LMFDB - Embedded newform 4018.2.a.u.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4018,2,Mod(1,4018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4018, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4018 = 2 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4018.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:	$32.0838915322$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{33}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 8 $ x^2 - x - 8
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 574)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-2.37228$ of defining polynomial
Character	$\chi$	$=$	4018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.37228 q^{3} +1.00000 q^{4} -2.37228 q^{5} -2.37228 q^{6} -1.00000 q^{8} +2.62772 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.37228 q^{3} +1.00000 q^{4} -2.37228 q^{5} -2.37228 q^{6} -1.00000 q^{8} +2.62772 q^{9} +2.37228 q^{10} -4.37228 q^{11} +2.37228 q^{12} +5.37228 q^{13} -5.62772 q^{15} +1.00000 q^{16} -6.74456 q^{17} -2.62772 q^{18} -0.372281 q^{19} -2.37228 q^{20} +4.37228 q^{22} +2.74456 q^{23} -2.37228 q^{24} +0.627719 q^{25} -5.37228 q^{26} -0.883156 q^{27} +10.1168 q^{29} +5.62772 q^{30} +8.74456 q^{31} -1.00000 q^{32} -10.3723 q^{33} +6.74456 q^{34} +2.62772 q^{36} -2.00000 q^{37} +0.372281 q^{38} +12.7446 q^{39} +2.37228 q^{40} +1.00000 q^{41} -0.627719 q^{43} -4.37228 q^{44} -6.23369 q^{45} -2.74456 q^{46} -8.00000 q^{47} +2.37228 q^{48} -0.627719 q^{50} -16.0000 q^{51} +5.37228 q^{52} -10.0000 q^{53} +0.883156 q^{54} +10.3723 q^{55} -0.883156 q^{57} -10.1168 q^{58} -5.37228 q^{59} -5.62772 q^{60} -8.37228 q^{61} -8.74456 q^{62} +1.00000 q^{64} -12.7446 q^{65} +10.3723 q^{66} -8.00000 q^{67} -6.74456 q^{68} +6.51087 q^{69} -0.255437 q^{71} -2.62772 q^{72} +4.11684 q^{73} +2.00000 q^{74} +1.48913 q^{75} -0.372281 q^{76} -12.7446 q^{78} -10.3723 q^{79} -2.37228 q^{80} -9.97825 q^{81} -1.00000 q^{82} -5.37228 q^{83} +16.0000 q^{85} +0.627719 q^{86} +24.0000 q^{87} +4.37228 q^{88} +2.00000 q^{89} +6.23369 q^{90} +2.74456 q^{92} +20.7446 q^{93} +8.00000 q^{94} +0.883156 q^{95} -2.37228 q^{96} -8.00000 q^{97} -11.4891 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - q^{3} + 2 q^{4} + q^{5} + q^{6} - 2 q^{8} + 11 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - q^3 + 2 * q^4 + q^5 + q^6 - 2 * q^8 + 11 * q^9	$ 2 q - 2 q^{2} - q^{3} + 2 q^{4} + q^{5} + q^{6} - 2 q^{8} + 11 q^{9} - q^{10} - 3 q^{11} - q^{12} + 5 q^{13} - 17 q^{15} + 2 q^{16} - 2 q^{17} - 11 q^{18} + 5 q^{19} + q^{20} + 3 q^{22} - 6 q^{23} + q^{24} + 7 q^{25} - 5 q^{26} - 19 q^{27} + 3 q^{29} + 17 q^{30} + 6 q^{31} - 2 q^{32} - 15 q^{33} + 2 q^{34} + 11 q^{36} - 4 q^{37} - 5 q^{38} + 14 q^{39} - q^{40} + 2 q^{41} - 7 q^{43} - 3 q^{44} + 22 q^{45} + 6 q^{46} - 16 q^{47} - q^{48} - 7 q^{50} - 32 q^{51} + 5 q^{52} - 20 q^{53} + 19 q^{54} + 15 q^{55} - 19 q^{57} - 3 q^{58} - 5 q^{59} - 17 q^{60} - 11 q^{61} - 6 q^{62} + 2 q^{64} - 14 q^{65} + 15 q^{66} - 16 q^{67} - 2 q^{68} + 36 q^{69} - 12 q^{71} - 11 q^{72} - 9 q^{73} + 4 q^{74} - 20 q^{75} + 5 q^{76} - 14 q^{78} - 15 q^{79} + q^{80} + 26 q^{81} - 2 q^{82} - 5 q^{83} + 32 q^{85} + 7 q^{86} + 48 q^{87} + 3 q^{88} + 4 q^{89} - 22 q^{90} - 6 q^{92} + 30 q^{93} + 16 q^{94} + 19 q^{95} + q^{96} - 16 q^{97}+O(q^{100}) $ 2 * q - 2 * q^2 - q^3 + 2 * q^4 + q^5 + q^6 - 2 * q^8 + 11 * q^9 - q^10 - 3 * q^11 - q^12 + 5 * q^13 - 17 * q^15 + 2 * q^16 - 2 * q^17 - 11 * q^18 + 5 * q^19 + q^20 + 3 * q^22 - 6 * q^23 + q^24 + 7 * q^25 - 5 * q^26 - 19 * q^27 + 3 * q^29 + 17 * q^30 + 6 * q^31 - 2 * q^32 - 15 * q^33 + 2 * q^34 + 11 * q^36 - 4 * q^37 - 5 * q^38 + 14 * q^39 - q^40 + 2 * q^41 - 7 * q^43 - 3 * q^44 + 22 * q^45 + 6 * q^46 - 16 * q^47 - q^48 - 7 * q^50 - 32 * q^51 + 5 * q^52 - 20 * q^53 + 19 * q^54 + 15 * q^55 - 19 * q^57 - 3 * q^58 - 5 * q^59 - 17 * q^60 - 11 * q^61 - 6 * q^62 + 2 * q^64 - 14 * q^65 + 15 * q^66 - 16 * q^67 - 2 * q^68 + 36 * q^69 - 12 * q^71 - 11 * q^72 - 9 * q^73 + 4 * q^74 - 20 * q^75 + 5 * q^76 - 14 * q^78 - 15 * q^79 + q^80 + 26 * q^81 - 2 * q^82 - 5 * q^83 + 32 * q^85 + 7 * q^86 + 48 * q^87 + 3 * q^88 + 4 * q^89 - 22 * q^90 - 6 * q^92 + 30 * q^93 + 16 * q^94 + 19 * q^95 + q^96 - 16 * q^97

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
$3$	2.37228	1.36964	0.684819	−	0.728714i	$-0.259881\pi$
$3$	2.37228	1.36964	0.684819	+	0.728714i	$0.259881\pi$
$4$	1.00000	0.500000
$5$	−2.37228	−1.06092	−0.530458	−	0.847711i	$-0.677980\pi$
$5$	−2.37228	−1.06092	−0.530458	+	0.847711i	$0.677980\pi$
$6$	−2.37228	−0.968480
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	2.62772	0.875906
$10$	2.37228	0.750181
$11$	−4.37228	−1.31829	−0.659146	−	0.752015i	$-0.729082\pi$
$11$	−4.37228	−1.31829	−0.659146	+	0.752015i	$0.729082\pi$
$12$	2.37228	0.684819
$13$	5.37228	1.49000	0.745001	−	0.667063i	$-0.232449\pi$
$13$	5.37228	1.49000	0.745001	+	0.667063i	$0.232449\pi$
$14$	0	0
$15$	−5.62772	−1.45307
$16$	1.00000	0.250000
$17$	−6.74456	−1.63580	−0.817898	−	0.575363i	$-0.804861\pi$
$17$	−6.74456	−1.63580	−0.817898	+	0.575363i	$0.804861\pi$
$18$	−2.62772	−0.619359
$19$	−0.372281	−0.0854072	−0.0427036	−	0.999088i	$-0.513597\pi$
$19$	−0.372281	−0.0854072	−0.0427036	+	0.999088i	$0.513597\pi$
$20$	−2.37228	−0.530458
$21$	0	0
$22$	4.37228	0.932174
$23$	2.74456	0.572281	0.286140	−	0.958188i	$-0.407628\pi$
$23$	2.74456	0.572281	0.286140	+	0.958188i	$0.407628\pi$
$24$	−2.37228	−0.484240
$25$	0.627719	0.125544
$26$	−5.37228	−1.05359
$27$	−0.883156	−0.169963
$28$	0	0
$29$	10.1168	1.87865	0.939325	−	0.343027i	$-0.111452\pi$
$29$	10.1168	1.87865	0.939325	+	0.343027i	$0.111452\pi$
$30$	5.62772	1.02748
$31$	8.74456	1.57057	0.785285	−	0.619135i	$-0.212516\pi$
$31$	8.74456	1.57057	0.785285	+	0.619135i	$0.212516\pi$
