LMFDB - Embedded newform 354.2.a.g.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,2,Mod(1,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("354.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	354.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:	$2.82670423155$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{11}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 11 $ x^2 - 11
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$3.31662$ of defining polynomial
Character	$\chi$	$=$	354.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.31662 q^{5} -1.00000 q^{6} +4.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.31662 q^{5} -1.00000 q^{6} +4.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -4.31662 q^{10} -2.00000 q^{11} +1.00000 q^{12} -4.31662 q^{13} -4.00000 q^{14} +4.31662 q^{15} +1.00000 q^{16} -6.63325 q^{17} -1.00000 q^{18} -2.00000 q^{19} +4.31662 q^{20} +4.00000 q^{21} +2.00000 q^{22} -4.63325 q^{23} -1.00000 q^{24} +13.6332 q^{25} +4.31662 q^{26} +1.00000 q^{27} +4.00000 q^{28} -8.31662 q^{29} -4.31662 q^{30} +2.31662 q^{31} -1.00000 q^{32} -2.00000 q^{33} +6.63325 q^{34} +17.2665 q^{35} +1.00000 q^{36} -4.31662 q^{37} +2.00000 q^{38} -4.31662 q^{39} -4.31662 q^{40} -2.63325 q^{41} -4.00000 q^{42} +4.00000 q^{43} -2.00000 q^{44} +4.31662 q^{45} +4.63325 q^{46} +8.63325 q^{47} +1.00000 q^{48} +9.00000 q^{49} -13.6332 q^{50} -6.63325 q^{51} -4.31662 q^{52} -3.68338 q^{53} -1.00000 q^{54} -8.63325 q^{55} -4.00000 q^{56} -2.00000 q^{57} +8.31662 q^{58} -1.00000 q^{59} +4.31662 q^{60} -4.31662 q^{61} -2.31662 q^{62} +4.00000 q^{63} +1.00000 q^{64} -18.6332 q^{65} +2.00000 q^{66} +4.63325 q^{67} -6.63325 q^{68} -4.63325 q^{69} -17.2665 q^{70} +6.31662 q^{71} -1.00000 q^{72} +11.2665 q^{73} +4.31662 q^{74} +13.6332 q^{75} -2.00000 q^{76} -8.00000 q^{77} +4.31662 q^{78} +4.31662 q^{80} +1.00000 q^{81} +2.63325 q^{82} -4.00000 q^{83} +4.00000 q^{84} -28.6332 q^{85} -4.00000 q^{86} -8.31662 q^{87} +2.00000 q^{88} +8.63325 q^{89} -4.31662 q^{90} -17.2665 q^{91} -4.63325 q^{92} +2.31662 q^{93} -8.63325 q^{94} -8.63325 q^{95} -1.00000 q^{96} -5.36675 q^{97} -9.00000 q^{98} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} + 8 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 + 8 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} + 8 q^{7} - 2 q^{8} + 2 q^{9} - 2 q^{10} - 4 q^{11} + 2 q^{12} - 2 q^{13} - 8 q^{14} + 2 q^{15} + 2 q^{16} - 2 q^{18} - 4 q^{19} + 2 q^{20} + 8 q^{21} + 4 q^{22} + 4 q^{23} - 2 q^{24} + 14 q^{25} + 2 q^{26} + 2 q^{27} + 8 q^{28} - 10 q^{29} - 2 q^{30} - 2 q^{31} - 2 q^{32} - 4 q^{33} + 8 q^{35} + 2 q^{36} - 2 q^{37} + 4 q^{38} - 2 q^{39} - 2 q^{40} + 8 q^{41} - 8 q^{42} + 8 q^{43} - 4 q^{44} + 2 q^{45} - 4 q^{46} + 4 q^{47} + 2 q^{48} + 18 q^{49} - 14 q^{50} - 2 q^{52} - 14 q^{53} - 2 q^{54} - 4 q^{55} - 8 q^{56} - 4 q^{57} + 10 q^{58} - 2 q^{59} + 2 q^{60} - 2 q^{61} + 2 q^{62} + 8 q^{63} + 2 q^{64} - 24 q^{65} + 4 q^{66} - 4 q^{67} + 4 q^{69} - 8 q^{70} + 6 q^{71} - 2 q^{72} - 4 q^{73} + 2 q^{74} + 14 q^{75} - 4 q^{76} - 16 q^{77} + 2 q^{78} + 2 q^{80} + 2 q^{81} - 8 q^{82} - 8 q^{83} + 8 q^{84} - 44 q^{85} - 8 q^{86} - 10 q^{87} + 4 q^{88} + 4 q^{89} - 2 q^{90} - 8 q^{91} + 4 q^{92} - 2 q^{93} - 4 q^{94} - 4 q^{95} - 2 q^{96} - 24 q^{97} - 18 q^{98} - 4 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 + 8 * q^7 - 2 * q^8 + 2 * q^9 - 2 * q^10 - 4 * q^11 + 2 * q^12 - 2 * q^13 - 8 * q^14 + 2 * q^15 + 2 * q^16 - 2 * q^18 - 4 * q^19 + 2 * q^20 + 8 * q^21 + 4 * q^22 + 4 * q^23 - 2 * q^24 + 14 * q^25 + 2 * q^26 + 2 * q^27 + 8 * q^28 - 10 * q^29 - 2 * q^30 - 2 * q^31 - 2 * q^32 - 4 * q^33 + 8 * q^35 + 2 * q^36 - 2 * q^37 + 4 * q^38 - 2 * q^39 - 2 * q^40 + 8 * q^41 - 8 * q^42 + 8 * q^43 - 4 * q^44 + 2 * q^45 - 4 * q^46 + 4 * q^47 + 2 * q^48 + 18 * q^49 - 14 * q^50 - 2 * q^52 - 14 * q^53 - 2 * q^54 - 4 * q^55 - 8 * q^56 - 4 * q^57 + 10 * q^58 - 2 * q^59 + 2 * q^60 - 2 * q^61 + 2 * q^62 + 8 * q^63 + 2 * q^64 - 24 * q^65 + 4 * q^66 - 4 * q^67 + 4 * q^69 - 8 * q^70 + 6 * q^71 - 2 * q^72 - 4 * q^73 + 2 * q^74 + 14 * q^75 - 4 * q^76 - 16 * q^77 + 2 * q^78 + 2 * q^80 + 2 * q^81 - 8 * q^82 - 8 * q^83 + 8 * q^84 - 44 * q^85 - 8 * q^86 - 10 * q^87 + 4 * q^88 + 4 * q^89 - 2 * q^90 - 8 * q^91 + 4 * q^92 - 2 * q^93 - 4 * q^94 - 4 * q^95 - 2 * q^96 - 24 * q^97 - 18 * q^98 - 4 * 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
$5$	4.31662	1.93045	0.965227	−	0.261414i	$-0.0841889\pi$
$5$	4.31662	1.93045	0.965227	+	0.261414i	$0.0841889\pi$
$6$	−1.00000	−0.408248
$7$	4.00000	1.51186	0.755929	−	0.654654i	$-0.227186\pi$
$7$	4.00000	1.51186	0.755929	+	0.654654i	$0.227186\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−4.31662	−1.36504
$11$	−2.00000	−0.603023	−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000	−0.603023	−0.301511	+	0.953463i	$0.597491\pi$
$12$	1.00000	0.288675
$13$	−4.31662	−1.19722	−0.598608	−	0.801042i	$-0.704279\pi$
$13$	−4.31662	−1.19722	−0.598608	+	0.801042i	$0.704279\pi$
$14$	−4.00000	−1.06904
$15$	4.31662	1.11455
$16$	1.00000	0.250000
$17$	−6.63325	−1.60880	−0.804400	−	0.594089i	$-0.797513\pi$
$17$	−6.63325	−1.60880	−0.804400	+	0.594089i	$0.797513\pi$
$18$	−1.00000	−0.235702
$19$	−2.00000	−0.458831	−0.229416	−	0.973329i	$-0.573682\pi$
$19$	−2.00000	−0.458831	−0.229416	+	0.973329i	$0.573682\pi$
$20$	4.31662	0.965227
$21$	4.00000	0.872872
$22$	2.00000	0.426401
$23$	−4.63325	−0.966099	−0.483050	−	0.875593i	$-0.660471\pi$
$23$	−4.63325	−0.966099	−0.483050	+	0.875593i	$0.660471\pi$
$24$	−1.00000	−0.204124
$25$	13.6332	2.72665
$26$	4.31662	0.846560
$27$	1.00000	0.192450
$28$	4.00000	0.755929
$29$	−8.31662	−1.54436	−0.772179	−	0.635405i	$-0.780833\pi$
$29$	−8.31662	−1.54436	−0.772179	+	0.635405i	$0.780833\pi$
$30$	−4.31662	−0.788104
$31$	2.31662	0.416078	0.208039	−	0.978121i	$-0.433292\pi$
$31$	2.31662	0.416078	0.208039	+	0.978121i	$0.433292\pi$
$32$	−1.00000	−0.176777
$33$	−2.00000	−0.348155
$34$	6.63325	1.13759
$35$	17.2665	2.91857
$36$	1.00000	0.166667
$37$	−4.31662	−0.709649	−0.354824	−	0.934933i	$-0.615459\pi$
