LMFDB - Embedded newform 6018.2.a.s.1.3

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			1.3
Root			$-2.36258$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.89711 q^{5} +1.00000 q^{6} +1.64158 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.89711 q^{5} +1.00000 q^{6} +1.64158 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.89711 q^{10} -3.44687 q^{11} -1.00000 q^{12} -5.40513 q^{13} -1.64158 q^{14} +1.89711 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} -5.05902 q^{19} -1.89711 q^{20} -1.64158 q^{21} +3.44687 q^{22} -7.56879 q^{23} +1.00000 q^{24} -1.40097 q^{25} +5.40513 q^{26} -1.00000 q^{27} +1.64158 q^{28} -2.54478 q^{29} -1.89711 q^{30} +1.76274 q^{31} -1.00000 q^{32} +3.44687 q^{33} +1.00000 q^{34} -3.11426 q^{35} +1.00000 q^{36} -2.74868 q^{37} +5.05902 q^{38} +5.40513 q^{39} +1.89711 q^{40} -1.58191 q^{41} +1.64158 q^{42} +1.82389 q^{43} -3.44687 q^{44} -1.89711 q^{45} +7.56879 q^{46} -7.14965 q^{47} -1.00000 q^{48} -4.30522 q^{49} +1.40097 q^{50} +1.00000 q^{51} -5.40513 q^{52} -3.26456 q^{53} +1.00000 q^{54} +6.53910 q^{55} -1.64158 q^{56} +5.05902 q^{57} +2.54478 q^{58} +1.00000 q^{59} +1.89711 q^{60} +3.88119 q^{61} -1.76274 q^{62} +1.64158 q^{63} +1.00000 q^{64} +10.2541 q^{65} -3.44687 q^{66} -3.05364 q^{67} -1.00000 q^{68} +7.56879 q^{69} +3.11426 q^{70} -1.57291 q^{71} -1.00000 q^{72} +12.9904 q^{73} +2.74868 q^{74} +1.40097 q^{75} -5.05902 q^{76} -5.65831 q^{77} -5.40513 q^{78} -5.95639 q^{79} -1.89711 q^{80} +1.00000 q^{81} +1.58191 q^{82} +9.77779 q^{83} -1.64158 q^{84} +1.89711 q^{85} -1.82389 q^{86} +2.54478 q^{87} +3.44687 q^{88} -5.77743 q^{89} +1.89711 q^{90} -8.87295 q^{91} -7.56879 q^{92} -1.76274 q^{93} +7.14965 q^{94} +9.59752 q^{95} +1.00000 q^{96} +8.85984 q^{97} +4.30522 q^{98} -3.44687 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−1.89711	−0.848414	−0.424207	−	0.905565i	$-0.639447\pi$
$5$	−1.89711	−0.848414	−0.424207	+	0.905565i	$0.639447\pi$
$6$	1.00000	0.408248
$7$	1.64158	0.620459	0.310229	−	0.950662i	$-0.399594\pi$
$7$	1.64158	0.620459	0.310229	+	0.950662i	$0.399594\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.89711	0.599919
$11$	−3.44687	−1.03927	−0.519635	−	0.854388i	$-0.673932\pi$
$11$	−3.44687	−1.03927	−0.519635	+	0.854388i	$0.673932\pi$
$12$	−1.00000	−0.288675
$13$	−5.40513	−1.49911	−0.749556	−	0.661940i	$-0.769733\pi$
$13$	−5.40513	−1.49911	−0.749556	+	0.661940i	$0.769733\pi$
$14$	−1.64158	−0.438731
$15$	1.89711	0.489832
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.00000	−0.235702
$19$	−5.05902	−1.16062	−0.580309	−	0.814396i	$-0.697068\pi$
$19$	−5.05902	−1.16062	−0.580309	+	0.814396i	$0.697068\pi$
$20$	−1.89711	−0.424207
$21$	−1.64158	−0.358222
$22$	3.44687	0.734875
$23$	−7.56879	−1.57820	−0.789101	−	0.614264i	$-0.789453\pi$
$23$	−7.56879	−1.57820	−0.789101	+	0.614264i	$0.789453\pi$
$24$	1.00000	0.204124
$25$	−1.40097	−0.280193
$26$	5.40513	1.06003
$27$	−1.00000	−0.192450
$28$	1.64158	0.310229
$29$	−2.54478	−0.472553	−0.236277	−	0.971686i	$-0.575927\pi$
$29$	−2.54478	−0.472553	−0.236277	+	0.971686i	$0.575927\pi$
$30$	−1.89711	−0.346364
$31$	1.76274	0.316598	0.158299	−	0.987391i	$-0.449399\pi$
$31$	1.76274	0.316598	0.158299	+	0.987391i	$0.449399\pi$
$32$	−1.00000	−0.176777
$33$	3.44687	0.600023
$34$	1.00000	0.171499
$35$	−3.11426	−0.526406
$36$	1.00000	0.166667
$37$	−2.74868	−0.451880	−0.225940	−	0.974141i	$-0.572545\pi$
$37$	−2.74868	−0.451880	−0.225940	+	0.974141i	$0.572545\pi$
$38$	5.05902	0.820681
$39$	5.40513	0.865513
$40$	1.89711	0.299960
$41$	−1.58191	−0.247053	−0.123527	−	0.992341i	$-0.539420\pi$
$41$	−1.58191	−0.247053	−0.123527	+	0.992341i	$0.539420\pi$
$42$	1.64158	0.253301
$43$	1.82389	0.278141	0.139070	−	0.990283i	$-0.455589\pi$
$43$	1.82389	0.278141	0.139070	+	0.990283i	$0.455589\pi$
$44$	−3.44687	−0.519635
$45$	−1.89711	−0.282805
$46$	7.56879	1.11596
$47$	−7.14965	−1.04288	−0.521442	−	0.853287i	$-0.674606\pi$
$47$	−7.14965	−1.04288	−0.521442	+	0.853287i	$0.674606\pi$
$48$	−1.00000	−0.144338
$49$	−4.30522	−0.615031
$50$	1.40097	0.198127
$51$	1.00000	0.140028
$52$	−5.40513	−0.749556
$53$	−3.26456	−0.448421	−0.224211	−	0.974541i	$-0.571980\pi$
$53$	−3.26456	−0.448421	−0.224211	+	0.974541i	$0.571980\pi$
$54$	1.00000	0.136083
$55$	6.53910	0.881731
$56$	−1.64158	−0.219365
$57$	5.05902	0.670083
$58$	2.54478	0.334146
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	1.89711	0.244916
$61$	3.88119	0.496935	0.248468	−	0.968640i	$-0.420073\pi$
$61$	3.88119	0.496935	0.248468	+	0.968640i	$0.420073\pi$
$62$	−1.76274	−0.223869
$63$	1.64158	0.206820
$64$	1.00000	0.125000
$65$	10.2541	1.27187
$66$	−3.44687	−0.424280
$67$	−3.05364	−0.373061	−0.186531	−	0.982449i	$-0.559724\pi$
$67$	−3.05364	−0.373061	−0.186531	+	0.982449i	$0.559724\pi$
$68$	−1.00000	−0.121268
$69$	7.56879	0.911175
$70$	3.11426	0.372225
$71$	−1.57291	−0.186670	−0.0933352	−	0.995635i	$-0.529753\pi$
$71$	−1.57291	−0.186670	−0.0933352	+	0.995635i	$0.529753\pi$
$72$	−1.00000	−0.117851
$73$	12.9904	1.52041	0.760203	−	0.649685i	$-0.225099\pi$
$73$	12.9904	1.52041	0.760203	+	0.649685i	$0.225099\pi$
$74$	2.74868	0.319528
$75$	1.40097	0.161770
$76$	−5.05902	−0.580309
$77$	−5.65831	−0.644824
$78$	−5.40513	−0.612010
$79$	−5.95639	−0.670146	−0.335073	−	0.942192i	$-0.608761\pi$
$79$	−5.95639	−0.670146	−0.335073	+	0.942192i	$0.608761\pi$
$80$	−1.89711	−0.212104
$81$	1.00000	0.111111
$82$	1.58191	0.174693
$83$	9.77779	1.07325	0.536626	−	0.843820i	$-0.319699\pi$