$32$	−1.00000	−0.176777
$33$	−10.3723	−1.80558
$34$	6.74456	1.15668
$35$	0	0
$36$	2.62772	0.437953
$37$	−2.00000	−0.328798	−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000	−0.328798	−0.164399	+	0.986394i	$0.552568\pi$
$38$	0.372281	0.0603920
$39$	12.7446	2.04076
$40$	2.37228	0.375091
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	−0.627719	−0.0957262	−0.0478631	−	0.998854i	$-0.515241\pi$
$43$	−0.627719	−0.0957262	−0.0478631	+	0.998854i	$0.515241\pi$
$44$	−4.37228	−0.659146
$45$	−6.23369	−0.929263
$46$	−2.74456	−0.404664
$47$	−8.00000	−1.16692	−0.583460	−	0.812142i	$-0.698301\pi$
$47$	−8.00000	−1.16692	−0.583460	+	0.812142i	$0.698301\pi$
$48$	2.37228	0.342409
$49$	0	0
$50$	−0.627719	−0.0887728
$51$	−16.0000	−2.24045
$52$	5.37228	0.745001
$53$	−10.0000	−1.37361	−0.686803	−	0.726844i	$-0.740986\pi$
$53$	−10.0000	−1.37361	−0.686803	+	0.726844i	$0.740986\pi$
$54$	0.883156	0.120182
$55$	10.3723	1.39860
$56$	0	0
$57$	−0.883156	−0.116977
$58$	−10.1168	−1.32841
$59$	−5.37228	−0.699411	−0.349706	−	0.936860i	$-0.613718\pi$
$59$	−5.37228	−0.699411	−0.349706	+	0.936860i	$0.613718\pi$
$60$	−5.62772	−0.726535
$61$	−8.37228	−1.07196	−0.535980	−	0.844230i	$-0.680058\pi$
$61$	−8.37228	−1.07196	−0.535980	+	0.844230i	$0.680058\pi$
$62$	−8.74456	−1.11056
$63$	0	0
$64$	1.00000	0.125000
$65$	−12.7446	−1.58077
$66$	10.3723	1.27674
$67$	−8.00000	−0.977356	−0.488678	−	0.872464i	$-0.662521\pi$
$67$	−8.00000	−0.977356	−0.488678	+	0.872464i	$0.662521\pi$
$68$	−6.74456	−0.817898
$69$	6.51087	0.783817
$70$	0	0
$71$	−0.255437	−0.0303148	−0.0151574	−	0.999885i	$-0.504825\pi$
$71$	−0.255437	−0.0303148	−0.0151574	+	0.999885i	$0.504825\pi$
$72$	−2.62772	−0.309680
$73$	4.11684	0.481840	0.240920	−	0.970545i	$-0.422551\pi$
$73$	4.11684	0.481840	0.240920	+	0.970545i	$0.422551\pi$
$74$	2.00000	0.232495
$75$	1.48913	0.171949
$76$	−0.372281	−0.0427036
$77$	0	0
$78$	−12.7446	−1.44304
$79$	−10.3723	−1.16697	−0.583486	−	0.812123i	$-0.698312\pi$
$79$	−10.3723	−1.16697	−0.583486	+	0.812123i	$0.698312\pi$
$80$	−2.37228	−0.265229
$81$	−9.97825	−1.10869
$82$	−1.00000	−0.110432
$83$	−5.37228	−0.589684	−0.294842	−	0.955546i	$-0.595267\pi$
$83$	−5.37228	−0.589684	−0.294842	+	0.955546i	$0.595267\pi$
$84$	0	0
$85$	16.0000	1.73544
$86$	0.627719	0.0676886
$87$	24.0000	2.57307
$88$	4.37228	0.466087
$89$	2.00000	0.212000	0.106000	−	0.994366i	$-0.466196\pi$
$89$	2.00000	0.212000	0.106000	+	0.994366i	$0.466196\pi$
$90$	6.23369	0.657088
$91$	0	0
$92$	2.74456	0.286140
$93$	20.7446	2.15111
$94$	8.00000	0.825137
$95$	0.883156	0.0906099
$96$	−2.37228	−0.242120
$97$	−8.00000	−0.812277	−0.406138	−	0.913812i	$-0.633125\pi$
$97$	−8.00000	−0.812277	−0.406138	+	0.913812i	$0.633125\pi$
$98$	0	0
$99$	−11.4891	−1.15470
$100$	0.627719	0.0627719
$101$	−14.7446	−1.46714	−0.733569	−	0.679615i	$-0.762147\pi$
$101$	−14.7446	−1.46714	−0.733569	+	0.679615i	$0.762147\pi$
$102$	16.0000	1.58424
$103$	−0.744563	−0.0733639	−0.0366820	−	0.999327i	$-0.511679\pi$
$103$	−0.744563	−0.0733639	−0.0366820	+	0.999327i	$0.511679\pi$
$104$	−5.37228	−0.526796
$105$	0	0
$106$	10.0000	0.971286
$107$	−16.1168	−1.55807	−0.779037	−	0.626978i	$-0.784292\pi$
$107$	−16.1168	−1.55807	−0.779037	+	0.626978i	$0.784292\pi$
$108$	−0.883156	−0.0849817
$109$	11.3723	1.08927	0.544633	−	0.838674i	$-0.316669\pi$
$109$	11.3723	1.08927	0.544633	+	0.838674i	$0.316669\pi$
$110$	−10.3723	−0.988958
$111$	−4.74456	−0.450334
$112$	0	0
$113$	−16.4891	−1.55117	−0.775583	−	0.631245i	$-0.782544\pi$
$113$	−16.4891	−1.55117	−0.775583	+	0.631245i	$0.782544\pi$
$114$	0.883156	0.0827151
$115$	−6.51087	−0.607142
$116$	10.1168	0.939325
$117$	14.1168	1.30510
$118$	5.37228	0.494559
$119$	0	0
$120$	5.62772	0.513738
$121$	8.11684	0.737895
$122$	8.37228	0.757991
$123$	2.37228	0.213901
$124$	8.74456	0.785285
$125$	10.3723	0.927725
$126$	0	0
$127$	−6.00000	−0.532414	−0.266207	−	0.963916i	$-0.585770\pi$
$127$	−6.00000	−0.532414	−0.266207	+	0.963916i	$0.585770\pi$
$128$	−1.00000	−0.0883883
$129$	−1.48913	−0.131110
$130$	12.7446	1.11777
$131$	12.0000	1.04844	0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000	1.04844	0.524222	+	0.851581i	$0.324356\pi$
$132$	−10.3723	−0.902791
$133$	0	0
$134$	8.00000	0.691095
$135$	2.09509	0.180317
$136$	6.74456	0.578341
$137$	−8.74456	−0.747098	−0.373549	−	0.927610i	$-0.621859\pi$
$137$	−8.74456	−0.747098	−0.373549	+	0.927610i	$0.621859\pi$
$138$	−6.51087	−0.554242
$139$	−16.7446	−1.42026	−0.710128	−	0.704073i	$-0.751363\pi$
$139$	−16.7446	−1.42026	−0.710128	+	0.704073i	$0.751363\pi$
$140$	0	0
$141$	−18.9783	−1.59826
$142$	0.255437	0.0214358
$143$	−23.4891	−1.96426
$144$	2.62772	0.218977
$145$	−24.0000	−1.99309
$146$	−4.11684	−0.340712
$147$	0	0
$148$	−2.00000	−0.164399
$149$	20.1168	1.64804	0.824018	−	0.566564i	$-0.191727\pi$
$149$	20.1168	1.64804	0.824018	+	0.566564i	$0.191727\pi$
$150$	−1.48913	−0.121587
$151$	−18.1168	−1.47433	−0.737164	−	0.675714i	$-0.763835\pi$
$151$	−18.1168	−1.47433	−0.737164	+	0.675714i	$0.763835\pi$
$152$	0.372281	0.0301960
$153$	−17.7228	−1.43280
$154$	0	0
$155$	−20.7446	−1.66624
$156$	12.7446	1.02038
$157$	−12.8614	−1.02645	−0.513226	−	0.858254i	$-0.671550\pi$
$157$	−12.8614	−1.02645	−0.513226	+	0.858254i	$0.671550\pi$
$158$	10.3723	0.825174
$159$	−23.7228	−1.88134
$160$	2.37228	0.187545
$161$	0	0
$162$	9.97825	0.783965
$163$	−4.11684	−0.322456	−0.161228	−	0.986917i	$-0.551545\pi$
$163$	−4.11684	−0.322456	−0.161228	+	0.986917i	$0.551545\pi$
$164$	1.00000	0.0780869
$165$	24.6060	1.91557
$166$	5.37228	0.416970
$167$	19.3723	1.49907	0.749536	−	0.661964i	$-0.230277\pi$
$167$	19.3723	1.49907	0.749536	+	0.661964i	$0.230277\pi$
$168$	0	0
$169$	15.8614	1.22011
$170$	−16.0000	−1.22714
$171$	−0.978251	−0.0748087
$172$	−0.627719	−0.0478631
$173$	−7.11684	−0.541084	−0.270542	−	0.962708i	$-0.587203\pi$
