LMFDB - Embedded newform 6018.2.a.w.1.3

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:	$9$
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} - x^{8} - 22x^{7} + 20x^{6} + 129x^{5} - 106x^{4} - 126x^{3} + 48x^{2} + 24x - 8 $ x^9 - x^8 - 22x^7 + 20x^6 + 129x^5 - 106x^4 - 126x^3 + 48x^2 + 24*x - 8
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			1.3
Root			$-0.637772$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.637772 q^{5} -1.00000 q^{6} -2.55112 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.637772 q^{5} -1.00000 q^{6} -2.55112 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.637772 q^{10} +3.01757 q^{11} +1.00000 q^{12} +4.51939 q^{13} +2.55112 q^{14} -0.637772 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} -0.204992 q^{19} -0.637772 q^{20} -2.55112 q^{21} -3.01757 q^{22} +1.62588 q^{23} -1.00000 q^{24} -4.59325 q^{25} -4.51939 q^{26} +1.00000 q^{27} -2.55112 q^{28} -5.48205 q^{29} +0.637772 q^{30} +2.31668 q^{31} -1.00000 q^{32} +3.01757 q^{33} -1.00000 q^{34} +1.62704 q^{35} +1.00000 q^{36} +1.11127 q^{37} +0.204992 q^{38} +4.51939 q^{39} +0.637772 q^{40} +5.08502 q^{41} +2.55112 q^{42} +1.39723 q^{43} +3.01757 q^{44} -0.637772 q^{45} -1.62588 q^{46} -6.68221 q^{47} +1.00000 q^{48} -0.491770 q^{49} +4.59325 q^{50} +1.00000 q^{51} +4.51939 q^{52} +9.49767 q^{53} -1.00000 q^{54} -1.92452 q^{55} +2.55112 q^{56} -0.204992 q^{57} +5.48205 q^{58} +1.00000 q^{59} -0.637772 q^{60} +9.48886 q^{61} -2.31668 q^{62} -2.55112 q^{63} +1.00000 q^{64} -2.88234 q^{65} -3.01757 q^{66} -1.80404 q^{67} +1.00000 q^{68} +1.62588 q^{69} -1.62704 q^{70} +14.5029 q^{71} -1.00000 q^{72} +0.762476 q^{73} -1.11127 q^{74} -4.59325 q^{75} -0.204992 q^{76} -7.69820 q^{77} -4.51939 q^{78} -4.77870 q^{79} -0.637772 q^{80} +1.00000 q^{81} -5.08502 q^{82} +14.7939 q^{83} -2.55112 q^{84} -0.637772 q^{85} -1.39723 q^{86} -5.48205 q^{87} -3.01757 q^{88} -0.444454 q^{89} +0.637772 q^{90} -11.5295 q^{91} +1.62588 q^{92} +2.31668 q^{93} +6.68221 q^{94} +0.130738 q^{95} -1.00000 q^{96} +0.884692 q^{97} +0.491770 q^{98} +3.01757 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 9 q^{2} + 9 q^{3} + 9 q^{4} + q^{5} - 9 q^{6} - 9 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q - 9 * q^2 + 9 * q^3 + 9 * q^4 + q^5 - 9 * q^6 - 9 * q^8 + 9 * q^9	$ 9 q - 9 q^{2} + 9 q^{3} + 9 q^{4} + q^{5} - 9 q^{6} - 9 q^{8} + 9 q^{9} - q^{10} + 6 q^{11} + 9 q^{12} + 2 q^{13} + q^{15} + 9 q^{16} + 9 q^{17} - 9 q^{18} - 5 q^{19} + q^{20} - 6 q^{22} + 15 q^{23} - 9 q^{24} - 2 q^{26} + 9 q^{27} + 11 q^{29} - q^{30} - 5 q^{31} - 9 q^{32} + 6 q^{33} - 9 q^{34} + 22 q^{35} + 9 q^{36} + 9 q^{37} + 5 q^{38} + 2 q^{39} - q^{40} + q^{41} + 4 q^{43} + 6 q^{44} + q^{45} - 15 q^{46} + 14 q^{47} + 9 q^{48} - q^{49} + 9 q^{51} + 2 q^{52} + 4 q^{53} - 9 q^{54} + 4 q^{55} - 5 q^{57} - 11 q^{58} + 9 q^{59} + q^{60} + 10 q^{61} + 5 q^{62} + 9 q^{64} + 8 q^{65} - 6 q^{66} - q^{67} + 9 q^{68} + 15 q^{69} - 22 q^{70} + 14 q^{71} - 9 q^{72} - q^{73} - 9 q^{74} - 5 q^{76} + 30 q^{77} - 2 q^{78} + 4 q^{79} + q^{80} + 9 q^{81} - q^{82} + 22 q^{83} + q^{85} - 4 q^{86} + 11 q^{87} - 6 q^{88} + 22 q^{89} - q^{90} - 3 q^{91} + 15 q^{92} - 5 q^{93} - 14 q^{94} + 43 q^{95} - 9 q^{96} - 15 q^{97} + q^{98} + 6 q^{99}+O(q^{100}) $ 9 * q - 9 * q^2 + 9 * q^3 + 9 * q^4 + q^5 - 9 * q^6 - 9 * q^8 + 9 * q^9 - q^10 + 6 * q^11 + 9 * q^12 + 2 * q^13 + q^15 + 9 * q^16 + 9 * q^17 - 9 * q^18 - 5 * q^19 + q^20 - 6 * q^22 + 15 * q^23 - 9 * q^24 - 2 * q^26 + 9 * q^27 + 11 * q^29 - q^30 - 5 * q^31 - 9 * q^32 + 6 * q^33 - 9 * q^34 + 22 * q^35 + 9 * q^36 + 9 * q^37 + 5 * q^38 + 2 * q^39 - q^40 + q^41 + 4 * q^43 + 6 * q^44 + q^45 - 15 * q^46 + 14 * q^47 + 9 * q^48 - q^49 + 9 * q^51 + 2 * q^52 + 4 * q^53 - 9 * q^54 + 4 * q^55 - 5 * q^57 - 11 * q^58 + 9 * q^59 + q^60 + 10 * q^61 + 5 * q^62 + 9 * q^64 + 8 * q^65 - 6 * q^66 - q^67 + 9 * q^68 + 15 * q^69 - 22 * q^70 + 14 * q^71 - 9 * q^72 - q^73 - 9 * q^74 - 5 * q^76 + 30 * q^77 - 2 * q^78 + 4 * q^79 + q^80 + 9 * q^81 - q^82 + 22 * q^83 + q^85 - 4 * q^86 + 11 * q^87 - 6 * q^88 + 22 * q^89 - q^90 - 3 * q^91 + 15 * q^92 - 5 * q^93 - 14 * q^94 + 43 * q^95 - 9 * q^96 - 15 * q^97 + q^98 + 6 * 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
$5$	−0.637772	−0.285220	−0.142610	−	0.989779i	$-0.545550\pi$
$5$	−0.637772	−0.285220	−0.142610	+	0.989779i	$0.545550\pi$
$6$	−1.00000	−0.408248
$7$	−2.55112	−0.964234	−0.482117	−	0.876107i	$-0.660132\pi$
$7$	−2.55112	−0.964234	−0.482117	+	0.876107i	$0.660132\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0.637772	0.201681
$11$	3.01757	0.909832	0.454916	−	0.890534i	$-0.349669\pi$
$11$	3.01757	0.909832	0.454916	+	0.890534i	$0.349669\pi$
$12$	1.00000	0.288675
$13$	4.51939	1.25345	0.626727	−	0.779239i	$-0.284394\pi$
$13$	4.51939	1.25345	0.626727	+	0.779239i	$0.284394\pi$
$14$	2.55112	0.681816
$15$	−0.637772	−0.164672
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.00000	−0.235702
$19$	−0.204992	−0.0470285	−0.0235142	−	0.999724i	$-0.507486\pi$
$19$	−0.204992	−0.0470285	−0.0235142	+	0.999724i	$0.507486\pi$
$20$	−0.637772	−0.142610
$21$	−2.55112	−0.556701
$22$	−3.01757	−0.643349
$23$	1.62588	0.339019	0.169509	−	0.985529i	$-0.445782\pi$
$23$	1.62588	0.339019	0.169509	+	0.985529i	$0.445782\pi$
$24$	−1.00000	−0.204124
$25$	−4.59325	−0.918649
$26$	−4.51939	−0.886325
$27$	1.00000	0.192450
$28$	−2.55112	−0.482117
$29$	−5.48205	−1.01799	−0.508995	−	0.860769i	$-0.669983\pi$
$29$	−5.48205	−1.01799	−0.508995	+	0.860769i	$0.669983\pi$
$30$	0.637772	0.116441
$31$	2.31668	0.416088	0.208044	−	0.978119i	$-0.433290\pi$
$31$	2.31668	0.416088	0.208044	+	0.978119i	$0.433290\pi$
$32$	−1.00000	−0.176777
$33$	3.01757	0.525292
$34$	−1.00000	−0.171499
$35$	1.62704	0.275019
$36$	1.00000	0.166667
$37$	1.11127	0.182691	0.0913454	−	0.995819i	$-0.470883\pi$
$37$	1.11127	0.182691	0.0913454	+	0.995819i	$0.470883\pi$
$38$	0.204992	0.0332541
$39$	4.51939	0.723682
$40$	0.637772	0.100841
$41$	5.08502	0.794146	0.397073	−	0.917787i	$-0.370026\pi$
$41$	5.08502	0.794146	0.397073	+	0.917787i	$0.370026\pi$
