LMFDB - Embedded newform 4002.2.a.bf.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4002,2,Mod(1,4002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4002, 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("4002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4002 = 2 \cdot 3 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4002.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:	$31.9561308889$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.61157024.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 8x^{4} + 8x^{3} + 17x^{2} - 4x - 4 $ x^6 - 2x^5 - 8x^4 + 8x^3 + 17x^2 - 4*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.430873$ of defining polynomial
Character	$\chi$	$=$	4002.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.56155 q^{5} -1.00000 q^{6} +1.95260 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.56155 q^{5} -1.00000 q^{6} +1.95260 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.56155 q^{10} -1.08018 q^{11} +1.00000 q^{12} -0.218439 q^{13} -1.95260 q^{14} -1.56155 q^{15} +1.00000 q^{16} +7.65567 q^{17} -1.00000 q^{18} -7.93745 q^{19} -1.56155 q^{20} +1.95260 q^{21} +1.08018 q^{22} +1.00000 q^{23} -1.00000 q^{24} -2.56155 q^{25} +0.218439 q^{26} +1.00000 q^{27} +1.95260 q^{28} +1.00000 q^{29} +1.56155 q^{30} +3.20285 q^{31} -1.00000 q^{32} -1.08018 q^{33} -7.65567 q^{34} -3.04909 q^{35} +1.00000 q^{36} -0.314128 q^{37} +7.93745 q^{38} -0.218439 q^{39} +1.56155 q^{40} +11.4749 q^{41} -1.95260 q^{42} +1.34602 q^{43} -1.08018 q^{44} -1.56155 q^{45} -1.00000 q^{46} +6.23438 q^{47} +1.00000 q^{48} -3.18735 q^{49} +2.56155 q^{50} +7.65567 q^{51} -0.218439 q^{52} -8.75180 q^{53} -1.00000 q^{54} +1.68677 q^{55} -1.95260 q^{56} -7.93745 q^{57} -1.00000 q^{58} +12.7224 q^{59} -1.56155 q^{60} +5.49373 q^{61} -3.20285 q^{62} +1.95260 q^{63} +1.00000 q^{64} +0.341103 q^{65} +1.08018 q^{66} +3.05066 q^{67} +7.65567 q^{68} +1.00000 q^{69} +3.04909 q^{70} +5.51706 q^{71} -1.00000 q^{72} -9.40614 q^{73} +0.314128 q^{74} -2.56155 q^{75} -7.93745 q^{76} -2.10917 q^{77} +0.218439 q^{78} -12.4263 q^{79} -1.56155 q^{80} +1.00000 q^{81} -11.4749 q^{82} +4.40445 q^{83} +1.95260 q^{84} -11.9547 q^{85} -1.34602 q^{86} +1.00000 q^{87} +1.08018 q^{88} -1.55379 q^{89} +1.56155 q^{90} -0.426524 q^{91} +1.00000 q^{92} +3.20285 q^{93} -6.23438 q^{94} +12.3948 q^{95} -1.00000 q^{96} +10.1777 q^{97} +3.18735 q^{98} -1.08018 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 6 q^{3} + 6 q^{4} + 3 q^{5} - 6 q^{6} + 2 q^{7} - 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 + 6 * q^3 + 6 * q^4 + 3 * q^5 - 6 * q^6 + 2 * q^7 - 6 * q^8 + 6 * q^9	\( 6 q - 6 q^{2} + 6 q^{3} + 6 q^{4} + 3 q^{5} - 6 q^{6} + 2 q^{7} - 6 q^{8} + 6 q^{9} - 3 q^{10} + 7 q^{11} + 6 q^{12} + 3 q^{13} - 2 q^{14} + 3 q^{15} + 6 q^{16} + 8 q^{17} - 6 q^{18} - 4 q^{19} + 3 q^{20} + 2 q^{21} - 7 q^{22} + 6 q^{23} - 6 q^{24} - 3 q^{25} - 3 q^{26} + 6 q^{27} + 2 q^{28} + 6 q^{29} - 3 q^{30} + q^{31} - 6 q^{32} + 7 q^{33} - 8 q^{34} + 18 q^{35} + 6 q^{36} + 7 q^{37} + 4 q^{38} + 3 q^{39} - 3 q^{40} + 13 q^{41} - 2 q^{42} + 7 q^{44} + 3 q^{45} - 6 q^{46} + 22 q^{47} + 6 q^{48} + 8 q^{49} + 3 q^{50} + 8 q^{51} + 3 q^{52} + 10 q^{53} - 6 q^{54} - 5 q^{55} - 2 q^{56} - 4 q^{57} - 6 q^{58} + 17 q^{59} + 3 q^{60} + q^{61} - q^{62} + 2 q^{63} + 6 q^{64} - 7 q^{65} - 7 q^{66} + 3 q^{67} + 8 q^{68} + 6 q^{69} - 18 q^{70} + 11 q^{71} - 6 q^{72} - 7 q^{74} - 3 q^{75} - 4 q^{76} - 3 q^{78} + 2 q^{79} + 3 q^{80} + 6 q^{81} - 13 q^{82} + 16 q^{83} + 2 q^{84} + 4 q^{85} + 6 q^{87} - 7 q^{88} + 16 q^{89} - 3 q^{90} - 28 q^{91} + 6 q^{92} + q^{93} - 22 q^{94} + 32 q^{95} - 6 q^{96} + 2 q^{97} - 8 q^{98} + 7 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + 6 * q^3 + 6 * q^4 + 3 * q^5 - 6 * q^6 + 2 * q^7 - 6 * q^8 + 6 * q^9 - 3 * q^10 + 7 * q^11 + 6 * q^12 + 3 * q^13 - 2 * q^14 + 3 * q^15 + 6 * q^16 + 8 * q^17 - 6 * q^18 - 4 * q^19 + 3 * q^20 + 2 * q^21 - 7 * q^22 + 6 * q^23 - 6 * q^24 - 3 * q^25 - 3 * q^26 + 6 * q^27 + 2 * q^28 + 6 * q^29 - 3 * q^30 + q^31 - 6 * q^32 + 7 * q^33 - 8 * q^34 + 18 * q^35 + 6 * q^36 + 7 * q^37 + 4 * q^38 + 3 * q^39 - 3 * q^40 + 13 * q^41 - 2 * q^42 + 7 * q^44 + 3 * q^45 - 6 * q^46 + 22 * q^47 + 6 * q^48 + 8 * q^49 + 3 * q^50 + 8 * q^51 + 3 * q^52 + 10 * q^53 - 6 * q^54 - 5 * q^55 - 2 * q^56 - 4 * q^57 - 6 * q^58 + 17 * q^59 + 3 * q^60 + q^61 - q^62 + 2 * q^63 + 6 * q^64 - 7 * q^65 - 7 * q^66 + 3 * q^67 + 8 * q^68 + 6 * q^69 - 18 * q^70 + 11 * q^71 - 6 * q^72 - 7 * q^74 - 3 * q^75 - 4 * q^76 - 3 * q^78 + 2 * q^79 + 3 * q^80 + 6 * q^81 - 13 * q^82 + 16 * q^83 + 2 * q^84 + 4 * q^85 + 6 * q^87 - 7 * q^88 + 16 * q^89 - 3 * q^90 - 28 * q^91 + 6 * q^92 + q^93 - 22 * q^94 + 32 * q^95 - 6 * q^96 + 2 * q^97 - 8 * q^98 + 7 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−1.56155	−0.698348	−0.349174	−	0.937058i	$-0.613538\pi$
$5$	−1.56155	−0.698348	−0.349174	+	0.937058i	$0.613538\pi$
$6$	−1.00000	−0.408248
$7$	1.95260	0.738014	0.369007	−	0.929427i	$-0.379698\pi$
$7$	1.95260	0.738014	0.369007	+	0.929427i	$0.379698\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.56155	0.493806
$11$	−1.08018	−0.325688	−0.162844	−	0.986652i	$-0.552067\pi$
$11$	−1.08018	−0.325688	−0.162844	+	0.986652i	$0.552067\pi$
$12$	1.00000	0.288675
$13$	−0.218439	−0.0605840	−0.0302920	−	0.999541i	$-0.509644\pi$
$13$	−0.218439	−0.0605840	−0.0302920	+	0.999541i	$0.509644\pi$
$14$	−1.95260	−0.521855
$15$	−1.56155	−0.403191
$16$	1.00000	0.250000
$17$	7.65567	1.85677	0.928387	−	0.371616i	$-0.121196\pi$
$17$	7.65567	1.85677	0.928387	+	0.371616i	$0.121196\pi$
$18$	−1.00000	−0.235702
$19$	−7.93745	−1.82098	−0.910488	−	0.413535i	$-0.864294\pi$
$19$	−7.93745	−1.82098	−0.910488	+	0.413535i	$0.864294\pi$
$20$	−1.56155	−0.349174
$21$	1.95260	0.426093
$22$	1.08018	0.230296
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−1.00000	−0.204124
$25$	−2.56155	−0.512311
$26$	0.218439	0.0428393
$27$	1.00000	0.192450
$28$	1.95260	0.369007
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	1.56155	0.285099
$31$	3.20285	0.575249	0.287624	−	0.957743i	$-0.407135\pi$
$31$	3.20285	0.575249	0.287624	+	0.957743i	$0.407135\pi$
