LMFDB - Embedded newform 6027.2.a.bh.1.13

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:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 4 x^{12} - 11 x^{11} + 56 x^{10} + 26 x^{9} - 263 x^{8} + 50 x^{7} + 478 x^{6} - 174 x^{5} + \cdots - 4 $ x^13 - 4x^12 - 11x^11 + 56x^10 + 26x^9 - 263x^8 + 50x^7 + 478x^6 - 174x^5 - 311x^4 + 84x^3 + 69x^2 - 12x - 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			1.13
Root			$-2.47258$ 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)

$f(q)$	$=$	$q+2.47258 q^{2} -1.00000 q^{3} +4.11367 q^{4} +4.25608 q^{5} -2.47258 q^{6} +5.22624 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.47258 q^{2} -1.00000 q^{3} +4.11367 q^{4} +4.25608 q^{5} -2.47258 q^{6} +5.22624 q^{8} +1.00000 q^{9} +10.5235 q^{10} -0.0562785 q^{11} -4.11367 q^{12} +0.121450 q^{13} -4.25608 q^{15} +4.69496 q^{16} +6.50188 q^{17} +2.47258 q^{18} -2.99714 q^{19} +17.5081 q^{20} -0.139153 q^{22} -7.44433 q^{23} -5.22624 q^{24} +13.1142 q^{25} +0.300296 q^{26} -1.00000 q^{27} +6.83272 q^{29} -10.5235 q^{30} +5.89005 q^{31} +1.15622 q^{32} +0.0562785 q^{33} +16.0764 q^{34} +4.11367 q^{36} -3.56058 q^{37} -7.41068 q^{38} -0.121450 q^{39} +22.2433 q^{40} -1.00000 q^{41} -11.9950 q^{43} -0.231511 q^{44} +4.25608 q^{45} -18.4067 q^{46} +12.7869 q^{47} -4.69496 q^{48} +32.4260 q^{50} -6.50188 q^{51} +0.499606 q^{52} -2.94688 q^{53} -2.47258 q^{54} -0.239526 q^{55} +2.99714 q^{57} +16.8945 q^{58} -10.7511 q^{59} -17.5081 q^{60} +9.07345 q^{61} +14.5636 q^{62} -6.53108 q^{64} +0.516902 q^{65} +0.139153 q^{66} +2.83719 q^{67} +26.7466 q^{68} +7.44433 q^{69} -2.41356 q^{71} +5.22624 q^{72} -7.14489 q^{73} -8.80383 q^{74} -13.1142 q^{75} -12.3293 q^{76} -0.300296 q^{78} +8.01738 q^{79} +19.9821 q^{80} +1.00000 q^{81} -2.47258 q^{82} +3.64416 q^{83} +27.6725 q^{85} -29.6587 q^{86} -6.83272 q^{87} -0.294125 q^{88} +7.76515 q^{89} +10.5235 q^{90} -30.6236 q^{92} -5.89005 q^{93} +31.6167 q^{94} -12.7561 q^{95} -1.15622 q^{96} +7.07757 q^{97} -0.0562785 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q - 4 q^{2} - 13 q^{3} + 12 q^{4} + 8 q^{5} + 4 q^{6} - 12 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q - 4 * q^2 - 13 * q^3 + 12 * q^4 + 8 * q^5 + 4 * q^6 - 12 * q^8 + 13 * q^9	$ 13 q - 4 q^{2} - 13 q^{3} + 12 q^{4} + 8 q^{5} + 4 q^{6} - 12 q^{8} + 13 q^{9} + q^{10} - 10 q^{11} - 12 q^{12} + 16 q^{13} - 8 q^{15} + 26 q^{16} + 12 q^{17} - 4 q^{18} + 11 q^{19} + 6 q^{20} + q^{22} - 15 q^{23} + 12 q^{24} + 15 q^{25} + 18 q^{26} - 13 q^{27} - 8 q^{29} - q^{30} + 9 q^{31} - 23 q^{32} + 10 q^{33} - 7 q^{34} + 12 q^{36} - 2 q^{37} + 20 q^{38} - 16 q^{39} + 49 q^{40} - 13 q^{41} - 7 q^{43} - 22 q^{44} + 8 q^{45} - 4 q^{46} + 26 q^{47} - 26 q^{48} - 15 q^{50} - 12 q^{51} + 24 q^{52} + 4 q^{53} + 4 q^{54} + q^{55} - 11 q^{57} + 39 q^{58} - 3 q^{59} - 6 q^{60} + 28 q^{61} + 7 q^{62} + 2 q^{64} - 20 q^{65} - q^{66} + 7 q^{67} + 55 q^{68} + 15 q^{69} - 40 q^{71} - 12 q^{72} - 2 q^{73} + q^{74} - 15 q^{75} - 26 q^{76} - 18 q^{78} + 13 q^{79} + 22 q^{80} + 13 q^{81} + 4 q^{82} + 14 q^{83} + 48 q^{85} - 49 q^{86} + 8 q^{87} + 20 q^{88} + 35 q^{89} + q^{90} - 105 q^{92} - 9 q^{93} - 2 q^{94} + 7 q^{95} + 23 q^{96} + 64 q^{97} - 10 q^{99}+O(q^{100}) $ 13 * q - 4 * q^2 - 13 * q^3 + 12 * q^4 + 8 * q^5 + 4 * q^6 - 12 * q^8 + 13 * q^9 + q^10 - 10 * q^11 - 12 * q^12 + 16 * q^13 - 8 * q^15 + 26 * q^16 + 12 * q^17 - 4 * q^18 + 11 * q^19 + 6 * q^20 + q^22 - 15 * q^23 + 12 * q^24 + 15 * q^25 + 18 * q^26 - 13 * q^27 - 8 * q^29 - q^30 + 9 * q^31 - 23 * q^32 + 10 * q^33 - 7 * q^34 + 12 * q^36 - 2 * q^37 + 20 * q^38 - 16 * q^39 + 49 * q^40 - 13 * q^41 - 7 * q^43 - 22 * q^44 + 8 * q^45 - 4 * q^46 + 26 * q^47 - 26 * q^48 - 15 * q^50 - 12 * q^51 + 24 * q^52 + 4 * q^53 + 4 * q^54 + q^55 - 11 * q^57 + 39 * q^58 - 3 * q^59 - 6 * q^60 + 28 * q^61 + 7 * q^62 + 2 * q^64 - 20 * q^65 - q^66 + 7 * q^67 + 55 * q^68 + 15 * q^69 - 40 * q^71 - 12 * q^72 - 2 * q^73 + q^74 - 15 * q^75 - 26 * q^76 - 18 * q^78 + 13 * q^79 + 22 * q^80 + 13 * q^81 + 4 * q^82 + 14 * q^83 + 48 * q^85 - 49 * q^86 + 8 * q^87 + 20 * q^88 + 35 * q^89 + q^90 - 105 * q^92 - 9 * q^93 - 2 * q^94 + 7 * q^95 + 23 * q^96 + 64 * q^97 - 10 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.47258	1.74838	0.874191	−	0.485583i	$-0.161393\pi$
$2$	2.47258	1.74838	0.874191	+	0.485583i	$0.161393\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.11367	2.05684
$5$	4.25608	1.90338	0.951688	−	0.307065i	$-0.0993470\pi$
$5$	4.25608	1.90338	0.951688	+	0.307065i	$0.0993470\pi$
$6$	−2.47258	−1.00943
$7$	0	0
$7$	0	0
$8$	5.22624	1.84775
$9$	1.00000	0.333333
$10$	10.5235	3.32783
$11$	−0.0562785	−0.0169686	−0.00848430	−	0.999964i	$-0.502701\pi$
$11$	−0.0562785	−0.0169686	−0.00848430	+	0.999964i	$0.502701\pi$
$12$	−4.11367	−1.18752
$13$	0.121450	0.0336842	0.0168421	−	0.999858i	$-0.494639\pi$
$13$	0.121450	0.0336842	0.0168421	+	0.999858i	$0.494639\pi$
$14$	0	0
$15$	−4.25608	−1.09892
$16$	4.69496	1.17374
$17$	6.50188	1.57694	0.788469	−	0.615075i	$-0.210874\pi$
$17$	6.50188	1.57694	0.788469	+	0.615075i	$0.210874\pi$
$18$	2.47258	0.582794
$19$	−2.99714	−0.687591	−0.343795	−	0.939045i	$-0.611713\pi$
$19$	−2.99714	−0.687591	−0.343795	+	0.939045i	$0.611713\pi$
$20$	17.5081	3.91494
$21$	0	0
$22$	−0.139153	−0.0296676
$23$	−7.44433	−1.55225	−0.776125	−	0.630579i	$-0.782818\pi$
$23$	−7.44433	−1.55225	−0.776125	+	0.630579i	$0.782818\pi$
$24$	−5.22624	−1.06680
$25$	13.1142	2.62284
$26$	0.300296	0.0588929
$27$	−1.00000	−0.192450
$28$	0	0
$29$	6.83272	1.26880	0.634402	−	0.773003i	$-0.281246\pi$
$29$	6.83272	1.26880	0.634402	+	0.773003i	$0.281246\pi$
$30$	−10.5235	−1.92132
$31$	5.89005	1.05788	0.528942	−	0.848658i	$-0.322589\pi$
$31$	5.89005	1.05788	0.528942	+	0.848658i	$0.322589\pi$
$32$	1.15622	0.204392
$33$	0.0562785	0.00979683
$34$	16.0764	2.75709
