LMFDB - Embedded newform 5610.2.a.bm.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5610,2,Mod(1,5610)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5610, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("5610.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5610.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:	$44.7960755339$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{17}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4 $ x^2 - x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.56155$ of defining polynomial
Character	$\chi$	$=$	5610.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +3.12311 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +3.12311 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} -1.00000 q^{12} +5.12311 q^{13} -3.12311 q^{14} +1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +3.12311 q^{19} -1.00000 q^{20} -3.12311 q^{21} +1.00000 q^{22} -3.12311 q^{23} +1.00000 q^{24} +1.00000 q^{25} -5.12311 q^{26} -1.00000 q^{27} +3.12311 q^{28} -8.24621 q^{29} -1.00000 q^{30} -10.2462 q^{31} -1.00000 q^{32} +1.00000 q^{33} +1.00000 q^{34} -3.12311 q^{35} +1.00000 q^{36} +2.00000 q^{37} -3.12311 q^{38} -5.12311 q^{39} +1.00000 q^{40} +10.0000 q^{41} +3.12311 q^{42} -7.12311 q^{43} -1.00000 q^{44} -1.00000 q^{45} +3.12311 q^{46} -4.00000 q^{47} -1.00000 q^{48} +2.75379 q^{49} -1.00000 q^{50} +1.00000 q^{51} +5.12311 q^{52} -9.12311 q^{53} +1.00000 q^{54} +1.00000 q^{55} -3.12311 q^{56} -3.12311 q^{57} +8.24621 q^{58} -7.12311 q^{59} +1.00000 q^{60} -2.00000 q^{61} +10.2462 q^{62} +3.12311 q^{63} +1.00000 q^{64} -5.12311 q^{65} -1.00000 q^{66} -4.00000 q^{67} -1.00000 q^{68} +3.12311 q^{69} +3.12311 q^{70} -4.87689 q^{71} -1.00000 q^{72} -1.12311 q^{73} -2.00000 q^{74} -1.00000 q^{75} +3.12311 q^{76} -3.12311 q^{77} +5.12311 q^{78} +11.1231 q^{79} -1.00000 q^{80} +1.00000 q^{81} -10.0000 q^{82} +4.00000 q^{83} -3.12311 q^{84} +1.00000 q^{85} +7.12311 q^{86} +8.24621 q^{87} +1.00000 q^{88} -12.2462 q^{89} +1.00000 q^{90} +16.0000 q^{91} -3.12311 q^{92} +10.2462 q^{93} +4.00000 q^{94} -3.12311 q^{95} +1.00000 q^{96} -8.24621 q^{97} -2.75379 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} - 2 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 - 2 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9} + 2 q^{10} - 2 q^{11} - 2 q^{12} + 2 q^{13} + 2 q^{14} + 2 q^{15} + 2 q^{16} - 2 q^{17} - 2 q^{18} - 2 q^{19} - 2 q^{20} + 2 q^{21} + 2 q^{22} + 2 q^{23} + 2 q^{24} + 2 q^{25} - 2 q^{26} - 2 q^{27} - 2 q^{28} - 2 q^{30} - 4 q^{31} - 2 q^{32} + 2 q^{33} + 2 q^{34} + 2 q^{35} + 2 q^{36} + 4 q^{37} + 2 q^{38} - 2 q^{39} + 2 q^{40} + 20 q^{41} - 2 q^{42} - 6 q^{43} - 2 q^{44} - 2 q^{45} - 2 q^{46} - 8 q^{47} - 2 q^{48} + 22 q^{49} - 2 q^{50} + 2 q^{51} + 2 q^{52} - 10 q^{53} + 2 q^{54} + 2 q^{55} + 2 q^{56} + 2 q^{57} - 6 q^{59} + 2 q^{60} - 4 q^{61} + 4 q^{62} - 2 q^{63} + 2 q^{64} - 2 q^{65} - 2 q^{66} - 8 q^{67} - 2 q^{68} - 2 q^{69} - 2 q^{70} - 18 q^{71} - 2 q^{72} + 6 q^{73} - 4 q^{74} - 2 q^{75} - 2 q^{76} + 2 q^{77} + 2 q^{78} + 14 q^{79} - 2 q^{80} + 2 q^{81} - 20 q^{82} + 8 q^{83} + 2 q^{84} + 2 q^{85} + 6 q^{86} + 2 q^{88} - 8 q^{89} + 2 q^{90} + 32 q^{91} + 2 q^{92} + 4 q^{93} + 8 q^{94} + 2 q^{95} + 2 q^{96} - 22 q^{98} - 2 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9 + 2 * q^10 - 2 * q^11 - 2 * q^12 + 2 * q^13 + 2 * q^14 + 2 * q^15 + 2 * q^16 - 2 * q^17 - 2 * q^18 - 2 * q^19 - 2 * q^20 + 2 * q^21 + 2 * q^22 + 2 * q^23 + 2 * q^24 + 2 * q^25 - 2 * q^26 - 2 * q^27 - 2 * q^28 - 2 * q^30 - 4 * q^31 - 2 * q^32 + 2 * q^33 + 2 * q^34 + 2 * q^35 + 2 * q^36 + 4 * q^37 + 2 * q^38 - 2 * q^39 + 2 * q^40 + 20 * q^41 - 2 * q^42 - 6 * q^43 - 2 * q^44 - 2 * q^45 - 2 * q^46 - 8 * q^47 - 2 * q^48 + 22 * q^49 - 2 * q^50 + 2 * q^51 + 2 * q^52 - 10 * q^53 + 2 * q^54 + 2 * q^55 + 2 * q^56 + 2 * q^57 - 6 * q^59 + 2 * q^60 - 4 * q^61 + 4 * q^62 - 2 * q^63 + 2 * q^64 - 2 * q^65 - 2 * q^66 - 8 * q^67 - 2 * q^68 - 2 * q^69 - 2 * q^70 - 18 * q^71 - 2 * q^72 + 6 * q^73 - 4 * q^74 - 2 * q^75 - 2 * q^76 + 2 * q^77 + 2 * q^78 + 14 * q^79 - 2 * q^80 + 2 * q^81 - 20 * q^82 + 8 * q^83 + 2 * q^84 + 2 * q^85 + 6 * q^86 + 2 * q^88 - 8 * q^89 + 2 * q^90 + 32 * q^91 + 2 * q^92 + 4 * q^93 + 8 * q^94 + 2 * q^95 + 2 * q^96 - 22 * q^98 - 2 * 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
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.00000	0.408248
$7$	3.12311	1.18042	0.590211	−	0.807249i	$-0.299044\pi$
$7$	3.12311	1.18042	0.590211	+	0.807249i	$0.299044\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−1.00000	−0.288675
$13$	5.12311	1.42089	0.710447	−	0.703751i	$-0.248493\pi$
$13$	5.12311	1.42089	0.710447	+	0.703751i	$0.248493\pi$
$14$	−3.12311	−0.834685
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.00000	−0.235702
$19$	3.12311	0.716490	0.358245	−	0.933628i	$-0.383375\pi$
$19$	3.12311	0.716490	0.358245	+	0.933628i	$0.383375\pi$
$20$	−1.00000	−0.223607
$21$	−3.12311	−0.681518
$22$	1.00000	0.213201
$23$	−3.12311	−0.651213	−0.325606	−	0.945505i	$-0.605568\pi$
$23$	−3.12311	−0.651213	−0.325606	+	0.945505i	$0.605568\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	−5.12311	−1.00472
$27$	−1.00000	−0.192450
$28$	3.12311	0.590211
$29$	−8.24621	−1.53128	−0.765641	−	0.643268i	$-0.777578\pi$
$29$	−8.24621	−1.53128	−0.765641	+	0.643268i	$0.777578\pi$
$30$	−1.00000	−0.182574
$31$	−10.2462	−1.84027	−0.920137	−	0.391597i	$-0.871923\pi$
$31$	−10.2462	−1.84027	−0.920137	+	0.391597i	$0.871923\pi$
$32$	−1.00000	−0.176777
$33$	1.00000	0.174078
$34$	1.00000	0.171499
$35$	−3.12311	−0.527901
$36$	1.00000	0.166667
$37$	2.00000	0.328798	0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000	0.328798	0.164399	+	0.986394i	$0.447432\pi$
$38$	−3.12311	−0.506635
$39$	−5.12311	−0.820353
$40$	1.00000	0.158114
$41$	10.0000	1.56174	0.780869	−	0.624695i	$-0.214777\pi$
$41$	10.0000	1.56174	0.780869	+	0.624695i	$0.214777\pi$
$42$	3.12311	0.481906
$43$	−7.12311	−1.08626	−0.543132	−	0.839648i	$-0.682762\pi$
