LMFDB - Embedded newform 5586.2.a.bg.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5586,2,Mod(1,5586)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5586, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("5586.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5586 = 2 \cdot 3 \cdot 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5586.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:	$44.6044345691$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 798)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.41421$ of defining polynomial
Character	$\chi$	$=$	5586.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.41421 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.41421 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -4.41421 q^{10} -1.00000 q^{11} -1.00000 q^{12} -2.82843 q^{13} +4.41421 q^{15} +1.00000 q^{16} +4.24264 q^{17} +1.00000 q^{18} +1.00000 q^{19} -4.41421 q^{20} -1.00000 q^{22} +0.585786 q^{23} -1.00000 q^{24} +14.4853 q^{25} -2.82843 q^{26} -1.00000 q^{27} +7.82843 q^{29} +4.41421 q^{30} +0.656854 q^{31} +1.00000 q^{32} +1.00000 q^{33} +4.24264 q^{34} +1.00000 q^{36} -8.24264 q^{37} +1.00000 q^{38} +2.82843 q^{39} -4.41421 q^{40} -3.41421 q^{41} -2.24264 q^{43} -1.00000 q^{44} -4.41421 q^{45} +0.585786 q^{46} +8.82843 q^{47} -1.00000 q^{48} +14.4853 q^{50} -4.24264 q^{51} -2.82843 q^{52} -3.82843 q^{53} -1.00000 q^{54} +4.41421 q^{55} -1.00000 q^{57} +7.82843 q^{58} -8.07107 q^{59} +4.41421 q^{60} +0.828427 q^{61} +0.656854 q^{62} +1.00000 q^{64} +12.4853 q^{65} +1.00000 q^{66} -2.00000 q^{67} +4.24264 q^{68} -0.585786 q^{69} +11.8995 q^{71} +1.00000 q^{72} -9.17157 q^{73} -8.24264 q^{74} -14.4853 q^{75} +1.00000 q^{76} +2.82843 q^{78} -5.82843 q^{79} -4.41421 q^{80} +1.00000 q^{81} -3.41421 q^{82} +11.1421 q^{83} -18.7279 q^{85} -2.24264 q^{86} -7.82843 q^{87} -1.00000 q^{88} +12.2426 q^{89} -4.41421 q^{90} +0.585786 q^{92} -0.656854 q^{93} +8.82843 q^{94} -4.41421 q^{95} -1.00000 q^{96} -8.41421 q^{97} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 6 q^{5} - 2 q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 6 * q^5 - 2 * q^6 + 2 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 6 q^{5} - 2 q^{6} + 2 q^{8} + 2 q^{9} - 6 q^{10} - 2 q^{11} - 2 q^{12} + 6 q^{15} + 2 q^{16} + 2 q^{18} + 2 q^{19} - 6 q^{20} - 2 q^{22} + 4 q^{23} - 2 q^{24} + 12 q^{25} - 2 q^{27} + 10 q^{29} + 6 q^{30} - 10 q^{31} + 2 q^{32} + 2 q^{33} + 2 q^{36} - 8 q^{37} + 2 q^{38} - 6 q^{40} - 4 q^{41} + 4 q^{43} - 2 q^{44} - 6 q^{45} + 4 q^{46} + 12 q^{47} - 2 q^{48} + 12 q^{50} - 2 q^{53} - 2 q^{54} + 6 q^{55} - 2 q^{57} + 10 q^{58} - 2 q^{59} + 6 q^{60} - 4 q^{61} - 10 q^{62} + 2 q^{64} + 8 q^{65} + 2 q^{66} - 4 q^{67} - 4 q^{69} + 4 q^{71} + 2 q^{72} - 24 q^{73} - 8 q^{74} - 12 q^{75} + 2 q^{76} - 6 q^{79} - 6 q^{80} + 2 q^{81} - 4 q^{82} - 6 q^{83} - 12 q^{85} + 4 q^{86} - 10 q^{87} - 2 q^{88} + 16 q^{89} - 6 q^{90} + 4 q^{92} + 10 q^{93} + 12 q^{94} - 6 q^{95} - 2 q^{96} - 14 q^{97} - 2 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 6 * q^5 - 2 * q^6 + 2 * q^8 + 2 * q^9 - 6 * q^10 - 2 * q^11 - 2 * q^12 + 6 * q^15 + 2 * q^16 + 2 * q^18 + 2 * q^19 - 6 * q^20 - 2 * q^22 + 4 * q^23 - 2 * q^24 + 12 * q^25 - 2 * q^27 + 10 * q^29 + 6 * q^30 - 10 * q^31 + 2 * q^32 + 2 * q^33 + 2 * q^36 - 8 * q^37 + 2 * q^38 - 6 * q^40 - 4 * q^41 + 4 * q^43 - 2 * q^44 - 6 * q^45 + 4 * q^46 + 12 * q^47 - 2 * q^48 + 12 * q^50 - 2 * q^53 - 2 * q^54 + 6 * q^55 - 2 * q^57 + 10 * q^58 - 2 * q^59 + 6 * q^60 - 4 * q^61 - 10 * q^62 + 2 * q^64 + 8 * q^65 + 2 * q^66 - 4 * q^67 - 4 * q^69 + 4 * q^71 + 2 * q^72 - 24 * q^73 - 8 * q^74 - 12 * q^75 + 2 * q^76 - 6 * q^79 - 6 * q^80 + 2 * q^81 - 4 * q^82 - 6 * q^83 - 12 * q^85 + 4 * q^86 - 10 * q^87 - 2 * q^88 + 16 * q^89 - 6 * q^90 + 4 * q^92 + 10 * q^93 + 12 * q^94 - 6 * q^95 - 2 * q^96 - 14 * q^97 - 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
$5$	−4.41421	−1.97410	−0.987048	−	0.160424i	$-0.948714\pi$
$5$	−4.41421	−1.97410	−0.987048	+	0.160424i	$0.948714\pi$
$6$	−1.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−4.41421	−1.39590
$11$	−1.00000	−0.301511	−0.150756	−	0.988571i	$-0.548171\pi$
$11$	−1.00000	−0.301511	−0.150756	+	0.988571i	$0.548171\pi$
$12$	−1.00000	−0.288675
$13$	−2.82843	−0.784465	−0.392232	−	0.919866i	$-0.628297\pi$
$13$	−2.82843	−0.784465	−0.392232	+	0.919866i	$0.628297\pi$
$14$	0	0
$15$	4.41421	1.13975
$16$	1.00000	0.250000
$17$	4.24264	1.02899	0.514496	−	0.857493i	$-0.327979\pi$
$17$	4.24264	1.02899	0.514496	+	0.857493i	$0.327979\pi$
$18$	1.00000	0.235702
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−4.41421	−0.987048
$21$	0	0
$22$	−1.00000	−0.213201
$23$	0.585786	0.122145	0.0610725	−	0.998133i	$-0.480548\pi$
$23$	0.585786	0.122145	0.0610725	+	0.998133i	$0.480548\pi$
$24$	−1.00000	−0.204124
$25$	14.4853	2.89706
$26$	−2.82843	−0.554700
$27$	−1.00000	−0.192450
$28$	0	0
$29$	7.82843	1.45370	0.726851	−	0.686795i	$-0.240983\pi$
$29$	7.82843	1.45370	0.726851	+	0.686795i	$0.240983\pi$
$30$	4.41421	0.805921
$31$	0.656854	0.117975	0.0589873	−	0.998259i	$-0.481213\pi$
$31$	0.656854	0.117975	0.0589873	+	0.998259i	$0.481213\pi$
$32$	1.00000	0.176777
$33$	1.00000	0.174078
$34$	4.24264	0.727607
$35$	0	0
$36$	1.00000	0.166667
$37$	−8.24264	−1.35508	−0.677541	−	0.735485i	$-0.736954\pi$
$37$	−8.24264	−1.35508	−0.677541	+	0.735485i	$0.736954\pi$
$38$	1.00000	0.162221
$39$	2.82843	0.452911
$40$	−4.41421	−0.697948
$41$	−3.41421	−0.533211	−0.266605	−	0.963806i	$-0.585902\pi$
$41$	−3.41421	−0.533211	−0.266605	+	0.963806i	$0.585902\pi$
$42$	0	0
$43$	−2.24264	−0.341999	−0.171000	−	0.985271i	$-0.554700\pi$
$43$	−2.24264	−0.341999	−0.171000	+	0.985271i	$0.554700\pi$
$44$	−1.00000	−0.150756
