LMFDB - Embedded newform 6018.2.a.s.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:	$8$
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} - 3x^{7} - 17x^{6} + 37x^{5} + 105x^{4} - 117x^{3} - 238x^{2} + 42x + 90 $ x^8 - 3x^7 - 17x^6 + 37x^5 + 105x^4 - 117x^3 - 238x^2 + 42*x + 90
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			1.2
Root			$2.14759$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.25098 q^{5} +1.00000 q^{6} +0.744783 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.25098 q^{5} +1.00000 q^{6} +0.744783 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.25098 q^{10} +2.33248 q^{11} -1.00000 q^{12} +1.46972 q^{13} -0.744783 q^{14} +2.25098 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +6.67430 q^{19} -2.25098 q^{20} -0.744783 q^{21} -2.33248 q^{22} -3.70644 q^{23} +1.00000 q^{24} +0.0669086 q^{25} -1.46972 q^{26} -1.00000 q^{27} +0.744783 q^{28} +2.98937 q^{29} -2.25098 q^{30} -0.755138 q^{31} -1.00000 q^{32} -2.33248 q^{33} +1.00000 q^{34} -1.67649 q^{35} +1.00000 q^{36} +10.9072 q^{37} -6.67430 q^{38} -1.46972 q^{39} +2.25098 q^{40} +1.43420 q^{41} +0.744783 q^{42} -2.14336 q^{43} +2.33248 q^{44} -2.25098 q^{45} +3.70644 q^{46} +7.97412 q^{47} -1.00000 q^{48} -6.44530 q^{49} -0.0669086 q^{50} +1.00000 q^{51} +1.46972 q^{52} -0.555658 q^{53} +1.00000 q^{54} -5.25037 q^{55} -0.744783 q^{56} -6.67430 q^{57} -2.98937 q^{58} +1.00000 q^{59} +2.25098 q^{60} +7.27359 q^{61} +0.755138 q^{62} +0.744783 q^{63} +1.00000 q^{64} -3.30831 q^{65} +2.33248 q^{66} +11.3321 q^{67} -1.00000 q^{68} +3.70644 q^{69} +1.67649 q^{70} -9.47926 q^{71} -1.00000 q^{72} -0.684684 q^{73} -10.9072 q^{74} -0.0669086 q^{75} +6.67430 q^{76} +1.73719 q^{77} +1.46972 q^{78} +2.55312 q^{79} -2.25098 q^{80} +1.00000 q^{81} -1.43420 q^{82} -10.4910 q^{83} -0.744783 q^{84} +2.25098 q^{85} +2.14336 q^{86} -2.98937 q^{87} -2.33248 q^{88} -4.18370 q^{89} +2.25098 q^{90} +1.09462 q^{91} -3.70644 q^{92} +0.755138 q^{93} -7.97412 q^{94} -15.0237 q^{95} +1.00000 q^{96} +6.31411 q^{97} +6.44530 q^{98} +2.33248 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} - 8 q^{3} + 8 q^{4} - q^{5} + 8 q^{6} + 6 q^{7} - 8 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 - q^5 + 8 * q^6 + 6 * q^7 - 8 * q^8 + 8 * q^9	$ 8 q - 8 q^{2} - 8 q^{3} + 8 q^{4} - q^{5} + 8 q^{6} + 6 q^{7} - 8 q^{8} + 8 q^{9} + q^{10} - 8 q^{12} + 6 q^{13} - 6 q^{14} + q^{15} + 8 q^{16} - 8 q^{17} - 8 q^{18} - 7 q^{19} - q^{20} - 6 q^{21} - 5 q^{23} + 8 q^{24} + 9 q^{25} - 6 q^{26} - 8 q^{27} + 6 q^{28} - 15 q^{29} - q^{30} + 21 q^{31} - 8 q^{32} + 8 q^{34} - 2 q^{35} + 8 q^{36} + 7 q^{37} + 7 q^{38} - 6 q^{39} + q^{40} - q^{41} + 6 q^{42} + 14 q^{43} - q^{45} + 5 q^{46} - 8 q^{47} - 8 q^{48} + 2 q^{49} - 9 q^{50} + 8 q^{51} + 6 q^{52} + 8 q^{53} + 8 q^{54} + 24 q^{55} - 6 q^{56} + 7 q^{57} + 15 q^{58} + 8 q^{59} + q^{60} - 21 q^{62} + 6 q^{63} + 8 q^{64} + 6 q^{65} + 15 q^{67} - 8 q^{68} + 5 q^{69} + 2 q^{70} - 22 q^{71} - 8 q^{72} + 13 q^{73} - 7 q^{74} - 9 q^{75} - 7 q^{76} - 6 q^{77} + 6 q^{78} + 26 q^{79} - q^{80} + 8 q^{81} + q^{82} + 30 q^{83} - 6 q^{84} + q^{85} - 14 q^{86} + 15 q^{87} - 6 q^{89} + q^{90} + 3 q^{91} - 5 q^{92} - 21 q^{93} + 8 q^{94} + 37 q^{95} + 8 q^{96} + 23 q^{97} - 2 q^{98}+O(q^{100}) $ 8 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 - q^5 + 8 * q^6 + 6 * q^7 - 8 * q^8 + 8 * q^9 + q^10 - 8 * q^12 + 6 * q^13 - 6 * q^14 + q^15 + 8 * q^16 - 8 * q^17 - 8 * q^18 - 7 * q^19 - q^20 - 6 * q^21 - 5 * q^23 + 8 * q^24 + 9 * q^25 - 6 * q^26 - 8 * q^27 + 6 * q^28 - 15 * q^29 - q^30 + 21 * q^31 - 8 * q^32 + 8 * q^34 - 2 * q^35 + 8 * q^36 + 7 * q^37 + 7 * q^38 - 6 * q^39 + q^40 - q^41 + 6 * q^42 + 14 * q^43 - q^45 + 5 * q^46 - 8 * q^47 - 8 * q^48 + 2 * q^49 - 9 * q^50 + 8 * q^51 + 6 * q^52 + 8 * q^53 + 8 * q^54 + 24 * q^55 - 6 * q^56 + 7 * q^57 + 15 * q^58 + 8 * q^59 + q^60 - 21 * q^62 + 6 * q^63 + 8 * q^64 + 6 * q^65 + 15 * q^67 - 8 * q^68 + 5 * q^69 + 2 * q^70 - 22 * q^71 - 8 * q^72 + 13 * q^73 - 7 * q^74 - 9 * q^75 - 7 * q^76 - 6 * q^77 + 6 * q^78 + 26 * q^79 - q^80 + 8 * q^81 + q^82 + 30 * q^83 - 6 * q^84 + q^85 - 14 * q^86 + 15 * q^87 - 6 * q^89 + q^90 + 3 * q^91 - 5 * q^92 - 21 * q^93 + 8 * q^94 + 37 * q^95 + 8 * q^96 + 23 * q^97 - 2 * q^98

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
$5$	−2.25098	−1.00667	−0.503334	−	0.864092i	$-0.667894\pi$
$5$	−2.25098	−1.00667	−0.503334	+	0.864092i	$0.667894\pi$
$6$	1.00000	0.408248
$7$	0.744783	0.281502	0.140751	−	0.990045i	$-0.455048\pi$
$7$	0.744783	0.281502	0.140751	+	0.990045i	$0.455048\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	2.25098	0.711822
$11$	2.33248	0.703269	0.351635	−	0.936137i	$-0.385626\pi$
$11$	2.33248	0.703269	0.351635	+	0.936137i	$0.385626\pi$
$12$	−1.00000	−0.288675
$13$	1.46972	0.407627	0.203813	−	0.979010i	$-0.434666\pi$
$13$	1.46972	0.407627	0.203813	+	0.979010i	$0.434666\pi$
$14$	−0.744783	−0.199052
$15$	2.25098	0.581200
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.00000	−0.235702
$19$	6.67430	1.53119	0.765595	−	0.643323i	$-0.222445\pi$
$19$	6.67430	1.53119	0.765595	+	0.643323i	$0.222445\pi$
$20$	−2.25098	−0.503334
$21$	−0.744783	−0.162525
$22$	−2.33248	−0.497287
$23$	−3.70644	−0.772847	−0.386423	−	0.922322i	$-0.626290\pi$
$23$	−3.70644	−0.772847	−0.386423	+	0.922322i	$0.626290\pi$
$24$	1.00000	0.204124
$25$	0.0669086	0.0133817
$26$	−1.46972	−0.288236
$27$	−1.00000	−0.192450
$28$	0.744783	0.140751
$29$	2.98937	0.555112	0.277556	−	0.960709i	$-0.410476\pi$
$29$	2.98937	0.555112	0.277556	+	0.960709i	$0.410476\pi$
$30$	−2.25098	−0.410971
$31$	−0.755138	−0.135627	−0.0678134	−	0.997698i	$-0.521602\pi$
$31$	−0.755138	−0.135627	−0.0678134	+	0.997698i	$0.521602\pi$
$32$	−1.00000	−0.176777
$33$	−2.33248	−0.406033
$34$	1.00000	0.171499
$35$	−1.67649	−0.283379
$36$	1.00000	0.166667
$37$	10.9072	1.79314	0.896568	−	0.442907i	$-0.146053\pi$
$37$	10.9072	1.79314	0.896568	+	0.442907i	$0.146053\pi$
$38$	−6.67430	−1.08271
$39$	−1.46972	−0.235343
$40$	2.25098	0.355911
$41$	1.43420	0.223985	0.111992	−	0.993709i	$-0.464277\pi$
