LMFDB - Embedded newform 8018.2.a.d.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$1$
Dimension:	$30$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.44219 q^{3} +1.00000 q^{4} -1.29569 q^{5} -1.44219 q^{6} +1.46621 q^{7} +1.00000 q^{8} -0.920075 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.44219 q^{3} +1.00000 q^{4} -1.29569 q^{5} -1.44219 q^{6} +1.46621 q^{7} +1.00000 q^{8} -0.920075 q^{9} -1.29569 q^{10} +4.03083 q^{11} -1.44219 q^{12} -4.55842 q^{13} +1.46621 q^{14} +1.86864 q^{15} +1.00000 q^{16} +4.46505 q^{17} -0.920075 q^{18} +1.00000 q^{19} -1.29569 q^{20} -2.11456 q^{21} +4.03083 q^{22} -5.71583 q^{23} -1.44219 q^{24} -3.32118 q^{25} -4.55842 q^{26} +5.65351 q^{27} +1.46621 q^{28} -2.18737 q^{29} +1.86864 q^{30} +2.09464 q^{31} +1.00000 q^{32} -5.81323 q^{33} +4.46505 q^{34} -1.89976 q^{35} -0.920075 q^{36} +0.932881 q^{37} +1.00000 q^{38} +6.57413 q^{39} -1.29569 q^{40} -5.12241 q^{41} -2.11456 q^{42} -5.26177 q^{43} +4.03083 q^{44} +1.19214 q^{45} -5.71583 q^{46} -4.83158 q^{47} -1.44219 q^{48} -4.85023 q^{49} -3.32118 q^{50} -6.43946 q^{51} -4.55842 q^{52} +11.7170 q^{53} +5.65351 q^{54} -5.22271 q^{55} +1.46621 q^{56} -1.44219 q^{57} -2.18737 q^{58} +6.23967 q^{59} +1.86864 q^{60} +7.92789 q^{61} +2.09464 q^{62} -1.34902 q^{63} +1.00000 q^{64} +5.90632 q^{65} -5.81323 q^{66} -5.85180 q^{67} +4.46505 q^{68} +8.24333 q^{69} -1.89976 q^{70} -9.87136 q^{71} -0.920075 q^{72} -1.85006 q^{73} +0.932881 q^{74} +4.78979 q^{75} +1.00000 q^{76} +5.91004 q^{77} +6.57413 q^{78} +15.3599 q^{79} -1.29569 q^{80} -5.39324 q^{81} -5.12241 q^{82} -6.53807 q^{83} -2.11456 q^{84} -5.78533 q^{85} -5.26177 q^{86} +3.15461 q^{87} +4.03083 q^{88} -14.9426 q^{89} +1.19214 q^{90} -6.68361 q^{91} -5.71583 q^{92} -3.02088 q^{93} -4.83158 q^{94} -1.29569 q^{95} -1.44219 q^{96} +14.1798 q^{97} -4.85023 q^{98} -3.70866 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9}+O(q^{10}) $ 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9} - 12 q^{10} - 17 q^{11} - 10 q^{12} - 19 q^{13} - 15 q^{14} - 8 q^{15} + 30 q^{16} - 18 q^{17} + 10 q^{18} + 30 q^{19} - 12 q^{20} - 14 q^{21} - 17 q^{22} - 15 q^{23} - 10 q^{24} - 4 q^{25} - 19 q^{26} - 37 q^{27} - 15 q^{28} - 37 q^{29} - 8 q^{30} - 11 q^{31} + 30 q^{32} + 6 q^{33} - 18 q^{34} - 4 q^{35} + 10 q^{36} - 46 q^{37} + 30 q^{38} - 12 q^{40} - 28 q^{41} - 14 q^{42} - 61 q^{43} - 17 q^{44} - 14 q^{45} - 15 q^{46} - 4 q^{47} - 10 q^{48} - q^{49} - 4 q^{50} - 8 q^{51} - 19 q^{52} - 19 q^{53} - 37 q^{54} - 17 q^{55} - 15 q^{56} - 10 q^{57} - 37 q^{58} - 6 q^{59} - 8 q^{60} - 32 q^{61} - 11 q^{62} - 24 q^{63} + 30 q^{64} - 24 q^{65} + 6 q^{66} - 44 q^{67} - 18 q^{68} - 2 q^{69} - 4 q^{70} + 10 q^{71} + 10 q^{72} - 58 q^{73} - 46 q^{74} - 42 q^{75} + 30 q^{76} - 32 q^{77} - 42 q^{79} - 12 q^{80} - 38 q^{81} - 28 q^{82} - 25 q^{83} - 14 q^{84} - 48 q^{85} - 61 q^{86} - 15 q^{87} - 17 q^{88} - 39 q^{89} - 14 q^{90} - 21 q^{91} - 15 q^{92} - 45 q^{93} - 4 q^{94} - 12 q^{95} - 10 q^{96} - 33 q^{97} - q^{98} - 38 q^{99}+O(q^{100}) \) 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9 - 12 * q^10 - 17 * q^11 - 10 * q^12 - 19 * q^13 - 15 * q^14 - 8 * q^15 + 30 * q^16 - 18 * q^17 + 10 * q^18 + 30 * q^19 - 12 * q^20 - 14 * q^21 - 17 * q^22 - 15 * q^23 - 10 * q^24 - 4 * q^25 - 19 * q^26 - 37 * q^27 - 15 * q^28 - 37 * q^29 - 8 * q^30 - 11 * q^31 + 30 * q^32 + 6 * q^33 - 18 * q^34 - 4 * q^35 + 10 * q^36 - 46 * q^37 + 30 * q^38 - 12 * q^40 - 28 * q^41 - 14 * q^42 - 61 * q^43 - 17 * q^44 - 14 * q^45 - 15 * q^46 - 4 * q^47 - 10 * q^48 - q^49 - 4 * q^50 - 8 * q^51 - 19 * q^52 - 19 * q^53 - 37 * q^54 - 17 * q^55 - 15 * q^56 - 10 * q^57 - 37 * q^58 - 6 * q^59 - 8 * q^60 - 32 * q^61 - 11 * q^62 - 24 * q^63 + 30 * q^64 - 24 * q^65 + 6 * q^66 - 44 * q^67 - 18 * q^68 - 2 * q^69 - 4 * q^70 + 10 * q^71 + 10 * q^72 - 58 * q^73 - 46 * q^74 - 42 * q^75 + 30 * q^76 - 32 * q^77 - 42 * q^79 - 12 * q^80 - 38 * q^81 - 28 * q^82 - 25 * q^83 - 14 * q^84 - 48 * q^85 - 61 * q^86 - 15 * q^87 - 17 * q^88 - 39 * q^89 - 14 * q^90 - 21 * q^91 - 15 * q^92 - 45 * q^93 - 4 * q^94 - 12 * q^95 - 10 * q^96 - 33 * q^97 - q^98 - 38 * 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
$3$	−1.44219	−0.832651	−0.416326	−	0.909216i	$-0.636682\pi$
$3$	−1.44219	−0.832651	−0.416326	+	0.909216i	$0.636682\pi$
$4$	1.00000	0.500000
$5$	−1.29569	−0.579451	−0.289726	−	0.957110i	$-0.593564\pi$
$5$	−1.29569	−0.579451	−0.289726	+	0.957110i	$0.593564\pi$
$6$	−1.44219	−0.588773
$7$	1.46621	0.554175	0.277088	−	0.960845i	$-0.410631\pi$
$7$	1.46621	0.554175	0.277088	+	0.960845i	$0.410631\pi$
$8$	1.00000	0.353553
$9$	−0.920075	−0.306692
$10$	−1.29569	−0.409734
$11$	4.03083	1.21534	0.607670	−	0.794190i	$-0.292104\pi$
$11$	4.03083	1.21534	0.607670	+	0.794190i	$0.292104\pi$
$12$	−1.44219	−0.416326
$13$	−4.55842	−1.26428	−0.632140	−	0.774855i	$-0.717823\pi$
$13$	−4.55842	−1.26428	−0.632140	+	0.774855i	$0.717823\pi$
$14$	1.46621	0.391861
$15$	1.86864	0.482481
$16$	1.00000	0.250000
$17$	4.46505	1.08293	0.541466	−	0.840722i	$-0.317869\pi$
$17$	4.46505	1.08293	0.541466	+	0.840722i	$0.317869\pi$
$18$	−0.920075	−0.216864
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−1.29569	−0.289726
$21$	−2.11456	−0.461435
$22$	4.03083	0.859375
$23$	−5.71583	−1.19183	−0.595916	−	0.803047i	$-0.703211\pi$
$23$	−5.71583	−1.19183	−0.595916	+	0.803047i	$0.703211\pi$
$24$	−1.44219	−0.294387
$25$	−3.32118	−0.664236
$26$	−4.55842	−0.893980
$27$	5.65351	1.08802
$28$	1.46621	0.277088
$29$	−2.18737	−0.406184	−0.203092	−	0.979160i	$-0.565099\pi$
$29$	−2.18737	−0.406184	−0.203092	+	0.979160i	$0.565099\pi$
$30$	1.86864	0.341166
$31$	2.09464	0.376209	0.188104	−	0.982149i	$-0.439766\pi$
$31$	2.09464	0.376209	0.188104	+	0.982149i	$0.439766\pi$
$32$	1.00000	0.176777
$33$	−5.81323	−1.01195
$34$	4.46505	0.765749
$35$	−1.89976	−0.321118
$36$	−0.920075	−0.153346
$37$	0.932881	0.153365	0.0766824	−	0.997056i	$-0.475567\pi$
$37$	0.932881	0.153365	0.0766824	+	0.997056i	$0.475567\pi$
$38$	1.00000	0.162221
$39$	6.57413	1.05270
$40$	−1.29569	−0.204867