$37$	−4.31662	−0.709649	−0.354824	+	0.934933i	$0.615459\pi$
$38$	2.00000	0.324443
$39$	−4.31662	−0.691213
$40$	−4.31662	−0.682518
$41$	−2.63325	−0.411244	−0.205622	−	0.978631i	$-0.565922\pi$
$41$	−2.63325	−0.411244	−0.205622	+	0.978631i	$0.565922\pi$
$42$	−4.00000	−0.617213
$43$	4.00000	0.609994	0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000	0.609994	0.304997	+	0.952353i	$0.401344\pi$
$44$	−2.00000	−0.301511
$45$	4.31662	0.643484
$46$	4.63325	0.683135
$47$	8.63325	1.25929	0.629644	−	0.776883i	$-0.283201\pi$
$47$	8.63325	1.25929	0.629644	+	0.776883i	$0.283201\pi$
$48$	1.00000	0.144338
$49$	9.00000	1.28571
$50$	−13.6332	−1.92803
$51$	−6.63325	−0.928841
$52$	−4.31662	−0.598608
$53$	−3.68338	−0.505950	−0.252975	−	0.967473i	$-0.581409\pi$
$53$	−3.68338	−0.505950	−0.252975	+	0.967473i	$0.581409\pi$
$54$	−1.00000	−0.136083
$55$	−8.63325	−1.16411
$56$	−4.00000	−0.534522
$57$	−2.00000	−0.264906
$58$	8.31662	1.09203
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	4.31662	0.557274
$61$	−4.31662	−0.552687	−0.276344	−	0.961059i	$-0.589123\pi$
$61$	−4.31662	−0.552687	−0.276344	+	0.961059i	$0.589123\pi$
$62$	−2.31662	−0.294212
$63$	4.00000	0.503953
$64$	1.00000	0.125000
$65$	−18.6332	−2.31117
$66$	2.00000	0.246183
$67$	4.63325	0.566042	0.283021	−	0.959114i	$-0.408663\pi$
$67$	4.63325	0.566042	0.283021	+	0.959114i	$0.408663\pi$
$68$	−6.63325	−0.804400
$69$	−4.63325	−0.557778
$70$	−17.2665	−2.06374
$71$	6.31662	0.749645	0.374823	−	0.927097i	$-0.377704\pi$
$71$	6.31662	0.749645	0.374823	+	0.927097i	$0.377704\pi$
$72$	−1.00000	−0.117851
$73$	11.2665	1.31864	0.659322	−	0.751861i	$-0.270843\pi$
$73$	11.2665	1.31864	0.659322	+	0.751861i	$0.270843\pi$
$74$	4.31662	0.501797
$75$	13.6332	1.57423
$76$	−2.00000	−0.229416
$77$	−8.00000	−0.911685
$78$	4.31662	0.488762
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	4.31662	0.482613
$81$	1.00000	0.111111
$82$	2.63325	0.290794
$83$	−4.00000	−0.439057	−0.219529	−	0.975606i	$-0.570452\pi$
$83$	−4.00000	−0.439057	−0.219529	+	0.975606i	$0.570452\pi$
$84$	4.00000	0.436436
$85$	−28.6332	−3.10571
$86$	−4.00000	−0.431331
$87$	−8.31662	−0.891636
$88$	2.00000	0.213201
$89$	8.63325	0.915123	0.457561	−	0.889178i	$-0.348723\pi$
$89$	8.63325	0.915123	0.457561	+	0.889178i	$0.348723\pi$
$90$	−4.31662	−0.455012
$91$	−17.2665	−1.81002
$92$	−4.63325	−0.483050
$93$	2.31662	0.240223
$94$	−8.63325	−0.890452
$95$	−8.63325	−0.885753
$96$	−1.00000	−0.102062
$97$	−5.36675	−0.544911	−0.272455	−	0.962168i	$-0.587836\pi$
$97$	−5.36675	−0.544911	−0.272455	+	0.962168i	$0.587836\pi$
$98$	−9.00000	−0.909137
$99$	−2.00000	−0.201008
$100$	13.6332	1.36332
$101$	−1.36675	−0.135997	−0.0679984	−	0.997685i	$-0.521661\pi$
$101$	−1.36675	−0.135997	−0.0679984	+	0.997685i	$0.521661\pi$
$102$	6.63325	0.656790
$103$	1.68338	0.165868	0.0829339	−	0.996555i	$-0.473571\pi$
$103$	1.68338	0.165868	0.0829339	+	0.996555i	$0.473571\pi$
$104$	4.31662	0.423280
$105$	17.2665	1.68504
$106$	3.68338	0.357761
$107$	12.6332	1.22130	0.610651	−	0.791900i	$-0.290908\pi$
$107$	12.6332	1.22130	0.610651	+	0.791900i	$0.290908\pi$
$108$	1.00000	0.0962250
$109$	12.9499	1.24037	0.620187	−	0.784454i	$-0.287057\pi$
$109$	12.9499	1.24037	0.620187	+	0.784454i	$0.287057\pi$
$110$	8.63325	0.823148
$111$	−4.31662	−0.409716
$112$	4.00000	0.377964
$113$	−14.0000	−1.31701	−0.658505	−	0.752577i	$-0.728811\pi$
$113$	−14.0000	−1.31701	−0.658505	+	0.752577i	$0.728811\pi$
$114$	2.00000	0.187317
$115$	−20.0000	−1.86501
$116$	−8.31662	−0.772179
$117$	−4.31662	−0.399072
$118$	1.00000	0.0920575
$119$	−26.5330	−2.43228
$120$	−4.31662	−0.394052
$121$	−7.00000	−0.636364
$122$	4.31662	0.390809
$123$	−2.63325	−0.237432
$124$	2.31662	0.208039
$125$	37.2665	3.33322
$126$	−4.00000	−0.356348
$127$	−17.8997	−1.58835	−0.794173	−	0.607692i	$-0.792096\pi$
$127$	−17.8997	−1.58835	−0.794173	+	0.607692i	$0.792096\pi$
$128$	−1.00000	−0.0883883
$129$	4.00000	0.352180
$130$	18.6332	1.63424
$131$	19.2665	1.68332	0.841661	−	0.540006i	$-0.181578\pi$
$131$	19.2665	1.68332	0.841661	+	0.540006i	$0.181578\pi$
$132$	−2.00000	−0.174078
$133$	−8.00000	−0.693688
$134$	−4.63325	−0.400252
$135$	4.31662	0.371516
$136$	6.63325	0.568796
$137$	14.6332	1.25020	0.625101	−	0.780544i	$-0.285058\pi$
$137$	14.6332	1.25020	0.625101	+	0.780544i	$0.285058\pi$
$138$	4.63325	0.394408
$139$	10.0000	0.848189	0.424094	−	0.905618i	$-0.360592\pi$
$139$	10.0000	0.848189	0.424094	+	0.905618i	$0.360592\pi$
$140$	17.2665	1.45929
$141$	8.63325	0.727051
$142$	−6.31662	−0.530079
$143$	8.63325	0.721949
$144$	1.00000	0.0833333
$145$	−35.8997	−2.98131
$146$	−11.2665	−0.932422
$147$	9.00000	0.742307
$148$	−4.31662	−0.354824
$149$	22.0000	1.80231	0.901155	−	0.433497i	$-0.142720\pi$
$149$	22.0000	1.80231	0.901155	+	0.433497i	$0.142720\pi$
$150$	−13.6332	−1.11315
$151$	14.3166	1.16507	0.582535	−	0.812805i	$-0.302061\pi$
$151$	14.3166	1.16507	0.582535	+	0.812805i	$0.302061\pi$
$152$	2.00000	0.162221
$153$	−6.63325	−0.536266
$154$	8.00000	0.644658
$155$	10.0000	0.803219
$156$	−4.31662	−0.345607
$157$	−13.5831	−1.08405	−0.542026	−	0.840362i	$-0.682342\pi$
$157$	−13.5831	−1.08405	−0.542026	+	0.840362i	$0.682342\pi$
$158$	0	0
$159$	−3.68338	−0.292111
$160$	−4.31662	−0.341259
$161$	−18.5330	−1.46060
$162$	−1.00000	−0.0785674
$163$	−10.0000	−0.783260	−0.391630	−	0.920123i	$-0.628089\pi$
$163$	−10.0000	−0.783260	−0.391630	+	0.920123i	$0.628089\pi$
$164$	−2.63325	−0.205622
$165$	−8.63325	−0.672098
$166$	4.00000	0.310460
$167$	18.3166	1.41738	0.708691	−	0.705519i	$-0.249286\pi$
$167$	18.3166	1.41738	0.708691	+	0.705519i	$0.249286\pi$
$168$	−4.00000	−0.308607
$169$	5.63325	0.433327
$170$	28.6332	2.19607
$171$	−2.00000	−0.152944
$172$	4.00000	0.304997
$173$	−22.6332	−1.72077	−0.860387	−	0.509641i	$-0.829778\pi$
$173$	−22.6332	−1.72077	−0.860387	+	0.509641i	$0.829778\pi$
$174$	8.31662	0.630482
$175$	54.5330	4.12231
$176$	−2.00000	−0.150756
$177$	−1.00000	−0.0751646
$178$	−8.63325	−0.647089
$179$	−4.00000	−0.298974	−0.149487	−	0.988764i	$-0.547762\pi$
$179$	−4.00000	−0.298974	−0.149487	+	0.988764i	$0.547762\pi$
