LMFDB - Embedded newform 6018.2.a.v.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6018,2,Mod(1,6018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6018, 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("6018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6018 = 2 \cdot 3 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6018.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:	$48.0539719364$
Analytic rank:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 3x^{8} - 21x^{7} + 42x^{6} + 121x^{5} - 127x^{4} - 141x^{3} + 27x^{2} + 26x - 1 $ x^9 - 3x^8 - 21x^7 + 42x^6 + 121x^5 - 127x^4 - 141x^3 + 27x^2 + 26x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-0.625332$ of defining polynomial
Character	$\chi$	$=$	6018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.62533 q^{5} +1.00000 q^{6} -4.68222 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.62533 q^{5} +1.00000 q^{6} -4.68222 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.62533 q^{10} +3.50360 q^{11} -1.00000 q^{12} +0.306705 q^{13} +4.68222 q^{14} -1.62533 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +7.98942 q^{19} +1.62533 q^{20} +4.68222 q^{21} -3.50360 q^{22} -0.450099 q^{23} +1.00000 q^{24} -2.35830 q^{25} -0.306705 q^{26} -1.00000 q^{27} -4.68222 q^{28} -2.74870 q^{29} +1.62533 q^{30} -9.09300 q^{31} -1.00000 q^{32} -3.50360 q^{33} +1.00000 q^{34} -7.61016 q^{35} +1.00000 q^{36} -0.508458 q^{37} -7.98942 q^{38} -0.306705 q^{39} -1.62533 q^{40} -3.01170 q^{41} -4.68222 q^{42} +5.17673 q^{43} +3.50360 q^{44} +1.62533 q^{45} +0.450099 q^{46} -13.6700 q^{47} -1.00000 q^{48} +14.9232 q^{49} +2.35830 q^{50} +1.00000 q^{51} +0.306705 q^{52} +1.19923 q^{53} +1.00000 q^{54} +5.69451 q^{55} +4.68222 q^{56} -7.98942 q^{57} +2.74870 q^{58} -1.00000 q^{59} -1.62533 q^{60} +5.58904 q^{61} +9.09300 q^{62} -4.68222 q^{63} +1.00000 q^{64} +0.498498 q^{65} +3.50360 q^{66} +2.15065 q^{67} -1.00000 q^{68} +0.450099 q^{69} +7.61016 q^{70} +1.51984 q^{71} -1.00000 q^{72} -3.09174 q^{73} +0.508458 q^{74} +2.35830 q^{75} +7.98942 q^{76} -16.4046 q^{77} +0.306705 q^{78} -1.76390 q^{79} +1.62533 q^{80} +1.00000 q^{81} +3.01170 q^{82} -5.70445 q^{83} +4.68222 q^{84} -1.62533 q^{85} -5.17673 q^{86} +2.74870 q^{87} -3.50360 q^{88} +14.6943 q^{89} -1.62533 q^{90} -1.43606 q^{91} -0.450099 q^{92} +9.09300 q^{93} +13.6700 q^{94} +12.9855 q^{95} +1.00000 q^{96} +17.0010 q^{97} -14.9232 q^{98} +3.50360 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 9 q^{2} - 9 q^{3} + 9 q^{4} + 6 q^{5} + 9 q^{6} - 11 q^{7} - 9 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q - 9 * q^2 - 9 * q^3 + 9 * q^4 + 6 * q^5 + 9 * q^6 - 11 * q^7 - 9 * q^8 + 9 * q^9	\( 9 q - 9 q^{2} - 9 q^{3} + 9 q^{4} + 6 q^{5} + 9 q^{6} - 11 q^{7} - 9 q^{8} + 9 q^{9} - 6 q^{10} + q^{11} - 9 q^{12} + 4 q^{13} + 11 q^{14} - 6 q^{15} + 9 q^{16} - 9 q^{17} - 9 q^{18} - 13 q^{19} + 6 q^{20} + 11 q^{21} - q^{22} - 6 q^{23} + 9 q^{24} + 9 q^{25} - 4 q^{26} - 9 q^{27} - 11 q^{28} + 10 q^{29} + 6 q^{30} + q^{31} - 9 q^{32} - q^{33} + 9 q^{34} + 6 q^{35} + 9 q^{36} - 2 q^{37} + 13 q^{38} - 4 q^{39} - 6 q^{40} + 20 q^{41} - 11 q^{42} - 17 q^{43} + q^{44} + 6 q^{45} + 6 q^{46} + 4 q^{47} - 9 q^{48} + 2 q^{49} - 9 q^{50} + 9 q^{51} + 4 q^{52} + 16 q^{53} + 9 q^{54} - 17 q^{55} + 11 q^{56} + 13 q^{57} - 10 q^{58} - 9 q^{59} - 6 q^{60} - 9 q^{61} - q^{62} - 11 q^{63} + 9 q^{64} + q^{66} - 8 q^{67} - 9 q^{68} + 6 q^{69} - 6 q^{70} - 8 q^{71} - 9 q^{72} - 20 q^{73} + 2 q^{74} - 9 q^{75} - 13 q^{76} - 32 q^{77} + 4 q^{78} - 29 q^{79} + 6 q^{80} + 9 q^{81} - 20 q^{82} - 16 q^{83} + 11 q^{84} - 6 q^{85} + 17 q^{86} - 10 q^{87} - q^{88} + 11 q^{89} - 6 q^{90} - 13 q^{91} - 6 q^{92} - q^{93} - 4 q^{94} + 5 q^{95} + 9 q^{96} + 17 q^{97} - 2 q^{98} + q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - 9 * q^3 + 9 * q^4 + 6 * q^5 + 9 * q^6 - 11 * q^7 - 9 * q^8 + 9 * q^9 - 6 * q^10 + q^11 - 9 * q^12 + 4 * q^13 + 11 * q^14 - 6 * q^15 + 9 * q^16 - 9 * q^17 - 9 * q^18 - 13 * q^19 + 6 * q^20 + 11 * q^21 - q^22 - 6 * q^23 + 9 * q^24 + 9 * q^25 - 4 * q^26 - 9 * q^27 - 11 * q^28 + 10 * q^29 + 6 * q^30 + q^31 - 9 * q^32 - q^33 + 9 * q^34 + 6 * q^35 + 9 * q^36 - 2 * q^37 + 13 * q^38 - 4 * q^39 - 6 * q^40 + 20 * q^41 - 11 * q^42 - 17 * q^43 + q^44 + 6 * q^45 + 6 * q^46 + 4 * q^47 - 9 * q^48 + 2 * q^49 - 9 * q^50 + 9 * q^51 + 4 * q^52 + 16 * q^53 + 9 * q^54 - 17 * q^55 + 11 * q^56 + 13 * q^57 - 10 * q^58 - 9 * q^59 - 6 * q^60 - 9 * q^61 - q^62 - 11 * q^63 + 9 * q^64 + q^66 - 8 * q^67 - 9 * q^68 + 6 * q^69 - 6 * q^70 - 8 * q^71 - 9 * q^72 - 20 * q^73 + 2 * q^74 - 9 * q^75 - 13 * q^76 - 32 * q^77 + 4 * q^78 - 29 * q^79 + 6 * q^80 + 9 * q^81 - 20 * q^82 - 16 * q^83 + 11 * q^84 - 6 * q^85 + 17 * q^86 - 10 * q^87 - q^88 + 11 * q^89 - 6 * q^90 - 13 * q^91 - 6 * q^92 - q^93 - 4 * q^94 + 5 * q^95 + 9 * q^96 + 17 * q^97 - 2 * q^98 + q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	1.62533	0.726870	0.363435	−	0.931619i	$-0.381604\pi$
$5$	1.62533	0.726870	0.363435	+	0.931619i	$0.381604\pi$
$6$	1.00000	0.408248
$7$	−4.68222	−1.76971	−0.884857	−	0.465863i	$-0.845744\pi$
$7$	−4.68222	−1.76971	−0.884857	+	0.465863i	$0.845744\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−1.62533	−0.513975
$11$	3.50360	1.05637	0.528187	−	0.849128i	$-0.322872\pi$
$11$	3.50360	1.05637	0.528187	+	0.849128i	$0.322872\pi$
$12$	−1.00000	−0.288675
$13$	0.306705	0.0850648	0.0425324	−	0.999095i	$-0.486457\pi$
$13$	0.306705	0.0850648	0.0425324	+	0.999095i	$0.486457\pi$
$14$	4.68222	1.25138
$15$	−1.62533	−0.419659
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.00000	−0.235702
$19$	7.98942	1.83290	0.916449	−	0.400151i	$-0.131042\pi$
$19$	7.98942	1.83290	0.916449	+	0.400151i	$0.131042\pi$
$20$	1.62533	0.363435
$21$	4.68222	1.02174
$22$	−3.50360	−0.746970
$23$	−0.450099	−0.0938521	−0.0469261	−	0.998898i	$-0.514943\pi$
$23$	−0.450099	−0.0938521	−0.0469261	+	0.998898i	$0.514943\pi$
$24$	1.00000	0.204124
$25$	−2.35830	−0.471659
$26$	−0.306705	−0.0601499
$27$	−1.00000	−0.192450
$28$	−4.68222	−0.884857
$29$	−2.74870	−0.510421	−0.255211	−	0.966885i	$-0.582145\pi$
$29$	−2.74870	−0.510421	−0.255211	+	0.966885i	$0.582145\pi$
