LMFDB - Embedded newform 1617.2.a.u.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1617,2,Mod(1,1617)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1617, 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("1617.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1617 = 3 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1617.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:	$12.9118100068$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.2624.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 3x^{2} + 2x + 1 $ x^4 - 2x^3 - 3x^2 + 2*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.814115$ of defining polynomial
Character	$\chi$	$=$	1617.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.185885 q^{2} -1.00000 q^{3} -1.96545 q^{4} +1.26288 q^{5} +0.185885 q^{6} +0.737118 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.185885 q^{2} -1.00000 q^{3} -1.96545 q^{4} +1.26288 q^{5} +0.185885 q^{6} +0.737118 q^{8} +1.00000 q^{9} -0.234751 q^{10} +1.00000 q^{11} +1.96545 q^{12} +6.93089 q^{13} -1.26288 q^{15} +3.79387 q^{16} -5.60799 q^{17} -0.185885 q^{18} -5.75932 q^{19} -2.48213 q^{20} -0.185885 q^{22} +4.13375 q^{23} -0.737118 q^{24} -3.40513 q^{25} -1.28835 q^{26} -1.00000 q^{27} -6.09131 q^{29} +0.234751 q^{30} +5.30532 q^{31} -2.17946 q^{32} -1.00000 q^{33} +1.04244 q^{34} -1.96545 q^{36} -3.73070 q^{37} +1.07057 q^{38} -6.93089 q^{39} +0.930893 q^{40} +11.4300 q^{41} -4.27866 q^{43} -1.96545 q^{44} +1.26288 q^{45} -0.768404 q^{46} +13.1938 q^{47} -3.79387 q^{48} +0.632964 q^{50} +5.60799 q^{51} -13.6223 q^{52} -5.52310 q^{53} +0.185885 q^{54} +1.26288 q^{55} +5.75932 q^{57} +1.13229 q^{58} +7.86821 q^{59} +2.48213 q^{60} +3.77690 q^{61} -0.986182 q^{62} -7.18262 q^{64} +8.75290 q^{65} +0.185885 q^{66} +16.1182 q^{67} +11.0222 q^{68} -4.13375 q^{69} +4.17353 q^{71} +0.737118 q^{72} +5.40040 q^{73} +0.693482 q^{74} +3.40513 q^{75} +11.3196 q^{76} +1.28835 q^{78} +9.55912 q^{79} +4.79121 q^{80} +1.00000 q^{81} -2.12467 q^{82} -6.73908 q^{83} -7.08223 q^{85} +0.795340 q^{86} +6.09131 q^{87} +0.737118 q^{88} -6.14867 q^{89} -0.234751 q^{90} -8.12467 q^{92} -5.30532 q^{93} -2.45253 q^{94} -7.27334 q^{95} +2.17946 q^{96} +15.3249 q^{97} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 4 q^{3} + 2 q^{4} + 8 q^{5} + 2 q^{6} + 4 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - 4 * q^3 + 2 * q^4 + 8 * q^5 + 2 * q^6 + 4 * q^9	$ 4 q - 2 q^{2} - 4 q^{3} + 2 q^{4} + 8 q^{5} + 2 q^{6} + 4 q^{9} - 2 q^{10} + 4 q^{11} - 2 q^{12} + 8 q^{13} - 8 q^{15} - 6 q^{16} - 2 q^{18} + 8 q^{19} + 14 q^{20} - 2 q^{22} + 12 q^{25} + 2 q^{26} - 4 q^{27} - 16 q^{29} + 2 q^{30} + 16 q^{31} - 2 q^{32} - 4 q^{33} - 4 q^{34} + 2 q^{36} - 4 q^{37} - 2 q^{38} - 8 q^{39} - 16 q^{40} + 4 q^{41} + 16 q^{43} + 2 q^{44} + 8 q^{45} + 8 q^{46} + 36 q^{47} + 6 q^{48} - 8 q^{50} - 22 q^{52} - 16 q^{53} + 2 q^{54} + 8 q^{55} - 8 q^{57} + 14 q^{58} - 14 q^{60} - 8 q^{61} + 8 q^{62} - 12 q^{64} - 4 q^{65} + 2 q^{66} + 20 q^{67} + 16 q^{68} - 20 q^{71} + 4 q^{73} - 30 q^{74} - 12 q^{75} + 30 q^{76} - 2 q^{78} + 16 q^{79} - 14 q^{80} + 4 q^{81} + 28 q^{82} + 24 q^{83} - 44 q^{86} + 16 q^{87} - 4 q^{89} - 2 q^{90} + 4 q^{92} - 16 q^{93} - 10 q^{94} + 28 q^{95} + 2 q^{96} + 16 q^{97} + 4 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 - 4 * q^3 + 2 * q^4 + 8 * q^5 + 2 * q^6 + 4 * q^9 - 2 * q^10 + 4 * q^11 - 2 * q^12 + 8 * q^13 - 8 * q^15 - 6 * q^16 - 2 * q^18 + 8 * q^19 + 14 * q^20 - 2 * q^22 + 12 * q^25 + 2 * q^26 - 4 * q^27 - 16 * q^29 + 2 * q^30 + 16 * q^31 - 2 * q^32 - 4 * q^33 - 4 * q^34 + 2 * q^36 - 4 * q^37 - 2 * q^38 - 8 * q^39 - 16 * q^40 + 4 * q^41 + 16 * q^43 + 2 * q^44 + 8 * q^45 + 8 * q^46 + 36 * q^47 + 6 * q^48 - 8 * q^50 - 22 * q^52 - 16 * q^53 + 2 * q^54 + 8 * q^55 - 8 * q^57 + 14 * q^58 - 14 * q^60 - 8 * q^61 + 8 * q^62 - 12 * q^64 - 4 * q^65 + 2 * q^66 + 20 * q^67 + 16 * q^68 - 20 * q^71 + 4 * q^73 - 30 * q^74 - 12 * q^75 + 30 * q^76 - 2 * q^78 + 16 * q^79 - 14 * q^80 + 4 * q^81 + 28 * q^82 + 24 * q^83 - 44 * q^86 + 16 * q^87 - 4 * q^89 - 2 * q^90 + 4 * q^92 - 16 * q^93 - 10 * q^94 + 28 * q^95 + 2 * q^96 + 16 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.185885	−0.131441	−0.0657204	−	0.997838i	$-0.520935\pi$
$2$	−0.185885	−0.131441	−0.0657204	+	0.997838i	$0.520935\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.96545	−0.982723
$5$	1.26288	0.564778	0.282389	−	0.959300i	$-0.408873\pi$
$5$	1.26288	0.564778	0.282389	+	0.959300i	$0.408873\pi$
$6$	0.185885	0.0758874
$7$	0	0
$7$	0	0
$8$	0.737118	0.260611
$9$	1.00000	0.333333
$10$	−0.234751	−0.0742348
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.96545	0.567376
$13$	6.93089	1.92228	0.961142	−	0.276055i	$-0.0890271\pi$
$13$	6.93089	1.92228	0.961142	+	0.276055i	$0.0890271\pi$
$14$	0	0
$15$	−1.26288	−0.326075
$16$	3.79387	0.948468
$17$	−5.60799	−1.36014	−0.680068	−	0.733149i	$-0.738050\pi$
$17$	−5.60799	−1.36014	−0.680068	+	0.733149i	$0.738050\pi$
$18$	−0.185885	−0.0438136
$19$	−5.75932	−1.32128	−0.660639	−	0.750703i	$-0.729715\pi$
$19$	−5.75932	−1.32128	−0.660639	+	0.750703i	$0.729715\pi$
$20$	−2.48213	−0.555020
$21$	0	0
$22$	−0.185885	−0.0396309
$23$	4.13375	0.861947	0.430973	−	0.902365i	$-0.358170\pi$
$23$	4.13375	0.861947	0.430973	+	0.902365i	$0.358170\pi$
$24$	−0.737118	−0.150464
$25$	−3.40513	−0.681026
$26$	−1.28835	−0.252667
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−6.09131	−1.13113	−0.565564	−	0.824705i	$-0.691341\pi$
$29$	−6.09131	−1.13113	−0.565564	+	0.824705i	$0.691341\pi$
$30$	0.234751	0.0428595
$31$	5.30532	0.952864	0.476432	−	0.879211i	$-0.341930\pi$
$31$	5.30532	0.952864	0.476432	+	0.879211i	$0.341930\pi$
$32$	−2.17946	−0.385278
$33$	−1.00000	−0.174078
$34$	1.04244	0.178777
$35$	0	0
$36$	−1.96545	−0.327574