$43$	−7.12311	−1.08626	−0.543132	+	0.839648i	$0.682762\pi$
$44$	−1.00000	−0.150756
$45$	−1.00000	−0.149071
$46$	3.12311	0.460477
$47$	−4.00000	−0.583460	−0.291730	−	0.956501i	$-0.594231\pi$
$47$	−4.00000	−0.583460	−0.291730	+	0.956501i	$0.594231\pi$
$48$	−1.00000	−0.144338
$49$	2.75379	0.393398
$50$	−1.00000	−0.141421
$51$	1.00000	0.140028
$52$	5.12311	0.710447
$53$	−9.12311	−1.25315	−0.626577	−	0.779359i	$-0.715545\pi$
$53$	−9.12311	−1.25315	−0.626577	+	0.779359i	$0.715545\pi$
$54$	1.00000	0.136083
$55$	1.00000	0.134840
$56$	−3.12311	−0.417343
$57$	−3.12311	−0.413665
$58$	8.24621	1.08278
$59$	−7.12311	−0.927349	−0.463675	−	0.886006i	$-0.653469\pi$
$59$	−7.12311	−0.927349	−0.463675	+	0.886006i	$0.653469\pi$
$60$	1.00000	0.129099
$61$	−2.00000	−0.256074	−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000	−0.256074	−0.128037	+	0.991769i	$0.540868\pi$
$62$	10.2462	1.30127
$63$	3.12311	0.393474
$64$	1.00000	0.125000
$65$	−5.12311	−0.635443
$66$	−1.00000	−0.123091
$67$	−4.00000	−0.488678	−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000	−0.488678	−0.244339	+	0.969690i	$0.578571\pi$
$68$	−1.00000	−0.121268
$69$	3.12311	0.375978
$70$	3.12311	0.373283
$71$	−4.87689	−0.578781	−0.289390	−	0.957211i	$-0.593453\pi$
$71$	−4.87689	−0.578781	−0.289390	+	0.957211i	$0.593453\pi$
$72$	−1.00000	−0.117851
$73$	−1.12311	−0.131450	−0.0657248	−	0.997838i	$-0.520936\pi$
$73$	−1.12311	−0.131450	−0.0657248	+	0.997838i	$0.520936\pi$
$74$	−2.00000	−0.232495
$75$	−1.00000	−0.115470
$76$	3.12311	0.358245
$77$	−3.12311	−0.355911
$78$	5.12311	0.580077
$79$	11.1231	1.25145	0.625724	−	0.780045i	$-0.284804\pi$
$79$	11.1231	1.25145	0.625724	+	0.780045i	$0.284804\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−10.0000	−1.10432
$83$	4.00000	0.439057	0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000	0.439057	0.219529	+	0.975606i	$0.429548\pi$
$84$	−3.12311	−0.340759
$85$	1.00000	0.108465
$86$	7.12311	0.768104
$87$	8.24621	0.884087
$88$	1.00000	0.106600
$89$	−12.2462	−1.29810	−0.649048	−	0.760748i	$-0.724833\pi$
$89$	−12.2462	−1.29810	−0.649048	+	0.760748i	$0.724833\pi$
$90$	1.00000	0.105409
$91$	16.0000	1.67726
$92$	−3.12311	−0.325606
$93$	10.2462	1.06248
$94$	4.00000	0.412568
$95$	−3.12311	−0.320424
$96$	1.00000	0.102062
$97$	−8.24621	−0.837276	−0.418638	−	0.908153i	$-0.637492\pi$
$97$	−8.24621	−0.837276	−0.418638	+	0.908153i	$0.637492\pi$
$98$	−2.75379	−0.278175
$99$	−1.00000	−0.100504
$100$	1.00000	0.100000
$101$	8.24621	0.820529	0.410264	−	0.911967i	$-0.365436\pi$
$101$	8.24621	0.820529	0.410264	+	0.911967i	$0.365436\pi$
$102$	−1.00000	−0.0990148
$103$	8.00000	0.788263	0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000	0.788263	0.394132	+	0.919054i	$0.371045\pi$
$104$	−5.12311	−0.502362
$105$	3.12311	0.304784
$106$	9.12311	0.886114
$107$	−1.75379	−0.169545	−0.0847726	−	0.996400i	$-0.527016\pi$
$107$	−1.75379	−0.169545	−0.0847726	+	0.996400i	$0.527016\pi$
$108$	−1.00000	−0.0962250
$109$	4.24621	0.406713	0.203357	−	0.979105i	$-0.434815\pi$
$109$	4.24621	0.406713	0.203357	+	0.979105i	$0.434815\pi$
$110$	−1.00000	−0.0953463
$111$	−2.00000	−0.189832
$112$	3.12311	0.295106
$113$	−6.87689	−0.646924	−0.323462	−	0.946241i	$-0.604847\pi$
$113$	−6.87689	−0.646924	−0.323462	+	0.946241i	$0.604847\pi$
$114$	3.12311	0.292506
$115$	3.12311	0.291231
$116$	−8.24621	−0.765641
$117$	5.12311	0.473631
$118$	7.12311	0.655735
$119$	−3.12311	−0.286295
$120$	−1.00000	−0.0912871
$121$	1.00000	0.0909091
$122$	2.00000	0.181071
$123$	−10.0000	−0.901670
$124$	−10.2462	−0.920137
$125$	−1.00000	−0.0894427
$126$	−3.12311	−0.278228
$127$	8.00000	0.709885	0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000	0.709885	0.354943	+	0.934888i	$0.384500\pi$
$128$	−1.00000	−0.0883883
$129$	7.12311	0.627154
$130$	5.12311	0.449326
$131$	−4.00000	−0.349482	−0.174741	−	0.984614i	$-0.555909\pi$
$131$	−4.00000	−0.349482	−0.174741	+	0.984614i	$0.555909\pi$
$132$	1.00000	0.0870388
$133$	9.75379	0.845761
$134$	4.00000	0.345547
$135$	1.00000	0.0860663
$136$	1.00000	0.0857493
$137$	20.2462	1.72975	0.864875	−	0.501987i	$-0.167397\pi$
$137$	20.2462	1.72975	0.864875	+	0.501987i	$0.167397\pi$
$138$	−3.12311	−0.265856
$139$	−12.0000	−1.01783	−0.508913	−	0.860818i	$-0.669953\pi$
$139$	−12.0000	−1.01783	−0.508913	+	0.860818i	$0.669953\pi$
$140$	−3.12311	−0.263951
$141$	4.00000	0.336861
$142$	4.87689	0.409260
$143$	−5.12311	−0.428416
$144$	1.00000	0.0833333
$145$	8.24621	0.684811
$146$	1.12311	0.0929489
$147$	−2.75379	−0.227129
$148$	2.00000	0.164399
$149$	18.0000	1.47462	0.737309	−	0.675556i	$-0.236096\pi$
$149$	18.0000	1.47462	0.737309	+	0.675556i	$0.236096\pi$
$150$	1.00000	0.0816497
$151$	−24.4924	−1.99317	−0.996583	−	0.0826029i	$-0.973677\pi$
$151$	−24.4924	−1.99317	−0.996583	+	0.0826029i	$0.973677\pi$
$152$	−3.12311	−0.253317
$153$	−1.00000	−0.0808452
$154$	3.12311	0.251667
$155$	10.2462	0.822995
$156$	−5.12311	−0.410177
$157$	−16.2462	−1.29659	−0.648294	−	0.761390i	$-0.724517\pi$
$157$	−16.2462	−1.29659	−0.648294	+	0.761390i	$0.724517\pi$
$158$	−11.1231	−0.884907
$159$	9.12311	0.723509
$160$	1.00000	0.0790569
$161$	−9.75379	−0.768706
$162$	−1.00000	−0.0785674
$163$	−16.4924	−1.29179	−0.645893	−	0.763428i	$-0.723515\pi$
$163$	−16.4924	−1.29179	−0.645893	+	0.763428i	$0.723515\pi$
$164$	10.0000	0.780869
$165$	−1.00000	−0.0778499
$166$	−4.00000	−0.310460
$167$	−18.2462	−1.41193	−0.705967	−	0.708245i	$-0.749487\pi$
$167$	−18.2462	−1.41193	−0.705967	+	0.708245i	$0.749487\pi$
$168$	3.12311	0.240953
$169$	13.2462	1.01894
$170$	−1.00000	−0.0766965
$171$	3.12311	0.238830
$172$	−7.12311	−0.543132
$173$	8.24621	0.626948	0.313474	−	0.949597i	$-0.398507\pi$
$173$	8.24621	0.626948	0.313474	+	0.949597i	$0.398507\pi$
$174$	−8.24621	−0.625144
$175$	3.12311	0.236085
$176$	−1.00000	−0.0753778
$177$	7.12311	0.535405
$178$	12.2462	0.917892
$179$	−0.876894	−0.0655422	−0.0327711	−	0.999463i	$-0.510433\pi$
$179$	−0.876894	−0.0655422	−0.0327711	+	0.999463i	$0.510433\pi$
$180$	−1.00000	−0.0745356