$41$	1.43420	0.223985	0.111992	+	0.993709i	$0.464277\pi$
$42$	0.744783	0.114923
$43$	−2.14336	−0.326859	−0.163429	−	0.986555i	$-0.552256\pi$
$43$	−2.14336	−0.326859	−0.163429	+	0.986555i	$0.552256\pi$
$44$	2.33248	0.351635
$45$	−2.25098	−0.335556
$46$	3.70644	0.546485
$47$	7.97412	1.16315	0.581573	−	0.813494i	$-0.302438\pi$
$47$	7.97412	1.16315	0.581573	+	0.813494i	$0.302438\pi$
$48$	−1.00000	−0.144338
$49$	−6.44530	−0.920757
$50$	−0.0669086	−0.00946230
$51$	1.00000	0.140028
$52$	1.46972	0.203813
$53$	−0.555658	−0.0763255	−0.0381627	−	0.999272i	$-0.512151\pi$
$53$	−0.555658	−0.0763255	−0.0381627	+	0.999272i	$0.512151\pi$
$54$	1.00000	0.136083
$55$	−5.25037	−0.707959
$56$	−0.744783	−0.0995258
$57$	−6.67430	−0.884033
$58$	−2.98937	−0.392524
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	2.25098	0.290600
$61$	7.27359	0.931288	0.465644	−	0.884972i	$-0.345823\pi$
$61$	7.27359	0.931288	0.465644	+	0.884972i	$0.345823\pi$
$62$	0.755138	0.0959026
$63$	0.744783	0.0938338
$64$	1.00000	0.125000
$65$	−3.30831	−0.410345
$66$	2.33248	0.287109
$67$	11.3321	1.38444	0.692219	−	0.721687i	$-0.256633\pi$
$67$	11.3321	1.38444	0.692219	+	0.721687i	$0.256633\pi$
$68$	−1.00000	−0.121268
$69$	3.70644	0.446203
$70$	1.67649	0.200379
$71$	−9.47926	−1.12498	−0.562490	−	0.826804i	$-0.690157\pi$
$71$	−9.47926	−1.12498	−0.562490	+	0.826804i	$0.690157\pi$
$72$	−1.00000	−0.117851
$73$	−0.684684	−0.0801362	−0.0400681	−	0.999197i	$-0.512757\pi$
$73$	−0.684684	−0.0801362	−0.0400681	+	0.999197i	$0.512757\pi$
$74$	−10.9072	−1.26794
$75$	−0.0669086	−0.00772594
$76$	6.67430	0.765595
$77$	1.73719	0.197971
$78$	1.46972	0.166413
$79$	2.55312	0.287249	0.143624	−	0.989632i	$-0.454124\pi$
$79$	2.55312	0.287249	0.143624	+	0.989632i	$0.454124\pi$
$80$	−2.25098	−0.251667
$81$	1.00000	0.111111
$82$	−1.43420	−0.158381
$83$	−10.4910	−1.15154	−0.575771	−	0.817611i	$-0.695298\pi$
$83$	−10.4910	−1.15154	−0.575771	+	0.817611i	$0.695298\pi$
$84$	−0.744783	−0.0812625
$85$	2.25098	0.244153
$86$	2.14336	0.231124
$87$	−2.98937	−0.320494
$88$	−2.33248	−0.248643
$89$	−4.18370	−0.443471	−0.221735	−	0.975107i	$-0.571172\pi$
$89$	−4.18370	−0.443471	−0.221735	+	0.975107i	$0.571172\pi$
$90$	2.25098	0.237274
$91$	1.09462	0.114748
$92$	−3.70644	−0.386423
$93$	0.755138	0.0783042
$94$	−7.97412	−0.822468
$95$	−15.0237	−1.54140
$96$	1.00000	0.102062
$97$	6.31411	0.641101	0.320550	−	0.947231i	$-0.396132\pi$
$97$	6.31411	0.641101	0.320550	+	0.947231i	$0.396132\pi$
$98$	6.44530	0.651073
$99$	2.33248	0.234423
$100$	0.0669086	0.00669086
$101$	−11.3149	−1.12588	−0.562938	−	0.826499i	$-0.690329\pi$
$101$	−11.3149	−1.12588	−0.562938	+	0.826499i	$0.690329\pi$
$102$	−1.00000	−0.0990148
$103$	−15.6380	−1.54086	−0.770430	−	0.637525i	$-0.779958\pi$
$103$	−15.6380	−1.54086	−0.770430	+	0.637525i	$0.779958\pi$
$104$	−1.46972	−0.144118
$105$	1.67649	0.163609
$106$	0.555658	0.0539703
$107$	10.6721	1.03171	0.515853	−	0.856677i	$-0.327475\pi$
$107$	10.6721	1.03171	0.515853	+	0.856677i	$0.327475\pi$
$108$	−1.00000	−0.0962250
$109$	−10.7884	−1.03334	−0.516672	−	0.856184i	$-0.672829\pi$
$109$	−10.7884	−1.03334	−0.516672	+	0.856184i	$0.672829\pi$
$110$	5.25037	0.500603
$111$	−10.9072	−1.03527
$112$	0.744783	0.0703754
$113$	2.51807	0.236880	0.118440	−	0.992961i	$-0.462211\pi$
$113$	2.51807	0.236880	0.118440	+	0.992961i	$0.462211\pi$
$114$	6.67430	0.625106
$115$	8.34313	0.778000
$116$	2.98937	0.277556
$117$	1.46972	0.135876
$118$	−1.00000	−0.0920575
$119$	−0.744783	−0.0682741
$120$	−2.25098	−0.205485
$121$	−5.55953	−0.505412
$122$	−7.27359	−0.658520
$123$	−1.43420	−0.129318
$124$	−0.755138	−0.0678134
$125$	11.1043	0.993198
$126$	−0.744783	−0.0663505
$127$	13.6560	1.21177	0.605887	−	0.795550i	$-0.292818\pi$
$127$	13.6560	1.21177	0.605887	+	0.795550i	$0.292818\pi$
$128$	−1.00000	−0.0883883
$129$	2.14336	0.188712
$130$	3.30831	0.290158
$131$	−15.8779	−1.38725	−0.693627	−	0.720334i	$-0.743988\pi$
$131$	−15.8779	−1.38725	−0.693627	+	0.720334i	$0.743988\pi$
$132$	−2.33248	−0.203016
$133$	4.97091	0.431032
$134$	−11.3321	−0.978946
$135$	2.25098	0.193733
$136$	1.00000	0.0857493
$137$	5.50898	0.470664	0.235332	−	0.971915i	$-0.424382\pi$
$137$	5.50898	0.470664	0.235332	+	0.971915i	$0.424382\pi$
$138$	−3.70644	−0.315513
$139$	−15.0899	−1.27991	−0.639956	−	0.768412i	$-0.721047\pi$
$139$	−15.0899	−1.27991	−0.639956	+	0.768412i	$0.721047\pi$
$140$	−1.67649	−0.141689
$141$	−7.97412	−0.671542
$142$	9.47926	0.795482
$143$	3.42809	0.286671
$144$	1.00000	0.0833333
$145$	−6.72902	−0.558814
$146$	0.684684	0.0566648
$147$	6.44530	0.531599
$148$	10.9072	0.896568
$149$	−10.7904	−0.883985	−0.441993	−	0.897019i	$-0.645728\pi$
$149$	−10.7904	−0.883985	−0.441993	+	0.897019i	$0.645728\pi$
$150$	0.0669086	0.00546306
$151$	−0.577797	−0.0470205	−0.0235102	−	0.999724i	$-0.507484\pi$
$151$	−0.577797	−0.0470205	−0.0235102	+	0.999724i	$0.507484\pi$
$152$	−6.67430	−0.541357
$153$	−1.00000	−0.0808452
$154$	−1.73719	−0.139987
$155$	1.69980	0.136531
$156$	−1.46972	−0.117672
$157$	19.5006	1.55632	0.778159	−	0.628068i	$-0.216154\pi$
$157$	19.5006	1.55632	0.778159	+	0.628068i	$0.216154\pi$
$158$	−2.55312	−0.203115
$159$	0.555658	0.0440665
$160$	2.25098	0.177956
$161$	−2.76050	−0.217558
$162$	−1.00000	−0.0785674
$163$	3.10700	0.243359	0.121679	−	0.992569i	$-0.461172\pi$
$163$	3.10700	0.243359	0.121679	+	0.992569i	$0.461172\pi$
$164$	1.43420	0.111992
$165$	5.25037	0.408740
$166$	10.4910	0.814263
$167$	−2.31460	−0.179109	−0.0895546	−	0.995982i	$-0.528544\pi$
$167$	−2.31460	−0.179109	−0.0895546	+	0.995982i	$0.528544\pi$
$168$	0.744783	0.0574613
$169$	−10.8399	−0.833841
$170$	−2.25098	−0.172642
$171$	6.67430	0.510397
$172$	−2.14336	−0.163429
$173$	8.26013	0.628006	0.314003	−	0.949422i	$-0.398330\pi$
$173$	8.26013	0.628006	0.314003	+	0.949422i	$0.398330\pi$
$174$	2.98937	0.226624
$175$	0.0498324	0.00376697
$176$	2.33248	0.175817
$177$	−1.00000	−0.0751646
$178$	4.18370	0.313581
$179$	−5.00744	−0.374274	−0.187137	−	0.982334i	$-0.559921\pi$
$179$	−5.00744	−0.374274	−0.187137	+	0.982334i	$0.559921\pi$
$180$	−2.25098	−0.167778