$30$	1.62533	0.296744
$31$	−9.09300	−1.63315	−0.816575	−	0.577239i	$-0.804130\pi$
$31$	−9.09300	−1.63315	−0.816575	+	0.577239i	$0.804130\pi$
$32$	−1.00000	−0.176777
$33$	−3.50360	−0.609898
$34$	1.00000	0.171499
$35$	−7.61016	−1.28635
$36$	1.00000	0.166667
$37$	−0.508458	−0.0835900	−0.0417950	−	0.999126i	$-0.513308\pi$
$37$	−0.508458	−0.0835900	−0.0417950	+	0.999126i	$0.513308\pi$
$38$	−7.98942	−1.29606
$39$	−0.306705	−0.0491122
$40$	−1.62533	−0.256987
$41$	−3.01170	−0.470349	−0.235174	−	0.971953i	$-0.575566\pi$
$41$	−3.01170	−0.470349	−0.235174	+	0.971953i	$0.575566\pi$
$42$	−4.68222	−0.722483
$43$	5.17673	0.789444	0.394722	−	0.918801i	$-0.370841\pi$
$43$	5.17673	0.789444	0.394722	+	0.918801i	$0.370841\pi$
$44$	3.50360	0.528187
$45$	1.62533	0.242290
$46$	0.450099	0.0663635
$47$	−13.6700	−1.99398	−0.996988	−	0.0775548i	$-0.975289\pi$
$47$	−13.6700	−1.99398	−0.996988	+	0.0775548i	$0.975289\pi$
$48$	−1.00000	−0.144338
$49$	14.9232	2.13189
$50$	2.35830	0.333514
$51$	1.00000	0.140028
$52$	0.306705	0.0425324
$53$	1.19923	0.164727	0.0823634	−	0.996602i	$-0.473753\pi$
$53$	1.19923	0.164727	0.0823634	+	0.996602i	$0.473753\pi$
$54$	1.00000	0.136083
$55$	5.69451	0.767848
$56$	4.68222	0.625688
$57$	−7.98942	−1.05822
$58$	2.74870	0.360922
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−1.62533	−0.209829
$61$	5.58904	0.715603	0.357802	−	0.933798i	$-0.383526\pi$
$61$	5.58904	0.715603	0.357802	+	0.933798i	$0.383526\pi$
$62$	9.09300	1.15481
$63$	−4.68222	−0.589905
$64$	1.00000	0.125000
$65$	0.498498	0.0618311
$66$	3.50360	0.431263
$67$	2.15065	0.262744	0.131372	−	0.991333i	$-0.458062\pi$
$67$	2.15065	0.262744	0.131372	+	0.991333i	$0.458062\pi$
$68$	−1.00000	−0.121268
$69$	0.450099	0.0541855
$70$	7.61016	0.909589
$71$	1.51984	0.180372	0.0901862	−	0.995925i	$-0.471254\pi$
$71$	1.51984	0.180372	0.0901862	+	0.995925i	$0.471254\pi$
$72$	−1.00000	−0.117851
$73$	−3.09174	−0.361861	−0.180931	−	0.983496i	$-0.557911\pi$
$73$	−3.09174	−0.361861	−0.180931	+	0.983496i	$0.557911\pi$
$74$	0.508458	0.0591070
$75$	2.35830	0.272313
$76$	7.98942	0.916449
$77$	−16.4046	−1.86948
$78$	0.306705	0.0347276
$79$	−1.76390	−0.198454	−0.0992271	−	0.995065i	$-0.531637\pi$
$79$	−1.76390	−0.198454	−0.0992271	+	0.995065i	$0.531637\pi$
$80$	1.62533	0.181718
$81$	1.00000	0.111111
$82$	3.01170	0.332587
$83$	−5.70445	−0.626145	−0.313073	−	0.949729i	$-0.601358\pi$
$83$	−5.70445	−0.626145	−0.313073	+	0.949729i	$0.601358\pi$
$84$	4.68222	0.510872
$85$	−1.62533	−0.176292
$86$	−5.17673	−0.558221
$87$	2.74870	0.294692
$88$	−3.50360	−0.373485
$89$	14.6943	1.55759	0.778796	−	0.627277i	$-0.215831\pi$
$89$	14.6943	1.55759	0.778796	+	0.627277i	$0.215831\pi$
$90$	−1.62533	−0.171325
$91$	−1.43606	−0.150540
$92$	−0.450099	−0.0469261
$93$	9.09300	0.942900
$94$	13.6700	1.40995
$95$	12.9855	1.33228
$96$	1.00000	0.102062
$97$	17.0010	1.72619	0.863095	−	0.505041i	$-0.168523\pi$
$97$	17.0010	1.72619	0.863095	+	0.505041i	$0.168523\pi$
$98$	−14.9232	−1.50747
$99$	3.50360	0.352125
$100$	−2.35830	−0.235830
$101$	2.22027	0.220925	0.110463	−	0.993880i	$-0.464767\pi$
$101$	2.22027	0.220925	0.110463	+	0.993880i	$0.464767\pi$
$102$	−1.00000	−0.0990148
$103$	−11.3558	−1.11892	−0.559458	−	0.828859i	$-0.688991\pi$
$103$	−11.3558	−1.11892	−0.559458	+	0.828859i	$0.688991\pi$
$104$	−0.306705	−0.0300749
$105$	7.61016	0.742676
$106$	−1.19923	−0.116479
$107$	−0.544607	−0.0526492	−0.0263246	−	0.999653i	$-0.508380\pi$
$107$	−0.544607	−0.0526492	−0.0263246	+	0.999653i	$0.508380\pi$
$108$	−1.00000	−0.0962250
$109$	8.09463	0.775325	0.387662	−	0.921801i	$-0.373283\pi$
$109$	8.09463	0.775325	0.387662	+	0.921801i	$0.373283\pi$
$110$	−5.69451	−0.542950
$111$	0.508458	0.0482607
$112$	−4.68222	−0.442428
$113$	11.0312	1.03773	0.518864	−	0.854857i	$-0.326355\pi$
$113$	11.0312	1.03773	0.518864	+	0.854857i	$0.326355\pi$
$114$	7.98942	0.748278
$115$	−0.731560	−0.0682183
$116$	−2.74870	−0.255211
$117$	0.306705	0.0283549
$118$	1.00000	0.0920575
$119$	4.68222	0.429219
$120$	1.62533	0.148372
$121$	1.27520	0.115928
$122$	−5.58904	−0.506008
$123$	3.01170	0.271556
$124$	−9.09300	−0.816575
$125$	−11.9597	−1.06971
$126$	4.68222	0.417125
$127$	7.38434	0.655254	0.327627	−	0.944807i	$-0.393751\pi$
$127$	7.38434	0.655254	0.327627	+	0.944807i	$0.393751\pi$
$128$	−1.00000	−0.0883883
$129$	−5.17673	−0.455786
$130$	−0.498498	−0.0437212
$131$	9.83137	0.858971	0.429486	−	0.903074i	$-0.358695\pi$
$131$	9.83137	0.858971	0.429486	+	0.903074i	$0.358695\pi$
$132$	−3.50360	−0.304949
$133$	−37.4082	−3.24371
$134$	−2.15065	−0.185788
$135$	−1.62533	−0.139886
$136$	1.00000	0.0857493
$137$	13.5747	1.15977	0.579884	−	0.814699i	$-0.303098\pi$
$137$	13.5747	1.15977	0.579884	+	0.814699i	$0.303098\pi$
$138$	−0.450099	−0.0383150
$139$	−3.26800	−0.277188	−0.138594	−	0.990349i	$-0.544258\pi$
$139$	−3.26800	−0.277188	−0.138594	+	0.990349i	$0.544258\pi$
$140$	−7.61016	−0.643176
$141$	13.6700	1.15122
$142$	−1.51984	−0.127543
$143$	1.07457	0.0898603
$144$	1.00000	0.0833333
$145$	−4.46755	−0.371010
$146$	3.09174	0.255874
$147$	−14.9232	−1.23085
$148$	−0.508458	−0.0417950
$149$	−9.55899	−0.783103	−0.391552	−	0.920156i	$-0.628062\pi$
$149$	−9.55899	−0.783103	−0.391552	+	0.920156i	$0.628062\pi$
$150$	−2.35830	−0.192554
$151$	−10.0285	−0.816111	−0.408055	−	0.912957i	$-0.633793\pi$
$151$	−10.0285	−0.816111	−0.408055	+	0.912957i	$0.633793\pi$
$152$	−7.98942	−0.648028
$153$	−1.00000	−0.0808452
$154$	16.4046	1.32192
$155$	−14.7791	−1.18709
$156$	−0.306705	−0.0245561
$157$	−8.01841	−0.639939	−0.319969	−	0.947428i	$-0.603673\pi$
$157$	−8.01841	−0.639939	−0.319969	+	0.947428i	$0.603673\pi$
$158$	1.76390	0.140328
$159$	−1.19923	−0.0951050
$160$	−1.62533	−0.128494
$161$	2.10746	0.166091
$162$	−1.00000	−0.0785674
$163$	−19.7380	−1.54600	−0.772998	−	0.634408i	$-0.781244\pi$
$163$	−19.7380	−1.54600	−0.772998	+	0.634408i	$0.781244\pi$
$164$	−3.01170	−0.235174
$165$	−5.69451	−0.443317
$166$	5.70445	0.442752
$167$	−10.0462	−0.777399	−0.388700	−	0.921364i	$-0.627076\pi$
$167$	−10.0462	−0.777399	−0.388700	+	0.921364i	$0.627076\pi$
$168$	−4.68222	−0.361241
$169$	−12.9059	−0.992764
$170$	1.62533	0.124657
$171$	7.98942	0.610966
$172$	5.17673	0.394722
