LMFDB - Embedded newform 6027.2.a.y.1.7

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			1.7
Root			$-1.69463$ 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)

$f(q)$	$=$	$q+2.69463 q^{2} -1.00000 q^{3} +5.26102 q^{4} +2.08082 q^{5} -2.69463 q^{6} +8.78724 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.69463 q^{2} -1.00000 q^{3} +5.26102 q^{4} +2.08082 q^{5} -2.69463 q^{6} +8.78724 q^{8} +1.00000 q^{9} +5.60704 q^{10} +3.71461 q^{11} -5.26102 q^{12} +6.98882 q^{13} -2.08082 q^{15} +13.1563 q^{16} -0.439561 q^{17} +2.69463 q^{18} -0.527622 q^{19} +10.9472 q^{20} +10.0095 q^{22} -7.76264 q^{23} -8.78724 q^{24} -0.670181 q^{25} +18.8323 q^{26} -1.00000 q^{27} -2.31439 q^{29} -5.60704 q^{30} -1.64558 q^{31} +17.8769 q^{32} -3.71461 q^{33} -1.18445 q^{34} +5.26102 q^{36} +9.81901 q^{37} -1.42175 q^{38} -6.98882 q^{39} +18.2847 q^{40} -1.00000 q^{41} -8.88126 q^{43} +19.5426 q^{44} +2.08082 q^{45} -20.9174 q^{46} -9.76026 q^{47} -13.1563 q^{48} -1.80589 q^{50} +0.439561 q^{51} +36.7684 q^{52} +1.90524 q^{53} -2.69463 q^{54} +7.72944 q^{55} +0.527622 q^{57} -6.23642 q^{58} +9.36489 q^{59} -10.9472 q^{60} -1.50981 q^{61} -4.43422 q^{62} +21.8589 q^{64} +14.5425 q^{65} -10.0095 q^{66} +1.04172 q^{67} -2.31254 q^{68} +7.76264 q^{69} -9.49670 q^{71} +8.78724 q^{72} +3.01125 q^{73} +26.4586 q^{74} +0.670181 q^{75} -2.77583 q^{76} -18.8323 q^{78} -13.8353 q^{79} +27.3759 q^{80} +1.00000 q^{81} -2.69463 q^{82} -13.6009 q^{83} -0.914648 q^{85} -23.9317 q^{86} +2.31439 q^{87} +32.6412 q^{88} -9.86142 q^{89} +5.60704 q^{90} -40.8394 q^{92} +1.64558 q^{93} -26.3003 q^{94} -1.09789 q^{95} -17.8769 q^{96} +5.45564 q^{97} +3.71461 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.69463	1.90539	0.952695	−	0.303928i	$-0.0982983\pi$
$2$	2.69463	1.90539	0.952695	+	0.303928i	$0.0982983\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.26102	2.63051
$5$	2.08082	0.930572	0.465286	−	0.885160i	$-0.345952\pi$
$5$	2.08082	0.930572	0.465286	+	0.885160i	$0.345952\pi$
$6$	−2.69463	−1.10008
$7$	0	0
$7$	0	0
$8$	8.78724	3.10676
$9$	1.00000	0.333333
$10$	5.60704	1.77310
$11$	3.71461	1.12000	0.559998	−	0.828494i	$-0.310802\pi$
$11$	3.71461	1.12000	0.559998	+	0.828494i	$0.310802\pi$
$12$	−5.26102	−1.51873
$13$	6.98882	1.93835	0.969176	−	0.246371i	$-0.0792382\pi$
$13$	6.98882	1.93835	0.969176	+	0.246371i	$0.0792382\pi$
$14$	0	0
$15$	−2.08082	−0.537266
$16$	13.1563	3.28908
$17$	−0.439561	−0.106609	−0.0533046	−	0.998578i	$-0.516975\pi$
$17$	−0.439561	−0.106609	−0.0533046	+	0.998578i	$0.516975\pi$
$18$	2.69463	0.635130
$19$	−0.527622	−0.121045	−0.0605224	−	0.998167i	$-0.519277\pi$
$19$	−0.527622	−0.121045	−0.0605224	+	0.998167i	$0.519277\pi$
$20$	10.9472	2.44788
$21$	0	0
$22$	10.0095	2.13403
$23$	−7.76264	−1.61862	−0.809311	−	0.587380i	$-0.800159\pi$
$23$	−7.76264	−1.61862	−0.809311	+	0.587380i	$0.800159\pi$
$24$	−8.78724	−1.79369
$25$	−0.670181	−0.134036
$26$	18.8323	3.69331
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−2.31439	−0.429771	−0.214886	−	0.976639i	$-0.568938\pi$
$29$	−2.31439	−0.429771	−0.214886	+	0.976639i	$0.568938\pi$
$30$	−5.60704	−1.02370
$31$	−1.64558	−0.295555	−0.147777	−	0.989021i	$-0.547212\pi$
$31$	−1.64558	−0.295555	−0.147777	+	0.989021i	$0.547212\pi$
$32$	17.8769	3.16021
$33$	−3.71461	−0.646630
$34$	−1.18445	−0.203132
$35$	0	0
$36$	5.26102	0.876837
$37$	9.81901	1.61424	0.807118	−	0.590390i	$-0.201026\pi$
$37$	9.81901	1.61424	0.807118	+	0.590390i	$0.201026\pi$
$38$	−1.42175	−0.230638
$39$	−6.98882	−1.11911
$40$	18.2847	2.89106
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	−8.88126	−1.35438	−0.677189	−	0.735809i	$-0.736802\pi$
$43$	−8.88126	−1.35438	−0.677189	+	0.735809i	$0.736802\pi$
$44$	19.5426	2.94616
$45$	2.08082	0.310191
$46$	−20.9174	−3.08411
$47$	−9.76026	−1.42368	−0.711840	−	0.702342i	$-0.752138\pi$
$47$	−9.76026	−1.42368	−0.711840	+	0.702342i	$0.752138\pi$
$48$	−13.1563	−1.89895
$49$	0	0
$50$	−1.80589	−0.255391
$51$	0.439561	0.0615509
$52$	36.7684	5.09885
$53$	1.90524	0.261705	0.130853	−	0.991402i	$-0.458229\pi$
$53$	1.90524	0.261705	0.130853	+	0.991402i	$0.458229\pi$
$54$	−2.69463	−0.366692
$55$	7.72944	1.04224
$56$	0	0
$57$	0.527622	0.0698853
$58$	−6.23642	−0.818882
$59$	9.36489	1.21920	0.609602	−	0.792707i	$-0.291329\pi$
$59$	9.36489	1.21920	0.609602	+	0.792707i	$0.291329\pi$
$60$	−10.9472	−1.41328
$61$	−1.50981	−0.193311	−0.0966555	−	0.995318i	$-0.530815\pi$
$61$	−1.50981	−0.193311	−0.0966555	+	0.995318i	$0.530815\pi$
$62$	−4.43422	−0.563147
$63$	0	0
$64$	21.8589	2.73236
$65$	14.5425	1.80377
$66$	−10.0095	−1.23208
$67$	1.04172	0.127266	0.0636331	−	0.997973i	$-0.479731\pi$
$67$	1.04172	0.127266	0.0636331	+	0.997973i	$0.479731\pi$
$68$	−2.31254	−0.280437
$69$	7.76264	0.934512
$70$	0	0
$71$	−9.49670	−1.12705	−0.563525	−	0.826099i	$-0.690555\pi$
$71$	−9.49670	−1.12705	−0.563525	+	0.826099i	$0.690555\pi$
$72$	8.78724	1.03559
$73$	3.01125	0.352441	0.176220	−	0.984351i	$-0.443613\pi$
$73$	3.01125	0.352441	0.176220	+	0.984351i	$0.443613\pi$
$74$	26.4586	3.07575
$75$	0.670181	0.0773859
$76$	−2.77583	−0.318410
$77$	0	0
$78$	−18.8323	−2.13234
$79$	−13.8353	−1.55659	−0.778295	−	0.627899i	$-0.783915\pi$
