LMFDB - Embedded newform 6027.2.a.y.1.1

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:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 6x^{5} + 16x^{4} + 14x^{3} - 20x^{2} - 10x + 4 $ x^7 - 3x^6 - 6x^5 + 16x^4 + 14x^3 - 20x^2 - 10x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 861)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.95889$ of defining polynomial
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)

$f(q)$	$=$	$q-1.95889 q^{2} -1.00000 q^{3} +1.83724 q^{4} +0.513172 q^{5} +1.95889 q^{6} +0.318823 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.95889 q^{2} -1.00000 q^{3} +1.83724 q^{4} +0.513172 q^{5} +1.95889 q^{6} +0.318823 q^{8} +1.00000 q^{9} -1.00525 q^{10} +5.65559 q^{11} -1.83724 q^{12} +0.337188 q^{13} -0.513172 q^{15} -4.29902 q^{16} -4.63097 q^{17} -1.95889 q^{18} +7.43860 q^{19} +0.942822 q^{20} -11.0787 q^{22} +3.51087 q^{23} -0.318823 q^{24} -4.73665 q^{25} -0.660514 q^{26} -1.00000 q^{27} +0.00385180 q^{29} +1.00525 q^{30} -2.90696 q^{31} +7.78366 q^{32} -5.65559 q^{33} +9.07154 q^{34} +1.83724 q^{36} +5.69784 q^{37} -14.5714 q^{38} -0.337188 q^{39} +0.163611 q^{40} -1.00000 q^{41} +6.32365 q^{43} +10.3907 q^{44} +0.513172 q^{45} -6.87741 q^{46} +10.1514 q^{47} +4.29902 q^{48} +9.27858 q^{50} +4.63097 q^{51} +0.619496 q^{52} -1.59568 q^{53} +1.95889 q^{54} +2.90229 q^{55} -7.43860 q^{57} -0.00754524 q^{58} -1.42494 q^{59} -0.942822 q^{60} -2.50182 q^{61} +5.69440 q^{62} -6.64927 q^{64} +0.173036 q^{65} +11.0787 q^{66} +9.61202 q^{67} -8.50821 q^{68} -3.51087 q^{69} +10.3934 q^{71} +0.318823 q^{72} -0.539898 q^{73} -11.1614 q^{74} +4.73665 q^{75} +13.6665 q^{76} +0.660514 q^{78} +7.84764 q^{79} -2.20614 q^{80} +1.00000 q^{81} +1.95889 q^{82} +13.6736 q^{83} -2.37648 q^{85} -12.3873 q^{86} -0.00385180 q^{87} +1.80313 q^{88} -15.4352 q^{89} -1.00525 q^{90} +6.45033 q^{92} +2.90696 q^{93} -19.8854 q^{94} +3.81728 q^{95} -7.78366 q^{96} -2.56452 q^{97} +5.65559 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 4 q^{2} - 7 q^{3} + 8 q^{4} - q^{5} - 4 q^{6} + 12 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q + 4 * q^2 - 7 * q^3 + 8 * q^4 - q^5 - 4 * q^6 + 12 * q^8 + 7 * q^9	$ 7 q + 4 q^{2} - 7 q^{3} + 8 q^{4} - q^{5} - 4 q^{6} + 12 q^{8} + 7 q^{9} + 3 q^{10} + 11 q^{11} - 8 q^{12} + 7 q^{13} + q^{15} + 6 q^{16} - 11 q^{17} + 4 q^{18} - 4 q^{19} + 7 q^{20} + 6 q^{22} + 7 q^{23} - 12 q^{24} + 2 q^{25} + 13 q^{26} - 7 q^{27} + 4 q^{29} - 3 q^{30} + 7 q^{31} + 18 q^{32} - 11 q^{33} + 20 q^{34} + 8 q^{36} - 4 q^{38} - 7 q^{39} + 9 q^{40} - 7 q^{41} + q^{43} + 18 q^{44} - q^{45} - 17 q^{46} - 14 q^{47} - 6 q^{48} + 19 q^{50} + 11 q^{51} + 27 q^{52} + 23 q^{53} - 4 q^{54} + 30 q^{55} + 4 q^{57} - 3 q^{58} - 8 q^{59} - 7 q^{60} + 3 q^{61} + 16 q^{62} + 6 q^{64} + 15 q^{65} - 6 q^{66} + 3 q^{67} - 7 q^{69} + 7 q^{71} + 12 q^{72} + 11 q^{73} - 13 q^{74} - 2 q^{75} + 40 q^{76} - 13 q^{78} - q^{79} + 43 q^{80} + 7 q^{81} - 4 q^{82} - 10 q^{85} - 12 q^{86} - 4 q^{87} + 10 q^{88} - 32 q^{89} + 3 q^{90} - 19 q^{92} - 7 q^{93} - 21 q^{94} - 8 q^{95} - 18 q^{96} + 25 q^{97} + 11 q^{99}+O(q^{100}) $ 7 * q + 4 * q^2 - 7 * q^3 + 8 * q^4 - q^5 - 4 * q^6 + 12 * q^8 + 7 * q^9 + 3 * q^10 + 11 * q^11 - 8 * q^12 + 7 * q^13 + q^15 + 6 * q^16 - 11 * q^17 + 4 * q^18 - 4 * q^19 + 7 * q^20 + 6 * q^22 + 7 * q^23 - 12 * q^24 + 2 * q^25 + 13 * q^26 - 7 * q^27 + 4 * q^29 - 3 * q^30 + 7 * q^31 + 18 * q^32 - 11 * q^33 + 20 * q^34 + 8 * q^36 - 4 * q^38 - 7 * q^39 + 9 * q^40 - 7 * q^41 + q^43 + 18 * q^44 - q^45 - 17 * q^46 - 14 * q^47 - 6 * q^48 + 19 * q^50 + 11 * q^51 + 27 * q^52 + 23 * q^53 - 4 * q^54 + 30 * q^55 + 4 * q^57 - 3 * q^58 - 8 * q^59 - 7 * q^60 + 3 * q^61 + 16 * q^62 + 6 * q^64 + 15 * q^65 - 6 * q^66 + 3 * q^67 - 7 * q^69 + 7 * q^71 + 12 * q^72 + 11 * q^73 - 13 * q^74 - 2 * q^75 + 40 * q^76 - 13 * q^78 - q^79 + 43 * q^80 + 7 * q^81 - 4 * q^82 - 10 * q^85 - 12 * q^86 - 4 * q^87 + 10 * q^88 - 32 * q^89 + 3 * q^90 - 19 * q^92 - 7 * q^93 - 21 * q^94 - 8 * q^95 - 18 * q^96 + 25 * q^97 + 11 * 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 $

$2$	−1.95889	−1.38514	−0.692572	−	0.721349i	$-0.743522\pi$
$2$	−1.95889	−1.38514	−0.692572	+	0.721349i	$0.743522\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.83724	0.918621
$5$	0.513172	0.229498	0.114749	−	0.993395i	$-0.463394\pi$
$5$	0.513172	0.229498	0.114749	+	0.993395i	$0.463394\pi$
$6$	1.95889	0.799713
$7$	0	0
$7$	0	0
$8$	0.318823	0.112721
$9$	1.00000	0.333333
$10$	−1.00525	−0.317887
$11$	5.65559	1.70522	0.852612	−	0.522544i	$-0.175017\pi$
$11$	5.65559	1.70522	0.852612	+	0.522544i	$0.175017\pi$
$12$	−1.83724	−0.530366
$13$	0.337188	0.0935191	0.0467596	−	0.998906i	$-0.485111\pi$
$13$	0.337188	0.0935191	0.0467596	+	0.998906i	$0.485111\pi$
$14$	0	0
$15$	−0.513172	−0.132500
$16$	−4.29902	−1.07476
$17$	−4.63097	−1.12317	−0.561587	−	0.827418i	$-0.689809\pi$
$17$	−4.63097	−1.12317	−0.561587	+	0.827418i	$0.689809\pi$
$18$	−1.95889	−0.461714
$19$	7.43860	1.70653	0.853266	−	0.521475i	$-0.174618\pi$
$19$	7.43860	1.70653	0.853266	+	0.521475i	$0.174618\pi$
$20$	0.942822	0.210821
$21$	0	0
$22$	−11.0787	−2.36198
$23$	3.51087	0.732068	0.366034	−	0.930602i	$-0.380715\pi$
$23$	3.51087	0.732068	0.366034	+	0.930602i	$0.380715\pi$
$24$	−0.318823	−0.0650796
$25$	−4.73665	−0.947331
$26$	−0.660514	−0.129537
$27$	−1.00000	−0.192450
$28$	0	0
$29$	0.00385180	0.000715261 0	0.000357630	−	1.00000i	$-0.499886\pi$
$29$	0.00385180	0.000715261 0	0.000357630		1.00000i	$0.499886\pi$
$30$	1.00525	0.183532
$31$	−2.90696	−0.522105	−0.261052	−	0.965325i	$-0.584070\pi$
$31$	−2.90696	−0.522105	−0.261052	+	0.965325i	$0.584070\pi$
$32$	7.78366	1.37597
$33$	−5.65559	−0.984512
$34$	9.07154	1.55576
$35$	0	0
$36$	1.83724	0.306207
$37$	5.69784	0.936719	0.468360	−	0.883538i	$-0.344845\pi$