$173$	−5.80330	−0.441217	−0.220608	−	0.975362i	$-0.570804\pi$
$173$	−5.80330	−0.441217	−0.220608	+	0.975362i	$0.570804\pi$
$174$	−2.74870	−0.208379
$175$	11.0421	0.834702
$176$	3.50360	0.264094
$177$	1.00000	0.0751646
$178$	−14.6943	−1.10138
$179$	3.99891	0.298892	0.149446	−	0.988770i	$-0.452251\pi$
$179$	3.99891	0.298892	0.149446	+	0.988770i	$0.452251\pi$
$180$	1.62533	0.121145
$181$	−19.1074	−1.42024	−0.710121	−	0.704080i	$-0.751360\pi$
$181$	−19.1074	−1.42024	−0.710121	+	0.704080i	$0.751360\pi$
$182$	1.43606	0.106448
$183$	−5.58904	−0.413154
$184$	0.450099	0.0331817
$185$	−0.826413	−0.0607591
$186$	−9.09300	−0.666731
$187$	−3.50360	−0.256208
$188$	−13.6700	−0.996988
$189$	4.68222	0.340582
$190$	−12.9855	−0.942064
$191$	−14.8667	−1.07572	−0.537858	−	0.843036i	$-0.680766\pi$
$191$	−14.8667	−1.07572	−0.537858	+	0.843036i	$0.680766\pi$
$192$	−1.00000	−0.0721688
$193$	−21.8472	−1.57260	−0.786299	−	0.617846i	$-0.788005\pi$
$193$	−21.8472	−1.57260	−0.786299	+	0.617846i	$0.788005\pi$
$194$	−17.0010	−1.22060
$195$	−0.498498	−0.0356982
$196$	14.9232	1.06594
$197$	8.07809	0.575540	0.287770	−	0.957699i	$-0.407086\pi$
$197$	8.07809	0.575540	0.287770	+	0.957699i	$0.407086\pi$
$198$	−3.50360	−0.248990
$199$	−1.22886	−0.0871118	−0.0435559	−	0.999051i	$-0.513869\pi$
$199$	−1.22886	−0.0871118	−0.0435559	+	0.999051i	$0.513869\pi$
$200$	2.35830	0.166757
$201$	−2.15065	−0.151695
$202$	−2.22027	−0.156218
$203$	12.8700	0.903299
$204$	1.00000	0.0700140
$205$	−4.89501	−0.341883
$206$	11.3558	0.791193
$207$	−0.450099	−0.0312840
$208$	0.306705	0.0212662
$209$	27.9917	1.93623
$210$	−7.61016	−0.525151
$211$	−24.4189	−1.68106	−0.840532	−	0.541762i	$-0.817758\pi$
$211$	−24.4189	−1.68106	−0.840532	+	0.541762i	$0.817758\pi$
$212$	1.19923	0.0823634
$213$	−1.51984	−0.104138
$214$	0.544607	0.0372286
$215$	8.41391	0.573824
$216$	1.00000	0.0680414
$217$	42.5754	2.89021
$218$	−8.09463	−0.548237
$219$	3.09174	0.208921
$220$	5.69451	0.383924
$221$	−0.306705	−0.0206312
$222$	−0.508458	−0.0341255
$223$	−12.7851	−0.856157	−0.428078	−	0.903742i	$-0.640809\pi$
$223$	−12.7851	−0.856157	−0.428078	+	0.903742i	$0.640809\pi$
$224$	4.68222	0.312844
$225$	−2.35830	−0.157220
$226$	−11.0312	−0.733785
$227$	1.76449	0.117113	0.0585567	−	0.998284i	$-0.481350\pi$
$227$	1.76449	0.117113	0.0585567	+	0.998284i	$0.481350\pi$
$228$	−7.98942	−0.529112
$229$	7.45559	0.492679	0.246339	−	0.969184i	$-0.420772\pi$
$229$	7.45559	0.492679	0.246339	+	0.969184i	$0.420772\pi$
$230$	0.731560	0.0482376
$231$	16.4046	1.07935
$232$	2.74870	0.180461
$233$	−23.0688	−1.51129	−0.755643	−	0.654984i	$-0.772675\pi$
$233$	−23.0688	−1.51129	−0.755643	+	0.654984i	$0.772675\pi$
$234$	−0.306705	−0.0200500
$235$	−22.2183	−1.44936
$236$	−1.00000	−0.0650945
$237$	1.76390	0.114578
$238$	−4.68222	−0.303503
$239$	2.30631	0.149183	0.0745914	−	0.997214i	$-0.476235\pi$
$239$	2.30631	0.149183	0.0745914	+	0.997214i	$0.476235\pi$
$240$	−1.62533	−0.104915
$241$	20.3974	1.31391	0.656956	−	0.753929i	$-0.271844\pi$
$241$	20.3974	1.31391	0.656956	+	0.753929i	$0.271844\pi$
$242$	−1.27520	−0.0819731
$243$	−1.00000	−0.0641500
$244$	5.58904	0.357802
$245$	24.2552	1.54960
$246$	−3.01170	−0.192019
$247$	2.45040	0.155915
$248$	9.09300	0.577406
$249$	5.70445	0.361505
$250$	11.9597	0.756396
$251$	26.3342	1.66220	0.831101	−	0.556122i	$-0.187711\pi$
$251$	26.3342	1.66220	0.831101	+	0.556122i	$0.187711\pi$
$252$	−4.68222	−0.294952
$253$	−1.57697	−0.0991430
$254$	−7.38434	−0.463335
$255$	1.62533	0.101782
$256$	1.00000	0.0625000
$257$	−5.75154	−0.358771	−0.179386	−	0.983779i	$-0.557411\pi$
$257$	−5.75154	−0.358771	−0.179386	+	0.983779i	$0.557411\pi$
$258$	5.17673	0.322289
$259$	2.38071	0.147930
$260$	0.498498	0.0309155
$261$	−2.74870	−0.170140
$262$	−9.83137	−0.607384
$263$	13.7497	0.847840	0.423920	−	0.905700i	$-0.360654\pi$
$263$	13.7497	0.847840	0.423920	+	0.905700i	$0.360654\pi$
$264$	3.50360	0.215632
$265$	1.94914	0.119735
$266$	37.4082	2.29365
$267$	−14.6943	−0.899276
$268$	2.15065	0.131372
$269$	−20.6179	−1.25710	−0.628549	−	0.777770i	$-0.716351\pi$
$269$	−20.6179	−1.25710	−0.628549	+	0.777770i	$0.716351\pi$
$270$	1.62533	0.0989145
$271$	21.7433	1.32081	0.660405	−	0.750909i	$-0.270385\pi$
$271$	21.7433	1.32081	0.660405	+	0.750909i	$0.270385\pi$
$272$	−1.00000	−0.0606339
$273$	1.43606	0.0869145
$274$	−13.5747	−0.820080
$275$	−8.26253	−0.498249
$276$	0.450099	0.0270928
$277$	−3.80661	−0.228717	−0.114359	−	0.993440i	$-0.536481\pi$
$277$	−3.80661	−0.228717	−0.114359	+	0.993440i	$0.536481\pi$
$278$	3.26800	0.196001
$279$	−9.09300	−0.544384
$280$	7.61016	0.454794
$281$	−7.46823	−0.445517	−0.222759	−	0.974874i	$-0.571506\pi$
$281$	−7.46823	−0.445517	−0.222759	+	0.974874i	$0.571506\pi$
$282$	−13.6700	−0.814037
$283$	−25.5910	−1.52123	−0.760614	−	0.649205i	$-0.775102\pi$
$283$	−25.5910	−1.52123	−0.760614	+	0.649205i	$0.775102\pi$
$284$	1.51984	0.0901862
$285$	−12.9855	−0.769192
$286$	−1.07457	−0.0635408
$287$	14.1015	0.832383
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	4.46755	0.262344
$291$	−17.0010	−0.996617
$292$	−3.09174	−0.180931
$293$	20.6677	1.20742	0.603709	−	0.797205i	$-0.293689\pi$
$293$	20.6677	1.20742	0.603709	+	0.797205i	$0.293689\pi$
$294$	14.9232	0.870339
$295$	−1.62533	−0.0946305
$296$	0.508458	0.0295535
$297$	−3.50360	−0.203299
$298$	9.55899	0.553738
$299$	−0.138048	−0.00798351
$300$	2.35830	0.136156
$301$	−24.2386	−1.39709
$302$	10.0285	0.577078
$303$	−2.22027	−0.127551
$304$	7.98942	0.458225
$305$	9.08404	0.520151
$306$	1.00000	0.0571662
$307$	8.87614	0.506588	0.253294	−	0.967389i	$-0.418486\pi$
$307$	8.87614	0.506588	0.253294	+	0.967389i	$0.418486\pi$
$308$	−16.4046	−0.934740
$309$	11.3558	0.646006
$310$	14.7791	0.839399
$311$	−20.4643	−1.16043	−0.580213	−	0.814465i	$-0.697031\pi$
$311$	−20.4643	−1.16043	−0.580213	+	0.814465i	$0.697031\pi$
$312$	0.306705	0.0173638
$313$	16.9378	0.957382	0.478691	−	0.877984i	$-0.341112\pi$
$313$	16.9378	0.957382	0.478691	+	0.877984i	$0.341112\pi$
$314$	8.01841	0.452505
$315$	−7.61016	−0.428784
$316$	−1.76390	−0.0992271
$317$	−8.70425	−0.488879	−0.244440	−	0.969664i	$-0.578604\pi$
$317$	−8.70425	−0.488879	−0.244440	+	0.969664i	$0.578604\pi$
$318$	1.19923	0.0672494