$41$	−5.12241	−0.799986	−0.399993	−	0.916518i	$-0.630987\pi$
$41$	−5.12241	−0.799986	−0.399993	+	0.916518i	$0.630987\pi$
$42$	−2.11456	−0.326284
$43$	−5.26177	−0.802413	−0.401206	−	0.915988i	$-0.631409\pi$
$43$	−5.26177	−0.802413	−0.401206	+	0.915988i	$0.631409\pi$
$44$	4.03083	0.607670
$45$	1.19214	0.177713
$46$	−5.71583	−0.842753
$47$	−4.83158	−0.704758	−0.352379	−	0.935857i	$-0.614627\pi$
$47$	−4.83158	−0.704758	−0.352379	+	0.935857i	$0.614627\pi$
$48$	−1.44219	−0.208163
$49$	−4.85023	−0.692890
$50$	−3.32118	−0.469686
$51$	−6.43946	−0.901705
$52$	−4.55842	−0.632140
$53$	11.7170	1.60946	0.804728	−	0.593644i	$-0.202311\pi$
$53$	11.7170	1.60946	0.804728	+	0.593644i	$0.202311\pi$
$54$	5.65351	0.769345
$55$	−5.22271	−0.704230
$56$	1.46621	0.195931
$57$	−1.44219	−0.191023
$58$	−2.18737	−0.287216
$59$	6.23967	0.812335	0.406168	−	0.913799i	$-0.366865\pi$
$59$	6.23967	0.812335	0.406168	+	0.913799i	$0.366865\pi$
$60$	1.86864	0.241241
$61$	7.92789	1.01506	0.507531	−	0.861634i	$-0.330558\pi$
$61$	7.92789	1.01506	0.507531	+	0.861634i	$0.330558\pi$
$62$	2.09464	0.266020
$63$	−1.34902	−0.169961
$64$	1.00000	0.125000
$65$	5.90632	0.732588
$66$	−5.81323	−0.715560
$67$	−5.85180	−0.714912	−0.357456	−	0.933930i	$-0.616356\pi$
$67$	−5.85180	−0.714912	−0.357456	+	0.933930i	$0.616356\pi$
$68$	4.46505	0.541466
$69$	8.24333	0.992381
$70$	−1.89976	−0.227065
$71$	−9.87136	−1.17152	−0.585758	−	0.810486i	$-0.699203\pi$
$71$	−9.87136	−1.17152	−0.585758	+	0.810486i	$0.699203\pi$
$72$	−0.920075	−0.108432
$73$	−1.85006	−0.216533	−0.108266	−	0.994122i	$-0.534530\pi$
$73$	−1.85006	−0.216533	−0.108266	+	0.994122i	$0.534530\pi$
$74$	0.932881	0.108445
$75$	4.78979	0.553077
$76$	1.00000	0.114708
$77$	5.91004	0.673511
$78$	6.57413	0.744374
$79$	15.3599	1.72812	0.864062	−	0.503385i	$-0.167912\pi$
$79$	15.3599	1.72812	0.864062	+	0.503385i	$0.167912\pi$
$80$	−1.29569	−0.144863
$81$	−5.39324	−0.599248
$82$	−5.12241	−0.565675
$83$	−6.53807	−0.717646	−0.358823	−	0.933406i	$-0.616822\pi$
$83$	−6.53807	−0.717646	−0.358823	+	0.933406i	$0.616822\pi$
$84$	−2.11456	−0.230717
$85$	−5.78533	−0.627507
$86$	−5.26177	−0.567391
$87$	3.15461	0.338210
$88$	4.03083	0.429687
$89$	−14.9426	−1.58392	−0.791958	−	0.610576i	$-0.790938\pi$
$89$	−14.9426	−1.58392	−0.791958	+	0.610576i	$0.790938\pi$
$90$	1.19214	0.125662
$91$	−6.68361	−0.700632
$92$	−5.71583	−0.595916
$93$	−3.02088	−0.313251
$94$	−4.83158	−0.498339
$95$	−1.29569	−0.132935
$96$	−1.44219	−0.147193
$97$	14.1798	1.43975	0.719873	−	0.694106i	$-0.244200\pi$
$97$	14.1798	1.43975	0.719873	+	0.694106i	$0.244200\pi$
$98$	−4.85023	−0.489947
$99$	−3.70866	−0.372735
$100$	−3.32118	−0.332118
$101$	−3.84467	−0.382559	−0.191279	−	0.981536i	$-0.561264\pi$
$101$	−3.84467	−0.382559	−0.191279	+	0.981536i	$0.561264\pi$
$102$	−6.43946	−0.637602
$103$	−12.3069	−1.21263	−0.606316	−	0.795224i	$-0.707353\pi$
$103$	−12.3069	−1.21263	−0.606316	+	0.795224i	$0.707353\pi$
$104$	−4.55842	−0.446990
$105$	2.73982	0.267379
$106$	11.7170	1.13806
$107$	−7.27339	−0.703146	−0.351573	−	0.936161i	$-0.614353\pi$
$107$	−7.27339	−0.703146	−0.351573	+	0.936161i	$0.614353\pi$
$108$	5.65351	0.544009
$109$	6.98340	0.668889	0.334444	−	0.942416i	$-0.391451\pi$
$109$	6.98340	0.668889	0.334444	+	0.942416i	$0.391451\pi$
$110$	−5.22271	−0.497966
$111$	−1.34540	−0.127699
$112$	1.46621	0.138544
$113$	12.9632	1.21948	0.609738	−	0.792603i	$-0.291275\pi$
$113$	12.9632	1.21948	0.609738	+	0.792603i	$0.291275\pi$
$114$	−1.44219	−0.135074
$115$	7.40596	0.690609
$116$	−2.18737	−0.203092
$117$	4.19409	0.387744
$118$	6.23967	0.574408
$119$	6.54670	0.600135
$120$	1.86864	0.170583
$121$	5.24755	0.477050
$122$	7.92789	0.717757
$123$	7.38751	0.666109
$124$	2.09464	0.188104
$125$	10.7817	0.964344
$126$	−1.34902	−0.120181
$127$	−11.4260	−1.01390	−0.506948	−	0.861977i	$-0.669226\pi$
$127$	−11.4260	−1.01390	−0.506948	+	0.861977i	$0.669226\pi$
$128$	1.00000	0.0883883
$129$	7.58850	0.668130
$130$	5.90632	0.518018
$131$	−9.61613	−0.840165	−0.420082	−	0.907486i	$-0.637999\pi$
$131$	−9.61613	−0.840165	−0.420082	+	0.907486i	$0.637999\pi$
$132$	−5.81323	−0.505977
$133$	1.46621	0.127137
$134$	−5.85180	−0.505519
$135$	−7.32521	−0.630454
$136$	4.46505	0.382875
$137$	−2.34078	−0.199986	−0.0999931	−	0.994988i	$-0.531882\pi$
$137$	−2.34078	−0.199986	−0.0999931	+	0.994988i	$0.531882\pi$
$138$	8.24333	0.701719
$139$	8.56107	0.726141	0.363070	−	0.931762i	$-0.381728\pi$
$139$	8.56107	0.726141	0.363070	+	0.931762i	$0.381728\pi$
$140$	−1.89976	−0.160559
$141$	6.96808	0.586818
$142$	−9.87136	−0.828386
$143$	−18.3742	−1.53653
$144$	−0.920075	−0.0766729
$145$	2.83416	0.235364
$146$	−1.85006	−0.153112
$147$	6.99497	0.576935
$148$	0.932881	0.0766824
$149$	7.47949	0.612743	0.306372	−	0.951912i	$-0.400885\pi$
$149$	7.47949	0.612743	0.306372	+	0.951912i	$0.400885\pi$
$150$	4.78979	0.391084
$151$	−12.5443	−1.02084	−0.510420	−	0.859926i	$-0.670510\pi$
$151$	−12.5443	−1.02084	−0.510420	+	0.859926i	$0.670510\pi$
$152$	1.00000	0.0811107
$153$	−4.10818	−0.332127
$154$	5.91004	0.476244
$155$	−2.71401	−0.217995
$156$	6.57413	0.526352
$157$	1.84383	0.147154	0.0735769	−	0.997290i	$-0.476559\pi$
$157$	1.84383	0.147154	0.0735769	+	0.997290i	$0.476559\pi$
$158$	15.3599	1.22197
$159$	−16.8982	−1.34012
$160$	−1.29569	−0.102434
$161$	−8.38060	−0.660484
$162$	−5.39324	−0.423733
$163$	−1.90813	−0.149456	−0.0747281	−	0.997204i	$-0.523809\pi$
$163$	−1.90813	−0.149456	−0.0747281	+	0.997204i	$0.523809\pi$
$164$	−5.12241	−0.399993
$165$	7.53216	0.586378
$166$	−6.53807	−0.507452
$167$	−10.1117	−0.782470	−0.391235	−	0.920291i	$-0.627952\pi$
$167$	−10.1117	−0.782470	−0.391235	+	0.920291i	$0.627952\pi$
$168$	−2.11456	−0.163142
$169$	7.77922	0.598401
$170$	−5.78533	−0.443714
$171$	−0.920075	−0.0703599
$172$	−5.26177	−0.401206
$173$	3.14349	0.238995	0.119498	−	0.992834i	$-0.461872\pi$
$173$	3.14349	0.238995	0.119498	+	0.992834i	$0.461872\pi$
$174$	3.15461	0.239150
$175$	−4.86955	−0.368103
$176$	4.03083	0.303835
$177$	−8.99881	−0.676392
$178$	−14.9426	−1.12000
$179$	−7.22917	−0.540334	−0.270167	−	0.962814i	$-0.587079\pi$