$37$	5.69784	0.936719	0.468360	+	0.883538i	$0.344845\pi$
$38$	−14.5714	−2.36379
$39$	−0.337188	−0.0539933
$40$	0.163611	0.0258692
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	6.32365	0.964347	0.482174	−	0.876076i	$-0.339847\pi$
$43$	6.32365	0.964347	0.482174	+	0.876076i	$0.339847\pi$
$44$	10.3907	1.56646
$45$	0.513172	0.0764992
$46$	−6.87741	−1.01402
$47$	10.1514	1.48073	0.740365	−	0.672205i	$-0.234653\pi$
$47$	10.1514	1.48073	0.740365	+	0.672205i	$0.234653\pi$
$48$	4.29902	0.620511
$49$	0	0
$50$	9.27858	1.31219
$51$	4.63097	0.648465
$52$	0.619496	0.0859087
$53$	−1.59568	−0.219183	−0.109592	−	0.993977i	$-0.534954\pi$
$53$	−1.59568	−0.219183	−0.109592	+	0.993977i	$0.534954\pi$
$54$	1.95889	0.266571
$55$	2.90229	0.391345
$56$	0	0
$57$	−7.43860	−0.985267
$58$	−0.00754524	−0.000990739 0
$59$	−1.42494	−0.185512	−0.0927559	−	0.995689i	$-0.529568\pi$
$59$	−1.42494	−0.185512	−0.0927559	+	0.995689i	$0.529568\pi$
$60$	−0.942822	−0.121718
$61$	−2.50182	−0.320325	−0.160163	−	0.987091i	$-0.551202\pi$
$61$	−2.50182	−0.320325	−0.160163	+	0.987091i	$0.551202\pi$
$62$	5.69440	0.723190
$63$	0	0
$64$	−6.64927	−0.831159
$65$	0.173036	0.0214624
$66$	11.0787	1.36369
$67$	9.61202	1.17430	0.587148	−	0.809480i	$-0.300251\pi$
$67$	9.61202	1.17430	0.587148	+	0.809480i	$0.300251\pi$
$68$	−8.50821	−1.03177
$69$	−3.51087	−0.422660
$70$	0	0
$71$	10.3934	1.23347	0.616733	−	0.787173i	$-0.288456\pi$
$71$	10.3934	1.23347	0.616733	+	0.787173i	$0.288456\pi$
$72$	0.318823	0.0375737
$73$	−0.539898	−0.0631903	−0.0315951	−	0.999501i	$-0.510059\pi$
$73$	−0.539898	−0.0631903	−0.0315951	+	0.999501i	$0.510059\pi$
$74$	−11.1614	−1.29749
$75$	4.73665	0.546942
$76$	13.6665	1.56766
$77$	0	0
$78$	0.660514	0.0747884
$79$	7.84764	0.882928	0.441464	−	0.897279i	$-0.354459\pi$
$79$	7.84764	0.882928	0.441464	+	0.897279i	$0.354459\pi$
$80$	−2.20614	−0.246654
$81$	1.00000	0.111111
$82$	1.95889	0.216323
$83$	13.6736	1.50088	0.750439	−	0.660940i	$-0.229842\pi$
$83$	13.6736	1.50088	0.750439	+	0.660940i	$0.229842\pi$
$84$	0	0
$85$	−2.37648	−0.257766
$86$	−12.3873	−1.33576
$87$	−0.00385180	−0.000412956 0
$88$	1.80313	0.192215
$89$	−15.4352	−1.63613	−0.818066	−	0.575125i	$-0.804953\pi$
$89$	−15.4352	−1.63613	−0.818066	+	0.575125i	$0.804953\pi$
$90$	−1.00525	−0.105962
$91$	0	0
$92$	6.45033	0.672493
$93$	2.90696	0.301437
$94$	−19.8854	−2.05102
$95$	3.81728	0.391645
$96$	−7.78366	−0.794417
$97$	−2.56452	−0.260388	−0.130194	−	0.991489i	$-0.541560\pi$
$97$	−2.56452	−0.260388	−0.130194	+	0.991489i	$0.541560\pi$
$98$	0	0
$99$	5.65559	0.568408
$100$	−8.70238	−0.870238
$101$	−16.0466	−1.59669	−0.798346	−	0.602198i	$-0.794292\pi$
$101$	−16.0466	−1.59669	−0.798346	+	0.602198i	$0.794292\pi$
$102$	−9.07154	−0.898217
$103$	12.2682	1.20882	0.604410	−	0.796673i	$-0.293409\pi$
$103$	12.2682	1.20882	0.604410	+	0.796673i	$0.293409\pi$
$104$	0.107503	0.0105416
$105$	0	0
$106$	3.12576	0.303600
$107$	1.06468	0.102926	0.0514631	−	0.998675i	$-0.483612\pi$
$107$	1.06468	0.102926	0.0514631	+	0.998675i	$0.483612\pi$
$108$	−1.83724	−0.176789
$109$	−7.49782	−0.718161	−0.359081	−	0.933307i	$-0.616910\pi$
$109$	−7.49782	−0.718161	−0.359081	+	0.933307i	$0.616910\pi$
$110$	−5.68526	−0.542069
$111$	−5.69784	−0.540815
$112$	0	0
$113$	−9.02374	−0.848882	−0.424441	−	0.905456i	$-0.639529\pi$
$113$	−9.02374	−0.848882	−0.424441	+	0.905456i	$0.639529\pi$
$114$	14.5714	1.36474
$115$	1.80168	0.168008
$116$	0.00707669	0.000657054 0
$117$	0.337188	0.0311730
$118$	2.79131	0.256961
$119$	0	0
$120$	−0.163611	−0.0149356
$121$	20.9857	1.90779
$122$	4.90079	0.443697
$123$	1.00000	0.0901670
$124$	−5.34079	−0.479617
$125$	−4.99658	−0.446908
$126$	0	0
$127$	6.16100	0.546700	0.273350	−	0.961915i	$-0.411868\pi$
$127$	6.16100	0.546700	0.273350	+	0.961915i	$0.411868\pi$
$128$	−2.54214	−0.224696
$129$	−6.32365	−0.556766
$130$	−0.338957	−0.0297285
$131$	−17.8524	−1.55977	−0.779884	−	0.625924i	$-0.784722\pi$
$131$	−17.8524	−1.55977	−0.779884	+	0.625924i	$0.784722\pi$
$132$	−10.3907	−0.904394
$133$	0	0
$134$	−18.8289	−1.62657
$135$	−0.513172	−0.0441668
$136$	−1.47646	−0.126605
$137$	13.1730	1.12545	0.562723	−	0.826646i	$-0.309754\pi$
$137$	13.1730	1.12545	0.562723	+	0.826646i	$0.309754\pi$
$138$	6.87741	0.585444
$139$	5.82242	0.493851	0.246926	−	0.969034i	$-0.420580\pi$
$139$	5.82242	0.493851	0.246926	+	0.969034i	$0.420580\pi$
$140$	0	0
$141$	−10.1514	−0.854900
$142$	−20.3594	−1.70853
$143$	1.90700	0.159471
$144$	−4.29902	−0.358252
$145$	0.00197664	0.000164151 0
$146$	1.05760	0.0875276
$147$	0	0
$148$	10.4683	0.860490
$149$	12.8687	1.05425	0.527124	−	0.849788i	$-0.323270\pi$
$149$	12.8687	1.05425	0.527124	+	0.849788i	$0.323270\pi$
$150$	−9.27858	−0.757593
$151$	−8.75604	−0.712557	−0.356278	−	0.934380i	$-0.615954\pi$
$151$	−8.75604	−0.712557	−0.356278	+	0.934380i	$0.615954\pi$
$152$	2.37160	0.192362
$153$	−4.63097	−0.374391
$154$	0	0
$155$	−1.49177	−0.119822
$156$	−0.619496	−0.0495994
$157$	4.49426	0.358681	0.179341	−	0.983787i	$-0.442604\pi$
$157$	4.49426	0.358681	0.179341	+	0.983787i	$0.442604\pi$
$158$	−15.3726	−1.22298
$159$	1.59568	0.126546
$160$	3.99436	0.315782
$161$	0	0
$162$	−1.95889	−0.153905
$163$	9.57653	0.750091	0.375046	−	0.927006i	$-0.377627\pi$
$163$	9.57653	0.750091	0.375046	+	0.927006i	$0.377627\pi$
$164$	−1.83724	−0.143465
$165$	−2.90229	−0.225943
$166$	−26.7851	−2.07893
$167$	6.49269	0.502419	0.251210	−	0.967933i	$-0.419172\pi$
$167$	6.49269	0.502419	0.251210	+	0.967933i	$0.419172\pi$
$168$	0	0
$169$	−12.8863	−0.991254
$170$	4.65526	0.357042
$171$	7.43860	0.568844
$172$	11.6181	0.885870
$173$	−0.203823	−0.0154963	−0.00774817	−	0.999970i	$-0.502466\pi$
$173$	−0.203823	−0.0154963	−0.00774817	+	0.999970i	$0.502466\pi$
$174$	0.00754524	0.000572003 0
$175$	0	0
$176$	−24.3135	−1.83270
$177$	1.42494	0.107105
$178$	30.2359	2.26628