$45$	−4.41421	−0.658032
$46$	0.585786	0.0863695
$47$	8.82843	1.28776	0.643879	−	0.765127i	$-0.277324\pi$
$47$	8.82843	1.28776	0.643879	+	0.765127i	$0.277324\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	14.4853	2.04853
$51$	−4.24264	−0.594089
$52$	−2.82843	−0.392232
$53$	−3.82843	−0.525875	−0.262937	−	0.964813i	$-0.584691\pi$
$53$	−3.82843	−0.525875	−0.262937	+	0.964813i	$0.584691\pi$
$54$	−1.00000	−0.136083
$55$	4.41421	0.595212
$56$	0	0
$57$	−1.00000	−0.132453
$58$	7.82843	1.02792
$59$	−8.07107	−1.05076	−0.525382	−	0.850867i	$-0.676077\pi$
$59$	−8.07107	−1.05076	−0.525382	+	0.850867i	$0.676077\pi$
$60$	4.41421	0.569873
$61$	0.828427	0.106069	0.0530346	−	0.998593i	$-0.483111\pi$
$61$	0.828427	0.106069	0.0530346	+	0.998593i	$0.483111\pi$
$62$	0.656854	0.0834206
$63$	0	0
$64$	1.00000	0.125000
$65$	12.4853	1.54861
$66$	1.00000	0.123091
$67$	−2.00000	−0.244339	−0.122169	−	0.992509i	$-0.538985\pi$
$67$	−2.00000	−0.244339	−0.122169	+	0.992509i	$0.538985\pi$
$68$	4.24264	0.514496
$69$	−0.585786	−0.0705204
$70$	0	0
$71$	11.8995	1.41221	0.706105	−	0.708107i	$-0.250451\pi$
$71$	11.8995	1.41221	0.706105	+	0.708107i	$0.250451\pi$
$72$	1.00000	0.117851
$73$	−9.17157	−1.07345	−0.536726	−	0.843757i	$-0.680339\pi$
$73$	−9.17157	−1.07345	−0.536726	+	0.843757i	$0.680339\pi$
$74$	−8.24264	−0.958188
$75$	−14.4853	−1.67262
$76$	1.00000	0.114708
$77$	0	0
$78$	2.82843	0.320256
$79$	−5.82843	−0.655749	−0.327875	−	0.944721i	$-0.606332\pi$
$79$	−5.82843	−0.655749	−0.327875	+	0.944721i	$0.606332\pi$
$80$	−4.41421	−0.493524
$81$	1.00000	0.111111
$82$	−3.41421	−0.377037
$83$	11.1421	1.22301	0.611504	−	0.791241i	$-0.290565\pi$
$83$	11.1421	1.22301	0.611504	+	0.791241i	$0.290565\pi$
$84$	0	0
$85$	−18.7279	−2.03133
$86$	−2.24264	−0.241830
$87$	−7.82843	−0.839295
$88$	−1.00000	−0.106600
$89$	12.2426	1.29772	0.648859	−	0.760909i	$-0.275247\pi$
$89$	12.2426	1.29772	0.648859	+	0.760909i	$0.275247\pi$
$90$	−4.41421	−0.465299
$91$	0	0
$92$	0.585786	0.0610725
$93$	−0.656854	−0.0681126
$94$	8.82843	0.910583
$95$	−4.41421	−0.452889
$96$	−1.00000	−0.102062
$97$	−8.41421	−0.854334	−0.427167	−	0.904173i	$-0.640488\pi$
$97$	−8.41421	−0.854334	−0.427167	+	0.904173i	$0.640488\pi$
$98$	0	0
$99$	−1.00000	−0.100504
$100$	14.4853	1.44853
$101$	−18.9706	−1.88764	−0.943821	−	0.330458i	$-0.892797\pi$
$101$	−18.9706	−1.88764	−0.943821	+	0.330458i	$0.892797\pi$
$102$	−4.24264	−0.420084
$103$	−1.51472	−0.149250	−0.0746248	−	0.997212i	$-0.523776\pi$
$103$	−1.51472	−0.149250	−0.0746248	+	0.997212i	$0.523776\pi$
$104$	−2.82843	−0.277350
$105$	0	0
$106$	−3.82843	−0.371850
$107$	−13.7279	−1.32713	−0.663564	−	0.748119i	$-0.730957\pi$
$107$	−13.7279	−1.32713	−0.663564	+	0.748119i	$0.730957\pi$
$108$	−1.00000	−0.0962250
$109$	10.2426	0.981067	0.490534	−	0.871422i	$-0.336802\pi$
$109$	10.2426	0.981067	0.490534	+	0.871422i	$0.336802\pi$
$110$	4.41421	0.420879
$111$	8.24264	0.782357
$112$	0	0
$113$	1.75736	0.165318	0.0826592	−	0.996578i	$-0.473659\pi$
$113$	1.75736	0.165318	0.0826592	+	0.996578i	$0.473659\pi$
$114$	−1.00000	−0.0936586
$115$	−2.58579	−0.241126
$116$	7.82843	0.726851
$117$	−2.82843	−0.261488
$118$	−8.07107	−0.743002
$119$	0	0
$120$	4.41421	0.402961
$121$	−10.0000	−0.909091
$122$	0.828427	0.0750023
$123$	3.41421	0.307849
$124$	0.656854	0.0589873
$125$	−41.8701	−3.74497
$126$	0	0
$127$	−0.171573	−0.0152246	−0.00761232	−	0.999971i	$-0.502423\pi$
$127$	−0.171573	−0.0152246	−0.00761232	+	0.999971i	$0.502423\pi$
$128$	1.00000	0.0883883
$129$	2.24264	0.197454
$130$	12.4853	1.09503
$131$	−18.3137	−1.60008	−0.800038	−	0.599949i	$-0.795187\pi$
$131$	−18.3137	−1.60008	−0.800038	+	0.599949i	$0.795187\pi$
$132$	1.00000	0.0870388
$133$	0	0
$134$	−2.00000	−0.172774
$135$	4.41421	0.379915
$136$	4.24264	0.363803
$137$	−11.6569	−0.995912	−0.497956	−	0.867202i	$-0.665916\pi$
$137$	−11.6569	−0.995912	−0.497956	+	0.867202i	$0.665916\pi$
$138$	−0.585786	−0.0498655
$139$	−11.8995	−1.00930	−0.504651	−	0.863323i	$-0.668379\pi$
$139$	−11.8995	−1.00930	−0.504651	+	0.863323i	$0.668379\pi$
$140$	0	0
$141$	−8.82843	−0.743488
$142$	11.8995	0.998583
$143$	2.82843	0.236525
$144$	1.00000	0.0833333
$145$	−34.5563	−2.86975
$146$	−9.17157	−0.759045
$147$	0	0
$148$	−8.24264	−0.677541
$149$	−1.51472	−0.124091	−0.0620453	−	0.998073i	$-0.519762\pi$
$149$	−1.51472	−0.124091	−0.0620453	+	0.998073i	$0.519762\pi$
$150$	−14.4853	−1.18272
$151$	−22.6569	−1.84379	−0.921894	−	0.387441i	$-0.873359\pi$
$151$	−22.6569	−1.84379	−0.921894	+	0.387441i	$0.873359\pi$
$152$	1.00000	0.0811107
$153$	4.24264	0.342997
$154$	0	0
$155$	−2.89949	−0.232893
$156$	2.82843	0.226455
$157$	12.4853	0.996434	0.498217	−	0.867052i	$-0.333988\pi$
$157$	12.4853	0.996434	0.498217	+	0.867052i	$0.333988\pi$
$158$	−5.82843	−0.463685
$159$	3.82843	0.303614
$160$	−4.41421	−0.348974
$161$	0	0
$162$	1.00000	0.0785674
$163$	−5.17157	−0.405069	−0.202534	−	0.979275i	$-0.564918\pi$
$163$	−5.17157	−0.405069	−0.202534	+	0.979275i	$0.564918\pi$
$164$	−3.41421	−0.266605
$165$	−4.41421	−0.343646
$166$	11.1421	0.864797
$167$	18.7279	1.44921	0.724605	−	0.689164i	$-0.242022\pi$
$167$	18.7279	1.44921	0.724605	+	0.689164i	$0.242022\pi$
$168$	0	0
$169$	−5.00000	−0.384615
$170$	−18.7279	−1.43637
$171$	1.00000	0.0764719
$172$	−2.24264	−0.171000
$173$	23.7990	1.80940	0.904702	−	0.426045i	$-0.140094\pi$
$173$	23.7990	1.80940	0.904702	+	0.426045i	$0.140094\pi$
$174$	−7.82843	−0.593472
$175$	0	0
$176$	−1.00000	−0.0753778
$177$	8.07107	0.606659
$178$	12.2426	0.917625
$179$	−24.4853	−1.83012	−0.915058	−	0.403322i	$-0.867855\pi$
$179$	−24.4853	−1.83012	−0.915058	+	0.403322i	$0.867855\pi$
$180$	−4.41421	−0.329016
$181$	−3.51472	−0.261247	−0.130623	−	0.991432i	$-0.541698\pi$
$181$	−3.51472	−0.261247	−0.130623	+	0.991432i	$0.541698\pi$
