LMFDB - Embedded newform 6018.2.a.x.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6018,2,Mod(1,6018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6018, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6018 = 2 \cdot 3 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6018.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.0539719364$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} - 34x^{8} + 30x^{7} + 341x^{6} - 276x^{5} - 1032x^{4} + 1176x^{3} + 416x^{2} - 896x + 272 $ x^10 - x^9 - 34x^8 + 30x^7 + 341x^6 - 276x^5 - 1032x^4 + 1176x^3 + 416x^2 - 896x + 272
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$0.931948$ of defining polynomial
Character	$\chi$	$=$	6018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.931948 q^{5} +1.00000 q^{6} -0.903548 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.931948 q^{5} +1.00000 q^{6} -0.903548 q^{7} -1.00000 q^{8} +1.00000 q^{9} -0.931948 q^{10} +3.44244 q^{11} -1.00000 q^{12} -6.04427 q^{13} +0.903548 q^{14} -0.931948 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} -6.86491 q^{19} +0.931948 q^{20} +0.903548 q^{21} -3.44244 q^{22} -0.440114 q^{23} +1.00000 q^{24} -4.13147 q^{25} +6.04427 q^{26} -1.00000 q^{27} -0.903548 q^{28} +4.22964 q^{29} +0.931948 q^{30} -9.99011 q^{31} -1.00000 q^{32} -3.44244 q^{33} -1.00000 q^{34} -0.842060 q^{35} +1.00000 q^{36} +4.29830 q^{37} +6.86491 q^{38} +6.04427 q^{39} -0.931948 q^{40} -7.07710 q^{41} -0.903548 q^{42} +6.87641 q^{43} +3.44244 q^{44} +0.931948 q^{45} +0.440114 q^{46} +8.17149 q^{47} -1.00000 q^{48} -6.18360 q^{49} +4.13147 q^{50} -1.00000 q^{51} -6.04427 q^{52} +3.86874 q^{53} +1.00000 q^{54} +3.20817 q^{55} +0.903548 q^{56} +6.86491 q^{57} -4.22964 q^{58} -1.00000 q^{59} -0.931948 q^{60} +8.73979 q^{61} +9.99011 q^{62} -0.903548 q^{63} +1.00000 q^{64} -5.63295 q^{65} +3.44244 q^{66} +1.38990 q^{67} +1.00000 q^{68} +0.440114 q^{69} +0.842060 q^{70} +1.13450 q^{71} -1.00000 q^{72} +5.84685 q^{73} -4.29830 q^{74} +4.13147 q^{75} -6.86491 q^{76} -3.11041 q^{77} -6.04427 q^{78} +11.4471 q^{79} +0.931948 q^{80} +1.00000 q^{81} +7.07710 q^{82} -12.3636 q^{83} +0.903548 q^{84} +0.931948 q^{85} -6.87641 q^{86} -4.22964 q^{87} -3.44244 q^{88} +2.42895 q^{89} -0.931948 q^{90} +5.46129 q^{91} -0.440114 q^{92} +9.99011 q^{93} -8.17149 q^{94} -6.39773 q^{95} +1.00000 q^{96} +10.3140 q^{97} +6.18360 q^{98} +3.44244 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + q^{5} + 10 q^{6} + 10 q^{7} - 10 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 - 10 * q^3 + 10 * q^4 + q^5 + 10 * q^6 + 10 * q^7 - 10 * q^8 + 10 * q^9	\( 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + q^{5} + 10 q^{6} + 10 q^{7} - 10 q^{8} + 10 q^{9} - q^{10} + 2 q^{11} - 10 q^{12} - 10 q^{14} - q^{15} + 10 q^{16} + 10 q^{17} - 10 q^{18} + 15 q^{19} + q^{20} - 10 q^{21} - 2 q^{22} + 19 q^{23} + 10 q^{24} + 19 q^{25} - 10 q^{27} + 10 q^{28} - q^{29} + q^{30} + 15 q^{31} - 10 q^{32} - 2 q^{33} - 10 q^{34} - 14 q^{35} + 10 q^{36} + q^{37} - 15 q^{38} - q^{40} - 5 q^{41} + 10 q^{42} + 26 q^{43} + 2 q^{44} + q^{45} - 19 q^{46} + 14 q^{47} - 10 q^{48} + 20 q^{49} - 19 q^{50} - 10 q^{51} - 2 q^{53} + 10 q^{54} + 4 q^{55} - 10 q^{56} - 15 q^{57} + q^{58} - 10 q^{59} - q^{60} + 4 q^{61} - 15 q^{62} + 10 q^{63} + 10 q^{64} - 20 q^{65} + 2 q^{66} + 15 q^{67} + 10 q^{68} - 19 q^{69} + 14 q^{70} + 14 q^{71} - 10 q^{72} + 43 q^{73} - q^{74} - 19 q^{75} + 15 q^{76} + 20 q^{77} + q^{80} + 10 q^{81} + 5 q^{82} - 4 q^{83} - 10 q^{84} + q^{85} - 26 q^{86} + q^{87} - 2 q^{88} - 22 q^{89} - q^{90} - q^{91} + 19 q^{92} - 15 q^{93} - 14 q^{94} - 37 q^{95} + 10 q^{96} + 37 q^{97} - 20 q^{98} + 2 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 - 10 * q^3 + 10 * q^4 + q^5 + 10 * q^6 + 10 * q^7 - 10 * q^8 + 10 * q^9 - q^10 + 2 * q^11 - 10 * q^12 - 10 * q^14 - q^15 + 10 * q^16 + 10 * q^17 - 10 * q^18 + 15 * q^19 + q^20 - 10 * q^21 - 2 * q^22 + 19 * q^23 + 10 * q^24 + 19 * q^25 - 10 * q^27 + 10 * q^28 - q^29 + q^30 + 15 * q^31 - 10 * q^32 - 2 * q^33 - 10 * q^34 - 14 * q^35 + 10 * q^36 + q^37 - 15 * q^38 - q^40 - 5 * q^41 + 10 * q^42 + 26 * q^43 + 2 * q^44 + q^45 - 19 * q^46 + 14 * q^47 - 10 * q^48 + 20 * q^49 - 19 * q^50 - 10 * q^51 - 2 * q^53 + 10 * q^54 + 4 * q^55 - 10 * q^56 - 15 * q^57 + q^58 - 10 * q^59 - q^60 + 4 * q^61 - 15 * q^62 + 10 * q^63 + 10 * q^64 - 20 * q^65 + 2 * q^66 + 15 * q^67 + 10 * q^68 - 19 * q^69 + 14 * q^70 + 14 * q^71 - 10 * q^72 + 43 * q^73 - q^74 - 19 * q^75 + 15 * q^76 + 20 * q^77 + q^80 + 10 * q^81 + 5 * q^82 - 4 * q^83 - 10 * q^84 + q^85 - 26 * q^86 + q^87 - 2 * q^88 - 22 * q^89 - q^90 - q^91 + 19 * q^92 - 15 * q^93 - 14 * q^94 - 37 * q^95 + 10 * q^96 + 37 * q^97 - 20 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	0.931948	0.416780	0.208390	−	0.978046i	$-0.433178\pi$
$5$	0.931948	0.416780	0.208390	+	0.978046i	$0.433178\pi$
$6$	1.00000	0.408248
$7$	−0.903548	−0.341509	−0.170755	−	0.985314i	$-0.554621\pi$
$7$	−0.903548	−0.341509	−0.170755	+	0.985314i	$0.554621\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−0.931948	−0.294708
$11$	3.44244	1.03793	0.518967	−	0.854794i	$-0.326317\pi$
$11$	3.44244	1.03793	0.518967	+	0.854794i	$0.326317\pi$
$12$	−1.00000	−0.288675
$13$	−6.04427	−1.67638	−0.838190	−	0.545379i	$-0.816386\pi$
$13$	−6.04427	−1.67638	−0.838190	+	0.545379i	$0.816386\pi$
$14$	0.903548	0.241483
$15$	−0.931948	−0.240628
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.00000	−0.235702
$19$	−6.86491	−1.57492	−0.787459	−	0.616367i	$-0.788604\pi$
$19$	−6.86491	−1.57492	−0.787459	+	0.616367i	$0.788604\pi$
$20$	0.931948	0.208390
$21$	0.903548	0.197170
$22$	−3.44244	−0.733930
$23$	−0.440114	−0.0917700	−0.0458850	−	0.998947i	$-0.514611\pi$
$23$	−0.440114	−0.0917700	−0.0458850	+	0.998947i	$0.514611\pi$
$24$	1.00000	0.204124
$25$	−4.13147	−0.826295
$26$	6.04427	1.18538
$27$	−1.00000	−0.192450
$28$	−0.903548	−0.170755
$29$	4.22964	0.785425	0.392712	−	0.919661i	$-0.371537\pi$
$29$	4.22964	0.785425	0.392712	+	0.919661i	$0.371537\pi$
$30$	0.931948	0.170150
$31$	−9.99011	−1.79428	−0.897138	−	0.441749i	$-0.854358\pi$
