LMFDB - Embedded newform 165.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,2,Mod(1,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("165.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	165.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:	$1.31753163335$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.17009$ of defining polynomial
Character	$\chi$	$=$	165.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.70928 q^{2} +1.00000 q^{3} +5.34017 q^{4} +1.00000 q^{5} -2.70928 q^{6} +1.07838 q^{7} -9.04945 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.70928 q^{2} +1.00000 q^{3} +5.34017 q^{4} +1.00000 q^{5} -2.70928 q^{6} +1.07838 q^{7} -9.04945 q^{8} +1.00000 q^{9} -2.70928 q^{10} +1.00000 q^{11} +5.34017 q^{12} -4.34017 q^{13} -2.92162 q^{14} +1.00000 q^{15} +13.8371 q^{16} +7.75872 q^{17} -2.70928 q^{18} +5.26180 q^{19} +5.34017 q^{20} +1.07838 q^{21} -2.70928 q^{22} -2.15676 q^{23} -9.04945 q^{24} +1.00000 q^{25} +11.7587 q^{26} +1.00000 q^{27} +5.75872 q^{28} +1.41855 q^{29} -2.70928 q^{30} -4.68035 q^{31} -19.3896 q^{32} +1.00000 q^{33} -21.0205 q^{34} +1.07838 q^{35} +5.34017 q^{36} -2.00000 q^{37} -14.2557 q^{38} -4.34017 q^{39} -9.04945 q^{40} -9.41855 q^{41} -2.92162 q^{42} +7.60197 q^{43} +5.34017 q^{44} +1.00000 q^{45} +5.84324 q^{46} +4.68035 q^{47} +13.8371 q^{48} -5.83710 q^{49} -2.70928 q^{50} +7.75872 q^{51} -23.1773 q^{52} +0.156755 q^{53} -2.70928 q^{54} +1.00000 q^{55} -9.75872 q^{56} +5.26180 q^{57} -3.84324 q^{58} +6.15676 q^{59} +5.34017 q^{60} -4.15676 q^{61} +12.6803 q^{62} +1.07838 q^{63} +24.8576 q^{64} -4.34017 q^{65} -2.70928 q^{66} -8.68035 q^{67} +41.4329 q^{68} -2.15676 q^{69} -2.92162 q^{70} -4.68035 q^{71} -9.04945 q^{72} -10.4969 q^{73} +5.41855 q^{74} +1.00000 q^{75} +28.0989 q^{76} +1.07838 q^{77} +11.7587 q^{78} -8.09890 q^{79} +13.8371 q^{80} +1.00000 q^{81} +25.5174 q^{82} -11.0205 q^{83} +5.75872 q^{84} +7.75872 q^{85} -20.5958 q^{86} +1.41855 q^{87} -9.04945 q^{88} -12.8371 q^{89} -2.70928 q^{90} -4.68035 q^{91} -11.5174 q^{92} -4.68035 q^{93} -12.6803 q^{94} +5.26180 q^{95} -19.3896 q^{96} +14.6803 q^{97} +15.8143 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - q^{2} + 3 q^{3} + 5 q^{4} + 3 q^{5} - q^{6} - 9 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - q^2 + 3 * q^3 + 5 * q^4 + 3 * q^5 - q^6 - 9 * q^8 + 3 * q^9	$ 3 q - q^{2} + 3 q^{3} + 5 q^{4} + 3 q^{5} - q^{6} - 9 q^{8} + 3 q^{9} - q^{10} + 3 q^{11} + 5 q^{12} - 2 q^{13} - 12 q^{14} + 3 q^{15} + 13 q^{16} - 2 q^{17} - q^{18} + 8 q^{19} + 5 q^{20} - q^{22} - 9 q^{24} + 3 q^{25} + 10 q^{26} + 3 q^{27} - 8 q^{28} - 10 q^{29} - q^{30} + 8 q^{31} - 29 q^{32} + 3 q^{33} - 30 q^{34} + 5 q^{36} - 6 q^{37} - 2 q^{39} - 9 q^{40} - 14 q^{41} - 12 q^{42} + 4 q^{43} + 5 q^{44} + 3 q^{45} + 24 q^{46} - 8 q^{47} + 13 q^{48} + 11 q^{49} - q^{50} - 2 q^{51} - 30 q^{52} - 6 q^{53} - q^{54} + 3 q^{55} - 4 q^{56} + 8 q^{57} - 18 q^{58} + 12 q^{59} + 5 q^{60} - 6 q^{61} + 16 q^{62} + 13 q^{64} - 2 q^{65} - q^{66} - 4 q^{67} + 42 q^{68} - 12 q^{70} + 8 q^{71} - 9 q^{72} - 14 q^{73} + 2 q^{74} + 3 q^{75} + 48 q^{76} + 10 q^{78} + 12 q^{79} + 13 q^{80} + 3 q^{81} + 26 q^{82} - 8 q^{84} - 2 q^{85} - 8 q^{86} - 10 q^{87} - 9 q^{88} - 10 q^{89} - q^{90} + 8 q^{91} + 16 q^{92} + 8 q^{93} - 16 q^{94} + 8 q^{95} - 29 q^{96} + 22 q^{97} + 39 q^{98} + 3 q^{99}+O(q^{100}) $ 3 * q - q^2 + 3 * q^3 + 5 * q^4 + 3 * q^5 - q^6 - 9 * q^8 + 3 * q^9 - q^10 + 3 * q^11 + 5 * q^12 - 2 * q^13 - 12 * q^14 + 3 * q^15 + 13 * q^16 - 2 * q^17 - q^18 + 8 * q^19 + 5 * q^20 - q^22 - 9 * q^24 + 3 * q^25 + 10 * q^26 + 3 * q^27 - 8 * q^28 - 10 * q^29 - q^30 + 8 * q^31 - 29 * q^32 + 3 * q^33 - 30 * q^34 + 5 * q^36 - 6 * q^37 - 2 * q^39 - 9 * q^40 - 14 * q^41 - 12 * q^42 + 4 * q^43 + 5 * q^44 + 3 * q^45 + 24 * q^46 - 8 * q^47 + 13 * q^48 + 11 * q^49 - q^50 - 2 * q^51 - 30 * q^52 - 6 * q^53 - q^54 + 3 * q^55 - 4 * q^56 + 8 * q^57 - 18 * q^58 + 12 * q^59 + 5 * q^60 - 6 * q^61 + 16 * q^62 + 13 * q^64 - 2 * q^65 - q^66 - 4 * q^67 + 42 * q^68 - 12 * q^70 + 8 * q^71 - 9 * q^72 - 14 * q^73 + 2 * q^74 + 3 * q^75 + 48 * q^76 + 10 * q^78 + 12 * q^79 + 13 * q^80 + 3 * q^81 + 26 * q^82 - 8 * q^84 - 2 * q^85 - 8 * q^86 - 10 * q^87 - 9 * q^88 - 10 * q^89 - q^90 + 8 * q^91 + 16 * q^92 + 8 * q^93 - 16 * q^94 + 8 * q^95 - 29 * q^96 + 22 * q^97 + 39 * 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 $

$2$	−2.70928	−1.91575	−0.957873	−	0.287190i	$-0.907279\pi$
$2$	−2.70928	−1.91575	−0.957873	+	0.287190i	$0.907279\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.34017	2.67009
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.70928	−1.10606
$7$	1.07838	0.407588	0.203794	−	0.979014i	$-0.434673\pi$
$7$	1.07838	0.407588	0.203794	+	0.979014i	$0.434673\pi$
$8$	−9.04945	−3.19946
$9$	1.00000	0.333333
$10$	−2.70928	−0.856748
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	5.34017	1.54158
$13$	−4.34017	−1.20375	−0.601874	−	0.798591i	$-0.705579\pi$
$13$	−4.34017	−1.20375	−0.601874	+	0.798591i	$0.705579\pi$
$14$	−2.92162	−0.780836
$15$	1.00000	0.258199
$16$	13.8371	3.45928
$17$	7.75872	1.88177	0.940883	−	0.338730i	$-0.109997\pi$
$17$	7.75872	1.88177	0.940883	+	0.338730i	$0.109997\pi$
$18$	−2.70928	−0.638582
$19$	5.26180	1.20714	0.603569	−	0.797311i	$-0.293745\pi$
$19$	5.26180	1.20714	0.603569	+	0.797311i	$0.293745\pi$
$20$	5.34017	1.19410
$21$	1.07838	0.235321
$22$	−2.70928	−0.577619
$23$	−2.15676	−0.449715	−0.224857	−	0.974392i	$-0.572192\pi$
$23$	−2.15676	−0.449715	−0.224857	+	0.974392i	$0.572192\pi$
$24$	−9.04945	−1.84721
$25$	1.00000	0.200000
$26$	11.7587	2.30608
$27$	1.00000	0.192450
$28$	5.75872	1.08830
$29$	1.41855	0.263418	0.131709	−	0.991288i	$-0.457954\pi$
$29$	1.41855	0.263418	0.131709	+	0.991288i	$0.457954\pi$
$30$	−2.70928	−0.494644
$31$	−4.68035	−0.840615	−0.420307	−	0.907382i	$-0.638078\pi$
$31$	−4.68035	−0.840615	−0.420307	+	0.907382i	$0.638078\pi$
$32$	−19.3896	−3.42763
$33$	1.00000	0.174078
$34$	−21.0205	−3.60499
$35$	1.07838	0.182279
$36$	5.34017	0.890029
$37$	−2.00000	−0.328798	−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000	−0.328798	−0.164399	+	0.986394i	$0.552568\pi$
$38$	−14.2557	−2.31257