$181$	4.27999	0.318129	0.159064	−	0.987268i	$-0.449152\pi$
$181$	4.27999	0.318129	0.159064	+	0.987268i	$0.449152\pi$
$182$	−1.09462	−0.0811388
$183$	−7.27359	−0.537679
$184$	3.70644	0.273243
$185$	−24.5519	−1.80509
$186$	−0.755138	−0.0553694
$187$	−2.33248	−0.170568
$188$	7.97412	0.581573
$189$	−0.744783	−0.0541750
$190$	15.0237	1.08994
$191$	−0.847670	−0.0613353	−0.0306676	−	0.999530i	$-0.509763\pi$
$191$	−0.847670	−0.0613353	−0.0306676	+	0.999530i	$0.509763\pi$
$192$	−1.00000	−0.0721688
$193$	14.5718	1.04890	0.524451	−	0.851441i	$-0.324271\pi$
$193$	14.5718	1.04890	0.524451	+	0.851441i	$0.324271\pi$
$194$	−6.31411	−0.453327
$195$	3.30831	0.236913
$196$	−6.44530	−0.460378
$197$	5.93431	0.422802	0.211401	−	0.977399i	$-0.432197\pi$
$197$	5.93431	0.422802	0.211401	+	0.977399i	$0.432197\pi$
$198$	−2.33248	−0.165762
$199$	−21.4599	−1.52125	−0.760625	−	0.649191i	$-0.775108\pi$
$199$	−21.4599	−1.52125	−0.760625	+	0.649191i	$0.775108\pi$
$200$	−0.0669086	−0.00473115
$201$	−11.3321	−0.799306
$202$	11.3149	0.796115
$203$	2.22643	0.156265
$204$	1.00000	0.0700140
$205$	−3.22836	−0.225479
$206$	15.6380	1.08955
$207$	−3.70644	−0.257616
$208$	1.46972	0.101907
$209$	15.5677	1.07684
$210$	−1.67649	−0.115689
$211$	12.1102	0.833698	0.416849	−	0.908976i	$-0.363134\pi$
$211$	12.1102	0.833698	0.416849	+	0.908976i	$0.363134\pi$
$212$	−0.555658	−0.0381627
$213$	9.47926	0.649508
$214$	−10.6721	−0.729527
$215$	4.82465	0.329038
$216$	1.00000	0.0680414
$217$	−0.562414	−0.0381792
$218$	10.7884	0.730684
$219$	0.684684	0.0462666
$220$	−5.25037	−0.353980
$221$	−1.46972	−0.0988640
$222$	10.9072	0.732044
$223$	12.2515	0.820419	0.410209	−	0.911991i	$-0.365456\pi$
$223$	12.2515	0.820419	0.410209	+	0.911991i	$0.365456\pi$
$224$	−0.744783	−0.0497629
$225$	0.0669086	0.00446057
$226$	−2.51807	−0.167500
$227$	25.7155	1.70679	0.853397	−	0.521261i	$-0.174538\pi$
$227$	25.7155	1.70679	0.853397	+	0.521261i	$0.174538\pi$
$228$	−6.67430	−0.442017
$229$	−1.91198	−0.126347	−0.0631736	−	0.998003i	$-0.520122\pi$
$229$	−1.91198	−0.126347	−0.0631736	+	0.998003i	$0.520122\pi$
$230$	−8.34313	−0.550129
$231$	−1.73719	−0.114299
$232$	−2.98937	−0.196262
$233$	12.2211	0.800634	0.400317	−	0.916377i	$-0.368900\pi$
$233$	12.2211	0.800634	0.400317	+	0.916377i	$0.368900\pi$
$234$	−1.46972	−0.0960785
$235$	−17.9496	−1.17090
$236$	1.00000	0.0650945
$237$	−2.55312	−0.165843
$238$	0.744783	0.0482771
$239$	17.2655	1.11681	0.558405	−	0.829569i	$-0.311414\pi$
$239$	17.2655	1.11681	0.558405	+	0.829569i	$0.311414\pi$
$240$	2.25098	0.145300
$241$	9.82240	0.632717	0.316358	−	0.948640i	$-0.397540\pi$
$241$	9.82240	0.632717	0.316358	+	0.948640i	$0.397540\pi$
$242$	5.55953	0.357380
$243$	−1.00000	−0.0641500
$244$	7.27359	0.465644
$245$	14.5082	0.926897
$246$	1.43420	0.0914415
$247$	9.80935	0.624154
$248$	0.755138	0.0479513
$249$	10.4910	0.664843
$250$	−11.1043	−0.702297
$251$	−5.65216	−0.356761	−0.178380	−	0.983962i	$-0.557086\pi$
$251$	−5.65216	−0.356761	−0.178380	+	0.983962i	$0.557086\pi$
$252$	0.744783	0.0469169
$253$	−8.64521	−0.543519
$254$	−13.6560	−0.856854
$255$	−2.25098	−0.140962
$256$	1.00000	0.0625000
$257$	−3.49579	−0.218061	−0.109031	−	0.994038i	$-0.534775\pi$
$257$	−3.49579	−0.218061	−0.109031	+	0.994038i	$0.534775\pi$
$258$	−2.14336	−0.133439
$259$	8.12351	0.504770
$260$	−3.30831	−0.205172
$261$	2.98937	0.185037
$262$	15.8779	0.980937
$263$	0.649961	0.0400783	0.0200392	−	0.999799i	$-0.493621\pi$
$263$	0.649961	0.0400783	0.0200392	+	0.999799i	$0.493621\pi$
$264$	2.33248	0.143554
$265$	1.25077	0.0768345
$266$	−4.97091	−0.304786
$267$	4.18370	0.256038
$268$	11.3321	0.692219
$269$	−2.49731	−0.152264	−0.0761318	−	0.997098i	$-0.524257\pi$
$269$	−2.49731	−0.152264	−0.0761318	+	0.997098i	$0.524257\pi$
$270$	−2.25098	−0.136990
$271$	25.5431	1.55163	0.775816	−	0.630959i	$-0.217339\pi$
$271$	25.5431	1.55163	0.775816	+	0.630959i	$0.217339\pi$
$272$	−1.00000	−0.0606339
$273$	−1.09462	−0.0662495
$274$	−5.50898	−0.332810
$275$	0.156063	0.00941095
$276$	3.70644	0.223102
$277$	−3.79244	−0.227866	−0.113933	−	0.993488i	$-0.536345\pi$
$277$	−3.79244	−0.227866	−0.113933	+	0.993488i	$0.536345\pi$
$278$	15.0899	0.905034
$279$	−0.755138	−0.0452089
$280$	1.67649	0.100190
$281$	22.4667	1.34025	0.670127	−	0.742247i	$-0.266240\pi$
$281$	22.4667	1.34025	0.670127	+	0.742247i	$0.266240\pi$
$282$	7.97412	0.474852
$283$	17.1466	1.01926	0.509630	−	0.860394i	$-0.329782\pi$
$283$	17.1466	1.01926	0.509630	+	0.860394i	$0.329782\pi$
$284$	−9.47926	−0.562490
$285$	15.0237	0.889928
$286$	−3.42809	−0.202707
$287$	1.06817	0.0630521
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	6.72902	0.395141
$291$	−6.31411	−0.370140
$292$	−0.684684	−0.0400681
$293$	−15.5636	−0.909236	−0.454618	−	0.890687i	$-0.650224\pi$
$293$	−15.5636	−0.909236	−0.454618	+	0.890687i	$0.650224\pi$
$294$	−6.44530	−0.375897
$295$	−2.25098	−0.131057
$296$	−10.9072	−0.633969
$297$	−2.33248	−0.135344
$298$	10.7904	0.625072
$299$	−5.44743	−0.315033
$300$	−0.0669086	−0.00386297
$301$	−1.59633	−0.0920112
$302$	0.577797	0.0332485
$303$	11.3149	0.650025
$304$	6.67430	0.382798
$305$	−16.3727	−0.937498
$306$	1.00000	0.0571662
$307$	5.47777	0.312633	0.156317	−	0.987707i	$-0.450038\pi$
$307$	5.47777	0.312633	0.156317	+	0.987707i	$0.450038\pi$
$308$	1.73719	0.0989857
$309$	15.6380	0.889616
$310$	−1.69980	−0.0965422
$311$	−22.2670	−1.26264	−0.631322	−	0.775521i	$-0.717487\pi$
$311$	−22.2670	−1.26264	−0.631322	+	0.775521i	$0.717487\pi$
$312$	1.46972	0.0832064
$313$	16.5391	0.934847	0.467424	−	0.884033i	$-0.345182\pi$
$313$	16.5391	0.934847	0.467424	+	0.884033i	$0.345182\pi$
$314$	−19.5006	−1.10048
$315$	−1.67649	−0.0944596
$316$	2.55312	0.143624
$317$	−1.48690	−0.0835125	−0.0417562	−	0.999128i	$-0.513295\pi$
$317$	−1.48690	−0.0835125	−0.0417562	+	0.999128i	$0.513295\pi$
$318$	−0.555658	−0.0311598
$319$	6.97265	0.390394
$320$	−2.25098	−0.125834
$321$	−10.6721	−0.595656
$322$	2.76050	0.153836
$323$	−6.67430	−0.371368
$324$	1.00000	0.0555556
$325$	0.0983368	0.00545475
$326$	−3.10700	−0.172081
$327$	10.7884	0.596601
$328$	−1.43420	−0.0791906
$329$	5.93899	0.327427