$181$	−16.2462	−1.20757	−0.603786	−	0.797147i	$-0.706342\pi$
$181$	−16.2462	−1.20757	−0.603786	+	0.797147i	$0.706342\pi$
$182$	−16.0000	−1.18600
$183$	2.00000	0.147844
$184$	3.12311	0.230238
$185$	−2.00000	−0.147043
$186$	−10.2462	−0.751289
$187$	1.00000	0.0731272
$188$	−4.00000	−0.291730
$189$	−3.12311	−0.227173
$190$	3.12311	0.226574
$191$	16.0000	1.15772	0.578860	−	0.815427i	$-0.303498\pi$
$191$	16.0000	1.15772	0.578860	+	0.815427i	$0.303498\pi$
$192$	−1.00000	−0.0721688
$193$	−18.8769	−1.35879	−0.679394	−	0.733773i	$-0.737757\pi$
$193$	−18.8769	−1.35879	−0.679394	+	0.733773i	$0.737757\pi$
$194$	8.24621	0.592043
$195$	5.12311	0.366873
$196$	2.75379	0.196699
$197$	6.49242	0.462566	0.231283	−	0.972887i	$-0.425708\pi$
$197$	6.49242	0.462566	0.231283	+	0.972887i	$0.425708\pi$
$198$	1.00000	0.0710669
$199$	18.2462	1.29344	0.646720	−	0.762728i	$-0.276140\pi$
$199$	18.2462	1.29344	0.646720	+	0.762728i	$0.276140\pi$
$200$	−1.00000	−0.0707107
$201$	4.00000	0.282138
$202$	−8.24621	−0.580201
$203$	−25.7538	−1.80756
$204$	1.00000	0.0700140
$205$	−10.0000	−0.698430
$206$	−8.00000	−0.557386
$207$	−3.12311	−0.217071
$208$	5.12311	0.355223
$209$	−3.12311	−0.216030
$210$	−3.12311	−0.215515
$211$	24.4924	1.68613	0.843064	−	0.537813i	$-0.180749\pi$
$211$	24.4924	1.68613	0.843064	+	0.537813i	$0.180749\pi$
$212$	−9.12311	−0.626577
$213$	4.87689	0.334159
$214$	1.75379	0.119887
$215$	7.12311	0.485792
$216$	1.00000	0.0680414
$217$	−32.0000	−2.17230
$218$	−4.24621	−0.287590
$219$	1.12311	0.0758924
$220$	1.00000	0.0674200
$221$	−5.12311	−0.344617
$222$	2.00000	0.134231
$223$	−28.4924	−1.90799	−0.953997	−	0.299817i	$-0.903075\pi$
$223$	−28.4924	−1.90799	−0.953997	+	0.299817i	$0.903075\pi$
$224$	−3.12311	−0.208671
$225$	1.00000	0.0666667
$226$	6.87689	0.457444
$227$	−1.75379	−0.116403	−0.0582015	−	0.998305i	$-0.518537\pi$
$227$	−1.75379	−0.116403	−0.0582015	+	0.998305i	$0.518537\pi$
$228$	−3.12311	−0.206833
$229$	−0.246211	−0.0162701	−0.00813505	−	0.999967i	$-0.502589\pi$
$229$	−0.246211	−0.0162701	−0.00813505	+	0.999967i	$0.502589\pi$
$230$	−3.12311	−0.205931
$231$	3.12311	0.205485
$232$	8.24621	0.541390
$233$	−0.246211	−0.0161298	−0.00806492	−	0.999967i	$-0.502567\pi$
$233$	−0.246211	−0.0161298	−0.00806492	+	0.999967i	$0.502567\pi$
$234$	−5.12311	−0.334908
$235$	4.00000	0.260931
$236$	−7.12311	−0.463675
$237$	−11.1231	−0.722523
$238$	3.12311	0.202441
$239$	4.49242	0.290591	0.145295	−	0.989388i	$-0.453587\pi$
$239$	4.49242	0.290591	0.145295	+	0.989388i	$0.453587\pi$
$240$	1.00000	0.0645497
$241$	29.1231	1.87598	0.937992	−	0.346657i	$-0.112683\pi$
$241$	29.1231	1.87598	0.937992	+	0.346657i	$0.112683\pi$
$242$	−1.00000	−0.0642824
$243$	−1.00000	−0.0641500
$244$	−2.00000	−0.128037
$245$	−2.75379	−0.175933
$246$	10.0000	0.637577
$247$	16.0000	1.01806
$248$	10.2462	0.650635
$249$	−4.00000	−0.253490
$250$	1.00000	0.0632456
$251$	2.63068	0.166047	0.0830236	−	0.996548i	$-0.473542\pi$
$251$	2.63068	0.166047	0.0830236	+	0.996548i	$0.473542\pi$
$252$	3.12311	0.196737
$253$	3.12311	0.196348
$254$	−8.00000	−0.501965
$255$	−1.00000	−0.0626224
$256$	1.00000	0.0625000
$257$	−0.246211	−0.0153582	−0.00767912	−	0.999971i	$-0.502444\pi$
$257$	−0.246211	−0.0153582	−0.00767912	+	0.999971i	$0.502444\pi$
$258$	−7.12311	−0.443465
$259$	6.24621	0.388121
$260$	−5.12311	−0.317722
$261$	−8.24621	−0.510428
$262$	4.00000	0.247121
$263$	24.0000	1.47990	0.739952	−	0.672660i	$-0.234848\pi$
$263$	24.0000	1.47990	0.739952	+	0.672660i	$0.234848\pi$
$264$	−1.00000	−0.0615457
$265$	9.12311	0.560428
$266$	−9.75379	−0.598043
$267$	12.2462	0.749456
$268$	−4.00000	−0.244339
$269$	2.00000	0.121942	0.0609711	−	0.998140i	$-0.480580\pi$
$269$	2.00000	0.121942	0.0609711	+	0.998140i	$0.480580\pi$
$270$	−1.00000	−0.0608581
$271$	18.2462	1.10838	0.554189	−	0.832391i	$-0.313028\pi$
$271$	18.2462	1.10838	0.554189	+	0.832391i	$0.313028\pi$
$272$	−1.00000	−0.0606339
$273$	−16.0000	−0.968364
$274$	−20.2462	−1.22312
$275$	−1.00000	−0.0603023
$276$	3.12311	0.187989
$277$	−28.7386	−1.72674	−0.863369	−	0.504574i	$-0.831650\pi$
$277$	−28.7386	−1.72674	−0.863369	+	0.504574i	$0.831650\pi$
$278$	12.0000	0.719712
$279$	−10.2462	−0.613425
$280$	3.12311	0.186641
$281$	4.24621	0.253308	0.126654	−	0.991947i	$-0.459576\pi$
$281$	4.24621	0.253308	0.126654	+	0.991947i	$0.459576\pi$
$282$	−4.00000	−0.238197
$283$	−8.49242	−0.504822	−0.252411	−	0.967620i	$-0.581224\pi$
$283$	−8.49242	−0.504822	−0.252411	+	0.967620i	$0.581224\pi$
$284$	−4.87689	−0.289390
$285$	3.12311	0.184997
$286$	5.12311	0.302936
$287$	31.2311	1.84351
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	−8.24621	−0.484234
$291$	8.24621	0.483401
$292$	−1.12311	−0.0657248
$293$	−18.4924	−1.08034	−0.540169	−	0.841556i	$-0.681640\pi$
$293$	−18.4924	−1.08034	−0.540169	+	0.841556i	$0.681640\pi$
$294$	2.75379	0.160604
$295$	7.12311	0.414723
$296$	−2.00000	−0.116248
$297$	1.00000	0.0580259
$298$	−18.0000	−1.04271
$299$	−16.0000	−0.925304
$300$	−1.00000	−0.0577350
$301$	−22.2462	−1.28225
$302$	24.4924	1.40938
$303$	−8.24621	−0.473732
$304$	3.12311	0.179122
$305$	2.00000	0.114520
$306$	1.00000	0.0571662
$307$	11.6155	0.662933	0.331467	−	0.943467i	$-0.392457\pi$
$307$	11.6155	0.662933	0.331467	+	0.943467i	$0.392457\pi$
$308$	−3.12311	−0.177955
$309$	−8.00000	−0.455104
$310$	−10.2462	−0.581946
$311$	−20.8769	−1.18382	−0.591910	−	0.806004i	$-0.701626\pi$
$311$	−20.8769	−1.18382	−0.591910	+	0.806004i	$0.701626\pi$
$312$	5.12311	0.290039
$313$	−32.2462	−1.82266	−0.911332	−	0.411673i	$-0.864945\pi$
$313$	−32.2462	−1.82266	−0.911332	+	0.411673i	$0.864945\pi$
$314$	16.2462	0.916827
$315$	−3.12311	−0.175967
$316$	11.1231	0.625724
$317$	−7.75379	−0.435496	−0.217748	−	0.976005i	$-0.569871\pi$
$317$	−7.75379	−0.435496	−0.217748	+	0.976005i	$0.569871\pi$
$318$	−9.12311	−0.511598
$319$	8.24621	0.461699
$320$	−1.00000	−0.0559017
$321$	1.75379	0.0978869
$322$	9.75379	0.543557
$323$	−3.12311	−0.173774
$324$	1.00000	0.0555556
$325$	5.12311	0.284179
$326$	16.4924	0.913431
$327$	−4.24621	−0.234816
$328$	−10.0000	−0.552158