$32$	−1.00000	−0.176777
$33$	−1.08018	−0.188036
$34$	−7.65567	−1.31294
$35$	−3.04909	−0.515390
$36$	1.00000	0.166667
$37$	−0.314128	−0.0516423	−0.0258212	−	0.999667i	$-0.508220\pi$
$37$	−0.314128	−0.0516423	−0.0258212	+	0.999667i	$0.508220\pi$
$38$	7.93745	1.28763
$39$	−0.218439	−0.0349782
$40$	1.56155	0.246903
$41$	11.4749	1.79208	0.896042	−	0.443969i	$-0.146430\pi$
$41$	11.4749	1.79208	0.896042	+	0.443969i	$0.146430\pi$
$42$	−1.95260	−0.301293
$43$	1.34602	0.205266	0.102633	−	0.994719i	$-0.467273\pi$
$43$	1.34602	0.205266	0.102633	+	0.994719i	$0.467273\pi$
$44$	−1.08018	−0.162844
$45$	−1.56155	−0.232783
$46$	−1.00000	−0.147442
$47$	6.23438	0.909378	0.454689	−	0.890650i	$-0.349750\pi$
$47$	6.23438	0.909378	0.454689	+	0.890650i	$0.349750\pi$
$48$	1.00000	0.144338
$49$	−3.18735	−0.455335
$50$	2.56155	0.362258
$51$	7.65567	1.07201
$52$	−0.218439	−0.0302920
$53$	−8.75180	−1.20215	−0.601076	−	0.799192i	$-0.705261\pi$
$53$	−8.75180	−1.20215	−0.601076	+	0.799192i	$0.705261\pi$
$54$	−1.00000	−0.136083
$55$	1.68677	0.227443
$56$	−1.95260	−0.260927
$57$	−7.93745	−1.05134
$58$	−1.00000	−0.131306
$59$	12.7224	1.65631	0.828155	−	0.560499i	$-0.189391\pi$
$59$	12.7224	1.65631	0.828155	+	0.560499i	$0.189391\pi$
$60$	−1.56155	−0.201596
$61$	5.49373	0.703400	0.351700	−	0.936113i	$-0.385604\pi$
$61$	5.49373	0.703400	0.351700	+	0.936113i	$0.385604\pi$
$62$	−3.20285	−0.406762
$63$	1.95260	0.246005
$64$	1.00000	0.125000
$65$	0.341103	0.0423087
$66$	1.08018	0.132962
$67$	3.05066	0.372698	0.186349	−	0.982484i	$-0.440335\pi$
$67$	3.05066	0.372698	0.186349	+	0.982484i	$0.440335\pi$
$68$	7.65567	0.928387
$69$	1.00000	0.120386
$70$	3.04909	0.364436
$71$	5.51706	0.654755	0.327377	−	0.944894i	$-0.393835\pi$
$71$	5.51706	0.654755	0.327377	+	0.944894i	$0.393835\pi$
$72$	−1.00000	−0.117851
$73$	−9.40614	−1.10091	−0.550453	−	0.834866i	$-0.685545\pi$
$73$	−9.40614	−1.10091	−0.550453	+	0.834866i	$0.685545\pi$
$74$	0.314128	0.0365166
$75$	−2.56155	−0.295783
$76$	−7.93745	−0.910488
$77$	−2.10917	−0.240362
$78$	0.218439	0.0247333
$79$	−12.4263	−1.39806	−0.699032	−	0.715090i	$-0.746386\pi$
$79$	−12.4263	−1.39806	−0.699032	+	0.715090i	$0.746386\pi$
$80$	−1.56155	−0.174587
$81$	1.00000	0.111111
$82$	−11.4749	−1.26719
$83$	4.40445	0.483451	0.241725	−	0.970345i	$-0.422287\pi$
$83$	4.40445	0.483451	0.241725	+	0.970345i	$0.422287\pi$
$84$	1.95260	0.213046
$85$	−11.9547	−1.29667
$86$	−1.34602	−0.145145
$87$	1.00000	0.107211
$88$	1.08018	0.115148
$89$	−1.55379	−0.164701	−0.0823506	−	0.996603i	$-0.526243\pi$
$89$	−1.55379	−0.164701	−0.0823506	+	0.996603i	$0.526243\pi$
$90$	1.56155	0.164602
$91$	−0.426524	−0.0447118
$92$	1.00000	0.104257
$93$	3.20285	0.332120
$94$	−6.23438	−0.643028
$95$	12.3948	1.27167
$96$	−1.00000	−0.102062
$97$	10.1777	1.03338	0.516692	−	0.856171i	$-0.327163\pi$
$97$	10.1777	1.03338	0.516692	+	0.856171i	$0.327163\pi$
$98$	3.18735	0.321970
$99$	−1.08018	−0.108563
$100$	−2.56155	−0.256155
$101$	4.92800	0.490354	0.245177	−	0.969478i	$-0.421154\pi$
$101$	4.92800	0.490354	0.245177	+	0.969478i	$0.421154\pi$
$102$	−7.65567	−0.758024
$103$	10.6010	1.04454	0.522271	−	0.852779i	$-0.325085\pi$
$103$	10.6010	1.04454	0.522271	+	0.852779i	$0.325085\pi$
$104$	0.218439	0.0214197
$105$	−3.04909	−0.297561
$106$	8.75180	0.850050
$107$	3.47034	0.335490	0.167745	−	0.985830i	$-0.446351\pi$
$107$	3.47034	0.335490	0.167745	+	0.985830i	$0.446351\pi$
$108$	1.00000	0.0962250
$109$	7.41070	0.709816	0.354908	−	0.934901i	$-0.384512\pi$
$109$	7.41070	0.709816	0.354908	+	0.934901i	$0.384512\pi$
$110$	−1.68677	−0.160827
$111$	−0.314128	−0.0298157
$112$	1.95260	0.184504
$113$	5.06424	0.476404	0.238202	−	0.971216i	$-0.423442\pi$
$113$	5.06424	0.476404	0.238202	+	0.971216i	$0.423442\pi$
$114$	7.93745	0.743411
$115$	−1.56155	−0.145616
$116$	1.00000	0.0928477
$117$	−0.218439	−0.0201947
$118$	−12.7224	−1.17119
$119$	14.9485	1.37033
$120$	1.56155	0.142550
$121$	−9.83320	−0.893927
$122$	−5.49373	−0.497379
$123$	11.4749	1.03466
$124$	3.20285	0.287624
$125$	11.8078	1.05612
$126$	−1.95260	−0.173952
$127$	−14.8620	−1.31878	−0.659392	−	0.751799i	$-0.729186\pi$
$127$	−14.8620	−1.31878	−0.659392	+	0.751799i	$0.729186\pi$
$128$	−1.00000	−0.0883883
$129$	1.34602	0.118511
$130$	−0.341103	−0.0299167
$131$	6.71575	0.586758	0.293379	−	0.955996i	$-0.405220\pi$
$131$	6.71575	0.586758	0.293379	+	0.955996i	$0.405220\pi$
$132$	−1.08018	−0.0940180
$133$	−15.4987	−1.34391
$134$	−3.05066	−0.263537
$135$	−1.56155	−0.134397
$136$	−7.65567	−0.656468
$137$	−11.3274	−0.967763	−0.483881	−	0.875134i	$-0.660773\pi$
$137$	−11.3274	−0.967763	−0.483881	+	0.875134i	$0.660773\pi$
$138$	−1.00000	−0.0851257
$139$	10.8315	0.918712	0.459356	−	0.888252i	$-0.348080\pi$
$139$	10.8315	0.918712	0.459356	+	0.888252i	$0.348080\pi$
$140$	−3.04909	−0.257695
$141$	6.23438	0.525030
$142$	−5.51706	−0.462982
$143$	0.235954	0.0197315
$144$	1.00000	0.0833333
$145$	−1.56155	−0.129680
$146$	9.40614	0.778458
$147$	−3.18735	−0.262888
$148$	−0.314128	−0.0258212
$149$	−8.53591	−0.699289	−0.349645	−	0.936882i	$-0.613698\pi$
$149$	−8.53591	−0.699289	−0.349645	+	0.936882i	$0.613698\pi$
$150$	2.56155	0.209150
$151$	20.9096	1.70160	0.850801	−	0.525489i	$-0.176118\pi$
$151$	20.9096	1.70160	0.850801	+	0.525489i	$0.176118\pi$
$152$	7.93745	0.643813
$153$	7.65567	0.618924
$154$	2.10917	0.169962
$155$	−5.00142	−0.401724
$156$	−0.218439	−0.0174891
$157$	−12.3989	−0.989541	−0.494770	−	0.869024i	$-0.664748\pi$
$157$	−12.3989	−0.989541	−0.494770	+	0.869024i	$0.664748\pi$
$158$	12.4263	0.988581
$159$	−8.75180	−0.694063
$160$	1.56155	0.123452
$161$	1.95260	0.153887
$162$	−1.00000	−0.0785674
$163$	−8.25813	−0.646827	−0.323414	−	0.946258i	$-0.604830\pi$
$163$	−8.25813	−0.646827	−0.323414	+	0.946258i	$0.604830\pi$
$164$	11.4749	0.896042
$165$	1.68677	0.131315
$166$	−4.40445	−0.341851
$167$	−6.64361	−0.514098	−0.257049	−	0.966398i	$-0.582750\pi$
$167$	−6.64361	−0.514098	−0.257049	+	0.966398i	$0.582750\pi$
$168$	−1.95260	−0.150647
$169$	−12.9523	−0.996330
$170$	11.9547	0.916886
$171$	−7.93745	−0.606992
$172$	1.34602	0.102633
$173$	16.6386	1.26501	0.632505	−	0.774557i	$-0.282027\pi$
$173$	16.6386	1.26501	0.632505	+	0.774557i	$0.282027\pi$