$83$	9.77779	1.07325	0.536626	+	0.843820i	$0.319699\pi$
$84$	−1.64158	−0.179111
$85$	1.89711	0.205771
$86$	−1.82389	−0.196675
$87$	2.54478	0.272829
$88$	3.44687	0.367437
$89$	−5.77743	−0.612406	−0.306203	−	0.951966i	$-0.599059\pi$
$89$	−5.77743	−0.612406	−0.306203	+	0.951966i	$0.599059\pi$
$90$	1.89711	0.199973
$91$	−8.87295	−0.930138
$92$	−7.56879	−0.789101
$93$	−1.76274	−0.182788
$94$	7.14965	0.737430
$95$	9.59752	0.984685
$96$	1.00000	0.102062
$97$	8.85984	0.899580	0.449790	−	0.893134i	$-0.351499\pi$
$97$	8.85984	0.899580	0.449790	+	0.893134i	$0.351499\pi$
$98$	4.30522	0.434892
$99$	−3.44687	−0.346423
$100$	−1.40097	−0.140097
$101$	−15.5253	−1.54482	−0.772411	−	0.635123i	$-0.780949\pi$
$101$	−15.5253	−1.54482	−0.772411	+	0.635123i	$0.780949\pi$
$102$	−1.00000	−0.0990148
$103$	16.1371	1.59004	0.795020	−	0.606584i	$-0.207460\pi$
$103$	16.1371	1.59004	0.795020	+	0.606584i	$0.207460\pi$
$104$	5.40513	0.530016
$105$	3.11426	0.303921
$106$	3.26456	0.317082
$107$	2.93007	0.283260	0.141630	−	0.989920i	$-0.454766\pi$
$107$	2.93007	0.283260	0.141630	+	0.989920i	$0.454766\pi$
$108$	−1.00000	−0.0962250
$109$	0.682996	0.0654192	0.0327096	−	0.999465i	$-0.489586\pi$
$109$	0.682996	0.0654192	0.0327096	+	0.999465i	$0.489586\pi$
$110$	−6.53910	−0.623478
$111$	2.74868	0.260893
$112$	1.64158	0.155115
$113$	−13.2238	−1.24399	−0.621994	−	0.783022i	$-0.713677\pi$
$113$	−13.2238	−1.24399	−0.621994	+	0.783022i	$0.713677\pi$
$114$	−5.05902	−0.473820
$115$	14.3588	1.33897
$116$	−2.54478	−0.236277
$117$	−5.40513	−0.499704
$118$	−1.00000	−0.0920575
$119$	−1.64158	−0.150483
$120$	−1.89711	−0.173182
$121$	0.880903	0.0800821
$122$	−3.88119	−0.351386
$123$	1.58191	0.142636
$124$	1.76274	0.158299
$125$	12.1433	1.08613
$126$	−1.64158	−0.146244
$127$	12.6998	1.12692	0.563462	−	0.826142i	$-0.309469\pi$
$127$	12.6998	1.12692	0.563462	+	0.826142i	$0.309469\pi$
$128$	−1.00000	−0.0883883
$129$	−1.82389	−0.160585
$130$	−10.2541	−0.899347
$131$	−9.76002	−0.852737	−0.426368	−	0.904550i	$-0.640207\pi$
$131$	−9.76002	−0.852737	−0.426368	+	0.904550i	$0.640207\pi$
$132$	3.44687	0.300011
$133$	−8.30478	−0.720116
$134$	3.05364	0.263794
$135$	1.89711	0.163277
$136$	1.00000	0.0857493
$137$	−0.796102	−0.0680156	−0.0340078	−	0.999422i	$-0.510827\pi$
$137$	−0.796102	−0.0680156	−0.0340078	+	0.999422i	$0.510827\pi$
$138$	−7.56879	−0.644298
$139$	−18.6484	−1.58174	−0.790868	−	0.611987i	$-0.790370\pi$
$139$	−18.6484	−1.58174	−0.790868	+	0.611987i	$0.790370\pi$
$140$	−3.11426	−0.263203
$141$	7.14965	0.602109
$142$	1.57291	0.131996
$143$	18.6308	1.55798
$144$	1.00000	0.0833333
$145$	4.82773	0.400921
$146$	−12.9904	−1.07509
$147$	4.30522	0.355088
$148$	−2.74868	−0.225940
$149$	7.50152	0.614548	0.307274	−	0.951621i	$-0.400583\pi$
$149$	7.50152	0.614548	0.307274	+	0.951621i	$0.400583\pi$
$150$	−1.40097	−0.114388
$151$	13.6733	1.11271	0.556357	−	0.830943i	$-0.312199\pi$
$151$	13.6733	1.11271	0.556357	+	0.830943i	$0.312199\pi$
$152$	5.05902	0.410340
$153$	−1.00000	−0.0808452
$154$	5.65831	0.455960
$155$	−3.34412	−0.268606
$156$	5.40513	0.432757
$157$	−5.84754	−0.466684	−0.233342	−	0.972395i	$-0.574966\pi$
$157$	−5.84754	−0.466684	−0.233342	+	0.972395i	$0.574966\pi$
$158$	5.95639	0.473865
$159$	3.26456	0.258896
$160$	1.89711	0.149980
$161$	−12.4248	−0.979209
$162$	−1.00000	−0.0785674
$163$	−15.6228	−1.22367	−0.611837	−	0.790984i	$-0.709569\pi$
$163$	−15.6228	−1.22367	−0.611837	+	0.790984i	$0.709569\pi$
$164$	−1.58191	−0.123527
$165$	−6.53910	−0.509068
$166$	−9.77779	−0.758904
$167$	−19.6048	−1.51707	−0.758534	−	0.651634i	$-0.774084\pi$
$167$	−19.6048	−1.51707	−0.758534	+	0.651634i	$0.774084\pi$
$168$	1.64158	0.126651
$169$	16.2154	1.24734
$170$	−1.89711	−0.145502
$171$	−5.05902	−0.386873
$172$	1.82389	0.139070
$173$	−16.9066	−1.28539	−0.642694	−	0.766123i	$-0.722183\pi$
$173$	−16.9066	−1.28539	−0.642694	+	0.766123i	$0.722183\pi$
$174$	−2.54478	−0.192919
$175$	−2.29980	−0.173848
$176$	−3.44687	−0.259817
$177$	−1.00000	−0.0751646
$178$	5.77743	0.433037
$179$	−1.04200	−0.0778827	−0.0389413	−	0.999241i	$-0.512399\pi$
$179$	−1.04200	−0.0778827	−0.0389413	+	0.999241i	$0.512399\pi$
$180$	−1.89711	−0.141402
$181$	−3.30426	−0.245603	−0.122802	−	0.992431i	$-0.539188\pi$
$181$	−3.30426	−0.245603	−0.122802	+	0.992431i	$0.539188\pi$
$182$	8.87295	0.657707
$183$	−3.88119	−0.286906
$184$	7.56879	0.557978
$185$	5.21455	0.383382
$186$	1.76274	0.129251
$187$	3.44687	0.252060
$188$	−7.14965	−0.521442
$189$	−1.64158	−0.119407
$190$	−9.59752	−0.696277
$191$	4.40428	0.318683	0.159341	−	0.987224i	$-0.449063\pi$
$191$	4.40428	0.318683	0.159341	+	0.987224i	$0.449063\pi$
$192$	−1.00000	−0.0721688
$193$	19.1064	1.37531	0.687654	−	0.726038i	$-0.258640\pi$
$193$	19.1064	1.37531	0.687654	+	0.726038i	$0.258640\pi$
$194$	−8.85984	−0.636099
$195$	−10.2541	−0.734314
$196$	−4.30522	−0.307515
$197$	6.75239	0.481088	0.240544	−	0.970638i	$-0.422674\pi$
$197$	6.75239	0.481088	0.240544	+	0.970638i	$0.422674\pi$
$198$	3.44687	0.244958
$199$	−0.156421	−0.0110884	−0.00554419	−	0.999985i	$-0.501765\pi$
$199$	−0.156421	−0.0110884	−0.00554419	+	0.999985i	$0.501765\pi$
$200$	1.40097	0.0990633
$201$	3.05364	0.215387
$202$	15.5253	1.09235
$203$	−4.17745	−0.293200
$204$	1.00000	0.0700140
$205$	3.00107	0.209604
$206$	−16.1371	−1.12433
$207$	−7.56879	−0.526067
$208$	−5.40513	−0.374778
$209$	17.4378	1.20620
$210$	−3.11426	−0.214904
$211$	−15.9898	−1.10078	−0.550390	−	0.834907i	$-0.685521\pi$
$211$	−15.9898	−1.10078	−0.550390	+	0.834907i	$0.685521\pi$
$212$	−3.26456	−0.224211