$182$	0	0
$183$	−0.828427	−0.0612391
$184$	0.585786	0.0431847
$185$	36.3848	2.67506
$186$	−0.656854	−0.0481629
$187$	−4.24264	−0.310253
$188$	8.82843	0.643879
$189$	0	0
$190$	−4.41421	−0.320241
$191$	10.1421	0.733859	0.366930	−	0.930249i	$-0.380409\pi$
$191$	10.1421	0.733859	0.366930	+	0.930249i	$0.380409\pi$
$192$	−1.00000	−0.0721688
$193$	1.72792	0.124379	0.0621893	−	0.998064i	$-0.480192\pi$
$193$	1.72792	0.124379	0.0621893	+	0.998064i	$0.480192\pi$
$194$	−8.41421	−0.604105
$195$	−12.4853	−0.894090
$196$	0	0
$197$	6.82843	0.486505	0.243253	−	0.969963i	$-0.421786\pi$
$197$	6.82843	0.486505	0.243253	+	0.969963i	$0.421786\pi$
$198$	−1.00000	−0.0710669
$199$	−8.48528	−0.601506	−0.300753	−	0.953702i	$-0.597238\pi$
$199$	−8.48528	−0.601506	−0.300753	+	0.953702i	$0.597238\pi$
$200$	14.4853	1.02426
$201$	2.00000	0.141069
$202$	−18.9706	−1.33476
$203$	0	0
$204$	−4.24264	−0.297044
$205$	15.0711	1.05261
$206$	−1.51472	−0.105535
$207$	0.585786	0.0407150
$208$	−2.82843	−0.196116
$209$	−1.00000	−0.0691714
$210$	0	0
$211$	−0.928932	−0.0639503	−0.0319752	−	0.999489i	$-0.510180\pi$
$211$	−0.928932	−0.0639503	−0.0319752	+	0.999489i	$0.510180\pi$
$212$	−3.82843	−0.262937
$213$	−11.8995	−0.815340
$214$	−13.7279	−0.938421
$215$	9.89949	0.675140
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	10.2426	0.693719
$219$	9.17157	0.619757
$220$	4.41421	0.297606
$221$	−12.0000	−0.807207
$222$	8.24264	0.553210
$223$	6.51472	0.436258	0.218129	−	0.975920i	$-0.430005\pi$
$223$	6.51472	0.436258	0.218129	+	0.975920i	$0.430005\pi$
$224$	0	0
$225$	14.4853	0.965685
$226$	1.75736	0.116898
$227$	20.8995	1.38715	0.693574	−	0.720385i	$-0.256035\pi$
$227$	20.8995	1.38715	0.693574	+	0.720385i	$0.256035\pi$
$228$	−1.00000	−0.0662266
$229$	19.7990	1.30835	0.654177	−	0.756341i	$-0.273015\pi$
$229$	19.7990	1.30835	0.654177	+	0.756341i	$0.273015\pi$
$230$	−2.58579	−0.170502
$231$	0	0
$232$	7.82843	0.513961
$233$	−10.8284	−0.709394	−0.354697	−	0.934981i	$-0.615416\pi$
$233$	−10.8284	−0.709394	−0.354697	+	0.934981i	$0.615416\pi$
$234$	−2.82843	−0.184900
$235$	−38.9706	−2.54216
$236$	−8.07107	−0.525382
$237$	5.82843	0.378597
$238$	0	0
$239$	−28.2843	−1.82956	−0.914779	−	0.403955i	$-0.867635\pi$
$239$	−28.2843	−1.82956	−0.914779	+	0.403955i	$0.867635\pi$
$240$	4.41421	0.284936
$241$	−30.5563	−1.96831	−0.984154	−	0.177317i	$-0.943258\pi$
$241$	−30.5563	−1.96831	−0.984154	+	0.177317i	$0.943258\pi$
$242$	−10.0000	−0.642824
$243$	−1.00000	−0.0641500
$244$	0.828427	0.0530346
$245$	0	0
$246$	3.41421	0.217682
$247$	−2.82843	−0.179969
$248$	0.656854	0.0417103
$249$	−11.1421	−0.706104
$250$	−41.8701	−2.64809
$251$	−21.0000	−1.32551	−0.662754	−	0.748837i	$-0.730613\pi$
$251$	−21.0000	−1.32551	−0.662754	+	0.748837i	$0.730613\pi$
$252$	0	0
$253$	−0.585786	−0.0368281
$254$	−0.171573	−0.0107654
$255$	18.7279	1.17279
$256$	1.00000	0.0625000
$257$	6.00000	0.374270	0.187135	−	0.982334i	$-0.440080\pi$
$257$	6.00000	0.374270	0.187135	+	0.982334i	$0.440080\pi$
$258$	2.24264	0.139621
$259$	0	0
$260$	12.4853	0.774304
$261$	7.82843	0.484567
$262$	−18.3137	−1.13142
$263$	19.5563	1.20590	0.602948	−	0.797780i	$-0.293993\pi$
$263$	19.5563	1.20590	0.602948	+	0.797780i	$0.293993\pi$
$264$	1.00000	0.0615457
$265$	16.8995	1.03813
$266$	0	0
$267$	−12.2426	−0.749237
$268$	−2.00000	−0.122169
$269$	1.00000	0.0609711	0.0304855	−	0.999535i	$-0.490295\pi$
$269$	1.00000	0.0609711	0.0304855	+	0.999535i	$0.490295\pi$
$270$	4.41421	0.268640
$271$	−10.8995	−0.662097	−0.331049	−	0.943614i	$-0.607402\pi$
$271$	−10.8995	−0.662097	−0.331049	+	0.943614i	$0.607402\pi$
$272$	4.24264	0.257248
$273$	0	0
$274$	−11.6569	−0.704216
$275$	−14.4853	−0.873495
$276$	−0.585786	−0.0352602
$277$	−22.2426	−1.33643	−0.668215	−	0.743968i	$-0.732942\pi$
$277$	−22.2426	−1.33643	−0.668215	+	0.743968i	$0.732942\pi$
$278$	−11.8995	−0.713684
$279$	0.656854	0.0393248
$280$	0	0
$281$	21.3137	1.27147	0.635735	−	0.771908i	$-0.280697\pi$
$281$	21.3137	1.27147	0.635735	+	0.771908i	$0.280697\pi$
$282$	−8.82843	−0.525725
$283$	−9.55635	−0.568066	−0.284033	−	0.958815i	$-0.591673\pi$
$283$	−9.55635	−0.568066	−0.284033	+	0.958815i	$0.591673\pi$
$284$	11.8995	0.706105
$285$	4.41421	0.261475
$286$	2.82843	0.167248
$287$	0	0
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	−34.5563	−2.02922
$291$	8.41421	0.493250
$292$	−9.17157	−0.536726
$293$	−23.0000	−1.34367	−0.671837	−	0.740699i	$-0.734495\pi$
$293$	−23.0000	−1.34367	−0.671837	+	0.740699i	$0.734495\pi$
$294$	0	0
$295$	35.6274	2.07431
$296$	−8.24264	−0.479094
$297$	1.00000	0.0580259
$298$	−1.51472	−0.0877453
$299$	−1.65685	−0.0958184
$300$	−14.4853	−0.836308
$301$	0	0
$302$	−22.6569	−1.30376
$303$	18.9706	1.08983
$304$	1.00000	0.0573539
$305$	−3.65685	−0.209391
$306$	4.24264	0.242536
$307$	4.58579	0.261725	0.130862	−	0.991401i	$-0.458225\pi$
$307$	4.58579	0.261725	0.130862	+	0.991401i	$0.458225\pi$
$308$	0	0
$309$	1.51472	0.0861693
$310$	−2.89949	−0.164680
$311$	13.7574	0.780108	0.390054	−	0.920792i	$-0.372456\pi$
$311$	13.7574	0.780108	0.390054	+	0.920792i	$0.372456\pi$
$312$	2.82843	0.160128
$313$	1.82843	0.103349	0.0516744	−	0.998664i	$-0.483544\pi$
$313$	1.82843	0.103349	0.0516744	+	0.998664i	$0.483544\pi$
$314$	12.4853	0.704585
$315$	0	0
$316$	−5.82843	−0.327875
$317$	7.48528	0.420415	0.210208	−	0.977657i	$-0.432586\pi$
$317$	7.48528	0.420415	0.210208	+	0.977657i	$0.432586\pi$
$318$	3.82843	0.214688
$319$	−7.82843	−0.438308
$320$	−4.41421	−0.246762
$321$	13.7279	0.766218
$322$	0	0
$323$	4.24264	0.236067
$324$	1.00000	0.0555556
$325$	−40.9706	−2.27264
$326$	−5.17157	−0.286427
$327$	−10.2426	−0.566419
$328$	−3.41421	−0.188518
$329$	0	0
$330$	−4.41421	−0.242994
$331$	32.3848	1.78003	0.890014	−	0.455933i	$-0.150694\pi$
