LMFDB - Embedded newform 6018.2.a.bb.1.2

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:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 4 x^{12} - 41 x^{11} + 179 x^{10} + 540 x^{9} - 2773 x^{8} - 2260 x^{7} + 17621 x^{6} + \cdots + 128 $ x^13 - 4x^12 - 41x^11 + 179x^10 + 540x^9 - 2773x^8 - 2260x^7 + 17621x^6 - 838x^5 - 44478x^4 + 16472x^3 + 29944x^2 - 6856x + 128
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-3.91861$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.91861 q^{5} +1.00000 q^{6} -4.71846 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.91861 q^{5} +1.00000 q^{6} -4.71846 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.91861 q^{10} -4.45672 q^{11} +1.00000 q^{12} -3.78968 q^{13} -4.71846 q^{14} -3.91861 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -5.42803 q^{19} -3.91861 q^{20} -4.71846 q^{21} -4.45672 q^{22} -5.61205 q^{23} +1.00000 q^{24} +10.3555 q^{25} -3.78968 q^{26} +1.00000 q^{27} -4.71846 q^{28} +8.21377 q^{29} -3.91861 q^{30} +0.794436 q^{31} +1.00000 q^{32} -4.45672 q^{33} +1.00000 q^{34} +18.4898 q^{35} +1.00000 q^{36} -1.18372 q^{37} -5.42803 q^{38} -3.78968 q^{39} -3.91861 q^{40} +3.76358 q^{41} -4.71846 q^{42} +1.63431 q^{43} -4.45672 q^{44} -3.91861 q^{45} -5.61205 q^{46} +1.69423 q^{47} +1.00000 q^{48} +15.2639 q^{49} +10.3555 q^{50} +1.00000 q^{51} -3.78968 q^{52} -7.69402 q^{53} +1.00000 q^{54} +17.4641 q^{55} -4.71846 q^{56} -5.42803 q^{57} +8.21377 q^{58} -1.00000 q^{59} -3.91861 q^{60} +1.91084 q^{61} +0.794436 q^{62} -4.71846 q^{63} +1.00000 q^{64} +14.8503 q^{65} -4.45672 q^{66} +9.79474 q^{67} +1.00000 q^{68} -5.61205 q^{69} +18.4898 q^{70} -6.44292 q^{71} +1.00000 q^{72} +6.22571 q^{73} -1.18372 q^{74} +10.3555 q^{75} -5.42803 q^{76} +21.0289 q^{77} -3.78968 q^{78} -11.3942 q^{79} -3.91861 q^{80} +1.00000 q^{81} +3.76358 q^{82} +3.99214 q^{83} -4.71846 q^{84} -3.91861 q^{85} +1.63431 q^{86} +8.21377 q^{87} -4.45672 q^{88} -2.36997 q^{89} -3.91861 q^{90} +17.8815 q^{91} -5.61205 q^{92} +0.794436 q^{93} +1.69423 q^{94} +21.2703 q^{95} +1.00000 q^{96} -5.12947 q^{97} +15.2639 q^{98} -4.45672 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 4 q^{5} + 13 q^{6} + 11 q^{7} + 13 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q + 13 * q^2 + 13 * q^3 + 13 * q^4 + 4 * q^5 + 13 * q^6 + 11 * q^7 + 13 * q^8 + 13 * q^9	\( 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 4 q^{5} + 13 q^{6} + 11 q^{7} + 13 q^{8} + 13 q^{9} + 4 q^{10} + 7 q^{11} + 13 q^{12} + 6 q^{13} + 11 q^{14} + 4 q^{15} + 13 q^{16} + 13 q^{17} + 13 q^{18} + 9 q^{19} + 4 q^{20} + 11 q^{21} + 7 q^{22} + 2 q^{23} + 13 q^{24} + 33 q^{25} + 6 q^{26} + 13 q^{27} + 11 q^{28} + 14 q^{29} + 4 q^{30} - 5 q^{31} + 13 q^{32} + 7 q^{33} + 13 q^{34} + 24 q^{35} + 13 q^{36} + 4 q^{37} + 9 q^{38} + 6 q^{39} + 4 q^{40} + 28 q^{41} + 11 q^{42} + q^{43} + 7 q^{44} + 4 q^{45} + 2 q^{46} + 12 q^{47} + 13 q^{48} + 32 q^{49} + 33 q^{50} + 13 q^{51} + 6 q^{52} + 22 q^{53} + 13 q^{54} - 7 q^{55} + 11 q^{56} + 9 q^{57} + 14 q^{58} - 13 q^{59} + 4 q^{60} - 9 q^{61} - 5 q^{62} + 11 q^{63} + 13 q^{64} + 34 q^{65} + 7 q^{66} + 26 q^{67} + 13 q^{68} + 2 q^{69} + 24 q^{70} + 8 q^{71} + 13 q^{72} + 4 q^{73} + 4 q^{74} + 33 q^{75} + 9 q^{76} + 38 q^{77} + 6 q^{78} - 17 q^{79} + 4 q^{80} + 13 q^{81} + 28 q^{82} + 14 q^{83} + 11 q^{84} + 4 q^{85} + q^{86} + 14 q^{87} + 7 q^{88} + 19 q^{89} + 4 q^{90} - 5 q^{91} + 2 q^{92} - 5 q^{93} + 12 q^{94} + 25 q^{95} + 13 q^{96} - 5 q^{97} + 32 q^{98} + 7 q^{99}+O(q^{100}) \) 13 * q + 13 * q^2 + 13 * q^3 + 13 * q^4 + 4 * q^5 + 13 * q^6 + 11 * q^7 + 13 * q^8 + 13 * q^9 + 4 * q^10 + 7 * q^11 + 13 * q^12 + 6 * q^13 + 11 * q^14 + 4 * q^15 + 13 * q^16 + 13 * q^17 + 13 * q^18 + 9 * q^19 + 4 * q^20 + 11 * q^21 + 7 * q^22 + 2 * q^23 + 13 * q^24 + 33 * q^25 + 6 * q^26 + 13 * q^27 + 11 * q^28 + 14 * q^29 + 4 * q^30 - 5 * q^31 + 13 * q^32 + 7 * q^33 + 13 * q^34 + 24 * q^35 + 13 * q^36 + 4 * q^37 + 9 * q^38 + 6 * q^39 + 4 * q^40 + 28 * q^41 + 11 * q^42 + q^43 + 7 * q^44 + 4 * q^45 + 2 * q^46 + 12 * q^47 + 13 * q^48 + 32 * q^49 + 33 * q^50 + 13 * q^51 + 6 * q^52 + 22 * q^53 + 13 * q^54 - 7 * q^55 + 11 * q^56 + 9 * q^57 + 14 * q^58 - 13 * q^59 + 4 * q^60 - 9 * q^61 - 5 * q^62 + 11 * q^63 + 13 * q^64 + 34 * q^65 + 7 * q^66 + 26 * q^67 + 13 * q^68 + 2 * q^69 + 24 * q^70 + 8 * q^71 + 13 * q^72 + 4 * q^73 + 4 * q^74 + 33 * q^75 + 9 * q^76 + 38 * q^77 + 6 * q^78 - 17 * q^79 + 4 * q^80 + 13 * q^81 + 28 * q^82 + 14 * q^83 + 11 * q^84 + 4 * q^85 + q^86 + 14 * q^87 + 7 * q^88 + 19 * q^89 + 4 * q^90 - 5 * q^91 + 2 * q^92 - 5 * q^93 + 12 * q^94 + 25 * q^95 + 13 * q^96 - 5 * q^97 + 32 * q^98 + 7 * 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
$5$	−3.91861	−1.75245	−0.876227	−	0.481899i	$-0.839947\pi$
$5$	−3.91861	−1.75245	−0.876227	+	0.481899i	$0.839947\pi$
$6$	1.00000	0.408248
$7$	−4.71846	−1.78341	−0.891705	−	0.452616i	$-0.850491\pi$
$7$	−4.71846	−1.78341	−0.891705	+	0.452616i	$0.850491\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−3.91861	−1.23917
$11$	−4.45672	−1.34375	−0.671876	−	0.740663i	$-0.734511\pi$
$11$	−4.45672	−1.34375	−0.671876	+	0.740663i	$0.734511\pi$
$12$	1.00000	0.288675
$13$	−3.78968	−1.05107	−0.525534	−	0.850773i	$-0.676134\pi$
$13$	−3.78968	−1.05107	−0.525534	+	0.850773i	$0.676134\pi$
$14$	−4.71846	−1.26106
$15$	−3.91861	−1.01178
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.00000	0.235702
$19$	−5.42803	−1.24528	−0.622638	−	0.782510i	$-0.713939\pi$
$19$	−5.42803	−1.24528	−0.622638	+	0.782510i	$0.713939\pi$
$20$	−3.91861	−0.876227
$21$	−4.71846	−1.02965
$22$	−4.45672	−0.950177
$23$	−5.61205	−1.17019	−0.585097	−	0.810963i	$-0.698944\pi$
$23$	−5.61205	−1.17019	−0.585097	+	0.810963i	$0.698944\pi$
$24$	1.00000	0.204124
$25$	10.3555	2.07109
$26$	−3.78968	−0.743217
$27$	1.00000	0.192450
$28$	−4.71846	−0.891705
$29$	8.21377	1.52526	0.762629	−	0.646836i	$-0.223908\pi$
$29$	8.21377	1.52526	0.762629	+	0.646836i	$0.223908\pi$
$30$	−3.91861	−0.715436
$31$	0.794436	0.142685	0.0713425	−	0.997452i	$-0.477272\pi$
$31$	0.794436	0.142685	0.0713425	+	0.997452i	$0.477272\pi$