$42$	2.55112	0.393647
$43$	1.39723	0.213075	0.106538	−	0.994309i	$-0.466024\pi$
$43$	1.39723	0.213075	0.106538	+	0.994309i	$0.466024\pi$
$44$	3.01757	0.454916
$45$	−0.637772	−0.0950735
$46$	−1.62588	−0.239722
$47$	−6.68221	−0.974700	−0.487350	−	0.873207i	$-0.662036\pi$
$47$	−6.68221	−0.974700	−0.487350	+	0.873207i	$0.662036\pi$
$48$	1.00000	0.144338
$49$	−0.491770	−0.0702528
$50$	4.59325	0.649583
$51$	1.00000	0.140028
$52$	4.51939	0.626727
$53$	9.49767	1.30461	0.652303	−	0.757959i	$-0.273803\pi$
$53$	9.49767	1.30461	0.652303	+	0.757959i	$0.273803\pi$
$54$	−1.00000	−0.136083
$55$	−1.92452	−0.259503
$56$	2.55112	0.340908
$57$	−0.204992	−0.0271519
$58$	5.48205	0.719828
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	−0.637772	−0.0823360
$61$	9.48886	1.21492	0.607462	−	0.794349i	$-0.292188\pi$
$61$	9.48886	1.21492	0.607462	+	0.794349i	$0.292188\pi$
$62$	−2.31668	−0.294219
$63$	−2.55112	−0.321411
$64$	1.00000	0.125000
$65$	−2.88234	−0.357510
$66$	−3.01757	−0.371438
$67$	−1.80404	−0.220398	−0.110199	−	0.993910i	$-0.535149\pi$
$67$	−1.80404	−0.220398	−0.110199	+	0.993910i	$0.535149\pi$
$68$	1.00000	0.121268
$69$	1.62588	0.195733
$70$	−1.62704	−0.194468
$71$	14.5029	1.72117	0.860586	−	0.509305i	$-0.170098\pi$
$71$	14.5029	1.72117	0.860586	+	0.509305i	$0.170098\pi$
$72$	−1.00000	−0.117851
$73$	0.762476	0.0892410	0.0446205	−	0.999004i	$-0.485792\pi$
$73$	0.762476	0.0892410	0.0446205	+	0.999004i	$0.485792\pi$
$74$	−1.11127	−0.129182
$75$	−4.59325	−0.530382
$76$	−0.204992	−0.0235142
$77$	−7.69820	−0.877291
$78$	−4.51939	−0.511720
$79$	−4.77870	−0.537646	−0.268823	−	0.963190i	$-0.586635\pi$
$79$	−4.77870	−0.537646	−0.268823	+	0.963190i	$0.586635\pi$
$80$	−0.637772	−0.0713051
$81$	1.00000	0.111111
$82$	−5.08502	−0.561546
$83$	14.7939	1.62384	0.811919	−	0.583770i	$-0.198423\pi$
$83$	14.7939	1.62384	0.811919	+	0.583770i	$0.198423\pi$
$84$	−2.55112	−0.278350
$85$	−0.637772	−0.0691761
$86$	−1.39723	−0.150667
$87$	−5.48205	−0.587737
$88$	−3.01757	−0.321674
$89$	−0.444454	−0.0471120	−0.0235560	−	0.999723i	$-0.507499\pi$
$89$	−0.444454	−0.0471120	−0.0235560	+	0.999723i	$0.507499\pi$
$90$	0.637772	0.0672271
$91$	−11.5295	−1.20862
$92$	1.62588	0.169509
$93$	2.31668	0.240229
$94$	6.68221	0.689217
$95$	0.130738	0.0134135
$96$	−1.00000	−0.102062
$97$	0.884692	0.0898269	0.0449134	−	0.998991i	$-0.485699\pi$
$97$	0.884692	0.0898269	0.0449134	+	0.998991i	$0.485699\pi$
$98$	0.491770	0.0496762
$99$	3.01757	0.303277
$100$	−4.59325	−0.459325
$101$	−8.85351	−0.880957	−0.440479	−	0.897763i	$-0.645191\pi$
$101$	−8.85351	−0.880957	−0.440479	+	0.897763i	$0.645191\pi$
$102$	−1.00000	−0.0990148
$103$	2.87562	0.283343	0.141672	−	0.989914i	$-0.454752\pi$
$103$	2.87562	0.283343	0.141672	+	0.989914i	$0.454752\pi$
$104$	−4.51939	−0.443163
$105$	1.62704	0.158782
$106$	−9.49767	−0.922495
$107$	2.47240	0.239016	0.119508	−	0.992833i	$-0.461868\pi$
$107$	2.47240	0.239016	0.119508	+	0.992833i	$0.461868\pi$
$108$	1.00000	0.0962250
$109$	−0.594478	−0.0569406	−0.0284703	−	0.999595i	$-0.509064\pi$
$109$	−0.594478	−0.0569406	−0.0284703	+	0.999595i	$0.509064\pi$
$110$	1.92452	0.183496
$111$	1.11127	0.105477
$112$	−2.55112	−0.241059
$113$	−19.7945	−1.86211	−0.931054	−	0.364882i	$-0.881109\pi$
$113$	−19.7945	−1.86211	−0.931054	+	0.364882i	$0.881109\pi$
$114$	0.204992	0.0191993
$115$	−1.03694	−0.0966950
$116$	−5.48205	−0.508995
$117$	4.51939	0.417818
$118$	−1.00000	−0.0920575
$119$	−2.55112	−0.233861
$120$	0.637772	0.0582204
$121$	−1.89426	−0.172205
$122$	−9.48886	−0.859081
$123$	5.08502	0.458500
$124$	2.31668	0.208044
$125$	6.11831	0.547238
$126$	2.55112	0.227272
$127$	−4.71056	−0.417995	−0.208997	−	0.977916i	$-0.567020\pi$
$127$	−4.71056	−0.417995	−0.208997	+	0.977916i	$0.567020\pi$
$128$	−1.00000	−0.0883883
$129$	1.39723	0.123019
$130$	2.88234	0.252798
$131$	−10.4772	−0.915394	−0.457697	−	0.889108i	$-0.651326\pi$
$131$	−10.4772	−0.915394	−0.457697	+	0.889108i	$0.651326\pi$
$132$	3.01757	0.262646
$133$	0.522961	0.0453464
$134$	1.80404	0.155845
$135$	−0.637772	−0.0548907
$136$	−1.00000	−0.0857493
$137$	7.58639	0.648149	0.324074	−	0.946032i	$-0.394947\pi$
$137$	7.58639	0.648149	0.324074	+	0.946032i	$0.394947\pi$
$138$	−1.62588	−0.138404
$139$	−4.56251	−0.386987	−0.193494	−	0.981102i	$-0.561982\pi$
$139$	−4.56251	−0.386987	−0.193494	+	0.981102i	$0.561982\pi$
$140$	1.62704	0.137510
$141$	−6.68221	−0.562743
$142$	−14.5029	−1.21705
$143$	13.6376	1.14043
$144$	1.00000	0.0833333
$145$	3.49630	0.290352
$146$	−0.762476	−0.0631029
$147$	−0.491770	−0.0405605
$148$	1.11127	0.0913454
$149$	5.57138	0.456425	0.228213	−	0.973611i	$-0.426712\pi$
$149$	5.57138	0.456425	0.228213	+	0.973611i	$0.426712\pi$
$150$	4.59325	0.375037
$151$	−22.8497	−1.85948	−0.929739	−	0.368218i	$-0.879968\pi$
$151$	−22.8497	−1.85948	−0.929739	+	0.368218i	$0.879968\pi$
$152$	0.204992	0.0166271
$153$	1.00000	0.0808452
$154$	7.69820	0.620339
$155$	−1.47751	−0.118677
$156$	4.51939	0.361841
$157$	8.32312	0.664257	0.332129	−	0.943234i	$-0.392233\pi$
$157$	8.32312	0.664257	0.332129	+	0.943234i	$0.392233\pi$
$158$	4.77870	0.380173
$159$	9.49767	0.753214
$160$	0.637772	0.0504203
$161$	−4.14781	−0.326893
$162$	−1.00000	−0.0785674
$163$	8.67759	0.679681	0.339841	−	0.940483i	$-0.389627\pi$
$163$	8.67759	0.679681	0.339841	+	0.940483i	$0.389627\pi$
$164$	5.08502	0.397073
$165$	−1.92452	−0.149824
$166$	−14.7939	−1.14823
$167$	−12.3061	−0.952275	−0.476137	−	0.879371i	$-0.657963\pi$
$167$	−12.3061	−0.952275	−0.476137	+	0.879371i	$0.657963\pi$
$168$	2.55112	0.196823
$169$	7.42489	0.571146
$170$	0.637772	0.0489149
$171$	−0.204992	−0.0156762
$172$	1.39723	0.106538
$173$	10.5416	0.801466	0.400733	−	0.916195i	$-0.368756\pi$
$173$	10.5416	0.801466	0.400733	+	0.916195i	$0.368756\pi$
$174$	5.48205	0.415593
$175$	11.7179	0.885793
$176$	3.01757	0.227458
$177$	1.00000	0.0751646
$178$	0.444454	0.0333132
$179$	5.30024	0.396159	0.198079	−	0.980186i	$-0.436530\pi$
$179$	5.30024	0.396159	0.198079	+	0.980186i	$0.436530\pi$
$180$	−0.637772	−0.0475367
$181$	4.77053	0.354590	0.177295	−	0.984158i	$-0.443265\pi$
