LMFDB - Embedded newform 8018.2.a.d.1.15

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			1.15
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)

$f(q)$	$=$	$q+1.00000 q^{2} -0.785531 q^{3} +1.00000 q^{4} -1.33472 q^{5} -0.785531 q^{6} +4.52537 q^{7} +1.00000 q^{8} -2.38294 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.785531 q^{3} +1.00000 q^{4} -1.33472 q^{5} -0.785531 q^{6} +4.52537 q^{7} +1.00000 q^{8} -2.38294 q^{9} -1.33472 q^{10} +1.48724 q^{11} -0.785531 q^{12} -4.61463 q^{13} +4.52537 q^{14} +1.04847 q^{15} +1.00000 q^{16} -0.964875 q^{17} -2.38294 q^{18} +1.00000 q^{19} -1.33472 q^{20} -3.55482 q^{21} +1.48724 q^{22} -0.651869 q^{23} -0.785531 q^{24} -3.21851 q^{25} -4.61463 q^{26} +4.22847 q^{27} +4.52537 q^{28} -2.58471 q^{29} +1.04847 q^{30} -0.662929 q^{31} +1.00000 q^{32} -1.16827 q^{33} -0.964875 q^{34} -6.04012 q^{35} -2.38294 q^{36} +0.132488 q^{37} +1.00000 q^{38} +3.62493 q^{39} -1.33472 q^{40} +6.87438 q^{41} -3.55482 q^{42} -4.27253 q^{43} +1.48724 q^{44} +3.18057 q^{45} -0.651869 q^{46} +0.671226 q^{47} -0.785531 q^{48} +13.4790 q^{49} -3.21851 q^{50} +0.757939 q^{51} -4.61463 q^{52} -10.9718 q^{53} +4.22847 q^{54} -1.98506 q^{55} +4.52537 q^{56} -0.785531 q^{57} -2.58471 q^{58} +4.28390 q^{59} +1.04847 q^{60} -13.9582 q^{61} -0.662929 q^{62} -10.7837 q^{63} +1.00000 q^{64} +6.15925 q^{65} -1.16827 q^{66} +8.43327 q^{67} -0.964875 q^{68} +0.512063 q^{69} -6.04012 q^{70} -9.36871 q^{71} -2.38294 q^{72} -2.16707 q^{73} +0.132488 q^{74} +2.52824 q^{75} +1.00000 q^{76} +6.73032 q^{77} +3.62493 q^{78} -10.6617 q^{79} -1.33472 q^{80} +3.82724 q^{81} +6.87438 q^{82} -18.0058 q^{83} -3.55482 q^{84} +1.28784 q^{85} -4.27253 q^{86} +2.03037 q^{87} +1.48724 q^{88} +6.72822 q^{89} +3.18057 q^{90} -20.8829 q^{91} -0.651869 q^{92} +0.520751 q^{93} +0.671226 q^{94} -1.33472 q^{95} -0.785531 q^{96} -14.1929 q^{97} +13.4790 q^{98} -3.54401 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.785531	−0.453526	−0.226763	−	0.973950i	$-0.572814\pi$
$3$	−0.785531	−0.453526	−0.226763	+	0.973950i	$0.572814\pi$
$4$	1.00000	0.500000
$5$	−1.33472	−0.596907	−0.298453	−	0.954424i	$-0.596471\pi$
$5$	−1.33472	−0.596907	−0.298453	+	0.954424i	$0.596471\pi$
$6$	−0.785531	−0.320692
$7$	4.52537	1.71043	0.855215	−	0.518274i	$-0.173425\pi$
$7$	4.52537	1.71043	0.855215	+	0.518274i	$0.173425\pi$
$8$	1.00000	0.353553
$9$	−2.38294	−0.794314
$10$	−1.33472	−0.422077
$11$	1.48724	0.448420	0.224210	−	0.974541i	$-0.428020\pi$
$11$	1.48724	0.448420	0.224210	+	0.974541i	$0.428020\pi$
$12$	−0.785531	−0.226763
$13$	−4.61463	−1.27987	−0.639934	−	0.768430i	$-0.721038\pi$
$13$	−4.61463	−1.27987	−0.639934	+	0.768430i	$0.721038\pi$
$14$	4.52537	1.20946
$15$	1.04847	0.270713
$16$	1.00000	0.250000
$17$	−0.964875	−0.234017	−0.117008	−	0.993131i	$-0.537330\pi$
$17$	−0.964875	−0.234017	−0.117008	+	0.993131i	$0.537330\pi$
$18$	−2.38294	−0.561665
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−1.33472	−0.298453
$21$	−3.55482	−0.775725
$22$	1.48724	0.317081
$23$	−0.651869	−0.135924	−0.0679620	−	0.997688i	$-0.521650\pi$
$23$	−0.651869	−0.135924	−0.0679620	+	0.997688i	$0.521650\pi$
$24$	−0.785531	−0.160346
$25$	−3.21851	−0.643702
$26$	−4.61463	−0.905003
$27$	4.22847	0.813769
$28$	4.52537	0.855215
$29$	−2.58471	−0.479969	−0.239984	−	0.970777i	$-0.577142\pi$
$29$	−2.58471	−0.479969	−0.239984	+	0.970777i	$0.577142\pi$
$30$	1.04847	0.191423
$31$	−0.662929	−0.119066	−0.0595328	−	0.998226i	$-0.518961\pi$
$31$	−0.662929	−0.119066	−0.0595328	+	0.998226i	$0.518961\pi$
$32$	1.00000	0.176777
$33$	−1.16827	−0.203370
$34$	−0.964875	−0.165475
$35$	−6.04012	−1.02097
$36$	−2.38294	−0.397157
$37$	0.132488	0.0217809	0.0108904	−	0.999941i	$-0.496533\pi$
$37$	0.132488	0.0217809	0.0108904	+	0.999941i	$0.496533\pi$
$38$	1.00000	0.162221
$39$	3.62493	0.580453
$40$	−1.33472	−0.211038
$41$	6.87438	1.07360	0.536799	−	0.843710i	$-0.319633\pi$
$41$	6.87438	1.07360	0.536799	+	0.843710i	$0.319633\pi$
$42$	−3.55482	−0.548520
$43$	−4.27253	−0.651554	−0.325777	−	0.945447i	$-0.605626\pi$
$43$	−4.27253	−0.651554	−0.325777	+	0.945447i	$0.605626\pi$
$44$	1.48724	0.224210
$45$	3.18057	0.474131
$46$	−0.651869	−0.0961128
$47$	0.671226	0.0979084	0.0489542	−	0.998801i	$-0.484411\pi$
$47$	0.671226	0.0979084	0.0489542	+	0.998801i	$0.484411\pi$
$48$	−0.785531	−0.113382
$49$	13.4790	1.92557
$50$	−3.21851	−0.455166
$51$	0.757939	0.106133
$52$	−4.61463	−0.639934
$53$	−10.9718	−1.50710	−0.753548	−	0.657393i	$-0.771659\pi$
$53$	−10.9718	−1.50710	−0.753548	+	0.657393i	$0.771659\pi$
$54$	4.22847	0.575421
$55$	−1.98506	−0.267665
$56$	4.52537	0.604728
$57$	−0.785531	−0.104046
$58$	−2.58471	−0.339389
$59$	4.28390	0.557717	0.278858	−	0.960332i	$-0.410044\pi$
$59$	4.28390	0.557717	0.278858	+	0.960332i	$0.410044\pi$
$60$	1.04847	0.135356
$61$	−13.9582	−1.78716	−0.893582	−	0.448899i	$-0.851816\pi$
$61$	−13.9582	−1.78716	−0.893582	+	0.448899i	$0.851816\pi$
$62$	−0.662929	−0.0841921
$63$	−10.7837	−1.35862
$64$	1.00000	0.125000
$65$	6.15925	0.763961
$66$	−1.16827	−0.143804
$67$	8.43327	1.03029	0.515144	−	0.857104i	$-0.327738\pi$
$67$	8.43327	1.03029	0.515144	+	0.857104i	$0.327738\pi$
$68$	−0.964875	−0.117008
$69$	0.512063	0.0616451
$70$	−6.04012	−0.721933
$71$	−9.36871	−1.11186	−0.555931	−	0.831229i	$-0.687638\pi$
$71$	−9.36871	−1.11186	−0.555931	+	0.831229i	$0.687638\pi$
$72$	−2.38294	−0.280832
$73$	−2.16707	−0.253636	−0.126818	−	0.991926i	$-0.540476\pi$
$73$	−2.16707	−0.253636	−0.126818	+	0.991926i	$0.540476\pi$
$74$	0.132488	0.0154014
$75$	2.52824	0.291936
