LMFDB - Embedded newform 6018.2.a.p.1.2

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:	$5$
Coefficient field:	5.5.1668357.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 11x^{3} + x^{2} + 17x - 2 $ x^5 - x^4 - 11x^3 + x^2 + 17x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-2.44651$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.37256 q^{5} -1.00000 q^{6} +2.44651 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.37256 q^{5} -1.00000 q^{6} +2.44651 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.37256 q^{10} +4.53685 q^{11} +1.00000 q^{12} -3.92241 q^{13} -2.44651 q^{14} -1.37256 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +1.28222 q^{19} -1.37256 q^{20} +2.44651 q^{21} -4.53685 q^{22} +3.17888 q^{23} -1.00000 q^{24} -3.11609 q^{25} +3.92241 q^{26} +1.00000 q^{27} +2.44651 q^{28} -4.44468 q^{29} +1.37256 q^{30} +5.90783 q^{31} -1.00000 q^{32} +4.53685 q^{33} +1.00000 q^{34} -3.35797 q^{35} +1.00000 q^{36} -1.11972 q^{37} -1.28222 q^{38} -3.92241 q^{39} +1.37256 q^{40} +5.71415 q^{41} -2.44651 q^{42} -3.32679 q^{43} +4.53685 q^{44} -1.37256 q^{45} -3.17888 q^{46} +12.7605 q^{47} +1.00000 q^{48} -1.01458 q^{49} +3.11609 q^{50} -1.00000 q^{51} -3.92241 q^{52} +6.22101 q^{53} -1.00000 q^{54} -6.22708 q^{55} -2.44651 q^{56} +1.28222 q^{57} +4.44468 q^{58} -1.00000 q^{59} -1.37256 q^{60} +4.28402 q^{61} -5.90783 q^{62} +2.44651 q^{63} +1.00000 q^{64} +5.38373 q^{65} -4.53685 q^{66} -14.1086 q^{67} -1.00000 q^{68} +3.17888 q^{69} +3.35797 q^{70} -10.3817 q^{71} -1.00000 q^{72} +11.6347 q^{73} +1.11972 q^{74} -3.11609 q^{75} +1.28222 q^{76} +11.0995 q^{77} +3.92241 q^{78} +14.0873 q^{79} -1.37256 q^{80} +1.00000 q^{81} -5.71415 q^{82} +9.20886 q^{83} +2.44651 q^{84} +1.37256 q^{85} +3.32679 q^{86} -4.44468 q^{87} -4.53685 q^{88} +14.8009 q^{89} +1.37256 q^{90} -9.59622 q^{91} +3.17888 q^{92} +5.90783 q^{93} -12.7605 q^{94} -1.75992 q^{95} -1.00000 q^{96} -6.25100 q^{97} +1.01458 q^{98} +4.53685 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 5 q^{2} + 5 q^{3} + 5 q^{4} - q^{5} - 5 q^{6} - q^{7} - 5 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 - q^5 - 5 * q^6 - q^7 - 5 * q^8 + 5 * q^9	\( 5 q - 5 q^{2} + 5 q^{3} + 5 q^{4} - q^{5} - 5 q^{6} - q^{7} - 5 q^{8} + 5 q^{9} + q^{10} + 6 q^{11} + 5 q^{12} - 2 q^{13} + q^{14} - q^{15} + 5 q^{16} - 5 q^{17} - 5 q^{18} + 4 q^{19} - q^{20} - q^{21} - 6 q^{22} + 12 q^{23} - 5 q^{24} + 4 q^{25} + 2 q^{26} + 5 q^{27} - q^{28} + 19 q^{29} + q^{30} + 5 q^{31} - 5 q^{32} + 6 q^{33} + 5 q^{34} - 4 q^{35} + 5 q^{36} - 11 q^{37} - 4 q^{38} - 2 q^{39} + q^{40} + 6 q^{41} + q^{42} + 2 q^{43} + 6 q^{44} - q^{45} - 12 q^{46} + 22 q^{47} + 5 q^{48} - 12 q^{49} - 4 q^{50} - 5 q^{51} - 2 q^{52} + 15 q^{53} - 5 q^{54} - 36 q^{55} + q^{56} + 4 q^{57} - 19 q^{58} - 5 q^{59} - q^{60} + 16 q^{61} - 5 q^{62} - q^{63} + 5 q^{64} - 2 q^{65} - 6 q^{66} + 25 q^{67} - 5 q^{68} + 12 q^{69} + 4 q^{70} - 5 q^{72} - 10 q^{73} + 11 q^{74} + 4 q^{75} + 4 q^{76} + 6 q^{77} + 2 q^{78} + 10 q^{79} - q^{80} + 5 q^{81} - 6 q^{82} + 19 q^{83} - q^{84} + q^{85} - 2 q^{86} + 19 q^{87} - 6 q^{88} + 23 q^{89} + q^{90} - 17 q^{91} + 12 q^{92} + 5 q^{93} - 22 q^{94} + q^{95} - 5 q^{96} + 8 q^{97} + 12 q^{98} + 6 q^{99}+O(q^{100}) \) 5 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 - q^5 - 5 * q^6 - q^7 - 5 * q^8 + 5 * q^9 + q^10 + 6 * q^11 + 5 * q^12 - 2 * q^13 + q^14 - q^15 + 5 * q^16 - 5 * q^17 - 5 * q^18 + 4 * q^19 - q^20 - q^21 - 6 * q^22 + 12 * q^23 - 5 * q^24 + 4 * q^25 + 2 * q^26 + 5 * q^27 - q^28 + 19 * q^29 + q^30 + 5 * q^31 - 5 * q^32 + 6 * q^33 + 5 * q^34 - 4 * q^35 + 5 * q^36 - 11 * q^37 - 4 * q^38 - 2 * q^39 + q^40 + 6 * q^41 + q^42 + 2 * q^43 + 6 * q^44 - q^45 - 12 * q^46 + 22 * q^47 + 5 * q^48 - 12 * q^49 - 4 * q^50 - 5 * q^51 - 2 * q^52 + 15 * q^53 - 5 * q^54 - 36 * q^55 + q^56 + 4 * q^57 - 19 * q^58 - 5 * q^59 - q^60 + 16 * q^61 - 5 * q^62 - q^63 + 5 * q^64 - 2 * q^65 - 6 * q^66 + 25 * q^67 - 5 * q^68 + 12 * q^69 + 4 * q^70 - 5 * q^72 - 10 * q^73 + 11 * q^74 + 4 * q^75 + 4 * q^76 + 6 * q^77 + 2 * q^78 + 10 * q^79 - q^80 + 5 * q^81 - 6 * q^82 + 19 * q^83 - q^84 + q^85 - 2 * q^86 + 19 * q^87 - 6 * q^88 + 23 * q^89 + q^90 - 17 * q^91 + 12 * q^92 + 5 * q^93 - 22 * q^94 + q^95 - 5 * q^96 + 8 * q^97 + 12 * q^98 + 6 * 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
$5$	−1.37256	−0.613826	−0.306913	−	0.951738i	$-0.599296\pi$
$5$	−1.37256	−0.613826	−0.306913	+	0.951738i	$0.599296\pi$
$6$	−1.00000	−0.408248
$7$	2.44651	0.924694	0.462347	−	0.886699i	$-0.347007\pi$
$7$	2.44651	0.924694	0.462347	+	0.886699i	$0.347007\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.37256	0.434040
$11$	4.53685	1.36791	0.683956	−	0.729524i	$-0.260258\pi$
$11$	4.53685	1.36791	0.683956	+	0.729524i	$0.260258\pi$
$12$	1.00000	0.288675
$13$	−3.92241	−1.08788	−0.543940	−	0.839124i	$-0.683068\pi$
$13$	−3.92241	−1.08788	−0.543940	+	0.839124i	$0.683068\pi$
$14$	−2.44651	−0.653858
$15$	−1.37256	−0.354392
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.00000	−0.235702
$19$	1.28222	0.294161	0.147081	−	0.989125i	$-0.453012\pi$
$19$	1.28222	0.294161	0.147081	+	0.989125i	$0.453012\pi$
$20$	−1.37256	−0.306913
$21$	2.44651	0.533873
$22$	−4.53685	−0.967259
$23$	3.17888	0.662841	0.331421	−	0.943483i	$-0.392472\pi$
$23$	3.17888	0.662841	0.331421	+	0.943483i	$0.392472\pi$
$24$	−1.00000	−0.204124
$25$	−3.11609	−0.623218
$26$	3.92241	0.769248
$27$	1.00000	0.192450
$28$	2.44651	0.462347
$29$	−4.44468	−0.825356	−0.412678	−	0.910877i	$-0.635406\pi$
$29$	−4.44468	−0.825356	−0.412678	+	0.910877i	$0.635406\pi$
$30$	1.37256	0.250593
$31$	5.90783	1.06108	0.530539	−	0.847661i	$-0.321990\pi$
$31$	5.90783	1.06108	0.530539	+	0.847661i	$0.321990\pi$
$32$	−1.00000	−0.176777
$33$	4.53685	0.789764
$34$	1.00000	0.171499
$35$	−3.35797	−0.567601
$36$	1.00000	0.166667
$37$	−1.11972	−0.184082	−0.0920408	−	0.995755i	$-0.529339\pi$
$37$	−1.11972	−0.184082	−0.0920408	+	0.995755i	$0.529339\pi$
$38$	−1.28222	−0.208003
$39$	−3.92241	−0.628088
$40$	1.37256	0.217020