$331$	32.3848	1.78003	0.890014	+	0.455933i	$0.150694\pi$
$332$	11.1421	0.611504
$333$	−8.24264	−0.451694
$334$	18.7279	1.02475
$335$	8.82843	0.482349
$336$	0	0
$337$	−12.0711	−0.657553	−0.328776	−	0.944408i	$-0.606636\pi$
$337$	−12.0711	−0.657553	−0.328776	+	0.944408i	$0.606636\pi$
$338$	−5.00000	−0.271964
$339$	−1.75736	−0.0954467
$340$	−18.7279	−1.01566
$341$	−0.656854	−0.0355707
$342$	1.00000	0.0540738
$343$	0	0
$344$	−2.24264	−0.120915
$345$	2.58579	0.139214
$346$	23.7990	1.27944
$347$	−34.0000	−1.82522	−0.912608	−	0.408836i	$-0.865935\pi$
$347$	−34.0000	−1.82522	−0.912608	+	0.408836i	$0.865935\pi$
$348$	−7.82843	−0.419648
$349$	−16.2426	−0.869449	−0.434724	−	0.900564i	$-0.643154\pi$
$349$	−16.2426	−0.869449	−0.434724	+	0.900564i	$0.643154\pi$
$350$	0	0
$351$	2.82843	0.150970
$352$	−1.00000	−0.0533002
$353$	33.8995	1.80429	0.902144	−	0.431435i	$-0.141993\pi$
$353$	33.8995	1.80429	0.902144	+	0.431435i	$0.141993\pi$
$354$	8.07107	0.428972
$355$	−52.5269	−2.78784
$356$	12.2426	0.648859
$357$	0	0
$358$	−24.4853	−1.29409
$359$	10.0000	0.527780	0.263890	−	0.964553i	$-0.414994\pi$
$359$	10.0000	0.527780	0.263890	+	0.964553i	$0.414994\pi$
$360$	−4.41421	−0.232649
$361$	1.00000	0.0526316
$362$	−3.51472	−0.184730
$363$	10.0000	0.524864
$364$	0	0
$365$	40.4853	2.11910
$366$	−0.828427	−0.0433026
$367$	−3.24264	−0.169264	−0.0846322	−	0.996412i	$-0.526972\pi$
$367$	−3.24264	−0.169264	−0.0846322	+	0.996412i	$0.526972\pi$
$368$	0.585786	0.0305362
$369$	−3.41421	−0.177737
$370$	36.3848	1.89155
$371$	0	0
$372$	−0.656854	−0.0340563
$373$	−16.4853	−0.853576	−0.426788	−	0.904352i	$-0.640355\pi$
$373$	−16.4853	−0.853576	−0.426788	+	0.904352i	$0.640355\pi$
$374$	−4.24264	−0.219382
$375$	41.8701	2.16216
$376$	8.82843	0.455291
$377$	−22.1421	−1.14038
$378$	0	0
$379$	−19.3137	−0.992079	−0.496039	−	0.868300i	$-0.665213\pi$
$379$	−19.3137	−0.992079	−0.496039	+	0.868300i	$0.665213\pi$
$380$	−4.41421	−0.226444
$381$	0.171573	0.00878994
$382$	10.1421	0.518917
$383$	4.34315	0.221924	0.110962	−	0.993825i	$-0.464607\pi$
$383$	4.34315	0.221924	0.110962	+	0.993825i	$0.464607\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	1.72792	0.0879489
$387$	−2.24264	−0.114000
$388$	−8.41421	−0.427167
$389$	28.8284	1.46166	0.730830	−	0.682560i	$-0.239133\pi$
$389$	28.8284	1.46166	0.730830	+	0.682560i	$0.239133\pi$
$390$	−12.4853	−0.632217
$391$	2.48528	0.125686
$392$	0	0
$393$	18.3137	0.923804
$394$	6.82843	0.344011
$395$	25.7279	1.29451
$396$	−1.00000	−0.0502519
$397$	−5.17157	−0.259554	−0.129777	−	0.991543i	$-0.541426\pi$
$397$	−5.17157	−0.259554	−0.129777	+	0.991543i	$0.541426\pi$
$398$	−8.48528	−0.425329
$399$	0	0
$400$	14.4853	0.724264
$401$	−14.1421	−0.706225	−0.353112	−	0.935581i	$-0.614877\pi$
$401$	−14.1421	−0.706225	−0.353112	+	0.935581i	$0.614877\pi$
$402$	2.00000	0.0997509
$403$	−1.85786	−0.0925468
$404$	−18.9706	−0.943821
$405$	−4.41421	−0.219344
$406$	0	0
$407$	8.24264	0.408573
$408$	−4.24264	−0.210042
$409$	11.1005	0.548885	0.274442	−	0.961604i	$-0.411507\pi$
$409$	11.1005	0.548885	0.274442	+	0.961604i	$0.411507\pi$
$410$	15.0711	0.744307
$411$	11.6569	0.574990
$412$	−1.51472	−0.0746248
$413$	0	0
$414$	0.585786	0.0287898
$415$	−49.1838	−2.41434
$416$	−2.82843	−0.138675
$417$	11.8995	0.582721
$418$	−1.00000	−0.0489116
$419$	2.97056	0.145121	0.0725607	−	0.997364i	$-0.476883\pi$
$419$	2.97056	0.145121	0.0725607	+	0.997364i	$0.476883\pi$
$420$	0	0
$421$	20.8284	1.01512	0.507558	−	0.861618i	$-0.330548\pi$
$421$	20.8284	1.01512	0.507558	+	0.861618i	$0.330548\pi$
$422$	−0.928932	−0.0452197
$423$	8.82843	0.429253
$424$	−3.82843	−0.185925
$425$	61.4558	2.98105
$426$	−11.8995	−0.576532
$427$	0	0
$428$	−13.7279	−0.663564
$429$	−2.82843	−0.136558
$430$	9.89949	0.477396
$431$	−33.8995	−1.63288	−0.816441	−	0.577429i	$-0.804056\pi$
$431$	−33.8995	−1.63288	−0.816441	+	0.577429i	$0.804056\pi$
$432$	−1.00000	−0.0481125
$433$	−25.1716	−1.20967	−0.604834	−	0.796351i	$-0.706761\pi$
$433$	−25.1716	−1.20967	−0.604834	+	0.796351i	$0.706761\pi$
$434$	0	0
$435$	34.5563	1.65685
$436$	10.2426	0.490534
$437$	0.585786	0.0280220
$438$	9.17157	0.438235
$439$	−28.4558	−1.35812	−0.679062	−	0.734081i	$-0.737613\pi$
$439$	−28.4558	−1.35812	−0.679062	+	0.734081i	$0.737613\pi$
$440$	4.41421	0.210439
$441$	0	0
$442$	−12.0000	−0.570782
$443$	−3.34315	−0.158838	−0.0794188	−	0.996841i	$-0.525306\pi$
$443$	−3.34315	−0.158838	−0.0794188	+	0.996841i	$0.525306\pi$
$444$	8.24264	0.391178
$445$	−54.0416	−2.56182
$446$	6.51472	0.308481
$447$	1.51472	0.0716437
$448$	0	0
$449$	5.75736	0.271707	0.135853	−	0.990729i	$-0.456622\pi$
$449$	5.75736	0.271707	0.135853	+	0.990729i	$0.456622\pi$
$450$	14.4853	0.682843
$451$	3.41421	0.160769
$452$	1.75736	0.0826592
$453$	22.6569	1.06451
$454$	20.8995	0.980862
$455$	0	0
$456$	−1.00000	−0.0468293
$457$	−26.1127	−1.22150	−0.610750	−	0.791823i	$-0.709132\pi$
$457$	−26.1127	−1.22150	−0.610750	+	0.791823i	$0.709132\pi$
$458$	19.7990	0.925146
$459$	−4.24264	−0.198030
$460$	−2.58579	−0.120563
$461$	5.31371	0.247484	0.123742	−	0.992314i	$-0.460510\pi$
$461$	5.31371	0.247484	0.123742	+	0.992314i	$0.460510\pi$
$462$	0	0
$463$	−9.65685	−0.448792	−0.224396	−	0.974498i	$-0.572041\pi$
$463$	−9.65685	−0.448792	−0.224396	+	0.974498i	$0.572041\pi$
$464$	7.82843	0.363426
$465$	2.89949	0.134461
$466$	−10.8284	−0.501617
$467$	−20.8284	−0.963825	−0.481912	−	0.876219i	$-0.660058\pi$
$467$	−20.8284	−0.963825	−0.481912	+	0.876219i	$0.660058\pi$
$468$	−2.82843	−0.130744
$469$	0	0
$470$	−38.9706	−1.79758
$471$	−12.4853	−0.575291
$472$	−8.07107	−0.371501
$473$	2.24264	0.103117
$474$	5.82843	0.267709
$475$	14.4853	0.664630
$476$	0	0
$477$	−3.82843	−0.175292
$478$	−28.2843	−1.29369
$479$	−21.3137	−0.973848	−0.486924	−	0.873444i	$-0.661881\pi$