$32$	1.00000	0.176777
$33$	−4.45672	−0.775816
$34$	1.00000	0.171499
$35$	18.4898	3.12535
$36$	1.00000	0.166667
$37$	−1.18372	−0.194602	−0.0973010	−	0.995255i	$-0.531021\pi$
$37$	−1.18372	−0.194602	−0.0973010	+	0.995255i	$0.531021\pi$
$38$	−5.42803	−0.880544
$39$	−3.78968	−0.606834
$40$	−3.91861	−0.619586
$41$	3.76358	0.587772	0.293886	−	0.955840i	$-0.405051\pi$
$41$	3.76358	0.587772	0.293886	+	0.955840i	$0.405051\pi$
$42$	−4.71846	−0.728074
$43$	1.63431	0.249231	0.124615	−	0.992205i	$-0.460230\pi$
$43$	1.63431	0.249231	0.124615	+	0.992205i	$0.460230\pi$
$44$	−4.45672	−0.671876
$45$	−3.91861	−0.584151
$46$	−5.61205	−0.827452
$47$	1.69423	0.247128	0.123564	−	0.992337i	$-0.460568\pi$
$47$	1.69423	0.247128	0.123564	+	0.992337i	$0.460568\pi$
$48$	1.00000	0.144338
$49$	15.2639	2.18055
$50$	10.3555	1.46449
$51$	1.00000	0.140028
$52$	−3.78968	−0.525534
$53$	−7.69402	−1.05685	−0.528427	−	0.848978i	$-0.677218\pi$
$53$	−7.69402	−1.05685	−0.528427	+	0.848978i	$0.677218\pi$
$54$	1.00000	0.136083
$55$	17.4641	2.35486
$56$	−4.71846	−0.630531
$57$	−5.42803	−0.718961
$58$	8.21377	1.07852
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−3.91861	−0.505890
$61$	1.91084	0.244658	0.122329	−	0.992490i	$-0.460964\pi$
$61$	1.91084	0.244658	0.122329	+	0.992490i	$0.460964\pi$
$62$	0.794436	0.100893
$63$	−4.71846	−0.594470
$64$	1.00000	0.125000
$65$	14.8503	1.84195
$66$	−4.45672	−0.548585
$67$	9.79474	1.19662	0.598309	−	0.801265i	$-0.295840\pi$
$67$	9.79474	1.19662	0.598309	+	0.801265i	$0.295840\pi$
$68$	1.00000	0.121268
$69$	−5.61205	−0.675612
$70$	18.4898	2.20995
$71$	−6.44292	−0.764634	−0.382317	−	0.924031i	$-0.624874\pi$
$71$	−6.44292	−0.764634	−0.382317	+	0.924031i	$0.624874\pi$
$72$	1.00000	0.117851
$73$	6.22571	0.728665	0.364332	−	0.931269i	$-0.381297\pi$
$73$	6.22571	0.728665	0.364332	+	0.931269i	$0.381297\pi$
$74$	−1.18372	−0.137604
$75$	10.3555	1.19575
$76$	−5.42803	−0.622638
$77$	21.0289	2.39646
$78$	−3.78968	−0.429097
$79$	−11.3942	−1.28195	−0.640974	−	0.767562i	$-0.721470\pi$
$79$	−11.3942	−1.28195	−0.640974	+	0.767562i	$0.721470\pi$
$80$	−3.91861	−0.438113
$81$	1.00000	0.111111
$82$	3.76358	0.415617
$83$	3.99214	0.438194	0.219097	−	0.975703i	$-0.429689\pi$
$83$	3.99214	0.438194	0.219097	+	0.975703i	$0.429689\pi$
$84$	−4.71846	−0.514826
$85$	−3.91861	−0.425032
$86$	1.63431	0.176233
$87$	8.21377	0.880608
$88$	−4.45672	−0.475088
$89$	−2.36997	−0.251216	−0.125608	−	0.992080i	$-0.540088\pi$
$89$	−2.36997	−0.251216	−0.125608	+	0.992080i	$0.540088\pi$
$90$	−3.91861	−0.413057
$91$	17.8815	1.87449
$92$	−5.61205	−0.585097
$93$	0.794436	0.0823792
$94$	1.69423	0.174746
$95$	21.2703	2.18229
$96$	1.00000	0.102062
$97$	−5.12947	−0.520819	−0.260409	−	0.965498i	$-0.583858\pi$
$97$	−5.12947	−0.520819	−0.260409	+	0.965498i	$0.583858\pi$
$98$	15.2639	1.54188
$99$	−4.45672	−0.447918
$100$	10.3555	1.03555
$101$	18.0874	1.79976	0.899880	−	0.436137i	$-0.143654\pi$
$101$	18.0874	1.79976	0.899880	+	0.436137i	$0.143654\pi$
$102$	1.00000	0.0990148
$103$	−10.9982	−1.08368	−0.541840	−	0.840482i	$-0.682272\pi$
$103$	−10.9982	−1.08368	−0.541840	+	0.840482i	$0.682272\pi$
$104$	−3.78968	−0.371609
$105$	18.4898	1.80442
$106$	−7.69402	−0.747309
$107$	−9.70005	−0.937739	−0.468869	−	0.883268i	$-0.655339\pi$
$107$	−9.70005	−0.937739	−0.468869	+	0.883268i	$0.655339\pi$
$108$	1.00000	0.0962250
$109$	8.81033	0.843877	0.421938	−	0.906624i	$-0.361350\pi$
$109$	8.81033	0.843877	0.421938	+	0.906624i	$0.361350\pi$
$110$	17.4641	1.66514
$111$	−1.18372	−0.112354
$112$	−4.71846	−0.445853
$113$	6.08320	0.572259	0.286130	−	0.958191i	$-0.407631\pi$
$113$	6.08320	0.572259	0.286130	+	0.958191i	$0.407631\pi$
$114$	−5.42803	−0.508382
$115$	21.9914	2.05071
$116$	8.21377	0.762629
$117$	−3.78968	−0.350356
$118$	−1.00000	−0.0920575
$119$	−4.71846	−0.432541
$120$	−3.91861	−0.357718
$121$	8.86238	0.805671
$122$	1.91084	0.172999
$123$	3.76358	0.339350
$124$	0.794436	0.0713425
$125$	−20.9860	−1.87704
$126$	−4.71846	−0.420354
$127$	−6.28642	−0.557830	−0.278915	−	0.960316i	$-0.589975\pi$
$127$	−6.28642	−0.557830	−0.278915	+	0.960316i	$0.589975\pi$
$128$	1.00000	0.0883883
$129$	1.63431	0.143893
$130$	14.8503	1.30245
$131$	−17.0406	−1.48884	−0.744421	−	0.667710i	$-0.767275\pi$
$131$	−17.0406	−1.48884	−0.744421	+	0.667710i	$0.767275\pi$
$132$	−4.45672	−0.387908
$133$	25.6120	2.22084
$134$	9.79474	0.846137
$135$	−3.91861	−0.337260
$136$	1.00000	0.0857493
$137$	3.69533	0.315713	0.157857	−	0.987462i	$-0.449542\pi$
$137$	3.69533	0.315713	0.157857	+	0.987462i	$0.449542\pi$
$138$	−5.61205	−0.477730
$139$	−18.5742	−1.57545	−0.787723	−	0.616029i	$-0.788740\pi$
$139$	−18.5742	−1.57545	−0.787723	+	0.616029i	$0.788740\pi$
$140$	18.4898	1.56267
$141$	1.69423	0.142680
$142$	−6.44292	−0.540678
$143$	16.8896	1.41238
$144$	1.00000	0.0833333
$145$	−32.1865	−2.67294
$146$	6.22571	0.515244
$147$	15.2639	1.25894
$148$	−1.18372	−0.0973010
$149$	4.09017	0.335080	0.167540	−	0.985865i	$-0.446418\pi$
$149$	4.09017	0.335080	0.167540	+	0.985865i	$0.446418\pi$
$150$	10.3555	0.845521
$151$	3.14599	0.256017	0.128009	−	0.991773i	$-0.459142\pi$
$151$	3.14599	0.256017	0.128009	+	0.991773i	$0.459142\pi$
$152$	−5.42803	−0.440272
$153$	1.00000	0.0808452
$154$	21.0289	1.69456
$155$	−3.11308	−0.250049
$156$	−3.78968	−0.303417
$157$	21.7172	1.73322	0.866609	−	0.498988i	$-0.166295\pi$
$157$	21.7172	1.73322	0.866609	+	0.498988i	$0.166295\pi$
$158$	−11.3942	−0.906475
$159$	−7.69402	−0.610175
$160$	−3.91861	−0.309793
$161$	26.4803	2.08694
$162$	1.00000	0.0785674
$163$	−3.36545	−0.263603	−0.131801	−	0.991276i	$-0.542076\pi$
$163$	−3.36545	−0.263603	−0.131801	+	0.991276i	$0.542076\pi$
$164$	3.76358	0.293886
$165$	17.4641	1.35958
$166$	3.99214	0.309850
$167$	−2.85566	−0.220978	−0.110489	−	0.993877i	$-0.535242\pi$
$167$	−2.85566	−0.220978	−0.110489	+	0.993877i	$0.535242\pi$
$168$	−4.71846	−0.364037
$169$	1.36167	0.104744
$170$	−3.91861	−0.300543
$171$	−5.42803	−0.415092
$172$	1.63431	0.124615
$173$	−0.558781	−0.0424833	−0.0212417	−	0.999774i	$-0.506762\pi$
$173$	−0.558781	−0.0424833	−0.0212417	+	0.999774i	$0.506762\pi$
$174$	8.21377	0.622684
$175$	−48.8619	−3.69361