$39$	−4.34017	−0.694984
$40$	−9.04945	−1.43084
$41$	−9.41855	−1.47093	−0.735465	−	0.677562i	$-0.763036\pi$
$41$	−9.41855	−1.47093	−0.735465	+	0.677562i	$0.763036\pi$
$42$	−2.92162	−0.450816
$43$	7.60197	1.15929	0.579645	−	0.814869i	$-0.303191\pi$
$43$	7.60197	1.15929	0.579645	+	0.814869i	$0.303191\pi$
$44$	5.34017	0.805061
$45$	1.00000	0.149071
$46$	5.84324	0.861539
$47$	4.68035	0.682699	0.341349	−	0.939937i	$-0.389116\pi$
$47$	4.68035	0.682699	0.341349	+	0.939937i	$0.389116\pi$
$48$	13.8371	1.99721
$49$	−5.83710	−0.833872
$50$	−2.70928	−0.383149
$51$	7.75872	1.08644
$52$	−23.1773	−3.21411
$53$	0.156755	0.0215320	0.0107660	−	0.999942i	$-0.496573\pi$
$53$	0.156755	0.0215320	0.0107660	+	0.999942i	$0.496573\pi$
$54$	−2.70928	−0.368686
$55$	1.00000	0.134840
$56$	−9.75872	−1.30406
$57$	5.26180	0.696942
$58$	−3.84324	−0.504643
$59$	6.15676	0.801541	0.400771	−	0.916178i	$-0.368742\pi$
$59$	6.15676	0.801541	0.400771	+	0.916178i	$0.368742\pi$
$60$	5.34017	0.689413
$61$	−4.15676	−0.532218	−0.266109	−	0.963943i	$-0.585738\pi$
$61$	−4.15676	−0.532218	−0.266109	+	0.963943i	$0.585738\pi$
$62$	12.6803	1.61041
$63$	1.07838	0.135863
$64$	24.8576	3.10720
$65$	−4.34017	−0.538332
$66$	−2.70928	−0.333489
$67$	−8.68035	−1.06047	−0.530237	−	0.847850i	$-0.677897\pi$
$67$	−8.68035	−1.06047	−0.530237	+	0.847850i	$0.677897\pi$
$68$	41.4329	5.02448
$69$	−2.15676	−0.259643
$70$	−2.92162	−0.349201
$71$	−4.68035	−0.555455	−0.277727	−	0.960660i	$-0.589581\pi$
$71$	−4.68035	−0.555455	−0.277727	+	0.960660i	$0.589581\pi$
$72$	−9.04945	−1.06649
$73$	−10.4969	−1.22857	−0.614286	−	0.789083i	$-0.710556\pi$
$73$	−10.4969	−1.22857	−0.614286	+	0.789083i	$0.710556\pi$
$74$	5.41855	0.629894
$75$	1.00000	0.115470
$76$	28.0989	3.22316
$77$	1.07838	0.122893
$78$	11.7587	1.33141
$79$	−8.09890	−0.911197	−0.455599	−	0.890185i	$-0.650575\pi$
$79$	−8.09890	−0.911197	−0.455599	+	0.890185i	$0.650575\pi$
$80$	13.8371	1.54703
$81$	1.00000	0.111111
$82$	25.5174	2.81793
$83$	−11.0205	−1.20966	−0.604830	−	0.796355i	$-0.706759\pi$
$83$	−11.0205	−1.20966	−0.604830	+	0.796355i	$0.706759\pi$
$84$	5.75872	0.628328
$85$	7.75872	0.841552
$86$	−20.5958	−2.22090
$87$	1.41855	0.152085
$88$	−9.04945	−0.964674
$89$	−12.8371	−1.36073	−0.680365	−	0.732873i	$-0.738179\pi$
$89$	−12.8371	−1.36073	−0.680365	+	0.732873i	$0.738179\pi$
$90$	−2.70928	−0.285583
$91$	−4.68035	−0.490634
$92$	−11.5174	−1.20078
$93$	−4.68035	−0.485329
$94$	−12.6803	−1.30788
$95$	5.26180	0.539849
$96$	−19.3896	−1.97894
$97$	14.6803	1.49056	0.745282	−	0.666750i	$-0.232315\pi$
$97$	14.6803	1.49056	0.745282	+	0.666750i	$0.232315\pi$
$98$	15.8143	1.59749
$99$	1.00000	0.100504
$100$	5.34017	0.534017
$101$	−15.5753	−1.54980	−0.774900	−	0.632083i	$-0.782200\pi$
$101$	−15.5753	−1.54980	−0.774900	+	0.632083i	$0.782200\pi$
$102$	−21.0205	−2.08134
$103$	6.83710	0.673680	0.336840	−	0.941562i	$-0.390642\pi$
$103$	6.83710	0.673680	0.336840	+	0.941562i	$0.390642\pi$
$104$	39.2762	3.85135
$105$	1.07838	0.105239
$106$	−0.424694	−0.0412499
$107$	6.34017	0.612928	0.306464	−	0.951882i	$-0.400854\pi$
$107$	6.34017	0.612928	0.306464	+	0.951882i	$0.400854\pi$
$108$	5.34017	0.513858
$109$	2.31351	0.221594	0.110797	−	0.993843i	$-0.464660\pi$
$109$	2.31351	0.221594	0.110797	+	0.993843i	$0.464660\pi$
$110$	−2.70928	−0.258319
$111$	−2.00000	−0.189832
$112$	14.9216	1.40996
$113$	−6.00000	−0.564433	−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000	−0.564433	−0.282216	+	0.959351i	$0.591070\pi$
$114$	−14.2557	−1.33516
$115$	−2.15676	−0.201118
$116$	7.57531	0.703350
$117$	−4.34017	−0.401249
$118$	−16.6803	−1.53555
$119$	8.36683	0.766987
$120$	−9.04945	−0.826098
$121$	1.00000	0.0909091
$122$	11.2618	1.01960
$123$	−9.41855	−0.849242
$124$	−24.9939	−2.24451
$125$	1.00000	0.0894427
$126$	−2.92162	−0.260279
$127$	−2.24128	−0.198881	−0.0994406	−	0.995044i	$-0.531705\pi$
$127$	−2.24128	−0.198881	−0.0994406	+	0.995044i	$0.531705\pi$
$128$	−28.5669	−2.52498
$129$	7.60197	0.669316
$130$	11.7587	1.03131
$131$	8.68035	0.758405	0.379203	−	0.925314i	$-0.376198\pi$
$131$	8.68035	0.758405	0.379203	+	0.925314i	$0.376198\pi$
$132$	5.34017	0.464802
$133$	5.67420	0.492016
$134$	23.5174	2.03160
$135$	1.00000	0.0860663
$136$	−70.2122	−6.02064
$137$	−15.3607	−1.31235	−0.656176	−	0.754608i	$-0.727827\pi$
$137$	−15.3607	−1.31235	−0.656176	+	0.754608i	$0.727827\pi$
$138$	5.84324	0.497410
$139$	8.58145	0.727869	0.363935	−	0.931425i	$-0.381433\pi$
$139$	8.58145	0.727869	0.363935	+	0.931425i	$0.381433\pi$
$140$	5.75872	0.486701
$141$	4.68035	0.394156
$142$	12.6803	1.06411
$143$	−4.34017	−0.362943
$144$	13.8371	1.15309
$145$	1.41855	0.117804
$146$	28.4391	2.35363
$147$	−5.83710	−0.481436
$148$	−10.6803	−0.877919
$149$	−18.0989	−1.48272	−0.741360	−	0.671108i	$-0.765819\pi$
$149$	−18.0989	−1.48272	−0.741360	+	0.671108i	$0.765819\pi$
$150$	−2.70928	−0.221211
$151$	22.9360	1.86651	0.933253	−	0.359221i	$-0.116958\pi$
$151$	22.9360	1.86651	0.933253	+	0.359221i	$0.116958\pi$
$152$	−47.6163	−3.86220
$153$	7.75872	0.627256
$154$	−2.92162	−0.235431
$155$	−4.68035	−0.375934
$156$	−23.1773	−1.85567
$157$	−10.9939	−0.877405	−0.438703	−	0.898632i	$-0.644562\pi$
$157$	−10.9939	−0.877405	−0.438703	+	0.898632i	$0.644562\pi$
$158$	21.9421	1.74562
$159$	0.156755	0.0124315
$160$	−19.3896	−1.53288
$161$	−2.32580	−0.183298
$162$	−2.70928	−0.212861
$163$	−6.52359	−0.510967	−0.255484	−	0.966813i	$-0.582235\pi$
$163$	−6.52359	−0.510967	−0.255484	+	0.966813i	$0.582235\pi$
$164$	−50.2967	−3.92751
$165$	1.00000	0.0778499
$166$	29.8576	2.31740
$167$	1.97334	0.152701	0.0763507	−	0.997081i	$-0.475673\pi$
$167$	1.97334	0.152701	0.0763507	+	0.997081i	$0.475673\pi$
$168$	−9.75872	−0.752902
$169$	5.83710	0.449008
$170$	−21.0205	−1.61220
$171$	5.26180	0.402380
$172$	40.5958	3.09540
$173$	3.75872	0.285770	0.142885	−	0.989739i	$-0.454362\pi$
$173$	3.75872	0.285770	0.142885	+	0.989739i	$0.454362\pi$
$174$	−3.84324	−0.291356
$175$	1.07838	0.0815177
$176$	13.8371	1.04301
$177$	6.15676	0.462770
$178$	34.7792	2.60681
$179$	15.1506	1.13241	0.566205	−	0.824264i	$-0.308411\pi$
$179$	15.1506	1.13241	0.566205	+	0.824264i	$0.308411\pi$
$180$	5.34017	0.398033
$181$	4.83710	0.359539	0.179769	−	0.983709i	$-0.442465\pi$