$76$	1.00000	0.114708
$77$	6.73032	0.766991
$78$	3.62493	0.410443
$79$	−10.6617	−1.19953	−0.599767	−	0.800174i	$-0.704740\pi$
$79$	−10.6617	−1.19953	−0.599767	+	0.800174i	$0.704740\pi$
$80$	−1.33472	−0.149227
$81$	3.82724	0.425248
$82$	6.87438	0.759148
$83$	−18.0058	−1.97639	−0.988197	−	0.153189i	$-0.951046\pi$
$83$	−18.0058	−1.97639	−0.988197	+	0.153189i	$0.951046\pi$
$84$	−3.55482	−0.387862
$85$	1.28784	0.139686
$86$	−4.27253	−0.460718
$87$	2.03037	0.217678
$88$	1.48724	0.158540
$89$	6.72822	0.713190	0.356595	−	0.934259i	$-0.383938\pi$
$89$	6.72822	0.713190	0.356595	+	0.934259i	$0.383938\pi$
$90$	3.18057	0.335262
$91$	−20.8829	−2.18912
$92$	−0.651869	−0.0679620
$93$	0.520751	0.0539994
$94$	0.671226	0.0692317
$95$	−1.33472	−0.136940
$96$	−0.785531	−0.0801729
$97$	−14.1929	−1.44107	−0.720536	−	0.693418i	$-0.756104\pi$
$97$	−14.1929	−1.44107	−0.720536	+	0.693418i	$0.756104\pi$
$98$	13.4790	1.36158
$99$	−3.54401	−0.356186
$100$	−3.21851	−0.321851
$101$	−1.21151	−0.120550	−0.0602750	−	0.998182i	$-0.519198\pi$
$101$	−1.21151	−0.120550	−0.0602750	+	0.998182i	$0.519198\pi$
$102$	0.757939	0.0750471
$103$	10.4983	1.03443	0.517213	−	0.855857i	$-0.326970\pi$
$103$	10.4983	1.03443	0.517213	+	0.855857i	$0.326970\pi$
$104$	−4.61463	−0.452501
$105$	4.74470	0.463035
$106$	−10.9718	−1.06568
$107$	−12.8117	−1.23856	−0.619279	−	0.785171i	$-0.712575\pi$
$107$	−12.8117	−1.23856	−0.619279	+	0.785171i	$0.712575\pi$
$108$	4.22847	0.406884
$109$	17.3509	1.66192	0.830959	−	0.556334i	$-0.187793\pi$
$109$	17.3509	1.66192	0.830959	+	0.556334i	$0.187793\pi$
$110$	−1.98506	−0.189268
$111$	−0.104073	−0.00987821
$112$	4.52537	0.427607
$113$	−7.90331	−0.743481	−0.371740	−	0.928337i	$-0.621239\pi$
$113$	−7.90331	−0.743481	−0.371740	+	0.928337i	$0.621239\pi$
$114$	−0.785531	−0.0735717
$115$	0.870065	0.0811340
$116$	−2.58471	−0.239984
$117$	10.9964	1.01662
$118$	4.28390	0.394365
$119$	−4.36642	−0.400269
$120$	1.04847	0.0957115
$121$	−8.78812	−0.798920
$122$	−13.9582	−1.26372
$123$	−5.40004	−0.486905
$124$	−0.662929	−0.0595328
$125$	10.9694	0.981137
$126$	−10.7837	−0.960688
$127$	−17.4311	−1.54676	−0.773380	−	0.633943i	$-0.781435\pi$
$127$	−17.4311	−1.54676	−0.773380	+	0.633943i	$0.781435\pi$
$128$	1.00000	0.0883883
$129$	3.35620	0.295497
$130$	6.15925	0.540202
$131$	2.66865	0.233161	0.116581	−	0.993181i	$-0.462807\pi$
$131$	2.66865	0.233161	0.116581	+	0.993181i	$0.462807\pi$
$132$	−1.16827	−0.101685
$133$	4.52537	0.392399
$134$	8.43327	0.728524
$135$	−5.64384	−0.485744
$136$	−0.964875	−0.0827374
$137$	16.2835	1.39119	0.695595	−	0.718434i	$-0.255141\pi$
$137$	16.2835	1.39119	0.695595	+	0.718434i	$0.255141\pi$
$138$	0.512063	0.0435897
$139$	−13.8370	−1.17364	−0.586819	−	0.809718i	$-0.699620\pi$
$139$	−13.8370	−1.17364	−0.586819	+	0.809718i	$0.699620\pi$
$140$	−6.04012	−0.510484
$141$	−0.527269	−0.0444040
$142$	−9.36871	−0.786205
$143$	−6.86306	−0.573918
$144$	−2.38294	−0.198578
$145$	3.44988	0.286497
$146$	−2.16707	−0.179348
$147$	−10.5882	−0.873296
$148$	0.132488	0.0108904
$149$	12.5642	1.02930	0.514650	−	0.857400i	$-0.327922\pi$
$149$	12.5642	1.02930	0.514650	+	0.857400i	$0.327922\pi$
$150$	2.52824	0.206430
$151$	15.8354	1.28867	0.644335	−	0.764743i	$-0.277134\pi$
$151$	15.8354	1.28867	0.644335	+	0.764743i	$0.277134\pi$
$152$	1.00000	0.0811107
$153$	2.29924	0.185883
$154$	6.73032	0.542344
$155$	0.884828	0.0710711
$156$	3.62493	0.290227
$157$	7.09521	0.566259	0.283130	−	0.959082i	$-0.408627\pi$
$157$	7.09521	0.566259	0.283130	+	0.959082i	$0.408627\pi$
$158$	−10.6617	−0.848199
$159$	8.61870	0.683508
$160$	−1.33472	−0.105519
$161$	−2.94995	−0.232488
$162$	3.82724	0.300696
$163$	−5.15118	−0.403471	−0.201736	−	0.979440i	$-0.564658\pi$
$163$	−5.15118	−0.403471	−0.201736	+	0.979440i	$0.564658\pi$
$164$	6.87438	0.536799
$165$	1.55932	0.121393
$166$	−18.0058	−1.39752
$167$	−17.7890	−1.37655	−0.688276	−	0.725449i	$-0.741632\pi$
$167$	−17.7890	−1.37655	−0.688276	+	0.725449i	$0.741632\pi$
$168$	−3.55482	−0.274260
$169$	8.29478	0.638060
$170$	1.28784	0.0987730
$171$	−2.38294	−0.182228
$172$	−4.27253	−0.325777
$173$	25.2983	1.92339	0.961696	−	0.274117i	$-0.0883855\pi$
$173$	25.2983	1.92339	0.961696	+	0.274117i	$0.0883855\pi$
$174$	2.03037	0.153922
$175$	−14.5650	−1.10101
$176$	1.48724	0.112105
$177$	−3.36514	−0.252939
$178$	6.72822	0.504302
$179$	12.8974	0.963995	0.481997	−	0.876173i	$-0.339911\pi$
$179$	12.8974	0.963995	0.481997	+	0.876173i	$0.339911\pi$
$180$	3.18057	0.237066
$181$	−14.3121	−1.06381	−0.531905	−	0.846804i	$-0.678524\pi$
$181$	−14.3121	−1.06381	−0.531905	+	0.846804i	$0.678524\pi$
$182$	−20.8829	−1.54794
$183$	10.9646	0.810526
$184$	−0.651869	−0.0480564
$185$	−0.176835	−0.0130012
$186$	0.520751	0.0381833
$187$	−1.43500	−0.104938
$188$	0.671226	0.0489542
$189$	19.1354	1.39189
$190$	−1.33472	−0.0968311
$191$	−4.14979	−0.300269	−0.150134	−	0.988666i	$-0.547971\pi$
$191$	−4.14979	−0.300269	−0.150134	+	0.988666i	$0.547971\pi$
$192$	−0.785531	−0.0566908
$193$	5.00873	0.360536	0.180268	−	0.983618i	$-0.442303\pi$
$193$	5.00873	0.360536	0.180268	+	0.983618i	$0.442303\pi$
$194$	−14.1929	−1.01899
$195$	−4.83828	−0.346477
$196$	13.4790	0.962785
$197$	−7.38557	−0.526200	−0.263100	−	0.964769i	$-0.584745\pi$
$197$	−7.38557	−0.526200	−0.263100	+	0.964769i	$0.584745\pi$
$198$	−3.54401	−0.251862
$199$	7.34587	0.520735	0.260368	−	0.965510i	$-0.416156\pi$
$199$	7.34587	0.520735	0.260368	+	0.965510i	$0.416156\pi$
$200$	−3.21851	−0.227583
$201$	−6.62459	−0.467263
$202$	−1.21151	−0.0852418
$203$	−11.6968	−0.820952
$204$	0.757939	0.0530663