$329$	−12.4924	−0.688730
$330$	1.00000	0.0550482
$331$	−20.0000	−1.09930	−0.549650	−	0.835395i	$-0.685239\pi$
$331$	−20.0000	−1.09930	−0.549650	+	0.835395i	$0.685239\pi$
$332$	4.00000	0.219529
$333$	2.00000	0.109599
$334$	18.2462	0.998388
$335$	4.00000	0.218543
$336$	−3.12311	−0.170379
$337$	3.36932	0.183538	0.0917692	−	0.995780i	$-0.470748\pi$
$337$	3.36932	0.183538	0.0917692	+	0.995780i	$0.470748\pi$
$338$	−13.2462	−0.720499
$339$	6.87689	0.373502
$340$	1.00000	0.0542326
$341$	10.2462	0.554863
$342$	−3.12311	−0.168878
$343$	−13.2614	−0.716046
$344$	7.12311	0.384052
$345$	−3.12311	−0.168142
$346$	−8.24621	−0.443319
$347$	−14.2462	−0.764777	−0.382388	−	0.924002i	$-0.624898\pi$
$347$	−14.2462	−0.764777	−0.382388	+	0.924002i	$0.624898\pi$
$348$	8.24621	0.442043
$349$	18.8769	1.01046	0.505228	−	0.862986i	$-0.331408\pi$
$349$	18.8769	1.01046	0.505228	+	0.862986i	$0.331408\pi$
$350$	−3.12311	−0.166937
$351$	−5.12311	−0.273451
$352$	1.00000	0.0533002
$353$	−24.2462	−1.29050	−0.645248	−	0.763973i	$-0.723246\pi$
$353$	−24.2462	−1.29050	−0.645248	+	0.763973i	$0.723246\pi$
$354$	−7.12311	−0.378589
$355$	4.87689	0.258839
$356$	−12.2462	−0.649048
$357$	3.12311	0.165292
$358$	0.876894	0.0463453
$359$	16.0000	0.844448	0.422224	−	0.906492i	$-0.361250\pi$
$359$	16.0000	0.844448	0.422224	+	0.906492i	$0.361250\pi$
$360$	1.00000	0.0527046
$361$	−9.24621	−0.486643
$362$	16.2462	0.853882
$363$	−1.00000	−0.0524864
$364$	16.0000	0.838628
$365$	1.12311	0.0587860
$366$	−2.00000	−0.104542
$367$	16.0000	0.835193	0.417597	−	0.908633i	$-0.362873\pi$
$367$	16.0000	0.835193	0.417597	+	0.908633i	$0.362873\pi$
$368$	−3.12311	−0.162803
$369$	10.0000	0.520579
$370$	2.00000	0.103975
$371$	−28.4924	−1.47925
$372$	10.2462	0.531241
$373$	33.6155	1.74055	0.870273	−	0.492570i	$-0.163942\pi$
$373$	33.6155	1.74055	0.870273	+	0.492570i	$0.163942\pi$
$374$	−1.00000	−0.0517088
$375$	1.00000	0.0516398
$376$	4.00000	0.206284
$377$	−42.2462	−2.17579
$378$	3.12311	0.160635
$379$	−6.24621	−0.320846	−0.160423	−	0.987048i	$-0.551286\pi$
$379$	−6.24621	−0.320846	−0.160423	+	0.987048i	$0.551286\pi$
$380$	−3.12311	−0.160212
$381$	−8.00000	−0.409852
$382$	−16.0000	−0.818631
$383$	−2.24621	−0.114776	−0.0573880	−	0.998352i	$-0.518277\pi$
$383$	−2.24621	−0.114776	−0.0573880	+	0.998352i	$0.518277\pi$
$384$	1.00000	0.0510310
$385$	3.12311	0.159168
$386$	18.8769	0.960809
$387$	−7.12311	−0.362088
$388$	−8.24621	−0.418638
$389$	−9.61553	−0.487527	−0.243763	−	0.969835i	$-0.578382\pi$
$389$	−9.61553	−0.487527	−0.243763	+	0.969835i	$0.578382\pi$
$390$	−5.12311	−0.259419
$391$	3.12311	0.157942
$392$	−2.75379	−0.139087
$393$	4.00000	0.201773
$394$	−6.49242	−0.327084
$395$	−11.1231	−0.559664
$396$	−1.00000	−0.0502519
$397$	−16.7386	−0.840088	−0.420044	−	0.907504i	$-0.637985\pi$
$397$	−16.7386	−0.840088	−0.420044	+	0.907504i	$0.637985\pi$
$398$	−18.2462	−0.914600
$399$	−9.75379	−0.488300
$400$	1.00000	0.0500000
$401$	17.1231	0.855087	0.427544	−	0.903995i	$-0.359379\pi$
$401$	17.1231	0.855087	0.427544	+	0.903995i	$0.359379\pi$
$402$	−4.00000	−0.199502
$403$	−52.4924	−2.61483
$404$	8.24621	0.410264
$405$	−1.00000	−0.0496904
$406$	25.7538	1.27814
$407$	−2.00000	−0.0991363
$408$	−1.00000	−0.0495074
$409$	−20.2462	−1.00111	−0.500555	−	0.865705i	$-0.666871\pi$
$409$	−20.2462	−1.00111	−0.500555	+	0.865705i	$0.666871\pi$
$410$	10.0000	0.493865
$411$	−20.2462	−0.998672
$412$	8.00000	0.394132
$413$	−22.2462	−1.09466
$414$	3.12311	0.153492
$415$	−4.00000	−0.196352
$416$	−5.12311	−0.251181
$417$	12.0000	0.587643
$418$	3.12311	0.152756
$419$	−4.00000	−0.195413	−0.0977064	−	0.995215i	$-0.531151\pi$
$419$	−4.00000	−0.195413	−0.0977064	+	0.995215i	$0.531151\pi$
$420$	3.12311	0.152392
$421$	−10.0000	−0.487370	−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000	−0.487370	−0.243685	+	0.969854i	$0.578356\pi$
$422$	−24.4924	−1.19227
$423$	−4.00000	−0.194487
$424$	9.12311	0.443057
$425$	−1.00000	−0.0485071
$426$	−4.87689	−0.236286
$427$	−6.24621	−0.302275
$428$	−1.75379	−0.0847726
$429$	5.12311	0.247346
$430$	−7.12311	−0.343507
$431$	−30.2462	−1.45691	−0.728454	−	0.685094i	$-0.759761\pi$
$431$	−30.2462	−1.45691	−0.728454	+	0.685094i	$0.759761\pi$
$432$	−1.00000	−0.0481125
$433$	−12.2462	−0.588515	−0.294258	−	0.955726i	$-0.595072\pi$
$433$	−12.2462	−0.588515	−0.294258	+	0.955726i	$0.595072\pi$
$434$	32.0000	1.53605
$435$	−8.24621	−0.395376
$436$	4.24621	0.203357
$437$	−9.75379	−0.466587
$438$	−1.12311	−0.0536641
$439$	3.12311	0.149058	0.0745288	−	0.997219i	$-0.476255\pi$
$439$	3.12311	0.149058	0.0745288	+	0.997219i	$0.476255\pi$
$440$	−1.00000	−0.0476731
$441$	2.75379	0.131133
$442$	5.12311	0.243681
$443$	−28.8769	−1.37198	−0.685991	−	0.727610i	$-0.740631\pi$
$443$	−28.8769	−1.37198	−0.685991	+	0.727610i	$0.740631\pi$
$444$	−2.00000	−0.0949158
$445$	12.2462	0.580526
$446$	28.4924	1.34916
$447$	−18.0000	−0.851371
$448$	3.12311	0.147553
$449$	2.87689	0.135769	0.0678845	−	0.997693i	$-0.478375\pi$
$449$	2.87689	0.135769	0.0678845	+	0.997693i	$0.478375\pi$
$450$	−1.00000	−0.0471405
$451$	−10.0000	−0.470882
$452$	−6.87689	−0.323462
$453$	24.4924	1.15075
$454$	1.75379	0.0823094
$455$	−16.0000	−0.750092
$456$	3.12311	0.146253
$457$	34.4924	1.61349	0.806744	−	0.590901i	$-0.201228\pi$
$457$	34.4924	1.61349	0.806744	+	0.590901i	$0.201228\pi$
$458$	0.246211	0.0115047
$459$	1.00000	0.0466760
$460$	3.12311	0.145616
$461$	−26.4924	−1.23388	−0.616938	−	0.787012i	$-0.711627\pi$
$461$	−26.4924	−1.23388	−0.616938	+	0.787012i	$0.711627\pi$
$462$	−3.12311	−0.145300
$463$	0	0		−	1.00000i	$-0.5\pi$
$463$	0	0			1.00000i	$0.5\pi$
$464$	−8.24621	−0.382821
$465$	−10.2462	−0.475157
$466$	0.246211	0.0114055
$467$	−28.8769	−1.33626	−0.668132	−	0.744043i	$-0.732906\pi$
$467$	−28.8769	−1.33626	−0.668132	+	0.744043i	$0.732906\pi$
$468$	5.12311	0.236816
$469$	−12.4924	−0.576846
$470$	−4.00000	−0.184506
$471$	16.2462	0.748586
$472$	7.12311	0.327868
$473$	7.12311	0.327521
$474$	11.1231	0.510901
$475$	3.12311	0.143298
$476$	−3.12311	−0.143147
$477$	−9.12311	−0.417718