$35$	0	0
$36$	4.11367	0.685612
$37$	−3.56058	−0.585356	−0.292678	−	0.956211i	$-0.594546\pi$
$37$	−3.56058	−0.585356	−0.292678	+	0.956211i	$0.594546\pi$
$38$	−7.41068	−1.20217
$39$	−0.121450	−0.0194476
$40$	22.2433	3.51697
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	−11.9950	−1.82922	−0.914611	−	0.404336i	$-0.867503\pi$
$43$	−11.9950	−1.82922	−0.914611	+	0.404336i	$0.867503\pi$
$44$	−0.231511	−0.0349017
$45$	4.25608	0.634459
$46$	−18.4067	−2.71393
$47$	12.7869	1.86516	0.932581	−	0.360961i	$-0.117551\pi$
$47$	12.7869	1.86516	0.932581	+	0.360961i	$0.117551\pi$
$48$	−4.69496	−0.677659
$49$	0	0
$50$	32.4260	4.58573
$51$	−6.50188	−0.910445
$52$	0.499606	0.0692829
$53$	−2.94688	−0.404784	−0.202392	−	0.979305i	$-0.564872\pi$
$53$	−2.94688	−0.404784	−0.202392	+	0.979305i	$0.564872\pi$
$54$	−2.47258	−0.336476
$55$	−0.239526	−0.0322977
$56$	0	0
$57$	2.99714	0.396981
$58$	16.8945	2.21835
$59$	−10.7511	−1.39968	−0.699838	−	0.714301i	$-0.746745\pi$
$59$	−10.7511	−1.39968	−0.699838	+	0.714301i	$0.746745\pi$
$60$	−17.5081	−2.26029
$61$	9.07345	1.16174	0.580868	−	0.813997i	$-0.302713\pi$
$61$	9.07345	1.16174	0.580868	+	0.813997i	$0.302713\pi$
$62$	14.5636	1.84958
$63$	0	0
$64$	−6.53108	−0.816385
$65$	0.516902	0.0641138
$66$	0.139153	0.0171286
$67$	2.83719	0.346618	0.173309	−	0.984867i	$-0.444554\pi$
$67$	2.83719	0.346618	0.173309	+	0.984867i	$0.444554\pi$
$68$	26.7466	3.24350
$69$	7.44433	0.896192
$70$	0	0
$71$	−2.41356	−0.286437	−0.143218	−	0.989691i	$-0.545745\pi$
$71$	−2.41356	−0.286437	−0.143218	+	0.989691i	$0.545745\pi$
$72$	5.22624	0.615918
$73$	−7.14489	−0.836246	−0.418123	−	0.908391i	$-0.637312\pi$
$73$	−7.14489	−0.836246	−0.418123	+	0.908391i	$0.637312\pi$
$74$	−8.80383	−1.02342
$75$	−13.1142	−1.51430
$76$	−12.3293	−1.41426
$77$	0	0
$78$	−0.300296	−0.0340018
$79$	8.01738	0.902026	0.451013	−	0.892517i	$-0.351063\pi$
$79$	8.01738	0.902026	0.451013	+	0.892517i	$0.351063\pi$
$80$	19.9821	2.23407
$81$	1.00000	0.111111
$82$	−2.47258	−0.273051
$83$	3.64416	0.399999	0.200000	−	0.979796i	$-0.435906\pi$
$83$	3.64416	0.399999	0.200000	+	0.979796i	$0.435906\pi$
$84$	0	0
$85$	27.6725	3.00151
$86$	−29.6587	−3.19818
$87$	−6.83272	−0.732544
$88$	−0.294125	−0.0313538
$89$	7.76515	0.823104	0.411552	−	0.911386i	$-0.364987\pi$
$89$	7.76515	0.823104	0.411552	+	0.911386i	$0.364987\pi$
$90$	10.5235	1.10928
$91$	0	0
$92$	−30.6236	−3.19273
$93$	−5.89005	−0.610770
$94$	31.6167	3.26101
$95$	−12.7561	−1.30874
$96$	−1.15622	−0.118006
$97$	7.07757	0.718619	0.359309	−	0.933219i	$-0.383012\pi$
$97$	7.07757	0.718619	0.359309	+	0.933219i	$0.383012\pi$
$98$	0	0
$99$	−0.0562785	−0.00565620
$100$	53.9476	5.39476
$101$	6.50521	0.647292	0.323646	−	0.946178i	$-0.395091\pi$
$101$	6.50521	0.647292	0.323646	+	0.946178i	$0.395091\pi$
$102$	−16.0764	−1.59181
$103$	−13.5776	−1.33784	−0.668921	−	0.743333i	$-0.733244\pi$
$103$	−13.5776	−1.33784	−0.668921	+	0.743333i	$0.733244\pi$
$104$	0.634727	0.0622401
$105$	0	0
$106$	−7.28640	−0.707718
$107$	0.630644	0.0609667	0.0304833	−	0.999535i	$-0.490295\pi$
$107$	0.630644	0.0609667	0.0304833	+	0.999535i	$0.490295\pi$
$108$	−4.11367	−0.395838
$109$	−5.08353	−0.486914	−0.243457	−	0.969912i	$-0.578282\pi$
$109$	−5.08353	−0.486914	−0.243457	+	0.969912i	$0.578282\pi$
$110$	−0.592248	−0.0564686
$111$	3.56058	0.337955
$112$	0	0
$113$	6.66772	0.627246	0.313623	−	0.949548i	$-0.398457\pi$
$113$	6.66772	0.627246	0.313623	+	0.949548i	$0.398457\pi$
$114$	7.41068	0.694074
$115$	−31.6837	−2.95452
$116$	28.1076	2.60972
$117$	0.121450	0.0112281
$118$	−26.5831	−2.44717
$119$	0	0
$120$	−22.2433	−2.03052
$121$	−10.9968	−0.999712
$122$	22.4349	2.03116
$123$	1.00000	0.0901670
$124$	24.2297	2.17589
$125$	34.5348	3.08888
$126$	0	0
$127$	2.79142	0.247699	0.123849	−	0.992301i	$-0.460476\pi$
$127$	2.79142	0.247699	0.123849	+	0.992301i	$0.460476\pi$
$128$	−18.4611	−1.63174
$129$	11.9950	1.05610
$130$	1.27808	0.112095
$131$	−7.04987	−0.615950	−0.307975	−	0.951394i	$-0.599651\pi$
$131$	−7.04987	−0.615950	−0.307975	+	0.951394i	$0.599651\pi$
$132$	0.231511	0.0201505
$133$	0	0
$134$	7.01520	0.606021
$135$	−4.25608	−0.366305
$136$	33.9804	2.91379
$137$	−11.9273	−1.01901	−0.509507	−	0.860466i	$-0.670172\pi$
$137$	−11.9273	−1.01901	−0.509507	+	0.860466i	$0.670172\pi$
$138$	18.4067	1.56689
$139$	−5.05946	−0.429138	−0.214569	−	0.976709i	$-0.568835\pi$
$139$	−5.05946	−0.429138	−0.214569	+	0.976709i	$0.568835\pi$
$140$	0	0
$141$	−12.7869	−1.07685
$142$	−5.96772	−0.500800
$143$	−0.00683503	−0.000571574 0
$144$	4.69496	0.391247
$145$	29.0806	2.41501
$146$	−17.6663	−1.46208
$147$	0	0
$148$	−14.6471	−1.20398
$149$	−13.3253	−1.09165	−0.545826	−	0.837898i	$-0.683784\pi$
$149$	−13.3253	−1.09165	−0.545826	+	0.837898i	$0.683784\pi$
$150$	−32.4260	−2.64757
$151$	−15.7379	−1.28073	−0.640364	−	0.768071i	$-0.721217\pi$
$151$	−15.7379	−1.28073	−0.640364	+	0.768071i	$0.721217\pi$
$152$	−15.6638	−1.27050
$153$	6.50188	0.525646
$154$	0	0
$155$	25.0685	2.01355
$156$	−0.499606	−0.0400005
$157$	−5.99751	−0.478653	−0.239327	−	0.970939i	$-0.576927\pi$
$157$	−5.99751	−0.478653	−0.239327	+	0.970939i	$0.576927\pi$
$158$	19.8236	1.57708
$159$	2.94688	0.233702
$160$	4.92095	0.389035
$161$	0	0
$162$	2.47258	0.194265
$163$	15.8335	1.24018	0.620090	−	0.784531i	$-0.287096\pi$
$163$	15.8335	1.24018	0.620090	+	0.784531i	$0.287096\pi$
$164$	−4.11367	−0.321224
$165$	0.239526	0.0186471
$166$	9.01050	0.699351
$167$	9.44704	0.731034	0.365517	−	0.930805i	$-0.380892\pi$
$167$	9.44704	0.731034	0.365517	+	0.930805i	$0.380892\pi$
$168$	0	0
$169$	−12.9852	−0.998865
$170$	68.4226	5.24778
$171$	−2.99714	−0.229197
$172$	−49.3435	−3.76241
$173$	−3.50248	−0.266288	−0.133144	−	0.991097i	$-0.542507\pi$
$173$	−3.50248	−0.266288	−0.133144	+	0.991097i	$0.542507\pi$
$174$	−16.8945	−1.28077
$175$	0	0
$176$	−0.264225	−0.0199167
$177$	10.7511	0.808104