$173$	−7.11684	−0.541084	−0.270542	+	0.962708i	$0.587203\pi$
$174$	−24.0000	−1.81944
$175$	0	0
$176$	−4.37228	−0.329573
$177$	−12.7446	−0.957940
$178$	−2.00000	−0.149906
$179$	7.62772	0.570122	0.285061	−	0.958509i	$-0.407986\pi$
$179$	7.62772	0.570122	0.285061	+	0.958509i	$0.407986\pi$
$180$	−6.23369	−0.464632
$181$	−0.510875	−0.0379730	−0.0189865	−	0.999820i	$-0.506044\pi$
$181$	−0.510875	−0.0379730	−0.0189865	+	0.999820i	$0.506044\pi$
$182$	0	0
$183$	−19.8614	−1.46820
$184$	−2.74456	−0.202332
$185$	4.74456	0.348827
$186$	−20.7446	−1.52107
$187$	29.4891	2.15646
$188$	−8.00000	−0.583460
$189$	0	0
$190$	−0.883156	−0.0640709
$191$	−19.3723	−1.40173	−0.700865	−	0.713294i	$-0.747202\pi$
$191$	−19.3723	−1.40173	−0.700865	+	0.713294i	$0.747202\pi$
$192$	2.37228	0.171205
$193$	12.7446	0.917374	0.458687	−	0.888598i	$-0.348320\pi$
$193$	12.7446	0.917374	0.458687	+	0.888598i	$0.348320\pi$
$194$	8.00000	0.574367
$195$	−30.2337	−2.16508
$196$	0	0
$197$	1.62772	0.115970	0.0579851	−	0.998317i	$-0.481532\pi$
$197$	1.62772	0.115970	0.0579851	+	0.998317i	$0.481532\pi$
$198$	11.4891	0.816497
$199$	3.37228	0.239055	0.119527	−	0.992831i	$-0.461862\pi$
$199$	3.37228	0.239055	0.119527	+	0.992831i	$0.461862\pi$
$200$	−0.627719	−0.0443864
$201$	−18.9783	−1.33862
$202$	14.7446	1.03742
$203$	0	0
$204$	−16.0000	−1.12022
$205$	−2.37228	−0.165687
$206$	0.744563	0.0518761
$207$	7.21194	0.501264
$208$	5.37228	0.372501
$209$	1.62772	0.112592
$210$	0	0
$211$	9.11684	0.627629	0.313815	−	0.949484i	$-0.398393\pi$
$211$	9.11684	0.627629	0.313815	+	0.949484i	$0.398393\pi$
$212$	−10.0000	−0.686803
$213$	−0.605969	−0.0415203
$214$	16.1168	1.10172
$215$	1.48913	0.101558
$216$	0.883156	0.0600912
$217$	0	0
$218$	−11.3723	−0.770228
$219$	9.76631	0.659946
$220$	10.3723	0.699299
$221$	−36.2337	−2.43734
$222$	4.74456	0.318434
$223$	−14.7446	−0.987369	−0.493684	−	0.869641i	$-0.664350\pi$
$223$	−14.7446	−0.987369	−0.493684	+	0.869641i	$0.664350\pi$
$224$	0	0
$225$	1.64947	0.109965
$226$	16.4891	1.09684
$227$	−5.62772	−0.373525	−0.186762	−	0.982405i	$-0.559799\pi$
$227$	−5.62772	−0.373525	−0.186762	+	0.982405i	$0.559799\pi$
$228$	−0.883156	−0.0584884
$229$	11.3723	0.751502	0.375751	−	0.926721i	$-0.377385\pi$
$229$	11.3723	0.751502	0.375751	+	0.926721i	$0.377385\pi$
$230$	6.51087	0.429314
$231$	0	0
$232$	−10.1168	−0.664203
$233$	−0.510875	−0.0334685	−0.0167343	−	0.999860i	$-0.505327\pi$
$233$	−0.510875	−0.0334685	−0.0167343	+	0.999860i	$0.505327\pi$
$234$	−14.1168	−0.922847
$235$	18.9783	1.23800
$236$	−5.37228	−0.349706
$237$	−24.6060	−1.59833
$238$	0	0
$239$	−13.6277	−0.881504	−0.440752	−	0.897629i	$-0.645288\pi$
$239$	−13.6277	−0.881504	−0.440752	+	0.897629i	$0.645288\pi$
$240$	−5.62772	−0.363268
$241$	24.1168	1.55350	0.776751	−	0.629808i	$-0.216866\pi$
$241$	24.1168	1.55350	0.776751	+	0.629808i	$0.216866\pi$
$242$	−8.11684	−0.521770
$243$	−21.0217	−1.34855
$244$	−8.37228	−0.535980
$245$	0	0
$246$	−2.37228	−0.151251
$247$	−2.00000	−0.127257
$248$	−8.74456	−0.555280
$249$	−12.7446	−0.807654
$250$	−10.3723	−0.656001
$251$	14.8614	0.938044	0.469022	−	0.883187i	$-0.344607\pi$
$251$	14.8614	0.938044	0.469022	+	0.883187i	$0.344607\pi$
$252$	0	0
$253$	−12.0000	−0.754434
$254$	6.00000	0.376473
$255$	37.9565	2.37693
$256$	1.00000	0.0625000
$257$	0	0		−	1.00000i	$-0.5\pi$
$257$	0	0			1.00000i	$0.5\pi$
$258$	1.48913	0.0927089
$259$	0	0
$260$	−12.7446	−0.790384
$261$	26.5842	1.64552
$262$	−12.0000	−0.741362
$263$	−19.3723	−1.19455	−0.597273	−	0.802038i	$-0.703749\pi$
$263$	−19.3723	−1.19455	−0.597273	+	0.802038i	$0.703749\pi$
$264$	10.3723	0.638370
$265$	23.7228	1.45728
$266$	0	0
$267$	4.74456	0.290363
$268$	−8.00000	−0.488678
$269$	23.3505	1.42371	0.711854	−	0.702328i	$-0.247856\pi$
$269$	23.3505	1.42371	0.711854	+	0.702328i	$0.247856\pi$
$270$	−2.09509	−0.127503
$271$	17.2554	1.04819	0.524097	−	0.851659i	$-0.324403\pi$
$271$	17.2554	1.04819	0.524097	+	0.851659i	$0.324403\pi$
$272$	−6.74456	−0.408949
$273$	0	0
$274$	8.74456	0.528278
$275$	−2.74456	−0.165503
$276$	6.51087	0.391909
$277$	−22.6060	−1.35826	−0.679131	−	0.734018i	$-0.737643\pi$
$277$	−22.6060	−1.35826	−0.679131	+	0.734018i	$0.737643\pi$
$278$	16.7446	1.00427
$279$	22.9783	1.37567
$280$	0	0
$281$	−18.7446	−1.11821	−0.559103	−	0.829098i	$-0.688855\pi$
$281$	−18.7446	−1.11821	−0.559103	+	0.829098i	$0.688855\pi$
$282$	18.9783	1.13014
$283$	25.3723	1.50823	0.754113	−	0.656745i	$-0.228067\pi$
$283$	25.3723	1.50823	0.754113	+	0.656745i	$0.228067\pi$
$284$	−0.255437	−0.0151574
$285$	2.09509	0.124103
$286$	23.4891	1.38894
$287$	0	0
$288$	−2.62772	−0.154840
$289$	28.4891	1.67583
$290$	24.0000	1.40933
$291$	−18.9783	−1.11252
$292$	4.11684	0.240920
$293$	7.37228	0.430693	0.215347	−	0.976538i	$-0.430912\pi$
$293$	7.37228	0.430693	0.215347	+	0.976538i	$0.430912\pi$
$294$	0	0
$295$	12.7446	0.742017
$296$	2.00000	0.116248
$297$	3.86141	0.224062
$298$	−20.1168	−1.16534
$299$	14.7446	0.852700
$300$	1.48913	0.0859747
$301$	0	0
$302$	18.1168	1.04251
$303$	−34.9783	−2.00945
$304$	−0.372281	−0.0213518
$305$	19.8614	1.13726
$306$	17.7228	1.01315
$307$	4.86141	0.277455	0.138728	−	0.990331i	$-0.455699\pi$
$307$	4.86141	0.277455	0.138728	+	0.990331i	$0.455699\pi$
$308$	0	0
$309$	−1.76631	−0.100482
$310$	20.7446	1.17821
$311$	−4.62772	−0.262414	−0.131207	−	0.991355i	$-0.541885\pi$
$311$	−4.62772	−0.262414	−0.131207	+	0.991355i	$0.541885\pi$
$312$	−12.7446	−0.721519
$313$	0	0		−	1.00000i	$-0.5\pi$
$313$	0	0			1.00000i	$0.5\pi$
$314$	12.8614	0.725811
$315$	0	0
$316$	−10.3723	−0.583486
$317$	−13.2554	−0.744500	−0.372250	−	0.928133i	$-0.621414\pi$
$317$	−13.2554	−0.744500	−0.372250	+	0.928133i	$0.621414\pi$
$318$	23.7228	1.33031
$319$	−44.2337	−2.47661
$320$	−2.37228	−0.132615
$321$	−38.2337	−2.13400
$322$	0	0
$323$	2.51087	0.139709