$181$	4.77053	0.354590	0.177295	+	0.984158i	$0.443265\pi$
$182$	11.5295	0.854625
$183$	9.48886	0.701437
$184$	−1.62588	−0.119861
$185$	−0.708734	−0.0521072
$186$	−2.31668	−0.169867
$187$	3.01757	0.220667
$188$	−6.68221	−0.487350
$189$	−2.55112	−0.185567
$190$	−0.130738	−0.00948476
$191$	20.7446	1.50102	0.750512	−	0.660857i	$-0.229807\pi$
$191$	20.7446	1.50102	0.750512	+	0.660857i	$0.229807\pi$
$192$	1.00000	0.0721688
$193$	−11.9029	−0.856788	−0.428394	−	0.903592i	$-0.640920\pi$
$193$	−11.9029	−0.856788	−0.428394	+	0.903592i	$0.640920\pi$
$194$	−0.884692	−0.0635172
$195$	−2.88234	−0.206409
$196$	−0.491770	−0.0351264
$197$	18.4369	1.31357	0.656787	−	0.754077i	$-0.271915\pi$
$197$	18.4369	1.31357	0.656787	+	0.754077i	$0.271915\pi$
$198$	−3.01757	−0.214450
$199$	23.3049	1.65204	0.826019	−	0.563642i	$-0.190600\pi$
$199$	23.3049	1.65204	0.826019	+	0.563642i	$0.190600\pi$
$200$	4.59325	0.324792
$201$	−1.80404	−0.127247
$202$	8.85351	0.622931
$203$	13.9854	0.981581
$204$	1.00000	0.0700140
$205$	−3.24308	−0.226507
$206$	−2.87562	−0.200354
$207$	1.62588	0.113006
$208$	4.51939	0.313363
$209$	−0.618579	−0.0427880
$210$	−1.62704	−0.112276
$211$	−2.15591	−0.148419	−0.0742095	−	0.997243i	$-0.523643\pi$
$211$	−2.15591	−0.148419	−0.0742095	+	0.997243i	$0.523643\pi$
$212$	9.49767	0.652303
$213$	14.5029	0.993719
$214$	−2.47240	−0.169010
$215$	−0.891112	−0.0607733
$216$	−1.00000	−0.0680414
$217$	−5.91014	−0.401206
$218$	0.594478	0.0402631
$219$	0.762476	0.0515233
$220$	−1.92452	−0.129751
$221$	4.51939	0.304007
$222$	−1.11127	−0.0745832
$223$	−18.2390	−1.22138	−0.610688	−	0.791871i	$-0.709107\pi$
$223$	−18.2390	−1.22138	−0.610688	+	0.791871i	$0.709107\pi$
$224$	2.55112	0.170454
$225$	−4.59325	−0.306216
$226$	19.7945	1.31671
$227$	12.5073	0.830140	0.415070	−	0.909789i	$-0.363757\pi$
$227$	12.5073	0.830140	0.415070	+	0.909789i	$0.363757\pi$
$228$	−0.204992	−0.0135759
$229$	−16.6494	−1.10022	−0.550112	−	0.835091i	$-0.685415\pi$
$229$	−16.6494	−1.10022	−0.550112	+	0.835091i	$0.685415\pi$
$230$	1.03694	0.0683737
$231$	−7.69820	−0.506504
$232$	5.48205	0.359914
$233$	27.1005	1.77541	0.887705	−	0.460412i	$-0.152298\pi$
$233$	27.1005	1.77541	0.887705	+	0.460412i	$0.152298\pi$
$234$	−4.51939	−0.295442
$235$	4.26173	0.278004
$236$	1.00000	0.0650945
$237$	−4.77870	−0.310410
$238$	2.55112	0.165365
$239$	23.0618	1.49175	0.745873	−	0.666089i	$-0.232033\pi$
$239$	23.0618	1.49175	0.745873	+	0.666089i	$0.232033\pi$
$240$	−0.637772	−0.0411680
$241$	28.9254	1.86325	0.931624	−	0.363423i	$-0.118392\pi$
$241$	28.9254	1.86325	0.931624	+	0.363423i	$0.118392\pi$
$242$	1.89426	0.121767
$243$	1.00000	0.0641500
$244$	9.48886	0.607462
$245$	0.313637	0.0200375
$246$	−5.08502	−0.324209
$247$	−0.926440	−0.0589480
$248$	−2.31668	−0.147109
$249$	14.7939	0.937523
$250$	−6.11831	−0.386956
$251$	18.6061	1.17441	0.587205	−	0.809438i	$-0.300228\pi$
$251$	18.6061	1.17441	0.587205	+	0.809438i	$0.300228\pi$
$252$	−2.55112	−0.160706
$253$	4.90620	0.308450
$254$	4.71056	0.295567
$255$	−0.637772	−0.0399388
$256$	1.00000	0.0625000
$257$	−1.42253	−0.0887352	−0.0443676	−	0.999015i	$-0.514127\pi$
$257$	−1.42253	−0.0887352	−0.0443676	+	0.999015i	$0.514127\pi$
$258$	−1.39723	−0.0869875
$259$	−2.83497	−0.176157
$260$	−2.88234	−0.178755
$261$	−5.48205	−0.339330
$262$	10.4772	0.647282
$263$	6.08824	0.375417	0.187709	−	0.982225i	$-0.439894\pi$
$263$	6.08824	0.375417	0.187709	+	0.982225i	$0.439894\pi$
$264$	−3.01757	−0.185719
$265$	−6.05735	−0.372100
$266$	−0.522961	−0.0320648
$267$	−0.444454	−0.0272001
$268$	−1.80404	−0.110199
$269$	9.37068	0.571340	0.285670	−	0.958328i	$-0.407784\pi$
$269$	9.37068	0.571340	0.285670	+	0.958328i	$0.407784\pi$
$270$	0.637772	0.0388136
$271$	17.2918	1.05040	0.525200	−	0.850979i	$-0.323990\pi$
$271$	17.2918	1.05040	0.525200	+	0.850979i	$0.323990\pi$
$272$	1.00000	0.0606339
$273$	−11.5295	−0.697799
$274$	−7.58639	−0.458310
$275$	−13.8605	−0.835817
$276$	1.62588	0.0978663
$277$	−1.01392	−0.0609206	−0.0304603	−	0.999536i	$-0.509697\pi$
$277$	−1.01392	−0.0609206	−0.0304603	+	0.999536i	$0.509697\pi$
$278$	4.56251	0.273641
$279$	2.31668	0.138696
$280$	−1.62704	−0.0972340
$281$	−5.16826	−0.308313	−0.154156	−	0.988046i	$-0.549266\pi$
$281$	−5.16826	−0.308313	−0.154156	+	0.988046i	$0.549266\pi$
$282$	6.68221	0.397920
$283$	−0.0666371	−0.00396116	−0.00198058	−	0.999998i	$-0.500630\pi$
$283$	−0.0666371	−0.00396116	−0.00198058	+	0.999998i	$0.500630\pi$
$284$	14.5029	0.860586
$285$	0.130738	0.00774427
$286$	−13.6376	−0.806408
$287$	−12.9725	−0.765743
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	−3.49630	−0.205310
$291$	0.884692	0.0518616
$292$	0.762476	0.0446205
$293$	26.7942	1.56533	0.782666	−	0.622442i	$-0.213859\pi$
$293$	26.7942	1.56533	0.782666	+	0.622442i	$0.213859\pi$
$294$	0.491770	0.0286806
$295$	−0.637772	−0.0371325
$296$	−1.11127	−0.0645910
$297$	3.01757	0.175097
$298$	−5.57138	−0.322741
$299$	7.34797	0.424944
$300$	−4.59325	−0.265191
$301$	−3.56450	−0.205454
$302$	22.8497	1.31485
$303$	−8.85351	−0.508621
$304$	−0.204992	−0.0117571
$305$	−6.05173	−0.346521
$306$	−1.00000	−0.0571662
$307$	34.5012	1.96909	0.984545	−	0.175134i	$-0.0560359\pi$
$307$	34.5012	1.96909	0.984545	+	0.175134i	$0.0560359\pi$
$308$	−7.69820	−0.438646
$309$	2.87562	0.163588
$310$	1.47751	0.0839172
$311$	3.93295	0.223017	0.111509	−	0.993763i	$-0.464432\pi$
$311$	3.93295	0.223017	0.111509	+	0.993763i	$0.464432\pi$
$312$	−4.51939	−0.255860
$313$	−12.5013	−0.706613	−0.353307	−	0.935508i	$-0.614943\pi$
$313$	−12.5013	−0.706613	−0.353307	+	0.935508i	$0.614943\pi$
$314$	−8.32312	−0.469701
$315$	1.62704	0.0916731
$316$	−4.77870	−0.268823
$317$	−5.09288	−0.286045	−0.143022	−	0.989719i	$-0.545682\pi$
$317$	−5.09288	−0.286045	−0.143022	+	0.989719i	$0.545682\pi$
$318$	−9.49767	−0.532603
$319$	−16.5425	−0.926201
$320$	−0.637772	−0.0356525
$321$	2.47240	0.137996
$322$	4.14781	0.231149
$323$	−0.204992	−0.0114061
$324$	1.00000	0.0555556
$325$	−20.7587	−1.15148
$326$	−8.67759	−0.480607
$327$	−0.594478	−0.0328747
$328$	−5.08502	−0.280773
$329$	17.0471	0.939839
$330$	1.92452	0.105942