$176$	−4.45672	−0.335938
$177$	−1.00000	−0.0751646
$178$	−2.36997	−0.177637
$179$	7.45996	0.557583	0.278792	−	0.960352i	$-0.410066\pi$
$179$	7.45996	0.557583	0.278792	+	0.960352i	$0.410066\pi$
$180$	−3.91861	−0.292076
$181$	−19.8339	−1.47425	−0.737123	−	0.675759i	$-0.763816\pi$
$181$	−19.8339	−1.47425	−0.737123	+	0.675759i	$0.763816\pi$
$182$	17.8815	1.32546
$183$	1.91084	0.141253
$184$	−5.61205	−0.413726
$185$	4.63852	0.341031
$186$	0.794436	0.0582509
$187$	−4.45672	−0.325908
$188$	1.69423	0.123564
$189$	−4.71846	−0.343218
$190$	21.2703	1.54311
$191$	1.15940	0.0838916	0.0419458	−	0.999120i	$-0.486644\pi$
$191$	1.15940	0.0838916	0.0419458	+	0.999120i	$0.486644\pi$
$192$	1.00000	0.0721688
$193$	10.7047	0.770544	0.385272	−	0.922803i	$-0.374108\pi$
$193$	10.7047	0.770544	0.385272	+	0.922803i	$0.374108\pi$
$194$	−5.12947	−0.368274
$195$	14.8503	1.06345
$196$	15.2639	1.09028
$197$	−6.86703	−0.489256	−0.244628	−	0.969617i	$-0.578666\pi$
$197$	−6.86703	−0.489256	−0.244628	+	0.969617i	$0.578666\pi$
$198$	−4.45672	−0.316726
$199$	−16.2794	−1.15402	−0.577009	−	0.816738i	$-0.695780\pi$
$199$	−16.2794	−1.15402	−0.577009	+	0.816738i	$0.695780\pi$
$200$	10.3555	0.732243
$201$	9.79474	0.690868
$202$	18.0874	1.27262
$203$	−38.7563	−2.72016
$204$	1.00000	0.0700140
$205$	−14.7480	−1.03004
$206$	−10.9982	−0.766277
$207$	−5.61205	−0.390065
$208$	−3.78968	−0.262767
$209$	24.1912	1.67334
$210$	18.4898	1.27592
$211$	19.4688	1.34029	0.670143	−	0.742232i	$-0.266233\pi$
$211$	19.4688	1.34029	0.670143	+	0.742232i	$0.266233\pi$
$212$	−7.69402	−0.528427
$213$	−6.44292	−0.441462
$214$	−9.70005	−0.663081
$215$	−6.40423	−0.436765
$216$	1.00000	0.0680414
$217$	−3.74852	−0.254466
$218$	8.81033	0.596711
$219$	6.22571	0.420695
$220$	17.4641	1.17743
$221$	−3.78968	−0.254921
$222$	−1.18372	−0.0794459
$223$	−14.4339	−0.966564	−0.483282	−	0.875465i	$-0.660555\pi$
$223$	−14.4339	−0.966564	−0.483282	+	0.875465i	$0.660555\pi$
$224$	−4.71846	−0.315265
$225$	10.3555	0.690365
$226$	6.08320	0.404648
$227$	5.52638	0.366799	0.183399	−	0.983039i	$-0.441290\pi$
$227$	5.52638	0.366799	0.183399	+	0.983039i	$0.441290\pi$
$228$	−5.42803	−0.359480
$229$	−23.9979	−1.58582	−0.792912	−	0.609336i	$-0.791436\pi$
$229$	−23.9979	−1.58582	−0.792912	+	0.609336i	$0.791436\pi$
$230$	21.9914	1.45007
$231$	21.0289	1.38360
$232$	8.21377	0.539260
$233$	6.90580	0.452414	0.226207	−	0.974079i	$-0.427367\pi$
$233$	6.90580	0.452414	0.226207	+	0.974079i	$0.427367\pi$
$234$	−3.78968	−0.247739
$235$	−6.63901	−0.433081
$236$	−1.00000	−0.0650945
$237$	−11.3942	−0.740134
$238$	−4.71846	−0.305852
$239$	−19.9781	−1.29227	−0.646137	−	0.763221i	$-0.723617\pi$
$239$	−19.9781	−1.29227	−0.646137	+	0.763221i	$0.723617\pi$
$240$	−3.91861	−0.252945
$241$	−30.7337	−1.97973	−0.989866	−	0.142006i	$-0.954645\pi$
$241$	−30.7337	−1.97973	−0.989866	+	0.142006i	$0.954645\pi$
$242$	8.86238	0.569695
$243$	1.00000	0.0641500
$244$	1.91084	0.122329
$245$	−59.8131	−3.82132
$246$	3.76358	0.239957
$247$	20.5705	1.30887
$248$	0.794436	0.0504467
$249$	3.99214	0.252991
$250$	−20.9860	−1.32727
$251$	19.4763	1.22933	0.614665	−	0.788788i	$-0.289291\pi$
$251$	19.4763	1.22933	0.614665	+	0.788788i	$0.289291\pi$
$252$	−4.71846	−0.297235
$253$	25.0114	1.57245
$254$	−6.28642	−0.394445
$255$	−3.91861	−0.245393
$256$	1.00000	0.0625000
$257$	1.46735	0.0915305	0.0457652	−	0.998952i	$-0.485427\pi$
$257$	1.46735	0.0915305	0.0457652	+	0.998952i	$0.485427\pi$
$258$	1.63431	0.101748
$259$	5.58533	0.347055
$260$	14.8503	0.920974
$261$	8.21377	0.508419
$262$	−17.0406	−1.05277
$263$	18.2418	1.12484	0.562418	−	0.826853i	$-0.309871\pi$
$263$	18.2418	1.12484	0.562418	+	0.826853i	$0.309871\pi$
$264$	−4.45672	−0.274292
$265$	30.1498	1.85209
$266$	25.6120	1.57037
$267$	−2.36997	−0.145040
$268$	9.79474	0.598309
$269$	25.1751	1.53495	0.767476	−	0.641077i	$-0.221512\pi$
$269$	25.1751	1.53495	0.767476	+	0.641077i	$0.221512\pi$
$270$	−3.91861	−0.238479
$271$	18.2494	1.10857	0.554287	−	0.832325i	$-0.312991\pi$
$271$	18.2494	1.10857	0.554287	+	0.832325i	$0.312991\pi$
$272$	1.00000	0.0606339
$273$	17.8815	1.08224
$274$	3.69533	0.223243
$275$	−46.1515	−2.78304
$276$	−5.61205	−0.337806
$277$	−18.9861	−1.14076	−0.570381	−	0.821380i	$-0.693204\pi$
$277$	−18.9861	−1.14076	−0.570381	+	0.821380i	$0.693204\pi$
$278$	−18.5742	−1.11401
$279$	0.794436	0.0475616
$280$	18.4898	1.10498
$281$	−4.49292	−0.268025	−0.134013	−	0.990980i	$-0.542786\pi$
$281$	−4.49292	−0.268025	−0.134013	+	0.990980i	$0.542786\pi$
$282$	1.69423	0.100890
$283$	26.7151	1.58805	0.794023	−	0.607888i	$-0.207983\pi$
$283$	26.7151	1.58805	0.794023	+	0.607888i	$0.207983\pi$
$284$	−6.44292	−0.382317
$285$	21.2703	1.25995
$286$	16.8896	0.998700
$287$	−17.7583	−1.04824
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	−32.1865	−1.89006
$291$	−5.12947	−0.300695
$292$	6.22571	0.364332
$293$	28.1574	1.64497	0.822485	−	0.568786i	$-0.192587\pi$
$293$	28.1574	1.64497	0.822485	+	0.568786i	$0.192587\pi$
$294$	15.2639	0.890207
$295$	3.91861	0.228150
$296$	−1.18372	−0.0688022
$297$	−4.45672	−0.258605
$298$	4.09017	0.236937
$299$	21.2679	1.22995
$300$	10.3555	0.597874
$301$	−7.71145	−0.444481
$302$	3.14599	0.181031
$303$	18.0874	1.03909
$304$	−5.42803	−0.311319
$305$	−7.48782	−0.428751
$306$	1.00000	0.0571662
$307$	21.9452	1.25248	0.626241	−	0.779630i	$-0.284593\pi$
$307$	21.9452	1.25248	0.626241	+	0.779630i	$0.284593\pi$
$308$	21.0289	1.19823
$309$	−10.9982	−0.625663
$310$	−3.11308	−0.176811
$311$	−7.74575	−0.439221	−0.219611	−	0.975588i	$-0.570479\pi$
$311$	−7.74575	−0.439221	−0.219611	+	0.975588i	$0.570479\pi$
$312$	−3.78968	−0.214548
$313$	19.6488	1.11062	0.555309	−	0.831644i	$-0.312600\pi$
$313$	19.6488	1.11062	0.555309	+	0.831644i	$0.312600\pi$
$314$	21.7172	1.22557
$315$	18.4898	1.04178
$316$	−11.3942	−0.640974
$317$	34.5637	1.94129	0.970646	−	0.240514i	$-0.0773159\pi$
$317$	34.5637	1.94129	0.970646	+	0.240514i	$0.0773159\pi$
$318$	−7.69402	−0.431459
$319$	−36.6065	−2.04957
$320$	−3.91861	−0.219057
$321$	−9.70005	−0.541404
$322$	26.4803	1.47569
$323$	−5.42803	−0.302024
$324$	1.00000	0.0555556
$325$	−39.2439	−2.17686