$324$	−9.97825	−0.554347
$325$	3.37228	0.187061
$326$	4.11684	0.228011
$327$	26.9783	1.49190
$328$	−1.00000	−0.0552158
$329$	0	0
$330$	−24.6060	−1.35451
$331$	10.7446	0.590575	0.295287	−	0.955409i	$-0.404585\pi$
$331$	10.7446	0.590575	0.295287	+	0.955409i	$0.404585\pi$
$332$	−5.37228	−0.294842
$333$	−5.25544	−0.287996
$334$	−19.3723	−1.06000
$335$	18.9783	1.03689
$336$	0	0
$337$	−5.00000	−0.272367	−0.136184	−	0.990684i	$-0.543484\pi$
$337$	−5.00000	−0.272367	−0.136184	+	0.990684i	$0.543484\pi$
$338$	−15.8614	−0.862747
$339$	−39.1168	−2.12454
$340$	16.0000	0.867722
$341$	−38.2337	−2.07047
$342$	0.978251	0.0528977
$343$	0	0
$344$	0.627719	0.0338443
$345$	−15.4456	−0.831565
$346$	7.11684	0.382604
$347$	24.6060	1.32092	0.660459	−	0.750862i	$-0.270362\pi$
$347$	24.6060	1.32092	0.660459	+	0.750862i	$0.270362\pi$
$348$	24.0000	1.28654
$349$	−11.2554	−0.602490	−0.301245	−	0.953547i	$-0.597402\pi$
$349$	−11.2554	−0.602490	−0.301245	+	0.953547i	$0.597402\pi$
$350$	0	0
$351$	−4.74456	−0.253246
$352$	4.37228	0.233043
$353$	35.0000	1.86286	0.931431	−	0.363918i	$-0.118561\pi$
$353$	35.0000	1.86286	0.931431	+	0.363918i	$0.118561\pi$
$354$	12.7446	0.677366
$355$	0.605969	0.0321615
$356$	2.00000	0.106000
$357$	0	0
$358$	−7.62772	−0.403137
$359$	12.5109	0.660299	0.330149	−	0.943929i	$-0.392901\pi$
$359$	12.5109	0.660299	0.330149	+	0.943929i	$0.392901\pi$
$360$	6.23369	0.328544
$361$	−18.8614	−0.992706
$362$	0.510875	0.0268510
$363$	19.2554	1.01065
$364$	0	0
$365$	−9.76631	−0.511192
$366$	19.8614	1.03817
$367$	10.0000	0.521996	0.260998	−	0.965339i	$-0.415948\pi$
$367$	10.0000	0.521996	0.260998	+	0.965339i	$0.415948\pi$
$368$	2.74456	0.143070
$369$	2.62772	0.136794
$370$	−4.74456	−0.246658
$371$	0	0
$372$	20.7446	1.07556
$373$	−20.3723	−1.05484	−0.527418	−	0.849606i	$-0.676840\pi$
$373$	−20.3723	−1.05484	−0.527418	+	0.849606i	$0.676840\pi$
$374$	−29.4891	−1.52485
$375$	24.6060	1.27065
$376$	8.00000	0.412568
$377$	54.3505	2.79919
$378$	0	0
$379$	5.13859	0.263952	0.131976	−	0.991253i	$-0.457868\pi$
$379$	5.13859	0.263952	0.131976	+	0.991253i	$0.457868\pi$
$380$	0.883156	0.0453049
$381$	−14.2337	−0.729214
$382$	19.3723	0.991172
$383$	33.4674	1.71010	0.855052	−	0.518543i	$-0.173525\pi$
$383$	33.4674	1.71010	0.855052	+	0.518543i	$0.173525\pi$
$384$	−2.37228	−0.121060
$385$	0	0
$386$	−12.7446	−0.648681
$387$	−1.64947	−0.0838472
$388$	−8.00000	−0.406138
$389$	15.1168	0.766454	0.383227	−	0.923654i	$-0.374813\pi$
$389$	15.1168	0.766454	0.383227	+	0.923654i	$0.374813\pi$
$390$	30.2337	1.53094
$391$	−18.5109	−0.936135
$392$	0	0
$393$	28.4674	1.43599
$394$	−1.62772	−0.0820033
$395$	24.6060	1.23806
$396$	−11.4891	−0.577350
$397$	14.0000	0.702640	0.351320	−	0.936255i	$-0.385733\pi$
$397$	14.0000	0.702640	0.351320	+	0.936255i	$0.385733\pi$
$398$	−3.37228	−0.169037
$399$	0	0
$400$	0.627719	0.0313859
$401$	−2.25544	−0.112631	−0.0563156	−	0.998413i	$-0.517935\pi$
$401$	−2.25544	−0.112631	−0.0563156	+	0.998413i	$0.517935\pi$
$402$	18.9783	0.946549
$403$	46.9783	2.34015
$404$	−14.7446	−0.733569
$405$	23.6712	1.17623
$406$	0	0
$407$	8.74456	0.433452
$408$	16.0000	0.792118
$409$	4.25544	0.210418	0.105209	−	0.994450i	$-0.466449\pi$
$409$	4.25544	0.210418	0.105209	+	0.994450i	$0.466449\pi$
$410$	2.37228	0.117159
$411$	−20.7446	−1.02325
$412$	−0.744563	−0.0366820
$413$	0	0
$414$	−7.21194	−0.354447
$415$	12.7446	0.625606
$416$	−5.37228	−0.263398
$417$	−39.7228	−1.94523
$418$	−1.62772	−0.0796143
$419$	−28.8614	−1.40997	−0.704986	−	0.709221i	$-0.749047\pi$
$419$	−28.8614	−1.40997	−0.704986	+	0.709221i	$0.749047\pi$
$420$	0	0
$421$	2.00000	0.0974740	0.0487370	−	0.998812i	$-0.484480\pi$
$421$	2.00000	0.0974740	0.0487370	+	0.998812i	$0.484480\pi$
$422$	−9.11684	−0.443801
$423$	−21.0217	−1.02211
$424$	10.0000	0.485643
$425$	−4.23369	−0.205364
$426$	0.605969	0.0293593
$427$	0	0
$428$	−16.1168	−0.779037
$429$	−55.7228	−2.69032
$430$	−1.48913	−0.0718120
$431$	13.4891	0.649748	0.324874	−	0.945757i	$-0.394678\pi$
$431$	13.4891	0.649748	0.324874	+	0.945757i	$0.394678\pi$
$432$	−0.883156	−0.0424909
$433$	16.3723	0.786802	0.393401	−	0.919367i	$-0.371298\pi$
$433$	16.3723	0.786802	0.393401	+	0.919367i	$0.371298\pi$
$434$	0	0
$435$	−56.9348	−2.72981
$436$	11.3723	0.544633
$437$	−1.02175	−0.0488769
$438$	−9.76631	−0.466652
$439$	−7.74456	−0.369628	−0.184814	−	0.982774i	$-0.559168\pi$
$439$	−7.74456	−0.369628	−0.184814	+	0.982774i	$0.559168\pi$
$440$	−10.3723	−0.494479
$441$	0	0
$442$	36.2337	1.72346
$443$	−18.3505	−0.871860	−0.435930	−	0.899981i	$-0.643580\pi$
$443$	−18.3505	−0.871860	−0.435930	+	0.899981i	$0.643580\pi$
$444$	−4.74456	−0.225167
$445$	−4.74456	−0.224914
$446$	14.7446	0.698175
$447$	47.7228	2.25721
$448$	0	0
$449$	−11.2337	−0.530151	−0.265075	−	0.964228i	$-0.585397\pi$
$449$	−11.2337	−0.530151	−0.265075	+	0.964228i	$0.585397\pi$
$450$	−1.64947	−0.0777567
$451$	−4.37228	−0.205883
$452$	−16.4891	−0.775583
$453$	−42.9783	−2.01929
$454$	5.62772	0.264122
$455$	0	0
$456$	0.883156	0.0413576
$457$	−8.23369	−0.385156	−0.192578	−	0.981282i	$-0.561685\pi$
$457$	−8.23369	−0.385156	−0.192578	+	0.981282i	$0.561685\pi$
$458$	−11.3723	−0.531392
$459$	5.95650	0.278026
$460$	−6.51087	−0.303571
$461$	−36.6060	−1.70491	−0.852455	−	0.522801i	$-0.824887\pi$
$461$	−36.6060	−1.70491	−0.852455	+	0.522801i	$0.824887\pi$
$462$	0	0
$463$	6.25544	0.290715	0.145357	−	0.989379i	$-0.453567\pi$
$463$	6.25544	0.290715	0.145357	+	0.989379i	$0.453567\pi$
$464$	10.1168	0.469663
$465$	−49.2119	−2.28215
$466$	0.510875	0.0236658
$467$	33.4891	1.54969	0.774846	−	0.632150i	$-0.217827\pi$
$467$	33.4891	1.54969	0.774846	+	0.632150i	$0.217827\pi$
$468$	14.1168	0.652551
$469$	0	0
$470$	−18.9783	−0.875401
$471$	−30.5109	−1.40587
$472$	5.37228	0.247279
$473$	2.74456	0.126195
$474$	24.6060	1.13019
