LMFDB - Embedded newform 6018.2.a.t.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:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 15x^{6} + 14x^{5} + 84x^{4} + 9x^{3} - 158x^{2} - 142x - 35 $ x^8 - 2x^7 - 15x^6 + 14x^5 + 84x^4 + 9x^3 - 158x^2 - 142*x - 35
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-2.13380$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.28626 q^{5} -1.00000 q^{6} -0.152464 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.28626 q^{5} -1.00000 q^{6} -0.152464 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.28626 q^{10} -4.49525 q^{11} +1.00000 q^{12} +2.76139 q^{13} +0.152464 q^{14} +1.28626 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} +1.11702 q^{19} +1.28626 q^{20} -0.152464 q^{21} +4.49525 q^{22} -5.93243 q^{23} -1.00000 q^{24} -3.34554 q^{25} -2.76139 q^{26} +1.00000 q^{27} -0.152464 q^{28} -5.75495 q^{29} -1.28626 q^{30} +1.89208 q^{31} -1.00000 q^{32} -4.49525 q^{33} -1.00000 q^{34} -0.196108 q^{35} +1.00000 q^{36} -2.00192 q^{37} -1.11702 q^{38} +2.76139 q^{39} -1.28626 q^{40} +9.29671 q^{41} +0.152464 q^{42} +6.20861 q^{43} -4.49525 q^{44} +1.28626 q^{45} +5.93243 q^{46} -8.79418 q^{47} +1.00000 q^{48} -6.97675 q^{49} +3.34554 q^{50} +1.00000 q^{51} +2.76139 q^{52} -12.8177 q^{53} -1.00000 q^{54} -5.78205 q^{55} +0.152464 q^{56} +1.11702 q^{57} +5.75495 q^{58} -1.00000 q^{59} +1.28626 q^{60} +5.20367 q^{61} -1.89208 q^{62} -0.152464 q^{63} +1.00000 q^{64} +3.55186 q^{65} +4.49525 q^{66} -3.55123 q^{67} +1.00000 q^{68} -5.93243 q^{69} +0.196108 q^{70} -10.2703 q^{71} -1.00000 q^{72} +0.304772 q^{73} +2.00192 q^{74} -3.34554 q^{75} +1.11702 q^{76} +0.685362 q^{77} -2.76139 q^{78} -14.0842 q^{79} +1.28626 q^{80} +1.00000 q^{81} -9.29671 q^{82} +6.59375 q^{83} -0.152464 q^{84} +1.28626 q^{85} -6.20861 q^{86} -5.75495 q^{87} +4.49525 q^{88} +8.70904 q^{89} -1.28626 q^{90} -0.421012 q^{91} -5.93243 q^{92} +1.89208 q^{93} +8.79418 q^{94} +1.43677 q^{95} -1.00000 q^{96} +7.20383 q^{97} +6.97675 q^{98} -4.49525 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 8 q^{3} + 8 q^{4} - 6 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 - 6 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^8 + 8 * q^9	\( 8 q - 8 q^{2} + 8 q^{3} + 8 q^{4} - 6 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{8} + 8 q^{9} + 6 q^{10} + q^{11} + 8 q^{12} - 2 q^{13} + 4 q^{14} - 6 q^{15} + 8 q^{16} + 8 q^{17} - 8 q^{18} + 4 q^{19} - 6 q^{20} - 4 q^{21} - q^{22} - 11 q^{23} - 8 q^{24} + 6 q^{25} + 2 q^{26} + 8 q^{27} - 4 q^{28} - 12 q^{29} + 6 q^{30} - 9 q^{31} - 8 q^{32} + q^{33} - 8 q^{34} - 28 q^{35} + 8 q^{36} - 22 q^{37} - 4 q^{38} - 2 q^{39} + 6 q^{40} - 19 q^{41} + 4 q^{42} - 5 q^{43} + q^{44} - 6 q^{45} + 11 q^{46} - 26 q^{47} + 8 q^{48} - 6 q^{50} + 8 q^{51} - 2 q^{52} - 21 q^{53} - 8 q^{54} - 13 q^{55} + 4 q^{56} + 4 q^{57} + 12 q^{58} - 8 q^{59} - 6 q^{60} + 9 q^{61} + 9 q^{62} - 4 q^{63} + 8 q^{64} + 14 q^{65} - q^{66} + 26 q^{67} + 8 q^{68} - 11 q^{69} + 28 q^{70} - 14 q^{71} - 8 q^{72} + 17 q^{73} + 22 q^{74} + 6 q^{75} + 4 q^{76} - 18 q^{77} + 2 q^{78} - 39 q^{79} - 6 q^{80} + 8 q^{81} + 19 q^{82} - 11 q^{83} - 4 q^{84} - 6 q^{85} + 5 q^{86} - 12 q^{87} - q^{88} + 6 q^{90} + 11 q^{91} - 11 q^{92} - 9 q^{93} + 26 q^{94} - 15 q^{95} - 8 q^{96} + 16 q^{97} + q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 - 6 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^8 + 8 * q^9 + 6 * q^10 + q^11 + 8 * q^12 - 2 * q^13 + 4 * q^14 - 6 * q^15 + 8 * q^16 + 8 * q^17 - 8 * q^18 + 4 * q^19 - 6 * q^20 - 4 * q^21 - q^22 - 11 * q^23 - 8 * q^24 + 6 * q^25 + 2 * q^26 + 8 * q^27 - 4 * q^28 - 12 * q^29 + 6 * q^30 - 9 * q^31 - 8 * q^32 + q^33 - 8 * q^34 - 28 * q^35 + 8 * q^36 - 22 * q^37 - 4 * q^38 - 2 * q^39 + 6 * q^40 - 19 * q^41 + 4 * q^42 - 5 * q^43 + q^44 - 6 * q^45 + 11 * q^46 - 26 * q^47 + 8 * q^48 - 6 * q^50 + 8 * q^51 - 2 * q^52 - 21 * q^53 - 8 * q^54 - 13 * q^55 + 4 * q^56 + 4 * q^57 + 12 * q^58 - 8 * q^59 - 6 * q^60 + 9 * q^61 + 9 * q^62 - 4 * q^63 + 8 * q^64 + 14 * q^65 - q^66 + 26 * q^67 + 8 * q^68 - 11 * q^69 + 28 * q^70 - 14 * q^71 - 8 * q^72 + 17 * q^73 + 22 * q^74 + 6 * q^75 + 4 * q^76 - 18 * q^77 + 2 * q^78 - 39 * q^79 - 6 * q^80 + 8 * q^81 + 19 * q^82 - 11 * q^83 - 4 * q^84 - 6 * q^85 + 5 * q^86 - 12 * q^87 - q^88 + 6 * q^90 + 11 * q^91 - 11 * q^92 - 9 * q^93 + 26 * q^94 - 15 * q^95 - 8 * q^96 + 16 * q^97 + 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
$5$	1.28626	0.575232	0.287616	−	0.957746i	$-0.407137\pi$
$5$	1.28626	0.575232	0.287616	+	0.957746i	$0.407137\pi$
$6$	−1.00000	−0.408248
$7$	−0.152464	−0.0576259	−0.0288129	−	0.999585i	$-0.509173\pi$
$7$	−0.152464	−0.0576259	−0.0288129	+	0.999585i	$0.509173\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−1.28626	−0.406751
$11$	−4.49525	−1.35537	−0.677684	−	0.735353i	$-0.737016\pi$
$11$	−4.49525	−1.35537	−0.677684	+	0.735353i	$0.737016\pi$
$12$	1.00000	0.288675
$13$	2.76139	0.765872	0.382936	−	0.923775i	$-0.374913\pi$
$13$	2.76139	0.765872	0.382936	+	0.923775i	$0.374913\pi$
$14$	0.152464	0.0407476
$15$	1.28626	0.332111
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.00000	−0.235702
$19$	1.11702	0.256261	0.128131	−	0.991757i	$-0.459102\pi$
$19$	1.11702	0.256261	0.128131	+	0.991757i	$0.459102\pi$
$20$	1.28626	0.287616
$21$	−0.152464	−0.0332703
$22$	4.49525	0.958390
$23$	−5.93243	−1.23700	−0.618499	−	0.785786i	$-0.712259\pi$
$23$	−5.93243	−1.23700	−0.618499	+	0.785786i	$0.712259\pi$
$24$	−1.00000	−0.204124
$25$	−3.34554	−0.669108
$26$	−2.76139	−0.541553
$27$	1.00000	0.192450
$28$	−0.152464	−0.0288129
$29$	−5.75495	−1.06867	−0.534334	−	0.845273i	$-0.679438\pi$
$29$	−5.75495	−1.06867	−0.534334	+	0.845273i	$0.679438\pi$
$30$	−1.28626	−0.234838
$31$	1.89208	0.339828	0.169914	−	0.985459i	$-0.445651\pi$
$31$	1.89208	0.339828	0.169914	+	0.985459i	$0.445651\pi$
$32$	−1.00000	−0.176777
$33$	−4.49525	−0.782522
$34$	−1.00000	−0.171499
$35$	−0.196108	−0.0331483
$36$	1.00000	0.166667
$37$	−2.00192	−0.329113	−0.164557	−	0.986368i	$-0.552619\pi$
$37$	−2.00192	−0.329113	−0.164557	+	0.986368i	$0.552619\pi$
$38$	−1.11702	−0.181204
