LMFDB - Embedded newform 6027.2.a.bo.1.9

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			1.9
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)

$f(q)$	$=$	$q-0.423828 q^{2} +1.00000 q^{3} -1.82037 q^{4} +3.41632 q^{5} -0.423828 q^{6} +1.61918 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.423828 q^{2} +1.00000 q^{3} -1.82037 q^{4} +3.41632 q^{5} -0.423828 q^{6} +1.61918 q^{8} +1.00000 q^{9} -1.44793 q^{10} +1.20844 q^{11} -1.82037 q^{12} +1.26276 q^{13} +3.41632 q^{15} +2.95449 q^{16} +2.17395 q^{17} -0.423828 q^{18} -7.30164 q^{19} -6.21897 q^{20} -0.512171 q^{22} +4.90922 q^{23} +1.61918 q^{24} +6.67126 q^{25} -0.535192 q^{26} +1.00000 q^{27} +0.506374 q^{29} -1.44793 q^{30} +6.04329 q^{31} -4.49055 q^{32} +1.20844 q^{33} -0.921382 q^{34} -1.82037 q^{36} +6.73103 q^{37} +3.09464 q^{38} +1.26276 q^{39} +5.53164 q^{40} -1.00000 q^{41} -7.21084 q^{43} -2.19981 q^{44} +3.41632 q^{45} -2.08066 q^{46} +5.13896 q^{47} +2.95449 q^{48} -2.82746 q^{50} +2.17395 q^{51} -2.29869 q^{52} -7.67647 q^{53} -0.423828 q^{54} +4.12842 q^{55} -7.30164 q^{57} -0.214615 q^{58} +3.05287 q^{59} -6.21897 q^{60} +1.50585 q^{61} -2.56131 q^{62} -4.00576 q^{64} +4.31399 q^{65} -0.512171 q^{66} +2.66239 q^{67} -3.95740 q^{68} +4.90922 q^{69} -8.67388 q^{71} +1.61918 q^{72} +12.5013 q^{73} -2.85280 q^{74} +6.67126 q^{75} +13.2917 q^{76} -0.535192 q^{78} +7.94958 q^{79} +10.0935 q^{80} +1.00000 q^{81} +0.423828 q^{82} -5.53811 q^{83} +7.42693 q^{85} +3.05615 q^{86} +0.506374 q^{87} +1.95668 q^{88} +4.64437 q^{89} -1.44793 q^{90} -8.93659 q^{92} +6.04329 q^{93} -2.17803 q^{94} -24.9448 q^{95} -4.49055 q^{96} -1.13053 q^{97} +1.20844 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.423828	−0.299691	−0.149846	−	0.988709i	$-0.547878\pi$
$2$	−0.423828	−0.299691	−0.149846	+	0.988709i	$0.547878\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.82037	−0.910185
$5$	3.41632	1.52783	0.763913	−	0.645319i	$-0.223276\pi$
$5$	3.41632	1.52783	0.763913	+	0.645319i	$0.223276\pi$
$6$	−0.423828	−0.173027
$7$	0	0
$7$	0	0
$8$	1.61918	0.572466
$9$	1.00000	0.333333
$10$	−1.44793	−0.457876
$11$	1.20844	0.364359	0.182179	−	0.983265i	$-0.441685\pi$
$11$	1.20844	0.364359	0.182179	+	0.983265i	$0.441685\pi$
$12$	−1.82037	−0.525496
$13$	1.26276	0.350226	0.175113	−	0.984548i	$-0.443971\pi$
$13$	1.26276	0.350226	0.175113	+	0.984548i	$0.443971\pi$
$14$	0	0
$15$	3.41632	0.882091
$16$	2.95449	0.738622
$17$	2.17395	0.527261	0.263631	−	0.964624i	$-0.415080\pi$
$17$	2.17395	0.527261	0.263631	+	0.964624i	$0.415080\pi$
$18$	−0.423828	−0.0998971
$19$	−7.30164	−1.67511	−0.837556	−	0.546352i	$-0.816016\pi$
$19$	−7.30164	−1.67511	−0.837556	+	0.546352i	$0.816016\pi$
$20$	−6.21897	−1.39060
$21$	0	0
$22$	−0.512171	−0.109195
$23$	4.90922	1.02364	0.511821	−	0.859092i	$-0.328971\pi$
$23$	4.90922	1.02364	0.511821	+	0.859092i	$0.328971\pi$
$24$	1.61918	0.330513
$25$	6.67126	1.33425
$26$	−0.535192	−0.104960
$27$	1.00000	0.192450
$28$	0	0
$29$	0.506374	0.0940313	0.0470156	−	0.998894i	$-0.485029\pi$
$29$	0.506374	0.0940313	0.0470156	+	0.998894i	$0.485029\pi$
$30$	−1.44793	−0.264355
$31$	6.04329	1.08541	0.542703	−	0.839925i	$-0.317401\pi$
$31$	6.04329	1.08541	0.542703	+	0.839925i	$0.317401\pi$
$32$	−4.49055	−0.793825
$33$	1.20844	0.210363
$34$	−0.921382	−0.158016
$35$	0	0
$36$	−1.82037	−0.303395
$37$	6.73103	1.10658	0.553288	−	0.832990i	$-0.313373\pi$
$37$	6.73103	1.10658	0.553288	+	0.832990i	$0.313373\pi$
$38$	3.09464	0.502017
$39$	1.26276	0.202203
$40$	5.53164	0.874629
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	−7.21084	−1.09964	−0.549821	−	0.835282i	$-0.685304\pi$
$43$	−7.21084	−1.09964	−0.549821	+	0.835282i	$0.685304\pi$
$44$	−2.19981	−0.331634
$45$	3.41632	0.509275
$46$	−2.08066	−0.306777
$47$	5.13896	0.749595	0.374797	−	0.927107i	$-0.377712\pi$
$47$	5.13896	0.749595	0.374797	+	0.927107i	$0.377712\pi$
$48$	2.95449	0.426444
$49$	0	0
$50$	−2.82746	−0.399864
$51$	2.17395	0.304414
$52$	−2.29869	−0.318771
$53$	−7.67647	−1.05444	−0.527222	−	0.849727i	$-0.676766\pi$
$53$	−7.67647	−1.05444	−0.527222	+	0.849727i	$0.676766\pi$
$54$	−0.423828	−0.0576756
$55$	4.12842	0.556677
$56$	0	0
$57$	−7.30164	−0.967126
$58$	−0.214615	−0.0281804
$59$	3.05287	0.397450	0.198725	−	0.980055i	$-0.436320\pi$
$59$	3.05287	0.397450	0.198725	+	0.980055i	$0.436320\pi$
$60$	−6.21897	−0.802866
$61$	1.50585	0.192805	0.0964024	−	0.995342i	$-0.469266\pi$
$61$	1.50585	0.192805	0.0964024	+	0.995342i	$0.469266\pi$
$62$	−2.56131	−0.325287
$63$	0	0
$64$	−4.00576	−0.500719
$65$	4.31399	0.535084
$66$	−0.512171	−0.0630438
$67$	2.66239	0.325263	0.162632	−	0.986687i	$-0.448002\pi$
$67$	2.66239	0.325263	0.162632	+	0.986687i	$0.448002\pi$
$68$	−3.95740	−0.479905
$69$	4.90922	0.591000
$70$	0	0
$71$	−8.67388	−1.02940	−0.514700	−	0.857370i	$-0.672097\pi$
$71$	−8.67388	−1.02940	−0.514700	+	0.857370i	$0.672097\pi$
$72$	1.61918	0.190822
$73$	12.5013	1.46316	0.731580	−	0.681755i	$-0.238783\pi$
$73$	12.5013	1.46316	0.731580	+	0.681755i	$0.238783\pi$
$74$	−2.85280	−0.331631
$75$	6.67126	0.770331
$76$	13.2917	1.52466
$77$	0	0
$78$	−0.535192	−0.0605985
$79$	7.94958	0.894397	0.447199	−	0.894435i	$-0.352422\pi$
$79$	7.94958	0.894397	0.447199	+	0.894435i	$0.352422\pi$
$80$	10.0935	1.12849
$81$	1.00000	0.111111