$178$	19.2000	1.43910
$179$	−0.908579	−0.0679104	−0.0339552	−	0.999423i	$-0.510810\pi$
$179$	−0.908579	−0.0679104	−0.0339552	+	0.999423i	$0.510810\pi$
$180$	17.5081	1.30498
$181$	−13.7972	−1.02554	−0.512768	−	0.858527i	$-0.671380\pi$
$181$	−13.7972	−1.02554	−0.512768	+	0.858527i	$0.671380\pi$
$182$	0	0
$183$	−9.07345	−0.670729
$184$	−38.9058	−2.86818
$185$	−15.1541	−1.11415
$186$	−14.5636	−1.06786
$187$	−0.365916	−0.0267584
$188$	52.6012	3.83633
$189$	0	0
$190$	−31.5405	−2.28818
$191$	−7.78497	−0.563301	−0.281650	−	0.959517i	$-0.590882\pi$
$191$	−7.78497	−0.563301	−0.281650	+	0.959517i	$0.590882\pi$
$192$	6.53108	0.471340
$193$	−1.33281	−0.0959379	−0.0479690	−	0.998849i	$-0.515275\pi$
$193$	−1.33281	−0.0959379	−0.0479690	+	0.998849i	$0.515275\pi$
$194$	17.4999	1.25642
$195$	−0.516902	−0.0370161
$196$	0	0
$197$	15.0128	1.06962	0.534810	−	0.844972i	$-0.320383\pi$
$197$	15.0128	1.06962	0.534810	+	0.844972i	$0.320383\pi$
$198$	−0.139153	−0.00988920
$199$	−7.95612	−0.563995	−0.281997	−	0.959415i	$-0.590997\pi$
$199$	−7.95612	−0.563995	−0.281997	+	0.959415i	$0.590997\pi$
$200$	68.5380	4.84637
$201$	−2.83719	−0.200120
$202$	16.0847	1.13171
$203$	0	0
$204$	−26.7466	−1.87264
$205$	−4.25608	−0.297258
$206$	−33.5718	−2.33906
$207$	−7.44433	−0.517417
$208$	0.570204	0.0395365
$209$	0.168675	0.0116675
$210$	0	0
$211$	16.4557	1.13286	0.566429	−	0.824111i	$-0.308325\pi$
$211$	16.4557	1.13286	0.566429	+	0.824111i	$0.308325\pi$
$212$	−12.1225	−0.832576
$213$	2.41356	0.165374
$214$	1.55932	0.106593
$215$	−51.0517	−3.48170
$216$	−5.22624	−0.355600
$217$	0	0
$218$	−12.5695	−0.851312
$219$	7.14489	0.482807
$220$	−0.985331	−0.0664310
$221$	0.789655	0.0531179
$222$	8.80383	0.590875
$223$	−5.34054	−0.357629	−0.178814	−	0.983883i	$-0.557226\pi$
$223$	−5.34054	−0.357629	−0.178814	+	0.983883i	$0.557226\pi$
$224$	0	0
$225$	13.1142	0.874281
$226$	16.4865	1.09667
$227$	−4.32524	−0.287076	−0.143538	−	0.989645i	$-0.545848\pi$
$227$	−4.32524	−0.287076	−0.143538	+	0.989645i	$0.545848\pi$
$228$	12.3293	0.816525
$229$	−9.09080	−0.600737	−0.300369	−	0.953823i	$-0.597110\pi$
$229$	−9.09080	−0.600737	−0.300369	+	0.953823i	$0.597110\pi$
$230$	−78.3406	−5.16562
$231$	0	0
$232$	35.7094	2.34444
$233$	12.2425	0.802035	0.401018	−	0.916070i	$-0.368657\pi$
$233$	12.2425	0.802035	0.401018	+	0.916070i	$0.368657\pi$
$234$	0.300296	0.0196310
$235$	54.4221	3.55011
$236$	−44.2266	−2.87891
$237$	−8.01738	−0.520785
$238$	0	0
$239$	−3.81168	−0.246557	−0.123279	−	0.992372i	$-0.539341\pi$
$239$	−3.81168	−0.246557	−0.123279	+	0.992372i	$0.539341\pi$
$240$	−19.9821	−1.28984
$241$	0.737748	0.0475225	0.0237613	−	0.999718i	$-0.492436\pi$
$241$	0.737748	0.0475225	0.0237613	+	0.999718i	$0.492436\pi$
$242$	−27.1906	−1.74788
$243$	−1.00000	−0.0641500
$244$	37.3252	2.38950
$245$	0	0
$246$	2.47258	0.157646
$247$	−0.364003	−0.0231610
$248$	30.7828	1.95471
$249$	−3.64416	−0.230940
$250$	85.3901	5.40054
$251$	11.7359	0.740763	0.370382	−	0.928880i	$-0.379227\pi$
$251$	11.7359	0.740763	0.370382	+	0.928880i	$0.379227\pi$
$252$	0	0
$253$	0.418956	0.0263395
$254$	6.90203	0.433072
$255$	−27.6725	−1.73292
$256$	−32.5844	−2.03653
$257$	2.38752	0.148929	0.0744646	−	0.997224i	$-0.476275\pi$
$257$	2.38752	0.148929	0.0744646	+	0.997224i	$0.476275\pi$
$258$	29.6587	1.84647
$259$	0	0
$260$	2.12636	0.131872
$261$	6.83272	0.422935
$262$	−17.4314	−1.07692
$263$	1.41800	0.0874378	0.0437189	−	0.999044i	$-0.486079\pi$
$263$	1.41800	0.0874378	0.0437189	+	0.999044i	$0.486079\pi$
$264$	0.294125	0.0181021
$265$	−12.5421	−0.770457
$266$	0	0
$267$	−7.76515	−0.475219
$268$	11.6713	0.712937
$269$	−11.1152	−0.677704	−0.338852	−	0.940840i	$-0.610039\pi$
$269$	−11.1152	−0.677704	−0.338852	+	0.940840i	$0.610039\pi$
$270$	−10.5235	−0.640441
$271$	−9.92507	−0.602905	−0.301452	−	0.953481i	$-0.597471\pi$
$271$	−9.92507	−0.602905	−0.301452	+	0.953481i	$0.597471\pi$
$272$	30.5261	1.85092
$273$	0	0
$274$	−29.4912	−1.78163
$275$	−0.738049	−0.0445060
$276$	30.6236	1.84332
$277$	7.48256	0.449583	0.224792	−	0.974407i	$-0.427830\pi$
$277$	7.48256	0.449583	0.224792	+	0.974407i	$0.427830\pi$
$278$	−12.5099	−0.750296
$279$	5.89005	0.352628
$280$	0	0
$281$	−15.0412	−0.897284	−0.448642	−	0.893712i	$-0.648092\pi$
$281$	−15.0412	−0.897284	−0.448642	+	0.893712i	$0.648092\pi$
$282$	−31.6167	−1.88275
$283$	−21.3617	−1.26982	−0.634912	−	0.772585i	$-0.718964\pi$
$283$	−21.3617	−1.26982	−0.634912	+	0.772585i	$0.718964\pi$
$284$	−9.92859	−0.589153
$285$	12.7561	0.755604
$286$	−0.0169002	−0.000999330 0
$287$	0	0
$288$	1.15622	0.0681307
$289$	25.2744	1.48673
$290$	71.9042	4.22236
$291$	−7.07757	−0.414895
$292$	−29.3917	−1.72002
$293$	10.9401	0.639129	0.319565	−	0.947564i	$-0.396463\pi$
$293$	10.9401	0.639129	0.319565	+	0.947564i	$0.396463\pi$
$294$	0	0
$295$	−45.7576	−2.66411
$296$	−18.6084	−1.08159
$297$	0.0562785	0.00326561
$298$	−32.9480	−1.90862
$299$	−0.904116	−0.0522864
$300$	−53.9476	−3.11467
$301$	0	0
$302$	−38.9132	−2.23920
$303$	−6.50521	−0.373714
$304$	−14.0715	−0.807053
$305$	38.6173	2.21122
$306$	16.0764	0.919029
$307$	15.2629	0.871097	0.435549	−	0.900165i	$-0.356554\pi$
$307$	15.2629	0.871097	0.435549	+	0.900165i	$0.356554\pi$
$308$	0	0
$309$	13.5776	0.772404
$310$	61.9840	3.52046
$311$	25.1312	1.42506	0.712530	−	0.701642i	$-0.247549\pi$
$311$	25.1312	1.42506	0.712530	+	0.701642i	$0.247549\pi$
$312$	−0.634727	−0.0359344
$313$	−30.3467	−1.71530	−0.857649	−	0.514235i	$-0.828076\pi$
$313$	−30.3467	−1.71530	−0.857649	+	0.514235i	$0.828076\pi$
$314$	−14.8293	−0.836868
$315$	0	0
$316$	32.9809	1.85532
$317$	23.5795	1.32436	0.662178	−	0.749347i	$-0.269632\pi$
$317$	23.5795	1.32436	0.662178	+	0.749347i	$0.269632\pi$
$318$	7.28640	0.408601
$319$	−0.384535	−0.0215298
$320$	−27.7968	−1.55389
$321$	−0.630644	−0.0351991
$322$	0	0
$323$	−19.4870	−1.08429
$324$	4.11367	0.228537