$180$	4.31662	0.321742
$181$	3.26650	0.242797	0.121398	−	0.992604i	$-0.461262\pi$
$181$	3.26650	0.242797	0.121398	+	0.992604i	$0.461262\pi$
$182$	17.2665	1.27988
$183$	−4.31662	−0.319094
$184$	4.63325	0.341568
$185$	−18.6332	−1.36994
$186$	−2.31662	−0.169863
$187$	13.2665	0.970143
$188$	8.63325	0.629644
$189$	4.00000	0.290957
$190$	8.63325	0.626322
$191$	0.633250	0.0458203	0.0229102	−	0.999738i	$-0.492707\pi$
$191$	0.633250	0.0458203	0.0229102	+	0.999738i	$0.492707\pi$
$192$	1.00000	0.0721688
$193$	−10.0000	−0.719816	−0.359908	−	0.932988i	$-0.617192\pi$
$193$	−10.0000	−0.719816	−0.359908	+	0.932988i	$0.617192\pi$
$194$	5.36675	0.385310
$195$	−18.6332	−1.33435
$196$	9.00000	0.642857
$197$	15.6834	1.11739	0.558697	−	0.829372i	$-0.311301\pi$
$197$	15.6834	1.11739	0.558697	+	0.829372i	$0.311301\pi$
$198$	2.00000	0.142134
$199$	24.6332	1.74620	0.873102	−	0.487537i	$-0.162105\pi$
$199$	24.6332	1.74620	0.873102	+	0.487537i	$0.162105\pi$
$200$	−13.6332	−0.964016
$201$	4.63325	0.326804
$202$	1.36675	0.0961642
$203$	−33.2665	−2.33485
$204$	−6.63325	−0.464420
$205$	−11.3668	−0.793888
$206$	−1.68338	−0.117286
$207$	−4.63325	−0.322033
$208$	−4.31662	−0.299304
$209$	4.00000	0.276686
$210$	−17.2665	−1.19150
$211$	16.6332	1.14508	0.572540	−	0.819877i	$-0.305958\pi$
$211$	16.6332	1.14508	0.572540	+	0.819877i	$0.305958\pi$
$212$	−3.68338	−0.252975
$213$	6.31662	0.432808
$214$	−12.6332	−0.863591
$215$	17.2665	1.17757
$216$	−1.00000	−0.0680414
$217$	9.26650	0.629051
$218$	−12.9499	−0.877076
$219$	11.2665	0.761319
$220$	−8.63325	−0.582054
$221$	28.6332	1.92608
$222$	4.31662	0.289713
$223$	−13.2665	−0.888390	−0.444195	−	0.895930i	$-0.646510\pi$
$223$	−13.2665	−0.888390	−0.444195	+	0.895930i	$0.646510\pi$
$224$	−4.00000	−0.267261
$225$	13.6332	0.908883
$226$	14.0000	0.931266
$227$	−21.2665	−1.41151	−0.705754	−	0.708457i	$-0.749391\pi$
$227$	−21.2665	−1.41151	−0.705754	+	0.708457i	$0.749391\pi$
$228$	−2.00000	−0.132453
$229$	−5.58312	−0.368943	−0.184472	−	0.982838i	$-0.559057\pi$
$229$	−5.58312	−0.368943	−0.184472	+	0.982838i	$0.559057\pi$
$230$	20.0000	1.31876
$231$	−8.00000	−0.526361
$232$	8.31662	0.546013
$233$	−20.6332	−1.35173	−0.675865	−	0.737026i	$-0.736230\pi$
$233$	−20.6332	−1.35173	−0.675865	+	0.737026i	$0.736230\pi$
$234$	4.31662	0.282187
$235$	37.2665	2.43100
$236$	−1.00000	−0.0650945
$237$	0	0
$238$	26.5330	1.71988
$239$	2.94987	0.190812	0.0954058	−	0.995438i	$-0.469585\pi$
$239$	2.94987	0.190812	0.0954058	+	0.995438i	$0.469585\pi$
$240$	4.31662	0.278637
$241$	−11.3668	−0.732197	−0.366098	−	0.930576i	$-0.619307\pi$
$241$	−11.3668	−0.732197	−0.366098	+	0.930576i	$0.619307\pi$
$242$	7.00000	0.449977
$243$	1.00000	0.0641500
$244$	−4.31662	−0.276344
$245$	38.8496	2.48201
$246$	2.63325	0.167890
$247$	8.63325	0.549321
$248$	−2.31662	−0.147106
$249$	−4.00000	−0.253490
$250$	−37.2665	−2.35694
$251$	−22.5330	−1.42227	−0.711135	−	0.703055i	$-0.751819\pi$
$251$	−22.5330	−1.42227	−0.711135	+	0.703055i	$0.751819\pi$
$252$	4.00000	0.251976
$253$	9.26650	0.582580
$254$	17.8997	1.12313
$255$	−28.6332	−1.79308
$256$	1.00000	0.0625000
$257$	−7.26650	−0.453272	−0.226636	−	0.973980i	$-0.572773\pi$
$257$	−7.26650	−0.453272	−0.226636	+	0.973980i	$0.572773\pi$
$258$	−4.00000	−0.249029
$259$	−17.2665	−1.07289
$260$	−18.6332	−1.15559
$261$	−8.31662	−0.514786
$262$	−19.2665	−1.19029
$263$	7.58312	0.467595	0.233798	−	0.972285i	$-0.424885\pi$
$263$	7.58312	0.467595	0.233798	+	0.972285i	$0.424885\pi$
$264$	2.00000	0.123091
$265$	−15.8997	−0.976714
$266$	8.00000	0.490511
$267$	8.63325	0.528346
$268$	4.63325	0.283021
$269$	2.00000	0.121942	0.0609711	−	0.998140i	$-0.480580\pi$
$269$	2.00000	0.121942	0.0609711	+	0.998140i	$0.480580\pi$
$270$	−4.31662	−0.262701
$271$	−26.5330	−1.61176	−0.805882	−	0.592076i	$-0.798309\pi$
$271$	−26.5330	−1.61176	−0.805882	+	0.592076i	$0.798309\pi$
$272$	−6.63325	−0.402200
$273$	−17.2665	−1.04502
$274$	−14.6332	−0.884027
$275$	−27.2665	−1.64423
$276$	−4.63325	−0.278889
$277$	−18.6332	−1.11956	−0.559782	−	0.828640i	$-0.689115\pi$
$277$	−18.6332	−1.11956	−0.559782	+	0.828640i	$0.689115\pi$
$278$	−10.0000	−0.599760
$279$	2.31662	0.138693
$280$	−17.2665	−1.03187
$281$	15.2665	0.910723	0.455361	−	0.890307i	$-0.349510\pi$
$281$	15.2665	0.910723	0.455361	+	0.890307i	$0.349510\pi$
$282$	−8.63325	−0.514103
$283$	−24.0000	−1.42665	−0.713326	−	0.700832i	$-0.752812\pi$
$283$	−24.0000	−1.42665	−0.713326	+	0.700832i	$0.752812\pi$
$284$	6.31662	0.374823
$285$	−8.63325	−0.511390
$286$	−8.63325	−0.510495
$287$	−10.5330	−0.621743
$288$	−1.00000	−0.0589256
$289$	27.0000	1.58824
$290$	35.8997	2.10811
$291$	−5.36675	−0.314604
$292$	11.2665	0.659322
$293$	−20.9499	−1.22390	−0.611952	−	0.790895i	$-0.709616\pi$
$293$	−20.9499	−1.22390	−0.611952	+	0.790895i	$0.709616\pi$
$294$	−9.00000	−0.524891
$295$	−4.31662	−0.251324
$296$	4.31662	0.250899
$297$	−2.00000	−0.116052
$298$	−22.0000	−1.27443
$299$	20.0000	1.15663
$300$	13.6332	0.787116
$301$	16.0000	0.922225
$302$	−14.3166	−0.823829
$303$	−1.36675	−0.0785178
$304$	−2.00000	−0.114708
$305$	−18.6332	−1.06694
$306$	6.63325	0.379198
$307$	19.2665	1.09960	0.549799	−	0.835297i	$-0.314704\pi$
$307$	19.2665	1.09960	0.549799	+	0.835297i	$0.314704\pi$
$308$	−8.00000	−0.455842
$309$	1.68338	0.0957639
$310$	−10.0000	−0.567962
$311$	2.31662	0.131364	0.0656819	−	0.997841i	$-0.479078\pi$
$311$	2.31662	0.131364	0.0656819	+	0.997841i	$0.479078\pi$
$312$	4.31662	0.244381
$313$	−18.6332	−1.05321	−0.526607	−	0.850109i	$-0.676536\pi$
$313$	−18.6332	−1.05321	−0.526607	+	0.850109i	$0.676536\pi$
$314$	13.5831	0.766540
$315$	17.2665	0.972857
$316$	0	0
$317$	−11.6834	−0.656204	−0.328102	−	0.944642i	$-0.606409\pi$
$317$	−11.6834	−0.656204	−0.328102	+	0.944642i	$0.606409\pi$
$318$	3.68338	0.206553
$319$	16.6332	0.931283
$320$	4.31662	0.241307
$321$	12.6332	0.705119
$322$	18.5330	1.03280
$323$	13.2665	0.738168
$324$	1.00000	0.0555556
$325$	−58.8496	−3.26439
$326$	10.0000	0.553849
$327$	12.9499	0.716130
$328$	2.63325	0.145397
$329$	34.5330	1.90387
$330$	8.63325	0.475245
$331$	−14.0000	−0.769510	−0.384755	−	0.923019i	$-0.625714\pi$
