LMFDB - Embedded newform 6027.2.a.bn.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6027,2,Mod(1,6027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6027, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6027 = 3 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6027.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:	$48.1258372982$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	6027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.37986 q^{2} -1.00000 q^{3} +3.66372 q^{4} -3.68734 q^{5} +2.37986 q^{6} -3.95941 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.37986 q^{2} -1.00000 q^{3} +3.66372 q^{4} -3.68734 q^{5} +2.37986 q^{6} -3.95941 q^{8} +1.00000 q^{9} +8.77534 q^{10} -6.26313 q^{11} -3.66372 q^{12} +3.25624 q^{13} +3.68734 q^{15} +2.09539 q^{16} -0.146265 q^{17} -2.37986 q^{18} +1.78602 q^{19} -13.5094 q^{20} +14.9053 q^{22} -3.11368 q^{23} +3.95941 q^{24} +8.59647 q^{25} -7.74938 q^{26} -1.00000 q^{27} +4.08462 q^{29} -8.77534 q^{30} -1.31731 q^{31} +2.93209 q^{32} +6.26313 q^{33} +0.348089 q^{34} +3.66372 q^{36} +3.67591 q^{37} -4.25047 q^{38} -3.25624 q^{39} +14.5997 q^{40} +1.00000 q^{41} -9.08247 q^{43} -22.9463 q^{44} -3.68734 q^{45} +7.41011 q^{46} -11.5238 q^{47} -2.09539 q^{48} -20.4584 q^{50} +0.146265 q^{51} +11.9299 q^{52} +4.41701 q^{53} +2.37986 q^{54} +23.0943 q^{55} -1.78602 q^{57} -9.72081 q^{58} -1.71894 q^{59} +13.5094 q^{60} -6.02287 q^{61} +3.13502 q^{62} -11.1687 q^{64} -12.0069 q^{65} -14.9053 q^{66} +1.38835 q^{67} -0.535872 q^{68} +3.11368 q^{69} +8.92495 q^{71} -3.95941 q^{72} -8.93911 q^{73} -8.74814 q^{74} -8.59647 q^{75} +6.54346 q^{76} +7.74938 q^{78} -10.3689 q^{79} -7.72642 q^{80} +1.00000 q^{81} -2.37986 q^{82} +10.6436 q^{83} +0.539327 q^{85} +21.6150 q^{86} -4.08462 q^{87} +24.7983 q^{88} +1.75624 q^{89} +8.77534 q^{90} -11.4076 q^{92} +1.31731 q^{93} +27.4251 q^{94} -6.58565 q^{95} -2.93209 q^{96} -5.53442 q^{97} -6.26313 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{2} - 24 q^{3} + 32 q^{4} - 4 q^{5} - 8 q^{6} + 24 q^{8} + 24 q^{9}+O(q^{10}) $ 24 * q + 8 * q^2 - 24 * q^3 + 32 * q^4 - 4 * q^5 - 8 * q^6 + 24 * q^8 + 24 * q^9	$ 24 q + 8 q^{2} - 24 q^{3} + 32 q^{4} - 4 q^{5} - 8 q^{6} + 24 q^{8} + 24 q^{9} + 4 q^{10} + 12 q^{11} - 32 q^{12} + 4 q^{15} + 44 q^{16} - 8 q^{17} + 8 q^{18} + 4 q^{19} - 28 q^{20} + 16 q^{22} + 20 q^{23} - 24 q^{24} + 48 q^{25} - 32 q^{26} - 24 q^{27} + 24 q^{29} - 4 q^{30} + 4 q^{31} + 36 q^{32} - 12 q^{33} - 16 q^{34} + 32 q^{36} + 64 q^{37} - 20 q^{38} + 48 q^{40} + 24 q^{41} + 20 q^{43} + 48 q^{44} - 4 q^{45} + 28 q^{46} - 32 q^{47} - 44 q^{48} - 20 q^{50} + 8 q^{51} + 76 q^{53} - 8 q^{54} + 24 q^{55} - 4 q^{57} + 28 q^{58} - 28 q^{59} + 28 q^{60} + 28 q^{61} + 4 q^{62} + 48 q^{64} + 28 q^{65} - 16 q^{66} + 44 q^{67} + 32 q^{68} - 20 q^{69} + 20 q^{71} + 24 q^{72} + 16 q^{73} + 44 q^{74} - 48 q^{75} + 16 q^{76} + 32 q^{78} + 4 q^{79} - 44 q^{80} + 24 q^{81} + 8 q^{82} - 8 q^{83} + 28 q^{85} + 56 q^{86} - 24 q^{87} + 60 q^{88} - 60 q^{89} + 4 q^{90} + 60 q^{92} - 4 q^{93} - 24 q^{94} + 28 q^{95} - 36 q^{96} + 48 q^{97} + 12 q^{99}+O(q^{100}) $ 24 * q + 8 * q^2 - 24 * q^3 + 32 * q^4 - 4 * q^5 - 8 * q^6 + 24 * q^8 + 24 * q^9 + 4 * q^10 + 12 * q^11 - 32 * q^12 + 4 * q^15 + 44 * q^16 - 8 * q^17 + 8 * q^18 + 4 * q^19 - 28 * q^20 + 16 * q^22 + 20 * q^23 - 24 * q^24 + 48 * q^25 - 32 * q^26 - 24 * q^27 + 24 * q^29 - 4 * q^30 + 4 * q^31 + 36 * q^32 - 12 * q^33 - 16 * q^34 + 32 * q^36 + 64 * q^37 - 20 * q^38 + 48 * q^40 + 24 * q^41 + 20 * q^43 + 48 * q^44 - 4 * q^45 + 28 * q^46 - 32 * q^47 - 44 * q^48 - 20 * q^50 + 8 * q^51 + 76 * q^53 - 8 * q^54 + 24 * q^55 - 4 * q^57 + 28 * q^58 - 28 * q^59 + 28 * q^60 + 28 * q^61 + 4 * q^62 + 48 * q^64 + 28 * q^65 - 16 * q^66 + 44 * q^67 + 32 * q^68 - 20 * q^69 + 20 * q^71 + 24 * q^72 + 16 * q^73 + 44 * q^74 - 48 * q^75 + 16 * q^76 + 32 * q^78 + 4 * q^79 - 44 * q^80 + 24 * q^81 + 8 * q^82 - 8 * q^83 + 28 * q^85 + 56 * q^86 - 24 * q^87 + 60 * q^88 - 60 * q^89 + 4 * q^90 + 60 * q^92 - 4 * q^93 - 24 * q^94 + 28 * q^95 - 36 * q^96 + 48 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.37986	−1.68281	−0.841406	−	0.540403i	$-0.818272\pi$
$2$	−2.37986	−1.68281	−0.841406	+	0.540403i	$0.818272\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.66372	1.83186
$5$	−3.68734	−1.64903	−0.824514	−	0.565841i	$-0.808551\pi$
$5$	−3.68734	−1.64903	−0.824514	+	0.565841i	$0.808551\pi$
$6$	2.37986	0.971572
$7$	0	0
$7$	0	0
$8$	−3.95941	−1.39986
$9$	1.00000	0.333333
$10$	8.77534	2.77501
$11$	−6.26313	−1.88840	−0.944202	−	0.329366i	$-0.893165\pi$
$11$	−6.26313	−1.88840	−0.944202	+	0.329366i	$0.893165\pi$
$12$	−3.66372	−1.05762
$13$	3.25624	0.903118	0.451559	−	0.892241i	$-0.350868\pi$
$13$	3.25624	0.903118	0.451559	+	0.892241i	$0.350868\pi$
$14$	0	0
$15$	3.68734	0.952067
$16$	2.09539	0.523848
$17$	−0.146265	−0.0354744	−0.0177372	−	0.999843i	$-0.505646\pi$
$17$	−0.146265	−0.0354744	−0.0177372	+	0.999843i	$0.505646\pi$
$18$	−2.37986	−0.560938
$19$	1.78602	0.409741	0.204870	−	0.978789i	$-0.434323\pi$
$19$	1.78602	0.409741	0.204870	+	0.978789i	$0.434323\pi$
$20$	−13.5094	−3.02079
$21$	0	0
$22$	14.9053	3.17783
$23$	−3.11368	−0.649247	−0.324623	−	0.945843i	$-0.605238\pi$
$23$	−3.11368	−0.649247	−0.324623	+	0.945843i	$0.605238\pi$
$24$	3.95941	0.808211
$25$	8.59647	1.71929
$26$	−7.74938	−1.51978
$27$	−1.00000	−0.192450
$28$	0	0
$29$	4.08462	0.758495	0.379247	−	0.925295i	$-0.376183\pi$
$29$	4.08462	0.758495	0.379247	+	0.925295i	$0.376183\pi$
$30$	−8.77534	−1.60215
$31$	−1.31731	−0.236596	−0.118298	−	0.992978i	$-0.537744\pi$
$31$	−1.31731	−0.236596	−0.118298	+	0.992978i	$0.537744\pi$
$32$	2.93209	0.518325
$33$	6.26313	1.09027
$34$	0.348089	0.0596967
$35$	0	0
$36$	3.66372	0.610620