$31$	−9.99011	−1.79428	−0.897138	+	0.441749i	$0.854358\pi$
$32$	−1.00000	−0.176777
$33$	−3.44244	−0.599251
$34$	−1.00000	−0.171499
$35$	−0.842060	−0.142334
$36$	1.00000	0.166667
$37$	4.29830	0.706636	0.353318	−	0.935503i	$-0.385053\pi$
$37$	4.29830	0.706636	0.353318	+	0.935503i	$0.385053\pi$
$38$	6.86491	1.11364
$39$	6.04427	0.967858
$40$	−0.931948	−0.147354
$41$	−7.07710	−1.10526	−0.552628	−	0.833428i	$-0.686375\pi$
$41$	−7.07710	−1.10526	−0.552628	+	0.833428i	$0.686375\pi$
$42$	−0.903548	−0.139421
$43$	6.87641	1.04864	0.524321	−	0.851520i	$-0.324319\pi$
$43$	6.87641	1.04864	0.524321	+	0.851520i	$0.324319\pi$
$44$	3.44244	0.518967
$45$	0.931948	0.138927
$46$	0.440114	0.0648912
$47$	8.17149	1.19193	0.595967	−	0.803009i	$-0.296769\pi$
$47$	8.17149	1.19193	0.595967	+	0.803009i	$0.296769\pi$
$48$	−1.00000	−0.144338
$49$	−6.18360	−0.883371
$50$	4.13147	0.584279
$51$	−1.00000	−0.140028
$52$	−6.04427	−0.838190
$53$	3.86874	0.531413	0.265706	−	0.964054i	$-0.414395\pi$
$53$	3.86874	0.531413	0.265706	+	0.964054i	$0.414395\pi$
$54$	1.00000	0.136083
$55$	3.20817	0.432589
$56$	0.903548	0.120742
$57$	6.86491	0.909279
$58$	−4.22964	−0.555379
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−0.931948	−0.120314
$61$	8.73979	1.11902	0.559508	−	0.828825i	$-0.310990\pi$
$61$	8.73979	1.11902	0.559508	+	0.828825i	$0.310990\pi$
$62$	9.99011	1.26875
$63$	−0.903548	−0.113836
$64$	1.00000	0.125000
$65$	−5.63295	−0.698681
$66$	3.44244	0.423735
$67$	1.38990	0.169804	0.0849018	−	0.996389i	$-0.472942\pi$
$67$	1.38990	0.169804	0.0849018	+	0.996389i	$0.472942\pi$
$68$	1.00000	0.121268
$69$	0.440114	0.0529835
$70$	0.842060	0.100645
$71$	1.13450	0.134640	0.0673202	−	0.997731i	$-0.478555\pi$
$71$	1.13450	0.134640	0.0673202	+	0.997731i	$0.478555\pi$
$72$	−1.00000	−0.117851
$73$	5.84685	0.684322	0.342161	−	0.939641i	$-0.388841\pi$
$73$	5.84685	0.684322	0.342161	+	0.939641i	$0.388841\pi$
$74$	−4.29830	−0.499667
$75$	4.13147	0.477062
$76$	−6.86491	−0.787459
$77$	−3.11041	−0.354464
$78$	−6.04427	−0.684379
$79$	11.4471	1.28790	0.643951	−	0.765067i	$-0.277294\pi$
$79$	11.4471	1.28790	0.643951	+	0.765067i	$0.277294\pi$
$80$	0.931948	0.104195
$81$	1.00000	0.111111
$82$	7.07710	0.781534
$83$	−12.3636	−1.35708	−0.678539	−	0.734564i	$-0.737387\pi$
$83$	−12.3636	−1.35708	−0.678539	+	0.734564i	$0.737387\pi$
$84$	0.903548	0.0985852
$85$	0.931948	0.101084
$86$	−6.87641	−0.741502
$87$	−4.22964	−0.453465
$88$	−3.44244	−0.366965
$89$	2.42895	0.257468	0.128734	−	0.991679i	$-0.458909\pi$
$89$	2.42895	0.257468	0.128734	+	0.991679i	$0.458909\pi$
$90$	−0.931948	−0.0982359
$91$	5.46129	0.572499
$92$	−0.440114	−0.0458850
$93$	9.99011	1.03593
$94$	−8.17149	−0.842825
$95$	−6.39773	−0.656394
$96$	1.00000	0.102062
$97$	10.3140	1.04722	0.523612	−	0.851957i	$-0.324584\pi$
$97$	10.3140	1.04722	0.523612	+	0.851957i	$0.324584\pi$
$98$	6.18360	0.624638
$99$	3.44244	0.345978
$100$	−4.13147	−0.413147
$101$	−3.26273	−0.324654	−0.162327	−	0.986737i	$-0.551900\pi$
$101$	−3.26273	−0.324654	−0.162327	+	0.986737i	$0.551900\pi$
$102$	1.00000	0.0990148
$103$	8.91836	0.878753	0.439376	−	0.898303i	$-0.355199\pi$
$103$	8.91836	0.878753	0.439376	+	0.898303i	$0.355199\pi$
$104$	6.04427	0.592690
$105$	0.842060	0.0821766
$106$	−3.86874	−0.375766
$107$	18.4900	1.78749	0.893746	−	0.448573i	$-0.148068\pi$
$107$	18.4900	1.78749	0.893746	+	0.448573i	$0.148068\pi$
$108$	−1.00000	−0.0962250
$109$	−13.7582	−1.31779	−0.658896	−	0.752234i	$-0.728976\pi$
$109$	−13.7582	−1.31779	−0.658896	+	0.752234i	$0.728976\pi$
$110$	−3.20817	−0.305887
$111$	−4.29830	−0.407977
$112$	−0.903548	−0.0853773
$113$	−0.756418	−0.0711578	−0.0355789	−	0.999367i	$-0.511328\pi$
$113$	−0.756418	−0.0711578	−0.0355789	+	0.999367i	$0.511328\pi$
$114$	−6.86491	−0.642958
$115$	−0.410163	−0.0382479
$116$	4.22964	0.392712
$117$	−6.04427	−0.558793
$118$	1.00000	0.0920575
$119$	−0.903548	−0.0828281
$120$	0.931948	0.0850748
$121$	0.850364	0.0773058
$122$	−8.73979	−0.791263
$123$	7.07710	0.638120
$124$	−9.99011	−0.897138
$125$	−8.51005	−0.761162
$126$	0.903548	0.0804945
$127$	2.39787	0.212777	0.106388	−	0.994325i	$-0.466071\pi$
$127$	2.39787	0.212777	0.106388	+	0.994325i	$0.466071\pi$
$128$	−1.00000	−0.0883883
$129$	−6.87641	−0.605434
$130$	5.63295	0.494042
$131$	9.95930	0.870148	0.435074	−	0.900395i	$-0.356722\pi$
$131$	9.95930	0.870148	0.435074	+	0.900395i	$0.356722\pi$
$132$	−3.44244	−0.299626
$133$	6.20278	0.537849
$134$	−1.38990	−0.120069
$135$	−0.931948	−0.0802093
$136$	−1.00000	−0.0857493
$137$	−17.6429	−1.50733	−0.753667	−	0.657256i	$-0.771717\pi$
$137$	−17.6429	−1.50733	−0.753667	+	0.657256i	$0.771717\pi$
$138$	−0.440114	−0.0374650
$139$	14.0824	1.19445	0.597225	−	0.802073i	$-0.296270\pi$
$139$	14.0824	1.19445	0.597225	+	0.802073i	$0.296270\pi$
$140$	−0.842060	−0.0711670
$141$	−8.17149	−0.688164
$142$	−1.13450	−0.0952051
$143$	−20.8070	−1.73997
$144$	1.00000	0.0833333
$145$	3.94180	0.327349
$146$	−5.84685	−0.483889
$147$	6.18360	0.510015
$148$	4.29830	0.353318
$149$	−1.09475	−0.0896858	−0.0448429	−	0.998994i	$-0.514279\pi$
$149$	−1.09475	−0.0896858	−0.0448429	+	0.998994i	$0.514279\pi$
$150$	−4.13147	−0.337333
$151$	11.9700	0.974103	0.487051	−	0.873373i	$-0.338072\pi$
$151$	11.9700	0.974103	0.487051	+	0.873373i	$0.338072\pi$
$152$	6.86491	0.556818
$153$	1.00000	0.0808452
$154$	3.11041	0.250644
$155$	−9.31026	−0.747818
$156$	6.04427	0.483929
$157$	−5.47098	−0.436631	−0.218316	−	0.975878i	$-0.570056\pi$
$157$	−5.47098	−0.436631	−0.218316	+	0.975878i	$0.570056\pi$
$158$	−11.4471	−0.910684
$159$	−3.86874	−0.306811
$160$	−0.931948	−0.0736769
$161$	0.397664	0.0313403
$162$	−1.00000	−0.0785674
$163$	11.5427	0.904091	0.452046	−	0.891995i	$-0.350694\pi$
$163$	11.5427	0.904091	0.452046	+	0.891995i	$0.350694\pi$
$164$	−7.07710	−0.552628
$165$	−3.20817	−0.249756
$166$	12.3636	0.959599
$167$	−19.2458	−1.48928	−0.744641	−	0.667465i	$-0.767379\pi$
$167$	−19.2458	−1.48928	−0.744641	+	0.667465i	$0.767379\pi$
$168$	−0.903548	−0.0697103
$169$	23.5332	1.81025
$170$	−0.931948	−0.0714771
$171$	−6.86491	−0.524973
$172$	6.87641	0.524321
$173$	19.4374	1.47780	0.738901	−	0.673814i	$-0.235345\pi$