$179$	−7.22917	−0.540334	−0.270167	+	0.962814i	$0.587079\pi$
$180$	1.19214	0.0888565
$181$	−18.0301	−1.34017	−0.670085	−	0.742285i	$-0.733742\pi$
$181$	−18.0301	−1.34017	−0.670085	+	0.742285i	$0.733742\pi$
$182$	−6.68361	−0.495422
$183$	−11.4336	−0.845193
$184$	−5.71583	−0.421376
$185$	−1.20873	−0.0888674
$186$	−3.02088	−0.221502
$187$	17.9978	1.31613
$188$	−4.83158	−0.352379
$189$	8.28923	0.602953
$190$	−1.29569	−0.0939994
$191$	−14.0248	−1.01480	−0.507398	−	0.861712i	$-0.669393\pi$
$191$	−14.0248	−1.01480	−0.507398	+	0.861712i	$0.669393\pi$
$192$	−1.44219	−0.104081
$193$	−24.0917	−1.73416	−0.867079	−	0.498171i	$-0.834005\pi$
$193$	−24.0917	−1.73416	−0.867079	+	0.498171i	$0.834005\pi$
$194$	14.1798	1.01805
$195$	−8.51806	−0.609991
$196$	−4.85023	−0.346445
$197$	−19.3440	−1.37820	−0.689101	−	0.724665i	$-0.741995\pi$
$197$	−19.3440	−1.37820	−0.689101	+	0.724665i	$0.741995\pi$
$198$	−3.70866	−0.263563
$199$	3.68411	0.261160	0.130580	−	0.991438i	$-0.458316\pi$
$199$	3.68411	0.261160	0.130580	+	0.991438i	$0.458316\pi$
$200$	−3.32118	−0.234843
$201$	8.43944	0.595272
$202$	−3.84467	−0.270510
$203$	−3.20714	−0.225097
$204$	−6.43946	−0.450853
$205$	6.63707	0.463553
$206$	−12.3069	−0.857460
$207$	5.25899	0.365525
$208$	−4.55842	−0.316070
$209$	4.03083	0.278818
$210$	2.73982	0.189066
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	11.7170	0.804728
$213$	14.2364	0.975464
$214$	−7.27339	−0.497199
$215$	6.81764	0.464959
$216$	5.65351	0.384673
$217$	3.07119	0.208486
$218$	6.98340	0.472976
$219$	2.66814	0.180296
$220$	−5.22271	−0.352115
$221$	−20.3536	−1.36913
$222$	−1.34540	−0.0902971
$223$	−8.59346	−0.575461	−0.287730	−	0.957711i	$-0.592901\pi$
$223$	−8.59346	−0.575461	−0.287730	+	0.957711i	$0.592901\pi$
$224$	1.46621	0.0979653
$225$	3.05574	0.203716
$226$	12.9632	0.862300
$227$	18.1353	1.20368	0.601840	−	0.798616i	$-0.294434\pi$
$227$	18.1353	1.20368	0.601840	+	0.798616i	$0.294434\pi$
$228$	−1.44219	−0.0955117
$229$	6.68049	0.441459	0.220729	−	0.975335i	$-0.429156\pi$
$229$	6.68049	0.441459	0.220729	+	0.975335i	$0.429156\pi$
$230$	7.40596	0.488334
$231$	−8.52342	−0.560800
$232$	−2.18737	−0.143608
$233$	24.7884	1.62394	0.811972	−	0.583696i	$-0.198394\pi$
$233$	24.7884	1.62394	0.811972	+	0.583696i	$0.198394\pi$
$234$	4.19409	0.274176
$235$	6.26024	0.408373
$236$	6.23967	0.406168
$237$	−22.1520	−1.43893
$238$	6.54670	0.424359
$239$	−1.48248	−0.0958934	−0.0479467	−	0.998850i	$-0.515268\pi$
$239$	−1.48248	−0.0958934	−0.0479467	+	0.998850i	$0.515268\pi$
$240$	1.86864	0.120620
$241$	3.49549	0.225164	0.112582	−	0.993642i	$-0.464088\pi$
$241$	3.49549	0.225164	0.112582	+	0.993642i	$0.464088\pi$
$242$	5.24755	0.337325
$243$	−9.18244	−0.589054
$244$	7.92789	0.507531
$245$	6.28441	0.401496
$246$	7.38751	0.471010
$247$	−4.55842	−0.290045
$248$	2.09464	0.133010
$249$	9.42916	0.597549
$250$	10.7817	0.681894
$251$	−30.2344	−1.90838	−0.954189	−	0.299203i	$-0.903279\pi$
$251$	−30.2344	−1.90838	−0.954189	+	0.299203i	$0.903279\pi$
$252$	−1.34902	−0.0849805
$253$	−23.0395	−1.44848
$254$	−11.4260	−0.716933
$255$	8.34357	0.522494
$256$	1.00000	0.0625000
$257$	−20.9504	−1.30685	−0.653425	−	0.756991i	$-0.726668\pi$
$257$	−20.9504	−1.30685	−0.653425	+	0.756991i	$0.726668\pi$
$258$	7.58850	0.472439
$259$	1.36780	0.0849910
$260$	5.90632	0.366294
$261$	2.01254	0.124573
$262$	−9.61613	−0.594086
$263$	25.0769	1.54631	0.773155	−	0.634217i	$-0.218677\pi$
$263$	25.0769	1.54631	0.773155	+	0.634217i	$0.218677\pi$
$264$	−5.81323	−0.357780
$265$	−15.1816	−0.932601
$266$	1.46621	0.0898991
$267$	21.5502	1.31885
$268$	−5.85180	−0.357456
$269$	−16.6717	−1.01649	−0.508245	−	0.861213i	$-0.669705\pi$
$269$	−16.6717	−1.01649	−0.508245	+	0.861213i	$0.669705\pi$
$270$	−7.32521	−0.445798
$271$	21.2874	1.29311	0.646557	−	0.762865i	$-0.276208\pi$
$271$	21.2874	1.29311	0.646557	+	0.762865i	$0.276208\pi$
$272$	4.46505	0.270733
$273$	9.63906	0.583382
$274$	−2.34078	−0.141412
$275$	−13.3871	−0.807272
$276$	8.24333	0.496190
$277$	−28.5155	−1.71333	−0.856665	−	0.515873i	$-0.827468\pi$
$277$	−28.5155	−1.71333	−0.856665	+	0.515873i	$0.827468\pi$
$278$	8.56107	0.513459
$279$	−1.92723	−0.115380
$280$	−1.89976	−0.113532
$281$	−4.77555	−0.284886	−0.142443	−	0.989803i	$-0.545496\pi$
$281$	−4.77555	−0.284886	−0.142443	+	0.989803i	$0.545496\pi$
$282$	6.96808	0.414943
$283$	−8.53132	−0.507134	−0.253567	−	0.967318i	$-0.581604\pi$
$283$	−8.53132	−0.507134	−0.253567	+	0.967318i	$0.581604\pi$
$284$	−9.87136	−0.585758
$285$	1.86864	0.110689
$286$	−18.3742	−1.08649
$287$	−7.51053	−0.443332
$288$	−0.920075	−0.0542160
$289$	2.93664	0.172743
$290$	2.83416	0.166427
$291$	−20.4501	−1.19881
$292$	−1.85006	−0.108266
$293$	−15.6409	−0.913754	−0.456877	−	0.889530i	$-0.651032\pi$
$293$	−15.6409	−0.913754	−0.456877	+	0.889530i	$0.651032\pi$
$294$	6.99497	0.407955
$295$	−8.08469	−0.470709
$296$	0.932881	0.0542226
$297$	22.7883	1.32231
$298$	7.47949	0.433275
$299$	26.0552	1.50681
$300$	4.78979	0.276538
$301$	−7.71486	−0.444677
$302$	−12.5443	−0.721842
$303$	5.54476	0.318538
$304$	1.00000	0.0573539
$305$	−10.2721	−0.588179
$306$	−4.10818	−0.234849
$307$	−6.75740	−0.385665	−0.192832	−	0.981232i	$-0.561767\pi$
$307$	−6.75740	−0.385665	−0.192832	+	0.981232i	$0.561767\pi$
$308$	5.91004	0.336756
$309$	17.7489	1.00970
$310$	−2.71401	−0.154146
$311$	5.51261	0.312591	0.156296	−	0.987710i	$-0.450045\pi$
$311$	5.51261	0.312591	0.156296	+	0.987710i	$0.450045\pi$
$312$	6.57413	0.372187
$313$	−7.64779	−0.432278	−0.216139	−	0.976363i	$-0.569347\pi$
$313$	−7.64779	−0.432278	−0.216139	+	0.976363i	$0.569347\pi$
$314$	1.84383	0.104053
$315$	1.74792	0.0984842
$316$	15.3599	0.864062
$317$	−14.7299	−0.827312	−0.413656	−	0.910433i	$-0.635748\pi$
$317$	−14.7299	−0.827312	−0.413656	+	0.910433i	$0.635748\pi$
$318$	−16.8982	−0.947605
$319$	−8.81690	−0.493652
$320$	−1.29569	−0.0724314
$321$	10.4896	0.585475
$322$	−8.38060	−0.467033
$323$	4.46505	0.248442
$324$	−5.39324	−0.299624
$325$	15.1393	0.839780
$326$	−1.90813	−0.105681
$327$	−10.0714	−0.556951
$328$	−5.12241	−0.282838
$329$	−7.08411	−0.390560
$330$	7.53216	0.414632