$319$	−9.63035	−0.539196
$320$	1.62533	0.0908588
$321$	0.544607	0.0303970
$322$	−2.10746	−0.117444
$323$	−7.98942	−0.444543
$324$	1.00000	0.0555556
$325$	−0.723303	−0.0401216
$326$	19.7380	1.09318
$327$	−8.09463	−0.447634
$328$	3.01170	0.166293
$329$	64.0060	3.52877
$330$	5.69451	0.313472
$331$	−18.6080	−1.02279	−0.511395	−	0.859346i	$-0.670871\pi$
$331$	−18.6080	−1.02279	−0.511395	+	0.859346i	$0.670871\pi$
$332$	−5.70445	−0.313073
$333$	−0.508458	−0.0278633
$334$	10.0462	0.549704
$335$	3.49553	0.190981
$336$	4.68222	0.255436
$337$	−30.0580	−1.63736	−0.818682	−	0.574247i	$-0.805295\pi$
$337$	−30.0580	−1.63736	−0.818682	+	0.574247i	$0.805295\pi$
$338$	12.9059	0.701990
$339$	−11.0312	−0.599133
$340$	−1.62533	−0.0881460
$341$	−31.8582	−1.72522
$342$	−7.98942	−0.432018
$343$	−37.0982	−2.00311
$344$	−5.17673	−0.279111
$345$	0.731560	0.0393859
$346$	5.80330	0.311987
$347$	−7.01610	−0.376644	−0.188322	−	0.982107i	$-0.560305\pi$
$347$	−7.01610	−0.376644	−0.188322	+	0.982107i	$0.560305\pi$
$348$	2.74870	0.147346
$349$	−11.7822	−0.630685	−0.315342	−	0.948978i	$-0.602119\pi$
$349$	−11.7822	−0.630685	−0.315342	+	0.948978i	$0.602119\pi$
$350$	−11.0421	−0.590223
$351$	−0.306705	−0.0163707
$352$	−3.50360	−0.186742
$353$	7.96293	0.423824	0.211912	−	0.977289i	$-0.432031\pi$
$353$	7.96293	0.423824	0.211912	+	0.977289i	$0.432031\pi$
$354$	−1.00000	−0.0531494
$355$	2.47025	0.131107
$356$	14.6943	0.778796
$357$	−4.68222	−0.247809
$358$	−3.99891	−0.211349
$359$	−12.1621	−0.641893	−0.320947	−	0.947097i	$-0.604001\pi$
$359$	−12.1621	−0.641893	−0.320947	+	0.947097i	$0.604001\pi$
$360$	−1.62533	−0.0856625
$361$	44.8308	2.35952
$362$	19.1074	1.00426
$363$	−1.27520	−0.0669308
$364$	−1.43606	−0.0752702
$365$	−5.02511	−0.263026
$366$	5.58904	0.292144
$367$	16.0356	0.837050	0.418525	−	0.908205i	$-0.362547\pi$
$367$	16.0356	0.837050	0.418525	+	0.908205i	$0.362547\pi$
$368$	−0.450099	−0.0234630
$369$	−3.01170	−0.156783
$370$	0.826413	0.0429632
$371$	−5.61505	−0.291519
$372$	9.09300	0.471450
$373$	−10.9908	−0.569082	−0.284541	−	0.958664i	$-0.591841\pi$
$373$	−10.9908	−0.569082	−0.284541	+	0.958664i	$0.591841\pi$
$374$	3.50360	0.181167
$375$	11.9597	0.617595
$376$	13.6700	0.704977
$377$	−0.843042	−0.0434189
$378$	−4.68222	−0.240828
$379$	−15.4450	−0.793354	−0.396677	−	0.917958i	$-0.629837\pi$
$379$	−15.4450	−0.793354	−0.396677	+	0.917958i	$0.629837\pi$
$380$	12.9855	0.666140
$381$	−7.38434	−0.378311
$382$	14.8667	0.760646
$383$	−15.9504	−0.815026	−0.407513	−	0.913199i	$-0.633604\pi$
$383$	−15.9504	−0.815026	−0.407513	+	0.913199i	$0.633604\pi$
$384$	1.00000	0.0510310
$385$	−26.6630	−1.35887
$386$	21.8472	1.11199
$387$	5.17673	0.263148
$388$	17.0010	0.863095
$389$	−10.6756	−0.541272	−0.270636	−	0.962682i	$-0.587234\pi$
$389$	−10.6756	−0.541272	−0.270636	+	0.962682i	$0.587234\pi$
$390$	0.498498	0.0252424
$391$	0.450099	0.0227625
$392$	−14.9232	−0.753736
$393$	−9.83137	−0.495927
$394$	−8.07809	−0.406969
$395$	−2.86692	−0.144251
$396$	3.50360	0.176062
$397$	−11.5482	−0.579586	−0.289793	−	0.957089i	$-0.593586\pi$
$397$	−11.5482	−0.579586	−0.289793	+	0.957089i	$0.593586\pi$
$398$	1.22886	0.0615974
$399$	37.4082	1.87275
$400$	−2.35830	−0.117915
$401$	−14.3310	−0.715658	−0.357829	−	0.933787i	$-0.616483\pi$
$401$	−14.3310	−0.715658	−0.357829	+	0.933787i	$0.616483\pi$
$402$	2.15065	0.107265
$403$	−2.78887	−0.138924
$404$	2.22027	0.110463
$405$	1.62533	0.0807634
$406$	−12.8700	−0.638729
$407$	−1.78143	−0.0883023
$408$	−1.00000	−0.0495074
$409$	−4.60814	−0.227858	−0.113929	−	0.993489i	$-0.536344\pi$
$409$	−4.60814	−0.227858	−0.113929	+	0.993489i	$0.536344\pi$
$410$	4.89501	0.241747
$411$	−13.5747	−0.669593
$412$	−11.3558	−0.559458
$413$	4.68222	0.230397
$414$	0.450099	0.0221212
$415$	−9.27163	−0.455126
$416$	−0.306705	−0.0150375
$417$	3.26800	0.160035
$418$	−27.9917	−1.36912
$419$	28.8597	1.40989	0.704945	−	0.709262i	$-0.250972\pi$
$419$	28.8597	1.40989	0.704945	+	0.709262i	$0.250972\pi$
$420$	7.61016	0.371338
$421$	23.3088	1.13600	0.568001	−	0.823028i	$-0.307717\pi$
$421$	23.3088	1.13600	0.568001	+	0.823028i	$0.307717\pi$
$422$	24.4189	1.18869
$423$	−13.6700	−0.664659
$424$	−1.19923	−0.0582397
$425$	2.35830	0.114394
$426$	1.51984	0.0736367
$427$	−26.1691	−1.26641
$428$	−0.544607	−0.0263246
$429$	−1.07457	−0.0518809
$430$	−8.41391	−0.405755
$431$	−30.6500	−1.47636	−0.738180	−	0.674603i	$-0.764315\pi$
$431$	−30.6500	−1.47636	−0.738180	+	0.674603i	$0.764315\pi$
$432$	−1.00000	−0.0481125
$433$	−0.208383	−0.0100142	−0.00500711	−	0.999987i	$-0.501594\pi$
$433$	−0.208383	−0.0100142	−0.00500711	+	0.999987i	$0.501594\pi$
$434$	−42.5754	−2.04369
$435$	4.46755	0.214203
$436$	8.09463	0.387662
$437$	−3.59603	−0.172021
$438$	−3.09174	−0.147729
$439$	−13.2415	−0.631981	−0.315990	−	0.948762i	$-0.602337\pi$
$439$	−13.2415	−0.631981	−0.315990	+	0.948762i	$0.602337\pi$
$440$	−5.69451	−0.271475
$441$	14.9232	0.710629
$442$	0.306705	0.0145885
$443$	−22.6761	−1.07737	−0.538686	−	0.842507i	$-0.681079\pi$
$443$	−22.6761	−1.07737	−0.538686	+	0.842507i	$0.681079\pi$
$444$	0.508458	0.0241303
$445$	23.8831	1.13217
$446$	12.7851	0.605394
$447$	9.55899	0.452125
$448$	−4.68222	−0.221214
$449$	6.65191	0.313923	0.156961	−	0.987605i	$-0.449830\pi$
$449$	6.65191	0.313923	0.156961	+	0.987605i	$0.449830\pi$
$450$	2.35830	0.111171
$451$	−10.5518	−0.496865
$452$	11.0312	0.518864
$453$	10.0285	0.471182
$454$	−1.76449	−0.0828117
$455$	−2.33408	−0.109423
$456$	7.98942	0.374139
$457$	−24.1943	−1.13176	−0.565881	−	0.824487i	$-0.691464\pi$
$457$	−24.1943	−1.13176	−0.565881	+	0.824487i	$0.691464\pi$
$458$	−7.45559	−0.348377
$459$	1.00000	0.0466760
$460$	−0.731560	−0.0341092
$461$	−17.1559	−0.799032	−0.399516	−	0.916726i	$-0.630822\pi$
$461$	−17.1559	−0.799032	−0.399516	+	0.916726i	$0.630822\pi$
$462$	−16.4046	−0.763212
$463$	5.99365	0.278548	0.139274	−	0.990254i	$-0.455523\pi$
$463$	5.99365	0.278548	0.139274	+	0.990254i	$0.455523\pi$
$464$	−2.74870	−0.127605
$465$	14.7791	0.685366
$466$	23.0688	1.06864
$467$	11.5345	0.533754	0.266877	−	0.963731i	$-0.414008\pi$
$467$	11.5345	0.533754	0.266877	+	0.963731i	$0.414008\pi$
$468$	0.306705	0.0141775
$469$	−10.0698	−0.464982
$470$	22.2183	1.02485