$173$	19.4374	1.47780	0.738901	+	0.673814i	$0.235345\pi$
$174$	4.22964	0.320648
$175$	3.73299	0.282187
$176$	3.44244	0.259483
$177$	1.00000	0.0751646
$178$	−2.42895	−0.182058
$179$	8.83310	0.660217	0.330108	−	0.943943i	$-0.392915\pi$
$179$	8.83310	0.660217	0.330108	+	0.943943i	$0.392915\pi$
$180$	0.931948	0.0694633
$181$	19.1010	1.41977	0.709883	−	0.704320i	$-0.248748\pi$
$181$	19.1010	1.41977	0.709883	+	0.704320i	$0.248748\pi$
$182$	−5.46129	−0.404818
$183$	−8.73979	−0.646064
$184$	0.440114	0.0324456
$185$	4.00579	0.294512
$186$	−9.99011	−0.732511
$187$	3.44244	0.251736
$188$	8.17149	0.595967
$189$	0.903548	0.0657235
$190$	6.39773	0.464140
$191$	−18.5916	−1.34524	−0.672619	−	0.739989i	$-0.734831\pi$
$191$	−18.5916	−1.34524	−0.672619	+	0.739989i	$0.734831\pi$
$192$	−1.00000	−0.0721688
$193$	−18.5855	−1.33781	−0.668906	−	0.743347i	$-0.733237\pi$
$193$	−18.5855	−1.33781	−0.668906	+	0.743347i	$0.733237\pi$
$194$	−10.3140	−0.740499
$195$	5.63295	0.403384
$196$	−6.18360	−0.441686
$197$	22.4569	1.59999	0.799993	−	0.600010i	$-0.204837\pi$
$197$	22.4569	1.59999	0.799993	+	0.600010i	$0.204837\pi$
$198$	−3.44244	−0.244643
$199$	13.6326	0.966388	0.483194	−	0.875513i	$-0.339477\pi$
$199$	13.6326	0.966388	0.483194	+	0.875513i	$0.339477\pi$
$200$	4.13147	0.292139
$201$	−1.38990	−0.0980361
$202$	3.26273	0.229565
$203$	−3.82169	−0.268230
$204$	−1.00000	−0.0700140
$205$	−6.59548	−0.460648
$206$	−8.91836	−0.621372
$207$	−0.440114	−0.0305900
$208$	−6.04427	−0.419095
$209$	−23.6320	−1.63466
$210$	−0.842060	−0.0581076
$211$	1.19832	0.0824954	0.0412477	−	0.999149i	$-0.486867\pi$
$211$	1.19832	0.0824954	0.0412477	+	0.999149i	$0.486867\pi$
$212$	3.86874	0.265706
$213$	−1.13450	−0.0777346
$214$	−18.4900	−1.26395
$215$	6.40845	0.437053
$216$	1.00000	0.0680414
$217$	9.02655	0.612762
$218$	13.7582	0.931819
$219$	−5.84685	−0.395093
$220$	3.20817	0.216295
$221$	−6.04427	−0.406582
$222$	4.29830	0.288483
$223$	−16.2758	−1.08991	−0.544954	−	0.838466i	$-0.683453\pi$
$223$	−16.2758	−1.08991	−0.544954	+	0.838466i	$0.683453\pi$
$224$	0.903548	0.0603709
$225$	−4.13147	−0.275432
$226$	0.756418	0.0503162
$227$	−0.976063	−0.0647835	−0.0323918	−	0.999475i	$-0.510312\pi$
$227$	−0.976063	−0.0647835	−0.0323918	+	0.999475i	$0.510312\pi$
$228$	6.86491	0.454640
$229$	−17.5112	−1.15717	−0.578585	−	0.815622i	$-0.696395\pi$
$229$	−17.5112	−1.15717	−0.578585	+	0.815622i	$0.696395\pi$
$230$	0.410163	0.0270453
$231$	3.11041	0.204650
$232$	−4.22964	−0.277690
$233$	5.78400	0.378922	0.189461	−	0.981888i	$-0.439326\pi$
$233$	5.78400	0.378922	0.189461	+	0.981888i	$0.439326\pi$
$234$	6.04427	0.395126
$235$	7.61540	0.496774
$236$	−1.00000	−0.0650945
$237$	−11.4471	−0.743570
$238$	0.903548	0.0585683
$239$	−17.9091	−1.15845	−0.579223	−	0.815169i	$-0.696644\pi$
$239$	−17.9091	−1.15845	−0.579223	+	0.815169i	$0.696644\pi$
$240$	−0.931948	−0.0601570
$241$	−2.68259	−0.172801	−0.0864003	−	0.996261i	$-0.527536\pi$
$241$	−2.68259	−0.172801	−0.0864003	+	0.996261i	$0.527536\pi$
$242$	−0.850364	−0.0546634
$243$	−1.00000	−0.0641500
$244$	8.73979	0.559508
$245$	−5.76279	−0.368171
$246$	−7.07710	−0.451219
$247$	41.4934	2.64016
$248$	9.99011	0.634373
$249$	12.3636	0.783510
$250$	8.51005	0.538223
$251$	5.07005	0.320019	0.160009	−	0.987115i	$-0.448848\pi$
$251$	5.07005	0.320019	0.160009	+	0.987115i	$0.448848\pi$
$252$	−0.903548	−0.0569182
$253$	−1.51506	−0.0952512
$254$	−2.39787	−0.150456
$255$	−0.931948	−0.0583608
$256$	1.00000	0.0625000
$257$	3.79336	0.236623	0.118312	−	0.992977i	$-0.462252\pi$
$257$	3.79336	0.236623	0.118312	+	0.992977i	$0.462252\pi$
$258$	6.87641	0.428107
$259$	−3.88372	−0.241323
$260$	−5.63295	−0.349340
$261$	4.22964	0.261808
$262$	−9.95930	−0.615288
$263$	29.5290	1.82084	0.910419	−	0.413688i	$-0.135760\pi$
$263$	29.5290	1.82084	0.910419	+	0.413688i	$0.135760\pi$
$264$	3.44244	0.211867
$265$	3.60547	0.221482
$266$	−6.20278	−0.380317
$267$	−2.42895	−0.148649
$268$	1.38990	0.0849018
$269$	−3.41252	−0.208065	−0.104033	−	0.994574i	$-0.533175\pi$
$269$	−3.41252	−0.208065	−0.104033	+	0.994574i	$0.533175\pi$
$270$	0.931948	0.0567165
$271$	−11.5819	−0.703550	−0.351775	−	0.936085i	$-0.614422\pi$
$271$	−11.5819	−0.703550	−0.351775	+	0.936085i	$0.614422\pi$
$272$	1.00000	0.0606339
$273$	−5.46129	−0.330533
$274$	17.6429	1.06585
$275$	−14.2223	−0.857639
$276$	0.440114	0.0264917
$277$	−8.58466	−0.515802	−0.257901	−	0.966171i	$-0.583031\pi$
$277$	−8.58466	−0.515802	−0.257901	+	0.966171i	$0.583031\pi$
$278$	−14.0824	−0.844604
$279$	−9.99011	−0.598092
$280$	0.842060	0.0503227
$281$	24.0209	1.43297	0.716484	−	0.697604i	$-0.245750\pi$
$281$	24.0209	1.43297	0.716484	+	0.697604i	$0.245750\pi$
$282$	8.17149	0.486605
$283$	−14.6026	−0.868033	−0.434017	−	0.900905i	$-0.642904\pi$
$283$	−14.6026	−0.868033	−0.434017	+	0.900905i	$0.642904\pi$
$284$	1.13450	0.0673202
$285$	6.39773	0.378969
$286$	20.8070	1.23034
$287$	6.39450	0.377455
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	−3.94180	−0.231471
$291$	−10.3140	−0.604615
$292$	5.84685	0.342161
$293$	−11.3509	−0.663127	−0.331563	−	0.943433i	$-0.607576\pi$
$293$	−11.3509	−0.663127	−0.331563	+	0.943433i	$0.607576\pi$
$294$	−6.18360	−0.360635
$295$	−0.931948	−0.0542601
$296$	−4.29830	−0.249834
$297$	−3.44244	−0.199750
$298$	1.09475	0.0634174
$299$	2.66017	0.153841
$300$	4.13147	0.238531
$301$	−6.21317	−0.358121
$302$	−11.9700	−0.688795
$303$	3.26273	0.187439
$304$	−6.86491	−0.393729
$305$	8.14503	0.466383
$306$	−1.00000	−0.0571662
$307$	25.7665	1.47057	0.735286	−	0.677757i	$-0.237048\pi$
$307$	25.7665	1.47057	0.735286	+	0.677757i	$0.237048\pi$
$308$	−3.11041	−0.177232
$309$	−8.91836	−0.507348
$310$	9.31026	0.528787
$311$	3.62805	0.205728	0.102864	−	0.994695i	$-0.467199\pi$
$311$	3.62805	0.205728	0.102864	+	0.994695i	$0.467199\pi$
$312$	−6.04427	−0.342190
$313$	8.86341	0.500990	0.250495	−	0.968118i	$-0.419407\pi$
$313$	8.86341	0.500990	0.250495	+	0.968118i	$0.419407\pi$
$314$	5.47098	0.308745
$315$	−0.842060	−0.0474447
$316$	11.4471	0.643951
$317$	−4.00925	−0.225182	−0.112591	−	0.993641i	$-0.535915\pi$
$317$	−4.00925	−0.225182	−0.112591	+	0.993641i	$0.535915\pi$
$318$	3.86874	0.216948
$319$	14.5603	0.815218