$213$	1.57291	0.107774
$214$	−2.93007	−0.200295
$215$	−3.46012	−0.235979
$216$	1.00000	0.0680414
$217$	2.89368	0.196436
$218$	−0.682996	−0.0462584
$219$	−12.9904	−0.877807
$220$	6.53910	0.440866
$221$	5.40513	0.363588
$222$	−2.74868	−0.184479
$223$	−18.4675	−1.23668	−0.618338	−	0.785912i	$-0.712194\pi$
$223$	−18.4675	−1.23668	−0.618338	+	0.785912i	$0.712194\pi$
$224$	−1.64158	−0.109683
$225$	−1.40097	−0.0933977
$226$	13.2238	0.879632
$227$	3.20751	0.212890	0.106445	−	0.994319i	$-0.466053\pi$
$227$	3.20751	0.212890	0.106445	+	0.994319i	$0.466053\pi$
$228$	5.05902	0.335042
$229$	10.7777	0.712213	0.356107	−	0.934445i	$-0.384104\pi$
$229$	10.7777	0.712213	0.356107	+	0.934445i	$0.384104\pi$
$230$	−14.3588	−0.946794
$231$	5.65831	0.372289
$232$	2.54478	0.167073
$233$	−19.2599	−1.26176	−0.630879	−	0.775881i	$-0.717306\pi$
$233$	−19.2599	−1.26176	−0.630879	+	0.775881i	$0.717306\pi$
$234$	5.40513	0.353344
$235$	13.5637	0.884797
$236$	1.00000	0.0650945
$237$	5.95639	0.386909
$238$	1.64158	0.106408
$239$	2.90935	0.188190	0.0940950	−	0.995563i	$-0.470004\pi$
$239$	2.90935	0.188190	0.0940950	+	0.995563i	$0.470004\pi$
$240$	1.89711	0.122458
$241$	−5.13160	−0.330556	−0.165278	−	0.986247i	$-0.552852\pi$
$241$	−5.13160	−0.330556	−0.165278	+	0.986247i	$0.552852\pi$
$242$	−0.880903	−0.0566266
$243$	−1.00000	−0.0641500
$244$	3.88119	0.248468
$245$	8.16748	0.521801
$246$	−1.58191	−0.100859
$247$	27.3446	1.73990
$248$	−1.76274	−0.111934
$249$	−9.77779	−0.619642
$250$	−12.1433	−0.768013
$251$	−15.3182	−0.966879	−0.483439	−	0.875378i	$-0.660613\pi$
$251$	−15.3182	−0.966879	−0.483439	+	0.875378i	$0.660613\pi$
$252$	1.64158	0.103410
$253$	26.0886	1.64018
$254$	−12.6998	−0.796856
$255$	−1.89711	−0.118802
$256$	1.00000	0.0625000
$257$	0.719244	0.0448652	0.0224326	−	0.999748i	$-0.492859\pi$
$257$	0.719244	0.0448652	0.0224326	+	0.999748i	$0.492859\pi$
$258$	1.82389	0.113550
$259$	−4.51218	−0.280373
$260$	10.2541	0.635934
$261$	−2.54478	−0.157518
$262$	9.76002	0.602976
$263$	1.50341	0.0927041	0.0463520	−	0.998925i	$-0.485240\pi$
$263$	1.50341	0.0927041	0.0463520	+	0.998925i	$0.485240\pi$
$264$	−3.44687	−0.212140
$265$	6.19323	0.380447
$266$	8.30478	0.509199
$267$	5.77743	0.353573
$268$	−3.05364	−0.186531
$269$	−15.5147	−0.945949	−0.472975	−	0.881076i	$-0.656820\pi$
$269$	−15.5147	−0.945949	−0.472975	+	0.881076i	$0.656820\pi$
$270$	−1.89711	−0.115455
$271$	16.4237	0.997671	0.498835	−	0.866697i	$-0.333761\pi$
$271$	16.4237	0.997671	0.498835	+	0.866697i	$0.333761\pi$
$272$	−1.00000	−0.0606339
$273$	8.87295	0.537015
$274$	0.796102	0.0480943
$275$	4.82895	0.291196
$276$	7.56879	0.455587
$277$	30.4972	1.83240	0.916199	−	0.400724i	$-0.131241\pi$
$277$	30.4972	1.83240	0.916199	+	0.400724i	$0.131241\pi$
$278$	18.6484	1.11846
$279$	1.76274	0.105533
$280$	3.11426	0.186113
$281$	−11.1904	−0.667561	−0.333781	−	0.942651i	$-0.608324\pi$
$281$	−11.1904	−0.667561	−0.333781	+	0.942651i	$0.608324\pi$
$282$	−7.14965	−0.425755
$283$	−1.61131	−0.0957824	−0.0478912	−	0.998853i	$-0.515250\pi$
$283$	−1.61131	−0.0957824	−0.0478912	+	0.998853i	$0.515250\pi$
$284$	−1.57291	−0.0933352
$285$	−9.59752	−0.568508
$286$	−18.6308	−1.10166
$287$	−2.59684	−0.153286
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	−4.82773	−0.283494
$291$	−8.85984	−0.519373
$292$	12.9904	0.760203
$293$	13.8449	0.808830	0.404415	−	0.914576i	$-0.367475\pi$
$293$	13.8449	0.808830	0.404415	+	0.914576i	$0.367475\pi$
$294$	−4.30522	−0.251085
$295$	−1.89711	−0.110454
$296$	2.74868	0.159764
$297$	3.44687	0.200008
$298$	−7.50152	−0.434551
$299$	40.9103	2.36590
$300$	1.40097	0.0808848
$301$	2.99406	0.172575
$302$	−13.6733	−0.786808
$303$	15.5253	0.891903
$304$	−5.05902	−0.290155
$305$	−7.36305	−0.421607
$306$	1.00000	0.0571662
$307$	6.07308	0.346609	0.173304	−	0.984868i	$-0.444556\pi$
$307$	6.07308	0.346609	0.173304	+	0.984868i	$0.444556\pi$
$308$	−5.65831	−0.322412
$309$	−16.1371	−0.918010
$310$	3.34412	0.189933
$311$	17.7884	1.00869	0.504344	−	0.863503i	$-0.331734\pi$
$311$	17.7884	1.00869	0.504344	+	0.863503i	$0.331734\pi$
$312$	−5.40513	−0.306005
$313$	17.9419	1.01413	0.507067	−	0.861906i	$-0.330730\pi$
$313$	17.9419	1.01413	0.507067	+	0.861906i	$0.330730\pi$
$314$	5.84754	0.329996
$315$	−3.11426	−0.175469
$316$	−5.95639	−0.335073
$317$	20.3677	1.14396	0.571982	−	0.820266i	$-0.306175\pi$
$317$	20.3677	1.14396	0.571982	+	0.820266i	$0.306175\pi$
$318$	−3.26456	−0.183067
$319$	8.77151	0.491110
$320$	−1.89711	−0.106052
$321$	−2.93007	−0.163540
$322$	12.4248	0.692405
$323$	5.05902	0.281491
$324$	1.00000	0.0555556
$325$	7.57240	0.420041
$326$	15.6228	0.865268
$327$	−0.682996	−0.0377698
$328$	1.58191	0.0873465
$329$	−11.7367	−0.647066
$330$	6.53910	0.359965
$331$	−3.32077	−0.182526	−0.0912631	−	0.995827i	$-0.529090\pi$
$331$	−3.32077	−0.182526	−0.0912631	+	0.995827i	$0.529090\pi$
$332$	9.77779	0.536626
$333$	−2.74868	−0.150627
$334$	19.6048	1.07273
$335$	5.79309	0.316510
$336$	−1.64158	−0.0895555
$337$	−34.0591	−1.85532	−0.927660	−	0.373426i	$-0.878183\pi$
$337$	−34.0591	−1.85532	−0.927660	+	0.373426i	$0.878183\pi$
$338$	−16.2154	−0.882002
$339$	13.2238	0.718216
$340$	1.89711	0.102885
$341$	−6.07594	−0.329031
$342$	5.05902	0.273560
$343$	−18.5584	−1.00206
$344$	−1.82389	−0.0983376
$345$	−14.3588	−0.773054
$346$	16.9066	0.908907
$347$	8.04200	0.431717	0.215859	−	0.976425i	$-0.430745\pi$
$347$	8.04200	0.431717	0.215859	+	0.976425i	$0.430745\pi$
$348$	2.54478	0.136414
$349$	−13.7280	−0.734841	−0.367420	−	0.930055i	$-0.619759\pi$