$82$	0.423828	0.0468039
$83$	−5.53811	−0.607886	−0.303943	−	0.952690i	$-0.598303\pi$
$83$	−5.53811	−0.607886	−0.303943	+	0.952690i	$0.598303\pi$
$84$	0	0
$85$	7.42693	0.805563
$86$	3.05615	0.329553
$87$	0.506374	0.0542890
$88$	1.95668	0.208583
$89$	4.64437	0.492303	0.246151	−	0.969231i	$-0.420834\pi$
$89$	4.64437	0.492303	0.246151	+	0.969231i	$0.420834\pi$
$90$	−1.44793	−0.152625
$91$	0	0
$92$	−8.93659	−0.931704
$93$	6.04329	0.626660
$94$	−2.17803	−0.224647
$95$	−24.9448	−2.55928
$96$	−4.49055	−0.458315
$97$	−1.13053	−0.114788	−0.0573940	−	0.998352i	$-0.518279\pi$
$97$	−1.13053	−0.114788	−0.0573940	+	0.998352i	$0.518279\pi$
$98$	0	0
$99$	1.20844	0.121453
$100$	−12.1442	−1.21442
$101$	5.31509	0.528871	0.264436	−	0.964403i	$-0.414814\pi$
$101$	5.31509	0.528871	0.264436	+	0.964403i	$0.414814\pi$
$102$	−0.921382	−0.0912304
$103$	−5.38877	−0.530972	−0.265486	−	0.964115i	$-0.585532\pi$
$103$	−5.38877	−0.530972	−0.265486	+	0.964115i	$0.585532\pi$
$104$	2.04463	0.200493
$105$	0	0
$106$	3.25350	0.316008
$107$	2.77874	0.268631	0.134315	−	0.990939i	$-0.457116\pi$
$107$	2.77874	0.268631	0.134315	+	0.990939i	$0.457116\pi$
$108$	−1.82037	−0.175165
$109$	11.6577	1.11661	0.558304	−	0.829637i	$-0.311452\pi$
$109$	11.6577	1.11661	0.558304	+	0.829637i	$0.311452\pi$
$110$	−1.74974	−0.166831
$111$	6.73103	0.638882
$112$	0	0
$113$	11.6261	1.09369	0.546844	−	0.837234i	$-0.315829\pi$
$113$	11.6261	1.09369	0.546844	+	0.837234i	$0.315829\pi$
$114$	3.09464	0.289839
$115$	16.7715	1.56395
$116$	−0.921788	−0.0855859
$117$	1.26276	0.116742
$118$	−1.29389	−0.119112
$119$	0	0
$120$	5.53164	0.504967
$121$	−9.53967	−0.867243
$122$	−0.638222	−0.0577819
$123$	−1.00000	−0.0901670
$124$	−11.0010	−0.987921
$125$	5.70956	0.510679
$126$	0	0
$127$	9.37534	0.831927	0.415964	−	0.909381i	$-0.363444\pi$
$127$	9.37534	0.831927	0.415964	+	0.909381i	$0.363444\pi$
$128$	10.6789	0.943886
$129$	−7.21084	−0.634879
$130$	−1.82839	−0.160360
$131$	5.63692	0.492500	0.246250	−	0.969206i	$-0.420802\pi$
$131$	5.63692	0.492500	0.246250	+	0.969206i	$0.420802\pi$
$132$	−2.19981	−0.191469
$133$	0	0
$134$	−1.12840	−0.0974785
$135$	3.41632	0.294030
$136$	3.52002	0.301839
$137$	6.59136	0.563138	0.281569	−	0.959541i	$-0.409145\pi$
$137$	6.59136	0.563138	0.281569	+	0.959541i	$0.409145\pi$
$138$	−2.08066	−0.177118
$139$	−9.80432	−0.831592	−0.415796	−	0.909458i	$-0.636497\pi$
$139$	−9.80432	−0.831592	−0.415796	+	0.909458i	$0.636497\pi$
$140$	0	0
$141$	5.13896	0.432779
$142$	3.67623	0.308502
$143$	1.52597	0.127608
$144$	2.95449	0.246207
$145$	1.72994	0.143663
$146$	−5.29838	−0.438497
$147$	0	0
$148$	−12.2530	−1.00719
$149$	−16.2225	−1.32900	−0.664501	−	0.747288i	$-0.731356\pi$
$149$	−16.2225	−1.32900	−0.664501	+	0.747288i	$0.731356\pi$
$150$	−2.82746	−0.230862
$151$	10.1199	0.823542	0.411771	−	0.911287i	$-0.364910\pi$
$151$	10.1199	0.823542	0.411771	+	0.911287i	$0.364910\pi$
$152$	−11.8227	−0.958944
$153$	2.17395	0.175754
$154$	0	0
$155$	20.6458	1.65831
$156$	−2.29869	−0.184042
$157$	9.73266	0.776751	0.388375	−	0.921501i	$-0.373036\pi$
$157$	9.73266	0.776751	0.388375	+	0.921501i	$0.373036\pi$
$158$	−3.36925	−0.268043
$159$	−7.67647	−0.608784
$160$	−15.3412	−1.21283
$161$	0	0
$162$	−0.423828	−0.0332990
$163$	−8.37276	−0.655805	−0.327902	−	0.944712i	$-0.606342\pi$
$163$	−8.37276	−0.655805	−0.327902	+	0.944712i	$0.606342\pi$
$164$	1.82037	0.142147
$165$	4.12842	0.321397
$166$	2.34720	0.182178
$167$	−8.10166	−0.626925	−0.313463	−	0.949601i	$-0.601489\pi$
$167$	−8.10166	−0.626925	−0.313463	+	0.949601i	$0.601489\pi$
$168$	0	0
$169$	−11.4054	−0.877342
$170$	−3.14774	−0.241420
$171$	−7.30164	−0.558370
$172$	13.1264	1.00088
$173$	−20.1515	−1.53209	−0.766045	−	0.642787i	$-0.777778\pi$
$173$	−20.1515	−1.53209	−0.766045	+	0.642787i	$0.777778\pi$
$174$	−0.214615	−0.0162699
$175$	0	0
$176$	3.57032	0.269123
$177$	3.05287	0.229468
$178$	−1.96841	−0.147539
$179$	−22.8501	−1.70790	−0.853949	−	0.520356i	$-0.825799\pi$
$179$	−22.8501	−1.70790	−0.853949	+	0.520356i	$0.825799\pi$
$180$	−6.21897	−0.463535
$181$	−4.04932	−0.300984	−0.150492	−	0.988611i	$-0.548086\pi$
$181$	−4.04932	−0.300984	−0.150492	+	0.988611i	$0.548086\pi$
$182$	0	0
$183$	1.50585	0.111316
$184$	7.94890	0.586001
$185$	22.9954	1.69065
$186$	−2.56131	−0.187805
$187$	2.62709	0.192112
$188$	−9.35481	−0.682270
$189$	0	0
$190$	10.5723	0.766994
$191$	−7.32116	−0.529741	−0.264870	−	0.964284i	$-0.585329\pi$
$191$	−7.32116	−0.529741	−0.264870	+	0.964284i	$0.585329\pi$
$192$	−4.00576	−0.289090
$193$	7.86097	0.565845	0.282922	−	0.959143i	$-0.408696\pi$
$193$	7.86097	0.565845	0.282922	+	0.959143i	$0.408696\pi$
$194$	0.479150	0.0344010
$195$	4.31399	0.308931
$196$	0	0
$197$	−15.2389	−1.08573	−0.542865	−	0.839820i	$-0.682660\pi$
$197$	−15.2389	−1.08573	−0.542865	+	0.839820i	$0.682660\pi$
$198$	−0.512171	−0.0363984
$199$	−0.755541	−0.0535589	−0.0267795	−	0.999641i	$-0.508525\pi$
$199$	−0.755541	−0.0535589	−0.0267795	+	0.999641i	$0.508525\pi$
$200$	10.8020	0.763814
$201$	2.66239	0.187791
$202$	−2.25268	−0.158498
$203$	0	0
$204$	−3.95740	−0.277073
$205$	−3.41632	−0.238606
$206$	2.28391	0.159128
$207$	4.90922	0.341214
$208$	3.73080	0.258685
$209$	−8.82360	−0.610341
$210$	0	0
$211$	18.4932	1.27312	0.636562	−	0.771225i	$-0.280356\pi$