$320$	0.931948	0.0520974
$321$	−18.4900	−1.03201
$322$	−0.397664	−0.0221609
$323$	−6.86491	−0.381974
$324$	1.00000	0.0555556
$325$	24.9718	1.38518
$326$	−11.5427	−0.639289
$327$	13.7582	0.760827
$328$	7.07710	0.390767
$329$	−7.38334	−0.407057
$330$	3.20817	0.176604
$331$	−22.6588	−1.24544	−0.622719	−	0.782446i	$-0.713972\pi$
$331$	−22.6588	−1.24544	−0.622719	+	0.782446i	$0.713972\pi$
$332$	−12.3636	−0.678539
$333$	4.29830	0.235545
$334$	19.2458	1.05308
$335$	1.29532	0.0707706
$336$	0.903548	0.0492926
$337$	31.7923	1.73184	0.865919	−	0.500184i	$-0.166734\pi$
$337$	31.7923	1.73184	0.865919	+	0.500184i	$0.166734\pi$
$338$	−23.5332	−1.28004
$339$	0.756418	0.0410830
$340$	0.931948	0.0505420
$341$	−34.3903	−1.86234
$342$	6.86491	0.371212
$343$	11.9120	0.643189
$344$	−6.87641	−0.370751
$345$	0.410163	0.0220824
$346$	−19.4374	−1.04496
$347$	25.0582	1.34519	0.672597	−	0.740009i	$-0.265179\pi$
$347$	25.0582	1.34519	0.672597	+	0.740009i	$0.265179\pi$
$348$	−4.22964	−0.226733
$349$	−3.05251	−0.163397	−0.0816985	−	0.996657i	$-0.526034\pi$
$349$	−3.05251	−0.163397	−0.0816985	+	0.996657i	$0.526034\pi$
$350$	−3.73299	−0.199537
$351$	6.04427	0.322619
$352$	−3.44244	−0.183482
$353$	30.5087	1.62382	0.811908	−	0.583785i	$-0.198429\pi$
$353$	30.5087	1.62382	0.811908	+	0.583785i	$0.198429\pi$
$354$	−1.00000	−0.0531494
$355$	1.05729	0.0561153
$356$	2.42895	0.128734
$357$	0.903548	0.0478209
$358$	−8.83310	−0.466844
$359$	6.07942	0.320860	0.160430	−	0.987047i	$-0.448712\pi$
$359$	6.07942	0.320860	0.160430	+	0.987047i	$0.448712\pi$
$360$	−0.931948	−0.0491179
$361$	28.1270	1.48037
$362$	−19.1010	−1.00393
$363$	−0.850364	−0.0446325
$364$	5.46129	0.286250
$365$	5.44896	0.285211
$366$	8.73979	0.456836
$367$	20.4984	1.07001	0.535004	−	0.844849i	$-0.320310\pi$
$367$	20.4984	1.07001	0.535004	+	0.844849i	$0.320310\pi$
$368$	−0.440114	−0.0229425
$369$	−7.07710	−0.368419
$370$	−4.00579	−0.208251
$371$	−3.49560	−0.181482
$372$	9.99011	0.517963
$373$	−19.8492	−1.02775	−0.513877	−	0.857864i	$-0.671791\pi$
$373$	−19.8492	−1.02775	−0.513877	+	0.857864i	$0.671791\pi$
$374$	−3.44244	−0.178004
$375$	8.51005	0.439457
$376$	−8.17149	−0.421413
$377$	−25.5651	−1.31667
$378$	−0.903548	−0.0464735
$379$	−17.5447	−0.901209	−0.450604	−	0.892724i	$-0.648791\pi$
$379$	−17.5447	−0.901209	−0.450604	+	0.892724i	$0.648791\pi$
$380$	−6.39773	−0.328197
$381$	−2.39787	−0.122847
$382$	18.5916	0.951227
$383$	−23.7500	−1.21357	−0.606783	−	0.794867i	$-0.707540\pi$
$383$	−23.7500	−1.21357	−0.606783	+	0.794867i	$0.707540\pi$
$384$	1.00000	0.0510310
$385$	−2.89874	−0.147733
$386$	18.5855	0.945975
$387$	6.87641	0.349548
$388$	10.3140	0.523612
$389$	−13.6646	−0.692821	−0.346411	−	0.938083i	$-0.612600\pi$
$389$	−13.6646	−0.692821	−0.346411	+	0.938083i	$0.612600\pi$
$390$	−5.63295	−0.285235
$391$	−0.440114	−0.0222575
$392$	6.18360	0.312319
$393$	−9.95930	−0.502380
$394$	−22.4569	−1.13136
$395$	10.6681	0.536771
$396$	3.44244	0.172989
$397$	6.33792	0.318091	0.159046	−	0.987271i	$-0.449158\pi$
$397$	6.33792	0.318091	0.159046	+	0.987271i	$0.449158\pi$
$398$	−13.6326	−0.683340
$399$	−6.20278	−0.310527
$400$	−4.13147	−0.206574
$401$	−10.0060	−0.499676	−0.249838	−	0.968288i	$-0.580377\pi$
$401$	−10.0060	−0.499676	−0.249838	+	0.968288i	$0.580377\pi$
$402$	1.38990	0.0693220
$403$	60.3830	3.00789
$404$	−3.26273	−0.162327
$405$	0.931948	0.0463088
$406$	3.82169	0.189667
$407$	14.7966	0.733441
$408$	1.00000	0.0495074
$409$	19.2584	0.952267	0.476134	−	0.879373i	$-0.342038\pi$
$409$	19.2584	0.952267	0.476134	+	0.879373i	$0.342038\pi$
$410$	6.59548	0.325728
$411$	17.6429	0.870260
$412$	8.91836	0.439376
$413$	0.903548	0.0444607
$414$	0.440114	0.0216304
$415$	−11.5222	−0.565603
$416$	6.04427	0.296345
$417$	−14.0824	−0.689616
$418$	23.6320	1.15588
$419$	12.5634	0.613761	0.306881	−	0.951748i	$-0.400715\pi$
$419$	12.5634	0.613761	0.306881	+	0.951748i	$0.400715\pi$
$420$	0.842060	0.0410883
$421$	−21.5266	−1.04914	−0.524571	−	0.851367i	$-0.675774\pi$
$421$	−21.5266	−1.04914	−0.524571	+	0.851367i	$0.675774\pi$
$422$	−1.19832	−0.0583331
$423$	8.17149	0.397312
$424$	−3.86874	−0.187883
$425$	−4.13147	−0.200406
$426$	1.13450	0.0549667
$427$	−7.89682	−0.382154
$428$	18.4900	0.893746
$429$	20.8070	1.00457
$430$	−6.40845	−0.309043
$431$	19.5172	0.940108	0.470054	−	0.882638i	$-0.344234\pi$
$431$	19.5172	0.940108	0.470054	+	0.882638i	$0.344234\pi$
$432$	−1.00000	−0.0481125
$433$	18.6986	0.898595	0.449298	−	0.893382i	$-0.351674\pi$
$433$	18.6986	0.898595	0.449298	+	0.893382i	$0.351674\pi$
$434$	−9.02655	−0.433288
$435$	−3.94180	−0.188995
$436$	−13.7582	−0.658896
$437$	3.02134	0.144530
$438$	5.84685	0.279373
$439$	−31.0232	−1.48066	−0.740328	−	0.672245i	$-0.765330\pi$
$439$	−31.0232	−1.48066	−0.740328	+	0.672245i	$0.765330\pi$
$440$	−3.20817	−0.152943
$441$	−6.18360	−0.294457
$442$	6.04427	0.287497
$443$	10.0095	0.475567	0.237783	−	0.971318i	$-0.423579\pi$
$443$	10.0095	0.475567	0.237783	+	0.971318i	$0.423579\pi$
$444$	−4.29830	−0.203988
$445$	2.26365	0.107308
$446$	16.2758	0.770681
$447$	1.09475	0.0517801
$448$	−0.903548	−0.0426887
$449$	39.1891	1.84945	0.924725	−	0.380637i	$-0.124295\pi$
$449$	39.1891	1.84945	0.924725	+	0.380637i	$0.124295\pi$
$450$	4.13147	0.194760
$451$	−24.3624	−1.14718
$452$	−0.756418	−0.0355789
$453$	−11.9700	−0.562398
$454$	0.976063	0.0458089
$455$	5.08964	0.238606
$456$	−6.86491	−0.321479
$457$	14.8001	0.692317	0.346159	−	0.938176i	$-0.387486\pi$
$457$	14.8001	0.692317	0.346159	+	0.938176i	$0.387486\pi$
$458$	17.5112	0.818243
$459$	−1.00000	−0.0466760
$460$	−0.410163	−0.0191239
$461$	−4.94088	−0.230119	−0.115060	−	0.993359i	$-0.536706\pi$
$461$	−4.94088	−0.230119	−0.115060	+	0.993359i	$0.536706\pi$
$462$	−3.11041	−0.144709
$463$	1.82094	0.0846265	0.0423132	−	0.999104i	$-0.486527\pi$
$463$	1.82094	0.0846265	0.0423132	+	0.999104i	$0.486527\pi$
$464$	4.22964	0.196356
$465$	9.31026	0.431753
$466$	−5.78400	−0.267938
$467$	28.1431	1.30231	0.651153	−	0.758946i	$-0.274286\pi$
$467$	28.1431	1.30231	0.651153	+	0.758946i	$0.274286\pi$
$468$	−6.04427	−0.279397
$469$	−1.25584	−0.0579895
$470$	−7.61540	−0.351272
$471$	5.47098	0.252089