$331$	−9.21502	−0.506503	−0.253252	−	0.967400i	$-0.581500\pi$
$331$	−9.21502	−0.506503	−0.253252	+	0.967400i	$0.581500\pi$
$332$	−6.53807	−0.358823
$333$	−0.858321	−0.0470357
$334$	−10.1117	−0.553290
$335$	7.58214	0.414257
$336$	−2.11456	−0.115359
$337$	−25.1254	−1.36867	−0.684333	−	0.729170i	$-0.739906\pi$
$337$	−25.1254	−1.36867	−0.684333	+	0.729170i	$0.739906\pi$
$338$	7.77922	0.423134
$339$	−18.6955	−1.01540
$340$	−5.78533	−0.313753
$341$	8.44314	0.457222
$342$	−0.920075	−0.0497520
$343$	−17.3749	−0.938158
$344$	−5.26177	−0.283696
$345$	−10.6808	−0.575036
$346$	3.14349	0.168995
$347$	−36.3139	−1.94943	−0.974716	−	0.223448i	$-0.928269\pi$
$347$	−36.3139	−1.94943	−0.974716	+	0.223448i	$0.928269\pi$
$348$	3.15461	0.169105
$349$	−29.8919	−1.60008	−0.800039	−	0.599948i	$-0.795188\pi$
$349$	−29.8919	−1.60008	−0.800039	+	0.599948i	$0.795188\pi$
$350$	−4.86955	−0.260288
$351$	−25.7711	−1.37556
$352$	4.03083	0.214844
$353$	34.5369	1.83821	0.919107	−	0.394009i	$-0.128912\pi$
$353$	34.5369	1.83821	0.919107	+	0.394009i	$0.128912\pi$
$354$	−8.99881	−0.478281
$355$	12.7903	0.678836
$356$	−14.9426	−0.791958
$357$	−9.44161	−0.499703
$358$	−7.22917	−0.382074
$359$	−33.5032	−1.76823	−0.884115	−	0.467269i	$-0.845238\pi$
$359$	−33.5032	−1.76823	−0.884115	+	0.467269i	$0.845238\pi$
$360$	1.19214	0.0628310
$361$	1.00000	0.0526316
$362$	−18.0301	−0.947643
$363$	−7.56799	−0.397216
$364$	−6.68361	−0.350316
$365$	2.39711	0.125470
$366$	−11.4336	−0.597641
$367$	6.31709	0.329750	0.164875	−	0.986315i	$-0.447278\pi$
$367$	6.31709	0.329750	0.164875	+	0.986315i	$0.447278\pi$
$368$	−5.71583	−0.297958
$369$	4.71300	0.245349
$370$	−1.20873	−0.0628388
$371$	17.1796	0.891921
$372$	−3.02088	−0.156625
$373$	−3.26221	−0.168911	−0.0844553	−	0.996427i	$-0.526915\pi$
$373$	−3.26221	−0.168911	−0.0844553	+	0.996427i	$0.526915\pi$
$374$	17.9978	0.930645
$375$	−15.5493	−0.802962
$376$	−4.83158	−0.249170
$377$	9.97095	0.513530
$378$	8.28923	0.426352
$379$	24.5061	1.25879	0.629397	−	0.777084i	$-0.283302\pi$
$379$	24.5061	1.25879	0.629397	+	0.777084i	$0.283302\pi$
$380$	−1.29569	−0.0664676
$381$	16.4786	0.844222
$382$	−14.0248	−0.717569
$383$	−1.79746	−0.0918457	−0.0459229	−	0.998945i	$-0.514623\pi$
$383$	−1.79746	−0.0918457	−0.0459229	+	0.998945i	$0.514623\pi$
$384$	−1.44219	−0.0735967
$385$	−7.65759	−0.390267
$386$	−24.0917	−1.22623
$387$	4.84123	0.246093
$388$	14.1798	0.719873
$389$	12.5599	0.636812	0.318406	−	0.947954i	$-0.396852\pi$
$389$	12.5599	0.636812	0.318406	+	0.947954i	$0.396852\pi$
$390$	−8.51806	−0.431328
$391$	−25.5214	−1.29067
$392$	−4.85023	−0.244973
$393$	13.8683	0.699564
$394$	−19.3440	−0.974536
$395$	−19.9017	−1.00136
$396$	−3.70866	−0.186367
$397$	14.9495	0.750293	0.375146	−	0.926966i	$-0.377592\pi$
$397$	14.9495	0.750293	0.375146	+	0.926966i	$0.377592\pi$
$398$	3.68411	0.184668
$399$	−2.11456	−0.105860
$400$	−3.32118	−0.166059
$401$	15.2745	0.762775	0.381387	−	0.924415i	$-0.375446\pi$
$401$	15.2745	0.762775	0.381387	+	0.924415i	$0.375446\pi$
$402$	8.43944	0.420921
$403$	−9.54827	−0.475633
$404$	−3.84467	−0.191279
$405$	6.98798	0.347235
$406$	−3.20714	−0.159168
$407$	3.76028	0.186390
$408$	−6.43946	−0.318801
$409$	14.6745	0.725605	0.362803	−	0.931866i	$-0.381820\pi$
$409$	14.6745	0.725605	0.362803	+	0.931866i	$0.381820\pi$
$410$	6.63707	0.327781
$411$	3.37586	0.166519
$412$	−12.3069	−0.606316
$413$	9.14866	0.450176
$414$	5.25899	0.258465
$415$	8.47133	0.415841
$416$	−4.55842	−0.223495
$417$	−12.3467	−0.604622
$418$	4.03083	0.197154
$419$	17.0859	0.834701	0.417351	−	0.908746i	$-0.362959\pi$
$419$	17.0859	0.834701	0.417351	+	0.908746i	$0.362959\pi$
$420$	2.73982	0.133690
$421$	−6.92230	−0.337373	−0.168686	−	0.985670i	$-0.553952\pi$
$421$	−6.92230	−0.337373	−0.168686	+	0.985670i	$0.553952\pi$
$422$	−1.00000	−0.0486792
$423$	4.44542	0.216144
$424$	11.7170	0.569028
$425$	−14.8292	−0.719323
$426$	14.2364	0.689757
$427$	11.6239	0.562522
$428$	−7.27339	−0.351573
$429$	26.4992	1.27939
$430$	6.81764	0.328776
$431$	27.7113	1.33481	0.667404	−	0.744696i	$-0.267405\pi$
$431$	27.7113	1.33481	0.667404	+	0.744696i	$0.267405\pi$
$432$	5.65351	0.272005
$433$	−8.07997	−0.388298	−0.194149	−	0.980972i	$-0.562195\pi$
$433$	−8.07997	−0.388298	−0.194149	+	0.980972i	$0.562195\pi$
$434$	3.07119	0.147422
$435$	−4.08741	−0.195976
$436$	6.98340	0.334444
$437$	−5.71583	−0.273425
$438$	2.66814	0.127489
$439$	41.2004	1.96639	0.983194	−	0.182566i	$-0.0584404\pi$
$439$	41.2004	1.96639	0.983194	+	0.182566i	$0.0584404\pi$
$440$	−5.22271	−0.248983
$441$	4.46258	0.212504
$442$	−20.3536	−0.968120
$443$	−11.8945	−0.565125	−0.282562	−	0.959249i	$-0.591184\pi$
$443$	−11.8945	−0.565125	−0.282562	+	0.959249i	$0.591184\pi$
$444$	−1.34540	−0.0638497
$445$	19.3611	0.917802
$446$	−8.59346	−0.406912
$447$	−10.7869	−0.510202
$448$	1.46621	0.0692719
$449$	−17.5206	−0.826849	−0.413425	−	0.910538i	$-0.635667\pi$
$449$	−17.5206	−0.826849	−0.413425	+	0.910538i	$0.635667\pi$
$450$	3.05574	0.144049
$451$	−20.6475	−0.972254
$452$	12.9632	0.609738
$453$	18.0913	0.850003
$454$	18.1353	0.851131
$455$	8.65990	0.405982
$456$	−1.44219	−0.0675369
$457$	−19.6238	−0.917963	−0.458982	−	0.888446i	$-0.651786\pi$
$457$	−19.6238	−0.917963	−0.458982	+	0.888446i	$0.651786\pi$
$458$	6.68049	0.312159
$459$	25.2432	1.17825
$460$	7.40596	0.345304
$461$	−42.1904	−1.96500	−0.982502	−	0.186250i	$-0.940366\pi$
$461$	−42.1904	−1.96500	−0.982502	+	0.186250i	$0.940366\pi$
$462$	−8.52342	−0.396545
$463$	8.95400	0.416128	0.208064	−	0.978115i	$-0.433284\pi$
$463$	8.95400	0.416128	0.208064	+	0.978115i	$0.433284\pi$
$464$	−2.18737	−0.101546
$465$	3.91413	0.181514
$466$	24.7884	1.14830
$467$	−26.9179	−1.24561	−0.622806	−	0.782376i	$-0.714008\pi$
$467$	−26.9179	−1.24561	−0.622806	+	0.782376i	$0.714008\pi$
$468$	4.19409	0.193872
$469$	−8.57998	−0.396186
$470$	6.26024	0.288763
$471$	−2.65916	−0.122528
$472$	6.23967	0.287204
$473$	−21.2093	−0.975204
$474$	−22.1520	−1.01747
$475$	−3.32118	−0.152386
$476$	6.54670	0.300067
$477$	−10.7805	−0.493607
$478$	−1.48248	−0.0678068
$479$	29.4731	1.34666	0.673331	−	0.739341i	$-0.264863\pi$