$39$	2.76139	0.442177
$40$	−1.28626	−0.203375
$41$	9.29671	1.45190	0.725951	−	0.687747i	$-0.241400\pi$
$41$	9.29671	1.45190	0.725951	+	0.687747i	$0.241400\pi$
$42$	0.152464	0.0235257
$43$	6.20861	0.946805	0.473402	−	0.880846i	$-0.343026\pi$
$43$	6.20861	0.946805	0.473402	+	0.880846i	$0.343026\pi$
$44$	−4.49525	−0.677684
$45$	1.28626	0.191744
$46$	5.93243	0.874690
$47$	−8.79418	−1.28276	−0.641382	−	0.767222i	$-0.721638\pi$
$47$	−8.79418	−1.28276	−0.641382	+	0.767222i	$0.721638\pi$
$48$	1.00000	0.144338
$49$	−6.97675	−0.996679
$50$	3.34554	0.473131
$51$	1.00000	0.140028
$52$	2.76139	0.382936
$53$	−12.8177	−1.76065	−0.880323	−	0.474374i	$-0.842674\pi$
$53$	−12.8177	−1.76065	−0.880323	+	0.474374i	$0.842674\pi$
$54$	−1.00000	−0.136083
$55$	−5.78205	−0.779651
$56$	0.152464	0.0203738
$57$	1.11702	0.147952
$58$	5.75495	0.755662
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	1.28626	0.166055
$61$	5.20367	0.666262	0.333131	−	0.942881i	$-0.391895\pi$
$61$	5.20367	0.666262	0.333131	+	0.942881i	$0.391895\pi$
$62$	−1.89208	−0.240295
$63$	−0.152464	−0.0192086
$64$	1.00000	0.125000
$65$	3.55186	0.440555
$66$	4.49525	0.553327
$67$	−3.55123	−0.433852	−0.216926	−	0.976188i	$-0.569603\pi$
$67$	−3.55123	−0.433852	−0.216926	+	0.976188i	$0.569603\pi$
$68$	1.00000	0.121268
$69$	−5.93243	−0.714181
$70$	0.196108	0.0234394
$71$	−10.2703	−1.21886	−0.609428	−	0.792842i	$-0.708601\pi$
$71$	−10.2703	−1.21886	−0.609428	+	0.792842i	$0.708601\pi$
$72$	−1.00000	−0.117851
$73$	0.304772	0.0356709	0.0178354	−	0.999841i	$-0.494323\pi$
$73$	0.304772	0.0356709	0.0178354	+	0.999841i	$0.494323\pi$
$74$	2.00192	0.232718
$75$	−3.34554	−0.386309
$76$	1.11702	0.128131
$77$	0.685362	0.0781042
$78$	−2.76139	−0.312666
$79$	−14.0842	−1.58459	−0.792296	−	0.610136i	$-0.791115\pi$
$79$	−14.0842	−1.58459	−0.792296	+	0.610136i	$0.791115\pi$
$80$	1.28626	0.143808
$81$	1.00000	0.111111
$82$	−9.29671	−1.02665
$83$	6.59375	0.723759	0.361879	−	0.932225i	$-0.382135\pi$
$83$	6.59375	0.723759	0.361879	+	0.932225i	$0.382135\pi$
$84$	−0.152464	−0.0166352
$85$	1.28626	0.139514
$86$	−6.20861	−0.669492
$87$	−5.75495	−0.616996
$88$	4.49525	0.479195
$89$	8.70904	0.923156	0.461578	−	0.887100i	$-0.347283\pi$
$89$	8.70904	0.923156	0.461578	+	0.887100i	$0.347283\pi$
$90$	−1.28626	−0.135584
$91$	−0.421012	−0.0441341
$92$	−5.93243	−0.618499
$93$	1.89208	0.196200
$94$	8.79418	0.907051
$95$	1.43677	0.147410
$96$	−1.00000	−0.102062
$97$	7.20383	0.731438	0.365719	−	0.930725i	$-0.380823\pi$
$97$	7.20383	0.731438	0.365719	+	0.930725i	$0.380823\pi$
$98$	6.97675	0.704759
$99$	−4.49525	−0.451789
$100$	−3.34554	−0.334554
$101$	−8.19362	−0.815295	−0.407648	−	0.913139i	$-0.633651\pi$
$101$	−8.19362	−0.815295	−0.407648	+	0.913139i	$0.633651\pi$
$102$	−1.00000	−0.0990148
$103$	2.22766	0.219498	0.109749	−	0.993959i	$-0.464995\pi$
$103$	2.22766	0.219498	0.109749	+	0.993959i	$0.464995\pi$
$104$	−2.76139	−0.270777
$105$	−0.196108	−0.0191382
$106$	12.8177	1.24497
$107$	7.84405	0.758313	0.379157	−	0.925333i	$-0.376214\pi$
$107$	7.84405	0.758313	0.379157	+	0.925333i	$0.376214\pi$
$108$	1.00000	0.0962250
$109$	−12.0448	−1.15369	−0.576843	−	0.816855i	$-0.695716\pi$
$109$	−12.0448	−1.15369	−0.576843	+	0.816855i	$0.695716\pi$
$110$	5.78205	0.551297
$111$	−2.00192	−0.190014
$112$	−0.152464	−0.0144065
$113$	1.34733	0.126746	0.0633729	−	0.997990i	$-0.479814\pi$
$113$	1.34733	0.126746	0.0633729	+	0.997990i	$0.479814\pi$
$114$	−1.11702	−0.104618
$115$	−7.63065	−0.711561
$116$	−5.75495	−0.534334
$117$	2.76139	0.255291
$118$	1.00000	0.0920575
$119$	−0.152464	−0.0139763
$120$	−1.28626	−0.117419
$121$	9.20724	0.837022
$122$	−5.20367	−0.471118
$123$	9.29671	0.838256
$124$	1.89208	0.169914
$125$	−10.7345	−0.960125
$126$	0.152464	0.0135825
$127$	9.16362	0.813140	0.406570	−	0.913620i	$-0.366725\pi$
$127$	9.16362	0.813140	0.406570	+	0.913620i	$0.366725\pi$
$128$	−1.00000	−0.0883883
$129$	6.20861	0.546638
$130$	−3.55186	−0.311519
$131$	9.48483	0.828694	0.414347	−	0.910119i	$-0.364010\pi$
$131$	9.48483	0.828694	0.414347	+	0.910119i	$0.364010\pi$
$132$	−4.49525	−0.391261
$133$	−0.170304	−0.0147673
$134$	3.55123	0.306779
$135$	1.28626	0.110704
$136$	−1.00000	−0.0857493
$137$	−3.31919	−0.283577	−0.141789	−	0.989897i	$-0.545285\pi$
$137$	−3.31919	−0.283577	−0.141789	+	0.989897i	$0.545285\pi$
$138$	5.93243	0.505002
$139$	−3.49560	−0.296493	−0.148246	−	0.988950i	$-0.547363\pi$
$139$	−3.49560	−0.296493	−0.148246	+	0.988950i	$0.547363\pi$
$140$	−0.196108	−0.0165741
$141$	−8.79418	−0.740604
$142$	10.2703	0.861861
$143$	−12.4131	−1.03804
$144$	1.00000	0.0833333
$145$	−7.40236	−0.614733
$146$	−0.304772	−0.0252231
$147$	−6.97675	−0.575433
$148$	−2.00192	−0.164557
$149$	−14.7027	−1.20449	−0.602245	−	0.798311i	$-0.705727\pi$
$149$	−14.7027	−1.20449	−0.602245	+	0.798311i	$0.705727\pi$
$150$	3.34554	0.273162
$151$	−14.7941	−1.20392	−0.601962	−	0.798525i	$-0.705614\pi$
$151$	−14.7941	−1.20392	−0.601962	+	0.798525i	$0.705614\pi$
$152$	−1.11702	−0.0906019
$153$	1.00000	0.0808452
$154$	−0.685362	−0.0552280
$155$	2.43371	0.195480
$156$	2.76139	0.221088
$157$	5.94041	0.474096	0.237048	−	0.971498i	$-0.423820\pi$
$157$	5.94041	0.474096	0.237048	+	0.971498i	$0.423820\pi$
$158$	14.0842	1.12048
$159$	−12.8177	−1.01651
$160$	−1.28626	−0.101688
$161$	0.904481	0.0712831
$162$	−1.00000	−0.0785674
$163$	−17.7566	−1.39080	−0.695402	−	0.718621i	$-0.744774\pi$
$163$	−17.7566	−1.39080	−0.695402	+	0.718621i	$0.744774\pi$
$164$	9.29671	0.725951
$165$	−5.78205	−0.450132
$166$	−6.59375	−0.511775
$167$	1.58263	0.122468	0.0612338	−	0.998123i	$-0.480496\pi$
$167$	1.58263	0.122468	0.0612338	+	0.998123i	$0.480496\pi$
$168$	0.152464	0.0117628
$169$	−5.37472	−0.413440
$170$	−1.28626	−0.0986515
$171$	1.11702	0.0854203
$172$	6.20861	0.473402
$173$	−23.5620	−1.79139	−0.895694	−	0.444671i	$-0.853321\pi$
$173$	−23.5620	−1.79139	−0.895694	+	0.444671i	$0.853321\pi$
$174$	5.75495	0.436282
$175$	0.510073	0.0385579
$176$	−4.49525	−0.338842
$177$	−1.00000	−0.0751646
$178$	−8.70904	−0.652770
$179$	3.86457	0.288852	0.144426	−	0.989516i	$-0.453866\pi$
$179$	3.86457	0.288852	0.144426	+	0.989516i	$0.453866\pi$