$181$	4.83710	0.359539	0.179769	+	0.983709i	$0.442465\pi$
$182$	12.6803	0.939930
$183$	−4.15676	−0.307276
$184$	19.5174	1.43885
$185$	−2.00000	−0.147043
$186$	12.6803	0.929768
$187$	7.75872	0.567374
$188$	24.9939	1.82286
$189$	1.07838	0.0784404
$190$	−14.2557	−1.03421
$191$	2.52359	0.182601	0.0913003	−	0.995823i	$-0.470898\pi$
$191$	2.52359	0.182601	0.0913003	+	0.995823i	$0.470898\pi$
$192$	24.8576	1.79394
$193$	0.0266620	0.00191917	0.000959586	−	1.00000i	$-0.499695\pi$
$193$	0.0266620	0.00191917	0.000959586		1.00000i	$0.499695\pi$
$194$	−39.7731	−2.85554
$195$	−4.34017	−0.310806
$196$	−31.1711	−2.22651
$197$	21.1194	1.50470	0.752348	−	0.658766i	$-0.228921\pi$
$197$	21.1194	1.50470	0.752348	+	0.658766i	$0.228921\pi$
$198$	−2.70928	−0.192540
$199$	10.5236	0.745998	0.372999	−	0.927832i	$-0.378330\pi$
$199$	10.5236	0.745998	0.372999	+	0.927832i	$0.378330\pi$
$200$	−9.04945	−0.639893
$201$	−8.68035	−0.612264
$202$	42.1978	2.96903
$203$	1.52973	0.107366
$204$	41.4329	2.90089
$205$	−9.41855	−0.657820
$206$	−18.5236	−1.29060
$207$	−2.15676	−0.149905
$208$	−60.0554	−4.16409
$209$	5.26180	0.363966
$210$	−2.92162	−0.201611
$211$	9.57531	0.659191	0.329596	−	0.944122i	$-0.393088\pi$
$211$	9.57531	0.659191	0.329596	+	0.944122i	$0.393088\pi$
$212$	0.837101	0.0574924
$213$	−4.68035	−0.320692
$214$	−17.1773	−1.17421
$215$	7.60197	0.518450
$216$	−9.04945	−0.615737
$217$	−5.04718	−0.342625
$218$	−6.26794	−0.424518
$219$	−10.4969	−0.709317
$220$	5.34017	0.360034
$221$	−33.6742	−2.26517
$222$	5.41855	0.363669
$223$	−2.15676	−0.144427	−0.0722135	−	0.997389i	$-0.523006\pi$
$223$	−2.15676	−0.144427	−0.0722135	+	0.997389i	$0.523006\pi$
$224$	−20.9093	−1.39706
$225$	1.00000	0.0666667
$226$	16.2557	1.08131
$227$	9.65983	0.641145	0.320573	−	0.947224i	$-0.396125\pi$
$227$	9.65983	0.641145	0.320573	+	0.947224i	$0.396125\pi$
$228$	28.0989	1.86089
$229$	−3.36069	−0.222081	−0.111040	−	0.993816i	$-0.535418\pi$
$229$	−3.36069	−0.222081	−0.111040	+	0.993816i	$0.535418\pi$
$230$	5.84324	0.385292
$231$	1.07838	0.0709520
$232$	−12.8371	−0.842797
$233$	−2.39803	−0.157100	−0.0785501	−	0.996910i	$-0.525029\pi$
$233$	−2.39803	−0.157100	−0.0785501	+	0.996910i	$0.525029\pi$
$234$	11.7587	0.768692
$235$	4.68035	0.305312
$236$	32.8781	2.14018
$237$	−8.09890	−0.526080
$238$	−22.6681	−1.46935
$239$	−7.20394	−0.465984	−0.232992	−	0.972479i	$-0.574852\pi$
$239$	−7.20394	−0.465984	−0.232992	+	0.972479i	$0.574852\pi$
$240$	13.8371	0.893181
$241$	−5.20394	−0.335215	−0.167608	−	0.985854i	$-0.553604\pi$
$241$	−5.20394	−0.335215	−0.167608	+	0.985854i	$0.553604\pi$
$242$	−2.70928	−0.174159
$243$	1.00000	0.0641500
$244$	−22.1978	−1.42107
$245$	−5.83710	−0.372919
$246$	25.5174	1.62693
$247$	−22.8371	−1.45309
$248$	42.3545	2.68952
$249$	−11.0205	−0.698397
$250$	−2.70928	−0.171350
$251$	15.3197	0.966968	0.483484	−	0.875353i	$-0.339371\pi$
$251$	15.3197	0.966968	0.483484	+	0.875353i	$0.339371\pi$
$252$	5.75872	0.362765
$253$	−2.15676	−0.135594
$254$	6.07223	0.381006
$255$	7.75872	0.485870
$256$	27.6803	1.73002
$257$	4.15676	0.259291	0.129646	−	0.991560i	$-0.458616\pi$
$257$	4.15676	0.259291	0.129646	+	0.991560i	$0.458616\pi$
$258$	−20.5958	−1.28224
$259$	−2.15676	−0.134014
$260$	−23.1773	−1.43739
$261$	1.41855	0.0878061
$262$	−23.5174	−1.45291
$263$	−18.7070	−1.15352	−0.576762	−	0.816912i	$-0.695684\pi$
$263$	−18.7070	−1.15352	−0.576762	+	0.816912i	$0.695684\pi$
$264$	−9.04945	−0.556955
$265$	0.156755	0.00962941
$266$	−15.3730	−0.942578
$267$	−12.8371	−0.785618
$268$	−46.3545	−2.83155
$269$	23.3607	1.42433	0.712163	−	0.702014i	$-0.247716\pi$
$269$	23.3607	1.42433	0.712163	+	0.702014i	$0.247716\pi$
$270$	−2.70928	−0.164881
$271$	−5.57531	−0.338676	−0.169338	−	0.985558i	$-0.554163\pi$
$271$	−5.57531	−0.338676	−0.169338	+	0.985558i	$0.554163\pi$
$272$	107.358	6.50955
$273$	−4.68035	−0.283267
$274$	41.6163	2.51414
$275$	1.00000	0.0603023
$276$	−11.5174	−0.693269
$277$	−26.0144	−1.56305	−0.781526	−	0.623872i	$-0.785558\pi$
$277$	−26.0144	−1.56305	−0.781526	+	0.623872i	$0.785558\pi$
$278$	−23.2495	−1.39441
$279$	−4.68035	−0.280205
$280$	−9.75872	−0.583195
$281$	−9.41855	−0.561864	−0.280932	−	0.959728i	$-0.590643\pi$
$281$	−9.41855	−0.561864	−0.280932	+	0.959728i	$0.590643\pi$
$282$	−12.6803	−0.755104
$283$	14.2413	0.846556	0.423278	−	0.906000i	$-0.360879\pi$
$283$	14.2413	0.846556	0.423278	+	0.906000i	$0.360879\pi$
$284$	−24.9939	−1.48311
$285$	5.26180	0.311682
$286$	11.7587	0.695308
$287$	−10.1568	−0.599534
$288$	−19.3896	−1.14254
$289$	43.1978	2.54105
$290$	−3.84324	−0.225683
$291$	14.6803	0.860577
$292$	−56.0554	−3.28039
$293$	−15.7587	−0.920634	−0.460317	−	0.887754i	$-0.652264\pi$
$293$	−15.7587	−0.920634	−0.460317	+	0.887754i	$0.652264\pi$
$294$	15.8143	0.922310
$295$	6.15676	0.358460
$296$	18.0989	1.05198
$297$	1.00000	0.0580259
$298$	49.0349	2.84052
$299$	9.36069	0.541343
$300$	5.34017	0.308315
$301$	8.19779	0.472513
$302$	−62.1399	−3.57575
$303$	−15.5753	−0.894778
$304$	72.8080	4.17582
$305$	−4.15676	−0.238015
$306$	−21.0205	−1.20166
$307$	−18.9216	−1.07991	−0.539957	−	0.841693i	$-0.681560\pi$
$307$	−18.9216	−1.07991	−0.539957	+	0.841693i	$0.681560\pi$
$308$	5.75872	0.328134
$309$	6.83710	0.388949
$310$	12.6803	0.720195
$311$	−20.8781	−1.18389	−0.591945	−	0.805978i	$-0.701640\pi$
$311$	−20.8781	−1.18389	−0.591945	+	0.805978i	$0.701640\pi$
$312$	39.2762	2.22358
$313$	6.31351	0.356861	0.178430	−	0.983953i	$-0.442898\pi$
$313$	6.31351	0.356861	0.178430	+	0.983953i	$0.442898\pi$
$314$	29.7854	1.68089
$315$	1.07838	0.0607597
$316$	−43.2495	−2.43297
$317$	31.3607	1.76139	0.880696	−	0.473682i	$-0.157075\pi$
$317$	31.3607	1.76139	0.880696	+	0.473682i	$0.157075\pi$
$318$	−0.424694	−0.0238156
$319$	1.41855	0.0794236
$320$	24.8576	1.38958
$321$	6.34017	0.353874
$322$	6.30122	0.351154
$323$	40.8248	2.27155
$324$	5.34017	0.296676
$325$	−4.34017	−0.240749
$326$	17.6742	0.978884
$327$	2.31351	0.127937
$328$	85.2327	4.70619
$329$	5.04718	0.278260
$330$	−2.70928	−0.149141
$331$	19.2039	1.05554	0.527772	−	0.849386i	$-0.323028\pi$
$331$	19.2039	1.05554	0.527772	+	0.849386i	$0.323028\pi$
$332$	−58.8515	−3.22989
$333$	−2.00000	−0.109599
$334$	−5.34632	−0.292537
