LMFDB - Embedded newform 5586.2.a.cf.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:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} - 22x^{6} + 60x^{5} + 87x^{4} - 176x^{3} - 40x^{2} + 64x + 16 $ x^8 - 4x^7 - 22x^6 + 60x^5 + 87x^4 - 176x^3 - 40x^2 + 64*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.514116$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.93854 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.93854 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -3.93854 q^{10} +1.27293 q^{11} +1.00000 q^{12} -5.94914 q^{13} -3.93854 q^{15} +1.00000 q^{16} +3.05310 q^{17} +1.00000 q^{18} +1.00000 q^{19} -3.93854 q^{20} +1.27293 q^{22} -0.148774 q^{23} +1.00000 q^{24} +10.5121 q^{25} -5.94914 q^{26} +1.00000 q^{27} -6.60877 q^{29} -3.93854 q^{30} -8.01988 q^{31} +1.00000 q^{32} +1.27293 q^{33} +3.05310 q^{34} +1.00000 q^{36} +6.14824 q^{37} +1.00000 q^{38} -5.94914 q^{39} -3.93854 q^{40} +6.28274 q^{41} +7.91174 q^{43} +1.27293 q^{44} -3.93854 q^{45} -0.148774 q^{46} +8.22182 q^{47} +1.00000 q^{48} +10.5121 q^{50} +3.05310 q^{51} -5.94914 q^{52} +11.3312 q^{53} +1.00000 q^{54} -5.01349 q^{55} +1.00000 q^{57} -6.60877 q^{58} +1.84029 q^{59} -3.93854 q^{60} +12.1881 q^{61} -8.01988 q^{62} +1.00000 q^{64} +23.4309 q^{65} +1.27293 q^{66} +2.61205 q^{67} +3.05310 q^{68} -0.148774 q^{69} -12.8117 q^{71} +1.00000 q^{72} -16.2859 q^{73} +6.14824 q^{74} +10.5121 q^{75} +1.00000 q^{76} -5.94914 q^{78} +7.44674 q^{79} -3.93854 q^{80} +1.00000 q^{81} +6.28274 q^{82} +12.1746 q^{83} -12.0248 q^{85} +7.91174 q^{86} -6.60877 q^{87} +1.27293 q^{88} -5.40934 q^{89} -3.93854 q^{90} -0.148774 q^{92} -8.01988 q^{93} +8.22182 q^{94} -3.93854 q^{95} +1.00000 q^{96} +11.2277 q^{97} +1.27293 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 4 q^{5} + 8 q^{6} + 8 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 4 * q^5 + 8 * q^6 + 8 * q^8 + 8 * q^9	$ 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 4 q^{5} + 8 q^{6} + 8 q^{8} + 8 q^{9} + 4 q^{10} + 8 q^{11} + 8 q^{12} - 4 q^{13} + 4 q^{15} + 8 q^{16} + 8 q^{17} + 8 q^{18} + 8 q^{19} + 4 q^{20} + 8 q^{22} + 4 q^{23} + 8 q^{24} + 24 q^{25} - 4 q^{26} + 8 q^{27} + 16 q^{29} + 4 q^{30} + 4 q^{31} + 8 q^{32} + 8 q^{33} + 8 q^{34} + 8 q^{36} + 12 q^{37} + 8 q^{38} - 4 q^{39} + 4 q^{40} + 16 q^{43} + 8 q^{44} + 4 q^{45} + 4 q^{46} + 12 q^{47} + 8 q^{48} + 24 q^{50} + 8 q^{51} - 4 q^{52} + 24 q^{53} + 8 q^{54} - 8 q^{55} + 8 q^{57} + 16 q^{58} - 8 q^{59} + 4 q^{60} + 4 q^{62} + 8 q^{64} + 8 q^{65} + 8 q^{66} + 8 q^{67} + 8 q^{68} + 4 q^{69} + 24 q^{71} + 8 q^{72} - 16 q^{73} + 12 q^{74} + 24 q^{75} + 8 q^{76} - 4 q^{78} + 20 q^{79} + 4 q^{80} + 8 q^{81} + 16 q^{83} + 48 q^{85} + 16 q^{86} + 16 q^{87} + 8 q^{88} + 4 q^{90} + 4 q^{92} + 4 q^{93} + 12 q^{94} + 4 q^{95} + 8 q^{96} - 8 q^{97} + 8 q^{99}+O(q^{100}) $ 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 4 * q^5 + 8 * q^6 + 8 * q^8 + 8 * q^9 + 4 * q^10 + 8 * q^11 + 8 * q^12 - 4 * q^13 + 4 * q^15 + 8 * q^16 + 8 * q^17 + 8 * q^18 + 8 * q^19 + 4 * q^20 + 8 * q^22 + 4 * q^23 + 8 * q^24 + 24 * q^25 - 4 * q^26 + 8 * q^27 + 16 * q^29 + 4 * q^30 + 4 * q^31 + 8 * q^32 + 8 * q^33 + 8 * q^34 + 8 * q^36 + 12 * q^37 + 8 * q^38 - 4 * q^39 + 4 * q^40 + 16 * q^43 + 8 * q^44 + 4 * q^45 + 4 * q^46 + 12 * q^47 + 8 * q^48 + 24 * q^50 + 8 * q^51 - 4 * q^52 + 24 * q^53 + 8 * q^54 - 8 * q^55 + 8 * q^57 + 16 * q^58 - 8 * q^59 + 4 * q^60 + 4 * q^62 + 8 * q^64 + 8 * q^65 + 8 * q^66 + 8 * q^67 + 8 * q^68 + 4 * q^69 + 24 * q^71 + 8 * q^72 - 16 * q^73 + 12 * q^74 + 24 * q^75 + 8 * q^76 - 4 * q^78 + 20 * q^79 + 4 * q^80 + 8 * q^81 + 16 * q^83 + 48 * q^85 + 16 * q^86 + 16 * q^87 + 8 * q^88 + 4 * q^90 + 4 * q^92 + 4 * q^93 + 12 * q^94 + 4 * q^95 + 8 * q^96 - 8 * q^97 + 8 * 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
$5$	−3.93854	−1.76137	−0.880685	−	0.473702i	$-0.842917\pi$
$5$	−3.93854	−1.76137	−0.880685	+	0.473702i	$0.842917\pi$
$6$	1.00000	0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−3.93854	−1.24548
$11$	1.27293	0.383803	0.191901	−	0.981414i	$-0.438535\pi$
$11$	1.27293	0.383803	0.191901	+	0.981414i	$0.438535\pi$
$12$	1.00000	0.288675
$13$	−5.94914	−1.64999	−0.824997	−	0.565137i	$-0.808823\pi$
$13$	−5.94914	−1.64999	−0.824997	+	0.565137i	$0.808823\pi$
$14$	0	0
$15$	−3.93854	−1.01693
$16$	1.00000	0.250000
$17$	3.05310	0.740486	0.370243	−	0.928935i	$-0.379274\pi$
$17$	3.05310	0.740486	0.370243	+	0.928935i	$0.379274\pi$
$18$	1.00000	0.235702
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−3.93854	−0.880685
$21$	0	0
$22$	1.27293	0.271390
$23$	−0.148774	−0.0310216	−0.0155108	−	0.999880i	$-0.504937\pi$
$23$	−0.148774	−0.0310216	−0.0155108	+	0.999880i	$0.504937\pi$
$24$	1.00000	0.204124
$25$	10.5121	2.10242
$26$	−5.94914	−1.16672
$27$	1.00000	0.192450
$28$	0	0
$29$	−6.60877	−1.22722	−0.613609	−	0.789610i	$-0.710283\pi$
$29$	−6.60877	−1.22722	−0.613609	+	0.789610i	$0.710283\pi$
$30$	−3.93854	−0.719076
$31$	−8.01988	−1.44041	−0.720206	−	0.693760i	$-0.755953\pi$
$31$	−8.01988	−1.44041	−0.720206	+	0.693760i	$0.755953\pi$
$32$	1.00000	0.176777
$33$	1.27293	0.221589
$34$	3.05310	0.523603
$35$	0	0
$36$	1.00000	0.166667
$37$	6.14824	1.01076	0.505382	−	0.862896i	$-0.331352\pi$
$37$	6.14824	1.01076	0.505382	+	0.862896i	$0.331352\pi$
$38$	1.00000	0.162221
$39$	−5.94914	−0.952624
$40$	−3.93854	−0.622738
$41$	6.28274	0.981198	0.490599	−	0.871385i	$-0.336778\pi$
$41$	6.28274	0.981198	0.490599	+	0.871385i	$0.336778\pi$
$42$	0	0
$43$	7.91174	1.20653	0.603264	−	0.797541i	$-0.293866\pi$
$43$	7.91174	1.20653	0.603264	+	0.797541i	$0.293866\pi$
$44$	1.27293	0.191901
$45$	−3.93854	−0.587123
$46$	−0.148774	−0.0219356