$174$	−1.00000	−0.0758098
$175$	−5.00169	−0.378092
$176$	−1.08018	−0.0814220
$177$	12.7224	0.956271
$178$	1.55379	0.116461
$179$	−3.99928	−0.298920	−0.149460	−	0.988768i	$-0.547754\pi$
$179$	−3.99928	−0.298920	−0.149460	+	0.988768i	$0.547754\pi$
$180$	−1.56155	−0.116391
$181$	22.8533	1.69867	0.849335	−	0.527854i	$-0.177003\pi$
$181$	22.8533	1.69867	0.849335	+	0.527854i	$0.177003\pi$
$182$	0.426524	0.0316160
$183$	5.49373	0.406108
$184$	−1.00000	−0.0737210
$185$	0.490527	0.0360643
$186$	−3.20285	−0.234844
$187$	−8.26954	−0.604729
$188$	6.23438	0.454689
$189$	1.95260	0.142031
$190$	−12.3948	−0.899210
$191$	9.55865	0.691639	0.345820	−	0.938301i	$-0.387601\pi$
$191$	9.55865	0.691639	0.345820	+	0.938301i	$0.387601\pi$
$192$	1.00000	0.0721688
$193$	24.3723	1.75435	0.877177	−	0.480167i	$-0.159424\pi$
$193$	24.3723	1.75435	0.877177	+	0.480167i	$0.159424\pi$
$194$	−10.1777	−0.730713
$195$	0.341103	0.0244269
$196$	−3.18735	−0.227668
$197$	14.8663	1.05918	0.529589	−	0.848254i	$-0.322346\pi$
$197$	14.8663	1.05918	0.529589	+	0.848254i	$0.322346\pi$
$198$	1.08018	0.0767654
$199$	20.6399	1.46313	0.731563	−	0.681774i	$-0.238791\pi$
$199$	20.6399	1.46313	0.731563	+	0.681774i	$0.238791\pi$
$200$	2.56155	0.181129
$201$	3.05066	0.215177
$202$	−4.92800	−0.346733
$203$	1.95260	0.137046
$204$	7.65567	0.536004
$205$	−17.9187	−1.25150
$206$	−10.6010	−0.738603
$207$	1.00000	0.0695048
$208$	−0.218439	−0.0151460
$209$	8.57392	0.593070
$210$	3.04909	0.210407
$211$	9.41556	0.648194	0.324097	−	0.946024i	$-0.394940\pi$
$211$	9.41556	0.648194	0.324097	+	0.946024i	$0.394940\pi$
$212$	−8.75180	−0.601076
$213$	5.51706	0.378023
$214$	−3.47034	−0.237228
$215$	−2.10188	−0.143347
$216$	−1.00000	−0.0680414
$217$	6.25389	0.424542
$218$	−7.41070	−0.501916
$219$	−9.40614	−0.635608
$220$	1.68677	0.113722
$221$	−1.67229	−0.112491
$222$	0.314128	0.0210829
$223$	29.7997	1.99554	0.997769	−	0.0667571i	$-0.0212652\pi$
$223$	29.7997	1.99554	0.997769	+	0.0667571i	$0.0212652\pi$
$224$	−1.95260	−0.130464
$225$	−2.56155	−0.170770
$226$	−5.06424	−0.336868
$227$	−23.3062	−1.54689	−0.773443	−	0.633866i	$-0.781467\pi$
$227$	−23.3062	−1.54689	−0.773443	+	0.633866i	$0.781467\pi$
$228$	−7.93745	−0.525671
$229$	−21.4977	−1.42061	−0.710304	−	0.703895i	$-0.751443\pi$
$229$	−21.4977	−1.42061	−0.710304	+	0.703895i	$0.751443\pi$
$230$	1.56155	0.102966
$231$	−2.10917	−0.138773
$232$	−1.00000	−0.0656532
$233$	5.22300	0.342170	0.171085	−	0.985256i	$-0.445273\pi$
$233$	5.22300	0.342170	0.171085	+	0.985256i	$0.445273\pi$
$234$	0.218439	0.0142798
$235$	−9.73532	−0.635062
$236$	12.7224	0.828155
$237$	−12.4263	−0.807173
$238$	−14.9485	−0.968966
$239$	−19.1291	−1.23736	−0.618680	−	0.785643i	$-0.712332\pi$
$239$	−19.1291	−1.23736	−0.618680	+	0.785643i	$0.712332\pi$
$240$	−1.56155	−0.100798
$241$	22.2742	1.43481	0.717404	−	0.696658i	$-0.245330\pi$
$241$	22.2742	1.43481	0.717404	+	0.696658i	$0.245330\pi$
$242$	9.83320	0.632102
$243$	1.00000	0.0641500
$244$	5.49373	0.351700
$245$	4.97721	0.317982
$246$	−11.4749	−0.731615
$247$	1.73385	0.110322
$248$	−3.20285	−0.203381
$249$	4.40445	0.279120
$250$	−11.8078	−0.746789
$251$	1.71943	0.108529	0.0542647	−	0.998527i	$-0.482719\pi$
$251$	1.71943	0.108529	0.0542647	+	0.998527i	$0.482719\pi$
$252$	1.95260	0.123002
$253$	−1.08018	−0.0679106
$254$	14.8620	0.932522
$255$	−11.9547	−0.748635
$256$	1.00000	0.0625000
$257$	−7.47689	−0.466395	−0.233198	−	0.972429i	$-0.574919\pi$
$257$	−7.47689	−0.466395	−0.233198	+	0.972429i	$0.574919\pi$
$258$	−1.34602	−0.0837996
$259$	−0.613367	−0.0381128
$260$	0.341103	0.0211543
$261$	1.00000	0.0618984
$262$	−6.71575	−0.414901
$263$	7.33253	0.452143	0.226072	−	0.974111i	$-0.427412\pi$
$263$	7.33253	0.452143	0.226072	+	0.974111i	$0.427412\pi$
$264$	1.08018	0.0664808
$265$	13.6664	0.839520
$266$	15.4987	0.950286
$267$	−1.55379	−0.0950903
$268$	3.05066	0.186349
$269$	−1.94389	−0.118521	−0.0592604	−	0.998243i	$-0.518874\pi$
$269$	−1.94389	−0.118521	−0.0592604	+	0.998243i	$0.518874\pi$
$270$	1.56155	0.0950331
$271$	21.8992	1.33028	0.665141	−	0.746718i	$-0.268371\pi$
$271$	21.8992	1.33028	0.665141	+	0.746718i	$0.268371\pi$
$272$	7.65567	0.464193
$273$	−0.426524	−0.0258144
$274$	11.3274	0.684312
$275$	2.76695	0.166853
$276$	1.00000	0.0601929
$277$	−16.9916	−1.02093	−0.510463	−	0.859900i	$-0.670526\pi$
$277$	−16.9916	−1.02093	−0.510463	+	0.859900i	$0.670526\pi$
$278$	−10.8315	−0.649627
$279$	3.20285	0.191750
$280$	3.04909	0.182218
$281$	1.32486	0.0790345	0.0395173	−	0.999219i	$-0.487418\pi$
$281$	1.32486	0.0790345	0.0395173	+	0.999219i	$0.487418\pi$
$282$	−6.23438	−0.371252
$283$	−33.2575	−1.97696	−0.988478	−	0.151365i	$-0.951633\pi$
$283$	−33.2575	−1.97696	−0.988478	+	0.151365i	$0.951633\pi$
$284$	5.51706	0.327377
$285$	12.3948	0.734202
$286$	−0.235954	−0.0139523
$287$	22.4060	1.32258
$288$	−1.00000	−0.0589256
$289$	41.6093	2.44761
$290$	1.56155	0.0916975
$291$	10.1777	0.596625
$292$	−9.40614	−0.550453
$293$	30.6145	1.78852	0.894260	−	0.447548i	$-0.147703\pi$
$293$	30.6145	1.78852	0.894260	+	0.447548i	$0.147703\pi$
$294$	3.18735	0.185890
$295$	−19.8666	−1.15668
$296$	0.314128	0.0182583
$297$	−1.08018	−0.0626787
$298$	8.53591	0.494472
$299$	−0.218439	−0.0126326
$300$	−2.56155	−0.147891
$301$	2.62824	0.151489
$302$	−20.9096	−1.20321
$303$	4.92800	0.283106
$304$	−7.93745	−0.455244
$305$	−8.57875	−0.491218
$306$	−7.65567	−0.437646
$307$	27.0042	1.54121	0.770607	−	0.637311i	$-0.219953\pi$
$307$	27.0042	1.54121	0.770607	+	0.637311i	$0.219953\pi$
$308$	−2.10917	−0.120181
$309$	10.6010	0.603067
$310$	5.00142	0.284061
$311$	11.6447	0.660313	0.330156	−	0.943926i	$-0.392899\pi$
$311$	11.6447	0.660313	0.330156	+	0.943926i	$0.392899\pi$
$312$	0.218439	0.0123666
$313$	−13.7637	−0.777973	−0.388986	−	0.921243i	$-0.627175\pi$
$313$	−13.7637	−0.777973	−0.388986	+	0.921243i	$0.627175\pi$
$314$	12.3989	0.699711
$315$	−3.04909	−0.171797
$316$	−12.4263	−0.699032
$317$	−14.3757	−0.807418	−0.403709	−	0.914887i	$-0.632279\pi$
$317$	−14.3757	−0.807418	−0.403709	+	0.914887i	$0.632279\pi$
$318$	8.75180	0.490777
$319$	−1.08018	−0.0604787
$320$	−1.56155	−0.0872935
$321$	3.47034	0.193696
$322$	−1.95260	−0.108814
$323$	−60.7665	−3.38114