$325$	1.59272	0.0883484
$326$	39.1498	2.16831
$327$	5.08353	0.281120
$328$	−5.22624	−0.288571
$329$	0	0
$330$	0.592248	0.0326022
$331$	1.06129	0.0583337	0.0291668	−	0.999575i	$-0.490715\pi$
$331$	1.06129	0.0583337	0.0291668	+	0.999575i	$0.490715\pi$
$332$	14.9909	0.822733
$333$	−3.56058	−0.195119
$334$	23.3586	1.27813
$335$	12.0753	0.659745
$336$	0	0
$337$	−10.9283	−0.595302	−0.297651	−	0.954675i	$-0.596203\pi$
$337$	−10.9283	−0.595302	−0.297651	+	0.954675i	$0.596203\pi$
$338$	−32.1071	−1.74640
$339$	−6.66772	−0.362141
$340$	113.836	6.17361
$341$	−0.331483	−0.0179508
$342$	−7.41068	−0.400724
$343$	0	0
$344$	−62.6887	−3.37995
$345$	31.6837	1.70579
$346$	−8.66017	−0.465574
$347$	−13.8479	−0.743394	−0.371697	−	0.928354i	$-0.621224\pi$
$347$	−13.8479	−0.743394	−0.371697	+	0.928354i	$0.621224\pi$
$348$	−28.1076	−1.50672
$349$	−5.37427	−0.287678	−0.143839	−	0.989601i	$-0.545945\pi$
$349$	−5.37427	−0.287678	−0.143839	+	0.989601i	$0.545945\pi$
$350$	0	0
$351$	−0.121450	−0.00648253
$352$	−0.0650702	−0.00346825
$353$	0.260123	0.0138449	0.00692247	−	0.999976i	$-0.497796\pi$
$353$	0.260123	0.0138449	0.00692247	+	0.999976i	$0.497796\pi$
$354$	26.5831	1.41287
$355$	−10.2723	−0.545197
$356$	31.9433	1.69299
$357$	0	0
$358$	−2.24654	−0.118733
$359$	15.3138	0.808231	0.404116	−	0.914708i	$-0.367579\pi$
$359$	15.3138	0.808231	0.404116	+	0.914708i	$0.367579\pi$
$360$	22.2433	1.17232
$361$	−10.0172	−0.527219
$362$	−34.1147	−1.79303
$363$	10.9968	0.577184
$364$	0	0
$365$	−30.4092	−1.59169
$366$	−22.4349	−1.17269
$367$	35.5332	1.85482	0.927409	−	0.374050i	$-0.122031\pi$
$367$	35.5332	1.85482	0.927409	+	0.374050i	$0.122031\pi$
$368$	−34.9509	−1.82194
$369$	−1.00000	−0.0520579
$370$	−37.4698	−1.94796
$371$	0	0
$372$	−24.2297	−1.25625
$373$	−32.4664	−1.68105	−0.840523	−	0.541776i	$-0.817752\pi$
$373$	−32.4664	−1.68105	−0.840523	+	0.541776i	$0.817752\pi$
$374$	−0.904758	−0.0467839
$375$	−34.5348	−1.78337
$376$	66.8274	3.44636
$377$	0.829835	0.0427387
$378$	0	0
$379$	21.1958	1.08876	0.544378	−	0.838840i	$-0.316766\pi$
$379$	21.1958	1.08876	0.544378	+	0.838840i	$0.316766\pi$
$380$	−52.4743	−2.69187
$381$	−2.79142	−0.143009
$382$	−19.2490	−0.984864
$383$	−5.79764	−0.296246	−0.148123	−	0.988969i	$-0.547323\pi$
$383$	−5.79764	−0.296246	−0.148123	+	0.988969i	$0.547323\pi$
$384$	18.4611	0.942088
$385$	0	0
$386$	−3.29549	−0.167736
$387$	−11.9950	−0.609740
$388$	29.1148	1.47808
$389$	−3.45633	−0.175243	−0.0876215	−	0.996154i	$-0.527927\pi$
$389$	−3.45633	−0.175243	−0.0876215	+	0.996154i	$0.527927\pi$
$390$	−1.27808	−0.0647182
$391$	−48.4022	−2.44780
$392$	0	0
$393$	7.04987	0.355619
$394$	37.1205	1.87011
$395$	34.1226	1.71689
$396$	−0.231511	−0.0116339
$397$	15.7246	0.789193	0.394597	−	0.918855i	$-0.370884\pi$
$397$	15.7246	0.789193	0.394597	+	0.918855i	$0.370884\pi$
$398$	−19.6722	−0.986077
$399$	0	0
$400$	61.5707	3.07854
$401$	6.00651	0.299951	0.149975	−	0.988690i	$-0.452081\pi$
$401$	6.00651	0.299951	0.149975	+	0.988690i	$0.452081\pi$
$402$	−7.01520	−0.349886
$403$	0.715347	0.0356340
$404$	26.7603	1.33137
$405$	4.25608	0.211486
$406$	0	0
$407$	0.200384	0.00993267
$408$	−33.9804	−1.68228
$409$	−33.3209	−1.64761	−0.823807	−	0.566871i	$-0.808154\pi$
$409$	−33.3209	−1.64761	−0.823807	+	0.566871i	$0.808154\pi$
$410$	−10.5235	−0.519719
$411$	11.9273	0.588328
$412$	−55.8539	−2.75172
$413$	0	0
$414$	−18.4067	−0.904642
$415$	15.5099	0.761349
$416$	0.140423	0.00688479
$417$	5.05946	0.247763
$418$	0.417062	0.0203992
$419$	28.2365	1.37944	0.689721	−	0.724075i	$-0.257733\pi$
$419$	28.2365	1.37944	0.689721	+	0.724075i	$0.257733\pi$
$420$	0	0
$421$	37.7688	1.84074	0.920369	−	0.391051i	$-0.127889\pi$
$421$	37.7688	1.84074	0.920369	+	0.391051i	$0.127889\pi$
$422$	40.6881	1.98067
$423$	12.7869	0.621721
$424$	−15.4011	−0.747942
$425$	85.2671	4.13606
$426$	5.96772	0.289137
$427$	0	0
$428$	2.59426	0.125398
$429$	0.00683503	0.000329999 0
$430$	−126.230	−6.08733
$431$	−27.7606	−1.33718	−0.668591	−	0.743630i	$-0.733102\pi$
$431$	−27.7606	−1.33718	−0.668591	+	0.743630i	$0.733102\pi$
$432$	−4.69496	−0.225886
$433$	3.18401	0.153014	0.0765068	−	0.997069i	$-0.475623\pi$
$433$	3.18401	0.153014	0.0765068	+	0.997069i	$0.475623\pi$
$434$	0	0
$435$	−29.0806	−1.39431
$436$	−20.9120	−1.00150
$437$	22.3117	1.06731
$438$	17.6663	0.844130
$439$	−31.3934	−1.49833	−0.749164	−	0.662385i	$-0.769544\pi$
$439$	−31.3934	−1.49833	−0.749164	+	0.662385i	$0.769544\pi$
$440$	−1.25182	−0.0596781
$441$	0	0
$442$	1.95249	0.0928704
$443$	22.4072	1.06460	0.532299	−	0.846556i	$-0.321328\pi$
$443$	22.4072	1.06460	0.532299	+	0.846556i	$0.321328\pi$
$444$	14.6471	0.695119
$445$	33.0491	1.56668
$446$	−13.2049	−0.625271
$447$	13.3253	0.630266
$448$	0	0
$449$	29.3945	1.38721	0.693606	−	0.720355i	$-0.256021\pi$
$449$	29.3945	1.38721	0.693606	+	0.720355i	$0.256021\pi$
$450$	32.4260	1.52858
$451$	0.0562785	0.00265005
$452$	27.4288	1.29014
$453$	15.7379	0.739429
$454$	−10.6945	−0.501919
$455$	0	0
$456$	15.6638	0.733523
$457$	39.1370	1.83075	0.915375	−	0.402601i	$-0.131894\pi$
$457$	39.1370	1.83075	0.915375	+	0.402601i	$0.131894\pi$
$458$	−22.4778	−1.05032
$459$	−6.50188	−0.303482
$460$	−130.336	−6.07696
$461$	−16.4385	−0.765617	−0.382809	−	0.923828i	$-0.625043\pi$
$461$	−16.4385	−0.765617	−0.382809	+	0.923828i	$0.625043\pi$
$462$	0	0
$463$	−8.45789	−0.393072	−0.196536	−	0.980497i	$-0.562969\pi$
$463$	−8.45789	−0.393072	−0.196536	+	0.980497i	$0.562969\pi$
$464$	32.0794	1.48925
$465$	−25.0685	−1.16252
$466$	30.2707	1.40226
$467$	29.3633	1.35877	0.679387	−	0.733780i	$-0.262246\pi$
$467$	29.3633	1.35877	0.679387	+	0.733780i	$0.262246\pi$
$468$	0.499606	0.0230943
$469$	0	0
$470$	134.563	6.20694
$471$	5.99751	0.276351
$472$	−56.1879	−2.58626
$473$	0.675061	0.0310393
$474$	−19.8236	−0.910530
$475$	−39.3051	−1.80344
$476$	0	0
$477$	−2.94688	−0.134928
