LMFDB - Embedded newform 8018.2.a.d.1.14

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			1.14
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)

$f(q)$	$=$	$q+1.00000 q^{2} -0.851234 q^{3} +1.00000 q^{4} -2.73591 q^{5} -0.851234 q^{6} +0.590237 q^{7} +1.00000 q^{8} -2.27540 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.851234 q^{3} +1.00000 q^{4} -2.73591 q^{5} -0.851234 q^{6} +0.590237 q^{7} +1.00000 q^{8} -2.27540 q^{9} -2.73591 q^{10} -1.85097 q^{11} -0.851234 q^{12} +1.88529 q^{13} +0.590237 q^{14} +2.32890 q^{15} +1.00000 q^{16} -4.96288 q^{17} -2.27540 q^{18} +1.00000 q^{19} -2.73591 q^{20} -0.502429 q^{21} -1.85097 q^{22} +9.18427 q^{23} -0.851234 q^{24} +2.48522 q^{25} +1.88529 q^{26} +4.49060 q^{27} +0.590237 q^{28} +5.21129 q^{29} +2.32890 q^{30} +2.14709 q^{31} +1.00000 q^{32} +1.57561 q^{33} -4.96288 q^{34} -1.61484 q^{35} -2.27540 q^{36} +4.56743 q^{37} +1.00000 q^{38} -1.60482 q^{39} -2.73591 q^{40} +2.66253 q^{41} -0.502429 q^{42} -2.82781 q^{43} -1.85097 q^{44} +6.22530 q^{45} +9.18427 q^{46} -5.33483 q^{47} -0.851234 q^{48} -6.65162 q^{49} +2.48522 q^{50} +4.22457 q^{51} +1.88529 q^{52} -4.12591 q^{53} +4.49060 q^{54} +5.06408 q^{55} +0.590237 q^{56} -0.851234 q^{57} +5.21129 q^{58} -1.38390 q^{59} +2.32890 q^{60} +2.88432 q^{61} +2.14709 q^{62} -1.34302 q^{63} +1.00000 q^{64} -5.15798 q^{65} +1.57561 q^{66} -5.02573 q^{67} -4.96288 q^{68} -7.81796 q^{69} -1.61484 q^{70} +3.68758 q^{71} -2.27540 q^{72} -2.34064 q^{73} +4.56743 q^{74} -2.11550 q^{75} +1.00000 q^{76} -1.09251 q^{77} -1.60482 q^{78} -5.28066 q^{79} -2.73591 q^{80} +3.00365 q^{81} +2.66253 q^{82} +4.69968 q^{83} -0.502429 q^{84} +13.5780 q^{85} -2.82781 q^{86} -4.43603 q^{87} -1.85097 q^{88} +11.7557 q^{89} +6.22530 q^{90} +1.11276 q^{91} +9.18427 q^{92} -1.82768 q^{93} -5.33483 q^{94} -2.73591 q^{95} -0.851234 q^{96} +14.6135 q^{97} -6.65162 q^{98} +4.21169 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.851234	−0.491460	−0.245730	−	0.969338i	$-0.579028\pi$
$3$	−0.851234	−0.491460	−0.245730	+	0.969338i	$0.579028\pi$
$4$	1.00000	0.500000
$5$	−2.73591	−1.22354	−0.611769	−	0.791037i	$-0.709542\pi$
$5$	−2.73591	−1.22354	−0.611769	+	0.791037i	$0.709542\pi$
$6$	−0.851234	−0.347515
$7$	0.590237	0.223088	0.111544	−	0.993759i	$-0.464420\pi$
$7$	0.590237	0.223088	0.111544	+	0.993759i	$0.464420\pi$
$8$	1.00000	0.353553
$9$	−2.27540	−0.758467
$10$	−2.73591	−0.865171
$11$	−1.85097	−0.558087	−0.279044	−	0.960278i	$-0.590017\pi$
$11$	−1.85097	−0.558087	−0.279044	+	0.960278i	$0.590017\pi$
$12$	−0.851234	−0.245730
$13$	1.88529	0.522884	0.261442	−	0.965219i	$-0.415802\pi$
$13$	1.88529	0.522884	0.261442	+	0.965219i	$0.415802\pi$
$14$	0.590237	0.157747
$15$	2.32890	0.601320
$16$	1.00000	0.250000
$17$	−4.96288	−1.20367	−0.601837	−	0.798619i	$-0.705564\pi$
$17$	−4.96288	−1.20367	−0.601837	+	0.798619i	$0.705564\pi$
$18$	−2.27540	−0.536317
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−2.73591	−0.611769
$21$	−0.502429	−0.109639
$22$	−1.85097	−0.394627
$23$	9.18427	1.91505	0.957526	−	0.288346i	$-0.0931053\pi$
$23$	9.18427	1.91505	0.957526	+	0.288346i	$0.0931053\pi$
$24$	−0.851234	−0.173757
$25$	2.48522	0.497043
$26$	1.88529	0.369735
$27$	4.49060	0.864217
$28$	0.590237	0.111544
$29$	5.21129	0.967712	0.483856	−	0.875148i	$-0.339236\pi$
$29$	5.21129	0.967712	0.483856	+	0.875148i	$0.339236\pi$
$30$	2.32890	0.425197
$31$	2.14709	0.385629	0.192814	−	0.981235i	$-0.438238\pi$
$31$	2.14709	0.385629	0.192814	+	0.981235i	$0.438238\pi$
$32$	1.00000	0.176777
$33$	1.57561	0.274278
$34$	−4.96288	−0.851126
$35$	−1.61484	−0.272957
$36$	−2.27540	−0.379233
$37$	4.56743	0.750881	0.375440	−	0.926847i	$-0.377491\pi$
$37$	4.56743	0.750881	0.375440	+	0.926847i	$0.377491\pi$
$38$	1.00000	0.162221
$39$	−1.60482	−0.256977
$40$	−2.73591	−0.432586
$41$	2.66253	0.415817	0.207909	−	0.978148i	$-0.433334\pi$
$41$	2.66253	0.415817	0.207909	+	0.978148i	$0.433334\pi$
$42$	−0.502429	−0.0775266
$43$	−2.82781	−0.431238	−0.215619	−	0.976478i	$-0.569177\pi$
$43$	−2.82781	−0.431238	−0.215619	+	0.976478i	$0.569177\pi$
$44$	−1.85097	−0.279044
$45$	6.22530	0.928012
$46$	9.18427	1.35415
$47$	−5.33483	−0.778165	−0.389083	−	0.921203i	$-0.627208\pi$
$47$	−5.33483	−0.778165	−0.389083	+	0.921203i	$0.627208\pi$
$48$	−0.851234	−0.122865
$49$	−6.65162	−0.950232
$50$	2.48522	0.351463
$51$	4.22457	0.591558
$52$	1.88529	0.261442
$53$	−4.12591	−0.566737	−0.283368	−	0.959011i	$-0.591452\pi$
$53$	−4.12591	−0.566737	−0.283368	+	0.959011i	$0.591452\pi$
$54$	4.49060	0.611093
$55$	5.06408	0.682841
$56$	0.590237	0.0788737
$57$	−0.851234	−0.112749
$58$	5.21129	0.684276
$59$	−1.38390	−0.180168	−0.0900842	−	0.995934i	$-0.528714\pi$
$59$	−1.38390	−0.180168	−0.0900842	+	0.995934i	$0.528714\pi$
$60$	2.32890	0.300660
$61$	2.88432	0.369299	0.184650	−	0.982804i	$-0.440885\pi$
$61$	2.88432	0.369299	0.184650	+	0.982804i	$0.440885\pi$
$62$	2.14709	0.272681
$63$	−1.34302	−0.169205
$64$	1.00000	0.125000
$65$	−5.15798	−0.639768
$66$	1.57561	0.193944
$67$	−5.02573	−0.613991	−0.306995	−	0.951711i	$-0.599324\pi$
$67$	−5.02573	−0.613991	−0.306995	+	0.951711i	$0.599324\pi$
$68$	−4.96288	−0.601837
$69$	−7.81796	−0.941172
$70$	−1.61484	−0.193010
$71$	3.68758	0.437635	0.218817	−	0.975766i	$-0.429780\pi$
$71$	3.68758	0.437635	0.218817	+	0.975766i	$0.429780\pi$
$72$	−2.27540	−0.268159
$73$	−2.34064	−0.273951	−0.136975	−	0.990574i	$-0.543738\pi$
$73$	−2.34064	−0.273951	−0.136975	+	0.990574i	$0.543738\pi$
$74$	4.56743	0.530953
$75$	−2.11550	−0.244277
$76$	1.00000	0.114708