$79$	−13.8353	−1.55659	−0.778295	+	0.627899i	$0.783915\pi$
$80$	27.3759	3.06072
$81$	1.00000	0.111111
$82$	−2.69463	−0.297572
$83$	−13.6009	−1.49289	−0.746445	−	0.665447i	$-0.768241\pi$
$83$	−13.6009	−1.49289	−0.746445	+	0.665447i	$0.768241\pi$
$84$	0	0
$85$	−0.914648	−0.0992076
$86$	−23.9317	−2.58062
$87$	2.31439	0.248129
$88$	32.6412	3.47956
$89$	−9.86142	−1.04531	−0.522654	−	0.852545i	$-0.675058\pi$
$89$	−9.86142	−1.04531	−0.522654	+	0.852545i	$0.675058\pi$
$90$	5.60704	0.591034
$91$	0	0
$92$	−40.8394	−4.25780
$93$	1.64558	0.170639
$94$	−26.3003	−2.71267
$95$	−1.09789	−0.112641
$96$	−17.8769	−1.82455
$97$	5.45564	0.553937	0.276968	−	0.960879i	$-0.410670\pi$
$97$	5.45564	0.553937	0.276968	+	0.960879i	$0.410670\pi$
$98$	0	0
$99$	3.71461	0.373332
$100$	−3.52584	−0.352584
$101$	−3.12132	−0.310583	−0.155292	−	0.987869i	$-0.549632\pi$
$101$	−3.12132	−0.310583	−0.155292	+	0.987869i	$0.549632\pi$
$102$	1.18445	0.117278
$103$	13.7132	1.35120	0.675601	−	0.737268i	$-0.263884\pi$
$103$	13.7132	1.35120	0.675601	+	0.737268i	$0.263884\pi$
$104$	61.4125	6.02199
$105$	0	0
$106$	5.13392	0.498651
$107$	−4.06184	−0.392673	−0.196337	−	0.980537i	$-0.562905\pi$
$107$	−4.06184	−0.392673	−0.196337	+	0.980537i	$0.562905\pi$
$108$	−5.26102	−0.506242
$109$	−8.07102	−0.773063	−0.386532	−	0.922276i	$-0.626327\pi$
$109$	−8.07102	−0.773063	−0.386532	+	0.922276i	$0.626327\pi$
$110$	20.8280	1.98587
$111$	−9.81901	−0.931979
$112$	0	0
$113$	−9.43020	−0.887119	−0.443559	−	0.896245i	$-0.646284\pi$
$113$	−9.43020	−0.887119	−0.443559	+	0.896245i	$0.646284\pi$
$114$	1.42175	0.133159
$115$	−16.1527	−1.50624
$116$	−12.1761	−1.13052
$117$	6.98882	0.646117
$118$	25.2349	2.32306
$119$	0	0
$120$	−18.2847	−1.66916
$121$	2.79832	0.254393
$122$	−4.06837	−0.368333
$123$	1.00000	0.0901670
$124$	−8.65742	−0.777460
$125$	−11.7986	−1.05530
$126$	0	0
$127$	−12.0758	−1.07156	−0.535779	−	0.844358i	$-0.679982\pi$
$127$	−12.0758	−1.07156	−0.535779	+	0.844358i	$0.679982\pi$
$128$	23.1479	2.04600
$129$	8.88126	0.781951
$130$	39.1866	3.43689
$131$	−12.5809	−1.09920	−0.549600	−	0.835428i	$-0.685220\pi$
$131$	−12.5809	−1.09920	−0.549600	+	0.835428i	$0.685220\pi$
$132$	−19.5426	−1.70097
$133$	0	0
$134$	2.80704	0.242492
$135$	−2.08082	−0.179089
$136$	−3.86253	−0.331209
$137$	13.6143	1.16315	0.581573	−	0.813494i	$-0.302437\pi$
$137$	13.6143	1.16315	0.581573	+	0.813494i	$0.302437\pi$
$138$	20.9174	1.78061
$139$	0.750677	0.0636716	0.0318358	−	0.999493i	$-0.489865\pi$
$139$	0.750677	0.0636716	0.0318358	+	0.999493i	$0.489865\pi$
$140$	0	0
$141$	9.76026	0.821962
$142$	−25.5901	−2.14747
$143$	25.9608	2.17095
$144$	13.1563	1.09636
$145$	−4.81583	−0.399933
$146$	8.11421	0.671537
$147$	0	0
$148$	51.6580	4.24626
$149$	6.69402	0.548396	0.274198	−	0.961673i	$-0.411588\pi$
$149$	6.69402	0.548396	0.274198	+	0.961673i	$0.411588\pi$
$150$	1.80589	0.147450
$151$	22.8919	1.86292	0.931460	−	0.363845i	$-0.118536\pi$
$151$	22.8919	1.86292	0.931460	+	0.363845i	$0.118536\pi$
$152$	−4.63634	−0.376057
$153$	−0.439561	−0.0355364
$154$	0	0
$155$	−3.42416	−0.275035
$156$	−36.7684	−2.94382
$157$	15.6112	1.24591	0.622955	−	0.782258i	$-0.285932\pi$
$157$	15.6112	1.24591	0.622955	+	0.782258i	$0.285932\pi$
$158$	−37.2809	−2.96591
$159$	−1.90524	−0.151096
$160$	37.1986	2.94081
$161$	0	0
$162$	2.69463	0.211710
$163$	2.98975	0.234175	0.117088	−	0.993122i	$-0.462644\pi$
$163$	2.98975	0.234175	0.117088	+	0.993122i	$0.462644\pi$
$164$	−5.26102	−0.410817
$165$	−7.72944	−0.601736
$166$	−36.6493	−2.84454
$167$	−23.3640	−1.80796	−0.903980	−	0.427576i	$-0.859368\pi$
$167$	−23.3640	−1.80796	−0.903980	+	0.427576i	$0.859368\pi$
$168$	0	0
$169$	35.8437	2.75721
$170$	−2.46464	−0.189029
$171$	−0.527622	−0.0403483
$172$	−46.7245	−3.56271
$173$	−0.0825921	−0.00627936	−0.00313968	−	0.999995i	$-0.500999\pi$
$173$	−0.0825921	−0.00627936	−0.00313968	+	0.999995i	$0.500999\pi$
$174$	6.23642	0.472782
$175$	0	0
$176$	48.8705	3.68375
$177$	−9.36489	−0.703908
$178$	−26.5729	−1.99172
$179$	20.6346	1.54230	0.771152	−	0.636651i	$-0.219681\pi$
$179$	20.6346	1.54230	0.771152	+	0.636651i	$0.219681\pi$
$180$	10.9472	0.815960
$181$	−17.1001	−1.27104	−0.635520	−	0.772084i	$-0.719214\pi$
$181$	−17.1001	−1.27104	−0.635520	+	0.772084i	$0.719214\pi$
$182$	0	0
$183$	1.50981	0.111608
$184$	−68.2122	−5.02867
$185$	20.4316	1.50216
$186$	4.43422	0.325133
$187$	−1.63280	−0.119402
$188$	−51.3489	−3.74501
$189$	0	0
$190$	−2.95840	−0.214625
$191$	19.7074	1.42598	0.712990	−	0.701174i	$-0.247340\pi$
$191$	19.7074	1.42598	0.712990	+	0.701174i	$0.247340\pi$
$192$	−21.8589	−1.57753
$193$	11.3362	0.815996	0.407998	−	0.912983i	$-0.366227\pi$
$193$	11.3362	0.815996	0.407998	+	0.912983i	$0.366227\pi$
$194$	14.7009	1.05547
$195$	−14.5425	−1.04141
$196$	0	0
$197$	14.0094	0.998128	0.499064	−	0.866565i	$-0.333677\pi$
$197$	14.0094	0.998128	0.499064	+	0.866565i	$0.333677\pi$
$198$	10.0095	0.711344
$199$	11.0903	0.786172	0.393086	−	0.919502i	$-0.371407\pi$
$199$	11.0903	0.786172	0.393086	+	0.919502i	$0.371407\pi$
$200$	−5.88904	−0.416418
$201$	−1.04172	−0.0734772
$202$	−8.41080	−0.591782
$203$	0	0
$204$	2.31254	0.161910
$205$	−2.08082	−0.145331
$206$	36.9520	2.57456
$207$	−7.76264	−0.539541
$208$	91.9471	6.37538