$37$	3.67591	0.604316	0.302158	−	0.953258i	$-0.402293\pi$
$37$	3.67591	0.604316	0.302158	+	0.953258i	$0.402293\pi$
$38$	−4.25047	−0.689517
$39$	−3.25624	−0.521415
$40$	14.5997	2.30841
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	−9.08247	−1.38506	−0.692532	−	0.721388i	$-0.743505\pi$
$43$	−9.08247	−1.38506	−0.692532	+	0.721388i	$0.743505\pi$
$44$	−22.9463	−3.45929
$45$	−3.68734	−0.549676
$46$	7.41011	1.09256
$47$	−11.5238	−1.68093	−0.840463	−	0.541869i	$-0.817717\pi$
$47$	−11.5238	−1.68093	−0.840463	+	0.541869i	$0.817717\pi$
$48$	−2.09539	−0.302444
$49$	0	0
$50$	−20.4584	−2.89325
$51$	0.146265	0.0204811
$52$	11.9299	1.65438
$53$	4.41701	0.606723	0.303361	−	0.952876i	$-0.401891\pi$
$53$	4.41701	0.606723	0.303361	+	0.952876i	$0.401891\pi$
$54$	2.37986	0.323857
$55$	23.0943	3.11403
$56$	0	0
$57$	−1.78602	−0.236564
$58$	−9.72081	−1.27640
$59$	−1.71894	−0.223786	−0.111893	−	0.993720i	$-0.535691\pi$
$59$	−1.71894	−0.223786	−0.111893	+	0.993720i	$0.535691\pi$
$60$	13.5094	1.74405
$61$	−6.02287	−0.771150	−0.385575	−	0.922677i	$-0.625997\pi$
$61$	−6.02287	−0.771150	−0.385575	+	0.922677i	$0.625997\pi$
$62$	3.13502	0.398147
$63$	0	0
$64$	−11.1687	−1.39609
$65$	−12.0069	−1.48927
$66$	−14.9053	−1.83472
$67$	1.38835	0.169615	0.0848073	−	0.996397i	$-0.472973\pi$
$67$	1.38835	0.169615	0.0848073	+	0.996397i	$0.472973\pi$
$68$	−0.535872	−0.0649840
$69$	3.11368	0.374843
$70$	0	0
$71$	8.92495	1.05920	0.529598	−	0.848249i	$-0.322343\pi$
$71$	8.92495	1.05920	0.529598	+	0.848249i	$0.322343\pi$
$72$	−3.95941	−0.466621
$73$	−8.93911	−1.04624	−0.523122	−	0.852258i	$-0.675233\pi$
$73$	−8.93911	−1.04624	−0.523122	+	0.852258i	$0.675233\pi$
$74$	−8.74814	−1.01695
$75$	−8.59647	−0.992635
$76$	6.54346	0.750587
$77$	0	0
$78$	7.74938	0.877445
$79$	−10.3689	−1.16659	−0.583294	−	0.812261i	$-0.698237\pi$
$79$	−10.3689	−1.16659	−0.583294	+	0.812261i	$0.698237\pi$
$80$	−7.72642	−0.863840
$81$	1.00000	0.111111
$82$	−2.37986	−0.262811
$83$	10.6436	1.16829	0.584146	−	0.811649i	$-0.301430\pi$
$83$	10.6436	1.16829	0.584146	+	0.811649i	$0.301430\pi$
$84$	0	0
$85$	0.539327	0.0584982
$86$	21.6150	2.33080
$87$	−4.08462	−0.437917
$88$	24.7983	2.64351
$89$	1.75624	0.186161	0.0930805	−	0.995659i	$-0.470329\pi$
$89$	1.75624	0.186161	0.0930805	+	0.995659i	$0.470329\pi$
$90$	8.77534	0.925002
$91$	0	0
$92$	−11.4076	−1.18933
$93$	1.31731	0.136599
$94$	27.4251	2.82868
$95$	−6.58565	−0.675674
$96$	−2.93209	−0.299255
$97$	−5.53442	−0.561935	−0.280968	−	0.959717i	$-0.590655\pi$
$97$	−5.53442	−0.561935	−0.280968	+	0.959717i	$0.590655\pi$
$98$	0	0
$99$	−6.26313	−0.629468
$100$	31.4950	3.14950
$101$	−15.9955	−1.59161	−0.795806	−	0.605552i	$-0.792952\pi$
$101$	−15.9955	−1.59161	−0.795806	+	0.605552i	$0.792952\pi$
$102$	−0.348089	−0.0344659
$103$	−18.2558	−1.79880	−0.899400	−	0.437127i	$-0.855996\pi$
$103$	−18.2558	−1.79880	−0.899400	+	0.437127i	$0.855996\pi$
$104$	−12.8928	−1.26424
$105$	0	0
$106$	−10.5118	−1.02100
$107$	−3.48468	−0.336877	−0.168439	−	0.985712i	$-0.553872\pi$
$107$	−3.48468	−0.336877	−0.168439	+	0.985712i	$0.553872\pi$
$108$	−3.66372	−0.352541
$109$	12.1345	1.16228	0.581138	−	0.813805i	$-0.302608\pi$
$109$	12.1345	1.16228	0.581138	+	0.813805i	$0.302608\pi$
$110$	−54.9611	−5.24033
$111$	−3.67591	−0.348902
$112$	0	0
$113$	11.1948	1.05312	0.526558	−	0.850139i	$-0.323482\pi$
$113$	11.1948	1.05312	0.526558	+	0.850139i	$0.323482\pi$
$114$	4.25047	0.398093
$115$	11.4812	1.07063
$116$	14.9649	1.38946
$117$	3.25624	0.301039
$118$	4.09082	0.376591
$119$	0	0
$120$	−14.5997	−1.33276
$121$	28.2268	2.56607
$122$	14.3336	1.29770
$123$	−1.00000	−0.0901670
$124$	−4.82626	−0.433411
$125$	−13.2614	−1.18614
$126$	0	0
$127$	−19.7467	−1.75224	−0.876119	−	0.482095i	$-0.839876\pi$
$127$	−19.7467	−1.75224	−0.876119	+	0.482095i	$0.839876\pi$
$128$	20.7158	1.83104
$129$	9.08247	0.799667
$130$	28.5746	2.50616
$131$	−19.2431	−1.68128	−0.840640	−	0.541594i	$-0.817821\pi$
$131$	−19.2431	−1.68128	−0.840640	+	0.541594i	$0.817821\pi$
$132$	22.9463	1.99722
$133$	0	0
$134$	−3.30408	−0.285429
$135$	3.68734	0.317356
$136$	0.579121	0.0496592
$137$	−3.63718	−0.310745	−0.155373	−	0.987856i	$-0.549658\pi$
$137$	−3.63718	−0.310745	−0.155373	+	0.987856i	$0.549658\pi$
$138$	−7.41011	−0.630790
$139$	−15.6912	−1.33091	−0.665457	−	0.746436i	$-0.731763\pi$
$139$	−15.6912	−1.33091	−0.665457	+	0.746436i	$0.731763\pi$
$140$	0	0
$141$	11.5238	0.970483
$142$	−21.2401	−1.78243
$143$	−20.3942	−1.70545
$144$	2.09539	0.174616
$145$	−15.0614	−1.25078
$146$	21.2738	1.76063
$147$	0	0
$148$	13.4675	1.10702
$149$	15.4694	1.26730	0.633651	−	0.773619i	$-0.281555\pi$
$149$	15.4694	1.26730	0.633651	+	0.773619i	$0.281555\pi$
$150$	20.4584	1.67042
$151$	−6.09366	−0.495895	−0.247947	−	0.968774i	$-0.579756\pi$
$151$	−6.09366	−0.495895	−0.247947	+	0.968774i	$0.579756\pi$
$152$	−7.07157	−0.573580
$153$	−0.146265	−0.0118248
$154$	0	0
$155$	4.85738	0.390154
$156$	−11.9299	−0.955160
$157$	−2.07672	−0.165740	−0.0828701	−	0.996560i	$-0.526409\pi$
$157$	−2.07672	−0.165740	−0.0828701	+	0.996560i	$0.526409\pi$
$158$	24.6764	1.96315
$159$	−4.41701	−0.350292
$160$	−10.8116	−0.854732
$161$	0	0
$162$	−2.37986	−0.186979
$163$	11.3480	0.888841	0.444421	−	0.895818i	$-0.353410\pi$
$163$	11.3480	0.888841	0.444421	+	0.895818i	$0.353410\pi$
$164$	3.66372	0.286088
$165$	−23.0943	−1.79789
$166$	−25.3303	−1.96602
$167$	−19.2640	−1.49069	−0.745347	−	0.666677i	$-0.767716\pi$
$167$	−19.2640	−1.49069	−0.745347	+	0.666677i	$0.767716\pi$
$168$	0	0
$169$	−2.39691	−0.184378
$170$	−1.28352	−0.0984416
$171$	1.78602	0.136580
$172$	−33.2756	−2.53724
$173$	11.0874	0.842961	0.421481	−	0.906837i	$-0.361511\pi$
$173$	11.0874	0.842961	0.421481	+	0.906837i	$0.361511\pi$
$174$	9.72081	0.736933
$175$	0	0
$176$	−13.1237	−0.989236