$472$	1.00000	0.0460287
$473$	23.6716	1.08842
$474$	11.4471	0.525784
$475$	28.3622	1.30135
$476$	−0.903548	−0.0414141
$477$	3.86874	0.177138
$478$	17.9091	0.819145
$479$	28.8030	1.31604	0.658021	−	0.753000i	$-0.271394\pi$
$479$	28.8030	1.31604	0.658021	+	0.753000i	$0.271394\pi$
$480$	0.931948	0.0425374
$481$	−25.9801	−1.18459
$482$	2.68259	0.122188
$483$	−0.397664	−0.0180943
$484$	0.850364	0.0386529
$485$	9.61207	0.436461
$486$	1.00000	0.0453609
$487$	−26.2664	−1.19024	−0.595122	−	0.803636i	$-0.702896\pi$
$487$	−26.2664	−1.19024	−0.595122	+	0.803636i	$0.702896\pi$
$488$	−8.73979	−0.395632
$489$	−11.5427	−0.521977
$490$	5.76279	0.260336
$491$	−14.4087	−0.650255	−0.325127	−	0.945670i	$-0.605407\pi$
$491$	−14.4087	−0.650255	−0.325127	+	0.945670i	$0.605407\pi$
$492$	7.07710	0.319060
$493$	4.22964	0.190493
$494$	−41.4934	−1.86688
$495$	3.20817	0.144196
$496$	−9.99011	−0.448569
$497$	−1.02508	−0.0459809
$498$	−12.3636	−0.554025
$499$	31.1672	1.39524	0.697618	−	0.716470i	$-0.254243\pi$
$499$	31.1672	1.39524	0.697618	+	0.716470i	$0.254243\pi$
$500$	−8.51005	−0.380581
$501$	19.2458	0.859837
$502$	−5.07005	−0.226288
$503$	8.96021	0.399516	0.199758	−	0.979845i	$-0.435984\pi$
$503$	8.96021	0.399516	0.199758	+	0.979845i	$0.435984\pi$
$504$	0.903548	0.0402472
$505$	−3.04069	−0.135309
$506$	1.51506	0.0673528
$507$	−23.5332	−1.04515
$508$	2.39787	0.106388
$509$	−5.79222	−0.256736	−0.128368	−	0.991727i	$-0.540974\pi$
$509$	−5.79222	−0.256736	−0.128368	+	0.991727i	$0.540974\pi$
$510$	0.931948	0.0412673
$511$	−5.28291	−0.233702
$512$	−1.00000	−0.0441942
$513$	6.86491	0.303093
$514$	−3.79336	−0.167318
$515$	8.31145	0.366246
$516$	−6.87641	−0.302717
$517$	28.1298	1.23715
$518$	3.88372	0.170641
$519$	−19.4374	−0.853209
$520$	5.63295	0.247021
$521$	−19.5408	−0.856097	−0.428049	−	0.903756i	$-0.640799\pi$
$521$	−19.5408	−0.856097	−0.428049	+	0.903756i	$0.640799\pi$
$522$	−4.22964	−0.185126
$523$	21.0705	0.921348	0.460674	−	0.887570i	$-0.347608\pi$
$523$	21.0705	0.921348	0.460674	+	0.887570i	$0.347608\pi$
$524$	9.95930	0.435074
$525$	−3.73299	−0.162921
$526$	−29.5290	−1.28753
$527$	−9.99011	−0.435176
$528$	−3.44244	−0.149813
$529$	−22.8063	−0.991578
$530$	−3.60547	−0.156611
$531$	−1.00000	−0.0433963
$532$	6.20278	0.268924
$533$	42.7759	1.85283
$534$	2.42895	0.105111
$535$	17.2317	0.744990
$536$	−1.38990	−0.0600346
$537$	−8.83310	−0.381176
$538$	3.41252	0.147124
$539$	−21.2866	−0.916881
$540$	−0.931948	−0.0401046
$541$	−16.9463	−0.728580	−0.364290	−	0.931285i	$-0.618688\pi$
$541$	−16.9463	−0.728580	−0.364290	+	0.931285i	$0.618688\pi$
$542$	11.5819	0.497485
$543$	−19.1010	−0.819702
$544$	−1.00000	−0.0428746
$545$	−12.8219	−0.549229
$546$	5.46129	0.233722
$547$	36.7513	1.57137	0.785685	−	0.618627i	$-0.212311\pi$
$547$	36.7513	1.57137	0.785685	+	0.618627i	$0.212311\pi$
$548$	−17.6429	−0.753667
$549$	8.73979	0.373005
$550$	14.2223	0.606442
$551$	−29.0361	−1.23698
$552$	−0.440114	−0.0187325
$553$	−10.3430	−0.439830
$554$	8.58466	0.364727
$555$	−4.00579	−0.170036
$556$	14.0824	0.597225
$557$	29.4742	1.24886	0.624432	−	0.781079i	$-0.285331\pi$
$557$	29.4742	1.24886	0.624432	+	0.781079i	$0.285331\pi$
$558$	9.99011	0.422915
$559$	−41.5629	−1.75792
$560$	−0.842060	−0.0355835
$561$	−3.44244	−0.145340
$562$	−24.0209	−1.01326
$563$	−18.4703	−0.778431	−0.389216	−	0.921147i	$-0.627254\pi$
$563$	−18.4703	−0.778431	−0.389216	+	0.921147i	$0.627254\pi$
$564$	−8.17149	−0.344082
$565$	−0.704942	−0.0296571
$566$	14.6026	0.613792
$567$	−0.903548	−0.0379455
$568$	−1.13450	−0.0476025
$569$	22.2465	0.932621	0.466311	−	0.884621i	$-0.345583\pi$
$569$	22.2465	0.932621	0.466311	+	0.884621i	$0.345583\pi$
$570$	−6.39773	−0.267972
$571$	−14.0779	−0.589140	−0.294570	−	0.955630i	$-0.595176\pi$
$571$	−14.0779	−0.589140	−0.294570	+	0.955630i	$0.595176\pi$
$572$	−20.8070	−0.869985
$573$	18.5916	0.776673
$574$	−6.39450	−0.266901
$575$	1.81832	0.0758291
$576$	1.00000	0.0416667
$577$	−6.95640	−0.289599	−0.144799	−	0.989461i	$-0.546254\pi$
$577$	−6.95640	−0.289599	−0.144799	+	0.989461i	$0.546254\pi$
$578$	−1.00000	−0.0415945
$579$	18.5855	0.772386
$580$	3.94180	0.163674
$581$	11.1711	0.463455
$582$	10.3140	0.427527
$583$	13.3179	0.551571
$584$	−5.84685	−0.241944
$585$	−5.63295	−0.232894
$586$	11.3509	0.468901
$587$	−23.8683	−0.985150	−0.492575	−	0.870270i	$-0.663944\pi$
$587$	−23.8683	−0.985150	−0.492575	+	0.870270i	$0.663944\pi$
$588$	6.18360	0.255007
$589$	68.5812	2.82584
$590$	0.931948	0.0383677
$591$	−22.4569	−0.923752
$592$	4.29830	0.176659
$593$	−38.9371	−1.59895	−0.799477	−	0.600697i	$-0.794890\pi$
$593$	−38.9371	−1.59895	−0.799477	+	0.600697i	$0.794890\pi$
$594$	3.44244	0.141245
$595$	−0.842060	−0.0345211
$596$	−1.09475	−0.0448429
$597$	−13.6326	−0.557944
$598$	−2.66017	−0.108782
$599$	30.4857	1.24561	0.622805	−	0.782377i	$-0.285993\pi$
$599$	30.4857	1.24561	0.622805	+	0.782377i	$0.285993\pi$
$600$	−4.13147	−0.168667
$601$	−31.2841	−1.27611	−0.638053	−	0.769992i	$-0.720260\pi$
$601$	−31.2841	−1.27611	−0.638053	+	0.769992i	$0.720260\pi$
$602$	6.21317	0.253230
$603$	1.38990	0.0566012
$604$	11.9700	0.487051
$605$	0.792494	0.0322195
$606$	−3.26273	−0.132539
$607$	26.4768	1.07466	0.537330	−	0.843372i	$-0.319433\pi$
$607$	26.4768	1.07466	0.537330	+	0.843372i	$0.319433\pi$
$608$	6.86491	0.278409
$609$	3.82169	0.154863
$610$	−8.14503	−0.329782
$611$	−49.3907	−1.99814
$612$	1.00000	0.0404226
$613$	15.9016	0.642258	0.321129	−	0.947035i	$-0.395938\pi$
$613$	15.9016	0.642258	0.321129	+	0.947035i	$0.395938\pi$
$614$	−25.7665	−1.03985
$615$	6.59548	0.265955
$616$	3.11041	0.125322
$617$	9.87679	0.397624	0.198812	−	0.980038i	$-0.436292\pi$
$617$	9.87679	0.397624	0.198812	+	0.980038i	$0.436292\pi$
$618$	8.91836	0.358749
$619$	17.1220	0.688193	0.344096	−	0.938934i	$-0.388185\pi$
$619$	17.1220	0.688193	0.344096	+	0.938934i	$0.388185\pi$
$620$	−9.31026	−0.373909
$621$	0.440114	0.0176612
$622$	−3.62805	−0.145471
$623$	−2.19467	−0.0879278
$624$	6.04427	0.241965
$625$	12.7264	0.509058
$626$	−8.86341	−0.354253
$627$	23.6320	0.943771
$628$	−5.47098	−0.218316
$629$	4.29830	0.171384
$630$	0.842060	0.0335485
$631$	14.0382	0.558852	0.279426	−	0.960167i	$-0.409856\pi$