$209$	−1.95991	−0.135570
$210$	0	0
$211$	22.8501	1.57306	0.786532	−	0.617550i	$-0.211875\pi$
$211$	22.8501	1.57306	0.786532	+	0.617550i	$0.211875\pi$
$212$	10.0235	0.688419
$213$	9.49670	0.650703
$214$	−10.9452	−0.748196
$215$	−18.4803	−1.26035
$216$	−8.78724	−0.597896
$217$	0	0
$218$	−21.7484	−1.47299
$219$	−3.01125	−0.203482
$220$	40.6647	2.74162
$221$	−3.07202	−0.206646
$222$	−26.4586	−1.77578
$223$	14.8028	0.991267	0.495634	−	0.868532i	$-0.334936\pi$
$223$	14.8028	0.991267	0.495634	+	0.868532i	$0.334936\pi$
$224$	0	0
$225$	−0.670181	−0.0446787
$226$	−25.4109	−1.69031
$227$	15.3884	1.02137	0.510683	−	0.859769i	$-0.329393\pi$
$227$	15.3884	1.02137	0.510683	+	0.859769i	$0.329393\pi$
$228$	2.77583	0.183834
$229$	19.3347	1.27767	0.638836	−	0.769343i	$-0.279416\pi$
$229$	19.3347	1.27767	0.638836	+	0.769343i	$0.279416\pi$
$230$	−43.5254	−2.86998
$231$	0	0
$232$	−20.3371	−1.33520
$233$	20.7893	1.36195	0.680977	−	0.732305i	$-0.261556\pi$
$233$	20.7893	1.36195	0.680977	+	0.732305i	$0.261556\pi$
$234$	18.8323	1.23110
$235$	−20.3094	−1.32484
$236$	49.2689	3.20713
$237$	13.8353	0.898697
$238$	0	0
$239$	−3.53932	−0.228940	−0.114470	−	0.993427i	$-0.536517\pi$
$239$	−3.53932	−0.228940	−0.114470	+	0.993427i	$0.536517\pi$
$240$	−27.3759	−1.76711
$241$	−14.4506	−0.930842	−0.465421	−	0.885089i	$-0.654097\pi$
$241$	−14.4506	−0.930842	−0.465421	+	0.885089i	$0.654097\pi$
$242$	7.54044	0.484718
$243$	−1.00000	−0.0641500
$244$	−7.94313	−0.508507
$245$	0	0
$246$	2.69463	0.171803
$247$	−3.68746	−0.234627
$248$	−14.4601	−0.918217
$249$	13.6009	0.861920
$250$	−31.7929	−2.01076
$251$	−8.31897	−0.525089	−0.262545	−	0.964920i	$-0.584562\pi$
$251$	−8.31897	−0.525089	−0.262545	+	0.964920i	$0.584562\pi$
$252$	0	0
$253$	−28.8352	−1.81285
$254$	−32.5399	−2.04174
$255$	0.914648	0.0572775
$256$	18.6571	1.16607
$257$	−3.68295	−0.229736	−0.114868	−	0.993381i	$-0.536645\pi$
$257$	−3.68295	−0.229736	−0.114868	+	0.993381i	$0.536645\pi$
$258$	23.9317	1.48992
$259$	0	0
$260$	76.5084	4.74485
$261$	−2.31439	−0.143257
$262$	−33.9009	−2.09440
$263$	4.39783	0.271182	0.135591	−	0.990765i	$-0.456707\pi$
$263$	4.39783	0.271182	0.135591	+	0.990765i	$0.456707\pi$
$264$	−32.6412	−2.00892
$265$	3.96447	0.243536
$266$	0	0
$267$	9.86142	0.603509
$268$	5.48050	0.334775
$269$	7.71053	0.470119	0.235060	−	0.971981i	$-0.424471\pi$
$269$	7.71053	0.470119	0.235060	+	0.971981i	$0.424471\pi$
$270$	−5.60704	−0.341234
$271$	5.03337	0.305756	0.152878	−	0.988245i	$-0.451146\pi$
$271$	5.03337	0.305756	0.152878	+	0.988245i	$0.451146\pi$
$272$	−5.78300	−0.350646
$273$	0	0
$274$	36.6854	2.21625
$275$	−2.48946	−0.150120
$276$	40.8394	2.45824
$277$	−21.8379	−1.31211	−0.656055	−	0.754713i	$-0.727776\pi$
$277$	−21.8379	−1.31211	−0.656055	+	0.754713i	$0.727776\pi$
$278$	2.02280	0.121319
$279$	−1.64558	−0.0985182
$280$	0	0
$281$	4.62047	0.275634	0.137817	−	0.990458i	$-0.455991\pi$
$281$	4.62047	0.275634	0.137817	+	0.990458i	$0.455991\pi$
$282$	26.3003	1.56616
$283$	−21.3099	−1.26674	−0.633371	−	0.773848i	$-0.718329\pi$
$283$	−21.3099	−1.26674	−0.633371	+	0.773848i	$0.718329\pi$
$284$	−49.9623	−2.96472
$285$	1.09789	0.0650333
$286$	69.9546	4.13650
$287$	0	0
$288$	17.8769	1.05340
$289$	−16.8068	−0.988634
$290$	−12.9769	−0.762028
$291$	−5.45564	−0.319815
$292$	15.8423	0.927099
$293$	14.5844	0.852030	0.426015	−	0.904716i	$-0.359917\pi$
$293$	14.5844	0.852030	0.426015	+	0.904716i	$0.359917\pi$
$294$	0	0
$295$	19.4867	1.13456
$296$	86.2820	5.01504
$297$	−3.71461	−0.215543
$298$	18.0379	1.04491
$299$	−54.2517	−3.13746
$300$	3.52584	0.203564
$301$	0	0
$302$	61.6853	3.54959
$303$	3.12132	0.179315
$304$	−6.94156	−0.398126
$305$	−3.14164	−0.179890
$306$	−1.18445	−0.0677107
$307$	−29.0776	−1.65954	−0.829772	−	0.558102i	$-0.811530\pi$
$307$	−29.0776	−1.65954	−0.829772	+	0.558102i	$0.811530\pi$
$308$	0	0
$309$	−13.7132	−0.780116
$310$	−9.22683	−0.524048
$311$	16.8938	0.957959	0.478979	−	0.877826i	$-0.341007\pi$
$311$	16.8938	0.957959	0.478979	+	0.877826i	$0.341007\pi$
$312$	−61.4125	−3.47680
$313$	7.10059	0.401349	0.200675	−	0.979658i	$-0.435687\pi$
$313$	7.10059	0.401349	0.200675	+	0.979658i	$0.435687\pi$
$314$	42.0664	2.37394
$315$	0	0
$316$	−72.7877	−4.09463
$317$	16.3844	0.920238	0.460119	−	0.887857i	$-0.347807\pi$
$317$	16.3844	0.920238	0.460119	+	0.887857i	$0.347807\pi$
$318$	−5.13392	−0.287896
$319$	−8.59705	−0.481343
$320$	45.4845	2.54266
$321$	4.06184	0.226710
$322$	0	0
$323$	0.231922	0.0129045
$324$	5.26102	0.292279
$325$	−4.68378	−0.259809
$326$	8.05626	0.446195
$327$	8.07102	0.446328
$328$	−8.78724	−0.485194
$329$	0	0
$330$	−20.8280	−1.14654
$331$	−6.23633	−0.342780	−0.171390	−	0.985203i	$-0.554826\pi$
$331$	−6.23633	−0.342780	−0.171390	+	0.985203i	$0.554826\pi$
$332$	−71.5545	−3.92706
$333$	9.81901	0.538079
$334$	−62.9572	−3.44487
$335$	2.16763	0.118430
$336$	0	0
$337$	−24.1319	−1.31455	−0.657273	−	0.753653i	$-0.728290\pi$
$337$	−24.1319	−1.31455	−0.657273	+	0.753653i	$0.728290\pi$
$338$	96.5854	5.25355
$339$	9.43020	0.512178
$340$	−4.81199	−0.260967
$341$	−6.11268	−0.331020
$342$	−1.42175	−0.0768792
$343$	0	0
$344$	−78.0417	−4.20773
$345$	16.1527	0.869630
$346$	−0.222555	−0.0119646
