LMFDB - Embedded newform 4018.2.a.bk.1.4

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:	$4$
Coefficient field:	4.4.113481.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 9x^{2} + 3x + 12 $ x^4 - 2x^3 - 9x^2 + 3*x + 12
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
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			1.4
Root			$1.26053$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.06659 q^{5} -1.00000 q^{6} -1.00000 q^{8} -2.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.06659 q^{5} -1.00000 q^{6} -1.00000 q^{8} -2.00000 q^{9} -4.06659 q^{10} -4.67159 q^{11} +1.00000 q^{12} +1.86554 q^{13} +4.06659 q^{15} +1.00000 q^{16} -2.54552 q^{17} +2.00000 q^{18} -6.45319 q^{19} +4.06659 q^{20} +4.67159 q^{22} -6.32712 q^{23} -1.00000 q^{24} +11.5371 q^{25} -1.86554 q^{26} -5.00000 q^{27} +0.932122 q^{29} -4.06659 q^{30} -8.38660 q^{31} -1.00000 q^{32} -4.67159 q^{33} +2.54552 q^{34} -2.00000 q^{36} -1.78160 q^{37} +6.45319 q^{38} +1.86554 q^{39} -4.06659 q^{40} -1.00000 q^{41} +9.99871 q^{43} -4.67159 q^{44} -8.13317 q^{45} +6.32712 q^{46} +6.19266 q^{47} +1.00000 q^{48} -11.5371 q^{50} -2.54552 q^{51} +1.86554 q^{52} +0.739466 q^{53} +5.00000 q^{54} -18.9974 q^{55} -6.45319 q^{57} -0.932122 q^{58} -11.7803 q^{59} +4.06659 q^{60} +2.18555 q^{61} +8.38660 q^{62} +1.00000 q^{64} +7.58636 q^{65} +4.67159 q^{66} +1.39500 q^{67} -2.54552 q^{68} -6.32712 q^{69} -14.1492 q^{71} +2.00000 q^{72} +1.45319 q^{73} +1.78160 q^{74} +11.5371 q^{75} -6.45319 q^{76} -1.86554 q^{78} -5.79895 q^{79} +4.06659 q^{80} +1.00000 q^{81} +1.00000 q^{82} -5.83050 q^{83} -10.3516 q^{85} -9.99871 q^{86} +0.932122 q^{87} +4.67159 q^{88} -5.45319 q^{89} +8.13317 q^{90} -6.32712 q^{92} -8.38660 q^{93} -6.19266 q^{94} -26.2425 q^{95} -1.00000 q^{96} -1.00710 q^{97} +9.34318 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} + 3 q^{5} - 4 q^{6} - 4 q^{8} - 8 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 + 3 * q^5 - 4 * q^6 - 4 * q^8 - 8 * q^9	$ 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} + 3 q^{5} - 4 q^{6} - 4 q^{8} - 8 q^{9} - 3 q^{10} + 4 q^{12} - q^{13} + 3 q^{15} + 4 q^{16} - 3 q^{17} + 8 q^{18} + 2 q^{19} + 3 q^{20} - 9 q^{23} - 4 q^{24} + 19 q^{25} + q^{26} - 20 q^{27} - 18 q^{29} - 3 q^{30} - 19 q^{31} - 4 q^{32} + 3 q^{34} - 8 q^{36} + 2 q^{37} - 2 q^{38} - q^{39} - 3 q^{40} - 4 q^{41} + 5 q^{43} - 6 q^{45} + 9 q^{46} + 4 q^{48} - 19 q^{50} - 3 q^{51} - q^{52} + 6 q^{53} + 20 q^{54} - 6 q^{55} + 2 q^{57} + 18 q^{58} - 3 q^{59} + 3 q^{60} - q^{61} + 19 q^{62} + 4 q^{64} - 24 q^{65} + 11 q^{67} - 3 q^{68} - 9 q^{69} - 9 q^{71} + 8 q^{72} - 22 q^{73} - 2 q^{74} + 19 q^{75} + 2 q^{76} + q^{78} - 28 q^{79} + 3 q^{80} + 4 q^{81} + 4 q^{82} - 12 q^{83} - 24 q^{85} - 5 q^{86} - 18 q^{87} + 6 q^{89} + 6 q^{90} - 9 q^{92} - 19 q^{93} - 27 q^{95} - 4 q^{96} + 11 q^{97}+O(q^{100}) $ 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 + 3 * q^5 - 4 * q^6 - 4 * q^8 - 8 * q^9 - 3 * q^10 + 4 * q^12 - q^13 + 3 * q^15 + 4 * q^16 - 3 * q^17 + 8 * q^18 + 2 * q^19 + 3 * q^20 - 9 * q^23 - 4 * q^24 + 19 * q^25 + q^26 - 20 * q^27 - 18 * q^29 - 3 * q^30 - 19 * q^31 - 4 * q^32 + 3 * q^34 - 8 * q^36 + 2 * q^37 - 2 * q^38 - q^39 - 3 * q^40 - 4 * q^41 + 5 * q^43 - 6 * q^45 + 9 * q^46 + 4 * q^48 - 19 * q^50 - 3 * q^51 - q^52 + 6 * q^53 + 20 * q^54 - 6 * q^55 + 2 * q^57 + 18 * q^58 - 3 * q^59 + 3 * q^60 - q^61 + 19 * q^62 + 4 * q^64 - 24 * q^65 + 11 * q^67 - 3 * q^68 - 9 * q^69 - 9 * q^71 + 8 * q^72 - 22 * q^73 - 2 * q^74 + 19 * q^75 + 2 * q^76 + q^78 - 28 * q^79 + 3 * q^80 + 4 * q^81 + 4 * q^82 - 12 * q^83 - 24 * q^85 - 5 * q^86 - 18 * q^87 + 6 * q^89 + 6 * q^90 - 9 * q^92 - 19 * q^93 - 27 * q^95 - 4 * q^96 + 11 * 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
$3$	1.00000	0.577350	0.288675	−	0.957427i	$-0.406785\pi$
$3$	1.00000	0.577350	0.288675	+	0.957427i	$0.406785\pi$
$4$	1.00000	0.500000
$5$	4.06659	1.81863	0.909316	−	0.416106i	$-0.136605\pi$
$5$	4.06659	1.81863	0.909316	+	0.416106i	$0.136605\pi$
$6$	−1.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	−2.00000	−0.666667
$10$	−4.06659	−1.28597
$11$	−4.67159	−1.40854	−0.704268	−	0.709934i	$-0.748725\pi$
$11$	−4.67159	−1.40854	−0.704268	+	0.709934i	$0.748725\pi$
$12$	1.00000	0.288675
$13$	1.86554	0.517407	0.258703	−	0.965957i	$-0.416705\pi$
$13$	1.86554	0.517407	0.258703	+	0.965957i	$0.416705\pi$
$14$	0	0
$15$	4.06659	1.04999
$16$	1.00000	0.250000
$17$	−2.54552	−0.617379	−0.308689	−	0.951163i	$-0.599890\pi$
$17$	−2.54552	−0.617379	−0.308689	+	0.951163i	$0.599890\pi$
$18$	2.00000	0.471405
$19$	−6.45319	−1.48046	−0.740232	−	0.672352i	$-0.765284\pi$
$19$	−6.45319	−1.48046	−0.740232	+	0.672352i	$0.765284\pi$
$20$	4.06659	0.909316
$21$	0	0
$22$	4.67159	0.995986
$23$	−6.32712	−1.31930	−0.659648	−	0.751575i	$-0.729295\pi$
$23$	−6.32712	−1.31930	−0.659648	+	0.751575i	$0.729295\pi$
$24$	−1.00000	−0.204124
$25$	11.5371	2.30742
$26$	−1.86554	−0.365862
$27$	−5.00000	−0.962250
$28$	0	0
$29$	0.932122	0.173091	0.0865454	−	0.996248i	$-0.472417\pi$
$29$	0.932122	0.173091	0.0865454	+	0.996248i	$0.472417\pi$
$30$	−4.06659	−0.742454
$31$	−8.38660	−1.50628	−0.753139	−	0.657861i	$-0.771461\pi$
$31$	−8.38660	−1.50628	−0.753139	+	0.657861i	$0.771461\pi$
$32$	−1.00000	−0.176777
$33$	−4.67159	−0.813219
$34$	2.54552	0.436553
$35$	0	0
$36$	−2.00000	−0.333333
$37$	−1.78160	−0.292893	−0.146447	−	0.989219i	$-0.546784\pi$
$37$	−1.78160	−0.292893	−0.146447	+	0.989219i	$0.546784\pi$
$38$	6.45319	1.04685
$39$	1.86554	0.298725
$40$	−4.06659	−0.642984
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	9.99871	1.52479	0.762394	−	0.647113i	$-0.224024\pi$
$43$	9.99871	1.52479	0.762394	+	0.647113i	$0.224024\pi$