$177$	1.71894	0.129203
$178$	−4.17960	−0.313274
$179$	15.7592	1.17790	0.588951	−	0.808169i	$-0.299541\pi$
$179$	15.7592	1.17790	0.588951	+	0.808169i	$0.299541\pi$
$180$	−13.5094	−1.00693
$181$	3.24953	0.241536	0.120768	−	0.992681i	$-0.461464\pi$
$181$	3.24953	0.241536	0.120768	+	0.992681i	$0.461464\pi$
$182$	0	0
$183$	6.02287	0.445223
$184$	12.3283	0.908856
$185$	−13.5543	−0.996534
$186$	−3.13502	−0.229871
$187$	0.916074	0.0669900
$188$	−42.2201	−3.07922
$189$	0	0
$190$	15.6729	1.13703
$191$	−0.889555	−0.0643660	−0.0321830	−	0.999482i	$-0.510246\pi$
$191$	−0.889555	−0.0643660	−0.0321830	+	0.999482i	$0.510246\pi$
$192$	11.1687	0.806034
$193$	−2.48347	−0.178764	−0.0893821	−	0.995997i	$-0.528489\pi$
$193$	−2.48347	−0.178764	−0.0893821	+	0.995997i	$0.528489\pi$
$194$	13.1711	0.945632
$195$	12.0069	0.859829
$196$	0	0
$197$	−16.0761	−1.14537	−0.572686	−	0.819775i	$-0.694099\pi$
$197$	−16.0761	−1.14537	−0.572686	+	0.819775i	$0.694099\pi$
$198$	14.9053	1.05928
$199$	−6.08609	−0.431432	−0.215716	−	0.976456i	$-0.569208\pi$
$199$	−6.08609	−0.431432	−0.215716	+	0.976456i	$0.569208\pi$
$200$	−34.0370	−2.40678
$201$	−1.38835	−0.0979270
$202$	38.0670	2.67838
$203$	0	0
$204$	0.535872	0.0375186
$205$	−3.68734	−0.257535
$206$	43.4462	3.02704
$207$	−3.11368	−0.216416
$208$	6.82309	0.473096
$209$	−11.1861	−0.773756
$210$	0	0
$211$	−26.1991	−1.80362	−0.901809	−	0.432135i	$-0.857761\pi$
$211$	−26.1991	−1.80362	−0.901809	+	0.432135i	$0.857761\pi$
$212$	16.1827	1.11143
$213$	−8.92495	−0.611527
$214$	8.29305	0.566901
$215$	33.4901	2.28401
$216$	3.95941	0.269404
$217$	0	0
$218$	−28.8784	−1.95589
$219$	8.93911	0.604049
$220$	84.6109	5.70447
$221$	−0.476272	−0.0320375
$222$	8.74814	0.587137
$223$	18.3279	1.22733	0.613663	−	0.789568i	$-0.289695\pi$
$223$	18.3279	1.22733	0.613663	+	0.789568i	$0.289695\pi$
$224$	0	0
$225$	8.59647	0.573098
$226$	−26.6420	−1.77220
$227$	−18.3473	−1.21776	−0.608878	−	0.793264i	$-0.708380\pi$
$227$	−18.3473	−1.21776	−0.608878	+	0.793264i	$0.708380\pi$
$228$	−6.54346	−0.433351
$229$	−4.23971	−0.280168	−0.140084	−	0.990140i	$-0.544737\pi$
$229$	−4.23971	−0.280168	−0.140084	+	0.990140i	$0.544737\pi$
$230$	−27.3236	−1.80166
$231$	0	0
$232$	−16.1727	−1.06179
$233$	16.9183	1.10836	0.554179	−	0.832398i	$-0.313032\pi$
$233$	16.9183	1.10836	0.554179	+	0.832398i	$0.313032\pi$
$234$	−7.74938	−0.506593
$235$	42.4923	2.77189
$236$	−6.29769	−0.409945
$237$	10.3689	0.673530
$238$	0	0
$239$	−12.6129	−0.815859	−0.407929	−	0.913014i	$-0.633749\pi$
$239$	−12.6129	−0.815859	−0.407929	+	0.913014i	$0.633749\pi$
$240$	7.72642	0.498738
$241$	−28.8035	−1.85539	−0.927697	−	0.373334i	$-0.878214\pi$
$241$	−28.8035	−1.85539	−0.927697	+	0.373334i	$0.878214\pi$
$242$	−67.1757	−4.31822
$243$	−1.00000	−0.0641500
$244$	−22.0661	−1.41264
$245$	0	0
$246$	2.37986	0.151734
$247$	5.81570	0.370044
$248$	5.21578	0.331202
$249$	−10.6436	−0.674513
$250$	31.5603	1.99605
$251$	−30.2514	−1.90945	−0.954726	−	0.297488i	$-0.903851\pi$
$251$	−30.2514	−1.90945	−0.954726	+	0.297488i	$0.903851\pi$
$252$	0	0
$253$	19.5014	1.22604
$254$	46.9943	2.94869
$255$	−0.539327	−0.0337740
$256$	−26.9632	−1.68520
$257$	−18.8356	−1.17493	−0.587466	−	0.809249i	$-0.699874\pi$
$257$	−18.8356	−1.17493	−0.587466	+	0.809249i	$0.699874\pi$
$258$	−21.6150	−1.34569
$259$	0	0
$260$	−43.9897	−2.72813
$261$	4.08462	0.252832
$262$	45.7959	2.82928
$263$	20.7414	1.27897	0.639486	−	0.768803i	$-0.279147\pi$
$263$	20.7414	1.27897	0.639486	+	0.768803i	$0.279147\pi$
$264$	−24.7983	−1.52623
$265$	−16.2870	−1.00050
$266$	0	0
$267$	−1.75624	−0.107480
$268$	5.08654	0.310710
$269$	2.26170	0.137898	0.0689492	−	0.997620i	$-0.478035\pi$
$269$	2.26170	0.137898	0.0689492	+	0.997620i	$0.478035\pi$
$270$	−8.77534	−0.534050
$271$	25.1898	1.53017	0.765086	−	0.643928i	$-0.222696\pi$
$271$	25.1898	1.53017	0.765086	+	0.643928i	$0.222696\pi$
$272$	−0.306481	−0.0185832
$273$	0	0
$274$	8.65597	0.522926
$275$	−53.8408	−3.24672
$276$	11.4076	0.686659
$277$	−10.2447	−0.615544	−0.307772	−	0.951460i	$-0.599583\pi$
$277$	−10.2447	−0.615544	−0.307772	+	0.951460i	$0.599583\pi$
$278$	37.3429	2.23968
$279$	−1.31731	−0.0788655
$280$	0	0
$281$	6.76403	0.403508	0.201754	−	0.979436i	$-0.435336\pi$
$281$	6.76403	0.403508	0.201754	+	0.979436i	$0.435336\pi$
$282$	−27.4251	−1.63314
$283$	−2.07715	−0.123474	−0.0617369	−	0.998092i	$-0.519664\pi$
$283$	−2.07715	−0.123474	−0.0617369	+	0.998092i	$0.519664\pi$
$284$	32.6985	1.94030
$285$	6.58565	0.390100
$286$	48.5354	2.86996
$287$	0	0
$288$	2.93209	0.172775
$289$	−16.9786	−0.998742
$290$	35.8439	2.10483
$291$	5.53442	0.324434
$292$	−32.7504	−1.91657
$293$	8.71064	0.508881	0.254440	−	0.967088i	$-0.418109\pi$
$293$	8.71064	0.508881	0.254440	+	0.967088i	$0.418109\pi$
$294$	0	0
$295$	6.33830	0.369030
$296$	−14.5544	−0.845959
$297$	6.26313	0.363424
$298$	−36.8150	−2.13263
$299$	−10.1389	−0.586346
$300$	−31.4950	−1.81837
$301$	0	0
$302$	14.5020	0.834498
$303$	15.9955	0.918918
$304$	3.74240	0.214642
$305$	22.2084	1.27165
$306$	0.348089	0.0198989
$307$	27.2743	1.55662	0.778312	−	0.627877i	$-0.216076\pi$
$307$	27.2743	1.55662	0.778312	+	0.627877i	$0.216076\pi$
$308$	0	0
$309$	18.2558	1.03854
$310$	−11.5599	−0.656556
$311$	−10.3281	−0.585654	−0.292827	−	0.956166i	$-0.594596\pi$
$311$	−10.3281	−0.585654	−0.292827	+	0.956166i	$0.594596\pi$
$312$	12.8928	0.729910
$313$	30.1284	1.70296	0.851480	−	0.524387i	$-0.175705\pi$
$313$	30.1284	1.70296	0.851480	+	0.524387i	$0.175705\pi$
$314$	4.94229	0.278910
$315$	0	0
$316$	−37.9886	−2.13703
$317$	19.6474	1.10351	0.551755	−	0.834006i	$-0.313958\pi$
$317$	19.6474	1.10351	0.551755	+	0.834006i	$0.313958\pi$
$318$	10.5118	0.589475
$319$	−25.5825	−1.43234
$320$	41.1829	2.30219
$321$	3.48468	0.194496
$322$	0	0
$323$	−0.261231	−0.0145353
$324$	3.66372	0.203540