$77$	−1.09251	−0.124503
$78$	−1.60482	−0.181710
$79$	−5.28066	−0.594121	−0.297060	−	0.954859i	$-0.596006\pi$
$79$	−5.28066	−0.594121	−0.297060	+	0.954859i	$0.596006\pi$
$80$	−2.73591	−0.305884
$81$	3.00365	0.333739
$82$	2.66253	0.294027
$83$	4.69968	0.515857	0.257929	−	0.966164i	$-0.416960\pi$
$83$	4.69968	0.515857	0.257929	+	0.966164i	$0.416960\pi$
$84$	−0.502429	−0.0548195
$85$	13.5780	1.47274
$86$	−2.82781	−0.304931
$87$	−4.43603	−0.475592
$88$	−1.85097	−0.197314
$89$	11.7557	1.24610	0.623051	−	0.782181i	$-0.285893\pi$
$89$	11.7557	1.24610	0.623051	+	0.782181i	$0.285893\pi$
$90$	6.22530	0.656204
$91$	1.11276	0.116649
$92$	9.18427	0.957526
$93$	−1.82768	−0.189521
$94$	−5.33483	−0.550246
$95$	−2.73591	−0.280699
$96$	−0.851234	−0.0868787
$97$	14.6135	1.48377	0.741887	−	0.670525i	$-0.233931\pi$
$97$	14.6135	1.48377	0.741887	+	0.670525i	$0.233931\pi$
$98$	−6.65162	−0.671915
$99$	4.21169	0.423291
$100$	2.48522	0.248522
$101$	−12.8472	−1.27835	−0.639173	−	0.769063i	$-0.720723\pi$
$101$	−12.8472	−1.27835	−0.639173	+	0.769063i	$0.720723\pi$
$102$	4.22457	0.418295
$103$	−16.3116	−1.60723	−0.803613	−	0.595152i	$-0.797092\pi$
$103$	−16.3116	−1.60723	−0.803613	+	0.595152i	$0.797092\pi$
$104$	1.88529	0.184867
$105$	1.37460	0.134148
$106$	−4.12591	−0.400743
$107$	−14.6131	−1.41270	−0.706350	−	0.707862i	$-0.749660\pi$
$107$	−14.6131	−1.41270	−0.706350	+	0.707862i	$0.749660\pi$
$108$	4.49060	0.432108
$109$	−13.7129	−1.31345	−0.656727	−	0.754128i	$-0.728060\pi$
$109$	−13.7129	−1.31345	−0.656727	+	0.754128i	$0.728060\pi$
$110$	5.06408	0.482841
$111$	−3.88795	−0.369028
$112$	0.590237	0.0557721
$113$	9.58561	0.901738	0.450869	−	0.892590i	$-0.351114\pi$
$113$	9.58561	0.901738	0.450869	+	0.892590i	$0.351114\pi$
$114$	−0.851234	−0.0797254
$115$	−25.1274	−2.34314
$116$	5.21129	0.483856
$117$	−4.28978	−0.396590
$118$	−1.38390	−0.127398
$119$	−2.92927	−0.268526
$120$	2.32890	0.212599
$121$	−7.57392	−0.688538
$122$	2.88432	0.261134
$123$	−2.26643	−0.204358
$124$	2.14709	0.192814
$125$	6.88023	0.615387
$126$	−1.34302	−0.119646
$127$	−11.2005	−0.993886	−0.496943	−	0.867783i	$-0.665544\pi$
$127$	−11.2005	−0.993886	−0.496943	+	0.867783i	$0.665544\pi$
$128$	1.00000	0.0883883
$129$	2.40713	0.211936
$130$	−5.15798	−0.452384
$131$	22.0343	1.92515	0.962573	−	0.271023i	$-0.0873619\pi$
$131$	22.0343	1.92515	0.962573	+	0.271023i	$0.0873619\pi$
$132$	1.57561	0.137139
$133$	0.590237	0.0511800
$134$	−5.02573	−0.434157
$135$	−12.2859	−1.05740
$136$	−4.96288	−0.425563
$137$	−12.8366	−1.09670	−0.548351	−	0.836248i	$-0.684744\pi$
$137$	−12.8366	−1.09670	−0.548351	+	0.836248i	$0.684744\pi$
$138$	−7.81796	−0.665509
$139$	−13.2901	−1.12725	−0.563625	−	0.826031i	$-0.690594\pi$
$139$	−13.2901	−1.12725	−0.563625	+	0.826031i	$0.690594\pi$
$140$	−1.61484	−0.136478
$141$	4.54119	0.382437
$142$	3.68758	0.309454
$143$	−3.48960	−0.291815
$144$	−2.27540	−0.189617
$145$	−14.2576	−1.18403
$146$	−2.34064	−0.193713
$147$	5.66209	0.467001
$148$	4.56743	0.375440
$149$	−9.18506	−0.752469	−0.376235	−	0.926524i	$-0.622781\pi$
$149$	−9.18506	−0.752469	−0.376235	+	0.926524i	$0.622781\pi$
$150$	−2.11550	−0.172730
$151$	−18.1659	−1.47832	−0.739161	−	0.673529i	$-0.764778\pi$
$151$	−18.1659	−1.47832	−0.739161	+	0.673529i	$0.764778\pi$
$152$	1.00000	0.0811107
$153$	11.2925	0.912947
$154$	−1.09251	−0.0880368
$155$	−5.87425	−0.471831
$156$	−1.60482	−0.128488
$157$	−6.86544	−0.547921	−0.273961	−	0.961741i	$-0.588334\pi$
$157$	−6.86544	−0.547921	−0.273961	+	0.961741i	$0.588334\pi$
$158$	−5.28066	−0.420107
$159$	3.51211	0.278529
$160$	−2.73591	−0.216293
$161$	5.42089	0.427226
$162$	3.00365	0.235989
$163$	−7.85359	−0.615141	−0.307570	−	0.951525i	$-0.599516\pi$
$163$	−7.85359	−0.615141	−0.307570	+	0.951525i	$0.599516\pi$
$164$	2.66253	0.207909
$165$	−4.31072	−0.335589
$166$	4.69968	0.364766
$167$	−3.06987	−0.237554	−0.118777	−	0.992921i	$-0.537897\pi$
$167$	−3.06987	−0.237554	−0.118777	+	0.992921i	$0.537897\pi$
$168$	−0.502429	−0.0387633
$169$	−9.44570	−0.726592
$170$	13.5780	1.04138
$171$	−2.27540	−0.174004
$172$	−2.82781	−0.215619
$173$	8.70636	0.661932	0.330966	−	0.943643i	$-0.392625\pi$
$173$	8.70636	0.661932	0.330966	+	0.943643i	$0.392625\pi$
$174$	−4.43603	−0.336294
$175$	1.46686	0.110885
$176$	−1.85097	−0.139522
$177$	1.17802	0.0885456
$178$	11.7557	0.881128
$179$	−18.7136	−1.39872	−0.699360	−	0.714769i	$-0.746532\pi$
$179$	−18.7136	−1.39872	−0.699360	+	0.714769i	$0.746532\pi$
$180$	6.22530	0.464006
$181$	−12.8415	−0.954498	−0.477249	−	0.878768i	$-0.658366\pi$
$181$	−12.8415	−0.954498	−0.477249	+	0.878768i	$0.658366\pi$
$182$	1.11276	0.0824836
$183$	−2.45523	−0.181496
$184$	9.18427	0.677073
$185$	−12.4961	−0.918731
$186$	−1.82768	−0.134012
$187$	9.18612	0.671755
$188$	−5.33483	−0.389083
$189$	2.65052	0.192797
$190$	−2.73591	−0.198484
$191$	18.4358	1.33396	0.666982	−	0.745074i	$-0.267586\pi$
$191$	18.4358	1.33396	0.666982	+	0.745074i	$0.267586\pi$
$192$	−0.851234	−0.0614325
$193$	1.16570	0.0839086	0.0419543	−	0.999120i	$-0.486642\pi$
$193$	1.16570	0.0839086	0.0419543	+	0.999120i	$0.486642\pi$
$194$	14.6135	1.04919
$195$	4.39064	0.314421
$196$	−6.65162	−0.475116
$197$	−0.461268	−0.0328640	−0.0164320	−	0.999865i	$-0.505231\pi$
$197$	−0.461268	−0.0328640	−0.0164320	+	0.999865i	$0.505231\pi$
$198$	4.21169	0.299312
$199$	−24.2470	−1.71883	−0.859413	−	0.511282i	$-0.829171\pi$
$199$	−24.2470	−1.71883	−0.859413	+	0.511282i	$0.829171\pi$
$200$	2.48522	0.175731
$201$	4.27807	0.301752
$202$	−12.8472	−0.903927
$203$	3.07589	0.215885
$204$	4.22457	0.295779