$211$	18.4932	1.27312	0.636562	+	0.771225i	$0.280356\pi$
$212$	13.9740	0.959739
$213$	−8.67388	−0.594324
$214$	−1.17771	−0.0805063
$215$	−24.6345	−1.68006
$216$	1.61918	0.110171
$217$	0	0
$218$	−4.94087	−0.334638
$219$	12.5013	0.844756
$220$	−7.51526	−0.506679
$221$	2.74518	0.184661
$222$	−2.85280	−0.191467
$223$	0.388827	0.0260378	0.0130189	−	0.999915i	$-0.495856\pi$
$223$	0.388827	0.0260378	0.0130189	+	0.999915i	$0.495856\pi$
$224$	0	0
$225$	6.67126	0.444751
$226$	−4.92745	−0.327769
$227$	3.86038	0.256223	0.128111	−	0.991760i	$-0.459109\pi$
$227$	3.86038	0.256223	0.128111	+	0.991760i	$0.459109\pi$
$228$	13.2917	0.880264
$229$	20.9616	1.38518	0.692591	−	0.721331i	$-0.256469\pi$
$229$	20.9616	1.38518	0.692591	+	0.721331i	$0.256469\pi$
$230$	−7.10821	−0.468702
$231$	0	0
$232$	0.819910	0.0538297
$233$	−4.79767	−0.314306	−0.157153	−	0.987574i	$-0.550232\pi$
$233$	−4.79767	−0.314306	−0.157153	+	0.987574i	$0.550232\pi$
$234$	−0.535192	−0.0349866
$235$	17.5564	1.14525
$236$	−5.55735	−0.361753
$237$	7.94958	0.516380
$238$	0	0
$239$	16.4100	1.06147	0.530737	−	0.847536i	$-0.321915\pi$
$239$	16.4100	1.06147	0.530737	+	0.847536i	$0.321915\pi$
$240$	10.0935	0.651532
$241$	29.2741	1.88571	0.942856	−	0.333199i	$-0.108128\pi$
$241$	29.2741	1.88571	0.942856	+	0.333199i	$0.108128\pi$
$242$	4.04318	0.259905
$243$	1.00000	0.0641500
$244$	−2.74121	−0.175488
$245$	0	0
$246$	0.423828	0.0270223
$247$	−9.22021	−0.586668
$248$	9.78516	0.621358
$249$	−5.53811	−0.350963
$250$	−2.41987	−0.153046
$251$	16.9300	1.06861	0.534305	−	0.845292i	$-0.320573\pi$
$251$	16.9300	1.06861	0.534305	+	0.845292i	$0.320573\pi$
$252$	0	0
$253$	5.93250	0.372973
$254$	−3.97353	−0.249321
$255$	7.42693	0.465092
$256$	3.48552	0.217845
$257$	17.2556	1.07637	0.538186	−	0.842826i	$-0.319110\pi$
$257$	17.2556	1.07637	0.538186	+	0.842826i	$0.319110\pi$
$258$	3.05615	0.190268
$259$	0	0
$260$	−7.85306	−0.487026
$261$	0.506374	0.0313438
$262$	−2.38908	−0.147598
$263$	20.1756	1.24408	0.622041	−	0.782984i	$-0.286304\pi$
$263$	20.1756	1.24408	0.622041	+	0.782984i	$0.286304\pi$
$264$	1.95668	0.120425
$265$	−26.2253	−1.61101
$266$	0	0
$267$	4.64437	0.284231
$268$	−4.84654	−0.296050
$269$	19.9933	1.21901	0.609506	−	0.792781i	$-0.291368\pi$
$269$	19.9933	1.21901	0.609506	+	0.792781i	$0.291368\pi$
$270$	−1.44793	−0.0881183
$271$	−30.7338	−1.86694	−0.933471	−	0.358652i	$-0.883236\pi$
$271$	−30.7338	−1.86694	−0.933471	+	0.358652i	$0.883236\pi$
$272$	6.42292	0.389447
$273$	0	0
$274$	−2.79360	−0.168768
$275$	8.06182	0.486146
$276$	−8.93659	−0.537920
$277$	17.0956	1.02718	0.513588	−	0.858037i	$-0.328316\pi$
$277$	17.0956	1.02718	0.513588	+	0.858037i	$0.328316\pi$
$278$	4.15534	0.249221
$279$	6.04329	0.361802
$280$	0	0
$281$	−6.90275	−0.411783	−0.205892	−	0.978575i	$-0.566009\pi$
$281$	−6.90275	−0.411783	−0.205892	+	0.978575i	$0.566009\pi$
$282$	−2.17803	−0.129700
$283$	−14.7476	−0.876653	−0.438326	−	0.898816i	$-0.644429\pi$
$283$	−14.7476	−0.876653	−0.438326	+	0.898816i	$0.644429\pi$
$284$	15.7897	0.936944
$285$	−24.9448	−1.47760
$286$	−0.646748	−0.0382430
$287$	0	0
$288$	−4.49055	−0.264608
$289$	−12.2739	−0.721996
$290$	−0.733195	−0.0430547
$291$	−1.13053	−0.0662729
$292$	−22.7569	−1.33175
$293$	−4.27776	−0.249910	−0.124955	−	0.992162i	$-0.539879\pi$
$293$	−4.27776	−0.249910	−0.124955	+	0.992162i	$0.539879\pi$
$294$	0	0
$295$	10.4296	0.607234
$296$	10.8987	0.633477
$297$	1.20844	0.0701208
$298$	6.87556	0.398290
$299$	6.19915	0.358506
$300$	−12.1442	−0.701144
$301$	0	0
$302$	−4.28907	−0.246808
$303$	5.31509	0.305344
$304$	−21.5726	−1.23727
$305$	5.14448	0.294572
$306$	−0.921382	−0.0526719
$307$	−13.5544	−0.773593	−0.386796	−	0.922165i	$-0.626418\pi$
$307$	−13.5544	−0.773593	−0.386796	+	0.922165i	$0.626418\pi$
$308$	0	0
$309$	−5.38877	−0.306557
$310$	−8.75027	−0.496982
$311$	−1.34293	−0.0761505	−0.0380753	−	0.999275i	$-0.512123\pi$
$311$	−1.34293	−0.0761505	−0.0380753	+	0.999275i	$0.512123\pi$
$312$	2.04463	0.115754
$313$	12.5685	0.710415	0.355208	−	0.934787i	$-0.384410\pi$
$313$	12.5685	0.710415	0.355208	+	0.934787i	$0.384410\pi$
$314$	−4.12497	−0.232785
$315$	0	0
$316$	−14.4712	−0.814067
$317$	−8.59197	−0.482573	−0.241287	−	0.970454i	$-0.577569\pi$
$317$	−8.59197	−0.482573	−0.241287	+	0.970454i	$0.577569\pi$
$318$	3.25350	0.182447
$319$	0.611923	0.0342611
$320$	−13.6850	−0.765012
$321$	2.77874	0.155094
$322$	0	0
$323$	−15.8734	−0.883221
$324$	−1.82037	−0.101132
$325$	8.42419	0.467290
$326$	3.54861	0.196539
$327$	11.6577	0.644674
$328$	−1.61918	−0.0894042
$329$	0	0
$330$	−1.74974	−0.0963200
$331$	35.0682	1.92752	0.963761	−	0.266766i	$-0.0859551\pi$
$331$	35.0682	1.92752	0.963761	+	0.266766i	$0.0859551\pi$
$332$	10.0814	0.553289
$333$	6.73103	0.368858
$334$	3.43371	0.187884
$335$	9.09559	0.496945
$336$	0	0
$337$	14.8438	0.808594	0.404297	−	0.914628i	$-0.367516\pi$
$337$	14.8438	0.808594	0.404297	+	0.914628i	$0.367516\pi$
$338$	4.83394	0.262932
$339$	11.6261	0.631441
$340$	−13.5198	−0.733212
$341$	7.30296	0.395477
$342$	3.09464	0.167339
$343$	0	0
$344$	−11.6756	−0.629508
$345$	16.7715	0.902946
$346$	8.54076	0.459154
$347$	−2.60346	−0.139761	−0.0698805	−	0.997555i	$-0.522262\pi$
$347$	−2.60346	−0.139761	−0.0698805	+	0.997555i	$0.522262\pi$
$348$	−0.921788	−0.0494130