$471$	8.01841	0.369469
$472$	1.00000	0.0460287
$473$	18.1372	0.833949
$474$	−1.76390	−0.0810186
$475$	−18.8414	−0.864504
$476$	4.68222	0.214609
$477$	1.19923	0.0549089
$478$	−2.30631	−0.105488
$479$	−6.12179	−0.279712	−0.139856	−	0.990172i	$-0.544664\pi$
$479$	−6.12179	−0.279712	−0.139856	+	0.990172i	$0.544664\pi$
$480$	1.62533	0.0741859
$481$	−0.155947	−0.00711056
$482$	−20.3974	−0.929077
$483$	−2.10746	−0.0958929
$484$	1.27520	0.0579638
$485$	27.6323	1.25472
$486$	1.00000	0.0453609
$487$	−12.1114	−0.548822	−0.274411	−	0.961612i	$-0.588483\pi$
$487$	−12.1114	−0.548822	−0.274411	+	0.961612i	$0.588483\pi$
$488$	−5.58904	−0.253004
$489$	19.7380	0.892581
$490$	−24.2552	−1.09574
$491$	−14.6409	−0.660737	−0.330368	−	0.943852i	$-0.607173\pi$
$491$	−14.6409	−0.660737	−0.330368	+	0.943852i	$0.607173\pi$
$492$	3.01170	0.135778
$493$	2.74870	0.123795
$494$	−2.45040	−0.110249
$495$	5.69451	0.255949
$496$	−9.09300	−0.408288
$497$	−7.11625	−0.319207
$498$	−5.70445	−0.255623
$499$	−30.4669	−1.36389	−0.681943	−	0.731405i	$-0.738865\pi$
$499$	−30.4669	−1.36389	−0.681943	+	0.731405i	$0.738865\pi$
$500$	−11.9597	−0.534853
$501$	10.0462	0.448832
$502$	−26.3342	−1.17535
$503$	−3.05282	−0.136118	−0.0680592	−	0.997681i	$-0.521681\pi$
$503$	−3.05282	−0.136118	−0.0680592	+	0.997681i	$0.521681\pi$
$504$	4.68222	0.208563
$505$	3.60868	0.160584
$506$	1.57697	0.0701047
$507$	12.9059	0.573173
$508$	7.38434	0.327627
$509$	1.79554	0.0795859	0.0397929	−	0.999208i	$-0.487330\pi$
$509$	1.79554	0.0795859	0.0397929	+	0.999208i	$0.487330\pi$
$510$	−1.62533	−0.0719709
$511$	14.4762	0.640391
$512$	−1.00000	−0.0441942
$513$	−7.98942	−0.352742
$514$	5.75154	0.253690
$515$	−18.4569	−0.813307
$516$	−5.17673	−0.227893
$517$	−47.8942	−2.10639
$518$	−2.38071	−0.104603
$519$	5.80330	0.254736
$520$	−0.498498	−0.0218606
$521$	31.9118	1.39808	0.699041	−	0.715081i	$-0.253610\pi$
$521$	31.9118	1.39808	0.699041	+	0.715081i	$0.253610\pi$
$522$	2.74870	0.120307
$523$	−30.2167	−1.32129	−0.660643	−	0.750700i	$-0.729716\pi$
$523$	−30.2167	−1.32129	−0.660643	+	0.750700i	$0.729716\pi$
$524$	9.83137	0.429486
$525$	−11.0421	−0.481915
$526$	−13.7497	−0.599514
$527$	9.09300	0.396097
$528$	−3.50360	−0.152475
$529$	−22.7974	−0.991192
$530$	−1.94914	−0.0846654
$531$	−1.00000	−0.0433963
$532$	−37.4082	−1.62185
$533$	−0.923705	−0.0400101
$534$	14.6943	0.635884
$535$	−0.885168	−0.0382691
$536$	−2.15065	−0.0928941
$537$	−3.99891	−0.172566
$538$	20.6179	0.888902
$539$	52.2849	2.25207
$540$	−1.62533	−0.0699431
$541$	−17.9114	−0.770070	−0.385035	−	0.922902i	$-0.625811\pi$
$541$	−17.9114	−0.770070	−0.385035	+	0.922902i	$0.625811\pi$
$542$	−21.7433	−0.933954
$543$	19.1074	0.819977
$544$	1.00000	0.0428746
$545$	13.1565	0.563561
$546$	−1.43606	−0.0614578
$547$	−37.6832	−1.61122	−0.805608	−	0.592449i	$-0.798161\pi$
$547$	−37.6832	−1.61122	−0.805608	+	0.592449i	$0.798161\pi$
$548$	13.5747	0.579884
$549$	5.58904	0.238534
$550$	8.26253	0.352315
$551$	−21.9605	−0.935550
$552$	−0.450099	−0.0191575
$553$	8.25897	0.351207
$554$	3.80661	0.161727
$555$	0.826413	0.0350793
$556$	−3.26800	−0.138594
$557$	22.7880	0.965557	0.482779	−	0.875742i	$-0.339628\pi$
$557$	22.7880	0.965557	0.482779	+	0.875742i	$0.339628\pi$
$558$	9.09300	0.384937
$559$	1.58773	0.0671539
$560$	−7.61016	−0.321588
$561$	3.50360	0.147922
$562$	7.46823	0.315028
$563$	−13.0376	−0.549470	−0.274735	−	0.961520i	$-0.588590\pi$
$563$	−13.0376	−0.549470	−0.274735	+	0.961520i	$0.588590\pi$
$564$	13.6700	0.575611
$565$	17.9294	0.754294
$566$	25.5910	1.07567
$567$	−4.68222	−0.196635
$568$	−1.51984	−0.0637713
$569$	0.155766	0.00653003	0.00326502	−	0.999995i	$-0.498961\pi$
$569$	0.155766	0.00653003	0.00326502	+	0.999995i	$0.498961\pi$
$570$	12.9855	0.543901
$571$	−1.70105	−0.0711866	−0.0355933	−	0.999366i	$-0.511332\pi$
$571$	−1.70105	−0.0711866	−0.0355933	+	0.999366i	$0.511332\pi$
$572$	1.07457	0.0449301
$573$	14.8667	0.621064
$574$	−14.1015	−0.588583
$575$	1.06147	0.0442662
$576$	1.00000	0.0416667
$577$	3.54080	0.147405	0.0737027	−	0.997280i	$-0.476518\pi$
$577$	3.54080	0.147405	0.0737027	+	0.997280i	$0.476518\pi$
$578$	−1.00000	−0.0415945
$579$	21.8472	0.907940
$580$	−4.46755	−0.185505
$581$	26.7095	1.10810
$582$	17.0010	0.704715
$583$	4.20162	0.174013
$584$	3.09174	0.127937
$585$	0.498498	0.0206104
$586$	−20.6677	−0.853773
$587$	−10.8194	−0.446566	−0.223283	−	0.974754i	$-0.571677\pi$
$587$	−10.8194	−0.446566	−0.223283	+	0.974754i	$0.571677\pi$
$588$	−14.9232	−0.615423
$589$	−72.6478	−2.99340
$590$	1.62533	0.0669138
$591$	−8.07809	−0.332288
$592$	−0.508458	−0.0208975
$593$	−5.26259	−0.216109	−0.108054	−	0.994145i	$-0.534462\pi$
$593$	−5.26259	−0.216109	−0.108054	+	0.994145i	$0.534462\pi$
$594$	3.50360	0.143754
$595$	7.61016	0.311986
$596$	−9.55899	−0.391552
$597$	1.22886	0.0502940
$598$	0.138048	0.00564519
$599$	39.1079	1.59791	0.798953	−	0.601393i	$-0.205387\pi$
$599$	39.1079	1.59791	0.798953	+	0.601393i	$0.205387\pi$
$600$	−2.35830	−0.0962771
$601$	36.2007	1.47666	0.738328	−	0.674442i	$-0.235616\pi$
$601$	36.2007	1.47666	0.738328	+	0.674442i	$0.235616\pi$
$602$	24.2386	0.987892
$603$	2.15065	0.0875814
$604$	−10.0285	−0.408055
$605$	2.07263	0.0842643
$606$	2.22027	0.0901925
$607$	−11.8771	−0.482079	−0.241039	−	0.970515i	$-0.577488\pi$
$607$	−11.8771	−0.482079	−0.241039	+	0.970515i	$0.577488\pi$
$608$	−7.98942	−0.324014
$609$	−12.8700	−0.521520
$610$	−9.08404	−0.367802
$611$	−4.19267	−0.169617
$612$	−1.00000	−0.0404226
$613$	15.8197	0.638952	0.319476	−	0.947594i	$-0.396493\pi$
$613$	15.8197	0.638952	0.319476	+	0.947594i	$0.396493\pi$
$614$	−8.87614	−0.358212
$615$	4.89501	0.197386
$616$	16.4046	0.660961
$617$	22.4478	0.903714	0.451857	−	0.892090i	$-0.350762\pi$
$617$	22.4478	0.903714	0.451857	+	0.892090i	$0.350762\pi$
$618$	−11.3558	−0.456795
$619$	−38.7149	−1.55609	−0.778043	−	0.628212i	$-0.783787\pi$
$619$	−38.7149	−1.55609	−0.778043	+	0.628212i	$0.783787\pi$
$620$	−14.7791	−0.593544
$621$	0.450099	0.0180618
$622$	20.4643	0.820545
$623$	−68.8019	−2.75649
$624$	−0.306705	−0.0122780
$625$	−7.64695	−0.305878
$626$	−16.9378	−0.676971
$627$	−27.9917	−1.11788
$628$	−8.01841	−0.319969
$629$	0.508458	0.0202735
$630$	7.61016	0.303196