$331$	−14.0000	−0.769510	−0.384755	+	0.923019i	$0.625714\pi$
$332$	−4.00000	−0.219529
$333$	−4.31662	−0.236550
$334$	−18.3166	−1.00224
$335$	20.0000	1.09272
$336$	4.00000	0.218218
$337$	19.2665	1.04951	0.524757	−	0.851252i	$-0.324156\pi$
$337$	19.2665	1.04951	0.524757	+	0.851252i	$0.324156\pi$
$338$	−5.63325	−0.306408
$339$	−14.0000	−0.760376
$340$	−28.6332	−1.55286
$341$	−4.63325	−0.250905
$342$	2.00000	0.108148
$343$	8.00000	0.431959
$344$	−4.00000	−0.215666
$345$	−20.0000	−1.07676
$346$	22.6332	1.21677
$347$	2.00000	0.107366	0.0536828	−	0.998558i	$-0.482904\pi$
$347$	2.00000	0.107366	0.0536828	+	0.998558i	$0.482904\pi$
$348$	−8.31662	−0.445818
$349$	28.9499	1.54965	0.774826	−	0.632175i	$-0.217838\pi$
$349$	28.9499	1.54965	0.774826	+	0.632175i	$0.217838\pi$
$350$	−54.5330	−2.91491
$351$	−4.31662	−0.230404
$352$	2.00000	0.106600
$353$	−14.0000	−0.745145	−0.372572	−	0.928003i	$-0.621524\pi$
$353$	−14.0000	−0.745145	−0.372572	+	0.928003i	$0.621524\pi$
$354$	1.00000	0.0531494
$355$	27.2665	1.44716
$356$	8.63325	0.457561
$357$	−26.5330	−1.40428
$358$	4.00000	0.211407
$359$	−18.3166	−0.966714	−0.483357	−	0.875423i	$-0.660583\pi$
$359$	−18.3166	−0.966714	−0.483357	+	0.875423i	$0.660583\pi$
$360$	−4.31662	−0.227506
$361$	−15.0000	−0.789474
$362$	−3.26650	−0.171683
$363$	−7.00000	−0.367405
$364$	−17.2665	−0.905010
$365$	48.6332	2.54558
$366$	4.31662	0.225634
$367$	22.3166	1.16492	0.582459	−	0.812860i	$-0.302091\pi$
$367$	22.3166	1.16492	0.582459	+	0.812860i	$0.302091\pi$
$368$	−4.63325	−0.241525
$369$	−2.63325	−0.137081
$370$	18.6332	0.968697
$371$	−14.7335	−0.764925
$372$	2.31662	0.120111
$373$	−3.26650	−0.169133	−0.0845665	−	0.996418i	$-0.526951\pi$
$373$	−3.26650	−0.169133	−0.0845665	+	0.996418i	$0.526951\pi$
$374$	−13.2665	−0.685994
$375$	37.2665	1.92443
$376$	−8.63325	−0.445226
$377$	35.8997	1.84893
$378$	−4.00000	−0.205738
$379$	20.0000	1.02733	0.513665	−	0.857991i	$-0.328287\pi$
$379$	20.0000	1.02733	0.513665	+	0.857991i	$0.328287\pi$
$380$	−8.63325	−0.442876
$381$	−17.8997	−0.917032
$382$	−0.633250	−0.0323999
$383$	32.2164	1.64618	0.823090	−	0.567911i	$-0.192248\pi$
$383$	32.2164	1.64618	0.823090	+	0.567911i	$0.192248\pi$
$384$	−1.00000	−0.0510310
$385$	−34.5330	−1.75996
$386$	10.0000	0.508987
$387$	4.00000	0.203331
$388$	−5.36675	−0.272455
$389$	12.3166	0.624478	0.312239	−	0.950004i	$-0.398921\pi$
$389$	12.3166	0.624478	0.312239	+	0.950004i	$0.398921\pi$
$390$	18.6332	0.943531
$391$	30.7335	1.55426
$392$	−9.00000	−0.454569
$393$	19.2665	0.971866
$394$	−15.6834	−0.790117
$395$	0	0
$396$	−2.00000	−0.100504
$397$	0.316625	0.0158909	0.00794547	−	0.999968i	$-0.497471\pi$
$397$	0.316625	0.0158909	0.00794547	+	0.999968i	$0.497471\pi$
$398$	−24.6332	−1.23475
$399$	−8.00000	−0.400501
$400$	13.6332	0.681662
$401$	21.8997	1.09362	0.546811	−	0.837256i	$-0.315842\pi$
$401$	21.8997	1.09362	0.546811	+	0.837256i	$0.315842\pi$
$402$	−4.63325	−0.231085
$403$	−10.0000	−0.498135
$404$	−1.36675	−0.0679984
$405$	4.31662	0.214495
$406$	33.2665	1.65099
$407$	8.63325	0.427934
$408$	6.63325	0.328395
$409$	−6.63325	−0.327993	−0.163997	−	0.986461i	$-0.552439\pi$
$409$	−6.63325	−0.327993	−0.163997	+	0.986461i	$0.552439\pi$
$410$	11.3668	0.561364
$411$	14.6332	0.721805
$412$	1.68338	0.0829339
$413$	−4.00000	−0.196827
$414$	4.63325	0.227712
$415$	−17.2665	−0.847579
$416$	4.31662	0.211640
$417$	10.0000	0.489702
$418$	−4.00000	−0.195646
$419$	−21.2665	−1.03894	−0.519468	−	0.854490i	$-0.673870\pi$
$419$	−21.2665	−1.03894	−0.519468	+	0.854490i	$0.673870\pi$
$420$	17.2665	0.842519
$421$	−15.6834	−0.764361	−0.382180	−	0.924088i	$-0.624827\pi$
$421$	−15.6834	−0.764361	−0.382180	+	0.924088i	$0.624827\pi$
$422$	−16.6332	−0.809694
$423$	8.63325	0.419763
$424$	3.68338	0.178881
$425$	−90.4327	−4.38663
$426$	−6.31662	−0.306041
$427$	−17.2665	−0.835584
$428$	12.6332	0.610651
$429$	8.63325	0.416817
$430$	−17.2665	−0.832665
$431$	−8.63325	−0.415849	−0.207924	−	0.978145i	$-0.566671\pi$
$431$	−8.63325	−0.415849	−0.207924	+	0.978145i	$0.566671\pi$
$432$	1.00000	0.0481125
$433$	20.6332	0.991571	0.495785	−	0.868445i	$-0.334880\pi$
$433$	20.6332	0.991571	0.495785	+	0.868445i	$0.334880\pi$
$434$	−9.26650	−0.444806
$435$	−35.8997	−1.72126
$436$	12.9499	0.620187
$437$	9.26650	0.443277
$438$	−11.2665	−0.538334
$439$	1.89975	0.0906701	0.0453350	−	0.998972i	$-0.485564\pi$
$439$	1.89975	0.0906701	0.0453350	+	0.998972i	$0.485564\pi$
$440$	8.63325	0.411574
$441$	9.00000	0.428571
$442$	−28.6332	−1.36194
$443$	−21.2665	−1.01040	−0.505201	−	0.863002i	$-0.668582\pi$
$443$	−21.2665	−1.01040	−0.505201	+	0.863002i	$0.668582\pi$
$444$	−4.31662	−0.204858
$445$	37.2665	1.76660
$446$	13.2665	0.628187
$447$	22.0000	1.04056
$448$	4.00000	0.188982
$449$	14.6332	0.690586	0.345293	−	0.938495i	$-0.387780\pi$
$449$	14.6332	0.690586	0.345293	+	0.938495i	$0.387780\pi$
$450$	−13.6332	−0.642678
$451$	5.26650	0.247990
$452$	−14.0000	−0.658505
$453$	14.3166	0.672654
$454$	21.2665	0.998086
$455$	−74.5330	−3.49416
$456$	2.00000	0.0936586
$457$	33.1662	1.55145	0.775726	−	0.631070i	$-0.217384\pi$
$457$	33.1662	1.55145	0.775726	+	0.631070i	$0.217384\pi$
$458$	5.58312	0.260882
$459$	−6.63325	−0.309614
$460$	−20.0000	−0.932505
$461$	−8.31662	−0.387344	−0.193672	−	0.981066i	$-0.562040\pi$
$461$	−8.31662	−0.387344	−0.193672	+	0.981066i	$0.562040\pi$
$462$	8.00000	0.372194
$463$	18.9499	0.880675	0.440338	−	0.897832i	$-0.354859\pi$
$463$	18.9499	0.880675	0.440338	+	0.897832i	$0.354859\pi$
$464$	−8.31662	−0.386090
$465$	10.0000	0.463739
$466$	20.6332	0.955817
$467$	−15.2665	−0.706449	−0.353225	−	0.935539i	$-0.614915\pi$
$467$	−15.2665	−0.706449	−0.353225	+	0.935539i	$0.614915\pi$
$468$	−4.31662	−0.199536
$469$	18.5330	0.855774
$470$	−37.2665	−1.71898
$471$	−13.5831	−0.625877
$472$	1.00000	0.0460287
$473$	−8.00000	−0.367840
$474$	0	0
$475$	−27.2665	−1.25107
$476$	−26.5330	−1.21614
$477$	−3.68338	−0.168650
$478$	−2.94987	−0.134924
$479$	−8.21637	−0.375416	−0.187708	−	0.982225i	$-0.560106\pi$
$479$	−8.21637	−0.375416	−0.187708	+	0.982225i	$0.560106\pi$