$330$	−5.25037	−0.289023
$331$	−11.7250	−0.644465	−0.322232	−	0.946661i	$-0.604433\pi$
$331$	−11.7250	−0.644465	−0.322232	+	0.946661i	$0.604433\pi$
$332$	−10.4910	−0.575771
$333$	10.9072	0.597712
$334$	2.31460	0.126649
$335$	−25.5084	−1.39367
$336$	−0.744783	−0.0406312
$337$	3.94487	0.214891	0.107445	−	0.994211i	$-0.465733\pi$
$337$	3.94487	0.214891	0.107445	+	0.994211i	$0.465733\pi$
$338$	10.8399	0.589614
$339$	−2.51807	−0.136763
$340$	2.25098	0.122077
$341$	−1.76135	−0.0953822
$342$	−6.67430	−0.360905
$343$	−10.0138	−0.540696
$344$	2.14336	0.115562
$345$	−8.34313	−0.449179
$346$	−8.26013	−0.444068
$347$	−6.95425	−0.373323	−0.186662	−	0.982424i	$-0.559767\pi$
$347$	−6.95425	−0.373323	−0.186662	+	0.982424i	$0.559767\pi$
$348$	−2.98937	−0.160247
$349$	1.00105	0.0535847	0.0267924	−	0.999641i	$-0.491471\pi$
$349$	1.00105	0.0535847	0.0267924	+	0.999641i	$0.491471\pi$
$350$	−0.0498324	−0.00266365
$351$	−1.46972	−0.0784478
$352$	−2.33248	−0.124322
$353$	−1.04474	−0.0556060	−0.0278030	−	0.999613i	$-0.508851\pi$
$353$	−1.04474	−0.0556060	−0.0278030	+	0.999613i	$0.508851\pi$
$354$	1.00000	0.0531494
$355$	21.3376	1.13248
$356$	−4.18370	−0.221735
$357$	0.744783	0.0394181
$358$	5.00744	0.264651
$359$	2.08008	0.109782	0.0548912	−	0.998492i	$-0.482519\pi$
$359$	2.08008	0.109782	0.0548912	+	0.998492i	$0.482519\pi$
$360$	2.25098	0.118637
$361$	25.5463	1.34454
$362$	−4.27999	−0.224951
$363$	5.55953	0.291800
$364$	1.09462	0.0573738
$365$	1.54121	0.0806705
$366$	7.27359	0.380197
$367$	3.17815	0.165898	0.0829491	−	0.996554i	$-0.473566\pi$
$367$	3.17815	0.165898	0.0829491	+	0.996554i	$0.473566\pi$
$368$	−3.70644	−0.193212
$369$	1.43420	0.0746616
$370$	24.5519	1.27639
$371$	−0.413845	−0.0214857
$372$	0.755138	0.0391521
$373$	24.6572	1.27670	0.638350	−	0.769746i	$-0.279617\pi$
$373$	24.6572	1.27670	0.638350	+	0.769746i	$0.279617\pi$
$374$	2.33248	0.120610
$375$	−11.1043	−0.573423
$376$	−7.97412	−0.411234
$377$	4.39354	0.226279
$378$	0.744783	0.0383075
$379$	37.0811	1.90473	0.952363	−	0.304966i	$-0.0986452\pi$
$379$	37.0811	1.90473	0.952363	+	0.304966i	$0.0986452\pi$
$380$	−15.0237	−0.770701
$381$	−13.6560	−0.699618
$382$	0.847670	0.0433706
$383$	6.62748	0.338648	0.169324	−	0.985560i	$-0.445841\pi$
$383$	6.62748	0.338648	0.169324	+	0.985560i	$0.445841\pi$
$384$	1.00000	0.0510310
$385$	−3.91038	−0.199292
$386$	−14.5718	−0.741686
$387$	−2.14336	−0.108953
$388$	6.31411	0.320550
$389$	−11.4197	−0.579001	−0.289500	−	0.957178i	$-0.593489\pi$
$389$	−11.4197	−0.579001	−0.289500	+	0.957178i	$0.593489\pi$
$390$	−3.30831	−0.167523
$391$	3.70644	0.187443
$392$	6.44530	0.325537
$393$	15.8779	0.800932
$394$	−5.93431	−0.298966
$395$	−5.74702	−0.289164
$396$	2.33248	0.117212
$397$	11.8768	0.596077	0.298039	−	0.954554i	$-0.403668\pi$
$397$	11.8768	0.596077	0.298039	+	0.954554i	$0.403668\pi$
$398$	21.4599	1.07569
$399$	−4.97091	−0.248857
$400$	0.0669086	0.00334543
$401$	23.7385	1.18544	0.592721	−	0.805407i	$-0.298053\pi$
$401$	23.7385	1.18544	0.592721	+	0.805407i	$0.298053\pi$
$402$	11.3321	0.565195
$403$	−1.10984	−0.0552851
$404$	−11.3149	−0.562938
$405$	−2.25098	−0.111852
$406$	−2.22643	−0.110496
$407$	25.4409	1.26106
$408$	−1.00000	−0.0495074
$409$	−28.1905	−1.39393	−0.696966	−	0.717105i	$-0.745467\pi$
$409$	−28.1905	−1.39393	−0.696966	+	0.717105i	$0.745467\pi$
$410$	3.22836	0.159437
$411$	−5.50898	−0.271738
$412$	−15.6380	−0.770430
$413$	0.744783	0.0366484
$414$	3.70644	0.182162
$415$	23.6151	1.15922
$416$	−1.46972	−0.0720589
$417$	15.0899	0.738957
$418$	−15.5677	−0.761440
$419$	−7.02938	−0.343408	−0.171704	−	0.985149i	$-0.554927\pi$
$419$	−7.02938	−0.343408	−0.171704	+	0.985149i	$0.554927\pi$
$420$	1.67649	0.0818044
$421$	−10.5205	−0.512740	−0.256370	−	0.966579i	$-0.582526\pi$
$421$	−10.5205	−0.512740	−0.256370	+	0.966579i	$0.582526\pi$
$422$	−12.1102	−0.589513
$423$	7.97412	0.387715
$424$	0.555658	0.0269851
$425$	−0.0669086	−0.00324554
$426$	−9.47926	−0.459272
$427$	5.41725	0.262159
$428$	10.6721	0.515853
$429$	−3.42809	−0.165510
$430$	−4.82465	−0.232665
$431$	9.69352	0.466920	0.233460	−	0.972366i	$-0.424995\pi$
$431$	9.69352	0.466920	0.233460	+	0.972366i	$0.424995\pi$
$432$	−1.00000	−0.0481125
$433$	−1.13605	−0.0545949	−0.0272975	−	0.999627i	$-0.508690\pi$
$433$	−1.13605	−0.0545949	−0.0272975	+	0.999627i	$0.508690\pi$
$434$	0.562414	0.0269967
$435$	6.72902	0.322632
$436$	−10.7884	−0.516672
$437$	−24.7379	−1.18338
$438$	−0.684684	−0.0327154
$439$	32.1368	1.53381	0.766903	−	0.641763i	$-0.221797\pi$
$439$	32.1368	1.53381	0.766903	+	0.641763i	$0.221797\pi$
$440$	5.25037	0.250301
$441$	−6.44530	−0.306919
$442$	1.46972	0.0699074
$443$	−18.1819	−0.863847	−0.431924	−	0.901910i	$-0.642165\pi$
$443$	−18.1819	−0.863847	−0.431924	+	0.901910i	$0.642165\pi$
$444$	−10.9072	−0.517633
$445$	9.41742	0.446428
$446$	−12.2515	−0.580124
$447$	10.7904	0.510369
$448$	0.744783	0.0351877
$449$	21.9530	1.03602	0.518012	−	0.855373i	$-0.326672\pi$
$449$	21.9530	1.03602	0.518012	+	0.855373i	$0.326672\pi$
$450$	−0.0669086	−0.00315410
$451$	3.34525	0.157522
$452$	2.51807	0.118440
$453$	0.577797	0.0271473
$454$	−25.7155	−1.20689
$455$	−2.46397	−0.115513
$456$	6.67430	0.312553
$457$	−2.49031	−0.116492	−0.0582459	−	0.998302i	$-0.518551\pi$
$457$	−2.49031	−0.116492	−0.0582459	+	0.998302i	$0.518551\pi$
$458$	1.91198	0.0893410
$459$	1.00000	0.0466760
$460$	8.34313	0.389000
$461$	40.8264	1.90148	0.950738	−	0.309995i	$-0.100327\pi$
$461$	40.8264	1.90148	0.950738	+	0.309995i	$0.100327\pi$
$462$	1.73719	0.0808215
$463$	0.959874	0.0446091	0.0223046	−	0.999751i	$-0.492900\pi$
$463$	0.959874	0.0446091	0.0223046	+	0.999751i	$0.492900\pi$
$464$	2.98937	0.138778
$465$	−1.69980	−0.0788264
$466$	−12.2211	−0.566134
$467$	7.88116	0.364696	0.182348	−	0.983234i	$-0.441630\pi$
$467$	7.88116	0.364696	0.182348	+	0.983234i	$0.441630\pi$
$468$	1.46972	0.0679378
$469$	8.43997	0.389722
$470$	17.9496	0.827953
$471$	−19.5006	−0.898540
$472$	−1.00000	−0.0460287
$473$	−4.99934	−0.229870
$474$	2.55312	0.117269
$475$	0.446568	0.0204900
$476$	−0.744783	−0.0341371
$477$	−0.555658	−0.0254418