$478$	−4.49242	−0.205479
$479$	12.4924	0.570793	0.285397	−	0.958409i	$-0.407875\pi$
$479$	12.4924	0.570793	0.285397	+	0.958409i	$0.407875\pi$
$480$	−1.00000	−0.0456435
$481$	10.2462	0.467187
$482$	−29.1231	−1.32652
$483$	9.75379	0.443813
$484$	1.00000	0.0454545
$485$	8.24621	0.374441
$486$	1.00000	0.0453609
$487$	3.50758	0.158944	0.0794718	−	0.996837i	$-0.474677\pi$
$487$	3.50758	0.158944	0.0794718	+	0.996837i	$0.474677\pi$
$488$	2.00000	0.0905357
$489$	16.4924	0.745813
$490$	2.75379	0.124403
$491$	14.7386	0.665145	0.332573	−	0.943078i	$-0.392083\pi$
$491$	14.7386	0.665145	0.332573	+	0.943078i	$0.392083\pi$
$492$	−10.0000	−0.450835
$493$	8.24621	0.371391
$494$	−16.0000	−0.719874
$495$	1.00000	0.0449467
$496$	−10.2462	−0.460068
$497$	−15.2311	−0.683206
$498$	4.00000	0.179244
$499$	14.2462	0.637748	0.318874	−	0.947797i	$-0.396695\pi$
$499$	14.2462	0.637748	0.318874	+	0.947797i	$0.396695\pi$
$500$	−1.00000	−0.0447214
$501$	18.2462	0.815181
$502$	−2.63068	−0.117413
$503$	−40.4924	−1.80547	−0.902734	−	0.430199i	$-0.858443\pi$
$503$	−40.4924	−1.80547	−0.902734	+	0.430199i	$0.858443\pi$
$504$	−3.12311	−0.139114
$505$	−8.24621	−0.366952
$506$	−3.12311	−0.138839
$507$	−13.2462	−0.588285
$508$	8.00000	0.354943
$509$	23.3693	1.03583	0.517913	−	0.855433i	$-0.326709\pi$
$509$	23.3693	1.03583	0.517913	+	0.855433i	$0.326709\pi$
$510$	1.00000	0.0442807
$511$	−3.50758	−0.155166
$512$	−1.00000	−0.0441942
$513$	−3.12311	−0.137888
$514$	0.246211	0.0108599
$515$	−8.00000	−0.352522
$516$	7.12311	0.313577
$517$	4.00000	0.175920
$518$	−6.24621	−0.274443
$519$	−8.24621	−0.361968
$520$	5.12311	0.224663
$521$	−15.8617	−0.694915	−0.347458	−	0.937696i	$-0.612955\pi$
$521$	−15.8617	−0.694915	−0.347458	+	0.937696i	$0.612955\pi$
$522$	8.24621	0.360927
$523$	2.63068	0.115032	0.0575159	−	0.998345i	$-0.481682\pi$
$523$	2.63068	0.115032	0.0575159	+	0.998345i	$0.481682\pi$
$524$	−4.00000	−0.174741
$525$	−3.12311	−0.136304
$526$	−24.0000	−1.04645
$527$	10.2462	0.446332
$528$	1.00000	0.0435194
$529$	−13.2462	−0.575922
$530$	−9.12311	−0.396282
$531$	−7.12311	−0.309116
$532$	9.75379	0.422880
$533$	51.2311	2.21906
$534$	−12.2462	−0.529945
$535$	1.75379	0.0758229
$536$	4.00000	0.172774
$537$	0.876894	0.0378408
$538$	−2.00000	−0.0862261
$539$	−2.75379	−0.118614
$540$	1.00000	0.0430331
$541$	10.4924	0.451104	0.225552	−	0.974231i	$-0.427581\pi$
$541$	10.4924	0.451104	0.225552	+	0.974231i	$0.427581\pi$
$542$	−18.2462	−0.783742
$543$	16.2462	0.697192
$544$	1.00000	0.0428746
$545$	−4.24621	−0.181888
$546$	16.0000	0.684737
$547$	−22.7386	−0.972234	−0.486117	−	0.873894i	$-0.661587\pi$
$547$	−22.7386	−0.972234	−0.486117	+	0.873894i	$0.661587\pi$
$548$	20.2462	0.864875
$549$	−2.00000	−0.0853579
$550$	1.00000	0.0426401
$551$	−25.7538	−1.09715
$552$	−3.12311	−0.132928
$553$	34.7386	1.47724
$554$	28.7386	1.22099
$555$	2.00000	0.0848953
$556$	−12.0000	−0.508913
$557$	30.4924	1.29201	0.646003	−	0.763335i	$-0.276439\pi$
$557$	30.4924	1.29201	0.646003	+	0.763335i	$0.276439\pi$
$558$	10.2462	0.433757
$559$	−36.4924	−1.54347
$560$	−3.12311	−0.131975
$561$	−1.00000	−0.0422200
$562$	−4.24621	−0.179116
$563$	−0.492423	−0.0207531	−0.0103766	−	0.999946i	$-0.503303\pi$
$563$	−0.492423	−0.0207531	−0.0103766	+	0.999946i	$0.503303\pi$
$564$	4.00000	0.168430
$565$	6.87689	0.289313
$566$	8.49242	0.356963
$567$	3.12311	0.131158
$568$	4.87689	0.204630
$569$	−10.0000	−0.419222	−0.209611	−	0.977785i	$-0.567220\pi$
$569$	−10.0000	−0.419222	−0.209611	+	0.977785i	$0.567220\pi$
$570$	−3.12311	−0.130812
$571$	−28.0000	−1.17176	−0.585882	−	0.810397i	$-0.699252\pi$
$571$	−28.0000	−1.17176	−0.585882	+	0.810397i	$0.699252\pi$
$572$	−5.12311	−0.214208
$573$	−16.0000	−0.668410
$574$	−31.2311	−1.30356
$575$	−3.12311	−0.130243
$576$	1.00000	0.0416667
$577$	8.24621	0.343294	0.171647	−	0.985158i	$-0.445091\pi$
$577$	8.24621	0.343294	0.171647	+	0.985158i	$0.445091\pi$
$578$	−1.00000	−0.0415945
$579$	18.8769	0.784497
$580$	8.24621	0.342405
$581$	12.4924	0.518273
$582$	−8.24621	−0.341816
$583$	9.12311	0.377840
$584$	1.12311	0.0464744
$585$	−5.12311	−0.211814
$586$	18.4924	0.763915
$587$	−12.8769	−0.531486	−0.265743	−	0.964044i	$-0.585617\pi$
$587$	−12.8769	−0.531486	−0.265743	+	0.964044i	$0.585617\pi$
$588$	−2.75379	−0.113564
$589$	−32.0000	−1.31854
$590$	−7.12311	−0.293254
$591$	−6.49242	−0.267063
$592$	2.00000	0.0821995
$593$	32.7386	1.34441	0.672207	−	0.740363i	$-0.265346\pi$
$593$	32.7386	1.34441	0.672207	+	0.740363i	$0.265346\pi$
$594$	−1.00000	−0.0410305
$595$	3.12311	0.128035
$596$	18.0000	0.737309
$597$	−18.2462	−0.746768
$598$	16.0000	0.654289
$599$	24.9848	1.02085	0.510427	−	0.859921i	$-0.329488\pi$
$599$	24.9848	1.02085	0.510427	+	0.859921i	$0.329488\pi$
$600$	1.00000	0.0408248
$601$	39.8617	1.62599	0.812997	−	0.582268i	$-0.197834\pi$
$601$	39.8617	1.62599	0.812997	+	0.582268i	$0.197834\pi$
$602$	22.2462	0.906688
$603$	−4.00000	−0.162893
$604$	−24.4924	−0.996583
$605$	−1.00000	−0.0406558
$606$	8.24621	0.334979
$607$	−41.3693	−1.67913	−0.839564	−	0.543260i	$-0.817190\pi$
$607$	−41.3693	−1.67913	−0.839564	+	0.543260i	$0.817190\pi$
$608$	−3.12311	−0.126659
$609$	25.7538	1.04360
$610$	−2.00000	−0.0809776
$611$	−20.4924	−0.829035
$612$	−1.00000	−0.0404226
$613$	−47.3693	−1.91323	−0.956614	−	0.291357i	$-0.905893\pi$
$613$	−47.3693	−1.91323	−0.956614	+	0.291357i	$0.905893\pi$
$614$	−11.6155	−0.468765
$615$	10.0000	0.403239
$616$	3.12311	0.125834
$617$	−17.6155	−0.709174	−0.354587	−	0.935023i	$-0.615379\pi$
$617$	−17.6155	−0.709174	−0.354587	+	0.935023i	$0.615379\pi$
$618$	8.00000	0.321807
$619$	42.7386	1.71781	0.858905	−	0.512134i	$-0.171145\pi$
$619$	42.7386	1.71781	0.858905	+	0.512134i	$0.171145\pi$
$620$	10.2462	0.411498
$621$	3.12311	0.125326
$622$	20.8769	0.837087
$623$	−38.2462	−1.53230
$624$	−5.12311	−0.205088
$625$	1.00000	0.0400000
$626$	32.2462	1.28882
$627$	3.12311	0.124725
$628$	−16.2462	−0.648294
$629$	−2.00000	−0.0797452
$630$	3.12311	0.124428
$631$	−3.50758	−0.139634	−0.0698172	−	0.997560i	$-0.522242\pi$