$631$	14.0382	0.558852	0.279426	+	0.960167i	$0.409856\pi$
$632$	−11.4471	−0.455342
$633$	−1.19832	−0.0476288
$634$	4.00925	0.159228
$635$	2.23469	0.0886811
$636$	−3.86874	−0.153406
$637$	37.3754	1.48087
$638$	−14.5603	−0.576447
$639$	1.13450	0.0448801
$640$	−0.931948	−0.0368385
$641$	5.72729	0.226214	0.113107	−	0.993583i	$-0.463920\pi$
$641$	5.72729	0.226214	0.113107	+	0.993583i	$0.463920\pi$
$642$	18.4900	0.729741
$643$	12.4340	0.490350	0.245175	−	0.969479i	$-0.421155\pi$
$643$	12.4340	0.490350	0.245175	+	0.969479i	$0.421155\pi$
$644$	0.397664	0.0156702
$645$	−6.40845	−0.252333
$646$	6.86491	0.270096
$647$	25.4536	1.00068	0.500341	−	0.865828i	$-0.333208\pi$
$647$	25.4536	1.00068	0.500341	+	0.865828i	$0.333208\pi$
$648$	−1.00000	−0.0392837
$649$	−3.44244	−0.135127
$650$	−24.9718	−0.979473
$651$	−9.02655	−0.353778
$652$	11.5427	0.452046
$653$	18.8692	0.738408	0.369204	−	0.929348i	$-0.379630\pi$
$653$	18.8692	0.738408	0.369204	+	0.929348i	$0.379630\pi$
$654$	−13.7582	−0.537986
$655$	9.28155	0.362660
$656$	−7.07710	−0.276314
$657$	5.84685	0.228107
$658$	7.38334	0.287833
$659$	−11.7694	−0.458469	−0.229235	−	0.973371i	$-0.573622\pi$
$659$	−11.7694	−0.458469	−0.229235	+	0.973371i	$0.573622\pi$
$660$	−3.20817	−0.124878
$661$	9.78604	0.380633	0.190316	−	0.981723i	$-0.439049\pi$
$661$	9.78604	0.380633	0.190316	+	0.981723i	$0.439049\pi$
$662$	22.6588	0.880658
$663$	6.04427	0.234740
$664$	12.3636	0.479800
$665$	5.78066	0.224164
$666$	−4.29830	−0.166556
$667$	−1.86152	−0.0720784
$668$	−19.2458	−0.744641
$669$	16.2758	0.629259
$670$	−1.29532	−0.0500424
$671$	30.0862	1.16146
$672$	−0.903548	−0.0348551
$673$	18.3158	0.706020	0.353010	−	0.935619i	$-0.385158\pi$
$673$	18.3158	0.706020	0.353010	+	0.935619i	$0.385158\pi$
$674$	−31.7923	−1.22459
$675$	4.13147	0.159021
$676$	23.5332	0.905124
$677$	23.2240	0.892570	0.446285	−	0.894891i	$-0.352747\pi$
$677$	23.2240	0.892570	0.446285	+	0.894891i	$0.352747\pi$
$678$	−0.756418	−0.0290501
$679$	−9.31916	−0.357636
$680$	−0.931948	−0.0357386
$681$	0.976063	0.0374028
$682$	34.3903	1.31687
$683$	−18.4111	−0.704482	−0.352241	−	0.935909i	$-0.614580\pi$
$683$	−18.4111	−0.704482	−0.352241	+	0.935909i	$0.614580\pi$
$684$	−6.86491	−0.262486
$685$	−16.4423	−0.628226
$686$	−11.9120	−0.454803
$687$	17.5112	0.668093
$688$	6.87641	0.262161
$689$	−23.3837	−0.890850
$690$	−0.410163	−0.0156146
$691$	−12.2502	−0.466020	−0.233010	−	0.972474i	$-0.574858\pi$
$691$	−12.2502	−0.466020	−0.233010	+	0.972474i	$0.574858\pi$
$692$	19.4374	0.738901
$693$	−3.11041	−0.118155
$694$	−25.0582	−0.951195
$695$	13.1240	0.497823
$696$	4.22964	0.160324
$697$	−7.07710	−0.268064
$698$	3.05251	0.115539
$699$	−5.78400	−0.218771
$700$	3.73299	0.141094
$701$	11.5069	0.434608	0.217304	−	0.976104i	$-0.430274\pi$
$701$	11.5069	0.434608	0.217304	+	0.976104i	$0.430274\pi$
$702$	−6.04427	−0.228126
$703$	−29.5074	−1.11289
$704$	3.44244	0.129742
$705$	−7.61540	−0.286813
$706$	−30.5087	−1.14821
$707$	2.94803	0.110872
$708$	1.00000	0.0375823
$709$	−22.0739	−0.829002	−0.414501	−	0.910049i	$-0.636044\pi$
$709$	−22.0739	−0.829002	−0.414501	+	0.910049i	$0.636044\pi$
$710$	−1.05729	−0.0396795
$711$	11.4471	0.429301
$712$	−2.42895	−0.0910288
$713$	4.39678	0.164661
$714$	−0.903548	−0.0338145
$715$	−19.3911	−0.725184
$716$	8.83310	0.330108
$717$	17.9091	0.668829
$718$	−6.07942	−0.226882
$719$	34.3660	1.28164	0.640819	−	0.767692i	$-0.278595\pi$
$719$	34.3660	1.28164	0.640819	+	0.767692i	$0.278595\pi$
$720$	0.931948	0.0347316
$721$	−8.05817	−0.300102
$722$	−28.1270	−1.04678
$723$	2.68259	0.0997664
$724$	19.1010	0.709883
$725$	−17.4747	−0.648992
$726$	0.850364	0.0315600
$727$	47.5174	1.76232	0.881162	−	0.472814i	$-0.156762\pi$
$727$	47.5174	1.76232	0.881162	+	0.472814i	$0.156762\pi$
$728$	−5.46129	−0.202409
$729$	1.00000	0.0370370
$730$	−5.44896	−0.201675
$731$	6.87641	0.254333
$732$	−8.73979	−0.323032
$733$	0.340611	0.0125808	0.00629038	−	0.999980i	$-0.497998\pi$
$733$	0.340611	0.0125808	0.00629038	+	0.999980i	$0.497998\pi$
$734$	−20.4984	−0.756610
$735$	5.76279	0.212564
$736$	0.440114	0.0162228
$737$	4.78465	0.176245
$738$	7.07710	0.260511
$739$	−14.8743	−0.547158	−0.273579	−	0.961849i	$-0.588208\pi$
$739$	−14.8743	−0.547158	−0.273579	+	0.961849i	$0.588208\pi$
$740$	4.00579	0.147256
$741$	−41.4934	−1.52430
$742$	3.49560	0.128327
$743$	26.1405	0.959002	0.479501	−	0.877541i	$-0.340818\pi$
$743$	26.1405	0.959002	0.479501	+	0.877541i	$0.340818\pi$
$744$	−9.99011	−0.366255
$745$	−1.02025	−0.0373792
$746$	19.8492	0.726732
$747$	−12.3636	−0.452359
$748$	3.44244	0.125868
$749$	−16.7066	−0.610445
$750$	−8.51005	−0.310743
$751$	49.6424	1.81148	0.905738	−	0.423837i	$-0.139317\pi$
$751$	49.6424	1.81148	0.905738	+	0.423837i	$0.139317\pi$
$752$	8.17149	0.297984
$753$	−5.07005	−0.184763
$754$	25.5651	0.931026
$755$	11.1554	0.405986
$756$	0.903548	0.0328617
$757$	13.8246	0.502464	0.251232	−	0.967927i	$-0.419164\pi$
$757$	13.8246	0.502464	0.251232	+	0.967927i	$0.419164\pi$
$758$	17.5447	0.637251
$759$	1.51506	0.0549933
$760$	6.39773	0.232070
$761$	−31.1983	−1.13094	−0.565469	−	0.824769i	$-0.691305\pi$
$761$	−31.1983	−1.13094	−0.565469	+	0.824769i	$0.691305\pi$
$762$	2.39787	0.0868658
$763$	12.4312	0.450038
$764$	−18.5916	−0.672619
$765$	0.931948	0.0336946
$766$	23.7500	0.858121
$767$	6.04427	0.218246
$768$	−1.00000	−0.0360844
$769$	35.3008	1.27298	0.636491	−	0.771284i	$-0.280385\pi$
$769$	35.3008	1.27298	0.636491	+	0.771284i	$0.280385\pi$
$770$	2.89874	0.104463
$771$	−3.79336	−0.136614
$772$	−18.5855	−0.668906
$773$	−10.1932	−0.366625	−0.183312	−	0.983055i	$-0.558682\pi$
$773$	−10.1932	−0.366625	−0.183312	+	0.983055i	$0.558682\pi$
$774$	−6.87641	−0.247167
$775$	41.2739	1.48260
$776$	−10.3140	−0.370249
$777$	3.88372	0.139328
$778$	13.6646	0.489899
$779$	48.5836	1.74069
$780$	5.63295	0.201692
$781$	3.90544	0.139748
$782$	0.440114	0.0157384
$783$	−4.22964	−0.151155
$784$	−6.18360	−0.220843
$785$	−5.09866	−0.181979
$786$	9.95930	0.355237
$787$	45.2509	1.61302	0.806510	−	0.591221i	$-0.201354\pi$
$787$	45.2509	1.61302	0.806510	+	0.591221i	$0.201354\pi$
$788$	22.4569	0.799993