$41$	5.71415	0.892400	0.446200	−	0.894933i	$-0.352777\pi$
$41$	5.71415	0.892400	0.446200	+	0.894933i	$0.352777\pi$
$42$	−2.44651	−0.377505
$43$	−3.32679	−0.507330	−0.253665	−	0.967292i	$-0.581636\pi$
$43$	−3.32679	−0.507330	−0.253665	+	0.967292i	$0.581636\pi$
$44$	4.53685	0.683956
$45$	−1.37256	−0.204609
$46$	−3.17888	−0.468700
$47$	12.7605	1.86131	0.930656	−	0.365895i	$-0.119237\pi$
$47$	12.7605	1.86131	0.930656	+	0.365895i	$0.119237\pi$
$48$	1.00000	0.144338
$49$	−1.01458	−0.144940
$50$	3.11609	0.440682
$51$	−1.00000	−0.140028
$52$	−3.92241	−0.543940
$53$	6.22101	0.854522	0.427261	−	0.904128i	$-0.359479\pi$
$53$	6.22101	0.854522	0.427261	+	0.904128i	$0.359479\pi$
$54$	−1.00000	−0.136083
$55$	−6.22708	−0.839659
$56$	−2.44651	−0.326929
$57$	1.28222	0.169834
$58$	4.44468	0.583615
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−1.37256	−0.177196
$61$	4.28402	0.548512	0.274256	−	0.961657i	$-0.411568\pi$
$61$	4.28402	0.548512	0.274256	+	0.961657i	$0.411568\pi$
$62$	−5.90783	−0.750295
$63$	2.44651	0.308231
$64$	1.00000	0.125000
$65$	5.38373	0.667769
$66$	−4.53685	−0.558447
$67$	−14.1086	−1.72364	−0.861818	−	0.507218i	$-0.830674\pi$
$67$	−14.1086	−1.72364	−0.861818	+	0.507218i	$0.830674\pi$
$68$	−1.00000	−0.121268
$69$	3.17888	0.382692
$70$	3.35797	0.401355
$71$	−10.3817	−1.23208	−0.616039	−	0.787716i	$-0.711264\pi$
$71$	−10.3817	−1.23208	−0.616039	+	0.787716i	$0.711264\pi$
$72$	−1.00000	−0.117851
$73$	11.6347	1.36174	0.680871	−	0.732404i	$-0.261602\pi$
$73$	11.6347	1.36174	0.680871	+	0.732404i	$0.261602\pi$
$74$	1.11972	0.130165
$75$	−3.11609	−0.359815
$76$	1.28222	0.147081
$77$	11.0995	1.26490
$78$	3.92241	0.444126
$79$	14.0873	1.58495	0.792473	−	0.609908i	$-0.208793\pi$
$79$	14.0873	1.58495	0.792473	+	0.609908i	$0.208793\pi$
$80$	−1.37256	−0.153456
$81$	1.00000	0.111111
$82$	−5.71415	−0.631022
$83$	9.20886	1.01080	0.505402	−	0.862884i	$-0.331344\pi$
$83$	9.20886	1.01080	0.505402	+	0.862884i	$0.331344\pi$
$84$	2.44651	0.266936
$85$	1.37256	0.148875
$86$	3.32679	0.358737
$87$	−4.44468	−0.476519
$88$	−4.53685	−0.483630
$89$	14.8009	1.56889	0.784443	−	0.620200i	$-0.212949\pi$
$89$	14.8009	1.56889	0.784443	+	0.620200i	$0.212949\pi$
$90$	1.37256	0.144680
$91$	−9.59622	−1.00596
$92$	3.17888	0.331421
$93$	5.90783	0.612613
$94$	−12.7605	−1.31615
$95$	−1.75992	−0.180564
$96$	−1.00000	−0.102062
$97$	−6.25100	−0.634692	−0.317346	−	0.948310i	$-0.602792\pi$
$97$	−6.25100	−0.634692	−0.317346	+	0.948310i	$0.602792\pi$
$98$	1.01458	0.102488
$99$	4.53685	0.455970
$100$	−3.11609	−0.311609
$101$	−7.31037	−0.727409	−0.363704	−	0.931514i	$-0.618488\pi$
$101$	−7.31037	−0.727409	−0.363704	+	0.931514i	$0.618488\pi$
$102$	1.00000	0.0990148
$103$	7.63233	0.752035	0.376018	−	0.926612i	$-0.377293\pi$
$103$	7.63233	0.752035	0.376018	+	0.926612i	$0.377293\pi$
$104$	3.92241	0.384624
$105$	−3.35797	−0.327705
$106$	−6.22101	−0.604238
$107$	−4.49082	−0.434144	−0.217072	−	0.976156i	$-0.569651\pi$
$107$	−4.49082	−0.434144	−0.217072	+	0.976156i	$0.569651\pi$
$108$	1.00000	0.0962250
$109$	−4.25283	−0.407347	−0.203674	−	0.979039i	$-0.565288\pi$
$109$	−4.25283	−0.407347	−0.203674	+	0.979039i	$0.565288\pi$
$110$	6.22708	0.593728
$111$	−1.11972	−0.106280
$112$	2.44651	0.231174
$113$	9.44831	0.888822	0.444411	−	0.895823i	$-0.353413\pi$
$113$	9.44831	0.888822	0.444411	+	0.895823i	$0.353413\pi$
$114$	−1.28222	−0.120091
$115$	−4.36318	−0.406869
$116$	−4.44468	−0.412678
$117$	−3.92241	−0.362627
$118$	1.00000	0.0920575
$119$	−2.44651	−0.224271
$120$	1.37256	0.125297
$121$	9.58299	0.871181
$122$	−4.28402	−0.387857
$123$	5.71415	0.515227
$124$	5.90783	0.530539
$125$	11.1398	0.996373
$126$	−2.44651	−0.217953
$127$	0.617352	0.0547811	0.0273906	−	0.999625i	$-0.491280\pi$
$127$	0.617352	0.0547811	0.0273906	+	0.999625i	$0.491280\pi$
$128$	−1.00000	−0.0883883
$129$	−3.32679	−0.292907
$130$	−5.38373	−0.472184
$131$	−4.86386	−0.424957	−0.212479	−	0.977166i	$-0.568154\pi$
$131$	−4.86386	−0.424957	−0.212479	+	0.977166i	$0.568154\pi$
$132$	4.53685	0.394882
$133$	3.13696	0.272009
$134$	14.1086	1.21879
$135$	−1.37256	−0.118131
$136$	1.00000	0.0857493
$137$	4.51260	0.385538	0.192769	−	0.981244i	$-0.438253\pi$
$137$	4.51260	0.385538	0.192769	+	0.981244i	$0.438253\pi$
$138$	−3.17888	−0.270604
$139$	−10.2338	−0.868016	−0.434008	−	0.900909i	$-0.642901\pi$
$139$	−10.2338	−0.868016	−0.434008	+	0.900909i	$0.642901\pi$
$140$	−3.35797	−0.283801
$141$	12.7605	1.07463
$142$	10.3817	0.871210
$143$	−17.7954	−1.48812
$144$	1.00000	0.0833333
$145$	6.10057	0.506624
$146$	−11.6347	−0.962896
$147$	−1.01458	−0.0836814
$148$	−1.11972	−0.0920408
$149$	15.1122	1.23804	0.619020	−	0.785375i	$-0.287530\pi$
$149$	15.1122	1.23804	0.619020	+	0.785375i	$0.287530\pi$
$150$	3.11609	0.254428
$151$	−18.4536	−1.50173	−0.750865	−	0.660456i	$-0.770363\pi$
$151$	−18.4536	−1.50173	−0.750865	+	0.660456i	$0.770363\pi$
$152$	−1.28222	−0.104002
$153$	−1.00000	−0.0808452
$154$	−11.0995	−0.894419
$155$	−8.10882	−0.651316
$156$	−3.92241	−0.314044
$157$	−7.52286	−0.600390	−0.300195	−	0.953878i	$-0.597052\pi$
$157$	−7.52286	−0.600390	−0.300195	+	0.953878i	$0.597052\pi$
$158$	−14.0873	−1.12073
$159$	6.22101	0.493358
$160$	1.37256	0.108510
$161$	7.77715	0.612926
$162$	−1.00000	−0.0785674
$163$	10.9961	0.861282	0.430641	−	0.902523i	$-0.358288\pi$
$163$	10.9961	0.861282	0.430641	+	0.902523i	$0.358288\pi$
$164$	5.71415	0.446200
$165$	−6.22708	−0.484777
$166$	−9.20886	−0.714746
$167$	−0.349234	−0.0270246	−0.0135123	−	0.999909i	$-0.504301\pi$
$167$	−0.349234	−0.0270246	−0.0135123	+	0.999909i	$0.504301\pi$
$168$	−2.44651	−0.188752
$169$	2.38530	0.183485
$170$	−1.37256	−0.105270
$171$	1.28222	0.0980537
$172$	−3.32679	−0.253665
$173$	−2.38590	−0.181397	−0.0906983	−	0.995878i	$-0.528910\pi$
$173$	−2.38590	−0.181397	−0.0906983	+	0.995878i	$0.528910\pi$
$174$	4.44468	0.336950
$175$	−7.62355	−0.576286
$176$	4.53685	0.341978
$177$	−1.00000	−0.0751646
$178$	−14.8009	−1.10937
$179$	−1.29654	−0.0969081	−0.0484541	−	0.998825i	$-0.515429\pi$
$179$	−1.29654	−0.0969081	−0.0484541	+	0.998825i	$0.515429\pi$
$180$	−1.37256	−0.102304