$47$	8.22182	1.19928	0.599638	−	0.800272i	$-0.295311\pi$
$47$	8.22182	1.19928	0.599638	+	0.800272i	$0.295311\pi$
$48$	1.00000	0.144338
$49$	0	0
$50$	10.5121	1.48664
$51$	3.05310	0.427520
$52$	−5.94914	−0.824997
$53$	11.3312	1.55646	0.778232	−	0.627977i	$-0.216117\pi$
$53$	11.3312	1.55646	0.778232	+	0.627977i	$0.216117\pi$
$54$	1.00000	0.136083
$55$	−5.01349	−0.676019
$56$	0	0
$57$	1.00000	0.132453
$58$	−6.60877	−0.867774
$59$	1.84029	0.239585	0.119793	−	0.992799i	$-0.461777\pi$
$59$	1.84029	0.239585	0.119793	+	0.992799i	$0.461777\pi$
$60$	−3.93854	−0.508464
$61$	12.1881	1.56053	0.780266	−	0.625448i	$-0.215084\pi$
$61$	12.1881	1.56053	0.780266	+	0.625448i	$0.215084\pi$
$62$	−8.01988	−1.01853
$63$	0	0
$64$	1.00000	0.125000
$65$	23.4309	2.90625
$66$	1.27293	0.156687
$67$	2.61205	0.319112	0.159556	−	0.987189i	$-0.448994\pi$
$67$	2.61205	0.319112	0.159556	+	0.987189i	$0.448994\pi$
$68$	3.05310	0.370243
$69$	−0.148774	−0.0179103
$70$	0	0
$71$	−12.8117	−1.52047	−0.760236	−	0.649647i	$-0.774917\pi$
$71$	−12.8117	−1.52047	−0.760236	+	0.649647i	$0.774917\pi$
$72$	1.00000	0.117851
$73$	−16.2859	−1.90612	−0.953059	−	0.302784i	$-0.902084\pi$
$73$	−16.2859	−1.90612	−0.953059	+	0.302784i	$0.902084\pi$
$74$	6.14824	0.714718
$75$	10.5121	1.21384
$76$	1.00000	0.114708
$77$	0	0
$78$	−5.94914	−0.673607
$79$	7.44674	0.837824	0.418912	−	0.908027i	$-0.362412\pi$
$79$	7.44674	0.837824	0.418912	+	0.908027i	$0.362412\pi$
$80$	−3.93854	−0.440343
$81$	1.00000	0.111111
$82$	6.28274	0.693812
$83$	12.1746	1.33634	0.668170	−	0.744009i	$-0.267078\pi$
$83$	12.1746	1.33634	0.668170	+	0.744009i	$0.267078\pi$
$84$	0	0
$85$	−12.0248	−1.30427
$86$	7.91174	0.853144
$87$	−6.60877	−0.708534
$88$	1.27293	0.135695
$89$	−5.40934	−0.573389	−0.286694	−	0.958022i	$-0.592556\pi$
$89$	−5.40934	−0.573389	−0.286694	+	0.958022i	$0.592556\pi$
$90$	−3.93854	−0.415159
$91$	0	0
$92$	−0.148774	−0.0155108
$93$	−8.01988	−0.831623
$94$	8.22182	0.848016
$95$	−3.93854	−0.404086
$96$	1.00000	0.102062
$97$	11.2277	1.14000	0.570002	−	0.821643i	$-0.306942\pi$
$97$	11.2277	1.14000	0.570002	+	0.821643i	$0.306942\pi$
$98$	0	0
$99$	1.27293	0.127934
$100$	10.5121	1.05121
$101$	4.38789	0.436612	0.218306	−	0.975880i	$-0.429947\pi$
$101$	4.38789	0.436612	0.218306	+	0.975880i	$0.429947\pi$
$102$	3.05310	0.302302
$103$	6.48370	0.638858	0.319429	−	0.947610i	$-0.396509\pi$
$103$	6.48370	0.638858	0.319429	+	0.947610i	$0.396509\pi$
$104$	−5.94914	−0.583361
$105$	0	0
$106$	11.3312	1.10059
$107$	4.09675	0.396047	0.198024	−	0.980197i	$-0.436548\pi$
$107$	4.09675	0.396047	0.198024	+	0.980197i	$0.436548\pi$
$108$	1.00000	0.0962250
$109$	5.93860	0.568815	0.284407	−	0.958704i	$-0.408203\pi$
$109$	5.93860	0.568815	0.284407	+	0.958704i	$0.408203\pi$
$110$	−5.01349	−0.478017
$111$	6.14824	0.583565
$112$	0	0
$113$	3.83385	0.360658	0.180329	−	0.983606i	$-0.442284\pi$
$113$	3.83385	0.360658	0.180329	+	0.983606i	$0.442284\pi$
$114$	1.00000	0.0936586
$115$	0.585954	0.0546405
$116$	−6.60877	−0.613609
$117$	−5.94914	−0.549998
$118$	1.84029	0.169412
$119$	0	0
$120$	−3.93854	−0.359538
$121$	−9.37965	−0.852695
$122$	12.1881	1.10346
$123$	6.28274	0.566495
$124$	−8.01988	−0.720206
$125$	−21.7097	−1.94178
$126$	0	0
$127$	−15.4576	−1.37164	−0.685821	−	0.727771i	$-0.740557\pi$
$127$	−15.4576	−1.37164	−0.685821	+	0.727771i	$0.740557\pi$
$128$	1.00000	0.0883883
$129$	7.91174	0.696589
$130$	23.4309	2.05503
$131$	−5.76015	−0.503267	−0.251633	−	0.967823i	$-0.580968\pi$
$131$	−5.76015	−0.503267	−0.251633	+	0.967823i	$0.580968\pi$
$132$	1.27293	0.110794
$133$	0	0
$134$	2.61205	0.225646
$135$	−3.93854	−0.338976
$136$	3.05310	0.261801
$137$	16.2798	1.39088	0.695440	−	0.718584i	$-0.255209\pi$
$137$	16.2798	1.39088	0.695440	+	0.718584i	$0.255209\pi$
$138$	−0.148774	−0.0126645
$139$	8.24825	0.699608	0.349804	−	0.936823i	$-0.386248\pi$
$139$	8.24825	0.699608	0.349804	+	0.936823i	$0.386248\pi$
$140$	0	0
$141$	8.22182	0.692402
$142$	−12.8117	−1.07514
$143$	−7.57283	−0.633272
$144$	1.00000	0.0833333
$145$	26.0289	2.16158
$146$	−16.2859	−1.34783
$147$	0	0
$148$	6.14824	0.505382
$149$	−5.92450	−0.485354	−0.242677	−	0.970107i	$-0.578026\pi$
$149$	−5.92450	−0.485354	−0.242677	+	0.970107i	$0.578026\pi$
$150$	10.5121	0.858311
$151$	−1.09856	−0.0893992	−0.0446996	−	0.999000i	$-0.514233\pi$
$151$	−1.09856	−0.0893992	−0.0446996	+	0.999000i	$0.514233\pi$
$152$	1.00000	0.0811107
$153$	3.05310	0.246829
$154$	0	0
$155$	31.5866	2.53710
$156$	−5.94914	−0.476312
$157$	−8.29607	−0.662098	−0.331049	−	0.943613i	$-0.607403\pi$
$157$	−8.29607	−0.662098	−0.331049	+	0.943613i	$0.607403\pi$
$158$	7.44674	0.592431
$159$	11.3312	0.898625
$160$	−3.93854	−0.311369
$161$	0	0
$162$	1.00000	0.0785674
$163$	12.5954	0.986550	0.493275	−	0.869873i	$-0.335800\pi$
$163$	12.5954	0.986550	0.493275	+	0.869873i	$0.335800\pi$
$164$	6.28274	0.490599
$165$	−5.01349	−0.390300
$166$	12.1746	0.944935
$167$	9.65057	0.746784	0.373392	−	0.927674i	$-0.378195\pi$
$167$	9.65057	0.746784	0.373392	+	0.927674i	$0.378195\pi$
$168$	0	0
$169$	22.3922	1.72248
$170$	−12.0248	−0.922258
$171$	1.00000	0.0764719
$172$	7.91174	0.603264
$173$	14.1088	1.07267	0.536335	−	0.844005i	$-0.319808\pi$
$173$	14.1088	1.07267	0.536335	+	0.844005i	$0.319808\pi$
$174$	−6.60877	−0.501009
$175$	0	0
$176$	1.27293	0.0959507
$177$	1.84029	0.138325
$178$	−5.40934	−0.405447
$179$	−12.4256	−0.928731	−0.464365	−	0.885644i	$-0.653718\pi$
$179$	−12.4256	−0.928731	−0.464365	+	0.885644i	$0.653718\pi$
$180$	−3.93854	−0.293562
$181$	−12.3729	−0.919671	−0.459836	−	0.888004i	$-0.652092\pi$
$181$	−12.3729	−0.919671	−0.459836	+	0.888004i	$0.652092\pi$
$182$	0	0
$183$	12.1881	0.900973
$184$	−0.148774	−0.0109678
$185$	−24.2151	−1.78033
$186$	−8.01988	−0.588046