$789$	−29.5290	−1.05126
$790$	−10.6681	−0.379555
$791$	0.683460	0.0243011
$792$	−3.44244	−0.122322
$793$	−52.8257	−1.87589
$794$	−6.33792	−0.224925
$795$	−3.60547	−0.127873
$796$	13.6326	0.483194
$797$	−48.1426	−1.70530	−0.852649	−	0.522484i	$-0.825005\pi$
$797$	−48.1426	−1.70530	−0.852649	+	0.522484i	$0.825005\pi$
$798$	6.20278	0.219576
$799$	8.17149	0.289087
$800$	4.13147	0.146070
$801$	2.42895	0.0858228
$802$	10.0060	0.353325
$803$	20.1274	0.710281
$804$	−1.38990	−0.0490181
$805$	0.370602	0.0130620
$806$	−60.3830	−2.12690
$807$	3.41252	0.120127
$808$	3.26273	0.114782
$809$	−4.57044	−0.160688	−0.0803440	−	0.996767i	$-0.525602\pi$
$809$	−4.57044	−0.160688	−0.0803440	+	0.996767i	$0.525602\pi$
$810$	−0.931948	−0.0327453
$811$	9.74887	0.342329	0.171165	−	0.985242i	$-0.445247\pi$
$811$	9.74887	0.342329	0.171165	+	0.985242i	$0.445247\pi$
$812$	−3.82169	−0.134115
$813$	11.5819	0.406195
$814$	−14.7966	−0.518621
$815$	10.7572	0.376807
$816$	−1.00000	−0.0350070
$817$	−47.2059	−1.65153
$818$	−19.2584	−0.673355
$819$	5.46129	0.190833
$820$	−6.59548	−0.230324
$821$	18.8932	0.659376	0.329688	−	0.944090i	$-0.393057\pi$
$821$	18.8932	0.659376	0.329688	+	0.944090i	$0.393057\pi$
$822$	−17.6429	−0.615367
$823$	18.0566	0.629412	0.314706	−	0.949189i	$-0.398094\pi$
$823$	18.0566	0.629412	0.314706	+	0.949189i	$0.398094\pi$
$824$	−8.91836	−0.310686
$825$	14.2223	0.495158
$826$	−0.903548	−0.0314385
$827$	−17.8737	−0.621530	−0.310765	−	0.950487i	$-0.600585\pi$
$827$	−17.8737	−0.621530	−0.310765	+	0.950487i	$0.600585\pi$
$828$	−0.440114	−0.0152950
$829$	−48.5062	−1.68469	−0.842346	−	0.538937i	$-0.818826\pi$
$829$	−48.5062	−1.68469	−0.842346	+	0.538937i	$0.818826\pi$
$830$	11.5222	0.399941
$831$	8.58466	0.297798
$832$	−6.04427	−0.209547
$833$	−6.18360	−0.214249
$834$	14.0824	0.487632
$835$	−17.9360	−0.620702
$836$	−23.6320	−0.817330
$837$	9.99011	0.345309
$838$	−12.5634	−0.433995
$839$	44.8772	1.54933	0.774666	−	0.632371i	$-0.217918\pi$
$839$	44.8772	1.54933	0.774666	+	0.632371i	$0.217918\pi$
$840$	−0.842060	−0.0290538
$841$	−11.1101	−0.383108
$842$	21.5266	0.741855
$843$	−24.0209	−0.827324
$844$	1.19832	0.0412477
$845$	21.9317	0.754475
$846$	−8.17149	−0.280942
$847$	−0.768345	−0.0264006
$848$	3.86874	0.132853
$849$	14.6026	0.501159
$850$	4.13147	0.141708
$851$	−1.89174	−0.0648480
$852$	−1.13450	−0.0388673
$853$	9.71948	0.332789	0.166394	−	0.986059i	$-0.446788\pi$
$853$	9.71948	0.332789	0.166394	+	0.986059i	$0.446788\pi$
$854$	7.89682	0.270224
$855$	−6.39773	−0.218798
$856$	−18.4900	−0.631974
$857$	−28.3788	−0.969401	−0.484700	−	0.874680i	$-0.661071\pi$
$857$	−28.3788	−0.969401	−0.484700	+	0.874680i	$0.661071\pi$
$858$	−20.8070	−0.710340
$859$	−54.9910	−1.87627	−0.938134	−	0.346273i	$-0.887447\pi$
$859$	−54.9910	−1.87627	−0.938134	+	0.346273i	$0.887447\pi$
$860$	6.40845	0.218526
$861$	−6.39450	−0.217924
$862$	−19.5172	−0.664757
$863$	22.6115	0.769706	0.384853	−	0.922978i	$-0.374252\pi$
$863$	22.6115	0.769706	0.384853	+	0.922978i	$0.374252\pi$
$864$	1.00000	0.0340207
$865$	18.1147	0.615917
$866$	−18.6986	−0.635403
$867$	−1.00000	−0.0339618
$868$	9.02655	0.306381
$869$	39.4060	1.33676
$870$	3.94180	0.133640
$871$	−8.40095	−0.284655
$872$	13.7582	0.465910
$873$	10.3140	0.349075
$874$	−3.02134	−0.102198
$875$	7.68925	0.259944
$876$	−5.84685	−0.197547
$877$	−19.0688	−0.643907	−0.321954	−	0.946755i	$-0.604340\pi$
$877$	−19.0688	−0.643907	−0.321954	+	0.946755i	$0.604340\pi$
$878$	31.0232	1.04698
$879$	11.3509	0.382856
$880$	3.20817	0.108147
$881$	−53.7455	−1.81073	−0.905367	−	0.424631i	$-0.860404\pi$
$881$	−53.7455	−1.81073	−0.905367	+	0.424631i	$0.860404\pi$
$882$	6.18360	0.208213
$883$	23.6620	0.796289	0.398144	−	0.917323i	$-0.369654\pi$
$883$	23.6620	0.796289	0.398144	+	0.917323i	$0.369654\pi$
$884$	−6.04427	−0.203291
$885$	0.931948	0.0313271
$886$	−10.0095	−0.336277
$887$	51.5824	1.73197	0.865984	−	0.500071i	$-0.166693\pi$
$887$	51.5824	1.73197	0.865984	+	0.500071i	$0.166693\pi$
$888$	4.29830	0.144242
$889$	−2.16660	−0.0726653
$890$	−2.26365	−0.0758779
$891$	3.44244	0.115326
$892$	−16.2758	−0.544954
$893$	−56.0965	−1.87720
$894$	−1.09475	−0.0366141
$895$	8.23198	0.275165
$896$	0.903548	0.0301854
$897$	−2.66017	−0.0888204
$898$	−39.1891	−1.30776
$899$	−42.2546	−1.40927
$900$	−4.13147	−0.137716
$901$	3.86874	0.128887
$902$	24.3624	0.811181
$903$	6.21317	0.206761
$904$	0.756418	0.0251581
$905$	17.8011	0.591729
$906$	11.9700	0.397676
$907$	−32.6268	−1.08335	−0.541677	−	0.840587i	$-0.682210\pi$
$907$	−32.6268	−1.08335	−0.541677	+	0.840587i	$0.682210\pi$
$908$	−0.976063	−0.0323918
$909$	−3.26273	−0.108218
$910$	−5.08964	−0.168720
$911$	1.23331	0.0408614	0.0204307	−	0.999791i	$-0.493496\pi$
$911$	1.23331	0.0408614	0.0204307	+	0.999791i	$0.493496\pi$
$912$	6.86491	0.227320
$913$	−42.5608	−1.40856
$914$	−14.8001	−0.489542
$915$	−8.14503	−0.269266
$916$	−17.5112	−0.578585
$917$	−8.99871	−0.297164
$918$	1.00000	0.0330049
$919$	46.7693	1.54278	0.771388	−	0.636365i	$-0.219563\pi$
$919$	46.7693	1.54278	0.771388	+	0.636365i	$0.219563\pi$
$920$	0.410163	0.0135227
$921$	−25.7665	−0.849035
$922$	4.94088	0.162719
$923$	−6.85722	−0.225708
$924$	3.11041	0.102325
$925$	−17.7583	−0.583890
$926$	−1.82094	−0.0598400
$927$	8.91836	0.292918
$928$	−4.22964	−0.138845
$929$	−9.56555	−0.313835	−0.156918	−	0.987612i	$-0.550156\pi$
$929$	−9.56555	−0.313835	−0.156918	+	0.987612i	$0.550156\pi$
$930$	−9.31026	−0.305295
$931$	42.4498	1.39124
$932$	5.78400	0.189461
$933$	−3.62805	−0.118777
$934$	−28.1431	−0.920870
$935$	3.20817	0.104918
$936$	6.04427	0.197563
$937$	−36.8669	−1.20439	−0.602194	−	0.798350i	$-0.705707\pi$
$937$	−36.8669	−1.20439	−0.602194	+	0.798350i	$0.705707\pi$
$938$	1.25584	0.0410047
$939$	−8.86341	−0.289247
$940$	7.61540	0.248387
$941$	−34.7755	−1.13365	−0.566824	−	0.823839i	$-0.691828\pi$
$941$	−34.7755	−1.13365	−0.566824	+	0.823839i	$0.691828\pi$
$942$	−5.47098	−0.178254
$943$	3.11473	0.101429
$944$	−1.00000	−0.0325472
$945$	0.842060	0.0273922
$946$	−23.6716	−0.769630
$947$	43.9102	1.42689	0.713446	−	0.700711i	$-0.247134\pi$
$947$	43.9102	1.42689	0.713446	+	0.700711i	$0.247134\pi$
$948$	−11.4471	−0.371785