$325$	27.9922	1.55273
$326$	−27.0065	−1.49575
$327$	−12.1345	−0.671040
$328$	−3.95941	−0.218622
$329$	0	0
$330$	54.9611	3.02551
$331$	−33.1392	−1.82150	−0.910748	−	0.412962i	$-0.864494\pi$
$331$	−33.1392	−1.82150	−0.910748	+	0.412962i	$0.864494\pi$
$332$	38.9953	2.14015
$333$	3.67591	0.201439
$334$	45.8456	2.50856
$335$	−5.11933	−0.279699
$336$	0	0
$337$	21.6674	1.18030	0.590148	−	0.807295i	$-0.299069\pi$
$337$	21.6674	1.18030	0.590148	+	0.807295i	$0.299069\pi$
$338$	5.70430	0.310273
$339$	−11.1948	−0.608017
$340$	1.97594	0.107161
$341$	8.25050	0.446790
$342$	−4.25047	−0.229839
$343$	0	0
$344$	35.9612	1.93890
$345$	−11.4812	−0.618126
$346$	−26.3865	−1.41855
$347$	21.5837	1.15867	0.579337	−	0.815088i	$-0.303311\pi$
$347$	21.5837	1.15867	0.579337	+	0.815088i	$0.303311\pi$
$348$	−14.9649	−0.802202
$349$	22.1900	1.18781	0.593903	−	0.804537i	$-0.297586\pi$
$349$	22.1900	1.18781	0.593903	+	0.804537i	$0.297586\pi$
$350$	0	0
$351$	−3.25624	−0.173805
$352$	−18.3640	−0.978807
$353$	−17.7402	−0.944215	−0.472108	−	0.881541i	$-0.656507\pi$
$353$	−17.7402	−0.944215	−0.472108	+	0.881541i	$0.656507\pi$
$354$	−4.09082	−0.217425
$355$	−32.9093	−1.74665
$356$	6.43436	0.341021
$357$	0	0
$358$	−37.5047	−1.98219
$359$	8.89293	0.469351	0.234675	−	0.972074i	$-0.424597\pi$
$359$	8.89293	0.469351	0.234675	+	0.972074i	$0.424597\pi$
$360$	14.5997	0.769471
$361$	−15.8101	−0.832113
$362$	−7.73343	−0.406460
$363$	−28.2268	−1.48152
$364$	0	0
$365$	32.9615	1.72529
$366$	−14.3336	−0.749228
$367$	0.601211	0.0313830	0.0156915	−	0.999877i	$-0.495005\pi$
$367$	0.601211	0.0313830	0.0156915	+	0.999877i	$0.495005\pi$
$368$	−6.52437	−0.340106
$369$	1.00000	0.0520579
$370$	32.2574	1.67698
$371$	0	0
$372$	4.82626	0.250230
$373$	2.16528	0.112114	0.0560570	−	0.998428i	$-0.482147\pi$
$373$	2.16528	0.112114	0.0560570	+	0.998428i	$0.482147\pi$
$374$	−2.18012	−0.112732
$375$	13.2614	0.684817
$376$	45.6276	2.35307
$377$	13.3005	0.685010
$378$	0	0
$379$	−5.85097	−0.300544	−0.150272	−	0.988645i	$-0.548015\pi$
$379$	−5.85097	−0.300544	−0.150272	+	0.988645i	$0.548015\pi$
$380$	−24.1280	−1.23774
$381$	19.7467	1.01165
$382$	2.11701	0.108316
$383$	−5.09873	−0.260533	−0.130267	−	0.991479i	$-0.541583\pi$
$383$	−5.09873	−0.260533	−0.130267	+	0.991479i	$0.541583\pi$
$384$	−20.7158	−1.05715
$385$	0	0
$386$	5.91030	0.300827
$387$	−9.08247	−0.461688
$388$	−20.2766	−1.02939
$389$	−38.2594	−1.93983	−0.969914	−	0.243449i	$-0.921721\pi$
$389$	−38.2594	−1.93983	−0.969914	+	0.243449i	$0.921721\pi$
$390$	−28.5746	−1.44693
$391$	0.455421	0.0230316
$392$	0	0
$393$	19.2431	0.970687
$394$	38.2587	1.92745
$395$	38.2335	1.92374
$396$	−22.9463	−1.15310
$397$	−25.6318	−1.28642	−0.643210	−	0.765689i	$-0.722398\pi$
$397$	−25.6318	−1.28642	−0.643210	+	0.765689i	$0.722398\pi$
$398$	14.4840	0.726018
$399$	0	0
$400$	18.0130	0.900649
$401$	−6.94500	−0.346817	−0.173408	−	0.984850i	$-0.555478\pi$
$401$	−6.94500	−0.346817	−0.173408	+	0.984850i	$0.555478\pi$
$402$	3.30408	0.164793
$403$	−4.28949	−0.213675
$404$	−58.6030	−2.91561
$405$	−3.68734	−0.183225
$406$	0	0
$407$	−23.0227	−1.14119
$408$	−0.579121	−0.0286708
$409$	35.3203	1.74648	0.873238	−	0.487294i	$-0.162016\pi$
$409$	35.3203	1.74648	0.873238	+	0.487294i	$0.162016\pi$
$410$	8.77534	0.433383
$411$	3.63718	0.179409
$412$	−66.8842	−3.29515
$413$	0	0
$414$	7.41011	0.364187
$415$	−39.2467	−1.92655
$416$	9.54758	0.468109
$417$	15.6912	0.768403
$418$	26.6212	1.30209
$419$	9.50778	0.464485	0.232243	−	0.972658i	$-0.425394\pi$
$419$	9.50778	0.464485	0.232243	+	0.972658i	$0.425394\pi$
$420$	0	0
$421$	−20.1034	−0.979781	−0.489891	−	0.871784i	$-0.662963\pi$
$421$	−20.1034	−0.979781	−0.489891	+	0.871784i	$0.662963\pi$
$422$	62.3500	3.03515
$423$	−11.5238	−0.560309
$424$	−17.4887	−0.849329
$425$	−1.25736	−0.0609909
$426$	21.2401	1.02909
$427$	0	0
$428$	−12.7669	−0.617111
$429$	20.3942	0.984643
$430$	−79.7017	−3.84356
$431$	−26.1665	−1.26040	−0.630199	−	0.776434i	$-0.717027\pi$
$431$	−26.1665	−1.26040	−0.630199	+	0.776434i	$0.717027\pi$
$432$	−2.09539	−0.100815
$433$	−35.2333	−1.69320	−0.846601	−	0.532227i	$-0.821355\pi$
$433$	−35.2333	−1.69320	−0.846601	+	0.532227i	$0.821355\pi$
$434$	0	0
$435$	15.0614	0.722138
$436$	44.4574	2.12912
$437$	−5.56108	−0.266023
$438$	−21.2738	−1.01650
$439$	10.1078	0.482419	0.241210	−	0.970473i	$-0.422456\pi$
$439$	10.1078	0.482419	0.241210	+	0.970473i	$0.422456\pi$
$440$	−91.4397	−4.35922
$441$	0	0
$442$	1.13346	0.0539132
$443$	24.3692	1.15782	0.578908	−	0.815393i	$-0.303479\pi$
$443$	24.3692	1.15782	0.578908	+	0.815393i	$0.303479\pi$
$444$	−13.4675	−0.639139
$445$	−6.47585	−0.306985
$446$	−43.6177	−2.06536
$447$	−15.4694	−0.731678
$448$	0	0
$449$	−19.5381	−0.922061	−0.461031	−	0.887384i	$-0.652520\pi$
$449$	−19.5381	−0.922061	−0.461031	+	0.887384i	$0.652520\pi$
$450$	−20.4584	−0.964417
$451$	−6.26313	−0.294919
$452$	41.0145	1.92916
$453$	6.09366	0.286305
$454$	43.6640	2.04926
$455$	0	0
$456$	7.07157	0.331157
$457$	26.2573	1.22826	0.614132	−	0.789203i	$-0.289506\pi$
$457$	26.2573	1.22826	0.614132	+	0.789203i	$0.289506\pi$
$458$	10.0899	0.471471
$459$	0.146265	0.00682705
$460$	42.0638	1.96124
$461$	−11.5537	−0.538110	−0.269055	−	0.963125i	$-0.586711\pi$
$461$	−11.5537	−0.538110	−0.269055	+	0.963125i	$0.586711\pi$
$462$	0	0
$463$	−1.17471	−0.0545936	−0.0272968	−	0.999627i	$-0.508690\pi$
$463$	−1.17471	−0.0545936	−0.0272968	+	0.999627i	$0.508690\pi$
$464$	8.55887	0.397336
$465$	−4.85738	−0.225256
$466$	−40.2632	−1.86516
$467$	−5.32580	−0.246449	−0.123224	−	0.992379i	$-0.539323\pi$
$467$	−5.32580	−0.246449	−0.123224	+	0.992379i	$0.539323\pi$
$468$	11.9299	0.551462
$469$	0	0
$470$	−101.126	−4.66458
$471$	2.07672	0.0956901
$472$	6.80597	0.313270
$473$	56.8847	2.61556
$474$	−24.6764	−1.13343