$37$	−3.73070	−0.613323	−0.306661	−	0.951819i	$-0.599212\pi$
$37$	−3.73070	−0.613323	−0.306661	+	0.951819i	$0.599212\pi$
$38$	1.07057	0.173670
$39$	−6.93089	−1.10983
$40$	0.930893	0.147187
$41$	11.4300	1.78506	0.892532	−	0.450983i	$-0.148927\pi$
$41$	11.4300	1.78506	0.892532	+	0.450983i	$0.148927\pi$
$42$	0	0
$43$	−4.27866	−0.652490	−0.326245	−	0.945285i	$-0.605783\pi$
$43$	−4.27866	−0.652490	−0.326245	+	0.945285i	$0.605783\pi$
$44$	−1.96545	−0.296302
$45$	1.26288	0.188259
$46$	−0.768404	−0.113295
$47$	13.1938	1.92451	0.962255	−	0.272150i	$-0.0877346\pi$
$47$	13.1938	1.92451	0.962255	+	0.272150i	$0.0877346\pi$
$48$	−3.79387	−0.547599
$49$	0	0
$50$	0.632964	0.0895146
$51$	5.60799	0.785275
$52$	−13.6223	−1.88907
$53$	−5.52310	−0.758656	−0.379328	−	0.925262i	$-0.623845\pi$
$53$	−5.52310	−0.758656	−0.379328	+	0.925262i	$0.623845\pi$
$54$	0.185885	0.0252958
$55$	1.26288	0.170287
$56$	0	0
$57$	5.75932	0.762841
$58$	1.13229	0.148676
$59$	7.86821	1.02435	0.512177	−	0.858880i	$-0.328839\pi$
$59$	7.86821	1.02435	0.512177	+	0.858880i	$0.328839\pi$
$60$	2.48213	0.320441
$61$	3.77690	0.483583	0.241791	−	0.970328i	$-0.422265\pi$
$61$	3.77690	0.483583	0.241791	+	0.970328i	$0.422265\pi$
$62$	−0.986182	−0.125245
$63$	0	0
$64$	−7.18262	−0.897827
$65$	8.75290	1.08566
$66$	0.185885	0.0228809
$67$	16.1182	1.96916	0.984579	−	0.174943i	$-0.0559742\pi$
$67$	16.1182	1.96916	0.984579	+	0.174943i	$0.0559742\pi$
$68$	11.0222	1.33664
$69$	−4.13375	−0.497645
$70$	0	0
$71$	4.17353	0.495307	0.247654	−	0.968849i	$-0.420340\pi$
$71$	4.17353	0.495307	0.247654	+	0.968849i	$0.420340\pi$
$72$	0.737118	0.0868702
$73$	5.40040	0.632069	0.316034	−	0.948748i	$-0.397649\pi$
$73$	5.40040	0.632069	0.316034	+	0.948748i	$0.397649\pi$
$74$	0.693482	0.0806156
$75$	3.40513	0.393191
$76$	11.3196	1.29845
$77$	0	0
$78$	1.28835	0.145877
$79$	9.55912	1.07549	0.537743	−	0.843109i	$-0.319277\pi$
$79$	9.55912	1.07549	0.537743	+	0.843109i	$0.319277\pi$
$80$	4.79121	0.535674
$81$	1.00000	0.111111
$82$	−2.12467	−0.234630
$83$	−6.73908	−0.739710	−0.369855	−	0.929089i	$-0.620593\pi$
$83$	−6.73908	−0.739710	−0.369855	+	0.929089i	$0.620593\pi$
$84$	0	0
$85$	−7.08223	−0.768175
$86$	0.795340	0.0857638
$87$	6.09131	0.653057
$88$	0.737118	0.0785771
$89$	−6.14867	−0.651758	−0.325879	−	0.945412i	$-0.605660\pi$
$89$	−6.14867	−0.651758	−0.325879	+	0.945412i	$0.605660\pi$
$90$	−0.234751	−0.0247449
$91$	0	0
$92$	−8.12467	−0.847055
$93$	−5.30532	−0.550137
$94$	−2.45253	−0.252959
$95$	−7.27334	−0.746229
$96$	2.17946	0.222440
$97$	15.3249	1.55600	0.778002	−	0.628262i	$-0.216233\pi$
$97$	15.3249	1.55600	0.778002	+	0.628262i	$0.216233\pi$
$98$	0	0
$99$	1.00000	0.100504
$100$	6.69260	0.669260
$101$	9.72803	0.967976	0.483988	−	0.875075i	$-0.339188\pi$
$101$	9.72803	0.967976	0.483988	+	0.875075i	$0.339188\pi$
$102$	−1.04244	−0.103217
$103$	1.24444	0.122619	0.0613093	−	0.998119i	$-0.480472\pi$
$103$	1.24444	0.122619	0.0613093	+	0.998119i	$0.480472\pi$
$104$	5.10889	0.500968
$105$	0	0
$106$	1.02666	0.0997184
$107$	2.09131	0.202174	0.101087	−	0.994878i	$-0.467768\pi$
$107$	2.09131	0.202174	0.101087	+	0.994878i	$0.467768\pi$
$108$	1.96545	0.189125
$109$	1.42537	0.136526	0.0682629	−	0.997667i	$-0.478254\pi$
$109$	1.42537	0.136526	0.0682629	+	0.997667i	$0.478254\pi$
$110$	−0.234751	−0.0223826
$111$	3.73070	0.354102
$112$	0	0
$113$	−11.7731	−1.10752	−0.553762	−	0.832675i	$-0.686808\pi$
$113$	−11.7731	−1.10752	−0.553762	+	0.832675i	$0.686808\pi$
$114$	−1.07057	−0.100268
$115$	5.22044	0.486808
$116$	11.9721	1.11159
$117$	6.93089	0.640761
$118$	−1.46258	−0.134642
$119$	0	0
$120$	−0.930893	−0.0849785
$121$	1.00000	0.0909091
$122$	−0.702071	−0.0635625
$123$	−11.4300	−1.03061
$124$	−10.4273	−0.936402
$125$	−10.6147	−0.949406
$126$	0	0
$127$	2.31914	0.205791	0.102895	−	0.994692i	$-0.467189\pi$
$127$	2.31914	0.205791	0.102895	+	0.994692i	$0.467189\pi$
$128$	5.69407	0.503289
$129$	4.27866	0.376715
$130$	−1.62704	−0.142700
$131$	6.61441	0.577904	0.288952	−	0.957344i	$-0.406693\pi$
$131$	6.61441	0.577904	0.288952	+	0.957344i	$0.406693\pi$
$132$	1.96545	0.171070
$133$	0	0
$134$	−2.99615	−0.258828
$135$	−1.26288	−0.108692
$136$	−4.13375	−0.354466
$137$	−18.3110	−1.56442	−0.782209	−	0.623016i	$-0.785907\pi$
$137$	−18.3110	−1.56442	−0.782209	+	0.623016i	$0.785907\pi$
$138$	0.768404	0.0654109
$139$	6.33129	0.537013	0.268506	−	0.963278i	$-0.413470\pi$
$139$	6.33129	0.537013	0.268506	+	0.963278i	$0.413470\pi$
$140$	0	0
$141$	−13.1938	−1.11112
$142$	−0.775799	−0.0651036
$143$	6.93089	0.579590
$144$	3.79387	0.316156
$145$	−7.69260	−0.638836
$146$	−1.00385	−0.0830796
$147$	0	0
$148$	7.33248	0.602726
$149$	−16.9069	−1.38507	−0.692533	−	0.721386i	$-0.743505\pi$
$149$	−16.9069	−1.38507	−0.692533	+	0.721386i	$0.743505\pi$
$150$	−0.632964	−0.0516813
$151$	6.48442	0.527695	0.263847	−	0.964564i	$-0.415008\pi$
$151$	6.48442	0.527695	0.263847	+	0.964564i	$0.415008\pi$
$152$	−4.24530	−0.344339
$153$	−5.60799	−0.453379
$154$	0	0
$155$	6.70000	0.538157
$156$	13.6223	1.09066
$157$	2.01285	0.160643	0.0803213	−	0.996769i	$-0.474405\pi$
$157$	2.01285	0.160643	0.0803213	+	0.996769i	$0.474405\pi$
$158$	−1.77690	−0.141363
$159$	5.52310	0.438011
$160$	−2.75240	−0.217597
$161$	0	0
$162$	−0.185885	−0.0146045
$163$	8.15341	0.638624	0.319312	−	0.947650i	$-0.396548\pi$
$163$	8.15341	0.638624	0.319312	+	0.947650i	$0.396548\pi$
$164$	−22.4650	−1.75422
$165$	−1.26288	−0.0983152
$166$	1.25270	0.0972281
$167$	15.8258	1.22463	0.612317	−	0.790612i	$-0.290238\pi$
$167$	15.8258	1.22463	0.612317	+	0.790612i	$0.290238\pi$
$168$	0	0
$169$	35.0373	2.69518
$170$	1.31648	0.100970
$171$	−5.75932	−0.440426
$172$	8.40948	0.641217
$173$	−4.21778	−0.320672	−0.160336	−	0.987063i	$-0.551258\pi$
$173$	−4.21778	−0.320672	−0.160336	+	0.987063i	$0.551258\pi$
$174$	−1.13229	−0.0858383
$175$	0	0
$176$	3.79387	0.285974