$326$	−3.36545	−0.186395
$327$	8.81033	0.487213
$328$	3.76358	0.207809
$329$	−7.99414	−0.440731
$330$	17.4641	0.961369
$331$	−14.4774	−0.795749	−0.397874	−	0.917440i	$-0.630252\pi$
$331$	−14.4774	−0.795749	−0.397874	+	0.917440i	$0.630252\pi$
$332$	3.99214	0.219097
$333$	−1.18372	−0.0648673
$334$	−2.85566	−0.156255
$335$	−38.3817	−2.09702
$336$	−4.71846	−0.257413
$337$	34.7556	1.89326	0.946630	−	0.322322i	$-0.104463\pi$
$337$	34.7556	1.89326	0.946630	+	0.322322i	$0.104463\pi$
$338$	1.36167	0.0740653
$339$	6.08320	0.330394
$340$	−3.91861	−0.212516
$341$	−3.54058	−0.191733
$342$	−5.42803	−0.293515
$343$	−38.9928	−2.10541
$344$	1.63431	0.0881163
$345$	21.9914	1.18398
$346$	−0.558781	−0.0300402
$347$	11.3614	0.609911	0.304956	−	0.952367i	$-0.401358\pi$
$347$	11.3614	0.609911	0.304956	+	0.952367i	$0.401358\pi$
$348$	8.21377	0.440304
$349$	−26.9003	−1.43994	−0.719971	−	0.694004i	$-0.755845\pi$
$349$	−26.9003	−1.43994	−0.719971	+	0.694004i	$0.755845\pi$
$350$	−48.8619	−2.61178
$351$	−3.78968	−0.202278
$352$	−4.45672	−0.237544
$353$	−25.7949	−1.37293	−0.686463	−	0.727165i	$-0.740838\pi$
$353$	−25.7949	−1.37293	−0.686463	+	0.727165i	$0.740838\pi$
$354$	−1.00000	−0.0531494
$355$	25.2473	1.33999
$356$	−2.36997	−0.125608
$357$	−4.71846	−0.249727
$358$	7.45996	0.394271
$359$	−6.31430	−0.333256	−0.166628	−	0.986020i	$-0.553288\pi$
$359$	−6.31430	−0.333256	−0.166628	+	0.986020i	$0.553288\pi$
$360$	−3.91861	−0.206529
$361$	10.4636	0.550714
$362$	−19.8339	−1.04245
$363$	8.86238	0.465154
$364$	17.8815	0.937243
$365$	−24.3961	−1.27695
$366$	1.91084	0.0998810
$367$	13.2057	0.689334	0.344667	−	0.938725i	$-0.387992\pi$
$367$	13.2057	0.689334	0.344667	+	0.938725i	$0.387992\pi$
$368$	−5.61205	−0.292549
$369$	3.76358	0.195924
$370$	4.63852	0.241145
$371$	36.3039	1.88481
$372$	0.794436	0.0411896
$373$	0.131396	0.00680342	0.00340171	−	0.999994i	$-0.498917\pi$
$373$	0.131396	0.00680342	0.00340171	+	0.999994i	$0.498917\pi$
$374$	−4.45672	−0.230452
$375$	−20.9860	−1.08371
$376$	1.69423	0.0873731
$377$	−31.1275	−1.60315
$378$	−4.71846	−0.242691
$379$	−26.7804	−1.37562	−0.687809	−	0.725891i	$-0.741427\pi$
$379$	−26.7804	−1.37562	−0.687809	+	0.725891i	$0.741427\pi$
$380$	21.2703	1.09114
$381$	−6.28642	−0.322063
$382$	1.15940	0.0593203
$383$	33.8185	1.72804	0.864022	−	0.503453i	$-0.167937\pi$
$383$	33.8185	1.72804	0.864022	+	0.503453i	$0.167937\pi$
$384$	1.00000	0.0510310
$385$	−82.4039	−4.19969
$386$	10.7047	0.544857
$387$	1.63431	0.0830769
$388$	−5.12947	−0.260409
$389$	35.6438	1.80721	0.903605	−	0.428366i	$-0.140911\pi$
$389$	35.6438	1.80721	0.903605	+	0.428366i	$0.140911\pi$
$390$	14.8503	0.751972
$391$	−5.61205	−0.283814
$392$	15.2639	0.770942
$393$	−17.0406	−0.859584
$394$	−6.86703	−0.345956
$395$	44.6494	2.24656
$396$	−4.45672	−0.223959
$397$	−20.3819	−1.02294	−0.511470	−	0.859301i	$-0.670899\pi$
$397$	−20.3819	−1.02294	−0.511470	+	0.859301i	$0.670899\pi$
$398$	−16.2794	−0.816013
$399$	25.6120	1.28220
$400$	10.3555	0.517774
$401$	17.5856	0.878183	0.439091	−	0.898442i	$-0.355300\pi$
$401$	17.5856	0.878183	0.439091	+	0.898442i	$0.355300\pi$
$402$	9.79474	0.488517
$403$	−3.01066	−0.149972
$404$	18.0874	0.899880
$405$	−3.91861	−0.194717
$406$	−38.7563	−1.92344
$407$	5.27550	0.261497
$408$	1.00000	0.0495074
$409$	−21.8356	−1.07970	−0.539850	−	0.841761i	$-0.681519\pi$
$409$	−21.8356	−1.07970	−0.539850	+	0.841761i	$0.681519\pi$
$410$	−14.7480	−0.728351
$411$	3.69533	0.182277
$412$	−10.9982	−0.541840
$413$	4.71846	0.232180
$414$	−5.61205	−0.275817
$415$	−15.6436	−0.767915
$416$	−3.78968	−0.185804
$417$	−18.5742	−0.909585
$418$	24.1912	1.18323
$419$	1.66256	0.0812213	0.0406106	−	0.999175i	$-0.487070\pi$
$419$	1.66256	0.0812213	0.0406106	+	0.999175i	$0.487070\pi$
$420$	18.4898	0.902209
$421$	13.3376	0.650035	0.325017	−	0.945708i	$-0.394630\pi$
$421$	13.3376	0.650035	0.325017	+	0.945708i	$0.394630\pi$
$422$	19.4688	0.947726
$423$	1.69423	0.0823761
$424$	−7.69402	−0.373655
$425$	10.3555	0.502314
$426$	−6.44292	−0.312161
$427$	−9.01621	−0.436325
$428$	−9.70005	−0.468869
$429$	16.8896	0.815435
$430$	−6.40423	−0.308840
$431$	−31.0415	−1.49522	−0.747609	−	0.664139i	$-0.768798\pi$
$431$	−31.0415	−1.49522	−0.747609	+	0.664139i	$0.768798\pi$
$432$	1.00000	0.0481125
$433$	−11.3394	−0.544938	−0.272469	−	0.962165i	$-0.587840\pi$
$433$	−11.3394	−0.544938	−0.272469	+	0.962165i	$0.587840\pi$
$434$	−3.74852	−0.179935
$435$	−32.1865	−1.54323
$436$	8.81033	0.421938
$437$	30.4624	1.45722
$438$	6.22571	0.297476
$439$	−29.2988	−1.39836	−0.699178	−	0.714948i	$-0.746450\pi$
$439$	−29.2988	−1.39836	−0.699178	+	0.714948i	$0.746450\pi$
$440$	17.4641	0.832570
$441$	15.2639	0.726851
$442$	−3.78968	−0.180257
$443$	33.8156	1.60663	0.803313	−	0.595557i	$-0.203069\pi$
$443$	33.8156	1.60663	0.803313	+	0.595557i	$0.203069\pi$
$444$	−1.18372	−0.0561768
$445$	9.28698	0.440245
$446$	−14.4339	−0.683464
$447$	4.09017	0.193458
$448$	−4.71846	−0.222926
$449$	24.9803	1.17889	0.589446	−	0.807808i	$-0.299346\pi$
$449$	24.9803	1.17889	0.589446	+	0.807808i	$0.299346\pi$
$450$	10.3555	0.488162
$451$	−16.7732	−0.789820
$452$	6.08320	0.286130
$453$	3.14599	0.147811
$454$	5.52638	0.259366
$455$	−70.0704	−3.28495
$456$	−5.42803	−0.254191
$457$	−12.2866	−0.574745	−0.287373	−	0.957819i	$-0.592782\pi$
$457$	−12.2866	−0.574745	−0.287373	+	0.957819i	$0.592782\pi$
$458$	−23.9979	−1.12135
$459$	1.00000	0.0466760
$460$	21.9914	1.02536
$461$	−12.9317	−0.602291	−0.301146	−	0.953578i	$-0.597369\pi$
$461$	−12.9317	−0.602291	−0.301146	+	0.953578i	$0.597369\pi$
$462$	21.0289	0.978352
$463$	−1.48470	−0.0689997	−0.0344999	−	0.999405i	$-0.510984\pi$
$463$	−1.48470	−0.0689997	−0.0344999	+	0.999405i	$0.510984\pi$
$464$	8.21377	0.381314
$465$	−3.11308	−0.144366
$466$	6.90580	0.319905
$467$	−5.57200	−0.257842	−0.128921	−	0.991655i	$-0.541151\pi$
$467$	−5.57200	−0.257842	−0.128921	+	0.991655i	$0.541151\pi$
$468$	−3.78968	−0.175178
$469$	−46.2161	−2.13406
$470$	−6.63901	−0.306235
$471$	21.7172	1.00067
$472$	−1.00000	−0.0460287
$473$	−7.28369	−0.334904
$474$	−11.3942	−0.523353
$475$	−56.2099	−2.57909
$476$	−4.71846	−0.216270
$477$	−7.69402	−0.352285