$181$	−7.64648	−0.568358	−0.284179	−	0.958771i	$-0.591721\pi$
$181$	−7.64648	−0.568358	−0.284179	+	0.958771i	$0.591721\pi$
$182$	9.59622	0.711319
$183$	4.28402	0.316684
$184$	−3.17888	−0.234350
$185$	1.53688	0.112994
$186$	−5.90783	−0.433183
$187$	−4.53685	−0.331767
$188$	12.7605	0.930656
$189$	2.44651	0.177958
$190$	1.75992	0.127678
$191$	14.1519	1.02399	0.511997	−	0.858987i	$-0.328906\pi$
$191$	14.1519	1.02399	0.511997	+	0.858987i	$0.328906\pi$
$192$	1.00000	0.0721688
$193$	16.3671	1.17813	0.589064	−	0.808086i	$-0.299496\pi$
$193$	16.3671	1.17813	0.589064	+	0.808086i	$0.299496\pi$
$194$	6.25100	0.448795
$195$	5.38373	0.385537
$196$	−1.01458	−0.0724702
$197$	4.28585	0.305354	0.152677	−	0.988276i	$-0.451211\pi$
$197$	4.28585	0.305354	0.152677	+	0.988276i	$0.451211\pi$
$198$	−4.53685	−0.322420
$199$	−20.6226	−1.46190	−0.730948	−	0.682434i	$-0.760922\pi$
$199$	−20.6226	−1.46190	−0.730948	+	0.682434i	$0.760922\pi$
$200$	3.11609	0.220341
$201$	−14.1086	−0.995141
$202$	7.31037	0.514356
$203$	−10.8739	−0.763202
$204$	−1.00000	−0.0700140
$205$	−7.84299	−0.547778
$206$	−7.63233	−0.531769
$207$	3.17888	0.220947
$208$	−3.92241	−0.271970
$209$	5.81723	0.402386
$210$	3.35797	0.231722
$211$	−3.27881	−0.225722	−0.112861	−	0.993611i	$-0.536002\pi$
$211$	−3.27881	−0.225722	−0.112861	+	0.993611i	$0.536002\pi$
$212$	6.22101	0.427261
$213$	−10.3817	−0.711340
$214$	4.49082	0.306986
$215$	4.56620	0.311412
$216$	−1.00000	−0.0680414
$217$	14.4536	0.981172
$218$	4.25283	0.288038
$219$	11.6347	0.786202
$220$	−6.22708	−0.419829
$221$	3.92241	0.263850
$222$	1.11972	0.0751510
$223$	7.89786	0.528880	0.264440	−	0.964402i	$-0.414813\pi$
$223$	7.89786	0.528880	0.264440	+	0.964402i	$0.414813\pi$
$224$	−2.44651	−0.163464
$225$	−3.11609	−0.207739
$226$	−9.44831	−0.628492
$227$	3.21878	0.213638	0.106819	−	0.994278i	$-0.465933\pi$
$227$	3.21878	0.213638	0.106819	+	0.994278i	$0.465933\pi$
$228$	1.28222	0.0849170
$229$	8.63791	0.570809	0.285405	−	0.958407i	$-0.407872\pi$
$229$	8.63791	0.570809	0.285405	+	0.958407i	$0.407872\pi$
$230$	4.36318	0.287700
$231$	11.0995	0.730290
$232$	4.44468	0.291807
$233$	−2.25951	−0.148026	−0.0740128	−	0.997257i	$-0.523581\pi$
$233$	−2.25951	−0.148026	−0.0740128	+	0.997257i	$0.523581\pi$
$234$	3.92241	0.256416
$235$	−17.5145	−1.14252
$236$	−1.00000	−0.0650945
$237$	14.0873	0.915068
$238$	2.44651	0.158584
$239$	25.9175	1.67647	0.838233	−	0.545312i	$-0.183589\pi$
$239$	25.9175	1.67647	0.838233	+	0.545312i	$0.183589\pi$
$240$	−1.37256	−0.0885981
$241$	14.0196	0.903084	0.451542	−	0.892250i	$-0.350874\pi$
$241$	14.0196	0.903084	0.451542	+	0.892250i	$0.350874\pi$
$242$	−9.58299	−0.616018
$243$	1.00000	0.0641500
$244$	4.28402	0.274256
$245$	1.39257	0.0889681
$246$	−5.71415	−0.364321
$247$	−5.02939	−0.320012
$248$	−5.90783	−0.375147
$249$	9.20886	0.583588
$250$	−11.1398	−0.704542
$251$	−10.4937	−0.662359	−0.331179	−	0.943568i	$-0.607446\pi$
$251$	−10.4937	−0.662359	−0.331179	+	0.943568i	$0.607446\pi$
$252$	2.44651	0.154116
$253$	14.4221	0.906708
$254$	−0.617352	−0.0387361
$255$	1.37256	0.0859528
$256$	1.00000	0.0625000
$257$	25.9848	1.62089	0.810445	−	0.585815i	$-0.199226\pi$
$257$	25.9848	1.62089	0.810445	+	0.585815i	$0.199226\pi$
$258$	3.32679	0.207117
$259$	−2.73942	−0.170219
$260$	5.38373	0.333885
$261$	−4.44468	−0.275119
$262$	4.86386	0.300490
$263$	16.6742	1.02818	0.514088	−	0.857738i	$-0.328131\pi$
$263$	16.6742	1.02818	0.514088	+	0.857738i	$0.328131\pi$
$264$	−4.53685	−0.279224
$265$	−8.53868	−0.524527
$266$	−3.13696	−0.192340
$267$	14.8009	0.905797
$268$	−14.1086	−0.861818
$269$	−17.1270	−1.04425	−0.522127	−	0.852868i	$-0.674861\pi$
$269$	−17.1270	−1.04425	−0.522127	+	0.852868i	$0.674861\pi$
$270$	1.37256	0.0835311
$271$	−16.7230	−1.01585	−0.507925	−	0.861401i	$-0.669587\pi$
$271$	−16.7230	−1.01585	−0.507925	+	0.861401i	$0.669587\pi$
$272$	−1.00000	−0.0606339
$273$	−9.59622	−0.580790
$274$	−4.51260	−0.272616
$275$	−14.1372	−0.852507
$276$	3.17888	0.191346
$277$	6.16976	0.370705	0.185353	−	0.982672i	$-0.440657\pi$
$277$	6.16976	0.370705	0.185353	+	0.982672i	$0.440657\pi$
$278$	10.2338	0.613780
$279$	5.90783	0.353692
$280$	3.35797	0.200677
$281$	−21.8738	−1.30488	−0.652440	−	0.757840i	$-0.726255\pi$
$281$	−21.8738	−1.30488	−0.652440	+	0.757840i	$0.726255\pi$
$282$	−12.7605	−0.759878
$283$	−3.51379	−0.208873	−0.104436	−	0.994532i	$-0.533304\pi$
$283$	−3.51379	−0.208873	−0.104436	+	0.994532i	$0.533304\pi$
$284$	−10.3817	−0.616039
$285$	−1.75992	−0.104248
$286$	17.7954	1.05226
$287$	13.9797	0.825197
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	−6.10057	−0.358238
$291$	−6.25100	−0.366440
$292$	11.6347	0.680871
$293$	9.89280	0.577944	0.288972	−	0.957338i	$-0.406687\pi$
$293$	9.89280	0.577944	0.288972	+	0.957338i	$0.406687\pi$
$294$	1.01458	0.0591717
$295$	1.37256	0.0799133
$296$	1.11972	0.0650827
$297$	4.53685	0.263255
$298$	−15.1122	−0.875426
$299$	−12.4689	−0.721092
$300$	−3.11609	−0.179908
$301$	−8.13902	−0.469125
$302$	18.4536	1.06188
$303$	−7.31037	−0.419970
$304$	1.28222	0.0735403
$305$	−5.88005	−0.336691
$306$	1.00000	0.0571662
$307$	13.8309	0.789370	0.394685	−	0.918817i	$-0.370854\pi$
$307$	13.8309	0.789370	0.394685	+	0.918817i	$0.370854\pi$
$308$	11.0995	0.632450
$309$	7.63233	0.434188
$310$	8.10882	0.460550
$311$	14.0500	0.796702	0.398351	−	0.917233i	$-0.369583\pi$
$311$	14.0500	0.796702	0.398351	+	0.917233i	$0.369583\pi$
$312$	3.92241	0.222063
$313$	−6.65585	−0.376211	−0.188106	−	0.982149i	$-0.560235\pi$
$313$	−6.65585	−0.376211	−0.188106	+	0.982149i	$0.560235\pi$
$314$	7.52286	0.424540
$315$	−3.35797	−0.189200
$316$	14.0873	0.792473
$317$	−8.10346	−0.455136	−0.227568	−	0.973762i	$-0.573077\pi$
$317$	−8.10346	−0.455136	−0.227568	+	0.973762i	$0.573077\pi$
$318$	−6.22101	−0.348857
$319$	−20.1648	−1.12901
$320$	−1.37256	−0.0767282
$321$	−4.49082	−0.250653
$322$	−7.77715	−0.433404
$323$	−1.28222	−0.0713446
$324$	1.00000	0.0555556
$325$	12.2226	0.677987
$326$	−10.9961	−0.609018
$327$	−4.25283	−0.235182
$328$	−5.71415	−0.315511
$329$	31.2187	1.72114
$330$	6.22708	0.342789