$187$	3.88638	0.284201
$188$	8.22182	0.599638
$189$	0	0
$190$	−3.93854	−0.285732
$191$	−4.07435	−0.294810	−0.147405	−	0.989076i	$-0.547092\pi$
$191$	−4.07435	−0.294810	−0.147405	+	0.989076i	$0.547092\pi$
$192$	1.00000	0.0721688
$193$	−4.50280	−0.324119	−0.162059	−	0.986781i	$-0.551814\pi$
$193$	−4.50280	−0.324119	−0.162059	+	0.986781i	$0.551814\pi$
$194$	11.2277	0.806105
$195$	23.4309	1.67792
$196$	0	0
$197$	0.322407	0.0229706	0.0114853	−	0.999934i	$-0.496344\pi$
$197$	0.322407	0.0229706	0.0114853	+	0.999934i	$0.496344\pi$
$198$	1.27293	0.0904632
$199$	22.6125	1.60296	0.801478	−	0.598024i	$-0.204047\pi$
$199$	22.6125	1.60296	0.801478	+	0.598024i	$0.204047\pi$
$200$	10.5121	0.743319
$201$	2.61205	0.184239
$202$	4.38789	0.308731
$203$	0	0
$204$	3.05310	0.213760
$205$	−24.7448	−1.72825
$206$	6.48370	0.451741
$207$	−0.148774	−0.0103405
$208$	−5.94914	−0.412498
$209$	1.27293	0.0880504
$210$	0	0
$211$	0.346997	0.0238882	0.0119441	−	0.999929i	$-0.496198\pi$
$211$	0.346997	0.0238882	0.0119441	+	0.999929i	$0.496198\pi$
$212$	11.3312	0.778232
$213$	−12.8117	−0.877844
$214$	4.09675	0.280048
$215$	−31.1607	−2.12514
$216$	1.00000	0.0680414
$217$	0	0
$218$	5.93860	0.402213
$219$	−16.2859	−1.10050
$220$	−5.01349	−0.338009
$221$	−18.1633	−1.22180
$222$	6.14824	0.412643
$223$	−2.29672	−0.153800	−0.0769000	−	0.997039i	$-0.524502\pi$
$223$	−2.29672	−0.153800	−0.0769000	+	0.997039i	$0.524502\pi$
$224$	0	0
$225$	10.5121	0.700808
$226$	3.83385	0.255024
$227$	15.3728	1.02033	0.510166	−	0.860076i	$-0.329584\pi$
$227$	15.3728	1.02033	0.510166	+	0.860076i	$0.329584\pi$
$228$	1.00000	0.0662266
$229$	−11.7178	−0.774336	−0.387168	−	0.922009i	$-0.626547\pi$
$229$	−11.7178	−0.774336	−0.387168	+	0.922009i	$0.626547\pi$
$230$	0.585954	0.0386367
$231$	0	0
$232$	−6.60877	−0.433887
$233$	13.7683	0.901989	0.450995	−	0.892527i	$-0.351069\pi$
$233$	13.7683	0.901989	0.450995	+	0.892527i	$0.351069\pi$
$234$	−5.94914	−0.388907
$235$	−32.3820	−2.11237
$236$	1.84029	0.119793
$237$	7.44674	0.483718
$238$	0	0
$239$	27.3226	1.76735	0.883676	−	0.468100i	$-0.155061\pi$
$239$	27.3226	1.76735	0.883676	+	0.468100i	$0.155061\pi$
$240$	−3.93854	−0.254232
$241$	−29.4781	−1.89885	−0.949427	−	0.313988i	$-0.898335\pi$
$241$	−29.4781	−1.89885	−0.949427	+	0.313988i	$0.898335\pi$
$242$	−9.37965	−0.602947
$243$	1.00000	0.0641500
$244$	12.1881	0.780266
$245$	0	0
$246$	6.28274	0.400573
$247$	−5.94914	−0.378534
$248$	−8.01988	−0.509263
$249$	12.1746	0.771536
$250$	−21.7097	−1.37304
$251$	22.6060	1.42688	0.713440	−	0.700716i	$-0.247136\pi$
$251$	22.6060	1.42688	0.713440	+	0.700716i	$0.247136\pi$
$252$	0	0
$253$	−0.189379	−0.0119062
$254$	−15.4576	−0.969897
$255$	−12.0248	−0.753021
$256$	1.00000	0.0625000
$257$	25.9880	1.62109	0.810543	−	0.585679i	$-0.199172\pi$
$257$	25.9880	1.62109	0.810543	+	0.585679i	$0.199172\pi$
$258$	7.91174	0.492563
$259$	0	0
$260$	23.4309	1.45312
$261$	−6.60877	−0.409072
$262$	−5.76015	−0.355863
$263$	6.16848	0.380365	0.190182	−	0.981749i	$-0.439092\pi$
$263$	6.16848	0.380365	0.190182	+	0.981749i	$0.439092\pi$
$264$	1.27293	0.0783434
$265$	−44.6285	−2.74151
$266$	0	0
$267$	−5.40934	−0.331046
$268$	2.61205	0.159556
$269$	10.1268	0.617442	0.308721	−	0.951153i	$-0.400099\pi$
$269$	10.1268	0.617442	0.308721	+	0.951153i	$0.400099\pi$
$270$	−3.93854	−0.239692
$271$	10.9731	0.666568	0.333284	−	0.942826i	$-0.391843\pi$
$271$	10.9731	0.666568	0.333284	+	0.942826i	$0.391843\pi$
$272$	3.05310	0.185122
$273$	0	0
$274$	16.2798	0.983501
$275$	13.3812	0.806916
$276$	−0.148774	−0.00895516
$277$	2.90574	0.174589	0.0872946	−	0.996183i	$-0.472178\pi$
$277$	2.90574	0.174589	0.0872946	+	0.996183i	$0.472178\pi$
$278$	8.24825	0.494697
$279$	−8.01988	−0.480138
$280$	0	0
$281$	13.5310	0.807191	0.403595	−	0.914938i	$-0.367760\pi$
$281$	13.5310	0.807191	0.403595	+	0.914938i	$0.367760\pi$
$282$	8.22182	0.489602
$283$	15.3969	0.915252	0.457626	−	0.889145i	$-0.348700\pi$
$283$	15.3969	0.915252	0.457626	+	0.889145i	$0.348700\pi$
$284$	−12.8117	−0.760236
$285$	−3.93854	−0.233299
$286$	−7.57283	−0.447791
$287$	0	0
$288$	1.00000	0.0589256
$289$	−7.67857	−0.451680
$290$	26.0289	1.52847
$291$	11.2277	0.658182
$292$	−16.2859	−0.953059
$293$	−14.5720	−0.851307	−0.425654	−	0.904886i	$-0.639956\pi$
$293$	−14.5720	−0.851307	−0.425654	+	0.904886i	$0.639956\pi$
$294$	0	0
$295$	−7.24806	−0.421998
$296$	6.14824	0.357359
$297$	1.27293	0.0738629
$298$	−5.92450	−0.343197
$299$	0.885079	0.0511854
$300$	10.5121	0.606918
$301$	0	0
$302$	−1.09856	−0.0632148
$303$	4.38789	0.252078
$304$	1.00000	0.0573539
$305$	−48.0035	−2.74867
$306$	3.05310	0.174534
$307$	−26.2382	−1.49749	−0.748745	−	0.662858i	$-0.769343\pi$
$307$	−26.2382	−1.49749	−0.748745	+	0.662858i	$0.769343\pi$
$308$	0	0
$309$	6.48370	0.368845
$310$	31.5866	1.79400
$311$	7.89074	0.447443	0.223721	−	0.974653i	$-0.428179\pi$
$311$	7.89074	0.447443	0.223721	+	0.974653i	$0.428179\pi$
$312$	−5.94914	−0.336804
$313$	−17.3496	−0.980655	−0.490327	−	0.871538i	$-0.663123\pi$
$313$	−17.3496	−0.980655	−0.490327	+	0.871538i	$0.663123\pi$
$314$	−8.29607	−0.468174
$315$	0	0
$316$	7.44674	0.418912
$317$	31.0193	1.74222	0.871108	−	0.491092i	$-0.163402\pi$
$317$	31.0193	1.74222	0.871108	+	0.491092i	$0.163402\pi$
$318$	11.3312	0.635424
$319$	−8.41250	−0.471009
$320$	−3.93854	−0.220171
$321$	4.09675	0.228658
$322$	0	0
$323$	3.05310	0.169879
$324$	1.00000	0.0555556
$325$	−62.5381	−3.46899
$326$	12.5954	0.697597
$327$	5.93860	0.328405
$328$	6.28274	0.346906
$329$	0	0
$330$	−5.01349	−0.275983
$331$	−27.7615	−1.52591	−0.762954	−	0.646453i	$-0.776252\pi$
$331$	−27.7615	−1.52591	−0.762954	+	0.646453i	$0.776252\pi$
$332$	12.1746	0.668170
$333$	6.14824	0.336921
$334$	9.65057	0.528056