$179$	−17.2933	−1.29256	−0.646282	−	0.763098i	$-0.723677\pi$
$179$	−17.2933	−1.29256	−0.646282	+	0.763098i	$0.723677\pi$
$180$	0.942822	0.0702738
$181$	9.90127	0.735955	0.367978	−	0.929835i	$-0.380050\pi$
$181$	9.90127	0.735955	0.367978	+	0.929835i	$0.380050\pi$
$182$	0	0
$183$	2.50182	0.184940
$184$	1.11935	0.0825195
$185$	2.92397	0.214975
$186$	−5.69440	−0.417534
$187$	−26.1908	−1.91526
$188$	18.6505	1.36023
$189$	0	0
$190$	−7.47763	−0.542484
$191$	−25.6289	−1.85444	−0.927222	−	0.374513i	$-0.877810\pi$
$191$	−25.6289	−1.85444	−0.927222	+	0.374513i	$0.877810\pi$
$192$	6.64927	0.479870
$193$	−14.1502	−1.01855	−0.509277	−	0.860603i	$-0.670087\pi$
$193$	−14.1502	−1.01855	−0.509277	+	0.860603i	$0.670087\pi$
$194$	5.02361	0.360674
$195$	−0.173036	−0.0123913
$196$	0	0
$197$	−13.9750	−0.995676	−0.497838	−	0.867270i	$-0.665873\pi$
$197$	−13.9750	−0.995676	−0.497838	+	0.867270i	$0.665873\pi$
$198$	−11.0787	−0.787327
$199$	−5.25791	−0.372723	−0.186362	−	0.982481i	$-0.559670\pi$
$199$	−5.25791	−0.372723	−0.186362	+	0.982481i	$0.559670\pi$
$200$	−1.51016	−0.106784
$201$	−9.61202	−0.677980
$202$	31.4334	2.21165
$203$	0	0
$204$	8.50821	0.595694
$205$	−0.513172	−0.0358415
$206$	−24.0320	−1.67439
$207$	3.51087	0.244023
$208$	−1.44958	−0.100510
$209$	42.0697	2.91002
$210$	0	0
$211$	2.92311	0.201235	0.100618	−	0.994925i	$-0.467918\pi$
$211$	2.92311	0.201235	0.100618	+	0.994925i	$0.467918\pi$
$212$	−2.93165	−0.201346
$213$	−10.3934	−0.712141
$214$	−2.08558	−0.142567
$215$	3.24512	0.221315
$216$	−0.318823	−0.0216932
$217$	0	0
$218$	14.6874	0.994756
$219$	0.539898	0.0364829
$220$	5.33221	0.359498
$221$	−1.56151	−0.105038
$222$	11.1614	0.749106
$223$	20.3713	1.36416	0.682082	−	0.731275i	$-0.261075\pi$
$223$	20.3713	1.36416	0.682082	+	0.731275i	$0.261075\pi$
$224$	0	0
$225$	−4.73665	−0.315777
$226$	17.6765	1.17582
$227$	−9.00865	−0.597925	−0.298962	−	0.954265i	$-0.596641\pi$
$227$	−9.00865	−0.597925	−0.298962	+	0.954265i	$0.596641\pi$
$228$	−13.6665	−0.905087
$229$	16.7740	1.10846	0.554230	−	0.832364i	$-0.313013\pi$
$229$	16.7740	1.10846	0.554230	+	0.832364i	$0.313013\pi$
$230$	−3.52930	−0.232715
$231$	0	0
$232$	0.00122804	8.06250e−5 0
$233$	20.9774	1.37428	0.687138	−	0.726527i	$-0.258867\pi$
$233$	20.9774	1.37428	0.687138	+	0.726527i	$0.258867\pi$
$234$	−0.660514	−0.0431791
$235$	5.20940	0.339824
$236$	−2.61797	−0.170415
$237$	−7.84764	−0.509759
$238$	0	0
$239$	−13.3300	−0.862246	−0.431123	−	0.902293i	$-0.641882\pi$
$239$	−13.3300	−0.862246	−0.431123	+	0.902293i	$0.641882\pi$
$240$	2.20614	0.142406
$241$	7.33366	0.472403	0.236201	−	0.971704i	$-0.424098\pi$
$241$	7.33366	0.472403	0.236201	+	0.971704i	$0.424098\pi$
$242$	−41.1086	−2.64256
$243$	−1.00000	−0.0641500
$244$	−4.59645	−0.294258
$245$	0	0
$246$	−1.95889	−0.124894
$247$	2.50821	0.159593
$248$	−0.926806	−0.0588522
$249$	−13.6736	−0.866532
$250$	9.78774	0.619031
$251$	−26.5835	−1.67794	−0.838969	−	0.544179i	$-0.816841\pi$
$251$	−26.5835	−1.67794	−0.838969	+	0.544179i	$0.816841\pi$
$252$	0	0
$253$	19.8561	1.24834
$254$	−12.0687	−0.757258
$255$	2.37648	0.148821
$256$	18.2783	1.14239
$257$	26.5995	1.65923	0.829615	−	0.558336i	$-0.188560\pi$
$257$	26.5995	1.65923	0.829615	+	0.558336i	$0.188560\pi$
$258$	12.3873	0.771201
$259$	0	0
$260$	0.317908	0.0197158
$261$	0.00385180	0.000238420 0
$262$	34.9708	2.16050
$263$	−6.28864	−0.387774	−0.193887	−	0.981024i	$-0.562110\pi$
$263$	−6.28864	−0.387774	−0.193887	+	0.981024i	$0.562110\pi$
$264$	−1.80313	−0.110975
$265$	−0.818858	−0.0503020
$266$	0	0
$267$	15.4352	0.944621
$268$	17.6596	1.07873
$269$	−12.8076	−0.780894	−0.390447	−	0.920625i	$-0.627680\pi$
$269$	−12.8076	−0.780894	−0.390447	+	0.920625i	$0.627680\pi$
$270$	1.00525	0.0611774
$271$	9.34578	0.567716	0.283858	−	0.958866i	$-0.408386\pi$
$271$	9.34578	0.567716	0.283858	+	0.958866i	$0.408386\pi$
$272$	19.9086	1.20714
$273$	0	0
$274$	−25.8044	−1.55890
$275$	−26.7886	−1.61541
$276$	−6.45033	−0.388264
$277$	−26.2243	−1.57567	−0.787833	−	0.615888i	$-0.788797\pi$
$277$	−26.2243	−1.57567	−0.787833	+	0.615888i	$0.788797\pi$
$278$	−11.4055	−0.684055
$279$	−2.90696	−0.174035
$280$	0	0
$281$	2.90948	0.173565	0.0867826	−	0.996227i	$-0.472341\pi$
$281$	2.90948	0.173565	0.0867826	+	0.996227i	$0.472341\pi$
$282$	19.8854	1.18416
$283$	2.90496	0.172682	0.0863411	−	0.996266i	$-0.472483\pi$
$283$	2.90496	0.172682	0.0863411	+	0.996266i	$0.472483\pi$
$284$	19.0951	1.13309
$285$	−3.81728	−0.226116
$286$	−3.73559	−0.220890
$287$	0	0
$288$	7.78366	0.458657
$289$	4.44585	0.261520
$290$	−0.00387201	−0.000227372 0
$291$	2.56452	0.150335
$292$	−0.991924	−0.0580479
$293$	11.7862	0.688560	0.344280	−	0.938867i	$-0.388123\pi$
$293$	11.7862	0.688560	0.344280	+	0.938867i	$0.388123\pi$
$294$	0	0
$295$	−0.731242	−0.0425745
$296$	1.81661	0.105588
$297$	−5.65559	−0.328171
$298$	−25.2084	−1.46028
$299$	1.18382	0.0684624
$300$	8.70238	0.502432
$301$	0	0
$302$	17.1521	0.986993
$303$	16.0466	0.921851
$304$	−31.9787	−1.83411
$305$	−1.28387	−0.0735139
$306$	9.07154	0.518586
$307$	−9.97122	−0.569088	−0.284544	−	0.958663i	$-0.591842\pi$
$307$	−9.97122	−0.569088	−0.284544	+	0.958663i	$0.591842\pi$
$308$	0	0
$309$	−12.2682	−0.697913
$310$	2.92221	0.165970
$311$	−23.9202	−1.35639	−0.678194	−	0.734883i	$-0.737237\pi$
$311$	−23.9202	−1.35639	−0.678194	+	0.734883i	$0.737237\pi$
$312$	−0.107503	−0.00608619
$313$	19.0421	1.07632	0.538160	−	0.842842i	$-0.319119\pi$
$313$	19.0421	1.07632	0.538160	+	0.842842i	$0.319119\pi$
$314$	−8.80376	−0.496825
$315$	0	0
$316$	14.4180	0.811077
$317$	−13.4871	−0.757510	−0.378755	−	0.925497i	$-0.623648\pi$
$317$	−13.4871	−0.757510	−0.378755	+	0.925497i	$0.623648\pi$
$318$	−3.12576	−0.175284
$319$	0.0217842	0.00121968
$320$	−3.41222	−0.190749
$321$	−1.06468	−0.0594245
$322$	0	0
$323$	−34.4479	−1.91673
$324$	1.83724	0.102069