$631$	−28.7544	−1.14469	−0.572347	−	0.820012i	$-0.693967\pi$
$631$	−28.7544	−1.14469	−0.572347	+	0.820012i	$0.693967\pi$
$632$	1.76390	0.0701642
$633$	24.4189	0.970563
$634$	8.70425	0.345690
$635$	12.0020	0.476285
$636$	−1.19923	−0.0475525
$637$	4.57703	0.181348
$638$	9.63035	0.381269
$639$	1.51984	0.0601241
$640$	−1.62533	−0.0642469
$641$	22.2994	0.880774	0.440387	−	0.897808i	$-0.354841\pi$
$641$	22.2994	0.880774	0.440387	+	0.897808i	$0.354841\pi$
$642$	−0.544607	−0.0214939
$643$	−48.9512	−1.93045	−0.965223	−	0.261430i	$-0.915806\pi$
$643$	−48.9512	−1.93045	−0.965223	+	0.261430i	$0.915806\pi$
$644$	2.10746	0.0830457
$645$	−8.41391	−0.331297
$646$	7.98942	0.314340
$647$	−3.17138	−0.124680	−0.0623399	−	0.998055i	$-0.519856\pi$
$647$	−3.17138	−0.124680	−0.0623399	+	0.998055i	$0.519856\pi$
$648$	−1.00000	−0.0392837
$649$	−3.50360	−0.137528
$650$	0.723303	0.0283703
$651$	−42.5754	−1.66866
$652$	−19.7380	−0.772998
$653$	−11.6477	−0.455811	−0.227905	−	0.973683i	$-0.573188\pi$
$653$	−11.6477	−0.455811	−0.227905	+	0.973683i	$0.573188\pi$
$654$	8.09463	0.316525
$655$	15.9792	0.624361
$656$	−3.01170	−0.117587
$657$	−3.09174	−0.120620
$658$	−64.0060	−2.49521
$659$	−9.79849	−0.381695	−0.190848	−	0.981620i	$-0.561124\pi$
$659$	−9.79849	−0.381695	−0.190848	+	0.981620i	$0.561124\pi$
$660$	−5.69451	−0.221658
$661$	−20.9428	−0.814580	−0.407290	−	0.913299i	$-0.633526\pi$
$661$	−20.9428	−0.814580	−0.407290	+	0.913299i	$0.633526\pi$
$662$	18.6080	0.723221
$663$	0.306705	0.0119115
$664$	5.70445	0.221376
$665$	−60.8008	−2.35775
$666$	0.508458	0.0197023
$667$	1.23719	0.0479041
$668$	−10.0462	−0.388700
$669$	12.7851	0.494302
$670$	−3.49553	−0.135044
$671$	19.5818	0.755945
$672$	−4.68222	−0.180621
$673$	37.5710	1.44825	0.724127	−	0.689666i	$-0.242243\pi$
$673$	37.5710	1.44825	0.724127	+	0.689666i	$0.242243\pi$
$674$	30.0580	1.15779
$675$	2.35830	0.0907709
$676$	−12.9059	−0.496382
$677$	−29.2120	−1.12271	−0.561354	−	0.827576i	$-0.689719\pi$
$677$	−29.2120	−1.12271	−0.561354	+	0.827576i	$0.689719\pi$
$678$	11.0312	0.423651
$679$	−79.6025	−3.05486
$680$	1.62533	0.0623286
$681$	−1.76449	−0.0676155
$682$	31.8582	1.21991
$683$	32.3264	1.23693	0.618467	−	0.785811i	$-0.287754\pi$
$683$	32.3264	1.23693	0.618467	+	0.785811i	$0.287754\pi$
$684$	7.98942	0.305483
$685$	22.0635	0.843002
$686$	37.0982	1.41642
$687$	−7.45559	−0.284448
$688$	5.17673	0.197361
$689$	0.367810	0.0140124
$690$	−0.731560	−0.0278500
$691$	12.9267	0.491754	0.245877	−	0.969301i	$-0.420924\pi$
$691$	12.9267	0.491754	0.245877	+	0.969301i	$0.420924\pi$
$692$	−5.80330	−0.220608
$693$	−16.4046	−0.623160
$694$	7.01610	0.266327
$695$	−5.31158	−0.201480
$696$	−2.74870	−0.104189
$697$	3.01170	0.114076
$698$	11.7822	0.445961
$699$	23.0688	0.872541
$700$	11.0421	0.417351
$701$	7.81292	0.295090	0.147545	−	0.989055i	$-0.452863\pi$
$701$	7.81292	0.295090	0.147545	+	0.989055i	$0.452863\pi$
$702$	0.306705	0.0115759
$703$	−4.06228	−0.153212
$704$	3.50360	0.132047
$705$	22.2183	0.836790
$706$	−7.96293	−0.299689
$707$	−10.3958	−0.390975
$708$	1.00000	0.0375823
$709$	31.2777	1.17466	0.587329	−	0.809348i	$-0.300179\pi$
$709$	31.2777	1.17466	0.587329	+	0.809348i	$0.300179\pi$
$710$	−2.47025	−0.0927069
$711$	−1.76390	−0.0661514
$712$	−14.6943	−0.550692
$713$	4.09275	0.153275
$714$	4.68222	0.175228
$715$	1.74654	0.0653168
$716$	3.99891	0.149446
$717$	−2.30631	−0.0861307
$718$	12.1621	0.453887
$719$	−18.7728	−0.700109	−0.350054	−	0.936729i	$-0.613837\pi$
$719$	−18.7728	−0.700109	−0.350054	+	0.936729i	$0.613837\pi$
$720$	1.62533	0.0605725
$721$	53.1702	1.98016
$722$	−44.8308	−1.66843
$723$	−20.3974	−0.758588
$724$	−19.1074	−0.710121
$725$	6.48226	0.240745
$726$	1.27520	0.0473272
$727$	−47.9490	−1.77833	−0.889166	−	0.457585i	$-0.848714\pi$
$727$	−47.9490	−1.77833	−0.889166	+	0.457585i	$0.848714\pi$
$728$	1.43606	0.0532240
$729$	1.00000	0.0370370
$730$	5.02511	0.185988
$731$	−5.17673	−0.191468
$732$	−5.58904	−0.206577
$733$	−41.0140	−1.51489	−0.757444	−	0.652901i	$-0.773552\pi$
$733$	−41.0140	−1.51489	−0.757444	+	0.652901i	$0.773552\pi$
$734$	−16.0356	−0.591884
$735$	−24.2552	−0.894665
$736$	0.450099	0.0165909
$737$	7.53503	0.277556
$738$	3.01170	0.110862
$739$	29.5579	1.08730	0.543652	−	0.839311i	$-0.317041\pi$
$739$	29.5579	1.08730	0.543652	+	0.839311i	$0.317041\pi$
$740$	−0.826413	−0.0303795
$741$	−2.45040	−0.0900177
$742$	5.61505	0.206135
$743$	20.0162	0.734324	0.367162	−	0.930157i	$-0.380329\pi$
$743$	20.0162	0.734324	0.367162	+	0.930157i	$0.380329\pi$
$744$	−9.09300	−0.333365
$745$	−15.5365	−0.569215
$746$	10.9908	0.402402
$747$	−5.70445	−0.208715
$748$	−3.50360	−0.128104
$749$	2.54997	0.0931740
$750$	−11.9597	−0.436706
$751$	−9.95068	−0.363105	−0.181553	−	0.983381i	$-0.558112\pi$
$751$	−9.95068	−0.363105	−0.181553	+	0.983381i	$0.558112\pi$
$752$	−13.6700	−0.498494
$753$	−26.3342	−0.959673
$754$	0.843042	0.0307018
$755$	−16.2997	−0.593207
$756$	4.68222	0.170291
$757$	23.0211	0.836715	0.418357	−	0.908282i	$-0.362606\pi$
$757$	23.0211	0.836715	0.418357	+	0.908282i	$0.362606\pi$
$758$	15.4450	0.560986
$759$	1.57697	0.0572402
$760$	−12.9855	−0.471032
$761$	33.4143	1.21127	0.605634	−	0.795743i	$-0.292920\pi$
$761$	33.4143	1.21127	0.605634	+	0.795743i	$0.292920\pi$
$762$	7.38434	0.267506
$763$	−37.9008	−1.37210
$764$	−14.8667	−0.537858
$765$	−1.62533	−0.0587640
$766$	15.9504	0.576310
$767$	−0.306705	−0.0110745
$768$	−1.00000	−0.0360844
$769$	−11.8518	−0.427387	−0.213694	−	0.976901i	$-0.568549\pi$
$769$	−11.8518	−0.427387	−0.213694	+	0.976901i	$0.568549\pi$
$770$	26.6630	0.960866
$771$	5.75154	0.207137
$772$	−21.8472	−0.786299
$773$	−26.2977	−0.945863	−0.472932	−	0.881099i	$-0.656804\pi$
$773$	−26.2977	−0.945863	−0.472932	+	0.881099i	$0.656804\pi$
$774$	−5.17673	−0.186074
$775$	21.4440	0.770291
$776$	−17.0010	−0.610301
$777$	−2.38071	−0.0854076
$778$	10.6756	0.382737
$779$	−24.0617	−0.862102
$780$	−0.498498	−0.0178491
$781$	5.32492	0.190541
$782$	−0.450099	−0.0160955
$783$	2.74870	0.0982306
$784$	14.9232	0.532972
$785$	−13.0326	−0.465152
$786$	9.83137	0.350674
$787$	21.9124	0.781092	0.390546	−	0.920583i	$-0.372286\pi$
$787$	21.9124	0.781092	0.390546	+	0.920583i	$0.372286\pi$
$788$	8.07809	0.287770