$335$	−10.2877	−0.562075
$336$	0	0
$337$	−11.9053	−0.648523	−0.324261	−	0.945968i	$-0.605116\pi$
$337$	−11.9053	−0.648523	−0.324261	+	0.945968i	$0.605116\pi$
$338$	22.3922	1.21798
$339$	3.83385	0.208226
$340$	−12.0248	−0.652135
$341$	−10.2087	−0.552834
$342$	1.00000	0.0540738
$343$	0	0
$344$	7.91174	0.426572
$345$	0.585954	0.0315467
$346$	14.1088	0.758493
$347$	18.8103	1.00979	0.504895	−	0.863181i	$-0.331531\pi$
$347$	18.8103	1.00979	0.504895	+	0.863181i	$0.331531\pi$
$348$	−6.60877	−0.354267
$349$	−8.76894	−0.469391	−0.234695	−	0.972069i	$-0.575409\pi$
$349$	−8.76894	−0.469391	−0.234695	+	0.972069i	$0.575409\pi$
$350$	0	0
$351$	−5.94914	−0.317541
$352$	1.27293	0.0678474
$353$	−29.8162	−1.58696	−0.793478	−	0.608599i	$-0.791732\pi$
$353$	−29.8162	−1.58696	−0.793478	+	0.608599i	$0.791732\pi$
$354$	1.84029	0.0978103
$355$	50.4595	2.67811
$356$	−5.40934	−0.286694
$357$	0	0
$358$	−12.4256	−0.656712
$359$	17.1263	0.903890	0.451945	−	0.892046i	$-0.350730\pi$
$359$	17.1263	0.903890	0.451945	+	0.892046i	$0.350730\pi$
$360$	−3.93854	−0.207579
$361$	1.00000	0.0526316
$362$	−12.3729	−0.650306
$363$	−9.37965	−0.492304
$364$	0	0
$365$	64.1426	3.35738
$366$	12.1881	0.637084
$367$	24.3662	1.27190	0.635952	−	0.771728i	$-0.280607\pi$
$367$	24.3662	1.27190	0.635952	+	0.771728i	$0.280607\pi$
$368$	−0.148774	−0.00775540
$369$	6.28274	0.327066
$370$	−24.2151	−1.25888
$371$	0	0
$372$	−8.01988	−0.415811
$373$	24.1414	1.24999	0.624997	−	0.780627i	$-0.285100\pi$
$373$	24.1414	1.24999	0.624997	+	0.780627i	$0.285100\pi$
$374$	3.88638	0.200960
$375$	−21.7097	−1.12109
$376$	8.22182	0.424008
$377$	39.3165	2.02490
$378$	0	0
$379$	8.51695	0.437486	0.218743	−	0.975782i	$-0.429804\pi$
$379$	8.51695	0.437486	0.218743	+	0.975782i	$0.429804\pi$
$380$	−3.93854	−0.202043
$381$	−15.4576	−0.791917
$382$	−4.07435	−0.208462
$383$	−17.3654	−0.887331	−0.443665	−	0.896193i	$-0.646322\pi$
$383$	−17.3654	−0.887331	−0.443665	+	0.896193i	$0.646322\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−4.50280	−0.229187
$387$	7.91174	0.402176
$388$	11.2277	0.570002
$389$	−22.5117	−1.14139	−0.570694	−	0.821163i	$-0.693326\pi$
$389$	−22.5117	−1.14139	−0.570694	+	0.821163i	$0.693326\pi$
$390$	23.4309	1.18647
$391$	−0.454223	−0.0229711
$392$	0	0
$393$	−5.76015	−0.290561
$394$	0.322407	0.0162426
$395$	−29.3293	−1.47572
$396$	1.27293	0.0639671
$397$	33.8779	1.70028	0.850140	−	0.526556i	$-0.176517\pi$
$397$	33.8779	1.70028	0.850140	+	0.526556i	$0.176517\pi$
$398$	22.6125	1.13346
$399$	0	0
$400$	10.5121	0.525606
$401$	33.1403	1.65495	0.827474	−	0.561504i	$-0.189777\pi$
$401$	33.1403	1.65495	0.827474	+	0.561504i	$0.189777\pi$
$402$	2.61205	0.130277
$403$	47.7114	2.37667
$404$	4.38789	0.218306
$405$	−3.93854	−0.195708
$406$	0	0
$407$	7.82627	0.387934
$408$	3.05310	0.151151
$409$	−28.2927	−1.39899	−0.699493	−	0.714639i	$-0.746591\pi$
$409$	−28.2927	−1.39899	−0.699493	+	0.714639i	$0.746591\pi$
$410$	−24.7448	−1.22206
$411$	16.2798	0.803025
$412$	6.48370	0.319429
$413$	0	0
$414$	−0.148774	−0.00731186
$415$	−47.9503	−2.35379
$416$	−5.94914	−0.291680
$417$	8.24825	0.403919
$418$	1.27293	0.0622610
$419$	24.5157	1.19767	0.598836	−	0.800872i	$-0.295630\pi$
$419$	24.5157	1.19767	0.598836	+	0.800872i	$0.295630\pi$
$420$	0	0
$421$	−36.4678	−1.77733	−0.888667	−	0.458553i	$-0.848368\pi$
$421$	−36.4678	−1.77733	−0.888667	+	0.458553i	$0.848368\pi$
$422$	0.346997	0.0168915
$423$	8.22182	0.399758
$424$	11.3312	0.550293
$425$	32.0946	1.55682
$426$	−12.8117	−0.620730
$427$	0	0
$428$	4.09675	0.198024
$429$	−7.57283	−0.365620
$430$	−31.1607	−1.50270
$431$	7.38080	0.355521	0.177760	−	0.984074i	$-0.443115\pi$
$431$	7.38080	0.355521	0.177760	+	0.984074i	$0.443115\pi$
$432$	1.00000	0.0481125
$433$	−11.4859	−0.551975	−0.275988	−	0.961161i	$-0.589005\pi$
$433$	−11.4859	−0.551975	−0.275988	+	0.961161i	$0.589005\pi$
$434$	0	0
$435$	26.0289	1.24799
$436$	5.93860	0.284407
$437$	−0.148774	−0.00711684
$438$	−16.2859	−0.778169
$439$	−22.2521	−1.06204	−0.531018	−	0.847360i	$-0.678191\pi$
$439$	−22.2521	−1.06204	−0.531018	+	0.847360i	$0.678191\pi$
$440$	−5.01349	−0.239009
$441$	0	0
$442$	−18.1633	−0.863941
$443$	−22.7804	−1.08233	−0.541165	−	0.840917i	$-0.682016\pi$
$443$	−22.7804	−1.08233	−0.541165	+	0.840917i	$0.682016\pi$
$444$	6.14824	0.291782
$445$	21.3049	1.00995
$446$	−2.29672	−0.108753
$447$	−5.92450	−0.280219
$448$	0	0
$449$	−8.19585	−0.386786	−0.193393	−	0.981121i	$-0.561949\pi$
$449$	−8.19585	−0.386786	−0.193393	+	0.981121i	$0.561949\pi$
$450$	10.5121	0.495546
$451$	7.99748	0.376587
$452$	3.83385	0.180329
$453$	−1.09856	−0.0516146
$454$	15.3728	0.721483
$455$	0	0
$456$	1.00000	0.0468293
$457$	−17.9078	−0.837691	−0.418846	−	0.908058i	$-0.637565\pi$
$457$	−17.9078	−0.837691	−0.418846	+	0.908058i	$0.637565\pi$
$458$	−11.7178	−0.547539
$459$	3.05310	0.142507
$460$	0.585954	0.0273203
$461$	−10.8937	−0.507372	−0.253686	−	0.967287i	$-0.581643\pi$
$461$	−10.8937	−0.507372	−0.253686	+	0.967287i	$0.581643\pi$
$462$	0	0
$463$	−39.6911	−1.84460	−0.922300	−	0.386475i	$-0.873693\pi$
$463$	−39.6911	−1.84460	−0.922300	+	0.386475i	$0.873693\pi$
$464$	−6.60877	−0.306804
$465$	31.5866	1.46480
$466$	13.7683	0.637803
$467$	32.0868	1.48480	0.742400	−	0.669956i	$-0.233687\pi$
$467$	32.0868	1.48480	0.742400	+	0.669956i	$0.233687\pi$
$468$	−5.94914	−0.274999
$469$	0	0
$470$	−32.3820	−1.49367
$471$	−8.29607	−0.382263
$472$	1.84029	0.0847062
$473$	10.0711	0.463069
$474$	7.44674	0.342040
$475$	10.5121	0.482329
$476$	0	0
$477$	11.3312	0.518821
$478$	27.3226	1.24971
$479$	−21.5125	−0.982933	−0.491466	−	0.870897i	$-0.663539\pi$
$479$	−21.5125	−0.982933	−0.491466	+	0.870897i	$0.663539\pi$
$480$	−3.93854	−0.179769
$481$	−36.5767	−1.66775
