LMFDB - Embedded newform 6018.2.a.o.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("6018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.0539719364$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.725.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 3x^{2} + x + 1 $ x^4 - x^3 - 3*x^2 + x + 1
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			1.1
Root			$-1.35567$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.97371 q^{5} +1.00000 q^{6} +4.16724 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.97371 q^{5} +1.00000 q^{6} +4.16724 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.97371 q^{10} -4.19353 q^{11} +1.00000 q^{12} +0.854102 q^{13} +4.16724 q^{14} -2.97371 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -5.91177 q^{19} -2.97371 q^{20} +4.16724 q^{21} -4.19353 q^{22} -4.66057 q^{23} +1.00000 q^{24} +3.84294 q^{25} +0.854102 q^{26} +1.00000 q^{27} +4.16724 q^{28} -6.51865 q^{29} -2.97371 q^{30} -6.77328 q^{31} +1.00000 q^{32} -4.19353 q^{33} +1.00000 q^{34} -12.3921 q^{35} +1.00000 q^{36} +4.01758 q^{37} -5.91177 q^{38} +0.854102 q^{39} -2.97371 q^{40} -5.28684 q^{41} +4.16724 q^{42} -8.96255 q^{43} -4.19353 q^{44} -2.97371 q^{45} -4.66057 q^{46} -1.57549 q^{47} +1.00000 q^{48} +10.3659 q^{49} +3.84294 q^{50} +1.00000 q^{51} +0.854102 q^{52} -8.73583 q^{53} +1.00000 q^{54} +12.4703 q^{55} +4.16724 q^{56} -5.91177 q^{57} -6.51865 q^{58} +1.00000 q^{59} -2.97371 q^{60} +1.25120 q^{61} -6.77328 q^{62} +4.16724 q^{63} +1.00000 q^{64} -2.53985 q^{65} -4.19353 q^{66} +1.32512 q^{67} +1.00000 q^{68} -4.66057 q^{69} -12.3921 q^{70} +10.2563 q^{71} +1.00000 q^{72} -2.48218 q^{73} +4.01758 q^{74} +3.84294 q^{75} -5.91177 q^{76} -17.4754 q^{77} +0.854102 q^{78} +6.76079 q^{79} -2.97371 q^{80} +1.00000 q^{81} -5.28684 q^{82} +13.2313 q^{83} +4.16724 q^{84} -2.97371 q^{85} -8.96255 q^{86} -6.51865 q^{87} -4.19353 q^{88} -1.90780 q^{89} -2.97371 q^{90} +3.55924 q^{91} -4.66057 q^{92} -6.77328 q^{93} -1.57549 q^{94} +17.5799 q^{95} +1.00000 q^{96} -4.72273 q^{97} +10.3659 q^{98} -4.19353 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - q^{5} + 4 q^{6} - q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 - q^5 + 4 * q^6 - q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - q^{5} + 4 q^{6} - q^{7} + 4 q^{8} + 4 q^{9} - q^{10} - 10 q^{11} + 4 q^{12} - 10 q^{13} - q^{14} - q^{15} + 4 q^{16} + 4 q^{17} + 4 q^{18} - 14 q^{19} - q^{20} - q^{21} - 10 q^{22} - 12 q^{23} + 4 q^{24} - 3 q^{25} - 10 q^{26} + 4 q^{27} - q^{28} - 7 q^{29} - q^{30} - 13 q^{31} + 4 q^{32} - 10 q^{33} + 4 q^{34} - 18 q^{35} + 4 q^{36} - 11 q^{37} - 14 q^{38} - 10 q^{39} - q^{40} - 6 q^{41} - q^{42} - 20 q^{43} - 10 q^{44} - q^{45} - 12 q^{46} - 4 q^{47} + 4 q^{48} - q^{49} - 3 q^{50} + 4 q^{51} - 10 q^{52} - 5 q^{53} + 4 q^{54} + 4 q^{55} - q^{56} - 14 q^{57} - 7 q^{58} + 4 q^{59} - q^{60} + 2 q^{61} - 13 q^{62} - q^{63} + 4 q^{64} - 20 q^{65} - 10 q^{66} - 7 q^{67} + 4 q^{68} - 12 q^{69} - 18 q^{70} + 20 q^{71} + 4 q^{72} - 16 q^{73} - 11 q^{74} - 3 q^{75} - 14 q^{76} - 6 q^{77} - 10 q^{78} + 22 q^{79} - q^{80} + 4 q^{81} - 6 q^{82} + 7 q^{83} - q^{84} - q^{85} - 20 q^{86} - 7 q^{87} - 10 q^{88} + 3 q^{89} - q^{90} + 25 q^{91} - 12 q^{92} - 13 q^{93} - 4 q^{94} + 3 q^{95} + 4 q^{96} - 16 q^{97} - q^{98} - 10 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 - q^5 + 4 * q^6 - q^7 + 4 * q^8 + 4 * q^9 - q^10 - 10 * q^11 + 4 * q^12 - 10 * q^13 - q^14 - q^15 + 4 * q^16 + 4 * q^17 + 4 * q^18 - 14 * q^19 - q^20 - q^21 - 10 * q^22 - 12 * q^23 + 4 * q^24 - 3 * q^25 - 10 * q^26 + 4 * q^27 - q^28 - 7 * q^29 - q^30 - 13 * q^31 + 4 * q^32 - 10 * q^33 + 4 * q^34 - 18 * q^35 + 4 * q^36 - 11 * q^37 - 14 * q^38 - 10 * q^39 - q^40 - 6 * q^41 - q^42 - 20 * q^43 - 10 * q^44 - q^45 - 12 * q^46 - 4 * q^47 + 4 * q^48 - q^49 - 3 * q^50 + 4 * q^51 - 10 * q^52 - 5 * q^53 + 4 * q^54 + 4 * q^55 - q^56 - 14 * q^57 - 7 * q^58 + 4 * q^59 - q^60 + 2 * q^61 - 13 * q^62 - q^63 + 4 * q^64 - 20 * q^65 - 10 * q^66 - 7 * q^67 + 4 * q^68 - 12 * q^69 - 18 * q^70 + 20 * q^71 + 4 * q^72 - 16 * q^73 - 11 * q^74 - 3 * q^75 - 14 * q^76 - 6 * q^77 - 10 * q^78 + 22 * q^79 - q^80 + 4 * q^81 - 6 * q^82 + 7 * q^83 - q^84 - q^85 - 20 * q^86 - 7 * q^87 - 10 * q^88 + 3 * q^89 - q^90 + 25 * q^91 - 12 * q^92 - 13 * q^93 - 4 * q^94 + 3 * q^95 + 4 * q^96 - 16 * q^97 - q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−2.97371	−1.32988	−0.664941	−	0.746896i	$-0.731543\pi$
$5$	−2.97371	−1.32988	−0.664941	+	0.746896i	$0.731543\pi$
$6$	1.00000	0.408248
$7$	4.16724	1.57507	0.787533	−	0.616272i	$-0.211358\pi$
$7$	4.16724	1.57507	0.787533	+	0.616272i	$0.211358\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−2.97371	−0.940369
$11$	−4.19353	−1.26440	−0.632198	−	0.774807i	$-0.717847\pi$
$11$	−4.19353	−1.26440	−0.632198	+	0.774807i	$0.717847\pi$
$12$	1.00000	0.288675
$13$	0.854102	0.236885	0.118443	−	0.992961i	$-0.462210\pi$
$13$	0.854102	0.236885	0.118443	+	0.992961i	$0.462210\pi$
$14$	4.16724	1.11374
$15$	−2.97371	−0.767808
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.00000	0.235702
$19$	−5.91177	−1.35625	−0.678127	−	0.734945i	$-0.737208\pi$
$19$	−5.91177	−1.35625	−0.678127	+	0.734945i	$0.737208\pi$
$20$	−2.97371	−0.664941
$21$	4.16724	0.909365
$22$	−4.19353	−0.894063
$23$	−4.66057	−0.971797	−0.485899	−	0.874015i	$-0.661508\pi$
$23$	−4.66057	−0.971797	−0.485899	+	0.874015i	$0.661508\pi$
$24$	1.00000	0.204124
$25$	3.84294	0.768588
$26$	0.854102	0.167503
$27$	1.00000	0.192450
$28$	4.16724	0.787533
$29$	−6.51865	−1.21048	−0.605241	−	0.796042i	$-0.706923\pi$
$29$	−6.51865	−1.21048	−0.605241	+	0.796042i	$0.706923\pi$
$30$	−2.97371	−0.542922
$31$	−6.77328	−1.21652	−0.608259	−	0.793739i	$-0.708132\pi$
$31$	−6.77328	−1.21652	−0.608259	+	0.793739i	$0.708132\pi$
$32$	1.00000	0.176777
$33$	−4.19353	−0.729999
$34$	1.00000	0.171499
$35$	−12.3921	−2.09465
$36$	1.00000	0.166667
$37$	4.01758	0.660487	0.330243	−	0.943896i	$-0.392869\pi$
$37$	4.01758	0.660487	0.330243	+	0.943896i	$0.392869\pi$
$38$	−5.91177	−0.959016