$480$	−4.31662	−0.197026
$481$	18.6332	0.849603
$482$	11.3668	0.517741
$483$	−18.5330	−0.843281
$484$	−7.00000	−0.318182
$485$	−23.1662	−1.05193
$486$	−1.00000	−0.0453609
$487$	0.633250	0.0286953	0.0143476	−	0.999897i	$-0.495433\pi$
$487$	0.633250	0.0286953	0.0143476	+	0.999897i	$0.495433\pi$
$488$	4.31662	0.195404
$489$	−10.0000	−0.452216
$490$	−38.8496	−1.75505
$491$	1.89975	0.0857345	0.0428672	−	0.999081i	$-0.486351\pi$
$491$	1.89975	0.0857345	0.0428672	+	0.999081i	$0.486351\pi$
$492$	−2.63325	−0.118716
$493$	55.1662	2.48456
$494$	−8.63325	−0.388428
$495$	−8.63325	−0.388036
$496$	2.31662	0.104020
$497$	25.2665	1.13336
$498$	4.00000	0.179244
$499$	−14.5330	−0.650586	−0.325293	−	0.945613i	$-0.605463\pi$
$499$	−14.5330	−0.650586	−0.325293	+	0.945613i	$0.605463\pi$
$500$	37.2665	1.66661
$501$	18.3166	0.818326
$502$	22.5330	1.00570
$503$	39.1662	1.74634	0.873168	−	0.487419i	$-0.162061\pi$
$503$	39.1662	1.74634	0.873168	+	0.487419i	$0.162061\pi$
$504$	−4.00000	−0.178174
$505$	−5.89975	−0.262535
$506$	−9.26650	−0.411946
$507$	5.63325	0.250181
$508$	−17.8997	−0.794173
$509$	11.8997	0.527447	0.263724	−	0.964598i	$-0.415049\pi$
$509$	11.8997	0.527447	0.263724	+	0.964598i	$0.415049\pi$
$510$	28.6332	1.26790
$511$	45.0660	1.99360
$512$	−1.00000	−0.0441942
$513$	−2.00000	−0.0883022
$514$	7.26650	0.320512
$515$	7.26650	0.320200
$516$	4.00000	0.176090
$517$	−17.2665	−0.759380
$518$	17.2665	0.758646
$519$	−22.6332	−0.993489
$520$	18.6332	0.817122
$521$	21.3668	0.936094	0.468047	−	0.883703i	$-0.344958\pi$
$521$	21.3668	0.936094	0.468047	+	0.883703i	$0.344958\pi$
$522$	8.31662	0.364009
$523$	−14.5330	−0.635484	−0.317742	−	0.948177i	$-0.602925\pi$
$523$	−14.5330	−0.635484	−0.317742	+	0.948177i	$0.602925\pi$
$524$	19.2665	0.841661
$525$	54.5330	2.38002
$526$	−7.58312	−0.330640
$527$	−15.3668	−0.669386
$528$	−2.00000	−0.0870388
$529$	−1.53300	−0.0666521
$530$	15.8997	0.690641
$531$	−1.00000	−0.0433963
$532$	−8.00000	−0.346844
$533$	11.3668	0.492349
$534$	−8.63325	−0.373597
$535$	54.5330	2.35767
$536$	−4.63325	−0.200126
$537$	−4.00000	−0.172613
$538$	−2.00000	−0.0862261
$539$	−18.0000	−0.775315
$540$	4.31662	0.185758
$541$	−3.05013	−0.131135	−0.0655676	−	0.997848i	$-0.520886\pi$
$541$	−3.05013	−0.131135	−0.0655676	+	0.997848i	$0.520886\pi$
$542$	26.5330	1.13969
$543$	3.26650	0.140179
$544$	6.63325	0.284398
$545$	55.8997	2.39448
$546$	17.2665	0.738938
$547$	−30.5330	−1.30550	−0.652748	−	0.757575i	$-0.726384\pi$
$547$	−30.5330	−1.30550	−0.652748	+	0.757575i	$0.726384\pi$
$548$	14.6332	0.625101
$549$	−4.31662	−0.184229
$550$	27.2665	1.16265
$551$	16.6332	0.708600
$552$	4.63325	0.197204
$553$	0	0
$554$	18.6332	0.791651
$555$	−18.6332	−0.790937
$556$	10.0000	0.424094
$557$	12.3166	0.521872	0.260936	−	0.965356i	$-0.415969\pi$
$557$	12.3166	0.521872	0.260936	+	0.965356i	$0.415969\pi$
$558$	−2.31662	−0.0980705
$559$	−17.2665	−0.730295
$560$	17.2665	0.729643
$561$	13.2665	0.560112
$562$	−15.2665	−0.643978
$563$	−14.0000	−0.590030	−0.295015	−	0.955493i	$-0.595325\pi$
$563$	−14.0000	−0.590030	−0.295015	+	0.955493i	$0.595325\pi$
$564$	8.63325	0.363525
$565$	−60.4327	−2.54242
$566$	24.0000	1.00880
$567$	4.00000	0.167984
$568$	−6.31662	−0.265040
$569$	−19.2665	−0.807694	−0.403847	−	0.914827i	$-0.632327\pi$
$569$	−19.2665	−0.807694	−0.403847	+	0.914827i	$0.632327\pi$
$570$	8.63325	0.361607
$571$	−17.2665	−0.722581	−0.361290	−	0.932453i	$-0.617664\pi$
$571$	−17.2665	−0.722581	−0.361290	+	0.932453i	$0.617664\pi$
$572$	8.63325	0.360974
$573$	0.633250	0.0264544
$574$	10.5330	0.439639
$575$	−63.1662	−2.63421
$576$	1.00000	0.0416667
$577$	−3.36675	−0.140160	−0.0700798	−	0.997541i	$-0.522325\pi$
$577$	−3.36675	−0.140160	−0.0700798	+	0.997541i	$0.522325\pi$
$578$	−27.0000	−1.12305
$579$	−10.0000	−0.415586
$580$	−35.8997	−1.49066
$581$	−16.0000	−0.663792
$582$	5.36675	0.222459
$583$	7.36675	0.305100
$584$	−11.2665	−0.466211
$585$	−18.6332	−0.770390
$586$	20.9499	0.865431
$587$	20.7335	0.855763	0.427882	−	0.903835i	$-0.359260\pi$
$587$	20.7335	0.855763	0.427882	+	0.903835i	$0.359260\pi$
$588$	9.00000	0.371154
$589$	−4.63325	−0.190910
$590$	4.31662	0.177713
$591$	15.6834	0.645128
$592$	−4.31662	−0.177412
$593$	19.2665	0.791180	0.395590	−	0.918427i	$-0.370540\pi$
$593$	19.2665	0.791180	0.395590	+	0.918427i	$0.370540\pi$
$594$	2.00000	0.0820610
$595$	−114.533	−4.69540
$596$	22.0000	0.901155
$597$	24.6332	1.00817
$598$	−20.0000	−0.817861
$599$	1.05013	0.0429070	0.0214535	−	0.999770i	$-0.493171\pi$
$599$	1.05013	0.0429070	0.0214535	+	0.999770i	$0.493171\pi$
$600$	−13.6332	−0.556575
$601$	20.7335	0.845737	0.422869	−	0.906191i	$-0.361023\pi$
$601$	20.7335	0.845737	0.422869	+	0.906191i	$0.361023\pi$
$602$	−16.0000	−0.652111
$603$	4.63325	0.188681
$604$	14.3166	0.582535
$605$	−30.2164	−1.22847
$606$	1.36675	0.0555204
$607$	5.89975	0.239463	0.119732	−	0.992806i	$-0.461797\pi$
$607$	5.89975	0.239463	0.119732	+	0.992806i	$0.461797\pi$
$608$	2.00000	0.0811107
$609$	−33.2665	−1.34803
$610$	18.6332	0.754438
$611$	−37.2665	−1.50764
$612$	−6.63325	−0.268133
$613$	20.9499	0.846157	0.423079	−	0.906093i	$-0.360949\pi$
$613$	20.9499	0.846157	0.423079	+	0.906093i	$0.360949\pi$
$614$	−19.2665	−0.777533
$615$	−11.3668	−0.458352
$616$	8.00000	0.322329
$617$	−14.0000	−0.563619	−0.281809	−	0.959470i	$-0.590935\pi$
$617$	−14.0000	−0.563619	−0.281809	+	0.959470i	$0.590935\pi$
$618$	−1.68338	−0.0677153
$619$	−18.7335	−0.752963	−0.376481	−	0.926424i	$-0.622866\pi$
$619$	−18.7335	−0.752963	−0.376481	+	0.926424i	$0.622866\pi$
$620$	10.0000	0.401610
$621$	−4.63325	−0.185926
$622$	−2.31662	−0.0928882
$623$	34.5330	1.38354
$624$	−4.31662	−0.172803
$625$	92.6992	3.70797
$626$	18.6332	0.744734
$627$	4.00000	0.159745
$628$	−13.5831	−0.542026
$629$	28.6332	1.14168
$630$	−17.2665	−0.687914
$631$	−34.5330	−1.37474	−0.687368	−	0.726309i	$-0.741234\pi$
$631$	−34.5330	−1.37474	−0.687368	+	0.726309i	$0.741234\pi$
$632$	0	0
$633$	16.6332	0.661112
$634$	11.6834	0.464006
$635$	−77.2665	−3.06623
$636$	−3.68338	−0.146055
$637$	−38.8496	−1.53928
$638$	−16.6332	−0.658517
$639$	6.31662	0.249882