$347$	−18.8453	−1.01167	−0.505834	−	0.862631i	$-0.668815\pi$
$347$	−18.8453	−1.01167	−0.505834	+	0.862631i	$0.668815\pi$
$348$	12.1761	0.652705
$349$	−22.1852	−1.18755	−0.593774	−	0.804632i	$-0.702363\pi$
$349$	−22.1852	−1.18755	−0.593774	+	0.804632i	$0.702363\pi$
$350$	0	0
$351$	−6.98882	−0.373036
$352$	66.4056	3.53943
$353$	−17.7563	−0.945075	−0.472537	−	0.881311i	$-0.656662\pi$
$353$	−17.7563	−0.945075	−0.472537	+	0.881311i	$0.656662\pi$
$354$	−25.2349	−1.34122
$355$	−19.7609	−1.04880
$356$	−51.8812	−2.74970
$357$	0	0
$358$	55.6027	2.93869
$359$	−26.6141	−1.40464	−0.702319	−	0.711862i	$-0.747852\pi$
$359$	−26.6141	−1.40464	−0.702319	+	0.711862i	$0.747852\pi$
$360$	18.2847	0.963687
$361$	−18.7216	−0.985348
$362$	−46.0784	−2.42183
$363$	−2.79832	−0.146874
$364$	0	0
$365$	6.26588	0.327971
$366$	4.06837	0.212657
$367$	28.4341	1.48425	0.742124	−	0.670263i	$-0.233819\pi$
$367$	28.4341	1.48425	0.742124	+	0.670263i	$0.233819\pi$
$368$	−102.128	−5.32377
$369$	−1.00000	−0.0520579
$370$	55.0556	2.86220
$371$	0	0
$372$	8.65742	0.448867
$373$	−14.4792	−0.749702	−0.374851	−	0.927085i	$-0.622306\pi$
$373$	−14.4792	−0.749702	−0.374851	+	0.927085i	$0.622306\pi$
$374$	−4.39978	−0.227507
$375$	11.7986	0.609279
$376$	−85.7658	−4.42303
$377$	−16.1749	−0.833048
$378$	0	0
$379$	27.0992	1.39199	0.695996	−	0.718046i	$-0.254963\pi$
$379$	27.0992	1.39199	0.695996	+	0.718046i	$0.254963\pi$
$380$	−5.77601	−0.296303
$381$	12.0758	0.618664
$382$	53.1042	2.71705
$383$	25.7679	1.31668	0.658339	−	0.752722i	$-0.271259\pi$
$383$	25.7679	1.31668	0.658339	+	0.752722i	$0.271259\pi$
$384$	−23.1479	−1.18126
$385$	0	0
$386$	30.5468	1.55479
$387$	−8.88126	−0.451460
$388$	28.7023	1.45714
$389$	−10.8688	−0.551069	−0.275535	−	0.961291i	$-0.588855\pi$
$389$	−10.8688	−0.551069	−0.275535	+	0.961291i	$0.588855\pi$
$390$	−39.1866	−1.98429
$391$	3.41215	0.172560
$392$	0	0
$393$	12.5809	0.634623
$394$	37.7501	1.90182
$395$	−28.7887	−1.44852
$396$	19.5426	0.982055
$397$	−18.4731	−0.927138	−0.463569	−	0.886061i	$-0.653431\pi$
$397$	−18.4731	−0.927138	−0.463569	+	0.886061i	$0.653431\pi$
$398$	29.8843	1.49797
$399$	0	0
$400$	−8.81711	−0.440855
$401$	−14.7562	−0.736889	−0.368445	−	0.929650i	$-0.620110\pi$
$401$	−14.7562	−0.736889	−0.368445	+	0.929650i	$0.620110\pi$
$402$	−2.80704	−0.140003
$403$	−11.5007	−0.572889
$404$	−16.4213	−0.816992
$405$	2.08082	0.103397
$406$	0	0
$407$	36.4738	1.80794
$408$	3.86253	0.191224
$409$	11.0730	0.547523	0.273761	−	0.961798i	$-0.411732\pi$
$409$	11.0730	0.547523	0.273761	+	0.961798i	$0.411732\pi$
$410$	−5.60704	−0.276912
$411$	−13.6143	−0.671543
$412$	72.1454	3.55435
$413$	0	0
$414$	−20.9174	−1.02804
$415$	−28.3010	−1.38924
$416$	124.938	6.12560
$417$	−0.750677	−0.0367608
$418$	−5.28123	−0.258313
$419$	7.32759	0.357976	0.178988	−	0.983851i	$-0.442718\pi$
$419$	7.32759	0.357976	0.178988	+	0.983851i	$0.442718\pi$
$420$	0	0
$421$	1.38217	0.0673629	0.0336815	−	0.999433i	$-0.489277\pi$
$421$	1.38217	0.0673629	0.0336815	+	0.999433i	$0.489277\pi$
$422$	61.5724	2.99730
$423$	−9.76026	−0.474560
$424$	16.7418	0.813055
$425$	0.294586	0.0142895
$426$	25.5901	1.23984
$427$	0	0
$428$	−21.3694	−1.03293
$429$	−25.9608	−1.25340
$430$	−49.7976	−2.40145
$431$	6.69985	0.322720	0.161360	−	0.986896i	$-0.448412\pi$
$431$	6.69985	0.322720	0.161360	+	0.986896i	$0.448412\pi$
$432$	−13.1563	−0.632983
$433$	35.4887	1.70548	0.852739	−	0.522337i	$-0.174940\pi$
$433$	35.4887	1.70548	0.852739	+	0.522337i	$0.174940\pi$
$434$	0	0
$435$	4.81583	0.230901
$436$	−42.4618	−2.03355
$437$	4.09574	0.195926
$438$	−8.11421	−0.387712
$439$	−17.5082	−0.835619	−0.417810	−	0.908535i	$-0.637202\pi$
$439$	−17.5082	−0.835619	−0.417810	+	0.908535i	$0.637202\pi$
$440$	67.9204	3.23798
$441$	0	0
$442$	−8.27794	−0.393742
$443$	−27.0536	−1.28535	−0.642677	−	0.766137i	$-0.722176\pi$
$443$	−27.0536	−1.28535	−0.642677	+	0.766137i	$0.722176\pi$
$444$	−51.6580	−2.45158
$445$	−20.5199	−0.972735
$446$	39.8880	1.88875
$447$	−6.69402	−0.316616
$448$	0	0
$449$	35.3056	1.66617	0.833087	−	0.553142i	$-0.186571\pi$
$449$	35.3056	1.66617	0.833087	+	0.553142i	$0.186571\pi$
$450$	−1.80589	−0.0851304
$451$	−3.71461	−0.174914
$452$	−49.6125	−2.33358
$453$	−22.8919	−1.07556
$454$	41.4661	1.94610
$455$	0	0
$456$	4.63634	0.217117
$457$	−2.67112	−0.124950	−0.0624749	−	0.998047i	$-0.519899\pi$
$457$	−2.67112	−0.124950	−0.0624749	+	0.998047i	$0.519899\pi$
$458$	52.0998	2.43446
$459$	0.439561	0.0205170
$460$	−84.9795	−3.96219
$461$	10.2093	0.475493	0.237747	−	0.971327i	$-0.423591\pi$
$461$	10.2093	0.475493	0.237747	+	0.971327i	$0.423591\pi$
$462$	0	0
$463$	−33.0579	−1.53633	−0.768166	−	0.640250i	$-0.778831\pi$
$463$	−33.0579	−1.53633	−0.768166	+	0.640250i	$0.778831\pi$
$464$	−30.4488	−1.41355
$465$	3.42416	0.158791
$466$	56.0195	2.59505
$467$	11.3902	0.527077	0.263538	−	0.964649i	$-0.415110\pi$
$467$	11.3902	0.527077	0.263538	+	0.964649i	$0.415110\pi$
$468$	36.7684	1.69962
$469$	0	0
$470$	−54.7262	−2.52433
$471$	−15.6112	−0.719326
$472$	82.2915	3.78777
$473$	−32.9904	−1.51690
$474$	37.2809	1.71237
$475$	0.353602	0.0162244
$476$	0	0
$477$	1.90524	0.0872351
$478$	−9.53715	−0.436219
$479$	15.3666	0.702119	0.351060	−	0.936353i	$-0.385821\pi$