$475$	15.3534	0.704465
$476$	0	0
$477$	4.41701	0.202241
$478$	30.0168	1.37294
$479$	−25.6439	−1.17170	−0.585849	−	0.810420i	$-0.699239\pi$
$479$	−25.6439	−1.17170	−0.585849	+	0.810420i	$0.699239\pi$
$480$	10.8116	0.493480
$481$	11.9696	0.545769
$482$	68.5481	3.12228
$483$	0	0
$484$	103.415	4.70068
$485$	20.4073	0.926647
$486$	2.37986	0.107952
$487$	−3.25149	−0.147339	−0.0736696	−	0.997283i	$-0.523471\pi$
$487$	−3.25149	−0.147339	−0.0736696	+	0.997283i	$0.523471\pi$
$488$	23.8470	1.07950
$489$	−11.3480	−0.513173
$490$	0	0
$491$	−19.5010	−0.880069	−0.440034	−	0.897981i	$-0.645034\pi$
$491$	−19.5010	−0.880069	−0.440034	+	0.897981i	$0.645034\pi$
$492$	−3.66372	−0.165173
$493$	−0.597435	−0.0269071
$494$	−13.8405	−0.622715
$495$	23.0943	1.03801
$496$	−2.76029	−0.123941
$497$	0	0
$498$	25.3303	1.13508
$499$	32.6281	1.46064	0.730318	−	0.683107i	$-0.239372\pi$
$499$	32.6281	1.46064	0.730318	+	0.683107i	$0.239372\pi$
$500$	−48.5861	−2.17284
$501$	19.2640	0.860652
$502$	71.9940	3.21325
$503$	21.7937	0.971732	0.485866	−	0.874033i	$-0.338504\pi$
$503$	21.7937	0.971732	0.485866	+	0.874033i	$0.338504\pi$
$504$	0	0
$505$	58.9808	2.62461
$506$	−46.4105	−2.06320
$507$	2.39691	0.106451
$508$	−72.3464	−3.20985
$509$	18.9583	0.840312	0.420156	−	0.907452i	$-0.361975\pi$
$509$	18.9583	0.840312	0.420156	+	0.907452i	$0.361975\pi$
$510$	1.28352	0.0568353
$511$	0	0
$512$	22.7369	1.00484
$513$	−1.78602	−0.0788546
$514$	44.8260	1.97719
$515$	67.3154	2.96627
$516$	33.2756	1.46488
$517$	72.1754	3.17427
$518$	0	0
$519$	−11.0874	−0.486684
$520$	47.5401	2.08477
$521$	3.35523	0.146995	0.0734975	−	0.997295i	$-0.476584\pi$
$521$	3.35523	0.146995	0.0734975	+	0.997295i	$0.476584\pi$
$522$	−9.72081	−0.425468
$523$	18.9321	0.827843	0.413922	−	0.910312i	$-0.364159\pi$
$523$	18.9321	0.827843	0.413922	+	0.910312i	$0.364159\pi$
$524$	−70.5014	−3.07987
$525$	0	0
$526$	−49.3617	−2.15227
$527$	0.192676	0.00839311
$528$	13.1237	0.571136
$529$	−13.3050	−0.578479
$530$	38.7608	1.68366
$531$	−1.71894	−0.0745955
$532$	0	0
$533$	3.25624	0.141043
$534$	4.17960	0.180869
$535$	12.8492	0.555520
$536$	−5.49706	−0.237437
$537$	−15.7592	−0.680062
$538$	−5.38253	−0.232057
$539$	0	0
$540$	13.5094	0.581351
$541$	28.6878	1.23339	0.616693	−	0.787204i	$-0.288472\pi$
$541$	28.6878	1.23339	0.616693	+	0.787204i	$0.288472\pi$
$542$	−59.9482	−2.57499
$543$	−3.24953	−0.139451
$544$	−0.428861	−0.0183872
$545$	−44.7441	−1.91662
$546$	0	0
$547$	25.8811	1.10659	0.553297	−	0.832984i	$-0.313369\pi$
$547$	25.8811	1.10659	0.553297	+	0.832984i	$0.313369\pi$
$548$	−13.3256	−0.569242
$549$	−6.02287	−0.257050
$550$	128.133	5.46363
$551$	7.29520	0.310786
$552$	−12.3283	−0.524728
$553$	0	0
$554$	24.3809	1.03585
$555$	13.5543	0.575349
$556$	−57.4883	−2.43805
$557$	23.2849	0.986614	0.493307	−	0.869855i	$-0.335788\pi$
$557$	23.2849	0.986614	0.493307	+	0.869855i	$0.335788\pi$
$558$	3.13502	0.132716
$559$	−29.5747	−1.25088
$560$	0	0
$561$	−0.916074	−0.0386767
$562$	−16.0974	−0.679029
$563$	32.5005	1.36973	0.684867	−	0.728668i	$-0.259860\pi$
$563$	32.5005	1.36973	0.684867	+	0.728668i	$0.259860\pi$
$564$	42.2201	1.77779
$565$	−41.2790	−1.73662
$566$	4.94332	0.207783
$567$	0	0
$568$	−35.3375	−1.48273
$569$	−17.0193	−0.713486	−0.356743	−	0.934203i	$-0.616113\pi$
$569$	−17.0193	−0.713486	−0.356743	+	0.934203i	$0.616113\pi$
$570$	−15.6729	−0.656466
$571$	29.9442	1.25313	0.626564	−	0.779370i	$-0.284461\pi$
$571$	29.9442	1.25313	0.626564	+	0.779370i	$0.284461\pi$
$572$	−74.7187	−3.12415
$573$	0.889555	0.0371617
$574$	0	0
$575$	−26.7666	−1.11625
$576$	−11.1687	−0.465364
$577$	22.0478	0.917862	0.458931	−	0.888472i	$-0.348233\pi$
$577$	22.0478	0.917862	0.458931	+	0.888472i	$0.348233\pi$
$578$	40.4066	1.68070
$579$	2.48347	0.103210
$580$	−55.1806	−2.29125
$581$	0	0
$582$	−13.1711	−0.545961
$583$	−27.6643	−1.14574
$584$	35.3936	1.46460
$585$	−12.0069	−0.496422
$586$	−20.7301	−0.856351
$587$	34.5456	1.42585	0.712924	−	0.701241i	$-0.247370\pi$
$587$	34.5456	1.42585	0.712924	+	0.701241i	$0.247370\pi$
$588$	0	0
$589$	−2.35274	−0.0969431
$590$	−15.0842	−0.621009
$591$	16.0761	0.661281
$592$	7.70247	0.316569
$593$	20.0432	0.823076	0.411538	−	0.911393i	$-0.364992\pi$
$593$	20.0432	0.823076	0.411538	+	0.911393i	$0.364992\pi$
$594$	−14.9053	−0.611574
$595$	0	0
$596$	56.6755	2.32152
$597$	6.08609	0.249087
$598$	24.1291	0.986711
$599$	28.6415	1.17026	0.585130	−	0.810940i	$-0.301044\pi$
$599$	28.6415	1.17026	0.585130	+	0.810940i	$0.301044\pi$
$600$	34.0370	1.38955
$601$	−19.4285	−0.792506	−0.396253	−	0.918141i	$-0.629690\pi$
$601$	−19.4285	−0.792506	−0.396253	+	0.918141i	$0.629690\pi$
$602$	0	0
$603$	1.38835	0.0565382
$604$	−22.3254	−0.908409
$605$	−104.082	−4.23153
$606$	−38.0670	−1.54637
$607$	9.75872	0.396094	0.198047	−	0.980193i	$-0.436540\pi$
$607$	9.75872	0.396094	0.198047	+	0.980193i	$0.436540\pi$
$608$	5.23676	0.212379
$609$	0	0
$610$	−52.8527	−2.13994
$611$	−37.5244	−1.51807
$612$	−0.535872	−0.0216613
$613$	16.3639	0.660934	0.330467	−	0.943818i	$-0.392794\pi$
$613$	16.3639	0.660934	0.330467	+	0.943818i	$0.392794\pi$
$614$	−64.9089	−2.61951
$615$	3.68734	0.148688
$616$	0	0
$617$	−6.22352	−0.250549	−0.125275	−	0.992122i	$-0.539981\pi$
$617$	−6.22352	−0.250549	−0.125275	+	0.992122i	$0.539981\pi$
$618$	−43.4462	−1.74766
$619$	36.5437	1.46882	0.734408	−	0.678709i	$-0.237460\pi$
$619$	36.5437	1.46882	0.734408	+	0.678709i	$0.237460\pi$
$620$	17.7961	0.714707
$621$	3.11368	0.124948
$622$	24.5794	0.985545
$623$	0	0
$624$	−6.82309	−0.273142
$625$	5.91698	0.236679
$626$	−71.7014	−2.86576
$627$	11.1861	0.446728
$628$	−7.60851	−0.303613
$629$	−0.537655	−0.0214377
$630$	0	0
$631$	34.5755	1.37643	0.688215	−	0.725506i	$-0.258394\pi$
$631$	34.5755	1.37643	0.688215	+	0.725506i	$0.258394\pi$
$632$	41.0546	1.63306