$205$	−7.28444	−0.508768
$206$	−16.3116	−1.13648
$207$	−20.8979	−1.45250
$208$	1.88529	0.130721
$209$	−1.85097	−0.128034
$210$	1.37460	0.0948566
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	−4.12591	−0.283368
$213$	−3.13899	−0.215080
$214$	−14.6131	−0.998930
$215$	7.73665	0.527635
$216$	4.49060	0.305547
$217$	1.26729	0.0860293
$218$	−13.7129	−0.928752
$219$	1.99243	0.134636
$220$	5.06408	0.341420
$221$	−9.35644	−0.629382
$222$	−3.88795	−0.260942
$223$	23.5388	1.57628	0.788138	−	0.615499i	$-0.211045\pi$
$223$	23.5388	1.57628	0.788138	+	0.615499i	$0.211045\pi$
$224$	0.590237	0.0394368
$225$	−5.65486	−0.376991
$226$	9.58561	0.637625
$227$	−22.4844	−1.49234	−0.746172	−	0.665754i	$-0.768110\pi$
$227$	−22.4844	−1.49234	−0.746172	+	0.665754i	$0.768110\pi$
$228$	−0.851234	−0.0563744
$229$	14.6615	0.968857	0.484428	−	0.874831i	$-0.339028\pi$
$229$	14.6615	0.968857	0.484428	+	0.874831i	$0.339028\pi$
$230$	−25.1274	−1.65685
$231$	0.929980	0.0611882
$232$	5.21129	0.342138
$233$	6.87666	0.450505	0.225252	−	0.974300i	$-0.427679\pi$
$233$	6.87666	0.450505	0.225252	+	0.974300i	$0.427679\pi$
$234$	−4.28978	−0.280432
$235$	14.5956	0.952114
$236$	−1.38390	−0.0900842
$237$	4.49508	0.291987
$238$	−2.92927	−0.189876
$239$	−13.6353	−0.881997	−0.440998	−	0.897508i	$-0.645376\pi$
$239$	−13.6353	−0.881997	−0.440998	+	0.897508i	$0.645376\pi$
$240$	2.32890	0.150330
$241$	9.32981	0.600986	0.300493	−	0.953784i	$-0.402849\pi$
$241$	9.32981	0.600986	0.300493	+	0.953784i	$0.402849\pi$
$242$	−7.57392	−0.486870
$243$	−16.0286	−1.02824
$244$	2.88432	0.184650
$245$	18.1983	1.16264
$246$	−2.26643	−0.144503
$247$	1.88529	0.119958
$248$	2.14709	0.136340
$249$	−4.00053	−0.253523
$250$	6.88023	0.435144
$251$	4.53768	0.286416	0.143208	−	0.989693i	$-0.454258\pi$
$251$	4.53768	0.286416	0.143208	+	0.989693i	$0.454258\pi$
$252$	−1.34302	−0.0846026
$253$	−16.9998	−1.06877
$254$	−11.2005	−0.702784
$255$	−11.5580	−0.723793
$256$	1.00000	0.0625000
$257$	−19.6876	−1.22808	−0.614039	−	0.789276i	$-0.710456\pi$
$257$	−19.6876	−1.22808	−0.614039	+	0.789276i	$0.710456\pi$
$258$	2.40713	0.149862
$259$	2.69586	0.167513
$260$	−5.15798	−0.319884
$261$	−11.8578	−0.733977
$262$	22.0343	1.36128
$263$	7.31531	0.451081	0.225541	−	0.974234i	$-0.427585\pi$
$263$	7.31531	0.451081	0.225541	+	0.974234i	$0.427585\pi$
$264$	1.57561	0.0969719
$265$	11.2881	0.693424
$266$	0.590237	0.0361897
$267$	−10.0069	−0.612410
$268$	−5.02573	−0.306995
$269$	22.7402	1.38650	0.693248	−	0.720699i	$-0.256179\pi$
$269$	22.7402	1.38650	0.693248	+	0.720699i	$0.256179\pi$
$270$	−12.2859	−0.747695
$271$	−0.653391	−0.0396907	−0.0198453	−	0.999803i	$-0.506317\pi$
$271$	−0.653391	−0.0396907	−0.0198453	+	0.999803i	$0.506317\pi$
$272$	−4.96288	−0.300919
$273$	−0.947223	−0.0573285
$274$	−12.8366	−0.775486
$275$	−4.60005	−0.277394
$276$	−7.81796	−0.470586
$277$	3.66730	0.220347	0.110173	−	0.993912i	$-0.464859\pi$
$277$	3.66730	0.220347	0.110173	+	0.993912i	$0.464859\pi$
$278$	−13.2901	−0.797086
$279$	−4.88549	−0.292487
$280$	−1.61484	−0.0965049
$281$	14.2063	0.847478	0.423739	−	0.905784i	$-0.360717\pi$
$281$	14.2063	0.847478	0.423739	+	0.905784i	$0.360717\pi$
$282$	4.54119	0.270424
$283$	14.2527	0.847236	0.423618	−	0.905841i	$-0.360760\pi$
$283$	14.2527	0.847236	0.423618	+	0.905841i	$0.360760\pi$
$284$	3.68758	0.218817
$285$	2.32890	0.137952
$286$	−3.48960	−0.206344
$287$	1.57152	0.0927640
$288$	−2.27540	−0.134079
$289$	7.63013	0.448831
$290$	−14.2576	−0.837237
$291$	−12.4395	−0.729216
$292$	−2.34064	−0.136975
$293$	−13.3014	−0.777073	−0.388537	−	0.921433i	$-0.627019\pi$
$293$	−13.3014	−0.777073	−0.388537	+	0.921433i	$0.627019\pi$
$294$	5.66209	0.330220
$295$	3.78623	0.220443
$296$	4.56743	0.265476
$297$	−8.31195	−0.482308
$298$	−9.18506	−0.532076
$299$	17.3150	1.00135
$300$	−2.11550	−0.122138
$301$	−1.66908	−0.0962041
$302$	−18.1659	−1.04533
$303$	10.9360	0.628256
$304$	1.00000	0.0573539
$305$	−7.89124	−0.451851
$306$	11.2925	0.645551
$307$	27.9110	1.59297	0.796483	−	0.604661i	$-0.206691\pi$
$307$	27.9110	1.59297	0.796483	+	0.604661i	$0.206691\pi$
$308$	−1.09251	−0.0622514
$309$	13.8850	0.789888
$310$	−5.87425	−0.333635
$311$	12.2226	0.693078	0.346539	−	0.938036i	$-0.387357\pi$
$311$	12.2226	0.693078	0.346539	+	0.938036i	$0.387357\pi$
$312$	−1.60482	−0.0908550
$313$	23.3705	1.32098	0.660490	−	0.750835i	$-0.270349\pi$
$313$	23.3705	1.32098	0.660490	+	0.750835i	$0.270349\pi$
$314$	−6.86544	−0.387439
$315$	3.67440	0.207029
$316$	−5.28066	−0.297060
$317$	−5.04135	−0.283151	−0.141575	−	0.989927i	$-0.545217\pi$
$317$	−5.04135	−0.283151	−0.141575	+	0.989927i	$0.545217\pi$
$318$	3.51211	0.196949
$319$	−9.64592	−0.540068
$320$	−2.73591	−0.152942
$321$	12.4392	0.694286
$322$	5.42089	0.302094
$323$	−4.96288	−0.276142
$324$	3.00365	0.166869
$325$	4.68534	0.259896
$326$	−7.85359	−0.434970
$327$	11.6729	0.645511
$328$	2.66253	0.147014
$329$	−3.14881	−0.173600
$330$	−4.31072	−0.237297
$331$	−27.5631	−1.51500	−0.757502	−	0.652833i	$-0.773580\pi$
$331$	−27.5631	−1.51500	−0.757502	+	0.652833i	$0.773580\pi$
$332$	4.69968	0.257929
$333$	−10.3927	−0.569518
$334$	−3.06987	−0.167976
$335$	13.7500	0.751241
$336$	−0.502429	−0.0274098
$337$	−10.5707	−0.575822	−0.287911	−	0.957657i	$-0.592961\pi$
$337$	−10.5707	−0.575822	−0.287911	+	0.957657i	$0.592961\pi$
$338$	−9.44570	−0.513778
$339$	−8.15960	−0.443168
$340$	13.5780	0.736370
$341$	−3.97419	−0.215215
$342$	−2.27540	−0.123040
$343$	−8.05769	−0.435074
$344$	−2.82781	−0.152466
$345$	21.3893	1.15156
$346$	8.70636	0.468057