$331$	−6.21793	−0.341768	−0.170884	−	0.985291i	$-0.554662\pi$
$331$	−6.21793	−0.341768	−0.170884	+	0.985291i	$0.554662\pi$
$332$	9.20886	0.505402
$333$	−1.11972	−0.0613605
$334$	0.349234	0.0191093
$335$	19.3648	1.05801
$336$	2.44651	0.133468
$337$	−5.56650	−0.303226	−0.151613	−	0.988440i	$-0.548447\pi$
$337$	−5.56650	−0.303226	−0.151613	+	0.988440i	$0.548447\pi$
$338$	−2.38530	−0.129743
$339$	9.44831	0.513162
$340$	1.37256	0.0744373
$341$	26.8029	1.45146
$342$	−1.28222	−0.0693344
$343$	−19.6078	−1.05872
$344$	3.32679	0.179368
$345$	−4.36318	−0.234906
$346$	2.38590	0.128267
$347$	24.3057	1.30480	0.652398	−	0.757877i	$-0.273763\pi$
$347$	24.3057	1.30480	0.652398	+	0.757877i	$0.273763\pi$
$348$	−4.44468	−0.238260
$349$	24.6813	1.32116	0.660579	−	0.750757i	$-0.270311\pi$
$349$	24.6813	1.32116	0.660579	+	0.750757i	$0.270311\pi$
$350$	7.62355	0.407496
$351$	−3.92241	−0.209363
$352$	−4.53685	−0.241815
$353$	30.3271	1.61415	0.807075	−	0.590449i	$-0.201049\pi$
$353$	30.3271	1.61415	0.807075	+	0.590449i	$0.201049\pi$
$354$	1.00000	0.0531494
$355$	14.2494	0.756281
$356$	14.8009	0.784443
$357$	−2.44651	−0.129483
$358$	1.29654	0.0685244
$359$	15.5771	0.822130	0.411065	−	0.911606i	$-0.365157\pi$
$359$	15.5771	0.822130	0.411065	+	0.911606i	$0.365157\pi$
$360$	1.37256	0.0723400
$361$	−17.3559	−0.913469
$362$	7.64648	0.401890
$363$	9.58299	0.502977
$364$	−9.59622	−0.502979
$365$	−15.9693	−0.835872
$366$	−4.28402	−0.223929
$367$	12.8664	0.671622	0.335811	−	0.941929i	$-0.390990\pi$
$367$	12.8664	0.671622	0.335811	+	0.941929i	$0.390990\pi$
$368$	3.17888	0.165710
$369$	5.71415	0.297467
$370$	−1.53688	−0.0798988
$371$	15.2198	0.790171
$372$	5.90783	0.306307
$373$	21.6663	1.12184	0.560919	−	0.827871i	$-0.310448\pi$
$373$	21.6663	1.12184	0.560919	+	0.827871i	$0.310448\pi$
$374$	4.53685	0.234595
$375$	11.1398	0.575256
$376$	−12.7605	−0.658073
$377$	17.4338	0.897889
$378$	−2.44651	−0.125835
$379$	23.2861	1.19613	0.598064	−	0.801448i	$-0.295937\pi$
$379$	23.2861	1.19613	0.598064	+	0.801448i	$0.295937\pi$
$380$	−1.75992	−0.0902818
$381$	0.617352	0.0316279
$382$	−14.1519	−0.724073
$383$	0.383389	0.0195902	0.00979512	−	0.999952i	$-0.496882\pi$
$383$	0.383389	0.0195902	0.00979512	+	0.999952i	$0.496882\pi$
$384$	−1.00000	−0.0510310
$385$	−15.2346	−0.776428
$386$	−16.3671	−0.833063
$387$	−3.32679	−0.169110
$388$	−6.25100	−0.317346
$389$	−3.45139	−0.174993	−0.0874963	−	0.996165i	$-0.527887\pi$
$389$	−3.45139	−0.174993	−0.0874963	+	0.996165i	$0.527887\pi$
$390$	−5.38373	−0.272616
$391$	−3.17888	−0.160763
$392$	1.01458	0.0512442
$393$	−4.86386	−0.245349
$394$	−4.28585	−0.215918
$395$	−19.3356	−0.972880
$396$	4.53685	0.227985
$397$	4.45900	0.223791	0.111895	−	0.993720i	$-0.464308\pi$
$397$	4.45900	0.223791	0.111895	+	0.993720i	$0.464308\pi$
$398$	20.6226	1.03372
$399$	3.13696	0.157045
$400$	−3.11609	−0.155805
$401$	−7.81142	−0.390084	−0.195042	−	0.980795i	$-0.562484\pi$
$401$	−7.81142	−0.390084	−0.195042	+	0.980795i	$0.562484\pi$
$402$	14.1086	0.703671
$403$	−23.1729	−1.15433
$404$	−7.31037	−0.363704
$405$	−1.37256	−0.0682028
$406$	10.8739	0.539665
$407$	−5.08002	−0.251807
$408$	1.00000	0.0495074
$409$	6.90534	0.341447	0.170724	−	0.985319i	$-0.445389\pi$
$409$	6.90534	0.341447	0.170724	+	0.985319i	$0.445389\pi$
$410$	7.84299	0.387337
$411$	4.51260	0.222590
$412$	7.63233	0.376018
$413$	−2.44651	−0.120385
$414$	−3.17888	−0.156233
$415$	−12.6397	−0.620457
$416$	3.92241	0.192312
$417$	−10.2338	−0.501149
$418$	−5.81723	−0.284530
$419$	10.4229	0.509192	0.254596	−	0.967048i	$-0.418058\pi$
$419$	10.4229	0.509192	0.254596	+	0.967048i	$0.418058\pi$
$420$	−3.35797	−0.163852
$421$	−27.6947	−1.34976	−0.674880	−	0.737928i	$-0.735804\pi$
$421$	−27.6947	−1.34976	−0.674880	+	0.737928i	$0.735804\pi$
$422$	3.27881	0.159610
$423$	12.7605	0.620437
$424$	−6.22101	−0.302119
$425$	3.11609	0.151153
$426$	10.3817	0.502994
$427$	10.4809	0.507206
$428$	−4.49082	−0.217072
$429$	−17.7954	−0.859169
$430$	−4.56620	−0.220202
$431$	13.8370	0.666504	0.333252	−	0.942838i	$-0.391854\pi$
$431$	13.8370	0.666504	0.333252	+	0.942838i	$0.391854\pi$
$432$	1.00000	0.0481125
$433$	−9.03973	−0.434422	−0.217211	−	0.976125i	$-0.569696\pi$
$433$	−9.03973	−0.434422	−0.217211	+	0.976125i	$0.569696\pi$
$434$	−14.4536	−0.693793
$435$	6.10057	0.292500
$436$	−4.25283	−0.203674
$437$	4.07601	0.194982
$438$	−11.6347	−0.555929
$439$	−6.09702	−0.290995	−0.145497	−	0.989359i	$-0.546478\pi$
$439$	−6.09702	−0.290995	−0.145497	+	0.989359i	$0.546478\pi$
$440$	6.22708	0.296864
$441$	−1.01458	−0.0483135
$442$	−3.92241	−0.186570
$443$	−21.3040	−1.01219	−0.506093	−	0.862479i	$-0.668911\pi$
$443$	−21.3040	−1.01219	−0.506093	+	0.862479i	$0.668911\pi$
$444$	−1.11972	−0.0531398
$445$	−20.3150	−0.963023
$446$	−7.89786	−0.373974
$447$	15.1122	0.714782
$448$	2.44651	0.115587
$449$	9.14428	0.431545	0.215773	−	0.976444i	$-0.430773\pi$
$449$	9.14428	0.431545	0.215773	+	0.976444i	$0.430773\pi$
$450$	3.11609	0.146894
$451$	25.9242	1.22072
$452$	9.44831	0.444411
$453$	−18.4536	−0.867024
$454$	−3.21878	−0.151065
$455$	13.1713	0.617482
$456$	−1.28222	−0.0600454
$457$	24.4679	1.14456	0.572280	−	0.820058i	$-0.306059\pi$
$457$	24.4679	1.14456	0.572280	+	0.820058i	$0.306059\pi$
$458$	−8.63791	−0.403623
$459$	−1.00000	−0.0466760
$460$	−4.36318	−0.203434
$461$	−0.986656	−0.0459531	−0.0229766	−	0.999736i	$-0.507314\pi$
$461$	−0.986656	−0.0459531	−0.0229766	+	0.999736i	$0.507314\pi$
$462$	−11.0995	−0.516393
$463$	10.0240	0.465856	0.232928	−	0.972494i	$-0.425169\pi$
$463$	10.0240	0.465856	0.232928	+	0.972494i	$0.425169\pi$
$464$	−4.44468	−0.206339
$465$	−8.10882	−0.376038
$466$	2.25951	0.104670
$467$	8.99505	0.416241	0.208121	−	0.978103i	$-0.433265\pi$
$467$	8.99505	0.416241	0.208121	+	0.978103i	$0.433265\pi$
$468$	−3.92241	−0.181313
$469$	−34.5168	−1.59384
$470$	17.5145	0.807884
$471$	−7.52286	−0.346635
$472$	1.00000	0.0460287
$473$	−15.0931	−0.693983
$474$	−14.0873	−0.647051
$475$	−3.99551	−0.183327
$476$	−2.44651	−0.112136
$477$	6.22101	0.284841
$478$	−25.9175	−1.18544
$479$	25.8738	1.18220	0.591102	−	0.806597i	$-0.298693\pi$