$475$	−0.233688	−0.0107223
$476$	0	0
$477$	−26.2772	−1.20315
$478$	13.6277	0.623317
$479$	−1.51087	−0.0690336	−0.0345168	−	0.999404i	$-0.510989\pi$
$479$	−1.51087	−0.0690336	−0.0345168	+	0.999404i	$0.510989\pi$
$480$	5.62772	0.256869
$481$	−10.7446	−0.489910
$482$	−24.1168	−1.09849
$483$	0	0
$484$	8.11684	0.368947
$485$	18.9783	0.861758
$486$	21.0217	0.953566
$487$	−24.7446	−1.12128	−0.560642	−	0.828059i	$-0.689445\pi$
$487$	−24.7446	−1.12128	−0.560642	+	0.828059i	$0.689445\pi$
$488$	8.37228	0.378995
$489$	−9.76631	−0.441648
$490$	0	0
$491$	0.116844	0.00527309	0.00263655	−	0.999997i	$-0.499161\pi$
$491$	0.116844	0.00527309	0.00263655	+	0.999997i	$0.499161\pi$
$492$	2.37228	0.106951
$493$	−68.2337	−3.07309
$494$	2.00000	0.0899843
$495$	27.2554	1.22504
$496$	8.74456	0.392642
$497$	0	0
$498$	12.7446	0.571098
$499$	6.74456	0.301928	0.150964	−	0.988539i	$-0.451762\pi$
$499$	6.74456	0.301928	0.150964	+	0.988539i	$0.451762\pi$
$500$	10.3723	0.463863
$501$	45.9565	2.05319
$502$	−14.8614	−0.663297
$503$	29.6277	1.32103	0.660517	−	0.750811i	$-0.270337\pi$
$503$	29.6277	1.32103	0.660517	+	0.750811i	$0.270337\pi$
$504$	0	0
$505$	34.9783	1.55651
$506$	12.0000	0.533465
$507$	37.6277	1.67111
$508$	−6.00000	−0.266207
$509$	−33.0951	−1.46691	−0.733457	−	0.679736i	$-0.762094\pi$
$509$	−33.0951	−1.46691	−0.733457	+	0.679736i	$0.762094\pi$
$510$	−37.9565	−1.68074
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	0.328782	0.0145161
$514$	0	0
$515$	1.76631	0.0778330
$516$	−1.48913	−0.0655551
$517$	34.9783	1.53834
$518$	0	0
$519$	−16.8832	−0.741088
$520$	12.7446	0.558886
$521$	12.7446	0.558349	0.279175	−	0.960240i	$-0.409939\pi$
$521$	12.7446	0.558349	0.279175	+	0.960240i	$0.409939\pi$
$522$	−26.5842	−1.16356
$523$	−40.4674	−1.76951	−0.884757	−	0.466052i	$-0.845676\pi$
$523$	−40.4674	−1.76951	−0.884757	+	0.466052i	$0.845676\pi$
$524$	12.0000	0.524222
$525$	0	0
$526$	19.3723	0.844672
$527$	−58.9783	−2.56913
$528$	−10.3723	−0.451396
$529$	−15.4674	−0.672495
$530$	−23.7228	−1.03045
$531$	−14.1168	−0.612619
$532$	0	0
$533$	5.37228	0.232699
$534$	−4.74456	−0.205317
$535$	38.2337	1.65299
$536$	8.00000	0.345547
$537$	18.0951	0.780861
$538$	−23.3505	−1.00671
$539$	0	0
$540$	2.09509	0.0901585
$541$	−16.9783	−0.729952	−0.364976	−	0.931017i	$-0.618923\pi$
$541$	−16.9783	−0.729952	−0.364976	+	0.931017i	$0.618923\pi$
$542$	−17.2554	−0.741184
$543$	−1.21194	−0.0520093
$544$	6.74456	0.289171
$545$	−26.9783	−1.15562
$546$	0	0
$547$	−17.4891	−0.747781	−0.373890	−	0.927473i	$-0.621976\pi$
$547$	−17.4891	−0.747781	−0.373890	+	0.927473i	$0.621976\pi$
$548$	−8.74456	−0.373549
$549$	−22.0000	−0.938937
$550$	2.74456	0.117029
$551$	−3.76631	−0.160450
$552$	−6.51087	−0.277121
$553$	0	0
$554$	22.6060	0.960436
$555$	11.2554	0.477767
$556$	−16.7446	−0.710128
$557$	16.3505	0.692794	0.346397	−	0.938088i	$-0.387405\pi$
$557$	16.3505	0.692794	0.346397	+	0.938088i	$0.387405\pi$
$558$	−22.9783	−0.972747
$559$	−3.37228	−0.142632
$560$	0	0
$561$	69.9565	2.95357
$562$	18.7446	0.790692
$563$	11.6277	0.490050	0.245025	−	0.969517i	$-0.421204\pi$
$563$	11.6277	0.490050	0.245025	+	0.969517i	$0.421204\pi$
$564$	−18.9783	−0.799129
$565$	39.1168	1.64566
$566$	−25.3723	−1.06648
$567$	0	0
$568$	0.255437	0.0107179
$569$	−29.8397	−1.25094	−0.625472	−	0.780247i	$-0.715093\pi$
$569$	−29.8397	−1.25094	−0.625472	+	0.780247i	$0.715093\pi$
$570$	−2.09509	−0.0877539
$571$	−14.6060	−0.611241	−0.305620	−	0.952153i	$-0.598864\pi$
$571$	−14.6060	−0.611241	−0.305620	+	0.952153i	$0.598864\pi$
$572$	−23.4891	−0.982130
$573$	−45.9565	−1.91986
$574$	0	0
$575$	1.72281	0.0718463
$576$	2.62772	0.109488
$577$	−32.7446	−1.36317	−0.681587	−	0.731737i	$-0.738710\pi$
$577$	−32.7446	−1.36317	−0.681587	+	0.731737i	$0.738710\pi$
$578$	−28.4891	−1.18499
$579$	30.2337	1.25647
$580$	−24.0000	−0.996546
$581$	0	0
$582$	18.9783	0.786674
$583$	43.7228	1.81081
$584$	−4.11684	−0.170356
$585$	−33.4891	−1.38460
$586$	−7.37228	−0.304546
$587$	−31.6277	−1.30542	−0.652708	−	0.757610i	$-0.726367\pi$
$587$	−31.6277	−1.30542	−0.652708	+	0.757610i	$0.726367\pi$
$588$	0	0
$589$	−3.25544	−0.134138
$590$	−12.7446	−0.524685
$591$	3.86141	0.158837
$592$	−2.00000	−0.0821995
$593$	8.23369	0.338117	0.169059	−	0.985606i	$-0.445927\pi$
$593$	8.23369	0.338117	0.169059	+	0.985606i	$0.445927\pi$
$594$	−3.86141	−0.158435
$595$	0	0
$596$	20.1168	0.824018
$597$	8.00000	0.327418
$598$	−14.7446	−0.602950
$599$	29.4891	1.20489	0.602446	−	0.798159i	$-0.294193\pi$
$599$	29.4891	1.20489	0.602446	+	0.798159i	$0.294193\pi$
$600$	−1.48913	−0.0607933
$601$	−26.0000	−1.06056	−0.530281	−	0.847822i	$-0.677914\pi$
$601$	−26.0000	−1.06056	−0.530281	+	0.847822i	$0.677914\pi$
$602$	0	0
$603$	−21.0217	−0.856072
$604$	−18.1168	−0.737164
$605$	−19.2554	−0.782845
$606$	34.9783	1.42089
$607$	−11.4891	−0.466329	−0.233165	−	0.972437i	$-0.574908\pi$
$607$	−11.4891	−0.466329	−0.233165	+	0.972437i	$0.574908\pi$
$608$	0.372281	0.0150980
$609$	0	0
$610$	−19.8614	−0.804165
$611$	−42.9783	−1.73871
$612$	−17.7228	−0.716402
$613$	−21.6277	−0.873535	−0.436768	−	0.899574i	$-0.643877\pi$
$613$	−21.6277	−0.873535	−0.436768	+	0.899574i	$0.643877\pi$
$614$	−4.86141	−0.196190
$615$	−5.62772	−0.226932
$616$	0	0
$617$	42.4891	1.71055	0.855274	−	0.518176i	$-0.173389\pi$
$617$	42.4891	1.71055	0.855274	+	0.518176i	$0.173389\pi$
$618$	1.76631	0.0710515
$619$	6.39403	0.256998	0.128499	−	0.991710i	$-0.458984\pi$
$619$	6.39403	0.256998	0.128499	+	0.991710i	$0.458984\pi$
$620$	−20.7446	−0.833122
$621$	−2.42388	−0.0972668
$622$	4.62772	0.185555
$623$	0	0
$624$	12.7446	0.510191
$625$	−27.7446	−1.10978
$626$	0	0
$627$	3.86141	0.154210
$628$	−12.8614	−0.513226
$629$	13.4891	0.537847
$630$	0	0
$631$	14.0000	0.557331	0.278666	−	0.960388i	$-0.410108\pi$
$631$	14.0000	0.557331	0.278666	+	0.960388i	$0.410108\pi$