$349$	−13.7280	−0.734841	−0.367420	+	0.930055i	$0.619759\pi$
$350$	2.29980	0.122929
$351$	5.40513	0.288504
$352$	3.44687	0.183719
$353$	−9.23440	−0.491497	−0.245749	−	0.969334i	$-0.579034\pi$
$353$	−9.23440	−0.491497	−0.245749	+	0.969334i	$0.579034\pi$
$354$	1.00000	0.0531494
$355$	2.98399	0.158374
$356$	−5.77743	−0.306203
$357$	1.64158	0.0868816
$358$	1.04200	0.0550714
$359$	−8.13040	−0.429106	−0.214553	−	0.976712i	$-0.568829\pi$
$359$	−8.13040	−0.429106	−0.214553	+	0.976712i	$0.568829\pi$
$360$	1.89711	0.0999866
$361$	6.59365	0.347034
$362$	3.30426	0.173668
$363$	−0.880903	−0.0462354
$364$	−8.87295	−0.465069
$365$	−24.6442	−1.28993
$366$	3.88119	0.202873
$367$	17.1748	0.896519	0.448259	−	0.893904i	$-0.352044\pi$
$367$	17.1748	0.896519	0.448259	+	0.893904i	$0.352044\pi$
$368$	−7.56879	−0.394550
$369$	−1.58191	−0.0823511
$370$	−5.21455	−0.271092
$371$	−5.35903	−0.278227
$372$	−1.76274	−0.0913940
$373$	−27.5634	−1.42718	−0.713590	−	0.700564i	$-0.752932\pi$
$373$	−27.5634	−1.42718	−0.713590	+	0.700564i	$0.752932\pi$
$374$	−3.44687	−0.178233
$375$	−12.1433	−0.627080
$376$	7.14965	0.368715
$377$	13.7548	0.708410
$378$	1.64158	0.0844338
$379$	5.51216	0.283141	0.141570	−	0.989928i	$-0.454785\pi$
$379$	5.51216	0.283141	0.141570	+	0.989928i	$0.454785\pi$
$380$	9.59752	0.492342
$381$	−12.6998	−0.650630
$382$	−4.40428	−0.225343
$383$	−2.23722	−0.114316	−0.0571582	−	0.998365i	$-0.518204\pi$
$383$	−2.23722	−0.114316	−0.0571582	+	0.998365i	$0.518204\pi$
$384$	1.00000	0.0510310
$385$	10.7344	0.547078
$386$	−19.1064	−0.972490
$387$	1.82389	0.0927136
$388$	8.85984	0.449790
$389$	−6.10635	−0.309604	−0.154802	−	0.987945i	$-0.549474\pi$
$389$	−6.10635	−0.309604	−0.154802	+	0.987945i	$0.549474\pi$
$390$	10.2541	0.519238
$391$	7.56879	0.382770
$392$	4.30522	0.217446
$393$	9.76002	0.492328
$394$	−6.75239	−0.340180
$395$	11.2999	0.568561
$396$	−3.44687	−0.173212
$397$	29.3351	1.47229	0.736144	−	0.676825i	$-0.236645\pi$
$397$	29.3351	1.47229	0.736144	+	0.676825i	$0.236645\pi$
$398$	0.156421	0.00784066
$399$	8.30478	0.415759
$400$	−1.40097	−0.0700483
$401$	19.4190	0.969740	0.484870	−	0.874586i	$-0.338867\pi$
$401$	19.4190	0.969740	0.484870	+	0.874586i	$0.338867\pi$
$402$	−3.05364	−0.152302
$403$	−9.52785	−0.474616
$404$	−15.5253	−0.772411
$405$	−1.89711	−0.0942683
$406$	4.17745	0.207324
$407$	9.47434	0.469626
$408$	−1.00000	−0.0495074
$409$	−10.6997	−0.529066	−0.264533	−	0.964377i	$-0.585218\pi$
$409$	−10.6997	−0.529066	−0.264533	+	0.964377i	$0.585218\pi$
$410$	−3.00107	−0.148212
$411$	0.796102	0.0392688
$412$	16.1371	0.795020
$413$	1.64158	0.0807769
$414$	7.56879	0.371986
$415$	−18.5496	−0.910562
$416$	5.40513	0.265008
$417$	18.6484	0.913215
$418$	−17.4378	−0.852909
$419$	37.7830	1.84582	0.922909	−	0.385018i	$-0.125805\pi$
$419$	37.7830	1.84582	0.922909	+	0.385018i	$0.125805\pi$
$420$	3.11426	0.151960
$421$	−2.48308	−0.121018	−0.0605089	−	0.998168i	$-0.519272\pi$
$421$	−2.48308	−0.121018	−0.0605089	+	0.998168i	$0.519272\pi$
$422$	15.9898	0.778370
$423$	−7.14965	−0.347628
$424$	3.26456	0.158541
$425$	1.40097	0.0679568
$426$	−1.57291	−0.0762079
$427$	6.37128	0.308328
$428$	2.93007	0.141630
$429$	−18.6308	−0.899502
$430$	3.46012	0.166862
$431$	20.0893	0.967669	0.483835	−	0.875160i	$-0.339244\pi$
$431$	20.0893	0.967669	0.483835	+	0.875160i	$0.339244\pi$
$432$	−1.00000	−0.0481125
$433$	16.2796	0.782346	0.391173	−	0.920317i	$-0.372069\pi$
$433$	16.2796	0.782346	0.391173	+	0.920317i	$0.372069\pi$
$434$	−2.89368	−0.138901
$435$	−4.82773	−0.231472
$436$	0.682996	0.0327096
$437$	38.2906	1.83169
$438$	12.9904	0.620703
$439$	3.62407	0.172967	0.0864837	−	0.996253i	$-0.472437\pi$
$439$	3.62407	0.172967	0.0864837	+	0.996253i	$0.472437\pi$
$440$	−6.53910	−0.311739
$441$	−4.30522	−0.205010
$442$	−5.40513	−0.257096
$443$	12.0827	0.574065	0.287032	−	0.957921i	$-0.407331\pi$
$443$	12.0827	0.574065	0.287032	+	0.957921i	$0.407331\pi$
$444$	2.74868	0.130447
$445$	10.9604	0.519574
$446$	18.4675	0.874462
$447$	−7.50152	−0.354810
$448$	1.64158	0.0775574
$449$	39.6035	1.86901	0.934503	−	0.355955i	$-0.115844\pi$
$449$	39.6035	1.86901	0.934503	+	0.355955i	$0.115844\pi$
$450$	1.40097	0.0660422
$451$	5.45265	0.256755
$452$	−13.2238	−0.621994
$453$	−13.6733	−0.642426
$454$	−3.20751	−0.150536
$455$	16.8330	0.789142
$456$	−5.05902	−0.236910
$457$	6.65164	0.311150	0.155575	−	0.987824i	$-0.450277\pi$
$457$	6.65164	0.311150	0.155575	+	0.987824i	$0.450277\pi$
$458$	−10.7777	−0.503611
$459$	1.00000	0.0466760
$460$	14.3588	0.669484
$461$	−13.1597	−0.612910	−0.306455	−	0.951885i	$-0.599143\pi$
$461$	−13.1597	−0.612910	−0.306455	+	0.951885i	$0.599143\pi$
$462$	−5.65831	−0.263248
$463$	14.8259	0.689019	0.344509	−	0.938783i	$-0.388045\pi$
$463$	14.8259	0.689019	0.344509	+	0.938783i	$0.388045\pi$
$464$	−2.54478	−0.118138
$465$	3.34412	0.155080
$466$	19.2599	0.892198
$467$	12.6007	0.583090	0.291545	−	0.956557i	$-0.405831\pi$
$467$	12.6007	0.583090	0.291545	+	0.956557i	$0.405831\pi$
$468$	−5.40513	−0.249852
$469$	−5.01279	−0.231469
$470$	−13.5637	−0.625646
$471$	5.84754	0.269440
$472$	−1.00000	−0.0460287
$473$	−6.28671	−0.289063
$474$	−5.95639	−0.273586
$475$	7.08751	0.325197
$476$	−1.64158	−0.0752417
$477$	−3.26456	−0.149474
$478$	−2.90935	−0.133070
$479$	−24.2587	−1.10841	−0.554205	−	0.832380i	$-0.686978\pi$
$479$	−24.2587	−1.10841	−0.554205	+	0.832380i	$0.686978\pi$
$480$	−1.89711	−0.0865909
$481$	14.8570	0.677420
$482$	5.13160	0.233738
$483$	12.4248	0.565346
$484$	0.880903	0.0400410