$325$	−1.59714	−0.0885936
$326$	−18.7593	−1.03898
$327$	7.49782	0.414631
$328$	−0.318823	−0.0176041
$329$	0	0
$330$	5.68526	0.312963
$331$	6.88877	0.378641	0.189320	−	0.981915i	$-0.439371\pi$
$331$	6.88877	0.378641	0.189320	+	0.981915i	$0.439371\pi$
$332$	25.1218	1.37874
$333$	5.69784	0.312240
$334$	−12.7184	−0.695922
$335$	4.93262	0.269498
$336$	0	0
$337$	32.2680	1.75775	0.878875	−	0.477051i	$-0.158294\pi$
$337$	32.2680	1.75775	0.878875	+	0.477051i	$0.158294\pi$
$338$	25.2428	1.37303
$339$	9.02374	0.490102
$340$	−4.36618	−0.236789
$341$	−16.4406	−0.890306
$342$	−14.5714	−0.787931
$343$	0	0
$344$	2.01613	0.108702
$345$	−1.80168	−0.0969993
$346$	0.399266	0.0214646
$347$	8.81735	0.473340	0.236670	−	0.971590i	$-0.423944\pi$
$347$	8.81735	0.473340	0.236670	+	0.971590i	$0.423944\pi$
$348$	−0.00707669	−0.000379350 0
$349$	−16.4848	−0.882410	−0.441205	−	0.897406i	$-0.645449\pi$
$349$	−16.4848	−0.882410	−0.441205	+	0.897406i	$0.645449\pi$
$350$	0	0
$351$	−0.337188	−0.0179978
$352$	44.0212	2.34634
$353$	10.5079	0.559281	0.279640	−	0.960105i	$-0.409785\pi$
$353$	10.5079	0.559281	0.279640	+	0.960105i	$0.409785\pi$
$354$	−2.79131	−0.148356
$355$	5.33358	0.283077
$356$	−28.3583	−1.50299
$357$	0	0
$358$	33.8757	1.79039
$359$	−10.6446	−0.561800	−0.280900	−	0.959737i	$-0.590633\pi$
$359$	−10.6446	−0.561800	−0.280900	+	0.959737i	$0.590633\pi$
$360$	0.163611	0.00862308
$361$	36.3328	1.91225
$362$	−19.3955	−1.01940
$363$	−20.9857	−1.10146
$364$	0	0
$365$	−0.277061	−0.0145020
$366$	−4.90079	−0.256168
$367$	26.4608	1.38124	0.690621	−	0.723217i	$-0.257337\pi$
$367$	26.4608	1.38124	0.690621	+	0.723217i	$0.257337\pi$
$368$	−15.0933	−0.786794
$369$	−1.00000	−0.0520579
$370$	−5.72774	−0.297771
$371$	0	0
$372$	5.34079	0.276907
$373$	−28.8140	−1.49193	−0.745966	−	0.665984i	$-0.768012\pi$
$373$	−28.8140	−1.49193	−0.745966	+	0.665984i	$0.768012\pi$
$374$	51.3049	2.65291
$375$	4.99658	0.258022
$376$	3.23650	0.166910
$377$	0.00129878	6.68906e−5 0
$378$	0	0
$379$	35.6547	1.83146	0.915728	−	0.401798i	$-0.131615\pi$
$379$	35.6547	1.83146	0.915728	+	0.401798i	$0.131615\pi$
$380$	7.01328	0.359774
$381$	−6.16100	−0.315638
$382$	50.2042	2.56867
$383$	−37.6215	−1.92237	−0.961185	−	0.275904i	$-0.911023\pi$
$383$	−37.6215	−1.92237	−0.961185	+	0.275904i	$0.911023\pi$
$384$	2.54214	0.129728
$385$	0	0
$386$	27.7187	1.41084
$387$	6.32365	0.321449
$388$	−4.71165	−0.239198
$389$	−3.09403	−0.156873	−0.0784367	−	0.996919i	$-0.524993\pi$
$389$	−3.09403	−0.156873	−0.0784367	+	0.996919i	$0.524993\pi$
$390$	0.338957	0.0171638
$391$	−16.2587	−0.822240
$392$	0	0
$393$	17.8524	0.900533
$394$	27.3754	1.37915
$395$	4.02719	0.202630
$396$	10.3907	0.522152
$397$	28.0868	1.40964	0.704818	−	0.709388i	$-0.251029\pi$
$397$	28.0868	1.40964	0.704818	+	0.709388i	$0.251029\pi$
$398$	10.2997	0.516275
$399$	0	0
$400$	20.3630	1.01815
$401$	−6.78324	−0.338739	−0.169369	−	0.985553i	$-0.554173\pi$
$401$	−6.78324	−0.338739	−0.169369	+	0.985553i	$0.554173\pi$
$402$	18.8289	0.939099
$403$	−0.980191	−0.0488268
$404$	−29.4814	−1.46676
$405$	0.513172	0.0254997
$406$	0	0
$407$	32.2246	1.59732
$408$	1.47646	0.0730957
$409$	22.9474	1.13468	0.567338	−	0.823485i	$-0.307973\pi$
$409$	22.9474	1.13468	0.567338	+	0.823485i	$0.307973\pi$
$410$	1.00525	0.0496456
$411$	−13.1730	−0.649776
$412$	22.5396	1.11045
$413$	0	0
$414$	−6.87741	−0.338006
$415$	7.01693	0.344448
$416$	2.62456	0.128680
$417$	−5.82242	−0.285125
$418$	−82.4098	−4.03080
$419$	1.76985	0.0864631	0.0432315	−	0.999065i	$-0.486235\pi$
$419$	1.76985	0.0864631	0.0432315	+	0.999065i	$0.486235\pi$
$420$	0	0
$421$	−36.4308	−1.77553	−0.887764	−	0.460299i	$-0.847742\pi$
$421$	−36.4308	−1.77553	−0.887764	+	0.460299i	$0.847742\pi$
$422$	−5.72605	−0.278740
$423$	10.1514	0.493577
$424$	−0.508740	−0.0247066
$425$	21.9353	1.06402
$426$	20.3594	0.986418
$427$	0	0
$428$	1.95607	0.0945502
$429$	−1.90700	−0.0920707
$430$	−6.35683	−0.306553
$431$	32.7586	1.57793	0.788963	−	0.614440i	$-0.210618\pi$
$431$	32.7586	1.57793	0.788963	+	0.614440i	$0.210618\pi$
$432$	4.29902	0.206837
$433$	−15.2131	−0.731097	−0.365548	−	0.930792i	$-0.619119\pi$
$433$	−15.2131	−0.731097	−0.365548	+	0.930792i	$0.619119\pi$
$434$	0	0
$435$	−0.00197664	−9.47724e−5 0
$436$	−13.7753	−0.659718
$437$	26.1160	1.24930
$438$	−1.05760	−0.0505341
$439$	12.8477	0.613186	0.306593	−	0.951841i	$-0.400811\pi$
$439$	12.8477	0.613186	0.306593	+	0.951841i	$0.400811\pi$
$440$	0.925319	0.0441128
$441$	0	0
$442$	3.05882	0.145493
$443$	−25.4783	−1.21051	−0.605254	−	0.796032i	$-0.706929\pi$
$443$	−25.4783	−1.21051	−0.605254	+	0.796032i	$0.706929\pi$
$444$	−10.4683	−0.496804
$445$	−7.92093	−0.375488
$446$	−39.9051	−1.88956
$447$	−12.8687	−0.608670
$448$	0	0
$449$	−24.5659	−1.15934	−0.579668	−	0.814853i	$-0.696818\pi$
$449$	−24.5659	−1.15934	−0.579668	+	0.814853i	$0.696818\pi$
$450$	9.27858	0.437396
$451$	−5.65559	−0.266311
$452$	−16.5788	−0.779801
$453$	8.75604	0.411395
$454$	17.6469	0.828211
$455$	0	0
$456$	−2.37160	−0.111060
$457$	−19.2097	−0.898592	−0.449296	−	0.893383i	$-0.648325\pi$
$457$	−19.2097	−0.898592	−0.449296	+	0.893383i	$0.648325\pi$
$458$	−32.8585	−1.53538
$459$	4.63097	0.216155
$460$	3.31013	0.154336
$461$	−2.22690	−0.103717	−0.0518586	−	0.998654i	$-0.516515\pi$
$461$	−2.22690	−0.103717	−0.0518586	+	0.998654i	$0.516515\pi$
$462$	0	0
$463$	−21.7689	−1.01169	−0.505844	−	0.862625i	$-0.668819\pi$
$463$	−21.7689	−1.01169	−0.505844	+	0.862625i	$0.668819\pi$
$464$	−0.0165590	−0.000768731 0
$465$	1.49177	0.0691792
$466$	−41.0924	−1.90357
$467$	15.6865	0.725885	0.362942	−	0.931812i	$-0.381772\pi$
$467$	15.6865	0.725885	0.362942	+	0.931812i	$0.381772\pi$
$468$	0.619496	0.0286362
$469$	0	0
$470$	−10.2046	−0.470705
$471$	−4.49426	−0.207085
$472$	−0.454306	−0.0209111
$473$	35.7640	1.64443
$474$	15.3726	0.706089