$479$	29.4731	1.34666	0.673331	+	0.739341i	$0.264863\pi$
$480$	1.86864	0.0852914
$481$	−4.25247	−0.193896
$482$	3.49549	0.159215
$483$	12.0865	0.549953
$484$	5.24755	0.238525
$485$	−18.3727	−0.834262
$486$	−9.18244	−0.416524
$487$	20.4895	0.928469	0.464234	−	0.885712i	$-0.346330\pi$
$487$	20.4895	0.928469	0.464234	+	0.885712i	$0.346330\pi$
$488$	7.92789	0.358879
$489$	2.75189	0.124445
$490$	6.28441	0.283900
$491$	−21.2564	−0.959288	−0.479644	−	0.877463i	$-0.659234\pi$
$491$	−21.2564	−0.959288	−0.479644	+	0.877463i	$0.659234\pi$
$492$	7.38751	0.333055
$493$	−9.76670	−0.439870
$494$	−4.55842	−0.205093
$495$	4.80529	0.215982
$496$	2.09464	0.0940522
$497$	−14.4735	−0.649225
$498$	9.42916	0.422531
$499$	−39.8369	−1.78334	−0.891672	−	0.452682i	$-0.850467\pi$
$499$	−39.8369	−1.78334	−0.891672	+	0.452682i	$0.850467\pi$
$500$	10.7817	0.482172
$501$	14.5831	0.651525
$502$	−30.2344	−1.34943
$503$	32.5936	1.45328	0.726639	−	0.687020i	$-0.241081\pi$
$503$	32.5936	1.45328	0.726639	+	0.687020i	$0.241081\pi$
$504$	−1.34902	−0.0600903
$505$	4.98151	0.221674
$506$	−23.0395	−1.02423
$507$	−11.2191	−0.498260
$508$	−11.4260	−0.506948
$509$	−4.79494	−0.212532	−0.106266	−	0.994338i	$-0.533889\pi$
$509$	−4.79494	−0.212532	−0.106266	+	0.994338i	$0.533889\pi$
$510$	8.34357	0.369459
$511$	−2.71257	−0.119997
$512$	1.00000	0.0441942
$513$	5.65351	0.249609
$514$	−20.9504	−0.924082
$515$	15.9459	0.702661
$516$	7.58850	0.334065
$517$	−19.4753	−0.856521
$518$	1.36780	0.0600977
$519$	−4.53353	−0.199000
$520$	5.90632	0.259009
$521$	17.4637	0.765097	0.382549	−	0.923935i	$-0.375046\pi$
$521$	17.4637	0.765097	0.382549	+	0.923935i	$0.375046\pi$
$522$	2.01254	0.0880866
$523$	−2.20374	−0.0963629	−0.0481814	−	0.998839i	$-0.515343\pi$
$523$	−2.20374	−0.0963629	−0.0481814	+	0.998839i	$0.515343\pi$
$524$	−9.61613	−0.420082
$525$	7.02283	0.306502
$526$	25.0769	1.09341
$527$	9.35268	0.407409
$528$	−5.81323	−0.252989
$529$	9.67068	0.420464
$530$	−15.1816	−0.659449
$531$	−5.74096	−0.249137
$532$	1.46621	0.0635683
$533$	23.3501	1.01141
$534$	21.5502	0.932567
$535$	9.42408	0.407439
$536$	−5.85180	−0.252759
$537$	10.4259	0.449910
$538$	−16.6717	−0.718766
$539$	−19.5504	−0.842096
$540$	−7.32521	−0.315227
$541$	−21.6585	−0.931173	−0.465586	−	0.885003i	$-0.654156\pi$
$541$	−21.6585	−0.931173	−0.465586	+	0.885003i	$0.654156\pi$
$542$	21.2874	0.914370
$543$	26.0030	1.11589
$544$	4.46505	0.191437
$545$	−9.04834	−0.387588
$546$	9.63906	0.412514
$547$	−8.55169	−0.365644	−0.182822	−	0.983146i	$-0.558523\pi$
$547$	−8.55169	−0.365644	−0.182822	+	0.983146i	$0.558523\pi$
$548$	−2.34078	−0.0999931
$549$	−7.29425	−0.311311
$550$	−13.3871	−0.570828
$551$	−2.18737	−0.0931850
$552$	8.24333	0.350860
$553$	22.5209	0.957684
$554$	−28.5155	−1.21151
$555$	1.74322	0.0739956
$556$	8.56107	0.363070
$557$	−11.3959	−0.482858	−0.241429	−	0.970419i	$-0.577616\pi$
$557$	−11.3959	−0.482858	−0.241429	+	0.970419i	$0.577616\pi$
$558$	−1.92723	−0.0815861
$559$	23.9854	1.01447
$560$	−1.89976	−0.0802794
$561$	−25.9564	−1.09588
$562$	−4.77555	−0.201445
$563$	−37.7400	−1.59055	−0.795276	−	0.606247i	$-0.792674\pi$
$563$	−37.7400	−1.59055	−0.795276	+	0.606247i	$0.792674\pi$
$564$	6.96808	0.293409
$565$	−16.7963	−0.706627
$566$	−8.53132	−0.358598
$567$	−7.90762	−0.332089
$568$	−9.87136	−0.414193
$569$	−0.998313	−0.0418515	−0.0209257	−	0.999781i	$-0.506661\pi$
$569$	−0.998313	−0.0418515	−0.0209257	+	0.999781i	$0.506661\pi$
$570$	1.86864	0.0782688
$571$	34.2041	1.43140	0.715698	−	0.698410i	$-0.246109\pi$
$571$	34.2041	1.43140	0.715698	+	0.698410i	$0.246109\pi$
$572$	−18.3742	−0.768264
$573$	20.2264	0.844971
$574$	−7.51053	−0.313483
$575$	18.9833	0.791658
$576$	−0.920075	−0.0383365
$577$	−39.0794	−1.62690	−0.813449	−	0.581637i	$-0.802412\pi$
$577$	−39.0794	−1.62690	−0.813449	+	0.581637i	$0.802412\pi$
$578$	2.93664	0.122148
$579$	34.7449	1.44395
$580$	2.83416	0.117682
$581$	−9.58618	−0.397702
$582$	−20.4501	−0.847684
$583$	47.2292	1.95603
$584$	−1.85006	−0.0765560
$585$	−5.43426	−0.224679
$586$	−15.6409	−0.646122
$587$	29.4932	1.21731	0.608656	−	0.793434i	$-0.291709\pi$
$587$	29.4932	1.21731	0.608656	+	0.793434i	$0.291709\pi$
$588$	6.99497	0.288468
$589$	2.09464	0.0863082
$590$	−8.08469	−0.332841
$591$	27.8978	1.14756
$592$	0.932881	0.0383412
$593$	−10.4827	−0.430471	−0.215236	−	0.976562i	$-0.569052\pi$
$593$	−10.4827	−0.430471	−0.215236	+	0.976562i	$0.569052\pi$
$594$	22.7883	0.935016
$595$	−8.48251	−0.347749
$596$	7.47949	0.306372
$597$	−5.31320	−0.217455
$598$	26.0552	1.06547
$599$	−30.3920	−1.24178	−0.620892	−	0.783896i	$-0.713229\pi$
$599$	−30.3920	−1.24178	−0.620892	+	0.783896i	$0.713229\pi$
$600$	4.78979	0.195542
$601$	31.7564	1.29537	0.647686	−	0.761907i	$-0.275737\pi$
$601$	31.7564	1.29537	0.647686	+	0.761907i	$0.275737\pi$
$602$	−7.71486	−0.314434
$603$	5.38410	0.219258
$604$	−12.5443	−0.510420
$605$	−6.79921	−0.276427
$606$	5.54476	0.225240
$607$	14.0798	0.571483	0.285742	−	0.958307i	$-0.407760\pi$
$607$	14.0798	0.571483	0.285742	+	0.958307i	$0.407760\pi$
$608$	1.00000	0.0405554
$609$	4.62532	0.187427
$610$	−10.2721	−0.415905
$611$	22.0244	0.891011
$612$	−4.10818	−0.166063
$613$	13.4374	0.542733	0.271366	−	0.962476i	$-0.412524\pi$
$613$	13.4374	0.542733	0.271366	+	0.962476i	$0.412524\pi$
$614$	−6.75740	−0.272706
$615$	−9.57194	−0.385978
$616$	5.91004	0.238122
$617$	−40.8722	−1.64545	−0.822726	−	0.568438i	$-0.807548\pi$
$617$	−40.8722	−1.64545	−0.822726	+	0.568438i	$0.807548\pi$
$618$	17.7489	0.713965
$619$	8.68986	0.349275	0.174637	−	0.984633i	$-0.444125\pi$
$619$	8.68986	0.349275	0.174637	+	0.984633i	$0.444125\pi$
$620$	−2.71401	−0.108997
$621$	−32.3145	−1.29674
$622$	5.51261	0.221035
$623$	−21.9090	−0.877767
$624$	6.57413	0.263176
$625$	2.63614	0.105446
$626$	−7.64779	−0.305667
$627$	−5.81323	−0.232158
$628$	1.84383	0.0735769
$629$	4.16536	0.166084
$630$	1.74792	0.0696388
$631$	−37.9916	−1.51242	−0.756211	−	0.654328i	$-0.772952\pi$
$631$	−37.9916	−1.51242	−0.756211	+	0.654328i	$0.772952\pi$
$632$	15.3599	0.610984
$633$	1.44219	0.0573221
$634$	−14.7299	−0.584998