$479$	15.3666	0.702119	0.351060	+	0.936353i	$0.385821\pi$
$480$	−37.1986	−1.69787
$481$	68.6234	3.12896
$482$	−38.9389	−1.77362
$483$	0	0
$484$	14.7220	0.669183
$485$	11.3522	0.515478
$486$	−2.69463	−0.122231
$487$	19.3061	0.874844	0.437422	−	0.899256i	$-0.355892\pi$
$487$	19.3061	0.874844	0.437422	+	0.899256i	$0.355892\pi$
$488$	−13.2670	−0.600570
$489$	−2.98975	−0.135201
$490$	0	0
$491$	−9.74439	−0.439758	−0.219879	−	0.975527i	$-0.570566\pi$
$491$	−9.74439	−0.439758	−0.219879	+	0.975527i	$0.570566\pi$
$492$	5.26102	0.237185
$493$	1.01732	0.0458176
$494$	−9.93633	−0.447057
$495$	7.72944	0.347412
$496$	−21.6497	−0.972102
$497$	0	0
$498$	36.6493	1.64229
$499$	34.5879	1.54837	0.774184	−	0.632960i	$-0.218160\pi$
$499$	34.5879	1.54837	0.774184	+	0.632960i	$0.218160\pi$
$500$	−62.0729	−2.77598
$501$	23.3640	1.04383
$502$	−22.4165	−1.00050
$503$	−11.6232	−0.518254	−0.259127	−	0.965843i	$-0.583435\pi$
$503$	−11.6232	−0.518254	−0.259127	+	0.965843i	$0.583435\pi$
$504$	0	0
$505$	−6.49491	−0.289020
$506$	−77.7001	−3.45419
$507$	−35.8437	−1.59187
$508$	−63.5313	−2.81874
$509$	−22.9053	−1.01526	−0.507629	−	0.861576i	$-0.669478\pi$
$509$	−22.9053	−1.01526	−0.507629	+	0.861576i	$0.669478\pi$
$510$	2.46464	0.109136
$511$	0	0
$512$	3.97829	0.175817
$513$	0.527622	0.0232951
$514$	−9.92419	−0.437737
$515$	28.5347	1.25739
$516$	46.7245	2.05693
$517$	−36.2556	−1.59452
$518$	0	0
$519$	0.0825921	0.00362539
$520$	127.788	5.60389
$521$	−23.6522	−1.03622	−0.518110	−	0.855314i	$-0.673364\pi$
$521$	−23.6522	−1.03622	−0.518110	+	0.855314i	$0.673364\pi$
$522$	−6.23642	−0.272961
$523$	−20.5658	−0.899279	−0.449639	−	0.893210i	$-0.648447\pi$
$523$	−20.5658	−0.899279	−0.449639	+	0.893210i	$0.648447\pi$
$524$	−66.1885	−2.89146
$525$	0	0
$526$	11.8505	0.516707
$527$	0.723332	0.0315089
$528$	−48.8705	−2.12682
$529$	37.2585	1.61994
$530$	10.6828	0.464030
$531$	9.36489	0.406401
$532$	0	0
$533$	−6.98882	−0.302720
$534$	26.5729	1.14992
$535$	−8.45197	−0.365411
$536$	9.15383	0.395385
$537$	−20.6346	−0.890450
$538$	20.7770	0.895761
$539$	0	0
$540$	−10.9472	−0.471095
$541$	0.768732	0.0330504	0.0165252	−	0.999863i	$-0.494740\pi$
$541$	0.768732	0.0330504	0.0165252	+	0.999863i	$0.494740\pi$
$542$	13.5631	0.582583
$543$	17.1001	0.733836
$544$	−7.85798	−0.336908
$545$	−16.7943	−0.719391
$546$	0	0
$547$	25.6661	1.09740	0.548701	−	0.836019i	$-0.315123\pi$
$547$	25.6661	1.09740	0.548701	+	0.836019i	$0.315123\pi$
$548$	71.6250	3.05967
$549$	−1.50981	−0.0644370
$550$	−6.70817	−0.286037
$551$	1.22112	0.0520216
$552$	68.2122	2.90330
$553$	0	0
$554$	−58.8450	−2.50008
$555$	−20.4316	−0.867274
$556$	3.94933	0.167489
$557$	−26.2390	−1.11178	−0.555890	−	0.831256i	$-0.687622\pi$
$557$	−26.2390	−1.11178	−0.555890	+	0.831256i	$0.687622\pi$
$558$	−4.43422	−0.187716
$559$	−62.0695	−2.62526
$560$	0	0
$561$	1.63280	0.0689368
$562$	12.4505	0.525191
$563$	−13.9758	−0.589009	−0.294505	−	0.955650i	$-0.595155\pi$
$563$	−13.9758	−0.589009	−0.294505	+	0.955650i	$0.595155\pi$
$564$	51.3489	2.16218
$565$	−19.6226	−0.825528
$566$	−57.4223	−2.41364
$567$	0	0
$568$	−83.4498	−3.50148
$569$	−6.10863	−0.256087	−0.128044	−	0.991769i	$-0.540870\pi$
$569$	−6.10863	−0.256087	−0.128044	+	0.991769i	$0.540870\pi$
$570$	2.95840	0.123914
$571$	11.4910	0.480885	0.240442	−	0.970663i	$-0.422707\pi$
$571$	11.4910	0.480885	0.240442	+	0.970663i	$0.422707\pi$
$572$	136.580	5.71070
$573$	−19.7074	−0.823290
$574$	0	0
$575$	5.20237	0.216954
$576$	21.8589	0.910788
$577$	33.2316	1.38345	0.691725	−	0.722161i	$-0.256851\pi$
$577$	33.2316	1.38345	0.691725	+	0.722161i	$0.256851\pi$
$578$	−45.2880	−1.88373
$579$	−11.3362	−0.471115
$580$	−25.3362	−1.05203
$581$	0	0
$582$	−14.7009	−0.609373
$583$	7.07724	0.293109
$584$	26.4606	1.09495
$585$	14.5425	0.601258
$586$	39.2995	1.62345
$587$	22.5690	0.931521	0.465760	−	0.884911i	$-0.345781\pi$
$587$	22.5690	0.931521	0.465760	+	0.884911i	$0.345781\pi$
$588$	0	0
$589$	0.868244	0.0357754
$590$	52.5093	2.16177
$591$	−14.0094	−0.576270
$592$	129.182	5.30934
$593$	−7.69128	−0.315843	−0.157921	−	0.987452i	$-0.550479\pi$
$593$	−7.69128	−0.315843	−0.157921	+	0.987452i	$0.550479\pi$
$594$	−10.0095	−0.410694
$595$	0	0
$596$	35.2174	1.44256
$597$	−11.0903	−0.453897
$598$	−146.188	−5.97808
$599$	−35.7330	−1.46001	−0.730005	−	0.683442i	$-0.760482\pi$
$599$	−35.7330	−1.46001	−0.730005	+	0.683442i	$0.760482\pi$
$600$	5.88904	0.240419
$601$	−12.9595	−0.528628	−0.264314	−	0.964437i	$-0.585146\pi$
$601$	−12.9595	−0.528628	−0.264314	+	0.964437i	$0.585146\pi$
$602$	0	0
$603$	1.04172	0.0424221
$604$	120.435	4.90043
$605$	5.82281	0.236731
$606$	8.41080	0.341665
$607$	−9.41614	−0.382189	−0.191095	−	0.981572i	$-0.561204\pi$
$607$	−9.41614	−0.382189	−0.191095	+	0.981572i	$0.561204\pi$
$608$	−9.43223	−0.382528
$609$	0	0
$610$	−8.46555	−0.342760
$611$	−68.2127	−2.75959
$612$	−2.31254	−0.0934789
$613$	−5.53895	−0.223716	−0.111858	−	0.993724i	$-0.535680\pi$
$613$	−5.53895	−0.223716	−0.111858	+	0.993724i	$0.535680\pi$
$614$	−78.3532	−3.16208
$615$	2.08082	0.0839068
$616$	0	0
$617$	3.96556	0.159647	0.0798237	−	0.996809i	$-0.474564\pi$
$617$	3.96556	0.159647	0.0798237	+	0.996809i	$0.474564\pi$
$618$	−36.9520	−1.48643
$619$	1.11331	0.0447478	0.0223739	−	0.999750i	$-0.492878\pi$