$349$	10.8091	0.578596	0.289298	−	0.957239i	$-0.406578\pi$
$349$	10.8091	0.578596	0.289298	+	0.957239i	$0.406578\pi$
$350$	0	0
$351$	1.26276	0.0674010
$352$	−5.42656	−0.289237
$353$	−28.5337	−1.51869	−0.759347	−	0.650686i	$-0.774482\pi$
$353$	−28.5337	−1.51869	−0.759347	+	0.650686i	$0.774482\pi$
$354$	−1.29389	−0.0687695
$355$	−29.6328	−1.57274
$356$	−8.45448	−0.448086
$357$	0	0
$358$	9.68452	0.511843
$359$	5.71023	0.301375	0.150687	−	0.988581i	$-0.451851\pi$
$359$	5.71023	0.301375	0.150687	+	0.988581i	$0.451851\pi$
$360$	5.53164	0.291543
$361$	34.3140	1.80600
$362$	1.71622	0.0902023
$363$	−9.53967	−0.500703
$364$	0	0
$365$	42.7083	2.23546
$366$	−0.638222	−0.0333604
$367$	−35.6658	−1.86174	−0.930869	−	0.365354i	$-0.880948\pi$
$367$	−35.6658	−1.86174	−0.930869	+	0.365354i	$0.880948\pi$
$368$	14.5042	0.756085
$369$	−1.00000	−0.0520579
$370$	−9.74608	−0.506675
$371$	0	0
$372$	−11.0010	−0.570376
$373$	−30.0359	−1.55520	−0.777600	−	0.628760i	$-0.783563\pi$
$373$	−30.0359	−1.55520	−0.777600	+	0.628760i	$0.783563\pi$
$374$	−1.11344	−0.0575744
$375$	5.70956	0.294841
$376$	8.32090	0.429118
$377$	0.639428	0.0329322
$378$	0	0
$379$	−31.5503	−1.62063	−0.810316	−	0.585994i	$-0.800704\pi$
$379$	−31.5503	−1.62063	−0.810316	+	0.585994i	$0.800704\pi$
$380$	45.4087	2.32942
$381$	9.37534	0.480313
$382$	3.10291	0.158759
$383$	−12.9828	−0.663392	−0.331696	−	0.943386i	$-0.607621\pi$
$383$	−12.9828	−0.663392	−0.331696	+	0.943386i	$0.607621\pi$
$384$	10.6789	0.544953
$385$	0	0
$386$	−3.33169	−0.169579
$387$	−7.21084	−0.366547
$388$	2.05798	0.104478
$389$	27.2660	1.38244	0.691220	−	0.722644i	$-0.257073\pi$
$389$	27.2660	1.38244	0.691220	+	0.722644i	$0.257073\pi$
$390$	−1.82839	−0.0925840
$391$	10.6724	0.539727
$392$	0	0
$393$	5.63692	0.284345
$394$	6.45868	0.325384
$395$	27.1583	1.36648
$396$	−2.19981	−0.110545
$397$	−13.0527	−0.655097	−0.327548	−	0.944834i	$-0.606222\pi$
$397$	−13.0527	−0.655097	−0.327548	+	0.944834i	$0.606222\pi$
$398$	0.320219	0.0160511
$399$	0	0
$400$	19.7102	0.985508
$401$	21.1440	1.05588	0.527940	−	0.849282i	$-0.322965\pi$
$401$	21.1440	1.05588	0.527940	+	0.849282i	$0.322965\pi$
$402$	−1.12840	−0.0562793
$403$	7.63121	0.380138
$404$	−9.67543	−0.481371
$405$	3.41632	0.169758
$406$	0	0
$407$	8.13406	0.403190
$408$	3.52002	0.174267
$409$	−21.5539	−1.06577	−0.532887	−	0.846186i	$-0.678893\pi$
$409$	−21.5539	−1.06577	−0.532887	+	0.846186i	$0.678893\pi$
$410$	1.44793	0.0715083
$411$	6.59136	0.325128
$412$	9.80956	0.483282
$413$	0	0
$414$	−2.08066	−0.102259
$415$	−18.9200	−0.928744
$416$	−5.67048	−0.278018
$417$	−9.80432	−0.480120
$418$	3.73969	0.182914
$419$	26.8639	1.31239	0.656194	−	0.754592i	$-0.272165\pi$
$419$	26.8639	1.31239	0.656194	+	0.754592i	$0.272165\pi$
$420$	0	0
$421$	35.5557	1.73288	0.866440	−	0.499282i	$-0.166403\pi$
$421$	35.5557	1.73288	0.866440	+	0.499282i	$0.166403\pi$
$422$	−7.83793	−0.381545
$423$	5.13896	0.249865
$424$	−12.4296	−0.603634
$425$	14.5030	0.703499
$426$	3.67623	0.178114
$427$	0	0
$428$	−5.05833	−0.244504
$429$	1.52597	0.0736744
$430$	10.4408	0.503500
$431$	−17.9655	−0.865366	−0.432683	−	0.901546i	$-0.642433\pi$
$431$	−17.9655	−0.865366	−0.432683	+	0.901546i	$0.642433\pi$
$432$	2.95449	0.142148
$433$	−1.94081	−0.0932692	−0.0466346	−	0.998912i	$-0.514850\pi$
$433$	−1.94081	−0.0932692	−0.0466346	+	0.998912i	$0.514850\pi$
$434$	0	0
$435$	1.72994	0.0829441
$436$	−21.2214	−1.01632
$437$	−35.8453	−1.71472
$438$	−5.29838	−0.253166
$439$	−19.9327	−0.951334	−0.475667	−	0.879626i	$-0.657793\pi$
$439$	−19.9327	−0.951334	−0.475667	+	0.879626i	$0.657793\pi$
$440$	6.68466	0.318678
$441$	0	0
$442$	−1.16348	−0.0553412
$443$	41.5846	1.97575	0.987873	−	0.155263i	$-0.0496226\pi$
$443$	41.5846	1.97575	0.987873	+	0.155263i	$0.0496226\pi$
$444$	−12.2530	−0.581500
$445$	15.8667	0.752153
$446$	−0.164796	−0.00780330
$447$	−16.2225	−0.767299
$448$	0	0
$449$	−25.2582	−1.19201	−0.596003	−	0.802982i	$-0.703245\pi$
$449$	−25.2582	−1.19201	−0.596003	+	0.802982i	$0.703245\pi$
$450$	−2.82746	−0.133288
$451$	−1.20844	−0.0569033
$452$	−21.1637	−0.995459
$453$	10.1199	0.475472
$454$	−1.63614	−0.0767877
$455$	0	0
$456$	−11.8227	−0.553647
$457$	24.9161	1.16552	0.582762	−	0.812643i	$-0.301972\pi$
$457$	24.9161	1.16552	0.582762	+	0.812643i	$0.301972\pi$
$458$	−8.88411	−0.415127
$459$	2.17395	0.101471
$460$	−30.5303	−1.42348
$461$	−21.5407	−1.00325	−0.501626	−	0.865085i	$-0.667265\pi$
$461$	−21.5407	−1.00325	−0.501626	+	0.865085i	$0.667265\pi$
$462$	0	0
$463$	4.53297	0.210665	0.105332	−	0.994437i	$-0.466409\pi$
$463$	4.53297	0.210665	0.105332	+	0.994437i	$0.466409\pi$
$464$	1.49608	0.0694536
$465$	20.6458	0.957427
$466$	2.03338	0.0941947
$467$	15.2773	0.706947	0.353474	−	0.935445i	$-0.385000\pi$
$467$	15.2773	0.706947	0.353474	+	0.935445i	$0.385000\pi$
$468$	−2.29869	−0.106257
$469$	0	0
$470$	−7.44087	−0.343222
$471$	9.73266	0.448457
$472$	4.94314	0.227526
$473$	−8.71387	−0.400664
$474$	−3.36925	−0.154755
$475$	−48.7112	−2.23502
$476$	0	0
$477$	−7.67647	−0.351481
$478$	−6.95501	−0.318115
$479$	−15.1805	−0.693616	−0.346808	−	0.937936i	$-0.612734\pi$
$479$	−15.1805	−0.693616	−0.346808	+	0.937936i	$0.612734\pi$
$480$	−15.3412	−0.700225
$481$	8.49967	0.387551
$482$	−12.4072	−0.565132
$483$	0	0
$484$	17.3657	0.789351