$478$	−17.2655	−0.789703
$479$	22.3279	1.02019	0.510093	−	0.860119i	$-0.329611\pi$
$479$	22.3279	1.02019	0.510093	+	0.860119i	$0.329611\pi$
$480$	−2.25098	−0.102743
$481$	16.0305	0.730930
$482$	−9.82240	−0.447398
$483$	2.76050	0.125607
$484$	−5.55953	−0.252706
$485$	−14.2129	−0.645376
$486$	1.00000	0.0453609
$487$	8.35612	0.378652	0.189326	−	0.981914i	$-0.439370\pi$
$487$	8.35612	0.378652	0.189326	+	0.981914i	$0.439370\pi$
$488$	−7.27359	−0.329260
$489$	−3.10700	−0.140503
$490$	−14.5082	−0.655415
$491$	−24.1809	−1.09127	−0.545635	−	0.838023i	$-0.683711\pi$
$491$	−24.1809	−1.09127	−0.545635	+	0.838023i	$0.683711\pi$
$492$	−1.43420	−0.0646589
$493$	−2.98937	−0.134635
$494$	−9.80935	−0.441343
$495$	−5.25037	−0.235986
$496$	−0.755138	−0.0339067
$497$	−7.05999	−0.316684
$498$	−10.4910	−0.470115
$499$	20.7556	0.929149	0.464574	−	0.885534i	$-0.346207\pi$
$499$	20.7556	0.929149	0.464574	+	0.885534i	$0.346207\pi$
$500$	11.1043	0.496599
$501$	2.31460	0.103409
$502$	5.65216	0.252268
$503$	7.78502	0.347117	0.173558	−	0.984824i	$-0.444473\pi$
$503$	7.78502	0.347117	0.173558	+	0.984824i	$0.444473\pi$
$504$	−0.744783	−0.0331753
$505$	25.4696	1.13338
$506$	8.64521	0.384326
$507$	10.8399	0.481418
$508$	13.6560	0.605887
$509$	9.16778	0.406355	0.203177	−	0.979142i	$-0.434873\pi$
$509$	9.16778	0.406355	0.203177	+	0.979142i	$0.434873\pi$
$510$	2.25098	0.0996750
$511$	−0.509941	−0.0225584
$512$	−1.00000	−0.0441942
$513$	−6.67430	−0.294678
$514$	3.49579	0.154193
$515$	35.2009	1.55114
$516$	2.14336	0.0943560
$517$	18.5995	0.818005
$518$	−8.12351	−0.356926
$519$	−8.26013	−0.362580
$520$	3.30831	0.145079
$521$	23.1482	1.01414	0.507070	−	0.861905i	$-0.330729\pi$
$521$	23.1482	1.01414	0.507070	+	0.861905i	$0.330729\pi$
$522$	−2.98937	−0.130841
$523$	7.35421	0.321577	0.160789	−	0.986989i	$-0.448596\pi$
$523$	7.35421	0.321577	0.160789	+	0.986989i	$0.448596\pi$
$524$	−15.8779	−0.693627
$525$	−0.0498324	−0.00217486
$526$	−0.649961	−0.0283397
$527$	0.755138	0.0328943
$528$	−2.33248	−0.101508
$529$	−9.26229	−0.402708
$530$	−1.25077	−0.0543302
$531$	1.00000	0.0433963
$532$	4.97091	0.215516
$533$	2.10788	0.0913022
$534$	−4.18370	−0.181046
$535$	−24.0226	−1.03859
$536$	−11.3321	−0.489473
$537$	5.00744	0.216087
$538$	2.49731	0.107667
$539$	−15.0335	−0.647540
$540$	2.25098	0.0968667
$541$	10.8733	0.467478	0.233739	−	0.972299i	$-0.424904\pi$
$541$	10.8733	0.467478	0.233739	+	0.972299i	$0.424904\pi$
$542$	−25.5431	−1.09717
$543$	−4.27999	−0.183672
$544$	1.00000	0.0428746
$545$	24.2845	1.04023
$546$	1.09462	0.0468455
$547$	−37.6511	−1.60984	−0.804922	−	0.593380i	$-0.797793\pi$
$547$	−37.6511	−1.60984	−0.804922	+	0.593380i	$0.797793\pi$
$548$	5.50898	0.235332
$549$	7.27359	0.310429
$550$	−0.156063	−0.00665455
$551$	19.9520	0.849983
$552$	−3.70644	−0.157757
$553$	1.90152	0.0808609
$554$	3.79244	0.161125
$555$	24.5519	1.04217
$556$	−15.0899	−0.639956
$557$	−10.0391	−0.425369	−0.212684	−	0.977121i	$-0.568221\pi$
$557$	−10.0391	−0.425369	−0.212684	+	0.977121i	$0.568221\pi$
$558$	0.755138	0.0319675
$559$	−3.15013	−0.133236
$560$	−1.67649	−0.0708447
$561$	2.33248	0.0984774
$562$	−22.4667	−0.947702
$563$	31.4267	1.32448	0.662240	−	0.749292i	$-0.269606\pi$
$563$	31.4267	1.32448	0.662240	+	0.749292i	$0.269606\pi$
$564$	−7.97412	−0.335771
$565$	−5.66813	−0.238460
$566$	−17.1466	−0.720725
$567$	0.744783	0.0312779
$568$	9.47926	0.397741
$569$	−5.84319	−0.244959	−0.122480	−	0.992471i	$-0.539085\pi$
$569$	−5.84319	−0.244959	−0.122480	+	0.992471i	$0.539085\pi$
$570$	−15.0237	−0.629274
$571$	−0.366490	−0.0153371	−0.00766856	−	0.999971i	$-0.502441\pi$
$571$	−0.366490	−0.0153371	−0.00766856	+	0.999971i	$0.502441\pi$
$572$	3.42809	0.143336
$573$	0.847670	0.0354119
$574$	−1.06817	−0.0445846
$575$	−0.247993	−0.0103420
$576$	1.00000	0.0416667
$577$	−37.0890	−1.54403	−0.772017	−	0.635602i	$-0.780752\pi$
$577$	−37.0890	−1.54403	−0.772017	+	0.635602i	$0.780752\pi$
$578$	−1.00000	−0.0415945
$579$	−14.5718	−0.605584
$580$	−6.72902	−0.279407
$581$	−7.81356	−0.324161
$582$	6.31411	0.261728
$583$	−1.29606	−0.0536774
$584$	0.684684	0.0283324
$585$	−3.30831	−0.136782
$586$	15.5636	0.642927
$587$	23.6078	0.974400	0.487200	−	0.873290i	$-0.338018\pi$
$587$	23.6078	0.974400	0.487200	+	0.873290i	$0.338018\pi$
$588$	6.44530	0.265800
$589$	−5.04002	−0.207670
$590$	2.25098	0.0926714
$591$	−5.93431	−0.244105
$592$	10.9072	0.448284
$593$	4.17885	0.171605	0.0858023	−	0.996312i	$-0.472655\pi$
$593$	4.17885	0.171605	0.0858023	+	0.996312i	$0.472655\pi$
$594$	2.33248	0.0957028
$595$	1.67649	0.0687294
$596$	−10.7904	−0.441993
$597$	21.4599	0.878294
$598$	5.44743	0.222762
$599$	−2.29628	−0.0938234	−0.0469117	−	0.998899i	$-0.514938\pi$
$599$	−2.29628	−0.0938234	−0.0469117	+	0.998899i	$0.514938\pi$
$600$	0.0669086	0.00273153
$601$	−12.9374	−0.527726	−0.263863	−	0.964560i	$-0.584997\pi$
$601$	−12.9374	−0.527726	−0.263863	+	0.964560i	$0.584997\pi$
$602$	1.59633	0.0650618
$603$	11.3321	0.461480
$604$	−0.577797	−0.0235102
$605$	12.5144	0.508783
$606$	−11.3149	−0.459637
$607$	−30.7070	−1.24636	−0.623179	−	0.782079i	$-0.714159\pi$
$607$	−30.7070	−1.24636	−0.623179	+	0.782079i	$0.714159\pi$
$608$	−6.67430	−0.270679
$609$	−2.22643	−0.0902196
$610$	16.3727	0.662911
$611$	11.7197	0.474129
$612$	−1.00000	−0.0404226
$613$	20.2545	0.818072	0.409036	−	0.912518i	$-0.365865\pi$
$613$	20.2545	0.818072	0.409036	+	0.912518i	$0.365865\pi$
$614$	−5.47777	−0.221065
$615$	3.22836	0.130180
$616$	−1.73719	−0.0699935
$617$	−11.9815	−0.482357	−0.241178	−	0.970481i	$-0.577534\pi$
$617$	−11.9815	−0.482357	−0.241178	+	0.970481i	$0.577534\pi$
$618$	−15.6380	−0.629053
$619$	40.8104	1.64031	0.820153	−	0.572144i	$-0.193888\pi$
$619$	40.8104	1.64031	0.820153	+	0.572144i	$0.193888\pi$
$620$	1.69980	0.0682656
$621$	3.70644	0.148734
$622$	22.2670	0.892824
$623$	−3.11595	−0.124838
$624$	−1.46972	−0.0588358
$625$	−25.3301	−1.01320
$626$	−16.5391	−0.661037
$627$	−15.5677	−0.621713
$628$	19.5006	0.778159
$629$	−10.9072	−0.434899
$630$	1.67649	0.0667930
$631$	4.38106	0.174407	0.0872036	−	0.996191i	$-0.472207\pi$