$39$	0.854102	0.136766
$40$	−2.97371	−0.470185
$41$	−5.28684	−0.825666	−0.412833	−	0.910807i	$-0.635461\pi$
$41$	−5.28684	−0.825666	−0.412833	+	0.910807i	$0.635461\pi$
$42$	4.16724	0.643018
$43$	−8.96255	−1.36678	−0.683388	−	0.730056i	$-0.739494\pi$
$43$	−8.96255	−1.36678	−0.683388	+	0.730056i	$0.739494\pi$
$44$	−4.19353	−0.632198
$45$	−2.97371	−0.443294
$46$	−4.66057	−0.687164
$47$	−1.57549	−0.229809	−0.114905	−	0.993377i	$-0.536656\pi$
$47$	−1.57549	−0.229809	−0.114905	+	0.993377i	$0.536656\pi$
$48$	1.00000	0.144338
$49$	10.3659	1.48084
$50$	3.84294	0.543474
$51$	1.00000	0.140028
$52$	0.854102	0.118443
$53$	−8.73583	−1.19996	−0.599979	−	0.800016i	$-0.704825\pi$
$53$	−8.73583	−1.19996	−0.599979	+	0.800016i	$0.704825\pi$
$54$	1.00000	0.136083
$55$	12.4703	1.68150
$56$	4.16724	0.556870
$57$	−5.91177	−0.783034
$58$	−6.51865	−0.855940
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	−2.97371	−0.383904
$61$	1.25120	0.160200	0.0800998	−	0.996787i	$-0.474476\pi$
$61$	1.25120	0.160200	0.0800998	+	0.996787i	$0.474476\pi$
$62$	−6.77328	−0.860208
$63$	4.16724	0.525022
$64$	1.00000	0.125000
$65$	−2.53985	−0.315030
$66$	−4.19353	−0.516188
$67$	1.32512	0.161889	0.0809446	−	0.996719i	$-0.474206\pi$
$67$	1.32512	0.161889	0.0809446	+	0.996719i	$0.474206\pi$
$68$	1.00000	0.121268
$69$	−4.66057	−0.561067
$70$	−12.3921	−1.48114
$71$	10.2563	1.21720	0.608599	−	0.793478i	$-0.291732\pi$
$71$	10.2563	1.21720	0.608599	+	0.793478i	$0.291732\pi$
$72$	1.00000	0.117851
$73$	−2.48218	−0.290517	−0.145259	−	0.989394i	$-0.546401\pi$
$73$	−2.48218	−0.290517	−0.145259	+	0.989394i	$0.546401\pi$
$74$	4.01758	0.467035
$75$	3.84294	0.443745
$76$	−5.91177	−0.678127
$77$	−17.4754	−1.99151
$78$	0.854102	0.0967080
$79$	6.76079	0.760648	0.380324	−	0.924853i	$-0.375812\pi$
$79$	6.76079	0.760648	0.380324	+	0.924853i	$0.375812\pi$
$80$	−2.97371	−0.332471
$81$	1.00000	0.111111
$82$	−5.28684	−0.583834
$83$	13.2313	1.45233	0.726164	−	0.687522i	$-0.241302\pi$
$83$	13.2313	1.45233	0.726164	+	0.687522i	$0.241302\pi$
$84$	4.16724	0.454683
$85$	−2.97371	−0.322544
$86$	−8.96255	−0.966456
$87$	−6.51865	−0.698872
$88$	−4.19353	−0.447031
$89$	−1.90780	−0.202227	−0.101113	−	0.994875i	$-0.532240\pi$
$89$	−1.90780	−0.202227	−0.101113	+	0.994875i	$0.532240\pi$
$90$	−2.97371	−0.313456
$91$	3.55924	0.373110
$92$	−4.66057	−0.485899
$93$	−6.77328	−0.702357
$94$	−1.57549	−0.162500
$95$	17.5799	1.80366
$96$	1.00000	0.102062
$97$	−4.72273	−0.479520	−0.239760	−	0.970832i	$-0.577069\pi$
$97$	−4.72273	−0.479520	−0.239760	+	0.970832i	$0.577069\pi$
$98$	10.3659	1.04711
$99$	−4.19353	−0.421465
$100$	3.84294	0.384294
$101$	−12.5766	−1.25142	−0.625710	−	0.780056i	$-0.715191\pi$
$101$	−12.5766	−1.25142	−0.625710	+	0.780056i	$0.715191\pi$
$102$	1.00000	0.0990148
$103$	0.717421	0.0706896	0.0353448	−	0.999375i	$-0.488747\pi$
$103$	0.717421	0.0706896	0.0353448	+	0.999375i	$0.488747\pi$
$104$	0.854102	0.0837516
$105$	−12.3921	−1.20935
$106$	−8.73583	−0.848499
$107$	15.4935	1.49781	0.748905	−	0.662677i	$-0.230580\pi$
$107$	15.4935	1.49781	0.748905	+	0.662677i	$0.230580\pi$
$108$	1.00000	0.0962250
$109$	10.2737	0.984038	0.492019	−	0.870585i	$-0.336259\pi$
$109$	10.2737	0.984038	0.492019	+	0.870585i	$0.336259\pi$
$110$	12.4703	1.18900
$111$	4.01758	0.381332
$112$	4.16724	0.393767
$113$	4.37965	0.412002	0.206001	−	0.978552i	$-0.433955\pi$
$113$	4.37965	0.412002	0.206001	+	0.978552i	$0.433955\pi$
$114$	−5.91177	−0.553688
$115$	13.8592	1.29238
$116$	−6.51865	−0.605241
$117$	0.854102	0.0789618
$118$	1.00000	0.0920575
$119$	4.16724	0.382010
$120$	−2.97371	−0.271461
$121$	6.58567	0.598697
$122$	1.25120	0.113278
$123$	−5.28684	−0.476698
$124$	−6.77328	−0.608259
$125$	3.44076	0.307751
$126$	4.16724	0.371247
$127$	−21.5339	−1.91083	−0.955413	−	0.295273i	$-0.904589\pi$
$127$	−21.5339	−1.91083	−0.955413	+	0.295273i	$0.904589\pi$
$128$	1.00000	0.0883883
$129$	−8.96255	−0.789108
$130$	−2.53985	−0.222760
$131$	−9.22227	−0.805754	−0.402877	−	0.915254i	$-0.631990\pi$
$131$	−9.22227	−0.805754	−0.402877	+	0.915254i	$0.631990\pi$
$132$	−4.19353	−0.365000
$133$	−24.6358	−2.13619
$134$	1.32512	0.114473
$135$	−2.97371	−0.255936
$136$	1.00000	0.0857493
$137$	−21.8186	−1.86409	−0.932044	−	0.362345i	$-0.881976\pi$
$137$	−21.8186	−1.86409	−0.932044	+	0.362345i	$0.881976\pi$
$138$	−4.66057	−0.396734
$139$	10.5040	0.890940	0.445470	−	0.895297i	$-0.353037\pi$
$139$	10.5040	0.890940	0.445470	+	0.895297i	$0.353037\pi$
$140$	−12.3921	−1.04733
$141$	−1.57549	−0.132680
$142$	10.2563	0.860688
$143$	−3.58170	−0.299517
$144$	1.00000	0.0833333
$145$	19.3846	1.60980
$146$	−2.48218	−0.205427
$147$	10.3659	0.854961
$148$	4.01758	0.330243
$149$	−12.8178	−1.05007	−0.525036	−	0.851080i	$-0.675948\pi$
$149$	−12.8178	−1.05007	−0.525036	+	0.851080i	$0.675948\pi$
$150$	3.84294	0.313775
$151$	17.7761	1.44659	0.723297	−	0.690537i	$-0.242626\pi$
$151$	17.7761	1.44659	0.723297	+	0.690537i	$0.242626\pi$
$152$	−5.91177	−0.479508
$153$	1.00000	0.0808452
$154$	−17.4754	−1.40821
$155$	20.1418	1.61783
$156$	0.854102	0.0683829
$157$	4.52424	0.361074	0.180537	−	0.983568i	$-0.442216\pi$
$157$	4.52424	0.361074	0.180537	+	0.983568i	$0.442216\pi$
$158$	6.76079	0.537859
$159$	−8.73583	−0.692796
$160$	−2.97371	−0.235092
$161$	−19.4217	−1.53065
$162$	1.00000	0.0785674
$163$	−14.6701	−1.14905	−0.574527	−	0.818486i	$-0.694814\pi$
$163$	−14.6701	−1.14905	−0.574527	+	0.818486i	$0.694814\pi$
$164$	−5.28684	−0.412833
$165$	12.4703	0.970814
$166$	13.2313	1.02695
$167$	−15.5463	−1.20301	−0.601503	−	0.798870i	$-0.705431\pi$
$167$	−15.5463	−1.20301	−0.601503	+	0.798870i	$0.705431\pi$
$168$	4.16724	0.321509
$169$	−12.2705	−0.943885
$170$	−2.97371	−0.228073
$171$	−5.91177	−0.452085
$172$	−8.96255	−0.683388
$173$	−7.63937	−0.580811	−0.290405	−	0.956904i	$-0.593790\pi$
$173$	−7.63937	−0.580811	−0.290405	+	0.956904i	$0.593790\pi$
$174$	−6.51865	−0.494177
$175$	16.0144	1.21058
$176$	−4.19353	−0.316099
$177$	1.00000	0.0751646
$178$	−1.90780	−0.142996
$179$	−16.6939	−1.24776	−0.623880	−	0.781520i	$-0.714445\pi$
$179$	−16.6939	−1.24776	−0.623880	+	0.781520i	$0.714445\pi$