$485$	−16.8081	−0.763217
$486$	1.00000	0.0453609
$487$	6.77627	0.307062	0.153531	−	0.988144i	$-0.450935\pi$
$487$	6.77627	0.307062	0.153531	+	0.988144i	$0.450935\pi$
$488$	−3.88119	−0.175693
$489$	15.6228	0.706488
$490$	−8.16748	−0.368969
$491$	−20.4446	−0.922651	−0.461325	−	0.887231i	$-0.652626\pi$
$491$	−20.4446	−0.922651	−0.461325	+	0.887231i	$0.652626\pi$
$492$	1.58191	0.0713181
$493$	2.54478	0.114611
$494$	−27.3446	−1.23029
$495$	6.53910	0.293910
$496$	1.76274	0.0791495
$497$	−2.58206	−0.115821
$498$	9.77779	0.438153
$499$	−10.8536	−0.485872	−0.242936	−	0.970042i	$-0.578111\pi$
$499$	−10.8536	−0.485872	−0.242936	+	0.970042i	$0.578111\pi$
$500$	12.1433	0.543067
$501$	19.6048	0.875879
$502$	15.3182	0.683686
$503$	18.6330	0.830805	0.415403	−	0.909638i	$-0.363641\pi$
$503$	18.6330	0.830805	0.415403	+	0.909638i	$0.363641\pi$
$504$	−1.64158	−0.0731218
$505$	29.4532	1.31065
$506$	−26.0886	−1.15978
$507$	−16.2154	−0.720152
$508$	12.6998	0.563462
$509$	−32.7411	−1.45123	−0.725613	−	0.688104i	$-0.758443\pi$
$509$	−32.7411	−1.45123	−0.725613	+	0.688104i	$0.758443\pi$
$510$	1.89711	0.0840055
$511$	21.3247	0.943350
$512$	−1.00000	−0.0441942
$513$	5.05902	0.223361
$514$	−0.719244	−0.0317245
$515$	−30.6140	−1.34901
$516$	−1.82389	−0.0802923
$517$	24.6439	1.08384
$518$	4.51218	0.198254
$519$	16.9066	0.742119
$520$	−10.2541	−0.449674
$521$	23.3427	1.02266	0.511331	−	0.859384i	$-0.329153\pi$
$521$	23.3427	1.02266	0.511331	+	0.859384i	$0.329153\pi$
$522$	2.54478	0.111382
$523$	−21.0948	−0.922412	−0.461206	−	0.887293i	$-0.652583\pi$
$523$	−21.0948	−0.922412	−0.461206	+	0.887293i	$0.652583\pi$
$524$	−9.76002	−0.426368
$525$	2.29980	0.100371
$526$	−1.50341	−0.0655517
$527$	−1.76274	−0.0767863
$528$	3.44687	0.150006
$529$	34.2865	1.49072
$530$	−6.19323	−0.269017
$531$	1.00000	0.0433963
$532$	−8.30478	−0.360058
$533$	8.55044	0.370361
$534$	−5.77743	−0.250014
$535$	−5.55866	−0.240322
$536$	3.05364	0.131897
$537$	1.04200	0.0449656
$538$	15.5147	0.668887
$539$	14.8395	0.639183
$540$	1.89711	0.0816387
$541$	−33.2119	−1.42789	−0.713946	−	0.700201i	$-0.753094\pi$
$541$	−33.2119	−1.42789	−0.713946	+	0.700201i	$0.753094\pi$
$542$	−16.4237	−0.705460
$543$	3.30426	0.141799
$544$	1.00000	0.0428746
$545$	−1.29572	−0.0555026
$546$	−8.87295	−0.379727
$547$	36.6248	1.56596	0.782982	−	0.622045i	$-0.213698\pi$
$547$	36.6248	1.56596	0.782982	+	0.622045i	$0.213698\pi$
$548$	−0.796102	−0.0340078
$549$	3.88119	0.165645
$550$	−4.82895	−0.205907
$551$	12.8741	0.548454
$552$	−7.56879	−0.322149
$553$	−9.77789	−0.415798
$554$	−30.4972	−1.29570
$555$	−5.21455	−0.221346
$556$	−18.6484	−0.790868
$557$	33.6439	1.42554	0.712769	−	0.701398i	$-0.247441\pi$
$557$	33.6439	1.42554	0.712769	+	0.701398i	$0.247441\pi$
$558$	−1.76274	−0.0746229
$559$	−9.85836	−0.416964
$560$	−3.11426	−0.131602
$561$	−3.44687	−0.145527
$562$	11.1904	0.472037
$563$	3.68008	0.155097	0.0775485	−	0.996989i	$-0.475291\pi$
$563$	3.68008	0.155097	0.0775485	+	0.996989i	$0.475291\pi$
$564$	7.14965	0.301054
$565$	25.0870	1.05542
$566$	1.61131	0.0677284
$567$	1.64158	0.0689399
$568$	1.57291	0.0659980
$569$	−13.5815	−0.569364	−0.284682	−	0.958622i	$-0.591888\pi$
$569$	−13.5815	−0.569364	−0.284682	+	0.958622i	$0.591888\pi$
$570$	9.59752	0.401996
$571$	−19.7884	−0.828118	−0.414059	−	0.910250i	$-0.635889\pi$
$571$	−19.7884	−0.828118	−0.414059	+	0.910250i	$0.635889\pi$
$572$	18.6308	0.778991
$573$	−4.40428	−0.183992
$574$	2.59684	0.108390
$575$	10.6036	0.442201
$576$	1.00000	0.0416667
$577$	−34.7501	−1.44667	−0.723333	−	0.690500i	$-0.757391\pi$
$577$	−34.7501	−1.44667	−0.723333	+	0.690500i	$0.757391\pi$
$578$	−1.00000	−0.0415945
$579$	−19.1064	−0.794035
$580$	4.82773	0.200460
$581$	16.0510	0.665909
$582$	8.85984	0.367252
$583$	11.2525	0.466031
$584$	−12.9904	−0.537545
$585$	10.2541	0.423956
$586$	−13.8449	−0.571929
$587$	12.6217	0.520954	0.260477	−	0.965480i	$-0.416120\pi$
$587$	12.6217	0.520954	0.260477	+	0.965480i	$0.416120\pi$
$588$	4.30522	0.177544
$589$	−8.91775	−0.367449
$590$	1.89711	0.0781029
$591$	−6.75239	−0.277756
$592$	−2.74868	−0.112970
$593$	−12.3892	−0.508763	−0.254382	−	0.967104i	$-0.581872\pi$
$593$	−12.3892	−0.508763	−0.254382	+	0.967104i	$0.581872\pi$
$594$	−3.44687	−0.141427
$595$	3.11426	0.127672
$596$	7.50152	0.307274
$597$	0.156421	0.00640187
$598$	−40.9103	−1.67295
$599$	15.3847	0.628601	0.314300	−	0.949324i	$-0.398230\pi$
$599$	15.3847	0.628601	0.314300	+	0.949324i	$0.398230\pi$
$600$	−1.40097	−0.0571942
$601$	23.5030	0.958708	0.479354	−	0.877622i	$-0.340871\pi$
$601$	23.5030	0.958708	0.479354	+	0.877622i	$0.340871\pi$
$602$	−2.99406	−0.122029
$603$	−3.05364	−0.124354
$604$	13.6733	0.556357
$605$	−1.67117	−0.0679428
$606$	−15.5253	−0.630671
$607$	0.973582	0.0395165	0.0197582	−	0.999805i	$-0.493710\pi$
$607$	0.973582	0.0395165	0.0197582	+	0.999805i	$0.493710\pi$
$608$	5.05902	0.205170
$609$	4.17745	0.169279
$610$	7.36305	0.298121
$611$	38.6448	1.56340
$612$	−1.00000	−0.0404226
$613$	−29.4366	−1.18893	−0.594466	−	0.804121i	$-0.702637\pi$
$613$	−29.4366	−1.18893	−0.594466	+	0.804121i	$0.702637\pi$
$614$	−6.07308	−0.245090
$615$	−3.00107	−0.121015
$616$	5.65831	0.227980
$617$	35.0549	1.41126	0.705629	−	0.708582i	$-0.250665\pi$
$617$	35.0549	1.41126	0.705629	+	0.708582i	$0.250665\pi$
$618$	16.1371	0.649131
$619$	−21.6754	−0.871208	−0.435604	−	0.900138i	$-0.643465\pi$
$619$	−21.6754	−0.871208	−0.435604	+	0.900138i	$0.643465\pi$
$620$	−3.34412	−0.134303
$621$	7.56879	0.303725
$622$	−17.7884	−0.713250
$623$	−9.48411	−0.379973