$633$	26.1991	1.04132
$634$	−46.7581	−1.85700
$635$	72.8128	2.88949
$636$	−16.1827	−0.641685
$637$	0	0
$638$	60.8827	2.41037
$639$	8.92495	0.353066
$640$	−76.3862	−3.01943
$641$	−45.6225	−1.80198	−0.900990	−	0.433839i	$-0.857159\pi$
$641$	−45.6225	−1.80198	−0.900990	+	0.433839i	$0.857159\pi$
$642$	−8.29305	−0.327300
$643$	6.12623	0.241595	0.120797	−	0.992677i	$-0.461455\pi$
$643$	6.12623	0.241595	0.120797	+	0.992677i	$0.461455\pi$
$644$	0	0
$645$	−33.4901	−1.31867
$646$	0.621693	0.0244602
$647$	21.5628	0.847720	0.423860	−	0.905728i	$-0.360675\pi$
$647$	21.5628	0.847720	0.423860	+	0.905728i	$0.360675\pi$
$648$	−3.95941	−0.155540
$649$	10.7659	0.422599
$650$	−66.6173	−2.61295
$651$	0	0
$652$	41.5757	1.62823
$653$	−2.57822	−0.100894	−0.0504468	−	0.998727i	$-0.516065\pi$
$653$	−2.57822	−0.100894	−0.0504468	+	0.998727i	$0.516065\pi$
$654$	28.8784	1.12923
$655$	70.9559	2.77248
$656$	2.09539	0.0818113
$657$	−8.93911	−0.348748
$658$	0	0
$659$	7.93310	0.309030	0.154515	−	0.987990i	$-0.450619\pi$
$659$	7.93310	0.309030	0.154515	+	0.987990i	$0.450619\pi$
$660$	−84.6109	−3.29348
$661$	2.46160	0.0957452	0.0478726	−	0.998853i	$-0.484756\pi$
$661$	2.46160	0.0957452	0.0478726	+	0.998853i	$0.484756\pi$
$662$	78.8666	3.06524
$663$	0.476272	0.0184969
$664$	−42.1425	−1.63545
$665$	0	0
$666$	−8.74814	−0.338983
$667$	−12.7182	−0.492450
$668$	−70.5779	−2.73074
$669$	−18.3279	−0.708597
$670$	12.1833	0.470681
$671$	37.7220	1.45624
$672$	0	0
$673$	46.3505	1.78668	0.893339	−	0.449383i	$-0.148356\pi$
$673$	46.3505	1.78668	0.893339	+	0.449383i	$0.148356\pi$
$674$	−51.5652	−1.98622
$675$	−8.59647	−0.330878
$676$	−8.78160	−0.337754
$677$	22.5487	0.866617	0.433309	−	0.901246i	$-0.357346\pi$
$677$	22.5487	0.866617	0.433309	+	0.901246i	$0.357346\pi$
$678$	26.6420	1.02318
$679$	0	0
$680$	−2.13542	−0.0818895
$681$	18.3473	0.703072
$682$	−19.6350	−0.751864
$683$	−5.94771	−0.227583	−0.113791	−	0.993505i	$-0.536300\pi$
$683$	−5.94771	−0.227583	−0.113791	+	0.993505i	$0.536300\pi$
$684$	6.54346	0.250196
$685$	13.4115	0.512428
$686$	0	0
$687$	4.23971	0.161755
$688$	−19.0313	−0.725562
$689$	14.3828	0.547942
$690$	27.3236	1.04019
$691$	−46.6357	−1.77411	−0.887054	−	0.461666i	$-0.847252\pi$
$691$	−46.6357	−1.77411	−0.887054	+	0.461666i	$0.847252\pi$
$692$	40.6212	1.54419
$693$	0	0
$694$	−51.3661	−1.94983
$695$	57.8589	2.19471
$696$	16.1727	0.613024
$697$	−0.146265	−0.00554017
$698$	−52.8091	−1.99885
$699$	−16.9183	−0.639910
$700$	0	0
$701$	−19.9123	−0.752078	−0.376039	−	0.926604i	$-0.622714\pi$
$701$	−19.9123	−0.752078	−0.376039	+	0.926604i	$0.622714\pi$
$702$	7.74938	0.292482
$703$	6.56524	0.247613
$704$	69.9512	2.63639
$705$	−42.4923	−1.60035
$706$	42.2191	1.58894
$707$	0	0
$708$	6.29769	0.236682
$709$	23.9798	0.900580	0.450290	−	0.892882i	$-0.351321\pi$
$709$	23.9798	0.900580	0.450290	+	0.892882i	$0.351321\pi$
$710$	78.3195	2.93928
$711$	−10.3689	−0.388863
$712$	−6.95367	−0.260600
$713$	4.10169	0.153609
$714$	0	0
$715$	75.2005	2.81234
$716$	57.7374	2.15775
$717$	12.6129	0.471036
$718$	−21.1639	−0.789830
$719$	16.6841	0.622213	0.311107	−	0.950375i	$-0.399300\pi$
$719$	16.6841	0.622213	0.311107	+	0.950375i	$0.399300\pi$
$720$	−7.72642	−0.287947
$721$	0	0
$722$	37.6259	1.40029
$723$	28.8035	1.07121
$724$	11.9054	0.442460
$725$	35.1133	1.30408
$726$	67.1757	2.49312
$727$	21.5134	0.797888	0.398944	−	0.916975i	$-0.369377\pi$
$727$	21.5134	0.797888	0.398944	+	0.916975i	$0.369377\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−78.4437	−2.90333
$731$	1.32844	0.0491342
$732$	22.0661	0.815586
$733$	−13.7896	−0.509330	−0.254665	−	0.967029i	$-0.581965\pi$
$733$	−13.7896	−0.509330	−0.254665	+	0.967029i	$0.581965\pi$
$734$	−1.43080	−0.0528116
$735$	0	0
$736$	−9.12958	−0.336521
$737$	−8.69544	−0.320301
$738$	−2.37986	−0.0876037
$739$	52.1005	1.91655	0.958273	−	0.285854i	$-0.0922773\pi$
$739$	52.1005	1.91655	0.958273	+	0.285854i	$0.0922773\pi$
$740$	−49.6592	−1.82551
$741$	−5.81570	−0.213645
$742$	0	0
$743$	−7.82960	−0.287240	−0.143620	−	0.989633i	$-0.545874\pi$
$743$	−7.82960	−0.287240	−0.143620	+	0.989633i	$0.545874\pi$
$744$	−5.21578	−0.191220
$745$	−57.0409	−2.08982
$746$	−5.15306	−0.188667
$747$	10.6436	0.389431
$748$	3.35624	0.122716
$749$	0	0
$750$	−31.5603	−1.15242
$751$	24.7094	0.901659	0.450829	−	0.892610i	$-0.351128\pi$
$751$	24.7094	0.901659	0.450829	+	0.892610i	$0.351128\pi$
$752$	−24.1470	−0.880549
$753$	30.2514	1.10242
$754$	−31.6533	−1.15274
$755$	22.4694	0.817744
$756$	0	0
$757$	3.24530	0.117952	0.0589762	−	0.998259i	$-0.481216\pi$
$757$	3.24530	0.117952	0.0589762	+	0.998259i	$0.481216\pi$
$758$	13.9245	0.505760
$759$	−19.5014	−0.707855
$760$	26.0753	0.945850
$761$	23.8904	0.866027	0.433013	−	0.901387i	$-0.357450\pi$
$761$	23.8904	0.866027	0.433013	+	0.901387i	$0.357450\pi$
$762$	−46.9943	−1.70243
$763$	0	0
$764$	−3.25908	−0.117909
$765$	0.539327	0.0194994
$766$	12.1343	0.438429
$767$	−5.59726	−0.202106
$768$	26.9632	0.972950
$769$	−7.71831	−0.278329	−0.139165	−	0.990269i	$-0.544442\pi$
$769$	−7.71831	−0.278329	−0.139165	+	0.990269i	$0.544442\pi$
$770$	0	0
$771$	18.8356	0.678347
$772$	−9.09873	−0.327471
$773$	−17.9179	−0.644461	−0.322231	−	0.946661i	$-0.604433\pi$
$773$	−17.9179	−0.644461	−0.322231	+	0.946661i	$0.604433\pi$
$774$	21.6150	0.776934
$775$	−11.3242	−0.406779
$776$	21.9130	0.786632
$777$	0	0
$778$	91.0518	3.26437
$779$	1.78602	0.0639907
$780$	43.9897	1.57509
$781$	−55.8981	−2.00019
$782$	−1.08384	−0.0387579
$783$	−4.08462	−0.145972
$784$	0	0
$785$	7.65757	0.273310
$786$	−45.7959	−1.63349
$787$	27.3832	0.976104	0.488052	−	0.872814i	$-0.337708\pi$
$787$	27.3832	0.976104	0.488052	+	0.872814i	$0.337708\pi$
$788$	−58.8982	−2.09816
$789$	−20.7414	−0.738415
$790$	−90.9903	−3.23729
$791$	0	0
$792$	24.7983	0.881169