$180$	−2.97371	−0.221647
$181$	−6.64941	−0.494247	−0.247124	−	0.968984i	$-0.579485\pi$
$181$	−6.64941	−0.494247	−0.247124	+	0.968984i	$0.579485\pi$
$182$	3.55924	0.263829
$183$	1.25120	0.0924913
$184$	−4.66057	−0.343582
$185$	−11.9471	−0.878370
$186$	−6.77328	−0.496641
$187$	−4.19353	−0.306661
$188$	−1.57549	−0.114905
$189$	4.16724	0.303122
$190$	17.5799	1.27538
$191$	−18.7494	−1.35666	−0.678331	−	0.734756i	$-0.737296\pi$
$191$	−18.7494	−1.35666	−0.678331	+	0.734756i	$0.737296\pi$
$192$	1.00000	0.0721688
$193$	20.8480	1.50067	0.750337	−	0.661056i	$-0.229891\pi$
$193$	20.8480	1.50067	0.750337	+	0.661056i	$0.229891\pi$
$194$	−4.72273	−0.339072
$195$	−2.53985	−0.181882
$196$	10.3659	0.740418
$197$	−3.06142	−0.218117	−0.109059	−	0.994035i	$-0.534784\pi$
$197$	−3.06142	−0.218117	−0.109059	+	0.994035i	$0.534784\pi$
$198$	−4.19353	−0.298021
$199$	1.57730	0.111812	0.0559060	−	0.998436i	$-0.482195\pi$
$199$	1.57730	0.111812	0.0559060	+	0.998436i	$0.482195\pi$
$200$	3.84294	0.271737
$201$	1.32512	0.0934667
$202$	−12.5766	−0.884887
$203$	−27.1647	−1.90659
$204$	1.00000	0.0700140
$205$	15.7215	1.09804
$206$	0.717421	0.0499851
$207$	−4.66057	−0.323932
$208$	0.854102	0.0592213
$209$	24.7912	1.71484
$210$	−12.3921	−0.855139
$211$	−11.0001	−0.757280	−0.378640	−	0.925544i	$-0.623608\pi$
$211$	−11.0001	−0.757280	−0.378640	+	0.925544i	$0.623608\pi$
$212$	−8.73583	−0.599979
$213$	10.2563	0.702749
$214$	15.4935	1.05911
$215$	26.6520	1.81765
$216$	1.00000	0.0680414
$217$	−28.2259	−1.91610
$218$	10.2737	0.695820
$219$	−2.48218	−0.167730
$220$	12.4703	0.840749
$221$	0.854102	0.0574531
$222$	4.01758	0.269643
$223$	24.3437	1.63017	0.815086	−	0.579340i	$-0.196690\pi$
$223$	24.3437	1.63017	0.815086	+	0.579340i	$0.196690\pi$
$224$	4.16724	0.278435
$225$	3.84294	0.256196
$226$	4.37965	0.291330
$227$	−11.5331	−0.765478	−0.382739	−	0.923857i	$-0.625019\pi$
$227$	−11.5331	−0.765478	−0.382739	+	0.923857i	$0.625019\pi$
$228$	−5.91177	−0.391517
$229$	−13.7537	−0.908872	−0.454436	−	0.890779i	$-0.650159\pi$
$229$	−13.7537	−0.908872	−0.454436	+	0.890779i	$0.650159\pi$
$230$	13.8592	0.913848
$231$	−17.4754	−1.14980
$232$	−6.51865	−0.427970
$233$	22.0235	1.44281	0.721404	−	0.692515i	$-0.243497\pi$
$233$	22.0235	1.44281	0.721404	+	0.692515i	$0.243497\pi$
$234$	0.854102	0.0558344
$235$	4.68506	0.305619
$236$	1.00000	0.0650945
$237$	6.76079	0.439160
$238$	4.16724	0.270122
$239$	22.2522	1.43937	0.719686	−	0.694299i	$-0.244286\pi$
$239$	22.2522	1.43937	0.719686	+	0.694299i	$0.244286\pi$
$240$	−2.97371	−0.191952
$241$	22.9990	1.48150	0.740748	−	0.671783i	$-0.234471\pi$
$241$	22.9990	1.48150	0.740748	+	0.671783i	$0.234471\pi$
$242$	6.58567	0.423343
$243$	1.00000	0.0641500
$244$	1.25120	0.0800998
$245$	−30.8250	−1.96934
$246$	−5.28684	−0.337077
$247$	−5.04926	−0.321277
$248$	−6.77328	−0.430104
$249$	13.2313	0.838501
$250$	3.44076	0.217613
$251$	−18.0222	−1.13755	−0.568774	−	0.822494i	$-0.692582\pi$
$251$	−18.0222	−1.13755	−0.568774	+	0.822494i	$0.692582\pi$
$252$	4.16724	0.262511
$253$	19.5442	1.22874
$254$	−21.5339	−1.35116
$255$	−2.97371	−0.186221
$256$	1.00000	0.0625000
$257$	29.0042	1.80923	0.904617	−	0.426225i	$-0.140157\pi$
$257$	29.0042	1.80923	0.904617	+	0.426225i	$0.140157\pi$
$258$	−8.96255	−0.557984
$259$	16.7422	1.04031
$260$	−2.53985	−0.157515
$261$	−6.51865	−0.403494
$262$	−9.22227	−0.569754
$263$	−9.70191	−0.598246	−0.299123	−	0.954215i	$-0.596694\pi$
$263$	−9.70191	−0.598246	−0.299123	+	0.954215i	$0.596694\pi$
$264$	−4.19353	−0.258094
$265$	25.9778	1.59580
$266$	−24.6358	−1.51051
$267$	−1.90780	−0.116756
$268$	1.32512	0.0809446
$269$	23.7567	1.44847	0.724236	−	0.689553i	$-0.242193\pi$
$269$	23.7567	1.44847	0.724236	+	0.689553i	$0.242193\pi$
$270$	−2.97371	−0.180974
$271$	−21.5562	−1.30945	−0.654724	−	0.755868i	$-0.727215\pi$
$271$	−21.5562	−1.30945	−0.654724	+	0.755868i	$0.727215\pi$
$272$	1.00000	0.0606339
$273$	3.55924	0.215415
$274$	−21.8186	−1.31811
$275$	−16.1155	−0.971800
$276$	−4.66057	−0.280534
$277$	5.41093	0.325111	0.162556	−	0.986699i	$-0.448026\pi$
$277$	5.41093	0.325111	0.162556	+	0.986699i	$0.448026\pi$
$278$	10.5040	0.629990
$279$	−6.77328	−0.405506
$280$	−12.3921	−0.740572
$281$	−24.3665	−1.45358	−0.726792	−	0.686858i	$-0.758989\pi$
$281$	−24.3665	−1.45358	−0.726792	+	0.686858i	$0.758989\pi$
$282$	−1.57549	−0.0938192
$283$	−10.8799	−0.646744	−0.323372	−	0.946272i	$-0.604817\pi$
$283$	−10.8799	−0.646744	−0.323372	+	0.946272i	$0.604817\pi$
$284$	10.2563	0.608599
$285$	17.5799	1.04134
$286$	−3.58170	−0.211790
$287$	−22.0315	−1.30048
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	19.3846	1.13830
$291$	−4.72273	−0.276851
$292$	−2.48218	−0.145259
$293$	−7.83492	−0.457721	−0.228861	−	0.973459i	$-0.573500\pi$
$293$	−7.83492	−0.457721	−0.228861	+	0.973459i	$0.573500\pi$
$294$	10.3659	0.604549
$295$	−2.97371	−0.173136
$296$	4.01758	0.233517
$297$	−4.19353	−0.243333
$298$	−12.8178	−0.742513
$299$	−3.98061	−0.230204
$300$	3.84294	0.221872
$301$	−37.3490	−2.15276
$302$	17.7761	1.02290
$303$	−12.5766	−0.722507
$304$	−5.91177	−0.339063
$305$	−3.72070	−0.213047
$306$	1.00000	0.0571662
$307$	30.0764	1.71655	0.858275	−	0.513191i	$-0.171537\pi$
$307$	30.0764	1.71655	0.858275	+	0.513191i	$0.171537\pi$
$308$	−17.4754	−0.995754
$309$	0.717421	0.0408127
$310$	20.1418	1.14398
$311$	−13.9010	−0.788251	−0.394126	−	0.919057i	$-0.628953\pi$
$311$	−13.9010	−0.788251	−0.394126	+	0.919057i	$0.628953\pi$
$312$	0.854102	0.0483540
$313$	24.6159	1.39137	0.695686	−	0.718346i	$-0.255101\pi$
$313$	24.6159	1.39137	0.695686	+	0.718346i	$0.255101\pi$
$314$	4.52424	0.255318
$315$	−12.3921	−0.698218
$316$	6.76079	0.380324
$317$	−22.2048	−1.24715	−0.623574	−	0.781765i	$-0.714320\pi$
$317$	−22.2048	−1.24715	−0.623574	+	0.781765i	$0.714320\pi$
$318$	−8.73583	−0.489881
$319$	27.3361	1.53053
$320$	−2.97371	−0.166235
$321$	15.4935	0.864761
$322$	−19.4217	−1.08233
$323$	−5.91177	−0.328940
$324$	1.00000	0.0555556
$325$	3.28226	0.182067
$326$	−14.6701	−0.812504
$327$	10.2737	0.568134
$328$	−5.28684	−0.291917
$329$	−6.56545	−0.361965