$479$	25.8738	1.18220	0.591102	+	0.806597i	$0.298693\pi$
$480$	1.37256	0.0626483
$481$	4.39202	0.200259
$482$	−14.0196	−0.638577
$483$	7.77715	0.353873
$484$	9.58299	0.435591
$485$	8.57984	0.389590
$486$	−1.00000	−0.0453609
$487$	1.84849	0.0837631	0.0418816	−	0.999123i	$-0.486665\pi$
$487$	1.84849	0.0837631	0.0418816	+	0.999123i	$0.486665\pi$
$488$	−4.28402	−0.193928
$489$	10.9961	0.497261
$490$	−1.39257	−0.0629100
$491$	−35.3045	−1.59327	−0.796636	−	0.604460i	$-0.793389\pi$
$491$	−35.3045	−1.59327	−0.796636	+	0.604460i	$0.793389\pi$
$492$	5.71415	0.257614
$493$	4.44468	0.200178
$494$	5.02939	0.226283
$495$	−6.22708	−0.279886
$496$	5.90783	0.265269
$497$	−25.3989	−1.13930
$498$	−9.20886	−0.412659
$499$	−9.67804	−0.433249	−0.216624	−	0.976255i	$-0.569505\pi$
$499$	−9.67804	−0.433249	−0.216624	+	0.976255i	$0.569505\pi$
$500$	11.1398	0.498186
$501$	−0.349234	−0.0156026
$502$	10.4937	0.468358
$503$	−40.2304	−1.79378	−0.896892	−	0.442249i	$-0.854181\pi$
$503$	−40.2304	−1.79378	−0.896892	+	0.442249i	$0.854181\pi$
$504$	−2.44651	−0.108976
$505$	10.0339	0.446502
$506$	−14.4221	−0.641139
$507$	2.38530	0.105935
$508$	0.617352	0.0273906
$509$	7.40618	0.328273	0.164137	−	0.986438i	$-0.447516\pi$
$509$	7.40618	0.328273	0.164137	+	0.986438i	$0.447516\pi$
$510$	−1.37256	−0.0607778
$511$	28.4645	1.25919
$512$	−1.00000	−0.0441942
$513$	1.28222	0.0566113
$514$	−25.9848	−1.14614
$515$	−10.4758	−0.461619
$516$	−3.32679	−0.146454
$517$	57.8925	2.54611
$518$	2.73942	0.120363
$519$	−2.38590	−0.104729
$520$	−5.38373	−0.236092
$521$	−36.4063	−1.59499	−0.797495	−	0.603325i	$-0.793842\pi$
$521$	−36.4063	−1.59499	−0.797495	+	0.603325i	$0.793842\pi$
$522$	4.44468	0.194538
$523$	18.1574	0.793966	0.396983	−	0.917826i	$-0.370057\pi$
$523$	18.1574	0.793966	0.396983	+	0.917826i	$0.370057\pi$
$524$	−4.86386	−0.212479
$525$	−7.62355	−0.332719
$526$	−16.6742	−0.727030
$527$	−5.90783	−0.257349
$528$	4.53685	0.197441
$529$	−12.8948	−0.560641
$530$	8.53868	0.370897
$531$	−1.00000	−0.0433963
$532$	3.13696	0.136005
$533$	−22.4132	−0.970825
$534$	−14.8009	−0.640495
$535$	6.16390	0.266489
$536$	14.1086	0.609397
$537$	−1.29654	−0.0559499
$538$	17.1270	0.738399
$539$	−4.60301	−0.198266
$540$	−1.37256	−0.0590654
$541$	−21.7888	−0.936774	−0.468387	−	0.883523i	$-0.655165\pi$
$541$	−21.7888	−0.936774	−0.468387	+	0.883523i	$0.655165\pi$
$542$	16.7230	0.718314
$543$	−7.64648	−0.328142
$544$	1.00000	0.0428746
$545$	5.83725	0.250040
$546$	9.59622	0.410680
$547$	18.3549	0.784799	0.392399	−	0.919795i	$-0.371645\pi$
$547$	18.3549	0.784799	0.392399	+	0.919795i	$0.371645\pi$
$548$	4.51260	0.192769
$549$	4.28402	0.182837
$550$	14.1372	0.602814
$551$	−5.69905	−0.242788
$552$	−3.17888	−0.135302
$553$	34.4647	1.46559
$554$	−6.16976	−0.262128
$555$	1.53688	0.0652371
$556$	−10.2338	−0.434008
$557$	19.9045	0.843382	0.421691	−	0.906740i	$-0.361437\pi$
$557$	19.9045	0.843382	0.421691	+	0.906740i	$0.361437\pi$
$558$	−5.90783	−0.250098
$559$	13.0490	0.551915
$560$	−3.35797	−0.141900
$561$	−4.53685	−0.191546
$562$	21.8738	0.922690
$563$	1.46278	0.0616487	0.0308244	−	0.999525i	$-0.490187\pi$
$563$	1.46278	0.0616487	0.0308244	+	0.999525i	$0.490187\pi$
$564$	12.7605	0.537315
$565$	−12.9683	−0.545582
$566$	3.51379	0.147695
$567$	2.44651	0.102744
$568$	10.3817	0.435605
$569$	−12.7127	−0.532942	−0.266471	−	0.963843i	$-0.585858\pi$
$569$	−12.7127	−0.532942	−0.266471	+	0.963843i	$0.585858\pi$
$570$	1.75992	0.0737148
$571$	−10.7548	−0.450073	−0.225037	−	0.974350i	$-0.572250\pi$
$571$	−10.7548	−0.450073	−0.225037	+	0.974350i	$0.572250\pi$
$572$	−17.7954	−0.744062
$573$	14.1519	0.591203
$574$	−13.9797	−0.583502
$575$	−9.90566	−0.413095
$576$	1.00000	0.0416667
$577$	−1.00812	−0.0419688	−0.0209844	−	0.999780i	$-0.506680\pi$
$577$	−1.00812	−0.0419688	−0.0209844	+	0.999780i	$0.506680\pi$
$578$	−1.00000	−0.0415945
$579$	16.3671	0.680193
$580$	6.10057	0.253312
$581$	22.5296	0.934684
$582$	6.25100	0.259112
$583$	28.2238	1.16891
$584$	−11.6347	−0.481448
$585$	5.38373	0.222590
$586$	−9.89280	−0.408668
$587$	−45.4167	−1.87455	−0.937273	−	0.348596i	$-0.886658\pi$
$587$	−45.4167	−1.87455	−0.937273	+	0.348596i	$0.886658\pi$
$588$	−1.01458	−0.0418407
$589$	7.57513	0.312128
$590$	−1.37256	−0.0565072
$591$	4.28585	0.176296
$592$	−1.11972	−0.0460204
$593$	−10.5736	−0.434207	−0.217103	−	0.976149i	$-0.569661\pi$
$593$	−10.5736	−0.434207	−0.217103	+	0.976149i	$0.569661\pi$
$594$	−4.53685	−0.186149
$595$	3.35797	0.137663
$596$	15.1122	0.619020
$597$	−20.6226	−0.844026
$598$	12.4689	0.509889
$599$	25.8614	1.05667	0.528335	−	0.849036i	$-0.322817\pi$
$599$	25.8614	1.05667	0.528335	+	0.849036i	$0.322817\pi$
$600$	3.11609	0.127214
$601$	−28.1495	−1.14824	−0.574122	−	0.818770i	$-0.694656\pi$
$601$	−28.1495	−1.14824	−0.574122	+	0.818770i	$0.694656\pi$
$602$	8.13902	0.331722
$603$	−14.1086	−0.574545
$604$	−18.4536	−0.750865
$605$	−13.1532	−0.534753
$606$	7.31037	0.296963
$607$	35.9274	1.45825	0.729124	−	0.684382i	$-0.239928\pi$
$607$	35.9274	1.45825	0.729124	+	0.684382i	$0.239928\pi$
$608$	−1.28222	−0.0520008
$609$	−10.8739	−0.440635
$610$	5.88005	0.238076
$611$	−50.0520	−2.02489
$612$	−1.00000	−0.0404226
$613$	18.1800	0.734285	0.367142	−	0.930165i	$-0.380336\pi$
$613$	18.1800	0.734285	0.367142	+	0.930165i	$0.380336\pi$
$614$	−13.8309	−0.558169
$615$	−7.84299	−0.316260
$616$	−11.0995	−0.447210
$617$	15.3181	0.616682	0.308341	−	0.951276i	$-0.400226\pi$
$617$	15.3181	0.616682	0.308341	+	0.951276i	$0.400226\pi$
$618$	−7.63233	−0.307017
$619$	−6.33812	−0.254750	−0.127375	−	0.991855i	$-0.540655\pi$
$619$	−6.33812	−0.254750	−0.127375	+	0.991855i	$0.540655\pi$
$620$	−8.10882	−0.325658
$621$	3.17888	0.127564
$622$	−14.0500	−0.563354
$623$	36.2104	1.45074
$624$	−3.92241	−0.157022
$625$	0.290476	0.0116190
$626$	6.65585	0.266021
$627$	5.81723	0.232318
$628$	−7.52286	−0.300195
$629$	1.11972	0.0446464
$630$	3.35797	0.133785
$631$	−8.70564	−0.346566	−0.173283	−	0.984872i	$-0.555438\pi$
$631$	−8.70564	−0.346566	−0.173283	+	0.984872i	$0.555438\pi$
$632$	−14.0873	−0.560363
$633$	−3.27881	−0.130321
$634$	8.10346	0.321829