$793$	−19.6119	−0.696439
$794$	60.9999	2.16481
$795$	16.2870	0.577641
$796$	−22.2977	−0.790322
$797$	11.0166	0.390229	0.195114	−	0.980781i	$-0.437492\pi$
$797$	11.0166	0.390229	0.195114	+	0.980781i	$0.437492\pi$
$798$	0	0
$799$	1.68553	0.0596298
$800$	25.2056	0.891153
$801$	1.75624	0.0620537
$802$	16.5281	0.583627
$803$	55.9868	1.97573
$804$	−5.08654	−0.179388
$805$	0	0
$806$	10.2084	0.359574
$807$	−2.26170	−0.0796157
$808$	63.3327	2.22804
$809$	−17.9023	−0.629413	−0.314706	−	0.949189i	$-0.601906\pi$
$809$	−17.9023	−0.629413	−0.314706	+	0.949189i	$0.601906\pi$
$810$	8.77534	0.308334
$811$	−30.4616	−1.06965	−0.534826	−	0.844962i	$-0.679623\pi$
$811$	−30.4616	−1.06965	−0.534826	+	0.844962i	$0.679623\pi$
$812$	0	0
$813$	−25.1898	−0.883446
$814$	54.7907	1.92041
$815$	−41.8438	−1.46572
$816$	0.306481	0.0107290
$817$	−16.2214	−0.567516
$818$	−84.0572	−2.93899
$819$	0	0
$820$	−13.5094	−0.471768
$821$	24.3154	0.848614	0.424307	−	0.905518i	$-0.360518\pi$
$821$	24.3154	0.848614	0.424307	+	0.905518i	$0.360518\pi$
$822$	−8.65597	−0.301912
$823$	−47.9101	−1.67004	−0.835020	−	0.550220i	$-0.814544\pi$
$823$	−47.9101	−1.67004	−0.835020	+	0.550220i	$0.814544\pi$
$824$	72.2823	2.51807
$825$	53.8408	1.87450
$826$	0	0
$827$	17.4163	0.605624	0.302812	−	0.953050i	$-0.402075\pi$
$827$	17.4163	0.605624	0.302812	+	0.953050i	$0.402075\pi$
$828$	−11.4076	−0.396443
$829$	−5.83275	−0.202580	−0.101290	−	0.994857i	$-0.532297\pi$
$829$	−5.83275	−0.202580	−0.101290	+	0.994857i	$0.532297\pi$
$830$	93.4016	3.24202
$831$	10.2447	0.355385
$832$	−36.3681	−1.26084
$833$	0	0
$834$	−37.3429	−1.29308
$835$	71.0329	2.45820
$836$	−40.9826	−1.41741
$837$	1.31731	0.0455330
$838$	−22.6271	−0.781642
$839$	−20.2271	−0.698316	−0.349158	−	0.937064i	$-0.613532\pi$
$839$	−20.2271	−0.698316	−0.349158	+	0.937064i	$0.613532\pi$
$840$	0	0
$841$	−12.3159	−0.424686
$842$	47.8433	1.64879
$843$	−6.76403	−0.232966
$844$	−95.9860	−3.30397
$845$	8.83822	0.304044
$846$	27.4251	0.942895
$847$	0	0
$848$	9.25536	0.317830
$849$	2.07715	0.0712876
$850$	2.99234	0.102636
$851$	−11.4456	−0.392350
$852$	−32.6985	−1.12023
$853$	12.0327	0.411992	0.205996	−	0.978553i	$-0.433957\pi$
$853$	12.0327	0.411992	0.205996	+	0.978553i	$0.433957\pi$
$854$	0	0
$855$	−6.58565	−0.225225
$856$	13.7973	0.471582
$857$	−0.405363	−0.0138469	−0.00692347	−	0.999976i	$-0.502204\pi$
$857$	−0.405363	−0.0138469	−0.00692347	+	0.999976i	$0.502204\pi$
$858$	−48.5354	−1.65697
$859$	15.9365	0.543748	0.271874	−	0.962333i	$-0.412357\pi$
$859$	15.9365	0.543748	0.271874	+	0.962333i	$0.412357\pi$
$860$	122.698	4.18398
$861$	0	0
$862$	62.2726	2.12101
$863$	−28.1342	−0.957698	−0.478849	−	0.877897i	$-0.658946\pi$
$863$	−28.1342	−0.957698	−0.478849	+	0.877897i	$0.658946\pi$
$864$	−2.93209	−0.0997517
$865$	−40.8831	−1.39007
$866$	83.8501	2.84934
$867$	16.9786	0.576624
$868$	0	0
$869$	64.9416	2.20299
$870$	−35.8439	−1.21522
$871$	4.52081	0.153182
$872$	−48.0455	−1.62703
$873$	−5.53442	−0.187312
$874$	13.2346	0.447666
$875$	0	0
$876$	32.7504	1.10653
$877$	4.69948	0.158690	0.0793451	−	0.996847i	$-0.474717\pi$
$877$	4.69948	0.158690	0.0793451	+	0.996847i	$0.474717\pi$
$878$	−24.0551	−0.811821
$879$	−8.71064	−0.293802
$880$	48.3916	1.63128
$881$	12.0182	0.404904	0.202452	−	0.979292i	$-0.435109\pi$
$881$	12.0182	0.404904	0.202452	+	0.979292i	$0.435109\pi$
$882$	0	0
$883$	59.0988	1.98883	0.994417	−	0.105520i	$-0.0336507\pi$
$883$	59.0988	1.98883	0.994417	+	0.105520i	$0.0336507\pi$
$884$	−1.74493	−0.0586883
$885$	−6.33830	−0.213060
$886$	−57.9952	−1.94839
$887$	−46.1453	−1.54941	−0.774704	−	0.632324i	$-0.782101\pi$
$887$	−46.1453	−1.54941	−0.774704	+	0.632324i	$0.782101\pi$
$888$	14.5544	0.488415
$889$	0	0
$890$	15.4116	0.516598
$891$	−6.26313	−0.209823
$892$	67.1482	2.24829
$893$	−20.5818	−0.688743
$894$	36.8150	1.23128
$895$	−58.1097	−1.94239
$896$	0	0
$897$	10.1389	0.338527
$898$	46.4980	1.55166
$899$	−5.38072	−0.179457
$900$	31.4950	1.04983
$901$	−0.646052	−0.0215231
$902$	14.9053	0.496294
$903$	0	0
$904$	−44.3247	−1.47422
$905$	−11.9821	−0.398300
$906$	−14.5020	−0.481798
$907$	21.7744	0.723008	0.361504	−	0.932370i	$-0.382263\pi$
$907$	21.7744	0.723008	0.361504	+	0.932370i	$0.382263\pi$
$908$	−67.2195	−2.23076
$909$	−15.9955	−0.530537
$910$	0	0
$911$	39.8850	1.32145	0.660724	−	0.750629i	$-0.270249\pi$
$911$	39.8850	1.32145	0.660724	+	0.750629i	$0.270249\pi$
$912$	−3.74240	−0.123923
$913$	−66.6625	−2.20621
$914$	−62.4886	−2.06694
$915$	−22.2084	−0.734186
$916$	−15.5331	−0.513228
$917$	0	0
$918$	−0.348089	−0.0114886
$919$	−50.3237	−1.66002	−0.830012	−	0.557745i	$-0.811667\pi$
$919$	−50.3237	−1.66002	−0.830012	+	0.557745i	$0.811667\pi$
$920$	−45.4587	−1.49873
$921$	−27.2743	−0.898718
$922$	27.4962	0.905538
$923$	29.0618	0.956580
$924$	0	0
$925$	31.5999	1.03900
$926$	2.79565	0.0918707
$927$	−18.2558	−0.599600
$928$	11.9765	0.393147
$929$	23.1421	0.759267	0.379633	−	0.925137i	$-0.376050\pi$
$929$	23.1421	0.759267	0.379633	+	0.925137i	$0.376050\pi$
$930$	11.5599	0.379063
$931$	0	0
$932$	61.9840	2.03035
$933$	10.3281	0.338127
$934$	12.6746	0.414727
$935$	−3.37788	−0.110468
$936$	−12.8928	−0.421414
$937$	28.0250	0.915535	0.457768	−	0.889072i	$-0.348649\pi$
$937$	28.0250	0.915535	0.457768	+	0.889072i	$0.348649\pi$
$938$	0	0
$939$	−30.1284	−0.983204
$940$	155.680	5.07772
$941$	−1.30089	−0.0424079	−0.0212040	−	0.999775i	$-0.506750\pi$
$941$	−1.30089	−0.0424079	−0.0212040	+	0.999775i	$0.506750\pi$
$942$	−4.94229	−0.161029
$943$	−3.11368	−0.101395
$944$	−3.60184	−0.117230
$945$	0	0
$946$	−135.377	−4.40150
$947$	−28.0944	−0.912944	−0.456472	−	0.889738i	$-0.650887\pi$
$947$	−28.0944	−0.912944	−0.456472	+	0.889738i	$0.650887\pi$
$948$	37.9886	1.23381
$949$	−29.1079	−0.944882
$950$	−36.5390	−1.18548
$951$	−19.6474	−0.637112
$952$	0	0