$479$	−21.3137	−0.973848	−0.486924	+	0.873444i	$0.661881\pi$
$480$	4.41421	0.201480
$481$	23.3137	1.06301
$482$	−30.5563	−1.39180
$483$	0	0
$484$	−10.0000	−0.454545
$485$	37.1421	1.68654
$486$	−1.00000	−0.0453609
$487$	0.798990	0.0362057	0.0181028	−	0.999836i	$-0.494237\pi$
$487$	0.798990	0.0362057	0.0181028	+	0.999836i	$0.494237\pi$
$488$	0.828427	0.0375011
$489$	5.17157	0.233867
$490$	0	0
$491$	19.1421	0.863872	0.431936	−	0.901904i	$-0.357831\pi$
$491$	19.1421	0.863872	0.431936	+	0.901904i	$0.357831\pi$
$492$	3.41421	0.153925
$493$	33.2132	1.49585
$494$	−2.82843	−0.127257
$495$	4.41421	0.198404
$496$	0.656854	0.0294936
$497$	0	0
$498$	−11.1421	−0.499291
$499$	−13.3137	−0.596003	−0.298002	−	0.954565i	$-0.596320\pi$
$499$	−13.3137	−0.596003	−0.298002	+	0.954565i	$0.596320\pi$
$500$	−41.8701	−1.87249
$501$	−18.7279	−0.836702
$502$	−21.0000	−0.937276
$503$	18.2426	0.813399	0.406700	−	0.913562i	$-0.366680\pi$
$503$	18.2426	0.813399	0.406700	+	0.913562i	$0.366680\pi$
$504$	0	0
$505$	83.7401	3.72639
$506$	−0.585786	−0.0260414
$507$	5.00000	0.222058
$508$	−0.171573	−0.00761232
$509$	8.31371	0.368499	0.184249	−	0.982880i	$-0.441015\pi$
$509$	8.31371	0.368499	0.184249	+	0.982880i	$0.441015\pi$
$510$	18.7279	0.829286
$511$	0	0
$512$	1.00000	0.0441942
$513$	−1.00000	−0.0441511
$514$	6.00000	0.264649
$515$	6.68629	0.294633
$516$	2.24264	0.0987268
$517$	−8.82843	−0.388274
$518$	0	0
$519$	−23.7990	−1.04466
$520$	12.4853	0.547516
$521$	−31.9411	−1.39937	−0.699683	−	0.714453i	$-0.746675\pi$
$521$	−31.9411	−1.39937	−0.699683	+	0.714453i	$0.746675\pi$
$522$	7.82843	0.342641
$523$	23.8995	1.04505	0.522526	−	0.852623i	$-0.324990\pi$
$523$	23.8995	1.04505	0.522526	+	0.852623i	$0.324990\pi$
$524$	−18.3137	−0.800038
$525$	0	0
$526$	19.5563	0.852697
$527$	2.78680	0.121395
$528$	1.00000	0.0435194
$529$	−22.6569	−0.985081
$530$	16.8995	0.734067
$531$	−8.07107	−0.350255
$532$	0	0
$533$	9.65685	0.418285
$534$	−12.2426	−0.529791
$535$	60.5980	2.61988
$536$	−2.00000	−0.0863868
$537$	24.4853	1.05662
$538$	1.00000	0.0431131
$539$	0	0
$540$	4.41421	0.189958
$541$	6.38478	0.274503	0.137251	−	0.990536i	$-0.456173\pi$
$541$	6.38478	0.274503	0.137251	+	0.990536i	$0.456173\pi$
$542$	−10.8995	−0.468173
$543$	3.51472	0.150831
$544$	4.24264	0.181902
$545$	−45.2132	−1.93672
$546$	0	0
$547$	−14.7279	−0.629720	−0.314860	−	0.949138i	$-0.601958\pi$
$547$	−14.7279	−0.629720	−0.314860	+	0.949138i	$0.601958\pi$
$548$	−11.6569	−0.497956
$549$	0.828427	0.0353564
$550$	−14.4853	−0.617654
$551$	7.82843	0.333502
$552$	−0.585786	−0.0249327
$553$	0	0
$554$	−22.2426	−0.944999
$555$	−36.3848	−1.54445
$556$	−11.8995	−0.504651
$557$	21.5858	0.914619	0.457310	−	0.889308i	$-0.348813\pi$
$557$	21.5858	0.914619	0.457310	+	0.889308i	$0.348813\pi$
$558$	0.656854	0.0278069
$559$	6.34315	0.268286
$560$	0	0
$561$	4.24264	0.179124
$562$	21.3137	0.899065
$563$	−15.1005	−0.636410	−0.318205	−	0.948022i	$-0.603080\pi$
$563$	−15.1005	−0.636410	−0.318205	+	0.948022i	$0.603080\pi$
$564$	−8.82843	−0.371744
$565$	−7.75736	−0.326355
$566$	−9.55635	−0.401683
$567$	0	0
$568$	11.8995	0.499292
$569$	22.6274	0.948591	0.474295	−	0.880366i	$-0.342703\pi$
$569$	22.6274	0.948591	0.474295	+	0.880366i	$0.342703\pi$
$570$	4.41421	0.184891
$571$	−30.5269	−1.27751	−0.638756	−	0.769410i	$-0.720551\pi$
$571$	−30.5269	−1.27751	−0.638756	+	0.769410i	$0.720551\pi$
$572$	2.82843	0.118262
$573$	−10.1421	−0.423694
$574$	0	0
$575$	8.48528	0.353861
$576$	1.00000	0.0416667
$577$	−1.48528	−0.0618331	−0.0309165	−	0.999522i	$-0.509843\pi$
$577$	−1.48528	−0.0618331	−0.0309165	+	0.999522i	$0.509843\pi$
$578$	1.00000	0.0415945
$579$	−1.72792	−0.0718100
$580$	−34.5563	−1.43487
$581$	0	0
$582$	8.41421	0.348780
$583$	3.82843	0.158557
$584$	−9.17157	−0.379522
$585$	12.4853	0.516203
$586$	−23.0000	−0.950121
$587$	−21.6274	−0.892659	−0.446330	−	0.894869i	$-0.647269\pi$
$587$	−21.6274	−0.892659	−0.446330	+	0.894869i	$0.647269\pi$
$588$	0	0
$589$	0.656854	0.0270652
$590$	35.6274	1.46676
$591$	−6.82843	−0.280884
$592$	−8.24264	−0.338770
$593$	−44.7696	−1.83847	−0.919233	−	0.393715i	$-0.871190\pi$
$593$	−44.7696	−1.83847	−0.919233	+	0.393715i	$0.871190\pi$
$594$	1.00000	0.0410305
$595$	0	0
$596$	−1.51472	−0.0620453
$597$	8.48528	0.347279
$598$	−1.65685	−0.0677538
$599$	29.7574	1.21585	0.607926	−	0.793993i	$-0.292002\pi$
$599$	29.7574	1.21585	0.607926	+	0.793993i	$0.292002\pi$
$600$	−14.4853	−0.591359
$601$	−32.4142	−1.32220	−0.661102	−	0.750296i	$-0.729911\pi$
$601$	−32.4142	−1.32220	−0.661102	+	0.750296i	$0.729911\pi$
$602$	0	0
$603$	−2.00000	−0.0814463
$604$	−22.6569	−0.921894
$605$	44.1421	1.79463
$606$	18.9706	0.770626
$607$	22.7990	0.925382	0.462691	−	0.886520i	$-0.346884\pi$
$607$	22.7990	0.925382	0.462691	+	0.886520i	$0.346884\pi$
$608$	1.00000	0.0405554
$609$	0	0
$610$	−3.65685	−0.148062
$611$	−24.9706	−1.01020
$612$	4.24264	0.171499
$613$	45.3553	1.83188	0.915942	−	0.401310i	$-0.131445\pi$
$613$	45.3553	1.83188	0.915942	+	0.401310i	$0.131445\pi$
$614$	4.58579	0.185067
$615$	−15.0711	−0.607724
$616$	0	0
$617$	−34.5269	−1.39000	−0.695001	−	0.719009i	$-0.744596\pi$
$617$	−34.5269	−1.39000	−0.695001	+	0.719009i	$0.744596\pi$
$618$	1.51472	0.0609309
$619$	33.7990	1.35850	0.679248	−	0.733909i	$-0.262306\pi$
$619$	33.7990	1.35850	0.679248	+	0.733909i	$0.262306\pi$
$620$	−2.89949	−0.116447
$621$	−0.585786	−0.0235068
$622$	13.7574	0.551620
$623$	0	0
$624$	2.82843	0.113228
$625$	112.397	4.49588
$626$	1.82843	0.0730786
$627$	1.00000	0.0399362
$628$	12.4853	0.498217
$629$	−34.9706	−1.39437
$630$	0	0
$631$	24.5563	0.977573	0.488786	−	0.872403i	$-0.337440\pi$
$631$	24.5563	0.977573	0.488786	+	0.872403i	$0.337440\pi$
$632$	−5.82843	−0.231842
$633$	0.928932	0.0369217
$634$	7.48528	0.297279