$478$	−19.9781	−0.913776
$479$	15.6138	0.713414	0.356707	−	0.934216i	$-0.383899\pi$
$479$	15.6138	0.713414	0.356707	+	0.934216i	$0.383899\pi$
$480$	−3.91861	−0.178859
$481$	4.48591	0.204540
$482$	−30.7337	−1.39988
$483$	26.4803	1.20489
$484$	8.86238	0.402835
$485$	20.1004	0.912711
$486$	1.00000	0.0453609
$487$	−29.7538	−1.34827	−0.674137	−	0.738606i	$-0.735484\pi$
$487$	−29.7538	−1.34827	−0.674137	+	0.738606i	$0.735484\pi$
$488$	1.91084	0.0864995
$489$	−3.36545	−0.152191
$490$	−59.8131	−2.70208
$491$	−0.0772158	−0.00348470	−0.00174235	−	0.999998i	$-0.500555\pi$
$491$	−0.0772158	−0.00348470	−0.00174235	+	0.999998i	$0.500555\pi$
$492$	3.76358	0.169675
$493$	8.21377	0.369929
$494$	20.5705	0.925511
$495$	17.4641	0.784955
$496$	0.794436	0.0356712
$497$	30.4007	1.36366
$498$	3.99214	0.178892
$499$	43.8706	1.96392	0.981959	−	0.189093i	$-0.0605546\pi$
$499$	43.8706	1.96392	0.981959	+	0.189093i	$0.0605546\pi$
$500$	−20.9860	−0.938522
$501$	−2.85566	−0.127582
$502$	19.4763	0.869268
$503$	−18.8757	−0.841628	−0.420814	−	0.907147i	$-0.638255\pi$
$503$	−18.8757	−0.841628	−0.420814	+	0.907147i	$0.638255\pi$
$504$	−4.71846	−0.210177
$505$	−70.8773	−3.15400
$506$	25.0114	1.11189
$507$	1.36167	0.0604741
$508$	−6.28642	−0.278915
$509$	7.44540	0.330012	0.165006	−	0.986293i	$-0.447236\pi$
$509$	7.44540	0.330012	0.165006	+	0.986293i	$0.447236\pi$
$510$	−3.91861	−0.173519
$511$	−29.3758	−1.29951
$512$	1.00000	0.0441942
$513$	−5.42803	−0.239654
$514$	1.46735	0.0647218
$515$	43.0974	1.89910
$516$	1.63431	0.0719467
$517$	−7.55070	−0.332079
$518$	5.58533	0.245405
$519$	−0.558781	−0.0245277
$520$	14.8503	0.651227
$521$	36.2690	1.58898	0.794488	−	0.607280i	$-0.207739\pi$
$521$	36.2690	1.58898	0.794488	+	0.607280i	$0.207739\pi$
$522$	8.21377	0.359507
$523$	11.4789	0.501937	0.250969	−	0.967995i	$-0.419251\pi$
$523$	11.4789	0.501937	0.250969	+	0.967995i	$0.419251\pi$
$524$	−17.0406	−0.744421
$525$	−48.8619	−2.13251
$526$	18.2418	0.795379
$527$	0.794436	0.0346062
$528$	−4.45672	−0.193954
$529$	8.49515	0.369354
$530$	30.1498	1.30962
$531$	−1.00000	−0.0433963
$532$	25.6120	1.11042
$533$	−14.2628	−0.617788
$534$	−2.36997	−0.102559
$535$	38.0107	1.64334
$536$	9.79474	0.423068
$537$	7.45996	0.321921
$538$	25.1751	1.08538
$539$	−68.0269	−2.93012
$540$	−3.91861	−0.168630
$541$	−13.5055	−0.580647	−0.290323	−	0.956929i	$-0.593763\pi$
$541$	−13.5055	−0.580647	−0.290323	+	0.956929i	$0.593763\pi$
$542$	18.2494	0.783880
$543$	−19.8339	−0.851156
$544$	1.00000	0.0428746
$545$	−34.5242	−1.47886
$546$	17.8815	0.765256
$547$	38.8769	1.66226	0.831128	−	0.556081i	$-0.187696\pi$
$547$	38.8769	1.66226	0.831128	+	0.556081i	$0.187696\pi$
$548$	3.69533	0.157857
$549$	1.91084	0.0815525
$550$	−46.1515	−1.96791
$551$	−44.5846	−1.89937
$552$	−5.61205	−0.238865
$553$	53.7631	2.28624
$554$	−18.9861	−0.806640
$555$	4.63852	0.196894
$556$	−18.5742	−0.787723
$557$	−11.5858	−0.490907	−0.245453	−	0.969408i	$-0.578937\pi$
$557$	−11.5858	−0.490907	−0.245453	+	0.969408i	$0.578937\pi$
$558$	0.794436	0.0336312
$559$	−6.19353	−0.261958
$560$	18.4898	0.781336
$561$	−4.45672	−0.188163
$562$	−4.49292	−0.189522
$563$	27.5850	1.16257	0.581285	−	0.813700i	$-0.302550\pi$
$563$	27.5850	1.16257	0.581285	+	0.813700i	$0.302550\pi$
$564$	1.69423	0.0713398
$565$	−23.8377	−1.00286
$566$	26.7151	1.12292
$567$	−4.71846	−0.198157
$568$	−6.44292	−0.270339
$569$	20.2714	0.849821	0.424911	−	0.905235i	$-0.360305\pi$
$569$	20.2714	0.849821	0.424911	+	0.905235i	$0.360305\pi$
$570$	21.2703	0.890916
$571$	25.5405	1.06884	0.534418	−	0.845220i	$-0.320531\pi$
$571$	25.5405	1.06884	0.534418	+	0.845220i	$0.320531\pi$
$572$	16.8896	0.706188
$573$	1.15940	0.0484348
$574$	−17.7583	−0.741217
$575$	−58.1155	−2.42358
$576$	1.00000	0.0416667
$577$	−31.7717	−1.32267	−0.661337	−	0.750089i	$-0.730010\pi$
$577$	−31.7717	−1.32267	−0.661337	+	0.750089i	$0.730010\pi$
$578$	1.00000	0.0415945
$579$	10.7047	0.444874
$580$	−32.1865	−1.33647
$581$	−18.8367	−0.781480
$582$	−5.12947	−0.212623
$583$	34.2901	1.42015
$584$	6.22571	0.257622
$585$	14.8503	0.613983
$586$	28.1574	1.16317
$587$	16.4294	0.678114	0.339057	−	0.940766i	$-0.389892\pi$
$587$	16.4294	0.678114	0.339057	+	0.940766i	$0.389892\pi$
$588$	15.2639	0.629472
$589$	−4.31223	−0.177682
$590$	3.91861	0.161326
$591$	−6.86703	−0.282472
$592$	−1.18372	−0.0486505
$593$	−13.9808	−0.574121	−0.287060	−	0.957912i	$-0.592678\pi$
$593$	−13.9808	−0.574121	−0.287060	+	0.957912i	$0.592678\pi$
$594$	−4.45672	−0.182862
$595$	18.4898	0.758008
$596$	4.09017	0.167540
$597$	−16.2794	−0.666272
$598$	21.2679	0.869709
$599$	−11.6783	−0.477163	−0.238581	−	0.971123i	$-0.576682\pi$
$599$	−11.6783	−0.477163	−0.238581	+	0.971123i	$0.576682\pi$
$600$	10.3555	0.422760
$601$	−40.4310	−1.64922	−0.824608	−	0.565705i	$-0.808604\pi$
$601$	−40.4310	−1.64922	−0.824608	+	0.565705i	$0.808604\pi$
$602$	−7.71145	−0.314295
$603$	9.79474	0.398873
$604$	3.14599	0.128009
$605$	−34.7282	−1.41190
$606$	18.0874	0.734749
$607$	36.4306	1.47867	0.739337	−	0.673335i	$-0.235139\pi$
$607$	36.4306	1.47867	0.739337	+	0.673335i	$0.235139\pi$
$608$	−5.42803	−0.220136
$609$	−38.7563	−1.57049
$610$	−7.48782	−0.303173
$611$	−6.42058	−0.259749
$612$	1.00000	0.0404226
$613$	−9.61479	−0.388338	−0.194169	−	0.980968i	$-0.562201\pi$
$613$	−9.61479	−0.388338	−0.194169	+	0.980968i	$0.562201\pi$
$614$	21.9452	0.885638
$615$	−14.7480	−0.594696
$616$	21.0289	0.847278
$617$	13.0429	0.525089	0.262545	−	0.964920i	$-0.415438\pi$
$617$	13.0429	0.525089	0.262545	+	0.964920i	$0.415438\pi$
$618$	−10.9982	−0.442411
$619$	30.9217	1.24285	0.621424	−	0.783475i	$-0.286555\pi$
$619$	30.9217	1.24285	0.621424	+	0.783475i	$0.286555\pi$
$620$	−3.11308	−0.125024
$621$	−5.61205	−0.225204
$622$	−7.74575	−0.310576
$623$	11.1826	0.448022
$624$	−3.78968	−0.151709
$625$	30.4585	1.21834
$626$	19.6488	0.785325
$627$	24.1912	0.966105
$628$	21.7172	0.866609
$629$	−1.18372	−0.0471979
$630$	18.4898	0.736651
$631$	33.7845	1.34494	0.672469	−	0.740125i	$-0.265234\pi$
$631$	33.7845	1.34494	0.672469	+	0.740125i	$0.265234\pi$
$632$	−11.3942	−0.453237
$633$	19.4688	0.773815
$634$	34.5637	1.37270
$635$	24.6340	0.977571