$205$	−9.17540	−0.640838
$206$	10.4983	0.731449
$207$	1.55337	0.107966
$208$	−4.61463	−0.319967
$209$	1.48724	0.102875
$210$	4.74470	0.327416
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	−10.9718	−0.753548
$213$	7.35941	0.504258
$214$	−12.8117	−0.875792
$215$	5.70265	0.388917
$216$	4.22847	0.287711
$217$	−3.00000	−0.203653
$218$	17.3509	1.17515
$219$	1.70230	0.115031
$220$	−1.98506	−0.133832
$221$	4.45254	0.299510
$222$	−0.104073	−0.00698495
$223$	29.6582	1.98606	0.993029	−	0.117867i	$-0.0376058\pi$
$223$	29.6582	1.98606	0.993029	+	0.117867i	$0.0376058\pi$
$224$	4.52537	0.302364
$225$	7.66952	0.511302
$226$	−7.90331	−0.525720
$227$	−26.9442	−1.78835	−0.894174	−	0.447719i	$-0.852236\pi$
$227$	−26.9442	−1.78835	−0.894174	+	0.447719i	$0.852236\pi$
$228$	−0.785531	−0.0520230
$229$	−25.0078	−1.65256	−0.826281	−	0.563259i	$-0.809547\pi$
$229$	−25.0078	−1.65256	−0.826281	+	0.563259i	$0.809547\pi$
$230$	0.870065	0.0573704
$231$	−5.28687	−0.347850
$232$	−2.58471	−0.169695
$233$	3.21801	0.210819	0.105410	−	0.994429i	$-0.466385\pi$
$233$	3.21801	0.210819	0.105410	+	0.994429i	$0.466385\pi$
$234$	10.9964	0.718856
$235$	−0.895902	−0.0584422
$236$	4.28390	0.278858
$237$	8.37509	0.544021
$238$	−4.36642	−0.283033
$239$	15.3880	0.995367	0.497684	−	0.867359i	$-0.334184\pi$
$239$	15.3880	0.995367	0.497684	+	0.867359i	$0.334184\pi$
$240$	1.04847	0.0676782
$241$	−19.9991	−1.28826	−0.644128	−	0.764918i	$-0.722780\pi$
$241$	−19.9991	−1.28826	−0.644128	+	0.764918i	$0.722780\pi$
$242$	−8.78812	−0.564921
$243$	−15.6918	−1.00663
$244$	−13.9582	−0.893582
$245$	−17.9907	−1.14939
$246$	−5.40004	−0.344294
$247$	−4.61463	−0.293622
$248$	−0.662929	−0.0420961
$249$	14.1441	0.896347
$250$	10.9694	0.693769
$251$	13.7911	0.870485	0.435243	−	0.900313i	$-0.356663\pi$
$251$	13.7911	0.870485	0.435243	+	0.900313i	$0.356663\pi$
$252$	−10.7837	−0.679309
$253$	−0.969486	−0.0609510
$254$	−17.4311	−1.09372
$255$	−1.01164	−0.0633513
$256$	1.00000	0.0625000
$257$	−7.85922	−0.490245	−0.245122	−	0.969492i	$-0.578828\pi$
$257$	−7.85922	−0.490245	−0.245122	+	0.969492i	$0.578828\pi$
$258$	3.35620	0.208948
$259$	0.599557	0.0372547
$260$	6.15925	0.381981
$261$	6.15921	0.381246
$262$	2.66865	0.164870
$263$	−18.4823	−1.13967	−0.569835	−	0.821759i	$-0.692993\pi$
$263$	−18.4823	−1.13967	−0.569835	+	0.821759i	$0.692993\pi$
$264$	−1.16827	−0.0719022
$265$	14.6444	0.899596
$266$	4.52537	0.277468
$267$	−5.28522	−0.323450
$268$	8.43327	0.515144
$269$	−3.97144	−0.242143	−0.121072	−	0.992644i	$-0.538633\pi$
$269$	−3.97144	−0.242143	−0.121072	+	0.992644i	$0.538633\pi$
$270$	−5.64384	−0.343473
$271$	−10.9405	−0.664587	−0.332293	−	0.943176i	$-0.607822\pi$
$271$	−10.9405	−0.664587	−0.332293	+	0.943176i	$0.607822\pi$
$272$	−0.964875	−0.0585042
$273$	16.4042	0.992825
$274$	16.2835	0.983720
$275$	−4.78670	−0.288649
$276$	0.512063	0.0308226
$277$	−4.64699	−0.279211	−0.139605	−	0.990207i	$-0.544583\pi$
$277$	−4.64699	−0.279211	−0.139605	+	0.990207i	$0.544583\pi$
$278$	−13.8370	−0.829887
$279$	1.57972	0.0945755
$280$	−6.04012	−0.360966
$281$	−6.71636	−0.400664	−0.200332	−	0.979728i	$-0.564202\pi$
$281$	−6.71636	−0.400664	−0.200332	+	0.979728i	$0.564202\pi$
$282$	−0.527269	−0.0313984
$283$	−23.8289	−1.41648	−0.708242	−	0.705970i	$-0.750511\pi$
$283$	−23.8289	−1.41648	−0.708242	+	0.705970i	$0.750511\pi$
$284$	−9.36871	−0.555931
$285$	1.04847	0.0621058
$286$	−6.86306	−0.405821
$287$	31.1091	1.83631
$288$	−2.38294	−0.140416
$289$	−16.0690	−0.945236
$290$	3.44988	0.202584
$291$	11.1490	0.653564
$292$	−2.16707	−0.126818
$293$	−14.9950	−0.876017	−0.438008	−	0.898971i	$-0.644316\pi$
$293$	−14.9950	−0.876017	−0.438008	+	0.898971i	$0.644316\pi$
$294$	−10.5882	−0.617514
$295$	−5.71783	−0.332905
$296$	0.132488	0.00770071
$297$	6.28875	0.364910
$298$	12.5642	0.727825
$299$	3.00813	0.173965
$300$	2.52824	0.145968
$301$	−19.3348	−1.11444
$302$	15.8354	0.911228
$303$	0.951681	0.0546726
$304$	1.00000	0.0573539
$305$	18.6304	1.06677
$306$	2.29924	0.131439
$307$	−4.36796	−0.249292	−0.124646	−	0.992201i	$-0.539780\pi$
$307$	−4.36796	−0.249292	−0.124646	+	0.992201i	$0.539780\pi$
$308$	6.73032	0.383495
$309$	−8.24671	−0.469139
$310$	0.884828	0.0502549
$311$	−29.5118	−1.67346	−0.836730	−	0.547616i	$-0.815536\pi$
$311$	−29.5118	−1.67346	−0.836730	+	0.547616i	$0.815536\pi$
$312$	3.62493	0.205221
$313$	13.5948	0.768422	0.384211	−	0.923245i	$-0.374474\pi$
$313$	13.5948	0.768422	0.384211	+	0.923245i	$0.374474\pi$
$314$	7.09521	0.400406
$315$	14.3933	0.810969
$316$	−10.6617	−0.599767
$317$	−11.3344	−0.636603	−0.318302	−	0.947989i	$-0.603112\pi$
$317$	−11.3344	−0.636603	−0.318302	+	0.947989i	$0.603112\pi$
$318$	8.61870	0.483313
$319$	−3.84409	−0.215227
$320$	−1.33472	−0.0746134
$321$	10.0640	0.561718
$322$	−2.94995	−0.164394
$323$	−0.964875	−0.0536871
$324$	3.82724	0.212624
$325$	14.8522	0.823853
$326$	−5.15118	−0.285297
$327$	−13.6297	−0.753723
$328$	6.87438	0.379574
$329$	3.03755	0.167465
$330$	1.55932	0.0858379
$331$	−31.5592	−1.73465	−0.867325	−	0.497742i	$-0.834162\pi$
$331$	−31.5592	−1.73465	−0.867325	+	0.497742i	$0.834162\pi$
$332$	−18.0058	−0.988197
$333$	−0.315711	−0.0173009
$334$	−17.7890	−0.973369
$335$	−11.2561	−0.614986
$336$	−3.55482	−0.193931
$337$	−19.4932	−1.06186	−0.530932	−	0.847415i	$-0.678158\pi$
$337$	−19.4932	−1.06186	−0.530932	+	0.847415i	$0.678158\pi$
$338$	8.29478	0.451176
$339$	6.20829	0.337188
$340$	1.28784	0.0698431
$341$	−0.985935	−0.0533914
$342$	−2.38294	−0.128855
$343$	29.3198	1.58312
$344$	−4.27253	−0.230359
$345$	−0.683463	−0.0367964