$330$	12.4703	0.686469
$331$	6.19973	0.340768	0.170384	−	0.985378i	$-0.445499\pi$
$331$	6.19973	0.340768	0.170384	+	0.985378i	$0.445499\pi$
$332$	13.2313	0.726164
$333$	4.01758	0.220162
$334$	−15.5463	−0.850654
$335$	−3.94052	−0.215294
$336$	4.16724	0.227341
$337$	0.597949	0.0325724	0.0162862	−	0.999867i	$-0.494816\pi$
$337$	0.597949	0.0325724	0.0162862	+	0.999867i	$0.494816\pi$
$338$	−12.2705	−0.667428
$339$	4.37965	0.237870
$340$	−2.97371	−0.161272
$341$	28.4039	1.53816
$342$	−5.91177	−0.319672
$343$	14.0263	0.757349
$344$	−8.96255	−0.483228
$345$	13.8592	0.746154
$346$	−7.63937	−0.410695
$347$	−6.96945	−0.374139	−0.187070	−	0.982347i	$-0.559899\pi$
$347$	−6.96945	−0.374139	−0.187070	+	0.982347i	$0.559899\pi$
$348$	−6.51865	−0.349436
$349$	−16.7848	−0.898469	−0.449235	−	0.893414i	$-0.648303\pi$
$349$	−16.7848	−0.898469	−0.449235	+	0.893414i	$0.648303\pi$
$350$	16.0144	0.856008
$351$	0.854102	0.0455886
$352$	−4.19353	−0.223516
$353$	−6.91683	−0.368146	−0.184073	−	0.982913i	$-0.558928\pi$
$353$	−6.91683	−0.368146	−0.184073	+	0.982913i	$0.558928\pi$
$354$	1.00000	0.0531494
$355$	−30.4992	−1.61873
$356$	−1.90780	−0.101113
$357$	4.16724	0.220553
$358$	−16.6939	−0.882300
$359$	18.5410	0.978555	0.489277	−	0.872128i	$-0.337261\pi$
$359$	18.5410	0.978555	0.489277	+	0.872128i	$0.337261\pi$
$360$	−2.97371	−0.156728
$361$	15.9491	0.839425
$362$	−6.64941	−0.349485
$363$	6.58567	0.345658
$364$	3.55924	0.186555
$365$	7.38127	0.386354
$366$	1.25120	0.0654012
$367$	13.2375	0.690994	0.345497	−	0.938420i	$-0.387710\pi$
$367$	13.2375	0.690994	0.345497	+	0.938420i	$0.387710\pi$
$368$	−4.66057	−0.242949
$369$	−5.28684	−0.275222
$370$	−11.9471	−0.621101
$371$	−36.4043	−1.89002
$372$	−6.77328	−0.351178
$373$	18.0201	0.933047	0.466524	−	0.884509i	$-0.345506\pi$
$373$	18.0201	0.933047	0.466524	+	0.884509i	$0.345506\pi$
$374$	−4.19353	−0.216842
$375$	3.44076	0.177680
$376$	−1.57549	−0.0812499
$377$	−5.56759	−0.286745
$378$	4.16724	0.214339
$379$	−14.4951	−0.744564	−0.372282	−	0.928120i	$-0.621425\pi$
$379$	−14.4951	−0.744564	−0.372282	+	0.928120i	$0.621425\pi$
$380$	17.5799	0.901829
$381$	−21.5339	−1.10322
$382$	−18.7494	−0.959305
$383$	−0.248698	−0.0127079	−0.00635393	−	0.999980i	$-0.502023\pi$
$383$	−0.248698	−0.0127079	−0.00635393	+	0.999980i	$0.502023\pi$
$384$	1.00000	0.0510310
$385$	51.9668	2.64847
$386$	20.8480	1.06114
$387$	−8.96255	−0.455592
$388$	−4.72273	−0.239760
$389$	10.7537	0.545233	0.272616	−	0.962123i	$-0.412111\pi$
$389$	10.7537	0.545233	0.272616	+	0.962123i	$0.412111\pi$
$390$	−2.53985	−0.128610
$391$	−4.66057	−0.235695
$392$	10.3659	0.523555
$393$	−9.22227	−0.465202
$394$	−3.06142	−0.154232
$395$	−20.1046	−1.01157
$396$	−4.19353	−0.210733
$397$	5.23774	0.262875	0.131437	−	0.991324i	$-0.458041\pi$
$397$	5.23774	0.262875	0.131437	+	0.991324i	$0.458041\pi$
$398$	1.57730	0.0790630
$399$	−24.6358	−1.23333
$400$	3.84294	0.192147
$401$	19.7517	0.986353	0.493177	−	0.869929i	$-0.335836\pi$
$401$	19.7517	0.986353	0.493177	+	0.869929i	$0.335836\pi$
$402$	1.32512	0.0660910
$403$	−5.78507	−0.288175
$404$	−12.5766	−0.625710
$405$	−2.97371	−0.147765
$406$	−27.1647	−1.34816
$407$	−16.8478	−0.835117
$408$	1.00000	0.0495074
$409$	−17.3791	−0.859343	−0.429671	−	0.902985i	$-0.641371\pi$
$409$	−17.3791	−0.859343	−0.429671	+	0.902985i	$0.641371\pi$
$410$	15.7215	0.776431
$411$	−21.8186	−1.07623
$412$	0.717421	0.0353448
$413$	4.16724	0.205056
$414$	−4.66057	−0.229055
$415$	−39.3461	−1.93142
$416$	0.854102	0.0418758
$417$	10.5040	0.514384
$418$	24.7912	1.21258
$419$	3.88043	0.189571	0.0947857	−	0.995498i	$-0.469783\pi$
$419$	3.88043	0.189571	0.0947857	+	0.995498i	$0.469783\pi$
$420$	−12.3921	−0.604675
$421$	−30.9429	−1.50806	−0.754032	−	0.656837i	$-0.771894\pi$
$421$	−30.9429	−1.50806	−0.754032	+	0.656837i	$0.771894\pi$
$422$	−11.0001	−0.535478
$423$	−1.57549	−0.0766031
$424$	−8.73583	−0.424249
$425$	3.84294	0.186410
$426$	10.2563	0.496919
$427$	5.21404	0.252325
$428$	15.4935	0.748905
$429$	−3.58170	−0.172926
$430$	26.6520	1.28527
$431$	0.678025	0.0326593	0.0163297	−	0.999867i	$-0.494802\pi$
$431$	0.678025	0.0326593	0.0163297	+	0.999867i	$0.494802\pi$
$432$	1.00000	0.0481125
$433$	5.51761	0.265159	0.132580	−	0.991172i	$-0.457674\pi$
$433$	5.51761	0.265159	0.132580	+	0.991172i	$0.457674\pi$
$434$	−28.2259	−1.35488
$435$	19.3846	0.929418
$436$	10.2737	0.492019
$437$	27.5523	1.31800
$438$	−2.48218	−0.118603
$439$	−5.00815	−0.239026	−0.119513	−	0.992833i	$-0.538133\pi$
$439$	−5.00815	−0.239026	−0.119513	+	0.992833i	$0.538133\pi$
$440$	12.4703	0.594499
$441$	10.3659	0.493612
$442$	0.854102	0.0406255
$443$	−7.14886	−0.339653	−0.169826	−	0.985474i	$-0.554321\pi$
$443$	−7.14886	−0.339653	−0.169826	+	0.985474i	$0.554321\pi$
$444$	4.01758	0.190666
$445$	5.67325	0.268938
$446$	24.3437	1.15271
$447$	−12.8178	−0.606260
$448$	4.16724	0.196883
$449$	−17.3252	−0.817625	−0.408812	−	0.912618i	$-0.634057\pi$
$449$	−17.3252	−0.817625	−0.408812	+	0.912618i	$0.634057\pi$
$450$	3.84294	0.181158
$451$	22.1705	1.04397
$452$	4.37965	0.206001
$453$	17.7761	0.835192
$454$	−11.5331	−0.541275
$455$	−10.5842	−0.496193
$456$	−5.91177	−0.276844
$457$	−23.2029	−1.08538	−0.542692	−	0.839931i	$-0.682595\pi$
$457$	−23.2029	−1.08538	−0.542692	+	0.839931i	$0.682595\pi$
$458$	−13.7537	−0.642670
$459$	1.00000	0.0466760
$460$	13.8592	0.646188
$461$	2.97349	0.138489	0.0692447	−	0.997600i	$-0.477941\pi$
$461$	2.97349	0.138489	0.0692447	+	0.997600i	$0.477941\pi$
$462$	−17.4754	−0.813030
$463$	21.3789	0.993560	0.496780	−	0.867877i	$-0.334516\pi$
$463$	21.3789	0.993560	0.496780	+	0.867877i	$0.334516\pi$
$464$	−6.51865	−0.302621
$465$	20.1418	0.934052
$466$	22.0235	1.02022
$467$	28.3583	1.31226	0.656132	−	0.754646i	$-0.272191\pi$
$467$	28.3583	1.31226	0.656132	+	0.754646i	$0.272191\pi$
$468$	0.854102	0.0394809
$469$	5.52208	0.254986
$470$	4.68506	0.216106
$471$	4.52424	0.208466
$472$	1.00000	0.0460287
$473$	37.5847	1.72815
$474$	6.76079	0.310533
$475$	−22.7186	−1.04240
$476$	4.16724	0.191005
$477$	−8.73583	−0.399986
$478$	22.2522	1.01779