$44$	−4.67159	−0.704268
$45$	−8.13317	−1.21242
$46$	6.32712	0.932883
$47$	6.19266	0.903292	0.451646	−	0.892197i	$-0.350837\pi$
$47$	6.19266	0.903292	0.451646	+	0.892197i	$0.350837\pi$
$48$	1.00000	0.144338
$49$	0	0
$50$	−11.5371	−1.63160
$51$	−2.54552	−0.356444
$52$	1.86554	0.258703
$53$	0.739466	0.101573	0.0507867	−	0.998710i	$-0.483827\pi$
$53$	0.739466	0.101573	0.0507867	+	0.998710i	$0.483827\pi$
$54$	5.00000	0.680414
$55$	−18.9974	−2.56161
$56$	0	0
$57$	−6.45319	−0.854746
$58$	−0.932122	−0.122394
$59$	−11.7803	−1.53367	−0.766833	−	0.641847i	$-0.778168\pi$
$59$	−11.7803	−1.53367	−0.766833	+	0.641847i	$0.778168\pi$
$60$	4.06659	0.524994
$61$	2.18555	0.279831	0.139916	−	0.990163i	$-0.455317\pi$
$61$	2.18555	0.279831	0.139916	+	0.990163i	$0.455317\pi$
$62$	8.38660	1.06510
$63$	0	0
$64$	1.00000	0.125000
$65$	7.58636	0.940972
$66$	4.67159	0.575033
$67$	1.39500	0.170426	0.0852131	−	0.996363i	$-0.472843\pi$
$67$	1.39500	0.170426	0.0852131	+	0.996363i	$0.472843\pi$
$68$	−2.54552	−0.308689
$69$	−6.32712	−0.761696
$70$	0	0
$71$	−14.1492	−1.67920	−0.839602	−	0.543202i	$-0.817212\pi$
$71$	−14.1492	−1.67920	−0.839602	+	0.543202i	$0.817212\pi$
$72$	2.00000	0.235702
$73$	1.45319	0.170083	0.0850415	−	0.996377i	$-0.472898\pi$
$73$	1.45319	0.170083	0.0850415	+	0.996377i	$0.472898\pi$
$74$	1.78160	0.207107
$75$	11.5371	1.33219
$76$	−6.45319	−0.740232
$77$	0	0
$78$	−1.86554	−0.211230
$79$	−5.79895	−0.652433	−0.326216	−	0.945295i	$-0.605774\pi$
$79$	−5.79895	−0.652433	−0.326216	+	0.945295i	$0.605774\pi$
$80$	4.06659	0.454658
$81$	1.00000	0.111111
$82$	1.00000	0.110432
$83$	−5.83050	−0.639981	−0.319990	−	0.947421i	$-0.603680\pi$
$83$	−5.83050	−0.639981	−0.319990	+	0.947421i	$0.603680\pi$
$84$	0	0
$85$	−10.3516	−1.12279
$86$	−9.99871	−1.07819
$87$	0.932122	0.0999340
$88$	4.67159	0.497993
$89$	−5.45319	−0.578037	−0.289018	−	0.957324i	$-0.593329\pi$
$89$	−5.45319	−0.578037	−0.289018	+	0.957324i	$0.593329\pi$
$90$	8.13317	0.857312
$91$	0	0
$92$	−6.32712	−0.659648
$93$	−8.38660	−0.869650
$94$	−6.19266	−0.638724
$95$	−26.2425	−2.69242
$96$	−1.00000	−0.102062
$97$	−1.00710	−0.102256	−0.0511279	−	0.998692i	$-0.516282\pi$
$97$	−1.00710	−0.102256	−0.0511279	+	0.998692i	$0.516282\pi$
$98$	0	0
$99$	9.34318	0.939025
$100$	11.5371	1.15371
$101$	−0.412346	−0.0410300	−0.0205150	−	0.999790i	$-0.506531\pi$
$101$	−0.412346	−0.0410300	−0.0205150	+	0.999790i	$0.506531\pi$
$102$	2.54552	0.252044
$103$	10.8816	1.07220	0.536098	−	0.844156i	$-0.319898\pi$
$103$	10.8816	1.07220	0.536098	+	0.844156i	$0.319898\pi$
$104$	−1.86554	−0.182931
$105$	0	0
$106$	−0.739466	−0.0718233
$107$	−2.35286	−0.227460	−0.113730	−	0.993512i	$-0.536280\pi$
$107$	−2.35286	−0.227460	−0.113730	+	0.993512i	$0.536280\pi$
$108$	−5.00000	−0.481125
$109$	−19.0653	−1.82612	−0.913062	−	0.407821i	$-0.866289\pi$
$109$	−19.0653	−1.82612	−0.913062	+	0.407821i	$0.866289\pi$
$110$	18.9974	1.81133
$111$	−1.78160	−0.169102
$112$	0	0
$113$	−8.26053	−0.777086	−0.388543	−	0.921431i	$-0.627021\pi$
$113$	−8.26053	−0.777086	−0.388543	+	0.921431i	$0.627021\pi$
$114$	6.45319	0.604397
$115$	−25.7298	−2.39931
$116$	0.932122	0.0865454
$117$	−3.73107	−0.344938
$118$	11.7803	1.08447
$119$	0	0
$120$	−4.06659	−0.371227
$121$	10.8237	0.983976
$122$	−2.18555	−0.197871
$123$	−1.00000	−0.0901670
$124$	−8.38660	−0.753139
$125$	26.5838	2.37773
$126$	0	0
$127$	−3.67288	−0.325915	−0.162958	−	0.986633i	$-0.552103\pi$
$127$	−3.67288	−0.325915	−0.162958	+	0.986633i	$0.552103\pi$
$128$	−1.00000	−0.0883883
$129$	9.99871	0.880337
$130$	−7.58636	−0.665368
$131$	−7.40266	−0.646773	−0.323387	−	0.946267i	$-0.604821\pi$
$131$	−7.40266	−0.646773	−0.323387	+	0.946267i	$0.604821\pi$
$132$	−4.67159	−0.406610
$133$	0	0
$134$	−1.39500	−0.120509
$135$	−20.3329	−1.74998
$136$	2.54552	0.218276
$137$	16.7719	1.43292	0.716461	−	0.697627i	$-0.245761\pi$
$137$	16.7719	1.43292	0.716461	+	0.697627i	$0.245761\pi$
$138$	6.32712	0.538600
$139$	−17.9224	−1.52016	−0.760081	−	0.649829i	$-0.774841\pi$
$139$	−17.9224	−1.52016	−0.760081	+	0.649829i	$0.774841\pi$
$140$	0	0
$141$	6.19266	0.521516
$142$	14.1492	1.18738
$143$	−8.71502	−0.728786
$144$	−2.00000	−0.166667
$145$	3.79056	0.314788
$146$	−1.45319	−0.120267
$147$	0	0
$148$	−1.78160	−0.146447
$149$	20.2145	1.65604	0.828019	−	0.560700i	$-0.189468\pi$
$149$	20.2145	1.65604	0.828019	+	0.560700i	$0.189468\pi$
$150$	−11.5371	−0.942002
$151$	2.15762	0.175585	0.0877925	−	0.996139i	$-0.472019\pi$
$151$	2.15762	0.175585	0.0877925	+	0.996139i	$0.472019\pi$
$152$	6.45319	0.523423
$153$	5.09104	0.411586
$154$	0	0
$155$	−34.1048	−2.73937
$156$	1.86554	0.149362
$157$	16.6037	1.32512	0.662560	−	0.749009i	$-0.269470\pi$
$157$	16.6037	1.32512	0.662560	+	0.749009i	$0.269470\pi$
$158$	5.79895	0.461340
$159$	0.739466	0.0586435
$160$	−4.06659	−0.321492
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	10.2908	0.806037	0.403019	−	0.915192i	$-0.367961\pi$
$163$	10.2908	0.806037	0.403019	+	0.915192i	$0.367961\pi$
$164$	−1.00000	−0.0780869
$165$	−18.9974	−1.47895
$166$	5.83050	0.452535
$167$	10.9334	0.846053	0.423026	−	0.906117i	$-0.360968\pi$
$167$	10.9334	0.846053	0.423026	+	0.906117i	$0.360968\pi$
$168$	0	0
$169$	−9.51978	−0.732290
$170$	10.3516	0.793929
$171$	12.9064	0.986976
$172$	9.99871	0.762394
$173$	−17.8053	−1.35371	−0.676857	−	0.736115i	$-0.736658\pi$
$173$	−17.8053	−1.35371	−0.676857	+	0.736115i	$0.736658\pi$
$174$	−0.932122	−0.0706640
$175$	0	0
$176$	−4.67159	−0.352134
$177$	−11.7803	−0.885462
$178$	5.45319	0.408734
$179$	2.58765	0.193410	0.0967052	−	0.995313i	$-0.469170\pi$
$179$	2.58765	0.193410	0.0967052	+	0.995313i	$0.469170\pi$
$180$	−8.13317	−0.606211
$181$	5.19976	0.386495	0.193248	−	0.981150i	$-0.438098\pi$