$347$	12.6630	0.679787	0.339894	−	0.940464i	$-0.389609\pi$
$347$	12.6630	0.679787	0.339894	+	0.940464i	$0.389609\pi$
$348$	−4.43603	−0.237796
$349$	−28.4933	−1.52521	−0.762606	−	0.646863i	$-0.776081\pi$
$349$	−28.4933	−1.52521	−0.762606	+	0.646863i	$0.776081\pi$
$350$	1.46686	0.0784072
$351$	8.46606	0.451885
$352$	−1.85097	−0.0986569
$353$	−21.5746	−1.14830	−0.574150	−	0.818750i	$-0.694667\pi$
$353$	−21.5746	−1.14830	−0.574150	+	0.818750i	$0.694667\pi$
$354$	1.17802	0.0626112
$355$	−10.0889	−0.535462
$356$	11.7557	0.623051
$357$	2.49349	0.131970
$358$	−18.7136	−0.989045
$359$	23.0994	1.21914	0.609571	−	0.792731i	$-0.291342\pi$
$359$	23.0994	1.21914	0.609571	+	0.792731i	$0.291342\pi$
$360$	6.22530	0.328102
$361$	1.00000	0.0526316
$362$	−12.8415	−0.674932
$363$	6.44718	0.338389
$364$	1.11276	0.0583247
$365$	6.40378	0.335189
$366$	−2.45523	−0.128337
$367$	−13.3317	−0.695910	−0.347955	−	0.937511i	$-0.613124\pi$
$367$	−13.3317	−0.695910	−0.347955	+	0.937511i	$0.613124\pi$
$368$	9.18427	0.478763
$369$	−6.05832	−0.315383
$370$	−12.4961	−0.649641
$371$	−2.43526	−0.126432
$372$	−1.82768	−0.0947606
$373$	−22.7148	−1.17613	−0.588063	−	0.808815i	$-0.700109\pi$
$373$	−22.7148	−1.17613	−0.588063	+	0.808815i	$0.700109\pi$
$374$	9.18612	0.475003
$375$	−5.85669	−0.302438
$376$	−5.33483	−0.275123
$377$	9.82476	0.506001
$378$	2.65052	0.136328
$379$	27.9622	1.43632	0.718162	−	0.695876i	$-0.244984\pi$
$379$	27.9622	1.43632	0.718162	+	0.695876i	$0.244984\pi$
$380$	−2.73591	−0.140349
$381$	9.53427	0.488456
$382$	18.4358	0.943255
$383$	−4.12225	−0.210637	−0.105319	−	0.994439i	$-0.533586\pi$
$383$	−4.12225	−0.210637	−0.105319	+	0.994439i	$0.533586\pi$
$384$	−0.851234	−0.0434394
$385$	2.98901	0.152334
$386$	1.16570	0.0593324
$387$	6.43441	0.327079
$388$	14.6135	0.741887
$389$	13.2545	0.672028	0.336014	−	0.941857i	$-0.390921\pi$
$389$	13.2545	0.672028	0.336014	+	0.941857i	$0.390921\pi$
$390$	4.39064	0.222329
$391$	−45.5804	−2.30510
$392$	−6.65162	−0.335958
$393$	−18.7563	−0.946133
$394$	−0.461268	−0.0232383
$395$	14.4474	0.726929
$396$	4.21169	0.211645
$397$	9.35973	0.469751	0.234876	−	0.972025i	$-0.424532\pi$
$397$	9.35973	0.469751	0.234876	+	0.972025i	$0.424532\pi$
$398$	−24.2470	−1.21539
$399$	−0.502429	−0.0251529
$400$	2.48522	0.124261
$401$	23.9174	1.19438	0.597188	−	0.802101i	$-0.296285\pi$
$401$	23.9174	1.19438	0.597188	+	0.802101i	$0.296285\pi$
$402$	4.27807	0.213371
$403$	4.04788	0.201639
$404$	−12.8472	−0.639173
$405$	−8.21772	−0.408342
$406$	3.07589	0.152654
$407$	−8.45416	−0.419057
$408$	4.22457	0.209147
$409$	−24.4329	−1.20813	−0.604065	−	0.796935i	$-0.706453\pi$
$409$	−24.4329	−1.20813	−0.604065	+	0.796935i	$0.706453\pi$
$410$	−7.28444	−0.359753
$411$	10.9269	0.538986
$412$	−16.3116	−0.803613
$413$	−0.816828	−0.0401935
$414$	−20.8979	−1.02708
$415$	−12.8579	−0.631170
$416$	1.88529	0.0924337
$417$	11.3130	0.553998
$418$	−1.85097	−0.0905337
$419$	7.08550	0.346149	0.173075	−	0.984909i	$-0.444630\pi$
$419$	7.08550	0.346149	0.173075	+	0.984909i	$0.444630\pi$
$420$	1.37460	0.0670738
$421$	−25.9286	−1.26368	−0.631841	−	0.775098i	$-0.717701\pi$
$421$	−25.9286	−1.26368	−0.631841	+	0.775098i	$0.717701\pi$
$422$	−1.00000	−0.0486792
$423$	12.1389	0.590213
$424$	−4.12591	−0.200372
$425$	−12.3338	−0.598278
$426$	−3.13899	−0.152085
$427$	1.70243	0.0823864
$428$	−14.6131	−0.706350
$429$	2.97047	0.143416
$430$	7.73665	0.373095
$431$	−22.2780	−1.07309	−0.536546	−	0.843871i	$-0.680271\pi$
$431$	−22.2780	−1.07309	−0.536546	+	0.843871i	$0.680271\pi$
$432$	4.49060	0.216054
$433$	−8.14495	−0.391422	−0.195711	−	0.980662i	$-0.562701\pi$
$433$	−8.14495	−0.391422	−0.195711	+	0.980662i	$0.562701\pi$
$434$	1.26729	0.0608319
$435$	12.1366	0.581904
$436$	−13.7129	−0.656727
$437$	9.18427	0.439343
$438$	1.99243	0.0952020
$439$	−23.9146	−1.14138	−0.570692	−	0.821164i	$-0.693325\pi$
$439$	−23.9146	−1.14138	−0.570692	+	0.821164i	$0.693325\pi$
$440$	5.06408	0.241421
$441$	15.1351	0.720719
$442$	−9.35644	−0.445040
$443$	−18.2748	−0.868262	−0.434131	−	0.900850i	$-0.642944\pi$
$443$	−18.2748	−0.868262	−0.434131	+	0.900850i	$0.642944\pi$
$444$	−3.88795	−0.184514
$445$	−32.1626	−1.52465
$446$	23.5388	1.11460
$447$	7.81864	0.369809
$448$	0.590237	0.0278861
$449$	−32.7585	−1.54597	−0.772984	−	0.634426i	$-0.781237\pi$
$449$	−32.7585	−1.54597	−0.772984	+	0.634426i	$0.781237\pi$
$450$	−5.65486	−0.266573
$451$	−4.92825	−0.232062
$452$	9.58561	0.450869
$453$	15.4635	0.726537
$454$	−22.4844	−1.05525
$455$	−3.04443	−0.142725
$456$	−0.851234	−0.0398627
$457$	−3.45841	−0.161777	−0.0808887	−	0.996723i	$-0.525776\pi$
$457$	−3.45841	−0.161777	−0.0808887	+	0.996723i	$0.525776\pi$
$458$	14.6615	0.685085
$459$	−22.2863	−1.04024
$460$	−25.1274	−1.17157
$461$	−30.8497	−1.43681	−0.718406	−	0.695624i	$-0.755128\pi$
$461$	−30.8497	−1.43681	−0.718406	+	0.695624i	$0.755128\pi$
$462$	0.929980	0.0432666
$463$	−39.7861	−1.84902	−0.924508	−	0.381163i	$-0.875524\pi$
$463$	−39.7861	−1.84902	−0.924508	+	0.381163i	$0.875524\pi$
$464$	5.21129	0.241928
$465$	5.00036	0.231886
$466$	6.87666	0.318555
$467$	−4.95261	−0.229180	−0.114590	−	0.993413i	$-0.536555\pi$
$467$	−4.95261	−0.229180	−0.114590	+	0.993413i	$0.536555\pi$
$468$	−4.28978	−0.198295
$469$	−2.96637	−0.136974
$470$	14.5956	0.673247
$471$	5.84409	0.269282
$472$	−1.38390	−0.0636991
$473$	5.23419	0.240668
$474$	4.49508	0.206466
$475$	2.48522	0.114029
$476$	−2.92927	−0.134263
$477$	9.38809	0.429851
$478$	−13.6353	−0.623666
$479$	1.34533	0.0614699	0.0307349	−	0.999528i	$-0.490215\pi$
$479$	1.34533	0.0614699	0.0307349	+	0.999528i	$0.490215\pi$