$478$	−9.42470	−0.431076
$479$	−13.9577	−0.637745	−0.318872	−	0.947798i	$-0.603304\pi$
$479$	−13.9577	−0.637745	−0.318872	+	0.947798i	$0.603304\pi$
$480$	−4.92095	−0.224610
$481$	−0.432433	−0.0197172
$482$	1.82414	0.0830875
$483$	0	0
$484$	−45.2374	−2.05624
$485$	30.1227	1.36780
$486$	−2.47258	−0.112159
$487$	−34.4999	−1.56334	−0.781671	−	0.623691i	$-0.785632\pi$
$487$	−34.4999	−1.56334	−0.781671	+	0.623691i	$0.785632\pi$
$488$	47.4200	2.14660
$489$	−15.8335	−0.716018
$490$	0	0
$491$	21.4412	0.967627	0.483813	−	0.875171i	$-0.339251\pi$
$491$	21.4412	0.967627	0.483813	+	0.875171i	$0.339251\pi$
$492$	4.11367	0.185459
$493$	44.4255	2.00083
$494$	−0.900028	−0.0404942
$495$	−0.239526	−0.0107659
$496$	27.6536	1.24168
$497$	0	0
$498$	−9.01050	−0.403770
$499$	−16.8887	−0.756043	−0.378022	−	0.925797i	$-0.623395\pi$
$499$	−16.8887	−0.756043	−0.378022	+	0.925797i	$0.623395\pi$
$500$	142.065	6.35333
$501$	−9.44704	−0.422063
$502$	29.0180	1.29514
$503$	3.72498	0.166089	0.0830444	−	0.996546i	$-0.473536\pi$
$503$	3.72498	0.166089	0.0830444	+	0.996546i	$0.473536\pi$
$504$	0	0
$505$	27.6867	1.23204
$506$	1.03590	0.0460515
$507$	12.9852	0.576695
$508$	11.4830	0.509476
$509$	9.14940	0.405540	0.202770	−	0.979226i	$-0.435006\pi$
$509$	9.14940	0.405540	0.202770	+	0.979226i	$0.435006\pi$
$510$	−68.4226	−3.02981
$511$	0	0
$512$	−43.6456	−1.92888
$513$	2.99714	0.132327
$514$	5.90334	0.260385
$515$	−57.7874	−2.54642
$516$	49.3435	2.17223
$517$	−0.719628	−0.0316492
$518$	0	0
$519$	3.50248	0.153742
$520$	2.70145	0.118466
$521$	−31.5175	−1.38081	−0.690403	−	0.723425i	$-0.742567\pi$
$521$	−31.5175	−1.38081	−0.690403	+	0.723425i	$0.742567\pi$
$522$	16.8945	0.739451
$523$	−5.84971	−0.255790	−0.127895	−	0.991788i	$-0.540822\pi$
$523$	−5.84971	−0.255790	−0.127895	+	0.991788i	$0.540822\pi$
$524$	−29.0009	−1.26691
$525$	0	0
$526$	3.50613	0.152875
$527$	38.2964	1.66822
$528$	0.264225	0.0114989
$529$	32.4181	1.40948
$530$	−31.0115	−1.34705
$531$	−10.7511	−0.466559
$532$	0	0
$533$	−0.121450	−0.00526059
$534$	−19.2000	−0.830864
$535$	2.68407	0.116043
$536$	14.8278	0.640465
$537$	0.908579	0.0392081
$538$	−27.4832	−1.18489
$539$	0	0
$540$	−17.5081	−0.753430
$541$	−22.8050	−0.980464	−0.490232	−	0.871592i	$-0.663088\pi$
$541$	−22.8050	−0.980464	−0.490232	+	0.871592i	$0.663088\pi$
$542$	−24.5406	−1.05411
$543$	13.7972	0.592094
$544$	7.51759	0.322314
$545$	−21.6359	−0.926781
$546$	0	0
$547$	0.777283	0.0332342	0.0166171	−	0.999862i	$-0.494710\pi$
$547$	0.777283	0.0332342	0.0166171	+	0.999862i	$0.494710\pi$
$548$	−49.0649	−2.09595
$549$	9.07345	0.387246
$550$	−1.82489	−0.0778135
$551$	−20.4786	−0.872418
$552$	38.9058	1.65594
$553$	0	0
$554$	18.5013	0.786043
$555$	15.1541	0.643256
$556$	−20.8130	−0.882666
$557$	24.2951	1.02941	0.514707	−	0.857366i	$-0.327901\pi$
$557$	24.2951	1.02941	0.514707	+	0.857366i	$0.327901\pi$
$558$	14.5636	0.616528
$559$	−1.45680	−0.0616159
$560$	0	0
$561$	0.365916	0.0154490
$562$	−37.1907	−1.56879
$563$	20.7301	0.873672	0.436836	−	0.899541i	$-0.356099\pi$
$563$	20.7301	0.873672	0.436836	+	0.899541i	$0.356099\pi$
$564$	−52.6012	−2.21491
$565$	28.3784	1.19389
$566$	−52.8187	−2.22014
$567$	0	0
$568$	−12.6138	−0.529264
$569$	−7.09221	−0.297321	−0.148660	−	0.988888i	$-0.547496\pi$
$569$	−7.09221	−0.297321	−0.148660	+	0.988888i	$0.547496\pi$
$570$	31.5405	1.32108
$571$	−8.85801	−0.370696	−0.185348	−	0.982673i	$-0.559341\pi$
$571$	−8.85801	−0.370696	−0.185348	+	0.982673i	$0.559341\pi$
$572$	−0.0281171	−0.00117564
$573$	7.78497	0.325222
$574$	0	0
$575$	−97.6266	−4.07131
$576$	−6.53108	−0.272128
$577$	18.0181	0.750103	0.375052	−	0.927004i	$-0.377625\pi$
$577$	18.0181	0.750103	0.375052	+	0.927004i	$0.377625\pi$
$578$	62.4932	2.59937
$579$	1.33281	0.0553898
$580$	119.628	4.96729
$581$	0	0
$582$	−17.4999	−0.725394
$583$	0.165846	0.00686863
$584$	−37.3409	−1.54518
$585$	0.516902	0.0213713
$586$	27.0504	1.11744
$587$	37.8110	1.56063	0.780313	−	0.625390i	$-0.215060\pi$
$587$	37.8110	1.56063	0.780313	+	0.625390i	$0.215060\pi$
$588$	0	0
$589$	−17.6533	−0.727392
$590$	−113.140	−4.65788
$591$	−15.0128	−0.617546
$592$	−16.7168	−0.687056
$593$	−40.4543	−1.66126	−0.830630	−	0.556825i	$-0.812020\pi$
$593$	−40.4543	−1.66126	−0.830630	+	0.556825i	$0.812020\pi$
$594$	0.139153	0.00570953
$595$	0	0
$596$	−54.8160	−2.24535
$597$	7.95612	0.325622
$598$	−2.23550	−0.0914165
$599$	−32.1277	−1.31270	−0.656351	−	0.754456i	$-0.727901\pi$
$599$	−32.1277	−1.31270	−0.656351	+	0.754456i	$0.727901\pi$
$600$	−68.5380	−2.79805
$601$	27.0868	1.10489	0.552447	−	0.833548i	$-0.313694\pi$
$601$	27.0868	1.10489	0.552447	+	0.833548i	$0.313694\pi$
$602$	0	0
$603$	2.83719	0.115539
$604$	−64.7404	−2.63425
$605$	−46.8034	−1.90283
$606$	−16.0847	−0.653395
$607$	−30.6006	−1.24204	−0.621020	−	0.783795i	$-0.713281\pi$
$607$	−30.6006	−1.24204	−0.621020	+	0.783795i	$0.713281\pi$
$608$	−3.46534	−0.140538
$609$	0	0
$610$	95.4847	3.86606
$611$	1.55297	0.0628265
$612$	26.7466	1.08117
$613$	−22.3532	−0.902835	−0.451418	−	0.892313i	$-0.649082\pi$
$613$	−22.3532	−0.902835	−0.451418	+	0.892313i	$0.649082\pi$
$614$	37.7387	1.52301
$615$	4.25608	0.171622
$616$	0	0
$617$	−47.6329	−1.91763	−0.958814	−	0.284035i	$-0.908327\pi$
$617$	−47.6329	−1.91763	−0.958814	+	0.284035i	$0.908327\pi$
$618$	33.5718	1.35046
$619$	−38.4435	−1.54518	−0.772588	−	0.634908i	$-0.781038\pi$
$619$	−38.4435	−1.54518	−0.772588	+	0.634908i	$0.781038\pi$
$620$	103.124	4.14155
$621$	7.44433	0.298731
$622$	62.1390	2.49155
$623$	0	0
$624$	−0.570204	−0.0228264
$625$	81.4116	3.25646
$626$	−75.0348	−2.99900
$627$	−0.168675	−0.00673621
$628$	−24.6718	−0.984511
$629$	−23.1505	−0.923069
$630$	0	0
$631$	1.60079	0.0637266	0.0318633	−	0.999492i	$-0.489856\pi$
$631$	1.60079	0.0637266	0.0318633	+	0.999492i	$0.489856\pi$
$632$	41.9007	1.66672
$633$	−16.4557	−0.654056
$634$	58.3023	2.31548