$180$	1.28626	0.0958721
$181$	17.8876	1.32957	0.664786	−	0.747034i	$-0.268523\pi$
$181$	17.8876	1.32957	0.664786	+	0.747034i	$0.268523\pi$
$182$	0.421012	0.0312075
$183$	5.20367	0.384667
$184$	5.93243	0.437345
$185$	−2.57499	−0.189317
$186$	−1.89208	−0.138734
$187$	−4.49525	−0.328725
$188$	−8.79418	−0.641382
$189$	−0.152464	−0.0110901
$190$	−1.43677	−0.104234
$191$	−1.53872	−0.111338	−0.0556691	−	0.998449i	$-0.517729\pi$
$191$	−1.53872	−0.111338	−0.0556691	+	0.998449i	$0.517729\pi$
$192$	1.00000	0.0721688
$193$	−8.97778	−0.646235	−0.323117	−	0.946359i	$-0.604731\pi$
$193$	−8.97778	−0.646235	−0.323117	+	0.946359i	$0.604731\pi$
$194$	−7.20383	−0.517205
$195$	3.55186	0.254354
$196$	−6.97675	−0.498340
$197$	−14.5269	−1.03500	−0.517498	−	0.855685i	$-0.673136\pi$
$197$	−14.5269	−1.03500	−0.517498	+	0.855685i	$0.673136\pi$
$198$	4.49525	0.319463
$199$	−21.0222	−1.49023	−0.745113	−	0.666938i	$-0.767605\pi$
$199$	−21.0222	−1.49023	−0.745113	+	0.666938i	$0.767605\pi$
$200$	3.34554	0.236565
$201$	−3.55123	−0.250484
$202$	8.19362	0.576501
$203$	0.877422	0.0615829
$204$	1.00000	0.0700140
$205$	11.9580	0.835181
$206$	−2.22766	−0.155208
$207$	−5.93243	−0.412333
$208$	2.76139	0.191468
$209$	−5.02126	−0.347328
$210$	0.196108	0.0135327
$211$	14.9326	1.02800	0.514002	−	0.857789i	$-0.328162\pi$
$211$	14.9326	1.02800	0.514002	+	0.857789i	$0.328162\pi$
$212$	−12.8177	−0.880323
$213$	−10.2703	−0.703706
$214$	−7.84405	−0.536208
$215$	7.98588	0.544633
$216$	−1.00000	−0.0680414
$217$	−0.288474	−0.0195829
$218$	12.0448	0.815779
$219$	0.304772	0.0205946
$220$	−5.78205	−0.389826
$221$	2.76139	0.185751
$222$	2.00192	0.134360
$223$	−14.8699	−0.995759	−0.497880	−	0.867246i	$-0.665888\pi$
$223$	−14.8699	−0.995759	−0.497880	+	0.867246i	$0.665888\pi$
$224$	0.152464	0.0101869
$225$	−3.34554	−0.223036
$226$	−1.34733	−0.0896228
$227$	−26.9014	−1.78551	−0.892754	−	0.450545i	$-0.851230\pi$
$227$	−26.9014	−1.78551	−0.892754	+	0.450545i	$0.851230\pi$
$228$	1.11702	0.0739762
$229$	28.9671	1.91420	0.957099	−	0.289762i	$-0.0935761\pi$
$229$	28.9671	1.91420	0.957099	+	0.289762i	$0.0935761\pi$
$230$	7.63065	0.503150
$231$	0.685362	0.0450935
$232$	5.75495	0.377831
$233$	23.5625	1.54363	0.771815	−	0.635847i	$-0.219349\pi$
$233$	23.5625	1.54363	0.771815	+	0.635847i	$0.219349\pi$
$234$	−2.76139	−0.180518
$235$	−11.3116	−0.737887
$236$	−1.00000	−0.0650945
$237$	−14.0842	−0.914865
$238$	0.152464	0.00988276
$239$	7.12658	0.460980	0.230490	−	0.973075i	$-0.425967\pi$
$239$	7.12658	0.460980	0.230490	+	0.973075i	$0.425967\pi$
$240$	1.28626	0.0830276
$241$	16.2003	1.04355	0.521776	−	0.853083i	$-0.325270\pi$
$241$	16.2003	1.04355	0.521776	+	0.853083i	$0.325270\pi$
$242$	−9.20724	−0.591864
$243$	1.00000	0.0641500
$244$	5.20367	0.333131
$245$	−8.97391	−0.573322
$246$	−9.29671	−0.592736
$247$	3.08452	0.196263
$248$	−1.89208	−0.120147
$249$	6.59375	0.417862
$250$	10.7345	0.678911
$251$	−29.3874	−1.85492	−0.927458	−	0.373928i	$-0.878011\pi$
$251$	−29.3874	−1.85492	−0.927458	+	0.373928i	$0.878011\pi$
$252$	−0.152464	−0.00960431
$253$	26.6678	1.67659
$254$	−9.16362	−0.574977
$255$	1.28626	0.0805486
$256$	1.00000	0.0625000
$257$	−26.2097	−1.63492	−0.817458	−	0.575988i	$-0.804618\pi$
$257$	−26.2097	−1.63492	−0.817458	+	0.575988i	$0.804618\pi$
$258$	−6.20861	−0.386531
$259$	0.305220	0.0189654
$260$	3.55186	0.220277
$261$	−5.75495	−0.356223
$262$	−9.48483	−0.585975
$263$	11.3586	0.700400	0.350200	−	0.936675i	$-0.386114\pi$
$263$	11.3586	0.700400	0.350200	+	0.936675i	$0.386114\pi$
$264$	4.49525	0.276663
$265$	−16.4869	−1.01278
$266$	0.170304	0.0104420
$267$	8.70904	0.532984
$268$	−3.55123	−0.216926
$269$	22.4028	1.36592	0.682960	−	0.730455i	$-0.260692\pi$
$269$	22.4028	1.36592	0.682960	+	0.730455i	$0.260692\pi$
$270$	−1.28626	−0.0782792
$271$	−16.6167	−1.00939	−0.504697	−	0.863297i	$-0.668396\pi$
$271$	−16.6167	−1.00939	−0.504697	+	0.863297i	$0.668396\pi$
$272$	1.00000	0.0606339
$273$	−0.421012	−0.0254808
$274$	3.31919	0.200519
$275$	15.0390	0.906887
$276$	−5.93243	−0.357091
$277$	22.3772	1.34451	0.672257	−	0.740318i	$-0.265325\pi$
$277$	22.3772	1.34451	0.672257	+	0.740318i	$0.265325\pi$
$278$	3.49560	0.209652
$279$	1.89208	0.113276
$280$	0.196108	0.0117197
$281$	23.0121	1.37279	0.686394	−	0.727230i	$-0.259193\pi$
$281$	23.0121	1.37279	0.686394	+	0.727230i	$0.259193\pi$
$282$	8.79418	0.523686
$283$	−27.5121	−1.63542	−0.817712	−	0.575627i	$-0.804758\pi$
$283$	−27.5121	−1.63542	−0.817712	+	0.575627i	$0.804758\pi$
$284$	−10.2703	−0.609428
$285$	1.43677	0.0851070
$286$	12.4131	0.734004
$287$	−1.41741	−0.0836671
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	7.40236	0.434682
$291$	7.20383	0.422296
$292$	0.304772	0.0178354
$293$	9.11672	0.532605	0.266302	−	0.963890i	$-0.414198\pi$
$293$	9.11672	0.532605	0.266302	+	0.963890i	$0.414198\pi$
$294$	6.97675	0.406893
$295$	−1.28626	−0.0748889
$296$	2.00192	0.116359
$297$	−4.49525	−0.260841
$298$	14.7027	0.851703
$299$	−16.3818	−0.947383
$300$	−3.34554	−0.193155
$301$	−0.946588	−0.0545604
$302$	14.7941	0.851303
$303$	−8.19362	−0.470711
$304$	1.11702	0.0640653
$305$	6.69327	0.383255
$306$	−1.00000	−0.0571662
$307$	−18.5738	−1.06006	−0.530031	−	0.847978i	$-0.677820\pi$
$307$	−18.5738	−1.06006	−0.530031	+	0.847978i	$0.677820\pi$
$308$	0.685362	0.0390521
$309$	2.22766	0.126727
$310$	−2.43371	−0.138225
$311$	−4.90015	−0.277862	−0.138931	−	0.990302i	$-0.544367\pi$
$311$	−4.90015	−0.277862	−0.138931	+	0.990302i	$0.544367\pi$
$312$	−2.76139	−0.156333
$313$	7.22211	0.408218	0.204109	−	0.978948i	$-0.434570\pi$
$313$	7.22211	0.408218	0.204109	+	0.978948i	$0.434570\pi$
$314$	−5.94041	−0.335237
$315$	−0.196108	−0.0110494
$316$	−14.0842	−0.792296
$317$	24.8696	1.39681	0.698407	−	0.715701i	$-0.253893\pi$
$317$	24.8696	1.39681	0.698407	+	0.715701i	$0.253893\pi$
$318$	12.8177	0.718781
$319$	25.8699	1.44844
$320$	1.28626	0.0719041
$321$	7.84405	0.437812
$322$	−0.904481	−0.0504048
$323$	1.11702	0.0621524
$324$	1.00000	0.0555556
$325$	−9.23834	−0.512451
$326$	17.7566	0.983447
$327$	−12.0448	−0.666081
$328$	−9.29671	−0.513325
$329$	1.34079	0.0739203
$330$	5.78205	0.318291