$335$	−8.68035	−0.474258
$336$	14.9216	0.814041
$337$	13.5031	0.735559	0.367780	−	0.929913i	$-0.380118\pi$
$337$	13.5031	0.735559	0.367780	+	0.929913i	$0.380118\pi$
$338$	−15.8143	−0.860185
$339$	−6.00000	−0.325875
$340$	41.4329	2.24702
$341$	−4.68035	−0.253455
$342$	−14.2557	−0.770857
$343$	−13.8432	−0.747465
$344$	−68.7936	−3.70910
$345$	−2.15676	−0.116116
$346$	−10.1834	−0.547464
$347$	6.34017	0.340358	0.170179	−	0.985413i	$-0.445565\pi$
$347$	6.34017	0.340358	0.170179	+	0.985413i	$0.445565\pi$
$348$	7.57531	0.406079
$349$	16.1568	0.864851	0.432426	−	0.901670i	$-0.357658\pi$
$349$	16.1568	0.864851	0.432426	+	0.901670i	$0.357658\pi$
$350$	−2.92162	−0.156167
$351$	−4.34017	−0.231661
$352$	−19.3896	−1.03347
$353$	−13.2039	−0.702775	−0.351387	−	0.936230i	$-0.614290\pi$
$353$	−13.2039	−0.702775	−0.351387	+	0.936230i	$0.614290\pi$
$354$	−16.6803	−0.886550
$355$	−4.68035	−0.248407
$356$	−68.5523	−3.63327
$357$	8.36683	0.442820
$358$	−41.0472	−2.16941
$359$	3.31965	0.175205	0.0876023	−	0.996156i	$-0.472080\pi$
$359$	3.31965	0.175205	0.0876023	+	0.996156i	$0.472080\pi$
$360$	−9.04945	−0.476948
$361$	8.68649	0.457184
$362$	−13.1050	−0.688786
$363$	1.00000	0.0524864
$364$	−24.9939	−1.31003
$365$	−10.4969	−0.549434
$366$	11.2618	0.588663
$367$	−36.1445	−1.88673	−0.943363	−	0.331762i	$-0.892357\pi$
$367$	−36.1445	−1.88673	−0.943363	+	0.331762i	$0.892357\pi$
$368$	−29.8432	−1.55569
$369$	−9.41855	−0.490310
$370$	5.41855	0.281697
$371$	0.169042	0.00877620
$372$	−24.9939	−1.29587
$373$	−2.81044	−0.145519	−0.0727595	−	0.997350i	$-0.523181\pi$
$373$	−2.81044	−0.145519	−0.0727595	+	0.997350i	$0.523181\pi$
$374$	−21.0205	−1.08695
$375$	1.00000	0.0516398
$376$	−42.3545	−2.18427
$377$	−6.15676	−0.317089
$378$	−2.92162	−0.150272
$379$	−20.0000	−1.02733	−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000	−1.02733	−0.513665	+	0.857991i	$0.671713\pi$
$380$	28.0989	1.44144
$381$	−2.24128	−0.114824
$382$	−6.83710	−0.349817
$383$	33.5585	1.71476	0.857379	−	0.514685i	$-0.172091\pi$
$383$	33.5585	1.71476	0.857379	+	0.514685i	$0.172091\pi$
$384$	−28.5669	−1.45780
$385$	1.07838	0.0549592
$386$	−0.0722347	−0.00367665
$387$	7.60197	0.386430
$388$	78.3956	3.97993
$389$	12.8371	0.650867	0.325433	−	0.945565i	$-0.394490\pi$
$389$	12.8371	0.650867	0.325433	+	0.945565i	$0.394490\pi$
$390$	11.7587	0.595426
$391$	−16.7337	−0.846258
$392$	52.8225	2.66794
$393$	8.68035	0.437866
$394$	−57.2183	−2.88262
$395$	−8.09890	−0.407500
$396$	5.34017	0.268354
$397$	−5.31965	−0.266986	−0.133493	−	0.991050i	$-0.542619\pi$
$397$	−5.31965	−0.266986	−0.133493	+	0.991050i	$0.542619\pi$
$398$	−28.5113	−1.42914
$399$	5.67420	0.284065
$400$	13.8371	0.691855
$401$	2.00000	0.0998752	0.0499376	−	0.998752i	$-0.484098\pi$
$401$	2.00000	0.0998752	0.0499376	+	0.998752i	$0.484098\pi$
$402$	23.5174	1.17294
$403$	20.3135	1.01189
$404$	−83.1748	−4.13810
$405$	1.00000	0.0496904
$406$	−4.14447	−0.205687
$407$	−2.00000	−0.0991363
$408$	−70.2122	−3.47602
$409$	26.1978	1.29540	0.647699	−	0.761897i	$-0.275732\pi$
$409$	26.1978	1.29540	0.647699	+	0.761897i	$0.275732\pi$
$410$	25.5174	1.26022
$411$	−15.3607	−0.757687
$412$	36.5113	1.79878
$413$	6.63931	0.326699
$414$	5.84324	0.287180
$415$	−11.0205	−0.540976
$416$	84.1543	4.12600
$417$	8.58145	0.420235
$418$	−14.2557	−0.697267
$419$	−2.83710	−0.138601	−0.0693007	−	0.997596i	$-0.522077\pi$
$419$	−2.83710	−0.138601	−0.0693007	+	0.997596i	$0.522077\pi$
$420$	5.75872	0.280997
$421$	11.4764	0.559326	0.279663	−	0.960098i	$-0.409777\pi$
$421$	11.4764	0.559326	0.279663	+	0.960098i	$0.409777\pi$
$422$	−25.9421	−1.26284
$423$	4.68035	0.227566
$424$	−1.41855	−0.0688909
$425$	7.75872	0.376353
$426$	12.6803	0.614365
$427$	−4.48255	−0.216926
$428$	33.8576	1.63657
$429$	−4.34017	−0.209546
$430$	−20.5958	−0.993219
$431$	23.5708	1.13536	0.567682	−	0.823248i	$-0.307840\pi$
$431$	23.5708	1.13536	0.567682	+	0.823248i	$0.307840\pi$
$432$	13.8371	0.665738
$433$	−14.9939	−0.720559	−0.360279	−	0.932844i	$-0.617319\pi$
$433$	−14.9939	−0.720559	−0.360279	+	0.932844i	$0.617319\pi$
$434$	13.6742	0.656383
$435$	1.41855	0.0680143
$436$	12.3545	0.591676
$437$	−11.3484	−0.542868
$438$	28.4391	1.35887
$439$	4.77924	0.228101	0.114050	−	0.993475i	$-0.463617\pi$
$439$	4.77924	0.228101	0.114050	+	0.993475i	$0.463617\pi$
$440$	−9.04945	−0.431416
$441$	−5.83710	−0.277957
$442$	91.2327	4.33950
$443$	20.1978	0.959626	0.479813	−	0.877371i	$-0.340704\pi$
$443$	20.1978	0.959626	0.479813	+	0.877371i	$0.340704\pi$
$444$	−10.6803	−0.506867
$445$	−12.8371	−0.608537
$446$	5.84324	0.276686
$447$	−18.0989	−0.856048
$448$	26.8059	1.26646
$449$	−21.5708	−1.01799	−0.508994	−	0.860770i	$-0.669982\pi$
$449$	−21.5708	−1.01799	−0.508994	+	0.860770i	$0.669982\pi$
$450$	−2.70928	−0.127716
$451$	−9.41855	−0.443502
$452$	−32.0410	−1.50708
$453$	22.9360	1.07763
$454$	−26.1711	−1.22827
$455$	−4.68035	−0.219418
$456$	−47.6163	−2.22984
$457$	28.1711	1.31779	0.658895	−	0.752235i	$-0.271024\pi$
$457$	28.1711	1.31779	0.658895	+	0.752235i	$0.271024\pi$
$458$	9.10504	0.425451
$459$	7.75872	0.362146
$460$	−11.5174	−0.537004
$461$	−1.47187	−0.0685520	−0.0342760	−	0.999412i	$-0.510913\pi$
$461$	−1.47187	−0.0685520	−0.0342760	+	0.999412i	$0.510913\pi$
$462$	−2.92162	−0.135926
$463$	−23.2039	−1.07838	−0.539189	−	0.842185i	$-0.681269\pi$
$463$	−23.2039	−1.07838	−0.539189	+	0.842185i	$0.681269\pi$
$464$	19.6286	0.911236
$465$	−4.68035	−0.217046
$466$	6.49693	0.300964
$467$	14.1568	0.655097	0.327548	−	0.944834i	$-0.393778\pi$
$467$	14.1568	0.655097	0.327548	+	0.944834i	$0.393778\pi$
$468$	−23.1773	−1.07137
$469$	−9.36069	−0.432237
$470$	−12.6803	−0.584901
$471$	−10.9939	−0.506570
$472$	−55.7152	−2.56450
$473$	7.60197	0.349539
$474$	21.9421	1.00784
$475$	5.26180	0.241428
$476$	44.6803	2.04792
$477$	0.156755	0.00717734
$478$	19.5174	0.892707
$479$	−13.8432	−0.632514	−0.316257	−	0.948674i	$-0.602426\pi$
$479$	−13.8432	−0.632514	−0.316257	+	0.948674i	$0.602426\pi$
$480$	−19.3896	−0.885011
$481$	8.68035	0.395790
$482$	14.0989	0.642187
$483$	−2.32580	−0.105827
$484$	5.34017	0.242735
$485$	14.6803	0.666600
$486$	−2.70928	−0.122895
$487$	−40.9939	−1.85761	−0.928804	−	0.370570i	$-0.879162\pi$