$479$	−32.0114	−1.46264	−0.731318	−	0.682037i	$-0.761094\pi$
$479$	−32.0114	−1.46264	−0.731318	+	0.682037i	$0.761094\pi$
$480$	−2.97371	−0.135731
$481$	3.43143	0.156460
$482$	22.9990	1.04758
$483$	−19.4217	−0.883719
$484$	6.58567	0.299349
$485$	14.0440	0.637706
$486$	1.00000	0.0453609
$487$	18.4344	0.835341	0.417670	−	0.908599i	$-0.362847\pi$
$487$	18.4344	0.835341	0.417670	+	0.908599i	$0.362847\pi$
$488$	1.25120	0.0566391
$489$	−14.6701	−0.663407
$490$	−30.8250	−1.39253
$491$	41.4725	1.87163	0.935815	−	0.352492i	$-0.114666\pi$
$491$	41.4725	1.87163	0.935815	+	0.352492i	$0.114666\pi$
$492$	−5.28684	−0.238349
$493$	−6.51865	−0.293585
$494$	−5.04926	−0.227177
$495$	12.4703	0.560499
$496$	−6.77328	−0.304129
$497$	42.7404	1.91717
$498$	13.2313	0.592910
$499$	8.90863	0.398805	0.199403	−	0.979918i	$-0.436100\pi$
$499$	8.90863	0.398805	0.199403	+	0.979918i	$0.436100\pi$
$500$	3.44076	0.153875
$501$	−15.5463	−0.694556
$502$	−18.0222	−0.804368
$503$	29.4783	1.31437	0.657187	−	0.753728i	$-0.271746\pi$
$503$	29.4783	1.31437	0.657187	+	0.753728i	$0.271746\pi$
$504$	4.16724	0.185623
$505$	37.3992	1.66424
$506$	19.5442	0.868848
$507$	−12.2705	−0.544952
$508$	−21.5339	−0.955413
$509$	−40.2991	−1.78622	−0.893112	−	0.449834i	$-0.851483\pi$
$509$	−40.2991	−1.78622	−0.893112	+	0.449834i	$0.851483\pi$
$510$	−2.97371	−0.131678
$511$	−10.3438	−0.457584
$512$	1.00000	0.0441942
$513$	−5.91177	−0.261011
$514$	29.0042	1.27932
$515$	−2.13340	−0.0940089
$516$	−8.96255	−0.394554
$517$	6.60687	0.290570
$518$	16.7422	0.735611
$519$	−7.63937	−0.335331
$520$	−2.53985	−0.111380
$521$	2.69755	0.118182	0.0590910	−	0.998253i	$-0.481180\pi$
$521$	2.69755	0.118182	0.0590910	+	0.998253i	$0.481180\pi$
$522$	−6.51865	−0.285313
$523$	13.0982	0.572746	0.286373	−	0.958118i	$-0.407550\pi$
$523$	13.0982	0.572746	0.286373	+	0.958118i	$0.407550\pi$
$524$	−9.22227	−0.402877
$525$	16.0144	0.698927
$526$	−9.70191	−0.423024
$527$	−6.77328	−0.295049
$528$	−4.19353	−0.182500
$529$	−1.27904	−0.0556105
$530$	25.9778	1.12840
$531$	1.00000	0.0433963
$532$	−24.6358	−1.06810
$533$	−4.51550	−0.195588
$534$	−1.90780	−0.0825587
$535$	−46.0731	−1.99191
$536$	1.32512	0.0572364
$537$	−16.6939	−0.720395
$538$	23.7567	1.02422
$539$	−43.4695	−1.87236
$540$	−2.97371	−0.127968
$541$	−33.4116	−1.43648	−0.718238	−	0.695797i	$-0.755051\pi$
$541$	−33.4116	−1.43648	−0.718238	+	0.695797i	$0.755051\pi$
$542$	−21.5562	−0.925919
$543$	−6.64941	−0.285354
$544$	1.00000	0.0428746
$545$	−30.5509	−1.30865
$546$	3.55924	0.152322
$547$	−13.8032	−0.590182	−0.295091	−	0.955469i	$-0.595350\pi$
$547$	−13.8032	−0.590182	−0.295091	+	0.955469i	$0.595350\pi$
$548$	−21.8186	−0.932044
$549$	1.25120	0.0533999
$550$	−16.1155	−0.687166
$551$	38.5368	1.64172
$552$	−4.66057	−0.198367
$553$	28.1738	1.19807
$554$	5.41093	0.229888
$555$	−11.9471	−0.507127
$556$	10.5040	0.445470
$557$	20.1342	0.853113	0.426556	−	0.904461i	$-0.359727\pi$
$557$	20.1342	0.853113	0.426556	+	0.904461i	$0.359727\pi$
$558$	−6.77328	−0.286736
$559$	−7.65493	−0.323769
$560$	−12.3921	−0.523664
$561$	−4.19353	−0.177051
$562$	−24.3665	−1.02784
$563$	−14.8882	−0.627461	−0.313730	−	0.949512i	$-0.601579\pi$
$563$	−14.8882	−0.627461	−0.313730	+	0.949512i	$0.601579\pi$
$564$	−1.57549	−0.0663402
$565$	−13.0238	−0.547915
$566$	−10.8799	−0.457317
$567$	4.16724	0.175007
$568$	10.2563	0.430344
$569$	−0.483673	−0.0202766	−0.0101383	−	0.999949i	$-0.503227\pi$
$569$	−0.483673	−0.0202766	−0.0101383	+	0.999949i	$0.503227\pi$
$570$	17.5799	0.736341
$571$	5.06849	0.212110	0.106055	−	0.994360i	$-0.466178\pi$
$571$	5.06849	0.212110	0.106055	+	0.994360i	$0.466178\pi$
$572$	−3.58170	−0.149758
$573$	−18.7494	−0.783269
$574$	−22.0315	−0.919578
$575$	−17.9103	−0.746912
$576$	1.00000	0.0416667
$577$	−1.72626	−0.0718653	−0.0359326	−	0.999354i	$-0.511440\pi$
$577$	−1.72626	−0.0718653	−0.0359326	+	0.999354i	$0.511440\pi$
$578$	1.00000	0.0415945
$579$	20.8480	0.866415
$580$	19.3846	0.804900
$581$	55.1381	2.28751
$582$	−4.72273	−0.195763
$583$	36.6339	1.51722
$584$	−2.48218	−0.102713
$585$	−2.53985	−0.105010
$586$	−7.83492	−0.323658
$587$	14.4174	0.595072	0.297536	−	0.954711i	$-0.403835\pi$
$587$	14.4174	0.595072	0.297536	+	0.954711i	$0.403835\pi$
$588$	10.3659	0.427480
$589$	40.0421	1.64991
$590$	−2.97371	−0.122426
$591$	−3.06142	−0.125930
$592$	4.01758	0.165122
$593$	−23.9070	−0.981741	−0.490870	−	0.871233i	$-0.663321\pi$
$593$	−23.9070	−0.981741	−0.490870	+	0.871233i	$0.663321\pi$
$594$	−4.19353	−0.172063
$595$	−12.3921	−0.508028
$596$	−12.8178	−0.525036
$597$	1.57730	0.0645547
$598$	−3.98061	−0.162779
$599$	0.520115	0.0212513	0.0106257	−	0.999944i	$-0.496618\pi$
$599$	0.520115	0.0212513	0.0106257	+	0.999944i	$0.496618\pi$
$600$	3.84294	0.156887
$601$	−0.193151	−0.00787879	−0.00393940	−	0.999992i	$-0.501254\pi$
$601$	−0.193151	−0.00787879	−0.00393940	+	0.999992i	$0.501254\pi$
$602$	−37.3490	−1.52223
$603$	1.32512	0.0539630
$604$	17.7761	0.723297
$605$	−19.5839	−0.796197
$606$	−12.5766	−0.510890
$607$	3.17626	0.128920	0.0644602	−	0.997920i	$-0.479467\pi$
$607$	3.17626	0.128920	0.0644602	+	0.997920i	$0.479467\pi$
$608$	−5.91177	−0.239754
$609$	−27.1647	−1.10077
$610$	−3.72070	−0.150647
$611$	−1.34563	−0.0544384
$612$	1.00000	0.0404226
$613$	−15.8021	−0.638239	−0.319119	−	0.947715i	$-0.603387\pi$
$613$	−15.8021	−0.638239	−0.319119	+	0.947715i	$0.603387\pi$
$614$	30.0764	1.21378
$615$	15.7215	0.633953
$616$	−17.4754	−0.704105
$617$	27.4777	1.10621	0.553104	−	0.833112i	$-0.313443\pi$
$617$	27.4777	1.10621	0.553104	+	0.833112i	$0.313443\pi$
$618$	0.717421	0.0288589
$619$	−21.9758	−0.883281	−0.441641	−	0.897192i	$-0.645603\pi$
$619$	−21.9758	−0.883281	−0.441641	+	0.897192i	$0.645603\pi$
$620$	20.1418	0.808913
$621$	−4.66057	−0.187022
$622$	−13.9010	−0.557378
$623$	−7.95027	−0.318521
$624$	0.854102	0.0341914
$625$	−29.4465	−1.17786
$626$	24.6159	0.983849
$627$	24.7912	0.990064
$628$	4.52424	0.180537
$629$	4.01758	0.160192
$630$	−12.3921	−0.493715
$631$	−14.0011	−0.557375	−0.278687	−	0.960382i	$-0.589899\pi$
$631$	−14.0011	−0.557375	−0.278687	+	0.960382i	$0.589899\pi$