$181$	5.19976	0.386495	0.193248	+	0.981150i	$0.438098\pi$
$182$	0	0
$183$	2.18555	0.161561
$184$	6.32712	0.466441
$185$	−7.24504	−0.532666
$186$	8.38660	0.614936
$187$	11.8916	0.869601
$188$	6.19266	0.451646
$189$	0	0
$190$	26.2425	1.90383
$191$	8.73817	0.632272	0.316136	−	0.948714i	$-0.397614\pi$
$191$	8.73817	0.632272	0.316136	+	0.948714i	$0.397614\pi$
$192$	1.00000	0.0721688
$193$	−1.88103	−0.135400	−0.0676999	−	0.997706i	$-0.521566\pi$
$193$	−1.88103	−0.135400	−0.0676999	+	0.997706i	$0.521566\pi$
$194$	1.00710	0.0723058
$195$	7.58636	0.543271
$196$	0	0
$197$	17.7111	1.26187	0.630933	−	0.775837i	$-0.282672\pi$
$197$	17.7111	1.26187	0.630933	+	0.775837i	$0.282672\pi$
$198$	−9.34318	−0.663991
$199$	17.6703	1.25261	0.626307	−	0.779576i	$-0.284566\pi$
$199$	17.6703	1.25261	0.626307	+	0.779576i	$0.284566\pi$
$200$	−11.5371	−0.815798
$201$	1.39500	0.0983956
$202$	0.412346	0.0290126
$203$	0	0
$204$	−2.54552	−0.178222
$205$	−4.06659	−0.284023
$206$	−10.8816	−0.758156
$207$	12.6542	0.879530
$208$	1.86554	0.129352
$209$	30.1466	2.08529
$210$	0	0
$211$	−7.06715	−0.486522	−0.243261	−	0.969961i	$-0.578217\pi$
$211$	−7.06715	−0.486522	−0.243261	+	0.969961i	$0.578217\pi$
$212$	0.739466	0.0507867
$213$	−14.1492	−0.969489
$214$	2.35286	0.160838
$215$	40.6606	2.77303
$216$	5.00000	0.340207
$217$	0	0
$218$	19.0653	1.29126
$219$	1.45319	0.0981975
$220$	−18.9974	−1.28081
$221$	−4.74876	−0.319436
$222$	1.78160	0.119573
$223$	−19.9974	−1.33913	−0.669563	−	0.742755i	$-0.733519\pi$
$223$	−19.9974	−1.33913	−0.669563	+	0.742755i	$0.733519\pi$
$224$	0	0
$225$	−23.0742	−1.53828
$226$	8.26053	0.549483
$227$	21.3592	1.41766	0.708831	−	0.705378i	$-0.249223\pi$
$227$	21.3592	1.41766	0.708831	+	0.705378i	$0.249223\pi$
$228$	−6.45319	−0.427373
$229$	21.8372	1.44304	0.721522	−	0.692392i	$-0.243443\pi$
$229$	21.8372	1.44304	0.721522	+	0.692392i	$0.243443\pi$
$230$	25.7298	1.69657
$231$	0	0
$232$	−0.932122	−0.0611968
$233$	−18.9672	−1.24258	−0.621290	−	0.783581i	$-0.713391\pi$
$233$	−18.9672	−1.24258	−0.621290	+	0.783581i	$0.713391\pi$
$234$	3.73107	0.243908
$235$	25.1830	1.64276
$236$	−11.7803	−0.766833
$237$	−5.79895	−0.376682
$238$	0	0
$239$	25.1901	1.62941	0.814705	−	0.579875i	$-0.196899\pi$
$239$	25.1901	1.62941	0.814705	+	0.579875i	$0.196899\pi$
$240$	4.06659	0.262497
$241$	4.13317	0.266241	0.133121	−	0.991100i	$-0.457500\pi$
$241$	4.13317	0.266241	0.133121	+	0.991100i	$0.457500\pi$
$242$	−10.8237	−0.695776
$243$	16.0000	1.02640
$244$	2.18555	0.139916
$245$	0	0
$246$	1.00000	0.0637577
$247$	−12.0387	−0.766001
$248$	8.38660	0.532550
$249$	−5.83050	−0.369493
$250$	−26.5838	−1.68131
$251$	−18.5287	−1.16952	−0.584762	−	0.811205i	$-0.698812\pi$
$251$	−18.5287	−1.16952	−0.584762	+	0.811205i	$0.698812\pi$
$252$	0	0
$253$	29.5577	1.85828
$254$	3.67288	0.230457
$255$	−10.3516	−0.648241
$256$	1.00000	0.0625000
$257$	−22.0817	−1.37742	−0.688709	−	0.725038i	$-0.741822\pi$
$257$	−22.0817	−1.37742	−0.688709	+	0.725038i	$0.741822\pi$
$258$	−9.99871	−0.622492
$259$	0	0
$260$	7.58636	0.470486
$261$	−1.86424	−0.115394
$262$	7.40266	0.457338
$263$	11.4532	0.706234	0.353117	−	0.935579i	$-0.385122\pi$
$263$	11.4532	0.706234	0.353117	+	0.935579i	$0.385122\pi$
$264$	4.67159	0.287516
$265$	3.00710	0.184725
$266$	0	0
$267$	−5.45319	−0.333730
$268$	1.39500	0.0852131
$269$	10.7971	0.658311	0.329155	−	0.944276i	$-0.393236\pi$
$269$	10.7971	0.658311	0.329155	+	0.944276i	$0.393236\pi$
$270$	20.3329	1.23742
$271$	14.4616	0.878479	0.439239	−	0.898370i	$-0.355248\pi$
$271$	14.4616	0.878479	0.439239	+	0.898370i	$0.355248\pi$
$272$	−2.54552	−0.154345
$273$	0	0
$274$	−16.7719	−1.01323
$275$	−53.8967	−3.25009
$276$	−6.32712	−0.380848
$277$	−13.1487	−0.790027	−0.395014	−	0.918675i	$-0.629260\pi$
$277$	−13.1487	−0.790027	−0.395014	+	0.918675i	$0.629260\pi$
$278$	17.9224	1.07492
$279$	16.7732	1.00419
$280$	0	0
$281$	−23.3911	−1.39540	−0.697699	−	0.716391i	$-0.745793\pi$
$281$	−23.3911	−1.39540	−0.697699	+	0.716391i	$0.745793\pi$
$282$	−6.19266	−0.368767
$283$	−14.7871	−0.879000	−0.439500	−	0.898242i	$-0.644844\pi$
$283$	−14.7871	−0.879000	−0.439500	+	0.898242i	$0.644844\pi$
$284$	−14.1492	−0.839602
$285$	−26.2425	−1.55447
$286$	8.71502	0.515330
$287$	0	0
$288$	2.00000	0.117851
$289$	−10.5203	−0.618843
$290$	−3.79056	−0.222589
$291$	−1.00710	−0.0590374
$292$	1.45319	0.0850415
$293$	−15.0914	−0.881647	−0.440824	−	0.897594i	$-0.645314\pi$
$293$	−15.0914	−0.881647	−0.440824	+	0.897594i	$0.645314\pi$
$294$	0	0
$295$	−47.9056	−2.78917
$296$	1.78160	0.103553
$297$	23.3579	1.35537
$298$	−20.2145	−1.17100
$299$	−11.8035	−0.682612
$300$	11.5371	0.666096
$301$	0	0
$302$	−2.15762	−0.124157
$303$	−0.412346	−0.0236887
$304$	−6.45319	−0.370116
$305$	8.88774	0.508911
$306$	−5.09104	−0.291035
$307$	17.7787	1.01468	0.507341	−	0.861745i	$-0.330628\pi$
$307$	17.7787	1.01468	0.507341	+	0.861745i	$0.330628\pi$
$308$	0	0
$309$	10.8816	0.619032
$310$	34.1048	1.93703
$311$	−24.2508	−1.37514	−0.687570	−	0.726118i	$-0.741322\pi$
$311$	−24.2508	−1.37514	−0.687570	+	0.726118i	$0.741322\pi$
$312$	−1.86554	−0.105615
$313$	6.07369	0.343305	0.171653	−	0.985158i	$-0.445089\pi$
$313$	6.07369	0.343305	0.171653	+	0.985158i	$0.445089\pi$
$314$	−16.6037	−0.937002
$315$	0	0
$316$	−5.79895	−0.326216
$317$	9.97426	0.560210	0.280105	−	0.959969i	$-0.409631\pi$
$317$	9.97426	0.560210	0.280105	+	0.959969i	$0.409631\pi$
$318$	−0.739466	−0.0414672
$319$	−4.35449	−0.243805
$320$	4.06659	0.227329
$321$	−2.35286	−0.131324
$322$	0	0
$323$	16.4267	0.914007
$324$	1.00000	0.0555556
$325$	21.5229	1.19388
$326$	−10.2908	−0.569954
$327$	−19.0653	−1.05431
$328$	1.00000	0.0552158
$329$	0	0
$330$	18.9974	1.04577
$331$	6.56505	0.360848	0.180424	−	0.983589i	$-0.442253\pi$