$482$	−29.4781	−1.34269
$483$	0	0
$484$	−9.37965	−0.426348
$485$	−44.2209	−2.00797
$486$	1.00000	0.0453609
$487$	−22.7496	−1.03088	−0.515441	−	0.856925i	$-0.672372\pi$
$487$	−22.7496	−1.03088	−0.515441	+	0.856925i	$0.672372\pi$
$488$	12.1881	0.551731
$489$	12.5954	0.569585
$490$	0	0
$491$	−26.4966	−1.19577	−0.597887	−	0.801581i	$-0.703993\pi$
$491$	−26.4966	−1.19577	−0.597887	+	0.801581i	$0.703993\pi$
$492$	6.28274	0.283248
$493$	−20.1772	−0.908737
$494$	−5.94914	−0.267664
$495$	−5.01349	−0.225340
$496$	−8.01988	−0.360103
$497$	0	0
$498$	12.1746	0.545558
$499$	20.4302	0.914580	0.457290	−	0.889318i	$-0.348820\pi$
$499$	20.4302	0.914580	0.457290	+	0.889318i	$0.348820\pi$
$500$	−21.7097	−0.970889
$501$	9.65057	0.431156
$502$	22.6060	1.00896
$503$	−0.0114171	−0.000509063 0	−0.000254532	−	1.00000i	$-0.500081\pi$
$503$	−0.0114171	−0.000509063 0	−0.000254532		1.00000i	$0.500081\pi$
$504$	0	0
$505$	−17.2819	−0.769035
$506$	−0.189379	−0.00841894
$507$	22.3922	0.994474
$508$	−15.4576	−0.685821
$509$	17.0678	0.756518	0.378259	−	0.925700i	$-0.376523\pi$
$509$	17.0678	0.756518	0.378259	+	0.925700i	$0.376523\pi$
$510$	−12.0248	−0.532466
$511$	0	0
$512$	1.00000	0.0441942
$513$	1.00000	0.0441511
$514$	25.9880	1.14628
$515$	−25.5363	−1.12527
$516$	7.91174	0.348295
$517$	10.4658	0.460285
$518$	0	0
$519$	14.1088	0.619307
$520$	23.4309	1.02751
$521$	6.84370	0.299828	0.149914	−	0.988699i	$-0.452100\pi$
$521$	6.84370	0.299828	0.149914	+	0.988699i	$0.452100\pi$
$522$	−6.60877	−0.289258
$523$	−10.9826	−0.480237	−0.240119	−	0.970744i	$-0.577186\pi$
$523$	−10.9826	−0.480237	−0.240119	+	0.970744i	$0.577186\pi$
$524$	−5.76015	−0.251633
$525$	0	0
$526$	6.16848	0.268958
$527$	−24.4855	−1.06661
$528$	1.27293	0.0553972
$529$	−22.9779	−0.999038
$530$	−44.6285	−1.93854
$531$	1.84029	0.0798618
$532$	0	0
$533$	−37.3769	−1.61897
$534$	−5.40934	−0.234085
$535$	−16.1352	−0.697586
$536$	2.61205	0.112823
$537$	−12.4256	−0.536203
$538$	10.1268	0.436597
$539$	0	0
$540$	−3.93854	−0.169488
$541$	18.7473	0.806011	0.403006	−	0.915197i	$-0.367965\pi$
$541$	18.7473	0.806011	0.403006	+	0.915197i	$0.367965\pi$
$542$	10.9731	0.471335
$543$	−12.3729	−0.530973
$544$	3.05310	0.130901
$545$	−23.3894	−1.00189
$546$	0	0
$547$	−5.12794	−0.219255	−0.109628	−	0.993973i	$-0.534966\pi$
$547$	−5.12794	−0.219255	−0.109628	+	0.993973i	$0.534966\pi$
$548$	16.2798	0.695440
$549$	12.1881	0.520177
$550$	13.3812	0.570576
$551$	−6.60877	−0.281543
$552$	−0.148774	−0.00633226
$553$	0	0
$554$	2.90574	0.123453
$555$	−24.2151	−1.02787
$556$	8.24825	0.349804
$557$	−19.8712	−0.841970	−0.420985	−	0.907068i	$-0.638316\pi$
$557$	−19.8712	−0.841970	−0.420985	+	0.907068i	$0.638316\pi$
$558$	−8.01988	−0.339509
$559$	−47.0680	−1.99076
$560$	0	0
$561$	3.88638	0.164083
$562$	13.5310	0.570770
$563$	−5.45760	−0.230010	−0.115005	−	0.993365i	$-0.536688\pi$
$563$	−5.45760	−0.230010	−0.115005	+	0.993365i	$0.536688\pi$
$564$	8.22182	0.346201
$565$	−15.0998	−0.635252
$566$	15.3969	0.647181
$567$	0	0
$568$	−12.8117	−0.537568
$569$	5.92409	0.248351	0.124175	−	0.992260i	$-0.460371\pi$
$569$	5.92409	0.248351	0.124175	+	0.992260i	$0.460371\pi$
$570$	−3.93854	−0.164967
$571$	22.8266	0.955265	0.477633	−	0.878560i	$-0.341495\pi$
$571$	22.8266	0.955265	0.477633	+	0.878560i	$0.341495\pi$
$572$	−7.57283	−0.316636
$573$	−4.07435	−0.170208
$574$	0	0
$575$	−1.56393	−0.0652206
$576$	1.00000	0.0416667
$577$	12.2583	0.510320	0.255160	−	0.966899i	$-0.417872\pi$
$577$	12.2583	0.510320	0.255160	+	0.966899i	$0.417872\pi$
$578$	−7.67857	−0.319386
$579$	−4.50280	−0.187130
$580$	26.0289	1.08079
$581$	0	0
$582$	11.2277	0.465405
$583$	14.4239	0.597375
$584$	−16.2859	−0.673915
$585$	23.4309	0.968750
$586$	−14.5720	−0.601965
$587$	−43.2598	−1.78552	−0.892762	−	0.450528i	$-0.851236\pi$
$587$	−43.2598	−1.78552	−0.892762	+	0.450528i	$0.851236\pi$
$588$	0	0
$589$	−8.01988	−0.330453
$590$	−7.24806	−0.298398
$591$	0.322407	0.0132621
$592$	6.14824	0.252691
$593$	18.4196	0.756403	0.378201	−	0.925723i	$-0.376543\pi$
$593$	18.4196	0.756403	0.378201	+	0.925723i	$0.376543\pi$
$594$	1.27293	0.0522289
$595$	0	0
$596$	−5.92450	−0.242677
$597$	22.6125	0.925467
$598$	0.885079	0.0361936
$599$	−6.36854	−0.260212	−0.130106	−	0.991500i	$-0.541532\pi$
$599$	−6.36854	−0.260212	−0.130106	+	0.991500i	$0.541532\pi$
$600$	10.5121	0.429156
$601$	−26.8167	−1.09388	−0.546939	−	0.837173i	$-0.684207\pi$
$601$	−26.8167	−1.09388	−0.546939	+	0.837173i	$0.684207\pi$
$602$	0	0
$603$	2.61205	0.106371
$604$	−1.09856	−0.0446996
$605$	36.9422	1.50191
$606$	4.38789	0.178246
$607$	−45.5076	−1.84710	−0.923549	−	0.383482i	$-0.874725\pi$
$607$	−45.5076	−1.84710	−0.923549	+	0.383482i	$0.874725\pi$
$608$	1.00000	0.0405554
$609$	0	0
$610$	−48.0035	−1.94361
$611$	−48.9127	−1.97880
$612$	3.05310	0.123414
$613$	−4.94269	−0.199633	−0.0998167	−	0.995006i	$-0.531826\pi$
$613$	−4.94269	−0.199633	−0.0998167	+	0.995006i	$0.531826\pi$
$614$	−26.2382	−1.05889
$615$	−24.7448	−0.997808
$616$	0	0
$617$	−41.7247	−1.67977	−0.839887	−	0.542762i	$-0.817379\pi$
$617$	−41.7247	−1.67977	−0.839887	+	0.542762i	$0.817379\pi$
$618$	6.48370	0.260813
$619$	28.8296	1.15876	0.579380	−	0.815058i	$-0.303295\pi$
$619$	28.8296	1.15876	0.579380	+	0.815058i	$0.303295\pi$
$620$	31.5866	1.26855
$621$	−0.148774	−0.00597011
$622$	7.89074	0.316390
$623$	0	0
$624$	−5.94914	−0.238156
$625$	32.9441	1.31777
$626$	−17.3496	−0.693428
$627$	1.27293	0.0508359
$628$	−8.29607	−0.331049
$629$	18.7712	0.748457
$630$	0	0
$631$	−18.8512	−0.750455	−0.375228	−	0.926933i	$-0.622435\pi$
$631$	−18.8512	−0.750455	−0.375228	+	0.926933i	$0.622435\pi$
$632$	7.44674	0.296215
$633$	0.346997	0.0137919
$634$	31.0193	1.23193
$635$	60.8805	2.41597
$636$	11.3312	0.449312