$635$	14.8046	0.587504
$636$	−16.8982	−0.670058
$637$	22.1094	0.876006
$638$	−8.81690	−0.349064
$639$	9.08240	0.359294
$640$	−1.29569	−0.0512168
$641$	−22.4366	−0.886193	−0.443096	−	0.896474i	$-0.646120\pi$
$641$	−22.4366	−0.886193	−0.443096	+	0.896474i	$0.646120\pi$
$642$	10.4896	0.413993
$643$	−47.1543	−1.85959	−0.929793	−	0.368083i	$-0.880014\pi$
$643$	−47.1543	−1.85959	−0.929793	+	0.368083i	$0.880014\pi$
$644$	−8.38060	−0.330242
$645$	−9.83236	−0.387149
$646$	4.46505	0.175675
$647$	−32.5549	−1.27987	−0.639933	−	0.768431i	$-0.721038\pi$
$647$	−32.5549	−1.27987	−0.639933	+	0.768431i	$0.721038\pi$
$648$	−5.39324	−0.211866
$649$	25.1510	0.987263
$650$	15.1393	0.593814
$651$	−4.42925	−0.173596
$652$	−1.90813	−0.0747281
$653$	38.4206	1.50351	0.751757	−	0.659440i	$-0.229207\pi$
$653$	38.4206	1.50351	0.751757	+	0.659440i	$0.229207\pi$
$654$	−10.0714	−0.393824
$655$	12.4595	0.486835
$656$	−5.12241	−0.199996
$657$	1.70219	0.0664089
$658$	−7.08411	−0.276167
$659$	14.8950	0.580225	0.290112	−	0.956993i	$-0.406307\pi$
$659$	14.8950	0.580225	0.290112	+	0.956993i	$0.406307\pi$
$660$	7.53216	0.293189
$661$	26.9981	1.05011	0.525053	−	0.851070i	$-0.324046\pi$
$661$	26.9981	1.05011	0.525053	+	0.851070i	$0.324046\pi$
$662$	−9.21502	−0.358152
$663$	29.3538	1.14001
$664$	−6.53807	−0.253726
$665$	−1.89976	−0.0736695
$666$	−0.858321	−0.0332593
$667$	12.5026	0.484103
$668$	−10.1117	−0.391235
$669$	12.3934	0.479158
$670$	7.58214	0.292924
$671$	31.9559	1.23364
$672$	−2.11456	−0.0815709
$673$	11.5558	0.445442	0.222721	−	0.974882i	$-0.428506\pi$
$673$	11.5558	0.445442	0.222721	+	0.974882i	$0.428506\pi$
$674$	−25.1254	−0.967793
$675$	−18.7763	−0.722701
$676$	7.77922	0.299201
$677$	−4.27317	−0.164231	−0.0821157	−	0.996623i	$-0.526168\pi$
$677$	−4.27317	−0.164231	−0.0821157	+	0.996623i	$0.526168\pi$
$678$	−18.6955	−0.717995
$679$	20.7906	0.797871
$680$	−5.78533	−0.221857
$681$	−26.1546	−1.00225
$682$	8.44314	0.323304
$683$	17.9501	0.686841	0.343421	−	0.939182i	$-0.388414\pi$
$683$	17.9501	0.686841	0.343421	+	0.939182i	$0.388414\pi$
$684$	−0.920075	−0.0351800
$685$	3.03293	0.115882
$686$	−17.3749	−0.663378
$687$	−9.63456	−0.367581
$688$	−5.26177	−0.200603
$689$	−53.4111	−2.03480
$690$	−10.6808	−0.406612
$691$	−4.46973	−0.170037	−0.0850183	−	0.996379i	$-0.527095\pi$
$691$	−4.46973	−0.170037	−0.0850183	+	0.996379i	$0.527095\pi$
$692$	3.14349	0.119498
$693$	−5.43768	−0.206560
$694$	−36.3139	−1.37846
$695$	−11.0925	−0.420763
$696$	3.15461	0.119575
$697$	−22.8718	−0.866331
$698$	−29.8919	−1.13143
$699$	−35.7497	−1.35218
$700$	−4.86955	−0.184052
$701$	−13.9807	−0.528043	−0.264022	−	0.964517i	$-0.585049\pi$
$701$	−13.9807	−0.528043	−0.264022	+	0.964517i	$0.585049\pi$
$702$	−25.7711	−0.972667
$703$	0.932881	0.0351843
$704$	4.03083	0.151917
$705$	−9.02849	−0.340033
$706$	34.5369	1.29981
$707$	−5.63709	−0.212005
$708$	−8.99881	−0.338196
$709$	30.6789	1.15217	0.576085	−	0.817390i	$-0.304580\pi$
$709$	30.6789	1.15217	0.576085	+	0.817390i	$0.304580\pi$
$710$	12.7903	0.480010
$711$	−14.1323	−0.530002
$712$	−14.9426	−0.559999
$713$	−11.9726	−0.448378
$714$	−9.44161	−0.353343
$715$	23.8073	0.890343
$716$	−7.22917	−0.270167
$717$	2.13802	0.0798457
$718$	−33.5032	−1.25033
$719$	20.2745	0.756112	0.378056	−	0.925783i	$-0.376593\pi$
$719$	20.2745	0.756112	0.378056	+	0.925783i	$0.376593\pi$
$720$	1.19214	0.0444283
$721$	−18.0445	−0.672011
$722$	1.00000	0.0372161
$723$	−5.04118	−0.187483
$724$	−18.0301	−0.670085
$725$	7.26464	0.269802
$726$	−7.56799	−0.280874
$727$	−13.6242	−0.505295	−0.252647	−	0.967558i	$-0.581301\pi$
$727$	−13.6242	−0.505295	−0.252647	+	0.967558i	$0.581301\pi$
$728$	−6.68361	−0.247711
$729$	29.4226	1.08972
$730$	2.39711	0.0887209
$731$	−23.4941	−0.868959
$732$	−11.4336	−0.422596
$733$	−41.9111	−1.54802	−0.774011	−	0.633173i	$-0.781752\pi$
$733$	−41.9111	−1.54802	−0.774011	+	0.633173i	$0.781752\pi$
$734$	6.31709	0.233168
$735$	−9.06333	−0.334306
$736$	−5.71583	−0.210688
$737$	−23.5876	−0.868860
$738$	4.71300	0.173488
$739$	8.66340	0.318688	0.159344	−	0.987223i	$-0.449062\pi$
$739$	8.66340	0.318688	0.159344	+	0.987223i	$0.449062\pi$
$740$	−1.20873	−0.0444337
$741$	6.57413	0.241507
$742$	17.1796	0.630683
$743$	34.8007	1.27671	0.638356	−	0.769741i	$-0.279615\pi$
$743$	34.8007	1.27671	0.638356	+	0.769741i	$0.279615\pi$
$744$	−3.02088	−0.110751
$745$	−9.69112	−0.355055
$746$	−3.26221	−0.119438
$747$	6.01551	0.220096
$748$	17.9978	0.658065
$749$	−10.6643	−0.389666
$750$	−15.5493	−0.567780
$751$	24.4616	0.892616	0.446308	−	0.894879i	$-0.352739\pi$
$751$	24.4616	0.892616	0.446308	+	0.894879i	$0.352739\pi$
$752$	−4.83158	−0.176190
$753$	43.6039	1.58901
$754$	9.97095	0.363121
$755$	16.2535	0.591527
$756$	8.28923	0.301477
$757$	−16.7086	−0.607284	−0.303642	−	0.952786i	$-0.598203\pi$
$757$	−16.7086	−0.607284	−0.303642	+	0.952786i	$0.598203\pi$
$758$	24.5061	0.890102
$759$	33.2274	1.20608
$760$	−1.29569	−0.0469997
$761$	39.3146	1.42515	0.712576	−	0.701595i	$-0.247528\pi$
$761$	39.3146	1.42515	0.712576	+	0.701595i	$0.247528\pi$
$762$	16.4786	0.596955
$763$	10.2391	0.370682
$764$	−14.0248	−0.507398
$765$	5.32294	0.192451
$766$	−1.79746	−0.0649448
$767$	−28.4430	−1.02702
$768$	−1.44219	−0.0520407
$769$	51.5686	1.85961	0.929806	−	0.368051i	$-0.119975\pi$
$769$	51.5686	1.85961	0.929806	+	0.368051i	$0.119975\pi$
$770$	−7.65759	−0.275960
$771$	30.2145	1.08815
$772$	−24.0917	−0.867079
$773$	11.0151	0.396187	0.198093	−	0.980183i	$-0.436525\pi$
$773$	11.0151	0.396187	0.198093	+	0.980183i	$0.436525\pi$
$774$	4.84123	0.174014
$775$	−6.95669	−0.249892
$776$	14.1798	0.509027
$777$	−1.97263	−0.0707678
$778$	12.5599	0.450294
$779$	−5.12241	−0.183529
$780$	−8.51806	−0.304995
$781$	−39.7897	−1.42379
$782$	−25.5214	−0.912644
$783$	−12.3663	−0.441936
$784$	−4.85023	−0.173222
$785$	−2.38904	−0.0852685
$786$	13.8683	0.494667
$787$	10.1016	0.360083	0.180041	−	0.983659i	$-0.442377\pi$
$787$	10.1016	0.360083	0.180041	+	0.983659i	$0.442377\pi$
$788$	−19.3440	−0.689101
$789$	−36.1658	−1.28754
$790$	−19.9017	−0.708071
$791$	19.0068	0.675804
$792$	−3.70866	−0.131782