$640$	−4.31662	−0.170630
$641$	26.6332	1.05195	0.525975	−	0.850500i	$-0.323701\pi$
$641$	26.6332	1.05195	0.525975	+	0.850500i	$0.323701\pi$
$642$	−12.6332	−0.498595
$643$	−5.26650	−0.207690	−0.103845	−	0.994593i	$-0.533115\pi$
$643$	−5.26650	−0.207690	−0.103845	+	0.994593i	$0.533115\pi$
$644$	−18.5330	−0.730302
$645$	17.2665	0.679868
$646$	−13.2665	−0.521963
$647$	0.416876	0.0163891	0.00819454	−	0.999966i	$-0.497392\pi$
$647$	0.416876	0.0163891	0.00819454	+	0.999966i	$0.497392\pi$
$648$	−1.00000	−0.0392837
$649$	2.00000	0.0785069
$650$	58.8496	2.30827
$651$	9.26650	0.363183
$652$	−10.0000	−0.391630
$653$	−11.6834	−0.457206	−0.228603	−	0.973520i	$-0.573416\pi$
$653$	−11.6834	−0.457206	−0.228603	+	0.973520i	$0.573416\pi$
$654$	−12.9499	−0.506380
$655$	83.1662	3.24957
$656$	−2.63325	−0.102811
$657$	11.2665	0.439548
$658$	−34.5330	−1.34624
$659$	5.26650	0.205154	0.102577	−	0.994725i	$-0.467291\pi$
$659$	5.26650	0.205154	0.102577	+	0.994725i	$0.467291\pi$
$660$	−8.63325	−0.336049
$661$	15.2665	0.593798	0.296899	−	0.954909i	$-0.404048\pi$
$661$	15.2665	0.593798	0.296899	+	0.954909i	$0.404048\pi$
$662$	14.0000	0.544125
$663$	28.6332	1.11202
$664$	4.00000	0.155230
$665$	−34.5330	−1.33913
$666$	4.31662	0.167266
$667$	38.5330	1.49200
$668$	18.3166	0.708691
$669$	−13.2665	−0.512912
$670$	−20.0000	−0.772667
$671$	8.63325	0.333283
$672$	−4.00000	−0.154303
$673$	−33.1662	−1.27846	−0.639232	−	0.769014i	$-0.720748\pi$
$673$	−33.1662	−1.27846	−0.639232	+	0.769014i	$0.720748\pi$
$674$	−19.2665	−0.742118
$675$	13.6332	0.524744
$676$	5.63325	0.216663
$677$	−19.6834	−0.756494	−0.378247	−	0.925705i	$-0.623473\pi$
$677$	−19.6834	−0.756494	−0.378247	+	0.925705i	$0.623473\pi$
$678$	14.0000	0.537667
$679$	−21.4670	−0.823828
$680$	28.6332	1.09803
$681$	−21.2665	−0.814934
$682$	4.63325	0.177416
$683$	−40.5330	−1.55095	−0.775476	−	0.631377i	$-0.782490\pi$
$683$	−40.5330	−1.55095	−0.775476	+	0.631377i	$0.782490\pi$
$684$	−2.00000	−0.0764719
$685$	63.1662	2.41346
$686$	−8.00000	−0.305441
$687$	−5.58312	−0.213009
$688$	4.00000	0.152499
$689$	15.8997	0.605732
$690$	20.0000	0.761387
$691$	−48.4327	−1.84247	−0.921234	−	0.389008i	$-0.872818\pi$
$691$	−48.4327	−1.84247	−0.921234	+	0.389008i	$0.872818\pi$
$692$	−22.6332	−0.860387
$693$	−8.00000	−0.303895
$694$	−2.00000	−0.0759190
$695$	43.1662	1.63739
$696$	8.31662	0.315241
$697$	17.4670	0.661610
$698$	−28.9499	−1.09577
$699$	−20.6332	−0.780421
$700$	54.5330	2.06115
$701$	37.1662	1.40375	0.701875	−	0.712300i	$-0.252347\pi$
$701$	37.1662	1.40375	0.701875	+	0.712300i	$0.252347\pi$
$702$	4.31662	0.162921
$703$	8.63325	0.325609
$704$	−2.00000	−0.0753778
$705$	37.2665	1.40354
$706$	14.0000	0.526897
$707$	−5.46700	−0.205608
$708$	−1.00000	−0.0375823
$709$	−31.2665	−1.17424	−0.587119	−	0.809501i	$-0.699738\pi$
$709$	−31.2665	−1.17424	−0.587119	+	0.809501i	$0.699738\pi$
$710$	−27.2665	−1.02329
$711$	0	0
$712$	−8.63325	−0.323545
$713$	−10.7335	−0.401973
$714$	26.5330	0.992973
$715$	37.2665	1.39369
$716$	−4.00000	−0.149487
$717$	2.94987	0.110165
$718$	18.3166	0.683570
$719$	41.8997	1.56260	0.781298	−	0.624158i	$-0.214558\pi$
$719$	41.8997	1.56260	0.781298	+	0.624158i	$0.214558\pi$
$720$	4.31662	0.160871
$721$	6.73350	0.250769
$722$	15.0000	0.558242
$723$	−11.3668	−0.422734
$724$	3.26650	0.121398
$725$	−113.383	−4.21092
$726$	7.00000	0.259794
$727$	−35.1662	−1.30424	−0.652122	−	0.758114i	$-0.726121\pi$
$727$	−35.1662	−1.30424	−0.652122	+	0.758114i	$0.726121\pi$
$728$	17.2665	0.639939
$729$	1.00000	0.0370370
$730$	−48.6332	−1.80000
$731$	−26.5330	−0.981358
$732$	−4.31662	−0.159547
$733$	−47.8997	−1.76922	−0.884609	−	0.466334i	$-0.845575\pi$
$733$	−47.8997	−1.76922	−0.884609	+	0.466334i	$0.845575\pi$
$734$	−22.3166	−0.823722
$735$	38.8496	1.43299
$736$	4.63325	0.170784
$737$	−9.26650	−0.341336
$738$	2.63325	0.0969313
$739$	18.5330	0.681747	0.340874	−	0.940109i	$-0.389277\pi$
$739$	18.5330	0.681747	0.340874	+	0.940109i	$0.389277\pi$
$740$	−18.6332	−0.684972
$741$	8.63325	0.317150
$742$	14.7335	0.540884
$743$	−20.2164	−0.741667	−0.370833	−	0.928699i	$-0.620928\pi$
$743$	−20.2164	−0.741667	−0.370833	+	0.928699i	$0.620928\pi$
$744$	−2.31662	−0.0849316
$745$	94.9657	3.47928
$746$	3.26650	0.119595
$747$	−4.00000	−0.146352
$748$	13.2665	0.485071
$749$	50.5330	1.84644
$750$	−37.2665	−1.36078
$751$	−20.8496	−0.760814	−0.380407	−	0.924819i	$-0.624216\pi$
$751$	−20.8496	−0.760814	−0.380407	+	0.924819i	$0.624216\pi$
$752$	8.63325	0.314822
$753$	−22.5330	−0.821148
$754$	−35.8997	−1.30739
$755$	61.7995	2.24911
$756$	4.00000	0.145479
$757$	11.2665	0.409488	0.204744	−	0.978816i	$-0.434364\pi$
$757$	11.2665	0.409488	0.204744	+	0.978816i	$0.434364\pi$
$758$	−20.0000	−0.726433
$759$	9.26650	0.336353
$760$	8.63325	0.313161
$761$	−33.1662	−1.20228	−0.601138	−	0.799145i	$-0.705286\pi$
$761$	−33.1662	−1.20228	−0.601138	+	0.799145i	$0.705286\pi$
$762$	17.8997	0.648439
$763$	51.7995	1.87527
$764$	0.633250	0.0229102
$765$	−28.6332	−1.03524
$766$	−32.2164	−1.16402
$767$	4.31662	0.155864
$768$	1.00000	0.0360844
$769$	−18.6332	−0.671932	−0.335966	−	0.941874i	$-0.609063\pi$
$769$	−18.6332	−0.671932	−0.335966	+	0.941874i	$0.609063\pi$
$770$	34.5330	1.24448
$771$	−7.26650	−0.261697
$772$	−10.0000	−0.359908
$773$	47.8997	1.72283	0.861417	−	0.507898i	$-0.169577\pi$
$773$	47.8997	1.72283	0.861417	+	0.507898i	$0.169577\pi$
$774$	−4.00000	−0.143777
$775$	31.5831	1.13450
$776$	5.36675	0.192655
$777$	−17.2665	−0.619432
$778$	−12.3166	−0.441572
$779$	5.26650	0.188692
$780$	−18.6332	−0.667177
$781$	−12.6332	−0.452053
$782$	−30.7335	−1.09903
$783$	−8.31662	−0.297212
$784$	9.00000	0.321429
$785$	−58.6332	−2.09271
$786$	−19.2665	−0.687213
$787$	−16.5330	−0.589338	−0.294669	−	0.955599i	$-0.595209\pi$
$787$	−16.5330	−0.589338	−0.294669	+	0.955599i	$0.595209\pi$
$788$	15.6834	0.558697
$789$	7.58312	0.269966
$790$	0	0
$791$	−56.0000	−1.99113
$792$	2.00000	0.0710669
$793$	18.6332	0.661686
$794$	−0.316625	−0.0112366
$795$	−15.8997	−0.563906
$796$	24.6332	0.873102
$797$	−12.7335	−0.451044	−0.225522	−	0.974238i	$-0.572409\pi$