$475$	−35.2341	−1.61665
$476$	0	0
$477$	−1.59568	−0.0730611
$478$	26.1120	1.19433
$479$	18.7627	0.857290	0.428645	−	0.903473i	$-0.358991\pi$
$479$	18.7627	0.857290	0.428645	+	0.903473i	$0.358991\pi$
$480$	−3.99436	−0.182317
$481$	1.92124	0.0876012
$482$	−14.3658	−0.654345
$483$	0	0
$484$	38.5558	1.75254
$485$	−1.31604	−0.0597584
$486$	1.95889	0.0888570
$487$	38.4308	1.74147	0.870733	−	0.491756i	$-0.163645\pi$
$487$	38.4308	1.74147	0.870733	+	0.491756i	$0.163645\pi$
$488$	−0.797640	−0.0361074
$489$	−9.57653	−0.433066
$490$	0	0
$491$	36.8009	1.66080	0.830402	−	0.557165i	$-0.188111\pi$
$491$	36.8009	1.66080	0.830402	+	0.557165i	$0.188111\pi$
$492$	1.83724	0.0828293
$493$	−0.0178375	−0.000803363 0
$494$	−4.91330	−0.221060
$495$	2.90229	0.130448
$496$	12.4971	0.561135
$497$	0	0
$498$	26.7851	1.20027
$499$	−9.91559	−0.443883	−0.221941	−	0.975060i	$-0.571239\pi$
$499$	−9.91559	−0.443883	−0.221941	+	0.975060i	$0.571239\pi$
$500$	−9.17993	−0.410539
$501$	−6.49269	−0.290072
$502$	52.0742	2.32418
$503$	27.2048	1.21300	0.606501	−	0.795083i	$-0.292573\pi$
$503$	27.2048	1.21300	0.606501	+	0.795083i	$0.292573\pi$
$504$	0	0
$505$	−8.23465	−0.366437
$506$	−38.8958	−1.72913
$507$	12.8863	0.572301
$508$	11.3193	0.502211
$509$	18.0939	0.801999	0.401000	−	0.916078i	$-0.368663\pi$
$509$	18.0939	0.801999	0.401000	+	0.916078i	$0.368663\pi$
$510$	−4.65526	−0.206139
$511$	0	0
$512$	−30.7209	−1.35768
$513$	−7.43860	−0.328422
$514$	−52.1054	−2.29827
$515$	6.29569	0.277421
$516$	−11.6181	−0.511457
$517$	57.4120	2.52498
$518$	0	0
$519$	0.203823	0.00894682
$520$	0.0551678	0.00241927
$521$	−23.3651	−1.02365	−0.511823	−	0.859091i	$-0.671029\pi$
$521$	−23.3651	−1.02365	−0.511823	+	0.859091i	$0.671029\pi$
$522$	−0.00754524	−0.000330246 0
$523$	−37.3684	−1.63401	−0.817004	−	0.576633i	$-0.804366\pi$
$523$	−37.3684	−1.63401	−0.817004	+	0.576633i	$0.804366\pi$
$524$	−32.7991	−1.43284
$525$	0	0
$526$	12.3187	0.537123
$527$	13.4620	0.586415
$528$	24.3135	1.05811
$529$	−10.6738	−0.464077
$530$	1.60405	0.0696755
$531$	−1.42494	−0.0618373
$532$	0	0
$533$	−0.337188	−0.0146052
$534$	−30.2359	−1.30844
$535$	0.546362	0.0236213
$536$	3.06454	0.132368
$537$	17.2933	0.746263
$538$	25.0887	1.08165
$539$	0	0
$540$	−0.942822	−0.0405726
$541$	31.1517	1.33931	0.669657	−	0.742670i	$-0.266441\pi$
$541$	31.1517	1.33931	0.669657	+	0.742670i	$0.266441\pi$
$542$	−18.3073	−0.786367
$543$	−9.90127	−0.424904
$544$	−36.0459	−1.54545
$545$	−3.84767	−0.164816
$546$	0	0
$547$	9.48991	0.405759	0.202880	−	0.979204i	$-0.434970\pi$
$547$	9.48991	0.405759	0.202880	+	0.979204i	$0.434970\pi$
$548$	24.2020	1.03386
$549$	−2.50182	−0.106775
$550$	52.4758	2.23758
$551$	0.0286520	0.00122062
$552$	−1.11935	−0.0476427
$553$	0	0
$554$	51.3705	2.18252
$555$	−2.92397	−0.124116
$556$	10.6972	0.453662
$557$	−17.2459	−0.730730	−0.365365	−	0.930864i	$-0.619056\pi$
$557$	−17.2459	−0.730730	−0.365365	+	0.930864i	$0.619056\pi$
$558$	5.69440	0.241063
$559$	2.13226	0.0901849
$560$	0	0
$561$	26.1908	1.10578
$562$	−5.69935	−0.240413
$563$	40.4074	1.70297	0.851485	−	0.524378i	$-0.175702\pi$
$563$	40.4074	1.70297	0.851485	+	0.524378i	$0.175702\pi$
$564$	−18.6505	−0.785329
$565$	−4.63073	−0.194816
$566$	−5.69050	−0.239190
$567$	0	0
$568$	3.31365	0.139038
$569$	13.6338	0.571560	0.285780	−	0.958295i	$-0.407747\pi$
$569$	13.6338	0.571560	0.285780	+	0.958295i	$0.407747\pi$
$570$	7.47763	0.313204
$571$	17.1020	0.715697	0.357849	−	0.933780i	$-0.383510\pi$
$571$	17.1020	0.715697	0.357849	+	0.933780i	$0.383510\pi$
$572$	3.50362	0.146494
$573$	25.6289	1.07066
$574$	0	0
$575$	−16.6298	−0.693510
$576$	−6.64927	−0.277053
$577$	13.9866	0.582270	0.291135	−	0.956682i	$-0.405967\pi$
$577$	13.9866	0.582270	0.291135	+	0.956682i	$0.405967\pi$
$578$	−8.70891	−0.362243
$579$	14.1502	0.588062
$580$	0.00363156	0.000150792 0
$581$	0	0
$582$	−5.02361	−0.208236
$583$	−9.02450	−0.373757
$584$	−0.172132	−0.00712288
$585$	0.173036	0.00715414
$586$	−23.0879	−0.953754
$587$	−12.3410	−0.509366	−0.254683	−	0.967025i	$-0.581971\pi$
$587$	−12.3410	−0.509366	−0.254683	+	0.967025i	$0.581971\pi$
$588$	0	0
$589$	−21.6237	−0.890989
$590$	1.43242	0.0589718
$591$	13.9750	0.574854
$592$	−24.4952	−1.00674
$593$	−0.617404	−0.0253538	−0.0126769	−	0.999920i	$-0.504035\pi$
$593$	−0.617404	−0.0253538	−0.0126769	+	0.999920i	$0.504035\pi$
$594$	11.0787	0.454563
$595$	0	0
$596$	23.6430	0.968455
$597$	5.25791	0.215192
$598$	−2.31898	−0.0948301
$599$	23.8114	0.972906	0.486453	−	0.873707i	$-0.338290\pi$
$599$	23.8114	0.972906	0.486453	+	0.873707i	$0.338290\pi$
$600$	1.51016	0.0616519
$601$	−19.7114	−0.804047	−0.402023	−	0.915629i	$-0.631693\pi$
$601$	−19.7114	−0.804047	−0.402023	+	0.915629i	$0.631693\pi$
$602$	0	0
$603$	9.61202	0.391432
$604$	−16.0870	−0.654570
$605$	10.7693	0.437833
$606$	−31.4334	−1.27690
$607$	18.1517	0.736753	0.368376	−	0.929677i	$-0.379914\pi$
$607$	18.1517	0.736753	0.368376	+	0.929677i	$0.379914\pi$
$608$	57.8996	2.34814
$609$	0	0
$610$	2.51495	0.101827
$611$	3.42292	0.138477
$612$	−8.50821	−0.343924
$613$	31.2630	1.26270	0.631351	−	0.775497i	$-0.282501\pi$
$613$	31.2630	1.26270	0.631351	+	0.775497i	$0.282501\pi$
$614$	19.5325	0.788268
$615$	0.513172	0.0206931
$616$	0	0
$617$	−12.3896	−0.498785	−0.249393	−	0.968402i	$-0.580231\pi$
$617$	−12.3896	−0.498785	−0.249393	+	0.968402i	$0.580231\pi$
$618$	24.0320	0.966709
$619$	32.7938	1.31809	0.659047	−	0.752102i	$-0.270960\pi$
$619$	32.7938	1.31809	0.659047	+	0.752102i	$0.270960\pi$
$620$	−2.74074	−0.110071
$621$	−3.51087	−0.140887
$622$	46.8569	1.87879
$623$	0	0
$624$	1.44958	0.0580296
$625$	21.1192	0.844767
$626$	−37.3013	−1.49086
$627$	−42.0697	−1.68010
$628$	8.25705	0.329492
$629$	−26.3865	−1.05210
$630$	0	0
$631$	−42.1403	−1.67758	−0.838790	−	0.544455i	$-0.816737\pi$
$631$	−42.1403	−1.67758	−0.838790	+	0.544455i	$0.816737\pi$