$346$	25.2983	1.36004
$347$	13.3386	0.716054	0.358027	−	0.933711i	$-0.383449\pi$
$347$	13.3386	0.716054	0.358027	+	0.933711i	$0.383449\pi$
$348$	2.03037	0.108839
$349$	23.8538	1.27686	0.638431	−	0.769679i	$-0.279584\pi$
$349$	23.8538	1.27686	0.638431	+	0.769679i	$0.279584\pi$
$350$	−14.5650	−0.778530
$351$	−19.5128	−1.04152
$352$	1.48724	0.0792702
$353$	−5.10964	−0.271959	−0.135979	−	0.990712i	$-0.543418\pi$
$353$	−5.10964	−0.271959	−0.135979	+	0.990712i	$0.543418\pi$
$354$	−3.36514	−0.178855
$355$	12.5046	0.663678
$356$	6.72822	0.356595
$357$	3.42996	0.181532
$358$	12.8974	0.681647
$359$	5.44774	0.287521	0.143760	−	0.989613i	$-0.454081\pi$
$359$	5.44774	0.287521	0.143760	+	0.989613i	$0.454081\pi$
$360$	3.18057	0.167631
$361$	1.00000	0.0526316
$362$	−14.3121	−0.752227
$363$	6.90333	0.362331
$364$	−20.8829	−1.09456
$365$	2.89244	0.151397
$366$	10.9646	0.573129
$367$	10.1954	0.532194	0.266097	−	0.963946i	$-0.414266\pi$
$367$	10.1954	0.532194	0.266097	+	0.963946i	$0.414266\pi$
$368$	−0.651869	−0.0339810
$369$	−16.3813	−0.852774
$370$	−0.176835	−0.00919321
$371$	−49.6516	−2.57778
$372$	0.520751	0.0269997
$373$	−16.0086	−0.828892	−0.414446	−	0.910074i	$-0.636025\pi$
$373$	−16.0086	−0.828892	−0.414446	+	0.910074i	$0.636025\pi$
$374$	−1.43500	−0.0742022
$375$	−8.61684	−0.444971
$376$	0.671226	0.0346158
$377$	11.9275	0.614296
$378$	19.1354	0.984218
$379$	−12.1725	−0.625261	−0.312630	−	0.949875i	$-0.601210\pi$
$379$	−12.1725	−0.625261	−0.312630	+	0.949875i	$0.601210\pi$
$380$	−1.33472	−0.0684699
$381$	13.6927	0.701496
$382$	−4.14979	−0.212322
$383$	−6.13654	−0.313563	−0.156781	−	0.987633i	$-0.550112\pi$
$383$	−6.13654	−0.313563	−0.156781	+	0.987633i	$0.550112\pi$
$384$	−0.785531	−0.0400864
$385$	−8.98312	−0.457822
$386$	5.00873	0.254937
$387$	10.1812	0.517539
$388$	−14.1929	−0.720536
$389$	−13.1518	−0.666821	−0.333410	−	0.942782i	$-0.608199\pi$
$389$	−13.1518	−0.666821	−0.333410	+	0.942782i	$0.608199\pi$
$390$	−4.83828	−0.244996
$391$	0.628972	0.0318085
$392$	13.4790	0.680792
$393$	−2.09631	−0.105745
$394$	−7.38557	−0.372080
$395$	14.2304	0.716011
$396$	−3.54401	−0.178093
$397$	−31.4511	−1.57848	−0.789242	−	0.614083i	$-0.789526\pi$
$397$	−31.4511	−1.57848	−0.789242	+	0.614083i	$0.789526\pi$
$398$	7.34587	0.368215
$399$	−3.55482	−0.177963
$400$	−3.21851	−0.160926
$401$	36.0847	1.80199	0.900993	−	0.433834i	$-0.142839\pi$
$401$	36.0847	1.80199	0.900993	+	0.433834i	$0.142839\pi$
$402$	−6.62459	−0.330405
$403$	3.05917	0.152388
$404$	−1.21151	−0.0602750
$405$	−5.10831	−0.253834
$406$	−11.6968	−0.580501
$407$	0.197041	0.00976698
$408$	0.757939	0.0375236
$409$	−17.9013	−0.885161	−0.442581	−	0.896729i	$-0.645937\pi$
$409$	−17.9013	−0.885161	−0.442581	+	0.896729i	$0.645937\pi$
$410$	−9.17540	−0.453141
$411$	−12.7912	−0.630941
$412$	10.4983	0.517213
$413$	19.3863	0.953935
$414$	1.55337	0.0763437
$415$	24.0328	1.17972
$416$	−4.61463	−0.226251
$417$	10.8694	0.532276
$418$	1.48724	0.0727433
$419$	7.72808	0.377542	0.188771	−	0.982021i	$-0.439550\pi$
$419$	7.72808	0.377542	0.188771	+	0.982021i	$0.439550\pi$
$420$	4.74470	0.231518
$421$	34.4132	1.67719	0.838597	−	0.544752i	$-0.183376\pi$
$421$	34.4132	1.67719	0.838597	+	0.544752i	$0.183376\pi$
$422$	−1.00000	−0.0486792
$423$	−1.59949	−0.0777700
$424$	−10.9718	−0.532839
$425$	3.10546	0.150637
$426$	7.35941	0.356565
$427$	−63.1661	−3.05682
$428$	−12.8117	−0.619279
$429$	5.39114	0.260287
$430$	5.70265	0.275006
$431$	38.5759	1.85814	0.929069	−	0.369907i	$-0.120611\pi$
$431$	38.5759	1.85814	0.929069	+	0.369907i	$0.120611\pi$
$432$	4.22847	0.203442
$433$	−19.6714	−0.945346	−0.472673	−	0.881238i	$-0.656711\pi$
$433$	−19.6714	−0.945346	−0.472673	+	0.881238i	$0.656711\pi$
$434$	−3.00000	−0.144005
$435$	−2.70998	−0.129934
$436$	17.3509	0.830959
$437$	−0.651869	−0.0311831
$438$	1.70230	0.0813389
$439$	7.86573	0.375411	0.187705	−	0.982225i	$-0.439895\pi$
$439$	7.86573	0.375411	0.187705	+	0.982225i	$0.439895\pi$
$440$	−1.98506	−0.0946338
$441$	−32.1196	−1.52951
$442$	4.45254	0.211786
$443$	−33.2036	−1.57755	−0.788775	−	0.614682i	$-0.789284\pi$
$443$	−33.2036	−1.57755	−0.788775	+	0.614682i	$0.789284\pi$
$444$	−0.104073	−0.00493910
$445$	−8.98032	−0.425708
$446$	29.6582	1.40436
$447$	−9.86957	−0.466815
$448$	4.52537	0.213804
$449$	−5.33328	−0.251693	−0.125847	−	0.992050i	$-0.540165\pi$
$449$	−5.33328	−0.251693	−0.125847	+	0.992050i	$0.540165\pi$
$450$	7.66952	0.361545
$451$	10.2239	0.481423
$452$	−7.90331	−0.371740
$453$	−12.4392	−0.584446
$454$	−26.9442	−1.26455
$455$	27.8729	1.30670
$456$	−0.785531	−0.0367858
$457$	15.5604	0.727884	0.363942	−	0.931422i	$-0.381431\pi$
$457$	15.5604	0.727884	0.363942	+	0.931422i	$0.381431\pi$
$458$	−25.0078	−1.16854
$459$	−4.07994	−0.190435
$460$	0.870065	0.0405670
$461$	0.313118	0.0145834	0.00729168	−	0.999973i	$-0.497679\pi$
$461$	0.313118	0.0145834	0.00729168	+	0.999973i	$0.497679\pi$
$462$	−5.28687	−0.245967
$463$	34.5413	1.60527	0.802635	−	0.596471i	$-0.203431\pi$
$463$	34.5413	1.60527	0.802635	+	0.596471i	$0.203431\pi$
$464$	−2.58471	−0.119992
$465$	−0.695059	−0.0322326
$466$	3.21801	0.149072
$467$	−10.4156	−0.481977	−0.240988	−	0.970528i	$-0.577472\pi$
$467$	−10.4156	−0.481977	−0.240988	+	0.970528i	$0.577472\pi$
$468$	10.9964	0.508308
$469$	38.1637	1.76224
$470$	−0.895902	−0.0413249
$471$	−5.57350	−0.256813
$472$	4.28390	0.197183
$473$	−6.35428	−0.292170
$474$	8.37509	0.384681
$475$	−3.21851	−0.147675
$476$	−4.36642	−0.200134
$477$	26.1452	1.19711
$478$	15.3880	0.703831
$479$	32.5625	1.48782	0.743909	−	0.668281i	$-0.232970\pi$