$177$	−7.86821	−0.591411
$178$	1.14295	0.0856676
$179$	16.2270	1.21286	0.606432	−	0.795135i	$-0.292600\pi$
$179$	16.2270	1.21286	0.606432	+	0.795135i	$0.292600\pi$
$180$	−2.48213	−0.185007
$181$	12.0684	0.897038	0.448519	−	0.893773i	$-0.351952\pi$
$181$	12.0684	0.897038	0.448519	+	0.893773i	$0.351952\pi$
$182$	0	0
$183$	−3.77690	−0.279197
$184$	3.04706	0.224633
$185$	−4.71143	−0.346391
$186$	0.986182	0.0723104
$187$	−5.60799	−0.410097
$188$	−25.9317	−1.89126
$189$	0	0
$190$	1.35201	0.0980849
$191$	−0.432653	−0.0313057	−0.0156528	−	0.999877i	$-0.504983\pi$
$191$	−0.432653	−0.0313057	−0.0156528	+	0.999877i	$0.504983\pi$
$192$	7.18262	0.518361
$193$	3.42537	0.246564	0.123282	−	0.992372i	$-0.460658\pi$
$193$	3.42537	0.246564	0.123282	+	0.992372i	$0.460658\pi$
$194$	−2.84867	−0.204522
$195$	−8.75290	−0.626808
$196$	0	0
$197$	17.7522	1.26479	0.632396	−	0.774645i	$-0.282072\pi$
$197$	17.7522	1.26479	0.632396	+	0.774645i	$0.282072\pi$
$198$	−0.185885	−0.0132103
$199$	−12.8840	−0.913322	−0.456661	−	0.889641i	$-0.650955\pi$
$199$	−12.8840	−0.913322	−0.456661	+	0.889641i	$0.650955\pi$
$200$	−2.50998	−0.177483
$201$	−16.1182	−1.13689
$202$	−1.80830	−0.127231
$203$	0	0
$204$	−11.0222	−0.771708
$205$	14.4347	1.00817
$206$	−0.231324	−0.0161171
$207$	4.13375	0.287316
$208$	26.2949	1.82323
$209$	−5.75932	−0.398381
$210$	0	0
$211$	18.2270	1.25480	0.627400	−	0.778697i	$-0.284119\pi$
$211$	18.2270	1.25480	0.627400	+	0.778697i	$0.284119\pi$
$212$	10.8554	0.745549
$213$	−4.17353	−0.285966
$214$	−0.388744	−0.0265740
$215$	−5.40344	−0.368512
$216$	−0.737118	−0.0501546
$217$	0	0
$218$	−0.264956	−0.0179451
$219$	−5.40040	−0.364925
$220$	−2.48213	−0.167345
$221$	−38.8684	−2.61457
$222$	−0.693482	−0.0465434
$223$	20.8782	1.39810	0.699052	−	0.715071i	$-0.253605\pi$
$223$	20.8782	1.39810	0.699052	+	0.715071i	$0.253605\pi$
$224$	0	0
$225$	−3.40513	−0.227009
$226$	2.18845	0.145574
$227$	−1.54589	−0.102604	−0.0513022	−	0.998683i	$-0.516337\pi$
$227$	−1.54589	−0.102604	−0.0513022	+	0.998683i	$0.516337\pi$
$228$	−11.3196	−0.749661
$229$	−4.82397	−0.318777	−0.159388	−	0.987216i	$-0.550952\pi$
$229$	−4.82397	−0.318777	−0.159388	+	0.987216i	$0.550952\pi$
$230$	−0.970403	−0.0639865
$231$	0	0
$232$	−4.49002	−0.294784
$233$	−9.81085	−0.642730	−0.321365	−	0.946955i	$-0.604142\pi$
$233$	−9.81085	−0.642730	−0.321365	+	0.946955i	$0.604142\pi$
$234$	−1.28835	−0.0842222
$235$	16.6622	1.08692
$236$	−15.4645	−1.00666
$237$	−9.55912	−0.620932
$238$	0	0
$239$	−27.3869	−1.77151	−0.885754	−	0.464155i	$-0.846358\pi$
$239$	−27.3869	−1.77151	−0.885754	+	0.464155i	$0.846358\pi$
$240$	−4.79121	−0.309271
$241$	−1.15399	−0.0743352	−0.0371676	−	0.999309i	$-0.511834\pi$
$241$	−1.15399	−0.0743352	−0.0371676	+	0.999309i	$0.511834\pi$
$242$	−0.185885	−0.0119492
$243$	−1.00000	−0.0641500
$244$	−7.42330	−0.475228
$245$	0	0
$246$	2.12467	0.135464
$247$	−39.9172	−2.53987
$248$	3.91065	0.248327
$249$	6.73908	0.427072
$250$	1.97311	0.124791
$251$	13.3869	0.844970	0.422485	−	0.906370i	$-0.361158\pi$
$251$	13.3869	0.844970	0.422485	+	0.906370i	$0.361158\pi$
$252$	0	0
$253$	4.13375	0.259887
$254$	−0.431095	−0.0270493
$255$	7.08223	0.443506
$256$	13.3068	0.831674
$257$	−10.2482	−0.639267	−0.319634	−	0.947541i	$-0.603560\pi$
$257$	−10.2482	−0.639267	−0.319634	+	0.947541i	$0.603560\pi$
$258$	−0.795340	−0.0495157
$259$	0	0
$260$	−17.2034	−1.06691
$261$	−6.09131	−0.377043
$262$	−1.22952	−0.0759601
$263$	−9.59949	−0.591930	−0.295965	−	0.955199i	$-0.595641\pi$
$263$	−9.59949	−0.591930	−0.295965	+	0.955199i	$0.595641\pi$
$264$	−0.737118	−0.0453665
$265$	−6.97502	−0.428472
$266$	0	0
$267$	6.14867	0.376293
$268$	−31.6796	−1.93514
$269$	7.07384	0.431300	0.215650	−	0.976471i	$-0.430813\pi$
$269$	7.07384	0.431300	0.215650	+	0.976471i	$0.430813\pi$
$270$	0.234751	0.0142865
$271$	−14.4835	−0.879809	−0.439904	−	0.898045i	$-0.644988\pi$
$271$	−14.4835	−0.879809	−0.439904	+	0.898045i	$0.644988\pi$
$272$	−21.2760	−1.29005
$273$	0	0
$274$	3.40376	0.205628
$275$	−3.40513	−0.205337
$276$	8.12467	0.489048
$277$	−8.61734	−0.517766	−0.258883	−	0.965909i	$-0.583354\pi$
$277$	−8.61734	−0.517766	−0.258883	+	0.965909i	$0.583354\pi$
$278$	−1.17689	−0.0705854
$279$	5.30532	0.317621
$280$	0	0
$281$	9.08125	0.541742	0.270871	−	0.962616i	$-0.412688\pi$
$281$	9.08125	0.541742	0.270871	+	0.962616i	$0.412688\pi$
$282$	2.45253	0.146046
$283$	−4.78975	−0.284721	−0.142360	−	0.989815i	$-0.545469\pi$
$283$	−4.78975	−0.284721	−0.142360	+	0.989815i	$0.545469\pi$
$284$	−8.20286	−0.486750
$285$	7.27334	0.430835
$286$	−1.28835	−0.0761818
$287$	0	0
$288$	−2.17946	−0.128426
$289$	14.4495	0.849973
$290$	1.42994	0.0839691
$291$	−15.3249	−0.898360
$292$	−10.6142	−0.621148
$293$	−13.0334	−0.761417	−0.380708	−	0.924695i	$-0.624320\pi$
$293$	−13.0334	−0.761417	−0.380708	+	0.924695i	$0.624320\pi$
$294$	0	0
$295$	9.93662	0.578532
$296$	−2.74996	−0.159838
$297$	−1.00000	−0.0580259
$298$	3.14274	0.182054
$299$	28.6506	1.65691
$300$	−6.69260	−0.386398
$301$	0	0
$302$	−1.20536	−0.0693606
$303$	−9.72803	−0.558861
$304$	−21.8501	−1.25319
$305$	4.76978	0.273117
$306$	1.04244	0.0595925
$307$	−11.3413	−0.647285	−0.323642	−	0.946179i	$-0.604907\pi$
$307$	−11.3413	−0.647285	−0.323642	+	0.946179i	$0.604907\pi$
$308$	0	0
$309$	−1.24444	−0.0707938
$310$	−1.24543	−0.0707357
$311$	−9.20020	−0.521695	−0.260848	−	0.965380i	$-0.584002\pi$
$311$	−9.20020	−0.521695	−0.260848	+	0.965380i	$0.584002\pi$
$312$	−5.10889	−0.289234
$313$	10.5085	0.593973	0.296987	−	0.954882i	$-0.404018\pi$
$313$	10.5085	0.593973	0.296987	+	0.954882i	$0.404018\pi$
$314$	−0.374159	−0.0211150
$315$	0	0
$316$	−18.7879	−1.05690
$317$	−25.2611	−1.41880	−0.709402	−	0.704804i	$-0.751035\pi$
$317$	−25.2611	−1.41880	−0.709402	+	0.704804i	$0.751035\pi$
$318$	−1.02666	−0.0575725
$319$	−6.09131	−0.341048
$320$	−9.07080	−0.507073