$331$	6.56505	0.360848	0.180424	+	0.983589i	$0.442253\pi$
$332$	−5.83050	−0.319990
$333$	3.56320	0.195262
$334$	−10.9334	−0.598250
$335$	5.67288	0.309943
$336$	0	0
$337$	−21.3698	−1.16409	−0.582044	−	0.813157i	$-0.697747\pi$
$337$	−21.3698	−1.16409	−0.582044	+	0.813157i	$0.697747\pi$
$338$	9.51978	0.517808
$339$	−8.26053	−0.448651
$340$	−10.3516	−0.561393
$341$	39.1788	2.12165
$342$	−12.9064	−0.697897
$343$	0	0
$344$	−9.99871	−0.539094
$345$	−25.7298	−1.38524
$346$	17.8053	0.957220
$347$	−27.7617	−1.49032	−0.745162	−	0.666883i	$-0.767628\pi$
$347$	−27.7617	−1.49032	−0.745162	+	0.666883i	$0.767628\pi$
$348$	0.932122	0.0499670
$349$	−14.7871	−0.791534	−0.395767	−	0.918351i	$-0.629521\pi$
$349$	−14.7871	−0.791534	−0.395767	+	0.918351i	$0.629521\pi$
$350$	0	0
$351$	−9.32768	−0.497875
$352$	4.67159	0.248996
$353$	18.1856	0.967919	0.483960	−	0.875090i	$-0.339198\pi$
$353$	18.1856	0.967919	0.483960	+	0.875090i	$0.339198\pi$
$354$	11.7803	0.626116
$355$	−57.5391	−3.05386
$356$	−5.45319	−0.289018
$357$	0	0
$358$	−2.58765	−0.136762
$359$	5.18426	0.273615	0.136807	−	0.990598i	$-0.456316\pi$
$359$	5.18426	0.273615	0.136807	+	0.990598i	$0.456316\pi$
$360$	8.13317	0.428656
$361$	22.6437	1.19177
$362$	−5.19976	−0.273293
$363$	10.8237	0.568099
$364$	0	0
$365$	5.90952	0.309319
$366$	−2.18555	−0.114241
$367$	15.1016	0.788298	0.394149	−	0.919047i	$-0.371039\pi$
$367$	15.1016	0.788298	0.394149	+	0.919047i	$0.371039\pi$
$368$	−6.32712	−0.329824
$369$	2.00000	0.104116
$370$	7.24504	0.376652
$371$	0	0
$372$	−8.38660	−0.434825
$373$	−16.8890	−0.874481	−0.437240	−	0.899345i	$-0.644044\pi$
$373$	−16.8890	−0.874481	−0.437240	+	0.899345i	$0.644044\pi$
$374$	−11.8916	−0.614901
$375$	26.5838	1.37278
$376$	−6.19266	−0.319362
$377$	1.73891	0.0895583
$378$	0	0
$379$	24.6464	1.26600	0.633000	−	0.774151i	$-0.281823\pi$
$379$	24.6464	1.26600	0.633000	+	0.774151i	$0.281823\pi$
$380$	−26.2425	−1.34621
$381$	−3.67288	−0.188167
$382$	−8.73817	−0.447084
$383$	32.8527	1.67869	0.839347	−	0.543595i	$-0.182937\pi$
$383$	32.8527	1.67869	0.839347	+	0.543595i	$0.182937\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	1.88103	0.0957421
$387$	−19.9974	−1.01653
$388$	−1.00710	−0.0511279
$389$	14.9961	0.760334	0.380167	−	0.924918i	$-0.375867\pi$
$389$	14.9961	0.760334	0.380167	+	0.924918i	$0.375867\pi$
$390$	−7.58636	−0.384150
$391$	16.1058	0.814505
$392$	0	0
$393$	−7.40266	−0.373415
$394$	−17.7111	−0.892274
$395$	−23.5819	−1.18654
$396$	9.34318	0.469512
$397$	−0.858433	−0.0430835	−0.0215418	−	0.999768i	$-0.506857\pi$
$397$	−0.858433	−0.0430835	−0.0215418	+	0.999768i	$0.506857\pi$
$398$	−17.6703	−0.885732
$399$	0	0
$400$	11.5371	0.576856
$401$	−27.5340	−1.37498	−0.687491	−	0.726193i	$-0.741288\pi$
$401$	−27.5340	−1.37498	−0.687491	+	0.726193i	$0.741288\pi$
$402$	−1.39500	−0.0695762
$403$	−15.6455	−0.779358
$404$	−0.412346	−0.0205150
$405$	4.06659	0.202070
$406$	0	0
$407$	8.32291	0.412551
$408$	2.54552	0.126022
$409$	−32.1299	−1.58872	−0.794360	−	0.607448i	$-0.792193\pi$
$409$	−32.1299	−1.58872	−0.794360	+	0.607448i	$0.792193\pi$
$410$	4.06659	0.200834
$411$	16.7719	0.827298
$412$	10.8816	0.536098
$413$	0	0
$414$	−12.6542	−0.621922
$415$	−23.7102	−1.16389
$416$	−1.86554	−0.0914654
$417$	−17.9224	−0.877665
$418$	−30.1466	−1.47452
$419$	−7.62760	−0.372633	−0.186316	−	0.982490i	$-0.559655\pi$
$419$	−7.62760	−0.372633	−0.186316	+	0.982490i	$0.559655\pi$
$420$	0	0
$421$	14.8971	0.726040	0.363020	−	0.931781i	$-0.381746\pi$
$421$	14.8971	0.726040	0.363020	+	0.931781i	$0.381746\pi$
$422$	7.06715	0.344023
$423$	−12.3853	−0.602194
$424$	−0.739466	−0.0359117
$425$	−29.3680	−1.42456
$426$	14.1492	0.685532
$427$	0	0
$428$	−2.35286	−0.113730
$429$	−8.71502	−0.420765
$430$	−40.6606	−1.96083
$431$	−26.9659	−1.29890	−0.649450	−	0.760404i	$-0.725001\pi$
$431$	−26.9659	−1.29890	−0.649450	+	0.760404i	$0.725001\pi$
$432$	−5.00000	−0.240563
$433$	6.96660	0.334793	0.167397	−	0.985890i	$-0.446464\pi$
$433$	6.96660	0.334793	0.167397	+	0.985890i	$0.446464\pi$
$434$	0	0
$435$	3.79056	0.181743
$436$	−19.0653	−0.913062
$437$	40.8301	1.95317
$438$	−1.45319	−0.0694361
$439$	−10.8980	−0.520132	−0.260066	−	0.965591i	$-0.583744\pi$
$439$	−10.8980	−0.520132	−0.260066	+	0.965591i	$0.583744\pi$
$440$	18.9974	0.905666
$441$	0	0
$442$	4.74876	0.225875
$443$	6.82082	0.324067	0.162033	−	0.986785i	$-0.448195\pi$
$443$	6.82082	0.324067	0.162033	+	0.986785i	$0.448195\pi$
$444$	−1.78160	−0.0845511
$445$	−22.1759	−1.05124
$446$	19.9974	0.946905
$447$	20.2145	0.956114
$448$	0	0
$449$	−33.4085	−1.57664	−0.788322	−	0.615263i	$-0.789050\pi$
$449$	−33.4085	−1.57664	−0.788322	+	0.615263i	$0.789050\pi$
$450$	23.0742	1.08773
$451$	4.67159	0.219977
$452$	−8.26053	−0.388543
$453$	2.15762	0.101374
$454$	−21.3592	−1.00244
$455$	0	0
$456$	6.45319	0.302198
$457$	8.40339	0.393094	0.196547	−	0.980494i	$-0.437027\pi$
$457$	8.40339	0.393094	0.196547	+	0.980494i	$0.437027\pi$
$458$	−21.8372	−1.02039
$459$	12.7276	0.594073
$460$	−25.7298	−1.19966
$461$	−21.2470	−0.989570	−0.494785	−	0.869015i	$-0.664753\pi$
$461$	−21.2470	−0.989570	−0.494785	+	0.869015i	$0.664753\pi$
$462$	0	0
$463$	30.8283	1.43271	0.716355	−	0.697736i	$-0.245809\pi$
$463$	30.8283	1.43271	0.716355	+	0.697736i	$0.245809\pi$
$464$	0.932122	0.0432727
$465$	−34.1048	−1.58157
$466$	18.9672	0.878636
$467$	21.1324	0.977893	0.488946	−	0.872314i	$-0.337381\pi$
$467$	21.1324	0.977893	0.488946	+	0.872314i	$0.337381\pi$
$468$	−3.73107	−0.172469
$469$	0	0
$470$	−25.1830	−1.16160
$471$	16.6037	0.765059
$472$	11.7803	0.542233
$473$	−46.7098	−2.14772
$474$	5.79895	0.266355
$475$	−74.4513	−3.41606
$476$	0	0
$477$	−1.47893	−0.0677157
$478$	−25.1901	−1.15217