$331$	7.52204	0.413449	0.206724	−	0.978399i	$-0.433720\pi$
$331$	7.52204	0.413449	0.206724	+	0.978399i	$0.433720\pi$
$332$	14.7939	0.811919
$333$	1.11127	0.0608970
$334$	12.3061	0.673360
$335$	1.15056	0.0628620
$336$	−2.55112	−0.139175
$337$	−3.41765	−0.186171	−0.0930856	−	0.995658i	$-0.529673\pi$
$337$	−3.41765	−0.186171	−0.0930856	+	0.995658i	$0.529673\pi$
$338$	−7.42489	−0.403861
$339$	−19.7945	−1.07509
$340$	−0.637772	−0.0345881
$341$	6.99075	0.378571
$342$	0.204992	0.0110847
$343$	19.1124	1.03197
$344$	−1.39723	−0.0753334
$345$	−1.03694	−0.0558269
$346$	−10.5416	−0.566722
$347$	5.24084	0.281343	0.140672	−	0.990056i	$-0.455074\pi$
$347$	5.24084	0.281343	0.140672	+	0.990056i	$0.455074\pi$
$348$	−5.48205	−0.293869
$349$	6.58009	0.352224	0.176112	−	0.984370i	$-0.443648\pi$
$349$	6.58009	0.352224	0.176112	+	0.984370i	$0.443648\pi$
$350$	−11.7179	−0.626350
$351$	4.51939	0.241227
$352$	−3.01757	−0.160837
$353$	−8.84253	−0.470640	−0.235320	−	0.971918i	$-0.575614\pi$
$353$	−8.84253	−0.470640	−0.235320	+	0.971918i	$0.575614\pi$
$354$	−1.00000	−0.0531494
$355$	−9.24951	−0.490913
$356$	−0.444454	−0.0235560
$357$	−2.55112	−0.135020
$358$	−5.30024	−0.280126
$359$	−5.89377	−0.311061	−0.155531	−	0.987831i	$-0.549709\pi$
$359$	−5.89377	−0.311061	−0.155531	+	0.987831i	$0.549709\pi$
$360$	0.637772	0.0336135
$361$	−18.9580	−0.997788
$362$	−4.77053	−0.250733
$363$	−1.89426	−0.0994227
$364$	−11.5295	−0.604311
$365$	−0.486286	−0.0254534
$366$	−9.48886	−0.495991
$367$	17.4632	0.911571	0.455786	−	0.890090i	$-0.349358\pi$
$367$	17.4632	0.911571	0.455786	+	0.890090i	$0.349358\pi$
$368$	1.62588	0.0847547
$369$	5.08502	0.264715
$370$	0.708734	0.0368453
$371$	−24.2297	−1.25794
$372$	2.31668	0.120114
$373$	18.0987	0.937114	0.468557	−	0.883433i	$-0.344774\pi$
$373$	18.0987	0.937114	0.468557	+	0.883433i	$0.344774\pi$
$374$	−3.01757	−0.156035
$375$	6.11831	0.315948
$376$	6.68221	0.344608
$377$	−24.7755	−1.27600
$378$	2.55112	0.131216
$379$	−35.1576	−1.80593	−0.902963	−	0.429719i	$-0.858613\pi$
$379$	−35.1576	−1.80593	−0.902963	+	0.429719i	$0.858613\pi$
$380$	0.130738	0.00670674
$381$	−4.71056	−0.241329
$382$	−20.7446	−1.06138
$383$	26.6004	1.35922	0.679609	−	0.733575i	$-0.262150\pi$
$383$	26.6004	1.35922	0.679609	+	0.733575i	$0.262150\pi$
$384$	−1.00000	−0.0510310
$385$	4.90970	0.250221
$386$	11.9029	0.605841
$387$	1.39723	0.0710250
$388$	0.884692	0.0449134
$389$	12.5616	0.636899	0.318449	−	0.947940i	$-0.396838\pi$
$389$	12.5616	0.636899	0.318449	+	0.947940i	$0.396838\pi$
$390$	2.88234	0.145953
$391$	1.62588	0.0822241
$392$	0.491770	0.0248381
$393$	−10.4772	−0.528503
$394$	−18.4369	−0.928836
$395$	3.04772	0.153348
$396$	3.01757	0.151639
$397$	−27.3798	−1.37415	−0.687077	−	0.726584i	$-0.741107\pi$
$397$	−27.3798	−1.37415	−0.687077	+	0.726584i	$0.741107\pi$
$398$	−23.3049	−1.16817
$399$	0.522961	0.0261808
$400$	−4.59325	−0.229662
$401$	−26.4916	−1.32293	−0.661464	−	0.749977i	$-0.730065\pi$
$401$	−26.4916	−1.32293	−0.661464	+	0.749977i	$0.730065\pi$
$402$	1.80404	0.0899771
$403$	10.4700	0.521547
$404$	−8.85351	−0.440479
$405$	−0.637772	−0.0316912
$406$	−13.9854	−0.694083
$407$	3.35332	0.166218
$408$	−1.00000	−0.0495074
$409$	−26.9138	−1.33080	−0.665402	−	0.746485i	$-0.731740\pi$
$409$	−26.9138	−1.33080	−0.665402	+	0.746485i	$0.731740\pi$
$410$	3.24308	0.160164
$411$	7.58639	0.374209
$412$	2.87562	0.141672
$413$	−2.55112	−0.125533
$414$	−1.62588	−0.0799075
$415$	−9.43512	−0.463152
$416$	−4.51939	−0.221581
$417$	−4.56251	−0.223427
$418$	0.618579	0.0302557
$419$	−28.3418	−1.38459	−0.692295	−	0.721615i	$-0.743400\pi$
$419$	−28.3418	−1.38459	−0.692295	+	0.721615i	$0.743400\pi$
$420$	1.62704	0.0793912
$421$	12.6370	0.615891	0.307946	−	0.951404i	$-0.400359\pi$
$421$	12.6370	0.615891	0.307946	+	0.951404i	$0.400359\pi$
$422$	2.15591	0.104948
$423$	−6.68221	−0.324900
$424$	−9.49767	−0.461248
$425$	−4.59325	−0.222805
$426$	−14.5029	−0.702665
$427$	−24.2072	−1.17147
$428$	2.47240	0.119508
$429$	13.6376	0.658429
$430$	0.891112	0.0429732
$431$	38.2170	1.84085	0.920425	−	0.390920i	$-0.127843\pi$
$431$	38.2170	1.84085	0.920425	+	0.390920i	$0.127843\pi$
$432$	1.00000	0.0481125
$433$	30.3893	1.46042	0.730208	−	0.683225i	$-0.239423\pi$
$433$	30.3893	1.46042	0.730208	+	0.683225i	$0.239423\pi$
$434$	5.91014	0.283696
$435$	3.49630	0.167635
$436$	−0.594478	−0.0284703
$437$	−0.333292	−0.0159435
$438$	−0.762476	−0.0364325
$439$	−3.61435	−0.172504	−0.0862519	−	0.996273i	$-0.527489\pi$
$439$	−3.61435	−0.172504	−0.0862519	+	0.996273i	$0.527489\pi$
$440$	1.92452	0.0917481
$441$	−0.491770	−0.0234176
$442$	−4.51939	−0.214966
$443$	37.4586	1.77971	0.889856	−	0.456242i	$-0.150805\pi$
$443$	37.4586	1.77971	0.889856	+	0.456242i	$0.150805\pi$
$444$	1.11127	0.0527383
$445$	0.283460	0.0134373
$446$	18.2390	0.863644
$447$	5.57138	0.263517
$448$	−2.55112	−0.120529
$449$	9.90182	0.467296	0.233648	−	0.972321i	$-0.424934\pi$
$449$	9.90182	0.467296	0.233648	+	0.972321i	$0.424934\pi$
$450$	4.59325	0.216528
$451$	15.3444	0.722540
$452$	−19.7945	−0.931054
$453$	−22.8497	−1.07357
$454$	−12.5073	−0.586998
$455$	7.35321	0.344724
$456$	0.204992	0.00959965
$457$	1.67390	0.0783016	0.0391508	−	0.999233i	$-0.487535\pi$
$457$	1.67390	0.0783016	0.0391508	+	0.999233i	$0.487535\pi$
$458$	16.6494	0.777976
$459$	1.00000	0.0466760
$460$	−1.03694	−0.0483475
$461$	−25.8894	−1.20579	−0.602894	−	0.797821i	$-0.705986\pi$
$461$	−25.8894	−1.20579	−0.602894	+	0.797821i	$0.705986\pi$
$462$	7.69820	0.358153
$463$	−9.26894	−0.430764	−0.215382	−	0.976530i	$-0.569100\pi$
$463$	−9.26894	−0.430764	−0.215382	+	0.976530i	$0.569100\pi$
$464$	−5.48205	−0.254498
$465$	−1.47751	−0.0685181
$466$	−27.1005	−1.25540
$467$	16.7863	0.776776	0.388388	−	0.921496i	$-0.373032\pi$
$467$	16.7863	0.776776	0.388388	+	0.921496i	$0.373032\pi$
$468$	4.51939	0.208909
$469$	4.60232	0.212515
$470$	−4.26173	−0.196579
$471$	8.32312	0.383509
$472$	−1.00000	−0.0460287
$473$	4.21623	0.193863
$474$	4.77870	0.219493
$475$	0.941580	0.0432027
$476$	−2.55112	−0.116931
$477$	9.49767	0.434868
$478$	−23.0618	−1.05482
