237663	+	0.971348i	$0.576381\pi$
$744$	−9.41742	−0.345260
$745$	−8.20871	−0.300744
$746$	−12.7477	−0.466727
$747$	−28.7477	−1.05182
$748$	−0.626136	−0.0228938
$749$	−7.91288	−0.289130
$750$	−2.79129	−0.101923
$751$	−8.74773	−0.319209	−0.159605	−	0.987181i	$-0.551022\pi$
$751$	−8.74773	−0.319209	−0.159605	+	0.987181i	$0.551022\pi$
$752$	−4.41742	−0.161087
$753$	−73.1561	−2.66596
$754$	−43.9129	−1.59921
$755$	10.7913	0.392735
$756$	8.95644	0.325743
$757$	−10.3303	−0.375461	−0.187731	−	0.982221i	$-0.560113\pi$
$757$	−10.3303	−0.375461	−0.187731	+	0.982221i	$0.560113\pi$
$758$	6.37386	0.231509
$759$	2.20871	0.0801712
$760$	5.79129	0.210072
$761$	−11.0436	−0.400329	−0.200164	−	0.979762i	$-0.564148\pi$
$761$	−11.0436	−0.400329	−0.200164	+	0.979762i	$0.564148\pi$
$762$	35.5826	1.28902
$763$	6.04356	0.218792
$764$	25.5826	0.925545
$765$	−3.79129	−0.137074
$766$	24.0000	0.867155
$767$	−78.6606	−2.84027
$768$	−2.79129	−0.100722
$769$	−40.3303	−1.45435	−0.727174	−	0.686453i	$-0.759167\pi$
$769$	−40.3303	−1.45435	−0.727174	+	0.686453i	$0.759167\pi$
$770$	1.41742	0.0510804
$771$	13.2523	0.477269
$772$	−20.7477	−0.746727
$773$	33.4955	1.20475	0.602374	−	0.798214i	$-0.294222\pi$
$773$	33.4955	1.20475	0.602374	+	0.798214i	$0.294222\pi$
$774$	−53.4955	−1.92285
$775$	−3.37386	−0.121193
$776$	7.95644	0.285620
$777$	−20.0000	−0.717496
$778$	20.7042	0.742280
$779$	−39.3303	−1.40915
$780$	16.1652	0.578805
$781$	−6.62614	−0.237102
$782$	−0.791288	−0.0282964
$783$	−37.9129	−1.35490
$784$	−3.79129	−0.135403
$785$	14.7477	0.526369
$786$	−25.5826	−0.912500
$787$	−17.5826	−0.626751	−0.313376	−	0.949629i	$-0.601460\pi$
$787$	−17.5826	−0.626751	−0.313376	+	0.949629i	$0.601460\pi$
$788$	−11.5390	−0.411060
$789$	−31.2867	−1.11384
$790$	8.00000	0.284627
$791$	−10.7477	−0.382145
$792$	3.79129	0.134718
$793$	60.0780	2.13343
$794$	15.5390	0.551459
$795$	16.7477	0.593981
$796$	−16.3303	−0.578812
$797$	−4.08712	−0.144773	−0.0723866	−	0.997377i	$-0.523062\pi$
$797$	−4.08712	−0.144773	−0.0723866	+	0.997377i	$0.523062\pi$
$798$	−28.9564	−1.02505
$799$	−3.49545	−0.123660
$800$	−1.00000	−0.0353553
$801$	72.6606	2.56734
$802$	4.74773	0.167648
$803$	−10.0871	−0.355967
$804$	−31.1652	−1.09911
$805$	1.79129	0.0631346
$806$	19.5390	0.688232
$807$	30.0000	1.05605
$808$	−4.41742	−0.155404
$809$	33.9564	1.19384	0.596922	−	0.802299i	$-0.296390\pi$
$809$	33.9564	1.19384	0.596922	+	0.802299i	$0.296390\pi$
$810$	−0.417424	−0.0146668