$479$	32.5625	1.48782	0.743909	+	0.668281i	$0.232970\pi$
$480$	1.04847	0.0478557
$481$	−0.611382	−0.0278766
$482$	−19.9991	−0.910935
$483$	2.31727	0.105440
$484$	−8.78812	−0.399460
$485$	18.9436	0.860186
$486$	−15.6918	−0.711795
$487$	−36.0060	−1.63159	−0.815794	−	0.578343i	$-0.803699\pi$
$487$	−36.0060	−1.63159	−0.815794	+	0.578343i	$0.803699\pi$
$488$	−13.9582	−0.631858
$489$	4.04641	0.182985
$490$	−17.9907	−0.812739
$491$	−38.4646	−1.73589	−0.867943	−	0.496665i	$-0.834558\pi$
$491$	−38.4646	−1.73589	−0.867943	+	0.496665i	$0.834558\pi$
$492$	−5.40004	−0.243452
$493$	2.49392	0.112321
$494$	−4.61463	−0.207622
$495$	4.73027	0.212610
$496$	−0.662929	−0.0297664
$497$	−42.3969	−1.90176
$498$	14.1441	0.633813
$499$	−1.73263	−0.0775634	−0.0387817	−	0.999248i	$-0.512348\pi$
$499$	−1.73263	−0.0775634	−0.0387817	+	0.999248i	$0.512348\pi$
$500$	10.9694	0.490569
$501$	13.9738	0.624302
$502$	13.7911	0.615526
$503$	−21.4042	−0.954365	−0.477182	−	0.878804i	$-0.658342\pi$
$503$	−21.4042	−0.954365	−0.477182	+	0.878804i	$0.658342\pi$
$504$	−10.7837	−0.480344
$505$	1.61704	0.0719572
$506$	−0.969486	−0.0430989
$507$	−6.51580	−0.289377
$508$	−17.4311	−0.773380
$509$	14.0876	0.624421	0.312211	−	0.950013i	$-0.398931\pi$
$509$	14.0876	0.624421	0.312211	+	0.950013i	$0.398931\pi$
$510$	−1.01164	−0.0447962
$511$	−9.80678	−0.433826
$512$	1.00000	0.0441942
$513$	4.22847	0.186691
$514$	−7.85922	−0.346655
$515$	−14.0123	−0.617456
$516$	3.35620	0.147749
$517$	0.998274	0.0439041
$518$	0.599557	0.0263430
$519$	−19.8726	−0.872309
$520$	6.15925	0.270101
$521$	15.2345	0.667436	0.333718	−	0.942673i	$-0.391697\pi$
$521$	15.2345	0.667436	0.333718	+	0.942673i	$0.391697\pi$
$522$	6.15921	0.269581
$523$	−17.7220	−0.774930	−0.387465	−	0.921884i	$-0.626649\pi$
$523$	−17.7220	−0.774930	−0.387465	+	0.921884i	$0.626649\pi$
$524$	2.66865	0.116581
$525$	11.4412	0.499336
$526$	−18.4823	−0.805868
$527$	0.639644	0.0278633
$528$	−1.16827	−0.0508426
$529$	−22.5751	−0.981525
$530$	14.6444	0.636110
$531$	−10.2083	−0.443002
$532$	4.52537	0.196200
$533$	−31.7227	−1.37406
$534$	−5.28522	−0.228714
$535$	17.1001	0.739303
$536$	8.43327	0.364262
$537$	−10.1313	−0.437197
$538$	−3.97144	−0.171221
$539$	20.0465	0.863464
$540$	−5.64384	−0.242872
$541$	5.34488	0.229794	0.114897	−	0.993377i	$-0.463346\pi$
$541$	5.34488	0.229794	0.114897	+	0.993377i	$0.463346\pi$
$542$	−10.9405	−0.469934
$543$	11.2426	0.482466
$544$	−0.964875	−0.0413687
$545$	−23.1587	−0.992010
$546$	16.4042	0.702033
$547$	28.9231	1.23666	0.618332	−	0.785917i	$-0.287809\pi$
$547$	28.9231	1.23666	0.618332	+	0.785917i	$0.287809\pi$
$548$	16.2835	0.695595
$549$	33.2616	1.41957
$550$	−4.78670	−0.204106
$551$	−2.58471	−0.110112
$552$	0.512063	0.0217948
$553$	−48.2482	−2.05172
$554$	−4.64699	−0.197432
$555$	0.138909	0.00589637
$556$	−13.8370	−0.586819
$557$	−29.9995	−1.27112	−0.635561	−	0.772051i	$-0.719231\pi$
$557$	−29.9995	−1.27112	−0.635561	+	0.772051i	$0.719231\pi$
$558$	1.57972	0.0668750
$559$	19.7161	0.833903
$560$	−6.04012	−0.255242
$561$	1.12724	0.0475920
$562$	−6.71636	−0.283312
$563$	18.8024	0.792425	0.396212	−	0.918159i	$-0.370324\pi$
$563$	18.8024	0.792425	0.396212	+	0.918159i	$0.370324\pi$
$564$	−0.527269	−0.0222020
$565$	10.5487	0.443789
$566$	−23.8289	−1.00160
$567$	17.3197	0.727358
$568$	−9.36871	−0.393102
$569$	19.5082	0.817826	0.408913	−	0.912573i	$-0.365908\pi$
$569$	19.5082	0.817826	0.408913	+	0.912573i	$0.365908\pi$
$570$	1.04847	0.0439154
$571$	−25.3545	−1.06105	−0.530526	−	0.847669i	$-0.678005\pi$
$571$	−25.3545	−1.06105	−0.530526	+	0.847669i	$0.678005\pi$
$572$	−6.86306	−0.286959
$573$	3.25979	0.136180
$574$	31.1091	1.29847
$575$	2.09805	0.0874946
$576$	−2.38294	−0.0992892
$577$	36.0228	1.49965	0.749825	−	0.661636i	$-0.230138\pi$
$577$	36.0228	1.49965	0.749825	+	0.661636i	$0.230138\pi$
$578$	−16.0690	−0.668383
$579$	−3.93451	−0.163513
$580$	3.44988	0.143248
$581$	−81.4830	−3.38048
$582$	11.1490	0.462139
$583$	−16.3177	−0.675812
$584$	−2.16707	−0.0896738
$585$	−14.6771	−0.606825
$586$	−14.9950	−0.619437
$587$	−10.4339	−0.430655	−0.215327	−	0.976542i	$-0.569082\pi$
$587$	−10.4339	−0.430655	−0.215327	+	0.976542i	$0.569082\pi$
$588$	−10.5882	−0.436648
$589$	−0.662929	−0.0273155
$590$	−5.71783	−0.235399
$591$	5.80159	0.238646
$592$	0.132488	0.00544522
$593$	40.1153	1.64734	0.823670	−	0.567070i	$-0.191923\pi$
$593$	40.1153	1.64734	0.823670	+	0.567070i	$0.191923\pi$
$594$	6.28875	0.258030
$595$	5.82797	0.238923
$596$	12.5642	0.514650
$597$	−5.77041	−0.236167
$598$	3.00813	0.123012
$599$	−17.1126	−0.699201	−0.349601	−	0.936899i	$-0.613683\pi$
$599$	−17.1126	−0.699201	−0.349601	+	0.936899i	$0.613683\pi$
$600$	2.52824	0.103215
$601$	28.6467	1.16852	0.584261	−	0.811566i	$-0.301384\pi$
$601$	28.6467	1.16852	0.584261	+	0.811566i	$0.301384\pi$
$602$	−19.3348	−0.788027
$603$	−20.0960	−0.818372
$604$	15.8354	0.644335
$605$	11.7297	0.476881
$606$	0.951681	0.0386594
$607$	31.1669	1.26503	0.632513	−	0.774550i	$-0.282023\pi$
$607$	31.1669	1.26503	0.632513	+	0.774550i	$0.282023\pi$
$608$	1.00000	0.0405554
$609$	9.18817	0.372324
$610$	18.6304	0.754321
$611$	−3.09746	−0.125310
$612$	2.29924	0.0929413
$613$	−33.5357	−1.35449	−0.677246	−	0.735757i	$-0.736827\pi$
$613$	−33.5357	−1.35449	−0.677246	+	0.735757i	$0.736827\pi$
$614$	−4.36796	−0.176276
$615$	7.20756	0.290637
$616$	6.73032	0.271172
$617$	28.6099	1.15179	0.575896	−	0.817523i	$-0.304653\pi$
$617$	28.6099	1.15179	0.575896	+	0.817523i	$0.304653\pi$
$618$	−8.24671	−0.331731
$619$	−20.2862	−0.815370	−0.407685	−	0.913123i	$-0.633664\pi$