$635$	0.757359	0.0300549
$636$	3.82843	0.151807
$637$	0	0
$638$	−7.82843	−0.309930
$639$	11.8995	0.470737
$640$	−4.41421	−0.174487
$641$	−21.4142	−0.845811	−0.422905	−	0.906174i	$-0.638990\pi$
$641$	−21.4142	−0.845811	−0.422905	+	0.906174i	$0.638990\pi$
$642$	13.7279	0.541798
$643$	33.7574	1.33126	0.665630	−	0.746282i	$-0.268163\pi$
$643$	33.7574	1.33126	0.665630	+	0.746282i	$0.268163\pi$
$644$	0	0
$645$	−9.89949	−0.389792
$646$	4.24264	0.166924
$647$	−27.3553	−1.07545	−0.537725	−	0.843120i	$-0.680716\pi$
$647$	−27.3553	−1.07545	−0.537725	+	0.843120i	$0.680716\pi$
$648$	1.00000	0.0392837
$649$	8.07107	0.316817
$650$	−40.9706	−1.60700
$651$	0	0
$652$	−5.17157	−0.202534
$653$	16.2132	0.634472	0.317236	−	0.948347i	$-0.397245\pi$
$653$	16.2132	0.634472	0.317236	+	0.948347i	$0.397245\pi$
$654$	−10.2426	−0.400519
$655$	80.8406	3.15870
$656$	−3.41421	−0.133303
$657$	−9.17157	−0.357817
$658$	0	0
$659$	−30.9706	−1.20644	−0.603221	−	0.797574i	$-0.706116\pi$
$659$	−30.9706	−1.20644	−0.603221	+	0.797574i	$0.706116\pi$
$660$	−4.41421	−0.171823
$661$	−4.38478	−0.170548	−0.0852740	−	0.996358i	$-0.527177\pi$
$661$	−4.38478	−0.170548	−0.0852740	+	0.996358i	$0.527177\pi$
$662$	32.3848	1.25867
$663$	12.0000	0.466041
$664$	11.1421	0.432399
$665$	0	0
$666$	−8.24264	−0.319396
$667$	4.58579	0.177562
$668$	18.7279	0.724605
$669$	−6.51472	−0.251874
$670$	8.82843	0.341072
$671$	−0.828427	−0.0319811
$672$	0	0
$673$	−27.7279	−1.06883	−0.534416	−	0.845221i	$-0.679469\pi$
$673$	−27.7279	−1.06883	−0.534416	+	0.845221i	$0.679469\pi$
$674$	−12.0711	−0.464960
$675$	−14.4853	−0.557539
$676$	−5.00000	−0.192308
$677$	0.313708	0.0120568	0.00602840	−	0.999982i	$-0.498081\pi$
$677$	0.313708	0.0120568	0.00602840	+	0.999982i	$0.498081\pi$
$678$	−1.75736	−0.0674910
$679$	0	0
$680$	−18.7279	−0.718183
$681$	−20.8995	−0.800870
$682$	−0.656854	−0.0251522
$683$	22.7574	0.870786	0.435393	−	0.900240i	$-0.356609\pi$
$683$	22.7574	0.870786	0.435393	+	0.900240i	$0.356609\pi$
$684$	1.00000	0.0382360
$685$	51.4558	1.96603
$686$	0	0
$687$	−19.7990	−0.755379
$688$	−2.24264	−0.0854999
$689$	10.8284	0.412530
$690$	2.58579	0.0984392
$691$	51.5563	1.96130	0.980648	−	0.195779i	$-0.0627236\pi$
$691$	51.5563	1.96130	0.980648	+	0.195779i	$0.0627236\pi$
$692$	23.7990	0.904702
$693$	0	0
$694$	−34.0000	−1.29062
$695$	52.5269	1.99246
$696$	−7.82843	−0.296736
$697$	−14.4853	−0.548669
$698$	−16.2426	−0.614793
$699$	10.8284	0.409569
$700$	0	0
$701$	−7.04163	−0.265959	−0.132979	−	0.991119i	$-0.542454\pi$
$701$	−7.04163	−0.265959	−0.132979	+	0.991119i	$0.542454\pi$
$702$	2.82843	0.106752
$703$	−8.24264	−0.310877
$704$	−1.00000	−0.0376889
$705$	38.9706	1.46772
$706$	33.8995	1.27582
$707$	0	0
$708$	8.07107	0.303329
$709$	−13.6152	−0.511330	−0.255665	−	0.966765i	$-0.582294\pi$
$709$	−13.6152	−0.511330	−0.255665	+	0.966765i	$0.582294\pi$
$710$	−52.5269	−1.97130
$711$	−5.82843	−0.218583
$712$	12.2426	0.458812
$713$	0.384776	0.0144100
$714$	0	0
$715$	−12.4853	−0.466923
$716$	−24.4853	−0.915058
$717$	28.2843	1.05630
$718$	10.0000	0.373197
$719$	3.17157	0.118280	0.0591399	−	0.998250i	$-0.481164\pi$
$719$	3.17157	0.118280	0.0591399	+	0.998250i	$0.481164\pi$
$720$	−4.41421	−0.164508
$721$	0	0
$722$	1.00000	0.0372161
$723$	30.5563	1.13640
$724$	−3.51472	−0.130623
$725$	113.397	4.21146
$726$	10.0000	0.371135
$727$	18.2721	0.677674	0.338837	−	0.940845i	$-0.389967\pi$
$727$	18.2721	0.677674	0.338837	+	0.940845i	$0.389967\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	40.4853	1.49843
$731$	−9.51472	−0.351915
$732$	−0.828427	−0.0306195
$733$	−42.1838	−1.55809	−0.779046	−	0.626966i	$-0.784296\pi$
$733$	−42.1838	−1.55809	−0.779046	+	0.626966i	$0.784296\pi$
$734$	−3.24264	−0.119688
$735$	0	0
$736$	0.585786	0.0215924
$737$	2.00000	0.0736709
$738$	−3.41421	−0.125679
$739$	2.44365	0.0898911	0.0449456	−	0.998989i	$-0.485689\pi$
$739$	2.44365	0.0898911	0.0449456	+	0.998989i	$0.485689\pi$
$740$	36.3848	1.33753
$741$	2.82843	0.103905
$742$	0	0
$743$	52.9117	1.94114	0.970571	−	0.240816i	$-0.0774150\pi$
$743$	52.9117	1.94114	0.970571	+	0.240816i	$0.0774150\pi$
$744$	−0.656854	−0.0240814
$745$	6.68629	0.244967
$746$	−16.4853	−0.603569
$747$	11.1421	0.407669
$748$	−4.24264	−0.155126
$749$	0	0
$750$	41.8701	1.52888
$751$	46.1127	1.68268	0.841338	−	0.540509i	$-0.181768\pi$
$751$	46.1127	1.68268	0.841338	+	0.540509i	$0.181768\pi$
$752$	8.82843	0.321940
$753$	21.0000	0.765283
$754$	−22.1421	−0.806369
$755$	100.012	3.63982
$756$	0	0
$757$	−41.2132	−1.49792	−0.748960	−	0.662616i	$-0.769446\pi$
$757$	−41.2132	−1.49792	−0.748960	+	0.662616i	$0.769446\pi$
$758$	−19.3137	−0.701505
$759$	0.585786	0.0212627
$760$	−4.41421	−0.160120
$761$	−22.1421	−0.802652	−0.401326	−	0.915935i	$-0.631451\pi$
$761$	−22.1421	−0.802652	−0.401326	+	0.915935i	$0.631451\pi$
$762$	0.171573	0.00621543
$763$	0	0
$764$	10.1421	0.366930
$765$	−18.7279	−0.677109
$766$	4.34315	0.156924
$767$	22.8284	0.824287
$768$	−1.00000	−0.0360844
$769$	44.6569	1.61037	0.805184	−	0.593026i	$-0.202067\pi$
$769$	44.6569	1.61037	0.805184	+	0.593026i	$0.202067\pi$
$770$	0	0
$771$	−6.00000	−0.216085
$772$	1.72792	0.0621893
$773$	10.6274	0.382242	0.191121	−	0.981567i	$-0.438788\pi$
$773$	10.6274	0.382242	0.191121	+	0.981567i	$0.438788\pi$
$774$	−2.24264	−0.0806101
$775$	9.51472	0.341779
$776$	−8.41421	−0.302053
$777$	0	0
$778$	28.8284	1.03355
$779$	−3.41421	−0.122327
$780$	−12.4853	−0.447045
$781$	−11.8995	−0.425797
$782$	2.48528	0.0888735
$783$	−7.82843	−0.279765
$784$	0	0
$785$	−55.1127	−1.96706
$786$	18.3137	0.653228
$787$	41.3137	1.47267	0.736337	−	0.676615i	$-0.236554\pi$
$787$	41.3137	1.47267	0.736337	+	0.676615i	$0.236554\pi$
$788$	6.82843	0.243253
$789$	−19.5563	−0.696224
$790$	25.7279	0.915358
$791$	0	0