$635$	−0.847350	−0.0336260
$636$	6.22101	0.246679
$637$	3.97961	0.157678
$638$	20.1648	0.798333
$639$	−10.3817	−0.410692
$640$	1.37256	0.0542550
$641$	−9.56592	−0.377831	−0.188916	−	0.981993i	$-0.560497\pi$
$641$	−9.56592	−0.377831	−0.188916	+	0.981993i	$0.560497\pi$
$642$	4.49082	0.177239
$643$	−19.2741	−0.760098	−0.380049	−	0.924966i	$-0.624093\pi$
$643$	−19.2741	−0.760098	−0.380049	+	0.924966i	$0.624093\pi$
$644$	7.77715	0.306463
$645$	4.56620	0.179794
$646$	1.28222	0.0504482
$647$	−23.7598	−0.934096	−0.467048	−	0.884232i	$-0.654682\pi$
$647$	−23.7598	−0.934096	−0.467048	+	0.884232i	$0.654682\pi$
$648$	−1.00000	−0.0392837
$649$	−4.53685	−0.178087
$650$	−12.2226	−0.479409
$651$	14.4536	0.566480
$652$	10.9961	0.430641
$653$	37.2182	1.45646	0.728230	−	0.685333i	$-0.240343\pi$
$653$	37.2182	1.45646	0.728230	+	0.685333i	$0.240343\pi$
$654$	4.25283	0.166299
$655$	6.67591	0.260850
$656$	5.71415	0.223100
$657$	11.6347	0.453914
$658$	−31.2187	−1.21703
$659$	10.3196	0.401995	0.200997	−	0.979592i	$-0.435582\pi$
$659$	10.3196	0.401995	0.200997	+	0.979592i	$0.435582\pi$
$660$	−6.22708	−0.242389
$661$	5.50184	0.213997	0.106998	−	0.994259i	$-0.465876\pi$
$661$	5.50184	0.213997	0.106998	+	0.994259i	$0.465876\pi$
$662$	6.21793	0.241667
$663$	3.92241	0.152334
$664$	−9.20886	−0.357373
$665$	−4.30566	−0.166966
$666$	1.11972	0.0433885
$667$	−14.1291	−0.547080
$668$	−0.349234	−0.0135123
$669$	7.89786	0.305349
$670$	−19.3648	−0.748127
$671$	19.4359	0.750316
$672$	−2.44651	−0.0943762
$673$	11.7544	0.453100	0.226550	−	0.974000i	$-0.427255\pi$
$673$	11.7544	0.453100	0.226550	+	0.974000i	$0.427255\pi$
$674$	5.56650	0.214413
$675$	−3.11609	−0.119938
$676$	2.38530	0.0917424
$677$	−36.9735	−1.42101	−0.710503	−	0.703694i	$-0.751533\pi$
$677$	−36.9735	−1.42101	−0.710503	+	0.703694i	$0.751533\pi$
$678$	−9.44831	−0.362860
$679$	−15.2931	−0.586896
$680$	−1.37256	−0.0526351
$681$	3.21878	0.123344
$682$	−26.8029	−1.02634
$683$	−14.5844	−0.558056	−0.279028	−	0.960283i	$-0.590012\pi$
$683$	−14.5844	−0.558056	−0.279028	+	0.960283i	$0.590012\pi$
$684$	1.28222	0.0490269
$685$	−6.19380	−0.236653
$686$	19.6078	0.748628
$687$	8.63791	0.329557
$688$	−3.32679	−0.126833
$689$	−24.4014	−0.929618
$690$	4.36318	0.166104
$691$	−16.4570	−0.626056	−0.313028	−	0.949744i	$-0.601343\pi$
$691$	−16.4570	−0.626056	−0.313028	+	0.949744i	$0.601343\pi$
$692$	−2.38590	−0.0906983
$693$	11.0995	0.421633
$694$	−24.3057	−0.922630
$695$	14.0464	0.532810
$696$	4.44468	0.168475
$697$	−5.71415	−0.216439
$698$	−24.6813	−0.934199
$699$	−2.25951	−0.0854626
$700$	−7.62355	−0.288143
$701$	30.3060	1.14464	0.572320	−	0.820030i	$-0.306043\pi$
$701$	30.3060	1.14464	0.572320	+	0.820030i	$0.306043\pi$
$702$	3.92241	0.148042
$703$	−1.43573	−0.0541497
$704$	4.53685	0.170989
$705$	−17.5145	−0.659635
$706$	−30.3271	−1.14138
$707$	−17.8849	−0.672631
$708$	−1.00000	−0.0375823
$709$	47.8644	1.79759	0.898793	−	0.438374i	$-0.144445\pi$
$709$	47.8644	1.79759	0.898793	+	0.438374i	$0.144445\pi$
$710$	−14.2494	−0.534771
$711$	14.0873	0.528315
$712$	−14.8009	−0.554685
$713$	18.7802	0.703326
$714$	2.44651	0.0915584
$715$	24.4252	0.913449
$716$	−1.29654	−0.0484541
$717$	25.9175	0.967908
$718$	−15.5771	−0.581334
$719$	−21.2687	−0.793190	−0.396595	−	0.917994i	$-0.629808\pi$
$719$	−21.2687	−0.793190	−0.396595	+	0.917994i	$0.629808\pi$
$720$	−1.37256	−0.0511521
$721$	18.6726	0.695403
$722$	17.3559	0.645920
$723$	14.0196	0.521396
$724$	−7.64648	−0.284179
$725$	13.8500	0.514377
$726$	−9.58299	−0.355658
$727$	7.60032	0.281880	0.140940	−	0.990018i	$-0.454987\pi$
$727$	7.60032	0.281880	0.140940	+	0.990018i	$0.454987\pi$
$728$	9.59622	0.355660
$729$	1.00000	0.0370370
$730$	15.9693	0.591050
$731$	3.32679	0.123046
$732$	4.28402	0.158342
$733$	43.2703	1.59823	0.799113	−	0.601181i	$-0.205303\pi$
$733$	43.2703	1.59823	0.799113	+	0.601181i	$0.205303\pi$
$734$	−12.8664	−0.474908
$735$	1.39257	0.0513658
$736$	−3.17888	−0.117175
$737$	−64.0084	−2.35778
$738$	−5.71415	−0.210341
$739$	25.2377	0.928384	0.464192	−	0.885735i	$-0.346345\pi$
$739$	25.2377	0.928384	0.464192	+	0.885735i	$0.346345\pi$
$740$	1.53688	0.0564970
$741$	−5.02939	−0.184759
$742$	−15.2198	−0.558735
$743$	−12.6389	−0.463675	−0.231838	−	0.972755i	$-0.574474\pi$
$743$	−12.6389	−0.463675	−0.231838	+	0.972755i	$0.574474\pi$
$744$	−5.90783	−0.216591
$745$	−20.7423	−0.759940
$746$	−21.6663	−0.793259
$747$	9.20886	0.336935
$748$	−4.53685	−0.165884
$749$	−10.9868	−0.401450
$750$	−11.1398	−0.406768
$751$	−30.5853	−1.11607	−0.558036	−	0.829817i	$-0.688445\pi$
$751$	−30.5853	−1.11607	−0.558036	+	0.829817i	$0.688445\pi$
$752$	12.7605	0.465328
$753$	−10.4937	−0.382413
$754$	−17.4338	−0.634903
$755$	25.3285	0.921800
$756$	2.44651	0.0889788
$757$	30.5441	1.11014	0.555072	−	0.831802i	$-0.312691\pi$
$757$	30.5441	1.11014	0.555072	+	0.831802i	$0.312691\pi$
$758$	−23.2861	−0.845790
$759$	14.4221	0.523488
$760$	1.75992	0.0638389
$761$	33.5608	1.21658	0.608289	−	0.793716i	$-0.291856\pi$
$761$	33.5608	1.21658	0.608289	+	0.793716i	$0.291856\pi$
$762$	−0.617352	−0.0223643
$763$	−10.4046	−0.376672
$764$	14.1519	0.511997
$765$	1.37256	0.0496249
$766$	−0.383389	−0.0138524
$767$	3.92241	0.141630
$768$	1.00000	0.0360844
$769$	−11.9763	−0.431875	−0.215938	−	0.976407i	$-0.569281\pi$
$769$	−11.9763	−0.431875	−0.215938	+	0.976407i	$0.569281\pi$
$770$	15.2346	0.549017
$771$	25.9848	0.935821
$772$	16.3671	0.589064
$773$	53.1645	1.91219	0.956097	−	0.293050i	$-0.0946703\pi$
$773$	53.1645	1.91219	0.956097	+	0.293050i	$0.0946703\pi$
$774$	3.32679	0.119579
$775$	−18.4093	−0.661283
$776$	6.25100	0.224398
$777$	−2.73942	−0.0982761
$778$	3.45139	0.123738
$779$	7.32679	0.262509
$780$	5.38373	0.192768
$781$	−47.1001	−1.68537
$782$	3.17888	0.113676
$783$	−4.44468	−0.158840
$784$	−1.01458	−0.0362351
$785$	10.3255	0.368535
$786$	4.86386	0.173488
$787$	10.3491	0.368905	0.184453	−	0.982841i	$-0.440949\pi$
$787$	10.3491	0.368905	0.184453	+	0.982841i	$0.440949\pi$
$788$	4.28585	0.152677
$789$	16.6742	0.593617
$790$	19.3356	0.687930
$791$	23.1154	0.821889
$792$	−4.53685	−0.161210