$479$	−13.5532	−0.619261	−0.309630	−	0.950857i	$-0.600205\pi$
$479$	−13.5532	−0.619261	−0.309630	+	0.950857i	$0.600205\pi$
$480$	−4.06659	−0.185613
$481$	−3.32364	−0.151545
$482$	−4.13317	−0.188261
$483$	0	0
$484$	10.8237	0.491988
$485$	−4.09547	−0.185966
$486$	−16.0000	−0.725775
$487$	−37.0392	−1.67841	−0.839204	−	0.543817i	$-0.816978\pi$
$487$	−37.0392	−1.67841	−0.839204	+	0.543817i	$0.816978\pi$
$488$	−2.18555	−0.0989353
$489$	10.2908	0.465366
$490$	0	0
$491$	−23.5847	−1.06436	−0.532182	−	0.846630i	$-0.678628\pi$
$491$	−23.5847	−1.06436	−0.532182	+	0.846630i	$0.678628\pi$
$492$	−1.00000	−0.0450835
$493$	−2.37273	−0.106863
$494$	12.0387	0.541645
$495$	37.9948	1.70774
$496$	−8.38660	−0.376570
$497$	0	0
$498$	5.83050	0.261271
$499$	−17.7288	−0.793651	−0.396826	−	0.917894i	$-0.629888\pi$
$499$	−17.7288	−0.793651	−0.396826	+	0.917894i	$0.629888\pi$
$500$	26.5838	1.18886
$501$	10.9334	0.488469
$502$	18.5287	0.826978
$503$	38.0691	1.69742	0.848708	−	0.528861i	$-0.177381\pi$
$503$	38.0691	1.69742	0.848708	+	0.528861i	$0.177381\pi$
$504$	0	0
$505$	−1.67684	−0.0746184
$506$	−29.5577	−1.31400
$507$	−9.51978	−0.422788
$508$	−3.67288	−0.162958
$509$	−4.33737	−0.192250	−0.0961252	−	0.995369i	$-0.530645\pi$
$509$	−4.33737	−0.192250	−0.0961252	+	0.995369i	$0.530645\pi$
$510$	10.3516	0.458375
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	32.2659	1.42458
$514$	22.0817	0.973981
$515$	44.2509	1.94993
$516$	9.99871	0.440169
$517$	−28.9295	−1.27232
$518$	0	0
$519$	−17.8053	−0.781567
$520$	−7.58636	−0.332684
$521$	−9.35213	−0.409724	−0.204862	−	0.978791i	$-0.565675\pi$
$521$	−9.35213	−0.409724	−0.204862	+	0.978791i	$0.565675\pi$
$522$	1.86424	0.0815958
$523$	−17.3445	−0.758421	−0.379210	−	0.925311i	$-0.623804\pi$
$523$	−17.3445	−0.758421	−0.379210	+	0.925311i	$0.623804\pi$
$524$	−7.40266	−0.323387
$525$	0	0
$526$	−11.4532	−0.499383
$527$	21.3483	0.929945
$528$	−4.67159	−0.203305
$529$	17.0324	0.740541
$530$	−3.00710	−0.130620
$531$	23.5606	1.02244
$532$	0	0
$533$	−1.86554	−0.0808053
$534$	5.45319	0.235983
$535$	−9.56812	−0.413666
$536$	−1.39500	−0.0602547
$537$	2.58765	0.111666
$538$	−10.7971	−0.465496
$539$	0	0
$540$	−20.3329	−0.874990
$541$	43.9961	1.89154	0.945771	−	0.324835i	$-0.105309\pi$
$541$	43.9961	1.89154	0.945771	+	0.324835i	$0.105309\pi$
$542$	−14.4616	−0.621178
$543$	5.19976	0.223143
$544$	2.54552	0.109138
$545$	−77.5307	−3.32105
$546$	0	0
$547$	23.6845	1.01268	0.506338	−	0.862335i	$-0.330999\pi$
$547$	23.6845	1.01268	0.506338	+	0.862335i	$0.330999\pi$
$548$	16.7719	0.716461
$549$	−4.37111	−0.186554
$550$	53.8967	2.29816
$551$	−6.01516	−0.256254
$552$	6.32712	0.269300
$553$	0	0
$554$	13.1487	0.558633
$555$	−7.24504	−0.307535
$556$	−17.9224	−0.760081
$557$	−3.08612	−0.130763	−0.0653816	−	0.997860i	$-0.520826\pi$
$557$	−3.08612	−0.130763	−0.0653816	+	0.997860i	$0.520826\pi$
$558$	−16.7732	−0.710066
$559$	18.6529	0.788936
$560$	0	0
$561$	11.8916	0.502064
$562$	23.3911	0.986695
$563$	12.4776	0.525870	0.262935	−	0.964814i	$-0.415310\pi$
$563$	12.4776	0.525870	0.262935	+	0.964814i	$0.415310\pi$
$564$	6.19266	0.260758
$565$	−33.5922	−1.41323
$566$	14.7871	0.621547
$567$	0	0
$568$	14.1492	0.593688
$569$	28.5380	1.19638	0.598188	−	0.801356i	$-0.295888\pi$
$569$	28.5380	1.19638	0.598188	+	0.801356i	$0.295888\pi$
$570$	26.2425	1.09918
$571$	−16.0071	−0.669876	−0.334938	−	0.942240i	$-0.608715\pi$
$571$	−16.0071	−0.669876	−0.334938	+	0.942240i	$0.608715\pi$
$572$	−8.71502	−0.364393
$573$	8.73817	0.365042
$574$	0	0
$575$	−72.9968	−3.04418
$576$	−2.00000	−0.0833333
$577$	34.3632	1.43056	0.715279	−	0.698839i	$-0.246300\pi$
$577$	34.3632	1.43056	0.715279	+	0.698839i	$0.246300\pi$
$578$	10.5203	0.437588
$579$	−1.88103	−0.0781731
$580$	3.79056	0.157394
$581$	0	0
$582$	1.00710	0.0417458
$583$	−3.45448	−0.143070
$584$	−1.45319	−0.0601334
$585$	−15.1727	−0.627315
$586$	15.0914	0.623419
$587$	−21.3063	−0.879405	−0.439702	−	0.898144i	$-0.644916\pi$
$587$	−21.3063	−0.879405	−0.439702	+	0.898144i	$0.644916\pi$
$588$	0	0
$589$	54.1203	2.22999
$590$	47.9056	1.97224
$591$	17.7111	0.728539
$592$	−1.78160	−0.0732234
$593$	−19.0547	−0.782483	−0.391242	−	0.920288i	$-0.627954\pi$
$593$	−19.0547	−0.782483	−0.391242	+	0.920288i	$0.627954\pi$
$594$	−23.3579	−0.958388
$595$	0	0
$596$	20.2145	0.828019
$597$	17.6703	0.723197
$598$	11.8035	0.482680
$599$	−38.2056	−1.56104	−0.780519	−	0.625133i	$-0.785045\pi$
$599$	−38.2056	−1.56104	−0.780519	+	0.625133i	$0.785045\pi$
$600$	−11.5371	−0.471001
$601$	−20.4940	−0.835969	−0.417985	−	0.908454i	$-0.637263\pi$
$601$	−20.4940	−0.835969	−0.417985	+	0.908454i	$0.637263\pi$
$602$	0	0
$603$	−2.79000	−0.113617
$604$	2.15762	0.0877925
$605$	44.0157	1.78949
$606$	0.412346	0.0167504
$607$	15.9016	0.645426	0.322713	−	0.946497i	$-0.395405\pi$
$607$	15.9016	0.645426	0.322713	+	0.946497i	$0.395405\pi$
$608$	6.45319	0.261711
$609$	0	0
$610$	−8.88774	−0.359854
$611$	11.5526	0.467369
$612$	5.09104	0.205793
$613$	−0.543668	−0.0219585	−0.0109793	−	0.999940i	$-0.503495\pi$
$613$	−0.543668	−0.0219585	−0.0109793	+	0.999940i	$0.503495\pi$
$614$	−17.7787	−0.717489
$615$	−4.06659	−0.163981
$616$	0	0
$617$	28.7179	1.15614	0.578070	−	0.815987i	$-0.303806\pi$
$617$	28.7179	1.15614	0.578070	+	0.815987i	$0.303806\pi$
$618$	−10.8816	−0.437722
$619$	44.5340	1.78997	0.894986	−	0.446094i	$-0.147185\pi$
$619$	44.5340	1.78997	0.894986	+	0.446094i	$0.147185\pi$
$620$	−34.1048	−1.36968
$621$	31.6356	1.26949
$622$	24.2508	0.972370
$623$	0	0
$624$	1.86554	0.0746812
$625$	50.4196	2.01678
$626$	−6.07369	−0.242753
$627$	30.1466	1.20394
$628$	16.6037	0.662560
$629$	4.53510	0.180826
$630$	0	0
$631$	8.21969	0.327221	0.163610	−	0.986525i	$-0.447686\pi$