$619$	−20.2862	−0.815370	−0.407685	+	0.913123i	$0.633664\pi$
$620$	0.884828	0.0355355
$621$	−2.75640	−0.110611
$622$	−29.5118	−1.18331
$623$	30.4477	1.21986
$624$	3.62493	0.145113
$625$	1.45137	0.0580546
$626$	13.5948	0.543356
$627$	−1.16827	−0.0466563
$628$	7.09521	0.283130
$629$	−0.127834	−0.00509709
$630$	14.3933	0.573441
$631$	22.1256	0.880804	0.440402	−	0.897801i	$-0.354836\pi$
$631$	22.1256	0.880804	0.440402	+	0.897801i	$0.354836\pi$
$632$	−10.6617	−0.424100
$633$	0.785531	0.0312220
$634$	−11.3344	−0.450146
$635$	23.2657	0.923271
$636$	8.61870	0.341754
$637$	−62.2005	−2.46447
$638$	−3.84409	−0.152189
$639$	22.3251	0.883167
$640$	−1.33472	−0.0527596
$641$	−9.92429	−0.391986	−0.195993	−	0.980605i	$-0.562793\pi$
$641$	−9.92429	−0.391986	−0.195993	+	0.980605i	$0.562793\pi$
$642$	10.0640	0.397195
$643$	35.3372	1.39356	0.696781	−	0.717284i	$-0.254615\pi$
$643$	35.3372	1.39356	0.696781	+	0.717284i	$0.254615\pi$
$644$	−2.94995	−0.116244
$645$	−4.47960	−0.176384
$646$	−0.964875	−0.0379625
$647$	50.2227	1.97446	0.987229	−	0.159306i	$-0.0509255\pi$
$647$	50.2227	1.97446	0.987229	+	0.159306i	$0.0509255\pi$
$648$	3.82724	0.150348
$649$	6.37119	0.250091
$650$	14.8522	0.582552
$651$	2.35659	0.0923622
$652$	−5.15118	−0.201736
$653$	−45.9899	−1.79972	−0.899862	−	0.436176i	$-0.856333\pi$
$653$	−45.9899	−1.79972	−0.899862	+	0.436176i	$0.856333\pi$
$654$	−13.6297	−0.532963
$655$	−3.56191	−0.139175
$656$	6.87438	0.268400
$657$	5.16399	0.201467
$658$	3.03755	0.118416
$659$	15.1580	0.590472	0.295236	−	0.955424i	$-0.404602\pi$
$659$	15.1580	0.590472	0.295236	+	0.955424i	$0.404602\pi$
$660$	1.55932	0.0606965
$661$	32.1229	1.24944	0.624718	−	0.780851i	$-0.285214\pi$
$661$	32.1229	1.24944	0.624718	+	0.780851i	$0.285214\pi$
$662$	−31.5592	−1.22658
$663$	−3.49761	−0.135836
$664$	−18.0058	−0.698761
$665$	−6.04012	−0.234226
$666$	−0.315711	−0.0122336
$667$	1.68489	0.0652393
$668$	−17.7890	−0.688276
$669$	−23.2974	−0.900730
$670$	−11.2561	−0.434861
$671$	−20.7592	−0.801400
$672$	−3.55482	−0.137130
$673$	−31.9772	−1.23263	−0.616315	−	0.787499i	$-0.711375\pi$
$673$	−31.9772	−1.23263	−0.616315	+	0.787499i	$0.711375\pi$
$674$	−19.4932	−0.750851
$675$	−13.6094	−0.523825
$676$	8.29478	0.319030
$677$	26.0429	1.00091	0.500454	−	0.865763i	$-0.333166\pi$
$677$	26.0429	1.00091	0.500454	+	0.865763i	$0.333166\pi$
$678$	6.20829	0.238428
$679$	−64.2282	−2.46485
$680$	1.28784	0.0493865
$681$	21.1655	0.811063
$682$	−0.985935	−0.0377534
$683$	35.2973	1.35061	0.675306	−	0.737538i	$-0.264012\pi$
$683$	35.2973	1.35061	0.675306	+	0.737538i	$0.264012\pi$
$684$	−2.38294	−0.0911141
$685$	−21.7339	−0.830411
$686$	29.3198	1.11944
$687$	19.6444	0.749480
$688$	−4.27253	−0.162889
$689$	50.6309	1.92888
$690$	−0.683463	−0.0260190
$691$	−10.4885	−0.399003	−0.199502	−	0.979897i	$-0.563932\pi$
$691$	−10.4885	−0.399003	−0.199502	+	0.979897i	$0.563932\pi$
$692$	25.2983	0.961696
$693$	−16.0380	−0.609231
$694$	13.3386	0.506327
$695$	18.4686	0.700553
$696$	2.03037	0.0769609
$697$	−6.63292	−0.251240
$698$	23.8538	0.902878
$699$	−2.52785	−0.0956120
$700$	−14.5650	−0.550504
$701$	1.94649	0.0735178	0.0367589	−	0.999324i	$-0.488297\pi$
$701$	1.94649	0.0735178	0.0367589	+	0.999324i	$0.488297\pi$
$702$	−19.5128	−0.736463
$703$	0.132488	0.00499688
$704$	1.48724	0.0560525
$705$	0.703758	0.0265051
$706$	−5.10964	−0.192304
$707$	−5.48255	−0.206192
$708$	−3.36514	−0.126470
$709$	−16.8116	−0.631371	−0.315686	−	0.948864i	$-0.602235\pi$
$709$	−16.8116	−0.631371	−0.315686	+	0.948864i	$0.602235\pi$
$710$	12.5046	0.469291
$711$	25.4062	0.952807
$712$	6.72822	0.252151
$713$	0.432143	0.0161839
$714$	3.42996	0.128363
$715$	9.16029	0.342576
$716$	12.8974	0.481997
$717$	−12.0877	−0.451425
$718$	5.44774	0.203308
$719$	0.0700285	0.00261162	0.00130581	−	0.999999i	$-0.499584\pi$
$719$	0.0700285	0.00261162	0.00130581	+	0.999999i	$0.499584\pi$
$720$	3.18057	0.118533
$721$	47.5086	1.76931
$722$	1.00000	0.0372161
$723$	15.7099	0.584258
$724$	−14.3121	−0.531905
$725$	8.31892	0.308957
$726$	6.90333	0.256207
$727$	−10.1670	−0.377072	−0.188536	−	0.982066i	$-0.560374\pi$
$727$	−10.1670	−0.377072	−0.188536	+	0.982066i	$0.560374\pi$
$728$	−20.8829	−0.773972
$729$	0.844685	0.0312846
$730$	2.89244	0.107054
$731$	4.12246	0.152475
$732$	10.9646	0.405263
$733$	28.6433	1.05797	0.528983	−	0.848632i	$-0.322573\pi$
$733$	28.6433	1.05797	0.528983	+	0.848632i	$0.322573\pi$
$734$	10.1954	0.376318
$735$	14.1323	0.521277
$736$	−0.651869	−0.0240282
$737$	12.5423	0.462002
$738$	−16.3813	−0.603002
$739$	−38.9553	−1.43299	−0.716497	−	0.697590i	$-0.754256\pi$
$739$	−38.9553	−1.43299	−0.716497	+	0.697590i	$0.754256\pi$
$740$	−0.176835	−0.00650058
$741$	3.62493	0.133165
$742$	−49.6516	−1.82277
$743$	−32.3995	−1.18862	−0.594312	−	0.804235i	$-0.702575\pi$
$743$	−32.3995	−1.18862	−0.594312	+	0.804235i	$0.702575\pi$
$744$	0.520751	0.0190917
$745$	−16.7698	−0.614396
$746$	−16.0086	−0.586115
$747$	42.9068	1.56988
$748$	−1.43500	−0.0524689
$749$	−57.9779	−2.11847
$750$	−8.61684	−0.314642
$751$	−43.1364	−1.57407	−0.787036	−	0.616907i	$-0.788385\pi$
$751$	−43.1364	−1.57407	−0.787036	+	0.616907i	$0.788385\pi$
$752$	0.671226	0.0244771
$753$	−10.8333	−0.394788
$754$	11.9275	0.434373
$755$	−21.1360	−0.769216
$756$	19.1354	0.695947
$757$	−27.1804	−0.987887	−0.493943	−	0.869494i	$-0.664445\pi$
$757$	−27.1804	−0.987887	−0.493943	+	0.869494i	$0.664445\pi$
$758$	−12.1725	−0.442126
$759$	0.761561	0.0276429
$760$	−1.33472	−0.0484155
$761$	−42.5952	−1.54408	−0.772038	−	0.635577i	$-0.780762\pi$
$761$	−42.5952	−1.54408	−0.772038	+	0.635577i	$0.780762\pi$