$479$	−9.12620	−0.416987	−0.208493	−	0.978024i	$-0.566856\pi$
$479$	−9.12620	−0.416987	−0.208493	+	0.978024i	$0.566856\pi$
$480$	0.637772	0.0291102
$481$	5.02224	0.228995
$482$	−28.9254	−1.31752
$483$	−4.14781	−0.188732
$484$	−1.89426	−0.0861025
$485$	−0.564232	−0.0256204
$486$	−1.00000	−0.0453609
$487$	−8.02089	−0.363461	−0.181731	−	0.983348i	$-0.558170\pi$
$487$	−8.02089	−0.363461	−0.181731	+	0.983348i	$0.558170\pi$
$488$	−9.48886	−0.429540
$489$	8.67759	0.392414
$490$	−0.313637	−0.0141687
$491$	39.5212	1.78357	0.891784	−	0.452462i	$-0.149454\pi$
$491$	39.5212	1.78357	0.891784	+	0.452462i	$0.149454\pi$
$492$	5.08502	0.229250
$493$	−5.48205	−0.246899
$494$	0.926440	0.0416825
$495$	−1.92452	−0.0865009
$496$	2.31668	0.104022
$497$	−36.9986	−1.65961
$498$	−14.7939	−0.662929
$499$	32.3760	1.44935	0.724674	−	0.689091i	$-0.241990\pi$
$499$	32.3760	1.44935	0.724674	+	0.689091i	$0.241990\pi$
$500$	6.11831	0.273619
$501$	−12.3061	−0.549796
$502$	−18.6061	−0.830433
$503$	37.7496	1.68317	0.841587	−	0.540122i	$-0.181622\pi$
$503$	37.7496	1.68317	0.841587	+	0.540122i	$0.181622\pi$
$504$	2.55112	0.113636
$505$	5.64652	0.251267
$506$	−4.90620	−0.218107
$507$	7.42489	0.329751
$508$	−4.71056	−0.208997
$509$	25.0431	1.11001	0.555007	−	0.831846i	$-0.312716\pi$
$509$	25.0431	1.11001	0.555007	+	0.831846i	$0.312716\pi$
$510$	0.637772	0.0282410
$511$	−1.94517	−0.0860492
$512$	−1.00000	−0.0441942
$513$	−0.204992	−0.00905063
$514$	1.42253	0.0627452
$515$	−1.83399	−0.0808152
$516$	1.39723	0.0615095
$517$	−20.1640	−0.886814
$518$	2.83497	0.124562
$519$	10.5416	0.462727
$520$	2.88234	0.126399
$521$	18.8627	0.826391	0.413195	−	0.910642i	$-0.364413\pi$
$521$	18.8627	0.826391	0.413195	+	0.910642i	$0.364413\pi$
$522$	5.48205	0.239943
$523$	−12.6767	−0.554313	−0.277157	−	0.960825i	$-0.589392\pi$
$523$	−12.6767	−0.554313	−0.277157	+	0.960825i	$0.589392\pi$
$524$	−10.4772	−0.457697
$525$	11.7179	0.511413
$526$	−6.08824	−0.265460
$527$	2.31668	0.100916
$528$	3.01757	0.131323
$529$	−20.3565	−0.885066
$530$	6.05735	0.263114
$531$	1.00000	0.0433963
$532$	0.522961	0.0226732
$533$	22.9812	0.995425
$534$	0.444454	0.0192334
$535$	−1.57683	−0.0681723
$536$	1.80404	0.0779225
$537$	5.30024	0.228722
$538$	−9.37068	−0.403999
$539$	−1.48395	−0.0639183
$540$	−0.637772	−0.0274453
$541$	−7.03523	−0.302468	−0.151234	−	0.988498i	$-0.548325\pi$
$541$	−7.03523	−0.302468	−0.151234	+	0.988498i	$0.548325\pi$
$542$	−17.2918	−0.742746
$543$	4.77053	0.204723
$544$	−1.00000	−0.0428746
$545$	0.379141	0.0162406
$546$	11.5295	0.493418
$547$	−29.8741	−1.27732	−0.638661	−	0.769488i	$-0.720512\pi$
$547$	−29.8741	−1.27732	−0.638661	+	0.769488i	$0.720512\pi$
$548$	7.58639	0.324074
$549$	9.48886	0.404975
$550$	13.8605	0.591012
$551$	1.12378	0.0478745
$552$	−1.62588	−0.0692019
$553$	12.1911	0.518417
$554$	1.01392	0.0430774
$555$	−0.708734	−0.0300841
$556$	−4.56251	−0.193494
$557$	17.2620	0.731415	0.365708	−	0.930730i	$-0.380827\pi$
$557$	17.2620	0.731415	0.365708	+	0.930730i	$0.380827\pi$
$558$	−2.31668	−0.0980729
$559$	6.31461	0.267080
$560$	1.62704	0.0687548
$561$	3.01757	0.127402
$562$	5.16826	0.218010
$563$	12.2198	0.515002	0.257501	−	0.966278i	$-0.417101\pi$
$563$	12.2198	0.515002	0.257501	+	0.966278i	$0.417101\pi$
$564$	−6.68221	−0.281372
$565$	12.6244	0.531111
$566$	0.0666371	0.00280096
$567$	−2.55112	−0.107137
$568$	−14.5029	−0.608526
$569$	−41.2961	−1.73122	−0.865610	−	0.500718i	$-0.833069\pi$
$569$	−41.2961	−1.73122	−0.865610	+	0.500718i	$0.833069\pi$
$570$	−0.130738	−0.00547603
$571$	19.8526	0.830805	0.415403	−	0.909638i	$-0.363641\pi$
$571$	19.8526	0.830805	0.415403	+	0.909638i	$0.363641\pi$
$572$	13.6376	0.570216
$573$	20.7446	0.866616
$574$	12.9725	0.541462
$575$	−7.46805	−0.311439
$576$	1.00000	0.0416667
$577$	−24.1860	−1.00688	−0.503439	−	0.864031i	$-0.667932\pi$
$577$	−24.1860	−1.00688	−0.503439	+	0.864031i	$0.667932\pi$
$578$	−1.00000	−0.0415945
$579$	−11.9029	−0.494667
$580$	3.49630	0.145176
$581$	−37.7410	−1.56576
$582$	−0.884692	−0.0366717
$583$	28.6599	1.18697
$584$	−0.762476	−0.0315515
$585$	−2.88234	−0.119170
$586$	−26.7942	−1.10686
$587$	27.7396	1.14493	0.572467	−	0.819927i	$-0.305986\pi$
$587$	27.7396	1.14493	0.572467	+	0.819927i	$0.305986\pi$
$588$	−0.491770	−0.0202802
$589$	−0.474902	−0.0195680
$590$	0.637772	0.0262567
$591$	18.4369	0.758392
$592$	1.11127	0.0456727
$593$	−43.5493	−1.78835	−0.894177	−	0.447714i	$-0.852238\pi$
$593$	−43.5493	−1.78835	−0.894177	+	0.447714i	$0.852238\pi$
$594$	−3.01757	−0.123813
$595$	1.62704	0.0667020
$596$	5.57138	0.228213
$597$	23.3049	0.953805
$598$	−7.34797	−0.300481
$599$	−27.7198	−1.13260	−0.566301	−	0.824198i	$-0.691626\pi$
$599$	−27.7198	−1.13260	−0.566301	+	0.824198i	$0.691626\pi$
$600$	4.59325	0.187519
$601$	30.5632	1.24670	0.623349	−	0.781944i	$-0.285772\pi$
$601$	30.5632	1.24670	0.623349	+	0.781944i	$0.285772\pi$
$602$	3.56450	0.145278
$603$	−1.80404	−0.0734660
$604$	−22.8497	−0.929739
$605$	1.20810	0.0491164
$606$	8.85351	0.359649
$607$	−34.3423	−1.39391	−0.696956	−	0.717114i	$-0.745463\pi$
$607$	−34.3423	−1.39391	−0.696956	+	0.717114i	$0.745463\pi$
$608$	0.204992	0.00831354
$609$	13.9854	0.566716
$610$	6.05173	0.245027
$611$	−30.1995	−1.22174
$612$	1.00000	0.0404226
$613$	31.2053	1.26037	0.630185	−	0.776445i	$-0.282979\pi$
$613$	31.2053	1.26037	0.630185	+	0.776445i	$0.282979\pi$
$614$	−34.5012	−1.39236
$615$	−3.24308	−0.130774
$616$	7.69820	0.310169
$617$	−42.4023	−1.70705	−0.853525	−	0.521051i	$-0.825540\pi$
$617$	−42.4023	−1.70705	−0.853525	+	0.521051i	$0.825540\pi$
$618$	−2.87562	−0.115674
$619$	19.8346	0.797221	0.398610	−	0.917120i	$-0.369493\pi$
$619$	19.8346	0.797221	0.398610	+	0.917120i	$0.369493\pi$
$620$	−1.47751	−0.0593384
$621$	1.62588	0.0652442
$622$	−3.93295	−0.157697
$623$	1.13386	0.0454270
$624$	4.51939	0.180920
$625$	19.0641	0.762566
$626$	12.5013	0.499651
$627$	−0.618579	−0.0247037
$628$	8.32312	0.332129
$629$	1.11127	0.0443090
$630$	−1.62704	−0.0648226
$631$	−4.73994	−0.188694	−0.0943470	−	0.995539i	$-0.530076\pi$
$631$	−4.73994	−0.188694	−0.0943470	+	0.995539i	$0.530076\pi$