$631$	8.21969	0.327221	0.163610	+	0.986525i	$0.447686\pi$
$632$	5.79895	0.230670
$633$	−7.06715	−0.280894
$634$	−9.97426	−0.396128
$635$	−14.9361	−0.592720
$636$	0.739466	0.0293217
$637$	0	0
$638$	4.35449	0.172396
$639$	28.2985	1.11947
$640$	−4.06659	−0.160746
$641$	30.2882	1.19631	0.598156	−	0.801380i	$-0.295900\pi$
$641$	30.2882	1.19631	0.598156	+	0.801380i	$0.295900\pi$
$642$	2.35286	0.0928601
$643$	21.1138	0.832647	0.416324	−	0.909217i	$-0.363318\pi$
$643$	21.1138	0.832647	0.416324	+	0.909217i	$0.363318\pi$
$644$	0	0
$645$	40.6606	1.60101
$646$	−16.4267	−0.646300
$647$	14.7031	0.578040	0.289020	−	0.957323i	$-0.406671\pi$
$647$	14.7031	0.578040	0.289020	+	0.957323i	$0.406671\pi$
$648$	−1.00000	−0.0392837
$649$	55.0328	2.16022
$650$	−21.5229	−0.844198
$651$	0	0
$652$	10.2908	0.403019
$653$	−21.3743	−0.836442	−0.418221	−	0.908345i	$-0.637346\pi$
$653$	−21.3743	−0.836442	−0.418221	+	0.908345i	$0.637346\pi$
$654$	19.0653	0.745512
$655$	−30.1036	−1.17624
$656$	−1.00000	−0.0390434
$657$	−2.90638	−0.113389
$658$	0	0
$659$	−32.2727	−1.25717	−0.628583	−	0.777742i	$-0.716365\pi$
$659$	−32.2727	−1.25717	−0.628583	+	0.777742i	$0.716365\pi$
$660$	−18.9974	−0.739473
$661$	22.4725	0.874078	0.437039	−	0.899443i	$-0.356027\pi$
$661$	22.4725	0.874078	0.437039	+	0.899443i	$0.356027\pi$
$662$	−6.56505	−0.255158
$663$	−4.74876	−0.184426
$664$	5.83050	0.226267
$665$	0	0
$666$	−3.56320	−0.138071
$667$	−5.89765	−0.228358
$668$	10.9334	0.423026
$669$	−19.9974	−0.773145
$670$	−5.67288	−0.219162
$671$	−10.2100	−0.394153
$672$	0	0
$673$	9.42874	0.363451	0.181726	−	0.983349i	$-0.441832\pi$
$673$	9.42874	0.363451	0.181726	+	0.983349i	$0.441832\pi$
$674$	21.3698	0.823134
$675$	−57.6856	−2.22032
$676$	−9.51978	−0.366145
$677$	−28.5745	−1.09821	−0.549103	−	0.835754i	$-0.685031\pi$
$677$	−28.5745	−1.09821	−0.549103	+	0.835754i	$0.685031\pi$
$678$	8.26053	0.317244
$679$	0	0
$680$	10.3516	0.396965
$681$	21.3592	0.818488
$682$	−39.1788	−1.50023
$683$	−21.7608	−0.832653	−0.416326	−	0.909215i	$-0.636683\pi$
$683$	−21.7608	−0.832653	−0.416326	+	0.909215i	$0.636683\pi$
$684$	12.9064	0.493488
$685$	68.2044	2.60596
$686$	0	0
$687$	21.8372	0.833142
$688$	9.99871	0.381197
$689$	1.37950	0.0525548
$690$	25.7298	0.979516
$691$	−16.6111	−0.631918	−0.315959	−	0.948773i	$-0.602326\pi$
$691$	−16.6111	−0.631918	−0.315959	+	0.948773i	$0.602326\pi$
$692$	−17.8053	−0.676857
$693$	0	0
$694$	27.7617	1.05382
$695$	−72.8831	−2.76461
$696$	−0.932122	−0.0353320
$697$	2.54552	0.0964184
$698$	14.7871	0.559699
$699$	−18.9672	−0.717404
$700$	0	0
$701$	−33.1306	−1.25133	−0.625663	−	0.780094i	$-0.715171\pi$
$701$	−33.1306	−1.25133	−0.625663	+	0.780094i	$0.715171\pi$
$702$	9.32768	0.352051
$703$	11.4970	0.433618
$704$	−4.67159	−0.176067
$705$	25.1830	0.948446
$706$	−18.1856	−0.684422
$707$	0	0
$708$	−11.7803	−0.442731
$709$	23.5761	0.885420	0.442710	−	0.896665i	$-0.354017\pi$
$709$	23.5761	0.885420	0.442710	+	0.896665i	$0.354017\pi$
$710$	57.5391	2.15940
$711$	11.5979	0.434955
$712$	5.45319	0.204367
$713$	53.0630	1.98723
$714$	0	0
$715$	−35.4404	−1.32539
$716$	2.58765	0.0967052
$717$	25.1901	0.940741
$718$	−5.18426	−0.193475
$719$	17.2647	0.643865	0.321933	−	0.946763i	$-0.395668\pi$
$719$	17.2647	0.643865	0.321933	+	0.946763i	$0.395668\pi$
$720$	−8.13317	−0.303105
$721$	0	0
$722$	−22.6437	−0.842710
$723$	4.13317	0.153714
$724$	5.19976	0.193248
$725$	10.7540	0.399394
$726$	−10.8237	−0.401707
$727$	20.6103	0.764392	0.382196	−	0.924081i	$-0.375168\pi$
$727$	20.6103	0.764392	0.382196	+	0.924081i	$0.375168\pi$
$728$	0	0
$729$	13.0000	0.481481
$730$	−5.90952	−0.218721
$731$	−25.4519	−0.941372
$732$	2.18555	0.0807804
$733$	−21.2463	−0.784751	−0.392376	−	0.919805i	$-0.628347\pi$
$733$	−21.2463	−0.784751	−0.392376	+	0.919805i	$0.628347\pi$
$734$	−15.1016	−0.557411
$735$	0	0
$736$	6.32712	0.233221
$737$	−6.51686	−0.240051
$738$	−2.00000	−0.0736210
$739$	−31.7427	−1.16767	−0.583837	−	0.811871i	$-0.698449\pi$
$739$	−31.7427	−1.16767	−0.583837	+	0.811871i	$0.698449\pi$
$740$	−7.24504	−0.266333
$741$	−12.0387	−0.442251
$742$	0	0
$743$	36.1357	1.32569	0.662845	−	0.748757i	$-0.269349\pi$
$743$	36.1357	1.32569	0.662845	+	0.748757i	$0.269349\pi$
$744$	8.38660	0.307468
$745$	82.2041	3.01173
$746$	16.8890	0.618351
$747$	11.6610	0.426654
$748$	11.8916	0.434800
$749$	0	0
$750$	−26.5838	−0.970702
$751$	−5.93049	−0.216407	−0.108203	−	0.994129i	$-0.534510\pi$
$751$	−5.93049	−0.216407	−0.108203	+	0.994129i	$0.534510\pi$
$752$	6.19266	0.225823
$753$	−18.5287	−0.675224
$754$	−1.73891	−0.0633273
$755$	8.77416	0.319324
$756$	0	0
$757$	−23.5475	−0.855847	−0.427923	−	0.903815i	$-0.640755\pi$
$757$	−23.5475	−0.855847	−0.427923	+	0.903815i	$0.640755\pi$
$758$	−24.6464	−0.895198
$759$	29.5577	1.07288
$760$	26.2425	0.951914
$761$	48.0312	1.74113	0.870564	−	0.492055i	$-0.163754\pi$
$761$	48.0312	1.74113	0.870564	+	0.492055i	$0.163754\pi$
$762$	3.67288	0.133054
$763$	0	0
$764$	8.73817	0.316136
$765$	20.7031	0.748524
$766$	−32.8527	−1.18702
$767$	−21.9766	−0.793529
$768$	1.00000	0.0360844
$769$	−25.8237	−0.931228	−0.465614	−	0.884988i	$-0.654166\pi$
$769$	−25.8237	−0.931228	−0.465614	+	0.884988i	$0.654166\pi$
$770$	0	0
$771$	−22.0817	−0.795253
$772$	−1.88103	−0.0676999
$773$	−9.71953	−0.349587	−0.174794	−	0.984605i	$-0.555926\pi$
$773$	−9.71953	−0.349587	−0.174794	+	0.984605i	$0.555926\pi$
$774$	19.9974	0.718792
$775$	−96.7573	−3.47562
$776$	1.00710	0.0361529
$777$	0	0
$778$	−14.9961	−0.537637
$779$	6.45319	0.231210
$780$	7.58636	0.271635
$781$	66.0994	2.36522
$782$	−16.1058	−0.575942
$783$	−4.66061	−0.166557
$784$	0	0
$785$	67.5204	2.40991
$786$	7.40266	0.264044
$787$	−4.61921	−0.164657	−0.0823285	−	0.996605i	$-0.526236\pi$
$787$	−4.61921	−0.164657	−0.0823285	+	0.996605i	$0.526236\pi$