$624$	5.40513	0.216378
$625$	−16.0325	−0.641299
$626$	−17.9419	−0.717101
$627$	−17.4378	−0.696397
$628$	−5.84754	−0.233342
$629$	2.74868	0.109597
$630$	3.11426	0.124075
$631$	29.5275	1.17547	0.587736	−	0.809053i	$-0.300019\pi$
$631$	29.5275	1.17547	0.587736	+	0.809053i	$0.300019\pi$
$632$	5.95639	0.236932
$633$	15.9898	0.635536
$634$	−20.3677	−0.808904
$635$	−24.0929	−0.956099
$636$	3.26456	0.129448
$637$	23.2702	0.922001
$638$	−8.77151	−0.347267
$639$	−1.57291	−0.0622235
$640$	1.89711	0.0749899
$641$	11.6315	0.459415	0.229707	−	0.973260i	$-0.426223\pi$
$641$	11.6315	0.459415	0.229707	+	0.973260i	$0.426223\pi$
$642$	2.93007	0.115640
$643$	−46.7060	−1.84191	−0.920953	−	0.389674i	$-0.872588\pi$
$643$	−46.7060	−1.84191	−0.920953	+	0.389674i	$0.872588\pi$
$644$	−12.4248	−0.489604
$645$	3.46012	0.136242
$646$	−5.05902	−0.199044
$647$	−15.3889	−0.605002	−0.302501	−	0.953149i	$-0.597822\pi$
$647$	−15.3889	−0.605002	−0.302501	+	0.953149i	$0.597822\pi$
$648$	−1.00000	−0.0392837
$649$	−3.44687	−0.135301
$650$	−7.57240	−0.297014
$651$	−2.89368	−0.113412
$652$	−15.6228	−0.611837
$653$	−41.4754	−1.62306	−0.811528	−	0.584313i	$-0.801364\pi$
$653$	−41.4754	−1.62306	−0.811528	+	0.584313i	$0.801364\pi$
$654$	0.682996	0.0267073
$655$	18.5159	0.723474
$656$	−1.58191	−0.0617633
$657$	12.9904	0.506802
$658$	11.7367	0.457545
$659$	−31.2622	−1.21780	−0.608901	−	0.793246i	$-0.708389\pi$
$659$	−31.2622	−1.21780	−0.608901	+	0.793246i	$0.708389\pi$
$660$	−6.53910	−0.254534
$661$	−32.2261	−1.25345	−0.626725	−	0.779240i	$-0.715605\pi$
$661$	−32.2261	−1.25345	−0.626725	+	0.779240i	$0.715605\pi$
$662$	3.32077	0.129065
$663$	−5.40513	−0.209918
$664$	−9.77779	−0.379452
$665$	15.7551	0.610956
$666$	2.74868	0.106509
$667$	19.2609	0.745784
$668$	−19.6048	−0.758534
$669$	18.4675	0.713996
$670$	−5.79309	−0.223807
$671$	−13.3779	−0.516450
$672$	1.64158	0.0633253
$673$	9.73950	0.375430	0.187715	−	0.982224i	$-0.439892\pi$
$673$	9.73950	0.375430	0.187715	+	0.982224i	$0.439892\pi$
$674$	34.0591	1.31191
$675$	1.40097	0.0539232
$676$	16.2154	0.623670
$677$	34.6683	1.33241	0.666206	−	0.745768i	$-0.267917\pi$
$677$	34.6683	1.33241	0.666206	+	0.745768i	$0.267917\pi$
$678$	−13.2238	−0.507856
$679$	14.5441	0.558152
$680$	−1.89711	−0.0727509
$681$	−3.20751	−0.122912
$682$	6.07594	0.232660
$683$	34.9730	1.33821	0.669103	−	0.743170i	$-0.266679\pi$
$683$	34.9730	1.33821	0.669103	+	0.743170i	$0.266679\pi$
$684$	−5.05902	−0.193436
$685$	1.51029	0.0577054
$686$	18.5584	0.708564
$687$	−10.7777	−0.411197
$688$	1.82389	0.0695352
$689$	17.6454	0.672234
$690$	14.3588	0.546632
$691$	−12.6028	−0.479434	−0.239717	−	0.970843i	$-0.577055\pi$
$691$	−12.6028	−0.479434	−0.239717	+	0.970843i	$0.577055\pi$
$692$	−16.9066	−0.642694
$693$	−5.65831	−0.214941
$694$	−8.04200	−0.305270
$695$	35.3781	1.34197
$696$	−2.54478	−0.0964595
$697$	1.58191	0.0599192
$698$	13.7280	0.519611
$699$	19.2599	0.728476
$700$	−2.29980	−0.0869242
$701$	3.58234	0.135303	0.0676515	−	0.997709i	$-0.478449\pi$
$701$	3.58234	0.135303	0.0676515	+	0.997709i	$0.478449\pi$
$702$	−5.40513	−0.204003
$703$	13.9056	0.524460
$704$	−3.44687	−0.129909
$705$	−13.5637	−0.510838
$706$	9.23440	0.347541
$707$	−25.4860	−0.958498
$708$	−1.00000	−0.0375823
$709$	−44.3463	−1.66546	−0.832730	−	0.553679i	$-0.813224\pi$
$709$	−44.3463	−1.66546	−0.832730	+	0.553679i	$0.813224\pi$
$710$	−2.98399	−0.111987
$711$	−5.95639	−0.223382
$712$	5.77743	0.216518
$713$	−13.3418	−0.499655
$714$	−1.64158	−0.0614346
$715$	−35.3447	−1.32182
$716$	−1.04200	−0.0389413
$717$	−2.90935	−0.108651
$718$	8.13040	0.303424
$719$	26.2125	0.977560	0.488780	−	0.872407i	$-0.337442\pi$
$719$	26.2125	0.977560	0.488780	+	0.872407i	$0.337442\pi$
$720$	−1.89711	−0.0707012
$721$	26.4904	0.986554
$722$	−6.59365	−0.245390
$723$	5.13160	0.190846
$724$	−3.30426	−0.122802
$725$	3.56515	0.132406
$726$	0.880903	0.0326934
$727$	5.92963	0.219918	0.109959	−	0.993936i	$-0.464928\pi$
$727$	5.92963	0.219918	0.109959	+	0.993936i	$0.464928\pi$
$728$	8.87295	0.328853
$729$	1.00000	0.0370370
$730$	24.6442	0.912122
$731$	−1.82389	−0.0674590
$732$	−3.88119	−0.143453
$733$	19.1224	0.706301	0.353150	−	0.935567i	$-0.385110\pi$
$733$	19.1224	0.706301	0.353150	+	0.935567i	$0.385110\pi$
$734$	−17.1748	−0.633935
$735$	−8.16748	−0.301262
$736$	7.56879	0.278989
$737$	10.5255	0.387711
$738$	1.58191	0.0582310
$739$	21.9969	0.809167	0.404584	−	0.914501i	$-0.367416\pi$
$739$	21.9969	0.809167	0.404584	+	0.914501i	$0.367416\pi$
$740$	5.21455	0.191691
$741$	−27.3446	−1.00453
$742$	5.35903	0.196736
$743$	−16.9961	−0.623527	−0.311763	−	0.950160i	$-0.600920\pi$
$743$	−16.9961	−0.623527	−0.311763	+	0.950160i	$0.600920\pi$
$744$	1.76274	0.0646253
$745$	−14.2312	−0.521392
$746$	27.5634	1.00917
$747$	9.77779	0.357751
$748$	3.44687	0.126030
$749$	4.80994	0.175751
$750$	12.1433	0.443412
$751$	28.2745	1.03175	0.515875	−	0.856664i	$-0.327467\pi$
$751$	28.2745	1.03175	0.515875	+	0.856664i	$0.327467\pi$
$752$	−7.14965	−0.260721
$753$	15.3182	0.558228
$754$	−13.7548	−0.500922
$755$	−25.9397	−0.944042
$756$	−1.64158	−0.0597037
$757$	−30.1222	−1.09481	−0.547405	−	0.836868i	$-0.684384\pi$
$757$	−30.1222	−1.09481	−0.547405	+	0.836868i	$0.684384\pi$
$758$	−5.51216	−0.200211
$759$	−26.0886	−0.946957
$760$	−9.59752	−0.348139
$761$	−18.0670	−0.654927	−0.327463	−	0.944864i	$-0.606194\pi$
$761$	−18.0670	−0.654927	−0.327463	+	0.944864i	$0.606194\pi$
$762$	12.6998	0.460065
$763$	1.12119	0.0405899
$764$	4.40428	0.159341
$765$	1.89711	0.0685902