$485$	−3.86226	−0.175376
$486$	−0.423828	−0.0192252
$487$	−6.13268	−0.277898	−0.138949	−	0.990300i	$-0.544372\pi$
$487$	−6.13268	−0.277898	−0.138949	+	0.990300i	$0.544372\pi$
$488$	2.43825	0.110374
$489$	−8.37276	−0.378629
$490$	0	0
$491$	26.8565	1.21202	0.606009	−	0.795457i	$-0.292769\pi$
$491$	26.8565	1.21202	0.606009	+	0.795457i	$0.292769\pi$
$492$	1.82037	0.0820686
$493$	1.10083	0.0495790
$494$	3.90778	0.175819
$495$	4.12842	0.185559
$496$	17.8548	0.801705
$497$	0	0
$498$	2.34720	0.105181
$499$	30.2368	1.35358	0.676792	−	0.736174i	$-0.263370\pi$
$499$	30.2368	1.35358	0.676792	+	0.736174i	$0.263370\pi$
$500$	−10.3935	−0.464812
$501$	−8.10166	−0.361955
$502$	−7.17539	−0.320253
$503$	−21.6645	−0.965971	−0.482985	−	0.875628i	$-0.660448\pi$
$503$	−21.6645	−0.965971	−0.482985	+	0.875628i	$0.660448\pi$
$504$	0	0
$505$	18.1581	0.808023
$506$	−2.51436	−0.111777
$507$	−11.4054	−0.506533
$508$	−17.0666	−0.757208
$509$	18.6777	0.827876	0.413938	−	0.910305i	$-0.364153\pi$
$509$	18.6777	0.827876	0.413938	+	0.910305i	$0.364153\pi$
$510$	−3.14774	−0.139384
$511$	0	0
$512$	−22.8350	−1.00917
$513$	−7.30164	−0.322375
$514$	−7.31338	−0.322580
$515$	−18.4098	−0.811232
$516$	13.1264	0.577857
$517$	6.21013	0.273121
$518$	0	0
$519$	−20.1515	−0.884552
$520$	6.98512	0.306318
$521$	39.8641	1.74648	0.873239	−	0.487291i	$-0.162015\pi$
$521$	39.8641	1.74648	0.873239	+	0.487291i	$0.162015\pi$
$522$	−0.214615	−0.00939346
$523$	−16.5889	−0.725381	−0.362690	−	0.931910i	$-0.618142\pi$
$523$	−16.5889	−0.725381	−0.362690	+	0.931910i	$0.618142\pi$
$524$	−10.2613	−0.448266
$525$	0	0
$526$	−8.55099	−0.372841
$527$	13.1378	0.572293
$528$	3.57032	0.155378
$529$	1.10041	0.0478441
$530$	11.1150	0.482805
$531$	3.05287	0.132483
$532$	0	0
$533$	−1.26276	−0.0546961
$534$	−1.96841	−0.0851816
$535$	9.49307	0.410421
$536$	4.31089	0.186202
$537$	−22.8501	−0.986056
$538$	−8.47371	−0.365328
$539$	0	0
$540$	−6.21897	−0.267622
$541$	22.9294	0.985813	0.492906	−	0.870082i	$-0.335935\pi$
$541$	22.9294	0.985813	0.492906	+	0.870082i	$0.335935\pi$
$542$	13.0258	0.559507
$543$	−4.04932	−0.173773
$544$	−9.76225	−0.418553
$545$	39.8266	1.70598
$546$	0	0
$547$	9.12814	0.390291	0.195146	−	0.980774i	$-0.437482\pi$
$547$	9.12814	0.390291	0.195146	+	0.980774i	$0.437482\pi$
$548$	−11.9987	−0.512560
$549$	1.50585	0.0642682
$550$	−3.41682	−0.145694
$551$	−3.69736	−0.157513
$552$	7.94890	0.338328
$553$	0	0
$554$	−7.24560	−0.307836
$555$	22.9954	0.976100
$556$	17.8475	0.756902
$557$	18.9625	0.803465	0.401732	−	0.915757i	$-0.368408\pi$
$557$	18.9625	0.803465	0.401732	+	0.915757i	$0.368408\pi$
$558$	−2.56131	−0.108429
$559$	−9.10554	−0.385123
$560$	0	0
$561$	2.62709	0.110916
$562$	2.92558	0.123408
$563$	41.9549	1.76819	0.884093	−	0.467310i	$-0.154777\pi$
$563$	41.9549	1.76819	0.884093	+	0.467310i	$0.154777\pi$
$564$	−9.35481	−0.393909
$565$	39.7184	1.67097
$566$	6.25043	0.262725
$567$	0	0
$568$	−14.0446	−0.589296
$569$	3.36971	0.141266	0.0706328	−	0.997502i	$-0.477498\pi$
$569$	3.36971	0.141266	0.0706328	+	0.997502i	$0.477498\pi$
$570$	10.5723	0.442824
$571$	−7.37068	−0.308454	−0.154227	−	0.988035i	$-0.549289\pi$
$571$	−7.37068	−0.308454	−0.154227	+	0.988035i	$0.549289\pi$
$572$	−2.77783	−0.116147
$573$	−7.32116	−0.305846
$574$	0	0
$575$	32.7507	1.36580
$576$	−4.00576	−0.166906
$577$	32.5328	1.35436	0.677180	−	0.735818i	$-0.263202\pi$
$577$	32.5328	1.35436	0.677180	+	0.735818i	$0.263202\pi$
$578$	5.20203	0.216376
$579$	7.86097	0.326691
$580$	−3.14913	−0.130760
$581$	0	0
$582$	0.479150	0.0198614
$583$	−9.27656	−0.384196
$584$	20.2418	0.837610
$585$	4.31399	0.178361
$586$	1.81303	0.0748957
$587$	29.8858	1.23352	0.616759	−	0.787152i	$-0.288445\pi$
$587$	29.8858	1.23352	0.616759	+	0.787152i	$0.288445\pi$
$588$	0	0
$589$	−44.1259	−1.81818
$590$	−4.42035	−0.181983
$591$	−15.2389	−0.626846
$592$	19.8868	0.817341
$593$	35.3874	1.45319	0.726594	−	0.687068i	$-0.241102\pi$
$593$	35.3874	1.45319	0.726594	+	0.687068i	$0.241102\pi$
$594$	−0.512171	−0.0210146
$595$	0	0
$596$	29.5310	1.20964
$597$	−0.755541	−0.0309222
$598$	−2.62737	−0.107441
$599$	−12.9486	−0.529064	−0.264532	−	0.964377i	$-0.585217\pi$
$599$	−12.9486	−0.529064	−0.264532	+	0.964377i	$0.585217\pi$
$600$	10.8020	0.440988
$601$	−31.0540	−1.26672	−0.633359	−	0.773858i	$-0.718324\pi$
$601$	−31.0540	−1.26672	−0.633359	+	0.773858i	$0.718324\pi$
$602$	0	0
$603$	2.66239	0.108421
$604$	−18.4219	−0.749575
$605$	−32.5906	−1.32500
$606$	−2.25268	−0.0915090
$607$	6.57550	0.266891	0.133446	−	0.991056i	$-0.457396\pi$
$607$	6.57550	0.266891	0.133446	+	0.991056i	$0.457396\pi$
$608$	32.7884	1.32974
$609$	0	0
$610$	−2.18037	−0.0882807
$611$	6.48927	0.262528
$612$	−3.95740	−0.159968
$613$	9.22564	0.372620	0.186310	−	0.982491i	$-0.440347\pi$
$613$	9.22564	0.372620	0.186310	+	0.982491i	$0.440347\pi$
$614$	5.74475	0.231839
$615$	−3.41632	−0.137759
$616$	0	0
$617$	−30.7333	−1.23727	−0.618637	−	0.785677i	$-0.712315\pi$
$617$	−30.7333	−1.23727	−0.618637	+	0.785677i	$0.712315\pi$
$618$	2.28391	0.0918724
$619$	−10.0098	−0.402328	−0.201164	−	0.979558i	$-0.564472\pi$
$619$	−10.0098	−0.402328	−0.201164	+	0.979558i	$0.564472\pi$
$620$	−37.5830	−1.50937
$621$	4.90922	0.197000
$622$	0.569171	0.0228217
$623$	0	0
$624$	3.73080	0.149352
$625$	−13.8506	−0.554023