$811$	−2.08712	−0.0732887	−0.0366444	−	0.999328i	$-0.511667\pi$
$811$	−2.08712	−0.0732887	−0.0366444	+	0.999328i	$0.511667\pi$
$812$	−13.5826	−0.476655
$813$	−50.5826	−1.77401
$814$	−3.16515	−0.110938
$815$	−8.62614	−0.302160
$816$	−2.20871	−0.0773204
$817$	64.6606	2.26219
$818$	18.2087	0.636653
$819$	−49.7042	−1.73680
$820$	6.79129	0.237162
$821$	21.1652	0.738669	0.369334	−	0.929297i	$-0.379586\pi$
$821$	21.1652	0.738669	0.369334	+	0.929297i	$0.379586\pi$
$822$	10.5826	0.369110
$823$	22.8348	0.795973	0.397986	−	0.917391i	$-0.369709\pi$
$823$	22.8348	0.795973	0.397986	+	0.917391i	$0.369709\pi$
$824$	6.37386	0.222044
$825$	2.20871	0.0768975
$826$	−24.3303	−0.846560
$827$	−23.0780	−0.802502	−0.401251	−	0.915968i	$-0.631424\pi$
$827$	−23.0780	−0.802502	−0.401251	+	0.915968i	$0.631424\pi$
$828$	4.79129	0.166509
$829$	23.4955	0.816031	0.408015	−	0.912975i	$-0.366221\pi$
$829$	23.4955	0.816031	0.408015	+	0.912975i	$0.366221\pi$
$830$	−6.00000	−0.208263
$831$	−47.9129	−1.66208
$832$	5.79129	0.200777
$833$	−3.00000	−0.103944
$834$	35.5826	1.23212
$835$	−18.3303	−0.634346
$836$	−4.58258	−0.158492
$837$	16.8693	0.583089
$838$	−20.8348	−0.719728
$839$	−31.5826	−1.09035	−0.545176	−	0.838322i	$-0.683537\pi$
$839$	−31.5826	−1.09035	−0.545176	+	0.838322i	$0.683537\pi$
$840$	5.00000	0.172516
$841$	28.4955	0.982602
$842$	−18.1216	−0.624511
$843$	−30.0000	−1.03325
$844$	−10.0000	−0.344214
$845$	−20.5390	−0.706564
$846$	21.1652	0.727673
$847$	18.5826	0.638505
$848$	6.00000	0.206041
$849$	−23.2523	−0.798016
$850$	−0.791288	−0.0271409
$851$	−4.00000	−0.137118
$852$	−23.3739	−0.800775
$853$	40.5390	1.38803	0.694015	−	0.719961i	$-0.255840\pi$
$853$	40.5390	1.38803	0.694015	+	0.719961i	$0.255840\pi$
$854$	18.5826	0.635883
$855$	−27.7477	−0.948952
$856$	−4.41742	−0.150984
$857$	−9.16515	−0.313076	−0.156538	−	0.987672i	$-0.550033\pi$
$857$	−9.16515	−0.313076	−0.156538	+	0.987672i	$0.550033\pi$
$858$	−12.7913	−0.436687
$859$	−26.7477	−0.912621	−0.456310	−	0.889821i	$-0.650829\pi$
$859$	−26.7477	−0.912621	−0.456310	+	0.889821i	$0.650829\pi$
$860$	−11.1652	−0.380729
$861$	−33.9564	−1.15723
$862$	−25.9129	−0.882596
$863$	−22.4174	−0.763098	−0.381549	−	0.924349i	$-0.624609\pi$
$863$	−22.4174	−0.763098	−0.381549	+	0.924349i	$0.624609\pi$
$864$	5.00000	0.170103
$865$	18.7913	0.638923
$866$	30.5390	1.03776
$867$	45.7042	1.55219
$868$	6.04356	0.205132
$869$	−6.33030	−0.214741
$870$	−21.1652	−0.717566