$331$	5.04518	0.277308	0.138654	−	0.990341i	$-0.455722\pi$
$331$	5.04518	0.277308	0.138654	+	0.990341i	$0.455722\pi$
$332$	6.59375	0.361879
$333$	−2.00192	−0.109704
$334$	−1.58263	−0.0865977
$335$	−4.56780	−0.249566
$336$	−0.152464	−0.00831758
$337$	27.3020	1.48724	0.743618	−	0.668605i	$-0.233108\pi$
$337$	27.3020	1.48724	0.743618	+	0.668605i	$0.233108\pi$
$338$	5.37472	0.292346
$339$	1.34733	0.0731767
$340$	1.28626	0.0697572
$341$	−8.50538	−0.460592
$342$	−1.11702	−0.0604013
$343$	2.13095	0.115060
$344$	−6.20861	−0.334746
$345$	−7.63065	−0.410820
$346$	23.5620	1.26670
$347$	−9.51129	−0.510593	−0.255296	−	0.966863i	$-0.582173\pi$
$347$	−9.51129	−0.510593	−0.255296	+	0.966863i	$0.582173\pi$
$348$	−5.75495	−0.308498
$349$	24.5246	1.31277	0.656386	−	0.754425i	$-0.272084\pi$
$349$	24.5246	1.31277	0.656386	+	0.754425i	$0.272084\pi$
$350$	−0.510073	−0.0272646
$351$	2.76139	0.147392
$352$	4.49525	0.239597
$353$	10.5939	0.563854	0.281927	−	0.959436i	$-0.409026\pi$
$353$	10.5939	0.563854	0.281927	+	0.959436i	$0.409026\pi$
$354$	1.00000	0.0531494
$355$	−13.2102	−0.701125
$356$	8.70904	0.461578
$357$	−0.152464	−0.00806924
$358$	−3.86457	−0.204249
$359$	11.6613	0.615458	0.307729	−	0.951474i	$-0.400431\pi$
$359$	11.6613	0.615458	0.307729	+	0.951474i	$0.400431\pi$
$360$	−1.28626	−0.0677918
$361$	−17.7523	−0.934330
$362$	−17.8876	−0.940149
$363$	9.20724	0.483255
$364$	−0.421012	−0.0220670
$365$	0.392016	0.0205190
$366$	−5.20367	−0.272000
$367$	30.4417	1.58905	0.794523	−	0.607234i	$-0.207721\pi$
$367$	30.4417	1.58905	0.794523	+	0.607234i	$0.207721\pi$
$368$	−5.93243	−0.309250
$369$	9.29671	0.483967
$370$	2.57499	0.133867
$371$	1.95423	0.101459
$372$	1.89208	0.0981000
$373$	−26.6699	−1.38092	−0.690458	−	0.723372i	$-0.742591\pi$
$373$	−26.6699	−1.38092	−0.690458	+	0.723372i	$0.742591\pi$
$374$	4.49525	0.232444
$375$	−10.7345	−0.554328
$376$	8.79418	0.453525
$377$	−15.8917	−0.818463
$378$	0.152464	0.00784189
$379$	4.34415	0.223144	0.111572	−	0.993756i	$-0.464411\pi$
$379$	4.34415	0.223144	0.111572	+	0.993756i	$0.464411\pi$
$380$	1.43677	0.0737048
$381$	9.16362	0.469467
$382$	1.53872	0.0787280
$383$	−18.2724	−0.933674	−0.466837	−	0.884343i	$-0.654607\pi$
$383$	−18.2724	−0.933674	−0.466837	+	0.884343i	$0.654607\pi$
$384$	−1.00000	−0.0510310
$385$	0.881553	0.0449281
$386$	8.97778	0.456957
$387$	6.20861	0.315602
$388$	7.20383	0.365719
$389$	−12.4799	−0.632758	−0.316379	−	0.948633i	$-0.602467\pi$
$389$	−12.4799	−0.632758	−0.316379	+	0.948633i	$0.602467\pi$
$390$	−3.55186	−0.179856
$391$	−5.93243	−0.300016
$392$	6.97675	0.352379
$393$	9.48483	0.478447
$394$	14.5269	0.731852
$395$	−18.1159	−0.911509
$396$	−4.49525	−0.225895
$397$	37.0725	1.86062	0.930308	−	0.366779i	$-0.119539\pi$
$397$	37.0725	1.86062	0.930308	+	0.366779i	$0.119539\pi$
$398$	21.0222	1.05375
$399$	−0.170304	−0.00852588
$400$	−3.34554	−0.167277
$401$	19.0730	0.952460	0.476230	−	0.879321i	$-0.342003\pi$
$401$	19.0730	0.952460	0.476230	+	0.879321i	$0.342003\pi$
$402$	3.55123	0.177119
$403$	5.22478	0.260265
$404$	−8.19362	−0.407648
$405$	1.28626	0.0639147
$406$	−0.877422	−0.0435457
$407$	8.99912	0.446070
$408$	−1.00000	−0.0495074
$409$	−28.5873	−1.41355	−0.706776	−	0.707437i	$-0.749851\pi$
$409$	−28.5873	−1.41355	−0.706776	+	0.707437i	$0.749851\pi$
$410$	−11.9580	−0.590562
$411$	−3.31919	−0.163723
$412$	2.22766	0.109749
$413$	0.152464	0.00750225
$414$	5.93243	0.291563
$415$	8.48127	0.416329
$416$	−2.76139	−0.135388
$417$	−3.49560	−0.171180
$418$	5.02126	0.245598
$419$	−3.34311	−0.163322	−0.0816609	−	0.996660i	$-0.526022\pi$
$419$	−3.34311	−0.163322	−0.0816609	+	0.996660i	$0.526022\pi$
$420$	−0.196108	−0.00956908
$421$	−27.7489	−1.35240	−0.676200	−	0.736718i	$-0.736374\pi$
$421$	−27.7489	−1.35240	−0.676200	+	0.736718i	$0.736374\pi$
$422$	−14.9326	−0.726909
$423$	−8.79418	−0.427588
$424$	12.8177	0.622483
$425$	−3.34554	−0.162282
$426$	10.2703	0.497596
$427$	−0.793371	−0.0383939
$428$	7.84405	0.379157
$429$	−12.4131	−0.599312
$430$	−7.98588	−0.385113
$431$	−23.5575	−1.13472	−0.567361	−	0.823469i	$-0.692036\pi$
$431$	−23.5575	−1.13472	−0.567361	+	0.823469i	$0.692036\pi$
$432$	1.00000	0.0481125
$433$	38.1391	1.83285	0.916425	−	0.400207i	$-0.131062\pi$
$433$	38.1391	1.83285	0.916425	+	0.400207i	$0.131062\pi$
$434$	0.288474	0.0138472
$435$	−7.40236	−0.354916
$436$	−12.0448	−0.576843
$437$	−6.62662	−0.316994
$438$	−0.304772	−0.0145626
$439$	29.8634	1.42530	0.712651	−	0.701518i	$-0.247494\pi$
$439$	29.8634	1.42530	0.712651	+	0.701518i	$0.247494\pi$
$440$	5.78205	0.275648
$441$	−6.97675	−0.332226
$442$	−2.76139	−0.131346
$443$	−15.1765	−0.721058	−0.360529	−	0.932748i	$-0.617404\pi$
$443$	−15.1765	−0.721058	−0.360529	+	0.932748i	$0.617404\pi$
$444$	−2.00192	−0.0950068
$445$	11.2021	0.531029
$446$	14.8699	0.704108
$447$	−14.7027	−0.695413
$448$	−0.152464	−0.00720323
$449$	−8.24532	−0.389121	−0.194560	−	0.980891i	$-0.562328\pi$
$449$	−8.24532	−0.389121	−0.194560	+	0.980891i	$0.562328\pi$
$450$	3.34554	0.157710
$451$	−41.7910	−1.96786
$452$	1.34733	0.0633729
$453$	−14.7941	−0.695086
$454$	26.9014	1.26254
$455$	−0.541530	−0.0253873
$456$	−1.11702	−0.0523091
$457$	−31.1186	−1.45567	−0.727833	−	0.685754i	$-0.759473\pi$
$457$	−31.1186	−1.45567	−0.727833	+	0.685754i	$0.759473\pi$
$458$	−28.9671	−1.35354
$459$	1.00000	0.0466760
$460$	−7.63065	−0.355781
$461$	−12.8218	−0.597169	−0.298584	−	0.954383i	$-0.596514\pi$
$461$	−12.8218	−0.597169	−0.298584	+	0.954383i	$0.596514\pi$
$462$	−0.685362	−0.0318859
$463$	23.7188	1.10230	0.551152	−	0.834405i	$-0.314188\pi$
$463$	23.7188	1.10230	0.551152	+	0.834405i	$0.314188\pi$
$464$	−5.75495	−0.267167
$465$	2.43371	0.112861
$466$	−23.5625	−1.09151
$467$	−34.1015	−1.57803	−0.789015	−	0.614374i	$-0.789409\pi$
$467$	−34.1015	−1.57803	−0.789015	+	0.614374i	$0.789409\pi$
$468$	2.76139	0.127645
$469$	0.541434	0.0250011
$470$	11.3116	0.521765
$471$	5.94041	0.273720
$472$	1.00000	0.0460287
$473$	−27.9092	−1.28327
$474$	14.0842	0.646907
$475$	−3.73702	−0.171466
$476$	−0.152464	−0.00698816
$477$	−12.8177	−0.586882
$478$	−7.12658	−0.325962
$479$	6.87279	0.314026	0.157013	−	0.987597i	$-0.449814\pi$