$626$	−5.32689	−0.212905
$627$	−8.82360	−0.352381
$628$	−17.7170	−0.706987
$629$	14.6330	0.583454
$630$	0	0
$631$	−36.9084	−1.46930	−0.734649	−	0.678447i	$-0.762653\pi$
$631$	−36.9084	−1.46930	−0.734649	+	0.678447i	$0.762653\pi$
$632$	12.8718	0.512012
$633$	18.4932	0.735039
$634$	3.64152	0.144623
$635$	32.0292	1.27104
$636$	13.9740	0.554106
$637$	0	0
$638$	−0.259350	−0.0102678
$639$	−8.67388	−0.343133
$640$	36.4824	1.44209
$641$	5.70866	0.225478	0.112739	−	0.993625i	$-0.464038\pi$
$641$	5.70866	0.225478	0.112739	+	0.993625i	$0.464038\pi$
$642$	−1.17771	−0.0464804
$643$	−18.1855	−0.717166	−0.358583	−	0.933498i	$-0.616740\pi$
$643$	−18.1855	−0.717166	−0.358583	+	0.933498i	$0.616740\pi$
$644$	0	0
$645$	−24.6345	−0.969984
$646$	6.72760	0.264694
$647$	−26.0068	−1.02243	−0.511217	−	0.859452i	$-0.670805\pi$
$647$	−26.0068	−1.02243	−0.511217	+	0.859452i	$0.670805\pi$
$648$	1.61918	0.0636073
$649$	3.68921	0.144814
$650$	−3.57040	−0.140043
$651$	0	0
$652$	15.2415	0.596904
$653$	35.2363	1.37890	0.689451	−	0.724332i	$-0.257852\pi$
$653$	35.2363	1.37890	0.689451	+	0.724332i	$0.257852\pi$
$654$	−4.94087	−0.193203
$655$	19.2575	0.752454
$656$	−2.95449	−0.115353
$657$	12.5013	0.487720
$658$	0	0
$659$	−44.6310	−1.73858	−0.869289	−	0.494304i	$-0.835423\pi$
$659$	−44.6310	−1.73858	−0.869289	+	0.494304i	$0.835423\pi$
$660$	−7.51526	−0.292531
$661$	−2.58592	−0.100581	−0.0502903	−	0.998735i	$-0.516015\pi$
$661$	−2.58592	−0.100581	−0.0502903	+	0.998735i	$0.516015\pi$
$662$	−14.8629	−0.577662
$663$	2.74518	0.106614
$664$	−8.96718	−0.347994
$665$	0	0
$666$	−2.85280	−0.110544
$667$	2.48590	0.0962544
$668$	14.7480	0.570618
$669$	0.388827	0.0150329
$670$	−3.85496	−0.148930
$671$	1.81973	0.0702501
$672$	0	0
$673$	−28.3612	−1.09324	−0.546621	−	0.837380i	$-0.684086\pi$
$673$	−28.3612	−1.09324	−0.546621	+	0.837380i	$0.684086\pi$
$674$	−6.29122	−0.242329
$675$	6.67126	0.256777
$676$	20.7621	0.798543
$677$	−27.6693	−1.06342	−0.531709	−	0.846927i	$-0.678450\pi$
$677$	−27.6693	−1.06342	−0.531709	+	0.846927i	$0.678450\pi$
$678$	−4.92745	−0.189237
$679$	0	0
$680$	12.0255	0.461158
$681$	3.86038	0.147930
$682$	−3.09519	−0.118521
$683$	−25.5819	−0.978863	−0.489432	−	0.872042i	$-0.662796\pi$
$683$	−25.5819	−0.978863	−0.489432	+	0.872042i	$0.662796\pi$
$684$	13.2917	0.508220
$685$	22.5182	0.860377
$686$	0	0
$687$	20.9616	0.799735
$688$	−21.3043	−0.812220
$689$	−9.69352	−0.369294
$690$	−7.10821	−0.270605
$691$	27.6456	1.05169	0.525845	−	0.850581i	$-0.323749\pi$
$691$	27.6456	1.05169	0.525845	+	0.850581i	$0.323749\pi$
$692$	36.6832	1.39448
$693$	0	0
$694$	1.10342	0.0418852
$695$	−33.4947	−1.27053
$696$	0.819910	0.0310786
$697$	−2.17395	−0.0823444
$698$	−4.58118	−0.173400
$699$	−4.79767	−0.181464
$700$	0	0
$701$	46.2861	1.74820	0.874101	−	0.485745i	$-0.161452\pi$
$701$	46.2861	1.74820	0.874101	+	0.485745i	$0.161452\pi$
$702$	−0.535192	−0.0201995
$703$	−49.1476	−1.85364
$704$	−4.84072	−0.182441
$705$	17.5564	0.661211
$706$	12.0934	0.455140
$707$	0	0
$708$	−5.55735	−0.208858
$709$	13.4057	0.503461	0.251730	−	0.967797i	$-0.419000\pi$
$709$	13.4057	0.503461	0.251730	+	0.967797i	$0.419000\pi$
$710$	12.5592	0.471338
$711$	7.94958	0.298132
$712$	7.52007	0.281827
$713$	29.6678	1.11107
$714$	0	0
$715$	5.21320	0.194963
$716$	41.5957	1.55450
$717$	16.4100	0.612843
$718$	−2.42015	−0.0903194
$719$	42.4424	1.58283	0.791417	−	0.611276i	$-0.209344\pi$
$719$	42.4424	1.58283	0.791417	+	0.611276i	$0.209344\pi$
$720$	10.0935	0.376162
$721$	0	0
$722$	−14.5432	−0.541242
$723$	29.2741	1.08872
$724$	7.37127	0.273951
$725$	3.37815	0.125461
$726$	4.04318	0.150056
$727$	−20.6826	−0.767077	−0.383538	−	0.923525i	$-0.625295\pi$
$727$	−20.6826	−0.767077	−0.383538	+	0.923525i	$0.625295\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−18.1010	−0.669947
$731$	−15.6760	−0.579799
$732$	−2.74121	−0.101318
$733$	−26.2703	−0.970314	−0.485157	−	0.874427i	$-0.661238\pi$
$733$	−26.2703	−0.970314	−0.485157	+	0.874427i	$0.661238\pi$
$734$	15.1161	0.557947
$735$	0	0
$736$	−22.0451	−0.812593
$737$	3.21734	0.118512
$738$	0.423828	0.0156013
$739$	−0.000930324 0	−3.42225e−5 0	−1.71113e−5	−	1.00000i	$-0.500005\pi$
$739$	−0.000930324 0	−3.42225e−5 0	−1.71113e−5		1.00000i	$0.500005\pi$
$740$	−41.8601	−1.53881
$741$	−9.22021	−0.338713
$742$	0	0
$743$	−12.6652	−0.464641	−0.232321	−	0.972639i	$-0.574632\pi$
$743$	−12.6652	−0.464641	−0.232321	+	0.972639i	$0.574632\pi$
$744$	9.78516	0.358741
$745$	−55.4214	−2.03048
$746$	12.7300	0.466080
$747$	−5.53811	−0.202629
$748$	−4.78228	−0.174858
$749$	0	0
$750$	−2.41987	−0.0883612
$751$	−10.0869	−0.368075	−0.184038	−	0.982919i	$-0.558917\pi$
$751$	−10.0869	−0.368075	−0.184038	+	0.982919i	$0.558917\pi$
$752$	15.1830	0.553667
$753$	16.9300	0.616963
$754$	−0.271007	−0.00986950
$755$	34.5727	1.25823
$756$	0	0
$757$	15.8957	0.577739	0.288869	−	0.957369i	$-0.406721\pi$
$757$	15.8957	0.577739	0.288869	+	0.957369i	$0.406721\pi$
$758$	13.3719	0.485689
$759$	5.93250	0.215336
$760$	−40.3900	−1.46510
$761$	6.40153	0.232055	0.116028	−	0.993246i	$-0.462984\pi$
$761$	6.40153	0.232055	0.116028	+	0.993246i	$0.462984\pi$
$762$	−3.97353	−0.143946
$763$	0	0
$764$	13.3272	0.482162
$765$	7.42693	0.268521
$766$	5.50249	0.198813
$767$	3.85503	0.139197
$768$	3.48552	0.125773