$321$	−2.09131	−0.116725
$322$	0	0
$323$	32.2982	1.79712
$324$	−1.96545	−0.109191
$325$	−23.6006	−1.30913
$326$	−1.51560	−0.0839412
$327$	−1.42537	−0.0788232
$328$	8.42526	0.465207
$329$	0	0
$330$	0.234751	0.0129226
$331$	−9.42091	−0.517820	−0.258910	−	0.965901i	$-0.583363\pi$
$331$	−9.42091	−0.517820	−0.258910	+	0.965901i	$0.583363\pi$
$332$	13.2453	0.726930
$333$	−3.73070	−0.204441
$334$	−2.94178	−0.160967
$335$	20.3554	1.11214
$336$	0	0
$337$	10.1636	0.553646	0.276823	−	0.960921i	$-0.410718\pi$
$337$	10.1636	0.553646	0.276823	+	0.960921i	$0.410718\pi$
$338$	−6.51292	−0.354256
$339$	11.7731	0.639429
$340$	13.9197	0.754904
$341$	5.30532	0.287299
$342$	1.07057	0.0578900
$343$	0	0
$344$	−3.15388	−0.170046
$345$	−5.22044	−0.281059
$346$	0.784023	0.0421493
$347$	34.0379	1.82725	0.913624	−	0.406560i	$-0.133272\pi$
$347$	34.0379	1.82725	0.913624	+	0.406560i	$0.133272\pi$
$348$	−11.9721	−0.641774
$349$	−27.2845	−1.46051	−0.730253	−	0.683177i	$-0.760598\pi$
$349$	−27.2845	−1.46051	−0.730253	+	0.683177i	$0.760598\pi$
$350$	0	0
$351$	−6.93089	−0.369944
$352$	−2.17946	−0.116166
$353$	19.9742	1.06312	0.531560	−	0.847021i	$-0.321606\pi$
$353$	19.9742	1.06312	0.531560	+	0.847021i	$0.321606\pi$
$354$	1.46258	0.0777355
$355$	5.27068	0.279739
$356$	12.0849	0.640498
$357$	0	0
$358$	−3.01637	−0.159420
$359$	−4.23888	−0.223719	−0.111860	−	0.993724i	$-0.535681\pi$
$359$	−4.23888	−0.223719	−0.111860	+	0.993724i	$0.535681\pi$
$360$	0.930893	0.0490624
$361$	14.1698	0.745777
$362$	−2.24334	−0.117907
$363$	−1.00000	−0.0524864
$364$	0	0
$365$	6.82006	0.356978
$366$	0.702071	0.0366978
$367$	4.17337	0.217848	0.108924	−	0.994050i	$-0.465259\pi$
$367$	4.17337	0.217848	0.108924	+	0.994050i	$0.465259\pi$
$368$	15.6829	0.817529
$369$	11.4300	0.595022
$370$	0.875785	0.0455299
$371$	0	0
$372$	10.4273	0.540632
$373$	36.1533	1.87195	0.935973	−	0.352071i	$-0.114522\pi$
$373$	36.1533	1.87195	0.935973	+	0.352071i	$0.114522\pi$
$374$	1.04244	0.0539034
$375$	10.6147	0.548140
$376$	9.72537	0.501548
$377$	−42.2182	−2.17435
$378$	0	0
$379$	25.7686	1.32364	0.661821	−	0.749662i	$-0.269784\pi$
$379$	25.7686	1.32364	0.661821	+	0.749662i	$0.269784\pi$
$380$	14.2954	0.733337
$381$	−2.31914	−0.118813
$382$	0.0804239	0.00411484
$383$	−6.22071	−0.317863	−0.158932	−	0.987290i	$-0.550805\pi$
$383$	−6.22071	−0.317863	−0.158932	+	0.987290i	$0.550805\pi$
$384$	−5.69407	−0.290574
$385$	0	0
$386$	−0.636726	−0.0324085
$387$	−4.27866	−0.217497
$388$	−30.1202	−1.52912
$389$	21.4171	1.08589	0.542946	−	0.839767i	$-0.317309\pi$
$389$	21.4171	1.08589	0.542946	+	0.839767i	$0.317309\pi$
$390$	1.62704	0.0823881
$391$	−23.1820	−1.17237
$392$	0	0
$393$	−6.61441	−0.333653
$394$	−3.29987	−0.166245
$395$	12.0720	0.607410
$396$	−1.96545	−0.0987674
$397$	−1.23743	−0.0621050	−0.0310525	−	0.999518i	$-0.509886\pi$
$397$	−1.23743	−0.0621050	−0.0310525	+	0.999518i	$0.509886\pi$
$398$	2.39494	0.120048
$399$	0	0
$400$	−12.9186	−0.645932
$401$	−17.4384	−0.870831	−0.435415	−	0.900230i	$-0.643399\pi$
$401$	−17.4384	−0.870831	−0.435415	+	0.900230i	$0.643399\pi$
$402$	2.99615	0.149434
$403$	36.7706	1.83168
$404$	−19.1199	−0.951252
$405$	1.26288	0.0627531
$406$	0	0
$407$	−3.73070	−0.184924
$408$	4.13375	0.204651
$409$	14.1632	0.700327	0.350163	−	0.936689i	$-0.386126\pi$
$409$	14.1632	0.700327	0.350163	+	0.936689i	$0.386126\pi$
$410$	−2.68320	−0.132514
$411$	18.3110	0.903217
$412$	−2.44588	−0.120500
$413$	0	0
$414$	−0.768404	−0.0377650
$415$	−8.51066	−0.417772
$416$	−15.1056	−0.740614
$417$	−6.33129	−0.310045
$418$	1.07057	0.0523635
$419$	−28.8378	−1.40882	−0.704409	−	0.709794i	$-0.748788\pi$
$419$	−28.8378	−1.40882	−0.704409	+	0.709794i	$0.748788\pi$
$420$	0	0
$421$	−26.1883	−1.27634	−0.638171	−	0.769895i	$-0.720309\pi$
$421$	−26.1883	−1.27634	−0.638171	+	0.769895i	$0.720309\pi$
$422$	−3.38814	−0.164932
$423$	13.1938	0.641503
$424$	−4.07118	−0.197714
$425$	19.0959	0.926289
$426$	0.775799	0.0375876
$427$	0	0
$428$	−4.11036	−0.198682
$429$	−6.93089	−0.334627
$430$	1.00442	0.0484375
$431$	−21.4952	−1.03539	−0.517694	−	0.855566i	$-0.673210\pi$
$431$	−21.4952	−1.03539	−0.517694	+	0.855566i	$0.673210\pi$
$432$	−3.79387	−0.182533
$433$	14.9303	0.717505	0.358752	−	0.933433i	$-0.383202\pi$
$433$	14.9303	0.717505	0.358752	+	0.933433i	$0.383202\pi$
$434$	0	0
$435$	7.69260	0.368832
$436$	−2.80149	−0.134167
$437$	−23.8076	−1.13887
$438$	1.00385	0.0479660
$439$	−24.8160	−1.18440	−0.592201	−	0.805790i	$-0.701741\pi$
$439$	−24.8160	−1.18440	−0.592201	+	0.805790i	$0.701741\pi$
$440$	0.930893	0.0443786
$441$	0	0
$442$	7.22506	0.343661
$443$	−31.6570	−1.50407	−0.752035	−	0.659123i	$-0.770928\pi$
$443$	−31.6570	−1.50407	−0.752035	+	0.659123i	$0.770928\pi$
$444$	−7.33248	−0.347984
$445$	−7.76504	−0.368098
$446$	−3.88094	−0.183768
$447$	16.9069	0.799668
$448$	0	0
$449$	−12.3117	−0.581027	−0.290514	−	0.956871i	$-0.593826\pi$
$449$	−12.3117	−0.581027	−0.290514	+	0.956871i	$0.593826\pi$
$450$	0.632964	0.0298382
$451$	11.4300	0.538217
$452$	23.1395	1.08839
$453$	−6.48442	−0.304665
$454$	0.287359	0.0134864
$455$	0	0
$456$	4.24530	0.198804
$457$	−9.99554	−0.467572	−0.233786	−	0.972288i	$-0.575111\pi$
$457$	−9.99554	−0.467572	−0.233786	+	0.972288i	$0.575111\pi$
$458$	0.896704	0.0419002
$459$	5.60799	0.261758
$460$	−10.2605	−0.478398
$461$	14.7163	0.685406	0.342703	−	0.939444i	$-0.388658\pi$
$461$	14.7163	0.685406	0.342703	+	0.939444i	$0.388658\pi$
$462$	0	0
$463$	28.7650	1.33682	0.668412	−	0.743791i	$-0.266974\pi$
$463$	28.7650	1.33682	0.668412	+	0.743791i	$0.266974\pi$
$464$	−23.1097	−1.07284
$465$	−6.70000	−0.310705
$466$	1.82369	0.0844809
$467$	−1.00462	−0.0464883	−0.0232442	−	0.999730i	$-0.507400\pi$
$467$	−1.00462	−0.0464883	−0.0232442	+	0.999730i	$0.507400\pi$
$468$	−13.6223	−0.629691
$469$	0	0
$470$	−3.09725	−0.142866
$471$	−2.01285	−0.0927470