$635$	11.8805	0.471464
$636$	12.1225	0.480688
$637$	0	0
$638$	−0.950796	−0.0376424
$639$	−2.41356	−0.0954788
$640$	−78.5718	−3.10582
$641$	−47.8953	−1.89175	−0.945875	−	0.324532i	$-0.894793\pi$
$641$	−47.8953	−1.89175	−0.945875	+	0.324532i	$0.894793\pi$
$642$	−1.55932	−0.0615415
$643$	8.11923	0.320191	0.160096	−	0.987102i	$-0.448820\pi$
$643$	8.11923	0.320191	0.160096	+	0.987102i	$0.448820\pi$
$644$	0	0
$645$	51.0517	2.01016
$646$	−48.1834	−1.89575
$647$	−38.7758	−1.52443	−0.762216	−	0.647322i	$-0.775889\pi$
$647$	−38.7758	−1.52443	−0.762216	+	0.647322i	$0.775889\pi$
$648$	5.22624	0.205306
$649$	0.605057	0.0237506
$650$	3.93814	0.154467
$651$	0	0
$652$	65.1340	2.55085
$653$	−32.2754	−1.26304	−0.631518	−	0.775362i	$-0.717568\pi$
$653$	−32.2754	−1.26304	−0.631518	+	0.775362i	$0.717568\pi$
$654$	12.5695	0.491505
$655$	−30.0048	−1.17239
$656$	−4.69496	−0.183307
$657$	−7.14489	−0.278749
$658$	0	0
$659$	15.0200	0.585096	0.292548	−	0.956251i	$-0.405497\pi$
$659$	15.0200	0.585096	0.292548	+	0.956251i	$0.405497\pi$
$660$	0.985331	0.0383540
$661$	36.4923	1.41939	0.709694	−	0.704510i	$-0.248833\pi$
$661$	36.4923	1.41939	0.709694	+	0.704510i	$0.248833\pi$
$662$	2.62412	0.101989
$663$	−0.789655	−0.0306676
$664$	19.0453	0.739100
$665$	0	0
$666$	−8.80383	−0.341142
$667$	−50.8650	−1.96950
$668$	38.8620	1.50362
$669$	5.34054	0.206477
$670$	29.8572	1.15349
$671$	−0.510640	−0.0197131
$672$	0	0
$673$	−28.9105	−1.11442	−0.557209	−	0.830372i	$-0.688128\pi$
$673$	−28.9105	−1.11442	−0.557209	+	0.830372i	$0.688128\pi$
$674$	−27.0211	−1.04081
$675$	−13.1142	−0.504766
$676$	−53.4171	−2.05450
$677$	−22.7874	−0.875790	−0.437895	−	0.899026i	$-0.644276\pi$
$677$	−22.7874	−0.875790	−0.437895	+	0.899026i	$0.644276\pi$
$678$	−16.4865	−0.633160
$679$	0	0
$680$	144.623	5.54604
$681$	4.32524	0.165744
$682$	−0.819620	−0.0313849
$683$	28.5285	1.09161	0.545807	−	0.837911i	$-0.316223\pi$
$683$	28.5285	1.09161	0.545807	+	0.837911i	$0.316223\pi$
$684$	−12.3293	−0.471421
$685$	−50.7634	−1.93957
$686$	0	0
$687$	9.09080	0.346836
$688$	−56.3161	−2.14703
$689$	−0.357899	−0.0136348
$690$	78.3406	2.98237
$691$	−37.7948	−1.43778	−0.718891	−	0.695122i	$-0.755350\pi$
$691$	−37.7948	−1.43778	−0.718891	+	0.695122i	$0.755350\pi$
$692$	−14.4080	−0.547712
$693$	0	0
$694$	−34.2401	−1.29974
$695$	−21.5335	−0.816811
$696$	−35.7094	−1.35356
$697$	−6.50188	−0.246276
$698$	−13.2883	−0.502971
$699$	−12.2425	−0.463055
$700$	0	0
$701$	−14.3043	−0.540267	−0.270133	−	0.962823i	$-0.587068\pi$
$701$	−14.3043	−0.540267	−0.270133	+	0.962823i	$0.587068\pi$
$702$	−0.300296	−0.0113339
$703$	10.6716	0.402485
$704$	0.367559	0.0138529
$705$	−54.4221	−2.04965
$706$	0.643176	0.0242062
$707$	0	0
$708$	44.2266	1.66214
$709$	−45.1453	−1.69547	−0.847733	−	0.530423i	$-0.822033\pi$
$709$	−45.1453	−1.69547	−0.847733	+	0.530423i	$0.822033\pi$
$710$	−25.3991	−0.953212
$711$	8.01738	0.300675
$712$	40.5825	1.52089
$713$	−43.8475	−1.64210
$714$	0	0
$715$	−0.0290905	−0.00108792
$716$	−3.73760	−0.139681
$717$	3.81168	0.142350
$718$	37.8646	1.41310
$719$	0.0777780	0.00290063	0.00145031	−	0.999999i	$-0.499538\pi$
$719$	0.0777780	0.00290063	0.00145031	+	0.999999i	$0.499538\pi$
$720$	19.9821	0.744690
$721$	0	0
$722$	−24.7683	−0.921779
$723$	−0.737748	−0.0274371
$724$	−56.7571	−2.10936
$725$	89.6058	3.32787
$726$	27.1906	1.00914
$727$	23.7853	0.882147	0.441073	−	0.897471i	$-0.354598\pi$
$727$	23.7853	0.882147	0.441073	+	0.897471i	$0.354598\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−75.1893	−2.78288
$731$	−77.9901	−2.88457
$732$	−37.3252	−1.37958
$733$	−1.78230	−0.0658307	−0.0329154	−	0.999458i	$-0.510479\pi$
$733$	−1.78230	−0.0658307	−0.0329154	+	0.999458i	$0.510479\pi$
$734$	87.8588	3.24293
$735$	0	0
$736$	−8.60727	−0.317268
$737$	−0.159673	−0.00588163
$738$	−2.47258	−0.0910171
$739$	−19.3781	−0.712834	−0.356417	−	0.934327i	$-0.616002\pi$
$739$	−19.3781	−0.712834	−0.356417	+	0.934327i	$0.616002\pi$
$740$	−62.3391	−2.29163
$741$	0.364003	0.0133720
$742$	0	0
$743$	3.78590	0.138891	0.0694455	−	0.997586i	$-0.477877\pi$
$743$	3.78590	0.138891	0.0694455	+	0.997586i	$0.477877\pi$
$744$	−30.7828	−1.12855
$745$	−56.7136	−2.07783
$746$	−80.2759	−2.93911
$747$	3.64416	0.133333
$748$	−1.50526	−0.0550377
$749$	0	0
$750$	−85.3901	−3.11801
$751$	4.49444	0.164005	0.0820023	−	0.996632i	$-0.473869\pi$
$751$	4.49444	0.164005	0.0820023	+	0.996632i	$0.473869\pi$
$752$	60.0340	2.18922
$753$	−11.7359	−0.427680
$754$	2.05184	0.0747235
$755$	−66.9816	−2.43771
$756$	0	0
$757$	9.09423	0.330535	0.165268	−	0.986249i	$-0.447151\pi$
$757$	9.09423	0.330535	0.165268	+	0.986249i	$0.447151\pi$
$758$	52.4085	1.90356
$759$	−0.418956	−0.0152071
$760$	−66.6662	−2.41824
$761$	7.54546	0.273523	0.136761	−	0.990604i	$-0.456331\pi$
$761$	7.54546	0.273523	0.136761	+	0.990604i	$0.456331\pi$
$762$	−6.90203	−0.250034
$763$	0	0
$764$	−32.0248	−1.15862
$765$	27.6725	1.00050
$766$	−14.3352	−0.517950
$767$	−1.30573	−0.0471470
$768$	32.5844	1.17579
$769$	−45.4058	−1.63738	−0.818688	−	0.574238i	$-0.805298\pi$
$769$	−45.4058	−1.63738	−0.818688	+	0.574238i	$0.805298\pi$
$770$	0	0
$771$	−2.38752	−0.0859844
$772$	−5.48275	−0.197329
$773$	33.6739	1.21117	0.605583	−	0.795782i	$-0.292940\pi$
$773$	33.6739	1.21117	0.605583	+	0.795782i	$0.292940\pi$
$774$	−29.6587	−1.06606
$775$	77.2434	2.77466
$776$	36.9891	1.32783
$777$	0	0
$778$	−8.54607	−0.306391
$779$	2.99714	0.107384
$780$	−2.12636	−0.0761361
$781$	0.135831	0.00486043
$782$	−119.678	−4.27969
$783$	−6.83272	−0.244181
$784$	0	0
$785$	−25.5259	−0.911057
$786$	17.4314	0.621758
$787$	38.9133	1.38711	0.693554	−	0.720404i	$-0.256044\pi$
$787$	38.9133	1.38711	0.693554	+	0.720404i	$0.256044\pi$
$788$	61.7579	2.20004
$789$	−1.41800	−0.0504822
$790$	84.3710	3.00179
$791$	0	0
$792$	−0.294125	−0.0104513
$793$	1.10197	0.0391322
$794$	38.8803	1.37981