$632$	10.3723	0.412587
$633$	21.6277	0.859625
$634$	13.2554	0.526441
$635$	14.2337	0.564847
$636$	−23.7228	−0.940671
$637$	0	0
$638$	44.2337	1.75123
$639$	−0.671218	−0.0265530
$640$	2.37228	0.0937727
$641$	30.4674	1.20339	0.601694	−	0.798726i	$-0.294492\pi$
$641$	30.4674	1.20339	0.601694	+	0.798726i	$0.294492\pi$
$642$	38.2337	1.50896
$643$	32.0951	1.26571	0.632853	−	0.774272i	$-0.281884\pi$
$643$	32.0951	1.26571	0.632853	+	0.774272i	$0.281884\pi$
$644$	0	0
$645$	3.53262	0.139097
$646$	−2.51087	−0.0987890
$647$	26.2337	1.03135	0.515676	−	0.856783i	$-0.327541\pi$
$647$	26.2337	1.03135	0.515676	+	0.856783i	$0.327541\pi$
$648$	9.97825	0.391983
$649$	23.4891	0.922029
$650$	−3.37228	−0.132272
$651$	0	0
$652$	−4.11684	−0.161228
$653$	−24.8614	−0.972902	−0.486451	−	0.873708i	$-0.661709\pi$
$653$	−24.8614	−0.972902	−0.486451	+	0.873708i	$0.661709\pi$
$654$	−26.9783	−1.05493
$655$	−28.4674	−1.11231
$656$	1.00000	0.0390434
$657$	10.8179	0.422047
$658$	0	0
$659$	−17.4891	−0.681280	−0.340640	−	0.940194i	$-0.610644\pi$
$659$	−17.4891	−0.681280	−0.340640	+	0.940194i	$0.610644\pi$
$660$	24.6060	0.957786
$661$	−23.6277	−0.919012	−0.459506	−	0.888175i	$-0.651973\pi$
$661$	−23.6277	−0.919012	−0.459506	+	0.888175i	$0.651973\pi$
$662$	−10.7446	−0.417599
$663$	−85.9565	−3.33827
$664$	5.37228	0.208485
$665$	0	0
$666$	5.25544	0.203644
$667$	27.7663	1.07512
$668$	19.3723	0.749536
$669$	−34.9783	−1.35234
$670$	−18.9783	−0.733194
$671$	36.6060	1.41316
$672$	0	0
$673$	−31.4891	−1.21382	−0.606908	−	0.794772i	$-0.707590\pi$
$673$	−31.4891	−1.21382	−0.606908	+	0.794772i	$0.707590\pi$
$674$	5.00000	0.192593
$675$	−0.554374	−0.0213378
$676$	15.8614	0.610054
$677$	31.1168	1.19592	0.597959	−	0.801527i	$-0.295979\pi$
$677$	31.1168	1.19592	0.597959	+	0.801527i	$0.295979\pi$
$678$	39.1168	1.50227
$679$	0	0
$680$	−16.0000	−0.613572
$681$	−13.3505	−0.511593
$682$	38.2337	1.46404
$683$	−9.25544	−0.354149	−0.177075	−	0.984197i	$-0.556663\pi$
$683$	−9.25544	−0.354149	−0.177075	+	0.984197i	$0.556663\pi$
$684$	−0.978251	−0.0374043
$685$	20.7446	0.792609
$686$	0	0
$687$	26.9783	1.02928
$688$	−0.627719	−0.0239316
$689$	−53.7228	−2.04668
$690$	15.4456	0.588005
$691$	−6.37228	−0.242413	−0.121207	−	0.992627i	$-0.538676\pi$
$691$	−6.37228	−0.242413	−0.121207	+	0.992627i	$0.538676\pi$
$692$	−7.11684	−0.270542
$693$	0	0
$694$	−24.6060	−0.934030
$695$	39.7228	1.50677
$696$	−24.0000	−0.909718
$697$	−6.74456	−0.255469
$698$	11.2554	0.426025
$699$	−1.21194	−0.0458397
$700$	0	0
$701$	−13.1168	−0.495416	−0.247708	−	0.968835i	$-0.579677\pi$
$701$	−13.1168	−0.495416	−0.247708	+	0.968835i	$0.579677\pi$
$702$	4.74456	0.179072
$703$	0.744563	0.0280817
$704$	−4.37228	−0.164787
$705$	45.0217	1.69562
$706$	−35.0000	−1.31724
$707$	0	0
$708$	−12.7446	−0.478970
$709$	36.6277	1.37558	0.687791	−	0.725908i	$-0.258580\pi$
$709$	36.6277	1.37558	0.687791	+	0.725908i	$0.258580\pi$
$710$	−0.605969	−0.0227416
$711$	−27.2554	−1.02216
$712$	−2.00000	−0.0749532
$713$	24.0000	0.898807
$714$	0	0
$715$	55.7228	2.08392
$716$	7.62772	0.285061
$717$	−32.3288	−1.20734
$718$	−12.5109	−0.466902
$719$	23.2337	0.866470	0.433235	−	0.901281i	$-0.357372\pi$
$719$	23.2337	0.866470	0.433235	+	0.901281i	$0.357372\pi$
$720$	−6.23369	−0.232316
$721$	0	0
$722$	18.8614	0.701949
$723$	57.2119	2.12773
$724$	−0.510875	−0.0189865
$725$	6.35053	0.235853
$726$	−19.2554	−0.714636
$727$	14.3505	0.532232	0.266116	−	0.963941i	$-0.414260\pi$
$727$	14.3505	0.532232	0.266116	+	0.963941i	$0.414260\pi$
$728$	0	0
$729$	−19.9348	−0.738324
$730$	9.76631	0.361467
$731$	4.23369	0.156589
$732$	−19.8614	−0.734099
$733$	40.7446	1.50493	0.752467	−	0.658630i	$-0.228864\pi$
$733$	40.7446	1.50493	0.752467	+	0.658630i	$0.228864\pi$
$734$	−10.0000	−0.369107
$735$	0	0
$736$	−2.74456	−0.101166
$737$	34.9783	1.28844
$738$	−2.62772	−0.0967277
$739$	17.3723	0.639050	0.319525	−	0.947578i	$-0.396477\pi$
$739$	17.3723	0.639050	0.319525	+	0.947578i	$0.396477\pi$
$740$	4.74456	0.174414
$741$	−4.74456	−0.174296
$742$	0	0
$743$	33.7228	1.23717	0.618585	−	0.785718i	$-0.287706\pi$
$743$	33.7228	1.23717	0.618585	+	0.785718i	$0.287706\pi$
$744$	−20.7446	−0.760533
$745$	−47.7228	−1.74843
$746$	20.3723	0.745882
$747$	−14.1168	−0.516508
$748$	29.4891	1.07823
$749$	0	0
$750$	−24.6060	−0.898483
$751$	−50.9565	−1.85943	−0.929715	−	0.368281i	$-0.879946\pi$
$751$	−50.9565	−1.85943	−0.929715	+	0.368281i	$0.879946\pi$
$752$	−8.00000	−0.291730
$753$	35.2554	1.28478
$754$	−54.3505	−1.97933
$755$	42.9783	1.56414
$756$	0	0
$757$	−42.3505	−1.53926	−0.769628	−	0.638492i	$-0.779558\pi$
$757$	−42.3505	−1.53926	−0.769628	+	0.638492i	$0.779558\pi$
$758$	−5.13859	−0.186642
$759$	−28.4674	−1.03330
$760$	−0.883156	−0.0320354
$761$	3.02175	0.109538	0.0547692	−	0.998499i	$-0.482558\pi$
$761$	3.02175	0.109538	0.0547692	+	0.998499i	$0.482558\pi$
$762$	14.2337	0.515632
$763$	0	0
$764$	−19.3723	−0.700865
$765$	42.0435	1.52009
$766$	−33.4674	−1.20923
$767$	−28.8614	−1.04212
$768$	2.37228	0.0856023
$769$	16.3723	0.590400	0.295200	−	0.955436i	$-0.404614\pi$
$769$	16.3723	0.590400	0.295200	+	0.955436i	$0.404614\pi$
$770$	0	0
$771$	0	0
$772$	12.7446	0.458687
$773$	−27.4891	−0.988715	−0.494358	−	0.869259i	$-0.664597\pi$
$773$	−27.4891	−0.988715	−0.494358	+	0.869259i	$0.664597\pi$
$774$	1.64947	0.0592889
$775$	5.48913	0.197175
$776$	8.00000	0.287183
$777$	0	0
$778$	−15.1168	−0.541965
$779$	−0.372281	−0.0133384
$780$	−30.2337	−1.08254
$781$	1.11684	0.0399638
$782$	18.5109	0.661948
$783$	−8.93475	−0.319302
$784$	0	0
$785$	30.5109	1.08898
$786$	−28.4674	−1.01540
$787$	−20.0000	−0.712923	−0.356462	−	0.934310i	$-0.616017\pi$
$787$	−20.0000	−0.712923	−0.356462	+	0.934310i	$0.616017\pi$
$788$	1.62772	0.0579851
$789$	−45.9565	−1.63609
$790$	−24.6060	−0.875441
$791$	0	0
$792$	11.4891	0.408248