$472$	5.79980	0.266958
$473$	−4.27866	−0.196733
$474$	1.77690	0.0816158
$475$	19.6112	0.899825
$476$	0	0
$477$	−5.52310	−0.252885
$478$	5.09081	0.232848
$479$	−15.0159	−0.686094	−0.343047	−	0.939318i	$-0.611459\pi$
$479$	−15.0159	−0.686094	−0.343047	+	0.939318i	$0.611459\pi$
$480$	2.75240	0.125629
$481$	−25.8571	−1.17898
$482$	0.214510	0.00977068
$483$	0	0
$484$	−1.96545	−0.0893385
$485$	19.3535	0.878797
$486$	0.185885	0.00843193
$487$	−2.55560	−0.115805	−0.0579027	−	0.998322i	$-0.518441\pi$
$487$	−2.55560	−0.115805	−0.0579027	+	0.998322i	$0.518441\pi$
$488$	2.78402	0.126027
$489$	−8.15341	−0.368710
$490$	0	0
$491$	−26.5637	−1.19880	−0.599402	−	0.800448i	$-0.704595\pi$
$491$	−26.5637	−1.19880	−0.599402	+	0.800448i	$0.704595\pi$
$492$	22.4650	1.01280
$493$	34.1600	1.53849
$494$	7.42003	0.333843
$495$	1.26288	0.0567623
$496$	20.1277	0.903762
$497$	0	0
$498$	−1.25270	−0.0561347
$499$	6.82270	0.305426	0.152713	−	0.988271i	$-0.451199\pi$
$499$	6.82270	0.305426	0.152713	+	0.988271i	$0.451199\pi$
$500$	20.8626	0.933004
$501$	−15.8258	−0.707043
$502$	−2.48842	−0.111064
$503$	5.42913	0.242073	0.121037	−	0.992648i	$-0.461378\pi$
$503$	5.42913	0.242073	0.121037	+	0.992648i	$0.461378\pi$
$504$	0	0
$505$	12.2854	0.546691
$506$	−0.768404	−0.0341597
$507$	−35.0373	−1.55606
$508$	−4.55815	−0.202235
$509$	−17.5157	−0.776370	−0.388185	−	0.921581i	$-0.626898\pi$
$509$	−17.5157	−0.776370	−0.388185	+	0.921581i	$0.626898\pi$
$510$	−1.31648	−0.0582948
$511$	0	0
$512$	−13.8617	−0.612605
$513$	5.75932	0.254280
$514$	1.90500	0.0840258
$515$	1.57158	0.0692522
$516$	−8.40948	−0.370207
$517$	13.1938	0.580262
$518$	0	0
$519$	4.21778	0.185140
$520$	6.45192	0.282935
$521$	38.6930	1.69517	0.847586	−	0.530658i	$-0.178055\pi$
$521$	38.6930	1.69517	0.847586	+	0.530658i	$0.178055\pi$
$522$	1.13229	0.0495588
$523$	1.05626	0.0461871	0.0230935	−	0.999733i	$-0.492648\pi$
$523$	1.05626	0.0461871	0.0230935	+	0.999733i	$0.492648\pi$
$524$	−13.0003	−0.567920
$525$	0	0
$526$	1.78440	0.0778037
$527$	−29.7522	−1.29603
$528$	−3.79387	−0.165107
$529$	−5.91210	−0.257048
$530$	1.29655	0.0563187
$531$	7.86821	0.341451
$532$	0	0
$533$	79.2201	3.43140
$534$	−1.14295	−0.0494602
$535$	2.64108	0.114184
$536$	11.8811	0.513183
$537$	−16.2270	−0.700248
$538$	−1.31492	−0.0566904
$539$	0	0
$540$	2.48213	0.106814
$541$	−14.1120	−0.606720	−0.303360	−	0.952876i	$-0.598109\pi$
$541$	−14.1120	−0.606720	−0.303360	+	0.952876i	$0.598109\pi$
$542$	2.69227	0.115643
$543$	−12.0684	−0.517905
$544$	12.2224	0.524031
$545$	1.80007	0.0771067
$546$	0	0
$547$	−2.08211	−0.0890247	−0.0445123	−	0.999009i	$-0.514173\pi$
$547$	−2.08211	−0.0890247	−0.0445123	+	0.999009i	$0.514173\pi$
$548$	35.9894	1.53739
$549$	3.77690	0.161194
$550$	0.632964	0.0269897
$551$	35.0818	1.49453
$552$	−3.04706	−0.129692
$553$	0	0
$554$	1.60184	0.0680556
$555$	4.71143	0.199989
$556$	−12.4438	−0.527735
$557$	−16.6785	−0.706689	−0.353345	−	0.935493i	$-0.614956\pi$
$557$	−16.6785	−0.706689	−0.353345	+	0.935493i	$0.614956\pi$
$558$	−0.986182	−0.0417484
$559$	−29.6549	−1.25427
$560$	0	0
$561$	5.60799	0.236769
$562$	−1.68807	−0.0712070
$563$	−35.7321	−1.50593	−0.752965	−	0.658061i	$-0.771377\pi$
$563$	−35.7321	−1.50593	−0.752965	+	0.658061i	$0.771377\pi$
$564$	25.9317	1.09192
$565$	−14.8681	−0.625505
$566$	0.890344	0.0374239
$567$	0	0
$568$	3.07639	0.129082
$569$	37.9050	1.58906	0.794530	−	0.607225i	$-0.207718\pi$
$569$	37.9050	1.58906	0.794530	+	0.607225i	$0.207718\pi$
$570$	−1.35201	−0.0566294
$571$	−37.9257	−1.58714	−0.793571	−	0.608477i	$-0.791781\pi$
$571$	−37.9257	−1.58714	−0.793571	+	0.608477i	$0.791781\pi$
$572$	−13.6223	−0.569577
$573$	0.432653	0.0180743
$574$	0	0
$575$	−14.0760	−0.587008
$576$	−7.18262	−0.299276
$577$	42.4001	1.76514	0.882569	−	0.470182i	$-0.155812\pi$
$577$	42.4001	1.76514	0.882569	+	0.470182i	$0.155812\pi$
$578$	−2.68596	−0.111721
$579$	−3.42537	−0.142354
$580$	15.1194	0.627799
$581$	0	0
$582$	2.84867	0.118081
$583$	−5.52310	−0.228744
$584$	3.98073	0.164724
$585$	8.75290	0.361888
$586$	2.42271	0.100081
$587$	−26.5924	−1.09758	−0.548792	−	0.835959i	$-0.684912\pi$
$587$	−26.5924	−1.09758	−0.548792	+	0.835959i	$0.684912\pi$
$588$	0	0
$589$	−30.5551	−1.25900
$590$	−1.84707	−0.0760427
$591$	−17.7522	−0.730228
$592$	−14.1538	−0.581717
$593$	−14.7749	−0.606734	−0.303367	−	0.952874i	$-0.598111\pi$
$593$	−14.7749	−0.606734	−0.303367	+	0.952874i	$0.598111\pi$
$594$	0.185885	0.00762697
$595$	0	0
$596$	33.2296	1.36114
$597$	12.8840	0.527307
$598$	−5.32573	−0.217785
$599$	3.12577	0.127716	0.0638578	−	0.997959i	$-0.479660\pi$
$599$	3.12577	0.127716	0.0638578	+	0.997959i	$0.479660\pi$
$600$	2.50998	0.102470
$601$	−19.2780	−0.786364	−0.393182	−	0.919461i	$-0.628626\pi$
$601$	−19.2780	−0.786364	−0.393182	+	0.919461i	$0.628626\pi$
$602$	0	0
$603$	16.1182	0.656386
$604$	−12.7448	−0.518578
$605$	1.26288	0.0513434
$606$	1.80830	0.0734571
$607$	−10.5994	−0.430216	−0.215108	−	0.976590i	$-0.569010\pi$
$607$	−10.5994	−0.430216	−0.215108	+	0.976590i	$0.569010\pi$
$608$	12.5522	0.509060
$609$	0	0
$610$	−0.886632	−0.0358987
$611$	91.4446	3.69945
$612$	11.0222	0.445546
$613$	25.1685	1.01655	0.508273	−	0.861196i	$-0.330284\pi$
$613$	25.1685	1.01655	0.508273	+	0.861196i	$0.330284\pi$
$614$	2.10819	0.0850796
$615$	−14.4347	−0.582064
$616$	0	0
$617$	−32.5595	−1.31080	−0.655399	−	0.755283i	$-0.727499\pi$
$617$	−32.5595	−1.31080	−0.655399	+	0.755283i	$0.727499\pi$
$618$	0.231324	0.00930520
$619$	−10.7770	−0.433165	−0.216582	−	0.976264i	$-0.569491\pi$
$619$	−10.7770	−0.433165	−0.216582	+	0.976264i	$0.569491\pi$
$620$	−13.1685	−0.528859
$621$	−4.13375	−0.165882
$622$	1.71018	0.0685720
$623$	0	0
$624$	−26.2949	−1.05264
$625$	3.62056	0.144822
$626$	−1.95337	−0.0780723
$627$	5.75932	0.230005
$628$	−3.95614	−0.157867
$629$	20.9217	0.834203
$630$	0	0