$632$	4.77870	0.190087
$633$	−2.15591	−0.0856898
$634$	5.09288	0.202264
$635$	3.00426	0.119221
$636$	9.49767	0.376607
$637$	−2.22250	−0.0880586
$638$	16.5425	0.654923
$639$	14.5029	0.573724
$640$	0.637772	0.0252102
$641$	48.8228	1.92838	0.964192	−	0.265206i	$-0.0854398\pi$
$641$	48.8228	1.92838	0.964192	+	0.265206i	$0.0854398\pi$
$642$	−2.47240	−0.0975779
$643$	−2.72136	−0.107320	−0.0536600	−	0.998559i	$-0.517089\pi$
$643$	−2.72136	−0.107320	−0.0536600	+	0.998559i	$0.517089\pi$
$644$	−4.14781	−0.163447
$645$	−0.891112	−0.0350875
$646$	0.204992	0.00806532
$647$	33.8135	1.32934	0.664672	−	0.747135i	$-0.268571\pi$
$647$	33.8135	1.32934	0.664672	+	0.747135i	$0.268571\pi$
$648$	−1.00000	−0.0392837
$649$	3.01757	0.118450
$650$	20.7587	0.814222
$651$	−5.91014	−0.231637
$652$	8.67759	0.339841
$653$	−14.9988	−0.586949	−0.293475	−	0.955967i	$-0.594812\pi$
$653$	−14.9988	−0.586949	−0.293475	+	0.955967i	$0.594812\pi$
$654$	0.594478	0.0232459
$655$	6.68205	0.261089
$656$	5.08502	0.198537
$657$	0.762476	0.0297470
$658$	−17.0471	−0.664566
$659$	−17.2021	−0.670098	−0.335049	−	0.942201i	$-0.608753\pi$
$659$	−17.2021	−0.670098	−0.335049	+	0.942201i	$0.608753\pi$
$660$	−1.92452	−0.0749120
$661$	−9.78919	−0.380755	−0.190378	−	0.981711i	$-0.560971\pi$
$661$	−9.78919	−0.380755	−0.190378	+	0.981711i	$0.560971\pi$
$662$	−7.52204	−0.292352
$663$	4.51939	0.175519
$664$	−14.7939	−0.574113
$665$	−0.333530	−0.0129337
$666$	−1.11127	−0.0430607
$667$	−8.91313	−0.345118
$668$	−12.3061	−0.476137
$669$	−18.2390	−0.705162
$670$	−1.15056	−0.0444501
$671$	28.6333	1.10538
$672$	2.55112	0.0984117
$673$	14.6001	0.562794	0.281397	−	0.959591i	$-0.409202\pi$
$673$	14.6001	0.562794	0.281397	+	0.959591i	$0.409202\pi$
$674$	3.41765	0.131643
$675$	−4.59325	−0.176794
$676$	7.42489	0.285573
$677$	−6.81897	−0.262074	−0.131037	−	0.991377i	$-0.541831\pi$
$677$	−6.81897	−0.262074	−0.131037	+	0.991377i	$0.541831\pi$
$678$	19.7945	0.760202
$679$	−2.25696	−0.0866141
$680$	0.637772	0.0244574
$681$	12.5073	0.479282
$682$	−6.99075	−0.267690
$683$	−30.7865	−1.17801	−0.589007	−	0.808128i	$-0.700481\pi$
$683$	−30.7865	−1.17801	−0.589007	+	0.808128i	$0.700481\pi$
$684$	−0.204992	−0.00783808
$685$	−4.83839	−0.184865
$686$	−19.1124	−0.729716
$687$	−16.6494	−0.635214
$688$	1.39723	0.0532688
$689$	42.9237	1.63526
$690$	1.03694	0.0394756
$691$	−0.329309	−0.0125275	−0.00626376	−	0.999980i	$-0.501994\pi$
$691$	−0.329309	−0.0125275	−0.00626376	+	0.999980i	$0.501994\pi$
$692$	10.5416	0.400733
$693$	−7.69820	−0.292430
$694$	−5.24084	−0.198940
$695$	2.90984	0.110377
$696$	5.48205	0.207796
$697$	5.08502	0.192609
$698$	−6.58009	−0.249060
$699$	27.1005	1.02503
$700$	11.7179	0.442896
$701$	37.0254	1.39843	0.699216	−	0.714911i	$-0.253533\pi$
$701$	37.0254	1.39843	0.699216	+	0.714911i	$0.253533\pi$
$702$	−4.51939	−0.170573
$703$	−0.227801	−0.00859167
$704$	3.01757	0.113729
$705$	4.26173	0.160506
$706$	8.84253	0.332793
$707$	22.5864	0.849449
$708$	1.00000	0.0375823
$709$	6.29042	0.236242	0.118121	−	0.992999i	$-0.462313\pi$
$709$	6.29042	0.236242	0.118121	+	0.992999i	$0.462313\pi$
$710$	9.24951	0.347128
$711$	−4.77870	−0.179215
$712$	0.444454	0.0166566
$713$	3.76664	0.141062
$714$	2.55112	0.0954734
$715$	−8.69768	−0.325275
$716$	5.30024	0.198079
$717$	23.0618	0.861260
$718$	5.89377	0.219953
$719$	−33.0181	−1.23137	−0.615684	−	0.787993i	$-0.711120\pi$
$719$	−33.0181	−1.23137	−0.615684	+	0.787993i	$0.711120\pi$
$720$	−0.637772	−0.0237684
$721$	−7.33606	−0.273209
$722$	18.9580	0.705543
$723$	28.9254	1.07575
$724$	4.77053	0.177295
$725$	25.1804	0.935176
$726$	1.89426	0.0703024
$727$	−4.41814	−0.163860	−0.0819299	−	0.996638i	$-0.526108\pi$
$727$	−4.41814	−0.163860	−0.0819299	+	0.996638i	$0.526108\pi$
$728$	11.5295	0.427313
$729$	1.00000	0.0370370
$730$	0.486286	0.0179982
$731$	1.39723	0.0516783
$732$	9.48886	0.350718
$733$	−23.9780	−0.885647	−0.442824	−	0.896609i	$-0.646023\pi$
$733$	−23.9780	−0.885647	−0.442824	+	0.896609i	$0.646023\pi$
$734$	−17.4632	−0.644578
$735$	0.313637	0.0115687
$736$	−1.62588	−0.0599306
$737$	−5.44381	−0.200525
$738$	−5.08502	−0.187182
$739$	−49.4667	−1.81966	−0.909830	−	0.414980i	$-0.863788\pi$
$739$	−49.4667	−1.81966	−0.909830	+	0.414980i	$0.863788\pi$
$740$	−0.708734	−0.0260536
$741$	−0.926440	−0.0340336
$742$	24.2297	0.889501
$743$	−38.0462	−1.39578	−0.697891	−	0.716204i	$-0.745878\pi$
$743$	−38.0462	−1.39578	−0.697891	+	0.716204i	$0.745878\pi$
$744$	−2.31668	−0.0849337
$745$	−3.55327	−0.130182
$746$	−18.0987	−0.662640
$747$	14.7939	0.541279
$748$	3.01757	0.110333
$749$	−6.30740	−0.230467
$750$	−6.11831	−0.223409
$751$	−50.3897	−1.83874	−0.919372	−	0.393388i	$-0.871303\pi$
$751$	−50.3897	−1.83874	−0.919372	+	0.393388i	$0.871303\pi$
$752$	−6.68221	−0.243675
$753$	18.6061	0.678046
$754$	24.7755	0.902271
$755$	14.5729	0.530361
$756$	−2.55112	−0.0927835
$757$	−11.0268	−0.400776	−0.200388	−	0.979717i	$-0.564220\pi$
$757$	−11.0268	−0.400776	−0.200388	+	0.979717i	$0.564220\pi$
$758$	35.1576	1.27698
$759$	4.90620	0.178084
$760$	−0.130738	−0.00474238
$761$	−35.8571	−1.29982	−0.649909	−	0.760012i	$-0.725193\pi$
$761$	−35.8571	−1.29982	−0.649909	+	0.760012i	$0.725193\pi$
$762$	4.71056	0.170646
$763$	1.51659	0.0549041
$764$	20.7446	0.750512
$765$	−0.637772	−0.0230587
$766$	−26.6004	−0.961112
$767$	4.51939	0.163186
$768$	1.00000	0.0360844
$769$	19.5019	0.703255	0.351627	−	0.936140i	$-0.385628\pi$
$769$	19.5019	0.703255	0.351627	+	0.936140i	$0.385628\pi$
$770$	−4.90970	−0.176933
$771$	−1.42253	−0.0512313
$772$	−11.9029	−0.428394
$773$	7.52845	0.270779	0.135390	−	0.990792i	$-0.456771\pi$
$773$	7.52845	0.270779	0.135390	+	0.990792i	$0.456771\pi$
$774$	−1.39723	−0.0502223
$775$	−10.6411	−0.382239
$776$	−0.884692	−0.0317586
$777$	−2.83497	−0.101704
$778$	−12.5616	−0.450355
$779$	−1.04239	−0.0373475
$780$	−2.88234	−0.103204
$781$	43.7634	1.56598
$782$	−1.62588	−0.0581412
$783$	−5.48205	−0.195912
$784$	−0.491770	−0.0175632
$785$	−5.30826	−0.189460
$786$	10.4772	0.373708
$787$	−25.0025	−0.891242	−0.445621	−	0.895222i	$-0.647017\pi$
$787$	−25.0025	−0.891242	−0.445621	+	0.895222i	$0.647017\pi$