$769$	−35.6888	−1.28697	−0.643485	−	0.765459i	$-0.722512\pi$
$769$	−35.6888	−1.28697	−0.643485	+	0.765459i	$0.722512\pi$
$770$	0	0
$771$	17.2556	0.621444
$772$	−14.3099	−0.515023
$773$	−33.3248	−1.19861	−0.599305	−	0.800521i	$-0.704556\pi$
$773$	−33.3248	−1.19861	−0.599305	+	0.800521i	$0.704556\pi$
$774$	3.05615	0.109851
$775$	40.3163	1.44821
$776$	−1.83053	−0.0657122
$777$	0	0
$778$	−11.5561	−0.414306
$779$	7.30164	0.261608
$780$	−7.85306	−0.281185
$781$	−10.4819	−0.375071
$782$	−4.52326	−0.161752
$783$	0.506374	0.0180963
$784$	0	0
$785$	33.2499	1.18674
$786$	−2.38908	−0.0852157
$787$	−41.0212	−1.46225	−0.731124	−	0.682244i	$-0.761004\pi$
$787$	−41.0212	−1.46225	−0.731124	+	0.682244i	$0.761004\pi$
$788$	27.7405	0.988214
$789$	20.1756	0.718271
$790$	−11.5104	−0.409523
$791$	0	0
$792$	1.95668	0.0695276
$793$	1.90153	0.0675252
$794$	5.53210	0.196327
$795$	−26.2253	−0.930116
$796$	1.37536	0.0487485
$797$	20.9473	0.741990	0.370995	−	0.928635i	$-0.379017\pi$
$797$	20.9473	0.741990	0.370995	+	0.928635i	$0.379017\pi$
$798$	0	0
$799$	11.1719	0.395232
$800$	−29.9576	−1.05916
$801$	4.64437	0.164101
$802$	−8.96140	−0.316438
$803$	15.1070	0.533115
$804$	−4.84654	−0.170924
$805$	0	0
$806$	−3.23432	−0.113924
$807$	19.9933	0.703797
$808$	8.60608	0.302761
$809$	23.3753	0.821832	0.410916	−	0.911673i	$-0.365209\pi$
$809$	23.3753	0.821832	0.410916	+	0.911673i	$0.365209\pi$
$810$	−1.44793	−0.0508751
$811$	−9.25028	−0.324821	−0.162411	−	0.986723i	$-0.551927\pi$
$811$	−9.25028	−0.324821	−0.162411	+	0.986723i	$0.551927\pi$
$812$	0	0
$813$	−30.7338	−1.07788
$814$	−3.44744	−0.120833
$815$	−28.6040	−1.00196
$816$	6.42292	0.224847
$817$	52.6509	1.84202
$818$	9.13516	0.319403
$819$	0	0
$820$	6.21897	0.217176
$821$	−23.9584	−0.836154	−0.418077	−	0.908412i	$-0.637296\pi$
$821$	−23.9584	−0.836154	−0.418077	+	0.908412i	$0.637296\pi$
$822$	−2.79360	−0.0974380
$823$	−39.7518	−1.38566	−0.692830	−	0.721101i	$-0.743636\pi$
$823$	−39.7518	−1.38566	−0.692830	+	0.721101i	$0.743636\pi$
$824$	−8.72539	−0.303963
$825$	8.06182	0.280677
$826$	0	0
$827$	27.1064	0.942581	0.471291	−	0.881978i	$-0.343788\pi$
$827$	27.1064	0.942581	0.471291	+	0.881978i	$0.343788\pi$
$828$	−8.93659	−0.310568
$829$	37.7500	1.31111	0.655556	−	0.755146i	$-0.272434\pi$
$829$	37.7500	1.31111	0.655556	+	0.755146i	$0.272434\pi$
$830$	8.01880	0.278337
$831$	17.0956	0.593041
$832$	−5.05830	−0.175365
$833$	0	0
$834$	4.15534	0.143888
$835$	−27.6779	−0.957832
$836$	16.0622	0.555524
$837$	6.04329	0.208887
$838$	−11.3857	−0.393311
$839$	−42.9086	−1.48137	−0.740684	−	0.671853i	$-0.765498\pi$
$839$	−42.9086	−1.48137	−0.740684	+	0.671853i	$0.765498\pi$
$840$	0	0
$841$	−28.7436	−0.991158
$842$	−15.0695	−0.519329
$843$	−6.90275	−0.237743
$844$	−33.6645	−1.15878
$845$	−38.9647	−1.34043
$846$	−2.17803	−0.0748824
$847$	0	0
$848$	−22.6800	−0.778836
$849$	−14.7476	−0.506136
$850$	−6.14678	−0.210833
$851$	33.0441	1.13274
$852$	15.7897	0.540945
$853$	−23.4761	−0.803806	−0.401903	−	0.915682i	$-0.631651\pi$
$853$	−23.4761	−0.803806	−0.401903	+	0.915682i	$0.631651\pi$
$854$	0	0
$855$	−24.9448	−0.853093
$856$	4.49927	0.153782
$857$	−43.1486	−1.47393	−0.736965	−	0.675931i	$-0.763742\pi$
$857$	−43.1486	−1.47393	−0.736965	+	0.675931i	$0.763742\pi$
$858$	−0.646748	−0.0220796
$859$	−33.5419	−1.14444	−0.572218	−	0.820102i	$-0.693917\pi$
$859$	−33.5419	−1.14444	−0.572218	+	0.820102i	$0.693917\pi$
$860$	44.8440	1.52917
$861$	0	0
$862$	7.61426	0.259343
$863$	−20.8609	−0.710112	−0.355056	−	0.934845i	$-0.615538\pi$
$863$	−20.8609	−0.710112	−0.355056	+	0.934845i	$0.615538\pi$
$864$	−4.49055	−0.152772
$865$	−68.8440	−2.34077
$866$	0.822568	0.0279520
$867$	−12.2739	−0.416844
$868$	0	0
$869$	9.60659	0.325881
$870$	−0.733195	−0.0248576
$871$	3.36196	0.113916
$872$	18.8759	0.639220
$873$	−1.13053	−0.0382627
$874$	15.1922	0.513885
$875$	0	0
$876$	−22.7569	−0.768885
$877$	−12.2475	−0.413569	−0.206784	−	0.978387i	$-0.566300\pi$
$877$	−12.2475	−0.413569	−0.206784	+	0.978387i	$0.566300\pi$
$878$	8.44801	0.285107
$879$	−4.27776	−0.144285
$880$	12.1974	0.411173
$881$	−42.3355	−1.42632	−0.713160	−	0.701002i	$-0.752737\pi$
$881$	−42.3355	−1.42632	−0.713160	+	0.701002i	$0.752737\pi$
$882$	0	0
$883$	33.7723	1.13653	0.568265	−	0.822846i	$-0.307615\pi$
$883$	33.7723	1.13653	0.568265	+	0.822846i	$0.307615\pi$
$884$	−4.99724	−0.168075
$885$	10.4296	0.350587
$886$	−17.6247	−0.592114
$887$	18.4300	0.618819	0.309410	−	0.950929i	$-0.399869\pi$
$887$	18.4300	0.618819	0.309410	+	0.950929i	$0.399869\pi$
$888$	10.8987	0.365738
$889$	0	0
$890$	−6.72474	−0.225414
$891$	1.20844	0.0404843
$892$	−0.707809	−0.0236992
$893$	−37.5229	−1.25565
$894$	6.87556	0.229953
$895$	−78.0634	−2.60937
$896$	0	0
$897$	6.19915	0.206984
$898$	10.7051	0.357234
$899$	3.06016	0.102062
$900$	−12.1442	−0.404805
$901$	−16.6883	−0.555968
$902$	0.512171	0.0170534
$903$	0	0
$904$	18.8247	0.626099
$905$	−13.8338	−0.459851
$906$	−4.28907	−0.142495
$907$	17.8679	0.593292	0.296646	−	0.954987i	$-0.404132\pi$
$907$	17.8679	0.593292	0.296646	+	0.954987i	$0.404132\pi$
$908$	−7.02733	−0.233210
$909$	5.31509	0.176290
$910$	0	0
$911$	−52.6939	−1.74583	−0.872913	−	0.487877i	$-0.837772\pi$
$911$	−52.6939	−1.74583	−0.872913	+	0.487877i	$0.837772\pi$
$912$	−21.5726	−0.714340
$913$	−6.69247	−0.221489