$631$	−3.50758	−0.139634	−0.0698172	+	0.997560i	$0.522242\pi$
$632$	−11.1231	−0.442453
$633$	−24.4924	−0.973486
$634$	7.75379	0.307942
$635$	−8.00000	−0.317470
$636$	9.12311	0.361755
$637$	14.1080	0.558977
$638$	−8.24621	−0.326471
$639$	−4.87689	−0.192927
$640$	1.00000	0.0395285
$641$	−2.38447	−0.0941810	−0.0470905	−	0.998891i	$-0.514995\pi$
$641$	−2.38447	−0.0941810	−0.0470905	+	0.998891i	$0.514995\pi$
$642$	−1.75379	−0.0692165
$643$	−8.49242	−0.334908	−0.167454	−	0.985880i	$-0.553555\pi$
$643$	−8.49242	−0.334908	−0.167454	+	0.985880i	$0.553555\pi$
$644$	−9.75379	−0.384353
$645$	−7.12311	−0.280472
$646$	3.12311	0.122877
$647$	8.49242	0.333872	0.166936	−	0.985968i	$-0.446613\pi$
$647$	8.49242	0.333872	0.166936	+	0.985968i	$0.446613\pi$
$648$	−1.00000	−0.0392837
$649$	7.12311	0.279606
$650$	−5.12311	−0.200945
$651$	32.0000	1.25418
$652$	−16.4924	−0.645893
$653$	14.4924	0.567132	0.283566	−	0.958953i	$-0.408482\pi$
$653$	14.4924	0.567132	0.283566	+	0.958953i	$0.408482\pi$
$654$	4.24621	0.166040
$655$	4.00000	0.156293
$656$	10.0000	0.390434
$657$	−1.12311	−0.0438165
$658$	12.4924	0.487005
$659$	−22.7386	−0.885771	−0.442886	−	0.896578i	$-0.646045\pi$
$659$	−22.7386	−0.885771	−0.442886	+	0.896578i	$0.646045\pi$
$660$	−1.00000	−0.0389249
$661$	−12.7386	−0.495475	−0.247738	−	0.968827i	$-0.579687\pi$
$661$	−12.7386	−0.495475	−0.247738	+	0.968827i	$0.579687\pi$
$662$	20.0000	0.777322
$663$	5.12311	0.198965
$664$	−4.00000	−0.155230
$665$	−9.75379	−0.378236
$666$	−2.00000	−0.0774984
$667$	25.7538	0.997191
$668$	−18.2462	−0.705967
$669$	28.4924	1.10158
$670$	−4.00000	−0.154533
$671$	2.00000	0.0772091
$672$	3.12311	0.120476
$673$	29.1231	1.12261	0.561307	−	0.827608i	$-0.310299\pi$
$673$	29.1231	1.12261	0.561307	+	0.827608i	$0.310299\pi$
$674$	−3.36932	−0.129781
$675$	−1.00000	−0.0384900
$676$	13.2462	0.509470
$677$	−14.0000	−0.538064	−0.269032	−	0.963131i	$-0.586704\pi$
$677$	−14.0000	−0.538064	−0.269032	+	0.963131i	$0.586704\pi$
$678$	−6.87689	−0.264106
$679$	−25.7538	−0.988340
$680$	−1.00000	−0.0383482
$681$	1.75379	0.0672053
$682$	−10.2462	−0.392348
$683$	28.9848	1.10907	0.554537	−	0.832159i	$-0.312895\pi$
$683$	28.9848	1.10907	0.554537	+	0.832159i	$0.312895\pi$
$684$	3.12311	0.119415
$685$	−20.2462	−0.773568
$686$	13.2614	0.506321
$687$	0.246211	0.00939355
$688$	−7.12311	−0.271566
$689$	−46.7386	−1.78060
$690$	3.12311	0.118895
$691$	−46.2462	−1.75929	−0.879644	−	0.475632i	$-0.842219\pi$
$691$	−46.2462	−1.75929	−0.879644	+	0.475632i	$0.842219\pi$
$692$	8.24621	0.313474
$693$	−3.12311	−0.118637
$694$	14.2462	0.540779
$695$	12.0000	0.455186
$696$	−8.24621	−0.312572
$697$	−10.0000	−0.378777
$698$	−18.8769	−0.714501
$699$	0.246211	0.00931256
$700$	3.12311	0.118042
$701$	−46.0000	−1.73740	−0.868698	−	0.495342i	$-0.835043\pi$
$701$	−46.0000	−1.73740	−0.868698	+	0.495342i	$0.835043\pi$
$702$	5.12311	0.193359
$703$	6.24621	0.235580
$704$	−1.00000	−0.0376889
$705$	−4.00000	−0.150649
$706$	24.2462	0.912518
$707$	25.7538	0.968571
$708$	7.12311	0.267703
$709$	−34.0000	−1.27690	−0.638448	−	0.769665i	$-0.720423\pi$
$709$	−34.0000	−1.27690	−0.638448	+	0.769665i	$0.720423\pi$
$710$	−4.87689	−0.183027
$711$	11.1231	0.417149
$712$	12.2462	0.458946
$713$	32.0000	1.19841
$714$	−3.12311	−0.116879
$715$	5.12311	0.191593
$716$	−0.876894	−0.0327711
$717$	−4.49242	−0.167773
$718$	−16.0000	−0.597115
$719$	49.3693	1.84116	0.920582	−	0.390548i	$-0.127715\pi$
$719$	49.3693	1.84116	0.920582	+	0.390548i	$0.127715\pi$
$720$	−1.00000	−0.0372678
$721$	24.9848	0.930484
$722$	9.24621	0.344108
$723$	−29.1231	−1.08310
$724$	−16.2462	−0.603786
$725$	−8.24621	−0.306257
$726$	1.00000	0.0371135
$727$	−24.9848	−0.926637	−0.463318	−	0.886192i	$-0.653341\pi$
$727$	−24.9848	−0.926637	−0.463318	+	0.886192i	$0.653341\pi$
$728$	−16.0000	−0.592999
$729$	1.00000	0.0370370
$730$	−1.12311	−0.0415680
$731$	7.12311	0.263458
$732$	2.00000	0.0739221
$733$	13.1231	0.484713	0.242356	−	0.970187i	$-0.422080\pi$
$733$	13.1231	0.484713	0.242356	+	0.970187i	$0.422080\pi$
$734$	−16.0000	−0.590571
$735$	2.75379	0.101575
$736$	3.12311	0.115119
$737$	4.00000	0.147342
$738$	−10.0000	−0.368105
$739$	43.1231	1.58631	0.793155	−	0.609020i	$-0.208437\pi$
$739$	43.1231	1.58631	0.793155	+	0.609020i	$0.208437\pi$
$740$	−2.00000	−0.0735215
$741$	−16.0000	−0.587775
$742$	28.4924	1.04599
$743$	−44.0000	−1.61420	−0.807102	−	0.590412i	$-0.798965\pi$
$743$	−44.0000	−1.61420	−0.807102	+	0.590412i	$0.798965\pi$
$744$	−10.2462	−0.375644
$745$	−18.0000	−0.659469
$746$	−33.6155	−1.23075
$747$	4.00000	0.146352
$748$	1.00000	0.0365636
$749$	−5.47727	−0.200135
$750$	−1.00000	−0.0365148
$751$	−7.50758	−0.273955	−0.136978	−	0.990574i	$-0.543739\pi$
$751$	−7.50758	−0.273955	−0.136978	+	0.990574i	$0.543739\pi$
$752$	−4.00000	−0.145865
$753$	−2.63068	−0.0958674
$754$	42.2462	1.53852
$755$	24.4924	0.891371
$756$	−3.12311	−0.113586
$757$	−10.0000	−0.363456	−0.181728	−	0.983349i	$-0.558169\pi$
$757$	−10.0000	−0.363456	−0.181728	+	0.983349i	$0.558169\pi$
$758$	6.24621	0.226873
$759$	−3.12311	−0.113362
$760$	3.12311	0.113287
$761$	−48.2462	−1.74892	−0.874462	−	0.485094i	$-0.838785\pi$
$761$	−48.2462	−1.74892	−0.874462	+	0.485094i	$0.838785\pi$
$762$	8.00000	0.289809
$763$	13.2614	0.480094
$764$	16.0000	0.578860
$765$	1.00000	0.0361551
$766$	2.24621	0.0811589
$767$	−36.4924	−1.31767
$768$	−1.00000	−0.0360844
$769$	50.9848	1.83856	0.919280	−	0.393604i	$-0.128772\pi$
$769$	50.9848	1.83856	0.919280	+	0.393604i	$0.128772\pi$
$770$	−3.12311	−0.112549
$771$	0.246211	0.00886708
$772$	−18.8769	−0.679394
$773$	38.1080	1.37065	0.685324	−	0.728238i	$-0.259661\pi$
$773$	38.1080	1.37065	0.685324	+	0.728238i	$0.259661\pi$
$774$	7.12311	0.256035
$775$	−10.2462	−0.368055
$776$	8.24621	0.296022
$777$	−6.24621	−0.224082
$778$	9.61553	0.344733
$779$	31.2311	1.11897
$780$	5.12311	0.183437
$781$	4.87689	0.174509
$782$	−3.12311	−0.111682
$783$	8.24621	0.294696
$784$	2.75379	0.0983496
$785$	16.2462	0.579852
$786$	−4.00000	−0.142675
$787$	−46.7386	−1.66605	−0.833026	−	0.553234i	$-0.813394\pi$