$788$	18.4369	0.656787
$789$	6.08824	0.216747
$790$	−3.04772	−0.108433
$791$	50.4981	1.79551
$792$	−3.01757	−0.107225
$793$	42.8839	1.52285
$794$	27.3798	0.971674
$795$	−6.05735	−0.214832
$796$	23.3049	0.826019
$797$	37.7283	1.33640	0.668202	−	0.743980i	$-0.267064\pi$
$797$	37.7283	1.33640	0.668202	+	0.743980i	$0.267064\pi$
$798$	−0.522961	−0.0185126
$799$	−6.68221	−0.236399
$800$	4.59325	0.162396
$801$	−0.444454	−0.0157040
$802$	26.4916	0.935452
$803$	2.30083	0.0811944
$804$	−1.80404	−0.0636234
$805$	2.64536	0.0932366
$806$	−10.4700	−0.368790
$807$	9.37068	0.329864
$808$	8.85351	0.311465
$809$	44.0640	1.54921	0.774604	−	0.632446i	$-0.217949\pi$
$809$	44.0640	1.54921	0.774604	+	0.632446i	$0.217949\pi$
$810$	0.637772	0.0224090
$811$	−28.7523	−1.00963	−0.504814	−	0.863228i	$-0.668439\pi$
$811$	−28.7523	−1.00963	−0.504814	+	0.863228i	$0.668439\pi$
$812$	13.9854	0.490791
$813$	17.2918	0.606449
$814$	−3.35332	−0.117534
$815$	−5.53432	−0.193859
$816$	1.00000	0.0350070
$817$	−0.286421	−0.0100206
$818$	26.9138	0.941021
$819$	−11.5295	−0.402874
$820$	−3.24308	−0.113253
$821$	−2.40596	−0.0839688	−0.0419844	−	0.999118i	$-0.513368\pi$
$821$	−2.40596	−0.0839688	−0.0419844	+	0.999118i	$0.513368\pi$
$822$	−7.58639	−0.264606
$823$	−26.0353	−0.907533	−0.453766	−	0.891121i	$-0.649920\pi$
$823$	−26.0353	−0.907533	−0.453766	+	0.891121i	$0.649920\pi$
$824$	−2.87562	−0.100177
$825$	−13.8605	−0.482559
$826$	2.55112	0.0887649
$827$	40.9336	1.42340	0.711701	−	0.702483i	$-0.247925\pi$
$827$	40.9336	1.42340	0.711701	+	0.702483i	$0.247925\pi$
$828$	1.62588	0.0565031
$829$	8.48235	0.294604	0.147302	−	0.989092i	$-0.452941\pi$
$829$	8.48235	0.294604	0.147302	+	0.989092i	$0.452941\pi$
$830$	9.43512	0.327498
$831$	−1.01392	−0.0351725
$832$	4.51939	0.156682
$833$	−0.491770	−0.0170388
$834$	4.56251	0.157987
$835$	7.84849	0.271608
$836$	−0.618579	−0.0213940
$837$	2.31668	0.0800762
$838$	28.3418	0.979052
$839$	25.1265	0.867462	0.433731	−	0.901042i	$-0.357197\pi$
$839$	25.1265	0.867462	0.433731	+	0.901042i	$0.357197\pi$
$840$	−1.62704	−0.0561381
$841$	1.05284	0.0363048
$842$	−12.6370	−0.435501
$843$	−5.16826	−0.178004
$844$	−2.15591	−0.0742095
$845$	−4.73539	−0.162902
$846$	6.68221	0.229739
$847$	4.83248	0.166046
$848$	9.49767	0.326151
$849$	−0.0666371	−0.00228698
$850$	4.59325	0.157547
$851$	1.80678	0.0619356
$852$	14.5029	0.496859
$853$	12.6607	0.433493	0.216746	−	0.976228i	$-0.430456\pi$
$853$	12.6607	0.433493	0.216746	+	0.976228i	$0.430456\pi$
$854$	24.2072	0.828355
$855$	0.130738	0.00447116
$856$	−2.47240	−0.0845050
$857$	−42.4988	−1.45173	−0.725866	−	0.687836i	$-0.758561\pi$
$857$	−42.4988	−1.45173	−0.725866	+	0.687836i	$0.758561\pi$
$858$	−13.6376	−0.465580
$859$	−44.7862	−1.52808	−0.764042	−	0.645166i	$-0.776788\pi$
$859$	−44.7862	−1.52808	−0.764042	+	0.645166i	$0.776788\pi$
$860$	−0.891112	−0.0303867
$861$	−12.9725	−0.442102
$862$	−38.2170	−1.30168
$863$	11.7128	0.398707	0.199354	−	0.979928i	$-0.436116\pi$
$863$	11.7128	0.398707	0.199354	+	0.979928i	$0.436116\pi$
$864$	−1.00000	−0.0340207
$865$	−6.72316	−0.228594
$866$	−30.3893	−1.03267
$867$	1.00000	0.0339618
$868$	−5.91014	−0.200603
$869$	−14.4201	−0.489168
$870$	−3.49630	−0.118536
$871$	−8.15314	−0.276259
$872$	0.594478	0.0201316
$873$	0.884692	0.0299423
$874$	0.333292	0.0112738
$875$	−15.6086	−0.527665
$876$	0.762476	0.0257617
$877$	28.5667	0.964629	0.482315	−	0.875998i	$-0.339796\pi$
$877$	28.5667	0.964629	0.482315	+	0.875998i	$0.339796\pi$
$878$	3.61435	0.121979
$879$	26.7942	0.903745
$880$	−1.92452	−0.0648757
$881$	−26.7921	−0.902648	−0.451324	−	0.892360i	$-0.649048\pi$
$881$	−26.7921	−0.902648	−0.451324	+	0.892360i	$0.649048\pi$
$882$	0.491770	0.0165587
$883$	53.1059	1.78716	0.893578	−	0.448907i	$-0.148187\pi$
$883$	53.1059	1.78716	0.893578	+	0.448907i	$0.148187\pi$
$884$	4.51939	0.152004
$885$	−0.637772	−0.0214385
$886$	−37.4586	−1.25845
$887$	40.0422	1.34449	0.672243	−	0.740331i	$-0.265331\pi$
$887$	40.0422	1.34449	0.672243	+	0.740331i	$0.265331\pi$
$888$	−1.11127	−0.0372916
$889$	12.0172	0.403045
$890$	−0.283460	−0.00950161
$891$	3.01757	0.101092
$892$	−18.2390	−0.610688
$893$	1.36980	0.0458386
$894$	−5.57138	−0.186335
$895$	−3.38035	−0.112992
$896$	2.55112	0.0852271
$897$	7.34797	0.245342
$898$	−9.90182	−0.330428
$899$	−12.7002	−0.423574
$900$	−4.59325	−0.153108
$901$	9.49767	0.316413
$902$	−15.3444	−0.510913
$903$	−3.56450	−0.118619
$904$	19.7945	0.658354
$905$	−3.04251	−0.101136
$906$	22.8497	0.759129
$907$	−32.1409	−1.06722	−0.533610	−	0.845731i	$-0.679165\pi$
$907$	−32.1409	−1.06722	−0.533610	+	0.845731i	$0.679165\pi$
$908$	12.5073	0.415070
$909$	−8.85351	−0.293652
$910$	−7.35321	−0.243757
$911$	−9.93568	−0.329184	−0.164592	−	0.986362i	$-0.552631\pi$
$911$	−9.93568	−0.329184	−0.164592	+	0.986362i	$0.552631\pi$
$912$	−0.204992	−0.00678797
$913$	44.6416	1.47742
$914$	−1.67390	−0.0553676
$915$	−6.05173	−0.200064
$916$	−16.6494	−0.550112
$917$	26.7285	0.882654
$918$	−1.00000	−0.0330049
$919$	−10.7304	−0.353963	−0.176981	−	0.984214i	$-0.556633\pi$
$919$	−10.7304	−0.353963	−0.176981	+	0.984214i	$0.556633\pi$
$920$	1.03694	0.0341869
$921$	34.5012	1.13685
$922$	25.8894	0.852621
$923$	65.5441	2.15741
$924$	−7.69820	−0.253252
$925$	−5.10432	−0.167829
$926$	9.26894	0.304596
$927$	2.87562	0.0944477
$928$	5.48205	0.179957
$929$	−47.4403	−1.55647	−0.778233	−	0.627976i	$-0.783883\pi$
$929$	−47.4403	−1.55647	−0.778233	+	0.627976i	$0.783883\pi$
$930$	1.47751	0.0484496
$931$	0.100809	0.00330388
$932$	27.1005	0.887705
$933$	3.93295	0.128759
$934$	−16.7863	−0.549264
$935$	−1.92452	−0.0629387
$936$	−4.51939	−0.147721
$937$	7.60497	0.248444	0.124222	−	0.992254i	$-0.460357\pi$
$937$	7.60497	0.248444	0.124222	+	0.992254i	$0.460357\pi$
$938$	−4.60232	−0.150271
$939$	−12.5013	−0.407963
$940$	4.26173	0.139002
$941$	−50.0965	−1.63310	−0.816550	−	0.577275i	$-0.804116\pi$
$941$	−50.0965	−1.63310	−0.816550	+	0.577275i	$0.804116\pi$
$942$	−8.32312	−0.271182
$943$	8.26761	0.269230
$944$	1.00000	0.0325472
$945$	1.62704	0.0529275
$946$	−4.21623	−0.137082