$914$	−10.5601	−0.349298
$915$	5.14448	0.170071
$916$	−38.1579	−1.26077
$917$	0	0
$918$	−0.921382	−0.0304101
$919$	−53.7884	−1.77432	−0.887158	−	0.461466i	$-0.847323\pi$
$919$	−53.7884	−1.77432	−0.887158	+	0.461466i	$0.847323\pi$
$920$	27.1560	0.895307
$921$	−13.5544	−0.446634
$922$	9.12956	0.300666
$923$	−10.9530	−0.360523
$924$	0	0
$925$	44.9045	1.47645
$926$	−1.92120	−0.0631345
$927$	−5.38877	−0.176991
$928$	−2.27390	−0.0746444
$929$	−1.19669	−0.0392621	−0.0196310	−	0.999807i	$-0.506249\pi$
$929$	−1.19669	−0.0392621	−0.0196310	+	0.999807i	$0.506249\pi$
$930$	−8.75027	−0.286933
$931$	0	0
$932$	8.73353	0.286076
$933$	−1.34293	−0.0439655
$934$	−6.47492	−0.211866
$935$	8.97500	0.293514
$936$	2.04463	0.0668308
$937$	−2.69258	−0.0879626	−0.0439813	−	0.999032i	$-0.514004\pi$
$937$	−2.69258	−0.0879626	−0.0439813	+	0.999032i	$0.514004\pi$
$938$	0	0
$939$	12.5685	0.410158
$940$	−31.9591	−1.04239
$941$	−7.77008	−0.253297	−0.126649	−	0.991948i	$-0.540422\pi$
$941$	−7.77008	−0.253297	−0.126649	+	0.991948i	$0.540422\pi$
$942$	−4.12497	−0.134399
$943$	−4.90922	−0.159866
$944$	9.01966	0.293565
$945$	0	0
$946$	3.69318	0.120076
$947$	22.8040	0.741032	0.370516	−	0.928826i	$-0.379181\pi$
$947$	22.8040	0.741032	0.370516	+	0.928826i	$0.379181\pi$
$948$	−14.4712	−0.470002
$949$	15.7861	0.512437
$950$	20.6451	0.669817
$951$	−8.59197	−0.278614
$952$	0	0
$953$	−13.6387	−0.441801	−0.220901	−	0.975296i	$-0.570900\pi$
$953$	−13.6387	−0.441801	−0.220901	+	0.975296i	$0.570900\pi$
$954$	3.25350	0.105336
$955$	−25.0114	−0.809351
$956$	−29.8723	−0.966138
$957$	0.611923	0.0197807
$958$	6.43393	0.207871
$959$	0	0
$960$	−13.6850	−0.441680
$961$	5.52132	0.178107
$962$	−3.60239	−0.116146
$963$	2.77874	0.0895436
$964$	−53.2898	−1.71635
$965$	26.8556	0.864512
$966$	0	0
$967$	28.6375	0.920920	0.460460	−	0.887680i	$-0.347684\pi$
$967$	28.6375	0.920920	0.460460	+	0.887680i	$0.347684\pi$
$968$	−15.4464	−0.496467
$969$	−15.8734	−0.509928
$970$	1.63693	0.0525587
$971$	18.7450	0.601555	0.300778	−	0.953694i	$-0.402754\pi$
$971$	18.7450	0.601555	0.300778	+	0.953694i	$0.402754\pi$
$972$	−1.82037	−0.0583884
$973$	0	0
$974$	2.59920	0.0832838
$975$	8.42419	0.269790
$976$	4.44902	0.142410
$977$	−0.0431378	−0.00138010	−0.000690050	−	1.00000i	$-0.500220\pi$
$977$	−0.0431378	−0.00138010	−0.000690050		1.00000i	$0.500220\pi$
$978$	3.54861	0.113472
$979$	5.61245	0.179375
$980$	0	0
$981$	11.6577	0.372203
$982$	−11.3825	−0.363232
$983$	18.2855	0.583217	0.291608	−	0.956538i	$-0.405810\pi$
$983$	18.2855	0.583217	0.291608	+	0.956538i	$0.405810\pi$
$984$	−1.61918	−0.0516175
$985$	−52.0611	−1.65881
$986$	−0.466564	−0.0148584
$987$	0	0
$988$	16.7842	0.533976
$989$	−35.3996	−1.12564
$990$	−1.74974	−0.0556104
$991$	0.164594	0.00522850	0.00261425	−	0.999997i	$-0.499168\pi$
$991$	0.164594	0.00522850	0.00261425	+	0.999997i	$0.499168\pi$
$992$	−27.1377	−0.861622
$993$	35.0682	1.11286
$994$	0	0
$995$	−2.58117	−0.0818287
$996$	10.0814	0.319442
$997$	8.72804	0.276420	0.138210	−	0.990403i	$-0.455865\pi$
$997$	8.72804	0.276420	0.138210	+	0.990403i	$0.455865\pi$
$998$	−12.8152	−0.405658
$999$	6.73103	0.212961

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bo.1.9	yes	24
7.6	odd	2		6027.2.a.bn.1.9	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6027.2.a.bn.1.9	✓	24	7.6	odd	2
6027.2.a.bo.1.9	yes	24	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:	\( N \)	\(=\)	\( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6027.a (trivial)

\(f(q)\)	\(=\)	\(q-0.423828 q^{2} +1.00000 q^{3} -1.82037 q^{4} +3.41632 q^{5} -0.423828 q^{6} +1.61918 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.423828 q^{2} +1.00000 q^{3} -1.82037 q^{4} +3.41632 q^{5} -0.423828 q^{6} +1.61918 q^{8} +1.00000 q^{9} -1.44793 q^{10} +1.20844 q^{11} -1.82037 q^{12} +1.26276 q^{13} +3.41632 q^{15} +2.95449 q^{16} +2.17395 q^{17} -0.423828 q^{18} -7.30164 q^{19} -6.21897 q^{20} -0.512171 q^{22} +4.90922 q^{23} +1.61918 q^{24} +6.67126 q^{25} -0.535192 q^{26} +1.00000 q^{27} +0.506374 q^{29} -1.44793 q^{30} +6.04329 q^{31} -4.49055 q^{32} +1.20844 q^{33} -0.921382 q^{34} -1.82037 q^{36} +6.73103 q^{37} +3.09464 q^{38} +1.26276 q^{39} +5.53164 q^{40} -1.00000 q^{41} -7.21084 q^{43} -2.19981 q^{44} +3.41632 q^{45} -2.08066 q^{46} +5.13896 q^{47} +2.95449 q^{48} -2.82746 q^{50} +2.17395 q^{51} -2.29869 q^{52} -7.67647 q^{53} -0.423828 q^{54} +4.12842 q^{55} -7.30164 q^{57} -0.214615 q^{58} +3.05287 q^{59} -6.21897 q^{60} +1.50585 q^{61} -2.56131 q^{62} -4.00576 q^{64} +4.31399 q^{65} -0.512171 q^{66} +2.66239 q^{67} -3.95740 q^{68} +4.90922 q^{69} -8.67388 q^{71} +1.61918 q^{72} +12.5013 q^{73} -2.85280 q^{74} +6.67126 q^{75} +13.2917 q^{76} -0.535192 q^{78} +7.94958 q^{79} +10.0935 q^{80} +1.00000 q^{81} +0.423828 q^{82} -5.53811 q^{83} +7.42693 q^{85} +3.05615 q^{86} +0.506374 q^{87} +1.95668 q^{88} +4.64437 q^{89} -1.44793 q^{90} -8.93659 q^{92} +6.04329 q^{93} -2.17803 q^{94} -24.9448 q^{95} -4.49055 q^{96} -1.13053 q^{97} +1.20844 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{2} + 24 q^{3} + 32 q^{4} + 4 q^{5} + 8 q^{6} + 24 q^{8} + 24 q^{9}+O(q^{10}) \) 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

Introduction

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