$632$	6.76079	0.268930
$633$	−11.0001	−0.437216
$634$	−22.2048	−0.881866
$635$	64.0356	2.54117
$636$	−8.73583	−0.346398
$637$	8.85349	0.350788
$638$	27.3361	1.08225
$639$	10.2563	0.405732
$640$	−2.97371	−0.117546
$641$	−29.9050	−1.18118	−0.590588	−	0.806973i	$-0.701104\pi$
$641$	−29.9050	−1.18118	−0.590588	+	0.806973i	$0.701104\pi$
$642$	15.4935	0.611479
$643$	25.1009	0.989881	0.494941	−	0.868927i	$-0.335190\pi$
$643$	25.1009	0.989881	0.494941	+	0.868927i	$0.335190\pi$
$644$	−19.4217	−0.765323
$645$	26.6520	1.04942
$646$	−5.91177	−0.232596
$647$	42.6085	1.67511	0.837556	−	0.546351i	$-0.183984\pi$
$647$	42.6085	1.67511	0.837556	+	0.546351i	$0.183984\pi$
$648$	1.00000	0.0392837
$649$	−4.19353	−0.164610
$650$	3.28226	0.128741
$651$	−28.2259	−1.10626
$652$	−14.6701	−0.574527
$653$	34.9986	1.36960	0.684801	−	0.728730i	$-0.259889\pi$
$653$	34.9986	1.36960	0.684801	+	0.728730i	$0.259889\pi$
$654$	10.2737	0.401732
$655$	27.4243	1.07156
$656$	−5.28684	−0.206416
$657$	−2.48218	−0.0968390
$658$	−6.56545	−0.255948
$659$	23.8406	0.928698	0.464349	−	0.885652i	$-0.346288\pi$
$659$	23.8406	0.928698	0.464349	+	0.885652i	$0.346288\pi$
$660$	12.4703	0.485407
$661$	−13.4324	−0.522458	−0.261229	−	0.965277i	$-0.584128\pi$
$661$	−13.4324	−0.522458	−0.261229	+	0.965277i	$0.584128\pi$
$662$	6.19973	0.240959
$663$	0.854102	0.0331706
$664$	13.2313	0.513475
$665$	73.2595	2.84088
$666$	4.01758	0.155678
$667$	30.3806	1.17634
$668$	−15.5463	−0.601503
$669$	24.3437	0.941180
$670$	−3.94052	−0.152236
$671$	−5.24694	−0.202556
$672$	4.16724	0.160755
$673$	−7.29103	−0.281048	−0.140524	−	0.990077i	$-0.544879\pi$
$673$	−7.29103	−0.281048	−0.140524	+	0.990077i	$0.544879\pi$
$674$	0.597949	0.0230321
$675$	3.84294	0.147915
$676$	−12.2705	−0.471943
$677$	−45.0342	−1.73080	−0.865402	−	0.501077i	$-0.832937\pi$
$677$	−45.0342	−1.73080	−0.865402	+	0.501077i	$0.832937\pi$
$678$	4.37965	0.168199
$679$	−19.6807	−0.755276
$680$	−2.97371	−0.114037
$681$	−11.5331	−0.441949
$682$	28.4039	1.08764
$683$	−18.6929	−0.715264	−0.357632	−	0.933863i	$-0.616416\pi$
$683$	−18.6929	−0.715264	−0.357632	+	0.933863i	$0.616416\pi$
$684$	−5.91177	−0.226042
$685$	64.8821	2.47902
$686$	14.0263	0.535526
$687$	−13.7537	−0.524738
$688$	−8.96255	−0.341694
$689$	−7.46129	−0.284253
$690$	13.8592	0.527610
$691$	−2.10581	−0.0801088	−0.0400544	−	0.999198i	$-0.512753\pi$
$691$	−2.10581	−0.0801088	−0.0400544	+	0.999198i	$0.512753\pi$
$692$	−7.63937	−0.290405
$693$	−17.4754	−0.663836
$694$	−6.96945	−0.264557
$695$	−31.2359	−1.18485
$696$	−6.51865	−0.247089
$697$	−5.28684	−0.200253
$698$	−16.7848	−0.635314
$699$	22.0235	0.833005
$700$	16.0144	0.605289
$701$	−39.9025	−1.50710	−0.753549	−	0.657392i	$-0.771660\pi$
$701$	−39.9025	−1.50710	−0.753549	+	0.657392i	$0.771660\pi$
$702$	0.854102	0.0322360
$703$	−23.7510	−0.895788
$704$	−4.19353	−0.158049
$705$	4.68506	0.176449
$706$	−6.91683	−0.260318
$707$	−52.4097	−1.97107
$708$	1.00000	0.0375823
$709$	−5.04961	−0.189642	−0.0948210	−	0.995494i	$-0.530228\pi$
$709$	−5.04961	−0.189642	−0.0948210	+	0.995494i	$0.530228\pi$
$710$	−30.4992	−1.14461
$711$	6.76079	0.253549
$712$	−1.90780	−0.0714980
$713$	31.5674	1.18221
$714$	4.16724	0.155955
$715$	10.6509	0.398322
$716$	−16.6939	−0.623880
$717$	22.2522	0.831022
$718$	18.5410	0.691943
$719$	25.6620	0.957033	0.478516	−	0.878079i	$-0.341175\pi$
$719$	25.6620	0.957033	0.478516	+	0.878079i	$0.341175\pi$
$720$	−2.97371	−0.110824
$721$	2.98966	0.111341
$722$	15.9491	0.593563
$723$	22.9990	0.855343
$724$	−6.64941	−0.247124
$725$	−25.0508	−0.930362
$726$	6.58567	0.244417
$727$	19.5319	0.724398	0.362199	−	0.932101i	$-0.382026\pi$
$727$	19.5319	0.724398	0.362199	+	0.932101i	$0.382026\pi$
$728$	3.55924	0.131914
$729$	1.00000	0.0370370
$730$	7.38127	0.273193
$731$	−8.96255	−0.331492
$732$	1.25120	0.0462456
$733$	−22.1951	−0.819794	−0.409897	−	0.912132i	$-0.634435\pi$
$733$	−22.1951	−0.819794	−0.409897	+	0.912132i	$0.634435\pi$
$734$	13.2375	0.488606
$735$	−30.8250	−1.13700
$736$	−4.66057	−0.171791
$737$	−5.55692	−0.204692
$738$	−5.28684	−0.194611
$739$	−44.5623	−1.63925	−0.819626	−	0.572899i	$-0.805819\pi$
$739$	−44.5623	−1.63925	−0.819626	+	0.572899i	$0.805819\pi$
$740$	−11.9471	−0.439185
$741$	−5.04926	−0.185489
$742$	−36.4043	−1.33644
$743$	43.9141	1.61105	0.805525	−	0.592561i	$-0.201883\pi$
$743$	43.9141	1.61105	0.805525	+	0.592561i	$0.201883\pi$
$744$	−6.77328	−0.248321
$745$	38.1163	1.39647
$746$	18.0201	0.659764
$747$	13.2313	0.484109
$748$	−4.19353	−0.153331
$749$	64.5649	2.35915
$750$	3.44076	0.125639
$751$	5.66380	0.206675	0.103338	−	0.994646i	$-0.467048\pi$
$751$	5.66380	0.206675	0.103338	+	0.994646i	$0.467048\pi$
$752$	−1.57549	−0.0574523
$753$	−18.0222	−0.656764
$754$	−5.56759	−0.202760
$755$	−52.8608	−1.92380
$756$	4.16724	0.151561
$757$	51.8284	1.88373	0.941867	−	0.335985i	$-0.109069\pi$
$757$	51.8284	1.88373	0.941867	+	0.335985i	$0.109069\pi$
$758$	−14.4951	−0.526487
$759$	19.5442	0.709411
$760$	17.5799	0.637690
$761$	19.2892	0.699232	0.349616	−	0.936893i	$-0.386312\pi$
$761$	19.2892	0.699232	0.349616	+	0.936893i	$0.386312\pi$
$762$	−21.5339	−0.780091
$763$	42.8127	1.54993
$764$	−18.7494	−0.678331
$765$	−2.97371	−0.107515
$766$	−0.248698	−0.00898581
$767$	0.854102	0.0308398
$768$	1.00000	0.0360844
$769$	−17.1522	−0.618523	−0.309261	−	0.950977i	$-0.600082\pi$
$769$	−17.1522	−0.618523	−0.309261	+	0.950977i	$0.600082\pi$
$770$	51.9668	1.87275
$771$	29.0042	1.04456
$772$	20.8480	0.750337
$773$	42.1904	1.51748	0.758741	−	0.651393i	$-0.225815\pi$
$773$	42.1904	1.51748	0.758741	+	0.651393i	$0.225815\pi$
$774$	−8.96255	−0.322152
$775$	−26.0293	−0.935001
$776$	−4.72273	−0.169536
$777$	16.7422	0.600624
$778$	10.7537	0.385538
$779$	31.2546	1.11981
$780$	−2.53985	−0.0909412
$781$	−43.0100	−1.53902
$782$	−4.66057	−0.166662
$783$	−6.51865	−0.232957
$784$	10.3659	0.370209
$785$	−13.4538	−0.480186
$786$	−9.22227	−0.328948
$787$	−43.6962	−1.55760	−0.778800	−	0.627272i	$-0.784171\pi$
$787$	−43.6962	−1.55760	−0.778800	+	0.627272i	$0.784171\pi$
$788$	−3.06142	−0.109059
$789$	−9.70191	−0.345397