$480$	2.32890	0.106299
$481$	8.61091	0.392624
$482$	9.32981	0.424961
$483$	−4.61445	−0.209965
$484$	−7.57392	−0.344269
$485$	−39.9812	−1.81545
$486$	−16.0286	−0.727073
$487$	−32.4030	−1.46832	−0.734160	−	0.678977i	$-0.762424\pi$
$487$	−32.4030	−1.46832	−0.734160	+	0.678977i	$0.762424\pi$
$488$	2.88432	0.130567
$489$	6.68524	0.302317
$490$	18.1983	0.822113
$491$	3.96106	0.178760	0.0893800	−	0.995998i	$-0.471511\pi$
$491$	3.96106	0.178760	0.0893800	+	0.995998i	$0.471511\pi$
$492$	−2.26643	−0.102179
$493$	−25.8630	−1.16481
$494$	1.88529	0.0848230
$495$	−11.5228	−0.517912
$496$	2.14709	0.0964072
$497$	2.17654	0.0976312
$498$	−4.00053	−0.179268
$499$	−14.9638	−0.669871	−0.334935	−	0.942241i	$-0.608715\pi$
$499$	−14.9638	−0.669871	−0.334935	+	0.942241i	$0.608715\pi$
$500$	6.88023	0.307693
$501$	2.61318	0.116748
$502$	4.53768	0.202526
$503$	2.73170	0.121801	0.0609003	−	0.998144i	$-0.480603\pi$
$503$	2.73170	0.121801	0.0609003	+	0.998144i	$0.480603\pi$
$504$	−1.34302	−0.0598231
$505$	35.1488	1.56410
$506$	−16.9998	−0.755732
$507$	8.04050	0.357091
$508$	−11.2005	−0.496943
$509$	8.11268	0.359588	0.179794	−	0.983704i	$-0.442457\pi$
$509$	8.11268	0.359588	0.179794	+	0.983704i	$0.442457\pi$
$510$	−11.5580	−0.511799
$511$	−1.38153	−0.0611153
$512$	1.00000	0.0441942
$513$	4.49060	0.198265
$514$	−19.6876	−0.868383
$515$	44.6270	1.96650
$516$	2.40713	0.105968
$517$	9.87460	0.434284
$518$	2.69586	0.118449
$519$	−7.41115	−0.325313
$520$	−5.15798	−0.226192
$521$	25.4442	1.11473	0.557366	−	0.830267i	$-0.311812\pi$
$521$	25.4442	1.11473	0.557366	+	0.830267i	$0.311812\pi$
$522$	−11.8578	−0.519000
$523$	−18.5770	−0.812315	−0.406157	−	0.913803i	$-0.633132\pi$
$523$	−18.5770	−0.812315	−0.406157	+	0.913803i	$0.633132\pi$
$524$	22.0343	0.962573
$525$	−1.24865	−0.0544954
$526$	7.31531	0.318962
$527$	−10.6557	−0.464171
$528$	1.57561	0.0685695
$529$	61.3508	2.66743
$530$	11.2881	0.490325
$531$	3.14893	0.136652
$532$	0.590237	0.0255900
$533$	5.01963	0.217424
$534$	−10.0069	−0.433039
$535$	39.9801	1.72849
$536$	−5.02573	−0.217079
$537$	15.9297	0.687415
$538$	22.7402	0.980400
$539$	12.3119	0.530312
$540$	−12.2859	−0.528701
$541$	9.21356	0.396122	0.198061	−	0.980190i	$-0.436536\pi$
$541$	9.21356	0.396122	0.198061	+	0.980190i	$0.436536\pi$
$542$	−0.653391	−0.0280656
$543$	10.9311	0.469098
$544$	−4.96288	−0.212782
$545$	37.5172	1.60706
$546$	−0.947223	−0.0405374
$547$	32.4664	1.38816	0.694082	−	0.719896i	$-0.255810\pi$
$547$	32.4664	1.38816	0.694082	+	0.719896i	$0.255810\pi$
$548$	−12.8366	−0.548351
$549$	−6.56298	−0.280101
$550$	−4.60005	−0.196147
$551$	5.21129	0.222008
$552$	−7.81796	−0.332755
$553$	−3.11684	−0.132541
$554$	3.66730	0.155809
$555$	10.6371	0.451520
$556$	−13.2901	−0.563625
$557$	22.9713	0.973325	0.486662	−	0.873590i	$-0.338214\pi$
$557$	22.9713	0.973325	0.486662	+	0.873590i	$0.338214\pi$
$558$	−4.88549	−0.206819
$559$	−5.33124	−0.225487
$560$	−1.61484	−0.0682392
$561$	−7.81954	−0.330141
$562$	14.2063	0.599258
$563$	46.2540	1.94937	0.974686	−	0.223577i	$-0.0717734\pi$
$563$	46.2540	1.94937	0.974686	+	0.223577i	$0.0717734\pi$
$564$	4.54119	0.191219
$565$	−26.2254	−1.10331
$566$	14.2527	0.599086
$567$	1.77286	0.0744533
$568$	3.68758	0.154727
$569$	−44.3647	−1.85987	−0.929933	−	0.367730i	$-0.880135\pi$
$569$	−44.3647	−1.85987	−0.929933	+	0.367730i	$0.880135\pi$
$570$	2.32890	0.0975470
$571$	−30.1679	−1.26249	−0.631244	−	0.775584i	$-0.717455\pi$
$571$	−30.1679	−1.26249	−0.631244	+	0.775584i	$0.717455\pi$
$572$	−3.48960	−0.145908
$573$	−15.6931	−0.655590
$574$	1.57152	0.0655940
$575$	22.8249	0.951864
$576$	−2.27540	−0.0948084
$577$	41.1781	1.71427	0.857133	−	0.515095i	$-0.172243\pi$
$577$	41.1781	1.71427	0.857133	+	0.515095i	$0.172243\pi$
$578$	7.63013	0.317372
$579$	−0.992280	−0.0412377
$580$	−14.2576	−0.592016
$581$	2.77392	0.115082
$582$	−12.4395	−0.515634
$583$	7.63692	0.316289
$584$	−2.34064	−0.0968563
$585$	11.7365	0.485243
$586$	−13.3014	−0.549474
$587$	−23.0521	−0.951462	−0.475731	−	0.879591i	$-0.657816\pi$
$587$	−23.0521	−0.951462	−0.475731	+	0.879591i	$0.657816\pi$
$588$	5.66209	0.233501
$589$	2.14709	0.0884693
$590$	3.78623	0.155877
$591$	0.392647	0.0161513
$592$	4.56743	0.187720
$593$	−10.5408	−0.432861	−0.216430	−	0.976298i	$-0.569441\pi$
$593$	−10.5408	−0.432861	−0.216430	+	0.976298i	$0.569441\pi$
$594$	−8.31195	−0.341044
$595$	8.01423	0.328551
$596$	−9.18506	−0.376235
$597$	20.6399	0.844735
$598$	17.3150	0.708062
$599$	−27.4181	−1.12027	−0.560136	−	0.828400i	$-0.689251\pi$
$599$	−27.4181	−1.12027	−0.560136	+	0.828400i	$0.689251\pi$
$600$	−2.11550	−0.0863649
$601$	46.3625	1.89117	0.945583	−	0.325382i	$-0.105493\pi$
$601$	46.3625	1.89117	0.945583	+	0.325382i	$0.105493\pi$
$602$	−1.66908	−0.0680266
$603$	11.4356	0.465692
$604$	−18.1659	−0.739161
$605$	20.7216	0.842452
$606$	10.9360	0.444244
$607$	−3.71754	−0.150890	−0.0754452	−	0.997150i	$-0.524038\pi$
$607$	−3.71754	−0.150890	−0.0754452	+	0.997150i	$0.524038\pi$
$608$	1.00000	0.0405554
$609$	−2.61830	−0.106099
$610$	−7.89124	−0.319507
$611$	−10.0577	−0.406890
$612$	11.2925	0.456473
$613$	−19.0907	−0.771067	−0.385534	−	0.922694i	$-0.625983\pi$
$613$	−19.0907	−0.771067	−0.385534	+	0.922694i	$0.625983\pi$
$614$	27.9110	1.12640
$615$	6.20077	0.250039
$616$	−1.09251	−0.0440184
$617$	−3.08331	−0.124130	−0.0620648	−	0.998072i	$-0.519769\pi$
$617$	−3.08331	−0.124130	−0.0620648	+	0.998072i	$0.519769\pi$
$618$	13.8850	0.558535
$619$	−20.1500	−0.809898	−0.404949	−	0.914339i	$-0.632711\pi$