$789$	−13.7497	−0.489501
$790$	2.86692	0.102001
$791$	−51.6506	−1.83648
$792$	−3.50360	−0.124495
$793$	1.71419	0.0608726
$794$	11.5482	0.409829
$795$	−1.94914	−0.0691290
$796$	−1.22886	−0.0435559
$797$	32.0720	1.13605	0.568025	−	0.823011i	$-0.307708\pi$
$797$	32.0720	1.13605	0.568025	+	0.823011i	$0.307708\pi$
$798$	−37.4082	−1.32424
$799$	13.6700	0.483610
$800$	2.35830	0.0833784
$801$	14.6943	0.519197
$802$	14.3310	0.506047
$803$	−10.8322	−0.382261
$804$	−2.15065	−0.0758477
$805$	3.42533	0.120727
$806$	2.78887	0.0982338
$807$	20.6179	0.725786
$808$	−2.22027	−0.0781090
$809$	21.0860	0.741345	0.370673	−	0.928764i	$-0.379127\pi$
$809$	21.0860	0.741345	0.370673	+	0.928764i	$0.379127\pi$
$810$	−1.62533	−0.0571083
$811$	−36.2723	−1.27369	−0.636846	−	0.770991i	$-0.719761\pi$
$811$	−36.2723	−1.27369	−0.636846	+	0.770991i	$0.719761\pi$
$812$	12.8700	0.451650
$813$	−21.7433	−0.762570
$814$	1.78143	0.0624392
$815$	−32.0807	−1.12374
$816$	1.00000	0.0350070
$817$	41.3591	1.44697
$818$	4.60814	0.161120
$819$	−1.43606	−0.0501801
$820$	−4.89501	−0.170941
$821$	7.96206	0.277878	0.138939	−	0.990301i	$-0.455631\pi$
$821$	7.96206	0.277878	0.138939	+	0.990301i	$0.455631\pi$
$822$	13.5747	0.473474
$823$	−31.7101	−1.10534	−0.552672	−	0.833399i	$-0.686392\pi$
$823$	−31.7101	−1.10534	−0.552672	+	0.833399i	$0.686392\pi$
$824$	11.3558	0.395596
$825$	8.26253	0.287664
$826$	−4.68222	−0.162915
$827$	41.7925	1.45327	0.726634	−	0.687024i	$-0.241083\pi$
$827$	41.7925	1.45327	0.726634	+	0.687024i	$0.241083\pi$
$828$	−0.450099	−0.0156420
$829$	50.3001	1.74699	0.873497	−	0.486829i	$-0.161846\pi$
$829$	50.3001	1.74699	0.873497	+	0.486829i	$0.161846\pi$
$830$	9.27163	0.321823
$831$	3.80661	0.132050
$832$	0.306705	0.0106331
$833$	−14.9232	−0.517058
$834$	−3.26800	−0.113162
$835$	−16.3284	−0.565069
$836$	27.9917	0.968114
$837$	9.09300	0.314300
$838$	−28.8597	−0.996942
$839$	−38.7270	−1.33701	−0.668503	−	0.743709i	$-0.733065\pi$
$839$	−38.7270	−1.33701	−0.668503	+	0.743709i	$0.733065\pi$
$840$	−7.61016	−0.262576
$841$	−21.4446	−0.739470
$842$	−23.3088	−0.803274
$843$	7.46823	0.257219
$844$	−24.4189	−0.840532
$845$	−20.9764	−0.721611
$846$	13.6700	0.469985
$847$	−5.97078	−0.205159
$848$	1.19923	0.0411817
$849$	25.5910	0.878281
$850$	−2.35830	−0.0808889
$851$	0.228856	0.00784510
$852$	−1.51984	−0.0520690
$853$	11.7188	0.401246	0.200623	−	0.979669i	$-0.435703\pi$
$853$	11.7188	0.401246	0.200623	+	0.979669i	$0.435703\pi$
$854$	26.1691	0.895489
$855$	12.9855	0.444093
$856$	0.544607	0.0186143
$857$	−33.7472	−1.15278	−0.576391	−	0.817174i	$-0.695539\pi$
$857$	−33.7472	−1.15278	−0.576391	+	0.817174i	$0.695539\pi$
$858$	1.07457	0.0366853
$859$	−9.88771	−0.337364	−0.168682	−	0.985671i	$-0.553951\pi$
$859$	−9.88771	−0.337364	−0.168682	+	0.985671i	$0.553951\pi$
$860$	8.41391	0.286912
$861$	−14.1015	−0.480576
$862$	30.6500	1.04394
$863$	45.8275	1.55999	0.779994	−	0.625787i	$-0.215222\pi$
$863$	45.8275	1.55999	0.779994	+	0.625787i	$0.215222\pi$
$864$	1.00000	0.0340207
$865$	−9.43228	−0.320707
$866$	0.208383	0.00708113
$867$	−1.00000	−0.0339618
$868$	42.5754	1.44510
$869$	−6.18000	−0.209642
$870$	−4.46755	−0.151464
$871$	0.659617	0.0223503
$872$	−8.09463	−0.274119
$873$	17.0010	0.575397
$874$	3.59603	0.121638
$875$	55.9978	1.89307
$876$	3.09174	0.104460
$877$	15.7204	0.530839	0.265419	−	0.964133i	$-0.414490\pi$
$877$	15.7204	0.530839	0.265419	+	0.964133i	$0.414490\pi$
$878$	13.2415	0.446878
$879$	−20.6677	−0.697103
$880$	5.69451	0.191962
$881$	−21.2569	−0.716165	−0.358082	−	0.933690i	$-0.616569\pi$
$881$	−21.2569	−0.716165	−0.358082	+	0.933690i	$0.616569\pi$
$882$	−14.9232	−0.502490
$883$	−28.3245	−0.953196	−0.476598	−	0.879121i	$-0.658130\pi$
$883$	−28.3245	−0.953196	−0.476598	+	0.879121i	$0.658130\pi$
$884$	−0.306705	−0.0103156
$885$	1.62533	0.0546349
$886$	22.6761	0.761817
$887$	−44.1739	−1.48321	−0.741606	−	0.670835i	$-0.765936\pi$
$887$	−44.1739	−1.48321	−0.741606	+	0.670835i	$0.765936\pi$
$888$	−0.508458	−0.0170627
$889$	−34.5751	−1.15961
$890$	−23.8831	−0.800563
$891$	3.50360	0.117375
$892$	−12.7851	−0.428078
$893$	−109.215	−3.65476
$894$	−9.55899	−0.319701
$895$	6.49955	0.217256
$896$	4.68222	0.156422
$897$	0.138048	0.00460928
$898$	−6.65191	−0.221977
$899$	24.9939	0.833595
$900$	−2.35830	−0.0786099
$901$	−1.19923	−0.0399521
$902$	10.5518	0.351336
$903$	24.2386	0.806610
$904$	−11.0312	−0.366893
$905$	−31.0558	−1.03233
$906$	−10.0285	−0.333176
$907$	12.1248	0.402597	0.201298	−	0.979530i	$-0.435484\pi$
$907$	12.1248	0.402597	0.201298	+	0.979530i	$0.435484\pi$
$908$	1.76449	0.0585567
$909$	2.22027	0.0736418
$910$	2.33408	0.0773740
$911$	10.8154	0.358331	0.179166	−	0.983819i	$-0.442660\pi$
$911$	10.8154	0.358331	0.179166	+	0.983819i	$0.442660\pi$
$912$	−7.98942	−0.264556
$913$	−19.9861	−0.661444
$914$	24.1943	0.800277
$915$	−9.08404	−0.300309
$916$	7.45559	0.246339
$917$	−46.0327	−1.52013
$918$	−1.00000	−0.0330049
$919$	−5.83398	−0.192445	−0.0962226	−	0.995360i	$-0.530676\pi$
$919$	−5.83398	−0.192445	−0.0962226	+	0.995360i	$0.530676\pi$
$920$	0.731560	0.0241188
$921$	−8.87614	−0.292479
$922$	17.1559	0.565001
$923$	0.466145	0.0153433
$924$	16.4046	0.539673
$925$	1.19909	0.0394260
$926$	−5.99365	−0.196963
$927$	−11.3558	−0.372972
$928$	2.74870	0.0902306
$929$	−19.5024	−0.639854	−0.319927	−	0.947442i	$-0.603658\pi$
$929$	−19.5024	−0.639854	−0.319927	+	0.947442i	$0.603658\pi$
$930$	−14.7791	−0.484627
$931$	119.228	3.90753
$932$	−23.0688	−0.755643
$933$	20.4643	0.669972
$934$	−11.5345	−0.377421
$935$	−5.69451	−0.186230
$936$	−0.306705	−0.0100250
$937$	−6.25657	−0.204393	−0.102197	−	0.994764i	$-0.532587\pi$
$937$	−6.25657	−0.204393	−0.102197	+	0.994764i	$0.532587\pi$
$938$	10.0698	0.328792
$939$	−16.9378	−0.552744
$940$	−22.2183	−0.724681
$941$	−34.5091	−1.12496	−0.562482	−	0.826810i	$-0.690153\pi$
$941$	−34.5091	−1.12496	−0.562482	+	0.826810i	$0.690153\pi$
$942$	−8.01841	−0.261254
$943$	1.35556	0.0441432
$944$	−1.00000	−0.0325472
$945$	7.61016	0.247559
$946$	−18.1372	−0.589691
$947$	54.8085	1.78104	0.890519	−	0.454946i	$-0.150342\pi$
$947$	54.8085	1.78104	0.890519	+	0.454946i	$0.150342\pi$
$948$	1.76390	0.0572888
$949$	−0.948255	−0.0307816
$950$	18.8414	0.611297