$479$	6.87279	0.314026	0.157013	+	0.987597i	$0.449814\pi$
$480$	−1.28626	−0.0587094
$481$	−5.52808	−0.252059
$482$	−16.2003	−0.737903
$483$	0.904481	0.0411553
$484$	9.20724	0.418511
$485$	9.26599	0.420747
$486$	−1.00000	−0.0453609
$487$	−41.9802	−1.90230	−0.951152	−	0.308723i	$-0.900098\pi$
$487$	−41.9802	−1.90230	−0.951152	+	0.308723i	$0.900098\pi$
$488$	−5.20367	−0.235559
$489$	−17.7566	−0.802981
$490$	8.97391	0.405400
$491$	−2.60497	−0.117560	−0.0587802	−	0.998271i	$-0.518721\pi$
$491$	−2.60497	−0.117560	−0.0587802	+	0.998271i	$0.518721\pi$
$492$	9.29671	0.419128
$493$	−5.75495	−0.259190
$494$	−3.08452	−0.138779
$495$	−5.78205	−0.259884
$496$	1.89208	0.0849571
$497$	1.56584	0.0702376
$498$	−6.59375	−0.295473
$499$	−27.6986	−1.23996	−0.619979	−	0.784618i	$-0.712859\pi$
$499$	−27.6986	−1.23996	−0.619979	+	0.784618i	$0.712859\pi$
$500$	−10.7345	−0.480062
$501$	1.58263	0.0707067
$502$	29.3874	1.31162
$503$	−25.2639	−1.12646	−0.563230	−	0.826300i	$-0.690442\pi$
$503$	−25.2639	−1.12646	−0.563230	+	0.826300i	$0.690442\pi$
$504$	0.152464	0.00679127
$505$	−10.5391	−0.468984
$506$	−26.6678	−1.18553
$507$	−5.37472	−0.238699
$508$	9.16362	0.406570
$509$	−1.86093	−0.0824845	−0.0412422	−	0.999149i	$-0.513132\pi$
$509$	−1.86093	−0.0824845	−0.0412422	+	0.999149i	$0.513132\pi$
$510$	−1.28626	−0.0569565
$511$	−0.0464667	−0.00205556
$512$	−1.00000	−0.0441942
$513$	1.11702	0.0493175
$514$	26.2097	1.15606
$515$	2.86535	0.126262
$516$	6.20861	0.273319
$517$	39.5320	1.73862
$518$	−0.305220	−0.0134106
$519$	−23.5620	−1.03426
$520$	−3.55186	−0.155760
$521$	−43.8667	−1.92184	−0.960918	−	0.276834i	$-0.910715\pi$
$521$	−43.8667	−1.92184	−0.960918	+	0.276834i	$0.910715\pi$
$522$	5.75495	0.251887
$523$	11.9220	0.521312	0.260656	−	0.965432i	$-0.416061\pi$
$523$	11.9220	0.521312	0.260656	+	0.965432i	$0.416061\pi$
$524$	9.48483	0.414347
$525$	0.510073	0.0222614
$526$	−11.3586	−0.495257
$527$	1.89208	0.0824205
$528$	−4.49525	−0.195630
$529$	12.1938	0.530164
$530$	16.4869	0.716144
$531$	−1.00000	−0.0433963
$532$	−0.170304	−0.00738363
$533$	25.6719	1.11197
$534$	−8.70904	−0.376877
$535$	10.0895	0.436206
$536$	3.55123	0.153390
$537$	3.86457	0.166769
$538$	−22.4028	−0.965852
$539$	31.3622	1.35087
$540$	1.28626	0.0553518
$541$	16.5843	0.713014	0.356507	−	0.934293i	$-0.383968\pi$
$541$	16.5843	0.713014	0.356507	+	0.934293i	$0.383968\pi$
$542$	16.6167	0.713749
$543$	17.8876	0.767628
$544$	−1.00000	−0.0428746
$545$	−15.4928	−0.663638
$546$	0.421012	0.0180177
$547$	43.6931	1.86818	0.934091	−	0.357034i	$-0.116212\pi$
$547$	43.6931	1.86818	0.934091	+	0.357034i	$0.116212\pi$
$548$	−3.31919	−0.141789
$549$	5.20367	0.222087
$550$	−15.0390	−0.641266
$551$	−6.42837	−0.273858
$552$	5.93243	0.252501
$553$	2.14732	0.0913135
$554$	−22.3772	−0.950715
$555$	−2.57499	−0.109302
$556$	−3.49560	−0.148246
$557$	−41.0431	−1.73905	−0.869526	−	0.493888i	$-0.835575\pi$
$557$	−41.0431	−1.73905	−0.869526	+	0.493888i	$0.835575\pi$
$558$	−1.89208	−0.0800983
$559$	17.1444	0.725131
$560$	−0.196108	−0.00828707
$561$	−4.49525	−0.189789
$562$	−23.0121	−0.970708
$563$	28.7951	1.21357	0.606785	−	0.794866i	$-0.292459\pi$
$563$	28.7951	1.21357	0.606785	+	0.794866i	$0.292459\pi$
$564$	−8.79418	−0.370302
$565$	1.73301	0.0729082
$566$	27.5121	1.15642
$567$	−0.152464	−0.00640287
$568$	10.2703	0.430930
$569$	17.3124	0.725773	0.362887	−	0.931833i	$-0.381791\pi$
$569$	17.3124	0.725773	0.362887	+	0.931833i	$0.381791\pi$
$570$	−1.43677	−0.0601797
$571$	−7.58918	−0.317597	−0.158799	−	0.987311i	$-0.550762\pi$
$571$	−7.58918	−0.317597	−0.158799	+	0.987311i	$0.550762\pi$
$572$	−12.4131	−0.519019
$573$	−1.53872	−0.0642811
$574$	1.41741	0.0591616
$575$	19.8472	0.827685
$576$	1.00000	0.0416667
$577$	−14.0247	−0.583856	−0.291928	−	0.956440i	$-0.594297\pi$
$577$	−14.0247	−0.583856	−0.291928	+	0.956440i	$0.594297\pi$
$578$	−1.00000	−0.0415945
$579$	−8.97778	−0.373104
$580$	−7.40236	−0.307366
$581$	−1.00531	−0.0417072
$582$	−7.20383	−0.298608
$583$	57.6187	2.38632
$584$	−0.304772	−0.0126116
$585$	3.55186	0.146852
$586$	−9.11672	−0.376608
$587$	−7.61162	−0.314165	−0.157083	−	0.987585i	$-0.550209\pi$
$587$	−7.61162	−0.314165	−0.157083	+	0.987585i	$0.550209\pi$
$588$	−6.97675	−0.287717
$589$	2.11349	0.0870847
$590$	1.28626	0.0529544
$591$	−14.5269	−0.597555
$592$	−2.00192	−0.0822783
$593$	−37.1012	−1.52356	−0.761782	−	0.647833i	$-0.775675\pi$
$593$	−37.1012	−1.52356	−0.761782	+	0.647833i	$0.775675\pi$
$594$	4.49525	0.184442
$595$	−0.196108	−0.00803964
$596$	−14.7027	−0.602245
$597$	−21.0222	−0.860383
$598$	16.3818	0.669901
$599$	−13.8415	−0.565550	−0.282775	−	0.959186i	$-0.591255\pi$
$599$	−13.8415	−0.565550	−0.282775	+	0.959186i	$0.591255\pi$
$600$	3.34554	0.136581
$601$	12.6122	0.514464	0.257232	−	0.966350i	$-0.417189\pi$
$601$	12.6122	0.514464	0.257232	+	0.966350i	$0.417189\pi$
$602$	0.946588	0.0385801
$603$	−3.55123	−0.144617
$604$	−14.7941	−0.601962
$605$	11.8429	0.481482
$606$	8.19362	0.332843
$607$	15.5374	0.630644	0.315322	−	0.948985i	$-0.397887\pi$
$607$	15.5374	0.630644	0.315322	+	0.948985i	$0.397887\pi$
$608$	−1.11702	−0.0453010
$609$	0.877422	0.0355549
$610$	−6.69327	−0.271003
$611$	−24.2842	−0.982433
$612$	1.00000	0.0404226
$613$	−14.7229	−0.594652	−0.297326	−	0.954776i	$-0.596095\pi$
$613$	−14.7229	−0.594652	−0.297326	+	0.954776i	$0.596095\pi$
$614$	18.5738	0.749578
$615$	11.9580	0.482192
$616$	−0.685362	−0.0276140
$617$	40.1984	1.61833	0.809164	−	0.587583i	$-0.199920\pi$
$617$	40.1984	1.61833	0.809164	+	0.587583i	$0.199920\pi$
$618$	−2.22766	−0.0896096
$619$	13.3060	0.534815	0.267408	−	0.963584i	$-0.413833\pi$
$619$	13.3060	0.534815	0.267408	+	0.963584i	$0.413833\pi$
$620$	2.43371	0.0977401
$621$	−5.93243	−0.238060
$622$	4.90015	0.196478
$623$	−1.32781	−0.0531977
$624$	2.76139	0.110544
$625$	2.92032	0.116813
$626$	−7.22211	−0.288654
$627$	−5.02126	−0.200530
$628$	5.94041	0.237048
$629$	−2.00192	−0.0798217
$630$	0.196108	0.00781312
$631$	−33.2545	−1.32384	−0.661919	−	0.749575i	$-0.730258\pi$
$631$	−33.2545	−1.32384	−0.661919	+	0.749575i	$0.730258\pi$
$632$	14.0842	0.560238
$633$	14.9326	0.593518
$634$	−24.8696	−0.987696
$635$	11.7868	0.467745