$787$	−46.7386	−1.66605	−0.833026	+	0.553234i	$0.813394\pi$
$788$	6.49242	0.231283
$789$	−24.0000	−0.854423
$790$	11.1231	0.395742
$791$	−21.4773	−0.763644
$792$	1.00000	0.0355335
$793$	−10.2462	−0.363854
$794$	16.7386	0.594032
$795$	−9.12311	−0.323563
$796$	18.2462	0.646720
$797$	22.8769	0.810341	0.405171	−	0.914241i	$-0.367212\pi$
$797$	22.8769	0.810341	0.405171	+	0.914241i	$0.367212\pi$
$798$	9.75379	0.345280
$799$	4.00000	0.141510
$800$	−1.00000	−0.0353553
$801$	−12.2462	−0.432699
$802$	−17.1231	−0.604638
$803$	1.12311	0.0396335
$804$	4.00000	0.141069
$805$	9.75379	0.343776
$806$	52.4924	1.84897
$807$	−2.00000	−0.0704033
$808$	−8.24621	−0.290101
$809$	49.2311	1.73087	0.865436	−	0.501020i	$-0.167042\pi$
$809$	49.2311	1.73087	0.865436	+	0.501020i	$0.167042\pi$
$810$	1.00000	0.0351364
$811$	2.24621	0.0788751	0.0394376	−	0.999222i	$-0.487443\pi$
$811$	2.24621	0.0788751	0.0394376	+	0.999222i	$0.487443\pi$
$812$	−25.7538	−0.903781
$813$	−18.2462	−0.639923
$814$	2.00000	0.0701000
$815$	16.4924	0.577704
$816$	1.00000	0.0350070
$817$	−22.2462	−0.778296
$818$	20.2462	0.707892
$819$	16.0000	0.559085
$820$	−10.0000	−0.349215
$821$	10.4924	0.366188	0.183094	−	0.983095i	$-0.441389\pi$
$821$	10.4924	0.366188	0.183094	+	0.983095i	$0.441389\pi$
$822$	20.2462	0.706168
$823$	18.7386	0.653188	0.326594	−	0.945165i	$-0.394099\pi$
$823$	18.7386	0.653188	0.326594	+	0.945165i	$0.394099\pi$
$824$	−8.00000	−0.278693
$825$	1.00000	0.0348155
$826$	22.2462	0.774045
$827$	−22.2462	−0.773577	−0.386788	−	0.922169i	$-0.626416\pi$
$827$	−22.2462	−0.773577	−0.386788	+	0.922169i	$0.626416\pi$
$828$	−3.12311	−0.108535
$829$	17.5076	0.608063	0.304032	−	0.952662i	$-0.401667\pi$
$829$	17.5076	0.608063	0.304032	+	0.952662i	$0.401667\pi$
$830$	4.00000	0.138842
$831$	28.7386	0.996932
$832$	5.12311	0.177612
$833$	−2.75379	−0.0954131
$834$	−12.0000	−0.415526
$835$	18.2462	0.631436
$836$	−3.12311	−0.108015
$837$	10.2462	0.354161
$838$	4.00000	0.138178
$839$	−9.36932	−0.323465	−0.161732	−	0.986835i	$-0.551708\pi$
$839$	−9.36932	−0.323465	−0.161732	+	0.986835i	$0.551708\pi$
$840$	−3.12311	−0.107757
$841$	39.0000	1.34483
$842$	10.0000	0.344623
$843$	−4.24621	−0.146247
$844$	24.4924	0.843064
$845$	−13.2462	−0.455684
$846$	4.00000	0.137523
$847$	3.12311	0.107311
$848$	−9.12311	−0.313289
$849$	8.49242	0.291459
$850$	1.00000	0.0342997
$851$	−6.24621	−0.214117
$852$	4.87689	0.167080
$853$	56.7386	1.94269	0.971347	−	0.237666i	$-0.0763824\pi$
$853$	56.7386	1.94269	0.971347	+	0.237666i	$0.0763824\pi$
$854$	6.24621	0.213741
$855$	−3.12311	−0.106808
$856$	1.75379	0.0599433
$857$	−6.49242	−0.221777	−0.110888	−	0.993833i	$-0.535370\pi$
$857$	−6.49242	−0.221777	−0.110888	+	0.993833i	$0.535370\pi$
$858$	−5.12311	−0.174900
$859$	24.4924	0.835671	0.417835	−	0.908523i	$-0.362789\pi$
$859$	24.4924	0.835671	0.417835	+	0.908523i	$0.362789\pi$
$860$	7.12311	0.242896
$861$	−31.2311	−1.06435
$862$	30.2462	1.03019
$863$	21.7538	0.740508	0.370254	−	0.928931i	$-0.379271\pi$
$863$	21.7538	0.740508	0.370254	+	0.928931i	$0.379271\pi$
$864$	1.00000	0.0340207
$865$	−8.24621	−0.280380
$866$	12.2462	0.416143
$867$	−1.00000	−0.0339618
$868$	−32.0000	−1.08615
$869$	−11.1231	−0.377326
$870$	8.24621	0.279573
$871$	−20.4924	−0.694359
$872$	−4.24621	−0.143795
$873$	−8.24621	−0.279092
$874$	9.75379	0.329927
$875$	−3.12311	−0.105580
$876$	1.12311	0.0379462
$877$	−32.2462	−1.08888	−0.544439	−	0.838801i	$-0.683257\pi$
$877$	−32.2462	−1.08888	−0.544439	+	0.838801i	$0.683257\pi$
$878$	−3.12311	−0.105400
$879$	18.4924	0.623734
$880$	1.00000	0.0337100
$881$	−37.1231	−1.25071	−0.625355	−	0.780341i	$-0.715046\pi$
$881$	−37.1231	−1.25071	−0.625355	+	0.780341i	$0.715046\pi$
$882$	−2.75379	−0.0927249
$883$	−50.2462	−1.69092	−0.845460	−	0.534039i	$-0.820674\pi$
$883$	−50.2462	−1.69092	−0.845460	+	0.534039i	$0.820674\pi$
$884$	−5.12311	−0.172309
$885$	−7.12311	−0.239441
$886$	28.8769	0.970138
$887$	−46.7386	−1.56933	−0.784665	−	0.619920i	$-0.787165\pi$
$887$	−46.7386	−1.56933	−0.784665	+	0.619920i	$0.787165\pi$
$888$	2.00000	0.0671156
$889$	24.9848	0.837965
$890$	−12.2462	−0.410494
$891$	−1.00000	−0.0335013
$892$	−28.4924	−0.953997
$893$	−12.4924	−0.418043
$894$	18.0000	0.602010
$895$	0.876894	0.0293113
$896$	−3.12311	−0.104336
$897$	16.0000	0.534224
$898$	−2.87689	−0.0960032
$899$	84.4924	2.81798
$900$	1.00000	0.0333333
$901$	9.12311	0.303935
$902$	10.0000	0.332964
$903$	22.2462	0.740308
$904$	6.87689	0.228722
$905$	16.2462	0.540042
$906$	−24.4924	−0.813706
$907$	12.0000	0.398453	0.199227	−	0.979953i	$-0.436157\pi$
$907$	12.0000	0.398453	0.199227	+	0.979953i	$0.436157\pi$
$908$	−1.75379	−0.0582015
$909$	8.24621	0.273510
$910$	16.0000	0.530395
$911$	−45.8617	−1.51947	−0.759734	−	0.650234i	$-0.774671\pi$
$911$	−45.8617	−1.51947	−0.759734	+	0.650234i	$0.774671\pi$
$912$	−3.12311	−0.103416
$913$	−4.00000	−0.132381
$914$	−34.4924	−1.14091
$915$	−2.00000	−0.0661180
$916$	−0.246211	−0.00813505
$917$	−12.4924	−0.412536
$918$	−1.00000	−0.0330049
$919$	−57.4773	−1.89600	−0.948000	−	0.318270i	$-0.896898\pi$
$919$	−57.4773	−1.89600	−0.948000	+	0.318270i	$0.896898\pi$
$920$	−3.12311	−0.102966
$921$	−11.6155	−0.382745
$922$	26.4924	0.872481
$923$	−24.9848	−0.822386
$924$	3.12311	0.102743
$925$	2.00000	0.0657596
$926$	0	0
$927$	8.00000	0.262754
$928$	8.24621	0.270695
$929$	34.8769	1.14427	0.572137	−	0.820158i	$-0.306115\pi$
$929$	34.8769	1.14427	0.572137	+	0.820158i	$0.306115\pi$
$930$	10.2462	0.335987
$931$	8.60037	0.281866
$932$	−0.246211	−0.00806492
$933$	20.8769	0.683479
$934$	28.8769	0.944881
$935$	−1.00000	−0.0327035
$936$	−5.12311	−0.167454
$937$	14.0000	0.457360	0.228680	−	0.973502i	$-0.426559\pi$
$937$	14.0000	0.457360	0.228680	+	0.973502i	$0.426559\pi$
$938$	12.4924	0.407892
$939$	32.2462	1.05232
$940$	4.00000	0.130466
$941$	34.4924	1.12442	0.562210	−	0.826994i	$-0.309951\pi$
$941$	34.4924	1.12442	0.562210	+	0.826994i	$0.309951\pi$
$942$	−16.2462	−0.529330
$943$	−31.2311	−1.01702
$944$	−7.12311	−0.231837
$945$	3.12311	0.101595