$632$	2.50201	0.0995247
$633$	−2.92311	−0.116183
$634$	26.4197	1.04926
$635$	3.16165	0.125466
$636$	2.93165	0.116247
$637$	0	0
$638$	−0.0426728	−0.00168943
$639$	10.3934	0.411155
$640$	−1.30456	−0.0515671
$641$	10.0868	0.398404	0.199202	−	0.979958i	$-0.436165\pi$
$641$	10.0868	0.398404	0.199202	+	0.979958i	$0.436165\pi$
$642$	2.08558	0.0823114
$643$	−26.4450	−1.04289	−0.521444	−	0.853286i	$-0.674606\pi$
$643$	−26.4450	−1.04289	−0.521444	+	0.853286i	$0.674606\pi$
$644$	0	0
$645$	−3.24512	−0.127777
$646$	67.4796	2.65495
$647$	17.7110	0.696292	0.348146	−	0.937440i	$-0.386811\pi$
$647$	17.7110	0.696292	0.348146	+	0.937440i	$0.386811\pi$
$648$	0.318823	0.0125246
$649$	−8.05890	−0.316339
$650$	3.12862	0.122715
$651$	0	0
$652$	17.5944	0.689050
$653$	−41.1025	−1.60846	−0.804232	−	0.594315i	$-0.797423\pi$
$653$	−41.1025	−1.60846	−0.804232	+	0.594315i	$0.797423\pi$
$654$	−14.6874	−0.574323
$655$	−9.16134	−0.357963
$656$	4.29902	0.167849
$657$	−0.539898	−0.0210634
$658$	0	0
$659$	39.6534	1.54468	0.772339	−	0.635211i	$-0.219087\pi$
$659$	39.6534	1.54468	0.772339	+	0.635211i	$0.219087\pi$
$660$	−5.33221	−0.207556
$661$	41.9575	1.63196	0.815979	−	0.578082i	$-0.196199\pi$
$661$	41.9575	1.63196	0.815979	+	0.578082i	$0.196199\pi$
$662$	−13.4943	−0.524472
$663$	1.56151	0.0606439
$664$	4.35948	0.169181
$665$	0	0
$666$	−11.1614	−0.432497
$667$	0.0135232	0.000523619 0
$668$	11.9286	0.461533
$669$	−20.3713	−0.787601
$670$	−9.66245	−0.373293
$671$	−14.1493	−0.546227
$672$	0	0
$673$	−27.1875	−1.04800	−0.524000	−	0.851718i	$-0.675561\pi$
$673$	−27.1875	−1.04800	−0.524000	+	0.851718i	$0.675561\pi$
$674$	−63.2094	−2.43474
$675$	4.73665	0.182314
$676$	−23.6753	−0.910587
$677$	17.9846	0.691206	0.345603	−	0.938381i	$-0.387674\pi$
$677$	17.9846	0.691206	0.345603	+	0.938381i	$0.387674\pi$
$678$	−17.6765	−0.678862
$679$	0	0
$680$	−0.757679	−0.0290556
$681$	9.00865	0.345212
$682$	32.2052	1.23320
$683$	−31.4508	−1.20343	−0.601716	−	0.798710i	$-0.705516\pi$
$683$	−31.4508	−1.20343	−0.601716	+	0.798710i	$0.705516\pi$
$684$	13.6665	0.522552
$685$	6.76002	0.258287
$686$	0	0
$687$	−16.7740	−0.639970
$688$	−27.1855	−1.03644
$689$	−0.538044	−0.0204978
$690$	3.52930	0.134358
$691$	42.5967	1.62045	0.810227	−	0.586117i	$-0.199344\pi$
$691$	42.5967	1.62045	0.810227	+	0.586117i	$0.199344\pi$
$692$	−0.374471	−0.0142353
$693$	0	0
$694$	−17.2722	−0.655644
$695$	2.98791	0.113338
$696$	−0.00122804	−4.65489e−5 0
$697$	4.63097	0.175410
$698$	32.2918	1.22226
$699$	−20.9774	−0.793439
$700$	0	0
$701$	18.0204	0.680619	0.340310	−	0.940313i	$-0.389468\pi$
$701$	18.0204	0.680619	0.340310	+	0.940313i	$0.389468\pi$
$702$	0.660514	0.0249295
$703$	42.3840	1.59854
$704$	−37.6056	−1.41731
$705$	−5.20940	−0.196197
$706$	−20.5839	−0.774684
$707$	0	0
$708$	2.61797	0.0983892
$709$	−8.47808	−0.318401	−0.159201	−	0.987246i	$-0.550892\pi$
$709$	−8.47808	−0.318401	−0.159201	+	0.987246i	$0.550892\pi$
$710$	−10.4479	−0.392103
$711$	7.84764	0.294309
$712$	−4.92111	−0.184427
$713$	−10.2060	−0.382216
$714$	0	0
$715$	0.978618	0.0365982
$716$	−31.7721	−1.18738
$717$	13.3300	0.497818
$718$	20.8516	0.778173
$719$	7.37205	0.274931	0.137466	−	0.990507i	$-0.456104\pi$
$719$	7.37205	0.274931	0.137466	+	0.990507i	$0.456104\pi$
$720$	−2.20614	−0.0822180
$721$	0	0
$722$	−71.1719	−2.64874
$723$	−7.33366	−0.272742
$724$	18.1910	0.676064
$725$	−0.0182446	−0.000677589 0
$726$	41.1086	1.52568
$727$	20.2474	0.750934	0.375467	−	0.926836i	$-0.377482\pi$
$727$	20.2474	0.750934	0.375467	+	0.926836i	$0.377482\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	0.542731	0.0200874
$731$	−29.2846	−1.08313
$732$	4.59645	0.169890
$733$	−3.10316	−0.114618	−0.0573090	−	0.998356i	$-0.518252\pi$
$733$	−3.10316	−0.114618	−0.0573090	+	0.998356i	$0.518252\pi$
$734$	−51.8337	−1.91322
$735$	0	0
$736$	27.3275	1.00730
$737$	54.3616	2.00244
$738$	1.95889	0.0721077
$739$	29.8501	1.09805	0.549026	−	0.835805i	$-0.314999\pi$
$739$	29.8501	1.09805	0.549026	+	0.835805i	$0.314999\pi$
$740$	5.37205	0.197480
$741$	−2.50821	−0.0921413
$742$	0	0
$743$	24.7526	0.908084	0.454042	−	0.890980i	$-0.349982\pi$
$743$	24.7526	0.908084	0.454042	+	0.890980i	$0.349982\pi$
$744$	0.926806	0.0339784
$745$	6.60388	0.241947
$746$	56.4434	2.06654
$747$	13.6736	0.500292
$748$	−48.1189	−1.75940
$749$	0	0
$750$	−9.78774	−0.357398
$751$	49.0314	1.78918	0.894591	−	0.446886i	$-0.147467\pi$
$751$	49.0314	1.78918	0.894591	+	0.446886i	$0.147467\pi$
$752$	−43.6410	−1.59142
$753$	26.5835	0.968758
$754$	−0.00254416	−9.26530e−5 0
$755$	−4.49336	−0.163530
$756$	0	0
$757$	37.5453	1.36461	0.682304	−	0.731069i	$-0.260978\pi$
$757$	37.5453	1.36461	0.682304	+	0.731069i	$0.260978\pi$
$758$	−69.8435	−2.53683
$759$	−19.8561	−0.720729
$760$	1.21704	0.0441467
$761$	30.7380	1.11425	0.557126	−	0.830428i	$-0.311904\pi$
$761$	30.7380	1.11425	0.557126	+	0.830428i	$0.311904\pi$
$762$	12.0687	0.437203
$763$	0	0
$764$	−47.0865	−1.70353
$765$	−2.37648	−0.0859219
$766$	73.6964	2.66276
$767$	−0.480474	−0.0173489
$768$	−18.2783	−0.659562
$769$	−16.6161	−0.599191	−0.299595	−	0.954066i	$-0.596852\pi$
$769$	−16.6161	−0.599191	−0.299595	+	0.954066i	$0.596852\pi$
$770$	0	0
$771$	−26.5995	−0.957957
$772$	−25.9974	−0.935665
$773$	15.0910	0.542785	0.271393	−	0.962469i	$-0.412516\pi$
$773$	15.0910	0.542785	0.271393	+	0.962469i	$0.412516\pi$
$774$	−12.3873	−0.445253
$775$	13.7692	0.494606
$776$	−0.817630	−0.0293512
$777$	0	0
$778$	6.06085	0.217292
$779$	−7.43860	−0.266516
$780$	−0.317908	−0.0113829
$781$	58.7806	2.10334
$782$	31.8490	1.13892
$783$	−0.00385180	−0.000137652 0
$784$	0	0
$785$	2.30633	0.0823165
$786$	−34.9708	−1.24737
$787$	−13.5486	−0.482954	−0.241477	−	0.970407i	$-0.577632\pi$
$787$	−13.5486	−0.482954	−0.241477	+	0.970407i	$0.577632\pi$
$788$	−25.6754	−0.914649
$789$	6.28864	0.223882