$636$	−12.8177	−0.508255
$637$	−19.2656	−0.763329
$638$	−25.8699	−1.02420
$639$	−10.2703	−0.406285
$640$	−1.28626	−0.0508438
$641$	2.63266	0.103984	0.0519918	−	0.998648i	$-0.483443\pi$
$641$	2.63266	0.103984	0.0519918	+	0.998648i	$0.483443\pi$
$642$	−7.84405	−0.309580
$643$	−38.2406	−1.50806	−0.754032	−	0.656838i	$-0.771894\pi$
$643$	−38.2406	−1.50806	−0.754032	+	0.656838i	$0.771894\pi$
$644$	0.904481	0.0356415
$645$	7.98588	0.314444
$646$	−1.11702	−0.0439484
$647$	43.6607	1.71648	0.858239	−	0.513250i	$-0.171559\pi$
$647$	43.6607	1.71648	0.858239	+	0.513250i	$0.171559\pi$
$648$	−1.00000	−0.0392837
$649$	4.49525	0.176454
$650$	9.23834	0.362358
$651$	−0.288474	−0.0113062
$652$	−17.7566	−0.695402
$653$	39.1582	1.53238	0.766189	−	0.642615i	$-0.222151\pi$
$653$	39.1582	1.53238	0.766189	+	0.642615i	$0.222151\pi$
$654$	12.0448	0.470991
$655$	12.1999	0.476691
$656$	9.29671	0.362975
$657$	0.304772	0.0118903
$658$	−1.34079	−0.0522696
$659$	−27.6248	−1.07611	−0.538054	−	0.842910i	$-0.680840\pi$
$659$	−27.6248	−1.07611	−0.538054	+	0.842910i	$0.680840\pi$
$660$	−5.78205	−0.225066
$661$	0.103194	0.00401380	0.00200690	−	0.999998i	$-0.499361\pi$
$661$	0.103194	0.00401380	0.00200690	+	0.999998i	$0.499361\pi$
$662$	−5.04518	−0.196087
$663$	2.76139	0.107244
$664$	−6.59375	−0.255887
$665$	−0.219056	−0.00849461
$666$	2.00192	0.0775728
$667$	34.1409	1.32194
$668$	1.58263	0.0612338
$669$	−14.8699	−0.574902
$670$	4.56780	0.176469
$671$	−23.3918	−0.903030
$672$	0.152464	0.00588142
$673$	−30.4959	−1.17553	−0.587766	−	0.809031i	$-0.699992\pi$
$673$	−30.4959	−1.17553	−0.587766	+	0.809031i	$0.699992\pi$
$674$	−27.3020	−1.05163
$675$	−3.34554	−0.128770
$676$	−5.37472	−0.206720
$677$	−50.0622	−1.92405	−0.962023	−	0.272967i	$-0.911995\pi$
$677$	−50.0622	−1.92405	−0.962023	+	0.272967i	$0.911995\pi$
$678$	−1.34733	−0.0517437
$679$	−1.09832	−0.0421497
$680$	−1.28626	−0.0493258
$681$	−26.9014	−1.03086
$682$	8.50538	0.325688
$683$	13.1163	0.501883	0.250941	−	0.968002i	$-0.419260\pi$
$683$	13.1163	0.501883	0.250941	+	0.968002i	$0.419260\pi$
$684$	1.11702	0.0427102
$685$	−4.26933	−0.163123
$686$	−2.13095	−0.0813600
$687$	28.9671	1.10516
$688$	6.20861	0.236701
$689$	−35.3947	−1.34843
$690$	7.63065	0.290494
$691$	12.3010	0.467953	0.233976	−	0.972242i	$-0.424826\pi$
$691$	12.3010	0.467953	0.233976	+	0.972242i	$0.424826\pi$
$692$	−23.5620	−0.895694
$693$	0.685362	0.0260347
$694$	9.51129	0.361043
$695$	−4.49625	−0.170552
$696$	5.75495	0.218141
$697$	9.29671	0.352138
$698$	−24.5246	−0.928271
$699$	23.5625	0.891215
$700$	0.510073	0.0192790
$701$	−32.2388	−1.21764	−0.608822	−	0.793307i	$-0.708358\pi$
$701$	−32.2388	−1.21764	−0.608822	+	0.793307i	$0.708358\pi$
$702$	−2.76139	−0.104222
$703$	−2.23617	−0.0843389
$704$	−4.49525	−0.169421
$705$	−11.3116	−0.426019
$706$	−10.5939	−0.398705
$707$	1.24923	0.0469821
$708$	−1.00000	−0.0375823
$709$	−24.0042	−0.901496	−0.450748	−	0.892651i	$-0.648843\pi$
$709$	−24.0042	−0.901496	−0.450748	+	0.892651i	$0.648843\pi$
$710$	13.2102	0.495770
$711$	−14.0842	−0.528198
$712$	−8.70904	−0.326385
$713$	−11.2247	−0.420367
$714$	0.152464	0.00570581
$715$	−15.9665	−0.597113
$716$	3.86457	0.144426
$717$	7.12658	0.266147
$718$	−11.6613	−0.435195
$719$	−3.63955	−0.135732	−0.0678661	−	0.997694i	$-0.521619\pi$
$719$	−3.63955	−0.135732	−0.0678661	+	0.997694i	$0.521619\pi$
$720$	1.28626	0.0479360
$721$	−0.339637	−0.0126488
$722$	17.7523	0.660671
$723$	16.2003	0.602495
$724$	17.8876	0.664786
$725$	19.2534	0.715054
$726$	−9.20724	−0.341713
$727$	−10.9051	−0.404446	−0.202223	−	0.979339i	$-0.564817\pi$
$727$	−10.9051	−0.404446	−0.202223	+	0.979339i	$0.564817\pi$
$728$	0.421012	0.0156037
$729$	1.00000	0.0370370
$730$	−0.392016	−0.0145092
$731$	6.20861	0.229634
$732$	5.20367	0.192333
$733$	−10.6067	−0.391766	−0.195883	−	0.980627i	$-0.562757\pi$
$733$	−10.6067	−0.391766	−0.195883	+	0.980627i	$0.562757\pi$
$734$	−30.4417	−1.12363
$735$	−8.97391	−0.331008
$736$	5.93243	0.218672
$737$	15.9636	0.588029
$738$	−9.29671	−0.342217
$739$	45.2169	1.66333	0.831665	−	0.555278i	$-0.187388\pi$
$739$	45.2169	1.66333	0.831665	+	0.555278i	$0.187388\pi$
$740$	−2.57499	−0.0946583
$741$	3.08452	0.113313
$742$	−1.95423	−0.0717422
$743$	19.6482	0.720822	0.360411	−	0.932794i	$-0.382637\pi$
$743$	19.6482	0.720822	0.360411	+	0.932794i	$0.382637\pi$
$744$	−1.89208	−0.0693672
$745$	−18.9114	−0.692862
$746$	26.6699	0.976455
$747$	6.59375	0.241253
$748$	−4.49525	−0.164362
$749$	−1.19593	−0.0436985
$750$	10.7345	0.391969
$751$	−40.6544	−1.48350	−0.741750	−	0.670677i	$-0.766004\pi$
$751$	−40.6544	−1.48350	−0.741750	+	0.670677i	$0.766004\pi$
$752$	−8.79418	−0.320691
$753$	−29.3874	−1.07094
$754$	15.8917	0.578741
$755$	−19.0290	−0.692536
$756$	−0.152464	−0.00554505
$757$	29.5024	1.07228	0.536142	−	0.844128i	$-0.319881\pi$
$757$	29.5024	1.07228	0.536142	+	0.844128i	$0.319881\pi$
$758$	−4.34415	−0.157787
$759$	26.6678	0.967978
$760$	−1.43677	−0.0521172
$761$	−2.09048	−0.0757797	−0.0378898	−	0.999282i	$-0.512064\pi$
$761$	−2.09048	−0.0757797	−0.0378898	+	0.999282i	$0.512064\pi$
$762$	−9.16362	−0.331963
$763$	1.83640	0.0664822
$764$	−1.53872	−0.0556691
$765$	1.28626	0.0465048
$766$	18.2724	0.660207
$767$	−2.76139	−0.0997081
$768$	1.00000	0.0360844
$769$	23.2263	0.837563	0.418781	−	0.908087i	$-0.362457\pi$
$769$	23.2263	0.837563	0.418781	+	0.908087i	$0.362457\pi$
$770$	−0.881553	−0.0317690
$771$	−26.2097	−0.943920
$772$	−8.97778	−0.323117
$773$	−24.0932	−0.866573	−0.433287	−	0.901256i	$-0.642646\pi$
$773$	−24.0932	−0.866573	−0.433287	+	0.901256i	$0.642646\pi$
$774$	−6.20861	−0.223164
$775$	−6.33004	−0.227382
$776$	−7.20383	−0.258602
$777$	0.305220	0.0109497
$778$	12.4799	0.447428
$779$	10.3846	0.372066
$780$	3.55186	0.127177
$781$	46.1673	1.65200
$782$	5.93243	0.212143
$783$	−5.75495	−0.205665
$784$	−6.97675	−0.249170
$785$	7.64090	0.272716
$786$	−9.48483	−0.338313
$787$	13.2159	0.471097	0.235549	−	0.971863i	$-0.424311\pi$
$787$	13.2159	0.471097	0.235549	+	0.971863i	$0.424311\pi$
$788$	−14.5269	−0.517498
$789$	11.3586	0.404376
$790$	18.1159	0.644534
$791$	−0.205418	−0.00730383
$792$	4.49525	0.159732
$793$	14.3694	0.510272