$790$	−20.1046	−0.715290
$791$	18.2510	0.648931
$792$	−4.19353	−0.149010
$793$	1.06865	0.0379489
$794$	5.23774	0.185881
$795$	25.9778	0.921338
$796$	1.57730	0.0559060
$797$	43.3066	1.53400	0.767000	−	0.641647i	$-0.221749\pi$
$797$	43.3066	1.53400	0.767000	+	0.641647i	$0.221749\pi$
$798$	−24.6358	−0.872096
$799$	−1.57549	−0.0557369
$800$	3.84294	0.135868
$801$	−1.90780	−0.0674089
$802$	19.7517	0.697457
$803$	10.4091	0.367329
$804$	1.32512	0.0467334
$805$	57.7545	2.03558
$806$	−5.78507	−0.203771
$807$	23.7567	0.836275
$808$	−12.5766	−0.442444
$809$	55.5542	1.95318	0.976591	−	0.215104i	$-0.0690091\pi$
$809$	55.5542	1.95318	0.976591	+	0.215104i	$0.0690091\pi$
$810$	−2.97371	−0.104485
$811$	7.86844	0.276298	0.138149	−	0.990411i	$-0.455885\pi$
$811$	7.86844	0.276298	0.138149	+	0.990411i	$0.455885\pi$
$812$	−27.1647	−0.953295
$813$	−21.5562	−0.756010
$814$	−16.8478	−0.590517
$815$	43.6247	1.52811
$816$	1.00000	0.0350070
$817$	52.9845	1.85369
$818$	−17.3791	−0.607647
$819$	3.55924	0.124370
$820$	15.7215	0.549019
$821$	−0.929517	−0.0324404	−0.0162202	−	0.999868i	$-0.505163\pi$
$821$	−0.929517	−0.0324404	−0.0162202	+	0.999868i	$0.505163\pi$
$822$	−21.8186	−0.761011
$823$	−8.34001	−0.290715	−0.145357	−	0.989379i	$-0.546433\pi$
$823$	−8.34001	−0.290715	−0.145357	+	0.989379i	$0.546433\pi$
$824$	0.717421	0.0249926
$825$	−16.1155	−0.561069
$826$	4.16724	0.144997
$827$	3.29089	0.114435	0.0572177	−	0.998362i	$-0.481777\pi$
$827$	3.29089	0.114435	0.0572177	+	0.998362i	$0.481777\pi$
$828$	−4.66057	−0.161966
$829$	5.39093	0.187235	0.0936173	−	0.995608i	$-0.470157\pi$
$829$	5.39093	0.187235	0.0936173	+	0.995608i	$0.470157\pi$
$830$	−39.3461	−1.36572
$831$	5.41093	0.187703
$832$	0.854102	0.0296107
$833$	10.3659	0.359155
$834$	10.5040	0.363725
$835$	46.2301	1.59986
$836$	24.7912	0.857421
$837$	−6.77328	−0.234119
$838$	3.88043	0.134047
$839$	39.7895	1.37369	0.686843	−	0.726806i	$-0.258996\pi$
$839$	39.7895	1.37369	0.686843	+	0.726806i	$0.258996\pi$
$840$	−12.3921	−0.427570
$841$	13.4928	0.465267
$842$	−30.9429	−1.06636
$843$	−24.3665	−0.839227
$844$	−11.0001	−0.378640
$845$	36.4889	1.25526
$846$	−1.57549	−0.0541666
$847$	27.4440	0.942988
$848$	−8.73583	−0.299990
$849$	−10.8799	−0.373398
$850$	3.84294	0.131812
$851$	−18.7243	−0.641859
$852$	10.2563	0.351375
$853$	23.0109	0.787880	0.393940	−	0.919136i	$-0.371112\pi$
$853$	23.0109	0.787880	0.393940	+	0.919136i	$0.371112\pi$
$854$	5.21404	0.178421
$855$	17.5799	0.601220
$856$	15.4935	0.529556
$857$	−1.39999	−0.0478227	−0.0239114	−	0.999714i	$-0.507612\pi$
$857$	−1.39999	−0.0478227	−0.0239114	+	0.999714i	$0.507612\pi$
$858$	−3.58170	−0.122277
$859$	22.5879	0.770689	0.385345	−	0.922773i	$-0.374083\pi$
$859$	22.5879	0.770689	0.385345	+	0.922773i	$0.374083\pi$
$860$	26.6520	0.908826
$861$	−22.0315	−0.750832
$862$	0.678025	0.0230936
$863$	12.9083	0.439404	0.219702	−	0.975567i	$-0.429491\pi$
$863$	12.9083	0.439404	0.219702	+	0.975567i	$0.429491\pi$
$864$	1.00000	0.0340207
$865$	22.7173	0.772410
$866$	5.51761	0.187496
$867$	1.00000	0.0339618
$868$	−28.2259	−0.958048
$869$	−28.3515	−0.961760
$870$	19.3846	0.657198
$871$	1.13179	0.0383491
$872$	10.2737	0.347910
$873$	−4.72273	−0.159840
$874$	27.5523	0.931969
$875$	14.3384	0.484728
$876$	−2.48218	−0.0838650
$877$	38.1819	1.28931	0.644655	−	0.764474i	$-0.277001\pi$
$877$	38.1819	1.28931	0.644655	+	0.764474i	$0.277001\pi$
$878$	−5.00815	−0.169017
$879$	−7.83492	−0.264265
$880$	12.4703	0.420375
$881$	−31.6504	−1.06633	−0.533165	−	0.846011i	$-0.678997\pi$
$881$	−31.6504	−1.06633	−0.533165	+	0.846011i	$0.678997\pi$
$882$	10.3659	0.349036
$883$	−44.4317	−1.49524	−0.747622	−	0.664124i	$-0.768805\pi$
$883$	−44.4317	−1.49524	−0.747622	+	0.664124i	$0.768805\pi$
$884$	0.854102	0.0287266
$885$	−2.97371	−0.0999601
$886$	−7.14886	−0.240171
$887$	−48.5564	−1.63037	−0.815183	−	0.579204i	$-0.803363\pi$
$887$	−48.5564	−1.63037	−0.815183	+	0.579204i	$0.803363\pi$
$888$	4.01758	0.134821
$889$	−89.7369	−3.00968
$890$	5.67325	0.190168
$891$	−4.19353	−0.140488
$892$	24.3437	0.815086
$893$	9.31396	0.311680
$894$	−12.8178	−0.428690
$895$	49.6428	1.65938
$896$	4.16724	0.139218
$897$	−3.98061	−0.132909
$898$	−17.3252	−0.578148
$899$	44.1526	1.47257
$900$	3.84294	0.128098
$901$	−8.73583	−0.291033
$902$	22.1705	0.738197
$903$	−37.3490	−1.24290
$904$	4.37965	0.145665
$905$	19.7734	0.657291
$906$	17.7761	0.590570
$907$	24.6158	0.817355	0.408678	−	0.912679i	$-0.365990\pi$
$907$	24.6158	0.817355	0.408678	+	0.912679i	$0.365990\pi$
$908$	−11.5331	−0.382739
$909$	−12.5766	−0.417140
$910$	−10.5842	−0.350861
$911$	13.9391	0.461824	0.230912	−	0.972975i	$-0.425829\pi$
$911$	13.9391	0.461824	0.230912	+	0.972975i	$0.425829\pi$
$912$	−5.91177	−0.195758
$913$	−55.4859	−1.83632
$914$	−23.2029	−0.767483
$915$	−3.72070	−0.123003
$916$	−13.7537	−0.454436
$917$	−38.4314	−1.26912
$918$	1.00000	0.0330049
$919$	−4.47878	−0.147741	−0.0738706	−	0.997268i	$-0.523535\pi$
$919$	−4.47878	−0.147741	−0.0738706	+	0.997268i	$0.523535\pi$
$920$	13.8592	0.456924
$921$	30.0764	0.991050
$922$	2.97349	0.0979267
$923$	8.75991	0.288336
$924$	−17.4754	−0.574899
$925$	15.4393	0.507642
$926$	21.3789	0.702553
$927$	0.717421	0.0235632
$928$	−6.51865	−0.213985
$929$	38.7061	1.26990	0.634952	−	0.772551i	$-0.281020\pi$
$929$	38.7061	1.26990	0.634952	+	0.772551i	$0.281020\pi$
$930$	20.1418	0.660475
$931$	−61.2806	−2.00839
$932$	22.0235	0.721404
$933$	−13.9010	−0.455097
$934$	28.3583	0.927911
$935$	12.4703	0.407823
$936$	0.854102	0.0279172
$937$	31.0896	1.01565	0.507827	−	0.861459i	$-0.330449\pi$
$937$	31.0896	1.01565	0.507827	+	0.861459i	$0.330449\pi$
$938$	5.52208	0.180302
$939$	24.6159	0.803309
$940$	4.68506	0.152810
$941$	11.4348	0.372764	0.186382	−	0.982477i	$-0.440324\pi$
$941$	11.4348	0.372764	0.186382	+	0.982477i	$0.440324\pi$
$942$	4.52424	0.147408
$943$	24.6397	0.802380
$944$	1.00000	0.0325472
$945$	−12.3921	−0.403116
$946$	37.5847	1.22198
$947$	−35.3536	−1.14884	−0.574419	−	0.818561i	$-0.694772\pi$
$947$	−35.3536	−1.14884	−0.574419	+	0.818561i	$0.694772\pi$
$948$	6.76079	0.219580