$871$	64.6606	2.19094
$872$	3.37386	0.114253
$873$	−38.1216	−1.29022
$874$	−5.79129	−0.195893
$875$	1.79129	0.0605566
$876$	−35.5826	−1.20222
$877$	−42.7042	−1.44202	−0.721009	−	0.692926i	$-0.756321\pi$
$877$	−42.7042	−1.44202	−0.721009	+	0.692926i	$0.756321\pi$
$878$	6.53901	0.220681
$879$	−76.7477	−2.58864
$880$	0.791288	0.0266743
$881$	30.3303	1.02185	0.510927	−	0.859624i	$-0.329302\pi$
$881$	30.3303	1.02185	0.510927	+	0.859624i	$0.329302\pi$
$882$	18.1652	0.611652
$883$	−34.9564	−1.17638	−0.588189	−	0.808724i	$-0.700159\pi$
$883$	−34.9564	−1.17638	−0.588189	+	0.808724i	$0.700159\pi$
$884$	4.58258	0.154129
$885$	−37.9129	−1.27443
$886$	39.7913	1.33681
$887$	15.1652	0.509196	0.254598	−	0.967047i	$-0.418057\pi$
$887$	15.1652	0.509196	0.254598	+	0.967047i	$0.418057\pi$
$888$	−11.1652	−0.374678
$889$	−22.8348	−0.765856
$890$	15.1652	0.508337
$891$	0.330303	0.0110656
$892$	−7.16515	−0.239907
$893$	−25.5826	−0.856088
$894$	22.9129	0.766321
$895$	−10.7477	−0.359257
$896$	1.79129	0.0598427
$897$	−16.1652	−0.539739
$898$	16.1216	0.537984
$899$	−25.5826	−0.853227
$900$	4.79129	0.159710
$901$	4.74773	0.158170
$902$	−5.37386	−0.178930
$903$	55.8258	1.85776
$904$	−6.00000	−0.199557
$905$	18.5390	0.616258
$906$	−30.1216	−1.00072
$907$	6.74773	0.224055	0.112027	−	0.993705i	$-0.464266\pi$
$907$	6.74773	0.224055	0.112027	+	0.993705i	$0.464266\pi$
$908$	−22.7477	−0.754910
$909$	21.1652	0.702004
$910$	−10.3739	−0.343890
$911$	4.41742	0.146356	0.0731779	−	0.997319i	$-0.476686\pi$
$911$	4.41742	0.146356	0.0731779	+	0.997319i	$0.476686\pi$
$912$	−16.1652	−0.535282
$913$	4.74773	0.157127
$914$	10.0000	0.330771
$915$	28.9564	0.957270
$916$	20.3303	0.671732
$917$	16.4174	0.542151
$918$	3.95644	0.130582
$919$	−55.1652	−1.81973	−0.909865	−	0.414904i	$-0.863815\pi$
$919$	−55.1652	−1.81973	−0.909865	+	0.414904i	$0.863815\pi$
$920$	1.00000	0.0329690
$921$	43.3739	1.42922
$922$	28.7477	0.946756
$923$	48.4955	1.59625
$924$	−3.95644	−0.130157
$925$	−4.00000	−0.131519
$926$	10.0000	0.328620
$927$	−30.5390	−1.00303
$928$	−7.58258	−0.248910
$929$	15.4955	0.508389	0.254195	−	0.967153i	$-0.418190\pi$
$929$	15.4955	0.508389	0.254195	+	0.967153i	$0.418190\pi$
$930$	9.41742	0.308810
$931$	−21.9564	−0.719593
$932$	−1.58258	−0.0518390
$933$	−33.4955	−1.09659
$934$	19.9129	0.651569
$935$	0.626136	0.0204769
$936$	−27.7477	−0.906963
$937$	44.6261	1.45787	0.728936	−	0.684582i	$-0.240015\pi$