$793$	−44.9783	−1.59722
$794$	−14.0000	−0.496841
$795$	56.2772	1.99595
$796$	3.37228	0.119527
$797$	52.7446	1.86831	0.934154	−	0.356870i	$-0.116156\pi$
$797$	52.7446	1.86831	0.934154	+	0.356870i	$0.116156\pi$
$798$	0	0
$799$	53.9565	1.90884
$800$	−0.627719	−0.0221932
$801$	5.25544	0.185692
$802$	2.25544	0.0796423
$803$	−18.0000	−0.635206
$804$	−18.9783	−0.669311
$805$	0	0
$806$	−46.9783	−1.65474
$807$	55.3940	1.94996
$808$	14.7446	0.518712
$809$	−21.4891	−0.755517	−0.377759	−	0.925904i	$-0.623305\pi$
$809$	−21.4891	−0.755517	−0.377759	+	0.925904i	$0.623305\pi$
$810$	−23.6712	−0.831722
$811$	−41.8397	−1.46919	−0.734595	−	0.678506i	$-0.762628\pi$
$811$	−41.8397	−1.46919	−0.734595	+	0.678506i	$0.762628\pi$
$812$	0	0
$813$	40.9348	1.43564
$814$	−8.74456	−0.306497
$815$	9.76631	0.342099
$816$	−16.0000	−0.560112
$817$	0.233688	0.00817571
$818$	−4.25544	−0.148788
$819$	0	0
$820$	−2.37228	−0.0828437
$821$	−2.60597	−0.0909490	−0.0454745	−	0.998966i	$-0.514480\pi$
$821$	−2.60597	−0.0909490	−0.0454745	+	0.998966i	$0.514480\pi$
$822$	20.7446	0.723550
$823$	0.883156	0.0307849	0.0153924	−	0.999882i	$-0.495100\pi$
$823$	0.883156	0.0307849	0.0153924	+	0.999882i	$0.495100\pi$
$824$	0.744563	0.0259381
$825$	−6.51087	−0.226680
$826$	0	0
$827$	−10.9783	−0.381751	−0.190876	−	0.981614i	$-0.561133\pi$
$827$	−10.9783	−0.381751	−0.190876	+	0.981614i	$0.561133\pi$
$828$	7.21194	0.250632
$829$	39.7228	1.37963	0.689815	−	0.723986i	$-0.257692\pi$
$829$	39.7228	1.37963	0.689815	+	0.723986i	$0.257692\pi$
$830$	−12.7446	−0.442370
$831$	−53.6277	−1.86032
$832$	5.37228	0.186250
$833$	0	0
$834$	39.7228	1.37549
$835$	−45.9565	−1.59039
$836$	1.62772	0.0562958
$837$	−7.72281	−0.266939
$838$	28.8614	0.997001
$839$	−55.2337	−1.90688	−0.953439	−	0.301585i	$-0.902484\pi$
$839$	−55.2337	−1.90688	−0.953439	+	0.301585i	$0.902484\pi$
$840$	0	0
$841$	73.3505	2.52933
$842$	−2.00000	−0.0689246
$843$	−44.4674	−1.53154
$844$	9.11684	0.313815
$845$	−37.6277	−1.29443
$846$	21.0217	0.722743
$847$	0	0
$848$	−10.0000	−0.343401
$849$	60.1902	2.06572
$850$	4.23369	0.145214
$851$	−5.48913	−0.188165
$852$	−0.605969	−0.0207602
$853$	22.6060	0.774014	0.387007	−	0.922077i	$-0.373509\pi$
$853$	22.6060	0.774014	0.387007	+	0.922077i	$0.373509\pi$
$854$	0	0
$855$	2.32069	0.0793658
$856$	16.1168	0.550862
$857$	−0.766312	−0.0261767	−0.0130884	−	0.999914i	$-0.504166\pi$
$857$	−0.766312	−0.0261767	−0.0130884	+	0.999914i	$0.504166\pi$
$858$	55.7228	1.90235
$859$	32.3505	1.10379	0.551893	−	0.833915i	$-0.313906\pi$
$859$	32.3505	1.10379	0.551893	+	0.833915i	$0.313906\pi$
$860$	1.48913	0.0507788
$861$	0	0
$862$	−13.4891	−0.459441
$863$	−28.5109	−0.970521	−0.485261	−	0.874370i	$-0.661275\pi$
$863$	−28.5109	−0.970521	−0.485261	+	0.874370i	$0.661275\pi$
$864$	0.883156	0.0300456
$865$	16.8832	0.574045
$866$	−16.3723	−0.556353
$867$	67.5842	2.29528
$868$	0	0
$869$	45.3505	1.53841
$870$	56.9348	1.93027
$871$	−42.9783	−1.45626
$872$	−11.3723	−0.385114
$873$	−21.0217	−0.711478
$874$	1.02175	0.0345612
$875$	0	0
$876$	9.76631	0.329973
$877$	−7.11684	−0.240319	−0.120159	−	0.992755i	$-0.538341\pi$
$877$	−7.11684	−0.240319	−0.120159	+	0.992755i	$0.538341\pi$
$878$	7.74456	0.261366
$879$	17.4891	0.589894
$880$	10.3723	0.349650
$881$	9.97825	0.336176	0.168088	−	0.985772i	$-0.446241\pi$
$881$	9.97825	0.336176	0.168088	+	0.985772i	$0.446241\pi$
$882$	0	0
$883$	−8.23369	−0.277086	−0.138543	−	0.990356i	$-0.544242\pi$
$883$	−8.23369	−0.277086	−0.138543	+	0.990356i	$0.544242\pi$
$884$	−36.2337	−1.21867
$885$	30.2337	1.01629
$886$	18.3505	0.616498
$887$	3.23369	0.108577	0.0542883	−	0.998525i	$-0.482711\pi$
$887$	3.23369	0.108577	0.0542883	+	0.998525i	$0.482711\pi$
$888$	4.74456	0.159217
$889$	0	0
$890$	4.74456	0.159038
$891$	43.6277	1.46158
$892$	−14.7446	−0.493684
$893$	2.97825	0.0996634
$894$	−47.7228	−1.59609
$895$	−18.0951	−0.604852
$896$	0	0
$897$	34.9783	1.16789
$898$	11.2337	0.374873
$899$	88.4674	2.95055
$900$	1.64947	0.0549823
$901$	67.4456	2.24694
$902$	4.37228	0.145581
$903$	0	0
$904$	16.4891	0.548420
$905$	1.21194	0.0402862
$906$	42.9783	1.42786
$907$	−22.8614	−0.759101	−0.379550	−	0.925171i	$-0.623921\pi$
$907$	−22.8614	−0.759101	−0.379550	+	0.925171i	$0.623921\pi$
$908$	−5.62772	−0.186762
$909$	−38.7446	−1.28508
$910$	0	0
$911$	−45.2554	−1.49938	−0.749690	−	0.661789i	$-0.769797\pi$
$911$	−45.2554	−1.49938	−0.749690	+	0.661789i	$0.769797\pi$
$912$	−0.883156	−0.0292442
$913$	23.4891	0.777377
$914$	8.23369	0.272346
$915$	47.1168	1.55763
$916$	11.3723	0.375751
$917$	0	0
$918$	−5.95650	−0.196594
$919$	33.0000	1.08857	0.544285	−	0.838901i	$-0.316801\pi$
$919$	33.0000	1.08857	0.544285	+	0.838901i	$0.316801\pi$
$920$	6.51087	0.214657
$921$	11.5326	0.380013
$922$	36.6060	1.20555
$923$	−1.37228	−0.0451692
$924$	0	0
$925$	−1.25544	−0.0412785
$926$	−6.25544	−0.205566
$927$	−1.95650	−0.0642599
$928$	−10.1168	−0.332102
$929$	−34.0000	−1.11550	−0.557752	−	0.830008i	$-0.688336\pi$
$929$	−34.0000	−1.11550	−0.557752	+	0.830008i	$0.688336\pi$
$930$	49.2119	1.61372
$931$	0	0
$932$	−0.510875	−0.0167343
$933$	−10.9783	−0.359412
$934$	−33.4891	−1.09580
$935$	−69.9565	−2.28782
$936$	−14.1168	−0.461423
$937$	−28.4674	−0.929989	−0.464994	−	0.885314i	$-0.653944\pi$
$937$	−28.4674	−0.929989	−0.464994	+	0.885314i	$0.653944\pi$
$938$	0	0
$939$	0	0
$940$	18.9783	0.619002
$941$	−40.6060	−1.32372	−0.661858	−	0.749629i	$-0.730232\pi$
$941$	−40.6060	−1.32372	−0.661858	+	0.749629i	$0.730232\pi$
$942$	30.5109	0.994098
$943$	2.74456	0.0893753
$944$	−5.37228	−0.174853
$945$	0	0
$946$	−2.74456	−0.0892334
$947$	45.0951	1.46539	0.732697	−	0.680555i	$-0.238261\pi$
$947$	45.0951	1.46539	0.732697	+	0.680555i	$0.238261\pi$
$948$	−24.6060	−0.799165
$949$	22.1168	0.717943
$950$	0.233688	0.00758184
$951$	−31.4456	−1.01969
$952$	0	0