$619$	−20.1500	−0.809898	−0.404949	+	0.914339i	$0.632711\pi$
$620$	−5.87425	−0.235915
$621$	41.2429	1.65502
$622$	12.2226	0.490080
$623$	6.93865	0.277991
$624$	−1.60482	−0.0642442
$625$	−31.2498	−1.24999
$626$	23.3705	0.934073
$627$	1.57561	0.0629236
$628$	−6.86544	−0.273961
$629$	−22.6676	−0.903816
$630$	3.67440	0.146391
$631$	22.4966	0.895576	0.447788	−	0.894140i	$-0.352212\pi$
$631$	22.4966	0.895576	0.447788	+	0.894140i	$0.352212\pi$
$632$	−5.28066	−0.210053
$633$	0.851234	0.0338335
$634$	−5.04135	−0.200218
$635$	30.6437	1.21606
$636$	3.51211	0.139264
$637$	−12.5402	−0.496861
$638$	−9.64592	−0.381886
$639$	−8.39071	−0.331931
$640$	−2.73591	−0.108146
$641$	−33.6952	−1.33088	−0.665440	−	0.746452i	$-0.731756\pi$
$641$	−33.6952	−1.33088	−0.665440	+	0.746452i	$0.731756\pi$
$642$	12.4392	0.490935
$643$	−0.279610	−0.0110267	−0.00551337	−	0.999985i	$-0.501755\pi$
$643$	−0.279610	−0.0110267	−0.00551337	+	0.999985i	$0.501755\pi$
$644$	5.42089	0.213613
$645$	−6.58570	−0.259312
$646$	−4.96288	−0.195262
$647$	35.1454	1.38171	0.690855	−	0.722994i	$-0.257234\pi$
$647$	35.1454	1.38171	0.690855	+	0.722994i	$0.257234\pi$
$648$	3.00365	0.117994
$649$	2.56155	0.100550
$650$	4.68534	0.183774
$651$	−1.07876	−0.0422800
$652$	−7.85359	−0.307570
$653$	43.4375	1.69984	0.849921	−	0.526910i	$-0.176650\pi$
$653$	43.4375	1.69984	0.849921	+	0.526910i	$0.176650\pi$
$654$	11.6729	0.456445
$655$	−60.2839	−2.35549
$656$	2.66253	0.103954
$657$	5.32589	0.207783
$658$	−3.14881	−0.122754
$659$	16.2510	0.633051	0.316525	−	0.948584i	$-0.397484\pi$
$659$	16.2510	0.633051	0.316525	+	0.948584i	$0.397484\pi$
$660$	−4.31072	−0.167795
$661$	−37.3742	−1.45369	−0.726843	−	0.686803i	$-0.759013\pi$
$661$	−37.3742	−1.45369	−0.726843	+	0.686803i	$0.759013\pi$
$662$	−27.5631	−1.07127
$663$	7.96452	0.309316
$664$	4.69968	0.182383
$665$	−1.61484	−0.0626206
$666$	−10.3927	−0.402710
$667$	47.8619	1.85322
$668$	−3.06987	−0.118777
$669$	−20.0370	−0.774677
$670$	13.7500	0.531207
$671$	−5.33878	−0.206101
$672$	−0.502429	−0.0193816
$673$	−21.8313	−0.841534	−0.420767	−	0.907169i	$-0.638239\pi$
$673$	−21.8313	−0.841534	−0.420767	+	0.907169i	$0.638239\pi$
$674$	−10.5707	−0.407168
$675$	11.1601	0.429553
$676$	−9.44570	−0.363296
$677$	−30.7230	−1.18078	−0.590390	−	0.807118i	$-0.701026\pi$
$677$	−30.7230	−1.18078	−0.590390	+	0.807118i	$0.701026\pi$
$678$	−8.15960	−0.313367
$679$	8.62541	0.331013
$680$	13.5780	0.520692
$681$	19.1395	0.733427
$682$	−3.97419	−0.152180
$683$	−50.1126	−1.91750	−0.958752	−	0.284245i	$-0.908257\pi$
$683$	−50.1126	−1.91750	−0.958752	+	0.284245i	$0.908257\pi$
$684$	−2.27540	−0.0870021
$685$	35.1197	1.34186
$686$	−8.05769	−0.307644
$687$	−12.4803	−0.476154
$688$	−2.82781	−0.107809
$689$	−7.77851	−0.296338
$690$	21.3893	0.814275
$691$	−33.4120	−1.27105	−0.635526	−	0.772079i	$-0.719217\pi$
$691$	−33.4120	−1.27105	−0.635526	+	0.772079i	$0.719217\pi$
$692$	8.70636	0.330966
$693$	2.48589	0.0944313
$694$	12.6630	0.480682
$695$	36.3605	1.37923
$696$	−4.43603	−0.168147
$697$	−13.2138	−0.500508
$698$	−28.4933	−1.07849
$699$	−5.85364	−0.221405
$700$	1.46686	0.0554423
$701$	−22.1771	−0.837619	−0.418809	−	0.908074i	$-0.637552\pi$
$701$	−22.1771	−0.837619	−0.418809	+	0.908074i	$0.637552\pi$
$702$	8.46606	0.319531
$703$	4.56743	0.172264
$704$	−1.85097	−0.0697609
$705$	−12.4243	−0.467926
$706$	−21.5746	−0.811970
$707$	−7.58289	−0.285184
$708$	1.17802	0.0442728
$709$	11.9572	0.449061	0.224531	−	0.974467i	$-0.427915\pi$
$709$	11.9572	0.449061	0.224531	+	0.974467i	$0.427915\pi$
$710$	−10.0889	−0.378629
$711$	12.0156	0.450621
$712$	11.7557	0.440564
$713$	19.7194	0.738499
$714$	2.49349	0.0933167
$715$	9.54724	0.357047
$716$	−18.7136	−0.699360
$717$	11.6069	0.433466
$718$	23.0994	0.862064
$719$	29.3090	1.09304	0.546521	−	0.837445i	$-0.315952\pi$
$719$	29.3090	1.09304	0.546521	+	0.837445i	$0.315952\pi$
$720$	6.22530	0.232003
$721$	−9.62768	−0.358554
$722$	1.00000	0.0372161
$723$	−7.94186	−0.295361
$724$	−12.8415	−0.477249
$725$	12.9512	0.480994
$726$	6.44718	0.239277
$727$	11.9179	0.442010	0.221005	−	0.975273i	$-0.429066\pi$
$727$	11.9179	0.442010	0.221005	+	0.975273i	$0.429066\pi$
$728$	1.11276	0.0412418
$729$	4.63315	0.171598
$730$	6.40378	0.237014
$731$	14.0341	0.519070
$732$	−2.45523	−0.0907480
$733$	−15.5131	−0.572991	−0.286496	−	0.958082i	$-0.592490\pi$
$733$	−15.5131	−0.572991	−0.286496	+	0.958082i	$0.592490\pi$
$734$	−13.3317	−0.492083
$735$	−15.4910	−0.571393
$736$	9.18427	0.338537
$737$	9.30246	0.342661
$738$	−6.05832	−0.223010
$739$	11.6483	0.428490	0.214245	−	0.976780i	$-0.431271\pi$
$739$	11.6483	0.428490	0.214245	+	0.976780i	$0.431271\pi$
$740$	−12.4961	−0.459365
$741$	−1.60482	−0.0589545
$742$	−2.43526	−0.0894012
$743$	0.558624	0.0204939	0.0102470	−	0.999947i	$-0.496738\pi$
$743$	0.558624	0.0204939	0.0102470	+	0.999947i	$0.496738\pi$
$744$	−1.82768	−0.0670059
$745$	25.1295	0.920674
$746$	−22.7148	−0.831647
$747$	−10.6937	−0.391261
$748$	9.18612	0.335878
$749$	−8.62518	−0.315157
$750$	−5.85669	−0.213856
$751$	−14.6166	−0.533368	−0.266684	−	0.963784i	$-0.585928\pi$
$751$	−14.6166	−0.533368	−0.266684	+	0.963784i	$0.585928\pi$
$752$	−5.33483	−0.194541
$753$	−3.86262	−0.140762
$754$	9.82476	0.357797
$755$	49.7004	1.80878
$756$	2.65052	0.0963984
$757$	−38.1142	−1.38528	−0.692642	−	0.721281i	$-0.743554\pi$
$757$	−38.1142	−1.38528	−0.692642	+	0.721281i	$0.743554\pi$
$758$	27.9622	1.01563
$759$	14.4708	0.525256
$760$	−2.73591	−0.0992420
$761$	11.4364	0.414568	0.207284	−	0.978281i	$-0.433538\pi$
$761$	11.4364	0.414568	0.207284	+	0.978281i	$0.433538\pi$