$793$	−16.8037	−0.596716
$794$	−4.45900	−0.158244
$795$	−8.53868	−0.302836
$796$	−20.6226	−0.730948
$797$	−11.0883	−0.392769	−0.196385	−	0.980527i	$-0.562920\pi$
$797$	−11.0883	−0.392769	−0.196385	+	0.980527i	$0.562920\pi$
$798$	−3.13696	−0.111047
$799$	−12.7605	−0.451435
$800$	3.11609	0.110170
$801$	14.8009	0.522962
$802$	7.81142	0.275831
$803$	52.7850	1.86274
$804$	−14.1086	−0.497571
$805$	−10.6746	−0.376229
$806$	23.1729	0.816231
$807$	−17.1270	−0.602900
$808$	7.31037	0.257178
$809$	36.1007	1.26923	0.634616	−	0.772828i	$-0.281158\pi$
$809$	36.1007	1.26923	0.634616	+	0.772828i	$0.281158\pi$
$810$	1.37256	0.0482267
$811$	−10.0801	−0.353960	−0.176980	−	0.984214i	$-0.556633\pi$
$811$	−10.0801	−0.353960	−0.176980	+	0.984214i	$0.556633\pi$
$812$	−10.8739	−0.381601
$813$	−16.7230	−0.586501
$814$	5.08002	0.178055
$815$	−15.0928	−0.528677
$816$	−1.00000	−0.0350070
$817$	−4.26567	−0.149237
$818$	−6.90534	−0.241440
$819$	−9.59622	−0.335319
$820$	−7.84299	−0.273889
$821$	21.5479	0.752025	0.376013	−	0.926614i	$-0.377295\pi$
$821$	21.5479	0.752025	0.376013	+	0.926614i	$0.377295\pi$
$822$	−4.51260	−0.157395
$823$	−28.9849	−1.01035	−0.505175	−	0.863017i	$-0.668572\pi$
$823$	−28.9849	−1.01035	−0.505175	+	0.863017i	$0.668572\pi$
$824$	−7.63233	−0.265885
$825$	−14.1372	−0.492195
$826$	2.44651	0.0851250
$827$	−8.30302	−0.288724	−0.144362	−	0.989525i	$-0.546113\pi$
$827$	−8.30302	−0.288724	−0.144362	+	0.989525i	$0.546113\pi$
$828$	3.17888	0.110474
$829$	11.8225	0.410611	0.205305	−	0.978698i	$-0.434181\pi$
$829$	11.8225	0.410611	0.205305	+	0.978698i	$0.434181\pi$
$830$	12.6397	0.438729
$831$	6.16976	0.214027
$832$	−3.92241	−0.135985
$833$	1.01458	0.0351532
$834$	10.2338	0.354366
$835$	0.479344	0.0165884
$836$	5.81723	0.201193
$837$	5.90783	0.204204
$838$	−10.4229	−0.360053
$839$	46.9065	1.61939	0.809696	−	0.586849i	$-0.199632\pi$
$839$	46.9065	1.61939	0.809696	+	0.586849i	$0.199632\pi$
$840$	3.35797	0.115861
$841$	−9.24486	−0.318788
$842$	27.6947	0.954424
$843$	−21.8738	−0.753373
$844$	−3.27881	−0.112861
$845$	−3.27396	−0.112628
$846$	−12.7605	−0.438715
$847$	23.4449	0.805576
$848$	6.22101	0.213630
$849$	−3.51379	−0.120593
$850$	−3.11609	−0.106881
$851$	−3.55947	−0.122017
$852$	−10.3817	−0.355670
$853$	−22.8736	−0.783176	−0.391588	−	0.920141i	$-0.628074\pi$
$853$	−22.8736	−0.783176	−0.391588	+	0.920141i	$0.628074\pi$
$854$	−10.4809	−0.358649
$855$	−1.75992	−0.0601879
$856$	4.49082	0.153493
$857$	−41.6744	−1.42357	−0.711785	−	0.702397i	$-0.752113\pi$
$857$	−41.6744	−1.42357	−0.711785	+	0.702397i	$0.752113\pi$
$858$	17.7954	0.607524
$859$	−28.1161	−0.959310	−0.479655	−	0.877457i	$-0.659238\pi$
$859$	−28.1161	−0.959310	−0.479655	+	0.877457i	$0.659238\pi$
$860$	4.56620	0.155706
$861$	13.9797	0.476428
$862$	−13.8370	−0.471290
$863$	−37.6570	−1.28186	−0.640930	−	0.767600i	$-0.721451\pi$
$863$	−37.6570	−1.28186	−0.640930	+	0.767600i	$0.721451\pi$
$864$	−1.00000	−0.0340207
$865$	3.27478	0.111346
$866$	9.03973	0.307183
$867$	1.00000	0.0339618
$868$	14.4536	0.490586
$869$	63.9119	2.16806
$870$	−6.10057	−0.206829
$871$	55.3396	1.87511
$872$	4.25283	0.144019
$873$	−6.25100	−0.211564
$874$	−4.07601	−0.137873
$875$	27.2536	0.921340
$876$	11.6347	0.393101
$877$	20.0188	0.675986	0.337993	−	0.941149i	$-0.390252\pi$
$877$	20.0188	0.675986	0.337993	+	0.941149i	$0.390252\pi$
$878$	6.09702	0.205764
$879$	9.89280	0.333676
$880$	−6.22708	−0.209915
$881$	−5.20291	−0.175290	−0.0876452	−	0.996152i	$-0.527934\pi$
$881$	−5.20291	−0.175290	−0.0876452	+	0.996152i	$0.527934\pi$
$882$	1.01458	0.0341628
$883$	7.60991	0.256094	0.128047	−	0.991768i	$-0.459129\pi$
$883$	7.60991	0.256094	0.128047	+	0.991768i	$0.459129\pi$
$884$	3.92241	0.131925
$885$	1.37256	0.0461380
$886$	21.3040	0.715723
$887$	−9.66067	−0.324374	−0.162187	−	0.986760i	$-0.551855\pi$
$887$	−9.66067	−0.324374	−0.162187	+	0.986760i	$0.551855\pi$
$888$	1.11972	0.0375755
$889$	1.51036	0.0506558
$890$	20.3150	0.680960
$891$	4.53685	0.151990
$892$	7.89786	0.264440
$893$	16.3618	0.547526
$894$	−15.1122	−0.505427
$895$	1.77958	0.0594847
$896$	−2.44651	−0.0817322
$897$	−12.4689	−0.416323
$898$	−9.14428	−0.305148
$899$	−26.2584	−0.875766
$900$	−3.11609	−0.103870
$901$	−6.22101	−0.207252
$902$	−25.9242	−0.863182
$903$	−8.13902	−0.270850
$904$	−9.44831	−0.314246
$905$	10.4952	0.348873
$906$	18.4536	0.613079
$907$	−5.93790	−0.197165	−0.0985824	−	0.995129i	$-0.531431\pi$
$907$	−5.93790	−0.197165	−0.0985824	+	0.995129i	$0.531431\pi$
$908$	3.21878	0.106819
$909$	−7.31037	−0.242470
$910$	−13.1713	−0.436626
$911$	−5.78904	−0.191799	−0.0958997	−	0.995391i	$-0.530573\pi$
$911$	−5.78904	−0.191799	−0.0958997	+	0.995391i	$0.530573\pi$
$912$	1.28222	0.0424585
$913$	41.7792	1.38269
$914$	−24.4679	−0.809326
$915$	−5.88005	−0.194389
$916$	8.63791	0.285405
$917$	−11.8995	−0.392955
$918$	1.00000	0.0330049
$919$	−9.84962	−0.324909	−0.162454	−	0.986716i	$-0.551941\pi$
$919$	−9.84962	−0.324909	−0.162454	+	0.986716i	$0.551941\pi$
$920$	4.36318	0.143850
$921$	13.8309	0.455743
$922$	0.986656	0.0324938
$923$	40.7212	1.34035
$924$	11.0995	0.365145
$925$	3.48916	0.114723
$926$	−10.0240	−0.329410
$927$	7.63233	0.250678
$928$	4.44468	0.145904
$929$	−26.2741	−0.862026	−0.431013	−	0.902346i	$-0.641844\pi$
$929$	−26.2741	−0.862026	−0.431013	+	0.902346i	$0.641844\pi$
$930$	8.10882	0.265899
$931$	−1.30092	−0.0426358
$932$	−2.25951	−0.0740128
$933$	14.0500	0.459976
$934$	−8.99505	−0.294327
$935$	6.22708	0.203647
$936$	3.92241	0.128208
$937$	43.4759	1.42029	0.710147	−	0.704053i	$-0.248628\pi$
$937$	43.4759	1.42029	0.710147	+	0.704053i	$0.248628\pi$
$938$	34.5168	1.12701
$939$	−6.65585	−0.217206
$940$	−17.5145	−0.571261
$941$	−49.9516	−1.62838	−0.814188	−	0.580601i	$-0.802818\pi$
$941$	−49.9516	−1.62838	−0.814188	+	0.580601i	$0.802818\pi$
$942$	7.52286	0.245108
$943$	18.1646	0.591520
$944$	−1.00000	−0.0325472
$945$	−3.35797	−0.109235
$946$	15.0931	0.490720
$947$	7.25843	0.235867	0.117934	−	0.993021i	$-0.462373\pi$
$947$	7.25843	0.235867	0.117934	+	0.993021i	$0.462373\pi$
$948$	14.0873	0.457534
$949$	−45.6362	−1.48141
$950$	3.99551	0.129631