$792$	−1.00000	−0.0355335
$793$	−2.34315	−0.0832075
$794$	−5.17157	−0.183532
$795$	−16.8995	−0.599363
$796$	−8.48528	−0.300753
$797$	−9.00000	−0.318796	−0.159398	−	0.987214i	$-0.550955\pi$
$797$	−9.00000	−0.318796	−0.159398	+	0.987214i	$0.550955\pi$
$798$	0	0
$799$	37.4558	1.32509
$800$	14.4853	0.512132
$801$	12.2426	0.432572
$802$	−14.1421	−0.499376
$803$	9.17157	0.323658
$804$	2.00000	0.0705346
$805$	0	0
$806$	−1.85786	−0.0654405
$807$	−1.00000	−0.0352017
$808$	−18.9706	−0.667382
$809$	2.87006	0.100906	0.0504529	−	0.998726i	$-0.483934\pi$
$809$	2.87006	0.100906	0.0504529	+	0.998726i	$0.483934\pi$
$810$	−4.41421	−0.155100
$811$	−27.5563	−0.967634	−0.483817	−	0.875169i	$-0.660750\pi$
$811$	−27.5563	−0.967634	−0.483817	+	0.875169i	$0.660750\pi$
$812$	0	0
$813$	10.8995	0.382262
$814$	8.24264	0.288904
$815$	22.8284	0.799645
$816$	−4.24264	−0.148522
$817$	−2.24264	−0.0784601
$818$	11.1005	0.388120
$819$	0	0
$820$	15.0711	0.526305
$821$	−45.1838	−1.57692	−0.788462	−	0.615083i	$-0.789122\pi$
$821$	−45.1838	−1.57692	−0.788462	+	0.615083i	$0.789122\pi$
$822$	11.6569	0.406579
$823$	−32.2843	−1.12536	−0.562679	−	0.826675i	$-0.690229\pi$
$823$	−32.2843	−1.12536	−0.562679	+	0.826675i	$0.690229\pi$
$824$	−1.51472	−0.0527677
$825$	14.4853	0.504313
$826$	0	0
$827$	2.27208	0.0790079	0.0395039	−	0.999219i	$-0.487422\pi$
$827$	2.27208	0.0790079	0.0395039	+	0.999219i	$0.487422\pi$
$828$	0.585786	0.0203575
$829$	−15.0294	−0.521994	−0.260997	−	0.965340i	$-0.584051\pi$
$829$	−15.0294	−0.521994	−0.260997	+	0.965340i	$0.584051\pi$
$830$	−49.1838	−1.70719
$831$	22.2426	0.771589
$832$	−2.82843	−0.0980581
$833$	0	0
$834$	11.8995	0.412046
$835$	−82.6690	−2.86088
$836$	−1.00000	−0.0345857
$837$	−0.656854	−0.0227042
$838$	2.97056	0.102616
$839$	10.7868	0.372402	0.186201	−	0.982512i	$-0.440383\pi$
$839$	10.7868	0.372402	0.186201	+	0.982512i	$0.440383\pi$
$840$	0	0
$841$	32.2843	1.11325
$842$	20.8284	0.717795
$843$	−21.3137	−0.734083
$844$	−0.928932	−0.0319752
$845$	22.0711	0.759268
$846$	8.82843	0.303528
$847$	0	0
$848$	−3.82843	−0.131469
$849$	9.55635	0.327973
$850$	61.4558	2.10792
$851$	−4.82843	−0.165516
$852$	−11.8995	−0.407670
$853$	−41.4975	−1.42085	−0.710423	−	0.703775i	$-0.751496\pi$
$853$	−41.4975	−1.42085	−0.710423	+	0.703775i	$0.751496\pi$
$854$	0	0
$855$	−4.41421	−0.150963
$856$	−13.7279	−0.469211
$857$	−41.3137	−1.41125	−0.705625	−	0.708586i	$-0.749334\pi$
$857$	−41.3137	−1.41125	−0.705625	+	0.708586i	$0.749334\pi$
$858$	−2.82843	−0.0965609
$859$	36.4264	1.24285	0.621426	−	0.783472i	$-0.286553\pi$
$859$	36.4264	1.24285	0.621426	+	0.783472i	$0.286553\pi$
$860$	9.89949	0.337570
$861$	0	0
$862$	−33.8995	−1.15462
$863$	29.7574	1.01295	0.506476	−	0.862254i	$-0.330948\pi$
$863$	29.7574	1.01295	0.506476	+	0.862254i	$0.330948\pi$
$864$	−1.00000	−0.0340207
$865$	−105.054	−3.57194
$866$	−25.1716	−0.855365
$867$	−1.00000	−0.0339618
$868$	0	0
$869$	5.82843	0.197716
$870$	34.5563	1.17157
$871$	5.65685	0.191675
$872$	10.2426	0.346860
$873$	−8.41421	−0.284778
$874$	0.585786	0.0198145
$875$	0	0
$876$	9.17157	0.309879
$877$	15.2721	0.515701	0.257851	−	0.966185i	$-0.416986\pi$
$877$	15.2721	0.515701	0.257851	+	0.966185i	$0.416986\pi$
$878$	−28.4558	−0.960338
$879$	23.0000	0.775771
$880$	4.41421	0.148803
$881$	43.9411	1.48041	0.740207	−	0.672379i	$-0.234727\pi$
$881$	43.9411	1.48041	0.740207	+	0.672379i	$0.234727\pi$
$882$	0	0
$883$	−6.87006	−0.231196	−0.115598	−	0.993296i	$-0.536878\pi$
$883$	−6.87006	−0.231196	−0.115598	+	0.993296i	$0.536878\pi$
$884$	−12.0000	−0.403604
$885$	−35.6274	−1.19760
$886$	−3.34315	−0.112315
$887$	−36.9289	−1.23995	−0.619976	−	0.784621i	$-0.712858\pi$
$887$	−36.9289	−1.23995	−0.619976	+	0.784621i	$0.712858\pi$
$888$	8.24264	0.276605
$889$	0	0
$890$	−54.0416	−1.81148
$891$	−1.00000	−0.0335013
$892$	6.51472	0.218129
$893$	8.82843	0.295432
$894$	1.51472	0.0506598
$895$	108.083	3.61282
$896$	0	0
$897$	1.65685	0.0553208
$898$	5.75736	0.192126
$899$	5.14214	0.171500
$900$	14.4853	0.482843
$901$	−16.2426	−0.541121
$902$	3.41421	0.113681
$903$	0	0
$904$	1.75736	0.0584489
$905$	15.5147	0.515727
$906$	22.6569	0.752724
$907$	35.8995	1.19202	0.596012	−	0.802976i	$-0.296751\pi$
$907$	35.8995	1.19202	0.596012	+	0.802976i	$0.296751\pi$
$908$	20.8995	0.693574
$909$	−18.9706	−0.629214
$910$	0	0
$911$	−23.1716	−0.767708	−0.383854	−	0.923394i	$-0.625403\pi$
$911$	−23.1716	−0.767708	−0.383854	+	0.923394i	$0.625403\pi$
$912$	−1.00000	−0.0331133
$913$	−11.1421	−0.368751
$914$	−26.1127	−0.863731
$915$	3.65685	0.120892
$916$	19.7990	0.654177
$917$	0	0
$918$	−4.24264	−0.140028
$919$	−51.6569	−1.70400	−0.852001	−	0.523540i	$-0.824611\pi$
$919$	−51.6569	−1.70400	−0.852001	+	0.523540i	$0.824611\pi$
$920$	−2.58579	−0.0852509
$921$	−4.58579	−0.151107
$922$	5.31371	0.174998
$923$	−33.6569	−1.10783
$924$	0	0
$925$	−119.397	−3.92575
$926$	−9.65685	−0.317344
$927$	−1.51472	−0.0497499
$928$	7.82843	0.256981
$929$	−17.0711	−0.560084	−0.280042	−	0.959988i	$-0.590348\pi$
$929$	−17.0711	−0.560084	−0.280042	+	0.959988i	$0.590348\pi$
$930$	2.89949	0.0950782
$931$	0	0
$932$	−10.8284	−0.354697
$933$	−13.7574	−0.450396
$934$	−20.8284	−0.681527
$935$	18.7279	0.612469
$936$	−2.82843	−0.0924500
$937$	29.1421	0.952032	0.476016	−	0.879437i	$-0.342080\pi$
$937$	29.1421	0.952032	0.476016	+	0.879437i	$0.342080\pi$
$938$	0	0
$939$	−1.82843	−0.0596685
$940$	−38.9706	−1.27108
$941$	−3.68629	−0.120170	−0.0600848	−	0.998193i	$-0.519137\pi$
$941$	−3.68629	−0.120170	−0.0600848	+	0.998193i	$0.519137\pi$
$942$	−12.4853	−0.406792
$943$	−2.00000	−0.0651290
$944$	−8.07107	−0.262691
$945$	0	0
$946$	2.24264	0.0729145
$947$	−20.3431	−0.661063	−0.330532	−	0.943795i	$-0.607228\pi$
$947$	−20.3431	−0.661063	−0.330532	+	0.943795i	$0.607228\pi$
$948$	5.82843	0.189299