$790$	−7.88882	−0.280671
$791$	0	0
$792$	1.80313	0.0640716
$793$	−0.843584	−0.0299566
$794$	−55.0189	−1.95255
$795$	0.818858	0.0290419
$796$	−9.66006	−0.342392
$797$	30.4556	1.07879	0.539396	−	0.842052i	$-0.318653\pi$
$797$	30.4556	1.07879	0.539396	+	0.842052i	$0.318653\pi$
$798$	0	0
$799$	−47.0107	−1.66312
$800$	−36.8685	−1.30350
$801$	−15.4352	−0.545377
$802$	13.2876	0.469202
$803$	−3.05344	−0.107754
$804$	−17.6596	−0.622807
$805$	0	0
$806$	1.92008	0.0676321
$807$	12.8076	0.450850
$808$	−5.11602	−0.179981
$809$	36.5584	1.28533	0.642663	−	0.766149i	$-0.277830\pi$
$809$	36.5584	1.28533	0.642663	+	0.766149i	$0.277830\pi$
$810$	−1.00525	−0.0353208
$811$	42.8439	1.50445	0.752226	−	0.658905i	$-0.228980\pi$
$811$	42.8439	1.50445	0.752226	+	0.658905i	$0.228980\pi$
$812$	0	0
$813$	−9.34578	−0.327771
$814$	−63.1245	−2.21251
$815$	4.91441	0.172144
$816$	−19.9086	−0.696942
$817$	47.0391	1.64569
$818$	−44.9514	−1.57169
$819$	0	0
$820$	−0.942822	−0.0329248
$821$	−38.0887	−1.32931	−0.664653	−	0.747152i	$-0.731421\pi$
$821$	−38.0887	−1.32931	−0.664653	+	0.747152i	$0.731421\pi$
$822$	25.8044	0.900033
$823$	23.4658	0.817965	0.408982	−	0.912542i	$-0.365884\pi$
$823$	23.4658	0.817965	0.408982	+	0.912542i	$0.365884\pi$
$824$	3.91139	0.136260
$825$	26.7886	0.932658
$826$	0	0
$827$	22.1287	0.769492	0.384746	−	0.923023i	$-0.374289\pi$
$827$	22.1287	0.769492	0.384746	+	0.923023i	$0.374289\pi$
$828$	6.45033	0.224164
$829$	−8.56171	−0.297360	−0.148680	−	0.988885i	$-0.547503\pi$
$829$	−8.56171	−0.297360	−0.148680	+	0.988885i	$0.547503\pi$
$830$	−13.7454	−0.477109
$831$	26.2243	0.909712
$832$	−2.24206	−0.0777293
$833$	0	0
$834$	11.4055	0.394939
$835$	3.33187	0.115304
$836$	77.2922	2.67321
$837$	2.90696	0.100479
$838$	−3.46695	−0.119764
$839$	5.19195	0.179246	0.0896231	−	0.995976i	$-0.471434\pi$
$839$	5.19195	0.179246	0.0896231	+	0.995976i	$0.471434\pi$
$840$	0	0
$841$	−29.0000	−0.999999
$842$	71.3638	2.45936
$843$	−2.90948	−0.100208
$844$	5.37047	0.184859
$845$	−6.61289	−0.227490
$846$	−19.8854	−0.683674
$847$	0	0
$848$	6.85986	0.235569
$849$	−2.90496	−0.0996981
$850$	−42.9688	−1.47382
$851$	20.0044	0.685742
$852$	−19.0951	−0.654188
$853$	−10.7872	−0.369348	−0.184674	−	0.982800i	$-0.559123\pi$
$853$	−10.7872	−0.369348	−0.184674	+	0.982800i	$0.559123\pi$
$854$	0	0
$855$	3.81728	0.130548
$856$	0.339444	0.0116020
$857$	−33.0347	−1.12844	−0.564221	−	0.825624i	$-0.690824\pi$
$857$	−33.0347	−1.12844	−0.564221	+	0.825624i	$0.690824\pi$
$858$	3.73559	0.127531
$859$	−30.0052	−1.02377	−0.511883	−	0.859055i	$-0.671052\pi$
$859$	−30.0052	−1.02377	−0.511883	+	0.859055i	$0.671052\pi$
$860$	5.96207	0.203305
$861$	0	0
$862$	−64.1704	−2.18565
$863$	−22.4627	−0.764639	−0.382320	−	0.924030i	$-0.624875\pi$
$863$	−22.4627	−0.764639	−0.382320	+	0.924030i	$0.624875\pi$
$864$	−7.78366	−0.264806
$865$	−0.104596	−0.00355637
$866$	29.8008	1.01267
$867$	−4.44585	−0.150989
$868$	0	0
$869$	44.3830	1.50559
$870$	0.00387201	0.000131273 0
$871$	3.24106	0.109819
$872$	−2.39048	−0.0809519
$873$	−2.56452	−0.0867960
$874$	−51.1583	−1.73046
$875$	0	0
$876$	0.991924	0.0335140
$877$	−39.4229	−1.33122	−0.665608	−	0.746302i	$-0.731828\pi$
$877$	−39.4229	−1.33122	−0.665608	+	0.746302i	$0.731828\pi$
$878$	−25.1671	−0.849350
$879$	−11.7862	−0.397540
$880$	−12.4770	−0.420600
$881$	43.8734	1.47813	0.739066	−	0.673633i	$-0.235267\pi$
$881$	43.8734	1.47813	0.739066	+	0.673633i	$0.235267\pi$
$882$	0	0
$883$	17.4922	0.588658	0.294329	−	0.955704i	$-0.404904\pi$
$883$	17.4922	0.588658	0.294329	+	0.955704i	$0.404904\pi$
$884$	−2.86887	−0.0964904
$885$	0.731242	0.0245804
$886$	49.9091	1.67673
$887$	−35.3835	−1.18806	−0.594030	−	0.804443i	$-0.702464\pi$
$887$	−35.3835	−1.18806	−0.594030	+	0.804443i	$0.702464\pi$
$888$	−1.81661	−0.0609613
$889$	0	0
$890$	15.5162	0.520105
$891$	5.65559	0.189469
$892$	37.4271	1.25315
$893$	75.5120	2.52691
$894$	25.2084	0.843095
$895$	−8.87446	−0.296640
$896$	0	0
$897$	−1.18382	−0.0395268
$898$	48.1218	1.60585
$899$	−0.0111970	−0.000373441 0
$900$	−8.70238	−0.290079
$901$	7.38953	0.246181
$902$	11.0787	0.368879
$903$	0	0
$904$	−2.87698	−0.0956869
$905$	5.08106	0.168900
$906$	−17.1521	−0.569841
$907$	−23.1267	−0.767910	−0.383955	−	0.923352i	$-0.625438\pi$
$907$	−23.1267	−0.767910	−0.383955	+	0.923352i	$0.625438\pi$
$908$	−16.5511	−0.549266
$909$	−16.0466	−0.532231
$910$	0	0
$911$	37.9418	1.25707	0.628534	−	0.777782i	$-0.283655\pi$
$911$	37.9418	1.25707	0.628534	+	0.777782i	$0.283655\pi$
$912$	31.9787	1.05892
$913$	77.3325	2.55933
$914$	37.6296	1.24468
$915$	1.28387	0.0424433
$916$	30.8180	1.01825
$917$	0	0
$918$	−9.07154	−0.299406
$919$	26.5698	0.876456	0.438228	−	0.898864i	$-0.355606\pi$
$919$	26.5698	0.876456	0.438228	+	0.898864i	$0.355606\pi$
$920$	0.574419	0.0189380
$921$	9.97122	0.328563
$922$	4.36225	0.143663
$923$	3.50452	0.115353
$924$	0	0
$925$	−26.9887	−0.887383
$926$	42.6429	1.40133
$927$	12.2682	0.402940
$928$	0.0299811	0.000984177 0
$929$	38.3519	1.25828	0.629142	−	0.777290i	$-0.283406\pi$
$929$	38.3519	1.25828	0.629142	+	0.777290i	$0.283406\pi$
$930$	−2.92221	−0.0958230
$931$	0	0
$932$	38.5406	1.26244
$933$	23.9202	0.783111
$934$	−30.7281	−1.00545
$935$	−13.4404	−0.439548
$936$	0.107503	0.00351386
$937$	29.1402	0.951969	0.475985	−	0.879454i	$-0.342092\pi$
$937$	29.1402	0.951969	0.475985	+	0.879454i	$0.342092\pi$
$938$	0	0
$939$	−19.0421	−0.621414
$940$	9.57093	0.312169
$941$	−39.2714	−1.28021	−0.640105	−	0.768287i	$-0.721109\pi$
$941$	−39.2714	−1.28021	−0.640105	+	0.768287i	$0.721109\pi$
$942$	8.80376	0.286842
$943$	−3.51087	−0.114330
$944$	6.12587	0.199380
$945$	0	0
$946$	−70.0576	−2.27777
$947$	−30.3126	−0.985028	−0.492514	−	0.870305i	$-0.663922\pi$
$947$	−30.3126	−0.985028	−0.492514	+	0.870305i	$0.663922\pi$
$948$	−14.4180	−0.468275
$949$	−0.182047	−0.00590950