$487$	−40.9939	−1.85761	−0.928804	+	0.370570i	$0.879162\pi$
$488$	37.6163	1.70281
$489$	−6.52359	−0.295007
$490$	15.8143	0.714418
$491$	34.8371	1.57218	0.786088	−	0.618114i	$-0.212103\pi$
$491$	34.8371	1.57218	0.786088	+	0.618114i	$0.212103\pi$
$492$	−50.2967	−2.26755
$493$	11.0061	0.495692
$494$	61.8720	2.78375
$495$	1.00000	0.0449467
$496$	−64.7624	−2.90792
$497$	−5.04718	−0.226397
$498$	29.8576	1.33795
$499$	15.1506	0.678235	0.339117	−	0.940744i	$-0.389872\pi$
$499$	15.1506	0.678235	0.339117	+	0.940744i	$0.389872\pi$
$500$	5.34017	0.238820
$501$	1.97334	0.0881622
$502$	−41.5052	−1.85247
$503$	−6.65368	−0.296673	−0.148337	−	0.988937i	$-0.547392\pi$
$503$	−6.65368	−0.296673	−0.148337	+	0.988937i	$0.547392\pi$
$504$	−9.75872	−0.434688
$505$	−15.5753	−0.693092
$506$	5.84324	0.259764
$507$	5.83710	0.259235
$508$	−11.9688	−0.531030
$509$	41.3484	1.83274	0.916368	−	0.400337i	$-0.131107\pi$
$509$	41.3484	1.83274	0.916368	+	0.400337i	$0.131107\pi$
$510$	−21.0205	−0.930804
$511$	−11.3197	−0.500752
$512$	−17.8599	−0.789303
$513$	5.26180	0.232314
$514$	−11.2618	−0.496736
$515$	6.83710	0.301279
$516$	40.5958	1.78713
$517$	4.68035	0.205841
$518$	5.84324	0.256737
$519$	3.75872	0.164990
$520$	39.2762	1.72237
$521$	7.67420	0.336213	0.168106	−	0.985769i	$-0.446235\pi$
$521$	7.67420	0.336213	0.168106	+	0.985769i	$0.446235\pi$
$522$	−3.84324	−0.168214
$523$	23.2351	1.01600	0.508001	−	0.861357i	$-0.330385\pi$
$523$	23.2351	1.01600	0.508001	+	0.861357i	$0.330385\pi$
$524$	46.3545	2.02501
$525$	1.07838	0.0470643
$526$	50.6824	2.20986
$527$	−36.3135	−1.58184
$528$	13.8371	0.602183
$529$	−18.3484	−0.797757
$530$	−0.424694	−0.0184475
$531$	6.15676	0.267180
$532$	30.3012	1.31372
$533$	40.8781	1.77063
$534$	34.7792	1.50505
$535$	6.34017	0.274110
$536$	78.5523	3.39294
$537$	15.1506	0.653797
$538$	−63.2905	−2.72865
$539$	−5.83710	−0.251422
$540$	5.34017	0.229804
$541$	−18.0000	−0.773880	−0.386940	−	0.922105i	$-0.626468\pi$
$541$	−18.0000	−0.773880	−0.386940	+	0.922105i	$0.626468\pi$
$542$	15.1050	0.648817
$543$	4.83710	0.207580
$544$	−150.439	−6.45001
$545$	2.31351	0.0990999
$546$	12.6803	0.542669
$547$	−23.0661	−0.986235	−0.493117	−	0.869963i	$-0.664143\pi$
$547$	−23.0661	−0.986235	−0.493117	+	0.869963i	$0.664143\pi$
$548$	−82.0288	−3.50409
$549$	−4.15676	−0.177406
$550$	−2.70928	−0.115524
$551$	7.46412	0.317982
$552$	19.5174	0.830718
$553$	−8.73367	−0.371393
$554$	70.4801	2.99441
$555$	−2.00000	−0.0848953
$556$	45.8264	1.94347
$557$	10.5958	0.448960	0.224480	−	0.974479i	$-0.427932\pi$
$557$	10.5958	0.448960	0.224480	+	0.974479i	$0.427932\pi$
$558$	12.6803	0.536802
$559$	−32.9939	−1.39549
$560$	14.9216	0.630554
$561$	7.75872	0.327574
$562$	25.5174	1.07639
$563$	−36.2122	−1.52616	−0.763080	−	0.646303i	$-0.776314\pi$
$563$	−36.2122	−1.52616	−0.763080	+	0.646303i	$0.776314\pi$
$564$	24.9939	1.05243
$565$	−6.00000	−0.252422
$566$	−38.5835	−1.62179
$567$	1.07838	0.0452876
$568$	42.3545	1.77716
$569$	−27.5753	−1.15602	−0.578008	−	0.816031i	$-0.696170\pi$
$569$	−27.5753	−1.15602	−0.578008	+	0.816031i	$0.696170\pi$
$570$	−14.2557	−0.597104
$571$	−27.9299	−1.16883	−0.584414	−	0.811456i	$-0.698676\pi$
$571$	−27.9299	−1.16883	−0.584414	+	0.811456i	$0.698676\pi$
$572$	−23.1773	−0.969091
$573$	2.52359	0.105425
$574$	27.5174	1.14856
$575$	−2.15676	−0.0899429
$576$	24.8576	1.03573
$577$	41.4017	1.72358	0.861788	−	0.507268i	$-0.169345\pi$
$577$	41.4017	1.72358	0.861788	+	0.507268i	$0.169345\pi$
$578$	−117.035	−4.86800
$579$	0.0266620	0.00110803
$580$	7.57531	0.314547
$581$	−11.8843	−0.493043
$582$	−39.7731	−1.64865
$583$	0.156755	0.00649215
$584$	94.9914	3.93077
$585$	−4.34017	−0.179444
$586$	42.6947	1.76370
$587$	8.48255	0.350112	0.175056	−	0.984558i	$-0.443989\pi$
$587$	8.48255	0.350112	0.175056	+	0.984558i	$0.443989\pi$
$588$	−31.1711	−1.28548
$589$	−24.6270	−1.01474
$590$	−16.6803	−0.686719
$591$	21.1194	0.868737
$592$	−27.6742	−1.13740
$593$	7.56093	0.310490	0.155245	−	0.987876i	$-0.450383\pi$
$593$	7.56093	0.310490	0.155245	+	0.987876i	$0.450383\pi$
$594$	−2.70928	−0.111163
$595$	8.36683	0.343007
$596$	−96.6512	−3.95899
$597$	10.5236	0.430702
$598$	−25.3607	−1.03708
$599$	5.67420	0.231842	0.115921	−	0.993258i	$-0.463018\pi$
$599$	5.67420	0.231842	0.115921	+	0.993258i	$0.463018\pi$
$600$	−9.04945	−0.369442
$601$	−1.31965	−0.0538298	−0.0269149	−	0.999638i	$-0.508568\pi$
$601$	−1.31965	−0.0538298	−0.0269149	+	0.999638i	$0.508568\pi$
$602$	−22.2101	−0.905215
$603$	−8.68035	−0.353491
$604$	122.482	4.98373
$605$	1.00000	0.0406558
$606$	42.1978	1.71417
$607$	−2.24128	−0.0909706	−0.0454853	−	0.998965i	$-0.514483\pi$
$607$	−2.24128	−0.0909706	−0.0454853	+	0.998965i	$0.514483\pi$
$608$	−102.024	−4.13763
$609$	1.52973	0.0619879
$610$	11.2618	0.455977
$611$	−20.3135	−0.821797
$612$	41.4329	1.67483
$613$	42.8638	1.73125	0.865626	−	0.500692i	$-0.166921\pi$
$613$	42.8638	1.73125	0.865626	+	0.500692i	$0.166921\pi$
$614$	51.2639	2.06884
$615$	−9.41855	−0.379793
$616$	−9.75872	−0.393190
$617$	11.3607	0.457364	0.228682	−	0.973501i	$-0.426558\pi$
$617$	11.3607	0.457364	0.228682	+	0.973501i	$0.426558\pi$
$618$	−18.5236	−0.745128
$619$	−45.1917	−1.81641	−0.908203	−	0.418530i	$-0.862545\pi$
$619$	−45.1917	−1.81641	−0.908203	+	0.418530i	$0.862545\pi$
$620$	−24.9939	−1.00378
$621$	−2.15676	−0.0865476
$622$	56.5646	2.26803
$623$	−13.8432	−0.554618
$624$	−60.0554	−2.40414
$625$	1.00000	0.0400000
$626$	−17.1050	−0.683655
$627$	5.26180	0.210136
$628$	−58.7091	−2.34275
$629$	−15.5174	−0.618721
$630$	−2.92162	−0.116400
$631$	−9.78992	−0.389731	−0.194865	−	0.980830i	$-0.562427\pi$
$631$	−9.78992	−0.389731	−0.194865	+	0.980830i	$0.562427\pi$
$632$	73.2905	2.91534
$633$	9.57531	0.380584
$634$	−84.9647	−3.37438
$635$	−2.24128	−0.0889423
$636$	0.837101	0.0331932
$637$	25.3340	1.00377
$638$	−3.84324	−0.152156
$639$	−4.68035	−0.185152
$640$	−28.5669	−1.12921
$641$	0.210079	0.00829764	0.00414882	−	0.999991i	$-0.498679\pi$
$641$	0.210079	0.00829764	0.00414882	+	0.999991i	$0.498679\pi$
$642$	−17.1773	−0.677933
$643$	14.5236	0.572754	0.286377	−	0.958117i	$-0.407549\pi$
$643$	14.5236	0.572754	0.286377	+	0.958117i	$0.407549\pi$
$644$	−12.4202	−0.489423
$645$	7.60197	0.299327