$637$	0	0
$638$	−8.41250	−0.333054
$639$	−12.8117	−0.506824
$640$	−3.93854	−0.155685
$641$	−12.1065	−0.478178	−0.239089	−	0.970998i	$-0.576849\pi$
$641$	−12.1065	−0.478178	−0.239089	+	0.970998i	$0.576849\pi$
$642$	4.09675	0.161686
$643$	40.2074	1.58563	0.792813	−	0.609465i	$-0.208616\pi$
$643$	40.2074	1.58563	0.792813	+	0.609465i	$0.208616\pi$
$644$	0	0
$645$	−31.1607	−1.22695
$646$	3.05310	0.120123
$647$	−18.0855	−0.711016	−0.355508	−	0.934673i	$-0.615692\pi$
$647$	−18.0855	−0.711016	−0.355508	+	0.934673i	$0.615692\pi$
$648$	1.00000	0.0392837
$649$	2.34256	0.0919535
$650$	−62.5381	−2.45294
$651$	0	0
$652$	12.5954	0.493275
$653$	−42.2280	−1.65251	−0.826255	−	0.563296i	$-0.809533\pi$
$653$	−42.2280	−1.65251	−0.826255	+	0.563296i	$0.809533\pi$
$654$	5.93860	0.232218
$655$	22.6866	0.886439
$656$	6.28274	0.245300
$657$	−16.2859	−0.635373
$658$	0	0
$659$	43.2743	1.68573	0.842864	−	0.538126i	$-0.180868\pi$
$659$	43.2743	1.68573	0.842864	+	0.538126i	$0.180868\pi$
$660$	−5.01349	−0.195150
$661$	−38.8777	−1.51217	−0.756083	−	0.654476i	$-0.772889\pi$
$661$	−38.8777	−1.51217	−0.756083	+	0.654476i	$0.772889\pi$
$662$	−27.7615	−1.07898
$663$	−18.1633	−0.705405
$664$	12.1746	0.472467
$665$	0	0
$666$	6.14824	0.238239
$667$	0.983215	0.0380702
$668$	9.65057	0.373392
$669$	−2.29672	−0.0887965
$670$	−10.2877	−0.397447
$671$	15.5146	0.598936
$672$	0	0
$673$	−13.3534	−0.514737	−0.257369	−	0.966313i	$-0.582855\pi$
$673$	−13.3534	−0.514737	−0.257369	+	0.966313i	$0.582855\pi$
$674$	−11.9053	−0.458575
$675$	10.5121	0.404612
$676$	22.3922	0.861239
$677$	−12.3254	−0.473704	−0.236852	−	0.971546i	$-0.576116\pi$
$677$	−12.3254	−0.473704	−0.236852	+	0.971546i	$0.576116\pi$
$678$	3.83385	0.147238
$679$	0	0
$680$	−12.0248	−0.461129
$681$	15.3728	0.589089
$682$	−10.2087	−0.390913
$683$	−14.1727	−0.542305	−0.271152	−	0.962536i	$-0.587405\pi$
$683$	−14.1727	−0.542305	−0.271152	+	0.962536i	$0.587405\pi$
$684$	1.00000	0.0382360
$685$	−64.1189	−2.44986
$686$	0	0
$687$	−11.7178	−0.447063
$688$	7.91174	0.301632
$689$	−67.4110	−2.56816
$690$	0.585954	0.0223069
$691$	41.6858	1.58580	0.792902	−	0.609350i	$-0.208569\pi$
$691$	41.6858	1.58580	0.792902	+	0.609350i	$0.208569\pi$
$692$	14.1088	0.536335
$693$	0	0
$694$	18.8103	0.714029
$695$	−32.4861	−1.23227
$696$	−6.60877	−0.250505
$697$	19.1818	0.726564
$698$	−8.76894	−0.331909
$699$	13.7683	0.520764
$700$	0	0
$701$	−17.0286	−0.643162	−0.321581	−	0.946882i	$-0.604214\pi$
$701$	−17.0286	−0.643162	−0.321581	+	0.946882i	$0.604214\pi$
$702$	−5.94914	−0.224536
$703$	6.14824	0.231885
$704$	1.27293	0.0479753
$705$	−32.3820	−1.21958
$706$	−29.8162	−1.12215
$707$	0	0
$708$	1.84029	0.0691623
$709$	32.3459	1.21478	0.607388	−	0.794405i	$-0.292217\pi$
$709$	32.3459	1.21478	0.607388	+	0.794405i	$0.292217\pi$
$710$	50.4595	1.89371
$711$	7.44674	0.279275
$712$	−5.40934	−0.202724
$713$	1.19315	0.0446839
$714$	0	0
$715$	29.8259	1.11543
$716$	−12.4256	−0.464365
$717$	27.3226	1.02038
$718$	17.1263	0.639146
$719$	−6.79180	−0.253291	−0.126646	−	0.991948i	$-0.540421\pi$
$719$	−6.79180	−0.253291	−0.126646	+	0.991948i	$0.540421\pi$
$720$	−3.93854	−0.146781
$721$	0	0
$722$	1.00000	0.0372161
$723$	−29.4781	−1.09630
$724$	−12.3729	−0.459836
$725$	−69.4722	−2.58013
$726$	−9.37965	−0.348111
$727$	−35.1033	−1.30191	−0.650955	−	0.759116i	$-0.725632\pi$
$727$	−35.1033	−1.30191	−0.650955	+	0.759116i	$0.725632\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	64.1426	2.37403
$731$	24.1553	0.893417
$732$	12.1881	0.450487
$733$	18.2408	0.673737	0.336869	−	0.941552i	$-0.390632\pi$
$733$	18.2408	0.673737	0.336869	+	0.941552i	$0.390632\pi$
$734$	24.3662	0.899373
$735$	0	0
$736$	−0.148774	−0.00548390
$737$	3.32495	0.122476
$738$	6.28274	0.231271
$739$	2.59627	0.0955054	0.0477527	−	0.998859i	$-0.484794\pi$
$739$	2.59627	0.0955054	0.0477527	+	0.998859i	$0.484794\pi$
$740$	−24.2151	−0.890165
$741$	−5.94914	−0.218547
$742$	0	0
$743$	5.38432	0.197531	0.0987657	−	0.995111i	$-0.468511\pi$
$743$	5.38432	0.197531	0.0987657	+	0.995111i	$0.468511\pi$
$744$	−8.01988	−0.294023
$745$	23.3339	0.854889
$746$	24.1414	0.883879
$747$	12.1746	0.445447
$748$	3.88638	0.142100
$749$	0	0
$750$	−21.7097	−0.792728
$751$	52.2522	1.90671	0.953356	−	0.301850i	$-0.0976041\pi$
$751$	52.2522	1.90671	0.953356	+	0.301850i	$0.0976041\pi$
$752$	8.22182	0.299819
$753$	22.6060	0.823810
$754$	39.3165	1.43182
$755$	4.32671	0.157465
$756$	0	0
$757$	−14.2585	−0.518233	−0.259116	−	0.965846i	$-0.583431\pi$
$757$	−14.2585	−0.518233	−0.259116	+	0.965846i	$0.583431\pi$
$758$	8.51695	0.309349
$759$	−0.189379	−0.00687403
$760$	−3.93854	−0.142866
$761$	4.51447	0.163649	0.0818247	−	0.996647i	$-0.473925\pi$
$761$	4.51447	0.163649	0.0818247	+	0.996647i	$0.473925\pi$
$762$	−15.4576	−0.559970
$763$	0	0
$764$	−4.07435	−0.147405
$765$	−12.0248	−0.434757
$766$	−17.3654	−0.627437
$767$	−10.9481	−0.395314
$768$	1.00000	0.0360844
$769$	16.9779	0.612239	0.306120	−	0.951993i	$-0.400969\pi$
$769$	16.9779	0.612239	0.306120	+	0.951993i	$0.400969\pi$
$770$	0	0
$771$	25.9880	0.935935
$772$	−4.50280	−0.162059
$773$	39.7267	1.42887	0.714435	−	0.699702i	$-0.246684\pi$
$773$	39.7267	1.42887	0.714435	+	0.699702i	$0.246684\pi$
$774$	7.91174	0.284381
$775$	−84.3060	−3.02836
$776$	11.2277	0.403052
$777$	0	0
$778$	−22.5117	−0.807083
$779$	6.28274	0.225102
$780$	23.4309	0.838962
$781$	−16.3084	−0.583561
$782$	−0.454223	−0.0162430
$783$	−6.60877	−0.236178
$784$	0	0
$785$	32.6744	1.16620
$786$	−5.76015	−0.205458
$787$	−54.3699	−1.93808	−0.969039	−	0.246908i	$-0.920586\pi$
$787$	−54.3699	−1.93808	−0.969039	+	0.246908i	$0.920586\pi$
$788$	0.322407	0.0114853
$789$	6.16848	0.219604
$790$	−29.3293	−1.04349
$791$	0	0
$792$	1.27293	0.0452316