$631$	−40.2884	−1.60386	−0.801928	−	0.597420i	$-0.796192\pi$
$631$	−40.2884	−1.60386	−0.801928	+	0.597420i	$0.796192\pi$
$632$	7.04621	0.280283
$633$	−18.2270	−0.724459
$634$	4.69566	0.186489
$635$	2.92880	0.116226
$636$	−10.8554	−0.430443
$637$	0	0
$638$	1.13229	0.0448276
$639$	4.17353	0.165102
$640$	7.19093	0.284247
$641$	−24.3884	−0.963284	−0.481642	−	0.876368i	$-0.659959\pi$
$641$	−24.3884	−0.963284	−0.481642	+	0.876368i	$0.659959\pi$
$642$	0.388744	0.0153425
$643$	23.0317	0.908280	0.454140	−	0.890930i	$-0.349947\pi$
$643$	23.0317	0.908280	0.454140	+	0.890930i	$0.349947\pi$
$644$	0	0
$645$	5.40344	0.212760
$646$	−6.00376	−0.236215
$647$	21.3671	0.840029	0.420015	−	0.907517i	$-0.362025\pi$
$647$	21.3671	0.840029	0.420015	+	0.907517i	$0.362025\pi$
$648$	0.737118	0.0289567
$649$	7.86821	0.308854
$650$	4.38700	0.172072
$651$	0	0
$652$	−16.0251	−0.627591
$653$	11.4924	0.449733	0.224866	−	0.974390i	$-0.427805\pi$
$653$	11.4924	0.449733	0.224866	+	0.974390i	$0.427805\pi$
$654$	0.264956	0.0103606
$655$	8.35322	0.326387
$656$	43.3639	1.69308
$657$	5.40040	0.210690
$658$	0	0
$659$	−2.40682	−0.0937563	−0.0468782	−	0.998901i	$-0.514927\pi$
$659$	−2.40682	−0.0937563	−0.0468782	+	0.998901i	$0.514927\pi$
$660$	2.48213	0.0966166
$661$	−16.5565	−0.643972	−0.321986	−	0.946744i	$-0.604350\pi$
$661$	−16.5565	−0.643972	−0.321986	+	0.946744i	$0.604350\pi$
$662$	1.75121	0.0680627
$663$	38.8684	1.50952
$664$	−4.96750	−0.192776
$665$	0	0
$666$	0.693482	0.0268719
$667$	−25.1800	−0.974972
$668$	−31.1047	−1.20348
$669$	−20.8782	−0.807196
$670$	−3.78378	−0.146180
$671$	3.77690	0.145806
$672$	0	0
$673$	43.2861	1.66856	0.834278	−	0.551344i	$-0.185885\pi$
$673$	43.2861	1.66856	0.834278	+	0.551344i	$0.185885\pi$
$674$	−1.88926	−0.0727717
$675$	3.40513	0.131064
$676$	−68.8639	−2.64861
$677$	−17.3727	−0.667689	−0.333844	−	0.942628i	$-0.608346\pi$
$677$	−17.3727	−0.667689	−0.333844	+	0.942628i	$0.608346\pi$
$678$	−2.18845	−0.0840471
$679$	0	0
$680$	−5.22044	−0.200195
$681$	1.54589	0.0592387
$682$	−0.986182	−0.0377629
$683$	12.0749	0.462035	0.231017	−	0.972950i	$-0.425795\pi$
$683$	12.0749	0.462035	0.231017	+	0.972950i	$0.425795\pi$
$684$	11.3196	0.432817
$685$	−23.1247	−0.883549
$686$	0	0
$687$	4.82397	0.184046
$688$	−16.2327	−0.618866
$689$	−38.2800	−1.45835
$690$	0.970403	0.0369426
$691$	35.4929	1.35022	0.675108	−	0.737719i	$-0.264097\pi$
$691$	35.4929	1.35022	0.675108	+	0.737719i	$0.264097\pi$
$692$	8.28982	0.315132
$693$	0	0
$694$	−6.32714	−0.240175
$695$	7.99567	0.303293
$696$	4.49002	0.170194
$697$	−64.0993	−2.42793
$698$	5.07179	0.191970
$699$	9.81085	0.371080
$700$	0	0
$701$	−9.81378	−0.370661	−0.185331	−	0.982676i	$-0.559336\pi$
$701$	−9.81378	−0.370661	−0.185331	+	0.982676i	$0.559336\pi$
$702$	1.28835	0.0486257
$703$	21.4863	0.810370
$704$	−7.18262	−0.270705
$705$	−16.6622	−0.627534
$706$	−3.71291	−0.139737
$707$	0	0
$708$	15.4645	0.581193
$709$	38.2551	1.43670	0.718349	−	0.695682i	$-0.244898\pi$
$709$	38.2551	1.43670	0.718349	+	0.695682i	$0.244898\pi$
$710$	−0.979742	−0.0367691
$711$	9.55912	0.358495
$712$	−4.53230	−0.169855
$713$	21.9309	0.821318
$714$	0	0
$715$	8.75290	0.327340
$716$	−31.8933	−1.19191
$717$	27.3869	1.02278
$718$	0.787945	0.0294059
$719$	18.5140	0.690456	0.345228	−	0.938519i	$-0.387802\pi$
$719$	18.5140	0.690456	0.345228	+	0.938519i	$0.387802\pi$
$720$	4.79121	0.178558
$721$	0	0
$722$	−2.63395	−0.0980256
$723$	1.15399	0.0429174
$724$	−23.7198	−0.881540
$725$	20.7417	0.770327
$726$	0.185885	0.00689885
$727$	41.0658	1.52305	0.761523	−	0.648138i	$-0.224452\pi$
$727$	41.0658	1.52305	0.761523	+	0.648138i	$0.224452\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−1.26775	−0.0469215
$731$	23.9947	0.887475
$732$	7.42330	0.274373
$733$	−10.0352	−0.370657	−0.185329	−	0.982677i	$-0.559335\pi$
$733$	−10.0352	−0.370657	−0.185329	+	0.982677i	$0.559335\pi$
$734$	−0.775769	−0.0286342
$735$	0	0
$736$	−9.00936	−0.332089
$737$	16.1182	0.593723
$738$	−2.12467	−0.0782101
$739$	14.4054	0.529911	0.264956	−	0.964261i	$-0.414643\pi$
$739$	14.4054	0.529911	0.264956	+	0.964261i	$0.414643\pi$
$740$	9.26006	0.340406
$741$	39.9172	1.46640
$742$	0	0
$743$	−6.03505	−0.221404	−0.110702	−	0.993854i	$-0.535310\pi$
$743$	−6.03505	−0.221404	−0.110702	+	0.993854i	$0.535310\pi$
$744$	−3.91065	−0.143371
$745$	−21.3514	−0.782255
$746$	−6.72037	−0.246050
$747$	−6.73908	−0.246570
$748$	11.0222	0.403012
$749$	0	0
$750$	−1.97311	−0.0720479
$751$	19.1240	0.697844	0.348922	−	0.937152i	$-0.386548\pi$
$751$	19.1240	0.697844	0.348922	+	0.937152i	$0.386548\pi$
$752$	50.0555	1.82534
$753$	−13.3869	−0.487844
$754$	7.84775	0.285798
$755$	8.18906	0.298030
$756$	0	0
$757$	−40.1103	−1.45783	−0.728917	−	0.684602i	$-0.759976\pi$
$757$	−40.1103	−1.45783	−0.728917	+	0.684602i	$0.759976\pi$
$758$	−4.79000	−0.173981
$759$	−4.13375	−0.150046
$760$	−5.36131	−0.194475
$761$	−34.9471	−1.26683	−0.633415	−	0.773812i	$-0.718347\pi$
$761$	−34.9471	−1.26683	−0.633415	+	0.773812i	$0.718347\pi$
$762$	0.431095	0.0156169
$763$	0	0
$764$	0.850356	0.0307648
$765$	−7.08223	−0.256058
$766$	1.15634	0.0417802
$767$	54.5337	1.96910
$768$	−13.3068	−0.480167
$769$	−7.83767	−0.282634	−0.141317	−	0.989964i	$-0.545134\pi$
$769$	−7.83767	−0.282634	−0.141317	+	0.989964i	$0.545134\pi$
$770$	0	0
$771$	10.2482	0.369081
$772$	−6.73238	−0.242304
$773$	−22.0496	−0.793069	−0.396535	−	0.918020i	$-0.629787\pi$
$773$	−22.0496	−0.793069	−0.396535	+	0.918020i	$0.629787\pi$
$774$	0.795340	0.0285879
$775$	−18.0653	−0.648925
$776$	11.2962	0.405511
$777$	0	0
$778$	−3.98113	−0.142731
$779$	−65.8290	−2.35857
$780$	17.2034	0.615979
$781$	4.17353	0.149341
$782$	4.30920	0.154097
$783$	6.09131	0.217686
$784$	0	0
$785$	2.54199	0.0907274
$786$	1.22952	0.0438556
$787$	32.6831	1.16503	0.582513	−	0.812821i	$-0.302069\pi$
$787$	32.6831	1.16503	0.582513	+	0.812821i	$0.302069\pi$