$937$	44.6261	1.45787	0.728936	+	0.684582i	$0.240015\pi$
$938$	20.0000	0.653023
$939$	12.9129	0.421396
$940$	4.41742	0.144080
$941$	32.0436	1.04459	0.522295	−	0.852765i	$-0.325076\pi$
$941$	32.0436	1.04459	0.522295	+	0.852765i	$0.325076\pi$
$942$	−41.1652	−1.34123
$943$	−6.79129	−0.221155
$944$	−13.5826	−0.442075
$945$	−8.95644	−0.291353
$946$	8.83485	0.287246
$947$	2.53901	0.0825069	0.0412534	−	0.999149i	$-0.486865\pi$
$947$	2.53901	0.0825069	0.0412534	+	0.999149i	$0.486865\pi$
$948$	−22.3303	−0.725255
$949$	73.8258	2.39649
$950$	−5.79129	−0.187894
$951$	−27.3303	−0.886246
$952$	1.41742	0.0459390
$953$	5.53901	0.179426	0.0897131	−	0.995968i	$-0.471405\pi$
$953$	5.53901	0.179426	0.0897131	+	0.995968i	$0.471405\pi$
$954$	−28.7477	−0.930742
$955$	−25.5826	−0.827833
$956$	−15.1652	−0.490476
$957$	16.7477	0.541377
$958$	−15.4955	−0.500635
$959$	−6.79129	−0.219302
$960$	2.79129	0.0900884
$961$	−19.6170	−0.632808
$962$	23.1652	0.746874
$963$	21.1652	0.682037
$964$	−28.0000	−0.901819
$965$	20.7477	0.667893
$966$	−5.00000	−0.160872
$967$	−32.7477	−1.05310	−0.526548	−	0.850145i	$-0.676514\pi$
$967$	−32.7477	−1.05310	−0.526548	+	0.850145i	$0.676514\pi$
$968$	10.3739	0.333429
$969$	−12.7913	−0.410915
$970$	−7.95644	−0.255466
$971$	15.9564	0.512067	0.256033	−	0.966668i	$-0.417584\pi$
$971$	15.9564	0.512067	0.256033	+	0.966668i	$0.417584\pi$
$972$	16.1652	0.518497
$973$	−22.8348	−0.732052
$974$	−6.41742	−0.205628
$975$	−16.1652	−0.517699
$976$	10.3739	0.332059
$977$	−34.1216	−1.09165	−0.545823	−	0.837900i	$-0.683783\pi$
$977$	−34.1216	−1.09165	−0.545823	+	0.837900i	$0.683783\pi$
$978$	24.0780	0.769930
$979$	−12.0000	−0.383522
$980$	3.79129	0.121108
$981$	−16.1652	−0.516114
$982$	−10.7477	−0.342974
$983$	−14.3739	−0.458455	−0.229228	−	0.973373i	$-0.573620\pi$
$983$	−14.3739	−0.458455	−0.229228	+	0.973373i	$0.573620\pi$
$984$	−18.9564	−0.604309
$985$	11.5390	0.367664
$986$	−6.00000	−0.191079
$987$	−22.0871	−0.703041
$988$	33.5390	1.06702
$989$	11.1652	0.355031
$990$	−3.79129	−0.120495
$991$	−33.2087	−1.05491	−0.527455	−	0.849583i	$-0.676854\pi$
$991$	−33.2087	−1.05491	−0.527455	+	0.849583i	$0.676854\pi$
$992$	3.37386	0.107120
$993$	57.9129	1.83781
$994$	15.0000	0.475771
$995$	16.3303	0.517705
$996$	16.7477	0.530672
$997$	−43.4955	−1.37751	−0.688757	−	0.724992i	$-0.741843\pi$
$997$	−43.4955	−1.37751	−0.688757	+	0.724992i	$0.741843\pi$
$998$	−4.83485	−0.153044