$797$	−12.7335	−0.451044	−0.225522	+	0.974238i	$0.572409\pi$
$798$	8.00000	0.283197
$799$	−57.2665	−2.02594
$800$	−13.6332	−0.482008
$801$	8.63325	0.305041
$802$	−21.8997	−0.773307
$803$	−22.5330	−0.795172
$804$	4.63325	0.163402
$805$	−80.0000	−2.81963
$806$	10.0000	0.352235
$807$	2.00000	0.0704033
$808$	1.36675	0.0480821
$809$	9.89975	0.348057	0.174028	−	0.984741i	$-0.444322\pi$
$809$	9.89975	0.348057	0.174028	+	0.984741i	$0.444322\pi$
$810$	−4.31662	−0.151671
$811$	25.8997	0.909463	0.454732	−	0.890629i	$-0.349735\pi$
$811$	25.8997	0.909463	0.454732	+	0.890629i	$0.349735\pi$
$812$	−33.2665	−1.16743
$813$	−26.5330	−0.930553
$814$	−8.63325	−0.302595
$815$	−43.1662	−1.51205
$816$	−6.63325	−0.232210
$817$	−8.00000	−0.279885
$818$	6.63325	0.231926
$819$	−17.2665	−0.603340
$820$	−11.3668	−0.396944
$821$	−51.0660	−1.78222	−0.891108	−	0.453792i	$-0.850071\pi$
$821$	−51.0660	−1.78222	−0.891108	+	0.453792i	$0.850071\pi$
$822$	−14.6332	−0.510393
$823$	−12.8496	−0.447910	−0.223955	−	0.974600i	$-0.571897\pi$
$823$	−12.8496	−0.447910	−0.223955	+	0.974600i	$0.571897\pi$
$824$	−1.68338	−0.0586432
$825$	−27.2665	−0.949298
$826$	4.00000	0.139178
$827$	−10.7335	−0.373240	−0.186620	−	0.982432i	$-0.559753\pi$
$827$	−10.7335	−0.373240	−0.186620	+	0.982432i	$0.559753\pi$
$828$	−4.63325	−0.161017
$829$	−14.0000	−0.486240	−0.243120	−	0.969996i	$-0.578171\pi$
$829$	−14.0000	−0.486240	−0.243120	+	0.969996i	$0.578171\pi$
$830$	17.2665	0.599329
$831$	−18.6332	−0.646380
$832$	−4.31662	−0.149652
$833$	−59.6992	−2.06846
$834$	−10.0000	−0.346272
$835$	79.0660	2.73619
$836$	4.00000	0.138343
$837$	2.31662	0.0800743
$838$	21.2665	0.734639
$839$	−1.89975	−0.0655866	−0.0327933	−	0.999462i	$-0.510440\pi$
$839$	−1.89975	−0.0655866	−0.0327933	+	0.999462i	$0.510440\pi$
$840$	−17.2665	−0.595751
$841$	40.1662	1.38504
$842$	15.6834	0.540485
$843$	15.2665	0.525806
$844$	16.6332	0.572540
$845$	24.3166	0.836517
$846$	−8.63325	−0.296817
$847$	−28.0000	−0.962091
$848$	−3.68338	−0.126488
$849$	−24.0000	−0.823678
$850$	90.4327	3.10182
$851$	20.0000	0.685591
$852$	6.31662	0.216404
$853$	17.1662	0.587761	0.293881	−	0.955842i	$-0.405053\pi$
$853$	17.1662	0.587761	0.293881	+	0.955842i	$0.405053\pi$
$854$	17.2665	0.590847
$855$	−8.63325	−0.295251
$856$	−12.6332	−0.431796
$857$	13.8997	0.474806	0.237403	−	0.971411i	$-0.423704\pi$
$857$	13.8997	0.474806	0.237403	+	0.971411i	$0.423704\pi$
$858$	−8.63325	−0.294734
$859$	25.8997	0.883688	0.441844	−	0.897092i	$-0.354324\pi$
$859$	25.8997	0.883688	0.441844	+	0.897092i	$0.354324\pi$
$860$	17.2665	0.588783
$861$	−10.5330	−0.358964
$862$	8.63325	0.294050
$863$	−14.1003	−0.479978	−0.239989	−	0.970776i	$-0.577144\pi$
$863$	−14.1003	−0.479978	−0.239989	+	0.970776i	$0.577144\pi$
$864$	−1.00000	−0.0340207
$865$	−97.6992	−3.32187
$866$	−20.6332	−0.701146
$867$	27.0000	0.916968
$868$	9.26650	0.314525
$869$	0	0
$870$	35.8997	1.21712
$871$	−20.0000	−0.677674
$872$	−12.9499	−0.438538
$873$	−5.36675	−0.181637
$874$	−9.26650	−0.313444
$875$	149.066	5.03935
$876$	11.2665	0.380660
$877$	−18.6332	−0.629200	−0.314600	−	0.949224i	$-0.601870\pi$
$877$	−18.6332	−0.629200	−0.314600	+	0.949224i	$0.601870\pi$
$878$	−1.89975	−0.0641134
$879$	−20.9499	−0.706622
$880$	−8.63325	−0.291027
$881$	37.8997	1.27687	0.638437	−	0.769674i	$-0.279581\pi$
$881$	37.8997	1.27687	0.638437	+	0.769674i	$0.279581\pi$
$882$	−9.00000	−0.303046
$883$	13.2665	0.446453	0.223227	−	0.974767i	$-0.428341\pi$
$883$	13.2665	0.446453	0.223227	+	0.974767i	$0.428341\pi$
$884$	28.6332	0.963040
$885$	−4.31662	−0.145102
$886$	21.2665	0.714462
$887$	14.7335	0.494703	0.247351	−	0.968926i	$-0.420440\pi$
$887$	14.7335	0.494703	0.247351	+	0.968926i	$0.420440\pi$
$888$	4.31662	0.144856
$889$	−71.5990	−2.40135
$890$	−37.2665	−1.24918
$891$	−2.00000	−0.0670025
$892$	−13.2665	−0.444195
$893$	−17.2665	−0.577801
$894$	−22.0000	−0.735790
$895$	−17.2665	−0.577155
$896$	−4.00000	−0.133631
$897$	20.0000	0.667781
$898$	−14.6332	−0.488318
$899$	−19.2665	−0.642574
$900$	13.6332	0.454442
$901$	24.4327	0.813973
$902$	−5.26650	−0.175355
$903$	16.0000	0.532447
$904$	14.0000	0.465633
$905$	14.1003	0.468708
$906$	−14.3166	−0.475638
$907$	−31.2665	−1.03819	−0.519094	−	0.854717i	$-0.673730\pi$
$907$	−31.2665	−1.03819	−0.519094	+	0.854717i	$0.673730\pi$
$908$	−21.2665	−0.705754
$909$	−1.36675	−0.0453322
$910$	74.5330	2.47074
$911$	47.5831	1.57650	0.788250	−	0.615356i	$-0.210988\pi$
$911$	47.5831	1.57650	0.788250	+	0.615356i	$0.210988\pi$
$912$	−2.00000	−0.0662266
$913$	8.00000	0.264761
$914$	−33.1662	−1.09704
$915$	−18.6332	−0.615996
$916$	−5.58312	−0.184472
$917$	77.0660	2.54494
$918$	6.63325	0.218930
$919$	−0.416876	−0.0137515	−0.00687574	−	0.999976i	$-0.502189\pi$
$919$	−0.416876	−0.0137515	−0.00687574	+	0.999976i	$0.502189\pi$
$920$	20.0000	0.659380
$921$	19.2665	0.634853
$922$	8.31662	0.273893
$923$	−27.2665	−0.897488
$924$	−8.00000	−0.263181
$925$	−58.8496	−1.93496
$926$	−18.9499	−0.622732
$927$	1.68338	0.0552893
$928$	8.31662	0.273007
$929$	31.3668	1.02911	0.514555	−	0.857457i	$-0.327957\pi$
$929$	31.3668	1.02911	0.514555	+	0.857457i	$0.327957\pi$
$930$	−10.0000	−0.327913
$931$	−18.0000	−0.589926
$932$	−20.6332	−0.675865
$933$	2.31662	0.0758429
$934$	15.2665	0.499535
$935$	57.2665	1.87281
$936$	4.31662	0.141093
$937$	12.7335	0.415985	0.207993	−	0.978130i	$-0.433307\pi$
$937$	12.7335	0.415985	0.207993	+	0.978130i	$0.433307\pi$
$938$	−18.5330	−0.605124
$939$	−18.6332	−0.608073
$940$	37.2665	1.21550
$941$	−6.63325	−0.216238	−0.108119	−	0.994138i	$-0.534483\pi$
$941$	−6.63325	−0.216238	−0.108119	+	0.994138i	$0.534483\pi$
$942$	13.5831	0.442562
$943$	12.2005	0.397303
$944$	−1.00000	−0.0325472
$945$	17.2665	0.561679
$946$	8.00000	0.260102
$947$	31.1662	1.01277	0.506383	−	0.862308i	$-0.330982\pi$
$947$	31.1662	1.01277	0.506383	+	0.862308i	$0.330982\pi$
$948$	0	0
$949$	−48.6332	−1.57870
$950$	27.2665	0.884642
$951$	−11.6834	−0.378859
$952$	26.5330	0.859939
$953$	−14.6332	−0.474017	−0.237009	−	0.971508i	$-0.576167\pi$
$953$	−14.6332	−0.474017	−0.237009	+	0.971508i	$0.576167\pi$
$954$	3.68338	0.119254