$762$	9.53427	0.345390
$763$	−8.09383	−0.293016
$764$	18.4358	0.666982
$765$	−30.8954	−1.11702
$766$	−4.12225	−0.148943
$767$	−2.60905	−0.0942072
$768$	−0.851234	−0.0307163
$769$	−1.30181	−0.0469444	−0.0234722	−	0.999724i	$-0.507472\pi$
$769$	−1.30181	−0.0469444	−0.0234722	+	0.999724i	$0.507472\pi$
$770$	2.98901	0.107716
$771$	16.7588	0.603552
$772$	1.16570	0.0419543
$773$	−14.9282	−0.536930	−0.268465	−	0.963289i	$-0.586516\pi$
$773$	−14.9282	−0.536930	−0.268465	+	0.963289i	$0.586516\pi$
$774$	6.43441	0.231280
$775$	5.33598	0.191674
$776$	14.6135	0.524593
$777$	−2.29481	−0.0823259
$778$	13.2545	0.475196
$779$	2.66253	0.0953950
$780$	4.39064	0.157210
$781$	−6.82558	−0.244238
$782$	−45.5804	−1.62995
$783$	23.4018	0.836313
$784$	−6.65162	−0.237558
$785$	18.7832	0.670402
$786$	−18.7563	−0.669017
$787$	15.7775	0.562407	0.281203	−	0.959648i	$-0.409266\pi$
$787$	15.7775	0.562407	0.281203	+	0.959648i	$0.409266\pi$
$788$	−0.461268	−0.0164320
$789$	−6.22704	−0.221688
$790$	14.4474	0.514016
$791$	5.65778	0.201167
$792$	4.21169	0.149656
$793$	5.43777	0.193101
$794$	9.35973	0.332164
$795$	−9.60883	−0.340790
$796$	−24.2470	−0.859413
$797$	4.18880	0.148375	0.0741875	−	0.997244i	$-0.476364\pi$
$797$	4.18880	0.148375	0.0741875	+	0.997244i	$0.476364\pi$
$798$	−0.502429	−0.0177858
$799$	26.4761	0.936658
$800$	2.48522	0.0878656
$801$	−26.7489	−0.945127
$802$	23.9174	0.844551
$803$	4.33244	0.152889
$804$	4.27807	0.150876
$805$	−14.8311	−0.522727
$806$	4.04788	0.142580
$807$	−19.3572	−0.681407
$808$	−12.8472	−0.451963
$809$	−32.8100	−1.15354	−0.576769	−	0.816907i	$-0.695687\pi$
$809$	−32.8100	−1.15354	−0.576769	+	0.816907i	$0.695687\pi$
$810$	−8.21772	−0.288741
$811$	−23.5911	−0.828394	−0.414197	−	0.910187i	$-0.635938\pi$
$811$	−23.5911	−0.828394	−0.414197	+	0.910187i	$0.635938\pi$
$812$	3.07589	0.107943
$813$	0.556189	0.0195064
$814$	−8.45416	−0.296318
$815$	21.4867	0.752647
$816$	4.22457	0.147889
$817$	−2.82781	−0.0989327
$818$	−24.4329	−0.854277
$819$	−2.53198	−0.0884747
$820$	−7.28444	−0.254384
$821$	20.2176	0.705598	0.352799	−	0.935699i	$-0.385230\pi$
$821$	20.2176	0.705598	0.352799	+	0.935699i	$0.385230\pi$
$822$	10.9269	0.381120
$823$	33.7231	1.17551	0.587757	−	0.809038i	$-0.300011\pi$
$823$	33.7231	1.17551	0.587757	+	0.809038i	$0.300011\pi$
$824$	−16.3116	−0.568240
$825$	3.91572	0.136328
$826$	−0.816828	−0.0284211
$827$	44.8266	1.55877	0.779387	−	0.626542i	$-0.215531\pi$
$827$	44.8266	1.55877	0.779387	+	0.626542i	$0.215531\pi$
$828$	−20.8979	−0.726252
$829$	49.8577	1.73163	0.865816	−	0.500363i	$-0.166800\pi$
$829$	49.8577	1.73163	0.865816	+	0.500363i	$0.166800\pi$
$830$	−12.8579	−0.446305
$831$	−3.12174	−0.108292
$832$	1.88529	0.0653605
$833$	33.0112	1.14377
$834$	11.3130	0.391736
$835$	8.39890	0.290656
$836$	−1.85097	−0.0640170
$837$	9.64172	0.333267
$838$	7.08550	0.244765
$839$	−50.0326	−1.72732	−0.863658	−	0.504078i	$-0.831832\pi$
$839$	−50.0326	−1.72732	−0.863658	+	0.504078i	$0.831832\pi$
$840$	1.37460	0.0474283
$841$	−1.84248	−0.0635340
$842$	−25.9286	−0.893558
$843$	−12.0929	−0.416502
$844$	−1.00000	−0.0344214
$845$	25.8426	0.889013
$846$	12.1389	0.417343
$847$	−4.47041	−0.153605
$848$	−4.12591	−0.141684
$849$	−12.1324	−0.416383
$850$	−12.3338	−0.423046
$851$	41.9485	1.43798
$852$	−3.13899	−0.107540
$853$	−43.1050	−1.47589	−0.737944	−	0.674862i	$-0.764203\pi$
$853$	−43.1050	−1.47589	−0.737944	+	0.674862i	$0.764203\pi$
$854$	1.70243	0.0582560
$855$	6.22530	0.212901
$856$	−14.6131	−0.499465
$857$	8.23730	0.281381	0.140690	−	0.990054i	$-0.455068\pi$
$857$	8.23730	0.281381	0.140690	+	0.990054i	$0.455068\pi$
$858$	2.97047	0.101410
$859$	5.09199	0.173737	0.0868683	−	0.996220i	$-0.472314\pi$
$859$	5.09199	0.173737	0.0868683	+	0.996220i	$0.472314\pi$
$860$	7.73665	0.263818
$861$	−1.33773	−0.0455898
$862$	−22.2780	−0.758791
$863$	44.4564	1.51331	0.756657	−	0.653812i	$-0.226831\pi$
$863$	44.4564	1.51331	0.756657	+	0.653812i	$0.226831\pi$
$864$	4.49060	0.152773
$865$	−23.8198	−0.809899
$866$	−8.14495	−0.276777
$867$	−6.49503	−0.220583
$868$	1.26729	0.0430146
$869$	9.77433	0.331571
$870$	12.1366	0.411468
$871$	−9.47494	−0.321046
$872$	−13.7129	−0.464376
$873$	−33.2515	−1.12539
$874$	9.18427	0.310663
$875$	4.06096	0.137286
$876$	1.99243	0.0673180
$877$	−20.3998	−0.688853	−0.344427	−	0.938813i	$-0.611927\pi$
$877$	−20.3998	−0.688853	−0.344427	+	0.938813i	$0.611927\pi$
$878$	−23.9146	−0.807080
$879$	11.3226	0.381901
$880$	5.06408	0.170710
$881$	−18.0011	−0.606473	−0.303237	−	0.952915i	$-0.598067\pi$
$881$	−18.0011	−0.606473	−0.303237	+	0.952915i	$0.598067\pi$
$882$	15.1351	0.509625
$883$	18.3131	0.616283	0.308142	−	0.951340i	$-0.400293\pi$
$883$	18.3131	0.616283	0.308142	+	0.951340i	$0.400293\pi$
$884$	−9.35644	−0.314691
$885$	−3.22297	−0.108339
$886$	−18.2748	−0.613954
$887$	−32.1648	−1.07999	−0.539994	−	0.841669i	$-0.681574\pi$
$887$	−32.1648	−1.07999	−0.539994	+	0.841669i	$0.681574\pi$
$888$	−3.88795	−0.130471
$889$	−6.61096	−0.221725
$890$	−32.1626	−1.07809
$891$	−5.55965	−0.186255
$892$	23.5388	0.788138
$893$	−5.33483	−0.178523
$894$	7.81864	0.261494
$895$	51.1988	1.71139
$896$	0.590237	0.0197184
$897$	−14.7391	−0.492124
$898$	−32.7585	−1.09316
$899$	11.1891	0.373177
$900$	−5.65486	−0.188495
$901$	20.4764	0.682166
$902$	−4.92825	−0.164093
$903$	1.42078	0.0472805
$904$	9.58561	0.318813
$905$	35.1331	1.16786
$906$	15.4635	0.513739
$907$	−20.0049	−0.664251	−0.332125	−	0.943235i	$-0.607766\pi$
$907$	−20.0049	−0.664251	−0.332125	+	0.943235i	$0.607766\pi$
$908$	−22.4844	−0.746172
$909$	29.2326	0.969583