$788$	17.7111	0.630933
$789$	11.4532	0.407744
$790$	23.5819	0.839007
$791$	0	0
$792$	−9.34318	−0.331995
$793$	4.07723	0.144787
$794$	0.858433	0.0304646
$795$	3.00710	0.106651
$796$	17.6703	0.626307
$797$	−1.43865	−0.0509595	−0.0254798	−	0.999675i	$-0.508111\pi$
$797$	−1.43865	−0.0509595	−0.0254798	+	0.999675i	$0.508111\pi$
$798$	0	0
$799$	−15.7635	−0.557673
$800$	−11.5371	−0.407899
$801$	10.9064	0.385358
$802$	27.5340	0.972259
$803$	−6.78870	−0.239568
$804$	1.39500	0.0491978
$805$	0	0
$806$	15.6455	0.551090
$807$	10.7971	0.380076
$808$	0.412346	0.0145063
$809$	−0.619208	−0.0217702	−0.0108851	−	0.999941i	$-0.503465\pi$
$809$	−0.619208	−0.0217702	−0.0108851	+	0.999941i	$0.503465\pi$
$810$	−4.06659	−0.142885
$811$	11.0534	0.388138	0.194069	−	0.980988i	$-0.437831\pi$
$811$	11.0534	0.388138	0.194069	+	0.980988i	$0.437831\pi$
$812$	0	0
$813$	14.4616	0.507190
$814$	−8.32291	−0.291718
$815$	41.8484	1.46589
$816$	−2.54552	−0.0891110
$817$	−64.5236	−2.25739
$818$	32.1299	1.12339
$819$	0	0
$820$	−4.06659	−0.142011
$821$	−44.9228	−1.56782	−0.783908	−	0.620877i	$-0.786777\pi$
$821$	−44.9228	−1.56782	−0.783908	+	0.620877i	$0.786777\pi$
$822$	−16.7719	−0.584988
$823$	−11.0182	−0.384072	−0.192036	−	0.981388i	$-0.561509\pi$
$823$	−11.0182	−0.384072	−0.192036	+	0.981388i	$0.561509\pi$
$824$	−10.8816	−0.379078
$825$	−53.8967	−1.87644
$826$	0	0
$827$	−29.1611	−1.01403	−0.507015	−	0.861937i	$-0.669251\pi$
$827$	−29.1611	−1.01403	−0.507015	+	0.861937i	$0.669251\pi$
$828$	12.6542	0.439765
$829$	−13.0122	−0.451932	−0.225966	−	0.974135i	$-0.572554\pi$
$829$	−13.0122	−0.451932	−0.225966	+	0.974135i	$0.572554\pi$
$830$	23.7102	0.822995
$831$	−13.1487	−0.456122
$832$	1.86554	0.0646758
$833$	0	0
$834$	17.9224	0.620603
$835$	44.4617	1.53866
$836$	30.1466	1.04264
$837$	41.9330	1.44942
$838$	7.62760	0.263491
$839$	−37.4822	−1.29403	−0.647014	−	0.762478i	$-0.723982\pi$
$839$	−37.4822	−1.29403	−0.647014	+	0.762478i	$0.723982\pi$
$840$	0	0
$841$	−28.1311	−0.970040
$842$	−14.8971	−0.513388
$843$	−23.3911	−0.805633
$844$	−7.06715	−0.243261
$845$	−38.7130	−1.33177
$846$	12.3853	0.425816
$847$	0	0
$848$	0.739466	0.0253934
$849$	−14.7871	−0.507491
$850$	29.3680	1.00731
$851$	11.2724	0.386413
$852$	−14.1492	−0.484745
$853$	−27.5677	−0.943901	−0.471950	−	0.881625i	$-0.656450\pi$
$853$	−27.5677	−0.943901	−0.471950	+	0.881625i	$0.656450\pi$
$854$	0	0
$855$	52.4849	1.79495
$856$	2.35286	0.0804192
$857$	−41.6520	−1.42280	−0.711402	−	0.702785i	$-0.751940\pi$
$857$	−41.6520	−1.42280	−0.711402	+	0.702785i	$0.751940\pi$
$858$	8.71502	0.297526
$859$	−10.8520	−0.370265	−0.185132	−	0.982714i	$-0.559271\pi$
$859$	−10.8520	−0.370265	−0.185132	+	0.982714i	$0.559271\pi$
$860$	40.6606	1.38652
$861$	0	0
$862$	26.9659	0.918461
$863$	−14.6477	−0.498613	−0.249307	−	0.968425i	$-0.580203\pi$
$863$	−14.6477	−0.498613	−0.249307	+	0.968425i	$0.580203\pi$
$864$	5.00000	0.170103
$865$	−72.4069	−2.46191
$866$	−6.96660	−0.236735
$867$	−10.5203	−0.357289
$868$	0	0
$869$	27.0903	0.918976
$870$	−3.79056	−0.128512
$871$	2.60242	0.0881796
$872$	19.0653	0.645632
$873$	2.01421	0.0681705
$874$	−40.8301	−1.38110
$875$	0	0
$876$	1.45319	0.0490987
$877$	46.2837	1.56289	0.781445	−	0.623975i	$-0.214483\pi$
$877$	46.2837	1.56289	0.781445	+	0.623975i	$0.214483\pi$
$878$	10.8980	0.367789
$879$	−15.0914	−0.509019
$880$	−18.9974	−0.640403
$881$	−34.3406	−1.15696	−0.578482	−	0.815695i	$-0.696355\pi$
$881$	−34.3406	−1.15696	−0.578482	+	0.815695i	$0.696355\pi$
$882$	0	0
$883$	−17.2734	−0.581298	−0.290649	−	0.956830i	$-0.593871\pi$
$883$	−17.2734	−0.581298	−0.290649	+	0.956830i	$0.593871\pi$
$884$	−4.74876	−0.159718
$885$	−47.9056	−1.61033
$886$	−6.82082	−0.229150
$887$	7.19920	0.241725	0.120863	−	0.992669i	$-0.461434\pi$
$887$	7.19920	0.241725	0.120863	+	0.992669i	$0.461434\pi$
$888$	1.78160	0.0597866
$889$	0	0
$890$	22.1759	0.743337
$891$	−4.67159	−0.156504
$892$	−19.9974	−0.669563
$893$	−39.9624	−1.33729
$894$	−20.2145	−0.676075
$895$	10.5229	0.351742
$896$	0	0
$897$	−11.8035	−0.394106
$898$	33.4085	1.11486
$899$	−7.81734	−0.260723
$900$	−23.0742	−0.769142
$901$	−1.88232	−0.0627093
$902$	−4.67159	−0.155547
$903$	0	0
$904$	8.26053	0.274741
$905$	21.1453	0.702892
$906$	−2.15762	−0.0716822
$907$	−9.26579	−0.307665	−0.153833	−	0.988097i	$-0.549162\pi$
$907$	−9.26579	−0.307665	−0.153833	+	0.988097i	$0.549162\pi$
$908$	21.3592	0.708831
$909$	0.824692	0.0273533
$910$	0	0
$911$	29.6538	0.982476	0.491238	−	0.871025i	$-0.336545\pi$
$911$	29.6538	0.982476	0.491238	+	0.871025i	$0.336545\pi$
$912$	−6.45319	−0.213686
$913$	27.2377	0.901437
$914$	−8.40339	−0.277960
$915$	8.88774	0.293820
$916$	21.8372	0.721522
$917$	0	0
$918$	−12.7276	−0.420073
$919$	−4.97426	−0.164086	−0.0820428	−	0.996629i	$-0.526144\pi$
$919$	−4.97426	−0.164086	−0.0820428	+	0.996629i	$0.526144\pi$
$920$	25.7298	0.848286
$921$	17.7787	0.585827
$922$	21.2470	0.699732
$923$	−26.3959	−0.868831
$924$	0	0
$925$	−20.5546	−0.675830
$926$	−30.8283	−1.01308
$927$	−21.7632	−0.714797
$928$	−0.932122	−0.0305984
$929$	−45.1116	−1.48006	−0.740032	−	0.672572i	$-0.765190\pi$
$929$	−45.1116	−1.48006	−0.740032	+	0.672572i	$0.765190\pi$
$930$	34.1048	1.11834
$931$	0	0
$932$	−18.9672	−0.621290
$933$	−24.2508	−0.793937
$934$	−21.1324	−0.691475
$935$	48.3583	1.58148
$936$	3.73107	0.121954
$937$	48.6606	1.58967	0.794836	−	0.606824i	$-0.207557\pi$
$937$	48.6606	1.58967	0.794836	+	0.606824i	$0.207557\pi$
$938$	0	0
$939$	6.07369	0.198207
$940$	25.1830	0.821378
$941$	−33.9022	−1.10518	−0.552590	−	0.833454i	$-0.686360\pi$
$941$	−33.9022	−1.10518	−0.552590	+	0.833454i	$0.686360\pi$
$942$	−16.6037	−0.540978
$943$	6.32712	0.206039
$944$	−11.7803	−0.383416
$945$	0	0