$324$	1.00000	0.0555556
$325$	0.559542	0.0310378
$326$	8.25813	0.457376
$327$	7.41070	0.409813
$328$	−11.4749	−0.633597
$329$	12.1733	0.671134
$330$	−1.68677	−0.0928534
$331$	3.42896	0.188472	0.0942362	−	0.995550i	$-0.469959\pi$
$331$	3.42896	0.188472	0.0942362	+	0.995550i	$0.469959\pi$
$332$	4.40445	0.241725
$333$	−0.314128	−0.0172141
$334$	6.64361	0.363522
$335$	−4.76377	−0.260272
$336$	1.95260	0.106523
$337$	22.6181	1.23209	0.616043	−	0.787713i	$-0.288735\pi$
$337$	22.6181	1.23209	0.616043	+	0.787713i	$0.288735\pi$
$338$	12.9523	0.704511
$339$	5.06424	0.275052
$340$	−11.9547	−0.648337
$341$	−3.45967	−0.187352
$342$	7.93745	0.429208
$343$	−19.8918	−1.07406
$344$	−1.34602	−0.0725726
$345$	−1.56155	−0.0840712
$346$	−16.6386	−0.894497
$347$	−24.2133	−1.29984	−0.649919	−	0.760004i	$-0.725197\pi$
$347$	−24.2133	−1.29984	−0.649919	+	0.760004i	$0.725197\pi$
$348$	1.00000	0.0536056
$349$	−28.4940	−1.52525	−0.762625	−	0.646840i	$-0.776090\pi$
$349$	−28.4940	−1.52525	−0.762625	+	0.646840i	$0.776090\pi$
$350$	5.00169	0.267352
$351$	−0.218439	−0.0116594
$352$	1.08018	0.0575740
$353$	18.5564	0.987657	0.493829	−	0.869559i	$-0.335597\pi$
$353$	18.5564	0.987657	0.493829	+	0.869559i	$0.335597\pi$
$354$	−12.7224	−0.676186
$355$	−8.61518	−0.457246
$356$	−1.55379	−0.0823506
$357$	14.9485	0.791158
$358$	3.99928	0.211369
$359$	−19.7032	−1.03989	−0.519947	−	0.854198i	$-0.674048\pi$
$359$	−19.7032	−1.03989	−0.519947	+	0.854198i	$0.674048\pi$
$360$	1.56155	0.0823011
$361$	44.0032	2.31596
$362$	−22.8533	−1.20114
$363$	−9.83320	−0.516109
$364$	−0.426524	−0.0223559
$365$	14.6882	0.768815
$366$	−5.49373	−0.287162
$367$	−19.1560	−0.999936	−0.499968	−	0.866044i	$-0.666655\pi$
$367$	−19.1560	−0.999936	−0.499968	+	0.866044i	$0.666655\pi$
$368$	1.00000	0.0521286
$369$	11.4749	0.597361
$370$	−0.490527	−0.0255013
$371$	−17.0888	−0.887206
$372$	3.20285	0.166060
$373$	−14.4799	−0.749739	−0.374869	−	0.927078i	$-0.622312\pi$
$373$	−14.4799	−0.749739	−0.374869	+	0.927078i	$0.622312\pi$
$374$	8.26954	0.427608
$375$	11.8078	0.609750
$376$	−6.23438	−0.321514
$377$	−0.218439	−0.0112502
$378$	−1.95260	−0.100431
$379$	20.8625	1.07164	0.535818	−	0.844333i	$-0.320003\pi$
$379$	20.8625	1.07164	0.535818	+	0.844333i	$0.320003\pi$
$380$	12.3948	0.635837
$381$	−14.8620	−0.761401
$382$	−9.55865	−0.489063
$383$	−8.98050	−0.458882	−0.229441	−	0.973323i	$-0.573690\pi$
$383$	−8.98050	−0.458882	−0.229441	+	0.973323i	$0.573690\pi$
$384$	−1.00000	−0.0510310
$385$	3.29358	0.167856
$386$	−24.3723	−1.24052
$387$	1.34602	0.0684221
$388$	10.1777	0.516692
$389$	5.48947	0.278327	0.139164	−	0.990269i	$-0.455559\pi$
$389$	5.48947	0.278327	0.139164	+	0.990269i	$0.455559\pi$
$390$	−0.341103	−0.0172724
$391$	7.65567	0.387164
$392$	3.18735	0.160985
$393$	6.71575	0.338765
$394$	−14.8663	−0.748952
$395$	19.4043	0.976335
$396$	−1.08018	−0.0542813
$397$	−0.752955	−0.0377897	−0.0188949	−	0.999821i	$-0.506015\pi$
$397$	−0.752955	−0.0377897	−0.0188949	+	0.999821i	$0.506015\pi$
$398$	−20.6399	−1.03459
$399$	−15.4987	−0.775905
$400$	−2.56155	−0.128078
$401$	−13.2125	−0.659798	−0.329899	−	0.944016i	$-0.607015\pi$
$401$	−13.2125	−0.659798	−0.329899	+	0.944016i	$0.607015\pi$
$402$	−3.05066	−0.152153
$403$	−0.699626	−0.0348508
$404$	4.92800	0.245177
$405$	−1.56155	−0.0775942
$406$	−1.95260	−0.0969060
$407$	0.339316	0.0168193
$408$	−7.65567	−0.379012
$409$	−14.3034	−0.707257	−0.353628	−	0.935386i	$-0.615052\pi$
$409$	−14.3034	−0.707257	−0.353628	+	0.935386i	$0.615052\pi$
$410$	17.9187	0.884943
$411$	−11.3274	−0.558738
$412$	10.6010	0.522271
$413$	24.8417	1.22238
$414$	−1.00000	−0.0491473
$415$	−6.87778	−0.337617
$416$	0.218439	0.0107098
$417$	10.8315	0.530418
$418$	−8.57392	−0.419364
$419$	23.1017	1.12859	0.564296	−	0.825572i	$-0.309148\pi$
$419$	23.1017	1.12859	0.564296	+	0.825572i	$0.309148\pi$
$420$	−3.04909	−0.148780
$421$	17.8515	0.870027	0.435013	−	0.900424i	$-0.356744\pi$
$421$	17.8515	0.870027	0.435013	+	0.900424i	$0.356744\pi$
$422$	−9.41556	−0.458342
$423$	6.23438	0.303126
$424$	8.75180	0.425025
$425$	−19.6104	−0.951245
$426$	−5.51706	−0.267303
$427$	10.7271	0.519119
$428$	3.47034	0.167745
$429$	0.235954	0.0113920
$430$	2.10188	0.101362
$431$	−3.79691	−0.182891	−0.0914455	−	0.995810i	$-0.529149\pi$
$431$	−3.79691	−0.182891	−0.0914455	+	0.995810i	$0.529149\pi$
$432$	1.00000	0.0481125
$433$	23.7716	1.14239	0.571196	−	0.820814i	$-0.306480\pi$
$433$	23.7716	1.14239	0.571196	+	0.820814i	$0.306480\pi$
$434$	−6.25389	−0.300196
$435$	−1.56155	−0.0748707
$436$	7.41070	0.354908
$437$	−7.93745	−0.379700
$438$	9.40614	0.449443
$439$	29.9716	1.43047	0.715234	−	0.698885i	$-0.246320\pi$
$439$	29.9716	1.43047	0.715234	+	0.698885i	$0.246320\pi$
$440$	−1.68677	−0.0804134
$441$	−3.18735	−0.151778
$442$	1.67229	0.0795429
$443$	25.1374	1.19432	0.597158	−	0.802124i	$-0.296297\pi$
$443$	25.1374	1.19432	0.597158	+	0.802124i	$0.296297\pi$
$444$	−0.314128	−0.0149079
$445$	2.42632	0.115019
$446$	−29.7997	−1.41106
$447$	−8.53591	−0.403735
$448$	1.95260	0.0922518
$449$	−28.5737	−1.34848	−0.674239	−	0.738513i	$-0.735528\pi$
$449$	−28.5737	−1.34848	−0.674239	+	0.738513i	$0.735528\pi$
$450$	2.56155	0.120753
$451$	−12.3951	−0.583660
$452$	5.06424	0.238202
$453$	20.9096	0.982420
$454$	23.3062	1.09381
$455$	0.666039	0.0312244
$456$	7.93745	0.371705
$457$	17.9657	0.840401	0.420201	−	0.907431i	$-0.361960\pi$
$457$	17.9657	0.840401	0.420201	+	0.907431i	$0.361960\pi$
$458$	21.4977	1.00452
$459$	7.65567	0.357336
$460$	−1.56155	−0.0728078
$461$	8.44900	0.393509	0.196755	−	0.980453i	$-0.436960\pi$
$461$	8.44900	0.393509	0.196755	+	0.980453i	$0.436960\pi$
$462$	2.10917	0.0981275
$463$	−15.7530	−0.732102	−0.366051	−	0.930595i	$-0.619290\pi$
$463$	−15.7530	−0.732102	−0.366051	+	0.930595i	$0.619290\pi$
$464$	1.00000	0.0464238
$465$	−5.00142	−0.231935
$466$	−5.22300	−0.241951
$467$	5.33447	0.246850	0.123425	−	0.992354i	$-0.460612\pi$
$467$	5.33447	0.246850	0.123425	+	0.992354i	$0.460612\pi$
$468$	−0.218439	−0.0100973
$469$	5.95673	0.275056
$470$	9.73532	0.449057
$471$	−12.3989	−0.571312
$472$	−12.7224	−0.585594
$473$	−1.45395	−0.0668528
$474$	12.4263	0.570757
$475$	20.3322	0.932906
$476$	14.9485	0.685163