$953$	−13.1386	−0.425601	−0.212800	−	0.977096i	$-0.568258\pi$
$953$	−13.1386	−0.425601	−0.212800	+	0.977096i	$0.568258\pi$
$954$	26.2772	0.850755
$955$	45.9565	1.48712
$956$	−13.6277	−0.440752
$957$	−104.935	−3.39206
$958$	1.51087	0.0488141
$959$	0	0
$960$	−5.62772	−0.181634
$961$	45.4674	1.46669
$962$	10.7446	0.346419
$963$	−42.3505	−1.36473
$964$	24.1168	0.776751
$965$	−30.2337	−0.973257
$966$	0	0
$967$	38.4891	1.23773	0.618863	−	0.785499i	$-0.287593\pi$
$967$	38.4891	1.23773	0.618863	+	0.785499i	$0.287593\pi$
$968$	−8.11684	−0.260885
$969$	5.95650	0.191350
$970$	−18.9783	−0.609355
$971$	−12.0000	−0.385098	−0.192549	−	0.981287i	$-0.561675\pi$
$971$	−12.0000	−0.385098	−0.192549	+	0.981287i	$0.561675\pi$
$972$	−21.0217	−0.674273
$973$	0	0
$974$	24.7446	0.792867
$975$	8.00000	0.256205
$976$	−8.37228	−0.267990
$977$	3.25544	0.104151	0.0520753	−	0.998643i	$-0.483416\pi$
$977$	3.25544	0.104151	0.0520753	+	0.998643i	$0.483416\pi$
$978$	9.76631	0.312292
$979$	−8.74456	−0.279477
$980$	0	0
$981$	29.8832	0.954096
$982$	−0.116844	−0.00372864
$983$	−12.0000	−0.382741	−0.191370	−	0.981518i	$-0.561293\pi$
$983$	−12.0000	−0.382741	−0.191370	+	0.981518i	$0.561293\pi$
$984$	−2.37228	−0.0756256
$985$	−3.86141	−0.123035
$986$	68.2337	2.17300
$987$	0	0
$988$	−2.00000	−0.0636285
$989$	−1.72281	−0.0547823
$990$	−27.2554	−0.866235
$991$	21.9783	0.698162	0.349081	−	0.937093i	$-0.386494\pi$
$991$	21.9783	0.698162	0.349081	+	0.937093i	$0.386494\pi$
$992$	−8.74456	−0.277640
$993$	25.4891	0.808873
$994$	0	0
$995$	−8.00000	−0.253617
$996$	−12.7446	−0.403827
$997$	20.3505	0.644508	0.322254	−	0.946653i	$-0.395560\pi$
$997$	20.3505	0.644508	0.322254	+	0.946653i	$0.395560\pi$
$998$	−6.74456	−0.213495
$999$	1.76631	0.0558836

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4018.2.a.u.1.2		2
7.3	odd	6		574.2.e.d.247.2	yes	4
7.5	odd	6		574.2.e.d.165.2	✓	4
7.6	odd	2		4018.2.a.v.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
574.2.e.d.165.2	✓	4	7.5	odd	6
574.2.e.d.247.2	yes	4	7.3	odd	6
4018.2.a.u.1.2		2	1.1	even	1	trivial
4018.2.a.v.1.1		2	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4018 = 2 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.37228 q^{3} +1.00000 q^{4} -2.37228 q^{5} -2.37228 q^{6} -1.00000 q^{8} +2.62772 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.37228 q^{3} +1.00000 q^{4} -2.37228 q^{5} -2.37228 q^{6} -1.00000 q^{8} +2.62772 q^{9} +2.37228 q^{10} -4.37228 q^{11} +2.37228 q^{12} +5.37228 q^{13} -5.62772 q^{15} +1.00000 q^{16} -6.74456 q^{17} -2.62772 q^{18} -0.372281 q^{19} -2.37228 q^{20} +4.37228 q^{22} +2.74456 q^{23} -2.37228 q^{24} +0.627719 q^{25} -5.37228 q^{26} -0.883156 q^{27} +10.1168 q^{29} +5.62772 q^{30} +8.74456 q^{31} -1.00000 q^{32} -10.3723 q^{33} +6.74456 q^{34} +2.62772 q^{36} -2.00000 q^{37} +0.372281 q^{38} +12.7446 q^{39} +2.37228 q^{40} +1.00000 q^{41} -0.627719 q^{43} -4.37228 q^{44} -6.23369 q^{45} -2.74456 q^{46} -8.00000 q^{47} +2.37228 q^{48} -0.627719 q^{50} -16.0000 q^{51} +5.37228 q^{52} -10.0000 q^{53} +0.883156 q^{54} +10.3723 q^{55} -0.883156 q^{57} -10.1168 q^{58} -5.37228 q^{59} -5.62772 q^{60} -8.37228 q^{61} -8.74456 q^{62} +1.00000 q^{64} -12.7446 q^{65} +10.3723 q^{66} -8.00000 q^{67} -6.74456 q^{68} +6.51087 q^{69} -0.255437 q^{71} -2.62772 q^{72} +4.11684 q^{73} +2.00000 q^{74} +1.48913 q^{75} -0.372281 q^{76} -12.7446 q^{78} -10.3723 q^{79} -2.37228 q^{80} -9.97825 q^{81} -1.00000 q^{82} -5.37228 q^{83} +16.0000 q^{85} +0.627719 q^{86} +24.0000 q^{87} +4.37228 q^{88} +2.00000 q^{89} +6.23369 q^{90} +2.74456 q^{92} +20.7446 q^{93} +8.00000 q^{94} +0.883156 q^{95} -2.37228 q^{96} -8.00000 q^{97} -11.4891 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - q^{3} + 2 q^{4} + q^{5} + q^{6} - 2 q^{8} + 11 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - q^3 + 2 * q^4 + q^5 + q^6 - 2 * q^8 + 11 * q^9	\( 2 q - 2 q^{2} - q^{3} + 2 q^{4} + q^{5} + q^{6} - 2 q^{8} + 11 q^{9} - q^{10} - 3 q^{11} - q^{12} + 5 q^{13} - 17 q^{15} + 2 q^{16} - 2 q^{17} - 11 q^{18} + 5 q^{19} + q^{20} + 3 q^{22} - 6 q^{23} + q^{24} + 7 q^{25} - 5 q^{26} - 19 q^{27} + 3 q^{29} + 17 q^{30} + 6 q^{31} - 2 q^{32} - 15 q^{33} + 2 q^{34} + 11 q^{36} - 4 q^{37} - 5 q^{38} + 14 q^{39} - q^{40} + 2 q^{41} - 7 q^{43} - 3 q^{44} + 22 q^{45} + 6 q^{46} - 16 q^{47} - q^{48} - 7 q^{50} - 32 q^{51} + 5 q^{52} - 20 q^{53} + 19 q^{54} + 15 q^{55} - 19 q^{57} - 3 q^{58} - 5 q^{59} - 17 q^{60} - 11 q^{61} - 6 q^{62} + 2 q^{64} - 14 q^{65} + 15 q^{66} - 16 q^{67} - 2 q^{68} + 36 q^{69} - 12 q^{71} - 11 q^{72} - 9 q^{73} + 4 q^{74} - 20 q^{75} + 5 q^{76} - 14 q^{78} - 15 q^{79} + q^{80} + 26 q^{81} - 2 q^{82} - 5 q^{83} + 32 q^{85} + 7 q^{86} + 48 q^{87} + 3 q^{88} + 4 q^{89} - 22 q^{90} - 6 q^{92} + 30 q^{93} + 16 q^{94} + 19 q^{95} + q^{96} - 16 q^{97}+O(q^{100}) \) 2 * q - 2 * q^2 - q^3 + 2 * q^4 + q^5 + q^6 - 2 * q^8 + 11 * q^9 - q^10 - 3 * q^11 - q^12 + 5 * q^13 - 17 * q^15 + 2 * q^16 - 2 * q^17 - 11 * q^18 + 5 * q^19 + q^20 + 3 * q^22 - 6 * q^23 + q^24 + 7 * q^25 - 5 * q^26 - 19 * q^27 + 3 * q^29 + 17 * q^30 + 6 * q^31 - 2 * q^32 - 15 * q^33 + 2 * q^34 + 11 * q^36 - 4 * q^37 - 5 * q^38 + 14 * q^39 - q^40 + 2 * q^41 - 7 * q^43 - 3 * q^44 + 22 * q^45 + 6 * q^46 - 16 * q^47 - q^48 - 7 * q^50 - 32 * q^51 + 5 * q^52 - 20 * q^53 + 19 * q^54 + 15 * q^55 - 19 * q^57 - 3 * q^58 - 5 * q^59 - 17 * q^60 - 11 * q^61 - 6 * q^62 + 2 * q^64 - 14 * q^65 + 15 * q^66 - 16 * q^67 - 2 * q^68 + 36 * q^69 - 12 * q^71 - 11 * q^72 - 9 * q^73 + 4 * q^74 - 20 * q^75 + 5 * q^76 - 14 * q^78 - 15 * q^79 + q^80 + 26 * q^81 - 2 * q^82 - 5 * q^83 + 32 * q^85 + 7 * q^86 + 48 * q^87 + 3 * q^88 + 4 * q^89 - 22 * q^90 - 6 * q^92 + 30 * q^93 + 16 * q^94 + 19 * q^95 + q^96 - 16 * q^97

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