$949$	−35.3399	−1.14718
$950$	−28.3622	−0.920191
$951$	4.00925	0.130009
$952$	0.903548	0.0292842
$953$	−26.4730	−0.857546	−0.428773	−	0.903412i	$-0.641054\pi$
$953$	−26.4730	−0.857546	−0.428773	+	0.903412i	$0.641054\pi$
$954$	−3.86874	−0.125255
$955$	−17.3264	−0.560668
$956$	−17.9091	−0.579223
$957$	−14.5603	−0.470667
$958$	−28.8030	−0.930582
$959$	15.9412	0.514769
$960$	−0.931948	−0.0300785
$961$	68.8023	2.21943
$962$	25.9801	0.837632
$963$	18.4900	0.595831
$964$	−2.68259	−0.0864003
$965$	−17.3207	−0.557572
$966$	0.397664	0.0127946
$967$	−12.4139	−0.399204	−0.199602	−	0.979877i	$-0.563965\pi$
$967$	−12.4139	−0.399204	−0.199602	+	0.979877i	$0.563965\pi$
$968$	−0.850364	−0.0273317
$969$	6.86491	0.220533
$970$	−9.61207	−0.308625
$971$	−18.7646	−0.602183	−0.301092	−	0.953595i	$-0.597351\pi$
$971$	−18.7646	−0.602183	−0.301092	+	0.953595i	$0.597351\pi$
$972$	−1.00000	−0.0320750
$973$	−12.7241	−0.407916
$974$	26.2664	0.841629
$975$	−24.9718	−0.799736
$976$	8.73979	0.279754
$977$	33.6734	1.07731	0.538654	−	0.842527i	$-0.318933\pi$
$977$	33.6734	1.07731	0.538654	+	0.842527i	$0.318933\pi$
$978$	11.5427	0.369094
$979$	8.36151	0.267235
$980$	−5.76279	−0.184086
$981$	−13.7582	−0.439264
$982$	14.4087	0.459799
$983$	−52.5925	−1.67744	−0.838721	−	0.544562i	$-0.816696\pi$
$983$	−52.5925	−1.67744	−0.838721	+	0.544562i	$0.816696\pi$
$984$	−7.07710	−0.225610
$985$	20.9286	0.666841
$986$	−4.22964	−0.134699
$987$	7.38334	0.235014
$988$	41.4934	1.32008
$989$	−3.02640	−0.0962340
$990$	−3.20817	−0.101962
$991$	15.0470	0.477984	0.238992	−	0.971022i	$-0.423183\pi$
$991$	15.0470	0.477984	0.238992	+	0.971022i	$0.423183\pi$
$992$	9.99011	0.317186
$993$	22.6588	0.719054
$994$	1.02508	0.0325134
$995$	12.7049	0.402771
$996$	12.3636	0.391755
$997$	7.97010	0.252416	0.126208	−	0.992004i	$-0.459719\pi$
$997$	7.97010	0.252416	0.126208	+	0.992004i	$0.459719\pi$
$998$	−31.1672	−0.986581
$999$	−4.29830	−0.135992

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.x.1.7	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.x.1.7	✓	10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.931948 q^{5} +1.00000 q^{6} -0.903548 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.931948 q^{5} +1.00000 q^{6} -0.903548 q^{7} -1.00000 q^{8} +1.00000 q^{9} -0.931948 q^{10} +3.44244 q^{11} -1.00000 q^{12} -6.04427 q^{13} +0.903548 q^{14} -0.931948 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} -6.86491 q^{19} +0.931948 q^{20} +0.903548 q^{21} -3.44244 q^{22} -0.440114 q^{23} +1.00000 q^{24} -4.13147 q^{25} +6.04427 q^{26} -1.00000 q^{27} -0.903548 q^{28} +4.22964 q^{29} +0.931948 q^{30} -9.99011 q^{31} -1.00000 q^{32} -3.44244 q^{33} -1.00000 q^{34} -0.842060 q^{35} +1.00000 q^{36} +4.29830 q^{37} +6.86491 q^{38} +6.04427 q^{39} -0.931948 q^{40} -7.07710 q^{41} -0.903548 q^{42} +6.87641 q^{43} +3.44244 q^{44} +0.931948 q^{45} +0.440114 q^{46} +8.17149 q^{47} -1.00000 q^{48} -6.18360 q^{49} +4.13147 q^{50} -1.00000 q^{51} -6.04427 q^{52} +3.86874 q^{53} +1.00000 q^{54} +3.20817 q^{55} +0.903548 q^{56} +6.86491 q^{57} -4.22964 q^{58} -1.00000 q^{59} -0.931948 q^{60} +8.73979 q^{61} +9.99011 q^{62} -0.903548 q^{63} +1.00000 q^{64} -5.63295 q^{65} +3.44244 q^{66} +1.38990 q^{67} +1.00000 q^{68} +0.440114 q^{69} +0.842060 q^{70} +1.13450 q^{71} -1.00000 q^{72} +5.84685 q^{73} -4.29830 q^{74} +4.13147 q^{75} -6.86491 q^{76} -3.11041 q^{77} -6.04427 q^{78} +11.4471 q^{79} +0.931948 q^{80} +1.00000 q^{81} +7.07710 q^{82} -12.3636 q^{83} +0.903548 q^{84} +0.931948 q^{85} -6.87641 q^{86} -4.22964 q^{87} -3.44244 q^{88} +2.42895 q^{89} -0.931948 q^{90} +5.46129 q^{91} -0.440114 q^{92} +9.99011 q^{93} -8.17149 q^{94} -6.39773 q^{95} +1.00000 q^{96} +10.3140 q^{97} +6.18360 q^{98} +3.44244 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + q^{5} + 10 q^{6} + 10 q^{7} - 10 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 - 10 * q^3 + 10 * q^4 + q^5 + 10 * q^6 + 10 * q^7 - 10 * q^8 + 10 * q^9	\( 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + q^{5} + 10 q^{6} + 10 q^{7} - 10 q^{8} + 10 q^{9} - q^{10} + 2 q^{11} - 10 q^{12} - 10 q^{14} - q^{15} + 10 q^{16} + 10 q^{17} - 10 q^{18} + 15 q^{19} + q^{20} - 10 q^{21} - 2 q^{22} + 19 q^{23} + 10 q^{24} + 19 q^{25} - 10 q^{27} + 10 q^{28} - q^{29} + q^{30} + 15 q^{31} - 10 q^{32} - 2 q^{33} - 10 q^{34} - 14 q^{35} + 10 q^{36} + q^{37} - 15 q^{38} - q^{40} - 5 q^{41} + 10 q^{42} + 26 q^{43} + 2 q^{44} + q^{45} - 19 q^{46} + 14 q^{47} - 10 q^{48} + 20 q^{49} - 19 q^{50} - 10 q^{51} - 2 q^{53} + 10 q^{54} + 4 q^{55} - 10 q^{56} - 15 q^{57} + q^{58} - 10 q^{59} - q^{60} + 4 q^{61} - 15 q^{62} + 10 q^{63} + 10 q^{64} - 20 q^{65} + 2 q^{66} + 15 q^{67} + 10 q^{68} - 19 q^{69} + 14 q^{70} + 14 q^{71} - 10 q^{72} + 43 q^{73} - q^{74} - 19 q^{75} + 15 q^{76} + 20 q^{77} + q^{80} + 10 q^{81} + 5 q^{82} - 4 q^{83} - 10 q^{84} + q^{85} - 26 q^{86} + q^{87} - 2 q^{88} - 22 q^{89} - q^{90} - q^{91} + 19 q^{92} - 15 q^{93} - 14 q^{94} - 37 q^{95} + 10 q^{96} + 37 q^{97} - 20 q^{98} + 2 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 - 10 * q^3 + 10 * q^4 + q^5 + 10 * q^6 + 10 * q^7 - 10 * q^8 + 10 * q^9 - q^10 + 2 * q^11 - 10 * q^12 - 10 * q^14 - q^15 + 10 * q^16 + 10 * q^17 - 10 * q^18 + 15 * q^19 + q^20 - 10 * q^21 - 2 * q^22 + 19 * q^23 + 10 * q^24 + 19 * q^25 - 10 * q^27 + 10 * q^28 - q^29 + q^30 + 15 * q^31 - 10 * q^32 - 2 * q^33 - 10 * q^34 - 14 * q^35 + 10 * q^36 + q^37 - 15 * q^38 - q^40 - 5 * q^41 + 10 * q^42 + 26 * q^43 + 2 * q^44 + q^45 - 19 * q^46 + 14 * q^47 - 10 * q^48 + 20 * q^49 - 19 * q^50 - 10 * q^51 - 2 * q^53 + 10 * q^54 + 4 * q^55 - 10 * q^56 - 15 * q^57 + q^58 - 10 * q^59 - q^60 + 4 * q^61 - 15 * q^62 + 10 * q^63 + 10 * q^64 - 20 * q^65 + 2 * q^66 + 15 * q^67 + 10 * q^68 - 19 * q^69 + 14 * q^70 + 14 * q^71 - 10 * q^72 + 43 * q^73 - q^74 - 19 * q^75 + 15 * q^76 + 20 * q^77 + q^80 + 10 * q^81 + 5 * q^82 - 4 * q^83 - 10 * q^84 + q^85 - 26 * q^86 + q^87 - 2 * q^88 - 22 * q^89 - q^90 - q^91 + 19 * q^92 - 15 * q^93 - 14 * q^94 - 37 * q^95 + 10 * q^96 + 37 * q^97 - 20 * q^98 + 2 * q^99

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