$953$	−32.4370	−1.05074	−0.525368	−	0.850875i	$-0.676073\pi$
$953$	−32.4370	−1.05074	−0.525368	+	0.850875i	$0.676073\pi$
$954$	−10.5118	−0.340334
$955$	3.28009	0.106141
$956$	−46.2100	−1.49454
$957$	25.5825	0.826965
$958$	61.0287	1.97175
$959$	0	0
$960$	−41.1829	−1.32917
$961$	−29.2647	−0.944022
$962$	−28.4860	−0.918426
$963$	−3.48468	−0.112292
$964$	−105.528	−3.39882
$965$	9.15740	0.294787
$966$	0	0
$967$	−50.6459	−1.62866	−0.814331	−	0.580401i	$-0.802896\pi$
$967$	−50.6459	−1.62866	−0.814331	+	0.580401i	$0.802896\pi$
$968$	−111.761	−3.59215
$969$	0.261231	0.00839195
$970$	−48.5664	−1.55937
$971$	11.8113	0.379042	0.189521	−	0.981877i	$-0.439307\pi$
$971$	11.8113	0.379042	0.189521	+	0.981877i	$0.439307\pi$
$972$	−3.66372	−0.117514
$973$	0	0
$974$	7.73808	0.247944
$975$	−27.9922	−0.896467
$976$	−12.6203	−0.403965
$977$	54.8172	1.75376	0.876879	−	0.480710i	$-0.159621\pi$
$977$	54.8172	1.75376	0.876879	+	0.480710i	$0.159621\pi$
$978$	27.0065	0.863573
$979$	−10.9996	−0.351547
$980$	0	0
$981$	12.1345	0.387425
$982$	46.4096	1.48099
$983$	5.79541	0.184845	0.0924224	−	0.995720i	$-0.470539\pi$
$983$	5.79541	0.184845	0.0924224	+	0.995720i	$0.470539\pi$
$984$	3.95941	0.126221
$985$	59.2779	1.88875
$986$	1.42181	0.0452797
$987$	0	0
$988$	21.3071	0.677868
$989$	28.2799	0.899248
$990$	−54.9611	−1.74678
$991$	−18.5305	−0.588642	−0.294321	−	0.955707i	$-0.595093\pi$
$991$	−18.5305	−0.588642	−0.294321	+	0.955707i	$0.595093\pi$
$992$	−3.86248	−0.122634
$993$	33.1392	1.05164
$994$	0	0
$995$	22.4415	0.711443
$996$	−38.9953	−1.23561
$997$	−40.1082	−1.27024	−0.635119	−	0.772414i	$-0.719049\pi$
$997$	−40.1082	−1.27024	−0.635119	+	0.772414i	$0.719049\pi$
$998$	−77.6503	−2.45798
$999$	−3.67591	−0.116301

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bn.1.2	✓	24
7.6	odd	2		6027.2.a.bo.1.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6027.2.a.bn.1.2	✓	24	1.1	even	1	trivial
6027.2.a.bo.1.2	yes	24	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:	\( N \)	\(=\)	\( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.37986 q^{2} -1.00000 q^{3} +3.66372 q^{4} -3.68734 q^{5} +2.37986 q^{6} -3.95941 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.37986 q^{2} -1.00000 q^{3} +3.66372 q^{4} -3.68734 q^{5} +2.37986 q^{6} -3.95941 q^{8} +1.00000 q^{9} +8.77534 q^{10} -6.26313 q^{11} -3.66372 q^{12} +3.25624 q^{13} +3.68734 q^{15} +2.09539 q^{16} -0.146265 q^{17} -2.37986 q^{18} +1.78602 q^{19} -13.5094 q^{20} +14.9053 q^{22} -3.11368 q^{23} +3.95941 q^{24} +8.59647 q^{25} -7.74938 q^{26} -1.00000 q^{27} +4.08462 q^{29} -8.77534 q^{30} -1.31731 q^{31} +2.93209 q^{32} +6.26313 q^{33} +0.348089 q^{34} +3.66372 q^{36} +3.67591 q^{37} -4.25047 q^{38} -3.25624 q^{39} +14.5997 q^{40} +1.00000 q^{41} -9.08247 q^{43} -22.9463 q^{44} -3.68734 q^{45} +7.41011 q^{46} -11.5238 q^{47} -2.09539 q^{48} -20.4584 q^{50} +0.146265 q^{51} +11.9299 q^{52} +4.41701 q^{53} +2.37986 q^{54} +23.0943 q^{55} -1.78602 q^{57} -9.72081 q^{58} -1.71894 q^{59} +13.5094 q^{60} -6.02287 q^{61} +3.13502 q^{62} -11.1687 q^{64} -12.0069 q^{65} -14.9053 q^{66} +1.38835 q^{67} -0.535872 q^{68} +3.11368 q^{69} +8.92495 q^{71} -3.95941 q^{72} -8.93911 q^{73} -8.74814 q^{74} -8.59647 q^{75} +6.54346 q^{76} +7.74938 q^{78} -10.3689 q^{79} -7.72642 q^{80} +1.00000 q^{81} -2.37986 q^{82} +10.6436 q^{83} +0.539327 q^{85} +21.6150 q^{86} -4.08462 q^{87} +24.7983 q^{88} +1.75624 q^{89} +8.77534 q^{90} -11.4076 q^{92} +1.31731 q^{93} +27.4251 q^{94} -6.58565 q^{95} -2.93209 q^{96} -5.53442 q^{97} -6.26313 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{2} - 24 q^{3} + 32 q^{4} - 4 q^{5} - 8 q^{6} + 24 q^{8} + 24 q^{9}+O(q^{10}) \) 24 * q + 8 * q^2 - 24 * q^3 + 32 * q^4 - 4 * q^5 - 8 * q^6 + 24 * q^8 + 24 * q^9	\( 24 q + 8 q^{2} - 24 q^{3} + 32 q^{4} - 4 q^{5} - 8 q^{6} + 24 q^{8} + 24 q^{9} + 4 q^{10} + 12 q^{11} - 32 q^{12} + 4 q^{15} + 44 q^{16} - 8 q^{17} + 8 q^{18} + 4 q^{19} - 28 q^{20} + 16 q^{22} + 20 q^{23} - 24 q^{24} + 48 q^{25} - 32 q^{26} - 24 q^{27} + 24 q^{29} - 4 q^{30} + 4 q^{31} + 36 q^{32} - 12 q^{33} - 16 q^{34} + 32 q^{36} + 64 q^{37} - 20 q^{38} + 48 q^{40} + 24 q^{41} + 20 q^{43} + 48 q^{44} - 4 q^{45} + 28 q^{46} - 32 q^{47} - 44 q^{48} - 20 q^{50} + 8 q^{51} + 76 q^{53} - 8 q^{54} + 24 q^{55} - 4 q^{57} + 28 q^{58} - 28 q^{59} + 28 q^{60} + 28 q^{61} + 4 q^{62} + 48 q^{64} + 28 q^{65} - 16 q^{66} + 44 q^{67} + 32 q^{68} - 20 q^{69} + 20 q^{71} + 24 q^{72} + 16 q^{73} + 44 q^{74} - 48 q^{75} + 16 q^{76} + 32 q^{78} + 4 q^{79} - 44 q^{80} + 24 q^{81} + 8 q^{82} - 8 q^{83} + 28 q^{85} + 56 q^{86} - 24 q^{87} + 60 q^{88} - 60 q^{89} + 4 q^{90} + 60 q^{92} - 4 q^{93} - 24 q^{94} + 28 q^{95} - 36 q^{96} + 48 q^{97} + 12 q^{99}+O(q^{100}) \) 24 * q + 8 * q^2 - 24 * q^3 + 32 * q^4 - 4 * q^5 - 8 * q^6 + 24 * q^8 + 24 * q^9 + 4 * q^10 + 12 * q^11 - 32 * q^12 + 4 * q^15 + 44 * q^16 - 8 * q^17 + 8 * q^18 + 4 * q^19 - 28 * q^20 + 16 * q^22 + 20 * q^23 - 24 * q^24 + 48 * q^25 - 32 * q^26 - 24 * q^27 + 24 * q^29 - 4 * q^30 + 4 * q^31 + 36 * q^32 - 12 * q^33 - 16 * q^34 + 32 * q^36 + 64 * q^37 - 20 * q^38 + 48 * q^40 + 24 * q^41 + 20 * q^43 + 48 * q^44 - 4 * q^45 + 28 * q^46 - 32 * q^47 - 44 * q^48 - 20 * q^50 + 8 * q^51 + 76 * q^53 - 8 * q^54 + 24 * q^55 - 4 * q^57 + 28 * q^58 - 28 * q^59 + 28 * q^60 + 28 * q^61 + 4 * q^62 + 48 * q^64 + 28 * q^65 - 16 * q^66 + 44 * q^67 + 32 * q^68 - 20 * q^69 + 20 * q^71 + 24 * q^72 + 16 * q^73 + 44 * q^74 - 48 * q^75 + 16 * q^76 + 32 * q^78 + 4 * q^79 - 44 * q^80 + 24 * q^81 + 8 * q^82 - 8 * q^83 + 28 * q^85 + 56 * q^86 - 24 * q^87 + 60 * q^88 - 60 * q^89 + 4 * q^90 + 60 * q^92 - 4 * q^93 - 24 * q^94 + 28 * q^95 - 36 * q^96 + 48 * q^97 + 12 * q^99

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