$766$	2.23722	0.0808340
$767$	−5.40513	−0.195168
$768$	−1.00000	−0.0360844
$769$	−33.0902	−1.19326	−0.596632	−	0.802515i	$-0.703495\pi$
$769$	−33.0902	−1.19326	−0.596632	+	0.802515i	$0.703495\pi$
$770$	−10.7344	−0.386843
$771$	−0.719244	−0.0259030
$772$	19.1064	0.687654
$773$	−42.3293	−1.52248	−0.761240	−	0.648471i	$-0.775409\pi$
$773$	−42.3293	−1.52248	−0.761240	+	0.648471i	$0.775409\pi$
$774$	−1.82389	−0.0655584
$775$	−2.46954	−0.0887086
$776$	−8.85984	−0.318050
$777$	4.51218	0.161874
$778$	6.10635	0.218923
$779$	8.00292	0.286734
$780$	−10.2541	−0.367157
$781$	5.42162	0.194001
$782$	−7.56879	−0.270659
$783$	2.54478	0.0909429
$784$	−4.30522	−0.153758
$785$	11.0934	0.395942
$786$	−9.76002	−0.348128
$787$	−18.2919	−0.652036	−0.326018	−	0.945363i	$-0.605707\pi$
$787$	−18.2919	−0.652036	−0.326018	+	0.945363i	$0.605707\pi$
$788$	6.75239	0.240544
$789$	−1.50341	−0.0535227
$790$	−11.2999	−0.402034
$791$	−21.7079	−0.771843
$792$	3.44687	0.122479
$793$	−20.9783	−0.744962
$794$	−29.3351	−1.04106
$795$	−6.19323	−0.219651
$796$	−0.156421	−0.00554419
$797$	−16.5718	−0.587004	−0.293502	−	0.955958i	$-0.594821\pi$
$797$	−16.5718	−0.587004	−0.293502	+	0.955958i	$0.594821\pi$
$798$	−8.30478	−0.293986
$799$	7.14965	0.252936
$800$	1.40097	0.0495316
$801$	−5.77743	−0.204135
$802$	−19.4190	−0.685710
$803$	−44.7761	−1.58011
$804$	3.05364	0.107693
$805$	23.5712	0.830775
$806$	9.52785	0.335604
$807$	15.5147	0.546144
$808$	15.5253	0.546177
$809$	45.0462	1.58374	0.791870	−	0.610690i	$-0.209108\pi$
$809$	45.0462	1.58374	0.791870	+	0.610690i	$0.209108\pi$
$810$	1.89711	0.0666577
$811$	11.7118	0.411258	0.205629	−	0.978630i	$-0.434076\pi$
$811$	11.7118	0.411258	0.205629	+	0.978630i	$0.434076\pi$
$812$	−4.17745	−0.146600
$813$	−16.4237	−0.576005
$814$	−9.47434	−0.332075
$815$	29.6382	1.03818
$816$	1.00000	0.0350070
$817$	−9.22709	−0.322815
$818$	10.6997	0.374106
$819$	−8.87295	−0.310046
$820$	3.00107	0.104802
$821$	−44.1705	−1.54156	−0.770781	−	0.637100i	$-0.780134\pi$
$821$	−44.1705	−1.54156	−0.770781	+	0.637100i	$0.780134\pi$
$822$	−0.796102	−0.0277672
$823$	30.2427	1.05419	0.527097	−	0.849805i	$-0.323280\pi$
$823$	30.2427	1.05419	0.527097	+	0.849805i	$0.323280\pi$
$824$	−16.1371	−0.562164
$825$	−4.82895	−0.168122
$826$	−1.64158	−0.0571179
$827$	−22.5771	−0.785082	−0.392541	−	0.919734i	$-0.628404\pi$
$827$	−22.5771	−0.785082	−0.392541	+	0.919734i	$0.628404\pi$
$828$	−7.56879	−0.263034
$829$	17.2204	0.598090	0.299045	−	0.954239i	$-0.403332\pi$
$829$	17.2204	0.598090	0.299045	+	0.954239i	$0.403332\pi$
$830$	18.5496	0.643865
$831$	−30.4972	−1.05794
$832$	−5.40513	−0.187389
$833$	4.30522	0.149167
$834$	−18.6484	−0.645741
$835$	37.1926	1.28710
$836$	17.4378	0.603098
$837$	−1.76274	−0.0609293
$838$	−37.7830	−1.30519
$839$	28.6974	0.990744	0.495372	−	0.868681i	$-0.335032\pi$
$839$	28.6974	0.990744	0.495372	+	0.868681i	$0.335032\pi$
$840$	−3.11426	−0.107452
$841$	−22.5241	−0.776694
$842$	2.48308	0.0855725
$843$	11.1904	0.385417
$844$	−15.9898	−0.550390
$845$	−30.7625	−1.05826
$846$	7.14965	0.245810
$847$	1.44607	0.0496876
$848$	−3.26456	−0.112105
$849$	1.61131	0.0553000
$850$	−1.40097	−0.0480527
$851$	20.8042	0.713158
$852$	1.57291	0.0538871
$853$	13.6587	0.467666	0.233833	−	0.972277i	$-0.424873\pi$
$853$	13.6587	0.467666	0.233833	+	0.972277i	$0.424873\pi$
$854$	−6.37128	−0.218021
$855$	9.59752	0.328228
$856$	−2.93007	−0.100148
$857$	−29.7710	−1.01696	−0.508479	−	0.861074i	$-0.669792\pi$
$857$	−29.7710	−1.01696	−0.508479	+	0.861074i	$0.669792\pi$
$858$	18.6308	0.636044
$859$	47.6772	1.62673	0.813363	−	0.581757i	$-0.197634\pi$
$859$	47.6772	1.62673	0.813363	+	0.581757i	$0.197634\pi$
$860$	−3.46012	−0.117989
$861$	2.59684	0.0884999
$862$	−20.0893	−0.684245
$863$	−27.2501	−0.927602	−0.463801	−	0.885939i	$-0.653515\pi$
$863$	−27.2501	−0.927602	−0.463801	+	0.885939i	$0.653515\pi$
$864$	1.00000	0.0340207
$865$	32.0738	1.09054
$866$	−16.2796	−0.553202
$867$	−1.00000	−0.0339618
$868$	2.89368	0.0982180
$869$	20.5309	0.696463
$870$	4.82773	0.163675
$871$	16.5053	0.559261
$872$	−0.682996	−0.0231292
$873$	8.85984	0.299860
$874$	−38.2906	−1.29520
$875$	19.9343	0.673902
$876$	−12.9904	−0.438904
$877$	−11.5598	−0.390347	−0.195173	−	0.980769i	$-0.562527\pi$
$877$	−11.5598	−0.390347	−0.195173	+	0.980769i	$0.562527\pi$
$878$	−3.62407	−0.122306
$879$	−13.8449	−0.466978
$880$	6.53910	0.220433
$881$	11.2574	0.379270	0.189635	−	0.981855i	$-0.439270\pi$
$881$	11.2574	0.379270	0.189635	+	0.981855i	$0.439270\pi$
$882$	4.30522	0.144964
$883$	−18.9534	−0.637832	−0.318916	−	0.947783i	$-0.603319\pi$
$883$	−18.9534	−0.637832	−0.318916	+	0.947783i	$0.603319\pi$
$884$	5.40513	0.181794
$885$	1.89711	0.0637707
$886$	−12.0827	−0.405925
$887$	−16.3876	−0.550241	−0.275121	−	0.961410i	$-0.588718\pi$
$887$	−16.3876	−0.550241	−0.275121	+	0.961410i	$0.588718\pi$
$888$	−2.74868	−0.0922397
$889$	20.8477	0.699211
$890$	−10.9604	−0.367394
$891$	−3.44687	−0.115474
$892$	−18.4675	−0.618338
$893$	36.1702	1.21039
$894$	7.50152	0.250888
$895$	1.97679	0.0660768
$896$	−1.64158	−0.0548413
$897$	−40.9103	−1.36595
$898$	−39.6035	−1.32159
$899$	−4.48579	−0.149609
$900$	−1.40097	−0.0466989
$901$	3.26456	0.108758
$902$	−5.45265	−0.181553
$903$	−2.99406	−0.0996361
$904$	13.2238	0.439816
$905$	6.26854	0.208373
$906$	13.6733	0.454264
$907$	13.2832	0.441062	0.220531	−	0.975380i	$-0.429221\pi$
$907$	13.2832	0.441062	0.220531	+	0.975380i	$0.429221\pi$
$908$	3.20751	0.106445
$909$	−15.5253	−0.514940
$910$	−16.8330	−0.558008