$949$	25.9411	0.842085
$950$	14.4853	0.469965
$951$	−7.48528	−0.242727
$952$	0	0
$953$	44.8284	1.45214	0.726068	−	0.687623i	$-0.241346\pi$
$953$	44.8284	1.45214	0.726068	+	0.687623i	$0.241346\pi$
$954$	−3.82843	−0.123950
$955$	−44.7696	−1.44871
$956$	−28.2843	−0.914779
$957$	7.82843	0.253057
$958$	−21.3137	−0.688615
$959$	0	0
$960$	4.41421	0.142468
$961$	−30.5685	−0.986082
$962$	23.3137	0.751664
$963$	−13.7279	−0.442376
$964$	−30.5563	−0.984154
$965$	−7.62742	−0.245535
$966$	0	0
$967$	0.556349	0.0178910	0.00894549	−	0.999960i	$-0.497153\pi$
$967$	0.556349	0.0178910	0.00894549	+	0.999960i	$0.497153\pi$
$968$	−10.0000	−0.321412
$969$	−4.24264	−0.136293
$970$	37.1421	1.19256
$971$	−11.0416	−0.354343	−0.177171	−	0.984180i	$-0.556695\pi$
$971$	−11.0416	−0.354343	−0.177171	+	0.984180i	$0.556695\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	0.798990	0.0256013
$975$	40.9706	1.31211
$976$	0.828427	0.0265173
$977$	−2.00000	−0.0639857	−0.0319928	−	0.999488i	$-0.510185\pi$
$977$	−2.00000	−0.0639857	−0.0319928	+	0.999488i	$0.510185\pi$
$978$	5.17157	0.165369
$979$	−12.2426	−0.391276
$980$	0	0
$981$	10.2426	0.327022
$982$	19.1421	0.610850
$983$	15.0294	0.479365	0.239682	−	0.970851i	$-0.422957\pi$
$983$	15.0294	0.479365	0.239682	+	0.970851i	$0.422957\pi$
$984$	3.41421	0.108841
$985$	−30.1421	−0.960408
$986$	33.2132	1.05772
$987$	0	0
$988$	−2.82843	−0.0899843
$989$	−1.31371	−0.0417735
$990$	4.41421	0.140293
$991$	33.6274	1.06821	0.534105	−	0.845418i	$-0.320649\pi$
$991$	33.6274	1.06821	0.534105	+	0.845418i	$0.320649\pi$
$992$	0.656854	0.0208551
$993$	−32.3848	−1.02770
$994$	0	0
$995$	37.4558	1.18743
$996$	−11.1421	−0.353052
$997$	8.82843	0.279599	0.139800	−	0.990180i	$-0.455354\pi$
$997$	8.82843	0.279599	0.139800	+	0.990180i	$0.455354\pi$
$998$	−13.3137	−0.421438
$999$	8.24264	0.260786

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5586.2.a.bg.1.1		2
7.2	even	3		798.2.j.h.571.2	yes	4
7.4	even	3		798.2.j.h.457.2	✓	4
7.6	odd	2		5586.2.a.br.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.j.h.457.2	✓	4	7.4	even	3
798.2.j.h.571.2	yes	4	7.2	even	3
5586.2.a.bg.1.1		2	1.1	even	1	trivial
5586.2.a.br.1.2		2	7.6	odd	2

Overview	Random
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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:	\( N \)	\(=\)	\( 5586 = 2 \cdot 3 \cdot 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5586.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.41421 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.41421 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -4.41421 q^{10} -1.00000 q^{11} -1.00000 q^{12} -2.82843 q^{13} +4.41421 q^{15} +1.00000 q^{16} +4.24264 q^{17} +1.00000 q^{18} +1.00000 q^{19} -4.41421 q^{20} -1.00000 q^{22} +0.585786 q^{23} -1.00000 q^{24} +14.4853 q^{25} -2.82843 q^{26} -1.00000 q^{27} +7.82843 q^{29} +4.41421 q^{30} +0.656854 q^{31} +1.00000 q^{32} +1.00000 q^{33} +4.24264 q^{34} +1.00000 q^{36} -8.24264 q^{37} +1.00000 q^{38} +2.82843 q^{39} -4.41421 q^{40} -3.41421 q^{41} -2.24264 q^{43} -1.00000 q^{44} -4.41421 q^{45} +0.585786 q^{46} +8.82843 q^{47} -1.00000 q^{48} +14.4853 q^{50} -4.24264 q^{51} -2.82843 q^{52} -3.82843 q^{53} -1.00000 q^{54} +4.41421 q^{55} -1.00000 q^{57} +7.82843 q^{58} -8.07107 q^{59} +4.41421 q^{60} +0.828427 q^{61} +0.656854 q^{62} +1.00000 q^{64} +12.4853 q^{65} +1.00000 q^{66} -2.00000 q^{67} +4.24264 q^{68} -0.585786 q^{69} +11.8995 q^{71} +1.00000 q^{72} -9.17157 q^{73} -8.24264 q^{74} -14.4853 q^{75} +1.00000 q^{76} +2.82843 q^{78} -5.82843 q^{79} -4.41421 q^{80} +1.00000 q^{81} -3.41421 q^{82} +11.1421 q^{83} -18.7279 q^{85} -2.24264 q^{86} -7.82843 q^{87} -1.00000 q^{88} +12.2426 q^{89} -4.41421 q^{90} +0.585786 q^{92} -0.656854 q^{93} +8.82843 q^{94} -4.41421 q^{95} -1.00000 q^{96} -8.41421 q^{97} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 6 q^{5} - 2 q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 6 * q^5 - 2 * q^6 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 6 q^{5} - 2 q^{6} + 2 q^{8} + 2 q^{9} - 6 q^{10} - 2 q^{11} - 2 q^{12} + 6 q^{15} + 2 q^{16} + 2 q^{18} + 2 q^{19} - 6 q^{20} - 2 q^{22} + 4 q^{23} - 2 q^{24} + 12 q^{25} - 2 q^{27} + 10 q^{29} + 6 q^{30} - 10 q^{31} + 2 q^{32} + 2 q^{33} + 2 q^{36} - 8 q^{37} + 2 q^{38} - 6 q^{40} - 4 q^{41} + 4 q^{43} - 2 q^{44} - 6 q^{45} + 4 q^{46} + 12 q^{47} - 2 q^{48} + 12 q^{50} - 2 q^{53} - 2 q^{54} + 6 q^{55} - 2 q^{57} + 10 q^{58} - 2 q^{59} + 6 q^{60} - 4 q^{61} - 10 q^{62} + 2 q^{64} + 8 q^{65} + 2 q^{66} - 4 q^{67} - 4 q^{69} + 4 q^{71} + 2 q^{72} - 24 q^{73} - 8 q^{74} - 12 q^{75} + 2 q^{76} - 6 q^{79} - 6 q^{80} + 2 q^{81} - 4 q^{82} - 6 q^{83} - 12 q^{85} + 4 q^{86} - 10 q^{87} - 2 q^{88} + 16 q^{89} - 6 q^{90} + 4 q^{92} + 10 q^{93} + 12 q^{94} - 6 q^{95} - 2 q^{96} - 14 q^{97} - 2 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 6 * q^5 - 2 * q^6 + 2 * q^8 + 2 * q^9 - 6 * q^10 - 2 * q^11 - 2 * q^12 + 6 * q^15 + 2 * q^16 + 2 * q^18 + 2 * q^19 - 6 * q^20 - 2 * q^22 + 4 * q^23 - 2 * q^24 + 12 * q^25 - 2 * q^27 + 10 * q^29 + 6 * q^30 - 10 * q^31 + 2 * q^32 + 2 * q^33 + 2 * q^36 - 8 * q^37 + 2 * q^38 - 6 * q^40 - 4 * q^41 + 4 * q^43 - 2 * q^44 - 6 * q^45 + 4 * q^46 + 12 * q^47 - 2 * q^48 + 12 * q^50 - 2 * q^53 - 2 * q^54 + 6 * q^55 - 2 * q^57 + 10 * q^58 - 2 * q^59 + 6 * q^60 - 4 * q^61 - 10 * q^62 + 2 * q^64 + 8 * q^65 + 2 * q^66 - 4 * q^67 - 4 * q^69 + 4 * q^71 + 2 * q^72 - 24 * q^73 - 8 * q^74 - 12 * q^75 + 2 * q^76 - 6 * q^79 - 6 * q^80 + 2 * q^81 - 4 * q^82 - 6 * q^83 - 12 * q^85 + 4 * q^86 - 10 * q^87 - 2 * q^88 + 16 * q^89 - 6 * q^90 + 4 * q^92 + 10 * q^93 + 12 * q^94 - 6 * q^95 - 2 * q^96 - 14 * q^97 - 2 * q^99

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