$762$	13.6927	0.496033
$763$	78.5194	2.84259
$764$	−4.14979	−0.150134
$765$	−3.06885	−0.110955
$766$	−6.13654	−0.221722
$767$	−19.7686	−0.713803
$768$	−0.785531	−0.0283454
$769$	−8.56664	−0.308921	−0.154461	−	0.987999i	$-0.549364\pi$
$769$	−8.56664	−0.308921	−0.154461	+	0.987999i	$0.549364\pi$
$770$	−8.98312	−0.323729
$771$	6.17366	0.222339
$772$	5.00873	0.180268
$773$	33.8724	1.21831	0.609153	−	0.793053i	$-0.291510\pi$
$773$	33.8724	1.21831	0.609153	+	0.793053i	$0.291510\pi$
$774$	10.1812	0.365955
$775$	2.13365	0.0766428
$776$	−14.1929	−0.509496
$777$	−0.470971	−0.0168960
$778$	−13.1518	−0.471514
$779$	6.87438	0.246300
$780$	−4.83828	−0.173238
$781$	−13.9335	−0.498581
$782$	0.628972	0.0224920
$783$	−10.9294	−0.390583
$784$	13.4790	0.481392
$785$	−9.47015	−0.338004
$786$	−2.09631	−0.0747728
$787$	−16.4589	−0.586698	−0.293349	−	0.956005i	$-0.594770\pi$
$787$	−16.4589	−0.586698	−0.293349	+	0.956005i	$0.594770\pi$
$788$	−7.38557	−0.263100
$789$	14.5184	0.516870
$790$	14.2304	0.506296
$791$	−35.7654	−1.27167
$792$	−3.54401	−0.125931
$793$	64.4119	2.28733
$794$	−31.4511	−1.11616
$795$	−11.5036	−0.407990
$796$	7.34587	0.260368
$797$	0.442603	0.0156778	0.00783890	−	0.999969i	$-0.497505\pi$
$797$	0.442603	0.0156778	0.00783890	+	0.999969i	$0.497505\pi$
$798$	−3.55482	−0.125839
$799$	−0.647649	−0.0229122
$800$	−3.21851	−0.113792
$801$	−16.0330	−0.566497
$802$	36.0847	1.27420
$803$	−3.22295	−0.113735
$804$	−6.62459	−0.233631
$805$	3.93737	0.138774
$806$	3.05917	0.107755
$807$	3.11969	0.109818
$808$	−1.21151	−0.0426209
$809$	−28.7421	−1.01052	−0.505259	−	0.862968i	$-0.668603\pi$
$809$	−28.7421	−1.01052	−0.505259	+	0.862968i	$0.668603\pi$
$810$	−5.10831	−0.179488
$811$	41.5537	1.45915	0.729574	−	0.683902i	$-0.239719\pi$
$811$	41.5537	1.45915	0.729574	+	0.683902i	$0.239719\pi$
$812$	−11.6968	−0.410476
$813$	8.59408	0.301407
$814$	0.197041	0.00690630
$815$	6.87540	0.240835
$816$	0.757939	0.0265332
$817$	−4.27253	−0.149477
$818$	−17.9013	−0.625904
$819$	49.7627	1.73885
$820$	−9.17540	−0.320419
$821$	33.3244	1.16303	0.581514	−	0.813536i	$-0.302461\pi$
$821$	33.3244	1.16303	0.581514	+	0.813536i	$0.302461\pi$
$822$	−12.7912	−0.446143
$823$	−6.41918	−0.223759	−0.111879	−	0.993722i	$-0.535687\pi$
$823$	−6.41918	−0.223759	−0.111879	+	0.993722i	$0.535687\pi$
$824$	10.4983	0.365725
$825$	3.76010	0.130910
$826$	19.3863	0.674534
$827$	−34.5689	−1.20208	−0.601039	−	0.799220i	$-0.705246\pi$
$827$	−34.5689	−1.20208	−0.601039	+	0.799220i	$0.705246\pi$
$828$	1.55337	0.0539832
$829$	−20.6219	−0.716229	−0.358114	−	0.933678i	$-0.616580\pi$
$829$	−20.6219	−0.716229	−0.358114	+	0.933678i	$0.616580\pi$
$830$	24.0328	0.834190
$831$	3.65035	0.126629
$832$	−4.61463	−0.159983
$833$	−13.0055	−0.450615
$834$	10.8694	0.376376
$835$	23.7434	0.821673
$836$	1.48724	0.0514373
$837$	−2.80317	−0.0968919
$838$	7.72808	0.266962
$839$	−14.4075	−0.497403	−0.248702	−	0.968580i	$-0.580004\pi$
$839$	−14.4075	−0.497403	−0.248702	+	0.968580i	$0.580004\pi$
$840$	4.74470	0.163708
$841$	−22.3193	−0.769630
$842$	34.4132	1.18596
$843$	5.27590	0.181712
$844$	−1.00000	−0.0344214
$845$	−11.0712	−0.380862
$846$	−1.59949	−0.0549917
$847$	−39.7695	−1.36650
$848$	−10.9718	−0.376774
$849$	18.7184	0.642412
$850$	3.10546	0.106516
$851$	−0.0863648	−0.00296055
$852$	7.35941	0.252129
$853$	−34.7785	−1.19079	−0.595396	−	0.803432i	$-0.703005\pi$
$853$	−34.7785	−1.19079	−0.595396	+	0.803432i	$0.703005\pi$
$854$	−63.1661	−2.16150
$855$	3.18057	0.108773
$856$	−12.8117	−0.437896
$857$	23.9704	0.818813	0.409406	−	0.912352i	$-0.365736\pi$
$857$	23.9704	0.818813	0.409406	+	0.912352i	$0.365736\pi$
$858$	5.39114	0.184051
$859$	−26.2240	−0.894752	−0.447376	−	0.894346i	$-0.647641\pi$
$859$	−26.2240	−0.894752	−0.447376	+	0.894346i	$0.647641\pi$
$860$	5.70265	0.194459
$861$	−24.4372	−0.832817
$862$	38.5759	1.31390
$863$	28.9721	0.986222	0.493111	−	0.869966i	$-0.335860\pi$
$863$	28.9721	0.986222	0.493111	+	0.869966i	$0.335860\pi$
$864$	4.22847	0.143855
$865$	−33.7662	−1.14809
$866$	−19.6714	−0.668461
$867$	12.6227	0.428689
$868$	−3.00000	−0.101827
$869$	−15.8565	−0.537895
$870$	−2.70998	−0.0918770
$871$	−38.9164	−1.31863
$872$	17.3509	0.587577
$873$	33.8209	1.14466
$874$	−0.651869	−0.0220498
$875$	49.6408	1.67817
$876$	1.70230	0.0575153
$877$	23.6996	0.800278	0.400139	−	0.916454i	$-0.368962\pi$
$877$	23.6996	0.800278	0.400139	+	0.916454i	$0.368962\pi$
$878$	7.86573	0.265456
$879$	11.7790	0.397297
$880$	−1.98506	−0.0669162
$881$	30.9644	1.04322	0.521609	−	0.853184i	$-0.325332\pi$
$881$	30.9644	1.04322	0.521609	+	0.853184i	$0.325332\pi$
$882$	−32.1196	−1.08152
$883$	42.5498	1.43191	0.715957	−	0.698144i	$-0.245991\pi$
$883$	42.5498	1.43191	0.715957	+	0.698144i	$0.245991\pi$
$884$	4.45254	0.149755
$885$	4.49153	0.150981
$886$	−33.2036	−1.11550
$887$	−2.39695	−0.0804816	−0.0402408	−	0.999190i	$-0.512813\pi$
$887$	−2.39695	−0.0804816	−0.0402408	+	0.999190i	$0.512813\pi$
$888$	−0.104073	−0.00349247
$889$	−78.8822	−2.64562
$890$	−8.98032	−0.301021
$891$	5.69202	0.190690
$892$	29.6582	0.993029
$893$	0.671226	0.0224617
$894$	−9.86957	−0.330088
$895$	−17.2144	−0.575415
$896$	4.52537	0.151182
$897$	−2.36298	−0.0788976
$898$	−5.33328	−0.177974
$899$	1.71348	0.0571478
$900$	7.66952	0.255651
$901$	10.5864	0.352685
$902$	10.2239	0.340417
$903$	15.1881	0.505427
$904$	−7.90331	−0.262860
$905$	19.1027	0.634995
$906$	−12.4392	−0.413266
$907$	15.5791	0.517296	0.258648	−	0.965972i	$-0.416723\pi$
$907$	15.5791	0.517296	0.258648	+	0.965972i	$0.416723\pi$
$908$	−26.9442	−0.894174