$793$	−36.1387	−1.28332
$794$	14.9495	0.530537
$795$	21.8949	0.776532
$796$	3.68411	0.130580
$797$	43.1521	1.52853	0.764263	−	0.644904i	$-0.223103\pi$
$797$	43.1521	1.52853	0.764263	+	0.644904i	$0.223103\pi$
$798$	−2.11456	−0.0748546
$799$	−21.5732	−0.763206
$800$	−3.32118	−0.117421
$801$	13.7483	0.485774
$802$	15.2745	0.539363
$803$	−7.45726	−0.263161
$804$	8.43944	0.297636
$805$	10.8587	0.382718
$806$	−9.54827	−0.336323
$807$	24.0438	0.846381
$808$	−3.84467	−0.135255
$809$	−3.43427	−0.120742	−0.0603712	−	0.998176i	$-0.519228\pi$
$809$	−3.43427	−0.120742	−0.0603712	+	0.998176i	$0.519228\pi$
$810$	6.98798	0.245532
$811$	−24.6057	−0.864025	−0.432012	−	0.901868i	$-0.642196\pi$
$811$	−24.6057	−0.864025	−0.432012	+	0.901868i	$0.642196\pi$
$812$	−3.20714	−0.112549
$813$	−30.7005	−1.07671
$814$	3.76028	0.131798
$815$	2.47235	0.0866026
$816$	−6.43946	−0.225426
$817$	−5.26177	−0.184086
$818$	14.6745	0.513080
$819$	6.14942	0.214878
$820$	6.63707	0.231776
$821$	8.57105	0.299132	0.149566	−	0.988752i	$-0.452212\pi$
$821$	8.57105	0.299132	0.149566	+	0.988752i	$0.452212\pi$
$822$	3.37586	0.117747
$823$	40.9895	1.42880	0.714402	−	0.699735i	$-0.246699\pi$
$823$	40.9895	1.42880	0.714402	+	0.699735i	$0.246699\pi$
$824$	−12.3069	−0.428730
$825$	19.3068	0.672176
$826$	9.14866	0.318323
$827$	−35.2591	−1.22608	−0.613039	−	0.790053i	$-0.710053\pi$
$827$	−35.2591	−1.22608	−0.613039	+	0.790053i	$0.710053\pi$
$828$	5.25899	0.182763
$829$	2.49867	0.0867823	0.0433912	−	0.999058i	$-0.486184\pi$
$829$	2.49867	0.0867823	0.0433912	+	0.999058i	$0.486184\pi$
$830$	8.47133	0.294044
$831$	41.1249	1.42661
$832$	−4.55842	−0.158035
$833$	−21.6565	−0.750353
$834$	−12.3467	−0.427532
$835$	13.1017	0.453404
$836$	4.03083	0.139409
$837$	11.8421	0.409322
$838$	17.0859	0.590223
$839$	9.19702	0.317516	0.158758	−	0.987317i	$-0.449251\pi$
$839$	9.19702	0.317516	0.158758	+	0.987317i	$0.449251\pi$
$840$	2.73982	0.0945328
$841$	−24.2154	−0.835014
$842$	−6.92230	−0.238558
$843$	6.88728	0.237210
$844$	−1.00000	−0.0344214
$845$	−10.0795	−0.346745
$846$	4.44542	0.152837
$847$	7.69401	0.264369
$848$	11.7170	0.402364
$849$	12.3038	0.422266
$850$	−14.8292	−0.508638
$851$	−5.33219	−0.182785
$852$	14.2364	0.487732
$853$	−0.381396	−0.0130588	−0.00652938	−	0.999979i	$-0.502078\pi$
$853$	−0.381396	−0.0130588	−0.00652938	+	0.999979i	$0.502078\pi$
$854$	11.6239	0.397763
$855$	1.19214	0.0407702
$856$	−7.27339	−0.248600
$857$	14.9111	0.509354	0.254677	−	0.967026i	$-0.418031\pi$
$857$	14.9111	0.509354	0.254677	+	0.967026i	$0.418031\pi$
$858$	26.4992	0.904667
$859$	−51.9534	−1.77263	−0.886313	−	0.463087i	$-0.846742\pi$
$859$	−51.9534	−1.77263	−0.886313	+	0.463087i	$0.846742\pi$
$860$	6.81764	0.232480
$861$	10.8316	0.369141
$862$	27.7113	0.943852
$863$	2.88329	0.0981483	0.0490742	−	0.998795i	$-0.484373\pi$
$863$	2.88329	0.0981483	0.0490742	+	0.998795i	$0.484373\pi$
$864$	5.65351	0.192336
$865$	−4.07300	−0.138486
$866$	−8.07997	−0.274568
$867$	−4.23520	−0.143835
$868$	3.07119	0.104243
$869$	61.9131	2.10026
$870$	−4.08741	−0.138576
$871$	26.6750	0.903848
$872$	6.98340	0.236488
$873$	−13.0465	−0.441558
$874$	−5.71583	−0.193341
$875$	15.8082	0.534416
$876$	2.66814	0.0901482
$877$	−13.8427	−0.467435	−0.233717	−	0.972305i	$-0.575089\pi$
$877$	−13.8427	−0.467435	−0.233717	+	0.972305i	$0.575089\pi$
$878$	41.2004	1.39045
$879$	22.5573	0.760838
$880$	−5.22271	−0.176058
$881$	32.3180	1.08882	0.544410	−	0.838819i	$-0.316754\pi$
$881$	32.3180	1.08882	0.544410	+	0.838819i	$0.316754\pi$
$882$	4.46258	0.150263
$883$	28.2011	0.949042	0.474521	−	0.880244i	$-0.342621\pi$
$883$	28.2011	0.949042	0.474521	+	0.880244i	$0.342621\pi$
$884$	−20.3536	−0.684565
$885$	11.6597	0.391936
$886$	−11.8945	−0.399603
$887$	20.5494	0.689980	0.344990	−	0.938606i	$-0.387882\pi$
$887$	20.5494	0.689980	0.344990	+	0.938606i	$0.387882\pi$
$888$	−1.34540	−0.0451485
$889$	−16.7530	−0.561876
$890$	19.3611	0.648984
$891$	−21.7392	−0.728290
$892$	−8.59346	−0.287730
$893$	−4.83158	−0.161683
$894$	−10.7869	−0.360767
$895$	9.36679	0.313097
$896$	1.46621	0.0489826
$897$	−37.5766	−1.25465
$898$	−17.5206	−0.584671
$899$	−4.58175	−0.152810
$900$	3.05574	0.101858
$901$	52.3170	1.74293
$902$	−20.6475	−0.687488
$903$	11.1263	0.370261
$904$	12.9632	0.431150
$905$	23.3615	0.776563
$906$	18.0913	0.601043
$907$	38.3338	1.27285	0.636427	−	0.771337i	$-0.280412\pi$
$907$	38.3338	1.27285	0.636427	+	0.771337i	$0.280412\pi$
$908$	18.1353	0.601840
$909$	3.53738	0.117328
$910$	8.65990	0.287073
$911$	−31.3294	−1.03799	−0.518995	−	0.854777i	$-0.673694\pi$
$911$	−31.3294	−1.03799	−0.518995	+	0.854777i	$0.673694\pi$
$912$	−1.44219	−0.0477558
$913$	−26.3538	−0.872184
$914$	−19.6238	−0.649098
$915$	14.8144	0.489748
$916$	6.68049	0.220729
$917$	−14.0993	−0.465599
$918$	25.2432	0.833149
$919$	−1.28254	−0.0423072	−0.0211536	−	0.999776i	$-0.506734\pi$
$919$	−1.28254	−0.0423072	−0.0211536	+	0.999776i	$0.506734\pi$
$920$	7.40596	0.244167
$921$	9.74548	0.321124
$922$	−42.1904	−1.38947
$923$	44.9979	1.48112
$924$	−8.52342	−0.280400
$925$	−3.09827	−0.101870
$926$	8.95400	0.294247
$927$	11.3232	0.371904
$928$	−2.18737	−0.0718039
$929$	−18.3101	−0.600734	−0.300367	−	0.953824i	$-0.597109\pi$
$929$	−18.3101	−0.600734	−0.300367	+	0.953824i	$0.597109\pi$
$930$	3.91413	0.128350
$931$	−4.85023	−0.158960
$932$	24.7884	0.811972
$933$	−7.95025	−0.260280
$934$	−26.9179	−0.880781
$935$	−23.3196	−0.762634
$936$	4.19409	0.137088
$937$	−34.3194	−1.12117	−0.560584	−	0.828098i	$-0.689423\pi$
$937$	−34.3194	−1.12117	−0.560584	+	0.828098i	$0.689423\pi$
$938$	−8.57998	−0.280146
$939$	11.0296	0.359937
$940$	6.26024	0.204187
$941$	8.89780	0.290060	0.145030	−	0.989427i	$-0.453672\pi$
$941$	8.89780	0.290060	0.145030	+	0.989427i	$0.453672\pi$
$942$	−2.65916	−0.0866403
$943$	29.2788	0.953449
$944$	6.23967	0.203084
$945$	−10.7403	−0.349382
$946$	−21.2093	−0.689573
$947$	−49.3282	−1.60295	−0.801475	−	0.598029i	$-0.795951\pi$
$947$	−49.3282	−1.60295	−0.801475	+	0.598029i	$0.795951\pi$
$948$	−22.1520	−0.719463
$949$	8.43335	0.273758
$950$	−3.32118	−0.107753