$619$	1.11331	0.0447478	0.0223739	+	0.999750i	$0.492878\pi$
$620$	−18.0146	−0.723482
$621$	7.76264	0.311504
$622$	45.5225	1.82528
$623$	0	0
$624$	−91.9471	−3.68083
$625$	−21.2000	−0.847998
$626$	19.1335	0.764727
$627$	1.95991	0.0782713
$628$	82.1309	3.27738
$629$	−4.31606	−0.172092
$630$	0	0
$631$	−11.4270	−0.454903	−0.227451	−	0.973789i	$-0.573039\pi$
$631$	−11.4270	−0.454903	−0.227451	+	0.973789i	$0.573039\pi$
$632$	−121.574	−4.83595
$633$	−22.8501	−0.908209
$634$	44.1498	1.75341
$635$	−25.1277	−0.997161
$636$	−10.0235	−0.397459
$637$	0	0
$638$	−23.1659	−0.917145
$639$	−9.49670	−0.375684
$640$	48.1666	1.90395
$641$	−24.4778	−0.966815	−0.483407	−	0.875395i	$-0.660601\pi$
$641$	−24.4778	−0.966815	−0.483407	+	0.875395i	$0.660601\pi$
$642$	10.9452	0.431971
$643$	−15.1314	−0.596724	−0.298362	−	0.954453i	$-0.596440\pi$
$643$	−15.1314	−0.596724	−0.298362	+	0.954453i	$0.596440\pi$
$644$	0	0
$645$	18.4803	0.727662
$646$	0.624944	0.0245881
$647$	39.3656	1.54762	0.773811	−	0.633417i	$-0.218348\pi$
$647$	39.3656	1.54762	0.773811	+	0.633417i	$0.218348\pi$
$648$	8.78724	0.345195
$649$	34.7869	1.36551
$650$	−12.6210	−0.495038
$651$	0	0
$652$	15.7291	0.616001
$653$	38.8681	1.52102	0.760512	−	0.649323i	$-0.224948\pi$
$653$	38.8681	1.52102	0.760512	+	0.649323i	$0.224948\pi$
$654$	21.7484	0.850429
$655$	−26.1787	−1.02288
$656$	−13.1563	−0.513667
$657$	3.01125	0.117480
$658$	0	0
$659$	−1.24009	−0.0483072	−0.0241536	−	0.999708i	$-0.507689\pi$
$659$	−1.24009	−0.0483072	−0.0241536	+	0.999708i	$0.507689\pi$
$660$	−40.6647	−1.58287
$661$	−14.1249	−0.549395	−0.274697	−	0.961531i	$-0.588578\pi$
$661$	−14.1249	−0.549395	−0.274697	+	0.961531i	$0.588578\pi$
$662$	−16.8046	−0.653129
$663$	3.07202	0.119307
$664$	−119.514	−4.63805
$665$	0	0
$666$	26.4586	1.02525
$667$	17.9658	0.695637
$668$	−122.918	−4.75586
$669$	−14.8028	−0.572309
$670$	5.84096	0.225656
$671$	−5.60834	−0.216508
$672$	0	0
$673$	−26.4023	−1.01773	−0.508867	−	0.860845i	$-0.669936\pi$
$673$	−26.4023	−1.01773	−0.508867	+	0.860845i	$0.669936\pi$
$674$	−65.0264	−2.50472
$675$	0.670181	0.0257953
$676$	188.574	7.25286
$677$	−22.2652	−0.855722	−0.427861	−	0.903844i	$-0.640733\pi$
$677$	−22.2652	−0.855722	−0.427861	+	0.903844i	$0.640733\pi$
$678$	25.4109	0.975899
$679$	0	0
$680$	−8.03724	−0.308214
$681$	−15.3884	−0.589685
$682$	−16.4714	−0.630723
$683$	−6.88159	−0.263317	−0.131658	−	0.991295i	$-0.542030\pi$
$683$	−6.88159	−0.263317	−0.131658	+	0.991295i	$0.542030\pi$
$684$	−2.77583	−0.106137
$685$	28.3289	1.08239
$686$	0	0
$687$	−19.3347	−0.737664
$688$	−116.845	−4.45466
$689$	13.3154	0.507277
$690$	43.5254	1.65698
$691$	−1.91499	−0.0728496	−0.0364248	−	0.999336i	$-0.511597\pi$
$691$	−1.91499	−0.0728496	−0.0364248	+	0.999336i	$0.511597\pi$
$692$	−0.434519	−0.0165179
$693$	0	0
$694$	−50.7811	−1.92762
$695$	1.56203	0.0592510
$696$	20.3371	0.770876
$697$	0.439561	0.0166496
$698$	−59.7810	−2.26274
$699$	−20.7893	−0.786324
$700$	0	0
$701$	6.28267	0.237293	0.118647	−	0.992937i	$-0.462144\pi$
$701$	6.28267	0.237293	0.118647	+	0.992937i	$0.462144\pi$
$702$	−18.8323	−0.710779
$703$	−5.18073	−0.195395
$704$	81.1973	3.06024
$705$	20.3094	0.764895
$706$	−47.8467	−1.80074
$707$	0	0
$708$	−49.2689	−1.85164
$709$	−12.3470	−0.463700	−0.231850	−	0.972752i	$-0.574478\pi$
$709$	−12.3470	−0.463700	−0.231850	+	0.972752i	$0.574478\pi$
$710$	−53.2484	−1.99838
$711$	−13.8353	−0.518863
$712$	−86.6547	−3.24752
$713$	12.7740	0.478391
$714$	0	0
$715$	54.0197	2.02022
$716$	108.559	4.05705
$717$	3.53932	0.132178
$718$	−71.7151	−2.67638
$719$	−40.6197	−1.51486	−0.757429	−	0.652917i	$-0.773545\pi$
$719$	−40.6197	−1.51486	−0.757429	+	0.652917i	$0.773545\pi$
$720$	27.3759	1.02024
$721$	0	0
$722$	−50.4478	−1.87747
$723$	14.4506	0.537422
$724$	−89.9640	−3.34349
$725$	1.55106	0.0576049
$726$	−7.54044	−0.279852
$727$	27.7416	1.02888	0.514439	−	0.857527i	$-0.328000\pi$
$727$	27.7416	1.02888	0.514439	+	0.857527i	$0.328000\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	16.8842	0.624913
$731$	3.90386	0.144389
$732$	7.94313	0.293586
$733$	0.517287	0.0191064	0.00955322	−	0.999954i	$-0.496959\pi$
$733$	0.517287	0.0191064	0.00955322	+	0.999954i	$0.496959\pi$
$734$	76.6193	2.82807
$735$	0	0
$736$	−138.772	−5.11519
$737$	3.86958	0.142538
$738$	−2.69463	−0.0991906
$739$	−49.2528	−1.81179	−0.905897	−	0.423498i	$-0.860802\pi$
$739$	−49.2528	−1.81179	−0.905897	+	0.423498i	$0.860802\pi$
$740$	107.491	3.95145
$741$	3.68746	0.135462
$742$	0	0
$743$	4.31629	0.158349	0.0791747	−	0.996861i	$-0.474771\pi$
$743$	4.31629	0.158349	0.0791747	+	0.996861i	$0.474771\pi$
$744$	14.4601	0.530133
$745$	13.9291	0.510321
$746$	−39.0159	−1.42847
$747$	−13.6009	−0.497630
$748$	−8.59019	−0.314088
$749$	0	0
$750$	31.7929	1.16091
$751$	23.1864	0.846084	0.423042	−	0.906110i	$-0.360962\pi$
$751$	23.1864	0.846084	0.423042	+	0.906110i	$0.360962\pi$
$752$	−128.409	−4.68259
$753$	8.31897	0.303160
$754$	−43.5852	−1.58728
$755$	47.6340	1.73358
$756$	0	0
$757$	−26.8333	−0.975274	−0.487637	−	0.873046i	$-0.662141\pi$
$757$	−26.8333	−0.975274	−0.487637	+	0.873046i	$0.662141\pi$
$758$	73.0222	2.65229
$759$	28.8352	1.04665
$760$	−9.64740	−0.349948