$477$	−8.75180	−0.400718
$478$	19.1291	0.874946
$479$	21.1083	0.964464	0.482232	−	0.876044i	$-0.339826\pi$
$479$	21.1083	0.964464	0.482232	+	0.876044i	$0.339826\pi$
$480$	1.56155	0.0712748
$481$	0.0686177	0.00312870
$482$	−22.2742	−1.01456
$483$	1.95260	0.0888465
$484$	−9.83320	−0.446964
$485$	−15.8929	−0.721661
$486$	−1.00000	−0.0453609
$487$	16.1217	0.730544	0.365272	−	0.930901i	$-0.380976\pi$
$487$	16.1217	0.730544	0.365272	+	0.930901i	$0.380976\pi$
$488$	−5.49373	−0.248690
$489$	−8.25813	−0.373446
$490$	−4.97721	−0.224847
$491$	−23.3137	−1.05213	−0.526067	−	0.850443i	$-0.676334\pi$
$491$	−23.3137	−1.05213	−0.526067	+	0.850443i	$0.676334\pi$
$492$	11.4749	0.517330
$493$	7.65567	0.344794
$494$	−1.73385	−0.0780094
$495$	1.68677	0.0758145
$496$	3.20285	0.143812
$497$	10.7726	0.483218
$498$	−4.40445	−0.197368
$499$	3.52795	0.157933	0.0789665	−	0.996877i	$-0.474838\pi$
$499$	3.52795	0.157933	0.0789665	+	0.996877i	$0.474838\pi$
$500$	11.8078	0.528059
$501$	−6.64361	−0.296815
$502$	−1.71943	−0.0767419
$503$	13.7589	0.613477	0.306738	−	0.951794i	$-0.400762\pi$
$503$	13.7589	0.613477	0.306738	+	0.951794i	$0.400762\pi$
$504$	−1.95260	−0.0869758
$505$	−7.69533	−0.342438
$506$	1.08018	0.0480201
$507$	−12.9523	−0.575231
$508$	−14.8620	−0.659392
$509$	−18.2597	−0.809347	−0.404673	−	0.914461i	$-0.632615\pi$
$509$	−18.2597	−0.809347	−0.404673	+	0.914461i	$0.632615\pi$
$510$	11.9547	0.529365
$511$	−18.3664	−0.812484
$512$	−1.00000	−0.0441942
$513$	−7.93745	−0.350447
$514$	7.47689	0.329791
$515$	−16.5539	−0.729454
$516$	1.34602	0.0592553
$517$	−6.73429	−0.296174
$518$	0.613367	0.0269498
$519$	16.6386	0.730353
$520$	−0.341103	−0.0149584
$521$	−11.6841	−0.511890	−0.255945	−	0.966691i	$-0.582387\pi$
$521$	−11.6841	−0.511890	−0.255945	+	0.966691i	$0.582387\pi$
$522$	−1.00000	−0.0437688
$523$	−30.3701	−1.32799	−0.663997	−	0.747736i	$-0.731141\pi$
$523$	−30.3701	−1.32799	−0.663997	+	0.747736i	$0.731141\pi$
$524$	6.71575	0.293379
$525$	−5.00169	−0.218292
$526$	−7.33253	−0.319713
$527$	24.5200	1.06811
$528$	−1.08018	−0.0470090
$529$	1.00000	0.0434783
$530$	−13.6664	−0.593631
$531$	12.7224	0.552104
$532$	−15.4987	−0.671953
$533$	−2.50657	−0.108572
$534$	1.55379	0.0672390
$535$	−5.41912	−0.234289
$536$	−3.05066	−0.131769
$537$	−3.99928	−0.172582
$538$	1.94389	0.0838069
$539$	3.44292	0.148297
$540$	−1.56155	−0.0671985
$541$	−24.1991	−1.04040	−0.520200	−	0.854044i	$-0.674143\pi$
$541$	−24.1991	−1.04040	−0.520200	+	0.854044i	$0.674143\pi$
$542$	−21.8992	−0.940652
$543$	22.8533	0.980728
$544$	−7.65567	−0.328234
$545$	−11.5722	−0.495699
$546$	0.426524	0.0182535
$547$	−16.3303	−0.698234	−0.349117	−	0.937079i	$-0.613518\pi$
$547$	−16.3303	−0.698234	−0.349117	+	0.937079i	$0.613518\pi$
$548$	−11.3274	−0.483881
$549$	5.49373	0.234467
$550$	−2.76695	−0.117983
$551$	−7.93745	−0.338147
$552$	−1.00000	−0.0425628
$553$	−24.2636	−1.03179
$554$	16.9916	0.721903
$555$	0.490527	0.0208217
$556$	10.8315	0.459356
$557$	16.2011	0.686464	0.343232	−	0.939251i	$-0.388478\pi$
$557$	16.2011	0.686464	0.343232	+	0.939251i	$0.388478\pi$
$558$	−3.20285	−0.135587
$559$	−0.294023	−0.0124358
$560$	−3.04909	−0.128848
$561$	−8.26954	−0.349140
$562$	−1.32486	−0.0558858
$563$	27.6059	1.16345	0.581724	−	0.813386i	$-0.302378\pi$
$563$	27.6059	1.16345	0.581724	+	0.813386i	$0.302378\pi$
$564$	6.23438	0.262515
$565$	−7.90808	−0.332695
$566$	33.2575	1.39792
$567$	1.95260	0.0820016
$568$	−5.51706	−0.231491
$569$	−8.83747	−0.370486	−0.185243	−	0.982693i	$-0.559307\pi$
$569$	−8.83747	−0.370486	−0.185243	+	0.982693i	$0.559307\pi$
$570$	−12.3948	−0.519159
$571$	−36.4500	−1.52539	−0.762693	−	0.646761i	$-0.776123\pi$
$571$	−36.4500	−1.52539	−0.762693	+	0.646761i	$0.776123\pi$
$572$	0.235954	0.00986573
$573$	9.55865	0.399318
$574$	−22.4060	−0.935208
$575$	−2.56155	−0.106824
$576$	1.00000	0.0416667
$577$	19.0695	0.793873	0.396936	−	0.917846i	$-0.370073\pi$
$577$	19.0695	0.793873	0.396936	+	0.917846i	$0.370073\pi$
$578$	−41.6093	−1.73072
$579$	24.3723	1.01288
$580$	−1.56155	−0.0648400
$581$	8.60013	0.356794
$582$	−10.1777	−0.421877
$583$	9.45356	0.391527
$584$	9.40614	0.389229
$585$	0.341103	0.0141029
$586$	−30.6145	−1.26467
$587$	41.3309	1.70591	0.852955	−	0.521984i	$-0.174808\pi$
$587$	41.3309	1.70591	0.852955	+	0.521984i	$0.174808\pi$
$588$	−3.18735	−0.131444
$589$	−25.4225	−1.04751
$590$	19.8666	0.817897
$591$	14.8663	0.611517
$592$	−0.314128	−0.0129106
$593$	19.7170	0.809682	0.404841	−	0.914387i	$-0.367327\pi$
$593$	19.7170	0.809682	0.404841	+	0.914387i	$0.367327\pi$
$594$	1.08018	0.0443205
$595$	−23.3428	−0.956963
$596$	−8.53591	−0.349645
$597$	20.6399	0.844736
$598$	0.218439	0.00893262
$599$	39.2709	1.60457	0.802283	−	0.596944i	$-0.203619\pi$
$599$	39.2709	1.60457	0.802283	+	0.596944i	$0.203619\pi$
$600$	2.56155	0.104575
$601$	−29.5200	−1.20415	−0.602073	−	0.798441i	$-0.705658\pi$
$601$	−29.5200	−1.20415	−0.602073	+	0.798441i	$0.705658\pi$
$602$	−2.62824	−0.107119
$603$	3.05066	0.124233
$604$	20.9096	0.850801
$605$	15.3551	0.624272
$606$	−4.92800	−0.200186
$607$	−5.41272	−0.219696	−0.109848	−	0.993948i	$-0.535036\pi$
$607$	−5.41272	−0.219696	−0.109848	+	0.993948i	$0.535036\pi$
$608$	7.93745	0.321906
$609$	1.95260	0.0791234
$610$	8.57875	0.347344
$611$	−1.36183	−0.0550937
$612$	7.65567	0.309462
$613$	36.3092	1.46651	0.733257	−	0.679952i	$-0.237999\pi$
$613$	36.3092	1.46651	0.733257	+	0.679952i	$0.237999\pi$
$614$	−27.0042	−1.08980
$615$	−17.9187	−0.722553
$616$	2.10917	0.0849809
$617$	40.4961	1.63031	0.815156	−	0.579242i	$-0.196651\pi$
$617$	40.4961	1.63031	0.815156	+	0.579242i	$0.196651\pi$
$618$	−10.6010	−0.426433
$619$	−39.7764	−1.59875	−0.799375	−	0.600833i	$-0.794836\pi$
$619$	−39.7764	−1.59875	−0.799375	+	0.600833i	$0.794836\pi$
$620$	−5.00142	−0.200862
$621$	1.00000	0.0401286
$622$	−11.6447	−0.466911
$623$	−3.03393	−0.121552
$624$	−0.218439	−0.00874454
$625$	−5.63068	−0.225227
$626$	13.7637	0.550110
$627$	8.57392	0.342409
$628$	−12.3989	−0.494770
$629$	−2.40486	−0.0958881
$630$	3.04909	0.121479
$631$	11.4739	0.456768	0.228384	−	0.973571i	$-0.426656\pi$
$631$	11.4739	0.456768	0.228384	+	0.973571i	$0.426656\pi$
$632$	12.4263	0.494290
$633$	9.41556	0.374235
$634$	14.3757	0.570931