$631$	4.38106	0.174407	0.0872036	+	0.996191i	$0.472207\pi$
$632$	−2.55312	−0.101558
$633$	−12.1102	−0.481336
$634$	1.48690	0.0590522
$635$	−30.7394	−1.21986
$636$	0.555658	0.0220333
$637$	−9.47278	−0.375325
$638$	−6.97265	−0.276050
$639$	−9.47926	−0.374994
$640$	2.25098	0.0889778
$641$	32.8368	1.29698	0.648488	−	0.761225i	$-0.275402\pi$
$641$	32.8368	1.29698	0.648488	+	0.761225i	$0.275402\pi$
$642$	10.6721	0.421192
$643$	12.7254	0.501840	0.250920	−	0.968008i	$-0.419267\pi$
$643$	12.7254	0.501840	0.250920	+	0.968008i	$0.419267\pi$
$644$	−2.76050	−0.108779
$645$	−4.82465	−0.189970
$646$	6.67430	0.262597
$647$	37.0464	1.45645	0.728223	−	0.685341i	$-0.240347\pi$
$647$	37.0464	1.45645	0.728223	+	0.685341i	$0.240347\pi$
$648$	−1.00000	−0.0392837
$649$	2.33248	0.0915579
$650$	−0.0983368	−0.00385709
$651$	0.562414	0.0220427
$652$	3.10700	0.121679
$653$	−37.8018	−1.47930	−0.739650	−	0.672992i	$-0.765009\pi$
$653$	−37.8018	−1.47930	−0.739650	+	0.672992i	$0.765009\pi$
$654$	−10.7884	−0.421861
$655$	35.7407	1.39651
$656$	1.43420	0.0559962
$657$	−0.684684	−0.0267121
$658$	−5.93899	−0.231526
$659$	−24.9348	−0.971321	−0.485661	−	0.874147i	$-0.661421\pi$
$659$	−24.9348	−0.971321	−0.485661	+	0.874147i	$0.661421\pi$
$660$	5.25037	0.204370
$661$	25.3582	0.986321	0.493160	−	0.869938i	$-0.335842\pi$
$661$	25.3582	0.986321	0.493160	+	0.869938i	$0.335842\pi$
$662$	11.7250	0.455705
$663$	1.46972	0.0570791
$664$	10.4910	0.407132
$665$	−11.1894	−0.433907
$666$	−10.9072	−0.422646
$667$	−11.0799	−0.429017
$668$	−2.31460	−0.0895546
$669$	−12.2515	−0.473669
$670$	25.5084	0.985474
$671$	16.9655	0.654946
$672$	0.744783	0.0287306
$673$	5.89157	0.227103	0.113552	−	0.993532i	$-0.463777\pi$
$673$	5.89157	0.227103	0.113552	+	0.993532i	$0.463777\pi$
$674$	−3.94487	−0.151951
$675$	−0.0669086	−0.00257531
$676$	−10.8399	−0.416920
$677$	−40.5600	−1.55885	−0.779423	−	0.626498i	$-0.784488\pi$
$677$	−40.5600	−1.55885	−0.779423	+	0.626498i	$0.784488\pi$
$678$	2.51807	0.0967060
$679$	4.70264	0.180471
$680$	−2.25098	−0.0863211
$681$	−25.7155	−0.985418
$682$	1.76135	0.0674454
$683$	10.6717	0.408342	0.204171	−	0.978935i	$-0.434550\pi$
$683$	10.6717	0.408342	0.204171	+	0.978935i	$0.434550\pi$
$684$	6.67430	0.255198
$685$	−12.4006	−0.473803
$686$	10.0138	0.382330
$687$	1.91198	0.0729466
$688$	−2.14336	−0.0817147
$689$	−0.816661	−0.0311123
$690$	8.34313	0.317617
$691$	11.1727	0.425029	0.212514	−	0.977158i	$-0.431835\pi$
$691$	11.1727	0.425029	0.212514	+	0.977158i	$0.431835\pi$
$692$	8.26013	0.314003
$693$	1.73719	0.0659905
$694$	6.95425	0.263980
$695$	33.9671	1.28845
$696$	2.98937	0.113312
$697$	−1.43420	−0.0543243
$698$	−1.00105	−0.0378901
$699$	−12.2211	−0.462246
$700$	0.0498324	0.00188349
$701$	−2.61307	−0.0986943	−0.0493472	−	0.998782i	$-0.515714\pi$
$701$	−2.61307	−0.0986943	−0.0493472	+	0.998782i	$0.515714\pi$
$702$	1.46972	0.0554710
$703$	72.7981	2.74563
$704$	2.33248	0.0879087
$705$	17.9496	0.676021
$706$	1.04474	0.0393194
$707$	−8.42716	−0.316936
$708$	−1.00000	−0.0375823
$709$	4.99299	0.187516	0.0937579	−	0.995595i	$-0.470112\pi$
$709$	4.99299	0.187516	0.0937579	+	0.995595i	$0.470112\pi$
$710$	−21.3376	−0.800786
$711$	2.55312	0.0957495
$712$	4.18370	0.156791
$713$	2.79888	0.104819
$714$	−0.744783	−0.0278728
$715$	−7.71656	−0.288583
$716$	−5.00744	−0.187137
$717$	−17.2655	−0.644790
$718$	−2.08008	−0.0776279
$719$	24.6175	0.918079	0.459039	−	0.888416i	$-0.348194\pi$
$719$	24.6175	0.918079	0.459039	+	0.888416i	$0.348194\pi$
$720$	−2.25098	−0.0838891
$721$	−11.6469	−0.433754
$722$	−25.5463	−0.950736
$723$	−9.82240	−0.365299
$724$	4.27999	0.159064
$725$	0.200015	0.00742836
$726$	−5.55953	−0.206334
$727$	−8.21807	−0.304791	−0.152396	−	0.988320i	$-0.548699\pi$
$727$	−8.21807	−0.304791	−0.152396	+	0.988320i	$0.548699\pi$
$728$	−1.09462	−0.0405694
$729$	1.00000	0.0370370
$730$	−1.54121	−0.0570427
$731$	2.14336	0.0792749
$732$	−7.27359	−0.268840
$733$	−22.9140	−0.846348	−0.423174	−	0.906049i	$-0.639084\pi$
$733$	−22.9140	−0.846348	−0.423174	+	0.906049i	$0.639084\pi$
$734$	−3.17815	−0.117308
$735$	−14.5082	−0.535144
$736$	3.70644	0.136621
$737$	26.4319	0.973633
$738$	−1.43420	−0.0527937
$739$	−5.90809	−0.217333	−0.108666	−	0.994078i	$-0.534658\pi$
$739$	−5.90809	−0.217333	−0.108666	+	0.994078i	$0.534658\pi$
$740$	−24.5519	−0.902546
$741$	−9.80935	−0.360355
$742$	0.413845	0.0151927
$743$	32.8388	1.20474	0.602370	−	0.798217i	$-0.294223\pi$
$743$	32.8388	1.20474	0.602370	+	0.798217i	$0.294223\pi$
$744$	−0.755138	−0.0276847
$745$	24.2890	0.889880
$746$	−24.6572	−0.902764
$747$	−10.4910	−0.383847
$748$	−2.33248	−0.0852839
$749$	7.94837	0.290427
$750$	11.1043	0.405471
$751$	18.5529	0.677003	0.338502	−	0.940966i	$-0.390080\pi$
$751$	18.5529	0.677003	0.338502	+	0.940966i	$0.390080\pi$
$752$	7.97412	0.290786
$753$	5.65216	0.205976
$754$	−4.39354	−0.160003
$755$	1.30061	0.0473340
$756$	−0.744783	−0.0270875
$757$	−9.78140	−0.355511	−0.177756	−	0.984075i	$-0.556884\pi$
$757$	−9.78140	−0.355511	−0.177756	+	0.984075i	$0.556884\pi$
$758$	−37.0811	−1.34684
$759$	8.64521	0.313801
$760$	15.0237	0.544968
$761$	−10.8795	−0.394380	−0.197190	−	0.980365i	$-0.563182\pi$
$761$	−10.8795	−0.394380	−0.197190	+	0.980365i	$0.563182\pi$
$762$	13.6560	0.494705
$763$	−8.03503	−0.290888
$764$	−0.847670	−0.0306676
$765$	2.25098	0.0813843
$766$	−6.62748	−0.239461
$767$	1.46972	0.0530685
$768$	−1.00000	−0.0360844
$769$	−2.02800	−0.0731314	−0.0365657	−	0.999331i	$-0.511642\pi$
$769$	−2.02800	−0.0731314	−0.0365657	+	0.999331i	$0.511642\pi$
$770$	3.91038	0.140920
$771$	3.49579	0.125898
$772$	14.5718	0.524451
$773$	−13.4984	−0.485503	−0.242751	−	0.970089i	$-0.578050\pi$
$773$	−13.4984	−0.485503	−0.242751	+	0.970089i	$0.578050\pi$
$774$	2.14336	0.0770413
$775$	−0.0505252	−0.00181492
$776$	−6.31411	−0.226663
$777$	−8.12351	−0.291429
$778$	11.4197	0.409415
$779$	9.57231	0.342964
$780$	3.30831	0.118456
$781$	−22.1102	−0.791165
$782$	−3.70644	−0.132542
$783$	−2.98937	−0.106831
$784$	−6.44530	−0.230189
$785$	−43.8955	−1.56670
$786$	−15.8779	−0.566344
$787$	51.1250	1.82241	0.911204	−	0.411956i	$-0.135154\pi$