$761$	28.9939	1.05103	0.525514	−	0.850785i	$-0.323873\pi$
$761$	28.9939	1.05103	0.525514	+	0.850785i	$0.323873\pi$
$762$	32.5399	1.17880
$763$	0	0
$764$	103.681	3.75106
$765$	−0.914648	−0.0330692
$766$	69.4349	2.50878
$767$	65.4496	2.36325
$768$	−18.6571	−0.673232
$769$	28.5947	1.03115	0.515576	−	0.856844i	$-0.327578\pi$
$769$	28.5947	1.03115	0.515576	+	0.856844i	$0.327578\pi$
$770$	0	0
$771$	3.68295	0.132638
$772$	59.6399	2.14649
$773$	21.4137	0.770197	0.385099	−	0.922875i	$-0.374167\pi$
$773$	21.4137	0.770197	0.385099	+	0.922875i	$0.374167\pi$
$774$	−23.9317	−0.860207
$775$	1.10284	0.0396150
$776$	47.9401	1.72095
$777$	0	0
$778$	−29.2873	−1.05000
$779$	0.527622	0.0189040
$780$	−76.5084	−2.73944
$781$	−35.2765	−1.26229
$782$	9.19449	0.328794
$783$	2.31439	0.0827095
$784$	0	0
$785$	32.4841	1.15941
$786$	33.9009	1.20921
$787$	37.1432	1.32401	0.662006	−	0.749499i	$-0.269705\pi$
$787$	37.1432	1.32401	0.662006	+	0.749499i	$0.269705\pi$
$788$	73.7038	2.62559
$789$	−4.39783	−0.156567
$790$	−77.5749	−2.75999
$791$	0	0
$792$	32.6412	1.15985
$793$	−10.5518	−0.374705
$794$	−49.7781	−1.76656
$795$	−3.96447	−0.140605
$796$	58.3464	2.06804
$797$	29.1409	1.03222	0.516111	−	0.856521i	$-0.327379\pi$
$797$	29.1409	1.03222	0.516111	+	0.856521i	$0.327379\pi$
$798$	0	0
$799$	4.29023	0.151777
$800$	−11.9807	−0.423583
$801$	−9.86142	−0.348436
$802$	−39.7625	−1.40406
$803$	11.1856	0.394732
$804$	−5.48050	−0.193282
$805$	0	0
$806$	−30.9900	−1.09158
$807$	−7.71053	−0.271424
$808$	−27.4278	−0.964907
$809$	22.1729	0.779558	0.389779	−	0.920908i	$-0.372551\pi$
$809$	22.1729	0.779558	0.389779	+	0.920908i	$0.372551\pi$
$810$	5.60704	0.197011
$811$	−10.4493	−0.366923	−0.183462	−	0.983027i	$-0.558730\pi$
$811$	−10.4493	−0.366923	−0.183462	+	0.983027i	$0.558730\pi$
$812$	0	0
$813$	−5.03337	−0.176528
$814$	98.2833	3.44483
$815$	6.22114	0.217917
$816$	5.78300	0.202446
$817$	4.68595	0.163941
$818$	29.8375	1.04324
$819$	0	0
$820$	−10.9472	−0.382294
$821$	−31.8282	−1.11081	−0.555405	−	0.831580i	$-0.687437\pi$
$821$	−31.8282	−1.11081	−0.555405	+	0.831580i	$0.687437\pi$
$822$	−36.6854	−1.27955
$823$	−6.19583	−0.215973	−0.107987	−	0.994152i	$-0.534440\pi$
$823$	−6.19583	−0.215973	−0.107987	+	0.994152i	$0.534440\pi$
$824$	120.501	4.19786
$825$	2.48946	0.0866719
$826$	0	0
$827$	−47.1531	−1.63967	−0.819837	−	0.572597i	$-0.805936\pi$
$827$	−47.1531	−1.63967	−0.819837	+	0.572597i	$0.805936\pi$
$828$	−40.8394	−1.41927
$829$	−18.5572	−0.644520	−0.322260	−	0.946651i	$-0.604442\pi$
$829$	−18.5572	−0.644520	−0.322260	+	0.946651i	$0.604442\pi$
$830$	−76.2606	−2.64705
$831$	21.8379	0.757548
$832$	152.768	5.29628
$833$	0	0
$834$	−2.02280	−0.0700437
$835$	−48.6163	−1.68244
$836$	−10.3111	−0.356618
$837$	1.64558	0.0568795
$838$	19.7451	0.682084
$839$	−38.4981	−1.32910	−0.664551	−	0.747243i	$-0.731377\pi$
$839$	−38.4981	−1.32910	−0.664551	+	0.747243i	$0.731377\pi$
$840$	0	0
$841$	−23.6436	−0.815297
$842$	3.72444	0.128353
$843$	−4.62047	−0.159138
$844$	120.215	4.13796
$845$	74.5843	2.56578
$846$	−26.3003	−0.904222
$847$	0	0
$848$	25.0660	0.860769
$849$	21.3099	0.731354
$850$	0.793799	0.0272271
$851$	−76.2214	−2.61284
$852$	49.9623	1.71168
$853$	−34.7856	−1.19104	−0.595518	−	0.803342i	$-0.703053\pi$
$853$	−34.7856	−1.19104	−0.595518	+	0.803342i	$0.703053\pi$
$854$	0	0
$855$	−1.09789	−0.0375470
$856$	−35.6924	−1.21994
$857$	45.7319	1.56217	0.781086	−	0.624423i	$-0.214666\pi$
$857$	45.7319	1.56217	0.781086	+	0.624423i	$0.214666\pi$
$858$	−69.9546	−2.38821
$859$	27.0766	0.923843	0.461921	−	0.886921i	$-0.347160\pi$
$859$	27.0766	0.923843	0.461921	+	0.886921i	$0.347160\pi$
$860$	−97.2253	−3.31536
$861$	0	0
$862$	18.0536	0.614908
$863$	24.4449	0.832113	0.416056	−	0.909339i	$-0.363412\pi$
$863$	24.4449	0.832113	0.416056	+	0.909339i	$0.363412\pi$
$864$	−17.8769	−0.608183
$865$	−0.171860	−0.00584340
$866$	95.6289	3.24960
$867$	16.8068	0.570788
$868$	0	0
$869$	−51.3926	−1.74338
$870$	12.9769	0.439957
$871$	7.28039	0.246687
$872$	−70.9220	−2.40172
$873$	5.45564	0.184646
$874$	11.0365	0.373315
$875$	0	0
$876$	−15.8423	−0.535261
$877$	−8.03269	−0.271245	−0.135622	−	0.990761i	$-0.543303\pi$
$877$	−8.03269	−0.271245	−0.135622	+	0.990761i	$0.543303\pi$
$878$	−47.1780	−1.59218
$879$	−14.5844	−0.491920
$880$	101.691	3.42800
$881$	35.4114	1.19304	0.596520	−	0.802598i	$-0.296550\pi$
$881$	35.4114	1.19304	0.596520	+	0.802598i	$0.296550\pi$
$882$	0	0
$883$	8.19851	0.275902	0.137951	−	0.990439i	$-0.455948\pi$
$883$	8.19851	0.275902	0.137951	+	0.990439i	$0.455948\pi$
$884$	−16.1619	−0.543585
$885$	−19.4867	−0.655037
$886$	−72.8994	−2.44910
$887$	−31.3125	−1.05137	−0.525685	−	0.850679i	$-0.676191\pi$
$887$	−31.3125	−1.05137	−0.525685	+	0.850679i	$0.676191\pi$
$888$	−86.2820	−2.89544
$889$	0	0
$890$	−55.2934	−1.85344
$891$	3.71461	0.124444
$892$	77.8777	2.60754
$893$	5.14973	0.172329
$894$	−18.0379	−0.603278
$895$	42.9370	1.43523
$896$	0	0
$897$	54.2517	1.81141
$898$	95.1355	3.17471
$899$	3.80851	0.127021
$900$	−3.52584	−0.117528
$901$	−0.837471	−0.0279002
$902$	−10.0095	−0.333280
$903$	0	0
$904$	−82.8655	−2.75606
$905$	−35.5823	−1.18279
$906$	−61.6853	−2.04936
$907$	2.33978	0.0776911	0.0388456	−	0.999245i	$-0.487632\pi$