$946$	46.7098	1.51867
$947$	6.64237	0.215848	0.107924	−	0.994159i	$-0.465580\pi$
$947$	6.64237	0.215848	0.107924	+	0.994159i	$0.465580\pi$
$948$	−5.79895	−0.188341
$949$	2.71098	0.0880021
$950$	74.4513	2.41552
$951$	9.97426	0.323437
$952$	0	0
$953$	−48.6772	−1.57681	−0.788405	−	0.615157i	$-0.789093\pi$
$953$	−48.6772	−1.57681	−0.788405	+	0.615157i	$0.789093\pi$
$954$	1.47893	0.0478822
$955$	35.5345	1.14987
$956$	25.1901	0.814705
$957$	−4.35449	−0.140761
$958$	13.5532	0.437883
$959$	0	0
$960$	4.06659	0.131249
$961$	39.3351	1.26887
$962$	3.32364	0.107159
$963$	4.70573	0.151640
$964$	4.13317	0.133121
$965$	−7.64938	−0.246242
$966$	0	0
$967$	42.1470	1.35536	0.677678	−	0.735359i	$-0.262986\pi$
$967$	42.1470	1.35536	0.677678	+	0.735359i	$0.262986\pi$
$968$	−10.8237	−0.347888
$969$	16.4267	0.527702
$970$	4.09547	0.131498
$971$	−14.6609	−0.470492	−0.235246	−	0.971936i	$-0.575590\pi$
$971$	−14.6609	−0.470492	−0.235246	+	0.971936i	$0.575590\pi$
$972$	16.0000	0.513200
$973$	0	0
$974$	37.0392	1.18681
$975$	21.5229	0.689285
$976$	2.18555	0.0699578
$977$	38.3282	1.22623	0.613113	−	0.789995i	$-0.289917\pi$
$977$	38.3282	1.22623	0.613113	+	0.789995i	$0.289917\pi$
$978$	−10.2908	−0.329063
$979$	25.4751	0.814186
$980$	0	0
$981$	38.1306	1.21742
$982$	23.5847	0.752619
$983$	23.3991	0.746316	0.373158	−	0.927768i	$-0.378275\pi$
$983$	23.3991	0.746316	0.373158	+	0.927768i	$0.378275\pi$
$984$	1.00000	0.0318788
$985$	72.0239	2.29487
$986$	2.37273	0.0755632
$987$	0	0
$988$	−12.0387	−0.383001
$989$	−63.2630	−2.01165
$990$	−37.9948	−1.20756
$991$	50.4325	1.60204	0.801021	−	0.598636i	$-0.204290\pi$
$991$	50.4325	1.60204	0.801021	+	0.598636i	$0.204290\pi$
$992$	8.38660	0.266275
$993$	6.56505	0.208336
$994$	0	0
$995$	71.8578	2.27804
$996$	−5.83050	−0.184747
$997$	−6.46925	−0.204883	−0.102442	−	0.994739i	$-0.532665\pi$
$997$	−6.46925	−0.204883	−0.102442	+	0.994739i	$0.532665\pi$
$998$	17.7288	0.561196
$999$	8.90801	0.281837

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4018.2.a.bk.1.4		4
7.2	even	3		574.2.e.f.165.1	✓	8
7.4	even	3		574.2.e.f.247.1	yes	8
7.6	odd	2		4018.2.a.bi.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
574.2.e.f.165.1	✓	8	7.2	even	3
574.2.e.f.247.1	yes	8	7.4	even	3
4018.2.a.bi.1.1		4	7.6	odd	2
4018.2.a.bk.1.4		4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.06659 q^{5} -1.00000 q^{6} -1.00000 q^{8} -2.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.06659 q^{5} -1.00000 q^{6} -1.00000 q^{8} -2.00000 q^{9} -4.06659 q^{10} -4.67159 q^{11} +1.00000 q^{12} +1.86554 q^{13} +4.06659 q^{15} +1.00000 q^{16} -2.54552 q^{17} +2.00000 q^{18} -6.45319 q^{19} +4.06659 q^{20} +4.67159 q^{22} -6.32712 q^{23} -1.00000 q^{24} +11.5371 q^{25} -1.86554 q^{26} -5.00000 q^{27} +0.932122 q^{29} -4.06659 q^{30} -8.38660 q^{31} -1.00000 q^{32} -4.67159 q^{33} +2.54552 q^{34} -2.00000 q^{36} -1.78160 q^{37} +6.45319 q^{38} +1.86554 q^{39} -4.06659 q^{40} -1.00000 q^{41} +9.99871 q^{43} -4.67159 q^{44} -8.13317 q^{45} +6.32712 q^{46} +6.19266 q^{47} +1.00000 q^{48} -11.5371 q^{50} -2.54552 q^{51} +1.86554 q^{52} +0.739466 q^{53} +5.00000 q^{54} -18.9974 q^{55} -6.45319 q^{57} -0.932122 q^{58} -11.7803 q^{59} +4.06659 q^{60} +2.18555 q^{61} +8.38660 q^{62} +1.00000 q^{64} +7.58636 q^{65} +4.67159 q^{66} +1.39500 q^{67} -2.54552 q^{68} -6.32712 q^{69} -14.1492 q^{71} +2.00000 q^{72} +1.45319 q^{73} +1.78160 q^{74} +11.5371 q^{75} -6.45319 q^{76} -1.86554 q^{78} -5.79895 q^{79} +4.06659 q^{80} +1.00000 q^{81} +1.00000 q^{82} -5.83050 q^{83} -10.3516 q^{85} -9.99871 q^{86} +0.932122 q^{87} +4.67159 q^{88} -5.45319 q^{89} +8.13317 q^{90} -6.32712 q^{92} -8.38660 q^{93} -6.19266 q^{94} -26.2425 q^{95} -1.00000 q^{96} -1.00710 q^{97} +9.34318 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} + 3 q^{5} - 4 q^{6} - 4 q^{8} - 8 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 + 3 * q^5 - 4 * q^6 - 4 * q^8 - 8 * q^9	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} + 3 q^{5} - 4 q^{6} - 4 q^{8} - 8 q^{9} - 3 q^{10} + 4 q^{12} - q^{13} + 3 q^{15} + 4 q^{16} - 3 q^{17} + 8 q^{18} + 2 q^{19} + 3 q^{20} - 9 q^{23} - 4 q^{24} + 19 q^{25} + q^{26} - 20 q^{27} - 18 q^{29} - 3 q^{30} - 19 q^{31} - 4 q^{32} + 3 q^{34} - 8 q^{36} + 2 q^{37} - 2 q^{38} - q^{39} - 3 q^{40} - 4 q^{41} + 5 q^{43} - 6 q^{45} + 9 q^{46} + 4 q^{48} - 19 q^{50} - 3 q^{51} - q^{52} + 6 q^{53} + 20 q^{54} - 6 q^{55} + 2 q^{57} + 18 q^{58} - 3 q^{59} + 3 q^{60} - q^{61} + 19 q^{62} + 4 q^{64} - 24 q^{65} + 11 q^{67} - 3 q^{68} - 9 q^{69} - 9 q^{71} + 8 q^{72} - 22 q^{73} - 2 q^{74} + 19 q^{75} + 2 q^{76} + q^{78} - 28 q^{79} + 3 q^{80} + 4 q^{81} + 4 q^{82} - 12 q^{83} - 24 q^{85} - 5 q^{86} - 18 q^{87} + 6 q^{89} + 6 q^{90} - 9 q^{92} - 19 q^{93} - 27 q^{95} - 4 q^{96} + 11 q^{97}+O(q^{100}) \) 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 + 3 * q^5 - 4 * q^6 - 4 * q^8 - 8 * q^9 - 3 * q^10 + 4 * q^12 - q^13 + 3 * q^15 + 4 * q^16 - 3 * q^17 + 8 * q^18 + 2 * q^19 + 3 * q^20 - 9 * q^23 - 4 * q^24 + 19 * q^25 + q^26 - 20 * q^27 - 18 * q^29 - 3 * q^30 - 19 * q^31 - 4 * q^32 + 3 * q^34 - 8 * q^36 + 2 * q^37 - 2 * q^38 - q^39 - 3 * q^40 - 4 * q^41 + 5 * q^43 - 6 * q^45 + 9 * q^46 + 4 * q^48 - 19 * q^50 - 3 * q^51 - q^52 + 6 * q^53 + 20 * q^54 - 6 * q^55 + 2 * q^57 + 18 * q^58 - 3 * q^59 + 3 * q^60 - q^61 + 19 * q^62 + 4 * q^64 - 24 * q^65 + 11 * q^67 - 3 * q^68 - 9 * q^69 - 9 * q^71 + 8 * q^72 - 22 * q^73 - 2 * q^74 + 19 * q^75 + 2 * q^76 + q^78 - 28 * q^79 + 3 * q^80 + 4 * q^81 + 4 * q^82 - 12 * q^83 - 24 * q^85 - 5 * q^86 - 18 * q^87 + 6 * q^89 + 6 * q^90 - 9 * q^92 - 19 * q^93 - 27 * q^95 - 4 * q^96 + 11 * q^97

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