$951$	21.2433	0.688862
$952$	6.54670	0.212180
$953$	37.3774	1.21077	0.605387	−	0.795932i	$-0.293019\pi$
$953$	37.3774	1.21077	0.605387	+	0.795932i	$0.293019\pi$
$954$	−10.7805	−0.349033
$955$	18.1718	0.588025
$956$	−1.48248	−0.0479467
$957$	12.7157	0.411040
$958$	29.4731	0.952234
$959$	−3.43207	−0.110827
$960$	1.86864	0.0603101
$961$	−26.6125	−0.858467
$962$	−4.25247	−0.137105
$963$	6.69207	0.215649
$964$	3.49549	0.112582
$965$	31.2154	1.00486
$966$	12.0865	0.388875
$967$	22.0195	0.708100	0.354050	−	0.935227i	$-0.384804\pi$
$967$	22.0195	0.708100	0.354050	+	0.935227i	$0.384804\pi$
$968$	5.24755	0.168663
$969$	−6.43946	−0.206865
$970$	−18.3727	−0.589913
$971$	35.7902	1.14856	0.574281	−	0.818658i	$-0.305282\pi$
$971$	35.7902	1.14856	0.574281	+	0.818658i	$0.305282\pi$
$972$	−9.18244	−0.294527
$973$	12.5523	0.402409
$974$	20.4895	0.656526
$975$	−21.8339	−0.699244
$976$	7.92789	0.253765
$977$	22.9157	0.733139	0.366570	−	0.930391i	$-0.380532\pi$
$977$	22.9157	0.733139	0.366570	+	0.930391i	$0.380532\pi$
$978$	2.75189	0.0879958
$979$	−60.2311	−1.92500
$980$	6.28441	0.200748
$981$	−6.42526	−0.205143
$982$	−21.2564	−0.678319
$983$	30.4755	0.972017	0.486008	−	0.873954i	$-0.338452\pi$
$983$	30.4755	0.972017	0.486008	+	0.873954i	$0.338452\pi$
$984$	7.38751	0.235505
$985$	25.0639	0.798602
$986$	−9.76670	−0.311035
$987$	10.2167	0.325200
$988$	−4.55842	−0.145023
$989$	30.0754	0.956341
$990$	4.80529	0.152722
$991$	−18.9649	−0.602441	−0.301221	−	0.953554i	$-0.597394\pi$
$991$	−18.9649	−0.602441	−0.301221	+	0.953554i	$0.597394\pi$
$992$	2.09464	0.0665050
$993$	13.2898	0.421740
$994$	−14.4735	−0.459071
$995$	−4.77347	−0.151329
$996$	9.42916	0.298775
$997$	−47.1509	−1.49328	−0.746642	−	0.665226i	$-0.768335\pi$
$997$	−47.1509	−1.49328	−0.746642	+	0.665226i	$0.768335\pi$
$998$	−39.8369	−1.26101
$999$	5.27406	0.166864

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.d.1.11	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.d.1.11	✓	30	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.44219 q^{3} +1.00000 q^{4} -1.29569 q^{5} -1.44219 q^{6} +1.46621 q^{7} +1.00000 q^{8} -0.920075 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.44219 q^{3} +1.00000 q^{4} -1.29569 q^{5} -1.44219 q^{6} +1.46621 q^{7} +1.00000 q^{8} -0.920075 q^{9} -1.29569 q^{10} +4.03083 q^{11} -1.44219 q^{12} -4.55842 q^{13} +1.46621 q^{14} +1.86864 q^{15} +1.00000 q^{16} +4.46505 q^{17} -0.920075 q^{18} +1.00000 q^{19} -1.29569 q^{20} -2.11456 q^{21} +4.03083 q^{22} -5.71583 q^{23} -1.44219 q^{24} -3.32118 q^{25} -4.55842 q^{26} +5.65351 q^{27} +1.46621 q^{28} -2.18737 q^{29} +1.86864 q^{30} +2.09464 q^{31} +1.00000 q^{32} -5.81323 q^{33} +4.46505 q^{34} -1.89976 q^{35} -0.920075 q^{36} +0.932881 q^{37} +1.00000 q^{38} +6.57413 q^{39} -1.29569 q^{40} -5.12241 q^{41} -2.11456 q^{42} -5.26177 q^{43} +4.03083 q^{44} +1.19214 q^{45} -5.71583 q^{46} -4.83158 q^{47} -1.44219 q^{48} -4.85023 q^{49} -3.32118 q^{50} -6.43946 q^{51} -4.55842 q^{52} +11.7170 q^{53} +5.65351 q^{54} -5.22271 q^{55} +1.46621 q^{56} -1.44219 q^{57} -2.18737 q^{58} +6.23967 q^{59} +1.86864 q^{60} +7.92789 q^{61} +2.09464 q^{62} -1.34902 q^{63} +1.00000 q^{64} +5.90632 q^{65} -5.81323 q^{66} -5.85180 q^{67} +4.46505 q^{68} +8.24333 q^{69} -1.89976 q^{70} -9.87136 q^{71} -0.920075 q^{72} -1.85006 q^{73} +0.932881 q^{74} +4.78979 q^{75} +1.00000 q^{76} +5.91004 q^{77} +6.57413 q^{78} +15.3599 q^{79} -1.29569 q^{80} -5.39324 q^{81} -5.12241 q^{82} -6.53807 q^{83} -2.11456 q^{84} -5.78533 q^{85} -5.26177 q^{86} +3.15461 q^{87} +4.03083 q^{88} -14.9426 q^{89} +1.19214 q^{90} -6.68361 q^{91} -5.71583 q^{92} -3.02088 q^{93} -4.83158 q^{94} -1.29569 q^{95} -1.44219 q^{96} +14.1798 q^{97} -4.85023 q^{98} -3.70866 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9}+O(q^{10}) \) 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9} - 12 q^{10} - 17 q^{11} - 10 q^{12} - 19 q^{13} - 15 q^{14} - 8 q^{15} + 30 q^{16} - 18 q^{17} + 10 q^{18} + 30 q^{19} - 12 q^{20} - 14 q^{21} - 17 q^{22} - 15 q^{23} - 10 q^{24} - 4 q^{25} - 19 q^{26} - 37 q^{27} - 15 q^{28} - 37 q^{29} - 8 q^{30} - 11 q^{31} + 30 q^{32} + 6 q^{33} - 18 q^{34} - 4 q^{35} + 10 q^{36} - 46 q^{37} + 30 q^{38} - 12 q^{40} - 28 q^{41} - 14 q^{42} - 61 q^{43} - 17 q^{44} - 14 q^{45} - 15 q^{46} - 4 q^{47} - 10 q^{48} - q^{49} - 4 q^{50} - 8 q^{51} - 19 q^{52} - 19 q^{53} - 37 q^{54} - 17 q^{55} - 15 q^{56} - 10 q^{57} - 37 q^{58} - 6 q^{59} - 8 q^{60} - 32 q^{61} - 11 q^{62} - 24 q^{63} + 30 q^{64} - 24 q^{65} + 6 q^{66} - 44 q^{67} - 18 q^{68} - 2 q^{69} - 4 q^{70} + 10 q^{71} + 10 q^{72} - 58 q^{73} - 46 q^{74} - 42 q^{75} + 30 q^{76} - 32 q^{77} - 42 q^{79} - 12 q^{80} - 38 q^{81} - 28 q^{82} - 25 q^{83} - 14 q^{84} - 48 q^{85} - 61 q^{86} - 15 q^{87} - 17 q^{88} - 39 q^{89} - 14 q^{90} - 21 q^{91} - 15 q^{92} - 45 q^{93} - 4 q^{94} - 12 q^{95} - 10 q^{96} - 33 q^{97} - q^{98} - 38 q^{99}+O(q^{100}) \) 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9 - 12 * q^10 - 17 * q^11 - 10 * q^12 - 19 * q^13 - 15 * q^14 - 8 * q^15 + 30 * q^16 - 18 * q^17 + 10 * q^18 + 30 * q^19 - 12 * q^20 - 14 * q^21 - 17 * q^22 - 15 * q^23 - 10 * q^24 - 4 * q^25 - 19 * q^26 - 37 * q^27 - 15 * q^28 - 37 * q^29 - 8 * q^30 - 11 * q^31 + 30 * q^32 + 6 * q^33 - 18 * q^34 - 4 * q^35 + 10 * q^36 - 46 * q^37 + 30 * q^38 - 12 * q^40 - 28 * q^41 - 14 * q^42 - 61 * q^43 - 17 * q^44 - 14 * q^45 - 15 * q^46 - 4 * q^47 - 10 * q^48 - q^49 - 4 * q^50 - 8 * q^51 - 19 * q^52 - 19 * q^53 - 37 * q^54 - 17 * q^55 - 15 * q^56 - 10 * q^57 - 37 * q^58 - 6 * q^59 - 8 * q^60 - 32 * q^61 - 11 * q^62 - 24 * q^63 + 30 * q^64 - 24 * q^65 + 6 * q^66 - 44 * q^67 - 18 * q^68 - 2 * q^69 - 4 * q^70 + 10 * q^71 + 10 * q^72 - 58 * q^73 - 46 * q^74 - 42 * q^75 + 30 * q^76 - 32 * q^77 - 42 * q^79 - 12 * q^80 - 38 * q^81 - 28 * q^82 - 25 * q^83 - 14 * q^84 - 48 * q^85 - 61 * q^86 - 15 * q^87 - 17 * q^88 - 39 * q^89 - 14 * q^90 - 21 * q^91 - 15 * q^92 - 45 * q^93 - 4 * q^94 - 12 * q^95 - 10 * q^96 - 33 * q^97 - q^98 - 38 * q^99

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