$788$	−34.8910	−1.24294
$789$	9.59949	0.341751
$790$	−2.24402	−0.0798385
$791$	0	0
$792$	0.737118	0.0261924
$793$	26.1773	0.929583
$794$	0.230021	0.00816313
$795$	6.97502	0.247379
$796$	25.3228	0.897543
$797$	35.1533	1.24519	0.622597	−	0.782543i	$-0.286078\pi$
$797$	35.1533	1.24519	0.622597	+	0.782543i	$0.286078\pi$
$798$	0	0
$799$	−73.9905	−2.61760
$800$	7.42135	0.262384
$801$	−6.14867	−0.217253
$802$	3.24154	0.114463
$803$	5.40040	0.190576
$804$	31.6796	1.11725
$805$	0	0
$806$	−6.83512	−0.240757
$807$	−7.07384	−0.249011
$808$	7.17071	0.252265
$809$	1.69745	0.0596791	0.0298396	−	0.999555i	$-0.490500\pi$
$809$	1.69745	0.0596791	0.0298396	+	0.999555i	$0.490500\pi$
$810$	−0.234751	−0.00824832
$811$	−7.74549	−0.271981	−0.135990	−	0.990710i	$-0.543422\pi$
$811$	−7.74549	−0.271981	−0.135990	+	0.990710i	$0.543422\pi$
$812$	0	0
$813$	14.4835	0.507958
$814$	0.693482	0.0243065
$815$	10.2968	0.360681
$816$	21.2760	0.744809
$817$	24.6422	0.862121
$818$	−2.63274	−0.0920515
$819$	0	0
$820$	−28.3707	−0.990747
$821$	−27.2852	−0.952260	−0.476130	−	0.879375i	$-0.657961\pi$
$821$	−27.2852	−0.952260	−0.476130	+	0.879375i	$0.657961\pi$
$822$	−3.40376	−0.118720
$823$	9.30028	0.324187	0.162094	−	0.986775i	$-0.448175\pi$
$823$	9.30028	0.324187	0.162094	+	0.986775i	$0.448175\pi$
$824$	0.917301	0.0319557
$825$	3.40513	0.118551
$826$	0	0
$827$	31.1262	1.08236	0.541182	−	0.840905i	$-0.317977\pi$
$827$	31.1262	1.08236	0.541182	+	0.840905i	$0.317977\pi$
$828$	−8.12467	−0.282352
$829$	−14.9080	−0.517776	−0.258888	−	0.965907i	$-0.583356\pi$
$829$	−14.9080	−0.517776	−0.258888	+	0.965907i	$0.583356\pi$
$830$	1.58201	0.0549123
$831$	8.61734	0.298932
$832$	−49.7820	−1.72588
$833$	0	0
$834$	1.17689	0.0407525
$835$	19.9861	0.691646
$836$	11.3196	0.391498
$837$	−5.30532	−0.183379
$838$	5.36052	0.185176
$839$	−23.3541	−0.806272	−0.403136	−	0.915140i	$-0.632080\pi$
$839$	−23.3541	−0.806272	−0.403136	+	0.915140i	$0.632080\pi$
$840$	0	0
$841$	8.10404	0.279450
$842$	4.86803	0.167763
$843$	−9.08125	−0.312775
$844$	−35.8242	−1.23312
$845$	44.2479	1.52218
$846$	−2.45253	−0.0843197
$847$	0	0
$848$	−20.9540	−0.719562
$849$	4.78975	0.164384
$850$	−3.54965	−0.121752
$851$	−15.4218	−0.528651
$852$	8.20286	0.281025
$853$	−15.0186	−0.514226	−0.257113	−	0.966381i	$-0.582771\pi$
$853$	−15.0186	−0.514226	−0.257113	+	0.966381i	$0.582771\pi$
$854$	0	0
$855$	−7.27334	−0.248743
$856$	1.54154	0.0526888
$857$	−51.7605	−1.76810	−0.884052	−	0.467389i	$-0.845195\pi$
$857$	−51.7605	−1.76810	−0.884052	+	0.467389i	$0.845195\pi$
$858$	1.28835	0.0439836
$859$	12.4297	0.424098	0.212049	−	0.977259i	$-0.431986\pi$
$859$	12.4297	0.424098	0.212049	+	0.977259i	$0.431986\pi$
$860$	10.6202	0.362145
$861$	0	0
$862$	3.99565	0.136092
$863$	−16.4050	−0.558433	−0.279217	−	0.960228i	$-0.590075\pi$
$863$	−16.4050	−0.558433	−0.279217	+	0.960228i	$0.590075\pi$
$864$	2.17946	0.0741468
$865$	−5.32655	−0.181108
$866$	−2.77533	−0.0943094
$867$	−14.4495	−0.490732
$868$	0	0
$869$	9.55912	0.324271
$870$	−1.42994	−0.0484796
$871$	111.714	3.78528
$872$	1.05067	0.0355801
$873$	15.3249	0.518668
$874$	4.42548	0.149694
$875$	0	0
$876$	10.6142	0.358620
$877$	24.8896	0.840462	0.420231	−	0.907417i	$-0.361949\pi$
$877$	24.8896	0.840462	0.420231	+	0.907417i	$0.361949\pi$
$878$	4.61293	0.155679
$879$	13.0334	0.439604
$880$	4.79121	0.161512
$881$	24.6591	0.830786	0.415393	−	0.909642i	$-0.363644\pi$
$881$	24.6591	0.830786	0.415393	+	0.909642i	$0.363644\pi$
$882$	0	0
$883$	−36.8851	−1.24128	−0.620641	−	0.784095i	$-0.713128\pi$
$883$	−36.8851	−1.24128	−0.620641	+	0.784095i	$0.713128\pi$
$884$	76.3937	2.56940
$885$	−9.93662	−0.334016
$886$	5.88458	0.197696
$887$	−13.0157	−0.437023	−0.218512	−	0.975834i	$-0.570120\pi$
$887$	−13.0157	−0.437023	−0.218512	+	0.975834i	$0.570120\pi$
$888$	2.74996	0.0922828
$889$	0	0
$890$	1.44341	0.0483831
$891$	1.00000	0.0335013
$892$	−41.0349	−1.37395
$893$	−75.9872	−2.54281
$894$	−3.14274	−0.105109
$895$	20.4928	0.684999
$896$	0	0
$897$	−28.6506	−0.956615
$898$	2.28857	0.0763707
$899$	−32.3164	−1.07781
$900$	6.69260	0.223087
$901$	30.9735	1.03188
$902$	−2.12467	−0.0707437
$903$	0	0
$904$	−8.67820	−0.288633
$905$	15.2410	0.506627
$906$	1.20536	0.0400454
$907$	26.7445	0.888038	0.444019	−	0.896017i	$-0.353552\pi$
$907$	26.7445	0.888038	0.444019	+	0.896017i	$0.353552\pi$
$908$	3.03837	0.100832
$909$	9.72803	0.322659
$910$	0	0
$911$	38.9528	1.29056	0.645282	−	0.763945i	$-0.276740\pi$
$911$	38.9528	1.29056	0.645282	+	0.763945i	$0.276740\pi$
$912$	21.8501	0.723530
$913$	−6.73908	−0.223031
$914$	1.85802	0.0614580
$915$	−4.76978	−0.157684
$916$	9.48125	0.313269
$917$	0	0
$918$	−1.04244	−0.0344057
$919$	40.6154	1.33978	0.669890	−	0.742461i	$-0.266341\pi$
$919$	40.6154	1.33978	0.669890	+	0.742461i	$0.266341\pi$
$920$	3.84808	0.126867
$921$	11.3413	0.373710
$922$	−2.73554	−0.0900903
$923$	28.9263	0.952121
$924$	0	0
$925$	12.7035	0.417689
$926$	−5.34700	−0.175713
$927$	1.24444	0.0408728
$928$	13.2758	0.435799
$929$	24.6644	0.809213	0.404607	−	0.914491i	$-0.367408\pi$
$929$	24.6644	0.809213	0.404607	+	0.914491i	$0.367408\pi$
$930$	1.24543	0.0408393
$931$	0	0
$932$	19.2827	0.631626
$933$	9.20020	0.301201
$934$	0.186744	0.00611046
$935$	−7.08223	−0.231614
$936$	5.10889	0.166989
$937$	−21.9210	−0.716127	−0.358064	−	0.933697i	$-0.616563\pi$
$937$	−21.9210	−0.716127	−0.358064	+	0.933697i	$0.616563\pi$
$938$	0	0
$939$	−10.5085	−0.342930
$940$	−32.7486	−1.06814
$941$	13.6736	0.445747	0.222874	−	0.974847i	$-0.428456\pi$
$941$	13.6736	0.445747	0.222874	+	0.974847i	$0.428456\pi$
$942$	0.374159	0.0121907
$943$	47.2487	1.53863
$944$	29.8510	0.971567
$945$	0	0
$946$	0.795340	0.0258587
$947$	11.4432	0.371855	0.185927	−	0.982563i	$-0.440471\pi$
$947$	11.4432	0.371855	0.185927	+	0.982563i	$0.440471\pi$
$948$	18.7879	0.610204
$949$	37.4296	1.21502