$635$	23.2077	0.920970
$636$	−8.75180	−0.347032
$637$	0.696239	0.0275860
$638$	1.08018	0.0427649
$639$	5.51706	0.218252
$640$	1.56155	0.0617258
$641$	4.72976	0.186814	0.0934071	−	0.995628i	$-0.470224\pi$
$641$	4.72976	0.186814	0.0934071	+	0.995628i	$0.470224\pi$
$642$	−3.47034	−0.136963
$643$	−34.9453	−1.37811	−0.689054	−	0.724710i	$-0.741974\pi$
$643$	−34.9453	−1.37811	−0.689054	+	0.724710i	$0.741974\pi$
$644$	1.95260	0.0769433
$645$	−2.10188	−0.0827616
$646$	60.7665	2.39083
$647$	21.6088	0.849531	0.424766	−	0.905303i	$-0.360357\pi$
$647$	21.6088	0.849531	0.424766	+	0.905303i	$0.360357\pi$
$648$	−1.00000	−0.0392837
$649$	−13.7425	−0.539440
$650$	−0.559542	−0.0219470
$651$	6.25389	0.245109
$652$	−8.25813	−0.323414
$653$	−35.8402	−1.40253	−0.701267	−	0.712899i	$-0.747382\pi$
$653$	−35.8402	−1.40253	−0.701267	+	0.712899i	$0.747382\pi$
$654$	−7.41070	−0.289781
$655$	−10.4870	−0.409761
$656$	11.4749	0.448021
$657$	−9.40614	−0.366968
$658$	−12.1733	−0.474564
$659$	27.4818	1.07054	0.535269	−	0.844682i	$-0.320210\pi$
$659$	27.4818	1.07054	0.535269	+	0.844682i	$0.320210\pi$
$660$	1.68677	0.0656573
$661$	−15.7667	−0.613252	−0.306626	−	0.951830i	$-0.599200\pi$
$661$	−15.7667	−0.613252	−0.306626	+	0.951830i	$0.599200\pi$
$662$	−3.42896	−0.133270
$663$	−1.67229	−0.0649465
$664$	−4.40445	−0.170926
$665$	24.2020	0.938514
$666$	0.314128	0.0121722
$667$	1.00000	0.0387202
$668$	−6.64361	−0.257049
$669$	29.7997	1.15212
$670$	4.76377	0.184040
$671$	−5.93425	−0.229089
$672$	−1.95260	−0.0753233
$673$	−40.2484	−1.55146	−0.775732	−	0.631063i	$-0.782619\pi$
$673$	−40.2484	−1.55146	−0.775732	+	0.631063i	$0.782619\pi$
$674$	−22.6181	−0.871216
$675$	−2.56155	−0.0985942
$676$	−12.9523	−0.498165
$677$	−45.6225	−1.75342	−0.876708	−	0.481024i	$-0.840265\pi$
$677$	−45.6225	−1.75342	−0.876708	+	0.481024i	$0.840265\pi$
$678$	−5.06424	−0.194491
$679$	19.8729	0.762652
$680$	11.9547	0.458443
$681$	−23.3062	−0.893095
$682$	3.45967	0.132478
$683$	−38.0942	−1.45763	−0.728817	−	0.684709i	$-0.759929\pi$
$683$	−38.0942	−1.45763	−0.728817	+	0.684709i	$0.759929\pi$
$684$	−7.93745	−0.303496
$685$	17.6883	0.675835
$686$	19.8918	0.759474
$687$	−21.4977	−0.820189
$688$	1.34602	0.0513166
$689$	1.91173	0.0728312
$690$	1.56155	0.0594473
$691$	20.2247	0.769383	0.384691	−	0.923045i	$-0.374308\pi$
$691$	20.2247	0.769383	0.384691	+	0.923045i	$0.374308\pi$
$692$	16.6386	0.632505
$693$	−2.10917	−0.0801208
$694$	24.2133	0.919124
$695$	−16.9139	−0.641580
$696$	−1.00000	−0.0379049
$697$	87.8484	3.32749
$698$	28.4940	1.07852
$699$	5.22300	0.197552
$700$	−5.00169	−0.189046
$701$	31.0939	1.17440	0.587200	−	0.809442i	$-0.300230\pi$
$701$	31.0939	1.17440	0.587200	+	0.809442i	$0.300230\pi$
$702$	0.218439	0.00824443
$703$	2.49338	0.0940395
$704$	−1.08018	−0.0407110
$705$	−9.73532	−0.366653
$706$	−18.5564	−0.698379
$707$	9.62242	0.361888
$708$	12.7224	0.478136
$709$	−46.3054	−1.73903	−0.869517	−	0.493903i	$-0.835570\pi$
$709$	−46.3054	−1.73903	−0.869517	+	0.493903i	$0.835570\pi$
$710$	8.61518	0.323322
$711$	−12.4263	−0.466021
$712$	1.55379	0.0582307
$713$	3.20285	0.119948
$714$	−14.9485	−0.559433
$715$	−0.368455	−0.0137794
$716$	−3.99928	−0.149460
$717$	−19.1291	−0.714390
$718$	19.7032	0.735317
$719$	11.0579	0.412389	0.206194	−	0.978511i	$-0.433892\pi$
$719$	11.0579	0.412389	0.206194	+	0.978511i	$0.433892\pi$
$720$	−1.56155	−0.0581956
$721$	20.6994	0.770887
$722$	−44.0032	−1.63763
$723$	22.2742	0.828386
$724$	22.8533	0.849335
$725$	−2.56155	−0.0951337
$726$	9.83320	0.364944
$727$	−27.2847	−1.01193	−0.505967	−	0.862553i	$-0.668864\pi$
$727$	−27.2847	−1.01193	−0.505967	+	0.862553i	$0.668864\pi$
$728$	0.426524	0.0158080
$729$	1.00000	0.0370370
$730$	−14.6882	−0.543634
$731$	10.3047	0.381133
$732$	5.49373	0.203054
$733$	−12.1670	−0.449399	−0.224700	−	0.974428i	$-0.572140\pi$
$733$	−12.1670	−0.449399	−0.224700	+	0.974428i	$0.572140\pi$
$734$	19.1560	0.707061
$735$	4.97721	0.183587
$736$	−1.00000	−0.0368605
$737$	−3.29528	−0.121383
$738$	−11.4749	−0.422398
$739$	48.1604	1.77161	0.885805	−	0.464057i	$-0.153607\pi$
$739$	48.1604	1.77161	0.885805	+	0.464057i	$0.153607\pi$
$740$	0.490527	0.0180321
$741$	1.73385	0.0636944
$742$	17.0888	0.627349
$743$	28.5856	1.04870	0.524352	−	0.851502i	$-0.324308\pi$
$743$	28.5856	1.04870	0.524352	+	0.851502i	$0.324308\pi$
$744$	−3.20285	−0.117422
$745$	13.3293	0.488347
$746$	14.4799	0.530145
$747$	4.40445	0.161150
$748$	−8.26954	−0.302364
$749$	6.77619	0.247597
$750$	−11.8078	−0.431159
$751$	−9.56676	−0.349096	−0.174548	−	0.984649i	$-0.555846\pi$
$751$	−9.56676	−0.349096	−0.174548	+	0.984649i	$0.555846\pi$
$752$	6.23438	0.227345
$753$	1.71943	0.0626595
$754$	0.218439	0.00795506
$755$	−32.6515	−1.18831
$756$	1.95260	0.0710155
$757$	9.20488	0.334557	0.167279	−	0.985910i	$-0.446502\pi$
$757$	9.20488	0.334557	0.167279	+	0.985910i	$0.446502\pi$
$758$	−20.8625	−0.757761
$759$	−1.08018	−0.0392082
$760$	−12.3948	−0.449605
$761$	−18.2963	−0.663242	−0.331621	−	0.943413i	$-0.607595\pi$
$761$	−18.2963	−0.663242	−0.331621	+	0.943413i	$0.607595\pi$
$762$	14.8620	0.538392
$763$	14.4702	0.523855
$764$	9.55865	0.345820
$765$	−11.9547	−0.432224
$766$	8.98050	0.324479
$767$	−2.77905	−0.100346
$768$	1.00000	0.0360844
$769$	−10.3329	−0.372615	−0.186308	−	0.982491i	$-0.559652\pi$
$769$	−10.3329	−0.372615	−0.186308	+	0.982491i	$0.559652\pi$
$770$	−3.29358	−0.118692
$771$	−7.47689	−0.269274
$772$	24.3723	0.877177
$773$	−10.4851	−0.377124	−0.188562	−	0.982061i	$-0.560383\pi$
$773$	−10.4851	−0.377124	−0.188562	+	0.982061i	$0.560383\pi$
$774$	−1.34602	−0.0483817
$775$	−8.20427	−0.294706
$776$	−10.1777	−0.365356
$777$	−0.613367	−0.0220044
$778$	−5.48947	−0.196807
$779$	−91.0818	−3.26334
$780$	0.341103	0.0122135
$781$	−5.95945	−0.213246
$782$	−7.65567	−0.273766
$783$	1.00000	0.0357371
$784$	−3.18735	−0.113834
$785$	19.3616	0.691044
$786$	−6.71575	−0.239543
$787$	−18.6908	−0.666254	−0.333127	−	0.942882i	$-0.608104\pi$
$787$	−18.6908	−0.666254	−0.333127	+	0.942882i	$0.608104\pi$
$788$	14.8663	0.529589
$789$	7.33253	0.261045
$790$	−19.4043	−0.690373
$791$	9.88844	0.351593
$792$	1.08018	0.0383827
$793$	−1.20004	−0.0426148
$794$	0.752955	0.0267214