$795$	12.5421	0.444824
$796$	−32.7289	−1.16004
$797$	−0.546002	−0.0193404	−0.00967019	−	0.999953i	$-0.503078\pi$
$797$	−0.546002	−0.0193404	−0.00967019	+	0.999953i	$0.503078\pi$
$798$	0	0
$799$	83.1389	2.94124
$800$	15.1629	0.536089
$801$	7.76515	0.274368
$802$	14.8516	0.524429
$803$	0.402103	0.0141899
$804$	−11.6713	−0.411614
$805$	0	0
$806$	1.76876	0.0623018
$807$	11.1152	0.391273
$808$	33.9977	1.19604
$809$	20.2053	0.710382	0.355191	−	0.934794i	$-0.384416\pi$
$809$	20.2053	0.710382	0.355191	+	0.934794i	$0.384416\pi$
$810$	10.5235	0.369759
$811$	49.1379	1.72546	0.862732	−	0.505661i	$-0.168751\pi$
$811$	49.1379	1.72546	0.862732	+	0.505661i	$0.168751\pi$
$812$	0	0
$813$	9.92507	0.348087
$814$	0.495467	0.0173661
$815$	67.3888	2.36053
$816$	−30.5261	−1.06863
$817$	35.9507	1.25776
$818$	−82.3888	−2.88066
$819$	0	0
$820$	−17.5081	−0.611410
$821$	−1.80057	−0.0628404	−0.0314202	−	0.999506i	$-0.510003\pi$
$821$	−1.80057	−0.0628404	−0.0314202	+	0.999506i	$0.510003\pi$
$822$	29.4912	1.02862
$823$	6.53927	0.227945	0.113972	−	0.993484i	$-0.463642\pi$
$823$	6.53927	0.227945	0.113972	+	0.993484i	$0.463642\pi$
$824$	−70.9598	−2.47200
$825$	0.738049	0.0256956
$826$	0	0
$827$	7.00477	0.243580	0.121790	−	0.992556i	$-0.461137\pi$
$827$	7.00477	0.243580	0.121790	+	0.992556i	$0.461137\pi$
$828$	−30.6236	−1.06424
$829$	−25.7578	−0.894605	−0.447303	−	0.894383i	$-0.647615\pi$
$829$	−25.7578	−0.894605	−0.447303	+	0.894383i	$0.647615\pi$
$830$	38.3494	1.33113
$831$	−7.48256	−0.259567
$832$	−0.793201	−0.0274993
$833$	0	0
$834$	12.5099	0.433184
$835$	40.2074	1.39143
$836$	0.693872	0.0239981
$837$	−5.89005	−0.203590
$838$	69.8170	2.41179
$839$	12.6958	0.438307	0.219154	−	0.975690i	$-0.429670\pi$
$839$	12.6958	0.438307	0.219154	+	0.975690i	$0.429670\pi$
$840$	0	0
$841$	17.6861	0.609864
$842$	93.3865	3.21831
$843$	15.0412	0.518047
$844$	67.6934	2.33010
$845$	−55.2663	−1.90122
$846$	31.6167	1.08700
$847$	0	0
$848$	−13.8355	−0.475112
$849$	21.3617	0.733133
$850$	210.830	7.23141
$851$	26.5061	0.908619
$852$	9.92859	0.340148
$853$	−30.9529	−1.05981	−0.529904	−	0.848058i	$-0.677772\pi$
$853$	−30.9529	−1.05981	−0.529904	+	0.848058i	$0.677772\pi$
$854$	0	0
$855$	−12.7561	−0.436248
$856$	3.29589	0.112651
$857$	27.8245	0.950467	0.475234	−	0.879860i	$-0.342364\pi$
$857$	27.8245	0.950467	0.475234	+	0.879860i	$0.342364\pi$
$858$	0.0169002	0.000576963 0
$859$	−18.8052	−0.641625	−0.320812	−	0.947143i	$-0.603956\pi$
$859$	−18.8052	−0.641625	−0.320812	+	0.947143i	$0.603956\pi$
$860$	−210.010	−7.16128
$861$	0	0
$862$	−68.6405	−2.33791
$863$	−43.9584	−1.49636	−0.748181	−	0.663495i	$-0.769072\pi$
$863$	−43.9584	−1.49636	−0.748181	+	0.663495i	$0.769072\pi$
$864$	−1.15622	−0.0393353
$865$	−14.9068	−0.506847
$866$	7.87273	0.267526
$867$	−25.2744	−0.858365
$868$	0	0
$869$	−0.451206	−0.0153061
$870$	−71.9042	−2.43778
$871$	0.344578	0.0116756
$872$	−26.5677	−0.899698
$873$	7.07757	0.239540
$874$	55.1676	1.86607
$875$	0	0
$876$	29.3917	0.993054
$877$	−22.0807	−0.745613	−0.372806	−	0.927909i	$-0.621604\pi$
$877$	−22.0807	−0.745613	−0.372806	+	0.927909i	$0.621604\pi$
$878$	−77.6229	−2.61965
$879$	−10.9401	−0.369001
$880$	−1.12456	−0.0379091
$881$	−12.8549	−0.433091	−0.216545	−	0.976273i	$-0.569479\pi$
$881$	−12.8549	−0.433091	−0.216545	+	0.976273i	$0.569479\pi$
$882$	0	0
$883$	−43.7208	−1.47132	−0.735661	−	0.677350i	$-0.763128\pi$
$883$	−43.7208	−1.47132	−0.735661	+	0.677350i	$0.763128\pi$
$884$	3.24838	0.109255
$885$	45.7576	1.53813
$886$	55.4037	1.86132
$887$	55.1423	1.85150	0.925749	−	0.378138i	$-0.123436\pi$
$887$	55.1423	1.85150	0.925749	+	0.378138i	$0.123436\pi$
$888$	18.6084	0.624458
$889$	0	0
$890$	81.7167	2.73915
$891$	−0.0562785	−0.00188540
$892$	−21.9692	−0.735584
$893$	−38.3241	−1.28247
$894$	32.9480	1.10194
$895$	−3.86698	−0.129259
$896$	0	0
$897$	0.904116	0.0301875
$898$	72.6804	2.42537
$899$	40.2451	1.34225
$900$	53.9476	1.79825
$901$	−19.1602	−0.638320
$902$	0.139153	0.00463330
$903$	0	0
$904$	34.8471	1.15900
$905$	−58.7219	−1.95198
$906$	38.9132	1.29280
$907$	55.6994	1.84947	0.924735	−	0.380612i	$-0.124287\pi$
$907$	55.6994	1.84947	0.924735	+	0.380612i	$0.124287\pi$
$908$	−17.7926	−0.590469
$909$	6.50521	0.215764
$910$	0	0
$911$	48.6812	1.61288	0.806441	−	0.591315i	$-0.201391\pi$
$911$	48.6812	1.61288	0.806441	+	0.591315i	$0.201391\pi$
$912$	14.0715	0.465952
$913$	−0.205088	−0.00678743
$914$	96.7695	3.20085
$915$	−38.6173	−1.27665
$916$	−37.3966	−1.23562
$917$	0	0
$918$	−16.0764	−0.530602
$919$	−11.1243	−0.366957	−0.183479	−	0.983024i	$-0.558736\pi$
$919$	−11.1243	−0.366957	−0.183479	+	0.983024i	$0.558736\pi$
$920$	−165.586	−5.45922
$921$	−15.2629	−0.502928
$922$	−40.6456	−1.33859
$923$	−0.293127	−0.00964839
$924$	0	0
$925$	−46.6942	−1.53530
$926$	−20.9129	−0.687239
$927$	−13.5776	−0.445947
$928$	7.90011	0.259334
$929$	−20.8350	−0.683574	−0.341787	−	0.939777i	$-0.611032\pi$
$929$	−20.8350	−0.683574	−0.341787	+	0.939777i	$0.611032\pi$
$930$	−61.9840	−2.03254
$931$	0	0
$932$	50.3618	1.64966
$933$	−25.1312	−0.822759
$934$	72.6034	2.37565
$935$	−1.55737	−0.0509314
$936$	0.634727	0.0207467
$937$	39.0100	1.27440	0.637201	−	0.770698i	$-0.280092\pi$
$937$	39.0100	1.27440	0.637201	+	0.770698i	$0.280092\pi$
$938$	0	0
$939$	30.3467	0.990328
$940$	223.875	7.30199
$941$	31.2865	1.01991	0.509955	−	0.860201i	$-0.329662\pi$
$941$	31.2865	1.01991	0.509955	+	0.860201i	$0.329662\pi$
$942$	14.8293	0.483166
$943$	7.44433	0.242421
$944$	−50.4761	−1.64286
$945$	0	0
$946$	1.66915	0.0542686
$947$	5.86329	0.190531	0.0952656	−	0.995452i	$-0.469630\pi$
$947$	5.86329	0.190531	0.0952656	+	0.995452i	$0.469630\pi$
$948$	−32.9809	−1.07117
$949$	−0.867748	−0.0281683
$950$	−97.1853	−3.15311
$951$	−23.5795	−0.764617
$952$	0	0
$953$	−3.51174	−0.113756	−0.0568782	−	0.998381i	$-0.518115\pi$
$953$	−3.51174	−0.113756	−0.0568782	+	0.998381i	$0.518115\pi$