$794$	−37.0725	−1.31565
$795$	−16.4869	−0.584729
$796$	−21.0222	−0.745113
$797$	41.4064	1.46669	0.733345	−	0.679857i	$-0.237958\pi$
$797$	41.4064	1.46669	0.733345	+	0.679857i	$0.237958\pi$
$798$	0.170304	0.00602871
$799$	−8.79418	−0.311116
$800$	3.34554	0.118283
$801$	8.70904	0.307719
$802$	−19.0730	−0.673491
$803$	−1.37003	−0.0483471
$804$	−3.55123	−0.125242
$805$	1.16340	0.0410043
$806$	−5.22478	−0.184035
$807$	22.4028	0.788615
$808$	8.19362	0.288250
$809$	14.7548	0.518751	0.259376	−	0.965777i	$-0.416483\pi$
$809$	14.7548	0.518751	0.259376	+	0.965777i	$0.416483\pi$
$810$	−1.28626	−0.0451945
$811$	−14.2361	−0.499897	−0.249949	−	0.968259i	$-0.580414\pi$
$811$	−14.2361	−0.499897	−0.249949	+	0.968259i	$0.580414\pi$
$812$	0.877422	0.0307915
$813$	−16.6167	−0.582774
$814$	−8.99912	−0.315419
$815$	−22.8396	−0.800036
$816$	1.00000	0.0350070
$817$	6.93512	0.242629
$818$	28.5873	0.999532
$819$	−0.421012	−0.0147114
$820$	11.9580	0.417590
$821$	−5.23597	−0.182737	−0.0913683	−	0.995817i	$-0.529124\pi$
$821$	−5.23597	−0.182737	−0.0913683	+	0.995817i	$0.529124\pi$
$822$	3.31919	0.115770
$823$	−25.1897	−0.878057	−0.439029	−	0.898473i	$-0.644677\pi$
$823$	−25.1897	−0.878057	−0.439029	+	0.898473i	$0.644677\pi$
$824$	−2.22766	−0.0776042
$825$	15.0390	0.523591
$826$	−0.152464	−0.00530489
$827$	29.7765	1.03543	0.517714	−	0.855554i	$-0.326783\pi$
$827$	29.7765	1.03543	0.517714	+	0.855554i	$0.326783\pi$
$828$	−5.93243	−0.206166
$829$	−26.5018	−0.920444	−0.460222	−	0.887804i	$-0.652230\pi$
$829$	−26.5018	−0.920444	−0.460222	+	0.887804i	$0.652230\pi$
$830$	−8.48127	−0.294389
$831$	22.3772	0.776256
$832$	2.76139	0.0957340
$833$	−6.97675	−0.241730
$834$	3.49560	0.121043
$835$	2.03567	0.0704474
$836$	−5.02126	−0.173664
$837$	1.89208	0.0654000
$838$	3.34311	0.115486
$839$	−8.31678	−0.287127	−0.143564	−	0.989641i	$-0.545856\pi$
$839$	−8.31678	−0.287127	−0.143564	+	0.989641i	$0.545856\pi$
$840$	0.196108	0.00676636
$841$	4.11949	0.142051
$842$	27.7489	0.956291
$843$	23.0121	0.792580
$844$	14.9326	0.514002
$845$	−6.91327	−0.237824
$846$	8.79418	0.302350
$847$	−1.40377	−0.0482341
$848$	−12.8177	−0.440162
$849$	−27.5121	−0.944213
$850$	3.34554	0.114751
$851$	11.8763	0.407113
$852$	−10.2703	−0.351853
$853$	−2.28613	−0.0782756	−0.0391378	−	0.999234i	$-0.512461\pi$
$853$	−2.28613	−0.0782756	−0.0391378	+	0.999234i	$0.512461\pi$
$854$	0.793371	0.0271486
$855$	1.43677	0.0491365
$856$	−7.84405	−0.268104
$857$	−0.545246	−0.0186252	−0.00931262	−	0.999957i	$-0.502964\pi$
$857$	−0.545246	−0.0186252	−0.00931262	+	0.999957i	$0.502964\pi$
$858$	12.4131	0.423777
$859$	−0.386278	−0.0131796	−0.00658982	−	0.999978i	$-0.502098\pi$
$859$	−0.386278	−0.0131796	−0.00658982	+	0.999978i	$0.502098\pi$
$860$	7.98588	0.272316
$861$	−1.41741	−0.0483052
$862$	23.5575	0.802370
$863$	−37.2882	−1.26931	−0.634653	−	0.772797i	$-0.718857\pi$
$863$	−37.2882	−1.26931	−0.634653	+	0.772797i	$0.718857\pi$
$864$	−1.00000	−0.0340207
$865$	−30.3069	−1.03046
$866$	−38.1391	−1.29602
$867$	1.00000	0.0339618
$868$	−0.288474	−0.00979145
$869$	63.3118	2.14771
$870$	7.40236	0.250963
$871$	−9.80633	−0.332275
$872$	12.0448	0.407890
$873$	7.20383	0.243813
$874$	6.62662	0.224149
$875$	1.63663	0.0553280
$876$	0.304772	0.0102973
$877$	23.1034	0.780145	0.390072	−	0.920784i	$-0.372450\pi$
$877$	23.1034	0.780145	0.390072	+	0.920784i	$0.372450\pi$
$878$	−29.8634	−1.00784
$879$	9.11672	0.307499
$880$	−5.78205	−0.194913
$881$	42.4725	1.43093	0.715467	−	0.698646i	$-0.246214\pi$
$881$	42.4725	1.43093	0.715467	+	0.698646i	$0.246214\pi$
$882$	6.97675	0.234920
$883$	38.9591	1.31108	0.655539	−	0.755161i	$-0.272441\pi$
$883$	38.9591	1.31108	0.655539	+	0.755161i	$0.272441\pi$
$884$	2.76139	0.0928757
$885$	−1.28626	−0.0432371
$886$	15.1765	0.509865
$887$	−15.7692	−0.529480	−0.264740	−	0.964320i	$-0.585286\pi$
$887$	−15.7692	−0.529480	−0.264740	+	0.964320i	$0.585286\pi$
$888$	2.00192	0.0671800
$889$	−1.39712	−0.0468579
$890$	−11.2021	−0.375494
$891$	−4.49525	−0.150596
$892$	−14.8699	−0.497880
$893$	−9.82324	−0.328722
$894$	14.7027	0.491731
$895$	4.97084	0.166157
$896$	0.152464	0.00509346
$897$	−16.3818	−0.546972
$898$	8.24532	0.275150
$899$	−10.8889	−0.363164
$900$	−3.34554	−0.111518
$901$	−12.8177	−0.427020
$902$	41.7910	1.39149
$903$	−0.946588	−0.0315005
$904$	−1.34733	−0.0448114
$905$	23.0080	0.764813
$906$	14.7941	0.491500
$907$	41.3639	1.37347	0.686733	−	0.726910i	$-0.259044\pi$
$907$	41.3639	1.37347	0.686733	+	0.726910i	$0.259044\pi$
$908$	−26.9014	−0.892754
$909$	−8.19362	−0.271765
$910$	0.541530	0.0179516
$911$	−31.5157	−1.04416	−0.522082	−	0.852896i	$-0.674844\pi$
$911$	−31.5157	−1.04416	−0.522082	+	0.852896i	$0.674844\pi$
$912$	1.11702	0.0369881
$913$	−29.6405	−0.980959
$914$	31.1186	1.02931
$915$	6.69327	0.221273
$916$	28.9671	0.957099
$917$	−1.44609	−0.0477542
$918$	−1.00000	−0.0330049
$919$	51.2116	1.68931	0.844657	−	0.535307i	$-0.179804\pi$
$919$	51.2116	1.68931	0.844657	+	0.535307i	$0.179804\pi$
$920$	7.63065	0.251575
$921$	−18.5738	−0.612028
$922$	12.8218	0.422262
$923$	−28.3602	−0.933487
$924$	0.685362	0.0225468
$925$	6.69750	0.220212
$926$	−23.7188	−0.779447
$927$	2.22766	0.0731660
$928$	5.75495	0.188916
$929$	−21.9818	−0.721199	−0.360600	−	0.932721i	$-0.617428\pi$
$929$	−21.9818	−0.721199	−0.360600	+	0.932721i	$0.617428\pi$
$930$	−2.43371	−0.0798045
$931$	−7.79315	−0.255410
$932$	23.5625	0.771815
$933$	−4.90015	−0.160424
$934$	34.1015	1.11584
$935$	−5.78205	−0.189093
$936$	−2.76139	−0.0902589
$937$	−13.2344	−0.432350	−0.216175	−	0.976355i	$-0.569358\pi$
$937$	−13.2344	−0.432350	−0.216175	+	0.976355i	$0.569358\pi$
$938$	−0.541434	−0.0176784
$939$	7.22211	0.235685
$940$	−11.3116	−0.368943
$941$	21.2518	0.692789	0.346394	−	0.938089i	$-0.387406\pi$
$941$	21.2518	0.692789	0.346394	+	0.938089i	$0.387406\pi$
$942$	−5.94041	−0.193549
$943$	−55.1521	−1.79600
$944$	−1.00000	−0.0325472
$945$	−0.196108	−0.00637939
$946$	27.9092	0.907408
$947$	1.43682	0.0466904	0.0233452	−	0.999727i	$-0.492568\pi$
$947$	1.43682	0.0466904	0.0233452	+	0.999727i	$0.492568\pi$
$948$	−14.0842	−0.457433
$949$	0.841595	0.0273193
$950$	3.73702	0.121245