$999$	20.0000	0.632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.a.a.1.1	✓	2
3.2	odd	2		2070.2.a.x.1.1		2
4.3	odd	2		1840.2.a.n.1.2		2
5.2	odd	4		1150.2.b.g.599.2		4
5.3	odd	4		1150.2.b.g.599.3		4
5.4	even	2		1150.2.a.o.1.2		2
8.3	odd	2		7360.2.a.bk.1.1		2
8.5	even	2		7360.2.a.bq.1.2		2
20.19	odd	2		9200.2.a.bs.1.1		2
23.22	odd	2		5290.2.a.e.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.a.a.1.1	✓	2	1.1	even	1	trivial
1150.2.a.o.1.2		2	5.4	even	2
1150.2.b.g.599.2		4	5.2	odd	4
1150.2.b.g.599.3		4	5.3	odd	4
1840.2.a.n.1.2		2	4.3	odd	2
2070.2.a.x.1.1		2	3.2	odd	2
5290.2.a.e.1.1		2	23.22	odd	2
7360.2.a.bk.1.1		2	8.3	odd	2
7360.2.a.bq.1.2		2	8.5	even	2
9200.2.a.bs.1.1		2	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.79129 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.79129 q^{6} -1.79129 q^{7} -1.00000 q^{8} +4.79129 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.79129 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.79129 q^{6} -1.79129 q^{7} -1.00000 q^{8} +4.79129 q^{9} +1.00000 q^{10} -0.791288 q^{11} -2.79129 q^{12} +5.79129 q^{13} +1.79129 q^{14} +2.79129 q^{15} +1.00000 q^{16} +0.791288 q^{17} -4.79129 q^{18} +5.79129 q^{19} -1.00000 q^{20} +5.00000 q^{21} +0.791288 q^{22} +1.00000 q^{23} +2.79129 q^{24} +1.00000 q^{25} -5.79129 q^{26} -5.00000 q^{27} -1.79129 q^{28} +7.58258 q^{29} -2.79129 q^{30} -3.37386 q^{31} -1.00000 q^{32} +2.20871 q^{33} -0.791288 q^{34} +1.79129 q^{35} +4.79129 q^{36} -4.00000 q^{37} -5.79129 q^{38} -16.1652 q^{39} +1.00000 q^{40} -6.79129 q^{41} -5.00000 q^{42} +11.1652 q^{43} -0.791288 q^{44} -4.79129 q^{45} -1.00000 q^{46} -4.41742 q^{47} -2.79129 q^{48} -3.79129 q^{49} -1.00000 q^{50} -2.20871 q^{51} +5.79129 q^{52} +6.00000 q^{53} +5.00000 q^{54} +0.791288 q^{55} +1.79129 q^{56} -16.1652 q^{57} -7.58258 q^{58} -13.5826 q^{59} +2.79129 q^{60} +10.3739 q^{61} +3.37386 q^{62} -8.58258 q^{63} +1.00000 q^{64} -5.79129 q^{65} -2.20871 q^{66} +11.1652 q^{67} +0.791288 q^{68} -2.79129 q^{69} -1.79129 q^{70} +8.37386 q^{71} -4.79129 q^{72} +12.7477 q^{73} +4.00000 q^{74} -2.79129 q^{75} +5.79129 q^{76} +1.41742 q^{77} +16.1652 q^{78} +8.00000 q^{79} -1.00000 q^{80} -0.417424 q^{81} +6.79129 q^{82} -6.00000 q^{83} +5.00000 q^{84} -0.791288 q^{85} -11.1652 q^{86} -21.1652 q^{87} +0.791288 q^{88} +15.1652 q^{89} +4.79129 q^{90} -10.3739 q^{91} +1.00000 q^{92} +9.41742 q^{93} +4.41742 q^{94} -5.79129 q^{95} +2.79129 q^{96} -7.95644 q^{97} +3.79129 