$907$	2.33978	0.0776911	0.0388456	+	0.999245i	$0.487632\pi$
$908$	80.9588	2.68671
$909$	−3.12132	−0.103528
$910$	0	0
$911$	2.17707	0.0721295	0.0360647	−	0.999349i	$-0.488518\pi$
$911$	2.17707	0.0721295	0.0360647	+	0.999349i	$0.488518\pi$
$912$	6.94156	0.229858
$913$	−50.5219	−1.67203
$914$	−7.19768	−0.238078
$915$	3.14164	0.103859
$916$	101.720	3.36093
$917$	0	0
$918$	1.18445	0.0390928
$919$	4.85889	0.160280	0.0801400	−	0.996784i	$-0.474463\pi$
$919$	4.85889	0.160280	0.0801400	+	0.996784i	$0.474463\pi$
$920$	−141.937	−4.67954
$921$	29.0776	0.958138
$922$	27.5102	0.906000
$923$	−66.3708	−2.18462
$924$	0	0
$925$	−6.58052	−0.216366
$926$	−89.0789	−2.92731
$927$	13.7132	0.450400
$928$	−41.3740	−1.35817
$929$	20.6103	0.676202	0.338101	−	0.941110i	$-0.390215\pi$
$929$	20.6103	0.676202	0.338101	+	0.941110i	$0.390215\pi$
$930$	9.22683	0.302560
$931$	0	0
$932$	109.373	3.58263
$933$	−16.8938	−0.553078
$934$	30.6924	1.00429
$935$	−3.39756	−0.111112
$936$	61.4125	2.00733
$937$	−12.8694	−0.420424	−0.210212	−	0.977656i	$-0.567415\pi$
$937$	−12.8694	−0.420424	−0.210212	+	0.977656i	$0.567415\pi$
$938$	0	0
$939$	−7.10059	−0.231719
$940$	−106.848	−3.48500
$941$	−40.3678	−1.31595	−0.657976	−	0.753039i	$-0.728587\pi$
$941$	−40.3678	−1.31595	−0.657976	+	0.753039i	$0.728587\pi$
$942$	−42.0664	−1.37060
$943$	7.76264	0.252786
$944$	123.207	4.01006
$945$	0	0
$946$	−88.8969	−2.89029
$947$	37.4055	1.21552	0.607758	−	0.794122i	$-0.292069\pi$
$947$	37.4055	1.21552	0.607758	+	0.794122i	$0.292069\pi$
$948$	72.7877	2.36403
$949$	21.0451	0.683154
$950$	0.952827	0.0309138
$951$	−16.3844	−0.531300
$952$	0	0
$953$	−41.4445	−1.34252	−0.671260	−	0.741222i	$-0.734247\pi$
$953$	−41.4445	−1.34252	−0.671260	+	0.741222i	$0.734247\pi$
$954$	5.13392	0.166217
$955$	41.0077	1.32698
$956$	−18.6204	−0.602228
$957$	8.59705	0.277903
$958$	41.4074	1.33781
$959$	0	0
$960$	−45.4845	−1.46801
$961$	−28.2921	−0.912647
$962$	184.914	5.96188
$963$	−4.06184	−0.130891
$964$	−76.0247	−2.44859
$965$	23.5886	0.759343
$966$	0	0
$967$	52.3364	1.68303	0.841513	−	0.540237i	$-0.181665\pi$
$967$	52.3364	1.68303	0.841513	+	0.540237i	$0.181665\pi$
$968$	24.5895	0.790337
$969$	−0.231922	−0.00745042
$970$	30.5900	0.982186
$971$	−51.5362	−1.65387	−0.826937	−	0.562295i	$-0.809919\pi$
$971$	−51.5362	−1.65387	−0.826937	+	0.562295i	$0.809919\pi$
$972$	−5.26102	−0.168747
$973$	0	0
$974$	52.0228	1.66692
$975$	4.68378	0.150001
$976$	−19.8635	−0.635814
$977$	8.48831	0.271565	0.135783	−	0.990739i	$-0.456645\pi$
$977$	8.48831	0.271565	0.135783	+	0.990739i	$0.456645\pi$
$978$	−8.05626	−0.257611
$979$	−36.6313	−1.17074
$980$	0	0
$981$	−8.07102	−0.257688
$982$	−26.2575	−0.837911
$983$	11.1950	0.357066	0.178533	−	0.983934i	$-0.442865\pi$
$983$	11.1950	0.357066	0.178533	+	0.983934i	$0.442865\pi$
$984$	8.78724	0.280127
$985$	29.1511	0.928830
$986$	2.74129	0.0873004
$987$	0	0
$988$	−19.3998	−0.617190
$989$	68.9420	2.19223
$990$	20.8280	0.661956
$991$	−29.2972	−0.930656	−0.465328	−	0.885138i	$-0.654064\pi$
$991$	−29.2972	−0.930656	−0.465328	+	0.885138i	$0.654064\pi$
$992$	−29.4178	−0.934016
$993$	6.23633	0.197904
$994$	0	0
$995$	23.0770	0.731590
$996$	71.5545	2.26729
$997$	48.6205	1.53983	0.769913	−	0.638149i	$-0.220300\pi$
$997$	48.6205	1.53983	0.769913	+	0.638149i	$0.220300\pi$
$998$	93.2016	2.95025
$999$	−9.81901	−0.310660

Twists

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

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

\(f(q)\)	\(=\)	\(q+2.69463 q^{2} -1.00000 q^{3} +5.26102 q^{4} +2.08082 q^{5} -2.69463 q^{6} +8.78724 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.69463 q^{2} -1.00000 q^{3} +5.26102 q^{4} +2.08082 q^{5} -2.69463 q^{6} +8.78724 q^{8} +1.00000 q^{9} +5.60704 q^{10} +3.71461 q^{11} -5.26102 q^{12} +6.98882 q^{13} -2.08082 q^{15} +13.1563 q^{16} -0.439561 q^{17} +2.69463 q^{18} -0.527622 q^{19} +10.9472 q^{20} +10.0095 q^{22} -7.76264 q^{23} -8.78724 q^{24} -0.670181 q^{25} +18.8323 q^{26} -1.00000 q^{27} -2.31439 q^{29} -5.60704 q^{30} -1.64558 q^{31} +17.8769 q^{32} -3.71461 q^{33} -1.18445 q^{34} +5.26102 q^{36} +9.81901 q^{37} -1.42175 q^{38} -6.98882 q^{39} +18.2847 q^{40} -1.00000 q^{41} -8.88126 q^{43} +19.5426 q^{44} +2.08082 q^{45} -20.9174 q^{46} -9.76026 q^{47} -13.1563 q^{48} -1.80589 q^{50} +0.439561 q^{51} +36.7684 q^{52} +1.90524 q^{53} -2.69463 q^{54} +7.72944 q^{55} +0.527622 q^{57} -6.23642 q^{58} +9.36489 q^{59} -10.9472 q^{60} -1.50981 q^{61} -4.43422 q^{62} +21.8589 q^{64} +14.5425 q^{65} -10.0095 q^{66} +1.04172 q^{67} -2.31254 q^{68} +7.76264 q^{69} -9.49670 q^{71} +8.78724 q^{72} +3.01125 q^{73} +26.4586 q^{74} +0.670181 q^{75} -2.77583 q^{76} -18.8323 q^{78} -13.8353 q^{79} +27.3759 q^{80} +1.00000 q^{81} -2.69463 q^{82} -13.6009 q^{83} -0.914648 q^{85} -23.9317 q^{86} +2.31439 q^{87} +32.6412 q^{88} -9.86142 q^{89} +5.60704 q^{90} -40.8394 q^{92} +1.64558 q^{93} -26.3003 q^{94} -1.09789 q^{95} -17.8769 q^{96} +5.45564 q^{97} +3.71461 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 4 q^{2} - 7 q^{3} + 8 q^{4} - q^{5} - 4 q^{6} + 12 q^{8} + 7 q^{9}+O(q^{10}) \) 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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