$636$	−7.69402	−0.305088
$637$	−57.8452	−2.29191
$638$	−36.6065	−1.44926
$639$	−6.44292	−0.254878
$640$	−3.91861	−0.154897
$641$	−39.5497	−1.56212	−0.781060	−	0.624456i	$-0.785321\pi$
$641$	−39.5497	−1.56212	−0.781060	+	0.624456i	$0.785321\pi$
$642$	−9.70005	−0.382830
$643$	−46.6193	−1.83849	−0.919243	−	0.393691i	$-0.871198\pi$
$643$	−46.6193	−1.83849	−0.919243	+	0.393691i	$0.871198\pi$
$644$	26.4803	1.04347
$645$	−6.40423	−0.252166
$646$	−5.42803	−0.213563
$647$	18.2873	0.718949	0.359474	−	0.933155i	$-0.382956\pi$
$647$	18.2873	0.718949	0.359474	+	0.933155i	$0.382956\pi$
$648$	1.00000	0.0392837
$649$	4.45672	0.174942
$650$	−39.2439	−1.53927
$651$	−3.74852	−0.146916
$652$	−3.36545	−0.131801
$653$	32.2956	1.26382	0.631912	−	0.775040i	$-0.282271\pi$
$653$	32.2956	1.26382	0.631912	+	0.775040i	$0.282271\pi$
$654$	8.81033	0.344511
$655$	66.7753	2.60913
$656$	3.76358	0.146943
$657$	6.22571	0.242888
$658$	−7.99414	−0.311644
$659$	20.2674	0.789504	0.394752	−	0.918788i	$-0.370830\pi$
$659$	20.2674	0.789504	0.394752	+	0.918788i	$0.370830\pi$
$660$	17.4641	0.679791
$661$	−24.1394	−0.938914	−0.469457	−	0.882955i	$-0.655550\pi$
$661$	−24.1394	−0.938914	−0.469457	+	0.882955i	$0.655550\pi$
$662$	−14.4774	−0.562679
$663$	−3.78968	−0.147179
$664$	3.99214	0.154925
$665$	−100.363	−3.89192
$666$	−1.18372	−0.0458681
$667$	−46.0961	−1.78485
$668$	−2.85566	−0.110489
$669$	−14.4339	−0.558046
$670$	−38.3817	−1.48282
$671$	−8.51607	−0.328759
$672$	−4.71846	−0.182019
$673$	11.9842	0.461955	0.230978	−	0.972959i	$-0.425808\pi$
$673$	11.9842	0.461955	0.230978	+	0.972959i	$0.425808\pi$
$674$	34.7556	1.33874
$675$	10.3555	0.398582
$676$	1.36167	0.0523721
$677$	−35.1751	−1.35189	−0.675944	−	0.736953i	$-0.736264\pi$
$677$	−35.1751	−1.35189	−0.675944	+	0.736953i	$0.736264\pi$
$678$	6.08320	0.233624
$679$	24.2032	0.928833
$680$	−3.91861	−0.150272
$681$	5.52638	0.211771
$682$	−3.54058	−0.135576
$683$	2.25333	0.0862214	0.0431107	−	0.999070i	$-0.486273\pi$
$683$	2.25333	0.0862214	0.0431107	+	0.999070i	$0.486273\pi$
$684$	−5.42803	−0.207546
$685$	−14.4805	−0.553273
$686$	−38.9928	−1.48875
$687$	−23.9979	−0.915576
$688$	1.63431	0.0623077
$689$	29.1579	1.11083
$690$	21.9914	0.837199
$691$	−29.2022	−1.11090	−0.555452	−	0.831549i	$-0.687455\pi$
$691$	−29.2022	−1.11090	−0.555452	+	0.831549i	$0.687455\pi$
$692$	−0.558781	−0.0212417
$693$	21.0289	0.798821
$694$	11.3614	0.431272
$695$	72.7851	2.76090
$696$	8.21377	0.311342
$697$	3.76358	0.142556
$698$	−26.9003	−1.01819
$699$	6.90580	0.261201
$700$	−48.8619	−1.84681
$701$	2.54538	0.0961376	0.0480688	−	0.998844i	$-0.484693\pi$
$701$	2.54538	0.0961376	0.0480688	+	0.998844i	$0.484693\pi$
$702$	−3.78968	−0.143032
$703$	6.42526	0.242333
$704$	−4.45672	−0.167969
$705$	−6.63901	−0.250040
$706$	−25.7949	−0.970805
$707$	−85.3445	−3.20971
$708$	−1.00000	−0.0375823
$709$	29.5244	1.10881	0.554405	−	0.832247i	$-0.312946\pi$
$709$	29.5244	1.10881	0.554405	+	0.832247i	$0.312946\pi$
$710$	25.2473	0.947514
$711$	−11.3942	−0.427316
$712$	−2.36997	−0.0888184
$713$	−4.45842	−0.166969
$714$	−4.71846	−0.176584
$715$	−66.1835	−2.47512
$716$	7.45996	0.278792
$717$	−19.9781	−0.746095
$718$	−6.31430	−0.235647
$719$	−16.0672	−0.599206	−0.299603	−	0.954064i	$-0.596854\pi$
$719$	−16.0672	−0.599206	−0.299603	+	0.954064i	$0.596854\pi$
$720$	−3.91861	−0.146038
$721$	51.8943	1.93265
$722$	10.4636	0.389414
$723$	−30.7337	−1.14300
$724$	−19.8339	−0.737123
$725$	85.0574	3.15895
$726$	8.86238	0.328914
$727$	28.3656	1.05202	0.526010	−	0.850478i	$-0.323687\pi$
$727$	28.3656	1.05202	0.526010	+	0.850478i	$0.323687\pi$
$728$	17.8815	0.662731
$729$	1.00000	0.0370370
$730$	−24.3961	−0.902941
$731$	1.63431	0.0604473
$732$	1.91084	0.0706265
$733$	−7.05180	−0.260464	−0.130232	−	0.991484i	$-0.541572\pi$
$733$	−7.05180	−0.260464	−0.130232	+	0.991484i	$0.541572\pi$
$734$	13.2057	0.487433
$735$	−59.8131	−2.20624
$736$	−5.61205	−0.206863
$737$	−43.6524	−1.60796
$738$	3.76358	0.138539
$739$	−40.7726	−1.49985	−0.749923	−	0.661525i	$-0.769909\pi$
$739$	−40.7726	−1.49985	−0.749923	+	0.661525i	$0.769909\pi$
$740$	4.63852	0.170515
$741$	20.5705	0.755677
$742$	36.3039	1.33276
$743$	14.7028	0.539394	0.269697	−	0.962945i	$-0.413077\pi$
$743$	14.7028	0.539394	0.269697	+	0.962945i	$0.413077\pi$
$744$	0.794436	0.0291254
$745$	−16.0278	−0.587211
$746$	0.131396	0.00481075
$747$	3.99214	0.146065
$748$	−4.45672	−0.162954
$749$	45.7693	1.67237
$750$	−20.9860	−0.766300
$751$	−46.6297	−1.70154	−0.850771	−	0.525537i	$-0.823865\pi$
$751$	−46.6297	−1.70154	−0.850771	+	0.525537i	$0.823865\pi$
$752$	1.69423	0.0617821
$753$	19.4763	0.709754
$754$	−31.1275	−1.13360
$755$	−12.3279	−0.448658
$756$	−4.71846	−0.171609
$757$	13.3551	0.485400	0.242700	−	0.970101i	$-0.421967\pi$
$757$	13.3551	0.485400	0.242700	+	0.970101i	$0.421967\pi$
$758$	−26.7804	−0.972709
$759$	25.0114	0.907855
$760$	21.2703	0.771556
$761$	−45.9381	−1.66525	−0.832627	−	0.553834i	$-0.813164\pi$
$761$	−45.9381	−1.66525	−0.832627	+	0.553834i	$0.813164\pi$
$762$	−6.28642	−0.227733
$763$	−41.5712	−1.50498
$764$	1.15940	0.0419458
$765$	−3.91861	−0.141677
$766$	33.8185	1.22191
$767$	3.78968	0.136837
$768$	1.00000	0.0360844
$769$	34.5657	1.24647	0.623235	−	0.782035i	$-0.285818\pi$
$769$	34.5657	1.24647	0.623235	+	0.782035i	$0.285818\pi$
$770$	−82.4039	−2.96963
$771$	1.46735	0.0528451
$772$	10.7047	0.385272
$773$	−48.9381	−1.76018	−0.880090	−	0.474807i	$-0.842518\pi$
$773$	−48.9381	−1.76018	−0.880090	+	0.474807i	$0.842518\pi$
$774$	1.63431	0.0587442
$775$	8.22676	0.295514
$776$	−5.12947	−0.184137
$777$	5.58533	0.200372
$778$	35.6438	1.27789
$779$	−20.4288	−0.731939
$780$	14.8503	0.531725
$781$	28.7143	1.02748
$782$	−5.61205	−0.200687
$783$	8.21377	0.293536
$784$	15.2639	0.545138
$785$	−85.1010	−3.03738
$786$	−17.0406	−0.607818
$787$	−41.5689	−1.48177	−0.740886	−	0.671631i	$-0.765594\pi$
$787$	−41.5689	−1.48177	−0.740886	+	0.671631i	$0.765594\pi$
$788$	−6.86703	−0.244628
$789$	18.2418	0.649424
$790$	44.6494	1.58856
$791$	−28.7033	−1.02057
$792$	−4.45672	−0.158363
$793$	−7.24146	−0.257152
$794$	−20.3819	−0.723328
$795$	30.1498	1.06930
$796$	−16.2794	−0.577009