$795$	13.6664	0.484697
$796$	20.6399	0.731563
$797$	−7.40081	−0.262150	−0.131075	−	0.991372i	$-0.541843\pi$
$797$	−7.40081	−0.262150	−0.131075	+	0.991372i	$0.541843\pi$
$798$	15.4987	0.548648
$799$	47.7284	1.68851
$800$	2.56155	0.0905646
$801$	−1.55379	−0.0549004
$802$	13.2125	0.466548
$803$	10.1604	0.358552
$804$	3.05066	0.107589
$805$	−3.04909	−0.107466
$806$	0.699626	0.0246433
$807$	−1.94389	−0.0684281
$808$	−4.92800	−0.173366
$809$	−9.23840	−0.324805	−0.162402	−	0.986725i	$-0.551924\pi$
$809$	−9.23840	−0.324805	−0.162402	+	0.986725i	$0.551924\pi$
$810$	1.56155	0.0548674
$811$	−21.9104	−0.769380	−0.384690	−	0.923046i	$-0.625692\pi$
$811$	−21.9104	−0.769380	−0.384690	+	0.923046i	$0.625692\pi$
$812$	1.95260	0.0685229
$813$	21.8992	0.768039
$814$	−0.339316	−0.0118930
$815$	12.8955	0.451710
$816$	7.65567	0.268002
$817$	−10.6840	−0.373785
$818$	14.3034	0.500106
$819$	−0.426524	−0.0149039
$820$	−17.9187	−0.625749
$821$	3.13743	0.109497	0.0547485	−	0.998500i	$-0.482564\pi$
$821$	3.13743	0.109497	0.0547485	+	0.998500i	$0.482564\pi$
$822$	11.3274	0.395088
$823$	−48.2908	−1.68331	−0.841655	−	0.540015i	$-0.818419\pi$
$823$	−48.2908	−1.68331	−0.841655	+	0.540015i	$0.818419\pi$
$824$	−10.6010	−0.369302
$825$	2.76695	0.0963328
$826$	−24.8417	−0.864354
$827$	−20.2922	−0.705629	−0.352814	−	0.935693i	$-0.614775\pi$
$827$	−20.2922	−0.705629	−0.352814	+	0.935693i	$0.614775\pi$
$828$	1.00000	0.0347524
$829$	−20.9619	−0.728037	−0.364018	−	0.931392i	$-0.618595\pi$
$829$	−20.9619	−0.728037	−0.364018	+	0.931392i	$0.618595\pi$
$830$	6.87778	0.238731
$831$	−16.9916	−0.589431
$832$	−0.218439	−0.00757299
$833$	−24.4013	−0.845454
$834$	−10.8315	−0.375062
$835$	10.3743	0.359019
$836$	8.57392	0.296535
$837$	3.20285	0.110707
$838$	−23.1017	−0.798035
$839$	−11.8894	−0.410468	−0.205234	−	0.978713i	$-0.565796\pi$
$839$	−11.8894	−0.410468	−0.205234	+	0.978713i	$0.565796\pi$
$840$	3.04909	0.105204
$841$	1.00000	0.0344828
$842$	−17.8515	−0.615202
$843$	1.32486	0.0456306
$844$	9.41556	0.324097
$845$	20.2257	0.695784
$846$	−6.23438	−0.214343
$847$	−19.2003	−0.659731
$848$	−8.75180	−0.300538
$849$	−33.2575	−1.14140
$850$	19.6104	0.672631
$851$	−0.314128	−0.0107682
$852$	5.51706	0.189011
$853$	17.2828	0.591752	0.295876	−	0.955226i	$-0.404389\pi$
$853$	17.2828	0.591752	0.295876	+	0.955226i	$0.404389\pi$
$854$	−10.7271	−0.367073
$855$	12.3948	0.423892
$856$	−3.47034	−0.118614
$857$	−44.4094	−1.51700	−0.758498	−	0.651675i	$-0.774067\pi$
$857$	−44.4094	−1.51700	−0.758498	+	0.651675i	$0.774067\pi$
$858$	−0.235954	−0.00805534
$859$	−32.8730	−1.12161	−0.560807	−	0.827947i	$-0.689509\pi$
$859$	−32.8730	−1.12161	−0.560807	+	0.827947i	$0.689509\pi$
$860$	−2.10188	−0.0716736
$861$	22.4060	0.763594
$862$	3.79691	0.129323
$863$	46.4125	1.57990	0.789951	−	0.613170i	$-0.210106\pi$
$863$	46.4125	1.57990	0.789951	+	0.613170i	$0.210106\pi$
$864$	−1.00000	−0.0340207
$865$	−25.9820	−0.883416
$866$	−23.7716	−0.807793
$867$	41.6093	1.41313
$868$	6.25389	0.212271
$869$	13.4227	0.455333
$870$	1.56155	0.0529416
$871$	−0.666382	−0.0225795
$872$	−7.41070	−0.250958
$873$	10.1777	0.344461
$874$	7.93745	0.268488
$875$	23.0559	0.779430
$876$	−9.40614	−0.317804
$877$	−18.8424	−0.636261	−0.318131	−	0.948047i	$-0.603055\pi$
$877$	−18.8424	−0.636261	−0.318131	+	0.948047i	$0.603055\pi$
$878$	−29.9716	−1.01149
$879$	30.6145	1.03260
$880$	1.68677	0.0568609
$881$	−48.0416	−1.61856	−0.809281	−	0.587422i	$-0.800143\pi$
$881$	−48.0416	−1.61856	−0.809281	+	0.587422i	$0.800143\pi$
$882$	3.18735	0.107323
$883$	−31.8886	−1.07314	−0.536568	−	0.843857i	$-0.680279\pi$
$883$	−31.8886	−1.07314	−0.536568	+	0.843857i	$0.680279\pi$
$884$	−1.67229	−0.0562453
$885$	−19.8666	−0.667810
$886$	−25.1374	−0.844508
$887$	21.8677	0.734247	0.367124	−	0.930172i	$-0.380343\pi$
$887$	21.8677	0.734247	0.367124	+	0.930172i	$0.380343\pi$
$888$	0.314128	0.0105414
$889$	−29.0195	−0.973282
$890$	−2.42632	−0.0813305
$891$	−1.08018	−0.0361876
$892$	29.7997	0.997769
$893$	−49.4851	−1.65596
$894$	8.53591	0.285484
$895$	6.24509	0.208750
$896$	−1.95260	−0.0652319
$897$	−0.218439	−0.00729345
$898$	28.5737	0.953518
$899$	3.20285	0.106821
$900$	−2.56155	−0.0853851
$901$	−67.0009	−2.23212
$902$	12.3951	0.412710
$903$	2.62824	0.0874625
$904$	−5.06424	−0.168434
$905$	−35.6866	−1.18626
$906$	−20.9096	−0.694676
$907$	15.8833	0.527396	0.263698	−	0.964605i	$-0.415058\pi$
$907$	15.8833	0.527396	0.263698	+	0.964605i	$0.415058\pi$
$908$	−23.3062	−0.773443
$909$	4.92800	0.163451
$910$	−0.666039	−0.0220790
$911$	22.9852	0.761533	0.380766	−	0.924671i	$-0.375660\pi$
$911$	22.9852	0.761533	0.380766	+	0.924671i	$0.375660\pi$
$912$	−7.93745	−0.262835
$913$	−4.75762	−0.157454
$914$	−17.9657	−0.594253
$915$	−8.57875	−0.283605
$916$	−21.4977	−0.710304
$917$	13.1132	0.433036
$918$	−7.65567	−0.252675
$919$	−22.0022	−0.725785	−0.362893	−	0.931831i	$-0.618211\pi$
$919$	−22.0022	−0.725785	−0.362893	+	0.931831i	$0.618211\pi$
$920$	1.56155	0.0514829
$921$	27.0042	0.889820
$922$	−8.44900	−0.278253
$923$	−1.20514	−0.0396676
$924$	−2.10917	−0.0693866
$925$	0.804655	0.0264569
$926$	15.7530	0.517674
$927$	10.6010	0.348181
$928$	−1.00000	−0.0328266
$929$	4.42206	0.145083	0.0725416	−	0.997365i	$-0.476889\pi$
$929$	4.42206	0.145083	0.0725416	+	0.997365i	$0.476889\pi$
$930$	5.00142	0.164003
$931$	25.2994	0.829154
$932$	5.22300	0.171085
$933$	11.6447	0.381232
$934$	−5.33447	−0.174549
$935$	12.9133	0.422311
$936$	0.218439	0.00713989
$937$	−21.1139	−0.689760	−0.344880	−	0.938647i	$-0.612080\pi$
$937$	−21.1139	−0.689760	−0.344880	+	0.938647i	$0.612080\pi$
$938$	−5.95673	−0.194494
$939$	−13.7637	−0.449163
$940$	−9.73532	−0.317531
$941$	−41.3716	−1.34868	−0.674338	−	0.738422i	$-0.735571\pi$
$941$	−41.3716	−1.34868	−0.674338	+	0.738422i	$0.735571\pi$
$942$	12.3989	0.403978
$943$	11.4749	0.373675
$944$	12.7224	0.414078
$945$	−3.04909	−0.0991869
$946$	1.45395	0.0472720
$947$	−49.4503	−1.60692	−0.803460	−	0.595359i	$-0.797010\pi$
$947$	−49.4503	−1.60692	−0.803460	+	0.595359i	$0.797010\pi$
$948$	−12.4263	−0.403586
$949$	2.05466	0.0666972
$950$	−20.3322	−0.659664
$951$	−14.3757	−0.466163
$952$	−14.9485	−0.484483
$953$	−26.6149	−0.862141	−0.431071	−	0.902318i	$-0.641864\pi$