$793$	−72.5089	−2.57487
$794$	33.8779	1.20228
$795$	−44.6285	−1.58281
$796$	22.6125	0.801478
$797$	17.4243	0.617201	0.308600	−	0.951192i	$-0.400139\pi$
$797$	17.4243	0.617201	0.308600	+	0.951192i	$0.400139\pi$
$798$	0	0
$799$	25.1020	0.888046
$800$	10.5121	0.371660
$801$	−5.40934	−0.191130
$802$	33.1403	1.17022
$803$	−20.7308	−0.731573
$804$	2.61205	0.0921197
$805$	0	0
$806$	47.7114	1.68056
$807$	10.1268	0.356480
$808$	4.38789	0.154366
$809$	31.2970	1.10034	0.550172	−	0.835051i	$-0.314562\pi$
$809$	31.2970	1.10034	0.550172	+	0.835051i	$0.314562\pi$
$810$	−3.93854	−0.138386
$811$	12.7410	0.447398	0.223699	−	0.974658i	$-0.428187\pi$
$811$	12.7410	0.447398	0.223699	+	0.974658i	$0.428187\pi$
$812$	0	0
$813$	10.9731	0.384843
$814$	7.82627	0.274311
$815$	−49.6077	−1.73768
$816$	3.05310	0.106880
$817$	7.91174	0.276797
$818$	−28.2927	−0.989233
$819$	0	0
$820$	−24.7448	−0.864127
$821$	−0.210997	−0.00736386	−0.00368193	−	0.999993i	$-0.501172\pi$
$821$	−0.210997	−0.00736386	−0.00368193	+	0.999993i	$0.501172\pi$
$822$	16.2798	0.567825
$823$	−26.1195	−0.910468	−0.455234	−	0.890372i	$-0.650444\pi$
$823$	−26.1195	−0.910468	−0.455234	+	0.890372i	$0.650444\pi$
$824$	6.48370	0.225870
$825$	13.3812	0.465873
$826$	0	0
$827$	−18.9617	−0.659364	−0.329682	−	0.944092i	$-0.606942\pi$
$827$	−18.9617	−0.659364	−0.329682	+	0.944092i	$0.606942\pi$
$828$	−0.148774	−0.00517027
$829$	7.91930	0.275049	0.137524	−	0.990498i	$-0.456085\pi$
$829$	7.91930	0.275049	0.137524	+	0.990498i	$0.456085\pi$
$830$	−47.9503	−1.66438
$831$	2.90574	0.100799
$832$	−5.94914	−0.206249
$833$	0	0
$834$	8.24825	0.285614
$835$	−38.0092	−1.31536
$836$	1.27293	0.0440252
$837$	−8.01988	−0.277208
$838$	24.5157	0.846882
$839$	1.11414	0.0384644	0.0192322	−	0.999815i	$-0.493878\pi$
$839$	1.11414	0.0384644	0.0192322	+	0.999815i	$0.493878\pi$
$840$	0	0
$841$	14.6758	0.506062
$842$	−36.4678	−1.25676
$843$	13.5310	0.466032
$844$	0.346997	0.0119441
$845$	−88.1928	−3.03392
$846$	8.22182	0.282672
$847$	0	0
$848$	11.3312	0.389116
$849$	15.3969	0.528421
$850$	32.0946	1.10084
$851$	−0.914700	−0.0313555
$852$	−12.8117	−0.438922
$853$	32.7675	1.12194	0.560969	−	0.827837i	$-0.310429\pi$
$853$	32.7675	1.12194	0.560969	+	0.827837i	$0.310429\pi$
$854$	0	0
$855$	−3.93854	−0.134695
$856$	4.09675	0.140024
$857$	−19.0262	−0.649921	−0.324960	−	0.945728i	$-0.605351\pi$
$857$	−19.0262	−0.649921	−0.324960	+	0.945728i	$0.605351\pi$
$858$	−7.57283	−0.258532
$859$	4.70887	0.160664	0.0803322	−	0.996768i	$-0.474402\pi$
$859$	4.70887	0.160664	0.0803322	+	0.996768i	$0.474402\pi$
$860$	−31.1607	−1.06257
$861$	0	0
$862$	7.38080	0.251391
$863$	3.17462	0.108065	0.0540326	−	0.998539i	$-0.482793\pi$
$863$	3.17462	0.108065	0.0540326	+	0.998539i	$0.482793\pi$
$864$	1.00000	0.0340207
$865$	−55.5680	−1.88937
$866$	−11.4859	−0.390306
$867$	−7.67857	−0.260778
$868$	0	0
$869$	9.47918	0.321559
$870$	26.0289	0.882463
$871$	−15.5394	−0.526533
$872$	5.93860	0.201106
$873$	11.2277	0.380001
$874$	−0.148774	−0.00503237
$875$	0	0
$876$	−16.2859	−0.550249
$877$	−1.38358	−0.0467201	−0.0233601	−	0.999727i	$-0.507436\pi$
$877$	−1.38358	−0.0467201	−0.0233601	+	0.999727i	$0.507436\pi$
$878$	−22.2521	−0.750974
$879$	−14.5720	−0.491503
$880$	−5.01349	−0.169005
$881$	0.922545	0.0310813	0.0155407	−	0.999879i	$-0.495053\pi$
$881$	0.922545	0.0310813	0.0155407	+	0.999879i	$0.495053\pi$
$882$	0	0
$883$	−57.2691	−1.92726	−0.963630	−	0.267241i	$-0.913888\pi$
$883$	−57.2691	−1.92726	−0.963630	+	0.267241i	$0.913888\pi$
$884$	−18.1633	−0.610899
$885$	−7.24806	−0.243641
$886$	−22.7804	−0.765322
$887$	52.8038	1.77298	0.886488	−	0.462751i	$-0.153138\pi$
$887$	52.8038	1.77298	0.886488	+	0.462751i	$0.153138\pi$
$888$	6.14824	0.206321
$889$	0	0
$890$	21.3049	0.714143
$891$	1.27293	0.0426447
$892$	−2.29672	−0.0769000
$893$	8.22182	0.275133
$894$	−5.92450	−0.198145
$895$	48.9386	1.63584
$896$	0	0
$897$	0.885079	0.0295519
$898$	−8.19585	−0.273499
$899$	53.0015	1.76770
$900$	10.5121	0.350404
$901$	34.5954	1.15254
$902$	7.99748	0.266287
$903$	0	0
$904$	3.83385	0.127512
$905$	48.7313	1.61988
$906$	−1.09856	−0.0364971
$907$	35.0561	1.16402	0.582009	−	0.813182i	$-0.302267\pi$
$907$	35.0561	1.16402	0.582009	+	0.813182i	$0.302267\pi$
$908$	15.3728	0.510166
$909$	4.38789	0.145537
$910$	0	0
$911$	23.3448	0.773449	0.386724	−	0.922195i	$-0.373606\pi$
$911$	23.3448	0.773449	0.386724	+	0.922195i	$0.373606\pi$
$912$	1.00000	0.0331133
$913$	15.4975	0.512891
$914$	−17.9078	−0.592337
$915$	−48.0035	−1.58695
$916$	−11.7178	−0.387168
$917$	0	0
$918$	3.05310	0.100767
$919$	2.68302	0.0885045	0.0442523	−	0.999020i	$-0.485909\pi$
$919$	2.68302	0.0885045	0.0442523	+	0.999020i	$0.485909\pi$
$920$	0.585954	0.0193183
$921$	−26.2382	−0.864577
$922$	−10.8937	−0.358766
$923$	76.2187	2.50877
$924$	0	0
$925$	64.6310	2.12506
$926$	−39.6911	−1.30433
$927$	6.48370	0.212953
$928$	−6.60877	−0.216943
$929$	16.0004	0.524955	0.262478	−	0.964938i	$-0.415460\pi$
$929$	16.0004	0.524955	0.262478	+	0.964938i	$0.415460\pi$
$930$	31.5866	1.03577
$931$	0	0
$932$	13.7683	0.450995
$933$	7.89074	0.258331
$934$	32.0868	1.04991
$935$	−15.3067	−0.500582
$936$	−5.94914	−0.194454
$937$	49.2753	1.60975	0.804876	−	0.593443i	$-0.202232\pi$
$937$	49.2753	1.60975	0.804876	+	0.593443i	$0.202232\pi$
$938$	0	0
$939$	−17.3496	−0.566181
$940$	−32.3820	−1.05618
$941$	12.9474	0.422074	0.211037	−	0.977478i	$-0.432316\pi$
$941$	12.9474	0.422074	0.211037	+	0.977478i	$0.432316\pi$
$942$	−8.29607	−0.270301
$943$	−0.934710	−0.0304383
$944$	1.84029	0.0598963
$945$	0	0
$946$	10.0711	0.327439
$947$	−24.6036	−0.799510	−0.399755	−	0.916622i	$-0.630905\pi$
$947$	−24.6036	−0.799510	−0.399755	+	0.916622i	$0.630905\pi$
$948$	7.44674	0.241859