$797$	−4.12568	−0.146139	−0.0730695	−	0.997327i	$-0.523280\pi$
$797$	−4.12568	−0.146139	−0.0730695	+	0.997327i	$0.523280\pi$
$798$	25.6120	0.906654
$799$	1.69423	0.0599374
$800$	10.3555	0.366121
$801$	−2.36997	−0.0837388
$802$	17.5856	0.620969
$803$	−27.7463	−0.979145
$804$	9.79474	0.345434
$805$	−103.766	−3.65726
$806$	−3.01066	−0.106046
$807$	25.1751	0.886205
$808$	18.0874	0.636311
$809$	20.9642	0.737063	0.368531	−	0.929615i	$-0.379861\pi$
$809$	20.9642	0.737063	0.368531	+	0.929615i	$0.379861\pi$
$810$	−3.91861	−0.137686
$811$	45.3720	1.59323	0.796614	−	0.604489i	$-0.206622\pi$
$811$	45.3720	1.59323	0.796614	+	0.604489i	$0.206622\pi$
$812$	−38.7563	−1.36008
$813$	18.2494	0.640036
$814$	5.27550	0.184906
$815$	13.1879	0.461951
$816$	1.00000	0.0350070
$817$	−8.87112	−0.310361
$818$	−21.8356	−0.763463
$819$	17.8815	0.624829
$820$	−14.7480	−0.515022
$821$	−7.06101	−0.246431	−0.123215	−	0.992380i	$-0.539321\pi$
$821$	−7.06101	−0.246431	−0.123215	+	0.992380i	$0.539321\pi$
$822$	3.69533	0.128889
$823$	26.4633	0.922452	0.461226	−	0.887283i	$-0.347410\pi$
$823$	26.4633	0.922452	0.461226	+	0.887283i	$0.347410\pi$
$824$	−10.9982	−0.383139
$825$	−46.1515	−1.60679
$826$	4.71846	0.164176
$827$	25.4006	0.883265	0.441633	−	0.897196i	$-0.354399\pi$
$827$	25.4006	0.883265	0.441633	+	0.897196i	$0.354399\pi$
$828$	−5.61205	−0.195032
$829$	22.2311	0.772118	0.386059	−	0.922474i	$-0.373836\pi$
$829$	22.2311	0.772118	0.386059	+	0.922474i	$0.373836\pi$
$830$	−15.6436	−0.542998
$831$	−18.9861	−0.658619
$832$	−3.78968	−0.131384
$833$	15.2639	0.528862
$834$	−18.5742	−0.643174
$835$	11.1902	0.387253
$836$	24.1912	0.836672
$837$	0.794436	0.0274597
$838$	1.66256	0.0574321
$839$	−22.6422	−0.781697	−0.390848	−	0.920455i	$-0.627818\pi$
$839$	−22.6422	−0.781697	−0.390848	+	0.920455i	$0.627818\pi$
$840$	18.4898	0.637958
$841$	38.4659	1.32641
$842$	13.3376	0.459644
$843$	−4.49292	−0.154744
$844$	19.4688	0.670143
$845$	−5.33586	−0.183559
$846$	1.69423	0.0582487
$847$	−41.8168	−1.43684
$848$	−7.69402	−0.264214
$849$	26.7151	0.916858
$850$	10.3555	0.355190
$851$	6.64309	0.227722
$852$	−6.44292	−0.220731
$853$	−0.553542	−0.0189529	−0.00947646	−	0.999955i	$-0.503016\pi$
$853$	−0.553542	−0.0189529	−0.00947646	+	0.999955i	$0.503016\pi$
$854$	−9.01621	−0.308528
$855$	21.2703	0.727430
$856$	−9.70005	−0.331541
$857$	−10.0285	−0.342567	−0.171284	−	0.985222i	$-0.554791\pi$
$857$	−10.0285	−0.342567	−0.171284	+	0.985222i	$0.554791\pi$
$858$	16.8896	0.576600
$859$	49.0405	1.67324	0.836620	−	0.547784i	$-0.184528\pi$
$859$	49.0405	1.67324	0.836620	+	0.547784i	$0.184528\pi$
$860$	−6.40423	−0.218383
$861$	−17.7583	−0.605201
$862$	−31.0415	−1.05728
$863$	19.0673	0.649058	0.324529	−	0.945876i	$-0.394794\pi$
$863$	19.0673	0.649058	0.324529	+	0.945876i	$0.394794\pi$
$864$	1.00000	0.0340207
$865$	2.18964	0.0744500
$866$	−11.3394	−0.385329
$867$	1.00000	0.0339618
$868$	−3.74852	−0.127233
$869$	50.7808	1.72262
$870$	−32.1865	−1.09122
$871$	−37.1189	−1.25773
$872$	8.81033	0.298356
$873$	−5.12947	−0.173606
$874$	30.4624	1.03041
$875$	99.0216	3.34754
$876$	6.22571	0.210347
$877$	24.5701	0.829672	0.414836	−	0.909896i	$-0.363839\pi$
$877$	24.5701	0.829672	0.414836	+	0.909896i	$0.363839\pi$
$878$	−29.2988	−0.988786
$879$	28.1574	0.949724
$880$	17.4641	0.588716
$881$	24.1442	0.813439	0.406720	−	0.913553i	$-0.366673\pi$
$881$	24.1442	0.813439	0.406720	+	0.913553i	$0.366673\pi$
$882$	15.2639	0.513961
$883$	20.8242	0.700791	0.350395	−	0.936602i	$-0.386047\pi$
$883$	20.8242	0.700791	0.350395	+	0.936602i	$0.386047\pi$
$884$	−3.78968	−0.127461
$885$	3.91861	0.131723
$886$	33.8156	1.13606
$887$	14.3390	0.481455	0.240727	−	0.970593i	$-0.422614\pi$
$887$	14.3390	0.481455	0.240727	+	0.970593i	$0.422614\pi$
$888$	−1.18372	−0.0397230
$889$	29.6622	0.994839
$890$	9.28698	0.311300
$891$	−4.45672	−0.149306
$892$	−14.4339	−0.483282
$893$	−9.19632	−0.307743
$894$	4.09017	0.136796
$895$	−29.2326	−0.977139
$896$	−4.71846	−0.157633
$897$	21.2679	0.710114
$898$	24.9803	0.833602
$899$	6.52531	0.217631
$900$	10.3555	0.345182
$901$	−7.69402	−0.256325
$902$	−16.7732	−0.558487
$903$	−7.71145	−0.256621
$904$	6.08320	0.202324
$905$	77.7214	2.58355
$906$	3.14599	0.104519
$907$	−37.7910	−1.25483	−0.627414	−	0.778686i	$-0.715887\pi$
$907$	−37.7910	−1.25483	−0.627414	+	0.778686i	$0.715887\pi$
$908$	5.52638	0.183399
$909$	18.0874	0.599920
$910$	−70.0704	−2.32281
$911$	−16.4277	−0.544275	−0.272138	−	0.962258i	$-0.587731\pi$
$911$	−16.4277	−0.544275	−0.272138	+	0.962258i	$0.587731\pi$
$912$	−5.42803	−0.179740
$913$	−17.7919	−0.588824
$914$	−12.2866	−0.406406
$915$	−7.48782	−0.247540
$916$	−23.9979	−0.792912
$917$	80.4053	2.65522
$918$	1.00000	0.0330049
$919$	5.11864	0.168848	0.0844242	−	0.996430i	$-0.473095\pi$
$919$	5.11864	0.168848	0.0844242	+	0.996430i	$0.473095\pi$
$920$	21.9914	0.725036
$921$	21.9452	0.723120
$922$	−12.9317	−0.425884
$923$	24.4166	0.803683
$924$	21.0289	0.691799
$925$	−12.2580	−0.403039
$926$	−1.48470	−0.0487902
$927$	−10.9982	−0.361227
$928$	8.21377	0.269630
$929$	5.69696	0.186911	0.0934556	−	0.995623i	$-0.470209\pi$
$929$	5.69696	0.186911	0.0934556	+	0.995623i	$0.470209\pi$
$930$	−3.11308	−0.102082
$931$	−82.8529	−2.71539
$932$	6.90580	0.226207
$933$	−7.74575	−0.253585
$934$	−5.57200	−0.182321
$935$	17.4641	0.571139
$936$	−3.78968	−0.123870
$937$	12.8867	0.420991	0.210496	−	0.977595i	$-0.432492\pi$
$937$	12.8867	0.420991	0.210496	+	0.977595i	$0.432492\pi$
$938$	−46.2161	−1.50901
$939$	19.6488	0.641215
$940$	−6.63901	−0.216541
$941$	34.7974	1.13436	0.567182	−	0.823592i	$-0.308034\pi$
$941$	34.7974	1.13436	0.567182	+	0.823592i	$0.308034\pi$
$942$	21.7172	0.707583
$943$	−21.1214	−0.687807
$944$	−1.00000	−0.0325472
$945$	18.4898	0.601473
$946$	−7.28369	−0.236813
$947$	8.14977	0.264832	0.132416	−	0.991194i	$-0.457727\pi$
$947$	8.14977	0.264832	0.132416	+	0.991194i	$0.457727\pi$
$948$	−11.3942	−0.370067
$949$	−23.5935	−0.765876
$950$	−56.2099	−1.82369
$951$	34.5637	1.12081
$952$	−4.71846	−0.152926
$953$	−52.3968	−1.69730	−0.848649	−	0.528956i	$-0.822584\pi$
$953$	−52.3968	−1.69730	−0.848649	+	0.528956i	$0.822584\pi$