$646$	−110.606	−4.35172
$647$	15.4641	0.607957	0.303979	−	0.952679i	$-0.401685\pi$
$647$	15.4641	0.607957	0.303979	+	0.952679i	$0.401685\pi$
$648$	−9.04945	−0.355496
$649$	6.15676	0.241674
$650$	11.7587	0.461215
$651$	−5.04718	−0.197815
$652$	−34.8371	−1.36433
$653$	−17.8310	−0.697779	−0.348890	−	0.937164i	$-0.613441\pi$
$653$	−17.8310	−0.697779	−0.348890	+	0.937164i	$0.613441\pi$
$654$	−6.26794	−0.245096
$655$	8.68035	0.339169
$656$	−130.325	−5.08835
$657$	−10.4969	−0.409524
$658$	−13.6742	−0.533076
$659$	−32.3135	−1.25876	−0.629378	−	0.777099i	$-0.716690\pi$
$659$	−32.3135	−1.25876	−0.629378	+	0.777099i	$0.716690\pi$
$660$	5.34017	0.207866
$661$	−5.68649	−0.221179	−0.110589	−	0.993866i	$-0.535274\pi$
$661$	−5.68649	−0.221179	−0.110589	+	0.993866i	$0.535274\pi$
$662$	−52.0288	−2.02215
$663$	−33.6742	−1.30780
$664$	99.7296	3.87026
$665$	5.67420	0.220036
$666$	5.41855	0.209965
$667$	−3.05947	−0.118463
$668$	10.5380	0.407726
$669$	−2.15676	−0.0833850
$670$	23.5174	0.908558
$671$	−4.15676	−0.160470
$672$	−20.9093	−0.806595
$673$	−21.0205	−0.810281	−0.405141	−	0.914254i	$-0.632777\pi$
$673$	−21.0205	−0.810281	−0.405141	+	0.914254i	$0.632777\pi$
$674$	−36.5835	−1.40915
$675$	1.00000	0.0384900
$676$	31.1711	1.19889
$677$	36.7526	1.41252	0.706258	−	0.707954i	$-0.250382\pi$
$677$	36.7526	1.41252	0.706258	+	0.707954i	$0.250382\pi$
$678$	16.2557	0.624295
$679$	15.8310	0.607536
$680$	−70.2122	−2.69251
$681$	9.65983	0.370165
$682$	12.6803	0.485556
$683$	−17.3074	−0.662248	−0.331124	−	0.943587i	$-0.607428\pi$
$683$	−17.3074	−0.662248	−0.331124	+	0.943587i	$0.607428\pi$
$684$	28.0989	1.07439
$685$	−15.3607	−0.586902
$686$	37.5052	1.43195
$687$	−3.36069	−0.128218
$688$	105.189	4.01030
$689$	−0.680346	−0.0259191
$690$	5.84324	0.222449
$691$	17.6742	0.672358	0.336179	−	0.941798i	$-0.390865\pi$
$691$	17.6742	0.672358	0.336179	+	0.941798i	$0.390865\pi$
$692$	20.0722	0.763032
$693$	1.07838	0.0409642
$694$	−17.1773	−0.652040
$695$	8.58145	0.325513
$696$	−12.8371	−0.486589
$697$	−73.0759	−2.76795
$698$	−43.7731	−1.65684
$699$	−2.39803	−0.0907019
$700$	5.75872	0.217659
$701$	−17.1050	−0.646048	−0.323024	−	0.946391i	$-0.604700\pi$
$701$	−17.1050	−0.646048	−0.323024	+	0.946391i	$0.604700\pi$
$702$	11.7587	0.443804
$703$	−10.5236	−0.396905
$704$	24.8576	0.936857
$705$	4.68035	0.176272
$706$	35.7731	1.34634
$707$	−16.7961	−0.631681
$708$	32.8781	1.23564
$709$	25.1506	0.944551	0.472276	−	0.881451i	$-0.343433\pi$
$709$	25.1506	0.944551	0.472276	+	0.881451i	$0.343433\pi$
$710$	12.6803	0.475885
$711$	−8.09890	−0.303732
$712$	116.169	4.35361
$713$	10.0944	0.378037
$714$	−22.6681	−0.848331
$715$	−4.34017	−0.162313
$716$	80.9069	3.02363
$717$	−7.20394	−0.269036
$718$	−8.99386	−0.335648
$719$	−1.78992	−0.0667528	−0.0333764	−	0.999443i	$-0.510626\pi$
$719$	−1.78992	−0.0667528	−0.0333764	+	0.999443i	$0.510626\pi$
$720$	13.8371	0.515678
$721$	7.37298	0.274584
$722$	−23.5341	−0.875848
$723$	−5.20394	−0.193536
$724$	25.8310	0.960000
$725$	1.41855	0.0526837
$726$	−2.70928	−0.100551
$727$	25.9877	0.963831	0.481915	−	0.876218i	$-0.339941\pi$
$727$	25.9877	0.963831	0.481915	+	0.876218i	$0.339941\pi$
$728$	42.3545	1.56976
$729$	1.00000	0.0370370
$730$	28.4391	1.05258
$731$	58.9816	2.18151
$732$	−22.1978	−0.820454
$733$	−41.0205	−1.51513	−0.757564	−	0.652761i	$-0.773610\pi$
$733$	−41.0205	−1.51513	−0.757564	+	0.652761i	$0.773610\pi$
$734$	97.9253	3.61449
$735$	−5.83710	−0.215305
$736$	41.8187	1.54146
$737$	−8.68035	−0.319745
$738$	25.5174	0.939310
$739$	−47.6163	−1.75160	−0.875798	−	0.482678i	$-0.839664\pi$
$739$	−47.6163	−1.75160	−0.875798	+	0.482678i	$0.839664\pi$
$740$	−10.6803	−0.392617
$741$	−22.8371	−0.838942
$742$	−0.457980	−0.0168130
$743$	0.550252	0.0201868	0.0100934	−	0.999949i	$-0.496787\pi$
$743$	0.550252	0.0201868	0.0100934	+	0.999949i	$0.496787\pi$
$744$	42.3545	1.55279
$745$	−18.0989	−0.663092
$746$	7.61425	0.278778
$747$	−11.0205	−0.403220
$748$	41.4329	1.51494
$749$	6.83710	0.249822
$750$	−2.70928	−0.0989287
$751$	41.5585	1.51649	0.758245	−	0.651969i	$-0.226057\pi$
$751$	41.5585	1.51649	0.758245	+	0.651969i	$0.226057\pi$
$752$	64.7624	2.36164
$753$	15.3197	0.558279
$754$	16.6803	0.607462
$755$	22.9360	0.834726
$756$	5.75872	0.209443
$757$	1.31965	0.0479636	0.0239818	−	0.999712i	$-0.492366\pi$
$757$	1.31965	0.0479636	0.0239818	+	0.999712i	$0.492366\pi$
$758$	54.1855	1.96811
$759$	−2.15676	−0.0782853
$760$	−47.6163	−1.72723
$761$	−2.21461	−0.0802797	−0.0401399	−	0.999194i	$-0.512780\pi$
$761$	−2.21461	−0.0802797	−0.0401399	+	0.999194i	$0.512780\pi$
$762$	6.07223	0.219974
$763$	2.49484	0.0903192
$764$	13.4764	0.487559
$765$	7.75872	0.280517
$766$	−90.9192	−3.28504
$767$	−26.7214	−0.964853
$768$	27.6803	0.998828
$769$	−14.3668	−0.518081	−0.259041	−	0.965866i	$-0.583406\pi$
$769$	−14.3668	−0.518081	−0.259041	+	0.965866i	$0.583406\pi$
$770$	−2.92162	−0.105288
$771$	4.15676	0.149702
$772$	0.142380	0.00512436
$773$	40.1568	1.44434	0.722169	−	0.691717i	$-0.243145\pi$
$773$	40.1568	1.44434	0.722169	+	0.691717i	$0.243145\pi$
$774$	−20.5958	−0.740302
$775$	−4.68035	−0.168123
$776$	−132.849	−4.76900
$777$	−2.15676	−0.0773732
$778$	−34.7792	−1.24690
$779$	−49.5585	−1.77562
$780$	−23.1773	−0.829880
$781$	−4.68035	−0.167476
$782$	45.3361	1.62122
$783$	1.41855	0.0506949
$784$	−80.7686	−2.88459
$785$	−10.9939	−0.392388
$786$	−23.5174	−0.838840
$787$	49.5897	1.76768	0.883841	−	0.467788i	$-0.154949\pi$
$787$	49.5897	1.76768	0.883841	+	0.467788i	$0.154949\pi$
$788$	112.781	4.01767
$789$	−18.7070	−0.665987
$790$	21.9421	0.780666
$791$	−6.47027	−0.230056
$792$	−9.04945	−0.321558
$793$	18.0410	0.640656
$794$	14.4124	0.511477
$795$	0.156755	0.00555954
$796$	56.1978	1.99188
$797$	−46.7091	−1.65452	−0.827261	−	0.561818i	$-0.810102\pi$
$797$	−46.7091	−1.65452	−0.827261	+	0.561818i	$0.810102\pi$
$798$	−15.3730	−0.544198
$799$	36.3135	1.28468
$800$	−19.3896	−0.685527
$801$	−12.8371	−0.453577
$802$	−5.41855	−0.191336
$803$	−10.4969	−0.370429
$804$	−46.3545	−1.63480
$805$	−2.32580	−0.0819736
$806$	−55.0349	−1.93852
$807$	23.3607	0.822335
$808$	140.948	4.95853
$809$	−18.5814	−0.653289	−0.326644	−	0.945147i	$-0.605918\pi$
$809$	−18.5814	−0.653289	−0.326644	+	0.945147i	$0.605918\pi$