$947$	−51.4013	−1.67032	−0.835159	−	0.550009i	$-0.814624\pi$
$947$	−51.4013	−1.67032	−0.835159	+	0.550009i	$0.814624\pi$
$948$	−4.77870	−0.155205
$949$	3.44593	0.111859
$950$	−0.941580	−0.0305489
$951$	−5.09288	−0.165148
$952$	2.55112	0.0826824
$953$	−44.9386	−1.45570	−0.727852	−	0.685734i	$-0.759481\pi$
$953$	−44.9386	−1.45570	−0.727852	+	0.685734i	$0.759481\pi$
$954$	−9.49767	−0.307498
$955$	−13.2303	−0.428122
$956$	23.0618	0.745873
$957$	−16.5425	−0.534742
$958$	9.12620	0.294854
$959$	−19.3538	−0.624967
$960$	−0.637772	−0.0205840
$961$	−25.6330	−0.826871
$962$	−5.02224	−0.161924
$963$	2.47240	0.0796720
$964$	28.9254	0.931624
$965$	7.59132	0.244373
$966$	4.14781	0.133454
$967$	−4.04497	−0.130077	−0.0650387	−	0.997883i	$-0.520717\pi$
$967$	−4.04497	−0.130077	−0.0650387	+	0.997883i	$0.520717\pi$
$968$	1.89426	0.0608837
$969$	−0.204992	−0.00658530
$970$	0.564232	0.0181164
$971$	20.1340	0.646130	0.323065	−	0.946377i	$-0.395287\pi$
$971$	20.1340	0.646130	0.323065	+	0.946377i	$0.395287\pi$
$972$	1.00000	0.0320750
$973$	11.6395	0.373146
$974$	8.02089	0.257006
$975$	−20.7587	−0.664810
$976$	9.48886	0.303731
$977$	24.7916	0.793154	0.396577	−	0.918001i	$-0.370198\pi$
$977$	24.7916	0.793154	0.396577	+	0.918001i	$0.370198\pi$
$978$	−8.67759	−0.277479
$979$	−1.34117	−0.0428640
$980$	0.313637	0.0100188
$981$	−0.594478	−0.0189802
$982$	−39.5212	−1.26117
$983$	1.31896	0.0420682	0.0210341	−	0.999779i	$-0.493304\pi$
$983$	1.31896	0.0420682	0.0210341	+	0.999779i	$0.493304\pi$
$984$	−5.08502	−0.162104
$985$	−11.7585	−0.374658
$986$	5.48205	0.174584
$987$	17.0471	0.542616
$988$	−0.926440	−0.0294740
$989$	2.27172	0.0722364
$990$	1.92452	0.0611654
$991$	−36.9500	−1.17375	−0.586877	−	0.809676i	$-0.699643\pi$
$991$	−36.9500	−1.17375	−0.586877	+	0.809676i	$0.699643\pi$
$992$	−2.31668	−0.0735547
$993$	7.52204	0.238705
$994$	36.9986	1.17352
$995$	−14.8632	−0.471195
$996$	14.7939	0.468762
$997$	21.9550	0.695323	0.347662	−	0.937620i	$-0.386976\pi$
$997$	21.9550	0.695323	0.347662	+	0.937620i	$0.386976\pi$
$998$	−32.3760	−1.02484
$999$	1.11127	0.0351589

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.w.1.3	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.w.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.637772 q^{5} -1.00000 q^{6} -2.55112 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.637772 q^{5} -1.00000 q^{6} -2.55112 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.637772 q^{10} +3.01757 q^{11} +1.00000 q^{12} +4.51939 q^{13} +2.55112 q^{14} -0.637772 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} -0.204992 q^{19} -0.637772 q^{20} -2.55112 q^{21} -3.01757 q^{22} +1.62588 q^{23} -1.00000 q^{24} -4.59325 q^{25} -4.51939 q^{26} +1.00000 q^{27} -2.55112 q^{28} -5.48205 q^{29} +0.637772 q^{30} +2.31668 q^{31} -1.00000 q^{32} +3.01757 q^{33} -1.00000 q^{34} +1.62704 q^{35} +1.00000 q^{36} +1.11127 q^{37} +0.204992 q^{38} +4.51939 q^{39} +0.637772 q^{40} +5.08502 q^{41} +2.55112 q^{42} +1.39723 q^{43} +3.01757 q^{44} -0.637772 q^{45} -1.62588 q^{46} -6.68221 q^{47} +1.00000 q^{48} -0.491770 q^{49} +4.59325 q^{50} +1.00000 q^{51} +4.51939 q^{52} +9.49767 q^{53} -1.00000 q^{54} -1.92452 q^{55} +2.55112 q^{56} -0.204992 q^{57} +5.48205 q^{58} +1.00000 q^{59} -0.637772 q^{60} +9.48886 q^{61} -2.31668 q^{62} -2.55112 q^{63} +1.00000 q^{64} -2.88234 q^{65} -3.01757 q^{66} -1.80404 q^{67} +1.00000 q^{68} +1.62588 q^{69} -1.62704 q^{70} +14.5029 q^{71} -1.00000 q^{72} +0.762476 q^{73} -1.11127 q^{74} -4.59325 q^{75} -0.204992 q^{76} -7.69820 q^{77} -4.51939 q^{78} -4.77870 q^{79} -0.637772 q^{80} +1.00000 q^{81} -5.08502 q^{82} +14.7939 q^{83} -2.55112 q^{84} -0.637772 q^{85} -1.39723 q^{86} -5.48205 q^{87} -3.01757 q^{88} -0.444454 q^{89} +0.637772 q^{90} -11.5295 q^{91} +1.62588 q^{92} +2.31668 q^{93} +6.68221 q^{94} +0.130738 q^{95} -1.00000 q^{96} +0.884692 q^{97} +0.491770 q^{98} +3.01757 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 9 q^{2} + 9 q^{3} + 9 q^{4} + q^{5} - 9 q^{6} - 9 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q - 9 * q^2 + 9 * q^3 + 9 * q^4 + q^5 - 9 * q^6 - 9 * q^8 + 9 * q^9	\( 9 q - 9 q^{2} + 9 q^{3} + 9 q^{4} + q^{5} - 9 q^{6} - 9 q^{8} + 9 q^{9} - q^{10} + 6 q^{11} + 9 q^{12} + 2 q^{13} + q^{15} + 9 q^{16} + 9 q^{17} - 9 q^{18} - 5 q^{19} + q^{20} - 6 q^{22} + 15 q^{23} - 9 q^{24} - 2 q^{26} + 9 q^{27} + 11 q^{29} - q^{30} - 5 q^{31} - 9 q^{32} + 6 q^{33} - 9 q^{34} + 22 q^{35} + 9 q^{36} + 9 q^{37} + 5 q^{38} + 2 q^{39} - q^{40} + q^{41} + 4 q^{43} + 6 q^{44} + q^{45} - 15 q^{46} + 14 q^{47} + 9 q^{48} - q^{49} + 9 q^{51} + 2 q^{52} + 4 q^{53} - 9 q^{54} + 4 q^{55} - 5 q^{57} - 11 q^{58} + 9 q^{59} + q^{60} + 10 q^{61} + 5 q^{62} + 9 q^{64} + 8 q^{65} - 6 q^{66} - q^{67} + 9 q^{68} + 15 q^{69} - 22 q^{70} + 14 q^{71} - 9 q^{72} - q^{73} - 9 q^{74} - 5 q^{76} + 30 q^{77} - 2 q^{78} + 4 q^{79} + q^{80} + 9 q^{81} - q^{82} + 22 q^{83} + q^{85} - 4 q^{86} + 11 q^{87} - 6 q^{88} + 22 q^{89} - q^{90} - 3 q^{91} + 15 q^{92} - 5 q^{93} - 14 q^{94} + 43 q^{95} - 9 q^{96} - 15 q^{97} + q^{98} + 6 q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 + 9 * q^3 + 9 * q^4 + q^5 - 9 * q^6 - 9 * q^8 + 9 * q^9 - q^10 + 6 * q^11 + 9 * q^12 + 2 * q^13 + q^15 + 9 * q^16 + 9 * q^17 - 9 * q^18 - 5 * q^19 + q^20 - 6 * q^22 + 15 * q^23 - 9 * q^24 - 2 * q^26 + 9 * q^27 + 11 * q^29 - q^30 - 5 * q^31 - 9 * q^32 + 6 * q^33 - 9 * q^34 + 22 * q^35 + 9 * q^36 + 9 * q^37 + 5 * q^38 + 2 * q^39 - q^40 + q^41 + 4 * q^43 + 6 * q^44 + q^45 - 15 * q^46 + 14 * q^47 + 9 * q^48 - q^49 + 9 * q^51 + 2 * q^52 + 4 * q^53 - 9 * q^54 + 4 * q^55 - 5 * q^57 - 11 * q^58 + 9 * q^59 + q^60 + 10 * q^61 + 5 * q^62 + 9 * q^64 + 8 * q^65 - 6 * q^66 - q^67 + 9 * q^68 + 15 * q^69 - 22 * q^70 + 14 * q^71 - 9 * q^72 - q^73 - 9 * q^74 - 5 * q^76 + 30 * q^77 - 2 * q^78 + 4 * q^79 + q^80 + 9 * q^81 - q^82 + 22 * q^83 + q^85 - 4 * q^86 + 11 * q^87 - 6 * q^88 + 22 * q^89 - q^90 - 3 * q^91 + 15 * q^92 - 5 * q^93 - 14 * q^94 + 43 * q^95 - 9 * q^96 - 15 * q^97 + q^98 + 6 * q^99

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