$954$	−7.28640	−0.235906
$955$	−33.1335	−1.07217
$956$	−15.6800	−0.507128
$957$	0.384535	0.0124303
$958$	−34.5116	−1.11502
$959$	0	0
$960$	27.7968	0.897138
$961$	3.69268	0.119119
$962$	−1.06923	−0.0344733
$963$	0.630644	0.0203222
$964$	3.03485	0.0977461
$965$	−5.67256	−0.182606
$966$	0	0
$967$	−30.0338	−0.965820	−0.482910	−	0.875670i	$-0.660420\pi$
$967$	−30.0338	−0.965820	−0.482910	+	0.875670i	$0.660420\pi$
$968$	−57.4720	−1.84722
$969$	19.4870	0.626014
$970$	74.4810	2.39144
$971$	0.448682	0.0143989	0.00719944	−	0.999974i	$-0.497708\pi$
$971$	0.448682	0.0143989	0.00719944	+	0.999974i	$0.497708\pi$
$972$	−4.11367	−0.131946
$973$	0	0
$974$	−85.3040	−2.73332
$975$	−1.59272	−0.0510080
$976$	42.5995	1.36358
$977$	0.955801	0.0305788	0.0152894	−	0.999883i	$-0.495133\pi$
$977$	0.955801	0.0305788	0.0152894	+	0.999883i	$0.495133\pi$
$978$	−39.1498	−1.25187
$979$	−0.437011	−0.0139669
$980$	0	0
$981$	−5.08353	−0.162305
$982$	53.0151	1.69178
$983$	−1.90830	−0.0608652	−0.0304326	−	0.999537i	$-0.509688\pi$
$983$	−1.90830	−0.0608652	−0.0304326	+	0.999537i	$0.509688\pi$
$984$	5.22624	0.166606
$985$	63.8959	2.03589
$986$	109.846	3.49820
$987$	0	0
$988$	−1.49739	−0.0476383
$989$	89.2948	2.83941
$990$	−0.592248	−0.0188229
$991$	32.5333	1.03346	0.516728	−	0.856150i	$-0.327150\pi$
$991$	32.5333	1.03346	0.516728	+	0.856150i	$0.327150\pi$
$992$	6.81018	0.216223
$993$	−1.06129	−0.0336790
$994$	0	0
$995$	−33.8619	−1.07349
$996$	−14.9909	−0.475005
$997$	9.69264	0.306969	0.153484	−	0.988151i	$-0.450951\pi$
$997$	9.69264	0.306969	0.153484	+	0.988151i	$0.450951\pi$
$998$	−41.7588	−1.32185
$999$	3.56058	0.112652

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bh.1.13		13
7.3	odd	6		861.2.i.f.247.1	✓	26
7.5	odd	6		861.2.i.f.739.1	yes	26
7.6	odd	2		6027.2.a.bi.1.13		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.i.f.247.1	✓	26	7.3	odd	6
861.2.i.f.739.1	yes	26	7.5	odd	6
6027.2.a.bh.1.13		13	1.1	even	1	trivial
6027.2.a.bi.1.13		13	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6027.a (trivial)

\(f(q)\)	\(=\)	\(q+2.47258 q^{2} -1.00000 q^{3} +4.11367 q^{4} +4.25608 q^{5} -2.47258 q^{6} +5.22624 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.47258 q^{2} -1.00000 q^{3} +4.11367 q^{4} +4.25608 q^{5} -2.47258 q^{6} +5.22624 q^{8} +1.00000 q^{9} +10.5235 q^{10} -0.0562785 q^{11} -4.11367 q^{12} +0.121450 q^{13} -4.25608 q^{15} +4.69496 q^{16} +6.50188 q^{17} +2.47258 q^{18} -2.99714 q^{19} +17.5081 q^{20} -0.139153 q^{22} -7.44433 q^{23} -5.22624 q^{24} +13.1142 q^{25} +0.300296 q^{26} -1.00000 q^{27} +6.83272 q^{29} -10.5235 q^{30} +5.89005 q^{31} +1.15622 q^{32} +0.0562785 q^{33} +16.0764 q^{34} +4.11367 q^{36} -3.56058 q^{37} -7.41068 q^{38} -0.121450 q^{39} +22.2433 q^{40} -1.00000 q^{41} -11.9950 q^{43} -0.231511 q^{44} +4.25608 q^{45} -18.4067 q^{46} +12.7869 q^{47} -4.69496 q^{48} +32.4260 q^{50} -6.50188 q^{51} +0.499606 q^{52} -2.94688 q^{53} -2.47258 q^{54} -0.239526 q^{55} +2.99714 q^{57} +16.8945 q^{58} -10.7511 q^{59} -17.5081 q^{60} +9.07345 q^{61} +14.5636 q^{62} -6.53108 q^{64} +0.516902 q^{65} +0.139153 q^{66} +2.83719 q^{67} +26.7466 q^{68} +7.44433 q^{69} -2.41356 q^{71} +5.22624 q^{72} -7.14489 q^{73} -8.80383 q^{74} -13.1142 q^{75} -12.3293 q^{76} -0.300296 q^{78} +8.01738 q^{79} +19.9821 q^{80} +1.00000 q^{81} -2.47258 q^{82} +3.64416 q^{83} +27.6725 q^{85} -29.6587 q^{86} -6.83272 q^{87} -0.294125 q^{88} +7.76515 q^{89} +10.5235 q^{90} -30.6236 q^{92} -5.89005 q^{93} +31.6167 q^{94} -12.7561 q^{95} -1.15622 q^{96} +7.07757 q^{97} -0.0562785 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q - 4 q^{2} - 13 q^{3} + 12 q^{4} + 8 q^{5} + 4 q^{6} - 12 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q - 4 * q^2 - 13 * q^3 + 12 * q^4 + 8 * q^5 + 4 * q^6 - 12 * q^8 + 13 * q^9	\( 13 q - 4 q^{2} - 13 q^{3} + 12 q^{4} + 8 q^{5} + 4 q^{6} - 12 q^{8} + 13 q^{9} + q^{10} - 10 q^{11} - 12 q^{12} + 16 q^{13} - 8 q^{15} + 26 q^{16} + 12 q^{17} - 4 q^{18} + 11 q^{19} + 6 q^{20} + q^{22} - 15 q^{23} + 12 q^{24} + 15 q^{25} + 18 q^{26} - 13 q^{27} - 8 q^{29} - q^{30} + 9 q^{31} - 23 q^{32} + 10 q^{33} - 7 q^{34} + 12 q^{36} - 2 q^{37} + 20 q^{38} - 16 q^{39} + 49 q^{40} - 13 q^{41} - 7 q^{43} - 22 q^{44} + 8 q^{45} - 4 q^{46} + 26 q^{47} - 26 q^{48} - 15 q^{50} - 12 q^{51} + 24 q^{52} + 4 q^{53} + 4 q^{54} + q^{55} - 11 q^{57} + 39 q^{58} - 3 q^{59} - 6 q^{60} + 28 q^{61} + 7 q^{62} + 2 q^{64} - 20 q^{65} - q^{66} + 7 q^{67} + 55 q^{68} + 15 q^{69} - 40 q^{71} - 12 q^{72} - 2 q^{73} + q^{74} - 15 q^{75} - 26 q^{76} - 18 q^{78} + 13 q^{79} + 22 q^{80} + 13 q^{81} + 4 q^{82} + 14 q^{83} + 48 q^{85} - 49 q^{86} + 8 q^{87} + 20 q^{88} + 35 q^{89} + q^{90} - 105 q^{92} - 9 q^{93} - 2 q^{94} + 7 q^{95} + 23 q^{96} + 64 q^{97} - 10 q^{99}+O(q^{100}) \) 13 * q - 4 * q^2 - 13 * q^3 + 12 * q^4 + 8 * q^5 + 4 * q^6 - 12 * q^8 + 13 * q^9 + q^10 - 10 * q^11 - 12 * q^12 + 16 * q^13 - 8 * q^15 + 26 * q^16 + 12 * q^17 - 4 * q^18 + 11 * q^19 + 6 * q^20 + q^22 - 15 * q^23 + 12 * q^24 + 15 * q^25 + 18 * q^26 - 13 * q^27 - 8 * q^29 - q^30 + 9 * q^31 - 23 * q^32 + 10 * q^33 - 7 * q^34 + 12 * q^36 - 2 * q^37 + 20 * q^38 - 16 * q^39 + 49 * q^40 - 13 * q^41 - 7 * q^43 - 22 * q^44 + 8 * q^45 - 4 * q^46 + 26 * q^47 - 26 * q^48 - 15 * q^50 - 12 * q^51 + 24 * q^52 + 4 * q^53 + 4 * q^54 + q^55 - 11 * q^57 + 39 * q^58 - 3 * q^59 - 6 * q^60 + 28 * q^61 + 7 * q^62 + 2 * q^64 - 20 * q^65 - q^66 + 7 * q^67 + 55 * q^68 + 15 * q^69 - 40 * q^71 - 12 * q^72 - 2 * q^73 + q^74 - 15 * q^75 - 26 * q^76 - 18 * q^78 + 13 * q^79 + 22 * q^80 + 13 * q^81 + 4 * q^82 + 14 * q^83 + 48 * q^85 - 49 * q^86 + 8 * q^87 + 20 * q^88 + 35 * q^89 + q^90 - 105 * q^92 - 9 * q^93 - 2 * q^94 + 7 * q^95 + 23 * q^96 + 64 * q^97 - 10 * q^99

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