$787$	51.1250	1.82241	0.911204	+	0.411956i	$0.135154\pi$
$788$	5.93431	0.211401
$789$	−0.649961	−0.0231392
$790$	5.74702	0.204470
$791$	1.87542	0.0666822
$792$	−2.33248	−0.0828811
$793$	10.6901	0.379618
$794$	−11.8768	−0.421490
$795$	−1.25077	−0.0443604
$796$	−21.4599	−0.760625
$797$	−23.5439	−0.833967	−0.416983	−	0.908914i	$-0.636913\pi$
$797$	−23.5439	−0.833967	−0.416983	+	0.908914i	$0.636913\pi$
$798$	4.97091	0.175968
$799$	−7.97412	−0.282104
$800$	−0.0669086	−0.00236558
$801$	−4.18370	−0.147824
$802$	−23.7385	−0.838235
$803$	−1.59701	−0.0563573
$804$	−11.3321	−0.399653
$805$	6.21382	0.219008
$806$	1.10984	0.0390925
$807$	2.49731	0.0879094
$808$	11.3149	0.398057
$809$	9.00040	0.316437	0.158219	−	0.987404i	$-0.449425\pi$
$809$	9.00040	0.316437	0.158219	+	0.987404i	$0.449425\pi$
$810$	2.25098	0.0790914
$811$	−34.6240	−1.21581	−0.607906	−	0.794009i	$-0.707990\pi$
$811$	−34.6240	−1.21581	−0.607906	+	0.794009i	$0.707990\pi$
$812$	2.22643	0.0781325
$813$	−25.5431	−0.895835
$814$	−25.4409	−0.891702
$815$	−6.99379	−0.244982
$816$	1.00000	0.0350070
$817$	−14.3054	−0.500483
$818$	28.1905	0.985658
$819$	1.09462	0.0382492
$820$	−3.22836	−0.112739
$821$	22.8376	0.797038	0.398519	−	0.917160i	$-0.369524\pi$
$821$	22.8376	0.797038	0.398519	+	0.917160i	$0.369524\pi$
$822$	5.50898	0.192148
$823$	17.0312	0.593672	0.296836	−	0.954928i	$-0.404069\pi$
$823$	17.0312	0.593672	0.296836	+	0.954928i	$0.404069\pi$
$824$	15.6380	0.544776
$825$	−0.156063	−0.00543342
$826$	−0.744783	−0.0259143
$827$	20.9520	0.728573	0.364287	−	0.931287i	$-0.381313\pi$
$827$	20.9520	0.728573	0.364287	+	0.931287i	$0.381313\pi$
$828$	−3.70644	−0.128808
$829$	−13.6782	−0.475065	−0.237532	−	0.971380i	$-0.576339\pi$
$829$	−13.6782	−0.475065	−0.237532	+	0.971380i	$0.576339\pi$
$830$	−23.6151	−0.819693
$831$	3.79244	0.131558
$832$	1.46972	0.0509533
$833$	6.44530	0.223316
$834$	−15.0899	−0.522522
$835$	5.21012	0.180304
$836$	15.5677	0.538420
$837$	0.755138	0.0261014
$838$	7.02938	0.242826
$839$	11.2419	0.388115	0.194058	−	0.980990i	$-0.437835\pi$
$839$	11.2419	0.388115	0.194058	+	0.980990i	$0.437835\pi$
$840$	−1.67649	−0.0578444
$841$	−20.0637	−0.691850
$842$	10.5205	0.362562
$843$	−22.4667	−0.773796
$844$	12.1102	0.416849
$845$	24.4005	0.839401
$846$	−7.97412	−0.274156
$847$	−4.14065	−0.142274
$848$	−0.555658	−0.0190814
$849$	−17.1466	−0.588470
$850$	0.0669086	0.00229495
$851$	−40.4270	−1.38582
$852$	9.47926	0.324754
$853$	−5.13625	−0.175862	−0.0879309	−	0.996127i	$-0.528025\pi$
$853$	−5.13625	−0.175862	−0.0879309	+	0.996127i	$0.528025\pi$
$854$	−5.41725	−0.185374
$855$	−15.0237	−0.513800
$856$	−10.6721	−0.364763
$857$	26.3242	0.899219	0.449609	−	0.893225i	$-0.351563\pi$
$857$	26.3242	0.899219	0.449609	+	0.893225i	$0.351563\pi$
$858$	3.42809	0.117033
$859$	−26.1048	−0.890686	−0.445343	−	0.895360i	$-0.646918\pi$
$859$	−26.1048	−0.890686	−0.445343	+	0.895360i	$0.646918\pi$
$860$	4.82465	0.164519
$861$	−1.06817	−0.0364031
$862$	−9.69352	−0.330163
$863$	30.1483	1.02626	0.513130	−	0.858311i	$-0.328486\pi$
$863$	30.1483	1.02626	0.513130	+	0.858311i	$0.328486\pi$
$864$	1.00000	0.0340207
$865$	−18.5934	−0.632194
$866$	1.13605	0.0386044
$867$	−1.00000	−0.0339618
$868$	−0.562414	−0.0190896
$869$	5.95511	0.202013
$870$	−6.72902	−0.228135
$871$	16.6550	0.564334
$872$	10.7884	0.365342
$873$	6.31411	0.213700
$874$	24.7379	0.836773
$875$	8.27029	0.279587
$876$	0.684684	0.0231333
$877$	−5.93599	−0.200444	−0.100222	−	0.994965i	$-0.531955\pi$
$877$	−5.93599	−0.200444	−0.100222	+	0.994965i	$0.531955\pi$
$878$	−32.1368	−1.08456
$879$	15.5636	0.524948
$880$	−5.25037	−0.176990
$881$	−54.0924	−1.82242	−0.911210	−	0.411941i	$-0.864851\pi$
$881$	−54.0924	−1.82242	−0.911210	+	0.411941i	$0.864851\pi$
$882$	6.44530	0.217024
$883$	−19.6268	−0.660493	−0.330247	−	0.943895i	$-0.607132\pi$
$883$	−19.6268	−0.660493	−0.330247	+	0.943895i	$0.607132\pi$
$884$	−1.46972	−0.0494320
$885$	2.25098	0.0756658
$886$	18.1819	0.610832
$887$	−16.7715	−0.563133	−0.281566	−	0.959542i	$-0.590854\pi$
$887$	−16.7715	−0.563133	−0.281566	+	0.959542i	$0.590854\pi$
$888$	10.9072	0.366022
$889$	10.1708	0.341116
$890$	−9.41742	−0.315673
$891$	2.33248	0.0781410
$892$	12.2515	0.410209
$893$	53.2217	1.78100
$894$	−10.7904	−0.360885
$895$	11.2716	0.376770
$896$	−0.744783	−0.0248815
$897$	5.44743	0.181884
$898$	−21.9530	−0.732580
$899$	−2.25739	−0.0752881
$900$	0.0669086	0.00223029
$901$	0.555658	0.0185117
$902$	−3.34525	−0.111385
$903$	1.59633	0.0531227
$904$	−2.51807	−0.0837499
$905$	−9.63416	−0.320250
$906$	−0.577797	−0.0191960
$907$	36.4018	1.20870	0.604351	−	0.796718i	$-0.293432\pi$
$907$	36.4018	1.20870	0.604351	+	0.796718i	$0.293432\pi$
$908$	25.7155	0.853397
$909$	−11.3149	−0.375292
$910$	2.46397	0.0816798
$911$	42.4720	1.40716	0.703579	−	0.710617i	$-0.251584\pi$
$911$	42.4720	1.40716	0.703579	+	0.710617i	$0.251584\pi$
$912$	−6.67430	−0.221008
$913$	−24.4702	−0.809844
$914$	2.49031	0.0823721
$915$	16.3727	0.541265
$916$	−1.91198	−0.0631736
$917$	−11.8256	−0.390514
$918$	−1.00000	−0.0330049
$919$	23.3770	0.771135	0.385568	−	0.922680i	$-0.374006\pi$
$919$	23.3770	0.771135	0.385568	+	0.922680i	$0.374006\pi$
$920$	−8.34313	−0.275065
$921$	−5.47777	−0.180499
$922$	−40.8264	−1.34455
$923$	−13.9318	−0.458572
$924$	−1.73719	−0.0571494
$925$	0.729786	0.0239952
$926$	−0.959874	−0.0315434
$927$	−15.6380	−0.513620
$928$	−2.98937	−0.0981310
$929$	−20.7973	−0.682338	−0.341169	−	0.940002i	$-0.610823\pi$
$929$	−20.7973	−0.682338	−0.341169	+	0.940002i	$0.610823\pi$
$930$	1.69980	0.0557387
$931$	−43.0179	−1.40985
$932$	12.2211	0.400317
$933$	22.2670	0.728988
$934$	−7.88116	−0.257879
$935$	5.25037	0.171705
$936$	−1.46972	−0.0480393
$937$	31.5794	1.03165	0.515827	−	0.856692i	$-0.327485\pi$
$937$	31.5794	1.03165	0.515827	+	0.856692i	$0.327485\pi$
$938$	−8.43997	−0.275575
$939$	−16.5391	−0.539734
$940$	−17.9496	−0.585451
$941$	15.2842	0.498250	0.249125	−	0.968471i	$-0.419857\pi$
$941$	15.2842	0.498250	0.249125	+	0.968471i	$0.419857\pi$
$942$	19.5006	0.635364
$943$	−5.31579	−0.173106
$944$	1.00000	0.0325472
$945$	1.67649	0.0545363