$951$	8.70425	0.282255
$952$	−4.68222	−0.151752
$953$	−40.6589	−1.31707	−0.658535	−	0.752550i	$-0.728824\pi$
$953$	−40.6589	−1.31707	−0.658535	+	0.752550i	$0.728824\pi$
$954$	−1.19923	−0.0388265
$955$	−24.1633	−0.781906
$956$	2.30631	0.0745914
$957$	9.63035	0.311305
$958$	6.12179	0.197786
$959$	−63.5600	−2.05246
$960$	−1.62533	−0.0524574
$961$	51.6826	1.66718
$962$	0.155947	0.00502793
$963$	−0.544607	−0.0175497
$964$	20.3974	0.656956
$965$	−35.5090	−1.14307
$966$	2.10746	0.0678065
$967$	−18.4249	−0.592506	−0.296253	−	0.955109i	$-0.595737\pi$
$967$	−18.4249	−0.592506	−0.296253	+	0.955109i	$0.595737\pi$
$968$	−1.27520	−0.0409866
$969$	7.98942	0.256657
$970$	−27.6323	−0.887219
$971$	7.68658	0.246674	0.123337	−	0.992365i	$-0.460640\pi$
$971$	7.68658	0.246674	0.123337	+	0.992365i	$0.460640\pi$
$972$	−1.00000	−0.0320750
$973$	15.3015	0.490543
$974$	12.1114	0.388076
$975$	0.723303	0.0231642
$976$	5.58904	0.178901
$977$	−45.9751	−1.47087	−0.735436	−	0.677594i	$-0.763023\pi$
$977$	−45.9751	−1.47087	−0.735436	+	0.677594i	$0.763023\pi$
$978$	−19.7380	−0.631150
$979$	51.4829	1.64540
$980$	24.2552	0.774802
$981$	8.09463	0.258442
$982$	14.6409	0.467211
$983$	62.0493	1.97906	0.989532	−	0.144313i	$-0.0460972\pi$
$983$	62.0493	1.97906	0.989532	+	0.144313i	$0.0460972\pi$
$984$	−3.01170	−0.0960095
$985$	13.1296	0.418343
$986$	−2.74870	−0.0875365
$987$	−64.0060	−2.03733
$988$	2.45040	0.0779576
$989$	−2.33004	−0.0740910
$990$	−5.69451	−0.180983
$991$	27.0267	0.858532	0.429266	−	0.903178i	$-0.358772\pi$
$991$	27.0267	0.858532	0.429266	+	0.903178i	$0.358772\pi$
$992$	9.09300	0.288703
$993$	18.6080	0.590508
$994$	7.11625	0.225714
$995$	−1.99731	−0.0633190
$996$	5.70445	0.180753
$997$	20.9677	0.664054	0.332027	−	0.943270i	$-0.392268\pi$
$997$	20.9677	0.664054	0.332027	+	0.943270i	$0.392268\pi$
$998$	30.4669	0.964413
$999$	0.508458	0.0160869

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.v.1.7	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.v.1.7	✓	9	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.62533 q^{5} +1.00000 q^{6} -4.68222 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.62533 q^{5} +1.00000 q^{6} -4.68222 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.62533 q^{10} +3.50360 q^{11} -1.00000 q^{12} +0.306705 q^{13} +4.68222 q^{14} -1.62533 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +7.98942 q^{19} +1.62533 q^{20} +4.68222 q^{21} -3.50360 q^{22} -0.450099 q^{23} +1.00000 q^{24} -2.35830 q^{25} -0.306705 q^{26} -1.00000 q^{27} -4.68222 q^{28} -2.74870 q^{29} +1.62533 q^{30} -9.09300 q^{31} -1.00000 q^{32} -3.50360 q^{33} +1.00000 q^{34} -7.61016 q^{35} +1.00000 q^{36} -0.508458 q^{37} -7.98942 q^{38} -0.306705 q^{39} -1.62533 q^{40} -3.01170 q^{41} -4.68222 q^{42} +5.17673 q^{43} +3.50360 q^{44} +1.62533 q^{45} +0.450099 q^{46} -13.6700 q^{47} -1.00000 q^{48} +14.9232 q^{49} +2.35830 q^{50} +1.00000 q^{51} +0.306705 q^{52} +1.19923 q^{53} +1.00000 q^{54} +5.69451 q^{55} +4.68222 q^{56} -7.98942 q^{57} +2.74870 q^{58} -1.00000 q^{59} -1.62533 q^{60} +5.58904 q^{61} +9.09300 q^{62} -4.68222 q^{63} +1.00000 q^{64} +0.498498 q^{65} +3.50360 q^{66} +2.15065 q^{67} -1.00000 q^{68} +0.450099 q^{69} +7.61016 q^{70} +1.51984 q^{71} -1.00000 q^{72} -3.09174 q^{73} +0.508458 q^{74} +2.35830 q^{75} +7.98942 q^{76} -16.4046 q^{77} +0.306705 q^{78} -1.76390 q^{79} +1.62533 q^{80} +1.00000 q^{81} +3.01170 q^{82} -5.70445 q^{83} +4.68222 q^{84} -1.62533 q^{85} -5.17673 q^{86} +2.74870 q^{87} -3.50360 q^{88} +14.6943 q^{89} -1.62533 q^{90} -1.43606 q^{91} -0.450099 q^{92} +9.09300 q^{93} +13.6700 q^{94} +12.9855 q^{95} +1.00000 q^{96} +17.0010 q^{97} -14.9232 q^{98} +3.50360 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 9 q^{2} - 9 q^{3} + 9 q^{4} + 6 q^{5} + 9 q^{6} - 11 q^{7} - 9 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q - 9 * q^2 - 9 * q^3 + 9 * q^4 + 6 * q^5 + 9 * q^6 - 11 * q^7 - 9 * q^8 + 9 * q^9	\( 9 q - 9 q^{2} - 9 q^{3} + 9 q^{4} + 6 q^{5} + 9 q^{6} - 11 q^{7} - 9 q^{8} + 9 q^{9} - 6 q^{10} + q^{11} - 9 q^{12} + 4 q^{13} + 11 q^{14} - 6 q^{15} + 9 q^{16} - 9 q^{17} - 9 q^{18} - 13 q^{19} + 6 q^{20} + 11 q^{21} - q^{22} - 6 q^{23} + 9 q^{24} + 9 q^{25} - 4 q^{26} - 9 q^{27} - 11 q^{28} + 10 q^{29} + 6 q^{30} + q^{31} - 9 q^{32} - q^{33} + 9 q^{34} + 6 q^{35} + 9 q^{36} - 2 q^{37} + 13 q^{38} - 4 q^{39} - 6 q^{40} + 20 q^{41} - 11 q^{42} - 17 q^{43} + q^{44} + 6 q^{45} + 6 q^{46} + 4 q^{47} - 9 q^{48} + 2 q^{49} - 9 q^{50} + 9 q^{51} + 4 q^{52} + 16 q^{53} + 9 q^{54} - 17 q^{55} + 11 q^{56} + 13 q^{57} - 10 q^{58} - 9 q^{59} - 6 q^{60} - 9 q^{61} - q^{62} - 11 q^{63} + 9 q^{64} + q^{66} - 8 q^{67} - 9 q^{68} + 6 q^{69} - 6 q^{70} - 8 q^{71} - 9 q^{72} - 20 q^{73} + 2 q^{74} - 9 q^{75} - 13 q^{76} - 32 q^{77} + 4 q^{78} - 29 q^{79} + 6 q^{80} + 9 q^{81} - 20 q^{82} - 16 q^{83} + 11 q^{84} - 6 q^{85} + 17 q^{86} - 10 q^{87} - q^{88} + 11 q^{89} - 6 q^{90} - 13 q^{91} - 6 q^{92} - q^{93} - 4 q^{94} + 5 q^{95} + 9 q^{96} + 17 q^{97} - 2 q^{98} + q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - 9 * q^3 + 9 * q^4 + 6 * q^5 + 9 * q^6 - 11 * q^7 - 9 * q^8 + 9 * q^9 - 6 * q^10 + q^11 - 9 * q^12 + 4 * q^13 + 11 * q^14 - 6 * q^15 + 9 * q^16 - 9 * q^17 - 9 * q^18 - 13 * q^19 + 6 * q^20 + 11 * q^21 - q^22 - 6 * q^23 + 9 * q^24 + 9 * q^25 - 4 * q^26 - 9 * q^27 - 11 * q^28 + 10 * q^29 + 6 * q^30 + q^31 - 9 * q^32 - q^33 + 9 * q^34 + 6 * q^35 + 9 * q^36 - 2 * q^37 + 13 * q^38 - 4 * q^39 - 6 * q^40 + 20 * q^41 - 11 * q^42 - 17 * q^43 + q^44 + 6 * q^45 + 6 * q^46 + 4 * q^47 - 9 * q^48 + 2 * q^49 - 9 * q^50 + 9 * q^51 + 4 * q^52 + 16 * q^53 + 9 * q^54 - 17 * q^55 + 11 * q^56 + 13 * q^57 - 10 * q^58 - 9 * q^59 - 6 * q^60 - 9 * q^61 - q^62 - 11 * q^63 + 9 * q^64 + q^66 - 8 * q^67 - 9 * q^68 + 6 * q^69 - 6 * q^70 - 8 * q^71 - 9 * q^72 - 20 * q^73 + 2 * q^74 - 9 * q^75 - 13 * q^76 - 32 * q^77 + 4 * q^78 - 29 * q^79 + 6 * q^80 + 9 * q^81 - 20 * q^82 - 16 * q^83 + 11 * q^84 - 6 * q^85 + 17 * q^86 - 10 * q^87 - q^88 + 11 * q^89 - 6 * q^90 - 13 * q^91 - 6 * q^92 - q^93 - 4 * q^94 + 5 * q^95 + 9 * q^96 + 17 * q^97 - 2 * q^98 + q^99

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