$810$	−2.70928	−0.0951942
$811$	27.3028	0.958732	0.479366	−	0.877615i	$-0.340867\pi$
$811$	27.3028	0.958732	0.479366	+	0.877615i	$0.340867\pi$
$812$	8.16904	0.286677
$813$	−5.57531	−0.195535
$814$	5.41855	0.189920
$815$	−6.52359	−0.228511
$816$	107.358	3.75829
$817$	40.0000	1.39942
$818$	−70.9770	−2.48165
$819$	−4.68035	−0.163545
$820$	−50.2967	−1.75644
$821$	−31.2085	−1.08918	−0.544592	−	0.838701i	$-0.683315\pi$
$821$	−31.2085	−1.08918	−0.544592	+	0.838701i	$0.683315\pi$
$822$	41.6163	1.45154
$823$	−50.1855	−1.74936	−0.874678	−	0.484704i	$-0.838927\pi$
$823$	−50.1855	−1.74936	−0.874678	+	0.484704i	$0.838927\pi$
$824$	−61.8720	−2.15541
$825$	1.00000	0.0348155
$826$	−17.9877	−0.625873
$827$	27.3874	0.952352	0.476176	−	0.879350i	$-0.342023\pi$
$827$	27.3874	0.952352	0.476176	+	0.879350i	$0.342023\pi$
$828$	−11.5174	−0.400259
$829$	−26.1978	−0.909887	−0.454943	−	0.890520i	$-0.650341\pi$
$829$	−26.1978	−0.909887	−0.454943	+	0.890520i	$0.650341\pi$
$830$	29.8576	1.03637
$831$	−26.0144	−0.902429
$832$	−107.886	−3.74029
$833$	−45.2885	−1.56915
$834$	−23.2495	−0.805065
$835$	1.97334	0.0682902
$836$	28.0989	0.971821
$837$	−4.68035	−0.161776
$838$	7.68649	0.265525
$839$	7.20394	0.248708	0.124354	−	0.992238i	$-0.460314\pi$
$839$	7.20394	0.248708	0.124354	+	0.992238i	$0.460314\pi$
$840$	−9.75872	−0.336708
$841$	−26.9877	−0.930611
$842$	−31.0928	−1.07153
$843$	−9.41855	−0.324392
$844$	51.1338	1.76010
$845$	5.83710	0.200802
$846$	−12.6803	−0.435959
$847$	1.07838	0.0370535
$848$	2.16904	0.0744852
$849$	14.2413	0.488759
$850$	−21.0205	−0.720998
$851$	4.31351	0.147865
$852$	−24.9939	−0.856275
$853$	39.8043	1.36287	0.681437	−	0.731877i	$-0.261356\pi$
$853$	39.8043	1.36287	0.681437	+	0.731877i	$0.261356\pi$
$854$	12.1445	0.415575
$855$	5.26180	0.179950
$856$	−57.3751	−1.96104
$857$	−36.9504	−1.26220	−0.631100	−	0.775701i	$-0.717396\pi$
$857$	−36.9504	−1.26220	−0.631100	+	0.775701i	$0.717396\pi$
$858$	11.7587	0.401436
$859$	57.5052	1.96205	0.981025	−	0.193879i	$-0.0621070\pi$
$859$	57.5052	1.96205	0.981025	+	0.193879i	$0.0621070\pi$
$860$	40.5958	1.38431
$861$	−10.1568	−0.346141
$862$	−63.8597	−2.17507
$863$	−1.89657	−0.0645599	−0.0322800	−	0.999479i	$-0.510277\pi$
$863$	−1.89657	−0.0645599	−0.0322800	+	0.999479i	$0.510277\pi$
$864$	−19.3896	−0.659648
$865$	3.75872	0.127800
$866$	40.6225	1.38041
$867$	43.1978	1.46707
$868$	−26.9528	−0.914838
$869$	−8.09890	−0.274736
$870$	−3.84324	−0.130298
$871$	37.6742	1.27654
$872$	−20.9360	−0.708982
$873$	14.6803	0.496854
$874$	30.7460	1.04000
$875$	1.07838	0.0364558
$876$	−56.0554	−1.89394
$877$	32.5380	1.09873	0.549365	−	0.835583i	$-0.314870\pi$
$877$	32.5380	1.09873	0.549365	+	0.835583i	$0.314870\pi$
$878$	−12.9483	−0.436983
$879$	−15.7587	−0.531529
$880$	13.8371	0.466449
$881$	18.1978	0.613099	0.306550	−	0.951855i	$-0.400825\pi$
$881$	18.1978	0.613099	0.306550	+	0.951855i	$0.400825\pi$
$882$	15.8143	0.532496
$883$	36.3956	1.22481	0.612405	−	0.790545i	$-0.290202\pi$
$883$	36.3956	1.22481	0.612405	+	0.790545i	$0.290202\pi$
$884$	−179.826	−6.04821
$885$	6.15676	0.206957
$886$	−54.7214	−1.83840
$887$	27.8699	0.935780	0.467890	−	0.883787i	$-0.345014\pi$
$887$	27.8699	0.935780	0.467890	+	0.883787i	$0.345014\pi$
$888$	18.0989	0.607359
$889$	−2.41694	−0.0810616
$890$	34.7792	1.16580
$891$	1.00000	0.0335013
$892$	−11.5174	−0.385633
$893$	24.6270	0.824112
$894$	49.0349	1.63997
$895$	15.1506	0.506429
$896$	−30.8059	−1.02915
$897$	9.36069	0.312544
$898$	58.4412	1.95021
$899$	−6.63931	−0.221433
$900$	5.34017	0.178006
$901$	1.21622	0.0405182
$902$	25.5174	0.849638
$903$	8.19779	0.272805
$904$	54.2967	1.80588
$905$	4.83710	0.160791
$906$	−62.1399	−2.06446
$907$	−27.9376	−0.927653	−0.463826	−	0.885926i	$-0.653524\pi$
$907$	−27.9376	−0.927653	−0.463826	+	0.885926i	$0.653524\pi$
$908$	51.5851	1.71191
$909$	−15.5753	−0.516600
$910$	12.6803	0.420349
$911$	−11.8843	−0.393744	−0.196872	−	0.980429i	$-0.563078\pi$
$911$	−11.8843	−0.393744	−0.196872	+	0.980429i	$0.563078\pi$
$912$	72.8080	2.41091
$913$	−11.0205	−0.364726
$914$	−76.3234	−2.52455
$915$	−4.15676	−0.137418
$916$	−17.9467	−0.592975
$917$	9.36069	0.309117
$918$	−21.0205	−0.693781
$919$	−45.6041	−1.50434	−0.752170	−	0.658970i	$-0.770993\pi$
$919$	−45.6041	−1.50434	−0.752170	+	0.658970i	$0.770993\pi$
$920$	19.5174	0.643471
$921$	−18.9216	−0.623489
$922$	3.98771	0.131328
$923$	20.3135	0.668627
$924$	5.75872	0.189448
$925$	−2.00000	−0.0657596
$926$	62.8659	2.06590
$927$	6.83710	0.224560
$928$	−27.5052	−0.902901
$929$	−25.1506	−0.825165	−0.412582	−	0.910920i	$-0.635373\pi$
$929$	−25.1506	−0.825165	−0.412582	+	0.910920i	$0.635373\pi$
$930$	12.6803	0.415805
$931$	−30.7136	−1.00660
$932$	−12.8059	−0.419471
$933$	−20.8781	−0.683520
$934$	−38.3545	−1.25500
$935$	7.75872	0.253737
$936$	39.2762	1.28378
$937$	5.33403	0.174255	0.0871276	−	0.996197i	$-0.472231\pi$
$937$	5.33403	0.174255	0.0871276	+	0.996197i	$0.472231\pi$
$938$	25.3607	0.828056
$939$	6.31351	0.206034
$940$	24.9939	0.815210
$941$	56.8203	1.85229	0.926144	−	0.377170i	$-0.123103\pi$
$941$	56.8203	1.85229	0.926144	+	0.377170i	$0.123103\pi$
$942$	29.7854	0.970460
$943$	20.3135	0.661499
$944$	85.1917	2.77275
$945$	1.07838	0.0350796
$946$	−20.5958	−0.669628
$947$	−20.9939	−0.682209	−0.341104	−	0.940025i	$-0.610801\pi$
$947$	−20.9939	−0.682209	−0.341104	+	0.940025i	$0.610801\pi$
$948$	−43.2495	−1.40468
$949$	45.5585	1.47889
$950$	−14.2557	−0.462514
$951$	31.3607	1.01694
$952$	−75.7152	−2.45395
$953$	−25.2351	−0.817446	−0.408723	−	0.912658i	$-0.634026\pi$
$953$	−25.2351	−0.817446	−0.408723	+	0.912658i	$0.634026\pi$
$954$	−0.424694	−0.0137500
$955$	2.52359	0.0816615
$956$	−38.4703	−1.24422
$957$	1.41855	0.0458552
$958$	37.5052	1.21174
$959$	−16.5646	−0.534900
$960$	24.8576	0.802276
$961$	−9.09436	−0.293367
$962$	−23.5174	−0.758233
$963$	6.34017	0.204309
$964$	−27.7899	−0.895053
$965$	0.0266620	0.000858280 0
$966$	6.30122	0.202739
$967$	13.1317	0.422287	0.211144	−	0.977455i	$-0.432281\pi$
$967$	13.1317	0.422287	0.211144	+	0.977455i	$0.432281\pi$
$968$	−9.04945	−0.290860
$969$	40.8248	1.31148
$970$	−39.7731	−1.27704
$971$	8.94053	0.286915	0.143458	−	0.989656i	$-0.454178\pi$