$910$	−3.04443	−0.100922
$911$	−18.5493	−0.614565	−0.307283	−	0.951618i	$-0.599420\pi$
$911$	−18.5493	−0.614565	−0.307283	+	0.951618i	$0.599420\pi$
$912$	−0.851234	−0.0281872
$913$	−8.69896	−0.287893
$914$	−3.45841	−0.114394
$915$	6.71730	0.222067
$916$	14.6615	0.484428
$917$	13.0054	0.429478
$918$	−22.2863	−0.735557
$919$	23.9314	0.789423	0.394711	−	0.918805i	$-0.370845\pi$
$919$	23.9314	0.789423	0.394711	+	0.918805i	$0.370845\pi$
$920$	−25.1274	−0.828424
$921$	−23.7588	−0.782879
$922$	−30.8497	−1.01598
$923$	6.95213	0.228832
$924$	0.929980	0.0305941
$925$	11.3510	0.373220
$926$	−39.7861	−1.30745
$927$	37.1153	1.21903
$928$	5.21129	0.171069
$929$	−27.6684	−0.907770	−0.453885	−	0.891060i	$-0.649962\pi$
$929$	−27.6684	−0.907770	−0.453885	+	0.891060i	$0.649962\pi$
$930$	5.00036	0.163968
$931$	−6.65162	−0.217998
$932$	6.87666	0.225252
$933$	−10.4043	−0.340620
$934$	−4.95261	−0.162054
$935$	−25.1324	−0.821918
$936$	−4.28978	−0.140216
$937$	−30.6488	−1.00125	−0.500626	−	0.865664i	$-0.666897\pi$
$937$	−30.6488	−1.00125	−0.500626	+	0.865664i	$0.666897\pi$
$938$	−2.96637	−0.0968554
$939$	−19.8938	−0.649209
$940$	14.5956	0.476057
$941$	−25.0236	−0.815745	−0.407873	−	0.913039i	$-0.633729\pi$
$941$	−25.0236	−0.815745	−0.407873	+	0.913039i	$0.633729\pi$
$942$	5.84409	0.190411
$943$	24.4534	0.796311
$944$	−1.38390	−0.0450421
$945$	−7.25158	−0.235894
$946$	5.23419	0.170178
$947$	35.9832	1.16930	0.584648	−	0.811287i	$-0.301233\pi$
$947$	35.9832	1.16930	0.584648	+	0.811287i	$0.301233\pi$
$948$	4.49508	0.145993
$949$	−4.41277	−0.143245
$950$	2.48522	0.0806310
$951$	4.29137	0.139157
$952$	−2.92927	−0.0949382
$953$	49.1700	1.59277	0.796386	−	0.604789i	$-0.206743\pi$
$953$	49.1700	1.59277	0.796386	+	0.604789i	$0.206743\pi$
$954$	9.38809	0.303951
$955$	−50.4386	−1.63215
$956$	−13.6353	−0.440998
$957$	8.21094	0.265422
$958$	1.34533	0.0434658
$959$	−7.57661	−0.244662
$960$	2.32890	0.0751650
$961$	−26.3900	−0.851291
$962$	8.61091	0.277627
$963$	33.2506	1.07149
$964$	9.32981	0.300493
$965$	−3.18924	−0.102665
$966$	−4.61445	−0.148467
$967$	27.1270	0.872345	0.436172	−	0.899863i	$-0.356334\pi$
$967$	27.1270	0.872345	0.436172	+	0.899863i	$0.356334\pi$
$968$	−7.57392	−0.243435
$969$	4.22457	0.135713
$970$	−39.9812	−1.28372
$971$	14.3827	0.461564	0.230782	−	0.973006i	$-0.425872\pi$
$971$	14.3827	0.461564	0.230782	+	0.973006i	$0.425872\pi$
$972$	−16.0286	−0.514118
$973$	−7.84429	−0.251476
$974$	−32.4030	−1.03826
$975$	−3.98832	−0.127729
$976$	2.88432	0.0923248
$977$	17.1218	0.547774	0.273887	−	0.961762i	$-0.411691\pi$
$977$	17.1218	0.547774	0.273887	+	0.961762i	$0.411691\pi$
$978$	6.68524	0.213770
$979$	−21.7594	−0.695434
$980$	18.1983	0.581322
$981$	31.2023	0.996211
$982$	3.96106	0.126402
$983$	−14.0672	−0.448675	−0.224338	−	0.974512i	$-0.572022\pi$
$983$	−14.0672	−0.448675	−0.224338	+	0.974512i	$0.572022\pi$
$984$	−2.26643	−0.0722513
$985$	1.26199	0.0402103
$986$	−25.8630	−0.823645
$987$	2.68038	0.0853174
$988$	1.88529	0.0599789
$989$	−25.9714	−0.825843
$990$	−11.5228	−0.366219
$991$	−2.44087	−0.0775367	−0.0387683	−	0.999248i	$-0.512343\pi$
$991$	−2.44087	−0.0775367	−0.0387683	+	0.999248i	$0.512343\pi$
$992$	2.14709	0.0681702
$993$	23.4626	0.744564
$994$	2.17654	0.0690357
$995$	66.3377	2.10305
$996$	−4.00053	−0.126762
$997$	20.7114	0.655936	0.327968	−	0.944689i	$-0.393636\pi$
$997$	20.7114	0.655936	0.327968	+	0.944689i	$0.393636\pi$
$998$	−14.9638	−0.473670
$999$	20.5105	0.648924

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.d.1.14	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.d.1.14	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.851234 q^{3} +1.00000 q^{4} -2.73591 q^{5} -0.851234 q^{6} +0.590237 q^{7} +1.00000 q^{8} -2.27540 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.851234 q^{3} +1.00000 q^{4} -2.73591 q^{5} -0.851234 q^{6} +0.590237 q^{7} +1.00000 q^{8} -2.27540 q^{9} -2.73591 q^{10} -1.85097 q^{11} -0.851234 q^{12} +1.88529 q^{13} +0.590237 q^{14} +2.32890 q^{15} +1.00000 q^{16} -4.96288 q^{17} -2.27540 q^{18} +1.00000 q^{19} -2.73591 q^{20} -0.502429 q^{21} -1.85097 q^{22} +9.18427 q^{23} -0.851234 q^{24} +2.48522 q^{25} +1.88529 q^{26} +4.49060 q^{27} +0.590237 q^{28} +5.21129 q^{29} +2.32890 q^{30} +2.14709 q^{31} +1.00000 q^{32} +1.57561 q^{33} -4.96288 q^{34} -1.61484 q^{35} -2.27540 q^{36} +4.56743 q^{37} +1.00000 q^{38} -1.60482 q^{39} -2.73591 q^{40} +2.66253 q^{41} -0.502429 q^{42} -2.82781 q^{43} -1.85097 q^{44} +6.22530 q^{45} +9.18427 q^{46} -5.33483 q^{47} -0.851234 q^{48} -6.65162 q^{49} +2.48522 q^{50} +4.22457 q^{51} +1.88529 q^{52} -4.12591 q^{53} +4.49060 q^{54} +5.06408 q^{55} +0.590237 q^{56} -0.851234 q^{57} +5.21129 q^{58} -1.38390 q^{59} +2.32890 q^{60} +2.88432 q^{61} +2.14709 q^{62} -1.34302 q^{63} +1.00000 q^{64} -5.15798 q^{65} +1.57561 q^{66} -5.02573 q^{67} -4.96288 q^{68} -7.81796 q^{69} -1.61484 q^{70} +3.68758 q^{71} -2.27540 q^{72} -2.34064 q^{73} +4.56743 q^{74} -2.11550 q^{75} +1.00000 q^{76} -1.09251 q^{77} -1.60482 q^{78} -5.28066 q^{79} -2.73591 q^{80} +3.00365 q^{81} +2.66253 q^{82} +4.69968 q^{83} -0.502429 q^{84} +13.5780 q^{85} -2.82781 q^{86} -4.43603 q^{87} -1.85097 q^{88} +11.7557 q^{89} +6.22530 q^{90} +1.11276 q^{91} +9.18427 q^{92} -1.82768 q^{93} -5.33483 q^{94} -2.73591 q^{95} -0.851234 q^{96} +14.6135 q^{97} -6.65162 q^{98} +4.21169 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9}+O(q^{10}) \) 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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