$911$	36.0021	1.19280	0.596401	−	0.802687i	$-0.296597\pi$
$911$	36.0021	1.19280	0.596401	+	0.802687i	$0.296597\pi$
$912$	5.05902	0.167521
$913$	−33.7028	−1.11540
$914$	−6.65164	−0.220017
$915$	7.36305	0.243415
$916$	10.7777	0.356107
$917$	−16.0219	−0.529088
$918$	−1.00000	−0.0330049
$919$	5.49079	0.181124	0.0905622	−	0.995891i	$-0.471134\pi$
$919$	5.49079	0.181124	0.0905622	+	0.995891i	$0.471134\pi$
$920$	−14.3588	−0.473397
$921$	−6.07308	−0.200115
$922$	13.1597	0.433393
$923$	8.50180	0.279840
$924$	5.65831	0.186145
$925$	3.85081	0.126614
$926$	−14.8259	−0.487210
$927$	16.1371	0.530013
$928$	2.54478	0.0835364
$929$	1.56932	0.0514877	0.0257438	−	0.999669i	$-0.491805\pi$
$929$	1.56932	0.0514877	0.0257438	+	0.999669i	$0.491805\pi$
$930$	−3.34412	−0.109658
$931$	21.7802	0.713816
$932$	−19.2599	−0.630879
$933$	−17.7884	−0.582366
$934$	−12.6007	−0.412307
$935$	−6.53910	−0.213851
$936$	5.40513	0.176672
$937$	−21.1769	−0.691819	−0.345910	−	0.938268i	$-0.612430\pi$
$937$	−21.1769	−0.691819	−0.345910	+	0.938268i	$0.612430\pi$
$938$	5.01279	0.163673
$939$	−17.9419	−0.585511
$940$	13.5637	0.442398
$941$	13.2646	0.432413	0.216207	−	0.976348i	$-0.430632\pi$
$941$	13.2646	0.432413	0.216207	+	0.976348i	$0.430632\pi$
$942$	−5.84754	−0.190523
$943$	11.9732	0.389900
$944$	1.00000	0.0325472
$945$	3.11426	0.101307
$946$	6.28671	0.204399
$947$	−3.69383	−0.120033	−0.0600167	−	0.998197i	$-0.519115\pi$
$947$	−3.69383	−0.120033	−0.0600167	+	0.998197i	$0.519115\pi$
$948$	5.95639	0.193454
$949$	−70.2146	−2.27926
$950$	−7.08751	−0.229949
$951$	−20.3677	−0.660468
$952$	1.64158	0.0532039
$953$	14.2069	0.460207	0.230103	−	0.973166i	$-0.426094\pi$
$953$	14.2069	0.460207	0.230103	+	0.973166i	$0.426094\pi$
$954$	3.26456	0.105694
$955$	−8.35542	−0.270375
$956$	2.90935	0.0940950
$957$	−8.77151	−0.283543
$958$	24.2587	0.783764
$959$	−1.30686	−0.0422009
$960$	1.89711	0.0612290
$961$	−27.8927	−0.899766
$962$	−14.8570	−0.479008
$963$	2.93007	0.0944200
$964$	−5.13160	−0.165278
$965$	−36.2470	−1.16683
$966$	−12.4248	−0.399760
$967$	−3.80175	−0.122256	−0.0611280	−	0.998130i	$-0.519470\pi$
$967$	−3.80175	−0.122256	−0.0611280	+	0.998130i	$0.519470\pi$
$968$	−0.880903	−0.0283133
$969$	−5.05902	−0.162519
$970$	16.8081	0.539676
$971$	−19.7360	−0.633359	−0.316679	−	0.948533i	$-0.602568\pi$
$971$	−19.7360	−0.633359	−0.316679	+	0.948533i	$0.602568\pi$
$972$	−1.00000	−0.0320750
$973$	−30.6128	−0.981401
$974$	−6.77627	−0.217126
$975$	−7.57240	−0.242511
$976$	3.88119	0.124234
$977$	30.0196	0.960413	0.480206	−	0.877156i	$-0.340562\pi$
$977$	30.0196	0.960413	0.480206	+	0.877156i	$0.340562\pi$
$978$	−15.6228	−0.499562
$979$	19.9140	0.636455
$980$	8.16748	0.260900
$981$	0.682996	0.0218064
$982$	20.4446	0.652413
$983$	−25.8730	−0.825220	−0.412610	−	0.910908i	$-0.635383\pi$
$983$	−25.8730	−0.825220	−0.412610	+	0.910908i	$0.635383\pi$
$984$	−1.58191	−0.0504295
$985$	−12.8100	−0.408162
$986$	−2.54478	−0.0810422
$987$	11.7367	0.373584
$988$	27.3446	0.869949
$989$	−13.8046	−0.438962
$990$	−6.53910	−0.207826
$991$	−5.55360	−0.176416	−0.0882079	−	0.996102i	$-0.528114\pi$
$991$	−5.55360	−0.176416	−0.0882079	+	0.996102i	$0.528114\pi$
$992$	−1.76274	−0.0559671
$993$	3.32077	0.105382
$994$	2.58206	0.0818980
$995$	0.296748	0.00940753
$996$	−9.77779	−0.309821
$997$	−16.6919	−0.528639	−0.264320	−	0.964435i	$-0.585147\pi$
$997$	−16.6919	−0.528639	−0.264320	+	0.964435i	$0.585147\pi$
$998$	10.8536	0.343563
$999$	2.74868	0.0869644

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.s.1.3	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.s.1.3	✓	8	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.89711 q^{5} +1.00000 q^{6} +1.64158 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.89711 q^{5} +1.00000 q^{6} +1.64158 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.89711 q^{10} -3.44687 q^{11} -1.00000 q^{12} -5.40513 q^{13} -1.64158 q^{14} +1.89711 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} -5.05902 q^{19} -1.89711 q^{20} -1.64158 q^{21} +3.44687 q^{22} -7.56879 q^{23} +1.00000 q^{24} -1.40097 q^{25} +5.40513 q^{26} -1.00000 q^{27} +1.64158 q^{28} -2.54478 q^{29} -1.89711 q^{30} +1.76274 q^{31} -1.00000 q^{32} +3.44687 q^{33} +1.00000 q^{34} -3.11426 q^{35} +1.00000 q^{36} -2.74868 q^{37} +5.05902 q^{38} +5.40513 q^{39} +1.89711 q^{40} -1.58191 q^{41} +1.64158 q^{42} +1.82389 q^{43} -3.44687 q^{44} -1.89711 q^{45} +7.56879 q^{46} -7.14965 q^{47} -1.00000 q^{48} -4.30522 q^{49} +1.40097 q^{50} +1.00000 q^{51} -5.40513 q^{52} -3.26456 q^{53} +1.00000 q^{54} +6.53910 q^{55} -1.64158 q^{56} +5.05902 q^{57} +2.54478 q^{58} +1.00000 q^{59} +1.89711 q^{60} +3.88119 q^{61} -1.76274 q^{62} +1.64158 q^{63} +1.00000 q^{64} +10.2541 q^{65} -3.44687 q^{66} -3.05364 q^{67} -1.00000 q^{68} +7.56879 q^{69} +3.11426 q^{70} -1.57291 q^{71} -1.00000 q^{72} +12.9904 q^{73} +2.74868 q^{74} +1.40097 q^{75} -5.05902 q^{76} -5.65831 q^{77} -5.40513 q^{78} -5.95639 q^{79} -1.89711 q^{80} +1.00000 q^{81} +1.58191 q^{82} +9.77779 q^{83} -1.64158 q^{84} +1.89711 q^{85} -1.82389 q^{86} +2.54478 q^{87} +3.44687 q^{88} -5.77743 q^{89} +1.89711 q^{90} -8.87295 q^{91} -7.56879 q^{92} -1.76274 q^{93} +7.14965 q^{94} +9.59752 q^{95} +1.00000 q^{96} +8.85984 q^{97} +4.30522 q^{98} -3.44687 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} - 8 q^{3} + 8 q^{4} - q^{5} + 8 q^{6} + 6 q^{7} - 8 q^{8} + 8 q^{9}+O(q^{10}) \) 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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