$951$	−8.10346	−0.262773
$952$	2.44651	0.0792919
$953$	−50.4910	−1.63556	−0.817781	−	0.575529i	$-0.804796\pi$
$953$	−50.4910	−1.63556	−0.817781	+	0.575529i	$0.804796\pi$
$954$	−6.22101	−0.201413
$955$	−19.4242	−0.628554
$956$	25.9175	0.838233
$957$	−20.1648	−0.651836
$958$	−25.8738	−0.835944
$959$	11.0401	0.356504
$960$	−1.37256	−0.0442990
$961$	3.90243	0.125885
$962$	−4.39202	−0.141604
$963$	−4.49082	−0.144715
$964$	14.0196	0.451542
$965$	−22.4647	−0.723165
$966$	−7.77715	−0.250226
$967$	30.9893	0.996548	0.498274	−	0.867020i	$-0.333967\pi$
$967$	30.9893	0.996548	0.498274	+	0.867020i	$0.333967\pi$
$968$	−9.58299	−0.308009
$969$	−1.28222	−0.0411908
$970$	−8.57984	−0.275482
$971$	41.1170	1.31951	0.659754	−	0.751482i	$-0.270661\pi$
$971$	41.1170	1.31951	0.659754	+	0.751482i	$0.270661\pi$
$972$	1.00000	0.0320750
$973$	−25.0370	−0.802649
$974$	−1.84849	−0.0592295
$975$	12.2226	0.391436
$976$	4.28402	0.137128
$977$	−26.5130	−0.848228	−0.424114	−	0.905609i	$-0.639414\pi$
$977$	−26.5130	−0.848228	−0.424114	+	0.905609i	$0.639414\pi$
$978$	−10.9961	−0.351617
$979$	67.1492	2.14610
$980$	1.39257	0.0444841
$981$	−4.25283	−0.135782
$982$	35.3045	1.12661
$983$	55.9913	1.78585	0.892923	−	0.450210i	$-0.148651\pi$
$983$	55.9913	1.78585	0.892923	+	0.450210i	$0.148651\pi$
$984$	−5.71415	−0.182160
$985$	−5.88257	−0.187434
$986$	−4.44468	−0.141547
$987$	31.2187	0.993703
$988$	−5.02939	−0.160006
$989$	−10.5754	−0.336279
$990$	6.22708	0.197909
$991$	18.0439	0.573182	0.286591	−	0.958053i	$-0.407478\pi$
$991$	18.0439	0.573182	0.286591	+	0.958053i	$0.407478\pi$
$992$	−5.90783	−0.187574
$993$	−6.21793	−0.197320
$994$	25.3989	0.805603
$995$	28.3056	0.897349
$996$	9.20886	0.291794
$997$	−13.3287	−0.422124	−0.211062	−	0.977473i	$-0.567692\pi$
$997$	−13.3287	−0.422124	−0.211062	+	0.977473i	$0.567692\pi$
$998$	9.67804	0.306353
$999$	−1.11972	−0.0354265

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.p.1.2	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.p.1.2	✓	5	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.37256 q^{5} -1.00000 q^{6} +2.44651 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.37256 q^{5} -1.00000 q^{6} +2.44651 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.37256 q^{10} +4.53685 q^{11} +1.00000 q^{12} -3.92241 q^{13} -2.44651 q^{14} -1.37256 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +1.28222 q^{19} -1.37256 q^{20} +2.44651 q^{21} -4.53685 q^{22} +3.17888 q^{23} -1.00000 q^{24} -3.11609 q^{25} +3.92241 q^{26} +1.00000 q^{27} +2.44651 q^{28} -4.44468 q^{29} +1.37256 q^{30} +5.90783 q^{31} -1.00000 q^{32} +4.53685 q^{33} +1.00000 q^{34} -3.35797 q^{35} +1.00000 q^{36} -1.11972 q^{37} -1.28222 q^{38} -3.92241 q^{39} +1.37256 q^{40} +5.71415 q^{41} -2.44651 q^{42} -3.32679 q^{43} +4.53685 q^{44} -1.37256 q^{45} -3.17888 q^{46} +12.7605 q^{47} +1.00000 q^{48} -1.01458 q^{49} +3.11609 q^{50} -1.00000 q^{51} -3.92241 q^{52} +6.22101 q^{53} -1.00000 q^{54} -6.22708 q^{55} -2.44651 q^{56} +1.28222 q^{57} +4.44468 q^{58} -1.00000 q^{59} -1.37256 q^{60} +4.28402 q^{61} -5.90783 q^{62} +2.44651 q^{63} +1.00000 q^{64} +5.38373 q^{65} -4.53685 q^{66} -14.1086 q^{67} -1.00000 q^{68} +3.17888 q^{69} +3.35797 q^{70} -10.3817 q^{71} -1.00000 q^{72} +11.6347 q^{73} +1.11972 q^{74} -3.11609 q^{75} +1.28222 q^{76} +11.0995 q^{77} +3.92241 q^{78} +14.0873 q^{79} -1.37256 q^{80} +1.00000 q^{81} -5.71415 q^{82} +9.20886 q^{83} +2.44651 q^{84} +1.37256 q^{85} +3.32679 q^{86} -4.44468 q^{87} -4.53685 q^{88} +14.8009 q^{89} +1.37256 q^{90} -9.59622 q^{91} +3.17888 q^{92} +5.90783 q^{93} -12.7605 q^{94} -1.75992 q^{95} -1.00000 q^{96} -6.25100 q^{97} +1.01458 q^{98} +4.53685 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 5 q^{2} + 5 q^{3} + 5 q^{4} - q^{5} - 5 q^{6} - q^{7} - 5 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 - q^5 - 5 * q^6 - q^7 - 5 * q^8 + 5 * q^9	\( 5 q - 5 q^{2} + 5 q^{3} + 5 q^{4} - q^{5} - 5 q^{6} - q^{7} - 5 q^{8} + 5 q^{9} + q^{10} + 6 q^{11} + 5 q^{12} - 2 q^{13} + q^{14} - q^{15} + 5 q^{16} - 5 q^{17} - 5 q^{18} + 4 q^{19} - q^{20} - q^{21} - 6 q^{22} + 12 q^{23} - 5 q^{24} + 4 q^{25} + 2 q^{26} + 5 q^{27} - q^{28} + 19 q^{29} + q^{30} + 5 q^{31} - 5 q^{32} + 6 q^{33} + 5 q^{34} - 4 q^{35} + 5 q^{36} - 11 q^{37} - 4 q^{38} - 2 q^{39} + q^{40} + 6 q^{41} + q^{42} + 2 q^{43} + 6 q^{44} - q^{45} - 12 q^{46} + 22 q^{47} + 5 q^{48} - 12 q^{49} - 4 q^{50} - 5 q^{51} - 2 q^{52} + 15 q^{53} - 5 q^{54} - 36 q^{55} + q^{56} + 4 q^{57} - 19 q^{58} - 5 q^{59} - q^{60} + 16 q^{61} - 5 q^{62} - q^{63} + 5 q^{64} - 2 q^{65} - 6 q^{66} + 25 q^{67} - 5 q^{68} + 12 q^{69} + 4 q^{70} - 5 q^{72} - 10 q^{73} + 11 q^{74} + 4 q^{75} + 4 q^{76} + 6 q^{77} + 2 q^{78} + 10 q^{79} - q^{80} + 5 q^{81} - 6 q^{82} + 19 q^{83} - q^{84} + q^{85} - 2 q^{86} + 19 q^{87} - 6 q^{88} + 23 q^{89} + q^{90} - 17 q^{91} + 12 q^{92} + 5 q^{93} - 22 q^{94} + q^{95} - 5 q^{96} + 8 q^{97} + 12 q^{98} + 6 q^{99}+O(q^{100}) \) 5 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 - q^5 - 5 * q^6 - q^7 - 5 * q^8 + 5 * q^9 + q^10 + 6 * q^11 + 5 * q^12 - 2 * q^13 + q^14 - q^15 + 5 * q^16 - 5 * q^17 - 5 * q^18 + 4 * q^19 - q^20 - q^21 - 6 * q^22 + 12 * q^23 - 5 * q^24 + 4 * q^25 + 2 * q^26 + 5 * q^27 - q^28 + 19 * q^29 + q^30 + 5 * q^31 - 5 * q^32 + 6 * q^33 + 5 * q^34 - 4 * q^35 + 5 * q^36 - 11 * q^37 - 4 * q^38 - 2 * q^39 + q^40 + 6 * q^41 + q^42 + 2 * q^43 + 6 * q^44 - q^45 - 12 * q^46 + 22 * q^47 + 5 * q^48 - 12 * q^49 - 4 * q^50 - 5 * q^51 - 2 * q^52 + 15 * q^53 - 5 * q^54 - 36 * q^55 + q^56 + 4 * q^57 - 19 * q^58 - 5 * q^59 - q^60 + 16 * q^61 - 5 * q^62 - q^63 + 5 * q^64 - 2 * q^65 - 6 * q^66 + 25 * q^67 - 5 * q^68 + 12 * q^69 + 4 * q^70 - 5 * q^72 - 10 * q^73 + 11 * q^74 + 4 * q^75 + 4 * q^76 + 6 * q^77 + 2 * q^78 + 10 * q^79 - q^80 + 5 * q^81 - 6 * q^82 + 19 * q^83 - q^84 + q^85 - 2 * q^86 + 19 * q^87 - 6 * q^88 + 23 * q^89 + q^90 - 17 * q^91 + 12 * q^92 + 5 * q^93 - 22 * q^94 + q^95 - 5 * q^96 + 8 * q^97 + 12 * q^98 + 6 * q^99

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