$946$	4.99934	0.162542
$947$	2.83073	0.0919863	0.0459932	−	0.998942i	$-0.485355\pi$
$947$	2.83073	0.0919863	0.0459932	+	0.998942i	$0.485355\pi$
$948$	−2.55312	−0.0829215
$949$	−1.00629	−0.0326656
$950$	−0.446568	−0.0144886
$951$	1.48690	0.0482159
$952$	0.744783	0.0241386
$953$	−20.5895	−0.666959	−0.333479	−	0.942757i	$-0.608223\pi$
$953$	−20.5895	−0.666959	−0.333479	+	0.942757i	$0.608223\pi$
$954$	0.555658	0.0179901
$955$	1.90809	0.0617443
$956$	17.2655	0.558405
$957$	−6.97265	−0.225394
$958$	−22.3279	−0.721381
$959$	4.10300	0.132493
$960$	2.25098	0.0726501
$961$	−30.4298	−0.981605
$962$	−16.0305	−0.516845
$963$	10.6721	0.343902
$964$	9.82240	0.316358
$965$	−32.8009	−1.05590
$966$	−2.76050	−0.0888175
$967$	39.4564	1.26883	0.634416	−	0.772992i	$-0.281241\pi$
$967$	39.4564	1.26883	0.634416	+	0.772992i	$0.281241\pi$
$968$	5.55953	0.178690
$969$	6.67430	0.214410
$970$	14.2129	0.456350
$971$	38.7634	1.24398	0.621989	−	0.783026i	$-0.286325\pi$
$971$	38.7634	1.24398	0.621989	+	0.783026i	$0.286325\pi$
$972$	−1.00000	−0.0320750
$973$	−11.2387	−0.360297
$974$	−8.35612	−0.267747
$975$	−0.0983368	−0.00314930
$976$	7.27359	0.232822
$977$	42.3730	1.35563	0.677816	−	0.735231i	$-0.262926\pi$
$977$	42.3730	1.35563	0.677816	+	0.735231i	$0.262926\pi$
$978$	3.10700	0.0993508
$979$	−9.75839	−0.311880
$980$	14.5082	0.463449
$981$	−10.7884	−0.344448
$982$	24.1809	0.771644
$983$	5.05137	0.161114	0.0805568	−	0.996750i	$-0.474330\pi$
$983$	5.05137	0.161114	0.0805568	+	0.996750i	$0.474330\pi$
$984$	1.43420	0.0457207
$985$	−13.3580	−0.425622
$986$	2.98937	0.0952010
$987$	−5.93899	−0.189040
$988$	9.80935	0.312077
$989$	7.94422	0.252612
$990$	5.25037	0.166868
$991$	29.3763	0.933169	0.466584	−	0.884477i	$-0.345484\pi$
$991$	29.3763	0.933169	0.466584	+	0.884477i	$0.345484\pi$
$992$	0.755138	0.0239757
$993$	11.7250	0.372082
$994$	7.05999	0.223929
$995$	48.3058	1.53140
$996$	10.4910	0.332422
$997$	19.7134	0.624329	0.312165	−	0.950028i	$-0.398946\pi$
$997$	19.7134	0.624329	0.312165	+	0.950028i	$0.398946\pi$
$998$	−20.7556	−0.657007
$999$	−10.9072	−0.345089

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.s.1.2	✓	8

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.25098 q^{5} +1.00000 q^{6} +0.744783 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.25098 q^{5} +1.00000 q^{6} +0.744783 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.25098 q^{10} +2.33248 q^{11} -1.00000 q^{12} +1.46972 q^{13} -0.744783 q^{14} +2.25098 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +6.67430 q^{19} -2.25098 q^{20} -0.744783 q^{21} -2.33248 q^{22} -3.70644 q^{23} +1.00000 q^{24} +0.0669086 q^{25} -1.46972 q^{26} -1.00000 q^{27} +0.744783 q^{28} +2.98937 q^{29} -2.25098 q^{30} -0.755138 q^{31} -1.00000 q^{32} -2.33248 q^{33} +1.00000 q^{34} -1.67649 q^{35} +1.00000 q^{36} +10.9072 q^{37} -6.67430 q^{38} -1.46972 q^{39} +2.25098 q^{40} +1.43420 q^{41} +0.744783 q^{42} -2.14336 q^{43} +2.33248 q^{44} -2.25098 q^{45} +3.70644 q^{46} +7.97412 q^{47} -1.00000 q^{48} -6.44530 q^{49} -0.0669086 q^{50} +1.00000 q^{51} +1.46972 q^{52} -0.555658 q^{53} +1.00000 q^{54} -5.25037 q^{55} -0.744783 q^{56} -6.67430 q^{57} -2.98937 q^{58} +1.00000 q^{59} +2.25098 q^{60} +7.27359 q^{61} +0.755138 q^{62} +0.744783 q^{63} +1.00000 q^{64} -3.30831 q^{65} +2.33248 q^{66} +11.3321 q^{67} -1.00000 q^{68} +3.70644 q^{69} +1.67649 q^{70} -9.47926 q^{71} -1.00000 q^{72} -0.684684 q^{73} -10.9072 q^{74} -0.0669086 q^{75} +6.67430 q^{76} +1.73719 q^{77} +1.46972 q^{78} +2.55312 q^{79} -2.25098 q^{80} +1.00000 q^{81} -1.43420 q^{82} -10.4910 q^{83} -0.744783 q^{84} +2.25098 q^{85} +2.14336 q^{86} -2.98937 q^{87} -2.33248 q^{88} -4.18370 q^{89} +2.25098 q^{90} +1.09462 q^{91} -3.70644 q^{92} +0.755138 q^{93} -7.97412 q^{94} -15.0237 q^{95} +1.00000 q^{96} +6.31411 q^{97} +6.44530 q^{98} +2.33248 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} - 8 q^{3} + 8 q^{4} - q^{5} + 8 q^{6} + 6 q^{7} - 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 - q^5 + 8 * q^6 + 6 * q^7 - 8 * q^8 + 8 * q^9	\( 8 q - 8 q^{2} - 8 q^{3} + 8 q^{4} - q^{5} + 8 q^{6} + 6 q^{7} - 8 q^{8} + 8 q^{9} + q^{10} - 8 q^{12} + 6 q^{13} - 6 q^{14} + q^{15} + 8 q^{16} - 8 q^{17} - 8 q^{18} - 7 q^{19} - q^{20} - 6 q^{21} - 5 q^{23} + 8 q^{24} + 9 q^{25} - 6 q^{26} - 8 q^{27} + 6 q^{28} - 15 q^{29} - q^{30} + 21 q^{31} - 8 q^{32} + 8 q^{34} - 2 q^{35} + 8 q^{36} + 7 q^{37} + 7 q^{38} - 6 q^{39} + q^{40} - q^{41} + 6 q^{42} + 14 q^{43} - q^{45} + 5 q^{46} - 8 q^{47} - 8 q^{48} + 2 q^{49} - 9 q^{50} + 8 q^{51} + 6 q^{52} + 8 q^{53} + 8 q^{54} + 24 q^{55} - 6 q^{56} + 7 q^{57} + 15 q^{58} + 8 q^{59} + q^{60} - 21 q^{62} + 6 q^{63} + 8 q^{64} + 6 q^{65} + 15 q^{67} - 8 q^{68} + 5 q^{69} + 2 q^{70} - 22 q^{71} - 8 q^{72} + 13 q^{73} - 7 q^{74} - 9 q^{75} - 7 q^{76} - 6 q^{77} + 6 q^{78} + 26 q^{79} - q^{80} + 8 q^{81} + q^{82} + 30 q^{83} - 6 q^{84} + q^{85} - 14 q^{86} + 15 q^{87} - 6 q^{89} + q^{90} + 3 q^{91} - 5 q^{92} - 21 q^{93} + 8 q^{94} + 37 q^{95} + 8 q^{96} + 23 q^{97} - 2 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 - q^5 + 8 * q^6 + 6 * q^7 - 8 * q^8 + 8 * q^9 + q^10 - 8 * q^12 + 6 * q^13 - 6 * q^14 + q^15 + 8 * q^16 - 8 * q^17 - 8 * q^18 - 7 * q^19 - q^20 - 6 * q^21 - 5 * q^23 + 8 * q^24 + 9 * q^25 - 6 * q^26 - 8 * q^27 + 6 * q^28 - 15 * q^29 - q^30 + 21 * q^31 - 8 * q^32 + 8 * q^34 - 2 * q^35 + 8 * q^36 + 7 * q^37 + 7 * q^38 - 6 * q^39 + q^40 - q^41 + 6 * q^42 + 14 * q^43 - q^45 + 5 * q^46 - 8 * q^47 - 8 * q^48 + 2 * q^49 - 9 * q^50 + 8 * q^51 + 6 * q^52 + 8 * q^53 + 8 * q^54 + 24 * q^55 - 6 * q^56 + 7 * q^57 + 15 * q^58 + 8 * q^59 + q^60 - 21 * q^62 + 6 * q^63 + 8 * q^64 + 6 * q^65 + 15 * q^67 - 8 * q^68 + 5 * q^69 + 2 * q^70 - 22 * q^71 - 8 * q^72 + 13 * q^73 - 7 * q^74 - 9 * q^75 - 7 * q^76 - 6 * q^77 + 6 * q^78 + 26 * q^79 - q^80 + 8 * q^81 + q^82 + 30 * q^83 - 6 * q^84 + q^85 - 14 * q^86 + 15 * q^87 - 6 * q^89 + q^90 + 3 * q^91 - 5 * q^92 - 21 * q^93 + 8 * q^94 + 37 * q^95 + 8 * q^96 + 23 * q^97 - 2 * q^98

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