$950$	69.0196	2.23929
$951$	13.4871	0.437348
$952$	0	0
$953$	52.1968	1.69082	0.845410	−	0.534118i	$-0.179356\pi$
$953$	52.1968	1.69082	0.845410	+	0.534118i	$0.179356\pi$
$954$	3.12576	0.101200
$955$	−13.1520	−0.425590
$956$	−24.4904	−0.792077
$957$	−0.0217842	−0.000704183 0
$958$	−36.7540	−1.18747
$959$	0	0
$960$	3.41222	0.110129
$961$	−22.5496	−0.727407
$962$	−3.76350	−0.121340
$963$	1.06468	0.0343087
$964$	13.4737	0.433959
$965$	−7.26149	−0.233756
$966$	0	0
$967$	−50.5470	−1.62548	−0.812741	−	0.582625i	$-0.802026\pi$
$967$	−50.5470	−1.62548	−0.812741	+	0.582625i	$0.802026\pi$
$968$	6.69073	0.215048
$969$	34.4479	1.10663
$970$	2.57798	0.0827739
$971$	30.5794	0.981339	0.490669	−	0.871346i	$-0.336752\pi$
$971$	30.5794	0.981339	0.490669	+	0.871346i	$0.336752\pi$
$972$	−1.83724	−0.0589296
$973$	0	0
$974$	−75.2816	−2.41218
$975$	1.59714	0.0511495
$976$	10.7554	0.344272
$977$	−21.3420	−0.682792	−0.341396	−	0.939919i	$-0.610900\pi$
$977$	−21.3420	−0.682792	−0.341396	+	0.939919i	$0.610900\pi$
$978$	18.7593	0.599858
$979$	−87.2953	−2.78997
$980$	0	0
$981$	−7.49782	−0.239387
$982$	−72.0889	−2.30045
$983$	−10.2173	−0.325880	−0.162940	−	0.986636i	$-0.552098\pi$
$983$	−10.2173	−0.325880	−0.162940	+	0.986636i	$0.552098\pi$
$984$	0.318823	0.0101637
$985$	−7.17157	−0.228505
$986$	0.0349418	0.00111277
$987$	0	0
$988$	4.60819	0.146606
$989$	22.2015	0.705968
$990$	−5.68526	−0.180690
$991$	−5.79546	−0.184099	−0.0920495	−	0.995754i	$-0.529342\pi$
$991$	−5.79546	−0.184099	−0.0920495	+	0.995754i	$0.529342\pi$
$992$	−22.6268	−0.718401
$993$	−6.88877	−0.218608
$994$	0	0
$995$	−2.69821	−0.0855391
$996$	−25.1218	−0.796015
$997$	−0.874723	−0.0277028	−0.0138514	−	0.999904i	$-0.504409\pi$
$997$	−0.874723	−0.0277028	−0.0138514	+	0.999904i	$0.504409\pi$
$998$	19.4235	0.614841
$999$	−5.69784	−0.180272

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.y.1.1		7
7.6	odd	2		861.2.a.m.1.1	✓	7
21.20	even	2		2583.2.a.u.1.7		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.a.m.1.1	✓	7	7.6	odd	2
2583.2.a.u.1.7		7	21.20	even	2
6027.2.a.y.1.1		7	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)

\(f(q)\)	\(=\)	\(q-1.95889 q^{2} -1.00000 q^{3} +1.83724 q^{4} +0.513172 q^{5} +1.95889 q^{6} +0.318823 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.95889 q^{2} -1.00000 q^{3} +1.83724 q^{4} +0.513172 q^{5} +1.95889 q^{6} +0.318823 q^{8} +1.00000 q^{9} -1.00525 q^{10} +5.65559 q^{11} -1.83724 q^{12} +0.337188 q^{13} -0.513172 q^{15} -4.29902 q^{16} -4.63097 q^{17} -1.95889 q^{18} +7.43860 q^{19} +0.942822 q^{20} -11.0787 q^{22} +3.51087 q^{23} -0.318823 q^{24} -4.73665 q^{25} -0.660514 q^{26} -1.00000 q^{27} +0.00385180 q^{29} +1.00525 q^{30} -2.90696 q^{31} +7.78366 q^{32} -5.65559 q^{33} +9.07154 q^{34} +1.83724 q^{36} +5.69784 q^{37} -14.5714 q^{38} -0.337188 q^{39} +0.163611 q^{40} -1.00000 q^{41} +6.32365 q^{43} +10.3907 q^{44} +0.513172 q^{45} -6.87741 q^{46} +10.1514 q^{47} +4.29902 q^{48} +9.27858 q^{50} +4.63097 q^{51} +0.619496 q^{52} -1.59568 q^{53} +1.95889 q^{54} +2.90229 q^{55} -7.43860 q^{57} -0.00754524 q^{58} -1.42494 q^{59} -0.942822 q^{60} -2.50182 q^{61} +5.69440 q^{62} -6.64927 q^{64} +0.173036 q^{65} +11.0787 q^{66} +9.61202 q^{67} -8.50821 q^{68} -3.51087 q^{69} +10.3934 q^{71} +0.318823 q^{72} -0.539898 q^{73} -11.1614 q^{74} +4.73665 q^{75} +13.6665 q^{76} +0.660514 q^{78} +7.84764 q^{79} -2.20614 q^{80} +1.00000 q^{81} +1.95889 q^{82} +13.6736 q^{83} -2.37648 q^{85} -12.3873 q^{86} -0.00385180 q^{87} +1.80313 q^{88} -15.4352 q^{89} -1.00525 q^{90} +6.45033 q^{92} +2.90696 q^{93} -19.8854 q^{94} +3.81728 q^{95} -7.78366 q^{96} -2.56452 q^{97} +5.65559 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 4 q^{2} - 7 q^{3} + 8 q^{4} - q^{5} - 4 q^{6} + 12 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q + 4 * q^2 - 7 * q^3 + 8 * q^4 - q^5 - 4 * q^6 + 12 * q^8 + 7 * q^9	\( 7 q + 4 q^{2} - 7 q^{3} + 8 q^{4} - q^{5} - 4 q^{6} + 12 q^{8} + 7 q^{9} + 3 q^{10} + 11 q^{11} - 8 q^{12} + 7 q^{13} + q^{15} + 6 q^{16} - 11 q^{17} + 4 q^{18} - 4 q^{19} + 7 q^{20} + 6 q^{22} + 7 q^{23} - 12 q^{24} + 2 q^{25} + 13 q^{26} - 7 q^{27} + 4 q^{29} - 3 q^{30} + 7 q^{31} + 18 q^{32} - 11 q^{33} + 20 q^{34} + 8 q^{36} - 4 q^{38} - 7 q^{39} + 9 q^{40} - 7 q^{41} + q^{43} + 18 q^{44} - q^{45} - 17 q^{46} - 14 q^{47} - 6 q^{48} + 19 q^{50} + 11 q^{51} + 27 q^{52} + 23 q^{53} - 4 q^{54} + 30 q^{55} + 4 q^{57} - 3 q^{58} - 8 q^{59} - 7 q^{60} + 3 q^{61} + 16 q^{62} + 6 q^{64} + 15 q^{65} - 6 q^{66} + 3 q^{67} - 7 q^{69} + 7 q^{71} + 12 q^{72} + 11 q^{73} - 13 q^{74} - 2 q^{75} + 40 q^{76} - 13 q^{78} - q^{79} + 43 q^{80} + 7 q^{81} - 4 q^{82} - 10 q^{85} - 12 q^{86} - 4 q^{87} + 10 q^{88} - 32 q^{89} + 3 q^{90} - 19 q^{92} - 7 q^{93} - 21 q^{94} - 8 q^{95} - 18 q^{96} + 25 q^{97} + 11 q^{99}+O(q^{100}) \) 7 * q + 4 * q^2 - 7 * q^3 + 8 * q^4 - q^5 - 4 * q^6 + 12 * q^8 + 7 * q^9 + 3 * q^10 + 11 * q^11 - 8 * q^12 + 7 * q^13 + q^15 + 6 * q^16 - 11 * q^17 + 4 * q^18 - 4 * q^19 + 7 * q^20 + 6 * q^22 + 7 * q^23 - 12 * q^24 + 2 * q^25 + 13 * q^26 - 7 * q^27 + 4 * q^29 - 3 * q^30 + 7 * q^31 + 18 * q^32 - 11 * q^33 + 20 * q^34 + 8 * q^36 - 4 * q^38 - 7 * q^39 + 9 * q^40 - 7 * q^41 + q^43 + 18 * q^44 - q^45 - 17 * q^46 - 14 * q^47 - 6 * q^48 + 19 * q^50 + 11 * q^51 + 27 * q^52 + 23 * q^53 - 4 * q^54 + 30 * q^55 + 4 * q^57 - 3 * q^58 - 8 * q^59 - 7 * q^60 + 3 * q^61 + 16 * q^62 + 6 * q^64 + 15 * q^65 - 6 * q^66 + 3 * q^67 - 7 * q^69 + 7 * q^71 + 12 * q^72 + 11 * q^73 - 13 * q^74 - 2 * q^75 + 40 * q^76 - 13 * q^78 - q^79 + 43 * q^80 + 7 * q^81 - 4 * q^82 - 10 * q^85 - 12 * q^86 - 4 * q^87 + 10 * q^88 - 32 * q^89 + 3 * q^90 - 19 * q^92 - 7 * q^93 - 21 * q^94 - 8 * q^95 - 18 * q^96 + 25 * q^97 + 11 * q^99

Introduction

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