$955$	2.73350	0.0884540
$956$	2.94987	0.0954058
$957$	16.6332	0.537677
$958$	8.21637	0.265459
$959$	58.5330	1.89013
$960$	4.31662	0.139318
$961$	−25.6332	−0.826879
$962$	−18.6332	−0.600760
$963$	12.6332	0.407101
$964$	−11.3668	−0.366098
$965$	−43.1662	−1.38957
$966$	18.5330	0.596289
$967$	−18.3166	−0.589023	−0.294511	−	0.955648i	$-0.595157\pi$
$967$	−18.3166	−0.589023	−0.294511	+	0.955648i	$0.595157\pi$
$968$	7.00000	0.224989
$969$	13.2665	0.426181
$970$	23.1662	0.743823
$971$	51.1662	1.64200	0.821002	−	0.570926i	$-0.193416\pi$
$971$	51.1662	1.64200	0.821002	+	0.570926i	$0.193416\pi$
$972$	1.00000	0.0320750
$973$	40.0000	1.28234
$974$	−0.633250	−0.0202906
$975$	−58.8496	−1.88470
$976$	−4.31662	−0.138172
$977$	−20.5330	−0.656909	−0.328454	−	0.944520i	$-0.606528\pi$
$977$	−20.5330	−0.656909	−0.328454	+	0.944520i	$0.606528\pi$
$978$	10.0000	0.319765
$979$	−17.2665	−0.551840
$980$	38.8496	1.24101
$981$	12.9499	0.413458
$982$	−1.89975	−0.0606234
$983$	−33.8997	−1.08123	−0.540617	−	0.841269i	$-0.681809\pi$
$983$	−33.8997	−1.08123	−0.540617	+	0.841269i	$0.681809\pi$
$984$	2.63325	0.0839449
$985$	67.6992	2.15708
$986$	−55.1662	−1.75685
$987$	34.5330	1.09920
$988$	8.63325	0.274660
$989$	−18.5330	−0.589315
$990$	8.63325	0.274383
$991$	−2.94987	−0.0937058	−0.0468529	−	0.998902i	$-0.514919\pi$
$991$	−2.94987	−0.0937058	−0.0468529	+	0.998902i	$0.514919\pi$
$992$	−2.31662	−0.0735529
$993$	−14.0000	−0.444277
$994$	−25.2665	−0.801405
$995$	106.332	3.37097
$996$	−4.00000	−0.126745
$997$	30.6332	0.970165	0.485082	−	0.874468i	$-0.338790\pi$
$997$	30.6332	0.970165	0.485082	+	0.874468i	$0.338790\pi$
$998$	14.5330	0.460034
$999$	−4.31662	−0.136572

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.2.a.g.1.2	✓	2
3.2	odd	2		1062.2.a.m.1.1		2
4.3	odd	2		2832.2.a.l.1.2		2
5.4	even	2		8850.2.a.bm.1.2		2
12.11	even	2		8496.2.a.z.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.2.a.g.1.2	✓	2	1.1	even	1	trivial
1062.2.a.m.1.1		2	3.2	odd	2
2832.2.a.l.1.2		2	4.3	odd	2
8496.2.a.z.1.1		2	12.11	even	2
8850.2.a.bm.1.2		2	5.4	even	2

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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	354.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.31662 q^{5} -1.00000 q^{6} +4.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.31662 q^{5} -1.00000 q^{6} +4.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -4.31662 q^{10} -2.00000 q^{11} +1.00000 q^{12} -4.31662 q^{13} -4.00000 q^{14} +4.31662 q^{15} +1.00000 q^{16} -6.63325 q^{17} -1.00000 q^{18} -2.00000 q^{19} +4.31662 q^{20} +4.00000 q^{21} +2.00000 q^{22} -4.63325 q^{23} -1.00000 q^{24} +13.6332 q^{25} +4.31662 q^{26} +1.00000 q^{27} +4.00000 q^{28} -8.31662 q^{29} -4.31662 q^{30} +2.31662 q^{31} -1.00000 q^{32} -2.00000 q^{33} +6.63325 q^{34} +17.2665 q^{35} +1.00000 q^{36} -4.31662 q^{37} +2.00000 q^{38} -4.31662 q^{39} -4.31662 q^{40} -2.63325 q^{41} -4.00000 q^{42} +4.00000 q^{43} -2.00000 q^{44} +4.31662 q^{45} +4.63325 q^{46} +8.63325 q^{47} +1.00000 q^{48} +9.00000 q^{49} -13.6332 q^{50} -6.63325 q^{51} -4.31662 q^{52} -3.68338 q^{53} -1.00000 q^{54} -8.63325 q^{55} -4.00000 q^{56} -2.00000 q^{57} +8.31662 q^{58} -1.00000 q^{59} +4.31662 q^{60} -4.31662 q^{61} -2.31662 q^{62} +4.00000 q^{63} +1.00000 q^{64} -18.6332 q^{65} +2.00000 q^{66} +4.63325 q^{67} -6.63325 q^{68} -4.63325 q^{69} -17.2665 q^{70} +6.31662 q^{71} -1.00000 q^{72} +11.2665 q^{73} +4.31662 q^{74} +13.6332 q^{75} -2.00000 q^{76} -8.00000 q^{77} +4.31662 q^{78} +4.31662 q^{80} +1.00000 q^{81} +2.63325 q^{82} -4.00000 q^{83} +4.00000 q^{84} -28.6332 q^{85} -4.00000 q^{86} -8.31662 q^{87} +2.00000 q^{88} +8.63325 q^{89} -4.31662 q^{90} -17.2665 q^{91} -4.63325 q^{92} +2.31662 q^{93} -8.63325 q^{94} -8.63325 q^{95} -1.00000 q^{96} -5.36675 q^{97} -9.00000 q^{98} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} + 8 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 + 8 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} + 8 q^{7} - 2 q^{8} + 2 q^{9} - 2 q^{10} - 4 q^{11} + 2 q^{12} - 2 q^{13} - 8 q^{14} + 2 q^{15} + 2 q^{16} - 2 q^{18} - 4 q^{19} + 2 q^{20} + 8 q^{21} + 4 q^{22} + 4 q^{23} - 2 q^{24} + 14 q^{25} + 2 q^{26} + 2 q^{27} + 8 q^{28} - 10 q^{29} - 2 q^{30} - 2 q^{31} - 2 q^{32} - 4 q^{33} + 8 q^{35} + 2 q^{36} - 2 q^{37} + 4 q^{38} - 2 q^{39} - 2 q^{40} + 8 q^{41} - 8 q^{42} + 8 q^{43} - 4 q^{44} + 2 q^{45} - 4 q^{46} + 4 q^{47} + 2 q^{48} + 18 q^{49} - 14 q^{50} - 2 q^{52} - 14 q^{53} - 2 q^{54} - 4 q^{55} - 8 q^{56} - 4 q^{57} + 10 q^{58} - 2 q^{59} + 2 q^{60} - 2 q^{61} + 2 q^{62} + 8 q^{63} + 2 q^{64} - 24 q^{65} + 4 q^{66} - 4 q^{67} + 4 q^{69} - 8 q^{70} + 6 q^{71} - 2 q^{72} - 4 q^{73} + 2 q^{74} + 14 q^{75} - 4 q^{76} - 16 q^{77} + 2 q^{78} + 2 q^{80} + 2 q^{81} - 8 q^{82} - 8 q^{83} + 8 q^{84} - 44 q^{85} - 8 q^{86} - 10 q^{87} + 4 q^{88} + 4 q^{89} - 2 q^{90} - 8 q^{91} + 4 q^{92} - 2 q^{93} - 4 q^{94} - 4 q^{95} - 2 q^{96} - 24 q^{97} - 18 q^{98} - 4 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 + 8 * q^7 - 2 * q^8 + 2 * q^9 - 2 * q^10 - 4 * q^11 + 2 * q^12 - 2 * q^13 - 8 * q^14 + 2 * q^15 + 2 * q^16 - 2 * q^18 - 4 * q^19 + 2 * q^20 + 8 * q^21 + 4 * q^22 + 4 * q^23 - 2 * q^24 + 14 * q^25 + 2 * q^26 + 2 * q^27 + 8 * q^28 - 10 * q^29 - 2 * q^30 - 2 * q^31 - 2 * q^32 - 4 * q^33 + 8 * q^35 + 2 * q^36 - 2 * q^37 + 4 * q^38 - 2 * q^39 - 2 * q^40 + 8 * q^41 - 8 * q^42 + 8 * q^43 - 4 * q^44 + 2 * q^45 - 4 * q^46 + 4 * q^47 + 2 * q^48 + 18 * q^49 - 14 * q^50 - 2 * q^52 - 14 * q^53 - 2 * q^54 - 4 * q^55 - 8 * q^56 - 4 * q^57 + 10 * q^58 - 2 * q^59 + 2 * q^60 - 2 * q^61 + 2 * q^62 + 8 * q^63 + 2 * q^64 - 24 * q^65 + 4 * q^66 - 4 * q^67 + 4 * q^69 - 8 * q^70 + 6 * q^71 - 2 * q^72 - 4 * q^73 + 2 * q^74 + 14 * q^75 - 4 * q^76 - 16 * q^77 + 2 * q^78 + 2 * q^80 + 2 * q^81 - 8 * q^82 - 8 * q^83 + 8 * q^84 - 44 * q^85 - 8 * q^86 - 10 * q^87 + 4 * q^88 + 4 * q^89 - 2 * q^90 - 8 * q^91 + 4 * q^92 - 2 * q^93 - 4 * q^94 - 4 * q^95 - 2 * q^96 - 24 * q^97 - 18 * q^98 - 4 * q^99

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