$951$	24.8696	0.806451
$952$	0.152464	0.00494138
$953$	−42.8726	−1.38878	−0.694389	−	0.719600i	$-0.744325\pi$
$953$	−42.8726	−1.38878	−0.694389	+	0.719600i	$0.744325\pi$
$954$	12.8177	0.414988
$955$	−1.97920	−0.0640453
$956$	7.12658	0.230490
$957$	25.8699	0.836256
$958$	−6.87279	−0.222050
$959$	0.506056	0.0163414
$960$	1.28626	0.0415138
$961$	−27.4200	−0.884517
$962$	5.52808	0.178232
$963$	7.84405	0.252771
$964$	16.2003	0.521776
$965$	−11.5478	−0.371735
$966$	−0.904481	−0.0291012
$967$	36.9245	1.18741	0.593706	−	0.804682i	$-0.297664\pi$
$967$	36.9245	1.18741	0.593706	+	0.804682i	$0.297664\pi$
$968$	−9.20724	−0.295932
$969$	1.11702	0.0358837
$970$	−9.26599	−0.297513
$971$	−27.9301	−0.896321	−0.448160	−	0.893953i	$-0.647921\pi$
$971$	−27.9301	−0.896321	−0.448160	+	0.893953i	$0.647921\pi$
$972$	1.00000	0.0320750
$973$	0.532952	0.0170857
$974$	41.9802	1.34513
$975$	−9.23834	−0.295864
$976$	5.20367	0.166565
$977$	2.99386	0.0957821	0.0478911	−	0.998853i	$-0.484750\pi$
$977$	2.99386	0.0957821	0.0478911	+	0.998853i	$0.484750\pi$
$978$	17.7566	0.567794
$979$	−39.1493	−1.25122
$980$	−8.97391	−0.286661
$981$	−12.0448	−0.384562
$982$	2.60497	0.0831278
$983$	−37.4642	−1.19492	−0.597461	−	0.801898i	$-0.703824\pi$
$983$	−37.4642	−1.19492	−0.597461	+	0.801898i	$0.703824\pi$
$984$	−9.29671	−0.296368
$985$	−18.6853	−0.595363
$986$	5.75495	0.183275
$987$	1.34079	0.0426779
$988$	3.08452	0.0981316
$989$	−36.8322	−1.17120
$990$	5.78205	0.183766
$991$	38.4025	1.21989	0.609947	−	0.792442i	$-0.291191\pi$
$991$	38.4025	1.21989	0.609947	+	0.792442i	$0.291191\pi$
$992$	−1.89208	−0.0600737
$993$	5.04518	0.160104
$994$	−1.56584	−0.0496655
$995$	−27.0400	−0.857226
$996$	6.59375	0.208931
$997$	50.4624	1.59816	0.799080	−	0.601224i	$-0.205320\pi$
$997$	50.4624	1.59816	0.799080	+	0.601224i	$0.205320\pi$
$998$	27.6986	0.876783
$999$	−2.00192	−0.0633379

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.t.1.7	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.t.1.7	✓	8	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.28626 q^{5} -1.00000 q^{6} -0.152464 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.28626 q^{5} -1.00000 q^{6} -0.152464 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.28626 q^{10} -4.49525 q^{11} +1.00000 q^{12} +2.76139 q^{13} +0.152464 q^{14} +1.28626 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} +1.11702 q^{19} +1.28626 q^{20} -0.152464 q^{21} +4.49525 q^{22} -5.93243 q^{23} -1.00000 q^{24} -3.34554 q^{25} -2.76139 q^{26} +1.00000 q^{27} -0.152464 q^{28} -5.75495 q^{29} -1.28626 q^{30} +1.89208 q^{31} -1.00000 q^{32} -4.49525 q^{33} -1.00000 q^{34} -0.196108 q^{35} +1.00000 q^{36} -2.00192 q^{37} -1.11702 q^{38} +2.76139 q^{39} -1.28626 q^{40} +9.29671 q^{41} +0.152464 q^{42} +6.20861 q^{43} -4.49525 q^{44} +1.28626 q^{45} +5.93243 q^{46} -8.79418 q^{47} +1.00000 q^{48} -6.97675 q^{49} +3.34554 q^{50} +1.00000 q^{51} +2.76139 q^{52} -12.8177 q^{53} -1.00000 q^{54} -5.78205 q^{55} +0.152464 q^{56} +1.11702 q^{57} +5.75495 q^{58} -1.00000 q^{59} +1.28626 q^{60} +5.20367 q^{61} -1.89208 q^{62} -0.152464 q^{63} +1.00000 q^{64} +3.55186 q^{65} +4.49525 q^{66} -3.55123 q^{67} +1.00000 q^{68} -5.93243 q^{69} +0.196108 q^{70} -10.2703 q^{71} -1.00000 q^{72} +0.304772 q^{73} +2.00192 q^{74} -3.34554 q^{75} +1.11702 q^{76} +0.685362 q^{77} -2.76139 q^{78} -14.0842 q^{79} +1.28626 q^{80} +1.00000 q^{81} -9.29671 q^{82} +6.59375 q^{83} -0.152464 q^{84} +1.28626 q^{85} -6.20861 q^{86} -5.75495 q^{87} +4.49525 q^{88} +8.70904 q^{89} -1.28626 q^{90} -0.421012 q^{91} -5.93243 q^{92} +1.89208 q^{93} +8.79418 q^{94} +1.43677 q^{95} -1.00000 q^{96} +7.20383 q^{97} +6.97675 q^{98} -4.49525 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 8 q^{3} + 8 q^{4} - 6 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 - 6 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^8 + 8 * q^9	\( 8 q - 8 q^{2} + 8 q^{3} + 8 q^{4} - 6 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{8} + 8 q^{9} + 6 q^{10} + q^{11} + 8 q^{12} - 2 q^{13} + 4 q^{14} - 6 q^{15} + 8 q^{16} + 8 q^{17} - 8 q^{18} + 4 q^{19} - 6 q^{20} - 4 q^{21} - q^{22} - 11 q^{23} - 8 q^{24} + 6 q^{25} + 2 q^{26} + 8 q^{27} - 4 q^{28} - 12 q^{29} + 6 q^{30} - 9 q^{31} - 8 q^{32} + q^{33} - 8 q^{34} - 28 q^{35} + 8 q^{36} - 22 q^{37} - 4 q^{38} - 2 q^{39} + 6 q^{40} - 19 q^{41} + 4 q^{42} - 5 q^{43} + q^{44} - 6 q^{45} + 11 q^{46} - 26 q^{47} + 8 q^{48} - 6 q^{50} + 8 q^{51} - 2 q^{52} - 21 q^{53} - 8 q^{54} - 13 q^{55} + 4 q^{56} + 4 q^{57} + 12 q^{58} - 8 q^{59} - 6 q^{60} + 9 q^{61} + 9 q^{62} - 4 q^{63} + 8 q^{64} + 14 q^{65} - q^{66} + 26 q^{67} + 8 q^{68} - 11 q^{69} + 28 q^{70} - 14 q^{71} - 8 q^{72} + 17 q^{73} + 22 q^{74} + 6 q^{75} + 4 q^{76} - 18 q^{77} + 2 q^{78} - 39 q^{79} - 6 q^{80} + 8 q^{81} + 19 q^{82} - 11 q^{83} - 4 q^{84} - 6 q^{85} + 5 q^{86} - 12 q^{87} - q^{88} + 6 q^{90} + 11 q^{91} - 11 q^{92} - 9 q^{93} + 26 q^{94} - 15 q^{95} - 8 q^{96} + 16 q^{97} + q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 - 6 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^8 + 8 * q^9 + 6 * q^10 + q^11 + 8 * q^12 - 2 * q^13 + 4 * q^14 - 6 * q^15 + 8 * q^16 + 8 * q^17 - 8 * q^18 + 4 * q^19 - 6 * q^20 - 4 * q^21 - q^22 - 11 * q^23 - 8 * q^24 + 6 * q^25 + 2 * q^26 + 8 * q^27 - 4 * q^28 - 12 * q^29 + 6 * q^30 - 9 * q^31 - 8 * q^32 + q^33 - 8 * q^34 - 28 * q^35 + 8 * q^36 - 22 * q^37 - 4 * q^38 - 2 * q^39 + 6 * q^40 - 19 * q^41 + 4 * q^42 - 5 * q^43 + q^44 - 6 * q^45 + 11 * q^46 - 26 * q^47 + 8 * q^48 - 6 * q^50 + 8 * q^51 - 2 * q^52 - 21 * q^53 - 8 * q^54 - 13 * q^55 + 4 * q^56 + 4 * q^57 + 12 * q^58 - 8 * q^59 - 6 * q^60 + 9 * q^61 + 9 * q^62 - 4 * q^63 + 8 * q^64 + 14 * q^65 - q^66 + 26 * q^67 + 8 * q^68 - 11 * q^69 + 28 * q^70 - 14 * q^71 - 8 * q^72 + 17 * q^73 + 22 * q^74 + 6 * q^75 + 4 * q^76 - 18 * q^77 + 2 * q^78 - 39 * q^79 - 6 * q^80 + 8 * q^81 + 19 * q^82 - 11 * q^83 - 4 * q^84 - 6 * q^85 + 5 * q^86 - 12 * q^87 - q^88 + 6 * q^90 + 11 * q^91 - 11 * q^92 - 9 * q^93 + 26 * q^94 - 15 * q^95 - 8 * q^96 + 16 * q^97 + q^99

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