$909$	2.88697	0.0957546
$910$	27.8729	0.923978
$911$	−29.8880	−0.990234	−0.495117	−	0.868826i	$-0.664875\pi$
$911$	−29.8880	−0.990234	−0.495117	+	0.868826i	$0.664875\pi$
$912$	−0.785531	−0.0260115
$913$	−26.7790	−0.886254
$914$	15.5604	0.514692
$915$	−14.6347	−0.483809
$916$	−25.0078	−0.826281
$917$	12.0766	0.398806
$918$	−4.07994	−0.134658
$919$	50.6550	1.67096	0.835478	−	0.549524i	$-0.185191\pi$
$919$	50.6550	1.67096	0.835478	+	0.549524i	$0.185191\pi$
$920$	0.870065	0.0286852
$921$	3.43116	0.113061
$922$	0.313118	0.0103120
$923$	43.2331	1.42303
$924$	−5.28687	−0.173925
$925$	−0.426414	−0.0140204
$926$	34.5413	1.13510
$927$	−25.0168	−0.821659
$928$	−2.58471	−0.0848473
$929$	34.0584	1.11742	0.558710	−	0.829363i	$-0.311296\pi$
$929$	34.0584	1.11742	0.558710	+	0.829363i	$0.311296\pi$
$930$	−0.695059	−0.0227919
$931$	13.4790	0.441756
$932$	3.21801	0.105410
$933$	23.1824	0.758958
$934$	−10.4156	−0.340809
$935$	1.91533	0.0626380
$936$	10.9964	0.359428
$937$	28.3162	0.925051	0.462525	−	0.886606i	$-0.346943\pi$
$937$	28.3162	0.925051	0.462525	+	0.886606i	$0.346943\pi$
$938$	38.1637	1.24609
$939$	−10.6791	−0.348499
$940$	−0.895902	−0.0292211
$941$	1.54472	0.0503563	0.0251782	−	0.999683i	$-0.491985\pi$
$941$	1.54472	0.0503563	0.0251782	+	0.999683i	$0.491985\pi$
$942$	−5.57350	−0.181595
$943$	−4.48119	−0.145928
$944$	4.28390	0.139429
$945$	−25.5405	−0.830831
$946$	−6.35428	−0.206595
$947$	33.3676	1.08430	0.542151	−	0.840281i	$-0.317610\pi$
$947$	33.3676	1.08430	0.542151	+	0.840281i	$0.317610\pi$
$948$	8.37509	0.272010
$949$	10.0002	0.324620
$950$	−3.21851	−0.104422
$951$	8.90352	0.288716
$952$	−4.36642	−0.141516
$953$	48.3612	1.56657	0.783286	−	0.621661i	$-0.213542\pi$
$953$	48.3612	1.56657	0.783286	+	0.621661i	$0.213542\pi$
$954$	26.1452	0.846483
$955$	5.53883	0.179232
$956$	15.3880	0.497684
$957$	3.01965	0.0976113
$958$	32.5625	1.05205
$959$	73.6887	2.37953
$960$	1.04847	0.0338391
$961$	−30.5605	−0.985823
$962$	−0.611382	−0.0197118
$963$	30.5296	0.983803
$964$	−19.9991	−0.644128
$965$	−6.68527	−0.215206
$966$	2.31727	0.0745571
$967$	−50.1503	−1.61273	−0.806363	−	0.591421i	$-0.798567\pi$
$967$	−50.1503	−1.61273	−0.806363	+	0.591421i	$0.798567\pi$
$968$	−8.78812	−0.282461
$969$	0.757939	0.0243485
$970$	18.9436	0.608243
$971$	45.5027	1.46025	0.730125	−	0.683313i	$-0.239462\pi$
$971$	45.5027	1.46025	0.730125	+	0.683313i	$0.239462\pi$
$972$	−15.6918	−0.503315
$973$	−62.6175	−2.00743
$974$	−36.0060	−1.15371
$975$	−11.6669	−0.373639
$976$	−13.9582	−0.446791
$977$	−29.7040	−0.950314	−0.475157	−	0.879901i	$-0.657609\pi$
$977$	−29.7040	−0.950314	−0.475157	+	0.879901i	$0.657609\pi$
$978$	4.04641	0.129390
$979$	10.0065	0.319809
$980$	−17.9907	−0.574693
$981$	−41.3462	−1.32008
$982$	−38.4646	−1.22746
$983$	−15.0044	−0.478567	−0.239283	−	0.970950i	$-0.576913\pi$
$983$	−15.0044	−0.478567	−0.239283	+	0.970950i	$0.576913\pi$
$984$	−5.40004	−0.172147
$985$	9.85770	0.314093
$986$	2.49392	0.0794227
$987$	−2.38609	−0.0759500
$988$	−4.61463	−0.146811
$989$	2.78513	0.0885619
$990$	4.73027	0.150338
$991$	−8.18906	−0.260134	−0.130067	−	0.991505i	$-0.541519\pi$
$991$	−8.18906	−0.260134	−0.130067	+	0.991505i	$0.541519\pi$
$992$	−0.662929	−0.0210480
$993$	24.7907	0.786709
$994$	−42.3969	−1.34475
$995$	−9.80472	−0.310830
$996$	14.1441	0.448173
$997$	34.5425	1.09397	0.546986	−	0.837142i	$-0.315775\pi$
$997$	34.5425	1.09397	0.546986	+	0.837142i	$0.315775\pi$
$998$	−1.73263	−0.0548456
$999$	0.560221	0.0177246

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.d.1.15	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.d.1.15	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.785531 q^{3} +1.00000 q^{4} -1.33472 q^{5} -0.785531 q^{6} +4.52537 q^{7} +1.00000 q^{8} -2.38294 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.785531 q^{3} +1.00000 q^{4} -1.33472 q^{5} -0.785531 q^{6} +4.52537 q^{7} +1.00000 q^{8} -2.38294 q^{9} -1.33472 q^{10} +1.48724 q^{11} -0.785531 q^{12} -4.61463 q^{13} +4.52537 q^{14} +1.04847 q^{15} +1.00000 q^{16} -0.964875 q^{17} -2.38294 q^{18} +1.00000 q^{19} -1.33472 q^{20} -3.55482 q^{21} +1.48724 q^{22} -0.651869 q^{23} -0.785531 q^{24} -3.21851 q^{25} -4.61463 q^{26} +4.22847 q^{27} +4.52537 q^{28} -2.58471 q^{29} +1.04847 q^{30} -0.662929 q^{31} +1.00000 q^{32} -1.16827 q^{33} -0.964875 q^{34} -6.04012 q^{35} -2.38294 q^{36} +0.132488 q^{37} +1.00000 q^{38} +3.62493 q^{39} -1.33472 q^{40} +6.87438 q^{41} -3.55482 q^{42} -4.27253 q^{43} +1.48724 q^{44} +3.18057 q^{45} -0.651869 q^{46} +0.671226 q^{47} -0.785531 q^{48} +13.4790 q^{49} -3.21851 q^{50} +0.757939 q^{51} -4.61463 q^{52} -10.9718 q^{53} +4.22847 q^{54} -1.98506 q^{55} +4.52537 q^{56} -0.785531 q^{57} -2.58471 q^{58} +4.28390 q^{59} +1.04847 q^{60} -13.9582 q^{61} -0.662929 q^{62} -10.7837 q^{63} +1.00000 q^{64} +6.15925 q^{65} -1.16827 q^{66} +8.43327 q^{67} -0.964875 q^{68} +0.512063 q^{69} -6.04012 q^{70} -9.36871 q^{71} -2.38294 q^{72} -2.16707 q^{73} +0.132488 q^{74} +2.52824 q^{75} +1.00000 q^{76} +6.73032 q^{77} +3.62493 q^{78} -10.6617 q^{79} -1.33472 q^{80} +3.82724 q^{81} +6.87438 q^{82} -18.0058 q^{83} -3.55482 q^{84} +1.28784 q^{85} -4.27253 q^{86} +2.03037 q^{87} +1.48724 q^{88} +6.72822 q^{89} +3.18057 q^{90} -20.8829 q^{91} -0.651869 q^{92} +0.520751 q^{93} +0.671226 q^{94} -1.33472 q^{95} -0.785531 q^{96} -14.1929 q^{97} +13.4790 q^{98} -3.54401 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9}+O(q^{10}) \) 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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