$950$	−3.64544	−0.118274
$951$	25.2611	0.819147
$952$	0	0
$953$	−1.02793	−0.0332978	−0.0166489	−	0.999861i	$-0.505300\pi$
$953$	−1.02793	−0.0332978	−0.0166489	+	0.999861i	$0.505300\pi$
$954$	1.02666	0.0332395
$955$	−0.546390	−0.0176808
$956$	53.8274	1.74090
$957$	6.09131	0.196904
$958$	2.79123	0.0901807
$959$	0	0
$960$	9.07080	0.292759
$961$	−2.85353	−0.0920494
$962$	4.80645	0.154966
$963$	2.09131	0.0673915
$964$	2.26811	0.0730509
$965$	4.32584	0.139254
$966$	0	0
$967$	2.74492	0.0882705	0.0441353	−	0.999026i	$-0.485947\pi$
$967$	2.74492	0.0882705	0.0441353	+	0.999026i	$0.485947\pi$
$968$	0.737118	0.0236919
$969$	−32.2982	−1.03757
$970$	−3.59753	−0.115510
$971$	−60.3616	−1.93709	−0.968547	−	0.248829i	$-0.919954\pi$
$971$	−60.3616	−1.93709	−0.968547	+	0.248829i	$0.919954\pi$
$972$	1.96545	0.0630417
$973$	0	0
$974$	0.475049	0.0152216
$975$	23.6006	0.755824
$976$	14.3291	0.458663
$977$	3.21291	0.102790	0.0513951	−	0.998678i	$-0.483633\pi$
$977$	3.21291	0.102790	0.0513951	+	0.998678i	$0.483633\pi$
$978$	1.51560	0.0484635
$979$	−6.14867	−0.196512
$980$	0	0
$981$	1.42537	0.0455086
$982$	4.93781	0.157572
$983$	17.6505	0.562965	0.281482	−	0.959566i	$-0.409174\pi$
$983$	17.6505	0.562965	0.281482	+	0.959566i	$0.409174\pi$
$984$	−8.42526	−0.268587
$985$	22.4189	0.714326
$986$	−6.34984	−0.202220
$987$	0	0
$988$	78.4552	2.49599
$989$	−17.6869	−0.562411
$990$	−0.234751	−0.00746088
$991$	−45.7816	−1.45430	−0.727151	−	0.686478i	$-0.759156\pi$
$991$	−45.7816	−1.45430	−0.727151	+	0.686478i	$0.759156\pi$
$992$	−11.5628	−0.367118
$993$	9.42091	0.298964
$994$	0	0
$995$	−16.2710	−0.515824
$996$	−13.2453	−0.419693
$997$	−58.4776	−1.85200	−0.926002	−	0.377519i	$-0.876777\pi$
$997$	−58.4776	−1.85200	−0.926002	+	0.377519i	$0.876777\pi$
$998$	−1.26824	−0.0401455
$999$	3.73070	0.118034

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1617.2.a.u.1.3	✓	4
3.2	odd	2		4851.2.a.bx.1.2		4
7.6	odd	2		1617.2.a.v.1.3	yes	4
21.20	even	2		4851.2.a.by.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1617.2.a.u.1.3	✓	4	1.1	even	1	trivial
1617.2.a.v.1.3	yes	4	7.6	odd	2
4851.2.a.bx.1.2		4	3.2	odd	2
4851.2.a.by.1.2		4	21.20	even	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:	\( N \)	\(=\)	\( 1617 = 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1617.a (trivial)

\(f(q)\)	\(=\)	\(q-0.185885 q^{2} -1.00000 q^{3} -1.96545 q^{4} +1.26288 q^{5} +0.185885 q^{6} +0.737118 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.185885 q^{2} -1.00000 q^{3} -1.96545 q^{4} +1.26288 q^{5} +0.185885 q^{6} +0.737118 q^{8} +1.00000 q^{9} -0.234751 q^{10} +1.00000 q^{11} +1.96545 q^{12} +6.93089 q^{13} -1.26288 q^{15} +3.79387 q^{16} -5.60799 q^{17} -0.185885 q^{18} -5.75932 q^{19} -2.48213 q^{20} -0.185885 q^{22} +4.13375 q^{23} -0.737118 q^{24} -3.40513 q^{25} -1.28835 q^{26} -1.00000 q^{27} -6.09131 q^{29} +0.234751 q^{30} +5.30532 q^{31} -2.17946 q^{32} -1.00000 q^{33} +1.04244 q^{34} -1.96545 q^{36} -3.73070 q^{37} +1.07057 q^{38} -6.93089 q^{39} +0.930893 q^{40} +11.4300 q^{41} -4.27866 q^{43} -1.96545 q^{44} +1.26288 q^{45} -0.768404 q^{46} +13.1938 q^{47} -3.79387 q^{48} +0.632964 q^{50} +5.60799 q^{51} -13.6223 q^{52} -5.52310 q^{53} +0.185885 q^{54} +1.26288 q^{55} +5.75932 q^{57} +1.13229 q^{58} +7.86821 q^{59} +2.48213 q^{60} +3.77690 q^{61} -0.986182 q^{62} -7.18262 q^{64} +8.75290 q^{65} +0.185885 q^{66} +16.1182 q^{67} +11.0222 q^{68} -4.13375 q^{69} +4.17353 q^{71} +0.737118 q^{72} +5.40040 q^{73} +0.693482 q^{74} +3.40513 q^{75} +11.3196 q^{76} +1.28835 q^{78} +9.55912 q^{79} +4.79121 q^{80} +1.00000 q^{81} -2.12467 q^{82} -6.73908 q^{83} -7.08223 q^{85} +0.795340 q^{86} +6.09131 q^{87} +0.737118 q^{88} -6.14867 q^{89} -0.234751 q^{90} -8.12467 q^{92} -5.30532 q^{93} -2.45253 q^{94} -7.27334 q^{95} +2.17946 q^{96} +15.3249 q^{97} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 4 q^{3} + 2 q^{4} + 8 q^{5} + 2 q^{6} + 4 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - 4 * q^3 + 2 * q^4 + 8 * q^5 + 2 * q^6 + 4 * q^9	\( 4 q - 2 q^{2} - 4 q^{3} + 2 q^{4} + 8 q^{5} + 2 q^{6} + 4 q^{9} - 2 q^{10} + 4 q^{11} - 2 q^{12} + 8 q^{13} - 8 q^{15} - 6 q^{16} - 2 q^{18} + 8 q^{19} + 14 q^{20} - 2 q^{22} + 12 q^{25} + 2 q^{26} - 4 q^{27} - 16 q^{29} + 2 q^{30} + 16 q^{31} - 2 q^{32} - 4 q^{33} - 4 q^{34} + 2 q^{36} - 4 q^{37} - 2 q^{38} - 8 q^{39} - 16 q^{40} + 4 q^{41} + 16 q^{43} + 2 q^{44} + 8 q^{45} + 8 q^{46} + 36 q^{47} + 6 q^{48} - 8 q^{50} - 22 q^{52} - 16 q^{53} + 2 q^{54} + 8 q^{55} - 8 q^{57} + 14 q^{58} - 14 q^{60} - 8 q^{61} + 8 q^{62} - 12 q^{64} - 4 q^{65} + 2 q^{66} + 20 q^{67} + 16 q^{68} - 20 q^{71} + 4 q^{73} - 30 q^{74} - 12 q^{75} + 30 q^{76} - 2 q^{78} + 16 q^{79} - 14 q^{80} + 4 q^{81} + 28 q^{82} + 24 q^{83} - 44 q^{86} + 16 q^{87} - 4 q^{89} - 2 q^{90} + 4 q^{92} - 16 q^{93} - 10 q^{94} + 28 q^{95} + 2 q^{96} + 16 q^{97} + 4 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 4 * q^3 + 2 * q^4 + 8 * q^5 + 2 * q^6 + 4 * q^9 - 2 * q^10 + 4 * q^11 - 2 * q^12 + 8 * q^13 - 8 * q^15 - 6 * q^16 - 2 * q^18 + 8 * q^19 + 14 * q^20 - 2 * q^22 + 12 * q^25 + 2 * q^26 - 4 * q^27 - 16 * q^29 + 2 * q^30 + 16 * q^31 - 2 * q^32 - 4 * q^33 - 4 * q^34 + 2 * q^36 - 4 * q^37 - 2 * q^38 - 8 * q^39 - 16 * q^40 + 4 * q^41 + 16 * q^43 + 2 * q^44 + 8 * q^45 + 8 * q^46 + 36 * q^47 + 6 * q^48 - 8 * q^50 - 22 * q^52 - 16 * q^53 + 2 * q^54 + 8 * q^55 - 8 * q^57 + 14 * q^58 - 14 * q^60 - 8 * q^61 + 8 * q^62 - 12 * q^64 - 4 * q^65 + 2 * q^66 + 20 * q^67 + 16 * q^68 - 20 * q^71 + 4 * q^73 - 30 * q^74 - 12 * q^75 + 30 * q^76 - 2 * q^78 + 16 * q^79 - 14 * q^80 + 4 * q^81 + 28 * q^82 + 24 * q^83 - 44 * q^86 + 16 * q^87 - 4 * q^89 - 2 * q^90 + 4 * q^92 - 16 * q^93 - 10 * q^94 + 28 * q^95 + 2 * q^96 + 16 * q^97 + 4 * q^99

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