$954$	−7.69402	−0.249103
$955$	−4.54325	−0.147016
$956$	−19.9781	−0.646137
$957$	−36.6065	−1.18332
$958$	15.6138	0.504460
$959$	−17.4363	−0.563047
$960$	−3.91861	−0.126472
$961$	−30.3689	−0.979641
$962$	4.48591	0.144632
$963$	−9.70005	−0.312580
$964$	−30.7337	−0.989866
$965$	−41.9477	−1.35034
$966$	26.4803	0.851988
$967$	45.3289	1.45768	0.728840	−	0.684684i	$-0.240060\pi$
$967$	45.3289	1.45768	0.728840	+	0.684684i	$0.240060\pi$
$968$	8.86238	0.284848
$969$	−5.42803	−0.174374
$970$	20.1004	0.645384
$971$	−29.1903	−0.936763	−0.468381	−	0.883526i	$-0.655163\pi$
$971$	−29.1903	−0.936763	−0.468381	+	0.883526i	$0.655163\pi$
$972$	1.00000	0.0320750
$973$	87.6419	2.80967
$974$	−29.7538	−0.953374
$975$	−39.2439	−1.25681
$976$	1.91084	0.0611644
$977$	16.9399	0.541954	0.270977	−	0.962586i	$-0.412653\pi$
$977$	16.9399	0.541954	0.270977	+	0.962586i	$0.412653\pi$
$978$	−3.36545	−0.107615
$979$	10.5623	0.337573
$980$	−59.8131	−1.91066
$981$	8.81033	0.281292
$982$	−0.0772158	−0.00246405
$983$	−28.2949	−0.902466	−0.451233	−	0.892406i	$-0.649016\pi$
$983$	−28.2949	−0.902466	−0.451233	+	0.892406i	$0.649016\pi$
$984$	3.76358	0.119978
$985$	26.9092	0.857398
$986$	8.21377	0.261580
$987$	−7.99414	−0.254456
$988$	20.5705	0.654435
$989$	−9.17186	−0.291648
$990$	17.4641	0.555047
$991$	−14.2672	−0.453212	−0.226606	−	0.973987i	$-0.572763\pi$
$991$	−14.2672	−0.453212	−0.226606	+	0.973987i	$0.572763\pi$
$992$	0.794436	0.0252234
$993$	−14.4774	−0.459426
$994$	30.4007	0.964251
$995$	63.7926	2.02236
$996$	3.99214	0.126496
$997$	−53.9524	−1.70869	−0.854345	−	0.519707i	$-0.826041\pi$
$997$	−53.9524	−1.70869	−0.854345	+	0.519707i	$0.826041\pi$
$998$	43.8706	1.38870
$999$	−1.18372	−0.0374512

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.bb.1.2	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.bb.1.2	✓	13	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.91861 q^{5} +1.00000 q^{6} -4.71846 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.91861 q^{5} +1.00000 q^{6} -4.71846 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.91861 q^{10} -4.45672 q^{11} +1.00000 q^{12} -3.78968 q^{13} -4.71846 q^{14} -3.91861 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -5.42803 q^{19} -3.91861 q^{20} -4.71846 q^{21} -4.45672 q^{22} -5.61205 q^{23} +1.00000 q^{24} +10.3555 q^{25} -3.78968 q^{26} +1.00000 q^{27} -4.71846 q^{28} +8.21377 q^{29} -3.91861 q^{30} +0.794436 q^{31} +1.00000 q^{32} -4.45672 q^{33} +1.00000 q^{34} +18.4898 q^{35} +1.00000 q^{36} -1.18372 q^{37} -5.42803 q^{38} -3.78968 q^{39} -3.91861 q^{40} +3.76358 q^{41} -4.71846 q^{42} +1.63431 q^{43} -4.45672 q^{44} -3.91861 q^{45} -5.61205 q^{46} +1.69423 q^{47} +1.00000 q^{48} +15.2639 q^{49} +10.3555 q^{50} +1.00000 q^{51} -3.78968 q^{52} -7.69402 q^{53} +1.00000 q^{54} +17.4641 q^{55} -4.71846 q^{56} -5.42803 q^{57} +8.21377 q^{58} -1.00000 q^{59} -3.91861 q^{60} +1.91084 q^{61} +0.794436 q^{62} -4.71846 q^{63} +1.00000 q^{64} +14.8503 q^{65} -4.45672 q^{66} +9.79474 q^{67} +1.00000 q^{68} -5.61205 q^{69} +18.4898 q^{70} -6.44292 q^{71} +1.00000 q^{72} +6.22571 q^{73} -1.18372 q^{74} +10.3555 q^{75} -5.42803 q^{76} +21.0289 q^{77} -3.78968 q^{78} -11.3942 q^{79} -3.91861 q^{80} +1.00000 q^{81} +3.76358 q^{82} +3.99214 q^{83} -4.71846 q^{84} -3.91861 q^{85} +1.63431 q^{86} +8.21377 q^{87} -4.45672 q^{88} -2.36997 q^{89} -3.91861 q^{90} +17.8815 q^{91} -5.61205 q^{92} +0.794436 q^{93} +1.69423 q^{94} +21.2703 q^{95} +1.00000 q^{96} -5.12947 q^{97} +15.2639 q^{98} -4.45672 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 4 q^{5} + 13 q^{6} + 11 q^{7} + 13 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q + 13 * q^2 + 13 * q^3 + 13 * q^4 + 4 * q^5 + 13 * q^6 + 11 * q^7 + 13 * q^8 + 13 * q^9	\( 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 4 q^{5} + 13 q^{6} + 11 q^{7} + 13 q^{8} + 13 q^{9} + 4 q^{10} + 7 q^{11} + 13 q^{12} + 6 q^{13} + 11 q^{14} + 4 q^{15} + 13 q^{16} + 13 q^{17} + 13 q^{18} + 9 q^{19} + 4 q^{20} + 11 q^{21} + 7 q^{22} + 2 q^{23} + 13 q^{24} + 33 q^{25} + 6 q^{26} + 13 q^{27} + 11 q^{28} + 14 q^{29} + 4 q^{30} - 5 q^{31} + 13 q^{32} + 7 q^{33} + 13 q^{34} + 24 q^{35} + 13 q^{36} + 4 q^{37} + 9 q^{38} + 6 q^{39} + 4 q^{40} + 28 q^{41} + 11 q^{42} + q^{43} + 7 q^{44} + 4 q^{45} + 2 q^{46} + 12 q^{47} + 13 q^{48} + 32 q^{49} + 33 q^{50} + 13 q^{51} + 6 q^{52} + 22 q^{53} + 13 q^{54} - 7 q^{55} + 11 q^{56} + 9 q^{57} + 14 q^{58} - 13 q^{59} + 4 q^{60} - 9 q^{61} - 5 q^{62} + 11 q^{63} + 13 q^{64} + 34 q^{65} + 7 q^{66} + 26 q^{67} + 13 q^{68} + 2 q^{69} + 24 q^{70} + 8 q^{71} + 13 q^{72} + 4 q^{73} + 4 q^{74} + 33 q^{75} + 9 q^{76} + 38 q^{77} + 6 q^{78} - 17 q^{79} + 4 q^{80} + 13 q^{81} + 28 q^{82} + 14 q^{83} + 11 q^{84} + 4 q^{85} + q^{86} + 14 q^{87} + 7 q^{88} + 19 q^{89} + 4 q^{90} - 5 q^{91} + 2 q^{92} - 5 q^{93} + 12 q^{94} + 25 q^{95} + 13 q^{96} - 5 q^{97} + 32 q^{98} + 7 q^{99}+O(q^{100}) \) 13 * q + 13 * q^2 + 13 * q^3 + 13 * q^4 + 4 * q^5 + 13 * q^6 + 11 * q^7 + 13 * q^8 + 13 * q^9 + 4 * q^10 + 7 * q^11 + 13 * q^12 + 6 * q^13 + 11 * q^14 + 4 * q^15 + 13 * q^16 + 13 * q^17 + 13 * q^18 + 9 * q^19 + 4 * q^20 + 11 * q^21 + 7 * q^22 + 2 * q^23 + 13 * q^24 + 33 * q^25 + 6 * q^26 + 13 * q^27 + 11 * q^28 + 14 * q^29 + 4 * q^30 - 5 * q^31 + 13 * q^32 + 7 * q^33 + 13 * q^34 + 24 * q^35 + 13 * q^36 + 4 * q^37 + 9 * q^38 + 6 * q^39 + 4 * q^40 + 28 * q^41 + 11 * q^42 + q^43 + 7 * q^44 + 4 * q^45 + 2 * q^46 + 12 * q^47 + 13 * q^48 + 32 * q^49 + 33 * q^50 + 13 * q^51 + 6 * q^52 + 22 * q^53 + 13 * q^54 - 7 * q^55 + 11 * q^56 + 9 * q^57 + 14 * q^58 - 13 * q^59 + 4 * q^60 - 9 * q^61 - 5 * q^62 + 11 * q^63 + 13 * q^64 + 34 * q^65 + 7 * q^66 + 26 * q^67 + 13 * q^68 + 2 * q^69 + 24 * q^70 + 8 * q^71 + 13 * q^72 + 4 * q^73 + 4 * q^74 + 33 * q^75 + 9 * q^76 + 38 * q^77 + 6 * q^78 - 17 * q^79 + 4 * q^80 + 13 * q^81 + 28 * q^82 + 14 * q^83 + 11 * q^84 + 4 * q^85 + q^86 + 14 * q^87 + 7 * q^88 + 19 * q^89 + 4 * q^90 - 5 * q^91 + 2 * q^92 - 5 * q^93 + 12 * q^94 + 25 * q^95 + 13 * q^96 - 5 * q^97 + 32 * q^98 + 7 * q^99

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