$949$	96.8869	3.14508
$950$	10.5121	0.341058
$951$	31.0193	1.00587
$952$	0	0
$953$	−33.2606	−1.07742	−0.538708	−	0.842493i	$-0.681087\pi$
$953$	−33.2606	−1.07742	−0.538708	+	0.842493i	$0.681087\pi$
$954$	11.3312	0.366862
$955$	16.0470	0.519269
$956$	27.3226	0.883676
$957$	−8.41250	−0.271937
$958$	−21.5125	−0.695038
$959$	0	0
$960$	−3.93854	−0.127116
$961$	33.3184	1.07479
$962$	−36.5767	−1.17928
$963$	4.09675	0.132016
$964$	−29.4781	−0.949427
$965$	17.7345	0.570893
$966$	0	0
$967$	−2.48135	−0.0797949	−0.0398974	−	0.999204i	$-0.512703\pi$
$967$	−2.48135	−0.0797949	−0.0398974	+	0.999204i	$0.512703\pi$
$968$	−9.37965	−0.301473
$969$	3.05310	0.0980798
$970$	−44.2209	−1.41985
$971$	9.65888	0.309968	0.154984	−	0.987917i	$-0.450467\pi$
$971$	9.65888	0.309968	0.154984	+	0.987917i	$0.450467\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	−22.7496	−0.728944
$975$	−62.5381	−2.00282
$976$	12.1881	0.390133
$977$	−34.6842	−1.10965	−0.554823	−	0.831968i	$-0.687214\pi$
$977$	−34.6842	−1.10965	−0.554823	+	0.831968i	$0.687214\pi$
$978$	12.5954	0.402758
$979$	−6.88571	−0.220068
$980$	0	0
$981$	5.93860	0.189605
$982$	−26.4966	−0.845539
$983$	−2.51987	−0.0803715	−0.0401857	−	0.999192i	$-0.512795\pi$
$983$	−2.51987	−0.0803715	−0.0401857	+	0.999192i	$0.512795\pi$
$984$	6.28274	0.200286
$985$	−1.26981	−0.0404597
$986$	−20.1772	−0.642574
$987$	0	0
$988$	−5.94914	−0.189267
$989$	−1.17706	−0.0374284
$990$	−5.01349	−0.159339
$991$	−40.5602	−1.28844	−0.644219	−	0.764841i	$-0.722817\pi$
$991$	−40.5602	−1.28844	−0.644219	+	0.764841i	$0.722817\pi$
$992$	−8.01988	−0.254631
$993$	−27.7615	−0.880983
$994$	0	0
$995$	−89.0603	−2.82340
$996$	12.1746	0.385768
$997$	−0.253401	−0.00802530	−0.00401265	−	0.999992i	$-0.501277\pi$
$997$	−0.253401	−0.00802530	−0.00401265	+	0.999992i	$0.501277\pi$
$998$	20.4302	0.646706
$999$	6.14824	0.194522

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5586.2.a.cf.1.1	yes	8
7.6	odd	2		5586.2.a.ce.1.8	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5586.2.a.ce.1.8	✓	8	7.6	odd	2
5586.2.a.cf.1.1	yes	8	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:	\( N \)	\(=\)	\( 5586 = 2 \cdot 3 \cdot 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5586.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.93854 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.93854 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -3.93854 q^{10} +1.27293 q^{11} +1.00000 q^{12} -5.94914 q^{13} -3.93854 q^{15} +1.00000 q^{16} +3.05310 q^{17} +1.00000 q^{18} +1.00000 q^{19} -3.93854 q^{20} +1.27293 q^{22} -0.148774 q^{23} +1.00000 q^{24} +10.5121 q^{25} -5.94914 q^{26} +1.00000 q^{27} -6.60877 q^{29} -3.93854 q^{30} -8.01988 q^{31} +1.00000 q^{32} +1.27293 q^{33} +3.05310 q^{34} +1.00000 q^{36} +6.14824 q^{37} +1.00000 q^{38} -5.94914 q^{39} -3.93854 q^{40} +6.28274 q^{41} +7.91174 q^{43} +1.27293 q^{44} -3.93854 q^{45} -0.148774 q^{46} +8.22182 q^{47} +1.00000 q^{48} +10.5121 q^{50} +3.05310 q^{51} -5.94914 q^{52} +11.3312 q^{53} +1.00000 q^{54} -5.01349 q^{55} +1.00000 q^{57} -6.60877 q^{58} +1.84029 q^{59} -3.93854 q^{60} +12.1881 q^{61} -8.01988 q^{62} +1.00000 q^{64} +23.4309 q^{65} +1.27293 q^{66} +2.61205 q^{67} +3.05310 q^{68} -0.148774 q^{69} -12.8117 q^{71} +1.00000 q^{72} -16.2859 q^{73} +6.14824 q^{74} +10.5121 q^{75} +1.00000 q^{76} -5.94914 q^{78} +7.44674 q^{79} -3.93854 q^{80} +1.00000 q^{81} +6.28274 q^{82} +12.1746 q^{83} -12.0248 q^{85} +7.91174 q^{86} -6.60877 q^{87} +1.27293 q^{88} -5.40934 q^{89} -3.93854 q^{90} -0.148774 q^{92} -8.01988 q^{93} +8.22182 q^{94} -3.93854 q^{95} +1.00000 q^{96} +11.2277 q^{97} +1.27293 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 4 q^{5} + 8 q^{6} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 4 * q^5 + 8 * q^6 + 8 * q^8 + 8 * q^9	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 4 q^{5} + 8 q^{6} + 8 q^{8} + 8 q^{9} + 4 q^{10} + 8 q^{11} + 8 q^{12} - 4 q^{13} + 4 q^{15} + 8 q^{16} + 8 q^{17} + 8 q^{18} + 8 q^{19} + 4 q^{20} + 8 q^{22} + 4 q^{23} + 8 q^{24} + 24 q^{25} - 4 q^{26} + 8 q^{27} + 16 q^{29} + 4 q^{30} + 4 q^{31} + 8 q^{32} + 8 q^{33} + 8 q^{34} + 8 q^{36} + 12 q^{37} + 8 q^{38} - 4 q^{39} + 4 q^{40} + 16 q^{43} + 8 q^{44} + 4 q^{45} + 4 q^{46} + 12 q^{47} + 8 q^{48} + 24 q^{50} + 8 q^{51} - 4 q^{52} + 24 q^{53} + 8 q^{54} - 8 q^{55} + 8 q^{57} + 16 q^{58} - 8 q^{59} + 4 q^{60} + 4 q^{62} + 8 q^{64} + 8 q^{65} + 8 q^{66} + 8 q^{67} + 8 q^{68} + 4 q^{69} + 24 q^{71} + 8 q^{72} - 16 q^{73} + 12 q^{74} + 24 q^{75} + 8 q^{76} - 4 q^{78} + 20 q^{79} + 4 q^{80} + 8 q^{81} + 16 q^{83} + 48 q^{85} + 16 q^{86} + 16 q^{87} + 8 q^{88} + 4 q^{90} + 4 q^{92} + 4 q^{93} + 12 q^{94} + 4 q^{95} + 8 q^{96} - 8 q^{97} + 8 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 4 * q^5 + 8 * q^6 + 8 * q^8 + 8 * q^9 + 4 * q^10 + 8 * q^11 + 8 * q^12 - 4 * q^13 + 4 * q^15 + 8 * q^16 + 8 * q^17 + 8 * q^18 + 8 * q^19 + 4 * q^20 + 8 * q^22 + 4 * q^23 + 8 * q^24 + 24 * q^25 - 4 * q^26 + 8 * q^27 + 16 * q^29 + 4 * q^30 + 4 * q^31 + 8 * q^32 + 8 * q^33 + 8 * q^34 + 8 * q^36 + 12 * q^37 + 8 * q^38 - 4 * q^39 + 4 * q^40 + 16 * q^43 + 8 * q^44 + 4 * q^45 + 4 * q^46 + 12 * q^47 + 8 * q^48 + 24 * q^50 + 8 * q^51 - 4 * q^52 + 24 * q^53 + 8 * q^54 - 8 * q^55 + 8 * q^57 + 16 * q^58 - 8 * q^59 + 4 * q^60 + 4 * q^62 + 8 * q^64 + 8 * q^65 + 8 * q^66 + 8 * q^67 + 8 * q^68 + 4 * q^69 + 24 * q^71 + 8 * q^72 - 16 * q^73 + 12 * q^74 + 24 * q^75 + 8 * q^76 - 4 * q^78 + 20 * q^79 + 4 * q^80 + 8 * q^81 + 16 * q^83 + 48 * q^85 + 16 * q^86 + 16 * q^87 + 8 * q^88 + 4 * q^90 + 4 * q^92 + 4 * q^93 + 12 * q^94 + 4 * q^95 + 8 * q^96 - 8 * q^97 + 8 * q^99

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