$946$	−7.12311	−0.231592
$947$	6.73863	0.218976	0.109488	−	0.993988i	$-0.465079\pi$
$947$	6.73863	0.218976	0.109488	+	0.993988i	$0.465079\pi$
$948$	−11.1231	−0.361262
$949$	−5.75379	−0.186776
$950$	−3.12311	−0.101327
$951$	7.75379	0.251434
$952$	3.12311	0.101220
$953$	−41.2311	−1.33560	−0.667802	−	0.744339i	$-0.732765\pi$
$953$	−41.2311	−1.33560	−0.667802	+	0.744339i	$0.732765\pi$
$954$	9.12311	0.295371
$955$	−16.0000	−0.517748
$956$	4.49242	0.145295
$957$	−8.24621	−0.266562
$958$	−12.4924	−0.403612
$959$	63.2311	2.04184
$960$	1.00000	0.0322749
$961$	73.9848	2.38661
$962$	−10.2462	−0.330351
$963$	−1.75379	−0.0565151
$964$	29.1231	0.937992
$965$	18.8769	0.607669
$966$	−9.75379	−0.313823
$967$	45.4773	1.46245	0.731225	−	0.682136i	$-0.238949\pi$
$967$	45.4773	1.46245	0.731225	+	0.682136i	$0.238949\pi$
$968$	−1.00000	−0.0321412
$969$	3.12311	0.100329
$970$	−8.24621	−0.264770
$971$	−35.6155	−1.14296	−0.571478	−	0.820617i	$-0.693630\pi$
$971$	−35.6155	−1.14296	−0.571478	+	0.820617i	$0.693630\pi$
$972$	−1.00000	−0.0320750
$973$	−37.4773	−1.20147
$974$	−3.50758	−0.112390
$975$	−5.12311	−0.164071
$976$	−2.00000	−0.0640184
$977$	20.2462	0.647734	0.323867	−	0.946103i	$-0.395017\pi$
$977$	20.2462	0.647734	0.323867	+	0.946103i	$0.395017\pi$
$978$	−16.4924	−0.527370
$979$	12.2462	0.391391
$980$	−2.75379	−0.0879666
$981$	4.24621	0.135571
$982$	−14.7386	−0.470329
$983$	−6.63068	−0.211486	−0.105743	−	0.994393i	$-0.533722\pi$
$983$	−6.63068	−0.211486	−0.105743	+	0.994393i	$0.533722\pi$
$984$	10.0000	0.318788
$985$	−6.49242	−0.206866
$986$	−8.24621	−0.262613
$987$	12.4924	0.397638
$988$	16.0000	0.509028
$989$	22.2462	0.707388
$990$	−1.00000	−0.0317821
$991$	−8.49242	−0.269771	−0.134885	−	0.990861i	$-0.543067\pi$
$991$	−8.49242	−0.269771	−0.134885	+	0.990861i	$0.543067\pi$
$992$	10.2462	0.325318
$993$	20.0000	0.634681
$994$	15.2311	0.483100
$995$	−18.2462	−0.578444
$996$	−4.00000	−0.126745
$997$	−34.9848	−1.10798	−0.553991	−	0.832523i	$-0.686896\pi$
$997$	−34.9848	−1.10798	−0.553991	+	0.832523i	$0.686896\pi$
$998$	−14.2462	−0.450956
$999$	−2.00000	−0.0632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5610.2.a.bm.1.2	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5610.2.a.bm.1.2	✓	2	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:	\( N \)	\(=\)	\( 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5610.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +3.12311 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +3.12311 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} -1.00000 q^{12} +5.12311 q^{13} -3.12311 q^{14} +1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +3.12311 q^{19} -1.00000 q^{20} -3.12311 q^{21} +1.00000 q^{22} -3.12311 q^{23} +1.00000 q^{24} +1.00000 q^{25} -5.12311 q^{26} -1.00000 q^{27} +3.12311 q^{28} -8.24621 q^{29} -1.00000 q^{30} -10.2462 q^{31} -1.00000 q^{32} +1.00000 q^{33} +1.00000 q^{34} -3.12311 q^{35} +1.00000 q^{36} +2.00000 q^{37} -3.12311 q^{38} -5.12311 q^{39} +1.00000 q^{40} +10.0000 q^{41} +3.12311 q^{42} -7.12311 q^{43} -1.00000 q^{44} -1.00000 q^{45} +3.12311 q^{46} -4.00000 q^{47} -1.00000 q^{48} +2.75379 q^{49} -1.00000 q^{50} +1.00000 q^{51} +5.12311 q^{52} -9.12311 q^{53} +1.00000 q^{54} +1.00000 q^{55} -3.12311 q^{56} -3.12311 q^{57} +8.24621 q^{58} -7.12311 q^{59} +1.00000 q^{60} -2.00000 q^{61} +10.2462 q^{62} +3.12311 q^{63} +1.00000 q^{64} -5.12311 q^{65} -1.00000 q^{66} -4.00000 q^{67} -1.00000 q^{68} +3.12311 q^{69} +3.12311 q^{70} -4.87689 q^{71} -1.00000 q^{72} -1.12311 q^{73} -2.00000 q^{74} -1.00000 q^{75} +3.12311 q^{76} -3.12311 q^{77} +5.12311 q^{78} +11.1231 q^{79} -1.00000 q^{80} +1.00000 q^{81} -10.0000 q^{82} +4.00000 q^{83} -3.12311 q^{84} +1.00000 q^{85} +7.12311 q^{86} +8.24621 q^{87} +1.00000 q^{88} -12.2462 q^{89} +1.00000 q^{90} +16.0000 q^{91} -3.12311 q^{92} +10.2462 q^{93} +4.00000 q^{94} -3.12311 q^{95} +1.00000 q^{96} -8.24621 q^{97} -2.75379 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9} + 2 q^{10} - 2 q^{11} - 2 q^{12} + 2 q^{13} + 2 q^{14} + 2 q^{15} + 2 q^{16} - 2 q^{17} - 2 q^{18} - 2 q^{19} - 2 q^{20} + 2 q^{21} + 2 q^{22} + 2 q^{23} + 2 q^{24} + 2 q^{25} - 2 q^{26} - 2 q^{27} - 2 q^{28} - 2 q^{30} - 4 q^{31} - 2 q^{32} + 2 q^{33} + 2 q^{34} + 2 q^{35} + 2 q^{36} + 4 q^{37} + 2 q^{38} - 2 q^{39} + 2 q^{40} + 20 q^{41} - 2 q^{42} - 6 q^{43} - 2 q^{44} - 2 q^{45} - 2 q^{46} - 8 q^{47} - 2 q^{48} + 22 q^{49} - 2 q^{50} + 2 q^{51} + 2 q^{52} - 10 q^{53} + 2 q^{54} + 2 q^{55} + 2 q^{56} + 2 q^{57} - 6 q^{59} + 2 q^{60} - 4 q^{61} + 4 q^{62} - 2 q^{63} + 2 q^{64} - 2 q^{65} - 2 q^{66} - 8 q^{67} - 2 q^{68} - 2 q^{69} - 2 q^{70} - 18 q^{71} - 2 q^{72} + 6 q^{73} - 4 q^{74} - 2 q^{75} - 2 q^{76} + 2 q^{77} + 2 q^{78} + 14 q^{79} - 2 q^{80} + 2 q^{81} - 20 q^{82} + 8 q^{83} + 2 q^{84} + 2 q^{85} + 6 q^{86} + 2 q^{88} - 8 q^{89} + 2 q^{90} + 32 q^{91} + 2 q^{92} + 4 q^{93} + 8 q^{94} + 2 q^{95} + 2 q^{96} - 22 q^{98} - 2 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9 + 2 * q^10 - 2 * q^11 - 2 * q^12 + 2 * q^13 + 2 * q^14 + 2 * q^15 + 2 * q^16 - 2 * q^17 - 2 * q^18 - 2 * q^19 - 2 * q^20 + 2 * q^21 + 2 * q^22 + 2 * q^23 + 2 * q^24 + 2 * q^25 - 2 * q^26 - 2 * q^27 - 2 * q^28 - 2 * q^30 - 4 * q^31 - 2 * q^32 + 2 * q^33 + 2 * q^34 + 2 * q^35 + 2 * q^36 + 4 * q^37 + 2 * q^38 - 2 * q^39 + 2 * q^40 + 20 * q^41 - 2 * q^42 - 6 * q^43 - 2 * q^44 - 2 * q^45 - 2 * q^46 - 8 * q^47 - 2 * q^48 + 22 * q^49 - 2 * q^50 + 2 * q^51 + 2 * q^52 - 10 * q^53 + 2 * q^54 + 2 * q^55 + 2 * q^56 + 2 * q^57 - 6 * q^59 + 2 * q^60 - 4 * q^61 + 4 * q^62 - 2 * q^63 + 2 * q^64 - 2 * q^65 - 2 * q^66 - 8 * q^67 - 2 * q^68 - 2 * q^69 - 2 * q^70 - 18 * q^71 - 2 * q^72 + 6 * q^73 - 4 * q^74 - 2 * q^75 - 2 * q^76 + 2 * q^77 + 2 * q^78 + 14 * q^79 - 2 * q^80 + 2 * q^81 - 20 * q^82 + 8 * q^83 + 2 * q^84 + 2 * q^85 + 6 * q^86 + 2 * q^88 - 8 * q^89 + 2 * q^90 + 32 * q^91 + 2 * q^92 + 4 * q^93 + 8 * q^94 + 2 * q^95 + 2 * q^96 - 22 * q^98 - 2 * q^99

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