q^{98} -3.79129 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - q^{3} + 2 q^{4} - 2 q^{5} + q^{6} + q^{7} - 2 q^{8} + 5 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - q^3 + 2 * q^4 - 2 * q^5 + q^6 + q^7 - 2 * q^8 + 5 * q^9	\( 2 q - 2 q^{2} - q^{3} + 2 q^{4} - 2 q^{5} + q^{6} + q^{7} - 2 q^{8} + 5 q^{9} + 2 q^{10} + 3 q^{11} - q^{12} + 7 q^{13} - q^{14} + q^{15} + 2 q^{16} - 3 q^{17} - 5 q^{18} + 7 q^{19} - 2 q^{20} + 10 q^{21} - 3 q^{22} + 2 q^{23} + q^{24} + 2 q^{25} - 7 q^{26} - 10 q^{27} + q^{28} + 6 q^{29} - q^{30} + 7 q^{31} - 2 q^{32} + 9 q^{33} + 3 q^{34} - q^{35} + 5 q^{36} - 8 q^{37} - 7 q^{38} - 14 q^{39} + 2 q^{40} - 9 q^{41} - 10 q^{42} + 4 q^{43} + 3 q^{44} - 5 q^{45} - 2 q^{46} - 18 q^{47} - q^{48} - 3 q^{49} - 2 q^{50} - 9 q^{51} + 7 q^{52} + 12 q^{53} + 10 q^{54} - 3 q^{55} - q^{56} - 14 q^{57} - 6 q^{58} - 18 q^{59} + q^{60} + 7 q^{61} - 7 q^{62} - 8 q^{63} + 2 q^{64} - 7 q^{65} - 9 q^{66} + 4 q^{67} - 3 q^{68} - q^{69} + q^{70} + 3 q^{71} - 5 q^{72} - 2 q^{73} + 8 q^{74} - q^{75} + 7 q^{76} + 12 q^{77} + 14 q^{78} + 16 q^{79} - 2 q^{80} - 10 q^{81} + 9 q^{82} - 12 q^{83} + 10 q^{84} + 3 q^{85} - 4 q^{86} - 24 q^{87} - 3 q^{88} + 12 q^{89} + 5 q^{90} - 7 q^{91} + 2 q^{92} + 28 q^{93} + 18 q^{94} - 7 q^{95} + q^{96} + 7 q^{97} + 3 q^{98} - 3 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - q^3 + 2 * q^4 - 2 * q^5 + q^6 + q^7 - 2 * q^8 + 5 * q^9 + 2 * q^10 + 3 * q^11 - q^12 + 7 * q^13 - q^14 + q^15 + 2 * q^16 - 3 * q^17 - 5 * q^18 + 7 * q^19 - 2 * q^20 + 10 * q^21 - 3 * q^22 + 2 * q^23 + q^24 + 2 * q^25 - 7 * q^26 - 10 * q^27 + q^28 + 6 * q^29 - q^30 + 7 * q^31 - 2 * q^32 + 9 * q^33 + 3 * q^34 - q^35 + 5 * q^36 - 8 * q^37 - 7 * q^38 - 14 * q^39 + 2 * q^40 - 9 * q^41 - 10 * q^42 + 4 * q^43 + 3 * q^44 - 5 * q^45 - 2 * q^46 - 18 * q^47 - q^48 - 3 * q^49 - 2 * q^50 - 9 * q^51 + 7 * q^52 + 12 * q^53 + 10 * q^54 - 3 * q^55 - q^56 - 14 * q^57 - 6 * q^58 - 18 * q^59 + q^60 + 7 * q^61 - 7 * q^62 - 8 * q^63 + 2 * q^64 - 7 * q^65 - 9 * q^66 + 4 * q^67 - 3 * q^68 - q^69 + q^70 + 3 * q^71 - 5 * q^72 - 2 * q^73 + 8 * q^74 - q^75 + 7 * q^76 + 12 * q^77 + 14 * q^78 + 16 * q^79 - 2 * q^80 - 10 * q^81 + 9 * q^82 - 12 * q^83 + 10 * q^84 + 3 * q^85 - 4 * q^86 - 24 * q^87 - 3 * q^88 + 12 * q^89 + 5 * q^90 - 7 * q^91 + 2 * q^92 + 28 * q^93 + 18 * q^94 - 7 * q^95 + q^96 + 7 * q^97 + 3 * q^98 - 3 * q^99

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