$953$	−26.6149	−0.862141	−0.431071	+	0.902318i	$0.641864\pi$
$954$	8.75180	0.283350
$955$	−14.9263	−0.483005
$956$	−19.1291	−0.618680
$957$	−1.08018	−0.0349174
$958$	−21.1083	−0.681979
$959$	−22.1179	−0.714223
$960$	−1.56155	−0.0503989
$961$	−20.7418	−0.669089
$962$	−0.0686177	−0.00221232
$963$	3.47034	0.111830
$964$	22.2742	0.717404
$965$	−38.0586	−1.22515
$966$	−1.95260	−0.0628239
$967$	21.6170	0.695156	0.347578	−	0.937651i	$-0.387004\pi$
$967$	21.6170	0.695156	0.347578	+	0.937651i	$0.387004\pi$
$968$	9.83320	0.316051
$969$	−60.7665	−1.95210
$970$	15.8929	0.510292
$971$	−38.8126	−1.24555	−0.622777	−	0.782399i	$-0.713996\pi$
$971$	−38.8126	−1.24555	−0.622777	+	0.782399i	$0.713996\pi$
$972$	1.00000	0.0320750
$973$	21.1495	0.678022
$974$	−16.1217	−0.516573
$975$	0.559542	0.0179197
$976$	5.49373	0.175850
$977$	−25.5190	−0.816425	−0.408213	−	0.912887i	$-0.633848\pi$
$977$	−25.5190	−0.816425	−0.408213	+	0.912887i	$0.633848\pi$
$978$	8.25813	0.264066
$979$	1.67838	0.0536412
$980$	4.97721	0.158991
$981$	7.41070	0.236605
$982$	23.3137	0.743970
$983$	23.3168	0.743691	0.371846	−	0.928295i	$-0.378725\pi$
$983$	23.3168	0.743691	0.371846	+	0.928295i	$0.378725\pi$
$984$	−11.4749	−0.365808
$985$	−23.2145	−0.739675
$986$	−7.65567	−0.243806
$987$	12.1733	0.387479
$988$	1.73385	0.0551610
$989$	1.34602	0.0428010
$990$	−1.68677	−0.0536089
$991$	−30.5696	−0.971076	−0.485538	−	0.874215i	$-0.661376\pi$
$991$	−30.5696	−0.971076	−0.485538	+	0.874215i	$0.661376\pi$
$992$	−3.20285	−0.101691
$993$	3.42896	0.108815
$994$	−10.7726	−0.341687
$995$	−32.2303	−1.02177
$996$	4.40445	0.139560
$997$	39.9078	1.26389	0.631947	−	0.775012i	$-0.282256\pi$
$997$	39.9078	1.26389	0.631947	+	0.775012i	$0.282256\pi$
$998$	−3.52795	−0.111675
$999$	−0.314128	−0.00993857

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4002.2.a.bf.1.3	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4002.2.a.bf.1.3	✓	6	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:	\( N \)	\(=\)	\( 4002 = 2 \cdot 3 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4002.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.56155 q^{5} -1.00000 q^{6} +1.95260 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.56155 q^{5} -1.00000 q^{6} +1.95260 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.56155 q^{10} -1.08018 q^{11} +1.00000 q^{12} -0.218439 q^{13} -1.95260 q^{14} -1.56155 q^{15} +1.00000 q^{16} +7.65567 q^{17} -1.00000 q^{18} -7.93745 q^{19} -1.56155 q^{20} +1.95260 q^{21} +1.08018 q^{22} +1.00000 q^{23} -1.00000 q^{24} -2.56155 q^{25} +0.218439 q^{26} +1.00000 q^{27} +1.95260 q^{28} +1.00000 q^{29} +1.56155 q^{30} +3.20285 q^{31} -1.00000 q^{32} -1.08018 q^{33} -7.65567 q^{34} -3.04909 q^{35} +1.00000 q^{36} -0.314128 q^{37} +7.93745 q^{38} -0.218439 q^{39} +1.56155 q^{40} +11.4749 q^{41} -1.95260 q^{42} +1.34602 q^{43} -1.08018 q^{44} -1.56155 q^{45} -1.00000 q^{46} +6.23438 q^{47} +1.00000 q^{48} -3.18735 q^{49} +2.56155 q^{50} +7.65567 q^{51} -0.218439 q^{52} -8.75180 q^{53} -1.00000 q^{54} +1.68677 q^{55} -1.95260 q^{56} -7.93745 q^{57} -1.00000 q^{58} +12.7224 q^{59} -1.56155 q^{60} +5.49373 q^{61} -3.20285 q^{62} +1.95260 q^{63} +1.00000 q^{64} +0.341103 q^{65} +1.08018 q^{66} +3.05066 q^{67} +7.65567 q^{68} +1.00000 q^{69} +3.04909 q^{70} +5.51706 q^{71} -1.00000 q^{72} -9.40614 q^{73} +0.314128 q^{74} -2.56155 q^{75} -7.93745 q^{76} -2.10917 q^{77} +0.218439 q^{78} -12.4263 q^{79} -1.56155 q^{80} +1.00000 q^{81} -11.4749 q^{82} +4.40445 q^{83} +1.95260 q^{84} -11.9547 q^{85} -1.34602 q^{86} +1.00000 q^{87} +1.08018 q^{88} -1.55379 q^{89} +1.56155 q^{90} -0.426524 q^{91} +1.00000 q^{92} +3.20285 q^{93} -6.23438 q^{94} +12.3948 q^{95} -1.00000 q^{96} +10.1777 q^{97} +3.18735 q^{98} -1.08018 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 6 q^{3} + 6 q^{4} + 3 q^{5} - 6 q^{6} + 2 q^{7} - 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 + 6 * q^3 + 6 * q^4 + 3 * q^5 - 6 * q^6 + 2 * q^7 - 6 * q^8 + 6 * q^9	\( 6 q - 6 q^{2} + 6 q^{3} + 6 q^{4} + 3 q^{5} - 6 q^{6} + 2 q^{7} - 6 q^{8} + 6 q^{9} - 3 q^{10} + 7 q^{11} + 6 q^{12} + 3 q^{13} - 2 q^{14} + 3 q^{15} + 6 q^{16} + 8 q^{17} - 6 q^{18} - 4 q^{19} + 3 q^{20} + 2 q^{21} - 7 q^{22} + 6 q^{23} - 6 q^{24} - 3 q^{25} - 3 q^{26} + 6 q^{27} + 2 q^{28} + 6 q^{29} - 3 q^{30} + q^{31} - 6 q^{32} + 7 q^{33} - 8 q^{34} + 18 q^{35} + 6 q^{36} + 7 q^{37} + 4 q^{38} + 3 q^{39} - 3 q^{40} + 13 q^{41} - 2 q^{42} + 7 q^{44} + 3 q^{45} - 6 q^{46} + 22 q^{47} + 6 q^{48} + 8 q^{49} + 3 q^{50} + 8 q^{51} + 3 q^{52} + 10 q^{53} - 6 q^{54} - 5 q^{55} - 2 q^{56} - 4 q^{57} - 6 q^{58} + 17 q^{59} + 3 q^{60} + q^{61} - q^{62} + 2 q^{63} + 6 q^{64} - 7 q^{65} - 7 q^{66} + 3 q^{67} + 8 q^{68} + 6 q^{69} - 18 q^{70} + 11 q^{71} - 6 q^{72} - 7 q^{74} - 3 q^{75} - 4 q^{76} - 3 q^{78} + 2 q^{79} + 3 q^{80} + 6 q^{81} - 13 q^{82} + 16 q^{83} + 2 q^{84} + 4 q^{85} + 6 q^{87} - 7 q^{88} + 16 q^{89} - 3 q^{90} - 28 q^{91} + 6 q^{92} + q^{93} - 22 q^{94} + 32 q^{95} - 6 q^{96} + 2 q^{97} - 8 q^{98} + 7 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + 6 * q^3 + 6 * q^4 + 3 * q^5 - 6 * q^6 + 2 * q^7 - 6 * q^8 + 6 * q^9 - 3 * q^10 + 7 * q^11 + 6 * q^12 + 3 * q^13 - 2 * q^14 + 3 * q^15 + 6 * q^16 + 8 * q^17 - 6 * q^18 - 4 * q^19 + 3 * q^20 + 2 * q^21 - 7 * q^22 + 6 * q^23 - 6 * q^24 - 3 * q^25 - 3 * q^26 + 6 * q^27 + 2 * q^28 + 6 * q^29 - 3 * q^30 + q^31 - 6 * q^32 + 7 * q^33 - 8 * q^34 + 18 * q^35 + 6 * q^36 + 7 * q^37 + 4 * q^38 + 3 * q^39 - 3 * q^40 + 13 * q^41 - 2 * q^42 + 7 * q^44 + 3 * q^45 - 6 * q^46 + 22 * q^47 + 6 * q^48 + 8 * q^49 + 3 * q^50 + 8 * q^51 + 3 * q^52 + 10 * q^53 - 6 * q^54 - 5 * q^55 - 2 * q^56 - 4 * q^57 - 6 * q^58 + 17 * q^59 + 3 * q^60 + q^61 - q^62 + 2 * q^63 + 6 * q^64 - 7 * q^65 - 7 * q^66 + 3 * q^67 + 8 * q^68 + 6 * q^69 - 18 * q^70 + 11 * q^71 - 6 * q^72 - 7 * q^74 - 3 * q^75 - 4 * q^76 - 3 * q^78 + 2 * q^79 + 3 * q^80 + 6 * q^81 - 13 * q^82 + 16 * q^83 + 2 * q^84 + 4 * q^85 + 6 * q^87 - 7 * q^88 + 16 * q^89 - 3 * q^90 - 28 * q^91 + 6 * q^92 + q^93 - 22 * q^94 + 32 * q^95 - 6 * q^96 + 2 * q^97 - 8 * q^98 + 7 * q^99

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