$971$	8.94053	0.286915	0.143458	+	0.989656i	$0.454178\pi$
$972$	5.34017	0.171286
$973$	9.25404	0.296671
$974$	111.064	3.55871
$975$	−4.34017	−0.138997
$976$	−57.5174	−1.84109
$977$	50.3956	1.61230	0.806149	−	0.591713i	$-0.201548\pi$
$977$	50.3956	1.61230	0.806149	+	0.591713i	$0.201548\pi$
$978$	17.6742	0.565159
$979$	−12.8371	−0.410276
$980$	−31.1711	−0.995725
$981$	2.31351	0.0738647
$982$	−94.3833	−3.01189
$983$	−32.1978	−1.02695	−0.513475	−	0.858105i	$-0.671642\pi$
$983$	−32.1978	−1.02695	−0.513475	+	0.858105i	$0.671642\pi$
$984$	85.2327	2.71712
$985$	21.1194	0.672921
$986$	−29.8187	−0.949620
$987$	5.04718	0.160654
$988$	−121.954	−3.87988
$989$	−16.3956	−0.521349
$990$	−2.70928	−0.0861064
$991$	−46.7747	−1.48585	−0.742924	−	0.669376i	$-0.766562\pi$
$991$	−46.7747	−1.48585	−0.742924	+	0.669376i	$0.766562\pi$
$992$	90.7501	2.88132
$993$	19.2039	0.609419
$994$	13.6742	0.433719
$995$	10.5236	0.333620
$996$	−58.8515	−1.86478
$997$	38.2122	1.21019	0.605096	−	0.796153i	$-0.293135\pi$
$997$	38.2122	1.21019	0.605096	+	0.796153i	$0.293135\pi$
$998$	−41.0472	−1.29933
$999$	−2.00000	−0.0632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.2.a.c.1.1	✓	3
3.2	odd	2		495.2.a.e.1.3		3
4.3	odd	2		2640.2.a.be.1.2		3
5.2	odd	4		825.2.c.g.199.1		6
5.3	odd	4		825.2.c.g.199.6		6
5.4	even	2		825.2.a.k.1.3		3
7.6	odd	2		8085.2.a.bk.1.1		3
11.10	odd	2		1815.2.a.m.1.3		3
12.11	even	2		7920.2.a.cj.1.2		3
15.2	even	4		2475.2.c.r.199.6		6
15.8	even	4		2475.2.c.r.199.1		6
15.14	odd	2		2475.2.a.bb.1.1		3
33.32	even	2		5445.2.a.z.1.1		3
55.54	odd	2		9075.2.a.cf.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.a.c.1.1	✓	3	1.1	even	1	trivial
495.2.a.e.1.3		3	3.2	odd	2
825.2.a.k.1.3		3	5.4	even	2
825.2.c.g.199.1		6	5.2	odd	4
825.2.c.g.199.6		6	5.3	odd	4
1815.2.a.m.1.3		3	11.10	odd	2
2475.2.a.bb.1.1		3	15.14	odd	2
2475.2.c.r.199.1		6	15.8	even	4
2475.2.c.r.199.6		6	15.2	even	4
2640.2.a.be.1.2		3	4.3	odd	2
5445.2.a.z.1.1		3	33.32	even	2
7920.2.a.cj.1.2		3	12.11	even	2
8085.2.a.bk.1.1		3	7.6	odd	2
9075.2.a.cf.1.1		3	55.54	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:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	165.a (trivial)

\(f(q)\)	\(=\)	\(q-2.70928 q^{2} +1.00000 q^{3} +5.34017 q^{4} +1.00000 q^{5} -2.70928 q^{6} +1.07838 q^{7} -9.04945 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.70928 q^{2} +1.00000 q^{3} +5.34017 q^{4} +1.00000 q^{5} -2.70928 q^{6} +1.07838 q^{7} -9.04945 q^{8} +1.00000 q^{9} -2.70928 q^{10} +1.00000 q^{11} +5.34017 q^{12} -4.34017 q^{13} -2.92162 q^{14} +1.00000 q^{15} +13.8371 q^{16} +7.75872 q^{17} -2.70928 q^{18} +5.26180 q^{19} +5.34017 q^{20} +1.07838 q^{21} -2.70928 q^{22} -2.15676 q^{23} -9.04945 q^{24} +1.00000 q^{25} +11.7587 q^{26} +1.00000 q^{27} +5.75872 q^{28} +1.41855 q^{29} -2.70928 q^{30} -4.68035 q^{31} -19.3896 q^{32} +1.00000 q^{33} -21.0205 q^{34} +1.07838 q^{35} +5.34017 q^{36} -2.00000 q^{37} -14.2557 q^{38} -4.34017 q^{39} -9.04945 q^{40} -9.41855 q^{41} -2.92162 q^{42} +7.60197 q^{43} +5.34017 q^{44} +1.00000 q^{45} +5.84324 q^{46} +4.68035 q^{47} +13.8371 q^{48} -5.83710 q^{49} -2.70928 q^{50} +7.75872 q^{51} -23.1773 q^{52} +0.156755 q^{53} -2.70928 q^{54} +1.00000 q^{55} -9.75872 q^{56} +5.26180 q^{57} -3.84324 q^{58} +6.15676 q^{59} +5.34017 q^{60} -4.15676 q^{61} +12.6803 q^{62} +1.07838 q^{63} +24.8576 q^{64} -4.34017 q^{65} -2.70928 q^{66} -8.68035 q^{67} +41.4329 q^{68} -2.15676 q^{69} -2.92162 q^{70} -4.68035 q^{71} -9.04945 q^{72} -10.4969 q^{73} +5.41855 q^{74} +1.00000 q^{75} +28.0989 q^{76} +1.07838 q^{77} +11.7587 q^{78} -8.09890 q^{79} +13.8371 q^{80} +1.00000 q^{81} +25.5174 q^{82} -11.0205 q^{83} +5.75872 q^{84} +7.75872 q^{85} -20.5958 q^{86} +1.41855 q^{87} -9.04945 q^{88} -12.8371 q^{89} -2.70928 q^{90} -4.68035 q^{91} -11.5174 q^{92} -4.68035 q^{93} -12.6803 q^{94} +5.26180 q^{95} -19.3896 q^{96} +14.6803 q^{97} +15.8143 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - q^{2} + 3 q^{3} + 5 q^{4} + 3 q^{5} - q^{6} - 9 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - q^2 + 3 * q^3 + 5 * q^4 + 3 * q^5 - q^6 - 9 * q^8 + 3 * q^9	\( 3 q - q^{2} + 3 q^{3} + 5 q^{4} + 3 q^{5} - q^{6} - 9 q^{8} + 3 q^{9} - q^{10} + 3 q^{11} + 5 q^{12} - 2 q^{13} - 12 q^{14} + 3 q^{15} + 13 q^{16} - 2 q^{17} - q^{18} + 8 q^{19} + 5 q^{20} - q^{22} - 9 q^{24} + 3 q^{25} + 10 q^{26} + 3 q^{27} - 8 q^{28} - 10 q^{29} - q^{30} + 8 q^{31} - 29 q^{32} + 3 q^{33} - 30 q^{34} + 5 q^{36} - 6 q^{37} - 2 q^{39} - 9 q^{40} - 14 q^{41} - 12 q^{42} + 4 q^{43} + 5 q^{44} + 3 q^{45} + 24 q^{46} - 8 q^{47} + 13 q^{48} + 11 q^{49} - q^{50} - 2 q^{51} - 30 q^{52} - 6 q^{53} - q^{54} + 3 q^{55} - 4 q^{56} + 8 q^{57} - 18 q^{58} + 12 q^{59} + 5 q^{60} - 6 q^{61} + 16 q^{62} + 13 q^{64} - 2 q^{65} - q^{66} - 4 q^{67} + 42 q^{68} - 12 q^{70} + 8 q^{71} - 9 q^{72} - 14 q^{73} + 2 q^{74} + 3 q^{75} + 48 q^{76} + 10 q^{78} + 12 q^{79} + 13 q^{80} + 3 q^{81} + 26 q^{82} - 8 q^{84} - 2 q^{85} - 8 q^{86} - 10 q^{87} - 9 q^{88} - 10 q^{89} - q^{90} + 8 q^{91} + 16 q^{92} + 8 q^{93} - 16 q^{94} + 8 q^{95} - 29 q^{96} + 22 q^{97} + 39 q^{98} + 3 q^{99}+O(q^{100}) \) 3 * q - q^2 + 3 * q^3 + 5 * q^4 + 3 * q^5 - q^6 - 9 * q^8 + 3 * q^9 - q^10 + 3 * q^11 + 5 * q^12 - 2 * q^13 - 12 * q^14 + 3 * q^15 + 13 * q^16 - 2 * q^17 - q^18 + 8 * q^19 + 5 * q^20 - q^22 - 9 * q^24 + 3 * q^25 + 10 * q^26 + 3 * q^27 - 8 * q^28 - 10 * q^29 - q^30 + 8 * q^31 - 29 * q^32 + 3 * q^33 - 30 * q^34 + 5 * q^36 - 6 * q^37 - 2 * q^39 - 9 * q^40 - 14 * q^41 - 12 * q^42 + 4 * q^43 + 5 * q^44 + 3 * q^45 + 24 * q^46 - 8 * q^47 + 13 * q^48 + 11 * q^49 - q^50 - 2 * q^51 - 30 * q^52 - 6 * q^53 - q^54 + 3 * q^55 - 4 * q^56 + 8 * q^57 - 18 * q^58 + 12 * q^59 + 5 * q^60 - 6 * q^61 + 16 * q^62 + 13 * q^64 - 2 * q^65 - q^66 - 4 * q^67 + 42 * q^68 - 12 * q^70 + 8 * q^71 - 9 * q^72 - 14 * q^73 + 2 * q^74 + 3 * q^75 + 48 * q^76 + 10 * q^78 + 12 * q^79 + 13 * q^80 + 3 * q^81 + 26 * q^82 - 8 * q^84 - 2 * q^85 - 8 * q^86 - 10 * q^87 - 9 * q^88 - 10 * q^89 - q^90 + 8 * q^91 + 16 * q^92 + 8 * q^93 - 16 * q^94 + 8 * q^95 - 29 * q^96 + 22 * q^97 + 39 * q^98 + 3 * q^99

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