$949$	−2.12003	−0.0688192
$950$	−22.7186	−0.737089
$951$	−22.2048	−0.720041
$952$	4.16724	0.135061
$953$	−25.2982	−0.819488	−0.409744	−	0.912201i	$-0.634382\pi$
$953$	−25.2982	−0.819488	−0.409744	+	0.912201i	$0.634382\pi$
$954$	−8.73583	−0.282833
$955$	55.7554	1.80420
$956$	22.2522	0.719686
$957$	27.3361	0.883651
$958$	−32.0114	−1.03424
$959$	−90.9232	−2.93606
$960$	−2.97371	−0.0959760
$961$	14.8774	0.479915
$962$	3.43143	0.110634
$963$	15.4935	0.499270
$964$	22.9990	0.740748
$965$	−61.9960	−1.99572
$966$	−19.4217	−0.624883
$967$	13.5851	0.436869	0.218434	−	0.975852i	$-0.429905\pi$
$967$	13.5851	0.436869	0.218434	+	0.975852i	$0.429905\pi$
$968$	6.58567	0.211671
$969$	−5.91177	−0.189914
$970$	14.0440	0.450926
$971$	8.29916	0.266333	0.133166	−	0.991094i	$-0.457486\pi$
$971$	8.29916	0.266333	0.133166	+	0.991094i	$0.457486\pi$
$972$	1.00000	0.0320750
$973$	43.7727	1.40329
$974$	18.4344	0.590675
$975$	3.28226	0.105117
$976$	1.25120	0.0400499
$977$	−25.1706	−0.805279	−0.402639	−	0.915359i	$-0.631907\pi$
$977$	−25.1706	−0.805279	−0.402639	+	0.915359i	$0.631907\pi$
$978$	−14.6701	−0.469099
$979$	8.00043	0.255695
$980$	−30.8250	−0.984669
$981$	10.2737	0.328013
$982$	41.4725	1.32344
$983$	−15.6528	−0.499246	−0.249623	−	0.968343i	$-0.580307\pi$
$983$	−15.6528	−0.499246	−0.249623	+	0.968343i	$0.580307\pi$
$984$	−5.28684	−0.168538
$985$	9.10378	0.290071
$986$	−6.51865	−0.207596
$987$	−6.56545	−0.208981
$988$	−5.04926	−0.160638
$989$	41.7706	1.32823
$990$	12.4703	0.396333
$991$	5.15296	0.163689	0.0818447	−	0.996645i	$-0.473919\pi$
$991$	5.15296	0.163689	0.0818447	+	0.996645i	$0.473919\pi$
$992$	−6.77328	−0.215052
$993$	6.19973	0.196743
$994$	42.7404	1.35564
$995$	−4.69044	−0.148697
$996$	13.2313	0.419251
$997$	24.4432	0.774125	0.387062	−	0.922054i	$-0.373490\pi$
$997$	24.4432	0.774125	0.387062	+	0.922054i	$0.373490\pi$
$998$	8.90863	0.281998
$999$	4.01758	0.127111

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.o.1.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.o.1.1	✓	4	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.97371 q^{5} +1.00000 q^{6} +4.16724 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.97371 q^{5} +1.00000 q^{6} +4.16724 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.97371 q^{10} -4.19353 q^{11} +1.00000 q^{12} +0.854102 q^{13} +4.16724 q^{14} -2.97371 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -5.91177 q^{19} -2.97371 q^{20} +4.16724 q^{21} -4.19353 q^{22} -4.66057 q^{23} +1.00000 q^{24} +3.84294 q^{25} +0.854102 q^{26} +1.00000 q^{27} +4.16724 q^{28} -6.51865 q^{29} -2.97371 q^{30} -6.77328 q^{31} +1.00000 q^{32} -4.19353 q^{33} +1.00000 q^{34} -12.3921 q^{35} +1.00000 q^{36} +4.01758 q^{37} -5.91177 q^{38} +0.854102 q^{39} -2.97371 q^{40} -5.28684 q^{41} +4.16724 q^{42} -8.96255 q^{43} -4.19353 q^{44} -2.97371 q^{45} -4.66057 q^{46} -1.57549 q^{47} +1.00000 q^{48} +10.3659 q^{49} +3.84294 q^{50} +1.00000 q^{51} +0.854102 q^{52} -8.73583 q^{53} +1.00000 q^{54} +12.4703 q^{55} +4.16724 q^{56} -5.91177 q^{57} -6.51865 q^{58} +1.00000 q^{59} -2.97371 q^{60} +1.25120 q^{61} -6.77328 q^{62} +4.16724 q^{63} +1.00000 q^{64} -2.53985 q^{65} -4.19353 q^{66} +1.32512 q^{67} +1.00000 q^{68} -4.66057 q^{69} -12.3921 q^{70} +10.2563 q^{71} +1.00000 q^{72} -2.48218 q^{73} +4.01758 q^{74} +3.84294 q^{75} -5.91177 q^{76} -17.4754 q^{77} +0.854102 q^{78} +6.76079 q^{79} -2.97371 q^{80} +1.00000 q^{81} -5.28684 q^{82} +13.2313 q^{83} +4.16724 q^{84} -2.97371 q^{85} -8.96255 q^{86} -6.51865 q^{87} -4.19353 q^{88} -1.90780 q^{89} -2.97371 q^{90} +3.55924 q^{91} -4.66057 q^{92} -6.77328 q^{93} -1.57549 q^{94} +17.5799 q^{95} +1.00000 q^{96} -4.72273 q^{97} +10.3659 q^{98} -4.19353 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - q^{5} + 4 q^{6} - q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 - q^5 + 4 * q^6 - q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - q^{5} + 4 q^{6} - q^{7} + 4 q^{8} + 4 q^{9} - q^{10} - 10 q^{11} + 4 q^{12} - 10 q^{13} - q^{14} - q^{15} + 4 q^{16} + 4 q^{17} + 4 q^{18} - 14 q^{19} - q^{20} - q^{21} - 10 q^{22} - 12 q^{23} + 4 q^{24} - 3 q^{25} - 10 q^{26} + 4 q^{27} - q^{28} - 7 q^{29} - q^{30} - 13 q^{31} + 4 q^{32} - 10 q^{33} + 4 q^{34} - 18 q^{35} + 4 q^{36} - 11 q^{37} - 14 q^{38} - 10 q^{39} - q^{40} - 6 q^{41} - q^{42} - 20 q^{43} - 10 q^{44} - q^{45} - 12 q^{46} - 4 q^{47} + 4 q^{48} - q^{49} - 3 q^{50} + 4 q^{51} - 10 q^{52} - 5 q^{53} + 4 q^{54} + 4 q^{55} - q^{56} - 14 q^{57} - 7 q^{58} + 4 q^{59} - q^{60} + 2 q^{61} - 13 q^{62} - q^{63} + 4 q^{64} - 20 q^{65} - 10 q^{66} - 7 q^{67} + 4 q^{68} - 12 q^{69} - 18 q^{70} + 20 q^{71} + 4 q^{72} - 16 q^{73} - 11 q^{74} - 3 q^{75} - 14 q^{76} - 6 q^{77} - 10 q^{78} + 22 q^{79} - q^{80} + 4 q^{81} - 6 q^{82} + 7 q^{83} - q^{84} - q^{85} - 20 q^{86} - 7 q^{87} - 10 q^{88} + 3 q^{89} - q^{90} + 25 q^{91} - 12 q^{92} - 13 q^{93} - 4 q^{94} + 3 q^{95} + 4 q^{96} - 16 q^{97} - q^{98} - 10 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 - q^5 + 4 * q^6 - q^7 + 4 * q^8 + 4 * q^9 - q^10 - 10 * q^11 + 4 * q^12 - 10 * q^13 - q^14 - q^15 + 4 * q^16 + 4 * q^17 + 4 * q^18 - 14 * q^19 - q^20 - q^21 - 10 * q^22 - 12 * q^23 + 4 * q^24 - 3 * q^25 - 10 * q^26 + 4 * q^27 - q^28 - 7 * q^29 - q^30 - 13 * q^31 + 4 * q^32 - 10 * q^33 + 4 * q^34 - 18 * q^35 + 4 * q^36 - 11 * q^37 - 14 * q^38 - 10 * q^39 - q^40 - 6 * q^41 - q^42 - 20 * q^43 - 10 * q^44 - q^45 - 12 * q^46 - 4 * q^47 + 4 * q^48 - q^49 - 3 * q^50 + 4 * q^51 - 10 * q^52 - 5 * q^53 + 4 * q^54 + 4 * q^55 - q^56 - 14 * q^57 - 7 * q^58 + 4 * q^59 - q^60 + 2 * q^61 - 13 * q^62 - q^63 + 4 * q^64 - 20 * q^65 - 10 * q^66 - 7 * q^67 + 4 * q^68 - 12 * q^69 - 18 * q^70 + 20 * q^71 + 4 * q^72 - 16 * q^73 - 11 * q^74 - 3 * q^75 - 14 * q^76 - 6 * q^77 - 10 * q^78 + 22 * q^79 - q^80 + 4 * q^81 - 6 * q^82 + 7 * q^83 - q^84 - q^85 - 20 * q^86 - 7 * q^87 - 10 * q^88 + 3 * q^89 - q^90 + 25 * q^91 - 12 * q^92 - 13 * q^93 - 4 * q^94 + 3 * q^95 + 4 * q^96 - 16 * q^97 - q^98 - 10 * q^99

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